LMFDB - Embedded newform 968.2.o.i.493.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(245,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("968.245");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.o (of order $10$, degree $4$, 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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			493.5
Character	$\chi$	$=$	968.493
Dual form			968.2.o.i.269.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.126804 + 1.40852i) q^{2} +(-1.10501 - 1.52092i) q^{3} +(-1.96784 - 0.357211i) q^{4} +(0.468972 - 0.152378i) q^{5} +(2.28236 - 1.36357i) q^{6} +(0.141392 + 0.102727i) q^{7} +(0.752668 - 2.72644i) q^{8} +(-0.165095 + 0.508111i) q^{9} +(0.155160 + 0.679877i) q^{10} +(1.63120 + 3.38766i) q^{12} +(-5.24957 - 1.70569i) q^{13} +(-0.162622 + 0.186127i) q^{14} +(-0.749976 - 0.544889i) q^{15} +(3.74480 + 1.40587i) q^{16} +(0.209682 + 0.645335i) q^{17} +(-0.694749 - 0.296970i) q^{18} +(-0.257018 - 0.353756i) q^{19} +(-0.977293 + 0.132334i) q^{20} -0.328562i q^{21} +6.88264 q^{23} +(-4.97842 + 1.86801i) q^{24} +(-3.84837 + 2.79600i) q^{25} +(3.06816 - 7.17782i) q^{26} +(-4.40862 + 1.43245i) q^{27} +(-0.241542 - 0.252658i) q^{28} +(0.829861 - 1.14221i) q^{29} +(0.862586 - 0.987260i) q^{30} +(-1.29020 + 3.97083i) q^{31} +(-2.45505 + 5.09635i) q^{32} +(-0.935553 + 0.213510i) q^{34} +(0.0819624 + 0.0266312i) q^{35} +(0.506385 - 0.940909i) q^{36} +(-3.83578 + 5.27950i) q^{37} +(0.530862 - 0.317157i) q^{38} +(3.20663 + 9.86900i) q^{39} +(-0.0624702 - 1.39332i) q^{40} +(-7.91468 + 5.75035i) q^{41} +(0.462785 + 0.0416629i) q^{42} -8.22782i q^{43} +0.263447i q^{45} +(-0.872747 + 9.69432i) q^{46} +(-6.27322 + 4.55776i) q^{47} +(-1.99984 - 7.24906i) q^{48} +(-2.15368 - 6.62835i) q^{49} +(-3.45023 - 5.77504i) q^{50} +(0.749802 - 1.03201i) q^{51} +(9.72103 + 5.23173i) q^{52} +(-9.43332 - 3.06507i) q^{53} +(-1.45860 - 6.39126i) q^{54} +(0.386502 - 0.308178i) q^{56} +(-0.254025 + 0.781810i) q^{57} +(1.50359 + 1.31371i) q^{58} +(5.55824 - 7.65026i) q^{59} +(1.28119 + 1.34016i) q^{60} +(-9.13658 + 2.96865i) q^{61} +(-5.42938 - 2.32079i) q^{62} +(-0.0755402 + 0.0548832i) q^{63} +(-6.86698 - 4.10421i) q^{64} -2.72181 q^{65} +5.24537i q^{67} +(-0.182100 - 1.34482i) q^{68} +(-7.60542 - 10.4680i) q^{69} +(-0.0479037 + 0.112068i) q^{70} +(1.42668 + 4.39088i) q^{71} +(1.26107 + 0.832562i) q^{72} +(-5.54545 - 4.02901i) q^{73} +(-6.94987 - 6.07222i) q^{74} +(8.50501 + 2.76344i) q^{75} +(0.379406 + 0.787945i) q^{76} +(-14.3073 + 3.26517i) q^{78} +(2.09346 - 6.44301i) q^{79} +(1.97043 + 0.0886875i) q^{80} +(8.34691 + 6.06438i) q^{81} +(-7.09586 - 11.8771i) q^{82} +(-6.92543 + 2.25021i) q^{83} +(-0.117366 + 0.646558i) q^{84} +(0.196670 + 0.270693i) q^{85} +(11.5890 + 1.04332i) q^{86} -2.65421 q^{87} -9.61762 q^{89} +(-0.371069 - 0.0334061i) q^{90} +(-0.567027 - 0.780446i) q^{91} +(-13.5440 - 2.45856i) q^{92} +(7.46502 - 2.42553i) q^{93} +(-5.62421 - 9.41388i) q^{94} +(-0.174439 - 0.126737i) q^{95} +(10.4640 - 1.89760i) q^{96} +(1.03707 - 3.19177i) q^{97} +(9.60923 - 2.19299i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} - q^{4} + 7 q^{6} + 10 q^{7} + 5 q^{8} + 20 q^{10} - 6 q^{12} + 2 q^{14} - 18 q^{15} + 15 q^{16} + 6 q^{17} + 20 q^{18} + 8 q^{20} - 8 q^{23} - 25 q^{24} - 4 q^{25} - 10 q^{26} - 32 q^{28}+ \cdots + 144 q^{98}+O(q^{100}) $ 40 * q + 5 * q^2 - q^4 + 7 * q^6 + 10 * q^7 + 5 * q^8 + 20 * q^10 - 6 * q^12 + 2 * q^14 - 18 * q^15 + 15 * q^16 + 6 * q^17 + 20 * q^18 + 8 * q^20 - 8 * q^23 - 25 * q^24 - 4 * q^25 - 10 * q^26 - 32 * q^28 + 28 * q^30 - 6 * q^31 - 20 * q^32 + 10 * q^34 + 18 * q^36 + 12 * q^38 + 34 * q^39 - 10 * q^40 + 14 * q^41 + 40 * q^42 - 18 * q^46 - 6 * q^47 + 18 * q^48 - 4 * q^49 - 61 * q^50 - 20 * q^52 - 108 * q^54 - 32 * q^56 + 26 * q^57 + 4 * q^58 - 46 * q^60 - 48 * q^62 - 60 * q^63 - 49 * q^64 + 36 * q^65 + 42 * q^68 - 8 * q^70 + 22 * q^71 + 101 * q^72 + 6 * q^73 - 54 * q^74 + 134 * q^76 - 12 * q^78 - 74 * q^79 - 44 * q^80 - 4 * q^81 - 31 * q^82 + 28 * q^84 - 15 * q^86 - 68 * q^87 - 16 * q^89 + 84 * q^90 - 4 * q^92 + 100 * q^94 - 66 * q^95 + 30 * q^96 + 10 * q^97 + 144 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.126804	+	1.40852i	−0.0896639	+	0.995972i
$2$	−0.126804	+	1.40852i	−0.0896639	+	0.995972i
$3$	−1.10501	−	1.52092i	−0.637980	−	0.878105i	0.360526	−	0.932749i	$-0.382597\pi$
$3$	−1.10501	−	1.52092i	−0.637980	−	0.878105i	−0.998506	+	0.0546447i	$0.982597\pi$
$4$	−1.96784	−	0.357211i	−0.983921	−	0.178606i
$5$	0.468972	−	0.152378i	0.209731	−	0.0681456i	−0.202267	−	0.979330i	$-0.564831\pi$
$5$	0.468972	−	0.152378i	0.209731	−	0.0681456i	0.411998	+	0.911185i	$0.364831\pi$
$6$	2.28236	−	1.36357i	0.931772	−	0.556676i
$7$	0.141392	+	0.102727i	0.0534412	+	0.0388273i	0.614185	−	0.789162i	$-0.289485\pi$
$7$	0.141392	+	0.102727i	0.0534412	+	0.0388273i	−0.560744	+	0.827989i	$0.689485\pi$
$8$	0.752668	−	2.72644i	0.266108	−	0.963943i
$9$	−0.165095	+	0.508111i	−0.0550318	+	0.169370i
$10$	0.155160	+	0.679877i	0.0490658	+	0.214996i
$11$		0			0
$11$		0			0
$12$	1.63120	+	3.38766i	0.470888	+	0.977932i
$13$	−5.24957	−	1.70569i	−1.45597	−	0.473073i	−0.529133	−	0.848539i	$-0.677483\pi$
$13$	−5.24957	−	1.70569i	−1.45597	−	0.473073i	−0.926836	+	0.375466i	$0.877483\pi$
$14$	−0.162622	+	0.186127i	−0.0434627	+	0.0497446i
$15$	−0.749976	−	0.544889i	−0.193643	−	0.140690i
$16$	3.74480	+	1.40587i	0.936200	+	0.351467i
$17$	0.209682	+	0.645335i	0.0508553	+	0.156517i	0.973259	−	0.229711i	$-0.0737780\pi$
$17$	0.209682	+	0.645335i	0.0508553	+	0.156517i	−0.922404	+	0.386227i	$0.873778\pi$
$18$	−0.694749	−	0.296970i	−0.163754	−	0.0699966i
$19$	−0.257018	−	0.353756i	−0.0589641	−	0.0811571i	0.778517	−	0.627624i	$-0.215972\pi$
$19$	−0.257018	−	0.353756i	−0.0589641	−	0.0811571i	−0.837481	+	0.546467i	$0.815972\pi$
$20$	−0.977293	+	0.132334i	−0.218529	+	0.0295908i
$21$		−	0.328562i		−	0.0716981i
$22$		0			0
$23$	6.88264			1.43513			0.717565	−	0.696491i	$-0.245256\pi$
$23$	6.88264			1.43513			0.717565	+	0.696491i	$0.245256\pi$
$24$	−4.97842	+	1.86801i	−1.01621	+	0.381306i
$25$	−3.84837	+	2.79600i	−0.769674	+	0.559201i
$26$	3.06816	−	7.17782i	0.601716	−	1.40769i
$27$	−4.40862	+	1.43245i	−0.848440	+	0.275675i
$28$	−0.241542	−	0.252658i	−0.0456472	−	0.0477479i
$29$	0.829861	−	1.14221i	0.154101	−	0.212102i	−0.724985	−	0.688764i	$-0.758153\pi$
$29$	0.829861	−	1.14221i	0.154101	−	0.212102i	0.879087	+	0.476662i	$0.158153\pi$
$30$	0.862586	−	0.987260i	0.157486	−	0.180248i
$31$	−1.29020	+	3.97083i	−0.231727	+	0.713183i	0.765812	+	0.643065i	$0.222337\pi$
$31$	−1.29020	+	3.97083i	−0.231727	+	0.713183i	−0.997539	+	0.0701176i	$0.977663\pi$
$32$	−2.45505	+	5.09635i	−0.433995	+	0.900915i
$33$		0			0
$34$	−0.935553	+	0.213510i	−0.160446	+	0.0366166i
$35$	0.0819624	+	0.0266312i	0.0138542	+	0.00450149i
$36$	0.506385	−	0.940909i	0.0843974	−	0.156818i
$37$	−3.83578	+	5.27950i	−0.630598	+	0.867944i	−0.998071	−	0.0620905i	$-0.980223\pi$
$37$	−3.83578	+	5.27950i	−0.630598	+	0.867944i	0.367472	+	0.930034i	$0.380223\pi$
$38$	0.530862	−	0.317157i	0.0861171	−	0.0514497i
$39$	3.20663	+	9.86900i	0.513472	+	1.58030i
$40$	−0.0624702	−	1.39332i	−0.00987741	−	0.220302i
$41$	−7.91468	+	5.75035i	−1.23607	+	0.898054i	−0.997330	−	0.0730301i	$-0.976733\pi$
$41$	−7.91468	+	5.75035i	−1.23607	+	0.898054i	−0.238736	+	0.971084i	$0.576733\pi$
$42$	0.462785	+	0.0416629i	0.0714093	+	0.00642873i
$43$		−	8.22782i		−	1.25473i	−0.778725	−	0.627365i	$-0.784133\pi$
$43$		−	8.22782i		−	1.25473i	0.778725	−	0.627365i	$-0.215867\pi$
$44$		0			0
$45$			0.263447i			0.0392723i
$46$	−0.872747	+	9.69432i	−0.128679	+	1.42935i
$47$	−6.27322	+	4.55776i	−0.915043	+	0.664818i	−0.942285	−	0.334811i	$-0.891327\pi$
$47$	−6.27322	+	4.55776i	−0.915043	+	0.664818i	0.0272423	+	0.999629i	$0.491327\pi$
$48$	−1.99984	−	7.24906i	−0.288652	−	1.04631i
$49$	−2.15368	−	6.62835i	−0.307669	−	0.946907i
$50$	−3.45023	−	5.77504i	−0.487936	−	0.816714i
$51$	0.749802	−	1.03201i	0.104993	−	0.144511i
$52$	9.72103	+	5.23173i	1.34806	+	0.725511i
$53$	−9.43332	−	3.06507i	−1.29577	−	0.421020i	−0.421660	−	0.906754i	$-0.638552\pi$
$53$	−9.43332	−	3.06507i	−1.29577	−	0.421020i	−0.874107	+	0.485734i	$0.838552\pi$
$54$	−1.45860	−	6.39126i	−0.198490	−	0.869740i
$55$		0			0
$56$	0.386502	−	0.308178i	0.0516485	−	0.0411820i
$57$	−0.254025	+	0.781810i	−0.0336465	+	0.103553i
$58$	1.50359	+	1.31371i	0.197431	+	0.172499i
$59$	5.55824	−	7.65026i	0.723621	−	0.995980i	−0.275774	−	0.961222i	$-0.588934\pi$
$59$	5.55824	−	7.65026i	0.723621	−	0.995980i	0.999396	−	0.0347571i	$-0.0110658\pi$
$60$	1.28119	+	1.34016i	0.165401	+	0.173013i
$61$	−9.13658	+	2.96865i	−1.16982	+	0.380097i	−0.828575	−	0.559878i	$-0.810848\pi$
$61$	−9.13658	+	2.96865i	−1.16982	+	0.380097i	−0.341244	+	0.939975i	$0.610848\pi$
$62$	−5.42938	−	2.32079i	−0.689532	−	0.294740i
$63$	−0.0755402	+	0.0548832i	−0.00951717	+	0.00691463i
$64$	−6.86698	−	4.10421i	−0.858373	−	0.513027i
$65$	−2.72181			−0.337599
$66$		0			0
$67$			5.24537i			0.640824i	0.947278	+	0.320412i	$0.103821\pi$
$67$			5.24537i			0.640824i	−0.947278	+	0.320412i	$0.896179\pi$
$68$	−0.182100	−	1.34482i	−0.0220829	−	0.163083i
