LMFDB - Embedded newform 575.2.k.g.101.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(26,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("575.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.k (of order $11$, degree $10$, 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:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 115)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			101.8
Character	$\chi$	$=$	575.101
Dual form			575.2.k.g.501.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34433 - 0.394732i) q^{2} +(1.70867 + 1.97191i) q^{3} +(-0.0310904 + 0.0199806i) q^{4} +(3.07540 + 1.97644i) q^{6} +(-1.22473 + 2.68179i) q^{7} +(-1.86894 + 2.15687i) q^{8} +(-0.541936 + 3.76925i) q^{9} +O(q^{10})$	\(q+(1.34433 - 0.394732i) q^{2} +(1.70867 + 1.97191i) q^{3} +(-0.0310904 + 0.0199806i) q^{4} +(3.07540 + 1.97644i) q^{6} +(-1.22473 + 2.68179i) q^{7} +(-1.86894 + 2.15687i) q^{8} +(-0.541936 + 3.76925i) q^{9} +(1.52091 + 0.446579i) q^{11} +(-0.0925233 - 0.0271673i) q^{12} +(-1.93920 - 4.24625i) q^{13} +(-0.587861 + 4.08866i) q^{14} +(-1.63039 + 3.57005i) q^{16} +(-1.11128 - 0.714176i) q^{17} +(0.759299 + 5.28104i) q^{18} +(4.70724 - 3.02516i) q^{19} +(-7.38094 + 2.16724i) q^{21} +2.22088 q^{22} +(1.60736 + 4.51845i) q^{23} -7.44658 q^{24} +(-4.28306 - 4.94291i) q^{26} +(-1.77358 + 1.13981i) q^{27} +(-0.0155063 - 0.107849i) q^{28} +(4.78017 + 3.07203i) q^{29} +(4.02560 - 4.64579i) q^{31} +(0.0297487 - 0.206907i) q^{32} +(1.71812 + 3.76216i) q^{33} +(-1.77584 - 0.521433i) q^{34} +(-0.0584628 - 0.128016i) q^{36} +(0.0325170 - 0.226161i) q^{37} +(5.13396 - 5.92491i) q^{38} +(5.05979 - 11.0794i) q^{39} +(-0.944912 - 6.57201i) q^{41} +(-9.06696 + 5.82698i) q^{42} +(4.05429 + 4.67889i) q^{43} +(-0.0562086 + 0.0165043i) q^{44} +(3.94440 + 5.43983i) q^{46} +9.26629 q^{47} +(-9.82563 + 2.88507i) q^{48} +(-1.10802 - 1.27872i) q^{49} +(-0.490520 - 3.41164i) q^{51} +(0.145133 + 0.0932714i) q^{52} +(-3.57091 + 7.81920i) q^{53} +(-1.93436 + 2.23238i) q^{54} +(-3.49533 - 7.65371i) q^{56} +(14.0085 + 4.11326i) q^{57} +(7.63876 + 2.24294i) q^{58} +(-4.84630 - 10.6119i) q^{59} +(-2.17039 + 2.50477i) q^{61} +(3.57791 - 7.83452i) q^{62} +(-9.44462 - 6.06969i) q^{63} +(-1.15877 - 8.05944i) q^{64} +(3.79477 + 4.37939i) q^{66} +(-10.1128 + 2.96939i) q^{67} +0.0488198 q^{68} +(-6.16355 + 10.8901i) q^{69} +(-7.18012 + 2.10827i) q^{71} +(-7.11694 - 8.21339i) q^{72} +(0.256729 - 0.164990i) q^{73} +(-0.0455592 - 0.316871i) q^{74} +(-0.0859054 + 0.188107i) q^{76} +(-3.06034 + 3.53182i) q^{77} +(2.42865 - 16.8916i) q^{78} +(3.42189 + 7.49289i) q^{79} +(5.68318 + 1.66873i) q^{81} +(-3.86445 - 8.46197i) q^{82} +(0.965140 - 6.71269i) q^{83} +(0.186174 - 0.214856i) q^{84} +(7.29721 + 4.68964i) q^{86} +(2.10997 + 14.6752i) q^{87} +(-3.80570 + 2.44578i) q^{88} +(-5.15177 - 5.94546i) q^{89} +13.7626 q^{91} +(-0.140255 - 0.108365i) q^{92} +16.0395 q^{93} +(12.4570 - 3.65770i) q^{94} +(0.458834 - 0.294875i) q^{96} +(-0.807595 - 5.61695i) q^{97} +(-1.99430 - 1.28166i) q^{98} +(-2.50750 + 5.49066i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9}+O(q^{10}) $ 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9	$ 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9} - 26 q^{11} + 26 q^{14} - 18 q^{16} + 14 q^{19} - 22 q^{21} + 68 q^{24} - 42 q^{26} + 24 q^{29} - 12 q^{31} - 8 q^{34} - 10 q^{36} - 14 q^{39} + 8 q^{41} - 166 q^{44} - 18 q^{46} - 32 q^{49} - 22 q^{51} - 116 q^{54} - 116 q^{56} - 50 q^{59} - 38 q^{61} - 10 q^{64} - 28 q^{66} - 80 q^{69} - 110 q^{71} - 22 q^{74} + 4 q^{76} - 42 q^{79} + 204 q^{81} - 56 q^{84} + 132 q^{86} + 66 q^{89} + 76 q^{91} + 70 q^{94} + 236 q^{96} + 60 q^{99}+O(q^{100}) $ 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9 - 26 * q^11 + 26 * q^14 - 18 * q^16 + 14 * q^19 - 22 * q^21 + 68 * q^24 - 42 * q^26 + 24 * q^29 - 12 * q^31 - 8 * q^34 - 10 * q^36 - 14 * q^39 + 8 * q^41 - 166 * q^44 - 18 * q^46 - 32 * q^49 - 22 * q^51 - 116 * q^54 - 116 * q^56 - 50 * q^59 - 38 * q^61 - 10 * q^64 - 28 * q^66 - 80 * q^69 - 110 * q^71 - 22 * q^74 + 4 * q^76 - 42 * q^79 + 204 * q^81 - 56 * q^84 + 132 * q^86 + 66 * q^89 + 76 * q^91 + 70 * q^94 + 236 * q^96 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/575\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	1.34433	−	0.394732i	0.950587	−	0.279117i	0.230555	−	0.973059i	$-0.425946\pi$
$2$	1.34433	−	0.394732i	0.950587	−	0.279117i	0.720031	+	0.693942i	$0.244128\pi$
$3$	1.70867	+	1.97191i	0.986503	+	1.13848i	0.990364	+	0.138492i	$0.0442256\pi$
$3$	1.70867	+	1.97191i	0.986503	+	1.13848i	−0.00386079	+	0.999993i	$0.501229\pi$
$4$	−0.0310904	+	0.0199806i	−0.0155452	+	0.00999030i
$5$		0			0
$5$		0			0
$6$	3.07540	+	1.97644i	1.25553	+	0.806878i
$7$	−1.22473	+	2.68179i	−0.462906	+	1.01362i	0.523909	+	0.851774i	$0.324473\pi$
$7$	−1.22473	+	2.68179i	−0.462906	+	1.01362i	−0.986816	+	0.161849i	$0.948254\pi$
$8$	−1.86894	+	2.15687i	−0.660771	+	0.762570i
$9$	−0.541936	+	3.76925i	−0.180645	+	1.25642i
$10$		0			0
$11$	1.52091	+	0.446579i	0.458571	+	0.134649i	0.502856	−	0.864370i	$-0.332283\pi$
$11$	1.52091	+	0.446579i	0.458571	+	0.134649i	−0.0442848	+	0.999019i	$0.514101\pi$
$12$	−0.0925233	−	0.0271673i	−0.0267092	−	0.00784252i
$13$	−1.93920	−	4.24625i	−0.537837	−	1.17770i	−0.962234	−	0.272222i	$-0.912241\pi$
$13$	−1.93920	−	4.24625i	−0.537837	−	1.17770i	0.424398	−	0.905476i	$-0.360486\pi$
$14$	−0.587861	+	4.08866i	−0.157113	+	1.09274i
$15$		0			0
$16$	−1.63039	+	3.57005i	−0.407597	+	0.892513i
$17$	−1.11128	−	0.714176i	−0.269525	−	0.173213i	0.398897	−	0.916996i	$-0.369393\pi$
$17$	−1.11128	−	0.714176i	−0.269525	−	0.173213i	−0.668421	+	0.743783i	$0.733030\pi$
$18$	0.759299	+	5.28104i	0.178968	+	1.24475i
$19$	4.70724	−	3.02516i	1.07991	−	0.694019i	0.125376	−	0.992109i	$-0.459986\pi$
$19$	4.70724	−	3.02516i	1.07991	−	0.694019i	0.954538	+	0.298091i	$0.0963498\pi$
$20$		0			0
$21$	−7.38094	+	2.16724i	−1.61065	+	0.472930i
$22$	2.22088			0.473494
$23$	1.60736	+	4.51845i	0.335157	+	0.942162i
$23$	1.60736	+	4.51845i	0.335157	+	0.942162i
$24$	−7.44658			−1.52003
$25$		0			0
$26$	−4.28306	−	4.94291i	−0.839976	−	0.969384i
$27$	−1.77358	+	1.13981i	−0.341326	+	0.219357i
$28$	−0.0155063	−	0.107849i	−0.00293042	−	0.0203815i
$29$	4.78017	+	3.07203i	0.887655	+	0.570461i	0.903105	−	0.429419i	$-0.141282\pi$
$29$	4.78017	+	3.07203i	0.887655	+	0.570461i	−0.0154501	+	0.999881i	$0.504918\pi$
$30$		0			0
$31$	4.02560	−	4.64579i	0.723020	−	0.834409i	−0.268647	−	0.963239i	$-0.586577\pi$
$31$	4.02560	−	4.64579i	0.723020	−	0.834409i	0.991667	+	0.128829i	$0.0411220\pi$
$32$	0.0297487	−	0.206907i	0.00525889	−	0.0365764i
$33$	1.71812	+	3.76216i	0.299086	+	0.654907i
$34$	−1.77584	−	0.521433i	−0.304553	−	0.0894249i
$35$		0			0
$36$	−0.0584628	−	0.128016i	−0.00974379	−	0.0213359i
$37$	0.0325170	−	0.226161i	0.00534577	−	0.0371806i	−0.986974	−	0.160880i	$-0.948567\pi$
$37$	0.0325170	−	0.226161i	0.00534577	−	0.0371806i	0.992320	+	0.123699i	$0.0394759\pi$
$38$	5.13396	−	5.92491i	0.832839	−	0.961147i
$39$	5.05979	−	11.0794i	0.810214	−	1.77412i
$40$		0			0
$41$	−0.944912	−	6.57201i	−0.147570	−	1.02637i	−0.920181	−	0.391494i	$-0.871958\pi$
$41$	−0.944912	−	6.57201i	−0.147570	−	1.02637i	0.772610	−	0.634881i	$-0.218951\pi$
$42$	−9.06696	+	5.82698i	−1.39906	+	0.899122i
$43$	4.05429	+	4.67889i	0.618273	+	0.713525i	0.975378	−	0.220539i	$-0.0707818\pi$
$43$	4.05429	+	4.67889i	0.618273	+	0.713525i	−0.357105	+	0.934064i	$0.616236\pi$
$44$	−0.0562086	+	0.0165043i	−0.00847376	+	0.00248812i
$45$		0			0
$46$	3.94440	+	5.43983i	0.581570	+	0.802059i
$47$	9.26629			1.35163			0.675813	−	0.737073i	$-0.263792\pi$
$47$	9.26629			1.35163			0.675813	+	0.737073i	$0.263792\pi$
$48$	−9.82563	+	2.88507i	−1.41821	+	0.416423i
$49$	−1.10802	−	1.27872i	−0.158289	−	0.182675i
$50$		0			0
$51$	−0.490520	−	3.41164i	−0.0686865	−	0.477725i
$52$	0.145133	+	0.0932714i	0.0201263	+	0.0129344i
$53$	−3.57091	+	7.81920i	−0.490502	+	1.07405i	0.488938	+	0.872318i	$0.337384\pi$
$53$	−3.57091	+	7.81920i	−0.490502	+	1.07405i	−0.979441	+	0.201732i	$0.935343\pi$
$54$	−1.93436	+	2.23238i	−0.263234	+	0.303788i
$55$		0			0
$56$	−3.49533	−	7.65371i	−0.467084	−	1.02277i
$57$	14.0085	+	4.11326i	1.85547	+	0.544814i
$58$	7.63876	+	2.24294i	1.00302	+	0.294513i
$59$	−4.84630	−	10.6119i	−0.630934	−	1.38155i	−0.907293	−	0.420499i	$-0.861855\pi$
$59$	−4.84630	−	10.6119i	−0.630934	−	1.38155i	0.276359	−	0.961055i	$-0.410872\pi$
$60$		0			0
$61$	−2.17039	+	2.50477i	−0.277891	+	0.320703i	−0.877488	−	0.479599i	$-0.840782\pi$
