LMFDB - Embedded newform 961.2.g.t.732.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(235,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([26])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.235"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,4,3,6,-3,11,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
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} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			732.1
Root			$-0.176392i$ of defining polynomial
Character	$\chi$	$=$	961.732
Dual form			961.2.g.t.235.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.996848 - 0.724253i) q^{2} +(1.89558 + 0.843968i) q^{3} +(-0.148869 - 0.458173i) q^{4} +(0.772811 - 1.33855i) q^{5} +(-1.27836 - 2.21419i) q^{6} +(-2.54521 + 2.82674i) q^{7} +(-0.944957 + 2.90828i) q^{8} +(0.873564 + 0.970191i) q^{9} +(-1.73982 + 0.774619i) q^{10} +(3.67933 + 0.782065i) q^{11} +(0.104489 - 0.994146i) q^{12} +(0.275439 + 2.62063i) q^{13} +(4.58447 - 0.974458i) q^{14} +(2.59462 - 1.88510i) q^{15} +(2.26882 - 1.64839i) q^{16} +(-3.69186 + 0.784729i) q^{17} +(-0.168147 - 1.59981i) q^{18} +(-0.637447 + 6.06491i) q^{19} +(-0.728335 - 0.154812i) q^{20} +(-7.21034 + 3.21025i) q^{21} +(-3.10132 - 3.44436i) q^{22} +(0.281158 - 0.865316i) q^{23} +(-4.24574 + 4.71537i) q^{24} +(1.30553 + 2.26124i) q^{25} +(1.62343 - 2.81186i) q^{26} +(-1.08650 - 3.34392i) q^{27} +(1.67404 + 0.745331i) q^{28} +(5.50827 + 4.00199i) q^{29} -3.95173 q^{30} +2.66037 q^{32} +(6.31443 + 4.58770i) q^{33} +(4.24857 + 1.89158i) q^{34} +(1.81676 + 5.59143i) q^{35} +(0.314468 - 0.544675i) q^{36} +(0.907032 + 1.57103i) q^{37} +(5.02796 - 5.58412i) q^{38} +(-1.68961 + 5.20008i) q^{39} +(3.16260 + 3.51242i) q^{40} +(0.307997 - 0.137129i) q^{41} +(9.51265 + 2.02198i) q^{42} +(-0.405988 + 3.86272i) q^{43} +(-0.189418 - 1.80219i) q^{44} +(1.97375 - 0.419533i) q^{45} +(-0.906980 + 0.658959i) q^{46} +(0.962040 - 0.698963i) q^{47} +(5.69192 - 1.20986i) q^{48} +(-0.780679 - 7.42766i) q^{49} +(0.336296 - 3.19964i) q^{50} +(-7.66052 - 1.62829i) q^{51} +(1.15970 - 0.516330i) q^{52} +(-1.56853 - 1.74202i) q^{53} +(-1.33876 + 4.12028i) q^{54} +(3.89026 - 4.32057i) q^{55} +(-5.81584 - 10.0733i) q^{56} +(-6.32692 + 10.9586i) q^{57} +(-2.59245 - 7.97875i) q^{58} +(7.10632 + 3.16394i) q^{59} +(-1.24996 - 0.908151i) q^{60} -2.72343 q^{61} -4.96588 q^{63} +(-7.18962 - 5.22357i) q^{64} +(3.72070 + 1.65656i) q^{65} +(-2.97187 - 9.14649i) q^{66} +(3.71059 - 6.42693i) q^{67} +(0.909147 + 1.57469i) q^{68} +(1.26326 - 1.40299i) q^{69} +(2.23857 - 6.88960i) q^{70} +(-3.41135 - 3.78869i) q^{71} +(-3.64706 + 1.62378i) q^{72} +(-5.27392 - 1.12101i) q^{73} +(0.233646 - 2.22299i) q^{74} +(0.566321 + 5.38818i) q^{75} +(2.87367 - 0.610818i) q^{76} +(-11.5754 + 8.40999i) q^{77} +(5.45046 - 3.95999i) q^{78} +(9.52444 - 2.02448i) q^{79} +(-0.453085 - 4.31082i) q^{80} +(1.17199 - 11.1508i) q^{81} +(-0.406342 - 0.0863707i) q^{82} +(-7.66935 + 3.41461i) q^{83} +(2.54425 + 2.82568i) q^{84} +(-1.80271 + 5.54818i) q^{85} +(3.20229 - 3.55651i) q^{86} +(7.06383 + 12.2349i) q^{87} +(-5.75127 + 9.96149i) q^{88} +(1.57463 + 4.84620i) q^{89} +(-2.27137 - 1.01128i) q^{90} +(-8.10889 - 5.89146i) q^{91} -0.438320 q^{92} -1.46523 q^{94} +(7.62555 + 5.54028i) q^{95} +(5.04296 + 2.24527i) q^{96} +(3.37268 + 10.3800i) q^{97} +(-4.60129 + 7.96966i) q^{98} +(2.45537 + 4.25283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} + 11 q^{6} + 12 q^{7} - 8 q^{8} + 5 q^{9} - 12 q^{10} - 2 q^{11} + 25 q^{12} + 18 q^{13} + 24 q^{14} + 4 q^{15} - 2 q^{16} - q^{17} - 8 q^{18} + 11 q^{19} - 18 q^{20}+ \cdots + 6 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 + 11 * q^6 + 12 * q^7 - 8 * q^8 + 5 * q^9 - 12 * q^10 - 2 * q^11 + 25 * q^12 + 18 * q^13 + 24 * q^14 + 4 * q^15 - 2 * q^16 - q^17 - 8 * q^18 + 11 * q^19 - 18 * q^20 - 31 * q^21 + 4 * q^22 + 21 * q^23 + 20 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 + 20 * q^28 + 26 * q^29 - 22 * q^30 - 42 * q^32 + 7 * q^33 + 28 * q^34 + 21 * q^35 + q^36 - 8 * q^37 + 3 * q^38 + 2 * q^39 + 29 * q^40 - 3 * q^41 + 39 * q^42 + 8 * q^43 - 41 * q^44 - 20 * q^45 - 16 * q^46 + 4 * q^47 + 49 * q^48 + 12 * q^49 + 48 * q^50 - 2 * q^51 - 6 * q^52 - 69 * q^53 + 39 * q^54 + 23 * q^55 - 30 * q^56 - 17 * q^57 + 10 * q^58 + 54 * q^59 + 35 * q^60 - 60 * q^61 - 46 * q^63 - 32 * q^64 - 27 * q^65 + 20 * q^66 + 13 * q^67 + 30 * q^68 - 27 * q^69 + 27 * q^70 + 6 * q^71 + 2 * q^72 - 18 * q^73 - 92 * q^74 + 13 * q^75 - 27 * q^76 - 42 * q^77 + 15 * q^78 - 22 * q^79 + 21 * q^80 - 22 * q^81 - 61 * q^82 - 71 * q^83 - 12 * q^84 - 63 * q^85 - 11 * q^86 + 15 * q^87 - 17 * q^88 + 26 * q^89 - 33 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 + 28 * q^95 + 58 * q^96 - 37 * q^97 - 10 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{15}\right)$

Coefficient data

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

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

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

$2$	−0.996848	−	0.724253i	−0.704878	−	0.512124i	0.176639	−	0.984276i	$-0.443477\pi$
$2$	−0.996848	−	0.724253i	−0.704878	−	0.512124i	−0.881517	+	0.472152i	$0.843477\pi$
$3$	1.89558	+	0.843968i	1.09442	+	0.487265i	0.872904	−	0.487892i	$-0.162234\pi$
$3$	1.89558	+	0.843968i	1.09442	+	0.487265i	0.221512	+	0.975158i	$0.428901\pi$
$4$	−0.148869	−	0.458173i	−0.0744347	−	0.229086i
$5$	0.772811	−	1.33855i	0.345612	−	0.598617i	−0.639853	−	0.768497i	$-0.721005\pi$
$5$	0.772811	−	1.33855i	0.345612	−	0.598617i	0.985465	+	0.169880i	$0.0543381\pi$
$6$	−1.27836	−	2.21419i	−0.521890	−	0.903939i
$7$	−2.54521	+	2.82674i	−0.961999	+	1.06841i	0.0356144	+	0.999366i	$0.488661\pi$
$7$	−2.54521	+	2.82674i	−0.961999	+	1.06841i	−0.997614	+	0.0690429i	$0.978005\pi$
$8$	−0.944957	+	2.90828i	−0.334093	+	1.02823i
$9$	0.873564	+	0.970191i	0.291188	+	0.323397i
$10$	−1.73982	+	0.774619i	−0.550180	+	0.244956i
$11$	3.67933	+	0.782065i	1.10936	+	0.235801i	0.725930	−	0.687769i	$-0.241410\pi$
$11$	3.67933	+	0.782065i	1.10936	+	0.235801i	0.383429	+	0.923570i	$0.374743\pi$
$12$	0.104489	−	0.994146i	0.0301634	−	0.286985i
$13$	0.275439	+	2.62063i	0.0763931	+	0.726831i	0.963941	+	0.266116i	$0.0857405\pi$
$13$	0.275439	+	2.62063i	0.0763931	+	0.726831i	−0.887548	+	0.460715i	$0.847593\pi$
$14$	4.58447	−	0.974458i	1.22525	−	0.260435i
$15$	2.59462	−	1.88510i	0.669928	−	0.486731i
$16$	2.26882	−	1.64839i	0.567204	−	0.412098i
$17$	−3.69186	+	0.784729i	−0.895408	+	0.190325i	−0.632559	−	0.774512i	$-0.717995\pi$
$17$	−3.69186	+	0.784729i	−0.895408	+	0.190325i	−0.262849	+	0.964837i	$0.584662\pi$
$18$	−0.168147	−	1.59981i	−0.0396327	−	0.377080i
$19$	−0.637447	+	6.06491i	−0.146240	+	1.39139i	0.637574	+	0.770390i	$0.279938\pi$
$19$	−0.637447	+	6.06491i	−0.146240	+	1.39139i	−0.783814	+	0.620996i	$0.786728\pi$
$20$	−0.728335	−	0.154812i	−0.162861	−	0.0346171i
$21$	−7.21034	+	3.21025i	−1.57343	+	0.700534i
$22$	−3.10132	−	3.44436i	−0.661203	−	0.734340i
$23$	0.281158	−	0.865316i	0.0586255	−	0.180431i	−0.917455	−	0.397839i	$-0.869760\pi$
$23$	0.281158	−	0.865316i	0.0586255	−	0.180431i	0.976081	+	0.217408i	$0.0697603\pi$
$24$	−4.24574	+	4.71537i	−0.866658	+	0.962521i
$25$	1.30553	+	2.26124i	0.261105	+	0.452247i
$26$	1.62343	−	2.81186i	0.318380	−	0.551450i
$27$	−1.08650	−	3.34392i	−0.209098	−	0.643537i
$28$	1.67404	+	0.745331i	0.316364	+	0.140854i
$29$	5.50827	+	4.00199i	1.02286	+	0.743151i	0.966867	−	0.255280i	$-0.0821678\pi$
$29$	5.50827	+	4.00199i	1.02286	+	0.743151i	0.0559922	+	0.998431i	$0.482168\pi$
$30$	−3.95173			−0.721485
$31$		0			0
$31$		0			0
$32$	2.66037			0.470292
$33$	6.31443	+	4.58770i	1.09920	+	0.798617i
$34$	4.24857	+	1.89158i	0.728623	+	0.324404i
$35$	1.81676	+	5.59143i	0.307089	+	0.945124i
$36$	0.314468	−	0.544675i	0.0524114	−	0.0907792i
$37$	0.907032	+	1.57103i	0.149115	+	0.258275i	0.930901	−	0.365272i	$-0.119024\pi$
$37$	0.907032	+	1.57103i	0.149115	+	0.258275i	−0.781786	+	0.623547i	$0.785691\pi$
$38$	5.02796	−	5.58412i	0.815643	−	0.905864i
$39$	−1.68961	+	5.20008i	−0.270554	+	0.832680i
$40$	3.16260	+	3.51242i	0.500051	+	0.555363i
$41$	0.307997	−	0.137129i	0.0481010	−	0.0214160i	−0.382545	−	0.923937i	$-0.624952\pi$
$41$	0.307997	−	0.137129i	0.0481010	−	0.0214160i	0.430646	+	0.902521i	$0.358286\pi$
$42$	9.51265	+	2.02198i	1.46783	+	0.311998i
$43$	−0.405988	+	3.86272i	−0.0619126	+	0.589059i	0.918952	+	0.394369i	$0.129037\pi$
$43$	−0.405988	+	3.86272i	−0.0619126	+	0.589059i	−0.980865	+	0.194690i	$0.937630\pi$
$44$	−0.189418	−	1.80219i	−0.0285559	−	0.271691i
$45$	1.97375	−	0.419533i	0.294229	−	0.0625403i
$46$	−0.906980	+	0.658959i	−0.133727	+	0.0971582i
$47$	0.962040	−	0.698963i	0.140328	−	0.101954i	−0.515407	−	0.856946i	$-0.672359\pi$
$47$	0.962040	−	0.698963i	0.140328	−	0.101954i	0.655735	+	0.754992i	$0.272359\pi$
$48$	5.69192	−	1.20986i	0.821558	−	0.174628i
$49$	−0.780679	−	7.42766i	−0.111526	−	1.06109i
$50$	0.336296	−	3.19964i	0.0475594	−	0.452497i
$51$	−7.66052	−	1.62829i	−1.07269	−	0.228007i
$52$	1.15970	−	0.516330i	0.160821	−	0.0716021i
$53$	−1.56853	−	1.74202i	−0.215454	−	0.239286i	0.625724	−	0.780045i	$-0.284804\pi$
$53$	−1.56853	−	1.74202i	−0.215454	−	0.239286i	−0.841177	+	0.540759i	$0.818137\pi$
$54$	−1.33876	+	4.12028i	−0.182182	+	0.560699i
$55$	3.89026	−	4.32057i	0.524562	−	0.582585i
$56$	−5.81584	−	10.0733i	−0.777175	−	1.34611i
$57$	−6.32692	+	10.9586i	−0.838022	+	1.45150i
$58$	−2.59245	−	7.97875i	−0.340406	−	1.04766i
$59$	7.10632	+	3.16394i	0.925164	+	0.411909i	0.813320	−	0.581816i	$-0.197658\pi$
$59$	7.10632	+	3.16394i	0.925164	+	0.411909i	0.111843	+	0.993726i	$0.464324\pi$
$60$	−1.24996	−	0.908151i	−0.161369	−	0.117242i
$61$	−2.72343			−0.348700			−0.174350	−	0.984684i	$-0.555782\pi$
