LMFDB - Embedded newform 11.7.d.a.8.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,7,Mod(2,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("11.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	11.d (of order $10$, 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:	$2.53059491982$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 825 x^{18} + 275175 x^{16} + 47589550 x^{14} + 4569013705 x^{12} + 245564683275 x^{10} + \cdots + 17\!\cdots\!25 $ x^20 + 825x^18 + 275175x^16 + 47589550x^14 + 4569013705x^12 + 245564683275x^10 + 7342625961605x^8 + 117784752305650x^6 + 929387807009775x^4 + 2945657032798125*x^2 + 1742746483878125
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 5\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			8.2
Root			$-3.41863i$ of defining polynomial
Character	$\chi$	$=$	11.8
Dual form			11.7.d.a.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.12745 - 4.30457i) q^{2} +(13.7792 + 42.4080i) q^{3} +(11.0287 - 33.9429i) q^{4} +(141.251 + 102.625i) q^{5} +(139.454 - 191.943i) q^{6} +(43.6363 + 14.1783i) q^{7} +(-504.462 + 163.910i) q^{8} +(-1018.80 + 740.201i) q^{9} +O(q^{10})$	\(q+(-3.12745 - 4.30457i) q^{2} +(13.7792 + 42.4080i) q^{3} +(11.0287 - 33.9429i) q^{4} +(141.251 + 102.625i) q^{5} +(139.454 - 191.943i) q^{6} +(43.6363 + 14.1783i) q^{7} +(-504.462 + 163.910i) q^{8} +(-1018.80 + 740.201i) q^{9} -928.982i q^{10} +(288.920 - 1299.26i) q^{11} +1591.42 q^{12} +(-610.524 - 840.314i) q^{13} +(-75.4391 - 232.178i) q^{14} +(-2405.80 + 7404.28i) q^{15} +(435.337 + 316.291i) q^{16} +(4591.05 - 6319.03i) q^{17} +(6372.49 + 2070.55i) q^{18} +(-6664.55 + 2165.44i) q^{19} +(5041.22 - 3662.66i) q^{20} +2045.90i q^{21} +(-6496.36 + 2819.71i) q^{22} +3548.64 q^{23} +(-13902.2 - 19134.7i) q^{24} +(4591.64 + 14131.6i) q^{25} +(-1707.81 + 5256.09i) q^{26} +(-19130.4 - 13899.1i) q^{27} +(962.506 - 1324.78i) q^{28} +(-10832.8 - 3519.80i) q^{29} +(39396.3 - 12800.6i) q^{30} +(-17077.9 + 12407.8i) q^{31} +31084.0i q^{32} +(59080.3 - 5650.29i) q^{33} -41559.0 q^{34} +(4708.64 + 6480.89i) q^{35} +(13888.5 + 42744.5i) q^{36} +(11988.4 - 36896.6i) q^{37} +(30164.4 + 21915.7i) q^{38} +(27223.5 - 37470.0i) q^{39} +(-88077.3 - 28618.0i) q^{40} +(73640.3 - 23927.2i) q^{41} +(8806.70 - 6398.45i) q^{42} +90422.5i q^{43} +(-40914.4 - 24136.0i) q^{44} -219870. q^{45} +(-11098.2 - 15275.4i) q^{46} +(-7062.11 - 21734.9i) q^{47} +(-7414.66 + 22820.0i) q^{48} +(-93476.9 - 67915.0i) q^{49} +(46470.4 - 63961.0i) q^{50} +(331238. + 107626. i) q^{51} +(-35256.0 + 11455.4i) q^{52} +(29877.9 - 21707.5i) q^{53} +125817. i q^{54} +(174147. - 153872. i) q^{55} -24336.9 q^{56} +(-183664. - 252792. i) q^{57} +(18727.9 + 57638.7i) q^{58} +(-93159.7 + 286716. i) q^{59} +(224790. + 163319. i) q^{60} +(-182387. + 251034. i) q^{61} +(106820. + 34708.1i) q^{62} +(-54951.5 + 17854.8i) q^{63} +(161665. - 117456. i) q^{64} -181351. i q^{65} +(-209093. - 236644. i) q^{66} +20396.5 q^{67} +(-163853. - 225524. i) q^{68} +(48897.5 + 150491. i) q^{69} +(13171.4 - 40537.4i) q^{70} +(116702. + 84788.8i) q^{71} +(392620. - 540395. i) q^{72} +(-298573. - 97012.3i) q^{73} +(-196317. + 63787.3i) q^{74} +(-536024. + 389444. i) q^{75} +250096. i q^{76} +(31028.8 - 52598.7i) q^{77} -246433. q^{78} +(288467. + 397041. i) q^{79} +(29032.5 + 89352.9i) q^{80} +(42142.0 - 129700. i) q^{81} +(-333303. - 242159. i) q^{82} +(-197159. + 271366. i) q^{83} +(69443.7 + 22563.6i) q^{84} +(1.29698e6 - 421415. i) q^{85} +(389230. - 282792. i) q^{86} -507898. i q^{87} +(67212.8 + 702787. i) q^{88} +484916. q^{89} +(687633. + 946446. i) q^{90} +(-14726.8 - 45324.4i) q^{91} +(39137.0 - 120451. i) q^{92} +(-761509. - 553269. i) q^{93} +(-71473.2 + 98374.4i) q^{94} +(-1.16361e6 - 378079. i) q^{95} +(-1.31821e6 + 428312. i) q^{96} +(311023. - 225972. i) q^{97} +614779. i q^{98} +(667365. + 1.53755e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{2} - 39 q^{3} + 215 q^{4} + 181 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} - 704 q^{9}+O(q^{10}) $ 20 * q - 5 * q^2 - 39 * q^3 + 215 * q^4 + 181 * q^5 - 405 * q^6 - 365 * q^7 + 1595 * q^8 - 704 * q^9	\( 20 q - 5 q^{2} - 39 q^{3} + 215 q^{4} + 181 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} - 704 q^{9} - 3498 q^{11} - 3006 q^{12} - 1805 q^{13} + 7170 q^{14} - 525 q^{15} - 2185 q^{16} + 3635 q^{17} + 11970 q^{18} + 23845 q^{19} + 5144 q^{20} - 2915 q^{22} + 7816 q^{23} - 123775 q^{24} - 30416 q^{25} - 131310 q^{26} - 18687 q^{27} + 226540 q^{28} + 134595 q^{29} + 220420 q^{30} - 71211 q^{31} + 5951 q^{33} - 228190 q^{34} - 377445 q^{35} - 119626 q^{36} - 205731 q^{37} + 127220 q^{38} + 443075 q^{39} + 704340 q^{40} + 490975 q^{41} - 20170 q^{42} - 537812 q^{44} - 805524 q^{45} - 714610 q^{46} + 25329 q^{47} - 935824 q^{48} + 304010 q^{49} + 417855 q^{50} + 1169565 q^{51} + 1468510 q^{52} - 110919 q^{53} - 5511 q^{55} - 862620 q^{56} - 1435995 q^{57} - 667940 q^{58} - 581009 q^{59} + 664640 q^{60} + 892675 q^{61} + 2337360 q^{62} + 900840 q^{63} + 124615 q^{64} + 272910 q^{66} - 960956 q^{67} - 1822680 q^{68} - 624034 q^{69} - 1987140 q^{70} - 288895 q^{71} + 954565 q^{72} - 806585 q^{73} - 404170 q^{74} - 550845 q^{75} + 623095 q^{77} + 1703080 q^{78} + 1662955 q^{79} + 1190956 q^{80} + 1465924 q^{81} - 282095 q^{82} + 14645 q^{83} - 2604390 q^{84} - 33365 q^{85} + 735635 q^{86} - 1860485 q^{88} + 1111620 q^{89} + 4118080 q^{90} + 650935 q^{91} + 4407784 q^{92} - 1556453 q^{93} - 5913080 q^{94} - 4329525 q^{95} - 6429020 q^{96} - 1189281 q^{97} + 252208 q^{99}+O(q^{100}) \) 20 * q - 5 * q^2 - 39 * q^3 + 215 * q^4 + 181 * q^5 - 405 * q^6 - 365 * q^7 + 1595 * q^8 - 704 * q^9 - 3498 * q^11 - 3006 * q^12 - 1805 * q^13 + 7170 * q^14 - 525 * q^15 - 2185 * q^16 + 3635 * q^17 + 11970 * q^18 + 23845 * q^19 + 5144 * q^20 - 2915 * q^22 + 7816 * q^23 - 123775 * q^24 - 30416 * q^25 - 131310 * q^26 - 18687 * q^27 + 226540 * q^28 + 134595 * q^29 + 220420 * q^30 - 71211 * q^31 + 5951 * q^33 - 228190 * q^34 - 377445 * q^35 - 119626 * q^36 - 205731 * q^37 + 127220 * q^38 + 443075 * q^39 + 704340 * q^40 + 490975 * q^41 - 20170 * q^42 - 537812 * q^44 - 805524 * q^45 - 714610 * q^46 + 25329 * q^47 - 935824 * q^48 + 304010 * q^49 + 417855 * q^50 + 1169565 * q^51 + 1468510 * q^52 - 110919 * q^53 - 5511 * q^55 - 862620 * q^56 - 1435995 * q^57 - 667940 * q^58 - 581009 * q^59 + 664640 * q^60 + 892675 * q^61 + 2337360 * q^62 + 900840 * q^63 + 124615 * q^64 + 272910 * q^66 - 960956 * q^67 - 1822680 * q^68 - 624034 * q^69 - 1987140 * q^70 - 288895 * q^71 + 954565 * q^72 - 806585 * q^73 - 404170 * q^74 - 550845 * q^75 + 623095 * q^77 + 1703080 * q^78 + 1662955 * q^79 + 1190956 * q^80 + 1465924 * q^81 - 282095 * q^82 + 14645 * q^83 - 2604390 * q^84 - 33365 * q^85 + 735635 * q^86 - 1860485 * q^88 + 1111620 * q^89 + 4118080 * q^90 + 650935 * q^91 + 4407784 * q^92 - 1556453 * q^93 - 5913080 * q^94 - 4329525 * q^95 - 6429020 * q^96 - 1189281 * q^97 + 252208 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−3.12745	−	4.30457i	−0.390932	−	0.538071i	0.567507	−	0.823368i	$-0.307908\pi$
$2$	−3.12745	−	4.30457i	−0.390932	−	0.538071i	−0.958439	+	0.285297i	$0.907908\pi$
$3$	13.7792	+	42.4080i	0.510341	+	1.57067i	0.791603	+	0.611036i	$0.209247\pi$
$3$	13.7792	+	42.4080i	0.510341	+	1.57067i	−0.281262	+	0.959631i	$0.590753\pi$
$4$	11.0287	−	33.9429i	0.172324	−	0.530358i
$5$	141.251	+	102.625i	1.13001	+	0.821001i	0.985696	−	0.168531i	$-0.0539023\pi$
$5$	141.251	+	102.625i	1.13001	+	0.821001i	0.144314	+	0.989532i	$0.453902\pi$
$6$	139.454	−	191.943i	0.645623	−	0.888623i
$7$	43.6363	+	14.1783i	0.127220	+	0.0413362i	0.371935	−	0.928259i	$-0.378694\pi$
$7$	43.6363	+	14.1783i	0.127220	+	0.0413362i	−0.244715	+	0.969595i	$0.578694\pi$
$8$	−504.462	+	163.910i	−0.985278	+	0.320136i
$9$	−1018.80	+	740.201i	−1.39753	+	1.01536i
$10$		−	928.982i		−	0.928982i
$11$	288.920	−	1299.26i	0.217070	−	0.976156i
$11$	288.920	−	1299.26i	0.217070	−	0.976156i
$12$	1591.42			0.920960
$13$	−610.524	−	840.314i	−0.277890	−	0.382483i	0.647144	−	0.762368i	$-0.275963\pi$
$13$	−610.524	−	840.314i	−0.277890	−	0.382483i	−0.925034	+	0.379885i	$0.875963\pi$
$14$	−75.4391	−	232.178i	−0.0274924	−	0.0846129i
$15$	−2405.80	+	7404.28i	−0.712828	+	2.19386i
$16$	435.337	+	316.291i	0.106283	+	0.0772194i
$17$	4591.05	−	6319.03i	0.934469	−	1.28619i	−0.0236216	−	0.999721i	$-0.507520\pi$
$17$	4591.05	−	6319.03i	0.934469	−	1.28619i	0.958091	−	0.286465i	$-0.0924803\pi$
$18$	6372.49	+	2070.55i	1.09268	+	0.355032i
$19$	−6664.55	+	2165.44i	−0.971651	+	0.315709i	−0.751482	−	0.659753i	$-0.770661\pi$
$19$	−6664.55	+	2165.44i	−0.971651	+	0.315709i	−0.220169	+	0.975462i	$0.570661\pi$
$20$	5041.22	−	3662.66i	0.630152	−	0.457832i
$21$			2045.90i			0.220915i
$22$	−6496.36	+	2819.71i	−0.610101	+	0.264811i
$23$	3548.64			0.291661			0.145831	−	0.989310i	$-0.453415\pi$
$23$	3548.64			0.291661			0.145831	+	0.989310i	$0.453415\pi$
$24$	−13902.2	−	19134.7i	−1.00565	−	1.38417i
$25$	4591.64	+	14131.6i	0.293865	+	0.904423i
$26$	−1707.81	+	5256.09i	−0.0971670	+	0.299049i
$27$	−19130.4	−	13899.1i	−0.971927	−	0.706146i
$28$	962.506	−	1324.78i	0.0438459	−	0.0603488i
$29$	−10832.8	−	3519.80i	−0.444168	−	0.144319i	0.0783896	−	0.996923i	$-0.475022\pi$
$29$	−10832.8	−	3519.80i	−0.444168	−	0.144319i	−0.522558	+	0.852604i	$0.675022\pi$
$30$	39396.3	−	12800.6i	1.45912	−	0.474097i
$31$	−17077.9	+	12407.8i	−0.573256	+	0.416495i	−0.836286	−	0.548293i	$-0.815278\pi$
$31$	−17077.9	+	12407.8i	−0.573256	+	0.416495i	0.263031	+	0.964787i	$0.415278\pi$
$32$			31084.0i			0.948607i
$33$	59080.3	−	5650.29i	1.64400	−	0.157228i
$34$	−41559.0			−1.05737
$35$	4708.64	+	6480.89i	0.109823	+	0.151158i
$36$	13888.5	+	42744.5i	0.297679	+	0.916162i
$37$	11988.4	−	36896.6i	0.236678	−	0.728419i	−0.760217	−	0.649669i	$-0.774907\pi$
$37$	11988.4	−	36896.6i	0.236678	−	0.728419i	0.996894	−	0.0787492i	$-0.0250926\pi$
$38$	30164.4	+	21915.7i	0.549723	+	0.399397i
$39$	27223.5	−	37470.0i	0.458934	−	0.631669i
$40$	−88077.3	−	28618.0i	−1.37621	−	0.447157i
$41$	73640.3	−	23927.2i	1.06847	−	0.347168i	0.278581	−	0.960413i	$-0.410136\pi$
