LMFDB - Embedded newform 961.2.g.l.732.2

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			732.2
Root			$-1.83925i$ of defining polynomial
Character	$\chi$	$=$	961.732
Dual form			961.2.g.l.235.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.557811 + 0.405274i) q^{2} +(0.824384 + 0.367040i) q^{3} +(-0.471127 - 1.44998i) q^{4} +(-1.85376 + 3.21080i) q^{5} +(0.311099 + 0.538840i) q^{6} +(0.510810 - 0.567312i) q^{7} +(0.750969 - 2.31124i) q^{8} +(-1.46250 - 1.62427i) q^{9} +(-2.33530 + 1.03974i) q^{10} +(-4.02569 - 0.855686i) q^{11} +(0.143810 - 1.36826i) q^{12} +(-0.304152 - 2.89381i) q^{13} +(0.514852 - 0.109435i) q^{14} +(-2.70670 + 1.96653i) q^{15} +(-1.11127 + 0.807384i) q^{16} +(1.27993 - 0.272057i) q^{17} +(-0.157525 - 1.49875i) q^{18} +(0.397160 - 3.77873i) q^{19} +(5.52896 + 1.17522i) q^{20} +(0.629330 - 0.280196i) q^{21} +(-1.89879 - 2.10882i) q^{22} +(1.01449 - 3.12228i) q^{23} +(1.46740 - 1.62972i) q^{24} +(-4.37284 - 7.57398i) q^{25} +(1.00313 - 1.73747i) q^{26} +(-1.44606 - 4.45052i) q^{27} +(-1.06325 - 0.473389i) q^{28} +(3.96065 + 2.87758i) q^{29} -2.30681 q^{30} -5.80746 q^{32} +(-3.00464 - 2.18300i) q^{33} +(0.824217 + 0.366965i) q^{34} +(0.874609 + 2.69177i) q^{35} +(-1.66614 + 2.88584i) q^{36} +(-5.20639 - 9.01773i) q^{37} +(1.75296 - 1.94686i) q^{38} +(0.811405 - 2.49725i) q^{39} +(6.02884 + 6.69570i) q^{40} +(0.690591 - 0.307471i) q^{41} +(0.464603 + 0.0987545i) q^{42} +(-0.748099 + 7.11768i) q^{43} +(0.655882 + 6.24030i) q^{44} +(7.92634 - 1.68480i) q^{45} +(1.83127 - 1.33050i) q^{46} +(0.708753 - 0.514939i) q^{47} +(-1.21245 + 0.257715i) q^{48} +(0.670783 + 6.38208i) q^{49} +(0.630315 - 5.99705i) q^{50} +(1.15501 + 0.245505i) q^{51} +(-4.05268 + 1.80437i) q^{52} +(-2.39261 - 2.65727i) q^{53} +(0.997049 - 3.06860i) q^{54} +(10.2101 - 11.3395i) q^{55} +(-0.927595 - 1.60664i) q^{56} +(1.71435 - 2.96935i) q^{57} +(1.04309 + 3.21029i) q^{58} +(0.847103 + 0.377155i) q^{59} +(4.12664 + 2.99818i) q^{60} -2.31704 q^{61} -1.66853 q^{63} +(-1.01693 - 0.738843i) q^{64} +(9.85528 + 4.38785i) q^{65} +(-0.791311 - 2.43540i) q^{66} +(1.04345 - 1.80731i) q^{67} +(-0.997488 - 1.72770i) q^{68} +(1.98233 - 2.20160i) q^{69} +(-0.603037 + 1.85596i) q^{70} +(-5.17645 - 5.74903i) q^{71} +(-4.85238 + 2.16042i) q^{72} +(-5.53385 - 1.17626i) q^{73} +(0.750466 - 7.14021i) q^{74} +(-0.824950 - 7.84887i) q^{75} +(-5.66619 + 1.20439i) q^{76} +(-2.54180 + 1.84673i) q^{77} +(1.46468 - 1.06415i) q^{78} +(-13.7867 + 2.93046i) q^{79} +(-0.532328 - 5.06476i) q^{80} +(-0.243989 + 2.32140i) q^{81} +(0.509829 + 0.108368i) q^{82} +(12.8880 - 5.73812i) q^{83} +(-0.702773 - 0.780508i) q^{84} +(-1.49916 + 4.61393i) q^{85} +(-3.30191 + 3.66714i) q^{86} +(2.20891 + 3.82595i) q^{87} +(-5.00086 + 8.66175i) q^{88} +(1.37043 + 4.21776i) q^{89} +(5.10420 + 2.27254i) q^{90} +(-1.79706 - 1.30564i) q^{91} -5.00520 q^{92} +0.604042 q^{94} +(11.3965 + 8.28005i) q^{95} +(-4.78758 - 2.13157i) q^{96} +(-1.63088 - 5.01933i) q^{97} +(-2.21232 + 3.83184i) q^{98} +(4.49770 + 7.79025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} + 12 q^{3} - 14 q^{4} - 3 q^{5} - 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9} - 2 q^{10} + 7 q^{11} - 5 q^{12} + 7 q^{13} - 6 q^{14} - 14 q^{15} - 2 q^{16} + 6 q^{17} - 3 q^{18} + 16 q^{19}+ \cdots - 6 q^{99}+O(q^{100}) $ 16 * q - 6 * q^2 + 12 * q^3 - 14 * q^4 - 3 * q^5 - 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9 - 2 * q^10 + 7 * q^11 - 5 * q^12 + 7 * q^13 - 6 * q^14 - 14 * q^15 - 2 * q^16 + 6 * q^17 - 3 * q^18 + 16 * q^19 + 37 * q^20 - 9 * q^21 - 9 * q^22 - q^23 + 20 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 - 30 * q^28 + 14 * q^29 + 22 * q^30 - 42 * q^32 - 13 * q^33 + 32 * q^34 - 9 * q^35 + q^36 + 8 * q^37 + 8 * q^38 - 3 * q^39 - q^40 - 8 * q^41 - 69 * q^42 - 23 * q^43 - 39 * q^44 + 65 * q^45 - 34 * q^46 + 14 * q^47 - 34 * q^48 + 2 * q^49 + 3 * q^50 - 42 * q^51 - 29 * q^52 - 6 * q^53 + 46 * q^54 + 7 * q^55 - 30 * q^56 + 17 * q^57 + 15 * q^58 + 4 * q^59 + 75 * q^60 + 60 * q^61 - 46 * q^63 + 23 * q^64 + 12 * q^65 - 30 * q^66 + 13 * q^67 - 30 * q^68 + 38 * q^69 + 12 * q^70 - 14 * q^71 + 37 * q^72 - 2 * q^73 - 13 * q^74 - 13 * q^75 - 12 * q^76 - 18 * q^77 - 15 * q^78 - 18 * q^79 + 36 * q^80 + 23 * q^81 + 14 * q^82 + 16 * q^83 - 8 * q^84 - 37 * q^85 + 26 * q^86 + 15 * q^87 + 17 * q^88 - q^89 - 23 * 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 $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.557811	+	0.405274i	0.394432	+	0.286572i	0.767269	−	0.641325i	$-0.221615\pi$
$2$	0.557811	+	0.405274i	0.394432	+	0.286572i	−0.372837	+	0.927897i	$0.621615\pi$
$3$	0.824384	+	0.367040i	0.475958	+	0.211910i	0.630673	−	0.776049i	$-0.282779\pi$
$3$	0.824384	+	0.367040i	0.475958	+	0.211910i	−0.154714	+	0.987959i	$0.549446\pi$
$4$	−0.471127	−	1.44998i	−0.235564	−	0.724990i
$5$	−1.85376	+	3.21080i	−0.829026	+	1.43591i	0.0697774	+	0.997563i	$0.477771\pi$
$5$	−1.85376	+	3.21080i	−0.829026	+	1.43591i	−0.898803	+	0.438352i	$0.855562\pi$
$6$	0.311099	+	0.538840i	0.127006	+	0.219981i
$7$	0.510810	−	0.567312i	0.193068	−	0.214424i	−0.638836	−	0.769343i	$-0.720584\pi$
$7$	0.510810	−	0.567312i	0.193068	−	0.214424i	0.831905	+	0.554919i	$0.187251\pi$
$8$	0.750969	−	2.31124i	0.265508	−	0.817148i
$9$	−1.46250	−	1.62427i	−0.487500	−	0.541424i
$10$	−2.33530	+	1.03974i	−0.738487	+	0.328796i
$11$	−4.02569	−	0.855686i	−1.21379	−	0.257999i	−0.443842	−	0.896105i	$-0.646385\pi$
$11$	−4.02569	−	0.855686i	−1.21379	−	0.257999i	−0.769948	+	0.638106i	$0.779718\pi$
$12$	0.143810	−	1.36826i	0.0415145	−	0.394984i
$13$	−0.304152	−	2.89381i	−0.0843565	−	0.802599i	−0.952141	−	0.305658i	$-0.901123\pi$
$13$	−0.304152	−	2.89381i	−0.0843565	−	0.802599i	0.867785	−	0.496940i	$-0.165543\pi$
$14$	0.514852	−	0.109435i	0.137600	−	0.0292478i
$15$	−2.70670	+	1.96653i	−0.698867	+	0.507757i
$16$	−1.11127	+	0.807384i	−0.277817	+	0.201846i
$17$	1.27993	−	0.272057i	0.310429	−	0.0659836i	−0.0500631	−	0.998746i	$-0.515942\pi$
$17$	1.27993	−	0.272057i	0.310429	−	0.0659836i	0.360492	+	0.932762i	$0.382609\pi$
$18$	−0.157525	−	1.49875i	−0.0371290	−	0.353259i
$19$	0.397160	−	3.77873i	0.0911148	−	0.866900i	−0.849538	−	0.527528i	$-0.823119\pi$
$19$	0.397160	−	3.77873i	0.0911148	−	0.866900i	0.940652	−	0.339371i	$-0.110214\pi$
$20$	5.52896	+	1.17522i	1.23631	+	0.262786i
$21$	0.629330	−	0.280196i	0.137331	−	0.0611437i
$22$	−1.89879	−	2.10882i	−0.404823	−	0.449601i
$23$	1.01449	−	3.12228i	0.211536	−	0.651040i	−0.787846	−	0.615873i	$-0.788804\pi$
$23$	1.01449	−	3.12228i	0.211536	−	0.651040i	0.999381	−	0.0351674i	$-0.0111964\pi$
$24$	1.46740	−	1.62972i	0.299533	−	0.332665i
$25$	−4.37284	−	7.57398i	−0.874568	−	1.51480i
$26$	1.00313	−	1.73747i	0.196729	−	0.340745i
$27$	−1.44606	−	4.45052i	−0.278295	−	0.856503i
$28$	−1.06325	−	0.473389i	−0.200935	−	0.0894620i
$29$	3.96065	+	2.87758i	0.735474	+	0.534353i	0.891290	−	0.453433i	$-0.149801\pi$
$29$	3.96065	+	2.87758i	0.735474	+	0.534353i	−0.155816	+	0.987786i	$0.549801\pi$
$30$	−2.30681			−0.421164
$31$		0			0
$31$		0			0
$32$	−5.80746			−1.02662
$33$	−3.00464	−	2.18300i	−0.523041	−	0.380012i
$34$	0.824217	+	0.366965i	0.141352	+	0.0629340i
$35$	0.874609	+	2.69177i	0.147836	+	0.454992i
$36$	−1.66614	+	2.88584i	−0.277690	+	0.480973i
$37$	−5.20639	−	9.01773i	−0.855925	−	1.48251i	−0.875784	−	0.482704i	$-0.839655\pi$
$37$	−5.20639	−	9.01773i	−0.855925	−	1.48251i	0.0198583	−	0.999803i	$-0.493679\pi$
$38$	1.75296	−	1.94686i	0.284368	−	0.315822i
$39$	0.811405	−	2.49725i	0.129929	−	0.399880i
$40$	6.02884	+	6.69570i	0.953243	+	1.05868i
$41$	0.690591	−	0.307471i	0.107852	−	0.0480189i	−0.352101	−	0.935962i	$-0.614533\pi$
$41$	0.690591	−	0.307471i	0.107852	−	0.0480189i	0.459953	+	0.887943i	$0.347866\pi$
$42$	0.464603	+	0.0987545i	0.0716898	+	0.0152381i
$43$	−0.748099	+	7.11768i	−0.114084	+	1.08544i	0.776343	+	0.630311i	$0.217072\pi$
$43$	−0.748099	+	7.11768i	−0.114084	+	1.08544i	−0.890427	+	0.455126i	$0.849594\pi$
$44$	0.655882	+	6.24030i	0.0988780	+	0.940761i
$45$	7.92634	−	1.68480i	1.18159	−	0.251154i
$46$	1.83127	−	1.33050i	0.270006	−	0.196171i
$47$	0.708753	−	0.514939i	0.103382	−	0.0751116i	−0.534893	−	0.844920i	$-0.679648\pi$
$47$	0.708753	−	0.514939i	0.103382	−	0.0751116i	0.638275	+	0.769808i	$0.279648\pi$
$48$	−1.21245	+	0.257715i	−0.175003	+	0.0371980i
$49$	0.670783	+	6.38208i	0.0958262	+	0.911725i
$50$	0.630315	−	5.99705i	0.0891400	−	0.848111i
$51$	1.15501	+	0.245505i	0.161734	+	0.0343776i
$52$	−4.05268	+	1.80437i	−0.562005	+	0.250221i
$53$	−2.39261	−	2.65727i	−0.328651	−	0.365004i	0.556062	−	0.831141i	$-0.312312\pi$
$53$	−2.39261	−	2.65727i	−0.328651	−	0.365004i	−0.884712	+	0.466138i	$0.845645\pi$
$54$	0.997049	−	3.06860i	0.135681	−	0.417584i
$55$	10.2101	−	11.3395i	1.37673	−	1.52901i
$56$	−0.927595	−	1.60664i	−0.123955	−	0.214696i
$57$	1.71435	−	2.96935i	0.227072	−	0.393300i
$58$	1.04309	+	3.21029i	0.136964	+	0.421532i
$59$	0.847103	+	0.377155i	0.110283	+	0.0491014i	0.461137	−	0.887329i	$-0.347442\pi$
$59$	0.847103	+	0.377155i	0.110283	+	0.0491014i	−0.350853	+	0.936430i	$0.614108\pi$
$60$	4.12664	+	2.99818i	0.532746	+	0.387063i
$61$	−2.31704			−0.296666			−0.148333	−	0.988937i	$-0.547391\pi$
$61$	−2.31704			−0.296666			−0.148333	+	0.988937i	$0.547391\pi$
$62$		0			0
$63$	−1.66853			−0.210215
$64$	−1.01693	−	0.738843i	−0.127116	−	0.0923554i
$65$	9.85528	+	4.38785i	1.22240	+	0.544246i
$66$	−0.791311	−	2.43540i	−0.0974036	−	0.299778i
$67$	1.04345	−	1.80731i	0.127478	−	0.220798i	−0.795221	−	0.606320i	$-0.792645\pi$
$67$	1.04345	−	1.80731i	0.127478	−	0.220798i	0.922699	+	0.385522i	$0.125979\pi$
$68$	−0.997488	−	1.72770i	−0.120963	−	0.209514i
$69$	1.98233	−	2.20160i	0.238644	−	0.265041i
