LMFDB - Embedded newform 117.2.t.c.25.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(25,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("117.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.t (of order $6$, degree $2$, 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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6x^{16} + 9x^{14} + 54x^{12} + 81x^{10} + 486x^{8} + 729x^{6} - 4374x^{4} + 59049 $ x^20 - 6x^16 + 9x^14 + 54x^12 + 81x^10 + 486x^8 + 729x^6 - 4374*x^4 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.4
Root			$1.65391 - 0.514376i$ of defining polynomial
Character	$\chi$	$=$	117.25
Dual form			117.2.t.c.103.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.929969 - 0.536918i) q^{2} +(-0.744247 - 1.56400i) q^{3} +(-0.423439 - 0.733417i) q^{4} +(-1.10543 + 0.638222i) q^{5} +(-0.147613 + 1.85407i) q^{6} +(-0.890926 - 0.514376i) q^{7} +3.05708i q^{8} +(-1.89219 + 2.32800i) q^{9} +1.37069 q^{10} +(-4.03796 - 2.33132i) q^{11} +(-0.831922 + 1.20810i) q^{12} +(2.29741 - 2.77883i) q^{13} +(0.552355 + 0.956708i) q^{14} +(1.82089 + 1.25390i) q^{15} +(0.794522 - 1.37615i) q^{16} -0.476187 q^{17} +(3.00963 - 1.14902i) q^{18} -6.69096i q^{19} +(0.936166 + 0.540496i) q^{20} +(-0.141416 + 1.77623i) q^{21} +(2.50345 + 4.33610i) q^{22} +(-0.479867 - 0.831155i) q^{23} +(4.78127 - 2.27522i) q^{24} +(-1.68535 + 2.91910i) q^{25} +(-3.62852 + 1.35071i) q^{26} +(5.04926 + 1.22678i) q^{27} +0.871227i q^{28} +(4.68880 - 8.12123i) q^{29} +(-1.02013 - 2.14376i) q^{30} +(1.66927 - 0.963754i) q^{31} +(3.81725 - 2.20389i) q^{32} +(-0.640940 + 8.05044i) q^{33} +(0.442839 + 0.255673i) q^{34} +1.31314 q^{35} +(2.50863 + 0.402000i) q^{36} +4.94666i q^{37} +(-3.59249 + 6.22238i) q^{38} +(-6.05593 - 1.52501i) q^{39} +(-1.95109 - 3.37939i) q^{40} +(1.31994 - 0.762068i) q^{41} +(1.08520 - 1.57591i) q^{42} +(-1.31426 + 2.27637i) q^{43} +3.94868i q^{44} +(0.605908 - 3.78109i) q^{45} +1.03060i q^{46} +(-5.92316 - 3.41974i) q^{47} +(-2.74362 - 0.218435i) q^{48} +(-2.97083 - 5.14564i) q^{49} +(3.13464 - 1.80978i) q^{50} +(0.354400 + 0.744756i) q^{51} +(-3.01086 - 0.508296i) q^{52} +0.582145 q^{53} +(-4.03697 - 3.85190i) q^{54} +5.95159 q^{55} +(1.57249 - 2.72363i) q^{56} +(-10.4647 + 4.97973i) q^{57} +(-8.72087 + 5.03499i) q^{58} +(3.64799 - 2.10617i) q^{59} +(0.148597 - 1.86643i) q^{60} +(-4.71645 + 8.16913i) q^{61} -2.06983 q^{62} +(2.88327 - 1.10078i) q^{63} -7.91132 q^{64} +(-0.766122 + 4.53807i) q^{65} +(4.91848 - 7.14253i) q^{66} +(2.01156 - 1.16138i) q^{67} +(0.201636 + 0.349243i) q^{68} +(-0.942786 + 1.36910i) q^{69} +(-1.22118 - 0.705051i) q^{70} +1.35071i q^{71} +(-7.11689 - 5.78458i) q^{72} +12.8687i q^{73} +(2.65595 - 4.60024i) q^{74} +(5.81979 + 0.463346i) q^{75} +(-4.90726 + 2.83321i) q^{76} +(2.39835 + 4.15406i) q^{77} +(4.81302 + 4.66975i) q^{78} +(6.45415 - 11.1789i) q^{79} +2.02833i q^{80} +(-1.83921 - 8.81007i) q^{81} -1.63667 q^{82} +(8.86189 + 5.11641i) q^{83} +(1.36260 - 0.648408i) q^{84} +(0.526392 - 0.303913i) q^{85} +(2.44445 - 1.41130i) q^{86} +(-16.1912 - 1.28907i) q^{87} +(7.12701 - 12.3444i) q^{88} -6.85985i q^{89} +(-2.59361 + 3.19097i) q^{90} +(-3.47619 + 1.29400i) q^{91} +(-0.406389 + 0.703886i) q^{92} +(-2.74966 - 1.89347i) q^{93} +(3.67224 + 6.36050i) q^{94} +(4.27032 + 7.39640i) q^{95} +(-6.28787 - 4.32994i) q^{96} +(14.9635 + 8.63918i) q^{97} +6.38037i q^{98} +(13.0679 - 4.98909i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} + 12 q^{4} - 2 q^{9} - 16 q^{10} - 2 q^{12} - 4 q^{13} - 18 q^{14} + 4 q^{16} - 12 q^{17} - 10 q^{22} + 24 q^{23} - 12 q^{25} - 12 q^{26} - 22 q^{27} + 12 q^{29} - 54 q^{30} - 12 q^{35} + 50 q^{36}+ \cdots + 24 q^{95}+O(q^{100}) $ 20 * q + 2 * q^3 + 12 * q^4 - 2 * q^9 - 16 * q^10 - 2 * q^12 - 4 * q^13 - 18 * q^14 + 4 * q^16 - 12 * q^17 - 10 * q^22 + 24 * q^23 - 12 * q^25 - 12 * q^26 - 22 * q^27 + 12 * q^29 - 54 * q^30 - 12 * q^35 + 50 * q^36 + 12 * q^38 - 8 * q^39 - 8 * q^40 + 6 * q^42 + 4 * q^43 + 38 * q^48 - 10 * q^49 - 78 * q^51 + 108 * q^53 + 20 * q^55 + 36 * q^56 - 2 * q^61 - 72 * q^62 + 8 * q^64 - 24 * q^65 + 78 * q^66 + 24 * q^68 + 72 * q^69 - 42 * q^74 - 8 * q^75 - 6 * q^77 + 66 * q^78 - 14 * q^79 + 46 * q^81 - 4 * q^82 - 54 * q^87 + 22 * q^88 + 24 * q^90 - 72 * q^91 - 84 * q^92 + 20 * q^94 + 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.929969	−	0.536918i	−0.657587	−	0.379658i	0.133770	−	0.991012i	$-0.457292\pi$
$2$	−0.929969	−	0.536918i	−0.657587	−	0.379658i	−0.791357	+	0.611354i	$0.790625\pi$
$3$	−0.744247	−	1.56400i	−0.429691	−	0.902976i
$3$	−0.744247	−	1.56400i	−0.429691	−	0.902976i
$4$	−0.423439	−	0.733417i	−0.211719	−	0.366709i
$5$	−1.10543	+	0.638222i	−0.494365	+	0.285422i	−0.726383	−	0.687290i	$-0.758800\pi$
$5$	−1.10543	+	0.638222i	−0.494365	+	0.285422i	0.232019	+	0.972711i	$0.425467\pi$
$6$	−0.147613	+	1.85407i	−0.0602627	+	0.756921i
$7$	−0.890926	−	0.514376i	−0.336738	−	0.194416i	0.322090	−	0.946709i	$-0.395614\pi$
$7$	−0.890926	−	0.514376i	−0.336738	−	0.194416i	−0.658829	+	0.752293i	$0.728948\pi$
$8$			3.05708i			1.08084i
$9$	−1.89219	+	2.32800i	−0.630731	+	0.776002i
$10$	1.37069			0.433450
$11$	−4.03796	−	2.33132i	−1.21749	−	0.702918i	−0.253110	−	0.967438i	$-0.581453\pi$
$11$	−4.03796	−	2.33132i	−1.21749	−	0.702918i	−0.964380	+	0.264519i	$0.914787\pi$
$12$	−0.831922	+	1.20810i	−0.240155	+	0.348749i
$13$	2.29741	−	2.77883i	0.637187	−	0.770709i
$13$	2.29741	−	2.77883i	0.637187	−	0.770709i
$14$	0.552355	+	0.956708i	0.147623	+	0.255691i
$15$	1.82089	+	1.25390i	0.470153	+	0.323756i
$16$	0.794522	−	1.37615i	0.198631	−	0.344038i
$17$	−0.476187			−0.115492			−0.0577461	−	0.998331i	$-0.518391\pi$
$17$	−0.476187			−0.115492			−0.0577461	+	0.998331i	$0.518391\pi$
$18$	3.00963	−	1.14902i	0.709376	−	0.270827i
$19$		−	6.69096i		−	1.53501i	−0.641042	−	0.767505i	$-0.721498\pi$
$19$		−	6.69096i		−	1.53501i	0.641042	−	0.767505i	$-0.278502\pi$
$20$	0.936166	+	0.540496i	0.209333	+	0.120859i
$21$	−0.141416	+	1.77623i	−0.0308594	+	0.387605i
$22$	2.50345	+	4.33610i	0.533737	+	0.924460i
$23$	−0.479867	−	0.831155i	−0.100059	−	0.173308i	0.811650	−	0.584145i	$-0.198570\pi$
$23$	−0.479867	−	0.831155i	−0.100059	−	0.173308i	−0.911709	+	0.410837i	$0.865237\pi$
$24$	4.78127	−	2.27522i	0.975973	−	0.464428i
$25$	−1.68535	+	2.91910i	−0.337069	+	0.583821i
$26$	−3.62852	+	1.35071i	−0.711612	+	0.264895i
$27$	5.04926	+	1.22678i	0.971730	+	0.236094i
$28$			0.871227i			0.164646i
$29$	4.68880	−	8.12123i	0.870687	−	1.50807i	0.00940050	−	0.999956i	$-0.497008\pi$
$29$	4.68880	−	8.12123i	0.870687	−	1.50807i	0.861287	−	0.508119i	$-0.169659\pi$
$30$	−1.02013	−	2.14376i	−0.186250	−	0.391395i
$31$	1.66927	−	0.963754i	0.299810	−	0.173095i	−0.342548	−	0.939500i	$-0.611290\pi$
$31$	1.66927	−	0.963754i	0.299810	−	0.173095i	0.642357	+	0.766405i	$0.277956\pi$
$32$	3.81725	−	2.20389i	0.674801	−	0.389597i
$33$	−0.640940	+	8.05044i	−0.111573	+	1.40140i
$34$	0.442839	+	0.255673i	0.0759462	+	0.0438476i
$35$	1.31314			0.221962
$36$	2.50863	+	0.402000i	0.418104	+	0.0669999i
$37$			4.94666i			0.813226i	0.913601	+	0.406613i	$0.133290\pi$
$37$			4.94666i			0.813226i	−0.913601	+	0.406613i	$0.866710\pi$
$38$	−3.59249	+	6.22238i	−0.582779	+	1.00940i
$39$	−6.05593	−	1.52501i	−0.969725	−	0.244198i
$40$	−1.95109	−	3.37939i	−0.308495	−	0.534329i
$41$	1.31994	−	0.762068i	0.206140	−	0.119015i	−0.393376	−	0.919378i	$-0.628693\pi$
$41$	1.31994	−	0.762068i	0.206140	−	0.119015i	0.599516	+	0.800363i	$0.295360\pi$
$42$	1.08520	−	1.57591i	0.167450	−	0.243168i
$43$	−1.31426	+	2.27637i	−0.200423	+	0.347143i	−0.948665	−	0.316283i	$-0.897565\pi$
$43$	−1.31426	+	2.27637i	−0.200423	+	0.347143i	0.748242	+	0.663426i	$0.230898\pi$
$44$			3.94868i			0.595285i
$45$	0.605908	−	3.78109i	0.0903235	−	0.563652i
$46$			1.03060i			0.151953i
$47$	−5.92316	−	3.41974i	−0.863982	−	0.498820i	0.00136148	−	0.999999i	$-0.499567\pi$
$47$	−5.92316	−	3.41974i	−0.863982	−	0.498820i	−0.865344	+	0.501179i	$0.832900\pi$
$48$	−2.74362	−	0.218435i	−0.396008	−	0.0315284i
$49$	−2.97083	−	5.14564i	−0.424405	−	0.735091i
$50$	3.13464	−	1.80978i	0.443305	−	0.255942i
$51$	0.354400	+	0.744756i	0.0496260	+	0.104287i
$52$	−3.01086	−	0.508296i	−0.417531	−	0.0704880i
$53$	0.582145			0.0799637			0.0399819	−	0.999200i	$-0.487270\pi$
$53$	0.582145			0.0799637			0.0399819	+	0.999200i	$0.487270\pi$
$54$	−4.03697	−	3.85190i	−0.549363	−	0.524178i
$55$	5.95159			0.802512
$56$	1.57249	−	2.72363i	0.210133	−	0.363960i
$57$	−10.4647	+	4.97973i	−1.38608	+	0.659581i
$58$	−8.72087	+	5.03499i	−1.14511	+	0.661127i
$59$	3.64799	−	2.10617i	0.474927	−	0.274199i	−0.243373	−	0.969933i	$-0.578254\pi$
$59$	3.64799	−	2.10617i	0.474927	−	0.274199i	0.718300	+	0.695733i	$0.244920\pi$
$60$	0.148597	−	1.86643i	0.0191837	−	0.240955i
$61$	−4.71645	+	8.16913i	−0.603880	+	1.04595i	0.388348	+	0.921513i	$0.373046\pi$
$61$	−4.71645	+	8.16913i	−0.603880	+	1.04595i	−0.992227	+	0.124437i	$0.960287\pi$
$62$	−2.06983			−0.262868
$63$	2.88327	−	1.10078i	0.363258	−	0.138685i
$64$	−7.91132			−0.988915
