LMFDB - Embedded newform 756.2.be.c.431.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(107,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.107"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.be (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,0,-4,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			431.3
Character	$\chi$	$=$	756.431
Dual form			756.2.be.c.107.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.04864 - 0.948869i) q^{2} +(0.199295 + 1.99005i) q^{4} +(-0.479813 + 0.277020i) q^{5} +(2.45883 + 0.976797i) q^{7} +(1.67930 - 2.27595i) q^{8} +(0.766008 + 0.164785i) q^{10} +(-2.96884 + 5.14218i) q^{11} +3.20224 q^{13} +(-1.65158 - 3.35742i) q^{14} +(-3.92056 + 0.793213i) q^{16} +(-2.48564 - 1.43509i) q^{17} +(-3.43890 + 1.98545i) q^{19} +(-0.646908 - 0.899641i) q^{20} +(7.99249 - 2.57526i) q^{22} +(0.145485 + 0.251987i) q^{23} +(-2.34652 + 4.06429i) q^{25} +(-3.35800 - 3.03851i) q^{26} +(-1.45384 + 5.08786i) q^{28} -4.13555i q^{29} +(-5.96048 - 3.44128i) q^{31} +(4.86392 + 2.88830i) q^{32} +(1.24484 + 3.86344i) q^{34} +(-1.45037 + 0.212467i) q^{35} +(1.20253 + 2.08285i) q^{37} +(5.49011 + 1.18104i) q^{38} +(-0.175268 + 1.55723i) q^{40} +2.27815i q^{41} +8.31569i q^{43} +(-10.8248 - 4.88331i) q^{44} +(0.0865415 - 0.402290i) q^{46} +(6.19284 + 10.7263i) q^{47} +(5.09174 + 4.80356i) q^{49} +(6.31714 - 2.03544i) q^{50} +(0.638192 + 6.37261i) q^{52} +(-4.21439 - 2.43318i) q^{53} -3.28971i q^{55} +(6.35227 - 3.95584i) q^{56} +(-3.92410 + 4.33671i) q^{58} +(-6.24666 + 10.8195i) q^{59} +(-0.305765 - 0.529601i) q^{61} +(2.98507 + 9.26438i) q^{62} +(-2.35988 - 7.64402i) q^{64} +(-1.53648 + 0.887087i) q^{65} +(3.70186 + 2.13727i) q^{67} +(2.36051 - 5.23254i) q^{68} +(1.72253 + 1.15341i) q^{70} +7.00902 q^{71} +(6.28996 - 10.8945i) q^{73} +(0.715324 - 3.32520i) q^{74} +(-4.63650 - 6.44788i) q^{76} +(-12.3227 + 9.74381i) q^{77} +(-5.20851 + 3.00714i) q^{79} +(1.66140 - 1.46667i) q^{80} +(2.16166 - 2.38896i) q^{82} -0.675423 q^{83} +1.59019 q^{85} +(7.89050 - 8.72017i) q^{86} +(6.71775 + 15.3922i) q^{88} +(11.1545 - 6.44005i) q^{89} +(7.87379 + 3.12794i) q^{91} +(-0.472472 + 0.339741i) q^{92} +(3.68380 - 17.1242i) q^{94} +(1.10002 - 1.90529i) q^{95} -3.00803 q^{97} +(-0.781450 - 9.86860i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{4} - 2 q^{7} - 20 q^{10} + 8 q^{13} + 12 q^{16} + 42 q^{19} + 4 q^{22} + 6 q^{25} - 28 q^{28} - 30 q^{31} + 24 q^{34} + 12 q^{37} + 36 q^{40} - 12 q^{46} - 14 q^{49} + 84 q^{52} + 28 q^{58}+ \cdots - 4 q^{97}+O(q^{100}) $ 28 * q - 4 * q^4 - 2 * q^7 - 20 * q^10 + 8 * q^13 + 12 * q^16 + 42 * q^19 + 4 * q^22 + 6 * q^25 - 28 * q^28 - 30 * q^31 + 24 * q^34 + 12 * q^37 + 36 * q^40 - 12 * q^46 - 14 * q^49 + 84 * q^52 + 28 * q^58 + 6 * q^61 + 8 * q^64 - 24 * q^67 + 128 * q^70 - 22 * q^73 - 48 * q^79 - 36 * q^82 - 24 * q^85 - 16 * q^88 - 16 * q^91 - 12 * q^94 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.04864	−	0.948869i	−0.741501	−	0.670952i
$2$	−1.04864	−	0.948869i	−0.741501	−	0.670952i
$3$		0			0
$3$		0			0
$4$	0.199295	+	1.99005i	0.0996476	+	0.995023i
$5$	−0.479813	+	0.277020i	−0.214579	+	0.123887i	−0.603438	−	0.797410i	$-0.706203\pi$
$5$	−0.479813	+	0.277020i	−0.214579	+	0.123887i	0.388859	+	0.921297i	$0.372869\pi$
$6$		0			0
$7$	2.45883	+	0.976797i	0.929352	+	0.369194i
$7$	2.45883	+	0.976797i	0.929352	+	0.369194i
$8$	1.67930	−	2.27595i	0.593723	−	0.804669i
$9$		0			0
$10$	0.766008	+	0.164785i	0.242233	+	0.0521096i
$11$	−2.96884	+	5.14218i	−0.895138	+	1.55042i	−0.0615040	+	0.998107i	$0.519590\pi$
$11$	−2.96884	+	5.14218i	−0.895138	+	1.55042i	−0.833634	+	0.552317i	$0.813744\pi$
$12$		0			0
$13$	3.20224			0.888143			0.444071	−	0.895991i	$-0.353534\pi$
$13$	3.20224			0.888143			0.444071	+	0.895991i	$0.353534\pi$
$14$	−1.65158	−	3.35742i	−0.441404	−	0.897308i
$15$		0			0
$16$	−3.92056	+	0.793213i	−0.980141	+	0.198303i
$17$	−2.48564	−	1.43509i	−0.602856	−	0.348059i	0.167308	−	0.985905i	$-0.446493\pi$
$17$	−2.48564	−	1.43509i	−0.602856	−	0.348059i	−0.770164	+	0.637845i	$0.779826\pi$
$18$		0			0
