LMFDB - Embedded newform 416.2.bi.a.395.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(99,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3, 2]))

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

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

chi := DirichletCharacter("416.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bi (of order $8$, 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			395.4
Character	$\chi$	$=$	416.395
Dual form			416.2.bi.a.99.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37040 - 0.349306i) q^{2} +(-0.598132 - 1.44402i) q^{3} +(1.75597 + 0.957376i) q^{4} +(0.944556 + 2.28036i) q^{5} +(0.315273 + 2.18781i) q^{6} -3.99101 q^{7} +(-2.07196 - 1.92536i) q^{8} +(0.393895 - 0.393895i) q^{9} +(-0.497872 - 3.45493i) q^{10} +(1.25590 - 0.520212i) q^{11} +(0.332166 - 3.10829i) q^{12} +(3.60343 + 0.123708i) q^{13} +(5.46926 + 1.39408i) q^{14} +(2.72791 - 2.72791i) q^{15} +(2.16686 + 3.36225i) q^{16} +2.50532 q^{17} +(-0.677382 + 0.402202i) q^{18} +(-0.0188665 + 0.0455478i) q^{19} +(-0.524549 + 4.90854i) q^{20} +(2.38715 + 5.76309i) q^{21} +(-1.90280 + 0.274202i) q^{22} +(2.76280 - 2.76280i) q^{23} +(-1.54094 + 4.14356i) q^{24} +(-0.772317 + 0.772317i) q^{25} +(-4.89491 - 1.42823i) q^{26} +(-5.13645 - 2.12759i) q^{27} +(-7.00809 - 3.82089i) q^{28} +(7.24960 - 3.00288i) q^{29} +(-4.69119 + 2.78544i) q^{30} +(6.59516 + 6.59516i) q^{31} +(-1.79501 - 5.36451i) q^{32} +(-1.50239 - 1.50239i) q^{33} +(-3.43329 - 0.875125i) q^{34} +(-3.76973 - 9.10093i) q^{35} +(1.06877 - 0.314563i) q^{36} +(2.30097 - 0.953092i) q^{37} +(0.0417647 - 0.0558283i) q^{38} +(-1.97669 - 5.27741i) q^{39} +(2.43342 - 6.54341i) q^{40} -7.91626i q^{41} +(-1.25826 - 8.73155i) q^{42} +(5.29406 + 2.19287i) q^{43} +(2.70337 + 0.288894i) q^{44} +(1.27028 + 0.526167i) q^{45} +(-4.75119 + 2.82106i) q^{46} +(-1.49919 - 1.49919i) q^{47} +(3.55907 - 5.14005i) q^{48} +8.92814 q^{49} +(1.32816 - 0.788605i) q^{50} +(-1.49851 - 3.61773i) q^{51} +(6.20908 + 3.66706i) q^{52} +(-7.29352 - 3.02108i) q^{53} +(6.29579 + 4.70983i) q^{54} +(2.37254 + 2.37254i) q^{55} +(8.26920 + 7.68411i) q^{56} +0.0770564 q^{57} +(-10.9837 + 1.58281i) q^{58} +(-4.15572 - 10.0328i) q^{59} +(7.40176 - 2.17849i) q^{60} +(-3.72929 + 1.54472i) q^{61} +(-6.73425 - 11.3417i) q^{62} +(-1.57204 + 1.57204i) q^{63} +(0.586014 + 7.97851i) q^{64} +(3.12154 + 8.33396i) q^{65} +(1.53408 + 2.58366i) q^{66} +(5.99293 + 2.48235i) q^{67} +(4.39927 + 2.39854i) q^{68} +(-5.64204 - 2.33701i) q^{69} +(1.98701 + 13.7887i) q^{70} +15.7489i q^{71} +(-1.57452 + 0.0577458i) q^{72} -10.3198 q^{73} +(-3.48616 + 0.502371i) q^{74} +(1.57719 + 0.653292i) q^{75} +(-0.0767354 + 0.0619182i) q^{76} +(-5.01232 + 2.07617i) q^{77} +(0.865413 + 7.92261i) q^{78} +11.8419 q^{79} +(-5.62041 + 8.11705i) q^{80} +7.01854i q^{81} +(-2.76520 + 10.8484i) q^{82} +(4.71040 - 11.3719i) q^{83} +(-1.32568 + 12.4052i) q^{84} +(2.36642 + 5.71304i) q^{85} +(-6.48897 - 4.85435i) q^{86} +(-8.67243 - 8.67243i) q^{87} +(-3.60377 - 1.34020i) q^{88} +12.7689i q^{89} +(-1.55699 - 1.16477i) q^{90} +(-14.3813 - 0.493721i) q^{91} +(7.49642 - 2.20635i) q^{92} +(5.57876 - 13.4683i) q^{93} +(1.53081 + 2.57816i) q^{94} -0.121686 q^{95} +(-6.67279 + 5.80070i) q^{96} +(-4.25886 + 4.25886i) q^{97} +(-12.2351 - 3.11866i) q^{98} +(0.289785 - 0.699603i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9} - 4 q^{11} + 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} - 4 q^{19} - 20 q^{20} - 16 q^{21} - 24 q^{22}+ \cdots - 116 q^{99}+O(q^{100}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9 - 4 * q^11 + 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 - 4 * q^19 - 20 * q^20 - 16 * q^21 - 24 * q^22 + 28 * q^24 - 4 * q^26 - 8 * q^27 - 24 * q^28 - 8 * q^29 + 16 * q^30 - 4 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 + 20 * q^39 - 8 * q^40 - 48 * q^42 + 32 * q^43 - 20 * q^44 + 4 * q^45 - 24 * q^46 - 8 * q^47 - 8 * q^48 + 168 * q^49 + 20 * q^50 - 4 * q^52 - 8 * q^53 + 20 * q^54 - 40 * q^55 - 56 * q^56 - 8 * q^57 + 32 * q^58 + 4 * q^59 - 36 * q^60 - 8 * q^61 - 72 * q^62 - 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 - 4 * q^70 + 56 * q^72 - 8 * q^73 - 8 * q^74 - 4 * q^76 - 56 * q^77 - 136 * q^78 - 16 * q^79 + 28 * q^80 + 88 * q^82 - 44 * q^83 + 44 * q^84 - 24 * q^85 + 64 * q^86 - 8 * q^87 - 64 * q^88 + 64 * q^90 + 16 * q^91 - 8 * q^92 + 56 * q^93 - 56 * q^94 - 28 * q^96 - 8 * q^97 - 76 * q^98 - 116 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.37040	−	0.349306i	−0.969016	−	0.246997i
$2$	−1.37040	−	0.349306i	−0.969016	−	0.246997i
$3$	−0.598132	−	1.44402i	−0.345331	−	0.833704i	−0.997158	−	0.0753360i	$-0.975997\pi$
$3$	−0.598132	−	1.44402i	−0.345331	−	0.833704i	0.651827	−	0.758368i	$-0.274003\pi$
$4$	1.75597	+	0.957376i	0.877985	+	0.478688i
$5$	0.944556	+	2.28036i	0.422418	+	1.01981i	0.981632	+	0.190784i	$0.0611030\pi$
$5$	0.944556	+	2.28036i	0.422418	+	1.01981i	−0.559214	+	0.829023i	$0.688897\pi$
$6$	0.315273	+	2.18781i	0.128710	+	0.893168i
$7$	−3.99101			−1.50846			−0.754230	−	0.656611i	$-0.771989\pi$
$7$	−3.99101			−1.50846			−0.754230	+	0.656611i	$0.771989\pi$
$8$	−2.07196	−	1.92536i	−0.732548	−	0.680716i
$9$	0.393895	−	0.393895i	0.131298	−	0.131298i
$10$	−0.497872	−	3.45493i	−0.157441	−	1.09255i
$11$	1.25590	−	0.520212i	0.378669	−	0.156850i	−0.185227	−	0.982696i	$-0.559302\pi$
$11$	1.25590	−	0.520212i	0.378669	−	0.156850i	0.563896	+	0.825846i	$0.309302\pi$
$12$	0.332166	−	3.10829i	0.0958881	−	0.897286i
$13$	3.60343	+	0.123708i	0.999411	+	0.0343105i
$13$	3.60343	+	0.123708i	0.999411	+	0.0343105i
$14$	5.46926	+	1.39408i	1.46172	+	0.372585i
$15$	2.72791	−	2.72791i	0.704343	−	0.704343i
$16$	2.16686	+	3.36225i	0.541716	+	0.840562i
$17$	2.50532			0.607630			0.303815	−	0.952731i	$-0.401739\pi$
$17$	2.50532			0.607630			0.303815	+	0.952731i	$0.401739\pi$
$18$	−0.677382	+	0.402202i	−0.159661	+	0.0948000i
$19$	−0.0188665	+	0.0455478i	−0.00432827	+	0.0104494i	−0.926029	−	0.377453i	$-0.876800\pi$
$19$	−0.0188665	+	0.0455478i	−0.00432827	+	0.0104494i	0.921701	+	0.387902i	$0.126800\pi$
$20$	−0.524549	+	4.90854i	−0.117293	+	1.09758i
$21$	2.38715	+	5.76309i	0.520918	+	1.25761i
$22$	−1.90280	+	0.274202i	−0.405678	+	0.0584600i
$23$	2.76280	−	2.76280i	0.576083	−	0.576083i	−0.357739	−	0.933822i	$-0.616452\pi$
$23$	2.76280	−	2.76280i	0.576083	−	0.576083i	0.933822	+	0.357739i	$0.116452\pi$
$24$	−1.54094	+	4.14356i	−0.314544	+	0.845800i
$25$	−0.772317	+	0.772317i	−0.154463	+	0.154463i
$26$	−4.89491	−	1.42823i	−0.959971	−	0.280099i
$27$	−5.13645	−	2.12759i	−0.988509	−	0.409454i
$28$	−7.00809	−	3.82089i	−1.32440	−	0.722081i
$29$	7.24960	−	3.00288i	1.34622	−	0.557621i	0.410980	−	0.911644i	$-0.365187\pi$
$29$	7.24960	−	3.00288i	1.34622	−	0.557621i	0.935237	+	0.354023i	$0.115187\pi$
$30$	−4.69119	+	2.78544i	−0.856491	+	0.508550i
$31$	6.59516	+	6.59516i	1.18453	+	1.18453i	0.978559	+	0.205968i	$0.0660342\pi$
$31$	6.59516	+	6.59516i	1.18453	+	1.18453i	0.205968	+	0.978559i	$0.433966\pi$
$32$	−1.79501	−	5.36451i	−0.317315	−	0.948320i
$33$	−1.50239	−	1.50239i	−0.261533	−	0.261533i
$34$	−3.43329	−	0.875125i	−0.588804	−	0.150083i
$35$	−3.76973	−	9.10093i	−0.637200	−	1.53834i
$36$	1.06877	−	0.314563i	0.178129	−	0.0524271i
$37$	2.30097	−	0.953092i	0.378277	−	0.156687i	−0.185440	−	0.982656i	$-0.559371\pi$
$37$	2.30097	−	0.953092i	0.378277	−	0.156687i	0.563717	+	0.825968i	$0.309371\pi$
$38$	0.0417647	−	0.0558283i	0.00677513	−	0.00905655i
$39$	−1.97669	−	5.27741i	−0.316523	−	0.845062i
$40$	2.43342	−	6.54341i	0.384758	−	1.03460i
$41$		−	7.91626i		−	1.23631i	−0.786055	−	0.618156i	$-0.787880\pi$
$41$		−	7.91626i		−	1.23631i	0.786055	−	0.618156i	$-0.212120\pi$
$42$	−1.25826	−	8.73155i	−0.194153	−	1.34731i
$43$	5.29406	+	2.19287i	0.807336	+	0.334410i	0.747891	−	0.663822i	$-0.231067\pi$
$43$	5.29406	+	2.19287i	0.807336	+	0.334410i	0.0594456	+	0.998232i	$0.481067\pi$
$44$	2.70337	+	0.288894i	0.407548	+	0.0435524i
$45$	1.27028	+	0.526167i	0.189362	+	0.0784363i
$46$	−4.75119	+	2.82106i	−0.700525	+	0.415943i
$47$	−1.49919	−	1.49919i	−0.218679	−	0.218679i	0.589263	−	0.807942i	$-0.299418\pi$
$47$	−1.49919	−	1.49919i	−0.218679	−	0.218679i	−0.807942	+	0.589263i	$0.799418\pi$
$48$	3.55907	−	5.14005i	0.513708	−	0.741903i
$49$	8.92814			1.27545
$50$	1.32816	−	0.788605i	0.187830	−	0.111526i
$51$	−1.49851	−	3.61773i	−0.209834	−	0.506584i
$52$	6.20908	+	3.66706i	0.861044	+	0.508530i
$53$	−7.29352	−	3.02108i	−1.00184	−	0.414977i	−0.179370	−	0.983782i	$-0.557406\pi$
$53$	−7.29352	−	3.02108i	−1.00184	−	0.414977i	−0.822472	+	0.568805i	$0.807406\pi$
$54$	6.29579	+	4.70983i	0.856748	+	0.640926i
$55$	2.37254	+	2.37254i	0.319913	+	0.319913i
$56$	8.26920	+	7.68411i	1.10502	+	1.02683i
$57$	0.0770564			0.0102064
$58$	−10.9837	+	1.58281i	−1.44224	+	0.207833i
$59$	−4.15572	−	10.0328i	−0.541029	−	1.30616i	−0.923997	−	0.382399i	$-0.875098\pi$
$59$	−4.15572	−	10.0328i	−0.541029	−	1.30616i	0.382968	−	0.923762i	$-0.374902\pi$
$60$	7.40176	−	2.17849i	0.955563	−	0.281242i
$61$	−3.72929	+	1.54472i	−0.477487	+	0.197781i	−0.608429	−	0.793609i	$-0.708200\pi$
$61$	−3.72929	+	1.54472i	−0.477487	+	0.197781i	0.130942	+	0.991390i	$0.458200\pi$
$62$	−6.73425	−	11.3417i	−0.855251	−	1.44040i