$65$	−0.766122	+	4.53807i	−0.0950257	+	0.562878i
$66$	4.91848	−	7.14253i	0.605423	−	0.879184i
$67$	2.01156	−	1.16138i	0.245751	−	0.141885i	−0.372066	−	0.928206i	$-0.621350\pi$
$67$	2.01156	−	1.16138i	0.245751	−	0.141885i	0.617817	+	0.786322i	$0.288017\pi$
$68$	0.201636	+	0.349243i	0.0244519	+	0.0423520i
$69$	−0.942786	+	1.36910i	−0.113498	+	0.164820i
$70$	−1.22118	−	0.705051i	−0.145959	−	0.0842697i
$71$			1.35071i			0.160299i	0.996783	+	0.0801497i	$0.0255398\pi$
$71$			1.35071i			0.160299i	−0.996783	+	0.0801497i	$0.974460\pi$
$72$	−7.11689	−	5.78458i	−0.838734	−	0.681719i
$73$			12.8687i			1.50617i	0.657923	+	0.753085i	$0.271435\pi$
$73$			12.8687i			1.50617i	−0.657923	+	0.753085i	$0.728565\pi$
$74$	2.65595	−	4.60024i	0.308748	−	0.534767i
$75$	5.81979	+	0.463346i	0.672012	+	0.0535026i
$76$	−4.90726	+	2.83321i	−0.562902	+	0.324991i
$77$	2.39835	+	4.15406i	0.273317	+	0.473399i
$78$	4.81302	+	4.66975i	0.544968	+	0.528745i
$79$	6.45415	−	11.1789i	0.726149	−	1.25773i	−0.232351	−	0.972632i	$-0.574642\pi$
$79$	6.45415	−	11.1789i	0.726149	−	1.25773i	0.958499	−	0.285094i	$-0.0920250\pi$
$80$			2.02833i			0.226774i
$81$	−1.83921	−	8.81007i	−0.204357	−	0.978896i
$82$	−1.63667			−0.180740
$83$	8.86189	+	5.11641i	0.972718	+	0.561599i	0.900064	−	0.435758i	$-0.143520\pi$
$83$	8.86189	+	5.11641i	0.972718	+	0.561599i	0.0726545	+	0.997357i	$0.476853\pi$
$84$	1.36260	−	0.648408i	0.148672	−	0.0707471i
$85$	0.526392	−	0.303913i	0.0570953	−	0.0329640i
$86$	2.44445	−	1.41130i	0.263591	−	0.152185i
$87$	−16.1912	−	1.28907i	−1.73588	−	0.138203i
$88$	7.12701	−	12.3444i	0.759742	−	1.31591i
$89$		−	6.85985i		−	0.727143i	−0.931566	−	0.363572i	$-0.881557\pi$
$89$		−	6.85985i		−	0.727143i	0.931566	−	0.363572i	$-0.118443\pi$
$90$	−2.59361	+	3.19097i	−0.273391	+	0.336358i
$91$	−3.47619	+	1.29400i	−0.364403	+	0.135648i
$92$	−0.406389	+	0.703886i	−0.0423690	+	0.0733852i
$93$	−2.74966	−	1.89347i	−0.285127	−	0.196344i
$94$	3.67224	+	6.36050i	0.378763	+	0.656036i
$95$	4.27032	+	7.39640i	0.438125	+	0.758855i
$96$	−6.28787	−	4.32994i	−0.641753	−	0.441923i
$97$	14.9635	+	8.63918i	1.51931	+	0.877175i	0.999741	+	0.0227483i	$0.00724164\pi$
$97$	14.9635	+	8.63918i	1.51931	+	0.877175i	0.519571	+	0.854427i	$0.326092\pi$
$98$			6.38037i			0.644515i
$99$	13.0679	−	4.98909i	1.31337	−	0.501422i
$100$	2.85456			0.285456
$101$	−6.76434	+	11.7162i	−0.673077	+	1.16580i	0.303950	+	0.952688i	$0.401694\pi$
$101$	−6.76434	+	11.7162i	−0.673077	+	1.16580i	−0.977027	+	0.213116i	$0.931639\pi$
$102$	0.0702913	−	0.882884i	0.00695987	−	0.0874185i
$103$	−0.0523553	−	0.0906821i	−0.00515873	−	0.00893517i	0.863435	−	0.504461i	$-0.168309\pi$
$103$	−0.0523553	−	0.0906821i	−0.00515873	−	0.00893517i	−0.868593	+	0.495526i	$0.834975\pi$
$104$	8.49510	+	7.02336i	0.833014	+	0.688697i
$105$	−0.977304	−	2.05376i	−0.0953751	−	0.200426i
$106$	−0.541376	−	0.312564i	−0.0525831	−	0.0303589i
$107$	12.4240			1.20107			0.600535	−	0.799598i	$-0.294954\pi$
$107$	12.4240			1.20107			0.600535	+	0.799598i	$0.294954\pi$
$108$	−1.23831	−	4.22268i	−0.119156	−	0.406328i
$109$		−	14.1160i		−	1.35207i	−0.736869	−	0.676036i	$-0.763696\pi$
$109$		−	14.1160i		−	1.35207i	0.736869	−	0.676036i	$-0.236304\pi$
$110$	−5.53479	−	3.19551i	−0.527722	−	0.304680i
$111$	7.73657	−	3.68154i	0.734323	−	0.349436i
$112$	−1.41572	+	0.817366i	−0.133773	+	0.0772339i
$113$	−5.84280	−	10.1200i	−0.549645	−	0.952013i	−0.998299	−	0.0583071i	$-0.981430\pi$
$113$	−5.84280	−	10.1200i	−0.549645	−	0.952013i	0.448654	−	0.893706i	$-0.351904\pi$
$114$	12.4055	+	0.987671i	1.16188	+	0.0925039i
$115$	1.06092	+	0.612524i	0.0989315	+	0.0571181i
$116$	−7.94167			−0.737365
$117$	2.12199	+	10.6065i	0.196178	+	0.980568i
$118$	−4.52335			−0.416408
$119$	0.424247	+	0.244939i	0.0388906	+	0.0224535i
$120$	−3.83328	+	5.56662i	−0.349929	+	0.508160i
$121$	5.37007	+	9.30123i	0.488188	+	0.845566i
$122$	8.77230	−	5.06469i	0.794207	−	0.458536i
$123$	−2.17424	−	1.49722i	−0.196044	−	0.135000i
$124$	−1.41367	−	0.816181i	−0.126951	−	0.0732952i
$125$		−	10.6847i		−	0.955670i
$126$	−3.27238	−	0.524389i	−0.291527	−	0.0467163i
$127$	−8.11161			−0.719789			−0.359894	−	0.932993i	$-0.617187\pi$
$127$	−8.11161			−0.719789			−0.359894	+	0.932993i	$0.617187\pi$
$128$	−0.277222	−	0.160054i	−0.0245032	−	0.0141469i
$129$	4.53838	+	0.361325i	0.399582	+	0.0318129i
$130$	3.14904	−	3.80892i	0.276189	−	0.334064i
$131$	−4.68039	−	8.10667i	−0.408927	−	0.708283i	0.585843	−	0.810425i	$-0.300764\pi$
$131$	−4.68039	−	8.10667i	−0.408927	−	0.708283i	−0.994770	+	0.102142i	$0.967430\pi$
$132$	6.17573	−	2.93879i	0.537528	−	0.255789i
$133$	−3.44167	+	5.96115i	−0.298431	+	0.516897i
$134$	−2.49425			−0.215471
$135$	−6.36457	+	1.86643i	−0.547775	+	0.160636i
$136$		−	1.45574i		−	0.124829i
$137$	0.512400	+	0.295834i	0.0437773	+	0.0252748i	0.521729	−	0.853111i	$-0.325287\pi$
$137$	0.512400	+	0.295834i	0.0437773	+	0.0252748i	−0.477952	+	0.878386i	$0.658621\pi$
$138$	1.61185	−	0.767019i	0.137210	−	0.0652930i
$139$	6.33633	+	10.9749i	0.537441	+	0.930875i	0.999041	+	0.0437867i	$0.0139422\pi$
$139$	6.33633	+	10.9749i	0.537441	+	0.930875i	−0.461600	+	0.887088i	$0.652724\pi$
$140$	−0.556036	−	0.963083i	−0.0469936	−	0.0813954i
$141$	−0.940177	+	11.8090i	−0.0791772	+	0.994494i
$142$	0.725218	−	1.25611i	0.0608589	−	0.105411i
$143$	−15.7552	+	5.86481i	−1.31751	+	0.490440i
$144$	1.70030	+	4.45360i	0.141692	+	0.371133i
$145$			11.9700i			0.994052i
$146$	6.90945	−	11.9675i	0.571830	−	0.990438i
$147$	−5.83674	+	8.47601i	−0.481406	+	0.699089i
$148$	3.62796	−	2.09461i	0.298217	−	0.172176i
$149$	−10.1242	+	5.84520i	−0.829406	+	0.478858i	−0.853649	−	0.520848i	$-0.825616\pi$
$149$	−10.1242	+	5.84520i	−0.829406	+	0.478858i	0.0242432	+	0.999706i	$0.492282\pi$
$150$	−5.16345	−	3.55565i	−0.421594	−	0.290317i
$151$	−8.83800	−	5.10262i	−0.719226	−	0.415245i	0.0952418	−	0.995454i	$-0.469638\pi$
$151$	−8.83800	−	5.10262i	−0.719226	−	0.415245i	−0.814468	+	0.580209i	$0.802971\pi$
$152$	20.4548			1.65910
$153$	0.901037	−	1.10856i	0.0728445	−	0.0896221i
$154$		−	5.15086i		−	0.415068i
$155$	−1.23018	+	2.13073i	−0.0988102	+	0.171144i
$156$	1.44585	+	5.08728i	0.115760	+	0.407308i
$157$	−5.47021	−	9.47468i	−0.436570	−	0.756162i	0.560852	−	0.827916i	$-0.310474\pi$
$157$	−5.47021	−	9.47468i	−0.436570	−	0.756162i	−0.997422	+	0.0717541i	$0.977140\pi$
$158$	−12.0043	+	6.93070i	−0.955012	+	0.551377i
$159$	−0.433259	−	0.910474i	−0.0343597	−	0.0722053i
$160$	−2.81314	+	4.87251i	−0.222399	+	0.385206i
$161$			0.987329i			0.0778125i
$162$	−3.01987	+	9.18059i	−0.237263	+	0.721296i
$163$		−	16.9633i		−	1.32867i	−0.747436	−	0.664334i	$-0.768715\pi$
$163$		−	16.9633i		−	1.32867i	0.747436	−	0.664334i	$-0.231285\pi$
$164$	−1.11783	−	0.645378i	−0.0872877	−	0.0503956i
$165$	−4.42945	−	9.30828i	−0.344832	−	0.724649i
$166$	−5.49419	−	9.51621i	−0.426431	−	0.738601i
$167$	−14.5559	+	8.40384i	−1.12637	+	0.650309i	−0.943019	−	0.332739i	$-0.892027\pi$
$167$	−14.5559	+	8.40384i	−1.12637	+	0.650309i	−0.183349	+	0.983048i	$0.558694\pi$
$168$	−5.43008	−	0.432318i	−0.418939	−	0.0333541i
$169$	−2.44381	−	12.7682i	−0.187985	−	0.982172i
$170$	−0.652705			−0.0500602
$171$	15.5766	+	12.6606i	1.19117	+	0.968179i
$172$	2.22604			0.169734
$173$	9.54320	−	16.5293i	0.725556	−	1.25670i	−0.233189	−	0.972431i	$-0.574916\pi$
$173$	9.54320	−	16.5293i	0.725556	−	1.25670i	0.958745	−	0.284268i	$-0.0917505\pi$
$174$	14.3652	+	9.89216i	1.08902	+	0.749922i
$175$	3.00303	−	1.73380i	0.227008	−	0.131063i
$176$	−6.41649	+	3.70456i	−0.483661	+	0.279242i
$177$	−6.00905	−	4.13794i	−0.451668	−	0.311027i
$178$	−3.68318	+	6.37945i	−0.276066	+	0.478160i
$179$	−8.33634			−0.623087			−0.311544	−	0.950232i	$-0.600846\pi$
$179$	−8.33634			−0.623087			−0.311544	+	0.950232i	$0.600846\pi$
$180$	−3.02968	+	1.15668i	−0.225819	+	0.0862136i
$181$	9.93629			0.738558			0.369279	−	0.929318i	$-0.379605\pi$
$181$	9.93629			0.738558			0.369279	+	0.929318i	$0.379605\pi$
$182$	3.92752	+	0.663048i	0.291127	+	0.0491484i
$183$	16.2867	+	1.29668i	1.20395	+	0.0958531i
$184$	2.54090	−	1.46699i	0.187318	−	0.108148i
$185$	−3.15707	−	5.46820i	−0.232112	−	0.402030i
$186$	1.54046	+	3.23721i	0.112952	+	0.237364i
$187$	1.92282	+	1.11014i	0.140611	+	0.0811816i
$188$			5.79220i			0.422440i
$189$	−3.86749	−	3.69019i	−0.281318	−	0.268422i
$190$		−	9.17123i		−	0.665351i
$191$	3.03797	−	5.26192i	0.219820	−	0.380739i	−0.734933	−	0.678140i	$-0.762786\pi$
$191$	3.03797	−	5.26192i	0.219820	−	0.380739i	0.954753	+	0.297401i	$0.0961197\pi$
$192$	5.88798	+	12.3733i	0.424928	+	0.892967i
$193$	−14.3007	+	8.25650i	−1.02939	+	0.594316i	−0.916809	−	0.399327i	$-0.869244\pi$
$193$	−14.3007	+	8.25650i	−1.02939	+	0.594316i	−0.112577	+	0.993643i	$0.535910\pi$
$194$	−9.27705	−	16.0683i	−0.666054	−	1.15364i
$195$	7.66773	−	2.17923i	0.549097	−	0.156058i
$196$	−2.51593	+	4.35772i	−0.179709	+	0.311266i
$197$		−	19.1696i		−	1.36578i	−0.730523	−	0.682888i	$-0.760724\pi$
$197$		−	19.1696i		−	1.36578i	0.730523	−	0.682888i	$-0.239276\pi$
$198$	−14.8315	−	2.37670i	−1.05403	−	0.168905i
$199$	9.06267			0.642436			0.321218	−	0.947005i	$-0.395908\pi$
