LMFDB - Embedded newform 400.2.bl.a.189.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(29,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 15, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("400.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.bl (of order $20$, degree $8$, 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$464$
Relative dimension:	$58$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			189.27
Character	$\chi$	$=$	400.189
Dual form			400.2.bl.a.309.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.199256 - 1.40011i) q^{2} +(0.983149 + 1.92954i) q^{3} +(-1.92059 + 0.557958i) q^{4} +(1.17859 - 1.90024i) q^{5} +(2.50566 - 1.76098i) q^{6} +0.337437 q^{7} +(1.16389 + 2.57786i) q^{8} +(-0.993180 + 1.36700i) q^{9} +O(q^{10})$	\(q+(-0.199256 - 1.40011i) q^{2} +(0.983149 + 1.92954i) q^{3} +(-1.92059 + 0.557958i) q^{4} +(1.17859 - 1.90024i) q^{5} +(2.50566 - 1.76098i) q^{6} +0.337437 q^{7} +(1.16389 + 2.57786i) q^{8} +(-0.993180 + 1.36700i) q^{9} +(-2.89538 - 1.27152i) q^{10} +(0.168908 - 1.06644i) q^{11} +(-2.96483 - 3.15730i) q^{12} +(4.26896 - 0.676137i) q^{13} +(-0.0672364 - 0.472448i) q^{14} +(4.82532 + 0.405912i) q^{15} +(3.37736 - 2.14322i) q^{16} +(1.29208 - 0.419821i) q^{17} +(2.11184 + 1.11818i) q^{18} +(-2.40298 + 4.71610i) q^{19} +(-1.20334 + 4.30720i) q^{20} +(0.331751 + 0.651098i) q^{21} +(-1.52679 - 0.0239942i) q^{22} +(0.226540 - 0.164591i) q^{23} +(-3.82980 + 4.78019i) q^{24} +(-2.22185 - 4.47922i) q^{25} +(-1.79728 - 5.84228i) q^{26} +(2.80262 + 0.443891i) q^{27} +(-0.648080 + 0.188276i) q^{28} +(6.90978 - 3.52071i) q^{29} +(-0.393154 - 6.83684i) q^{30} +(1.69748 + 5.22431i) q^{31} +(-3.67370 - 4.30162i) q^{32} +(2.22381 - 0.722558i) q^{33} +(-0.845248 - 1.72539i) q^{34} +(0.397700 - 0.641213i) q^{35} +(1.14477 - 3.17960i) q^{36} +(0.130366 + 0.823099i) q^{37} +(7.08185 + 2.42471i) q^{38} +(5.50166 + 7.57238i) q^{39} +(6.27031 + 0.826563i) q^{40} +(1.79636 - 2.47248i) q^{41} +(0.845504 - 0.594222i) q^{42} +(-4.82814 - 4.82814i) q^{43} +(0.270627 + 2.14245i) q^{44} +(1.42707 + 3.49841i) q^{45} +(-0.275584 - 0.284384i) q^{46} +(-2.30680 - 0.749523i) q^{47} +(7.45588 + 4.40965i) q^{48} -6.88614 q^{49} +(-5.82866 + 4.00334i) q^{50} +(2.08037 + 2.08037i) q^{51} +(-7.82169 + 3.68049i) q^{52} +(-8.22391 + 4.19029i) q^{53} +(0.0630567 - 4.01241i) q^{54} +(-1.82743 - 1.57787i) q^{55} +(0.392740 + 0.869866i) q^{56} -11.4624 q^{57} +(-6.30618 - 8.97290i) q^{58} +(-4.60509 + 0.729375i) q^{59} +(-9.49397 + 1.91274i) q^{60} +(-8.58235 - 1.35931i) q^{61} +(6.97636 - 3.41763i) q^{62} +(-0.335136 + 0.461275i) q^{63} +(-5.29072 + 6.00069i) q^{64} +(3.74653 - 8.90896i) q^{65} +(-1.45476 - 2.96959i) q^{66} +(-4.75211 - 2.42132i) q^{67} +(-2.24731 + 1.52723i) q^{68} +(0.540307 + 0.275300i) q^{69} +(-0.977011 - 0.429057i) q^{70} +(12.3535 + 4.01390i) q^{71} +(-4.67987 - 0.969246i) q^{72} +(-8.25632 + 5.99857i) q^{73} +(1.12645 - 0.346534i) q^{74} +(6.45841 - 8.69088i) q^{75} +(1.98375 - 10.3985i) q^{76} +(0.0569959 - 0.359858i) q^{77} +(9.50590 - 9.21174i) q^{78} +(-2.56248 + 7.88650i) q^{79} +(-0.0921200 - 8.94380i) q^{80} +(3.46532 + 10.6652i) q^{81} +(-3.81966 - 2.02244i) q^{82} +(-12.6973 - 6.46961i) q^{83} +(-1.00045 - 1.06539i) q^{84} +(0.725066 - 2.95006i) q^{85} +(-5.79788 + 7.72195i) q^{86} +(13.5867 + 9.87130i) q^{87} +(2.94573 - 0.805803i) q^{88} +(5.62268 + 7.73896i) q^{89} +(4.61379 - 2.69513i) q^{90} +(1.44051 - 0.228154i) q^{91} +(-0.343257 + 0.442512i) q^{92} +(-8.41163 + 8.41163i) q^{93} +(-0.589770 + 3.37911i) q^{94} +(6.12963 + 10.1246i) q^{95} +(4.68834 - 11.3177i) q^{96} +(-6.60997 - 2.14771i) q^{97} +(1.37210 + 9.64132i) q^{98} +(1.29007 + 1.29007i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 464 q - 10 q^{2} - 10 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} - 40 q^{8}+O(q^{10}) $ 464 * q - 10 * q^2 - 10 * q^3 - 6 * q^4 - 8 * q^5 - 6 * q^6 - 40 * q^8	$ 464 q - 10 q^{2} - 10 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} - 40 q^{8} - 2 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 18 q^{14} - 16 q^{15} - 6 q^{16} - 20 q^{17} - 6 q^{19} + 6 q^{20} - 24 q^{21} - 10 q^{22} - 16 q^{24} - 36 q^{26} - 10 q^{27} - 50 q^{28} - 6 q^{29} + 14 q^{30} - 36 q^{31} - 20 q^{33} - 46 q^{34} - 36 q^{35} + 38 q^{36} - 10 q^{37} + 60 q^{38} - 84 q^{40} - 70 q^{42} + 36 q^{44} - 24 q^{45} + 2 q^{46} - 20 q^{47} - 140 q^{48} + 336 q^{49} - 46 q^{50} - 28 q^{51} + 80 q^{52} - 10 q^{53} - 30 q^{54} - 48 q^{56} - 10 q^{58} - 6 q^{59} + 112 q^{60} - 6 q^{61} - 10 q^{62} - 160 q^{63} - 24 q^{64} - 48 q^{65} - 104 q^{66} - 70 q^{67} + 6 q^{69} - 100 q^{70} - 10 q^{72} + 28 q^{74} - 46 q^{75} + 44 q^{76} - 80 q^{77} - 10 q^{78} - 52 q^{79} - 2 q^{80} + 72 q^{81} - 10 q^{83} + 28 q^{84} - 18 q^{85} + 34 q^{86} + 100 q^{88} + 74 q^{90} - 48 q^{91} + 80 q^{92} - 6 q^{94} - 40 q^{95} + 54 q^{96} - 20 q^{97} - 100 q^{98} - 64 q^{99}+O(q^{100}) $ 464 * q - 10 * q^2 - 10 * q^3 - 6 * q^4 - 8 * q^5 - 6 * q^6 - 40 * q^8 - 2 * q^10 - 6 * q^11 - 10 * q^12 - 10 * q^13 - 18 * q^14 - 16 * q^15 - 6 * q^16 - 20 * q^17 - 6 * q^19 + 6 * q^20 - 24 * q^21 - 10 * q^22 - 16 * q^24 - 36 * q^26 - 10 * q^27 - 50 * q^28 - 6 * q^29 + 14 * q^30 - 36 * q^31 - 20 * q^33 - 46 * q^34 - 36 * q^35 + 38 * q^36 - 10 * q^37 + 60 * q^38 - 84 * q^40 - 70 * q^42 + 36 * q^44 - 24 * q^45 + 2 * q^46 - 20 * q^47 - 140 * q^48 + 336 * q^49 - 46 * q^50 - 28 * q^51 + 80 * q^52 - 10 * q^53 - 30 * q^54 - 48 * q^56 - 10 * q^58 - 6 * q^59 + 112 * q^60 - 6 * q^61 - 10 * q^62 - 160 * q^63 - 24 * q^64 - 48 * q^65 - 104 * q^66 - 70 * q^67 + 6 * q^69 - 100 * q^70 - 10 * q^72 + 28 * q^74 - 46 * q^75 + 44 * q^76 - 80 * q^77 - 10 * q^78 - 52 * q^79 - 2 * q^80 + 72 * q^81 - 10 * q^83 + 28 * q^84 - 18 * q^85 + 34 * q^86 + 100 * q^88 + 74 * q^90 - 48 * q^91 + 80 * q^92 - 6 * q^94 - 40 * q^95 + 54 * q^96 - 20 * q^97 - 100 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	−0.199256	−	1.40011i	−0.140895	−	0.990025i
$2$	−0.199256	−	1.40011i	−0.140895	−	0.990025i
$3$	0.983149	+	1.92954i	0.567621	+	1.11402i	0.979248	+	0.202667i	$0.0649608\pi$
$3$	0.983149	+	1.92954i	0.567621	+	1.11402i	−0.411627	+	0.911353i	$0.635039\pi$
$4$	−1.92059	+	0.557958i	−0.960297	+	0.278979i
$5$	1.17859	−	1.90024i	0.527081	−	0.849815i
$5$	1.17859	−	1.90024i	0.527081	−	0.849815i
$6$	2.50566	−	1.76098i	1.02293	−	0.718919i
$7$	0.337437			0.127539			0.0637697	−	0.997965i	$-0.479688\pi$
$7$	0.337437			0.127539			0.0637697	+	0.997965i	$0.479688\pi$
$8$	1.16389	+	2.57786i	0.411497	+	0.911411i
$9$	−0.993180	+	1.36700i	−0.331060	+	0.455665i
$10$	−2.89538	−	1.27152i	−0.915601	−	0.402089i
$11$	0.168908	−	1.06644i	0.0509277	−	0.321545i	−0.949052	−	0.315121i	$-0.897955\pi$
$11$	0.168908	−	1.06644i	0.0509277	−	0.321545i	0.999979	−	0.00642437i	$-0.00204495\pi$
$12$	−2.96483	−	3.15730i	−0.855873	−	0.911435i
$13$	4.26896	−	0.676137i	1.18400	−	0.187527i	0.466778	−	0.884375i	$-0.345415\pi$
$13$	4.26896	−	0.676137i	1.18400	−	0.187527i	0.717219	+	0.696848i	$0.245415\pi$
$14$	−0.0672364	−	0.472448i	−0.0179697	−	0.126267i
$15$	4.82532	+	0.405912i	1.24589	+	0.104806i
$16$	3.37736	−	2.14322i	0.844341	−	0.535806i
$17$	1.29208	−	0.419821i	0.313375	−	0.101822i	−0.148107	−	0.988971i	$-0.547318\pi$
$17$	1.29208	−	0.419821i	0.313375	−	0.101822i	0.461482	+	0.887150i	$0.347318\pi$
$18$	2.11184	+	1.11818i	0.497764	+	0.263557i
$19$	−2.40298	+	4.71610i	−0.551280	+	1.08195i	0.432342	+	0.901709i	$0.357687\pi$
$19$	−2.40298	+	4.71610i	−0.551280	+	1.08195i	−0.983623	+	0.180239i	$0.942313\pi$
$20$	−1.20334	+	4.30720i	−0.269074	+	0.963119i
$21$	0.331751	+	0.651098i	0.0723940	+	0.142081i
$22$	−1.52679	−	0.0239942i	−0.325513	−	0.00511558i
$23$	0.226540	−	0.164591i	0.0472369	−	0.0343196i	−0.563916	−	0.825832i	$-0.690706\pi$
$23$	0.226540	−	0.164591i	0.0472369	−	0.0343196i	0.611153	+	0.791512i	$0.290706\pi$
$24$	−3.82980	+	4.78019i	−0.781755	+	0.975752i
$25$	−2.22185	−	4.47922i	−0.444370	−	0.895843i
$26$	−1.79728	−	5.84228i	−0.352475	−	1.14576i
$27$	2.80262	+	0.443891i	0.539364	+	0.0854268i
$28$	−0.648080	+	0.188276i	−0.122476	+	0.0355808i
$29$	6.90978	−	3.52071i	1.28311	−	0.653779i	0.326516	−	0.945192i	$-0.394125\pi$
$29$	6.90978	−	3.52071i	1.28311	−	0.653779i	0.956597	+	0.291413i	$0.0941253\pi$
$30$	−0.393154	−	6.83684i	−0.0717798	−	1.24823i
$31$	1.69748	+	5.22431i	0.304877	+	0.938314i	0.979723	+	0.200356i	$0.0642099\pi$
$31$	1.69748	+	5.22431i	0.304877	+	0.938314i	−0.674846	+	0.737958i	$0.735790\pi$
$32$	−3.67370	−	4.30162i	−0.649425	−	0.760426i
$33$	2.22381	−	0.722558i	0.387115	−	0.125781i
$34$	−0.845248	−	1.72539i	−0.144959	−	0.295902i
$35$	0.397700	−	0.641213i	0.0672236	−	0.108385i
$36$	1.14477	−	3.17960i	0.190795	−	0.529933i
$37$	0.130366	+	0.823099i	0.0214320	+	0.135317i	0.996084	−	0.0884087i	$-0.0281781\pi$
$37$	0.130366	+	0.823099i	0.0214320	+	0.135317i	−0.974652	+	0.223725i	$0.928178\pi$
$38$	7.08185	+	2.42471i	1.14883	+	0.393340i
$39$	5.50166	+	7.57238i	0.880970	+	1.21255i
$40$	6.27031	+	0.826563i	0.991423	+	0.130691i
$41$	1.79636	−	2.47248i	0.280544	−	0.386136i	−0.645370	−	0.763870i	$-0.723297\pi$
$41$	1.79636	−	2.47248i	0.280544	−	0.386136i	0.925914	+	0.377734i	$0.123297\pi$
$42$	0.845504	−	0.594222i	0.130464	−	0.0916904i
$43$	−4.82814	−	4.82814i	−0.736285	−	0.736285i	0.235572	−	0.971857i	$-0.424304\pi$
$43$	−4.82814	−	4.82814i	−0.736285	−	0.736285i	−0.971857	+	0.235572i	$0.924304\pi$
$44$	0.270627	+	2.14245i	0.0407986	+	0.322986i
$45$	1.42707	+	3.49841i	0.212735	+	0.521512i
$46$	−0.275584	−	0.284384i	−0.0406327	−	0.0419302i
$47$	−2.30680	−	0.749523i	−0.336481	−	0.109329i	0.135903	−	0.990722i	$-0.456606\pi$
$47$	−2.30680	−	0.749523i	−0.336481	−	0.109329i	−0.472384	+	0.881393i	$0.656606\pi$
$48$	7.45588	+	4.40965i	1.07616	+	0.636478i
$49$	−6.88614			−0.983734
$50$	−5.82866	+	4.00334i	−0.824297	+	0.566158i