$70$	−0.603037	+	1.85596i	−0.0720767	+	0.221829i
$71$	−5.17645	−	5.74903i	−0.614332	−	0.682284i	0.353051	−	0.935604i	$-0.385144\pi$
$71$	−5.17645	−	5.74903i	−0.614332	−	0.682284i	−0.967383	+	0.253320i	$0.918478\pi$
$72$	−4.85238	+	2.16042i	−0.571858	+	0.254608i
$73$	−5.53385	−	1.17626i	−0.647688	−	0.137670i	−0.127658	−	0.991818i	$-0.540746\pi$
$73$	−5.53385	−	1.17626i	−0.647688	−	0.137670i	−0.520030	+	0.854148i	$0.674079\pi$
$74$	0.750466	−	7.14021i	0.0872399	−	0.830032i
$75$	−0.824950	−	7.84887i	−0.0952570	−	0.906310i
$76$	−5.66619	+	1.20439i	−0.649957	+	0.138153i
$77$	−2.54180	+	1.84673i	−0.289665	+	0.210454i
$78$	1.46468	−	1.06415i	0.165842	−	0.120492i
$79$	−13.7867	+	2.93046i	−1.55113	+	0.329702i	−0.902257	−	0.431198i	$-0.858091\pi$
$79$	−13.7867	+	2.93046i	−1.55113	+	0.329702i	−0.648869	+	0.760900i	$0.724758\pi$
$80$	−0.532328	−	5.06476i	−0.0595161	−	0.566257i
$81$	−0.243989	+	2.32140i	−0.0271098	+	0.257933i
$82$	0.509829	+	0.108368i	0.0563012	+	0.0119672i
$83$	12.8880	−	5.73812i	1.41465	−	0.629841i	0.449913	−	0.893072i	$-0.351455\pi$
$83$	12.8880	−	5.73812i	1.41465	−	0.629841i	0.964733	+	0.263231i	$0.0847883\pi$
$84$	−0.702773	−	0.780508i	−0.0766788	−	0.0851604i
$85$	−1.49916	+	4.61393i	−0.162606	+	0.500451i
$86$	−3.30191	+	3.66714i	−0.356054	+	0.395438i
$87$	2.20891	+	3.82595i	0.236820	+	0.410184i
$88$	−5.00086	+	8.66175i	−0.533094	+	0.923346i
$89$	1.37043	+	4.21776i	0.145266	+	0.447081i	0.997045	−	0.0768191i	$-0.0244764\pi$
$89$	1.37043	+	4.21776i	0.145266	+	0.447081i	−0.851780	+	0.523900i	$0.824476\pi$
$90$	5.10420	+	2.27254i	0.538030	+	0.239547i
$91$	−1.79706	−	1.30564i	−0.188383	−	0.136868i
$92$	−5.00520			−0.521828
$93$		0			0
$94$	0.604042			0.0623021
$95$	11.3965	+	8.28005i	1.16926	+	0.849515i
$96$	−4.78758	−	2.13157i	−0.488630	−	0.217552i
$97$	−1.63088	−	5.01933i	−0.165591	−	0.509636i	0.833489	−	0.552537i	$-0.186340\pi$
$97$	−1.63088	−	5.01933i	−0.165591	−	0.509636i	−0.999079	+	0.0429007i	$0.986340\pi$
$98$	−2.21232	+	3.83184i	−0.223478	+	0.387075i
$99$	4.49770	+	7.79025i	0.452036	+	0.782949i
$100$	−8.92196	+	9.90884i	−0.892196	+	0.990884i
$101$	1.17656	−	3.62108i	0.117072	−	0.360311i	−0.875301	−	0.483578i	$-0.839337\pi$
$101$	1.17656	−	3.62108i	0.117072	−	0.360311i	0.992374	+	0.123267i	$0.0393371\pi$
$102$	0.544781	+	0.605040i	0.0539413	+	0.0599079i
$103$	−5.70573	+	2.54035i	−0.562202	+	0.250308i	−0.668104	−	0.744068i	$-0.732894\pi$
$103$	−5.70573	+	2.54035i	−0.562202	+	0.250308i	0.105902	+	0.994377i	$0.466227\pi$
$104$	−6.91671	−	1.47019i	−0.678239	−	0.144164i
$105$	−0.266972	+	2.54007i	−0.0260538	+	0.247885i
$106$	−0.257707	−	2.45192i	−0.0250307	−	0.238151i
$107$	−2.27653	+	0.483890i	−0.220080	+	0.0467795i	−0.316632	−	0.948548i	$-0.602552\pi$
$107$	−2.27653	+	0.483890i	−0.220080	+	0.0467795i	0.0965518	+	0.995328i	$0.469219\pi$
$108$	−5.77189	+	4.19352i	−0.555400	+	0.403522i
$109$	−1.19478	+	0.868057i	−0.114439	+	0.0831448i	−0.643533	−	0.765419i	$-0.722532\pi$
$109$	−1.19478	+	0.868057i	−0.114439	+	0.0831448i	0.529094	+	0.848563i	$0.322532\pi$
$110$	10.2909	−	2.18740i	0.981197	−	0.208560i
$111$	−0.982202	−	9.34503i	−0.0932265	−	0.886991i
$112$	−0.109609	+	1.04286i	−0.0103570	+	0.0985407i
$113$	−6.24112	−	1.32659i	−0.587115	−	0.124795i	−0.0952299	−	0.995455i	$-0.530359\pi$
$113$	−6.24112	−	1.32659i	−0.587115	−	0.124795i	−0.491885	+	0.870660i	$0.663692\pi$
$114$	2.15969	−	0.961554i	0.202273	−	0.0900578i
$115$	8.14440	+	9.04528i	0.759470	+	0.843476i
$116$	2.30647	−	7.09857i	0.214150	−	0.659086i
$117$	−4.25551	+	4.72623i	−0.393422	+	0.436940i
$118$	0.319673	+	0.553690i	0.0294283	+	0.0509713i
$119$	0.499460	−	0.865089i	0.0457854	−	0.0793026i
$120$	2.51249	+	7.73265i	0.229358	+	0.705891i
$121$	5.42495	+	2.41534i	0.493178	+	0.219577i
$122$	−1.29247	−	0.939035i	−0.117015	−	0.0850162i
$123$	0.682166			0.0615089
$124$		0			0
$125$	13.8872			1.24211
$126$	−0.930724	−	0.676211i	−0.0829155	−	0.0602417i
$127$	1.30821	+	0.582453i	0.116085	+	0.0516843i	0.463957	−	0.885858i	$-0.346429\pi$
$127$	1.30821	+	0.582453i	0.116085	+	0.0516843i	−0.347872	+	0.937542i	$0.613096\pi$
$128$	3.32139	+	10.2222i	0.293572	+	0.903521i
$129$	−3.22919	+	5.59312i	−0.284314	+	0.492447i
$130$	3.71911	+	6.44168i	0.326187	+	0.564973i
$131$	4.21077	−	4.67654i	0.367897	−	0.408591i	−0.530564	−	0.847645i	$-0.678020\pi$
$131$	4.21077	−	4.67654i	0.367897	−	0.408591i	0.898461	+	0.439054i	$0.144686\pi$
$132$	−1.74974	+	5.38514i	−0.152295	+	0.468717i
$133$	−1.94084	−	2.15553i	−0.168293	−	0.186908i
$134$	1.31450	−	0.585254i	0.113556	−	0.0505582i
$135$	16.9704	+	3.60717i	1.46058	+	0.310456i
$136$	0.332396	−	3.16254i	0.0285027	−	0.271185i
$137$	1.33273	+	12.6801i	0.113863	+	1.08333i	0.891001	+	0.454001i	$0.150004\pi$
$137$	1.33273	+	12.6801i	0.113863	+	1.08333i	−0.777139	+	0.629330i	$0.783330\pi$
$138$	1.99802	−	0.424691i	0.170082	−	0.0361521i
$139$	15.1397	−	10.9997i	1.28414	−	0.932979i	0.284466	−	0.958686i	$-0.408184\pi$
$139$	15.1397	−	10.9997i	1.28414	−	0.932979i	0.999670	+	0.0257067i	$0.00818361\pi$
$140$	3.49096	−	2.53633i	0.295040	−	0.214359i
$141$	0.773288	−	0.164367i	0.0651226	−	0.0138422i
$142$	−0.557552	−	5.30475i	−0.0467887	−	0.445165i
$143$	−1.25177	+	11.9098i	−0.104679	+	0.995950i
$144$	2.93664	+	0.624203i	0.244720	+	0.0520169i
$145$	−16.5814	+	7.38253i	−1.37701	+	0.613086i
$146$	−2.61014	−	2.89885i	−0.216017	−	0.239911i
$147$	−1.78949	+	5.50749i	−0.147595	+	0.454250i
$148$	−10.6227	+	11.7977i	−0.873178	+	0.969762i
$149$	10.0677	+	17.4377i	0.824774	+	1.42855i	0.902092	+	0.431545i	$0.142031\pi$
$149$	10.0677	+	17.4377i	0.824774	+	1.42855i	−0.0773172	+	0.997007i	$0.524635\pi$
$150$	2.72078	−	4.71252i	0.222150	−	0.384776i
$151$	−4.75035	−	14.6201i	−0.386578	−	1.18977i	−0.935329	−	0.353779i	$-0.884896\pi$
$151$	−4.75035	−	14.6201i	−0.386578	−	1.18977i	0.548751	−	0.835986i	$-0.315104\pi$
$152$	−8.43531	−	3.75564i	−0.684194	−	0.304623i
$153$	−2.31379	−	1.68107i	−0.187059	−	0.135906i
$154$	−2.16628			−0.174564
$155$		0			0
$156$	−4.00324			−0.320515
$157$	−12.2544	−	8.90334i	−0.978008	−	0.710564i	−0.0207452	−	0.999785i	$-0.506604\pi$
$157$	−12.2544	−	8.90334i	−0.978008	−	0.710564i	−0.957262	+	0.289221i	$0.906604\pi$
$158$	−8.87802	−	3.95275i	−0.706298	−	0.314464i
$159$	−0.997111	−	3.06879i	−0.0790760	−	0.243371i
$160$	10.7656	−	18.6466i	0.851098	−	1.47414i
$161$	−1.25310	−	2.17042i	−0.0987577	−	0.171053i
$162$	−1.07690	+	1.19602i	−0.0846093	+	0.0939681i
$163$	−0.322882	+	0.993730i	−0.0252901	+	0.0778349i	−0.962905	−	0.269841i	$-0.913029\pi$
$163$	−0.322882	+	0.993730i	−0.0252901	+	0.0778349i	0.937615	+	0.347676i	$0.113029\pi$
$164$	−0.771183	−	0.856485i	−0.0602193	−	0.0668803i
$165$	12.5791	−	5.60056i	0.979279	−	0.436003i
$166$	9.51460	+	2.02239i	0.738477	+	0.156968i
$167$	−1.18006	+	11.2276i	−0.0913161	+	0.868815i	0.848973	+	0.528437i	$0.177222\pi$
$167$	−1.18006	+	11.2276i	−0.0913161	+	0.868815i	−0.940289	+	0.340378i	$0.889445\pi$
$168$	−0.174994	−	1.66495i	−0.0135011	−	0.128454i
$169$	4.43428	−	0.942536i	0.341099	−	0.0725028i
$170$	−2.70615	+	1.96613i	−0.207552	+	0.150796i
$171$	−6.71853	+	4.88129i	−0.513778	+	0.373282i
$172$	10.6730	−	2.26861i	0.813805	−	0.172980i
$173$	2.15879	+	20.5395i	0.164130	+	1.56159i	0.698045	+	0.716054i	$0.254054\pi$
$173$	2.15879	+	20.5395i	0.164130	+	1.56159i	−0.533915	+	0.845538i	$0.679280\pi$
$174$	−0.318400	+	3.02937i	−0.0241378	+	0.229656i
$175$	−6.53050	−	1.38810i	−0.493660	−	0.104931i
$176$	5.16449	−	2.29938i	0.389288	−	0.173322i
$177$	0.559908	+	0.621841i	0.0420853	+	0.0467404i
$178$	−0.944903	+	2.90811i	−0.0708235	+	0.217972i
$179$	0.0880993	−	0.0978442i	0.00658485	−	0.00731322i	−0.739843	−	0.672779i	$-0.765100\pi$
$179$	0.0880993	−	0.0978442i	0.00658485	−	0.00731322i	0.746428	+	0.665466i	$0.231767\pi$
$180$	−6.17723	−	10.6993i	−0.460424	−	0.797477i
$181$	3.86599	−	6.69610i	0.287357	−	0.497717i	−0.685821	−	0.727770i	$-0.740557\pi$
$181$	3.86599	−	6.69610i	0.287357	−	0.497717i	0.973178	+	0.230053i	$0.0738901\pi$
$182$	−0.473278	−	1.45660i	−0.0350817	−	0.107970i
$183$	−1.91013	−	0.850445i	−0.141201	−	0.0628667i
$184$	−6.45450	−	4.68947i	−0.475832	−	0.345712i
$185$	38.6056			2.83834
$186$		0			0
$187$	−5.38539			−0.393819
$188$	−1.08056	−	0.785076i	−0.0788083	−	0.0572576i
$189$	−3.26350	−	1.45300i	−0.237385	−	0.105690i
$190$	3.00142	+	9.23741i	0.217746	+	0.670152i
$191$	10.5513	−	18.2755i	0.763468	−	1.32237i	−0.177585	−	0.984106i	$-0.556828\pi$
$191$	10.5513	−	18.2755i	0.763468	−	1.32237i	0.941053	−	0.338260i	$-0.109838\pi$
$192$	−0.567157	−	0.982344i	−0.0409310	−	0.0708946i
$193$	3.78944	−	4.20860i	0.272770	−	0.302942i	−0.591159	−	0.806555i	$-0.701330\pi$
$193$	3.78944	−	4.20860i	0.272770	−	0.302942i	0.863929	+	0.503613i	$0.167996\pi$
$194$	1.12448	−	3.46079i	0.0807330	−	0.248471i
$195$	6.51402	+	7.23456i	0.466479	+	0.518077i
$196$	8.93786	−	3.97939i	0.638419	−	0.284242i
$197$	15.5670	+	3.30887i	1.10910	+	0.235747i	0.725821	−	0.687883i	$-0.241460\pi$
$197$	15.5670	+	3.30887i	1.10910	+	0.235747i	0.383283	+	0.923631i	$0.374793\pi$
$198$	−0.648313	+	6.16829i	−0.0460736	+	0.438361i
$199$	−0.445443	−	4.23811i	−0.0315766	−	0.300432i	−0.998900	−	0.0468866i	$-0.985070\pi$
$199$	−0.445443	−	4.23811i	−0.0315766	−	0.300432i	0.967324	−	0.253545i	$-0.0815966\pi$
$200$	−20.7892	+	4.41888i	−1.47002	+	0.312462i
$201$	1.52356	−	1.10693i	0.107463	−	0.0780767i
$202$	2.12383	−	1.54305i	0.149432	−	0.108569i
$203$	3.65563	−	0.777027i	0.256575	−	0.0545366i
$204$	−0.188179	−	1.79041i	−0.0131752	−	0.125353i
$205$	−0.292960	+	2.78733i	−0.0204612	+	0.194675i
$206$	−4.21226	−	0.895343i	−0.293482	−	0.0623815i
$207$	−6.55512	+	2.91853i	−0.455612	+	0.202852i