$61$	−2.17039	+	2.50477i	−0.277891	+	0.320703i	0.599597	+	0.800302i	$0.295328\pi$
$62$	3.57791	−	7.83452i	0.454395	−	0.994986i
$63$	−9.44462	−	6.06969i	−1.18991	−	0.764709i
$64$	−1.15877	−	8.05944i	−0.144847	−	1.00743i
$65$		0			0
$66$	3.79477	+	4.37939i	0.467103	+	0.539066i
$67$	−10.1128	+	2.96939i	−1.23548	+	0.362769i	−0.833315	−	0.552799i	$-0.813560\pi$
$67$	−10.1128	+	2.96939i	−1.23548	+	0.362769i	−0.402163	+	0.915568i	$0.631741\pi$
$68$	0.0488198			0.00592027
$69$	−6.16355	+	10.8901i	−0.742004	+	1.31102i
$70$		0			0
$71$	−7.18012	+	2.10827i	−0.852123	+	0.250206i	−0.678495	−	0.734605i	$-0.737367\pi$
$71$	−7.18012	+	2.10827i	−0.852123	+	0.250206i	−0.173628	+	0.984811i	$0.555549\pi$
$72$	−7.11694	−	8.21339i	−0.838740	−	0.967957i
$73$	0.256729	−	0.164990i	0.0300479	−	0.0193106i	−0.525531	−	0.850775i	$-0.676133\pi$
$73$	0.256729	−	0.164990i	0.0300479	−	0.0193106i	0.555579	+	0.831464i	$0.312497\pi$
$74$	−0.0455592	−	0.316871i	−0.00529615	−	0.0368355i
$75$		0			0
$76$	−0.0859054	+	0.188107i	−0.00985403	+	0.0215773i
$77$	−3.06034	+	3.53182i	−0.348758	+	0.402488i
$78$	2.42865	−	16.8916i	0.274990	−	1.91260i
$79$	3.42189	+	7.49289i	0.384992	+	0.843016i	0.998574	+	0.0533846i	$0.0170009\pi$
$79$	3.42189	+	7.49289i	0.384992	+	0.843016i	−0.613582	+	0.789631i	$0.710272\pi$
$80$		0			0
$81$	5.68318	+	1.66873i	0.631465	+	0.185415i
$82$	−3.86445	−	8.46197i	−0.426758	−	0.934469i
$83$	0.965140	−	6.71269i	0.105938	−	0.736814i	−0.865738	−	0.500497i	$-0.833151\pi$
$83$	0.965140	−	6.71269i	0.105938	−	0.736814i	0.971676	−	0.236317i	$-0.0759403\pi$
$84$	0.186174	−	0.214856i	0.0203132	−	0.0234427i
$85$		0			0
$86$	7.29721	+	4.68964i	0.786879	+	0.505696i
$87$	2.10997	+	14.6752i	0.226213	+	1.57334i
$88$	−3.80570	+	2.44578i	−0.405689	+	0.260721i
$89$	−5.15177	−	5.94546i	−0.546086	−	0.630217i	0.413881	−	0.910331i	$-0.364173\pi$
$89$	−5.15177	−	5.94546i	−0.546086	−	0.630217i	−0.959967	+	0.280114i	$0.909628\pi$
$90$		0			0
$91$	13.7626			1.44271
$92$	−0.140255	−	0.108365i	−0.0146226	−	0.0112978i
$93$	16.0395			1.66322
$94$	12.4570	−	3.65770i	1.28484	−	0.377263i
$95$		0			0
$96$	0.458834	−	0.294875i	0.0468295	−	0.0300955i
$97$	−0.807595	−	5.61695i	−0.0819989	−	0.570315i	−0.988856	−	0.148876i	$-0.952434\pi$
$97$	−0.807595	−	5.61695i	−0.0819989	−	0.570315i	0.906857	−	0.421438i	$-0.138475\pi$
$98$	−1.99430	−	1.28166i	−0.201455	−	0.129467i
$99$	−2.50750	+	5.49066i	−0.252013	+	0.551832i
$100$		0			0
$101$	0.745671	−	5.18625i	0.0741970	−	0.516052i	−0.918500	−	0.395420i	$-0.870599\pi$
$101$	0.745671	−	5.18625i	0.0741970	−	0.516052i	0.992697	−	0.120631i	$-0.0384919\pi$
$102$	−2.00610	−	4.39275i	−0.198634	−	0.434947i
$103$	−17.8877	−	5.25232i	−1.76253	−	0.517526i	−0.769844	−	0.638232i	$-0.779666\pi$
$103$	−17.8877	−	5.25232i	−1.76253	−	0.517526i	−0.992688	+	0.120706i	$0.961484\pi$
$104$	12.7829	+	3.75339i	1.25346	+	0.368050i
$105$		0			0
$106$	−1.71400	+	11.9212i	−0.166479	+	1.15789i
$107$	5.07730	−	5.85951i	0.490841	−	0.566460i	−0.455249	−	0.890364i	$-0.650450\pi$
$107$	5.07730	−	5.85951i	0.490841	−	0.566460i	0.946090	+	0.323904i	$0.104995\pi$
$108$	0.0323673	−	0.0708745i	0.00311454	−	0.00681990i
$109$	−4.92636	−	3.16598i	−0.471860	−	0.303246i	0.283014	−	0.959116i	$-0.408666\pi$
$109$	−4.92636	−	3.16598i	−0.471860	−	0.303246i	−0.754874	+	0.655870i	$0.772302\pi$
$110$		0			0
$111$	0.501531	−	0.322314i	0.0476032	−	0.0305927i
$112$	−7.57735	−	8.74473i	−0.715992	−	0.826299i
$113$	8.72074	−	2.56064i	0.820378	−	0.240885i	0.155499	−	0.987836i	$-0.450301\pi$
$113$	8.72074	−	2.56064i	0.820378	−	0.240885i	0.664879	+	0.746951i	$0.268483\pi$
$114$	20.4557			1.91585
$115$		0			0
$116$	−0.209998			−0.0194979
$117$	17.0561	−	5.00812i	1.57684	−	0.463001i
$118$	−10.7039	−	12.3530i	−0.985374	−	1.13718i
$119$	3.27629	−	2.10555i	0.300337	−	0.193015i
$120$		0			0
$121$	−7.14006	−	4.58864i	−0.649096	−	0.417149i
$122$	−1.92902	+	4.22397i	−0.174645	+	0.382420i
$123$	11.3449	−	13.0927i	1.02293	−	1.18053i
$124$	−0.0323319	+	0.224874i	−0.00290349	+	0.0201942i
$125$		0			0
$126$	−15.0926	−	4.43159i	−1.34456	−	0.394797i
$127$	6.07417	+	1.78354i	0.538996	+	0.158263i	0.539889	−	0.841736i	$-0.318466\pi$
$127$	6.07417	+	1.78354i	0.538996	+	0.158263i	−0.000893287		1.00000i	$0.500284\pi$
$128$	−4.56542	−	9.99687i	−0.403530	−	0.883607i
$129$	−2.29893	+	15.9894i	−0.202409	+	1.40779i
$130$		0			0
$131$	−1.99588	+	4.37037i	−0.174381	+	0.381841i	−0.976561	−	0.215241i	$-0.930946\pi$
$131$	−1.99588	+	4.37037i	−0.174381	+	0.381841i	0.802180	+	0.597082i	$0.203673\pi$
$132$	−0.128587	−	0.0826379i	−0.0111921	−	0.00719271i
$133$	2.34773	+	16.3289i	0.203574	+	1.41589i
$134$	−12.4229	+	7.98370i	−1.07317	+	0.689687i
$135$		0			0
$136$	3.61730	−	1.06214i	0.310181	−	0.0910774i
$137$	−4.56852			−0.390315			−0.195158	−	0.980772i	$-0.562522\pi$
$137$	−4.56852			−0.390315			−0.195158	+	0.980772i	$0.562522\pi$
$138$	−3.98718	+	17.0729i	−0.339411	+	1.45334i
$139$	15.2156			1.29057			0.645284	−	0.763943i	$-0.276739\pi$
$139$	15.2156			1.29057			0.645284	+	0.763943i	$0.276739\pi$
$140$		0			0
$141$	15.8331	+	18.2723i	1.33338	+	1.53881i
$142$	−8.82026	+	5.66844i	−0.740180	+	0.475685i
$143$	−1.05306	−	7.32416i	−0.0880609	−	0.612477i
$144$	−12.5728	−	8.08007i	−1.04774	−	0.673339i
$145$		0			0
$146$	0.280003	−	0.323141i	0.0231732	−	0.0267433i
$147$	0.628289	−	4.36984i	0.0518204	−	0.360419i
$148$	0.00350786	+	0.00768115i	0.000288345	+	0.000631386i
$149$	−9.48896	−	2.78621i	−0.777366	−	0.228255i	−0.131101	−	0.991369i	$-0.541851\pi$
$149$	−9.48896	−	2.78621i	−0.777366	−	0.228255i	−0.646264	+	0.763114i	$0.723670\pi$
$150$		0			0
$151$	−7.52665	−	16.4811i	−0.612510	−	1.34121i	−0.920844	−	0.389932i	$-0.872499\pi$
$151$	−7.52665	−	16.4811i	−0.612510	−	1.34121i	0.308333	−	0.951278i	$-0.400229\pi$
$152$	−2.27267	+	15.8068i	−0.184338	+	1.28210i
$153$	3.29415	−	3.80165i	0.266316	−	0.307345i
$154$	−2.71999	+	5.95596i	−0.219183	+	0.479945i
$155$		0			0
$156$	0.0640619	+	0.445560i	0.00512905	+	0.0356734i
$157$	−19.0071	+	12.2151i	−1.51693	+	0.974873i	−0.524590	+	0.851355i	$0.675781\pi$
$157$	−19.0071	+	12.2151i	−1.51693	+	0.974873i	−0.992342	+	0.123518i	$0.960582\pi$
$158$	7.55784	+	8.72221i	0.601269	+	0.693902i
$159$	−21.5203	+	6.31893i	−1.70667	+	0.501124i
$160$		0			0
$161$	−14.0861	−	1.22330i	−1.11014	−	0.0964095i
$162$	8.29879			0.652014
$163$	−6.18810	+	1.81699i	−0.484689	+	0.142318i	−0.514943	−	0.857225i	$-0.672187\pi$
$163$	−6.18810	+	1.81699i	−0.484689	+	0.142318i	0.0302534	+	0.999542i	$0.490369\pi$
$164$	0.160690	+	0.185446i	0.0125478	+	0.0144809i
$165$		0			0
$166$	−1.35224	−	9.40506i	−0.104954	−	0.729974i
$167$	−8.22194	−	5.28392i	−0.636233	−	0.408882i	0.182380	−	0.983228i	$-0.441620\pi$
$167$	−8.22194	−	5.28392i	−0.636233	−	0.408882i	−0.818613	+	0.574346i	$0.805256\pi$
$168$	9.12008	−	19.9702i	0.703630	−	1.54073i
$169$	−5.75697	+	6.64390i	−0.442844	+	0.511069i
$170$		0			0
$171$	8.85154	+	19.3822i	0.676894	+	1.48219i
$172$	−0.219536	−	0.0644617i	−0.0167395	−	0.00491516i
$173$	8.63190	+	2.53455i	0.656271	+	0.192699i	0.592881	−	0.805290i	$-0.297991\pi$
$173$	8.63190	+	2.53455i	0.656271	+	0.192699i	0.0633903	+	0.997989i	$0.479809\pi$
$174$	8.62926	+	18.8954i	0.654182	+	1.43246i
$175$		0			0
$176$	−4.07398	+	4.70162i	−0.307088	+	0.354398i
$177$	12.6450	−	27.6888i	0.950459	−	2.08122i
$178$	−9.27255	−	5.95910i	−0.695007	−	0.446654i
$179$	−1.93200	−	13.4374i	−0.144405	−	1.00436i	−0.925175	−	0.379540i	$-0.876082\pi$
$179$	−1.93200	−	13.4374i	−0.144405	−	1.00436i	0.780771	−	0.624818i	$-0.214827\pi$
$180$		0			0
$181$	−2.05334	−	2.36968i	−0.152623	−	0.176137i	0.674289	−	0.738468i	$-0.264450\pi$
$181$	−2.05334	−	2.36968i	−0.152623	−	0.176137i	−0.826912	+	0.562331i	$0.809905\pi$
$182$	18.5015	−	5.43252i	1.37142	−	0.402685i
$183$	−8.64768			−0.639255
$184$	−12.7498	−	4.97785i	−0.939927	−	0.366972i
$185$		0			0
$186$	21.5625	−	6.33131i	1.58104	−	0.464235i
$187$	−1.37122	−	1.58247i	−0.100273	−	0.115722i
$188$	−0.288093	+	0.185146i	−0.0210113	+	0.0135032i
$189$	−0.884575	−	6.15235i	−0.0643433	−	0.447518i
$190$		0			0
$191$	0.574624	−	1.25825i	0.0415783	−	0.0910439i	−0.887703	−	0.460416i	$-0.847700\pi$
$191$	0.574624	−	1.25825i	0.0415783	−	0.0910439i	0.929281	+	0.369373i	$0.120427\pi$
$192$	13.9126	−	16.0559i	1.00405	−	1.15874i
$193$	0.374166	−	2.60238i	0.0269331	−	0.187324i	−0.971914	−	0.235338i	$-0.924380\pi$
$193$	0.374166	−	2.60238i	0.0269331	−	0.187324i	0.998847	+	0.0480145i	$0.0152894\pi$
$194$	−3.30286	−	7.23226i	−0.237132	−	0.519246i
$195$		0			0
$196$	0.0599985	+	0.0176172i	0.00428561	+	0.00125837i
