LMFDB - Embedded newform 961.2.g.n.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			235.1
Root			$0.176392i$ of defining polynomial
Character	$\chi$	$=$	961.235
Dual form			961.2.g.n.732.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.996848 + 0.724253i) q^{2} +(-1.89558 + 0.843968i) q^{3} +(-0.148869 + 0.458173i) q^{4} +(0.772811 + 1.33855i) q^{5} +(1.27836 - 2.21419i) q^{6} +(-2.54521 - 2.82674i) q^{7} +(-0.944957 - 2.90828i) q^{8} +(0.873564 - 0.970191i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 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	\( 16 q + 4 q^{2} - 3 q^{3} + 6 q^{4} - 3 q^{5} - 11 q^{6} + 12 q^{7} - 8 q^{8} + 5 q^{9} - 12 q^{10} + 2 q^{11} - 25 q^{12} - 18 q^{13} + 24 q^{14} - 4 q^{15} - 2 q^{16} + q^{17} - 8 q^{18} + 11 q^{19} - 18 q^{20} + 31 q^{21} - 4 q^{22} - 21 q^{23} - 20 q^{24} - 13 q^{25} - 9 q^{26} - 9 q^{27} + 20 q^{28} - 26 q^{29} + 22 q^{30} - 42 q^{32} + 7 q^{33} - 28 q^{34} + 21 q^{35} + q^{36} + 8 q^{37} + 3 q^{38} + 2 q^{39} + 29 q^{40} - 3 q^{41} - 39 q^{42} - 8 q^{43} + 41 q^{44} - 20 q^{45} + 16 q^{46} + 4 q^{47} - 49 q^{48} + 12 q^{49} + 48 q^{50} - 2 q^{51} + 6 q^{52} + 69 q^{53} - 39 q^{54} - 23 q^{55} - 30 q^{56} + 17 q^{57} - 10 q^{58} + 54 q^{59} - 35 q^{60} + 60 q^{61} - 46 q^{63} - 32 q^{64} + 27 q^{65} + 20 q^{66} + 13 q^{67} - 30 q^{68} - 27 q^{69} + 27 q^{70} + 6 q^{71} + 2 q^{72} + 18 q^{73} + 92 q^{74} - 13 q^{75} - 27 q^{76} + 42 q^{77} + 15 q^{78} + 22 q^{79} + 21 q^{80} - 22 q^{81} - 61 q^{82} + 71 q^{83} + 12 q^{84} + 63 q^{85} + 11 q^{86} + 15 q^{87} + 17 q^{88} - 26 q^{89} - 33 q^{90} - 8 q^{91} + 64 q^{92} + 44 q^{94} + 28 q^{95} - 58 q^{96} - 37 q^{97} - 10 q^{98} - 6 q^{99}+O(q^{100}) \) 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{13}{15}\right)$

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	−0.881517	−	0.472152i	$-0.843477\pi$
$2$	−0.996848	+	0.724253i	−0.704878	+	0.512124i	0.176639	+	0.984276i	$0.443477\pi$
$3$	−1.89558	+	0.843968i	−1.09442	+	0.487265i	−0.872904	−	0.487892i	$-0.837766\pi$
$3$	−1.89558	+	0.843968i	−1.09442	+	0.487265i	−0.221512	+	0.975158i	$0.571099\pi$
$4$	−0.148869	+	0.458173i	−0.0744347	+	0.229086i
$5$	0.772811	+	1.33855i	0.345612	+	0.598617i	0.985465	−	0.169880i	$-0.0543381\pi$
$5$	0.772811	+	1.33855i	0.345612	+	0.598617i	−0.639853	+	0.768497i	$0.721005\pi$
$6$	1.27836	−	2.21419i	0.521890	−	0.903939i
$7$	−2.54521	−	2.82674i	−0.961999	−	1.06841i	−0.997614	−	0.0690429i	$-0.978005\pi$
$7$	−2.54521	−	2.82674i	−0.961999	−	1.06841i	0.0356144	−	0.999366i	$-0.488661\pi$
$8$	−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	$-0.758590\pi$
$11$	−3.67933	+	0.782065i	−1.10936	+	0.235801i	−0.383429	+	0.923570i	$0.625257\pi$
$12$	−0.104489	−	0.994146i	−0.0301634	−	0.286985i
$13$	−0.275439	+	2.62063i	−0.0763931	+	0.726831i	0.887548	+	0.460715i	$0.152407\pi$
$13$	−0.275439	+	2.62063i	−0.0763931	+	0.726831i	−0.963941	+	0.266116i	$0.914260\pi$
$14$	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	$-0.282005\pi$
$17$	3.69186	+	0.784729i	0.895408	+	0.190325i	0.262849	+	0.964837i	$0.415338\pi$
$18$	−0.168147	+	1.59981i	−0.0396327	+	0.377080i
$19$	−0.637447	−	6.06491i	−0.146240	−	1.39139i	−0.783814	−	0.620996i	$-0.786728\pi$
$19$	−0.637447	−	6.06491i	−0.146240	−	1.39139i	0.637574	−	0.770390i	$-0.279938\pi$
$20$	−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	$-0.130240\pi$
$23$	−0.281158	−	0.865316i	−0.0586255	−	0.180431i	−0.976081	+	0.217408i	$0.930240\pi$
$24$	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	$-0.917832\pi$
$29$	−5.50827	+	4.00199i	−1.02286	+	0.743151i	−0.0559922	+	0.998431i	$0.517832\pi$
$30$	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	$-0.880976\pi$
$37$	−0.907032	+	1.57103i	−0.149115	+	0.258275i	0.781786	+	0.623547i	$0.214309\pi$
$38$	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	0.430646	−	0.902521i	$-0.358286\pi$
$41$	0.307997	+	0.137129i	0.0481010	+	0.0214160i	−0.382545	+	0.923937i	$0.624952\pi$
$42$	−9.51265	+	2.02198i	−1.46783	+	0.311998i
$43$	0.405988	+	3.86272i	0.0619126	+	0.589059i	0.980865	+	0.194690i	$0.0623701\pi$
$43$	0.405988	+	3.86272i	0.0619126	+	0.589059i	−0.918952	+	0.394369i	$0.870963\pi$
$44$	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	0.655735	−	0.754992i	$-0.272359\pi$
$47$	0.962040	+	0.698963i	0.140328	+	0.101954i	−0.515407	+	0.856946i	$0.672359\pi$
$48$	−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	$-0.715196\pi$
$53$	1.56853	−	1.74202i	0.215454	−	0.239286i	0.841177	+	0.540759i	$0.181863\pi$
