LMFDB - Embedded newform 450.2.q.b.331.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [450,2,Mod(31,450)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("450.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(450, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([10, 12])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.q (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [112] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			331.12
Character	$\chi$	$=$	450.331
Dual form			450.2.q.b.121.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.978148 - 0.207912i) q^{2} +(1.62578 + 0.597357i) q^{3} +(0.913545 + 0.406737i) q^{4} +(0.605543 - 2.15251i) q^{5} +(-1.46606 - 0.922322i) q^{6} +(-0.294886 + 0.510758i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.28633 + 1.94234i) q^{9} +(-1.03984 + 1.97958i) q^{10} +(0.140938 + 0.0299574i) q^{11} +(1.24226 + 1.20698i) q^{12} +(4.09952 - 0.871380i) q^{13} +(0.394635 - 0.438287i) q^{14} +(2.27030 - 3.13779i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-1.93882 - 1.40864i) q^{17} +(-1.83253 - 2.37525i) q^{18} +(1.37124 + 0.996265i) q^{19} +(1.42870 - 1.72012i) q^{20} +(-0.784526 + 0.654229i) q^{21} +(-0.131630 - 0.0586055i) q^{22} +(3.81363 - 4.23547i) q^{23} +(-0.964167 - 1.43888i) q^{24} +(-4.26663 - 2.60688i) q^{25} -4.19110 q^{26} +(2.55680 + 4.52358i) q^{27} +(-0.477136 + 0.346660i) q^{28} +(-0.195996 - 1.86478i) q^{29} +(-2.87307 + 2.59720i) q^{30} +(-0.586948 + 5.58444i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.211240 + 0.132895i) q^{33} +(1.60358 + 1.78096i) q^{34} +(0.920848 + 0.944033i) q^{35} +(1.29864 + 2.70435i) q^{36} +(0.528080 - 1.62526i) q^{37} +(-1.13414 - 1.25959i) q^{38} +(7.18544 + 1.03220i) q^{39} +(-1.75511 + 1.38549i) q^{40} +(-0.630574 + 0.134033i) q^{41} +(0.903404 - 0.476820i) q^{42} +(-3.45722 + 5.98808i) q^{43} +(0.116569 + 0.0846923i) q^{44} +(5.56539 - 3.74518i) q^{45} +(-4.61090 + 3.35001i) q^{46} +(-0.564316 - 5.36911i) q^{47} +(0.643937 + 1.60790i) q^{48} +(3.32608 + 5.76095i) q^{49} +(3.63140 + 3.43700i) q^{50} +(-2.31064 - 3.44831i) q^{51} +(4.09952 + 0.871380i) q^{52} +(3.80623 - 2.76539i) q^{53} +(-1.56042 - 4.95632i) q^{54} +(0.149828 - 0.285232i) q^{55} +(0.538784 - 0.239882i) q^{56} +(1.63421 + 2.43883i) q^{57} +(-0.195996 + 1.86478i) q^{58} +(7.22978 - 1.53674i) q^{59} +(3.35028 - 1.94310i) q^{60} +(-4.51033 - 0.958701i) q^{61} +(1.73519 - 5.34037i) q^{62} +(-1.66628 + 0.594991i) q^{63} +(0.309017 + 0.951057i) q^{64} +(0.606779 - 9.35193i) q^{65} +(-0.178993 - 0.173910i) q^{66} +(-0.357376 + 3.40021i) q^{67} +(-1.19826 - 2.07545i) q^{68} +(8.73021 - 4.60784i) q^{69} +(-0.704450 - 1.11486i) q^{70} +(-12.7343 + 9.25198i) q^{71} +(-0.707999 - 2.91526i) q^{72} +(-4.82838 - 14.8602i) q^{73} +(-0.854451 + 1.47995i) q^{74} +(-5.37938 - 6.78692i) q^{75} +(0.847474 + 1.46787i) q^{76} +(-0.0568618 + 0.0631515i) q^{77} +(-6.81382 - 2.50358i) q^{78} +(-0.00170289 - 0.0162019i) q^{79} +(2.00482 - 0.990307i) q^{80} +(1.45461 + 8.88167i) q^{81} +0.644661 q^{82} +(-10.2980 + 4.58495i) q^{83} +(-0.982799 + 0.278572i) q^{84} +(-4.20616 + 3.32036i) q^{85} +(4.62666 - 5.13843i) q^{86} +(0.795290 - 3.14880i) q^{87} +(-0.0964131 - 0.107078i) q^{88} +(3.02707 + 9.31636i) q^{89} +(-6.22244 + 2.50623i) q^{90} +(-0.763828 + 2.35082i) q^{91} +(5.20664 - 2.31815i) q^{92} +(-4.29015 + 8.72846i) q^{93} +(-0.564316 + 5.36911i) q^{94} +(2.97482 - 2.34833i) q^{95} +(-0.295565 - 1.70665i) q^{96} +(-0.981903 - 9.34218i) q^{97} +(-2.05563 - 6.32659i) q^{98} +(0.264044 + 0.342243i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 14 q^{2} + 2 q^{3} + 14 q^{4} + 9 q^{5} - 7 q^{6} - 8 q^{7} - 28 q^{8} + 8 q^{9} - 8 q^{10} - 3 q^{11} - 3 q^{14} + 32 q^{15} + 14 q^{16} + 10 q^{17} - 6 q^{18} - 32 q^{19} - 6 q^{20} - 7 q^{21}+ \cdots + 68 q^{99}+O(q^{100}) $ 112 * q + 14 * q^2 + 2 * q^3 + 14 * q^4 + 9 * q^5 - 7 * q^6 - 8 * q^7 - 28 * q^8 + 8 * q^9 - 8 * q^10 - 3 * q^11 - 3 * q^14 + 32 * q^15 + 14 * q^16 + 10 * q^17 - 6 * q^18 - 32 * q^19 - 6 * q^20 - 7 * q^21 + 2 * q^22 - 5 * q^23 + 2 * q^24 + 21 * q^25 + 20 * q^26 - 16 * q^27 - 14 * q^28 + 18 * q^29 + 3 * q^30 - 27 * q^31 - 56 * q^32 - 25 * q^33 - 15 * q^34 - 12 * q^35 - 7 * q^36 + 16 * q^37 - 9 * q^38 + 12 * q^39 - q^40 + 16 * q^41 - 13 * q^42 - 44 * q^43 - 4 * q^44 + 69 * q^45 - 10 * q^46 + 27 * q^47 + 3 * q^48 - 64 * q^49 + 11 * q^50 + 138 * q^51 - 14 * q^53 - 30 * q^54 - 8 * q^55 + 7 * q^56 - 50 * q^57 + 18 * q^58 + 14 * q^59 - 20 * q^60 - 5 * q^61 - 66 * q^62 - 12 * q^63 - 28 * q^64 - 102 * q^65 + 18 * q^66 + 11 * q^67 + 40 * q^68 - 78 * q^69 + 6 * q^70 + 38 * q^71 - 17 * q^72 - 44 * q^73 + 12 * q^74 + 10 * q^75 - 14 * q^76 - 3 * q^77 - 55 * q^78 + 16 * q^79 + 12 * q^80 + 72 * q^81 + 28 * q^82 - 56 * q^83 - 30 * q^84 + 35 * q^85 + 21 * q^86 - 44 * q^87 - 3 * q^88 - 64 * q^89 + 38 * q^90 - 40 * q^91 + 5 * q^92 - 22 * q^93 + 27 * q^94 + 24 * q^95 + 5 * q^96 + 34 * q^97 + 38 * q^98 + 68 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.978148	−	0.207912i	−0.691655	−	0.147016i
$2$	−0.978148	−	0.207912i	−0.691655	−	0.147016i
$3$	1.62578	+	0.597357i	0.938645	+	0.344884i
$3$	1.62578	+	0.597357i	0.938645	+	0.344884i
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	0.605543	−	2.15251i	0.270807	−	0.962634i
$5$	0.605543	−	2.15251i	0.270807	−	0.962634i
$6$	−1.46606	−	0.922322i	−0.598515	−	0.376536i
$7$	−0.294886	+	0.510758i	−0.111457	+	0.193048i	−0.916358	−	0.400360i	$-0.868885\pi$
$7$	−0.294886	+	0.510758i	−0.111457	+	0.193048i	0.804901	+	0.593409i	$0.202218\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	2.28633	+	1.94234i	0.762110	+	0.647448i
$10$	−1.03984	+	1.97958i	−0.328827	+	0.625997i
$11$	0.140938	+	0.0299574i	0.0424946	+	0.00903250i	0.229110	−	0.973401i	$-0.426418\pi$
$11$	0.140938	+	0.0299574i	0.0424946	+	0.00903250i	−0.186615	+	0.982433i	$0.559752\pi$
$12$	1.24226	+	1.20698i	0.358609	+	0.348424i
$13$	4.09952	−	0.871380i	1.13700	−	0.241677i	0.399311	−	0.916816i	$-0.369249\pi$
$13$	4.09952	−	0.871380i	1.13700	−	0.241677i	0.737691	+	0.675138i	$0.235916\pi$
$14$	0.394635	−	0.438287i	0.105471	−	0.117137i
$15$	2.27030	−	3.13779i	0.586189	−	0.810174i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−1.93882	−	1.40864i	−0.470234	−	0.341645i	0.327299	−	0.944921i	$-0.393862\pi$
$17$	−1.93882	−	1.40864i	−0.470234	−	0.341645i	−0.797532	+	0.603276i	$0.793862\pi$
$18$	−1.83253	−	2.37525i	−0.431932	−	0.559852i
$19$	1.37124	+	0.996265i	0.314584	+	0.228559i	0.733861	−	0.679300i	$-0.237716\pi$
$19$	1.37124	+	0.996265i	0.314584	+	0.228559i	−0.419277	+	0.907858i	$0.637716\pi$
$20$	1.42870	−	1.72012i	0.319467	−	0.384631i
$21$	−0.784526	+	0.654229i	−0.171198	+	0.142764i
$22$	−0.131630	−	0.0586055i	−0.0280636	−	0.0124947i
$23$	3.81363	−	4.23547i	0.795197	−	0.883156i	−0.200125	−	0.979770i	$-0.564135\pi$
$23$	3.81363	−	4.23547i	0.795197	−	0.883156i	0.995322	+	0.0966147i	$0.0308014\pi$
$24$	−0.964167	−	1.43888i	−0.196810	−	0.293711i
$25$	−4.26663	−	2.60688i	−0.853327	−	0.521376i
$26$	−4.19110			−0.821943
$27$	2.55680	+	4.52358i	0.492056	+	0.870563i
$28$	−0.477136	+	0.346660i	−0.0901703	+	0.0655125i
$29$	−0.195996	−	1.86478i	−0.0363955	−	0.346280i	−0.997532	−	0.0702078i	$-0.977634\pi$
$29$	−0.195996	−	1.86478i	−0.0363955	−	0.346280i	0.961137	−	0.276072i	$-0.0890329\pi$
$30$	−2.87307	+	2.59720i	−0.524549	+	0.474182i
$31$	−0.586948	+	5.58444i	−0.105419	+	1.00300i	0.806112	+	0.591763i	$0.201568\pi$
$31$	−0.586948	+	5.58444i	−0.105419	+	1.00300i	−0.911531	+	0.411232i	$0.865099\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.211240	+	0.132895i	0.0367721	+	0.0231340i
$34$	1.60358	+	1.78096i	0.275012	+	0.305432i
$35$	0.920848	+	0.944033i	0.155652	+	0.159571i
$36$	1.29864	+	2.70435i	0.216441	+	0.450725i
$37$	0.528080	−	1.62526i	0.0868158	−	0.267192i	−0.898219	−	0.439549i	$-0.855138\pi$
$37$	0.528080	−	1.62526i	0.0868158	−	0.267192i	0.985035	+	0.172357i	$0.0551383\pi$
$38$	−1.13414	−	1.25959i	−0.183982	−	0.204333i
$39$	7.18544	+	1.03220i	1.15059	+	0.165285i
$40$	−1.75511	+	1.38549i	−0.277507	+	0.219065i
$41$	−0.630574	+	0.134033i	−0.0984791	+	0.0209324i	−0.256888	−	0.966441i	$-0.582697\pi$
$41$	−0.630574	+	0.134033i	−0.0984791	+	0.0209324i	0.158409	+	0.987374i	$0.449364\pi$
$42$	0.903404	−	0.476820i	0.139398	−	0.0735750i
$43$	−3.45722	+	5.98808i	−0.527221	+	0.913174i	0.472275	+	0.881451i	$0.343433\pi$
$43$	−3.45722	+	5.98808i	−0.527221	+	0.913174i	−0.999497	+	0.0317230i	$0.989901\pi$
$44$	0.116569	+	0.0846923i	0.0175734	+	0.0127678i
$45$	5.56539	−	3.74518i	0.829640	−	0.558299i
$46$	−4.61090	+	3.35001i	−0.679840	+	0.493932i
$47$	−0.564316	−	5.36911i	−0.0823140	−	0.783165i	−0.955343	−	0.295498i	$-0.904515\pi$
$47$	−0.564316	−	5.36911i	−0.0823140	−	0.783165i	0.873029	−	0.487668i	$-0.162152\pi$
$48$	0.643937	+	1.60790i	0.0929444	+	0.232080i
$49$	3.32608	+	5.76095i	0.475155	+	0.822992i
$50$	3.63140	+	3.43700i	0.513557	+	0.486065i
$51$	−2.31064	−	3.44831i	−0.323555	−	0.482860i
$52$	4.09952	+	0.871380i	0.568501	+	0.120839i
$53$	3.80623	−	2.76539i	0.522826	−	0.379856i	−0.294841	−	0.955546i	$-0.595267\pi$
$53$	3.80623	−	2.76539i	0.522826	−	0.379856i	0.817668	+	0.575691i	$0.195267\pi$
$54$	−1.56042	−	4.95632i	−0.212347	−	0.674469i
$55$	0.149828	−	0.285232i	0.0202028	−	0.0384606i
$56$	0.538784	−	0.239882i	0.0719981	−	0.0320556i
$57$	1.63421	+	2.43883i	0.216457	+	0.323031i
$58$	−0.195996	+	1.86478i	−0.0257355	+	0.244857i
$59$	7.22978	−	1.53674i	0.941237	−	0.200066i	0.288353	−	0.957524i	$-0.406892\pi$
$59$	7.22978	−	1.53674i	0.941237	−	0.200066i	0.652884	+	0.757458i	$0.273559\pi$
$60$	3.35028	−	1.94310i	0.432519	−	0.250853i
$61$	−4.51033	−	0.958701i	−0.577489	−	0.122749i	−0.0900980	−	0.995933i	$-0.528718\pi$
