LMFDB - Embedded newform 11.7.d.a.7.5

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			7.5
Root			$-12.6102i$ of defining polynomial
Character	$\chi$	$=$	11.7
Dual form			11.7.d.a.8.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.29405 - 8.66302i) q^{2} +(3.74624 - 11.5298i) q^{3} +(-15.6557 - 48.1834i) q^{4} +(-15.2392 + 11.0719i) q^{5} +(-76.3035 - 105.023i) q^{6} +(51.6547 - 16.7836i) q^{7} +(135.823 + 44.1317i) q^{8} +(470.872 + 342.109i) q^{9} +O(q^{10})$	\(q+(6.29405 - 8.66302i) q^{2} +(3.74624 - 11.5298i) q^{3} +(-15.6557 - 48.1834i) q^{4} +(-15.2392 + 11.0719i) q^{5} +(-76.3035 - 105.023i) q^{6} +(51.6547 - 16.7836i) q^{7} +(135.823 + 44.1317i) q^{8} +(470.872 + 342.109i) q^{9} +201.705i q^{10} +(-903.134 + 977.706i) q^{11} -614.193 q^{12} +(-502.918 + 692.207i) q^{13} +(179.720 - 553.123i) q^{14} +(70.5668 + 217.182i) q^{15} +(3860.38 - 2804.73i) q^{16} +(-3998.21 - 5503.06i) q^{17} +(5927.39 - 1925.93i) q^{18} +(-819.988 - 266.430i) q^{19} +(772.065 + 560.938i) q^{20} -658.441i q^{21} +(2785.52 + 13977.6i) q^{22} -20739.3 q^{23} +(1017.65 - 1400.68i) q^{24} +(-4718.74 + 14522.8i) q^{25} +(2831.21 + 8713.57i) q^{26} +(12858.3 - 9342.11i) q^{27} +(-1617.39 - 2226.14i) q^{28} +(21841.3 - 7096.68i) q^{29} +(2325.61 + 755.636i) q^{30} +(8066.57 + 5860.71i) q^{31} -41955.6i q^{32} +(7889.35 + 14075.6i) q^{33} -72838.1 q^{34} +(-601.349 + 827.686i) q^{35} +(9112.12 - 28044.2i) q^{36} +(-3362.77 - 10349.5i) q^{37} +(-7469.14 + 5426.65i) q^{38} +(6096.92 + 8391.69i) q^{39} +(-2558.46 + 831.294i) q^{40} +(85983.0 + 27937.6i) q^{41} +(-5704.09 - 4144.26i) q^{42} -26427.6i q^{43} +(61248.5 + 28209.4i) q^{44} -10963.5 q^{45} +(-130534. + 179665. i) q^{46} +(41521.0 - 127789. i) q^{47} +(-17875.9 - 55016.4i) q^{48} +(-92793.5 + 67418.4i) q^{49} +(96111.3 + 132286. i) q^{50} +(-78427.2 + 25482.5i) q^{51} +(41226.4 + 13395.3i) q^{52} +(-12038.9 - 8746.77i) q^{53} -170192. i q^{54} +(2937.95 - 24898.9i) q^{55} +7756.60 q^{56} +(-6143.75 + 8456.15i) q^{57} +(75991.9 - 233879. i) q^{58} +(-92965.2 - 286117. i) q^{59} +(9359.82 - 6800.31i) q^{60} +(218947. + 301355. i) q^{61} +(101543. - 32993.3i) q^{62} +(30064.6 + 9768.58i) q^{63} +(-116398. - 84568.3i) q^{64} -16116.9i q^{65} +(171594. + 20247.2i) q^{66} -189715. q^{67} +(-202561. + 278802. i) q^{68} +(-77694.4 + 239119. i) q^{69} +(3385.34 + 10419.0i) q^{70} +(-333295. + 242153. i) q^{71} +(48857.6 + 67246.7i) q^{72} +(102292. - 33236.7i) q^{73} +(-110824. - 36008.8i) q^{74} +(149767. + 108812. i) q^{75} +43681.0i q^{76} +(-30241.6 + 65661.0i) q^{77} +111072. q^{78} +(312971. - 430768. i) q^{79} +(-27775.3 + 85483.7i) q^{80} +(71574.1 + 220282. i) q^{81} +(783205. - 569032. i) q^{82} +(-435941. - 600021. i) q^{83} +(-31726.0 + 10308.4i) q^{84} +(121859. + 39594.4i) q^{85} +(-228943. - 166337. i) q^{86} -278411. i q^{87} +(-165814. + 92938.5i) q^{88} -493938. q^{89} +(-69005.0 + 94977.3i) q^{90} +(-14360.3 + 44196.5i) q^{91} +(324689. + 999290. i) q^{92} +(97791.9 - 71049.9i) q^{93} +(-845700. - 1.16401e6i) q^{94} +(15445.9 - 5018.67i) q^{95} +(-483738. - 157176. i) q^{96} +(1.03679e6 + 753274. i) q^{97} +1.22821e6i q^{98} +(-759743. + 151405. i) 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 $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	6.29405	−	8.66302i	0.786757	−	1.08288i	−0.207748	−	0.978182i	$-0.566613\pi$
$2$	6.29405	−	8.66302i	0.786757	−	1.08288i	0.994504	−	0.104695i	$-0.0333867\pi$
$3$	3.74624	−	11.5298i	0.138750	−	0.427028i	−0.857405	−	0.514643i	$-0.827925\pi$
$3$	3.74624	−	11.5298i	0.138750	−	0.427028i	0.996154	+	0.0876149i	$0.0279245\pi$
$4$	−15.6557	−	48.1834i	−0.244621	−	0.752866i
$5$	−15.2392	+	11.0719i	−0.121914	+	0.0885754i	−0.647071	−	0.762430i	$-0.724006\pi$
$5$	−15.2392	+	11.0719i	−0.121914	+	0.0885754i	0.525158	+	0.851005i	$0.324006\pi$
$6$	−76.3035	−	105.023i	−0.353257	−	0.486216i
$7$	51.6547	−	16.7836i	0.150597	−	0.0489318i	−0.232749	−	0.972537i	$-0.574772\pi$
$7$	51.6547	−	16.7836i	0.150597	−	0.0489318i	0.383345	+	0.923605i	$0.374772\pi$
$8$	135.823	+	44.1317i	0.265280	+	0.0861946i
$9$	470.872	+	342.109i	0.645916	+	0.469285i
$10$			201.705i			0.201705i
$11$	−903.134	+	977.706i	−0.678538	+	0.734565i
$11$	−903.134	+	977.706i	−0.678538	+	0.734565i
$12$	−614.193			−0.355436
$13$	−502.918	+	692.207i	−0.228911	+	0.315069i	−0.907986	−	0.418999i	$-0.862381\pi$
$13$	−502.918	+	692.207i	−0.228911	+	0.315069i	0.679075	+	0.734069i	$0.262381\pi$
$14$	179.720	−	553.123i	0.0654958	−	0.201575i
$15$	70.5668	+	217.182i	0.0209087	+	0.0643503i
$16$	3860.38	−	2804.73i	0.942475	−	0.684748i
$17$	−3998.21	−	5503.06i	−0.813802	−	1.12010i	−0.990726	−	0.135878i	$-0.956615\pi$
$17$	−3998.21	−	5503.06i	−0.813802	−	1.12010i	0.176924	−	0.984225i	$-0.443385\pi$
$18$	5927.39	−	1925.93i	1.01636	−	0.330234i
$19$	−819.988	−	266.430i	−0.119549	−	0.0388439i	0.248631	−	0.968598i	$-0.420019\pi$
$19$	−819.988	−	266.430i	−0.119549	−	0.0388439i	−0.368181	+	0.929754i	$0.620019\pi$
$20$	772.065	+	560.938i	0.0965081	+	0.0701172i
$21$		−	658.441i		−	0.0710983i
$22$	2785.52	+	13977.6i	0.261600	+	1.31270i
$23$	−20739.3			−1.70455			−0.852276	−	0.523093i	$-0.824778\pi$
$23$	−20739.3			−1.70455			−0.852276	+	0.523093i	$0.824778\pi$
$24$	1017.65	−	1400.68i	0.0736150	−	0.101322i
$25$	−4718.74	+	14522.8i	−0.302000	+	0.929459i
$26$	2831.21	+	8713.57i	0.161084	+	0.495765i
$27$	12858.3	−	9342.11i	0.653270	−	0.474629i
$28$	−1617.39	−	2226.14i	−0.0736783	−	0.101409i
$29$	21841.3	−	7096.68i	0.895541	−	0.290979i	0.175145	−	0.984543i	$-0.443960\pi$
$29$	21841.3	−	7096.68i	0.895541	−	0.290979i	0.720395	+	0.693564i	$0.243960\pi$
$30$	2325.61	+	755.636i	0.0861336	+	0.0279865i
$31$	8066.57	+	5860.71i	0.270772	+	0.196727i	0.714882	−	0.699245i	$-0.246480\pi$
$31$	8066.57	+	5860.71i	0.270772	+	0.196727i	−0.444110	+	0.895972i	$0.646480\pi$
$32$		−	41955.6i		−	1.28038i
$33$	7889.35	+	14075.6i	0.219533	+	0.391675i
$34$	−72838.1			−1.85320
$35$	−601.349	+	827.686i	−0.0140256	+	0.0193046i
$36$	9112.12	−	28044.2i	0.195304	−	0.601085i
$37$	−3362.77	−	10349.5i	−0.0663884	−	0.204322i	0.912359	−	0.409390i	$-0.134259\pi$
$37$	−3362.77	−	10349.5i	−0.0663884	−	0.204322i	−0.978748	+	0.205068i	$0.934259\pi$
$38$	−7469.14	+	5426.65i	−0.136119	+	0.0988965i
$39$	6096.92	+	8391.69i	0.102782	+	0.141467i
$40$	−2558.46	+	831.294i	−0.0399760	+	0.0129890i
$41$	85983.0	+	27937.6i	1.24756	+	0.405356i	0.857045	−	0.515241i	$-0.172298\pi$
$41$	85983.0	+	27937.6i	1.24756	+	0.405356i	0.390513	+	0.920597i	$0.372298\pi$
$42$	−5704.09	−	4144.26i	−0.0769908	−	0.0559371i
$43$		−	26427.6i		−	0.332394i	−0.986093	−	0.166197i	$-0.946851\pi$
$43$		−	26427.6i		−	0.332394i	0.986093	−	0.166197i	$-0.0531487\pi$
$44$	61248.5	+	28209.4i	0.719014	+	0.331158i
$45$	−10963.5			−0.120313
$46$	−130534.	+	179665.i	−1.34107	+	1.84582i
$47$	41521.0	−	127789.i	0.399921	−	1.23083i	−0.525141	−	0.851015i	$-0.675987\pi$
$47$	41521.0	−	127789.i	0.399921	−	1.23083i	0.925062	−	0.379816i	$-0.124013\pi$
$48$	−17875.9	−	55016.4i	−0.161638	−	0.497472i
$49$	−92793.5	+	67418.4i	−0.788732	+	0.573047i
$50$	96111.3	+	132286.i	0.768891	+	1.05829i
$51$	−78427.2	+	25482.5i	−0.591230	+	0.192102i
$52$	41226.4	+	13395.3i	0.293201	+	0.0952669i
$53$	−12038.9	−	8746.77i	−0.0808647	−	0.0587516i	0.546618	−	0.837382i	$-0.315915\pi$
$53$	−12038.9	−	8746.77i	−0.0808647	−	0.0587516i	−0.627483	+	0.778630i	$0.715915\pi$
$54$		−	170192.i		−	1.08083i
$55$	2937.95	−	24898.9i	0.0176586	−	0.149655i
$56$	7756.60			0.0441679
$57$	−6143.75	+	8456.15i	−0.0331749	+	0.0456613i
$58$	75991.9	−	233879.i	0.389478	−	1.19869i
$59$	−92965.2	−	286117.i	−0.452652	−	1.39312i	−0.873870	−	0.486160i	$-0.838397\pi$
$59$	−92965.2	−	286117.i	−0.452652	−	1.39312i	0.421218	−	0.906959i	$-0.361603\pi$
$60$	9359.82	−	6800.31i	0.0433325	−	0.0314829i
$61$	218947.	+	301355.i	0.964606	+	1.32767i	0.944725	+	0.327863i	$0.106329\pi$
$61$	218947.	+	301355.i	0.964606	+	1.32767i	0.0198806	+	0.999802i	$0.493671\pi$
$62$	101543.	−	32993.3i	0.426064	−	0.138436i
$63$	30064.6	+	9768.58i	0.120236	+	0.0390670i
$64$	−116398.	−	84568.3i	−0.444024	−	0.322602i
$65$		−	16116.9i		−	0.0586871i
$66$	171594.	+	20247.2i	0.596856	+	0.0704260i
$67$	−189715.			−0.630781			−0.315390	−	0.948962i	$-0.602135\pi$
$67$	−189715.			−0.630781			−0.315390	+	0.948962i	$0.602135\pi$
$68$	−202561.	+	278802.i	−0.644214	+	0.886684i
$69$	−77694.4	+	239119.i	−0.236506	+	0.727891i
$70$	3385.34	+	10419.0i	0.00986979	+	0.0303761i
$71$	−333295.	+	242153.i	−0.931222	+	0.676572i	−0.946292	−	0.323314i	$-0.895203\pi$
$71$	−333295.	+	242153.i	−0.931222	+	0.676572i	0.0150699	+	0.999886i	$0.495203\pi$
$72$	48857.6	+	67246.7i	0.130899	+	0.180166i
$73$	102292.	−	33236.7i	0.262950	−	0.0854377i	−0.174575	−	0.984644i	$-0.555855\pi$
$73$	102292.	−	33236.7i	0.262950	−	0.0854377i	0.437525	+	0.899206i	$0.355855\pi$
$74$	−110824.	−	36008.8i	−0.273488	−	0.0888616i
$75$	149767.	+	108812.i	0.355003	+	0.257925i
$76$			43681.0i			0.0995066i
$77$	−30241.6	+	65661.0i	−0.0662420	+	0.143825i
$78$	111072.			0.234056
$79$	312971.	−	430768.i	0.634780	−	0.873700i	−0.363544	−	0.931577i	$-0.618433\pi$
$79$	312971.	−	430768.i	0.634780	−	0.873700i	0.998324	+	0.0578773i	$0.0184332\pi$
$80$	−27775.3	+	85483.7i	−0.0542487	+	0.166960i
$81$	71574.1	+	220282.i	0.134679	+	0.414500i