$208$	2.67441	+	2.97024i	0.185437	+	0.205949i
$209$	−4.83225	+	14.8721i	−0.334254	+	1.02873i
$210$	−1.17834	+	1.30868i	−0.0813134	+	0.0903077i
$211$	5.75414	+	9.96646i	0.396131	+	0.686120i	0.993245	−	0.116037i	$-0.0370191\pi$
$211$	5.75414	+	9.96646i	0.396131	+	0.686120i	−0.597113	+	0.802157i	$0.703686\pi$
$212$	−2.72576	+	4.72115i	−0.187206	+	0.324250i
$213$	−2.15726	−	6.63937i	−0.147813	−	0.454922i
$214$	−1.46598	−	0.652696i	−0.100212	−	0.0446174i
$215$	−21.4667	−	15.5965i	−1.46402	−	1.06367i
$216$	−11.3722			−0.773780
$217$		0			0
$218$	−1.01826			−0.0689654
$219$	−4.13028	−	3.00083i	−0.279099	−	0.202777i
$220$	−21.2522	−	9.46211i	−1.43283	−	0.637935i
$221$	−1.17658	−	3.62113i	−0.0791450	−	0.243583i
$222$	3.23941	−	5.61082i	0.217415	−	0.376574i
$223$	4.71196	+	8.16135i	0.315536	+	0.546524i	0.979551	−	0.201195i	$-0.0644824\pi$
$223$	4.71196	+	8.16135i	0.315536	+	0.546524i	−0.664015	+	0.747719i	$0.731149\pi$
$224$	−2.96651	+	3.29464i	−0.198208	+	0.220133i
$225$	−5.90692	+	18.1796i	−0.393795	+	1.21197i
$226$	−2.94373	−	3.26935i	−0.195814	−	0.217474i
$227$	19.8815	−	8.85182i	1.31958	−	0.587516i	0.378471	−	0.925613i	$-0.376450\pi$
$227$	19.8815	−	8.85182i	1.31958	−	0.587516i	0.941111	+	0.338097i	$0.109783\pi$
$228$	−5.11318	−	1.08684i	−0.338629	−	0.0719777i
$229$	1.77237	−	16.8630i	0.117122	−	1.11434i	−0.765233	−	0.643754i	$-0.777376\pi$
$229$	1.77237	−	16.8630i	0.117122	−	1.11434i	0.882355	−	0.470585i	$-0.155957\pi$
$230$	0.877228	+	8.34627i	0.0578427	+	0.550337i
$231$	−2.77324	+	0.589471i	−0.182466	+	0.0387844i
$232$	9.62511	−	6.99305i	0.631920	−	0.459117i
$233$	7.95758	−	5.78152i	0.521318	−	0.378760i	−0.295782	−	0.955255i	$-0.595580\pi$
$233$	7.95758	−	5.78152i	0.521318	−	0.378760i	0.817100	+	0.576496i	$0.195580\pi$
$234$	−4.28919	+	0.911695i	−0.280393	+	0.0595994i
$235$	0.339512	+	3.23024i	0.0221473	+	0.210718i
$236$	0.147774	−	1.40597i	0.00961924	−	0.0915209i
$237$	−12.4411	−	2.64445i	−0.808139	−	0.171775i
$238$	0.629202	−	0.280139i	0.0407851	−	0.0181587i
$239$	−0.395212	−	0.438927i	−0.0255641	−	0.0283919i	0.730227	−	0.683204i	$-0.239414\pi$
$239$	−0.395212	−	0.438927i	−0.0255641	−	0.0283919i	−0.755791	+	0.654813i	$0.772748\pi$
$240$	1.42012	−	4.37069i	0.0916687	−	0.282127i
$241$	−10.2848	+	11.4225i	−0.662504	+	0.735786i	−0.976945	−	0.213491i	$-0.931516\pi$
$241$	−10.2848	+	11.4225i	−0.662504	+	0.735786i	0.314440	+	0.949277i	$0.398183\pi$
$242$	2.04722	+	3.54590i	0.131601	+	0.227939i
$243$	−8.07252	+	13.9820i	−0.517852	+	0.896946i
$244$	1.09162	+	3.35966i	0.0698838	+	0.215080i
$245$	−21.7351	−	9.67707i	−1.38860	−	0.618245i
$246$	0.380520	+	0.276464i	0.0242611	+	0.0176267i
$247$	−11.0557			−0.703459
$248$		0			0
$249$	12.7308			0.806783
$250$	7.74642	+	5.62810i	0.489926	+	0.355952i
$251$	5.52832	+	2.46137i	0.348945	+	0.155360i	0.573722	−	0.819050i	$-0.305499\pi$
$251$	5.52832	+	2.46137i	0.348945	+	0.155360i	−0.224778	+	0.974410i	$0.572166\pi$
$252$	0.786090	+	2.41933i	0.0495190	+	0.152404i
$253$	−6.75571	+	11.7012i	−0.424728	+	0.735650i
$254$	0.493682	+	0.855082i	0.0309763	+	0.0536526i
$255$	−2.92938	+	3.25340i	−0.183445	+	0.203736i
$256$	−3.06694	+	9.43906i	−0.191684	+	0.589942i
$257$	−3.02972	−	3.36484i	−0.188988	−	0.209893i	0.641203	−	0.767371i	$-0.278436\pi$
$257$	−3.02972	−	3.36484i	−0.188988	−	0.209893i	−0.830192	+	0.557478i	$0.811769\pi$
$258$	−4.06803	+	1.81120i	−0.253264	+	0.112760i
$259$	−7.77535	−	1.65270i	−0.483137	−	0.102694i
$260$	1.71921	−	16.3572i	0.106621	−	1.01443i
$261$	−1.11848	−	10.6416i	−0.0692322	−	0.658700i
$262$	4.24409	−	0.902110i	0.262201	−	0.0557325i
$263$	−2.02971	+	1.47467i	−0.125157	+	0.0909322i	−0.648603	−	0.761127i	$-0.724646\pi$
$263$	−2.02971	+	1.47467i	−0.125157	+	0.0909322i	0.523445	+	0.852059i	$0.324646\pi$
$264$	−7.30184	+	5.30510i	−0.449397	+	0.326506i
$265$	12.9673	−	2.75628i	0.796574	−	0.169317i
$266$	−0.209047	−	1.98895i	−0.0128175	−	0.121950i
$267$	−0.418321	+	3.98005i	−0.0256008	+	0.243575i
$268$	−3.11216	−	0.661509i	−0.190105	−	0.0404081i
$269$	−12.1865	+	5.42577i	−0.743023	+	0.330815i	−0.743096	−	0.669185i	$-0.766643\pi$
$269$	−12.1865	+	5.42577i	−0.743023	+	0.330815i	7.27860e−5		1.00000i	$0.499977\pi$
$270$	8.00439	+	8.88978i	0.487132	+	0.541015i
$271$	−4.27190	+	13.1476i	−0.259500	+	0.798658i	0.733410	+	0.679787i	$0.237928\pi$
$271$	−4.27190	+	13.1476i	−0.259500	+	0.798658i	−0.992910	+	0.118871i	$0.962072\pi$
$272$	−1.20269	+	1.33572i	−0.0729239	+	0.0809902i
$273$	−1.00225	−	1.73594i	−0.0606586	−	0.105064i
$274$	−4.39548	+	7.61320i	−0.265541	+	0.459930i
$275$	11.1227	+	34.2322i	0.670726	+	2.06428i
$276$	−4.12621	−	1.83711i	−0.248368	−	0.110581i
$277$	9.36093	+	6.80111i	0.562444	+	0.408639i	0.832353	−	0.554247i	$-0.186994\pi$
$277$	9.36093	+	6.80111i	0.562444	+	0.408639i	−0.269909	+	0.962886i	$0.586994\pi$
$278$	12.9030			0.773870
$279$		0			0
$280$	6.87814			0.411048
$281$	12.4583	+	9.05151i	0.743202	+	0.539968i	0.893712	−	0.448641i	$-0.148092\pi$
$281$	12.4583	+	9.05151i	0.743202	+	0.539968i	−0.150510	+	0.988608i	$0.548092\pi$
$282$	0.497962	+	0.221707i	0.0296532	+	0.0132025i
$283$	−7.01336	−	21.5849i	−0.416901	−	1.28309i	−0.910539	−	0.413422i	$-0.864333\pi$
$283$	−7.01336	−	21.5849i	−0.416901	−	1.28309i	0.493638	−	0.869667i	$-0.335667\pi$
$284$	−5.89722	+	10.2143i	−0.349935	+	0.606106i
$285$	6.35600	+	11.0089i	0.376497	+	0.652112i
$286$	−5.52500	+	6.13613i	−0.326700	+	0.362837i
$287$	0.178329	−	0.548840i	0.0105264	−	0.0323970i
$288$	8.49342	+	9.43289i	0.500479	+	0.555839i
$289$	−13.9661	+	6.21809i	−0.821533	+	0.365770i
$290$	−12.2413	−	2.60196i	−0.718831	−	0.152792i
$291$	0.497822	−	4.73646i	0.0291828	−	0.277656i
$292$	0.901599	+	8.57814i	0.0527621	+	0.501998i
$293$	−12.1299	+	2.57828i	−0.708635	+	0.150625i	−0.548109	−	0.836407i	$-0.684652\pi$
$293$	−12.1299	+	2.57828i	−0.708635	+	0.150625i	−0.160525	+	0.987032i	$0.551319\pi$
$294$	−3.23024	+	2.34690i	−0.188391	+	0.136874i
$295$	−2.78129	+	2.02073i	−0.161933	+	0.117651i
$296$	−24.7520	+	5.26121i	−1.43868	+	0.305801i
$297$	2.01314	+	19.1538i	0.116814	+	1.11142i
$298$	−1.45118	+	13.8071i	−0.0840649	+	0.799824i
$299$	−9.34384	−	1.98610i	−0.540368	−	0.114859i
$300$	−10.9921	+	4.89398i	−0.634627	+	0.282554i
$301$	3.65581	+	4.06019i	0.210718	+	0.234026i
$302$	3.27533	−	10.0804i	0.188474	−	0.580064i
$303$	2.29902	−	2.55332i	0.132075	−	0.146684i
$304$	2.60953	+	4.51984i	0.149667	+	0.259231i
$305$	4.29523	−	7.43956i	0.245944	−	0.425988i
$306$	−0.609367	−	1.87544i	−0.0348352	−	0.107212i
$307$	28.0641	+	12.4949i	1.60170	+	0.713124i	0.996551	−	0.0829855i	$-0.0264455\pi$
$307$	28.0641	+	12.4949i	1.60170	+	0.713124i	0.605152	+	0.796110i	$0.293112\pi$
$308$	3.87523	+	2.81552i	0.220812	+	0.160429i
$309$	−5.63612			−0.320628
$310$		0			0
$311$	2.38141			0.135037			0.0675187	−	0.997718i	$-0.478492\pi$
$311$	2.38141			0.135037			0.0675187	+	0.997718i	$0.478492\pi$
$312$	−5.16241	−	3.75071i	−0.292264	−	0.212342i
$313$	−9.81659	−	4.37063i	−0.554866	−	0.247042i	0.110094	−	0.993921i	$-0.464885\pi$
$313$	−9.81659	−	4.37063i	−0.554866	−	0.247042i	−0.664960	+	0.746879i	$0.731551\pi$
$314$	−3.22735	−	9.93277i	−0.182130	−	0.560539i
$315$	3.09305	−	5.35732i	0.174274	−	0.301851i
$316$	10.7444	+	18.6098i	0.604420	+	1.04689i
$317$	5.85245	−	6.49980i	0.328706	−	0.365065i	−0.556026	−	0.831165i	$-0.687674\pi$
$317$	5.85245	−	6.49980i	0.328706	−	0.365065i	0.884732	+	0.466100i	$0.154341\pi$
$318$	0.687501	−	2.11591i	0.0385531	−	0.118654i
$319$	−13.4820	−	14.9733i	−0.754849	−	0.838344i
$320$	4.25742	−	1.89553i	0.237997	−	0.105963i
$321$	−2.05434	−	0.436663i	−0.114662	−	0.0243722i
$322$	0.180625	−	1.71853i	0.0100658	−	0.0957701i
$323$	−0.519694	−	4.94456i	−0.0289165	−	0.275122i
$324$	3.48093	−	0.739894i	0.193385	−	0.0411052i
$325$	−20.5877	+	14.9578i	−1.14200	+	0.829710i
$326$	−0.582840	+	0.423458i	−0.0322805	+	0.0234532i
$327$	−1.30357	+	0.277082i	−0.0720874	+	0.0153227i
$328$	−0.192028	−	1.82703i	−0.0106030	−	0.100881i
$329$	0.0699070	−	0.665120i	0.00385410	−	0.0366693i
$330$	9.28650	+	1.97391i	0.511205	+	0.108660i
$331$	29.5706	−	13.1657i	1.62535	−	0.723652i	0.626889	−	0.779109i	$-0.284328\pi$
$331$	29.5706	−	13.1657i	1.62535	−	0.723652i	0.998461	+	0.0554567i	$0.0176615\pi$
$332$	−14.3921	−	15.9840i	−0.789868	−	0.877237i
$333$	−7.03290	+	21.6450i	−0.385400	+	1.18614i
$334$	−5.20849	+	5.78461i	−0.284996	+	0.316520i
$335$	3.86860	+	6.70062i	0.211364	+	0.366094i
$336$	−0.473129	+	0.819484i	−0.0258113	+	0.0447065i
$337$	−8.57021	−	26.3764i	−0.466849	−	1.43681i	−0.856642	−	0.515912i	$-0.827453\pi$
$337$	−8.57021	−	26.3764i	−0.466849	−	1.43681i	0.389792	−	0.920903i	$-0.372547\pi$
$338$	2.85548	+	1.27134i	0.155318	+	0.0691518i
$339$	−4.65817	−	3.38436i	−0.252997	−	0.183813i
$340$	7.39640			0.401126
$341$		0			0
$342$	−5.72593			−0.309623
$343$	8.28646	+	6.02047i	0.447427	+	0.325075i
$344$	15.8889	+	7.07420i	0.856672	+	0.381415i
$345$	3.39414	+	10.4461i	0.182735	+	0.562399i
$346$	−7.11994	+	12.3321i	−0.382770	+	0.662977i
$347$	−12.9580	−	22.4440i	−0.695624	−	1.20486i	−0.969970	−	0.243224i	$-0.921795\pi$
$347$	−12.9580	−	22.4440i	−0.695624	−	1.20486i	0.274347	−	0.961631i	$-0.411538\pi$
$348$	4.50687	−	5.00539i	0.241594	−	0.268317i
$349$	1.72862	−	5.32015i	0.0925309	−	0.284781i	−0.894071	−	0.447924i	$-0.852163\pi$
$349$	1.72862	−	5.32015i	0.0925309	−	0.284781i	0.986602	+	0.163144i	$0.0521634\pi$
$350$	−3.08023	−	3.42094i	−0.164645	−	0.182857i
$351$	−12.4391	+	5.53827i	−0.663953	+	0.295611i
$352$	23.3790	+	4.96936i	1.24611	+	0.264868i
$353$	1.21974	−	11.6051i	0.0649202	−	0.617675i	−0.912893	−	0.408198i	$-0.866157\pi$
$353$	1.21974	−	11.6051i	0.0649202	−	0.617675i	0.977814	−	0.209477i	$-0.0671760\pi$