$61$	−4.51033	−	0.958701i	−0.577489	−	0.122749i	−0.487391	+	0.873184i	$0.662051\pi$
$62$	1.73519	−	5.34037i	0.220370	−	0.678228i
$63$	−1.66628	+	0.594991i	−0.209931	+	0.0749618i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	0.606779	−	9.35193i	0.0752617	−	1.15996i
$66$	−0.178993	−	0.173910i	−0.0220326	−	0.0214068i
$67$	−0.357376	+	3.40021i	−0.0436604	+	0.415401i	0.950761	+	0.309924i	$0.100304\pi$
$67$	−0.357376	+	3.40021i	−0.0436604	+	0.415401i	−0.994422	+	0.105477i	$0.966363\pi$
$68$	−1.19826	−	2.07545i	−0.145310	−	0.251685i
$69$	8.73021	−	4.60784i	1.05099	−	0.554719i
$70$	−0.704450	−	1.11486i	−0.0841978	−	0.133251i
$71$	−12.7343	+	9.25198i	−1.51128	+	1.09801i	−0.545673	+	0.837998i	$0.683726\pi$
$71$	−12.7343	+	9.25198i	−1.51128	+	1.09801i	−0.965606	+	0.260010i	$0.916274\pi$
$72$	−0.707999	−	2.91526i	−0.0834385	−	0.343567i
$73$	−4.82838	−	14.8602i	−0.565119	−	1.73926i	−0.667597	−	0.744523i	$-0.732677\pi$
$73$	−4.82838	−	14.8602i	−0.565119	−	1.73926i	0.102478	−	0.994735i	$-0.467323\pi$
$74$	−0.854451	+	1.47995i	−0.0993279	+	0.172041i
$75$	−5.37938	−	6.78692i	−0.621157	−	0.783686i
$76$	0.847474	+	1.46787i	0.0972119	+	0.168376i
$77$	−0.0568618	+	0.0631515i	−0.00648001	+	0.00719678i
$78$	−6.81382	−	2.50358i	−0.771513	−	0.283475i
$79$	−0.00170289	−	0.0162019i	−0.000191590	−	0.00182285i	0.994426	−	0.105440i	$-0.0336250\pi$
$79$	−0.00170289	−	0.0162019i	−0.000191590	−	0.00182285i	−0.994617	+	0.103617i	$0.966958\pi$
$80$	2.00482	−	0.990307i	0.224145	−	0.110720i
$81$	1.45461	+	8.88167i	0.161623	+	0.986853i
$82$	0.644661			0.0711909
$83$	−10.2980	+	4.58495i	−1.13035	+	0.503264i	−0.884731	−	0.466102i	$-0.845658\pi$
$83$	−10.2980	+	4.58495i	−1.13035	+	0.503264i	−0.245619	+	0.969366i	$0.578991\pi$
$84$	−0.982799	+	0.278572i	−0.107232	+	0.0303947i
$85$	−4.20616	+	3.32036i	−0.456222	+	0.360143i
$86$	4.62666	−	5.13843i	0.498906	−	0.554091i
$87$	0.795290	−	3.14880i	0.0852640	−	0.337586i
$88$	−0.0964131	−	0.107078i	−0.0102777	−	0.0114145i
$89$	3.02707	+	9.31636i	0.320869	+	0.987533i	0.973271	+	0.229660i	$0.0737613\pi$
$89$	3.02707	+	9.31636i	0.320869	+	0.987533i	−0.652402	+	0.757873i	$0.726239\pi$
$90$	−6.22244	+	2.50623i	−0.655903	+	0.264180i
$91$	−0.763828	+	2.35082i	−0.0800709	+	0.246433i
$92$	5.20664	−	2.31815i	0.542830	−	0.241684i
$93$	−4.29015	+	8.72846i	−0.444868	+	0.905099i
$94$	−0.564316	+	5.36911i	−0.0582048	+	0.553781i
$95$	2.97482	−	2.34833i	0.305210	−	0.240934i
$96$	−0.295565	−	1.70665i	−0.0301659	−	0.174184i
$97$	−0.981903	−	9.34218i	−0.0996971	−	0.948555i	−0.923997	−	0.382401i	$-0.875097\pi$
$97$	−0.981903	−	9.34218i	−0.0996971	−	0.948555i	0.824299	−	0.566154i	$-0.191569\pi$
$98$	−2.05563	−	6.32659i	−0.207650	−	0.639082i
$99$	0.264044	+	0.342243i	0.0265375	+	0.0343968i
$100$	−2.83745	−	4.11690i	−0.283745	−	0.411690i
$101$	−8.51933	+	14.7559i	−0.847705	+	1.46827i	0.0355453	+	0.999368i	$0.488683\pi$
$101$	−8.51933	+	14.7559i	−0.847705	+	1.46827i	−0.883251	+	0.468901i	$0.844650\pi$
$102$	1.54321	+	3.85336i	0.152800	+	0.381540i
$103$	10.3961	+	4.62863i	1.02436	+	0.456073i	0.848978	−	0.528428i	$-0.177218\pi$
$103$	10.3961	+	4.62863i	1.02436	+	0.456073i	0.175379	+	0.984501i	$0.443885\pi$
$104$	−3.82876	−	1.70468i	−0.375441	−	0.167157i
$105$	0.933172	+	2.08487i	0.0910683	+	0.203462i
$106$	−4.29801	+	1.91360i	−0.417460	+	0.185865i
$107$	−10.6321			−1.02785			−0.513923	−	0.857836i	$-0.671808\pi$
$107$	−10.6321			−1.02785			−0.513923	+	0.857836i	$0.671808\pi$
$108$	0.495848	+	5.17244i	0.0477130	+	0.497718i
$109$	−2.30939	+	7.10757i	−0.221199	+	0.680782i	0.777456	+	0.628938i	$0.216510\pi$
$109$	−2.30939	+	7.10757i	−0.221199	+	0.680782i	−0.998655	+	0.0518442i	$0.983490\pi$
$110$	−0.205857	+	0.247848i	−0.0196277	+	0.0236313i
$111$	1.82940	−	2.32687i	0.173639	−	0.220857i
$112$	−0.576885	+	0.122621i	−0.0545105	+	0.0115866i
$113$	−16.9810	+	3.60943i	−1.59744	+	0.339546i	−0.918738	−	0.394868i	$-0.870790\pi$
$113$	−16.9810	+	3.60943i	−1.59744	+	0.339546i	−0.678702	+	0.734414i	$0.737457\pi$
$114$	−1.09144	−	2.72531i	−0.102223	−	0.255248i
$115$	−6.80758	−	10.7737i	−0.634810	−	1.00465i
$116$	0.579421	−	1.78328i	0.0537979	−	0.165573i
$117$	11.0654	+	5.97041i	1.02299	+	0.551965i
$118$	−7.39130			−0.680424
$119$	1.29121	−	0.574882i	0.118365	−	0.0526994i
$120$	−3.68106	+	1.20408i	−0.336033	+	0.109917i
$121$	−10.0300	−	4.46566i	−0.911821	−	0.405969i
$122$	4.21245	+	1.87550i	0.381377	+	0.169800i
$123$	−1.10524	−	0.158770i	−0.0996562	−	0.0143158i
$124$	−2.80760	+	4.86291i	−0.252130	+	0.436702i
$125$	−8.19498	+	7.60541i	−0.732981	+	0.680249i
$126$	1.75357	−	0.235551i	0.156220	−	0.0209846i
$127$	3.64339	+	11.2132i	0.323298	+	0.995010i	0.972203	+	0.234140i	$0.0752274\pi$
$127$	3.64339	+	11.2132i	0.323298	+	0.995010i	−0.648905	+	0.760870i	$0.724773\pi$
$128$	−0.104528	−	0.994522i	−0.00923910	−	0.0879041i
$129$	−9.19771	+	7.67012i	−0.809813	+	0.675316i
$130$	−2.53789	+	9.02141i	−0.222588	+	0.791230i
$131$	−0.0710957	+	0.676431i	−0.00621166	+	0.0591000i	−0.997189	−	0.0749323i	$-0.976126\pi$
$131$	−0.0710957	+	0.676431i	−0.00621166	+	0.0591000i	0.990977	+	0.134032i	$0.0427926\pi$
$132$	0.138924	+	0.207324i	0.0120918	+	0.0180453i
$133$	−0.913211	+	0.406588i	−0.0791854	+	0.0352556i
$134$	1.05651	−	3.25160i	0.0912685	−	0.280895i
$135$	11.2853	−	2.76433i	0.971286	−	0.237915i
$136$	0.740565	+	2.27922i	0.0635029	+	0.195442i
$137$	−12.3801	−	13.7495i	−1.05770	−	1.17470i	−0.984137	−	0.177409i	$-0.943229\pi$
$137$	−12.3801	−	13.7495i	−1.05770	−	1.17470i	−0.0735663	−	0.997290i	$-0.523438\pi$
$138$	−9.49746	+	2.69204i	−0.808478	+	0.229161i
$139$	−11.9997	+	13.3270i	−1.01780	+	1.13038i	−0.0263805	+	0.999652i	$0.508398\pi$
$139$	−11.9997	+	13.3270i	−1.01780	+	1.13038i	−0.991418	+	0.130728i	$0.958269\pi$
$140$	0.457263	+	1.23696i	0.0386458	+	0.104542i
$141$	2.28982	−	9.06610i	0.192838	−	0.763503i
$142$	14.3796	−	6.40220i	1.20671	−	0.537261i
$143$	0.603884			0.0504993
$144$	0.0864111	+	2.99876i	0.00720093	+	0.249896i
$145$	−4.13264	−	0.707318i	−0.343197	−	0.0587396i
$146$	1.63325	+	15.5394i	0.135169	+	1.28605i
$147$	1.96614	+	11.3529i	0.162165	+	0.936371i
$148$	1.14348	−	1.26996i	0.0939934	−	0.104390i
$149$	−0.462567	−	0.801189i	−0.0378949	−	0.0656360i	0.846456	−	0.532459i	$-0.178732\pi$
$149$	−0.462567	−	0.801189i	−0.0378949	−	0.0656360i	−0.884351	+	0.466823i	$0.845399\pi$
$150$	3.85074	+	7.75705i	0.314412	+	0.633360i
$151$	10.7306	−	18.5859i	0.873244	−	1.51250i	0.0146217	−	0.999893i	$-0.495346\pi$
$151$	10.7306	−	18.5859i	0.873244	−	1.51250i	0.858622	−	0.512609i	$-0.171321\pi$
$152$	−0.523768	−	1.61199i	−0.0424832	−	0.130750i
$153$	−1.69673	−	6.98647i	−0.137173	−	0.564823i
$154$	0.0687492	−	0.0499492i	0.00553997	−	0.00402502i
$155$	11.6652	+	4.64504i	0.936969	+	0.373098i
$156$	6.14440	+	3.86555i	0.491945	+	0.309492i
$157$	−5.56007	−	9.63032i	−0.443742	−	0.768583i	0.554222	−	0.832369i	$-0.313016\pi$
$157$	−5.56007	−	9.63032i	−0.443742	−	0.768583i	−0.997964	+	0.0637858i	$0.979683\pi$
$158$	−0.00170289	+	0.0162019i	−0.000135474	+	0.00128895i
$159$	7.84003	−	2.22224i	0.621755	−	0.176235i
$160$	−2.16690	+	0.551841i	−0.171309	+	0.0436269i
$161$	1.03871	+	3.19682i	0.0818619	+	0.251945i
$162$	0.423783	−	8.99002i	0.0332955	−	0.706322i
$163$	3.05141	−	9.39126i	0.239005	−	0.735580i	−0.757560	−	0.652765i	$-0.773609\pi$
$163$	3.05141	−	9.39126i	0.239005	−	0.735580i	0.996565	−	0.0828152i	$-0.0263911\pi$
$164$	−0.630574	−	0.134033i	−0.0492395	−	0.0104662i
$165$	0.413973	−	0.374223i	0.0322277	−	0.0291332i
$166$	11.0262	−	2.34369i	0.855800	−	0.181906i
$167$	0.466747	−	4.44080i	0.0361180	−	0.343640i	−0.961508	−	0.274776i	$-0.911396\pi$
$167$	0.466747	−	4.44080i	0.0361180	−	0.343640i	0.997626	−	0.0688631i	$-0.0219372\pi$
$168$	1.01924	−	0.0681496i	0.0786361	−	0.00525785i
$169$	4.17066	−	1.85690i	0.320820	−	0.142838i
$170$	4.80458	−	2.37329i	0.368495	−	0.182023i
$171$	1.20002	+	4.94121i	0.0917679	+	0.377864i
$172$	−5.59390	+	4.06421i	−0.426531	+	0.309893i
$173$	−2.50967	−	0.533448i	−0.190807	−	0.0405573i	0.111517	−	0.993763i	$-0.464429\pi$
$173$	−2.50967	−	0.533448i	−0.190807	−	0.0405573i	−0.302324	+	0.953205i	$0.597762\pi$
$174$	−1.43258	+	2.91464i	−0.108604	+	0.220958i
$175$	2.58966	−	1.41048i	0.195760	−	0.106623i
$176$	0.0720436	+	0.124783i	0.00543049	+	0.00940588i
$177$	12.6720	+	1.82036i	0.952488	+	0.136827i
$178$	−1.02394	−	9.74214i	−0.0767476	−	0.730204i
$179$	0.137544	−	0.0999317i	0.0102805	−	0.00746925i	−0.582633	−	0.812735i	$-0.697978\pi$
$179$	0.137544	−	0.0999317i	0.0102805	−	0.00746925i	0.592914	+	0.805266i	$0.297978\pi$
$180$	6.60754	−	1.15775i	0.492497	−	0.0862934i
$181$	−3.82985	−	2.78255i	−0.284670	−	0.206825i	0.436282	−	0.899810i	$-0.356295\pi$
$181$	−3.82985	−	2.78255i	−0.284670	−	0.206825i	−0.720952	+	0.692985i	$0.756295\pi$
$182$	1.23590	−	2.14064i	0.0916110	−	0.158675i
$183$	−6.76013	−	4.25292i	−0.499723	−	0.314385i
$184$	−5.57484	+	1.18497i	−0.410982	+	0.0873570i
$185$	−3.17863	−	2.12087i	−0.233697	−	0.155929i
$186$	6.01115	−	7.64575i	0.440759	−	0.560614i
$187$	−0.231056	−	0.256613i	−0.0168965	−	0.0187654i
$188$	1.66829	−	5.13445i	0.121672	−	0.374469i
$189$	−3.06442	−	0.0280352i	−0.222904	−	0.00203926i
$190$	−3.39806	+	1.67852i	−0.246521	+	0.121772i
$191$	9.28017	+	10.3067i	0.671489	+	0.745764i	0.978569	−	0.205919i	$-0.0660185\pi$
$191$	9.28017	+	10.3067i	0.671489	+	0.745764i	−0.307080	+	0.951684i	$0.599352\pi$
$192$	−0.0657260	+	1.73080i	−0.00474337	+	0.124910i
$193$	−1.58283	−	2.74154i	−0.113934	−	0.197340i	0.803419	−	0.595414i	$-0.203012\pi$
$193$	−1.58283	−	2.74154i	−0.113934	−	0.197340i	−0.917353	+	0.398074i	$0.869679\pi$
$194$	−0.981903	+	9.34218i	−0.0704965	+	0.670730i
$195$	6.57293	−	14.8417i	0.470697	−	1.06284i
$196$	0.695341	+	6.61573i	0.0496672	+	0.472552i