$63$	−1.57204	+	1.57204i	−0.198058	+	0.198058i
$64$	0.586014	+	7.97851i	0.0732517	+	0.997313i
$65$	3.12154	+	8.33396i	0.387179	+	1.03370i
$66$	1.53408	+	2.58366i	0.188832	+	0.318027i
$67$	5.99293	+	2.48235i	0.732153	+	0.303268i	0.717436	−	0.696624i	$-0.245315\pi$
$67$	5.99293	+	2.48235i	0.732153	+	0.303268i	0.0147163	+	0.999892i	$0.495315\pi$
$68$	4.39927	+	2.39854i	0.533490	+	0.290865i
$69$	−5.64204	−	2.33701i	−0.679222	−	0.281343i
$70$	1.98701	+	13.7887i	0.237493	+	1.64806i
$71$			15.7489i			1.86905i	0.355897	+	0.934525i	$0.384175\pi$
$71$			15.7489i			1.86905i	−0.355897	+	0.934525i	$0.615825\pi$
$72$	−1.57452	+	0.0577458i	−0.185559	+	0.00680540i
$73$	−10.3198			−1.20784			−0.603920	−	0.797045i	$-0.706395\pi$
$73$	−10.3198			−1.20784			−0.603920	+	0.797045i	$0.706395\pi$
$74$	−3.48616	+	0.502371i	−0.405258	+	0.0583994i
$75$	1.57719	+	0.653292i	0.182118	+	0.0754357i
$76$	−0.0767354	+	0.0619182i	−0.00880215	+	0.00710250i
$77$	−5.01232	+	2.07617i	−0.571207	+	0.236602i
$78$	0.865413	+	7.92261i	0.0979887	+	0.897059i
$79$	11.8419			1.33231			0.666157	−	0.745811i	$-0.267938\pi$
$79$	11.8419			1.33231			0.666157	+	0.745811i	$0.267938\pi$
$80$	−5.62041	+	8.11705i	−0.628381	+	0.907514i
$81$			7.01854i			0.779837i
$82$	−2.76520	+	10.8484i	−0.305365	+	1.19801i
$83$	4.71040	−	11.3719i	0.517034	−	1.24823i	−0.422684	−	0.906277i	$-0.638912\pi$
$83$	4.71040	−	11.3719i	0.517034	−	1.24823i	0.939717	−	0.341952i	$-0.111088\pi$
$84$	−1.32568	+	12.4052i	−0.144643	+	1.35352i
$85$	2.36642	+	5.71304i	0.256674	+	0.619666i
$86$	−6.48897	−	4.85435i	−0.699724	−	0.523458i
$87$	−8.67243	−	8.67243i	−0.929782	−	0.929782i
$88$	−3.60377	−	1.34020i	−0.384163	−	0.142866i
$89$			12.7689i			1.35350i	0.736213	+	0.676749i	$0.236612\pi$
$89$			12.7689i			1.35350i	−0.736213	+	0.676749i	$0.763388\pi$
$90$	−1.55699	−	1.16477i	−0.164121	−	0.122778i
$91$	−14.3813	−	0.493721i	−1.50757	−	0.0517560i
$92$	7.49642	−	2.20635i	0.781556	−	0.230028i
$93$	5.57876	−	13.4683i	0.578490	−	1.39660i
$94$	1.53081	+	2.57816i	0.157890	+	0.265917i
$95$	−0.121686			−0.0124847
$96$	−6.67279	+	5.80070i	−0.681039	+	0.592032i
$97$	−4.25886	+	4.25886i	−0.432421	+	0.432421i	−0.889451	−	0.457030i	$-0.848913\pi$
$97$	−4.25886	+	4.25886i	−0.432421	+	0.432421i	0.457030	+	0.889451i	$0.348913\pi$
$98$	−12.2351	−	3.11866i	−1.23593	−	0.315032i
$99$	0.289785	−	0.699603i	0.0291245	−	0.0703128i
$100$	−2.09556	+	0.616768i	−0.209556	+	0.0616768i
$101$	3.07479	+	1.27362i	0.305953	+	0.126730i	0.530377	−	0.847762i	$-0.322050\pi$
$101$	3.07479	+	1.27362i	0.305953	+	0.126730i	−0.224425	+	0.974491i	$0.572050\pi$
$102$	0.789861	+	5.48116i	0.0782078	+	0.542716i
$103$	8.07721	+	8.07721i	0.795871	+	0.795871i	0.982442	−	0.186570i	$-0.0597372\pi$
$103$	8.07721	+	8.07721i	0.795871	+	0.795871i	−0.186570	+	0.982442i	$0.559737\pi$
$104$	−7.22797	−	7.19420i	−0.708760	−	0.705449i
$105$	−10.8871	+	10.8871i	−1.06247	+	1.06247i
$106$	8.93973	+	6.68774i	0.868304	+	0.649571i
$107$	1.31983	−	3.18634i	0.127592	−	0.308035i	−0.847155	−	0.531346i	$-0.821686\pi$
$107$	1.31983	−	3.18634i	0.127592	−	0.308035i	0.974747	+	0.223311i	$0.0716864\pi$
$108$	−6.98255	−	8.65348i	−0.671896	−	0.832682i
$109$	−8.80704	−	3.64800i	−0.843562	−	0.349415i	−0.0813049	−	0.996689i	$-0.525909\pi$
$109$	−8.80704	−	3.64800i	−0.843562	−	0.349415i	−0.762257	+	0.647274i	$0.775909\pi$
$110$	−2.42258	−	4.08006i	−0.230984	−	0.389019i
$111$	−2.75256	−	2.75256i	−0.261262	−	0.261262i
$112$	−8.64797	−	13.4188i	−0.817156	−	1.26795i
$113$			2.59394i			0.244018i	0.992529	+	0.122009i	$0.0389336\pi$
$113$			2.59394i			0.244018i	−0.992529	+	0.122009i	$0.961066\pi$
$114$	−0.105598	−	0.0269163i	−0.00989014	−	0.00252094i
$115$	8.90978	+	3.69055i	0.830842	+	0.344146i
$116$	15.6050	+	1.66762i	1.44888	+	0.154834i
$117$	1.46810	−	1.37065i	0.135726	−	0.126716i
$118$	2.19047	+	15.2005i	0.201649	+	1.39932i
$119$	−9.99877			−0.916585
$120$	−10.9043	+	0.399917i	−0.995422	+	0.0365072i
$121$	−6.47150	+	6.47150i	−0.588318	+	0.588318i
$122$	5.65019	−	0.814217i	0.511544	−	0.0737158i
$123$	−11.4312	+	4.73497i	−1.03072	+	0.426938i
$124$	5.26686	+	17.8950i	0.472978	+	1.60702i
$125$	8.91114	+	3.69111i	0.797036	+	0.330143i
$126$	2.70344	−	1.60519i	0.240841	−	0.143002i
$127$	4.63435			0.411232			0.205616	−	0.978633i	$-0.434080\pi$
$127$	4.63435			0.411232			0.205616	+	0.978633i	$0.434080\pi$
$128$	1.98387	−	11.1384i	0.175351	−	0.984506i
$129$		−	8.95634i		−	0.788562i
$130$	−1.36664	−	12.5112i	−0.119862	−	1.09730i
$131$	−4.94654	−	11.9420i	−0.432181	−	1.04338i	−0.978583	−	0.205854i	$-0.934003\pi$
$131$	−4.94654	−	11.9420i	−0.432181	−	1.04338i	0.546402	−	0.837523i	$-0.315997\pi$
$132$	−1.19980	−	4.07651i	−0.104429	−	0.354814i
$133$	0.0752964	−	0.181782i	0.00652902	−	0.0157625i
$134$	−7.34558	−	5.49517i	−0.634562	−	0.474711i
$135$		−	13.7226i		−	1.18105i
$136$	−5.19092	−	4.82364i	−0.445118	−	0.413624i
$137$	6.00387			0.512945			0.256472	−	0.966552i	$-0.417440\pi$
$137$	6.00387			0.512945			0.256472	+	0.966552i	$0.417440\pi$
$138$	6.91550	+	5.17343i	0.588687	+	0.440392i
$139$	−1.26567	+	3.05560i	−0.107353	+	0.259173i	−0.968423	−	0.249314i	$-0.919795\pi$
$139$	−1.26567	+	3.05560i	−0.107353	+	0.259173i	0.861070	+	0.508487i	$0.169795\pi$
$140$	2.09348	−	19.5900i	0.176931	−	1.65566i
$141$	−1.26814	+	3.06156i	−0.106797	+	0.257830i
$142$	5.50119	−	21.5822i	0.461650	−	1.81114i
$143$	4.58991	−	1.71918i	0.383828	−	0.143765i
$144$	2.17789	+	0.470856i	0.181491	+	0.0392380i
$145$	13.6953	+	13.6953i	1.13733	+	1.13733i
$146$	14.1422	+	3.60477i	1.17042	+	0.298333i
$147$	−5.34020	−	12.8924i	−0.440453	−	1.06335i
$148$	4.95290	+	0.529289i	0.407126	+	0.0435073i
$149$	4.67896	−	1.93809i	0.383315	−	0.158774i	−0.182701	−	0.983169i	$-0.558484\pi$
$149$	4.67896	−	1.93809i	0.383315	−	0.158774i	0.566016	+	0.824394i	$0.308484\pi$
$150$	−1.93317	−	1.44619i	−0.157843	−	0.118081i
$151$			12.5444i			1.02085i	0.859922	+	0.510426i	$0.170512\pi$
$151$			12.5444i			1.02085i	−0.859922	+	0.510426i	$0.829488\pi$
$152$	0.126786	−	0.0580483i	0.0102837	−	0.00470834i
$153$	0.986835	−	0.986835i	0.0797809	−	0.0797809i
$154$	7.59408	−	1.09434i	0.611948	−	0.0881845i
$155$	−8.80984	+	21.2688i	−0.707624	+	1.70835i
$156$	1.58146	−	11.1594i	0.126618	−	0.893467i
$157$	−20.7501	+	8.59498i	−1.65604	+	0.685954i	−0.997765	−	0.0668236i	$-0.978714\pi$
$157$	−20.7501	+	8.59498i	−1.65604	+	0.685954i	−0.658275	+	0.752778i	$0.728714\pi$
$158$	−16.2281	−	4.13644i	−1.29103	−	0.329077i
$159$			12.3390i			0.978545i
$160$	10.5375	−	9.16034i	0.833064	−	0.724188i
$161$	−11.0263	+	11.0263i	−0.868998	+	0.868998i
$162$	2.45162	−	9.61818i	0.192617	−	0.755675i
$163$	−4.15971	+	10.0424i	−0.325814	+	0.786584i	0.673080	+	0.739569i	$0.264971\pi$
$163$	−4.15971	+	10.0424i	−0.325814	+	0.786584i	−0.998894	+	0.0470148i	$0.985029\pi$
$164$	7.57884	−	13.9007i	0.591808	−	1.08546i
$165$	2.00690	−	4.84508i	0.156237	−	0.377189i
$166$	−10.4274	+	13.9387i	−0.809323	+	1.08185i
$167$	11.0815			0.857510			0.428755	−	0.903421i	$-0.358952\pi$
$167$	11.0815			0.857510			0.428755	+	0.903421i	$0.358952\pi$
$168$	6.14992	−	16.5370i	0.474476	−	1.27586i
$169$	12.9694	+	0.891548i	0.997646	+	0.0685806i
$170$	−1.24733	−	8.65573i	−0.0956658	−	0.663864i
$171$	0.0105096	+	0.0253725i	0.000803691	+	0.00194028i
$172$	7.19681	+	8.91902i	0.548751	+	0.680069i
$173$	−20.4716	+	8.47961i	−1.55643	+	0.644693i	−0.984464	−	0.175587i	$-0.943818\pi$
$173$	−20.4716	+	8.47961i	−1.55643	+	0.644693i	−0.571963	+	0.820280i	$0.693818\pi$
$174$	8.85533	+	14.9140i	0.671321	+	1.13063i
$175$	3.08232	−	3.08232i	0.233002	−	0.233002i
$176$	4.47045	+	3.09543i	0.336973	+	0.233327i
$177$	−12.0019	+	12.0019i	−0.902116	+	0.902116i
$178$	4.46025	−	17.4984i	0.334310	−	1.31156i
$179$	−3.12282	−	7.53915i	−0.233411	−	0.563503i	0.763164	−	0.646205i	$-0.223645\pi$
$179$	−3.12282	−	7.53915i	−0.233411	−	0.563503i	−0.996574	+	0.0827023i	$0.973645\pi$
$180$	1.72683	+	2.14007i	0.128710	+	0.159511i
$181$	5.96815	−	14.4084i	0.443609	−	1.07097i	−0.531063	−	0.847332i	$-0.678207\pi$
$181$	5.96815	−	14.4084i	0.443609	−	1.07097i	0.974673	−	0.223636i	$-0.0717926\pi$
$182$	19.5356	+	5.70007i	1.44808	+	0.422518i
$183$	4.46121	+	4.46121i	0.329782	+	0.329782i
$184$	−11.0438	+	0.405031i	−0.814157	+	0.0298593i
$185$	4.34678	+	4.34678i	0.319582	+	0.319582i
$186$	−12.3497	+	16.5082i	−0.905522	+	1.21044i
$187$	3.14644	−	1.30330i	0.230091	−	0.0953067i
$188$	−1.19724	−	4.06781i	−0.0873179	−	0.296676i
$189$	20.4996	+	8.49121i	1.49113	+	0.617645i
$190$	0.166758	+	0.0425056i	0.0120979	+	0.00308368i
$191$		−	3.48429i		−	0.252114i	−0.992023	−	0.126057i	$-0.959768\pi$
$191$		−	3.48429i		−	0.252114i	0.992023	−	0.126057i	$-0.0402323\pi$
$192$	11.1706	−	5.61841i	0.806168	−	0.405474i
$193$	−4.18981	−	4.18981i	−0.301589	−	0.301589i	0.540046	−	0.841635i	$-0.318407\pi$
$193$	−4.18981	−	4.18981i	−0.301589	−	0.301589i	−0.841635	+	0.540046i	$0.818407\pi$
$194$	7.32396	−	4.34867i	0.525830	−	0.312217i
$195$	10.1673	−	9.49236i	0.728095	−	0.679762i
$196$	15.6776	+	8.54759i	1.11983	+	0.610542i
$197$	−5.95330	−	14.3725i	−0.424155	−	1.02400i	−0.981109	−	0.193458i	$-0.938030\pi$
$197$	−5.95330	−	14.3725i	−0.424155	−	1.02400i	0.556953	−	0.830544i	$-0.311970\pi$
$198$	−0.641496	+	0.857510i	−0.0455891	+	0.0609406i