$69$	−7.60542	−	10.4680i	−0.915585	−	1.26019i
$70$	−0.0479037	+	0.112068i	−0.00572558	+	0.0133947i
$71$	1.42668	+	4.39088i	0.169316	+	0.521102i	0.999328	−	0.0366434i	$-0.0116666\pi$
$71$	1.42668	+	4.39088i	0.169316	+	0.521102i	−0.830012	+	0.557745i	$0.811667\pi$
$72$	1.26107	+	0.832562i	0.148619	+	0.0981184i
$73$	−5.54545	−	4.02901i	−0.649046	−	0.471560i	0.213900	−	0.976856i	$-0.431383\pi$
$73$	−5.54545	−	4.02901i	−0.649046	−	0.471560i	−0.862946	+	0.505296i	$0.831383\pi$
$74$	−6.94987	−	6.07222i	−0.807906	−	0.705881i
$75$	8.50501	+	2.76344i	0.982074	+	0.319095i
$76$	0.379406	+	0.787945i	0.0435209	+	0.0903835i
$77$		0			0
$78$	−14.3073	+	3.26517i	−1.61998	+	0.369708i
$79$	2.09346	−	6.44301i	0.235533	−	0.724895i	−0.761518	−	0.648144i	$-0.775545\pi$
$79$	2.09346	−	6.44301i	0.235533	−	0.724895i	0.997050	−	0.0767507i	$-0.0244546\pi$
$80$	1.97043	+	0.0886875i	0.220301	+	0.00991556i
$81$	8.34691	+	6.06438i	0.927434	+	0.673820i
$82$	−7.09586	−	11.8771i	−0.783607	−	1.31161i
$83$	−6.92543	+	2.25021i	−0.760164	+	0.246992i	−0.663349	−	0.748310i	$-0.730866\pi$
$83$	−6.92543	+	2.25021i	−0.760164	+	0.246992i	−0.0968151	+	0.995302i	$0.530866\pi$
$84$	−0.117366	+	0.646558i	−0.0128057	+	0.0705452i
$85$	0.196670	+	0.270693i	0.0213318	+	0.0293608i
$86$	11.5890	+	1.04332i	1.24968	+	0.112504i
$87$	−2.65421			−0.284562
$88$		0			0
$89$	−9.61762			−1.01947			−0.509733	−	0.860333i	$-0.670256\pi$
$89$	−9.61762			−1.01947			−0.509733	+	0.860333i	$0.670256\pi$
$90$	−0.371069	−	0.0334061i	−0.0391142	−	0.00352131i
$91$	−0.567027	−	0.780446i	−0.0594406	−	0.0818130i
$92$	−13.5440	−	2.45856i	−1.41205	−	0.256322i
$93$	7.46502	−	2.42553i	0.774086	−	0.251516i
$94$	−5.62421	−	9.41388i	−0.580093	−	0.970967i
$95$	−0.174439	−	0.126737i	−0.0178971	−	0.0130030i
$96$	10.4640	−	1.89760i	1.06798	−	0.193673i
$97$	1.03707	−	3.19177i	0.105298	−	0.324075i	−0.884502	−	0.466537i	$-0.845502\pi$
$97$	1.03707	−	3.19177i	0.105298	−	0.324075i	0.989800	+	0.142461i	$0.0455016\pi$
$98$	9.60923	−	2.19299i	0.970679	−	0.221526i
$99$		0			0
$100$	8.57175	−	4.12741i	0.857175	−	0.412741i
$101$	6.71393	+	2.18149i	0.668061	+	0.217066i	0.623361	−	0.781934i	$-0.285767\pi$
$101$	6.71393	+	2.18149i	0.668061	+	0.217066i	0.0447002	+	0.999000i	$0.485767\pi$
$102$	1.35853	+	1.18697i	0.134515	+	0.117528i
$103$	3.33029	+	2.41960i	0.328144	+	0.238410i	0.739642	−	0.673000i	$-0.234995\pi$
$103$	3.33029	+	2.41960i	0.328144	+	0.238410i	−0.411499	+	0.911410i	$0.634995\pi$
$104$	−8.60165	+	13.0288i	−0.843461	+	1.27758i
$105$	−0.0500657	−	0.154086i	−0.00488591	−	0.0150373i
$106$	5.51339	−	12.8983i	0.535508	−	1.25280i
$107$	−4.02442	−	5.53914i	−0.389056	−	0.535489i	0.568900	−	0.822407i	$-0.307369\pi$
$107$	−4.02442	−	5.53914i	−0.389056	−	0.535489i	−0.957955	+	0.286918i	$0.907369\pi$
$108$	9.18716	−	1.24402i	0.884034	−	0.119706i
$109$			11.3993i			1.09186i	0.837832	+	0.545928i	$0.183823\pi$
$109$			11.3993i			1.09186i	−0.837832	+	0.545928i	$0.816177\pi$
$110$		0			0
$111$	12.2683			1.16445
$112$	0.385064	+	0.583473i	0.0363851	+	0.0551330i
$113$	−7.54218	+	5.47971i	−0.709508	+	0.515488i	−0.883015	−	0.469345i	$-0.844490\pi$
$113$	−7.54218	+	5.47971i	−0.709508	+	0.515488i	0.173507	+	0.984833i	$0.444490\pi$
$114$	−1.06898	−	0.456936i	−0.100119	−	0.0427960i
$115$	3.22777	−	1.04876i	0.300991	−	0.0977978i
$116$	−2.04104	+	1.95124i	−0.189506	+	0.181169i
$117$	1.73336	−	2.38577i	0.160249	−	0.220564i
$118$	10.0707	+	8.79896i	0.927085	+	0.810010i
$119$	−0.0366462	+	0.112785i	−0.00335935	+	0.0103390i
$120$	−2.05009	+	1.63465i	−0.187147	+	0.149222i
$121$		0			0
$122$	−3.02285	−	13.2455i	−0.273676	−	1.19919i
$123$	17.4917	+	5.68339i	1.57717	+	0.512454i
$124$	3.95734	−	7.35309i	0.355379	−	0.660327i
$125$	−2.82793	+	3.89231i	−0.252938	+	0.348139i
$126$	−0.0677251	−	0.113359i	−0.00603343	−	0.0100988i
$127$	6.00703	+	18.4878i	0.533038	+	1.64052i	0.747850	+	0.663867i	$0.231086\pi$
$127$	6.00703	+	18.4878i	0.533038	+	1.64052i	−0.214812	+	0.976655i	$0.568914\pi$
$128$	6.65162	−	9.15183i	0.587925	−	0.808915i
$129$	−12.5139	+	9.09186i	−1.10178	+	0.800494i
$130$	0.345136	−	3.83372i	0.0302705	−	0.336239i
$131$			6.43523i			0.562249i	0.959671	+	0.281124i	$0.0907073\pi$
$131$			6.43523i			0.562249i	−0.959671	+	0.281124i	$0.909293\pi$
$132$		0			0
$133$		−	0.0764211i		−	0.00662655i
$134$	−7.38820	−	0.665134i	−0.638243	−	0.0574588i
$135$	−1.84925	+	1.34356i	−0.159158	+	0.115635i
$136$	1.91729	−	0.0859629i	0.164406	−	0.00737126i
$137$	−2.74125	−	8.43670i	−0.234201	−	0.720796i	−0.997226	−	0.0744276i	$-0.976287\pi$
$137$	−2.74125	−	8.43670i	−0.234201	−	0.720796i	0.763026	−	0.646368i	$-0.223713\pi$
$138$	15.7087	−	9.38499i	1.33721	−	0.798903i
$139$	−1.54439	+	2.12568i	−0.130994	+	0.180297i	−0.869476	−	0.493976i	$-0.835543\pi$
$139$	−1.54439	+	2.12568i	−0.130994	+	0.180297i	0.738482	+	0.674273i	$0.235543\pi$
$140$	−0.151776	−	0.0816838i	−0.0128274	−	0.00690355i
$141$	13.8640	+	4.50468i	1.16756	+	0.379363i
$142$	−6.36554	+	1.45273i	−0.534185	+	0.121910i
$143$		0			0
$144$	−1.33259	+	1.67067i	−0.111049	+	0.139223i
$145$	0.215134	−	0.662115i	0.0178659	−	0.0549857i
$146$	6.37811	−	7.29997i	0.527856	−	0.604150i
$147$	−7.70135	+	10.6000i	−0.635197	+	0.874273i
$148$	9.43410	−	9.01903i	0.775478	−	0.741360i
$149$	17.9239	−	5.82382i	1.46838	−	0.477106i	0.537763	−	0.843096i	$-0.319270\pi$
$149$	17.9239	−	5.82382i	1.46838	−	0.477106i	0.930619	+	0.365990i	$0.119270\pi$
$150$	−4.97083	+	11.6290i	−0.405866	+	0.949507i
$151$	13.1346	−	9.54284i	1.06888	−	0.776586i	0.0931680	−	0.995650i	$-0.470301\pi$
$151$	13.1346	−	9.54284i	1.06888	−	0.776586i	0.975710	+	0.219065i	$0.0703006\pi$
$152$	−1.15794	+	0.434486i	−0.0939216	+	0.0352414i
$153$	−0.362519			−0.0293080
$154$		0			0
$155$			2.05881i			0.165367i
$156$	−2.78483	−	20.5661i	−0.222965	−	1.64660i
$157$	12.0482	+	16.5829i	0.961552	+	1.32346i	0.946200	+	0.323581i	$0.104887\pi$
$157$	12.0482	+	16.5829i	0.961552	+	1.32346i	0.0153519	+	0.999882i	$0.495113\pi$
$158$	8.80963	+	3.76567i	0.700856	+	0.299581i
$159$	5.76222	+	17.7343i	0.456974	+	1.40642i
$160$	−0.374776	+	2.76414i	−0.0296287	+	0.218524i
$161$	0.973152	+	0.707037i	0.0766952	+	0.0557223i
$162$	−9.60021	+	10.9878i	−0.754264	+	0.863281i
$163$	−14.5067	−	4.71351i	−1.13625	−	0.369190i	−0.320303	−	0.947315i	$-0.603785\pi$
$163$	−14.5067	−	4.71351i	−1.13625	−	0.369190i	−0.815948	+	0.578125i	$0.803785\pi$
$164$	17.6289	−	8.48857i	1.37659	−	0.662846i
$165$		0			0
$166$	−2.29128	−	10.0399i	−0.177838	−	0.779249i
$167$	3.61930	−	11.1390i	0.280070	−	0.861966i	−0.707764	−	0.706449i	$-0.750296\pi$
$167$	3.61930	−	11.1390i	0.280070	−	0.861966i	0.987833	−	0.155516i	$-0.0497041\pi$
$168$	−0.895805	−	0.247298i	−0.0691129	−	0.0190795i
$169$	14.1314	+	10.2671i	1.08703	+	0.789775i
$170$	−0.406214	+	0.242688i	−0.0311552	+	0.0186133i
$171$	0.222180	−	0.0721906i	0.0169905	−	0.00552055i
$172$	−2.93907	+	16.1910i	−0.224102	+	1.23456i
$173$	−10.1845	−	14.0177i	−0.774311	−	1.06575i	−0.995887	−	0.0906046i	$-0.971120\pi$
$173$	−10.1845	−	14.0177i	−0.774311	−	1.06575i	0.221576	−	0.975143i	$-0.428880\pi$
$174$	0.336565	−	3.73851i	0.0255149	−	0.283416i
$175$	−0.831356			−0.0628446
$176$		0			0
$177$	−17.7774			−1.33623
$178$	1.21955	−	13.5466i	0.0914093	−	1.01536i
$179$	−1.18508	−	1.63112i	−0.0885767	−	0.121915i	0.762429	−	0.647072i	$-0.224007\pi$
$179$	−1.18508	−	1.63112i	−0.0885767	−	0.121915i	−0.851006	+	0.525157i	$0.824007\pi$
$180$	0.0941062	−	0.518422i	0.00701426	−	0.0386409i
$181$	6.46367	−	2.10017i	0.480441	−	0.156105i	−0.0587768	−	0.998271i	$-0.518720\pi$
$181$	6.46367	−	2.10017i	0.480441	−	0.156105i	0.539218	+	0.842166i	$0.318720\pi$
$182$	1.17117	−	0.699704i	0.0868132	−	0.0518655i
$183$	14.6111	+	10.6156i	1.08009	+	0.784729i
$184$	5.18035	−	18.7651i	0.381900	−	1.38338i
$185$	−0.994392	+	3.06042i	−0.0731092	+	0.225007i
$186$	2.46981	+	10.8222i	0.181095	+	0.793520i
$187$		0			0
$188$	13.9728	−	6.72808i	1.01907	−	0.490696i
$189$	−0.770497	−	0.250350i	−0.0560454	−	0.0182102i
$190$	0.200631	−	0.229630i	0.0145553	−	0.0166591i
$191$	−7.97694	−	5.79559i	−0.577191	−	0.419354i	0.260519	−	0.965469i	$-0.416106\pi$
$191$	−7.97694	−	5.79559i	−0.577191	−	0.419354i	−0.837710	+	0.546115i	$0.816106\pi$
$192$	1.34592	+	14.9794i	0.0971338	+	1.08104i
$193$	−4.17089	−	12.8367i	−0.300227	−	0.924005i	−0.981415	−	0.191896i	$-0.938536\pi$
$193$	−4.17089	−	12.8367i	−0.300227	−	0.924005i	0.681188	−	0.732109i	$-0.261464\pi$
$194$	4.36416	+	1.86546i	0.313328	+	0.133932i
$195$	3.00764	+	4.13966i	0.215382	+	0.296447i
$196$	1.87038	+	13.8129i	0.133599	+	0.986632i
$197$		−	14.2852i		−	1.01778i	−0.860833	−	0.508888i	$-0.830057\pi$
$197$		−	14.2852i		−	1.01778i	0.860833	−	0.508888i	$-0.169943\pi$
$198$		0			0
$199$	9.46384			0.670874			0.335437	−	0.942063i	$-0.391116\pi$
$199$	9.46384			0.670874			0.335437	+	0.942063i	$0.391116\pi$
$200$	4.72660	+	12.5968i	0.334221	+	0.890730i
$201$	7.97780	−	5.79621i	0.562711	−	0.408833i
$202$	−3.92402	+	9.18007i	−0.276093	+	0.645907i
$203$	0.234672	−	0.0762495i	0.0164707	−	0.00535167i
$204$	−1.84414	+	1.76300i	−0.129115	+	0.123435i
$205$	−2.83553	+	3.90278i	−0.198042	+	0.272582i
$206$	−3.83034	+	4.38396i	−0.266873	+	0.305445i
