LMFDB - Embedded newform 961.2.g.k.235.2

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			235.2
Root			$2.52368i$ of defining polynomial
Character	$\chi$	$=$	961.235
Dual form			961.2.g.k.732.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.284315 + 0.206567i) q^{2} +(-2.64315 + 1.17681i) q^{3} +(-0.579869 + 1.78465i) q^{4} +(-1.48661 - 2.57489i) q^{5} +(0.508398 - 0.880572i) q^{6} +(-0.724084 - 0.804176i) q^{7} +(-0.420982 - 1.29565i) q^{8} +(3.59399 - 3.99153i) q^{9} +(0.954554 + 0.424995i) q^{10} +(2.37824 - 0.505510i) q^{11} +(-0.567511 - 5.39951i) q^{12} +(-0.300378 + 2.85791i) q^{13} +(0.371984 + 0.0790676i) q^{14} +(6.95951 + 5.05638i) q^{15} +(-2.64890 - 1.92454i) q^{16} +(1.78489 + 0.379390i) q^{17} +(-0.197307 + 1.87725i) q^{18} +(-0.221420 - 2.10667i) q^{19} +(5.45733 - 1.15999i) q^{20} +(2.86023 + 1.27345i) q^{21} +(-0.571747 + 0.634989i) q^{22} +(-0.136652 - 0.420572i) q^{23} +(2.63745 + 2.92919i) q^{24} +(-1.92005 + 3.32562i) q^{25} +(-0.504947 - 0.874594i) q^{26} +(-2.11998 + 6.52462i) q^{27} +(1.85505 - 0.825921i) q^{28} +(2.55579 - 1.85689i) q^{29} -3.02317 q^{30} +3.87532 q^{32} +(-5.69116 + 4.13487i) q^{33} +(-0.585840 + 0.260833i) q^{34} +(-0.994234 + 3.05994i) q^{35} +(5.03946 + 8.72860i) q^{36} +(-1.57338 + 2.72517i) q^{37} +(0.498121 + 0.553219i) q^{38} +(-2.56926 - 7.90738i) q^{39} +(-2.71032 + 3.01011i) q^{40} +(-6.34570 - 2.82529i) q^{41} +(-1.07626 + 0.228766i) q^{42} +(0.879333 + 8.36630i) q^{43} +(-0.476906 + 4.53746i) q^{44} +(-15.6207 - 3.32027i) q^{45} +(0.125728 + 0.0913471i) q^{46} +(6.44144 + 4.67998i) q^{47} +(9.26627 + 1.96961i) q^{48} +(0.609297 - 5.79707i) q^{49} +(-0.141065 - 1.34214i) q^{50} +(-5.16421 + 1.09769i) q^{51} +(-4.92620 - 2.19328i) q^{52} +(-3.33026 + 3.69863i) q^{53} +(-0.745029 - 2.29296i) q^{54} +(-4.83716 - 5.37221i) q^{55} +(-0.737104 + 1.27670i) q^{56} +(3.06439 + 5.30768i) q^{57} +(-0.343078 + 1.05588i) q^{58} +(-10.9753 + 4.88651i) q^{59} +(-13.0595 + 9.48827i) q^{60} -14.4351 q^{61} -5.81225 q^{63} +(4.19600 - 3.04857i) q^{64} +(7.80536 - 3.47517i) q^{65} +(0.763955 - 2.35121i) q^{66} +(3.21879 + 5.57511i) q^{67} +(-1.71208 + 2.96541i) q^{68} +(0.856125 + 0.950823i) q^{69} +(-0.349406 - 1.07536i) q^{70} +(1.12272 - 1.24690i) q^{71} +(-6.68463 - 2.97619i) q^{72} +(-14.0464 + 2.98565i) q^{73} +(-0.115595 - 1.09981i) q^{74} +(1.16137 - 11.0497i) q^{75} +(3.88807 + 0.826435i) q^{76} +(-2.12856 - 1.54649i) q^{77} +(2.36388 + 1.71746i) q^{78} +(3.37230 + 0.716805i) q^{79} +(-1.01759 + 9.68169i) q^{80} +(-0.390488 - 3.71525i) q^{81} +(2.38779 - 0.507540i) q^{82} +(11.7424 + 5.22804i) q^{83} +(-3.93123 + 4.36607i) q^{84} +(-1.67655 - 5.15991i) q^{85} +(-1.97821 - 2.19702i) q^{86} +(-4.57015 + 7.91573i) q^{87} +(-1.65616 - 2.86855i) q^{88} +(0.698188 - 2.14880i) q^{89} +(5.12704 - 2.28271i) q^{90} +(2.51576 - 1.82781i) q^{91} +0.829816 q^{92} -2.79812 q^{94} +(-5.09528 + 3.70194i) q^{95} +(-10.2431 + 4.56051i) q^{96} +(1.05463 - 3.24582i) q^{97} +(1.02425 + 1.77405i) q^{98} +(6.52961 - 11.3096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} + 3 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9} - 17 q^{10} - 7 q^{11} - 10 q^{12} + 8 q^{13} - 21 q^{14} + 14 q^{15} - 2 q^{16} + 9 q^{17} + 12 q^{18} - 29 q^{19}+ \cdots + 6 q^{99}+O(q^{100}) $ 16 * q - 6 * q^2 + 3 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9 - 17 * q^10 - 7 * q^11 - 10 * q^12 + 8 * q^13 - 21 * q^14 + 14 * q^15 - 2 * q^16 + 9 * q^17 + 12 * q^18 - 29 * q^19 - 8 * q^20 - 6 * q^21 - 21 * q^22 + q^23 - 5 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 + 45 * q^28 - 14 * q^29 - 22 * q^30 - 42 * q^32 - 13 * q^33 - 17 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 23 * q^38 - 3 * q^39 - q^40 - 8 * q^41 - 51 * q^42 - 37 * q^43 - 6 * q^44 - 70 * q^45 + 34 * q^46 + 14 * q^47 + 4 * q^48 - 43 * q^49 + 3 * q^50 + 33 * q^51 - 46 * q^52 - 9 * q^53 - 46 * q^54 + 8 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 - 11 * q^59 - 75 * q^60 - 60 * q^61 - 46 * q^63 + 23 * q^64 + 18 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 - 37 * q^69 + 12 * q^70 + 31 * q^71 - 38 * q^72 - 13 * q^73 + 43 * q^74 - 17 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 - 12 * q^79 + 6 * q^80 - 22 * q^81 - q^82 + 44 * q^83 + 23 * q^84 + 37 * q^85 + 19 * q^86 + 15 * q^87 - 17 * q^88 + q^89 + 7 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 - 22 * q^95 + 8 * q^96 + 3 * q^97 - 10 * q^98 + 6 * q^99

Character values

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

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

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 $

$2$	−0.284315	+	0.206567i	−0.201041	+	0.146065i	−0.683751	−	0.729715i	$-0.739653\pi$
$2$	−0.284315	+	0.206567i	−0.201041	+	0.146065i	0.482710	+	0.875780i	$0.339653\pi$
$3$	−2.64315	+	1.17681i	−1.52603	+	0.679430i	−0.986683	−	0.162656i	$-0.947994\pi$
$3$	−2.64315	+	1.17681i	−1.52603	+	0.679430i	−0.539343	+	0.842086i	$0.681327\pi$
$4$	−0.579869	+	1.78465i	−0.289934	+	0.892327i
$5$	−1.48661	−	2.57489i	−0.664834	−	1.15153i	−0.979330	−	0.202268i	$-0.935169\pi$
$5$	−1.48661	−	2.57489i	−0.664834	−	1.15153i	0.314496	−	0.949259i	$-0.398165\pi$
$6$	0.508398	−	0.880572i	0.207553	−	0.359492i
$7$	−0.724084	−	0.804176i	−0.273678	−	0.303950i	0.590600	−	0.806964i	$-0.298891\pi$
$7$	−0.724084	−	0.804176i	−0.273678	−	0.303950i	−0.864278	+	0.503014i	$0.832224\pi$
$8$	−0.420982	−	1.29565i	−0.148840	−	0.458081i
$9$	3.59399	−	3.99153i	1.19800	−	1.33051i
$10$	0.954554	+	0.424995i	0.301856	+	0.134395i
$11$	2.37824	−	0.505510i	0.717066	−	0.152417i	0.165092	−	0.986278i	$-0.447208\pi$
$11$	2.37824	−	0.505510i	0.717066	−	0.152417i	0.551974	+	0.833861i	$0.313875\pi$
$12$	−0.567511	−	5.39951i	−0.163826	−	1.55870i
$13$	−0.300378	+	2.85791i	−0.0833100	+	0.792642i	0.870487	+	0.492191i	$0.163804\pi$
$13$	−0.300378	+	2.85791i	−0.0833100	+	0.792642i	−0.953797	+	0.300451i	$0.902863\pi$
$14$	0.371984	+	0.0790676i	0.0994169	+	0.0211317i
$15$	6.95951	+	5.05638i	1.79694	+	1.30555i
$16$	−2.64890	−	1.92454i	−0.662226	−	0.481135i
$17$	1.78489	+	0.379390i	0.432899	+	0.0920156i	0.419207	−	0.907891i	$-0.362308\pi$
$17$	1.78489	+	0.379390i	0.432899	+	0.0920156i	0.0136923	+	0.999906i	$0.495641\pi$
$18$	−0.197307	+	1.87725i	−0.0465057	+	0.442473i
$19$	−0.221420	−	2.10667i	−0.0507972	−	0.483303i	−0.990115	−	0.140256i	$-0.955208\pi$
$19$	−0.221420	−	2.10667i	−0.0507972	−	0.483303i	0.939318	−	0.343047i	$-0.111459\pi$
$20$	5.45733	−	1.15999i	1.22030	−	0.259382i
$21$	2.86023	+	1.27345i	0.624152	+	0.277890i
$22$	−0.571747	+	0.634989i	−0.121897	+	0.135380i
$23$	−0.136652	−	0.420572i	−0.0284939	−	0.0876953i	0.935798	−	0.352536i	$-0.114681\pi$
$23$	−0.136652	−	0.420572i	−0.0284939	−	0.0876953i	−0.964292	+	0.264841i	$0.914681\pi$
$24$	2.63745	+	2.92919i	0.538367	+	0.597917i
$25$	−1.92005	+	3.32562i	−0.384010	+	0.665124i
$26$	−0.504947	−	0.874594i	−0.0990283	−	0.171522i
$27$	−2.11998	+	6.52462i	−0.407990	+	1.25566i
$28$	1.85505	−	0.825921i	0.350571	−	0.156084i
$29$	2.55579	−	1.85689i	0.474599	−	0.344816i	−0.324632	−	0.945840i	$-0.605240\pi$
$29$	2.55579	−	1.85689i	0.474599	−	0.344816i	0.799231	+	0.601024i	$0.205240\pi$
$30$	−3.02317			−0.551953
$31$		0			0
$31$		0			0
$32$	3.87532			0.685067
$33$	−5.69116	+	4.13487i	−0.990704	+	0.719789i
$34$	−0.585840	+	0.260833i	−0.100471	+	0.0447324i
$35$	−0.994234	+	3.05994i	−0.168056	+	0.517224i
$36$	5.03946	+	8.72860i	0.839910	+	1.45477i
$37$	−1.57338	+	2.72517i	−0.258661	+	0.448015i	−0.965884	−	0.258977i	$-0.916615\pi$
$37$	−1.57338	+	2.72517i	−0.258661	+	0.448015i	0.707222	+	0.706991i	$0.249948\pi$
$38$	0.498121	+	0.553219i	0.0808059	+	0.0897440i
$39$	−2.56926	−	7.90738i	−0.411412	−	1.26619i
$40$	−2.71032	+	3.01011i	−0.428539	+	0.475941i
$41$	−6.34570	−	2.82529i	−0.991032	−	0.441236i	−0.153811	−	0.988100i	$-0.549155\pi$
$41$	−6.34570	−	2.82529i	−0.991032	−	0.441236i	−0.837221	+	0.546864i	$0.815821\pi$
$42$	−1.07626	+	0.228766i	−0.166070	+	0.0352993i
$43$	0.879333	+	8.36630i	0.134097	+	1.27585i	0.830021	+	0.557732i	$0.188328\pi$
$43$	0.879333	+	8.36630i	0.134097	+	1.27585i	−0.695924	+	0.718116i	$0.745005\pi$
$44$	−0.476906	+	4.53746i	−0.0718963	+	0.684048i
$45$	−15.6207	−	3.32027i	−2.32859	−	0.494957i
$46$	0.125728	+	0.0913471i	0.0185377	+	0.0134684i
$47$	6.44144	+	4.67998i	0.939580	+	0.682645i	0.948320	−	0.317317i	$-0.102782\pi$
$47$	6.44144	+	4.67998i	0.939580	+	0.682645i	−0.00873953	+	0.999962i	$0.502782\pi$
$48$	9.26627	+	1.96961i	1.33747	+	0.284288i
$49$	0.609297	−	5.79707i	0.0870424	−	0.828153i
$50$	−0.141065	−	1.34214i	−0.0199496	−	0.189807i
$51$	−5.16421	+	1.09769i	−0.723134	+	0.153707i
$52$	−4.92620	−	2.19328i	−0.683141	−	0.304154i
$53$	−3.33026	+	3.69863i	−0.457447	+	0.508046i	−0.927105	−	0.374802i	$-0.877711\pi$
$53$	−3.33026	+	3.69863i	−0.457447	+	0.508046i	0.469658	+	0.882848i	$0.344377\pi$
$54$	−0.745029	−	2.29296i	−0.101386	−	0.312033i
$55$	−4.83716	−	5.37221i	−0.652243	−	0.724389i
$56$	−0.737104	+	1.27670i	−0.0984997	+	0.170606i
$57$	3.06439	+	5.30768i	0.405889	+	0.703020i
$58$	−0.343078	+	1.05588i	−0.0450483	+	0.138644i
$59$	−10.9753	+	4.88651i	−1.42886	+	0.636169i	−0.967919	−	0.251262i	$-0.919154\pi$
$59$	−10.9753	+	4.88651i	−1.42886	+	0.636169i	−0.460940	+	0.887431i	$0.652488\pi$
$60$	−13.0595	+	9.48827i	−1.68597	+	1.22493i
$61$	−14.4351			−1.84823			−0.924115	−	0.382115i	$-0.875196\pi$
$61$	−14.4351			−1.84823			−0.924115	+	0.382115i	$0.875196\pi$
$62$		0			0
$63$	−5.81225			−0.732274
$64$	4.19600	−	3.04857i	0.524499	−	0.381071i
$65$	7.80536	−	3.47517i	0.968136	−	0.431042i
$66$	0.763955	−	2.35121i	0.0940363	−	0.289414i
$67$	3.21879	+	5.57511i	0.393238	+	0.681108i	0.992875	−	0.119164i	$-0.0380215\pi$