$199$	9.06267			0.642436			0.321218	+	0.947005i	$0.395908\pi$
$200$	−8.92393	−	5.15223i	−0.631017	−	0.364318i
$201$	−3.31349	−	2.28173i	−0.233716	−	0.160941i
$202$	12.5813	−	7.26379i	0.885214	−	0.511078i
$203$	−8.35474	+	4.82361i	−0.586387	+	0.338551i
$204$	0.396150	−	0.575282i	0.0277360	−	0.0402778i
$205$	−0.972737	+	1.68483i	−0.0679389	+	0.117674i
$206$			0.112442i			0.00783421i
$207$	2.84293	+	0.455571i	0.197598	+	0.0316644i
$208$	−1.99875	−	5.36943i	−0.138589	−	0.372303i
$209$	−15.5987	+	27.0178i	−1.07899	+	1.86886i
$210$	−0.193837	+	2.43466i	−0.0133760	+	0.168008i
$211$	7.34882	+	12.7285i	0.505913	+	0.876268i	0.999977	+	0.00684175i	$0.00217781\pi$
$211$	7.34882	+	12.7285i	0.505913	+	0.876268i	−0.494063	+	0.869426i	$0.664489\pi$
$212$	−0.246503	−	0.426955i	−0.0169299	−	0.0293234i
$213$	2.11250	−	1.00526i	0.144746	−	0.0688792i
$214$	−11.5539	−	6.67065i	−0.789809	−	0.455996i
$215$		−	3.35516i		−	0.228820i
$216$	−3.75036	+	15.4360i	−0.255180	+	1.05029i
$217$	−1.98293			−0.134610
$218$	−7.57916	+	13.1275i	−0.513325	+	0.889105i
$219$	20.1267	−	9.57751i	1.36004	−	0.647188i
$220$	−2.52013	−	4.36500i	−0.169907	−	0.294288i
$221$	−1.09400	+	1.32324i	−0.0735901	+	0.0890109i
$222$	−9.17145	−	0.730190i	−0.615548	−	0.0490072i
$223$	−17.4983	−	10.1026i	−1.17177	−	0.676521i	−0.217673	−	0.976022i	$-0.569847\pi$
$223$	−17.4983	−	10.1026i	−1.17177	−	0.676521i	−0.954096	+	0.299500i	$0.903180\pi$
$224$	−4.53452			−0.302975
$225$	−3.60669	−	9.44700i	−0.240446	−	0.629800i
$226$			12.5484i			0.834709i
$227$	17.8003	+	10.2770i	1.18145	+	0.682109i	0.956349	−	0.292228i	$-0.0943965\pi$
$227$	17.8003	+	10.2770i	1.18145	+	0.682109i	0.225098	+	0.974336i	$0.427730\pi$
$228$	8.08336	+	5.56635i	0.535333	+	0.368641i
$229$	17.2270	−	9.94602i	1.13839	−	0.657251i	0.192361	−	0.981324i	$-0.438386\pi$
$229$	17.2270	−	9.94602i	1.13839	−	0.657251i	0.946032	+	0.324073i	$0.105052\pi$
$230$	−0.657750	−	1.13926i	−0.0433707	−	0.0751203i
$231$	4.71198	−	6.84266i	0.310026	−	0.450214i
$232$	24.8272	+	14.3340i	1.62999	+	0.941074i
$233$	28.3932			1.86010			0.930049	−	0.367436i	$-0.119764\pi$
$233$	28.3932			1.86010			0.930049	+	0.367436i	$0.119764\pi$
$234$	3.72142	−	11.0030i	0.243277	−	0.719290i
$235$	8.73021			0.569496
$236$	−3.08940	−	1.78366i	−0.201103	−	0.116107i
$237$	−22.2873	−	1.77442i	−1.44772	−	0.115261i
$238$	−0.263024	−	0.455571i	−0.0170493	−	0.0295303i
$239$	−12.7434	+	7.35741i	−0.824302	+	0.475911i	−0.851898	−	0.523708i	$-0.824548\pi$
$239$	−12.7434	+	7.35741i	−0.824302	+	0.475911i	0.0275956	+	0.999619i	$0.491215\pi$
$240$	3.17230	−	1.50958i	0.204771	−	0.0974427i
$241$	11.4631	+	6.61822i	0.738403	+	0.426317i	0.821488	−	0.570225i	$-0.193144\pi$
$241$	11.4631	+	6.61822i	0.738403	+	0.426317i	−0.0830856	+	0.996542i	$0.526477\pi$
$242$		−	11.5331i		−	0.741378i
$243$	−12.4101	+	9.43340i	−0.796109	+	0.605153i
$244$	7.98851			0.511412
$245$	6.56812	+	3.79210i	0.419622	+	0.242269i
$246$	1.21809	+	2.55975i	0.0776624	+	0.163204i
$247$	−18.5930	−	15.3719i	−1.18305	−	0.978089i
$248$	2.94627	+	5.10309i	0.187088	+	0.324047i
$249$	1.40664	−	17.6679i	0.0891420	−	1.11966i
$250$	−5.73681	+	9.93645i	−0.362828	+	0.628437i
$251$	−11.9439			−0.753893			−0.376946	−	0.926235i	$-0.623026\pi$
$251$	−11.9439			−0.753893			−0.376946	+	0.926235i	$0.623026\pi$
$252$	−2.02822	−	1.64853i	−0.127766	−	0.103848i
$253$			4.47489i			0.281334i
$254$	7.54354	+	4.35527i	0.473324	+	0.273274i
$255$	−0.867085	−	0.597091i	−0.0542990	−	0.0373913i
$256$	8.08319	+	14.0005i	0.505200	+	0.875032i
$257$	7.48243	+	12.9600i	0.466741	+	0.808419i	0.999278	−	0.0379872i	$-0.0120946\pi$
$257$	7.48243	+	12.9600i	0.466741	+	0.808419i	−0.532537	+	0.846407i	$0.678761\pi$
$258$	−4.02655	−	2.77276i	−0.250682	−	0.172624i
$259$	2.54444	−	4.40710i	0.158104	−	0.273844i
$260$	3.65270	−	1.35971i	0.226531	−	0.0843255i
$261$	10.0342	+	26.2825i	0.621099	+	1.62684i
$262$			10.0519i			0.621010i
$263$	−0.774621	+	1.34168i	−0.0477652	+	0.0827317i	−0.888919	−	0.458063i	$-0.848543\pi$
$263$	−0.774621	+	1.34168i	−0.0477652	+	0.0827317i	0.841154	+	0.540795i	$0.181877\pi$
$264$	−24.6108	−	1.95940i	−1.51469	−	0.120593i
$265$	−0.643522	+	0.371538i	−0.0395312	+	0.0228234i
$266$	6.40129	−	3.69579i	0.392488	−	0.226603i
$267$	−10.7288	+	5.10543i	−0.656593	+	0.312447i
$268$	−1.70355	−	0.983543i	−0.104061	−	0.0600794i
$269$	21.0293			1.28218			0.641090	−	0.767466i	$-0.278483\pi$
$269$	21.0293			1.28218			0.641090	+	0.767466i	$0.278483\pi$
$270$	6.92097	+	1.68153i	0.421197	+	0.102335i
$271$		−	12.7508i		−	0.774554i	−0.921963	−	0.387277i	$-0.873416\pi$
$271$		−	12.7508i		−	0.774554i	0.921963	−	0.387277i	$-0.126584\pi$
$272$	−0.378341	+	0.655305i	−0.0229403	+	0.0397337i
$273$	4.61096	+	4.47370i	0.279068	+	0.270761i
$274$	−0.317677	−	0.550233i	−0.0191916	−	0.0332408i
$275$	13.6107	−	7.85814i	0.820756	−	0.473864i
$276$	1.40333	+	0.111727i	0.0844706	+	0.00672518i
$277$	5.81364	−	10.0695i	0.349308	−	0.605019i	−0.636819	−	0.771013i	$-0.719750\pi$
$277$	5.81364	−	10.0695i	0.349308	−	0.605019i	0.986127	+	0.165995i	$0.0530835\pi$
$278$		−	13.6084i		−	0.816175i
$279$	−0.914958	+	5.70968i	−0.0547771	+	0.341829i
$280$			4.01439i			0.239905i
$281$	14.9681	+	8.64183i	0.892921	+	0.515528i	0.874897	−	0.484309i	$-0.160929\pi$
$281$	14.9681	+	8.64183i	0.892921	+	0.515528i	0.0180245	+	0.999838i	$0.494262\pi$
$282$	7.21478	−	10.4772i	0.429634	−	0.623906i
$283$	−10.8047	−	18.7143i	−0.642273	−	1.11245i	−0.984924	−	0.172987i	$-0.944658\pi$
$283$	−10.8047	−	18.7143i	−0.642273	−	1.11245i	0.342651	−	0.939463i	$-0.388675\pi$
$284$	0.990631	−	0.571941i	0.0587831	−	0.0339385i
$285$	8.38981	−	12.1835i	0.496969	−	0.721690i
$286$	17.8007	+	3.00514i	1.05258	+	0.177698i
$287$	−1.56796			−0.0925536
$288$	−2.09231	+	13.0568i	−0.123290	+	0.769378i
$289$	−16.7732			−0.986662
$290$	6.42689	−	11.1317i	0.377400	−	0.653676i
$291$	2.37514	−	29.8326i	0.139233	−	1.74882i
$292$	9.43814	−	5.44912i	0.552326	−	0.318885i
$293$	−0.0618730	+	0.0357224i	−0.00361466	+	0.00208692i	−0.501806	−	0.864980i	$-0.667331\pi$
$293$	−0.0618730	+	0.0357224i	−0.00361466	+	0.00208692i	0.498192	+	0.867067i	$0.333998\pi$
$294$	9.97891	−	4.74858i	0.581982	−	0.276943i
$295$	−2.68840	+	4.65645i	−0.156525	+	0.271109i
$296$	−15.1223			−0.878967
$297$	−17.5287	−	16.7251i	−1.01712	−	0.970489i
$298$	12.5536			0.727209
$299$	−3.41209	−	0.576033i	−0.197326	−	0.0333129i
$300$	−2.12450	−	4.46453i	−0.122658	−	0.257760i
$301$	2.34182	−	1.35205i	0.134980	−	0.0779309i
$302$	5.47937	+	9.49055i	0.315303	+	0.546120i
$303$	23.3584	+	1.85970i	1.34191	+	0.106837i
$304$	−9.20778	−	5.31611i	−0.528102	−	0.304900i
$305$		−	12.0406i		−	0.689441i
$306$	−1.43314	+	0.547148i	−0.0819274	+	0.0312784i
$307$			19.9335i			1.13766i	0.822454	+	0.568831i	$0.192604\pi$
$307$			19.9335i			1.13766i	−0.822454	+	0.568831i	$0.807396\pi$
$308$	2.03111	−	3.51798i	0.115733	−	0.200455i
$309$	−0.102862	+	0.149374i	−0.00585159	+	0.00849757i
$310$	2.28805	−	1.32101i	0.129953	−	0.0750282i
$311$	−3.04014	−	5.26567i	−0.172390	−	0.298589i	0.766865	−	0.641809i	$-0.221816\pi$
$311$	−3.04014	−	5.26567i	−0.172390	−	0.298589i	−0.939255	+	0.343220i	$0.888482\pi$
$312$	4.66208	−	18.5135i	0.263939	−	1.04812i
$313$	−3.04622	+	5.27620i	−0.172182	+	0.298228i	−0.939183	−	0.343418i	$-0.888415\pi$
$313$	−3.04622	+	5.27620i	−0.172182	+	0.298228i	0.767000	+	0.641647i	$0.221748\pi$
$314$			11.7482i			0.662990i
$315$	−2.48472	+	3.05701i	−0.139998	+	0.172243i
$316$	−10.9317			−0.614959
$317$	8.25032	+	4.76332i	0.463384	+	0.267535i	0.713466	−	0.700690i	$-0.247124\pi$
$317$	8.25032	+	4.76332i	0.463384	+	0.267535i	−0.250082	+	0.968225i	$0.580458\pi$
$318$	−0.0859321	+	1.07934i	−0.00481883	+	0.0605262i
$319$	−37.8663	+	21.8621i	−2.12011	+	1.22404i
$320$	8.74544	−	5.04918i	0.488885	−	0.282258i
$321$	−9.24650	−	19.4311i	−0.516089	−	1.08454i
$322$	0.530115	−	0.918186i	0.0295421	−	0.0511685i
$323$			3.18614i			0.177282i
$324$	−5.68266	+	5.07943i	−0.315703	+	0.282191i
$325$	4.23977	+	11.3897i	0.235180	+	0.631785i
$326$	−9.10790	+	15.7753i	−0.504440	+	0.873715i
$327$	−22.0775	+	10.5058i	−1.22089	+	0.580974i
$328$	2.32970	+	4.03516i	0.128636	+	0.222804i
$329$	3.51807	+	6.09347i	0.193957	+	0.335944i
$330$	−0.878531	+	11.0347i	−0.0483615	+	0.607438i
$331$	−15.7143	−	9.07268i	−0.863739	−	0.498680i	0.00152386	−	0.999999i	$-0.499515\pi$
$331$	−15.7143	−	9.07268i	−0.863739	−	0.498680i	−0.865262	+	0.501319i	$0.832848\pi$
$332$		−	8.66595i		−	0.475606i
$333$	−11.5158	−	9.36003i	−0.631064	−	0.512927i
$334$	18.0487			0.987580
$335$	−1.48243	+	2.56765i	−0.0809938	+	0.140285i
$336$	2.33201	+	1.60586i	0.127221	+	0.0876071i
$337$	4.00930	+	6.94430i	0.218400	+	0.378280i	0.954319	−	0.298789i	$-0.0965828\pi$
$337$	4.00930	+	6.94430i	0.218400	+	0.378280i	−0.735919	+	0.677070i	$0.763250\pi$
$338$	−4.58283	+	13.1862i	−0.249273	+	0.717234i
$339$	−11.4792	+	16.6700i	−0.623467	+	0.905387i
$340$	−0.445790	−	0.257377i	−0.0241763	−	0.0139582i
$341$	−8.98726			−0.486687
$342$	−7.68804	−	20.1373i	−0.415722	−	1.08890i