$51$	2.08037	+	2.08037i	0.291309	+	0.291309i
$52$	−7.82169	+	3.68049i	−1.08467	+	0.510392i
$53$	−8.22391	+	4.19029i	−1.12964	+	0.575581i	−0.915939	−	0.401318i	$-0.868552\pi$
$53$	−8.22391	+	4.19029i	−1.12964	+	0.575581i	−0.213702	+	0.976899i	$0.568552\pi$
$54$	0.0630567	−	4.01241i	0.00858093	−	0.546019i
$55$	−1.82743	−	1.57787i	−0.246411	−	0.212759i
$56$	0.392740	+	0.869866i	0.0524821	+	0.116241i
$57$	−11.4624			−1.51823
$58$	−6.30618	−	8.97290i	−0.828042	−	1.17820i
$59$	−4.60509	+	0.729375i	−0.599532	+	0.0949565i	−0.448821	−	0.893621i	$-0.648156\pi$
$59$	−4.60509	+	0.729375i	−0.599532	+	0.0949565i	−0.150710	+	0.988578i	$0.548156\pi$
$60$	−9.49397	+	1.91274i	−1.22567	+	0.246933i
$61$	−8.58235	−	1.35931i	−1.09886	−	0.174042i	−0.419432	−	0.907787i	$-0.637771\pi$
$61$	−8.58235	−	1.35931i	−1.09886	−	0.174042i	−0.679425	+	0.733745i	$0.737771\pi$
$62$	6.97636	−	3.41763i	0.885998	−	0.434039i
$63$	−0.335136	+	0.461275i	−0.0422232	+	0.0581152i
$64$	−5.29072	+	6.00069i	−0.661340	+	0.750087i
$65$	3.74653	−	8.90896i	0.464700	−	1.10502i
$66$	−1.45476	−	2.96959i	−0.179069	−	0.365531i
$67$	−4.75211	−	2.42132i	−0.580563	−	0.295812i	0.138940	−	0.990301i	$-0.455630\pi$
$67$	−4.75211	−	2.42132i	−0.580563	−	0.295812i	−0.719503	+	0.694489i	$0.755630\pi$
$68$	−2.24731	+	1.52723i	−0.272527	+	0.185204i
$69$	0.540307	+	0.275300i	0.0650453	+	0.0331422i
$70$	−0.977011	−	0.429057i	−0.116775	−	0.0512821i
$71$	12.3535	+	4.01390i	1.46609	+	0.476362i	0.929925	−	0.367750i	$-0.119872\pi$
$71$	12.3535	+	4.01390i	1.46609	+	0.476362i	0.536167	+	0.844112i	$0.319872\pi$
$72$	−4.67987	−	0.969246i	−0.551528	−	0.114227i
$73$	−8.25632	+	5.99857i	−0.966329	+	0.702079i	−0.954612	−	0.297852i	$-0.903730\pi$
$73$	−8.25632	+	5.99857i	−0.966329	+	0.702079i	−0.0117170	+	0.999931i	$0.503730\pi$
$74$	1.12645	−	0.346534i	0.130947	−	0.0402837i
$75$	6.45841	−	8.69088i	0.745752	−	1.00354i
$76$	1.98375	−	10.3985i	0.227552	−	1.19279i
$77$	0.0569959	−	0.359858i	0.00649529	−	0.0410096i
$78$	9.50590	−	9.21174i	1.07633	−	1.04302i
$79$	−2.56248	+	7.88650i	−0.288301	+	0.887301i	0.697088	+	0.716985i	$0.254479\pi$
$79$	−2.56248	+	7.88650i	−0.288301	+	0.887301i	−0.985390	+	0.170315i	$0.945521\pi$
$80$	−0.0921200	−	8.94380i	−0.0102993	−	0.999947i
$81$	3.46532	+	10.6652i	0.385036	+	1.18502i
$82$	−3.81966	−	2.02244i	−0.421811	−	0.223341i
$83$	−12.6973	−	6.46961i	−1.39371	−	0.710132i	−0.413950	−	0.910299i	$-0.635851\pi$
$83$	−12.6973	−	6.46961i	−1.39371	−	0.710132i	−0.979762	+	0.200168i	$0.935851\pi$
$84$	−1.00045	−	1.06539i	−0.109158	−	0.116244i
$85$	0.725066	−	2.95006i	0.0786445	−	0.319979i
$86$	−5.79788	+	7.72195i	−0.625201	+	0.832679i
$87$	13.5867	+	9.87130i	1.45664	+	1.05831i
$88$	2.94573	−	0.805803i	0.314016	−	0.0858988i
$89$	5.62268	+	7.73896i	0.596003	+	0.820328i	0.995335	−	0.0964786i	$-0.0307579\pi$
$89$	5.62268	+	7.73896i	0.596003	+	0.820328i	−0.399332	+	0.916806i	$0.630758\pi$
$90$	4.61379	−	2.69513i	0.486337	−	0.284092i
$91$	1.44051	−	0.228154i	0.151006	−	0.0239170i
$92$	−0.343257	+	0.442512i	−0.0357870	+	0.0461351i
$93$	−8.41163	+	8.41163i	−0.872246	+	0.872246i
$94$	−0.589770	+	3.37911i	−0.0608301	+	0.348528i
$95$	6.12963	+	10.1246i	0.628886	+	1.03876i
$96$	4.68834	−	11.3177i	0.478502	−	1.15511i
$97$	−6.60997	−	2.14771i	−0.671140	−	0.218067i	−0.0464280	−	0.998922i	$-0.514784\pi$
$97$	−6.60997	−	2.14771i	−0.671140	−	0.218067i	−0.624712	+	0.780855i	$0.714784\pi$
$98$	1.37210	+	9.64132i	0.138603	+	0.973921i
$99$	1.29007	+	1.29007i	0.129657	+	0.129657i
$100$	6.76649	+	7.36305i	0.676649	+	0.736305i
$101$	−8.68705	+	8.68705i	−0.864394	+	0.864394i	−0.991845	−	0.127451i	$-0.959320\pi$
$101$	−8.68705	+	8.68705i	−0.864394	+	0.864394i	0.127451	+	0.991845i	$0.459320\pi$
$102$	2.49821	−	3.32726i	0.247359	−	0.329448i
$103$	5.45281	−	16.7820i	0.537282	−	1.65358i	−0.201386	−	0.979512i	$-0.564544\pi$
$103$	5.45281	−	16.7820i	0.537282	−	1.65358i	0.738667	−	0.674070i	$-0.235456\pi$
$104$	6.71159	+	10.2178i	0.658126	+	1.00194i
$105$	1.62824	+	0.136970i	0.158900	+	0.0133669i
$106$	7.50552	+	10.6794i	0.729000	+	1.03728i
$107$	5.05330	+	5.05330i	0.488521	+	0.488521i	0.907839	−	0.419319i	$-0.137731\pi$
$107$	5.05330	+	5.05330i	0.488521	+	0.488521i	−0.419319	+	0.907839i	$0.637731\pi$
$108$	−5.63036	+	0.711209i	−0.541782	+	0.0684361i
$109$	−0.576898	−	3.64239i	−0.0552568	−	0.348878i	−0.999791	−	0.0204635i	$-0.993486\pi$
$109$	−0.576898	−	3.64239i	−0.0552568	−	0.348878i	0.944534	−	0.328414i	$-0.106514\pi$
$110$	−1.84505	+	2.87299i	−0.175919	+	0.273929i
$111$	−1.46003	+	1.06077i	−0.138580	+	0.100684i
$112$	1.13965	−	0.723204i	0.107687	−	0.0683363i
$113$	6.44200	−	8.86666i	0.606013	−	0.834105i	−0.390229	−	0.920718i	$-0.627604\pi$
$113$	6.44200	−	8.86666i	0.606013	−	0.834105i	0.996242	+	0.0866127i	$0.0276043\pi$
$114$	2.28395	+	16.0486i	0.213911	+	1.50309i
$115$	−0.0457652	−	0.624466i	−0.00426763	−	0.0582318i
$116$	−11.3065	+	10.6172i	−1.04978	+	0.985784i
$117$	−3.31557	+	6.50718i	−0.306525	+	0.601589i
$118$	1.93879	+	6.30228i	0.178480	+	0.580172i
$119$	0.435995	−	0.141663i	0.0399676	−	0.0129863i
$120$	4.56976	+	12.9114i	0.417160	+	1.17865i
$121$	9.35285	+	3.03892i	0.850259	+	0.276266i
$122$	−0.193096	+	12.2871i	−0.0174821	+	1.11242i
$123$	6.53682	+	1.03533i	0.589406	+	0.0933527i
$124$	−6.17512	−	9.08666i	−0.554542	−	0.816006i
$125$	−11.1303	−	1.05710i	−0.995520	−	0.0945496i
$126$	0.712612	+	0.377314i	0.0634845	+	0.0336138i
$127$	−1.62066	−	2.23065i	−0.143810	−	0.197938i	0.731035	−	0.682340i	$-0.239037\pi$
$127$	−1.62066	−	2.23065i	−0.143810	−	0.197938i	−0.874846	+	0.484401i	$0.839037\pi$
$128$	9.45581	+	6.21189i	0.835784	+	0.549059i
$129$	4.56930	−	14.0629i	0.402305	−	1.23817i
$130$	−13.2200	−	3.47038i	−1.15947	−	0.304372i
$131$	−7.21094	+	14.1523i	−0.630023	+	1.23649i	0.326601	+	0.945162i	$0.394097\pi$
$131$	−7.21094	+	14.1523i	−0.630023	+	1.23649i	−0.956624	+	0.291327i	$0.905903\pi$
$132$	−3.86787	+	2.62853i	−0.336655	+	0.228784i
$133$	−0.810854	+	1.59139i	−0.0703099	+	0.137991i
$134$	−2.44322	+	7.13592i	−0.211062	+	0.616450i
$135$	4.14663	−	4.80249i	0.356885	−	0.413332i
$136$	2.58608	+	2.84217i	0.221754	+	0.243714i
$137$	−8.60930	−	6.25502i	−0.735542	−	0.534403i	0.155770	−	0.987793i	$-0.450214\pi$
$137$	−8.60930	−	6.25502i	−0.735542	−	0.534403i	−0.891312	+	0.453391i	$0.850214\pi$
$138$	0.277790	−	0.811342i	0.0236471	−	0.0690660i
$139$	1.47072	−	9.28576i	0.124745	−	0.787608i	−0.843413	−	0.537266i	$-0.819457\pi$
$139$	1.47072	−	9.28576i	0.124745	−	0.787608i	0.968158	−	0.250342i	$-0.0805430\pi$
$140$	−0.406050	+	1.45341i	−0.0343175	+	0.122836i
$141$	−0.821689	−	5.18794i	−0.0691987	−	0.436904i
$142$	3.15838	−	18.0960i	0.265045	−	1.51858i
$143$		−	4.66681i		−	0.390259i
$144$	−0.424555	+	6.74545i	−0.0353796	+	0.562121i
$145$	1.45359	−	17.2797i	0.120714	−	1.43500i
$146$	10.0437	+	10.3645i	0.831227	+	0.857770i
$147$	−6.77010	−	13.2871i	−0.558388	−	1.09590i
$148$	−0.709635	−	1.50810i	−0.0583317	−	0.123965i
$149$	7.50255	−	7.50255i	0.614633	−	0.614633i	−0.329517	−	0.944150i	$-0.606886\pi$
$149$	7.50255	−	7.50255i	0.614633	−	0.614633i	0.944150	+	0.329517i	$0.106886\pi$
$150$	−13.4550	−	7.31074i	−1.09860	−	0.596920i
$151$			9.37199i			0.762681i	0.924435	+	0.381341i	$0.124538\pi$
$151$			9.37199i			0.762681i	−0.924435	+	0.381341i	$0.875462\pi$
$152$	−14.9543	−	0.705503i	−1.21295	−	0.0572238i
$153$	−0.709372	+	2.18322i	−0.0573493	+	0.176503i
$154$	−0.515196	−	0.00809653i	−0.0415157	−	0.000652437i
$155$	11.9281	+	2.93169i	0.958088	+	0.235479i
$156$	−14.7915	−	11.4738i	−1.18427	−	0.918637i
$157$	−14.7527	+	14.7527i	−1.17739	+	1.17739i	−0.196985	+	0.980407i	$0.563115\pi$
$157$	−14.7527	+	14.7527i	−1.17739	+	1.17739i	−0.980407	+	0.196985i	$0.936885\pi$
$158$	11.5525	+	2.01631i	0.919070	+	0.160409i
$159$	−16.1707	−	11.7487i	−1.28242	−	0.931730i
$160$	−12.5039	+	1.91108i	−0.988521	+	0.151084i
$161$	0.0764431	−	0.0555391i	0.00602456	−	0.00437710i
$162$	14.2419	−	6.97691i	1.11895	−	0.548158i
$163$	5.65513	−	0.895685i	0.442944	−	0.0701555i	0.0690211	−	0.997615i	$-0.478012\pi$
$163$	5.65513	−	0.895685i	0.442944	−	0.0701555i	0.373923	+	0.927460i	$0.378012\pi$
$164$	−2.07054	+	5.75092i	−0.161682	+	0.449071i
$165$	1.24792	−	5.07737i	0.0971503	−	0.395273i
$166$	−6.52812	+	19.0667i	−0.506681	+	1.47986i
$167$	5.51860	+	16.9845i	0.427042	+	1.31430i	0.901025	+	0.433766i	$0.142816\pi$
$167$	5.51860	+	16.9845i	0.427042	+	1.31430i	−0.473983	+	0.880534i	$0.657184\pi$
$168$	−1.29232	+	1.61302i	−0.0997045	+	0.124447i
$169$	5.40314	−	1.75559i	0.415626	−	0.135045i
$170$	−4.27487	−	0.427353i	−0.327867	−	0.0327765i
$171$	−4.06030	−	7.96880i	−0.310499	−	0.609389i
$172$	11.9668	+	6.57900i	0.912461	+	0.501644i
$173$	2.12022	−	13.3865i	0.161197	−	1.01776i	−0.765906	−	0.642952i	$-0.777709\pi$
$173$	2.12022	−	13.3865i	0.161197	−	1.01776i	0.927103	−	0.374806i	$-0.122291\pi$
$174$	11.1136	−	20.9897i	0.842523	−	1.59123i
$175$	−0.749736	−	1.51146i	−0.0566747	−	0.114255i
$176$	−1.71516	−	3.96378i	−0.129285	−	0.298781i
$177$	−5.93485	−	8.16861i	−0.446090	−	0.613991i
$178$	9.71501	−	9.41438i	0.728171	−	0.705638i
$179$	−13.2984	+	6.77586i	−0.993967	+	0.506451i	−0.873791	−	0.486301i	$-0.838346\pi$
$179$	−13.2984	+	6.77586i	−0.993967	+	0.506451i	−0.120175	+	0.992753i	$0.538346\pi$
$180$	−4.69279	−	5.92278i	−0.349780	−	0.441458i
$181$	5.70125	+	2.90493i	0.423770	+	0.215922i	0.652852	−	0.757485i	$-0.273572\pi$
$181$	5.70125	+	2.90493i	0.423770	+	0.215922i	−0.229082	+	0.973407i	$0.573572\pi$
$182$	−0.606469	−	1.97140i	−0.0449545	−	0.146130i
$183$	−5.81489	−	17.8964i	−0.429849	−	1.32294i
$184$	0.687960	+	0.392422i	0.0507171	+	0.0289298i
$185$	1.71774	+	0.722369i	0.126291	+	0.0531096i
$186$	13.4532	+	10.1011i	0.986440	+	0.740649i
$187$	−0.229474	−	1.44884i	−0.0167808	−	0.105950i
$188$	4.84862	+	0.152434i	0.353622	+	0.0111174i
$189$	0.945707	+	0.149785i	0.0687901	+	0.0108953i
$190$	12.9541	−	10.5995i	0.939792	−	0.768969i