$199$	−14.0679	−	14.0679i	−0.997248	−	0.997248i	0.00274833	−	0.999996i	$-0.499125\pi$
$199$	−14.0679	−	14.0679i	−0.997248	−	0.997248i	−0.999996	+	0.00274833i	$0.999125\pi$
$200$	3.08719	−	0.113223i	0.218298	−	0.00800609i
$201$		−	10.1387i		−	0.715126i
$202$	−3.76879	−	2.81940i	−0.265171	−	0.198372i
$203$	−28.9332	+	11.9845i	−2.03071	+	0.841149i
$204$	0.832183	−	7.78727i	0.0582645	−	0.545218i
$205$	18.0519	−	7.47735i	1.26080	−	0.522241i
$206$	−8.24756	−	13.8904i	−0.574635	−	0.967790i
$207$		−	2.17651i		−	0.151278i
$208$	7.39220	+	12.3837i	0.512557	+	0.858653i
$209$			0.0670182i			0.00463574i
$210$	18.7226	−	11.1167i	1.29198	−	0.767126i
$211$	−9.31229	+	3.85728i	−0.641084	+	0.265546i	−0.679454	−	0.733718i	$-0.737783\pi$
$211$	−9.31229	+	3.85728i	−0.641084	+	0.265546i	0.0383700	+	0.999264i	$0.487783\pi$
$212$	−9.91491	−	12.2876i	−0.680959	−	0.843913i
$213$	22.7417	−	9.41992i	1.55823	−	0.645442i
$214$	−2.92169	+	3.90553i	−0.199723	+	0.266976i
$215$			14.1436i			0.964588i
$216$	6.54614	+	14.2977i	0.445408	+	0.972839i
$217$	−26.3214	−	26.3214i	−1.78681	−	1.78681i
$218$	10.7949	+	8.07556i	0.731121	+	0.546946i
$219$	6.17259	+	14.9020i	0.417105	+	1.00698i
$220$	1.89470	+	6.43752i	0.127740	+	0.434018i
$221$	9.02775	+	0.309929i	0.607273	+	0.0208481i
$222$	2.81061	+	4.73359i	0.188636	+	0.317698i
$223$	−3.57447	−	3.57447i	−0.239364	−	0.239364i	0.577223	−	0.816587i	$-0.304136\pi$
$223$	−3.57447	−	3.57447i	−0.239364	−	0.239364i	−0.816587	+	0.577223i	$0.804136\pi$
$224$	7.16389	+	21.4098i	0.478657	+	1.43050i
$225$			0.608424i			0.0405616i
$226$	0.906080	−	3.55473i	0.0602715	−	0.236457i
$227$	10.8096	+	4.47750i	0.717462	+	0.297182i	0.711388	−	0.702799i	$-0.248067\pi$
$227$	10.8096	+	4.47750i	0.717462	+	0.297182i	0.00607335	+	0.999982i	$0.498067\pi$
$228$	0.135309	+	0.0737720i	0.00896104	+	0.00488567i
$229$	14.4414	−	5.98182i	0.954313	−	0.395290i	0.149463	−	0.988767i	$-0.452246\pi$
$229$	14.4414	−	5.98182i	0.954313	−	0.395290i	0.804850	+	0.593478i	$0.202246\pi$
$230$	−10.9208	−	8.16976i	−0.720096	−	0.538698i
$231$	5.99605	+	5.99605i	0.394511	+	0.394511i
$232$	−20.8025	−	7.73621i	−1.36575	−	0.507907i
$233$	−10.5598	−	10.5598i	−0.691799	−	0.691799i	0.270829	−	0.962628i	$-0.412702\pi$
$233$	−10.5598	−	10.5598i	−0.691799	−	0.691799i	−0.962628	+	0.270829i	$0.912702\pi$
$234$	−2.49066	+	1.36551i	−0.162819	+	0.0892661i
$235$	2.00262	−	4.83475i	0.130637	−	0.315384i
$236$	2.30784	−	21.5959i	0.150227	−	1.40577i
$237$	−7.08300	−	17.0999i	−0.460090	−	1.11076i
$238$	13.7023	+	3.49263i	0.888186	+	0.226394i
$239$	13.1406	−	13.1406i	0.849992	−	0.849992i	−0.140140	−	0.990132i	$-0.544755\pi$
$239$	13.1406	−	13.1406i	0.849992	−	0.849992i	0.990132	+	0.140140i	$0.0447552\pi$
$240$	15.0829	+	3.26090i	0.973598	+	0.210490i
$241$	−3.83639	+	3.83639i	−0.247124	+	0.247124i	−0.819789	−	0.572665i	$-0.805909\pi$
$241$	−3.83639	+	3.83639i	−0.247124	+	0.247124i	0.572665	+	0.819789i	$0.305909\pi$
$242$	11.1291	−	6.60799i	0.715403	−	0.424777i
$243$	−5.27445	+	2.18475i	−0.338356	+	0.140152i
$244$	−8.02740	−	0.857845i	−0.513902	−	0.0549179i
$245$	8.43313	+	20.3594i	0.538773	+	1.30071i
$246$	17.3193	−	2.49578i	1.10424	−	0.159125i
$247$	−0.0736187	+	0.161794i	−0.00468425	+	0.0102947i
$248$	−0.966863	−	26.3629i	−0.0613959	−	1.67405i
$249$	−19.2387			−1.21920
$250$	−10.9225	−	8.17100i	−0.690797	−	0.516780i
$251$	0.445627	−	1.07584i	0.0281277	−	0.0679064i	−0.909192	−	0.416378i	$-0.863299\pi$
$251$	0.445627	−	1.07584i	0.0281277	−	0.0679064i	0.937319	+	0.348472i	$0.113299\pi$
$252$	−4.26549	+	1.25542i	−0.268700	+	0.0790841i
$253$	2.03256	−	4.90705i	0.127786	−	0.308503i
$254$	−6.35090	−	1.61881i	−0.398491	−	0.101573i
$255$	6.83430	−	6.83430i	0.427980	−	0.427980i
$256$	−6.60941	+	14.5711i	−0.413088	+	0.910691i
$257$		−	2.06870i		−	0.129042i	−0.997916	−	0.0645210i	$-0.979448\pi$
$257$		−	2.06870i		−	0.129042i	0.997916	−	0.0645210i	$-0.0205519\pi$
$258$	−3.12850	+	12.2737i	−0.194772	+	0.764129i
$259$	−9.18318	+	3.80380i	−0.570615	+	0.236356i
$260$	−2.49740	+	17.6227i	−0.154882	+	1.09291i
$261$	1.67276	−	4.03840i	0.103541	−	0.249971i
$262$	2.60730	+	18.0931i	0.161080	+	1.11780i
$263$	−6.83532	+	6.83532i	−0.421484	+	0.421484i	−0.885714	−	0.464231i	$-0.846331\pi$
$263$	−6.83532	+	6.83532i	−0.421484	+	0.421484i	0.464231	+	0.885714i	$0.346331\pi$
$264$	0.220253	+	6.00552i	0.0135557	+	0.369615i
$265$		−	19.4854i		−	1.19698i
$266$	−0.166683	+	0.222811i	−0.0102200	+	0.0136614i
$267$	18.4385	−	7.63747i	1.12842	−	0.467406i
$268$	8.14686	+	10.0964i	0.497649	+	0.616737i
$269$	3.61403	+	8.72505i	0.220352	+	0.531976i	0.994938	−	0.100493i	$-0.0320419\pi$
$269$	3.61403	+	8.72505i	0.220352	+	0.531976i	−0.774586	+	0.632468i	$0.782042\pi$
$270$	−4.79338	+	18.8053i	−0.291716	+	1.14446i
$271$	−9.77094	−	9.77094i	−0.593543	−	0.593543i	0.345044	−	0.938587i	$-0.387864\pi$
$271$	−9.77094	−	9.77094i	−0.593543	−	0.593543i	−0.938587	+	0.345044i	$0.887864\pi$
$272$	5.42869	+	8.42352i	0.329163	+	0.510751i
$273$	7.88898	+	21.0622i	0.477463	+	1.27474i
$274$	−8.22767	−	2.09719i	−0.497052	−	0.126696i
$275$	−0.568187	+	1.37172i	−0.0342630	+	0.0827181i
$276$	−7.66986	−	9.50528i	−0.461672	−	0.572151i
$277$	8.70567	−	21.0174i	0.523073	−	1.26281i	−0.412912	−	0.910771i	$-0.635488\pi$
$277$	8.70567	−	21.0174i	0.523073	−	1.26281i	0.935985	−	0.352039i	$-0.114512\pi$
$278$	2.80181	−	3.74528i	0.168042	−	0.224627i
$279$	5.19561			0.311053
$280$	−9.71181	+	26.1148i	−0.580392	+	1.56066i
$281$		−	19.4402i		−	1.15970i	−0.814722	−	0.579851i	$-0.803111\pi$
$281$		−	19.4402i		−	1.15970i	0.814722	−	0.579851i	$-0.196889\pi$
$282$	2.80728	−	3.75259i	0.167171	−	0.223463i
$283$	0.871315	−	2.10354i	0.0517943	−	0.125042i	−0.895864	−	0.444327i	$-0.853443\pi$
$283$	0.871315	−	2.10354i	0.0517943	−	0.125042i	0.947659	+	0.319285i	$0.103443\pi$
$284$	−15.0776	+	27.6546i	−0.894692	+	1.64100i
$285$	0.0727841	+	0.175716i	0.00431136	+	0.0104085i
$286$	−6.89052	+	0.752674i	−0.407445	+	0.0445066i
$287$			31.5939i			1.86493i
$288$	−2.82010	−	1.40601i	−0.166176	−	0.0828499i
$289$	−10.7234			−0.630785
$290$	−13.9841	−	23.5518i	−0.821176	−	1.38301i
$291$	8.69722	+	3.60251i	0.509840	+	0.211183i
$292$	−18.1212	−	9.87991i	−1.06047	−	0.578178i
$293$	−10.1294	+	4.19575i	−0.591769	+	0.245119i	−0.658411	−	0.752658i	$-0.728771\pi$
$293$	−10.1294	+	4.19575i	−0.591769	+	0.245119i	0.0666427	+	0.997777i	$0.478771\pi$
$294$	2.81480	+	19.5331i	0.164163	+	1.13919i
$295$	18.9531	−	18.9531i	1.10349	−	1.10349i
$296$	−6.60255	−	2.45541i	−0.383765	−	0.142718i
$297$	−7.55767			−0.438541
$298$	−7.08901	+	1.02156i	−0.410656	+	0.0591773i
$299$	10.2973	−	9.61376i	0.595510	−	0.555978i
$300$	2.14405	+	2.65712i	0.123787	+	0.153409i
$301$	−21.1286	−	8.75176i	−1.21783	−	0.504443i
$302$	4.38185	−	17.1908i	0.252147	−	0.989221i
$303$		−	5.20183i		−	0.298838i
$304$	−0.194024	+	0.0352619i	−0.0111280	+	0.00202241i
$305$	−7.04504	−	7.04504i	−0.403398	−	0.403398i
$306$	−1.69706	+	1.00765i	−0.0970146	+	0.0576034i
$307$	−17.0226	−	7.05097i	−0.971528	−	0.402420i	−0.160248	−	0.987077i	$-0.551229\pi$
$307$	−17.0226	−	7.05097i	−0.971528	−	0.402420i	−0.811281	+	0.584657i	$0.801229\pi$
$308$	−10.7892	−	1.15298i	−0.614769	−	0.0656971i
$309$	6.83240	−	16.4949i	0.388682	−	0.938360i
$310$	19.5023	−	26.0694i	1.10766	−	1.48064i
$311$	−13.6580	+	13.6580i	−0.774475	+	0.774475i	−0.978885	−	0.204411i	$-0.934472\pi$
$311$	−13.6580	+	13.6580i	−0.774475	+	0.774475i	0.204411	+	0.978885i	$0.434472\pi$
$312$	−6.06527	+	14.7404i	−0.343378	+	0.834510i
$313$	16.6480	+	16.6480i	0.940998	+	0.940998i	0.998354	−	0.0573554i	$-0.0182668\pi$
$313$	16.6480	+	16.6480i	0.940998	+	0.940998i	−0.0573554	+	0.998354i	$0.518267\pi$
$314$	31.4382	−	4.53038i	1.77416	−	0.255664i
$315$	−5.06969	−	2.09993i	−0.285645	−	0.118318i
$316$	20.7940	+	11.3371i	1.16975	+	0.637763i
$317$	−13.2372	+	31.9574i	−0.743475	+	1.79491i	−0.152352	+	0.988326i	$0.548685\pi$
$317$	−13.2372	+	31.9574i	−0.743475	+	1.79491i	−0.591123	+	0.806582i	$0.701315\pi$
$318$	4.31008	−	16.9093i	0.241697	−	0.948226i
$319$	7.54266	−	7.54266i	0.422308	−	0.422308i
$320$	−17.6403	+	8.87246i	−0.986125	+	0.495986i
$321$	−5.39057			−0.300872
$322$	18.9620	−	11.2589i	1.05671	−	0.627433i
$323$	−0.0472667	+	0.114112i	−0.00262999	+	0.00634936i
$324$	−6.71938	+	12.3243i	−0.373299	+	0.684686i
$325$	−2.87853	+	2.68745i	−0.159672	+	0.149073i
$326$	9.20834	−	12.3091i	0.510003	−	0.681738i
$327$			14.8995i			0.823945i
$328$	−15.2416	+	16.4022i	−0.841577	+	0.905657i
$329$	5.98327	+	5.98327i	0.329868	+	0.329868i
$330$	−4.44266	+	5.93866i	−0.244561	+	0.326912i
$331$	5.15554	+	12.4466i	0.283374	+	0.684126i	0.999910	−	0.0134245i	$-0.00427327\pi$
$331$	5.15554	+	12.4466i	0.283374	+	0.684126i	−0.716536	+	0.697551i	$0.754273\pi$
$332$	19.1585	−	15.4591i	1.05146	−	0.848429i
$333$	0.530922	−	1.28176i	0.0290943	−	0.0702399i
$334$	−15.1860	−	3.87083i	−0.830941	−	0.211802i
$335$			16.0107i			0.874760i
$336$	−14.2043	+	20.5140i	−0.774908	+	1.11913i
$337$	21.0080			1.14438			0.572190	−	0.820121i	$-0.306094\pi$
$337$	21.0080			1.14438			0.572190	+	0.820121i	$0.306094\pi$
$338$	−17.4618	−	5.75206i	−0.949796	−	0.312871i
$339$	3.74570	−	1.55152i	0.203438	−	0.0842669i
$340$	−1.31416	+	12.2975i	−0.0712706	+	0.666924i
$341$	11.7138	+	4.85200i	0.634336	+	0.262751i