$343$			13.3138i			0.718876i
$344$	−6.95904	−	4.01780i	−0.375206	−	0.216625i
$345$	0.168399	−	2.11515i	0.00906630	−	0.113876i
$346$	−17.7497	+	10.2478i	−0.954232	+	0.550926i
$347$	−8.31364	−	14.3996i	−0.446299	−	0.773013i	0.551842	−	0.833949i	$-0.313925\pi$
$347$	−8.31364	−	14.3996i	−0.446299	−	0.773013i	−0.998142	+	0.0609351i	$0.980592\pi$
$348$	5.91056	+	12.4208i	0.316839	+	0.665823i
$349$	−0.155013	−	0.0894966i	−0.00829764	−	0.00479065i	0.495845	−	0.868411i	$-0.334858\pi$
$349$	−0.155013	−	0.0894966i	−0.00829764	−	0.00479065i	−0.504143	+	0.863620i	$0.668192\pi$
$350$	−3.72364			−0.199037
$351$	15.0092	−	11.2126i	0.801134	−	0.598486i
$352$	−20.5519			−1.09542
$353$	14.6540	+	8.46052i	0.779956	+	0.450308i	0.836415	−	0.548097i	$-0.184648\pi$
$353$	14.6540	+	8.46052i	0.779956	+	0.450308i	−0.0564585	+	0.998405i	$0.517981\pi$
$354$	3.36649	+	7.07452i	0.178927	+	0.376007i
$355$	−0.862050	−	1.49311i	−0.0457529	−	0.0792463i
$356$	−5.03114	+	2.90473i	−0.266650	+	0.153950i
$357$	0.0673402	−	0.845817i	0.00356402	−	0.0447654i
$358$	7.75253	+	4.47593i	0.409734	+	0.236560i
$359$			34.4410i			1.81773i	0.417093	+	0.908864i	$0.363049\pi$
$359$			34.4410i			1.81773i	−0.417093	+	0.908864i	$0.636951\pi$
$360$	11.5591	+	1.85231i	0.609218	+	0.0976252i
$361$	−25.7689			−1.35626
$362$	−9.24044	−	5.33497i	−0.485667	−	0.280400i
$363$	10.5505	−	15.3212i	0.553756	−	0.804154i
$364$	2.42099	+	2.00157i	0.126895	+	0.104911i
$365$	−8.21310	−	14.2255i	−0.429893	−	0.744597i
$366$	−14.4499	−	9.95050i	−0.755310	−	0.520121i
$367$	−12.5426	+	21.7244i	−0.654717	+	1.13400i	0.327248	+	0.944939i	$0.393879\pi$
$367$	−12.5426	+	21.7244i	−0.654717	+	1.13400i	−0.981965	+	0.189064i	$0.939455\pi$
$368$	−1.52506			−0.0794993
$369$	−0.723484	+	4.51481i	−0.0376630	+	0.235031i
$370$			6.78034i			0.352493i
$371$	−0.518648	−	0.299441i	−0.0269268	−	0.0155462i
$372$	−0.224390	+	2.81842i	−0.0116341	+	0.146128i
$373$	−5.47530	−	9.48350i	−0.283500	−	0.491037i	0.688744	−	0.725005i	$-0.258162\pi$
$373$	−5.47530	−	9.48350i	−0.283500	−	0.491037i	−0.972244	+	0.233968i	$0.924829\pi$
$374$	−1.19211	−	2.06479i	−0.0616425	−	0.106768i
$375$	−16.7109	+	7.95207i	−0.862947	+	0.410643i
$376$	10.4544	−	18.1076i	0.539145	−	0.933827i
$377$	−11.7954	−	31.6872i	−0.607496	−	1.63197i
$378$	1.61532	+	5.50828i	0.0830829	+	0.283315i
$379$		−	11.1048i		−	0.570415i	−0.958466	−	0.285208i	$-0.907937\pi$
$379$		−	11.1048i		−	0.570415i	0.958466	−	0.285208i	$-0.0920626\pi$
$380$	3.61643	−	6.26385i	0.185519	−	0.321329i
$381$	6.03704	+	12.6866i	0.309287	+	0.649952i
$382$	−5.65043	+	3.26228i	−0.289101	+	0.166913i
$383$	5.09111	−	2.93935i	0.260144	−	0.150194i	−0.364256	−	0.931299i	$-0.618677\pi$
$383$	5.09111	−	2.93935i	0.260144	−	0.150194i	0.624400	+	0.781105i	$0.285344\pi$
$384$	−0.0440032	+	0.552696i	−0.00224553	+	0.0282046i
$385$	−5.30242	−	3.06135i	−0.270236	−	0.156021i
$386$	17.7322			0.902548
$387$	−2.81256	−	7.36694i	−0.142970	−	0.374482i
$388$		−	14.6326i		−	0.742860i
$389$	0.0401383	−	0.0695217i	0.00203510	−	0.00352489i	−0.865006	−	0.501761i	$-0.832686\pi$
$389$	0.0401383	−	0.0695217i	0.00203510	−	0.00352489i	0.867041	+	0.498237i	$0.166019\pi$
$390$	−8.30081	−	2.09032i	−0.420328	−	0.105848i
$391$	0.228506	+	0.395785i	0.0115561	+	0.0200157i
$392$	15.7306	−	9.08207i	0.794516	−	0.458714i
$393$	−9.19546	+	13.3535i	−0.463850	+	0.673594i
$394$	−10.2925	+	17.8271i	−0.518528	+	0.898117i
$395$			16.4767i			0.829034i
$396$	−9.19254	−	7.47166i	−0.461943	−	0.375465i
$397$		−	1.33964i		−	0.0672345i	−0.999435	−	0.0336172i	$-0.989297\pi$
$397$		−	1.33964i		−	0.0672345i	0.999435	−	0.0336172i	$-0.0107027\pi$
$398$	−8.42800	−	4.86591i	−0.422458	−	0.243906i
$399$	11.8847	+	0.946206i	0.594978	+	0.0473695i
$400$	2.67809	+	4.63858i	0.133904	+	0.231929i
$401$	27.4333	−	15.8386i	1.36995	−	0.790942i	0.379030	−	0.925384i	$-0.376258\pi$
$401$	27.4333	−	15.8386i	1.36995	−	0.790942i	0.990921	+	0.134442i	$0.0429243\pi$
$402$	1.85634	+	3.90101i	0.0925858	+	0.194565i
$403$	1.15689	−	6.85276i	0.0576288	−	0.341360i
$404$	11.4571			0.570014
$405$	7.65591	+	8.56511i	0.380425	+	0.425604i
$406$	10.3595			0.514135
$407$	11.5322	−	19.9744i	0.571631	−	0.990094i
$408$	−2.27678	+	1.08343i	−0.112717	+	0.0536378i
$409$	−2.92633	+	1.68952i	−0.144698	+	0.0835412i	−0.570601	−	0.821227i	$-0.693290\pi$
$409$	−2.92633	+	1.68952i	−0.144698	+	0.0835412i	0.425903	+	0.904769i	$0.359956\pi$
$410$	1.80923	−	1.04456i	0.0893515	−	0.0515871i
$411$	0.0813326	−	1.02157i	0.00401184	−	0.0503902i
$412$	−0.0443386	+	0.0767966i	−0.00218440	+	0.00378350i
$413$	−4.33345			−0.213235
$414$	−2.39924	−	1.95009i	−0.117916	−	0.0958416i
$415$	−13.0616			−0.641170
$416$	2.64555	−	15.6707i	0.129709	−	0.768322i
$417$	12.4489	−	18.0780i	0.609624	−	0.885285i
$418$	29.0127	−	16.7505i	1.41906	−	0.819293i
$419$	10.8330	+	18.7633i	0.529228	+	0.916649i	0.999419	+	0.0340847i	$0.0108516\pi$
$419$	10.8330	+	18.7633i	0.529228	+	0.916649i	−0.470191	+	0.882565i	$0.655815\pi$
$420$	−1.09243	+	1.58641i	−0.0533053	+	0.0774090i
$421$	12.1688	+	7.02566i	0.593071	+	0.342409i	0.766311	−	0.642470i	$-0.222090\pi$
$421$	12.1688	+	7.02566i	0.593071	+	0.342409i	−0.173240	+	0.984880i	$0.555424\pi$
$422$		−	15.7828i		−	0.768297i
$423$	19.1689	−	7.31835i	0.932026	−	0.355830i
$424$			1.77966i			0.0864280i
$425$	0.802539	−	1.39004i	0.0389288	−	0.0674267i
$426$	−2.50430	−	0.199382i	−0.121334	−	0.00966007i
$427$	8.40401	−	4.85206i	0.406699	−	0.234808i
$428$	−5.26079	−	9.11195i	−0.254290	−	0.440443i
$429$	20.8983	+	20.2762i	1.00898	+	0.978946i
$430$	−1.80145	+	3.12020i	−0.0868735	+	0.150469i
$431$			26.5547i			1.27909i	0.768752	+	0.639547i	$0.220878\pi$
$431$			26.5547i			1.27909i	−0.768752	+	0.639547i	$0.779122\pi$
$432$	5.69998	−	5.97385i	0.274241	−	0.287417i
$433$	21.7861			1.04697			0.523485	−	0.852035i	$-0.324631\pi$
$433$	21.7861			1.04697			0.523485	+	0.852035i	$0.324631\pi$
$434$	1.84406	+	1.06467i	0.0885178	+	0.0511058i
$435$	18.7210	−	8.90861i	0.897605	−	0.427135i
$436$	−10.3530	+	5.97728i	−0.495817	+	0.286260i
$437$	−5.56122	+	3.21077i	−0.266029	+	0.153592i
$438$	−23.8595	−	1.89959i	−1.14005	−	0.0907659i
$439$	3.89690	−	6.74963i	0.185989	−	0.322142i	−0.757920	−	0.652347i	$-0.773784\pi$
$439$	3.89690	−	6.74963i	0.185989	−	0.322142i	0.943909	+	0.330205i	$0.107118\pi$
$440$			18.1945i			0.867387i
$441$	17.6005	+	2.82042i	0.838117	+	0.134306i
$442$	1.72785	−	0.643188i	0.0821857	−	0.0305933i
$443$	−8.00154	+	13.8591i	−0.380165	+	0.658465i	−0.991086	−	0.133227i	$-0.957466\pi$
$443$	−8.00154	+	13.8591i	−0.380165	+	0.658465i	0.610921	+	0.791692i	$0.290799\pi$
$444$	−5.97607	−	4.11523i	−0.283612	−	0.195300i
$445$	4.37811	+	7.58311i	0.207542	+	0.359474i
$446$	10.8486	+	18.7902i	0.513694	+	0.889744i
$447$	16.6768	+	11.4840i	0.788786	+	0.543173i
$448$	7.04840	+	4.06940i	0.333006	+	0.192261i
$449$		−	8.58501i		−	0.405151i	−0.979267	−	0.202576i	$-0.935069\pi$
$449$		−	8.58501i		−	0.405151i	0.979267	−	0.202576i	$-0.0649312\pi$
$450$	−1.71815	+	10.7219i	−0.0809945	+	0.505436i
$451$	−7.10648			−0.334631
$452$	−4.94814	+	8.57043i	−0.232741	+	0.403119i
$453$	−1.40284	+	17.6202i	−0.0659114	+	0.827871i
$454$	−11.0358	−	19.1146i	−0.517936	−	0.897092i
$455$	3.01683	−	3.64901i	0.141431	−	0.171068i
$456$	−15.2234	−	31.9913i	−0.712901	−	1.49813i
$457$	4.76629	+	2.75182i	0.222958	+	0.128725i	0.607319	−	0.794458i	$-0.292245\pi$
$457$	4.76629	+	2.75182i	0.222958	+	0.128725i	−0.384361	+	0.923183i	$0.625578\pi$
$458$	−21.3608			−0.998123
$459$	−2.40439	−	0.584176i	−0.112227	−	0.0272670i
$460$		−	1.03747i		−	0.0483721i
$461$	−19.9077	−	11.4937i	−0.927196	−	0.535317i	−0.0412725	−	0.999148i	$-0.513141\pi$
$461$	−19.9077	−	11.4937i	−0.927196	−	0.535317i	−0.885924	+	0.463831i	$0.846475\pi$
$462$	−8.05594	+	3.83351i	−0.374796	+	0.178351i
$463$	21.8412	−	12.6100i	1.01505	−	0.586037i	0.102381	−	0.994745i	$-0.467354\pi$
$463$	21.8412	−	12.6100i	1.01505	−	0.586037i	0.912665	+	0.408708i	$0.134021\pi$
$464$	−7.45070	−	12.9050i	−0.345890	−	0.599099i
$465$	4.24802	+	0.338208i	0.196997	+	0.0156840i
$466$	−26.4048	−	15.2448i	−1.22318	−	0.706201i
$467$	18.1098			0.838023			0.419012	−	0.907981i	$-0.362377\pi$
$467$	18.1098			0.838023			0.419012	+	0.907981i	$0.362377\pi$
$468$	6.88043	−	6.04749i	0.318048	−	0.279545i
$469$	−2.38954			−0.110338
$470$	−8.11883	−	4.68741i	−0.374494	−	0.216214i
$471$	−10.7472	+	15.6069i	−0.495206	+	0.719129i
$472$	6.43871	+	11.1522i	0.296366	+	0.513321i
$473$	10.6139	−	6.12792i	0.488026	−	0.281762i
$474$	19.7738	+	13.6166i	0.908240	+	0.625431i
$475$	19.5316	+	11.2766i	0.896171	+	0.517405i
$476$		−	0.414867i		−	0.0190154i
$477$	−1.10153	+	1.35524i	−0.0504356	+	0.0620520i
$478$	15.8013			0.722734
$479$	14.3564	+	8.28869i	0.655962	+	0.378720i	0.790737	−	0.612157i	$-0.209698\pi$
$479$	14.3564	+	8.28869i	0.655962	+	0.378720i	−0.134775	+	0.990876i	$0.543031\pi$
$480$	9.71428	+	0.773408i	0.443394	+	0.0353011i
$481$	13.7459	+	11.3645i	0.626760	+	0.518177i
$482$	−7.10688	−	12.3095i	−0.323709	−	0.560681i
$483$	1.54418	−	0.734817i	0.0702628	−	0.0334353i