$67$	3.21879	+	5.57511i	0.393238	+	0.681108i	−0.599636	+	0.800273i	$0.704688\pi$
$68$	−1.71208	+	2.96541i	−0.207620	+	0.359609i
$69$	0.856125	+	0.950823i	0.103065	+	0.114466i
$70$	−0.349406	−	1.07536i	−0.0417620	−	0.128530i
$71$	1.12272	−	1.24690i	0.133242	−	0.147980i	−0.672831	−	0.739796i	$-0.734922\pi$
$71$	1.12272	−	1.24690i	0.133242	−	0.147980i	0.806073	+	0.591816i	$0.201589\pi$
$72$	−6.68463	−	2.97619i	−0.787792	−	0.350747i
$73$	−14.0464	+	2.98565i	−1.64400	+	0.349443i	−0.934694	−	0.355455i	$-0.884326\pi$
$73$	−14.0464	+	2.98565i	−1.64400	+	0.349443i	−0.709309	+	0.704898i	$0.750993\pi$
$74$	−0.115595	−	1.09981i	−0.0134376	−	0.127851i
$75$	1.16137	−	11.0497i	0.134103	−	1.27590i
$76$	3.88807	+	0.826435i	0.445992	+	0.0947985i
$77$	−2.12856	−	1.54649i	−0.242572	−	0.176239i
$78$	2.36388	+	1.71746i	0.267657	+	0.194464i
$79$	3.37230	+	0.716805i	0.379414	+	0.0806469i	0.393671	−	0.919251i	$-0.371205\pi$
$79$	3.37230	+	0.716805i	0.379414	+	0.0806469i	−0.0142570	+	0.999898i	$0.504538\pi$
$80$	−1.01759	+	9.68169i	−0.113770	+	1.08245i
$81$	−0.390488	−	3.71525i	−0.0433876	−	0.412805i
$82$	2.38779	−	0.507540i	0.263687	−	0.0560484i
$83$	11.7424	+	5.22804i	1.28889	+	0.573851i	0.932731	−	0.360573i	$-0.117419\pi$
$83$	11.7424	+	5.22804i	1.28889	+	0.573851i	0.356161	+	0.934425i	$0.384086\pi$
$84$	−3.93123	+	4.36607i	−0.428932	+	0.476378i
$85$	−1.67655	−	5.15991i	−0.181848	−	0.559670i
$86$	−1.97821	−	2.19702i	−0.213315	−	0.236911i
$87$	−4.57015	+	7.91573i	−0.489972	+	0.848656i
$88$	−1.65616	−	2.86855i	−0.176547	−	0.305789i
$89$	0.698188	−	2.14880i	0.0740078	−	0.227773i	−0.907209	−	0.420680i	$-0.861792\pi$
$89$	0.698188	−	2.14880i	0.0740078	−	0.227773i	0.981217	+	0.192907i	$0.0617916\pi$
$90$	5.12704	−	2.28271i	0.540438	−	0.240618i
$91$	2.51576	−	1.82781i	0.263724	−	0.191606i
$92$	0.829816			0.0865143
$93$		0			0
$94$	−2.79812			−0.288604
$95$	−5.09528	+	3.70194i	−0.522765	+	0.379811i
$96$	−10.2431	+	4.56051i	−1.04543	+	0.465455i
$97$	1.05463	−	3.24582i	0.107082	−	0.329563i	−0.883132	−	0.469125i	$-0.844569\pi$
$97$	1.05463	−	3.24582i	0.107082	−	0.329563i	0.990213	+	0.139562i	$0.0445693\pi$
$98$	1.02425	+	1.77405i	0.103465	+	0.179207i
$99$	6.52961	−	11.3096i	0.656251	−	1.13666i
$100$	−4.82170	−	5.35504i	−0.482170	−	0.535504i
$101$	5.47495	+	16.8502i	0.544778	+	1.67665i	0.721518	+	0.692395i	$0.243445\pi$
$101$	5.47495	+	16.8502i	0.544778	+	1.67665i	−0.176741	+	0.984257i	$0.556555\pi$
$102$	1.24152	−	1.37884i	0.122928	−	0.136526i
$103$	7.37583	+	3.28393i	0.726762	+	0.323575i	0.736556	−	0.676377i	$-0.236451\pi$
$103$	7.37583	+	3.28393i	0.726762	+	0.323575i	−0.00979397	+	0.999952i	$0.503118\pi$
$104$	3.82930	−	0.813944i	0.375494	−	0.0798137i
$105$	−0.973045	−	9.25791i	−0.0949595	−	0.903479i
$106$	0.182829	−	1.73950i	0.0177579	−	0.168955i
$107$	11.8857	+	2.52638i	1.14903	+	0.244234i	0.742785	−	0.669530i	$-0.233505\pi$
$107$	11.8857	+	2.52638i	1.14903	+	0.244234i	0.406245	+	0.913764i	$0.366838\pi$
$108$	−10.4149	−	7.56685i	−1.00217	−	0.728121i
$109$	0.511381	+	0.371540i	0.0489815	+	0.0355871i	0.612007	−	0.790853i	$-0.290363\pi$
$109$	0.511381	+	0.371540i	0.0489815	+	0.0355871i	−0.563025	+	0.826440i	$0.690363\pi$
$110$	2.48500	+	0.528202i	0.236935	+	0.0503621i
$111$	0.951676	−	9.05459i	0.0903291	−	0.859424i
$112$	0.370357	+	3.52371i	0.0349955	+	0.332960i
$113$	11.0534	−	2.34947i	1.03982	−	0.221020i	0.343798	−	0.939044i	$-0.388286\pi$
$113$	11.0534	−	2.34947i	1.03982	−	0.221020i	0.696019	+	0.718024i	$0.254953\pi$
$114$	−1.96764	−	0.876051i	−0.184287	−	0.0820497i
$115$	−0.879779	+	0.977093i	−0.0820398	+	0.0911144i
$116$	1.83188	+	5.63796i	0.170086	+	0.523472i
$117$	10.3279	+	11.4703i	0.954813	+	1.06043i
$118$	2.11104	−	3.65643i	0.194337	−	0.336602i
$119$	−0.987313	−	1.71008i	−0.0905068	−	0.156762i
$120$	3.62146	−	11.1457i	0.330593	−	1.01746i
$121$	−4.64852	+	2.06965i	−0.422593	+	0.188150i
$122$	4.10412	−	2.98182i	0.371570	−	0.269961i
$123$	20.0975			1.81213
$124$		0			0
$125$	−3.44866			−0.308458
$126$	1.65251	−	1.20062i	0.147217	−	0.106960i
$127$	0.107621	−	0.0479161i	0.00954985	−	0.00425186i	−0.401956	−	0.915659i	$-0.631670\pi$
$127$	0.107621	−	0.0479161i	0.00954985	−	0.00425186i	0.411506	+	0.911407i	$0.365003\pi$
$128$	−2.95833	+	9.10481i	−0.261482	+	0.804759i
$129$	−12.1697	−	21.0786i	−1.07149	−	1.85587i
$130$	−1.50132	+	2.60037i	−0.131675	+	0.228068i
$131$	3.87022	+	4.29831i	0.338143	+	0.375545i	0.888102	−	0.459646i	$-0.152024\pi$
$131$	3.87022	+	4.29831i	0.338143	+	0.375545i	−0.549960	+	0.835191i	$0.685357\pi$
$132$	−4.07918	−	12.5544i	−0.355047	−	1.09272i
$133$	−1.53381	+	1.70347i	−0.132998	+	0.147709i
$134$	−2.06678	−	0.920192i	−0.178543	−	0.0794924i
$135$	19.9518	−	4.24089i	1.71718	−	0.364997i
$136$	−0.259850	−	2.47231i	−0.0222820	−	0.211999i
$137$	−1.23400	+	11.7408i	−0.105428	+	1.00308i	0.806083	+	0.591803i	$0.201584\pi$
$137$	−1.23400	+	11.7408i	−0.105428	+	1.00308i	−0.911510	+	0.411277i	$0.865083\pi$
$138$	−0.439818	−	0.0934861i	−0.0374398	−	0.00795807i
$139$	12.4767	+	9.06482i	1.05826	+	0.768868i	0.973765	−	0.227556i	$-0.0730734\pi$
$139$	12.4767	+	9.06482i	1.05826	+	0.768868i	0.0844915	+	0.996424i	$0.473073\pi$
$140$	−4.88440	−	3.54873i	−0.412807	−	0.299922i
$141$	−22.5331	−	4.78957i	−1.89763	−	0.403354i
$142$	−0.0616362	+	0.586429i	−0.00517240	+	0.0492121i
$143$	0.730331	+	6.94864i	0.0610734	+	0.581074i
$144$	−17.2020	+	3.65640i	−1.43350	+	0.304700i
$145$	−8.58078	−	3.82041i	−0.712595	−	0.317268i
$146$	3.37685	−	3.75038i	0.279470	−	0.310383i
$147$	5.21157	+	16.0396i	0.429843	+	1.32292i
$148$	−3.95112	−	4.38817i	−0.324780	−	0.360705i
$149$	5.97511	−	10.3492i	0.489500	−	0.847840i	−0.510427	−	0.859921i	$-0.670512\pi$
$149$	5.97511	−	10.3492i	0.489500	−	0.847840i	0.999927	+	0.0120817i	$0.00384583\pi$
$150$	1.95230	+	3.38148i	0.159404	+	0.276097i
$151$	−1.33561	+	4.11059i	−0.108691	+	0.334515i	−0.990579	−	0.136943i	$-0.956272\pi$
$151$	−1.33561	+	4.11059i	−0.108691	+	0.334515i	0.881888	+	0.471458i	$0.156272\pi$
$152$	−2.63629	+	1.17375i	−0.213831	+	0.0952039i
$153$	7.92923	−	5.76092i	0.641040	−	0.465743i
$154$	0.924636			0.0745093
$155$		0			0
$156$	15.6018			1.24914
$157$	7.04204	−	5.11634i	0.562016	−	0.408328i	−0.270180	−	0.962810i	$-0.587083\pi$
$157$	7.04204	−	5.11634i	0.562016	−	0.408328i	0.832196	+	0.554481i	$0.187083\pi$
$158$	−1.10686	+	0.492808i	−0.0880574	+	0.0392057i
$159$	4.44982	−	13.6951i	0.352893	−	1.08609i
$160$	−5.76111	−	9.97854i	−0.455456	−	0.788873i
$161$	−0.239267	+	0.414422i	−0.0188568	+	0.0326610i
$162$	0.878469	+	0.975638i	0.0690190	+	0.0766534i
$163$	0.966575	+	2.97481i	0.0757080	+	0.233005i	0.981748	−	0.190187i	$-0.0609095\pi$
$163$	0.966575	+	2.97481i	0.0757080	+	0.233005i	−0.906040	+	0.423192i	$0.860909\pi$
$164$	8.72184	−	9.68658i	0.681061	−	0.756395i
$165$	19.1074	+	8.50717i	1.48751	+	0.662282i
$166$	−4.41847	+	0.939174i	−0.342939	+	0.0728940i
$167$	1.39597	+	13.2818i	0.108023	+	1.02777i	0.905477	+	0.424395i	$0.139513\pi$
$167$	1.39597	+	13.2818i	0.108023	+	1.02777i	−0.797454	+	0.603380i	$0.793820\pi$
$168$	0.445847	−	4.24195i	0.0343978	−	0.327274i
$169$	4.63850	+	0.985943i	0.356807	+	0.0758417i
$170$	1.54253	+	1.12072i	0.118307	+	0.0859551i
$171$	−9.20462	−	6.68755i	−0.703895	−	0.511410i
$172$	−15.4408	−	3.28205i	−1.17735	−	0.250254i
$173$	−1.99072	+	18.9404i	−0.151351	+	1.44001i	0.610374	+	0.792113i	$0.291019\pi$
$173$	−1.99072	+	18.9404i	−0.151351	+	1.44001i	−0.761726	+	0.647900i	$0.775648\pi$
$174$	−0.335766	−	3.19460i	−0.0254544	−	0.242182i
$175$	4.06466	−	0.863970i	0.307259	−	0.0653100i
$176$	−7.27260	−	3.23797i	−0.548193	−	0.244071i
$177$	23.2589	−	25.8316i	1.74824	−	1.94162i
$178$	0.245366	+	0.755159i	0.0183910	+	0.0566016i
$179$	−0.0530821	−	0.0589537i	−0.00396754	−	0.00440640i	0.741158	−	0.671331i	$-0.234277\pi$
$179$	−0.0530821	−	0.0589537i	−0.00396754	−	0.00440640i	−0.745125	+	0.666924i	$0.767610\pi$
$180$	14.9835	−	25.9521i	1.11680	−	1.93436i
$181$	−1.08143	−	1.87308i	−0.0803817	−	0.139225i	0.823032	−	0.567995i	$-0.192281\pi$
$181$	−1.08143	−	1.87308i	−0.0803817	−	0.139225i	−0.903414	+	0.428769i	$0.858947\pi$
$182$	−0.337704	+	1.03935i	−0.0250323	+	0.0770415i
$183$	38.1543	−	16.9874i	2.82045	−	1.25574i
$184$	−0.487386	+	0.354107i	−0.0359306	+	0.0261051i
$185$	9.35601			0.687868
$186$		0			0
$187$	4.43668			0.324442
$188$	−12.0873	+	8.78195i	−0.881559	+	0.640490i
$189$	6.78199	−	3.01954i	0.493317	−	0.219639i
$190$	0.683966	−	2.10503i	0.0496201	−	0.152715i
$191$	2.67085	+	4.62604i	0.193256	+	0.334729i	0.946327	−	0.323210i	$-0.104762\pi$
$191$	2.67085	+	4.62604i	0.193256	+	0.334729i	−0.753072	+	0.657939i	$0.771429\pi$
$192$	−7.50308	+	12.9957i	−0.541488	+	0.937885i
$193$	−1.42771	−	1.58563i	−0.102769	−	0.114136i	0.689566	−	0.724223i	$-0.257801\pi$
$193$	−1.42771	−	1.58563i	−0.102769	−	0.114136i	−0.792335	+	0.610087i	$0.791135\pi$
$194$	0.370632	+	1.14069i	0.0266098	+	0.0818966i
$195$	−16.5412	+	18.3708i	−1.18454	+	1.31556i
$196$	9.99245	+	4.44893i	0.713746	+	0.317780i
$197$	5.74733	−	1.22163i	0.409480	−	0.0870377i	0.00143405	−	0.999999i	$-0.499544\pi$
$197$	5.74733	−	1.22163i	0.409480	−	0.0870377i	0.408046	+	0.912961i	$0.366210\pi$
$198$	0.479727	+	4.56429i	0.0340927	+	0.324370i
$199$	−0.724169	+	6.89001i	−0.0513350	+	0.488420i	0.938405	+	0.345538i	$0.112304\pi$
$199$	−0.724169	+	6.89001i	−0.0513350	+	0.488420i	−0.989740	+	0.142882i	$0.954363\pi$
$200$	5.11714	+	1.08768i	0.361837	+	0.0769108i
$201$	−15.0686	−	10.9480i	−1.06286	−	0.772211i
$202$	−5.03729	−	3.65981i	−0.354423	−	0.257503i
$203$	−3.34388	−	0.710763i	−0.234694	−	0.0498858i
$204$	1.03557	−	9.85283i	0.0725047	−	0.689836i
$205$	2.15880	+	20.5396i	0.150777	+	1.43455i