$61$	−2.72343			−0.348700			−0.174350	+	0.984684i	$0.555782\pi$
$62$		0			0
$63$	−4.96588			−0.625642
$64$	−7.18962	−	5.22357i	−0.898703	−	0.652946i
$65$	3.72070	+	1.65656i	0.461496	+	0.205471i
$66$	−2.97187	−	9.14649i	−0.365812	−	1.12586i
$67$	3.71059	−	6.42693i	0.453321	−	0.785175i	−0.545269	−	0.838261i	$-0.683573\pi$
$67$	3.71059	−	6.42693i	0.453321	−	0.785175i	0.998590	+	0.0530864i	$0.0169059\pi$
$68$	0.909147	+	1.57469i	0.110250	+	0.190959i
$69$	1.26326	−	1.40299i	0.152078	−	0.168900i
$70$	2.23857	−	6.88960i	0.267560	−	0.823465i
$71$	−3.41135	−	3.78869i	−0.404853	−	0.449634i	0.505897	−	0.862594i	$-0.331162\pi$
$71$	−3.41135	−	3.78869i	−0.404853	−	0.449634i	−0.910749	+	0.412960i	$0.864495\pi$
$72$	−3.64706	+	1.62378i	−0.429811	+	0.191364i
$73$	−5.27392	−	1.12101i	−0.617266	−	0.131204i	−0.111342	−	0.993782i	$-0.535515\pi$
$73$	−5.27392	−	1.12101i	−0.617266	−	0.131204i	−0.505924	+	0.862578i	$0.668848\pi$
$74$	0.233646	−	2.22299i	0.0271608	−	0.258418i
$75$	0.566321	+	5.38818i	0.0653931	+	0.622174i
$76$	2.87367	−	0.610818i	0.329633	−	0.0700656i
$77$	−11.5754	+	8.40999i	−1.31913	+	0.958407i
$78$	5.45046	−	3.95999i	0.617143	−	0.448380i
$79$	9.52444	−	2.02448i	1.07158	−	0.227772i	0.361846	−	0.932238i	$-0.382147\pi$
$79$	9.52444	−	2.02448i	1.07158	−	0.227772i	0.709738	+	0.704466i	$0.248813\pi$
$80$	−0.453085	−	4.31082i	−0.0506565	−	0.481964i
$81$	1.17199	−	11.1508i	0.130221	−	1.23897i
$82$	−0.406342	−	0.0863707i	−0.0448730	−	0.00953805i
$83$	−7.66935	+	3.41461i	−0.841820	+	0.374803i	−0.781902	−	0.623401i	$-0.785751\pi$
$83$	−7.66935	+	3.41461i	−0.841820	+	0.374803i	−0.0599178	+	0.998203i	$0.519084\pi$
$84$	2.54425	+	2.82568i	0.277600	+	0.308306i
$85$	−1.80271	+	5.54818i	−0.195532	+	0.601785i
$86$	3.20229	−	3.55651i	0.345312	−	0.383508i
$87$	7.06383	+	12.2349i	0.757322	+	1.31172i
$88$	−5.75127	+	9.96149i	−0.613087	+	1.06190i
$89$	1.57463	+	4.84620i	0.166910	+	0.513696i	0.999172	−	0.0406863i	$-0.0129544\pi$
$89$	1.57463	+	4.84620i	0.166910	+	0.513696i	−0.832262	+	0.554383i	$0.812954\pi$
$90$	−2.27137	−	1.01128i	−0.239424	−	0.106598i
$91$	−8.10889	−	5.89146i	−0.850043	−	0.617592i
$92$	−0.438320			−0.0456980
$93$		0			0
$94$	−1.46523			−0.151127
$95$	7.62555	+	5.54028i	0.782365	+	0.568421i
$96$	5.04296	+	2.24527i	0.514695	+	0.229157i
$97$	3.37268	+	10.3800i	0.342444	+	1.05393i	0.962938	+	0.269723i	$0.0869320\pi$
$97$	3.37268	+	10.3800i	0.342444	+	1.05393i	−0.620494	+	0.784211i	$0.713068\pi$
$98$	−4.60129	+	7.96966i	−0.464800	+	0.805057i
$99$	2.45537	+	4.25283i	0.246774	+	0.427426i
$100$	0.841684	−	0.934785i	0.0841684	−	0.0934785i
$101$	−0.123213	+	0.379212i	−0.0122602	+	0.0377330i	−0.956999	−	0.290090i	$-0.906315\pi$
$101$	−0.123213	+	0.379212i	−0.0122602	+	0.0377330i	0.944739	+	0.327823i	$0.106315\pi$
$102$	6.45708	+	7.17131i	0.639346	+	0.710066i
$103$	2.99351	−	1.33280i	0.294959	−	0.131324i	−0.253922	−	0.967225i	$-0.581721\pi$
$103$	2.99351	−	1.33280i	0.294959	−	0.131324i	0.548881	+	0.835900i	$0.315054\pi$
$104$	−7.88180	−	1.67533i	−0.772874	−	0.164279i
$105$	−1.27516	+	12.1323i	−0.124443	+	1.18399i
$106$	0.301917	+	2.87254i	0.0293247	+	0.279006i
$107$	−3.08786	+	0.656345i	−0.298515	+	0.0634513i	−0.354734	−	0.934967i	$-0.615429\pi$
$107$	−3.08786	+	0.656345i	−0.298515	+	0.0634513i	0.0562195	+	0.998418i	$0.482095\pi$
$108$	−1.37035	+	0.995614i	−0.131862	+	0.0958030i
$109$	−5.62770	+	4.08876i	−0.539036	+	0.391632i	−0.823727	−	0.566987i	$-0.808109\pi$
$109$	−5.62770	+	4.08876i	−0.539036	+	0.391632i	0.284691	+	0.958619i	$0.408109\pi$
$110$	−7.00718	+	1.48942i	−0.668108	+	0.142011i
$111$	0.393459	+	3.74352i	0.0373455	+	0.355319i
$112$	−1.11504	+	10.6089i	−0.105361	+	1.00244i
$113$	14.9136	+	3.16999i	1.40295	+	0.298207i	0.846375	−	0.532587i	$-0.178780\pi$
$113$	14.9136	+	3.16999i	1.40295	+	0.298207i	0.556579	+	0.830795i	$0.312114\pi$
$114$	14.2437	−	6.34172i	1.33405	−	0.593957i
$115$	−0.940985	−	1.04507i	−0.0877473	−	0.0974533i
$116$	1.01359	−	3.11951i	0.0941096	−	0.289639i
$117$	−2.30190	+	2.55651i	−0.212810	+	0.236350i
$118$	−4.79243	−	8.30073i	−0.441179	−	0.764144i
$119$	7.17834	−	12.4332i	0.658037	−	1.13975i
$120$	3.03060	+	9.32722i	0.276655	+	0.851455i
$121$	2.87681	+	1.28084i	0.261529	+	0.116440i
$122$	2.71485	+	1.97245i	0.245791	+	0.178578i
$123$	0.699567			0.0630778
$124$		0			0
$125$	11.7638			1.05219
$126$	4.95023	+	3.59655i	0.441002	+	0.320407i
$127$	−18.4777	−	8.22681i	−1.63963	−	0.730011i	−0.640356	−	0.768078i	$-0.721213\pi$
$127$	−18.4777	−	8.22681i	−1.63963	−	0.730011i	−0.999275	+	0.0380671i	$0.987880\pi$
$128$	1.73958	+	5.35388i	0.153759	+	0.473220i
$129$	−4.02960	+	6.97946i	−0.354786	+	0.614508i
$130$	−2.50920	−	4.34607i	−0.220072	−	0.381175i
$131$	8.46536	−	9.40173i	0.739622	−	0.821433i	−0.249524	−	0.968369i	$-0.580274\pi$
$131$	8.46536	−	9.40173i	0.739622	−	0.821433i	0.989146	+	0.146935i	$0.0469409\pi$
$132$	1.16194	−	3.57607i	0.101134	−	0.311257i
$133$	−15.5215	−	17.2384i	−1.34588	−	1.49476i
$134$	−8.35362	+	3.71927i	−0.721643	+	0.321296i
$135$	−5.31566	−	1.12988i	−0.457499	−	0.0972444i
$136$	1.20644	−	11.4785i	0.103451	−	0.984273i
$137$	1.03253	+	9.82390i	0.0882153	+	0.839312i	0.945752	+	0.324890i	$0.105327\pi$
$137$	1.03253	+	9.82390i	0.0882153	+	0.839312i	−0.857537	+	0.514423i	$0.828006\pi$
$138$	−2.27540	+	0.483650i	−0.193695	+	0.0411711i
$139$	12.5389	−	9.11007i	1.06354	−	0.772706i	0.0887990	−	0.996050i	$-0.471697\pi$
$139$	12.5389	−	9.11007i	1.06354	−	0.772706i	0.974740	+	0.223343i	$0.0716971\pi$
$140$	2.29138	−	1.66479i	0.193657	−	0.140700i
$141$	2.41353	−	0.513012i	0.203256	−	0.0432034i
$142$	0.656631	+	6.24742i	0.0551032	+	0.524272i
$143$	−1.03607	+	9.85756i	−0.0866406	+	0.824330i
$144$	3.58121	+	0.761210i	0.298434	+	0.0634342i
$145$	9.61371	−	4.28030i	0.798375	−	0.355459i
$146$	4.44541	+	4.93713i	0.367905	+	0.408599i
$147$	4.78887	−	14.7386i	0.394979	−	1.21562i
$148$	0.584772	−	0.649455i	0.0480680	−	0.0533849i
$149$	7.62162	+	13.2010i	0.624388	+	1.08147i	0.988659	+	0.150178i	$0.0479848\pi$
$149$	7.62162	+	13.2010i	0.624388	+	1.08147i	−0.364271	+	0.931293i	$0.618682\pi$
$150$	3.33787	−	5.78136i	0.272536	−	0.472046i
$151$	−0.0809093	−	0.249013i	−0.00658430	−	0.0202644i	0.947710	−	0.319132i	$-0.103391\pi$
$151$	−0.0809093	−	0.249013i	−0.00658430	−	0.0202644i	−0.954295	+	0.298867i	$0.903391\pi$
$152$	−17.0361	−	7.58495i	−1.38181	−	0.615221i
$153$	−3.98641	−	2.89630i	−0.322282	−	0.234152i
$154$	17.6298			1.42065
$155$		0			0
$156$	2.63407			0.210894
$157$	−12.8848	−	9.36138i	−1.02832	−	0.747120i	−0.0603497	−	0.998177i	$-0.519222\pi$
$157$	−12.8848	−	9.36138i	−1.02832	−	0.747120i	−0.967972	+	0.251058i	$0.919222\pi$
$158$	−10.9607	−	4.88000i	−0.871984	−	0.388232i
$159$	−1.50306	−	4.62594i	−0.119200	−	0.366861i
$160$	2.05597	−	3.56104i	0.162538	−	0.281525i
$161$	1.73042	+	2.99717i	0.136376	+	0.236210i
$162$	−9.24426	+	10.2668i	−0.726298	+	0.806636i
$163$	−0.0411534	+	0.126657i	−0.00322339	+	0.00992056i	−0.952655	−	0.304053i	$-0.901660\pi$
$163$	−0.0411534	+	0.126657i	−0.00322339	+	0.00992056i	0.949432	+	0.313973i	$0.101660\pi$
$164$	−0.108680	−	0.120702i	−0.00848650	−	0.00942521i
$165$	11.0207	−	4.90674i	0.857963	−	0.381990i
$166$	10.1182	+	2.15069i	0.785326	+	0.166926i
$167$	0.412760	−	3.92715i	0.0319403	−	0.303892i	−0.966876	−	0.255247i	$-0.917843\pi$
$167$	0.412760	−	3.92715i	0.0319403	−	0.303892i	0.998816	−	0.0486446i	$-0.0154902\pi$
$168$	−2.52284	−	24.0032i	−0.194641	−	1.85189i
$169$	5.92409	−	1.25920i	0.455699	−	0.0968619i
$170$	5.81532	−	4.22508i	0.446015	−	0.324049i
$171$	−6.44097	+	4.67964i	−0.492553	+	0.357861i
$172$	1.83023	−	0.389028i	0.139554	−	0.0296631i
$173$	1.51116	+	14.3777i	0.114891	+	1.09312i	0.888316	+	0.459232i	$0.151875\pi$
$173$	1.51116	+	14.3777i	0.114891	+	1.09312i	−0.773425	+	0.633888i	$0.781458\pi$
$174$	1.81960	−	17.3123i	0.137944	−	1.31245i
$175$	−9.71477	−	2.06494i	−0.734368	−	0.156095i
$176$	9.63687	−	4.29061i	0.726406	−	0.323417i
$177$	10.8004	+	11.9950i	0.811805	+	0.901600i
$178$	1.94021	−	5.97136i	0.145425	−	0.447572i
$179$	−11.8569	+	13.1684i	−0.886228	+	0.984256i	−0.999957	−	0.00925620i	$-0.997054\pi$
$179$	−11.8569	+	13.1684i	−0.886228	+	0.984256i	0.113729	+	0.993512i	$0.463720\pi$
$180$	−0.486049	−	0.841862i	−0.0362280	−	0.0627487i
$181$	6.02958	−	10.4435i	0.448175	−	0.776262i	−0.550092	−	0.835104i	$-0.685407\pi$
$181$	6.02958	−	10.4435i	0.448175	−	0.776262i	0.998267	+	0.0588418i	$0.0187408\pi$
$182$	3.81643	+	11.7458i	0.282893	+	0.870655i
$183$	−5.16250	−	2.29849i	−0.381623	−	0.169909i
$184$	2.25090	+	1.63537i	0.165938	+	0.120561i
$185$	2.80386			0.206144
$186$		0			0
$187$	−14.1973			−1.03821
$188$	−0.463464	−	0.336727i	−0.0338016	−	0.0245583i
$189$	12.2178	+	5.43971i	0.888713	+	0.395680i
$190$	−3.58895	−	11.0456i	−0.260370	−	0.801335i
$191$	−2.53576	+	4.39207i	−0.183481	+	0.317799i	−0.943064	−	0.332612i	$-0.892070\pi$
$191$	−2.53576	+	4.39207i	−0.183481	+	0.317799i	0.759583	+	0.650411i	$0.225403\pi$
$192$	−9.22001	−	15.9695i	−0.665397	−	1.15250i
$193$	−13.4105	+	14.8939i	−0.965312	+	1.07209i	0.0320489	+	0.999486i	$0.489797\pi$
$193$	−13.4105	+	14.8939i	−0.965312	+	1.07209i	−0.997361	+	0.0726015i	$0.976870\pi$
$194$	4.15572	−	12.7900i	0.298364	−	0.918269i
$195$	5.65481	+	6.28031i	0.404950	+	0.449742i
$196$	−3.28693	+	1.46344i	−0.234781	+	0.104531i
$197$	−21.2340	−	4.51342i	−1.51286	−	0.321568i	−0.624612	−	0.780935i	$-0.714743\pi$
$197$	−21.2340	−	4.51342i	−1.51286	−	0.321568i	−0.888246	+	0.459367i	$0.848076\pi$
$198$	0.632490	−	6.01774i	0.0449491	−	0.427662i
$199$	−1.58523	−	15.0824i	−0.112374	−	1.06917i	−0.894814	−	0.446439i	$-0.852692\pi$
$199$	−1.58523	−	15.0824i	−0.112374	−	1.06917i	0.782440	−	0.622726i	$-0.213975\pi$
$200$	−7.80997	+	1.66006i	−0.552248	+	0.117384i