$207$	−1.13629	+	3.49715i	−0.0789778	+	0.243069i
$208$	−17.2606	−	13.7677i	−1.19681	−	0.954617i
$209$		0			0
$210$	0.223382	−	0.0509796i	0.0154148	−	0.00351793i
$211$	−5.61754	−	1.82525i	−0.386727	−	0.125655i	0.109199	−	0.994020i	$-0.465171\pi$
$211$	−5.61754	−	1.82525i	−0.386727	−	0.125655i	−0.495926	+	0.868365i	$0.665171\pi$
$212$	17.4684	+	9.40127i	1.19974	+	0.645682i
$213$	5.10168	−	7.02186i	0.349562	−	0.481130i
$214$	8.31229	−	4.96608i	0.568216	−	0.339474i
$215$	−1.25374	−	3.85862i	−0.0855044	−	0.263155i
$216$	0.587258	+	13.0980i	0.0399579	+	0.891207i
$217$	−0.590338	+	0.428906i	−0.0400747	+	0.0291160i
$218$	−16.0561	−	1.44548i	−1.08746	−	0.0979000i
$219$			12.8863i			0.870777i
$220$		0			0
$221$		−	3.74538i		−	0.251942i
$222$	−1.55567	+	17.2801i	−0.104410	+	1.15976i
$223$	18.2705	−	13.2743i	1.22348	−	0.888913i	0.227100	−	0.973872i	$-0.427076\pi$
$223$	18.2705	−	13.2743i	1.22348	−	0.888913i	0.996385	+	0.0849584i	$0.0270757\pi$
$224$	−0.870659	+	0.468383i	−0.0581734	+	0.0312951i
$225$	−0.785333	−	2.41701i	−0.0523556	−	0.161134i
$226$	−6.76189	−	11.3181i	−0.449794	−	0.752871i
$227$	−6.07085	+	8.35581i	−0.402936	+	0.554594i	−0.961478	−	0.274882i	$-0.911361\pi$
$227$	−6.07085	+	8.35581i	−0.402936	+	0.554594i	0.558542	+	0.829477i	$0.311361\pi$
$228$	0.779153	−	1.44774i	0.0516007	−	0.0958787i
$229$	−1.18831	−	0.386105i	−0.0785258	−	0.0255146i	0.269491	−	0.963003i	$-0.413145\pi$
$229$	−1.18831	−	0.386105i	−0.0785258	−	0.0255146i	−0.348016	+	0.937488i	$0.613145\pi$
$230$	1.06791	+	4.67935i	0.0704159	+	0.308547i
$231$		0			0
$232$	−2.48955	−	3.12227i	−0.163447	−	0.204987i
$233$	−1.83061	+	5.63403i	−0.119927	+	0.369098i	−0.992943	−	0.118594i	$-0.962161\pi$
$233$	−1.83061	+	5.63403i	−0.119927	+	0.369098i	0.873016	+	0.487692i	$0.162161\pi$
$234$	3.14060	+	2.74399i	0.205307	+	0.179380i
$235$	−2.24746	+	3.09336i	−0.146608	+	0.201789i
$236$	−13.6705	+	13.0690i	−0.889874	+	0.850722i
$237$	−12.1126	+	3.93563i	−0.786799	+	0.255646i
$238$	−0.154213	−	0.0659184i	−0.00999616	−	0.00427286i
$239$	−3.15323	+	2.29096i	−0.203966	+	0.148190i	−0.685079	−	0.728469i	$-0.740232\pi$
$239$	−3.15323	+	2.29096i	−0.203966	+	0.148190i	0.481114	+	0.876658i	$0.340232\pi$
$240$	−2.04247	−	3.09487i	−0.131841	−	0.199773i
$241$	12.3613			0.796264			0.398132	−	0.917328i	$-0.369659\pi$
$241$	12.3613			0.796264			0.398132	+	0.917328i	$0.369659\pi$
$242$		0			0
$243$		−	5.48973i		−	0.352166i
$244$	19.0398	−	2.57815i	1.21890	−	0.165049i
$245$	−2.02003	−	2.78033i	−0.129055	−	0.177629i
$246$	−10.2232	+	23.9167i	−0.651805	+	1.52487i
$247$	0.745840	+	2.29546i	0.0474566	+	0.146057i
$248$	9.85515	+	6.50638i	0.625803	+	0.413156i
$249$	11.0751	+	8.04652i	0.701855	+	0.509927i
$250$	−5.12379	−	4.47675i	−0.324057	−	0.283134i
$251$	−12.2326	−	3.97460i	−0.772113	−	0.250875i	−0.103644	−	0.994614i	$-0.533050\pi$
$251$	−12.2326	−	3.97460i	−0.772113	−	0.250875i	−0.668469	+	0.743740i	$0.733050\pi$
$252$	0.168256	−	0.0810176i	0.0105991	−	0.00510363i
$253$		0			0
$254$	−26.8020	+	6.11669i	−1.68171	+	0.383795i
$255$	0.194380	−	0.598239i	0.0121725	−	0.0374632i
$256$	12.0471	+	10.5294i	0.752941	+	0.658088i
$257$	0.0268767	+	0.0195271i	0.00167653	+	0.00121807i	0.588623	−	0.808408i	$-0.299670\pi$
$257$	0.0268767	+	0.0195271i	0.00167653	+	0.00121807i	−0.586947	+	0.809626i	$0.699670\pi$
$258$	−11.2192	−	18.7789i	−0.698479	−	1.16912i
$259$	−1.08470	+	0.352440i	−0.0673999	+	0.0218996i
$260$	5.35609	+	0.972261i	0.332171	+	0.0602971i
$261$	0.443362	+	0.610235i	0.0274434	+	0.0377726i
$262$	−9.06413	−	0.816013i	−0.559984	−	0.0504134i
$263$	−6.83713			−0.421596			−0.210798	−	0.977530i	$-0.567606\pi$
$263$	−6.83713			−0.421596			−0.210798	+	0.977530i	$0.567606\pi$
$264$		0			0
$265$	−4.89101			−0.300453
$266$	0.107640	+	0.00969050i	0.00659986	+	0.000594163i
$267$	10.6276	+	14.6276i	0.650399	+	0.895198i
$268$	1.87371	−	10.3221i	0.114455	−	0.630520i
$269$	−26.5809	+	8.63665i	−1.62066	+	0.526586i	−0.972098	−	0.234573i	$-0.924631\pi$
$269$	−26.5809	+	8.63665i	−1.62066	+	0.526586i	−0.648565	+	0.761159i	$0.724631\pi$
$270$	−1.65793	−	2.77506i	−0.100898	−	0.168885i
$271$	−5.14699	−	3.73950i	−0.312657	−	0.227159i	0.420379	−	0.907349i	$-0.361897\pi$
$271$	−5.14699	−	3.73950i	−0.312657	−	0.227159i	−0.733036	+	0.680190i	$0.761897\pi$
$272$	−0.122040	+	2.71143i	−0.00739973	+	0.164405i
$273$	−0.560424	+	1.72481i	−0.0339184	+	0.104390i
$274$	12.2308	−	2.79129i	0.738892	−	0.168628i
$275$		0			0
$276$	11.2270	+	23.3160i	0.675785	+	1.40346i
$277$	12.6404	+	4.10712i	0.759490	+	0.246773i	0.663060	−	0.748567i	$-0.269258\pi$
$277$	12.6404	+	4.10712i	0.759490	+	0.246773i	0.0964302	+	0.995340i	$0.469258\pi$
$278$	−2.79821	−	2.44485i	−0.167826	−	0.146632i
$279$	−1.80462	−	1.31113i	−0.108040	−	0.0784954i
$280$	0.134299	−	0.203421i	0.00802589	−	0.0121567i
$281$	−7.02374	−	21.6168i	−0.419001	−	1.28955i	−0.908623	−	0.417618i	$-0.862865\pi$
$281$	−7.02374	−	21.6168i	−0.419001	−	1.28955i	0.489622	−	0.871935i	$-0.337135\pi$
$282$	−8.10293	+	18.9565i	−0.482523	+	1.12884i
$283$	13.6643	+	18.8073i	0.812259	+	1.11798i	0.990971	+	0.134077i	$0.0428071\pi$
$283$	13.6643	+	18.8073i	0.812259	+	1.11798i	−0.178712	+	0.983902i	$0.557193\pi$
$284$	−1.23902	−	9.15019i	−0.0735221	−	0.542964i
$285$			0.405355i			0.0240111i
$286$		0			0
$287$	−1.70979			−0.100926
$288$	−2.18419	−	2.08882i	−0.128705	−	0.123085i
$289$	13.3808	−	9.72172i	0.787106	−	0.571866i
$290$	0.905321	+	0.386979i	0.0531623	+	0.0227242i
$291$	−6.00041	+	1.94965i	−0.351750	+	0.114291i
$292$	9.47337	+	9.90935i	0.554387	+	0.579901i
$293$	−12.5499	+	17.2734i	−0.733172	+	1.00913i	0.265810	+	0.964025i	$0.414361\pi$
$293$	−12.5499	+	17.2734i	−0.733172	+	1.00913i	−0.998982	+	0.0450998i	$0.985639\pi$
$294$	−13.9537	−	12.1916i	−0.813797	−	0.711029i
$295$	1.44093	−	4.43471i	0.0838939	−	0.258199i
$296$	11.5072	+	14.4317i	0.668841	+	0.838828i
$297$		0			0
$298$	5.93013	+	25.9846i	0.343523	+	1.50525i
$299$	−36.1309	−	11.7397i	−2.08951	−	0.678922i
$300$	−15.7494	−	8.47610i	−0.909290	−	0.489368i
$301$	0.845223	−	1.16335i	0.0487178	−	0.0670544i
$302$	11.7757	+	19.7104i	0.677618	+	1.13420i
$303$	−4.10112	−	12.6219i	−0.235603	−	0.725111i
$304$	−0.465148	−	1.68608i	−0.0266781	−	0.0967032i
$305$	−3.83244	+	2.78443i	−0.219445	+	0.159436i
$306$	0.0459689	−	0.510615i	0.00262787	−	0.0291899i
$307$		−	4.08838i		−	0.233336i	−0.993171	−	0.116668i	$-0.962779\pi$
$307$		−	4.08838i		−	0.233336i	0.993171	−	0.116668i	$-0.0372214\pi$
$308$		0			0
$309$		−	7.73881i		−	0.440245i
$310$	−2.89987	−	0.261065i	−0.164701	−	0.0148275i
$311$	−1.07450	+	0.780672i	−0.0609294	+	0.0442678i	−0.617833	−	0.786309i	$-0.711989\pi$
$311$	−1.07450	+	0.780672i	−0.0609294	+	0.0442678i	0.556904	+	0.830577i	$0.311989\pi$
$312$	29.3208	−	1.31462i	1.65996	−	0.0744256i
$313$	−4.69517	−	14.4502i	−0.265387	−	0.816776i	−0.991604	−	0.129311i	$-0.958723\pi$
$313$	−4.69517	−	14.4502i	−0.265387	−	0.816776i	0.726218	−	0.687465i	$-0.241277\pi$
$314$	−24.8851	+	14.8673i	−1.40435	+	0.839012i
$315$	−0.0270632	+	0.0372493i	−0.00152484	+	0.00209876i
$316$	−6.42111	+	11.9310i	−0.361216	+	0.671172i
$317$	6.13879	+	1.99461i	0.344789	+	0.112029i	0.476292	−	0.879287i	$-0.341980\pi$
$317$	6.13879	+	1.99461i	0.344789	+	0.112029i	−0.131503	+	0.991316i	$0.541980\pi$
$318$	−25.7097	+	5.86741i	−1.44173	+	0.329028i
$319$		0			0
$320$	−3.84581	−	0.878382i	−0.214987	−	0.0491031i
$321$	−3.97756	+	12.2417i	−0.222006	+	0.683263i
$322$	−1.11927	+	1.28105i	−0.0623746	+	0.0713899i
$323$	0.174399	−	0.240039i	0.00970380	−	0.0133561i
$324$	−14.2591	−	14.9154i	−0.792174	−	0.828631i
$325$	24.9714	−	8.11370i	1.38516	−	0.450067i
$326$	8.47856	−	19.8352i	0.469584	−	1.09857i
$327$	17.3374	−	12.5964i	0.958763	−	0.696582i
$328$	9.72088	+	25.9070i	0.536746	+	1.43048i
$329$	−1.35519			−0.0747141
$330$		0			0
$331$			6.10154i			0.335371i	0.985841	+	0.167685i	$0.0536293\pi$
$331$			6.10154i			0.335371i	−0.985841	+	0.167685i	$0.946371\pi$
$332$	14.4319	−	1.95421i	0.792056	−	0.107251i
$333$	−2.04930	−	2.82062i	−0.112301	−	0.154569i
$334$	15.2306	+	6.51032i	0.833381	+	0.356229i
$335$	0.799281	+	2.45993i	0.0436694	+	0.134400i
$336$	0.461915	−	1.23040i	0.0251995	−	0.0671237i
$337$	−17.0126	−	12.3604i	−0.926737	−	0.673314i	0.0184547	−	0.999830i	$-0.494125\pi$
$337$	−17.0126	−	12.3604i	−0.926737	−	0.673314i	−0.945192	+	0.326516i	$0.894125\pi$
$338$	−16.2533	+	18.6024i	−0.884061	+	1.01184i
$339$	16.6684	+	5.41590i	0.905305	+	0.294151i
$340$	−0.290321	−	0.602933i	−0.0157448	−	0.0326986i
$341$		0			0
$342$	0.0735084	+	0.322098i	0.00397488	+	0.0174171i
$343$	0.754449	−	2.32195i	0.0407364	−	0.125374i
$344$	−22.4327	−	6.19282i	−1.20949	−	0.333894i
$345$	−5.16182	−	3.75028i	−0.277903	−	0.201908i
$346$	21.0356	−	12.5675i	1.13088	−	0.675633i
$347$	6.65166	−	2.16126i	0.357080	−	0.116022i	−0.124983	−	0.992159i	$-0.539888\pi$
$347$	6.65166	−	2.16126i	0.357080	−	0.116022i	0.482063	+	0.876137i	$0.339888\pi$
$348$	5.22307	+	0.948115i	0.279986	+	0.0508243i
$349$	13.4245	+	18.4773i	0.718599	+	0.989067i	0.999569	+	0.0293507i	$0.00934396\pi$
$349$	13.4245	+	18.4773i	0.718599	+	0.989067i	−0.280970	+	0.959717i	$0.590656\pi$
$350$	0.105419	−	1.17098i	0.00563489	−	0.0625915i