$191$	9.98689	+	7.25590i	0.722626	+	0.525018i	0.887222	−	0.461343i	$-0.152632\pi$
$191$	9.98689	+	7.25590i	0.722626	+	0.525018i	−0.164596	+	0.986361i	$0.552632\pi$
$192$	−16.7801	−	4.30907i	−1.21100	−	0.310980i
$193$		−	21.3259i		−	1.53508i	−0.641004	−	0.767538i	$-0.721482\pi$
$193$		−	21.3259i		−	1.53508i	0.641004	−	0.767538i	$-0.278518\pi$
$194$	−1.68995	+	9.68260i	−0.121331	+	0.695170i
$195$	20.8736	−	1.52976i	1.49479	−	0.109548i
$196$	13.2255	−	3.84218i	0.944677	−	0.274441i
$197$	−1.00721	+	0.513197i	−0.0717604	+	0.0365638i	−0.489502	−	0.872002i	$-0.662822\pi$
$197$	−1.00721	+	0.513197i	−0.0717604	+	0.0365638i	0.417742	+	0.908566i	$0.362822\pi$
$198$	1.54918	−	2.06328i	0.110095	−	0.146631i
$199$		−	2.35601i		−	0.167013i	−0.996507	−	0.0835065i	$-0.973388\pi$
$199$		−	2.35601i		−	0.167013i	0.996507	−	0.0835065i	$-0.0266119\pi$
$200$	8.96079	−	10.9409i	0.633624	−	0.773641i
$201$		−	11.5499i		−	0.814667i
$202$	13.8937	+	10.4318i	0.977560	+	0.733982i
$203$	2.33162	−	1.18802i	0.163647	−	0.0833825i
$204$	−5.15629	−	2.83478i	−0.361013	−	0.198474i
$205$	−2.58114	−	6.32755i	−0.180274	−	0.441935i
$206$	−24.5831	−	4.29060i	−1.71279	−	0.298940i
$207$			0.473148i			0.0328860i
$208$	12.9687	−	11.4329i	0.899219	−	0.792729i
$209$	4.62358	+	3.35923i	0.319820	+	0.232363i
$210$	−0.132665	−	2.30701i	−0.00915475	−	0.159199i
$211$	−9.20296	−	1.45761i	−0.633558	−	0.100346i	−0.168609	−	0.985683i	$-0.553927\pi$
$211$	−9.20296	−	1.45761i	−0.633558	−	0.100346i	−0.464949	+	0.885337i	$0.653927\pi$
$212$	13.4568	−	12.6365i	0.924216	−	0.867875i
$213$	4.40037	+	27.7828i	0.301508	+	1.90365i
$214$	6.06825	−	8.08205i	0.414817	−	0.552477i
$215$	−14.8651	+	3.48425i	−1.01379	+	0.237624i
$216$	2.11765	+	7.74139i	0.144088	+	0.526735i
$217$	0.572794	+	1.76288i	0.0388838	+	0.119672i
$218$	−4.98478	+	1.53349i	−0.337612	+	0.103861i
$219$	−19.6917	−	10.0334i	−1.33064	−	0.677994i
$220$	4.39014	+	2.01081i	0.295983	+	0.135569i
$221$	5.23197	−	2.66582i	0.351940	−	0.179323i
$222$	1.77612	+	1.83283i	0.119205	+	0.123012i
$223$	−11.4107	−	15.7054i	−0.764114	−	1.05171i	−0.996861	−	0.0791750i	$-0.974771\pi$
$223$	−11.4107	−	15.7054i	−0.764114	−	1.05171i	0.232747	−	0.972537i	$-0.425229\pi$
$224$	−1.23964	−	1.45153i	−0.0828272	−	0.0969843i
$225$	8.32977	+	1.41141i	0.555318	+	0.0940938i
$226$	−13.6979	−	7.25276i	−0.911169	−	0.482446i
$227$	2.84577	−	17.9675i	0.188881	−	1.19255i	−0.692952	−	0.720984i	$-0.743690\pi$
$227$	2.84577	−	17.9675i	0.188881	−	1.19255i	0.881833	−	0.471562i	$-0.156310\pi$
$228$	22.0146	−	6.39554i	1.45795	−	0.423555i
$229$	−9.88142	−	19.3934i	−0.652982	−	1.28155i	−0.945603	−	0.325321i	$-0.894527\pi$
$229$	−9.88142	−	19.3934i	−0.652982	−	1.28155i	0.292621	−	0.956228i	$-0.405473\pi$
$230$	−0.865200	+	0.188505i	−0.0570496	+	0.0124296i
$231$	0.750395	−	0.243818i	0.0493724	−	0.0160421i
$232$	17.1181	+	13.7147i	1.12386	+	0.900415i
$233$	2.99825	+	9.22767i	0.196422	+	0.604525i	0.999957	+	0.00926720i	$0.00294988\pi$
$233$	2.99825	+	9.22767i	0.196422	+	0.604525i	−0.803535	+	0.595257i	$0.797050\pi$
$234$	9.77138	+	3.34556i	0.638775	+	0.218706i
$235$	−4.14304	+	3.50009i	−0.270262	+	0.228321i
$236$	8.43755	−	3.97028i	0.549238	−	0.258443i
$237$	−17.7366	+	2.80920i	−1.15212	+	0.182477i
$238$	−0.285218	−	0.582212i	−0.0184880	−	0.0377392i
$239$	17.5429	−	12.7457i	1.13476	−	0.824451i	0.148378	−	0.988931i	$-0.452595\pi$
$239$	17.5429	−	12.7457i	1.13476	−	0.824451i	0.986380	+	0.164480i	$0.0525946\pi$
$240$	17.1668	−	8.97083i	1.10811	−	0.579065i
$241$	22.4697	+	16.3252i	1.44740	+	1.05160i	0.986430	+	0.164183i	$0.0524987\pi$
$241$	22.4697	+	16.3252i	1.44740	+	1.05160i	0.460971	+	0.887415i	$0.347501\pi$
$242$	2.39121	−	13.7005i	0.153713	−	0.880702i
$243$	−11.1526	+	11.1526i	−0.715437	+	0.715437i
$244$	17.2417	−	2.17791i	1.10378	−	0.139426i
$245$	−8.11593	+	13.0853i	−0.518508	+	0.835991i
$246$	0.147074	−	9.35854i	0.00937707	−	0.596679i
$247$	−7.06948	+	21.7576i	−0.449820	+	1.38440i
$248$	−11.4919	+	10.4564i	−0.729734	+	0.663982i
$249$		−	30.8606i		−	1.95571i
$250$	0.737720	+	15.7942i	0.0466575	+	0.998911i
$251$	−12.3477	+	12.3477i	−0.779380	+	0.779380i	−0.979725	−	0.200346i	$-0.935793\pi$
$251$	−12.3477	+	12.3477i	−0.779380	+	0.779380i	0.200346	+	0.979725i	$0.435793\pi$
$252$	0.386288	−	1.07291i	0.0243339	−	0.0675873i
$253$	−0.137263	−	0.269393i	−0.00862962	−	0.0169366i
$254$	−2.80022	+	2.71357i	−0.175701	+	0.170264i
$255$	6.40510	−	1.50130i	0.401103	−	0.0940153i
$256$	6.81318	−	14.4769i	0.425824	−	0.904806i
$257$		−	8.40090i		−	0.524034i	−0.965063	−	0.262017i	$-0.915612\pi$
$257$		−	8.40090i		−	0.524034i	0.965063	−	0.262017i	$-0.0843876\pi$
$258$	−20.6000	−	3.59540i	−1.28250	−	0.223840i
$259$	0.0439904	+	0.277744i	0.00273343	+	0.0172582i
$260$	−2.22474	+	19.2009i	−0.137972	+	1.19079i
$261$	−2.04986	+	12.9423i	−0.126883	+	0.801110i
$262$	21.2515	+	7.27616i	1.31292	+	0.449523i
$263$	8.02478	+	5.83035i	0.494829	+	0.359515i	0.807038	−	0.590499i	$-0.201069\pi$
$263$	8.02478	+	5.83035i	0.494829	+	0.359515i	−0.312209	+	0.950013i	$0.601069\pi$
$264$	4.45092	+	4.89168i	0.273935	+	0.301062i
$265$	−1.73004	+	20.5661i	−0.106276	+	1.26336i
$266$	2.38968	+	0.818188i	0.146521	+	0.0501663i
$267$	−9.40468	+	18.4577i	−0.575557	+	1.12959i
$268$	10.4779	+	1.99890i	0.640038	+	0.122102i
$269$	1.01172	−	1.98562i	0.0616858	−	0.121065i	−0.858105	−	0.513474i	$-0.828358\pi$
$269$	1.01172	−	1.98562i	0.0616858	−	0.121065i	0.919791	+	0.392409i	$0.128358\pi$
$270$	−7.55023	−	4.84880i	−0.459493	−	0.295089i
$271$	4.26385	−	13.1228i	0.259011	−	0.797153i	−0.734002	−	0.679147i	$-0.762350\pi$
$271$	4.26385	−	13.1228i	0.259011	−	0.797153i	0.993013	−	0.118006i	$-0.0376501\pi$
$272$	3.46404	−	4.18710i	0.210039	−	0.253880i
$273$	1.85647	+	2.55520i	0.112358	+	0.154648i
$274$	−7.04224	+	13.3003i	−0.425438	+	0.803500i
$275$	−5.15212	+	1.61290i	−0.310685	+	0.0972618i
$276$	−1.19132	−	0.227271i	−0.0717088	−	0.0136801i
$277$	14.4164	+	2.28333i	0.866195	+	0.137192i	0.573690	−	0.819072i	$-0.305511\pi$
$277$	14.4164	+	2.28333i	0.866195	+	0.137192i	0.292505	+	0.956264i	$0.405511\pi$
$278$	−13.2941	−	0.208923i	−0.797327	−	0.0125303i
$279$	−8.82751	−	2.86823i	−0.528489	−	0.171717i
$280$	2.11584	+	0.278913i	0.126445	+	0.0166683i
$281$	26.0445	−	8.46237i	1.55368	−	0.504823i	0.598573	−	0.801069i	$-0.295735\pi$
$281$	26.0445	−	8.46237i	1.55368	−	0.504823i	0.955112	+	0.296246i	$0.0957348\pi$
$282$	−7.09994	+	2.18418i	−0.422795	+	0.130066i
$283$	−1.25983	+	2.47255i	−0.0748891	+	0.146978i	−0.925415	−	0.378955i	$-0.876284\pi$
$283$	−1.25983	+	2.47255i	−0.0748891	+	0.146978i	0.850526	+	0.525933i	$0.176284\pi$
$284$	−25.9657	−	0.816325i	−1.54078	−	0.0484400i
$285$	−13.5095	+	21.7813i	−0.800231	+	1.29021i
$286$	−6.53403	+	0.929890i	−0.386366	+	0.0549855i
$287$	0.606159	−	0.834306i	0.0357804	−	0.0492475i
$288$	9.52894	−	0.749648i	0.561498	−	0.0441734i
$289$	−12.2601	+	8.90747i	−0.721181	+	0.523969i
$290$	−24.4831	+	1.40791i	−1.43770	+	0.0826750i
$291$	−2.35450	−	14.8657i	−0.138023	−	0.871443i
$292$	12.5101	−	16.1275i	0.732097	−	0.943790i
$293$	21.7840	+	21.7840i	1.27263	+	1.27263i	0.944701	+	0.327933i	$0.106352\pi$
$293$	21.7840	+	21.7840i	1.27263	+	1.27263i	0.327933	+	0.944701i	$0.393648\pi$
$294$	−17.2543	+	12.1264i	−1.00629	+	0.707225i
$295$	−4.04152	+	9.61043i	−0.235307	+	0.559541i
$296$	−1.97010	+	1.29406i	−0.114510	+	0.0752159i
$297$	0.946769	−	2.91386i	0.0549371	−	0.169079i
$298$	−11.9993	−	9.00944i	−0.695100	−	0.521903i
$299$	0.855805	−	0.855805i	0.0494925	−	0.0494925i
$300$	−7.55482	+	20.2952i	−0.436178	+	1.17174i
$301$	−1.62920	−	1.62920i	−0.0939053	−	0.0939053i
$302$	13.1218	−	1.86742i	0.755073	−	0.107458i
$303$	−25.3027	−	8.22133i	−1.45360	−	0.472303i
$304$	1.99194	+	21.0781i	0.114246	+	1.20891i
$305$	−12.6981	+	14.7065i	−0.727091	+	0.842091i
$306$	3.19809	+	0.558176i	0.182823	+	0.0319088i
$307$	−17.3242	+	17.3242i	−0.988746	+	0.988746i	−0.999937	−	0.0111910i	$-0.996438\pi$
$307$	−17.3242	+	17.3242i	−0.988746	+	0.988746i	0.0111910	+	0.999937i	$0.496438\pi$
$308$	0.0913198	+	0.722943i	0.00520343	+	0.0411935i
$309$	37.7425	−	5.97782i	2.14710	−	0.340066i
$310$	1.72794	−	17.2848i	0.0981402	−	0.981709i
$311$	−17.4879	−	24.0700i	−0.991648	−	1.36489i	−0.930312	−	0.366769i	$-0.880464\pi$
$311$	−17.4879	−	24.0700i	−0.991648	−	1.36489i	−0.0613360	−	0.998117i	$-0.519536\pi$
$312$	−13.1172	+	22.9959i	−0.742616	+	1.30189i
$313$	23.5173	+	17.0863i	1.32927	+	0.965774i	0.999766	+	0.0216217i	$0.00688295\pi$
$313$	23.5173	+	17.0863i	1.32927	+	0.965774i	0.329508	+	0.944153i	$0.393117\pi$
$314$	23.5949	+	17.7157i	1.33153	+	0.999757i
$315$	0.481548	+	1.18049i	0.0271321	+	0.0665133i
$316$	0.521143	−	16.5765i	0.0293166	−	0.932502i
$317$	18.6155	+	9.48505i	1.04555	+	0.532733i	0.890410	−	0.455160i	$-0.150418\pi$
$317$	18.6155	+	9.48505i	1.04555	+	0.532733i	0.155138	+	0.987893i	$0.450418\pi$
$318$	−13.2273	+	24.9816i	−0.741750	+	1.40090i
$319$	−2.58752	−	7.96357i	−0.144873	−	0.445874i
$320$	5.16719	+	17.1260i	0.288855	+	0.957373i
$321$	−4.78239	+	14.7187i	−0.266927	+	0.821516i
$322$	−0.0929924	−	0.0959619i	−0.00518227	−	0.00534775i
$323$	−1.12491	+	7.10239i	−0.0625916	+	0.395188i
$324$	−12.6062	−	18.5499i	−0.700344	−	1.03055i
$325$	−12.5136	−	17.6193i	−0.694128	−	0.977344i
$326$	−2.38087	−	7.73932i	−0.131864	−	0.428641i
$327$	6.46095	−	4.69416i	0.357292	−	0.259588i
$328$	8.46446	+	1.75307i	0.467372	+	0.0967970i
$329$	−0.778399	−	0.252917i	−0.0429145	−	0.0139438i
$330$	−7.35752	−	0.735522i	−0.405018	−	0.0404891i
$331$	−8.24078	−	4.19889i	−0.452954	−	0.230792i	0.212603	−	0.977139i	$-0.431806\pi$
$331$	−8.24078	−	4.19889i	−0.452954	−	0.230792i	−0.665557	+	0.746347i	$0.731806\pi$
$332$	27.9962	+	5.34091i	1.53649	+	0.293121i
$333$	−1.25465	−	0.639276i	−0.0687544	−	0.0350321i
$334$	22.6805	−	11.1109i	1.24102	−	0.607961i
$335$	−10.2019	+	6.17643i	−0.557389	+	0.337454i