$342$	−0.00553958	−	0.0384414i	−0.000299546	−	0.00207867i
$343$	−7.69523			−0.415503
$344$	−6.74701	−	14.7365i	−0.363774	−	0.794538i
$345$		−	15.0733i		−	0.811520i
$346$	31.0162	−	4.46957i	1.66744	−	0.240286i
$347$	7.24218	+	2.99981i	0.388781	+	0.161038i	0.568507	−	0.822678i	$-0.307521\pi$
$347$	7.24218	+	2.99981i	0.388781	+	0.161038i	−0.179726	+	0.983717i	$0.557521\pi$
$348$	−6.92575	−	23.5313i	−0.371259	−	1.26141i
$349$	−21.3656	−	8.84992i	−1.14367	−	0.473726i	−0.271267	−	0.962504i	$-0.587443\pi$
$349$	−21.3656	−	8.84992i	−1.14367	−	0.473726i	−0.872408	+	0.488779i	$0.837443\pi$
$350$	−5.30068	+	3.14733i	−0.283333	+	0.168232i
$351$	−18.2456	−	8.30202i	−0.973879	−	0.443129i
$352$	−5.04504	−	5.80352i	−0.268901	−	0.309329i
$353$	−11.0991	+	11.0991i	−0.590746	+	0.590746i	−0.937833	−	0.347087i	$-0.887171\pi$
$353$	−11.0991	+	11.0991i	−0.590746	+	0.590746i	0.347087	+	0.937833i	$0.387171\pi$
$354$	20.6397	−	12.2550i	1.09699	−	0.651346i
$355$	−35.9131	+	14.8757i	−1.90607	+	0.789521i
$356$	−12.2246	+	22.4218i	−0.647904	+	1.18835i
$357$	5.98058	+	14.4384i	0.316526	+	0.764161i
$358$	1.64603	+	11.4224i	0.0869952	+	0.603695i
$359$	−33.1007			−1.74699			−0.873495	−	0.486832i	$-0.838152\pi$
$359$	−33.1007			−1.74699			−0.873495	+	0.486832i	$0.838152\pi$
$360$	−1.61890	−	3.53593i	−0.0853238	−	0.186360i
$361$	13.4333	+	13.4333i	0.707016	+	0.707016i
$362$	−13.2117	+	17.6605i	−0.694390	+	0.928215i
$363$	13.2158	+	5.47415i	0.693648	+	0.287319i
$364$	−24.7805	−	14.6353i	−1.29885	−	0.767097i
$365$	−9.74761	−	23.5328i	−0.510213	−	1.23176i
$366$	−4.55530	−	7.67196i	−0.238109	−	0.401020i
$367$	−12.6816			−0.661975			−0.330988	−	0.943635i	$-0.607382\pi$
$367$	−12.6816			−0.661975			−0.330988	+	0.943635i	$0.607382\pi$
$368$	15.2758	+	3.30260i	0.796307	+	0.172160i
$369$	−3.11818	−	3.11818i	−0.162326	−	0.162326i
$370$	−4.43846	−	7.47517i	−0.230744	−	0.388616i
$371$	29.1085	+	12.0571i	1.51124	+	0.625975i
$372$	22.6904	−	18.3090i	1.17644	−	0.949277i
$373$	24.9962	+	10.3538i	1.29425	+	0.536098i	0.920251	−	0.391329i	$-0.127985\pi$
$373$	24.9962	+	10.3538i	1.29425	+	0.536098i	0.374004	+	0.927427i	$0.377985\pi$
$374$	−4.76712	+	0.686964i	−0.246502	+	0.0355221i
$375$		−	15.0756i		−	0.778501i
$376$	0.219784	+	5.99272i	0.0113345	+	0.309051i
$377$	26.4949	−	9.92383i	1.36456	−	0.511103i
$378$	−25.1265	−	18.7970i	−1.29237	−	0.966811i
$379$	5.57935	−	2.31104i	0.286592	−	0.118710i	−0.234756	−	0.972054i	$-0.575429\pi$
$379$	5.57935	−	2.31104i	0.286592	−	0.118710i	0.521348	+	0.853344i	$0.325429\pi$
$380$	−0.213677	−	0.116499i	−0.0109614	−	0.00597627i
$381$	−2.77195	−	6.69209i	−0.142011	−	0.342846i
$382$	−1.21708	+	4.77486i	−0.0622714	+	0.244303i
$383$	19.7375	+	19.7375i	1.00854	+	1.00854i	0.999963	+	0.00857352i	$0.00272907\pi$
$383$	19.7375	+	19.7375i	1.00854	+	1.00854i	0.00857352	+	0.999963i	$0.497271\pi$
$384$	−17.2707	+	3.79749i	−0.881341	+	0.193790i
$385$	−9.46883	−	9.46883i	−0.482576	−	0.482576i
$386$	4.27817	+	7.20523i	0.217753	+	0.366736i
$387$	2.94907	−	1.22154i	0.149909	−	0.0620945i
$388$	−11.5558	+	3.40110i	−0.586654	+	0.172665i
$389$	7.16766	+	2.96894i	0.363415	+	0.150531i	0.556916	−	0.830569i	$-0.311984\pi$
$389$	7.16766	+	2.96894i	0.363415	+	0.150531i	−0.193501	+	0.981100i	$0.561984\pi$
$390$	−17.2490	+	9.45680i	−0.873435	+	0.478863i
$391$	6.92170	−	6.92170i	0.350045	−	0.350045i
$392$	−18.4987	−	17.1898i	−0.934327	−	0.868218i
$393$	−14.2858	+	14.2858i	−0.720622	+	0.720622i
$394$	3.13796	+	21.7756i	0.158088	+	1.09704i
$395$	11.1853	+	27.0037i	0.562794	+	1.35870i
$396$	1.17864	−	0.951049i	0.0592287	−	0.0477920i
$397$	−6.15623	+	14.8625i	−0.308973	+	0.745926i	0.690766	+	0.723078i	$0.257273\pi$
$397$	−6.15623	+	14.8625i	−0.308973	+	0.745926i	−0.999739	+	0.0228477i	$0.992727\pi$
$398$	14.3646	+	24.1926i	0.720032	+	1.21267i
$399$	−0.307533			−0.0153959
$400$	−4.27023	−	0.923215i	−0.213511	−	0.0461608i
$401$	6.79073	−	6.79073i	0.339113	−	0.339113i	−0.516921	−	0.856033i	$-0.672922\pi$
$401$	6.79073	−	6.79073i	0.339113	−	0.339113i	0.856033	+	0.516921i	$0.172922\pi$
$402$	−3.54150	+	13.8940i	−0.176634	+	0.692969i
$403$	22.9493	+	24.5811i	1.14319	+	1.22447i
$404$	4.17990	+	5.18016i	0.207958	+	0.257723i
$405$	−16.0048	+	6.62940i	−0.795284	+	0.329417i
$406$	43.8362	−	6.31700i	2.17555	−	0.313507i
$407$	2.39398	−	2.39398i	0.118665	−	0.118665i
$408$	−3.86056	+	10.3810i	−0.191126	+	0.513934i
$409$	−22.4604			−1.11060			−0.555298	−	0.831652i	$-0.687396\pi$
$409$	−22.4604			−1.11060			−0.555298	+	0.831652i	$0.687396\pi$
$410$	−27.3502	+	3.94128i	−1.35073	+	0.194646i
$411$	−3.59110	−	8.66969i	−0.177136	−	0.427644i
$412$	6.45042	+	21.9163i	0.317789	+	1.07974i
$413$	16.5855	+	40.0410i	0.816121	+	1.97029i
$414$	−0.760267	+	2.98267i	−0.0373651	+	0.146590i
$415$	30.3813			1.49136
$416$	−5.80454	−	19.5527i	−0.284591	−	0.958649i
$417$	5.16938			0.253146
$418$	0.0234099	−	0.0918414i	0.00114501	−	0.00449211i
$419$	−3.48891	−	8.42297i	−0.170444	−	0.411489i	0.815457	−	0.578818i	$-0.196486\pi$
$419$	−3.48891	−	8.42297i	−0.170444	−	0.411489i	−0.985901	+	0.167329i	$0.946486\pi$
$420$	−29.5405	+	8.69438i	−1.44143	+	0.424243i
$421$	−12.9995	−	31.3835i	−0.633556	−	1.52954i	−0.835122	−	0.550064i	$-0.814603\pi$
$421$	−12.9995	−	31.3835i	−0.633556	−	1.52954i	0.201567	−	0.979475i	$-0.435397\pi$
$422$	14.1089	−	2.03316i	0.686810	−	0.0989724i
$423$	−1.18105			−0.0574244
$424$	9.29522	+	20.3022i	0.451416	+	0.985960i
$425$	−1.93490	+	1.93490i	−0.0938567	+	0.0938567i
$426$	−34.4556	+	4.96520i	−1.66938	+	0.240565i
$427$	14.8836	−	6.16500i	0.720269	−	0.298345i
$428$	5.36810	−	4.33155i	0.259477	−	0.209374i
$429$	−5.22790	−	5.59962i	−0.252405	−	0.270352i
$430$	4.94046	−	19.3824i	0.238250	−	0.934702i
$431$	−24.0861	+	24.0861i	−1.16019	+	1.16019i	−0.175754	+	0.984434i	$0.556236\pi$
$431$	−24.0861	+	24.0861i	−1.16019	+	1.16019i	−0.984434	+	0.175754i	$0.943764\pi$
$432$	−3.97651	−	21.8802i	−0.191320	−	1.05271i
$433$	10.6659			0.512571			0.256285	−	0.966601i	$-0.417501\pi$
$433$	10.6659			0.512571			0.256285	+	0.966601i	$0.417501\pi$
$434$	26.8765	+	45.2649i	1.29011	+	2.17278i
$435$	11.5847	−	27.9678i	0.555442	−	1.34096i
$436$	−11.9724	−	14.8374i	−0.573374	−	0.710584i
$437$	0.0737149	+	0.177964i	0.00352626	+	0.00851315i
$438$	−3.25355	−	22.5777i	−0.155461	−	1.07880i
$439$	−22.9852	+	22.9852i	−1.09702	+	1.09702i	−0.102267	+	0.994757i	$0.532610\pi$
$439$	−22.9852	+	22.9852i	−1.09702	+	1.09702i	−0.994757	+	0.102267i	$0.967390\pi$
$440$	−0.347819	−	9.48378i	−0.0165816	−	0.452122i
$441$	3.51675	−	3.51675i	0.167464	−	0.167464i
$442$	−12.2633	−	3.57818i	−0.583308	−	0.170197i
$443$	17.0012	+	7.04213i	0.807752	+	0.334582i	0.748057	−	0.663635i	$-0.230987\pi$
$443$	17.0012	+	7.04213i	0.807752	+	0.334582i	0.0596951	+	0.998217i	$0.480987\pi$
$444$	−2.19818	−	7.46865i	−0.104321	−	0.354447i
$445$	−29.1176	+	12.0609i	−1.38031	+	0.571742i
$446$	3.64986	+	6.14703i	0.172826	+	0.291070i
$447$	−5.59727	−	5.59727i	−0.264742	−	0.264742i
$448$	−2.33878	−	31.8423i	−0.110497	−	1.50441i
$449$	2.64543	+	2.64543i	0.124846	+	0.124846i	0.766769	−	0.641923i	$-0.221863\pi$
$449$	2.64543	+	2.64543i	0.124846	+	0.124846i	−0.641923	+	0.766769i	$0.721863\pi$
$450$	0.212526	−	0.833782i	0.0100186	−	0.0393049i
$451$	−4.11813	−	9.94206i	−0.193915	−	0.468153i
$452$	−2.48338	+	4.55488i	−0.116808	+	0.214244i
$453$	18.1144	−	7.50322i	0.851087	−	0.352532i
$454$	−13.2495	−	9.91183i	−0.621829	−	0.465185i
$455$	−12.4581	−	33.2609i	−0.584044	−	1.55929i
$456$	−0.159658	−	0.148361i	−0.00747665	−	0.00694764i
$457$		−	35.3190i		−	1.65215i	−0.563559	−	0.826076i	$-0.690568\pi$
$457$		−	35.3190i		−	1.65215i	0.563559	−	0.826076i	$-0.309432\pi$
$458$	−21.8799	+	3.15299i	−1.02238	+	0.147330i
$459$	−12.8685	−	5.33029i	−0.600648	−	0.248797i
$460$	12.1121	+	15.0105i	0.564728	+	0.699869i
$461$	28.8366	+	11.9445i	1.34306	+	0.556312i	0.934351	−	0.356355i	$-0.115980\pi$
$461$	28.8366	+	11.9445i	1.34306	+	0.556312i	0.408705	+	0.912667i	$0.365980\pi$
$462$	−6.12251	−	10.3114i	−0.284845	−	0.479731i
$463$	19.9050	+	19.9050i	0.925065	+	0.925065i	0.997382	−	0.0723166i	$-0.0230392\pi$
$463$	19.9050	+	19.9050i	0.925065	+	0.925065i	−0.0723166	+	0.997382i	$0.523039\pi$
$464$	25.8053	+	17.8681i	1.19798	+	0.829506i
$465$	35.9820			1.66863
$466$	10.7826	+	18.1598i	0.499492	+	0.841236i
$467$	−10.1495	−	24.5031i	−0.469663	−	1.13387i	−0.964311	−	0.264773i	$-0.914703\pi$
$467$	−10.1495	−	24.5031i	−0.469663	−	1.13387i	0.494648	−	0.869094i	$-0.335297\pi$
$468$	3.89016	−	1.00129i	0.179823	−	0.0462845i
$469$	−23.9178	−	9.90708i	−1.10442	−	0.457467i
$470$	−4.43319	+	5.92600i	−0.204488	+	0.273346i
$471$	24.8226	+	24.8226i	1.14377	+	1.14377i
$472$	−10.7062	+	28.7888i	−0.492794	+	1.32511i
$473$	7.78958			0.358165
$474$	3.73342	+	25.9077i	0.171482	+	1.18998i
$475$	−0.0206064	−	0.0497483i	−0.000945487	−	0.00228261i
$476$	−17.5575	−	9.57258i	−0.804748	−	0.438758i
$477$	−4.06287	+	1.68290i	−0.186026	+	0.0770545i
$478$	−22.5978	+	13.4177i	−1.03360	+	0.613711i
$479$	−2.03700	+	2.03700i	−0.0930728	+	0.0930728i	−0.752110	−	0.659037i	$-0.770964\pi$
$479$	−2.03700	+	2.03700i	−0.0930728	+	0.0930728i	0.659037	+	0.752110i	$0.270964\pi$
$480$	−19.5305	−	9.73728i	−0.891442	−	0.444444i
$481$	8.40928	−	3.14975i	0.383430	−	0.143616i
