LMFDB - Embedded newform 605.2.j.h.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(9,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

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

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

chi := DirichletCharacter("605.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.j (of order $10$, degree $4$, not 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{14} + 25x^{12} - 57x^{10} + 194x^{8} - 303x^{6} + 235x^{4} - 33x^{2} + 121 $ x^16 - 7x^14 + 25x^12 - 57x^10 + 194x^8 - 303x^6 + 235x^4 - 33*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			9.1
Root			$-1.92464 + 0.625353i$ of defining polynomial
Character	$\chi$	$=$	605.9
Dual form			605.2.j.h.269.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.92464 - 0.625353i) q^{2} +(-1.54035 - 2.12011i) q^{3} +(1.69513 + 1.23158i) q^{4} +(-2.19919 + 0.404418i) q^{5} +(1.63880 + 5.04369i) q^{6} +(0.567697 - 0.781367i) q^{7} +(-0.113351 - 0.156015i) q^{8} +(-1.19513 + 3.67823i) q^{9} +O(q^{10})$	\(q+(-1.92464 - 0.625353i) q^{2} +(-1.54035 - 2.12011i) q^{3} +(1.69513 + 1.23158i) q^{4} +(-2.19919 + 0.404418i) q^{5} +(1.63880 + 5.04369i) q^{6} +(0.567697 - 0.781367i) q^{7} +(-0.113351 - 0.156015i) q^{8} +(-1.19513 + 3.67823i) q^{9} +(4.48555 + 0.596911i) q^{10} -5.49092i q^{12} +(4.30362 + 1.39833i) q^{13} +(-1.58124 + 1.14884i) q^{14} +(4.24493 + 4.03957i) q^{15} +(-1.17437 - 3.61433i) q^{16} +(3.17338 - 1.03109i) q^{17} +(4.60038 - 6.33188i) q^{18} +(2.65163 - 1.92652i) q^{19} +(-4.22599 - 2.02295i) q^{20} -2.53103 q^{21} +3.36643i q^{23} +(-0.156167 + 0.480634i) q^{24} +(4.67289 - 1.77879i) q^{25} +(-7.40846 - 5.38256i) q^{26} +(2.16214 - 0.702522i) q^{27} +(1.92464 - 0.625353i) q^{28} +(3.97470 + 2.88779i) q^{29} +(-5.64379 - 10.4293i) q^{30} +(-0.129282 + 0.397889i) q^{31} +8.07636i q^{32} -6.75241 q^{34} +(-0.932474 + 1.94796i) q^{35} +(-6.55594 + 4.76317i) q^{36} +(3.72512 - 5.12719i) q^{37} +(-6.30817 + 2.04965i) q^{38} +(-3.66446 - 11.2780i) q^{39} +(0.312377 + 0.297265i) q^{40} +(-4.68068 + 3.40071i) q^{41} +(4.87132 + 1.58279i) q^{42} +2.26205i q^{43} +(1.14077 - 8.57246i) q^{45} +(2.10520 - 6.47915i) q^{46} +(-2.54173 - 3.49838i) q^{47} +(-5.85383 + 8.05710i) q^{48} +(1.87486 + 5.77024i) q^{49} +(-10.1060 + 0.501317i) q^{50} +(-7.07414 - 5.13966i) q^{51} +(5.57303 + 7.67061i) q^{52} +(2.53047 + 0.822201i) q^{53} -4.60066 q^{54} -0.186254 q^{56} +(-8.16885 - 2.65422i) q^{57} +(-5.84397 - 8.04353i) q^{58} +(-8.19153 - 5.95150i) q^{59} +(2.22063 + 12.0756i) q^{60} +(-0.763537 - 2.34993i) q^{61} +(0.497642 - 0.684945i) q^{62} +(2.19558 + 3.02195i) q^{63} +(2.70184 - 8.31540i) q^{64} +(-10.0300 - 1.33473i) q^{65} -9.60059i q^{67} +(6.64917 + 2.16045i) q^{68} +(7.13718 - 5.18546i) q^{69} +(3.01284 - 3.16600i) q^{70} +(-1.68510 - 5.18621i) q^{71} +(0.709327 - 0.230474i) q^{72} +(-0.843791 + 1.16138i) q^{73} +(-10.3758 + 7.53847i) q^{74} +(-10.9691 - 7.16707i) q^{75} +6.86752 q^{76} +23.9977i q^{78} +(-0.310240 + 0.954820i) q^{79} +(4.04436 + 7.47367i) q^{80} +(4.56679 + 3.31797i) q^{81} +(11.1353 - 3.61806i) q^{82} +(7.03346 - 2.28531i) q^{83} +(-4.29042 - 3.11717i) q^{84} +(-6.56188 + 3.55095i) q^{85} +(1.41458 - 4.35363i) q^{86} -12.8750i q^{87} +12.1964 q^{89} +(-7.55639 + 15.7855i) q^{90} +(3.53576 - 2.56888i) q^{91} +(-4.14603 + 5.70652i) q^{92} +(1.04271 - 0.338796i) q^{93} +(2.70418 + 8.32259i) q^{94} +(-5.05232 + 5.30915i) q^{95} +(17.1227 - 12.4404i) q^{96} +(-2.87147 - 0.932997i) q^{97} -12.2781i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{4} - 2 q^{5} + 12 q^{6} + 2 q^{9}+O(q^{10}) $ 16 * q + 6 * q^4 - 2 * q^5 + 12 * q^6 + 2 * q^9	$ 16 q + 6 q^{4} - 2 q^{5} + 12 q^{6} + 2 q^{9} + 8 q^{14} + 24 q^{15} + 6 q^{16} + 6 q^{19} + 12 q^{20} + 8 q^{21} - 4 q^{24} + 24 q^{25} - 50 q^{26} + 22 q^{29} - 4 q^{30} - 22 q^{31} - 16 q^{34} - 8 q^{35} - 30 q^{36} + 12 q^{40} + 18 q^{41} + 12 q^{45} + 38 q^{46} - 20 q^{49} - 12 q^{50} - 12 q^{51} - 40 q^{54} - 20 q^{56} - 8 q^{59} - 2 q^{60} + 20 q^{61} + 22 q^{64} - 40 q^{65} + 6 q^{69} + 26 q^{70} + 6 q^{71} - 52 q^{74} + 40 q^{75} + 56 q^{76} - 22 q^{79} - 6 q^{80} - 32 q^{81} - 18 q^{84} - 62 q^{85} - 68 q^{86} + 24 q^{89} - 32 q^{90} - 56 q^{94} - 22 q^{95} + 94 q^{96}+O(q^{100}) $ 16 * q + 6 * q^4 - 2 * q^5 + 12 * q^6 + 2 * q^9 + 8 * q^14 + 24 * q^15 + 6 * q^16 + 6 * q^19 + 12 * q^20 + 8 * q^21 - 4 * q^24 + 24 * q^25 - 50 * q^26 + 22 * q^29 - 4 * q^30 - 22 * q^31 - 16 * q^34 - 8 * q^35 - 30 * q^36 + 12 * q^40 + 18 * q^41 + 12 * q^45 + 38 * q^46 - 20 * q^49 - 12 * q^50 - 12 * q^51 - 40 * q^54 - 20 * q^56 - 8 * q^59 - 2 * q^60 + 20 * q^61 + 22 * q^64 - 40 * q^65 + 6 * q^69 + 26 * q^70 + 6 * q^71 - 52 * q^74 + 40 * q^75 + 56 * q^76 - 22 * q^79 - 6 * q^80 - 32 * q^81 - 18 * q^84 - 62 * q^85 - 68 * q^86 + 24 * q^89 - 32 * q^90 - 56 * q^94 - 22 * q^95 + 94 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.92464	−	0.625353i	−1.36092	−	0.442191i	−0.464572	−	0.885535i	$-0.653792\pi$
$2$	−1.92464	−	0.625353i	−1.36092	−	0.442191i	−0.896352	+	0.443344i	$0.853792\pi$
$3$	−1.54035	−	2.12011i	−0.889320	−	1.22404i	−0.973751	−	0.227614i	$-0.926907\pi$
$3$	−1.54035	−	2.12011i	−0.889320	−	1.22404i	0.0844316	−	0.996429i	$-0.473093\pi$
$4$	1.69513	+	1.23158i	0.847564	+	0.615791i
$5$	−2.19919	+	0.404418i	−0.983509	+	0.180861i
$5$	−2.19919	+	0.404418i	−0.983509	+	0.180861i
$6$	1.63880	+	5.04369i	0.669035	+	2.05908i
$7$	0.567697	−	0.781367i	0.214569	−	0.295329i	−0.688142	−	0.725576i	$-0.741573\pi$
$7$	0.567697	−	0.781367i	0.214569	−	0.295329i	0.902711	+	0.430247i	$0.141573\pi$
$8$	−0.113351	−	0.156015i	−0.0400758	−	0.0551595i
$9$	−1.19513	+	3.67823i	−0.398376	+	1.22608i
$10$	4.48555	+	0.596911i	1.41846	+	0.188760i
$11$		0			0
$11$		0			0
$12$		−	5.49092i		−	1.58509i
$13$	4.30362	+	1.39833i	1.19361	+	0.387827i	0.837406	−	0.546581i	$-0.184071\pi$
$13$	4.30362	+	1.39833i	1.19361	+	0.387827i	0.356203	+	0.934408i	$0.384071\pi$
$14$	−1.58124	+	1.14884i	−0.422604	+	0.307040i
$15$	4.24493	+	4.03957i	1.09604	+	1.04301i
$16$	−1.17437	−	3.61433i	−0.293592	−	0.903582i
$17$	3.17338	−	1.03109i	0.769658	−	0.250077i	0.102239	−	0.994760i	$-0.467399\pi$
$17$	3.17338	−	1.03109i	0.769658	−	0.250077i	0.667419	+	0.744683i	$0.267399\pi$
$18$	4.60038	−	6.33188i	1.08432	−	1.49244i
$19$	2.65163	−	1.92652i	0.608325	−	0.441974i	−0.240499	−	0.970649i	$-0.577311\pi$
$19$	2.65163	−	1.92652i	0.608325	−	0.441974i	0.848824	+	0.528675i	$0.177311\pi$
$20$	−4.22599	−	2.02295i	−0.944960	−	0.452344i
$21$	−2.53103			−0.552316
$22$		0			0
$23$			3.36643i			0.701948i	0.936385	+	0.350974i	$0.114149\pi$
$23$			3.36643i			0.701948i	−0.936385	+	0.350974i	$0.885851\pi$
$24$	−0.156167	+	0.480634i	−0.0318775	+	0.0981089i
$25$	4.67289	−	1.77879i	0.934578	−	0.355758i
$26$	−7.40846	−	5.38256i	−1.45292	−	1.05561i
$27$	2.16214	−	0.702522i	0.416104	−	0.135200i
$28$	1.92464	−	0.625353i	0.363722	−	0.118181i
$29$	3.97470	+	2.88779i	0.738083	+	0.536249i	0.892110	−	0.451818i	$-0.149224\pi$
$29$	3.97470	+	2.88779i	0.738083	+	0.536249i	−0.154027	+	0.988067i	$0.549224\pi$
$30$	−5.64379	−	10.4293i	−1.03041	−	1.90412i
$31$	−0.129282	+	0.397889i	−0.0232197	+	0.0714629i	−0.961995	−	0.273067i	$-0.911962\pi$
$31$	−0.129282	+	0.397889i	−0.0232197	+	0.0714629i	0.938775	+	0.344530i	$0.111962\pi$
$32$			8.07636i			1.42771i
$33$		0			0
$34$	−6.75241			−1.15803
$35$	−0.932474	+	1.94796i	−0.157617	+	0.329266i
$36$	−6.55594	+	4.76317i	−1.09266	+	0.793861i
$37$	3.72512	−	5.12719i	0.612406	−	0.842905i	−0.384367	−	0.923181i	$-0.625580\pi$
$37$	3.72512	−	5.12719i	0.612406	−	0.842905i	0.996773	+	0.0802758i	$0.0255801\pi$
$38$	−6.30817	+	2.04965i	−1.02332	+	0.332497i
$39$	−3.66446	−	11.2780i	−0.586783	−	1.80593i
$40$	0.312377	+	0.297265i	0.0493911	+	0.0470017i
$41$	−4.68068	+	3.40071i	−0.730999	+	0.531102i	−0.889879	−	0.456196i	$-0.849212\pi$
$41$	−4.68068	+	3.40071i	−0.730999	+	0.531102i	0.158880	+	0.987298i	$0.449212\pi$
$42$	4.87132	+	1.58279i	0.751660	+	0.244229i
$43$			2.26205i			0.344960i	0.985013	+	0.172480i	$0.0551780\pi$
$43$			2.26205i			0.344960i	−0.985013	+	0.172480i	$0.944822\pi$
$44$		0			0
$45$	1.14077	−	8.57246i	0.170057	−	1.27791i
$46$	2.10520	−	6.47915i	0.310395	−	0.955298i
$47$	−2.54173	−	3.49838i	−0.370749	−	0.510292i	0.582355	−	0.812934i	$-0.302131\pi$
$47$	−2.54173	−	3.49838i	−0.370749	−	0.510292i	−0.953104	+	0.302642i	$0.902131\pi$
$48$	−5.85383	+	8.05710i	−0.844927	+	1.16294i
$49$	1.87486	+	5.77024i	0.267838	+	0.824320i
$50$	−10.1060	+	0.501317i	−1.42920	+	0.0708969i
$51$	−7.07414	−	5.13966i	−0.990577	−	0.719697i
$52$	5.57303	+	7.67061i	0.772840	+	1.06372i
$53$	2.53047	+	0.822201i	0.347587	+	0.112938i	0.477607	−	0.878573i	$-0.341504\pi$
$53$	2.53047	+	0.822201i	0.347587	+	0.112938i	−0.130020	+	0.991511i	$0.541504\pi$
$54$	−4.60066			−0.626071
$55$		0			0
$56$	−0.186254			−0.0248892
$57$	−8.16885	−	2.65422i	−1.08199	−	0.351560i
$58$	−5.84397	−	8.04353i	−0.767350	−	1.05617i
$59$	−8.19153	−	5.95150i	−1.06645	−	0.774819i	−0.0911765	−	0.995835i	$-0.529063\pi$
$59$	−8.19153	−	5.95150i	−1.06645	−	0.774819i	−0.975270	+	0.221016i	$0.929063\pi$