$19$	−3.43890	+	1.98545i	−0.788938	+	0.455494i	−0.839589	−	0.543223i	$-0.817204\pi$
$19$	−3.43890	+	1.98545i	−0.788938	+	0.455494i	0.0506503	+	0.998716i	$0.483871\pi$
$20$	−0.646908	−	0.899641i	−0.144653	−	0.201166i
$21$		0			0
$22$	7.99249	−	2.57526i	1.70401	−	0.549047i
$23$	0.145485	+	0.251987i	0.0303357	+	0.0525430i	0.880795	−	0.473498i	$-0.157009\pi$
$23$	0.145485	+	0.251987i	0.0303357	+	0.0525430i	−0.850459	+	0.526041i	$0.823676\pi$
$24$		0			0
$25$	−2.34652	+	4.06429i	−0.469304	+	0.812858i
$26$	−3.35800	−	3.03851i	−0.658559	−	0.595901i
$27$		0			0
$28$	−1.45384	+	5.08786i	−0.274749	+	0.961516i
$29$		−	4.13555i		−	0.767953i	−0.923343	−	0.383976i	$-0.874554\pi$
$29$		−	4.13555i		−	0.767953i	0.923343	−	0.383976i	$-0.125446\pi$
$30$		0			0
$31$	−5.96048	−	3.44128i	−1.07053	−	0.618073i	−0.142206	−	0.989837i	$-0.545420\pi$
$31$	−5.96048	−	3.44128i	−1.07053	−	0.618073i	−0.928327	+	0.371764i	$0.878753\pi$
$32$	4.86392	+	2.88830i	0.859827	+	0.510585i
$33$		0			0
$34$	1.24484	+	3.86344i	0.213488	+	0.662574i
$35$	−1.45037	+	0.212467i	−0.245158	+	0.0359135i
$36$		0			0
$37$	1.20253	+	2.08285i	0.197695	+	0.342418i	0.947781	−	0.318923i	$-0.103321\pi$
$37$	1.20253	+	2.08285i	0.197695	+	0.342418i	−0.750086	+	0.661341i	$0.769988\pi$
$38$	5.49011	+	1.18104i	0.890613	+	0.191590i
$39$		0			0
$40$	−0.175268	+	1.55723i	−0.0277123	+	0.246220i
$41$			2.27815i			0.355787i	0.984050	+	0.177893i	$0.0569282\pi$
$41$			2.27815i			0.355787i	−0.984050	+	0.177893i	$0.943072\pi$
$42$		0			0
$43$			8.31569i			1.26813i	0.773280	+	0.634065i	$0.218615\pi$
$43$			8.31569i			1.26813i	−0.773280	+	0.634065i	$0.781385\pi$
$44$	−10.8248	−	4.88331i	−1.63191	−	0.736186i
$45$		0			0
$46$	0.0865415	−	0.402290i	0.0127598	−	0.0593145i
$47$	6.19284	+	10.7263i	0.903318	+	1.56459i	0.823159	+	0.567811i	$0.192210\pi$
$47$	6.19284	+	10.7263i	0.903318	+	1.56459i	0.0801597	+	0.996782i	$0.474457\pi$
$48$		0			0
$49$	5.09174	+	4.80356i	0.727391	+	0.686223i
$50$	6.31714	−	2.03544i	0.893378	−	0.287855i
$51$		0			0
$52$	0.638192	+	6.37261i	0.0885013	+	0.883722i
$53$	−4.21439	−	2.43318i	−0.578892	−	0.334223i	0.181801	−	0.983335i	$-0.441807\pi$
$53$	−4.21439	−	2.43318i	−0.578892	−	0.334223i	−0.760693	+	0.649112i	$0.775141\pi$
$54$		0			0
$55$		−	3.28971i		−	0.443585i
$56$	6.35227	−	3.95584i	0.848858	−	0.528622i
$57$		0			0
$58$	−3.92410	+	4.33671i	−0.515259	+	0.569438i
$59$	−6.24666	+	10.8195i	−0.813246	+	1.40858i	0.0973349	+	0.995252i	$0.468968\pi$
$59$	−6.24666	+	10.8195i	−0.813246	+	1.40858i	−0.910581	+	0.413331i	$0.864365\pi$
$60$		0			0
$61$	−0.305765	−	0.529601i	−0.0391492	−	0.0678085i	0.845787	−	0.533521i	$-0.179131\pi$
$61$	−0.305765	−	0.529601i	−0.0391492	−	0.0678085i	−0.884936	+	0.465712i	$0.845798\pi$
$62$	2.98507	+	9.26438i	0.379105	+	1.17658i
$63$		0			0
$64$	−2.35988	−	7.64402i	−0.294985	−	0.955502i
$65$	−1.53648	+	0.887087i	−0.190577	+	0.110030i
$66$		0			0
$67$	3.70186	+	2.13727i	0.452254	+	0.261109i	0.708782	−	0.705428i	$-0.249245\pi$
$67$	3.70186	+	2.13727i	0.452254	+	0.261109i	−0.256528	+	0.966537i	$0.582578\pi$
$68$	2.36051	−	5.23254i	0.286254	−	0.634539i
$69$		0			0
$70$	1.72253	+	1.15341i	0.205881	+	0.137859i
$71$	7.00902			0.831818			0.415909	−	0.909406i	$-0.363464\pi$
$71$	7.00902			0.831818			0.415909	+	0.909406i	$0.363464\pi$
$72$		0			0
$73$	6.28996	−	10.8945i	0.736184	−	1.27511i	−0.218017	−	0.975945i	$-0.569959\pi$
$73$	6.28996	−	10.8945i	0.736184	−	1.27511i	0.954202	−	0.299164i	$-0.0967078\pi$
$74$	0.715324	−	3.32520i	0.0831547	−	0.386547i
$75$		0			0
$76$	−4.63650	−	6.44788i	−0.531843	−	0.739623i
$77$	−12.3227	+	9.74381i	−1.40431	+	1.11041i
$78$		0			0
$79$	−5.20851	+	3.00714i	−0.586003	+	0.338329i	−0.763516	−	0.645789i	$-0.776528\pi$
$79$	−5.20851	+	3.00714i	−0.586003	+	0.338329i	0.177512	+	0.984119i	$0.443195\pi$
$80$	1.66140	−	1.46667i	0.185750	−	0.163979i
$81$		0			0
$82$	2.16166	−	2.38896i	0.238716	−	0.263816i
$83$	−0.675423			−0.0741373			−0.0370686	−	0.999313i	$-0.511802\pi$
$83$	−0.675423			−0.0741373			−0.0370686	+	0.999313i	$0.511802\pi$
$84$		0			0
$85$	1.59019			0.172480