$201$	12.4579	−	9.05117i	0.878710	−	0.638420i
$202$	0.397470	−	0.288779i	0.0279659	−	0.0203184i
$203$	−25.3323	+	5.38455i	−1.77798	+	0.377921i
$204$	0.394377	+	3.75225i	0.0276119	+	0.262710i
$205$	0.0544696	−	0.518244i	0.00380432	−	0.0361957i
$206$	−3.94935	−	0.839461i	−0.275165	−	0.0584880i
$207$	1.08513	−	0.483131i	0.0754218	−	0.0335800i
$208$	4.94474	+	5.49169i	0.342856	+	0.380781i
$209$	−7.08853	+	21.8162i	−0.490324	+	1.50906i
$210$	10.0580	−	11.1705i	0.694068	−	0.770840i
$211$	−3.15220	−	5.45978i	−0.217007	−	0.375867i	0.736885	−	0.676018i	$-0.236296\pi$
$211$	−3.15220	−	5.45978i	−0.217007	−	0.375867i	−0.953891	+	0.300152i	$0.902963\pi$
$212$	−0.564643	+	0.977990i	−0.0387798	+	0.0671687i
$213$	−3.26897	−	10.0608i	−0.223986	−	0.689358i
$214$	3.55349	+	1.58212i	0.242912	+	0.108151i
$215$	4.85668	+	3.52859i	0.331223	+	0.240648i
$216$	10.7517			0.731564
$217$		0			0
$218$	8.57126			0.580519
$219$	−9.05107	−	6.57598i	−0.611614	−	0.444364i
$220$	−2.55871	−	1.13921i	−0.172508	−	0.0768055i
$221$	−3.07337	−	9.45885i	−0.206737	−	0.636271i
$222$	2.31903	−	4.01668i	0.155643	−	0.269582i
$223$	−3.69455	−	6.39915i	−0.247406	−	0.428519i	0.715400	−	0.698716i	$-0.246245\pi$
$223$	−3.69455	−	6.39915i	−0.247406	−	0.428519i	−0.962805	+	0.270196i	$0.912911\pi$
$224$	−6.77121	+	7.52019i	−0.452420	+	0.502464i
$225$	−1.05337	+	3.24194i	−0.0702247	+	0.216129i
$226$	−12.5707	−	13.9612i	−0.836193	−	0.928686i
$227$	17.5764	−	7.82553i	1.16659	−	0.519398i	0.270259	−	0.962788i	$-0.412891\pi$
$227$	17.5764	−	7.82553i	1.16659	−	0.519398i	0.896329	+	0.443389i	$0.146224\pi$
$228$	5.96280	+	1.26743i	0.394896	+	0.0839377i
$229$	0.636276	−	6.05376i	0.0420463	−	0.400044i	−0.953177	−	0.302414i	$-0.902207\pi$
$229$	0.636276	−	6.05376i	0.0420463	−	0.400044i	0.995223	−	0.0976293i	$-0.0311260\pi$
$230$	0.181125	+	1.72329i	0.0119430	+	0.113630i
$231$	−29.0398	+	6.17261i	−1.91068	+	0.406128i
$232$	−16.8440	+	12.2379i	−1.10586	+	0.803455i
$233$	−14.1805	+	10.3027i	−0.928995	+	0.674954i	−0.945746	−	0.324906i	$-0.894667\pi$
$233$	−14.1805	+	10.3027i	−0.928995	+	0.674954i	0.0167519	+	0.999860i	$0.494667\pi$
$234$	4.14620	−	0.881303i	0.271046	−	0.0576125i
$235$	−0.192120	−	1.82790i	−0.0125326	−	0.119239i
$236$	0.391717	−	3.72694i	0.0254986	−	0.242603i
$237$	19.7630	+	4.20075i	1.28374	+	0.272868i
$238$	−16.1605	+	7.19513i	−1.04753	+	0.466391i
$239$	−18.6768	−	20.7427i	−1.20810	−	1.34173i	−0.923742	−	0.383016i	$-0.874886\pi$
$239$	−18.6768	−	20.7427i	−1.20810	−	1.34173i	−0.284360	−	0.958718i	$-0.591781\pi$
$240$	2.77933	−	8.55391i	0.179405	−	0.552152i
$241$	15.2225	−	16.9063i	0.980570	−	1.08903i	−0.0154476	−	0.999881i	$-0.504917\pi$
$241$	15.2225	−	16.9063i	0.980570	−	1.08903i	0.996018	−	0.0891530i	$-0.0284160\pi$
$242$	−1.94010	−	3.36034i	−0.124714	−	0.216011i
$243$	6.35849	−	11.0132i	0.407897	−	0.706499i
$244$	0.405436	+	1.24780i	0.0259554	+	0.0798824i
$245$	−10.5456	−	4.69521i	−0.673734	−	0.299966i
$246$	−0.697362	−	0.506663i	−0.0444622	−	0.0323037i
$247$	−16.0694			−1.02247
$248$		0			0
$249$	−17.4197			−1.10393
$250$	−11.7267	−	8.51997i	−0.741664	−	0.538850i
$251$	−14.8310	−	6.60317i	−0.936121	−	0.416788i	−0.118766	−	0.992922i	$-0.537894\pi$
$251$	−14.8310	−	6.60317i	−0.936121	−	0.416788i	−0.817355	+	0.576134i	$0.804561\pi$
$252$	0.739268	+	2.27523i	0.0465695	+	0.143326i
$253$	1.71121	−	2.96390i	0.107583	−	0.186339i
$254$	12.4612	+	21.5834i	0.781884	+	1.35426i
$255$	−8.09969	+	8.99561i	−0.507222	+	0.563327i
$256$	−3.34892	+	10.3069i	−0.209307	+	0.644182i
$257$	15.6256	+	17.3540i	0.974699	+	1.08251i	0.996570	+	0.0827516i	$0.0263708\pi$
$257$	15.6256	+	17.3540i	0.974699	+	1.08251i	−0.0218716	+	0.999761i	$0.506963\pi$
$258$	9.07179	−	4.03902i	0.564785	−	0.251459i
$259$	−6.74947	−	1.43464i	−0.419392	−	0.0891445i
$260$	0.205094	−	1.95134i	0.0127194	−	0.121017i
$261$	0.929128	+	8.84006i	0.0575116	+	0.547186i
$262$	−15.2479	+	3.24104i	−0.942019	+	0.200232i
$263$	8.40921	−	6.10965i	0.518534	−	0.376737i	−0.297517	−	0.954716i	$-0.596159\pi$
$263$	8.40921	−	6.10965i	0.518534	−	0.376737i	0.816051	+	0.577979i	$0.196159\pi$
$264$	−19.3092	+	14.0289i	−1.18840	+	0.863422i
$265$	−3.54396	+	0.753292i	−0.217704	+	0.0462743i
$266$	2.98764	+	28.4255i	0.183184	+	1.74288i
$267$	−1.10520	+	10.5153i	−0.0676374	+	0.643527i
$268$	−3.49704	−	0.743319i	−0.213616	−	0.0454054i
$269$	−4.03609	+	1.79698i	−0.246084	+	0.109564i	−0.526073	−	0.850440i	$-0.676336\pi$
$269$	−4.03609	+	1.79698i	−0.246084	+	0.109564i	0.279988	+	0.960003i	$0.409669\pi$
$270$	4.48059	+	4.97620i	0.272680	+	0.302842i
$271$	1.90134	−	5.85172i	0.115498	−	0.355467i	−0.876552	−	0.481306i	$-0.840162\pi$
$271$	1.90134	−	5.85172i	0.115498	−	0.355467i	0.992051	+	0.125840i	$0.0401625\pi$
$272$	−7.08262	+	7.86604i	−0.429447	+	0.476949i
$273$	−10.3989	−	18.0114i	−0.629369	−	1.09010i
$274$	6.08571	−	10.5408i	0.367651	−	0.636790i
$275$	3.03502	+	9.34083i	0.183019	+	0.563273i
$276$	−0.830873	−	0.369928i	−0.0500127	−	0.0222671i
$277$	−17.8367	−	12.9591i	−1.07171	−	0.778639i	−0.0954872	−	0.995431i	$-0.530441\pi$
$277$	−17.8367	−	12.9591i	−1.07171	−	0.778639i	−0.976218	+	0.216791i	$0.930441\pi$
$278$	−19.0974			−1.14539
$279$		0			0
$280$	−17.9782			−1.07440
$281$	24.8963	+	18.0882i	1.48519	+	1.07905i	0.975838	+	0.218497i	$0.0701154\pi$
$281$	24.8963	+	18.0882i	1.48519	+	1.07905i	0.509353	+	0.860557i	$0.329885\pi$
$282$	−2.77747	−	1.23661i	−0.165396	−	0.0736391i
$283$	−6.59605	−	20.3005i	−0.392094	−	1.20674i	−0.931202	−	0.364505i	$-0.881238\pi$
$283$	−6.59605	−	20.3005i	−0.392094	−	1.20674i	0.539107	−	0.842237i	$-0.318762\pi$
$284$	−1.22803	+	2.12701i	−0.0728701	+	0.126215i
$285$	9.77904	+	16.9378i	0.579260	+	1.00331i
$286$	8.17217	−	9.07611i	0.483230	−	0.536682i
$287$	−0.396289	+	1.21965i	−0.0233922	+	0.0719937i
$288$	2.32400	+	2.58107i	0.136943	+	0.152091i
$289$	−2.51624	+	1.12030i	−0.148014	+	0.0659000i
$290$	−12.6834	−	2.69595i	−0.744796	−	0.158311i
$291$	−2.36723	+	22.5227i	−0.138769	+	1.32030i
$292$	0.271511	+	2.58325i	0.0158890	+	0.151173i
$293$	1.75971	−	0.374039i	0.102804	−	0.0218516i	−0.156223	−	0.987722i	$-0.549932\pi$
$293$	1.75971	−	0.374039i	0.102804	−	0.0218516i	0.259026	+	0.965870i	$0.416598\pi$
$294$	−15.4483	+	11.2238i	−0.900961	+	0.654587i
$295$	9.72692	−	7.06702i	0.566323	−	0.411458i
$296$	−5.42609	+	1.15335i	−0.315385	+	0.0670371i
$297$	−1.38244	−	13.1531i	−0.0802176	−	0.763219i
$298$	1.96329	−	18.6794i	0.113730	−	1.08207i
$299$	2.34511	+	0.498469i	0.135621	+	0.0288272i
$300$	2.38441	−	1.06161i	0.137664	−	0.0612920i
$301$	−9.88559	−	10.9791i	−0.569796	−	0.632822i
$302$	−0.0996942	+	0.306827i	−0.00573676	+	0.0176559i
$303$	−0.553604	+	0.614840i	−0.0318037	+	0.0353216i
$304$	8.55109	+	14.8109i	0.490439	+	0.849465i
$305$	−2.10470	+	3.64545i	−0.120515	+	0.208738i
$306$	1.87620	+	5.77434i	0.107255	+	0.330097i
$307$	24.4551	+	10.8881i	1.39572	+	0.621417i	0.960341	−	0.278829i	$-0.0899461\pi$
$307$	24.4551	+	10.8881i	1.39572	+	0.621417i	0.435383	+	0.900245i	$0.356613\pi$
$308$	5.57645	+	4.05153i	0.317748	+	0.230857i
$309$	6.79928			0.386798
$310$		0			0
$311$	4.18114			0.237090			0.118545	−	0.992949i	$-0.462177\pi$
$311$	4.18114			0.237090			0.118545	+	0.992949i	$0.462177\pi$
$312$	−13.5267	−	9.82771i	−0.765798	−	0.556384i
$313$	−10.3622	−	4.61354i	−0.585706	−	0.260773i	0.0924186	−	0.995720i	$-0.470540\pi$
$313$	−10.3622	−	4.61354i	−0.585706	−	0.260773i	−0.678124	+	0.734947i	$0.737207\pi$
$314$	6.06422	+	18.6638i	0.342224	+	1.05326i
$315$	−3.83769	+	6.64708i	−0.216229	+	0.374520i
$316$	−2.34546	−	4.06246i	−0.131943	−	0.228531i
$317$	17.3180	−	19.2336i	0.972676	−	1.08027i	−0.0240746	−	0.999710i	$-0.507664\pi$
$317$	17.3180	−	19.2336i	0.972676	−	1.08027i	0.996750	−	0.0805554i	$-0.0256694\pi$
$318$	−1.85203	+	5.69996i	−0.103857	+	0.319638i
$319$	17.1369	+	19.0324i	0.959482	+	1.06561i
$320$	−12.5482	+	5.58683i	−0.701467	+	0.312313i
$321$	−6.40723	−	1.36190i	−0.357617	−	0.0760138i
$322$	0.445746	−	4.24099i	0.0248404	−	0.236341i
$323$	−2.40594	−	22.8910i	−0.133870	−	1.27369i
$324$	−5.28345	+	1.12303i	−0.293525	+	0.0623906i
$325$	−5.56627	+	4.04413i	−0.308761	+	0.224328i
$326$	0.132756	−	0.0964526i	0.00735265	−	0.00534202i
$327$	−14.1186	+	3.00099i	−0.780758	+	0.165955i
$328$	0.107766	+	1.02532i	0.00595037	+	0.0566139i
$329$	−0.472806	+	4.49845i	−0.0260666	+	0.248008i
$330$	−14.5397	−	3.09051i	−0.800385	−	0.170127i
$331$	0.699582	−	0.311474i	0.0384525	−	0.0171202i	−0.387420	−	0.921903i	$-0.626634\pi$
$331$	0.699582	−	0.311474i	0.0384525	−	0.0171202i	0.425873	+	0.904783i	$0.359967\pi$
$332$	2.70621	+	3.00556i	0.148523	+	0.164951i
$333$	−0.731844	+	2.25238i	−0.0401048	+	0.123430i
$334$	−3.25571	+	3.61583i	−0.178144	+	0.197849i
$335$	−5.73517	−	9.93361i	−0.313346	−	0.542731i
$336$	−11.0672	+	19.1689i	−0.603765	+	1.04575i
$337$	0.739892	+	2.27715i	0.0403045	+	0.124044i	0.969184	−	0.246337i	$-0.0792270\pi$
$337$	0.739892	+	2.27715i	0.0403045	+	0.124044i	−0.928880	+	0.370381i	$0.879227\pi$
$338$	−6.81740	−	3.03530i	−0.370818	−	0.165099i
$339$	25.5946	+	18.5956i	1.39011	+	1.00997i
$340$	2.81040			0.152415
$341$		0			0
$342$	9.80991			0.530459
$343$	1.44195	+	1.04764i	0.0778580	+	0.0565672i
$344$	−10.8502	−	4.83083i	−0.585005	−	0.260461i
$345$	−0.901710	−	2.77518i	−0.0485465	−	0.149411i
$346$	8.90672	−	15.4269i	0.478828	−	0.829355i
$347$	−2.82890	−	4.89980i	−0.151863	−	0.263035i	0.780049	−	0.625718i	$-0.215194\pi$
$347$	−2.82890	−	4.89980i	−0.151863	−	0.263035i	−0.931912	+	0.362683i	$0.881861\pi$
$348$	4.55412	−	5.05786i	0.244126	−	0.271130i
$349$	8.98238	−	27.6449i	0.480816	−	1.47980i	−0.357134	−	0.934053i	$-0.616246\pi$
$349$	8.98238	−	27.6449i	0.480816	−	1.47980i	0.837950	−	0.545746i	$-0.183754\pi$