$197$	5.80756	+	12.7168i	0.413771	+	0.906033i	0.995686	+	0.0927834i	$0.0295764\pi$
$197$	5.80756	+	12.7168i	0.413771	+	0.906033i	−0.581915	+	0.813250i	$0.697696\pi$
$198$	−1.20358	+	8.37106i	−0.0855345	+	0.594905i
$199$	−8.88720	+	10.2564i	−0.629997	+	0.727055i	−0.977573	−	0.210597i	$-0.932459\pi$
$199$	−8.88720	+	10.2564i	−0.629997	+	0.727055i	0.347576	+	0.937652i	$0.387005\pi$
$200$		0			0
$201$	−23.1349	−	14.8679i	−1.63181	−	1.04870i
$202$	−1.04475	−	7.26639i	−0.0735083	−	0.511261i
$203$	−14.0930	+	9.05701i	−0.989134	+	0.635678i
$204$	0.0834170	+	0.0962684i	0.00584036	+	0.00674013i
$205$		0			0
$206$	−26.1203			−1.81989
$207$	−17.9022	+	3.60982i	−1.24429	+	0.250900i
$208$	18.3210			1.27033
$209$	8.51024	−	2.49883i	0.588666	−	0.172848i
$210$		0			0
$211$	5.33889	−	3.43110i	0.367545	−	0.236207i	−0.343811	−	0.939039i	$-0.611718\pi$
$211$	5.33889	−	3.43110i	0.367545	−	0.236207i	0.711356	+	0.702832i	$0.248082\pi$
$212$	−0.0452113	−	0.314451i	−0.00310512	−	0.0215966i
$213$	−16.4258	−	10.5562i	−1.12548	−	0.723300i
$214$	4.51264	−	9.88130i	0.308478	−	0.675472i
$215$		0			0
$216$	0.856291	−	5.95564i	0.0582632	−	0.405230i
$217$	7.52877	+	16.4857i	0.511086	+	1.11912i
$218$	−7.87238	−	2.31154i	−0.533185	−	0.156557i
$219$	0.764012	+	0.224334i	0.0516272	+	0.0151591i
$220$		0			0
$221$	−0.877579	+	6.10370i	−0.0590324	+	0.410579i
$222$	0.546997	−	0.631268i	0.0367120	−	0.0423679i
$223$	4.00377	−	8.76703i	0.268112	−	0.587084i	−0.726911	−	0.686732i	$-0.759045\pi$
$223$	4.00377	−	8.76703i	0.268112	−	0.587084i	0.995023	+	0.0996485i	$0.0317718\pi$
$224$	0.518448	+	0.333186i	0.0346403	+	0.0222619i
$225$		0			0
$226$	10.7128	−	6.88471i	0.712606	−	0.457964i
$227$	12.2919	+	14.1856i	0.815841	+	0.941530i	0.999137	−	0.0415273i	$-0.0132223\pi$
$227$	12.2919	+	14.1856i	0.815841	+	0.941530i	−0.183297	+	0.983058i	$0.558677\pi$
$228$	−0.517714	+	0.152015i	−0.0342865	+	0.0100674i
$229$	16.6093			1.09757			0.548786	−	0.835963i	$-0.315090\pi$
$229$	16.6093			1.09757			0.548786	+	0.835963i	$0.315090\pi$
$230$		0			0
$231$	−12.1936			−0.802278
$232$	−15.5598	+	4.56878i	−1.02155	+	0.299955i
$233$	−8.84581	−	10.2086i	−0.579509	−	0.668789i	0.387990	−	0.921663i	$-0.373169\pi$
$233$	−8.84581	−	10.2086i	−0.579509	−	0.668789i	−0.967499	+	0.252875i	$0.918624\pi$
$234$	20.9522	−	13.4652i	1.36969	−	0.880245i
$235$		0			0
$236$	0.362706	+	0.233097i	0.0236101	+	0.0151733i
$237$	−8.92844	+	19.5506i	−0.579965	+	1.26995i
$238$	3.57330	−	4.12381i	0.231623	−	0.267307i
$239$	0.556606	−	3.87128i	0.0360038	−	0.250412i	−0.963869	−	0.266378i	$-0.914173\pi$
$239$	0.556606	−	3.87128i	0.0360038	−	0.250412i	0.999873	+	0.0159656i	$0.00508221\pi$
$240$		0			0
$241$	9.35355	+	2.74645i	0.602515	+	0.176914i	0.568743	−	0.822515i	$-0.307430\pi$
$241$	9.35355	+	2.74645i	0.602515	+	0.176914i	0.0337718	+	0.999430i	$0.489248\pi$
$242$	−11.4099	−	3.35025i	−0.733456	−	0.215362i
$243$	9.04751	+	19.8113i	0.580398	+	1.27089i
$244$	0.0174317	−	0.121240i	0.00111595	−	0.00776160i
$245$		0			0
$246$	10.0832	−	22.0791i	0.642881	−	1.40771i
$247$	−21.9738	−	14.1217i	−1.39816	−	0.898544i
$248$	2.49677	+	17.3654i	0.158545	+	1.10271i
$249$	14.8860	−	9.56662i	0.943359	−	0.606260i
$250$		0			0
$251$	16.5033	−	4.84581i	1.04168	−	0.305865i	0.284228	−	0.958757i	$-0.408263\pi$
$251$	16.5033	−	4.84581i	1.04168	−	0.305865i	0.757451	+	0.652892i	$0.226444\pi$
$252$	0.414913			0.0261371
$253$	0.426798	+	7.58996i	0.0268326	+	0.477177i
$254$	8.86973			0.556536
$255$		0			0
$256$	0.580645	+	0.670100i	0.0362903	+	0.0418812i
$257$	−7.47940	+	4.80672i	−0.466552	+	0.299835i	−0.752715	−	0.658346i	$-0.771256\pi$
$257$	−7.47940	+	4.80672i	−0.466552	+	0.299835i	0.286163	+	0.958181i	$0.407620\pi$
$258$	3.22100	+	22.4025i	0.200531	+	1.39472i
$259$	0.566693	+	0.364191i	0.0352126	+	0.0226297i
$260$		0			0
$261$	−14.1698	+	16.3528i	−0.877087	+	1.01221i
$262$	−0.958004	+	6.66307i	−0.0591857	+	0.411646i
$263$	1.07753	+	2.35945i	0.0664431	+	0.145490i	0.939940	−	0.341339i	$-0.110881\pi$
$263$	1.07753	+	2.35945i	0.0664431	+	0.145490i	−0.873497	+	0.486830i	$0.838153\pi$
$264$	−11.3256	−	3.32548i	−0.697040	−	0.204669i
$265$		0			0
$266$	9.60165	+	21.0247i	0.588715	+	1.28911i
$267$	2.92124	−	20.3177i	0.178777	−	1.24342i
$268$	0.255081	−	0.294380i	0.0155816	−	0.0179821i
$269$	1.13907	−	2.49422i	0.0694504	−	0.152075i	−0.871723	−	0.489999i	$-0.836997\pi$
$269$	1.13907	−	2.49422i	0.0694504	−	0.152075i	0.941174	+	0.337924i	$0.109725\pi$
$270$		0			0
$271$	1.97254	+	13.7193i	0.119823	+	0.833390i	0.957749	+	0.287606i	$0.0928593\pi$
$271$	1.97254	+	13.7193i	0.119823	+	0.833390i	−0.837925	+	0.545785i	$0.816232\pi$
$272$	4.36146	−	2.80294i	0.264452	−	0.169953i
$273$	23.5157	+	27.1386i	1.42324	+	1.64250i
$274$	−6.14161	+	1.80334i	−0.371028	+	0.108944i
$275$		0			0
$276$	−0.0259640	−	0.461730i	−0.00156285	−	0.0277929i
$277$	2.92978			0.176033			0.0880167	−	0.996119i	$-0.471947\pi$
$277$	2.92978			0.176033			0.0880167	+	0.996119i	$0.471947\pi$
$278$	20.4548	−	6.00607i	1.22680	−	0.360220i
$279$	15.3295	+	17.6912i	0.917754	+	1.05915i
$280$		0			0
$281$	3.47962	+	24.2013i	0.207577	+	1.44373i	0.781032	+	0.624491i	$0.214694\pi$
$281$	3.47962	+	24.2013i	0.207577	+	1.44373i	−0.573455	+	0.819237i	$0.694397\pi$
$282$	28.4975	+	18.3143i	1.69700	+	1.09060i
$283$	−8.27096	+	18.1109i	−0.491657	+	1.07658i	0.487434	+	0.873160i	$0.337933\pi$
$283$	−8.27096	+	18.1109i	−0.491657	+	1.07658i	−0.979092	+	0.203420i	$0.934794\pi$
$284$	0.181108	−	0.209010i	0.0107468	−	0.0124025i
$285$		0			0
$286$	−4.30673	−	9.43043i	−0.254663	−	0.557633i
$287$	18.7820	+	5.51490i	1.10867	+	0.325534i
$288$	0.763762	+	0.224261i	0.0450051	+	0.0132147i
$289$	−6.33716	−	13.8764i	−0.372774	−	0.816262i
$290$		0			0
$291$	9.69622	−	11.1900i	0.568402	−	0.655971i
$292$	−0.00468522	+	0.0102592i	−0.000274182	+	0.000600375i
$293$	9.43634	+	6.06437i	0.551277	+	0.354284i	0.786435	−	0.617673i	$-0.211924\pi$
$293$	9.43634	+	6.06437i	0.551277	+	0.354284i	−0.235158	+	0.971957i	$0.575561\pi$
$294$	−0.880287	−	6.12253i	−0.0513394	−	0.357073i
$295$		0			0
$296$	0.427028	+	0.492817i	0.0248205	+	0.0286444i
$297$	−3.20647	+	0.941505i	−0.186058	+	0.0546317i
$298$	−13.8561			−0.802663
$299$	16.0695	−	15.5874i	0.929323	−	0.901443i
$300$		0			0
$301$	−17.5133	+	5.14236i	−1.00945	+	0.296400i
$302$	−16.6239	−	19.1850i	−0.956599	−	1.10397i
$303$	11.5010	−	7.39121i	0.660713	−	0.424614i
$304$	3.12534	+	21.7372i	0.179251	+	1.24672i
$305$		0			0
$306$	2.92780	−	6.41098i	0.167371	−	0.366491i
$307$	4.97852	−	5.74551i	0.284139	−	0.327914i	−0.595681	−	0.803221i	$-0.703118\pi$
$307$	4.97852	−	5.74551i	0.284139	−	0.327914i	0.879820	+	0.475307i	$0.157663\pi$
$308$	0.0245794	−	0.170953i	0.00140054	−	0.00974096i
$309$	−20.2072	−	44.2476i	−1.14955	−	2.51716i
$310$		0			0
$311$	16.5580	+	4.86186i	0.938916	+	0.275691i	0.715165	−	0.698956i	$-0.246351\pi$
$311$	16.5580	+	4.86186i	0.938916	+	0.275691i	0.223751	+	0.974646i	$0.428170\pi$
$312$	14.4404	+	31.6200i	0.817526	+	1.79013i
$313$	0.385977	−	2.68453i	0.0218167	−	0.151738i	−0.976001	−	0.217765i	$-0.930123\pi$
$313$	0.385977	−	2.68453i	0.0218167	−	0.151738i	0.997818	+	0.0660270i	$0.0210323\pi$
$314$	−20.7302	+	23.9239i	−1.16987	+	1.35010i
$315$		0			0
$316$	−0.256100	−	0.164586i	−0.0144068	−	0.00925867i
$317$	0.417211	+	2.90177i	0.0234329	+	0.162980i	0.998178	−	0.0603419i	$-0.0192191\pi$
$317$	0.417211	+	2.90177i	0.0234329	+	0.162980i	−0.974745	+	0.223322i	$0.928310\pi$
$318$	−26.4362	+	16.9895i	−1.48247	+	0.952724i
$319$	5.89829	+	6.80699i	0.330241	+	0.381118i
$320$		0			0
$321$	20.2299			1.12912
$322$	−19.4193	+	3.91572i	−1.08220	+	0.218215i
$323$	−7.39154			−0.411277
$324$	−0.210035	+	0.0616717i	−0.0116686	+	0.00342621i
$325$		0			0
$326$	−7.60164	+	4.88528i	−0.421016	+	0.270570i
$327$	−2.17450	−	15.1240i	−0.120250	−	0.836358i
$328$	15.9410	+	10.2446i	0.880193	+	0.565666i
$329$	−11.3487	+	24.8503i	−0.625676	+	1.37004i
$330$		0			0
$331$	−1.19997	+	8.34600i	−0.0659565	+	0.458738i	0.929901	+	0.367810i	$0.119892\pi$
$331$	−1.19997	+	8.34600i	−0.0659565	+	0.458738i	−0.995857	+	0.0909277i	$0.971017\pi$
$332$	0.104117	+	0.227984i	0.00571416	+	0.0125123i
$333$	0.834834	+	0.245129i	0.0457486	+	0.0134330i
$334$	−13.1388	−	3.85789i	−0.718921	−	0.211094i
$335$		0			0
$336$	4.29664	−	29.8838i	0.234401	−	1.63029i
$337$	−2.23956	+	2.58459i	−0.121997	+	0.140792i	−0.813462	−	0.581618i	$-0.802420\pi$
$337$	−2.23956	+	2.58459i	−0.121997	+	0.140792i	0.691465	+	0.722410i	$0.256965\pi$
$338$	−5.11672	+	11.2041i	−0.278313	+	0.609421i
$339$	19.9503	+	12.8213i	1.08355	+	0.696355i
$340$		0			0