$86$	7.89050	−	8.72017i	0.850854	−	0.940320i
$87$		0			0
$88$	6.71775	+	15.3922i	0.716114	+	1.64081i
$89$	11.1545	−	6.44005i	1.18237	−	0.682644i	0.225811	−	0.974171i	$-0.427497\pi$
$89$	11.1545	−	6.44005i	1.18237	−	0.682644i	0.956562	+	0.291527i	$0.0941635\pi$
$90$		0			0
$91$	7.87379	+	3.12794i	0.825397	+	0.327897i
$92$	−0.472472	+	0.339741i	−0.0492586	+	0.0354205i
$93$		0			0
$94$	3.68380	−	17.1242i	0.379955	−	1.76623i
$95$	1.10002	−	1.90529i	0.112860	−	0.195479i
$96$		0			0
$97$	−3.00803			−0.305420			−0.152710	−	0.988271i	$-0.548800\pi$
$97$	−3.00803			−0.305420			−0.152710	+	0.988271i	$0.548800\pi$
$98$	−0.781450	−	9.86860i	−0.0789384	−	0.996879i
$99$		0			0
$100$	−8.55577	−	3.85969i	−0.855577	−	0.385969i
$101$	15.3276	+	8.84940i	1.52515	+	0.880548i	0.999555	+	0.0298150i	$0.00949180\pi$
$101$	15.3276	+	8.84940i	1.52515	+	0.880548i	0.525598	+	0.850733i	$0.323842\pi$
$102$		0			0
$103$	4.01639	−	2.31886i	0.395746	−	0.228484i	−0.288901	−	0.957359i	$-0.593290\pi$
$103$	4.01639	−	2.31886i	0.395746	−	0.228484i	0.684647	+	0.728875i	$0.259956\pi$
$104$	5.37754	−	7.28814i	0.527311	−	0.714661i
$105$		0			0
$106$	2.11062	+	6.55044i	0.205001	+	0.636235i
$107$	3.39483	+	5.88002i	0.328191	+	0.568443i	0.982153	−	0.188084i	$-0.0602279\pi$
$107$	3.39483	+	5.88002i	0.328191	+	0.568443i	−0.653962	+	0.756527i	$0.726895\pi$
$108$		0			0
$109$	−6.48848	+	11.2384i	−0.621483	+	1.07644i	0.367726	+	0.929934i	$0.380136\pi$
$109$	−6.48848	+	11.2384i	−0.621483	+	1.07644i	−0.989210	+	0.146507i	$0.953197\pi$
$110$	−3.12151	+	3.44973i	−0.297624	+	0.328919i
$111$		0			0
$112$	−10.4148	−	1.87921i	−0.984108	−	0.177569i
$113$			12.0732i			1.13575i	0.823115	+	0.567875i	$0.192234\pi$
$113$			12.0732i			1.13575i	−0.823115	+	0.567875i	$0.807766\pi$
$114$		0			0
$115$	−0.139611	−	0.0806045i	−0.0130188	−	0.00751641i
$116$	8.22994	−	0.824196i	0.764130	−	0.0765247i
$117$		0			0
$118$	16.8168	−	5.41854i	1.54811	−	0.498817i
$119$	−4.70999	−	5.95660i	−0.431764	−	0.546041i
$120$		0			0
$121$	−12.1280	−	21.0063i	−1.10254	−	1.90966i
$122$	−0.181884	+	0.845493i	−0.0164670	+	0.0765473i
$123$		0			0
$124$	5.66042	−	12.5475i	0.508320	−	1.12679i
$125$		−	5.37034i		−	0.480338i
$126$		0			0
$127$		−	19.0672i		−	1.69194i	−0.533233	−	0.845968i	$-0.679023\pi$
$127$		−	19.0672i		−	1.69194i	0.533233	−	0.845968i	$-0.320977\pi$
$128$	−4.77850	+	10.2550i	−0.422364	+	0.906426i
$129$		0			0
$130$	2.45294	+	0.527682i	0.215137	+	0.0462808i
$131$	0.945219	+	1.63717i	0.0825842	+	0.143040i	0.904359	−	0.426772i	$-0.140349\pi$
$131$	0.945219	+	1.63717i	0.0825842	+	0.143040i	−0.821775	+	0.569812i	$0.807016\pi$
$132$		0			0
$133$	−10.3951	+	1.52279i	−0.901367	+	0.132042i
$134$	−1.85393	−	5.75381i	−0.160155	−	0.497053i
$135$		0			0
$136$	−7.44032	+	3.24725i	−0.638002	+	0.278449i
$137$	−16.9097	−	9.76280i	−1.44469	−	0.834092i	−0.446533	−	0.894767i	$-0.647341\pi$
$137$	−16.9097	−	9.76280i	−1.44469	−	0.834092i	−0.998158	+	0.0606749i	$0.980675\pi$
$138$		0			0
$139$		−	16.3163i		−	1.38393i	−0.721931	−	0.691965i	$-0.756745\pi$
$139$		−	16.3163i		−	1.38393i	0.721931	−	0.691965i	$-0.243255\pi$
$140$	−0.711872	−	2.84397i	−0.0601642	−	0.240359i
$141$		0			0
$142$	−7.34995	−	6.65064i	−0.616794	−	0.558110i
$143$	−9.50694	+	16.4665i	−0.795010	+	1.37700i
$144$		0			0
$145$	1.14563	+	1.98429i	0.0951395	+	0.164787i
$146$	−16.9334	+	5.45610i	−1.40142	+	0.451550i
$147$		0			0
$148$	−3.90530	+	2.80819i	−0.321014	+	0.230832i
$149$	−11.3984	+	6.58089i	−0.933797	+	0.539128i	−0.888010	−	0.459823i	$-0.847913\pi$
$149$	−11.3984	+	6.58089i	−0.933797	+	0.539128i	−0.0457864	+	0.998951i	$0.514579\pi$
$150$		0			0
$151$	11.8095	+	6.81819i	0.961040	+	0.554856i	0.896493	−	0.443058i	$-0.146106\pi$
$151$	11.8095	+	6.81819i	0.961040	+	0.554856i	0.0645468	+	0.997915i	$0.479440\pi$
$152$	−1.25618	+	11.1609i	−0.101889	+	0.905272i
$153$		0			0
$154$	22.1677	+	1.47491i	1.78633	+	0.118851i
$155$	3.81322			0.306285
$156$		0			0
$157$	−5.63724	+	9.76398i	−0.449900	+	0.779250i	−0.998379	−	0.0569142i	$-0.981874\pi$
$157$	−5.63724	+	9.76398i	−0.449900	+	0.779250i	0.548479	+	0.836165i	$0.315207\pi$