$197$	0.715723	−	0.520003i	0.0509932	−	0.0370487i	−0.561997	−	0.827139i	$-0.689967\pi$
$197$	0.715723	−	0.520003i	0.0509932	−	0.0370487i	0.612990	+	0.790091i	$0.289967\pi$
$198$	−0.187118	−	0.389662i	−0.0132979	−	0.0276921i
$199$	−7.48275			−0.530438			−0.265219	−	0.964188i	$-0.585444\pi$
$199$	−7.48275			−0.530438			−0.265219	+	0.964188i	$0.585444\pi$
$200$	1.91949	+	4.61688i	0.135729	+	0.326462i
$201$	−2.61215	+	5.31451i	−0.184247	+	0.374857i
$202$	11.4011	−	12.6622i	0.802178	−	0.890909i
$203$	1.01025	+	0.449790i	0.0709053	+	0.0315691i
$204$	−0.708326	−	4.09001i	−0.0495927	−	0.286358i
$205$	−0.0933326	+	1.43848i	−0.00651863	+	0.100468i
$206$	−9.20656	−	6.68896i	−0.641451	−	0.466042i
$207$	16.9459	−	2.27629i	1.17782	−	0.158213i
$208$	3.39067	+	2.46347i	0.235101	+	0.170811i
$209$	0.163415	+	0.181491i	0.0113037	+	0.0125540i
$210$	−0.479312	−	2.23332i	−0.0330757	−	0.154114i
$211$	12.4984	−	13.8808i	0.860423	−	0.955596i	−0.138975	−	0.990296i	$-0.544381\pi$
$211$	12.4984	−	13.8808i	0.860423	−	0.955596i	0.999398	+	0.0346998i	$0.0110475\pi$
$212$	4.60195	−	0.978175i	0.316063	−	0.0671813i
$213$	−26.2299	+	7.43480i	−1.79724	+	0.509424i
$214$	10.3998	+	2.21054i	0.710915	+	0.151110i
$215$	10.7959	+	11.0678i	0.736277	+	0.754815i
$216$	0.590398	−	5.16250i	0.0401715	−	0.351264i
$217$	−2.67922	−	1.94656i	−0.181877	−	0.132141i
$218$	3.73667	−	6.47210i	0.253079	−	0.438346i
$219$	1.02697	−	27.0437i	0.0693960	−	1.82745i
$220$	0.252889	−	0.199631i	0.0170498	−	0.0134591i
$221$	−9.17570	−	4.08529i	−0.617225	−	0.274806i
$222$	−2.27321	+	1.89567i	−0.152568	+	0.127229i
$223$	27.8242	+	5.91422i	1.86325	+	0.396045i	0.994982	−	0.100055i	$-0.0319020\pi$
$223$	27.8242	+	5.91422i	1.86325	+	0.396045i	0.868265	+	0.496101i	$0.165235\pi$
$224$	0.589773			0.0394059
$225$	−4.69148	−	14.2475i	−0.312765	−	0.949830i
$226$	17.3604			1.15480
$227$	−11.0377	−	2.34613i	−0.732597	−	0.155718i	−0.173515	−	0.984831i	$-0.555513\pi$
$227$	−11.0377	−	2.34613i	−0.732597	−	0.155718i	−0.559081	+	0.829113i	$0.688846\pi$
$228$	0.500966	+	2.89268i	0.0331773	+	0.191572i
$229$	18.1820	+	8.09517i	1.20150	+	0.534944i	0.907172	−	0.420760i	$-0.138237\pi$
$229$	18.1820	+	8.09517i	1.20150	+	0.534944i	0.294331	+	0.955704i	$0.404903\pi$
$230$	4.41885	+	11.9536i	0.291370	+	0.788197i
$231$	−0.130169	+	0.0687037i	−0.00856448	+	0.00452037i
$232$	−0.937523	+	1.62384i	−0.0615514	+	0.106610i
$233$	14.3052	+	10.3933i	0.937165	+	0.680890i	0.947737	−	0.319054i	$-0.103365\pi$
$233$	14.3052	+	10.3933i	0.937165	+	0.680890i	−0.0105717	+	0.999944i	$0.503365\pi$
$234$	−9.58225	−	8.14056i	−0.626411	−	0.532165i
$235$	−11.8988	−	2.03653i	−0.776192	−	0.132849i
$236$	7.22978	+	1.53674i	0.470619	+	0.100033i
$237$	0.00690978	−	0.0273580i	0.000448839	−	0.00177709i
$238$	−1.38252	+	0.293863i	−0.0896152	+	0.0190483i
$239$	8.29050	−	9.20753i	0.536268	−	0.595585i	−0.412736	−	0.910851i	$-0.635427\pi$
$239$	8.29050	−	9.20753i	0.536268	−	0.595585i	0.949004	+	0.315265i	$0.102093\pi$
$240$	3.85096	−	0.412431i	0.248578	−	0.0266223i
$241$	−14.8751	−	16.5205i	−0.958190	−	1.06418i	−0.997887	−	0.0649661i	$-0.979306\pi$
$241$	−14.8751	−	16.5205i	−0.958190	−	1.06418i	0.0396975	−	0.999212i	$-0.487361\pi$
$242$	8.88239	+	6.45343i	0.570982	+	0.414842i
$243$	−2.94065	+	15.3086i	−0.188643	+	0.982046i
$244$	−3.73046	−	2.71033i	−0.238818	−	0.173511i
$245$	14.4146	−	3.67094i	0.920915	−	0.234528i
$246$	1.04808	+	0.385093i	0.0668230	+	0.0245526i
$247$	6.48955	+	2.88934i	0.412920	+	0.183844i
$248$	3.75730	−	4.17291i	0.238589	−	0.264980i
$249$	−19.4811	+	1.30257i	−1.23457	+	0.0825469i
$250$	9.59715	−	5.73538i	0.606977	−	0.362738i
$251$	16.6434			1.05052			0.525260	−	0.850942i	$-0.323968\pi$
$251$	16.6434			1.05052			0.525260	+	0.850942i	$0.323968\pi$
$252$	−1.76422	−	0.134184i	−0.111136	−	0.00845278i
$253$	0.664371	−	0.482694i	0.0417686	−	0.0303467i
$254$	−1.23242	−	11.7257i	−0.0773287	−	0.735733i
$255$	−8.82173	+	2.88560i	−0.552438	+	0.180703i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	9.70071	+	16.8021i	0.605113	+	1.04809i	0.992034	+	0.125974i	$0.0402056\pi$
$257$	9.70071	+	16.8021i	0.605113	+	1.04809i	−0.386920	+	0.922113i	$0.626461\pi$
$258$	10.5914	−	5.59020i	0.659393	−	0.348030i
$259$	0.674393	+	0.748989i	0.0419047	+	0.0465399i
$260$	4.35809	−	8.29661i	0.270277	−	0.514534i
$261$	3.17392	−	4.64418i	0.196461	−	0.287468i
$262$	0.210180	−	0.646868i	0.0129850	−	0.0399636i
$263$	14.5304	+	16.1376i	0.895981	+	0.995088i	1.00000		0.000512589i	$0.000163162\pi$
$263$	14.5304	+	16.1376i	0.895981	+	0.995088i	−0.104019	+	0.994575i	$0.533170\pi$
$264$	−0.0927831	−	0.231678i	−0.00571040	−	0.0142588i
$265$	−3.64770	−	9.86753i	−0.224077	−	0.606158i
$266$	0.977790	−	0.207836i	0.0599521	−	0.0127432i
$267$	−0.643839	+	16.9546i	−0.0394023	+	1.03761i
$268$	−1.70947	+	2.96088i	−0.104422	+	0.180865i
$269$	5.63382	+	4.09321i	0.343500	+	0.249567i	0.746137	−	0.665792i	$-0.231906\pi$
$269$	5.63382	+	4.09321i	0.343500	+	0.249567i	−0.402637	+	0.915360i	$0.631906\pi$
$270$	−11.6134	+	0.357569i	−0.706772	+	0.0217609i
$271$	−13.3833	+	9.72352i	−0.812976	+	0.590662i	−0.914692	−	0.404152i	$-0.867567\pi$
$271$	−13.3833	+	9.72352i	−0.812976	+	0.590662i	0.101716	+	0.994814i	$0.467567\pi$
$272$	−0.250504	−	2.38339i	−0.0151891	−	0.144514i
$273$	−2.64610	+	3.36564i	−0.160149	+	0.203698i
$274$	9.25089	+	16.0230i	0.558867	+	0.967985i
$275$	−0.523238	−	0.495227i	−0.0315524	−	0.0298633i
$276$	9.84963	−	0.658577i	0.592878	−	0.0396416i
$277$	17.9874	+	3.82334i	1.08076	+	0.229722i	0.713683	−	0.700469i	$-0.247026\pi$
$277$	17.9874	+	3.82334i	1.08076	+	0.229722i	0.367075	+	0.930191i	$0.380359\pi$
$278$	14.5083	−	10.5409i	0.870149	−	0.632200i
$279$	−12.1889	+	11.6278i	−0.729728	+	0.696139i
$280$	−0.190093	−	1.30500i	−0.0113602	−	0.0779887i
$281$	−14.8441	+	6.60902i	−0.885524	+	0.394261i	−0.798535	−	0.601948i	$-0.794391\pi$
$281$	−14.8441	+	6.60902i	−0.885524	+	0.394261i	−0.0869894	+	0.996209i	$0.527725\pi$
$282$	−4.12473	+	8.39190i	−0.245624	+	0.499730i
$283$	−1.14024	+	10.8487i	−0.0677804	+	0.644888i	0.906909	+	0.421326i	$0.138435\pi$
$283$	−1.14024	+	10.8487i	−0.0677804	+	0.644888i	−0.974690	+	0.223562i	$0.928232\pi$
$284$	−15.3964	+	3.27262i	−0.913611	+	0.194194i
$285$	6.23920	−	2.04085i	0.369578	−	0.120889i
$286$	−0.590688	−	0.125555i	−0.0349281	−	0.00742420i
$287$	0.117489	−	0.361595i	0.00693518	−	0.0213443i
$288$	0.538953	−	2.95119i	0.0317581	−	0.173901i
$289$	−3.47851	−	10.7058i	−0.204618	−	0.629750i
$290$	3.89527	+	1.55109i	0.228738	+	0.0910829i
$291$	3.98426	−	15.7749i	0.233561	−	0.924741i
$292$	1.63325	−	15.5394i	0.0955789	−	0.909373i
$293$	−0.761176	−	1.31840i	−0.0444684	−	0.0770215i	0.842935	−	0.538016i	$-0.180826\pi$
$293$	−0.761176	−	1.31840i	−0.0444684	−	0.0770215i	−0.887403	+	0.460995i	$0.847493\pi$
$294$	0.437220	−	11.5136i	0.0254992	−	0.671486i
$295$	1.07010	−	16.4928i	0.0623034	−	0.960246i
$296$	−1.38253	+	1.00447i	−0.0803580	+	0.0583835i
$297$	0.224837	+	0.714142i	0.0130464	+	0.0414387i
$298$	0.285882	+	0.879854i	0.0165607	+	0.0509686i
$299$	11.9434	−	20.6865i	0.690702	−	1.19633i
$300$	−2.15382	−	8.38815i	−0.124351	−	0.484290i
$301$	−2.03897	−	3.53161i	−0.117525	−	0.203559i
$302$	−14.3603	+	15.9488i	−0.826345	+	0.917749i
$303$	−22.6651	+	18.9008i	−1.30208	+	1.08582i
$304$	0.177170	+	1.68566i	0.0101614	+	0.0966794i
$305$	−4.79482	+	9.12802i	−0.274551	+	0.522669i
$306$	0.207086	+	7.18657i	0.0118383	+	0.410829i
$307$	−15.7451			−0.898618			−0.449309	−	0.893376i	$-0.648330\pi$
$307$	−15.7451			−0.898618			−0.449309	+	0.893376i	$0.648330\pi$
$308$	−0.0776319	+	0.0345639i	−0.00442349	+	0.00196946i
$309$	14.1368	+	13.7353i	0.804215	+	0.781375i
$310$	−10.4445	−	6.96886i	−0.593208	−	0.395804i
$311$	2.85314	−	3.16873i	0.161786	−	0.179682i	−0.656801	−	0.754064i	$-0.728091\pi$
$311$	2.85314	−	3.16873i	0.161786	−	0.179682i	0.818587	+	0.574382i	$0.194758\pi$
$312$	−5.20643	−	5.05857i	−0.294756	−	0.286385i
$313$	16.0777	+	17.8561i	0.908767	+	1.00929i	0.999910	+	0.0134497i	$0.00428131\pi$
$313$	16.0777	+	17.8561i	0.908767	+	1.00929i	−0.0911430	+	0.995838i	$0.529052\pi$
$314$	3.43631	+	10.5759i	0.193922	+	0.596831i
$315$	0.271725	+	3.94697i	0.0153100	+	0.222387i
$316$	0.00503424	−	0.0154938i	0.000283198	−	0.000871594i
$317$	−23.8765	+	10.6305i	−1.34104	+	0.597069i	−0.946766	−	0.321923i	$-0.895671\pi$
$317$	−23.8765	+	10.6305i	−1.34104	+	0.597069i	−0.394274	+	0.918993i	$0.629004\pi$
$318$	−8.13073	+	0.543646i	−0.455949	+	0.0304862i
$319$	0.0282405	−	0.268690i	0.00158116	−	0.0150438i
$320$	2.23429	−	0.0892576i	0.124900	−	0.00498965i
$321$	−17.2855	−	6.35117i	−0.964783	−	0.354488i
$322$	−0.351356	−	3.34293i	−0.0195803	−	0.186294i
$323$	−1.25522	−	3.86317i	−0.0698422	−	0.214952i
$324$	−2.28365	+	8.70545i	−0.126870	+	0.483636i
$325$	−19.7627	−	6.96910i	−1.09624	−	0.386576i
$326$	−4.93728	+	8.55162i	−0.273451	+	0.473630i
$327$	−8.00032	+	10.1758i	−0.442419	+	0.562725i
$328$	0.588927	+	0.262207i	0.0325181	+	0.0144780i
$329$	2.90873	+	1.29505i	0.160363	+	0.0713983i
$330$	−0.482732	+	0.279976i	−0.0265735	+	0.0154122i
$331$	25.9679	−	11.5616i	1.42732	−	0.635485i	0.459743	−	0.888052i	$-0.347942\pi$
$331$	25.9679	−	11.5616i	1.42732	−	0.635485i	0.967579	+	0.252567i	$0.0812749\pi$
$332$	−11.2725			−0.618661
$333$	4.36418	−	2.69017i	0.239156	−	0.147421i
$334$	−1.37984	+	4.24672i	−0.0755016	+	0.232370i
$335$	7.10258	+	2.82823i	0.388056	+	0.154523i
$336$	−1.01114	−	0.145252i	−0.0551620	−	0.00792413i
$337$	−8.04455	+	1.70992i	−0.438214	+	0.0931454i	−0.421736	−	0.906719i	$-0.638579\pi$
$337$	−8.04455	+	1.70992i	−0.438214	+	0.0931454i	−0.0164789	+	0.999864i	$0.505246\pi$
$338$	−4.46559	+	0.949190i	−0.242896	+	0.0516292i
$339$	−29.7635	−	4.27559i	−1.61653	−	0.232218i
$340$	−5.19302	+	1.32250i	−0.281631	+	0.0717225i