$336$	2.51589	+	1.48798i	0.137253	+	0.0811759i
$337$	−6.41167	+	8.82491i	−0.349266	+	0.480724i	−0.947119	−	0.320882i	$-0.896021\pi$
$337$	−6.41167	+	8.82491i	−0.349266	+	0.480724i	0.597853	+	0.801606i	$0.296021\pi$
$338$	−3.53461	−	7.21516i	−0.192258	−	0.392453i
$339$	23.4420	+	3.71285i	1.27319	+	0.201654i
$340$	0.253452	+	6.07042i	0.0137454	+	0.329215i
$341$	5.85815	−	0.927840i	0.317237	−	0.0502454i
$342$	−10.3481	+	7.27269i	−0.559562	+	0.393262i
$343$	−4.68570			−0.253004
$344$	6.82684	−	18.0657i	0.368079	−	0.974038i
$345$	1.15994	−	0.702249i	0.0624490	−	0.0378078i
$346$	−19.1650	−	0.301186i	−1.03032	−	0.0161919i
$347$	5.38900	−	2.74583i	0.289296	−	0.147404i	−0.303320	−	0.952889i	$-0.598095\pi$
$347$	5.38900	−	2.74583i	0.289296	−	0.147404i	0.592616	+	0.805485i	$0.298095\pi$
$348$	−31.6023	−	11.3780i	−1.69406	−	0.609923i
$349$	−6.78894	−	6.78894i	−0.363404	−	0.363404i	0.501661	−	0.865064i	$-0.332723\pi$
$349$	−6.78894	−	6.78894i	−0.363404	−	0.363404i	−0.865064	+	0.501661i	$0.832723\pi$
$350$	−1.96681	+	1.35088i	−0.105130	+	0.0722074i
$351$	12.2644			0.654625
$352$	−5.20795	+	3.19122i	−0.277585	+	0.170092i
$353$	8.27300	+	2.68806i	0.440328	+	0.143071i	0.520787	−	0.853687i	$-0.325639\pi$
$353$	8.27300	+	2.68806i	0.440328	+	0.143071i	−0.0804592	+	0.996758i	$0.525639\pi$
$354$	−10.2544	+	9.93706i	−0.545014	+	0.528149i
$355$	22.1871	−	18.7439i	1.17757	−	0.994825i
$356$	−15.1169	−	11.7262i	−0.801194	−	0.621486i
$357$	0.701993	+	0.701993i	0.0371534	+	0.0371534i
$358$	12.1367	+	17.2690i	0.641444	+	0.912695i
$359$	−13.7351	+	18.9047i	−0.724911	+	0.997754i	0.274436	+	0.961605i	$0.411509\pi$
$359$	−13.7351	+	18.9047i	−0.724911	+	0.997754i	−0.999346	+	0.0361486i	$0.988491\pi$
$360$	−7.35745	+	7.75056i	−0.387772	+	0.408490i
$361$	−5.29943	−	7.29404i	−0.278917	−	0.383897i
$362$	2.93120	−	8.56117i	0.154061	−	0.449965i
$363$	3.33152	+	21.0344i	0.174859	+	1.10402i
$364$	−2.63933	+	1.24193i	−0.138338	+	0.0650951i
$365$	1.66793	+	22.7589i	0.0873032	+	1.19125i
$366$	−23.8982	+	11.7074i	−1.24918	+	0.611956i
$367$	4.85089	−	1.57615i	0.253215	−	0.0822744i	−0.179659	−	0.983729i	$-0.557500\pi$
$367$	4.85089	−	1.57615i	0.253215	−	0.0822744i	0.432874	+	0.901454i	$0.357500\pi$
$368$	0.412353	−	1.04141i	0.0214954	−	0.0542872i
$369$	1.59575	+	4.91123i	0.0830717	+	0.255668i
$370$	0.669124	−	2.54895i	0.0347861	−	0.132514i
$371$	−2.77506	+	1.41396i	−0.144074	+	0.0734092i
$372$	11.4620	−	20.8487i	0.594277	−	1.08095i
$373$	−8.87524	−	1.40570i	−0.459543	−	0.0727844i	−0.0776288	−	0.996982i	$-0.524735\pi$
$373$	−8.87524	−	1.40570i	−0.459543	−	0.0727844i	−0.381914	+	0.924198i	$0.624735\pi$
$374$	−1.98280	+	0.609977i	−0.102528	+	0.0315412i
$375$	−8.90299	−	22.5155i	−0.459748	−	1.16270i
$376$	−0.752692	−	6.81896i	−0.0388171	−	0.351661i
$377$	27.1171	−	19.7017i	1.39660	−	1.01469i
$378$	0.0212777	−	1.35394i	0.00109441	−	0.0696390i
$379$	−7.24669	−	14.2224i	−0.372238	−	0.730557i	0.626571	−	0.779365i	$-0.284458\pi$
$379$	−7.24669	−	14.2224i	−0.372238	−	0.730557i	−0.998808	+	0.0488073i	$0.984458\pi$
$380$	−17.4216	−	16.0252i	−0.893711	−	0.822073i
$381$	2.71077	−	5.32019i	0.138877	−	0.272562i
$382$	8.16908	−	15.4285i	0.417967	−	0.789390i
$383$	28.4178	−	9.23349i	1.45208	−	0.471809i	0.526439	−	0.850213i	$-0.323527\pi$
$383$	28.4178	−	9.23349i	1.45208	−	0.471809i	0.925641	+	0.378404i	$0.123527\pi$
$384$	−2.68961	+	24.3526i	−0.137254	+	1.24274i
$385$	−0.616643	−	0.532431i	−0.0314271	−	0.0271352i
$386$	−29.8586	+	4.24932i	−1.51976	+	0.216285i
$387$	11.3953	−	1.80483i	0.579254	−	0.0917448i
$388$	13.8934	+	0.436789i	0.705330	+	0.0221746i
$389$	4.50057	−	28.4155i	0.228188	−	1.44072i	−0.561634	−	0.827386i	$-0.689827\pi$
$389$	4.50057	−	28.4155i	0.228188	−	1.44072i	0.789822	−	0.613336i	$-0.210173\pi$
$390$	−6.30100	−	28.9204i	−0.319064	−	1.46444i
$391$	0.223608	−	0.307771i	0.0113084	−	0.0155646i
$392$	−8.01471	−	17.7515i	−0.404804	−	0.896586i
$393$	−34.3968			−1.73509
$394$	0.919222	+	1.30794i	0.0463097	+	0.0658929i
$395$	11.9662	+	14.1643i	0.602083	+	0.712683i
$396$	−3.19750	−	1.75789i	−0.160680	−	0.0883374i
$397$	1.50049	+	2.94487i	0.0753072	+	0.147799i	0.925590	−	0.378527i	$-0.123569\pi$
$397$	1.50049	+	2.94487i	0.0753072	+	0.147799i	−0.850283	+	0.526326i	$0.823569\pi$
$398$	−3.29866	+	0.469448i	−0.165347	+	0.0235313i
$399$	−3.86784			−0.193634
$400$	−17.1040	−	10.3660i	−0.855198	−	0.518301i
$401$	14.0370			0.700976			0.350488	−	0.936567i	$-0.386016\pi$
$401$	14.0370			0.700976			0.350488	+	0.936567i	$0.386016\pi$
$402$	−16.1711	+	2.30138i	−0.806541	+	0.114783i
$403$	10.7788	+	21.1547i	0.536932	+	1.05379i
$404$	11.8373	−	21.5313i	0.588927	−	1.07122i
$405$	24.3506	+	5.98490i	1.20999	+	0.297392i
$406$	−2.12794	−	3.02779i	−0.105608	−	0.150267i
$407$	0.899809			0.0446019
$408$	−2.94157	+	7.78421i	−0.145629	+	0.385376i
$409$	−16.7230	+	23.0173i	−0.826900	+	1.13813i	0.161592	+	0.986858i	$0.448337\pi$
$409$	−16.7230	+	23.0173i	−0.826900	+	1.13813i	−0.988492	+	0.151272i	$0.951663\pi$
$410$	−8.34494	+	4.87467i	−0.412127	+	0.240743i
$411$	3.60508	−	22.7616i	0.177826	−	1.12275i
$412$	−1.10896	+	35.2739i	−0.0546347	+	1.73782i
$413$	−1.55393	+	0.246118i	−0.0764639	+	0.0121107i
$414$	0.662457	−	0.0942774i	0.0325580	−	0.00463348i
$415$	−27.2588	+	16.5030i	−1.33808	+	0.810100i
$416$	−18.5914	−	15.8795i	−0.911517	−	0.778558i
$417$	19.3632	−	6.29147i	0.948218	−	0.308095i
$418$	3.78200	−	7.14285i	0.184984	−	0.349368i
$419$	−13.5902	+	26.6723i	−0.663924	+	1.30302i	0.275841	+	0.961203i	$0.411044\pi$
$419$	−13.5902	+	26.6723i	−0.663924	+	1.30302i	−0.939765	+	0.341821i	$0.888956\pi$
$420$	−3.20362	+	0.645429i	−0.156321	+	0.0314937i
$421$	−9.72797	−	19.0922i	−0.474112	−	0.930497i	−0.996948	−	0.0780641i	$-0.975126\pi$
$421$	−9.72797	−	19.0922i	−0.474112	−	0.930497i	0.522836	−	0.852433i	$-0.324874\pi$
$422$	−0.207060	+	13.1756i	−0.0100795	+	0.641376i
$423$	3.31566	−	2.40897i	0.161213	−	0.117128i
$424$	−20.3737	−	16.3230i	−0.989435	−	0.792717i
$425$	−4.75127	−	4.85471i	−0.230471	−	0.235488i
$426$	38.0221	−	11.6969i	1.84218	−	0.566715i
$427$	−2.89601	−	0.458682i	−0.140148	−	0.0221972i
$428$	−12.5249	−	6.88580i	−0.605412	−	0.332838i
$429$	9.00479	−	4.58817i	0.434756	−	0.221519i
$430$	7.84027	+	20.1184i	0.378091	+	0.970195i
$431$	3.12790	+	9.62670i	0.150666	+	0.463702i	0.997696	−	0.0678430i	$-0.0216117\pi$
$431$	3.12790	+	9.62670i	0.150666	+	0.463702i	−0.847030	+	0.531545i	$0.821612\pi$
$432$	10.4168	−	4.50745i	0.501179	−	0.216865i
$433$	−16.7538	+	5.44364i	−0.805136	+	0.261605i	−0.682536	−	0.730852i	$-0.739123\pi$
$433$	−16.7538	+	5.44364i	−0.805136	+	0.261605i	−0.122600	+	0.992456i	$0.539123\pi$
$434$	2.35408	−	1.15324i	0.113000	−	0.0553571i
$435$	34.7710	−	14.1838i	1.66714	−	0.680061i
$436$	3.14029	+	6.67367i	0.150393	+	0.319611i
$437$	0.231858	+	1.46389i	0.0110913	+	0.0700276i
$438$	−10.1241	+	29.5696i	−0.483750	+	1.41289i
$439$	15.2588	+	21.0019i	0.728261	+	1.00236i	0.999209	+	0.0397709i	$0.0126628\pi$
$439$	15.2588	+	21.0019i	0.728261	+	1.00236i	−0.270948	+	0.962594i	$0.587337\pi$
$440$	1.94059	−	6.54732i	0.0925140	−	0.312131i
$441$	6.83917	−	9.41331i	0.325675	−	0.448253i
$442$	−4.77493	−	6.79413i	−0.227120	−	0.323164i
$443$	−27.7820	−	27.7820i	−1.31996	−	1.31996i	−0.913802	−	0.406159i	$-0.866868\pi$
$443$	−27.7820	−	27.7820i	−1.31996	−	1.31996i	−0.406159	−	0.913802i	$-0.633132\pi$
$444$	2.21226	−	2.85196i	0.104989	−	0.135348i
$445$	21.3327	−	1.56341i	1.01127	−	0.0741127i
$446$	−19.7156	+	19.1055i	−0.933561	+	0.904672i
$447$	21.8526	+	7.10033i	1.03359	+	0.335834i
$448$	−1.78529	+	2.02486i	−0.0843468	+	0.0956656i
$449$	−10.8418			−0.511654			−0.255827	−	0.966723i	$-0.582348\pi$
$449$	−10.8418			−0.511654			−0.255827	+	0.966723i	$0.582348\pi$
$450$	0.316365	−	11.9438i	0.0149136	−	0.563035i
$451$	−2.33334	−	2.33334i	−0.109873	−	0.109873i
$452$	−7.42525	+	20.6236i	−0.349254	+	0.970054i
$453$	−18.0836	+	9.21406i	−0.849642	+	0.432914i
$454$	−25.7235	−	0.404255i	−1.20726	−	0.0189726i
$455$	1.26422	−	3.00622i	0.0592675	−	0.140934i
$456$	−13.3410	−	29.5484i	−0.624748	−	1.38373i
$457$	−28.4452			−1.33061			−0.665304	−	0.746572i	$-0.731698\pi$
$457$	−28.4452			−1.33061			−0.665304	+	0.746572i	$0.731698\pi$
$458$	−25.1838	+	17.6993i	−1.17676	+	0.827033i
$459$	3.80755	−	0.603057i	0.177721	−	0.0281483i
$460$	0.436323	+	1.17381i	0.0203437	+	0.0547292i
$461$	38.9087	+	6.16253i	1.81216	+	0.287018i	0.968345	−	0.249617i	$-0.0803049\pi$
$461$	38.9087	+	6.16253i	1.81216	+	0.287018i	0.843814	+	0.536635i	$0.180305\pi$
$462$	−0.490892	−	1.00205i	−0.0228384	−	0.0466196i
$463$	2.59949	−	3.57789i	0.120809	−	0.166279i	−0.744329	−	0.667813i	$-0.767231\pi$
$463$	2.59949	−	3.57789i	0.120809	−	0.166279i	0.865138	+	0.501534i	$0.167231\pi$
$464$	15.7912	−	26.6999i	0.733087	−	1.23951i
$465$	6.07029	+	25.8980i	0.281503	+	1.20099i
$466$	12.3223	−	6.03653i	0.570819	−	0.279637i
$467$	−32.2563	−	16.4354i	−1.49264	−	0.760539i	−0.498324	−	0.866991i	$-0.666051\pi$
$467$	−32.2563	−	16.4354i	−1.49264	−	0.760539i	−0.994318	+	0.106451i	$0.966051\pi$
$468$	2.73713	−	14.3476i	0.126524	−	0.663218i
$469$	−1.60354	−	0.817045i	−0.0740446	−	0.0377276i
$470$	5.72603	+	5.10328i	0.264122	+	0.235397i
$471$	−42.9699	−	13.9618i	−1.97995	−	0.643324i
$472$	−7.24005	−	11.0224i	−0.333250	−	0.507345i
$473$	−5.96446	+	4.33343i	−0.274246	+	0.199251i
$474$	7.46730	+	24.2734i	0.342985	+	1.11491i
$475$	26.4635	+	0.284956i	1.21423	+	0.0130747i
$476$	−0.758328	+	0.515345i	−0.0347579	+	0.0236208i
$477$	2.43972	−	15.4038i	0.111707	−	0.705290i
$478$	−21.3409	−	22.0223i	−0.976108	−	1.00728i
$479$	−6.68957	+	20.5884i	−0.305654	+	0.940707i	0.673778	+	0.738934i	$0.264670\pi$
$479$	−6.68957	+	20.5884i	−0.305654	+	0.940707i	−0.979432	+	0.201773i	$0.935330\pi$
$480$	−15.9807	−	22.2479i	−0.729416	−	1.01547i
$481$	1.11306	+	3.42563i	0.0507510	+	0.156195i
$482$	18.3798	−	34.7129i	0.837176	−	1.58113i