$350$	8.18862	+	9.09438i	0.437700	+	0.486115i
$351$	8.46390	−	3.76837i	0.451769	−	0.201141i
$352$	9.78837	+	2.08058i	0.521722	+	0.110895i
$353$	2.01481	−	19.1696i	0.107237	−	1.02030i	−0.800093	−	0.599876i	$-0.795216\pi$
$353$	2.01481	−	19.1696i	0.107237	−	1.02030i	0.907330	−	0.420419i	$-0.138117\pi$
$354$	−2.07890	−	19.7794i	−0.110492	−	1.05126i
$355$	−7.70767	+	1.63832i	−0.409081	+	0.0869528i
$356$	1.98598	−	1.44290i	0.105257	−	0.0764737i
$357$	24.1004	−	17.5100i	1.27553	−	0.926726i
$358$	21.3568	−	4.53953i	1.12874	−	0.239922i
$359$	−1.08127	−	10.2876i	−0.0570673	−	0.542959i	−0.985285	−	0.170921i	$-0.945326\pi$
$359$	−1.08127	−	10.2876i	−0.0570673	−	0.542959i	0.928217	−	0.372038i	$-0.121341\pi$
$360$	−0.644988	+	6.13665i	−0.0339938	+	0.323430i
$361$	−17.7920	−	3.78180i	−0.936419	−	0.199042i
$362$	−13.5743	+	6.04368i	−0.713451	+	0.317649i
$363$	4.37225	+	4.85588i	0.229484	+	0.254868i
$364$	−1.49214	+	4.59233i	−0.0782094	+	0.240704i
$365$	−5.57627	+	6.19307i	−0.291875	+	0.324160i
$366$	3.48154	+	6.03020i	0.181983	+	0.315203i
$367$	0.0682819	−	0.118268i	0.00356428	−	0.00617352i	−0.864238	−	0.503084i	$-0.832199\pi$
$367$	0.0682819	−	0.118268i	0.00356428	−	0.00617352i	0.867802	+	0.496910i	$0.165532\pi$
$368$	−0.788484	−	2.42670i	−0.0411025	−	0.126501i
$369$	0.402096	+	0.179025i	0.0209323	+	0.00931966i
$370$	−2.79502	−	2.03070i	−0.145306	−	0.105571i
$371$	8.91649			0.462921
$372$		0			0
$373$	−7.36393			−0.381290			−0.190645	−	0.981659i	$-0.561058\pi$
$373$	−7.36393			−0.381290			−0.190645	+	0.981659i	$0.561058\pi$
$374$	14.1525	+	10.2824i	0.731810	+	0.531691i
$375$	22.2993	+	9.92828i	1.15153	+	0.512694i
$376$	1.12369	+	3.45837i	0.0579500	+	0.178352i
$377$	−8.97053	+	15.5374i	−0.462006	+	0.800218i
$378$	−8.23955	−	14.2713i	−0.423797	−	0.734038i
$379$	−3.08344	+	3.42451i	−0.158386	+	0.175905i	−0.817115	−	0.576475i	$-0.804428\pi$
$379$	−3.08344	+	3.42451i	−0.158386	+	0.175905i	0.658729	+	0.752380i	$0.271094\pi$
$380$	1.40320	−	4.31860i	0.0719825	−	0.221539i
$381$	−28.0829	−	31.1892i	−1.43873	−	1.59787i
$382$	5.70873	−	2.54169i	0.292084	−	0.130044i
$383$	31.5891	+	6.71446i	1.61413	+	0.343093i	0.924532	−	0.381104i	$-0.124456\pi$
$383$	31.5891	+	6.71446i	1.61413	+	0.343093i	0.689593	+	0.724197i	$0.257789\pi$
$384$	−1.22098	+	11.6169i	−0.0623080	+	0.592821i
$385$	2.31161	+	21.9935i	0.117811	+	1.12089i
$386$	24.1552	−	5.13435i	1.22947	−	0.261332i
$387$	−4.10223	+	2.98044i	−0.208528	+	0.151504i
$388$	4.25377	−	3.09054i	0.215952	−	0.156898i
$389$	34.5005	−	7.33331i	1.74925	−	0.371814i	0.781532	−	0.623866i	$-0.214439\pi$
$389$	34.5005	−	7.33331i	1.74925	−	0.371814i	0.967714	+	0.252052i	$0.0811054\pi$
$390$	−1.08846	−	10.3560i	−0.0551164	−	0.524398i
$391$	−0.358958	+	3.41526i	−0.0181533	+	0.172717i
$392$	22.3394	+	4.74839i	1.12831	+	0.239830i
$393$	23.9816	−	10.6773i	1.20971	−	0.538598i
$394$	17.8982	+	19.8780i	0.901698	+	1.00144i
$395$	4.65073	−	14.3135i	0.234004	−	0.720189i
$396$	1.58300	−	1.75810i	0.0795489	−	0.0883479i
$397$	2.01701	+	3.49356i	0.101231	+	0.175337i	0.912192	−	0.409763i	$-0.134389\pi$
$397$	2.01701	+	3.49356i	0.101231	+	0.175337i	−0.810961	+	0.585100i	$0.801055\pi$
$398$	−9.34326	+	16.1830i	−0.468335	+	0.811181i
$399$	−14.8737	−	45.7764i	−0.744614	−	2.29169i
$400$	6.68940	+	2.97831i	0.334470	+	0.148916i
$401$	−20.1309	−	14.6260i	−1.00529	−	0.730387i	−0.0420750	−	0.999114i	$-0.513397\pi$
$401$	−20.1309	−	14.6260i	−1.00529	−	0.730387i	−0.963216	+	0.268728i	$0.913397\pi$
$402$	−18.9739			−0.946334
$403$		0			0
$404$	0.192087			0.00955671
$405$	−14.0201	−	10.1862i	−0.696664	−	0.506156i
$406$	29.1522	+	12.9794i	1.44680	+	0.644157i
$407$	2.10862	+	6.48967i	0.104521	+	0.321681i
$408$	11.9744	−	20.7403i	0.592821	−	1.02680i
$409$	−1.75361	−	3.03734i	−0.0867105	−	0.150187i	0.819408	−	0.573210i	$-0.194302\pi$
$409$	−1.75361	−	3.03734i	−0.0867105	−	0.150187i	−0.906119	+	0.423023i	$0.860969\pi$
$410$	−0.429637	+	0.477161i	−0.0212183	+	0.0235653i
$411$	−6.33381	+	19.4935i	−0.312424	+	0.961541i
$412$	−1.05629	−	1.17313i	−0.0520398	−	0.0577961i
$413$	−27.0307	+	12.0348i	−1.33009	+	0.592196i
$414$	−1.43162	−	0.304300i	−0.0703603	−	0.0149555i
$415$	−1.35633	+	12.9046i	−0.0665798	+	0.633464i
$416$	0.732770	+	6.97185i	0.0359270	+	0.341823i
$417$	31.4572	−	6.68644i	1.54047	−	0.327436i
$418$	22.8667	−	16.6136i	1.11844	−	0.812598i
$419$	−3.33340	+	2.42186i	−0.162847	+	0.118316i	−0.666224	−	0.745751i	$-0.732091\pi$
$419$	−3.33340	+	2.42186i	−0.162847	+	0.118316i	0.503377	+	0.864067i	$0.332091\pi$
$420$	5.74853	−	1.22189i	0.280499	−	0.0596220i
$421$	−2.88513	−	27.4502i	−0.140613	−	1.33784i	−0.806254	−	0.591569i	$-0.798509\pi$
$421$	−2.88513	−	27.4502i	−0.140613	−	1.33784i	0.665642	−	0.746272i	$-0.268158\pi$
$422$	−0.811989	+	7.72556i	−0.0395270	+	0.376074i
$423$	1.51853	+	0.322774i	0.0738335	+	0.0156938i
$424$	6.54848	−	2.91557i	0.318022	−	0.141593i
$425$	−6.59428	−	7.32369i	−0.319869	−	0.355251i
$426$	−4.02793	+	12.3967i	−0.195154	+	0.600622i
$427$	6.93171	−	7.69845i	0.335449	−	0.372554i
$428$	0.760408	+	1.31706i	0.0367557	+	0.0636627i
$429$	−10.2834	+	17.8114i	−0.496488	+	0.859943i
$430$	−2.28579	−	7.03493i	−0.110230	−	0.339255i
$431$	−13.5880	−	6.04978i	−0.654512	−	0.291407i	0.0524876	−	0.998622i	$-0.483285\pi$
$431$	−13.5880	−	6.04978i	−0.654512	−	0.291407i	−0.706999	+	0.707214i	$0.749952\pi$
$432$	−7.97717	−	5.79575i	−0.383802	−	0.278848i
$433$	9.26195			0.445101			0.222550	−	0.974921i	$-0.428562\pi$
$433$	9.26195			0.445101			0.222550	+	0.974921i	$0.428562\pi$
$434$		0			0
$435$	21.8360			1.04696
$436$	2.71115	+	1.96977i	0.129841	+	0.0943348i
$437$	5.06884	+	2.25679i	0.242475	+	0.107957i
$438$	4.25987	+	13.1105i	0.203544	+	0.626445i
$439$	−8.85909	+	15.3444i	−0.422821	+	0.732348i	−0.996214	−	0.0869324i	$-0.972294\pi$
$439$	−8.85909	+	15.3444i	−0.422821	+	0.732348i	0.573393	+	0.819281i	$0.305627\pi$
$440$	8.88929	+	15.3967i	0.423780	+	0.734009i
$441$	6.52428	−	7.24594i	0.310680	−	0.345045i
$442$	−3.78692	+	11.6549i	−0.180125	+	0.554369i
$443$	−12.3456	−	13.7112i	−0.586558	−	0.651439i	0.374682	−	0.927154i	$-0.377752\pi$
$443$	−12.3456	−	13.7112i	−0.586558	−	0.651439i	−0.961239	+	0.275715i	$0.911085\pi$
$444$	1.65660	−	0.737568i	0.0786189	−	0.0350034i
$445$	7.70376	+	1.63749i	0.365193	+	0.0776243i
$446$	−0.951695	+	9.05478i	−0.0450641	+	0.428756i
$447$	3.30617	+	31.4561i	0.156376	+	1.48782i
$448$	33.0648	−	7.02814i	1.56216	−	0.332048i
$449$	−18.3730	+	13.3487i	−0.867073	+	0.629966i	−0.929800	−	0.368065i	$-0.880020\pi$
$449$	−18.3730	+	13.3487i	−0.867073	+	0.629966i	0.0627268	+	0.998031i	$0.480020\pi$
$450$	3.39804	−	2.46882i	0.160185	−	0.116381i
$451$	1.24047	−	0.263669i	0.0584112	−	0.0124157i
$452$	−0.767779	−	7.30493i	−0.0361133	−	0.343595i
$453$	0.0567889	−	0.540310i	0.00266817	−	0.0253860i
$454$	−23.1887	−	4.92891i	−1.08830	−	0.231325i
$455$	−14.1526	+	6.30116i	−0.663486	+	0.295403i
$456$	−25.8919	−	28.7558i	−1.21250	−	1.34661i
$457$	−4.99429	+	15.3708i	−0.233623	+	0.719018i	0.763678	+	0.645597i	$0.223392\pi$
$457$	−4.99429	+	15.3708i	−0.233623	+	0.719018i	−0.997301	+	0.0734205i	$0.976608\pi$
$458$	−5.01872	+	5.57385i	−0.234509	+	0.260449i
$459$	6.63529	+	11.4927i	0.309709	+	0.536432i
$460$	−0.338739	+	0.586713i	−0.0157938	+	0.0273556i
$461$	6.65584	+	20.4846i	0.309993	+	0.954062i	0.977766	+	0.209697i	$0.0672476\pi$
$461$	6.65584	+	20.4846i	0.309993	+	0.954062i	−0.667773	+	0.744365i	$0.732752\pi$
$462$	33.4188	+	14.8790i	1.55478	+	0.692235i
$463$	14.1657	+	10.2920i	0.658337	+	0.478310i	0.866101	−	0.499869i	$-0.166619\pi$
$463$	14.1657	+	10.2920i	0.658337	+	0.478310i	−0.207764	+	0.978179i	$0.566619\pi$
$464$	19.0941			0.886421
$465$		0			0
$466$	21.5976			1.00049
$467$	9.55176	+	6.93976i	0.442003	+	0.321134i	0.786430	−	0.617679i	$-0.211927\pi$
$467$	9.55176	+	6.93976i	0.442003	+	0.321134i	−0.344427	+	0.938813i	$0.611927\pi$
$468$	1.51401	+	0.674079i	0.0699850	+	0.0311593i
$469$	8.72305	+	26.8468i	0.402793	+	1.23967i
$470$	−1.13235	+	1.96129i	−0.0522314	+	0.0904674i
$471$	−16.5236	−	28.6197i	−0.761366	−	1.31872i
$472$	−15.9168	+	17.6774i	−0.732629	+	0.813667i
$473$	−4.51466	+	13.8947i	−0.207584	+	0.638879i
$474$	−16.6583	−	18.5009i	−0.765141	−	0.849775i
$475$	−14.5464	+	6.47647i	−0.667434	+	0.297161i
$476$	−6.76521	−	1.43799i	−0.310083	−	0.0659102i
$477$	0.319889	−	3.04354i	0.0146467	−	0.139354i
$478$	3.59499	+	34.2040i	0.164431	+	1.56446i
$479$	15.4633	−	3.28682i	0.706534	−	0.150179i	0.159389	−	0.987216i	$-0.449048\pi$
$479$	15.4633	−	3.28682i	0.706534	−	0.150179i	0.547146	+	0.837037i	$0.315714\pi$
$480$	6.90266	−	5.01507i	0.315062	−	0.228906i
$481$	−3.86724	+	2.80972i	−0.176331	+	0.128112i
$482$	−27.4190	+	5.82810i	−1.24890	+	0.265462i
$483$	0.750635	+	7.14181i	0.0341551	+	0.324964i
$484$	0.158577	−	1.50876i	0.00720803	−	0.0685798i
$485$	16.5006	+	3.50732i	0.749255	+	0.159259i
$486$	−14.3148	+	6.37336i	−0.649333	+	0.289102i
$487$	8.55928	+	9.50604i	0.387858	+	0.430760i	0.905178	−	0.425032i	$-0.139737\pi$
$487$	8.55928	+	9.50604i	0.387858	+	0.430760i	−0.517320	+	0.855792i	$0.673070\pi$
$488$	2.57353	−	7.92050i	0.116498	−	0.358544i
$489$	−0.184905	+	0.205357i	−0.00836167	+	0.00928658i
$490$	7.11185	+	12.3181i	0.321281	+	0.556475i
$491$	9.26410	−	16.0459i	0.418083	−	0.724141i	−0.577664	−	0.816275i	$-0.696036\pi$
$491$	9.26410	−	16.0459i	0.418083	−	0.724141i	0.995747	+	0.0921341i	$0.0293688\pi$
$492$	−0.104144	−	0.320523i	−0.00469518	−	0.0144503i
$493$	−23.4762	−	10.4523i	−1.05732	−	0.470747i
$494$	16.0188	+	11.6383i	0.720720	+	0.523634i
$495$	7.59016			0.341152
$496$		0			0
$497$	19.3922			0.869861
$498$	17.3648	+	12.6163i	0.778136	+	0.565349i
$499$	37.3524	+	16.6303i	1.67212	+	0.744476i	0.999992	+	0.00404299i	$0.00128693\pi$
