LMFDB - Embedded newform 26.7.f.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,7,Mod(7,26)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([11]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("26.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	26.f (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.98140617412$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 5712 x^{10} + 12204858 x^{8} + 11783014920 x^{6} + 4783763172609 x^{4} + 532462287988296 x^{2} + 172998936244836 $ x^12 + 5712x^10 + 12204858x^8 + 11783014920x^6 + 4783763172609x^4 + 532462287988296*x^2 + 172998936244836
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.2
Root			$13.1145i$ of defining polynomial
Character	$\chi$	$=$	26.11
Dual form			26.7.f.a.19.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.46410 - 5.46410i) q^{2} +(6.55725 + 11.3575i) q^{3} +(-27.7128 - 16.0000i) q^{4} +(-97.4789 - 97.4789i) q^{5} +(71.6589 - 19.2009i) q^{6} +(-87.6994 - 327.299i) q^{7} +(-128.000 + 128.000i) q^{8} +(278.505 - 482.385i) q^{9} +O(q^{10})$	\(q+(1.46410 - 5.46410i) q^{2} +(6.55725 + 11.3575i) q^{3} +(-27.7128 - 16.0000i) q^{4} +(-97.4789 - 97.4789i) q^{5} +(71.6589 - 19.2009i) q^{6} +(-87.6994 - 327.299i) q^{7} +(-128.000 + 128.000i) q^{8} +(278.505 - 482.385i) q^{9} +(-675.354 + 389.916i) q^{10} +(-873.242 - 233.984i) q^{11} -419.664i q^{12} +(-2062.55 + 756.755i) q^{13} -1916.79 q^{14} +(467.922 - 1746.31i) q^{15} +(512.000 + 886.810i) q^{16} +(2111.30 + 1218.96i) q^{17} +(-2228.04 - 2228.04i) q^{18} +(10376.3 - 2780.31i) q^{19} +(1141.75 + 4261.08i) q^{20} +(3142.22 - 3142.22i) q^{21} +(-2557.03 + 4428.91i) q^{22} +(2521.36 - 1455.71i) q^{23} +(-2293.09 - 614.430i) q^{24} +3379.27i q^{25} +(1115.20 + 12378.0i) q^{26} +16865.4 q^{27} +(-2806.38 + 10473.6i) q^{28} +(15347.0 + 26581.8i) q^{29} +(-8856.92 - 5113.54i) q^{30} +(-28381.0 - 28381.0i) q^{31} +(5595.24 - 1499.24i) q^{32} +(-3068.59 - 11452.1i) q^{33} +(9751.66 - 9751.66i) q^{34} +(-23355.9 + 40453.6i) q^{35} +(-15436.3 + 8912.16i) q^{36} +(8580.33 + 2299.09i) q^{37} -60767.6i q^{38} +(-22119.5 - 18463.2i) q^{39} +24954.6 q^{40} +(24163.5 - 90179.3i) q^{41} +(-12568.9 - 21770.0i) q^{42} +(-42128.5 - 24322.9i) q^{43} +(20456.2 + 20456.2i) q^{44} +(-74170.7 + 19874.0i) q^{45} +(-4262.61 - 15908.3i) q^{46} +(-91926.6 + 91926.6i) q^{47} +(-6714.62 + 11630.1i) q^{48} +(2453.76 - 1416.68i) q^{49} +(18464.7 + 4947.60i) q^{50} +31972.0i q^{51} +(69267.3 + 12029.1i) q^{52} +62841.7 q^{53} +(24692.6 - 92154.1i) q^{54} +(62314.1 + 107931. i) q^{55} +(53119.8 + 30668.7i) q^{56} +(99617.0 + 99617.0i) q^{57} +(167715. - 44939.2i) q^{58} +(29695.0 + 110823. i) q^{59} +(-40908.4 + 40908.4i) q^{60} +(-5099.27 + 8832.20i) q^{61} +(-196629. + 113524. i) q^{62} +(-182309. - 48849.5i) q^{63} -32768.0i q^{64} +(274823. + 127288. i) q^{65} -67068.3 q^{66} +(132374. - 494028. i) q^{67} +(-39006.6 - 67561.5i) q^{68} +(33066.4 + 19090.9i) q^{69} +(186847. + 186847. i) q^{70} +(-436191. + 116877. i) q^{71} +(26096.6 + 97393.9i) q^{72} +(424686. - 424686. i) q^{73} +(25124.9 - 43517.7i) q^{74} +(-38380.0 + 22158.7i) q^{75} +(-332040. - 88970.0i) q^{76} +306331. i q^{77} +(-133270. + 93831.2i) q^{78} +81421.6 q^{79} +(36536.1 - 136354. i) q^{80} +(-92439.8 - 160110. i) q^{81} +(-457371. - 264063. i) q^{82} +(-320512. - 320512. i) q^{83} +(-137355. + 36804.3i) q^{84} +(-86984.2 - 324630. i) q^{85} +(-194583. + 194583. i) q^{86} +(-201268. + 348607. i) q^{87} +(141725. - 81825.0i) q^{88} +(-136331. - 36529.9i) q^{89} +434374. i q^{90} +(428570. + 608704. i) q^{91} -93165.4 q^{92} +(136235. - 508437. i) q^{93} +(367706. + 636886. i) q^{94} +(-1.28249e6 - 740445. i) q^{95} +(53717.0 + 53717.0i) q^{96} +(1.64142e6 - 439816. i) q^{97} +(-4148.32 - 15481.7i) q^{98} +(-356073. + 356073. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{2} + 150 q^{5} - 1026 q^{7} - 1536 q^{8} - 1338 q^{9}+O(q^{10}) $ 12 * q - 24 * q^2 + 150 * q^5 - 1026 * q^7 - 1536 * q^8 - 1338 * q^9	\( 12 q - 24 q^{2} + 150 q^{5} - 1026 q^{7} - 1536 q^{8} - 1338 q^{9} - 2472 q^{10} - 414 q^{11} - 2586 q^{13} + 11040 q^{14} - 19494 q^{15} + 6144 q^{16} - 11592 q^{17} + 10704 q^{18} + 2100 q^{19} + 12288 q^{20} + 23076 q^{21} - 5376 q^{22} + 23124 q^{23} - 11064 q^{26} + 83844 q^{27} - 32832 q^{28} + 8118 q^{29} + 101760 q^{30} + 32496 q^{31} + 24576 q^{32} - 139596 q^{33} - 55344 q^{34} - 223188 q^{35} - 27264 q^{36} - 36816 q^{37} - 53364 q^{39} - 38400 q^{40} + 186168 q^{41} - 92304 q^{42} + 64290 q^{43} + 43008 q^{44} - 46614 q^{45} - 106416 q^{46} - 211932 q^{47} + 48744 q^{49} - 273312 q^{50} - 54144 q^{52} + 826032 q^{53} + 159552 q^{54} + 120276 q^{55} + 86016 q^{56} + 720600 q^{57} - 61176 q^{58} - 140202 q^{59} - 433536 q^{60} - 511572 q^{61} - 648528 q^{62} - 378180 q^{63} + 1436640 q^{65} + 1161984 q^{66} + 1837104 q^{67} + 221376 q^{68} - 1103952 q^{69} + 1785504 q^{70} - 173352 q^{71} + 280320 q^{72} - 1877034 q^{73} - 1089480 q^{74} - 4264686 q^{75} - 67200 q^{76} + 1108080 q^{78} - 794880 q^{79} + 393216 q^{80} + 1086270 q^{81} - 2141544 q^{82} + 2905464 q^{83} + 368256 q^{84} - 855852 q^{85} - 944400 q^{86} - 3153372 q^{87} - 66048 q^{88} - 2794182 q^{89} + 2486574 q^{91} + 222720 q^{92} + 3523116 q^{93} + 847728 q^{94} - 3175842 q^{95} + 4229166 q^{97} - 659496 q^{98} - 3795372 q^{99}+O(q^{100}) \) 12 * q - 24 * q^2 + 150 * q^5 - 1026 * q^7 - 1536 * q^8 - 1338 * q^9 - 2472 * q^10 - 414 * q^11 - 2586 * q^13 + 11040 * q^14 - 19494 * q^15 + 6144 * q^16 - 11592 * q^17 + 10704 * q^18 + 2100 * q^19 + 12288 * q^20 + 23076 * q^21 - 5376 * q^22 + 23124 * q^23 - 11064 * q^26 + 83844 * q^27 - 32832 * q^28 + 8118 * q^29 + 101760 * q^30 + 32496 * q^31 + 24576 * q^32 - 139596 * q^33 - 55344 * q^34 - 223188 * q^35 - 27264 * q^36 - 36816 * q^37 - 53364 * q^39 - 38400 * q^40 + 186168 * q^41 - 92304 * q^42 + 64290 * q^43 + 43008 * q^44 - 46614 * q^45 - 106416 * q^46 - 211932 * q^47 + 48744 * q^49 - 273312 * q^50 - 54144 * q^52 + 826032 * q^53 + 159552 * q^54 + 120276 * q^55 + 86016 * q^56 + 720600 * q^57 - 61176 * q^58 - 140202 * q^59 - 433536 * q^60 - 511572 * q^61 - 648528 * q^62 - 378180 * q^63 + 1436640 * q^65 + 1161984 * q^66 + 1837104 * q^67 + 221376 * q^68 - 1103952 * q^69 + 1785504 * q^70 - 173352 * q^71 + 280320 * q^72 - 1877034 * q^73 - 1089480 * q^74 - 4264686 * q^75 - 67200 * q^76 + 1108080 * q^78 - 794880 * q^79 + 393216 * q^80 + 1086270 * q^81 - 2141544 * q^82 + 2905464 * q^83 + 368256 * q^84 - 855852 * q^85 - 944400 * q^86 - 3153372 * q^87 - 66048 * q^88 - 2794182 * q^89 + 2486574 * q^91 + 222720 * q^92 + 3523116 * q^93 + 847728 * q^94 - 3175842 * q^95 + 4229166 * q^97 - 659496 * q^98 - 3795372 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{7}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.46410	−	5.46410i	0.183013	−	0.683013i
$2$	1.46410	−	5.46410i	0.183013	−	0.683013i
$3$	6.55725	+	11.3575i	0.242861	+	0.420647i	0.961528	−	0.274707i	$-0.0885808\pi$
$3$	6.55725	+	11.3575i	0.242861	+	0.420647i	−0.718667	+	0.695354i	$0.755247\pi$
$4$	−27.7128	−	16.0000i	−0.433013	−	0.250000i
$5$	−97.4789	−	97.4789i	−0.779831	−	0.779831i	0.199971	−	0.979802i	$-0.435915\pi$
$5$	−97.4789	−	97.4789i	−0.779831	−	0.779831i	−0.979802	+	0.199971i	$0.935915\pi$
$6$	71.6589	−	19.2009i	0.331754	−	0.0888933i
$7$	−87.6994	−	327.299i	−0.255683	−	0.954224i	−0.967709	−	0.252070i	$-0.918889\pi$
$7$	−87.6994	−	327.299i	−0.255683	−	0.954224i	0.712026	−	0.702154i	$-0.247778\pi$
$8$	−128.000	+	128.000i	−0.250000	+	0.250000i
$9$	278.505	−	482.385i	0.382037	−	0.661708i
$10$	−675.354	+	389.916i	−0.675354	+	0.389916i
$11$	−873.242	−	233.984i	−0.656080	−	0.175796i	−0.0846035	−	0.996415i	$-0.526962\pi$
$11$	−873.242	−	233.984i	−0.656080	−	0.175796i	−0.571476	+	0.820619i	$0.693629\pi$
$12$		−	419.664i		−	0.242861i
$13$	−2062.55	+	756.755i	−0.938805	+	0.344449i
$13$	−2062.55	+	756.755i	−0.938805	+	0.344449i
$14$	−1916.79			−0.698540
$15$	467.922	−	1746.31i	0.138644	−	0.517425i
$16$	512.000	+	886.810i	0.125000	+	0.216506i
$17$	2111.30	+	1218.96i	0.429737	+	0.248109i	0.699234	−	0.714892i	$-0.253524\pi$
$17$	2111.30	+	1218.96i	0.429737	+	0.248109i	−0.269498	+	0.963001i	$0.586858\pi$
$18$	−2228.04	−	2228.04i	−0.382037	−	0.382037i
$19$	10376.3	−	2780.31i	1.51280	−	0.405352i	0.595433	−	0.803405i	$-0.296981\pi$
$19$	10376.3	−	2780.31i	1.51280	−	0.405352i	0.917362	+	0.398053i	$0.130314\pi$
$20$	1141.75	+	4261.08i	0.142719	+	0.532635i
$21$	3142.22	−	3142.22i	0.339296	−	0.339296i
$22$	−2557.03	+	4428.91i	−0.240142	+	0.415938i
$23$	2521.36	−	1455.71i	0.207230	−	0.119644i	−0.392794	−	0.919627i	$-0.628491\pi$
$23$	2521.36	−	1455.71i	0.207230	−	0.119644i	0.600023	+	0.799983i	$0.295158\pi$
$24$	−2293.09	−	614.430i	−0.165877	−	0.0444466i
$25$			3379.27i			0.216273i
$26$	1115.20	+	12378.0i	0.0634499	+	0.704254i
$27$	16865.4			0.856849
$28$	−2806.38	+	10473.6i	−0.127842	+	0.477112i
$29$	15347.0	+	26581.8i	0.629260	+	1.08991i	0.987701	+	0.156357i	$0.0499751\pi$
$29$	15347.0	+	26581.8i	0.629260	+	1.08991i	−0.358441	+	0.933552i	$0.616692\pi$
$30$	−8856.92	−	5113.54i	−0.328034	−	0.189391i
$31$	−28381.0	−	28381.0i	−0.952670	−	0.952670i	0.0462599	−	0.998929i	$-0.485270\pi$
$31$	−28381.0	−	28381.0i	−0.952670	−	0.952670i	−0.998929	+	0.0462599i	$0.985270\pi$
$32$	5595.24	−	1499.24i	0.170753	−	0.0457532i
$33$	−3068.59	−	11452.1i	−0.0853880	−	0.318672i
$34$	9751.66	−	9751.66i	0.248109	−	0.248109i
$35$	−23355.9	+	40453.6i	−0.544743	+	0.943523i
$36$	−15436.3	+	8912.16i	−0.330854	+	0.191019i
$37$	8580.33	+	2299.09i	0.169394	+	0.0453891i	0.342519	−	0.939511i	$-0.388720\pi$
$37$	8580.33	+	2299.09i	0.169394	+	0.0453891i	−0.173125	+	0.984900i	$0.555386\pi$
$38$		−	60767.6i		−	1.10744i
$39$	−22119.5	−	18463.2i	−0.372891	−	0.311253i
$40$	24954.6			0.389916
$41$	24163.5	−	90179.3i	0.350596	−	1.30844i	−0.535340	−	0.844637i	$-0.679816\pi$
$41$	24163.5	−	90179.3i	0.350596	−	1.30844i	0.885936	−	0.463807i	$-0.153517\pi$
$42$	−12568.9	−	21770.0i	−0.169648	−	0.293839i
$43$	−42128.5	−	24322.9i	−0.529872	−	0.305922i	0.211092	−	0.977466i	$-0.432298\pi$
$43$	−42128.5	−	24322.9i	−0.529872	−	0.305922i	−0.740964	+	0.671544i	$0.765631\pi$