$483$	0.182320	+	0.0928966i	0.00829584	+	0.00422694i
$484$	−19.6586	−	0.618040i	−0.893574	−	0.0280927i
$485$	−11.8716	+	10.0293i	−0.539062	+	0.455406i
$486$	17.8370	+	13.3926i	0.809102	+	0.607498i
$487$	12.4896	+	9.07421i	0.565957	+	0.411192i	0.833634	−	0.552317i	$-0.186256\pi$
$487$	12.4896	+	9.07421i	0.565957	+	0.411192i	−0.267677	+	0.963509i	$0.586256\pi$
$488$	−6.48481	−	23.7062i	−0.293553	−	1.07313i
$489$	7.28810	+	10.0312i	0.329579	+	0.453627i
$490$	19.9380	+	8.75583i	0.900707	+	0.395548i
$491$	−10.8516	+	1.71873i	−0.489727	+	0.0775651i	−0.396414	−	0.918072i	$-0.629746\pi$
$491$	−10.8516	+	1.71873i	−0.489727	+	0.0775651i	−0.0933126	+	0.995637i	$0.529746\pi$
$492$	−13.1323	+	1.65883i	−0.592048	+	0.0747856i
$493$	7.44990	−	7.44990i	0.335526	−	0.335526i
$494$	31.8716	+	5.56269i	1.43397	+	0.250277i
$495$	3.97190	−	0.930982i	0.178524	−	0.0418445i
$496$	16.9299	+	14.0063i	0.760174	+	0.628902i
$497$	4.16854	+	1.35444i	0.186984	+	0.0607549i
$498$	−43.2081	+	6.14914i	−1.93620	+	0.275550i
$499$	18.8806	+	18.8806i	0.845211	+	0.845211i	0.989531	−	0.144320i	$-0.0460995\pi$
$499$	18.8806	+	18.8806i	0.845211	+	0.845211i	−0.144320	+	0.989531i	$0.546099\pi$
$500$	21.9665	−	4.17997i	0.982373	−	0.186934i
$501$	−27.3466	+	27.3466i	−1.22176	+	1.22176i
$502$	19.7484	+	14.8277i	0.881416	+	0.661794i
$503$	6.21176	−	19.1178i	0.276969	−	0.852422i	−0.711723	−	0.702460i	$-0.752085\pi$
$503$	6.21176	−	19.1178i	0.276969	−	0.852422i	0.988692	−	0.149962i	$-0.0479150\pi$
$504$	−1.57916	−	0.327060i	−0.0703416	−	0.0145684i
$505$	6.26905	+	26.7460i	0.278969	+	1.19018i
$506$	−0.349828	+	0.245860i	−0.0155518	+	0.0109298i
$507$	8.69956	+	8.69956i	0.386361	+	0.386361i
$508$	4.35724	+	3.37991i	0.193321	+	0.149959i
$509$	3.23499	+	20.4249i	0.143388	+	0.905319i	0.949548	+	0.313621i	$0.101542\pi$
$509$	3.23499	+	20.4249i	0.143388	+	0.905319i	−0.806160	+	0.591698i	$0.798458\pi$
$510$	−3.37824	−	8.66867i	−0.149591	−	0.383855i
$511$	−2.78599	+	2.02414i	−0.123245	+	0.0895427i
$512$	−21.6268	−	6.65458i	−0.955777	−	0.294093i
$513$	−8.82805	+	12.1508i	−0.389768	+	0.536470i
$514$	−11.7622	+	1.67393i	−0.518806	+	0.0738338i
$515$	−25.4633	−	30.1408i	−1.12205	−	1.32816i
$516$	−0.929280	+	29.5586i	−0.0409093	+	1.30124i
$517$	−1.18896	+	2.33347i	−0.0522904	+	0.102626i
$518$	0.380106	−	0.116933i	0.0167009	−	0.00513776i
$519$	27.9143	−	9.06990i	1.22530	−	0.398124i
$520$	27.3266	−	0.711025i	1.19835	−	0.0311805i
$521$	−7.15296	−	2.32414i	−0.313377	−	0.101822i	0.148106	−	0.988972i	$-0.452682\pi$
$521$	−7.15296	−	2.32414i	−0.313377	−	0.101822i	−0.461483	+	0.887149i	$0.652682\pi$
$522$	18.5291	+	0.291193i	0.810996	+	0.0127452i
$523$	−8.59081	−	1.36065i	−0.375650	−	0.0594971i	−0.0342450	−	0.999413i	$-0.510903\pi$
$523$	−8.59081	−	1.36065i	−0.375650	−	0.0594971i	−0.341405	+	0.939916i	$0.610903\pi$
$524$	5.95291	−	31.2042i	0.260054	−	1.36316i
$525$	2.17931	−	2.93263i	0.0951128	−	0.127990i
$526$	6.56412	−	12.3973i	0.286209	−	0.540547i
$527$	4.38655	+	6.03757i	0.191081	+	0.263001i
$528$	5.96200	−	7.20646i	0.259463	−	0.313621i
$529$	−7.08316	+	21.7997i	−0.307964	+	0.947814i
$530$	29.1394	−	1.67567i	1.26573	−	0.0727863i
$531$	3.57663	−	7.01954i	0.155213	−	0.304622i
$532$	0.669392	−	3.50884i	0.0290218	−	0.152127i
$533$	5.99685	−	11.7695i	0.259753	−	0.509793i
$534$	27.7167	+	9.48974i	1.19942	+	0.410661i
$535$	15.5583	−	3.64673i	0.672642	−	0.157662i
$536$	0.710889	−	15.0684i	0.0307057	−	0.650857i
$537$	−26.1485	−	18.9980i	−1.12839	−	0.819826i
$538$	−2.98167	−	1.02087i	−0.128549	−	0.0440130i
$539$	−1.16312	+	7.34368i	−0.0500993	+	0.316315i
$540$	−5.28441	+	11.5373i	−0.227405	+	0.496485i
$541$	−1.01848	−	6.43040i	−0.0437877	−	0.276464i	0.956074	−	0.293127i	$-0.0946959\pi$
$541$	−1.01848	−	6.43040i	−0.0437877	−	0.276464i	−0.999861	+	0.0166626i	$0.994696\pi$
$542$	−19.2229	−	3.35505i	−0.825694	−	0.144112i
$543$			13.8567i			0.594650i
$544$	−6.55262	−	4.01573i	−0.280941	−	0.172173i
$545$	−7.60135	−	3.19664i	−0.325606	−	0.136929i
$546$	3.20765	−	3.10839i	0.137275	−	0.133027i
$547$	13.3685	+	26.2371i	0.571594	+	1.12182i	0.978094	+	0.208165i	$0.0667492\pi$
$547$	13.3685	+	26.2371i	0.571594	+	1.12182i	−0.406500	+	0.913651i	$0.633251\pi$
$548$	20.0250	+	7.20973i	0.855426	+	0.307984i
$549$	10.3820	−	10.3820i	0.443093	−	0.443093i
$550$	3.28483	+	6.89214i	0.140066	+	0.293882i
$551$			41.0474i			1.74868i
$552$	−0.0808269	+	1.71325i	−0.00344022	+	0.0729210i
$553$	−0.864677	+	2.66120i	−0.0367698	+	0.113166i
$554$	0.324357	−	20.6394i	0.0137806	−	0.876884i
$555$	0.294953	+	4.02463i	0.0125200	+	0.170836i
$556$	2.35641	+	18.6548i	0.0999342	+	0.791139i
$557$	26.7263	−	26.7263i	1.13243	−	1.13243i	0.142656	−	0.989772i	$-0.454436\pi$
$557$	26.7263	−	26.7263i	1.13243	−	1.13243i	0.989772	−	0.142656i	$-0.0455642\pi$
$558$	−2.25690	+	12.9310i	−0.0955421	+	0.547412i
$559$	−23.8756	−	17.3467i	−1.00983	−	0.733686i
$560$	−0.0310847	−	3.01797i	−0.00131357	−	0.127533i
$561$	2.56998	−	1.86720i	0.108505	−	0.0788333i
$562$	−17.0377	−	34.7789i	−0.718693	−	1.46706i
$563$	−15.7912	+	2.50108i	−0.665521	+	0.105408i	−0.480049	−	0.877242i	$-0.659381\pi$
$563$	−15.7912	+	2.50108i	−0.665521	+	0.105408i	−0.185471	+	0.982650i	$0.559381\pi$
$564$	4.47279	+	9.50546i	0.188338	+	0.400252i
$565$	−9.25633	−	22.6915i	−0.389417	−	0.954640i
$566$	3.71287	+	1.27122i	0.156063	+	0.0534335i
$567$	1.16933	+	3.59882i	0.0491072	+	0.151136i
$568$	4.03087	+	36.5174i	0.169131	+	1.53223i
$569$	10.5520	−	3.42854i	0.442362	−	0.143732i	−0.0793633	−	0.996846i	$-0.525289\pi$
$569$	10.5520	−	3.42854i	0.442362	−	0.143732i	0.521725	+	0.853114i	$0.325289\pi$
$570$	33.1880	+	14.5746i	1.39009	+	0.610463i
$571$	−9.43266	−	18.5126i	−0.394745	−	0.774730i	0.605025	−	0.796207i	$-0.293163\pi$
$571$	−9.43266	−	18.5126i	−0.394745	−	0.774730i	−0.999769	+	0.0214769i	$0.993163\pi$
$572$	2.60389	+	8.96305i	0.108874	+	0.374764i
$573$	−4.18194	+	26.4037i	−0.174703	+	1.10303i
$574$	−1.28890	−	0.682446i	−0.0537975	−	0.0284848i
$575$	−1.24058	−	0.649025i	−0.0517356	−	0.0270662i
$576$	−2.94828	−	13.1922i	−0.122845	−	0.549673i
$577$	4.61654	+	6.35412i	0.192189	+	0.264525i	0.894227	−	0.447614i	$-0.147726\pi$
$577$	4.61654	+	6.35412i	0.192189	+	0.264525i	−0.702038	+	0.712140i	$0.747726\pi$
$578$	14.9143	+	15.3905i	0.620353	+	0.640162i
$579$	41.1492	−	20.9666i	1.71010	−	0.871341i
$580$	6.84961	+	33.9984i	0.284415	+	1.41171i
$581$	−4.28455	−	2.18309i	−0.177753	−	0.0905698i
$582$	−20.3444	+	6.25862i	−0.843303	+	0.259428i
$583$	3.07963	+	9.47812i	0.127545	+	0.392543i
$584$	−25.0729	−	14.3020i	−1.03752	−	0.591819i
$585$	8.45752	+	13.9697i	0.349675	+	0.577575i
$586$	26.1593	−	34.8405i	1.08063	−	1.43925i
$587$	0.414128	+	2.61470i	0.0170929	+	0.107920i	0.994760	−	0.102241i	$-0.0326012\pi$
$587$	0.414128	+	2.61470i	0.0170929	+	0.107920i	−0.977667	+	0.210161i	$0.932601\pi$
$588$	20.4162	+	21.7416i	0.841951	+	0.896609i
$589$	−28.7174	−	4.54839i	−1.18328	−	0.187413i
$590$	14.2609	+	3.74363i	0.587113	+	0.154123i
$591$	−1.98047	−	1.43889i	−0.0814655	−	0.0591881i
$592$	2.20438	+	2.50050i	0.0905994	+	0.102770i
$593$		−	24.9723i		−	1.02549i	−0.858541	−	0.512744i	$-0.828629\pi$
$593$		−	24.9723i		−	1.02549i	0.858541	−	0.512744i	$-0.171371\pi$
$594$	−4.26836	−	0.744975i	−0.175133	−	0.0305667i
$595$	0.244664	−	0.995460i	0.0100303	−	0.0408099i
$596$	−10.2232	+	18.5955i	−0.418760	+	0.761700i
$597$	4.54601	−	2.31631i	0.186056	−	0.0948001i
$598$	−1.36874	−	1.02769i	−0.0559720	−	0.0420255i
$599$		−	31.8153i		−	1.29994i	−0.759961	−	0.649968i	$-0.774782\pi$
$599$		−	31.8153i		−	1.29994i	0.759961	−	0.649968i	$-0.225218\pi$
$600$	29.9208	+	6.53362i	1.22151	+	0.266734i
$601$			36.7619i			1.49955i	0.661694	+	0.749774i	$0.269838\pi$
$601$			36.7619i			1.49955i	−0.661694	+	0.749774i	$0.730162\pi$
$602$	−1.95642	+	2.60567i	−0.0797378	+	0.106199i
$603$	8.02964	−	4.09131i	0.326992	−	0.166611i
$604$	−5.22918	−	17.9998i	−0.212772	−	0.732401i
$605$	16.7979	−	14.1910i	0.682931	−	0.576948i
$606$	−6.46904	+	37.0646i	−0.262787	+	1.50564i
$607$			2.22253i			0.0902095i	0.998982	+	0.0451048i	$0.0143622\pi$
$607$			2.22253i			0.0902095i	−0.998982	+	0.0451048i	$0.985638\pi$
$608$	29.1147	−	6.98887i	1.18076	−	0.283436i
$609$	4.58465	+	3.33095i	0.185780	+	0.134977i
$610$	23.1208	+	14.8483i	0.936134	+	0.601191i
$611$	−10.3544	−	1.63998i	−0.418894	−	0.0663463i
$612$	0.144268	−	4.58888i	0.00583170	−	0.185495i
$613$	−0.267111	−	1.68647i	−0.0107885	−	0.0681159i	0.981707	−	0.190399i	$-0.0609783\pi$
$613$	−0.267111	−	1.68647i	−0.0107885	−	0.0681159i	−0.992495	+	0.122283i	$0.960978\pi$
$614$	27.7077	+	20.8038i	1.11819	+	0.839574i
$615$	9.67161	−	11.2013i	0.389997	−	0.451681i
$616$	0.994001	−	0.271908i	0.0400494	−	0.0109555i
$617$	−8.18889	−	25.2028i	−0.329672	−	1.01463i	−0.969287	−	0.245932i	$-0.920906\pi$
$617$	−8.18889	−	25.2028i	−0.329672	−	1.01463i	0.639615	−	0.768696i	$-0.279094\pi$
$618$	−15.8900	−	51.6524i	−0.639189	−	2.07776i
$619$	37.7463	+	19.2327i	1.51715	+	0.773027i	0.996724	−	0.0808797i	$-0.0257730\pi$
$619$	37.7463	+	19.2327i	1.51715	+	0.773027i	0.520427	+	0.853906i	$0.325773\pi$
$620$	−24.5448	+	1.02480i	−0.985743	+	0.0411568i
$621$	0.707965	−	0.360726i	0.0284097	−	0.0144754i
$622$	−30.2160	+	29.2810i	−1.21155	+	1.17406i
$623$	1.89730	+	2.61141i	0.0760138	+	0.104624i
$624$	34.8104	+	13.7834i	1.39353	+	0.551778i
$625$	−15.1267	+	19.9043i	−0.605070	+	0.796172i
$626$	19.2367	−	36.3312i	0.768852	−	1.45209i
$627$	−1.93609	+	12.2240i	−0.0773200	+	0.488179i
$628$	20.1025	−	36.5653i	0.802178	−	1.45911i
$629$	0.513997	+	1.00878i	0.0204944	+	0.0402226i
$630$	1.55687	−	0.909438i	0.0620271	−	0.0362329i
$631$	−10.6741	+	3.46822i	−0.424929	+	0.138068i	−0.513672	−	0.857987i	$-0.671715\pi$
$631$	−10.6741	+	3.46822i	−0.424929	+	0.138068i	0.0887429	+	0.996055i	$0.471715\pi$
$632$	−23.3127	+	2.57331i	−0.927331	+	0.102361i
$633$	−6.23538	−	19.1905i	−0.247834	−	0.762754i
$634$	9.57084	−	27.9536i	0.380106	−	1.11018i