$206$	−2.77541	+	0.589931i	−0.193372	+	0.0411025i
$207$	−2.16985	−	0.966082i	−0.150815	−	0.0671473i
$208$	6.29584	−	6.99224i	0.436538	−	0.484824i
$209$	−1.59153	−	4.89823i	−0.110089	−	0.338818i
$210$	2.18903	+	2.43116i	0.151057	+	0.167766i
$211$	−8.35437	+	14.4702i	−0.575139	+	0.996170i	0.420888	+	0.907113i	$0.361719\pi$
$211$	−8.35437	+	14.4702i	−0.575139	+	0.996170i	−0.996027	+	0.0890568i	$0.971615\pi$
$212$	−4.66966	−	8.08808i	−0.320713	−	0.555492i
$213$	−1.50015	+	4.61698i	−0.102788	+	0.316350i
$214$	−3.90114	+	1.73690i	−0.266676	+	0.118732i
$215$	20.2351	−	14.7016i	1.38002	−	1.00264i
$216$	9.34610			0.635921
$217$		0			0
$218$	−0.222141			−0.0150453
$219$	33.6132	−	24.4214i	2.27137	−	1.65024i
$220$	12.3925	−	5.51747i	0.835499	−	0.371988i
$221$	−1.62040	+	4.98709i	−0.109000	+	0.335468i
$222$	1.59980	+	2.77094i	0.107372	+	0.185973i
$223$	3.13078	−	5.42267i	0.209653	−	0.363129i	−0.741952	−	0.670453i	$-0.766100\pi$
$223$	3.13078	−	5.42267i	0.209653	−	0.363129i	0.951605	+	0.307323i	$0.0994333\pi$
$224$	−2.80606	−	3.11644i	−0.187488	−	0.208226i
$225$	6.37369	+	19.6162i	0.424912	+	1.30775i
$226$	−2.65732	+	2.95126i	−0.176763	+	0.196315i
$227$	−7.16906	−	3.19187i	−0.475827	−	0.211852i	0.154788	−	0.987948i	$-0.450531\pi$
$227$	−7.16906	−	3.19187i	−0.475827	−	0.211852i	−0.630615	+	0.776096i	$0.717197\pi$
$228$	−11.2493	+	2.39112i	−0.745004	+	0.158356i
$229$	−1.33514	−	12.7030i	−0.0882286	−	0.839439i	−0.945729	−	0.324956i	$-0.894651\pi$
$229$	−1.33514	−	12.7030i	−0.0882286	−	0.839439i	0.857501	−	0.514483i	$-0.172016\pi$
$230$	0.0482991	−	0.459535i	0.00318475	−	0.0303009i
$231$	7.44604	+	1.58271i	0.489914	+	0.104134i
$232$	−3.48183	−	2.52969i	−0.228593	−	0.166083i
$233$	−10.2887	−	7.47514i	−0.674032	−	0.489713i	0.197340	−	0.980335i	$-0.436770\pi$
$233$	−10.2887	−	7.47514i	−0.674032	−	0.489713i	−0.871373	+	0.490622i	$0.836770\pi$
$234$	−5.30575	−	1.12777i	−0.346848	−	0.0737248i
$235$	2.47450	−	23.5433i	0.161419	−	1.53580i
$236$	−2.35650	−	22.4206i	−0.153395	−	1.45946i
$237$	−9.75706	+	2.07393i	−0.633789	+	0.134716i
$238$	0.633953	+	0.282254i	0.0410930	+	0.0182958i
$239$	−17.0124	+	18.8942i	−1.10044	+	1.22216i	−0.127320	+	0.991862i	$0.540638\pi$
$239$	−17.0124	+	18.8942i	−1.10044	+	1.22216i	−0.973120	+	0.230301i	$0.926029\pi$
$240$	−8.70385	−	26.7877i	−0.561831	−	1.72914i
$241$	1.57980	+	1.75455i	0.101764	+	0.113021i	0.791875	−	0.610683i	$-0.209105\pi$
$241$	1.57980	+	1.75455i	0.101764	+	0.113021i	−0.690111	+	0.723703i	$0.742438\pi$
$242$	0.894121	−	1.54866i	0.0574763	−	0.0995519i
$243$	−4.88634	−	8.46339i	−0.313459	−	0.542927i
$244$	8.37048	−	25.7617i	0.535865	−	1.64922i
$245$	−15.8326	+	7.04914i	−1.01151	+	0.450353i
$246$	−5.71401	+	4.15147i	−0.364312	+	0.264688i
$247$	6.08718			0.387318
$248$		0			0
$249$	−37.1893			−2.35677
$250$	0.980506	−	0.712379i	0.0620126	−	0.0450548i
$251$	2.15289	−	0.958530i	0.135889	−	0.0605019i	−0.337665	−	0.941266i	$-0.609637\pi$
$251$	2.15289	−	0.958530i	0.135889	−	0.0605019i	0.473555	+	0.880764i	$0.342971\pi$
$252$	3.37034	−	10.3728i	0.212312	−	0.653428i
$253$	−0.537595	−	0.931142i	−0.0337983	−	0.0585404i
$254$	−0.0207005	+	0.0358542i	−0.00129886	+	0.00224970i
$255$	10.5036	+	11.6654i	0.657762	+	0.730518i
$256$	2.16580	+	6.66565i	0.135363	+	0.416603i
$257$	−17.4068	+	19.3322i	−1.08580	+	1.20591i	−0.108494	+	0.994097i	$0.534603\pi$
$257$	−17.4068	+	19.3322i	−1.08580	+	1.20591i	−0.977311	+	0.211811i	$0.932064\pi$
$258$	7.81418	+	3.47909i	0.486489	+	0.216599i
$259$	3.33077	−	0.707977i	0.206964	−	0.0439915i
$260$	1.67589	+	15.9450i	0.103934	+	0.988867i
$261$	1.77366	−	16.8752i	0.109786	−	1.04455i
$262$	−1.98825	−	0.422616i	−0.122834	−	0.0261093i
$263$	−18.5552	−	13.4812i	−1.14417	−	0.831285i	−0.156471	−	0.987683i	$-0.550012\pi$
$263$	−18.5552	−	13.4812i	−1.14417	−	0.831285i	−0.987694	+	0.156398i	$0.950012\pi$
$264$	7.75322	+	5.63304i	0.477178	+	0.346690i
$265$	14.4744	+	3.07663i	0.889155	+	0.188996i
$266$	0.0842047	−	0.801154i	0.00516292	−	0.0491219i
$267$	0.683309	+	6.50125i	0.0418178	+	0.397870i
$268$	−11.8161	+	2.51159i	−0.721784	+	0.153420i
$269$	−15.5735	−	6.93377i	−0.949534	−	0.422760i	−0.127271	−	0.991868i	$-0.540622\pi$
$269$	−15.5735	−	6.93377i	−0.949534	−	0.422760i	−0.822263	+	0.569108i	$0.807288\pi$
$270$	−4.79657	+	5.32713i	−0.291910	+	0.324199i
$271$	2.23929	+	6.89184i	0.136027	+	0.418649i	0.995748	−	0.0921146i	$-0.0293626\pi$
$271$	2.23929	+	6.89184i	0.136027	+	0.418649i	−0.859721	+	0.510764i	$0.829363\pi$
$272$	−3.99785	−	4.44006i	−0.242405	−	0.269218i
$273$	−4.49857	+	7.79175i	−0.272266	+	0.471578i
$274$	−2.07440	−	3.59297i	−0.125319	−	0.217059i
$275$	−2.88520	+	8.87972i	−0.173984	+	0.535467i
$276$	−2.19333	+	0.976534i	−0.132023	+	0.0587804i
$277$	−12.2188	+	8.87748i	−0.734157	+	0.533396i	−0.890876	−	0.454247i	$-0.849908\pi$
$277$	−12.2188	+	8.87748i	−0.734157	+	0.533396i	0.156719	+	0.987643i	$0.449908\pi$
$278$	−5.41979			−0.325058
$279$		0			0
$280$	4.38316			0.261944
$281$	2.01209	−	1.46187i	0.120031	−	0.0872078i	−0.526150	−	0.850392i	$-0.676365\pi$
$281$	2.01209	−	1.46187i	0.120031	−	0.0872078i	0.646181	+	0.763184i	$0.276365\pi$
$282$	7.39587	−	3.29285i	0.440418	−	0.196087i
$283$	−1.46052	+	4.49503i	−0.0868192	+	0.267202i	−0.985035	−	0.172352i	$-0.944863\pi$
$283$	−1.46052	+	4.49503i	−0.0868192	+	0.267202i	0.898216	+	0.439554i	$0.144863\pi$
$284$	1.57426	+	2.72670i	0.0934153	+	0.161800i
$285$	9.11114	−	15.7810i	0.539697	−	0.934783i
$286$	−1.64300	−	1.82474i	−0.0971527	−	0.107899i
$287$	2.32279	+	7.14881i	0.137110	+	0.421981i
$288$	13.9279	−	15.4685i	0.820708	−	0.911489i
$289$	−12.4884	−	5.56018i	−0.734611	−	0.327070i
$290$	3.22881	−	0.686306i	0.189602	−	0.0403013i
$291$	1.03216	+	9.82031i	0.0605061	+	0.575677i
$292$	2.81671	−	26.7992i	0.164835	−	1.56830i
$293$	10.3184	+	2.19324i	0.602806	+	0.128130i	0.499198	−	0.866488i	$-0.333628\pi$
$293$	10.3184	+	2.19324i	0.602806	+	0.128130i	0.103608	+	0.994618i	$0.466961\pi$
$294$	−4.79497	−	3.48375i	−0.279648	−	0.203177i
$295$	28.8982	+	20.9958i	1.68252	+	1.22242i
$296$	4.19322	+	0.891297i	0.243726	+	0.0518056i
$297$	−1.74355	+	16.5888i	−0.101171	+	0.962579i
$298$	0.438988	+	4.17669i	0.0254299	+	0.241949i
$299$	1.24300	−	0.264209i	0.0718848	−	0.0152796i
$300$	19.0464	+	8.47998i	1.09964	+	0.489592i
$301$	6.09127	−	6.76504i	0.351095	−	0.389930i
$302$	−0.469377	−	1.44459i	−0.0270096	−	0.0831271i
$303$	−34.3005	−	38.0946i	−1.97051	−	2.18848i
$304$	−3.46785	+	6.00650i	−0.198895	+	0.344496i
$305$	21.4595	+	37.1689i	1.22877	+	2.12829i
$306$	−1.06438	+	3.27583i	−0.0608467	+	0.187267i
$307$	2.41953	−	1.07724i	0.138090	−	0.0614815i	−0.336528	−	0.941673i	$-0.609253\pi$
$307$	2.41953	−	1.07724i	0.138090	−	0.0614815i	0.474618	+	0.880192i	$0.342586\pi$
$308$	3.99424	−	2.90198i	0.227593	−	0.165356i
$309$	−23.3600			−1.32890
$310$		0			0
$311$	5.51283			0.312604			0.156302	−	0.987709i	$-0.450043\pi$
$311$	5.51283			0.312604			0.156302	+	0.987709i	$0.450043\pi$
$312$	−9.16358	+	6.65773i	−0.518786	+	0.376920i
$313$	−24.3692	+	10.8499i	−1.37743	+	0.613272i	−0.955940	−	0.293561i	$-0.905160\pi$
$313$	−24.3692	+	10.8499i	−1.37743	+	0.613272i	−0.421491	+	0.906833i	$0.638493\pi$
$314$	−0.945290	+	2.90930i	−0.0533458	+	0.164181i
$315$	8.64057	+	14.9659i	0.486841	+	0.843234i
$316$	−3.23474	+	5.60274i	−0.181969	+	0.315179i
$317$	7.18662	+	7.98155i	0.403641	+	0.448288i	0.910357	−	0.413825i	$-0.135807\pi$
$317$	7.18662	+	7.98155i	0.403641	+	0.448288i	−0.506716	+	0.862113i	$0.669141\pi$
$318$	1.56381	+	4.81291i	0.0876941	+	0.269895i
$319$	5.13961	−	5.70812i	0.287763	−	0.319593i
$320$	−14.0876	−	6.27219i	−0.787519	−	0.350626i
$321$	−34.3887	+	7.30954i	−1.91939	+	0.407979i
$322$	−0.0175788	−	0.167251i	−0.000979626	−	0.00932052i
$323$	0.404039	−	3.84418i	0.0224813	−	0.213896i
$324$	6.85686	+	1.45747i	0.380937	+	0.0809706i
$325$	−8.92758	−	6.48627i	−0.495213	−	0.359793i
$326$	−0.889309	−	0.646121i	−0.0492543	−	0.0357853i
$327$	−1.78889	−	0.380241i	−0.0989259	−	0.0210274i
$328$	−0.989157	+	9.41120i	−0.0546171	+	0.519647i
$329$	−0.900611	−	8.56874i	−0.0496523	−	0.472410i
$330$	−7.18982	+	1.52824i	−0.395787	+	0.0841271i
$331$	17.9490	+	7.99140i	0.986565	+	0.439247i	0.835628	−	0.549296i	$-0.185104\pi$
$331$	17.9490	+	7.99140i	0.986565	+	0.439247i	0.150938	+	0.988543i	$0.451771\pi$
$332$	−16.1393	+	17.9245i	−0.885757	+	0.983733i
$333$	5.22289	+	16.0744i	0.286213	+	0.880872i
$334$	−3.14047	−	3.48784i	−0.171839	−	0.190846i
$335$	9.57021	−	16.5761i	0.522876	−	0.905649i
$336$	−5.12565	−	8.87788i	−0.279627	−	0.484328i
$337$	5.92655	−	18.2401i	0.322840	−	0.993599i	−0.649566	−	0.760305i	$-0.725050\pi$
$337$	5.92655	−	18.2401i	0.322840	−	0.993599i	0.972406	−	0.233294i	$-0.0749505\pi$
$338$	−1.52246	+	0.677841i	−0.0828107	+	0.0368697i
$339$	−26.4510	+	19.2178i	−1.43662	+	1.04376i
$340$	10.1808			0.552133
$341$		0			0
$342$	3.99844			0.216211
$343$	−11.2313	+	8.15999i	−0.606431	+	0.440598i
$344$	10.4696	−	4.66137i	0.564483	−	0.251324i
$345$	1.17554	−	3.61794i	0.0632889	−	0.194783i
$346$	−3.34647	−	5.79626i	−0.179907	−	0.311609i
$347$	−5.32998	+	9.23180i	−0.286128	+	0.495589i	−0.972882	−	0.231301i	$-0.925702\pi$
$347$	−5.32998	+	9.23180i	−0.286128	+	0.495589i	0.686754	+	0.726890i	$0.259035\pi$
$348$	−11.4767	−	12.7462i	−0.615218	−	0.683269i
$349$	−5.77910	−	17.7862i	−0.309348	−	0.952075i	−0.978019	−	0.208517i	$-0.933136\pi$
$349$	−5.77910	−	17.7862i	−0.309348	−	0.952075i	0.668671	−	0.743559i	$-0.266864\pi$
$350$	−0.977176	+	1.08526i	−0.0522322	+	0.0580098i
$351$	−18.0100	−	8.01857i	−0.961302	−	0.427999i
$352$	9.21644	−	1.95901i	0.491238	−	0.104416i
$353$	1.32356	+	12.5929i	0.0704463	+	0.670251i	0.971580	+	0.236711i	$0.0760693\pi$