$44$	20456.2	+	20456.2i	0.240142	+	0.240142i
$45$	−74170.7	+	19874.0i	−0.813945	+	0.218096i
$46$	−4262.61	−	15908.3i	−0.0437928	−	0.163437i
$47$	−91926.6	+	91926.6i	−0.885416	+	0.885416i	−0.994079	−	0.108663i	$-0.965343\pi$
$47$	−91926.6	+	91926.6i	−0.885416	+	0.885416i	0.108663	+	0.994079i	$0.465343\pi$
$48$	−6714.62	+	11630.1i	−0.0607152	+	0.105162i
$49$	2453.76	−	1416.68i	0.0208566	−	0.0120416i
$50$	18464.7	+	4947.60i	0.147718	+	0.0395808i
$51$			31972.0i			0.241024i
$52$	69267.3	+	12029.1i	0.492627	+	0.0855504i
$53$	62841.7			0.422105			0.211052	−	0.977475i	$-0.432311\pi$
$53$	62841.7			0.422105			0.211052	+	0.977475i	$0.432311\pi$
$54$	24692.6	−	92154.1i	0.156814	−	0.585239i
$55$	62314.1	+	107931.i	0.374540	+	0.648723i
$56$	53119.8	+	30668.7i	0.302477	+	0.174635i
$57$	99617.0	+	99617.0i	0.537909	+	0.537909i
$58$	167715.	−	44939.2i	0.859585	−	0.230325i
$59$	29695.0	+	110823.i	0.144586	+	0.539604i	0.999773	+	0.0212845i	$0.00677556\pi$
$59$	29695.0	+	110823.i	0.144586	+	0.539604i	−0.855187	+	0.518320i	$0.826558\pi$
$60$	−40908.4	+	40908.4i	−0.189391	+	0.189391i
$61$	−5099.27	+	8832.20i	−0.0224656	+	0.0389116i	−0.877040	−	0.480418i	$-0.840485\pi$
$61$	−5099.27	+	8832.20i	−0.0224656	+	0.0389116i	0.854574	+	0.519330i	$0.173818\pi$
$62$	−196629.	+	113524.i	−0.825036	+	0.476335i
$63$	−182309.	−	48849.5i	−0.729098	−	0.195361i
$64$		−	32768.0i		−	0.125000i
$65$	274823.	+	127288.i	1.00072	+	0.463497i
$66$	−67068.3			−0.233284
$67$	132374.	−	494028.i	0.440129	−	1.64258i	−0.288359	−	0.957523i	$-0.593110\pi$
$67$	132374.	−	494028.i	0.440129	−	1.64258i	0.728487	−	0.685060i	$-0.240224\pi$
$68$	−39006.6	−	67561.5i	−0.124054	−	0.214868i
$69$	33066.4	+	19090.9i	0.100656	+	0.0581138i
$70$	186847.	+	186847.i	0.544743	+	0.544743i
$71$	−436191.	+	116877.i	−1.21871	+	0.326553i	−0.810175	−	0.586189i	$-0.800628\pi$
$71$	−436191.	+	116877.i	−1.21871	+	0.326553i	−0.408538	+	0.912741i	$0.633961\pi$
$72$	26096.6	+	97393.9i	0.0699176	+	0.260936i
$73$	424686.	−	424686.i	1.09169	−	1.09169i	0.0963427	−	0.995348i	$-0.469286\pi$
$73$	424686.	−	424686.i	1.09169	−	1.09169i	0.995348	−	0.0963427i	$-0.0307145\pi$
$74$	25124.9	−	43517.7i	0.0620026	−	0.107392i
$75$	−38380.0	+	22158.7i	−0.0909749	+	0.0525244i
$76$	−332040.	−	88970.0i	−0.756398	−	0.202676i
$77$			306331.i			0.670995i
$78$	−133270.	+	93831.2i	−0.280833	+	0.197726i
$79$	81421.6			0.165142			0.0825711	−	0.996585i	$-0.473687\pi$
$79$	81421.6			0.165142			0.0825711	+	0.996585i	$0.473687\pi$
$80$	36536.1	−	136354.i	0.0713595	−	0.266317i
$81$	−92439.8	−	160110.i	−0.173942	−	0.301276i
$82$	−457371.	−	264063.i	−0.829520	−	0.478924i
$83$	−320512.	−	320512.i	−0.560544	−	0.560544i	0.368918	−	0.929462i	$-0.379728\pi$
$83$	−320512.	−	320512.i	−0.560544	−	0.560544i	−0.929462	+	0.368918i	$0.879728\pi$
$84$	−137355.	+	36804.3i	−0.231744	+	0.0620955i
$85$	−86984.2	−	324630.i	−0.141639	−	0.528605i
$86$	−194583.	+	194583.i	−0.305922	+	0.305922i
$87$	−201268.	+	348607.i	−0.305645	+	0.529393i
$88$	141725.	−	81825.0i	0.207969	−	0.120071i
$89$	−136331.	−	36529.9i	−0.193386	−	0.0518177i	0.160826	−	0.986983i	$-0.448584\pi$
$89$	−136331.	−	36529.9i	−0.193386	−	0.0518177i	−0.354212	+	0.935165i	$0.615251\pi$
$90$			434374.i			0.595849i
$91$	428570.	+	608704.i	0.568718	+	0.807760i
$92$	−93165.4			−0.119644
$93$	136235.	−	508437.i	0.169372	−	0.632104i
$94$	367706.	+	636886.i	0.442708	+	0.766793i
$95$	−1.28249e6	−	740445.i	−1.49583	−	0.863619i
$96$	53717.0	+	53717.0i	0.0607152	+	0.0607152i
$97$	1.64142e6	−	439816.i	1.79847	−	0.481899i	0.804732	−	0.593638i	$-0.202309\pi$
$97$	1.64142e6	−	439816.i	1.79847	−	0.481899i	0.993738	+	0.111739i	$0.0356421\pi$
$98$	−4148.32	−	15481.7i	−0.00440752	−	0.0164491i
$99$	−356073.	+	356073.i	−0.366972	+	0.366972i
$100$	54068.4	−	93649.2i	0.0540684	−	0.0936492i
$101$	1.12542e6	−	649764.i	1.09233	−	0.630654i	0.158131	−	0.987418i	$-0.449453\pi$
$101$	1.12542e6	−	649764.i	1.09233	−	0.630654i	0.934195	+	0.356764i	$0.116120\pi$
$102$	174698.	+	46810.3i	0.164622	+	0.0441104i
$103$			973997.i			0.891346i	0.895196	+	0.445673i	$0.147036\pi$
$103$			973997.i			0.891346i	−0.895196	+	0.445673i	$0.852964\pi$
$104$	167142.	−	360872.i	0.148589	−	0.320814i
$105$	−612601.			−0.529188
$106$	92006.6	−	343373.i	0.0772505	−	0.288303i
$107$	72186.9	+	125031.i	0.0589260	+	0.102063i	0.893984	−	0.448100i	$-0.147899\pi$
$107$	72186.9	+	125031.i	0.0589260	+	0.102063i	−0.835058	+	0.550163i	$0.814566\pi$
$108$	−467387.	−	269846.i	−0.371027	−	0.214212i
$109$	1.34667e6	+	1.34667e6i	1.03988	+	1.03988i	0.999171	+	0.0407067i	$0.0129609\pi$
$109$	1.34667e6	+	1.34667e6i	1.03988	+	1.03988i	0.0407067	+	0.999171i	$0.487039\pi$
$110$	680981.	−	182468.i	0.511631	−	0.137091i
$111$	30151.4	+	112527.i	0.0220465	+	0.0822785i
$112$	245350.	−	245350.i	0.174635	−	0.174635i
$113$	−1.13179e6	+	1.96032e6i	−0.784390	+	1.35860i	0.144973	+	0.989436i	$0.453690\pi$
$113$	−1.13179e6	+	1.96032e6i	−0.784390	+	1.35860i	−0.929363	+	0.369167i	$0.879643\pi$
$114$	690167.	−	398468.i	0.465843	−	0.268955i
$115$	−387681.	−	103879.i	−0.254906	−	0.0683020i
$116$		−	982209.i		−	0.629260i
$117$	−209385.	+	1.20571e6i	−0.130734	+	0.752807i
$118$	649027.			0.395018
$119$	213804.	−	797927.i	0.126875	−	0.473502i
$120$	163633.	+	283421.i	0.0946953	+	0.164017i
$121$	−826414.	−	477130.i	−0.466489	−	0.269328i
$122$	40794.2	+	40794.2i	0.0224656	+	0.0224656i
$123$	1.18266e6	−	316891.i	0.635540	−	0.170292i
$124$	332421.	+	1.24061e6i	0.174351	+	0.650685i
$125$	−1.19370e6	+	1.19370e6i	−0.611174	+	0.611174i
$126$	−533837.	+	924633.i	−0.266868	+	0.462229i
$127$	468444.	−	270456.i	0.228689	−	0.132034i	−0.381278	−	0.924460i	$-0.624516\pi$
$127$	468444.	−	270456.i	0.228689	−	0.132034i	0.609967	+	0.792427i	$0.291183\pi$
$128$	−179048.	−	47975.7i	−0.0853766	−	0.0228766i
$129$		−	637966.i		−	0.297186i
$130$	1.09788e6	−	1.31530e6i	0.499719	−	0.598680i
$131$	−3.28871e6			−1.46289			−0.731446	−	0.681900i	$-0.761154\pi$
$131$	−3.28871e6			−1.46289			−0.731446	+	0.681900i	$0.761154\pi$
$132$	−98194.8	+	366468.i	−0.0426940	+	0.159336i
$133$	−1.81998e6	−	3.15231e6i	−0.773593	−	1.33990i
$134$	−2.50561e6	−	1.44661e6i	−1.04136	−	0.601227i
$135$	−1.64402e6	−	1.64402e6i	−0.668198	−	0.668198i
$136$	−426273.	+	114219.i	−0.169461	+	0.0454070i
$137$	1.01674e6	+	3.79452e6i	0.395409	+	1.47569i	0.821082	+	0.570811i	$0.193371\pi$
$137$	1.01674e6	+	3.79452e6i	0.395409	+	1.47569i	−0.425672	+	0.904877i	$0.639962\pi$
$138$	152727.	−	152727.i	0.0581138	−	0.0581138i
$139$	736760.	−	1.27611e6i	0.274335	−	0.475162i	−0.695632	−	0.718398i	$-0.744876\pi$
$139$	736760.	−	1.27611e6i	0.274335	−	0.475162i	0.969967	+	0.243236i	$0.0782089\pi$
$140$	1.29451e6	−	747388.i	0.471762	−	0.272372i
$141$	−1.64684e6	−	441269.i	−0.587481	−	0.157415i
$142$			2.55451e6i			0.892159i
$143$	1.97818e6	−	178224.i	0.676484	−	0.0609479i
$144$	570378.			0.191019
$145$	1.09516e6	−	4.08718e6i	0.359229	−	1.34066i
$146$	−1.69875e6	−	2.94231e6i	−0.545845	−	0.945432i
$147$	32179.8	+	18579.0i	0.0101305	+	0.00584885i
$148$	−201000.	−	201000.i	−0.0620026	−	0.0620026i
$149$	3.52642e6	−	944901.i	1.06604	−	0.285645i	0.317177	−	0.948366i	$-0.397265\pi$
$149$	3.52642e6	−	944901.i	1.06604	−	0.285645i	0.748866	+	0.662721i	$0.230598\pi$
$150$	64885.2	+	242155.i	0.0192253	+	0.0717496i
$151$	1.26043e6	−	1.26043e6i	0.366091	−	0.366091i	−0.499959	−	0.866049i	$-0.666651\pi$
$151$	1.26043e6	−	1.26043e6i	0.366091	−	0.366091i	0.866049	+	0.499959i	$0.166651\pi$
$152$	−972282.	+	1.68404e6i	−0.276861	+	0.479537i
$153$	1.17601e6	−	678972.i	0.328351	−	0.189573i
$154$	1.67383e6	+	448500.i	0.458298	+	0.122801i
$155$			5.53309e6i			1.48584i
$156$	317583.	+	865579.i	0.0836533	+	0.227999i
$157$	−5.04600e6			−1.30391			−0.651956	−	0.758257i	$-0.726051\pi$
$157$	−5.04600e6			−1.30391			−0.651956	+	0.758257i	$0.726051\pi$
$158$	119209.	−	444896.i	0.0302231	−	0.112794i
$159$	412068.	+	713723.i	0.102513	+	0.177557i
$160$	−691562.	−	399274.i	−0.168838	−	0.0974789i
$161$	−697574.	−	697574.i	−0.167152	−	0.167152i
$162$	−1.01020e6	+	270683.i	−0.237609	+	0.0636671i
$163$	1.99221e6	+	7.43502e6i	0.460015	+	1.71680i	0.672910	+	0.739724i	$0.265044\pi$
$163$	1.99221e6	+	7.43502e6i	0.460015	+	1.71680i	−0.212896	+	0.977075i	$0.568289\pi$
$164$	−2.11251e6	+	2.11251e6i	−0.478924	+	0.478924i
$165$	−817218.	+	1.41546e6i	−0.181922	+	0.315099i
$166$	−2.22057e6	+	1.28205e6i	−0.485445	+	0.280272i
$167$	2.83120e6	+	758618.i	0.607885	+	0.162882i	0.549614	−	0.835419i	$-0.314775\pi$
$167$	2.83120e6	+	758618.i	0.607885	+	0.162882i	0.0582707	+	0.998301i	$0.481441\pi$
$168$			804409.i			0.169648i
$169$	3.68145e6	−	3.12170e6i	0.762709	−	0.646741i
$170$	−1.90116e6			−0.386966
$171$	1.54866e6	−	5.77968e6i	0.309719	−	1.15589i
$172$	778334.	+	1.34811e6i	0.152961	+	0.264936i
$173$	3.58931e6	+	2.07229e6i	0.693222	+	0.400232i	0.804818	−	0.593522i	$-0.202263\pi$
$173$	3.58931e6	+	2.07229e6i	0.693222	+	0.400232i	−0.111596	+	0.993754i	$0.535596\pi$
$174$	1.61015e6	+	1.61015e6i	0.305645	+	0.305645i
$175$	1.10603e6	−	296360.i	0.206373	−	0.0552976i
$176$	−239600.	−	894200.i	−0.0439490	−	0.164020i
$177$	−1.06396e6	+	1.06396e6i	−0.191869	+	0.191869i
$178$	−399206.	+	691445.i	−0.0707843	+	0.122602i
$179$	5.80624e6	−	3.35224e6i	1.01236	−	0.584488i	0.100480	−	0.994939i	$-0.467962\pi$
$179$	5.80624e6	−	3.35224e6i	1.01236	−	0.584488i	0.911883	+	0.410451i	$0.134629\pi$
$180$	2.37346e6	+	635968.i	0.406972	+	0.109048i
$181$			3.99099e6i			0.673046i	0.941675	+	0.336523i	$0.109251\pi$
$181$			3.99099e6i			0.673046i	−0.941675	+	0.336523i	$0.890749\pi$
$182$	3.95349e6	−	1.45054e6i	0.655793	−	0.240612i
$183$	−133749.			−0.0218241
$184$	−136404.	+	509065.i	−0.0218964	+	0.0817184i
$185$	−612288.	−	1.06051e6i	−0.0967031	−	0.167495i
$186$	−2.57869e6	−	1.48881e6i	−0.400738	−	0.231366i
$187$	−1.55846e6	−	1.55846e6i	−0.238325	−	0.238325i
$188$	4.01837e6	−	1.07672e6i	0.604751	−	0.162042i
$189$	−1.47908e6	−	5.52001e6i	−0.219082	−	0.817626i
$190$	−5.92356e6	+	5.92356e6i	−0.863619	+	0.863619i
$191$	717369.	−	1.24252e6i	0.102954	−	0.178321i	−0.809947	−	0.586504i	$-0.800504\pi$
$191$	717369.	−	1.24252e6i	0.102954	−	0.178321i	0.912900	+	0.408183i	$0.133837\pi$