$41$	73640.3	−	23927.2i	1.06847	−	0.347168i	0.789893	+	0.613245i	$0.210136\pi$
$42$	8806.70	−	6398.45i	0.118868	−	0.0863628i
$43$			90422.5i			1.13729i	0.822583	+	0.568645i	$0.192532\pi$
$43$			90422.5i			1.13729i	−0.822583	+	0.568645i	$0.807468\pi$
$44$	−40914.4	−	24136.0i	−0.480306	−	0.283340i
$45$	−219870.			−2.41284
$46$	−11098.2	−	15275.4i	−0.114020	−	0.156935i
$47$	−7062.11	−	21734.9i	−0.0680207	−	0.209346i	0.911268	−	0.411813i	$-0.135104\pi$
$47$	−7062.11	−	21734.9i	−0.0680207	−	0.209346i	−0.979289	+	0.202467i	$0.935104\pi$
$48$	−7414.66	+	22820.0i	−0.0670452	+	0.206344i
$49$	−93476.9	−	67915.0i	−0.794541	−	0.577268i
$50$	46470.4	−	63961.0i	0.371763	−	0.511688i
$51$	331238.	+	107626.i	2.49707	+	0.811346i
$52$	−35256.0	+	11455.4i	−0.250740	+	0.0814703i
$53$	29877.9	−	21707.5i	0.200688	−	0.145809i	−0.482902	−	0.875674i	$-0.660417\pi$
$53$	29877.9	−	21707.5i	0.200688	−	0.145809i	0.683591	+	0.729866i	$0.260417\pi$
$54$			125817.i			0.799021i
$55$	174147.	−	153872.i	1.04672	−	0.924852i
$56$	−24336.9			−0.138580
$57$	−183664.	−	252792.i	−0.991746	−	1.36502i
$58$	18727.9	+	57638.7i	0.0959856	+	0.295413i
$59$	−93159.7	+	286716.i	−0.453599	+	1.39603i	0.419174	+	0.907906i	$0.362320\pi$
$59$	−93159.7	+	286716.i	−0.453599	+	1.39603i	−0.872772	+	0.488127i	$0.837680\pi$
$60$	224790.	+	163319.i	1.04069	+	0.756109i
$61$	−182387.	+	251034.i	−0.803533	+	1.10597i	0.188756	+	0.982024i	$0.439555\pi$
$61$	−182387.	+	251034.i	−0.803533	+	1.10597i	−0.992289	+	0.123945i	$0.960445\pi$
$62$	106820.	+	34708.1i	0.448208	+	0.145632i
$63$	−54951.5	+	17854.8i	−0.219765	+	0.0714058i
$64$	161665.	−	117456.i	0.616702	−	0.448060i
$65$		−	181351.i		−	0.660357i
$66$	−209093.	−	236644.i	−0.727290	−	0.823122i
$67$	20396.5			0.0678160			0.0339080	−	0.999425i	$-0.489205\pi$
$67$	20396.5			0.0678160			0.0339080	+	0.999425i	$0.489205\pi$
$68$	−163853.	−	225524.i	−0.521108	−	0.717244i
$69$	48897.5	+	150491.i	0.148847	+	0.458103i
$70$	13171.4	−	40537.4i	0.0384006	−	0.118185i
$71$	116702.	+	84788.8i	0.326064	+	0.236899i	0.738758	−	0.673970i	$-0.235412\pi$
$71$	116702.	+	84788.8i	0.326064	+	0.236899i	−0.412695	+	0.910869i	$0.635412\pi$
$72$	392620.	−	540395.i	1.05190	−	1.44782i
$73$	−298573.	−	97012.3i	−0.767507	−	0.249378i	−0.101009	−	0.994885i	$-0.532207\pi$
$73$	−298573.	−	97012.3i	−0.767507	−	0.249378i	−0.666497	+	0.745507i	$0.732207\pi$
$74$	−196317.	+	63787.3i	−0.484466	+	0.157413i
$75$	−536024.	+	389444.i	−1.27058	+	0.923128i
$76$			250096.i			0.569727i
$77$	31028.8	−	52598.7i	0.0679661	−	0.115213i
$78$	−246433.			−0.519295
$79$	288467.	+	397041.i	0.585080	+	0.805294i	0.994241	−	0.107168i	$-0.0341784\pi$
$79$	288467.	+	397041.i	0.585080	+	0.805294i	−0.409161	+	0.912462i	$0.634178\pi$
$80$	29032.5	+	89352.9i	0.0567041	+	0.174517i
$81$	42142.0	−	129700.i	0.0792977	−	0.244053i
$82$	−333303.	−	242159.i	−0.604502	−	0.439196i
$83$	−197159.	+	271366.i	−0.344812	+	0.474593i	−0.945839	−	0.324636i	$-0.894758\pi$
$83$	−197159.	+	271366.i	−0.344812	+	0.474593i	0.601027	+	0.799229i	$0.294758\pi$
$84$	69443.7	+	22563.6i	0.117164	+	0.0380689i
$85$	1.29698e6	−	421415.i	2.11192	−	0.686204i
$86$	389230.	−	282792.i	0.611943	−	0.444603i
$87$		−	507898.i		−	0.771292i
$88$	67212.8	+	702787.i	0.0986288	+	1.03128i
$89$	484916.			0.687854			0.343927	−	0.938996i	$-0.388243\pi$
$89$	484916.			0.687854			0.343927	+	0.938996i	$0.388243\pi$
$90$	687633.	+	946446.i	0.943255	+	1.29828i
$91$	−14726.8	−	45324.4i	−0.0195427	−	0.0601462i
$92$	39137.0	−	120451.i	0.0502602	−	0.154685i
$93$	−761509.	−	553269.i	−0.946730	−	0.687840i
$94$	−71473.2	+	98374.4i	−0.0860517	+	0.118440i
$95$	−1.16361e6	−	378079.i	−1.35717	−	0.440972i
$96$	−1.31821e6	+	428312.i	−1.48995	+	0.484113i
$97$	311023.	−	225972.i	0.340783	−	0.247593i	−0.404209	−	0.914667i	$-0.632453\pi$
$97$	311023.	−	225972.i	0.340783	−	0.247593i	0.744992	+	0.667073i	$0.232453\pi$
$98$			614779.i			0.653192i
$99$	667365.	+	1.53755e6i	0.687793	+	1.58461i
$100$	530308.			0.530308
$101$	−595824.	−	820081.i	−0.578301	−	0.795962i	0.415207	−	0.909727i	$-0.363709\pi$
$101$	−595824.	−	820081.i	−0.578301	−	0.795962i	−0.993508	+	0.113764i	$0.963709\pi$
$102$	−572650.	−	1.76243e6i	−0.539621	−	1.66078i
$103$	610320.	−	1.87837e6i	0.558530	−	1.71898i	−0.127905	−	0.991786i	$-0.540825\pi$
$103$	610320.	−	1.87837e6i	0.558530	−	1.71898i	0.686435	−	0.727191i	$-0.259175\pi$
$104$	445722.	+	323836.i	0.396246	+	0.287889i
$105$	−209960.	+	288986.i	−0.181372	+	0.249637i
$106$	−186883.	−	60722.1i	−0.156911	−	0.0509834i
$107$	−1.00865e6	+	327730.i	−0.823358	+	0.267525i	−0.690245	−	0.723576i	$-0.742497\pi$
$107$	−1.00865e6	+	327730.i	−0.823358	+	0.267525i	−0.133113	+	0.991101i	$0.542497\pi$
$108$	−682759.	+	496054.i	−0.541996	+	0.393783i
$109$		−	5885.12i		−	0.00454440i	−0.999997	−	0.00227220i	$-0.999277\pi$
$109$		−	5885.12i		−	0.00454440i	0.999997	−	0.00227220i	$-0.000723264\pi$
$110$	−1.20699e6	−	268401.i	−0.906831	−	0.201654i
$111$	1.72990e6			1.26489
$112$	14512.0	+	19974.1i	0.0103294	+	0.0142172i
$113$	341419.	+	1.05078e6i	0.236620	+	0.728242i	0.996902	+	0.0786492i	$0.0250607\pi$
$113$	341419.	+	1.05078e6i	0.236620	+	0.728242i	−0.760282	+	0.649593i	$0.774939\pi$
$114$	−513761.	+	1.58119e6i	−0.346774	+	1.06726i
$115$	501251.	+	364180.i	0.329580	+	0.239454i
$116$	−238944.	+	328879.i	−0.153082	+	0.210699i
$117$	1.24400e6	+	404201.i	0.776719	+	0.252371i
$118$	1.52554e6	−	495679.i	0.928492	−	0.301685i
$119$	289930.	−	210646.i	0.172049	−	0.125001i
$120$		−	4.12951e6i		−	2.38977i
$121$	−1.60461e6	−	750766.i	−0.905761	−	0.423788i
$122$	1.65100e6			0.909217
$123$	2.02941e6	+	2.79324e6i	1.09057	+	1.50104i
$124$	232810.	+	716515.i	0.122106	+	0.375803i
$125$	41336.0	−	127219.i	0.0211640	−	0.0651362i
$126$	248715.	+	180702.i	0.124334	+	0.0903342i
$127$	−773325.	+	1.06439e6i	−0.377529	+	0.519625i	−0.954928	−	0.296838i	$-0.904068\pi$
$127$	−773325.	+	1.06439e6i	−0.377529	+	0.519625i	0.577398	+	0.816462i	$0.304068\pi$
$128$	880809.	+	286192.i	0.420002	+	0.136467i
$129$	−3.83464e6	+	1.24595e6i	−1.78630	+	0.580405i
$130$	−780637.	+	567166.i	−0.355319	+	0.258155i
$131$		−	1.12543e6i		−	0.500618i	−0.968166	−	0.250309i	$-0.919468\pi$
$131$		−	1.12543e6i		−	0.500618i	0.968166	−	0.250309i	$-0.0805322\pi$
$132$	459792.	−	2.06767e6i	0.199913	−	0.899000i
$133$	−321519.			−0.136663
$134$	−63789.3	−	87798.4i	−0.0265114	−	0.0364899i
$135$	−1.27581e6	−	3.92652e6i	−0.518541	−	1.59591i
$136$	−1.28026e6	+	3.94023e6i	−0.508957	+	1.56641i
$137$	2.00080e6	+	1.45367e6i	0.778112	+	0.565331i	0.904412	−	0.426661i	$-0.140310\pi$
$137$	2.00080e6	+	1.45367e6i	0.778112	+	0.565331i	−0.126300	+	0.991992i	$0.540310\pi$
$138$	494874.	−	681136.i	0.188303	−	0.259177i
$139$	−2.70026e6	−	877366.i	−1.00545	−	0.326691i	−0.240409	−	0.970672i	$-0.577282\pi$
$139$	−2.70026e6	−	877366.i	−1.00545	−	0.326691i	−0.765041	+	0.643981i	$0.777282\pi$
$140$	271911.	−	88349.1i	0.0990928	−	0.0321972i
$141$	824425.	−	598980.i	0.294099	−	0.213676i
$142$		−	767524.i		−	0.268057i
$143$	−1.26818e6	+	550448.i	−0.433684	+	0.188239i
$144$	−677639.			−0.226940
$145$	−1.16893e6	−	1.60890e6i	−0.383429	−	0.527745i
$146$	516178.	+	1.58863e6i	0.165860	+	0.510463i
$147$	1.59210e6	−	4.89998e6i	0.501209	−	1.54256i
$148$	−1.12016e6	−	813844.i	−0.345537	−	0.251048i
$149$	−283491.	+	390191.i	−0.0856998	+	0.117956i	−0.849714	−	0.527243i	$-0.823226\pi$
$149$	−283491.	+	390191.i	−0.0856998	+	0.117956i	0.764014	+	0.645199i	$0.223226\pi$
$150$	3.35278e6	+	1.08939e6i	0.993417	+	0.322781i
$151$	1.88534e6	−	612583.i	0.547593	−	0.177924i	−0.0221381	−	0.999755i	$-0.507047\pi$
$151$	1.88534e6	−	612583.i	0.547593	−	0.177924i	0.569731	+	0.821831i	$0.307047\pi$
$152$	3.00708e6	−	2.18477e6i	0.856277	−	0.622121i
$153$			9.83612e6i			2.74631i
$154$	−323456.	+	30934.5i	−0.0885632	+	0.00846996i
$155$	−3.68562e6			−0.989728
$156$	−971599.	−	1.33729e6i	−0.255925	−	0.352251i
$157$	71189.9	+	219100.i	0.0183958	+	0.0566165i	0.959833	−	0.280572i	$-0.0905241\pi$
$157$	71189.9	+	219100.i	0.0183958	+	0.0566165i	−0.941437	+	0.337188i	$0.890524\pi$
$158$	806924.	−	2.48346e6i	0.204579	−	0.629630i
$159$	1.33227e6	+	967948.i	0.331436	+	0.240802i
$160$	−3.19000e6	+	4.39065e6i	−0.778807	+	1.07194i
$161$	154850.	+	50313.8i	0.0371051	+	0.0120562i
$162$	−690099.	+	224227.i	−0.162318	+	0.0527403i
$163$	−3.42492e6	+	2.48835e6i	−0.790839	+	0.574578i	−0.908212	−	0.418510i	$-0.862553\pi$
$163$	−3.42492e6	+	2.48835e6i	−0.790839	+	0.574578i	0.117373	+	0.993088i	$0.462553\pi$
$164$		−	2.76345e6i		−	0.626499i
$165$	8.92503e6	+	5.26501e6i	1.98682	+	1.17205i
$166$	1.78472e6			0.390163
$167$	885953.	+	1.21941e6i	0.190222	+	0.261819i	0.893467	−	0.449130i	$-0.148266\pi$
$167$	885953.	+	1.21941e6i	0.190222	+	0.261819i	−0.703244	+	0.710948i	$0.748266\pi$
$168$	−335342.	−	1.03208e6i	−0.0707230	−	0.217663i
$169$	1.15818e6	−	3.56450e6i	0.239947	−	0.738480i
$170$	−5.87027e6	−	4.26500e6i	−1.19484	−	0.868105i
$171$	5.18698e6	−	7.13926e6i	1.03735	−	1.42779i
$172$	3.06920e6	+	997245.i	0.603171	+	0.195982i
$173$	9.35472e6	−	3.03953e6i	1.80673	−	0.587041i	0.806734	−	0.590915i	$-0.201233\pi$
$173$	9.35472e6	−	3.03953e6i	1.80673	−	0.587041i	0.999992	+	0.00387417i	$0.00123319\pi$
$174$	−2.18629e6	+	1.58843e6i	−0.415010	+	0.301523i
$175$			681753.i			0.127208i
$176$	536722.	−	474234.i	0.0984491	−	0.0869871i
$177$	−1.34427e7			−2.42419
$178$	−1.51655e6	−	2.08735e6i	−0.268904	−	0.370115i
$179$	2.07303e6	+	6.38012e6i	0.361448	+	1.11242i	0.952176	+	0.305551i	$0.0988407\pi$
$179$	2.07303e6	+	6.38012e6i	0.361448	+	1.11242i	−0.590728	+	0.806871i	$0.701159\pi$
$180$	−2.42488e6	+	7.46303e6i	−0.415789	+	1.27967i
$181$	−3.50548e6	−	2.54688e6i	−0.591169	−	0.429509i	0.251564	−	0.967841i	$-0.419055\pi$
$181$	−3.50548e6	−	2.54688e6i	−0.591169	−	0.429509i	−0.842733	+	0.538331i	$0.819055\pi$
$182$	−149045.	+	205143.i	−0.0247231	+	0.0340284i
$183$	−1.31590e7	−	4.27561e6i	−2.14718	−	0.697662i
$184$	−1.79016e6	+	581658.i	−0.287368	+	0.0933714i
$185$	5.47990e6	−	3.98138e6i	0.865480	−	0.628808i
$186$			5.00829e6i			0.778307i
$187$	−6.88365e6	−	7.79067e6i	−1.05267	−	1.19138i
$188$	−815633.			−0.122750