$482$	6.59745	−	3.91730i	0.300506	−	0.178428i
$483$	22.5174	+	9.32703i	1.02458	+	0.424395i
$484$	−17.5594	+	5.16811i	−0.798156	+	0.234914i
$485$	−13.7344	−	5.68899i	−0.623649	−	0.258324i
$486$	7.99122	−	1.15157i	0.362489	−	0.0522363i
$487$		−	22.1626i		−	1.00428i	−0.864786	−	0.502141i	$-0.832546\pi$
$487$		−	22.1626i		−	1.00428i	0.864786	−	0.502141i	$-0.167454\pi$
$488$	10.7011	+	3.97961i	0.484415	+	0.180148i
$489$	16.9895			0.768292
$490$	−4.44507	−	30.8461i	−0.200808	−	1.39349i
$491$	−5.11912	−	2.12041i	−0.231023	−	0.0956927i	0.264169	−	0.964476i	$-0.414902\pi$
$491$	−5.11912	−	2.12041i	−0.231023	−	0.0956927i	−0.495192	+	0.868784i	$0.664902\pi$
$492$	−24.6060	−	2.62951i	−1.10933	−	0.118548i
$493$	18.1626	−	7.52319i	0.818002	−	0.338827i
$494$	0.157403	−	0.196007i	0.00708188	−	0.00881875i
$495$	1.86906			0.0840082
$496$	−7.88375	+	36.4654i	−0.353991	+	1.63734i
$497$		−	62.8540i		−	2.81939i
$498$	26.3646	+	6.72019i	1.18143	+	0.301139i
$499$	5.20650	−	12.5696i	0.233075	−	0.562693i	−0.763461	−	0.645854i	$-0.776502\pi$
$499$	5.20650	−	12.5696i	0.233075	−	0.562693i	0.996536	+	0.0831611i	$0.0265016\pi$
$500$	12.1139	+	15.0128i	0.541750	+	0.671393i
$501$	−6.62818	−	16.0018i	−0.296125	−	0.714909i
$502$	−0.986483	+	1.31867i	−0.0440289	+	0.0588549i
$503$	−24.7473	−	24.7473i	−1.10343	−	1.10343i	−0.993994	−	0.109433i	$-0.965096\pi$
$503$	−24.7473	−	24.7473i	−1.10343	−	1.10343i	−0.109433	−	0.993994i	$-0.534904\pi$
$504$	6.28393	−	0.230464i	0.279909	−	0.0102657i
$505$			8.21462i			0.365546i
$506$	−4.49948	+	6.01461i	−0.200026	+	0.267382i
$507$	−6.46999	−	19.2613i	−0.287342	−	0.855424i
$508$	8.13779	+	4.43682i	0.361056	+	0.196852i
$509$	4.70711	−	11.3640i	0.208639	−	0.503699i	−0.784570	−	0.620040i	$-0.787116\pi$
$509$	4.70711	−	11.3640i	0.208639	−	0.503699i	0.993209	+	0.116341i	$0.0371164\pi$
$510$	−11.7530	+	6.97843i	−0.520430	+	0.309010i
$511$	41.1863			1.82198
$512$	14.1473	−	17.6594i	0.625227	−	0.780443i
$513$	0.193814	−	0.193814i	0.00855708	−	0.00855708i
$514$	−0.722610	+	2.83494i	−0.0318730	+	0.125044i
$515$	−10.7896	+	26.0483i	−0.475445	+	1.14783i
$516$	8.57458	−	15.7271i	0.377475	−	0.692345i
$517$	−2.66273	−	1.10294i	−0.117107	−	0.0485072i
$518$	13.9133	−	2.00497i	0.611314	−	0.0880932i
$519$	24.4894	+	24.4894i	1.07497	+	1.07497i
$520$	9.57814	−	23.2777i	0.420029	−	1.02079i
$521$	15.8642	−	15.8642i	0.695024	−	0.695024i	−0.268309	−	0.963333i	$-0.586465\pi$
$521$	15.8642	−	15.8642i	0.695024	−	0.695024i	0.963333	+	0.268309i	$0.0864649\pi$
$522$	−3.70298	+	4.94990i	−0.162075	+	0.216651i
$523$	−9.94596	+	24.0117i	−0.434906	+	1.04996i	0.542778	+	0.839876i	$0.317373\pi$
$523$	−9.94596	+	24.0117i	−0.434906	+	1.04996i	−0.977684	+	0.210081i	$0.932627\pi$
$524$	2.74701	−	25.7055i	0.120004	−	1.12295i
$525$	−6.29457	−	2.60729i	−0.274717	−	0.113792i
$526$	11.7547	−	6.97947i	0.512530	−	0.304319i
$527$	16.5230	+	16.5230i	0.719754	+	0.719754i
$528$	1.79593	−	8.30688i	0.0781580	−	0.361511i
$529$			7.73390i			0.336257i
$530$	−6.80638	+	26.7027i	−0.295650	+	1.15989i
$531$	−5.58879	−	2.31495i	−0.242533	−	0.100460i
$532$	0.306251	−	0.247116i	0.0132777	−	0.0107138i
$533$	0.979307	−	28.5257i	0.0424185	−	1.23558i
$534$	−27.9358	+	4.02568i	−1.20890	+	0.174208i
$535$	8.51266			0.368034
$536$	−7.63768	−	16.6818i	−0.329898	−	0.720546i
$537$	−9.01881	+	9.01881i	−0.389191	+	0.389191i
$538$	−1.90494	−	13.2192i	−0.0821279	−	0.569919i
$539$	11.2129	−	4.64453i	0.482973	−	0.200054i
$540$	13.1376	−	24.0964i	0.565354	−	1.03694i
$541$	−33.3080	−	13.7966i	−1.43202	−	0.593163i	−0.474172	−	0.880432i	$-0.657253\pi$
$541$	−33.3080	−	13.7966i	−1.43202	−	0.593163i	−0.957850	+	0.287269i	$0.907253\pi$
$542$	9.97701	+	16.8031i	0.428549	+	0.721756i
$543$	−24.3757			−1.04606
$544$	−4.49707	−	13.4398i	−0.192810	−	0.576228i
$545$		−	23.5290i		−	1.00787i
$546$	−3.45387	−	31.6192i	−0.147812	−	1.35318i
$547$	0.238358	+	0.575447i	0.0101915	+	0.0246043i	0.928893	−	0.370347i	$-0.120761\pi$
$547$	0.238358	+	0.575447i	0.0101915	+	0.0246043i	−0.918702	+	0.394952i	$0.870761\pi$
$548$	10.5426	+	5.74796i	0.450358	+	0.245540i
$549$	−0.860491	+	2.07741i	−0.0367248	+	0.0886616i
$550$	1.25779	−	1.68133i	0.0536325	−	0.0716923i
$551$			0.386857i			0.0164807i
$552$	7.19050	+	15.7051i	0.306048	+	0.668455i
$553$	−47.2610			−2.00974
$554$	−19.2717	+	25.7611i	−0.818776	+	1.09449i
$555$	3.67688	−	8.87678i	0.156075	−	0.376798i
$556$	−5.14784	+	4.15382i	−0.218317	+	0.176161i
$557$	9.18486	−	22.1742i	0.389175	−	0.939552i	−0.600940	−	0.799294i	$-0.705207\pi$
$557$	9.18486	−	22.1742i	0.389175	−	0.939552i	0.990115	−	0.140258i	$-0.0447931\pi$
$558$	−7.12004	−	1.81486i	−0.301415	−	0.0768291i
$559$	18.8055	+	8.55677i	0.795387	+	0.361913i
$560$	22.4311	−	32.3952i	0.947886	−	1.36895i
$561$	−3.76397	−	3.76397i	−0.158915	−	0.158915i
$562$	−6.79057	+	26.6407i	−0.286443	+	1.12377i
$563$	5.70650	+	13.7767i	0.240500	+	0.580619i	0.997333	−	0.0729898i	$-0.0232540\pi$
$563$	5.70650	+	13.7767i	0.240500	+	0.580619i	−0.756832	+	0.653609i	$0.773254\pi$
$564$	−5.15789	+	4.16193i	−0.217186	+	0.175249i
$565$	−5.91512	+	2.45012i	−0.248851	+	0.103077i
$566$	−1.92883	+	2.57833i	−0.0810746	+	0.108375i
$567$		−	28.0110i		−	1.17635i
$568$	30.3222	−	32.6310i	1.27229	−	1.36917i
$569$	−1.97766	+	1.97766i	−0.0829080	+	0.0829080i	−0.747345	−	0.664437i	$-0.768672\pi$
$569$	−1.97766	+	1.97766i	−0.0829080	+	0.0829080i	0.664437	+	0.747345i	$0.268672\pi$
$570$	−0.0383642	−	0.266225i	−0.00160690	−	0.0111509i
$571$	−2.59622	+	6.26783i	−0.108649	+	0.262301i	−0.968848	−	0.247658i	$-0.920339\pi$
$571$	−2.59622	+	6.26783i	−0.108649	+	0.262301i	0.860199	+	0.509958i	$0.170339\pi$
$572$	9.70565	+	1.37544i	0.405814	+	0.0575100i
$573$	−5.03137	+	2.08406i	−0.210189	+	0.0870630i
$574$	11.0359	−	43.2961i	0.460631	−	1.80714i
$575$			4.26751i			0.177968i
$576$	3.37352	+	2.91187i	0.140563	+	0.121328i
$577$	28.0044	−	28.0044i	1.16584	−	1.16584i	0.182661	−	0.983176i	$-0.441529\pi$
$577$	28.0044	−	28.0044i	1.16584	−	1.16584i	0.983176	−	0.182661i	$-0.0584711\pi$
$578$	14.6952	+	3.74573i	0.611241	+	0.155802i
$579$	−3.54410	+	8.55622i	−0.147288	+	0.355584i
$580$	10.9370	+	37.1601i	0.454134	+	1.54299i
$581$	−18.7992	+	45.3854i	−0.779924	+	1.88290i
$582$	−10.6603	−	7.97485i	−0.441882	−	0.330568i
$583$	−10.7316			−0.444456
$584$	21.3822	+	19.8693i	0.884800	+	0.822196i
$585$	4.51227	+	2.05315i	0.186559	+	0.0848872i
$586$	15.3470	−	2.21157i	0.633977	−	0.0913589i
$587$	−3.71049	−	8.95791i	−0.153148	−	0.369732i	0.828621	−	0.559810i	$-0.189126\pi$
$587$	−3.71049	−	8.95791i	−0.153148	−	0.369732i	−0.981769	+	0.190078i	$0.939126\pi$
$588$	2.96563	−	27.7512i	0.122300	−	1.14444i
$589$	−0.424823	+	0.175967i	−0.0175045	+	0.00725061i
$590$	−32.5937	+	19.3528i	−1.34186	+	0.796742i
$591$	−17.1933	+	17.1933i	−0.707240	+	0.707240i
$592$	8.19041	+	5.67120i	0.336624	+	0.233085i
$593$	−14.5157	+	14.5157i	−0.596089	+	0.596089i	−0.939270	−	0.343180i	$-0.888496\pi$
$593$	−14.5157	+	14.5157i	−0.596089	+	0.596089i	0.343180	+	0.939270i	$0.388496\pi$
$594$	10.3570	+	2.63994i	0.424953	+	0.108318i
$595$	−9.44439	−	22.8008i	−0.387182	−	0.934741i
$596$	10.0716	+	1.07630i	0.412549	+	0.0440868i
$597$	−11.8998	+	28.7288i	−0.487028	+	1.17579i
$598$	−17.4696	+	9.57774i	−0.714383	+	0.391663i
$599$	−19.4724	−	19.4724i	−0.795620	−	0.795620i	0.186781	−	0.982402i	$-0.440194\pi$
$599$	−19.4724	−	19.4724i	−0.795620	−	0.795620i	−0.982402	+	0.186781i	$0.940194\pi$
$600$	−2.01004	−	4.39024i	−0.0820597	−	0.179231i
$601$	21.2213	+	21.2213i	0.865636	+	0.865636i	0.991986	−	0.126350i	$-0.0403262\pi$
$601$	21.2213	+	21.2213i	0.865636	+	0.865636i	−0.126350	+	0.991986i	$0.540326\pi$
$602$	25.8975	+	19.3737i	1.05550	+	0.789615i
$603$	3.33837	−	1.38280i	0.135949	−	0.0563119i
$604$	−12.0097	+	22.0276i	−0.488669	+	0.896292i
$605$	−20.8700	−	8.64465i	−0.848488	−	0.351455i
$606$	−1.81703	+	7.12857i	−0.0738119	+	0.289578i
$607$			24.3906i			0.989984i	0.868898	+	0.494992i	$0.164829\pi$
$607$			24.3906i			0.989984i	−0.868898	+	0.494992i	$0.835171\pi$
$608$	0.278207	+	0.0194510i	0.0112828	+	0.000788841i
$609$	34.6117	+	34.6117i	1.40254	+	1.40254i
$610$	7.19362	+	12.1154i	0.291261	+	0.490537i
$611$	−5.21675	−	5.58768i	−0.211047	−	0.226053i
$612$	2.67762	−	0.788081i	0.108237	−	0.0318563i
$613$	10.2175	+	24.6671i	0.412679	+	0.996295i	0.984416	+	0.175858i	$0.0562699\pi$
$613$	10.2175	+	24.6671i	0.412679	+	0.996295i	−0.571737	+	0.820437i	$0.693730\pi$
$614$	20.8647	+	15.6087i	0.842030	+	0.629916i
$615$	−21.5948	−	21.5948i	−0.870788	−	0.870788i
$616$	14.3827	+	5.34876i	0.579494	+	0.215508i
$617$		−	3.03840i		−	0.122321i	−0.998128	−	0.0611607i	$-0.980520\pi$
$617$		−	3.03840i		−	0.122321i	0.998128	−	0.0611607i	$-0.0194802\pi$
$618$	−15.1249	+	20.2179i	−0.608411	+	0.813283i
$619$	3.26323	−	1.35167i	0.131160	−	0.0543284i	−0.316138	−	0.948713i	$-0.602386\pi$
$619$	3.26323	−	1.35167i	0.131160	−	0.0543284i	0.447298	+	0.894385i	$0.352386\pi$
$620$	−35.8321	+	28.9131i	−1.43905	+	1.16118i
$621$	−20.0690	+	8.31287i	−0.805343	+	0.333584i
$622$	23.4877	−	13.9461i	0.941771	−	0.559186i
$623$		−	50.9607i		−	2.04170i
$624$	13.4607	−	18.0815i	0.538861	−	0.723841i
$625$			29.2682i			1.17073i
$626$	−16.9991	−	28.6295i	−0.679419	−	1.14427i