$635$	−6.14887	+	0.450632i	−0.244011	+	0.0178828i
$636$	37.6125	+	13.5419i	1.49143	+	0.536970i
$637$	−29.3967	+	4.65597i	−1.16474	+	0.184476i
$638$	−10.6343	+	5.20959i	−0.421014	+	0.206250i
$639$	−17.7562	+	12.9007i	−0.702426	+	0.510342i
$640$	22.9486	−	10.6471i	0.907124	−	0.420863i
$641$	−9.43533	−	6.85517i	−0.372673	−	0.270763i	0.385645	−	0.922647i	$-0.373979\pi$
$641$	−9.43533	−	6.85517i	−0.372673	−	0.270763i	−0.758319	+	0.651884i	$0.773979\pi$
$642$	21.5606	+	3.76307i	0.850930	+	0.148516i
$643$	23.6810	−	23.6810i	0.933886	−	0.933886i	−0.0640601	−	0.997946i	$-0.520405\pi$
$643$	23.6810	−	23.6810i	0.933886	−	0.933886i	0.997946	+	0.0640601i	$0.0204049\pi$
$644$	−0.115828	+	0.149320i	−0.00456425	+	0.00588404i
$645$	−21.3375	−	25.2571i	−0.840165	−	0.994499i
$646$	10.1682	+	0.159798i	0.400064	+	0.00628718i
$647$	6.00640	−	18.4858i	0.236136	−	0.726751i	−0.760833	−	0.648948i	$-0.775209\pi$
$647$	6.00640	−	18.4858i	0.236136	−	0.726751i	0.996969	−	0.0778035i	$-0.0247907\pi$
$648$	−23.4600	+	21.3462i	−0.921597	+	0.838558i
$649$			5.03427i			0.197612i
$650$	−22.1755	+	21.0311i	−0.869796	+	0.824907i
$651$	−2.83840	+	2.83840i	−0.111246	+	0.111246i
$652$	−10.3615	+	4.87558i	−0.405786	+	0.190942i
$653$	−11.0000	−	21.5887i	−0.430464	−	0.844832i	−0.999743	−	0.0226879i	$-0.992778\pi$
$653$	−11.0000	−	21.5887i	−0.430464	−	0.844832i	0.569279	−	0.822144i	$-0.307222\pi$
$654$	−7.85970	−	8.11068i	−0.307339	−	0.317153i
$655$	18.3940	+	30.3823i	0.718714	+	1.18713i
$656$	0.767890	−	12.2004i	0.0299811	−	0.476348i
$657$		−	17.2440i		−	0.672753i
$658$	−0.199010	+	1.14024i	−0.00775823	+	0.0444510i
$659$	−0.596486	−	3.76606i	−0.0232358	−	0.146705i	0.973343	−	0.229355i	$-0.0736617\pi$
$659$	−0.596486	−	3.76606i	−0.0232358	−	0.146705i	−0.996579	+	0.0826499i	$0.973662\pi$
$660$	0.436219	+	10.4479i	0.0169798	+	0.406682i
$661$	5.64145	−	35.6187i	0.219427	−	1.38541i	−0.594340	−	0.804214i	$-0.702586\pi$
$661$	5.64145	−	35.6187i	0.219427	−	1.38541i	0.813766	−	0.581192i	$-0.197414\pi$
$662$	−4.23687	+	12.3746i	−0.164670	+	0.480953i
$663$	10.2876	+	7.47439i	0.399538	+	0.290281i
$664$	1.89945	−	40.2618i	0.0737129	−	1.56246i
$665$	2.06837	+	3.41642i	0.0802078	+	0.132483i
$666$	−0.645058	+	1.88402i	−0.0249955	+	0.0730043i
$667$	0.985864	−	1.93487i	0.0381728	−	0.0749184i
$668$	−20.0756	−	29.5412i	−0.776750	−	1.14298i
$669$	19.0858	−	37.4580i	0.737901	−	1.44821i
$670$	10.6804	+	13.0530i	0.412621	+	0.504283i
$671$	−2.89926	+	8.92300i	−0.111925	+	0.344468i
$672$	1.58202	−	3.81901i	0.0610279	−	0.147321i
$673$	5.81725	+	8.00676i	0.224239	+	0.308638i	0.906282	−	0.422674i	$-0.138908\pi$
$673$	5.81725	+	8.00676i	0.224239	+	0.308638i	−0.682043	+	0.731312i	$0.738908\pi$
$674$	13.6334	+	7.21861i	0.525138	+	0.278050i
$675$	−4.23872	−	13.5398i	−0.163148	−	0.521146i
$676$	−9.39769	+	6.38650i	−0.361450	+	0.245635i
$677$	2.02844	+	0.321273i	0.0779593	+	0.0123475i	0.195292	−	0.980745i	$-0.437434\pi$
$677$	2.02844	+	0.321273i	0.0779593	+	0.0123475i	−0.117333	+	0.993093i	$0.537434\pi$
$678$	0.527427	−	33.5611i	0.0202557	−	1.28891i
$679$	−2.23045	−	0.724717i	−0.0855968	−	0.0278121i
$680$	8.44873	−	1.56443i	0.323994	−	0.0599930i
$681$	37.4668	−	12.1737i	1.43573	−	0.466497i
$682$	−2.46635	−	8.01716i	−0.0944413	−	0.306993i
$683$	11.1722	−	21.9267i	0.427494	−	0.839003i	−0.572326	−	0.820026i	$-0.693959\pi$
$683$	11.1722	−	21.9267i	0.427494	−	0.839003i	0.999820	−	0.0189774i	$-0.00604107\pi$
$684$	12.2445	+	13.0393i	0.468178	+	0.498572i
$685$	−22.0329	+	8.98766i	−0.841834	+	0.343401i
$686$	0.933653	+	6.56048i	0.0356470	+	0.250480i
$687$	27.7053	−	38.1331i	1.05702	−	1.45487i
$688$	−26.6542	−	5.95861i	−1.01618	−	0.227170i
$689$	−32.2744	+	23.4487i	−1.22956	+	0.893324i
$690$	−1.21435	−	1.48411i	−0.0462294	−	0.0564991i
$691$	−6.40318	−	40.4281i	−0.243589	−	1.53796i	−0.741633	−	0.670806i	$-0.765948\pi$
$691$	−6.40318	−	40.4281i	−0.243589	−	1.53796i	0.498044	−	0.867152i	$-0.334052\pi$
$692$	3.39705	+	26.8931i	0.129136	+	1.02232i
$693$	0.435317	+	0.435317i	0.0165363	+	0.0165363i
$694$	−4.91824	−	6.99804i	−0.186694	−	0.265642i
$695$	−15.9118	−	13.7388i	−0.603570	−	0.521144i
$696$	−9.63341	+	46.5137i	−0.365154	+	1.76310i
$697$	1.28304	−	3.94878i	0.0485984	−	0.149571i
$698$	−8.15250	+	10.8580i	−0.308577	+	0.410980i
$699$	−14.8574	+	14.8574i	−0.561959	+	0.561959i
$700$	2.28327	+	2.48457i	0.0862994	+	0.0939079i
$701$	−1.49153	−	1.49153i	−0.0563343	−	0.0563343i	0.678378	−	0.734713i	$-0.262683\pi$
$701$	−1.49153	−	1.49153i	−0.0563343	−	0.0563343i	−0.734713	+	0.678378i	$0.762683\pi$
$702$	−2.44375	−	17.1714i	−0.0922334	−	0.648094i
$703$	−4.19509	−	1.36307i	−0.158221	−	0.0514090i
$704$	5.50576	+	6.65582i	0.207506	+	0.250851i
$705$	−10.8268	−	4.55305i	−0.407760	−	0.171478i
$706$	2.11513	−	12.1187i	0.0796039	−	0.456093i
$707$	−2.93134	+	2.93134i	−0.110244	+	0.110244i
$708$	15.9562	+	12.3772i	0.599670	+	0.465163i
$709$	41.1384	−	6.51568i	1.54498	−	0.244701i	0.675013	−	0.737805i	$-0.264138\pi$
$709$	41.1384	−	6.51568i	1.54498	−	0.244701i	0.869970	+	0.493104i	$0.164138\pi$
$710$	−30.6644	−	27.3295i	−1.15082	−	1.02566i
$711$	−8.23581	−	11.3356i	−0.308867	−	0.425119i
$712$	−13.4058	+	23.5018i	−0.502402	+	0.880766i
$713$	1.24442	+	0.904125i	0.0466040	+	0.0338598i
$714$	0.842989	−	1.12274i	0.0315481	−	0.0420175i
$715$	−8.86808	−	5.50026i	−0.331647	−	0.205698i
$716$	21.7601	−	20.4336i	0.813214	−	0.763640i
$717$	41.8406	+	21.3189i	1.56257	+	0.796168i
$718$	29.2054	+	15.4637i	1.08994	+	0.577101i
$719$	−2.38428	−	7.33805i	−0.0889185	−	0.273663i	0.896703	−	0.442634i	$-0.145956\pi$
$719$	−2.38428	−	7.33805i	−0.0889185	−	0.273663i	−0.985621	+	0.168971i	$0.945956\pi$
$720$	12.3176	+	8.75687i	0.459051	+	0.326349i
$721$	1.83998	−	5.66288i	0.0685245	−	0.210897i
$722$	−9.15649	+	8.87315i	−0.340769	+	0.330224i
$723$	−9.40902	+	59.4062i	−0.349925	+	2.20934i
$724$	−12.5706	−	2.39813i	−0.467183	−	0.0891259i
$725$	−31.1225	−	23.1279i	−1.15586	−	0.858948i
$726$	28.7866	−	8.85571i	1.06837	−	0.328666i
$727$	−28.9701	+	21.0480i	−1.07444	+	0.780627i	−0.976705	−	0.214586i	$-0.931160\pi$
$727$	−28.9701	+	21.0480i	−1.07444	+	0.780627i	−0.0977355	+	0.995212i	$0.531160\pi$
$728$	2.26474	+	3.44788i	0.0839369	+	0.127787i
$729$	−0.488420	−	0.158697i	−0.0180896	−	0.00587767i
$730$	31.5325	−	6.87011i	1.16707	−	0.254274i
$731$	−8.26529	−	4.21138i	−0.305703	−	0.155763i
$732$	21.1535	+	31.1272i	0.781855	+	1.15049i
$733$	8.40448	+	4.28230i	0.310427	+	0.158170i	0.602262	−	0.798298i	$-0.294266\pi$
$733$	8.40448	+	4.28230i	0.310427	+	0.158170i	−0.291836	+	0.956468i	$0.594266\pi$
$734$	−3.17335	−	6.47771i	−0.117130	−	0.239097i
$735$	−33.2278	−	2.79516i	−1.22563	−	0.103101i
$736$	−1.54025	−	0.369831i	−0.0567743	−	0.0136322i
$737$	−3.38487	+	4.65888i	−0.124683	+	0.171612i
$738$	6.55828	−	3.21282i	0.241413	−	0.118265i
$739$	5.38604	+	0.853065i	0.198129	+	0.0313805i	0.254710	−	0.967017i	$-0.418020\pi$
$739$	5.38604	+	0.853065i	0.198129	+	0.0313805i	−0.0565812	+	0.998398i	$0.518020\pi$
$740$	−3.70213	−	0.428951i	−0.136093	−	0.0157686i
$741$	−48.9325	+	7.75014i	−1.79758	+	0.284709i
$742$	2.53264	+	3.60363i	0.0929762	+	0.132294i
$743$	−36.7485			−1.34817			−0.674086	−	0.738653i	$-0.735462\pi$
$743$	−36.7485			−1.34817			−0.674086	+	0.738653i	$0.735462\pi$
$744$	−31.4742	−	11.8938i	−1.15390	−	0.436047i
$745$	−5.41424	−	23.0991i	−0.198362	−	0.846285i
$746$	−0.199686	+	12.7064i	−0.00731103	+	0.465213i
$747$	21.4547	−	10.9317i	0.784985	−	0.399970i
$748$	1.24912	+	2.65460i	0.0456723	+	0.0970616i
$749$	1.70517	+	1.70517i	0.0623056	+	0.0623056i
$750$	−29.7502	+	16.9515i	−1.08632	+	0.618980i
$751$	−25.1704			−0.918481			−0.459241	−	0.888312i	$-0.651878\pi$
$751$	−25.1704			−0.918481			−0.459241	+	0.888312i	$0.651878\pi$
$752$	−9.39728	+	2.41257i	−0.342684	+	0.0879772i
$753$	−35.9650	−	11.6857i	−1.31064	−	0.425852i
$754$	−32.9877	−	34.0411i	−1.20134	−	1.23970i
$755$	17.8091	+	11.0457i	0.648138	+	0.401995i
$756$	−1.89989	+	0.239989i	−0.0690985	+	0.00872830i
$757$	−14.3263	−	14.3263i	−0.520697	−	0.520697i	0.397085	−	0.917782i	$-0.370022\pi$
$757$	−14.3263	−	14.3263i	−0.520697	−	0.520697i	−0.917782	+	0.397085i	$0.870022\pi$
$758$	−18.4690	+	12.9800i	−0.670823	+	0.471456i
$759$	0.384854	−	0.529707i	0.0139693	−	0.0192271i
$760$	−18.9656	+	27.5852i	−0.687953	+	1.00062i
$761$	20.5190	+	28.2420i	0.743813	+	1.02377i	0.998390	+	0.0567187i	$0.0180638\pi$
$761$	20.5190	+	28.2420i	0.743813	+	1.02377i	−0.254577	+	0.967053i	$0.581936\pi$
$762$	−7.98897	−	2.73529i	−0.289410	−	0.0990891i
$763$	−0.194667	−	1.22908i	−0.00704742	−	0.0444956i
$764$	−23.2292	−	8.36337i	−0.840405	−	0.302576i
$765$	3.31259	+	3.92110i	0.119767	+	0.141768i
$766$	−18.5903	−	37.9480i	−0.671694	−	1.37112i
$767$	−19.1658	+	6.22735i	−0.692037	+	0.224856i
$768$	34.6321	−	1.08664i	1.24968	−	0.0392109i
$769$	−0.666968	−	2.05272i	−0.0240515	−	0.0740228i	0.938310	−	0.345794i	$-0.112391\pi$
$769$	−0.666968	−	2.05272i	−0.0240515	−	0.0740228i	−0.962362	+	0.271771i	$0.912391\pi$
$770$	−0.622590	+	0.969456i	−0.0224366	+	0.0349368i
$771$	16.2099	−	8.25934i	0.583784	−	0.297453i
$772$	11.8990	+	40.9585i	0.428254	+	1.47413i
$773$	30.0383	+	4.75760i	1.08040	+	0.171119i	0.671164	−	0.741309i	$-0.265795\pi$
$773$	30.0383	+	4.75760i	1.08040	+	0.171119i	0.409238	+	0.912428i	$0.365795\pi$
$774$	−4.79753	−	15.5950i	−0.172444	−	0.560549i
$775$	19.6293	−	19.2110i	0.705104	−	0.690081i
$776$	−2.15679	−	19.5393i	−0.0774242	−	0.701419i
$777$	−0.492669	+	0.357945i	−0.0176744	+	0.0128412i
$778$	−40.6815	−	0.639327i	−1.45850	−	0.0229210i
$779$	7.34385	+	14.4131i	0.263121	+	0.516403i
$780$	−39.2361	+	14.5846i	−1.40488	+	0.522213i
$781$	6.36721	−	12.4963i	0.227837	−	0.447154i
$782$	−0.475467	−	0.251750i	−0.0170027	−	0.00900258i
$783$	20.9283	−	6.80000i	0.747915	−	0.243012i
$784$	−23.2570	+	14.7585i	−0.830607	+	0.527090i
$785$	10.6463	+	45.4210i	0.379984	+	1.62115i