$82$	783205.	−	569032.i	1.42048	−	1.03204i
$83$	−435941.	−	600021.i	−0.762418	−	1.04938i	−0.997009	−	0.0772844i	$-0.975375\pi$
$83$	−435941.	−	600021.i	−0.762418	−	1.04938i	0.234591	−	0.972094i	$-0.424625\pi$
$84$	−31726.0	+	10308.4i	−0.0535275	+	0.0173921i
$85$	121859.	+	39594.4i	0.198427	+	0.0644729i
$86$	−228943.	−	166337.i	−0.359942	−	0.261513i
$87$		−	278411.i		−	0.422794i
$88$	−165814.	+	92938.5i	−0.243318	+	0.136379i
$89$	−493938.			−0.700652			−0.350326	−	0.936628i	$-0.613929\pi$
$89$	−493938.			−0.700652			−0.350326	+	0.936628i	$0.613929\pi$
$90$	−69005.0	+	94977.3i	−0.0946571	+	0.130284i
$91$	−14360.3	+	44196.5i	−0.0190563	+	0.0586494i
$92$	324689.	+	999290.i	0.416969	+	1.28330i
$93$	97791.9	−	71049.9i	0.121578	−	0.0883314i
$94$	−845700.	−	1.16401e6i	−1.01820	−	1.40143i
$95$	15445.9	−	5018.67i	0.0180153	−	0.00585352i
$96$	−483738.	−	157176.i	−0.546760	−	0.177653i
$97$	1.03679e6	+	753274.i	1.13600	+	0.825349i	0.986556	−	0.163422i	$-0.0522531\pi$
$97$	1.03679e6	+	753274.i	1.13600	+	0.825349i	0.149440	+	0.988771i	$0.452253\pi$
$98$			1.22821e6i			1.30495i
$99$	−759743.	+	151405.i	−0.782999	+	0.156039i
$100$	773634.			0.773634
$101$	1.01791e6	−	1.40103e6i	0.987969	−	1.35982i	0.0555452	−	0.998456i	$-0.482310\pi$
$101$	1.01791e6	−	1.40103e6i	0.987969	−	1.35982i	0.932424	−	0.361367i	$-0.117690\pi$
$102$	−272869.	+	839805.i	−0.257131	+	0.791367i
$103$	25916.8	+	79763.8i	0.0237176	+	0.0729952i	0.962215	−	0.272292i	$-0.0877816\pi$
$103$	25916.8	+	79763.8i	0.0237176	+	0.0729952i	−0.938497	+	0.345287i	$0.887782\pi$
$104$	−98856.1	+	71823.2i	−0.0878827	+	0.0638506i
$105$	7290.22	+	10034.1i	0.00629756	+	0.00866785i
$106$	−151547.	+	49240.6i	−0.127242	+	0.0413433i
$107$	1.02699e6	+	333690.i	0.838332	+	0.272391i	0.696551	−	0.717507i	$-0.254717\pi$
$107$	1.02699e6	+	333690.i	0.838332	+	0.272391i	0.141781	+	0.989898i	$0.454717\pi$
$108$	−651442.	−	473300.i	−0.517135	−	0.375721i
$109$			852922.i			0.658612i	0.944223	+	0.329306i	$0.106815\pi$
$109$			852922.i			0.658612i	−0.944223	+	0.329306i	$0.893185\pi$
$110$	−197208.	−	182167.i	−0.148165	−	0.136864i
$111$	−131925.			−0.0964628
$112$	152333.	−	209668.i	0.108428	−	0.149238i
$113$	−371008.	+	1.14184e6i	−0.257127	+	0.791355i	0.736276	+	0.676681i	$0.236582\pi$
$113$	−371008.	+	1.14184e6i	−0.257127	+	0.791355i	−0.993403	+	0.114674i	$0.963418\pi$
$114$	34586.7	+	106447.i	0.0233450	+	0.0718487i
$115$	316050.	−	229624.i	0.207808	−	0.150981i
$116$	−683885.	−	941287.i	−0.438136	−	0.603043i
$117$	−473620.	+	153889.i	−0.295714	+	0.0960834i
$118$	−3.06377e6	−	995479.i	−1.86470	−	0.605879i
$119$	−298887.	−	217154.i	−0.177365	−	0.128863i
$120$			32612.7i			0.0188731i
$121$	−140258.	−	1.76600e6i	−0.0791723	−	0.996861i
$122$	3.98871e6			2.19661
$123$	644226.	−	886702.i	0.346197	−	0.476499i
$124$	156101.	−	480429.i	0.0818729	−	0.251979i
$125$	−179836.	−	553480.i	−0.0920763	−	0.283382i
$126$	273854.	−	198966.i	0.136901	−	0.0994644i
$127$	1.53331e6	+	2.11042e6i	0.748546	+	1.03028i	0.998081	+	0.0619190i	$0.0197221\pi$
$127$	1.53331e6	+	2.11042e6i	0.748546	+	1.03028i	−0.249536	+	0.968366i	$0.580278\pi$
$128$	1.08850e6	−	353677.i	0.519040	−	0.168646i
$129$	−304704.	−	99004.3i	−0.141941	−	0.0461195i
$130$	−139621.	−	101441.i	−0.0635510	−	0.0461725i
$131$		−	536161.i		−	0.238496i	−0.992864	−	0.119248i	$-0.961952\pi$
$131$		−	536161.i		−	0.238496i	0.992864	−	0.119248i	$-0.0380484\pi$
$132$	554699.	−	600501.i	0.241177	−	0.261091i
$133$	−46827.9			−0.0199044
$134$	−1.19408e6	+	1.64351e6i	−0.496271	+	0.683058i
$135$	−92515.3	+	284733.i	−0.0376021	+	0.115727i
$136$	−300191.	−	923891.i	−0.119338	−	0.367286i
$137$	−2.82752e6	+	2.05431e6i	−1.09962	+	0.798922i	−0.980998	−	0.194017i	$-0.937848\pi$
$137$	−2.82752e6	+	2.05431e6i	−1.09962	+	0.798922i	−0.118624	+	0.992939i	$0.537848\pi$
$138$	1.58248e6	+	2.17810e6i	0.602144	+	0.828781i
$139$	−3.95169e6	+	1.28398e6i	−1.47143	+	0.478096i	−0.931539	−	0.363641i	$-0.881533\pi$
$139$	−3.95169e6	+	1.28398e6i	−1.47143	+	0.478096i	−0.539888	+	0.841737i	$0.681533\pi$
$140$	49295.3	+	16017.0i	0.0179648	+	0.00583711i
$141$	−1.31782e6	−	957455.i	−0.470110	−	0.341555i
$142$			4.41146e6i			1.54070i
$143$	−222573.	−	1.11686e6i	−0.0761139	−	0.381936i
$144$	2.77727e6			0.930102
$145$	−254271.	+	349974.i	−0.0834050	+	0.114797i
$146$	355902.	−	1.09535e6i	0.114359	−	0.351962i
$147$	429691.	+	1.32245e6i	0.135271	+	0.416321i
$148$	−446030.	+	324060.i	−0.137587	+	0.0999632i
$149$	−843162.	−	1.16051e6i	−0.254890	−	0.350825i	0.662327	−	0.749215i	$-0.269569\pi$
$149$	−843162.	−	1.16051e6i	−0.254890	−	0.350825i	−0.917216	+	0.398390i	$0.869569\pi$
$150$	1.88528e6	−	612565.i	0.558602	−	0.181501i
$151$	2.20041e6	+	714956.i	0.639105	+	0.207658i	0.610604	−	0.791936i	$-0.290927\pi$
$151$	2.20041e6	+	714956.i	0.639105	+	0.207658i	0.0285010	+	0.999594i	$0.490927\pi$
$152$	−99615.5	−	72374.9i	−0.0283659	−	0.0206090i
$153$		−	3.95906e6i		−	1.10540i
$154$	378480.	+	675258.i	0.103629	+	0.184887i
$155$	−187817.			−0.0504360
$156$	308889.	−	425149.i	0.0813632	−	0.111987i
$157$	1.36058e6	−	4.18744e6i	0.351581	−	1.08206i	−0.606384	−	0.795172i	$-0.707380\pi$
$157$	1.36058e6	−	4.18744e6i	0.351581	−	1.08206i	0.957965	−	0.286884i	$-0.0926196\pi$
$158$	−1.76190e6	−	5.42256e6i	−0.446693	−	1.37478i
$159$	−145949.	+	106038.i	−0.0363086	+	0.0263797i
$160$	464530.	+	639370.i	0.113411	+	0.156096i
$161$	−1.07128e6	+	348080.i	−0.256700	+	0.0834068i
$162$	2.35880e6	+	766421.i	0.554813	+	0.180270i
$163$	3.94124e6	+	2.86348e6i	0.910060	+	0.661197i	0.941030	−	0.338323i	$-0.109860\pi$
$163$	3.94124e6	+	2.86348e6i	0.910060	+	0.661197i	−0.0309703	+	0.999520i	$0.509860\pi$
$164$		−	4.58034e6i		−	1.03840i
$165$	−276072.	−	127151.i	−0.0614569	−	0.0283054i
$166$	−7.94183e6			−1.73619
$167$	−709616.	+	976703.i	−0.152361	+	0.209707i	−0.878374	−	0.477974i	$-0.841371\pi$
$167$	−709616.	+	976703.i	−0.152361	+	0.209707i	0.726013	+	0.687681i	$0.241371\pi$
$168$	29058.1	−	89431.6i	0.00612829	−	0.0188609i
$169$	1.26534e6	+	3.89432e6i	0.262149	+	0.806811i
$170$	1.10999e6	−	806458.i	0.225930	−	0.164148i
$171$	−294962.	−	405980.i	−0.0589899	−	0.0811926i
$172$	−1.27337e6	+	413744.i	−0.250248	+	0.0813105i
$173$	3.40987e6	+	1.10793e6i	0.658566	+	0.213981i	0.619188	−	0.785243i	$-0.287462\pi$
$173$	3.40987e6	+	1.10793e6i	0.658566	+	0.213981i	0.0393789	+	0.999224i	$0.487462\pi$
$174$	−2.41188e6	−	1.75234e6i	−0.457834	−	0.332636i
$175$			829368.i			0.154751i
$176$	−744238.	+	6.30736e6i	−0.136513	+	1.15694i
$177$	−3.64713e6			−0.657706
$178$	−3.10887e6	+	4.27900e6i	−0.551243	+	0.758721i
$179$	−751089.	+	2.31161e6i	−0.130958	+	0.403047i	−0.994939	−	0.100476i	$-0.967963\pi$
$179$	−751089.	+	2.31161e6i	−0.130958	+	0.403047i	0.863981	+	0.503524i	$0.167963\pi$
$180$	171642.	+	528260.i	0.0294311	+	0.0905796i
$181$	4.34791e6	−	3.15894e6i	0.733238	−	0.532729i	−0.157348	−	0.987543i	$-0.550294\pi$
$181$	4.34791e6	−	3.15894e6i	0.733238	−	0.532729i	0.890586	+	0.454815i	$0.150294\pi$
$182$	292491.	+	402579.i	0.0485174	+	0.0667785i
$183$	4.29478e6	−	1.39546e6i	0.700789	−	0.227700i
$184$	−2.81688e6	−	915259.i	−0.452183	−	0.146923i
$185$	165835.	+	120486.i	0.0261916	+	0.0190293i
$186$		−	1.29437e6i		−	0.201149i
$187$	8.99130e6	+	1.06093e6i	1.37498	+	0.162241i
$188$	−6.80734e6			−1.02448
$189$	507398.	−	698373.i	0.0751559	−	0.103443i
$190$	53740.3	−	165396.i	0.00783500	−	0.0241137i
$191$	3.21642e6	+	9.89914e6i	0.461608	+	1.42068i	0.863199	+	0.504864i	$0.168457\pi$
$191$	3.21642e6	+	9.89914e6i	0.461608	+	1.42068i	−0.401591	+	0.915819i	$0.631543\pi$
$192$	−1.41111e6	+	1.02523e6i	−0.199369	+	0.144850i
$193$	−4.37365e6	−	6.01982e6i	−0.608377	−	0.837359i	0.388066	−	0.921632i	$-0.373143\pi$
$193$	−4.37365e6	−	6.01982e6i	−0.608377	−	0.837359i	−0.996443	+	0.0842729i	$0.973143\pi$
$194$	1.30513e7	−	4.24061e6i	1.78750	−	0.580796i
$195$	−185824.	−	60378.0i	−0.0250610	−	0.00814282i
$196$	4.70120e6	+	3.41562e6i	0.624368	+	0.453630i
$197$		−	9.81016e6i		−	1.28315i	−0.767060	−	0.641575i	$-0.778281\pi$
$197$		−	9.81016e6i		−	1.28315i	0.767060	−	0.641575i	$-0.221719\pi$
$198$	−3.47024e6	+	7.53462e6i	−0.447058	+	0.970657i
$199$	−1.15052e7			−1.45994			−0.729969	−	0.683481i	$-0.760465\pi$
$199$	−1.15052e7			−1.45994			−0.729969	+	0.683481i	$0.760465\pi$
$200$	−1.28183e6	+	1.76429e6i	−0.160229	+	0.220536i
$201$	−710721.	+	2.18737e6i	−0.0875207	+	0.269361i
$202$	−5.73037e6	−	1.76363e7i	−0.695230	−	2.13970i
$203$	1.00910e6	−	733154.i	0.120627	−	0.0876409i
$204$	2.45567e6	+	3.37994e6i	0.289254	+	0.398125i
$205$	−1.61963e6	+	526251.i	−0.187999	+	0.0610846i
$206$	854117.	+	277520.i	0.0977048	+	0.0317462i
$207$	−9.76556e6	−	7.09509e6i	−1.10100	−	0.799921i
$208$			4.08273e6i			0.453691i
$209$	1.00105e6	−	561085.i	0.109652	−	0.0614597i
$210$	132811.			0.0143409
$211$	1.45262e6	−	1.99937e6i	0.154634	−	0.212836i	−0.724670	−	0.689096i	$-0.758008\pi$
$211$	1.45262e6	−	1.99937e6i	0.154634	−	0.212836i	0.879305	+	0.476260i	$0.158008\pi$
$212$	−232971.	+	717013.i	−0.0244509	+	0.0752522i
$213$	1.54336e6	+	4.74997e6i	0.159708	+	0.491532i
$214$	9.35472e6	−	6.79660e6i	0.954530	−	0.693506i
$215$	292605.	+	402736.i	0.0294419	+	0.0405233i
$216$	2.15874e6	−	701418.i	0.214210	−	0.0696010i
$217$	515040.	+	167347.i	0.0504036	+	0.0163771i
$218$	7.38888e6	+	5.36833e6i	0.713196	+	0.518167i
$219$		−	1.30392e6i		−	0.124142i