$627$	0.0967754	−	0.0400857i	0.00386484	−	0.00160087i
$628$	−44.6652	−	4.77313i	−1.78234	−	0.190469i
$629$	5.76467	−	2.38780i	0.229852	−	0.0952080i
$630$	6.21396	+	4.64862i	0.247570	+	0.185205i
$631$		−	13.5342i		−	0.538788i	−0.963030	−	0.269394i	$-0.913177\pi$
$631$		−	13.5342i		−	0.538788i	0.963030	−	0.269394i	$-0.0868233\pi$
$632$	−24.5358	−	22.7998i	−0.975984	−	0.906928i
$633$	11.1399	+	11.1399i	0.442773	+	0.442773i
$634$	29.3031	−	39.1705i	1.16378	−	1.55566i
$635$	4.37740	+	10.5680i	0.173712	+	0.419378i
$636$	−11.8130	+	21.6669i	−0.468417	+	0.859148i
$637$	32.1719	+	1.10449i	1.27470	+	0.0437613i
$638$	−12.9711	+	7.70173i	−0.513532	+	0.304914i
$639$	6.20342	+	6.20342i	0.245403	+	0.245403i
$640$	27.2735	−	5.99691i	1.07808	−	0.237049i
$641$			25.6960i			1.01493i	0.861672	+	0.507466i	$0.169418\pi$
$641$			25.6960i			1.01493i	−0.861672	+	0.507466i	$0.830582\pi$
$642$	7.38721	+	1.88296i	0.291550	+	0.0743144i
$643$	−23.9769	−	9.93155i	−0.945556	−	0.391662i	−0.143997	−	0.989578i	$-0.545996\pi$
$643$	−23.9769	−	9.93155i	−0.945556	−	0.391662i	−0.801559	+	0.597916i	$0.795996\pi$
$644$	−29.9183	+	8.80558i	−1.17895	+	0.346988i
$645$	20.4237	−	8.45976i	0.804181	−	0.333103i
$646$	0.104634	−	0.139868i	0.00411677	−	0.00550303i
$647$	21.0878	+	21.0878i	0.829046	+	0.829046i	0.987385	−	0.158339i	$-0.0506138\pi$
$647$	21.0878	+	21.0878i	0.829046	+	0.829046i	−0.158339	+	0.987385i	$0.550614\pi$
$648$	13.5132	−	14.5421i	0.530848	−	0.571268i
$649$	−10.4384	−	10.4384i	−0.409742	−	0.409742i
$650$	4.88347	−	2.67738i	0.191545	−	0.105015i
$651$	−22.2649	+	53.7521i	−0.872629	+	2.10671i
$652$	−16.9187	+	13.6518i	−0.662588	+	0.534646i
$653$	5.74269	+	13.8641i	0.224729	+	0.542543i	0.995521	−	0.0945436i	$-0.0301392\pi$
$653$	5.74269	+	13.8641i	0.224729	+	0.542543i	−0.770792	+	0.637087i	$0.780139\pi$
$654$	5.20449	−	20.4182i	0.203512	−	0.798416i
$655$	22.5598	−	22.5598i	0.881483	−	0.881483i
$656$	26.6164	−	17.1535i	1.03920	−	0.669730i
$657$	−4.06491	+	4.06491i	−0.158587	+	0.158587i
$658$	−6.10945	−	10.2894i	−0.238171	−	0.401124i
$659$	−3.85239	+	1.59571i	−0.150068	+	0.0621601i	−0.456453	−	0.889747i	$-0.650880\pi$
$659$	−3.85239	+	1.59571i	−0.150068	+	0.0621601i	0.306385	+	0.951908i	$0.400880\pi$
$660$	8.16262	−	6.58646i	0.317729	−	0.256378i
$661$	−15.8872	−	38.3551i	−0.617941	−	1.49184i	−0.854091	−	0.520124i	$-0.825886\pi$
$661$	−15.8872	−	38.3551i	−0.617941	−	1.49184i	0.236150	−	0.971717i	$-0.424114\pi$
$662$	−2.71747	−	18.8576i	−0.105617	−	0.732922i
$663$	−4.95224	−	13.2216i	−0.192329	−	0.513485i
$664$	−31.6547	+	14.4929i	−1.22844	+	0.562434i
$665$	0.485649			0.0188326
$666$	−1.17530	+	1.57106i	−0.0455419	+	0.0608774i
$667$	11.7328	−	28.3255i	0.454296	−	1.09677i
$668$	19.4587	+	10.6091i	0.752881	+	0.410480i
$669$	−3.02359	+	7.29960i	−0.116899	+	0.282219i
$670$	5.59265	−	21.9411i	0.216063	−	0.847657i
$671$	−3.88004	+	3.88004i	−0.149787	+	0.149787i
$672$	26.6312	−	23.1507i	1.02732	−	0.893056i
$673$			36.3609i			1.40161i	0.713353	+	0.700805i	$0.247176\pi$
$673$			36.3609i			1.40161i	−0.713353	+	0.700805i	$0.752824\pi$
$674$	−28.7893	−	7.33823i	−1.10892	−	0.282658i
$675$	5.61014	−	2.32379i	0.215934	−	0.0894429i
$676$	21.9203	+	13.9821i	0.843089	+	0.537774i
$677$	−16.3965	+	39.5845i	−0.630167	+	1.52136i	0.209246	+	0.977863i	$0.432899\pi$
$677$	−16.3965	+	39.5845i	−0.630167	+	1.52136i	−0.839413	+	0.543494i	$0.817101\pi$
$678$	−5.67504	+	0.817799i	−0.217949	+	0.0314074i
$679$	16.9971	−	16.9971i	0.652290	−	0.652290i
$680$	6.09651	−	16.3934i	0.233791	−	0.628657i
$681$		−	18.2875i		−	0.700777i
$682$	−14.3577	−	10.7409i	−0.549784	−	0.411289i
$683$	29.8010	−	12.3440i	1.14030	−	0.472329i	0.269032	−	0.963131i	$-0.413296\pi$
$683$	29.8010	−	12.3440i	1.14030	−	0.472329i	0.871271	+	0.490802i	$0.163296\pi$
$684$	−0.00583641	+	0.0546150i	−0.000223161	+	0.00208826i
$685$	5.67098	+	13.6910i	0.216677	+	0.523105i
$686$	10.5455	+	2.68799i	0.402630	+	0.102628i
$687$	−17.2757	−	17.2757i	−0.659109	−	0.659109i
$688$	4.09853	+	22.5516i	0.156255	+	0.859771i
$689$	−25.9080	−	11.7885i	−0.987015	−	0.449106i
$690$	−5.26521	+	20.6564i	−0.200443	+	0.786376i
$691$	−4.33850	+	10.4741i	−0.165045	+	0.398453i	−0.984665	−	0.174454i	$-0.944184\pi$
$691$	−4.33850	+	10.4741i	−0.165045	+	0.398453i	0.819621	+	0.572906i	$0.194184\pi$
$692$	−44.0657	−	4.70906i	−1.67513	−	0.179012i
$693$	−1.15653	+	2.79212i	−0.0439331	+	0.106064i
$694$	−8.87680	−	6.64067i	−0.336959	−	0.252076i
$695$	−8.16337			−0.309654
$696$	1.27139	+	34.6664i	0.0481921	+	1.31403i
$697$		−	19.8328i		−	0.751221i
$698$	26.1880	+	19.5910i	0.991231	+	0.741532i
$699$	−8.93243	+	21.5648i	−0.337855	+	0.815655i
$700$	8.36341	−	2.46153i	0.316107	−	0.0930370i
$701$	−5.34799	−	12.9112i	−0.201991	−	0.487649i	0.790129	−	0.612940i	$-0.210013\pi$
$701$	−5.34799	−	12.9112i	−0.201991	−	0.487649i	−0.992120	+	0.125292i	$0.960013\pi$
$702$	22.1038	+	17.7504i	0.834253	+	0.669944i
$703$			0.122785i			0.00463094i
$704$	4.88649	+	9.71538i	0.184167	+	0.366162i
$705$	−8.17930			−0.308050
$706$	19.0872	−	11.3332i	0.718355	−	0.426530i
$707$	−12.2715	−	5.08302i	−0.461517	−	0.191167i
$708$	−32.5652	+	9.58463i	−1.22388	+	0.360213i
$709$	−10.5623	+	4.37503i	−0.396674	+	0.164308i	−0.572098	−	0.820185i	$-0.693870\pi$
$709$	−10.5623	+	4.37503i	−0.396674	+	0.164308i	0.175424	+	0.984493i	$0.443870\pi$
$710$	54.4114	−	7.84093i	2.04202	−	0.294265i
$711$	4.66446	−	4.66446i	0.174931	−	0.174931i
$712$	24.5846	−	26.4566i	0.921348	−	0.991502i
$713$	36.4422			1.36477
$714$	−3.15234	−	21.8754i	−0.117973	−	0.818665i
$715$	8.25578	+	8.84278i	0.308749	+	0.330701i
$716$	1.73422	−	16.2282i	0.0648110	−	0.606478i
$717$	−26.8350	−	11.1154i	−1.00217	−	0.415113i
$718$	45.3611	+	11.5623i	1.69286	+	0.431501i
$719$			20.6911i			0.771646i	0.922573	+	0.385823i	$0.126083\pi$
$719$			20.6911i			0.771646i	−0.922573	+	0.385823i	$0.873917\pi$
$720$	0.983418	+	5.41112i	0.0366498	+	0.201661i
$721$	−32.2362	−	32.2362i	−1.20054	−	1.20054i
$722$	−13.7166	−	23.1013i	−0.510480	−	0.859741i
$723$	7.83449	+	3.24515i	0.291368	+	0.120688i
$724$	24.2742	−	19.5870i	0.902142	−	0.727943i
$725$	−3.27981	+	7.91817i	−0.121809	+	0.294073i
$726$	−16.1987	−	12.1181i	−0.601190	−	0.449745i
$727$	−4.67967	+	4.67967i	−0.173559	+	0.173559i	−0.788541	−	0.614982i	$-0.789163\pi$
$727$	−4.67967	+	4.67967i	−0.173559	+	0.173559i	0.614982	+	0.788541i	$0.289163\pi$
$728$	28.8469	+	28.7121i	1.06914	+	1.06414i
$729$	21.1982	+	21.1982i	0.785118	+	0.785118i
$730$	5.13793	+	35.6542i	0.190163	+	1.31962i
$731$	13.2633	+	5.49385i	0.490562	+	0.203197i
$732$	3.56270	+	12.1048i	0.131681	+	0.447407i
$733$	−6.76484	+	16.3318i	−0.249865	+	0.603228i	−0.998192	−	0.0601022i	$-0.980857\pi$
$733$	−6.76484	+	16.3318i	−0.249865	+	0.603228i	0.748327	+	0.663330i	$0.230857\pi$
$734$	17.3788	+	4.42977i	0.641465	+	0.163506i
$735$	24.3552	−	24.3552i	0.898354	−	0.898354i
$736$	−19.7803	−	9.86181i	−0.729111	−	0.363511i
$737$	8.81788			0.324811
$738$	3.18394	+	5.36234i	0.117202	+	0.197390i
$739$	16.4515	−	39.7173i	0.605177	−	1.46103i	−0.263013	−	0.964792i	$-0.584716\pi$
$739$	16.4515	−	39.7173i	0.605177	−	1.46103i	0.868189	−	0.496233i	$-0.165284\pi$
$740$	3.47132	+	11.7943i	0.127608	+	0.433568i
$741$	0.277667	+	0.00953252i	0.0102004	+	0.000350186i
$742$	−35.6786	−	26.6908i	−1.30980	−	0.979852i
$743$			5.56777i			0.204262i	0.994771	+	0.102131i	$0.0325661\pi$
$743$			5.56777i			0.204262i	−0.994771	+	0.102131i	$0.967434\pi$
$744$	−37.4902	+	17.1647i	−1.37446	+	0.629287i
$745$	8.83908	+	8.83908i	0.323839	+	0.323839i
$746$	−30.6381	−	22.9201i	−1.12174	−	0.839164i
$747$	−2.62394	−	6.33475i	−0.0960049	−	0.231776i
$748$	6.77281	+	0.723774i	0.247638	+	0.0264638i
$749$	−5.26744	+	12.7167i	−0.192468	+	0.464659i
$750$	−5.26601	+	20.6596i	−0.192287	+	0.754380i
$751$			4.44081i			0.162047i	0.996712	+	0.0810237i	$0.0258189\pi$
$751$			4.44081i			0.162047i	−0.996712	+	0.0810237i	$0.974181\pi$
$752$	1.79210	−	8.28917i	0.0653513	−	0.302275i
$753$	−1.82007			−0.0663272
$754$	−39.7749	+	4.34475i	−1.44852	+	0.158227i
$755$	−28.6058	+	11.8489i	−1.04107	+	0.431226i
$756$	27.8674	+	34.5361i	1.01353	+	1.25607i
$757$	26.6022	+	11.0190i	0.966874	+	0.400493i	0.809548	−	0.587054i	$-0.199712\pi$
$757$	26.6022	+	11.0190i	0.966874	+	0.400493i	0.157327	+	0.987547i	$0.449712\pi$
$758$	−8.45318	+	1.21814i	−0.307033	+	0.0442449i
$759$	−8.30160			−0.301329
$760$	0.252128	+	0.234288i	0.00914563	+	0.00849853i
$761$			11.2799i			0.408897i	0.978877	+	0.204449i	$0.0655401\pi$
$761$			11.2799i			0.408897i	−0.978877	+	0.204449i	$0.934460\pi$
$762$	1.46109	+	10.1391i	0.0529295	+	0.367300i
$763$	35.1490	+	14.5592i	1.27248	+	0.527078i
$764$	3.33577	−	6.11831i	0.120684	−	0.221353i
$765$	3.18246	+	1.31822i	0.115062	+	0.0476603i
$766$	−20.1537	−	33.9425i	−0.728183	−	1.22639i
$767$	−13.7337	−	36.6666i	−0.495896	−	1.32395i
$768$	24.9942	+	0.828690i	0.901899	+	0.0299028i
$769$	37.3630	−	37.3630i	1.34734	−	1.34734i	0.458808	−	0.888535i	$-0.348277\pi$
$769$	37.3630	−	37.3630i	1.34734	−	1.34734i	0.888535	−	0.458808i	$-0.151723\pi$
$770$	9.66852	+	16.2836i	0.348429	+	0.586819i
$771$	−2.98724	+	1.23735i	−0.107583	+	0.0445622i
$772$	−3.34596	−	11.3684i	−0.120424	−	0.409158i
$773$	17.5740	+	42.4275i	0.632094	+	1.52601i	0.836986	+	0.547225i	$0.184316\pi$