$54$	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	0.111843	−	0.993726i	$-0.464324\pi$
$59$	7.10632	−	3.16394i	0.925164	−	0.411909i	0.813320	+	0.581816i	$0.197658\pi$
$60$	1.24996	−	0.908151i	0.161369	−	0.117242i
$61$	2.72343			0.348700			0.174350	−	0.984684i	$-0.444218\pi$
$61$	2.72343			0.348700			0.174350	+	0.984684i	$0.444218\pi$
$62$		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	0.998590	−	0.0530864i	$-0.0169059\pi$
$67$	3.71059	+	6.42693i	0.453321	+	0.785175i	−0.545269	+	0.838261i	$0.683573\pi$
$68$	−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	−0.910749	−	0.412960i	$-0.864495\pi$
$71$	−3.41135	+	3.78869i	−0.404853	+	0.449634i	0.505897	+	0.862594i	$0.331162\pi$
$72$	−3.64706	−	1.62378i	−0.429811	−	0.191364i
$73$	5.27392	−	1.12101i	0.617266	−	0.131204i	0.111342	−	0.993782i	$-0.464485\pi$
$73$	5.27392	−	1.12101i	0.617266	−	0.131204i	0.505924	+	0.862578i	$0.331152\pi$
$74$	−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	$-0.617853\pi$
$79$	−9.52444	−	2.02448i	−1.07158	−	0.227772i	−0.709738	+	0.704466i	$0.751187\pi$
$80$	−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	$-0.214249\pi$
$83$	7.66935	+	3.41461i	0.841820	+	0.374803i	0.0599178	+	0.998203i	$0.480916\pi$
$84$	−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	$-0.987046\pi$
$89$	−1.57463	+	4.84620i	−0.166910	+	0.513696i	0.832262	+	0.554383i	$0.187046\pi$
$90$	−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	−0.620494	−	0.784211i	$-0.713068\pi$
$97$	3.37268	−	10.3800i	0.342444	−	1.05393i	0.962938	−	0.269723i	$-0.0869320\pi$
$98$	−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	0.944739	−	0.327823i	$-0.106315\pi$
$101$	−0.123213	−	0.379212i	−0.0122602	−	0.0377330i	−0.956999	+	0.290090i	$0.906315\pi$
$102$	6.45708	−	7.17131i	0.639346	−	0.710066i
$103$	2.99351	+	1.33280i	0.294959	+	0.131324i	0.548881	−	0.835900i	$-0.315054\pi$
$103$	2.99351	+	1.33280i	0.294959	+	0.131324i	−0.253922	+	0.967225i	$0.581721\pi$
$104$	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	0.0562195	−	0.998418i	$-0.482095\pi$
$107$	−3.08786	−	0.656345i	−0.298515	−	0.0634513i	−0.354734	+	0.934967i	$0.615429\pi$
$108$	1.37035	+	0.995614i	0.131862	+	0.0958030i
$109$	−5.62770	−	4.08876i	−0.539036	−	0.391632i	0.284691	−	0.958619i	$-0.408109\pi$
$109$	−5.62770	−	4.08876i	−0.539036	−	0.391632i	−0.823727	+	0.566987i	$0.808109\pi$
$110$	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	0.556579	−	0.830795i	$-0.312114\pi$
$113$	14.9136	−	3.16999i	1.40295	−	0.298207i	0.846375	+	0.532587i	$0.178780\pi$
$114$	−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	$-0.278787\pi$
$127$	18.4777	−	8.22681i	1.63963	−	0.730011i	0.999275	+	0.0380671i	$0.0121201\pi$
$128$	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	0.989146	−	0.146935i	$-0.0469409\pi$
$131$	8.46536	+	9.40173i	0.739622	+	0.821433i	−0.249524	+	0.968369i	$0.580274\pi$
$132$	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	0.857537	+	0.514423i	$0.171994\pi$
$137$	−1.03253	+	9.82390i	−0.0882153	+	0.839312i	−0.945752	+	0.324890i	$0.894673\pi$
$138$	−2.27540	−	0.483650i	−0.193695	−	0.0411711i
$139$	−12.5389	−	9.11007i	−1.06354	−	0.772706i	−0.0887990	−	0.996050i	$-0.528303\pi$
$139$	−12.5389	−	9.11007i	−1.06354	−	0.772706i	−0.974740	+	0.223343i	$0.928303\pi$
$140$	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	−0.364271	−	0.931293i	$-0.618682\pi$
$149$	7.62162	−	13.2010i	0.624388	−	1.08147i	0.988659	−	0.150178i	$-0.0479848\pi$
$150$	−3.33787	−	5.78136i	−0.272536	−	0.472046i
$151$	0.0809093	−	0.249013i	0.00658430	−	0.0202644i	−0.947710	−	0.319132i	$-0.896609\pi$
$151$	0.0809093	−	0.249013i	0.00658430	−	0.0202644i	0.954295	+	0.298867i	$0.0966088\pi$
$152$	−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	−0.967972	−	0.251058i	$-0.919222\pi$
$157$	−12.8848	+	9.36138i	−1.02832	+	0.747120i	−0.0603497	+	0.998177i	$0.519222\pi$
$158$	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	0.949432	−	0.313973i	$-0.101660\pi$
$163$	−0.0411534	−	0.126657i	−0.00322339	−	0.00992056i	−0.952655	+	0.304053i	$0.901660\pi$
$164$	−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	−0.998816	−	0.0486446i	$-0.984510\pi$
$167$	−0.412760	−	3.92715i	−0.0319403	−	0.303892i	0.966876	−	0.255247i	$-0.0821568\pi$
$168$	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	−0.773425	−	0.633888i	$-0.781458\pi$
$173$	1.51116	−	14.3777i	0.114891	−	1.09312i	0.888316	−	0.459232i	$-0.151875\pi$
$174$	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	$-0.00294638\pi$