$220$	−1.24571e6	+	248250.i	−0.116990	+	0.0233143i
$221$	5.82003e6			0.539198
$222$	−830346.	+	1.14287e6i	−0.0758927	+	0.104457i
$223$	3.25468e6	−	1.00169e7i	0.293490	−	0.903270i	−0.690234	−	0.723586i	$-0.742492\pi$
$223$	3.25468e6	−	1.00169e7i	0.293490	−	0.903270i	0.983724	−	0.179684i	$-0.0575075\pi$
$224$	−704167.	−	2.16720e6i	−0.0626515	−	0.192822i
$225$	−7.19031e6	+	5.22406e6i	−0.631248	+	0.458628i
$226$	7.55668e6	+	1.04009e7i	0.654645	+	0.901041i
$227$	−1.17117e7	+	3.80537e6i	−1.00125	+	0.325327i	−0.763366	−	0.645966i	$-0.776455\pi$
$227$	−1.17117e7	+	3.80537e6i	−1.00125	+	0.325327i	−0.237887	+	0.971293i	$0.576455\pi$
$228$	503631.	+	163640.i	0.0424921	+	0.0138065i
$229$	2.94323e6	+	2.13838e6i	0.245086	+	0.178065i	0.703546	−	0.710650i	$-0.251599\pi$
$229$	2.94323e6	+	2.13838e6i	0.245086	+	0.178065i	−0.458460	+	0.888715i	$0.651599\pi$
$230$		−	4.18321e6i		−	0.343816i
$231$	643762.	+	594661.i	0.0522263	+	0.0482429i
$232$	3.27975e6			0.262650
$233$	−9.83723e6	+	1.35398e7i	−0.777687	+	1.07039i	0.217846	+	0.975983i	$0.430097\pi$
$233$	−9.83723e6	+	1.35398e7i	−0.777687	+	1.07039i	−0.995533	+	0.0944113i	$0.969903\pi$
$234$	−1.64785e6	+	5.07156e6i	−0.128609	+	0.395817i
$235$	782119.	+	2.40711e6i	0.0602655	+	0.185478i
$236$	−1.23307e7	+	8.95876e6i	−0.938104	+	0.681573i
$237$	−3.79418e6	−	5.22225e6i	−0.285019	−	0.392295i
$238$	−3.76243e6	+	1.22249e6i	−0.279085	+	0.0906804i
$239$	3.93372e6	+	1.27814e6i	0.288144	+	0.0936237i	0.449523	−	0.893269i	$-0.351594\pi$
$239$	3.93372e6	+	1.27814e6i	0.288144	+	0.0936237i	−0.161379	+	0.986893i	$0.551594\pi$
$240$	881553.	+	640485.i	0.0637697	+	0.0463314i
$241$			2.30972e7i			1.65009i	0.565065	+	0.825047i	$0.308851\pi$
$241$			2.30972e7i			1.65009i	−0.565065	+	0.825047i	$0.691149\pi$
$242$	−1.61817e7	−	9.90024e6i	−1.14177	−	0.698553i
$243$	1.43945e7			1.00318
$244$	1.10925e7	−	1.52676e7i	0.763592	−	1.05099i
$245$	667647.	−	2.05481e6i	0.0453993	−	0.139725i
$246$	−3.62672e6	−	1.11619e7i	−0.243618	−	0.749778i
$247$	596811.	−	433609.i	0.0396047	−	0.0287745i
$248$	836985.	+	1.15201e6i	0.0548735	+	0.0755269i
$249$	−8.55124e6	+	2.77847e6i	−0.553899	+	0.179973i
$250$	−5.92671e6	−	1.92570e6i	−0.379309	−	0.123245i
$251$	−1.31042e7	−	9.52073e6i	−0.828682	−	0.602073i	0.0905041	−	0.995896i	$-0.471152\pi$
$251$	−1.31042e7	−	9.52073e6i	−0.828682	−	0.602073i	−0.919186	+	0.393823i	$0.871152\pi$
$252$		−	1.60155e6i		−	0.100078i
$253$	1.87304e7	−	2.02769e7i	1.15660	−	1.25210i
$254$	2.79333e7			1.70460
$255$	913027.	−	1.25667e6i	0.0550634	−	0.0757883i
$256$	6.63265e6	−	2.04132e7i	0.395337	−	1.21672i
$257$	2.86526e6	+	8.81838e6i	0.168797	+	0.519504i	0.999296	−	0.0375160i	$-0.0119445\pi$
$257$	2.86526e6	+	8.81838e6i	0.168797	+	0.519504i	−0.830499	+	0.557020i	$0.811945\pi$
$258$	−2.77550e6	+	2.01652e6i	−0.161615	+	0.117420i
$259$	−347406.	−	478163.i	−0.0199957	−	0.0275218i
$260$	−776570.	+	252323.i	−0.0441835	+	0.0143561i
$261$	1.27123e7	+	4.13049e6i	0.714996	+	0.232316i
$262$	−4.64478e6	−	3.37463e6i	−0.258262	−	0.187639i
$263$		−	2.02512e7i		−	1.11322i	−0.830772	−	0.556612i	$-0.812101\pi$
$263$		−	2.02512e7i		−	1.11322i	0.830772	−	0.556612i	$-0.187899\pi$
$264$	450376.	+	2.25997e6i	0.0244773	+	0.122826i
$265$	280307.			0.0150625
$266$	−294737.	+	405671.i	−0.0156599	+	0.0215541i
$267$	−1.85041e6	+	5.69498e6i	−0.0972153	+	0.299198i
$268$	2.97014e6	+	9.14114e6i	0.154302	+	0.474893i
$269$	−7.50185e6	+	5.45041e6i	−0.385400	+	0.280009i	−0.763568	−	0.645728i	$-0.776554\pi$
$269$	−7.50185e6	+	5.45041e6i	−0.385400	+	0.280009i	0.378168	+	0.925737i	$0.376554\pi$
$270$	1.88435e6	+	2.59359e6i	0.0957349	+	0.131768i
$271$	−1.08022e7	+	3.50985e6i	−0.542756	+	0.176352i	−0.567548	−	0.823340i	$-0.692108\pi$
$271$	−1.08022e7	+	3.50985e6i	−0.542756	+	0.176352i	0.0247915	+	0.999693i	$0.492108\pi$
$272$	−3.08692e7	−	1.00300e7i	−1.53398	−	0.498419i
$273$	455777.	+	331142.i	0.0224009	+	0.0162752i
$274$			3.74248e7i			1.81931i
$275$	−9.93738e6	−	1.77296e7i	−0.477830	−	0.852512i
$276$	1.27379e7			0.605859
$277$	6.94198e6	−	9.55481e6i	0.326621	−	0.449555i	−0.613853	−	0.789420i	$-0.710381\pi$
$277$	6.94198e6	−	9.55481e6i	0.326621	−	0.449555i	0.940474	+	0.339865i	$0.110381\pi$
$278$	−1.37490e7	+	4.23151e7i	−0.639936	+	1.96952i
$279$	1.79333e6	+	5.51929e6i	0.0825747	+	0.254139i
$280$	−118204.	+	85880.5i	−0.00538467	+	0.00391219i
$281$	1.78909e6	+	2.46247e6i	0.0806330	+	0.110982i	0.847428	−	0.530910i	$-0.178150\pi$
$281$	1.78909e6	+	2.46247e6i	0.0806330	+	0.110982i	−0.766795	+	0.641892i	$0.778150\pi$
$282$	−1.65889e7	+	5.39006e6i	−0.739725	+	0.240351i
$283$	−1.06616e7	−	3.46416e6i	−0.470394	−	0.152840i	0.0642213	−	0.997936i	$-0.479544\pi$
$283$	−1.06616e7	−	3.46416e6i	−0.470394	−	0.152840i	−0.534616	+	0.845095i	$0.679544\pi$
$284$	1.68857e7	+	1.22682e7i	0.737165	+	0.535582i
$285$		−	196888.i		−	0.00850521i
$286$	−1.10763e7	−	5.10143e6i	−0.473474	−	0.218069i
$287$	4.91032e6			0.207713
$288$	1.43534e7	−	1.97557e7i	0.600865	−	0.827020i
$289$	−6.83910e6	+	2.10486e7i	−0.283338	+	0.872026i
$290$	1.43144e6	+	4.40551e6i	0.0586918	+	0.180635i
$291$	1.25691e7	−	9.13202e6i	0.510066	−	0.370585i
$292$	−3.20292e6	−	4.40844e6i	−0.128646	−	0.177066i
$293$	3.62774e7	−	1.17872e7i	1.44223	−	0.468607i	0.519635	−	0.854388i	$-0.326068\pi$
$293$	3.62774e7	−	1.17872e7i	1.44223	−	0.468607i	0.922590	+	0.385781i	$0.126068\pi$
$294$	1.41609e7	+	4.60117e6i	0.557250	+	0.181061i
$295$	4.58459e6	+	3.33090e6i	0.178581	+	0.129746i
$296$		−	1.55411e6i		−	0.0599250i
$297$	−2.47894e6	+	2.10088e7i	−0.0946230	+	0.801923i
$298$	−1.53604e7			−0.580437
$299$	1.04301e7	−	1.43559e7i	0.390191	−	0.537051i
$300$	2.89822e6	−	8.91981e6i	0.107342	−	0.330363i
$301$	−443551.	−	1.36511e6i	−0.0162646	−	0.0500574i
$302$	2.00432e7	−	1.45622e7i	0.727688	−	0.528697i
$303$	−1.23402e7	−	1.69848e7i	−0.443602	−	0.610566i
$304$	−3.91273e6	+	1.27132e6i	−0.139270	+	0.0452517i
$305$	−6.67316e6	−	2.16824e6i	−0.235197	−	0.0764202i
$306$	−3.42974e7	−	2.49186e7i	−1.19701	−	0.869678i
$307$			1.75338e7i			0.605984i	0.952993	+	0.302992i	$0.0979856\pi$
$307$			1.75338e7i			0.605984i	−0.952993	+	0.302992i	$0.902014\pi$
$308$	3.63723e6	+	429175.i	0.124485	+	0.0146887i
$309$	1.01675e6			0.0344618
$310$	−1.18213e6	+	1.62707e6i	−0.0396809	+	0.0546160i
$311$	3.44362e6	−	1.05984e7i	0.114481	−	0.352337i	−0.877357	−	0.479838i	$-0.840696\pi$
$311$	3.44362e6	−	1.05984e7i	0.114481	−	0.352337i	0.991838	+	0.127501i	$0.0406956\pi$
$312$	457764.	+	1.40885e6i	0.0150723	+	0.0463876i
$313$	−2.29654e6	+	1.66854e6i	−0.0748930	+	0.0544130i	−0.624602	−	0.780943i	$-0.714739\pi$
$313$	−2.29654e6	+	1.66854e6i	−0.0748930	+	0.0544130i	0.549709	+	0.835356i	$0.314739\pi$
$314$	−2.77123e7	−	3.81428e7i	−0.895126	−	1.23204i
$315$	−566317.	+	184008.i	−0.0181188	+	0.00588714i
$316$	−2.56557e7	−	8.33604e6i	−0.813060	−	0.264179i
$317$	2.63384e7	+	1.91360e7i	0.826821	+	0.600721i	0.918658	−	0.395053i	$-0.129274\pi$
$317$	2.63384e7	+	1.91360e7i	0.826821	+	0.600721i	−0.0918372	+	0.995774i	$0.529274\pi$
$318$			1.93177e6i			0.0600721i
$319$	−1.27872e7	+	2.77637e7i	−0.393916	+	0.855273i
$320$	2.71015e6			0.0827072
$321$	7.69474e6	−	1.05909e7i	0.232637	−	0.320197i
$322$	−3.72727e6	+	1.14714e7i	−0.111641	+	0.343595i
$323$	1.81230e6	+	5.57769e6i	0.0537803	+	0.165519i
$324$	9.49341e6	−	6.89737e6i	0.279118	−	0.202791i
$325$	−7.67964e6	−	1.05701e7i	−0.223713	−	0.307914i
$326$	4.96127e7	−	1.61202e7i	1.43199	−	0.465282i
$327$	9.83398e6	+	3.19525e6i	0.281246	+	0.0913823i
$328$	1.04456e7	+	7.58914e6i	0.296013	+	0.215066i
$329$		−	7.29775e6i		−	0.204928i
$330$	−2.83913e6	+	1.59132e6i	−0.0790029	+	0.0442809i
$331$	−2.80029e7			−0.772182			−0.386091	−	0.922461i	$-0.626175\pi$
$331$	−2.80029e7			−0.772182			−0.386091	+	0.922461i	$0.626175\pi$
$332$	−2.20861e7	+	3.03989e7i	−0.603538	+	0.830699i
$333$	1.95724e6	−	6.02375e6i	0.0530042	−	0.163130i
$334$	3.99484e6	+	1.22948e7i	0.107216	+	0.329977i
$335$	2.89111e6	−	2.10052e6i	0.0769008	−	0.0558717i
$336$	−1.84675e6	−	2.54183e6i	−0.0486844	−	0.0670084i
$337$	−2.49741e7	+	8.11459e6i	−0.652530	+	0.212020i	−0.616530	−	0.787332i	$-0.711462\pi$
$337$	−2.49741e7	+	8.11459e6i	−0.652530	+	0.212020i	−0.0360008	+	0.999352i	$0.511462\pi$
$338$	4.17007e7	+	1.35494e7i	1.07992	+	0.350889i
$339$	1.17753e7	+	8.55525e6i	0.302254	+	0.219601i
$340$		−	6.49147e6i		−	0.165160i
$341$	−1.30152e7	+	2.59373e6i	−0.328238	+	0.0654127i
$342$	−5.37352e6			−0.134332
$343$	−7.41756e6	+	1.02094e7i	−0.183814	+	0.252998i
$344$	1.16629e6	−	3.58949e6i	0.0286505	−	0.0881773i
$345$	−1.46351e6	−	4.50421e6i	−0.0356399	−	0.109688i
$346$	3.10600e7	−	2.25664e7i	0.749847	−	0.544796i
$347$	8.04953e6	+	1.10792e7i	0.192656	+	0.265168i	0.894407	−	0.447254i	$-0.147598\pi$
$347$	8.04953e6	+	1.10792e7i	0.192656	+	0.265168i	−0.701751	+	0.712422i	$0.747598\pi$
$348$	−1.34148e7	+	4.35874e6i	−0.318307	+	0.103424i
$349$	−1.25681e7	−	4.08362e6i	−0.295660	−	0.0960658i	0.157431	−	0.987530i	$-0.449679\pi$
$349$	−1.25681e7	−	4.08362e6i	−0.295660	−	0.0960658i	−0.453091	+	0.891464i	$0.649679\pi$
$350$	7.18484e6	+	5.22009e6i	0.167576	+	0.121751i
$351$			1.35989e7i			0.314473i
$352$	4.10203e7	+	3.78916e7i	0.940526	+	0.868789i
$353$	−3.41261e7			−0.775822			−0.387911	−	0.921697i	$-0.626803\pi$
$353$	−3.41261e7			−0.775822			−0.387911	+	0.921697i	$0.626803\pi$