$189$	−637717.	−	877742.i	−0.0944588	−	0.130011i
$190$	2.01166e6	+	6.19125e6i	0.293287	+	0.902646i
$191$	−1.37788e6	+	4.24066e6i	−0.197747	+	0.608603i	0.802187	+	0.597073i	$0.203670\pi$
$191$	−1.37788e6	+	4.24066e6i	−0.197747	+	0.608603i	−0.999934	+	0.0115291i	$0.996330\pi$
$192$	7.20870e6	+	5.23742e6i	1.01848	+	0.739970i
$193$	5.05160e6	−	6.95292e6i	0.702678	−	0.967154i	−0.297245	−	0.954801i	$-0.596068\pi$
$193$	5.05160e6	−	6.95292e6i	0.702678	−	0.967154i	0.999924	−	0.0123527i	$-0.00393209\pi$
$194$	−1.94542e6	−	632106.i	−0.266446	−	0.0865734i
$195$	7.69072e6	−	2.49887e6i	1.03720	−	0.337007i
$196$	−3.33616e6	+	2.42386e6i	−0.443077	+	0.321914i
$197$			5.26147e6i			0.688191i	0.938935	+	0.344095i	$0.111814\pi$
$197$			5.26147e6i			0.688191i	−0.938935	+	0.344095i	$0.888186\pi$
$198$	4.53133e6	−	7.68133e6i	0.583754	−	0.989557i
$199$	1.02227e7			1.29720			0.648600	−	0.761130i	$-0.275355\pi$
$199$	1.02227e7			1.29720			0.648600	+	0.761130i	$0.275355\pi$
$200$	−4.63262e6	−	6.37625e6i	−0.579077	−	0.797032i
$201$	281048.	+	864977.i	0.0346093	+	0.106516i
$202$	−1.66669e6	+	5.12953e6i	−0.202209	+	0.622334i
$203$	−422800.	−	307182.i	−0.0505414	−	0.0367204i
$204$	7.30627e6	−	1.00562e7i	0.860608	−	1.18453i
$205$	1.28573e7	+	4.17759e6i	1.49241	+	0.484914i
$206$	−9.99434e6	+	3.24736e6i	−1.14328	+	0.371474i
$207$	−3.61536e6	+	2.62671e6i	−0.407605	+	0.296143i
$208$		−	558923.i		−	0.0621100i
$209$	887961.	+	9.28465e6i	0.0972647	+	1.01701i
$210$	1.90060e6			0.205226
$211$	−2.30856e6	−	3.17746e6i	−0.245750	−	0.338246i	0.668267	−	0.743921i	$-0.267036\pi$
$211$	−2.30856e6	−	3.17746e6i	−0.245750	−	0.338246i	−0.914017	+	0.405675i	$0.867036\pi$
$212$	−407302.	−	1.25355e6i	−0.0427474	−	0.131563i
$213$	−1.98767e6	+	6.11741e6i	−0.205686	+	0.633036i
$214$	4.56524e6	+	3.31684e6i	0.465824	+	0.338441i
$215$	−9.27962e6	+	1.27723e7i	−0.933716	+	1.28515i
$216$	1.19288e7	+	3.87589e6i	1.18368	+	0.384601i
$217$	−921137.	+	299296.i	−0.0901457	+	0.0292901i
$218$	−25332.9	+	18405.5i	−0.00244521	+	0.00177655i
$219$		−	1.39986e7i		−	1.33277i
$220$	−3.30225e6	−	7.60809e6i	−0.310129	−	0.714508i
$221$	−8.11292e6			−0.751624
$222$	−5.41019e6	−	7.44648e6i	−0.494485	−	0.680601i
$223$	1.79274e6	+	5.51747e6i	0.161660	+	0.497537i	0.998775	−	0.0494897i	$-0.0157595\pi$
$223$	1.79274e6	+	5.51747e6i	0.161660	+	0.497537i	−0.837115	+	0.547027i	$0.815760\pi$
$224$	−440718.	+	1.35639e6i	−0.0392118	+	0.120682i
$225$	−1.51382e7	−	1.09985e7i	−1.32900	−	0.965578i
$226$	3.45538e6	−	4.75592e6i	0.299344	−	0.412012i
$227$	3.58120e6	+	1.16360e6i	0.306161	+	0.0994779i	0.458068	−	0.888917i	$-0.348541\pi$
$227$	3.58120e6	+	1.16360e6i	0.306161	+	0.0994779i	−0.151907	+	0.988395i	$0.548541\pi$
$228$	−1.06061e7	+	3.44613e6i	−0.894851	+	0.290755i
$229$	8.50917e6	−	6.18227e6i	0.708567	−	0.514804i	−0.174144	−	0.984720i	$-0.555716\pi$
$229$	8.50917e6	−	6.18227e6i	0.708567	−	0.514804i	0.882711	+	0.469916i	$0.155716\pi$
$230$		−	3.29663e6i		−	0.270948i
$231$	2.65816e6	+	591100.i	0.215648	+	0.0479540i
$232$	6.04168e6			0.483831
$233$	−4.48416e6	−	6.17191e6i	−0.354497	−	0.487924i	0.594108	−	0.804385i	$-0.297505\pi$
$233$	−4.48416e6	−	6.17191e6i	−0.354497	−	0.487924i	−0.948605	+	0.316462i	$0.897505\pi$
$234$	−2.15065e6	−	6.61902e6i	−0.167850	−	0.516590i
$235$	1.23302e6	−	3.79484e6i	0.0950093	−	0.292408i
$236$	8.70454e6	+	6.32422e6i	0.662232	+	0.481140i
$237$	−1.28629e7	+	1.77042e7i	−0.966258	+	1.32994i
$238$	−1.81348e6	−	589236.i	−0.134519	−	0.0437078i
$239$	3.57291e6	−	1.16091e6i	0.261715	−	0.0850362i	−0.175221	−	0.984529i	$-0.556064\pi$
$239$	3.57291e6	−	1.16091e6i	0.261715	−	0.0850362i	0.436935	+	0.899493i	$0.356064\pi$
$240$	−3.38923e6	+	2.46242e6i	−0.245170	+	0.178127i
$241$			1.88724e7i			1.34827i	0.738609	+	0.674134i	$0.235483\pi$
$241$			1.88724e7i			1.34827i	−0.738609	+	0.674134i	$0.764517\pi$
$242$	1.78662e6	+	9.25515e6i	0.126063	+	0.653037i
$243$	−1.11573e7			−0.777572
$244$	6.50933e6	+	8.95932e6i	0.448092	+	0.616745i
$245$	−6.23396e6	−	1.91862e7i	−0.423902	−	1.30464i
$246$	5.67682e6	−	1.74715e7i	0.381329	−	1.17361i
$247$	5.88853e6	+	4.27826e6i	0.390765	+	0.283907i
$248$	6.58138e6	−	9.05850e6i	0.431481	−	0.593883i
$249$	−1.42248e7	−	4.62191e6i	−0.921399	−	0.299381i
$250$	−676900.	+	219938.i	−0.0433216	+	0.0140760i
$251$	4.35033e6	−	3.16070e6i	0.275106	−	0.199877i	−0.441674	−	0.897176i	$-0.645615\pi$
$251$	4.35033e6	−	3.16070e6i	0.275106	−	0.199877i	0.716780	+	0.697299i	$0.245615\pi$
$252$			2.06213e6i			0.128859i
$253$	1.02527e6	−	4.61062e6i	0.0633109	−	0.284707i
$254$	7.00028e6			0.427183
$255$	3.57428e7	+	4.91957e7i	2.15560	+	2.96692i
$256$	−5.47478e6	−	1.68496e7i	−0.326322	−	1.00432i
$257$	4.15769e6	−	1.27961e7i	0.244936	−	0.753836i	−0.750711	−	0.660631i	$-0.770289\pi$
$257$	4.15769e6	−	1.27961e7i	0.244936	−	0.753836i	0.995647	−	0.0932050i	$-0.0297112\pi$
$258$	1.73559e7	+	1.26098e7i	1.01062	+	0.734260i
$259$	1.04626e6	−	1.44006e6i	0.0602201	−	0.0828858i
$260$	−6.15557e6	−	2.00007e6i	−0.350226	−	0.113795i
$261$	1.36418e7	−	4.43250e6i	0.767275	−	0.249303i
$262$	−4.84452e6	+	3.51975e6i	−0.269368	+	0.195708i
$263$		−	9.60229e6i		−	0.527847i	−0.964544	−	0.263923i	$-0.914983\pi$
$263$		−	9.60229e6i		−	0.527847i	0.964544	−	0.263923i	$-0.0850166\pi$
$264$	−2.88776e7	+	1.25342e7i	−1.56946	+	0.681216i
$265$	6.44803e6			0.346489
$266$	1.00554e6	+	1.38400e6i	0.0534260	+	0.0735346i
$267$	6.68175e6	+	2.05643e7i	0.351040	+	1.08039i
$268$	224948.	−	692318.i	0.0116863	−	0.0359668i
$269$	−2.51197e7	−	1.82505e7i	−1.29050	−	0.937602i	−0.290683	−	0.956819i	$-0.593882\pi$
$269$	−2.51197e7	−	1.82505e7i	−1.29050	−	0.937602i	−0.999815	+	0.0192178i	$0.993882\pi$
$270$	−1.29120e7	+	1.77718e7i	−0.655997	+	0.902902i
$271$	−3.10725e7	−	1.00961e7i	−1.56123	−	0.507275i	−0.604096	−	0.796911i	$-0.706466\pi$
$271$	−3.10725e7	−	1.00961e7i	−1.56123	−	0.507275i	−0.957137	+	0.289636i	$0.906466\pi$
$272$	3.99730e6	−	1.29880e6i	0.198637	−	0.0645411i
$273$	1.71920e6	−	1.24907e6i	0.0844962	−	0.0613901i
$274$		−	1.31589e7i		−	0.639686i
$275$	1.96873e7	−	1.88285e6i	0.946647	−	0.0905350i
$276$	5.64738e6			0.268608
$277$	8.18611e6	+	1.12672e7i	0.385158	+	0.530124i	0.956942	−	0.290280i	$-0.0937485\pi$
$277$	8.18611e6	+	1.12672e7i	0.385158	+	0.530124i	−0.571784	+	0.820404i	$0.693749\pi$
$278$	4.66824e6	+	1.43674e7i	0.217280	+	0.668718i
$279$	8.21465e6	−	2.52821e7i	0.378248	−	1.16413i
$280$	−3.43761e6	−	2.49757e6i	−0.156597	−	0.113774i
$281$	−1.64278e7	+	2.26109e7i	−0.740390	+	1.01906i	0.258207	+	0.966090i	$0.416868\pi$
$281$	−1.64278e7	+	2.26109e7i	−0.740390	+	1.01906i	−0.998596	+	0.0529690i	$0.983132\pi$
$282$	−5.15671e6	−	1.67552e6i	−0.229946	−	0.0747138i
$283$	8.01791e6	−	2.60518e6i	0.353755	−	0.114942i	−0.126748	−	0.991935i	$-0.540454\pi$
$283$	8.01791e6	−	2.60518e6i	0.353755	−	0.114942i	0.480503	+	0.876993i	$0.340454\pi$
$284$	4.16505e6	−	3.02609e6i	0.181830	−	0.132107i
$285$		−	5.45558e7i		−	2.35671i
$286$	6.33563e6	+	3.73748e6i	0.270827	+	0.159765i
$287$	3.55264e6			0.150281
$288$	−2.30084e7	−	3.16683e7i	−0.963182	−	1.32571i
$289$	−1.13936e7	−	3.50658e7i	−0.472026	−	1.45275i
$290$	−3.26983e6	+	1.00635e7i	−0.134070	+	0.412624i
$291$	1.38687e7	+	1.00762e7i	0.562802	+	0.408899i
$292$	−6.58576e6	+	9.06452e6i	−0.264519	+	0.364080i
$293$	4.44147e7	+	1.44312e7i	1.76573	+	0.573720i	0.997768	−	0.0667757i	$-0.0212712\pi$
$293$	4.44147e7	+	1.44312e7i	1.76573	+	0.573720i	0.767962	+	0.640496i	$0.221271\pi$
$294$	−2.60716e7	+	8.47116e6i	−1.02595	+	0.333350i
$295$	−4.25832e7	+	3.09385e7i	−1.65872	+	1.20513i
$296$			2.05780e7i			0.793464i
$297$	−2.35857e7	+	2.08398e7i	−0.900285	+	0.795469i
$298$	2.56621e6			0.0969714
$299$	−2.16653e6	−	2.98198e6i	−0.0810498	−	0.111555i
$300$	7.30722e6	+	2.24893e7i	0.270638	+	0.832937i
$301$	−1.28204e6	+	3.94571e6i	−0.0470112	+	0.144686i
$302$	−8.53321e6	−	6.19974e6i	−0.309807	−	0.225088i
$303$	2.65680e7	−	3.65677e7i	0.955061	−	1.31453i
$304$	−3.58623e6	−	1.16524e6i	−0.127649	−	0.0414757i
$305$	−5.15248e7	+	1.67414e7i	−1.81600	+	0.590055i
$306$	4.23403e7	−	3.07620e7i	1.47771	−	1.07362i
$307$			3.09115e7i			1.06833i	0.845380	+	0.534165i	$0.179374\pi$
$307$			3.09115e7i			1.06833i	−0.845380	+	0.534165i	$0.820626\pi$
$308$	−1.44315e6	−	1.63330e6i	−0.0493922	−	0.0559004i
$309$	8.80678e7			2.98498
$310$	1.15266e7	+	1.58650e7i	0.386916	+	0.532544i
$311$	−9.80421e6	−	3.01743e7i	−0.325935	−	1.00313i	−0.971017	−	0.239012i	$-0.923177\pi$
$311$	−9.80421e6	−	3.01743e7i	−0.325935	−	1.00313i	0.645081	−	0.764114i	$-0.276823\pi$
$312$	−7.59155e6	+	2.33644e7i	−0.249958	+	0.769291i
$313$	9.60711e6	+	6.97997e6i	0.313299	+	0.227625i	0.733311	−	0.679893i	$-0.237974\pi$
$313$	9.60711e6	+	6.97997e6i	0.313299	+	0.227625i	−0.420012	+	0.907519i	$0.637974\pi$
$314$	720488.	−	991667.i	0.0232722	−	0.0320315i
$315$	−9.59432e6	−	3.11738e6i	−0.306960	−	0.0997375i
$316$	1.66582e7	−	5.41257e6i	0.527917	−	0.171531i
$317$	3.89940e7	−	2.83308e7i	1.22411	−	0.889367i	0.227674	−	0.973737i	$-0.426888\pi$
$317$	3.89940e7	−	2.83308e7i	1.22411	−	0.889367i	0.996434	+	0.0843708i	$0.0268880\pi$
$318$		−	8.76205e6i		−	0.272474i
$319$	−7.70297e6	+	1.30578e7i	−0.237294	+	0.402250i
$320$	3.48893e7			1.06474
$321$	−2.77967e7	−	3.82589e7i	−0.840386	−	1.15669i
$322$	−267707.	−	823916.i	−0.00801847	−	0.0246783i
$323$	−1.69138e7	+	5.20552e7i	−0.501918	+	1.54474i
$324$	−3.93762e6	−	2.86085e6i	−0.115771	−	0.0841123i
$325$	9.07169e6	−	1.24861e7i	0.264264	−	0.363728i
$326$	2.14226e7	+	6.96062e6i	0.618328	+	0.200907i
$327$	249576.	−	81092.3i	0.00713773	−	0.00231919i
$328$	−3.32269e7	+	2.41407e7i	−0.941603	+	0.684114i
$329$		−	1.04856e6i		−	0.0294447i
$330$	−5.24902e6	−	5.48845e7i	−0.146062	−	1.52724i
$331$	−6.32735e7			−1.74477			−0.872385	−	0.488820i	$-0.837427\pi$
$331$	−6.32735e7			−1.74477			−0.872385	+	0.488820i	$0.837427\pi$
$332$	7.03654e6	+	9.68497e6i	0.192285	+	0.264657i
$333$	1.50971e7	+	4.64640e7i	0.408847	+	1.25830i
$334$	2.47826e6	−	7.62730e6i	0.0665131	−	0.204706i
$335$	2.88104e6	+	2.09320e6i	0.0766328	+	0.0556770i
$336$	−647097.	+	890653.i	−0.0170589	+	0.0234796i
$337$	3.37639e6	+	1.09706e6i	0.0882192	+	0.0286642i	0.352794	−	0.935701i	$-0.385232\pi$