$341$	−0.250019	+	0.769479i	−0.0135393	+	0.0416696i
$342$	−0.146462	−	5.08273i	−0.00791977	−	0.274843i
$343$	−8.05168			−0.434750
$344$	6.31666	−	2.81236i	0.340571	−	0.151632i
$345$	−4.63193	−	21.5822i	−0.249375	−	1.16194i
$346$	2.34392	+	1.04358i	0.126010	+	0.0561033i
$347$	14.8953	+	6.63180i	0.799619	+	0.356014i	0.765526	−	0.643405i	$-0.222479\pi$
$347$	14.8953	+	6.63180i	0.799619	+	0.356014i	0.0340936	+	0.999419i	$0.489146\pi$
$348$	2.00726	−	2.55309i	0.107601	−	0.136860i
$349$	−0.951760	+	1.64850i	−0.0509466	+	0.0882420i	−0.890374	−	0.455230i	$-0.849557\pi$
$349$	−0.951760	+	1.64850i	−0.0509466	+	0.0882420i	0.839427	+	0.543472i	$0.182890\pi$
$350$	−2.82632	+	0.841242i	−0.151073	+	0.0449663i
$351$	14.4234	+	16.3166i	0.769864	+	0.870913i
$352$	−0.0445254	−	0.137035i	−0.00237321	−	0.00730399i
$353$	−2.90299	−	27.6201i	−0.154510	−	1.47007i	−0.747179	−	0.664623i	$-0.768592\pi$
$353$	−2.90299	−	27.6201i	−0.154510	−	1.47007i	0.592669	−	0.805446i	$-0.298074\pi$
$354$	−12.0166	−	4.41524i	−0.638677	−	0.234667i
$355$	12.2039	+	33.0132i	0.647714	+	1.75216i
$356$	−1.02394	+	9.74214i	−0.0542687	+	0.516332i
$357$	2.44263	−	0.163322i	0.129278	−	0.00864390i
$358$	−0.155315	+	0.0691509i	−0.00820868	+	0.00365474i
$359$	6.03032	−	18.5594i	0.318268	−	0.979528i	−0.656120	−	0.754656i	$-0.727804\pi$
$359$	6.03032	−	18.5594i	0.318268	−	0.979528i	0.974388	−	0.224872i	$-0.0721963\pi$
$360$	−6.70386	−	0.241338i	−0.353325	−	0.0127196i
$361$	−4.98356	−	15.3378i	−0.262293	−	0.807254i
$362$	3.16763	+	3.51801i	0.166487	+	0.184902i
$363$	−13.6391	−	13.2517i	−0.715864	−	0.695534i
$364$	−1.65396	+	1.83690i	−0.0866909	+	0.0962800i
$365$	−34.9106	+	1.39465i	−1.82731	+	0.0729992i
$366$	5.72817	+	5.56549i	0.299416	+	0.290913i
$367$	−14.7705	+	6.57626i	−0.771015	+	0.343278i	−0.754255	−	0.656582i	$-0.772002\pi$
$367$	−14.7705	+	6.57626i	−0.771015	+	0.343278i	−0.0167600	+	0.999860i	$0.505335\pi$
$368$	5.69938			0.297101
$369$	−1.70204	−	0.918348i	−0.0886045	−	0.0478073i
$370$	2.66821	+	2.73539i	0.138714	+	0.142206i
$371$	0.290039	+	2.75954i	0.0150581	+	0.143268i
$372$	−7.46944	+	6.22889i	−0.387272	+	0.322953i
$373$	18.3731	−	20.4054i	0.951324	−	1.05655i	−0.0470119	−	0.998894i	$-0.514970\pi$
$373$	18.3731	−	20.4054i	0.951324	−	1.05655i	0.998336	−	0.0576585i	$-0.0183635\pi$
$374$	0.172654	+	0.299045i	0.00892771	+	0.0154633i
$375$	−17.8664	+	7.46941i	−0.922616	+	0.385719i
$376$	−2.69934	+	4.67540i	−0.139208	+	0.241115i
$377$	−2.42841	−	7.47389i	−0.125070	−	0.384925i
$378$	2.99163	+	0.664551i	0.153873	+	0.0341808i
$379$	18.4747	−	13.4226i	0.948981	−	0.689475i	−0.00158453	−	0.999999i	$-0.500504\pi$
$379$	18.4747	−	13.4226i	0.948981	−	0.689475i	0.950566	+	0.310524i	$0.100504\pi$
$380$	3.67279	−	0.935342i	0.188410	−	0.0479820i
$381$	−0.774926	+	20.4066i	−0.0397006	+	1.04546i
$382$	−6.93450	−	12.0109i	−0.354800	−	0.614531i
$383$	−1.56373	+	14.8779i	−0.0799028	+	0.760225i	0.879064	+	0.476705i	$0.158169\pi$
$383$	−1.56373	+	14.8779i	−0.0799028	+	0.760225i	−0.958966	+	0.283520i	$0.908498\pi$
$384$	0.424144	−	1.67932i	0.0216445	−	0.0856972i
$385$	0.101502	+	0.160637i	0.00517303	+	0.00818681i
$386$	0.978241	+	3.01072i	0.0497912	+	0.153241i
$387$	−19.5353	+	6.97562i	−0.993033	+	0.354591i
$388$	2.90279	−	8.93388i	0.147367	−	0.453549i
$389$	−1.71772	−	0.365112i	−0.0870917	−	0.0185119i	0.164160	−	0.986434i	$-0.447509\pi$
$389$	−1.71772	−	0.365112i	−0.0870917	−	0.0185119i	−0.251251	+	0.967922i	$0.580842\pi$
$390$	−9.51506	+	13.1508i	−0.481814	+	0.665917i
$391$	−13.3602	+	2.83980i	−0.675654	+	0.143615i
$392$	0.695341	−	6.61573i	0.0351200	−	0.334145i
$393$	−0.519657	+	1.05726i	−0.0262132	+	0.0533317i
$394$	−0.808198	+	0.359833i	−0.0407164	+	0.0181281i
$395$	−0.0359060	−	0.00614545i	−0.00180662	−	0.000309211i
$396$	0.102014	+	0.420051i	0.00512637	+	0.0211084i
$397$	24.2401	−	17.6115i	1.21658	−	0.883894i	0.220765	−	0.975327i	$-0.429145\pi$
$397$	24.2401	−	17.6115i	1.21658	−	0.883894i	0.995811	+	0.0914331i	$0.0291448\pi$
$398$	7.31924	+	1.55575i	0.366880	+	0.0779828i
$399$	−1.72756	+	0.115510i	−0.0864861	+	0.00578273i
$400$	−0.917646	−	4.91507i	−0.0458823	−	0.245754i
$401$	1.82034	+	3.15292i	0.0909035	+	0.157450i	0.907892	−	0.419205i	$-0.137691\pi$
$401$	1.82034	+	3.15292i	0.0909035	+	0.157450i	−0.816988	+	0.576655i	$0.804358\pi$
$402$	3.66002	−	4.65528i	0.182545	−	0.232184i
$403$	2.45996	+	23.4050i	0.122539	+	1.16588i
$404$	−13.7846	+	10.0151i	−0.685808	+	0.498269i
$405$	19.9988	+	2.24717i	0.993746	+	0.111663i
$406$	−0.894653	−	0.650003i	−0.0444009	−	0.0322591i
$407$	0.123115	−	0.213242i	0.00610261	−	0.0105700i
$408$	−0.157514	+	4.14790i	−0.00779808	+	0.205352i
$409$	−12.1441	+	2.58131i	−0.600487	+	0.127637i	−0.498118	−	0.867109i	$-0.665975\pi$
$409$	−12.1441	+	2.58131i	−0.600487	+	0.127637i	−0.102369	+	0.994747i	$0.532642\pi$
$410$	0.390370	−	1.38764i	0.0192790	−	0.0685308i
$411$	−11.9140	−	29.7490i	−0.587674	−	1.46741i
$412$	7.61466	+	8.45694i	0.375147	+	0.416643i
$413$	−1.34706	+	4.14583i	−0.0662846	+	0.204003i
$414$	−17.0489	−	1.29671i	−0.837908	−	0.0637298i
$415$	3.63331	+	24.9429i	0.178352	+	1.22440i
$416$	−2.80440	−	3.11460i	−0.137497	−	0.152706i
$417$	−27.4698	+	14.4987i	−1.34520	+	0.710003i
$418$	−0.122110	−	0.211501i	−0.00597260	−	0.0103448i
$419$	−0.108116	+	1.02866i	−0.00528181	+	0.0502531i	−0.996845	−	0.0793686i	$-0.974710\pi$
$419$	−0.108116	+	1.02866i	−0.00528181	+	0.0502531i	0.991564	+	0.129622i	$0.0413763\pi$
$420$	0.00450391	+	2.28418i	0.000219768	+	0.111456i
$421$	−3.11165	−	29.6054i	−0.151653	−	1.44288i	−0.760369	−	0.649492i	$-0.774982\pi$
$421$	−3.11165	−	29.6054i	−0.151653	−	1.44288i	0.608716	−	0.793388i	$-0.291685\pi$
$422$	−15.1112	+	10.9789i	−0.735603	+	0.534447i
$423$	9.13844	−	13.3717i	0.444326	−	0.650152i
$424$	−4.70476			−0.228483
$425$	4.60010	+	11.0644i	0.223138	+	0.536704i
$426$	27.2025	−	1.81884i	1.31796	−	0.0881231i
$427$	1.81970	−	2.02098i	0.0880615	−	0.0978022i
$428$	−9.71293	−	4.32447i	−0.469492	−	0.209031i
$429$	0.981784	+	0.360734i	0.0474010	+	0.0174164i
$430$	−8.25890	−	13.0705i	−0.398280	−	0.630316i
$431$	28.8507	+	20.9612i	1.38969	+	1.00967i	0.995899	+	0.0904668i	$0.0288359\pi$
$431$	28.8507	+	20.9612i	1.38969	+	1.00967i	0.393789	+	0.919201i	$0.371164\pi$
$432$	−1.65084	+	4.92694i	−0.0794261	+	0.237047i
$433$	29.4426	+	21.3913i	1.41492	+	1.02800i	0.992584	+	0.121564i	$0.0387911\pi$
$433$	29.4426	+	21.3913i	1.41492	+	1.02800i	0.422340	+	0.906438i	$0.361209\pi$
$434$	2.21596	+	2.46107i	0.106369	+	0.118135i
$435$	−6.29625	−	3.61860i	−0.301882	−	0.173499i
$436$	−5.00064	+	5.55378i	−0.239487	+	0.265978i
$437$	9.44906	−	2.00846i	0.452010	−	0.0960776i
$438$	−6.62723	+	26.2393i	−0.316662	+	1.25376i
$439$	−7.32832	−	1.55768i	−0.349762	−	0.0743441i	0.0296810	−	0.999559i	$-0.490551\pi$
$439$	−7.32832	−	1.55768i	−0.349762	−	0.0743441i	−0.379443	+	0.925215i	$0.623884\pi$
$440$	−0.288868	+	0.142690i	−0.0137713	+	0.00680250i
$441$	−3.58521	+	19.6318i	−0.170724	+	0.934849i
$442$	8.12581	+	5.90375i	0.386506	+	0.280813i
$443$	0.645949	−	1.11882i	0.0306899	−	0.0531565i	−0.850272	−	0.526343i	$-0.823563\pi$
$443$	0.645949	−	1.11882i	0.0306899	−	0.0531565i	0.880962	+	0.473186i	$0.156896\pi$
$444$	2.61767	−	1.38162i	0.124229	−	0.0655686i
$445$	21.8866	−	0.874350i	1.03753	−	0.0414482i
$446$	−25.9865	−	11.5700i	−1.23050	−	0.547853i
$447$	−0.273437	−	1.57888i	−0.0129331	−	0.0746782i
$448$	−0.576885	−	0.122621i	−0.0272552	−	0.00579328i
$449$	35.3485			1.66820			0.834100	−	0.551613i	$-0.185987\pi$
$449$	35.3485			1.66820			0.834100	+	0.551613i	$0.185987\pi$
$450$	1.62674	+	14.9115i	0.0766855	+	0.702936i
$451$	−0.0928874			−0.00437390
$452$	−16.9810	−	3.60943i	−0.798720	−	0.169773i
$453$	28.5480	−	23.8067i	1.34130	−	1.11854i
$454$	10.3087	+	4.58973i	0.483811	+	0.215407i
$455$	4.59764	+	3.06767i	0.215541	+	0.143815i
$456$	0.111402	−	2.93362i	0.00521688	−	0.137379i
$457$	−9.45832	+	16.3823i	−0.442442	+	0.766332i	−0.997870	−	0.0652328i	$-0.979221\pi$
$457$	−9.45832	+	16.3823i	−0.442442	+	0.766332i	0.555428	+	0.831564i	$0.312554\pi$
$458$	−16.1016	−	11.6985i	−0.752380	−	0.546636i
$459$	1.41490	−	12.3720i	0.0660419	−	0.577477i
$460$	−1.83700	−	12.6111i	−0.0856504	−	0.587996i
$461$	−39.0560	−	8.30161i	−1.81902	−	0.386645i	−0.833000	−	0.553273i	$-0.813379\pi$
$461$	−39.0560	−	8.30161i	−1.81902	−	0.386645i	−0.986020	+	0.166628i	$0.946712\pi$
$462$	0.141609	−	0.0401387i	0.00658823	−	0.00186742i
$463$	9.14188	−	1.94317i	0.424859	−	0.0903067i	0.00948032	−	0.999955i	$-0.496982\pi$
$463$	9.14188	−	1.94317i	0.424859	−	0.0903067i	0.415379	+	0.909648i	$0.363649\pi$
$464$	1.25465	−	1.39343i	0.0582457	−	0.0646884i
$465$	16.1903	+	14.5201i	0.750806	+	0.673353i
$466$	−11.8317	−	13.1404i	−0.548093	−	0.608719i
$467$	−29.1383	−	21.1702i	−1.34836	−	0.979641i	−0.999091	−	0.0426188i	$-0.986430\pi$
$467$	−29.1383	−	21.1702i	−1.34836	−	0.979641i	−0.349269	−	0.937022i	$-0.613570\pi$
$468$	7.68033	+	9.95493i	0.355024	+	0.460167i
$469$	−1.63130	−	1.18521i	−0.0753263	−	0.0547278i
$470$	11.2154	+	4.46593i	0.517326	+	0.205998i
$471$	−3.28672	−	18.9781i	−0.151444	−	0.874466i
$472$	−6.75229	−	3.00631i	−0.310799	−	0.138377i
$473$	−0.666643	+	0.740382i	−0.0306523	+	0.0340428i
$474$	−0.0124468	+	0.0253235i	−0.000571702	+	0.00116315i
$475$	−3.25344	−	7.82536i	−0.149278	−	0.359052i
$476$	1.41340			0.0647832
$477$	14.0736	+	1.07042i	0.644388	+	0.0490110i
$478$	−10.0237	+	7.28263i	−0.458473	+	0.333100i
$479$	−2.34014	−	22.2650i	−0.106924	−	1.01731i	−0.908063	−	0.418834i	$-0.862439\pi$
$479$	−2.34014	−	22.2650i	−0.106924	−	1.01731i	0.801139	−	0.598479i	$-0.204228\pi$
$480$	−3.85256	−	0.397241i	−0.175844	−	0.0181315i
$481$	0.748653	−	7.12295i	0.0341356	−	0.324779i
$482$	11.1153	+	19.2522i	0.506286	+	0.876913i