$353$	1.32356	+	12.5929i	0.0704463	+	0.670251i	−0.901134	+	0.433541i	$0.857264\pi$
$354$	−1.27689	+	12.1488i	−0.0678660	+	0.645702i
$355$	−4.87969	−	1.03721i	−0.258987	−	0.0550494i
$356$	3.43001	+	2.49205i	0.181790	+	0.132078i
$357$	4.62205	+	3.35812i	0.244625	+	0.177730i
$358$	0.0272699	+	0.00579640i	0.00144126	+	0.000306349i
$359$	2.37051	−	22.5539i	0.125111	−	1.19035i	−0.734214	−	0.678918i	$-0.762449\pi$
$359$	2.37051	−	22.5539i	0.125111	−	1.19035i	0.859325	−	0.511431i	$-0.170884\pi$
$360$	2.27411	+	21.6367i	0.119856	+	1.14035i
$361$	14.1958	−	3.01741i	0.747146	−	0.158811i
$362$	0.694383	+	0.309159i	0.0364959	+	0.0162490i
$363$	9.85117	−	10.9408i	0.517052	−	0.574245i
$364$	1.80319	+	5.54965i	0.0945129	+	0.290881i
$365$	28.5692	+	31.7294i	1.49538	+	1.66079i
$366$	−7.33880	+	12.7112i	−0.383605	+	0.664424i
$367$	−4.35984	−	7.55147i	−0.227582	−	0.394183i	0.729509	−	0.683971i	$-0.239749\pi$
$367$	−4.35984	−	7.55147i	−0.227582	−	0.394183i	−0.957091	+	0.289788i	$0.906415\pi$
$368$	−0.447430	+	1.37705i	−0.0233239	+	0.0717836i
$369$	−34.0836	+	15.1750i	−1.77432	+	0.789980i
$370$	−2.66005	+	1.93264i	−0.138290	+	0.100473i
$371$	5.38574			0.279614
$372$		0			0
$373$	25.4134			1.31586			0.657928	−	0.753081i	$-0.271433\pi$
$373$	25.4134			1.31586			0.657928	+	0.753081i	$0.271433\pi$
$374$	−1.26141	+	0.916471i	−0.0652262	+	0.0473896i
$375$	9.11535	−	4.05841i	0.470714	−	0.209576i
$376$	3.35188	−	10.3160i	0.172860	−	0.532009i
$377$	4.53913	+	7.86200i	0.233777	+	0.404914i
$378$	−1.30448	+	2.25943i	−0.0670954	+	0.116213i
$379$	14.7864	+	16.4219i	0.759525	+	0.843538i	0.991624	−	0.129154i	$-0.0412263\pi$
$379$	14.7864	+	16.4219i	0.759525	+	0.843538i	−0.232100	+	0.972692i	$0.574560\pi$
$380$	−3.65208	−	11.2399i	−0.187348	−	0.576597i
$381$	−0.228072	+	0.253299i	−0.0116845	+	0.0129769i
$382$	−1.71495	−	0.763544i	−0.0877444	−	0.0390663i
$383$	26.0604	−	5.53931i	1.33163	−	0.283046i	0.513502	−	0.858088i	$-0.328348\pi$
$383$	26.0604	−	5.53931i	1.33163	−	0.283046i	0.818123	+	0.575043i	$0.195015\pi$
$384$	−2.89528	−	27.5468i	−0.147749	−	1.40574i
$385$	−0.817696	+	7.77986i	−0.0416737	+	0.396498i
$386$	0.733457	+	0.155901i	0.0373320	+	0.00793516i
$387$	36.5547	+	26.5585i	1.85818	+	1.35005i
$388$	5.18112	+	3.76430i	0.263032	+	0.191104i
$389$	12.6720	+	2.69351i	0.642494	+	0.136566i	0.517626	−	0.855607i	$-0.326816\pi$
$389$	12.6720	+	2.69351i	0.642494	+	0.136566i	0.124868	+	0.992173i	$0.460149\pi$
$390$	0.908095	−	8.63995i	0.0459832	−	0.437501i
$391$	−0.0843482	−	0.802519i	−0.00426567	−	0.0405851i
$392$	−7.76747	+	1.65103i	−0.392317	+	0.0833895i
$393$	−15.2879	−	6.80660i	−0.771171	−	0.343348i
$394$	−1.38170	+	1.53454i	−0.0696092	+	0.0773088i
$395$	−3.16762	−	9.74894i	−0.159380	−	0.490522i
$396$	16.3974	+	18.2112i	0.824002	+	0.915147i
$397$	1.46363	−	2.53508i	0.0734574	−	0.127232i	−0.826957	−	0.562265i	$-0.809930\pi$
$397$	1.46363	−	2.53508i	0.0734574	−	0.127232i	0.900414	+	0.435033i	$0.143263\pi$
$398$	−1.21736	−	2.10852i	−0.0610205	−	0.105691i
$399$	2.04944	−	6.30752i	0.102600	−	0.315771i
$400$	11.4863	−	5.11404i	0.574316	−	0.255702i
$401$	9.93025	−	7.21475i	0.495893	−	0.360287i	−0.311553	−	0.950229i	$-0.600849\pi$
$401$	9.93025	−	7.21475i	0.495893	−	0.360287i	0.807446	+	0.589942i	$0.200849\pi$
$402$	6.54572			0.326471
$403$		0			0
$404$	−33.2464			−1.65407
$405$	−8.98586	+	6.52861i	−0.446511	+	0.324409i
$406$	1.09753	−	0.488654i	0.0544697	−	0.0242515i
$407$	−2.36426	+	7.27645i	−0.117192	+	0.360680i
$408$	3.59625	+	6.22889i	0.178041	+	0.308376i
$409$	8.59861	−	14.8932i	0.425174	−	0.736423i	−0.571263	−	0.820767i	$-0.693546\pi$
$409$	8.59861	−	14.8932i	0.425174	−	0.736423i	0.996437	+	0.0843442i	$0.0268795\pi$
$410$	−4.85658	−	5.39378i	−0.239850	−	0.266380i
$411$	−10.5549	−	32.4848i	−0.520637	−	1.60236i
$412$	−10.1377	+	11.2590i	−0.499448	+	0.554693i
$413$	11.8766	+	5.28782i	0.584411	+	0.260196i
$414$	0.816482	−	0.173549i	0.0401279	−	0.00852945i
$415$	−3.99474	−	38.0074i	−0.196094	−	1.86571i
$416$	−1.16406	+	11.0753i	−0.0570729	+	0.543012i
$417$	−43.6453	−	9.27709i	−2.13732	−	0.454301i
$418$	1.46431	+	1.06388i	0.0716217	+	0.0520362i
$419$	−18.7251	−	13.6046i	−0.914782	−	0.664628i	0.0274378	−	0.999624i	$-0.491265\pi$
$419$	−18.7251	−	13.6046i	−0.914782	−	0.664628i	−0.942220	+	0.334996i	$0.891265\pi$
$420$	17.0864	+	3.63182i	0.833731	+	0.177215i
$421$	−3.05037	+	29.0224i	−0.148666	+	1.41446i	0.624878	+	0.780722i	$0.285149\pi$
$421$	−3.05037	+	29.0224i	−0.148666	+	1.41446i	−0.773545	+	0.633742i	$0.781518\pi$
$422$	−0.613791	−	5.83983i	−0.0298789	−	0.284278i
$423$	41.8308	−	8.89140i	2.03388	−	0.432315i
$424$	6.19411	+	2.75779i	0.300813	+	0.133930i
$425$	−4.68878	+	5.20742i	−0.227439	+	0.252597i
$426$	−0.527201	−	1.62256i	−0.0255430	−	0.0786132i
$427$	10.4522	+	11.6084i	0.505819	+	0.561769i
$428$	−11.4008	+	19.7468i	−0.551080	+	0.954498i
$429$	−10.1076	−	17.5069i	−0.487999	−	0.845239i
$430$	−2.71626	+	8.35979i	−0.130990	+	0.403145i
$431$	27.7281	−	12.3454i	1.33562	−	0.594655i	0.390264	−	0.920703i	$-0.372384\pi$
$431$	27.7281	−	12.3454i	1.33562	−	0.594655i	0.945353	+	0.326048i	$0.105717\pi$
$432$	18.1725	−	13.2031i	0.874326	−	0.635235i
$433$	−13.8400			−0.665107			−0.332553	−	0.943084i	$-0.607910\pi$
$433$	−13.8400			−0.665107			−0.332553	+	0.943084i	$0.607910\pi$
$434$		0			0
$435$	27.1762			1.30300
$436$	−0.959605	+	0.697194i	−0.0459567	+	0.0333895i
$437$	−0.855749	+	0.381004i	−0.0409360	+	0.0182259i
$438$	−4.51207	+	13.8867i	−0.215595	+	0.663534i
$439$	−6.46006	−	11.1892i	−0.308322	−	0.534029i	0.669674	−	0.742656i	$-0.266434\pi$
$439$	−6.46006	−	11.1892i	−0.308322	−	0.534029i	−0.977995	+	0.208626i	$0.933101\pi$
$440$	−4.92414	+	8.52887i	−0.234749	+	0.406598i
$441$	−20.9494	−	23.2667i	−0.997590	−	1.10794i
$442$	−0.569463	−	1.75263i	−0.0270866	−	0.0833639i
$443$	15.8974	−	17.6558i	0.755307	−	0.838854i	−0.235816	−	0.971798i	$-0.575776\pi$
$443$	15.8974	−	17.6558i	0.755307	−	0.838854i	0.991124	+	0.132944i	$0.0424430\pi$
$444$	15.6075	+	6.94889i	0.740697	+	0.329780i
$445$	−6.57087	+	1.39668i	−0.311489	+	0.0662091i
$446$	0.230017	+	2.18846i	0.0108916	+	0.103627i
$447$	−3.61412	+	34.3861i	−0.170942	+	1.62641i
$448$	−5.48984	−	1.16690i	−0.259370	−	0.0551309i
$449$	15.7054	+	11.4106i	0.741181	+	0.538500i	0.893081	−	0.449896i	$-0.148539\pi$
$449$	15.7054	+	11.4106i	0.741181	+	0.538500i	−0.151900	+	0.988396i	$0.548539\pi$
$450$	−5.86419	−	4.26058i	−0.276440	−	0.200846i
$451$	−16.5198	−	3.51139i	−0.777888	−	0.165345i
$452$	−2.21653	+	21.0889i	−0.104257	+	0.991937i
$453$	−1.30715	−	12.4367i	−0.0614152	−	0.584326i
$454$	2.69761	−	0.573394i	0.126605	−	0.0269107i
$455$	−8.44638	−	3.76057i	−0.395972	−	0.176298i
$456$	5.58684	−	6.20482i	0.261628	−	0.290567i
$457$	7.52208	+	23.1506i	0.351868	+	1.08294i	0.957803	+	0.287424i	$0.0927990\pi$
$457$	7.52208	+	23.1506i	0.351868	+	1.08294i	−0.605935	+	0.795514i	$0.707201\pi$
$458$	3.00362	+	3.33586i	0.140350	+	0.155874i
$459$	−6.25931	+	10.8414i	−0.292159	+	0.506035i
$460$	−1.23362	−	2.13669i	−0.0575177	−	0.0996235i
$461$	−11.8487	+	36.4665i	−0.551848	+	1.69841i	0.152279	+	0.988338i	$0.451339\pi$
$461$	−11.8487	+	36.4665i	−0.551848	+	1.69841i	−0.704126	+	0.710075i	$0.748661\pi$
$462$	−2.44395	+	1.08812i	−0.113703	+	0.0506239i
$463$	5.33489	−	3.87603i	0.247934	−	0.180134i	−0.456877	−	0.889530i	$-0.651032\pi$
$463$	5.33489	−	3.87603i	0.247934	−	0.180134i	0.704810	+	0.709396i	$0.251032\pi$
$464$	−10.3437			−0.480195
$465$		0			0
$466$	4.46933			0.207038
$467$	−31.0674	+	22.5718i	−1.43763	+	1.04450i	−0.449096	+	0.893484i	$0.648254\pi$
$467$	−31.0674	+	22.5718i	−1.43763	+	1.04450i	−0.988532	+	0.151014i	$0.951746\pi$
$468$	−26.4593	+	11.7804i	−1.22308	+	0.544551i
$469$	2.15270	−	6.62532i	0.0994024	−	0.305929i
$470$	4.15973	+	7.20487i	0.191874	+	0.332336i
$471$	−12.5922	+	21.8104i	−0.580220	+	1.00497i
$472$	10.9516	+	12.1630i	0.504088	+	0.559846i
$473$	6.32051	+	19.4525i	0.290617	+	0.894429i
$474$	2.34567	−	2.60513i	0.107740	−	0.119658i
$475$	7.43112	+	3.30855i	0.340963	+	0.151807i
$476$	3.62440	−	0.770391i	0.166124	−	0.0353108i
$477$	2.79427	+	26.5857i	0.127941	+	1.21728i
$478$	0.933965	−	8.88609i	0.0427186	−	0.406440i
$479$	−7.36071	−	1.56457i	−0.336319	−	0.0714869i	0.0366565	−	0.999328i	$-0.488329\pi$
$479$	−7.36071	−	1.56457i	−0.336319	−	0.0714869i	−0.372976	+	0.927841i	$0.621663\pi$
$480$	26.9703	+	19.5951i	1.23102	+	0.894389i
$481$	−7.31567	−	5.31515i	−0.333566	−	0.242350i
$482$	−0.811594	−	0.172510i	−0.0369671	−	0.00785760i
$483$	0.144723	−	1.37695i	0.00658514	−	0.0626534i
$484$	−0.998083	−	9.49612i	−0.0453674	−	0.431642i
$485$	−9.92548	+	2.10973i	−0.450693	+	0.0957977i
$486$	3.13751	+	1.39691i	0.142321	+	0.0633652i
$487$	16.7498	−	18.6026i	0.759008	−	0.842964i	−0.232556	−	0.972583i	$-0.574709\pi$
$487$	16.7498	−	18.6026i	0.759008	−	0.842964i	0.991564	+	0.129619i	$0.0413755\pi$
$488$	6.07693	+	18.7029i	0.275090	+	0.846639i
$489$	−6.05559	−	6.72541i	−0.273843	−	0.304134i
$490$	3.04533	−	5.27467i	0.137574	−	0.238285i
$491$	19.8550	+	34.3899i	0.896044	+	1.55199i	0.832507	+	0.554015i	$0.186905\pi$
$491$	19.8550	+	34.3899i	0.896044	+	1.55199i	0.0635377	+	0.997979i	$0.479762\pi$
$492$	−11.6539	+	35.8670i	−0.525399	+	1.61701i
$493$	5.26630	−	2.34471i	0.237182	−	0.105600i
$494$	−1.73068	+	1.25741i	−0.0778668	+	0.0565735i
$495$	−38.8281			−1.74519
$496$		0			0
$497$	−1.81567			−0.0814440
$498$	10.5735	−	7.68207i	0.473808	−	0.344242i
$499$	−21.6091	+	9.62098i	−0.967355	+	0.430694i	−0.828729	−	0.559651i	$-0.810935\pi$
$499$	−21.6091	+	9.62098i	−0.967355	+	0.430694i	−0.138626	+	0.990345i	$0.544269\pi$
$500$	1.99977	−	6.15467i	0.0894325	−	0.275245i
$501$	−19.3199	−	33.4630i	−0.863148	−	1.49502i
$502$	−0.414099	+	0.717241i	−0.0184822	+	0.0320120i