$179$	11.8569	+	13.1684i	0.886228	+	0.984256i	−0.113729	+	0.993512i	$0.536280\pi$
$180$	−0.486049	+	0.841862i	−0.0362280	+	0.0627487i
$181$	−6.02958	−	10.4435i	−0.448175	−	0.776262i	0.550092	−	0.835104i	$-0.314593\pi$
$181$	−6.02958	−	10.4435i	−0.448175	−	0.776262i	−0.998267	+	0.0588418i	$0.981259\pi$
$182$	−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	0.759583	−	0.650411i	$-0.225403\pi$
$191$	−2.53576	−	4.39207i	−0.183481	−	0.317799i	−0.943064	+	0.332612i	$0.892070\pi$
$192$	9.22001	−	15.9695i	0.665397	−	1.15250i
$193$	−13.4105	−	14.8939i	−0.965312	−	1.07209i	−0.997361	−	0.0726015i	$-0.976870\pi$
$193$	−13.4105	−	14.8939i	−0.965312	−	1.07209i	0.0320489	−	0.999486i	$-0.489797\pi$
$194$	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	$-0.285257\pi$
$197$	21.2340	−	4.51342i	1.51286	−	0.321568i	0.888246	+	0.459367i	$0.151924\pi$
$198$	−0.632490	−	6.01774i	−0.0449491	−	0.427662i
$199$	1.58523	−	15.0824i	0.112374	−	1.06917i	−0.782440	−	0.622726i	$-0.786025\pi$
$199$	1.58523	−	15.0824i	0.112374	−	1.06917i	0.894814	−	0.446439i	$-0.147308\pi$
$200$	−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	−0.953891	−	0.300152i	$-0.902963\pi$
$211$	−3.15220	+	5.45978i	−0.217007	+	0.375867i	0.736885	+	0.676018i	$0.236296\pi$
$212$	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	$-0.753755\pi$
$223$	3.69455	−	6.39915i	0.247406	−	0.428519i	0.962805	+	0.270196i	$0.0870887\pi$
$224$	−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	0.896329	−	0.443389i	$-0.146224\pi$
$227$	17.5764	+	7.82553i	1.16659	+	0.519398i	0.270259	+	0.962788i	$0.412891\pi$
$228$	−5.96280	+	1.26743i	−0.394896	+	0.0839377i
$229$	−0.636276	−	6.05376i	−0.0420463	−	0.400044i	−0.995223	−	0.0976293i	$-0.968874\pi$
$229$	−0.636276	−	6.05376i	−0.0420463	−	0.400044i	0.953177	−	0.302414i	$-0.0977926\pi$
$230$	−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	0.0167519	−	0.999860i	$-0.494667\pi$
$233$	−14.1805	−	10.3027i	−0.928995	−	0.674954i	−0.945746	+	0.324906i	$0.894667\pi$
$234$	−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	0.284360	−	0.958718i	$-0.408219\pi$
$239$	18.6768	−	20.7427i	1.20810	−	1.34173i	0.923742	−	0.383016i	$-0.125114\pi$
$240$	−2.77933	−	8.55391i	−0.179405	−	0.552152i
$241$	−15.2225	−	16.9063i	−0.980570	−	1.08903i	−0.996018	−	0.0891530i	$-0.971584\pi$
$241$	−15.2225	−	16.9063i	−0.980570	−	1.08903i	0.0154476	−	0.999881i	$-0.495083\pi$
$242$	−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	$-0.462106\pi$
$251$	14.8310	−	6.60317i	0.936121	−	0.416788i	0.817355	+	0.576134i	$0.195439\pi$
$252$	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	−0.0218716	−	0.999761i	$-0.506963\pi$
$257$	15.6256	−	17.3540i	0.974699	−	1.08251i	0.996570	−	0.0827516i	$-0.0263708\pi$
$258$	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	$-0.403841\pi$
$263$	−8.40921	−	6.10965i	−0.518534	−	0.376737i	−0.816051	+	0.577979i	$0.803841\pi$
$264$	−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	$-0.323664\pi$
$269$	4.03609	+	1.79698i	0.246084	+	0.109564i	−0.279988	+	0.960003i	$0.590331\pi$
$270$	−4.48059	+	4.97620i	−0.272680	+	0.302842i
$271$	−1.90134	−	5.85172i	−0.115498	−	0.355467i	0.876552	−	0.481306i	$-0.159838\pi$
$271$	−1.90134	−	5.85172i	−0.115498	−	0.355467i	−0.992051	+	0.125840i	$0.959838\pi$
$272$	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	$-0.469559\pi$
$277$	17.8367	−	12.9591i	1.07171	−	0.778639i	0.976218	+	0.216791i	$0.0695591\pi$
$278$	19.0974			1.14539
$279$		0			0
$280$	−17.9782			−1.07440
$281$	24.8963	−	18.0882i	1.48519	−	1.07905i	0.509353	−	0.860557i	$-0.329885\pi$
$281$	24.8963	−	18.0882i	1.48519	−	1.07905i	0.975838	−	0.218497i	$-0.0701154\pi$
$282$	2.77747	−	1.23661i	0.165396	−	0.0736391i
$283$	−6.59605	+	20.3005i	−0.392094	+	1.20674i	0.539107	+	0.842237i	$0.318762\pi$
$283$	−6.59605	+	20.3005i	−0.392094	+	1.20674i	−0.931202	+	0.364505i	$0.881238\pi$
$284$	−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	0.259026	−	0.965870i	$-0.416598\pi$
$293$	1.75971	+	0.374039i	0.102804	+	0.0218516i	−0.156223	+	0.987722i	$0.549932\pi$
$294$	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	0.435383	−	0.900245i	$-0.356613\pi$
$307$	24.4551	−	10.8881i	1.39572	−	0.621417i	0.960341	+	0.278829i	$0.0899461\pi$
$308$	−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	$-0.529460\pi$
$313$	10.3622	−	4.61354i	0.585706	−	0.260773i	0.678124	+	0.734947i	$0.262793\pi$
$314$	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	0.996750	+	0.0805554i	$0.0256694\pi$