$484$	4.54779	−	7.87700i	0.206718	−	0.358045i
$485$	−22.0548			−1.00146
$486$	16.6060	−	2.10955i	0.753263	−	0.0956913i
$487$		−	5.78932i		−	0.262339i	−0.991360	−	0.131170i	$-0.958127\pi$
$487$		−	5.78932i		−	0.262339i	0.991360	−	0.131170i	$-0.0418732\pi$
$488$	−24.9737	−	14.4186i	−1.13051	−	0.652697i
$489$	−26.5306	+	12.6249i	−1.19976	+	0.570917i
$490$	−4.07210	−	7.05308i	−0.183959	−	0.318626i
$491$	5.23530	+	9.06781i	0.236266	+	0.409224i	0.959640	−	0.281232i	$-0.0907430\pi$
$491$	5.23530	+	9.06781i	0.236266	+	0.409224i	−0.723374	+	0.690456i	$0.757410\pi$
$492$	−0.177431	+	2.22860i	−0.00799923	+	0.100473i
$493$	−2.23274	+	3.86722i	−0.100558	+	0.174171i
$494$	9.03752	+	24.2783i	0.406617	+	1.09233i
$495$	−11.2616	+	13.8553i	−0.506169	+	0.622751i
$496$		−	3.06289i		−	0.137528i
$497$	0.694771	−	1.20338i	0.0311647	−	0.0539789i
$498$	−10.7943	+	15.6753i	−0.483705	+	0.702428i
$499$	7.82629	−	4.51851i	0.350353	−	0.202276i	−0.314488	−	0.949262i	$-0.601833\pi$
$499$	7.82629	−	4.51851i	0.350353	−	0.202276i	0.664841	+	0.746985i	$0.268499\pi$
$500$	−7.83636	+	4.52432i	−0.350453	+	0.202334i
$501$	23.9768	+	16.5109i	1.07120	+	0.737651i
$502$	11.1075	+	6.41289i	0.495750	+	0.286221i
$503$	−9.96486			−0.444311			−0.222155	−	0.975011i	$-0.571309\pi$
$503$	−9.96486			−0.444311			−0.222155	+	0.975011i	$0.571309\pi$
$504$	3.36517	+	8.81439i	0.149897	+	0.392624i
$505$		−	17.2686i		−	0.768443i
$506$	2.40265	−	4.16151i	0.106811	−	0.185002i
$507$	−18.1507	+	13.3248i	−0.806102	+	0.591777i
$508$	3.43477	+	5.94920i	0.152393	+	0.263953i
$509$	−30.5593	+	17.6434i	−1.35452	+	0.782030i	−0.988878	−	0.148727i	$-0.952482\pi$
$509$	−30.5593	+	17.6434i	−1.35452	+	0.782030i	−0.365638	+	0.930757i	$0.619149\pi$
$510$	0.485773	+	1.02083i	0.0215104	+	0.0452031i
$511$	6.61936	−	11.4651i	0.292823	−	0.507185i
$512$		−	16.7198i		−	0.738919i
$513$	8.20832	−	33.7844i	0.362406	−	1.49162i
$514$		−	16.0698i		−	0.708808i
$515$	0.115751	+	0.0668287i	0.00510058	+	0.00294482i
$516$	−1.65672	−	3.48152i	−0.0729331	−	0.153266i
$517$	15.9450	+	27.6175i	0.701260	+	1.21462i
$518$	−4.73251	+	2.73231i	−0.207934	+	0.120051i
$519$	−32.9543	−	2.62368i	−1.44653	−	0.115167i
$520$	−13.8732	−	2.34209i	−0.608381	−	0.102708i
$521$	12.9544			0.567541			0.283770	−	0.958892i	$-0.408415\pi$
$521$	12.9544			0.567541			0.283770	+	0.958892i	$0.408415\pi$
$522$	4.78007	−	29.8294i	0.209218	−	1.30560i
$523$	−0.367139			−0.0160539			−0.00802694	−	0.999968i	$-0.502555\pi$
$523$	−0.367139			−0.0160539			−0.00802694	+	0.999968i	$0.502555\pi$
$524$	−3.96371	+	6.86535i	−0.173156	+	0.299914i
$525$	−4.94667	−	3.40637i	−0.215890	−	0.148666i
$526$	1.44075	−	0.831815i	0.0628195	−	0.0362689i
$527$	−0.794884	+	0.458927i	−0.0346257	+	0.0199912i
$528$	10.5694	+	7.27828i	0.459974	+	0.316747i
$529$	11.0395	−	19.1209i	0.479976	−	0.831343i
$530$	0.797940			0.0346603
$531$	−1.99953	+	12.4778i	−0.0867721	+	0.541490i
$532$	5.82934			0.252734
$533$	0.914787	−	5.41867i	0.0396238	−	0.234709i
$534$	12.7187	+	1.01260i	0.550390	+	0.0438196i
$535$	−13.7339	+	7.92925i	−0.593767	+	0.342811i
$536$	3.55042	+	6.14950i	0.153355	+	0.265618i
$537$	6.20429	+	13.0380i	0.267735	+	0.562633i
$538$	−19.5566	−	11.2910i	−0.843145	−	0.486790i
$539$			27.7038i			1.19329i
$540$	4.06388	+	3.87757i	0.174881	+	0.166864i
$541$		−	42.0316i		−	1.80708i	−0.428504	−	0.903540i	$-0.640959\pi$
$541$		−	42.0316i		−	1.80708i	0.428504	−	0.903540i	$-0.359041\pi$
$542$	−6.84612	+	11.8578i	−0.294066	+	0.509337i
$543$	−7.39505	−	15.5404i	−0.317352	−	0.666901i
$544$	−1.81772	+	1.04946i	−0.0779343	+	0.0449954i
$545$	9.00917	+	15.6043i	0.385911	+	0.668417i
$546$	−1.88604	−	6.63611i	−0.0807149	−	0.283999i
$547$	14.2892	−	24.7496i	0.610962	−	1.05822i	−0.380116	−	0.924939i	$-0.624116\pi$
$547$	14.2892	−	24.7496i	0.610962	−	1.05822i	0.991079	−	0.133279i	$-0.0425506\pi$
$548$		−	0.501071i		−	0.0214047i
$549$	−10.0933	−	26.4375i	−0.430774	−	1.12832i
$550$	−16.8767			−0.719625
$551$	−54.3388	−	31.3725i	−2.31491	−	1.33651i
$552$	−4.18544	−	2.88217i	−0.178144	−	0.122673i
$553$	−11.5003	+	6.63972i	−0.489044	+	0.282350i
$554$	−10.8130	+	6.24289i	−0.459401	+	0.265235i
$555$	−6.20263	+	9.00734i	−0.263287	+	0.382340i
$556$	5.36610	−	9.29435i	0.227573	−	0.394168i
$557$			3.59187i			0.152192i	0.997100	+	0.0760961i	$0.0242456\pi$
$557$			3.59187i			0.152192i	−0.997100	+	0.0760961i	$0.975754\pi$
$558$	3.91651	−	4.81857i	0.165799	−	0.203986i
$559$	3.30625	+	8.88187i	0.139839	+	0.375663i
$560$	1.04332	−	1.80709i	0.0440884	−	0.0763634i
$561$	0.305207	−	3.83351i	0.0128859	−	0.161851i
$562$	−9.27991	−	16.0733i	−0.391449	−	0.678010i
$563$	15.3227	+	26.5396i	0.645774	+	1.11851i	0.984122	+	0.177492i	$0.0567983\pi$
$563$	15.3227	+	26.5396i	0.645774	+	1.11851i	−0.338349	+	0.941021i	$0.609868\pi$
$564$	9.05900	−	4.31083i	0.381453	−	0.181519i
$565$	12.9177	+	7.45801i	0.543450	+	0.313761i
$566$			23.2050i			0.975377i
$567$	−2.89309	+	8.79516i	−0.121498	+	0.369362i
$568$	−4.12921			−0.173258
$569$	17.3324	−	30.0206i	0.726612	−	1.25853i	−0.231695	−	0.972788i	$-0.574427\pi$
$569$	17.3324	−	30.0206i	0.726612	−	1.25853i	0.958307	−	0.285740i	$-0.0922395\pi$
$570$	−14.3438	+	6.82566i	−0.600796	+	0.285896i
$571$	7.76050	+	13.4416i	0.324767	+	0.562512i	0.981465	−	0.191641i	$-0.0613809\pi$
$571$	7.76050	+	13.4416i	0.324767	+	0.562512i	−0.656698	+	0.754153i	$0.728048\pi$
$572$	10.9727	+	9.07173i	0.458792	+	0.379308i
$573$	−10.4906	−	0.835218i	−0.438253	−	0.0348917i
$574$	1.45815	+	0.841864i	0.0608621	+	0.0351387i
$575$	3.23497			0.134908
$576$	14.9697	−	18.4176i	0.623739	−	0.767400i
$577$			18.6264i			0.775426i	0.921780	+	0.387713i	$0.126735\pi$
$577$			18.6264i			0.775426i	−0.921780	+	0.387713i	$0.873265\pi$
$578$	15.5986	+	9.00585i	0.648816	+	0.374594i
$579$	23.5564	+	16.2214i	0.978971	+	0.674138i
$580$	8.77898	−	5.06855i	0.364527	−	0.210460i
$581$	−5.26352	−	9.11669i	−0.218368	−	0.378224i
$582$	−18.2264	+	26.4681i	−0.755511	+	1.09714i
$583$	−2.35068	−	1.35716i	−0.0973550	−	0.0562080i
$584$	−39.3407			−1.62793
$585$	−9.11500	−	10.3704i	−0.376859	−	0.428765i
$586$	0.0767199			0.00316927
$587$	−30.6515	−	17.6966i	−1.26512	−	0.730418i	−0.291060	−	0.956705i	$-0.594008\pi$
$587$	−30.6515	−	17.6966i	−1.26512	−	0.730418i	−0.974061	+	0.226287i	$0.927341\pi$
$588$	8.68795	+	0.691696i	0.358285	+	0.0285251i
$589$	−6.44844	−	11.1690i	−0.265703	−	0.460211i
$590$	5.00026	−	2.88690i	0.205857	−	0.118852i
$591$	−29.9812	+	14.2669i	−1.23326	+	0.586862i
$592$	6.80736	+	3.93023i	0.279781	+	0.161531i
$593$			2.41535i			0.0991864i	0.998770	+	0.0495932i	$0.0157925\pi$
$593$			2.41535i			0.0991864i	−0.998770	+	0.0495932i	$0.984208\pi$
$594$	7.32113	+	24.9653i	0.300389	+	1.02434i
$595$	−0.625302			−0.0256349
$596$	8.57395	+	4.95017i	0.351203	+	0.202767i
$597$	−6.74487	−	14.1740i	−0.276049	−	0.580104i
$598$	2.86386	+	2.36771i	0.117112	+	0.0968227i
$599$	−20.4683	−	35.4522i	−0.836314	−	1.44854i	−0.892956	−	0.450143i	$-0.851373\pi$
$599$	−20.4683	−	35.4522i	−0.836314	−	1.44854i	0.0566424	−	0.998395i	$-0.481960\pi$
$600$	−1.41648	+	17.7916i	−0.0578278	+	0.726337i
$601$	8.82077	−	15.2780i	0.359807	−	0.623203i	−0.628122	−	0.778115i	$-0.716176\pi$
$601$	8.82077	−	15.2780i	0.359807	−	0.623203i	0.987928	+	0.154912i	$0.0495093\pi$
$602$	−2.90376			−0.118348
$603$	−1.10257	+	6.88047i	−0.0449003	+	0.280194i
$604$			8.64259i			0.351662i
$605$	−11.8725	−	6.85459i	−0.482686	−	0.278679i
$606$	−20.7241	−	14.2710i	−0.841860	−	0.579721i
$607$	9.22956	+	15.9861i	0.374616	+	0.648854i	0.990270	−	0.139163i	$-0.0444412\pi$
$607$	9.22956	+	15.9861i	0.374616	+	0.648854i	−0.615653	+	0.788017i	$0.711108\pi$
$608$	−14.7461	−	25.5411i	−0.598035	−	1.03583i
$609$	13.7621	+	9.47685i	0.557669	+	0.384021i
$610$	−6.46480	+	11.1974i	−0.261752	+	0.453368i
$611$	−23.1108	+	8.60293i	−0.934964	+	0.348037i
$612$	−1.19457	−	0.191427i	−0.0482878	−	0.00773797i
$613$		−	7.01548i		−	0.283352i	−0.989913	−	0.141676i	$-0.954751\pi$
$613$		−	7.01548i		−	0.283352i	0.989913	−	0.141676i	$-0.0452492\pi$
$614$	10.7026	−	18.5375i	0.431923	−	0.748112i
$615$	3.35903	+	0.267431i	0.135449	+	0.0107839i
$616$	−12.6993	+	7.33193i	−0.511669	+	0.295412i
$617$	−8.78344	+	5.07112i	−0.353608	+	0.204156i	−0.666273	−	0.745708i	$-0.732112\pi$
$617$	−8.78344	+	5.07112i	−0.353608	+	0.204156i	0.312665	+	0.949863i	$0.398778\pi$
$618$	0.175859	−	0.0836847i	0.00707410	−	0.00336629i
$619$	−8.11092	−	4.68284i	−0.326005	−	0.188219i	0.328061	−	0.944657i	$-0.393605\pi$
$619$	−8.11092	−	4.68284i	−0.326005	−	0.188219i	−0.654066	+	0.756437i	$0.726938\pi$
$620$	2.08362			0.0836802
$621$	−1.40333	−	4.78541i	−0.0563138	−	0.192032i
$622$			6.52922i			0.261798i
$623$	−3.52855	+	6.11162i	−0.141368	+	0.244857i
$624$	−6.91022	+	7.12223i	−0.276630	+	0.285117i
$625$	−1.60751	−	2.78428i	−0.0643002	−	0.111371i
$626$	5.66577	−	3.27113i	0.226450	−	0.130741i
$627$	53.8652	+	4.28850i	2.15117	+	0.171266i
$628$	−4.63260	+	8.02389i	−0.184861	+	0.320188i
$629$		−	2.35553i		−	0.0939212i
$630$	3.95208	−	1.50883i	0.157454	−	0.0601132i
$631$			0.999379i			0.0397846i	0.999802	+	0.0198923i	$0.00633234\pi$