$60$	2.22063	+	12.0756i	0.286682	+	1.55895i
$61$	−0.763537	−	2.34993i	−0.0977609	−	0.300877i	0.890202	−	0.455565i	$-0.150563\pi$
$61$	−0.763537	−	2.34993i	−0.0977609	−	0.300877i	−0.987963	+	0.154688i	$0.950563\pi$
$62$	0.497642	−	0.684945i	0.0632005	−	0.0869881i
$63$	2.19558	+	3.02195i	0.276617	+	0.380730i
$64$	2.70184	−	8.31540i	0.337729	−	1.03942i
$65$	−10.0300	−	1.33473i	−1.24407	−	0.165553i
$66$		0			0
$67$		−	9.60059i		−	1.17290i	−0.809986	−	0.586449i	$-0.800525\pi$
$67$		−	9.60059i		−	1.17290i	0.809986	−	0.586449i	$-0.199475\pi$
$68$	6.64917	+	2.16045i	0.806330	+	0.261992i
$69$	7.13718	−	5.18546i	0.859215	−	0.624256i
$70$	3.01284	−	3.16600i	0.360103	−	0.378409i
$71$	−1.68510	−	5.18621i	−0.199985	−	0.615490i	−0.999882	−	0.0153533i	$-0.995113\pi$
$71$	−1.68510	−	5.18621i	−0.199985	−	0.615490i	0.799897	−	0.600137i	$-0.204887\pi$
$72$	0.709327	−	0.230474i	0.0835950	−	0.0271617i
$73$	−0.843791	+	1.16138i	−0.0987582	+	0.135929i	−0.855536	−	0.517743i	$-0.826772\pi$
$73$	−0.843791	+	1.16138i	−0.0987582	+	0.135929i	0.756778	+	0.653672i	$0.226772\pi$
$74$	−10.3758	+	7.53847i	−1.20616	+	0.876329i
$75$	−10.9691	−	7.16707i	−1.26660	−	0.827582i
$76$	6.86752			0.787758
$77$		0			0
$78$			23.9977i			2.71721i
$79$	−0.310240	+	0.954820i	−0.0349047	+	0.107426i	−0.966991	−	0.254811i	$-0.917987\pi$
$79$	−0.310240	+	0.954820i	−0.0349047	+	0.107426i	0.932086	+	0.362237i	$0.117987\pi$
$80$	4.04436	+	7.47367i	0.452173	+	0.835582i
$81$	4.56679	+	3.31797i	0.507421	+	0.368663i
$82$	11.1353	−	3.61806i	1.22968	−	0.399548i
$83$	7.03346	−	2.28531i	0.772022	−	0.250845i	0.103592	−	0.994620i	$-0.466966\pi$
$83$	7.03346	−	2.28531i	0.772022	−	0.250845i	0.668430	+	0.743775i	$0.266966\pi$
$84$	−4.29042	−	3.11717i	−0.468123	−	0.340112i
$85$	−6.56188	+	3.55095i	−0.711736	+	0.385154i
$86$	1.41458	−	4.35363i	0.152538	−	0.469464i
$87$		−	12.8750i		−	1.38034i
$88$		0			0
$89$	12.1964			1.29282			0.646410	−	0.762991i	$-0.276270\pi$
$89$	12.1964			1.29282			0.646410	+	0.762991i	$0.276270\pi$
$90$	−7.55639	+	15.7855i	−0.796513	+	1.66394i
$91$	3.53576	−	2.56888i	0.370648	−	0.269292i
$92$	−4.14603	+	5.70652i	−0.432254	+	0.594946i
$93$	1.04271	−	0.338796i	0.108124	−	0.0351315i
$94$	2.70418	+	8.32259i	0.278914	+	0.858410i
$95$	−5.05232	+	5.30915i	−0.518357	+	0.544708i
$96$	17.1227	−	12.4404i	1.74758	−	1.26969i
$97$	−2.87147	−	0.932997i	−0.291553	−	0.0947315i	0.159589	−	0.987184i	$-0.448983\pi$
$97$	−2.87147	−	0.932997i	−0.291553	−	0.0947315i	−0.451142	+	0.892452i	$0.648983\pi$
$98$		−	12.2781i		−	1.24027i
$99$		0			0
$100$	10.1119	+	2.73978i	1.01119	+	0.273978i
$101$	4.69588	−	14.4524i	0.467258	−	1.43807i	−0.388863	−	0.921296i	$-0.627132\pi$
$101$	4.69588	−	14.4524i	0.467258	−	1.43807i	0.856120	−	0.516776i	$-0.172868\pi$
$102$	10.4010	+	14.3158i	1.02986	+	1.41748i
$103$	5.72909	−	7.88542i	0.564504	−	0.776974i	−0.427386	−	0.904069i	$-0.640565\pi$
$103$	5.72909	−	7.88542i	0.564504	−	0.776974i	0.991890	+	0.127096i	$0.0405655\pi$
$104$	−0.269661	−	0.829931i	−0.0264424	−	0.0813814i
$105$	5.56622	−	1.02360i	0.543208	−	0.0998927i
$106$	−4.35608	−	3.16488i	−0.423100	−	0.307400i
$107$	−4.49173	−	6.18234i	−0.434232	−	0.597669i	0.534686	−	0.845051i	$-0.320430\pi$
$107$	−4.49173	−	6.18234i	−0.434232	−	0.597669i	−0.968918	+	0.247382i	$0.920430\pi$
$108$	4.53032	+	1.47199i	0.435930	+	0.141642i
$109$	9.85576			0.944010			0.472005	−	0.881596i	$-0.343530\pi$
$109$	9.85576			0.944010			0.472005	+	0.881596i	$0.343530\pi$
$110$		0			0
$111$	−16.6082			−1.57638
$112$	−3.49080	−	1.13423i	−0.329850	−	0.107175i
$113$	2.94987	+	4.06014i	0.277500	+	0.381946i	0.924904	−	0.380201i	$-0.124145\pi$
$113$	2.94987	+	4.06014i	0.277500	+	0.381946i	−0.647404	+	0.762147i	$0.724145\pi$
$114$	14.0623	+	10.2168i	1.31705	+	0.956893i
$115$	−1.36144	−	7.40342i	−0.126955	−	0.690372i
$116$	3.18107	+	9.79034i	0.295355	+	0.909010i
$117$	−10.2868	+	14.1585i	−0.951011	+	1.30895i
$118$	12.0439	+	16.5771i	1.10873	+	1.52604i
$119$	0.995855	−	3.06493i	0.0912898	−	0.280961i
$120$	0.149065	−	1.12016i	0.0136077	−	0.102256i
$121$		0			0
$122$			5.00023i			0.452700i
$123$	14.4197	+	4.68526i	1.30018	+	0.422455i
$124$	−0.709183	+	0.515251i	−0.0636865	+	0.0462709i
$125$	−9.55721	+	5.80170i	−0.854823	+	0.518920i
$126$	−2.33590	−	7.18917i	−0.208099	−	0.640462i
$127$	−6.74338	+	2.19106i	−0.598378	+	0.194425i	−0.592517	−	0.805558i	$-0.701866\pi$
$127$	−6.74338	+	2.19106i	−0.598378	+	0.194425i	−0.00586102	+	0.999983i	$0.501866\pi$
$128$	−0.905782	+	1.24670i	−0.0800605	+	0.110194i
$129$	4.79579	−	3.48435i	0.422246	−	0.306780i
$130$	18.4694	+	8.84116i	1.61988	+	0.775421i
$131$	7.21704			0.630556			0.315278	−	0.948999i	$-0.397902\pi$
$131$	7.21704			0.630556			0.315278	+	0.948999i	$0.397902\pi$
$132$		0			0
$133$		−	3.16557i		−	0.274490i
$134$	−6.00375	+	18.4776i	−0.518645	+	1.59623i
$135$	−4.47085	+	2.41939i	−0.384790	+	0.208228i
$136$	−0.520573	−	0.378218i	−0.0446388	−	0.0324320i
$137$	−8.07522	+	2.62380i	−0.689913	+	0.224166i	−0.632930	−	0.774209i	$-0.718148\pi$
$137$	−8.07522	+	2.62380i	−0.689913	+	0.224166i	−0.0569827	+	0.998375i	$0.518148\pi$
$138$	−16.9792	+	5.51688i	−1.44537	+	0.469628i
$139$	6.26192	+	4.54955i	0.531129	+	0.385888i	0.820780	−	0.571245i	$-0.193539\pi$
$139$	6.26192	+	4.54955i	0.531129	+	0.385888i	−0.289651	+	0.957132i	$0.593539\pi$
$140$	−3.97974	+	2.15363i	−0.336350	+	0.182015i
$141$	−3.50181	+	10.7775i	−0.294905	+	0.907625i
$142$			11.0354i			0.926067i
$143$		0			0
$144$	14.6978			1.22482
$145$	−9.90900	−	4.74336i	−0.822898	−	0.393914i
$146$	2.35026	−	1.70756i	0.194509	−	0.141319i
$147$	9.34557	−	12.8631i	0.770810	−	1.06093i
$148$	12.6291	−	4.10345i	1.03811	−	0.337301i
$149$	5.21723	+	16.0570i	0.427412	+	1.31544i	0.900666	+	0.434513i	$0.143079\pi$
$149$	5.21723	+	16.0570i	0.427412	+	1.31544i	−0.473254	+	0.880926i	$0.656921\pi$
$150$	16.6296	+	20.6536i	1.35780	+	1.68636i
$151$	9.93687	−	7.21956i	0.808651	−	0.587519i	−0.104788	−	0.994495i	$-0.533416\pi$
$151$	9.93687	−	7.21956i	0.808651	−	0.587519i	0.913439	+	0.406975i	$0.133416\pi$
$152$	−0.601131	−	0.195319i	−0.0487582	−	0.0158425i
$153$			12.9047i			1.04328i
$154$		0			0
$155$	0.123402	−	0.927318i	0.00991190	−	0.0744840i
$156$	7.67812	−	23.6308i	0.614741	−	1.89198i
$157$	−2.47441	−	3.40573i	−0.197479	−	0.271807i	0.698781	−	0.715336i	$-0.253726\pi$
$157$	−2.47441	−	3.40573i	−0.197479	−	0.271807i	−0.896260	+	0.443529i	$0.853726\pi$
$158$	1.19420	−	1.64367i	0.0950053	−	0.130764i
$159$	−2.15466	−	6.63135i	−0.170875	−	0.525900i
$160$	−3.26623	−	17.7615i	−0.258218	−	1.40417i
$161$	2.63041	+	1.91111i	0.207306	+	0.150616i
$162$	−6.71452	−	9.24174i	−0.527542	−	0.726100i
$163$	15.7624	+	5.12151i	1.23461	+	0.401148i	0.852381	−	0.522922i	$-0.175158\pi$
$163$	15.7624	+	5.12151i	1.23461	+	0.401148i	0.382225	+	0.924069i	$0.375158\pi$
$164$	−12.1226			−0.946617
$165$		0			0
$166$	−14.9660			−1.16159
$167$	8.71813	+	2.83269i	0.674629	+	0.219200i	0.626242	−	0.779628i	$-0.284592\pi$
$167$	8.71813	+	2.83269i	0.674629	+	0.219200i	0.0483867	+	0.998829i	$0.484592\pi$
$168$	0.286896	+	0.394878i	0.0221345	+	0.0304655i
$169$	6.04859	+	4.39456i	0.465276	+	0.338043i
$170$	14.8498	−	2.73080i	1.13893	−	0.209443i
$171$	3.91714	+	12.0557i	0.299551	+	0.921924i
$172$	−2.78591	+	3.83447i	−0.212423	+	0.292376i
$173$	−2.41560	−	3.32479i	−0.183655	−	0.252779i	0.707256	−	0.706958i	$-0.249933\pi$
$173$	−2.41560	−	3.32479i	−0.183655	−	0.252779i	−0.890911	+	0.454178i	$0.849933\pi$
$174$	−8.05140	+	24.7797i	−0.610375	+	1.87854i
$175$	1.26290	−	4.66106i	0.0954661	−	0.352343i
$176$		0			0
$177$			26.5343i			1.99444i
$178$	−23.4737	−	7.62707i	−1.75943	−	0.571673i
$179$	−13.1838	+	9.57858i	−0.985403	+	0.715937i	−0.958910	−	0.283712i	$-0.908434\pi$
$179$	−13.1838	+	9.57858i	−0.985403	+	0.715937i	−0.0264932	+	0.999649i	$0.508434\pi$
$180$	12.4915	−	13.1265i	0.931058	−	0.978389i
$181$	−1.71408	−	5.27541i	−0.127407	−	0.392118i	0.866925	−	0.498438i	$-0.166093\pi$
$181$	−1.71408	−	5.27541i	−0.127407	−	0.392118i	−0.994332	+	0.106321i	$0.966093\pi$
$182$	−8.41151	+	2.73307i	−0.623503	+	0.202588i
$183$	−3.80598	+	5.23848i	−0.281346	+	0.387240i
$184$	0.525212	−	0.381589i	0.0387191	−	0.0281311i
$185$	−6.11873	+	12.7822i	−0.449858	+	0.939765i
$186$	−2.21870			−0.162683
$187$		0			0
$188$		−	9.06056i		−	0.660809i
$189$	0.678512	−	2.08825i	0.0493545	−	0.151898i
$190$	13.0440	−	7.05872i	0.946309	−	0.512093i
$191$	−17.6496	−	12.8232i	−1.27708	−	0.927854i	−0.277621	−	0.960691i	$-0.589546\pi$
$191$	−17.6496	−	12.8232i	−1.27708	−	0.927854i	−0.999461	+	0.0328370i	$0.989546\pi$
$192$	−21.7913	+	7.08042i	−1.57265	+	0.510985i
$193$	21.3787	−	6.94637i	1.53887	−	0.500010i	0.587808	−	0.809000i	$-0.299991\pi$
$193$	21.3787	−	6.94637i	1.53887	−	0.500010i	0.951065	+	0.308990i	$0.0999910\pi$
$194$	4.94308	+	3.59136i	0.354893	+	0.257845i
$195$	12.6199	+	23.3206i	0.903730	+	1.67002i
$196$	−3.92839	+	12.0903i	−0.280599	+	0.863596i
$197$		−	25.7479i		−	1.83446i	−0.398358	−	0.917230i	$-0.630420\pi$
$197$		−	25.7479i		−	1.83446i	0.398358	−	0.917230i	$-0.369580\pi$
$198$		0			0