$337$	3.37639e6	+	1.09706e6i	0.0882192	+	0.0286642i	−0.264575	+	0.964365i	$0.585232\pi$
$338$	−1.89658e7	+	6.16236e6i	−0.491158	+	0.159587i
$339$	−3.98569e7	+	2.89578e7i	−1.02307	+	0.743303i
$340$		−	4.86711e7i		−	1.23832i
$341$	1.11869e7	+	2.57735e7i	0.282127	+	0.649996i
$342$	−4.69535e7			−1.17379
$343$	−6.28892e6	−	8.65595e6i	−0.155845	−	0.214503i
$344$	−1.48211e7	−	4.56148e7i	−0.364088	−	1.12055i
$345$	−8.53731e6	+	2.62751e7i	−0.207905	+	0.639864i
$346$	−4.23403e7	−	3.07621e7i	−1.02218	−	0.742655i
$347$	3.52917e7	−	4.85748e7i	0.844664	−	1.16258i	−0.140349	−	0.990102i	$-0.544823\pi$
$347$	3.52917e7	−	4.85748e7i	0.844664	−	1.16258i	0.985013	−	0.172478i	$-0.0551774\pi$
$348$	−1.72396e7	−	5.60147e6i	−0.409061	−	0.132912i
$349$	1.10840e6	−	360141.i	0.0260748	−	0.00847221i	−0.295951	−	0.955203i	$-0.595636\pi$
$349$	1.10840e6	−	360141.i	0.0260748	−	0.00847221i	0.322025	+	0.946731i	$0.395636\pi$
$350$	2.93466e6	−	2.13215e6i	0.0684468	−	0.0497295i
$351$			2.45613e7i			0.567976i
$352$	4.03863e7	+	8.98078e6i	0.925989	+	0.205914i
$353$	−5.49643e7			−1.24956			−0.624780	−	0.780801i	$-0.714811\pi$
$353$	−5.49643e7			−1.24956			−0.624780	+	0.780801i	$0.714811\pi$
$354$	4.20415e7	+	5.78651e7i	0.947694	+	1.30439i
$355$	7.78282e6	+	2.39531e7i	0.173961	+	0.535397i
$356$	5.34800e6	−	1.64595e7i	0.118534	−	0.364809i
$357$	1.29281e7	+	9.39280e6i	0.284138	+	0.206438i
$358$	2.09804e7	−	2.88770e7i	0.457261	−	0.629366i
$359$	1.80004e7	+	5.84868e6i	0.389044	+	0.126408i	0.497006	−	0.867747i	$-0.334433\pi$
$359$	1.80004e7	+	5.84868e6i	0.389044	+	0.126408i	−0.107962	+	0.994155i	$0.534433\pi$
$360$	1.10916e8	−	3.60388e7i	2.37732	−	0.772437i
$361$	1.66620e6	−	1.21057e6i	0.0354165	−	0.0257316i
$362$			2.30548e7i			0.486000i
$363$	9.72825e6	−	7.83933e7i	0.203383	−	1.63893i
$364$	−1.70086e6			−0.0352667
$365$	−3.22180e7	−	4.43442e7i	−0.662551	−	0.911924i
$366$	2.27494e7	+	7.00156e7i	0.464010	+	1.42808i
$367$	2.82113e7	−	8.68255e7i	0.570723	−	1.75650i	−0.0795800	−	0.996828i	$-0.525358\pi$
$367$	2.82113e7	−	8.68255e7i	0.570723	−	1.75650i	0.650303	−	0.759675i	$-0.274642\pi$
$368$	1.54485e6	+	1.12240e6i	0.0309987	+	0.0225219i
$369$	−5.73137e7	+	7.88856e7i	−1.14072	+	1.57007i
$370$	−3.42763e7	−	1.11370e7i	−0.676688	−	0.219869i
$371$	1.61154e6	−	523620.i	0.0315587	−	0.0102540i
$372$	−2.71780e7	+	1.97460e7i	−0.527945	+	0.383575i
$373$			7.30282e7i			1.40723i	0.710583	+	0.703614i	$0.248431\pi$
$373$			7.30282e7i			1.40723i	−0.710583	+	0.703614i	$0.751569\pi$
$374$	−1.20072e7	+	5.39961e7i	−0.229524	+	1.03216i
$375$	5.96468e6			0.113108
$376$	7.12514e6	+	9.80691e6i	0.134039	+	0.184488i
$377$	3.65596e6	+	1.12519e7i	0.0682304	+	0.209992i
$378$	−1.78387e6	+	5.49019e6i	−0.0330285	+	0.101651i
$379$	8.28026e7	+	6.01596e7i	1.52099	+	1.10506i	0.960994	+	0.276569i	$0.0891973\pi$
$379$	8.28026e7	+	6.01596e7i	1.52099	+	1.10506i	0.559996	+	0.828495i	$0.310803\pi$
$380$	−2.56662e7	+	3.53265e7i	−0.467746	+	0.643798i
$381$	−5.57945e7	−	1.81287e7i	−1.00883	−	0.327787i
$382$	2.25635e7	−	7.33132e6i	0.404777	−	0.131520i
$383$	6.14329e7	−	4.46336e7i	1.09346	−	0.794448i	0.113483	−	0.993540i	$-0.463799\pi$
$383$	6.14329e7	−	4.46336e7i	1.09346	−	0.794448i	0.979981	+	0.199092i	$0.0637992\pi$
$384$			4.12968e7i			0.729329i
$385$	9.78080e6	−	4.24531e6i	0.171393	−	0.0743922i
$386$	−4.57280e7			−0.795097
$387$	−6.69308e7	−	9.21224e7i	−1.15476	−	1.58940i
$388$	−4.23995e6	−	1.30492e7i	−0.0725881	−	0.223403i
$389$	1.92476e7	−	5.92381e7i	0.326985	−	1.00636i	−0.643551	−	0.765403i	$-0.722540\pi$
$389$	1.92476e7	−	5.92381e7i	0.326985	−	1.00636i	0.970537	−	0.240954i	$-0.0774603\pi$
$390$	−3.48089e7	−	2.52902e7i	−0.586809	−	0.426342i
$391$	1.62920e7	−	2.24240e7i	0.272549	−	0.375131i
$392$	5.82875e7	+	1.89388e7i	0.967648	+	0.314408i
$393$	4.77274e7	−	1.55076e7i	0.786304	−	0.255486i
$394$	2.26484e7	−	1.64550e7i	0.370296	−	0.269036i
$395$			8.56866e7i			1.39034i
$396$	5.95490e7	−	5.69512e6i	0.958935	−	0.0917102i
$397$	−3.16884e7			−0.506441			−0.253220	−	0.967409i	$-0.581490\pi$
$397$	−3.16884e7			−0.506441			−0.253220	+	0.967409i	$0.581490\pi$
$398$	−3.19710e7	−	4.40044e7i	−0.507116	−	0.697986i
$399$	−4.43027e6	−	1.36350e7i	−0.0697448	−	0.214652i
$400$	−2.47079e6	+	7.60430e6i	−0.0386060	+	0.118817i
$401$	−3.18623e7	−	2.31493e7i	−0.494134	−	0.359009i	0.312638	−	0.949872i	$-0.398787\pi$
$401$	−3.18623e7	−	2.31493e7i	−0.494134	−	0.359009i	−0.806772	+	0.590863i	$0.798787\pi$
$402$	2.84439e6	−	3.91497e6i	0.0437835	−	0.0602629i
$403$	2.08529e7	+	6.77552e6i	0.318604	+	0.103521i
$404$	−3.44071e7	+	1.11795e7i	−0.521800	+	0.169543i
$405$	1.92631e7	−	1.39954e7i	0.289975	−	0.210679i
$406$			2.78067e6i			0.0415501i
$407$	−4.44747e7	−	2.62363e7i	−0.659675	−	0.389152i
$408$	−1.84738e8			−2.72005
$409$	6.60781e7	+	9.09487e7i	0.965801	+	1.32931i	0.944140	+	0.329546i	$0.106896\pi$
$409$	6.60781e7	+	9.09487e7i	0.965801	+	1.32931i	0.0216617	+	0.999765i	$0.493104\pi$
$410$	−2.22279e7	−	6.84105e7i	−0.322513	−	0.992593i
$411$	−3.40777e7	+	1.04880e8i	−0.490845	+	1.51067i
$412$	−5.70264e7	−	4.14321e7i	−0.815426	−	0.592441i
$413$	−8.13029e6	+	1.11904e7i	−0.115413	+	0.158853i
$414$	2.26137e7	+	7.34764e6i	0.318692	+	0.103549i
$415$	−5.56979e7	+	1.80974e7i	−0.779282	+	0.253204i
$416$	2.61203e7	−	1.89775e7i	0.362826	−	0.263608i
$417$		−	1.26602e8i		−	1.74595i
$418$	3.71894e7	−	3.28596e7i	0.509202	−	0.449918i
$419$	4.10970e7			0.558687			0.279343	−	0.960191i	$-0.409883\pi$
$419$	4.10970e7			0.558687			0.279343	+	0.960191i	$0.409883\pi$
$420$	7.49342e6	+	1.03138e7i	0.101142	+	0.139210i
$421$	2.29794e7	+	7.07232e7i	0.307958	+	0.947798i	0.978557	+	0.205978i	$0.0660374\pi$
$421$	2.29794e7	+	7.07232e7i	0.307958	+	0.947798i	−0.670598	+	0.741821i	$0.733963\pi$
$422$	−6.45769e6	+	1.98747e7i	−0.0859290	+	0.264462i
$423$	2.32831e7	+	1.69162e7i	0.307624	+	0.223502i
$424$	−1.15142e7	+	1.58479e7i	−0.151055	+	0.207910i
$425$	1.10379e8	+	3.58642e7i	1.43786	+	0.467190i
$426$	3.25492e7	−	1.05759e7i	0.421028	−	0.136800i
$427$	−1.15179e7	+	8.36826e6i	−0.147942	+	0.107486i
$428$			3.78509e7i			0.482775i
$429$	−4.08180e7	−	4.61964e7i	−0.516987	−	0.585108i
$430$	8.40009e7			1.05652
$431$	−6.09932e7	−	8.39500e7i	−0.761816	−	1.04855i	−0.997061	−	0.0766133i	$-0.975589\pi$
$431$	−6.09932e7	−	8.39500e7i	−0.761816	−	1.04855i	0.235245	−	0.971936i	$-0.424411\pi$
$432$	−3.93203e6	−	1.21015e7i	−0.0487715	−	0.150103i
$433$	−3.12375e7	+	9.61392e7i	−0.384780	+	1.18423i	0.551859	+	0.833937i	$0.313919\pi$
$433$	−3.12375e7	+	9.61392e7i	−0.384780	+	1.18423i	−0.936640	+	0.350295i	$0.886081\pi$
$434$	4.16915e6	+	3.02907e6i	0.0510010	+	0.0370544i
$435$	5.21231e7	−	7.17413e7i	0.633232	−	0.871569i
$436$	−199758.	−	64905.4i	−0.00241016	−	0.000783107i
$437$	−2.36501e7	+	7.68439e6i	−0.283393	+	0.0920800i
$438$	−6.02582e7	+	4.37801e7i	−0.717123	+	0.521020i
$439$		−	1.54033e8i		−	1.82063i	−0.413920	−	0.910313i	$-0.635841\pi$
$439$		−	1.54033e8i		−	1.82063i	0.413920	−	0.910313i	$-0.364159\pi$
$440$	−6.26297e7	+	1.06167e8i	−0.735228	+	1.24633i
$441$	1.45505e8			1.69653
$442$	2.53728e7	+	3.49226e7i	0.293834	+	0.404427i
$443$	2.13073e7	+	6.55770e7i	0.245085	+	0.754293i	0.995622	+	0.0934658i	$0.0297946\pi$
$443$	2.13073e7	+	6.55770e7i	0.245085	+	0.754293i	−0.750538	+	0.660828i	$0.770205\pi$
$444$	1.90786e7	−	5.87179e7i	0.217970	−	0.670844i
$445$	6.84950e7	+	4.97645e7i	0.777282	+	0.564729i
$446$	1.81437e7	−	2.49726e7i	0.204513	−	0.281488i
$447$	−2.04535e7	−	6.64575e6i	−0.229005	−	0.0744083i
$448$	8.71979e6	−	2.83323e6i	0.0969777	−	0.0315100i
$449$	−1.04048e8	+	7.55955e7i	−1.14947	+	0.835136i	−0.988410	−	0.151809i	$-0.951490\pi$
$449$	−1.04048e8	+	7.55955e7i	−1.14947	+	0.835136i	−0.161056	+	0.986945i	$0.551490\pi$
$450$			9.95608e7i			1.09257i
$451$	−9.81157e6	−	1.02591e8i	−0.106957	−	1.11836i
$452$	3.94319e7			0.427004
$453$	5.19568e7	+	7.15124e7i	0.558918	+	0.769284i
$454$	−6.19122e6	−	1.90546e7i	−0.0661620	−	0.203626i
$455$	2.57125e6	−	7.91348e6i	0.0272966	−	0.0840104i
$456$	1.34087e8	+	9.74198e7i	1.41414	+	1.02743i
$457$	7.25556e7	−	9.98642e7i	0.760190	−	1.04631i	−0.237008	−	0.971508i	$-0.576167\pi$
$457$	7.25556e7	−	9.98642e7i	0.760190	−	1.04631i	0.997198	−	0.0748042i	$-0.0238332\pi$
$458$	−5.32241e7	−	1.72936e7i	−0.554002	−	0.180006i
$459$	−1.75657e8	+	5.70745e7i	−1.81647	+	0.590207i
$460$	1.78895e7	−	1.29975e7i	0.183791	−	0.133532i
$461$			4.45105e7i			0.454318i	0.973858	+	0.227159i	$0.0729437\pi$
$461$			4.45105e7i			0.454318i	−0.973858	+	0.227159i	$0.927056\pi$
$462$	−5.76884e6	−	1.32909e7i	−0.0585009	−	0.134781i
$463$	−3.56679e7			−0.359364			−0.179682	−	0.983725i	$-0.557507\pi$
$463$	−3.56679e7			−0.359364			−0.179682	+	0.983725i	$0.557507\pi$
$464$	−3.60265e6	−	4.95862e6i	−0.0360635	−	0.0496371i
$465$	−5.07849e7	−	1.56300e8i	−0.505098	−	1.55453i
$466$	−1.25434e7	+	3.86047e7i	−0.123954	+	0.381490i
$467$	−8.97959e7	−	6.52406e7i	−0.881670	−	0.640571i	0.0520229	−	0.998646i	$-0.483433\pi$
$467$	−8.97959e7	−	6.52406e7i	−0.881670	−	0.640571i	−0.933693	+	0.358075i	$0.883433\pi$
$468$	2.74395e7	−	3.77673e7i	0.267694	−	0.368449i
$469$	890031.	+	289188.i	0.00862753	+	0.00280325i
$470$	−2.01914e7	+	6.56057e6i	−0.194479	+	0.0631900i
$471$	−8.31065e6	+	6.03804e6i	−0.0795376	+	0.0577874i
$472$		−	1.59907e8i		−	1.52069i
$473$	1.17483e8	+	2.61249e7i	1.11017	+	0.246871i
$474$	1.16437e8			1.09334
$475$	−6.12024e7	−	8.42379e7i	−0.571068	−	0.786008i
$476$	−3.95239e6	−	1.21642e7i	−0.0366471	−	0.112788i
$477$	−1.43716e7	+	4.42312e7i	−0.132419	+	0.407543i
$478$	−1.61713e7	−	1.17491e7i	−0.148068	−	0.107578i
$479$	−1.23271e8	+	1.69668e8i	−1.12164	+	1.54381i	−0.318599	+	0.947890i	$0.603212\pi$
$479$	−1.23271e8	+	1.69668e8i	−1.12164	+	1.54381i	−0.803044	+	0.595919i	$0.796788\pi$
$480$	−2.30154e8	−	7.47817e7i	−2.08111	−	0.676194i
$481$	−3.83240e7	+	1.24522e7i	−0.344378	+	0.111895i
$482$	8.12376e7	−	5.90226e7i	0.725464	−	0.527081i
$483$			7.26016e6i			0.0644324i
$484$	−4.31800e7	+	4.61852e7i	−0.380844	+	0.407349i
$485$	6.71228e7			0.588362
$486$	3.48940e7	+	4.80275e7i	0.303978	+	0.418389i
$487$	4.10001e7	+	1.26185e8i	0.354975	+	1.09250i	0.956024	+	0.293289i	$0.0947497\pi$