$192$	372162.	−	214868.i	0.0525809	−	0.0303576i
$193$	−1.05090e7	−	2.81587e6i	−1.46180	−	0.391689i	−0.561690	−	0.827348i	$-0.689849\pi$
$193$	−1.05090e7	−	2.81587e6i	−1.46180	−	0.391689i	−0.900112	+	0.435659i	$0.856515\pi$
$194$		−	9.61279e6i		−	1.31657i
$195$	356413.	+	3.95596e6i	0.0480673	+	0.533516i
$196$	−90667.4			−0.0120416
$197$	−2.10338e6	+	7.84992e6i	−0.275118	+	1.02675i	0.680644	+	0.732614i	$0.261700\pi$
$197$	−2.10338e6	+	7.84992e6i	−0.275118	+	1.02675i	−0.955762	+	0.294140i	$0.904967\pi$
$198$	1.42429e6	+	2.46695e6i	0.183486	+	0.317807i
$199$	−1.08125e7	−	6.24258e6i	−1.37204	−	0.792146i	−0.380852	−	0.924636i	$-0.624369\pi$
$199$	−1.08125e7	−	6.24258e6i	−1.37204	−	0.792146i	−0.991184	+	0.132490i	$0.957703\pi$
$200$	−432547.	−	432547.i	−0.0540684	−	0.0540684i
$201$	6.47892e6	−	1.73602e6i	0.797838	−	0.213780i
$202$	−1.90264e6	−	7.10075e6i	−0.230836	−	0.861490i
$203$	7.35427e6	−	7.35427e6i	0.879126	−	0.879126i
$204$	511552.	−	886035.i	0.0602559	−	0.104366i
$205$	−1.11460e7	+	6.43515e6i	−1.29377	+	0.746959i
$206$	5.32202e6	+	1.42603e6i	0.608800	+	0.163128i
$207$		−	1.62169e6i		−	0.182834i
$208$	−1.72713e6	−	1.44164e6i	−0.191926	−	0.160201i
$209$	−9.71154e6			−1.06377
$210$	−896910.	+	3.34731e6i	−0.0968481	+	0.361442i
$211$	2.93566e6	+	5.08471e6i	0.312506	+	0.541276i	0.978904	−	0.204320i	$-0.0654983\pi$
$211$	2.93566e6	+	5.08471e6i	0.312506	+	0.541276i	−0.666398	+	0.745596i	$0.732165\pi$
$212$	−1.74152e6	−	1.00547e6i	−0.182777	−	0.105526i
$213$	−4.18764e6	−	4.18764e6i	−0.433341	−	0.433341i
$214$	788873.	−	211378.i	0.0804945	−	0.0215684i
$215$	1.73567e6	+	6.47762e6i	0.174643	+	0.651778i
$216$	−2.15877e6	+	2.15877e6i	−0.214212	+	0.214212i
$217$	−6.80006e6	+	1.17781e7i	−0.665478	+	1.15264i
$218$	9.33002e6	−	5.38669e6i	0.900561	−	0.519939i
$219$	7.60814e6	+	2.03859e6i	0.724346	+	0.194088i
$220$		−	3.98810e6i		−	0.374540i
$221$	−5.27712e6	−	916433.i	−0.488900	−	0.0849031i
$222$	659002.			0.0602320
$223$	2.13006e6	−	7.94947e6i	0.192077	−	0.716843i	−0.800927	−	0.598762i	$-0.795659\pi$
$223$	2.13006e6	−	7.94947e6i	0.192077	−	0.716843i	0.993004	−	0.118080i	$-0.0376740\pi$
$224$	−981399.	−	1.69983e6i	−0.0873175	−	0.151238i
$225$	1.63011e6	+	941145.i	0.143110	+	0.0826245i
$226$	9.05435e6	+	9.05435e6i	0.784390	+	0.784390i
$227$	−1.05974e7	+	2.83956e6i	−0.905984	+	0.242758i	−0.681584	−	0.731740i	$-0.738709\pi$
$227$	−1.05974e7	+	2.83956e6i	−0.905984	+	0.242758i	−0.224399	+	0.974497i	$0.572042\pi$
$228$	−1.16680e6	−	4.35454e6i	−0.0984442	−	0.367399i
$229$	1.23222e7	−	1.23222e7i	1.02608	−	1.02608i	0.0264290	−	0.999651i	$-0.491586\pi$
$229$	1.23222e7	−	1.23222e7i	1.02608	−	1.02608i	0.999651	−	0.0264290i	$-0.00841359\pi$
$230$	−1.13521e6	+	1.96624e6i	−0.0933022	+	0.161604i
$231$	−3.47915e6	+	2.00869e6i	−0.282252	+	0.162958i
$232$	−5.36689e6	−	1.43805e6i	−0.429792	−	0.115163i
$233$			1.59252e7i			1.25898i	0.777009	+	0.629489i	$0.216736\pi$
$233$			1.59252e7i			1.25898i	−0.777009	+	0.629489i	$0.783264\pi$
$234$	6.28154e6	+	2.90937e6i	0.490251	+	0.227066i
$235$	1.79218e7			1.38095
$236$	950241.	−	3.54635e6i	0.0722932	−	0.269802i
$237$	533901.	+	924744.i	0.0401066	+	0.0694667i
$238$	−4.04692e6	−	2.33649e6i	−0.300188	−	0.173314i
$239$	952071.	+	952071.i	0.0697390	+	0.0697390i	0.741116	−	0.671377i	$-0.234297\pi$
$239$	952071.	+	952071.i	0.0697390	+	0.0697390i	−0.671377	+	0.741116i	$0.734297\pi$
$240$	1.78822e6	−	479152.i	0.129356	−	0.0346609i
$241$	368269.	+	1.37440e6i	0.0263096	+	0.0981888i	0.977832	−	0.209390i	$-0.0671479\pi$
$241$	368269.	+	1.37440e6i	0.0263096	+	0.0981888i	−0.951523	+	0.307579i	$0.900481\pi$
$242$	−3.81704e6	+	3.81704e6i	−0.269328	+	0.269328i
$243$	7.35973e6	−	1.27474e7i	0.512912	−	0.888390i
$244$	282630.	−	163177.i	0.0194558	−	0.0112328i
$245$	−377286.	−	101093.i	−0.0256550	−	0.00687424i
$246$		−	6.92611e6i		−	0.465247i
$247$	−1.92976e7	+	1.35868e7i	−1.28060	+	0.901628i
$248$	7.26553e6			0.476335
$249$	1.53853e6	−	5.74188e6i	0.0996571	−	0.371925i
$250$	4.77480e6	+	8.27020e6i	0.305587	+	0.529293i
$251$	2.30459e7	+	1.33056e7i	1.45738	+	0.841419i	0.998882	−	0.0472767i	$-0.0150542\pi$
$251$	2.30459e7	+	1.33056e7i	1.45738	+	0.841419i	0.458498	+	0.888695i	$0.348388\pi$
$252$	4.27070e6	+	4.27070e6i	0.266868	+	0.266868i
$253$	−2.54237e6	+	681227.i	−0.156992	+	0.0420659i
$254$	−791950.	−	2.95560e6i	−0.0483278	−	0.180362i
$255$	3.11660e6	−	3.11660e6i	0.187958	−	0.187958i
$256$	−524288.	+	908093.i	−0.0312500	+	0.0541266i
$257$	2.00030e6	−	1.15487e6i	0.117841	−	0.0680354i	−0.439921	−	0.898036i	$-0.644994\pi$
$257$	2.00030e6	−	1.15487e6i	0.117841	−	0.0680354i	0.557762	+	0.830001i	$0.311660\pi$
$258$	−3.48591e6	−	934047.i	−0.202982	−	0.0543888i
$259$		−	3.00996e6i		−	0.173245i
$260$	−5.57952e6	−	7.92468e6i	−0.317451	−	0.450881i
$261$	1.70969e7			0.961602
$262$	−4.81501e6	+	1.79699e7i	−0.267728	+	0.999173i
$263$	−3.76470e6	−	6.52065e6i	−0.206949	−	0.358446i	0.743803	−	0.668399i	$-0.233020\pi$
$263$	−3.76470e6	−	6.52065e6i	−0.206949	−	0.358446i	−0.950752	+	0.309953i	$0.899687\pi$
$264$	1.85865e6	+	1.07309e6i	0.101015	+	0.0583211i
$265$	−6.12574e6	−	6.12574e6i	−0.329171	−	0.329171i
$266$	−1.98892e7	+	5.32928e6i	−1.05675	+	0.283155i
$267$	−479071.	−	1.78792e6i	−0.0251690	−	0.0939319i
$268$	−1.15729e7	+	1.15729e7i	−0.601227	+	0.601227i
$269$	1.49775e7	−	2.59417e7i	0.769452	−	1.33273i	−0.168409	−	0.985717i	$-0.553863\pi$
$269$	1.49775e7	−	2.59417e7i	0.769452	−	1.33273i	0.937861	−	0.347012i	$-0.112804\pi$
$270$	−1.13901e7	+	6.57607e6i	−0.578676	+	0.334099i
$271$	−2.99537e7	−	8.02606e6i	−1.50502	−	0.403269i	−0.590241	−	0.807227i	$-0.700967\pi$
$271$	−2.99537e7	−	8.02606e6i	−1.50502	−	0.403269i	−0.914777	+	0.403958i	$0.867634\pi$
$272$			2.49643e6i			0.124054i
$273$	−4.10311e6	+	8.85890e6i	−0.201663	+	0.435403i
$274$	2.22222e7			1.08028
$275$	790698.	−	2.95092e6i	0.0380200	−	0.141893i
$276$	−610909.	−	1.05812e6i	−0.0290569	−	0.0503280i
$277$	3.15477e7	+	1.82141e7i	1.48432	+	0.856975i	0.999841	−	0.0178261i	$-0.00567453\pi$
$277$	3.15477e7	+	1.82141e7i	1.48432	+	0.856975i	0.484483	+	0.874801i	$0.339008\pi$
$278$	−5.89408e6	−	5.89408e6i	−0.274335	−	0.274335i
$279$	−2.15948e7	+	5.78631e6i	−0.994344	+	0.266434i
$280$	−2.18850e6	−	8.16761e6i	−0.0996950	−	0.372067i
$281$	6.23880e6	−	6.23880e6i	0.281178	−	0.281178i	−0.552400	−	0.833579i	$-0.686288\pi$
$281$	6.23880e6	−	6.23880e6i	0.281178	−	0.281178i	0.833579	+	0.552400i	$0.186288\pi$
$282$	−4.82228e6	+	8.35243e6i	−0.215033	+	0.372448i
$283$	−2.66693e6	+	1.53975e6i	−0.117666	+	0.0679347i	−0.557678	−	0.830057i	$-0.688308\pi$
$283$	−2.66693e6	+	1.53975e6i	−0.117666	+	0.0679347i	0.440012	+	0.897992i	$0.354974\pi$
$284$	1.39581e7	+	3.74006e6i	0.609356	+	0.163276i
$285$		−	1.94211e7i		−	0.838957i
$286$	1.92242e6	−	1.10699e7i	0.0821769	−	0.473201i
$287$	−3.16347e7			−1.33819
$288$	835092.	−	3.11661e6i	0.0349588	−	0.130468i
$289$	−9.09707e6	−	1.57566e7i	−0.376884	−	0.652783i
$290$	−2.07293e7	−	1.19681e7i	−0.849946	−	0.490716i
$291$	1.57584e7	+	1.57584e7i	0.639488	+	0.639488i
$292$	−1.85642e7	+	4.97427e6i	−0.745639	+	0.199793i
$293$	−1.53050e6	−	5.71192e6i	−0.0608459	−	0.227080i	0.928807	−	0.370565i	$-0.120836\pi$
$293$	−1.53050e6	−	5.71192e6i	−0.0608459	−	0.227080i	−0.989653	+	0.143485i	$0.954169\pi$
$294$	148632.	−	148632.i	0.00584885	−	0.00584885i
$295$	7.90830e6	−	1.36976e7i	0.308047	−	0.533553i
$296$	−1.39257e6	+	803998.i	−0.0536958	+	0.0310013i
$297$	−1.47275e7	−	3.94623e6i	−0.562162	−	0.150631i
$298$		−	2.06521e7i		−	0.780398i
$299$	−4.09883e6	+	4.91053e6i	−0.153337	+	0.183703i
$300$	1.41816e6			0.0525244
$301$	−4.26621e6	+	1.59217e7i	−0.156438	+	0.583836i
$302$	−5.04173e6	−	8.73253e6i	−0.183045	−	0.317044i
$303$	1.47594e7	+	8.52132e6i	0.530566	+	0.306323i
$304$	7.77825e6	+	7.77825e6i	0.276861	+	0.276861i
$305$	1.35802e6	−	363881.i	0.0478639	−	0.0128251i
$306$	−1.98817e6	−	7.41994e6i	−0.0693887	−	0.258962i
$307$	−8.09702e6	+	8.09702e6i	−0.279840	+	0.279840i	−0.833045	−	0.553205i	$-0.813405\pi$
$307$	−8.09702e6	+	8.09702e6i	−0.279840	+	0.279840i	0.553205	+	0.833045i	$0.313405\pi$
$308$	4.90130e6	−	8.48930e6i	0.167749	−	0.290549i
$309$	−1.10622e7	+	6.38674e6i	−0.374942	+	0.216473i
$310$	3.02334e7	+	8.10101e6i	1.01485	+	0.271928i
$311$		−	3.00209e7i		−	0.998027i	−0.866594	−	0.499013i	$-0.833696\pi$
$311$		−	3.00209e7i		−	0.998027i	0.866594	−	0.499013i	$-0.166304\pi$
$312$	5.19459e6	−	468007.i	0.171036	−	0.0154095i
$313$	4.58497e7			1.49521			0.747607	−	0.664141i	$-0.231203\pi$
$313$	4.58497e7			1.49521			0.747607	+	0.664141i	$0.231203\pi$
$314$	−7.38785e6	+	2.75718e7i	−0.238632	+	0.890588i
$315$	1.30095e7	+	2.25330e7i	0.416224	+	0.720922i
$316$	−2.25642e6	−	1.30275e6i	−0.0715087	−	0.0412856i
$317$	−1.20135e7	−	1.20135e7i	−0.377131	−	0.377131i	0.492935	−	0.870066i	$-0.335924\pi$
$317$	−1.20135e7	−	1.20135e7i	−0.377131	−	0.377131i	−0.870066	+	0.492935i	$0.835924\pi$
$318$	4.50317e6	−	1.20662e6i	0.140035	−	0.0375223i
$319$	−7.18193e6	−	2.68033e7i	−0.221243	−	0.825689i
$320$	−3.19419e6	+	3.19419e6i	−0.0974789	+	0.0974789i
$321$	−946695.	+	1.63972e6i	−0.0286217	+	0.0495742i
$322$	−4.83293e6	+	2.79030e6i	−0.144758	+	0.0835762i
$323$	2.52965e7	+	6.77816e6i	0.750675	+	0.201143i
$324$			5.91615e6i			0.173942i
$325$	−2.55728e6	−	6.96994e6i	−0.0744952	−	0.203039i
$326$	4.35425e7			1.25678
$327$	−6.46434e6	+	2.41253e7i	−0.184876	+	0.689968i
$328$	8.45002e6	+	1.46359e7i	0.239462	+	0.414760i
$329$	3.81494e7	+	2.20255e7i	1.07127	+	0.618499i
$330$	6.53774e6	+	6.53774e6i	0.181922	+	0.181922i
$331$	−6.29026e6	+	1.68547e6i	−0.173454	+	0.0464769i	−0.344501	−	0.938786i	$-0.611952\pi$
$331$	−6.29026e6	+	1.68547e6i	−0.173454	+	0.0464769i	0.171047	+	0.985263i	$0.445285\pi$
$332$	3.75409e6	+	1.40105e7i	0.102587	+	0.382858i
$333$	3.49871e6	−	3.49871e6i	0.0947492	−	0.0947492i
$334$	8.29033e6	−	1.43593e7i	0.222501	−	0.385384i
$335$	−6.10610e7	+	3.52536e7i	−1.62416	+	0.937711i
$336$	4.39537e6	+	1.17774e6i	0.115872	+	0.0310478i
$337$			3.42205e7i			0.894122i	0.894503	+	0.447061i	$0.147529\pi$
$337$			3.42205e7i			0.894122i	−0.894503	+	0.447061i	$0.852471\pi$
$338$	−1.16672e7	−	2.46863e7i	−0.302147	−	0.639302i