$786$	6.85375	+	48.1591i	0.244465	+	1.71778i
$787$	17.2915	−	2.73871i	0.616377	−	0.0976245i	0.159564	−	0.987188i	$-0.448991\pi$
$787$	17.2915	−	2.73871i	0.616377	−	0.0976245i	0.456812	+	0.889563i	$0.348991\pi$
$788$	1.64809	−	1.54762i	0.0587108	−	0.0551317i
$789$	−3.36032	+	21.2162i	−0.119631	+	0.755317i
$790$	17.4472	−	19.5762i	0.620743	−	0.696490i
$791$	2.17377	−	2.99194i	0.0772905	−	0.106381i
$792$	−1.82411	+	4.82711i	−0.0648171	+	0.171524i
$793$	−37.5568			−1.33368
$794$	3.82415	−	2.68762i	0.135714	−	0.0953801i
$795$	−41.3839	+	16.8813i	−1.46774	+	0.598719i
$796$	1.31456	+	4.52494i	0.0465932	+	0.160382i
$797$	−13.7741	−	27.0331i	−0.487902	−	0.957562i	−0.995391	−	0.0959035i	$-0.969426\pi$
$797$	−13.7741	−	27.0331i	−0.487902	−	0.957562i	0.507488	−	0.861659i	$-0.330574\pi$
$798$	0.770689	+	5.41538i	0.0272821	+	0.191703i
$799$	−3.29522			−0.116577
$800$	−11.1055	+	26.0129i	−0.392637	+	0.919693i
$801$	−16.1635			−0.571107
$802$	−2.79696	−	19.6533i	−0.0987640	−	0.693983i
$803$	5.00258	+	9.81811i	0.176537	+	0.346473i
$804$	6.44437	+	22.1827i	0.227275	+	0.782323i
$805$	−0.0154429	−	0.210718i	−0.000544290	−	0.00742685i
$806$	27.4710	−	19.3067i	0.967625	−	0.680050i
$807$	4.82600			0.169883
$808$	−32.5048	−	12.2832i	−1.14351	−	0.432122i
$809$	−17.8906	+	24.6243i	−0.629000	+	0.865744i	−0.997969	−	0.0636976i	$-0.979711\pi$
$809$	−17.8906	+	24.6243i	−0.629000	+	0.865744i	0.368969	+	0.929442i	$0.379711\pi$
$810$	3.52749	−	35.2859i	0.123943	−	1.23982i
$811$	−3.87801	+	24.4848i	−0.136175	+	0.859776i	0.821139	+	0.570728i	$0.193339\pi$
$811$	−3.87801	+	24.4848i	−0.136175	+	0.859776i	−0.957314	+	0.289048i	$0.906661\pi$
$812$	−3.81523	+	3.58265i	−0.133888	+	0.125726i
$813$	29.5129	−	4.67439i	1.03506	−	0.163938i
$814$	−0.179292	−	1.25983i	−0.00628418	−	0.0441569i
$815$	4.96306	−	11.8018i	0.173848	−	0.413398i
$816$	11.4848	+	2.56746i	0.402050	+	0.0898792i
$817$	34.3719	−	11.1681i	1.20252	−	0.390723i
$818$	35.5588	+	18.8277i	1.24328	+	0.658294i
$819$	−1.11880	+	2.19576i	−0.0390940	+	0.0767262i
$820$	8.48783	+	10.7125i	0.296408	+	0.374097i
$821$	−3.23273	−	6.34460i	−0.112823	−	0.221428i	0.827690	−	0.561186i	$-0.189655\pi$
$821$	−3.23273	−	6.34460i	−0.112823	−	0.221428i	−0.940513	+	0.339758i	$0.889655\pi$
$822$	−32.5870	−	0.512119i	−1.13660	−	0.0178622i
$823$	13.9133	−	10.1086i	0.484987	−	0.352363i	−0.318266	−	0.948001i	$-0.603101\pi$
$823$	13.9133	−	10.1086i	0.484987	−	0.352363i	0.803253	+	0.595638i	$0.203101\pi$
$824$	49.6082	−	5.47586i	1.72818	−	0.190761i
$825$	−8.17746	−	8.35549i	−0.284703	−	0.290901i
$826$	0.654221	+	2.12663i	0.0227633	+	0.0739948i
$827$	−22.8450	−	3.61829i	−0.794397	−	0.125820i	−0.253971	−	0.967212i	$-0.581737\pi$
$827$	−22.8450	−	3.61829i	−0.794397	−	0.125820i	−0.540426	+	0.841392i	$0.681737\pi$
$828$	−0.263997	−	0.908724i	−0.00917452	−	0.0315804i
$829$	−40.6939	+	20.7346i	−1.41336	+	0.720141i	−0.983186	−	0.182606i	$-0.941547\pi$
$829$	−40.6939	+	20.7346i	−1.41336	+	0.720141i	−0.430171	+	0.902747i	$0.641547\pi$
$830$	28.5374	+	34.8768i	0.990548	+	1.21059i
$831$	9.76766	+	30.0618i	0.338836	+	1.04283i
$832$	−18.5286	+	29.1940i	−0.642363	+	1.01212i
$833$	−8.89742	+	2.89095i	−0.308277	+	0.100165i
$834$	−12.6670	−	25.8569i	−0.438621	−	0.895350i
$835$	38.7789	+	9.53108i	1.34200	+	0.329837i
$836$	−10.7543	−	3.87195i	−0.371946	−	0.133914i
$837$	2.43837	+	15.3952i	0.0842822	+	0.532137i
$838$	40.0519	+	13.7131i	1.38357	+	0.473711i
$839$	−26.3237	−	36.2315i	−0.908795	−	1.25085i	−0.967577	−	0.252578i	$-0.918722\pi$
$839$	−26.3237	−	36.2315i	−0.908795	−	1.25085i	0.0587815	−	0.998271i	$-0.481278\pi$
$840$	1.54201	+	4.35680i	0.0532044	+	0.150324i
$841$	18.3039	−	25.1931i	0.631168	−	0.868728i
$842$	−24.7928	+	17.4244i	−0.854415	+	0.600485i
$843$	41.9341	+	41.9341i	1.44429	+	1.44429i
$844$	18.4884	−	2.33540i	0.636398	−	0.0803878i
$845$	3.03204	−	12.3364i	0.104305	−	0.424385i
$846$	−4.03347	−	4.16227i	−0.138674	−	0.143102i
$847$	3.15600	+	1.02545i	0.108441	+	0.0352348i
$848$	−18.7944	+	31.7778i	−0.645403	+	1.09126i
$849$	−6.00949			−0.206245
$850$	−5.85039	+	7.61962i	−0.200667	+	0.261351i
$851$	0.165008	+	0.165008i	0.00565639	+	0.00565639i
$852$	−23.9530	−	50.9043i	−0.820616	−	1.74395i
$853$	31.0440	−	15.8177i	1.06293	−	0.541587i	0.167075	−	0.985944i	$-0.446568\pi$
$853$	31.0440	−	15.8177i	1.06293	−	0.541587i	0.895850	+	0.444357i	$0.146568\pi$
$854$	−0.0651579	+	4.14611i	−0.00222966	+	0.141877i
$855$	−19.9281	−	1.67637i	−0.681526	−	0.0573308i
$856$	−7.14520	+	18.9082i	−0.244218	+	0.646268i
$857$	37.9688			1.29699			0.648494	−	0.761219i	$-0.275399\pi$
$857$	37.9688			1.29699			0.648494	+	0.761219i	$0.275399\pi$
$858$	−8.21818	−	11.6934i	−0.280564	−	0.399208i
$859$	−20.9353	+	3.31582i	−0.714302	+	0.113134i	−0.503000	−	0.864286i	$-0.667770\pi$
$859$	−20.9353	+	3.31582i	−0.714302	+	0.113134i	−0.211302	+	0.977421i	$0.567770\pi$
$860$	26.6057	−	14.9859i	0.907246	−	0.511015i
$861$	2.20577	+	0.349359i	0.0751724	+	0.0119061i
$862$	12.8551	−	6.29757i	0.437848	−	0.214496i
$863$	5.59589	−	7.70208i	0.190486	−	0.262182i	−0.703082	−	0.711108i	$-0.748193\pi$
$863$	5.59589	−	7.70208i	0.190486	−	0.262182i	0.893569	+	0.448926i	$0.148193\pi$
$864$	−8.38652	−	13.6865i	−0.285315	−	0.465624i
$865$	−22.9388	−	19.8061i	−0.779942	−	0.673429i
$866$	10.9600	+	22.3724i	0.372435	+	0.760246i
$867$	−29.2408	−	14.8989i	−0.993069	−	0.505994i
$868$	−2.08372	−	3.06618i	−0.0707260	−	0.104073i
$869$	7.97769	+	4.06483i	0.270625	+	0.137890i
$870$	−26.7871	−	45.8569i	−0.908169	−	1.55469i
$871$	−21.9237	−	7.12345i	−0.742857	−	0.241369i
$872$	8.71812	−	5.72650i	0.295233	−	0.193924i
$873$	9.50079	−	6.90273i	0.321553	−	0.233622i
$874$	2.00341	−	0.616315i	0.0677663	−	0.0208472i
$875$	−3.75576	−	0.356704i	−0.126968	−	0.0120588i
$876$	43.4179	+	8.28296i	1.46695	+	0.279855i
$877$	1.94875	−	12.3039i	0.0658047	−	0.415475i	−0.932693	−	0.360672i	$-0.882547\pi$
$877$	1.94875	−	12.3039i	0.0658047	−	0.415475i	0.998497	−	0.0548021i	$-0.0174528\pi$
$878$	26.3645	−	25.5486i	0.889757	−	0.862224i
$879$	−20.6161	+	63.4499i	−0.695365	+	2.14011i
$880$	−9.55362	−	1.41244i	−0.322052	−	0.0476133i
$881$	−6.15911	−	18.9558i	−0.207506	−	0.638637i	−0.999601	−	0.0282396i	$-0.991010\pi$
$881$	−6.15911	−	18.9558i	−0.207506	−	0.638637i	0.792095	−	0.610397i	$-0.208990\pi$
$882$	−14.5424	−	7.69991i	−0.489668	−	0.259269i
$883$	−31.3983	−	15.9983i	−1.05664	−	0.538384i	−0.162747	−	0.986668i	$-0.552035\pi$
$883$	−31.3983	−	15.9983i	−1.05664	−	0.538384i	−0.893891	+	0.448284i	$0.852035\pi$
$884$	−8.56108	+	8.03919i	−0.287940	+	0.270387i
$885$	−22.5171	+	1.65021i	−0.756904	+	0.0554711i
$886$	−33.3620	+	44.4334i	−1.12082	+	1.49277i
$887$	15.5451	+	11.2942i	0.521955	+	0.379223i	0.817340	−	0.576156i	$-0.195448\pi$
$887$	15.5451	+	11.2942i	0.521955	+	0.379223i	−0.295385	+	0.955378i	$0.595448\pi$
$888$	−4.43385	−	2.52913i	−0.148790	−	0.0848720i
$889$	−0.546872	−	0.752705i	−0.0183415	−	0.0252449i
$890$	−6.43961	−	29.5566i	−0.215856	−	0.990739i
$891$	11.9591	−	1.89414i	0.400645	−	0.0634560i
$892$	30.6782	+	23.7971i	1.02718	+	0.796784i
$893$	9.07800	−	9.07800i	0.303784	−	0.303784i
$894$	5.58696	−	32.0107i	0.186856	−	1.07060i
$895$	−2.79754	+	33.2561i	−0.0935115	+	1.11163i
$896$	3.19075	+	2.09613i	0.106595	+	0.0700266i
$897$	2.49269	+	0.809924i	0.0832285	+	0.0270426i
$898$	2.16028	+	15.1796i	0.0720895	+	0.506550i
$899$	30.1225	+	30.1225i	1.00464	+	1.00464i
$900$	−16.7856	+	1.93692i	−0.559520	+	0.0645641i
$901$	−8.86675	+	8.86675i	−0.295394	+	0.295394i
$902$	−2.80199	+	3.73185i	−0.0932960	+	0.124257i
$903$	1.54185	−	4.74534i	0.0513097	−	0.157915i
$904$	30.3548	+	6.28676i	1.00959	+	0.209095i
$905$	12.2395	−	7.41004i	0.406855	−	0.246318i
$906$	16.5039	+	23.4830i	0.548306	+	0.780171i
$907$	26.0438	+	26.0438i	0.864771	+	0.864771i	0.991888	−	0.127116i	$-0.0405722\pi$
$907$	26.0438	+	26.0438i	0.864771	+	0.864771i	−0.127116	+	0.991888i	$0.540572\pi$
$908$	4.55955	+	36.0961i	0.151314	+	1.19789i
$909$	−3.24735	−	20.5030i	−0.107708	−	0.680040i
$910$	−4.46092	−	1.17104i	−0.147878	−	0.0388194i
$911$	24.1823	−	17.5695i	0.801195	−	0.582102i	−0.110069	−	0.993924i	$-0.535107\pi$
$911$	24.1823	−	17.5695i	0.801195	−	0.582102i	0.911264	+	0.411822i	$0.135107\pi$
$912$	−38.7127	+	24.5665i	−1.28190	+	0.813477i
$913$	−9.04416	+	12.4482i	−0.299318	+	0.411976i
$914$	5.66786	+	39.8262i	0.187476	+	1.31734i
$915$	−40.8608	−	10.0428i	−1.35082	−	0.332004i
$916$	29.7989	+	31.7334i	0.984583	+	1.04850i
$917$	−2.43324	+	4.77550i	−0.0803527	+	0.157701i
$918$	−1.60302	−	5.21081i	−0.0529075	−	0.171982i
$919$	−12.8192	+	4.16521i	−0.422866	+	0.137398i	−0.512717	−	0.858558i	$-0.671361\pi$
$919$	−12.8192	+	4.16521i	−0.422866	+	0.137398i	0.0898507	+	0.995955i	$0.471361\pi$
$920$	1.55652	−	0.844787i	0.0513170	−	0.0278518i
$921$	−50.4601	−	16.3955i	−1.66272	−	0.540249i
$922$	0.875416	−	55.7042i	0.0288303	−	1.83452i
$923$	55.4506	+	8.78251i	1.82518	+	0.289080i
$924$	−1.30516	+	0.886965i	−0.0429368	+	0.0291790i
$925$	3.39718	−	2.41274i	0.111699	−	0.0793305i
$926$	−5.52740	−	2.92665i	−0.181641	−	0.0961757i
$927$	17.5253	+	24.1215i	0.575607	+	0.792255i
$928$	−40.5292	−	16.7892i	−1.33044	−	0.551133i
$929$	9.26967	−	28.5291i	0.304128	−	0.936009i	−0.675873	−	0.737018i	$-0.736233\pi$
$929$	9.26967	−	28.5291i	0.304128	−	0.936009i	0.980001	−	0.198992i	$-0.0637666\pi$
$930$	35.0504	−	13.6594i	1.14935	−	0.447909i
$931$	16.5472	−	32.4757i	0.542313	−	1.06435i
$932$	−10.9071	−	16.0497i	−0.357273	−	0.525726i
$933$	29.2508	−	57.4080i	0.957629	−	1.87945i
$934$	−16.5840	+	48.4371i	−0.542646	+	1.58491i
$935$	−3.02360	−	1.27153i	−0.0988824	−	0.0415835i
$936$	−20.6335	−	0.973437i	−0.674429	−	0.0318178i
$937$	−13.3444	−	9.69527i	−0.435942	−	0.316731i	0.348078	−	0.937465i	$-0.386834\pi$
$937$	−13.3444	−	9.69527i	−0.435942	−	0.316731i	−0.784021	+	0.620735i	$0.786834\pi$
$938$	−0.824435	+	2.40793i	−0.0269187	+	0.0786216i