$631$			0.999379i			0.0397846i	−0.999802	+	0.0198923i	$0.993668\pi$
$632$	34.1748	+	19.7308i	1.35940	+	0.784851i
$633$	14.4381	−	20.9667i	0.573862	−	0.833352i
$634$	−5.11503	−	8.85948i	−0.203144	−	0.351855i
$635$	8.96684	−	5.17701i	0.355838	−	0.205443i
$636$	−0.484299	+	0.703290i	−0.0192037	+	0.0278873i
$637$	−21.1241	−	3.56619i	−0.836967	−	0.141298i
$638$	46.9526			1.85887
$639$	−3.14445	−	2.55580i	−0.124393	−	0.101106i
$640$	0.408601			0.0161514
$641$	4.27107	−	7.39770i	0.168697	−	0.292192i	−0.769265	−	0.638930i	$-0.779377\pi$
$641$	4.27107	−	7.39770i	0.168697	−	0.292192i	0.937962	+	0.346738i	$0.112711\pi$
$642$	−1.83394	+	23.0349i	−0.0723798	+	0.909116i
$643$	−0.783139	+	0.452145i	−0.0308840	+	0.0178309i	−0.515362	−	0.856972i	$-0.672343\pi$
$643$	−0.783139	+	0.452145i	−0.0308840	+	0.0178309i	0.484479	+	0.874803i	$0.339009\pi$
$644$	0.724124	−	0.418073i	0.0285345	−	0.0164744i
$645$	−5.24748	+	2.49707i	−0.206619	+	0.0983221i
$646$	1.71070	−	2.96301i	0.0673065	−	0.116578i
$647$	20.5148			0.806518			0.403259	−	0.915086i	$-0.367877\pi$
$647$	20.5148			0.806518			0.403259	+	0.915086i	$0.367877\pi$
$648$	26.9331	−	5.62262i	1.05803	−	0.220877i
$649$	−19.6406			−0.770959
$650$	2.17247	−	12.8684i	0.0852111	−	0.504742i
$651$	1.47579	+	3.10130i	0.0578407	+	0.121550i
$652$	−12.4412	+	7.18292i	−0.487234	+	0.281305i
$653$	−4.68449	−	8.11378i	−0.183318	−	0.317517i	0.759690	−	0.650285i	$-0.225351\pi$
$653$	−4.68449	−	8.11378i	−0.183318	−	0.317517i	−0.943009	+	0.332768i	$0.892017\pi$
$654$	26.1721	+	2.08371i	1.02341	+	0.0814795i
$655$	10.3477	+	5.97425i	0.404318	+	0.233433i
$656$		−	2.42192i		−	0.0945600i
$657$	−29.9585	−	24.3501i	−1.16879	−	0.949988i
$658$		−	7.55565i		−	0.294550i
$659$	−17.6521	+	30.5743i	−0.687627	+	1.19101i	0.284976	+	0.958535i	$0.408014\pi$
$659$	−17.6521	+	30.5743i	−0.687627	+	1.19101i	−0.972603	+	0.232471i	$0.925319\pi$
$660$	−4.95126	+	7.19012i	−0.192727	+	0.279875i
$661$	20.2167	−	11.6721i	0.786337	−	0.453992i	−0.0523346	−	0.998630i	$-0.516666\pi$
$661$	20.2167	−	11.6721i	0.786337	−	0.453992i	0.838671	+	0.544638i	$0.183333\pi$
$662$	9.74257	+	16.8746i	0.378656	+	0.655851i
$663$	2.88375	+	0.726191i	0.111996	+	0.0282029i
$664$	−15.6413	+	27.0915i	−0.606999	+	1.05135i
$665$		−	8.78619i		−	0.340714i
$666$	5.68381	+	14.8876i	0.220243	+	0.576883i
$667$	−9.00000			−0.348481
$668$	12.3270	+	7.11702i	0.476948	+	0.275366i
$669$	−2.77748	+	34.8861i	−0.107383	+	1.34877i
$670$	2.75723	−	1.59189i	0.106521	−	0.0615000i
$671$	38.0897	−	21.9911i	1.47043	−	0.848956i
$672$	3.37480	+	7.09199i	0.130186	+	0.273579i
$673$	−24.9264	+	43.1738i	−0.960842	+	1.66423i	−0.240449	+	0.970662i	$0.577295\pi$
$673$	−24.9264	+	43.1738i	−0.960842	+	1.66423i	−0.720393	+	0.693566i	$0.756039\pi$
$674$		−	8.61065i		−	0.331670i
$675$	−12.0908	+	12.6718i	−0.465377	+	0.487736i
$676$	−8.32964	+	7.19890i	−0.320371	+	0.276881i
$677$	−5.45592	+	9.44994i	−0.209688	+	0.363191i	−0.951616	−	0.307289i	$-0.900578\pi$
$677$	−5.45592	+	9.44994i	−0.209688	+	0.363191i	0.741928	+	0.670479i	$0.233912\pi$
$678$	19.6257	−	9.33912i	0.753722	−	0.358667i
$679$	−8.88757	−	15.3937i	−0.341074	−	0.590757i
$680$	0.929085	+	1.60922i	0.0356288	+	0.0617109i
$681$	2.82542	−	35.4883i	0.108270	−	1.35991i
$682$	8.35787	+	4.82542i	0.320039	+	0.184775i
$683$		−	24.0595i		−	0.920610i	−0.887761	−	0.460305i	$-0.847740\pi$
$683$		−	24.0595i		−	0.920610i	0.887761	−	0.460305i	$-0.152260\pi$
$684$	2.68976	−	16.7851i	0.102846	−	0.641795i
$685$	−0.755232			−0.0288559
$686$	7.14840	−	12.3814i	0.272927	−	0.472724i
$687$	−28.3767	−	19.5407i	−1.08264	−	0.745526i
$688$	2.08842	+	3.61725i	0.0796203	+	0.137906i
$689$	1.33743	−	1.61768i	0.0509518	−	0.0616288i
$690$	−1.29227	+	1.87661i	−0.0491958	+	0.0714413i
$691$	25.4878	+	14.7154i	0.969600	+	0.559799i	0.899114	−	0.437714i	$-0.144212\pi$
$691$	25.4878	+	14.7154i	0.969600	+	0.559799i	0.0704856	+	0.997513i	$0.477545\pi$
$692$	−16.1638			−0.614457
$693$	−14.2088	−	2.27692i	−0.539748	−	0.0864929i
$694$			17.8550i			0.677765i
$695$	−14.0088	−	8.08798i	−0.531383	−	0.306794i
$696$	3.94080	−	49.4978i	0.149376	−	1.87621i
$697$	−0.628538	+	0.362886i	−0.0238076	+	0.0137453i
$698$	0.0961047	+	0.166458i	0.00363762	+	0.00630053i
$699$	−21.1315	−	44.4069i	−0.799268	−	1.67962i
$700$	−2.54320	−	1.46832i	−0.0961240	−	0.0554972i
$701$	16.6961			0.630604			0.315302	−	0.948991i	$-0.397894\pi$
$701$	16.6961			0.630604			0.315302	+	0.948991i	$0.397894\pi$
$702$	−19.9784	+	2.36867i	−0.754035	+	0.0893996i
$703$	33.0979			1.24831
$704$	31.9456	+	18.4438i	1.20399	+	0.695127i
$705$	−6.49744	−	13.6541i	−0.244708	−	0.514242i
$706$	−9.08520	−	15.7360i	−0.341926	−	0.592234i
$707$	12.0530	−	6.95883i	0.453302	−	0.261714i
$708$	−0.490376	+	6.15930i	−0.0184295	+	0.231481i
$709$	−28.9718	−	16.7269i	−1.08806	−	0.628191i	−0.155000	−	0.987915i	$-0.549538\pi$
$709$	−28.9718	−	16.7269i	−1.08806	−	0.628191i	−0.933059	+	0.359724i	$0.882871\pi$
$710$			1.85140i			0.0694818i
$711$	13.8121	+	36.1780i	0.517993	+	1.35678i
$712$	20.9711			0.785925
$713$	−1.60206	−	0.924948i	−0.0599975	−	0.0346396i
$714$	−0.516759	+	0.750427i	−0.0193392	+	0.0280840i
$715$	13.6732	−	16.5385i	0.511350	−	0.618503i
$716$	3.52993	+	6.11401i	0.131920	+	0.228491i
$717$	20.9912	+	14.4550i	0.783932	+	0.539830i
$718$	18.4920	−	32.0291i	0.690115	−	1.19531i
$719$	−31.3183			−1.16797			−0.583987	−	0.811763i	$-0.698508\pi$
$719$	−31.3183			−1.16797			−0.583987	+	0.811763i	$0.698508\pi$
$720$	−4.72195	−	3.83798i	−0.175977	−	0.143033i
$721$			0.107721i			0.00401175i
$722$	23.9643	+	13.8358i	0.891858	+	0.514915i
$723$	1.81952	−	22.8539i	0.0676688	−	0.849944i
$724$	−4.20741	−	7.28745i	−0.156367	−	0.270836i
$725$	15.8045	+	27.3742i	0.586964	+	1.01665i
$726$	−18.0378	+	8.58350i	−0.669447	+	0.318564i
$727$	−18.8915	+	32.7210i	−0.700646	+	1.21356i	0.267593	+	0.963532i	$0.413772\pi$
$727$	−18.8915	+	32.7210i	−0.700646	+	1.21356i	−0.968240	+	0.250023i	$0.919562\pi$
$728$	−3.95586	−	10.6270i	−0.146614	−	0.393862i
$729$	23.9900	+	12.3886i	0.888520	+	0.458839i
$730$			17.6390i			0.652850i
$731$	0.625834	−	1.08398i	0.0231473	−	0.0400923i
$732$	−5.94543	−	12.4940i	−0.219749	−	0.461793i
$733$	−5.55072	+	3.20471i	−0.205021	+	0.118369i	−0.598995	−	0.800753i	$-0.704433\pi$
$733$	−5.55072	+	3.20471i	−0.205021	+	0.118369i	0.393975	+	0.919121i	$0.371100\pi$
$734$	23.3284	−	13.4687i	0.861067	−	0.497137i
$735$	1.04255	−	13.0948i	0.0384550	−	0.483009i
$736$	−3.66355	−	2.11515i	−0.135040	−	0.0779655i
$737$	−10.8301			−0.398933
$738$	3.09690	−	3.81018i	0.113998	−	0.140255i
$739$			26.2292i			0.964856i	0.875936	+	0.482428i	$0.160245\pi$
$739$			26.2292i			0.964856i	−0.875936	+	0.482428i	$0.839755\pi$
$740$	−2.67365	+	4.63089i	−0.0982852	+	0.170235i
$741$	−10.2038	+	40.5200i	−0.374846	+	1.48854i
$742$	0.321551	+	0.556942i	0.0118045	+	0.0204460i
$743$	23.7541	−	13.7144i	0.871454	−	0.503134i	0.00362278	−	0.999993i	$-0.498847\pi$
$743$	23.7541	−	13.7144i	0.871454	−	0.503134i	0.867831	+	0.496859i	$0.165513\pi$
$744$	5.78848	−	8.40593i	0.212216	−	0.308176i
$745$	7.46108	−	12.9230i	0.273353	−	0.473461i
$746$			11.7591i			0.430533i
$747$	−28.6794	+	10.9493i	−1.04933	+	0.400613i
$748$		−	1.88031i		−	0.0687508i
$749$	−11.0688	−	6.39059i	−0.404446	−	0.233507i
$750$	19.8102	+	1.57720i	0.723367	+	0.0575913i
$751$	7.31837	+	12.6758i	0.267051	+	0.462546i	0.968099	−	0.250568i	$-0.0806174\pi$
$751$	7.31837	+	12.6758i	0.267051	+	0.462546i	−0.701048	+	0.713114i	$0.747284\pi$
$752$	−9.41217	+	5.43412i	−0.343227	+	0.198162i
$753$	8.88921	+	18.6803i	0.323941	+	0.680747i
$754$	−6.04401	+	35.8013i	−0.220110	+	1.30381i
$755$	13.0264			0.474080
$756$	−1.06880	+	4.39905i	−0.0388720	+	0.159992i
$757$	4.79203			0.174169			0.0870846	−	0.996201i	$-0.472245\pi$
$757$	4.79203			0.174169			0.0870846	+	0.996201i	$0.472245\pi$
$758$	−5.96236	+	10.3271i	−0.216563	+	0.375098i
$759$	6.99873	−	3.33042i	0.254038	−	0.120887i
$760$	−22.6114	+	13.0547i	−0.820201	+	0.473543i
$761$	16.7477	−	9.66927i	0.607103	−	0.350511i	−0.164728	−	0.986339i	$-0.552675\pi$
$761$	16.7477	−	9.66927i	0.607103	−	0.350511i	0.771831	+	0.635828i	$0.219341\pi$
$762$	1.19738	−	15.0395i	0.0433764	−	0.544824i
$763$	−7.26096	+	12.5763i	−0.262864	+	0.455294i
$764$	−5.14558			−0.186160
$765$	−0.288525	+	1.80051i	−0.0104317	+	0.0650974i
$766$	−6.31277			−0.228089
$767$	2.52824	−	14.9759i	0.0912895	−	0.540747i
$768$	15.8809	−	23.0620i	0.573052	−	0.832177i
$769$	−8.74040	+	5.04627i	−0.315187	+	0.181973i	−0.649245	−	0.760579i	$-0.724915\pi$
$769$	−8.74040	+	5.04627i	−0.315187	+	0.181973i	0.334058	+	0.942552i	$0.391582\pi$
$770$	3.28739	+	5.69393i	0.118469	+	0.205195i
$771$	14.7006	−	21.3479i	0.529429	−	0.768827i
$772$	12.1109	+	6.99224i	0.435882	+	0.251656i
$773$			8.43470i			0.303375i	0.988428	+	0.151688i	$0.0484708\pi$
$773$			8.43470i			0.303375i	−0.988428	+	0.151688i	$0.951529\pi$
$774$	−1.33985	+	8.36113i	−0.0481598	+	0.300535i
$775$			6.49703i			0.233380i
$776$	−26.4106	+	45.7446i	−0.948087	+	1.64213i