$339$	−2.96858e7			−0.761991
$340$	−2.78350e6	+	1.03881e7i	−0.0708196	+	0.264303i
$341$	1.81428e7	+	3.14242e7i	0.457552	+	0.792503i
$342$	−2.93134e7	−	1.69241e7i	−0.732804	−	0.423084i
$343$	−2.88675e7	−	2.88675e7i	−0.715363	−	0.715363i
$344$	8.50579e6	−	2.27912e6i	0.208949	−	0.0559876i
$345$	−1.36232e6	−	5.08424e6i	−0.0331758	−	0.123814i
$346$	1.65783e7	−	1.65783e7i	0.400232	−	0.400232i
$347$	−6.30679e6	+	1.09237e7i	−0.150945	+	0.261445i	−0.931575	−	0.363548i	$-0.881565\pi$
$347$	−6.30679e6	+	1.09237e7i	−0.150945	+	0.261445i	0.780630	+	0.624994i	$0.214898\pi$
$348$	1.11554e7	−	6.44058e6i	0.264696	−	0.152823i
$349$	2.27764e7	+	6.10291e6i	0.535807	+	0.143569i	0.516568	−	0.856246i	$-0.327209\pi$
$349$	2.27764e7	+	6.10291e6i	0.535807	+	0.143569i	0.0192383	+	0.999815i	$0.493876\pi$
$350$		−	6.47737e6i		−	0.151076i
$351$	−3.47857e7	+	1.27629e7i	−0.804415	+	0.295141i
$352$	−5.23680e6			−0.120071
$353$	−1.32616e7	+	4.94931e7i	−0.301490	+	1.12518i	0.634434	+	0.772977i	$0.281233\pi$
$353$	−1.32616e7	+	4.94931e7i	−0.301490	+	1.12518i	−0.935925	+	0.352200i	$0.885434\pi$
$354$	4.25583e6	+	7.37131e6i	0.0959343	+	0.166163i
$355$	5.39124e7	+	3.11263e7i	1.20505	+	0.695734i
$356$	3.19365e6	+	3.19365e6i	0.0707843	+	0.0707843i
$357$	1.04644e7	−	2.80393e6i	0.229990	−	0.0616257i
$358$	−9.81603e6	−	3.66339e7i	−0.213937	−	0.798425i
$359$	4.21733e7	−	4.21733e7i	0.911495	−	0.911495i	−0.0848953	−	0.996390i	$-0.527056\pi$
$359$	4.21733e7	−	4.21733e7i	0.911495	−	0.911495i	0.996390	+	0.0848953i	$0.0270556\pi$
$360$	6.94998e6	−	1.20377e7i	0.148962	−	0.258010i
$361$	5.91938e7	−	3.41755e7i	1.25821	−	0.726430i
$362$	2.18072e7	+	5.84321e6i	0.459699	+	0.123176i
$363$		−	1.25146e7i		−	0.261637i
$364$	−2.13760e6	−	2.37260e7i	−0.0443223	−	0.491950i
$365$	−8.27959e7			−1.70267
$366$	−195822.	+	730816.i	−0.00399409	+	0.0149061i
$367$	−1.09077e7	−	1.88926e7i	−0.220665	−	0.382203i	0.734345	−	0.678776i	$-0.237489\pi$
$367$	−1.09077e7	−	1.88926e7i	−0.220665	−	0.382203i	−0.955010	+	0.296573i	$0.904156\pi$
$368$	2.58188e6	+	1.49065e6i	0.0518074	+	0.0299110i
$369$	−3.67715e7	−	3.67715e7i	−0.731867	−	0.731867i
$370$	−6.69121e6	+	1.79290e6i	−0.132099	+	0.0353958i
$371$	−5.51118e6	−	2.05680e7i	−0.107925	−	0.402782i
$372$	−1.19105e7	+	1.19105e7i	−0.231366	+	0.231366i
$373$	4.29205e6	−	7.43405e6i	0.0827062	−	0.143251i	−0.821705	−	0.569913i	$-0.806977\pi$
$373$	4.29205e6	−	7.43405e6i	0.0827062	−	0.143251i	0.904411	+	0.426661i	$0.140310\pi$
$374$	−1.07973e7	+	6.23382e6i	−0.206396	+	0.119163i
$375$	−2.13848e7	−	5.73004e6i	−0.405519	−	0.108659i
$376$		−	2.35332e7i		−	0.442708i
$377$	−5.17700e7	−	4.32125e7i	−0.966171	−	0.806465i
$378$	−3.23274e7			−0.598544
$379$	5.41500e6	−	2.02090e7i	0.0994674	−	0.371217i	−0.898191	−	0.439604i	$-0.855119\pi$
$379$	5.41500e6	−	2.02090e7i	0.0994674	−	0.371217i	0.997659	+	0.0683872i	$0.0217853\pi$
$380$	2.36942e7	+	4.10396e7i	0.431809	+	0.747916i
$381$	6.14340e6	+	3.54689e6i	0.111079	+	0.0641318i
$382$	−5.73895e6	−	5.73895e6i	−0.102954	−	0.102954i
$383$	−1.29977e7	+	3.48273e6i	−0.231351	+	0.0619903i	−0.372632	−	0.927979i	$-0.621545\pi$
$383$	−1.29977e7	+	3.48273e6i	−0.231351	+	0.0619903i	0.141281	+	0.989970i	$0.454878\pi$
$384$	−629177.	−	2.34812e6i	−0.0111117	−	0.0414693i
$385$	2.98608e7	−	2.98608e7i	0.523263	−	0.523263i
$386$	−3.07724e7	+	5.32994e7i	−0.535057	+	0.926745i
$387$	−2.34660e7	+	1.35481e7i	−0.404862	+	0.233747i
$388$	−5.25253e7	−	1.40741e7i	−0.899235	−	0.240949i
$389$			1.04578e7i			0.177661i	0.996047	+	0.0888307i	$0.0283130\pi$
$389$			1.04578e7i			0.177661i	−0.996047	+	0.0888307i	$0.971687\pi$
$390$	2.21376e7	+	3.84445e6i	0.373195	+	0.0648097i
$391$	7.09780e6			0.118739
$392$	−132746.	+	495416.i	−0.00220376	+	0.00822454i
$393$	−2.15649e7	−	3.73515e7i	−0.355279	−	0.615362i
$394$	3.98132e7	+	2.29862e7i	0.650936	+	0.375818i
$395$	−7.93689e6	−	7.93689e6i	−0.128783	−	0.128783i
$396$	1.55649e7	−	4.17062e6i	0.250647	−	0.0671606i
$397$	7.76097e6	+	2.89643e7i	0.124035	+	0.462905i	0.999803	−	0.0198264i	$-0.00631136\pi$
$397$	7.76097e6	+	2.89643e7i	0.124035	+	0.462905i	−0.875768	+	0.482732i	$0.839645\pi$
$398$	−4.99407e7	+	4.99407e7i	−0.792146	+	0.792146i
$399$	2.38682e7	−	4.13409e7i	0.375751	−	0.650820i
$400$	−2.99677e6	+	1.73019e6i	−0.0468246	+	0.0270342i
$401$	7.51750e7	+	2.01431e7i	1.16584	+	0.312387i	0.789297	−	0.614011i	$-0.210445\pi$
$401$	7.51750e7	+	2.01431e7i	1.16584	+	0.312387i	0.376546	+	0.926398i	$0.377112\pi$
$402$		−	3.79432e7i		−	0.584058i
$403$	8.00148e7	+	3.70599e7i	1.22252	+	0.566225i
$404$	−4.15849e7			−0.630654
$405$	−6.59646e6	+	2.46183e7i	−0.0992992	+	0.370590i
$406$	−2.94171e7	−	5.09519e7i	−0.439563	−	0.761346i
$407$	−6.95475e6	−	4.01533e6i	−0.103157	−	0.0595577i
$408$	−4.09242e6	−	4.09242e6i	−0.0602559	−	0.0602559i
$409$	−2.53349e6	+	678846.i	−0.0370296	+	0.00992205i	−0.277286	−	0.960787i	$-0.589435\pi$
$409$	−2.53349e6	+	678846.i	−0.0370296	+	0.00992205i	0.240257	+	0.970709i	$0.422768\pi$
$410$	1.88434e7	+	7.03246e7i	0.273406	+	1.02037i
$411$	−3.64291e7	+	3.64291e7i	−0.524715	+	0.524715i
$412$	1.55840e7	−	2.69922e7i	0.222836	−	0.385964i
$413$	3.36681e7	−	1.94383e7i	0.477935	−	0.275936i
$414$	−8.86108e6	−	2.37432e6i	−0.124878	−	0.0334609i
$415$			6.24862e7i			0.874259i
$416$	−1.04059e7	+	7.32649e6i	−0.144544	+	0.101769i
$417$	1.93245e7			0.266501
$418$	−1.42187e7	+	5.30648e7i	−0.194684	+	0.726571i
$419$	−3.18743e7	−	5.52079e7i	−0.433310	−	0.750514i	0.563846	−	0.825880i	$-0.309321\pi$
$419$	−3.18743e7	−	5.52079e7i	−0.433310	−	0.750514i	−0.997156	+	0.0753655i	$0.975988\pi$
$420$	1.69769e7	+	9.80161e6i	0.229145	+	0.132297i
$421$	2.29904e6	+	2.29904e6i	0.0308106	+	0.0308106i	0.722344	−	0.691534i	$-0.243065\pi$
$421$	2.29904e6	+	2.29904e6i	0.0308106	+	0.0308106i	−0.691534	+	0.722344i	$0.743065\pi$
$422$	3.20815e7	−	8.59620e6i	0.426891	−	0.114385i
$423$	1.87420e7	+	6.99460e7i	0.247625	+	0.924149i
$424$	−8.04374e6	+	8.04374e6i	−0.105526	+	0.105526i
$425$	−4.11919e6	+	7.13465e6i	−0.0536593	+	0.0929407i
$426$	−2.90128e7	+	1.67505e7i	−0.375285	+	0.216671i
$427$	3.33797e6	+	894406.i	0.0428745	+	0.0114882i
$428$		−	4.61996e6i		−	0.0589260i
$429$	1.49956e7	+	2.12985e7i	0.189929	+	0.269759i
$430$	3.79356e7			0.477135
$431$	1.46568e7	−	5.46998e7i	0.183065	−	0.683209i	−0.811971	−	0.583698i	$-0.801605\pi$
$431$	1.46568e7	−	5.46998e7i	0.183065	−	0.683209i	0.995036	−	0.0995114i	$-0.0317280\pi$
$432$	8.63507e6	+	1.49564e7i	0.107106	+	0.185513i
$433$	−8.10855e7	−	4.68147e7i	−0.998803	−	0.576659i	−0.0909088	−	0.995859i	$-0.528977\pi$
$433$	−8.10855e7	−	4.68147e7i	−0.998803	−	0.576659i	−0.907894	+	0.419200i	$0.862311\pi$
$434$	5.44005e7	+	5.44005e7i	0.665478	+	0.665478i
$435$	5.36012e7	−	1.43624e7i	0.651189	−	0.174486i
$436$	−1.57733e7	−	5.88668e7i	−0.190311	−	0.710250i
$437$	2.21150e7	−	2.21150e7i	0.264998	−	0.264998i
$438$	2.22782e7	−	3.85869e7i	0.265129	−	0.459217i
$439$	5.98698e7	−	3.45659e7i	0.707643	−	0.408558i	−0.102544	−	0.994728i	$-0.532698\pi$
$439$	5.98698e7	−	3.45659e7i	0.707643	−	0.408558i	0.810188	+	0.586170i	$0.199365\pi$
$440$	−2.17914e7	−	5.83899e6i	−0.255816	−	0.0685456i
$441$		−	1.57821e6i		−	0.0184013i
$442$	−1.27337e7	+	2.74930e7i	−0.147465	+	0.318386i
$443$	1.63760e8			1.88364			0.941818	−	0.336124i	$-0.109116\pi$
$443$	1.63760e8			1.88364			0.941818	+	0.336124i	$0.109116\pi$
$444$	964845.	−	3.60085e6i	0.0110232	−	0.0411392i
$445$	9.72854e6	+	1.68503e7i	0.110400	+	0.191218i
$446$	−4.03181e7	−	2.32777e7i	−0.454460	−	0.262383i
$447$	3.38553e7	+	3.38553e7i	0.379056	+	0.379056i
$448$	−1.07249e7	+	2.87373e6i	−0.119278	+	0.0319604i
$449$	5.70565e6	+	2.12938e7i	0.0630327	+	0.235241i	0.990254	−	0.139272i	$-0.0444764\pi$
$449$	5.70565e6	+	2.12938e7i	0.0630327	+	0.235241i	−0.927221	+	0.374514i	$0.877810\pi$
$450$	7.52916e6	−	7.52916e6i	0.0826245	−	0.0826245i
$451$	−4.22011e7	+	7.30944e7i	−0.460038	+	0.796810i
$452$	6.27304e7	−	3.62174e7i	0.679301	−	0.392195i
$453$	2.25803e7	+	6.05038e6i	0.242904	+	0.0650860i
$454$			6.20625e7i			0.663226i
$455$	1.75593e7	−	1.01112e8i	0.186412	−	1.07342i
$456$	−2.55020e7			−0.268955
$457$	2.97673e6	−	1.11093e7i	0.0311883	−	0.116396i	−0.948577	−	0.316547i	$-0.897477\pi$
$457$	2.97673e6	−	1.11093e7i	0.0311883	−	0.116396i	0.979765	+	0.200151i	$0.0641432\pi$
$458$	−4.92887e7	−	8.53706e7i	−0.513040	−	0.888611i
$459$	3.56078e7	+	2.05582e7i	0.368220	+	0.212592i
$460$	9.08166e6	+	9.08166e6i	0.0933022	+	0.0933022i
$461$	−1.27546e8	+	3.41757e7i	−1.30185	+	0.348831i	−0.842151	−	0.539242i	$-0.818711\pi$
$461$	−1.27546e8	+	3.41757e7i	−1.30185	+	0.348831i	−0.459704	+	0.888072i	$0.652044\pi$
$462$	5.88185e6	+	2.19514e7i	0.0596469	+	0.222605i
$463$	−7.30109e7	+	7.30109e7i	−0.735605	+	0.735605i	−0.971724	−	0.236119i	$-0.924124\pi$
$463$	−7.30109e7	+	7.30109e7i	−0.735605	+	0.735605i	0.236119	+	0.971724i	$0.424124\pi$
$464$	−1.57153e7	+	2.72198e7i	−0.157315	+	0.272477i
$465$	−6.28420e7	+	3.62819e7i	−0.625016	+	0.360853i
$466$	8.70171e7	+	2.33162e7i	0.859898	+	0.230409i
$467$		−	2.89840e6i		−	0.0284582i	−0.999899	−	0.0142291i	$-0.995471\pi$
$467$		−	2.89840e6i		−	0.0284582i	0.999899	−	0.0142291i	$-0.00452942\pi$
$468$	2.50939e7	−	3.00633e7i	0.244811	−	0.293292i
$469$	−1.73304e8			−1.67992
$470$	2.62393e7	−	9.79265e7i	0.252731	−	0.943207i
$471$	−3.30878e7	−	5.73098e7i	−0.316669	−	0.548487i
$472$	−1.79864e7	−	1.03844e7i	−0.171048	−	0.0987544i
$473$	3.10972e7	+	3.10972e7i	0.293859	+	0.293859i
$474$	5.83458e6	−	1.56337e6i	0.0547866	−	0.0146800i
$475$	9.39543e6	+	3.50642e7i	0.0876670	+	0.327178i
$476$	−1.86919e7	+	1.86919e7i	−0.173314	+	0.173314i
$477$	1.75017e7	−	3.03139e7i	0.161260	−	0.279310i
$478$	6.59614e6	−	3.80828e6i	0.0603957	−	0.0348695i
$479$	−1.84101e8	−	4.93298e7i	−1.67514	−	0.448852i	−0.708648	−	0.705562i	$-0.750695\pi$
$479$	−1.84101e8	−	4.93298e7i	−1.67514	−	0.448852i	−0.966488	+	0.256710i	$0.917361\pi$
$480$		−	1.04725e7i		−	0.0946953i
$481$	−1.94372e7	+	1.75120e6i	−0.174662	+	0.0157362i
$482$	8.04904e6			0.0718792
$483$	3.34852e6	−	1.24968e7i	0.0297175	−	0.110907i
$484$	1.52682e7	+	2.64452e7i	0.134664	+	0.233245i
$485$	−2.02876e8	−	1.17131e8i	−1.77830	−	1.02670i
$486$	−5.88778e7	−	5.88778e7i	−0.512912	−	0.512912i