$939$	−9.84768	+	62.1758i	−0.321367	+	2.02903i
$940$	6.00420	−	9.03390i	0.195835	−	0.294653i
$941$	6.26617	+	39.5630i	0.204271	+	1.28972i	0.850257	+	0.526368i	$0.176447\pi$
$941$	6.26617	+	39.5630i	0.204271	+	1.28972i	−0.645985	+	0.763350i	$0.723553\pi$
$942$	−10.9860	+	62.9444i	−0.357942	+	2.05084i
$943$		−	0.855779i		−	0.0278680i
$944$	−13.9899	+	12.3331i	−0.455331	+	0.401408i
$945$	1.39923	−	1.62054i	0.0455169	−	0.0527161i
$946$	7.25572	+	7.48741i	0.235904	+	0.243437i
$947$	−8.34412	−	16.3763i	−0.271147	−	0.532157i	0.714776	−	0.699353i	$-0.246529\pi$
$947$	−8.34412	−	16.3763i	−0.271147	−	0.532157i	−0.985924	+	0.167197i	$0.946529\pi$
$948$	32.4974	−	15.2916i	1.05547	−	0.496649i
$949$	−31.1901	+	31.1901i	−1.01247	+	1.01247i
$950$	−4.87404	−	37.1085i	−0.158135	−	1.20396i
$951$			45.2444i			1.46715i
$952$	0.872639	+	0.959054i	0.0282824	+	0.0310831i
$953$	8.04762	−	24.7680i	0.260688	−	0.802315i	−0.731968	−	0.681339i	$-0.761398\pi$
$953$	8.04762	−	24.7680i	0.260688	−	0.802315i	0.992656	−	0.120975i	$-0.0386022\pi$
$954$	−22.0530	−	0.346573i	−0.713993	−	0.0112207i
$955$	25.5584	−	10.4258i	0.827051	−	0.337371i
$956$	−26.5813	+	34.2675i	−0.859701	+	1.10829i
$957$	12.8221	−	12.8221i	0.414479	−	0.414479i
$958$	30.1588	+	5.26375i	0.974388	+	0.170064i
$959$	−2.90510	−	2.11068i	−0.0938106	−	0.0681574i
$960$	−27.9652	+	26.8077i	−0.902572	+	0.865215i
$961$	0.667537	−	0.484994i	0.0215334	−	0.0156450i
$962$	4.57447	−	2.24097i	0.147487	−	0.0722519i
$963$	−11.9267	+	1.88900i	−0.384331	+	0.0608721i
$964$	−52.2640	−	18.8169i	−1.68331	−	0.606052i
$965$	−40.5245	−	25.1345i	−1.30453	−	0.809110i
$966$	0.0937368	−	0.273777i	0.00301593	−	0.00880864i
$967$	−14.3979	−	44.3123i	−0.463006	−	1.42499i	−0.861473	−	0.507804i	$-0.830458\pi$
$967$	−14.3979	−	44.3123i	−0.463006	−	1.42499i	0.398467	−	0.917183i	$-0.369542\pi$
$968$	3.05177	+	27.6473i	0.0980877	+	0.888618i
$969$	−14.8103	+	4.81215i	−0.475775	+	0.154589i
$970$	16.4075	+	14.6231i	0.526814	+	0.469520i
$971$	13.2347	+	25.9746i	0.424723	+	0.833566i	0.999880	+	0.0155225i	$0.00494117\pi$
$971$	13.2347	+	25.9746i	0.424723	+	0.833566i	−0.575156	+	0.818043i	$0.695059\pi$
$972$	15.1969	−	27.6422i	0.487440	−	0.886624i
$973$	0.496276	−	3.13336i	0.0159099	−	0.100451i
$974$	10.2162	−	19.2948i	0.327349	−	0.618246i
$975$	21.6945	−	41.4678i	0.694779	−	1.32803i
$976$	−31.8990	+	13.8030i	−1.02106	+	0.441824i
$977$	3.11312	+	4.28484i	0.0995975	+	0.137084i	0.855907	−	0.517130i	$-0.173000\pi$
$977$	3.11312	+	4.28484i	0.0995975	+	0.137084i	−0.756309	+	0.654214i	$0.773000\pi$
$978$	12.5926	−	12.2029i	0.402665	−	0.390205i
$979$	9.20288	−	4.68910i	0.294125	−	0.149864i
$980$	8.28633	−	29.6600i	0.264697	−	0.947453i
$981$	5.55209	+	2.82893i	0.177265	+	0.0903209i
$982$	4.56865	+	14.8510i	0.145791	+	0.473913i
$983$	−0.121546	−	0.374079i	−0.00387670	−	0.0119313i	0.949099	−	0.314977i	$-0.101997\pi$
$983$	−0.121546	−	0.374079i	−0.00387670	−	0.0119313i	−0.952976	+	0.303045i	$0.901997\pi$
$984$	4.93921	+	18.0560i	0.157456	+	0.575605i
$985$	−0.211883	+	2.51878i	−0.00675115	+	0.0802551i
$986$	−11.9151	−	8.94621i	−0.379453	−	0.284905i
$987$	−0.277269	−	1.75061i	−0.00882556	−	0.0557224i
$988$	1.43775	−	45.7320i	0.0457410	−	1.45493i
$989$	−1.88844	−	0.299099i	−0.0600488	−	0.00951079i
$990$	−2.09490	−	5.37558i	−0.0665802	−	0.170847i
$991$	−17.9810	−	13.0640i	−0.571187	−	0.414992i	0.264349	−	0.964427i	$-0.414843\pi$
$991$	−17.9810	−	13.0640i	−0.571187	−	0.414992i	−0.835536	+	0.549435i	$0.814843\pi$
$992$	16.2370	−	26.4945i	0.515524	−	0.841200i
$993$		−	20.0290i		−	0.635602i
$994$	1.06575	−	6.10627i	0.0338037	−	0.193679i
$995$	−4.47699	−	2.77677i	−0.141930	−	0.0880295i
$996$	17.2189	+	59.2706i	0.545602	+	1.87806i
$997$	−40.0956	+	20.4297i	−1.26984	+	0.647016i	−0.953432	−	0.301607i	$-0.902477\pi$
$997$	−40.0956	+	20.4297i	−1.26984	+	0.647016i	−0.316408	+	0.948623i	$0.602477\pi$
$998$	22.6728	−	30.1969i	0.717694	−	0.955866i
$999$			2.36470i			0.0748157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.bl.a.189.27	yes	464
16.5	even	4	inner	400.2.bl.a.389.9	yes	464
25.9	even	10	inner	400.2.bl.a.109.9	✓	464
400.309	even	20	inner	400.2.bl.a.309.27	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.bl.a.109.9	✓	464	25.9	even	10	inner
400.2.bl.a.189.27	yes	464	1.1	even	1	trivial
400.2.bl.a.309.27	yes	464	400.309	even	20	inner
400.2.bl.a.389.9	yes	464	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.bl (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.199256 - 1.40011i) q^{2} +(0.983149 + 1.92954i) q^{3} +(-1.92059 + 0.557958i) q^{4} +(1.17859 - 1.90024i) q^{5} +(2.50566 - 1.76098i) q^{6} +0.337437 q^{7} +(1.16389 + 2.57786i) q^{8} +(-0.993180 + 1.36700i) q^{9} +O(q^{10})\)	\(q+(-0.199256 - 1.40011i) q^{2} +(0.983149 + 1.92954i) q^{3} +(-1.92059 + 0.557958i) q^{4} +(1.17859 - 1.90024i) q^{5} +(2.50566 - 1.76098i) q^{6} +0.337437 q^{7} +(1.16389 + 2.57786i) q^{8} +(-0.993180 + 1.36700i) q^{9} +(-2.89538 - 1.27152i) q^{10} +(0.168908 - 1.06644i) q^{11} +(-2.96483 - 3.15730i) q^{12} +(4.26896 - 0.676137i) q^{13} +(-0.0672364 - 0.472448i) q^{14} +(4.82532 + 0.405912i) q^{15} +(3.37736 - 2.14322i) q^{16} +(1.29208 - 0.419821i) q^{17} +(2.11184 + 1.11818i) q^{18} +(-2.40298 + 4.71610i) q^{19} +(-1.20334 + 4.30720i) q^{20} +(0.331751 + 0.651098i) q^{21} +(-1.52679 - 0.0239942i) q^{22} +(0.226540 - 0.164591i) q^{23} +(-3.82980 + 4.78019i) q^{24} +(-2.22185 - 4.47922i) q^{25} +(-1.79728 - 5.84228i) q^{26} +(2.80262 + 0.443891i) q^{27} +(-0.648080 + 0.188276i) q^{28} +(6.90978 - 3.52071i) q^{29} +(-0.393154 - 6.83684i) q^{30} +(1.69748 + 5.22431i) q^{31} +(-3.67370 - 4.30162i) q^{32} +(2.22381 - 0.722558i) q^{33} +(-0.845248 - 1.72539i) q^{34} +(0.397700 - 0.641213i) q^{35} +(1.14477 - 3.17960i) q^{36} +(0.130366 + 0.823099i) q^{37} +(7.08185 + 2.42471i) q^{38} +(5.50166 + 7.57238i) q^{39} +(6.27031 + 0.826563i) q^{40} +(1.79636 - 2.47248i) q^{41} +(0.845504 - 0.594222i) q^{42} +(-4.82814 - 4.82814i) q^{43} +(0.270627 + 2.14245i) q^{44} +(1.42707 + 3.49841i) q^{45} +(-0.275584 - 0.284384i) q^{46} +(-2.30680 - 0.749523i) q^{47} +(7.45588 + 4.40965i) q^{48} -6.88614 q^{49} +(-5.82866 + 4.00334i) q^{50} +(2.08037 + 2.08037i) q^{51} +(-7.82169 + 3.68049i) q^{52} +(-8.22391 + 4.19029i) q^{53} +(0.0630567 - 4.01241i) q^{54} +(-1.82743 - 1.57787i) q^{55} +(0.392740 + 0.869866i) q^{56} -11.4624 q^{57} +(-6.30618 - 8.97290i) q^{58} +(-4.60509 + 0.729375i) q^{59} +(-9.49397 + 1.91274i) q^{60} +(-8.58235 - 1.35931i) q^{61} +(6.97636 - 3.41763i) q^{62} +(-0.335136 + 0.461275i) q^{63} +(-5.29072 + 6.00069i) q^{64} +(3.74653 - 8.90896i) q^{65} +(-1.45476 - 2.96959i) q^{66} +(-4.75211 - 2.42132i) q^{67} +(-2.24731 + 1.52723i) q^{68} +(0.540307 + 0.275300i) q^{69} +(-0.977011 - 0.429057i) q^{70} +(12.3535 + 4.01390i) q^{71} +(-4.67987 - 0.969246i) q^{72} +(-8.25632 + 5.99857i) q^{73} +(1.12645 - 0.346534i) q^{74} +(6.45841 - 8.69088i) q^{75} +(1.98375 - 10.3985i) q^{76} +(0.0569959 - 0.359858i) q^{77} +(9.50590 - 9.21174i) q^{78} +(-2.56248 + 7.88650i) q^{79} +(-0.0921200 - 8.94380i) q^{80} +(3.46532 + 10.6652i) q^{81} +(-3.81966 - 2.02244i) q^{82} +(-12.6973 - 6.46961i) q^{83} +(-1.00045 - 1.06539i) q^{84} +(0.725066 - 2.95006i) q^{85} +(-5.79788 + 7.72195i) q^{86} +(13.5867 + 9.87130i) q^{87} +(2.94573 - 0.805803i) q^{88} +(5.62268 + 7.73896i) q^{89} +(4.61379 - 2.69513i) q^{90} +(1.44051 - 0.228154i) q^{91} +(-0.343257 + 0.442512i) q^{92} +(-8.41163 + 8.41163i) q^{93} +(-0.589770 + 3.37911i) q^{94} +(6.12963 + 10.1246i) q^{95} +(4.68834 - 11.3177i) q^{96} +(-6.60997 - 2.14771i) q^{97} +(1.37210 + 9.64132i) q^{98} +(1.29007 + 1.29007i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q - 10 q^{2} - 10 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} - 40 q^{8}+O(q^{10}) \) 464 * q - 10 * q^2 - 10 * q^3 - 6 * q^4 - 8 * q^5 - 6 * q^6 - 40 * q^8	\( 464 q - 10 q^{2} - 10 q^{3} - 6 q^{4} - 8 q^{5} - 6 q^{6} - 40 q^{8} - 2 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 18 q^{14} - 16 q^{15} - 6 q^{16} - 20 q^{17} - 6 q^{19} + 6 q^{20} - 24 q^{21} - 10 q^{22} - 16 q^{24} - 36 q^{26} - 10 q^{27} - 50 q^{28} - 6 q^{29} + 14 q^{30} - 36 q^{31} - 20 q^{33} - 46 q^{34} - 36 q^{35} + 38 q^{36} - 10 q^{37} + 60 q^{38} - 84 q^{40} - 70 q^{42} + 36 q^{44} - 24 q^{45} + 2 q^{46} - 20 q^{47} - 140 q^{48} + 336 q^{49} - 46 q^{50} - 28 q^{51} + 80 q^{52} - 10 q^{53} - 30 q^{54} - 48 q^{56} - 10 q^{58} - 6 q^{59} + 112 q^{60} - 6 q^{61} - 10 q^{62} - 160 q^{63} - 24 q^{64} - 48 q^{65} - 104 q^{66} - 70 q^{67} + 6 q^{69} - 100 q^{70} - 10 q^{72} + 28 q^{74} - 46 q^{75} + 44 q^{76} - 80 q^{77} - 10 q^{78} - 52 q^{79} - 2 q^{80} + 72 q^{81} - 10 q^{83} + 28 q^{84} - 18 q^{85} + 34 q^{86} + 100 q^{88} + 74 q^{90} - 48 q^{91} + 80 q^{92} - 6 q^{94} - 40 q^{95} + 54 q^{96} - 20 q^{97} - 100 q^{98} - 64 q^{99}+O(q^{100}) \) 464 * q - 10 * q^2 - 10 * q^3 - 6 * q^4 - 8 * q^5 - 6 * q^6 - 40 * q^8 - 2 * q^10 - 6 * q^11 - 10 * q^12 - 10 * q^13 - 18 * q^14 - 16 * q^15 - 6 * q^16 - 20 * q^17 - 6 * q^19 + 6 * q^20 - 24 * q^21 - 10 * q^22 - 16 * q^24 - 36 * q^26 - 10 * q^27 - 50 * q^28 - 6 * q^29 + 14 * q^30 - 36 * q^31 - 20 * q^33 - 46 * q^34 - 36 * q^35 + 38 * q^36 - 10 * q^37 + 60 * q^38 - 84 * q^40 - 70 * q^42 + 36 * q^44 - 24 * q^45 + 2 * q^46 - 20 * q^47 - 140 * q^48 + 336 * q^49 - 46 * q^50 - 28 * q^51 + 80 * q^52 - 10 * q^53 - 30 * q^54 - 48 * q^56 - 10 * q^58 - 6 * q^59 + 112 * q^60 - 6 * q^61 - 10 * q^62 - 160 * q^63 - 24 * q^64 - 48 * q^65 - 104 * q^66 - 70 * q^67 + 6 * q^69 - 100 * q^70 - 10 * q^72 + 28 * q^74 - 46 * q^75 + 44 * q^76 - 80 * q^77 - 10 * q^78 - 52 * q^79 - 2 * q^80 + 72 * q^81 - 10 * q^83 + 28 * q^84 - 18 * q^85 + 34 * q^86 + 100 * q^88 + 74 * q^90 - 48 * q^91 + 80 * q^92 - 6 * q^94 - 40 * q^95 + 54 * q^96 - 20 * q^97 - 100 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more