$351$	25.5867			1.36572
$352$		0			0
$353$	−5.72528			−0.304726			−0.152363	−	0.988325i	$-0.548688\pi$
$353$	−5.72528			−0.304726			−0.152363	+	0.988325i	$0.548688\pi$
$354$	2.25424	−	25.0398i	0.119812	−	1.33085i
$355$	1.33815	+	1.84180i	0.0710216	+	0.0977529i
$356$	18.9260	+	3.43552i	1.00307	+	0.182082i
$357$	0.212032	−	0.0688935i	0.0112219	−	0.00364623i
$358$	2.44773	−	1.46237i	0.129366	−	0.0772885i
$359$	11.2078	+	8.14298i	0.591527	+	0.429770i	0.842861	−	0.538131i	$-0.180869\pi$
$359$	11.2078	+	8.14298i	0.591527	+	0.429770i	−0.251334	+	0.967900i	$0.580869\pi$
$360$	0.718273	+	0.198288i	0.0378563	+	0.0104507i
$361$	5.81224	−	17.8882i	0.305907	−	0.941486i
$362$	2.13851	+	9.37050i	0.112398	+	0.492503i
$363$		0			0
$364$	0.837036	+	1.73834i	0.0438726	+	0.0911139i
$365$	−3.21460	−	1.04449i	−0.168260	−	0.0546709i
$366$	−16.8050	+	19.2339i	−0.878413	+	1.00537i
$367$	−23.2670	−	16.9045i	−1.21453	−	0.882405i	−0.218893	−	0.975749i	$-0.570244\pi$
$367$	−23.2670	−	16.9045i	−1.21453	−	0.882405i	−0.995634	+	0.0933437i	$0.970244\pi$
$368$	25.7741	+	9.67610i	1.34357	+	0.504402i
$369$	−1.61514	−	4.97090i	−0.0840810	−	0.258775i
$370$	−4.18457	−	1.78869i	−0.217545	−	0.0929897i
$371$	−1.01893	−	1.40244i	−0.0529003	−	0.0728110i
$372$	−15.5564	+	2.10647i	−0.806562	+	0.109216i
$373$		−	25.9293i		−	1.34257i	−0.741199	−	0.671285i	$-0.765743\pi$
$373$		−	25.9293i		−	1.34257i	0.741199	−	0.671285i	$-0.234257\pi$
$374$		0			0
$375$	9.04480			0.467072
$376$	7.70482	+	20.5341i	0.397346	+	1.05896i
$377$	−6.30467	+	4.58061i	−0.324707	+	0.235913i
$378$	0.450324	−	1.05351i	0.0231621	−	0.0541868i
$379$	4.63646	−	1.50648i	0.238159	−	0.0773825i	−0.187506	−	0.982263i	$-0.560040\pi$
$379$	4.63646	−	1.50648i	0.238159	−	0.0773825i	0.425665	+	0.904881i	$0.360040\pi$
$380$	0.297996	+	0.311711i	0.0152869	+	0.0159904i
$381$	21.4806	−	29.5655i	1.10048	−	1.51468i
$382$	9.17469	−	10.5008i	0.469418	−	0.537266i
$383$	−1.32699	+	4.08407i	−0.0678062	+	0.208686i	−0.979218	−	0.202809i	$-0.934993\pi$
$383$	−1.32699	+	4.08407i	−0.0678062	+	0.208686i	0.911412	+	0.411495i	$0.134993\pi$
$384$	−21.2694	−	0.00368342i	−1.08540	−	0.000187969i
$385$		0			0
$386$	18.6096	−	4.24703i	0.947203	−	0.216168i
$387$	4.18065	+	1.35838i	0.212514	+	0.0690501i
$388$	−3.18092	+	5.91045i	−0.161487	+	0.300058i
$389$	12.0892	−	16.6394i	0.612948	−	0.843651i	−0.383868	−	0.923388i	$-0.625408\pi$
$389$	12.0892	−	16.6394i	0.612948	−	0.843651i	0.996816	+	0.0797372i	$0.0254081\pi$
$390$	−6.21217	+	3.71139i	−0.314565	+	0.187933i
$391$	1.44317	+	4.44161i	0.0729840	+	0.224622i
$392$	−19.6928	+	0.882941i	−0.994637	+	0.0445952i
$393$	9.78748	−	7.11102i	0.493713	−	0.358704i
$394$	20.1209	+	1.81142i	1.01368	+	0.0912579i
$395$		−	3.34059i		−	0.168083i
$396$		0			0
$397$		−	12.1985i		−	0.612226i	−0.951995	−	0.306113i	$-0.900971\pi$
$397$		−	12.1985i		−	0.612226i	0.951995	−	0.306113i	$-0.0990285\pi$
$398$	−1.20005	+	13.3300i	−0.0601532	+	0.668171i
$399$	−0.116231	+	0.0844464i	−0.00581881	+	0.00422761i
$400$	−18.3422	+	5.06017i	−0.917110	+	0.253009i
$401$	−1.59290	−	4.90244i	−0.0795456	−	0.244816i	0.903373	−	0.428855i	$-0.141083\pi$
$401$	−1.59290	−	4.90244i	−0.0795456	−	0.244816i	−0.982919	+	0.184039i	$0.941083\pi$
$402$	7.15245	+	11.9719i	0.356732	+	0.597102i
$403$	13.5460	−	18.6445i	0.674775	−	0.928748i
$404$	−12.4327	−	6.69111i	−0.618550	−	0.332895i
$405$	4.83854	+	1.57214i	0.240429	+	0.0781202i
$406$	0.0776414	+	0.340208i	0.00385328	+	0.0168842i
$407$		0			0
$408$	−2.24937	−	2.82106i	−0.111361	−	0.139663i
$409$	−0.933387	+	2.87267i	−0.0461530	+	0.142044i	−0.971477	−	0.237132i	$-0.923793\pi$
$409$	−0.933387	+	2.87267i	−0.0461530	+	0.142044i	0.925324	+	0.379176i	$0.123793\pi$
$410$	−5.13757	−	4.48879i	−0.253727	−	0.221685i
$411$	−9.80244	+	13.4919i	−0.483519	+	0.665506i
$412$	−5.68918	−	5.95101i	−0.280286	−	0.293185i
$413$	1.57178	−	0.510704i	0.0773424	−	0.0251301i
$414$	−4.78171	−	2.04394i	−0.235008	−	0.100454i
$415$	−2.90495	+	2.11057i	−0.142598	+	0.103604i
$416$	21.5807	−	22.5661i	1.05808	−	1.10639i
$417$	4.93956			0.241891
$418$		0			0
$419$			6.15734i			0.300806i	0.988625	+	0.150403i	$0.0480570\pi$
$419$			6.15734i			0.300806i	−0.988625	+	0.150403i	$0.951943\pi$
$420$	0.0434799	+	0.321101i	0.00212160	+	0.0156681i
$421$	−1.57696	−	2.17050i	−0.0768565	−	0.105784i	0.768858	−	0.639420i	$-0.220825\pi$
$421$	−1.57696	−	2.17050i	−0.0768565	−	0.105784i	−0.845714	+	0.533636i	$0.820825\pi$
$422$	3.28322	−	7.68095i	0.159825	−	0.373903i
$423$	−1.28017	−	3.93996i	−0.0622440	−	0.191567i
$424$	−15.4569	+	23.4124i	−0.750654	+	1.13701i
$425$	−2.61129	−	1.89721i	−0.126666	−	0.0920284i
$426$	9.24350	+	8.07621i	0.447849	+	0.391294i
$427$	−1.59680	−	0.518833i	−0.0772747	−	0.0251081i
$428$	5.94078	+	12.3377i	0.287159	+	0.596366i
$429$		0			0
$430$	5.59391	−	1.27663i	0.269762	−	0.0615644i
$431$	−3.45224	+	10.6249i	−0.166289	+	0.511784i	−0.999129	−	0.0417294i	$-0.986713\pi$
$431$	−3.45224	+	10.6249i	−0.166289	+	0.511784i	0.832840	+	0.553513i	$0.186713\pi$
$432$	−18.5232	−	0.833717i	−0.891200	−	0.0401122i
$433$	−18.7670	−	13.6351i	−0.901886	−	0.655259i	0.0370636	−	0.999313i	$-0.488200\pi$
$433$	−18.7670	−	13.6351i	−0.901886	−	0.655259i	−0.938950	+	0.344054i	$0.888200\pi$
$434$	−0.529264	−	0.885888i	−0.0254055	−	0.0425240i
$435$	−1.24475	+	0.404444i	−0.0596813	+	0.0193916i
$436$	4.07196	−	22.4320i	0.195011	−	1.07430i
$437$	−1.76897	−	2.43477i	−0.0846211	−	0.116471i
$438$	−18.1506	−	1.63404i	−0.867269	−	0.0780773i
$439$	−21.6484			−1.03322			−0.516611	−	0.856220i	$-0.672807\pi$
$439$	−21.6484			−1.03322			−0.516611	+	0.856220i	$0.672807\pi$
$440$		0			0
$441$	3.72350			0.177310
$442$	5.27544	+	0.474929i	0.250927	+	0.0225901i
$443$	−21.5950	−	29.7229i	−1.02601	−	1.41218i	−0.907904	−	0.419179i	$-0.862318\pi$
$443$	−21.5950	−	29.7229i	−1.02601	−	1.41218i	−0.118105	−	0.993001i	$-0.537682\pi$
$444$	−24.1421	−	4.38237i	−1.14573	−	0.207978i
$445$	−4.51039	+	1.46552i	−0.213813	+	0.0694721i
$446$	16.3803	+	27.4176i	0.775630	+	1.29826i
$447$	−28.6637	−	20.8254i	−1.35575	−	0.985008i
$448$	−0.549322	−	1.28573i	−0.0259530	−	0.0607451i
$449$	−3.30409	+	10.1689i	−0.155929	+	0.479902i	−0.998254	−	0.0590693i	$-0.981187\pi$
$449$	−3.30409	+	10.1689i	−0.155929	+	0.479902i	0.842324	+	0.538971i	$0.181187\pi$
$450$	3.50398	−	0.799670i	0.165179	−	0.0376968i
$451$		0			0
$452$	16.7992	−	8.08905i	0.790169	−	0.380477i
$453$	−29.0278	−	9.43172i	−1.36385	−	0.443141i
$454$	−10.9995	−	9.61044i	−0.516232	−	0.451040i
$455$	−0.384843	−	0.279605i	−0.0180417	−	0.0131081i
$456$	1.94036	+	1.28103i	0.0908658	+	0.0599897i
$457$	3.28209	+	10.1012i	0.153530	+	0.472516i	0.998009	−	0.0630724i	$-0.0200899\pi$
$457$	3.28209	+	10.1012i	0.153530	+	0.472516i	−0.844479	+	0.535588i	$0.820090\pi$
$458$	0.694519	−	1.62480i	0.0324527	−	0.0759217i
$459$	−1.84882	−	2.54468i	−0.0862954	−	0.118775i
$460$	−6.72636	+	0.910809i	−0.313618	+	0.0424667i
$461$			22.4809i			1.04704i	0.852014	+	0.523519i	$0.175381\pi$
$461$			22.4809i			1.04704i	−0.852014	+	0.523519i	$0.824619\pi$
$462$		0			0
$463$	−31.1360			−1.44701			−0.723506	−	0.690318i	$-0.757471\pi$
$463$	−31.1360			−1.44701			−0.723506	+	0.690318i	$0.757471\pi$
$464$	4.71346	−	3.11066i	0.218817	−	0.144409i
$465$	3.13128	−	2.27501i	0.145210	−	0.105501i
$466$	−7.70350	−	3.29286i	−0.356858	−	0.152539i
$467$	4.72144	−	1.53409i	0.218482	−	0.0709891i	−0.197731	−	0.980256i	$-0.563357\pi$
$467$	4.72144	−	1.53409i	0.218482	−	0.0709891i	0.416213	+	0.909267i	$0.363357\pi$
$468$	−4.26320	+	4.07563i	−0.197067	+	0.188396i
$469$	−0.538844	+	0.741655i	−0.0248815	+	0.0342464i
$470$	−4.07207	−	3.55784i	−0.187830	−	0.164111i
$471$	11.9079	−	36.6488i	0.548688	−	1.68869i
$472$	−16.6745	−	20.9123i	−0.767506	−	0.962568i
$473$		0			0
$474$	−4.00747	−	17.5599i	−0.184069	−	0.806552i
$475$	1.97820	+	0.642757i	0.0907662	+	0.0294917i
$476$	0.112402	−	0.208853i	0.00515194	−	0.00957278i
$477$	3.11480	−	4.28715i	0.142617	−	0.196295i
$478$	−2.82701	−	4.73188i	−0.129304	−	0.216431i
$479$	−8.52738	−	26.2446i	−0.389626	−	1.19914i	−0.933069	−	0.359699i	$-0.882879\pi$
$479$	−8.52738	−	26.2446i	−0.389626	−	1.19914i	0.543443	−	0.839446i	$-0.317121\pi$
$480$	4.61817	−	2.48441i	0.210790	−	0.113397i
$481$	29.1414	−	21.1725i	1.32873	−	0.965381i
$482$	−1.56747	+	17.4112i	−0.0713962	+	0.793057i
$483$		−	2.26137i		−	0.102896i
$484$		0			0
$485$		−	1.65488i		−	0.0751441i
$486$	7.73238	+	0.696119i	0.350748	+	0.0315766i
$487$	14.4263	−	10.4813i	0.653716	−	0.474952i	−0.210819	−	0.977525i	$-0.567613\pi$
$487$	14.4263	−	10.4813i	0.653716	−	0.474952i	0.864535	+	0.502573i	$0.167613\pi$
$488$	1.21705	+	27.1448i	0.0550935	+	1.22879i
$489$	8.86122	+	27.2720i	0.400718	+	1.23328i
$490$	4.17230	−	2.49269i	0.188485	−	0.112608i
$491$	5.95381	−	8.19471i	0.268692	−	0.369822i	−0.653256	−	0.757137i	$-0.726597\pi$
$491$	5.95381	−	8.19471i	0.268692	−	0.369822i	0.921947	+	0.387315i	$0.126597\pi$
$492$	−32.3907	−	17.4322i	−1.46028	−	0.785906i
$493$	0.911112	+	0.296038i	0.0410344	+	0.0133329i
$494$	−3.32777	+	0.759455i	−0.149723	+	0.0341695i
$495$		0			0
$496$	−10.4140	+	13.0561i	−0.467603	+	0.586237i
$497$	−0.249342	+	0.767396i	−0.0111845	+	0.0344224i