$773$	17.5740	+	42.4275i	0.632094	+	1.52601i	−0.204892	+	0.978785i	$0.565684\pi$
$774$	−4.46808	+	0.643870i	−0.160602	+	0.0231434i
$775$	−10.1871			−0.365932
$776$	17.0240	−	0.624356i	0.611125	−	0.0224131i
$777$	10.9855	+	10.9855i	0.394103	+	0.394103i
$778$	−8.78546	−	6.57234i	−0.314974	−	0.235630i
$779$	0.360568	+	0.149352i	0.0129187	+	0.00535110i
$780$	26.9412	−	6.93439i	0.964650	−	0.248291i
$781$	8.19277	+	19.7791i	0.293160	+	0.707752i
$782$	−11.9033	+	7.06768i	−0.425660	+	0.252740i
$783$	−43.6261			−1.55907
$784$	19.3461	+	30.0186i	0.690931	+	1.07209i
$785$	−39.1993	−	39.1993i	−1.39908	−	1.39908i
$786$	24.5673	−	14.5871i	0.876285	−	0.520303i
$787$	36.6456	+	15.1791i	1.30627	+	0.541076i	0.923795	−	0.382888i	$-0.125070\pi$
$787$	36.6456	+	15.1791i	1.30627	+	0.541076i	0.382479	+	0.923964i	$0.375070\pi$
$788$	3.30610	−	30.9373i	0.117775	−	1.10210i
$789$	13.9587	+	5.78190i	0.496944	+	0.205841i
$790$	−5.89573	−	40.9129i	−0.209761	−	1.45561i
$791$		−	10.3524i		−	0.368090i
$792$	−1.94741	+	0.891609i	−0.0691981	+	0.0316819i
$793$	−13.6293	+	5.10495i	−0.483992	+	0.181282i
$794$	13.6280	−	18.2170i	0.483641	−	0.646499i
$795$	−28.1373	+	11.6548i	−0.997927	+	0.413355i
$796$	−11.2346	−	38.1711i	−0.398198	−	1.35294i
$797$	4.78083	+	11.5419i	0.169346	+	0.408837i	0.985654	−	0.168780i	$-0.0539828\pi$
$797$	4.78083	+	11.5419i	0.169346	+	0.408837i	−0.816308	+	0.577617i	$0.803983\pi$
$798$	0.421442	+	0.107423i	0.0149189	+	0.00380274i
$799$	−3.75595	−	3.75595i	−0.132876	−	0.132876i
$800$	5.52942	+	2.75679i	0.195494	+	0.0974672i
$801$	5.02960	+	5.02960i	0.177712	+	0.177712i
$802$	−11.6780	+	6.93394i	−0.412365	+	0.244846i
$803$	−12.9606	+	5.36848i	−0.457371	+	0.189449i
$804$	9.70651	−	17.8032i	0.342322	−	0.627870i
$805$	−35.5590	−	14.7290i	−1.25329	−	0.519130i
$806$	−22.8633	−	41.7022i	−0.805327	−	1.46890i
$807$	10.4375	−	10.4375i	0.367416	−	0.367416i
$808$	−3.91866	−	8.55894i	−0.137858	−	0.301102i
$809$	10.3909	−	10.3909i	0.365325	−	0.365325i	−0.500444	−	0.865769i	$-0.666830\pi$
$809$	10.3909	−	10.3909i	0.365325	−	0.365325i	0.865769	+	0.500444i	$0.166830\pi$
$810$	24.2486	−	3.49433i	0.852008	−	0.122778i
$811$	4.25668	+	10.2765i	0.149472	+	0.360858i	0.980826	−	0.194886i	$-0.0624336\pi$
$811$	4.25668	+	10.2765i	0.149472	+	0.360858i	−0.831354	+	0.555744i	$0.812434\pi$
$812$	−62.2795	−	6.65548i	−2.18558	−	0.233561i
$813$	−8.26510	+	19.9537i	−0.289870	+	0.699808i
$814$	−4.11694	+	2.44447i	−0.144299	+	0.0856786i
$815$	−26.8294			−0.939794
$816$	8.91663	−	12.8775i	0.312145	−	0.450803i
$817$	−0.199761	+	0.199761i	−0.00698874	+	0.00698874i
$818$	30.7796	+	7.84556i	1.07619	+	0.274314i
$819$	−5.85920	+	5.47026i	−0.204737	+	0.191146i
$820$	38.8573	+	4.15247i	1.35695	+	0.145010i
$821$	−27.2181	+	11.2741i	−0.949918	+	0.393469i	−0.803200	−	0.595709i	$-0.796871\pi$
$821$	−27.2181	+	11.2741i	−0.949918	+	0.393469i	−0.146718	+	0.989178i	$0.546871\pi$
$822$	1.89286	+	13.1353i	0.0660209	+	0.458146i
$823$	−17.5446	+	17.5446i	−0.611568	+	0.611568i	−0.943354	−	0.331787i	$-0.892349\pi$
$823$	−17.5446	+	17.5446i	−0.611568	+	0.611568i	0.331787	+	0.943354i	$0.392349\pi$
$824$	−1.18413	−	32.2871i	−0.0412513	−	1.12478i
$825$	2.32064			0.0807945
$826$	−8.74217	−	60.6655i	−0.304179	−	2.11082i
$827$	−13.8647	−	33.4723i	−0.482122	−	1.16394i	−0.958599	−	0.284758i	$-0.908087\pi$
$827$	−13.8647	−	33.4723i	−0.482122	−	1.16394i	0.476478	−	0.879187i	$-0.341913\pi$
$828$	2.08373	−	3.82188i	0.0724147	−	0.132819i
$829$	17.1854	+	41.4892i	0.596873	+	1.44098i	0.876751	+	0.480944i	$0.159706\pi$
$829$	17.1854	+	41.4892i	0.596873	+	1.44098i	−0.279878	+	0.960036i	$0.590294\pi$
$830$	−41.6344	−	10.6124i	−1.44515	−	0.368361i
$831$	−35.5566			−1.23344
$832$	1.12465	+	28.8225i	0.0389902	+	0.999240i
$833$	22.3679			0.775001
$834$	−7.08410	−	1.80570i	−0.245302	−	0.0625262i
$835$	10.4671	+	25.2697i	0.362228	+	0.874495i
$836$	−0.0641616	+	0.117682i	−0.00221907	+	0.00407011i
$837$	−19.8439	−	47.9075i	−0.685906	−	1.65592i
$838$	1.83899	+	12.7615i	0.0635268	+	0.440839i
$839$	−44.4389			−1.53420			−0.767100	−	0.641528i	$-0.778301\pi$
$839$	−44.4389			−1.53420			−0.767100	+	0.641528i	$0.778301\pi$
$840$	43.5192	−	1.59607i	1.50155	−	0.0550697i
$841$	23.0333	−	23.0333i	0.794251	−	0.794251i
$842$	6.85197	+	47.5486i	0.236135	+	1.63863i
$843$	−28.0719	+	11.6278i	−0.966849	+	0.400482i
$844$	−20.0450	−	2.14210i	−0.689976	−	0.0737340i
$845$	10.2173	+	30.4170i	0.351484	+	1.04638i
$846$	1.61850	+	0.412547i	0.0556452	+	0.0141836i
$847$	25.8278	−	25.8278i	0.887454	−	0.887454i
$848$	−5.64646	−	31.0689i	−0.193900	−	1.06691i
$849$	−3.55871			−0.122135
$850$	3.32746	−	1.97571i	0.114131	−	0.0677663i
$851$	3.72391	−	8.99030i	0.127654	−	0.308184i
$852$	48.9521	+	5.23125i	1.67707	+	0.179220i
$853$	11.0412	+	26.6558i	0.378044	+	0.912679i	0.992332	+	0.123597i	$0.0394431\pi$
$853$	11.0412	+	26.6558i	0.378044	+	0.912679i	−0.614288	+	0.789082i	$0.710557\pi$
$854$	−22.5499	+	3.24955i	−0.771643	+	0.111197i
$855$	−0.0479314	+	0.0479314i	−0.00163922	+	0.00163922i
$856$	−8.86947	+	4.06083i	−0.303152	+	0.138796i
$857$	−22.5929	+	22.5929i	−0.771758	+	0.771758i	−0.978414	−	0.206656i	$-0.933742\pi$
$857$	−22.5929	+	22.5929i	−0.771758	+	0.771758i	0.206656	+	0.978414i	$0.433742\pi$
$858$	5.20831	+	9.49983i	0.177809	+	0.324319i
$859$	−33.2293	−	13.7640i	−1.13377	−	0.469623i	−0.264709	−	0.964328i	$-0.585276\pi$
$859$	−33.2293	−	13.7640i	−1.13377	−	0.469623i	−0.869061	+	0.494705i	$0.835276\pi$
$860$	−13.5408	+	24.8358i	−0.461737	+	0.846894i
$861$	45.6221	−	18.8973i	1.55480	−	0.644018i
$862$	41.4210	−	24.5941i	1.41080	−	0.837678i
$863$	−33.3213	−	33.3213i	−1.13427	−	1.13427i	−0.989459	−	0.144810i	$-0.953743\pi$
$863$	−33.3213	−	33.3213i	−1.13427	−	1.13427i	−0.144810	−	0.989459i	$-0.546257\pi$
$864$	−2.19350	+	31.3735i	−0.0746242	+	1.06735i
$865$	−38.6731	−	38.6731i	−1.31493	−	1.31493i
$866$	−14.6165	−	3.72567i	−0.496689	−	0.126603i
$867$	6.41398	+	15.4847i	0.217830	+	0.525888i
$868$	−21.0201	−	71.4189i	−0.713468	−	2.42412i
$869$	14.8722	−	6.16028i	0.504506	−	0.208973i
$870$	−25.6449	+	34.2804i	−0.869444	+	1.16222i
$871$	21.2880	+	9.68635i	0.721316	+	0.328210i
$872$	11.2241	+	24.5152i	0.380097	+	0.830189i
$873$			3.35509i			0.113552i
$874$	−0.0388548	−	0.269630i	−0.00131428	−	0.00912036i
$875$	−35.5644	−	14.7313i	−1.20230	−	0.498008i
$876$	−3.42788	+	32.0769i	−0.115817	+	1.08378i
$877$	−26.5727	−	11.0068i	−0.897296	−	0.371672i	−0.114116	−	0.993467i	$-0.536404\pi$
$877$	−26.5727	−	11.0068i	−0.897296	−	0.371672i	−0.783180	+	0.621795i	$0.786404\pi$
$878$	39.5277	−	23.4700i	1.33400	−	0.792073i
$879$	12.1175	+	12.1175i	0.408713	+	0.408713i
$880$	−2.83610	+	13.1180i	−0.0956048	+	0.442209i
$881$	15.0441			0.506848			0.253424	−	0.967355i	$-0.418443\pi$
$881$	15.0441			0.506848			0.253424	+	0.967355i	$0.418443\pi$
$882$	−6.04777	+	3.59092i	−0.203639	+	0.120913i
$883$	−11.4904	−	27.7403i	−0.386683	−	0.933536i	−0.990638	−	0.136517i	$-0.956409\pi$
$883$	−11.4904	−	27.7403i	−0.386683	−	0.933536i	0.603955	−	0.797019i	$-0.293591\pi$
$884$	15.5558	+	9.18718i	0.523196	+	0.308998i
$885$	−38.7050	−	16.0321i	−1.30106	−	0.538915i
$886$	−20.8385	−	15.5891i	−0.700084	−	0.523727i
$887$	−20.9518	−	20.9518i	−0.703493	−	0.703493i	0.261666	−	0.965159i	$-0.415728\pi$
$887$	−20.9518	−	20.9518i	−0.703493	−	0.703493i	−0.965159	+	0.261666i	$0.915728\pi$
$888$	0.403531	+	11.0029i	0.0135416	+	0.369232i
$889$	−18.4957			−0.620327
$890$	44.1156	−	6.35726i	1.47876	−	0.213096i
$891$	3.65113	+	8.81460i	0.122317	+	0.295300i
$892$	−2.85455	−	9.69878i	−0.0955775	−	0.324739i
$893$	0.0965691	−	0.0400002i	0.00323156	−	0.00133856i
$894$	5.71531	+	9.62563i	0.191149	+	0.321929i
$895$	14.2423	−	14.2423i	0.476068	−	0.476068i
$896$	−7.91765	+	44.4535i	−0.264510	+	1.48509i
$897$	−20.0416	−	9.11922i	−0.669169	−	0.304482i
$898$	−2.70122	−	4.54935i	−0.0901409	−	0.151814i
$899$	67.6168	+	28.0078i	2.25515	+	0.934112i
$900$	−0.582491	+	1.06837i	−0.0194164	+	0.0356125i
$901$	−18.2726	−	7.56877i	−0.608750	−	0.252152i
$902$	2.17065	+	15.0630i	0.0722748	+	0.501544i
$903$			35.7448i			1.18951i
$904$	4.99426	−	5.37454i	0.166107	−	0.178754i
$905$	38.4936			1.27957
$906$	−27.4448	+	3.95492i	−0.911792	+	0.131393i
$907$	−43.9852	−	18.2193i	−1.46050	−	0.604961i	−0.495833	−	0.868418i	$-0.665137\pi$
$907$	−43.9852	−	18.2193i	−1.46050	−	0.604961i	−0.964671	+	0.263457i	$0.915137\pi$
$908$	14.6948	+	18.2113i	0.487663	+	0.604362i
$909$	1.71281	−	0.709471i	0.0568105	−	0.0235317i
$910$	5.45427	+	49.9323i	0.180807	+	1.65524i
$911$	−35.2123			−1.16664			−0.583318	−	0.812244i	$-0.698246\pi$
$911$	−35.2123			−1.16664			−0.583318	+	0.812244i	$0.698246\pi$
$912$	0.166971	+	0.259083i	0.00552895	+	0.00857909i
$913$		−	16.7324i		−	0.553763i
$914$	−12.3371	+	48.4010i	−0.408076	+	1.60096i
$915$	−5.95930	+	14.3870i	−0.197008	+	0.475621i
$916$	31.0855	+	3.32194i	1.02709	+	0.109760i
$917$	19.7417	+	47.6606i	0.651927	+	1.57389i
$918$	15.7730	+	11.7996i	0.520586	+	0.389446i
$919$	7.91073	+	7.91073i	0.260951	+	0.260951i	0.825440	−	0.564489i	$-0.190927\pi$
$919$	7.91073	+	7.91073i	0.260951	+	0.260951i	−0.564489	+	0.825440i	$0.690927\pi$
$920$	−11.3551	−	24.8012i	−0.374365	−	0.817670i
$921$			28.7983i			0.948935i
$922$	−35.3453	−	26.4415i	−1.16404	−	0.870806i