$341$	8.19728	−	5.26808i	0.443908	−	0.285282i
$342$	19.5502	+	22.5621i	1.05715	+	1.22002i
$343$	−15.0153	+	4.40888i	−0.810748	+	0.238057i
$344$	−17.6690			−0.952649
$345$		0			0
$346$	12.6046			0.677628
$347$	6.96754	−	2.04586i	0.374037	−	0.109827i	−0.0893103	−	0.996004i	$-0.528466\pi$
$347$	6.96754	−	2.04586i	0.374037	−	0.109827i	0.463348	+	0.886177i	$0.346648\pi$
$348$	−0.358818	−	0.414099i	−0.0192347	−	0.0221980i
$349$	−29.2341	+	18.7876i	−1.56487	+	1.00568i	−0.583825	+	0.811879i	$0.698445\pi$
$349$	−29.2341	+	18.7876i	−1.56487	+	1.00568i	−0.981041	+	0.193799i	$0.937919\pi$
$350$		0			0
$351$	8.27926	+	5.32076i	0.441914	+	0.284001i
$352$	0.137645	−	0.301401i	0.00733653	−	0.0160648i
$353$	15.6748	−	18.0897i	0.834284	−	0.962815i	−0.165442	−	0.986220i	$-0.552905\pi$
$353$	15.6748	−	18.0897i	0.834284	−	0.962815i	0.999726	+	0.0234042i	$0.00745047\pi$
$354$	6.06950	−	42.2143i	0.322590	−	2.24367i
$355$		0			0
$356$	0.278964	+	0.0819113i	0.0147851	+	0.00434129i
$357$	9.75007	+	2.86288i	0.516028	+	0.151520i
$358$	−7.90142	−	17.3017i	−0.417603	−	0.914423i
$359$	−1.74258	+	12.1199i	−0.0919697	+	0.639663i	0.890740	+	0.454512i	$0.150186\pi$
$359$	−1.74258	+	12.1199i	−0.0919697	+	0.639663i	−0.982710	+	0.185151i	$0.940723\pi$
$360$		0			0
$361$	5.11361	−	11.1972i	0.269137	−	0.589328i
$362$	−3.69575	−	2.37512i	−0.194244	−	0.124833i
$363$	−3.15163	−	21.9201i	−0.165418	−	1.15051i
$364$	−0.427884	+	0.274984i	−0.0224272	+	0.0144131i
$365$		0			0
$366$	−11.6254	+	3.41351i	−0.607667	+	0.178427i
$367$	−0.210443			−0.0109850			−0.00549251	−	0.999985i	$-0.501748\pi$
$367$	−0.210443			−0.0109850			−0.00549251	+	0.999985i	$0.501748\pi$
$368$	−18.7517	−	1.62848i	−0.977501	−	0.0848903i
$369$	25.2836			1.31621
$370$		0			0
$371$	−16.5961	−	19.1529i	−0.861626	−	0.994369i
$372$	−0.498676	+	0.320480i	−0.0258551	+	0.0166161i
$373$	1.62071	+	11.2723i	0.0839170	+	0.583655i	0.987783	+	0.155839i	$0.0498080\pi$
$373$	1.62071	+	11.2723i	0.0839170	+	0.583655i	−0.903866	+	0.427817i	$0.859283\pi$
$374$	−2.46802	−	1.58610i	−0.127618	−	0.0820154i
$375$		0			0
$376$	−17.3182	+	19.9862i	−0.893115	+	1.03071i
$377$	3.77491	−	26.2551i	0.194418	−	1.35220i
$378$	−3.61769	−	7.92164i	−0.186074	−	0.407445i
$379$	−8.35975	−	2.45465i	−0.429412	−	0.126087i	0.0598825	−	0.998205i	$-0.480927\pi$
$379$	−8.35975	−	2.45465i	−0.429412	−	0.126087i	−0.489294	+	0.872119i	$0.662746\pi$
$380$		0			0
$381$	6.86179	+	15.0252i	0.351540	+	0.769766i
$382$	0.275814	−	1.91833i	0.0141119	−	0.0981503i
$383$	5.31344	−	6.13203i	0.271504	−	0.313332i	−0.603581	−	0.797302i	$-0.706260\pi$
$383$	5.31344	−	6.13203i	0.271504	−	0.313332i	0.875085	+	0.483969i	$0.160805\pi$
$384$	11.9122	−	26.0840i	0.607890	−	1.33109i
$385$		0			0
$386$	−0.524239	−	3.64616i	−0.0266831	−	0.185585i
$387$	−19.8331	+	12.7459i	−1.00817	+	0.647912i
$388$	0.137338	+	0.158497i	0.00697230	+	0.00804646i
$389$	29.3900	−	8.62967i	1.49013	−	0.437542i	0.567548	−	0.823341i	$-0.307892\pi$
$389$	29.3900	−	8.62967i	1.49013	−	0.437542i	0.922583	+	0.385799i	$0.126074\pi$
$390$		0			0
$391$	1.44074	−	6.16920i	0.0728616	−	0.311990i
$392$	4.82887			0.243895
$393$	−12.0283	+	3.53183i	−0.606747	+	0.178157i
$394$	12.8270	+	14.8032i	0.646215	+	0.745772i
$395$		0			0
$396$	−0.0317474	−	0.220808i	−0.00159537	−	0.0110960i
$397$	−21.8887	−	14.0670i	−1.09856	−	0.706004i	−0.139792	−	0.990181i	$-0.544643\pi$
$397$	−21.8887	−	14.0670i	−1.09856	−	0.706004i	−0.958772	+	0.284177i	$0.908280\pi$
$398$	−7.89883	+	17.2960i	−0.395933	+	0.866972i
$399$	−28.1876	+	32.5302i	−1.41114	+	1.62855i
$400$		0			0
$401$	−13.4921	−	29.5435i	−0.673762	−	1.47533i	−0.869120	−	0.494601i	$-0.835314\pi$
$401$	−13.4921	−	29.5435i	−0.673762	−	1.47533i	0.195358	−	0.980732i	$-0.437413\pi$
$402$	−36.9698	−	10.8553i	−1.84389	−	0.541414i
$403$	−27.5336	−	8.08461i	−1.37155	−	0.402723i
$404$	0.0804412	+	0.176142i	0.00400210	+	0.00876338i
$405$		0			0
$406$	−15.3706	+	17.7386i	−0.762828	+	0.880351i
$407$	0.150454	−	0.329449i	0.00745774	−	0.0163302i
$408$	8.27523	+	5.31816i	0.409685	+	0.263288i
$409$	2.99322	+	20.8183i	0.148005	+	1.02940i	0.919479	+	0.393138i	$0.128611\pi$
$409$	2.99322	+	20.8183i	0.148005	+	1.02940i	−0.771474	+	0.636261i	$0.780480\pi$
$410$		0			0
$411$	−7.80611	−	9.00873i	−0.385047	−	0.444368i
$412$	0.661082	−	0.194111i	0.0325692	−	0.00956317i
$413$	34.3944			1.69244
$414$	−22.6417	+	11.9194i	−1.11278	+	0.585805i
$415$		0			0
$416$	−0.936268	+	0.274913i	−0.0459043	+	0.0134787i
$417$	25.9984	+	30.0038i	1.27315	+	1.46929i
$418$	10.4542	−	6.71852i	0.511333	−	0.328614i
$419$	−1.82939	−	12.7237i	−0.0893716	−	0.621593i	−0.984447	−	0.175679i	$-0.943788\pi$
$419$	−1.82939	−	12.7237i	−0.0893716	−	0.621593i	0.895076	−	0.445914i	$-0.147121\pi$
$420$		0			0
$421$	−10.5373	+	23.0735i	−0.513558	+	1.12453i	0.458264	+	0.888816i	$0.348471\pi$
$421$	−10.5373	+	23.0735i	−0.513558	+	1.12453i	−0.971821	+	0.235718i	$0.924256\pi$
$422$	5.82288	−	6.71997i	0.283454	−	0.327123i
$423$	−5.02173	+	34.9269i	−0.244165	+	1.69820i
$424$	−10.1912	−	22.3156i	−0.494929	−	1.08374i
$425$		0			0
$426$	−26.2486	−	7.70729i	−1.27175	−	0.373419i
$427$	−4.05912	−	8.88823i	−0.196435	−	0.430132i
$428$	−0.0407787	+	0.283622i	−0.00197111	+	0.0137094i
$429$	12.6433	−	14.5911i	0.610424	−	0.704466i
$430$		0			0
$431$	16.3004	+	10.4756i	0.785163	+	0.504594i	0.870743	−	0.491738i	$-0.163638\pi$
$431$	16.3004	+	10.4756i	0.785163	+	0.504594i	−0.0855803	+	0.996331i	$0.527274\pi$
$432$	−1.17756	−	8.19012i	−0.0566554	−	0.394047i
$433$	6.50727	−	4.18197i	0.312720	−	0.200973i	−0.374860	−	0.927081i	$-0.622309\pi$
$433$	6.50727	−	4.18197i	0.312720	−	0.200973i	0.687580	+	0.726109i	$0.258673\pi$
$434$	16.6286	+	19.1904i	0.798198	+	0.921170i
$435$		0			0
$436$	0.216421			0.0103647
$437$	21.2352	+	16.4069i	1.01582	+	0.784849i
$438$	1.11564			0.0533073
$439$	−23.5703	+	6.92087i	−1.12495	+	0.330315i	−0.790721	−	0.612177i	$-0.790294\pi$
$439$	−23.5703	+	6.92087i	−1.12495	+	0.330315i	−0.334229	+	0.942492i	$0.608476\pi$
$440$		0			0
$441$	5.42030	−	3.48342i	0.258110	−	0.165877i
$442$	1.22956	+	8.55181i	0.0584844	+	0.406768i
$443$	−23.2021	−	14.9111i	−1.10236	−	0.708446i	−0.142748	−	0.989759i	$-0.545594\pi$
$443$	−23.2021	−	14.9111i	−1.10236	−	0.708446i	−0.959616	+	0.281313i	$0.909230\pi$
$444$	−0.00915277	+	0.0200418i	−0.000434371	+	0.000951140i
$445$		0			0
$446$	1.92177	−	13.3662i	0.0909985	−	0.632909i
$447$	−10.7194	−	23.4721i	−0.507008	−	1.11019i
$448$	23.0329	+	6.76308i	1.08820	+	0.319526i
$449$	29.4956	+	8.66069i	1.39198	+	0.408723i	0.889923	−	0.456110i	$-0.150758\pi$
$449$	29.4956	+	8.66069i	1.39198	+	0.408723i	0.502059	+	0.864833i	$0.332576\pi$
$450$		0			0
$451$	1.49780	−	10.4174i	0.0705284	−	0.490536i
$452$	−0.219968	+	0.253857i	−0.0103464	+	0.0119404i
$453$	19.6387	−	43.0027i	0.922705	−	2.02044i
$454$	22.1239	+	14.2181i	1.03832	+	0.667291i
$455$		0			0
$456$	−35.0528	+	22.5271i	−1.64150	+	1.05493i
$457$	−5.91082	−	6.82146i	−0.276497	−	0.319094i	0.600468	−	0.799649i	$-0.294981\pi$
$457$	−5.91082	−	6.82146i	−0.276497	−	0.319094i	−0.876965	+	0.480554i	$0.840435\pi$
$458$	22.3284	−	6.55621i	1.04334	−	0.306352i
$459$	2.78497			0.129991
$460$		0			0
$461$	30.1893			1.40606			0.703028	−	0.711162i	$-0.251831\pi$
$461$	30.1893			1.40606			0.703028	+	0.711162i	$0.251831\pi$
$462$	−16.3922	+	4.81319i	−0.762635	+	0.223930i
$463$	19.0501	+	21.9850i	0.885332	+	1.02173i	0.999600	+	0.0282782i	$0.00900242\pi$
$463$	19.0501	+	21.9850i	0.885332	+	1.02173i	−0.114268	+	0.993450i	$0.536452\pi$
$464$	−18.7608	+	12.0568i	−0.870949	+	0.559725i
$465$		0			0
$466$	−15.9214	−	10.2320i	−0.737544	−	0.473990i
$467$	−8.87127	+	19.4254i	−0.410513	+	0.898899i	0.585582	+	0.810613i	$0.300866\pi$
$467$	−8.87127	+	19.4254i	−0.410513	+	0.898899i	−0.996095	+	0.0882857i	$0.971861\pi$
$468$	−0.430215	+	0.496495i	−0.0198867	+	0.0229505i
$469$	4.42222	−	30.7572i	0.204199	−	1.42024i
$470$		0			0
$471$	−56.5641	−	16.6087i	−2.60634	−	0.765289i
$472$	31.9460	+	9.38020i	1.47043	+	0.431758i
$473$	4.07670	+	8.92673i	0.187447	+	0.410451i
$474$	−4.28557	+	29.8068i	−0.196843	+	1.36907i
$475$		0			0
$476$	−0.0597912	+	0.130925i	−0.00274053	+	0.00600092i
$477$	−27.5373	−	17.6971i	−1.26085	−	0.810297i
$478$	−0.779853	−	5.42400i	−0.0356696	−	0.248088i
$479$	−21.8930	+	14.0698i	−1.00032	+	0.642865i	−0.934870	−	0.354991i	$-0.884484\pi$
$479$	−21.8930	+	14.0698i	−1.00032	+	0.642865i	−0.0654482	+	0.997856i	$0.520848\pi$
$480$		0			0
$481$	−1.02339	+	0.300495i	−0.0466627	+	0.0137014i
$482$	13.6584			0.622123
$483$	−21.6564	−	29.8669i	−0.985399	−	1.35899i