$158$	8.31524	+	1.78879i	0.661525	+	0.142308i
$159$		0			0
$160$	−3.13389	−	0.0384429i	−0.247756	−	0.00303918i
$161$	0.111583	+	0.761704i	0.00879397	+	0.0600307i
$162$		0			0
$163$	−12.4495	+	7.18771i	−0.975118	+	0.562985i	−0.900793	−	0.434249i	$-0.857014\pi$
$163$	−12.4495	+	7.18771i	−0.975118	+	0.562985i	−0.0743256	+	0.997234i	$0.523680\pi$
$164$	−4.53362	+	0.454024i	−0.354016	+	0.0354533i
$165$		0			0
$166$	0.708276	+	0.640888i	0.0549729	+	0.0497425i
$167$	−7.45155			−0.576618			−0.288309	−	0.957537i	$-0.593093\pi$
$167$	−7.45155			−0.576618			−0.288309	+	0.957537i	$0.593093\pi$
$168$		0			0
$169$	−2.74563			−0.211203
$170$	−1.66754	−	1.50888i	−0.127894	−	0.115726i
$171$		0			0
$172$	−16.5486	+	1.65728i	−1.26182	+	0.126366i
$173$	12.9948	−	7.50257i	0.987978	−	0.570410i	0.0833090	−	0.996524i	$-0.473451\pi$
$173$	12.9948	−	7.50257i	0.987978	−	0.570410i	0.904669	+	0.426114i	$0.140118\pi$
$174$		0			0
$175$	−9.73969	+	7.70135i	−0.736251	+	0.582167i
$176$	7.56067	−	22.5151i	0.569907	−	1.69714i
$177$		0			0
$178$	−17.8078	−	3.83085i	−1.33475	−	0.287135i
$179$	3.35522	−	5.81141i	0.250781	−	0.434365i	−0.712960	−	0.701205i	$-0.752646\pi$
$179$	3.35522	−	5.81141i	0.250781	−	0.434365i	0.963741	+	0.266839i	$0.0859793\pi$
$180$		0			0
$181$	5.69773			0.423509			0.211755	−	0.977323i	$-0.432082\pi$
$181$	5.69773			0.423509			0.211755	+	0.977323i	$0.432082\pi$
$182$	−5.28877	−	10.7513i	−0.392030	−	0.796938i
$183$		0			0
$184$	0.817823	+	0.0920469i	0.0602907	+	0.00678579i
$185$	−1.15398	−	0.666251i	−0.0848424	−	0.0489838i
$186$		0			0
$187$	14.7589	−	8.52107i	1.07928	−	0.623122i
$188$	−20.1116	+	14.4617i	−1.46679	+	1.05473i
$189$		0			0
$190$	−2.96140	+	0.954191i	−0.214842	+	0.0692243i
$191$	−2.01847	−	3.49609i	−0.146051	−	0.252968i	0.783713	−	0.621123i	$-0.213323\pi$
$191$	−2.01847	−	3.49609i	−0.146051	−	0.252968i	−0.929765	+	0.368154i	$0.879990\pi$
$192$		0			0
$193$	9.24035	−	16.0047i	0.665135	−	1.15205i	−0.314114	−	0.949385i	$-0.601707\pi$
$193$	9.24035	−	16.0047i	0.665135	−	1.15205i	0.979249	−	0.202662i	$-0.0649592\pi$
$194$	3.15435	+	2.85423i	0.226469	+	0.204922i
$195$		0			0
$196$	−8.54455	+	11.0901i	−0.610325	+	0.792151i
$197$		−	8.91601i		−	0.635239i	−0.948218	−	0.317620i	$-0.897117\pi$
$197$		−	8.91601i		−	0.635239i	0.948218	−	0.317620i	$-0.102883\pi$
$198$		0			0
$199$	6.08418	+	3.51270i	0.431296	+	0.249009i	0.699898	−	0.714242i	$-0.253229\pi$
$199$	6.08418	+	3.51270i	0.431296	+	0.249009i	−0.268603	+	0.963251i	$0.586562\pi$
$200$	5.30960	+	12.1657i	0.375445	+	0.860247i
$201$		0			0
$202$	−7.67623	−	23.8237i	−0.540098	−	1.67623i
$203$	4.03959	−	10.1686i	0.283524	−	0.713698i
$204$		0			0
$205$	−0.631093	−	1.09309i	−0.0440775	−	0.0763444i
$206$	−6.41205	−	1.37937i	−0.446748	−	0.0961054i
$207$		0			0
$208$	−12.5546	+	2.54006i	−0.870505	+	0.176122i
$209$		−	23.5779i		−	1.63092i
$210$		0			0
$211$		−	10.6524i		−	0.733339i	−0.930351	−	0.366669i	$-0.880498\pi$
$211$		−	10.6524i		−	0.733339i	0.930351	−	0.366669i	$-0.119502\pi$
$212$	4.00223	−	8.87176i	0.274875	−	0.609315i
$213$		0			0
$214$	2.01941	−	9.38727i	0.138044	−	0.641701i
$215$	−2.30361	−	3.98998i	−0.157105	−	0.272114i
$216$		0			0
$217$	−11.2944	−	14.2837i	−0.766714	−	0.969642i
$218$	17.4678	−	5.62830i	1.18307	−	0.381197i
$219$		0			0
$220$	6.54668	−	0.655624i	0.441377	−	0.0442022i
$221$	−7.95963	−	4.59549i	−0.535422	−	0.309126i
$222$		0			0
$223$			0.485215i			0.0324924i	0.999868	+	0.0162462i	$0.00517155\pi$
$223$			0.485215i			0.0324924i	−0.999868	+	0.0162462i	$0.994828\pi$
$224$	9.13828	+	11.8529i	0.610577	+	0.791957i
$225$		0			0
$226$	11.4559	−	12.6604i	0.762033	−	0.842159i
$227$	8.05240	−	13.9472i	0.534456	−	0.925705i	−0.464733	−	0.885451i	$-0.653850\pi$
$227$	8.05240	−	13.9472i	0.534456	−	0.925705i	0.999189	−	0.0402546i	$-0.0128169\pi$
$228$		0			0
$229$	6.98446	+	12.0974i	0.461546	+	0.799421i	0.999038	−	0.0438475i	$-0.0139616\pi$
$229$	6.98446	+	12.0974i	0.461546	+	0.799421i	−0.537492	+	0.843269i	$0.680628\pi$
$230$	0.0699188	+	0.216998i	0.00461031	+	0.0143084i