$487$	4.10001e7	+	1.26185e8i	0.354975	+	1.09250i	−0.601049	+	0.799212i	$0.705250\pi$
$488$	5.08604e7	−	1.56532e8i	0.437643	−	1.34693i
$489$	−1.52719e8	−	1.10957e8i	−1.30607	−	0.948914i
$490$	−6.30918e7	+	8.68384e7i	−0.536271	+	0.738114i
$491$	4.11431e7	+	1.33682e7i	0.347578	+	0.112935i	0.477603	−	0.878576i	$-0.341506\pi$
$491$	4.11431e7	+	1.33682e7i	0.347578	+	0.112935i	−0.130025	+	0.991511i	$0.541506\pi$
$492$	1.17192e8	−	3.80781e7i	0.984021	−	0.319728i
$493$	−7.19757e7	+	5.22934e7i	−0.600683	+	0.436422i
$494$		−	3.87277e7i		−	0.321248i
$495$	−6.35248e7	+	2.85669e8i	−0.523754	+	2.35531i
$496$	−1.13591e7			−0.0930890
$497$	3.89028e6	+	5.35450e6i	0.0316892	+	0.0436164i
$498$	2.45920e7	+	7.56864e7i	0.199116	+	0.612816i
$499$	−1.57757e7	+	4.85526e7i	−0.126966	+	0.390761i	−0.994254	−	0.107045i	$-0.965861\pi$
$499$	−1.57757e7	+	4.85526e7i	−0.126966	+	0.390761i	0.867288	+	0.497806i	$0.165861\pi$
$500$	−3.86230e6	−	2.80613e6i	−0.0308984	−	0.0224490i
$501$	−3.95050e7	+	5.43740e7i	−0.314152	+	0.432393i
$502$	−2.72109e7	−	8.84136e6i	−0.215096	−	0.0698888i
$503$	1.82776e8	−	5.93876e7i	1.43620	−	0.466650i	0.515491	−	0.856895i	$-0.327609\pi$
$503$	1.82776e8	−	5.93876e7i	1.43620	−	0.466650i	0.920711	+	0.390244i	$0.127609\pi$
$504$	2.47944e7	−	1.80142e7i	0.193670	−	0.140709i
$505$		−	1.76984e8i		−	1.37423i
$506$	−2.30533e7	+	1.00062e7i	−0.177943	+	0.0772352i
$507$	1.67122e8			1.28236
$508$	2.75997e7	+	3.79878e7i	0.210530	+	0.289769i
$509$	−5.63680e7	−	1.73483e8i	−0.427444	−	1.31554i	−0.900635	−	0.434577i	$-0.856898\pi$
$509$	−5.63680e7	−	1.73483e8i	−0.427444	−	1.31554i	0.473191	−	0.880960i	$-0.343102\pi$
$510$	9.99825e7	−	3.07715e8i	0.753726	−	2.31973i
$511$	−1.16532e7	−	8.46653e6i	−0.0873336	−	0.0634516i
$512$	−2.05687e7	+	2.83104e7i	−0.153249	+	0.210929i
$513$	1.57593e8	+	5.12052e7i	1.16731	+	0.379282i
$514$	−6.80846e7	+	2.21220e7i	−0.501371	+	0.162905i
$515$	2.78977e8	−	2.02689e8i	2.04243	−	1.48391i
$516$			1.43900e8i			1.04740i
$517$	−3.02798e7	+	2.89589e6i	−0.219120	+	0.0209561i
$518$	−9.47096e6			−0.0681404
$519$	2.57801e8	+	3.54833e8i	1.84409	+	2.53817i
$520$	2.97252e7	+	9.14846e7i	0.211404	+	0.650636i
$521$	−3.92489e7	+	1.20796e8i	−0.277533	+	0.854158i	0.711005	+	0.703187i	$0.248240\pi$
$521$	−3.92489e7	+	1.20796e8i	−0.277533	+	0.854158i	−0.988538	+	0.150971i	$0.951760\pi$
$522$	−6.17442e7	−	4.48598e7i	−0.434095	−	0.315388i
$523$	−1.12314e7	+	1.54586e7i	−0.0785105	+	0.108060i	−0.846466	−	0.532443i	$-0.821274\pi$
$523$	−1.12314e7	+	1.54586e7i	−0.0785105	+	0.108060i	0.767956	+	0.640503i	$0.221274\pi$
$524$	−3.82005e7	−	1.24121e7i	−0.265507	−	0.0862684i
$525$	−2.89118e7	+	9.39401e6i	−0.199801	+	0.0649192i
$526$	−4.13338e7	+	3.00307e7i	−0.284019	+	0.206352i
$527$			1.64880e8i			1.12652i
$528$	2.75069e7	+	1.62267e7i	0.186870	+	0.110238i
$529$	−1.35443e8			−0.914934
$530$	−2.01659e7	−	2.77560e7i	−0.135453	−	0.186436i
$531$	−1.17316e8	−	3.61063e8i	−0.783565	−	2.41157i
$532$	−3.54594e6	+	1.09133e7i	−0.0235503	+	0.0724805i
$533$	−6.50655e7	−	4.72729e7i	−0.429704	−	0.312198i
$534$	6.76237e7	−	9.30760e7i	0.444094	−	0.611243i
$535$	−1.76106e8	−	5.72204e7i	−1.15004	−	0.373671i
$536$	−1.02893e7	+	3.34319e6i	−0.0668176	+	0.0217104i
$537$	−2.42003e8	+	1.75826e8i	−1.56278	+	1.13543i
$538$			1.65207e8i			1.06092i
$539$	−1.15247e8	+	1.01829e8i	−0.735974	+	0.650288i
$540$	−1.47348e8			−0.935758
$541$	−4.04847e7	−	5.57224e7i	−0.255681	−	0.351915i	0.661809	−	0.749672i	$-0.269789\pi$
$541$	−4.04847e7	−	5.57224e7i	−0.255681	−	0.351915i	−0.917491	+	0.397757i	$0.869789\pi$
$542$	5.37185e7	+	1.65329e8i	0.337385	+	1.03837i
$543$	5.97054e7	−	1.83754e8i	0.372919	−	1.14773i
$544$	1.96421e8	+	1.42708e8i	1.22009	+	0.886444i
$545$	603962.	−	831282.i	0.00373095	−	0.00513522i
$546$	−1.07534e7	−	3.49400e6i	−0.0660645	−	0.0214657i
$547$	−1.60112e7	+	5.20235e6i	−0.0978276	+	0.0317861i	−0.357522	−	0.933905i	$-0.616378\pi$
$547$	−1.60112e7	+	5.20235e6i	−0.0978276	+	0.0317861i	0.259694	+	0.965691i	$0.416378\pi$
$548$	7.14079e7	−	5.18809e7i	0.433915	−	0.315258i
$549$		−	3.90756e8i		−	2.36150i
$550$	−6.96760e7	−	7.88569e7i	−0.418789	−	0.473971i
$551$	7.98179e7			0.477139
$552$	−4.93339e7	−	6.79022e7i	−0.293311	−	0.403708i
$553$	6.95829e6	+	2.14154e7i	0.0411460	+	0.126634i
$554$	2.28988e7	−	7.04754e7i	0.134674	−	0.414485i
$555$	2.44351e8	+	1.77531e8i	1.42934	+	1.03847i
$556$	−5.95607e7	+	8.19783e7i	−0.346526	+	0.476952i
$557$	−5.39903e7	−	1.75425e7i	−0.312428	−	0.101514i	0.148606	−	0.988896i	$-0.452521\pi$
$557$	−5.39903e7	−	1.75425e7i	−0.312428	−	0.101514i	−0.461034	+	0.887382i	$0.652521\pi$
$558$	−1.34520e8	+	4.37081e7i	−0.774253	+	0.251570i
$559$	7.59834e7	−	5.52051e7i	0.434994	−	0.316042i
$560$			4.31067e6i			0.0245460i
$561$	2.35536e8	−	3.99271e8i	1.33404	−	2.26141i
$562$	1.48707e8			0.837768
$563$	−7.90138e7	−	1.08753e8i	−0.442769	−	0.609420i	0.528055	−	0.849210i	$-0.322921\pi$
$563$	−7.90138e7	−	1.08753e8i	−0.442769	−	0.609420i	−0.970825	+	0.239790i	$0.922921\pi$
$564$	−1.12388e7	−	3.45894e7i	−0.0626443	−	0.192799i
$565$	−5.96104e7	+	1.83462e8i	−0.330504	+	1.01719i
$566$	−3.62898e7	−	2.63661e7i	−0.200141	−	0.145411i
$567$	3.67785e6	−	5.06212e6i	0.0201764	−	0.0277705i
$568$	−7.27694e7	−	2.36442e7i	−0.397103	−	0.129027i
$569$	3.51808e7	−	1.14309e7i	0.190971	−	0.0620504i	−0.211970	−	0.977276i	$-0.567988\pi$
$569$	3.51808e7	−	1.14309e7i	0.190971	−	0.0620504i	0.402941	+	0.915226i	$0.367988\pi$
$570$	−2.34839e8	+	1.70621e8i	−1.26808	+	0.921314i
$571$		−	8.81736e7i		−	0.473620i	−0.971556	−	0.236810i	$-0.923898\pi$
$571$		−	8.81736e7i		−	0.473620i	0.971556	−	0.236810i	$-0.0761019\pi$
$572$	4.69739e6	+	4.91166e7i	0.0250997	+	0.262446i
$573$	−1.98824e8			−1.05683
$574$	−1.11107e7	−	1.52926e7i	−0.0587498	−	0.0808621i
$575$	1.62941e7	+	5.01481e7i	0.0857090	+	0.263785i
$576$	−7.77626e7	+	2.39329e8i	−0.406915	+	1.25235i
$577$	7.65365e7	+	5.56070e7i	0.398420	+	0.289469i	0.768897	−	0.639372i	$-0.220806\pi$
$577$	7.65365e7	+	5.56070e7i	0.398420	+	0.289469i	−0.370477	+	0.928842i	$0.620806\pi$
$578$	−1.15310e8	+	1.58711e8i	−0.597151	+	0.821908i
$579$	3.64467e8	+	1.18422e8i	1.87768	+	0.610096i
$580$	−6.75024e7	+	2.19329e7i	−0.345968	+	0.112412i
$581$	−1.24508e7	+	9.04604e6i	−0.0634847	+	0.0461243i
$582$		−	9.12114e7i		−	0.462679i
$583$	−1.95715e7	−	4.50910e7i	−0.0987685	−	0.227554i
$584$	1.66520e8			0.836043
$585$	1.34236e8	+	1.84760e8i	0.670504	+	0.922869i
$586$	−7.67848e7	−	2.36319e8i	−0.381577	−	1.17437i
$587$	−2.85052e7	+	8.77299e7i	−0.140932	+	0.433744i	−0.996465	−	0.0840036i	$-0.973229\pi$
$587$	−2.85052e7	+	8.77299e7i	−0.140932	+	0.433744i	0.855534	+	0.517747i	$0.173229\pi$
$588$	−1.48761e8	−	1.08081e8i	−0.731740	−	0.531640i
$589$	8.69479e7	−	1.19674e8i	0.425514	−	0.585669i
$590$	2.66354e8	+	8.65436e7i	1.29689	+	0.421385i
$591$	−2.23129e8	+	7.24989e7i	−1.08092	+	0.351212i
$592$	1.68890e7	−	1.22706e7i	0.0814029	−	0.0591427i
$593$			9.19601e7i			0.440997i	0.975387	+	0.220498i	$0.0707684\pi$
$593$			9.19601e7i			0.440997i	−0.975387	+	0.220498i	$0.929232\pi$
$594$	1.63469e8	+	3.63510e7i	0.779969	+	0.173443i
$595$	6.25705e7			0.297043
$596$	1.01177e7	+	1.39258e7i	0.0477906	+	0.0657782i
$597$	1.40861e8	+	4.33525e8i	0.662013	+	2.03747i
$598$	−6.06040e6	+	1.86520e7i	−0.0283399	+	0.0872211i
$599$	−6.35768e7	−	4.61912e7i	−0.295814	−	0.214921i	0.429972	−	0.902842i	$-0.358523\pi$
$599$	−6.35768e7	−	4.61912e7i	−0.295814	−	0.214921i	−0.725785	+	0.687921i	$0.758523\pi$
$600$	2.06570e8	−	2.84320e8i	0.956344	−	1.31630i
$601$	−1.24570e7	−	4.04754e6i	−0.0573841	−	0.0186452i	0.280184	−	0.959946i	$-0.409604\pi$
$601$	−1.24570e7	−	4.04754e6i	−0.0573841	−	0.0186452i	−0.337568	+	0.941301i	$0.609604\pi$
$602$	2.09941e7	−	6.82140e6i	0.0962294	−	0.0312668i
$603$	−2.07800e7	+	1.50975e7i	−0.0947749	+	0.0688580i
$604$		−	7.07498e7i		−	0.321081i
$605$	−1.49606e8	−	2.70720e8i	−0.675590	−	1.22252i
$606$	−2.40499e8			−1.08067
$607$	−1.77139e8	−	2.43811e8i	−0.792041	−	1.09015i	−0.993851	−	0.110727i	$-0.964682\pi$
$607$	−1.77139e8	−	2.43811e8i	−0.792041	−	1.09015i	0.201810	−	0.979425i	$-0.435318\pi$
$608$	−6.73106e7	−	2.07161e8i	−0.299483	−	0.921715i
$609$	7.20114e6	−	2.21628e7i	0.0318823	−	0.0981236i
$610$	2.33206e8	+	1.69434e8i	1.02742	+	0.746468i
$611$	−1.39526e7	+	1.92041e7i	−0.0611690	+	0.0841919i
$612$	3.33867e8	+	1.08480e8i	1.45653	+	0.473254i
$613$	4.03675e8	−	1.31162e8i	1.75247	−	0.569411i	0.756092	−	0.654465i	$-0.227106\pi$
$613$	4.03675e8	−	1.31162e8i	1.75247	−	0.569411i	0.996376	+	0.0850539i	$0.0271062\pi$
$614$	1.33061e8	−	9.66744e7i	0.574838	−	0.417644i
$615$			6.02817e8i			2.59155i
$616$	−7.03140e6	+	3.16200e7i	−0.0300815	+	0.135276i
$617$	−2.69745e8			−1.14841			−0.574207	−	0.818710i	$-0.694690\pi$
$617$	−2.69745e8			−1.14841			−0.574207	+	0.818710i	$0.694690\pi$
$618$	−2.75428e8	−	3.79094e8i	−1.16692	−	1.60613i
$619$	5.59585e7	+	1.72222e8i	0.235936	+	0.726136i	0.996996	+	0.0774543i	$0.0246792\pi$
$619$	5.59585e7	+	1.72222e8i	0.235936	+	0.726136i	−0.761060	+	0.648681i	$0.775321\pi$
$620$	−4.06477e7	+	1.25101e8i	−0.170554	+	0.524910i
$621$	−6.78871e7	−	4.93229e7i	−0.283473	−	0.205956i
$622$	−9.92250e7	+	1.36572e8i	−0.412335	+	0.567530i
$623$	2.11600e7	+	6.87528e6i	0.0875086	+	0.0284333i
$624$	2.37028e7	−	7.70150e6i	0.0975541	−	0.0316973i
$625$	2.06724e8	−	1.50194e8i	0.846741	−	0.615193i
$626$		−	6.31840e7i		−	0.257563i
$627$	−3.81508e8	+	1.65592e8i	−1.54775	+	0.671794i
$628$	8.22202e6			0.0331971
$629$	−1.78111e8	−	2.45149e8i	−0.715714	−	0.985096i
$630$	1.65868e7	+	5.10489e7i	0.0663347	+	0.204157i
$631$	5.69934e7	−	1.75408e8i	0.226849	−	0.698169i	−0.771250	−	0.636533i	$-0.780368\pi$
$631$	5.69934e7	−	1.75408e8i	0.226849	−	0.698169i	0.998099	−	0.0616364i	$-0.0196319\pi$
$632$	−2.10600e8	−	1.53010e8i	−0.834271	−	0.606133i
$633$	1.02940e8	−	1.41684e8i	0.405855	−	0.558612i
$634$	−2.43904e8	−	7.92491e7i	−0.957086	−	0.310976i
$635$	−2.18466e8	+	7.09840e7i	−0.853225	+	0.277229i
$636$	4.75482e7	−	3.45458e7i	0.184826	−	0.134284i
$637$			1.20014e8i			0.464315i
$638$	8.02987e7	−	7.67957e6i	0.309205	−	0.0295716i
$639$	−1.81656e8			−0.696222
$640$	9.50450e7	+	1.30818e8i	0.362568	+	0.499032i
$641$	7.97948e7	+	2.45583e8i	0.302971	+	0.932448i	0.980427	+	0.196885i	$0.0630825\pi$