$484$	0.313671			0.0142578
$485$		0			0
$486$	19.9830	+	23.0616i	0.906447	+	1.04610i
$487$	13.6005	−	8.74048i	0.616295	−	0.396069i	−0.194918	−	0.980820i	$-0.562444\pi$
$487$	13.6005	−	8.74048i	0.616295	−	0.396069i	0.811213	+	0.584751i	$0.198808\pi$
$488$	−1.34613	−	9.36254i	−0.0609364	−	0.423822i
$489$	−14.1564	−	9.09775i	−0.640174	−	0.411415i
$490$		0			0
$491$	−11.1213	+	12.8347i	−0.501899	+	0.579223i	−0.949006	−	0.315258i	$-0.897909\pi$
$491$	−11.1213	+	12.8347i	−0.501899	+	0.579223i	0.447107	+	0.894481i	$0.352454\pi$
$492$	−0.0911173	+	0.633735i	−0.00410788	+	0.0285710i
$493$	−3.11813	−	6.82776i	−0.140434	−	0.307507i
$494$	−35.1144	−	10.3105i	−1.57987	−	0.463893i
$495$		0			0
$496$	10.0224	+	21.9461i	0.450020	+	0.985407i
$497$	3.13978	−	21.8377i	0.140839	−	0.979553i
$498$	16.2354	−	18.7367i	0.727527	−	0.839611i
$499$	8.55147	−	18.7251i	0.382816	−	0.838251i	−0.615911	−	0.787816i	$-0.711212\pi$
$499$	8.55147	−	18.7251i	0.382816	−	0.838251i	0.998727	−	0.0504351i	$-0.0160608\pi$
$500$		0			0
$501$	−3.62917	−	25.2415i	−0.162139	−	1.12770i
$502$	20.2731	−	13.0288i	0.904834	−	0.581502i
$503$	−3.69991	−	4.26993i	−0.164971	−	0.190387i	0.667245	−	0.744838i	$-0.267473\pi$
$503$	−3.69991	−	4.26993i	−0.164971	−	0.190387i	−0.832216	+	0.554452i	$0.812928\pi$
$504$	30.7430	−	9.02695i	1.36940	−	0.402092i
$505$		0			0
$506$	3.56976	+	10.0350i	0.158695	+	0.446108i
$507$	−22.9380			−1.01871
$508$	−0.224485	+	0.0659147i	−0.00995990	+	0.00292449i
$509$	23.0053	+	26.5496i	1.01969	+	1.17679i	0.984135	+	0.177421i	$0.0567754\pi$
$509$	23.0053	+	26.5496i	1.01969	+	1.17679i	0.0355580	+	0.999368i	$0.488679\pi$
$510$		0			0
$511$	0.128044	+	0.890564i	0.00566432	+	0.0393962i
$512$	19.5359	+	12.5549i	0.863372	+	0.554855i
$513$	−4.90056	+	10.7307i	−0.216365	+	0.473773i
$514$	−8.15743	+	9.41418i	−0.359809	+	0.415242i
$515$		0			0
$516$	−0.248003	−	0.543051i	−0.0109177	−	0.0239065i
$517$	14.0932	+	4.13813i	0.619817	+	0.181995i
$518$	0.905581	+	0.265903i	0.0397889	+	0.0116831i
$519$	9.75117	+	21.3521i	0.428029	+	0.937252i
$520$		0			0
$521$	6.79035	−	7.83648i	0.297491	−	0.343323i	−0.587250	−	0.809405i	$-0.699790\pi$
$521$	6.79035	−	7.83648i	0.297491	−	0.343323i	0.884741	+	0.466083i	$0.154335\pi$
$522$	−12.5939	+	27.5768i	−0.551221	+	1.20701i
$523$	−33.2219	−	21.3504i	−1.45269	−	0.933589i	−0.999102	−	0.0423796i	$-0.986506\pi$
$523$	−33.2219	−	21.3504i	−1.45269	−	0.933589i	−0.453592	−	0.891210i	$-0.649858\pi$
$524$	−0.0252698	−	0.175755i	−0.00110392	−	0.00767791i
$525$		0			0
$526$	2.37990	+	2.74655i	0.103769	+	0.119755i
$527$	−7.79148	+	2.28779i	−0.339402	+	0.0996575i
$528$	−16.2323			−0.706420
$529$	−17.8328	+	14.5255i	−0.775339	+	0.631545i
$530$		0			0
$531$	42.6253	−	12.5159i	1.84978	−	0.543145i
$532$	−0.399252	−	0.460761i	−0.0173098	−	0.0199765i
$533$	−26.0740	+	16.7568i	−1.12939	+	0.725816i
$534$	−4.09291	−	28.4668i	−0.177118	−	1.23188i
$535$		0			0
$536$	12.4957	−	27.3617i	0.539731	−	1.18185i
$537$	23.1962	−	26.7698i	1.00099	−	1.15520i
$538$	0.546744	−	3.80269i	0.0235718	−	0.163945i
$539$	−1.11415	−	2.43964i	−0.0479897	−	0.105083i
$540$		0			0
$541$	4.70539	+	1.38163i	0.202300	+	0.0594007i	0.381313	−	0.924446i	$-0.375472\pi$
$541$	4.70539	+	1.38163i	0.202300	+	0.0594007i	−0.179013	+	0.983847i	$0.557290\pi$
$542$	8.06721	+	17.6647i	0.346516	+	0.758765i
$543$	1.16432	−	8.09800i	0.0499656	−	0.347519i
$544$	−0.180827	+	0.208686i	−0.00775290	+	0.00894732i
$545$		0			0
$546$	42.3254	+	27.2009i	1.81136	+	1.16409i
$547$	−2.78626	−	19.3788i	−0.119132	−	0.828579i	−0.958516	−	0.285040i	$-0.907993\pi$
$547$	−2.78626	−	19.3788i	−0.119132	−	0.828579i	0.839384	−	0.543539i	$-0.182916\pi$
$548$	0.142037	−	0.0912818i	0.00606753	−	0.00389936i
$549$	−8.26488	−	9.53818i	−0.352736	−	0.407079i
$550$		0			0
$551$	31.7947			1.35450
$552$	−11.9693	−	33.6470i	−0.509448	−	1.43211i
$553$	−24.2853			−1.03272
$554$	3.93860	−	1.15648i	0.167335	−	0.0491340i
$555$		0			0
$556$	−0.473058	+	0.304016i	−0.0200621	+	0.0128932i
$557$	−2.98516	−	20.7623i	−0.126485	−	0.879725i	−0.949960	−	0.312372i	$-0.898876\pi$
$557$	−2.98516	−	20.7623i	−0.126485	−	0.879725i	0.823474	−	0.567353i	$-0.192033\pi$
$558$	27.5913	+	17.7318i	1.16803	+	0.750648i
$559$	12.0057	−	26.2888i	0.507787	−	1.11190i
$560$		0			0
$561$	0.777531	−	5.40784i	0.0328274	−	0.228319i
$562$	14.2308	+	31.1611i	0.600289	+	1.31445i
$563$	2.35894	+	0.692647i	0.0994174	+	0.0291916i	0.331063	−	0.943609i	$-0.392593\pi$
$563$	2.35894	+	0.692647i	0.0994174	+	0.0291916i	−0.231645	+	0.972800i	$0.574411\pi$
$564$	−0.857348	−	0.251740i	−0.0361009	−	0.0106002i
$565$		0			0
$566$	−3.96998	+	27.6118i	−0.166871	+	1.16061i
$567$	−11.4356	+	13.1974i	−0.480249	+	0.554237i
$568$	8.87194	−	19.4268i	0.372258	−	0.815132i
$569$	4.13174	+	2.65531i	0.173212	+	0.111316i	0.624374	−	0.781126i	$-0.285354\pi$
$569$	4.13174	+	2.65531i	0.173212	+	0.111316i	−0.451162	+	0.892442i	$0.648990\pi$
$570$		0			0
$571$	−6.45163	+	4.14621i	−0.269992	+	0.173514i	−0.668631	−	0.743595i	$-0.733119\pi$
$571$	−6.45163	+	4.14621i	−0.269992	+	0.173514i	0.398638	+	0.917108i	$0.369483\pi$
$572$	0.179081	+	0.206670i	0.00748775	+	0.00864133i
$573$	3.46301	−	1.01683i	0.144669	−	0.0424787i
$574$	27.4262			1.14475
$575$		0			0
$576$	31.0060			1.29192
$577$	−33.2974	+	9.77699i	−1.38619	+	0.407021i	−0.887918	−	0.460001i	$-0.847849\pi$
$577$	−33.2974	+	9.77699i	−1.38619	+	0.407021i	−0.498269	+	0.867022i	$0.666031\pi$
$578$	−13.9967	−	16.1531i	−0.582187	−	0.671880i
$579$	5.77100	−	3.70880i	0.239835	−	0.154132i
$580$		0			0
$581$	16.8200	+	10.8096i	0.697812	+	0.448457i
$582$	8.61788	−	18.8705i	0.357223	−	0.782209i
$583$	−8.92292	+	10.2976i	−0.369550	+	0.426483i
$584$	−0.123950	+	0.862089i	−0.00512908	+	0.0356735i
$585$		0			0
$586$	15.0794	+	4.42770i	0.622923	+	0.182907i
$587$	−21.6933	−	6.36972i	−0.895377	−	0.262906i	−0.198503	−	0.980100i	$-0.563608\pi$
$587$	−21.6933	−	6.36972i	−0.895377	−	0.262906i	−0.696874	+	0.717194i	$0.745426\pi$
$588$	0.0677783	+	0.148414i	0.00279513	+	0.00612048i
$589$	4.89521	−	34.0469i	0.201704	−	1.40288i
$590$		0			0
$591$	−15.1532	+	33.1808i	−0.623318	+	1.36488i
$592$	0.754391	+	0.484818i	0.0310053	+	0.0199259i
$593$	−1.92471	−	13.3866i	−0.0790383	−	0.549723i	−0.990412	−	0.138144i	$-0.955886\pi$
$593$	−1.92471	−	13.3866i	−0.0790383	−	0.549723i	0.911374	−	0.411579i	$-0.135023\pi$
$594$	−3.93892	+	2.53139i	−0.161616	+	0.103864i
$595$		0			0
$596$	0.350686	−	0.102971i	0.0143646	−	0.00421784i
$597$	−35.4100			−1.44923
$598$	15.4499	−	27.2978i	0.631793	−	1.11629i
$599$	−24.1718			−0.987634			−0.493817	−	0.869566i	$-0.664399\pi$
$599$	−24.1718			−0.987634			−0.493817	+	0.869566i	$0.664399\pi$
$600$		0			0
$601$	3.63800	+	4.19847i	0.148397	+	0.171259i	0.825081	−	0.565014i	$-0.191129\pi$
$601$	3.63800	+	4.19847i	0.148397	+	0.171259i	−0.676684	+	0.736273i	$0.736584\pi$
$602$	−21.5138	+	13.8261i	−0.876836	+	0.563509i
$603$	−5.71187	−	39.7269i	−0.232605	−	1.61781i
$604$	0.563308	+	0.362016i	0.0229207	+	0.0147302i
$605$		0			0
$606$	12.5436	−	14.4760i	0.509547	−	0.588049i
$607$	1.96959	−	13.6988i	0.0799431	−	0.556016i	−0.910006	−	0.414594i	$-0.863923\pi$
$607$	1.96959	−	13.6988i	0.0799431	−	0.556016i	0.989949	−	0.141422i	$-0.0451675\pi$
$608$	−0.485892	−	1.06396i	−0.0197055	−	0.0431491i
$609$	−41.9399	−	12.3147i	−1.69949	−	0.499016i
$610$		0			0
$611$	−17.9692	−	39.3470i	−0.726955	−	1.59181i
$612$	−0.0264572	+	0.184014i	−0.00106947	+	0.00743831i
$613$	2.21258	−	2.55345i	0.0893651	−	0.103133i	−0.709306	−	0.704901i	$-0.750991\pi$
$613$	2.21258	−	2.55345i	0.0893651	−	0.103133i	0.798671	+	0.601768i	$0.205537\pi$
$614$	4.42484	−	9.68906i	0.178572	−	0.391019i
$615$		0			0
$616$	−1.89809	−	13.2015i	−0.0764764	−	0.531905i
$617$	32.6389	−	20.9757i	1.31399	−	0.844451i	0.319331	−	0.947643i	$-0.396542\pi$
$617$	32.6389	−	20.9757i	1.31399	−	0.844451i	0.994661	+	0.103192i	$0.0329056\pi$
$618$	−44.6311	−	51.5070i	−1.79533	−	2.07192i
$619$	−2.59883	+	0.763087i	−0.104456	+	0.0306710i	−0.333543	−	0.942735i	$-0.608244\pi$
$619$	−2.59883	+	0.763087i	−0.104456	+	0.0306710i	0.229087	+	0.973406i	$0.426426\pi$
$620$		0			0
$621$	−8.00097	−	6.18176i	−0.321068	−	0.248066i
$622$	24.1785			0.969471
$623$	22.2540	−	6.53437i	0.891589	−	0.261794i
$624$	31.3046	+	36.1274i	1.25319	+	1.44625i
$625$		0			0
$626$	−0.540786	−	3.76125i	−0.0216142	−	0.150330i
$627$	19.4687	+	12.5118i	0.777505	+	0.499672i
$628$	0.346873	−	0.759546i	0.0138418	−	0.0303092i
$629$	−0.197654	+	0.228105i	−0.00788099	+	0.00909515i
$630$		0			0
$631$	−16.5157	−	36.1643i	−0.657480	−	1.43968i	−0.884852	−	0.465872i	$-0.845741\pi$