$499$	37.3524	+	16.6303i	1.67212	+	0.744476i	0.672130	+	0.740433i	$0.265380\pi$
$500$	−1.75127	−	5.38986i	−0.0783193	−	0.241042i
$501$	4.09681	−	7.09588i	0.183032	−	0.317021i
$502$	10.0018	+	17.3237i	0.446404	+	0.773195i
$503$	13.4342	−	14.9202i	0.599001	−	0.665258i	−0.365046	−	0.930990i	$-0.618947\pi$
$503$	13.4342	−	14.9202i	0.599001	−	0.665258i	0.964047	+	0.265731i	$0.0856133\pi$
$504$	4.69255	−	14.4422i	0.209023	−	0.643306i
$505$	0.412373	+	0.457987i	0.0183504	+	0.0203801i
$506$	−3.85242	+	1.71521i	−0.171261	+	0.0762503i
$507$	12.2923	+	2.61282i	0.545922	+	0.116039i
$508$	−1.01853	+	9.69071i	−0.0451901	+	0.429956i
$509$	3.33563	+	31.7364i	0.147849	+	1.40669i	0.777045	+	0.629445i	$0.216718\pi$
$509$	3.33563	+	31.7364i	0.147849	+	1.40669i	−0.629196	+	0.777247i	$0.716616\pi$
$510$	14.5893	−	3.10104i	0.646023	−	0.137316i
$511$	16.5920	−	12.0548i	0.733989	−	0.533274i
$512$	19.9117	−	14.4667i	0.879983	−	0.639345i
$513$	20.9731	−	4.45798i	0.925987	−	0.196825i
$514$	−3.00768	−	28.6162i	−0.132663	−	1.26221i
$515$	0.529405	−	5.03696i	0.0233284	−	0.221955i
$516$	3.79769	+	0.807223i	0.167184	+	0.0355360i
$517$	4.08629	−	1.81934i	0.179715	−	0.0800143i
$518$	5.68915	+	6.31845i	0.249967	+	0.277617i
$519$	−9.26983	+	28.5296i	−0.406900	+	1.25231i
$520$	−8.33365	+	9.25545i	−0.365455	+	0.405879i
$521$	−1.05378	−	1.82520i	−0.0461670	−	0.0799635i	0.842019	−	0.539449i	$-0.181367\pi$
$521$	−1.05378	−	1.82520i	−0.0461670	−	0.0799635i	−0.888185	+	0.459485i	$0.848034\pi$
$522$	5.47624	−	9.48512i	0.239688	−	0.415152i
$523$	1.51658	+	4.66757i	0.0663156	+	0.204098i	0.978723	−	0.205184i	$-0.0657792\pi$
$523$	1.51658	+	4.66757i	0.0663156	+	0.204098i	−0.912408	+	0.409282i	$0.865779\pi$
$524$	−5.56785	−	2.47897i	−0.243233	−	0.108294i
$525$	−16.6724	−	12.1132i	−0.727644	−	0.528664i
$526$	−12.8076			−0.558440
$527$		0			0
$528$	21.8886			0.952580
$529$	17.9377	+	13.0325i	0.779899	+	0.566630i
$530$	4.07836	+	1.81580i	0.177153	+	0.0788735i
$531$	3.13820	+	9.65838i	0.136186	+	0.419138i
$532$	−5.58748	+	9.67780i	−0.242248	+	0.419586i
$533$	0.444199	+	0.769375i	0.0192404	+	0.0333253i
$534$	8.71747	−	9.68173i	0.377242	−	0.418969i
$535$	−1.50778	+	4.64048i	−0.0651872	+	0.200626i
$536$	15.1850	+	16.8646i	0.655890	+	0.728440i
$537$	−33.5895	+	14.9550i	−1.44950	+	0.645357i
$538$	5.32483	+	1.13183i	0.229570	+	0.0487966i
$539$	2.93654	−	27.9393i	0.126486	−	1.20343i
$540$	0.273659	+	2.60370i	0.0117764	+	0.112045i
$541$	12.1652	−	2.58580i	0.523025	−	0.111172i	0.0611690	−	0.998127i	$-0.480517\pi$
$541$	12.1652	−	2.58580i	0.523025	−	0.111172i	0.461856	+	0.886955i	$0.347184\pi$
$542$	−6.13347	+	4.45623i	−0.263455	+	0.191411i
$543$	20.2436	−	14.7078i	0.868736	−	0.631173i
$544$	−9.82172	+	2.08767i	−0.421103	+	0.0895082i
$545$	1.12386	+	10.6928i	0.0481408	+	0.458029i
$546$	−2.67869	+	25.4861i	−0.114637	+	1.09070i
$547$	13.6598	+	2.90349i	0.584053	+	0.124144i	0.490456	−	0.871466i	$-0.336830\pi$
$547$	13.6598	+	2.90349i	0.584053	+	0.124144i	0.0935967	+	0.995610i	$0.470164\pi$
$548$	4.34733	−	1.93556i	0.185709	−	0.0826829i
$549$	−2.37909	−	2.64225i	−0.101537	−	0.112768i
$550$	3.73967	−	11.5095i	0.159460	−	0.490767i
$551$	−27.7829	+	30.8561i	−1.18359	+	1.31451i
$552$	2.88656	+	4.99967i	0.122860	+	0.212800i
$553$	−18.5190	+	32.0759i	−0.787509	+	1.36401i
$554$	8.39482	+	25.8366i	0.356662	+	1.09769i
$555$	5.31495	+	2.36637i	0.225607	+	0.100447i
$556$	−6.04065	−	4.38879i	−0.256181	−	0.186126i
$557$	−37.2207			−1.57709			−0.788546	−	0.614976i	$-0.789166\pi$
$557$	−37.2207			−1.57709			−0.788546	+	0.614976i	$0.789166\pi$
$558$		0			0
$559$	−10.2346			−0.432876
$560$	13.3388	+	9.69119i	0.563666	+	0.409527i
$561$	−26.9121	−	11.9820i	−1.13623	−	0.505882i
$562$	−11.7174	−	36.0625i	−0.494269	−	1.52120i
$563$	15.0134	−	26.0039i	0.632738	−	1.09593i	−0.354252	−	0.935150i	$-0.615264\pi$
$563$	15.0134	−	26.0039i	0.632738	−	1.09593i	0.986990	−	0.160784i	$-0.0514023\pi$
$564$	−0.594349	−	1.02944i	−0.0250266	−	0.0433474i
$565$	15.7686	−	17.5128i	0.663389	−	0.736768i
$566$	−8.12746	+	25.0138i	−0.341623	+	1.05141i
$567$	28.5374	+	31.6939i	1.19846	+	1.33102i
$568$	14.2421	−	6.34101i	0.597587	−	0.266063i
$569$	39.4891	+	8.39367i	1.65547	+	0.351881i	0.938515	−	0.345239i	$-0.112202\pi$
$569$	39.4891	+	8.39367i	1.65547	+	0.351881i	0.716955	+	0.697120i	$0.245536\pi$
$570$	2.51902	−	23.9669i	0.105510	−	1.00386i
$571$	−4.45307	−	42.3682i	−0.186355	−	1.77305i	−0.543894	−	0.839154i	$-0.683051\pi$
$571$	−4.45307	−	42.3682i	−0.186355	−	1.77305i	0.357538	−	0.933898i	$-0.383616\pi$
$572$	4.67071	−	0.992789i	0.195292	−	0.0415106i
$573$	−8.51351	+	6.18543i	−0.355657	+	0.258400i
$574$	1.27837	−	0.928794i	0.0533583	−	0.0387671i
$575$	2.32374	−	0.493927i	0.0969068	−	0.0205982i
$576$	−1.21274	−	11.5384i	−0.0505307	−	0.480767i
$577$	0.683383	−	6.50195i	0.0284496	−	0.270680i	−0.971045	−	0.238896i	$-0.923215\pi$
$577$	0.683383	−	6.50195i	0.0284496	−	0.270680i	0.999495	−	0.0317838i	$-0.0101188\pi$
$578$	3.31969	+	0.705621i	0.138081	+	0.0293500i
$579$	−37.9908	+	16.9146i	−1.57884	+	0.702947i
$580$	−3.39230	−	3.76753i	−0.140858	−	0.156438i
$581$	9.86787	−	30.3702i	0.409388	−	1.25997i
$582$	18.6719	−	20.7372i	0.773974	−	0.859585i
$583$	−4.40874	−	7.63617i	−0.182591	−	0.316258i
$584$	8.24383	−	14.2787i	0.341132	−	0.590858i
$585$	1.64309	+	5.05690i	0.0679333	+	0.209077i
$586$	−2.02507	−	0.901618i	−0.0836547	−	0.0372455i
$587$	17.2949	+	12.5655i	0.713838	+	0.518634i	0.884410	−	0.466712i	$-0.154561\pi$
$587$	17.2949	+	12.5655i	0.713838	+	0.518634i	−0.170572	+	0.985345i	$0.554561\pi$
$588$	−7.46576			−0.307883
$589$		0			0
$590$	−14.8146			−0.609907
$591$	−36.4416	−	26.4764i	−1.49901	−	1.08909i
$592$	4.64756	+	2.06923i	0.191013	+	0.0850446i
$593$	8.03153	+	24.7185i	0.329816	+	1.01507i	0.969220	+	0.246197i	$0.0791811\pi$
$593$	8.03153	+	24.7185i	0.329816	+	1.01507i	−0.639404	+	0.768871i	$0.720819\pi$
$594$	−8.14807	+	14.1129i	−0.334319	+	0.579058i
$595$	−11.0950	−	19.2171i	−0.454851	−	0.787824i
$596$	4.91373	−	5.45725i	0.201274	−	0.223538i
$597$	9.72416	−	29.9279i	0.397983	−	1.22487i
$598$	−1.97670	−	2.19535i	−0.0808335	−	0.0897747i
$599$	−8.39362	+	3.73708i	−0.342954	+	0.152693i	−0.570984	−	0.820961i	$-0.693438\pi$
$599$	−8.39362	+	3.73708i	−0.342954	+	0.152693i	0.228030	+	0.973654i	$0.426772\pi$
$600$	−16.2055	−	3.44458i	−0.661586	−	0.140625i
$601$	−3.48279	+	33.1365i	−0.142066	+	1.35167i	0.658572	+	0.752518i	$0.271161\pi$
$601$	−3.48279	+	33.1365i	−0.142066	+	1.35167i	−0.800638	+	0.599149i	$0.795506\pi$
$602$	1.90282	+	18.1041i	0.0775531	+	0.737869i
$603$	9.47679	−	2.01435i	0.385925	−	0.0820308i
$604$	−0.102046	+	0.0741409i	−0.00415220	+	0.00301675i
$605$	3.93770	−	2.86091i	0.160090	−	0.116312i
$606$	0.997159	−	0.211953i	0.0405068	−	0.00860999i
$607$	5.09062	+	48.4340i	0.206622	+	1.96587i	0.254666	+	0.967029i	$0.418035\pi$
$607$	5.09062	+	48.4340i	0.206622	+	1.96587i	−0.0480438	+	0.998845i	$0.515299\pi$
$608$	−1.69585	+	16.1349i	−0.0687757	+	0.654357i
$609$	−52.5639	−	11.1728i	−2.13000	−	0.452745i
$610$	4.73829	−	2.10962i	0.191848	−	0.0854161i
$611$	2.09671	+	2.32863i	0.0848237	+	0.0942062i
$612$	−0.733551	+	2.25764i	−0.0296520	+	0.0912595i
$613$	13.9942	−	15.5421i	0.565220	−	0.627741i	−0.390999	−	0.920391i	$-0.627870\pi$
$613$	13.9942	−	15.5421i	0.565220	−	0.627741i	0.956220	+	0.292650i	$0.0945371\pi$
$614$	−16.4923	−	28.5654i	−0.665573	−	1.15281i
$615$	0.540633	−	0.936404i	0.0218004	−	0.0377594i
$616$	−13.5204	−	41.6114i	−0.544752	−	1.67657i
$617$	41.4603	+	18.4593i	1.66913	+	0.743144i	1.00000		1.59016e-6i	$-5.06163e-7\pi$
$617$	41.4603	+	18.4593i	1.66913	+	0.743144i	0.669129	+	0.743146i	$0.266667\pi$
$618$	−6.77785	−	4.92440i	−0.272645	−	0.198088i
$619$	−10.2462			−0.411832			−0.205916	−	0.978570i	$-0.566017\pi$
$619$	−10.2462			−0.411832			−0.205916	+	0.978570i	$0.566017\pi$
$620$		0			0
$621$	−3.19902			−0.128372
$622$	−4.16796	−	3.02820i	−0.167120	−	0.121420i
$623$	−17.7067	−	7.88354i	−0.709405	−	0.315847i
$624$	4.73836	+	14.5832i	0.189686	+	0.583794i
$625$	2.56358	−	4.44025i	0.102543	−	0.177610i
$626$	6.98816	+	12.1038i	0.279303	+	0.483767i
$627$	−31.8491	+	35.3720i	−1.27193	+	1.41262i
$628$	−2.37097	+	7.29711i	−0.0946121	+	0.291186i
$629$	−4.58147	−	5.08823i	−0.182675	−	0.202881i
$630$	8.63976	−	3.84667i	0.344216	−	0.153255i
$631$	10.4437	+	2.21987i	0.415755	+	0.0883715i	0.411040	−	0.911617i	$-0.365166\pi$
$631$	10.4437	+	2.21987i	0.415755	+	0.0883715i	0.00471535	+	0.999989i	$0.498499\pi$
$632$	−3.11243	+	29.6128i	−0.123806	+	1.17793i
$633$	−1.36739	−	13.0098i	−0.0543488	−	0.517094i
$634$	−31.1934	+	6.63036i	−1.23885	+	0.263325i
$635$	−25.2918	+	18.3755i	−1.00367	+	0.729211i
$636$	−1.89572	+	1.37732i	−0.0751702	+	0.0546144i
$637$	19.2501	−	4.09174i	0.762717	−	0.162121i
$638$	−3.29858	−	31.3839i	−0.130592	−	1.24250i
$639$	0.695718	−	6.61932i	0.0275222	−	0.261856i
$640$	8.51079	+	1.80902i	0.336419	+	0.0715080i
$641$	21.7991	−	9.70559i	0.861013	−	0.383348i	0.0717646	−	0.997422i	$-0.477137\pi$
$641$	21.7991	−	9.70559i	0.861013	−	0.383348i	0.789249	+	0.614074i	$0.210470\pi$
$642$	5.40068	+	5.99806i	0.213148	+	0.236725i
$643$	−2.45337	+	7.55069i	−0.0967513	+	0.297770i	−0.987706	−	0.156322i	$-0.950036\pi$
$643$	−2.45337	+	7.55069i	−0.0967513	+	0.297770i	0.890955	+	0.454092i	$0.150036\pi$
$644$	1.11562	−	1.23902i	0.0439615	−	0.0488242i
$645$	6.22823	+	10.7876i	0.245237	+	0.424762i
$646$	−14.1805	+	24.5614i	−0.557925	+	0.966355i
$647$	0.765625	+	2.35635i	0.0300998	+	0.0926377i	0.964978	−	0.262331i	$-0.0844914\pi$
$647$	0.765625	+	2.35635i	0.0300998	+	0.0926377i	−0.934878	+	0.354969i	$0.884491\pi$
$648$	31.3220	+	13.9455i	1.23045	+	0.547830i
$649$	23.6721	+	17.1988i	0.929209	+	0.675110i