$354$	0.0603073	+	0.573786i	0.00320530	+	0.0304964i
$355$	28.0549	−	5.96325i	1.48900	−	0.316497i
$356$	5.47002	−	3.97420i	0.289910	−	0.210632i
$357$	0.729269	−	0.529845i	0.0385970	−	0.0280424i
$358$	0.0887965	−	0.0188743i	0.00469304	−	0.000997537i
$359$	−2.73863	−	26.0563i	−0.144539	−	1.37520i	−0.790796	−	0.612080i	$-0.790333\pi$
$359$	−2.73863	−	26.0563i	−0.144539	−	1.37520i	0.646257	−	0.763120i	$-0.276334\pi$
$360$	2.05846	−	19.5849i	0.108490	−	1.03222i
$361$	4.46376	+	0.948801i	0.234935	+	0.0499369i
$362$	4.87025	−	2.16837i	0.255974	−	0.113967i
$363$	3.58572	+	3.98234i	0.188201	+	0.209019i
$364$	−1.04651	+	3.22082i	−0.0548519	+	0.168817i
$365$	14.0351	−	15.5876i	0.734633	−	0.815893i
$366$	−0.720830	−	1.24851i	−0.0376784	−	0.0652608i
$367$	13.5073	−	23.3953i	0.705076	−	1.22123i	−0.261589	−	0.965179i	$-0.584246\pi$
$367$	13.5073	−	23.3953i	0.705076	−	1.22123i	0.966664	−	0.256047i	$-0.0824203\pi$
$368$	1.39351	+	4.28877i	0.0726416	+	0.223568i
$369$	−1.50941	−	0.672031i	−0.0785765	−	0.0349845i
$370$	21.5346	+	15.6458i	1.11953	+	0.813387i
$371$	−2.72967			−0.141717
$372$		0			0
$373$	−12.4058			−0.642351			−0.321175	−	0.947020i	$-0.604078\pi$
$373$	−12.4058			−0.642351			−0.321175	+	0.947020i	$0.604078\pi$
$374$	−3.00403	−	2.18256i	−0.155335	−	0.112857i
$375$	11.4484	+	5.09714i	0.591191	+	0.263215i
$376$	−0.657899	−	2.02480i	−0.0339285	−	0.104421i
$377$	7.12253	−	12.3366i	0.366829	−	0.635367i
$378$	−1.23155	−	2.13311i	−0.0633442	−	0.109715i
$379$	−3.10411	+	3.44746i	−0.159447	+	0.177084i	−0.817575	−	0.575822i	$-0.804682\pi$
$379$	−3.10411	+	3.44746i	−0.159447	+	0.177084i	0.658128	+	0.752906i	$0.271349\pi$
$380$	6.63670	−	20.4257i	0.340456	−	1.04782i
$381$	0.864685	+	0.960330i	0.0442991	+	0.0491992i
$382$	13.2922	−	5.91808i	0.680089	−	0.302795i
$383$	−4.91161	−	1.04399i	−0.250971	−	0.0533456i	0.0807080	−	0.996738i	$-0.474282\pi$
$383$	−4.91161	−	1.04399i	−0.250971	−	0.0533456i	−0.331679	+	0.943392i	$0.607615\pi$
$384$	−1.01384	+	9.64608i	−0.0517375	+	0.492250i
$385$	−1.21759	−	11.5846i	−0.0620542	−	0.590407i
$386$	3.81943	−	0.811845i	0.194404	−	0.0413218i
$387$	12.6551	−	9.19450i	0.643297	−	0.467383i
$388$	−6.50958	+	4.72949i	−0.330474	+	0.240103i
$389$	18.1953	−	3.86754i	0.922540	−	0.196092i	0.277928	−	0.960602i	$-0.410352\pi$
$389$	18.1953	−	3.86754i	0.922540	−	0.196092i	0.644612	+	0.764510i	$0.277019\pi$
$390$	0.701621	+	6.67548i	0.0355280	+	0.338026i
$391$	0.449036	−	4.27230i	0.0227087	−	0.216059i
$392$	15.2543	+	3.24240i	0.770457	+	0.163766i
$393$	5.18777	−	2.30974i	0.261688	−	0.116511i
$394$	7.34246	+	8.15463i	0.369908	+	0.410824i
$395$	16.1481	−	49.6988i	0.812500	−	2.50062i
$396$	9.17672	−	10.1918i	0.461147	−	0.512156i
$397$	−16.2794	−	28.1968i	−0.817040	−	1.41515i	−0.907854	−	0.419287i	$-0.862280\pi$
$397$	−16.2794	−	28.1968i	−0.817040	−	1.41515i	0.0908142	−	0.995868i	$-0.471053\pi$
$398$	1.46912	−	2.54459i	0.0736404	−	0.127549i
$399$	−0.808838	−	2.48935i	−0.0404926	−	0.124623i
$400$	10.9745	+	4.88617i	0.548725	+	0.244308i
$401$	−10.0239	−	7.28282i	−0.500572	−	0.363687i	0.308664	−	0.951171i	$-0.400118\pi$
$401$	−10.0239	−	7.28282i	−0.500572	−	0.363687i	−0.809235	+	0.587485i	$0.800118\pi$
$402$	1.29847			0.0647616
$403$		0			0
$404$	−5.80481			−0.288800
$405$	−7.00125	−	5.08671i	−0.347895	−	0.252760i
$406$	2.35406	+	1.04809i	0.116830	+	0.0520161i
$407$	13.2429	+	40.7576i	0.656429	+	2.02028i
$408$	1.43480	−	2.48514i	0.0710331	−	0.123033i
$409$	−1.72404	−	2.98613i	−0.0852484	−	0.147654i	0.820249	−	0.572007i	$-0.193835\pi$
$409$	−1.72404	−	2.98613i	−0.0852484	−	0.147654i	−0.905497	+	0.424353i	$0.860502\pi$
$410$	−1.29305	+	1.43607i	−0.0638590	+	0.0709227i
$411$	−3.55540	+	10.9424i	−0.175375	+	0.539749i
$412$	6.37158	+	7.07636i	0.313905	+	0.348627i
$413$	0.646673	−	0.287918i	0.0318207	−	0.0141675i
$414$	−4.83932	−	1.02863i	−0.237840	−	0.0505544i
$415$	−5.46732	+	52.0180i	−0.268380	+	2.55347i
$416$	1.76635	+	16.8057i	0.0866024	+	0.823967i
$417$	16.5183	−	3.51107i	0.808903	−	0.171938i
$418$	−8.72276	+	6.33746i	−0.426644	+	0.309975i
$419$	32.3988	−	23.5391i	1.58279	−	1.14996i	0.669374	−	0.742926i	$-0.266563\pi$
$419$	32.3988	−	23.5391i	1.58279	−	1.14996i	0.913412	−	0.407035i	$-0.133437\pi$
$420$	3.80883	−	0.809592i	0.185852	−	0.0395040i
$421$	−2.26664	−	21.5656i	−0.110469	−	1.05104i	−0.899569	−	0.436779i	$-0.856119\pi$
$421$	−2.26664	−	21.5656i	−0.110469	−	1.05104i	0.789100	−	0.614265i	$-0.210548\pi$
$422$	−0.829421	+	7.89141i	−0.0403756	+	0.384148i
$423$	−1.87295	−	0.398108i	−0.0910660	−	0.0193567i
$424$	−7.93837	+	3.53439i	−0.385521	+	0.171645i
$425$	−7.65748	−	8.50450i	−0.371442	−	0.412529i
$426$	1.48742	−	4.57780i	0.0720656	−	0.221795i
$427$	−1.18357	+	1.31448i	−0.0572768	+	0.0636124i
$428$	1.77417	+	3.07294i	0.0857575	+	0.148536i
$429$	−5.40332	+	9.35883i	−0.260875	+	0.451849i
$430$	−5.65353	−	17.3998i	−0.272637	−	0.839091i
$431$	−10.6160	−	4.72655i	−0.511355	−	0.227670i	0.134805	−	0.990872i	$-0.456959\pi$
$431$	−10.6160	−	4.72655i	−0.511355	−	0.227670i	−0.646160	+	0.763202i	$0.723626\pi$
$432$	5.20024	+	3.77820i	0.250197	+	0.181779i
$433$	−24.5964			−1.18203			−0.591015	−	0.806661i	$-0.701272\pi$
$433$	−24.5964			−1.18203			−0.591015	+	0.806661i	$0.701272\pi$
$434$		0			0
$435$	−16.3791			−0.785320
$436$	1.82156	+	1.32344i	0.0872368	+	0.0633813i
$437$	−11.3953	−	5.07353i	−0.545112	−	0.242700i
$438$	−1.08776	−	3.34779i	−0.0519753	−	0.159964i
$439$	−9.09662	+	15.7558i	−0.434158	+	0.751984i	−0.997227	−	0.0744265i	$-0.976287\pi$
$439$	−9.09662	+	15.7558i	−0.434158	+	0.751984i	0.563068	+	0.826410i	$0.309621\pi$
$440$	−18.5408	−	32.1136i	−0.883897	−	1.53096i
$441$	9.38520	−	10.4233i	0.446914	−	0.496349i
$442$	0.811240	−	2.49674i	0.0385868	−	0.118758i
$443$	11.8840	+	13.1985i	0.564625	+	0.627080i	0.956076	−	0.293119i	$-0.0946933\pi$
$443$	11.8840	+	13.1985i	0.564625	+	0.627080i	−0.391451	+	0.920199i	$0.628027\pi$
$444$	−13.0874	+	5.82687i	−0.621099	+	0.276531i
$445$	−16.0828	−	3.41851i	−0.762400	−	0.162053i
$446$	−0.679196	+	6.46212i	−0.0321609	+	0.305990i
$447$	1.89929	+	18.0706i	0.0898336	+	0.854709i
$448$	−0.938613	+	0.199508i	−0.0443453	+	0.00942588i
$449$	−7.44180	+	5.40679i	−0.351200	+	0.255162i	−0.749372	−	0.662149i	$-0.769645\pi$
$449$	−7.44180	+	5.40679i	−0.351200	+	0.255162i	0.398172	+	0.917311i	$0.369645\pi$
$450$	−10.6627	+	7.74688i	−0.502643	+	0.365192i
$451$	−3.04320	+	0.646852i	−0.143299	+	0.0304591i
$452$	1.01683	+	9.67449i	0.0478277	+	0.455050i
$453$	1.45003	−	13.7961i	0.0681284	−	0.648199i
$454$	14.6775	+	3.11981i	0.688851	+	0.146420i
$455$	7.52346	−	3.34966i	0.352705	−	0.157035i
$456$	−5.57547	−	6.19218i	−0.261095	−	0.289975i
$457$	9.64130	−	29.6729i	0.451001	−	1.38804i	−0.424766	−	0.905303i	$-0.639644\pi$
$457$	9.64130	−	29.6729i	0.451001	−	1.38804i	0.875767	−	0.482735i	$-0.160356\pi$
$458$	7.82278	−	8.68808i	0.365535	−	0.405967i
$459$	−3.06166	−	5.30294i	−0.142906	−	0.247520i
$460$	9.27842	−	16.0707i	0.432609	−	0.749300i
$461$	2.06067	+	6.34209i	0.0959750	+	0.295381i	0.987507	−	0.157578i	$-0.0503685\pi$
$461$	2.06067	+	6.34209i	0.0959750	+	0.295381i	−0.891532	+	0.452959i	$0.850369\pi$
$462$	−1.78584	−	0.795109i	−0.0830850	−	0.0369918i
$463$	28.5732	+	20.7597i	1.32791	+	0.964784i	0.999797	+	0.0201457i	$0.00641301\pi$
$463$	28.5732	+	20.7597i	1.32791	+	0.964784i	0.328114	+	0.944638i	$0.393587\pi$
$464$	−6.72466			−0.312184
$465$		0			0
$466$	6.78192			0.314167
$467$	−29.0789	−	21.1270i	−1.34561	−	0.977642i	−0.999218	−	0.0395520i	$-0.987407\pi$
$467$	−29.0789	−	21.1270i	−1.34561	−	0.977642i	−0.346391	−	0.938090i	$-0.612593\pi$
$468$	8.85782	+	3.94376i	0.409453	+	0.182300i
$469$	−0.492303	−	1.51515i	−0.0227324	−	0.0699632i
$470$	−1.11975	+	1.93946i	−0.0516501	+	0.0894606i
$471$	−6.83446	−	11.8376i	−0.314915	−	0.545449i
$472$	1.50784	−	1.67463i	0.0694042	−	0.0770811i
$473$	9.10211	−	28.0134i	0.418516	−	1.28806i
$474$	−5.86809	−	6.51717i	−0.269530	−	0.299344i
$475$	−30.3567	+	13.5157i	−1.39286	+	0.620142i
$476$	−1.48967	−	0.316640i	−0.0682790	−	0.0145131i
$477$	−0.816923	+	7.77251i	−0.0374043	+	0.355879i
$478$	−0.0425680	−	0.405008i	−0.00194702	−	0.0185246i
$479$	−32.5179	+	6.91190i	−1.48578	+	0.315813i	−0.878142	−	0.478400i	$-0.841217\pi$
$479$	−32.5179	+	6.91190i	−1.48578	+	0.315813i	−0.607640	+	0.794212i	$0.707884\pi$
$480$	15.7191	−	11.4206i	0.717474	−	0.521275i
$481$	−24.5121	+	17.8091i	−1.11765	+	0.812024i
$482$	−10.3662	+	2.20341i	−0.472168	+	0.100363i
$483$	−0.236400	−	2.24920i	−0.0107566	−	0.102342i
$484$	0.946360	−	9.00401i	0.0430163	−	0.409273i
$485$	19.1393	+	4.06819i	0.869073	+	0.184727i
$486$	−10.1695	+	4.52775i	−0.461297	+	0.205383i
$487$	−19.0805	−	21.1910i	−0.864620	−	0.960258i	0.134912	−	0.990858i	$-0.456925\pi$
$487$	−19.0805	−	21.1910i	−0.864620	−	0.960258i	−0.999532	+	0.0305999i	$0.990258\pi$
$488$	−1.74002	+	5.35524i	−0.0787672	+	0.242420i
$489$	−0.630917	+	0.700705i	−0.0285311	+	0.0316870i
$490$	−8.20220	−	14.2066i	−0.370538	−	0.641790i
$491$	−13.9818	+	24.2172i	−0.630991	+	1.09291i	0.356359	+	0.934349i	$0.384018\pi$
$491$	−13.9818	+	24.2172i	−0.630991	+	1.09291i	−0.987350	+	0.158559i	$0.949315\pi$
$492$	−0.321387	−	0.989128i	−0.0144892	−	0.0445933i
$493$	5.85222	+	2.60558i	0.263571	+	0.117349i
$494$	−6.16701	−	4.48059i	−0.277467	−	0.201591i
$495$	−33.3506			−1.49900
$496$		0			0
$497$	−5.90568			−0.264906
$498$	7.10139	+	5.15946i	0.318221	+	0.231201i
$499$	37.7340	+	16.8002i	1.68920	+	0.752082i	0.999611	+	0.0278849i	$0.00887720\pi$
$499$	37.7340	+	16.8002i	1.68920	+	0.752082i	0.689593	+	0.724197i	$0.257789\pi$
$500$	−6.54262	−	20.1361i	−0.292595	−	0.900514i
$501$	−5.09378	+	8.82269i	−0.227573	+	0.394169i
$502$	2.08623	+	3.61346i	0.0931132	+	0.161277i