$503$	−13.5074	−	15.0014i	−0.602263	−	0.668881i	0.362505	−	0.931982i	$-0.381922\pi$
$503$	−13.5074	−	15.0014i	−0.602263	−	0.668881i	−0.964768	+	0.263101i	$0.915255\pi$
$504$	2.44685	+	7.53063i	0.108991	+	0.335441i
$505$	35.2482	−	39.1471i	1.56852	−	1.74202i
$506$	0.345189	+	0.153688i	0.0153455	+	0.00683227i
$507$	−13.4205	+	2.85262i	−0.596026	+	0.126689i
$508$	0.0231073	+	0.219852i	0.00102522	+	0.00975434i
$509$	−1.23751	+	11.7742i	−0.0548518	+	0.521880i	0.932253	+	0.361806i	$0.117840\pi$
$509$	−1.23751	+	11.7742i	−0.0548518	+	0.521880i	−0.987105	+	0.160074i	$0.948827\pi$
$510$	−5.39603	−	1.14696i	−0.238940	−	0.0507883i
$511$	12.5717	+	9.13389i	0.556140	+	0.404060i
$512$	−17.4827	−	12.7019i	−0.772633	−	0.561351i
$513$	14.2146	+	3.02141i	0.627591	+	0.133399i
$514$	0.955617	−	9.09209i	0.0421504	−	0.401035i
$515$	−2.50925	−	23.8739i	−0.110571	−	1.05201i
$516$	44.6748	−	9.49593i	1.96670	−	0.418035i
$517$	17.6851	+	7.87389i	0.777788	+	0.346293i
$518$	−0.800743	+	0.889315i	−0.0351826	+	0.0390742i
$519$	−17.0275	−	52.4051i	−0.747422	−	2.30033i
$520$	−7.78852	−	8.65002i	−0.341549	−	0.379329i
$521$	16.3742	−	28.3610i	0.717368	−	1.24252i	−0.244672	−	0.969606i	$-0.578680\pi$
$521$	16.3742	−	28.3610i	0.717368	−	1.24252i	0.962039	−	0.272911i	$-0.0879865\pi$
$522$	2.98158	+	5.16425i	0.130500	+	0.226033i
$523$	−9.11682	+	28.0587i	−0.398651	+	1.22692i	0.527431	+	0.849598i	$0.323155\pi$
$523$	−9.11682	+	28.0587i	−0.398651	+	1.22692i	−0.926082	+	0.377323i	$0.876845\pi$
$524$	−9.91522	+	4.41454i	−0.433148	+	0.192850i
$525$	−9.72679	+	7.06693i	−0.424512	+	0.308426i
$526$	8.06030			0.351446
$527$		0			0
$528$	23.0331			1.00239
$529$	18.4492	−	13.4041i	0.802138	−	0.582788i
$530$	−4.75081	+	2.11520i	−0.206362	+	0.0918784i
$531$	−19.9404	+	61.3703i	−0.865340	+	2.66324i
$532$	−2.15069	−	3.72510i	−0.0932441	−	0.161504i
$533$	9.98053	−	17.2868i	0.432305	−	0.748774i
$534$	−1.53722	−	1.70725i	−0.0665219	−	0.0738801i
$535$	−11.1643	−	34.3600i	−0.482673	−	1.48551i
$536$	5.86834	−	6.51745i	0.253474	−	0.281511i
$537$	0.209681	+	0.0933561i	0.00904842	+	0.00402861i
$538$	5.86007	−	1.24560i	0.252645	−	0.0537014i
$539$	−1.48143	−	14.0948i	−0.0638095	−	0.607107i
$540$	−4.00092	+	38.0662i	−0.172172	+	1.63811i
$541$	−12.9759	−	2.75812i	−0.557879	−	0.118581i	−0.0796610	−	0.996822i	$-0.525384\pi$
$541$	−12.9759	−	2.75812i	−0.557879	−	0.118581i	−0.478218	+	0.878241i	$0.658717\pi$
$542$	−2.06029	−	1.49689i	−0.0884970	−	0.0642968i
$543$	5.06264	+	3.67822i	0.217258	+	0.157848i
$544$	6.91702	+	1.47026i	0.296565	+	0.0630368i
$545$	0.196449	−	1.86909i	0.00841496	−	0.0800630i
$546$	−0.330507	−	3.14456i	−0.0141444	−	0.134575i
$547$	−36.9386	+	7.85155i	−1.57938	+	0.335708i	−0.912379	−	0.409347i	$-0.865756\pi$
$547$	−36.9386	+	7.85155i	−1.57938	+	0.335708i	−0.667003	+	0.745055i	$0.732423\pi$
$548$	−20.2376	−	9.01036i	−0.864508	−	0.384904i
$549$	−51.8798	+	57.6183i	−2.21417	+	2.45909i
$550$	−1.01395	−	3.12062i	−0.0432351	−	0.133064i
$551$	−4.47776	−	4.97306i	−0.190759	−	0.211860i
$552$	0.871520	−	1.50952i	0.0370944	−	0.0642493i
$553$	−1.86539	−	3.23095i	−0.0793245	−	0.137394i
$554$	1.64019	−	5.04800i	0.0696852	−	0.214469i
$555$	−24.7294	+	11.0102i	−1.04970	+	0.467358i
$556$	−23.4124	+	17.0101i	−0.992907	+	0.721389i
$557$	−11.3637			−0.481496			−0.240748	−	0.970588i	$-0.577393\pi$
$557$	−11.3637			−0.481496			−0.240748	+	0.970588i	$0.577393\pi$
$558$		0			0
$559$	−24.1743			−1.02246
$560$	8.52261	−	6.19204i	0.360146	−	0.261661i
$561$	−11.7268	+	5.22112i	−0.495107	+	0.220436i
$562$	−0.270094	+	0.831262i	−0.0113932	+	0.0350647i
$563$	10.0933	+	17.4821i	0.425381	+	0.736781i	0.996456	−	0.0841167i	$-0.0268068\pi$
$563$	10.0933	+	17.4821i	0.425381	+	0.736781i	−0.571075	+	0.820898i	$0.693474\pi$
$564$	21.6140	−	37.4365i	0.910113	−	1.57636i
$565$	−22.4818	−	24.9686i	−0.945816	−	1.05044i
$566$	−0.513276	−	1.57970i	−0.0215746	−	0.0663998i
$567$	−2.70497	+	3.00417i	−0.113598	+	0.126163i
$568$	−2.08819	−	0.929724i	−0.0876187	−	0.0390103i
$569$	30.3125	−	6.44311i	1.27076	−	0.270109i	0.477308	−	0.878736i	$-0.341613\pi$
$569$	30.3125	−	6.44311i	1.27076	−	0.270109i	0.793457	+	0.608627i	$0.208279\pi$
$570$	0.669390	+	6.36882i	0.0280377	+	0.266761i
$571$	1.08706	−	10.3427i	0.0454922	−	0.432830i	−0.947944	−	0.318438i	$-0.896842\pi$
$571$	1.08706	−	10.3427i	0.0454922	−	0.432830i	0.993436	−	0.114391i	$-0.0364918\pi$
$572$	−12.8244	−	2.72591i	−0.536215	−	0.113976i
$573$	−12.5034	−	9.08427i	−0.522338	−	0.379501i
$574$	−2.13711	−	1.55270i	−0.0892012	−	0.0648085i
$575$	1.66104	+	0.353065i	0.0692702	+	0.0147238i
$576$	2.91191	−	27.7050i	0.121330	−	1.15437i
$577$	−0.565902	−	5.38420i	−0.0235588	−	0.224147i	−0.999966	−	0.00821097i	$-0.997386\pi$
$577$	−0.565902	−	5.38420i	−0.0235588	−	0.224147i	0.976407	−	0.215936i	$-0.0692803\pi$
$578$	4.69918	−	0.998842i	0.195460	−	0.0415463i
$579$	5.63963	+	2.51093i	0.234375	+	0.104351i
$580$	11.7938	−	13.0984i	0.489712	−	0.543881i
$581$	−4.29819	−	13.2285i	−0.178319	−	0.548809i
$582$	−2.32201	−	2.57885i	−0.0962503	−	0.106897i
$583$	−6.05046	+	10.4797i	−0.250585	+	0.434025i
$584$	9.78162	+	16.9423i	0.404766	+	0.701076i
$585$	14.1811	−	43.6451i	0.586318	−	1.80450i
$586$	−3.38672	+	1.50786i	−0.139904	+	0.0622893i
$587$	10.1635	−	7.38424i	0.419494	−	0.304780i	−0.357940	−	0.933744i	$-0.616521\pi$
$587$	10.1635	−	7.38424i	0.419494	−	0.304780i	0.777434	+	0.628964i	$0.216521\pi$
$588$	−31.6471			−1.30510
$589$		0			0
$590$	−12.5532			−0.516809
$591$	−13.7535	+	9.99247i	−0.565741	+	0.411035i
$592$	9.41241	−	4.19068i	0.386848	−	0.172236i
$593$	8.36510	−	25.7451i	0.343513	−	1.05723i	−0.618861	−	0.785500i	$-0.712406\pi$
$593$	8.36510	−	25.7451i	0.343513	−	1.05723i	0.962375	−	0.271726i	$-0.0875943\pi$
$594$	−2.93098	−	5.07660i	−0.120259	−	0.208295i
$595$	−2.93551	+	5.08445i	−0.120344	+	0.208442i
$596$	15.0050	+	16.6647i	0.614627	+	0.682612i
$597$	−6.19413	−	19.0636i	−0.253509	−	0.780220i
$598$	−0.298828	+	0.331882i	−0.0122200	+	0.0135717i
$599$	−13.1140	−	5.83874i	−0.535824	−	0.238564i	0.120941	−	0.992660i	$-0.461409\pi$
$599$	−13.1140	−	5.83874i	−0.535824	−	0.238564i	−0.656765	+	0.754095i	$0.728076\pi$
$600$	−14.8054	+	3.14698i	−0.604427	+	0.128475i
$601$	−0.0669000	−	0.636511i	−0.00272891	−	0.0259638i	0.993073	−	0.117501i	$-0.0374885\pi$
$601$	−0.0669000	−	0.636511i	−0.00272891	−	0.0259638i	−0.995802	+	0.0915377i	$0.970822\pi$
$602$	−0.334405	+	3.18165i	−0.0136293	+	0.129675i
$603$	33.8216	+	7.18900i	1.37732	+	0.292759i
$604$	−6.56150	−	4.76721i	−0.266984	−	0.193975i
$605$	12.2397	+	8.89266i	0.497614	+	0.361538i
$606$	17.6212	+	3.74551i	0.715813	+	0.152151i
$607$	0.681298	−	6.48211i	0.0276530	−	0.263101i	−0.971957	−	0.235160i	$-0.924438\pi$
$607$	0.681298	−	6.48211i	0.0276530	−	0.263101i	0.999610	−	0.0279405i	$-0.00889489\pi$
$608$	−0.858073	−	8.16402i	−0.0347995	−	0.331095i
$609$	9.67482	−	2.05645i	0.392043	−	0.0833314i
$610$	−13.7791	−	6.13486i	−0.557900	−	0.248393i
$611$	−15.3098	+	17.0033i	−0.619369	+	0.687879i
$612$	5.68333	+	17.4915i	0.229735	+	0.707052i
$613$	6.98929	+	7.76239i	0.282295	+	0.313520i	0.867570	−	0.497314i	$-0.165680\pi$
$613$	6.98929	+	7.76239i	0.282295	+	0.313520i	−0.585276	+	0.810834i	$0.699014\pi$
$614$	−0.465385	+	0.806070i	−0.0187814	+	0.0325303i
$615$	−29.8772	−	51.7489i	−1.20477	−	2.08672i
$616$	−1.10762	+	3.40892i	−0.0446274	+	0.137349i
$617$	19.8270	−	8.82755i	0.798205	−	0.355384i	0.0332333	−	0.999448i	$-0.489420\pi$
$617$	19.8270	−	8.82755i	0.798205	−	0.355384i	0.764972	+	0.644064i	$0.222753\pi$
$618$	6.64159	−	4.82540i	0.267164	−	0.194106i
$619$	28.5478			1.14743			0.573716	−	0.819054i	$-0.305501\pi$
$619$	28.5478			1.14743			0.573716	+	0.819054i	$0.305501\pi$
$620$		0			0
$621$	3.03377			0.121741
$622$	−1.56738	+	1.13877i	−0.0628462	+	0.0456604i
$623$	−2.23356	+	0.994446i	−0.0894858	+	0.0398416i
$624$	−8.41235	+	25.8906i	−0.336764	+	1.03645i
$625$	14.7271	+	25.5080i	0.589083	+	1.02032i
$626$	4.68731	−	8.11866i	0.187343	−	0.324487i
$627$	9.97095	+	11.0739i	0.398201	+	0.442247i
$628$	5.04743	+	15.5344i	0.201414	+	0.619890i
$629$	−3.84220	+	4.26720i	−0.153199	+	0.170144i
$630$	−5.54810	−	2.47018i	−0.221042	−	0.0984141i
$631$	−26.6452	+	5.66362i	−1.06073	+	0.225465i	−0.705061	−	0.709147i	$-0.749080\pi$
$631$	−26.6452	+	5.66362i	−1.06073	+	0.225465i	−0.355669	+	0.934612i	$0.615747\pi$
$632$	−0.490951	−	4.67109i	−0.0195290	−	0.185806i
$633$	5.05325	−	48.0784i	0.200849	−	1.91095i
$634$	−3.69199	−	0.784756i	−0.146627	−	0.0311666i
$635$	−0.283370	−	0.205880i	−0.0112452	−	0.00817012i
$636$	21.8607	+	15.8828i	0.866835	+	0.629792i
$637$	16.3845	+	3.48263i	0.649177	+	0.137987i
$638$	−0.282160	+	2.68458i	−0.0111708	+	0.106283i
$639$	−0.942021	−	8.96273i	−0.0372658	−	0.354560i
$640$	27.8418	−	5.91796i	1.10054	−	0.233928i
$641$	37.6455	+	16.7608i	1.48691	+	0.662013i	0.979820	−	0.199882i	$-0.0640558\pi$
$641$	37.6455	+	16.7608i	1.48691	+	0.662013i	0.507086	+	0.861895i	$0.330722\pi$
$642$	8.26731	−	9.18177i	0.326285	−	0.362376i
$643$	−9.52156	−	29.3044i	−0.375494	−	1.15565i	−0.943145	−	0.332382i	$-0.892148\pi$
$643$	−9.52156	−	29.3044i	−0.375494	−	1.15565i	0.567651	−	0.823269i	$-0.307852\pi$
$644$	−0.600856	−	0.667318i	−0.0236770	−	0.0262960i
$645$	−36.1834	+	62.6715i	−1.42472	+	2.46769i
$646$	0.679205	+	1.17642i	0.0267230	+	0.0462855i
$647$	2.75525	−	8.47978i	0.108320	−	0.333375i	−0.882175	−	0.470921i	$-0.843922\pi$
$647$	2.75525	−	8.47978i	0.108320	−	0.333375i	0.990495	+	0.137547i	$0.0439217\pi$
$648$	−4.64927	+	2.06999i	−0.182641	+	0.0813168i
$649$	−23.6317	+	17.1694i	−0.927623	+	0.673958i
$650$	3.87809			0.152111
$651$		0			0
$652$	−5.86949			−0.229867
$653$	−31.7469	+	23.0655i	−1.24235	+	0.902623i	−0.997753	−	0.0670010i	$-0.978657\pi$