$650$	8.47769			0.332523
$651$		0			0
$652$	0.0641574			0.00251260
$653$	−18.1981	−	13.2217i	−0.712145	−	0.517404i	0.171720	−	0.985146i	$-0.445068\pi$
$653$	−18.1981	−	13.2217i	−0.712145	−	0.517404i	−0.883865	+	0.467742i	$0.845068\pi$
$654$	16.2475	+	7.23387i	0.635329	+	0.282867i
$655$	−6.04255	−	18.5971i	−0.236102	−	0.726647i
$656$	0.472746	−	0.818821i	0.0184576	−	0.0319696i
$657$	−3.51952	−	6.09598i	−0.137309	−	0.237827i
$658$	3.72933	−	4.14184i	0.145384	−	0.161466i
$659$	−3.69573	+	11.3743i	−0.143965	+	0.443079i	−0.996876	−	0.0789765i	$-0.974835\pi$
$659$	−3.69573	+	11.3743i	−0.143965	+	0.443079i	0.852911	+	0.522056i	$0.174835\pi$
$660$	−3.88879	−	4.31894i	−0.151371	−	0.168114i
$661$	21.7752	−	9.69496i	0.846959	−	0.377090i	0.0630832	−	0.998008i	$-0.479907\pi$
$661$	21.7752	−	9.69496i	0.846959	−	0.377090i	0.783876	+	0.620918i	$0.213240\pi$
$662$	−0.922963	−	0.196182i	−0.0358720	−	0.00762482i
$663$	2.15715	−	20.5239i	0.0837766	−	0.797081i
$664$	−2.68344	−	25.5313i	−0.104138	−	0.990805i
$665$	−35.0696	+	7.45427i	−1.35994	+	0.289064i
$666$	2.36083	−	1.71525i	0.0914804	−	0.0664644i
$667$	5.01168	−	3.64120i	0.194053	−	0.140988i
$668$	−1.86076	+	0.395517i	−0.0719950	+	0.0153030i
$669$	−1.60265	−	15.2482i	−0.0619621	−	0.589530i
$670$	−1.47735	+	14.0560i	−0.0570749	+	0.543031i
$671$	−10.0204	−	2.12990i	−0.386833	−	0.0822239i
$672$	−19.1822	+	8.54046i	−0.739969	+	0.329455i
$673$	2.33802	+	2.59664i	0.0901242	+	0.100093i	0.786520	−	0.617565i	$-0.211881\pi$
$673$	2.33802	+	2.59664i	0.0901242	+	0.100093i	−0.696396	+	0.717658i	$0.745214\pi$
$674$	0.911675	−	2.80585i	0.0351164	−	0.108077i
$675$	6.14293	−	6.82241i	0.236441	−	0.262595i
$676$	−1.45885	−	2.52680i	−0.0561096	−	0.0971847i
$677$	9.62287	−	16.6673i	0.369837	−	0.640576i	−0.619703	−	0.784836i	$-0.712747\pi$
$677$	9.62287	−	16.6673i	0.369837	−	0.640576i	0.989540	+	0.144260i	$0.0460803\pi$
$678$	−12.0461	−	37.0740i	−0.462626	−	1.42382i
$679$	−37.9259	−	16.8857i	−1.45546	−	0.648014i
$680$	−14.4322	−	10.4856i	−0.553449	−	0.402104i
$681$	39.9221			1.52982
$682$		0			0
$683$	−39.8738			−1.52573			−0.762865	−	0.646558i	$-0.776208\pi$
$683$	−39.8738			−1.52573			−0.762865	+	0.646558i	$0.776208\pi$
$684$	3.10295	+	2.25442i	0.118644	+	0.0862000i
$685$	13.9477	+	6.20992i	0.532915	+	0.237269i
$686$	−0.678651	−	2.08867i	−0.0259110	−	0.0797459i
$687$	6.31529	−	10.9384i	0.240944	−	0.417326i
$688$	5.44616	+	9.43303i	0.207633	+	0.359631i
$689$	4.13317	−	4.59035i	0.157461	−	0.174878i
$690$	−1.11106	+	3.41950i	−0.0422974	+	0.130178i
$691$	25.7016	+	28.5445i	0.977735	+	1.08588i	0.996290	+	0.0860571i	$0.0274267\pi$
$691$	25.7016	+	28.5445i	0.977735	+	1.08588i	−0.0185551	+	0.999828i	$0.505907\pi$
$692$	6.36253	−	2.83278i	0.241867	−	0.107686i
$693$	−18.2711	−	3.88364i	−0.694062	−	0.147527i
$694$	−0.728708	+	6.93320i	−0.0276614	+	0.263181i
$695$	−2.50404	−	23.8243i	−0.0949836	−	0.903709i
$696$	−42.2575	+	8.98212i	−1.60177	+	0.340466i
$697$	−1.02947	+	0.747956i	−0.0389941	+	0.0283308i
$698$	−28.9760	+	21.0523i	−1.09676	+	0.796841i
$699$	−35.5755	+	7.56180i	−1.34559	+	0.286014i
$700$	0.500133	+	4.75845i	0.0189033	+	0.179853i
$701$	3.70297	−	35.2314i	0.139859	−	1.33067i	−0.669261	−	0.743028i	$-0.733389\pi$
$701$	3.70297	−	35.2314i	0.139859	−	1.33067i	0.809120	−	0.587644i	$-0.199944\pi$
$702$	−11.1665	−	2.37351i	−0.421451	−	0.0895823i
$703$	−10.1063	+	4.49962i	−0.381167	+	0.169706i
$704$	−22.3678	−	24.8420i	−0.843018	−	0.936266i
$705$	1.17851	−	3.62709i	0.0443854	−	0.136604i
$706$	−15.8921	+	17.6500i	−0.598107	+	0.664265i
$707$	−0.758331	−	1.31347i	−0.0285200	−	0.0493980i
$708$	3.88795	−	6.73412i	0.146118	−	0.253084i
$709$	−7.97551	−	24.5461i	−0.299526	−	0.921848i	−0.981663	−	0.190623i	$-0.938949\pi$
$709$	−7.97551	−	24.5461i	−0.299526	−	0.921848i	0.682137	−	0.731225i	$-0.261051\pi$
$710$	8.86993	+	3.94915i	0.332883	+	0.148209i
$711$	10.2843	+	7.47201i	0.385693	+	0.280222i
$712$	−15.5821			−0.583962
$713$		0			0
$714$	−36.7061			−1.37369
$715$	12.3941	+	9.00486i	0.463514	+	0.336763i
$716$	7.79856	+	3.47214i	0.291446	+	0.129760i
$717$	−17.8973	−	55.0821i	−0.668386	−	2.05708i
$718$	−6.37296	+	11.0383i	−0.237837	+	0.411945i
$719$	19.5234	+	33.8155i	0.728099	+	1.26110i	0.957686	+	0.287816i	$0.0929291\pi$
$719$	19.5234	+	33.8155i	0.728099	+	1.26110i	−0.229587	+	0.973288i	$0.573738\pi$
$720$	3.78652	−	4.20535i	0.141115	−	0.156724i
$721$	−3.85164	+	11.8541i	−0.143443	+	0.441471i
$722$	14.9969	+	16.6558i	0.558127	+	0.619863i
$723$	43.1240	−	19.2001i	1.60380	−	0.714058i
$724$	−5.68257	−	1.20787i	−0.211191	−	0.0448900i
$725$	−1.85826	+	17.6802i	−0.0690141	+	0.656626i
$726$	−0.841590	−	8.00719i	−0.0312343	−	0.297175i
$727$	−24.4377	+	5.19439i	−0.906344	+	0.192649i	−0.637424	−	0.770513i	$-0.720000\pi$
$727$	−24.4377	+	5.19439i	−0.906344	+	0.192649i	−0.268920	+	0.963163i	$0.586667\pi$
$728$	24.7966	−	18.0158i	0.919021	−	0.667708i
$729$	−5.86467	+	4.26093i	−0.217210	+	0.157812i
$730$	10.0440	−	2.13493i	0.371747	−	0.0790172i
$731$	−1.53234	−	14.5792i	−0.0566755	−	0.539232i
$732$	−0.284569	+	2.70749i	−0.0105180	+	0.100072i
$733$	16.5787	+	3.52390i	0.612347	+	0.130158i	0.503637	−	0.863915i	$-0.331995\pi$
$733$	16.5787	+	3.52390i	0.612347	+	0.130158i	0.108710	+	0.994074i	$0.465328\pi$
$734$	−0.153722	+	0.0684416i	−0.00567400	+	0.00252623i
$735$	−16.0275	−	17.8003i	−0.591182	−	0.656574i
$736$	0.747985	−	2.30206i	0.0275711	−	0.0848551i
$737$	18.6787	−	20.7449i	0.688041	−	0.764146i
$738$	−0.271170	−	0.469680i	−0.00998190	−	0.0172892i
$739$	−7.19107	+	12.4553i	−0.264528	+	0.458175i	−0.967440	−	0.253101i	$-0.918549\pi$
$739$	−7.19107	+	12.4553i	−0.264528	+	0.458175i	0.702912	+	0.711277i	$0.251883\pi$
$740$	−0.417409	−	1.28465i	−0.0153442	−	0.0472247i
$741$	−30.4610	−	13.5621i	−1.11901	−	0.498216i
$742$	−8.88838	−	6.45779i	−0.326303	−	0.237073i
$743$	−27.7705			−1.01880			−0.509400	−	0.860530i	$-0.670133\pi$
$743$	−27.7705			−1.01880			−0.509400	+	0.860530i	$0.670133\pi$
$744$		0			0
$745$	23.5603			0.863183
$746$	7.34072	+	5.33334i	0.268763	+	0.195268i
$747$	−10.0125	−	4.45785i	−0.366338	−	0.163104i
$748$	2.11354	+	6.50480i	0.0772786	+	0.237839i
$749$	6.00394	−	10.3991i	0.219379	−	0.379976i
$750$	−15.0384	−	26.0473i	−0.549126	−	0.951113i
$751$	−29.1542	+	32.3790i	−1.06385	+	1.18153i	−0.0810773	+	0.996708i	$0.525836\pi$
$751$	−29.1542	+	32.3790i	−1.06385	+	1.18153i	−0.982773	+	0.184817i	$0.940831\pi$
$752$	1.03053	−	3.17164i	0.0375795	−	0.115658i
$753$	−22.5405	−	25.0337i	−0.821420	−	0.912279i
$754$	20.1953	−	8.99152i	0.735469	−	0.327452i
$755$	−0.395844	−	0.0841392i	−0.0144062	−	0.00306214i
$756$	0.673472	−	6.40766i	0.0244940	−	0.233044i
$757$	−2.63590	−	25.0790i	−0.0958036	−	0.911510i	−0.931848	−	0.362849i	$-0.881804\pi$
$757$	−2.63590	−	25.0790i	−0.0958036	−	0.911510i	0.836044	−	0.548662i	$-0.184862\pi$
$758$	5.55394	−	1.18053i	0.201728	−	0.0428786i
$759$	5.74517	−	4.17411i	0.208536	−	0.151511i
$760$	−23.3185	+	16.9419i	−0.845851	+	0.614547i
$761$	2.55877	−	0.543883i	0.0927552	−	0.0197157i	−0.161300	−	0.986905i	$-0.551569\pi$
$761$	2.55877	−	0.543883i	0.0927552	−	0.0197157i	0.254055	+	0.967190i	$0.418235\pi$
$762$	5.40551	+	51.4300i	0.195821	+	1.86311i
$763$	2.76580	−	26.3148i	0.100129	−	0.952660i
$764$	2.38982	+	0.507973i	0.0864608	+	0.0183778i
$765$	−6.95758	+	3.09771i	−0.251552	+	0.111998i
$766$	−26.6265	−	29.5718i	−0.962056	−	1.06847i
$767$	−6.33414	+	19.4945i	−0.228713	+	0.703905i
$768$	−15.0469	+	16.7112i	−0.542957	+	0.603015i
$769$	−5.67534	−	9.82998i	−0.204658	−	0.354478i	0.745366	−	0.666656i	$-0.232275\pi$
$769$	−5.67534	−	9.82998i	−0.204658	−	0.354478i	−0.950024	+	0.312178i	$0.898942\pi$
$770$	13.6245	−	23.5984i	0.490994	−	0.850427i
$771$	14.9734	+	46.0835i	0.539255	+	1.65966i
$772$	8.82041	+	3.92710i	0.317454	+	0.141339i
$773$	9.23685	+	6.71097i	0.332226	+	0.241377i	0.741375	−	0.671091i	$-0.234174\pi$
$773$	9.23685	+	6.71097i	0.332226	+	0.241377i	−0.409148	+	0.912468i	$0.634174\pi$
$774$	6.24789			0.224576
$775$		0			0
$776$	−33.3751			−1.19810
$777$	−11.5834	−	8.41583i	−0.415552	−	0.301916i
$778$	−39.7029	−	17.6769i	−1.42342	−	0.633747i
$779$	0.635343	+	1.95539i	0.0227635	+	0.0700590i
$780$	2.03564	−	3.52583i	0.0728875	−	0.126245i
$781$	−9.58846	−	16.6077i	−0.343102	−	0.594270i
$782$	2.83134	−	3.14452i	0.101248	−	0.112448i
$783$	7.39756	−	22.7674i	0.264367	−	0.813639i
$784$	−14.0149	−	15.5651i	−0.500533	−	0.555898i
$785$	−22.4882	+	10.0124i	−0.802639	+	0.357358i
$786$	−31.6390	−	6.72508i	−1.12853	−	0.239876i
$787$	2.83159	−	26.9408i	0.100935	−	0.960336i	−0.820458	−	0.571706i	$-0.806282\pi$
$787$	2.83159	−	26.9408i	0.100935	−	0.960336i	0.921394	−	0.388630i	$-0.127052\pi$
$788$	1.09316	+	10.4007i	0.0389423	+	0.370511i
$789$	21.0967	−	4.48425i	0.751063	−	0.159643i
$790$	−15.0026	+	10.9001i	−0.533770	+	0.387807i
$791$	−46.9190	+	34.0887i	−1.66825	+	1.21205i
$792$	−14.6886	+	3.12217i	−0.521938	+	0.110941i
$793$	−0.750140	−	7.13711i	−0.0266383	−	0.253446i
$794$	0.519570	−	4.94338i	0.0184388	−	0.175434i
$795$	−7.35363	−	1.56306i	−0.260806	−	0.0554361i
$796$	−6.67437	+	2.97162i	−0.236567	+	0.105326i
$797$	32.5571	+	36.1583i	1.15323	+	1.28079i	0.953652	+	0.300912i	$0.0972911\pi$
$797$	32.5571	+	36.1583i	1.15323	+	1.28079i	0.199580	+	0.979882i	$0.436042\pi$
$798$	−18.3269	+	56.4044i	−0.648766	+	1.99670i
$799$	−3.00322	+	3.33542i	−0.106246	+	0.117999i
$800$	3.47318	+	6.01573i	0.122796	+	0.212688i
$801$	−3.32620	+	5.76115i	−0.117526	+	0.203560i
$802$	9.47458	+	29.1598i	0.334559	+	1.02967i
$803$	−18.5278	−	8.24910i	−0.653831	−	0.291104i
$804$	−6.00159	−	4.36041i	−0.211660	−	0.153780i
$805$	5.34915			0.188533
$806$		0			0
$807$	−9.16733			−0.322705
$808$	−0.986423	−	0.716678i	−0.0347022	−	0.0252127i