$487$	6.86230e7	−	1.83875e7i	0.594132	−	0.159197i	0.0507911	−	0.998709i	$-0.483826\pi$
$487$	6.86230e7	−	1.83875e7i	0.594132	−	0.159197i	0.543341	+	0.839512i	$0.317159\pi$
$488$	−477814.	−	1.78323e6i	−0.00411150	−	0.0153443i
$489$	−7.13797e7	+	7.13797e7i	−0.610448	+	0.610448i
$490$	−1.10477e6	+	1.91352e6i	−0.00939039	+	0.0162646i
$491$	7.83285e7	−	4.52230e7i	0.661722	−	0.382045i	−0.131211	−	0.991354i	$-0.541887\pi$
$491$	7.83285e7	−	4.52230e7i	0.661722	−	0.382045i	0.792933	+	0.609309i	$0.208553\pi$
$492$	−3.78450e7	−	1.01405e7i	−0.317770	−	0.0851462i
$493$			7.48294e7i			0.624499i
$494$	4.59862e7	+	1.25337e8i	0.381458	+	1.03967i
$495$	6.94192e7			0.572353
$496$	1.06375e7	−	3.96996e7i	0.0871753	−	0.325343i
$497$	7.65073e7	+	1.32515e8i	0.623209	+	1.07943i
$498$	−2.91216e7	−	1.68134e7i	−0.235791	−	0.136134i
$499$	2.60484e7	+	2.60484e7i	0.209643	+	0.209643i	0.804116	−	0.594473i	$-0.202639\pi$
$499$	2.60484e7	+	2.60484e7i	0.209643	+	0.209643i	−0.594473	+	0.804116i	$0.702639\pi$
$500$	5.21800e7	−	1.39816e7i	0.417440	−	0.111853i
$501$	9.94889e6	+	3.71298e7i	0.0791155	+	0.295263i
$502$	1.06445e8	−	1.06445e8i	0.841419	−	0.841419i
$503$	−4.17082e7	+	7.22408e7i	−0.327731	+	0.567647i	−0.982061	−	0.188562i	$-0.939617\pi$
$503$	−4.17082e7	+	7.22408e7i	−0.327731	+	0.567647i	0.654330	+	0.756209i	$0.272951\pi$
$504$	2.95882e7	−	1.70828e7i	0.231115	−	0.133434i
$505$	−1.73043e8	−	4.63668e7i	−1.34363	−	0.360025i
$506$			1.48892e7i			0.114926i
$507$	5.95948e7	+	2.13423e7i	0.457282	+	0.163764i
$508$	−1.73092e7			−0.132034
$509$	5.28310e7	−	1.97168e8i	0.400623	−	1.49515i	−0.411365	−	0.911471i	$-0.634948\pi$
$509$	5.28310e7	−	1.97168e8i	0.400623	−	1.49515i	0.811988	−	0.583675i	$-0.198386\pi$
$510$	−1.24664e7	−	2.15924e7i	−0.0939789	−	0.162776i
$511$	−1.76244e8	−	1.01755e8i	−1.32084	−	0.762590i
$512$	4.19430e6	+	4.19430e6i	0.0312500	+	0.0312500i
$513$	1.74999e8	−	4.68910e7i	1.29624	−	0.347326i
$514$	−3.38170e6	−	1.26207e7i	−0.0249027	−	0.0929381i
$515$	9.49442e7	−	9.49442e7i	0.695099	−	0.695099i
$516$	−1.02075e7	+	1.76798e7i	−0.0742965	+	0.128685i
$517$	1.01784e8	−	5.87647e7i	0.736556	−	0.425251i
$518$	−1.64467e7	−	4.40689e6i	−0.118329	−	0.0317061i
$519$			5.43540e7i			0.388803i
$520$	−5.14702e7	+	1.88845e7i	−0.366055	+	0.134306i
$521$	−7.86210e7			−0.555937			−0.277968	−	0.960590i	$-0.589661\pi$
$521$	−7.86210e7			−0.555937			−0.277968	+	0.960590i	$0.589661\pi$
$522$	2.50316e7	−	9.34191e7i	0.175985	−	0.656786i
$523$	6.36106e7	+	1.10177e8i	0.444656	+	0.770167i	0.998028	−	0.0627671i	$-0.0199925\pi$
$523$	6.36106e7	+	1.10177e8i	0.444656	+	0.770167i	−0.553372	+	0.832934i	$0.686659\pi$
$524$	9.11395e7	+	5.26194e7i	0.633450	+	0.365723i
$525$	1.06184e7	+	1.06184e7i	0.0733808	+	0.0733808i
$526$	−4.11414e7	+	1.10238e7i	−0.282697	+	0.0757485i
$527$	−2.53255e7	−	9.45159e7i	−0.173032	−	0.645763i
$528$	8.58474e6	−	8.58474e6i	0.0583211	−	0.0583211i
$529$	−6.97798e7	+	1.20862e8i	−0.471371	+	0.816438i
$530$	−4.24404e7	+	2.45030e7i	−0.285070	+	0.164585i
$531$	6.17297e7	+	1.65404e7i	0.412298	+	0.110475i
$532$			1.16479e8i			0.773593i
$533$	1.84051e7	+	2.04285e8i	0.121551	+	1.34914i
$534$	−1.04708e7			−0.0687630
$535$	5.15122e6	−	1.92246e7i	0.0336395	−	0.125544i
$536$	4.62917e7	+	8.01795e7i	0.300613	+	0.520678i
$537$	7.61459e7	+	4.39629e7i	0.491727	+	0.283899i
$538$	−1.19820e8	−	1.19820e8i	−0.769452	−	0.769452i
$539$	−2.47421e6	+	662962.i	−0.0158005	+	0.00423372i
$540$	1.92561e7	+	7.18646e7i	0.122289	+	0.456388i
$541$	−2.46914e7	+	2.46914e7i	−0.155939	+	0.155939i	−0.780764	−	0.624826i	$-0.785170\pi$
$541$	−2.46914e7	+	2.46914e7i	−0.155939	+	0.155939i	0.624826	+	0.780764i	$0.285170\pi$
$542$	−8.77104e7	+	1.51919e8i	−0.550875	+	0.954144i
$543$	−4.53276e7	+	2.61699e7i	−0.283115	+	0.163457i
$544$	1.36407e7	+	3.65502e6i	0.0847307	+	0.0227035i
$545$		−	2.62544e8i		−	1.62186i
$546$	4.23985e7	+	3.53902e7i	0.260479	+	0.217423i
$547$	−8.22220e7			−0.502373			−0.251186	−	0.967939i	$-0.580821\pi$
$547$	−8.22220e7			−0.502373			−0.251186	+	0.967939i	$0.580821\pi$
$548$	3.25356e7	−	1.21424e8i	0.197705	−	0.737844i
$549$	2.84035e6	+	4.91962e6i	0.0171654	+	0.0297314i
$550$	−1.49665e7	−	8.64090e6i	−0.0899563	−	0.0519363i
$551$	2.33150e8	+	2.33150e8i	1.39374	+	1.39374i
$552$	−6.67613e6	+	1.78886e6i	−0.0396924	+	0.0106356i
$553$	−7.14062e6	−	2.66492e7i	−0.0422241	−	0.157583i
$554$	1.45713e8	−	1.45713e8i	0.856975	−	0.856975i
$555$	8.02984e6	−	1.39081e7i	0.0469708	−	0.0813559i
$556$	−4.08354e7	+	2.35763e7i	−0.237581	+	0.137168i
$557$	2.35224e8	+	6.30282e7i	1.36118	+	0.364728i	0.864251	−	0.503061i	$-0.167793\pi$
$557$	2.35224e8	+	6.30282e7i	1.36118	+	0.364728i	0.496933	+	0.867789i	$0.334460\pi$
$558$			1.26468e8i			0.727910i
$559$	1.05299e8	+	1.82864e7i	0.602821	+	0.104687i
$560$	−4.78328e7			−0.272372
$561$	7.48096e6	−	2.79193e7i	0.0423710	−	0.158131i
$562$	−2.49552e7	−	4.32237e7i	−0.140589	−	0.243508i
$563$	−2.46962e7	−	1.42583e7i	−0.138390	−	0.0798995i	0.429206	−	0.903206i	$-0.358793\pi$
$563$	−2.46962e7	−	1.42583e7i	−0.138390	−	0.0798995i	−0.567596	+	0.823307i	$0.692127\pi$
$564$	3.85782e7	+	3.85782e7i	0.215033	+	0.215033i
$565$	3.01416e8	−	8.07642e7i	1.67117	−	0.447789i
$566$	4.50871e6	+	1.68267e7i	0.0248658	+	0.0928005i
$567$	−4.42970e7	+	4.42970e7i	−0.243011	+	0.243011i
$568$	4.08721e7	−	7.07926e7i	0.223040	−	0.386316i
$569$	−1.66093e8	+	9.58938e7i	−0.901601	+	0.520539i	−0.877719	−	0.479175i	$-0.840936\pi$
$569$	−1.66093e8	+	9.58938e7i	−0.901601	+	0.520539i	−0.0238815	+	0.999715i	$0.507602\pi$
$570$	−1.06119e8	−	2.84345e7i	−0.573018	−	0.153540i
$571$			1.06284e8i			0.570902i	0.958393	+	0.285451i	$0.0921434\pi$
$571$			1.06284e8i			0.570902i	−0.958393	+	0.285451i	$0.907857\pi$
$572$	−5.76725e7	−	2.67118e7i	−0.308163	−	0.142730i
$573$	1.88158e7			0.100014
$574$	−4.63164e7	+	1.72855e8i	−0.244906	+	0.914001i
$575$	4.91924e6	+	8.52038e6i	0.0258758	+	0.0448183i
$576$	−1.58068e7	−	9.12605e6i	−0.0827135	−	0.0477546i
$577$	5.51484e6	+	5.51484e6i	0.0287082	+	0.0287082i	0.721315	−	0.692607i	$-0.243538\pi$
$577$	5.51484e6	+	5.51484e6i	0.0287082	+	0.0287082i	−0.692607	+	0.721315i	$0.743538\pi$
$578$	−9.94146e7	+	2.66381e7i	−0.514833	+	0.137949i
$579$	−3.69287e7	−	1.37820e8i	−0.190252	−	0.710029i
$580$	−9.57446e7	+	9.57446e7i	−0.490716	+	0.490716i
$581$	−7.67944e7	+	1.33012e8i	−0.391562	+	0.678206i
$582$	1.09177e8	−	6.30334e7i	0.553812	−	0.319744i
$583$	−5.48760e7	−	1.47040e7i	−0.276934	−	0.0742043i
$584$			1.08720e8i			0.545845i
$585$	1.37941e8	−	9.71202e7i	0.689012	−	0.485112i
$586$	−3.34513e7			−0.166234
$587$	9.14624e7	−	3.41342e8i	0.452198	−	1.68763i	−0.244000	−	0.969775i	$-0.578460\pi$
$587$	9.14624e7	−	3.41342e8i	0.452198	−	1.68763i	0.696198	−	0.717850i	$-0.254874\pi$
$588$	−594529.	−	1.02975e6i	−0.00292443	−	0.00506526i
$589$	−3.73396e8	−	2.15581e8i	−1.82736	−	1.05503i
$590$	−6.32664e7	−	6.32664e7i	−0.308047	−	0.308047i
$591$	−1.02948e8	+	2.75847e7i	−0.498717	+	0.133631i
$592$	2.35427e6	+	8.78625e6i	0.0113473	+	0.0423486i
$593$	−9.25280e7	+	9.25280e7i	−0.443720	+	0.443720i	−0.893260	−	0.449540i	$-0.851588\pi$
$593$	−9.25280e7	+	9.25280e7i	−0.443720	+	0.443720i	0.449540	+	0.893260i	$0.351588\pi$
$594$	−4.31253e7	+	7.46951e7i	−0.205765	+	0.356396i
$595$	−9.86224e7	+	5.69397e7i	−0.468193	+	0.270311i
$596$	−1.12845e8	−	3.02368e7i	−0.533022	−	0.142823i
$597$		−	1.63737e8i		−	0.769525i
$598$	2.08306e7	+	2.95860e7i	0.0974086	+	0.138351i
$599$	1.39283e8			0.648063			0.324031	−	0.946046i	$-0.394962\pi$
$599$	1.39283e8			0.648063			0.324031	+	0.946046i	$0.394962\pi$
$600$	2.07633e6	−	7.74896e6i	0.00961263	−	0.0358748i
$601$	−6.87543e7	−	1.19086e8i	−0.316721	−	0.548576i	0.663081	−	0.748548i	$-0.269248\pi$
$601$	−6.87543e7	−	1.19086e8i	−0.316721	−	0.548576i	−0.979802	+	0.199971i	$0.935915\pi$
$602$	8.07518e7	+	4.66221e7i	0.370137	+	0.213699i
$603$	−2.01445e8	−	2.01445e8i	−0.918764	−	0.918764i
$604$	−5.50971e7	+	1.47632e7i	−0.250045	+	0.0669993i
$605$	3.40478e7	+	1.27068e8i	0.153753	+	0.573813i
$606$	6.81706e7	−	6.81706e7i	0.306323	−	0.306323i
$607$	1.18722e8	−	2.05632e8i	0.530840	−	0.919441i	−0.468513	−	0.883457i	$-0.655210\pi$
$607$	1.18722e8	−	2.05632e8i	0.530840	−	0.919441i	0.999352	−	0.0359846i	$-0.0114567\pi$
$608$	5.38893e7	−	3.11130e7i	0.239768	−	0.138430i
$609$	1.31750e8	+	3.53022e7i	0.583308	+	0.156297i
$610$		−	7.95314e6i		−	0.0350388i
$611$	1.20038e8	−	2.59169e8i	0.526252	−	1.13621i
$612$	−4.34542e7			−0.189573
$613$	−2.11474e7	+	7.89232e7i	−0.0918070	+	0.342628i	−0.996516	−	0.0834016i	$-0.973422\pi$
$613$	−2.11474e7	+	7.89232e7i	−0.0918070	+	0.342628i	0.904709	+	0.426030i	$0.140088\pi$
$614$	3.23881e7	+	5.60978e7i	0.139920	+	0.242349i
$615$	−1.46174e8	−	8.43937e7i	−0.628413	−	0.362814i
$616$	−3.92104e7	−	3.92104e7i	−0.167749	−	0.167749i
$617$	−2.96374e7	+	7.94130e6i	−0.126178	+	0.0338093i	−0.321355	−	0.946959i	$-0.604138\pi$
$617$	−2.96374e7	+	7.94130e6i	−0.126178	+	0.0338093i	0.195177	+	0.980768i	$0.437472\pi$
$618$	1.87017e7	+	6.97956e7i	0.0792346	+	0.295708i
$619$	−2.63179e8	+	2.63179e8i	−1.10963	+	1.10963i	−0.116435	+	0.993198i	$0.537147\pi$
$619$	−2.63179e8	+	2.63179e8i	−1.10963	+	1.10963i	−0.993198	+	0.116435i	$0.962853\pi$
$620$	8.85295e7	−	1.53338e8i	0.371461	−	0.643389i
$621$	4.25237e7	−	2.45511e7i	0.177565	−	0.102517i
$622$	−1.64037e8	−	4.39536e7i	−0.681665	−	0.182652i
$623$			4.78247e7i			0.197783i
$624$	5.04816e6	−	2.90690e7i	0.0207768	−	0.119640i
$625$	2.85522e8			1.16950
$626$	6.71286e7	−	2.50527e8i	0.273643	−	1.02125i
$627$	−6.36809e7	−	1.10299e8i	−0.258349	−	0.447474i
$628$	1.39839e8	+	8.07360e7i	0.564610	+	0.325978i
$629$	1.53131e7	+	1.53131e7i	0.0615335	+	0.0615335i
$630$	1.42170e8	−	3.80943e7i	0.568573	−	0.152349i
$631$	7.34823e7	+	2.74240e8i	0.292479	+	1.09155i	0.943199	+	0.332228i	$0.107800\pi$
$631$	7.34823e7	+	2.74240e8i	0.292479	+	1.09155i	−0.650720	+	0.759318i	$0.725533\pi$
$632$	−1.04220e7	+	1.04220e7i	−0.0412856	+	0.0412856i
$633$	−3.84996e7	+	6.66833e7i	−0.151791	+	0.262909i
$634$	−8.32320e7	+	4.80540e7i	−0.326605	+	0.188565i
$635$	−7.20271e7	−	1.92996e7i	−0.281303	−	0.0753750i
$636$		−	2.63724e7i		−	0.102513i
$637$	−3.98893e6	+	4.77887e6i	−0.0154326	+	0.0184887i