$199$	−16.9671			−1.20277			−0.601385	−	0.798960i	$-0.705384\pi$
$199$	−16.9671			−1.20277			−0.601385	+	0.798960i	$0.705384\pi$
$200$	−0.807196	−	0.527412i	−0.0570774	−	0.0372937i
$201$	−20.3543	+	14.7882i	−1.43568	+	1.04308i
$202$	−18.0757	+	24.8791i	−1.27181	+	1.75049i
$203$	4.51284	−	1.46631i	0.316740	−	0.102915i
$204$	−5.66165	−	17.4248i	−0.396395	−	1.21998i
$205$	8.91840	−	9.37177i	0.622888	−	0.654553i
$206$	−15.9576	+	11.5939i	−1.11182	+	0.807783i
$207$	−12.3825	−	4.02331i	−0.860642	−	0.279639i
$208$		−	17.1969i		−	1.19239i
$209$		0			0
$210$	−11.3531	−	1.51080i	−0.783436	−	0.104255i
$211$	−1.80045	+	5.54121i	−0.123948	+	0.381472i	−0.993708	−	0.112002i	$-0.964274\pi$
$211$	−1.80045	+	5.54121i	−0.123948	+	0.381472i	0.869760	+	0.493475i	$0.164274\pi$
$212$	3.27687	+	4.51023i	0.225056	+	0.309764i
$213$	−8.39968	+	11.5612i	−0.575537	+	0.792158i
$214$	4.77881	+	14.7077i	0.326673	+	1.00540i
$215$	−0.914816	−	4.97469i	−0.0623899	−	0.339271i
$216$	−0.354686	−	0.257694i	−0.0241333	−	0.0175339i
$217$	0.237504	+	0.326897i	0.0161229	+	0.0221912i
$218$	−18.9688	−	6.16332i	−1.28473	−	0.417433i
$219$	3.76197			0.254211
$220$		0			0
$221$	15.0988			1.01566
$222$	31.9647	+	10.3860i	2.14533	+	0.697060i
$223$	11.1810	+	15.3893i	0.748736	+	1.03055i	0.998068	+	0.0621285i	$0.0197889\pi$
$223$	11.1810	+	15.3893i	0.748736	+	1.03055i	−0.249332	+	0.968418i	$0.580211\pi$
$224$	6.31060	+	4.58492i	0.421645	+	0.306343i
$225$	0.958080	+	19.3138i	0.0638720	+	1.28759i
$226$	−3.13840	−	9.65900i	−0.208763	−	0.642507i
$227$	16.7319	−	23.0294i	1.11053	−	1.52852i	0.289902	−	0.957056i	$-0.406377\pi$
$227$	16.7319	−	23.0294i	1.11053	−	1.52852i	0.820630	−	0.571460i	$-0.193623\pi$
$228$	−10.5784	−	14.5599i	−0.700569	−	0.964250i
$229$	7.84636	−	24.1486i	0.518502	−	1.59579i	−0.258316	−	0.966060i	$-0.583168\pi$
$229$	7.84636	−	24.1486i	0.518502	−	1.59579i	0.776818	−	0.629725i	$-0.216832\pi$
$230$	−2.00946	+	15.1003i	−0.132500	+	0.995682i
$231$		0			0
$232$		−	0.947446i		−	0.0622029i
$233$	−11.9048	−	3.86810i	−0.779908	−	0.253407i	−0.108107	−	0.994139i	$-0.534479\pi$
$233$	−11.9048	−	3.86810i	−0.779908	−	0.253407i	−0.671801	+	0.740732i	$0.734479\pi$
$234$	28.6523	−	20.8171i	1.87306	−	1.36086i
$235$	7.00455	+	6.66570i	0.456927	+	0.434822i
$236$	−6.55594	−	20.1771i	−0.426755	−	1.31342i
$237$	2.50220	−	0.813013i	0.162535	−	0.0528108i
$238$	−3.83332	+	5.27611i	−0.248477	+	0.341999i
$239$	16.4939	−	11.9835i	1.06690	−	0.775149i	0.0915488	−	0.995801i	$-0.470818\pi$
$239$	16.4939	−	11.9835i	1.06690	−	0.775149i	0.975353	+	0.220651i	$0.0708183\pi$
$240$	9.61525	−	20.0865i	0.620662	−	1.29658i
$241$	−22.7935			−1.46826			−0.734129	−	0.679010i	$-0.762409\pi$
$241$	−22.7935			−1.46826			−0.734129	+	0.679010i	$0.762409\pi$
$242$		0			0
$243$		−	21.6131i		−	1.38648i
$244$	1.59983	−	4.92378i	0.102419	−	0.315213i
$245$	−6.45678	−	11.9316i	−0.412508	−	0.762284i
$246$	−24.8228	−	18.0348i	−1.58265	−	1.14986i
$247$	14.1055	−	4.58316i	0.897512	−	0.291619i
$248$	0.0767308	−	0.0249314i	0.00487241	−	0.00158314i
$249$	−15.6791	−	11.3915i	−0.993620	−	0.721907i
$250$	22.0223	−	5.18954i	1.39281	−	0.328215i
$251$	5.23870	−	16.1231i	0.330664	−	1.01768i	−0.638155	−	0.769908i	$-0.720302\pi$
$251$	5.23870	−	16.1231i	0.330664	−	1.01768i	0.968819	−	0.247771i	$-0.0796980\pi$
$252$			7.82663i			0.493031i
$253$		0			0
$254$	14.3487			0.900320
$255$	17.6360	+	8.44219i	1.10441	+	0.528671i
$256$	−11.6241	+	8.44538i	−0.726504	+	0.527836i
$257$	2.78366	−	3.83138i	0.173640	−	0.238995i	−0.713323	−	0.700835i	$-0.752811\pi$
$257$	2.78366	−	3.83138i	0.173640	−	0.238995i	0.886963	+	0.461841i	$0.152811\pi$
$258$	−11.4091	+	3.70704i	−0.710300	+	0.230790i
$259$	−1.89148	−	5.82138i	−0.117531	−	0.361723i
$260$	−15.3583	−	14.6153i	−0.952481	−	0.906404i
$261$	−15.3722	+	11.1686i	−0.951516	+	0.691317i
$262$	−13.8902	−	4.51319i	−0.858138	−	0.278826i
$263$			18.1037i			1.11632i	0.829732	+	0.558162i	$0.188493\pi$
$263$			18.1037i			1.11632i	−0.829732	+	0.558162i	$0.811507\pi$
$264$		0			0
$265$	−5.89751	−	0.784807i	−0.362281	−	0.0482103i
$266$	−1.97960	+	6.09258i	−0.121377	+	0.373560i
$267$	−18.7867	−	25.8577i	−1.14973	−	1.58247i
$268$	11.8239	−	16.2742i	0.722261	−	0.994107i
$269$	0.710127	+	2.18555i	0.0432972	+	0.133255i	0.970368	−	0.241630i	$-0.0776821\pi$
$269$	0.710127	+	2.18555i	0.0432972	+	0.133255i	−0.927071	+	0.374885i	$0.877682\pi$
$270$	10.1177	−	1.86059i	0.615746	−	0.113232i
$271$	−0.651815	−	0.473572i	−0.0395950	−	0.0287674i	0.567812	−	0.823158i	$-0.307790\pi$
$271$	−0.651815	−	0.473572i	−0.0395950	−	0.0287674i	−0.607407	+	0.794391i	$0.707790\pi$
$272$	−7.45343	−	10.2588i	−0.451930	−	0.622029i
$273$	−10.8926	−	3.53922i	−0.659250	−	0.214203i
$274$	17.1827			1.03804
$275$		0			0
$276$	18.4848			1.11265
$277$	−11.2538	−	3.65657i	−0.676173	−	0.219702i	−0.0492539	−	0.998786i	$-0.515684\pi$
$277$	−11.2538	−	3.65657i	−0.676173	−	0.219702i	−0.626919	+	0.779084i	$0.715684\pi$
$278$	−9.20685	−	12.6721i	−0.552190	−	0.760025i
$279$	−1.30902	−	0.951057i	−0.0783688	−	0.0569383i
$280$	0.409608	−	0.0753246i	0.0244788	−	0.00450150i
$281$	1.92496	+	5.92441i	0.114833	+	0.353420i	0.991912	−	0.126926i	$-0.0405110\pi$
$281$	1.92496	+	5.92441i	0.114833	+	0.353420i	−0.877079	+	0.480346i	$0.840511\pi$
$282$	13.4794	−	18.5528i	0.802687	−	1.10480i
$283$	−5.08178	−	6.99448i	−0.302081	−	0.415778i	0.630810	−	0.775937i	$-0.282723\pi$
$283$	−5.08178	−	6.99448i	−0.302081	−	0.415778i	−0.932891	+	0.360159i	$0.882723\pi$
$284$	3.53079	−	10.8666i	0.209514	−	0.644817i
$285$	19.0383	+	2.53351i	1.12773	+	0.150072i
$286$		0			0
$287$			5.58790i			0.329843i
$288$	−29.7067	−	9.65228i	−1.75048	−	0.568766i
$289$	−4.74609	+	3.44824i	−0.279182	+	0.202838i
$290$	16.1050	+	15.3259i	0.945716	+	0.899965i
$291$	2.44501	+	7.52496i	0.143329	+	0.441121i
$292$	−2.86067	+	0.929487i	−0.167408	+	0.0543941i
$293$	−3.41532	+	4.70078i	−0.199525	+	0.274622i	−0.897042	−	0.441946i	$-0.854288\pi$
$293$	−3.41532	+	4.70078i	−0.199525	+	0.274622i	0.697517	+	0.716568i	$0.254288\pi$
$294$	−26.0308	+	18.9125i	−1.51815	+	1.10300i
$295$	20.4216	+	9.77568i	1.18899	+	0.569162i
$296$	−1.22216			−0.0710369
$297$		0			0
$298$		−	34.1665i		−	1.97921i
$299$	−4.70738	+	14.4878i	−0.272235	+	0.837852i
$300$	−9.76717	−	25.6585i	−0.563908	−	1.48139i
$301$	1.76749	+	1.28416i	0.101877	+	0.0740177i
$302$	−23.6396	+	7.68098i	−1.36031	+	0.441991i
$303$	−37.8740	+	12.3060i	−2.17580	+	0.706962i
$304$	−10.0771	−	7.32141i	−0.577959	−	0.419912i
$305$	2.62952	+	4.85915i	0.150566	+	0.278234i
$306$	8.06999	−	24.8369i	0.461331	−	1.41983i
$307$			18.4721i			1.05426i	0.849785	+	0.527130i	$0.176732\pi$
$307$			18.4721i			1.05426i	−0.849785	+	0.527130i	$0.823268\pi$
$308$		0			0
$309$	−25.5427			−1.45307
$310$	−0.817405	+	1.70758i	−0.0464255	+	0.0969841i
$311$	9.16726	−	6.66041i	0.519828	−	0.377677i	−0.296711	−	0.954967i	$-0.595890\pi$
$311$	9.16726	−	6.66041i	0.519828	−	0.377677i	0.816539	+	0.577290i	$0.195890\pi$
$312$	−1.34417	+	1.85009i	−0.0760986	+	0.104741i
$313$	−4.86464	+	1.58062i	−0.274966	+	0.0893418i	−0.443254	−	0.896396i	$-0.646176\pi$
$313$	−4.86464	+	1.58062i	−0.274966	+	0.0893418i	0.168288	+	0.985738i	$0.446176\pi$
$314$	2.63256	+	8.10217i	0.148564	+	0.457232i
$315$	−6.05063	−	5.75792i	−0.340914	−	0.324422i
$316$	−1.70184	+	1.23646i	−0.0957357	+	0.0695561i
$317$	11.2351	+	3.65051i	0.631027	+	0.205033i	0.607030	−	0.794679i	$-0.292361\pi$
$317$	11.2351	+	3.65051i	0.631027	+	0.205033i	0.0239968	+	0.999712i	$0.492361\pi$
$318$			14.1104i			0.791270i
$319$		0			0
$320$	−2.57896	+	19.3798i	−0.144168	+	1.08337i
$321$	−6.18839	+	19.0459i	−0.345402	+	1.06304i
$322$	−3.86748	−	5.32313i	−0.215526	−	0.296646i
$323$	6.42820	−	8.84766i	0.357675	−	0.492297i
$324$	3.65494	+	11.2488i	0.203052	+	0.624931i
$325$	22.5977	−	1.12098i	1.25349	−	0.0621807i
$326$	−27.1341	−	19.7141i	−1.50282	−	1.09186i
$327$	−15.1813	−	20.8952i	−0.839527	−	1.15551i
$328$	1.06112	+	0.344780i	0.0585907	+	0.0190373i
$329$	−4.17645			−0.230255
$330$		0			0
$331$	29.2692			1.60878			0.804391	−	0.594100i	$-0.202492\pi$
$331$	29.2692			1.60878			0.804391	+	0.594100i	$0.202492\pi$
$332$	14.7372	+	4.78839i	0.808807	+	0.262797i
$333$	14.4070	+	19.8295i	0.789497	+	1.08665i
$334$	−15.0078	−	10.9038i	−0.821191	−	0.596630i
$335$	3.88265	+	21.1135i	0.212132	+	1.15356i
$336$	2.97236	+	9.14798i	0.162155	+	0.499063i
$337$	−15.6610	+	21.5555i	−0.853109	+	1.17420i	0.130060	+	0.991506i	$0.458483\pi$
$337$	−15.6610	+	21.5555i	−0.853109	+	1.17420i	−0.983169	+	0.182698i	$0.941517\pi$
$338$	−8.89320	−	12.2404i	−0.483726	−	0.665792i
$339$	4.06411	−	12.5081i	0.220732	−	0.679344i
$340$	−15.4965	−	2.06219i	−0.840417	−	0.111838i
$341$		0			0
$342$		−	25.6525i		−	1.38713i
$343$	12.0029	+	3.89998i	0.648095	+	0.210579i
$344$	0.352914	−	0.256407i	0.0190278	−	0.0138245i
$345$	−13.5989	+	14.2902i	−0.732142	+	0.769360i
$346$	2.56999	+	7.90962i	0.138164	+	0.425224i
$347$	−4.10028	+	1.33226i	−0.220114	+	0.0715195i	−0.416998	−	0.908907i	$-0.636918\pi$
$347$	−4.10028	+	1.33226i	−0.220114	+	0.0715195i	0.196884	+	0.980427i	$0.436918\pi$
$348$	15.8566	−	21.8247i	0.850003	−	1.16993i