$923$	−1.94827	+	56.7500i	−0.0641281	+	1.86795i
$924$	4.78841	+	16.2694i	0.157527	+	0.535223i
$925$	−1.04099	+	2.51317i	−0.0342275	+	0.0826324i
$926$	−20.3248	−	34.2307i	−0.667915	−	1.12489i
$927$	6.36315			0.208993
$928$	−29.1221	−	33.5003i	−0.955978	−	1.09970i
$929$	−28.5036	+	28.5036i	−0.935173	+	0.935173i	−0.998023	−	0.0628496i	$-0.979981\pi$
$929$	−28.5036	+	28.5036i	−0.935173	+	0.935173i	0.0628496	+	0.998023i	$0.479981\pi$
$930$	−49.3096	−	12.5687i	−1.61693	−	0.412145i
$931$	−0.168443	+	0.406657i	−0.00552049	+	0.0133276i
$932$	−8.43304	−	28.6525i	−0.276233	−	0.938545i
$933$	27.8917	+	11.5531i	0.913133	+	0.378232i
$934$	5.34976	+	37.1242i	0.175050	+	1.21474i
$935$	5.94398	+	5.94398i	0.194389	+	0.194389i
$936$	−5.68082	+	0.0133012i	−0.185683	+	0.000434765i
$937$	−34.3011	+	34.3011i	−1.12057	+	1.12057i	−0.128911	+	0.991656i	$0.541148\pi$
$937$	−34.3011	+	34.3011i	−1.12057	+	1.12057i	−0.991656	+	0.128911i	$0.958852\pi$
$938$	29.3163	+	21.9313i	0.957210	+	0.716081i
$939$	14.0823	−	33.9976i	0.459558	−	1.10947i
$940$	8.14522	−	6.57242i	0.265668	−	0.214369i
$941$	26.3979	+	10.9344i	0.860546	+	0.356450i	0.768921	−	0.639344i	$-0.220794\pi$
$941$	26.3979	+	10.9344i	0.860546	+	0.356450i	0.0916251	+	0.995794i	$0.470794\pi$
$942$	−25.3461	−	42.6875i	−0.825821	−	1.39083i
$943$	−21.8710	−	21.8710i	−0.712218	−	0.712218i
$944$	24.7279	−	35.7123i	0.804824	−	1.16234i
$945$			54.7668i			1.78157i
$946$	−10.6748	−	2.72095i	−0.347068	−	0.0884657i
$947$	10.1690	+	4.21214i	0.330448	+	0.136876i	0.541738	−	0.840547i	$-0.317766\pi$
$947$	10.1690	+	4.21214i	0.330448	+	0.136876i	−0.211290	+	0.977423i	$0.567766\pi$
$948$	3.93347	−	36.8080i	0.127753	−	1.19547i
$949$	−37.1866	−	1.27664i	−1.20713	−	0.0414416i
$950$	0.0108616	+	0.0753728i	0.000352395	+	0.00244542i
$951$	54.0647			1.75317
$952$	20.7170	+	19.2512i	0.671442	+	0.623934i
$953$	14.3930	−	14.3930i	0.466236	−	0.466236i	−0.434457	−	0.900693i	$-0.643060\pi$
$953$	14.3930	−	14.3930i	0.466236	−	0.466236i	0.900693	+	0.434457i	$0.143060\pi$
$954$	6.15559	−	0.887048i	0.199295	−	0.0287192i
$955$	7.94543	−	3.29110i	0.257108	−	0.106498i
$956$	35.6549	−	10.4940i	1.15316	−	0.339399i
$957$	−15.4032	−	6.38023i	−0.497916	−	0.206243i
$958$	3.50303	−	2.07996i	0.113178	−	0.0672003i
$959$	−23.9615			−0.773756
$960$	23.3632	+	20.1661i	0.754045	+	0.650857i
$961$			55.9924i			1.80621i
$962$	−12.6243	+	1.37899i	−0.407023	+	0.0444605i
$963$	−0.735212	−	1.77496i	−0.0236919	−	0.0571972i
$964$	−10.4095	+	3.06372i	−0.335266	+	0.0986758i
$965$	5.59676	−	13.5118i	0.180166	−	0.434960i
$966$	−27.5998	−	20.6472i	−0.888010	−	0.664313i
$967$			42.8379i			1.37757i	0.724964	+	0.688787i	$0.241856\pi$
$967$			42.8379i			1.37757i	−0.724964	+	0.688787i	$0.758144\pi$
$968$	25.8686	−	0.948734i	0.831449	−	0.0304935i
$969$	0.193051			0.00620170
$970$	16.8344	+	12.5937i	0.540521	+	0.404359i
$971$	−15.0356	+	36.2992i	−0.482517	+	1.16490i	0.475893	+	0.879503i	$0.342125\pi$
$971$	−15.0356	+	36.2992i	−0.482517	+	1.16490i	−0.958410	+	0.285395i	$0.907875\pi$
$972$	−11.3534	−	1.21328i	−0.364160	−	0.0389158i
$973$	5.05131	−	12.1949i	0.161937	−	0.390952i
$974$	−7.74152	+	30.3715i	−0.248054	+	0.973165i
$975$	5.60246	+	2.54920i	0.179422	+	0.0816398i
$976$	−13.2746	−	9.19159i	−0.424910	−	0.294216i
$977$	12.4041	+	12.4041i	0.396842	+	0.396842i	0.877118	−	0.480275i	$-0.159463\pi$
$977$	12.4041	+	12.4041i	0.396842	+	0.396842i	−0.480275	+	0.877118i	$0.659463\pi$
$978$	−23.2823	−	5.93454i	−0.744487	−	0.189766i
$979$	6.64253	+	16.0365i	0.212296	+	0.512528i
$980$	−4.68325	+	43.8241i	−0.149601	+	1.39991i
$981$	−4.90598	+	2.03212i	−0.156636	+	0.0648807i
$982$	6.27455	+	4.69394i	0.200229	+	0.149790i
$983$			27.8749i			0.889070i	0.895761	+	0.444535i	$0.146631\pi$
$983$			27.8749i			0.889070i	−0.895761	+	0.444535i	$0.853369\pi$
$984$	32.8015	+	12.1985i	1.04567	+	0.388874i
$985$	27.1513	−	27.1513i	0.865114	−	0.865114i
$986$	−27.5178	+	3.96544i	−0.876346	+	0.126285i
$987$	5.06116	−	12.2187i	0.161099	−	0.388926i
$988$	−0.284170	+	0.213625i	−0.00904066	+	0.00679632i
$989$	20.6849	−	8.56795i	0.657740	−	0.272445i
$990$	−2.56136	−	0.652876i	−0.0814053	−	0.0207498i
$991$			29.5857i			0.939821i	0.882714	+	0.469911i	$0.155714\pi$
$991$			29.5857i			0.939821i	−0.882714	+	0.469911i	$0.844286\pi$
$992$	23.5415	−	47.2182i	0.747442	−	1.49918i
$993$	14.8894	−	14.8894i	0.472501	−	0.472501i
$994$	−21.9553	+	86.1348i	−0.696380	+	2.73203i
$995$	18.7920	−	45.3678i	0.595745	−	1.43826i
$996$	−33.7826	−	18.4186i	−1.07044	−	0.583617i
$997$	−6.41937	+	15.4977i	−0.203303	+	0.490818i	−0.992341	−	0.123527i	$-0.960579\pi$
$997$	−6.41937	+	15.4977i	−0.203303	+	0.490818i	0.789038	+	0.614345i	$0.210579\pi$
$998$	−11.5256	+	15.4067i	−0.364837	+	0.487690i
$999$	−13.8466			−0.438086

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bi.a.395.4	yes	216
13.8	odd	4		416.2.bd.a.203.32	✓	216
32.3	odd	8		416.2.bd.a.291.32	yes	216
416.99	even	8	inner	416.2.bi.a.99.4	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bd.a.203.32	✓	216	13.8	odd	4
416.2.bd.a.291.32	yes	216	32.3	odd	8
416.2.bi.a.99.4	yes	216	416.99	even	8	inner
416.2.bi.a.395.4	yes	216	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bi (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37040 - 0.349306i) q^{2} +(-0.598132 - 1.44402i) q^{3} +(1.75597 + 0.957376i) q^{4} +(0.944556 + 2.28036i) q^{5} +(0.315273 + 2.18781i) q^{6} -3.99101 q^{7} +(-2.07196 - 1.92536i) q^{8} +(0.393895 - 0.393895i) q^{9} +(-0.497872 - 3.45493i) q^{10} +(1.25590 - 0.520212i) q^{11} +(0.332166 - 3.10829i) q^{12} +(3.60343 + 0.123708i) q^{13} +(5.46926 + 1.39408i) q^{14} +(2.72791 - 2.72791i) q^{15} +(2.16686 + 3.36225i) q^{16} +2.50532 q^{17} +(-0.677382 + 0.402202i) q^{18} +(-0.0188665 + 0.0455478i) q^{19} +(-0.524549 + 4.90854i) q^{20} +(2.38715 + 5.76309i) q^{21} +(-1.90280 + 0.274202i) q^{22} +(2.76280 - 2.76280i) q^{23} +(-1.54094 + 4.14356i) q^{24} +(-0.772317 + 0.772317i) q^{25} +(-4.89491 - 1.42823i) q^{26} +(-5.13645 - 2.12759i) q^{27} +(-7.00809 - 3.82089i) q^{28} +(7.24960 - 3.00288i) q^{29} +(-4.69119 + 2.78544i) q^{30} +(6.59516 + 6.59516i) q^{31} +(-1.79501 - 5.36451i) q^{32} +(-1.50239 - 1.50239i) q^{33} +(-3.43329 - 0.875125i) q^{34} +(-3.76973 - 9.10093i) q^{35} +(1.06877 - 0.314563i) q^{36} +(2.30097 - 0.953092i) q^{37} +(0.0417647 - 0.0558283i) q^{38} +(-1.97669 - 5.27741i) q^{39} +(2.43342 - 6.54341i) q^{40} -7.91626i q^{41} +(-1.25826 - 8.73155i) q^{42} +(5.29406 + 2.19287i) q^{43} +(2.70337 + 0.288894i) q^{44} +(1.27028 + 0.526167i) q^{45} +(-4.75119 + 2.82106i) q^{46} +(-1.49919 - 1.49919i) q^{47} +(3.55907 - 5.14005i) q^{48} +8.92814 q^{49} +(1.32816 - 0.788605i) q^{50} +(-1.49851 - 3.61773i) q^{51} +(6.20908 + 3.66706i) q^{52} +(-7.29352 - 3.02108i) q^{53} +(6.29579 + 4.70983i) q^{54} +(2.37254 + 2.37254i) q^{55} +(8.26920 + 7.68411i) q^{56} +0.0770564 q^{57} +(-10.9837 + 1.58281i) q^{58} +(-4.15572 - 10.0328i) q^{59} +(7.40176 - 2.17849i) q^{60} +(-3.72929 + 1.54472i) q^{61} +(-6.73425 - 11.3417i) q^{62} +(-1.57204 + 1.57204i) q^{63} +(0.586014 + 7.97851i) q^{64} +(3.12154 + 8.33396i) q^{65} +(1.53408 + 2.58366i) q^{66} +(5.99293 + 2.48235i) q^{67} +(4.39927 + 2.39854i) q^{68} +(-5.64204 - 2.33701i) q^{69} +(1.98701 + 13.7887i) q^{70} +15.7489i q^{71} +(-1.57452 + 0.0577458i) q^{72} -10.3198 q^{73} +(-3.48616 + 0.502371i) q^{74} +(1.57719 + 0.653292i) q^{75} +(-0.0767354 + 0.0619182i) q^{76} +(-5.01232 + 2.07617i) q^{77} +(0.865413 + 7.92261i) q^{78} +11.8419 q^{79} +(-5.62041 + 8.11705i) q^{80} +7.01854i q^{81} +(-2.76520 + 10.8484i) q^{82} +(4.71040 - 11.3719i) q^{83} +(-1.32568 + 12.4052i) q^{84} +(2.36642 + 5.71304i) q^{85} +(-6.48897 - 4.85435i) q^{86} +(-8.67243 - 8.67243i) q^{87} +(-3.60377 - 1.34020i) q^{88} +12.7689i q^{89} +(-1.55699 - 1.16477i) q^{90} +(-14.3813 - 0.493721i) q^{91} +(7.49642 - 2.20635i) q^{92} +(5.57876 - 13.4683i) q^{93} +(1.53081 + 2.57816i) q^{94} -0.121686 q^{95} +(-6.67279 + 5.80070i) q^{96} +(-4.25886 + 4.25886i) q^{97} +(-12.2351 - 3.11866i) q^{98} +(0.289785 - 0.699603i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9} - 4 q^{11} + 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} - 4 q^{19} - 20 q^{20} - 16 q^{21} - 24 q^{22}+ \cdots - 116 q^{99}+O(q^{100}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 4 * q^8 - 8 * q^9 - 4 * q^11 + 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 - 4 * q^19 - 20 * q^20 - 16 * q^21 - 24 * q^22 + 28 * q^24 - 4 * q^26 - 8 * q^27 - 24 * q^28 - 8 * q^29 + 16 * q^30 - 4 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 + 20 * q^39 - 8 * q^40 - 48 * q^42 + 32 * q^43 - 20 * q^44 + 4 * q^45 - 24 * q^46 - 8 * q^47 - 8 * q^48 + 168 * q^49 + 20 * q^50 - 4 * q^52 - 8 * q^53 + 20 * q^54 - 40 * q^55 - 56 * q^56 - 8 * q^57 + 32 * q^58 + 4 * q^59 - 36 * q^60 - 8 * q^61 - 72 * q^62 - 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 - 4 * q^70 + 56 * q^72 - 8 * q^73 - 8 * q^74 - 4 * q^76 - 56 * q^77 - 136 * q^78 - 16 * q^79 + 28 * q^80 + 88 * q^82 - 44 * q^83 + 44 * q^84 - 24 * q^85 + 64 * q^86 - 8 * q^87 - 64 * q^88 + 64 * q^90 + 16 * q^91 - 8 * q^92 + 56 * q^93 - 56 * q^94 - 28 * q^96 - 8 * q^97 - 76 * q^98 - 116 * q^99

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