$354$	−2.29553e7	+	3.15952e7i	−0.517455	+	0.712215i
$355$	2.39805e6	−	7.38043e6i	0.0536009	−	0.164967i
$356$	7.73297e6	+	2.37996e7i	0.171394	+	0.527497i
$357$	−3.62344e6	+	2.63259e6i	−0.0796373	+	0.0578599i
$358$	1.52982e7	+	2.10561e7i	0.333419	+	0.458912i
$359$	−3.38074e6	+	1.09847e6i	−0.0730682	+	0.0237413i	−0.345323	−	0.938484i	$-0.612231\pi$
$359$	−3.38074e6	+	1.09847e6i	−0.0730682	+	0.0237413i	0.272255	+	0.962225i	$0.412231\pi$
$360$	−1.48910e6	−	483839.i	−0.0319166	−	0.0103703i
$361$	−3.74595e7	−	2.72159e7i	−0.796234	−	0.578498i
$362$		−	5.75486e7i		−	1.21314i
$363$	−2.08870e7	−	4.99872e6i	−0.436673	−	0.104505i
$364$	2.35436e6			0.0488167
$365$	−1.19086e6	+	1.63907e6i	−0.0244895	+	0.0337069i
$366$	1.49427e7	−	4.59888e7i	0.304779	−	0.938014i
$367$	−2.13562e7	−	6.57278e7i	−0.432043	−	1.32969i	−0.896087	−	0.443879i	$-0.853602\pi$
$367$	−2.13562e7	−	6.57278e7i	−0.432043	−	1.32969i	0.464044	−	0.885812i	$-0.346398\pi$
$368$	−8.00615e7	+	5.81681e7i	−1.60650	+	1.16719i
$369$	3.09293e7	+	4.25706e7i	0.615590	+	0.847287i
$370$	2.08755e6	−	678287.i	0.0412128	−	0.0133909i
$371$	−768668.	−	249755.i	−0.0150528	−	0.00489095i
$372$	−4.95444e6	−	3.59961e6i	−0.0962422	−	0.0699240i
$373$		−	5.99195e7i		−	1.15463i	−0.816522	−	0.577314i	$-0.804101\pi$
$373$		−	5.99195e7i		−	1.15463i	0.816522	−	0.577314i	$-0.195899\pi$
$374$	6.57826e7	−	7.12143e7i	1.25747	−	1.36129i
$375$	−7.05520e6			−0.133787
$376$	1.12790e7	−	1.55243e7i	0.212182	−	0.292044i
$377$	−6.07202e6	+	1.86878e7i	−0.113321	+	0.348765i
$378$	−2.85643e6	−	8.79120e6i	−0.0528870	−	0.162769i
$379$	−171708.	+	124753.i	−0.00315409	+	0.00229158i	−0.589361	−	0.807870i	$-0.700620\pi$
$379$	−171708.	+	124753.i	−0.00315409	+	0.00229158i	0.586207	+	0.810161i	$0.300620\pi$
$380$	−483633.	−	665664.i	−0.00881384	−	0.0121312i
$381$	3.00767e7	−	9.77253e6i	0.543821	−	0.176698i
$382$	1.06001e8	+	3.44417e7i	1.90160	+	0.617867i
$383$	4.64727e7	+	3.37644e7i	0.827183	+	0.600984i	0.918761	−	0.394814i	$-0.129191\pi$
$383$	4.64727e7	+	3.37644e7i	0.827183	+	0.600984i	−0.0915776	+	0.995798i	$0.529191\pi$
$384$		−	1.38752e7i		−	0.245044i
$385$	−266135.	−	1.33545e6i	−0.00466358	−	0.0234017i
$386$	−7.96778e7			−1.38540
$387$	9.04112e6	−	1.24440e7i	0.155987	−	0.214698i
$388$	2.00636e7	−	6.17493e7i	0.343489	−	1.05715i
$389$	−3.00023e7	−	9.23376e7i	−0.509690	−	1.56866i	−0.792741	−	0.609559i	$-0.791347\pi$
$389$	−3.00023e7	−	9.23376e7i	−0.509690	−	1.56866i	0.283051	−	0.959105i	$-0.408653\pi$
$390$	−1.69265e6	+	1.22978e6i	−0.0285346	+	0.0207316i
$391$	8.29200e7	+	1.14130e8i	1.38717	+	1.90927i
$392$	−1.55788e7	+	5.06186e6i	−0.258628	+	0.0840334i
$393$	−6.18181e6	−	2.00859e6i	−0.101845	−	0.0330913i
$394$	−8.49856e7	−	6.17457e7i	−1.38949	−	1.00953i
$395$			1.00298e7i			0.162742i
$396$	1.91895e7	+	3.42367e7i	0.309015	+	0.551323i
$397$	5.17953e7			0.827787			0.413893	−	0.910325i	$-0.364169\pi$
$397$	5.17953e7			0.827787			0.413893	+	0.910325i	$0.364169\pi$
$398$	−7.24142e7	+	9.96696e7i	−1.14862	+	1.58093i
$399$	−175429.	+	539914.i	−0.00276174	+	0.00849975i
$400$	2.25164e7	+	6.92983e7i	0.351819	+	1.08279i
$401$	−6.36464e7	+	4.62418e7i	−0.987053	+	0.717136i	−0.959274	−	0.282478i	$-0.908844\pi$
$401$	−6.36464e7	+	4.62418e7i	−0.987053	+	0.717136i	−0.0277795	+	0.999614i	$0.508844\pi$
$402$	1.44759e7	+	1.99244e7i	0.222828	+	0.306696i
$403$	−8.11364e6	+	2.63628e6i	−0.123965	+	0.0402788i
$404$	−8.34424e7	−	2.71121e7i	−1.26544	−	0.411167i
$405$	−3.52968e6	−	2.56446e6i	−0.0531338	−	0.0386039i
$406$		−	1.33564e7i		−	0.199577i
$407$	1.31559e7	+	6.05923e6i	0.195135	+	0.0898740i
$408$	−1.17768e7			−0.173400
$409$	−1.85958e6	+	2.55950e6i	−0.0271798	+	0.0374098i	−0.822391	−	0.568923i	$-0.807360\pi$
$409$	−1.85958e6	+	2.55950e6i	−0.0271798	+	0.0374098i	0.795211	+	0.606333i	$0.207360\pi$
$410$	−5.63514e6	+	1.73432e7i	−0.0817623	+	0.251639i
$411$	1.30931e7	+	4.02965e7i	0.188590	+	0.580420i
$412$	3.43755e6	−	2.49752e6i	0.0491538	−	0.0357123i
$413$	−9.60417e6	−	1.32190e7i	−0.136336	−	0.187650i
$414$	−1.22930e8	+	3.99423e7i	−1.73243	+	0.562902i
$415$	1.32868e7	+	4.31714e6i	0.185898	+	0.0604020i
$416$	2.90420e7	+	2.11002e7i	0.403409	+	0.293094i
$417$			5.03722e7i			0.694676i
$418$	1.43997e6	−	1.22036e7i	0.0197162	−	0.167094i
$419$	5.46803e7			0.743342			0.371671	−	0.928365i	$-0.378785\pi$
$419$	5.46803e7			0.743342			0.371671	+	0.928365i	$0.378785\pi$
$420$	369345.	−	508359.i	0.00498522	−	0.00686156i
$421$	1.53752e7	−	4.73201e7i	0.206051	−	0.634160i	−0.793617	−	0.608417i	$-0.791805\pi$
$421$	1.53752e7	−	4.73201e7i	0.206051	−	0.634160i	0.999669	−	0.0257432i	$-0.00819521\pi$
$422$	−8.17765e6	−	2.51682e7i	−0.108816	−	0.334900i
$423$	6.32687e7	−	4.59674e7i	0.835926	−	0.607336i
$424$	−1.24915e6	−	1.71931e6i	−0.0163877	−	0.0225557i
$425$	9.87864e7	−	3.20976e7i	1.28686	−	0.418125i
$426$	5.08630e7	+	1.65264e7i	0.657921	+	0.213771i
$427$	1.63675e7	+	1.18917e7i	0.210232	+	0.152742i
$428$		−	5.47082e7i		−	0.697785i
$429$	−1.37109e7	−	1.61782e6i	−0.173658	−	0.0204908i
$430$	5.33058e6			0.0670454
$431$	−4.62130e7	+	6.36067e7i	−0.577208	+	0.794459i	−0.993386	−	0.114825i	$-0.963369\pi$
$431$	−4.62130e7	+	6.36067e7i	−0.577208	+	0.794459i	0.416178	+	0.909283i	$0.363369\pi$
$432$	2.34359e7	−	7.21282e7i	0.290690	−	0.894651i
$433$	−3.08343e7	−	9.48982e7i	−0.379813	−	1.16895i	−0.940173	−	0.340696i	$-0.889337\pi$
$433$	−3.08343e7	−	9.48982e7i	−0.379813	−	1.16895i	0.560360	−	0.828249i	$-0.310663\pi$
$434$	4.69142e6	−	3.40851e6i	0.0573898	−	0.0416961i
$435$	3.08255e6	+	4.24277e6i	0.0374492	+	0.0515444i
$436$	4.10967e7	−	1.33531e7i	0.495847	−	0.161110i
$437$	1.70060e7	+	5.52557e6i	0.203778	+	0.0662114i
$438$	−1.12958e7	−	8.20692e6i	−0.134430	−	0.0976692i
$439$		−	8.24629e7i		−	0.974687i	−0.873210	−	0.487343i	$-0.837966\pi$
$439$		−	8.24629e7i		−	0.974687i	0.873210	−	0.487343i	$-0.162034\pi$
$440$	1.49787e6	−	3.25219e6i	0.0175840	−	0.0381785i
$441$	−6.67584e7			−0.778377
$442$	3.66316e7	−	5.04190e7i	0.424217	−	0.583885i
$443$	−7.94839e6	+	2.44626e7i	−0.0914257	+	0.281379i	−0.986306	−	0.164928i	$-0.947261\pi$
$443$	−7.94839e6	+	2.44626e7i	−0.0914257	+	0.281379i	0.894880	+	0.446307i	$0.147261\pi$
$444$	2.06539e6	+	6.35662e6i	0.0235968	+	0.0726236i
$445$	7.52722e6	−	5.46885e6i	0.0854190	−	0.0620606i
$446$	−6.62913e7	−	9.12421e7i	−0.747226	−	1.02847i
$447$	−1.65391e7	+	5.37388e6i	−0.185178	+	0.0601680i
$448$	−7.43188e6	−	2.41476e6i	−0.0826541	−	0.0268560i
$449$	4.09473e7	+	2.97499e7i	0.452362	+	0.328660i	0.790528	−	0.612426i	$-0.209806\pi$
$449$	4.09473e7	+	2.97499e7i	0.452362	+	0.328660i	−0.338166	+	0.941087i	$0.609806\pi$
$450$			9.51703e7i			1.04439i
$451$	−1.04969e8	+	5.88347e7i	−1.14428	+	0.641363i
$452$	6.08264e7			0.658683
$453$	1.64865e7	−	2.26918e7i	0.177351	−	0.244103i
$454$	−4.07482e7	+	1.25410e8i	−0.435453	+	1.34019i
$455$	−270501.	−	832516.i	−0.00287167	−	0.00883808i
$456$	−1.20765e6	+	877408.i	−0.0127364	+	0.00925352i
$457$	−9.39161e7	−	1.29264e8i	−0.983992	−	1.35435i	−0.934651	−	0.355567i	$-0.884288\pi$
$457$	−9.39161e7	−	1.29264e8i	−0.983992	−	1.35435i	−0.0493411	−	0.998782i	$-0.515712\pi$
$458$	3.70497e7	−	1.20382e7i	0.385646	−	0.125304i
$459$	−1.02820e8	−	3.34084e7i	−1.06327	−	0.345476i
$460$	−1.60121e7	−	1.16334e7i	−0.164503	−	0.119518i
$461$			1.88579e8i			1.92482i	0.271592	+	0.962412i	$0.412450\pi$
$461$			1.88579e8i			1.92482i	−0.271592	+	0.962412i	$0.587550\pi$
$462$	9.20343e6	−	1.83410e6i	0.0933306	−	0.0185993i
$463$	3.06398e7			0.308705			0.154352	−	0.988016i	$-0.450671\pi$
$463$	3.06398e7			0.308705			0.154352	+	0.988016i	$0.450671\pi$
$464$	6.44116e7	−	8.86549e7i	0.644778	−	0.887460i
$465$	−703610.	+	2.16549e6i	−0.00699799	+	0.0215376i
$466$	5.53794e7	+	1.70440e8i	0.547256	+	1.68428i
$467$	4.18735e7	−	3.04229e7i	0.411139	−	0.298710i	−0.362924	−	0.931819i	$-0.618221\pi$
$467$	4.18735e7	−	3.04229e7i	0.411139	−	0.298710i	0.774063	+	0.633109i	$0.218221\pi$
$468$	1.48298e7	+	2.04114e7i	0.144676	+	0.199129i
$469$	−9.79969e6	+	3.18411e6i	−0.0949935	+	0.0308653i
$470$	2.57756e7	+	8.37499e6i	0.248265	+	0.0806661i
$471$	−4.31831e7	−	3.13744e7i	−0.413287	−	0.300270i
$472$		−	4.29641e7i		−	0.408583i
$473$	2.58385e7	+	2.38677e7i	0.244165	+	0.225542i
$474$	−6.91212e7			−0.649047
$475$	7.73863e6	−	1.06513e7i	0.0722077	−	0.0993853i
$476$	−5.78394e6	+	1.78011e7i	−0.0536294	+	0.165054i
$477$	−2.67644e6	−	8.23723e6i	−0.0246605	−	0.0758972i
$478$	3.58316e7	−	2.60332e7i	0.328082	−	0.238366i
$479$	−2.75219e7	−	3.78807e7i	−0.250422	−	0.344676i	0.665237	−	0.746632i	$-0.268330\pi$
$479$	−2.75219e7	−	3.78807e7i	−0.250422	−	0.344676i	−0.915659	+	0.401956i	$0.868330\pi$
$480$	9.11202e6	−	2.96068e6i	0.0823932	−	0.0267712i
$481$	8.85522e6	+	2.87724e6i	0.0795727	+	0.0258547i
$482$	2.00092e8	+	1.45375e8i	1.78685	+	1.29822i
$483$			1.36556e7i			0.121191i
$484$	−8.28961e7	+	3.44062e7i	−0.731136	+	0.303459i
$485$	−2.41401e7			−0.211599
$486$	9.05996e7	−	1.24700e8i	0.789256	−	1.08632i
$487$	−5.62986e7	+	1.73269e8i	−0.487428	+	1.50015i	0.341005	+	0.940061i	$0.389233\pi$
$487$	−5.62986e7	+	1.73269e8i	−0.487428	+	1.50015i	−0.828433	+	0.560088i	$0.810767\pi$
$488$	1.64388e7	+	5.05935e7i	0.141453	+	0.435347i
$489$	4.77800e7	−	3.47142e7i	0.408620	−	0.296880i
$490$	−1.35986e7	−	1.87169e7i	−0.115586	−	0.159091i
$491$	1.21359e8	−	3.94319e7i	1.02524	−	0.333122i	0.252335	−	0.967640i	$-0.418802\pi$