$503$	−17.1204	+	19.0141i	−0.763361	+	0.847798i	−0.992069	−	0.125697i	$-0.959883\pi$
$503$	−17.1204	+	19.0141i	−0.763361	+	0.847798i	0.228708	+	0.973495i	$0.426550\pi$
$504$	−1.25301	+	3.85638i	−0.0558136	+	0.171777i
$505$	9.44552	+	10.4903i	0.420320	+	0.466813i
$506$	−8.51061	+	3.78917i	−0.378343	+	0.168449i
$507$	4.00150	+	0.850545i	0.177713	+	0.0377741i
$508$	0.228212	−	2.17129i	0.0101253	−	0.0963353i
$509$	−2.55758	−	24.3337i	−0.113363	−	1.07857i	−0.892291	−	0.451461i	$-0.850903\pi$
$509$	−2.55758	−	24.3337i	−0.113363	−	1.07857i	0.778928	−	0.627113i	$-0.215764\pi$
$510$	−2.95256	+	0.627585i	−0.130741	+	0.0277900i
$511$	−3.49405	+	2.53858i	−0.154568	+	0.112300i
$512$	11.8548	−	8.61304i	0.523915	−	0.380646i
$513$	−17.3916	+	3.69670i	−0.767859	+	0.163213i
$514$	−0.326329	−	3.10481i	−0.0143937	−	0.136947i
$515$	2.42046	−	23.0292i	0.106658	−	1.01479i
$516$	9.63128	+	2.04719i	0.423994	+	0.0901226i
$517$	−3.29384	+	1.46651i	−0.144863	+	0.0644972i
$518$	−3.66738	−	4.07304i	−0.161135	−	0.178959i
$519$	−5.75915	+	17.7248i	−0.252799	+	0.778034i
$520$	17.5424	−	19.4828i	0.769286	−	0.854378i
$521$	−7.48279	−	12.9606i	−0.327827	−	0.567813i	0.654253	−	0.756275i	$-0.272983\pi$
$521$	−7.48279	−	12.9606i	−0.327827	−	0.567813i	−0.982080	+	0.188462i	$0.939650\pi$
$522$	3.68887	−	6.38931i	0.161458	−	0.279653i
$523$	6.47873	+	19.9395i	0.283295	+	0.871893i	0.986904	+	0.161306i	$0.0515706\pi$
$523$	6.47873	+	19.9395i	0.283295	+	0.871893i	−0.703609	+	0.710587i	$0.748429\pi$
$524$	−8.76470	−	3.90229i	−0.382887	−	0.170472i
$525$	−4.87415	−	3.54128i	−0.212726	−	0.154554i
$526$	−1.72984			−0.0754247
$527$		0			0
$528$	5.10148			0.222014
$529$	9.88796	+	7.18402i	0.429911	+	0.312349i
$530$	8.35035	+	3.71781i	0.362716	+	0.161492i
$531$	−0.626287	−	1.92751i	−0.0271786	−	0.0836470i
$532$	−2.21109	+	3.82971i	−0.0958628	+	0.166039i
$533$	−1.09981	−	1.90492i	−0.0476379	−	0.0825113i
$534$	−1.84636	+	2.05059i	−0.0798996	+	0.0887375i
$535$	2.66645	−	8.20649i	0.115281	−	0.354798i
$536$	−3.39353	−	3.76890i	−0.146578	−	0.162791i
$537$	0.108540	−	0.0483253i	0.00468386	−	0.00208539i
$538$	−8.99669	−	1.91230i	−0.387875	−	0.0824453i
$539$	2.76069	−	26.2662i	0.118911	−	1.13137i
$540$	−2.76489	−	26.3062i	−0.118982	−	1.13204i
$541$	−1.69347	+	0.359958i	−0.0728079	+	0.0154758i	−0.244172	−	0.969732i	$-0.578516\pi$
$541$	−1.69347	+	0.359958i	−0.0728079	+	0.0154758i	0.171364	+	0.985208i	$0.445183\pi$
$542$	−7.71128	+	5.60257i	−0.331228	+	0.240651i
$543$	5.64480	−	4.10118i	0.242241	−	0.175999i
$544$	−7.43314	+	1.57996i	−0.318693	+	0.0677404i
$545$	−0.572331	−	5.44536i	−0.0245160	−	0.233254i
$546$	0.144467	−	1.37451i	0.00618261	−	0.0588236i
$547$	12.8347	+	2.72810i	0.548772	+	0.116645i	0.473950	−	0.880552i	$-0.342828\pi$
$547$	12.8347	+	2.72810i	0.548772	+	0.116645i	0.0748220	+	0.997197i	$0.476161\pi$
$548$	17.7580	−	7.90635i	0.758582	−	0.337743i
$549$	3.38867	+	3.76350i	0.144625	+	0.160622i
$550$	−7.66904	+	23.6029i	−0.327009	+	1.00643i
$551$	12.4466	−	13.8234i	0.530243	−	0.588895i
$552$	−3.59977	−	6.23498i	−0.153216	−	0.265378i
$553$	−5.37991	+	9.31828i	−0.228777	+	0.396254i
$554$	2.46532	+	7.58748i	0.104741	+	0.322361i
$555$	31.8258	+	14.1698i	1.35093	+	0.601473i
$556$	−23.0820	−	16.7701i	−0.978897	−	0.711210i
$557$	28.0246			1.18744			0.593721	−	0.804671i	$-0.297658\pi$
$557$	28.0246			1.18744			0.593721	+	0.804671i	$0.297658\pi$
$558$		0			0
$559$	20.8248			0.880794
$560$	−3.14522	−	2.28514i	−0.132910	−	0.0965646i
$561$	−4.43963	−	1.97665i	−0.187441	−	0.0834543i
$562$	3.28106	+	10.0981i	0.138403	+	0.425961i
$563$	−11.3259	+	19.6171i	−0.477331	+	0.826762i	−0.999662	−	0.0259808i	$-0.991729\pi$
$563$	−11.3259	+	19.6171i	−0.477331	+	0.826762i	0.522331	+	0.852743i	$0.325062\pi$
$564$	−0.602646	−	1.04381i	−0.0253760	−	0.0439525i
$565$	15.8289	−	17.5798i	0.665928	−	0.739589i
$566$	4.83566	−	14.8826i	0.203258	−	0.625564i
$567$	1.19232	+	1.32421i	0.0500729	+	0.0556116i
$568$	−17.1748	+	7.64670i	−0.720637	+	0.320848i
$569$	−45.4271	−	9.65584i	−1.90441	−	0.404794i	−0.904634	−	0.426189i	$-0.859856\pi$
$569$	−45.4271	−	9.65584i	−1.90441	−	0.404794i	−0.999771	+	0.0213953i	$0.993189\pi$
$570$	−0.916174	+	8.71682i	−0.0383743	+	0.365107i
$571$	−1.30643	−	12.4299i	−0.0546726	−	0.520175i	−0.987247	−	0.159197i	$-0.949110\pi$
$571$	−1.30643	−	12.4299i	−0.0546726	−	0.520175i	0.932574	−	0.360978i	$-0.117557\pi$
$572$	17.8588	−	3.79600i	0.746713	−	0.158719i
$573$	15.4062	−	11.1932i	0.643602	−	0.467604i
$574$	0.321904	−	0.233877i	0.0134360	−	0.00976184i
$575$	−28.0843	+	5.96950i	−1.17120	+	0.248945i
$576$	0.287179	+	2.73233i	0.0119658	+	0.113847i
$577$	3.18648	−	30.3173i	0.132655	−	1.26213i	−0.702330	−	0.711852i	$-0.747857\pi$
$577$	3.18648	−	30.3173i	0.132655	−	1.26213i	0.834984	−	0.550274i	$-0.185477\pi$
$578$	−10.3105	−	2.19156i	−0.428859	−	0.0911567i
$579$	4.66868	−	2.07863i	0.194024	−	0.0863850i
$580$	18.5165	+	20.5646i	0.768855	+	0.853900i
$581$	3.32803	−	10.2426i	0.138070	−	0.424936i
$582$	2.19725	−	2.44030i	0.0910790	−	0.101153i
$583$	7.35812	+	12.7446i	0.304742	+	0.527829i
$584$	−6.87436	+	11.9067i	−0.284463	+	0.492705i
$585$	−7.28629	−	22.4249i	−0.301251	−	0.927155i
$586$	−7.81109	−	3.47772i	−0.322673	−	0.143663i
$587$	27.2300	+	19.7837i	1.12390	+	0.816562i	0.984796	−	0.173716i	$-0.0555774\pi$
$587$	27.2300	+	19.7837i	1.12390	+	0.816562i	0.139105	+	0.990278i	$0.455577\pi$
$588$	8.82883			0.364095
$589$		0			0
$590$	−2.37039			−0.0975872
$591$	11.6187	+	8.44150i	0.477930	+	0.347237i
$592$	13.0665	+	5.81757i	0.537029	+	0.239101i
$593$	−13.8711	−	42.6909i	−0.569619	−	1.75311i	−0.653812	−	0.756657i	$-0.726831\pi$
$593$	−13.8711	−	42.6909i	−0.569619	−	1.75311i	0.0841933	−	0.996449i	$-0.473169\pi$
$594$	−6.63957	+	11.5001i	−0.272425	+	0.471854i
$595$	1.85175	+	3.20733i	0.0759145	+	0.131488i
$596$	20.5412	−	22.8133i	0.841399	−	0.934468i
$597$	1.18834	−	3.65733i	0.0486354	−	0.149684i
$598$	−4.40719	−	4.89468i	−0.180223	−	0.200158i
$599$	−17.8914	+	7.96578i	−0.731024	+	0.325473i	−0.738274	−	0.674501i	$-0.764359\pi$
$599$	−17.8914	+	7.96578i	−0.731024	+	0.325473i	0.00724987	+	0.999974i	$0.497692\pi$
$600$	−18.7602	−	3.98760i	−0.765881	−	0.162793i
$601$	3.18388	−	30.2926i	0.129873	−	1.23566i	−0.714396	−	0.699742i	$-0.753298\pi$
$601$	3.18388	−	30.2926i	0.129873	−	1.23566i	0.844269	−	0.535919i	$-0.180035\pi$
$602$	0.393765	+	3.74642i	0.0160487	+	0.152693i
$603$	−4.46160	+	0.948342i	−0.181690	+	0.0386195i
$604$	−18.9608	+	13.7758i	−0.771504	+	0.560531i
$605$	−17.8117	+	12.9410i	−0.724150	+	0.526126i
$606$	2.31721	−	0.492538i	0.0941302	−	0.0200080i
$607$	1.39802	+	13.3013i	0.0567440	+	0.539883i	0.985558	+	0.169337i	$0.0541627\pi$
$607$	1.39802	+	13.3013i	0.0567440	+	0.539883i	−0.928814	+	0.370546i	$0.879171\pi$
$608$	−2.30649	+	21.9448i	−0.0935406	+	0.889980i
$609$	3.29884	+	0.701190i	0.133676	+	0.0284137i
$610$	5.41099	−	2.40913i	0.219084	−	0.0975427i
$611$	−1.70570	−	1.89438i	−0.0690054	−	0.0766383i
$612$	−1.34743	+	4.14695i	−0.0544665	+	0.167631i
$613$	3.47627	−	3.86079i	0.140405	−	0.155936i	−0.668841	−	0.743406i	$-0.733209\pi$
$613$	3.47627	−	3.86079i	0.140405	−	0.155936i	0.809246	+	0.587470i	$0.199876\pi$
$614$	10.5906	+	18.3435i	0.427402	+	0.740282i
$615$	−1.26457	+	2.19030i	−0.0509924	+	0.0883215i
$616$	2.35942	+	7.26156i	0.0950639	+	0.292577i
$617$	−27.4183	−	12.2074i	−1.10382	−	0.491452i	−0.227790	−	0.973710i	$-0.573150\pi$
$617$	−27.4183	−	12.2074i	−1.10382	−	0.491452i	−0.876029	+	0.482258i	$0.839817\pi$
$618$	−3.14389	−	2.28417i	−0.126466	−	0.0918828i
$619$	−18.3260			−0.736584			−0.368292	−	0.929710i	$-0.620057\pi$
$619$	−18.3260			−0.736584			−0.368292	+	0.929710i	$0.620057\pi$
$620$		0			0
$621$	−15.3628			−0.616487
$622$	1.32838	+	0.965124i	0.0532631	+	0.0386979i
$623$	3.09282	+	1.37701i	0.123911	+	0.0551687i
$624$	1.11455	+	3.43023i	0.0446177	+	0.137319i
$625$	−3.87924	+	6.71905i	−0.155170	+	0.268762i
$626$	−3.70450	−	6.41639i	−0.148062	−	0.256450i
$627$	−9.44229	+	10.4867i	−0.377089	+	0.418799i
$628$	−7.13629	+	21.9632i	−0.284769	+	0.876429i
$629$	−9.11716	−	10.1256i	−0.363525	−	0.403735i
$630$	3.89652	−	1.73484i	0.155241	−	0.0691178i
$631$	10.1094	+	2.14881i	0.402447	+	0.0855428i	0.404688	−	0.914455i	$-0.367380\pi$
$631$	10.1094	+	2.14881i	0.402447	+	0.0855428i	−0.00224100	+	0.999997i	$0.500713\pi$
$632$	−3.58039	+	34.0651i	−0.142420	+	1.35504i
$633$	1.08554	+	10.3282i	0.0431462	+	0.410509i
$634$	5.89876	−	1.25382i	0.234270	−	0.0497956i
$635$	−4.29525	+	3.12068i	−0.170452	+	0.123840i
$636$	−3.97992	+	2.89158i	−0.157814	+	0.114659i
$637$	18.2645	−	3.88224i	0.723666	−	0.153820i
$638$	−1.45214	−	13.8162i	−0.0574908	−	0.546988i
$639$	−1.76742	+	16.8159i	−0.0699182	+	0.665228i
$640$	−38.9785	−	8.28513i	−1.54076	−	0.327498i
$641$	−0.0924983	+	0.0411829i	−0.00365346	+	0.00162663i	−0.408563	−	0.912730i	$-0.633970\pi$
$641$	−0.0924983	+	0.0411829i	−0.00365346	+	0.00162663i	0.404909	+	0.914357i	$0.367303\pi$
$642$	−0.968965	−	1.07615i	−0.0382420	−	0.0424721i
$643$	4.23719	−	13.0407i	0.167098	−	0.514276i	−0.832086	−	0.554646i	$-0.812854\pi$
$643$	4.23719	−	13.0407i	0.167098	−	0.514276i	0.999185	+	0.0403701i	$0.0128537\pi$
$644$	−2.55671	+	2.83951i	−0.100748	+	0.111892i
$645$	−11.9723	−	20.7366i	−0.471408	−	0.816503i
$646$	1.71401	−	2.96875i	0.0674367	−	0.116804i
$647$	3.34800	+	10.3041i	0.131624	+	0.405096i	0.995050	−	0.0993798i	$-0.0316859\pi$
$647$	3.34800	+	10.3041i	0.131624	+	0.405096i	−0.863426	+	0.504476i	$0.831686\pi$
$648$	5.18208	+	2.30721i	0.203572	+	0.0906359i
$649$	−3.08745	−	2.24316i	−0.121193	−	0.0880518i
$650$	−17.5460			−0.688212
$651$		0			0
$652$	1.59301			0.0623870
$653$	19.6204	+	14.2551i	0.767807	+	0.557844i	0.901295	−	0.433206i	$-0.142618\pi$