$483$	−0.220927	+	5.81782i	−0.0100525	+	0.264720i
$484$	−7.34654	−	8.15916i	−0.333934	−	0.370871i
$485$	−20.7038	−	3.54354i	−0.940110	−	0.160904i
$486$	6.05923	−	14.3627i	0.274852	−	0.651503i
$487$	−5.33649	+	16.4240i	−0.241820	+	0.744244i	0.754324	+	0.656503i	$0.227965\pi$
$487$	−5.33649	+	16.4240i	−0.241820	+	0.744244i	−0.996143	+	0.0877416i	$0.972035\pi$
$488$	3.08543	+	3.42671i	0.139671	+	0.155120i
$489$	10.5709	−	13.4454i	0.478030	−	0.608020i
$490$	−14.8628	+	0.593757i	−0.671435	+	0.0268232i
$491$	−2.59070	+	0.550670i	−0.116917	+	0.0248514i	−0.265998	−	0.963973i	$-0.585702\pi$
$491$	−2.59070	+	0.550670i	−0.116917	+	0.0248514i	0.149082	+	0.988825i	$0.452368\pi$
$492$	−0.945110	−	0.594585i	−0.0426088	−	0.0268060i
$493$	−2.24679	+	3.89156i	−0.101190	+	0.175267i
$494$	−5.74702	−	4.17545i	−0.258570	−	0.187862i
$495$	0.896574	−	0.361116i	0.0402980	−	0.0162310i
$496$	−4.54279	+	3.30053i	−0.203977	+	0.148198i
$497$	−0.970366	−	9.23241i	−0.0435268	−	0.414130i
$498$	19.3262	+	2.77625i	0.866029	+	0.124407i
$499$	−3.71614	−	6.43654i	−0.166357	−	0.288139i	0.770779	−	0.637102i	$-0.219867\pi$
$499$	−3.71614	−	6.43654i	−0.166357	−	0.288139i	−0.937136	+	0.348963i	$0.886534\pi$
$500$	−10.5799	+	3.61469i	−0.473147	+	0.161654i
$501$	3.41157	−	6.94096i	0.152418	−	0.310099i
$502$	−16.2797	−	3.46035i	−0.726597	−	0.154443i
$503$	24.6462	−	17.9065i	1.09892	−	0.798413i	0.118038	−	0.993009i	$-0.462340\pi$
$503$	24.6462	−	17.9065i	1.09892	−	0.798413i	0.980883	+	0.194596i	$0.0623397\pi$
$504$	1.69777	+	0.498054i	0.0756248	+	0.0221851i
$505$	26.6035	+	27.2733i	1.18384	+	1.21365i
$506$	−0.750210	+	0.334015i	−0.0333509	+	0.0148488i
$507$	7.88981	−	0.527537i	0.350399	−	0.0234287i
$508$	−1.23242	+	11.7257i	−0.0546796	+	0.520242i
$509$	42.8615	−	9.11049i	1.89980	−	0.403815i	0.900296	−	0.435278i	$-0.143350\pi$
$509$	42.8615	−	9.11049i	1.89980	−	0.403815i	0.999505	+	0.0314627i	$0.0100165\pi$
$510$	9.22890	−	0.988399i	0.408663	−	0.0437670i
$511$	9.01381	+	1.91594i	0.398747	+	0.0847564i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−1.00069	+	8.75017i	−0.0441817	+	0.386329i
$514$	−5.99537	−	18.4518i	−0.264444	−	0.813876i
$515$	16.2585	−	19.5749i	0.716434	−	0.862572i
$516$	−11.5222	+	3.26596i	−0.507238	+	0.143776i
$517$	0.0813107	−	0.773620i	0.00357604	−	0.0340238i
$518$	−0.503932	−	0.872836i	−0.0221415	−	0.0383502i
$519$	−3.76152	−	2.36644i	−0.165113	−	0.103875i
$520$	−5.98782	+	7.20921i	−0.262583	+	0.316145i
$521$	7.54994	−	5.48535i	0.330769	−	0.240318i	−0.409988	−	0.912091i	$-0.634467\pi$
$521$	7.54994	−	5.48535i	0.330769	−	0.240318i	0.740757	+	0.671773i	$0.234467\pi$
$522$	−4.07014	+	3.88280i	−0.178145	+	0.169946i
$523$	3.63232	+	11.1791i	0.158830	+	0.488829i	0.998529	−	0.0542238i	$-0.0172684\pi$
$523$	3.63232	+	11.1791i	0.158830	+	0.488829i	−0.839699	+	0.543053i	$0.817268\pi$
$524$	−0.340078	+	0.589033i	−0.0148564	+	0.0257320i
$525$	5.05278	−	0.746190i	0.220521	−	0.0325664i
$526$	−10.8577	−	18.8060i	−0.473416	−	0.819981i
$527$	9.00445	−	10.0005i	0.392240	−	0.435627i
$528$	0.0425870	+	0.245906i	0.00185336	+	0.0107017i
$529$	−0.991239	−	9.43101i	−0.0430973	−	0.410044i
$530$	1.51642	+	10.4103i	0.0658689	+	0.452195i
$531$	19.5145	+	10.5292i	0.846859	+	0.456930i
$532$	−0.999634			−0.0433396
$533$	−2.46826	+	1.09894i	−0.106912	+	0.0476003i
$534$	4.15483	−	16.4502i	0.179797	−	0.711872i
$535$	−6.43821	+	22.8858i	−0.278348	+	0.989439i
$536$	2.28771	−	2.54076i	0.0988142	−	0.109744i
$537$	0.283312	−	0.0803041i	0.0122258	−	0.00346538i
$538$	−4.65968	−	5.17510i	−0.200893	−	0.223114i
$539$	0.296190	+	0.911580i	0.0127578	+	0.0392645i
$540$	11.4340	+	2.06482i	0.492041	+	0.0888556i
$541$	−1.89517	+	5.83274i	−0.0814798	+	0.250769i	−0.983495	−	0.180935i	$-0.942088\pi$
$541$	−1.89517	+	5.83274i	−0.0814798	+	0.250769i	0.902015	+	0.431704i	$0.142088\pi$
$542$	15.1125	−	6.72850i	0.649136	−	0.289014i
$543$	−4.56432	−	6.81159i	−0.195874	−	0.292314i
$544$	−0.250504	+	2.38339i	−0.0107403	+	0.102187i
$545$	13.9007	+	9.27494i	0.595441	+	0.397295i
$546$	3.28803	−	2.74194i	0.140715	−	0.117344i
$547$	0.421941	+	4.01450i	0.0180409	+	0.171648i	0.999832	−	0.0183147i	$-0.00583008\pi$
$547$	0.421941	+	4.01450i	0.0180409	+	0.171648i	−0.981791	+	0.189962i	$0.939163\pi$
$548$	−5.71736	−	17.5962i	−0.244234	−	0.751674i
$549$	−8.44998	−	10.9525i	−0.360637	−	0.467442i
$550$	0.408840	+	0.593192i	0.0174330	+	0.0252938i
$551$	1.58905	−	2.75232i	0.0676959	−	0.117253i
$552$	−9.77131	−	1.40367i	−0.415895	−	0.0597441i
$553$	0.00877740	+	0.00390795i	0.000373253	+	0.000166183i
$554$	−16.7994	−	7.47958i	−0.713739	−	0.317777i
$555$	−3.90084	−	5.34684i	−0.165581	−	0.226961i
$556$	−16.3828	+	7.29410i	−0.694786	+	0.309339i
$557$	−33.5130			−1.41999			−0.709996	−	0.704205i	$-0.751303\pi$
$557$	−33.5130			−1.41999			−0.709996	+	0.704205i	$0.751303\pi$
$558$	14.3401	−	8.83952i	0.607063	−	0.374207i
$559$	−8.95505	+	27.5608i	−0.378758	+	1.16570i
$560$	−0.0853860	+	1.31600i	−0.00360822	+	0.0556114i
$561$	−0.222356	−	0.555220i	−0.00938790	−	0.0234414i
$562$	15.8938	−	3.37833i	0.670440	−	0.142506i
$563$	−7.02607	+	1.49344i	−0.296114	+	0.0629409i	−0.353573	−	0.935407i	$-0.615033\pi$
$563$	−7.02607	+	1.49344i	−0.296114	+	0.0629409i	0.0574593	+	0.998348i	$0.481700\pi$
$564$	5.77937	−	7.35094i	0.243355	−	0.309530i
$565$	−2.51340	+	38.7376i	−0.105739	+	1.62970i
$566$	3.37090	−	10.3746i	0.141689	−	0.436075i
$567$	−4.96533	−	1.87613i	−0.208524	−	0.0787901i
$568$	15.7404			0.660453
$569$	−34.1370	+	15.1988i	−1.43110	+	0.637166i	−0.968412	−	0.249356i	$-0.919781\pi$
$569$	−34.1370	+	15.1988i	−1.43110	+	0.637166i	−0.462687	+	0.886522i	$0.653114\pi$
$570$	−6.52718	+	0.699049i	−0.273393	+	0.0292799i
$571$	−34.4286	−	15.3286i	−1.44079	−	0.641482i	−0.470277	−	0.882519i	$-0.655846\pi$
$571$	−34.4286	−	15.3286i	−1.44079	−	0.641482i	−0.970516	+	0.241036i	$0.922513\pi$
$572$	0.551676	+	0.245622i	0.0230667	+	0.0102700i
$573$	8.93076	+	22.3000i	0.373088	+	0.931594i
$574$	−0.190102	+	0.329266i	−0.00793470	+	0.0137433i
$575$	−27.3127	+	8.12951i	−1.13902	+	0.339024i
$576$	−1.14076	+	2.77465i	−0.0475318	+	0.115610i
$577$	−8.73421	−	26.8811i	−0.363610	−	1.11908i	−0.950847	−	0.309661i	$-0.899784\pi$
$577$	−8.73421	−	26.8811i	−0.363610	−	1.11908i	0.587237	−	0.809415i	$-0.300216\pi$
$578$	1.17665	+	11.1950i	0.0489420	+	0.465652i
$579$	−0.935655	−	5.40265i	−0.0388845	−	0.224527i
$580$	−3.48766	−	2.32706i	−0.144817	−	0.0966260i
$581$	0.694930	−	6.61182i	0.0288306	−	0.274304i
$582$	−7.17698	+	14.6018i	−0.297495	+	0.605264i
$583$	0.619289	−	0.275725i	0.0256483	−	0.0114194i
$584$	−4.82838	+	14.8602i	−0.199800	+	0.614920i
$585$	19.5520	−	20.2030i	0.808374	−	0.835292i
$586$	0.470433	+	1.44784i	0.0194334	+	0.0598099i
$587$	29.1571	+	32.3823i	1.20344	+	1.33656i	0.926785	+	0.375592i	$0.122560\pi$
$587$	29.1571	+	32.3823i	1.20344	+	1.33656i	0.276659	+	0.960968i	$0.410773\pi$
$588$	−2.82148	+	11.1711i	−0.116356	+	0.460688i
$589$	−6.36843	+	7.07286i	−0.262407	+	0.291432i
$590$	−4.47575	+	15.9099i	−0.184264	+	0.654999i
$591$	1.47424	−	0.417870i	0.0606420	−	0.0171889i
$592$	1.56116	−	0.695073i	0.0641633	−	0.0285673i
$593$	27.2179			1.11770			0.558852	−	0.829267i	$-0.311242\pi$
$593$	27.2179			1.11770			0.558852	+	0.829267i	$0.311242\pi$
$594$	−0.0714453	−	0.745282i	−0.00293144	−	0.0305793i
$595$	−0.455561	−	3.12746i	−0.0186762	−	0.128213i
$596$	−0.0967028	−	0.920065i	−0.00396110	−	0.0376873i
$597$	−12.1653	−	4.46987i	−0.497893	−	0.182940i
$598$	−15.9833	+	17.7513i	−0.653607	+	0.725904i
$599$	−5.08770	−	8.81216i	−0.207878	−	0.360055i	0.743168	−	0.669105i	$-0.233322\pi$
$599$	−5.08770	−	8.81216i	−0.207878	−	0.360055i	−0.951046	+	0.309050i	$0.899989\pi$
$600$	0.362755	+	8.65265i	0.0148094	+	0.353243i
$601$	−13.2363	+	22.9260i	−0.539920	+	0.935169i	0.458987	+	0.888443i	$0.348212\pi$
$601$	−13.2363	+	22.9260i	−0.539920	+	0.935169i	−0.998908	+	0.0467267i	$0.985121\pi$
$602$	1.26016	+	3.87836i	0.0513601	+	0.158070i
$603$	−7.42145	+	7.07984i	−0.302225	+	0.288314i
$604$	17.3625	−	12.6146i	0.706469	−	0.513280i
$605$	−15.6860	+	18.8856i	−0.637727	+	0.767810i
$606$	26.0995	−	13.7754i	1.06022	−	0.559589i
$607$	−9.02693	−	15.6351i	−0.366392	−	0.634609i	0.622607	−	0.782535i	$-0.286074\pi$
$607$	−9.02693	−	15.6351i	−0.366392	−	0.634609i	−0.988998	+	0.147926i	$0.952740\pi$
$608$	0.177170	−	1.68566i	0.00718520	−	0.0683626i
$609$	1.37375	+	1.33474i	0.0556673	+	0.0540863i
$610$	6.58786	−	7.93165i	0.266735	−	0.321143i
$611$	−6.99196	−	21.5190i	−0.282864	−	0.870567i
$612$	1.29161	−	7.07258i	0.0522103	−	0.285892i
$613$	6.04512	−	18.6050i	0.244160	−	0.751448i	−0.751613	−	0.659604i	$-0.770724\pi$
$613$	6.04512	−	18.6050i	0.244160	−	0.751448i	0.995773	−	0.0918436i	$-0.0292760\pi$
$614$	15.4010	+	3.27358i	0.621534	+	0.132111i
$615$	−1.01103	+	2.28290i	−0.0407685	+	0.0920555i
$616$	0.0831217	−	0.0176681i	0.00334907	−	0.000711866i
$617$	2.30619	−	21.9419i	0.0928437	−	0.883349i	−0.844644	−	0.535329i	$-0.820188\pi$
$617$	2.30619	−	21.9419i	0.0928437	−	0.883349i	0.937487	−	0.348020i	$-0.113146\pi$
$618$	−10.9722	−	16.3744i	−0.441365	−	0.658674i
$619$	−40.7055	+	18.1232i	−1.63609	+	0.728434i	−0.999099	−	0.0424365i	$-0.986488\pi$
$619$	−40.7055	+	18.1232i	−1.63609	+	0.728434i	−0.636991	+	0.770871i	$0.719821\pi$
$620$	8.76735	+	8.98810i	0.352105	+	0.360971i
$621$	28.9102	+	6.42202i	1.16012	+	0.257707i
$622$	−3.44960	+	2.50628i	−0.138316	+	0.100493i
$623$	−5.65105	−	1.20117i	−0.226405	−	0.0481238i
$624$	4.04093	+	6.03050i	0.161766	+	0.241413i
$625$	11.4083	+	22.2452i	0.456334	+	0.889809i
$626$	−12.0139	−	20.8087i	−0.480172	−	0.831682i
$627$	0.157262	+	0.392682i	0.00628046	+	0.0156822i
$628$	−1.16237	−	11.0592i	−0.0463836	−	0.441311i
$629$	−3.31326	+	2.40723i	−0.132108	+	0.0959824i
$630$	0.554835	−	3.91722i	0.0221051	−	0.156066i