$491$	1.21359e8	−	3.94319e7i	1.02524	−	0.333122i	0.772908	+	0.634518i	$0.218802\pi$
$492$	−5.28102e7	−	1.71591e7i	−0.443427	−	0.144078i
$493$	−1.26380e8	−	9.18202e7i	−1.05472	−	0.766298i
$494$		−	7.89935e6i		−	0.0655255i
$495$	9.90153e6	−	1.07191e7i	0.0816370	−	0.0883778i
$496$	4.75777e7			0.389905
$497$	−1.31520e7	+	1.81022e7i	−0.107133	+	0.147456i
$498$	−2.97520e7	+	9.15674e7i	−0.240896	+	0.741400i
$499$	2.31942e7	+	7.13844e7i	0.186671	+	0.574516i	0.999973	−	0.00732652i	$-0.00233212\pi$
$499$	2.31942e7	+	7.13844e7i	0.186671	+	0.574516i	−0.813302	+	0.581842i	$0.802332\pi$
$500$	−2.38531e7	+	1.73303e7i	−0.190825	+	0.138642i
$501$	8.60275e6	+	1.18407e7i	0.0684107	+	0.0941593i
$502$	−1.64957e8	+	5.35976e7i	−1.30394	+	0.423677i
$503$	−1.93782e8	−	6.29636e7i	−1.52268	−	0.494750i	−0.576147	−	0.817346i	$-0.695444\pi$
$503$	−1.93782e8	−	6.29636e7i	−1.52268	−	0.494750i	−0.946537	+	0.322597i	$0.895444\pi$
$504$	3.65237e6	+	2.65360e6i	0.0285288	+	0.0207274i
$505$			3.26207e7i			0.253291i
$506$	−5.77696e7	−	2.89885e8i	−0.445911	−	2.23756i
$507$	4.96409e7			0.380904
$508$	7.76821e7	−	1.06920e8i	0.592556	−	0.815584i
$509$	4.68326e6	−	1.44136e7i	0.0355137	−	0.109300i	−0.931728	−	0.363156i	$-0.881699\pi$
$509$	4.68326e6	−	1.44136e7i	0.0355137	−	0.109300i	0.967242	+	0.253857i	$0.0816991\pi$
$510$	−5.13995e6	−	1.58192e7i	−0.0387479	−	0.119254i
$511$	4.72603e6	−	3.43366e6i	0.0354188	−	0.0257333i
$512$	−9.20388e7	−	1.26681e8i	−0.685743	−	0.943844i
$513$	−1.30327e7	+	4.23458e6i	−0.0965344	+	0.0313659i
$514$	9.44279e7	+	3.06815e7i	0.695362	+	0.225937i
$515$	−1.27809e6	−	928587.i	−0.00935707	−	0.00679831i
$516$			1.62317e7i			0.118145i
$517$	8.74407e7	+	1.56006e8i	0.632764	+	1.12893i
$518$	−6.32893e6			−0.0455345
$519$	2.55484e7	−	3.51644e7i	0.182752	−	0.251536i
$520$	711267.	−	2.18906e6i	0.00505851	−	0.0155685i
$521$	2.71207e7	+	8.34689e7i	0.191773	+	0.590217i	0.999999	+	0.00134433i	$0.000427915\pi$
$521$	2.71207e7	+	8.34689e7i	0.191773	+	0.590217i	−0.808226	+	0.588872i	$0.799572\pi$
$522$	1.15795e8	−	8.41297e7i	0.814098	−	0.591477i
$523$	4.63756e6	+	6.38306e6i	0.0324179	+	0.0446194i	0.824918	−	0.565252i	$-0.191221\pi$
$523$	4.63756e6	+	6.38306e6i	0.0324179	+	0.0446194i	−0.792500	+	0.609871i	$0.791221\pi$
$524$	−2.58341e7	+	8.39401e6i	−0.179556	+	0.0583412i
$525$	9.56241e6	+	3.10702e6i	0.0660830	+	0.0214717i
$526$	−1.75436e8	−	1.27462e8i	−1.20549	−	0.875837i
$527$		−	6.78232e7i		−	0.463390i
$528$	6.99343e7	+	3.22098e7i	0.475103	+	0.218820i
$529$	2.82082e8			1.90550
$530$	1.76427e6	−	2.42830e6i	0.0118505	−	0.0163108i
$531$	5.41086e7	−	1.66529e8i	0.361395	−	1.11226i
$532$	733126.	+	2.25633e6i	0.00486904	+	0.0149854i
$533$	−6.25809e7	+	4.54677e7i	−0.413295	+	0.300276i
$534$	3.76892e7	+	5.18747e7i	0.247510	+	0.340668i
$535$	−1.93452e7	+	6.28562e6i	−0.126331	+	0.0410475i
$536$	−2.57678e7	−	8.37246e6i	−0.167333	−	0.0543699i
$537$	2.38386e7	+	1.73197e7i	0.153942	+	0.111845i
$538$			9.92939e7i			0.637640i
$539$	1.78896e7	−	1.51613e8i	0.114244	−	0.968209i
$540$	1.51678e7			0.0963255
$541$	−3.58789e7	+	4.93831e7i	−0.226594	+	0.311879i	−0.907143	−	0.420823i	$-0.861741\pi$
$541$	−3.58789e7	+	4.93831e7i	−0.226594	+	0.311879i	0.680549	+	0.732703i	$0.261741\pi$
$542$	−3.75838e7	+	1.15671e8i	−0.236049	+	0.726485i
$543$	−2.01335e7	−	6.19645e7i	−0.125753	−	0.387029i
$544$	−2.30884e8	+	1.67747e8i	−1.43416	+	1.04198i
$545$	−9.44349e6	−	1.29978e7i	−0.0583368	−	0.0802938i
$546$	5.73738e6	−	1.86419e6i	0.0352481	−	0.0114528i
$547$	5.16864e7	+	1.67939e7i	0.315802	+	0.102610i	0.462629	−	0.886552i	$-0.346906\pi$
$547$	5.16864e7	+	1.67939e7i	0.315802	+	0.102610i	−0.146827	+	0.989162i	$0.546906\pi$
$548$	1.43251e8	+	1.04078e8i	0.870472	+	0.632435i
$549$			2.16804e8i			1.31024i
$550$	−2.16138e8	−	2.55032e7i	−1.29910	−	0.153288i
$551$	−1.98004e7			−0.118364
$552$	−2.11054e7	+	2.90491e7i	−0.125481	+	0.172709i
$553$	8.93659e6	−	2.75040e7i	0.0528441	−	0.162637i
$554$	−3.90804e7	−	1.20277e8i	−0.229842	−	0.707381i
$555$	2.01044e6	−	1.46067e6i	0.0117601	−	0.00854423i
$556$	1.23733e8	+	1.70304e8i	0.719884	+	0.990835i
$557$	−1.18087e8	+	3.83689e7i	−0.683342	+	0.222031i	−0.630058	−	0.776548i	$-0.716969\pi$
$557$	−1.18087e8	+	3.83689e7i	−0.683342	+	0.222031i	−0.0532840	+	0.998579i	$0.516969\pi$
$558$	5.91010e7	+	1.92031e7i	0.340167	+	0.110527i
$559$	1.82934e7	+	1.32909e7i	0.104727	+	0.0760886i
$560$			4.88180e6i			0.0277982i
$561$	4.59158e7	−	9.96929e7i	0.260060	−	0.564645i
$562$	3.25931e7			0.183618
$563$	−1.41524e8	+	1.94792e8i	−0.793060	+	1.09155i	0.200660	+	0.979661i	$0.435691\pi$
$563$	−1.41524e8	+	1.94792e8i	−0.793060	+	1.09155i	−0.993720	+	0.111893i	$0.964309\pi$
$564$	−2.55019e7	+	7.84869e7i	−0.142146	+	0.437482i
$565$	−6.98855e6	−	2.15086e7i	−0.0387474	−	0.119252i
$566$	−9.71146e7	+	7.05579e7i	−0.535593	+	0.389131i
$567$	7.39427e6	+	1.01773e7i	0.0405645	+	0.0558322i
$568$	−5.59557e7	+	1.81811e7i	−0.305351	+	0.0992146i
$569$	3.92758e7	+	1.27615e7i	0.213201	+	0.0692731i	0.413670	−	0.910427i	$-0.364247\pi$
$569$	3.92758e7	+	1.27615e7i	0.213201	+	0.0692731i	−0.200469	+	0.979700i	$0.564247\pi$
$570$	−1.70565e6	−	1.23922e6i	−0.00921010	−	0.00669153i
$571$		−	1.43171e8i		−	0.769036i	−0.923117	−	0.384518i	$-0.874368\pi$
$571$		−	1.43171e8i		−	0.769036i	0.923117	−	0.384518i	$-0.125632\pi$
$572$	−5.03297e7	+	2.82096e7i	−0.268928	+	0.150733i
$573$	1.26184e8			0.670719
$574$	3.09058e7	−	4.25382e7i	0.163420	−	0.224928i
$575$	9.78634e7	−	3.01192e8i	0.514774	−	1.58431i
$576$	−2.58772e7	−	7.96418e7i	−0.135410	−	0.416748i
$577$	−4.64963e7	+	3.37815e7i	−0.242042	+	0.175854i	−0.702193	−	0.711987i	$-0.747795\pi$
$577$	−4.64963e7	+	3.37815e7i	−0.242042	+	0.175854i	0.460151	+	0.887841i	$0.347795\pi$
$578$	1.39299e8	+	1.91728e8i	0.721379	+	0.992893i
$579$	−8.57918e7	+	2.78755e7i	−0.441988	+	0.143611i
$580$	2.08437e7	+	6.77254e6i	0.106830	+	0.0347110i
$581$	−3.25889e7	−	2.36772e7i	−0.166166	−	0.120726i
$582$		−	1.66364e8i		−	0.843900i
$583$	1.94245e7	−	3.87100e6i	0.0980267	−	0.0195352i
$584$	1.53604e7			0.0771197
$585$	5.51375e6	−	7.58903e6i	0.0275410	−	0.0379069i
$586$	1.26219e8	−	3.88461e8i	0.627236	−	1.93043i
$587$	−2.68257e7	−	8.25610e7i	−0.132628	−	0.408188i	0.862585	−	0.505912i	$-0.168844\pi$
$587$	−2.68257e7	−	8.25610e7i	−0.132628	−	0.408188i	−0.995214	+	0.0977235i	$0.968844\pi$
$588$	5.69932e7	−	4.14080e7i	0.280344	−	0.203682i
$589$	−5.05302e6	−	6.95489e6i	−0.0247289	−	0.0340365i
$590$	5.77113e7	−	1.87515e7i	0.280999	−	0.0913021i
$591$	−1.13109e8	−	3.67513e7i	−0.547941	−	0.178037i
$592$	−4.20092e7	−	3.05215e7i	−0.202479	−	0.147110i
$593$		−	3.67388e7i		−	0.176182i	−0.996112	−	0.0880910i	$-0.971923\pi$
$593$		−	3.67388e7i		−	0.176182i	0.996112	−	0.0880910i	$-0.0280766\pi$
$594$	1.66397e8	+	1.53706e8i	0.793939	+	0.733384i
$595$	6.95912e6			0.0330372
$596$	−4.27171e7	+	5.87951e7i	−0.201773	+	0.277717i
$597$	−4.31012e7	+	1.32652e8i	−0.202566	+	0.623434i
$598$	−5.87173e7	−	1.80713e8i	−0.274576	−	0.845058i
$599$	2.16574e8	−	1.57350e8i	1.00769	−	0.732127i	0.0439638	−	0.999033i	$-0.486001\pi$
$599$	2.16574e8	−	1.57350e8i	1.00769	−	0.732127i	0.963723	+	0.266906i	$0.0860014\pi$
$600$	1.55398e7	+	2.13887e7i	0.0719434	+	0.0990215i
$601$	3.18892e8	−	1.03614e8i	1.46899	−	0.477305i	0.538189	−	0.842824i	$-0.319109\pi$
$601$	3.18892e8	−	1.03614e8i	1.46899	−	0.477305i	0.930804	+	0.365519i	$0.119109\pi$
$602$	−1.46177e7	−	4.74958e6i	−0.0670023	−	0.0217704i
$603$	−8.93318e7	−	6.49034e7i	−0.407431	−	0.296016i
$604$		−	1.17216e8i		−	0.531958i
$605$	2.16905e7	+	2.53595e7i	0.0979496	+	0.114518i
$606$	−2.24809e8			−1.01017
$607$	−1.15747e8	+	1.59312e8i	−0.517540	+	0.712333i	−0.985168	−	0.171593i	$-0.945109\pi$
$607$	−1.15747e8	+	1.59312e8i	−0.517540	+	0.712333i	0.467628	+	0.883925i	$0.345109\pi$
$608$	−1.11783e7	+	3.44031e7i	−0.0497351	+	0.153069i
$609$	−4.67275e6	−	1.43812e7i	−0.0206881	−	0.0636714i
$610$	−6.07848e7	+	4.41627e7i	−0.267797	+	0.194566i
$611$	6.75745e7	+	9.30083e7i	0.296250	+	0.407754i
$612$	−1.90761e8	+	6.19821e7i	−0.832216	+	0.270403i
$613$	1.61182e8	+	5.23711e7i	0.699736	+	0.227358i	0.637216	−	0.770686i	$-0.280086\pi$
$613$	1.61182e8	+	5.23711e7i	0.699736	+	0.227358i	0.0625205	+	0.998044i	$0.480086\pi$
$614$	1.51896e8	+	1.10359e8i	0.656207	+	0.476762i
$615$			2.06455e7i			0.0887563i
$616$	−7.00525e6	+	7.58367e6i	−0.0299696	+	0.0324442i
$617$	−1.33996e8			−0.570473			−0.285236	−	0.958457i	$-0.592072\pi$
$617$	−1.33996e8			−0.570473			−0.285236	+	0.958457i	$0.592072\pi$
$618$	6.39947e6	−	8.80811e6i	0.0271130	−	0.0373179i
$619$	−1.01673e8	+	3.12917e8i	−0.428680	+	1.31934i	0.470745	+	0.882269i	$0.343985\pi$
$619$	−1.01673e8	+	3.12917e8i	−0.428680	+	1.31934i	−0.899426	+	0.437073i	$0.856015\pi$
$620$	2.94042e6	+	9.04969e6i	0.0123377	+	0.0379716i
$621$	−2.66672e8	+	1.93749e8i	−1.11353	+	0.809029i
$622$	−7.01396e7	−	9.65389e7i	−0.291469	−	0.401172i
$623$	−2.55142e7	+	8.29007e6i	−0.105516	+	0.0342842i
$624$	4.70728e7	+	1.52949e7i	0.193739	+	0.0629496i
$625$	−1.84160e8	−	1.33800e8i	−0.754319	−	0.548045i
$626$			3.03968e7i			0.123910i
$627$	−2.71900e6	−	1.36438e7i	−0.0110308	−	0.0553520i
$628$	−2.23066e8			−0.900648
$629$	−4.35091e7	+	5.98852e7i	−0.174835	+	0.240640i
$630$	−1.97037e6	+	6.06417e6i	−0.00788000	+	0.0242521i
$631$	1.11007e8	+	3.41644e8i	0.441837	+	1.35983i	0.885916	+	0.463846i	$0.153531\pi$