$653$	19.6204	+	14.2551i	0.767807	+	0.557844i	−0.133488	+	0.991050i	$0.542618\pi$
$654$	−0.839439	−	0.373742i	−0.0328246	−	0.0146145i
$655$	7.20968	+	22.1891i	0.281706	+	0.867001i
$656$	−0.519185	+	0.899255i	−0.0202708	+	0.0351100i
$657$	6.18270	+	10.7087i	0.241210	+	0.417788i
$658$	0.308551	−	0.342680i	0.0120286	−	0.0133591i
$659$	−2.63699	+	8.11583i	−0.102723	+	0.316148i	−0.989189	−	0.146645i	$-0.953153\pi$
$659$	−2.63699	+	8.11583i	−0.102723	+	0.316148i	0.886467	+	0.462793i	$0.153153\pi$
$660$	−14.0470	−	15.6008i	−0.546780	−	0.607261i
$661$	34.6089	−	15.4089i	1.34613	−	0.599337i	0.398050	−	0.917364i	$-0.369687\pi$
$661$	34.6089	−	15.4089i	1.34613	−	0.599337i	0.948082	+	0.318027i	$0.103020\pi$
$662$	21.8306	+	4.64023i	0.848469	+	0.180348i
$663$	0.359146	−	3.41705i	0.0139481	−	0.132707i
$664$	−3.58369	−	34.0966i	−0.139074	−	1.32320i
$665$	10.5188	−	2.23585i	0.407903	−	0.0867024i
$666$	−12.6952	+	9.22360i	−0.491929	+	0.357407i
$667$	13.0026	−	9.44697i	0.503464	−	0.365788i
$668$	16.8357	−	3.57854i	0.651393	−	0.138458i
$669$	0.888925	+	8.45756i	0.0343678	+	0.326988i
$670$	−0.557633	+	5.30552i	−0.0215432	+	0.204970i
$671$	9.32767	+	1.98266i	0.360091	+	0.0765397i
$672$	−3.65481	+	1.62723i	−0.140987	+	0.0627716i
$673$	−4.76428	−	5.29127i	−0.183650	−	0.203963i	0.644289	−	0.764782i	$-0.277153\pi$
$673$	−4.76428	−	5.29127i	−0.183650	−	0.203963i	−0.827939	+	0.560818i	$0.810487\pi$
$674$	5.90910	−	18.1863i	0.227610	−	0.700512i
$675$	−27.3848	+	30.4139i	−1.05404	+	1.17063i
$676$	−3.45577	−	5.98557i	−0.132914	−	0.230214i
$677$	24.0305	−	41.6220i	0.923567	−	1.59966i	0.129716	−	0.991551i	$-0.458593\pi$
$677$	24.0305	−	41.6220i	0.923567	−	1.59966i	0.793850	−	0.608113i	$-0.208073\pi$
$678$	−1.22679	−	3.77566i	−0.0471145	−	0.145004i
$679$	−3.68060	−	1.63871i	−0.141248	−	0.0628879i
$680$	9.53810	+	6.92984i	0.365769	+	0.265747i
$681$	19.6390			0.752567
$682$		0			0
$683$	32.5731			1.24638			0.623188	−	0.782072i	$-0.285837\pi$
$683$	32.5731			1.24638			0.623188	+	0.782072i	$0.285837\pi$
$684$	10.2431	+	7.44202i	0.391653	+	0.284553i
$685$	−43.1837	−	19.2266i	−1.64997	−	0.734612i
$686$	2.18235	+	6.71657i	0.0833224	+	0.256440i
$687$	7.65051	−	13.2511i	0.291885	−	0.505560i
$688$	−4.91537	−	8.51366i	−0.187397	−	0.324580i
$689$	−6.96191	+	7.73198i	−0.265228	+	0.294565i
$690$	−2.34024	+	7.20251i	−0.0890913	+	0.274195i
$691$	18.2359	+	20.2530i	0.693725	+	0.770460i	0.982364	−	0.186978i	$-0.0598693\pi$
$691$	18.2359	+	20.2530i	0.693725	+	0.770460i	−0.288639	+	0.957438i	$0.593203\pi$
$692$	28.7649	−	12.8069i	1.09348	−	0.486847i
$693$	6.71698	+	1.42774i	0.255157	+	0.0542353i
$694$	1.86781	−	17.7710i	0.0709012	−	0.674580i
$695$	7.25234	+	69.0014i	0.275097	+	2.61737i
$696$	10.5015	−	2.23217i	0.398059	−	0.0846101i
$697$	0.800258	−	0.581421i	0.0303119	−	0.0220229i
$698$	3.12036	−	2.26707i	0.118107	−	0.0858100i
$699$	8.68215	−	1.84545i	0.328389	−	0.0698012i
$700$	1.06398	+	10.1231i	0.0402146	+	0.382616i
$701$	−0.887358	+	8.44265i	−0.0335150	+	0.318874i	0.964901	+	0.262614i	$0.0845845\pi$
$701$	−0.887358	+	8.44265i	−0.0335150	+	0.318874i	−0.998416	+	0.0562607i	$0.982082\pi$
$702$	−9.18321	−	1.95195i	−0.346598	−	0.0736717i
$703$	−36.1433	+	16.0920i	−1.36317	+	0.606923i
$704$	3.46162	+	3.84452i	0.130465	+	0.144896i
$705$	−0.905737	+	2.78757i	−0.0341120	+	0.104986i
$706$	5.38361	−	5.97910i	0.202615	−	0.225026i
$707$	−1.45328	−	2.51716i	−0.0546564	−	0.0946676i
$708$	0.637869	−	1.10482i	0.0239726	−	0.0415217i
$709$	7.22670	+	22.2415i	0.271404	+	0.835297i	0.990148	+	0.140022i	$0.0447174\pi$
$709$	7.22670	+	22.2415i	0.271404	+	0.835297i	−0.718744	+	0.695275i	$0.755283\pi$
$710$	18.0661	+	8.04354i	0.678008	+	0.301869i
$711$	24.9229	+	18.1076i	0.934683	+	0.679087i
$712$	10.7774			0.403901
$713$		0			0
$714$	0.621526			0.0232600
$715$	−35.9197	−	26.0972i	−1.34332	−	0.975978i
$716$	−0.183378	−	0.0816452i	−0.00685317	−	0.00305123i
$717$	−0.164703	−	0.506903i	−0.00615094	−	0.0189306i
$718$	9.03230	−	15.6444i	0.337083	−	0.583844i
$719$	6.48843	+	11.2383i	0.241978	+	0.419118i	0.961278	−	0.275582i	$-0.0888706\pi$
$719$	6.48843	+	11.2383i	0.241978	+	0.419118i	−0.719300	+	0.694700i	$0.755537\pi$
$720$	−7.44802	+	8.27186i	−0.277571	+	0.308274i
$721$	−1.47337	+	4.53457i	−0.0548712	+	0.168876i
$722$	2.10541	+	2.33830i	0.0783553	+	0.0870224i
$723$	−12.6712	+	5.64156i	−0.471245	+	0.209812i
$724$	−11.5306	−	2.45090i	−0.428531	−	0.0910870i
$725$	4.47545	−	42.5811i	0.166214	−	1.58142i
$726$	0.386215	+	3.67459i	0.0143338	+	0.136377i
$727$	12.1515	−	2.58289i	0.450676	−	0.0957941i	0.0230186	−	0.999735i	$-0.492672\pi$
$727$	12.1515	−	2.58289i	0.450676	−	0.0957941i	0.427657	+	0.903941i	$0.359339\pi$
$728$	−4.36719	+	3.17295i	−0.161859	+	0.117597i
$729$	−6.12163	+	4.44762i	−0.226727	+	0.164727i
$730$	14.1462	−	3.00687i	0.523575	−	0.111289i
$731$	0.978905	+	9.31366i	0.0362061	+	0.344478i
$732$	−0.333214	+	3.17032i	−0.0123159	+	0.117178i
$733$	33.4109	+	7.10171i	1.23406	+	0.262308i	0.778356	−	0.627823i	$-0.216054\pi$
$733$	33.4109	+	7.10171i	1.23406	+	0.262308i	0.455705	+	0.890131i	$0.349387\pi$
$734$	17.0160	−	7.57603i	0.628074	−	0.279636i
$735$	−14.3662	−	15.9553i	−0.529904	−	0.588518i
$736$	−5.89161	+	18.1325i	−0.217168	+	0.668373i
$737$	−5.74708	+	6.38278i	−0.211697	+	0.235113i
$738$	−0.569607	−	0.986589i	−0.0209675	−	0.0363168i
$739$	−6.18747	+	10.7170i	−0.227610	+	0.394231i	−0.957099	−	0.289761i	$-0.906424\pi$
$739$	−6.18747	+	10.7170i	−0.227610	+	0.394231i	0.729490	+	0.683992i	$0.239758\pi$
$740$	−18.1881	−	55.9773i	−0.668609	−	2.05777i
$741$	−9.11416	−	4.05789i	−0.334817	−	0.149070i
$742$	−1.52264	−	1.10626i	−0.0558979	−	0.0406122i
$743$	16.2455			0.595990			0.297995	−	0.954567i	$-0.403682\pi$
$743$	16.2455			0.595990			0.297995	+	0.954567i	$0.403682\pi$
$744$		0			0
$745$	−74.6520			−2.73504
$746$	−6.92012	−	5.02776i	−0.253364	−	0.184080i
$747$	−28.1690	−	12.5417i	−1.03065	−	0.458875i
$748$	2.53720	+	7.80871i	0.0927694	+	0.285515i
$749$	−0.888356	+	1.53868i	−0.0324598	+	0.0562220i
$750$	4.32029	+	7.48296i	0.157755	+	0.273239i
$751$	−7.21876	+	8.01725i	−0.263416	+	0.292554i	−0.860315	−	0.509763i	$-0.829733\pi$
$751$	−7.21876	+	8.01725i	−0.263416	+	0.292554i	0.596898	+	0.802317i	$0.296400\pi$
$752$	−0.371861	+	1.14447i	−0.0135604	+	0.0417346i
$753$	3.65404	+	4.05823i	0.133161	+	0.147890i
$754$	8.97273	−	3.99492i	0.326767	−	0.145486i
$755$	55.7482	+	11.8496i	2.02888	+	0.431253i
$756$	−0.569303	+	5.41656i	−0.0207054	+	0.196998i
$757$	4.29629	+	40.8765i	0.156151	+	1.48568i	0.739333	+	0.673340i	$0.235141\pi$
$757$	4.29629	+	40.8765i	0.156151	+	1.48568i	−0.583181	+	0.812342i	$0.698192\pi$
$758$	−3.12867	+	0.665019i	−0.113638	+	0.0241546i
$759$	−9.86411	+	7.16670i	−0.358045	+	0.260135i
$760$	27.6956	−	20.1221i	1.00463	−	0.729904i
$761$	19.2309	−	4.08765i	0.697119	−	0.148177i	0.154296	−	0.988025i	$-0.450689\pi$
$761$	19.2309	−	4.08765i	0.697119	−	0.148177i	0.542823	+	0.839847i	$0.317356\pi$
$762$	0.0931346	+	0.886117i	0.00337391	+	0.0321006i
$763$	−0.117845	+	1.12122i	−0.00426629	+	0.0405911i
$764$	−31.4701	−	6.68917i	−1.13855	−	0.242006i
$765$	9.68679	−	4.31284i	0.350227	−	0.155931i
$766$	−2.31665	−	2.57290i	−0.0837038	−	0.0929625i
$767$	0.833766	−	2.56607i	0.0301056	−	0.0926554i
$768$	−5.99284	+	6.65573i	−0.216248	+	0.240168i
$769$	−1.89417	−	3.28080i	−0.0683055	−	0.118309i	0.829850	−	0.557986i	$-0.188426\pi$
$769$	−1.89417	−	3.28080i	−0.0683055	−	0.118309i	−0.898155	+	0.439678i	$0.855093\pi$
$770$	4.01575	−	6.95549i	0.144718	−	0.250658i
$771$	−1.26262	−	3.88595i	−0.0454722	−	0.139949i
$772$	−7.88770	−	3.51183i	−0.283885	−	0.126394i
$773$	−20.5244	−	14.9119i	−0.738212	−	0.536342i	0.153939	−	0.988080i	$-0.450804\pi$
$773$	−20.5244	−	14.9119i	−0.738212	−	0.536342i	−0.892151	+	0.451738i	$0.850804\pi$
$774$	10.7855			0.387676
$775$		0			0
$776$	−12.8256			−0.460414
$777$	−5.80327	−	4.21632i	−0.208191	−	0.151260i
$778$	11.7170	+	5.21674i	0.420074	+	0.187029i
$779$	−0.887573	−	2.73167i	−0.0318006	−	0.0978722i
$780$	7.42103	−	12.8536i	0.265716	−	0.460233i
$781$	15.9194	+	27.5732i	0.569641	+	0.986647i
$782$	1.98193	−	2.20115i	0.0708736	−	0.0787131i
$783$	7.07939	−	21.7881i	0.252997	−	0.778644i
$784$	−5.89821	−	6.55062i	−0.210650	−	0.233951i
$785$	51.3036	−	22.8418i	1.83110	−	0.815260i
$786$	3.82987	+	0.814065i	0.136607	+	0.0290367i
$787$	−2.71216	+	25.8045i	−0.0966780	+	0.919829i	0.833450	+	0.552594i	$0.186362\pi$
$787$	−2.71216	+	25.8045i	−0.0966780	+	0.919829i	−0.930128	+	0.367235i	$0.880305\pi$
$788$	−2.53625	−	24.1308i	−0.0903501	−	0.859623i
$789$	−2.21453	+	0.470712i	−0.0788392	+	0.0167578i
$790$	29.1492	−	21.1781i	1.03708	−	0.753484i
$791$	−3.94062	+	2.86303i	−0.140112	+	0.101797i
$792$	21.3828	−	4.54505i	0.759805	−	0.161501i
$793$	0.704732	+	6.70507i	0.0250258	+	0.238104i
$794$	2.34657	−	22.3261i	0.0832765	−	0.792323i
$795$	11.7017	+	2.48727i	0.415016	+	0.0882144i
$796$	−5.93532	+	2.64257i	−0.210372	+	0.0936635i
$797$	12.3807	+	13.7501i	0.438546	+	0.487054i	0.921383	−	0.388656i	$-0.127060\pi$
$797$	12.3807	+	13.7501i	0.438546	+	0.487054i	−0.482837	+	0.875710i	$0.660394\pi$
$798$	0.557688	−	1.71639i	0.0197419	−	0.0607595i
$799$	0.767061	−	0.851907i	0.0271367	−	0.0301383i
$800$	25.3951	+	43.9856i	0.897852	+	1.55513i
$801$	4.84652	−	8.39442i	0.171243	−	0.296602i
$802$	−2.63993	−	8.12488i	−0.0932192	−	0.286899i
$803$	21.2710	+	9.47047i	0.750638	+	0.334206i
$804$	−2.32281	−	1.68762i	−0.0819193	−	0.0595178i
$805$	9.29174			0.327491
$806$		0			0
$807$	−12.0378			−0.423751
$808$	−7.48564	−	5.43864i	−0.263344	−	0.191331i
$809$	−33.5708	−	14.9467i	−1.18029	−	0.525498i	−0.279664	−	0.960098i	$-0.590223\pi$