$638$	−1.56971e8			−0.604446
$639$	−6.51016e7	+	2.42963e8i	−0.249511	+	0.931187i
$640$	1.27768e7	+	2.21300e7i	0.0487395	+	0.0844192i
$641$	1.88467e8	+	1.08812e8i	0.715586	+	0.413144i	0.813126	−	0.582088i	$-0.197764\pi$
$641$	1.88467e8	+	1.08812e8i	0.715586	+	0.413144i	−0.0975398	+	0.995232i	$0.531097\pi$
$642$	7.57356e6	+	7.57356e6i	0.0286217	+	0.0286217i
$643$	−4.56345e8	+	1.22277e8i	−1.71657	+	0.459953i	−0.977019	−	0.213152i	$-0.931627\pi$
$643$	−4.56345e8	+	1.22277e8i	−1.71657	+	0.459953i	−0.739547	+	0.673105i	$0.764960\pi$
$644$	8.17055e6	+	3.04929e7i	0.0305910	+	0.114167i
$645$	−6.21882e7	+	6.21882e7i	−0.231755	+	0.231755i
$646$	7.40732e7	−	1.28298e8i	0.274766	−	0.475909i
$647$	1.19769e8	−	6.91486e7i	0.442213	−	0.255312i	−0.262323	−	0.964980i	$-0.584489\pi$
$647$	1.19769e8	−	6.91486e7i	0.442213	−	0.255312i	0.704536	+	0.709669i	$0.251155\pi$
$648$	3.23264e7	+	8.66184e6i	0.118804	+	0.0318336i
$649$		−	1.03724e8i		−	0.379441i
$650$	−4.18286e7	+	3.76855e6i	−0.152312	+	0.0137225i
$651$	−1.78359e8			−0.646474
$652$	6.37507e7	−	2.37921e8i	0.230007	−	0.858399i
$653$	1.32227e8	+	2.29023e8i	0.474875	+	0.822507i	0.999586	−	0.0287732i	$-0.00916006\pi$
$653$	1.32227e8	+	2.29023e8i	0.474875	+	0.822507i	−0.524711	+	0.851280i	$0.675827\pi$
$654$	1.22358e8	+	7.06437e7i	0.437422	+	0.252546i
$655$	3.20580e8	+	3.20580e8i	1.14081	+	1.14081i
$656$	9.23436e7	−	2.47434e7i	0.327111	−	0.0876491i
$657$	−8.65850e7	−	3.23140e8i	−0.305314	−	1.13945i
$658$	1.76204e8	−	1.76204e8i	0.618499	−	0.618499i
$659$	−2.32298e8	+	4.02352e8i	−0.811688	+	1.40588i	0.0999946	+	0.994988i	$0.468117\pi$
$659$	−2.32298e8	+	4.02352e8i	−0.811688	+	1.40588i	−0.911682	+	0.410896i	$0.865216\pi$
$660$	4.52948e7	−	2.61510e7i	0.157549	−	0.0909612i
$661$	1.74263e8	+	4.66935e7i	0.603392	+	0.161679i	0.547567	−	0.836762i	$-0.315554\pi$
$661$	1.74263e8	+	4.66935e7i	0.603392	+	0.161679i	0.0558257	+	0.998441i	$0.482221\pi$
$662$			3.68383e7i			0.126977i
$663$	−2.41950e7	−	6.59440e7i	−0.0830204	−	0.226274i
$664$	8.20510e7			0.280272
$665$	−1.29873e8	+	4.84693e8i	−0.441626	+	1.64817i
$666$	−1.39948e7	−	2.42398e7i	−0.0473746	−	0.0820552i
$667$	7.73908e7	+	4.46816e7i	0.260803	+	0.150574i
$668$	−6.63227e7	−	6.63227e7i	−0.222501	−	0.222501i
$669$	1.04253e8	−	2.79346e7i	0.348186	−	0.0932962i
$670$	1.03230e8	+	3.85258e8i	0.343226	+	1.28094i
$671$	6.51949e6	−	6.51949e6i	0.0215797	−	0.0215797i
$672$	1.28705e7	−	2.22924e7i	0.0424120	−	0.0734598i
$673$	3.32008e8	−	1.91685e8i	1.08919	−	0.628844i	0.155829	−	0.987784i	$-0.450195\pi$
$673$	3.32008e8	−	1.91685e8i	1.08919	−	0.628844i	0.933360	+	0.358941i	$0.116862\pi$
$674$	1.86984e8	+	5.01023e7i	0.610697	+	0.163636i
$675$			5.69927e7i			0.185314i
$676$	−1.51971e8	+	2.76077e7i	−0.491948	+	0.0893698i
$677$	1.35385e7			0.0436320			0.0218160	−	0.999762i	$-0.493055\pi$
$677$	1.35385e7			0.0436320			0.0218160	+	0.999762i	$0.493055\pi$
$678$	−4.34630e7	+	1.62206e8i	−0.139454	+	0.520449i
$679$	−2.87902e8	−	4.98661e8i	−0.919678	−	1.59293i
$680$	5.26866e7	+	3.04186e7i	0.167561	+	0.0967414i
$681$	−1.01740e8	−	1.01740e8i	−0.322143	−	0.322143i
$682$	1.98268e8	−	5.31257e7i	0.625027	−	0.167476i
$683$	3.33716e7	+	1.24544e8i	0.104740	+	0.390897i	0.998316	−	0.0580169i	$-0.0184777\pi$
$683$	3.33716e7	+	1.24544e8i	0.104740	+	0.390897i	−0.893575	+	0.448914i	$0.851811\pi$
$684$	−1.35393e8	+	1.35393e8i	−0.423084	+	0.423084i
$685$	2.70775e8	−	4.68996e8i	0.842435	−	1.45914i
$686$	−2.00000e8	+	1.15470e8i	−0.619523	+	0.357682i
$687$	2.20748e8	+	5.91494e7i	0.680813	+	0.182423i
$688$		−	4.98134e7i		−	0.152961i
$689$	−1.29614e8	+	4.75558e7i	−0.396274	+	0.145394i
$690$	−2.97753e7			−0.0906378
$691$	−9.17967e7	+	3.42590e8i	−0.278223	+	1.03834i	0.675428	+	0.737426i	$0.263959\pi$
$691$	−9.17967e7	+	3.42590e8i	−0.278223	+	1.03834i	−0.953651	+	0.300916i	$0.902708\pi$
$692$	−6.63132e7	−	1.14858e8i	−0.200116	−	0.346611i
$693$	1.47770e8	+	8.53148e7i	0.444002	+	0.256345i
$694$	5.04543e7	+	5.04543e7i	0.150945	+	0.150945i
$695$	−1.96212e8	+	5.25748e7i	−0.584482	+	0.156611i
$696$	−1.88593e7	−	7.03840e7i	−0.0559369	−	0.208760i
$697$	1.60941e8	−	1.60941e8i	0.475300	−	0.475300i
$698$	6.66938e7	−	1.15517e8i	0.196119	−	0.339688i
$699$	−1.80871e8	+	1.04426e8i	−0.529586	+	0.305757i
$700$	−3.53930e7	−	9.48353e6i	−0.103187	−	0.0276488i
$701$		−	1.11662e8i		−	0.324153i	−0.986778	−	0.162077i	$-0.948181\pi$
$701$		−	1.11662e8i		−	0.324153i	0.986778	−	0.162077i	$-0.0518192\pi$
$702$	1.88082e7	+	2.08759e8i	0.0543671	+	0.603440i
$703$	9.54239e7			0.274657
$704$	−7.66720e6	+	2.86144e7i	−0.0219745	+	0.0820100i
$705$	1.17518e8	+	2.03547e8i	0.335379	+	0.580893i
$706$	2.51019e8	+	1.44926e8i	0.713334	+	0.411843i
$707$	−3.11366e8	−	3.11366e8i	−0.881075	−	0.881075i
$708$	4.65085e7	−	1.24619e7i	0.131049	−	0.0351144i
$709$	−6.87046e7	−	2.56409e8i	−0.192773	−	0.719440i	−0.992832	−	0.119518i	$-0.961865\pi$
$709$	−6.87046e7	−	2.56409e8i	−0.192773	−	0.719440i	0.800059	−	0.599922i	$-0.204802\pi$
$710$	2.49011e8	−	2.49011e8i	0.695734	−	0.695734i
$711$	2.26763e7	−	3.92765e7i	0.0630905	−	0.109276i
$712$	2.21262e7	−	1.27746e7i	0.0613010	−	0.0353921i
$713$	−1.12873e8	−	3.02443e7i	−0.311403	−	0.0834401i
$714$		−	6.12838e7i		−	0.168365i
$715$	−2.10204e8	−	1.75458e8i	−0.575072	−	0.480014i
$716$	−2.14543e8			−0.584488
$717$	−4.57016e6	+	1.70561e7i	−0.0123986	+	0.0462724i
$718$	−1.68693e8	−	2.92185e8i	−0.455747	−	0.789377i
$719$	3.53312e8	+	2.03985e8i	0.950542	+	0.548796i	0.893249	−	0.449562i	$-0.148420\pi$
$719$	3.53312e8	+	2.03985e8i	0.950542	+	0.548796i	0.0572927	+	0.998357i	$0.481753\pi$
$720$	−5.55999e7	−	5.55999e7i	−0.148962	−	0.148962i
$721$	3.18788e8	−	8.54190e7i	0.850543	−	0.227902i
$722$	−1.00073e8	−	3.73477e8i	−0.265892	−	0.992322i
$723$	−1.31949e7	+	1.31949e7i	−0.0349133	+	0.0349133i
$724$	6.38558e7	−	1.10601e8i	0.168261	−	0.291437i
$725$	−8.98272e7	+	5.18618e7i	−0.235719	+	0.136092i
$726$	−6.83813e7	−	1.83227e7i	−0.178701	−	0.0478828i
$727$		−	1.29055e8i		−	0.335870i	−0.985798	−	0.167935i	$-0.946290\pi$
$727$		−	1.29055e8i		−	0.335870i	0.985798	−	0.167935i	$-0.0537099\pi$
$728$	−1.32771e8	−	2.30572e7i	−0.344120	−	0.0597604i
$729$	5.82609e7			0.150382
$730$	−1.21222e8	+	4.52405e8i	−0.311610	+	1.16294i
$731$	−5.92972e7	−	1.02706e8i	−0.151804	−	0.262932i
$732$	3.70655e6	+	2.13998e6i	0.00945011	+	0.00545602i
$733$	−1.46571e8	−	1.46571e8i	−0.372166	−	0.372166i	0.496100	−	0.868266i	$-0.334765\pi$
$733$	−1.46571e8	−	1.46571e8i	−0.372166	−	0.372166i	−0.868266	+	0.496100i	$0.834765\pi$
$734$	−1.19201e8	+	3.19399e7i	−0.301434	+	0.0807690i
$735$	−1.32579e6	−	4.94791e6i	−0.00333897	−	0.0124612i
$736$	1.19252e7	−	1.19252e7i	0.0299110	−	0.0299110i
$737$	−2.31190e8	+	4.00432e8i	−0.577519	+	1.00029i
$738$	−2.54760e8	+	1.47086e8i	−0.633815	+	0.365933i
$739$	2.70757e8	+	7.25492e7i	0.670883	+	0.179763i	0.578153	−	0.815929i	$-0.303774\pi$
$739$	2.70757e8	+	7.25492e7i	0.670883	+	0.179763i	0.0927305	+	0.995691i	$0.470441\pi$
$740$			3.91864e7i			0.0967031i
$741$	−2.80851e8	−	1.30080e8i	−0.690274	−	0.319709i
$742$	−1.20455e8			−0.294857
$743$	−4.13598e7	+	1.54357e8i	−0.100835	+	0.376322i	−0.997839	−	0.0657001i	$-0.979072\pi$
$743$	−4.13598e7	+	1.54357e8i	−0.100835	+	0.376322i	0.897004	+	0.442022i	$0.145739\pi$
$744$	4.76419e7	+	8.25181e7i	0.115683	+	0.200369i
$745$	−4.35859e8	−	2.51643e8i	−1.05409	−	0.608579i
$746$	−3.43364e7	−	3.43364e7i	−0.0827062	−	0.0827062i
$747$	−2.43874e8	+	6.53459e7i	−0.585065	+	0.156768i
$748$	1.82539e7	+	6.81245e7i	0.0436165	+	0.162779i
$749$	3.45919e7	−	3.45919e7i	0.0823244	−	0.0823244i
$750$	−6.26191e7	+	1.08459e8i	−0.148430	+	0.257089i
$751$	6.10667e8	−	3.52569e8i	1.44173	−	0.832385i	0.443767	−	0.896142i	$-0.353642\pi$
$751$	6.10667e8	−	3.52569e8i	1.44173	−	0.832385i	0.997965	+	0.0637573i	$0.0203084\pi$
$752$	−1.28588e8	−	3.44550e7i	−0.302375	−	0.0810212i
$753$			3.48991e8i			0.817391i
$754$	−3.11914e8	+	2.19609e8i	−0.727647	+	0.512313i
$755$	−2.45731e8			−0.570978
$756$	−4.73307e7	+	1.76640e8i	−0.109541	+	0.408813i
$757$	3.18653e8	+	5.51923e8i	0.734565	+	1.27230i	0.954914	+	0.296882i	$0.0959469\pi$
$757$	3.18653e8	+	5.51923e8i	0.734565	+	1.27230i	−0.220350	+	0.975421i	$0.570720\pi$
$758$	−1.02496e8	−	5.91762e7i	−0.235342	−	0.135875i
$759$	−2.44080e7	−	2.44080e7i	−0.0558222	−	0.0558222i
$760$	2.58935e8	−	6.93816e7i	0.589862	−	0.158053i
$761$	−1.94300e8	−	7.25137e8i	−0.440878	−	1.64538i	−0.726595	−	0.687066i	$-0.758898\pi$
$761$	−1.94300e8	−	7.25137e8i	−0.440878	−	1.64538i	0.285716	−	0.958314i	$-0.407769\pi$
$762$	2.83751e7	−	2.83751e7i	0.0641318	−	0.0641318i
$763$	3.22662e8	−	5.58866e8i	0.726396	−	1.25816i
$764$	−3.97606e7	+	2.29558e7i	−0.0891606	+	0.0514769i
$765$	−1.80822e8	−	4.84511e7i	−0.403894	−	0.108223i
$766$			7.61200e7i			0.169361i
$767$	−1.45114e8	−	2.06107e8i	−0.321605	−	0.456780i
$768$	−1.37515e7			−0.0303576
$769$	−1.26864e8	+	4.73463e8i	−0.278971	+	1.04113i	0.674162	+	0.738583i	$0.264505\pi$
$769$	−1.26864e8	+	4.73463e8i	−0.278971	+	1.04113i	−0.953133	+	0.302551i	$0.902162\pi$
$770$	−1.19443e8	−	2.06882e8i	−0.261631	−	0.453159i
$771$	2.62329e7	+	1.51456e7i	0.0572379	+	0.0330463i
$772$	2.46179e8	+	2.46179e8i	0.535057	+	0.535057i
$773$	−3.33403e8	+	8.93350e7i	−0.721823	+	0.193412i	−0.600985	−	0.799260i	$-0.705225\pi$
$773$	−3.33403e8	+	8.93350e7i	−0.721823	+	0.193412i	−0.120838	+	0.992672i	$0.538558\pi$
$774$	3.96716e7	+	1.48057e8i	0.0855573	+	0.319304i
$775$	9.59071e7	−	9.59071e7i	0.206037	−	0.206037i
$776$	−1.53805e8	+	2.66398e8i	−0.329143	+	0.570092i
$777$	3.41856e7	−	1.97370e7i	0.0728752	−	0.0420745i
$778$	5.71427e7	+	1.53113e7i	0.121345	+	0.0325143i
$779$		−	1.00291e9i		−	2.12152i
$780$	5.34181e7	−	1.15333e8i	0.112565	−	0.243036i
$781$	4.08247e8			0.856979
$782$	1.03919e7	−	3.87831e7i	0.0217307	−	0.0811002i
$783$	2.58833e8	+	4.48312e8i	0.539181	+	0.933888i
$784$	2.51265e6	+	1.45068e6i	0.00521415	+	0.00301039i
$785$	4.91878e8	+	4.91878e8i	1.01683	+	1.01683i
$786$	−2.35666e8	+	6.31464e7i	−0.485320	+	0.130041i
$787$	394370.	+	1.47181e6i	0.000809058	+	0.00301944i	0.966329	−	0.257309i	$-0.0828358\pi$
$787$	394370.	+	1.47181e6i	0.000809058	+	0.00301944i	−0.965520	+	0.260328i	$0.916169\pi$
$788$	1.83889e8	−	1.83889e8i	0.375818	−	0.375818i