$317$	17.3180	+	19.2336i	0.972676	+	1.08027i	−0.0240746	+	0.999710i	$0.507664\pi$
$318$	−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	$-0.373366\pi$
$331$	−0.699582	−	0.311474i	−0.0384525	−	0.0171202i	−0.425873	+	0.904783i	$0.640033\pi$
$332$	−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	$-0.920773\pi$
$337$	−0.739892	+	2.27715i	−0.0403045	+	0.124044i	0.928880	+	0.370381i	$0.120773\pi$
$338$	−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	$-0.784806\pi$
$347$	2.82890	−	4.89980i	0.151863	−	0.263035i	0.931912	+	0.362683i	$0.118139\pi$
$348$	4.55412	+	5.05786i	0.244126	+	0.271130i
$349$	8.98238	+	27.6449i	0.480816	+	1.47980i	0.837950	+	0.545746i	$0.183754\pi$
$349$	8.98238	+	27.6449i	0.480816	+	1.47980i	−0.357134	+	0.934053i	$0.616246\pi$
$350$	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	−0.907330	−	0.420419i	$-0.861883\pi$
$353$	−2.01481	−	19.1696i	−0.107237	−	1.02030i	0.800093	−	0.599876i	$-0.204784\pi$
$354$	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	0.928217	+	0.372038i	$0.121341\pi$
$359$	−1.08127	+	10.2876i	−0.0570673	+	0.542959i	−0.985285	+	0.170921i	$0.945326\pi$
$360$	−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	$-0.167801\pi$
$367$	−0.0682819	−	0.118268i	−0.00356428	−	0.00617352i	−0.867802	+	0.496910i	$0.834468\pi$
$368$	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	0.658729	−	0.752380i	$-0.271094\pi$
$379$	−3.08344	−	3.42451i	−0.158386	−	0.175905i	−0.817115	+	0.576475i	$0.804428\pi$
$380$	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	$-0.875544\pi$
$383$	−31.5891	+	6.71446i	−1.61413	+	0.343093i	−0.689593	+	0.724197i	$0.742211\pi$
$384$	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	$-0.785561\pi$
$389$	−34.5005	−	7.33331i	−1.74925	−	0.371814i	−0.967714	+	0.252052i	$0.918895\pi$
$390$	−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	−0.810961	−	0.585100i	$-0.801055\pi$
$397$	2.01701	−	3.49356i	0.101231	−	0.175337i	0.912192	+	0.409763i	$0.134389\pi$
$398$	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	$-0.486603\pi$
$401$	20.1309	−	14.6260i	1.00529	−	0.730387i	0.963216	+	0.268728i	$0.0866032\pi$
$402$	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	$-0.805698\pi$
$409$	1.75361	−	3.03734i	0.0867105	−	0.150187i	0.906119	+	0.423023i	$0.139031\pi$
$410$	−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	0.503377	−	0.864067i	$-0.332091\pi$
$419$	−3.33340	−	2.42186i	−0.162847	−	0.118316i	−0.666224	+	0.745751i	$0.732091\pi$
$420$	−5.74853	−	1.22189i	−0.280499	−	0.0596220i
$421$	−2.88513	+	27.4502i	−0.140613	+	1.33784i	0.665642	+	0.746272i	$0.268158\pi$
$421$	−2.88513	+	27.4502i	−0.140613	+	1.33784i	−0.806254	+	0.591569i	$0.798509\pi$
$422$	−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	−0.706999	−	0.707214i	$-0.749952\pi$
$431$	−13.5880	+	6.04978i	−0.654512	+	0.291407i	0.0524876	+	0.998622i	$0.483285\pi$
$432$	7.97717	−	5.79575i	0.383802	−	0.278848i
$433$	−9.26195			−0.445101			−0.222550	−	0.974921i	$-0.571438\pi$
$433$	−9.26195			−0.445101			−0.222550	+	0.974921i	$0.571438\pi$
$434$		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	0.573393	−	0.819281i	$-0.305627\pi$
$439$	−8.85909	−	15.3444i	−0.422821	−	0.732348i	−0.996214	+	0.0869324i	$0.972294\pi$
$440$	−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	−0.961239	−	0.275715i	$-0.911085\pi$
$443$	−12.3456	+	13.7112i	−0.586558	+	0.651439i	0.374682	+	0.927154i	$0.377752\pi$
$444$	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	$-0.119980\pi$
$449$	18.3730	+	13.3487i	0.867073	+	0.629966i	−0.0627268	+	0.998031i	$0.519980\pi$
$450$	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	0.997301	+	0.0734205i	$0.0233915\pi$
$457$	4.99429	+	15.3708i	0.233623	+	0.719018i	−0.763678	+	0.645597i	$0.776608\pi$
$458$	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	0.667773	+	0.744365i	$0.267248\pi$
$461$	−6.65584	+	20.4846i	−0.309993	+	0.954062i	−0.977766	+	0.209697i	$0.932752\pi$
$462$	33.4188	−	14.8790i	1.55478	−	0.692235i
$463$	−14.1657	+	10.2920i	−0.658337	+	0.478310i	−0.866101	−	0.499869i	$-0.833381\pi$
$463$	−14.1657	+	10.2920i	−0.658337	+	0.478310i	0.207764	+	0.978179i	$0.433381\pi$
$464$	−19.0941			−0.886421
$465$		0			0
$466$	21.5976			1.00049
$467$	9.55176	−	6.93976i	0.442003	−	0.321134i	−0.344427	−	0.938813i	$-0.611927\pi$
$467$	9.55176	−	6.93976i	0.442003	−	0.321134i	0.786430	+	0.617679i	$0.211927\pi$
$468$	−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	0.547146	−	0.837037i	$-0.315714\pi$