$641$	7.97948e7	+	2.45583e8i	0.302971	+	0.932448i	−0.677456	+	0.735563i	$0.736918\pi$
$642$	−7.77553e7	+	2.39306e8i	−0.293849	+	0.904375i
$643$	−2.02159e8	−	1.46877e8i	−0.760431	−	0.552485i	0.138612	−	0.990347i	$-0.455736\pi$
$643$	−2.02159e8	−	1.46877e8i	−0.760431	−	0.552485i	−0.899042	+	0.437862i	$0.855736\pi$
$644$	3.41559e6	−	4.70116e6i	0.0127882	−	0.0176014i
$645$	−6.69514e8	−	2.17538e8i	−2.49506	−	0.810693i
$646$	2.76972e8	−	8.99937e7i	1.02740	−	0.333822i
$647$	1.70168e8	−	1.23634e8i	0.628296	−	0.456484i	−0.227514	−	0.973775i	$-0.573060\pi$
$647$	1.70168e8	−	1.23634e8i	0.628296	−	0.456484i	0.855809	+	0.517291i	$0.173060\pi$
$648$			7.23362e7i			0.265846i
$649$	3.45604e8	+	2.03877e8i	1.26428	+	0.745820i
$650$	−8.21187e7			−0.299021
$651$	−2.53851e7	−	3.49395e7i	−0.0920100	−	0.126641i
$652$	4.66894e7	+	1.43695e8i	0.168452	+	0.518441i
$653$	−4.75624e7	+	1.46382e8i	−0.170814	+	0.525712i	−0.999418	−	0.0341241i	$-0.989136\pi$
$653$	−4.75624e7	+	1.46382e8i	−0.170814	+	0.525712i	0.828603	+	0.559836i	$0.189136\pi$
$654$	−1.12961e6	−	820707.i	−0.00403826	−	0.00293396i
$655$	1.15498e8	−	1.58969e8i	0.411008	−	0.565704i
$656$	3.96262e7	+	1.28753e7i	0.140369	+	0.0456087i
$657$	3.75995e8	−	1.22168e8i	1.32582	−	0.430786i
$658$	−4.51361e6	+	3.27933e6i	−0.0158433	+	0.0115109i
$659$			1.56373e8i			0.546394i	0.961958	+	0.273197i	$0.0880811\pi$
$659$			1.56373e8i			0.546394i	−0.961958	+	0.273197i	$0.911919\pi$
$660$	2.77141e8	−	2.44875e8i	0.963983	−	0.851752i
$661$	−2.91747e7			−0.101019			−0.0505093	−	0.998724i	$-0.516084\pi$
$661$	−2.91747e7			−0.101019			−0.0505093	+	0.998724i	$0.516084\pi$
$662$	1.97885e8	+	2.72365e8i	0.682086	+	0.938810i
$663$	−1.11790e8	−	3.44053e8i	−0.383584	−	1.18055i
$664$	5.49798e7	−	1.69210e8i	0.187801	−	0.577993i
$665$	−4.54150e7	−	3.29959e7i	−0.154431	−	0.112201i
$666$	1.52792e8	−	2.10301e8i	0.517224	−	0.711898i
$667$	−3.84418e7	−	1.24905e7i	−0.129547	−	0.0420923i
$668$	5.11613e7	−	1.66233e7i	0.171637	−	0.0557684i
$669$	−2.09283e8	+	1.52053e8i	−0.698964	+	0.507827i
$670$		−	1.89480e7i		−	0.0629998i
$671$	2.73464e8	+	3.09497e8i	0.905175	+	1.02445i
$672$	−6.35946e7			−0.209562
$673$	2.38549e8	+	3.28335e8i	0.782588	+	1.07714i	0.994992	+	0.0999574i	$0.0318707\pi$
$673$	2.38549e8	+	3.28335e8i	0.782588	+	1.07714i	−0.212404	+	0.977182i	$0.568129\pi$
$674$	−5.83715e6	−	1.79649e7i	−0.0190643	−	0.0586740i
$675$	1.08576e8	−	3.34163e8i	0.353040	−	1.08654i
$676$	−1.08216e8	−	7.86238e7i	−0.350310	−	0.254515i
$677$	−2.39834e8	+	3.30103e8i	−0.772937	+	1.06386i	0.223089	+	0.974798i	$0.428386\pi$
$677$	−2.39834e8	+	3.30103e8i	−0.772937	+	1.06386i	−0.996026	+	0.0890585i	$0.971614\pi$
$678$	2.49302e8	+	8.10030e7i	0.799900	+	0.259903i
$679$	1.67758e7	−	5.45079e6i	0.0535888	−	0.0174121i
$680$	−5.85205e8	+	4.25176e8i	−1.86115	+	1.35220i
$681$			1.67905e8i			0.531645i
$682$	7.59575e7	−	1.28760e8i	0.239452	−	0.405909i
$683$	1.76997e8			0.555526			0.277763	−	0.960650i	$-0.410407\pi$
$683$	1.76997e8			0.555526			0.277763	+	0.960650i	$0.410407\pi$
$684$	−1.85122e8	−	2.54798e8i	−0.578481	−	0.796210i
$685$	1.33433e8	+	4.10665e8i	0.415137	+	1.27766i
$686$	−1.75919e7	+	5.41422e7i	−0.0544929	+	0.167712i
$687$	3.79427e8	+	2.75670e8i	1.17020	+	0.850197i
$688$	−2.85998e7	+	3.93642e7i	−0.0878208	+	0.120875i
$689$	−3.64823e7	−	1.18538e7i	−0.111538	−	0.0362411i
$690$	1.39803e8	−	4.54249e7i	0.425569	−	0.138276i
$691$	−5.91273e7	+	4.29585e7i	−0.179206	+	0.130201i	−0.673772	−	0.738939i	$-0.735327\pi$
$691$	−5.91273e7	+	4.29585e7i	−0.179206	+	0.130201i	0.494566	+	0.869140i	$0.335327\pi$
$692$		−	3.51049e8i		−	1.05937i
$693$	7.32154e6	+	7.65550e7i	0.0219990	+	0.230025i
$694$	−3.19467e8			−0.955757
$695$	−2.91375e8	−	4.01043e8i	−0.867956	−	1.19464i
$696$	8.32495e7	+	2.56216e8i	0.246919	+	0.759938i
$697$	1.86889e8	−	5.75186e8i	0.551933	−	1.69867i
$698$	−5.01673e6	−	3.64487e6i	−0.0147521	−	0.0107180i
$699$	1.99950e8	−	2.75208e8i	0.585451	−	0.805804i
$700$	2.31407e7	+	7.51887e6i	0.0674656	+	0.0219209i
$701$	3.53717e8	−	1.14930e8i	1.02684	−	0.333640i	0.253299	−	0.967388i	$-0.418484\pi$
$701$	3.53717e8	−	1.14930e8i	1.02684	−	0.333640i	0.773539	+	0.633748i	$0.218484\pi$
$702$	1.05726e8	−	7.68143e7i	0.305612	−	0.222040i
$703$			2.71860e8i			0.782490i
$704$	−1.05899e8	−	2.43981e8i	−0.303509	−	0.699258i
$705$	1.77922e8			0.507763
$706$	1.71898e8	+	2.36598e8i	0.488492	+	0.672352i
$707$	−1.43722e7	−	4.42331e7i	−0.0406692	−	0.125167i
$708$	−1.48256e8	+	4.56285e8i	−0.417746	+	1.28569i
$709$	−3.89666e8	−	2.83109e8i	−1.09334	−	0.794355i	−0.113376	−	0.993552i	$-0.536166\pi$
$709$	−3.89666e8	−	2.83109e8i	−1.09334	−	0.794355i	−0.979959	+	0.199197i	$0.936166\pi$
$710$	7.87672e7	−	1.08414e8i	0.220075	−	0.302907i
$711$	−5.87781e8	−	1.90982e8i	−1.63533	−	0.531352i
$712$	−2.44622e8	+	7.94824e7i	−0.677728	+	0.220207i
$713$	−6.06033e7	+	4.40308e7i	−0.167197	+	0.121475i
$714$		−	8.50254e7i		−	0.233590i
$715$	−2.35622e8	−	5.23958e7i	−0.644612	−	0.143344i
$716$	2.39423e8			0.652268
$717$	9.84635e7	+	1.35523e8i	0.267127	+	0.367669i
$718$	−3.11193e7	−	9.57755e7i	−0.0840731	−	0.258750i
$719$	4.25877e7	−	1.31071e8i	0.114577	−	0.352632i	−0.877282	−	0.479976i	$-0.840645\pi$
$719$	4.25877e7	−	1.31071e8i	0.114577	−	0.352632i	0.991859	+	0.127344i	$0.0406453\pi$
$720$	−9.57174e7	−	6.95428e7i	−0.256445	−	0.186318i
$721$	5.32643e7	−	7.33120e7i	0.142112	−	0.195600i
$722$	−1.04219e7	−	3.38629e6i	−0.0276909	−	0.00899732i
$723$	−8.00341e8	+	2.60047e8i	−2.11768	+	0.688076i
$724$	−1.25109e8	+	9.08973e7i	−0.329666	+	0.239516i
$725$		−	1.69247e8i		−	0.444127i
$726$	−3.67874e8	+	2.03296e8i	−0.961368	+	0.531273i
$727$	−4.81011e8			−1.25185			−0.625924	−	0.779884i	$-0.715278\pi$
$727$	−4.81011e8			−1.25185			−0.625924	+	0.779884i	$0.715278\pi$
$728$	1.48582e7	+	2.04506e7i	0.0385100	+	0.0530044i
$729$	−1.84460e8	−	5.67711e8i	−0.476124	−	1.46536i
$730$	−9.01227e7	+	2.77369e8i	−0.231668	+	0.713000i
$731$	5.71383e8	+	4.15134e8i	1.46277	+	1.06276i
$732$	−2.90254e8	+	3.99500e8i	−0.740022	+	1.01855i
$733$	6.77304e8	+	2.20069e8i	1.71978	+	0.558789i	0.991911	−	0.126933i	$-0.0405132\pi$
$733$	6.77304e8	+	2.20069e8i	1.71978	+	0.558789i	0.727864	+	0.685721i	$0.240513\pi$
$734$	−4.61976e8	+	1.50105e8i	−1.16824	+	0.379584i
$735$	7.27748e8	−	5.28740e8i	1.83282	−	1.33162i
$736$			1.10306e8i			0.276672i
$737$	5.89297e6	−	2.65005e7i	0.0147208	−	0.0661990i
$738$	5.18815e8			1.29075
$739$	4.31139e7	+	5.93413e7i	0.106828	+	0.147036i	0.859084	−	0.511835i	$-0.171034\pi$
$739$	4.31139e7	+	5.93413e7i	0.106828	+	0.147036i	−0.752256	+	0.658871i	$0.771034\pi$
$740$	−7.47033e7	−	2.29913e8i	−0.184351	−	0.567373i
$741$	−1.00293e8	+	3.08672e8i	−0.246501	+	0.758651i
$742$	−7.29397e6	−	5.29938e6i	−0.0178547	−	0.0129722i
$743$	3.69812e8	−	5.09002e8i	0.901601	−	1.24095i	−0.0683542	−	0.997661i	$-0.521775\pi$
$743$	3.69812e8	−	5.09002e8i	0.901601	−	1.24095i	0.969955	−	0.243286i	$-0.0782252\pi$
$744$	4.74839e8	+	1.54285e8i	1.15300	+	0.374631i
$745$	−8.00869e7	+	2.60218e7i	−0.193683	+	0.0629316i
$746$	3.14355e8	−	2.28392e8i	0.757189	−	0.550130i
$747$		−	4.22405e8i		−	1.01337i
$748$	−3.40356e8	+	1.47730e8i	−0.813259	+	0.352991i
$749$	−4.86604e7			−0.115806
$750$	−1.86543e7	−	2.56754e7i	−0.0442175	−	0.0608602i
$751$	−1.77822e8	−	5.47281e8i	−0.419824	−	1.29208i	−0.907865	−	0.419264i	$-0.862288\pi$
$751$	−1.77822e8	−	5.47281e8i	−0.419824	−	1.29208i	0.488041	−	0.872821i	$-0.337712\pi$
$752$	3.80016e6	−	1.16957e7i	0.00893611	−	0.0275025i
$753$	1.93983e8	+	1.40937e8i	0.454337	+	0.330095i
$754$	3.70008e7	−	5.09272e7i	0.0863170	−	0.118805i
$755$	3.29173e8	+	1.06955e8i	0.764862	+	0.248519i
$756$	−3.68263e7	+	1.19656e7i	−0.0852301	+	0.0276929i
$757$	−4.43484e8	+	3.22210e8i	−1.02233	+	0.742765i	−0.966759	−	0.255689i	$-0.917698\pi$
$757$	−4.43484e8	+	3.22210e8i	−1.02233	+	0.742765i	−0.0555699	+	0.998455i	$0.517698\pi$
$758$		−	5.44576e8i		−	1.25041i
$759$	2.09655e8	−	2.00509e7i	0.479490	−	0.0458572i
$760$	6.48966e8			1.47836
$761$	1.82239e8	+	2.50831e8i	0.413512	+	0.569150i	0.964071	−	0.265646i	$-0.0855854\pi$
$761$	1.82239e8	+	2.50831e8i	0.413512	+	0.569150i	−0.550559	+	0.834796i	$0.685585\pi$
$762$	9.64583e7	+	2.96868e8i	0.218009	+	0.670963i
$763$	83441.1	−	256805.i	0.000187848	−	0.000578136i
$764$	1.28744e8	+	9.35382e7i	0.288701	+	0.209753i
$765$	−1.00943e9	+	1.38937e9i	−2.25472	+	3.10336i
$766$	−3.84257e8	−	1.24853e8i	−0.854940	−	0.277787i
$767$	2.97808e8	−	9.67636e7i	0.660009	−	0.214450i
$768$	6.39122e8	−	4.64349e8i	1.41091	−	1.02509i
$769$			9.65570e7i			0.212327i	0.994349	+	0.106163i	$0.0338566\pi$
$769$			9.65570e7i			0.212327i	−0.994349	+	0.106163i	$0.966143\pi$
$770$	−4.88633e7	−	2.88252e7i	−0.107031	−	0.0631393i
$771$	5.99945e8			1.30903
$772$	−1.80290e8	−	2.48148e8i	−0.391850	−	0.539335i
$773$	3.16457e6	+	9.73954e6i	0.00685135	+	0.0210863i	0.954424	−	0.298455i	$-0.0964712\pi$
$773$	3.16457e6	+	9.73954e6i	0.00685135	+	0.0210863i	−0.947572	+	0.319541i	$0.896471\pi$
$774$	−1.87224e8	+	5.76217e8i	−0.403775	+	1.24269i
$775$	−2.53758e8	−	1.84366e8i	−0.545147	−	0.396073i
$776$	−1.19861e8	+	1.64974e8i	−0.256502	+	0.353045i
$777$	7.54866e7	+	2.45271e7i	0.160919	+	0.0522857i
$778$	−3.15191e8	+	1.02412e8i	−0.669321	+	0.217476i
$779$	−4.38966e8	+	3.18928e8i	−0.928579	+	0.674652i
$780$		−	2.88605e8i		−	0.608162i
$781$	1.43880e8	−	1.27129e8i	0.302029	−	0.266865i
$782$	−1.47478e8			−0.308395
$783$	1.58315e8	+	2.17901e8i	0.329789	+	0.453915i
$784$	−1.92131e7	−	5.91317e7i	−0.0398702	−	0.122708i
$785$	−1.24295e7	+	3.82540e7i	−0.0256947	+	0.0790803i
$786$	−2.16019e8	−	1.56947e8i	−0.444861	−	0.323210i
$787$	−2.20252e8	+	3.03151e8i	−0.451851	+	0.621920i	−0.972794	−	0.231672i	$-0.925581\pi$
$787$	−2.20252e8	+	3.03151e8i	−0.451851	+	0.621920i	0.520943	+	0.853592i	$0.325581\pi$
$788$	1.78590e8	+	5.80273e7i	0.364987	+	0.118592i
$789$	4.07214e8	−	1.32312e8i	0.829071	−	0.269382i
$790$	3.68844e8	−	2.67981e8i	0.748104	−	0.543529i
$791$			5.06929e7i			0.102428i
$792$	−5.88680e8	−	6.66247e8i	−1.18496	−	1.34110i
$793$	3.22299e8			0.646308
$794$	9.91040e7	+	1.36405e8i	0.197984	+	0.272501i
$795$	8.88486e7	+	2.73448e8i	0.176827	+	0.544218i