$789$	4.93721e7	−	8.55150e7i	0.100520	−	0.174105i
$790$	−5.49884e7	+	3.17475e7i	−0.111529	+	0.0643915i
$791$	7.40869e8	+	1.98515e8i	1.49697	+	0.401111i
$792$		−	9.11547e7i		−	0.183486i
$793$	3.83372e6	−	2.20758e7i	0.00768777	−	0.0442687i
$794$	1.69627e8			0.338870
$795$	2.94050e7	−	1.09741e8i	0.0585221	−	0.218407i
$796$	1.99763e8	+	3.45999e8i	0.396073	+	0.686018i
$797$	4.86259e8	+	2.80742e8i	0.960489	+	0.554539i	0.896324	−	0.443401i	$-0.146228\pi$
$797$	4.86259e8	+	2.80742e8i	0.960489	+	0.554539i	0.0641657	+	0.997939i	$0.479561\pi$
$798$	−1.90945e8	−	1.90945e8i	−0.375751	−	0.375751i
$799$	−3.06139e8	+	8.20297e7i	−0.600175	+	0.160816i
$800$	5.06634e6	+	1.89078e7i	0.00989520	+	0.0369294i
$801$	−5.55904e7	+	5.55904e7i	−0.108169	+	0.108169i
$802$	2.20128e8	−	3.81272e8i	0.426728	−	0.739115i
$803$	−4.70224e8	+	2.71484e8i	−0.908151	+	0.524321i
$804$	−2.07326e8	−	5.55527e7i	−0.398919	−	0.106890i
$805$			1.35998e8i			0.260701i
$806$	3.19649e8	−	3.82949e8i	0.610475	−	0.731368i
$807$	3.92844e8			0.747479
$808$	−6.08845e7	+	2.27224e8i	−0.115418	+	0.430745i
$809$	−1.33071e7	−	2.30485e7i	−0.0251326	−	0.0435309i	0.853186	−	0.521608i	$-0.174667\pi$
$809$	−1.33071e7	−	2.30485e7i	−0.0251326	−	0.0435309i	−0.878318	+	0.478077i	$0.841334\pi$
$810$	1.24859e8	+	7.20875e7i	0.234945	+	0.135645i
$811$	2.09052e8	+	2.09052e8i	0.391915	+	0.391915i	0.875370	−	0.483454i	$-0.160618\pi$
$811$	2.09052e8	+	2.09052e8i	0.391915	+	0.391915i	−0.483454	+	0.875370i	$0.660618\pi$
$812$	−3.21476e8	+	8.61392e7i	−0.600454	+	0.160891i
$813$	−1.05258e8	−	3.92827e8i	−0.195876	−	0.731021i
$814$	−3.21226e7	+	3.21226e7i	−0.0595577	+	0.0595577i
$815$	5.30560e8	−	9.18956e8i	0.980079	−	1.69755i
$816$	−2.83531e7	+	1.63697e7i	−0.0521831	+	0.0301280i
$817$	−5.04762e8	−	1.35251e8i	−0.925594	−	0.248012i
$818$			1.48371e7i			0.0271075i
$819$	4.12989e8	−	3.72083e7i	0.751773	−	0.0677311i
$820$	4.11849e8			0.746959
$821$	−1.50923e8	+	5.63251e8i	−0.272725	+	1.01782i	0.684626	+	0.728895i	$0.259966\pi$
$821$	−1.50923e8	+	5.63251e8i	−0.272725	+	1.01782i	−0.957351	+	0.288929i	$0.906701\pi$
$822$	1.45717e8	+	2.52389e8i	0.262358	+	0.454417i
$823$	3.85230e8	+	2.22413e8i	0.691068	+	0.398988i	0.804012	−	0.594613i	$-0.202695\pi$
$823$	3.85230e8	+	2.22413e8i	0.691068	+	0.398988i	−0.112944	+	0.993601i	$0.536028\pi$
$824$	−1.24672e8	−	1.24672e8i	−0.222836	−	0.222836i
$825$	3.86999e7	−	1.03696e7i	0.0689204	−	0.0184672i
$826$	−5.69193e7	−	2.12426e8i	−0.100999	−	0.376935i
$827$	−6.46168e8	+	6.46168e8i	−1.14243	+	1.14243i	−0.154423	+	0.988005i	$0.549352\pi$
$827$	−6.46168e8	+	6.46168e8i	−1.14243	+	1.14243i	−0.988005	+	0.154423i	$0.950648\pi$
$828$	−2.59470e7	+	4.49416e7i	−0.0457085	+	0.0791694i
$829$	−3.30399e8	+	1.90756e8i	−0.579929	+	0.334822i	−0.761105	−	0.648628i	$-0.775343\pi$
$829$	−3.30399e8	+	1.90756e8i	−0.579929	+	0.334822i	0.181176	+	0.983451i	$0.442010\pi$
$830$	3.41431e8	+	9.14862e7i	0.597130	+	0.160001i
$831$			4.77737e8i			0.832503i
$832$	2.47973e7	+	6.75858e7i	0.0430562	+	0.117351i
$833$	6.90748e6			0.0119505
$834$	2.82930e7	−	1.05591e8i	0.0487731	−	0.182024i
$835$	−2.02033e8	−	3.49932e8i	−0.347027	−	0.601068i
$836$	2.69134e8	+	1.55385e8i	0.460627	+	0.265943i
$837$	−4.78656e8	−	4.78656e8i	−0.816294	−	0.816294i
$838$	−3.48329e8	+	9.33344e7i	−0.591912	+	0.158602i
$839$	1.54009e8	+	5.74768e8i	0.260771	+	0.973210i	0.964788	+	0.263027i	$0.0847209\pi$
$839$	1.54009e8	+	5.74768e8i	0.260771	+	0.973210i	−0.704018	+	0.710182i	$0.748612\pi$
$840$	7.84129e7	−	7.84129e7i	0.132297	−	0.132297i
$841$	−1.73650e8	+	3.00771e8i	−0.291935	+	0.505647i
$842$	1.59282e7	−	9.19616e6i	0.0266828	−	0.0154053i
$843$	1.11766e8	+	2.99477e7i	0.186564	+	0.0499897i
$844$		−	1.87882e8i		−	0.312506i
$845$	−6.63164e8	−	5.45645e7i	−1.09913	−	0.0904357i
$846$	4.09632e8			0.676524
$847$	−8.36881e7	+	3.12328e8i	−0.137725	+	0.513998i
$848$	3.21749e7	+	5.57286e7i	0.0527631	+	0.0913884i
$849$	−3.49754e7	−	2.01931e7i	−0.0571531	−	0.0329974i
$850$	3.29535e7	+	3.29535e7i	0.0536593	+	0.0536593i
$851$	2.49809e7	−	6.69362e6i	0.0405340	−	0.0108611i
$852$	4.90490e7	+	1.83053e8i	0.0793070	+	0.295978i
$853$	5.30632e8	−	5.30632e8i	0.854962	−	0.854962i	−0.135778	−	0.990739i	$-0.543353\pi$
$853$	5.30632e8	−	5.30632e8i	0.854962	−	0.854962i	0.990739	+	0.135778i	$0.0433533\pi$
$854$	9.77425e6	−	1.69295e7i	0.0156931	−	0.0271813i
$855$	−7.14359e8	+	4.12435e8i	−1.14293	+	0.659869i
$856$	−2.52439e7	−	6.76410e6i	−0.0402472	−	0.0107842i
$857$		−	5.45727e7i		−	0.0867028i	−0.999060	−	0.0433514i	$-0.986196\pi$
$857$		−	5.45727e7i		−	0.0867028i	0.999060	−	0.0433514i	$-0.0138035\pi$
$858$	1.38332e8	−	5.07543e7i	0.219008	−	0.0803546i
$859$	−1.51122e8			−0.238422			−0.119211	−	0.992869i	$-0.538037\pi$
$859$	−1.51122e8			−0.238422			−0.119211	+	0.992869i	$0.538037\pi$
$860$	5.55415e7	−	2.07284e8i	0.0873217	−	0.325889i
$861$	−2.07436e8	−	3.59290e8i	−0.324994	−	0.562906i
$862$	−2.77426e8	−	1.60172e8i	−0.433137	−	0.250072i
$863$	3.36535e8	+	3.36535e8i	0.523598	+	0.523598i	0.918656	−	0.395058i	$-0.129276\pi$
$863$	3.36535e8	+	3.36535e8i	0.523598	+	0.523598i	−0.395058	+	0.918656i	$0.629276\pi$
$864$	9.43658e7	−	2.52852e7i	0.146310	−	0.0392036i
$865$	−1.47877e8	−	5.51886e8i	−0.228483	−	0.852710i
$866$	−3.74518e8	+	3.74518e8i	−0.576659	+	0.576659i
$867$	1.19303e8	−	2.06640e8i	0.183061	−	0.317071i
$868$	3.76898e8	−	2.17602e8i	0.576321	−	0.332739i
$869$	−7.11007e7	−	1.90514e7i	−0.108346	−	0.0290313i
$870$		−	3.13911e8i		−	0.476703i
$871$	1.00829e8	+	1.11913e9i	0.152591	+	1.69367i
$872$	−3.44748e8			−0.519939
$873$	2.44982e8	−	9.14285e8i	0.368206	−	1.37416i
$874$	−8.84600e7	−	1.53217e8i	−0.132499	−	0.229495i
$875$	4.95383e8	+	2.86010e8i	0.739464	+	0.426930i
$876$	−1.78225e8	−	1.78225e8i	−0.265129	−	0.265129i
$877$	−5.31319e8	+	1.42367e8i	−0.787692	+	0.211062i	−0.630173	−	0.776454i	$-0.717016\pi$
$877$	−5.31319e8	+	1.42367e8i	−0.787692	+	0.211062i	−0.157519	+	0.987516i	$0.550350\pi$
$878$	−1.01216e8	−	3.77743e8i	−0.149543	−	0.558101i
$879$	5.48371e7	−	5.48371e7i	0.0807436	−	0.0807436i
$880$	−6.38097e7	+	1.10522e8i	−0.0936350	+	0.162181i
$881$	−6.35011e8	+	3.66624e8i	−0.928653	+	0.536158i	−0.886385	−	0.462948i	$-0.846792\pi$
$881$	−6.35011e8	+	3.66624e8i	−0.928653	+	0.536158i	−0.0422675	+	0.999106i	$0.513458\pi$
$882$	−8.62349e6	−	2.31066e6i	−0.0125683	−	0.00336767i
$883$		−	5.91057e8i		−	0.858514i	−0.903182	−	0.429257i	$-0.858776\pi$
$883$		−	5.91057e8i		−	0.858514i	0.903182	−	0.429257i	$-0.141224\pi$
$884$	1.31581e8	+	1.09831e8i	0.190474	+	0.158989i
$885$	2.07427e8			0.299250
$886$	2.39761e8	−	8.94802e8i	0.344729	−	1.28655i
$887$	−4.47665e8	−	7.75378e8i	−0.641478	−	1.11107i	−0.985103	−	0.171966i	$-0.944988\pi$
$887$	−4.47665e8	−	7.75378e8i	−0.641478	−	1.11107i	0.343625	−	0.939107i	$-0.388345\pi$
$888$	−1.82628e7	−	1.05440e7i	−0.0260812	−	0.0150580i
$889$	−1.29602e8	−	1.29602e8i	−0.184462	−	0.184462i
$890$	1.06315e8	−	2.84871e7i	0.150809	−	0.0404091i
$891$	4.32590e7	+	1.61445e8i	0.0611566	+	0.228239i
$892$	−1.86221e8	+	1.86221e8i	−0.262383	+	0.262383i
$893$	−6.98270e8	+	1.20944e9i	−0.980548	+	1.69836i
$894$	2.34556e8	−	1.35421e8i	0.328272	−	0.189528i
$895$	−8.92759e8	−	2.39214e8i	−1.24527	−	0.333670i
$896$			6.28095e7i			0.0873175i
$897$	−8.26484e7	−	1.43528e7i	−0.114514	−	0.0198866i
$898$	1.24705e8			0.172209
$899$	3.18854e8	−	1.18998e9i	0.438847	−	1.63780i
$900$	−3.01166e7	−	5.21635e7i	−0.0413123	−	0.0715549i
$901$	1.32677e8	+	7.66014e7i	0.181394	+	0.104728i
$902$	3.37609e8	+	3.37609e8i	0.460038	+	0.460038i
$903$	−2.08805e8	+	5.59492e7i	−0.283582	+	0.0759855i
$904$	−1.06052e8	−	3.95791e8i	−0.143553	−	0.535748i
$905$	3.89037e8	−	3.89037e8i	0.524862	−	0.524862i
$906$	6.61197e7	−	1.14523e8i	0.0889092	−	0.153995i
$907$	−6.59198e8	+	3.80588e8i	−0.883475	+	0.510075i	−0.871803	−	0.489857i	$-0.837049\pi$
$907$	−6.59198e8	+	3.80588e8i	−0.883475	+	0.510075i	−0.0116725	+	0.999932i	$0.503716\pi$
$908$	3.39116e8	+	9.08658e7i	0.452992	+	0.121379i
$909$		−	7.23850e8i		−	0.963734i
$910$	−5.26780e8	−	2.43985e8i	−0.699044	−	0.323771i
$911$	−5.26681e7			−0.0696615			−0.0348307	−	0.999393i	$-0.511089\pi$
$911$	−5.26681e7			−0.0696615			−0.0348307	+	0.999393i	$0.511089\pi$
$912$	−3.73375e7	+	1.39345e8i	−0.0492221	+	0.183699i
$913$	2.04889e8	+	3.54879e8i	0.269220	+	0.466303i
$914$	−5.63442e7	−	3.25304e7i	−0.0737923	−	0.0426040i
$915$	1.30377e7	+	1.30377e7i	0.0170191	+	0.0170191i
$916$	−5.38637e8	+	1.44327e8i	−0.700825	+	0.187786i
$917$	2.88418e8	+	1.07639e9i	0.374037	+	1.39593i
$918$	1.64465e8	−	1.64465e8i	0.212592	−	0.212592i
$919$	3.02317e8	−	5.23629e8i	0.389508	−	0.674647i	−0.602875	−	0.797835i	$-0.705978\pi$
$919$	3.02317e8	−	5.23629e8i	0.389508	−	0.674647i	0.992383	+	0.123188i	$0.0393118\pi$
$920$	6.29196e7	−	3.63267e7i	0.0808021	−	0.0466511i
$921$	−1.45056e8	−	3.88676e7i	−0.185676	−	0.0497518i
$922$			7.46959e8i			0.953024i
$923$	8.11220e8	−	5.71154e8i	1.03165	−	0.726354i
$924$	1.28556e8			0.162958
$925$	−7.76926e6	+	2.89953e7i	−0.00981645	+	0.0366355i
$926$	2.92044e8	+	5.05834e8i	0.367803	+	0.637053i
$927$	4.69842e8	+	2.71263e8i	0.589810	+	0.340527i
$928$	1.25723e8	+	1.25723e8i	0.157315	+	0.157315i
$929$	1.31045e9	−	3.51135e8i	1.63446	−	0.437952i	0.679255	−	0.733902i	$-0.262303\pi$
$929$	1.31045e9	−	3.51135e8i	1.63446	−	0.437952i	0.955203	+	0.295950i	$0.0956363\pi$
$930$	1.06241e8	+	3.96495e8i	0.132081	+	0.492935i
$931$	2.15220e7	−	2.15220e7i	0.0266707	−	0.0266707i
$932$	2.54804e8	−	4.41333e8i	0.314745	−	0.545154i
$933$	3.40962e8	−	1.96854e8i	0.419817	−	0.242382i
$934$	−1.58372e7	−	4.24356e6i	−0.0194373	−	0.00520822i
$935$			3.03833e8i			0.371707i
$936$	−1.27529e8	−	1.81132e8i	−0.155518	−	0.220885i
$937$	1.25501e8			0.152555			0.0762777	−	0.997087i	$-0.475696\pi$
$937$	1.25501e8			0.152555			0.0762777	+	0.997087i	$0.475696\pi$
$938$	−2.53734e8	+	9.46950e8i	−0.307447	+	1.14741i
$939$	3.00648e8	+	5.20737e8i	0.363129	+	0.628958i
$940$	−4.96664e8	−	2.86749e8i	−0.597969	−	0.345238i
$941$	−8.94688e8	−	8.94688e8i	−1.07375	−	1.07375i	−0.997055	−	0.0766943i	$-0.975563\pi$
$941$	−8.94688e8	−	8.94688e8i	−1.07375	−	1.07375i	−0.0766943	−	0.997055i	$-0.524437\pi$