$231$		0			0
$232$	−9.41230	−	6.94485i	−0.617948	−	0.455951i
$233$	18.4130	−	10.6308i	1.20628	−	0.696445i	0.244333	−	0.969691i	$-0.421431\pi$
$233$	18.4130	−	10.6308i	1.20628	−	0.696445i	0.961944	+	0.273247i	$0.0880975\pi$
$234$		0			0
$235$	−5.94281	−	3.43108i	−0.387666	−	0.223819i
$236$	−22.7763	−	10.2749i	−1.48261	−	0.668836i
$237$		0			0
$238$	−0.712945	+	10.7155i	−0.0462134	+	0.694583i
$239$	−13.8556			−0.896247			−0.448123	−	0.893972i	$-0.647907\pi$
$239$	−13.8556			−0.896247			−0.448123	+	0.893972i	$0.647907\pi$
$240$		0			0
$241$	4.31224	−	7.46902i	0.277776	−	0.481122i	−0.693056	−	0.720884i	$-0.743736\pi$
$241$	4.31224	−	7.46902i	0.277776	−	0.481122i	0.970832	+	0.239762i	$0.0770694\pi$
$242$	−7.21431	+	33.5359i	−0.463753	+	2.15577i
$243$		0			0
$244$	0.992993	−	0.714034i	0.0635698	−	0.0457113i
$245$	−3.77377	−	0.894299i	−0.241097	−	0.0571347i
$246$		0			0
$247$	−11.0122	+	6.35790i	−0.700690	+	0.404543i
$248$	−17.8416	+	7.78678i	−1.13294	+	0.494461i
$249$		0			0
$250$	−5.09575	+	5.63156i	−0.322283	+	0.356171i
$251$	10.0174			0.632293			0.316147	−	0.948710i	$-0.397611\pi$
$251$	10.0174			0.632293			0.316147	+	0.948710i	$0.397611\pi$
$252$		0			0
$253$	−1.72768			−0.108619
$254$	−18.0922	+	19.9946i	−1.13521	+	1.25457i
$255$		0			0
$256$	14.7416	−	6.21968i	0.921352	−	0.388730i
$257$	−8.40598	+	4.85319i	−0.524351	+	0.302734i	−0.738713	−	0.674020i	$-0.764566\pi$
$257$	−8.40598	+	4.85319i	−0.524351	+	0.302734i	0.214362	+	0.976754i	$0.431233\pi$
$258$		0			0
$259$	0.922309	+	6.29600i	0.0573095	+	0.391215i
$260$	−2.07156	−	2.88087i	−0.128472	−	0.178664i
$261$		0			0
$262$	0.562262	−	2.61369i	0.0347367	−	0.161474i
$263$	5.83530	−	10.1070i	0.359820	−	0.623226i	−0.628111	−	0.778124i	$-0.716171\pi$
$263$	5.83530	−	10.1070i	0.359820	−	0.623226i	0.987931	+	0.154898i	$0.0495048\pi$
$264$		0			0
$265$	2.69616			0.165624
$266$	12.3456	+	8.26671i	0.756959	+	0.506864i
$267$		0			0
$268$	−3.51550	+	7.79281i	−0.214743	+	0.476022i
$269$	12.2044	+	7.04622i	0.744116	+	0.429616i	0.823564	−	0.567223i	$-0.191982\pi$
$269$	12.2044	+	7.04622i	0.744116	+	0.429616i	−0.0794480	+	0.996839i	$0.525316\pi$
$270$		0			0
$271$	4.52302	−	2.61137i	0.274754	−	0.158629i	−0.356292	−	0.934375i	$-0.615959\pi$
$271$	4.52302	−	2.61137i	0.274754	−	0.158629i	0.631046	+	0.775745i	$0.282626\pi$
$272$	10.8834	+	3.65470i	0.659905	+	0.221599i
$273$		0			0
$274$	8.46855	+	26.2827i	0.511604	+	1.58780i
$275$	−13.9329	−	24.1324i	−0.840183	−	1.45524i
$276$		0			0
$277$	−5.09716	+	8.82854i	−0.306259	+	0.530456i	−0.977541	−	0.210746i	$-0.932411\pi$
$277$	−5.09716	+	8.82854i	−0.306259	+	0.530456i	0.671282	+	0.741202i	$0.265744\pi$
$278$	−15.4820	+	17.1099i	−0.928550	+	1.02619i
$279$		0			0
$280$	−1.95205	+	3.65777i	−0.116658	+	0.218594i
$281$			28.3097i			1.68881i	0.535702	+	0.844407i	$0.320047\pi$
$281$			28.3097i			1.68881i	−0.535702	+	0.844407i	$0.679953\pi$
$282$		0			0
$283$	7.18829	+	4.15016i	0.427300	+	0.246702i	0.698196	−	0.715907i	$-0.253987\pi$
$283$	7.18829	+	4.15016i	0.427300	+	0.246702i	−0.270896	+	0.962609i	$0.587320\pi$
$284$	1.39686	+	13.9483i	0.0828887	+	0.827678i
$285$		0			0
$286$	25.5939	−	8.24661i	1.51340	−	0.487632i
$287$	−2.22529	+	5.60159i	−0.131355	+	0.330651i
$288$		0			0
$289$	−4.38106	−	7.58822i	−0.257710	−	0.446366i
$290$	0.681477	−	3.16786i	0.0400177	−	0.186023i
$291$		0			0
$292$	22.9342	+	10.3461i	1.34212	+	0.605459i
$293$			18.3982i			1.07483i	0.843317	+	0.537416i	$0.180599\pi$
$293$			18.3982i			1.07483i	−0.843317	+	0.537416i	$0.819401\pi$
$294$		0			0
$295$		−	6.92181i		−	0.403003i
$296$	6.75986	+	0.760830i	0.392909	+	0.0442224i
$297$		0			0
$298$	18.1973	+	3.91463i	1.05414	+	0.226769i
$299$	0.465878	+	0.806925i	0.0269424	+	0.0466657i
$300$		0			0
$301$	−8.12274	+	20.4469i	−0.468187	+	1.17854i
$302$	−5.91430	−	18.3555i	−0.340330	−	1.05624i
$303$		0			0
$304$	11.9075	−	10.5119i	0.682945	−	0.602897i
$305$	0.293421	+	0.169406i	0.0168012	+	0.00970018i
$306$		0			0
$307$		−	5.96914i		−	0.340677i	−0.985386	−	0.170338i	$-0.945514\pi$
$307$		−	5.96914i		−	0.340677i	0.985386	−	0.170338i	$-0.0544861\pi$