$479$	15.4633	+	3.28682i	0.706534	+	0.150179i	0.159389	+	0.987216i	$0.449048\pi$
$480$	−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	$-0.860263\pi$
$487$	−8.55928	+	9.50604i	−0.387858	+	0.430760i	0.517320	+	0.855792i	$0.326930\pi$
$488$	−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	$-0.303964\pi$
$491$	−9.26410	−	16.0459i	−0.418083	−	0.724141i	−0.995747	+	0.0921341i	$0.970631\pi$
$492$	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	−0.672130	+	0.740433i	$0.734620\pi$
$499$	−37.3524	+	16.6303i	−1.67212	+	0.744476i	−0.999992	+	0.00404299i	$0.998713\pi$
$500$	−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	0.964047	−	0.265731i	$-0.0856133\pi$
$503$	13.4342	+	14.9202i	0.599001	+	0.665258i	−0.365046	+	0.930990i	$0.618947\pi$
$504$	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	0.629196	+	0.777247i	$0.283384\pi$
$509$	−3.33563	+	31.7364i	−0.147849	+	1.40669i	−0.777045	+	0.629445i	$0.783282\pi$
$510$	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	−0.888185	−	0.459485i	$-0.848034\pi$
$521$	−1.05378	+	1.82520i	−0.0461670	+	0.0799635i	0.842019	+	0.539449i	$0.181367\pi$
$522$	−5.47624	−	9.48512i	−0.239688	−	0.415152i
$523$	−1.51658	+	4.66757i	−0.0663156	+	0.204098i	−0.978723	−	0.205184i	$-0.934221\pi$
$523$	−1.51658	+	4.66757i	−0.0663156	+	0.204098i	0.912408	+	0.409282i	$0.134221\pi$
$524$	−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	0.461856	−	0.886955i	$-0.347184\pi$
$541$	12.1652	+	2.58580i	0.523025	+	0.111172i	0.0611690	+	0.998127i	$0.480517\pi$
$542$	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	0.0935967	−	0.995610i	$-0.470164\pi$
$547$	13.6598	−	2.90349i	0.584053	−	0.124144i	0.490456	+	0.871466i	$0.336830\pi$
$548$	−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	$-0.210834\pi$
$557$	37.2207			1.57709			0.788546	+	0.614976i	$0.210834\pi$
$558$		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	0.986990	+	0.160784i	$0.0514023\pi$
$563$	15.0134	+	26.0039i	0.632738	+	1.09593i	−0.354252	+	0.935150i	$0.615264\pi$
$564$	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	$-0.887798\pi$
$569$	−39.4891	+	8.39367i	−1.65547	+	0.351881i	−0.716955	+	0.697120i	$0.754464\pi$
$570$	−2.51902	−	23.9669i	−0.105510	−	1.00386i
$571$	4.45307	−	42.3682i	0.186355	−	1.77305i	−0.357538	−	0.933898i	$-0.616384\pi$
$571$	4.45307	−	42.3682i	0.186355	−	1.77305i	0.543894	−	0.839154i	$-0.316949\pi$
$572$	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	0.999495	+	0.0317838i	$0.0101188\pi$
$577$	0.683383	+	6.50195i	0.0284496	+	0.270680i	−0.971045	+	0.238896i	$0.923215\pi$
$578$	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	$-0.845439\pi$
$587$	−17.2949	+	12.5655i	−0.713838	+	0.518634i	0.170572	+	0.985345i	$0.445439\pi$
$588$	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	−0.639404	−	0.768871i	$-0.720819\pi$
$593$	8.03153	−	24.7185i	0.329816	−	1.01507i	0.969220	−	0.246197i	$-0.0791811\pi$
$594$	−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	0.228030	−	0.973654i	$-0.426772\pi$
$599$	−8.39362	−	3.73708i	−0.342954	−	0.152693i	−0.570984	+	0.820961i	$0.693438\pi$
$600$	16.2055	−	3.44458i	0.661586	−	0.140625i
$601$	3.48279	+	33.1365i	0.142066	+	1.35167i	0.800638	+	0.599149i	$0.204494\pi$
$601$	3.48279	+	33.1365i	0.142066	+	1.35167i	−0.658572	+	0.752518i	$0.728839\pi$
$602$	−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	−0.0480438	−	0.998845i	$-0.515299\pi$
$607$	5.09062	−	48.4340i	0.206622	−	1.96587i	0.254666	−	0.967029i	$-0.418035\pi$
$608$	−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	$-0.372130\pi$
$613$	−13.9942	−	15.5421i	−0.565220	−	0.627741i	−0.956220	+	0.292650i	$0.905463\pi$
$614$	−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	0.669129	−	0.743146i	$-0.266667\pi$
$617$	41.4603	−	18.4593i	1.66913	−	0.743144i	1.00000		1.59016e-6i	$5.06163e-7\pi$
$618$	6.77785	−	4.92440i	0.272645	−	0.198088i
$619$	10.2462			0.411832			0.205916	−	0.978570i	$-0.433983\pi$
$619$	10.2462			0.411832			0.205916	+	0.978570i	$0.433983\pi$
$620$		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	$-0.634834\pi$
$631$	−10.4437	+	2.21987i	−0.415755	+	0.0883715i	−0.00471535	+	0.999989i	$0.501501\pi$
$632$	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	$-0.522863\pi$
$641$	−21.7991	−	9.70559i	−0.861013	−	0.383348i	−0.789249	+	0.614074i	$0.789530\pi$
$642$	−5.40068	+	5.99806i	−0.213148	+	0.236725i
$643$	2.45337	+	7.55069i	0.0967513	+	0.297770i	0.987706	−	0.156322i	$-0.0499637\pi$
$643$	2.45337	+	7.55069i	0.0967513	+	0.297770i	−0.890955	+	0.454092i	$0.849964\pi$