$349$	−10.6543	+	7.74083i	−0.570314	+	0.414357i	−0.835219	−	0.549917i	$-0.814659\pi$
$349$	−10.6543	+	7.74083i	−0.570314	+	0.414357i	0.264905	+	0.964274i	$0.414659\pi$
$350$	−5.34542	+	8.18109i	−0.285725	+	0.437297i
$351$	10.2874			0.549100
$352$		0			0
$353$		−	25.4904i		−	1.35672i	−0.734732	−	0.678358i	$-0.762692\pi$
$353$		−	25.4904i		−	1.35672i	0.734732	−	0.678358i	$-0.237308\pi$
$354$	16.5933	−	51.0689i	0.881923	−	2.71428i
$355$	5.80327	+	10.7240i	0.308005	+	0.569171i
$356$	20.6745	+	15.0209i	1.09575	+	0.796107i
$357$	−8.03193	+	2.60973i	−0.425095	+	0.138122i
$358$	31.3640	−	10.1908i	1.65764	−	0.538600i
$359$	21.2562	+	15.4435i	1.12186	+	0.815079i	0.984490	−	0.175441i	$-0.0561351\pi$
$359$	21.2562	+	15.4435i	1.12186	+	0.815079i	0.137370	+	0.990520i	$0.456135\pi$
$360$	−1.46674	+	0.793722i	−0.0773039	+	0.0418328i
$361$	−2.55168	+	7.85325i	−0.134299	+	0.413329i
$362$			11.2252i			0.589981i
$363$		0			0
$364$	9.15736			0.479976
$365$	1.38597	−	2.89534i	0.0725452	−	0.151549i
$366$	10.6010	−	7.70209i	0.554124	−	0.402595i
$367$	1.18658	−	1.63319i	0.0619391	−	0.0852518i	−0.776924	−	0.629595i	$-0.783221\pi$
$367$	1.18658	−	1.63319i	0.0619391	−	0.0852518i	0.838863	+	0.544343i	$0.183221\pi$
$368$	12.1674	−	3.95342i	0.634268	−	0.206086i
$369$	−6.91458	−	21.2809i	−0.359959	−	1.10784i
$370$	19.7697	−	20.7747i	1.02778	−	1.08003i
$371$	2.07898	−	1.51047i	0.107935	−	0.0784197i
$372$	2.18477	+	0.709876i	0.113275	+	0.0368054i
$373$			8.87153i			0.459351i	0.973267	+	0.229675i	$0.0737664\pi$
$373$			8.87153i			0.459351i	−0.973267	+	0.229675i	$0.926234\pi$
$374$		0			0
$375$	27.0216	+	11.3257i	1.39539	+	0.584855i
$376$	−0.257692	+	0.793093i	−0.0132894	+	0.0409007i
$377$	13.0675	+	17.9859i	0.673011	+	0.926320i
$378$	−2.61178	+	3.59481i	−0.134335	+	0.184897i
$379$	−6.50916	−	20.0331i	−0.334353	−	1.02903i	−0.967040	−	0.254625i	$-0.918048\pi$
$379$	−6.50916	−	20.0331i	−0.334353	−	1.02903i	0.632686	−	0.774408i	$-0.281952\pi$
$380$	−15.1030	+	2.77735i	−0.774767	+	0.142475i
$381$	15.0324	+	10.9217i	0.770134	+	0.559535i
$382$	25.9501	+	35.7172i	1.32772	+	1.82745i
$383$	−24.7080	−	8.02812i	−1.26252	−	0.410218i	−0.400129	−	0.916459i	$-0.631035\pi$
$383$	−24.7080	−	8.02812i	−1.26252	−	0.410218i	−0.862392	+	0.506241i	$0.831035\pi$
$384$	4.03836			0.206082
$385$		0			0
$386$	−45.4902			−2.31539
$387$	−8.32034	−	2.70344i	−0.422947	−	0.137424i
$388$	−3.71845	−	5.11800i	−0.188775	−	0.259827i
$389$	−1.32987	−	0.966206i	−0.0674270	−	0.0489886i	0.553561	−	0.832809i	$-0.313269\pi$
$389$	−1.32987	−	0.966206i	−0.0674270	−	0.0489886i	−0.620988	+	0.783820i	$0.713269\pi$
$390$	−9.70512	−	52.7756i	−0.491438	−	2.67240i
$391$	3.47110	+	10.6830i	0.175541	+	0.540260i
$392$	0.687724	−	0.946571i	0.0347353	−	0.0478090i
$393$	−11.1167	−	15.3009i	−0.560766	−	0.771828i
$394$	−16.1015	+	49.5553i	−0.811182	+	2.49656i
$395$	0.296130	−	2.22530i	0.0148999	−	0.111967i
$396$		0			0
$397$			16.7088i			0.838588i	0.907850	+	0.419294i	$0.137722\pi$
$397$			16.7088i			0.838588i	−0.907850	+	0.419294i	$0.862278\pi$
$398$	32.6556	+	10.6104i	1.63688	+	0.531854i
$399$	−6.71135	+	4.87608i	−0.335988	+	0.244109i
$400$	−11.9168	−	14.8004i	−0.595841	−	0.740021i
$401$	8.58819	+	26.4317i	0.428874	+	1.31994i	0.899236	+	0.437464i	$0.144123\pi$
$401$	8.58819	+	26.4317i	0.428874	+	1.31994i	−0.470362	+	0.882474i	$0.655877\pi$
$402$	48.4224	−	15.7334i	2.41509	−	0.784711i
$403$	−1.11276	+	1.53158i	−0.0554305	+	0.0762936i
$404$	25.7595	−	18.7154i	1.28158	−	0.931125i
$405$	−11.3851	−	5.44995i	−0.565730	−	0.270810i
$406$	−9.60255			−0.476567
$407$		0			0
$408$			1.68626i			0.0834822i
$409$	−12.1855	+	37.5030i	−0.602532	+	1.85440i	−0.0895906	+	0.995979i	$0.528556\pi$
$409$	−12.1855	+	37.5030i	−0.602532	+	1.85440i	−0.512941	+	0.858424i	$0.671444\pi$
$410$	−23.0253	+	12.4601i	−1.13714	+	0.615361i
$411$	18.0014	+	13.0788i	0.887942	+	0.645128i
$412$	19.4231	−	6.31095i	0.956908	−	0.310918i
$413$	−9.30061	+	3.02195i	−0.457653	+	0.148700i
$414$	21.3158	+	15.4868i	1.04761	+	0.761136i
$415$	−14.5437	+	7.87029i	−0.713922	+	0.386338i
$416$	−11.2934	+	34.7576i	−0.553705	+	1.70413i
$417$		−	20.2838i		−	0.993303i
$418$		0			0
$419$	−14.7812			−0.722111			−0.361055	−	0.932544i	$-0.617583\pi$
$419$	−14.7812			−0.722111			−0.361055	+	0.932544i	$0.617583\pi$
$420$	10.6961	+	5.12014i	0.521917	+	0.249837i
$421$	8.71900	−	6.33473i	0.424938	−	0.308736i	−0.354684	−	0.934986i	$-0.615411\pi$
$421$	8.71900	−	6.33473i	0.424938	−	0.308736i	0.779622	+	0.626251i	$0.215411\pi$
$422$	6.93042	−	9.53890i	0.337367	−	0.464346i
$423$	15.9055	−	5.16802i	0.773354	−	0.251278i
$424$	−0.158557	−	0.487989i	−0.00770022	−	0.0236988i
$425$	12.9948	−	10.4630i	0.630339	−	0.507528i
$426$	23.3961	−	16.9983i	1.13355	−	0.823570i
$427$	−2.26961	−	0.737442i	−0.109834	−	0.0356873i
$428$		−	16.0118i		−	0.773960i
$429$		0			0
$430$	−1.35025	+	10.1466i	−0.0651146	+	0.489310i
$431$	9.94774	−	30.6160i	0.479166	−	1.47472i	−0.361090	−	0.932531i	$-0.617595\pi$
$431$	9.94774	−	30.6160i	0.479166	−	1.47472i	0.840256	−	0.542190i	$-0.182405\pi$
$432$	−5.07829	−	6.98967i	−0.244330	−	0.336291i
$433$	−0.224905	+	0.309555i	−0.0108082	+	0.0148763i	−0.814387	−	0.580322i	$-0.802927\pi$
$433$	−0.224905	+	0.309555i	−0.0108082	+	0.0148763i	0.803579	+	0.595199i	$0.202927\pi$
$434$	−0.252684	−	0.777682i	−0.0121292	−	0.0373299i
$435$	5.20688	+	28.3145i	0.249651	+	1.35758i
$436$	16.7068	+	12.1382i	0.800109	+	0.581314i
$437$	6.48548	+	8.92650i	0.310243	+	0.427013i
$438$	−7.24044	−	2.35256i	−0.345961	−	0.112410i
$439$	−26.5331			−1.26635			−0.633177	−	0.774007i	$-0.718249\pi$
$439$	−26.5331			−1.26635			−0.633177	+	0.774007i	$0.718249\pi$
$440$		0			0
$441$	−23.4649			−1.11738
$442$	−29.0598	−	9.44210i	−1.38223	−	0.449115i
$443$	−8.52347	−	11.7316i	−0.404962	−	0.557383i	0.557018	−	0.830500i	$-0.311945\pi$
$443$	−8.52347	−	11.7316i	−0.404962	−	0.557383i	−0.961981	+	0.273117i	$0.911945\pi$
$444$	−28.1530	−	20.4543i	−1.33608	−	0.970720i
$445$	−26.8223	+	4.93246i	−1.27150	+	0.233821i
$446$	−11.8956	−	36.6110i	−0.563274	−	1.73358i
$447$	26.0062	−	35.7944i	1.23005	−	1.69302i
$448$	−4.96356	−	6.83175i	−0.234506	−	0.322770i
$449$	−3.12540	+	9.61898i	−0.147497	+	0.453948i	−0.997324	−	0.0731139i	$-0.976706\pi$
$449$	−3.12540	+	9.61898i	−0.147497	+	0.453948i	0.849827	+	0.527062i	$0.176706\pi$
$450$	10.2340	−	37.7713i	0.482435	−	1.78055i
$451$		0			0
$452$			10.5155i			0.494606i
$453$	−30.6125	−	9.94659i	−1.43830	−	0.467332i
$454$	−46.6043	+	33.8600i	−2.18725	+	1.58913i
$455$	−6.73691	+	7.07939i	−0.315831	+	0.331887i
$456$	0.511853	+	1.57532i	0.0239697	+	0.0737712i
$457$	−37.1756	+	12.0791i	−1.73900	+	0.565036i	−0.994701	−	0.102809i	$-0.967217\pi$
$457$	−37.1756	+	12.0791i	−1.73900	+	0.565036i	−0.744301	+	0.667845i	$0.767217\pi$
$458$	−30.2028	+	41.5706i	−1.41128	+	1.94247i
$459$	6.13693	−	4.45874i	0.286448	−	0.208116i
$460$	6.81010	−	14.2265i	0.317522	−	0.663313i
$461$	39.1322			1.82257			0.911285	−	0.411776i	$-0.135092\pi$
$461$	39.1322			1.82257			0.911285	+	0.411776i	$0.135092\pi$
$462$		0			0
$463$			12.9189i			0.600392i	0.953878	+	0.300196i	$0.0970521\pi$
$463$			12.9189i			0.600392i	−0.953878	+	0.300196i	$0.902948\pi$
$464$	5.76966	−	17.7572i	0.267850	−	0.824357i
$465$	−2.15609	+	1.16677i	−0.0999865	+	0.0541075i
$466$	20.4934	+	14.8894i	0.949341	+	0.689736i
$467$	10.6985	−	3.47616i	0.495069	−	0.160858i	−0.0508323	−	0.998707i	$-0.516187\pi$
$467$	10.6985	−	3.47616i	0.495069	−	0.160858i	0.545901	+	0.837850i	$0.316187\pi$
$468$	−34.8747	+	11.3315i	−1.61209	+	0.523798i
$469$	−7.50158	−	5.45022i	−0.346391	−	0.251668i
$470$	−9.31281	−	17.2094i	−0.429568	−	0.793809i
$471$	−3.40906	+	10.4920i	−0.157081	+	0.483446i
$472$			1.95261i			0.0898762i
$473$		0			0
$474$	−5.32424			−0.244550
$475$	8.96389	−	13.7191i	0.411292	−	0.629475i
$476$	5.46281	−	3.96896i	0.250388	−	0.181917i
$477$	−6.04848	+	8.32503i	−0.276941	+	0.381177i
$478$	−39.2387	+	12.7494i	−1.79474	+	0.583145i
$479$	−6.47894	−	19.9401i	−0.296030	−	0.911087i	−0.982873	−	0.184282i	$-0.941004\pi$
$479$	−6.47894	−	19.9401i	−0.296030	−	0.911087i	0.686843	−	0.726806i	$-0.258996\pi$
$480$	−32.6250	+	34.2836i	−1.48912	+	1.56482i
$481$	23.2010	−	16.8565i	1.05788	−	0.768591i
$482$	43.8692	+	14.2540i	1.99819	+	0.649250i
$483$		−	8.52053i		−	0.387697i
$484$		0			0
$485$	6.69223	+	0.890564i	0.303879	+	0.0404384i
$486$	−13.5158	+	41.5974i	−0.613090	+	1.88690i
$487$	−13.2658	−	18.2588i	−0.601130	−	0.827385i	0.394681	−	0.918818i	$-0.370855\pi$
$487$	−13.2658	−	18.2588i	−0.601130	−	0.827385i	−0.995811	+	0.0914336i	$0.970855\pi$
$488$	−0.280075	+	0.385490i	−0.0126784	+	0.0174503i
$489$	−13.4214	−	41.3068i	−0.606937	−	1.86796i
$490$	4.96548	+	27.0018i	0.224317	+	1.21982i
$491$	16.2420	+	11.8005i	0.732991	+	0.532549i	0.890508	−	0.454967i	$-0.150349\pi$
$491$	16.2420	+	11.8005i	0.732991	+	0.532549i	−0.157518	+	0.987516i	$0.550349\pi$
$492$	18.6730	+	25.7012i	0.841845	+	1.15870i
$493$	15.5908	+	5.06576i	0.702175	+	0.228150i
$494$	−30.0141			−1.35040
$495$		0			0
$496$	1.58993			0.0713898
$497$	−5.00897	−	1.62751i	−0.224683	−	0.0730039i