$631$	−16.5157	−	36.1643i	−0.657480	−	1.43968i	0.227373	−	0.973808i	$-0.426986\pi$
$632$	−22.5565	−	6.62319i	−0.897250	−	0.263456i
$633$	15.8883	+	4.66521i	0.631501	+	0.185426i
$634$	1.70629	+	3.73626i	0.0677655	+	0.148386i
$635$		0			0
$636$	0.542819	−	0.626447i	0.0215242	−	0.0248402i
$637$	−3.28111	+	7.18464i	−0.130002	+	0.284666i
$638$	10.6162	+	6.82262i	0.420299	+	0.270110i
$639$	−4.05544	−	28.2062i	−0.160431	−	1.11582i
$640$		0			0
$641$	−6.33688	−	7.31315i	−0.250292	−	0.288852i	0.616675	−	0.787218i	$-0.288479\pi$
$641$	−6.33688	−	7.31315i	−0.250292	−	0.288852i	−0.866967	+	0.498366i	$0.833934\pi$
$642$	27.1957	−	7.98538i	1.07333	−	0.315158i
$643$	32.3558			1.27599			0.637994	−	0.770041i	$-0.279765\pi$
$643$	32.3558			1.27599			0.637994	+	0.770041i	$0.279765\pi$
$644$	0.462386	−	0.243417i	0.0182206	−	0.00959196i
$645$		0			0
$646$	−9.93669	+	2.91768i	−0.390954	+	0.114794i
$647$	−14.4060	−	16.6254i	−0.566357	−	0.653611i	0.398258	−	0.917274i	$-0.369615\pi$
$647$	−14.4060	−	16.6254i	−0.566357	−	0.653611i	−0.964615	+	0.263662i	$0.915070\pi$
$648$	−14.2208	+	9.13914i	−0.558645	+	0.359019i
$649$	−2.63172	−	18.3040i	−0.103304	−	0.718495i
$650$		0			0
$651$	−19.6442	+	43.0148i	−0.769916	+	1.68588i
$652$	0.156086	−	0.180133i	0.00611280	−	0.00705454i
$653$	−0.296923	+	2.06514i	−0.0116195	+	0.0808152i	−0.994806	−	0.101789i	$-0.967543\pi$
$653$	−0.296923	+	2.06514i	−0.0116195	+	0.0808152i	0.983187	+	0.182604i	$0.0584526\pi$
$654$	−8.89317	−	19.4733i	−0.347750	−	0.761467i
$655$		0			0
$656$	25.0030	+	7.34153i	0.976202	+	0.286639i
$657$	0.482757	+	1.05709i	0.0188341	+	0.0412410i
$658$	−5.44729	+	37.8867i	−0.212358	+	1.47698i
$659$	−2.87363	+	3.31634i	−0.111941	+	0.129186i	−0.808954	−	0.587871i	$-0.799966\pi$
$659$	−2.87363	+	3.31634i	−0.111941	+	0.129186i	0.697014	+	0.717058i	$0.254512\pi$
$660$		0			0
$661$	−18.4504	−	11.8574i	−0.717639	−	0.461199i	0.130176	−	0.991491i	$-0.458446\pi$
$661$	−18.4504	−	11.8574i	−0.717639	−	0.461199i	−0.847815	+	0.530292i	$0.822082\pi$
$662$	1.68127	+	11.6935i	0.0653443	+	0.454480i
$663$	−13.5355	+	8.69871i	−0.525674	+	0.337830i
$664$	12.6746	+	14.6273i	0.491871	+	0.567650i
$665$		0			0
$666$	1.21906			0.0472374
$667$	−6.19737	+	26.5368i	−0.239963	+	1.02751i
$668$	0.361199			0.0139752
$669$	24.1290	−	7.08490i	0.932879	−	0.273918i
$670$		0			0
$671$	−4.41955	+	2.84027i	−0.170615	+	0.109647i
$672$	0.228843	+	1.59164i	0.00882783	+	0.0613989i
$673$	27.8003	+	17.8662i	1.07162	+	0.688690i	0.952608	−	0.304202i	$-0.0983898\pi$
$673$	27.8003	+	17.8662i	1.07162	+	0.688690i	0.119016	+	0.992892i	$0.462026\pi$
$674$	−1.99050	+	4.35858i	−0.0766711	+	0.167886i
$675$		0			0
$676$	0.0462375	−	0.321589i	0.00177837	−	0.0123688i
$677$	−13.1705	−	28.8393i	−0.506182	−	1.10838i	−0.974410	−	0.224777i	$-0.927835\pi$
$677$	−13.1705	−	28.8393i	−0.506182	−	1.10838i	0.468228	−	0.883608i	$-0.344893\pi$
$678$	31.8807	+	9.36103i	1.22437	+	0.359508i
$679$	16.0526	+	4.71346i	0.616042	+	0.180886i
$680$		0			0
$681$	−6.96995	+	48.4770i	−0.267089	+	1.85764i
$682$	8.94040	−	10.3178i	0.342346	−	0.395088i
$683$	−6.46599	+	14.1586i	−0.247414	+	0.541762i	−0.992070	−	0.125687i	$-0.959886\pi$
$683$	−6.46599	+	14.1586i	−0.247414	+	0.541762i	0.744656	+	0.667449i	$0.232614\pi$
$684$	−0.662465	−	0.425741i	−0.0253300	−	0.0162786i
$685$		0			0
$686$	−18.4452	+	11.8540i	−0.704240	+	0.452588i
$687$	28.3798	+	32.7521i	1.08276	+	1.24957i
$688$	−23.3139	+	6.84559i	−0.888836	+	0.260986i
$689$	40.1270			1.52872
$690$		0			0
$691$	−42.2733			−1.60815			−0.804076	−	0.594527i	$-0.797339\pi$
$691$	−42.2733			−1.60815			−0.804076	+	0.594527i	$0.797339\pi$
$692$	−0.319011	+	0.0936701i	−0.0121270	+	0.00356080i
$693$	−11.6538	−	13.4492i	−0.442691	−	0.510893i
$694$	8.55913	−	5.50062i	0.324900	−	0.208801i
$695$		0			0
$696$	−35.5959	−	22.8761i	−1.34926	−	0.867116i
$697$	−3.64351	+	7.97817i	−0.138008	+	0.302195i
$698$	−31.8843	+	36.7964i	−1.20684	+	1.39277i
$699$	5.01590	−	34.8864i	0.189719	−	1.31952i
$700$		0			0
$701$	41.6290	+	12.2234i	1.57231	+	0.461671i	0.947672	−	0.319246i	$-0.103430\pi$
$701$	41.6290	+	12.2234i	1.57231	+	0.461671i	0.624635	+	0.780917i	$0.285248\pi$
$702$	13.2303	+	3.88478i	0.499347	+	0.146622i
$703$	−0.531107	−	1.16296i	−0.0200311	−	0.0438620i
$704$	1.83679	−	12.7751i	0.0692266	−	0.481481i
$705$		0			0
$706$	13.9316	−	30.5058i	0.524321	−	1.14810i
$707$	12.9952	+	8.35152i	0.488736	+	0.314091i
$708$	0.160099	+	1.11351i	0.00601688	+	0.0418483i
$709$	−30.2132	+	19.4168i	−1.13468	+	0.729215i	−0.966532	−	0.256547i	$-0.917415\pi$
$709$	−30.2132	+	19.4168i	−1.13468	+	0.729215i	−0.168148	+	0.985762i	$0.553779\pi$
$710$		0			0
$711$	−30.0970	+	8.83727i	−1.12873	+	0.331424i
$712$	22.4519			0.841422
$713$	27.4624	+	10.7220i	1.02847	+	0.401544i
$714$	14.2374			0.532821
$715$		0			0
$716$	0.328554	+	0.379171i	0.0122786	+	0.0141703i
$717$	8.58489	−	5.51717i	0.320608	−	0.206043i
$718$	2.44150	+	16.9810i	0.0911160	+	0.633725i
$719$	−0.284312	−	0.182716i	−0.0106030	−	0.00681416i	0.535329	−	0.844644i	$-0.320188\pi$
$719$	−0.284312	−	0.182716i	−0.0106030	−	0.00681416i	−0.545932	+	0.837830i	$0.683824\pi$
$720$		0			0
$721$	35.9934	−	41.5386i	1.34046	−	1.54698i
$722$	2.45448	−	17.0713i	0.0913465	−	0.635329i
$723$	10.5664	+	23.1372i	0.392968	+	0.860481i
$724$	0.111187	+	0.0326473i	0.00413222	+	0.00121333i
$725$		0			0
$726$	−12.8894	−	28.2238i	−0.478370	−	1.04748i
$727$	−0.474610	+	3.30099i	−0.0176023	+	0.122427i	−0.996728	−	0.0808290i	$-0.974243\pi$
$727$	−0.474610	+	3.30099i	−0.0176023	+	0.122427i	0.979126	+	0.203256i	$0.0651523\pi$
$728$	−25.7214	+	29.6841i	−0.953300	+	1.10017i
$729$	−16.2253	+	35.5284i	−0.600936	+	1.31587i
$730$		0			0
$731$	−1.16389	−	8.09503i	−0.0430480	−	0.299405i
$732$	0.268860	−	0.172786i	0.00993735	−	0.00638635i
$733$	−24.8826	−	28.7160i	−0.919060	−	1.06065i	−0.997965	−	0.0637693i	$-0.979688\pi$
$733$	−24.8826	−	28.7160i	−0.919060	−	1.06065i	0.0789050	−	0.996882i	$-0.474858\pi$
$734$	−0.282905	+	0.0830684i	−0.0104422	+	0.00306611i
$735$		0			0
$736$	0.982716	−	0.198155i	0.0362234	−	0.00730411i
$737$	−16.7067			−0.615400
$738$	33.9896	−	9.98023i	1.25117	−	0.367377i
$739$	−10.3211	−	11.9112i	−0.379668	−	0.438161i	0.533465	−	0.845822i	$-0.320890\pi$
$739$	−10.3211	−	11.9112i	−0.379668	−	0.438161i	−0.913133	+	0.407662i	$0.866344\pi$
$740$		0			0
$741$	−9.69927	−	67.4599i	−0.356312	−	2.47820i
$742$	−29.8709	−	19.1969i	−1.09660	−	0.704739i
$743$	10.6998	−	23.4293i	0.392538	−	0.859538i	−0.605435	−	0.795895i	$-0.707001\pi$
$743$	10.6998	−	23.4293i	0.392538	−	0.859538i	0.997973	−	0.0636434i	$-0.0202720\pi$
$744$	−29.9770	+	34.5953i	−1.09901	+	1.26832i
$745$		0			0
$746$	6.62828	+	14.5139i	0.242679	+	0.531392i
$747$	24.7787	+	7.27570i	0.906607	+	0.266204i
$748$	0.0742504	+	0.0218019i	0.00271486	+	0.000797155i
$749$	9.49567	+	20.7926i	0.346964	+	0.759746i
$750$		0			0
$751$	−26.6918	+	30.8040i	−0.973998	+	1.12405i	0.0182565	+	0.999833i	$0.494188\pi$
$751$	−26.6918	+	30.8040i	−0.973998	+	1.12405i	−0.992255	+	0.124220i	$0.960357\pi$
$752$	−15.1076	+	33.0811i	−0.550919	+	1.20634i
$753$	37.7543	+	24.2632i	1.37584	+	0.884200i
$754$	−5.28897	−	36.7856i	−0.192613	−	1.33965i
$755$		0			0
$756$	0.150429	+	0.173605i	0.00547107	+	0.00631395i
$757$	−31.8344	+	9.34741i	−1.15704	+	0.339737i	−0.803281	−	0.595600i	$-0.796915\pi$
$757$	−31.8344	+	9.34741i	−1.15704	+	0.339737i	−0.353758	+	0.935337i	$0.615096\pi$
$758$	−12.2072			−0.443386
$759$	−14.2375	+	13.8104i	−0.516788	+	0.501285i
$760$		0			0
$761$	−27.2664	+	8.00614i	−0.988407	+	0.290222i	−0.735690	−	0.677318i	$-0.763142\pi$
$761$	−27.2664	+	8.00614i	−0.988407	+	0.290222i	−0.252716	+	0.967540i	$0.581324\pi$
$762$	15.1555	+	17.4903i	0.549025	+	0.633608i
$763$	14.5240	−	9.33400i	0.525804	−	0.337914i
$764$	0.00727531	+	0.0506009i	0.000263211	+	0.00183068i
$765$		0			0
$766$	4.72252	−	10.3409i	0.170632	−	0.373631i
$767$	−35.6629	+	41.1572i	−1.28771	+	1.48610i
$768$	−0.329247	+	2.28996i	−0.0118807	+	0.0826319i
$769$	4.94521	+	10.8285i	0.178329	+	0.390486i	0.977596	−	0.210490i	$-0.0675060\pi$
$769$	4.94521	+	10.8285i	0.178329	+	0.390486i	−0.799267	+	0.600976i	$0.794779\pi$
$770$		0			0
$771$	−22.2583	−	6.53562i	−0.801612	−	0.235375i
$772$	0.0403642	+	0.0883852i	0.00145274	+	0.00318105i
$773$	3.44832	−	23.9836i	0.124027	−	0.862629i	−0.828893	−	0.559408i	$-0.811029\pi$
$773$	3.44832	−	23.9836i	0.124027	−	0.862629i	0.952920	−	0.303222i	$-0.0980622\pi$
$774$	−21.6310	+	24.9635i	−0.777511	+	0.897295i
$775$		0			0
$776$	13.6244	+	8.75587i	0.489087	+	0.314317i