$498$	−12.7380	+	14.5791i	−0.570805	+	0.653306i
$499$	22.5457	−	31.0315i	1.00928	−	1.38916i	0.0898336	−	0.995957i	$-0.471366\pi$
$499$	22.5457	−	31.0315i	1.00928	−	1.38916i	0.919451	−	0.393204i	$-0.128634\pi$
$500$	6.95529	−	6.64928i	0.311050	−	0.297365i
$501$	−20.9410	+	6.80414i	−0.935575	+	0.303987i
$502$	7.14943	−	16.7258i	0.319095	−	0.746508i
$503$	14.0550	−	10.2115i	0.626680	−	0.455310i	−0.228569	−	0.973528i	$-0.573405\pi$
$503$	14.0550	−	10.2115i	0.626680	−	0.455310i	0.855248	+	0.518218i	$0.173405\pi$
$504$	0.0927791	+	0.247265i	0.00413271	+	0.0110141i
$505$	3.48106			0.154905
$506$		0			0
$507$		−	32.8380i		−	1.45839i
$508$	−5.21686	−	38.5267i	−0.231461	−	1.70935i
$509$	13.2030	+	18.1724i	0.585213	+	0.805476i	0.994255	−	0.107039i	$-0.0341371\pi$
$509$	13.2030	+	18.1724i	0.585213	+	0.805476i	−0.409042	+	0.912516i	$0.634137\pi$
$510$	0.817982	+	0.349646i	0.0362208	+	0.0154826i
$511$	−0.370194	−	1.13934i	−0.0163764	−	0.0504015i
$512$	−16.3585	+	15.6333i	−0.722949	+	0.690902i
$513$	1.63983	+	1.19141i	0.0724004	+	0.0526020i
$514$	−0.0309123	+	0.0353802i	−0.00136348	+	0.00156056i
$515$	1.93051	+	0.627260i	0.0850683	+	0.0276404i
$516$	27.8730	−	13.4212i	1.22704	−	0.590837i
$517$		0			0
$518$	−0.358874	−	1.57251i	−0.0157680	−	0.0690920i
$519$	−10.0659	+	30.9796i	−0.441843	+	1.35985i
$520$	−2.04862	+	7.42086i	−0.0898380	+	0.325426i
$521$	−23.8045	−	17.2950i	−1.04289	−	0.757707i	−0.0720457	−	0.997401i	$-0.522953\pi$
$521$	−23.8045	−	17.2950i	−1.04289	−	0.757707i	−0.970848	+	0.239694i	$0.922953\pi$
$522$	−0.915747	+	0.547102i	−0.0400811	+	0.0239460i
$523$	−10.4671	+	3.40098i	−0.457696	+	0.148714i	−0.528786	−	0.848755i	$-0.677352\pi$
$523$	−10.4671	+	3.40098i	−0.457696	+	0.148714i	0.0710894	+	0.997470i	$0.477352\pi$
$524$	2.29874	−	12.6635i	0.100421	−	0.553208i
$525$	0.918660	+	1.26443i	0.0400936	+	0.0551841i
$526$	0.866975	−	9.63022i	0.0378019	−	0.419897i
$527$	−2.83305			−0.123409
$528$		0			0
$529$	24.3708			1.05960
$530$	0.620200	−	6.88908i	0.0269398	−	0.299242i
$531$	2.96955	+	4.08723i	0.128867	+	0.177371i
$532$	−0.0272985	+	0.150385i	−0.00118354	+	0.00652000i
$533$	51.3570	−	16.6869i	2.22452	−	0.722790i
$534$	−21.9509	+	13.1143i	−0.949909	+	0.567512i
$535$	−2.73138	−	1.98447i	−0.118088	−	0.0857960i
$536$	14.3012	+	3.94803i	0.617718	+	0.170529i
$537$	−1.17127	+	3.60481i	−0.0505442	+	0.155559i
$538$	−8.79430	−	38.5348i	−0.379149	−	1.66135i
$539$		0			0
$540$	4.11896	−	1.98333i	0.177252	−	0.0853491i
$541$	6.13318	+	1.99279i	0.263686	+	0.0856768i	0.437876	−	0.899035i	$-0.355731\pi$
$541$	6.13318	+	1.99279i	0.263686	+	0.0856768i	−0.174190	+	0.984712i	$0.555731\pi$
$542$	5.91982	−	6.77544i	0.254278	−	0.291030i
$543$	−10.3366	−	7.51001i	−0.443588	−	0.322286i
$544$	−3.80363	−	0.515715i	−0.163079	−	0.0221111i
$545$	1.73700	+	5.34595i	0.0744051	+	0.228995i
$546$	−2.35836	−	1.00808i	−0.100928	−	0.0431418i
$547$	−4.91913	−	6.77061i	−0.210327	−	0.289490i	0.690800	−	0.723046i	$-0.257259\pi$
$547$	−4.91913	−	6.77061i	−0.210327	−	0.289490i	−0.901127	+	0.433556i	$0.857259\pi$
$548$	2.38066	+	17.5813i	0.101697	+	0.751035i
$549$		−	5.13251i		−	0.219050i
$550$		0			0
$551$	−0.617351			−0.0263001
$552$	−34.2647	+	12.8568i	−1.45840	+	0.547224i
$553$	0.957873	−	0.695935i	0.0407329	−	0.0295942i
$554$	−7.38781	+	17.2835i	−0.313878	+	0.734304i
$555$	5.75348	−	1.86942i	0.244222	−	0.0793525i
$556$	3.79844	−	3.63132i	0.161090	−	0.154002i
$557$	−1.86891	+	2.57233i	−0.0791881	+	0.108993i	−0.846773	−	0.531954i	$-0.821458\pi$
$557$	−1.86891	+	2.57233i	−0.0791881	+	0.108993i	0.767585	+	0.640947i	$0.221458\pi$
$558$	2.07559	−	2.37558i	0.0878665	−	0.100566i
$559$	−14.0341	+	43.1925i	−0.593579	+	1.82685i
$560$	0.269493	+	0.214957i	0.0113881	+	0.00908359i
$561$		0			0
$562$	31.3383	−	7.15195i	1.32193	−	0.301687i
$563$	31.4236	+	10.2101i	1.32435	+	0.430306i	0.883985	−	0.467515i	$-0.154851\pi$
$563$	31.4236	+	10.2101i	1.32435	+	0.430306i	0.440360	+	0.897821i	$0.354851\pi$
$564$	−25.6730	−	13.8169i	−1.08103	−	0.581795i
$565$	−2.70208	+	3.71909i	−0.113677	+	0.156463i
$566$	−28.2231	+	16.8616i	−1.18631	+	0.708745i
$567$	0.557209	+	1.71491i	0.0234006	+	0.0720196i
$568$	13.0453	−	0.584895i	0.547369	−	0.0245417i
$569$	2.09326	−	1.52084i	0.0877541	−	0.0637571i	−0.543043	−	0.839705i	$-0.682728\pi$
$569$	2.09326	−	1.52084i	0.0877541	−	0.0637571i	0.630797	+	0.775948i	$0.282728\pi$
$570$	−0.570949	−	0.0514006i	−0.0239144	−	0.00215293i
$571$			17.5956i			0.736352i	0.929756	+	0.368176i	$0.120018\pi$
$571$			17.5956i			0.736352i	−0.929756	+	0.368176i	$0.879982\pi$
$572$		0			0
$573$			18.5365i			0.774374i
$574$	0.216809	−	2.40827i	0.00904942	−	0.100519i
$575$	−26.4870	+	19.2439i	−1.10458	+	0.802526i
$576$	3.21910	−	2.81160i	0.134129	−	0.117150i
$577$	5.44803	+	16.7673i	0.226805	+	0.698032i	0.998103	+	0.0615594i	$0.0196074\pi$
$577$	5.44803	+	16.7673i	0.226805	+	0.698032i	−0.771299	+	0.636473i	$0.780393\pi$
$578$	11.9965	+	20.0798i	0.498987	+	0.835211i
$579$	−14.9147	+	20.5283i	−0.619834	+	0.853128i
$580$	−0.659865	+	1.22609i	−0.0273994	+	0.0509106i
$581$	−1.21036	−	0.393270i	−0.0502142	−	0.0163156i
$582$	−1.98524	−	8.69891i	−0.0822909	−	0.360581i
$583$		0			0
$584$	−15.1587	+	12.0869i	−0.627274	+	0.500158i
$585$	0.449359	−	1.38298i	0.0185787	−	0.0571793i
$586$	−22.7386	−	19.8671i	−0.939321	−	0.820701i
$587$	9.60257	−	13.2168i	0.396340	−	0.545516i	−0.563480	−	0.826129i	$-0.690538\pi$
$587$	9.60257	−	13.2168i	0.396340	−	0.545516i	0.959821	+	0.280614i	$0.0905380\pi$
$588$	18.9415	−	18.1081i	0.781133	−	0.746766i
$589$	1.73631	−	0.564161i	0.0715434	−	0.0232459i
$590$	6.06365	+	2.59191i	0.249637	+	0.106707i
$591$	−21.7266	+	15.7853i	−0.893714	+	0.649322i
$592$	−21.7865	+	14.3781i	−0.895420	+	0.590934i
$593$	−44.6152			−1.83213			−0.916063	−	0.401035i	$-0.868651\pi$
$593$	−44.6152			−1.83213			−0.916063	+	0.401035i	$0.868651\pi$
$594$		0			0
$595$			0.0584772i			0.00239733i
$596$	−37.3517	+	5.05775i	−1.52998	+	0.207173i
$597$	−10.4577	−	14.3938i	−0.428004	−	0.589097i
$598$	21.1171	−	49.4024i	0.863540	−	2.02021i
$599$	−10.3581	−	31.8788i	−0.423219	−	1.30253i	−0.904689	−	0.426072i	$-0.859897\pi$
$599$	−10.3581	−	31.8788i	−0.423219	−	1.30253i	0.481470	−	0.876462i	$-0.340103\pi$
$600$	13.9358	−	21.1085i	0.568928	−	0.861749i
$601$	−18.3021	−	13.2973i	−0.746559	−	0.542407i	0.148200	−	0.988957i	$-0.452652\pi$
$601$	−18.3021	−	13.2973i	−0.746559	−	0.542407i	−0.894758	+	0.446551i	$0.852652\pi$
$602$	1.53142	+	1.33803i	0.0624160	+	0.0545340i
$603$	−2.66523	−	0.865987i	−0.108537	−	0.0352657i
$604$	−29.2556	+	14.0870i	−1.19039	+	0.573191i
$605$		0			0
$606$	18.2983	−	4.17598i	0.743316	−	0.169638i
$607$	−3.68637	+	11.3455i	−0.149625	+	0.460499i	−0.997577	−	0.0695747i	$-0.977836\pi$
$607$	−3.68637	+	11.3455i	−0.149625	+	0.460499i	0.847952	+	0.530074i	$0.177836\pi$
$608$	2.43385	−	0.441368i	0.0987058	−	0.0178998i
$609$	−0.375285	−	0.272661i	−0.0152073	−	0.0110488i
$610$	−3.43595	−	5.75113i	−0.139118	−	0.232857i
$611$	40.7058	−	13.2261i	1.64678	−	0.535072i
$612$	0.713381	+	0.129496i	0.0288367	+	0.00523456i
$613$	−11.2544	−	15.4903i	−0.454559	−	0.625647i	0.518810	−	0.854890i	$-0.326375\pi$
$613$	−11.2544	−	15.4903i	−0.454559	−	0.625647i	−0.973369	+	0.229242i	$0.926375\pi$
$614$	5.75856	+	0.518423i	0.232396	+	0.0209218i
$615$	9.06913			0.365703
$616$		0			0
$617$	−3.14690			−0.126689			−0.0633446	−	0.997992i	$-0.520177\pi$
$617$	−3.14690			−0.126689			−0.0633446	+	0.997992i	$0.520177\pi$
$618$	10.9002	+	0.981312i	0.438472	+	0.0394741i
$619$	19.8074	+	27.2626i	0.796129	+	1.09578i	0.993318	+	0.115412i	$0.0368187\pi$
$619$	19.8074	+	27.2626i	0.796129	+	1.09578i	−0.197189	+	0.980365i	$0.563181\pi$
$620$	0.735429	−	4.05141i	0.0295355	−	0.162708i
$621$	−30.3430	+	9.85903i	−1.21762	+	0.395629i
$622$	−0.963338	−	1.61245i	−0.0386263	−	0.0646532i
$623$	−1.35986	−	0.987994i	−0.0544815	−	0.0395831i
$624$	−1.86633	+	41.4655i	−0.0747130	+	1.65995i
$625$	6.61662	−	20.3638i	0.264665	−	0.814554i
$626$	20.9488	−	4.78088i	0.837282	−	0.191082i
$627$		0			0
$628$	−17.7854	−	36.9364i	−0.709713	−	1.47392i
$629$	−4.21134	−	1.36835i	−0.167917	−	0.0545595i
$630$	−0.0490346	−	0.0428424i	−0.00195359	−	0.00170688i
$631$	33.7776	+	24.5408i	1.34466	+	0.976956i	0.999259	+	0.0385022i	$0.0122587\pi$
$631$	33.7776	+	24.5408i	1.34466	+	0.976956i	0.345406	+	0.938453i	$0.387741\pi$
$632$	−15.9908	−	10.5571i	−0.636080	−	0.419941i
$633$	3.43140	+	10.5608i	0.136386	+	0.419753i
$634$	−3.58787	+	8.39367i	−0.142493	+	0.333355i
$635$	5.63426	+	7.75489i	0.223589	+	0.307744i
$636$	−5.00425	−	36.9566i	−0.198432	−	1.46543i
$637$			38.4695i			1.52422i
$638$		0			0
$639$	−2.46660			−0.0975771
$640$	1.72488	−	5.30551i	0.0681819	−	0.209719i
$641$	−11.9370	+	8.67273i	−0.471482	+	0.342552i	−0.798019	−	0.602633i	$-0.794118\pi$
$641$	−11.9370	+	8.67273i	−0.471482	+	0.342552i	0.326536	+	0.945185i	$0.394118\pi$
$642$	−16.7382	−	7.15475i	−0.660605	−	0.282375i
$643$	−18.3528	+	5.96318i	−0.723763	+	0.235165i	−0.647654	−	0.761935i	$-0.724250\pi$
$643$	−18.3528	+	5.96318i	−0.723763	+	0.235165i	−0.0761091	+	0.997099i	$0.524250\pi$
$644$	−1.66245	−	1.73896i	−0.0655096	−	0.0685245i