$653$	−31.7469	+	23.0655i	−1.24235	+	0.902623i	−0.244601	+	0.969624i	$0.578657\pi$
$654$	0.587153	−	0.261418i	0.0229595	−	0.0102222i
$655$	5.31417	−	16.3553i	0.207642	−	0.639056i
$656$	11.3718	+	19.6965i	0.443993	+	0.769018i
$657$	−38.5652	+	66.7969i	−1.50457	+	2.60600i
$658$	2.02608	+	2.25018i	0.0789846	+	0.0877213i
$659$	10.1832	+	31.3407i	0.396681	+	1.22086i	0.927644	+	0.373465i	$0.121830\pi$
$659$	10.1832	+	31.3407i	0.396681	+	1.22086i	−0.530963	+	0.847395i	$0.678170\pi$
$660$	−26.2621	+	29.1671i	−1.02225	+	1.13533i
$661$	−0.155006	−	0.0690131i	−0.00602903	−	0.00268430i	0.403720	−	0.914883i	$-0.367717\pi$
$661$	−0.155006	−	0.0690131i	−0.00602903	−	0.00268430i	−0.409749	+	0.912198i	$0.634384\pi$
$662$	−6.75392	+	1.43559i	−0.262499	+	0.0557958i
$663$	−1.58587	−	15.0886i	−0.0615901	−	0.585991i
$664$	1.83038	−	17.4149i	0.0710325	−	0.675829i
$665$	6.66642	+	1.41699i	0.258513	+	0.0549486i
$666$	−4.80539	−	3.49132i	−0.186205	−	0.135286i
$667$	−1.13021	−	0.821147i	−0.0437620	−	0.0317950i
$668$	−24.5128	−	5.21036i	−0.948430	−	0.201595i
$669$	−1.89369	+	18.0173i	−0.0732144	+	0.696589i
$670$	0.703118	+	6.68972i	0.0271638	+	0.258446i
$671$	−34.3302	+	7.29711i	−1.32530	+	0.281702i
$672$	11.0843	+	4.93504i	0.427586	+	0.190373i
$673$	−9.76017	+	10.8398i	−0.376227	+	0.417842i	−0.901287	−	0.433223i	$-0.857376\pi$
$673$	−9.76017	+	10.8398i	−0.376227	+	0.417842i	0.525060	+	0.851065i	$0.324043\pi$
$674$	2.08278	+	6.41015i	0.0802258	+	0.246910i
$675$	−17.6280	−	19.5778i	−0.678501	−	0.753551i
$676$	−4.44929	+	7.70639i	−0.171126	+	0.296400i
$677$	−7.88341	−	13.6545i	−0.302984	−	0.524784i	0.673826	−	0.738890i	$-0.264650\pi$
$677$	−7.88341	−	13.6545i	−0.302984	−	0.524784i	−0.976810	+	0.214106i	$0.931316\pi$
$678$	3.55065	−	10.9278i	0.136362	−	0.419679i
$679$	−3.37386	+	1.50214i	−0.129477	+	0.0576467i
$680$	−5.97963	+	4.34445i	−0.229308	+	0.166602i
$681$	22.7051			0.870063
$682$		0			0
$683$	20.5935			0.787988			0.393994	−	0.919113i	$-0.371093\pi$
$683$	20.5935			0.787988			0.393994	+	0.919113i	$0.371093\pi$
$684$	17.2724	−	12.5492i	0.660428	−	0.479829i
$685$	32.0657	−	14.2766i	1.22517	−	0.545479i
$686$	1.50763	−	4.64001i	0.0575616	−	0.177156i
$687$	18.4780	+	32.0048i	0.704979	+	1.22106i
$688$	13.7720	−	23.8538i	0.525053	−	0.909418i
$689$	−9.57002	−	10.6286i	−0.364589	−	0.404917i
$690$	0.413123	+	1.27146i	0.0157273	+	0.0484037i
$691$	−3.98247	+	4.42298i	−0.151500	+	0.168258i	−0.814118	−	0.580700i	$-0.802779\pi$
$691$	−3.98247	+	4.42298i	−0.151500	+	0.168258i	0.662617	+	0.748958i	$0.269446\pi$
$692$	−32.6477	−	14.5357i	−1.24108	−	0.552564i
$693$	−13.8229	+	2.93815i	−0.525089	+	0.111611i
$694$	−0.391590	−	3.72573i	−0.0148646	−	0.141427i
$695$	4.79296	−	45.6020i	0.181807	−	1.72978i
$696$	12.1800	+	2.58893i	0.461680	+	0.0981332i
$697$	−10.2545	−	7.45032i	−0.388417	−	0.282201i
$698$	5.31713	+	3.86312i	0.201256	+	0.146221i
$699$	35.9913	+	7.65019i	1.36132	+	0.289357i
$700$	−0.815083	+	7.75500i	−0.0308072	+	0.293111i
$701$	2.78364	+	26.4845i	0.105136	+	1.00031i	0.912173	+	0.409805i	$0.134403\pi$
$701$	2.78364	+	26.4845i	0.105136	+	1.00031i	−0.807037	+	0.590502i	$0.798930\pi$
$702$	6.77688	−	1.44047i	0.255777	−	0.0543670i
$703$	6.08940	+	2.71118i	0.229666	+	0.102254i
$704$	8.43800	−	9.37135i	0.318019	−	0.353196i
$705$	21.1655	+	65.1407i	0.797138	+	2.45334i
$706$	−2.97758	−	3.30694i	−0.112063	−	0.124458i
$707$	9.58617	−	16.6037i	0.360525	−	0.624448i
$708$	32.6133	+	56.4879i	1.22568	+	2.12295i
$709$	−0.816662	+	2.51343i	−0.0306704	+	0.0943938i	−0.965220	−	0.261439i	$-0.915803\pi$
$709$	−0.816662	+	2.51343i	−0.0306704	+	0.0943938i	0.934550	+	0.355833i	$0.115803\pi$
$710$	1.60162	−	0.713088i	0.0601078	−	0.0267617i
$711$	14.9812	−	10.8845i	0.561839	−	0.408200i
$712$	−3.07802			−0.115354
$713$		0			0
$714$	−2.00779			−0.0751398
$715$	16.8063	−	12.2105i	0.628519	−	0.456646i
$716$	0.135992	−	0.0605478i	0.00508228	−	0.00226278i
$717$	22.7315	−	69.9605i	0.848925	−	2.61272i
$718$	3.98491	+	6.90207i	0.148716	+	0.257583i
$719$	−2.59912	+	4.50181i	−0.0969308	+	0.167889i	−0.910413	−	0.413701i	$-0.864236\pi$
$719$	−2.59912	+	4.50181i	−0.0969308	+	0.167889i	0.813482	+	0.581590i	$0.197569\pi$
$720$	34.9876	+	38.8577i	1.30391	+	1.44814i
$721$	−2.69986	−	8.30930i	−0.100548	−	0.309455i
$722$	−3.41277	+	3.79027i	−0.127010	+	0.141059i
$723$	−6.24044	−	2.77842i	−0.232084	−	0.103331i
$724$	3.96989	−	0.843826i	0.147540	−	0.0313606i
$725$	1.26807	+	12.0649i	0.0470951	+	0.448080i
$726$	−0.540821	+	5.14556i	−0.0200717	+	0.190970i
$727$	−23.6775	−	5.03280i	−0.878149	−	0.186656i	−0.253286	−	0.967391i	$-0.581512\pi$
$727$	−23.6775	−	5.03280i	−0.878149	−	0.186656i	−0.624862	+	0.780735i	$0.714845\pi$
$728$	−3.42729	−	2.49007i	−0.127024	−	0.0922882i
$729$	31.9419	+	23.2071i	1.18303	+	0.859524i
$730$	−14.6769	−	3.11967i	−0.543216	−	0.115464i
$731$	−1.60458	+	15.2665i	−0.0593474	+	0.564653i
$732$	8.19210	+	77.9426i	0.302789	+	2.88084i
$733$	−39.4807	+	8.39189i	−1.45825	+	0.309961i	−0.867721	−	0.497052i	$-0.834416\pi$
$733$	−39.4807	+	8.39189i	−1.45825	+	0.309961i	−0.590533	+	0.807013i	$0.701083\pi$
$734$	2.79945	+	1.24640i	0.103330	+	0.0460053i
$735$	33.5526	−	37.2639i	1.23761	−	1.37450i
$736$	−0.529571	−	1.62985i	−0.0195202	−	0.0600771i
$737$	10.4733	+	11.6318i	0.385790	+	0.428464i
$738$	6.55583	−	11.3550i	0.241324	−	0.417985i
$739$	−3.04893	−	5.28089i	−0.112157	−	0.194261i	0.804483	−	0.593976i	$-0.202442\pi$
$739$	−3.04893	−	5.28089i	−0.112157	−	0.194261i	−0.916640	+	0.399715i	$0.869109\pi$
$740$	−5.42526	+	16.6972i	−0.199437	+	0.613803i
$741$	−16.0894	+	7.16344i	−0.591057	+	0.263156i
$742$	−1.53125	+	1.11251i	−0.0562138	+	0.0408417i
$743$	16.2263			0.595284			0.297642	−	0.954678i	$-0.403800\pi$
$743$	16.2263			0.595284			0.297642	+	0.954678i	$0.403800\pi$
$744$		0			0
$745$	−35.5308			−1.30175
$746$	−7.22540	+	5.24956i	−0.264541	+	0.192200i
$747$	63.0698	−	28.0805i	2.30760	−	1.02741i
$748$	−2.57269	+	7.91793i	−0.0940670	+	0.289508i
$749$	−6.57456	−	11.3875i	−0.240229	−	0.416089i
$750$	−1.75329	+	3.03680i	−0.0640213	+	0.110888i
$751$	24.3861	+	27.0835i	0.889862	+	0.988291i	0.999984	−	0.00562661i	$-0.00179101\pi$
$751$	24.3861	+	27.0835i	0.889862	+	0.988291i	−0.110123	+	0.993918i	$0.535124\pi$
$752$	−8.05593	−	24.7936i	−0.293770	−	0.904130i
$753$	−4.56243	+	5.06709i	−0.166264	+	0.184655i
$754$	−2.91457	−	1.29765i	−0.106142	−	0.0472576i
$755$	12.5699	−	2.67181i	0.457464	−	0.0972370i
$756$	1.45616	+	13.8544i	0.0529600	+	0.503881i
$757$	−4.55349	+	43.3236i	−0.165499	+	1.57462i	0.524881	+	0.851175i	$0.324110\pi$
$757$	−4.55349	+	43.3236i	−0.165499	+	1.57462i	−0.690381	+	0.723446i	$0.742557\pi$
$758$	−7.59621	−	1.61462i	−0.275907	−	0.0586458i
$759$	2.51672	+	1.82851i	0.0913512	+	0.0663705i
$760$	6.94144	+	5.04325i	0.251792	+	0.182938i
$761$	−3.22718	−	0.685959i	−0.116985	−	0.0248660i	0.149047	−	0.988830i	$-0.452379\pi$
$761$	−3.22718	−	0.685959i	−0.116985	−	0.0248660i	−0.266032	+	0.963964i	$0.585713\pi$
$762$	0.0125209	−	0.119129i	0.000453586	−	0.00431558i
$763$	−0.0714990	−	0.680267i	−0.00258844	−	0.0246273i
$764$	−9.80462	+	2.08404i	−0.354719	+	0.0753978i
$765$	−26.6215	−	11.8526i	−0.962501	−	0.428533i
$766$	−6.26513	+	6.95813i	−0.226368	+	0.251407i
$767$	−10.6685	−	32.8342i	−0.385216	−	1.18557i
$768$	−13.5687	−	15.0696i	−0.489620	−	0.543778i
$769$	22.8568	−	39.5891i	0.824237	−	1.42762i	−0.0782634	−	0.996933i	$-0.524938\pi$
$769$	22.8568	−	39.5891i	0.824237	−	1.42762i	0.902501	−	0.430688i	$-0.141729\pi$
$770$	−1.37458	−	2.38084i	−0.0495363	−	0.0857995i
$771$	23.2585	−	71.5823i	0.837635	−	2.57798i
$772$	3.65768	−	1.62851i	0.131643	−	0.0586112i
$773$	−24.2710	+	17.6339i	−0.872969	+	0.634249i	−0.931382	−	0.364044i	$-0.881396\pi$
$773$	−24.2710	+	17.6339i	−0.872969	+	0.634249i	0.0584131	+	0.998292i	$0.481396\pi$
$774$	−15.8791			−0.570764
$775$		0			0
$776$	−4.64943			−0.166905
$777$	−7.97058	+	5.79097i	−0.285943	+	0.207750i
$778$	−4.15921	+	1.85180i	−0.149115	+	0.0663903i
$779$	−4.54689	+	13.9939i	−0.162909	+	0.501383i
$780$	−23.1938	−	40.1729i	−0.830472	−	1.43842i
$781$	2.03977	−	3.53298i	0.0729886	−	0.126420i
$782$	0.189755	+	0.210745i	0.00678564	+	0.00753621i
$783$	6.69730	+	20.6122i	0.239342	+	0.736619i
$784$	−12.7707	+	14.1833i	−0.456095	+	0.506545i
$785$	−23.6428	−	10.5265i	−0.843848	−	0.375706i
$786$	5.75259	−	1.22275i	0.205188	−	0.0436141i
$787$	4.51897	+	42.9951i	0.161084	+	1.53261i	0.714458	+	0.699679i	$0.246673\pi$
$787$	4.51897	+	42.9951i	0.161084	+	1.53261i	−0.553374	+	0.832933i	$0.686660\pi$
$788$	−1.15251	+	10.9654i	−0.0410564	+	0.390625i
$789$	64.9091	+	13.7969i	2.31083	+	0.491181i
$790$	2.91441	+	2.11744i	0.103690	+	0.0753352i
$791$	−9.89298	−	7.18767i	−0.351754	−	0.255564i
$792$	−17.4022	−	3.69894i	−0.618359	−	0.131436i
$793$	4.33600	−	41.2543i	0.153976	−	1.46498i
$794$	0.107532	+	1.02310i	0.00381616	+	0.0363084i
$795$	−41.8786	+	8.90158i	−1.48528	+	0.315707i
$796$	−11.8764	−	5.28769i	−0.420946	−	0.187417i
$797$	15.2721	−	16.9613i	0.540964	−	0.600802i	−0.409241	−	0.912426i	$-0.634206\pi$
$797$	15.2721	−	16.9613i	0.540964	−	0.600802i	0.950205	+	0.311625i	$0.100873\pi$
$798$	0.720239	+	2.21667i	0.0254962	+	0.0784691i
$799$	9.72172	+	10.7971i	0.343930	+	0.381972i
$800$	−7.44080	+	12.8878i	−0.263072	+	0.455654i
$801$	−6.06773	−	10.5096i	−0.214393	−	0.371339i
$802$	−1.33299	+	4.10252i	−0.0470695	+	0.144865i
$803$	−31.8963	+	14.2012i	−1.12560	+	0.501148i
$804$	28.2762	−	20.5438i	0.997223	−	0.724525i
$805$	1.42279			0.0501467
$806$		0			0
$807$	49.3229			1.73625
$808$	19.5270	−	14.1872i	0.686959	−	0.499105i
$809$	−19.4023	+	8.63844i	−0.682147	+	0.303711i	−0.718399	−	0.695631i	$-0.755125\pi$
$809$	−19.4023	+	8.63844i	−0.682147	+	0.303711i	0.0362519	+	0.999343i	$0.488458\pi$