$777$	0.250139	+	1.73975i	0.00897367	+	0.0624133i
$778$	36.1035	−	23.2023i	1.29437	−	0.831843i
$779$	−24.3293	−	28.0775i	−0.871687	−	1.00598i
$780$		0			0
$781$	−11.8618			−0.424449
$782$	−0.498336	−	8.86216i	−0.0178205	−	0.316910i
$783$	−11.9796			−0.428115
$784$	6.37162	−	1.87088i	0.227558	−	0.0668170i
$785$		0			0
$786$	−14.7759	+	9.49590i	−0.527039	+	0.338708i
$787$	−3.15980	−	21.9769i	−0.112635	−	0.783391i	−0.965339	−	0.260998i	$-0.915948\pi$
$787$	−3.15980	−	21.9769i	−0.112635	−	0.783391i	0.852705	−	0.522393i	$-0.174961\pi$
$788$	−0.434648	−	0.279331i	−0.0154837	−	0.00995077i
$789$	−2.81150	+	6.15632i	−0.100092	+	0.219171i
$790$		0			0
$791$	−3.81348	+	26.5233i	−0.135592	+	0.943061i
$792$	−7.15629	−	15.6701i	−0.254288	−	0.556812i
$793$	14.8447	+	4.35880i	0.527151	+	0.154785i
$794$	−34.9784	−	10.2706i	−1.24134	−	0.364490i
$795$		0			0
$796$	0.0713782	−	0.496446i	0.00252993	−	0.0175961i
$797$	−5.71446	+	6.59484i	−0.202417	+	0.233601i	−0.847878	−	0.530192i	$-0.822120\pi$
$797$	−5.71446	+	6.59484i	−0.202417	+	0.233601i	0.645461	+	0.763793i	$0.276665\pi$
$798$	−25.0528	+	54.8579i	−0.886859	+	1.94195i
$799$	−10.2974	−	6.61776i	−0.364297	−	0.234119i
$800$		0			0
$801$	25.2018	−	16.1962i	0.890462	−	0.572265i
$802$	−29.7996	−	34.3906i	−1.05226	−	1.21437i
$803$	0.464143	−	0.136285i	0.0163792	−	0.00480938i
$804$	1.01634			0.0358436
$805$		0			0
$806$	−40.2056			−1.41618
$807$	6.86468	−	2.01565i	0.241648	−	0.0709543i
$808$	9.79248	+	11.3011i	0.344498	+	0.397572i
$809$	42.8271	−	27.5233i	1.50572	−	0.967669i	0.511621	−	0.859211i	$-0.329045\pi$
$809$	42.8271	−	27.5233i	1.50572	−	0.967669i	0.994101	−	0.108457i	$-0.0345910\pi$
$810$		0			0
$811$	0.148167	+	0.0952212i	0.00520285	+	0.00334367i	0.543240	−	0.839578i	$-0.317198\pi$
$811$	0.148167	+	0.0952212i	0.00520285	+	0.00334367i	−0.538037	+	0.842921i	$0.680834\pi$
$812$	0.257192	−	0.563172i	0.00902568	−	0.0197635i
$813$	−23.6829	+	27.3315i	−0.830596	+	0.958559i
$814$	0.0722166	−	0.502277i	0.00253119	−	0.0176048i
$815$		0			0
$816$	12.9795	+	3.81111i	0.454372	+	0.133416i
$817$	33.2389	+	9.75981i	1.16288	+	0.341453i
$818$	12.2415	+	26.8052i	0.428015	+	0.937222i
$819$	−7.45843	+	51.8745i	−0.260619	+	1.81264i
$820$		0			0
$821$	12.4719	−	27.3097i	0.435273	−	0.953115i	−0.557169	−	0.830399i	$-0.688112\pi$
$821$	12.4719	−	27.3097i	0.435273	−	0.953115i	0.992442	−	0.122716i	$-0.0391603\pi$
$822$	−14.0500	−	9.02941i	−0.490051	−	0.314937i
$823$	−0.297567	−	2.06963i	−0.0103725	−	0.0721426i	0.983978	−	0.178292i	$-0.0570570\pi$
$823$	−0.297567	−	2.06963i	−0.0103725	−	0.0721426i	−0.994350	+	0.106149i	$0.966148\pi$
$824$	44.7597	−	28.7653i	1.55928	−	1.00209i
$825$		0			0
$826$	46.2375	−	13.5766i	1.60881	−	0.472389i
$827$	3.18639			0.110802			0.0554008	−	0.998464i	$-0.482356\pi$
$827$	3.18639			0.110802			0.0554008	+	0.998464i	$0.482356\pi$
$828$	0.484462	−	0.469928i	0.0168362	−	0.0163311i
$829$	−31.5021			−1.09411			−0.547057	−	0.837095i	$-0.684252\pi$
$829$	−31.5021			−1.09411			−0.547057	+	0.837095i	$0.684252\pi$
$830$		0			0
$831$	5.00603	+	5.77727i	0.173657	+	0.200411i
$832$	−31.9753	+	20.5493i	−1.10854	+	0.712418i
$833$	0.318087	+	2.21234i	0.0110211	+	0.0766531i
$834$	46.7940	+	30.0727i	1.62034	+	1.04133i
$835$		0			0
$836$	−0.214659	+	0.247729i	−0.00742413	+	0.00856790i
$837$	−1.84441	+	12.8281i	−0.0637520	+	0.443405i
$838$	−7.48176	−	16.3828i	−0.258453	−	0.565933i
$839$	−11.4981	−	3.37616i	−0.396960	−	0.116558i	0.0771588	−	0.997019i	$-0.475415\pi$
$839$	−11.4981	−	3.37616i	−0.396960	−	0.116558i	−0.474119	+	0.880461i	$0.657233\pi$
$840$		0			0
$841$	1.36562	+	2.99030i	0.0470904	+	0.103114i
$842$	−5.05782	+	35.1779i	−0.174304	+	1.21231i
$843$	−41.7773	+	48.2136i	−1.43889	+	1.66057i
$844$	−0.0974330	+	0.213348i	−0.00335378	+	0.00734376i
$845$		0			0
$846$	7.03588	+	48.9356i	0.241899	+	1.68244i
$847$	21.0505	−	13.5283i	0.723302	−	0.464838i
$848$	−22.0930	−	25.4967i	−0.758676	−	0.875559i
$849$	−49.8454	+	14.6359i	−1.71069	+	0.502304i
$850$		0			0
$851$	1.07416	−	0.216595i	0.0368219	−	0.00742478i
$852$	0.721604			0.0247218
$853$	−49.2681	+	14.4664i	−1.68691	+	0.495321i	−0.977758	−	0.209736i	$-0.932739\pi$
$853$	−49.2681	+	14.4664i	−1.68691	+	0.495321i	−0.709150	+	0.705057i	$0.750921\pi$
$854$	−8.96527	−	10.3465i	−0.306785	−	0.354049i
$855$		0			0
$856$	3.14906	+	21.9022i	0.107633	+	0.748601i
$857$	−0.651877	−	0.418936i	−0.0222677	−	0.0143106i	0.529460	−	0.848335i	$-0.322395\pi$
$857$	−0.651877	−	0.418936i	−0.0222677	−	0.0143106i	−0.551727	+	0.834025i	$0.686031\pi$
$858$	11.2372	−	24.6060i	0.383632	−	0.840036i
$859$	−12.2578	+	14.1463i	−0.418231	+	0.482664i	−0.925297	−	0.379243i	$-0.876184\pi$
$859$	−12.2578	+	14.1463i	−0.418231	+	0.482664i	0.507066	+	0.861907i	$0.330730\pi$
$860$		0			0
$861$	21.2174	+	46.4597i	0.723088	+	1.58334i
$862$	26.0482	+	7.64845i	0.887207	+	0.260507i
$863$	−34.1937	−	10.0402i	−1.16397	−	0.341772i	−0.357994	−	0.933724i	$-0.616539\pi$
$863$	−34.1937	−	10.0402i	−1.16397	−	0.341772i	−0.805973	+	0.591952i	$0.798357\pi$
$864$	0.183073	+	0.400875i	0.00622828	+	0.0136380i
$865$		0			0
$866$	7.09718	−	8.19059i	0.241172	−	0.278327i
$867$	16.5350	−	36.2066i	0.561559	−	1.22964i
$868$	−0.563467	−	0.362118i	−0.0191253	−	0.0122911i
$869$	1.85821	+	12.9241i	0.0630355	+	0.438421i
$870$		0			0
$871$	32.2195	+	37.1833i	1.09172	+	1.25991i
$872$	16.0357	−	4.70851i	0.543037	−	0.159450i
$873$	21.6093			0.731365
$874$	35.0235	+	13.6741i	1.18469	+	0.462534i
$875$		0			0
$876$	−0.0282358	+	0.00829078i	−0.000953999	+	0.000280119i
$877$	26.4562	+	30.5321i	0.893362	+	1.03099i	0.999329	+	0.0366249i	$0.0116607\pi$
$877$	26.4562	+	30.5321i	0.893362	+	1.03099i	−0.105967	+	0.994370i	$0.533794\pi$
$878$	−28.9544	+	18.6079i	−0.977165	+	0.627986i
$879$	4.16521	+	28.9697i	0.140489	+	0.977122i
$880$		0			0
$881$	5.52226	−	12.0921i	0.186050	−	0.407392i	−0.793507	−	0.608561i	$-0.791747\pi$
$881$	5.52226	−	12.0921i	0.186050	−	0.407392i	0.979556	+	0.201169i	$0.0644742\pi$
$882$	5.91168	−	6.82244i	0.199056	−	0.229723i
$883$	−4.25750	+	29.6115i	−0.143276	+	0.996508i	0.783633	+	0.621223i	$0.213364\pi$
$883$	−4.25750	+	29.6115i	−0.143276	+	0.996508i	−0.926910	+	0.375284i	$0.877545\pi$
$884$	−0.0946712	−	0.207301i	−0.00318414	−	0.00697229i
$885$		0			0
$886$	−37.0772	−	10.8868i	−1.24563	−	0.365750i
$887$	−13.9669	−	30.5833i	−0.468964	−	1.02689i	−0.985352	−	0.170533i	$-0.945451\pi$
$887$	−13.9669	−	30.5833i	−0.468964	−	1.02689i	0.516388	−	0.856355i	$-0.327276\pi$
$888$	−0.242141	+	1.68413i	−0.00812571	+	0.0565156i
$889$	−12.2223	+	14.1053i	−0.409924	+	0.473077i
$890$		0			0
$891$	7.89837	+	5.07598i	0.264605	+	0.170052i
$892$	0.0506916	+	0.352568i	0.00169728	+	0.0118049i
$893$	43.6186	−	28.0320i	1.45964	−	0.938054i
$894$	−23.6756	−	27.3231i	−0.791830	−	0.913820i
$895$		0			0
$896$	32.4010			1.08244
$897$	58.1945	+	5.05386i	1.94306	+	0.168743i
$898$	43.0705			1.43728
$899$	33.5151	−	9.84091i	1.11779	−	0.328213i
$900$		0			0
$901$	9.55256	−	6.13906i	0.318242	−	0.204522i
$902$	−2.09854	−	14.5957i	−0.0698737	−	0.485983i
$903$	−40.0647	−	25.7480i	−1.33327	−	0.856841i
$904$	−10.7756	+	23.5952i	−0.358390	+	0.784766i
$905$		0			0
$906$	9.42637	−	65.5619i	0.313170	−	2.17815i
$907$	15.1098	+	33.0858i	0.501712	+	1.09860i	0.975909	+	0.218177i	$0.0700111\pi$
$907$	15.1098	+	33.0858i	0.501712	+	1.09860i	−0.474197	+	0.880419i	$0.657262\pi$
$908$	−0.665596	−	0.195437i	−0.0220886	−	0.00648579i
$909$	19.1442	+	5.62123i	0.634972	+	0.186445i
$910$		0			0
$911$	−4.37201	+	30.4080i	−0.144851	+	1.00746i	0.779632	+	0.626238i	$0.215406\pi$
$911$	−4.37201	+	30.4080i	−0.144851	+	1.00746i	−0.924483	+	0.381223i	$0.875503\pi$
$912$	−37.5238	+	43.3048i	−1.24254	+	1.43396i
$913$	4.46564	−	9.77838i	0.147791	−	0.323617i
$914$	−10.6388	−	6.83711i	−0.351899	−	0.226152i
$915$		0			0
$916$	−0.516390	+	0.331863i	−0.0170620	+	0.0109651i
$917$	−9.27601	−	10.7051i	−0.306321	−	0.353513i
$918$	3.74393	−	1.09932i	0.123568	−	0.0362828i
$919$	19.6529			0.648290			0.324145	−	0.946007i	$-0.394923\pi$
$919$	19.6529			0.648290			0.324145	+	0.946007i	$0.394923\pi$
$920$		0			0
$921$	19.8363			0.653629
$922$	40.5845	−	11.9167i	1.33658	−	0.392455i
$923$	22.8759	+	26.4002i	0.752970	+	0.868974i
$924$	0.379103	−	0.243635i	0.0124716	−	0.00801499i
$925$		0			0
$926$	34.2878	+	22.0354i	1.12677	+	0.724129i
$927$	29.4913	−	64.5769i	0.968621	−	2.12098i
$928$	0.777828	−	0.897662i	0.0255335	−	0.0294672i
$929$	−1.48994	+	10.3628i	−0.0488834	+	0.339991i	0.950673	+	0.310196i	$0.100395\pi$
$929$	−1.48994	+	10.3628i	−0.0488834	+	0.339991i	−0.999556	+	0.0297953i	$0.990514\pi$