$631$	1.11007e8	+	3.41644e8i	0.441837	+	1.35983i	−0.444079	+	0.895988i	$0.646469\pi$
$632$	6.15193e7	−	4.46964e7i	0.243703	−	0.177060i
$633$	−1.76103e7	−	2.42385e7i	−0.0694314	−	0.0955641i
$634$	3.31550e8	−	1.07727e8i	1.30101	−	0.422725i
$635$	−4.67328e7	−	1.51844e7i	−0.182516	−	0.0593030i
$636$	7.39421e6	+	5.37221e6i	0.0287422	+	0.0208825i
$637$		−	9.81382e7i		−	0.379682i
$638$	1.60034e8	+	2.85522e8i	0.616241	+	1.09945i
$639$	−2.39782e8			−0.918996
$640$	−1.26721e7	+	1.74416e7i	−0.0483401	+	0.0665344i
$641$	2.27804e6	−	7.01109e6i	0.00864944	−	0.0266202i	−0.946639	−	0.322297i	$-0.895545\pi$
$641$	2.27804e6	−	7.01109e6i	0.00864944	−	0.0266202i	0.955288	+	0.295677i	$0.0955451\pi$
$642$	−4.33181e7	−	1.33319e8i	−0.163706	−	0.503835i
$643$	2.70427e8	−	1.96477e8i	1.01722	−	0.739057i	0.0515126	−	0.998672i	$-0.483596\pi$
$643$	2.70427e8	−	1.96477e8i	1.01722	−	0.739057i	0.965712	+	0.259615i	$0.0835958\pi$
$644$	3.35434e7	+	4.61685e7i	0.125588	+	0.172858i
$645$	5.73961e6	−	1.86491e6i	0.0213896	−	0.00694992i
$646$	5.97264e7	+	1.94063e7i	0.221548	+	0.0719854i
$647$	1.81707e8	+	1.32018e8i	0.670902	+	0.487439i	0.870327	−	0.492474i	$-0.163907\pi$
$647$	1.81707e8	+	1.32018e8i	0.670902	+	0.487439i	−0.199425	+	0.979913i	$0.563907\pi$
$648$			3.30781e7i			0.121567i
$649$	3.63699e8	+	1.67510e8i	1.33048	+	0.612782i
$650$	−1.39905e8			−0.509441
$651$	3.85893e6	−	5.31136e6i	0.0139870	−	0.0192514i
$652$	7.62691e7	−	2.34732e8i	0.275173	−	0.846896i
$653$	4.94382e7	+	1.52155e8i	0.177551	+	0.546446i	0.999741	−	0.0227678i	$-0.00724783\pi$
$653$	4.94382e7	+	1.52155e8i	0.177551	+	0.546446i	−0.822190	+	0.569213i	$0.807248\pi$
$654$	8.95761e7	−	6.50809e7i	0.320228	−	0.232659i
$655$	5.93634e6	+	8.17067e6i	0.0211249	+	0.0290759i
$656$	4.10284e8	−	1.33309e8i	1.45336	−	0.472225i
$657$	5.95371e7	+	1.93448e7i	0.209938	+	0.0682131i
$658$	−6.32206e7	−	4.59324e7i	−0.221912	−	0.161228i
$659$		−	4.77342e8i		−	1.66791i	−0.551830	−	0.833957i	$-0.686070\pi$
$659$		−	4.77342e8i		−	1.66791i	0.551830	−	0.833957i	$-0.313930\pi$
$660$	−1.80447e6	+	1.52927e7i	−0.00627650	+	0.0531929i
$661$	−4.51585e8			−1.56363			−0.781816	−	0.623509i	$-0.785707\pi$
$661$	−4.51585e8			−1.56363			−0.781816	+	0.623509i	$0.785707\pi$
$662$	−1.76252e8	+	2.42590e8i	−0.607519	+	0.836178i
$663$	2.18032e7	−	6.71035e7i	0.0748136	−	0.230253i
$664$	−3.27310e7	−	1.00736e8i	−0.111803	−	0.344095i
$665$	713620.	−	518475.i	0.00242662	−	0.00176304i
$666$	−3.98649e7	−	5.48694e7i	−0.134949	−	0.185741i
$667$	−4.52974e8	+	1.47180e8i	−1.52650	+	0.495988i
$668$	5.81705e7	+	1.89007e7i	0.195152	+	0.0634088i
$669$	−1.03299e8	−	7.50513e7i	−0.345000	−	0.250657i
$670$		−	3.82665e7i		−	0.127232i
$671$	−4.92375e8	−	5.80979e7i	−1.62978	−	0.192306i
$672$	−2.76253e7			−0.0910331
$673$	3.31408e8	−	4.56145e8i	1.08722	−	1.49643i	0.235909	−	0.971775i	$-0.424193\pi$
$673$	3.31408e8	−	4.56145e8i	1.08722	−	1.49643i	0.851313	−	0.524658i	$-0.175807\pi$
$674$	−8.68917e7	+	2.67425e8i	−0.283791	+	0.873419i
$675$	7.49986e7	+	2.30822e8i	0.243861	+	0.750526i
$676$	1.67832e8	−	1.21937e8i	0.543294	−	0.394726i
$677$	−2.68657e8	−	3.69775e8i	−0.865830	−	1.19171i	−0.980148	−	0.198268i	$-0.936468\pi$
$677$	−2.68657e8	−	3.69775e8i	−0.865830	−	1.19171i	0.114318	−	0.993444i	$-0.463532\pi$
$678$	1.48229e8	−	4.81624e7i	0.475601	−	0.154532i
$679$	6.61979e7	+	2.15090e7i	0.211463	+	0.0687085i
$680$	1.48039e7	+	1.07557e7i	0.0470815	+	0.0342067i
$681$			1.49289e8i			0.472702i
$682$	−5.94491e7	+	1.29076e8i	−0.187410	+	0.406906i
$683$	−2.34096e8			−0.734737			−0.367368	−	0.930076i	$-0.619741\pi$
$683$	−2.34096e8			−0.734737			−0.367368	+	0.930076i	$0.619741\pi$
$684$	−1.49437e7	+	2.05682e7i	−0.0466970	+	0.0642729i
$685$	2.03439e7	−	6.26121e7i	0.0632940	−	0.194799i
$686$	4.17577e7	+	1.28517e8i	0.129349	+	0.398096i
$687$	3.56811e7	−	2.59238e7i	0.110044	−	0.0799520i
$688$	−7.41223e7	−	1.02021e8i	−0.227606	−	0.313273i
$689$	1.21091e7	−	3.93450e6i	0.0370216	−	0.0120291i
$690$	−4.82314e7	−	1.56713e7i	−0.146819	−	0.0477044i
$691$	5.15218e8	+	3.74328e8i	1.56155	+	1.13454i	0.934722	+	0.355380i	$0.115649\pi$
$691$	5.15218e8	+	3.74328e8i	1.56155	+	1.13454i	0.626832	+	0.779155i	$0.284351\pi$
$692$		−	1.81645e8i		−	0.548157i
$693$	−3.67032e7	+	2.05720e7i	−0.110282	+	0.0618126i
$694$	1.46644e8			0.438718
$695$	4.60045e7	−	6.33197e7i	0.137039	−	0.188619i
$696$	1.22867e7	−	3.78147e7i	0.0364426	−	0.112159i
$697$	−1.90036e8	−	5.84870e8i	−0.561225	−	1.72727i
$698$	−1.14481e8	+	8.31751e7i	−0.336640	+	0.244583i
$699$	1.19258e8	+	1.64144e8i	0.349184	+	0.480611i
$700$	3.99618e7	−	1.29844e7i	0.116507	−	0.0378553i
$701$	2.38237e8	+	7.74079e7i	0.691601	+	0.224715i	0.633667	−	0.773606i	$-0.281549\pi$
$701$	2.38237e8	+	7.74079e7i	0.691601	+	0.224715i	0.0579334	+	0.998320i	$0.481549\pi$
$702$	1.17808e8	+	8.55924e7i	0.340536	+	0.247414i
$703$			9.38245e6i			0.0270054i
$704$	1.87806e8	−	3.74268e7i	0.538260	−	0.107267i
$705$	3.06834e7			0.0875662
$706$	−2.14791e8	+	2.95635e8i	−0.610384	+	0.840121i
$707$	2.90653e7	−	8.94537e7i	0.0822463	−	0.253128i
$708$	5.70986e7	+	1.75731e8i	0.160889	+	0.495165i
$709$	−1.02055e8	+	7.41470e7i	−0.286348	+	0.208044i	−0.721681	−	0.692225i	$-0.756630\pi$
$709$	−1.02055e8	+	7.41470e7i	−0.286348	+	0.208044i	0.435334	+	0.900269i	$0.356630\pi$
$710$	−4.88434e7	−	6.72271e7i	−0.136468	−	0.187832i
$711$	2.94739e8	−	9.57666e7i	0.820029	−	0.266444i
$712$	−6.70883e7	−	2.17983e7i	−0.185869	−	0.0603925i
$713$	−1.67295e8	−	1.21547e8i	−0.461545	−	0.335332i
$714$			4.79596e7i			0.131759i
$715$	1.57576e7	+	1.45558e7i	0.0431095	+	0.0398214i
$716$	1.23140e8			0.335476
$717$	2.94734e7	−	4.05666e7i	0.0799599	−	0.110055i
$718$	−1.17625e7	+	3.62013e7i	−0.0317780	+	0.0978026i
$719$	1.04693e8	+	3.22212e8i	0.281664	+	0.866872i	0.987379	+	0.158376i	$0.0506259\pi$
$719$	1.04693e8	+	3.22212e8i	0.281664	+	0.866872i	−0.705715	+	0.708496i	$0.749374\pi$
$720$	−4.23234e7	+	3.07497e7i	−0.113392	+	0.0823842i
$721$	2.67745e6	+	3.68519e6i	0.00714358	+	0.00983229i
$722$	−4.71544e8	+	1.53214e8i	−1.25288	+	0.407087i
$723$	2.66305e8	+	8.65278e7i	0.704636	+	0.228950i
$724$	−2.20279e8	−	1.60042e8i	−0.580439	−	0.421714i
$725$			3.50685e8i			0.920244i
$726$	−1.74768e8	+	1.49482e8i	−0.456722	+	0.390643i
$727$	4.78349e8			1.24492			0.622461	−	0.782651i	$-0.286133\pi$
$727$	4.78349e8			1.24492			0.622461	+	0.782651i	$0.286133\pi$
$728$	−3.90093e6	+	5.36917e6i	−0.0101105	+	0.0139159i
$729$	1.74776e6	−	5.37904e6i	0.00451126	−	0.0138842i
$730$	6.70401e6	+	2.06328e7i	0.0172332	+	0.0530383i
$731$	−1.45433e8	+	1.05663e8i	−0.372315	+	0.270503i
$732$	−1.34476e8	−	1.85090e8i	−0.342856	−	0.471900i
$733$	−4.32554e8	+	1.40545e8i	−1.09832	+	0.356866i	−0.801456	−	0.598054i	$-0.795941\pi$
$733$	−4.32554e8	+	1.40545e8i	−1.09832	+	0.356866i	−0.296864	+	0.954920i	$0.595941\pi$
$734$	−7.03819e8	−	2.28684e8i	−1.77981	−	0.578294i
$735$	−2.11902e7	−	1.53956e7i	−0.0533671	−	0.0387735i
$736$			8.70129e8i			2.18248i
$737$	1.71339e8	−	1.85486e8i	0.428009	−	0.463350i
$738$	5.63461e8			1.40183
$739$	−3.76932e7	+	5.18803e7i	−0.0933963	+	0.128549i	−0.853158	−	0.521653i	$-0.825316\pi$
$739$	−3.76932e7	+	5.18803e7i	−0.0933963	+	0.128549i	0.759762	+	0.650202i	$0.225316\pi$
$740$	3.20917e6	−	9.87683e6i	0.00791951	−	0.0243737i
$741$	−2.76360e6	−	8.50549e6i	−0.00679236	−	0.0209047i
$742$	−7.00167e6	+	5.08701e6i	−0.0171392	+	0.0124523i
$743$	2.88045e8	+	3.96460e8i	0.702254	+	0.966569i	0.999929	+	0.0119022i	$0.00378868\pi$
$743$	2.88045e8	+	3.96460e8i	0.702254	+	0.966569i	−0.297675	+	0.954667i	$0.596211\pi$
$744$	1.64180e7	−	5.33452e6i	0.0398658	−	0.0129532i
$745$	2.56982e7	+	8.34986e6i	0.0621490	+	0.0201934i
$746$	−5.19084e8	−	3.77137e8i	−1.25032	−	0.908411i
$747$		−	4.31673e8i		−	1.03560i
$748$	−8.96463e7	−	4.49841e8i	−0.214204	−	1.07487i
$749$	5.86495e7			0.139579
$750$	−4.44058e7	+	6.11193e7i	−0.105258	+	0.144875i
$751$	−4.18385e7	+	1.28766e8i	−0.0987771	+	0.304005i	−0.988220	−	0.153042i	$-0.951093\pi$
$751$	−4.18385e7	+	1.28766e8i	−0.0987771	+	0.304005i	0.889442	+	0.457047i	$0.151093\pi$
$752$	−1.98125e8	−	6.09767e8i	−0.465894	−	1.43387i
$753$	−1.58863e8	+	1.15421e8i	−0.372081	+	0.270333i
$754$	1.23675e8	+	1.70224e8i	0.288514	+	0.397106i
$755$	−4.14484e7	+	1.34674e7i	−0.0963090	+	0.0312927i
$756$	−4.15937e7	−	1.35146e7i	−0.0962636	−	0.0312779i
$757$	4.02431e8	+	2.92383e8i	0.927692	+	0.674008i	0.945427	−	0.325835i	$-0.105645\pi$
$757$	4.02431e8	+	2.92383e8i	0.927692	+	0.674008i	−0.0177347	+	0.999843i	$0.505645\pi$
$758$			2.27272e6i			0.00521841i
$759$	−1.63620e8	−	2.91919e8i	−0.374205	−	0.667631i
$760$	2.31939e6			0.00528364
$761$	3.72611e8	−	5.12855e8i	0.845477	−	1.16370i	−0.139364	−	0.990241i	$-0.544506\pi$
$761$	3.72611e8	−	5.12855e8i	0.845477	−	1.16370i	0.984841	−	0.173458i	$-0.0554941\pi$
$762$	1.04645e8	−	3.22064e8i	0.236512	−	0.727910i
$763$	1.43151e7	+	4.40574e7i	0.0322271	+	0.0991848i
$764$	4.26619e8	−	3.09957e8i	0.956665	−	0.695058i
$765$	4.38345e7	+	6.03330e7i	0.0979110	+	0.134763i
$766$	5.85004e8	−	1.90079e8i	1.30158	−	0.422910i
$767$	2.44806e8	+	7.95424e7i	0.542546	+	0.176284i
$768$	−2.10512e8	−	1.52946e8i	−0.464721	−	0.337640i
$769$		−	1.62690e8i		−	0.357752i	−0.983872	−	0.178876i	$-0.942754\pi$
$769$		−	1.62690e8i		−	0.357752i	0.983872	−	0.178876i	$-0.0572461\pi$