$498$	23.0528	+	31.7295i	1.03302	+	1.42183i
$499$	3.76342	+	2.73429i	0.168474	+	0.122403i	0.668827	−	0.743418i	$-0.266797\pi$
$499$	3.76342	+	2.73429i	0.168474	+	0.122403i	−0.500353	+	0.865821i	$0.666797\pi$
$500$	−23.3460	−	1.93587i	−1.04406	−	0.0865748i
$501$	−7.42334	−	22.8467i	−0.331650	−	1.02071i
$502$	−20.1652	+	27.7550i	−0.900017	+	1.23877i
$503$	7.63957	+	10.5150i	0.340632	+	0.468839i	0.944626	−	0.328149i	$-0.106425\pi$
$503$	7.63957	+	10.5150i	0.340632	+	0.468839i	−0.603994	+	0.796989i	$0.706425\pi$
$504$	0.222597	−	0.685085i	0.00991528	−	0.0305161i
$505$	−4.48232	+	33.6828i	−0.199460	+	1.49887i
$506$		0			0
$507$		−	19.5928i		−	0.870147i
$508$	−14.1294	−	4.59091i	−0.626889	−	0.203689i
$509$	23.9020	−	17.3658i	1.05944	−	0.769727i	0.0854540	−	0.996342i	$-0.472766\pi$
$509$	23.9020	−	17.3658i	1.05944	−	0.769727i	0.973984	+	0.226615i	$0.0727659\pi$
$510$	−28.6635	−	27.2768i	−1.26924	−	1.20784i
$511$	0.428446	+	1.31862i	0.0189533	+	0.0583323i
$512$	30.5846	−	9.93755i	1.35166	−	0.439182i
$513$	4.37977	−	6.02824i	0.193372	−	0.266153i
$514$	−7.75350	+	5.63324i	−0.341992	+	0.248472i
$515$	−9.41037	+	19.6585i	−0.414670	+	0.866257i
$516$	12.4207			0.546793
$517$		0			0
$518$			12.3869i			0.544248i
$519$	−3.32804	+	10.2427i	−0.146085	+	0.449603i
$520$	0.928675	+	1.71612i	0.0407251	+	0.0752569i
$521$	25.4446	+	18.4866i	1.11475	+	0.809911i	0.983405	−	0.181426i	$-0.0580712\pi$
$521$	25.4446	+	18.4866i	1.11475	+	0.809911i	0.131343	+	0.991337i	$0.458071\pi$
$522$	36.5702	−	11.8824i	1.60064	−	0.520078i
$523$	8.57873	−	2.78740i	0.375121	−	0.121884i	−0.115387	−	0.993321i	$-0.536811\pi$
$523$	8.57873	−	2.78740i	0.375121	−	0.121884i	0.490509	+	0.871436i	$0.336811\pi$
$524$	12.2338	+	8.88838i	0.534437	+	0.388291i
$525$	−11.8272	+	4.50217i	−0.516183	+	0.196491i
$526$	11.3212	−	34.8431i	0.493628	−	1.51923i
$527$			1.39595i			0.0608088i
$528$		0			0
$529$	11.6672			0.507269
$530$	10.8598	+	5.19849i	0.471719	+	0.225808i
$531$	31.6809	−	23.0175i	1.37483	−	0.998875i
$532$	3.89867	−	5.36605i	0.169029	−	0.232648i
$533$	−24.8992	+	8.09024i	−1.07850	+	0.350427i
$534$	19.9875	+	61.5151i	0.864942	+	2.66202i
$535$	12.3784	+	11.7796i	0.535166	+	0.509277i
$536$	−1.49783	+	1.08824i	−0.0646965	+	0.0470048i
$537$	40.6152	+	13.1967i	1.75268	+	0.569479i
$538$		−	4.65046i		−	0.200496i
$539$		0			0
$540$	−10.5583	−	1.40504i	−0.454359	−	0.0604635i
$541$	−2.64213	+	8.13165i	−0.113594	+	0.349607i	−0.991651	−	0.128949i	$-0.958840\pi$
$541$	−2.64213	+	8.13165i	−0.113594	+	0.349607i	0.878057	+	0.478556i	$0.158840\pi$
$542$	0.958359	+	1.31907i	0.0411650	+	0.0566588i
$543$	−8.54414	+	11.7600i	−0.366664	+	0.504670i
$544$	8.32748	+	25.6294i	0.357038	+	1.09885i
$545$	−21.6747	+	3.98585i	−0.928442	+	0.170735i
$546$	18.7510	+	13.6234i	0.802470	+	0.583029i
$547$	19.9435	+	27.4499i	0.852725	+	1.17367i	0.983256	+	0.182230i	$0.0583317\pi$
$547$	19.9435	+	27.4499i	0.852725	+	1.17367i	−0.130531	+	0.991444i	$0.541668\pi$
$548$	−16.9200	−	5.49763i	−0.722785	−	0.234847i
$549$	9.55608			0.407844
$550$		0			0
$551$	16.1028			0.686002
$552$	−1.61802	−	0.525726i	−0.0688674	−	0.0223764i
$553$	0.569943	+	0.784459i	0.0242364	+	0.0333586i
$554$	19.3728	+	14.0751i	0.823070	+	0.597995i
$555$	36.5245	−	6.71665i	1.55038	−	0.285106i
$556$	5.01161	+	15.4241i	0.212540	+	0.654129i
$557$	−13.4842	+	18.5594i	−0.571342	+	0.786385i	−0.992713	−	0.120503i	$-0.961549\pi$
$557$	−13.4842	+	18.5594i	−0.571342	+	0.786385i	0.421371	+	0.906888i	$0.361549\pi$
$558$	1.92464	+	2.64904i	0.0814764	+	0.112143i
$559$	−3.16310	+	9.73501i	−0.133785	+	0.411747i
$560$	8.13565	+	1.08265i	0.343794	+	0.0457501i
$561$		0			0
$562$		−	12.6061i		−	0.531757i
$563$	−8.82830	−	2.86849i	−0.372068	−	0.120892i	0.117013	−	0.993130i	$-0.462668\pi$
$563$	−8.82830	−	2.86849i	−0.372068	−	0.120892i	−0.489082	+	0.872238i	$0.662668\pi$
$564$	−19.2093	+	13.9564i	−0.808859	+	0.587670i
$565$	−8.12932	−	7.73605i	−0.342003	−	0.325458i
$566$	5.40658	+	16.6397i	0.227255	+	0.699420i
$567$	5.18510	−	1.68474i	0.217754	−	0.0707525i
$568$	−0.618117	+	0.850765i	−0.0259356	+	0.0356973i
$569$	25.0206	−	18.1785i	1.04892	−	0.762083i	0.0769109	−	0.997038i	$-0.475494\pi$
$569$	25.0206	−	18.1785i	1.04892	−	0.762083i	0.972006	+	0.234955i	$0.0754943\pi$
$570$	−35.0575	−	16.7817i	−1.46840	−	0.702909i
$571$	−2.63736			−0.110370			−0.0551851	−	0.998476i	$-0.517575\pi$
$571$	−2.63736			−0.110370			−0.0551851	+	0.998476i	$0.517575\pi$
$572$		0			0
$573$			57.1712i			2.38836i
$574$	3.49441	−	10.7547i	0.145854	−	0.448892i
$575$	5.98816	+	15.7309i	0.249723	+	0.656026i
$576$	27.3569	+	19.8759i	1.13987	+	0.828164i
$577$	34.8377	−	11.3194i	1.45031	−	0.471235i	0.525216	−	0.850969i	$-0.323985\pi$
$577$	34.8377	−	11.3194i	1.45031	−	0.471235i	0.925096	+	0.379734i	$0.123985\pi$
$578$	11.2909	−	3.66863i	0.469638	−	0.152595i
$579$	−47.6577	−	34.6253i	−1.98058	−	1.43898i
$580$	−10.9552	−	20.2444i	−0.454889	−	0.840601i
$581$	2.20720	−	6.79308i	0.0915703	−	0.281824i
$582$		−	16.0118i		−	0.663710i
$583$		0			0
$584$	0.276837			0.0114556
$585$	16.8966	−	35.2974i	0.698588	−	1.45937i
$586$	9.51289	−	6.91152i	0.392974	−	0.285512i
$587$	8.08348	−	11.1259i	0.333641	−	0.459217i	−0.608930	−	0.793224i	$-0.708401\pi$
$587$	8.08348	−	11.1259i	0.333641	−	0.459217i	0.942571	+	0.334007i	$0.108401\pi$
$588$	31.6839	−	10.2947i	1.30662	−	0.424547i
$589$	0.423733	+	1.30412i	0.0174596	+	0.0537352i
$590$	−33.1910	−	31.5854i	−1.36645	−	1.30035i
$591$	−54.5882	+	39.6607i	−2.24546	+	1.63142i
$592$	−22.9060	−	7.44261i	−0.941431	−	0.305890i
$593$		−	20.1550i		−	0.827668i	−0.910352	−	0.413834i	$-0.864189\pi$
$593$		−	20.1550i		−	0.827668i	0.910352	−	0.413834i	$-0.135811\pi$
$594$		0			0
$595$	−0.950563	+	7.14310i	−0.0389693	+	0.292839i
$596$	−10.9316	+	33.6441i	−0.447777	+	1.37812i
$597$	26.1353	+	35.9721i	1.06965	+	1.47224i
$598$	18.1200	−	24.9400i	0.740981	−	1.01987i
$599$	−1.33594	−	4.11159i	−0.0545849	−	0.167995i	0.920047	−	0.391807i	$-0.128150\pi$
$599$	−1.33594	−	4.11159i	−0.0545849	−	0.167995i	−0.974632	+	0.223812i	$0.928150\pi$
$600$	0.125192	+	2.52374i	0.00511095	+	0.103031i
$601$	−29.1161	−	21.1541i	−1.18767	−	0.862894i	−0.194655	−	0.980872i	$-0.562359\pi$
$601$	−29.1161	−	21.1541i	−1.18767	−	0.862894i	−0.993016	+	0.117978i	$0.962359\pi$
$602$	−2.59873	−	3.57685i	−0.105916	−	0.145781i
$603$	35.3131	+	11.4739i	1.43806	+	0.467255i
$604$	25.7358			1.04717
$605$		0			0
$606$	80.5893			3.27372
$607$	37.7092	+	12.2525i	1.53057	+	0.497313i	0.948756	−	0.316009i	$-0.102343\pi$
$607$	37.7092	+	12.2525i	1.53057	+	0.497313i	0.581815	+	0.813321i	$0.302343\pi$
$608$	15.5593	+	21.4155i	0.631011	+	0.868513i
$609$	−10.0601	−	7.30908i	−0.407655	−	0.296179i
$610$	−2.02219	−	10.9965i	−0.0818759	−	0.445234i
$611$	−6.04672	−	18.6099i	−0.244624	−	0.752875i
$612$	−15.8932	+	21.8751i	−0.642445	+	0.884250i
$613$	−2.24234	−	3.08631i	−0.0905671	−	0.124655i	0.761329	−	0.648366i	$-0.224547\pi$
$613$	−2.24234	−	3.08631i	−0.0905671	−	0.124655i	−0.851896	+	0.523711i	$0.824547\pi$
$614$	11.5516	−	35.5521i	0.466184	−	1.43477i
$615$	−33.6066	−	4.47217i	−1.35515	−	0.180335i
$616$		0			0
$617$			28.4055i			1.14356i	0.820407	+	0.571781i	$0.193747\pi$
$617$			28.4055i			1.14356i	−0.820407	+	0.571781i	$0.806253\pi$
$618$	49.1605	+	15.9732i	1.97752	+	0.642537i
$619$	19.4737	−	14.1485i	0.782715	−	0.568676i	−0.123077	−	0.992397i	$-0.539276\pi$
$619$	19.4737	−	14.1485i	0.782715	−	0.568676i	0.905793	+	0.423721i	$0.139276\pi$
$620$	1.35125	−	1.41994i	0.0542676	−	0.0570263i
$621$	2.36499	+	7.27869i	0.0949037	+	0.292084i
$622$	−21.8088	+	7.08610i	−0.874452	+	0.284127i
$623$	6.92387	−	9.52989i	0.277399	−	0.381807i
$624$	−36.4591	+	26.4891i	−1.45953	+	1.06041i
$625$	18.6718	−	16.6242i	0.746873	−	0.664967i
$626$	10.3511			0.413714
$627$		0			0
$628$		−	8.82059i		−	0.351980i
$629$	6.53462	−	20.1115i	0.260552	−	0.801897i
$630$	8.04453	+	14.8657i	0.320502	+	0.592263i
$631$	−15.4697	−	11.2394i	−0.615838	−	0.447432i	0.235627	−	0.971843i	$-0.424286\pi$
$631$	−15.4697	−	11.2394i	−0.615838	−	0.447432i	−0.851465	+	0.524411i	$0.824286\pi$
$632$	0.184132	−	0.0598281i	0.00732438	−	0.00237984i
$633$	14.5213	−	4.71824i	0.577168	−	0.187533i
$634$	−19.3407	−	14.0518i	−0.768115	−	0.558069i
$635$	13.9439	−	7.54570i	0.553346	−	0.299442i
$636$	4.51464	−	13.8946i	0.179017	−	0.550958i
$637$			27.4546i			1.08779i
$638$		0			0
$639$	21.0900			0.834307
$640$	1.48780	−	3.10805i	0.0588104	−	0.122856i
$641$	−9.69123	+	7.04109i	−0.382780	+	0.278106i	−0.762491	−	0.646999i	$-0.776024\pi$
$641$	−9.69123	+	7.04109i	−0.382780	+	0.278106i	0.379710	+	0.925105i	$0.376024\pi$
$642$	23.8208	−	32.7865i	0.940132	−	1.29398i
$643$	24.4810	−	7.95435i	0.965435	−	0.313689i	0.216463	−	0.976291i	$-0.430548\pi$
$643$	24.4810	−	7.95435i	0.965435	−	0.313689i	0.748972	+	0.662602i	$0.230548\pi$
$644$	2.10520	+	6.47915i	0.0829566	+	0.255314i
$645$	−9.13773	+	9.60225i	−0.359798	+	0.378088i
$646$	−17.9049	+	13.0086i	−0.704457	+	0.511818i
$647$	−8.84699	−	2.87456i	−0.347811	−	0.113011i	0.129901	−	0.991527i	$-0.458534\pi$
$647$	−8.84699	−	2.87456i	−0.347811	−	0.113011i	−0.477712	+	0.878516i	$0.658534\pi$