$777$	−8.78641	−	0.699535i	−0.315211	−	0.0250957i
$778$	−0.0746548	+	0.0431020i	−0.00267651	+	0.00154528i
$779$	−5.09896	−	8.83166i	−0.182689	−	0.316427i
$780$	−4.84510	−	4.70087i	−0.173482	−	0.168318i
$781$	3.14892	−	5.45409i	0.112677	−	0.195163i
$782$		−	0.490757i		−	0.0175494i
$783$	33.6379	−	35.2541i	1.20212	−	1.25988i
$784$	−9.44157			−0.337199
$785$	12.0939	+	6.98242i	0.431650	+	0.249213i
$786$	15.7212	−	7.48112i	0.560757	−	0.266843i
$787$	11.0977	−	6.40724i	0.395589	−	0.228393i	−0.288990	−	0.957332i	$-0.593319\pi$
$787$	11.0977	−	6.40724i	0.395589	−	0.228393i	0.684579	+	0.728939i	$0.259986\pi$
$788$	−14.0593	+	8.11714i	−0.500842	+	0.289161i
$789$	2.67490	+	0.212964i	0.0952290	+	0.00758171i
$790$	8.84665	−	15.3228i	0.314750	−	0.545162i
$791$			12.0216i			0.427439i
$792$	15.2520	+	39.9496i	0.541957	+	1.41955i
$793$	11.8650	+	31.8741i	0.421339	+	1.13188i
$794$	−0.719275	+	1.24582i	−0.0255261	+	0.0442125i
$795$	1.06002	+	0.729953i	0.0375952	+	0.0258888i
$796$	−3.83749	−	6.64672i	−0.136016	−	0.235587i
$797$	−14.6074	−	25.3008i	−0.517421	−	0.896200i	−0.999795	−	0.0202344i	$-0.993559\pi$
$797$	−14.6074	−	25.3008i	−0.517421	−	0.896200i	0.482374	−	0.875965i	$-0.339775\pi$
$798$	−10.5444	−	7.26104i	−0.373266	−	0.257038i
$799$	2.82053	+	1.62843i	0.0997832	+	0.0576099i
$800$			14.8573i			0.525284i
$801$	15.9698	+	12.9802i	0.564264	+	0.458632i
$802$	−34.0161			−1.20115
$803$	30.0011	−	51.9634i	1.05871	−	1.83375i
$804$	−0.270402	+	3.39634i	−0.00953634	+	0.119780i
$805$	−0.630135	−	1.09143i	−0.0222094	−	0.0384677i
$806$	−4.75524	+	5.75170i	−0.167496	+	0.202595i
$807$	−15.6510	−	32.8898i	−0.550941	−	1.15778i
$808$	−35.8173	−	20.6791i	−1.26005	−	0.727489i
$809$	−11.3570			−0.399292			−0.199646	−	0.979868i	$-0.563979\pi$
$809$	−11.3570			−0.399292			−0.199646	+	0.979868i	$0.563979\pi$
$810$	−2.52099	−	12.0759i	−0.0885787	−	0.424303i
$811$		−	26.8826i		−	0.943974i	−0.881605	−	0.471987i	$-0.843537\pi$
$811$		−	26.8826i		−	0.943974i	0.881605	−	0.471987i	$-0.156463\pi$
$812$	7.07544	+	4.08500i	0.248299	+	0.143356i
$813$	−19.9422	+	9.48973i	−0.699404	+	0.332819i
$814$	−21.4492	+	12.3837i	−0.751795	+	0.434049i
$815$	10.8264	+	18.7518i	0.379231	+	0.656847i
$816$	1.30648	+	0.104016i	0.0457358	+	0.00364128i
$817$	15.2311	+	8.79367i	0.532868	+	0.307652i
$818$	3.62852			0.126868
$819$	3.56518	−	10.5411i	0.124577	−	0.368335i
$820$	1.64758			0.0575359
$821$	14.2700	+	8.23880i	0.498027	+	0.287536i	0.727898	−	0.685685i	$-0.240497\pi$
$821$	14.2700	+	8.23880i	0.498027	+	0.287536i	−0.229871	+	0.973221i	$0.573831\pi$
$822$	−0.624134	+	0.906357i	−0.0217692	+	0.0316128i
$823$	−4.10205	−	7.10496i	−0.142988	−	0.247663i	0.785632	−	0.618694i	$-0.212338\pi$
$823$	−4.10205	−	7.10496i	−0.142988	−	0.247663i	−0.928621	+	0.371031i	$0.879005\pi$
$824$	0.277222	−	0.160054i	0.00965750	−	0.00557576i
$825$	−22.4199	−	15.4387i	−0.780560	−	0.537508i
$826$	4.02997	+	2.32670i	0.140221	+	0.0809564i
$827$		−	43.6569i		−	1.51810i	−0.651033	−	0.759049i	$-0.725664\pi$
$827$		−	43.6569i		−	1.51810i	0.651033	−	0.759049i	$-0.274336\pi$
$828$	−0.869684	−	2.27796i	−0.0302236	−	0.0791647i
$829$	23.3338			0.810415			0.405208	−	0.914225i	$-0.367199\pi$
$829$	23.3338			0.810415			0.405208	+	0.914225i	$0.367199\pi$
$830$	12.1469	+	7.01302i	0.421625	+	0.243425i
$831$	−20.0755	−	1.59832i	−0.696412	−	0.0554452i
$832$	−18.1756	+	21.9842i	−0.630124	+	0.762166i
$833$	1.41467	+	2.45028i	0.0490155	+	0.0848973i
$834$	−21.2835	+	10.1280i	−0.736987	+	0.350703i
$835$	10.7270	−	18.5798i	0.371224	−	0.642979i
$836$	26.4204			0.913770
$837$	9.61089	−	2.81842i	0.332201	−	0.0974187i
$838$		−	23.2658i		−	0.803702i
$839$	−11.8836	−	6.86099i	−0.410267	−	0.236868i	0.280638	−	0.959814i	$-0.409454\pi$
$839$	−11.8836	−	6.86099i	−0.410267	−	0.236868i	−0.690904	+	0.722946i	$0.742787\pi$
$840$	6.27850	−	2.98769i	0.216629	−	0.103085i
$841$	−29.4696	−	51.0428i	−1.01619	−	1.76010i
$842$	−7.54440	−	13.0673i	−0.259997	−	0.450328i
$843$	2.37587	−	29.8418i	0.0818292	−	1.02780i
$844$	6.22355	−	10.7795i	0.214223	−	0.371046i
$845$	10.8504	+	12.5547i	0.373266	+	0.431896i
$846$	−21.7559	−	3.48631i	−0.747982	−	0.119862i
$847$		−	11.0489i		−	0.379646i
$848$	0.462527	−	0.801120i	0.0158832	−	0.0275106i
$849$	−21.2278	+	30.8266i	−0.728536	+	1.05797i
$850$	−1.49267	+	0.861795i	−0.0511982	+	0.0295593i
$851$	4.11144	−	2.37374i	0.140938	−	0.0813708i
$852$	−1.63179	−	1.12368i	−0.0559042	−	0.0384967i
$853$	13.2769	+	7.66545i	0.454594	+	0.262460i	0.709768	−	0.704435i	$-0.248800\pi$
$853$	13.2769	+	7.66545i	0.454594	+	0.262460i	−0.255175	+	0.966895i	$0.582133\pi$
$854$	−10.4206			−0.356587
$855$	−25.2991	−	4.05411i	−0.865212	−	0.138647i
$856$			37.9810i			1.29817i
$857$	−21.3961	+	37.0590i	−0.730875	+	1.26591i	0.225634	+	0.974212i	$0.427555\pi$
$857$	−21.3961	+	37.0590i	−0.730875	+	1.26591i	−0.956510	+	0.291701i	$0.905779\pi$
$858$	−8.54811	−	30.0769i	−0.291828	−	1.02681i
$859$	13.1536	+	22.7826i	0.448793	+	0.777333i	0.998308	−	0.0581513i	$-0.0185206\pi$
$859$	13.1536	+	22.7826i	0.448793	+	0.777333i	−0.549514	+	0.835484i	$0.685187\pi$
$860$	−2.46074	+	1.42071i	−0.0839104	+	0.0484457i
$861$	1.16695	+	2.45229i	0.0397695	+	0.0835737i
$862$	14.2577	−	24.6950i	0.485618	−	0.841116i
$863$		−	8.03444i		−	0.273495i	−0.990606	−	0.136748i	$-0.956335\pi$
$863$		−	8.03444i		−	0.273495i	0.990606	−	0.136748i	$-0.0436650\pi$
$864$	21.9780	−	6.44510i	0.747706	−	0.219267i
$865$			24.3627i			0.828357i
$866$	−20.2603	−	11.6973i	−0.688475	−	0.397491i
$867$	12.4834	+	26.2334i	0.423960	+	0.890932i
$868$	0.839648	+	1.45431i	0.0284995	+	0.0493626i
$869$	−52.1232	+	30.0933i	−1.76816	+	1.02085i
$870$	−22.1932	−	1.76692i	−0.752419	−	0.0599042i
$871$	1.39412	−	8.25795i	0.0472378	−	0.279810i
$872$	43.1539			1.46137
$873$	−48.4259	+	18.4881i	−1.63897	+	0.625727i
$874$	6.89568			0.233250
$875$	−5.49596	+	9.51929i	−0.185797	+	0.321811i
$876$	−15.5467	−	10.7058i	−0.525275	−	0.361714i
$877$	−6.03899	+	3.48661i	−0.203922	+	0.117735i	−0.598484	−	0.801135i	$-0.704230\pi$
$877$	−6.03899	+	3.48661i	−0.203922	+	0.117735i	0.394561	+	0.918870i	$0.370897\pi$
$878$	−7.24799	+	4.18463i	−0.244608	+	0.141224i
$879$	0.101919	+	0.0701831i	0.00343763	+	0.00236722i
$880$	4.72867	−	8.19029i	0.159403	−	0.276095i
$881$	30.4317			1.02527			0.512635	−	0.858606i	$-0.328669\pi$
$881$	30.4317			1.02527			0.512635	+	0.858606i	$0.328669\pi$
$882$	−14.8535	−	12.0729i	−0.500145	−	0.406516i
$883$	−1.51291			−0.0509134			−0.0254567	−	0.999676i	$-0.508104\pi$
$883$	−1.51291			−0.0509134			−0.0254567	+	0.999676i	$0.508104\pi$
$884$	1.43373	+	0.242044i	0.0482215	+	0.00814081i
$885$	9.28352	+	0.739113i	0.312062	+	0.0248450i
$886$	14.8824	−	8.59234i	0.499983	−	0.288665i
$887$	18.4472	+	31.9514i	0.619395	+	1.07282i	0.989596	+	0.143872i	$0.0459554\pi$
$887$	18.4472	+	31.9514i	0.619395	+	1.07282i	−0.370201	+	0.928952i	$0.620711\pi$
$888$	11.2547	+	23.6513i	0.377684	+	0.793686i
$889$	7.22684	+	4.17242i	0.242380	+	0.139938i
$890$		−	9.40274i		−	0.315181i
$891$	−13.1124	+	39.8625i	−0.439281	+	1.33544i
$892$			17.1114i			0.572931i
$893$	−22.8813	+	39.6316i	−0.765695	+	1.32622i
$894$	−9.34296	−	19.6338i	−0.312475	−	0.656652i
$895$	9.21526	−	5.32043i	0.308032	−	0.177842i
$896$	0.164656	+	0.285193i	0.00550078	+	0.00952763i
$897$	1.63852	+	5.76522i	0.0547087	+	0.192495i
$898$	−4.60944	+	7.98379i	−0.153819	+	0.266422i
$899$		−	18.0754i		−	0.602848i
$900$	−5.40138	+	6.64543i	−0.180046	+	0.221514i
$901$	−0.277209			−0.00923519
$902$	6.60881	+	3.81560i	0.220049	+	0.127045i
$903$	−3.85750	−	2.65635i	−0.128370	−	0.0883977i
$904$	30.9377	−	17.8619i	1.02897	−	0.594078i
$905$	−10.9839	+	6.34156i	−0.365117	+	0.210801i
$906$	10.7652	−	15.6331i	0.357650	−	0.519374i
$907$	−14.3940	+	24.9312i	−0.477946	+	0.827827i	−0.999680	−	0.0252808i	$-0.991952\pi$
$907$	−14.3940	+	24.9312i	−0.477946	+	0.827827i	0.521734	+	0.853108i	$0.325285\pi$
$908$		−	17.4067i		−	0.577662i
$909$	−14.4759	−	37.9167i	−0.480135	−	1.25762i
$910$	−4.76478	+	1.77367i	−0.157951	+	0.0587967i
$911$	19.8931	−	34.4559i	0.659089	−	1.14158i	−0.321763	−	0.946820i	$-0.604275\pi$
$911$	19.8931	−	34.4559i	0.659089	−	1.14158i	0.980852	−	0.194755i	$-0.0623912\pi$
$912$	−1.46154	+	18.3575i	−0.0483964	+	0.607876i
$913$	−23.8559	−	41.3197i	−0.789517	−	1.36748i
$914$	−2.95500	−	5.11822i	−0.0977428	−	0.169296i
$915$	−18.8315	+	8.96116i	−0.622549	+	0.296247i
$916$	−14.5892	−	8.42306i	−0.482039	−	0.278306i
$917$			9.62991i			0.318008i
$918$	1.92235	+	1.83422i	0.0634471	+	0.0605384i
$919$	28.4990			0.940095			0.470047	−	0.882641i	$-0.344237\pi$
$919$	28.4990			0.940095			0.470047	+	0.882641i	$0.344237\pi$
$920$	−1.87253	+	3.24332i	−0.0617356	+	0.106929i
$921$	31.1759	−	14.8354i	1.02728	−	0.488844i
$922$	12.3424	+	21.3776i	0.406475	+	0.704035i
$923$	3.75338	+	3.10313i	0.123544	+	0.102141i
$924$	−7.01376	−	0.558405i	−0.230736	−	0.0183702i
$925$	−14.4398	−	8.33683i	−0.474778	−	0.274113i
$926$	−27.0822			−0.889975
$927$	0.310175	+	0.0497045i	0.0101875	+	0.00163251i
$928$		−	41.3344i		−	1.35687i