$809$	−17.1830	−	7.65036i	−0.604122	−	0.268972i	0.0817985	−	0.996649i	$-0.473934\pi$
$809$	−17.1830	−	7.65036i	−0.604122	−	0.268972i	−0.685921	+	0.727676i	$0.740600\pi$
$810$	6.59853	+	20.3082i	0.231849	+	0.713557i
$811$	19.7693	−	34.2414i	0.694193	−	1.20238i	−0.276259	−	0.961083i	$-0.589095\pi$
$811$	19.7693	−	34.2414i	0.694193	−	1.20238i	0.970452	−	0.241294i	$-0.0775720\pi$
$812$	6.23826	+	10.8050i	0.218920	+	0.379180i
$813$	8.54282	−	9.48776i	0.299610	−	0.332750i
$814$	2.59819	−	7.99639i	0.0910664	−	0.280273i
$815$	0.137733	+	0.152968i	0.00482458	+	0.00535824i
$816$	−20.0644	+	8.93324i	−0.702394	+	0.312726i
$817$	−23.1682	−	4.92456i	−0.810554	−	0.172289i
$818$	−0.451720	+	4.29783i	−0.0157940	+	0.150270i
$819$	−1.36780	−	13.0137i	−0.0477947	−	0.454737i
$820$	−0.245554	+	0.0521941i	−0.00857512	+	0.00182270i
$821$	11.8414	−	8.60325i	0.413266	−	0.300255i	−0.361657	−	0.932311i	$-0.617789\pi$
$821$	11.8414	−	8.60325i	0.413266	−	0.300255i	0.774923	+	0.632056i	$0.217789\pi$
$822$	20.4320	−	14.8447i	0.712649	−	0.517770i
$823$	−40.8736	+	8.68794i	−1.42476	+	0.302843i	−0.854855	−	0.518866i	$-0.826354\pi$
$823$	−40.8736	+	8.68794i	−1.42476	+	0.302843i	−0.569907	+	0.821709i	$0.693021\pi$
$824$	1.04740	+	9.96539i	0.0364881	+	0.347161i
$825$	−2.13023	+	20.2678i	−0.0741651	+	0.705634i
$826$	35.6618	+	7.58015i	1.24083	+	0.263747i
$827$	−8.59293	+	3.82582i	−0.298805	+	0.133037i	−0.550663	−	0.834728i	$-0.685625\pi$
$827$	−8.59293	+	3.82582i	−0.298805	+	0.133037i	0.251858	+	0.967764i	$0.418958\pi$
$828$	−0.382901	−	0.425254i	−0.0133067	−	0.0147786i
$829$	12.4629	−	38.3568i	0.432854	−	1.33219i	−0.462416	−	0.886663i	$-0.653017\pi$
$829$	12.4629	−	38.3568i	0.432854	−	1.33219i	0.895270	−	0.445524i	$-0.146983\pi$
$830$	10.6983	−	11.8816i	0.371343	−	0.412418i
$831$	−22.8739	−	39.6188i	−0.793487	−	1.37436i
$832$	11.7087	−	20.2801i	0.405927	−	0.703086i
$833$	8.71086	+	26.8093i	0.301813	+	0.928886i
$834$	−36.2007	−	16.1176i	−1.25353	−	0.558107i
$835$	−4.93769	−	3.58744i	−0.170876	−	0.124149i
$836$	11.0509			0.382203
$837$		0			0
$838$	5.07693			0.175380
$839$	−5.78419	−	4.20246i	−0.199692	−	0.145085i	0.483445	−	0.875374i	$-0.339385\pi$
$839$	−5.78419	−	4.20246i	−0.199692	−	0.145085i	−0.683138	+	0.730290i	$0.739385\pi$
$840$	−34.0792	−	15.1730i	−1.17584	−	0.523519i
$841$	5.36358	+	16.5074i	0.184951	+	0.569221i
$842$	−17.0048	+	29.4532i	−0.586025	+	1.01503i
$843$	31.9272	+	55.2995i	1.09963	+	1.90462i
$844$	−2.03226	+	2.25705i	−0.0699531	+	0.0776908i
$845$	2.89270	−	8.90281i	0.0995119	−	0.306266i
$846$	−1.27998	−	1.42156i	−0.0440065	−	0.0488741i
$847$	−10.9427	+	4.87201i	−0.375996	+	0.167404i
$848$	−6.43024	−	1.36679i	−0.220815	−	0.0469357i
$849$	4.62966	−	44.0482i	0.158889	−	1.51173i
$850$	1.26929	+	12.0765i	0.0435364	+	0.414221i
$851$	1.61445	−	0.343163i	0.0553427	−	0.0117635i
$852$	−4.12296	+	2.99550i	−0.141250	+	0.102624i
$853$	−0.911496	+	0.662240i	−0.0312090	+	0.0226747i	−0.603280	−	0.797529i	$-0.706140\pi$
$853$	−0.911496	+	0.662240i	−0.0312090	+	0.0226747i	0.572071	+	0.820204i	$0.306140\pi$
$854$	−12.4855	+	2.65387i	−0.427244	+	0.0908136i
$855$	1.28627	+	12.2380i	0.0439894	+	0.418532i
$856$	1.00906	−	9.60058i	0.0344890	−	0.328141i
$857$	23.3328	+	4.95953i	0.797032	+	0.169414i	0.588390	−	0.808578i	$-0.299762\pi$
$857$	23.3328	+	4.95953i	0.797032	+	0.169414i	0.208642	+	0.977992i	$0.433096\pi$
$858$	23.1510	−	10.3075i	0.790361	−	0.351892i
$859$	21.7238	+	24.1267i	0.741206	+	0.823193i	0.989354	−	0.145530i	$-0.0464886\pi$
$859$	21.7238	+	24.1267i	0.741206	+	0.823193i	−0.248148	+	0.968722i	$0.579822\pi$
$860$	0.893692	−	2.75050i	0.0304746	−	0.0937913i
$861$	−1.78054	+	1.97750i	−0.0606808	+	0.0673929i
$862$	9.16363	+	15.8719i	0.312114	+	0.540598i
$863$	11.9209	−	20.6476i	0.405793	−	0.702853i	−0.588621	−	0.808409i	$-0.700329\pi$
$863$	11.9209	−	20.6476i	0.405793	−	0.702853i	0.994413	+	0.105556i	$0.0336622\pi$
$864$	−2.89051	−	8.89606i	−0.0983370	−	0.302650i
$865$	20.4131	+	9.08852i	0.694068	+	0.309019i
$866$	−9.23276	−	6.70799i	−0.313742	−	0.227947i
$867$	−5.71523			−0.194099
$868$		0			0
$869$	36.6268			1.24248
$870$	−21.7672	−	15.8148i	−0.737977	−	0.536172i
$871$	17.8646	+	7.95385i	0.605320	+	0.269506i
$872$	−6.57333	−	20.2306i	−0.222601	−	0.685095i
$873$	−7.12437	+	12.3398i	−0.241123	+	0.417638i
$874$	−3.41837	−	5.92080i	−0.115628	−	0.200274i
$875$	−29.9414	+	33.2533i	−1.01220	+	1.12417i
$876$	−1.66551	+	5.12592i	−0.0562724	+	0.173189i
$877$	19.5886	+	21.7553i	0.661459	+	0.734624i	0.976753	−	0.214370i	$-0.0687698\pi$
$877$	19.5886	+	21.7553i	0.661459	+	0.734624i	−0.315294	+	0.948994i	$0.602103\pi$
$878$	19.9444	−	8.87982i	0.673091	−	0.299679i
$879$	3.65136	+	0.776121i	0.123157	+	0.0261779i
$880$	1.70429	−	16.2152i	0.0574516	−	0.546616i
$881$	−0.943900	−	8.98061i	−0.0318008	−	0.302564i	−0.998849	−	0.0479702i	$-0.984725\pi$
$881$	−0.943900	−	8.98061i	−0.0318008	−	0.302564i	0.967048	−	0.254594i	$-0.0819419\pi$
$882$	−11.7516	+	2.49788i	−0.395697	+	0.0841080i
$883$	−17.3191	+	12.5831i	−0.582834	+	0.423454i	−0.839745	−	0.542981i	$-0.817295\pi$
$883$	−17.3191	+	12.5831i	−0.582834	+	0.423454i	0.256911	+	0.966435i	$0.417295\pi$
$884$	−3.87626	+	2.81627i	−0.130373	+	0.0947213i
$885$	24.4025	−	5.18692i	0.820282	−	0.174356i
$886$	2.37634	+	22.6093i	0.0798346	+	0.759575i
$887$	−2.57088	+	24.4603i	−0.0863216	+	0.821296i	0.862622	+	0.505849i	$0.168821\pi$
$887$	−2.57088	+	24.4603i	−0.0863216	+	0.821296i	−0.948943	+	0.315446i	$0.897846\pi$
$888$	−11.2590	−	2.39317i	−0.377827	−	0.0803096i
$889$	70.2847	−	31.2928i	2.35727	−	1.04953i
$890$	−6.49353	−	7.21180i	−0.217664	−	0.241740i
$891$	13.0328	−	40.1107i	0.436614	−	1.34376i
$892$	−2.38191	+	2.64538i	−0.0797524	+	0.0885740i
$893$	3.62590	+	6.28024i	0.121336	+	0.210160i
$894$	19.4864	−	33.7514i	0.651723	−	1.12882i
$895$	8.46344	+	26.0478i	0.282902	+	0.870681i
$896$	−19.5616	−	8.70940i	−0.653508	−	0.290961i
$897$	4.02467	+	2.92409i	0.134380	+	0.0976326i
$898$	27.9829			0.933801
$899$		0			0
$900$	1.64218			0.0547395
$901$	7.15780	+	5.20044i	0.238461	+	0.173252i
$902$	−1.42752	−	0.635572i	−0.0475312	−	0.0211622i
$903$	−9.47298	−	29.1548i	−0.315241	−	0.970212i
$904$	−23.3119	+	40.3774i	−0.775343	+	1.34293i
$905$	−9.31946	−	16.1418i	−0.309789	−	0.536571i
$906$	−0.447931	+	0.497478i	−0.0148815	+	0.0165276i
$907$	−6.10812	+	18.7989i	−0.202817	+	0.624206i	0.796979	+	0.604007i	$0.206430\pi$
$907$	−6.10812	+	18.7989i	−0.202817	+	0.624206i	−0.999796	+	0.0201992i	$0.993570\pi$
$908$	−6.20204	−	6.88806i	−0.205822	−	0.228588i
$909$	−0.475543	+	0.211725i	−0.0157728	+	0.00702248i
$910$	18.6717	+	3.96879i	0.618960	+	0.131564i
$911$	3.72347	−	35.4264i	0.123364	−	1.17373i	−0.741227	−	0.671254i	$-0.765756\pi$
$911$	3.72347	−	35.4264i	0.123364	−	1.17373i	0.864591	−	0.502476i	$-0.167578\pi$
$912$	3.70936	+	35.2922i	0.122829	+	1.16864i
$913$	−30.8885	+	6.56555i	−1.02226	+	0.217288i
$914$	16.1109	−	11.7053i	0.532902	−	0.387176i
$915$	−7.06628	+	5.13395i	−0.233604	+	0.169723i
$916$	−2.86839	+	0.609695i	−0.0947743	+	0.0201449i
$917$	5.03016	+	47.8588i	0.166111	+	1.58044i
$918$	1.70921	−	16.2621i	0.0564124	−	0.536728i
$919$	16.7814	+	3.56700i	0.553568	+	0.117665i	0.476198	−	0.879338i	$-0.342014\pi$
$919$	16.7814	+	3.56700i	0.553568	+	0.117665i	0.0773698	+	0.997002i	$0.475348\pi$
$920$	3.92855	−	1.74910i	0.129520	−	0.0576662i
$921$	37.1674	+	41.2786i	1.22471	+	1.36018i
$922$	8.20114	−	25.2405i	0.270090	−	0.831252i
$923$	8.98912	−	9.98343i	0.295880	−	0.328609i
$924$	7.15126	+	12.3863i	0.235259	+	0.407481i
$925$	−2.36831	+	4.10203i	−0.0778694	+	0.134874i
$926$	−6.66707	−	20.5191i	−0.219094	−	0.674301i
$927$	3.90809	+	1.73999i	0.128358	+	0.0571488i
$928$	14.6540	+	10.6468i	0.481042	+	0.349498i
$929$	45.5222			1.49353			0.746767	−	0.665086i	$-0.231605\pi$
$929$	45.5222			1.49353			0.746767	+	0.665086i	$0.231605\pi$
$930$		0			0
$931$	45.5457			1.49270
$932$	6.83147	+	4.96335i	0.223772	+	0.162580i
$933$	7.92569	+	3.52875i	0.259476	+	0.115526i
$934$	−4.49552	−	13.8358i	−0.147098	−	0.452720i
$935$	−10.9718	+	19.0037i	−0.358817	+	0.621489i
$936$	−5.25986	−	9.11035i	−0.171924	−	0.297781i
$937$	17.1414	−	19.0375i	0.559986	−	0.621928i	−0.394963	−	0.918697i	$-0.629243\pi$
$937$	17.1414	−	19.0375i	0.559986	−	0.621928i	0.954949	+	0.296769i	$0.0959092\pi$
$938$	10.7483	−	33.0799i	0.350944	−	1.08010i
$939$	−15.7487	−	17.4907i	−0.513940	−	0.570788i
$940$	−0.808895	+	0.360143i	−0.0263833	+	0.0117466i
$941$	−11.8589	−	2.52069i	−0.386589	−	0.0821721i	0.0105171	−	0.999945i	$-0.496652\pi$
$941$	−11.8589	−	2.52069i	−0.386589	−	0.0821721i	−0.397106	+	0.917773i	$0.629986\pi$
$942$	−4.25638	+	40.4967i	−0.138680	+	1.31945i
$943$	−0.0320641	−	0.305070i	−0.00104415	−	0.00993444i
$944$	21.3383	−	4.53560i	0.694504	−	0.147621i
$945$	16.7233	−	12.1502i	0.544011	−	0.395247i
$946$	14.5637	−	10.5811i	0.473507	−	0.344023i
$947$	26.6067	−	5.65542i	0.864600	−	0.183776i	0.245796	−	0.969322i	$-0.420951\pi$
$947$	26.6067	−	5.65542i	0.864600	−	0.183776i	0.618804	+	0.785545i	$0.287617\pi$
$948$	−1.01743	−	9.68023i	−0.0330447	−	0.314399i
$949$	1.48510	−	14.1298i	0.0482083	−	0.458671i
$950$	19.1911	+	4.07920i	0.622643	+	0.132347i
$951$	49.0602	−	21.8430i	1.59089	−	0.708309i
$952$	29.3761	+	32.6255i	0.952086	+	1.05740i
$953$	7.69226	−	23.6743i	0.249177	−	0.766887i	−0.745745	−	0.666232i	$-0.767906\pi$
$953$	7.69226	−	23.6743i	0.249177	−	0.766887i	0.994921	−	0.100655i	$-0.0320939\pi$
$954$	−2.52317	+	2.80227i	−0.0816907	+	0.0907267i
$955$	3.91933	+	6.78848i	0.126826	+	0.219670i
$956$	−6.72333	+	11.6452i	−0.217448	+	0.376631i
$957$	16.4216	+	50.5406i	0.530836	+	1.63374i
$958$	−17.7950	−	7.92285i	−0.574931	−	0.255976i
$959$	−30.3977	−	22.0852i	−0.981592	−	0.713168i
$960$	−28.5013			−0.919876