$308$	−21.8465	−	22.5809i	−1.24482	−	1.28667i
$309$		0			0
$310$	−3.99870	−	3.61825i	−0.227111	−	0.205503i
$311$	14.9380	−	25.8734i	0.847058	−	1.46715i	−0.0367643	−	0.999324i	$-0.511705\pi$
$311$	14.9380	−	25.8734i	0.847058	−	1.46715i	0.883822	−	0.467823i	$-0.154962\pi$
$312$		0			0
$313$	−0.862490	−	1.49388i	−0.0487508	−	0.0844389i	0.840620	−	0.541625i	$-0.182191\pi$
$313$	−0.862490	−	1.49388i	−0.0487508	−	0.0844389i	−0.889371	+	0.457186i	$0.848857\pi$
$314$	15.1762	−	4.88991i	0.856441	−	0.275954i
$315$		0			0
$316$	−7.02237	−	9.76587i	−0.395039	−	0.549373i
$317$	−1.24055	+	0.716235i	−0.0696765	+	0.0402277i	−0.534434	−	0.845211i	$-0.679475\pi$
$317$	−1.24055	+	0.716235i	−0.0696765	+	0.0402277i	0.464757	+	0.885438i	$0.346142\pi$
$318$		0			0
$319$	21.2657	+	12.2778i	1.19065	+	0.687423i
$320$	3.24985	+	3.01397i	0.181672	+	0.168486i
$321$		0			0
$322$	0.605747	−	0.904632i	0.0337570	−	0.0504132i
$323$	11.3972			0.634155
$324$		0			0
$325$	−7.51413	+	13.0149i	−0.416809	+	0.721934i
$326$	19.8752	+	4.27560i	1.10079	+	0.236803i
$327$		0			0
$328$	5.18495	+	3.82570i	0.286291	+	0.211239i
$329$	4.74974	+	32.4234i	0.261862	+	1.78756i
$330$		0			0
$331$	−17.0867	+	9.86503i	−0.939172	+	0.542231i	−0.889701	−	0.456545i	$-0.849087\pi$
$331$	−17.0867	+	9.86503i	−0.939172	+	0.542231i	−0.0494711	+	0.998776i	$0.515754\pi$
$332$	−0.134609	−	1.34412i	−0.00738760	−	0.0737683i
$333$		0			0
$334$	7.81400	+	7.07054i	0.427563	+	0.386883i
$335$	−2.36827			−0.129392
$336$		0			0
$337$	3.45266			0.188079			0.0940393	−	0.995568i	$-0.470022\pi$
$337$	3.45266			0.188079			0.0940393	+	0.995568i	$0.470022\pi$
$338$	2.87918	+	2.60525i	0.156607	+	0.141707i
$339$		0			0
$340$	0.316917	+	3.16455i	0.0171873	+	0.171622i
$341$	35.3914	−	20.4332i	1.91655	−	1.10652i
$342$		0			0
$343$	7.82763	+	16.7848i	0.422652	+	0.906292i
$344$	18.9261	+	13.9646i	1.02043	+	0.752919i
$345$		0			0
$346$	−20.7459	−	4.46289i	−1.11530	−	0.239926i
$347$	7.69485	−	13.3279i	0.413081	−	0.715478i	−0.582144	−	0.813086i	$-0.697786\pi$
$347$	7.69485	−	13.3279i	0.413081	−	0.715478i	0.995225	+	0.0976081i	$0.0311192\pi$
$348$		0			0
$349$	35.4402			1.89707			0.948534	−	0.316676i	$-0.102567\pi$
$349$	35.4402			1.89707			0.948534	+	0.316676i	$0.102567\pi$
$350$	17.5210	+	1.16574i	0.936537	+	0.0623115i
$351$		0			0
$352$	−29.2923	+	16.4362i	−1.56129	+	0.876053i
$353$	9.96600	+	5.75387i	0.530436	+	0.306248i	0.741194	−	0.671291i	$-0.234260\pi$
$353$	9.96600	+	5.75387i	0.530436	+	0.306248i	−0.210758	+	0.977538i	$0.567593\pi$
$354$		0			0
$355$	−3.36302	+	1.94164i	−0.178491	+	0.103052i
$356$	15.0390	+	20.9145i	0.797067	+	1.10846i
$357$		0			0
$358$	−9.03269	+	2.91042i	−0.477392	+	0.153820i
$359$	−7.16808	−	12.4155i	−0.378317	−	0.655264i	0.612501	−	0.790470i	$-0.290164\pi$
$359$	−7.16808	−	12.4155i	−0.378317	−	0.655264i	−0.990817	+	0.135206i	$0.956830\pi$
$360$		0			0
$361$	−1.61596	+	2.79893i	−0.0850508	+	0.147312i
$362$	−5.97488	−	5.40640i	−0.314033	−	0.284154i
$363$		0			0
$364$	−4.65554	+	16.2926i	−0.244016	+	0.853963i
$365$			6.96979i			0.364815i
$366$		0			0
$367$	−26.6088	−	15.3626i	−1.38897	−	0.801921i	−0.395770	−	0.918350i	$-0.629522\pi$
$367$	−26.6088	−	15.3626i	−1.38897	−	0.801921i	−0.993199	+	0.116428i	$0.962855\pi$
$368$	−0.770262	−	0.872531i	−0.0401527	−	0.0454838i
$369$		0			0
$370$	0.577927	+	1.79364i	0.0300450	+	0.0932467i
$371$	−7.98577	−	10.0994i	−0.414601	−	0.524335i
$372$		0			0
$373$	7.94955	+	13.7690i	0.411612	+	0.712933i	0.995066	−	0.0992132i	$-0.0316326\pi$
$373$	7.94955	+	13.7690i	0.411612	+	0.712933i	−0.583454	+	0.812146i	$0.698299\pi$
$374$	−23.5622	−	5.06874i	−1.21837	−	0.262098i
$375$		0			0
$376$	34.8122	+	3.91815i	1.79530	+	0.202063i
$377$		−	13.2430i		−	0.682051i
$378$		0			0
$379$			23.8379i			1.22447i	0.790675	+	0.612236i	$0.209730\pi$
$379$			23.8379i			1.22447i	−0.790675	+	0.612236i	$0.790270\pi$
$380$	4.01085	+	1.80938i	0.205752	+	0.0928190i
$381$		0			0
$382$	−1.20068	+	5.58141i	−0.0614323	+	0.285570i
$383$	3.63573	+	6.29726i	0.185777	+	0.321775i	0.943838	−	0.330408i	$-0.107186\pi$