$631$	26.9639	+	19.5904i	1.07342	+	0.779882i	0.976523	−	0.215413i	$-0.0691096\pi$
$631$	26.9639	+	19.5904i	1.07342	+	0.779882i	0.0968927	+	0.995295i	$0.469110\pi$
$632$	−0.00814556	+	0.0141085i	−0.000324013	+	0.000561207i
$633$	28.6114	−	15.1012i	1.13720	−	0.600220i
$634$	25.5650	−	5.43401i	1.01532	−	0.215812i
$635$	26.3428	−	1.05237i	1.04538	−	0.0417620i
$636$	8.06609	+	1.15871i	0.319841	+	0.0459458i
$637$	18.6553	+	20.7188i	0.739150	+	0.820910i
$638$	−0.0834872	+	0.256947i	−0.00330529	+	0.0101726i
$639$	−47.0852	−	3.58122i	−1.86266	−	0.141671i
$640$	−2.20402	−	0.377227i	−0.0871215	−	0.0149112i
$641$	30.6868	+	34.0811i	1.21205	+	1.34612i	0.921071	+	0.389395i	$0.127316\pi$
$641$	30.6868	+	34.0811i	1.21205	+	1.34612i	0.290984	+	0.956728i	$0.406017\pi$
$642$	15.5873	+	9.80624i	0.615181	+	0.387022i
$643$	−23.3328	−	40.4136i	−0.920155	−	1.59376i	−0.799173	−	0.601101i	$-0.794729\pi$
$643$	−23.3328	−	40.4136i	−0.920155	−	1.59376i	−0.120983	−	0.992655i	$-0.538605\pi$
$644$	−0.351356	+	3.34293i	−0.0138454	+	0.131730i
$645$	10.9404	+	24.4428i	0.430779	+	0.962434i
$646$	0.424592	+	4.03972i	0.0167053	+	0.158941i
$647$	−19.0254	+	13.8227i	−0.747964	+	0.543428i	−0.895195	−	0.445674i	$-0.852964\pi$
$647$	−19.0254	+	13.8227i	−0.747964	+	0.543428i	0.147231	+	0.989102i	$0.452964\pi$
$648$	4.04371	−	8.04042i	0.158852	−	0.315858i
$649$	1.06499			0.0418046
$650$	17.8819	+	10.9257i	0.701386	+	0.428542i
$651$	−3.19303	−	4.76514i	−0.125145	−	0.186760i
$652$	6.60737	−	7.33822i	0.258764	−	0.287387i
$653$	−12.8067	−	5.70192i	−0.501166	−	0.223133i	0.140553	−	0.990073i	$-0.455112\pi$
$653$	−12.8067	−	5.70192i	−0.501166	−	0.223133i	−0.641719	+	0.766940i	$0.721779\pi$
$654$	9.94117	−	8.29010i	0.388730	−	0.324169i
$655$	1.41298	+	0.562643i	0.0552095	+	0.0219843i
$656$	−0.521542	−	0.378922i	−0.0203628	−	0.0147944i
$657$	17.8244	−	43.3537i	0.695395	−	1.69139i
$658$	−2.57591	−	1.87151i	−0.100419	−	0.0729589i
$659$	−15.6040	−	17.3300i	−0.607846	−	0.675082i	0.358142	−	0.933667i	$-0.383410\pi$
$659$	−15.6040	−	17.3300i	−0.607846	−	0.675082i	−0.965988	+	0.258585i	$0.916744\pi$
$660$	0.530393	−	0.173492i	0.0206455	−	0.00675317i
$661$	18.8177	−	20.8992i	0.731923	−	0.812883i	−0.256188	−	0.966627i	$-0.582466\pi$
$661$	18.8177	−	20.8992i	0.731923	−	0.812883i	0.988111	+	0.153744i	$0.0491331\pi$
$662$	−27.8042	+	5.90996i	−1.08064	+	0.229697i
$663$	−12.4773	−	12.1230i	−0.484579	−	0.470816i
$664$	11.0262	+	2.34369i	0.427900	+	0.0909529i
$665$	0.322197	+	2.21191i	0.0124943	+	0.0857740i
$666$	−4.82813	+	1.72402i	−0.187086	+	0.0668045i
$667$	−8.64565	−	6.28143i	−0.334761	−	0.243218i
$668$	2.23263	−	3.86703i	0.0863831	−	0.149620i
$669$	41.7032	+	26.2362i	1.61234	+	1.01435i
$670$	−6.35935	−	4.24314i	−0.245683	−	0.163927i
$671$	−0.606959	−	0.270236i	−0.0234314	−	0.0104323i
$672$	0.958842	+	0.352305i	0.0369881	+	0.0135905i
$673$	9.41198	+	2.00058i	0.362805	+	0.0771167i	0.385708	−	0.922621i	$-0.373957\pi$
$673$	9.41198	+	2.00058i	0.362805	+	0.0771167i	−0.0229023	+	0.999738i	$0.507291\pi$
$674$	8.22427			0.316787
$675$	0.883499	−	25.9657i	0.0340059	−	0.999422i
$676$	4.56535			0.175591
$677$	−31.0509	−	6.60007i	−1.19338	−	0.253661i	−0.431945	−	0.901900i	$-0.642173\pi$
$677$	−31.0509	−	6.60007i	−1.19338	−	0.253661i	−0.761437	+	0.648239i	$0.775506\pi$
$678$	28.2242	+	10.3703i	1.08394	+	0.398271i
$679$	5.06115	+	2.25337i	0.194229	+	0.0864763i
$680$	5.35451	−	0.213907i	0.205336	−	0.00820298i
$681$	−16.5434	−	10.4077i	−0.633944	−	0.398825i
$682$	0.404539	−	0.700682i	0.0154906	−	0.0268305i
$683$	−20.8093	−	15.1188i	−0.796246	−	0.578506i	0.113565	−	0.993531i	$-0.463773\pi$
$683$	−20.8093	−	15.1188i	−0.796246	−	0.578506i	−0.909810	+	0.415024i	$0.863773\pi$
$684$	−0.913498	+	5.00211i	−0.0349285	+	0.191261i
$685$	−37.0927	+	18.3224i	−1.41724	+	0.700064i
$686$	7.87573	+	1.67404i	0.300697	+	0.0639151i
$687$	24.7243	+	24.0221i	0.943292	+	0.916502i
$688$	−6.76334	+	1.43759i	−0.257850	+	0.0548077i
$689$	13.1940	−	14.6534i	0.502652	−	0.558252i
$690$	0.0435244	+	22.0736i	0.00165694	+	0.840326i
$691$	0.0590924	+	0.0656287i	0.00224798	+	0.00249663i	0.744268	−	0.667881i	$-0.232799\pi$
$691$	0.0590924	+	0.0656287i	0.00224798	+	0.00249663i	−0.742020	+	0.670378i	$0.766132\pi$
$692$	−2.07573	−	1.50811i	−0.0789074	−	0.0573296i
$693$	−0.252667	+	0.0339399i	−0.00959801	+	0.00128927i
$694$	−13.1909	−	9.58378i	−0.500721	−	0.363795i
$695$	21.4202	+	33.8995i	0.812515	+	1.28588i
$696$	−2.49422	+	2.07997i	−0.0945431	+	0.0788410i
$697$	1.41138	+	0.628385i	0.0534596	+	0.0238018i
$698$	1.27370	−	1.41459i	0.0482104	−	0.0535431i
$699$	17.0486	+	25.4426i	0.644837	+	0.962328i
$700$	2.93947	−	0.235233i	0.111101	−	0.00889098i
$701$	28.3556			1.07097			0.535487	−	0.844543i	$-0.320128\pi$
$701$	28.3556			1.07097			0.535487	+	0.844543i	$0.320128\pi$
$702$	−10.7158	−	18.9588i	−0.404442	−	0.715554i
$703$	2.34332	−	1.70252i	0.0883799	−	0.0642118i
$704$	0.0150612	+	0.143298i	0.000567641	+	0.00540074i
$705$	−18.1283	−	10.4188i	−0.682752	−	0.392394i
$706$	−2.90299	+	27.6201i	−0.109255	+	1.03950i
$707$	−5.02447	−	8.70264i	−0.188965	−	0.327296i
$708$	10.8361	+	6.81716i	0.407244	+	0.256204i
$709$	−7.86397	−	8.73383i	−0.295338	−	0.328006i	0.577153	−	0.816636i	$-0.304163\pi$
$709$	−7.86397	−	8.73383i	−0.295338	−	0.328006i	−0.872491	+	0.488630i	$0.837497\pi$
$710$	−5.07337	−	34.8291i	−0.190400	−	1.30711i
$711$	0.0275763	−	0.0403504i	0.00103419	−	0.00151326i
$712$	3.02707	−	9.31636i	0.113444	−	0.349145i
$713$	21.4143	+	23.7830i	0.801972	+	0.890680i
$714$	−2.42321	−	0.348098i	−0.0906863	−	0.0130273i
$715$	0.365678	−	1.29987i	0.0136756	−	0.0486124i
$716$	0.166299	−	0.0353479i	0.00621488	−	0.00132101i
$717$	18.9787	−	10.0170i	0.708773	−	0.374093i
$718$	−9.75726	+	16.9001i	−0.364138	+	0.630705i
$719$	1.79216	+	1.30208i	0.0668364	+	0.0485595i	0.620702	−	0.784047i	$-0.286848\pi$
$719$	1.79216	+	1.30208i	0.0668364	+	0.0485595i	−0.553865	+	0.832606i	$0.686848\pi$
$720$	6.50719	+	1.62987i	0.242509	+	0.0607419i
$721$	−5.42978	+	3.94496i	−0.202215	+	0.146918i
$722$	1.68575	+	16.0388i	0.0627370	+	0.596903i
$723$	−14.3151	−	35.7444i	−0.532383	−	1.32935i
$724$	−2.36697	−	4.09972i	−0.0879679	−	0.152365i
$725$	−4.02500	+	8.46725i	−0.149485	+	0.314466i
$726$	10.5858	+	15.7978i	0.392877	+	0.586312i
$727$	−14.7461	−	3.13438i	−0.546902	−	0.116248i	−0.0738293	−	0.997271i	$-0.523522\pi$
$727$	−14.7461	−	3.13438i	−0.546902	−	0.116248i	−0.473073	+	0.881023i	$0.656855\pi$
$728$	1.99973	−	1.45289i	0.0741148	−	0.0538476i
$729$	−13.9255	+	23.1318i	−0.515761	+	0.856733i
$730$	34.4377	+	5.89416i	1.27460	+	0.218153i
$731$	15.1380	−	6.73987i	0.559899	−	0.249283i
$732$	−4.44587	−	6.63482i	−0.164324	−	0.245230i
$733$	−2.27696	+	21.6638i	−0.0841015	+	0.800172i	0.868446	+	0.495783i	$0.165119\pi$
$733$	−2.27696	+	21.6638i	−0.0841015	+	0.800172i	−0.952548	+	0.304389i	$0.901548\pi$
$734$	15.8150	−	3.36159i	0.583744	−	0.124079i
$735$	25.6279	+	2.64252i	0.945298	+	0.0974707i
$736$	−5.57484	−	1.18497i	−0.205491	−	0.0436785i
$737$	−0.152229	+	0.468514i	−0.00560744	+	0.0172579i
$738$	1.47391	+	1.25215i	0.0542553	+	0.0460924i
$739$	−6.17927	−	19.0178i	−0.227308	−	0.699583i	−0.998049	−	0.0624339i	$-0.980114\pi$
$739$	−6.17927	−	19.0178i	−0.227308	−	0.699583i	0.770741	−	0.637149i	$-0.219886\pi$
$740$	−2.04119	−	3.23037i	−0.0750355	−	0.118751i
$741$	8.82463	+	8.57401i	0.324181	+	0.314974i
$742$	0.290039	−	2.75954i	0.0106477	−	0.101306i
$743$	−17.5409	−	30.3818i	−0.643514	−	1.11460i	−0.984643	−	0.174583i	$-0.944142\pi$
$743$	−17.5409	−	30.3818i	−0.643514	−	1.11460i	0.341128	−	0.940017i	$-0.389191\pi$
$744$	8.60127	−	4.53979i	0.315338	−	0.166437i
$745$	−2.00467	+	0.510527i	−0.0734456	+	0.0187043i
$746$	−22.2142	+	16.1395i	−0.813318	+	0.590910i
$747$	−32.4501	−	9.51948i	−1.18729	−	0.348300i
$748$	−0.106706	−	0.328407i	−0.00390155	−	0.0120077i
$749$	3.13527	−	5.43044i	0.114560	−	0.198424i
$750$	19.0289	−	3.59155i	0.694839	−	0.131145i
$751$	3.17972	+	5.50744i	0.116030	+	0.200969i	0.918191	−	0.396138i	$-0.129650\pi$
$751$	3.17972	+	5.50744i	0.116030	+	0.200969i	−0.802161	+	0.597108i	$0.796317\pi$
$752$	3.61243	−	4.01200i	0.131732	−	0.146303i
$753$	27.0585	+	9.94202i	0.986065	+	0.362308i
$754$	0.821439	+	7.81547i	0.0299150	+	0.284622i
$755$	−33.5087	−	34.3524i	−1.21950	−	1.25021i
$756$	−2.78808	−	1.27202i	−0.101402	−	0.0462631i
$757$	42.2532			1.53572			0.767860	−	0.640618i	$-0.221322\pi$
$757$	42.2532			1.53572			0.767860	+	0.640618i	$0.221322\pi$
$758$	−20.8617	+	9.28823i	−0.757731	+	0.337364i
$759$	1.36846	−	0.387888i	0.0496720	−	0.0140794i
$760$	−3.78700	+	0.151287i	−0.137369	+	0.00548775i
$761$	24.9413	−	27.7002i	0.904123	−	1.00413i	−0.0958389	−	0.995397i	$-0.530553\pi$
$761$	24.9413	−	27.7002i	0.904123	−	1.00413i	0.999962	−	0.00873345i	$-0.00277998\pi$
$762$	5.00076	−	19.7996i	0.181159	−	0.717262i
$763$	−2.94924	−	3.27547i	−0.106770	−	0.118580i
$764$	4.28575	+	13.1902i	0.155053	+	0.477204i
$765$	−16.0659	−	0.578370i	−0.580865	−	0.0209110i
$766$	4.62284	−	14.2277i	0.167030	−	0.514066i
$767$	28.2995	−	12.5998i	1.02184	−	0.454951i
$768$	−0.764025	+	1.55443i	−0.0275694	+	0.0560908i
$769$	1.04274	−	9.92100i	0.0376021	−	0.357760i	−0.959501	−	0.281704i	$-0.909100\pi$
$769$	1.04274	−	9.92100i	0.0376021	−	0.357760i	0.997104	−	0.0760565i	$-0.0242329\pi$
$770$	−0.0658858	−	0.178230i	−0.00237436	−	0.00642296i
$771$	5.73437	+	33.1114i	0.206518	+	1.19248i
$772$	−0.330901	−	3.14831i	−0.0119094	−	0.113310i
$773$	−12.9908	−	39.9816i	−0.467247	−	1.43804i	−0.856135	−	0.516752i	$-0.827141\pi$
$773$	−12.9908	−	39.9816i	−0.467247	−	1.43804i	0.388889	−	0.921285i	$-0.372859\pi$
$774$	20.5587	−	2.76158i	0.738966	−	0.0992629i
$775$	17.0623	−	22.2967i	0.612895	−	0.800920i
$776$	−4.69682	+	8.13513i	−0.168606	+	0.292034i