$961$		0			0
$962$	5.89000			0.189901
$963$	−3.33422	−	2.42246i	−0.107444	−	0.0780625i
$964$	−10.0122	−	4.45772i	−0.322471	−	0.143573i
$965$	9.57241	+	29.4609i	0.308147	+	0.948378i
$966$	4.42421	−	7.66295i	0.142347	−	0.246551i
$967$	−26.0999	−	45.2064i	−0.839316	−	1.45374i	−0.890467	−	0.455048i	$-0.849622\pi$
$967$	−26.0999	−	45.2064i	−0.839316	−	1.45374i	0.0511507	−	0.998691i	$-0.483711\pi$
$968$	−6.44351	+	7.15624i	−0.207102	+	0.230010i
$969$	14.7586	−	45.4224i	0.474115	−	1.45918i
$970$	−13.9084	−	15.4469i	−0.446573	−	0.495970i
$971$	−18.2351	+	8.11880i	−0.585193	+	0.260545i	−0.677907	−	0.735148i	$-0.737113\pi$
$971$	−18.2351	+	8.11880i	−0.585193	+	0.260545i	0.0927134	+	0.995693i	$0.470446\pi$
$972$	−5.99255	−	1.27376i	−0.192211	−	0.0408557i
$973$	−6.16241	+	58.6314i	−0.197558	+	1.87964i
$974$	−1.64753	−	15.6752i	−0.0527901	−	0.502265i
$975$	−13.9644	+	2.96823i	−0.447220	+	0.0950596i
$976$	−6.17897	+	4.48929i	−0.197784	+	0.143699i
$977$	48.7438	−	35.4144i	1.55945	−	1.13301i	0.622994	−	0.782227i	$-0.285916\pi$
$977$	48.7438	−	35.4144i	1.55945	−	1.13301i	0.936458	−	0.350781i	$-0.114084\pi$
$978$	0.333052	−	0.0707925i	0.0106498	−	0.00226369i
$979$	2.00352	+	19.0622i	0.0640328	+	0.609231i
$980$	−0.581298	+	5.53068i	−0.0185689	+	0.176671i
$981$	−8.88303	−	1.88815i	−0.283613	−	0.0602839i
$982$	−20.8562	+	9.28577i	−0.665547	+	0.296321i
$983$	−7.72091	−	8.57494i	−0.246259	−	0.273498i	0.607325	−	0.794453i	$-0.292243\pi$
$983$	−7.72091	−	8.57494i	−0.246259	−	0.273498i	−0.853584	+	0.520955i	$0.825576\pi$
$984$	−0.661060	+	2.03453i	−0.0210738	+	0.0648586i
$985$	−22.4513	+	24.9347i	−0.715358	+	0.794485i
$986$	15.8321	+	27.4221i	0.504198	+	0.873297i
$987$	−4.69279	+	8.12816i	−0.149373	+	0.258722i
$988$	2.39225	+	7.36259i	0.0761076	+	0.234235i
$989$	3.22832	+	1.43734i	0.102655	+	0.0457048i
$990$	−7.56624	−	5.49719i	−0.240471	−	0.174712i
$991$	37.3423			1.18622			0.593109	−	0.805122i	$-0.297900\pi$
$991$	37.3423			1.18622			0.593109	+	0.805122i	$0.297900\pi$
$992$		0			0
$993$	1.58899			0.0504251
$994$	−19.3311	−	14.0449i	−0.613146	−	0.445477i
$995$	−21.4136	−	9.53397i	−0.678858	−	0.302247i
$996$	2.59326	+	7.98124i	0.0821707	+	0.252895i
$997$	−10.4012	+	18.0154i	−0.329410	+	0.570555i	−0.982395	−	0.186816i	$-0.940183\pi$
$997$	−10.4012	+	18.0154i	−0.329410	+	0.570555i	0.652985	+	0.757371i	$0.273516\pi$
$998$	−25.1901	−	43.6305i	−0.797378	−	1.38110i
$999$	4.26788	−	4.73997i	0.135030	−	0.149966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.t.732.1		16
31.2	even	5		961.2.g.k.448.2		16
31.3	odd	30		961.2.d.q.388.2		16
31.4	even	5		961.2.c.j.521.5		16
31.5	even	3		961.2.g.s.816.1		16
31.6	odd	6		961.2.d.q.374.2		16
31.7	even	15		961.2.a.i.1.5		8
31.8	even	5		31.2.g.a.7.2	✓	16
31.9	even	15		961.2.g.k.547.2		16
31.10	even	15		31.2.g.a.9.2	yes	16
31.11	odd	30		961.2.c.i.439.5		16
31.12	odd	30		961.2.d.n.628.3		16
31.13	odd	30		961.2.g.n.235.1		16
31.14	even	15		961.2.d.o.531.3		16
31.15	odd	10		961.2.g.m.338.1		16
31.16	even	5		961.2.g.s.338.1		16
31.17	odd	30		961.2.d.n.531.3		16
31.18	even	15	inner	961.2.g.t.235.1		16
31.19	even	15		961.2.d.o.628.3		16
31.20	even	15		961.2.c.j.439.5		16
31.21	odd	30		961.2.g.l.846.2		16
31.22	odd	30		961.2.g.j.547.2		16
31.23	odd	10		961.2.g.l.844.2		16
31.24	odd	30		961.2.a.j.1.5		8
31.25	even	3		961.2.d.p.374.2		16
31.26	odd	6		961.2.g.m.816.1		16
31.27	odd	10		961.2.c.i.521.5		16
31.28	even	15		961.2.d.p.388.2		16
31.29	odd	10		961.2.g.j.448.2		16
31.30	odd	2		961.2.g.n.732.1		16
93.8	odd	10		279.2.y.c.100.1		16
93.38	odd	30		8649.2.a.bf.1.4		8
93.41	odd	30		279.2.y.c.226.1		16
93.86	even	30		8649.2.a.be.1.4		8
124.39	odd	10		496.2.bg.c.193.2		16
124.103	odd	30		496.2.bg.c.257.2		16
155.8	odd	20		775.2.ck.a.224.3		32
155.39	even	10		775.2.bl.a.751.1		16
155.72	odd	60		775.2.ck.a.474.3		32
155.103	odd	60		775.2.ck.a.474.2		32
155.132	odd	20		775.2.ck.a.224.2		32
155.134	even	30		775.2.bl.a.226.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.7.2	✓	16	31.8	even	5
31.2.g.a.9.2	yes	16	31.10	even	15
279.2.y.c.100.1		16	93.8	odd	10
279.2.y.c.226.1		16	93.41	odd	30
496.2.bg.c.193.2		16	124.39	odd	10
496.2.bg.c.257.2		16	124.103	odd	30
775.2.bl.a.226.1		16	155.134	even	30
775.2.bl.a.751.1		16	155.39	even	10
775.2.ck.a.224.2		32	155.132	odd	20
775.2.ck.a.224.3		32	155.8	odd	20
775.2.ck.a.474.2		32	155.103	odd	60
775.2.ck.a.474.3		32	155.72	odd	60
961.2.a.i.1.5		8	31.7	even	15
961.2.a.j.1.5		8	31.24	odd	30
961.2.c.i.439.5		16	31.11	odd	30
961.2.c.i.521.5		16	31.27	odd	10
961.2.c.j.439.5		16	31.20	even	15
961.2.c.j.521.5		16	31.4	even	5
961.2.d.n.531.3		16	31.17	odd	30
961.2.d.n.628.3		16	31.12	odd	30
961.2.d.o.531.3		16	31.14	even	15
961.2.d.o.628.3		16	31.19	even	15
961.2.d.p.374.2		16	31.25	even	3
961.2.d.p.388.2		16	31.28	even	15
961.2.d.q.374.2		16	31.6	odd	6
961.2.d.q.388.2		16	31.3	odd	30
961.2.g.j.448.2		16	31.29	odd	10
961.2.g.j.547.2		16	31.22	odd	30
961.2.g.k.448.2		16	31.2	even	5
961.2.g.k.547.2		16	31.9	even	15
961.2.g.l.844.2		16	31.23	odd	10
961.2.g.l.846.2		16	31.21	odd	30
961.2.g.m.338.1		16	31.15	odd	10
961.2.g.m.816.1		16	31.26	odd	6
961.2.g.n.235.1		16	31.13	odd	30
961.2.g.n.732.1		16	31.30	odd	2
961.2.g.s.338.1		16	31.16	even	5
961.2.g.s.816.1		16	31.5	even	3
961.2.g.t.235.1		16	31.18	even	15	inner
961.2.g.t.732.1		16	1.1	even	1	trivial
8649.2.a.be.1.4		8	93.86	even	30
8649.2.a.bf.1.4		8	93.38	odd	30

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.996848 - 0.724253i) q^{2} +(1.89558 + 0.843968i) q^{3} +(-0.148869 - 0.458173i) q^{4} +(0.772811 - 1.33855i) q^{5} +(-1.27836 - 2.21419i) q^{6} +(-2.54521 + 2.82674i) q^{7} +(-0.944957 + 2.90828i) q^{8} +(0.873564 + 0.970191i) q^{9} +(-1.73982 + 0.774619i) q^{10} +(3.67933 + 0.782065i) q^{11} +(0.104489 - 0.994146i) q^{12} +(0.275439 + 2.62063i) q^{13} +(4.58447 - 0.974458i) q^{14} +(2.59462 - 1.88510i) q^{15} +(2.26882 - 1.64839i) q^{16} +(-3.69186 + 0.784729i) q^{17} +(-0.168147 - 1.59981i) q^{18} +(-0.637447 + 6.06491i) q^{19} +(-0.728335 - 0.154812i) q^{20} +(-7.21034 + 3.21025i) q^{21} +(-3.10132 - 3.44436i) q^{22} +(0.281158 - 0.865316i) q^{23} +(-4.24574 + 4.71537i) q^{24} +(1.30553 + 2.26124i) q^{25} +(1.62343 - 2.81186i) q^{26} +(-1.08650 - 3.34392i) q^{27} +(1.67404 + 0.745331i) q^{28} +(5.50827 + 4.00199i) q^{29} -3.95173 q^{30} +2.66037 q^{32} +(6.31443 + 4.58770i) q^{33} +(4.24857 + 1.89158i) q^{34} +(1.81676 + 5.59143i) q^{35} +(0.314468 - 0.544675i) q^{36} +(0.907032 + 1.57103i) q^{37} +(5.02796 - 5.58412i) q^{38} +(-1.68961 + 5.20008i) q^{39} +(3.16260 + 3.51242i) q^{40} +(0.307997 - 0.137129i) q^{41} +(9.51265 + 2.02198i) q^{42} +(-0.405988 + 3.86272i) q^{43} +(-0.189418 - 1.80219i) q^{44} +(1.97375 - 0.419533i) q^{45} +(-0.906980 + 0.658959i) q^{46} +(0.962040 - 0.698963i) q^{47} +(5.69192 - 1.20986i) q^{48} +(-0.780679 - 7.42766i) q^{49} +(0.336296 - 3.19964i) q^{50} +(-7.66052 - 1.62829i) q^{51} +(1.15970 - 0.516330i) q^{52} +(-1.56853 - 1.74202i) q^{53} +(-1.33876 + 4.12028i) q^{54} +(3.89026 - 4.32057i) q^{55} +(-5.81584 - 10.0733i) q^{56} +(-6.32692 + 10.9586i) q^{57} +(-2.59245 - 7.97875i) q^{58} +(7.10632 + 3.16394i) q^{59} +(-1.24996 - 0.908151i) q^{60} -2.72343 q^{61} -4.96588 q^{63} +(-7.18962 - 5.22357i) q^{64} +(3.72070 + 1.65656i) q^{65} +(-2.97187 - 9.14649i) q^{66} +(3.71059 - 6.42693i) q^{67} +(0.909147 + 1.57469i) q^{68} +(1.26326 - 1.40299i) q^{69} +(2.23857 - 6.88960i) q^{70} +(-3.41135 - 3.78869i) q^{71} +(-3.64706 + 1.62378i) q^{72} +(-5.27392 - 1.12101i) q^{73} +(0.233646 - 2.22299i) q^{74} +(0.566321 + 5.38818i) q^{75} +(2.87367 - 0.610818i) q^{76} +(-11.5754 + 8.40999i) q^{77} +(5.45046 - 3.95999i) q^{78} +(9.52444 - 2.02448i) q^{79} +(-0.453085 - 4.31082i) q^{80} +(1.17199 - 11.1508i) q^{81} +(-0.406342 - 0.0863707i) q^{82} +(-7.66935 + 3.41461i) q^{83} +(2.54425 + 2.82568i) q^{84} +(-1.80271 + 5.54818i) q^{85} +(3.20229 - 3.55651i) q^{86} +(7.06383 + 12.2349i) q^{87} +(-5.75127 + 9.96149i) q^{88} +(1.57463 + 4.84620i) q^{89} +(-2.27137 - 1.01128i) q^{90} +(-8.10889 - 5.89146i) q^{91} -0.438320 q^{92} -1.46523 q^{94} +(7.62555 + 5.54028i) q^{95} +(5.04296 + 2.24527i) q^{96} +(3.37268 + 10.3800i) q^{97} +(-4.60129 + 7.96966i) q^{98} +(2.45537 + 4.25283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} + 11 q^{6} + 12 q^{7} - 8 q^{8} + 5 q^{9} - 12 q^{10} - 2 q^{11} + 25 q^{12} + 18 q^{13} + 24 q^{14} + 4 q^{15} - 2 q^{16} - q^{17} - 8 q^{18} + 11 q^{19} - 18 q^{20}+ \cdots + 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 + 11 * q^6 + 12 * q^7 - 8 * q^8 + 5 * q^9 - 12 * q^10 - 2 * q^11 + 25 * q^12 + 18 * q^13 + 24 * q^14 + 4 * q^15 - 2 * q^16 - q^17 - 8 * q^18 + 11 * q^19 - 18 * q^20 - 31 * q^21 + 4 * q^22 + 21 * q^23 + 20 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 + 20 * q^28 + 26 * q^29 - 22 * q^30 - 42 * q^32 + 7 * q^33 + 28 * q^34 + 21 * q^35 + q^36 - 8 * q^37 + 3 * q^38 + 2 * q^39 + 29 * q^40 - 3 * q^41 + 39 * q^42 + 8 * q^43 - 41 * q^44 - 20 * q^45 - 16 * q^46 + 4 * q^47 + 49 * q^48 + 12 * q^49 + 48 * q^50 - 2 * q^51 - 6 * q^52 - 69 * q^53 + 39 * q^54 + 23 * q^55 - 30 * q^56 - 17 * q^57 + 10 * q^58 + 54 * q^59 + 35 * q^60 - 60 * q^61 - 46 * q^63 - 32 * q^64 - 27 * q^65 + 20 * q^66 + 13 * q^67 + 30 * q^68 - 27 * q^69 + 27 * q^70 + 6 * q^71 + 2 * q^72 - 18 * q^73 - 92 * q^74 + 13 * q^75 - 27 * q^76 - 42 * q^77 + 15 * q^78 - 22 * q^79 + 21 * q^80 - 22 * q^81 - 61 * q^82 - 71 * q^83 - 12 * q^84 - 63 * q^85 - 11 * q^86 + 15 * q^87 - 17 * q^88 + 26 * q^89 - 33 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 + 28 * q^95 + 58 * q^96 - 37 * q^97 - 10 * q^98 + 6 * q^99

Introduction

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