$383$	3.63573	+	6.29726i	0.185777	+	0.321775i	−0.758061	+	0.652184i	$0.773853\pi$
$384$		0			0
$385$	3.21338	−	8.08886i	0.163769	−	0.412246i
$386$	−24.8762	+	8.01536i	−1.26617	+	0.407971i
$387$		0			0
$388$	−0.599487	−	5.98613i	−0.0304343	−	0.303900i
$389$	−13.6345	−	7.87187i	−0.691295	−	0.399120i	0.112802	−	0.993618i	$-0.464017\pi$
$389$	−13.6345	−	7.87187i	−0.691295	−	0.399120i	−0.804097	+	0.594498i	$0.797351\pi$
$390$		0			0
$391$		−	0.835133i		−	0.0422345i
$392$	19.4832	−	3.52189i	0.984052	−	0.177882i
$393$		0			0
$394$	−8.46012	+	9.34969i	−0.426215	+	0.471031i
$395$	1.66608	−	2.88573i	0.0838293	−	0.145197i
$396$		0			0
$397$	4.93160	+	8.54177i	0.247510	+	0.428699i	0.962834	−	0.270093i	$-0.0870545\pi$
$397$	4.93160	+	8.54177i	0.247510	+	0.428699i	−0.715325	+	0.698792i	$0.753721\pi$
$398$	−3.04702	−	9.45665i	−0.152733	−	0.474019i
$399$		0			0
$400$	5.97583	−	17.7956i	0.298791	−	0.889780i
$401$	22.7516	−	13.1357i	1.13616	−	0.655964i	0.190685	−	0.981651i	$-0.438929\pi$
$401$	22.7516	−	13.1357i	1.13616	−	0.655964i	0.945477	+	0.325688i	$0.105596\pi$
$402$		0			0
$403$	−19.0869	−	11.0198i	−0.950786	−	0.548937i
$404$	−14.5560	+	32.2663i	−0.724187	+	1.60531i
$405$		0			0
$406$	−13.8848	+	6.83020i	−0.689090	+	0.338977i
$407$	−14.2805			−0.707857
$408$		0			0
$409$	12.3008	−	21.3056i	0.608234	−	1.05349i	−0.383298	−	0.923625i	$-0.625212\pi$
$409$	12.3008	−	21.3056i	0.608234	−	1.05349i	0.991531	−	0.129867i	$-0.0414551\pi$
$410$	−0.375405	+	1.74508i	−0.0185399	+	0.0861833i
$411$		0			0
$412$	5.41509	+	7.53066i	0.266782	+	0.371009i
$413$	−25.9280	+	20.5017i	−1.27583	+	1.00882i
$414$		0			0
$415$	0.324077	−	0.187106i	0.0159083	−	0.00918466i
$416$	15.5755	+	9.24906i	0.763649	+	0.453472i
$417$		0			0
$418$	−22.3724	+	24.7248i	−1.09427	+	1.20933i
$419$	22.1374			1.08148			0.540742	−	0.841189i	$-0.318144\pi$
$419$	22.1374			1.08148			0.540742	+	0.841189i	$0.318144\pi$
$420$		0			0
$421$	6.42567			0.313168			0.156584	−	0.987665i	$-0.449952\pi$
$421$	6.42567			0.313168			0.156584	+	0.987665i	$0.449952\pi$
$422$	−10.1077	+	11.1705i	−0.492035	+	0.543772i
$423$		0			0
$424$	−12.6150	+	5.50569i	−0.612641	+	0.267380i
$425$	11.6652	−	6.73491i	0.565846	−	0.326691i
$426$		0			0
$427$	−0.234514	−	1.60087i	−0.0113489	−	0.0774716i
$428$	−11.0249	+	7.92772i	−0.532910	+	0.383201i
$429$		0			0
$430$	−1.37030	+	6.36988i	−0.0660818	+	0.307183i
$431$	14.9953	−	25.9727i	0.722299	−	1.25106i	−0.237777	−	0.971320i	$-0.576419\pi$
$431$	14.9953	−	25.9727i	0.722299	−	1.25106i	0.960076	−	0.279739i	$-0.0902479\pi$
$432$		0			0
$433$	33.6049			1.61495			0.807475	−	0.589902i	$-0.200833\pi$
$433$	33.6049			1.61495			0.807475	+	0.589902i	$0.200833\pi$
$434$	−1.70962	+	25.6954i	−0.0820643	+	1.23342i
$435$		0			0
$436$	−23.6580	−	10.6726i	−1.13301	−	0.511125i
$437$	−1.00062	−	0.577706i	−0.0478660	−	0.0276354i
$438$		0			0
$439$	−9.83511	+	5.67831i	−0.469404	+	0.271011i	−0.715990	−	0.698110i	$-0.754025\pi$
$439$	−9.83511	+	5.67831i	−0.469404	+	0.271011i	0.246586	+	0.969121i	$0.420691\pi$
$440$	−7.48721	−	5.52442i	−0.356939	−	0.263367i
$441$		0			0
$442$	3.98627	+	12.3717i	0.189607	+	0.588460i
$443$	14.1468	+	24.5029i	0.672132	+	1.16417i	0.977298	+	0.211868i	$0.0679548\pi$
$443$	14.1468	+	24.5029i	0.672132	+	1.16417i	−0.305166	+	0.952299i	$0.598712\pi$
$444$		0			0
$445$	−3.56805	+	6.18004i	−0.169142	+	0.292962i
$446$	0.460406	−	0.508816i	0.0218008	−	0.0240932i
$447$		0			0
$448$	1.66409	−	21.1005i	0.0786210	−	0.996905i
$449$			29.4996i			1.39217i	0.717959	+	0.696086i	$0.245077\pi$
$449$			29.4996i			1.39217i	−0.717959	+	0.696086i	$0.754923\pi$
$450$		0			0
$451$	−11.7146	−	6.76345i	−0.551621	−	0.318478i
$452$	−24.0262	+	2.40613i	−1.13010	+	0.113175i
$453$		0			0
$454$	−21.6781	+	6.98489i	−1.01740	+	0.327817i
$455$	−4.64445	+	0.680372i	−0.217735	+	0.0318963i
$456$		0			0
$457$	1.43214	+	2.48054i	0.0669926	+	0.116035i	0.897576	−	0.440859i	$-0.145326\pi$
$457$	1.43214	+	2.48054i	0.0669926	+	0.116035i	−0.830584	+	0.556894i	$0.811993\pi$
$458$	4.15470	−	19.3132i	0.194136	−	0.902447i