$648$		−	1.08858i		−	0.0427636i
$649$		0			0
$650$	−44.1933	−	11.9740i	−1.73341	−	0.469661i
$651$	0.327217	−	1.00707i	0.0128246	−	0.0394701i
$652$	20.4117	+	28.0943i	0.799384	+	1.10026i
$653$	−22.0129	+	30.2982i	−0.861432	+	1.18566i	0.119794	+	0.992799i	$0.461777\pi$
$653$	−22.0129	+	30.2982i	−0.861432	+	1.18566i	−0.981226	+	0.192861i	$0.938223\pi$
$654$	16.1516	+	49.7094i	0.631576	+	1.94379i
$655$	−15.8717	+	2.91870i	−0.620157	+	0.114043i
$656$	17.7881	+	12.9238i	0.694510	+	0.504591i
$657$	−3.26337	−	4.49165i	−0.127316	−	0.175236i
$658$	8.03815	+	2.61175i	0.313360	+	0.101817i
$659$	4.93753			0.192339			0.0961693	−	0.995365i	$-0.469341\pi$
$659$	4.93753			0.192339			0.0961693	+	0.995365i	$0.469341\pi$
$660$		0			0
$661$	−4.82155			−0.187537			−0.0937683	−	0.995594i	$-0.529891\pi$
$661$	−4.82155			−0.187537			−0.0937683	+	0.995594i	$0.529891\pi$
$662$	−56.3327	−	18.3036i	−2.18943	−	0.711389i
$663$	−23.2574	−	32.0111i	−0.903244	−	1.24321i
$664$	−1.15379	−	0.838280i	−0.0447759	−	0.0325316i
$665$	1.28022	+	6.96170i	0.0496447	+	0.269963i
$666$	−15.3278	−	47.1740i	−0.593939	−	1.82796i
$667$	−9.72152	+	13.3805i	−0.376419	+	0.518096i
$668$	11.2897	+	15.5389i	0.436810	+	0.601217i
$669$	15.4044	−	47.4098i	0.595568	−	1.83297i
$670$	5.73070	−	43.0639i	0.221396	−	1.66370i
$671$		0			0
$672$		−	20.4415i		−	0.788548i
$673$	31.3031	+	10.1710i	1.20665	+	0.392063i	0.842202	−	0.539162i	$-0.181259\pi$
$673$	31.3031	+	10.1710i	1.20665	+	0.392063i	0.364445	+	0.931225i	$0.381259\pi$
$674$	43.6215	−	31.6929i	1.68024	−	1.22077i
$675$	8.85381	−	7.12880i	0.340783	−	0.274388i
$676$	4.84088	+	14.8987i	0.186188	+	0.573026i
$677$	16.3035	−	5.29734i	0.626596	−	0.203593i	0.0215294	−	0.999768i	$-0.493146\pi$
$677$	16.3035	−	5.29734i	0.626596	−	0.203593i	0.605067	+	0.796175i	$0.293146\pi$
$678$	−15.6439	+	21.5320i	−0.600800	+	0.826930i
$679$	−2.35914	+	1.71401i	−0.0905353	+	0.0657778i
$680$	1.29780	+	0.621246i	0.0497683	+	0.0238237i
$681$	−74.5977			−2.85859
$682$		0			0
$683$			19.3586i			0.740737i	0.928885	+	0.370368i	$0.120769\pi$
$683$			19.3586i			0.740737i	−0.928885	+	0.370368i	$0.879231\pi$
$684$	−8.20756	+	25.2603i	−0.313824	+	0.965851i
$685$	16.6979	−	9.03601i	0.637992	−	0.345248i
$686$	−20.6624	−	15.0121i	−0.788892	−	0.573164i
$687$	−63.2837	+	20.5621i	−2.41442	+	0.784494i
$688$	8.17580	−	2.65648i	0.311700	−	0.101277i
$689$	9.74049	+	7.07688i	0.371083	+	0.269608i
$690$	35.1094	−	18.9994i	1.33659	−	0.723295i
$691$	−2.82486	+	8.69404i	−0.107463	+	0.330737i	−0.990301	−	0.138941i	$-0.955630\pi$
$691$	−2.82486	+	8.69404i	−0.107463	+	0.330737i	0.882838	+	0.469678i	$0.155630\pi$
$692$		−	8.61097i		−	0.327340i
$693$		0			0
$694$	8.72467			0.331184
$695$	−15.6111	−	7.47290i	−0.592162	−	0.283463i
$696$	−2.00869	+	1.45940i	−0.0761390	+	0.0553183i
$697$	−11.3471	+	15.6180i	−0.429803	+	0.591573i
$698$	25.3465	−	8.23558i	0.959379	−	0.311721i
$699$	10.1367	+	31.1976i	0.383406	+	1.18000i
$700$	7.88125	−	6.34573i	0.297883	−	0.239846i
$701$	12.3727	−	8.98928i	0.467310	−	0.339520i	−0.329082	−	0.944301i	$-0.606739\pi$
$701$	12.3727	−	8.98928i	0.467310	−	0.339520i	0.796392	+	0.604781i	$0.206739\pi$
$702$	−19.7995	−	6.43325i	−0.747284	−	0.242807i
$703$		−	20.7719i		−	0.783428i
$704$		0			0
$705$	3.34254	−	25.1179i	0.125887	−	0.945994i
$706$	−15.9405	+	49.0597i	−0.599927	+	1.84639i
$707$	−8.62683	−	11.8738i	−0.324445	−	0.446561i
$708$	−32.6792	+	44.9790i	−1.22816	+	1.69042i
$709$	−13.2608	−	40.8126i	−0.498020	−	1.53275i	−0.812197	−	0.583383i	$-0.801729\pi$
$709$	−13.2608	−	40.8126i	−0.498020	−	1.53275i	0.314177	−	0.949364i	$-0.398271\pi$
$710$	−4.46291	−	24.2689i	−0.167490	−	0.910795i
$711$	−3.14127	−	2.28226i	−0.117807	−	0.0855916i
$712$	−1.38248	−	1.90282i	−0.0518107	−	0.0713113i
$713$	−1.33946	−	0.435218i	−0.0501633	−	0.0162990i
$714$	17.0905			0.639598
$715$		0			0
$716$	−34.1450			−1.27606
$717$	−50.8126	−	16.5100i	−1.89763	−	0.616578i
$718$	−31.2528	−	43.0158i	−1.16635	−	1.60534i
$719$	3.89401	+	2.82916i	0.145222	+	0.105510i	0.658024	−	0.752997i	$-0.271393\pi$
$719$	3.89401	+	2.82916i	0.145222	+	0.105510i	−0.512802	+	0.858507i	$0.671393\pi$
$720$	−32.3234	+	5.94408i	−1.20462	+	0.221523i
$721$	−2.90902	−	8.95305i	−0.108338	−	0.333429i
$722$	9.82210	−	13.5190i	0.365541	−	0.503124i
$723$	35.1099	+	48.3246i	1.30575	+	1.79721i
$724$	3.59151	−	11.0535i	0.133477	−	0.410801i
$725$	23.7101	+	6.42417i	0.880571	+	0.238588i
$726$		0			0
$727$		−	21.8922i		−	0.811937i	−0.913887	−	0.405969i	$-0.866934\pi$
$727$		−	21.8922i		−	0.811937i	0.913887	−	0.405969i	$-0.133066\pi$
$728$	−0.801566	−	0.260445i	−0.0297080	−	0.00965272i
$729$	−32.1218	+	23.3378i	−1.18969	+	0.864364i
$730$	−4.47811	+	4.70575i	−0.165742	+	0.174168i
$731$	2.33239	+	7.17836i	0.0862665	+	0.265501i
$732$	−12.9032	+	4.19252i	−0.476918	+	0.154960i
$733$	28.2310	−	38.8567i	1.04274	−	1.43520i	0.147797	−	0.989018i	$-0.452782\pi$
$733$	28.2310	−	38.8567i	1.04274	−	1.43520i	0.894940	−	0.446187i	$-0.147218\pi$
$734$	−3.30506	+	2.40127i	−0.121992	+	0.0886324i
$735$	−15.3506	+	32.0679i	−0.566217	+	1.18284i
$736$	−27.1885			−1.00218
$737$		0			0
$738$			45.2820i			1.66685i
$739$	10.5398	−	32.4380i	0.387711	−	1.19325i	−0.546783	−	0.837274i	$-0.684148\pi$
$739$	10.5398	−	32.4380i	0.387711	−	1.19325i	0.934494	−	0.355978i	$-0.115852\pi$
$740$	−26.1143	+	14.1317i	−0.959982	+	0.519492i
$741$	−31.4441	−	22.8455i	−1.15513	−	0.839251i
$742$	−4.94586	+	1.60701i	−0.181568	+	0.0589951i
$743$	−25.1461	+	8.17046i	−0.922521	+	0.299745i	−0.731501	−	0.681841i	$-0.761180\pi$
$743$	−25.1461	+	8.17046i	−0.922521	+	0.299745i	−0.191020	+	0.981586i	$0.561180\pi$
$744$	−0.171049	−	0.124274i	−0.00627097	−	0.00455612i
$745$	−17.9674	−	33.2024i	−0.658276	−	1.21644i
$746$	5.54784	−	17.0745i	0.203121	−	0.625141i
$747$			28.6019i			1.04649i
$748$		0			0
$749$	−7.38062			−0.269682
$750$	−44.9243	−	38.6958i	−1.64040	−	1.41297i
$751$	−37.1665	+	27.0030i	−1.35622	+	0.985355i	−0.357549	+	0.933894i	$0.616388\pi$
$751$	−37.1665	+	27.0030i	−1.35622	+	0.985355i	−0.998675	+	0.0514603i	$0.983612\pi$
$752$	−9.65940	+	13.2950i	−0.352242	+	0.484819i
$753$	−42.2520	+	13.7285i	−1.53975	+	0.500295i
$754$	−13.9027	−	42.7881i	−0.506306	−	1.55825i
$755$	−18.9334	+	19.8958i	−0.689056	+	0.724084i
$756$	3.72201	−	2.70420i	0.135368	−	0.0983509i
$757$	−29.3455	−	9.53493i	−1.06658	−	0.346553i	−0.277426	−	0.960747i	$-0.589481\pi$
$757$	−29.3455	−	9.53493i	−1.06658	−	0.346553i	−0.789155	+	0.614194i	$0.789481\pi$
$758$			42.6271i			1.54828i
$759$		0			0
$760$	1.40099	+	0.186436i	0.0508194	+	0.00676275i
$761$	−4.38726	+	13.5026i	−0.159038	+	0.489469i	−0.998548	−	0.0538760i	$-0.982842\pi$
$761$	−4.38726	+	13.5026i	−0.159038	+	0.489469i	0.839510	+	0.543345i	$0.182842\pi$
$762$	−22.1020	−	30.4208i	−0.800672	−	1.10203i
$763$	5.59508	−	7.70097i	0.202555	−	0.278794i
$764$	−14.1255	−	43.4739i	−0.511044	−	1.57283i
$765$	−5.21890	−	28.3799i	−0.188690	−	1.02608i
$766$	42.5336	+	30.9024i	1.53680	+	1.11655i
$767$	−26.9311	−	37.0674i	−0.972425	−	1.33843i
$768$	35.8102	+	11.6354i	1.29219	+	0.419858i
$769$	30.0208			1.08258			0.541290	−	0.840836i	$-0.317936\pi$
$769$	30.0208			1.08258			0.541290	+	0.840836i	$0.317936\pi$
$770$		0			0
$771$	−12.4107			−0.446961
$772$	44.7947	+	14.5547i	1.61220	+	0.523834i
$773$	−17.8859	−	24.6179i	−0.643313	−	0.885444i	0.355474	−	0.934686i	$-0.384319\pi$
$773$	−17.8859	−	24.6179i	−0.643313	−	0.885444i	−0.998787	+	0.0492422i	$0.984319\pi$
$774$	14.3230	+	10.4063i	0.514831	+	0.374047i
$775$	0.103639	+	2.08926i	0.00372284	+	0.0750483i
$776$	0.179924	+	0.553748i	0.00645888	+	0.0198784i
$777$	−9.42840	+	12.9771i	−0.338242	+	0.465550i
$778$	1.95530	+	2.69123i	0.0701007	+	0.0964854i
$779$	−5.85988	+	18.0348i	−0.209952	+	0.646165i
$780$	−7.32892	+	55.0739i	−0.262417	+	1.97196i
$781$		0			0
$782$		−	22.7315i		−	0.812876i
$783$	10.6226	+	3.45149i	0.379621	+	0.123346i
$784$	18.6538	−	13.5527i	0.666206	−	0.484027i
$785$	6.81904	+	6.48916i	0.243382	+	0.231608i
$786$	11.8273	+	36.4005i	0.421864	+	1.29836i
$787$	−28.9737	+	9.41413i	−1.03280	+	0.335577i	−0.775897	−	0.630859i	$-0.782702\pi$
$787$	−28.9737	+	9.41413i	−1.03280	+	0.335577i	−0.256904	+	0.966437i	$0.582702\pi$
$788$	31.7106	−	43.6460i	1.12964	−	1.55482i
$789$	38.3818	−	27.8860i	1.36643	−	0.992768i
$790$	−1.96154	+	4.09771i	−0.0697884	+	0.145790i
$791$	4.84709			0.172343
$792$		0			0
$793$		−	11.1809i		−	0.397044i
$794$	10.4489	−	32.1583i	0.370816	−	1.14126i
$795$	7.42034	+	13.7122i	0.263172	+	0.486323i
$796$	−28.7615	−	20.8964i	−1.01942	−	0.740655i
$797$	31.4278	−	10.2115i	1.11323	−	0.361711i	0.306050	−	0.952015i	$-0.400992\pi$
$797$	31.4278	−	10.2115i	1.11323	−	0.361711i	0.807180	+	0.590305i	$0.200992\pi$
$798$	15.9662	−	5.18773i	0.565197	−	0.183644i
$799$	−11.6730	−	8.48095i	−0.412962	−	0.300034i
$800$	14.3661	+	37.7399i	0.507919	+	1.33431i
$801$	−14.5763	+	44.8613i	−0.515028	+	1.58509i
$802$		−	56.2421i		−	1.98598i
$803$		0			0
$804$	−52.7160			−1.85915
$805$	−6.55767	−	3.13911i	−0.231128	−	0.110639i
$806$	3.09944	−	2.25187i	0.109173	−	0.0793189i