$770$	−1.32441e7	−	6.09989e6i	−0.0290102	−	0.0133613i
$771$	1.12408e8			0.245263
$772$	−2.21583e8	+	3.04982e8i	−0.481597	+	0.662862i
$773$	−3.61365e7	+	1.11217e8i	−0.0782361	+	0.240786i	−0.982524	−	0.186138i	$-0.940403\pi$
$773$	−3.61365e7	+	1.11217e8i	−0.0782361	+	0.240786i	0.904287	+	0.426924i	$0.140403\pi$
$774$	−5.08977e7	−	1.56647e8i	−0.109768	−	0.337831i
$775$	−1.23178e8	+	8.94940e7i	−0.264623	+	0.192260i
$776$	1.07577e8	+	1.48068e8i	0.230216	+	0.316865i
$777$	−6.81457e6	+	2.21419e6i	−0.0145270	+	0.00472010i
$778$	−9.88759e8	−	3.21267e8i	−2.09967	−	0.682225i
$779$	−6.30616e7	−	4.58169e7i	−0.133399	−	0.0969201i
$780$			9.89892e6i			0.0208595i
$781$	6.42555e7	−	5.44560e8i	0.134883	−	1.14312i
$782$	1.51061e9			3.15887
$783$	2.14545e8	−	2.95296e8i	0.446923	−	0.615137i
$784$	−1.69128e8	+	5.20521e8i	−0.350967	+	1.08017i
$785$	2.56289e7	+	7.88776e7i	0.0529811	+	0.163059i
$786$	−5.63091e7	+	4.09110e7i	−0.115961	+	0.0842504i
$787$	1.01366e8	+	1.39518e8i	0.207954	+	0.286224i	0.900235	−	0.435403i	$-0.143394\pi$
$787$	1.01366e8	+	1.39518e8i	0.207954	+	0.286224i	−0.692281	+	0.721628i	$0.743394\pi$
$788$	−4.72687e8	+	1.53585e8i	−0.966040	+	0.313885i
$789$	−2.33491e8	−	7.58658e7i	−0.475378	−	0.154460i
$790$	8.68880e7	+	6.31278e7i	0.176230	+	0.128038i
$791$			6.52084e7i			0.131757i
$792$	−1.09873e8	−	1.29644e7i	−0.221164	−	0.0260962i
$793$	−3.18712e8			−0.639115
$794$	3.26002e8	−	4.48703e8i	0.651267	−	0.896392i
$795$	1.05010e6	−	3.23187e6i	0.00208991	−	0.00643209i
$796$	1.80122e8	+	5.54359e8i	0.357131	+	1.09914i
$797$	−7.66508e8	+	5.56901e8i	−1.51406	+	1.10003i	−0.549718	+	0.835350i	$0.685265\pi$
$797$	−7.66508e8	+	5.56901e8i	−1.51406	+	1.10003i	−0.964337	+	0.264676i	$0.914735\pi$
$798$	3.57313e6	+	4.91799e6i	0.00703137	+	0.00967786i
$799$	−8.69238e8	+	2.82433e8i	−1.70411	+	0.553700i
$800$	6.09313e8	+	1.97978e8i	1.19006	+	0.386676i
$801$	−2.32582e8	−	1.68981e8i	−0.452562	−	0.328806i
$802$			8.42418e8i			1.63307i
$803$	−5.98877e7	+	1.30029e8i	−0.115662	+	0.251127i
$804$	1.16522e8			0.224202
$805$	1.24715e7	−	1.71656e7i	0.0239074	−	0.0329057i
$806$	−2.82295e7	+	8.68815e7i	−0.0539136	+	0.165929i
$807$	3.47382e7	+	1.06913e8i	0.0660977	+	0.203428i
$808$	2.00085e8	−	1.45370e8i	0.379298	−	0.275576i
$809$	−9.80041e7	−	1.34891e8i	−0.185097	−	0.254764i	0.706377	−	0.707835i	$-0.250328\pi$
$809$	−9.80041e7	−	1.34891e8i	−0.185097	−	0.254764i	−0.891474	+	0.453072i	$0.850328\pi$
$810$	−4.44320e7	+	1.44368e7i	−0.0836067	+	0.0271655i
$811$	−6.69467e8	−	2.17523e8i	−1.25507	−	0.407796i	−0.395332	−	0.918538i	$-0.629371\pi$
$811$	−6.69467e8	−	2.17523e8i	−1.25507	−	0.407796i	−0.859734	+	0.510742i	$0.829371\pi$
$812$	−5.11241e7	−	3.71438e7i	−0.0954899	−	0.0693775i
$813$			1.37696e8i			0.256241i
$814$	1.35295e8	−	7.58323e7i	0.250846	−	0.140599i
$815$	−9.17655e7			−0.169514
$816$	−2.31287e8	+	3.18339e8i	−0.425678	+	0.585895i
$817$	−7.04112e6	+	2.16703e7i	−0.0129115	+	0.0397374i
$818$	1.04687e7	+	3.22192e7i	0.0191263	+	0.0588648i
$819$	−2.18819e7	+	1.58981e7i	−0.0398321	+	0.0289397i
$820$	5.07132e7	+	6.98007e7i	0.0919770	+	0.126595i
$821$	5.19388e8	−	1.68759e8i	0.938561	−	0.304957i	0.200502	−	0.979693i	$-0.435743\pi$
$821$	5.19388e8	−	1.68759e8i	0.938561	−	0.304957i	0.738059	+	0.674736i	$0.235743\pi$
$822$	4.31499e8	+	1.40202e8i	0.776898	+	0.252429i
$823$	2.58729e8	+	1.87978e8i	0.464136	+	0.337215i	0.795152	−	0.606411i	$-0.207391\pi$
$823$	2.58729e8	+	1.87978e8i	0.464136	+	0.337215i	−0.331015	+	0.943625i	$0.607391\pi$
$824$			1.19775e7i			0.0214085i
$825$	−2.41646e8	+	4.81562e7i	−0.430345	+	0.0857610i
$826$	−1.74966e8			−0.310465
$827$	1.29958e8	−	1.78872e8i	0.229767	−	0.316247i	−0.678531	−	0.734572i	$-0.737383\pi$
$827$	1.29958e8	−	1.78872e8i	0.229767	−	0.316247i	0.908297	+	0.418326i	$0.137383\pi$
$828$	−1.88979e8	+	5.81617e8i	−0.332906	+	1.02458i
$829$	−1.72498e8	−	5.30893e8i	−0.302775	−	0.931845i	−0.980498	−	0.196528i	$-0.937033\pi$
$829$	−1.72498e8	−	5.30893e8i	−0.302775	−	0.931845i	0.677723	−	0.735317i	$-0.262967\pi$
$830$	1.21027e8	−	8.79314e7i	0.211665	−	0.153783i
$831$	−8.41583e7	−	1.15834e8i	−0.146654	−	0.201852i
$832$	1.17077e8	−	3.80408e7i	0.203284	−	0.0660510i
$833$	7.42016e8	+	2.41096e8i	1.28374	+	0.417113i
$834$	4.36375e8	+	3.17045e8i	0.752249	+	0.546541i
$835$		−	2.27410e7i		−	0.0390616i
$836$	−4.27072e7	−	3.94498e7i	−0.0730941	−	0.0675190i
$837$	1.58474e8			0.270260
$838$	3.44161e8	−	4.73696e8i	0.584829	−	0.804949i
$839$	−4.54757e7	+	1.39960e8i	−0.0770005	+	0.236983i	−0.982146	−	0.188118i	$-0.939761\pi$
$839$	−4.54757e7	+	1.39960e8i	−0.0770005	+	0.236983i	0.905146	+	0.425101i	$0.139761\pi$
$840$	547359.	+	1.68460e6i	0.000923494	+	0.00284222i
$841$	−5.45408e7	+	3.96262e7i	−0.0916924	+	0.0666184i
$842$	−3.13162e8	−	4.31031e8i	−0.524606	−	0.722058i
$843$	3.50940e7	−	1.14027e7i	0.0585802	−	0.0190339i
$844$	−1.19078e8	−	3.86909e7i	−0.198064	−	0.0643548i
$845$	−6.24005e7	−	4.53366e7i	−0.103423	−	0.0751413i
$846$		−	8.37420e8i		−	1.38303i
$847$	−3.68849e7	−	8.88681e7i	−0.0607013	−	0.146250i
$848$	−7.10070e7			−0.116443
$849$	−7.98818e7	+	1.09948e8i	−0.130534	+	0.179665i
$850$	3.43704e8	−	1.05781e9i	0.559665	−	1.72247i
$851$	6.97415e7	+	2.14642e8i	0.113162	+	0.348278i
$852$	2.04707e8	−	1.48729e8i	0.330990	−	0.240478i
$853$	−5.83905e8	−	8.03676e8i	−0.940795	−	1.29489i	−0.955497	−	0.295002i	$-0.904680\pi$
$853$	−5.83905e8	−	8.03676e8i	−0.940795	−	1.29489i	0.0147015	−	0.999892i	$-0.495320\pi$
$854$	2.06035e8	−	6.69450e7i	0.330802	−	0.107484i
$855$	8.98996e6	+	2.92102e6i	0.0143833	+	0.00467343i
$856$	1.24763e8	+	9.06458e7i	0.198914	+	0.144520i
$857$			6.22213e8i			0.988545i	0.869307	+	0.494272i	$0.164565\pi$
$857$			6.22213e8i			0.988545i	−0.869307	+	0.494272i	$0.835435\pi$
$858$	−1.00313e8	+	1.08596e8i	−0.158816	+	0.171929i
$859$	−8.76900e8			−1.38347			−0.691736	−	0.722150i	$-0.743154\pi$
$859$	−8.76900e8			−1.38347			−0.691736	+	0.722150i	$0.743154\pi$
$860$	1.48243e7	−	2.04038e7i	0.0233065	−	0.0320787i
$861$	1.83952e7	−	5.66147e7i	0.0288201	−	0.0886993i
$862$	2.60159e8	+	8.00688e8i	0.406179	+	1.25009i
$863$	7.00358e8	−	5.08840e8i	1.08965	−	0.791678i	0.110311	−	0.993897i	$-0.464815\pi$
$863$	7.00358e8	−	5.08840e8i	1.08965	−	0.791678i	0.979340	+	0.202219i	$0.0648153\pi$
$864$	−3.91954e8	−	5.39479e8i	−0.607707	−	0.836437i
$865$	−6.42307e7	+	2.08698e7i	−0.0992417	+	0.0322456i
$866$	−1.01618e9	−	3.30176e8i	−1.56465	−	0.508384i
$867$	2.17064e8	+	1.57706e8i	0.333066	+	0.241987i
$868$		−	2.74363e7i		−	0.0419534i
$869$	1.38510e8	+	6.95036e8i	0.211067	+	1.05913i
$870$	5.61569e7			0.0852796
$871$	9.54113e7	−	1.31322e8i	0.144393	−	0.198739i
$872$	−3.76408e7	+	1.15847e8i	−0.0567688	+	0.174716i
$873$	2.30495e8	+	7.09392e8i	0.346433	+	1.06621i
$874$	1.54905e8	−	1.12545e8i	0.232022	−	0.168574i
$875$	−1.85788e7	−	2.55715e7i	−0.0277328	−	0.0381709i
$876$	−6.28271e7	+	2.04138e7i	−0.0934620	+	0.0303676i
$877$	9.10694e8	+	2.95903e8i	1.35012	+	0.438682i	0.892734	−	0.450584i	$-0.148784\pi$
$877$	9.10694e8	+	2.95903e8i	1.35012	+	0.438682i	0.457391	+	0.889266i	$0.348784\pi$
$878$	−7.14378e8	−	5.19026e8i	−1.05547	−	0.766841i
$879$		−	4.62427e8i		−	0.680890i
$880$	−5.84931e7	−	1.04359e8i	−0.0858334	−	0.153138i
$881$	−2.49548e7			−0.0364945			−0.0182472	−	0.999834i	$-0.505809\pi$
$881$	−2.49548e7			−0.0364945			−0.0182472	+	0.999834i	$0.505809\pi$
$882$	−4.20181e8	+	5.78329e8i	−0.612393	+	0.842887i
$883$	−8.30922e7	+	2.55731e8i	−0.120692	+	0.371451i	−0.993092	−	0.117342i	$-0.962563\pi$
$883$	−8.30922e7	+	2.55731e8i	−0.120692	+	0.371451i	0.872400	+	0.488793i	$0.162563\pi$
$884$	−9.11168e7	−	2.80429e8i	−0.131899	−	0.405944i
$885$	5.55794e7	−	4.03808e7i	0.0801833	−	0.0582566i
$886$	1.61893e8	+	2.22826e8i	0.232770	+	0.320380i
$887$	−2.90873e8	+	9.45104e7i	−0.416805	+	0.135428i	−0.509909	−	0.860228i	$-0.670321\pi$
$887$	−2.90873e8	+	9.45104e7i	−0.416805	+	0.135428i	0.0931044	+	0.995656i	$0.470321\pi$
$888$	−1.79186e7	−	5.82209e6i	−0.0255896	−	0.00831458i
$889$	1.14623e8	+	8.32785e7i	0.163142	+	0.118530i
$890$		−	9.96297e7i		−	0.141325i
$891$	−2.80012e8	−	1.28966e8i	−0.395862	−	0.182323i
$892$	−5.33602e8			−0.751835
$893$	−6.80935e7	+	9.37227e7i	−0.0956206	+	0.131610i
$894$	−5.75440e7	+	1.77102e8i	−0.0805355	+	0.247863i
$895$	−1.41480e7	−	4.35431e7i	−0.0197345	−	0.0607366i
$896$	5.02904e7	−	3.65381e7i	0.0699135	−	0.0507951i
$897$	−1.26446e8	−	1.74038e8i	−0.175197	−	0.241138i
$898$	5.15449e8	−	1.67479e8i	0.711798	−	0.231277i
$899$	2.17776e8	+	7.07598e7i	0.299731	+	0.0973885i
$900$	3.64283e8	+	2.64667e8i	0.499702	+	0.363055i
$901$			1.01222e8i			0.138389i
$902$	−1.50993e8	+	1.27966e9i	−0.205749	+	1.74371i
$903$	−1.74010e7			−0.0236326
$904$	−1.00783e8	+	1.38716e8i	−0.136421	+	0.187768i
$905$	−3.12831e7	+	9.62795e7i	−0.0422050	+	0.129894i
$906$	−9.28121e7	−	2.85646e8i	−0.124802	−	0.384100i
$907$	1.11375e9	−	8.09189e8i	1.49268	−	1.08450i	0.519497	−	0.854472i	$-0.326119\pi$
$907$	1.11375e9	−	8.09189e8i	1.49268	−	1.08450i	0.973185	−	0.230025i	$-0.0738807\pi$
$908$	3.66712e8	+	5.04736e8i	0.489855	+	0.674227i
$909$	9.58607e8	−	3.11470e8i	1.27629	−	0.414692i
$910$	−8.91465e6	−	2.89654e6i	−0.0118299	−	0.00384376i
$911$	−7.28847e8	−	5.29539e8i	−0.964010	−	0.700394i	−0.00993113	−	0.999951i	$-0.503161\pi$
$911$	−7.28847e8	−	5.29539e8i	−0.964010	−	0.700394i	−0.954079	+	0.299557i	$0.903161\pi$