$929$	26.1642	+	15.1059i	0.858421	+	0.495610i	0.863483	−	0.504378i	$-0.168278\pi$
$929$	26.1642	+	15.1059i	0.858421	+	0.495610i	−0.00506213	+	0.999987i	$0.501611\pi$
$930$	−3.76893	−	2.59536i	−0.123588	−	0.0851052i
$931$	−34.4292	+	19.8777i	−1.12837	+	0.651466i
$932$	−12.0228	−	20.8240i	−0.393819	−	0.682114i
$933$	−5.97290	+	8.67374i	−0.195544	+	0.283965i
$934$	−16.8416	−	9.72349i	−0.551073	−	0.318162i
$935$	−2.83407			−0.0926839
$936$	−32.4248	+	6.48709i	−1.05984	+	0.212037i
$937$	6.31683			0.206362			0.103181	−	0.994663i	$-0.467098\pi$
$937$	6.31683			0.206362			0.103181	+	0.994663i	$0.467098\pi$
$938$	2.22219	+	1.28298i	0.0725572	+	0.0418909i
$939$	10.5191	+	0.837485i	0.343278	+	0.0273303i
$940$	−3.69671	−	6.40289i	−0.120573	−	0.208839i
$941$	−36.5433	+	21.0983i	−1.19128	+	0.687784i	−0.958596	−	0.284769i	$-0.908083\pi$
$941$	−36.5433	+	21.0983i	−1.19128	+	0.687784i	−0.232681	+	0.972553i	$0.574750\pi$
$942$	18.3742	−	8.74357i	0.598664	−	0.284881i
$943$	−1.26679	−	0.731383i	−0.0412524	−	0.0238171i
$944$		−	6.69358i		−	0.217857i
$945$	6.63041	+	1.61094i	0.215687	+	0.0524038i
$946$	−13.1608			−0.427893
$947$	−11.7977	−	6.81143i	−0.383375	−	0.221342i	0.295910	−	0.955216i	$-0.404377\pi$
$947$	−11.7977	−	6.81143i	−0.383375	−	0.221342i	−0.679286	+	0.733874i	$0.737710\pi$
$948$	8.13592	+	17.0973i	0.264242	+	0.555293i
$949$	35.7600	+	29.5647i	1.16082	+	0.959712i
$950$	−12.1092	−	20.9737i	−0.392874	−	0.680477i
$951$	1.30956	−	16.4486i	0.0424655	−	0.533382i
$952$	−0.748798	+	1.29696i	−0.0242687	+	0.0420346i
$953$	−43.5443			−1.41054			−0.705268	−	0.708940i	$-0.749174\pi$
$953$	−43.5443			−1.41054			−0.705268	+	0.708940i	$0.749174\pi$
$954$	1.75204	−	0.668896i	0.0567243	−	0.0216563i
$955$			7.75560i			0.250965i
$956$	10.7921	+	6.23082i	0.349041	+	0.201519i
$957$	62.3743	+	42.9521i	2.01627	+	1.38844i
$958$	−8.90068	−	15.4164i	−0.287568	−	0.498082i
$959$	−0.304340	−	0.527132i	−0.00982765	−	0.0170220i
$960$	−14.4057	−	9.92003i	−0.464941	−	0.320167i
$961$	−13.6424	+	23.6293i	−0.440076	+	0.762234i
$962$	−6.68148	−	17.9491i	−0.215420	−	0.578701i
$963$	−23.5085	+	28.9231i	−0.757552	+	0.932033i
$964$		−	11.2096i		−	0.361038i
$965$	10.5390	−	18.2540i	0.339261	−	0.587618i
$966$	−1.83058	−	0.145743i	−0.0588979	−	0.00468919i
$967$	13.9813	−	8.07210i	0.449608	−	0.259581i	−0.258057	−	0.966130i	$-0.583082\pi$
$967$	13.9813	−	8.07210i	0.449608	−	0.259581i	0.707665	+	0.706549i	$0.249749\pi$
$968$	−28.4346	+	16.4167i	−0.913922	+	0.527653i
$969$	4.98313	−	2.37128i	0.160081	−	0.0761764i
$970$	20.5103	+	11.8416i	0.658547	+	0.380212i
$971$	−0.206193			−0.00661704			−0.00330852	−	0.999995i	$-0.501053\pi$
$971$	−0.206193			−0.00661704			−0.00330852	+	0.999995i	$0.501053\pi$
$972$	12.1735	+	5.10733i	0.390466	+	0.163818i
$973$		−	13.0370i		−	0.417948i
$974$	−3.10839	+	5.38389i	−0.0995992	+	0.172511i
$975$	14.6580	−	15.1077i	0.469432	−	0.483834i
$976$	7.49465	+	12.9811i	0.239898	+	0.415515i
$977$	−6.91568	+	3.99277i	−0.221252	+	0.127740i	−0.606530	−	0.795061i	$-0.707439\pi$
$977$	−6.91568	+	3.99277i	−0.221252	+	0.127740i	0.385278	+	0.922801i	$0.374106\pi$
$978$	31.4512	+	2.50400i	1.00570	+	0.0800691i
$979$	−15.9925	+	27.6998i	−0.511122	+	0.885289i
$980$		−	6.42289i		−	0.205172i
$981$	32.8622	+	26.7103i	1.04921	+	0.852794i
$982$		−	11.2437i		−	0.358801i
$983$	−24.1512	−	13.9437i	−0.770304	−	0.444735i	0.0626793	−	0.998034i	$-0.480035\pi$
$983$	−24.1512	−	13.9437i	−0.770304	−	0.444735i	−0.832983	+	0.553299i	$0.813369\pi$
$984$	4.57712	−	6.64681i	0.145913	−	0.211893i
$985$	12.2344	+	21.1907i	0.389822	+	0.675191i
$986$	4.15276	−	2.39760i	0.132251	−	0.0763550i
$987$	6.91188	−	10.0373i	0.220007	−	0.319491i
$988$	−3.40099	+	20.1455i	−0.108200	+	0.640914i
$989$	2.52269			0.0802168
$990$	17.9121	−	6.83849i	0.569283	−	0.217342i
$991$	−8.84780			−0.281059			−0.140530	−	0.990076i	$-0.544881\pi$
$991$	−8.84780			−0.281059			−0.140530	+	0.990076i	$0.544881\pi$
$992$	4.24802	−	7.35778i	0.134875	−	0.233610i
$993$	−2.49432	+	31.3296i	−0.0791549	+	0.994213i
$994$	−1.29223	+	0.746070i	−0.0409871	+	0.0236639i
$995$	−10.0182	+	5.78400i	−0.317598	+	0.183365i
$996$	−13.5535	+	6.44961i	−0.429460	+	0.204364i
$997$	12.7226	−	22.0362i	0.402929	−	0.697893i	−0.591149	−	0.806562i	$-0.701326\pi$
$997$	12.7226	−	22.0362i	0.402929	−	0.697893i	0.994078	+	0.108669i	$0.0346590\pi$
$998$	−9.70427			−0.307183
$999$	−6.06846	+	24.9770i	−0.191997	+	0.790236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.t.c.25.4	✓	20
3.2	odd	2		351.2.t.c.181.7		20
9.2	odd	6		1053.2.b.i.649.4		10
9.4	even	3	inner	117.2.t.c.103.7	yes	20
9.5	odd	6		351.2.t.c.64.4		20
9.7	even	3		1053.2.b.j.649.7		10
13.12	even	2	inner	117.2.t.c.25.7	yes	20
39.38	odd	2		351.2.t.c.181.4		20
117.25	even	6		1053.2.b.j.649.4		10
117.38	odd	6		1053.2.b.i.649.7		10
117.77	odd	6		351.2.t.c.64.7		20
117.103	even	6	inner	117.2.t.c.103.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.t.c.25.4	✓	20	1.1	even	1	trivial
117.2.t.c.25.7	yes	20	13.12	even	2	inner
117.2.t.c.103.4	yes	20	117.103	even	6	inner
117.2.t.c.103.7	yes	20	9.4	even	3	inner
351.2.t.c.64.4		20	9.5	odd	6
351.2.t.c.64.7		20	117.77	odd	6
351.2.t.c.181.4		20	39.38	odd	2
351.2.t.c.181.7		20	3.2	odd	2
1053.2.b.i.649.4		10	9.2	odd	6
1053.2.b.i.649.7		10	117.38	odd	6
1053.2.b.j.649.4		10	117.25	even	6
1053.2.b.j.649.7		10	9.7	even	3

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.929969 - 0.536918i) q^{2} +(-0.744247 - 1.56400i) q^{3} +(-0.423439 - 0.733417i) q^{4} +(-1.10543 + 0.638222i) q^{5} +(-0.147613 + 1.85407i) q^{6} +(-0.890926 - 0.514376i) q^{7} +3.05708i q^{8} +(-1.89219 + 2.32800i) q^{9} +1.37069 q^{10} +(-4.03796 - 2.33132i) q^{11} +(-0.831922 + 1.20810i) q^{12} +(2.29741 - 2.77883i) q^{13} +(0.552355 + 0.956708i) q^{14} +(1.82089 + 1.25390i) q^{15} +(0.794522 - 1.37615i) q^{16} -0.476187 q^{17} +(3.00963 - 1.14902i) q^{18} -6.69096i q^{19} +(0.936166 + 0.540496i) q^{20} +(-0.141416 + 1.77623i) q^{21} +(2.50345 + 4.33610i) q^{22} +(-0.479867 - 0.831155i) q^{23} +(4.78127 - 2.27522i) q^{24} +(-1.68535 + 2.91910i) q^{25} +(-3.62852 + 1.35071i) q^{26} +(5.04926 + 1.22678i) q^{27} +0.871227i q^{28} +(4.68880 - 8.12123i) q^{29} +(-1.02013 - 2.14376i) q^{30} +(1.66927 - 0.963754i) q^{31} +(3.81725 - 2.20389i) q^{32} +(-0.640940 + 8.05044i) q^{33} +(0.442839 + 0.255673i) q^{34} +1.31314 q^{35} +(2.50863 + 0.402000i) q^{36} +4.94666i q^{37} +(-3.59249 + 6.22238i) q^{38} +(-6.05593 - 1.52501i) q^{39} +(-1.95109 - 3.37939i) q^{40} +(1.31994 - 0.762068i) q^{41} +(1.08520 - 1.57591i) q^{42} +(-1.31426 + 2.27637i) q^{43} +3.94868i q^{44} +(0.605908 - 3.78109i) q^{45} +1.03060i q^{46} +(-5.92316 - 3.41974i) q^{47} +(-2.74362 - 0.218435i) q^{48} +(-2.97083 - 5.14564i) q^{49} +(3.13464 - 1.80978i) q^{50} +(0.354400 + 0.744756i) q^{51} +(-3.01086 - 0.508296i) q^{52} +0.582145 q^{53} +(-4.03697 - 3.85190i) q^{54} +5.95159 q^{55} +(1.57249 - 2.72363i) q^{56} +(-10.4647 + 4.97973i) q^{57} +(-8.72087 + 5.03499i) q^{58} +(3.64799 - 2.10617i) q^{59} +(0.148597 - 1.86643i) q^{60} +(-4.71645 + 8.16913i) q^{61} -2.06983 q^{62} +(2.88327 - 1.10078i) q^{63} -7.91132 q^{64} +(-0.766122 + 4.53807i) q^{65} +(4.91848 - 7.14253i) q^{66} +(2.01156 - 1.16138i) q^{67} +(0.201636 + 0.349243i) q^{68} +(-0.942786 + 1.36910i) q^{69} +(-1.22118 - 0.705051i) q^{70} +1.35071i q^{71} +(-7.11689 - 5.78458i) q^{72} +12.8687i q^{73} +(2.65595 - 4.60024i) q^{74} +(5.81979 + 0.463346i) q^{75} +(-4.90726 + 2.83321i) q^{76} +(2.39835 + 4.15406i) q^{77} +(4.81302 + 4.66975i) q^{78} +(6.45415 - 11.1789i) q^{79} +2.02833i q^{80} +(-1.83921 - 8.81007i) q^{81} -1.63667 q^{82} +(8.86189 + 5.11641i) q^{83} +(1.36260 - 0.648408i) q^{84} +(0.526392 - 0.303913i) q^{85} +(2.44445 - 1.41130i) q^{86} +(-16.1912 - 1.28907i) q^{87} +(7.12701 - 12.3444i) q^{88} -6.85985i q^{89} +(-2.59361 + 3.19097i) q^{90} +(-3.47619 + 1.29400i) q^{91} +(-0.406389 + 0.703886i) q^{92} +(-2.74966 - 1.89347i) q^{93} +(3.67224 + 6.36050i) q^{94} +(4.27032 + 7.39640i) q^{95} +(-6.28787 - 4.32994i) q^{96} +(14.9635 + 8.63918i) q^{97} +6.38037i q^{98} +(13.0679 - 4.98909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} + 12 q^{4} - 2 q^{9} - 16 q^{10} - 2 q^{12} - 4 q^{13} - 18 q^{14} + 4 q^{16} - 12 q^{17} - 10 q^{22} + 24 q^{23} - 12 q^{25} - 12 q^{26} - 22 q^{27} + 12 q^{29} - 54 q^{30} - 12 q^{35} + 50 q^{36}+ \cdots + 24 q^{95}+O(q^{100}) \) 20 * q + 2 * q^3 + 12 * q^4 - 2 * q^9 - 16 * q^10 - 2 * q^12 - 4 * q^13 - 18 * q^14 + 4 * q^16 - 12 * q^17 - 10 * q^22 + 24 * q^23 - 12 * q^25 - 12 * q^26 - 22 * q^27 + 12 * q^29 - 54 * q^30 - 12 * q^35 + 50 * q^36 + 12 * q^38 - 8 * q^39 - 8 * q^40 + 6 * q^42 + 4 * q^43 + 38 * q^48 - 10 * q^49 - 78 * q^51 + 108 * q^53 + 20 * q^55 + 36 * q^56 - 2 * q^61 - 72 * q^62 + 8 * q^64 - 24 * q^65 + 78 * q^66 + 24 * q^68 + 72 * q^69 - 42 * q^74 - 8 * q^75 - 6 * q^77 + 66 * q^78 - 14 * q^79 + 46 * q^81 - 4 * q^82 - 54 * q^87 + 22 * q^88 + 24 * q^90 - 72 * q^91 - 84 * q^92 + 20 * q^94 + 24 * q^95

Introduction

L-functions

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