$809$	−33.5708	−	14.9467i	−1.18029	−	0.525498i	−0.900623	+	0.434600i	$0.856890\pi$
$810$	−1.84387	−	5.67484i	−0.0647869	−	0.199394i
$811$	19.7151	−	34.1475i	0.692289	−	1.19908i	−0.278797	−	0.960350i	$-0.589936\pi$
$811$	19.7151	−	34.1475i	0.692289	−	1.19908i	0.971086	−	0.238730i	$-0.0767310\pi$
$812$	−2.84894	−	4.93451i	−0.0999782	−	0.173167i
$813$	−8.34737	+	9.27069i	−0.292755	+	0.325137i
$814$	−9.13092	+	28.1021i	−0.320039	+	0.984977i
$815$	−2.59213	−	2.87885i	−0.0907982	−	0.100842i
$816$	−1.48174	+	0.659715i	−0.0518714	+	0.0230946i
$817$	26.5987	+	5.65372i	0.930570	+	0.197799i
$818$	0.248509	−	2.36440i	0.00868891	−	0.0826694i
$819$	0.507486	+	4.82841i	0.0177330	+	0.168718i
$820$	4.17959	−	0.888400i	0.145958	−	0.0310243i
$821$	1.19782	−	0.870264i	0.0418041	−	0.0303724i	−0.566687	−	0.823933i	$-0.691775\pi$
$821$	1.19782	−	0.870264i	0.0418041	−	0.0303724i	0.608491	+	0.793561i	$0.291775\pi$
$822$	−6.41791	+	4.66289i	−0.223850	+	0.162637i
$823$	−38.0159	+	8.08053i	−1.32515	+	0.281670i	−0.815523	−	0.578725i	$-0.803551\pi$
$823$	−38.0159	+	8.08053i	−1.32515	+	0.281670i	−0.509629	+	0.860394i	$0.670217\pi$
$824$	1.58655	+	15.0950i	0.0552702	+	0.525861i
$825$	−3.39518	+	32.3030i	−0.118205	+	1.12465i
$826$	0.477407	+	0.101476i	0.0166111	+	0.00353080i
$827$	−31.0023	+	13.8031i	−1.07806	+	0.479982i	−0.867417	−	0.497582i	$-0.834221\pi$
$827$	−31.0023	+	13.8031i	−1.07806	+	0.479982i	−0.210640	+	0.977564i	$0.567555\pi$
$828$	7.32010	+	8.12980i	0.254391	+	0.282530i
$829$	−5.10827	+	15.7216i	−0.177417	+	0.546035i	−0.999736	−	0.0229933i	$-0.992680\pi$
$829$	−5.10827	+	15.7216i	−0.177417	+	0.546035i	0.822318	+	0.569028i	$0.192680\pi$
$830$	−24.1313	+	26.8005i	−0.837609	+	0.930259i
$831$	5.22073	+	9.04256i	0.181105	+	0.313683i
$832$	−1.82877	+	3.16752i	−0.0634012	+	0.109814i
$833$	2.59485	+	7.98612i	0.0899061	+	0.276703i
$834$	10.6370	+	4.73591i	0.368330	+	0.163991i
$835$	−33.8619	−	24.6021i	−1.17184	−	0.851392i
$836$	23.8409			0.824555
$837$		0			0
$838$	27.6122			0.953848
$839$	43.7501	+	31.7863i	1.51042	+	1.09738i	0.965990	+	0.258579i	$0.0832542\pi$
$839$	43.7501	+	31.7863i	1.51042	+	1.09738i	0.544430	+	0.838806i	$0.316746\pi$
$840$	5.67023	+	2.52455i	0.195642	+	0.0871053i
$841$	−1.55522	−	4.78647i	−0.0536282	−	0.165051i
$842$	7.47562	−	12.9482i	0.257627	−	0.446223i
$843$	6.94819	+	12.0346i	0.239308	+	0.414494i
$844$	11.7402	−	13.0389i	0.404116	−	0.448816i
$845$	−5.19379	+	15.9848i	−0.178672	+	0.549896i
$846$	−0.883411	−	0.981127i	−0.0303723	−	0.0337319i
$847$	4.14138	−	1.84386i	0.142299	−	0.0633558i
$848$	4.80427	+	1.02118i	0.164979	+	0.0350674i
$849$	2.14081	−	20.3684i	0.0734724	−	0.699043i
$850$	−0.824782	−	7.84728i	−0.0282898	−	0.269160i
$851$	−33.4377	+	7.10741i	−1.14623	+	0.243639i
$852$	−8.61062	+	6.25598i	−0.294995	+	0.214326i
$853$	−32.0178	+	23.2623i	−1.09627	+	0.796487i	−0.980447	−	0.196783i	$-0.936950\pi$
$853$	−32.0178	+	23.2623i	−1.09627	+	0.796487i	−0.115823	+	0.993270i	$0.536950\pi$
$854$	−1.19293	+	0.253566i	−0.0408213	+	0.00867684i
$855$	−3.21836	−	30.6206i	−0.110065	−	1.04720i
$856$	−0.591211	+	5.62499i	−0.0202072	+	0.192258i
$857$	−12.4470	−	2.64569i	−0.425180	−	0.0903749i	−0.00964843	−	0.999953i	$-0.503071\pi$
$857$	−12.4470	−	2.64569i	−0.425180	−	0.0903749i	−0.415532	+	0.909579i	$0.636405\pi$
$858$	−6.80692	+	3.03064i	−0.232384	+	0.103464i
$859$	14.1550	+	15.7207i	0.482963	+	0.536385i	0.934545	−	0.355845i	$-0.115807\pi$
$859$	14.1550	+	15.7207i	0.482963	+	0.536385i	−0.451582	+	0.892230i	$0.649140\pi$
$860$	−12.5010	+	38.4742i	−0.426281	+	1.31196i
$861$	0.348457	−	0.387001i	0.0118754	−	0.0131890i
$862$	−4.00618	−	6.93891i	−0.136451	−	0.236340i
$863$	4.66987	−	8.08845i	0.158964	−	0.275334i	−0.775531	−	0.631309i	$-0.782518\pi$
$863$	4.66987	−	8.08845i	0.158964	−	0.275334i	0.934495	+	0.355975i	$0.115851\pi$
$864$	8.39795	+	25.8462i	0.285704	+	0.879307i
$865$	−69.9503	−	31.1439i	−2.37838	−	1.05892i
$866$	−13.7202	−	9.96829i	−0.466230	−	0.338736i
$867$	−13.7957			−0.468526
$868$		0			0
$869$	58.0085			1.96780
$870$	−9.13647	−	6.63804i	−0.309755	−	0.225051i
$871$	−5.54737	−	2.46985i	−0.187965	−	0.0836876i
$872$	1.10905	+	3.41331i	0.0375572	+	0.115589i
$873$	−5.76760	+	9.98977i	−0.195204	+	0.338102i
$874$	−4.30028	−	7.44830i	−0.145459	−	0.251942i
$875$	7.09370	−	7.87836i	0.239811	−	0.266337i
$876$	−2.40525	+	7.40260i	−0.0812659	+	0.250111i
$877$	15.0121	+	16.6726i	0.506923	+	0.562995i	0.941228	−	0.337771i	$-0.109673\pi$
$877$	15.0121	+	16.6726i	0.506923	+	0.562995i	−0.434305	+	0.900766i	$0.643006\pi$
$878$	−11.4596	+	5.10215i	−0.386743	+	0.172189i
$879$	−10.9460	−	2.32665i	−0.369200	−	0.0784758i
$880$	−2.19086	+	20.8446i	−0.0738539	+	0.702673i
$881$	−4.85341	−	46.1771i	−0.163516	−	1.55575i	−0.701425	−	0.712744i	$-0.747452\pi$
$881$	−4.85341	−	46.1771i	−0.163516	−	1.55575i	0.537909	−	0.843003i	$-0.319214\pi$
$882$	9.45947	−	2.01067i	0.318517	−	0.0677029i
$883$	29.5611	−	21.4774i	0.994811	−	0.722773i	0.0338419	−	0.999427i	$-0.489226\pi$
$883$	29.5611	−	21.4774i	0.994811	−	0.722773i	0.960969	+	0.276654i	$0.0892257\pi$
$884$	−4.69625	+	3.41202i	−0.157952	+	0.114759i
$885$	−3.03454	+	0.645012i	−0.102005	+	0.0216818i
$886$	1.28002	+	12.1785i	0.0430030	+	0.409146i
$887$	−2.99840	+	28.5279i	−0.100677	+	0.957873i	0.821266	+	0.570546i	$0.193268\pi$
$887$	−2.99840	+	28.5279i	−0.100677	+	0.957873i	−0.921942	+	0.387327i	$0.873398\pi$
$888$	−22.3362	−	4.74772i	−0.749555	−	0.159323i
$889$	0.998680	−	0.444641i	0.0334946	−	0.0149128i
$890$	−7.58576	−	8.42484i	−0.254275	−	0.282401i
$891$	2.96861	−	9.13643i	0.0994521	−	0.306082i
$892$	9.61386	−	10.6773i	0.321896	−	0.357502i
$893$	−1.66433	−	2.88270i	−0.0556945	−	0.0964658i
$894$	−6.26408	+	10.8497i	−0.209502	+	0.362869i
$895$	0.150844	+	0.464249i	0.00504215	+	0.0155181i
$896$	7.49577	+	3.33733i	0.250416	+	0.111492i
$897$	−6.97394	−	5.06687i	−0.232853	−	0.169178i
$898$	−6.34235			−0.211647
$899$		0			0
$900$	29.1430			0.971434
$901$	−3.78531	−	2.75019i	−0.126107	−	0.0916220i
$902$	−1.95968	−	0.872508i	−0.0652503	−	0.0290513i
$903$	1.52354	+	4.68898i	0.0507004	+	0.156040i
$904$	−7.75296	+	13.4285i	−0.257860	+	0.446626i
$905$	14.3332	+	24.8259i	0.476453	+	0.825240i
$906$	6.40005	−	7.10798i	0.212627	−	0.236147i
$907$	−6.85697	+	21.1036i	−0.227682	+	0.700733i	0.770326	+	0.637650i	$0.220093\pi$
$907$	−6.85697	+	21.1036i	−0.227682	+	0.700733i	−0.998008	+	0.0630831i	$0.979907\pi$
$908$	−22.2017	−	24.6575i	−0.736789	−	0.818287i
$909$	−7.60234	+	3.38478i	−0.252154	+	0.112266i
$910$	5.55420	+	1.18058i	0.184120	+	0.0391359i
$911$	−3.01381	+	28.6745i	−0.0998520	+	0.950028i	0.823822	+	0.566849i	$0.191838\pi$
$911$	−3.01381	+	28.6745i	−0.0998520	+	0.950028i	−0.923674	+	0.383179i	$0.874829\pi$
$912$	0.492297	+	4.68389i	0.0163016	+	0.155099i
$913$	−56.7932	+	12.0718i	−1.87958	+	0.399517i
$914$	17.4037	−	12.6445i	0.575662	−	0.418243i
$915$	6.27153	−	4.55653i	0.207330	−	0.150634i
$916$	−25.2860	+	5.37471i	−0.835474	+	0.177586i
$917$	−0.502151	−	4.77764i	−0.0165825	−	0.157772i
$918$	0.441317	−	4.19885i	0.0145656	−	0.138583i
$919$	−47.0121	−	9.99272i	−1.55078	−	0.329629i	−0.648651	−	0.761086i	$-0.724667\pi$
$919$	−47.0121	−	9.99272i	−1.55078	−	0.329629i	−0.902134	+	0.431456i	$0.858000\pi$
$920$	27.0220	−	12.0310i	0.890890	−	0.396650i
$921$	18.5495	+	20.6013i	0.611226	+	0.678835i
$922$	−1.42082	+	4.37283i	−0.0467921	+	0.144011i
$923$	−15.0622	+	16.7282i	−0.495778	+	0.550617i
$924$	2.16127	+	3.74343i	0.0711007	+	0.123150i
$925$	−45.5334	+	78.8662i	−1.49713	+	2.59310i
$926$	7.52513	+	23.1600i	0.247291	+	0.761084i
$927$	12.4708	+	5.55238i	0.409596	+	0.182364i
$928$	−23.0013	−	16.7114i	−0.755055	−	0.548580i
$929$	−7.01617			−0.230193			−0.115097	−	0.993354i	$-0.536718\pi$
$929$	−7.01617			−0.230193			−0.115097	+	0.993354i	$0.536718\pi$
$930$		0			0
$931$	24.3825			0.799105
$932$	−12.1321	−	8.81450i	−0.397401	−	0.288729i
$933$	1.96320	+	0.874072i	0.0642722	+	0.0286158i
$934$	−7.65829	−	23.5698i	−0.250587	−	0.771227i
$935$	9.98321	−	17.2914i	0.326486	−	0.565490i
$936$	7.72770	+	13.3848i	0.252588	+	0.437495i
$937$	−8.61884	+	9.57219i	−0.281565	+	0.312710i	−0.867293	−	0.497798i	$-0.834142\pi$
$937$	−8.61884	+	9.57219i	−0.281565	+	0.312710i	0.585728	+	0.810508i	$0.300809\pi$
$938$	0.339439	−	1.04469i	0.0110831	−	0.0341102i
$939$	−6.48845	−	7.20615i	−0.211742	−	0.235164i
$940$	4.52383	−	2.01414i	0.147551	−	0.0656940i
$941$	−48.9458	−	10.4037i	−1.59559	−	0.339152i	−0.677497	−	0.735526i	$-0.736935\pi$
$941$	−48.9458	−	10.4037i	−1.59559	−	0.339152i	−0.918089	+	0.396373i	$0.870269\pi$
$942$	0.985141	−	9.37299i	0.0320976	−	0.305388i
$943$	−0.259412	−	2.46814i	−0.00844763	−	0.0803738i
$944$	−1.24587	+	0.264817i	−0.0405496	+	0.00861907i
$945$	10.7150	−	7.78494i	0.348560	−	0.253244i
$946$	16.4304	−	11.9374i	0.534197	−	0.388117i
$947$	50.7345	−	10.7840i	1.64865	−	0.350431i	0.712402	−	0.701772i	$-0.247607\pi$
$947$	50.7345	−	10.7840i	1.64865	−	0.350431i	0.936248	+	0.351340i	$0.114274\pi$
$948$	2.02697	+	19.2853i	0.0658328	+	0.626357i
$949$	−1.72073	+	16.3717i	−0.0558573	+	0.531447i
$950$	−22.4109	−	4.76358i	−0.727105	−	0.154551i
$951$	7.21035	−	3.21026i	0.233812	−	0.104100i
$952$	−1.62435	−	1.80403i	−0.0526456	−	0.0584689i
$953$	−5.78950	+	17.8183i	−0.187540	+	0.577190i	−0.999983	−	0.00585146i	$-0.998137\pi$
$953$	−5.78950	+	17.8183i	−0.187540	+	0.577190i	0.812443	+	0.583041i	$0.198137\pi$
$954$	−3.60568	+	4.00451i	−0.116738	+	0.129651i
$955$	39.1193	+	67.7565i	1.26587	+	2.19255i
$956$	−0.450241	+	0.779840i	−0.0145618	+	0.0252218i
$957$	−5.61857	−	17.2922i	−0.181623	−	0.558977i
$958$	−20.9401	−	9.32313i	−0.676543	−	0.301217i
$959$	7.87432	+	5.72103i	0.254275	+	0.184742i
$960$	4.20549			0.135731