$942$	−3.61591e8	+	9.68879e7i	−0.432578	+	0.115909i
$943$	−7.03500e7	−	2.62550e8i	−0.0838936	−	0.313095i
$944$	−8.30754e7	+	8.30754e7i	−0.0987544	+	0.0987544i
$945$	−3.93905e8	+	6.82264e8i	−0.466763	+	0.808458i
$946$	2.15448e8	−	1.24389e8i	0.254489	−	0.146929i
$947$	6.86969e7	+	1.84073e7i	0.0808885	+	0.0216740i	0.299036	−	0.954242i	$-0.403335\pi$
$947$	6.86969e7	+	1.84073e7i	0.0808885	+	0.0216740i	−0.218148	+	0.975916i	$0.570001\pi$
$948$		−	3.41697e7i		−	0.0401066i
$949$	−5.54555e8	+	1.19732e9i	−0.648853	+	1.40092i
$950$	2.05350e8			0.239511
$951$	5.76677e7	−	2.15219e8i	0.0670488	−	0.250229i
$952$	7.47677e7	+	1.29501e8i	0.0866569	+	0.150094i
$953$	−7.73647e8	−	4.46665e8i	−0.893849	−	0.516064i	−0.0186495	−	0.999826i	$-0.505937\pi$
$953$	−7.73647e8	−	4.46665e8i	−0.893849	−	0.516064i	−0.875200	+	0.483762i	$0.839270\pi$
$954$	−1.40014e8	−	1.40014e8i	−0.161260	−	0.161260i
$955$	−1.91048e8	+	5.11911e7i	−0.219347	+	0.0587738i
$956$	−1.11514e7	−	4.16177e7i	−0.0127631	−	0.0476326i
$957$	2.57325e8	−	2.57325e8i	0.293593	−	0.293593i
$958$	−5.39086e8	+	9.33724e8i	−0.613143	+	1.06199i
$959$	1.15277e9	−	6.65554e8i	1.30704	−	0.754618i
$960$	−5.72230e7	−	1.53329e7i	−0.0646781	−	0.0173304i
$961$			7.23456e8i			0.815158i
$962$	−1.88893e7	+	1.08771e8i	−0.0212174	+	0.122177i
$963$	8.04177e7			0.0900477
$964$	1.17846e7	−	4.39808e7i	0.0131548	−	0.0490944i
$965$	7.49915e8	+	1.29889e9i	0.834508	+	1.44541i
$966$	−6.33815e7	−	3.65933e7i	−0.0703123	−	0.0405948i
$967$	8.33646e8	+	8.33646e8i	0.921940	+	0.921940i	0.997166	−	0.0752269i	$-0.0239681\pi$
$967$	8.33646e8	+	8.33646e8i	0.921940	+	0.921940i	−0.0752269	+	0.997166i	$0.523968\pi$
$968$	1.66854e8	−	4.47083e7i	0.183954	−	0.0492904i
$969$	8.88922e7	+	3.31750e8i	0.0976995	+	0.364619i
$970$	−9.37045e8	+	9.37045e8i	−1.02670	+	1.02670i
$971$	3.83278e8	−	6.63856e8i	0.418655	−	0.725131i	−0.577150	−	0.816638i	$-0.695835\pi$
$971$	3.83278e8	−	6.63856e8i	0.418655	−	0.725131i	0.995804	+	0.0915074i	$0.0291685\pi$
$972$	−4.07918e8	+	2.35511e8i	−0.444195	+	0.256456i
$973$	−4.82281e8	−	1.29227e8i	−0.523554	−	0.140286i
$974$		−	4.01884e8i		−	0.434935i
$975$	6.23922e7	−	7.47479e7i	0.0673157	−	0.0806464i
$976$	−1.04433e7			−0.0112328
$977$	8.37892e7	−	3.12705e8i	0.0898471	−	0.335314i	−0.906341	−	0.422548i	$-0.861136\pi$
$977$	8.37892e7	−	3.12705e8i	0.0898471	−	0.335314i	0.996188	+	0.0872335i	$0.0278026\pi$
$978$	2.85519e8	+	4.94533e8i	0.305224	+	0.528663i
$979$	1.10503e8	+	6.37988e7i	0.117767	+	0.0679931i
$980$	8.83816e6	+	8.83816e6i	0.00939039	+	0.00939039i
$981$	1.02467e9	−	2.74559e8i	1.08537	−	0.290823i
$982$	−1.32422e8	−	4.94206e8i	−0.139838	−	0.521883i
$983$	4.88573e8	−	4.88573e8i	0.514362	−	0.514362i	−0.401498	−	0.915860i	$-0.631510\pi$
$983$	4.88573e8	−	4.88573e8i	0.514362	−	0.514362i	0.915860	+	0.401498i	$0.131510\pi$
$984$	−1.10818e8	+	1.91942e8i	−0.116312	+	0.201458i
$985$	9.70236e8	−	5.60166e8i	1.01524	−	0.586149i
$986$	4.08876e8	+	1.09558e8i	0.426541	+	0.114291i
$987$			5.77707e8i			0.600837i
$988$	7.52180e8	−	6.77678e7i	0.779921	−	0.0702672i
$989$	−1.41629e8			−0.146407
$990$	1.01637e8	−	3.79314e8i	0.104748	−	0.390924i
$991$	−6.95639e8	−	1.20488e9i	−0.714764	−	1.23801i	−0.963050	−	0.269321i	$-0.913201\pi$
$991$	−6.95639e8	−	1.20488e9i	−0.714764	−	1.23801i	0.248286	−	0.968687i	$-0.420133\pi$
$992$	−2.01348e8	−	1.16248e8i	−0.206259	−	0.119084i
$993$	−6.03895e7	−	6.03895e7i	−0.0616756	−	0.0616756i
$994$	8.36088e8	−	2.24029e8i	0.851320	−	0.228110i
$995$	4.45468e8	+	1.66251e9i	0.452217	+	1.68770i
$996$	−1.34507e8	+	1.34507e8i	−0.136134	+	0.136134i
$997$	−1.53148e8	+	2.65259e8i	−0.154534	+	0.267661i	−0.932889	−	0.360163i	$-0.882721\pi$
$997$	−1.53148e8	+	2.65259e8i	−0.154534	+	0.267661i	0.778355	+	0.627824i	$0.216054\pi$
$998$	1.80469e8	−	1.04194e8i	0.181556	−	0.104821i
$999$	1.44710e8	+	3.87750e7i	0.145145	+	0.0388916i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.7.f.a.11.2	✓	12
13.6	odd	12	inner	26.7.f.a.19.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.7.f.a.11.2	✓	12	1.1	even	1	trivial
26.7.f.a.19.2	yes	12	13.6	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	26.f (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.46410 - 5.46410i) q^{2} +(6.55725 + 11.3575i) q^{3} +(-27.7128 - 16.0000i) q^{4} +(-97.4789 - 97.4789i) q^{5} +(71.6589 - 19.2009i) q^{6} +(-87.6994 - 327.299i) q^{7} +(-128.000 + 128.000i) q^{8} +(278.505 - 482.385i) q^{9} +O(q^{10})\)	\(q+(1.46410 - 5.46410i) q^{2} +(6.55725 + 11.3575i) q^{3} +(-27.7128 - 16.0000i) q^{4} +(-97.4789 - 97.4789i) q^{5} +(71.6589 - 19.2009i) q^{6} +(-87.6994 - 327.299i) q^{7} +(-128.000 + 128.000i) q^{8} +(278.505 - 482.385i) q^{9} +(-675.354 + 389.916i) q^{10} +(-873.242 - 233.984i) q^{11} -419.664i q^{12} +(-2062.55 + 756.755i) q^{13} -1916.79 q^{14} +(467.922 - 1746.31i) q^{15} +(512.000 + 886.810i) q^{16} +(2111.30 + 1218.96i) q^{17} +(-2228.04 - 2228.04i) q^{18} +(10376.3 - 2780.31i) q^{19} +(1141.75 + 4261.08i) q^{20} +(3142.22 - 3142.22i) q^{21} +(-2557.03 + 4428.91i) q^{22} +(2521.36 - 1455.71i) q^{23} +(-2293.09 - 614.430i) q^{24} +3379.27i q^{25} +(1115.20 + 12378.0i) q^{26} +16865.4 q^{27} +(-2806.38 + 10473.6i) q^{28} +(15347.0 + 26581.8i) q^{29} +(-8856.92 - 5113.54i) q^{30} +(-28381.0 - 28381.0i) q^{31} +(5595.24 - 1499.24i) q^{32} +(-3068.59 - 11452.1i) q^{33} +(9751.66 - 9751.66i) q^{34} +(-23355.9 + 40453.6i) q^{35} +(-15436.3 + 8912.16i) q^{36} +(8580.33 + 2299.09i) q^{37} -60767.6i q^{38} +(-22119.5 - 18463.2i) q^{39} +24954.6 q^{40} +(24163.5 - 90179.3i) q^{41} +(-12568.9 - 21770.0i) q^{42} +(-42128.5 - 24322.9i) q^{43} +(20456.2 + 20456.2i) q^{44} +(-74170.7 + 19874.0i) q^{45} +(-4262.61 - 15908.3i) q^{46} +(-91926.6 + 91926.6i) q^{47} +(-6714.62 + 11630.1i) q^{48} +(2453.76 - 1416.68i) q^{49} +(18464.7 + 4947.60i) q^{50} +31972.0i q^{51} +(69267.3 + 12029.1i) q^{52} +62841.7 q^{53} +(24692.6 - 92154.1i) q^{54} +(62314.1 + 107931. i) q^{55} +(53119.8 + 30668.7i) q^{56} +(99617.0 + 99617.0i) q^{57} +(167715. - 44939.2i) q^{58} +(29695.0 + 110823. i) q^{59} +(-40908.4 + 40908.4i) q^{60} +(-5099.27 + 8832.20i) q^{61} +(-196629. + 113524. i) q^{62} +(-182309. - 48849.5i) q^{63} -32768.0i q^{64} +(274823. + 127288. i) q^{65} -67068.3 q^{66} +(132374. - 494028. i) q^{67} +(-39006.6 - 67561.5i) q^{68} +(33066.4 + 19090.9i) q^{69} +(186847. + 186847. i) q^{70} +(-436191. + 116877. i) q^{71} +(26096.6 + 97393.9i) q^{72} +(424686. - 424686. i) q^{73} +(25124.9 - 43517.7i) q^{74} +(-38380.0 + 22158.7i) q^{75} +(-332040. - 88970.0i) q^{76} +306331. i q^{77} +(-133270. + 93831.2i) q^{78} +81421.6 q^{79} +(36536.1 - 136354. i) q^{80} +(-92439.8 - 160110. i) q^{81} +(-457371. - 264063. i) q^{82} +(-320512. - 320512. i) q^{83} +(-137355. + 36804.3i) q^{84} +(-86984.2 - 324630. i) q^{85} +(-194583. + 194583. i) q^{86} +(-201268. + 348607. i) q^{87} +(141725. - 81825.0i) q^{88} +(-136331. - 36529.9i) q^{89} +434374. i q^{90} +(428570. + 608704. i) q^{91} -93165.4 q^{92} +(136235. - 508437. i) q^{93} +(367706. + 636886. i) q^{94} +(-1.28249e6 - 740445. i) q^{95} +(53717.0 + 53717.0i) q^{96} +(1.64142e6 - 439816. i) q^{97} +(-4148.32 - 15481.7i) q^{98} +(-356073. + 356073. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{2} + 150 q^{5} - 1026 q^{7} - 1536 q^{8} - 1338 q^{9}+O(q^{10}) \) 12 * q - 24 * q^2 + 150 * q^5 - 1026 * q^7 - 1536 * q^8 - 1338 * q^9	\( 12 q - 24 q^{2} + 150 q^{5} - 1026 q^{7} - 1536 q^{8} - 1338 q^{9} - 2472 q^{10} - 414 q^{11} - 2586 q^{13} + 11040 q^{14} - 19494 q^{15} + 6144 q^{16} - 11592 q^{17} + 10704 q^{18} + 2100 q^{19} + 12288 q^{20} + 23076 q^{21} - 5376 q^{22} + 23124 q^{23} - 11064 q^{26} + 83844 q^{27} - 32832 q^{28} + 8118 q^{29} + 101760 q^{30} + 32496 q^{31} + 24576 q^{32} - 139596 q^{33} - 55344 q^{34} - 223188 q^{35} - 27264 q^{36} - 36816 q^{37} - 53364 q^{39} - 38400 q^{40} + 186168 q^{41} - 92304 q^{42} + 64290 q^{43} + 43008 q^{44} - 46614 q^{45} - 106416 q^{46} - 211932 q^{47} + 48744 q^{49} - 273312 q^{50} - 54144 q^{52} + 826032 q^{53} + 159552 q^{54} + 120276 q^{55} + 86016 q^{56} + 720600 q^{57} - 61176 q^{58} - 140202 q^{59} - 433536 q^{60} - 511572 q^{61} - 648528 q^{62} - 378180 q^{63} + 1436640 q^{65} + 1161984 q^{66} + 1837104 q^{67} + 221376 q^{68} - 1103952 q^{69} + 1785504 q^{70} - 173352 q^{71} + 280320 q^{72} - 1877034 q^{73} - 1089480 q^{74} - 4264686 q^{75} - 67200 q^{76} + 1108080 q^{78} - 794880 q^{79} + 393216 q^{80} + 1086270 q^{81} - 2141544 q^{82} + 2905464 q^{83} + 368256 q^{84} - 855852 q^{85} - 944400 q^{86} - 3153372 q^{87} - 66048 q^{88} - 2794182 q^{89} + 2486574 q^{91} + 222720 q^{92} + 3523116 q^{93} + 847728 q^{94} - 3175842 q^{95} + 4229166 q^{97} - 659496 q^{98} - 3795372 q^{99}+O(q^{100}) \) 12 * q - 24 * q^2 + 150 * q^5 - 1026 * q^7 - 1536 * q^8 - 1338 * q^9 - 2472 * q^10 - 414 * q^11 - 2586 * q^13 + 11040 * q^14 - 19494 * q^15 + 6144 * q^16 - 11592 * q^17 + 10704 * q^18 + 2100 * q^19 + 12288 * q^20 + 23076 * q^21 - 5376 * q^22 + 23124 * q^23 - 11064 * q^26 + 83844 * q^27 - 32832 * q^28 + 8118 * q^29 + 101760 * q^30 + 32496 * q^31 + 24576 * q^32 - 139596 * q^33 - 55344 * q^34 - 223188 * q^35 - 27264 * q^36 - 36816 * q^37 - 53364 * q^39 - 38400 * q^40 + 186168 * q^41 - 92304 * q^42 + 64290 * q^43 + 43008 * q^44 - 46614 * q^45 - 106416 * q^46 - 211932 * q^47 + 48744 * q^49 - 273312 * q^50 - 54144 * q^52 + 826032 * q^53 + 159552 * q^54 + 120276 * q^55 + 86016 * q^56 + 720600 * q^57 - 61176 * q^58 - 140202 * q^59 - 433536 * q^60 - 511572 * q^61 - 648528 * q^62 - 378180 * q^63 + 1436640 * q^65 + 1161984 * q^66 + 1837104 * q^67 + 221376 * q^68 - 1103952 * q^69 + 1785504 * q^70 - 173352 * q^71 + 280320 * q^72 - 1877034 * q^73 - 1089480 * q^74 - 4264686 * q^75 - 67200 * q^76 + 1108080 * q^78 - 794880 * q^79 + 393216 * q^80 + 1086270 * q^81 - 2141544 * q^82 + 2905464 * q^83 + 368256 * q^84 - 855852 * q^85 - 944400 * q^86 - 3153372 * q^87 - 66048 * q^88 - 2794182 * q^89 + 2486574 * q^91 + 222720 * q^92 + 3523116 * q^93 + 847728 * q^94 - 3175842 * q^95 + 4229166 * q^97 - 659496 * q^98 - 3795372 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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