$796$	1.12743e8	−	3.46988e8i	0.223538	−	0.687980i
$797$	4.22100e7	+	3.06674e7i	0.0833759	+	0.0605761i	0.628692	−	0.777654i	$-0.283591\pi$
$797$	4.22100e7	+	3.06674e7i	0.0833759	+	0.0605761i	−0.545316	+	0.838230i	$0.683591\pi$
$798$	−4.48373e7	+	6.17132e7i	−0.0882329	+	0.121442i
$799$	−1.69766e8	−	5.51604e7i	−0.332821	−	0.108140i
$800$	−4.39267e8	+	1.42726e8i	−0.857942	+	0.278762i
$801$	−4.94032e8	+	3.58935e8i	−0.961296	+	0.698423i
$802$			2.09552e8i			0.406227i
$803$	−2.12308e8	+	3.59897e8i	−0.410035	+	0.695074i
$804$	3.24594e7			0.0624558
$805$	1.67093e7	+	2.29984e7i	0.0320310	+	0.0440869i
$806$	−3.60508e7	−	1.10953e8i	−0.0688509	−	0.211901i
$807$	4.27839e8	−	1.31675e9i	0.814066	−	2.50544i
$808$	4.34990e8	+	3.16039e8i	0.824603	+	0.599109i
$809$	5.29395e8	−	7.28650e8i	0.999849	−	1.37617i	0.0744312	−	0.997226i	$-0.476286\pi$
$809$	5.29395e8	−	7.28650e8i	0.999849	−	1.37617i	0.925418	−	0.378948i	$-0.123714\pi$
$810$	−1.20489e8	−	3.91492e7i	−0.226721	−	0.0736661i
$811$	−1.70972e8	+	5.55523e7i	−0.320526	+	0.104145i	−0.464861	−	0.885384i	$-0.653896\pi$
$811$	−1.70972e8	+	5.55523e7i	−0.320526	+	0.104145i	0.144335	+	0.989529i	$0.453896\pi$
$812$	−1.50896e7	+	1.09632e7i	−0.0281845	+	0.0204772i
$813$		−	1.45684e9i		−	2.71106i
$814$	2.61566e7	+	2.73497e8i	0.0484963	+	0.507084i
$815$	−7.39143e8			−1.36539
$816$	1.10159e8	+	1.51621e8i	0.202745	+	0.279055i
$817$	−1.95805e8	−	6.02626e8i	−0.359052	−	1.10505i
$818$	1.84839e8	−	5.68876e8i	0.337702	−	1.03934i
$819$	4.85529e7	+	3.52757e7i	0.0883818	+	0.0642132i
$820$	2.83599e8	−	3.90341e8i	0.514356	−	0.707950i
$821$	−8.65694e8	−	2.81281e8i	−1.56435	−	0.508289i	−0.606387	−	0.795169i	$-0.707382\pi$
$821$	−8.65694e8	−	2.81281e8i	−1.56435	−	0.508289i	−0.957967	+	0.286880i	$0.907382\pi$
$822$	5.58041e8	−	1.81319e8i	1.00473	−	0.326458i
$823$	−7.72658e8	+	5.61369e8i	−1.38608	+	1.00704i	−0.389796	+	0.920901i	$0.627454\pi$
$823$	−7.72658e8	+	5.61369e8i	−1.38608	+	1.00704i	−0.996283	+	0.0861434i	$0.972546\pi$
$824$			1.04761e9i			1.87248i
$825$	3.51123e8	+	8.08955e8i	0.625313	+	1.44066i
$826$	7.35970e7			0.130593
$827$	4.56072e8	+	6.27730e8i	0.806338	+	1.10983i	0.991878	+	0.127192i	$0.0405966\pi$
$827$	4.56072e8	+	6.27730e8i	0.806338	+	1.10983i	−0.185540	+	0.982637i	$0.559403\pi$
$828$	4.92854e7	+	1.51685e8i	0.0868215	+	0.267209i
$829$	−935361.	+	2.87875e6i	−0.00164178	+	0.00505289i	−0.951874	−	0.306489i	$-0.900846\pi$
$829$	−935361.	+	2.87875e6i	−0.00164178	+	0.00505289i	0.950232	+	0.311542i	$0.100846\pi$
$830$	2.52094e8	+	1.83157e8i	0.440888	+	0.320324i
$831$	−3.65022e8	+	5.02410e8i	−0.636086	+	0.875498i
$832$	−1.97400e8	−	6.41393e7i	−0.342751	−	0.111366i
$833$	−8.58314e8	+	2.78883e8i	−1.48495	+	0.482489i
$834$	−5.44967e8	+	3.95942e8i	−0.939446	+	0.682548i
$835$			2.63164e8i			0.452031i
$836$	3.24941e8	+	7.22579e7i	0.556142	+	0.123671i
$837$	4.99164e8			0.851269
$838$	−1.28529e8	−	1.76905e8i	−0.218408	−	0.300614i
$839$	2.30650e8	+	7.09867e8i	0.390541	+	1.20196i	0.932380	+	0.361480i	$0.117728\pi$
$839$	2.30650e8	+	7.09867e8i	0.390541	+	1.20196i	−0.541838	+	0.840483i	$0.682272\pi$
$840$	5.85495e7	−	1.80197e8i	0.0987837	−	0.304025i
$841$	−3.76261e8	−	2.73370e8i	−0.632559	−	0.459581i
$842$	2.32566e8	−	3.20100e8i	0.389592	−	0.536228i
$843$	−1.18525e9	−	3.85110e8i	−1.97845	−	0.642838i
$844$	−1.33313e8	+	4.33159e7i	−0.221740	+	0.0720477i
$845$	5.29402e8	−	3.84633e8i	0.877435	−	0.637494i
$846$		−	1.53128e8i		−	0.252897i
$847$	−5.93748e7	−	5.55114e7i	−0.0977129	−	0.0913549i
$848$	1.98728e7			0.0325891
$849$	2.20961e8	+	3.04126e8i	0.361071	+	0.496971i
$850$	−1.90824e8	−	5.87296e8i	−0.310725	−	0.956313i
$851$	4.25427e7	−	1.30933e8i	0.0690297	−	0.212452i
$852$	1.85721e8	+	1.34934e8i	0.300291	+	0.218174i
$853$	−5.15864e8	+	7.10026e8i	−0.831167	+	1.14400i	0.156538	+	0.987672i	$0.449967\pi$
$853$	−5.15864e8	+	7.10026e8i	−0.831167	+	1.14400i	−0.987705	+	0.156331i	$0.950033\pi$
$854$	7.20436e7	+	2.34084e7i	0.115670	+	0.0375835i
$855$	1.46533e9	−	4.76116e8i	2.34444	−	0.761754i
$856$	4.55107e8	−	3.30655e8i	0.725592	−	0.527174i
$857$		−	3.55199e8i		−	0.564324i	−0.959367	−	0.282162i	$-0.908948\pi$
$857$		−	3.55199e8i		−	0.564324i	0.959367	−	0.282162i	$-0.0910516\pi$
$858$	−7.11993e7	+	3.20181e8i	−0.112723	+	0.506913i
$859$	−2.83335e8			−0.447014			−0.223507	−	0.974702i	$-0.571751\pi$
$859$	−2.83335e8			−0.447014			−0.223507	+	0.974702i	$0.571751\pi$
$860$	3.31187e8	+	4.55840e8i	0.520688	+	0.716666i
$861$	4.89525e7	+	1.50660e8i	0.0766947	+	0.236042i
$862$	−1.70615e8	+	5.25100e8i	−0.266376	+	0.819823i
$863$	−3.30926e8	−	2.40432e8i	−0.514871	−	0.374076i	0.299797	−	0.954003i	$-0.403081\pi$
$863$	−3.30926e8	−	2.40432e8i	−0.514871	−	0.374076i	−0.814668	+	0.579927i	$0.803081\pi$
$864$	4.32038e8	−	5.94650e8i	0.669855	−	0.921977i
$865$	1.63330e9	+	5.30691e8i	2.52358	+	0.819961i
$866$	5.11532e8	−	1.66207e8i	0.787624	−	0.255915i
$867$	1.33007e9	−	9.66356e8i	2.04089	−	1.48279i
$868$			3.45669e7i			0.0528569i
$869$	5.99205e8	−	2.60082e8i	0.913096	−	0.396325i
$870$	−4.71828e8			−0.716517
$871$	−1.24526e7	−	1.71395e7i	−0.0188454	−	0.0259384i
$872$	964630.	+	2.96882e6i	0.00145483	+	0.00447749i
$873$	−1.49606e8	+	4.60439e8i	−0.224857	+	0.692038i
$874$	1.07043e8	+	7.77711e7i	0.160333	+	0.116489i
$875$	3.60750e6	−	4.96530e6i	0.00538496	−	0.00741176i
$876$	−4.75155e8	−	1.54387e8i	−0.706843	−	0.229667i
$877$	3.85320e8	−	1.25198e8i	0.571246	−	0.185609i	−0.00912902	−	0.999958i	$-0.502906\pi$
$877$	3.85320e8	−	1.25198e8i	0.571246	−	0.185609i	0.580375	+	0.814349i	$0.302906\pi$
$878$	−6.63047e8	+	4.81732e8i	−0.979627	+	0.711741i
$879$			2.08239e9i			3.06617i
$880$	1.24481e8	−	1.19051e7i	0.182665	−	0.0174696i
$881$	2.11235e8			0.308914			0.154457	−	0.987999i	$-0.450637\pi$
$881$	2.11235e8			0.308914			0.154457	+	0.987999i	$0.450637\pi$
$882$	−4.55060e8	−	6.26336e8i	−0.663228	−	0.912855i
$883$	5.58637e6	+	1.71931e7i	0.00811424	+	0.0249731i	0.955032	−	0.296504i	$-0.0958208\pi$
$883$	5.58637e6	+	1.71931e7i	0.00811424	+	0.0249731i	−0.946917	+	0.321477i	$0.895821\pi$
$884$	−8.94751e7	+	2.75376e8i	−0.129523	+	0.398630i
$885$	−1.89880e9	−	1.37956e9i	−2.73936	−	1.99026i
$886$	2.15643e8	−	2.96808e8i	0.310052	−	0.426750i
$887$	−7.64302e8	−	2.48337e8i	−1.09520	−	0.355853i	−0.294948	−	0.955513i	$-0.595302\pi$
$887$	−7.64302e8	−	2.48337e8i	−1.09520	−	0.355853i	−0.800254	+	0.599661i	$0.795302\pi$
$888$	−8.72670e8	+	2.83548e8i	−1.24627	+	0.404937i
$889$	−4.88363e7	+	3.54817e7i	−0.0695085	+	0.0505009i
$890$		−	4.50478e8i		−	0.639004i
$891$	−1.56339e8	−	9.22265e7i	−0.221021	−	0.130383i
$892$	2.07051e8			0.291731
$893$	9.41316e7	+	1.29561e8i	0.132185	+	0.181937i
$894$	3.53603e7	+	1.08828e8i	0.0494884	+	0.152310i
$895$	−3.61943e8	+	1.11394e9i	−0.504859	+	1.55380i
$896$	3.43776e7	+	2.49768e7i	0.0477915	+	0.0347226i
$897$	9.66066e7	−	1.32968e8i	0.133853	−	0.184233i
$898$	6.50813e8	+	2.11462e8i	0.898726	+	0.292014i
$899$	2.28674e8	−	7.43008e7i	0.314730	−	0.102262i
$900$	−5.40277e8	+	3.92534e8i	−0.741121	+	0.538456i
$901$		−	2.88460e8i		−	0.394376i
$902$	−4.10926e8	+	3.63084e8i	−0.559943	+	0.494752i
$903$	−1.84995e8			−0.251245
$904$	−3.44466e8	−	4.74117e8i	−0.466274	−	0.641771i
$905$	−2.33780e8	−	7.19500e8i	−0.315400	−	0.970700i
$906$	1.45338e8	−	4.47304e8i	0.195431	−	0.601475i
$907$	1.67507e8	+	1.21701e8i	0.224497	+	0.163107i	0.694349	−	0.719639i	$-0.255693\pi$
$907$	1.67507e8	+	1.21701e8i	0.224497	+	0.163107i	−0.469851	+	0.882745i	$0.655693\pi$
$908$	7.89920e7	−	1.08723e8i	0.105518	−	0.145233i
$909$	1.21405e9	+	3.94468e8i	1.61638	+	0.525195i
$910$	−4.21056e7	+	1.36809e7i	−0.0558748	+	0.0181548i
$911$	−4.74838e8	+	3.44990e8i	−0.628045	+	0.456301i	−0.855722	−	0.517435i	$-0.826887\pi$
$911$	−4.74838e8	+	3.44990e8i	−0.628045	+	0.456301i	0.227678	+	0.973737i	$0.426887\pi$
$912$		−	1.68141e8i		−	0.221661i
$913$	2.95613e8	+	3.34565e8i	0.388429	+	0.439610i
$914$	−6.56787e8			−0.860173
$915$	−1.41994e9	−	1.95438e9i	−1.85356	−	2.55121i
$916$	−1.15999e8	−	3.57009e8i	−0.150927	−	0.464507i
$917$	1.59568e7	−	4.91099e7i	0.0206936	−	0.0636885i
$918$	7.95042e8	+	5.77632e8i	1.02769	+	0.746660i
$919$	7.71800e8	−	1.06229e9i	0.994393	−	1.36866i	0.0656905	−	0.997840i	$-0.479075\pi$
$919$	7.71800e8	−	1.06229e9i	0.994393	−	1.36866i	0.928703	−	0.370825i	$-0.120925\pi$
$920$	−3.12555e8	−	1.01555e8i	−0.401387	−	0.130418i
$921$	−1.31090e9	+	4.25936e8i	−1.67799	+	0.545212i
$922$	1.91599e8	−	1.39205e8i	0.244455	−	0.177607i
$923$		−	1.49832e8i		−	0.190546i
$924$	4.93797e7	−	8.37066e7i	0.0625940	−	0.106107i
$925$	5.76455e8			0.728350
$926$	1.11550e8	+	1.53535e8i	0.140487	+	0.193363i
$927$	7.68579e8	+	2.36544e9i	0.964827	+	2.96943i
$928$	1.09409e8	−	3.36727e8i	0.136902	−	0.421341i
$929$	1.85998e8	+	1.35135e8i	0.231985	+	0.168547i	0.697705	−	0.716385i	$-0.254205\pi$
$929$	1.85998e8	+	1.35135e8i	0.231985	+	0.168547i	−0.465720	+	0.884932i	$0.654205\pi$
$930$	−5.13977e8	+	7.07428e8i	−0.638991	+	0.879495i
$931$	7.70048e8	+	2.50204e8i	0.954265	+	0.310059i
$932$	−2.58947e8	+	8.41370e7i	−0.319863	+	0.103930i
$933$	1.14454e9	−	8.31554e8i	1.40924	−	1.02387i
$934$			5.90570e8i			0.724821i
$935$	−1.72805e8	−	1.80688e9i	−0.211408	−	2.21052i
$936$	−6.93805e8			−0.846077
$937$	−6.46240e8	−	8.89474e8i	−0.785553	−	1.08122i	−0.994648	−	0.103325i	$-0.967052\pi$
$937$	−6.46240e8	−	8.89474e8i	−0.785553	−	1.08122i	0.209095	−	0.977895i	$-0.432948\pi$
$938$	−1.53870e6	−	4.73562e6i	−0.00186442	−	0.00573811i
$939$	−1.63628e8	+	5.03597e8i	−0.197634	+	0.608255i
$940$	−1.15209e8	−	8.37045e7i	−0.138709	−	0.100778i
$941$	−1.28540e8	+	1.76920e8i	−0.154265	+	0.212328i	−0.879154	−	0.476538i	$-0.841891\pi$
$941$	−1.28540e8	+	1.76920e8i	−0.154265	+	0.212328i	0.724888	+	0.688866i	$0.241891\pi$
$942$	5.19824e7	+	1.68901e7i	0.0621875	+	0.0202059i
$943$	2.61323e8	−	8.49090e7i	0.311632	−	0.101256i
$944$	−1.31241e8	+	9.53524e7i	−0.156011	+	0.113348i
$945$		−	1.89428e8i		−	0.224465i
$946$	−2.54965e8	−	5.87417e8i	−0.301167	−	0.693862i
$947$	6.29801e8			0.741572			0.370786	−	0.928718i	$-0.379088\pi$
$947$	6.29801e8			0.741572			0.370786	+	0.928718i	$0.379088\pi$
$948$	4.59072e8	+	6.31859e8i	0.538835	+	0.741643i