$644$	−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	$-0.915509\pi$
$647$	−0.765625	+	2.35635i	−0.0300998	+	0.0926377i	0.934878	+	0.354969i	$0.115509\pi$
$648$	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	−0.883865	−	0.467742i	$-0.845068\pi$
$653$	−18.1981	+	13.2217i	−0.712145	+	0.517404i	0.171720	+	0.985146i	$0.445068\pi$
$654$	−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	0.852911	−	0.522056i	$-0.174835\pi$
$659$	−3.69573	−	11.3743i	−0.143965	−	0.443079i	−0.996876	+	0.0789765i	$0.974835\pi$
$660$	−3.88879	+	4.31894i	−0.151371	+	0.168114i
$661$	21.7752	+	9.69496i	0.846959	+	0.377090i	0.783876	−	0.620918i	$-0.213240\pi$
$661$	21.7752	+	9.69496i	0.846959	+	0.377090i	0.0630832	+	0.998008i	$0.479907\pi$
$662$	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	$-0.788119\pi$
$673$	−2.33802	+	2.59664i	−0.0901242	+	0.100093i	0.696396	+	0.717658i	$0.254786\pi$
$674$	−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	$-0.287253\pi$
$677$	−9.62287	−	16.6673i	−0.369837	−	0.640576i	−0.989540	+	0.144260i	$0.953920\pi$
$678$	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	−0.0185551	−	0.999828i	$-0.505907\pi$
$691$	25.7016	−	28.5445i	0.977735	−	1.08588i	0.996290	−	0.0860571i	$-0.0274267\pi$
$692$	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	0.809120	+	0.587644i	$0.199944\pi$
$701$	3.70297	+	35.2314i	0.139859	+	1.33067i	−0.669261	+	0.743028i	$0.733389\pi$
$702$	−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	−0.682137	−	0.731225i	$-0.738949\pi$
$709$	7.97551	−	24.5461i	0.299526	−	0.921848i	0.981663	−	0.190623i	$-0.0610508\pi$
$710$	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	0.229587	+	0.973288i	$0.426262\pi$
$719$	−19.5234	+	33.8155i	−0.728099	+	1.26110i	−0.957686	+	0.287816i	$0.907071\pi$
$720$	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	−0.268920	−	0.963163i	$-0.586667\pi$
$727$	−24.4377	−	5.19439i	−0.906344	−	0.192649i	−0.637424	+	0.770513i	$0.720000\pi$
$728$	−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	0.108710	−	0.994074i	$-0.465328\pi$
$733$	16.5787	−	3.52390i	0.612347	−	0.130158i	0.503637	+	0.863915i	$0.331995\pi$
$734$	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	$-0.0814506\pi$
$739$	7.19107	+	12.4553i	0.264528	+	0.458175i	−0.702912	+	0.711277i	$0.748117\pi$
$740$	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	$-0.329867\pi$
$743$	27.7705			1.01880			0.509400	+	0.860530i	$0.329867\pi$
$744$		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	−0.982773	−	0.184817i	$-0.940831\pi$
$751$	−29.1542	−	32.3790i	−1.06385	−	1.18153i	−0.0810773	−	0.996708i	$-0.525836\pi$
$752$	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	−0.836044	−	0.548662i	$-0.815138\pi$
$757$	2.63590	−	25.0790i	0.0958036	−	0.911510i	0.931848	−	0.362849i	$-0.118196\pi$
$758$	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	$-0.448431\pi$
$761$	−2.55877	−	0.543883i	−0.0927552	−	0.0197157i	−0.254055	+	0.967190i	$0.581765\pi$
$762$	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	−0.950024	−	0.312178i	$-0.898942\pi$
$769$	−5.67534	+	9.82998i	−0.204658	+	0.354478i	0.745366	+	0.666656i	$0.232275\pi$
$770$	−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	$-0.765826\pi$
$773$	−9.23685	+	6.71097i	−0.332226	+	0.241377i	0.409148	+	0.912468i	$0.365826\pi$
$774$	−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	−0.921394	−	0.388630i	$-0.872948\pi$
$787$	−2.83159	−	26.9408i	−0.100935	−	0.960336i	0.820458	−	0.571706i	$-0.193718\pi$
$788$	−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	−0.199580	+	0.979882i	$0.563958\pi$
$797$	−32.5571	+	36.1583i	−1.15323	+	1.28079i	−0.953652	+	0.300912i	$0.902709\pi$
$798$	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	$-0.526066\pi$
$809$	17.1830	−	7.65036i	0.604122	−	0.268972i	0.685921	+	0.727676i	$0.259400\pi$
$810$	6.59853	−	20.3082i	0.231849	−	0.713557i
$811$	19.7693	+	34.2414i	0.694193	+	1.20238i	0.970452	+	0.241294i	$0.0775720\pi$
$811$	19.7693	+	34.2414i	0.694193	+	1.20238i	−0.276259	+	0.961083i	$0.589095\pi$
$812$	−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	$-0.382211\pi$
$821$	−11.8414	−	8.60325i	−0.413266	−	0.300255i	−0.774923	+	0.632056i	$0.782211\pi$
$822$	20.4320	+	14.8447i	0.712649	+	0.517770i
$823$	40.8736	+	8.68794i	1.42476	+	0.302843i	0.854855	−	0.518866i	$-0.173646\pi$
$823$	40.8736	+	8.68794i	1.42476	+	0.302843i	0.569907	+	0.821709i	$0.306979\pi$
$824$	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	$-0.314375\pi$