$645$	−4.48325	+	6.17067i	−0.176528	+	0.242970i
$646$	0.315985	+	0.276081i	0.0124323	+	0.0108623i
$647$	8.33188	−	25.6429i	0.327560	−	1.00813i	−0.642712	−	0.766108i	$-0.722191\pi$
$647$	8.33188	−	25.6429i	0.327560	−	1.00813i	0.970272	−	0.242018i	$-0.0778092\pi$
$648$	22.8166	−	18.1929i	0.896323	−	0.714685i
$649$		0			0
$650$	8.26182	+	36.2015i	0.324055	+	1.41994i
$651$	1.30466	+	0.423911i	0.0511338	+	0.0166144i
$652$	26.8631	+	14.4574i	1.05204	+	0.566195i
$653$	−18.5621	+	25.5486i	−0.726392	+	0.999793i	0.272895	+	0.962044i	$0.412019\pi$
$653$	−18.5621	+	25.5486i	−0.726392	+	0.999793i	−0.999287	+	0.0377490i	$0.987981\pi$
$654$	15.5438	+	26.0174i	0.607810	+	1.01736i
$655$	0.980589	+	3.01794i	0.0383148	+	0.117921i
$656$	−37.7232	+	10.4069i	−1.47284	+	0.406322i
$657$	2.96271	−	2.15254i	0.115587	−	0.0839785i
$658$	0.171844	−	1.90881i	0.00669916	−	0.0744132i
$659$		−	31.9283i		−	1.24375i	−0.783116	−	0.621876i	$-0.786371\pi$
$659$		−	31.9283i		−	1.24375i	0.783116	−	0.621876i	$-0.213629\pi$
$660$		0			0
$661$			48.2943i			1.87843i	0.343328	+	0.939216i	$0.388446\pi$
$661$			48.2943i			1.87843i	−0.343328	+	0.939216i	$0.611554\pi$
$662$	−8.59412	−	0.773699i	−0.334020	−	0.0300707i
$663$	−5.69643	+	4.13870i	−0.221231	+	0.160734i
$664$	0.922514	+	20.5754i	0.0358005	+	0.798482i
$665$	−0.0116449	−	0.0358394i	−0.000451570	−	0.00138979i
$666$	4.23276	−	2.52881i	0.164016	−	0.0979895i
$667$	5.71164	−	7.86140i	0.221156	−	0.304395i
$668$	−11.1012	+	20.6270i	−0.429518	+	0.798084i
$669$	−40.3784	−	13.1197i	−1.56112	−	0.507238i
$670$	−3.56621	+	0.813871i	−0.137775	+	0.0314426i
$671$		0			0
$672$	1.67446	+	0.806635i	0.0645939	+	0.0311166i
$673$	−2.09903	+	6.46015i	−0.0809117	+	0.249020i	−0.983327	−	0.181847i	$-0.941792\pi$
$673$	−2.09903	+	6.46015i	−0.0809117	+	0.249020i	0.902415	+	0.430868i	$0.141792\pi$
$674$	19.5671	−	22.3952i	0.753697	−	0.862632i
$675$	12.9609	−	17.8391i	0.498864	−	0.686628i
$676$	−24.1409	−	25.2519i	−0.928495	−	0.971225i
$677$	−15.0472	+	4.88914i	−0.578312	+	0.187905i	−0.583544	−	0.812081i	$-0.698334\pi$
$677$	−15.0472	+	4.88914i	−0.578312	+	0.187905i	0.00523234	+	0.999986i	$0.498334\pi$
$678$	−9.74201	+	22.7910i	−0.374140	+	0.875283i
$679$	0.474516	−	0.344756i	0.0182103	−	0.0132305i
$680$	0.886056	−	0.332467i	0.0339787	−	0.0127495i
$681$	19.4169			0.744057
$682$		0			0
$683$			47.5045i			1.81771i	0.417113	+	0.908855i	$0.363042\pi$
$683$			47.5045i			1.81771i	−0.417113	+	0.908855i	$0.636958\pi$
$684$	−0.463002	+	0.0626945i	−0.0177033	+	0.00239719i
$685$	−2.57114	−	3.53887i	−0.0982381	−	0.135213i
$686$	3.17485	+	1.35709i	0.121216	+	0.0518138i
$687$	0.725864	+	2.23398i	0.0276934	+	0.0852316i
$688$	11.5672	−	30.8115i	0.440997	−	1.17468i
$689$	44.2929	+	32.1806i	1.68742	+	1.22598i
$690$	5.93687	−	6.79496i	0.226013	−	0.258680i
$691$	35.0513	+	11.3888i	1.33341	+	0.433252i	0.887080	−	0.461615i	$-0.152730\pi$
$691$	35.0513	+	11.3888i	1.33341	+	0.433252i	0.446332	+	0.894867i	$0.352730\pi$
$692$	15.0341	+	31.2227i	0.571512	+	1.18691i
$693$		0			0
$694$	2.20071	+	9.64303i	0.0835378	+	0.366045i
$695$	−0.400370	+	1.23221i	−0.0151869	+	0.0467405i
$696$	−1.99774	+	7.23657i	−0.0757243	+	0.274301i
$697$	−5.37047	−	3.90187i	−0.203421	−	0.147794i
$698$	−27.7279	+	16.5657i	−1.04952	+	0.627021i
$699$	10.5918	−	3.44147i	0.400618	−	0.130169i
$700$	1.63598	+	0.296970i	0.0618341	+	0.0112244i
$701$	19.9175	+	27.4141i	0.752275	+	1.03542i	0.997817	+	0.0660321i	$0.0210340\pi$
$701$	19.9175	+	27.4141i	0.752275	+	1.03542i	−0.245542	+	0.969386i	$0.578966\pi$
$702$	−3.24449	+	36.0393i	−0.122456	+	1.36022i
$703$	2.85352			0.107622
$704$		0			0
$705$	7.18824			0.270725
$706$	0.725988	−	8.06415i	0.0273229	−	0.303498i
$707$	0.725199	+	0.998150i	0.0272739	+	0.0375393i
$708$	34.9831	+	6.35028i	1.31474	+	0.238658i
$709$	10.8541	−	3.52672i	0.407635	−	0.132449i	−0.0980197	−	0.995184i	$-0.531251\pi$
$709$	10.8541	−	3.52672i	0.407635	−	0.132449i	0.505655	+	0.862736i	$0.331251\pi$
$710$	−2.76390	+	1.65126i	−0.103727	+	0.0619706i
$711$	2.92814	+	2.12742i	0.109814	+	0.0797845i
$712$	−7.23888	+	26.2219i	−0.271288	+	0.982707i
$713$	−8.88000	+	27.3298i	−0.332559	+	1.02351i
$714$	0.0701511	+	0.307387i	0.00262534	+	0.0115037i
$715$		0			0
$716$	1.74939	+	3.63310i	0.0653777	+	0.135775i
$717$	6.96873	+	2.26428i	0.260252	+	0.0845610i
$718$	−12.8907	+	14.7539i	−0.481077	+	0.550610i
$719$	2.72204	+	1.97768i	0.101515	+	0.0737550i	0.637385	−	0.770546i	$-0.280016\pi$
$719$	2.72204	+	1.97768i	0.101515	+	0.0737550i	−0.535870	+	0.844301i	$0.680016\pi$
$720$	−0.370372	+	0.986556i	−0.0138030	+	0.0367668i
$721$	0.222318	+	0.684225i	0.00827956	+	0.0254819i
$722$	24.4589	+	10.4549i	0.910265	+	0.389092i
$723$	−13.6595	−	18.8006i	−0.508001	−	0.699203i
$724$	−13.4697	+	1.82391i	−0.500597	+	0.0677852i
$725$			6.71593i			0.249423i
$726$		0			0
$727$	−43.9520			−1.63009			−0.815045	−	0.579398i	$-0.803288\pi$
$727$	−43.9520			−1.63009			−0.815045	+	0.579398i	$0.803288\pi$
$728$	−2.55463	+	0.958551i	−0.0946807	+	0.0355263i
$729$	16.6913	−	12.1269i	0.618195	−	0.449145i
$730$	1.87880	−	4.39537i	0.0695375	−	0.162680i
$731$	5.30970	−	1.72522i	0.196386	−	0.0638097i
$732$	−24.9604	−	26.1091i	−0.922563	−	0.965021i
$733$	6.34147	−	8.72828i	0.234227	−	0.322386i	−0.675682	−	0.737193i	$-0.736151\pi$
$733$	6.34147	−	8.72828i	0.234227	−	0.322386i	0.909910	+	0.414807i	$0.136151\pi$
$734$	26.7606	−	30.6284i	0.987750	−	1.13051i
$735$	−1.99651	+	6.14462i	−0.0736423	+	0.226648i
$736$	−16.8972	+	35.0763i	−0.622840	+	1.29293i
$737$		0			0
$738$	7.20640	−	1.64463i	0.265271	−	0.0605395i
$739$	−19.9870	−	6.49418i	−0.735235	−	0.238892i	−0.0826191	−	0.996581i	$-0.526328\pi$
$739$	−19.9870	−	6.49418i	−0.735235	−	0.238892i	−0.652616	+	0.757689i	$0.726328\pi$
$740$	3.05002	−	5.66722i	0.112121	−	0.208331i
$741$	2.66705	−	3.67088i	0.0979765	−	0.134853i
$742$	2.10456	−	1.25735i	0.0772610	−	0.0461587i
$743$	−13.4658	−	41.4433i	−0.494011	−	1.52041i	−0.818493	−	0.574516i	$-0.805190\pi$
$743$	−13.4658	−	41.4433i	−0.494011	−	1.52041i	0.324483	−	0.945892i	$-0.394810\pi$
$744$	−0.994391	−	22.1786i	−0.0364561	−	0.813105i
$745$	7.51837	−	5.46242i	0.275452	−	0.200127i
$746$	36.5219	+	3.28794i	1.33716	+	0.120380i
$747$		−	3.89039i		−	0.142342i
$748$		0			0
$749$		−	1.19661i		−	0.0437232i
$750$	−1.14692	+	12.7398i	−0.0418795	+	0.465190i
$751$	27.7765	−	20.1808i	1.01358	−	0.736409i	0.0486234	−	0.998817i	$-0.484517\pi$
$751$	27.7765	−	20.1808i	1.01358	−	0.736409i	0.964957	+	0.262408i	$0.0845166\pi$
$752$	−29.8996	+	8.24857i	−1.09032	+	0.300794i
$753$	7.47210	+	22.9968i	0.272299	+	0.838049i
$754$	−5.65241	−	9.46107i	−0.205849	−	0.344552i
$755$	4.70563	−	6.47675i	0.171256	−	0.235713i
$756$	1.42679	+	0.767878i	0.0518918	+	0.0279275i
$757$	−11.4551	−	3.72200i	−0.416344	−	0.135279i	0.0933513	−	0.995633i	$-0.470242\pi$
$757$	−11.4551	−	3.72200i	−0.416344	−	0.135279i	−0.509696	+	0.860355i	$0.670242\pi$
$758$	1.53398	+	6.72156i	0.0557165	+	0.244138i
$759$		0			0
$760$	−0.476837	+	0.380207i	−0.0172967	+	0.0137916i
$761$	4.72812	−	14.5517i	0.171394	−	0.527497i	−0.828056	−	0.560645i	$-0.810553\pi$
$761$	4.72812	−	14.5517i	0.171394	−	0.527497i	0.999450	+	0.0331477i	$0.0105532\pi$
$762$	38.9196	+	34.0048i	1.40991	+	1.23186i
$763$	−1.17102	+	1.61177i	−0.0423938	+	0.0583501i
$764$	13.6271	+	14.2543i	0.493012	+	0.515701i
$765$	−0.170011	+	0.0552400i	−0.00614677	+	0.00199721i
$766$	−5.58421	−	2.38697i	−0.201766	−	0.0862447i
$767$	−42.2274	+	30.6800i	−1.52474	+	1.10779i
$768$	2.70223	−	29.9578i	0.0975082	−	1.08101i
$769$	30.4165			1.09685			0.548424	−	0.836200i	$-0.315228\pi$
$769$	30.4165			1.09685			0.548424	+	0.836200i	$0.315228\pi$
$770$		0			0
$771$		−	0.0624552i		−	0.00224927i
$772$	3.62225	+	26.7505i	0.130368	+	0.962770i
$773$	−9.93774	−	13.6781i	−0.357436	−	0.491968i	0.591996	−	0.805941i	$-0.298340\pi$
$773$	−9.93774	−	13.6781i	−0.357436	−	0.491968i	−0.949432	+	0.313973i	$0.898340\pi$
$774$	−2.44342	+	5.71627i	−0.0878268	+	0.205467i
$775$	−6.13729	−	18.8886i	−0.220458	−	0.678500i
$776$	−7.92161	−	5.22986i	−0.284369	−	0.187741i
$777$	1.73464	+	1.26029i	0.0622299	+	0.0452127i
$778$	21.9039	+	19.1378i	0.785293	+	0.686124i
$779$	4.06844	+	1.32192i	0.145767	+	0.0473626i
$780$	−4.43983	−	9.22056i	−0.158971	−	0.330149i
$781$		0			0
$782$	−6.43908	+	1.46951i	−0.230261	+	0.0525496i
$783$	−2.02239	+	6.22429i	−0.0722745	+	0.222438i
$784$	1.25349	−	27.8496i	0.0447675	−	0.994630i
$785$	8.17715	+	5.94105i	0.291855	+	0.212045i
$786$	8.77490	+	14.6875i	0.312990	+	0.523887i
$787$	−35.7363	+	11.6114i	−1.27386	+	0.413903i	−0.866414	−	0.499326i	$-0.833581\pi$
$787$	−35.7363	+	11.6114i	−1.27386	+	0.413903i	−0.407447	+	0.913229i	$0.633581\pi$
$788$	−5.10282	+	28.1110i	−0.181781	+	1.00141i
$789$	7.55513	+	10.3987i	0.268970	+	0.370205i
$790$	4.70527	+	0.423600i	0.167406	+	0.0150710i
$791$	−1.62932			−0.0579320
$792$		0			0
$793$	53.0267			1.88303
$794$	17.1818	+	1.54682i	0.609760	+	0.0548946i
$795$	5.40464	+	7.43885i	0.191683	+	0.263829i
$796$	−18.6233	−	3.38059i	−0.660087	−	0.119822i
$797$	−11.2717	+	3.66239i	−0.399264	+	0.129729i	−0.501764	−	0.865004i	$-0.667316\pi$
$797$	−11.2717	+	3.66239i	−0.399264	+	0.129729i	0.102501	+	0.994733i	$0.467316\pi$