$949$	1.00765e8	+	3.10124e8i	0.117900	+	0.362858i
$950$	−1.71200e8	+	5.26901e8i	−0.199680	+	0.614551i
$951$	1.73876e9	+	1.26328e9i	2.02161	+	1.46879i
$952$	−1.11732e8	+	1.53785e8i	−0.129499	+	0.178240i
$953$	−1.16788e9	−	3.79469e8i	−1.34934	−	0.438427i	−0.456869	−	0.889534i	$-0.651029\pi$
$953$	−1.16788e9	−	3.79469e8i	−1.34934	−	0.438427i	−0.892470	+	0.451107i	$0.851029\pi$
$954$	2.35343e8	−	7.64676e7i	0.271054	−	0.0880709i
$955$	−6.29825e8	+	4.57595e8i	−0.723119	+	0.525377i
$956$		−	1.34078e8i		−	0.153456i
$957$	−6.59894e8	−	1.46742e8i	−0.752902	−	0.167424i
$958$	1.11587e9			1.26917
$959$	6.66971e7	+	9.18006e7i	0.0756225	+	0.104085i
$960$	4.80747e8	+	1.47959e9i	0.543379	+	1.67235i
$961$	−1.36554e8	+	4.20269e8i	−0.153863	+	0.473540i
$962$	1.73458e8	+	1.26025e8i	0.194836	+	0.141557i
$963$	7.85025e8	−	1.08049e9i	0.879031	−	1.20988i
$964$	6.40584e8	+	2.08139e8i	0.715065	+	0.232339i
$965$	1.42709e9	−	4.63689e8i	1.58807	−	0.515995i
$966$	3.12519e7	−	2.27058e7i	0.0346693	−	0.0251887i
$967$		−	7.11485e8i		−	0.786840i	−0.919359	−	0.393420i	$-0.871292\pi$
$967$		−	7.11485e8i		−	0.786840i	0.919359	−	0.393420i	$-0.128708\pi$
$968$	9.32524e8	+	1.15722e8i	1.02810	+	0.127582i
$969$	−2.44061e9			−2.68243
$970$	−2.09924e8	−	2.88935e8i	−0.230010	−	0.316581i
$971$	1.22670e7	+	3.77539e7i	0.0133992	+	0.0412386i	0.957533	−	0.288325i	$-0.0930984\pi$
$971$	1.22670e7	+	3.77539e7i	0.0133992	+	0.0412386i	−0.944133	+	0.329564i	$0.893098\pi$
$972$	−1.23051e8	+	3.78712e8i	−0.133994	+	0.412392i
$973$	−1.05390e8	−	7.65701e7i	−0.114409	−	0.0831229i
$974$	4.14948e8	−	5.71127e8i	0.449073	−	0.618095i
$975$	6.54512e8	+	2.12664e8i	0.706161	+	0.229446i
$976$	−1.58799e8	+	5.15970e7i	−0.170804	+	0.0554977i
$977$	−5.53831e8	+	4.02382e8i	−0.593873	+	0.431474i	−0.843699	−	0.536817i	$-0.819627\pi$
$977$	−5.53831e8	+	4.02382e8i	−0.593873	+	0.431474i	0.249826	+	0.968291i	$0.419627\pi$
$978$			1.00440e9i			1.07372i
$979$	1.40102e8	−	6.30033e8i	0.149312	−	0.671453i
$980$	−7.19987e8			−0.764973
$981$	4.35617e6	+	5.99576e6i	0.00461422	+	0.00635093i
$982$	−7.11288e7	−	2.18912e8i	−0.0751123	−	0.231172i
$983$	−3.98495e7	+	1.22644e8i	−0.0419529	+	0.129118i	−0.969839	−	0.243745i	$-0.921624\pi$
$983$	−3.98495e7	+	1.22644e8i	−0.0419529	+	0.129118i	0.927886	+	0.372863i	$0.121624\pi$
$984$	−1.48160e9	−	1.07644e9i	−1.55505	−	1.12981i
$985$	−5.39959e8	+	7.43190e8i	−0.565005	+	0.777663i
$986$	4.50202e8	+	1.46279e8i	0.469652	+	0.152599i
$987$	4.44674e7	−	1.44483e7i	0.0462477	−	0.0150268i
$988$	2.10160e8	−	1.52690e8i	0.217911	−	0.158321i
$989$			3.20877e8i			0.331704i
$990$	1.42835e9	−	6.19970e8i	1.47208	−	0.638947i
$991$	−4.87597e8			−0.501003			−0.250501	−	0.968116i	$-0.580595\pi$
$991$	−4.87597e8			−0.501003			−0.250501	+	0.968116i	$0.580595\pi$
$992$	−3.85683e8	−	5.30848e8i	−0.395090	−	0.543795i
$993$	−8.71858e8	−	2.68330e9i	−0.890426	−	2.74045i
$994$	1.08822e7	−	3.34919e7i	0.0110804	−	0.0341021i
$995$	1.44397e9	+	1.04911e9i	1.46585	+	1.06500i
$996$	−3.13762e8	+	4.31857e8i	−0.317558	+	0.437081i
$997$	−3.79675e8	−	1.23364e8i	−0.383113	−	0.124481i	0.111128	−	0.993806i	$-0.464554\pi$
$997$	−3.79675e8	−	1.23364e8i	−0.383113	−	0.124481i	−0.494240	+	0.869325i	$0.664554\pi$
$998$	2.58336e8	−	8.39385e7i	0.259892	−	0.0844441i
$999$	−7.42172e8	+	5.39220e8i	−0.744403	+	0.540840i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.7.d.a.8.2	yes	20
3.2	odd	2		99.7.k.a.19.4		20
11.2	odd	10		121.7.b.c.120.6		20
11.7	odd	10	inner	11.7.d.a.7.2	✓	20
11.9	even	5		121.7.b.c.120.15		20
33.29	even	10		99.7.k.a.73.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.7.d.a.7.2	✓	20	11.7	odd	10	inner
11.7.d.a.8.2	yes	20	1.1	even	1	trivial
99.7.k.a.19.4		20	3.2	odd	2
99.7.k.a.73.4		20	33.29	even	10
121.7.b.c.120.6		20	11.2	odd	10
121.7.b.c.120.15		20	11.9	even	5

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:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	11.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.12745 - 4.30457i) q^{2} +(13.7792 + 42.4080i) q^{3} +(11.0287 - 33.9429i) q^{4} +(141.251 + 102.625i) q^{5} +(139.454 - 191.943i) q^{6} +(43.6363 + 14.1783i) q^{7} +(-504.462 + 163.910i) q^{8} +(-1018.80 + 740.201i) q^{9} +O(q^{10})\)	\(q+(-3.12745 - 4.30457i) q^{2} +(13.7792 + 42.4080i) q^{3} +(11.0287 - 33.9429i) q^{4} +(141.251 + 102.625i) q^{5} +(139.454 - 191.943i) q^{6} +(43.6363 + 14.1783i) q^{7} +(-504.462 + 163.910i) q^{8} +(-1018.80 + 740.201i) q^{9} -928.982i q^{10} +(288.920 - 1299.26i) q^{11} +1591.42 q^{12} +(-610.524 - 840.314i) q^{13} +(-75.4391 - 232.178i) q^{14} +(-2405.80 + 7404.28i) q^{15} +(435.337 + 316.291i) q^{16} +(4591.05 - 6319.03i) q^{17} +(6372.49 + 2070.55i) q^{18} +(-6664.55 + 2165.44i) q^{19} +(5041.22 - 3662.66i) q^{20} +2045.90i q^{21} +(-6496.36 + 2819.71i) q^{22} +3548.64 q^{23} +(-13902.2 - 19134.7i) q^{24} +(4591.64 + 14131.6i) q^{25} +(-1707.81 + 5256.09i) q^{26} +(-19130.4 - 13899.1i) q^{27} +(962.506 - 1324.78i) q^{28} +(-10832.8 - 3519.80i) q^{29} +(39396.3 - 12800.6i) q^{30} +(-17077.9 + 12407.8i) q^{31} +31084.0i q^{32} +(59080.3 - 5650.29i) q^{33} -41559.0 q^{34} +(4708.64 + 6480.89i) q^{35} +(13888.5 + 42744.5i) q^{36} +(11988.4 - 36896.6i) q^{37} +(30164.4 + 21915.7i) q^{38} +(27223.5 - 37470.0i) q^{39} +(-88077.3 - 28618.0i) q^{40} +(73640.3 - 23927.2i) q^{41} +(8806.70 - 6398.45i) q^{42} +90422.5i q^{43} +(-40914.4 - 24136.0i) q^{44} -219870. q^{45} +(-11098.2 - 15275.4i) q^{46} +(-7062.11 - 21734.9i) q^{47} +(-7414.66 + 22820.0i) q^{48} +(-93476.9 - 67915.0i) q^{49} +(46470.4 - 63961.0i) q^{50} +(331238. + 107626. i) q^{51} +(-35256.0 + 11455.4i) q^{52} +(29877.9 - 21707.5i) q^{53} +125817. i q^{54} +(174147. - 153872. i) q^{55} -24336.9 q^{56} +(-183664. - 252792. i) q^{57} +(18727.9 + 57638.7i) q^{58} +(-93159.7 + 286716. i) q^{59} +(224790. + 163319. i) q^{60} +(-182387. + 251034. i) q^{61} +(106820. + 34708.1i) q^{62} +(-54951.5 + 17854.8i) q^{63} +(161665. - 117456. i) q^{64} -181351. i q^{65} +(-209093. - 236644. i) q^{66} +20396.5 q^{67} +(-163853. - 225524. i) q^{68} +(48897.5 + 150491. i) q^{69} +(13171.4 - 40537.4i) q^{70} +(116702. + 84788.8i) q^{71} +(392620. - 540395. i) q^{72} +(-298573. - 97012.3i) q^{73} +(-196317. + 63787.3i) q^{74} +(-536024. + 389444. i) q^{75} +250096. i q^{76} +(31028.8 - 52598.7i) q^{77} -246433. q^{78} +(288467. + 397041. i) q^{79} +(29032.5 + 89352.9i) q^{80} +(42142.0 - 129700. i) q^{81} +(-333303. - 242159. i) q^{82} +(-197159. + 271366. i) q^{83} +(69443.7 + 22563.6i) q^{84} +(1.29698e6 - 421415. i) q^{85} +(389230. - 282792. i) q^{86} -507898. i q^{87} +(67212.8 + 702787. i) q^{88} +484916. q^{89} +(687633. + 946446. i) q^{90} +(-14726.8 - 45324.4i) q^{91} +(39137.0 - 120451. i) q^{92} +(-761509. - 553269. i) q^{93} +(-71473.2 + 98374.4i) q^{94} +(-1.16361e6 - 378079. i) q^{95} +(-1.31821e6 + 428312. i) q^{96} +(311023. - 225972. i) q^{97} +614779. i q^{98} +(667365. + 1.53755e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{2} - 39 q^{3} + 215 q^{4} + 181 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} - 704 q^{9}+O(q^{10}) \) 20 * q - 5 * q^2 - 39 * q^3 + 215 * q^4 + 181 * q^5 - 405 * q^6 - 365 * q^7 + 1595 * q^8 - 704 * q^9	\( 20 q - 5 q^{2} - 39 q^{3} + 215 q^{4} + 181 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} - 704 q^{9} - 3498 q^{11} - 3006 q^{12} - 1805 q^{13} + 7170 q^{14} - 525 q^{15} - 2185 q^{16} + 3635 q^{17} + 11970 q^{18} + 23845 q^{19} + 5144 q^{20} - 2915 q^{22} + 7816 q^{23} - 123775 q^{24} - 30416 q^{25} - 131310 q^{26} - 18687 q^{27} + 226540 q^{28} + 134595 q^{29} + 220420 q^{30} - 71211 q^{31} + 5951 q^{33} - 228190 q^{34} - 377445 q^{35} - 119626 q^{36} - 205731 q^{37} + 127220 q^{38} + 443075 q^{39} + 704340 q^{40} + 490975 q^{41} - 20170 q^{42} - 537812 q^{44} - 805524 q^{45} - 714610 q^{46} + 25329 q^{47} - 935824 q^{48} + 304010 q^{49} + 417855 q^{50} + 1169565 q^{51} + 1468510 q^{52} - 110919 q^{53} - 5511 q^{55} - 862620 q^{56} - 1435995 q^{57} - 667940 q^{58} - 581009 q^{59} + 664640 q^{60} + 892675 q^{61} + 2337360 q^{62} + 900840 q^{63} + 124615 q^{64} + 272910 q^{66} - 960956 q^{67} - 1822680 q^{68} - 624034 q^{69} - 1987140 q^{70} - 288895 q^{71} + 954565 q^{72} - 806585 q^{73} - 404170 q^{74} - 550845 q^{75} + 623095 q^{77} + 1703080 q^{78} + 1662955 q^{79} + 1190956 q^{80} + 1465924 q^{81} - 282095 q^{82} + 14645 q^{83} - 2604390 q^{84} - 33365 q^{85} + 735635 q^{86} - 1860485 q^{88} + 1111620 q^{89} + 4118080 q^{90} + 650935 q^{91} + 4407784 q^{92} - 1556453 q^{93} - 5913080 q^{94} - 4329525 q^{95} - 6429020 q^{96} - 1189281 q^{97} + 252208 q^{99}+O(q^{100}) \) 20 * q - 5 * q^2 - 39 * q^3 + 215 * q^4 + 181 * q^5 - 405 * q^6 - 365 * q^7 + 1595 * q^8 - 704 * q^9 - 3498 * q^11 - 3006 * q^12 - 1805 * q^13 + 7170 * q^14 - 525 * q^15 - 2185 * q^16 + 3635 * q^17 + 11970 * q^18 + 23845 * q^19 + 5144 * q^20 - 2915 * q^22 + 7816 * q^23 - 123775 * q^24 - 30416 * q^25 - 131310 * q^26 - 18687 * q^27 + 226540 * q^28 + 134595 * q^29 + 220420 * q^30 - 71211 * q^31 + 5951 * q^33 - 228190 * q^34 - 377445 * q^35 - 119626 * q^36 - 205731 * q^37 + 127220 * q^38 + 443075 * q^39 + 704340 * q^40 + 490975 * q^41 - 20170 * q^42 - 537812 * q^44 - 805524 * q^45 - 714610 * q^46 + 25329 * q^47 - 935824 * q^48 + 304010 * q^49 + 417855 * q^50 + 1169565 * q^51 + 1468510 * q^52 - 110919 * q^53 - 5511 * q^55 - 862620 * q^56 - 1435995 * q^57 - 667940 * q^58 - 581009 * q^59 + 664640 * q^60 + 892675 * q^61 + 2337360 * q^62 + 900840 * q^63 + 124615 * q^64 + 272910 * q^66 - 960956 * q^67 - 1822680 * q^68 - 624034 * q^69 - 1987140 * q^70 - 288895 * q^71 + 954565 * q^72 - 806585 * q^73 - 404170 * q^74 - 550845 * q^75 + 623095 * q^77 + 1703080 * q^78 + 1662955 * q^79 + 1190956 * q^80 + 1465924 * q^81 - 282095 * q^82 + 14645 * q^83 - 2604390 * q^84 - 33365 * q^85 + 735635 * q^86 - 1860485 * q^88 + 1111620 * q^89 + 4118080 * q^90 + 650935 * q^91 + 4407784 * q^92 - 1556453 * q^93 - 5913080 * q^94 - 4329525 * q^95 - 6429020 * q^96 - 1189281 * q^97 + 252208 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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