$810$	1.20622	−	3.71236i	0.0423822	−	0.130439i
$811$	−1.06157	−	1.83869i	−0.0372767	−	0.0645652i	0.846785	−	0.531935i	$-0.178535\pi$
$811$	−1.06157	−	1.83869i	−0.0372767	−	0.0645652i	−0.884062	+	0.467370i	$0.845202\pi$
$812$	3.20748	−	5.55551i	0.112560	−	0.194960i
$813$	−14.0292	−	15.5810i	−0.492024	−	0.546448i
$814$	−0.830879	−	2.55718i	−0.0291223	−	0.0896292i
$815$	6.22290	−	6.91123i	0.217979	−	0.242090i
$816$	15.7920	+	7.03106i	0.552832	+	0.246136i
$817$	17.4303	−	3.70493i	0.609810	−	0.129619i
$818$	0.631735	+	6.01056i	0.0220881	+	0.210154i
$819$	1.74587	−	16.6109i	0.0610058	−	0.580431i
$820$	−37.9079	−	8.05758i	−1.32380	−	0.281383i
$821$	−33.8104	−	24.5647i	−1.17999	−	0.857313i	−0.187819	−	0.982204i	$-0.560142\pi$
$821$	−33.8104	−	24.5647i	−1.17999	−	0.857313i	−0.992171	+	0.124891i	$0.960142\pi$
$822$	9.71121	+	7.05561i	0.338717	+	0.246093i
$823$	−15.9423	−	3.38865i	−0.555715	−	0.118121i	−0.0785108	−	0.996913i	$-0.525016\pi$
$823$	−15.9423	−	3.38865i	−0.555715	−	0.118121i	−0.477204	+	0.878792i	$0.658350\pi$
$824$	1.14973	−	10.9390i	0.0400528	−	0.381077i
$825$	−2.82371	−	26.8658i	−0.0983089	−	0.935347i
$826$	−4.46899	+	0.949913i	−0.155496	+	0.0330517i
$827$	−28.4017	−	12.6452i	−0.987623	−	0.439718i	−0.151618	−	0.988439i	$-0.548448\pi$
$827$	−28.4017	−	12.6452i	−0.987623	−	0.439718i	−0.836006	+	0.548721i	$0.815115\pi$
$828$	2.98235	−	3.31224i	0.103644	−	0.115108i
$829$	−8.66756	−	26.6760i	−0.301037	−	0.926496i	−0.981126	−	0.193367i	$-0.938059\pi$
$829$	−8.66756	−	26.6760i	−0.301037	−	0.926496i	0.680090	−	0.733129i	$-0.261941\pi$
$830$	8.98683	+	9.98089i	0.311937	+	0.346442i
$831$	21.8491	−	37.8437i	0.757936	−	1.31278i
$832$	7.45215	+	12.9075i	0.258357	+	0.447487i
$833$	3.28688	−	10.1160i	0.113884	−	0.350498i
$834$	14.3253	−	6.37805i	0.496046	−	0.220854i
$835$	32.1239	−	23.3394i	1.11169	−	0.807692i
$836$	9.66453			0.334255
$837$		0			0
$838$	8.13409			0.280987
$839$	18.6621	−	13.5588i	0.644287	−	0.468102i	−0.217034	−	0.976164i	$-0.569638\pi$
$839$	18.6621	−	13.5588i	0.644287	−	0.468102i	0.861320	+	0.508062i	$0.169638\pi$
$840$	−11.5854	+	5.15814i	−0.399733	+	0.177973i
$841$	−5.87746	+	18.0890i	−0.202671	+	0.623757i
$842$	−5.12779	−	8.88160i	−0.176715	−	0.306080i
$843$	−3.59793	+	6.23179i	−0.123919	+	0.214634i
$844$	−20.9798	−	23.3005i	−0.722156	−	0.802035i
$845$	−4.35696	−	13.4093i	−0.149884	−	0.461296i
$846$	−10.0564	+	11.1688i	−0.345747	+	0.383991i
$847$	5.03028	+	2.23963i	0.172843	+	0.0769545i
$848$	15.9397	−	3.38809i	0.547372	−	0.116347i
$849$	−1.42940	−	13.5998i	−0.0490568	−	0.466745i
$850$	0.257410	−	2.44909i	0.00882909	−	0.0840032i
$851$	1.36113	+	0.289318i	0.0466591	+	0.00991769i
$852$	−7.36982	−	5.35449i	−0.252486	−	0.183442i
$853$	−24.2874	−	17.6458i	−0.831585	−	0.604182i	0.0884221	−	0.996083i	$-0.471818\pi$
$853$	−24.2874	−	17.6458i	−0.831585	−	0.604182i	−0.920007	+	0.391901i	$0.871818\pi$
$854$	−5.36964	−	1.14135i	−0.183745	−	0.0390562i
$855$	−3.53599	+	33.6427i	−0.120928	+	1.15056i
$856$	−1.73035	−	16.4632i	−0.0591422	−	0.562701i
$857$	53.3945	−	11.3494i	1.82392	−	0.387687i	0.836781	−	0.547538i	$-0.184435\pi$
$857$	53.3945	−	11.3494i	1.82392	−	0.387687i	0.987141	+	0.159851i	$0.0511015\pi$
$858$	6.49007	+	2.88957i	0.221567	+	0.0986482i
$859$	6.24728	−	6.93830i	0.213154	−	0.236732i	−0.627081	−	0.778954i	$-0.715750\pi$
$859$	6.24728	−	6.93830i	0.213154	−	0.236732i	0.840235	+	0.542223i	$0.182417\pi$
$860$	14.5036	+	44.6376i	0.494570	+	1.52213i
$861$	−14.5523	−	16.1619i	−0.495940	−	0.550797i
$862$	−5.33338	+	9.23768i	−0.181656	+	0.314637i
$863$	−6.65836	−	11.5326i	−0.226653	−	0.392575i	0.730161	−	0.683275i	$-0.239445\pi$
$863$	−6.65836	−	11.5326i	−0.226653	−	0.392575i	−0.956814	+	0.290700i	$0.906112\pi$
$864$	−8.21560	+	25.2850i	−0.279500	+	0.860214i
$865$	51.7289	−	23.0312i	1.75884	−	0.783085i
$866$	3.93491	−	2.85888i	0.133714	−	0.0971487i
$867$	39.5520			1.34326
$868$		0			0
$869$	8.38250			0.284357
$870$	−7.72660	+	5.61370i	−0.261956	+	0.190322i
$871$	−16.9000	+	7.52438i	−0.572636	+	0.254954i
$872$	0.266104	−	0.818983i	0.00901141	−	0.0277343i
$873$	−9.16547	−	15.8751i	−0.310204	−	0.537290i
$874$	0.164599	−	0.285094i	0.00556766	−	0.00964346i
$875$	2.49712	+	2.77333i	0.0844181	+	0.0937558i
$876$	24.0925	+	74.1490i	0.814010	+	2.50526i
$877$	−28.4822	+	31.6327i	−0.961777	+	1.06816i	0.0358529	+	0.999357i	$0.488585\pi$
$877$	−28.4822	+	31.6327i	−0.961777	+	1.06816i	−0.997630	+	0.0688047i	$0.978081\pi$
$878$	4.14800	+	1.84681i	0.139988	+	0.0623268i
$879$	−29.8541	+	6.34568i	−1.00695	+	0.214034i
$880$	2.47413	+	23.5398i	0.0834029	+	0.793526i
$881$	0.603457	−	5.74151i	0.0203310	−	0.193436i	−0.979642	−	0.200751i	$-0.935662\pi$
$881$	0.603457	−	5.74151i	0.0203310	−	0.193436i	0.999973	+	0.00731486i	$0.00232841\pi$
$882$	10.7623	+	2.28761i	0.362387	+	0.0770277i
$883$	−22.0029	−	15.9860i	−0.740457	−	0.537973i	0.152397	−	0.988319i	$-0.451301\pi$
$883$	−22.0029	−	15.9860i	−0.740457	−	0.537973i	−0.892854	+	0.450346i	$0.851301\pi$
$884$	−7.96061	−	5.78372i	−0.267744	−	0.194528i
$885$	−101.091	−	21.4875i	−3.39812	−	0.722293i
$886$	−0.872753	+	8.30369i	−0.0293207	+	0.278968i
$887$	0.770551	+	7.33131i	0.0258726	+	0.246161i	0.999813	+	0.0193557i	$0.00616149\pi$
$887$	0.770551	+	7.33131i	0.0258726	+	0.246161i	−0.973940	+	0.226805i	$0.927172\pi$
$888$	−12.1322	+	2.57878i	−0.407131	+	0.0865383i
$889$	−0.116460	−	0.0518512i	−0.00390594	−	0.00173903i
$890$	1.57969	−	1.75442i	0.0529513	−	0.0588084i
$891$	−2.80677	−	8.63835i	−0.0940304	−	0.289396i
$892$	7.86215	+	8.73180i	0.263244	+	0.292362i
$893$	8.43290	−	14.6062i	0.282196	−	0.488778i
$894$	−6.07548	−	10.5230i	−0.203194	−	0.351943i
$895$	−0.0728867	+	0.224322i	−0.00243633	+	0.00749826i
$896$	9.46395	−	4.21362i	0.316168	−	0.140767i
$897$	−2.97453	+	2.16112i	−0.0993166	+	0.0721578i
$898$	−6.82232			−0.227664
$899$		0			0
$900$	−38.7040			−1.29013
$901$	−7.34737	+	5.33818i	−0.244776	+	0.177841i
$902$	5.42217	−	2.41410i	0.180538	−	0.0803809i
$903$	−8.13900	+	25.0493i	−0.270849	+	0.833588i
$904$	−7.69738	−	13.3322i	−0.256011	−	0.443424i
$905$	−3.21533	+	5.56911i	−0.106881	+	0.185123i
$906$	2.94065	+	3.26592i	0.0976964	+	0.108503i
$907$	5.09354	+	15.6763i	0.169128	+	0.520523i	0.999317	−	0.0369599i	$-0.0117674\pi$
$907$	5.09354	+	15.6763i	0.169128	+	0.520523i	−0.830189	+	0.557482i	$0.811767\pi$
$908$	9.85350	−	10.9434i	0.327000	−	0.363170i
$909$	86.9349	+	38.7059i	2.88345	+	1.28379i
$910$	3.17824	−	0.675556i	0.105358	−	0.0223945i
$911$	−4.68361	−	44.5616i	−0.155175	−	1.47639i	−0.744027	−	0.668150i	$-0.767087\pi$
$911$	−4.68361	−	44.5616i	−0.155175	−	1.47639i	0.588852	−	0.808241i	$-0.299580\pi$
$912$	2.09757	−	19.9571i	0.0694576	−	0.660845i
$913$	30.5690	+	6.49763i	1.01169	+	0.215040i
$914$	−6.92078	−	5.02824i	−0.228919	−	0.166319i
$915$	−100.461	−	72.9895i	−3.32115	−	2.41296i
$916$	23.4447	+	4.98332i	0.774634	+	0.164654i
$917$	0.654240	−	6.22468i	0.0216049	−	0.205557i
$918$	−0.459867	−	4.37535i	−0.0151779	−	0.144408i
$919$	10.1305	−	2.15330i	0.334174	−	0.0710309i	−0.0377687	−	0.999287i	$-0.512025\pi$
$919$	10.1305	−	2.15330i	0.334174	−	0.0710309i	0.371943	+	0.928256i	$0.378692\pi$
$920$	1.63634	+	0.728546i	0.0539486	+	0.0240195i
$921$	−5.12747	+	5.69464i	−0.168956	+	0.187645i
$922$	−4.16401	−	12.8155i	−0.137134	−	0.422056i
$923$	3.22630	+	3.58317i	0.106195	+	0.117941i
$924$	−7.14231	+	12.3708i	−0.234965	+	0.406971i
$925$	−6.04191	−	10.4649i	−0.198657	−	0.344084i
$926$	−0.716131	+	2.20402i	−0.0235335	+	0.0724287i
$927$	39.6166	−	17.6384i	1.30118	−	0.579322i
$928$	9.90452	−	7.19606i	0.325132	−	0.236222i
$929$	44.0624			1.44564			0.722820	−	0.691037i	$-0.242846\pi$
$929$	44.0624			1.44564			0.722820	+	0.691037i	$0.242846\pi$
$930$		0			0
$931$	−12.3474			−0.404671
$932$	19.3066	−	14.0271i	0.632409	−	0.459472i
$933$	−14.5713	+	6.48754i	−0.477042	+	0.212393i
$934$	4.17034	−	12.8350i	0.136458	−	0.419974i
$935$	−6.59563	−	11.4240i	−0.215700	−	0.373604i
$936$	10.5136	−	18.2101i	0.343648	−	0.595216i
$937$	−23.1298	−	25.6882i	−0.755617	−	0.839198i	0.235543	−	0.971864i	$-0.424313\pi$
$937$	−23.1298	−	25.6882i	−0.755617	−	0.839198i	−0.991161	+	0.132666i	$0.957646\pi$
$938$	0.756528	+	2.32835i	0.0247015	+	0.0760235i
$939$	51.6434	−	57.3558i	1.68532	−	1.87174i
$940$	40.5818	+	18.0682i	1.32363	+	0.589319i
$941$	21.6651	−	4.60505i	0.706261	−	0.150120i	0.159241	−	0.987240i	$-0.449095\pi$
$941$	21.6651	−	4.60505i	0.706261	−	0.150120i	0.547020	+	0.837119i	$0.315762\pi$
$942$	−0.925144	−	8.80216i	−0.0301428	−	0.286790i
$943$	−0.321084	+	3.05491i	−0.0104559	+	0.0994815i
$944$	38.4767	+	8.17848i	1.25231	+	0.266187i
$945$	−17.8572	−	12.9740i	−0.580894	−	0.422044i
$946$	−5.81526	−	4.22504i	−0.189071	−	0.137368i
$947$	27.4689	+	5.83869i	0.892619	+	0.189732i	0.631317	−	0.775525i	$-0.282515\pi$
$947$	27.4689	+	5.83869i	0.892619	+	0.189732i	0.261302	+	0.965257i	$0.415848\pi$
$948$	1.95658	−	18.6156i	0.0635466	−	0.604606i
$949$	−4.31348	−	41.0401i	−0.140022	−	1.33222i
$950$	−2.79621	+	0.594354i	−0.0907212	+	0.0192834i
$951$	−28.3881	−	12.6392i	−0.920547	−	0.409854i
$952$	−1.80002	+	1.99912i	−0.0583389	+	0.0647919i
$953$	2.36916	+	7.29152i	0.0767446	+	0.236196i	0.982068	−	0.188527i	$-0.0603715\pi$
$953$	2.36916	+	7.29152i	0.0767446	+	0.236196i	−0.905323	+	0.424723i	$0.860371\pi$
$954$	−6.28618	−	6.98151i	−0.203523	−	0.226035i
$955$	7.94104	−	13.7543i	0.256966	−	0.445078i
$956$	−23.8546	−	41.3173i	−0.771512	−	1.33630i
$957$	−6.86743	+	21.1358i	−0.221992	+	0.683222i
$958$	2.41595	−	1.07565i	0.0780557	−	0.0347526i
$959$	10.3352	−	7.50893i	0.333740	−	0.242476i
$960$	44.6168			1.44000
$961$		0			0
$962$	3.17789			0.102459
$963$	52.8011	−	38.3622i	1.70149	−	1.23621i