$807$	3.53975	−	4.87204i	0.124605	−	0.171504i
$808$	−2.78708	+	0.905577i	−0.0980491	+	0.0318581i
$809$	−3.39595	−	10.4517i	−0.119395	−	0.367461i	0.873443	−	0.486926i	$-0.161882\pi$
$809$	−3.39595	−	10.4517i	−0.119395	−	0.367461i	−0.992838	+	0.119465i	$0.961882\pi$
$810$	18.5040	+	17.6089i	0.650166	+	0.618713i
$811$	−32.9745	+	23.9573i	−1.15789	+	0.841256i	−0.989510	−	0.144466i	$-0.953854\pi$
$811$	−32.9745	+	23.9573i	−1.15789	+	0.841256i	−0.168380	+	0.985722i	$0.553854\pi$
$812$	9.45574	+	3.07235i	0.331831	+	0.107819i
$813$			2.11138i			0.0740494i
$814$		0			0
$815$	−36.7358	−	4.88858i	−1.28680	−	0.171240i
$816$	−10.2688	+	31.6041i	−0.359480	+	1.10637i
$817$	4.35789	+	5.99812i	0.152463	+	0.209848i
$818$	46.9052	−	64.5594i	1.64000	−	2.25727i
$819$	5.22324	+	16.0755i	0.182515	+	0.561722i
$820$	26.6600	−	4.90261i	0.931006	−	0.171207i
$821$	−12.2223	−	8.88003i	−0.426562	−	0.309915i	0.353711	−	0.935355i	$-0.384920\pi$
$821$	−12.2223	−	8.88003i	−0.426562	−	0.309915i	−0.780273	+	0.625439i	$0.784920\pi$
$822$	−26.4673	−	36.4291i	−0.923152	−	1.27061i
$823$	−34.6482	−	11.2579i	−1.20776	−	0.392425i	−0.365150	−	0.930949i	$-0.618982\pi$
$823$	−34.6482	−	11.2579i	−1.20776	−	0.392425i	−0.842610	+	0.538524i	$0.818982\pi$
$824$	−1.87964			−0.0654805
$825$		0			0
$826$	19.7901			0.688585
$827$	3.61727	+	1.17532i	0.125785	+	0.0408700i	0.371233	−	0.928540i	$-0.378935\pi$
$827$	3.61727	+	1.17532i	0.125785	+	0.0408700i	−0.245448	+	0.969410i	$0.578935\pi$
$828$	−16.0348	−	22.0701i	−0.557250	−	0.766988i
$829$	−22.0912	−	16.0502i	−0.767261	−	0.557447i	0.133868	−	0.990999i	$-0.457260\pi$
$829$	−22.0912	−	16.0502i	−0.767261	−	0.557447i	−0.901129	+	0.433552i	$0.857260\pi$
$830$	32.9131	−	6.05252i	1.14243	−	0.210086i
$831$	9.58238	+	29.4915i	0.332409	+	1.02305i
$832$	23.2553	−	32.0082i	0.806234	−	1.10969i
$833$	11.8993	+	16.3780i	0.412287	+	0.567464i
$834$	−12.6845	+	39.0390i	−0.439230	+	1.35181i
$835$	−20.3184	−	2.70386i	−0.703148	−	0.0935710i
$836$		0			0
$837$			0.951115i			0.0328754i
$838$	28.4485	+	9.24348i	0.982738	+	0.319311i
$839$	22.9154	−	16.6490i	0.791128	−	0.574788i	−0.117170	−	0.993112i	$-0.537382\pi$
$839$	22.9154	−	16.6490i	0.791128	−	0.574788i	0.908298	+	0.418324i	$0.137382\pi$
$840$	−0.790635	−	0.752387i	−0.0272795	−	0.0259598i
$841$	−1.50258	−	4.62448i	−0.0518132	−	0.159465i
$842$	−20.7424	+	6.73960i	−0.714829	+	0.232262i
$843$	9.59527	−	13.2068i	0.330479	−	0.454865i
$844$	−9.87645	+	7.17566i	−0.339961	+	0.246996i
$845$	−15.0793	−	7.21832i	−0.518742	−	0.248318i
$846$	−33.8442			−1.16359
$847$		0			0
$848$		−	10.1115i		−	0.347232i
$849$	−7.00132	+	21.5478i	−0.240285	+	0.739520i
$850$	−31.5533	+	12.0111i	−1.08227	+	0.411977i
$851$	17.2603	+	12.5403i	0.591676	+	0.429877i
$852$	−28.4771	+	9.25276i	−0.975608	+	0.316994i
$853$	7.93484	−	2.57818i	0.271684	−	0.0882754i	−0.170007	−	0.985443i	$-0.554379\pi$
$853$	7.93484	−	2.57818i	0.271684	−	0.0882754i	0.441690	+	0.897168i	$0.354379\pi$
$854$	3.90702	+	2.83862i	0.133695	+	0.0971354i
$855$	−13.4901	−	24.9287i	−0.461352	−	0.852543i
$856$	−0.455392	+	1.40155i	−0.0155650	+	0.0479041i
$857$		−	8.59547i		−	0.293616i	−0.989165	−	0.146808i	$-0.953100\pi$
$857$		−	8.59547i		−	0.293616i	0.989165	−	0.146808i	$-0.0468999\pi$
$858$		0			0
$859$	−9.40807			−0.320999			−0.160500	−	0.987036i	$-0.551311\pi$
$859$	−9.40807			−0.320999			−0.160500	+	0.987036i	$0.551311\pi$
$860$	4.57601	−	9.55941i	0.156041	−	0.325973i
$861$	11.8469	−	8.60731i	0.403743	−	0.293336i
$862$	−38.2916	+	52.7039i	−1.30422	+	1.79510i
$863$	−9.82067	+	3.19093i	−0.334299	+	0.108620i	−0.471357	−	0.881943i	$-0.656236\pi$
$863$	−9.82067	+	3.19093i	−0.334299	+	0.108620i	0.137057	+	0.990563i	$0.456236\pi$
$864$	5.67382	+	17.4622i	0.193027	+	0.594077i
$865$	6.65698	+	6.33494i	0.226344	+	0.215394i
$866$	0.626441	−	0.455136i	0.0212873	−	0.0154662i
$867$	14.6213	+	4.75074i	0.496564	+	0.161343i
$868$			0.846638i			0.0287368i
$869$		0			0
$870$	7.68522	−	57.7514i	0.260553	−	1.95795i
$871$	13.4248	−	41.3173i	0.454882	−	1.39998i
$872$	−1.11716	−	1.53764i	−0.0378319	−	0.0520712i
$873$	6.86355	−	9.44686i	0.232296	−	0.319728i
$874$	−6.89999	−	21.2360i	−0.233396	−	0.718318i
$875$	−0.892338	+	10.7613i	−0.0301665	+	0.363798i
$876$	6.37703	+	4.63318i	0.215460	+	0.156541i
$877$	−17.5179	−	24.1113i	−0.591536	−	0.814180i	0.403364	−	0.915039i	$-0.367841\pi$
$877$	−17.5179	−	24.1113i	−0.591536	−	0.814180i	−0.994901	+	0.100859i	$0.967841\pi$
$878$	51.0665	+	16.5925i	1.72341	+	0.559970i
$879$	15.2269			0.513591
$880$		0			0
$881$	30.1175			1.01469			0.507343	−	0.861744i	$-0.330628\pi$
$881$	30.1175			1.01469			0.507343	+	0.861744i	$0.330628\pi$
$882$	45.1615	+	14.6739i	1.52067	+	0.494095i
$883$	29.6020	+	40.7436i	0.996185	+	1.37113i	0.927637	+	0.373484i	$0.121837\pi$
$883$	29.6020	+	40.7436i	0.996185	+	1.37113i	0.0685488	+	0.997648i	$0.478163\pi$
$884$	25.5945	+	18.5955i	0.860835	+	0.625433i
$885$	−10.7310	−	58.3540i	−0.360717	−	1.96155i
$886$	9.06824	+	27.9092i	0.304653	+	0.937627i
$887$	24.3375	−	33.4977i	0.817173	−	1.12474i	−0.173003	−	0.984921i	$-0.555347\pi$
$887$	24.3375	−	33.4977i	0.817173	−	1.12474i	0.990177	−	0.139821i	$-0.0446528\pi$
$888$	1.88256	+	2.59112i	0.0631745	+	0.0869522i
$889$	−2.11617	+	6.51291i	−0.0709741	+	0.218436i
$890$	54.7077	+	7.28019i	1.83381	+	0.244033i
$891$		0			0
$892$			39.8572i			1.33452i
$893$	−13.4794	−	4.37973i	−0.451071	−	0.146562i
$894$	−72.4365	+	52.6282i	−2.42264	+	1.76015i
$895$	25.1199	−	26.3969i	0.839667	−	0.882352i
$896$	0.459923	+	1.41550i	0.0153649	+	0.0472884i
$897$	37.9667	−	12.3361i	1.26767	−	0.411891i
$898$	12.0305	−	16.5586i	0.401463	−	0.552567i
$899$	−1.66287	+	1.20815i	−0.0554600	+	0.0402940i
$900$	−22.1625	+	33.9194i	−0.738751	+	1.13065i
$901$	8.87793			0.295767
$902$		0			0
$903$		−	5.72532i		−	0.190527i
$904$	0.299071	−	0.920445i	0.00994694	−	0.0306135i
$905$	5.90307	+	10.9084i	0.196225	+	0.362608i
$906$	52.6977	+	38.2872i	1.75077	+	1.27201i
$907$	4.40544	−	1.43142i	0.146280	−	0.0475294i	−0.234962	−	0.972005i	$-0.575496\pi$
$907$	4.40544	−	1.43142i	0.146280	−	0.0475294i	0.381242	+	0.924475i	$0.375496\pi$
$908$	56.7253	−	18.4312i	1.88249	−	0.611660i
$909$	47.5472	+	34.5451i	1.57704	+	1.14579i
$910$	17.3932	−	9.41231i	0.576580	−	0.312015i
$911$	2.15649	−	6.63699i	0.0714477	−	0.219893i	−0.908956	−	0.416892i	$-0.863119\pi$
$911$	2.15649	−	6.63699i	0.0714477	−	0.219893i	0.980404	+	0.196998i	$0.0631194\pi$
$912$			32.6419i			1.08088i
$913$		0			0
$914$	79.1032			2.61650
$915$	6.25154	−	13.0596i	0.206669	−	0.431738i
$916$	43.0416	−	31.2716i	1.42213	−	1.03324i
$917$	4.09709	−	5.63916i	0.135298	−	0.186221i
$918$	−14.5997	+	4.74372i	−0.481860	+	0.156566i
$919$	7.23738	+	22.2744i	0.238739	+	0.734763i	0.996603	+	0.0823512i	$0.0262429\pi$
$919$	7.23738	+	22.2744i	0.238739	+	0.734763i	−0.757864	+	0.652412i	$0.773757\pi$
$920$	−1.00072	+	1.05159i	−0.0329928	+	0.0346700i
$921$	39.1628	−	28.4535i	1.29046	−	0.937574i
$922$	−75.3154	−	24.4714i	−2.48038	−	0.805924i
$923$		−	24.6758i		−	0.812215i
$924$		0			0
$925$	8.28691	−	30.5850i	0.272472	−	1.00563i
$926$	8.07887	−	24.8642i	0.265488	−	0.817088i
$927$	22.1574	+	30.4970i	0.727744	+	1.00165i
$928$	−23.3228	+	32.1011i	−0.765608	+	1.05377i
$929$	5.59027	+	17.2051i	0.183411	+	0.564480i	0.999917	−	0.0128560i	$-0.00409231\pi$
$929$	5.59027	+	17.2051i	0.183411	+	0.564480i	−0.816507	+	0.577336i	$0.804092\pi$
$930$	4.87934	−	0.897282i	0.160000	−	0.0294230i
$931$	16.0879	+	11.6886i	0.527260	+	0.383077i
$932$	−15.4162	−	21.2186i	−0.504976	−	0.695039i
$933$	−28.2415	−	9.17623i	−0.924586	−	0.300416i
$934$	−22.7646			−0.744881
$935$		0			0
$936$	3.37495			0.110314
$937$	10.4708	+	3.40215i	0.342065	+	0.111144i	0.475011	−	0.879980i	$-0.342444\pi$
$937$	10.4708	+	3.40215i	0.342065	+	0.111144i	−0.132947	+	0.991123i	$0.542444\pi$
$938$	11.0295	+	15.1808i	0.360127	+	0.495672i
$939$	10.8443	+	7.87885i	0.353891	+	0.257117i
$940$	3.66426	+	19.9259i	0.119515	+	0.649911i
$941$	10.4388	+	32.1275i	0.340297	+	1.04733i	0.964054	+	0.265707i	$0.0856055\pi$
$941$	10.4388	+	32.1275i	0.340297	+	1.04733i	−0.623757	+	0.781618i	$0.714395\pi$
$942$	13.1224	−	18.0615i	0.427551	−	0.588474i
$943$	−11.4482	−	15.7572i	−0.372806	−	0.513124i
$944$	−11.8908	+	36.5961i	−0.387013	+	1.19110i
$945$	−0.647654	+	4.86686i	−0.0210682	+	0.158319i
$946$		0			0
$947$		−	46.9853i		−	1.52682i	−0.645915	−	0.763409i	$-0.723524\pi$
$947$		−	46.9853i		−	1.52682i	0.645915	−	0.763409i	$-0.276476\pi$
$948$	5.24284	+	1.70350i	0.170279	+	0.0553271i
$949$	−5.25534	+	3.81823i	−0.170596	+	0.123945i
$950$	−25.8315	+	20.7987i	−0.838085	+	0.674799i
$951$	−9.56650	−	29.4427i	−0.310215	−	0.954744i
$952$	−0.591055	+	0.192045i	−0.0191562	+	0.00622423i
$953$	−24.9754	+	34.3757i	−0.809032	+	1.11354i	0.182440	+	0.983217i	$0.441600\pi$
$953$	−24.9754	+	34.3757i	−0.809032	+	1.11354i	−0.991472	+	0.130320i	$0.958400\pi$
$954$	16.8472	−	12.2402i	0.545449	−	0.396292i
$955$	44.0008	+	21.0628i	1.42383	+	0.681577i
$956$	42.7180			1.38160
$957$		0			0
$958$			42.4291i			1.37082i
$959$	−2.53413	+	7.79924i	−0.0818312	+	0.251850i
$960$	45.0598	−	24.3840i	1.45430	−	0.786990i