$930$		0			0
$931$	−9.08406	−	2.66732i	−0.297718	−	0.0874179i
$932$	0.478994	+	0.140645i	0.0156900	+	0.00460699i
$933$	18.7050	+	40.9582i	0.612374	+	1.34091i
$934$	−4.25813	+	29.6159i	−0.139330	+	0.969063i
$935$		0			0
$936$	−21.0749	+	46.1477i	−0.688856	+	1.50838i
$937$	46.1608	+	29.6657i	1.50801	+	0.969137i	0.993765	+	0.111491i	$0.0355625\pi$
$937$	46.1608	+	29.6657i	1.50801	+	0.969137i	0.514241	+	0.857646i	$0.328074\pi$
$938$	−6.19591	−	43.0935i	−0.202304	−	1.40705i
$939$	5.95316	−	3.82586i	0.194274	−	0.124852i
$940$		0			0
$941$	−25.1608	+	7.38787i	−0.820218	+	0.240838i	−0.664810	−	0.747013i	$-0.731487\pi$
$941$	−25.1608	+	7.38787i	−0.820218	+	0.240838i	−0.155408	+	0.987850i	$0.549669\pi$
$942$	−82.5969			−2.69115
$943$	28.1765	−	14.8331i	0.917552	−	0.483032i
$944$	45.7864			1.49022
$945$		0			0
$946$	9.00410	+	10.3913i	0.292749	+	0.337850i
$947$	−7.71640	+	4.95903i	−0.250749	+	0.161147i	−0.659978	−	0.751285i	$-0.729434\pi$
$947$	−7.71640	+	4.95903i	−0.250749	+	0.161147i	0.409228	+	0.912432i	$0.365798\pi$
$948$	−0.113043	−	0.786231i	−0.00367146	−	0.0255356i
$949$	−1.19844	−	0.770189i	−0.0389029	−	0.0250014i
$950$		0			0
$951$	−5.00916	+	5.78088i	−0.162433	+	0.187458i
$952$	−1.58180	+	11.0017i	−0.0512666	+	0.356567i
$953$	17.2960	+	37.8730i	0.560273	+	1.22683i	0.951817	+	0.306667i	$0.0992139\pi$
$953$	17.2960	+	37.8730i	0.560273	+	1.22683i	−0.391544	+	0.920159i	$0.628059\pi$
$954$	−44.0049	−	12.9210i	−1.42471	−	0.418333i
$955$		0			0
$956$	0.0600453	+	0.131481i	0.00194201	+	0.00425240i
$957$	−3.34455	+	23.2618i	−0.108114	+	0.751949i
$958$	−23.8777	+	27.5564i	−0.771454	+	0.890305i
$959$	5.59523	−	12.2518i	0.180679	−	0.395632i
$960$		0			0
$961$	−0.966159	−	6.71978i	−0.0311664	−	0.216767i
$962$	−1.25717	+	0.807931i	−0.0405327	+	0.0260488i
$963$	19.3344	+	22.3131i	0.623042	+	0.719028i
$964$	−0.345681	+	0.101501i	−0.0111336	+	0.00326913i
$965$		0			0
$966$	−40.9028	−	31.6026i	−1.31602	−	1.01680i
$967$	−13.6682			−0.439540			−0.219770	−	0.975552i	$-0.570531\pi$
$967$	−13.6682			−0.439540			−0.219770	+	0.975552i	$0.570531\pi$
$968$	23.2415	−	6.82431i	0.747009	−	0.219342i
$969$	−12.6297	−	14.5755i	−0.405725	−	0.468232i
$970$		0			0
$971$	3.95275	+	27.4920i	0.126850	+	0.882259i	0.949512	+	0.313729i	$0.101578\pi$
$971$	3.95275	+	27.4920i	0.126850	+	0.882259i	−0.822663	+	0.568530i	$0.807512\pi$
$972$	−0.677132	−	0.435166i	−0.0217190	−	0.0139580i
$973$	−18.6350	+	40.8050i	−0.597412	+	1.30815i
$974$	14.8334	−	17.1186i	0.475292	−	0.548516i
$975$		0			0
$976$	−5.40357	−	11.8322i	−0.172964	−	0.378738i
$977$	4.56457	+	1.34028i	0.146034	+	0.0428793i	0.353932	−	0.935271i	$-0.384844\pi$
$977$	4.56457	+	1.34028i	0.146034	+	0.0428793i	−0.207899	+	0.978150i	$0.566662\pi$
$978$	−22.6220	−	6.64243i	−0.723373	−	0.212402i
$979$	−5.18025	−	11.3432i	−0.165561	−	0.362529i
$980$		0			0
$981$	14.6031	−	16.8529i	0.466242	−	0.538072i
$982$	−9.88451	+	21.6441i	−0.315428	+	0.690690i
$983$	31.1033	+	19.9889i	0.992040	+	0.637545i	0.932685	−	0.360692i	$-0.117459\pi$
$983$	31.1033	+	19.9889i	0.992040	+	0.637545i	0.0593548	+	0.998237i	$0.481096\pi$
$984$	7.03636	+	48.9390i	0.224311	+	1.56012i
$985$		0			0
$986$	−6.88694	−	7.94795i	−0.219325	−	0.253114i
$987$	−68.3939	+	20.0823i	−2.17700	+	0.639225i
$988$	0.965336			0.0307114
$989$	−14.6247	+	25.8397i	−0.465037	+	0.821656i
$990$		0			0
$991$	32.7309	−	9.61067i	1.03973	−	0.305293i	0.283070	−	0.959099i	$-0.408647\pi$
$991$	32.7309	−	9.61067i	1.03973	−	0.305293i	0.756662	+	0.653806i	$0.226829\pi$
$992$	−0.841491	−	0.971132i	−0.0267174	−	0.0308335i
$993$	−18.5080	+	11.8943i	−0.587332	+	0.377456i
$994$	−4.39911	−	30.5965i	−0.139531	−	0.970461i
$995$		0			0
$996$	−0.271664	+	0.594860i	−0.00860799	+	0.0188489i
$997$	−20.5939	+	23.7667i	−0.652217	+	0.752698i	−0.981485	−	0.191538i	$-0.938652\pi$
$997$	−20.5939	+	23.7667i	−0.652217	+	0.752698i	0.329268	+	0.944236i	$0.393198\pi$
$998$	4.10463	−	28.5483i	0.129930	−	0.903681i
$999$	0.200109	+	0.438179i	0.00633118	+	0.0138634i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.k.g.101.8		100
5.2	odd	4		115.2.j.a.9.8	yes	100
5.3	odd	4		115.2.j.a.9.3	✓	100
5.4	even	2	inner	575.2.k.g.101.3		100
23.18	even	11	inner	575.2.k.g.501.8		100
115.18	odd	44		115.2.j.a.64.8	yes	100
115.64	even	22	inner	575.2.k.g.501.3		100
115.87	odd	44		115.2.j.a.64.3	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.j.a.9.3	✓	100	5.3	odd	4
115.2.j.a.9.8	yes	100	5.2	odd	4
115.2.j.a.64.3	yes	100	115.87	odd	44
115.2.j.a.64.8	yes	100	115.18	odd	44
575.2.k.g.101.3		100	5.4	even	2	inner
575.2.k.g.101.8		100	1.1	even	1	trivial
575.2.k.g.501.3		100	115.64	even	22	inner
575.2.k.g.501.8		100	23.18	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.k (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34433 - 0.394732i) q^{2} +(1.70867 + 1.97191i) q^{3} +(-0.0310904 + 0.0199806i) q^{4} +(3.07540 + 1.97644i) q^{6} +(-1.22473 + 2.68179i) q^{7} +(-1.86894 + 2.15687i) q^{8} +(-0.541936 + 3.76925i) q^{9} +O(q^{10})\)	\(q+(1.34433 - 0.394732i) q^{2} +(1.70867 + 1.97191i) q^{3} +(-0.0310904 + 0.0199806i) q^{4} +(3.07540 + 1.97644i) q^{6} +(-1.22473 + 2.68179i) q^{7} +(-1.86894 + 2.15687i) q^{8} +(-0.541936 + 3.76925i) q^{9} +(1.52091 + 0.446579i) q^{11} +(-0.0925233 - 0.0271673i) q^{12} +(-1.93920 - 4.24625i) q^{13} +(-0.587861 + 4.08866i) q^{14} +(-1.63039 + 3.57005i) q^{16} +(-1.11128 - 0.714176i) q^{17} +(0.759299 + 5.28104i) q^{18} +(4.70724 - 3.02516i) q^{19} +(-7.38094 + 2.16724i) q^{21} +2.22088 q^{22} +(1.60736 + 4.51845i) q^{23} -7.44658 q^{24} +(-4.28306 - 4.94291i) q^{26} +(-1.77358 + 1.13981i) q^{27} +(-0.0155063 - 0.107849i) q^{28} +(4.78017 + 3.07203i) q^{29} +(4.02560 - 4.64579i) q^{31} +(0.0297487 - 0.206907i) q^{32} +(1.71812 + 3.76216i) q^{33} +(-1.77584 - 0.521433i) q^{34} +(-0.0584628 - 0.128016i) q^{36} +(0.0325170 - 0.226161i) q^{37} +(5.13396 - 5.92491i) q^{38} +(5.05979 - 11.0794i) q^{39} +(-0.944912 - 6.57201i) q^{41} +(-9.06696 + 5.82698i) q^{42} +(4.05429 + 4.67889i) q^{43} +(-0.0562086 + 0.0165043i) q^{44} +(3.94440 + 5.43983i) q^{46} +9.26629 q^{47} +(-9.82563 + 2.88507i) q^{48} +(-1.10802 - 1.27872i) q^{49} +(-0.490520 - 3.41164i) q^{51} +(0.145133 + 0.0932714i) q^{52} +(-3.57091 + 7.81920i) q^{53} +(-1.93436 + 2.23238i) q^{54} +(-3.49533 - 7.65371i) q^{56} +(14.0085 + 4.11326i) q^{57} +(7.63876 + 2.24294i) q^{58} +(-4.84630 - 10.6119i) q^{59} +(-2.17039 + 2.50477i) q^{61} +(3.57791 - 7.83452i) q^{62} +(-9.44462 - 6.06969i) q^{63} +(-1.15877 - 8.05944i) q^{64} +(3.79477 + 4.37939i) q^{66} +(-10.1128 + 2.96939i) q^{67} +0.0488198 q^{68} +(-6.16355 + 10.8901i) q^{69} +(-7.18012 + 2.10827i) q^{71} +(-7.11694 - 8.21339i) q^{72} +(0.256729 - 0.164990i) q^{73} +(-0.0455592 - 0.316871i) q^{74} +(-0.0859054 + 0.188107i) q^{76} +(-3.06034 + 3.53182i) q^{77} +(2.42865 - 16.8916i) q^{78} +(3.42189 + 7.49289i) q^{79} +(5.68318 + 1.66873i) q^{81} +(-3.86445 - 8.46197i) q^{82} +(0.965140 - 6.71269i) q^{83} +(0.186174 - 0.214856i) q^{84} +(7.29721 + 4.68964i) q^{86} +(2.10997 + 14.6752i) q^{87} +(-3.80570 + 2.44578i) q^{88} +(-5.15177 - 5.94546i) q^{89} +13.7626 q^{91} +(-0.140255 - 0.108365i) q^{92} +16.0395 q^{93} +(12.4570 - 3.65770i) q^{94} +(0.458834 - 0.294875i) q^{96} +(-0.807595 - 5.61695i) q^{97} +(-1.99430 - 1.28166i) q^{98} +(-2.50750 + 5.49066i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9}+O(q^{10}) \) 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9	\( 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9} - 26 q^{11} + 26 q^{14} - 18 q^{16} + 14 q^{19} - 22 q^{21} + 68 q^{24} - 42 q^{26} + 24 q^{29} - 12 q^{31} - 8 q^{34} - 10 q^{36} - 14 q^{39} + 8 q^{41} - 166 q^{44} - 18 q^{46} - 32 q^{49} - 22 q^{51} - 116 q^{54} - 116 q^{56} - 50 q^{59} - 38 q^{61} - 10 q^{64} - 28 q^{66} - 80 q^{69} - 110 q^{71} - 22 q^{74} + 4 q^{76} - 42 q^{79} + 204 q^{81} - 56 q^{84} + 132 q^{86} + 66 q^{89} + 76 q^{91} + 70 q^{94} + 236 q^{96} + 60 q^{99}+O(q^{100}) \) 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9 - 26 * q^11 + 26 * q^14 - 18 * q^16 + 14 * q^19 - 22 * q^21 + 68 * q^24 - 42 * q^26 + 24 * q^29 - 12 * q^31 - 8 * q^34 - 10 * q^36 - 14 * q^39 + 8 * q^41 - 166 * q^44 - 18 * q^46 - 32 * q^49 - 22 * q^51 - 116 * q^54 - 116 * q^56 - 50 * q^59 - 38 * q^61 - 10 * q^64 - 28 * q^66 - 80 * q^69 - 110 * q^71 - 22 * q^74 + 4 * q^76 - 42 * q^79 + 204 * q^81 - 56 * q^84 + 132 * q^86 + 66 * q^89 + 76 * q^91 + 70 * q^94 + 236 * q^96 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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