$964$	−4.04734	+	1.80199i	−0.130356	+	0.0580383i
$965$	−1.96038	+	6.03342i	−0.0631067	+	0.194223i
$966$	0.243285	+	0.421383i	0.00782758	+	0.0135578i
$967$	0.925182	−	1.60246i	0.0297518	−	0.0515317i	−0.850766	−	0.525545i	$-0.823862\pi$
$967$	0.925182	−	1.60246i	0.0297518	−	0.0515317i	0.880518	+	0.474013i	$0.157195\pi$
$968$	4.63849	+	5.15156i	0.149087	+	0.165578i
$969$	3.45592	+	10.6362i	0.111020	+	0.341685i
$970$	2.38616	−	2.65010i	0.0766150	−	0.0850896i
$971$	45.1031	+	20.0812i	1.44743	+	0.644436i	0.971928	−	0.235280i	$-0.0756009\pi$
$971$	45.1031	+	20.0812i	1.44743	+	0.644436i	0.475499	+	0.879716i	$0.342268\pi$
$972$	17.9376	−	3.81276i	0.575350	−	0.122294i
$973$	−1.74443	−	16.5971i	−0.0559238	−	0.532079i
$974$	−0.919552	+	8.74896i	−0.0294644	+	0.280335i
$975$	31.2301	+	6.63816i	1.00016	+	0.212591i
$976$	38.2373	+	27.7810i	1.22395	+	0.889248i
$977$	28.8192	+	20.9383i	0.922007	+	0.669877i	0.944023	−	0.329881i	$-0.107008\pi$
$977$	28.8192	+	20.9383i	0.922007	+	0.669877i	−0.0220160	+	0.999758i	$0.507008\pi$
$978$	3.11094	+	0.661251i	0.0994769	+	0.0211445i
$979$	0.574217	−	5.46331i	0.0183520	−	0.174608i
$980$	−3.39942	−	32.3433i	−0.108590	−	1.03317i
$981$	3.32092	−	0.705883i	0.106029	−	0.0225371i
$982$	−12.7489	−	5.67617i	−0.406833	−	0.181134i
$983$	−4.27146	+	4.74393i	−0.136238	+	0.151308i	−0.807403	−	0.590000i	$-0.799128\pi$
$983$	−4.27146	+	4.74393i	−0.136238	+	0.151308i	0.671165	+	0.741308i	$0.265794\pi$
$984$	−8.46068	−	26.0393i	−0.269717	−	0.830103i
$985$	−11.6896	−	12.9827i	−0.372463	−	0.413662i
$986$	−1.01295	+	1.75448i	−0.0322588	+	0.0558739i
$987$	12.4642	+	21.5887i	0.396740	+	0.687175i
$988$	−3.52977	+	10.8635i	−0.112297	+	0.345614i
$989$	3.39847	−	1.51310i	0.108065	−	0.0481136i
$990$	11.0394	−	8.02059i	0.350855	−	0.254911i
$991$	−44.2919			−1.40698			−0.703489	−	0.710706i	$-0.748376\pi$
$991$	−44.2919			−1.40698			−0.703489	+	0.710706i	$0.748376\pi$
$992$		0			0
$993$	−56.8463			−1.80396
$994$	0.516222	−	0.375058i	0.0163736	−	0.0118961i
$995$	18.8176	−	8.37813i	0.596558	−	0.265605i
$996$	21.5649	−	66.3699i	0.683310	−	2.10301i
$997$	−2.66158	−	4.60999i	−0.0842931	−	0.146000i	0.820797	−	0.571220i	$-0.193530\pi$
$997$	−2.66158	−	4.60999i	−0.0842931	−	0.146000i	−0.905090	+	0.425221i	$0.860197\pi$
$998$	4.15641	−	7.19911i	0.131569	−	0.227884i
$999$	−14.4452	−	16.0430i	−0.457025	−	0.507577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.k.235.2		16
31.2	even	5		31.2.g.a.10.2	✓	16
31.3	odd	30		961.2.g.n.844.1		16
31.4	even	5		961.2.g.t.846.1		16
31.5	even	3		961.2.d.o.388.3		16
31.6	odd	6		961.2.g.l.338.2		16
31.7	even	15		961.2.g.s.448.1		16
31.8	even	5		961.2.c.j.439.4		16
31.9	even	15		961.2.a.i.1.4		8
31.10	even	15		961.2.d.o.374.3		16
31.11	odd	30		961.2.d.q.628.2		16
31.12	odd	30		961.2.g.j.732.2		16
31.13	odd	30		961.2.d.q.531.2		16
31.14	even	15		961.2.c.j.521.4		16
31.15	odd	10		961.2.g.m.547.1		16
31.16	even	5		961.2.g.s.547.1		16
31.17	odd	30		961.2.c.i.521.4		16
31.18	even	15		961.2.d.p.531.2		16
31.19	even	15	inner	961.2.g.k.732.2		16
31.20	even	15		961.2.d.p.628.2		16
31.21	odd	30		961.2.d.n.374.3		16
31.22	odd	30		961.2.a.j.1.4		8
31.23	odd	10		961.2.c.i.439.4		16
31.24	odd	30		961.2.g.m.448.1		16
31.25	even	3		31.2.g.a.28.2	yes	16
31.26	odd	6		961.2.d.n.388.3		16
31.27	odd	10		961.2.g.n.846.1		16
31.28	even	15		961.2.g.t.844.1		16
31.29	odd	10		961.2.g.l.816.2		16
31.30	odd	2		961.2.g.j.235.2		16
93.2	odd	10		279.2.y.c.10.1		16
93.53	even	30		8649.2.a.be.1.5		8
93.56	odd	6		279.2.y.c.28.1		16
93.71	odd	30		8649.2.a.bf.1.5		8
124.87	odd	6		496.2.bg.c.369.1		16
124.95	odd	10		496.2.bg.c.289.1		16
155.2	odd	20		775.2.ck.a.599.3		32
155.33	odd	20		775.2.ck.a.599.2		32
155.64	even	10		775.2.bl.a.351.1		16
155.87	odd	12		775.2.ck.a.524.2		32
155.118	odd	12		775.2.ck.a.524.3		32
155.149	even	6		775.2.bl.a.276.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.10.2	✓	16	31.2	even	5
31.2.g.a.28.2	yes	16	31.25	even	3
279.2.y.c.10.1		16	93.2	odd	10
279.2.y.c.28.1		16	93.56	odd	6
496.2.bg.c.289.1		16	124.95	odd	10
496.2.bg.c.369.1		16	124.87	odd	6
775.2.bl.a.276.1		16	155.149	even	6
775.2.bl.a.351.1		16	155.64	even	10
775.2.ck.a.524.2		32	155.87	odd	12
775.2.ck.a.524.3		32	155.118	odd	12
775.2.ck.a.599.2		32	155.33	odd	20
775.2.ck.a.599.3		32	155.2	odd	20
961.2.a.i.1.4		8	31.9	even	15
961.2.a.j.1.4		8	31.22	odd	30
961.2.c.i.439.4		16	31.23	odd	10
961.2.c.i.521.4		16	31.17	odd	30
961.2.c.j.439.4		16	31.8	even	5
961.2.c.j.521.4		16	31.14	even	15
961.2.d.n.374.3		16	31.21	odd	30
961.2.d.n.388.3		16	31.26	odd	6
961.2.d.o.374.3		16	31.10	even	15
961.2.d.o.388.3		16	31.5	even	3
961.2.d.p.531.2		16	31.18	even	15
961.2.d.p.628.2		16	31.20	even	15
961.2.d.q.531.2		16	31.13	odd	30
961.2.d.q.628.2		16	31.11	odd	30
961.2.g.j.235.2		16	31.30	odd	2
961.2.g.j.732.2		16	31.12	odd	30
961.2.g.k.235.2		16	1.1	even	1	trivial
961.2.g.k.732.2		16	31.19	even	15	inner
961.2.g.l.338.2		16	31.6	odd	6
961.2.g.l.816.2		16	31.29	odd	10
961.2.g.m.448.1		16	31.24	odd	30
961.2.g.m.547.1		16	31.15	odd	10
961.2.g.n.844.1		16	31.3	odd	30
961.2.g.n.846.1		16	31.27	odd	10
961.2.g.s.448.1		16	31.7	even	15
961.2.g.s.547.1		16	31.16	even	5
961.2.g.t.844.1		16	31.28	even	15
961.2.g.t.846.1		16	31.4	even	5
8649.2.a.be.1.5		8	93.53	even	30
8649.2.a.bf.1.5		8	93.71	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.284315 + 0.206567i) q^{2} +(-2.64315 + 1.17681i) q^{3} +(-0.579869 + 1.78465i) q^{4} +(-1.48661 - 2.57489i) q^{5} +(0.508398 - 0.880572i) q^{6} +(-0.724084 - 0.804176i) q^{7} +(-0.420982 - 1.29565i) q^{8} +(3.59399 - 3.99153i) q^{9} +(0.954554 + 0.424995i) q^{10} +(2.37824 - 0.505510i) q^{11} +(-0.567511 - 5.39951i) q^{12} +(-0.300378 + 2.85791i) q^{13} +(0.371984 + 0.0790676i) q^{14} +(6.95951 + 5.05638i) q^{15} +(-2.64890 - 1.92454i) q^{16} +(1.78489 + 0.379390i) q^{17} +(-0.197307 + 1.87725i) q^{18} +(-0.221420 - 2.10667i) q^{19} +(5.45733 - 1.15999i) q^{20} +(2.86023 + 1.27345i) q^{21} +(-0.571747 + 0.634989i) q^{22} +(-0.136652 - 0.420572i) q^{23} +(2.63745 + 2.92919i) q^{24} +(-1.92005 + 3.32562i) q^{25} +(-0.504947 - 0.874594i) q^{26} +(-2.11998 + 6.52462i) q^{27} +(1.85505 - 0.825921i) q^{28} +(2.55579 - 1.85689i) q^{29} -3.02317 q^{30} +3.87532 q^{32} +(-5.69116 + 4.13487i) q^{33} +(-0.585840 + 0.260833i) q^{34} +(-0.994234 + 3.05994i) q^{35} +(5.03946 + 8.72860i) q^{36} +(-1.57338 + 2.72517i) q^{37} +(0.498121 + 0.553219i) q^{38} +(-2.56926 - 7.90738i) q^{39} +(-2.71032 + 3.01011i) q^{40} +(-6.34570 - 2.82529i) q^{41} +(-1.07626 + 0.228766i) q^{42} +(0.879333 + 8.36630i) q^{43} +(-0.476906 + 4.53746i) q^{44} +(-15.6207 - 3.32027i) q^{45} +(0.125728 + 0.0913471i) q^{46} +(6.44144 + 4.67998i) q^{47} +(9.26627 + 1.96961i) q^{48} +(0.609297 - 5.79707i) q^{49} +(-0.141065 - 1.34214i) q^{50} +(-5.16421 + 1.09769i) q^{51} +(-4.92620 - 2.19328i) q^{52} +(-3.33026 + 3.69863i) q^{53} +(-0.745029 - 2.29296i) q^{54} +(-4.83716 - 5.37221i) q^{55} +(-0.737104 + 1.27670i) q^{56} +(3.06439 + 5.30768i) q^{57} +(-0.343078 + 1.05588i) q^{58} +(-10.9753 + 4.88651i) q^{59} +(-13.0595 + 9.48827i) q^{60} -14.4351 q^{61} -5.81225 q^{63} +(4.19600 - 3.04857i) q^{64} +(7.80536 - 3.47517i) q^{65} +(0.763955 - 2.35121i) q^{66} +(3.21879 + 5.57511i) q^{67} +(-1.71208 + 2.96541i) q^{68} +(0.856125 + 0.950823i) q^{69} +(-0.349406 - 1.07536i) q^{70} +(1.12272 - 1.24690i) q^{71} +(-6.68463 - 2.97619i) q^{72} +(-14.0464 + 2.98565i) q^{73} +(-0.115595 - 1.09981i) q^{74} +(1.16137 - 11.0497i) q^{75} +(3.88807 + 0.826435i) q^{76} +(-2.12856 - 1.54649i) q^{77} +(2.36388 + 1.71746i) q^{78} +(3.37230 + 0.716805i) q^{79} +(-1.01759 + 9.68169i) q^{80} +(-0.390488 - 3.71525i) q^{81} +(2.38779 - 0.507540i) q^{82} +(11.7424 + 5.22804i) q^{83} +(-3.93123 + 4.36607i) q^{84} +(-1.67655 - 5.15991i) q^{85} +(-1.97821 - 2.19702i) q^{86} +(-4.57015 + 7.91573i) q^{87} +(-1.65616 - 2.86855i) q^{88} +(0.698188 - 2.14880i) q^{89} +(5.12704 - 2.28271i) q^{90} +(2.51576 - 1.82781i) q^{91} +0.829816 q^{92} -2.79812 q^{94} +(-5.09528 + 3.70194i) q^{95} +(-10.2431 + 4.56051i) q^{96} +(1.05463 - 3.24582i) q^{97} +(1.02425 + 1.77405i) q^{98} +(6.52961 - 11.3096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 3 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} - 13 q^{7} + 17 q^{8} + 5 q^{9} - 17 q^{10} - 7 q^{11} - 10 q^{12} + 8 q^{13} - 21 q^{14} + 14 q^{15} - 2 q^{16} + 9 q^{17} + 12 q^{18} - 29 q^{19}+ \cdots + 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 + 3 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 - 13 * q^7 + 17 * q^8 + 5 * q^9 - 17 * q^10 - 7 * q^11 - 10 * q^12 + 8 * q^13 - 21 * q^14 + 14 * q^15 - 2 * q^16 + 9 * q^17 + 12 * q^18 - 29 * q^19 - 8 * q^20 - 6 * q^21 - 21 * q^22 + q^23 - 5 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 + 45 * q^28 - 14 * q^29 - 22 * q^30 - 42 * q^32 - 13 * q^33 - 17 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 23 * q^38 - 3 * q^39 - q^40 - 8 * q^41 - 51 * q^42 - 37 * q^43 - 6 * q^44 - 70 * q^45 + 34 * q^46 + 14 * q^47 + 4 * q^48 - 43 * q^49 + 3 * q^50 + 33 * q^51 - 46 * q^52 - 9 * q^53 - 46 * q^54 + 8 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 - 11 * q^59 - 75 * q^60 - 60 * q^61 - 46 * q^63 + 23 * q^64 + 18 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 - 37 * q^69 + 12 * q^70 + 31 * q^71 - 38 * q^72 - 13 * q^73 + 43 * q^74 - 17 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 - 12 * q^79 + 6 * q^80 - 22 * q^81 - q^82 + 44 * q^83 + 23 * q^84 + 37 * q^85 + 19 * q^86 + 15 * q^87 - 17 * q^88 + q^89 + 7 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 - 22 * q^95 + 8 * q^96 + 3 * q^97 - 10 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more