$961$	24.9379	+	18.1185i	0.804449	+	0.584467i
$962$	−55.1948	+	17.9339i	−1.77955	+	0.578211i
$963$	28.1082	−	9.13292i	0.905776	−	0.294304i
$964$	−38.6379	−	28.0721i	−1.24444	−	0.904140i
$965$	−44.2067	+	23.9223i	−1.42306	+	0.770087i
$966$	−5.32833	+	16.3989i	−0.171436	+	0.527627i
$967$			54.1642i			1.74180i	0.491458	+	0.870901i	$0.336464\pi$
$967$			54.1642i			1.74180i	−0.491458	+	0.870901i	$0.663536\pi$
$968$		0			0
$969$	−28.6596			−0.920680
$970$	−12.3232	−	5.89902i	−0.395674	−	0.189406i
$971$	−4.23802	+	3.07910i	−0.136004	+	0.0988130i	−0.653707	−	0.756747i	$-0.726787\pi$
$971$	−4.23802	+	3.07910i	−0.136004	+	0.0988130i	0.517703	+	0.855560i	$0.326787\pi$
$972$	26.6184	−	36.6370i	0.853784	−	1.17513i
$973$	7.10974	−	2.31009i	0.227928	−	0.0740582i
$974$	14.1136	+	43.4373i	0.452230	+	1.39182i
$975$	−37.1849	−	46.1828i	−1.19087	−	1.47903i
$976$	−7.59673	+	5.51935i	−0.243165	+	0.176670i
$977$	−7.40057	−	2.40459i	−0.236765	−	0.0769297i	0.188231	−	0.982125i	$-0.439725\pi$
$977$	−7.40057	−	2.40459i	−0.236765	−	0.0769297i	−0.424996	+	0.905195i	$0.639725\pi$
$978$			87.8938i			2.81053i
$979$		0			0
$980$	3.74973	−	28.1777i	0.119781	−	0.900104i
$981$	−11.7789	+	36.2517i	−0.376071	+	1.15743i
$982$	−23.8805	−	32.8686i	−0.762056	−	1.04888i
$983$	−30.2789	+	41.6754i	−0.965748	+	1.32924i	−0.0215828	+	0.999767i	$0.506871\pi$
$983$	−30.2789	+	41.6754i	−0.965748	+	1.32924i	−0.944166	+	0.329471i	$0.893129\pi$
$984$	−0.903528	−	2.78077i	−0.0288034	−	0.0886478i
$985$	10.4129	+	56.6245i	0.331783	+	1.80421i
$986$	−26.8388	−	19.4995i	−0.854721	−	0.620991i
$987$	6.43318	+	8.85452i	0.204771	+	0.281842i
$988$	29.5552	+	9.60306i	0.940276	+	0.305514i
$989$	−7.61503			−0.242144
$990$		0			0
$991$	−22.3382			−0.709596			−0.354798	−	0.934943i	$-0.615450\pi$
$991$	−22.3382			−0.709596			−0.354798	+	0.934943i	$0.615450\pi$
$992$	−3.21349	−	1.04413i	−0.102028	−	0.0331511i
$993$	−45.0848	−	62.0539i	−1.43072	−	1.96922i
$994$	8.62267	+	6.26474i	0.273495	+	0.198705i
$995$	37.3140	−	6.86183i	1.18293	−	0.217535i
$996$	−12.5484	−	38.6201i	−0.397613	−	1.22373i
$997$	0.108473	−	0.149301i	0.00343539	−	0.00472840i	−0.807296	−	0.590147i	$-0.799070\pi$
$997$	0.108473	−	0.149301i	0.00343539	−	0.00472840i	0.810731	+	0.585419i	$0.199070\pi$
$998$	−5.53333	−	7.61597i	−0.175154	−	0.241079i
$999$	4.45227	−	13.7027i	0.140864	−	0.433534i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.j.h.9.1		16
5.4	even	2	inner	605.2.j.h.9.4		16
11.2	odd	10		605.2.j.d.124.1		16
11.3	even	5		55.2.j.a.4.1	✓	16
11.4	even	5		605.2.b.g.364.1		8
11.5	even	5	inner	605.2.j.h.269.4		16
11.6	odd	10		605.2.j.g.269.1		16
11.7	odd	10		605.2.b.f.364.8		8
11.8	odd	10		605.2.j.d.444.4		16
11.9	even	5		55.2.j.a.14.4	yes	16
11.10	odd	2		605.2.j.g.9.4		16
33.14	odd	10		495.2.ba.a.334.4		16
33.20	odd	10		495.2.ba.a.289.1		16
44.3	odd	10		880.2.cd.c.609.1		16
44.31	odd	10		880.2.cd.c.289.4		16
55.3	odd	20		275.2.h.d.26.4		16
55.4	even	10		605.2.b.g.364.8		8
55.7	even	20		3025.2.a.bk.1.1		8
55.9	even	10		55.2.j.a.14.1	yes	16
55.14	even	10		55.2.j.a.4.4	yes	16
55.18	even	20		3025.2.a.bk.1.8		8
55.19	odd	10		605.2.j.d.444.1		16
55.24	odd	10		605.2.j.d.124.4		16
55.29	odd	10		605.2.b.f.364.1		8
55.37	odd	20		3025.2.a.bl.1.8		8
55.39	odd	10		605.2.j.g.269.4		16
55.42	odd	20		275.2.h.d.201.1		16
55.47	odd	20		275.2.h.d.26.1		16
55.48	odd	20		3025.2.a.bl.1.1		8
55.49	even	10	inner	605.2.j.h.269.1		16
55.53	odd	20		275.2.h.d.201.4		16
55.54	odd	2		605.2.j.g.9.1		16
165.14	odd	10		495.2.ba.a.334.1		16
165.119	odd	10		495.2.ba.a.289.4		16
220.119	odd	10		880.2.cd.c.289.1		16
220.179	odd	10		880.2.cd.c.609.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.4.1	✓	16	11.3	even	5
55.2.j.a.4.4	yes	16	55.14	even	10
55.2.j.a.14.1	yes	16	55.9	even	10
55.2.j.a.14.4	yes	16	11.9	even	5
275.2.h.d.26.1		16	55.47	odd	20
275.2.h.d.26.4		16	55.3	odd	20
275.2.h.d.201.1		16	55.42	odd	20
275.2.h.d.201.4		16	55.53	odd	20
495.2.ba.a.289.1		16	33.20	odd	10
495.2.ba.a.289.4		16	165.119	odd	10
495.2.ba.a.334.1		16	165.14	odd	10
495.2.ba.a.334.4		16	33.14	odd	10
605.2.b.f.364.1		8	55.29	odd	10
605.2.b.f.364.8		8	11.7	odd	10
605.2.b.g.364.1		8	11.4	even	5
605.2.b.g.364.8		8	55.4	even	10
605.2.j.d.124.1		16	11.2	odd	10
605.2.j.d.124.4		16	55.24	odd	10
605.2.j.d.444.1		16	55.19	odd	10
605.2.j.d.444.4		16	11.8	odd	10
605.2.j.g.9.1		16	55.54	odd	2
605.2.j.g.9.4		16	11.10	odd	2
605.2.j.g.269.1		16	11.6	odd	10
605.2.j.g.269.4		16	55.39	odd	10
605.2.j.h.9.1		16	1.1	even	1	trivial
605.2.j.h.9.4		16	5.4	even	2	inner
605.2.j.h.269.1		16	55.49	even	10	inner
605.2.j.h.269.4		16	11.5	even	5	inner
880.2.cd.c.289.1		16	220.119	odd	10
880.2.cd.c.289.4		16	44.31	odd	10
880.2.cd.c.609.1		16	44.3	odd	10
880.2.cd.c.609.4		16	220.179	odd	10
3025.2.a.bk.1.1		8	55.7	even	20
3025.2.a.bk.1.8		8	55.18	even	20
3025.2.a.bl.1.1		8	55.48	odd	20
3025.2.a.bl.1.8		8	55.37	odd	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.92464 - 0.625353i) q^{2} +(-1.54035 - 2.12011i) q^{3} +(1.69513 + 1.23158i) q^{4} +(-2.19919 + 0.404418i) q^{5} +(1.63880 + 5.04369i) q^{6} +(0.567697 - 0.781367i) q^{7} +(-0.113351 - 0.156015i) q^{8} +(-1.19513 + 3.67823i) q^{9} +O(q^{10})\)	\(q+(-1.92464 - 0.625353i) q^{2} +(-1.54035 - 2.12011i) q^{3} +(1.69513 + 1.23158i) q^{4} +(-2.19919 + 0.404418i) q^{5} +(1.63880 + 5.04369i) q^{6} +(0.567697 - 0.781367i) q^{7} +(-0.113351 - 0.156015i) q^{8} +(-1.19513 + 3.67823i) q^{9} +(4.48555 + 0.596911i) q^{10} -5.49092i q^{12} +(4.30362 + 1.39833i) q^{13} +(-1.58124 + 1.14884i) q^{14} +(4.24493 + 4.03957i) q^{15} +(-1.17437 - 3.61433i) q^{16} +(3.17338 - 1.03109i) q^{17} +(4.60038 - 6.33188i) q^{18} +(2.65163 - 1.92652i) q^{19} +(-4.22599 - 2.02295i) q^{20} -2.53103 q^{21} +3.36643i q^{23} +(-0.156167 + 0.480634i) q^{24} +(4.67289 - 1.77879i) q^{25} +(-7.40846 - 5.38256i) q^{26} +(2.16214 - 0.702522i) q^{27} +(1.92464 - 0.625353i) q^{28} +(3.97470 + 2.88779i) q^{29} +(-5.64379 - 10.4293i) q^{30} +(-0.129282 + 0.397889i) q^{31} +8.07636i q^{32} -6.75241 q^{34} +(-0.932474 + 1.94796i) q^{35} +(-6.55594 + 4.76317i) q^{36} +(3.72512 - 5.12719i) q^{37} +(-6.30817 + 2.04965i) q^{38} +(-3.66446 - 11.2780i) q^{39} +(0.312377 + 0.297265i) q^{40} +(-4.68068 + 3.40071i) q^{41} +(4.87132 + 1.58279i) q^{42} +2.26205i q^{43} +(1.14077 - 8.57246i) q^{45} +(2.10520 - 6.47915i) q^{46} +(-2.54173 - 3.49838i) q^{47} +(-5.85383 + 8.05710i) q^{48} +(1.87486 + 5.77024i) q^{49} +(-10.1060 + 0.501317i) q^{50} +(-7.07414 - 5.13966i) q^{51} +(5.57303 + 7.67061i) q^{52} +(2.53047 + 0.822201i) q^{53} -4.60066 q^{54} -0.186254 q^{56} +(-8.16885 - 2.65422i) q^{57} +(-5.84397 - 8.04353i) q^{58} +(-8.19153 - 5.95150i) q^{59} +(2.22063 + 12.0756i) q^{60} +(-0.763537 - 2.34993i) q^{61} +(0.497642 - 0.684945i) q^{62} +(2.19558 + 3.02195i) q^{63} +(2.70184 - 8.31540i) q^{64} +(-10.0300 - 1.33473i) q^{65} -9.60059i q^{67} +(6.64917 + 2.16045i) q^{68} +(7.13718 - 5.18546i) q^{69} +(3.01284 - 3.16600i) q^{70} +(-1.68510 - 5.18621i) q^{71} +(0.709327 - 0.230474i) q^{72} +(-0.843791 + 1.16138i) q^{73} +(-10.3758 + 7.53847i) q^{74} +(-10.9691 - 7.16707i) q^{75} +6.86752 q^{76} +23.9977i q^{78} +(-0.310240 + 0.954820i) q^{79} +(4.04436 + 7.47367i) q^{80} +(4.56679 + 3.31797i) q^{81} +(11.1353 - 3.61806i) q^{82} +(7.03346 - 2.28531i) q^{83} +(-4.29042 - 3.11717i) q^{84} +(-6.56188 + 3.55095i) q^{85} +(1.41458 - 4.35363i) q^{86} -12.8750i q^{87} +12.1964 q^{89} +(-7.55639 + 15.7855i) q^{90} +(3.53576 - 2.56888i) q^{91} +(-4.14603 + 5.70652i) q^{92} +(1.04271 - 0.338796i) q^{93} +(2.70418 + 8.32259i) q^{94} +(-5.05232 + 5.30915i) q^{95} +(17.1227 - 12.4404i) q^{96} +(-2.87147 - 0.932997i) q^{97} -12.2781i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{4} - 2 q^{5} + 12 q^{6} + 2 q^{9}+O(q^{10}) \) 16 * q + 6 * q^4 - 2 * q^5 + 12 * q^6 + 2 * q^9	\( 16 q + 6 q^{4} - 2 q^{5} + 12 q^{6} + 2 q^{9} + 8 q^{14} + 24 q^{15} + 6 q^{16} + 6 q^{19} + 12 q^{20} + 8 q^{21} - 4 q^{24} + 24 q^{25} - 50 q^{26} + 22 q^{29} - 4 q^{30} - 22 q^{31} - 16 q^{34} - 8 q^{35} - 30 q^{36} + 12 q^{40} + 18 q^{41} + 12 q^{45} + 38 q^{46} - 20 q^{49} - 12 q^{50} - 12 q^{51} - 40 q^{54} - 20 q^{56} - 8 q^{59} - 2 q^{60} + 20 q^{61} + 22 q^{64} - 40 q^{65} + 6 q^{69} + 26 q^{70} + 6 q^{71} - 52 q^{74} + 40 q^{75} + 56 q^{76} - 22 q^{79} - 6 q^{80} - 32 q^{81} - 18 q^{84} - 62 q^{85} - 68 q^{86} + 24 q^{89} - 32 q^{90} - 56 q^{94} - 22 q^{95} + 94 q^{96}+O(q^{100}) \) 16 * q + 6 * q^4 - 2 * q^5 + 12 * q^6 + 2 * q^9 + 8 * q^14 + 24 * q^15 + 6 * q^16 + 6 * q^19 + 12 * q^20 + 8 * q^21 - 4 * q^24 + 24 * q^25 - 50 * q^26 + 22 * q^29 - 4 * q^30 - 22 * q^31 - 16 * q^34 - 8 * q^35 - 30 * q^36 + 12 * q^40 + 18 * q^41 + 12 * q^45 + 38 * q^46 - 20 * q^49 - 12 * q^50 - 12 * q^51 - 40 * q^54 - 20 * q^56 - 8 * q^59 - 2 * q^60 + 20 * q^61 + 22 * q^64 - 40 * q^65 + 6 * q^69 + 26 * q^70 + 6 * q^71 - 52 * q^74 + 40 * q^75 + 56 * q^76 - 22 * q^79 - 6 * q^80 - 32 * q^81 - 18 * q^84 - 62 * q^85 - 68 * q^86 + 24 * q^89 - 32 * q^90 - 56 * q^94 - 22 * q^95 + 94 * q^96

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