$961$		0			0
$962$	−20.8907			−0.673542
$963$	4.11539	+	2.99001i	0.132617	+	0.0963516i
$964$	21.4078	+	9.53138i	0.689499	+	0.306985i
$965$	6.48829	+	19.9689i	0.208865	+	0.642821i
$966$	0.779674	−	1.35044i	0.0250856	−	0.0434496i
$967$	−23.8923	−	41.3827i	−0.768324	−	1.33078i	−0.938471	−	0.345358i	$-0.887757\pi$
$967$	−23.8923	−	41.3827i	−0.768324	−	1.33078i	0.170146	−	0.985419i	$-0.445576\pi$
$968$	9.65642	−	10.7245i	0.310369	−	0.344700i
$969$	1.38642	−	4.26696i	0.0445382	−	0.137075i
$970$	9.02741	+	10.0260i	0.289853	+	0.321914i
$971$	−28.4119	+	12.6498i	−0.911780	+	0.405951i	−0.808361	−	0.588687i	$-0.799645\pi$
$971$	−28.4119	+	12.6498i	−0.911780	+	0.405951i	−0.103419	+	0.994638i	$0.532978\pi$
$972$	24.0768	+	5.11769i	0.772265	+	0.164150i
$973$	1.49329	−	14.2077i	0.0478727	−	0.455478i
$974$	−2.05515	−	19.5534i	−0.0658512	−	0.626532i
$975$	−22.4622	+	4.77450i	−0.719368	+	0.152906i
$976$	2.57485	−	1.87074i	0.0824191	−	0.0598810i
$977$	17.8624	−	12.9778i	0.571469	−	0.415197i	−0.264170	−	0.964476i	$-0.585098\pi$
$977$	17.8624	−	12.9778i	0.571469	−	0.415197i	0.835639	+	0.549280i	$0.185098\pi$
$978$	−0.635910	+	0.135167i	−0.0203342	+	0.00432216i
$979$	−1.90785	−	18.1520i	−0.0609753	−	0.580141i
$980$	−3.79159	+	36.0745i	−0.121118	+	1.15236i
$981$	3.15732	+	0.671110i	0.100806	+	0.0214269i
$982$	−17.6138	+	7.84218i	−0.562080	+	0.250254i
$983$	25.1438	+	27.9251i	0.801964	+	0.890671i	0.995911	−	0.0903411i	$-0.0287957\pi$
$983$	25.1438	+	27.9251i	0.801964	+	0.890671i	−0.193947	+	0.981012i	$0.562129\pi$
$984$	0.512285	−	1.57665i	0.0163311	−	0.0502618i
$985$	−39.4816	+	43.8488i	−1.25799	+	1.39714i
$986$	2.20846	+	3.82517i	0.0703318	+	0.121818i
$987$	0.301756	−	0.522656i	0.00960499	−	0.0166363i
$988$	5.20865	+	16.0306i	0.165709	+	0.510001i
$989$	21.4645	+	9.55659i	0.682530	+	0.303882i
$990$	−18.6033	−	13.5161i	−0.591253	−	0.429571i
$991$	6.77397			0.215182			0.107591	−	0.994195i	$-0.465686\pi$
$991$	6.77397			0.215182			0.107591	+	0.994195i	$0.465686\pi$
$992$		0			0
$993$	29.2099			0.926948
$994$	−3.29426	−	2.39342i	−0.104487	−	0.0759146i
$995$	14.4335	+	6.42620i	0.457572	+	0.203724i
$996$	−5.99783	−	18.4594i	−0.190049	−	0.584909i
$997$	14.7866	−	25.6112i	0.468298	−	0.811115i	−0.531046	−	0.847343i	$-0.678201\pi$
$997$	14.7866	−	25.6112i	0.468298	−	0.811115i	0.999344	+	0.0362278i	$0.0115342\pi$
$998$	14.2397	+	24.6639i	0.450751	+	0.780724i
$999$	−32.6049	+	36.2114i	−1.03157	+	1.14568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.l.732.2		16
31.2	even	5		961.2.g.n.448.1		16
31.3	odd	30		961.2.d.o.388.4		16
31.4	even	5		961.2.c.i.521.3		16
31.5	even	3		961.2.g.j.816.2		16
31.6	odd	6		961.2.d.o.374.4		16
31.7	even	15		961.2.a.j.1.3		8
31.8	even	5		961.2.g.m.844.1		16
31.9	even	15		961.2.g.n.547.1		16
31.10	even	15		961.2.g.m.846.1		16
31.11	odd	30		961.2.c.j.439.3		16
31.12	odd	30		961.2.d.p.628.1		16
31.13	odd	30		31.2.g.a.18.2	✓	16
31.14	even	15		961.2.d.q.531.1		16
31.15	odd	10		961.2.g.k.338.2		16
31.16	even	5		961.2.g.j.338.2		16
31.17	odd	30		961.2.d.p.531.1		16
31.18	even	15	inner	961.2.g.l.235.2		16
31.19	even	15		961.2.d.q.628.1		16
31.20	even	15		961.2.c.i.439.3		16
31.21	odd	30		961.2.g.s.846.1		16
31.22	odd	30		961.2.g.t.547.1		16
31.23	odd	10		961.2.g.s.844.1		16
31.24	odd	30		961.2.a.i.1.3		8
31.25	even	3		961.2.d.n.374.4		16
31.26	odd	6		961.2.g.k.816.2		16
31.27	odd	10		961.2.c.j.521.3		16
31.28	even	15		961.2.d.n.388.4		16
31.29	odd	10		961.2.g.t.448.1		16
31.30	odd	2		31.2.g.a.19.2	yes	16
93.38	odd	30		8649.2.a.be.1.6		8
93.44	even	30		279.2.y.c.235.1		16
93.86	even	30		8649.2.a.bf.1.6		8
93.92	even	2		279.2.y.c.19.1		16
124.75	even	30		496.2.bg.c.49.1		16
124.123	even	2		496.2.bg.c.81.1		16
155.13	even	60		775.2.ck.a.49.2		32
155.44	odd	30		775.2.bl.a.576.1		16
155.92	even	4		775.2.ck.a.174.2		32
155.123	even	4		775.2.ck.a.174.3		32
155.137	even	60		775.2.ck.a.49.3		32
155.154	odd	2		775.2.bl.a.701.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.18.2	✓	16	31.13	odd	30
31.2.g.a.19.2	yes	16	31.30	odd	2
279.2.y.c.19.1		16	93.92	even	2
279.2.y.c.235.1		16	93.44	even	30
496.2.bg.c.49.1		16	124.75	even	30
496.2.bg.c.81.1		16	124.123	even	2
775.2.bl.a.576.1		16	155.44	odd	30
775.2.bl.a.701.1		16	155.154	odd	2
775.2.ck.a.49.2		32	155.13	even	60
775.2.ck.a.49.3		32	155.137	even	60
775.2.ck.a.174.2		32	155.92	even	4
775.2.ck.a.174.3		32	155.123	even	4
961.2.a.i.1.3		8	31.24	odd	30
961.2.a.j.1.3		8	31.7	even	15
961.2.c.i.439.3		16	31.20	even	15
961.2.c.i.521.3		16	31.4	even	5
961.2.c.j.439.3		16	31.11	odd	30
961.2.c.j.521.3		16	31.27	odd	10
961.2.d.n.374.4		16	31.25	even	3
961.2.d.n.388.4		16	31.28	even	15
961.2.d.o.374.4		16	31.6	odd	6
961.2.d.o.388.4		16	31.3	odd	30
961.2.d.p.531.1		16	31.17	odd	30
961.2.d.p.628.1		16	31.12	odd	30
961.2.d.q.531.1		16	31.14	even	15
961.2.d.q.628.1		16	31.19	even	15
961.2.g.j.338.2		16	31.16	even	5
961.2.g.j.816.2		16	31.5	even	3
961.2.g.k.338.2		16	31.15	odd	10
961.2.g.k.816.2		16	31.26	odd	6
961.2.g.l.235.2		16	31.18	even	15	inner
961.2.g.l.732.2		16	1.1	even	1	trivial
961.2.g.m.844.1		16	31.8	even	5
961.2.g.m.846.1		16	31.10	even	15
961.2.g.n.448.1		16	31.2	even	5
961.2.g.n.547.1		16	31.9	even	15
961.2.g.s.844.1		16	31.23	odd	10
961.2.g.s.846.1		16	31.21	odd	30
961.2.g.t.448.1		16	31.29	odd	10
961.2.g.t.547.1		16	31.22	odd	30
8649.2.a.be.1.6		8	93.38	odd	30
8649.2.a.bf.1.6		8	93.86	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+(0.557811 + 0.405274i) q^{2} +(0.824384 + 0.367040i) q^{3} +(-0.471127 - 1.44998i) q^{4} +(-1.85376 + 3.21080i) q^{5} +(0.311099 + 0.538840i) q^{6} +(0.510810 - 0.567312i) q^{7} +(0.750969 - 2.31124i) q^{8} +(-1.46250 - 1.62427i) q^{9} +(-2.33530 + 1.03974i) q^{10} +(-4.02569 - 0.855686i) q^{11} +(0.143810 - 1.36826i) q^{12} +(-0.304152 - 2.89381i) q^{13} +(0.514852 - 0.109435i) q^{14} +(-2.70670 + 1.96653i) q^{15} +(-1.11127 + 0.807384i) q^{16} +(1.27993 - 0.272057i) q^{17} +(-0.157525 - 1.49875i) q^{18} +(0.397160 - 3.77873i) q^{19} +(5.52896 + 1.17522i) q^{20} +(0.629330 - 0.280196i) q^{21} +(-1.89879 - 2.10882i) q^{22} +(1.01449 - 3.12228i) q^{23} +(1.46740 - 1.62972i) q^{24} +(-4.37284 - 7.57398i) q^{25} +(1.00313 - 1.73747i) q^{26} +(-1.44606 - 4.45052i) q^{27} +(-1.06325 - 0.473389i) q^{28} +(3.96065 + 2.87758i) q^{29} -2.30681 q^{30} -5.80746 q^{32} +(-3.00464 - 2.18300i) q^{33} +(0.824217 + 0.366965i) q^{34} +(0.874609 + 2.69177i) q^{35} +(-1.66614 + 2.88584i) q^{36} +(-5.20639 - 9.01773i) q^{37} +(1.75296 - 1.94686i) q^{38} +(0.811405 - 2.49725i) q^{39} +(6.02884 + 6.69570i) q^{40} +(0.690591 - 0.307471i) q^{41} +(0.464603 + 0.0987545i) q^{42} +(-0.748099 + 7.11768i) q^{43} +(0.655882 + 6.24030i) q^{44} +(7.92634 - 1.68480i) q^{45} +(1.83127 - 1.33050i) q^{46} +(0.708753 - 0.514939i) q^{47} +(-1.21245 + 0.257715i) q^{48} +(0.670783 + 6.38208i) q^{49} +(0.630315 - 5.99705i) q^{50} +(1.15501 + 0.245505i) q^{51} +(-4.05268 + 1.80437i) q^{52} +(-2.39261 - 2.65727i) q^{53} +(0.997049 - 3.06860i) q^{54} +(10.2101 - 11.3395i) q^{55} +(-0.927595 - 1.60664i) q^{56} +(1.71435 - 2.96935i) q^{57} +(1.04309 + 3.21029i) q^{58} +(0.847103 + 0.377155i) q^{59} +(4.12664 + 2.99818i) q^{60} -2.31704 q^{61} -1.66853 q^{63} +(-1.01693 - 0.738843i) q^{64} +(9.85528 + 4.38785i) q^{65} +(-0.791311 - 2.43540i) q^{66} +(1.04345 - 1.80731i) q^{67} +(-0.997488 - 1.72770i) q^{68} +(1.98233 - 2.20160i) q^{69} +(-0.603037 + 1.85596i) q^{70} +(-5.17645 - 5.74903i) q^{71} +(-4.85238 + 2.16042i) q^{72} +(-5.53385 - 1.17626i) q^{73} +(0.750466 - 7.14021i) q^{74} +(-0.824950 - 7.84887i) q^{75} +(-5.66619 + 1.20439i) q^{76} +(-2.54180 + 1.84673i) q^{77} +(1.46468 - 1.06415i) q^{78} +(-13.7867 + 2.93046i) q^{79} +(-0.532328 - 5.06476i) q^{80} +(-0.243989 + 2.32140i) q^{81} +(0.509829 + 0.108368i) q^{82} +(12.8880 - 5.73812i) q^{83} +(-0.702773 - 0.780508i) q^{84} +(-1.49916 + 4.61393i) q^{85} +(-3.30191 + 3.66714i) q^{86} +(2.20891 + 3.82595i) q^{87} +(-5.00086 + 8.66175i) q^{88} +(1.37043 + 4.21776i) q^{89} +(5.10420 + 2.27254i) q^{90} +(-1.79706 - 1.30564i) q^{91} -5.00520 q^{92} +0.604042 q^{94} +(11.3965 + 8.28005i) q^{95} +(-4.78758 - 2.13157i) q^{96} +(-1.63088 - 5.01933i) q^{97} +(-2.21232 + 3.83184i) q^{98} +(4.49770 + 7.79025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 12 q^{3} - 14 q^{4} - 3 q^{5} - 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9} - 2 q^{10} + 7 q^{11} - 5 q^{12} + 7 q^{13} - 6 q^{14} - 14 q^{15} - 2 q^{16} + 6 q^{17} - 3 q^{18} + 16 q^{19}+ \cdots - 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 + 12 * q^3 - 14 * q^4 - 3 * q^5 - 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9 - 2 * q^10 + 7 * q^11 - 5 * q^12 + 7 * q^13 - 6 * q^14 - 14 * q^15 - 2 * q^16 + 6 * q^17 - 3 * q^18 + 16 * q^19 + 37 * q^20 - 9 * q^21 - 9 * q^22 - q^23 + 20 * q^24 - 13 * q^25 - 9 * q^26 - 9 * q^27 - 30 * q^28 + 14 * q^29 + 22 * q^30 - 42 * q^32 - 13 * q^33 + 32 * q^34 - 9 * q^35 + q^36 + 8 * q^37 + 8 * q^38 - 3 * q^39 - q^40 - 8 * q^41 - 69 * q^42 - 23 * q^43 - 39 * q^44 + 65 * q^45 - 34 * q^46 + 14 * q^47 - 34 * q^48 + 2 * q^49 + 3 * q^50 - 42 * q^51 - 29 * q^52 - 6 * q^53 + 46 * q^54 + 7 * q^55 - 30 * q^56 + 17 * q^57 + 15 * q^58 + 4 * q^59 + 75 * q^60 + 60 * q^61 - 46 * q^63 + 23 * q^64 + 12 * q^65 - 30 * q^66 + 13 * q^67 - 30 * q^68 + 38 * q^69 + 12 * q^70 - 14 * q^71 + 37 * q^72 - 2 * q^73 - 13 * q^74 - 13 * q^75 - 12 * q^76 - 18 * q^77 - 15 * q^78 - 18 * q^79 + 36 * q^80 + 23 * q^81 + 14 * q^82 + 16 * q^83 - 8 * q^84 - 37 * q^85 + 26 * q^86 + 15 * q^87 + 17 * q^88 - q^89 - 23 * 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

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