$827$	8.59293	+	3.82582i	0.298805	+	0.133037i	−0.251858	+	0.967764i	$0.581042\pi$
$828$	0.382901	−	0.425254i	0.0133067	−	0.0147786i
$829$	−12.4629	−	38.3568i	−0.432854	−	1.33219i	−0.895270	−	0.445524i	$-0.853017\pi$
$829$	−12.4629	−	38.3568i	−0.432854	−	1.33219i	0.462416	−	0.886663i	$-0.346983\pi$
$830$	−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	−0.683138	−	0.730290i	$-0.739385\pi$
$839$	−5.78419	+	4.20246i	−0.199692	+	0.145085i	0.483445	+	0.875374i	$0.339385\pi$
$840$	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	0.572071	−	0.820204i	$-0.306140\pi$
$853$	−0.911496	−	0.662240i	−0.0312090	−	0.0226747i	−0.603280	+	0.797529i	$0.706140\pi$
$854$	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	0.208642	−	0.977992i	$-0.433096\pi$
$857$	23.3328	−	4.95953i	0.797032	−	0.169414i	0.588390	+	0.808578i	$0.299762\pi$
$858$	−23.1510	−	10.3075i	−0.790361	−	0.351892i
$859$	−21.7238	+	24.1267i	−0.741206	+	0.823193i	−0.989354	−	0.145530i	$-0.953511\pi$
$859$	−21.7238	+	24.1267i	−0.741206	+	0.823193i	0.248148	+	0.968722i	$0.420178\pi$
$860$	−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	$-0.299671\pi$
$863$	−11.9209	−	20.6476i	−0.405793	−	0.702853i	−0.994413	+	0.105556i	$0.966338\pi$
$864$	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	−0.315294	−	0.948994i	$-0.602103\pi$
$877$	19.5886	−	21.7553i	0.661459	−	0.734624i	0.976753	+	0.214370i	$0.0687698\pi$
$878$	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	−0.967048	−	0.254594i	$-0.918058\pi$
$881$	0.943900	−	8.98061i	0.0318008	−	0.302564i	0.998849	−	0.0479702i	$-0.0152752\pi$
$882$	−11.7516	−	2.49788i	−0.395697	−	0.0841080i
$883$	17.3191	+	12.5831i	0.582834	+	0.423454i	0.839745	−	0.542981i	$-0.182705\pi$
$883$	17.3191	+	12.5831i	0.582834	+	0.423454i	−0.256911	+	0.966435i	$0.582705\pi$
$884$	−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	−0.948943	−	0.315446i	$-0.897846\pi$
$887$	−2.57088	−	24.4603i	−0.0863216	−	0.821296i	0.862622	−	0.505849i	$-0.168821\pi$
$888$	−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	−0.999796	−	0.0201992i	$-0.993570\pi$
$907$	−6.10812	−	18.7989i	−0.202817	−	0.624206i	0.796979	−	0.604007i	$-0.206430\pi$
$908$	−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	−0.864591	−	0.502476i	$-0.832422\pi$
$911$	−3.72347	−	35.4264i	−0.123364	−	1.17373i	0.741227	−	0.671254i	$-0.234244\pi$
$912$	−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	0.0773698	−	0.997002i	$-0.475348\pi$
$919$	16.7814	−	3.56700i	0.553568	−	0.117665i	0.476198	+	0.879338i	$0.342014\pi$
$920$	−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	$-0.768395\pi$
$929$	−45.5222			−1.49353			−0.746767	+	0.665086i	$0.768395\pi$
$930$		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	0.954949	−	0.296769i	$-0.0959092\pi$
$937$	17.1414	+	19.0375i	0.559986	+	0.621928i	−0.394963	+	0.918697i	$0.629243\pi$
$938$	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	$-0.503348\pi$
$941$	11.8589	−	2.52069i	0.386589	−	0.0821721i	0.397106	+	0.917773i	$0.370014\pi$
$942$	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	$-0.579049\pi$
$947$	−26.6067	−	5.65542i	−0.864600	−	0.183776i	−0.618804	+	0.785545i	$0.712383\pi$
$948$	−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	−0.994921	−	0.100655i	$-0.967906\pi$
$953$	−7.69226	−	23.6743i	−0.249177	−	0.766887i	0.745745	−	0.666232i	$-0.232094\pi$
$954$	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	−0.0511507	−	0.998691i	$-0.516289\pi$
$967$	26.0999	−	45.2064i	0.839316	−	1.45374i	0.890467	−	0.455048i	$-0.150378\pi$
$968$	−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	0.0927134	−	0.995693i	$-0.470446\pi$
$971$	−18.2351	−	8.11880i	−0.585193	−	0.260545i	−0.677907	+	0.735148i	$0.737113\pi$
$972$	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	0.936458	+	0.350781i	$0.114084\pi$
$977$	48.7438	+	35.4144i	1.55945	+	1.13301i	0.622994	+	0.782227i	$0.285916\pi$
$978$	−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	$-0.707757\pi$
$983$	7.72091	−	8.57494i	0.246259	−	0.273498i	0.853584	+	0.520955i	$0.174424\pi$
$984$	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	$-0.702100\pi$
$991$	−37.3423			−1.18622			−0.593109	+	0.805122i	$0.702100\pi$
$992$		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	0.652985	−	0.757371i	$-0.273516\pi$
$997$	−10.4012	−	18.0154i	−0.329410	−	0.570555i	−0.982395	+	0.186816i	$0.940183\pi$
$998$	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.n.235.1		16
31.2	even	5		961.2.g.m.816.1		16
31.3	odd	30		31.2.g.a.7.2	✓	16