$912$			4.98755e7i			0.0657511i
$913$	9.80357e8	+	1.15677e8i	1.28817	+	0.151997i
$914$	−1.71093e9			−2.24076
$915$	−4.99986e7	+	6.88171e7i	−0.0652671	+	0.0898325i
$916$	5.69562e7	−	1.75293e8i	0.0741062	−	0.228075i
$917$	−8.99873e6	−	2.76952e7i	−0.0116701	−	0.0359168i
$918$	−9.36575e8	+	6.80462e8i	−1.21064	+	0.879581i
$919$	3.79359e8	+	5.22144e8i	0.488770	+	0.672734i	0.980161	−	0.198205i	$-0.0635113\pi$
$919$	3.79359e8	+	5.22144e8i	0.488770	+	0.672734i	−0.491391	+	0.870939i	$0.663511\pi$
$920$	5.30606e7	−	1.72404e7i	0.0681411	−	0.0221404i
$921$	2.02161e8	+	6.56860e7i	0.258772	+	0.0840802i
$922$	1.63367e9	+	1.18693e9i	2.08435	+	1.51437i
$923$		−	3.52491e8i		−	0.448274i
$924$	1.85742e7	−	4.03285e7i	0.0235448	−	0.0511207i
$925$	1.66172e8			0.209959
$926$	1.92849e8	−	2.65433e8i	0.242876	−	0.334290i
$927$	−1.50844e7	+	4.64250e7i	−0.0189360	+	0.0582790i
$928$	−2.97746e8	−	9.16367e8i	−0.372565	−	1.14664i
$929$	−9.90957e8	+	7.19972e8i	−1.23597	+	0.897984i	−0.997323	−	0.0731224i	$-0.976704\pi$
$929$	−9.90957e8	+	7.19972e8i	−1.23597	+	0.897984i	−0.238646	+	0.971107i	$0.576704\pi$
$930$	1.43311e7	+	1.97251e7i	0.0178169	+	0.0245228i
$931$	9.40519e7	−	3.05593e7i	0.116552	−	0.0378699i
$932$	8.06402e8	+	2.62016e8i	0.996102	+	0.323653i
$933$	−1.09296e8	−	7.94082e7i	−0.134573	−	0.0977733i
$934$		−	5.54235e8i		−	0.680226i
$935$	−1.48767e8	+	8.33833e7i	−0.182000	+	0.102010i
$936$	−7.11200e7			−0.0867290
$937$	−2.82316e8	+	3.88575e8i	−0.343176	+	0.472342i	−0.945366	−	0.326011i	$-0.894295\pi$
$937$	−2.82316e8	+	3.88575e8i	−0.343176	+	0.472342i	0.602189	+	0.798353i	$0.294295\pi$
$938$	−3.40958e7	+	1.04936e8i	−0.0413135	+	0.127150i
$939$	1.06344e7	+	3.27293e7i	0.0128445	+	0.0395312i
$940$	1.03738e8	−	7.53703e7i	0.124898	−	0.0907438i
$941$	−5.94541e7	−	8.18315e7i	−0.0713531	−	0.0982091i	0.771849	−	0.635806i	$-0.219332\pi$
$941$	−5.94541e7	−	8.18315e7i	−0.0713531	−	0.0982091i	−0.843202	+	0.537597i	$0.819332\pi$
$942$	−5.43594e8	+	1.76624e8i	−0.650312	+	0.211299i
$943$	−1.78322e9	−	5.79405e8i	−2.12653	−	0.690951i
$944$	−1.16136e9	−	8.43779e8i	−1.38055	−	1.00303i
$945$			1.62605e7i			0.0192681i
$946$	3.69395e8	−	7.36146e7i	0.436332	−	0.0869542i
$947$	8.37572e7			0.0986216			0.0493108	−	0.998783i	$-0.484298\pi$
$947$	8.37572e7			0.0986216			0.0493108	+	0.998783i	$0.484298\pi$
$948$	−1.92225e8	+	2.64575e8i	−0.225624	+	0.310544i
$949$	−2.84378e7	+	8.75226e7i	−0.0332734	+	0.102405i
$950$	−4.35652e7	−	1.34080e8i	−0.0508123	−	0.156384i
$951$	3.19303e8	−	2.31987e8i	0.371246	−	0.269726i
$952$	−3.10125e7	−	4.26850e7i	−0.0359439	−	0.0494726i
$953$	5.13353e8	−	1.66798e8i	0.593113	−	0.192714i	0.00294638	−	0.999996i	$-0.499062\pi$
$953$	5.13353e8	−	1.66798e8i	0.593113	−	0.192714i	0.590166	+	0.807282i	$0.299062\pi$
$954$	−8.82049e7	−	2.86595e7i	−0.101589	−	0.0330083i
$955$	−1.58618e8	−	1.15243e8i	−0.182114	−	0.132314i
$956$		−	2.09550e8i		−	0.239836i
$957$	2.72204e8	+	2.51443e8i	0.310570	+	0.286882i
$958$	−5.01386e8			−0.570263
$959$	−1.11576e8	+	1.53571e8i	−0.126507	+	0.174122i
$960$	1.01529e7	−	3.12474e7i	0.0114756	−	0.0353183i
$961$	−2.43532e8	−	7.49515e8i	−0.274401	−	0.844520i
$962$	8.06608e7	−	5.86035e7i	0.0906019	−	0.0658261i
$963$	3.69424e8	+	5.08469e8i	0.413663	+	0.569358i
$964$	1.11290e9	−	3.61604e8i	1.24230	−	0.403648i
$965$	1.33302e8	+	4.33124e7i	0.148339	+	0.0481982i
$966$	1.18299e8	+	8.59491e7i	0.131235	+	0.0953476i
$967$		−	8.10234e8i		−	0.896048i	−0.894022	−	0.448024i	$-0.852128\pi$
$967$		−	8.10234e8i		−	0.896048i	0.894022	−	0.448024i	$-0.147872\pi$
$968$	5.88861e7	−	2.46054e8i	0.0649213	−	0.271271i
$969$	7.10987e7			0.0781431
$970$	−1.51939e8	+	2.09126e8i	−0.166477	+	0.229136i
$971$	4.89962e8	−	1.50795e9i	0.535186	−	1.64713i	−0.208060	−	0.978116i	$-0.566715\pi$
$971$	4.89962e8	−	1.50795e9i	0.535186	−	1.64713i	0.743246	−	0.669018i	$-0.233285\pi$
$972$	−2.25356e8	−	6.93576e8i	−0.245398	−	0.755257i
$973$	−1.82574e8	+	1.32647e8i	−0.198198	+	0.143999i
$974$	1.14669e9	+	1.57828e9i	1.24099	+	1.70808i
$975$	−1.50641e8	+	4.89461e7i	−0.162528	+	0.0528086i
$976$	1.69044e9	+	5.49257e8i	1.81823	+	0.590780i
$977$	−1.42486e8	−	1.03522e8i	−0.152788	−	0.111007i	0.508765	−	0.860905i	$-0.330102\pi$
$977$	−1.42486e8	−	1.03522e8i	−0.152788	−	0.111007i	−0.661553	+	0.749899i	$0.730102\pi$
$978$		−	6.32413e8i		−	0.676058i
$979$	4.46092e8	−	4.82926e8i	0.475419	−	0.514675i
$980$	−1.09460e8			−0.116299
$981$	−2.91792e8	+	4.01617e8i	−0.309077	+	0.425408i
$982$	4.22240e8	−	1.29952e9i	0.445887	−	1.37230i
$983$	5.07734e7	+	1.56265e8i	0.0534535	+	0.164513i	0.974219	−	0.225603i	$-0.0724351\pi$
$983$	5.07734e7	+	1.56265e8i	0.0534535	+	0.164513i	−0.920766	+	0.390115i	$0.872435\pi$
$984$	1.26633e8	−	9.20039e7i	0.132911	−	0.0965653i
$985$	1.08617e8	+	1.49499e8i	0.113656	+	0.156433i
$986$	−1.59088e9	+	5.16909e8i	−1.65961	+	0.539241i
$987$	−8.41413e7	−	2.73392e7i	−0.0875100	−	0.0284337i
$988$	−3.02363e7	−	2.19680e7i	−0.0313515	−	0.0227782i
$989$			5.48090e8i			0.566582i
$990$	−3.05391e7	−	1.53244e8i	−0.0314739	−	0.157935i
$991$	6.30732e8			0.648073			0.324036	−	0.946045i	$-0.394960\pi$
$991$	6.30732e8			0.648073			0.324036	+	0.946045i	$0.394960\pi$
$992$	2.45890e8	−	3.38438e8i	0.251887	−	0.346692i
$993$	−1.04906e8	+	3.22867e8i	−0.107140	+	0.329743i
$994$	7.40403e7	+	2.27872e8i	0.0753891	+	0.232024i
$995$	1.75330e8	−	1.27385e8i	0.177986	−	0.129315i
$996$	2.67752e8	+	3.68529e8i	0.270991	+	0.372987i
$997$	−5.48001e8	+	1.78056e8i	−0.552962	+	0.179668i	−0.572152	−	0.820148i	$-0.693891\pi$
$997$	−5.48001e8	+	1.78056e8i	−0.552962	+	0.179668i	0.0191898	+	0.999816i	$0.493891\pi$
$998$	7.64391e8	+	2.48366e8i	0.768995	+	0.249862i
$999$	−1.39926e8	−	1.01662e8i	−0.140347	−	0.101968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.7.d.a.7.5	✓	20
3.2	odd	2		99.7.k.a.73.1		20
11.5	even	5		121.7.b.c.120.17		20
11.6	odd	10		121.7.b.c.120.4		20
11.8	odd	10	inner	11.7.d.a.8.5	yes	20
33.8	even	10		99.7.k.a.19.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.7.d.a.7.5	✓	20	1.1	even	1	trivial
11.7.d.a.8.5	yes	20	11.8	odd	10	inner
99.7.k.a.19.1		20	33.8	even	10
99.7.k.a.73.1		20	3.2	odd	2
121.7.b.c.120.4		20	11.6	odd	10
121.7.b.c.120.17		20	11.5	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)

\(f(q)\)	\(=\)	\(q+(6.29405 - 8.66302i) q^{2} +(3.74624 - 11.5298i) q^{3} +(-15.6557 - 48.1834i) q^{4} +(-15.2392 + 11.0719i) q^{5} +(-76.3035 - 105.023i) q^{6} +(51.6547 - 16.7836i) q^{7} +(135.823 + 44.1317i) q^{8} +(470.872 + 342.109i) q^{9} +O(q^{10})\)	\(q+(6.29405 - 8.66302i) q^{2} +(3.74624 - 11.5298i) q^{3} +(-15.6557 - 48.1834i) q^{4} +(-15.2392 + 11.0719i) q^{5} +(-76.3035 - 105.023i) q^{6} +(51.6547 - 16.7836i) q^{7} +(135.823 + 44.1317i) q^{8} +(470.872 + 342.109i) q^{9} +201.705i q^{10} +(-903.134 + 977.706i) q^{11} -614.193 q^{12} +(-502.918 + 692.207i) q^{13} +(179.720 - 553.123i) q^{14} +(70.5668 + 217.182i) q^{15} +(3860.38 - 2804.73i) q^{16} +(-3998.21 - 5503.06i) q^{17} +(5927.39 - 1925.93i) q^{18} +(-819.988 - 266.430i) q^{19} +(772.065 + 560.938i) q^{20} -658.441i q^{21} +(2785.52 + 13977.6i) q^{22} -20739.3 q^{23} +(1017.65 - 1400.68i) q^{24} +(-4718.74 + 14522.8i) q^{25} +(2831.21 + 8713.57i) q^{26} +(12858.3 - 9342.11i) q^{27} +(-1617.39 - 2226.14i) q^{28} +(21841.3 - 7096.68i) q^{29} +(2325.61 + 755.636i) q^{30} +(8066.57 + 5860.71i) q^{31} -41955.6i q^{32} +(7889.35 + 14075.6i) q^{33} -72838.1 q^{34} +(-601.349 + 827.686i) q^{35} +(9112.12 - 28044.2i) q^{36} +(-3362.77 - 10349.5i) q^{37} +(-7469.14 + 5426.65i) q^{38} +(6096.92 + 8391.69i) q^{39} +(-2558.46 + 831.294i) q^{40} +(85983.0 + 27937.6i) q^{41} +(-5704.09 - 4144.26i) q^{42} -26427.6i q^{43} +(61248.5 + 28209.4i) q^{44} -10963.5 q^{45} +(-130534. + 179665. i) q^{46} +(41521.0 - 127789. i) q^{47} +(-17875.9 - 55016.4i) q^{48} +(-92793.5 + 67418.4i) q^{49} +(96111.3 + 132286. i) q^{50} +(-78427.2 + 25482.5i) q^{51} +(41226.4 + 13395.3i) q^{52} +(-12038.9 - 8746.77i) q^{53} -170192. i q^{54} +(2937.95 - 24898.9i) q^{55} +7756.60 q^{56} +(-6143.75 + 8456.15i) q^{57} +(75991.9 - 233879. i) q^{58} +(-92965.2 - 286117. i) q^{59} +(9359.82 - 6800.31i) q^{60} +(218947. + 301355. i) q^{61} +(101543. - 32993.3i) q^{62} +(30064.6 + 9768.58i) q^{63} +(-116398. - 84568.3i) q^{64} -16116.9i q^{65} +(171594. + 20247.2i) q^{66} -189715. q^{67} +(-202561. + 278802. i) q^{68} +(-77694.4 + 239119. i) q^{69} +(3385.34 + 10419.0i) q^{70} +(-333295. + 242153. i) q^{71} +(48857.6 + 67246.7i) q^{72} +(102292. - 33236.7i) q^{73} +(-110824. - 36008.8i) q^{74} +(149767. + 108812. i) q^{75} +43681.0i q^{76} +(-30241.6 + 65661.0i) q^{77} +111072. q^{78} +(312971. - 430768. i) q^{79} +(-27775.3 + 85483.7i) q^{80} +(71574.1 + 220282. i) q^{81} +(783205. - 569032. i) q^{82} +(-435941. - 600021. i) q^{83} +(-31726.0 + 10308.4i) q^{84} +(121859. + 39594.4i) q^{85} +(-228943. - 166337. i) q^{86} -278411. i q^{87} +(-165814. + 92938.5i) q^{88} -493938. q^{89} +(-69005.0 + 94977.3i) q^{90} +(-14360.3 + 44196.5i) q^{91} +(324689. + 999290. i) q^{92} +(97791.9 - 71049.9i) q^{93} +(-845700. - 1.16401e6i) q^{94} +(15445.9 - 5018.67i) q^{95} +(-483738. - 157176. i) q^{96} +(1.03679e6 + 753274. i) q^{97} +1.22821e6i q^{98} +(-759743. + 151405. i) 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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