$798$	−0.104206	−	0.174421i	−0.00368884	−	0.00617443i
$799$	−4.25666	−	3.09264i	−0.150590	−	0.109410i
$800$	−4.80147	−	26.4769i	−0.169758	−	0.936101i
$801$	1.58783	−	4.88682i	0.0561030	−	0.172667i
$802$	7.10716	−	1.62198i	0.250963	−	0.0572740i
$803$		0			0
$804$	−17.7695	+	8.55627i	−0.626683	+	0.301756i
$805$	0.564118	+	0.183293i	0.0198825	+	0.00646023i
$806$	24.5434	+	21.4440i	0.864504	+	0.755332i
$807$	42.5079	+	30.8838i	1.49635	+	1.08716i
$808$	11.0011	−	16.6632i	0.387016	−	0.586210i
$809$	8.22636	+	25.3181i	0.289223	+	0.890138i	0.985101	+	0.171978i	$0.0550156\pi$
$809$	8.22636	+	25.3181i	0.289223	+	0.890138i	−0.695877	+	0.718161i	$0.744984\pi$
$810$	−2.82793	+	6.61582i	−0.0993634	+	0.232456i
$811$	−25.6391	−	35.2892i	−0.900311	−	1.23917i	−0.970369	−	0.241629i	$-0.922318\pi$
$811$	−25.6391	−	35.2892i	−0.900311	−	1.23917i	0.0700576	−	0.997543i	$-0.477682\pi$
$812$	−0.489034	+	0.0662195i	−0.0171617	+	0.00232385i
$813$			11.9604i			0.419469i
$814$		0			0
$815$	−7.52146			−0.263465
$816$	4.25874	−	2.81056i	0.149086	−	0.0983893i
$817$	−2.91064	+	2.11470i	−0.101830	+	0.0739840i
$818$	−3.92785	−	1.67896i	−0.137334	−	0.0587034i
$819$	0.490167	−	0.159265i	0.0171278	−	0.00556517i
$820$	6.97400	−	6.66717i	0.243543	−	0.232828i
$821$	−22.3108	+	30.7081i	−0.778651	+	1.07172i	0.216778	+	0.976221i	$0.430445\pi$
$821$	−22.3108	+	30.7081i	−0.778651	+	1.07172i	−0.995429	+	0.0955006i	$0.969555\pi$
$822$	−17.7606	−	15.5177i	−0.619471	−	0.541243i
$823$	−4.74802	+	14.6129i	−0.165506	+	0.509374i	−0.999073	−	0.0430436i	$-0.986295\pi$
$823$	−4.74802	+	14.6129i	−0.165506	+	0.509374i	0.833568	+	0.552417i	$0.186295\pi$
$824$	9.10351	−	7.25870i	0.317136	−	0.252869i
$825$		0			0
$826$	0.520026	+	2.27864i	0.0180940	+	0.0792842i
$827$	19.4118	+	6.30729i	0.675016	+	0.219326i	0.626412	−	0.779492i	$-0.284523\pi$
$827$	19.4118	+	6.30729i	0.675016	+	0.219326i	0.0486040	+	0.998818i	$0.484523\pi$
$828$	3.48527	−	6.47594i	0.121121	−	0.225055i
$829$	−9.09411	+	12.5170i	−0.315851	+	0.434732i	−0.937195	−	0.348806i	$-0.886587\pi$
$829$	−9.09411	+	12.5170i	−0.315851	+	0.434732i	0.621344	+	0.783538i	$0.286587\pi$
$830$	−2.60441	−	4.35930i	−0.0904005	−	0.151313i
$831$	−7.72124	−	23.7635i	−0.267847	−	0.824348i
$832$	29.0482	+	33.2583i	1.00707	+	1.15302i
$833$	3.82591	−	2.77969i	0.132560	−	0.0963105i
$834$	−0.626356	+	6.95746i	−0.0216889	+	0.240917i
$835$		−	5.77540i		−	0.199866i
$836$		0			0
$837$		−	19.3540i		−	0.668974i
$838$	−8.67271	−	0.780775i	−0.299594	−	0.0269714i
$839$	−24.9516	+	18.1284i	−0.861425	+	0.625862i	−0.928272	−	0.371902i	$-0.878706\pi$
$839$	−24.9516	+	18.1284i	−0.861425	+	0.625862i	0.0668475	+	0.997763i	$0.478706\pi$
$840$	−0.457790	+	0.0205253i	−0.0157953	+	0.000708191i
$841$	8.34553	+	25.6849i	0.287777	+	0.885686i
$842$	3.25716	−	1.94595i	0.112249	−	0.0670619i
$843$	−25.1162	+	34.5695i	−0.865048	+	1.19064i
$844$	10.4024	+	5.59845i	0.358066	+	0.192707i
$845$	8.19171	+	2.66165i	0.281803	+	0.0915635i
$846$	5.71183	−	1.30354i	0.196377	−	0.0448166i
$847$		0			0
$848$	−31.0168	−	24.7401i	−1.06512	−	0.849579i
$849$	13.5052	−	41.5647i	0.463497	−	1.42650i
$850$	3.00338	−	3.43747i	0.103015	−	0.117904i
$851$	−26.4003	+	36.3369i	−0.904991	+	1.24561i
$852$	−12.5476	+	11.9955i	−0.429873	+	0.410960i
$853$	19.2765	−	6.26330i	0.660014	−	0.214451i	0.0401894	−	0.999192i	$-0.487204\pi$
$853$	19.2765	−	6.26330i	0.660014	−	0.214451i	0.619824	+	0.784741i	$0.287204\pi$
$854$	0.933266	−	2.18334i	0.0319357	−	0.0747122i
$855$	0.0931958	−	0.0677107i	0.00318723	−	0.00231566i
$856$	−18.1312	+	6.80322i	−0.619712	+	0.232529i
$857$	−52.7137			−1.80066			−0.900332	−	0.435203i	$-0.856677\pi$
$857$	−52.7137			−1.80066			−0.900332	+	0.435203i	$0.856677\pi$
$858$		0			0
$859$		−	35.6585i		−	1.21665i	−0.793687	−	0.608326i	$-0.791841\pi$
$859$		−	35.6585i		−	1.21665i	0.793687	−	0.608326i	$-0.208159\pi$
$860$	1.08882	+	8.04099i	0.0371285	+	0.274196i
$861$	1.88935	+	2.60046i	0.0643888	+	0.0886235i
$862$	−14.5276	−	6.20983i	−0.494813	−	0.211508i
$863$	−7.25777	−	22.3371i	−0.247057	−	0.760364i	−0.995291	−	0.0969293i	$-0.969098\pi$
$863$	−7.25777	−	22.3371i	−0.247057	−	0.760364i	0.748234	−	0.663435i	$-0.230902\pi$
$864$	3.52313	−	25.9846i	0.119859	−	0.884014i
$865$	−6.91223	−	5.02203i	−0.235023	−	0.170754i
$866$	21.5849	−	24.7047i	0.733486	−	0.839500i
$867$	−29.5720	−	9.60851i	−1.00432	−	0.326322i
$868$	1.31490	−	0.633143i	0.0446307	−	0.0214903i
$869$		0			0
$870$	−0.411827	−	1.80454i	−0.0139623	−	0.0611796i
$871$	8.94698	−	27.5360i	0.303157	−	0.933021i
$872$	31.0795	+	8.57989i	1.05249	+	0.290552i
$873$	1.45056	+	1.05389i	0.0490940	+	0.0356689i
$874$	3.65373	−	2.18288i	0.123589	−	0.0738371i
$875$	−0.799694	+	0.259836i	−0.0270346	+	0.00878408i
$876$	4.60314	−	25.3582i	0.155526	−	0.856775i
$877$	4.39339	+	6.04699i	0.148354	+	0.204192i	0.876726	−	0.480990i	$-0.159723\pi$
$877$	4.39339	+	6.04699i	0.148354	+	0.204192i	−0.728372	+	0.685182i	$0.759723\pi$
$878$	2.74510	−	30.4922i	0.0926428	−	1.02906i
$879$	40.1394			1.35387
$880$		0			0
$881$	28.0269			0.944250			0.472125	−	0.881532i	$-0.343487\pi$
$881$	28.0269			0.944250			0.472125	+	0.881532i	$0.343487\pi$
$882$	−0.472155	+	5.24462i	−0.0158983	+	0.176595i
$883$	−8.49703	−	11.6952i	−0.285948	−	0.393574i	0.641745	−	0.766918i	$-0.278211\pi$
$883$	−8.49703	−	11.6952i	−0.285948	−	0.393574i	−0.927693	+	0.373345i	$0.878211\pi$
$884$	−1.33789	+	7.37032i	−0.0449982	+	0.247891i
$885$	−8.33710	+	2.70889i	−0.280248	+	0.0910582i
$886$	44.6036	−	26.6479i	1.49849	−	0.895254i
$887$	26.7582	+	19.4410i	0.898452	+	0.652764i	0.938068	−	0.346451i	$-0.112613\pi$
$887$	26.7582	+	19.4410i	0.898452	+	0.652764i	−0.0396157	+	0.999215i	$0.512613\pi$
$888$	9.23395	−	33.4488i	0.309871	−	1.12247i
$889$	−1.04985	+	3.23111i	−0.0352109	+	0.108368i
$890$	−1.49227	−	6.53880i	−0.0500209	−	0.219181i
$891$		0			0
$892$	−40.6952	+	19.5953i	−1.36258	+	0.656099i
$893$	3.22467	+	1.04776i	0.107909	+	0.0350619i
$894$	32.9676	−	37.7326i	1.10260	−	1.26197i
$895$	−0.804313	−	0.584368i	−0.0268852	−	0.0195333i
$896$	1.88063	−	0.610694i	0.0628275	−	0.0204019i
$897$	22.0701	+	67.9248i	0.736900	+	2.26794i
$898$	−13.9041	−	5.94332i	−0.463987	−	0.198331i
$899$	3.46482	+	4.76892i	0.115558	+	0.159052i
$900$	0.682030	+	5.03682i	0.0227343	+	0.167894i
$901$		−	6.73034i		−	0.224220i
$902$		0			0
$903$	−2.70335			−0.0899618
$904$	9.26336	+	24.6877i	0.308095	+	0.821101i
$905$	2.71126	−	1.96984i	0.0901253	−	0.0654798i
$906$	16.9656	−	39.6902i	0.563644	−	1.31862i
$907$	6.68909	−	2.17342i	0.222107	−	0.0721671i	−0.195849	−	0.980634i	$-0.562746\pi$
$907$	6.68909	−	2.17342i	0.222107	−	0.0721671i	0.417957	+	0.908467i	$0.362746\pi$
$908$	14.9313	−	14.2743i	0.495511	−	0.473710i
$909$	−2.21688	+	3.05127i	−0.0735292	+	0.101204i
$910$	0.442628	−	0.506603i	0.0146730	−	0.0167937i
$911$	0.480856	−	1.47992i	0.0159315	−	0.0490321i	−0.942775	−	0.333430i	$-0.891794\pi$
$911$	0.480856	−	1.47992i	0.0159315	−	0.0490321i	0.958706	+	0.284398i	$0.0917938\pi$
$912$	−2.05040	+	2.57060i	−0.0678954	+	0.0851209i
$913$		0			0
$914$	−14.6439	+	3.34200i	−0.484379	+	0.110544i
$915$	8.46980	+	2.75201i	0.280003	+	0.0909785i
$916$	2.20049	+	1.18427i	0.0727061	+	0.0391295i
$917$	−0.661075	+	0.909891i	−0.0218306	+	0.0300473i
$918$	3.81866	−	2.28141i	0.126035	−	0.0752979i
$919$	14.6551	+	45.1038i	0.483427	+	1.48784i	0.834246	+	0.551393i	$0.185904\pi$
$919$	14.6551	+	45.1038i	0.483427	+	1.48784i	−0.350818	+	0.936444i	$0.614096\pi$
$920$	−0.429960	−	9.58969i	−0.0141754	−	0.316163i
$921$	−6.21811	+	4.51772i	−0.204894	+	0.148864i
$922$	−31.6647	−	2.85066i	−1.04282	−	0.0938815i
$923$		−	25.4837i		−	0.838807i
$924$		0			0
$925$		−	31.0423i		−	1.02066i
$926$	3.94817	−	43.8556i	0.129745	−	1.44118i
$927$	−1.77924	+	1.29270i	−0.0584380	+	0.0424577i
$928$	3.78373	+	7.03343i	0.124207	+	0.230884i
$929$	−0.534570	−	1.64524i	−0.0175387	−	0.0539784i	0.941904	−	0.335882i	$-0.109034\pi$
$929$	−0.534570	−	1.64524i	−0.0175387	−	0.0539784i	−0.959443	+	0.281903i	$0.909034\pi$
$930$	2.80733	+	4.69895i	0.0920561	+	0.154085i
$931$	−1.79128	+	2.46548i	−0.0587068	+	0.0808030i
$932$	5.61489	−	10.4330i	0.183922	−	0.341743i
$933$	2.37468	+	0.771581i	0.0777436	+	0.0252604i
$934$	1.56209	+	6.84475i	0.0511132	+	0.223967i
$935$		0			0
$936$	−5.20001	−	6.52160i	−0.169968	−	0.213165i
$937$	9.56394	−	29.4348i	0.312440	−	0.961592i	−0.664355	−	0.747417i	$-0.731294\pi$
$937$	9.56394	−	29.4348i	0.312440	−	0.961592i	0.976795	−	0.214175i	$-0.0687063\pi$
$938$	−0.976306	−	0.853016i	−0.0318775	−	0.0278520i
$939$	−16.7895	+	23.1087i	−0.547903	+	0.754124i
$940$	5.52763	−	5.28443i	0.180291	−	0.172359i
$941$	−12.3695	+	4.01909i	−0.403234	+	0.131019i	−0.503610	−	0.863931i	$-0.667995\pi$
$941$	−12.3695	+	4.01909i	−0.403234	+	0.131019i	0.100376	+	0.994950i	$0.467995\pi$
$942$	50.1105	+	21.4197i	1.63269	+	0.697892i
$943$	−54.4740	+	39.5776i	−1.77392	+	1.28883i
$944$	31.5698	−	20.8345i	1.02751	−	0.678107i
$945$	−0.399489			−0.0129954
$946$		0			0
$947$		−	56.9355i		−	1.85016i	−0.379776	−	0.925078i	$-0.623999\pi$
$947$		−	56.9355i		−	1.85016i	0.379776	−	0.925078i	$-0.376001\pi$
$948$	25.2415	−	3.41793i	0.819807	−	0.111009i