$777$	0.649001	+	1.62055i	0.0232828	+	0.0581367i
$778$	1.60427	+	0.714266i	0.0575158	+	0.0256077i
$779$	−0.998201	−	0.444428i	−0.0357643	−	0.0159233i
$780$	12.0413	−	10.8851i	0.431149	−	0.389751i
$781$	−2.07191	+	0.922475i	−0.0741389	+	0.0330087i
$782$	13.6587			0.488433
$783$	7.93434	−	5.65446i	0.283550	−	0.202074i
$784$	−2.05563	+	6.32659i	−0.0734155	+	0.225950i
$785$	−24.0963	+	6.13655i	−0.860032	+	0.219023i
$786$	0.728117	−	0.926113i	0.0259711	−	0.0330333i
$787$	−22.5138	+	4.78546i	−0.802531	+	0.170583i	−0.590877	−	0.806761i	$-0.701218\pi$
$787$	−22.5138	+	4.78546i	−0.802531	+	0.170583i	−0.211654	+	0.977345i	$0.567885\pi$
$788$	0.865350	−	0.183936i	0.0308268	−	0.00655244i
$789$	13.9833	+	34.9160i	0.497819	+	1.24304i
$790$	0.0338436	+	0.0134764i	0.00120410	+	0.000479470i
$791$	3.16393	−	9.73757i	0.112496	−	0.346228i
$792$	−0.0124507	−	0.432082i	−0.000442417	−	0.0153534i
$793$	−19.3256			−0.686272
$794$	−27.3720	+	12.1868i	−0.971397	+	0.432494i
$795$	−0.0359288	−	18.2214i	−0.00127426	−	0.646248i
$796$	−6.83584	−	3.04351i	−0.242290	−	0.107874i
$797$	−11.8396	−	5.27134i	−0.419381	−	0.186720i	0.186187	−	0.982514i	$-0.440387\pi$
$797$	−11.8396	−	5.27134i	−0.419381	−	0.186720i	−0.605567	+	0.795794i	$0.707054\pi$
$798$	1.71382	+	0.246194i	0.0606687	+	0.00871517i
$799$	−6.46902	+	11.2047i	−0.228858	+	0.396393i
$800$	−0.124308	+	4.99845i	−0.00439494	+	0.176722i
$801$	−11.1747	+	27.1799i	−0.394838	+	0.960354i
$802$	−1.12503	−	3.46250i	−0.0397263	−	0.122265i
$803$	−0.235331	−	2.23902i	−0.00830464	−	0.0790134i
$804$	−4.54792	+	3.79259i	−0.160393	+	0.133754i
$805$	7.51019	−	0.300025i	0.264700	−	0.0105745i
$806$	2.45996	−	23.4050i	0.0866485	−	0.824405i
$807$	6.71425	+	10.0201i	0.236353	+	0.352723i
$808$	15.5656	−	6.93025i	0.547596	−	0.243805i
$809$	−8.15709	+	25.1049i	−0.286788	+	0.882643i	0.699069	+	0.715054i	$0.253598\pi$
$809$	−8.15709	+	25.1049i	−0.286788	+	0.882643i	−0.985857	+	0.167589i	$0.946402\pi$
$810$	−19.0945	−	6.35604i	−0.670913	−	0.223329i
$811$	3.62031	+	11.1422i	0.127126	+	0.391255i	0.994283	−	0.106782i	$-0.0340546\pi$
$811$	3.62031	+	11.1422i	0.127126	+	0.391255i	−0.867156	+	0.498036i	$0.834055\pi$
$812$	0.739959	+	0.821808i	0.0259675	+	0.0288398i
$813$	−27.5667	+	7.81373i	−0.966806	+	0.274039i
$814$	−0.164761	+	0.182985i	−0.00577486	+	0.00641363i
$815$	−18.3671	−	12.2550i	−0.643370	−	0.429274i
$816$	1.01647	−	4.02451i	0.0355835	−	0.140886i
$817$	−10.7064	+	4.76680i	−0.374570	+	0.166769i
$818$	12.4154			0.434094
$819$	−6.31246	+	3.89114i	−0.220575	+	0.135967i
$820$	−0.670347	+	1.27616i	−0.0234095	+	0.0445653i
$821$	−2.32902	−	22.1591i	−0.0812833	−	0.773359i	−0.956913	−	0.290376i	$-0.906220\pi$
$821$	−2.32902	−	22.1591i	−0.0812833	−	0.773359i	0.875629	−	0.482984i	$-0.160447\pi$
$822$	5.46847	+	31.5760i	0.190735	+	1.10134i
$823$	−11.6200	+	12.9053i	−0.405046	+	0.449849i	−0.910812	−	0.412822i	$-0.864543\pi$
$823$	−11.6200	+	12.9053i	−0.405046	+	0.449849i	0.505766	+	0.862671i	$0.331210\pi$
$824$	−5.68997	−	9.85531i	−0.198219	−	0.343326i
$825$	−0.554843	−	1.11769i	−0.0193171	−	0.0389130i
$826$	2.17959	−	3.77517i	0.0758378	−	0.131355i
$827$	1.56494	+	4.81641i	0.0544185	+	0.167483i	0.974572	−	0.224075i	$-0.0719362\pi$
$827$	1.56494	+	4.81641i	0.0544185	+	0.167483i	−0.920153	+	0.391558i	$0.871936\pi$
$828$	16.4067	+	4.81304i	0.570174	+	0.167265i
$829$	15.0796	−	10.9560i	0.523736	−	0.380517i	−0.294273	−	0.955721i	$-0.595078\pi$
$829$	15.0796	−	10.9560i	0.523736	−	0.380517i	0.818010	+	0.575205i	$0.195078\pi$
$830$	1.63201	−	25.1533i	0.0566480	−	0.873083i
$831$	26.9597	+	16.9608i	0.935221	+	0.588364i
$832$	2.09555	+	3.62960i	0.0726502	+	0.125834i
$833$	1.66640	−	15.8547i	0.0577372	−	0.549333i
$834$	29.8840	−	8.47055i	1.03480	−	0.293311i
$835$	−9.27625	−	3.69378i	−0.321018	−	0.127828i
$836$	0.0754682	+	0.232267i	0.00261012	+	0.00803313i
$837$	−26.7624	+	11.6232i	−0.925043	+	0.401756i
$838$	0.319623	−	0.983698i	0.0110412	−	0.0339813i
$839$	1.19343	+	0.253671i	0.0412017	+	0.00875769i	0.228466	−	0.973552i	$-0.426629\pi$
$839$	1.19343	+	0.253671i	0.0412017	+	0.00875769i	−0.187265	+	0.982309i	$0.559962\pi$
$840$	0.470501	−	2.23520i	0.0162338	−	0.0771216i
$841$	24.9273	−	5.29846i	0.859562	−	0.182706i
$842$	−3.11165	+	29.6054i	−0.107235	+	1.02027i
$843$	−28.0812	+	1.87760i	−0.967168	+	0.0646678i
$844$	17.0637	−	7.59723i	0.587356	−	0.261508i
$845$	−1.47148	−	10.1018i	−0.0506205	−	0.347514i
$846$	−11.7189	+	11.1795i	−0.402903	+	0.384358i
$847$	5.23859	−	3.80606i	0.180000	−	0.130778i
$848$	4.60195	+	0.978175i	0.158032	+	0.0335907i
$849$	−8.33433	+	16.9565i	−0.286033	+	0.581945i
$850$	−2.19916	−	11.7791i	−0.0754304	−	0.404018i
$851$	−4.86984	−	8.43482i	−0.166936	−	0.289142i
$852$	−26.9862	−	3.87661i	−0.924531	−	0.132811i
$853$	0.662117	+	6.29962i	0.0226704	+	0.215695i	0.999992	+	0.00393538i	$0.00125267\pi$
$853$	0.662117	+	6.29962i	0.0226704	+	0.215695i	−0.977322	+	0.211759i	$0.932081\pi$
$854$	−2.20012	+	1.59848i	−0.0752866	+	0.0546989i
$855$	11.3627	+	0.409055i	0.388596	+	0.0139894i
$856$	8.60157	+	6.24941i	0.293996	+	0.213600i
$857$	15.3073	−	26.5131i	0.522888	−	0.905669i	−0.476757	−	0.879035i	$-0.658188\pi$
$857$	15.3073	−	26.5131i	0.522888	−	0.905669i	0.999645	−	0.0266336i	$-0.00847874\pi$
$858$	−0.885328	−	0.556976i	−0.0302246	−	0.0190148i
$859$	−43.0122	+	9.14252i	−1.46756	+	0.311939i	−0.871259	−	0.490824i	$-0.836696\pi$
$859$	−43.0122	+	9.14252i	−1.46756	+	0.311939i	−0.596298	+	0.802763i	$0.703362\pi$
$860$	5.36091	+	14.5020i	0.182806	+	0.494514i
$861$	0.407013	−	0.517691i	0.0138710	−	0.0176429i
$862$	−23.8621	−	26.5016i	−0.812748	−	0.902648i
$863$	−8.41499	+	25.8987i	−0.286450	+	0.881601i	0.699511	+	0.714622i	$0.253401\pi$
$863$	−8.41499	+	25.8987i	−0.286450	+	0.881601i	−0.985960	+	0.166979i	$0.946599\pi$
$864$	2.63913	−	4.47604i	0.0897852	−	0.152278i
$865$	−2.66797	+	5.07909i	−0.0907137	+	0.172694i
$866$	−24.3517	−	27.0454i	−0.827506	−	0.919038i
$867$	0.739858	−	19.4831i	0.0251269	−	0.661682i
$868$	−1.65585	−	2.86801i	−0.0562031	−	0.0973466i
$869$	0.000245364	−	0.00233448i	8.32341e−6	−	7.91919e-5i
$870$	5.40631	+	4.84859i	0.183291	+	0.164383i
$871$	1.49780	+	14.2506i	0.0507510	+	0.482864i
$872$	6.04606	−	4.39272i	0.204745	−	0.148756i
$873$	15.9008	−	23.2665i	0.538159	−	0.787452i
$874$	−9.66015			−0.326760
$875$	−1.46794	−	6.42839i	−0.0496254	−	0.217319i
$876$	11.9379	−	24.2880i	0.403343	−	0.820615i
$877$	5.73212	−	6.36616i	0.193560	−	0.214970i	−0.638551	−	0.769580i	$-0.720466\pi$
$877$	5.73212	−	6.36616i	0.193560	−	0.214970i	0.832111	+	0.554610i	$0.187132\pi$
$878$	6.84432	+	3.04729i	0.230985	+	0.102841i
$879$	−0.449953	−	2.59812i	−0.0151766	−	0.0876323i
$880$	0.312223	−	0.0795132i	0.0105250	−	0.00268039i
$881$	30.0664	+	21.8445i	1.01296	+	0.735960i	0.964828	−	0.262881i	$-0.0846726\pi$
$881$	30.0664	+	21.8445i	1.01296	+	0.735960i	0.0481339	+	0.998841i	$0.484673\pi$
$882$	7.58855	−	18.4574i	0.255520	−	0.621493i
$883$	40.1424	+	29.1652i	1.35090	+	0.981486i	0.998966	+	0.0454611i	$0.0144757\pi$
$883$	40.1424	+	29.1652i	1.35090	+	0.981486i	0.351934	+	0.936025i	$0.385524\pi$
$884$	−6.72079	−	7.46419i	−0.226045	−	0.251048i
$885$	11.5918	−	26.1744i	0.389654	−	0.879843i
$886$	−0.864448	+	0.960067i	−0.0290417	+	0.0322541i
$887$	28.9582	−	6.15525i	0.972321	−	0.206673i	0.305747	−	0.952113i	$-0.401094\pi$
$887$	28.9582	−	6.15525i	0.972321	−	0.206673i	0.666573	+	0.745440i	$0.267760\pi$
$888$	−2.84772	+	0.807180i	−0.0955632	+	0.0270872i
$889$	−6.80162	−	1.44573i	−0.228119	−	0.0484882i
$890$	−21.5901	−	3.69524i	−0.723703	−	0.123865i
$891$	−0.0610616	+	1.29535i	−0.00204564	+	0.0433957i
$892$	23.0132	+	16.7200i	0.770537	+	0.559828i
$893$	4.57524	−	7.92456i	0.153105	−	0.265185i
$894$	−0.0608053	+	1.60122i	−0.00203363	+	0.0535529i
$895$	−0.131815	−	0.356579i	−0.00440610	−	0.0119191i
$896$	0.538784	+	0.239882i	0.0179995	+	0.00801390i
$897$	31.7745	−	26.4973i	1.06092	−	0.884718i
$898$	−34.5761	−	7.34937i	−1.15382	−	0.245252i
$899$	10.5288			0.351154
$900$	1.50909	−	14.9239i	0.0503028	−	0.497463i
$901$	−11.2751			−0.375626
$902$	0.0908576	+	0.0193124i	0.00302523	+	0.000643032i
$903$	−1.20530	−	6.95962i	−0.0401098	−	0.231602i
$904$	15.8595	+	7.06111i	0.527479	+	0.234849i
$905$	−8.30861	+	6.55884i	−0.276187	+	0.218023i
$906$	−32.8739	+	17.3510i	−1.09216	+	0.576448i
$907$	−4.28109	+	7.41506i	−0.142151	+	0.246213i	−0.928306	−	0.371816i	$-0.878735\pi$
$907$	−4.28109	+	7.41506i	−0.142151	+	0.246213i	0.786155	+	0.618029i	$0.212069\pi$
$908$	−9.12917	−	6.63273i	−0.302962	−	0.220115i
$909$	−48.1391	+	17.1894i	−1.59667	+	0.570137i
$910$	−3.85937	−	3.95654i	−0.127937	−	0.131158i
$911$	−15.1963	−	3.23008i	−0.503476	−	0.107017i	−0.0508300	−	0.998707i	$-0.516187\pi$
$911$	−15.1963	−	3.23008i	−0.503476	−	0.107017i	−0.452646	+	0.891690i	$0.649520\pi$
$912$	−0.718902	+	2.84635i	−0.0238052	+	0.0942521i
$913$	−1.58873	+	0.337696i	−0.0525794	+	0.0111761i
$914$	12.6577	−	14.0578i	0.418680	−	0.464991i
$915$	−13.2480	+	11.9759i	−0.437966	+	0.395913i
$916$	13.3175	+	14.7906i	0.440023	+	0.488695i
$917$	−0.324527	−	0.235783i	−0.0107168	−	0.00778624i
$918$	−3.95627	+	11.8075i	−0.130576	+	0.389706i
$919$	4.35119	+	3.16132i	0.143533	+	0.104282i	0.657234	−	0.753686i	$-0.271726\pi$
$919$	4.35119	+	3.16132i	0.143533	+	0.104282i	−0.513702	+	0.857969i	$0.671726\pi$
$920$	−0.825144	+	12.7175i	−0.0272042	+	0.419282i
$921$	−25.5980	−	9.40542i	−0.843484	−	0.309919i
$922$	36.4765	+	16.2404i	1.20129	+	0.534849i
$923$	−44.1423	+	49.0250i	−1.45296	+	1.61368i
$924$	−0.146859	+	0.00981948i	−0.00483132	+	0.000323037i
$925$	−6.48999	+	5.55776i	−0.213390	+	0.182738i
$926$	−9.34612			−0.307133
$927$	14.7785	+	30.7753i	0.485389	+	1.01079i
$928$	−1.51694	+	1.10212i	−0.0497961	+	0.0361790i