31.4	even	5		961.2.g.l.846.2		16
31.5	even	3		961.2.d.q.388.2		16
31.6	odd	6		961.2.g.s.338.1		16
31.7	even	15		961.2.g.j.448.2		16
31.8	even	5		961.2.c.i.439.5		16
31.9	even	15		961.2.a.j.1.5		8
31.10	even	15		961.2.d.q.374.2		16
31.11	odd	30		961.2.d.o.628.3		16
31.12	odd	30		961.2.g.t.732.1		16
31.13	odd	30		961.2.d.o.531.3		16
31.14	even	15		961.2.c.i.521.5		16
31.15	odd	10		961.2.g.k.547.2		16
31.16	even	5		961.2.g.j.547.2		16
31.17	odd	30		961.2.c.j.521.5		16
31.18	even	15		961.2.d.n.531.3		16
31.19	even	15	inner	961.2.g.n.732.1		16
31.20	even	15		961.2.d.n.628.3		16
31.21	odd	30		961.2.d.p.374.2		16
31.22	odd	30		961.2.a.i.1.5		8
31.23	odd	10		961.2.c.j.439.5		16
31.24	odd	30		961.2.g.k.448.2		16
31.25	even	3		961.2.g.m.338.1		16
31.26	odd	6		961.2.d.p.388.2		16
31.27	odd	10		31.2.g.a.9.2	yes	16
31.28	even	15		961.2.g.l.844.2		16
31.29	odd	10		961.2.g.s.816.1		16
31.30	odd	2		961.2.g.t.235.1		16
93.53	even	30		8649.2.a.bf.1.4		8
93.65	even	30		279.2.y.c.100.1		16
93.71	odd	30		8649.2.a.be.1.4		8
93.89	even	10		279.2.y.c.226.1		16
124.3	even	30		496.2.bg.c.193.2		16
124.27	even	10		496.2.bg.c.257.2		16
155.3	even	60		775.2.ck.a.224.3		32
155.27	even	20		775.2.ck.a.474.3		32
155.34	odd	30		775.2.bl.a.751.1		16
155.58	even	20		775.2.ck.a.474.2		32
155.89	odd	10		775.2.bl.a.226.1		16
155.127	even	60		775.2.ck.a.224.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.7.2	✓	16	31.3	odd	30
31.2.g.a.9.2	yes	16	31.27	odd	10
279.2.y.c.100.1		16	93.65	even	30
279.2.y.c.226.1		16	93.89	even	10
496.2.bg.c.193.2		16	124.3	even	30
496.2.bg.c.257.2		16	124.27	even	10
775.2.bl.a.226.1		16	155.89	odd	10
775.2.bl.a.751.1		16	155.34	odd	30
775.2.ck.a.224.2		32	155.127	even	60
775.2.ck.a.224.3		32	155.3	even	60
775.2.ck.a.474.2		32	155.58	even	20
775.2.ck.a.474.3		32	155.27	even	20
961.2.a.i.1.5		8	31.22	odd	30
961.2.a.j.1.5		8	31.9	even	15
961.2.c.i.439.5		16	31.8	even	5
961.2.c.i.521.5		16	31.14	even	15
961.2.c.j.439.5		16	31.23	odd	10
961.2.c.j.521.5		16	31.17	odd	30
961.2.d.n.531.3		16	31.18	even	15
961.2.d.n.628.3		16	31.20	even	15
961.2.d.o.531.3		16	31.13	odd	30
961.2.d.o.628.3		16	31.11	odd	30
961.2.d.p.374.2		16	31.21	odd	30
961.2.d.p.388.2		16	31.26	odd	6
961.2.d.q.374.2		16	31.10	even	15
961.2.d.q.388.2		16	31.5	even	3
961.2.g.j.448.2		16	31.7	even	15
961.2.g.j.547.2		16	31.16	even	5
961.2.g.k.448.2		16	31.24	odd	30
961.2.g.k.547.2		16	31.15	odd	10
961.2.g.l.844.2		16	31.28	even	15
961.2.g.l.846.2		16	31.4	even	5
961.2.g.m.338.1		16	31.25	even	3
961.2.g.m.816.1		16	31.2	even	5
961.2.g.n.235.1		16	1.1	even	1	trivial
961.2.g.n.732.1		16	31.19	even	15	inner
961.2.g.s.338.1		16	31.6	odd	6
961.2.g.s.816.1		16	31.29	odd	10
961.2.g.t.235.1		16	31.30	odd	2
961.2.g.t.732.1		16	31.12	odd	30
8649.2.a.be.1.4		8	93.71	odd	30
8649.2.a.bf.1.4		8	93.53	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.996848 + 0.724253i) q^{2} +(-1.89558 + 0.843968i) q^{3} +(-0.148869 + 0.458173i) q^{4} +(0.772811 + 1.33855i) q^{5} +(1.27836 - 2.21419i) q^{6} +(-2.54521 - 2.82674i) q^{7} +(-0.944957 - 2.90828i) q^{8} +(0.873564 - 0.970191i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 3 q^{3} + 6 q^{4} - 3 q^{5} - 11 q^{6} + 12 q^{7} - 8 q^{8} + 5 q^{9}+O(q^{10}) \) 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	\( 16 q + 4 q^{2} - 3 q^{3} + 6 q^{4} - 3 q^{5} - 11 q^{6} + 12 q^{7} - 8 q^{8} + 5 q^{9} - 12 q^{10} + 2 q^{11} - 25 q^{12} - 18 q^{13} + 24 q^{14} - 4 q^{15} - 2 q^{16} + q^{17} - 8 q^{18} + 11 q^{19} - 18 q^{20} + 31 q^{21} - 4 q^{22} - 21 q^{23} - 20 q^{24} - 13 q^{25} - 9 q^{26} - 9 q^{27} + 20 q^{28} - 26 q^{29} + 22 q^{30} - 42 q^{32} + 7 q^{33} - 28 q^{34} + 21 q^{35} + q^{36} + 8 q^{37} + 3 q^{38} + 2 q^{39} + 29 q^{40} - 3 q^{41} - 39 q^{42} - 8 q^{43} + 41 q^{44} - 20 q^{45} + 16 q^{46} + 4 q^{47} - 49 q^{48} + 12 q^{49} + 48 q^{50} - 2 q^{51} + 6 q^{52} + 69 q^{53} - 39 q^{54} - 23 q^{55} - 30 q^{56} + 17 q^{57} - 10 q^{58} + 54 q^{59} - 35 q^{60} + 60 q^{61} - 46 q^{63} - 32 q^{64} + 27 q^{65} + 20 q^{66} + 13 q^{67} - 30 q^{68} - 27 q^{69} + 27 q^{70} + 6 q^{71} + 2 q^{72} + 18 q^{73} + 92 q^{74} - 13 q^{75} - 27 q^{76} + 42 q^{77} + 15 q^{78} + 22 q^{79} + 21 q^{80} - 22 q^{81} - 61 q^{82} + 71 q^{83} + 12 q^{84} + 63 q^{85} + 11 q^{86} + 15 q^{87} + 17 q^{88} - 26 q^{89} - 33 q^{90} - 8 q^{91} + 64 q^{92} + 44 q^{94} + 28 q^{95} - 58 q^{96} - 37 q^{97} - 10 q^{98} - 6 q^{99}+O(q^{100}) \) 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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