$949$	22.2390	+	30.6094i	0.721909	+	0.993623i
$950$	−1.15618	+	2.70483i	−0.0375114	+	0.0877563i
$951$	−3.74980	−	11.5407i	−0.121596	−	0.374233i
$952$	0.279920	+	0.184804i	0.00907227	+	0.00598952i
$953$	33.0979	+	24.0470i	1.07215	+	0.778960i	0.976297	−	0.216436i	$-0.0694432\pi$
$953$	33.0979	+	24.0470i	1.07215	+	0.778960i	0.0958498	+	0.995396i	$0.469443\pi$
$954$	5.64356	+	4.93087i	0.182717	+	0.159643i
$955$	−4.62408	−	1.50246i	−0.149632	−	0.0486183i
$956$	7.02341	−	3.38187i	0.227153	−	0.109377i
$957$		0			0
$958$	38.0472	−	8.68304i	1.22925	−	0.280536i
$959$	0.479089	−	1.47448i	0.0154706	−	0.0476136i
$960$	2.91373	+	6.81981i	0.0940402	+	0.220108i
$961$	10.9766	+	7.97500i	0.354085	+	0.257258i
$962$	26.1265	+	43.7309i	0.842353	+	1.40994i
$963$	3.47891	−	1.13037i	0.112106	−	0.0364256i
$964$	−24.3252	−	4.41561i	−0.783461	−	0.142217i
$965$	−3.91206	−	5.38449i	−0.125934	−	0.173333i
$966$	3.18518	+	0.286751i	0.102482	+	0.00922607i
$967$	−33.5254			−1.07810			−0.539052	−	0.842272i	$-0.681217\pi$
$967$	−33.5254			−1.07810			−0.539052	+	0.842272i	$0.681217\pi$
$968$		0			0
$969$	−0.557793			−0.0179189
$970$	2.33092	+	0.209845i	0.0748414	+	0.00673772i
$971$	−19.3960	−	26.6963i	−0.622447	−	0.856725i	0.375081	−	0.926992i	$-0.377615\pi$
$971$	−19.3960	−	26.6963i	−0.622447	−	0.856725i	−0.997528	+	0.0702673i	$0.977615\pi$
$972$	−1.96099	+	10.8029i	−0.0628989	+	0.346504i
$973$	−0.436730	+	0.141902i	−0.0140009	+	0.00454918i
$974$	12.9338	+	21.6487i	0.414425	+	0.693669i
$975$	−39.9341	−	29.0138i	−1.27891	−	0.929185i
$976$	−38.3882	−	1.72782i	−1.22878	−	0.0553063i
$977$	−8.80381	+	27.0954i	−0.281659	+	0.866857i	0.705721	+	0.708490i	$0.250623\pi$
$977$	−8.80381	+	27.0954i	−0.281659	+	0.866857i	−0.987380	+	0.158368i	$0.949377\pi$
$978$	−39.5368	+	9.02298i	−1.26425	+	0.288523i
$979$		0			0
$980$	2.98193	+	6.19283i	0.0952544	+	0.197823i
$981$	−5.79212	−	1.88197i	−0.184928	−	0.0600868i
$982$	10.7874	+	9.42516i	0.344241	+	0.300769i
$983$	32.4442	+	23.5721i	1.03481	+	0.751834i	0.969266	−	0.246016i	$-0.0791214\pi$
$983$	32.4442	+	23.5721i	1.03481	+	0.751834i	0.0655449	+	0.997850i	$0.479121\pi$
$984$	28.6609	−	43.4124i	0.913675	−	1.38394i
$985$	−2.17675	−	6.69935i	−0.0693570	−	0.213459i
$986$	−0.532508	+	1.24578i	−0.0169585	+	0.0396737i
$987$	1.49751	+	2.06114i	0.0476661	+	0.0656068i
$988$	−0.647731	−	4.78352i	−0.0206071	−	0.152184i
$989$		−	56.6292i		−	1.80070i
$990$		0			0
$991$	−26.7150			−0.848631			−0.424316	−	0.905514i	$-0.639485\pi$
$991$	−26.7150			−0.848631			−0.424316	+	0.905514i	$0.639485\pi$
$992$	−17.0692	−	16.3239i	−0.541949	−	0.518284i
$993$	9.27996	−	6.74229i	0.294491	−	0.213960i
$994$	−1.04927	−	0.448512i	−0.0332809	−	0.0142259i
$995$	4.43827	−	1.44208i	0.140703	−	0.0457171i
$996$	−18.9197	−	19.7904i	−0.599494	−	0.627083i
$997$	15.5329	−	21.3792i	0.491933	−	0.677088i	−0.488810	−	0.872390i	$-0.662569\pi$
$997$	15.5329	−	21.3792i	0.491933	−	0.677088i	0.980743	+	0.195303i	$0.0625689\pi$
$998$	40.8495	+	35.6909i	1.29307	+	1.12978i
$999$	9.34789	−	28.7699i	0.295754	−	0.910238i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.o.i.493.5		40
8.5	even	2	inner	968.2.o.i.493.3		40
11.2	odd	10		968.2.o.j.245.3		40
11.3	even	5		968.2.o.d.565.10		40
11.4	even	5		968.2.c.i.485.4		20
11.5	even	5	inner	968.2.o.i.269.3		40
11.6	odd	10		88.2.o.a.5.8	yes	40
11.7	odd	10		968.2.c.h.485.17		20
11.8	odd	10		968.2.o.j.565.1		40
11.9	even	5		968.2.o.d.245.8		40
11.10	odd	2		88.2.o.a.53.6	yes	40
33.17	even	10		792.2.br.b.181.3		40
33.32	even	2		792.2.br.b.757.5		40
44.7	even	10		3872.2.c.h.1937.5		20
44.15	odd	10		3872.2.c.i.1937.5		20
44.39	even	10		352.2.w.a.49.3		40
44.43	even	2		352.2.w.a.273.8		40
88.5	even	10	inner	968.2.o.i.269.5		40
88.13	odd	10		968.2.o.j.245.1		40
88.21	odd	2		88.2.o.a.53.8	yes	40
88.29	odd	10		968.2.c.h.485.18		20
88.37	even	10		968.2.c.i.485.3		20
88.43	even	2		352.2.w.a.273.3		40
88.51	even	10		3872.2.c.h.1937.16		20
88.53	even	10		968.2.o.d.245.10		40
88.59	odd	10		3872.2.c.i.1937.16		20
88.61	odd	10		88.2.o.a.5.6	✓	40
88.69	even	10		968.2.o.d.565.8		40
88.83	even	10		352.2.w.a.49.8		40
88.85	odd	10		968.2.o.j.565.3		40
264.149	even	10		792.2.br.b.181.5		40
264.197	even	2		792.2.br.b.757.3		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.o.a.5.6	✓	40	88.61	odd	10
88.2.o.a.5.8	yes	40	11.6	odd	10
88.2.o.a.53.6	yes	40	11.10	odd	2
88.2.o.a.53.8	yes	40	88.21	odd	2
352.2.w.a.49.3		40	44.39	even	10
352.2.w.a.49.8		40	88.83	even	10
352.2.w.a.273.3		40	88.43	even	2
352.2.w.a.273.8		40	44.43	even	2
792.2.br.b.181.3		40	33.17	even	10
792.2.br.b.181.5		40	264.149	even	10
792.2.br.b.757.3		40	264.197	even	2
792.2.br.b.757.5		40	33.32	even	2
968.2.c.h.485.17		20	11.7	odd	10
968.2.c.h.485.18		20	88.29	odd	10
968.2.c.i.485.3		20	88.37	even	10
968.2.c.i.485.4		20	11.4	even	5
968.2.o.d.245.8		40	11.9	even	5
968.2.o.d.245.10		40	88.53	even	10
968.2.o.d.565.8		40	88.69	even	10
968.2.o.d.565.10		40	11.3	even	5
968.2.o.i.269.3		40	11.5	even	5	inner
968.2.o.i.269.5		40	88.5	even	10	inner
968.2.o.i.493.3		40	8.5	even	2	inner
968.2.o.i.493.5		40	1.1	even	1	trivial
968.2.o.j.245.1		40	88.13	odd	10
968.2.o.j.245.3		40	11.2	odd	10
968.2.o.j.565.1		40	11.8	odd	10
968.2.o.j.565.3		40	88.85	odd	10
3872.2.c.h.1937.5		20	44.7	even	10
3872.2.c.h.1937.16		20	88.51	even	10
3872.2.c.i.1937.5		20	44.15	odd	10
3872.2.c.i.1937.16		20	88.59	odd	10

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.126804 + 1.40852i) q^{2} +(-1.10501 - 1.52092i) q^{3} +(-1.96784 - 0.357211i) q^{4} +(0.468972 - 0.152378i) q^{5} +(2.28236 - 1.36357i) q^{6} +(0.141392 + 0.102727i) q^{7} +(0.752668 - 2.72644i) q^{8} +(-0.165095 + 0.508111i) q^{9} +(0.155160 + 0.679877i) q^{10} +(1.63120 + 3.38766i) q^{12} +(-5.24957 - 1.70569i) q^{13} +(-0.162622 + 0.186127i) q^{14} +(-0.749976 - 0.544889i) q^{15} +(3.74480 + 1.40587i) q^{16} +(0.209682 + 0.645335i) q^{17} +(-0.694749 - 0.296970i) q^{18} +(-0.257018 - 0.353756i) q^{19} +(-0.977293 + 0.132334i) q^{20} -0.328562i q^{21} +6.88264 q^{23} +(-4.97842 + 1.86801i) q^{24} +(-3.84837 + 2.79600i) q^{25} +(3.06816 - 7.17782i) q^{26} +(-4.40862 + 1.43245i) q^{27} +(-0.241542 - 0.252658i) q^{28} +(0.829861 - 1.14221i) q^{29} +(0.862586 - 0.987260i) q^{30} +(-1.29020 + 3.97083i) q^{31} +(-2.45505 + 5.09635i) q^{32} +(-0.935553 + 0.213510i) q^{34} +(0.0819624 + 0.0266312i) q^{35} +(0.506385 - 0.940909i) q^{36} +(-3.83578 + 5.27950i) q^{37} +(0.530862 - 0.317157i) q^{38} +(3.20663 + 9.86900i) q^{39} +(-0.0624702 - 1.39332i) q^{40} +(-7.91468 + 5.75035i) q^{41} +(0.462785 + 0.0416629i) q^{42} -8.22782i q^{43} +0.263447i q^{45} +(-0.872747 + 9.69432i) q^{46} +(-6.27322 + 4.55776i) q^{47} +(-1.99984 - 7.24906i) q^{48} +(-2.15368 - 6.62835i) q^{49} +(-3.45023 - 5.77504i) q^{50} +(0.749802 - 1.03201i) q^{51} +(9.72103 + 5.23173i) q^{52} +(-9.43332 - 3.06507i) q^{53} +(-1.45860 - 6.39126i) q^{54} +(0.386502 - 0.308178i) q^{56} +(-0.254025 + 0.781810i) q^{57} +(1.50359 + 1.31371i) q^{58} +(5.55824 - 7.65026i) q^{59} +(1.28119 + 1.34016i) q^{60} +(-9.13658 + 2.96865i) q^{61} +(-5.42938 - 2.32079i) q^{62} +(-0.0755402 + 0.0548832i) q^{63} +(-6.86698 - 4.10421i) q^{64} -2.72181 q^{65} +5.24537i q^{67} +(-0.182100 - 1.34482i) q^{68} +(-7.60542 - 10.4680i) q^{69} +(-0.0479037 + 0.112068i) q^{70} +(1.42668 + 4.39088i) q^{71} +(1.26107 + 0.832562i) q^{72} +(-5.54545 - 4.02901i) q^{73} +(-6.94987 - 6.07222i) q^{74} +(8.50501 + 2.76344i) q^{75} +(0.379406 + 0.787945i) q^{76} +(-14.3073 + 3.26517i) q^{78} +(2.09346 - 6.44301i) q^{79} +(1.97043 + 0.0886875i) q^{80} +(8.34691 + 6.06438i) q^{81} +(-7.09586 - 11.8771i) q^{82} +(-6.92543 + 2.25021i) q^{83} +(-0.117366 + 0.646558i) q^{84} +(0.196670 + 0.270693i) q^{85} +(11.5890 + 1.04332i) q^{86} -2.65421 q^{87} -9.61762 q^{89} +(-0.371069 - 0.0334061i) q^{90} +(-0.567027 - 0.780446i) q^{91} +(-13.5440 - 2.45856i) q^{92} +(7.46502 - 2.42553i) q^{93} +(-5.62421 - 9.41388i) q^{94} +(-0.174439 - 0.126737i) q^{95} +(10.4640 - 1.89760i) q^{96} +(1.03707 - 3.19177i) q^{97} +(9.60923 - 2.19299i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} - q^{4} + 7 q^{6} + 10 q^{7} + 5 q^{8} + 20 q^{10} - 6 q^{12} + 2 q^{14} - 18 q^{15} + 15 q^{16} + 6 q^{17} + 20 q^{18} + 8 q^{20} - 8 q^{23} - 25 q^{24} - 4 q^{25} - 10 q^{26} - 32 q^{28}+ \cdots + 144 q^{98}+O(q^{100}) \) 40 * q + 5 * q^2 - q^4 + 7 * q^6 + 10 * q^7 + 5 * q^8 + 20 * q^10 - 6 * q^12 + 2 * q^14 - 18 * q^15 + 15 * q^16 + 6 * q^17 + 20 * q^18 + 8 * q^20 - 8 * q^23 - 25 * q^24 - 4 * q^25 - 10 * q^26 - 32 * q^28 + 28 * q^30 - 6 * q^31 - 20 * q^32 + 10 * q^34 + 18 * q^36 + 12 * q^38 + 34 * q^39 - 10 * q^40 + 14 * q^41 + 40 * q^42 - 18 * q^46 - 6 * q^47 + 18 * q^48 - 4 * q^49 - 61 * q^50 - 20 * q^52 - 108 * q^54 - 32 * q^56 + 26 * q^57 + 4 * q^58 - 46 * q^60 - 48 * q^62 - 60 * q^63 - 49 * q^64 + 36 * q^65 + 42 * q^68 - 8 * q^70 + 22 * q^71 + 101 * q^72 + 6 * q^73 - 54 * q^74 + 134 * q^76 - 12 * q^78 - 74 * q^79 - 44 * q^80 - 4 * q^81 - 31 * q^82 + 28 * q^84 - 15 * q^86 - 68 * q^87 - 16 * q^89 + 84 * q^90 - 4 * q^92 + 100 * q^94 - 66 * q^95 + 30 * q^96 + 10 * q^97 + 144 * q^98

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