$929$	2.26289	+	21.5300i	0.0742432	+	0.706377i	0.966816	+	0.255473i	$0.0822313\pi$
$929$	2.26289	+	21.5300i	0.0742432	+	0.706377i	−0.892573	+	0.450903i	$0.851102\pi$
$930$	−12.8176	−	17.5689i	−0.420305	−	0.576108i
$931$	−1.17857	+	11.2133i	−0.0386260	+	0.367501i
$932$	8.84110	+	15.3132i	0.289600	+	0.501602i
$933$	6.53143	−	3.44732i	0.213830	−	0.112860i
$934$	24.1000	+	26.7658i	0.788577	+	0.875804i
$935$	−0.692278	+	0.341960i	−0.0226399	+	0.0111833i
$936$	−5.44275	−	11.3342i	−0.177902	−	0.370471i
$937$	−0.833405	+	2.56496i	−0.0272262	+	0.0837935i	−0.963746	−	0.266820i	$-0.914027\pi$
$937$	−0.833405	+	2.56496i	−0.0272262	+	0.0837935i	0.936520	+	0.350614i	$0.114027\pi$
$938$	1.34923	+	1.49847i	0.0440540	+	0.0489269i
$939$	15.4724	+	38.6343i	0.504922	+	1.26078i
$940$	−10.0418	−	6.70014i	−0.327526	−	0.218535i
$941$	13.2701	−	2.82066i	0.432594	−	0.0919508i	0.0135324	−	0.999908i	$-0.495692\pi$
$941$	13.2701	−	2.82066i	0.432594	−	0.0919508i	0.419062	+	0.907958i	$0.362359\pi$
$942$	−0.730882	+	19.2468i	−0.0238134	+	0.627094i
$943$	−1.83708	+	3.18192i	−0.0598237	+	0.103618i
$944$	5.97969	+	4.34450i	0.194622	+	0.141401i
$945$	−1.91599	+	6.57923i	−0.0623270	+	0.214022i
$946$	0.806009	−	0.585600i	0.0262056	−	0.0190395i
$947$	−4.05237	−	38.5557i	−0.131684	−	1.25289i	−0.838266	−	0.545261i	$-0.816430\pi$
$947$	−4.05237	−	38.5557i	−0.131684	−	1.25289i	0.706582	−	0.707632i	$-0.250236\pi$
$948$	0.0174399	−	0.0221823i	0.000566421	−	0.000720447i
$949$	−32.7429	−	56.7124i	−1.06288	−	1.84096i
$950$	1.55536	+	8.33079i	0.0504626	+	0.270286i
$951$	−45.1682	+	3.02009i	−1.46468	+	0.0979331i
$952$	−1.38252	−	0.293863i	−0.0448076	−	0.00952414i
$953$	2.73635	−	1.98808i	0.0886392	−	0.0644001i	−0.542583	−	0.840002i	$-0.682554\pi$
$953$	2.73635	−	1.98808i	0.0886392	−	0.0644001i	0.631222	+	0.775602i	$0.282554\pi$
$954$	−13.5435	−	3.97310i	−0.438488	−	0.128634i
$955$	27.8048	−	13.7346i	0.899742	−	0.444440i
$956$	11.3188	−	5.03945i	0.366076	−	0.162987i
$957$	0.206417	−	0.419962i	0.00667250	−	0.0135754i
$958$	−2.34014	+	22.2650i	−0.0756066	+	0.719349i
$959$	10.6734	−	2.26870i	0.344662	−	0.0732601i
$960$	3.68578	+	1.18955i	0.118958	+	0.0383926i
$961$	−0.518905	−	0.110297i	−0.0167389	−	0.00355795i
$962$	−2.21324	+	6.81165i	−0.0713577	+	0.219616i
$963$	−24.3085	−	20.6512i	−0.783332	−	0.665477i
$964$	−6.86960	−	21.1425i	−0.221255	−	0.680953i
$965$	−6.85967	+	1.74694i	−0.220821	+	0.0562359i
$966$	1.42569	−	5.64475i	0.0458709	−	0.181617i
$967$	−4.38998	+	41.7678i	−0.141172	+	1.34316i	0.662934	+	0.748678i	$0.269311\pi$
$967$	−4.38998	+	41.7678i	−0.141172	+	1.34316i	−0.804106	+	0.594485i	$0.797356\pi$
$968$	5.48962	+	9.50830i	0.176443	+	0.305608i
$969$	0.266977	−	7.03048i	0.00857654	−	0.225851i
$970$	19.5146	+	7.77066i	0.626576	+	0.249501i
$971$	−2.30465	+	1.67442i	−0.0739596	+	0.0537348i	−0.624151	−	0.781304i	$-0.714555\pi$
$971$	−2.30465	+	1.67442i	−0.0739596	+	0.0537348i	0.550191	+	0.835039i	$0.314555\pi$
$972$	−8.91298	+	12.7890i	−0.285884	+	0.410208i
$973$	−3.26833	−	10.0589i	−0.104778	−	0.322473i
$974$	8.63463	−	14.9556i	0.276671	−	0.479209i
$975$	−27.9668	−	23.1356i	−0.895656	−	0.740933i
$976$	−2.30555	−	3.99333i	−0.0737988	−	0.127823i
$977$	−10.8148	+	12.0110i	−0.345995	+	0.384266i	−0.890876	−	0.454247i	$-0.849908\pi$
$977$	−10.8148	+	12.0110i	−0.345995	+	0.384266i	0.544881	+	0.838514i	$0.316575\pi$
$978$	−13.1353	+	10.9537i	−0.420021	+	0.350262i
$979$	0.147537	+	1.40372i	0.00471529	+	0.0448630i
$980$	14.6615	+	2.50938i	0.468345	+	0.0801591i
$981$	−19.0854	+	11.7646i	−0.609349	+	0.375616i
$982$	2.64857			0.0845194
$983$	−38.1596	+	16.9897i	−1.21710	+	0.541889i	−0.911905	−	0.410401i	$-0.865389\pi$
$983$	−38.1596	+	16.9897i	−1.21710	+	0.541889i	−0.305196	+	0.952289i	$0.598722\pi$
$984$	0.800836	+	0.778091i	0.0255297	+	0.0248046i
$985$	−0.685913	−	1.85549i	−0.0218550	−	0.0591208i
$986$	3.00679	−	3.33938i	0.0957559	−	0.106348i
$987$	3.95535	+	3.84301i	0.125900	+	0.122324i
$988$	4.75330	+	5.27908i	0.151223	+	0.167950i
$989$	12.1778	+	37.4793i	0.387230	+	1.19177i
$990$	−0.952062	+	0.166816i	−0.0302585	+	0.00530178i
$991$	−10.0696	+	30.9911i	−0.319872	+	0.984464i	0.653831	+	0.756641i	$0.273161\pi$
$991$	−10.0696	+	30.9911i	−0.319872	+	0.984464i	−0.973702	+	0.227823i	$0.926839\pi$
$992$	5.12974	−	2.28391i	0.162869	−	0.0725142i
$993$	49.1245	−	3.28461i	1.55892	−	0.104234i
$994$	−0.970366	+	9.23241i	−0.0307781	+	0.292834i
$995$	−4.53113	+	16.1067i	−0.143647	+	0.510618i
$996$	−18.3267	−	6.73373i	−0.580703	−	0.213366i
$997$	−0.945387	−	8.99476i	−0.0299407	−	0.284867i	−0.999240	−	0.0389825i	$-0.987588\pi$
$997$	−0.945387	−	8.99476i	−0.0299407	−	0.284867i	0.969299	−	0.245884i	$-0.0790783\pi$
$998$	2.29670	+	7.06851i	0.0727007	+	0.223750i
$999$	8.70220	−	1.76666i	0.275325	−	0.0558947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.q.b.331.12	yes	112
9.4	even	3	inner	450.2.q.b.31.8	✓	112
25.21	even	5	inner	450.2.q.b.421.8	yes	112
225.121	even	15	inner	450.2.q.b.121.12	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.q.b.31.8	✓	112	9.4	even	3	inner
450.2.q.b.121.12	yes	112	225.121	even	15	inner
450.2.q.b.331.12	yes	112	1.1	even	1	trivial
450.2.q.b.421.8	yes	112	25.21	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.978148 - 0.207912i) q^{2} +(1.62578 + 0.597357i) q^{3} +(0.913545 + 0.406737i) q^{4} +(0.605543 - 2.15251i) q^{5} +(-1.46606 - 0.922322i) q^{6} +(-0.294886 + 0.510758i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.28633 + 1.94234i) q^{9} +(-1.03984 + 1.97958i) q^{10} +(0.140938 + 0.0299574i) q^{11} +(1.24226 + 1.20698i) q^{12} +(4.09952 - 0.871380i) q^{13} +(0.394635 - 0.438287i) q^{14} +(2.27030 - 3.13779i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-1.93882 - 1.40864i) q^{17} +(-1.83253 - 2.37525i) q^{18} +(1.37124 + 0.996265i) q^{19} +(1.42870 - 1.72012i) q^{20} +(-0.784526 + 0.654229i) q^{21} +(-0.131630 - 0.0586055i) q^{22} +(3.81363 - 4.23547i) q^{23} +(-0.964167 - 1.43888i) q^{24} +(-4.26663 - 2.60688i) q^{25} -4.19110 q^{26} +(2.55680 + 4.52358i) q^{27} +(-0.477136 + 0.346660i) q^{28} +(-0.195996 - 1.86478i) q^{29} +(-2.87307 + 2.59720i) q^{30} +(-0.586948 + 5.58444i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.211240 + 0.132895i) q^{33} +(1.60358 + 1.78096i) q^{34} +(0.920848 + 0.944033i) q^{35} +(1.29864 + 2.70435i) q^{36} +(0.528080 - 1.62526i) q^{37} +(-1.13414 - 1.25959i) q^{38} +(7.18544 + 1.03220i) q^{39} +(-1.75511 + 1.38549i) q^{40} +(-0.630574 + 0.134033i) q^{41} +(0.903404 - 0.476820i) q^{42} +(-3.45722 + 5.98808i) q^{43} +(0.116569 + 0.0846923i) q^{44} +(5.56539 - 3.74518i) q^{45} +(-4.61090 + 3.35001i) q^{46} +(-0.564316 - 5.36911i) q^{47} +(0.643937 + 1.60790i) q^{48} +(3.32608 + 5.76095i) q^{49} +(3.63140 + 3.43700i) q^{50} +(-2.31064 - 3.44831i) q^{51} +(4.09952 + 0.871380i) q^{52} +(3.80623 - 2.76539i) q^{53} +(-1.56042 - 4.95632i) q^{54} +(0.149828 - 0.285232i) q^{55} +(0.538784 - 0.239882i) q^{56} +(1.63421 + 2.43883i) q^{57} +(-0.195996 + 1.86478i) q^{58} +(7.22978 - 1.53674i) q^{59} +(3.35028 - 1.94310i) q^{60} +(-4.51033 - 0.958701i) q^{61} +(1.73519 - 5.34037i) q^{62} +(-1.66628 + 0.594991i) q^{63} +(0.309017 + 0.951057i) q^{64} +(0.606779 - 9.35193i) q^{65} +(-0.178993 - 0.173910i) q^{66} +(-0.357376 + 3.40021i) q^{67} +(-1.19826 - 2.07545i) q^{68} +(8.73021 - 4.60784i) q^{69} +(-0.704450 - 1.11486i) q^{70} +(-12.7343 + 9.25198i) q^{71} +(-0.707999 - 2.91526i) q^{72} +(-4.82838 - 14.8602i) q^{73} +(-0.854451 + 1.47995i) q^{74} +(-5.37938 - 6.78692i) q^{75} +(0.847474 + 1.46787i) q^{76} +(-0.0568618 + 0.0631515i) q^{77} +(-6.81382 - 2.50358i) q^{78} +(-0.00170289 - 0.0162019i) q^{79} +(2.00482 - 0.990307i) q^{80} +(1.45461 + 8.88167i) q^{81} +0.644661 q^{82} +(-10.2980 + 4.58495i) q^{83} +(-0.982799 + 0.278572i) q^{84} +(-4.20616 + 3.32036i) q^{85} +(4.62666 - 5.13843i) q^{86} +(0.795290 - 3.14880i) q^{87} +(-0.0964131 - 0.107078i) q^{88} +(3.02707 + 9.31636i) q^{89} +(-6.22244 + 2.50623i) q^{90} +(-0.763828 + 2.35082i) q^{91} +(5.20664 - 2.31815i) q^{92} +(-4.29015 + 8.72846i) q^{93} +(-0.564316 + 5.36911i) q^{94} +(2.97482 - 2.34833i) q^{95} +(-0.295565 - 1.70665i) q^{96} +(-0.981903 - 9.34218i) q^{97} +(-2.05563 - 6.32659i) q^{98} +(0.264044 + 0.342243i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 14 q^{2} + 2 q^{3} + 14 q^{4} + 9 q^{5} - 7 q^{6} - 8 q^{7} - 28 q^{8} + 8 q^{9} - 8 q^{10} - 3 q^{11} - 3 q^{14} + 32 q^{15} + 14 q^{16} + 10 q^{17} - 6 q^{18} - 32 q^{19} - 6 q^{20} - 7 q^{21}+ \cdots + 68 q^{99}+O(q^{100}) \) 112 * q + 14 * q^2 + 2 * q^3 + 14 * q^4 + 9 * q^5 - 7 * q^6 - 8 * q^7 - 28 * q^8 + 8 * q^9 - 8 * q^10 - 3 * q^11 - 3 * q^14 + 32 * q^15 + 14 * q^16 + 10 * q^17 - 6 * q^18 - 32 * q^19 - 6 * q^20 - 7 * q^21 + 2 * q^22 - 5 * q^23 + 2 * q^24 + 21 * q^25 + 20 * q^26 - 16 * q^27 - 14 * q^28 + 18 * q^29 + 3 * q^30 - 27 * q^31 - 56 * q^32 - 25 * q^33 - 15 * q^34 - 12 * q^35 - 7 * q^36 + 16 * q^37 - 9 * q^38 + 12 * q^39 - q^40 + 16 * q^41 - 13 * q^42 - 44 * q^43 - 4 * q^44 + 69 * q^45 - 10 * q^46 + 27 * q^47 + 3 * q^48 - 64 * q^49 + 11 * q^50 + 138 * q^51 - 14 * q^53 - 30 * q^54 - 8 * q^55 + 7 * q^56 - 50 * q^57 + 18 * q^58 + 14 * q^59 - 20 * q^60 - 5 * q^61 - 66 * q^62 - 12 * q^63 - 28 * q^64 - 102 * q^65 + 18 * q^66 + 11 * q^67 + 40 * q^68 - 78 * q^69 + 6 * q^70 + 38 * q^71 - 17 * q^72 - 44 * q^73 + 12 * q^74 + 10 * q^75 - 14 * q^76 - 3 * q^77 - 55 * q^78 + 16 * q^79 + 12 * q^80 + 72 * q^81 + 28 * q^82 - 56 * q^83 - 30 * q^84 + 35 * q^85 + 21 * q^86 - 44 * q^87 - 3 * q^88 - 64 * q^89 + 38 * q^90 - 40 * q^91 + 5 * q^92 - 22 * q^93 + 27 * q^94 + 24 * q^95 + 5 * q^96 + 34 * q^97 + 38 * q^98 + 68 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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