$459$		0			0
$460$	0.132583	−	0.293897i	0.00618171	−	0.0137030i
$461$		−	21.1377i		−	0.984482i	−0.870459	−	0.492241i	$-0.836178\pi$
$461$		−	21.1377i		−	0.984482i	0.870459	−	0.492241i	$-0.163822\pi$
$462$		0			0
$463$			39.2453i			1.82389i	0.410317	+	0.911943i	$0.365418\pi$
$463$			39.2453i			1.82389i	−0.410317	+	0.911943i	$0.634582\pi$
$464$	3.28037	+	16.2137i	0.152288	+	0.752702i
$465$		0			0
$466$	−29.3959	−	6.32369i	−1.36174	−	0.292940i
$467$	−14.6992	−	25.4597i	−0.680196	−	1.17813i	−0.974921	−	0.222552i	$-0.928561\pi$
$467$	−14.6992	−	25.4597i	−0.680196	−	1.17813i	0.294725	−	0.955582i	$-0.404772\pi$
$468$		0			0
$469$	7.01458	+	8.87115i	0.323903	+	0.409632i
$470$	2.97623	+	9.23693i	0.137283	+	0.426068i
$471$		0			0
$472$	14.1347	+	32.3863i	0.650600	+	1.49070i
$473$	−42.7607	−	24.6879i	−1.96614	−	1.13515i
$474$		0			0
$475$		−	18.6356i		−	0.855060i
$476$	10.9152	−	10.5602i	0.500299	−	0.484027i
$477$		0			0
$478$	14.5296	+	13.1472i	0.664568	+	0.601338i
$479$	9.81732	−	17.0041i	0.448565	−	0.776937i	−0.549728	−	0.835344i	$-0.685269\pi$
$479$	9.81732	−	17.0041i	0.448565	−	0.776937i	0.998293	+	0.0584067i	$0.0186020\pi$
$480$		0			0
$481$	3.85080	+	6.66978i	0.175581	+	0.304116i
$482$	−11.6091	+	3.74057i	−0.528781	+	0.170378i
$483$		0			0
$484$	39.3864	−	28.3217i	1.79029	−	1.28735i
$485$	1.44330	−	0.833287i	0.0655367	−	0.0378376i
$486$		0			0
$487$	−0.798307	−	0.460903i	−0.0361748	−	0.0208855i	0.481804	−	0.876279i	$-0.339982\pi$
$487$	−0.798307	−	0.460903i	−0.0361748	−	0.0208855i	−0.517978	+	0.855394i	$0.673315\pi$
$488$	−1.71882	−	0.193455i	−0.0778072	−	0.00875729i
$489$		0			0
$490$	3.10875	+	4.51861i	0.140439	+	0.204130i
$491$	−31.2381			−1.40976			−0.704878	−	0.709329i	$-0.748998\pi$
$491$	−31.2381			−1.40976			−0.704878	+	0.709329i	$0.748998\pi$
$492$		0			0
$493$	−5.93487	+	10.2795i	−0.267293	+	0.462965i
$494$	17.5807	+	3.78199i	0.790991	+	0.170160i
$495$		0			0
$496$	26.0981	+	8.76384i	1.17184	+	0.393508i
$497$	17.2340	+	6.84639i	0.773052	+	0.307103i
$498$		0			0
$499$	12.1999	−	7.04359i	0.546141	−	0.315314i	−0.201423	−	0.979504i	$-0.564557\pi$
$499$	12.1999	−	7.04359i	0.546141	−	0.315314i	0.747564	+	0.664190i	$0.231223\pi$
$500$	10.6872	−	1.07028i	0.477947	−	0.0478645i
$501$		0			0
$502$	−10.5047	−	9.50521i	−0.468846	−	0.424238i
$503$	21.4391			0.955922			0.477961	−	0.878381i	$-0.341376\pi$
$503$	21.4391			0.955922			0.477961	+	0.878381i	$0.341376\pi$
$504$		0			0
$505$	−9.80585			−0.436355
$506$	1.81172	+	1.63935i	0.0805408	+	0.0728778i
$507$		0			0
$508$	37.9445	−	3.79999i	1.68352	−	0.168597i
$509$	32.8654	−	18.9749i	1.45673	−	0.841046i	0.457885	−	0.889011i	$-0.348607\pi$
$509$	32.8654	−	18.9749i	1.45673	−	0.841046i	0.998849	+	0.0479657i	$0.0152738\pi$
$510$		0			0
$511$	26.1077	−	20.6438i	1.15494	−	0.913230i
$512$	−21.3603	−	7.46566i	−0.944002	−	0.329938i
$513$		0			0
$514$	13.4199	+	2.88691i	0.591926	+	0.127336i
$515$	−1.28474	+	2.22524i	−0.0566126	+	0.0980559i
$516$		0			0
$517$	−73.5421			−3.23438
$518$	5.00691	−	7.47740i	0.219991	−	0.328538i
$519$		0			0
$520$	−0.561251	+	4.98663i	−0.0246125	+	0.218678i
$521$	−24.5753	−	14.1886i	−1.07666	−	0.621613i	−0.146670	−	0.989185i	$-0.546856\pi$
$521$	−24.5753	−	14.1886i	−1.07666	−	0.621613i	−0.929995	+	0.367573i	$0.880189\pi$
$522$		0			0
$523$	13.2425	−	7.64559i	0.579056	−	0.334318i	−0.181702	−	0.983354i	$-0.558161\pi$
$523$	13.2425	−	7.64559i	0.579056	−	0.334318i	0.760758	+	0.649035i	$0.224827\pi$
$524$	−3.06966	+	2.20731i	−0.134099	+	0.0964267i
$525$		0			0
$526$	−15.7094	+	5.06171i	−0.684961	+	0.220701i
$527$	9.87707	+	17.1076i	0.430252	+	0.745218i
$528$		0			0
$529$	11.4577	−	19.8453i	0.498159	−	0.862838i
$530$	−2.82731	−	2.55831i	−0.122810	−	0.111126i
$531$		0			0
$532$	−5.10211	−	20.3832i	−0.221204	−	0.883723i
$533$			7.29518i			0.315990i
$534$		0			0
$535$	−3.25777	−	1.88087i	−0.140846	−	0.0813172i
$536$	11.0809	−	4.83611i	0.478620	−	0.208888i
$537$		0			0
$538$	−6.11210	−	18.9693i	−0.263511	−	0.817826i
$539$	−39.8173	+	11.9216i	−1.71505	+	0.513500i
$540$		0			0
$541$	4.90969	+	8.50383i	0.211084	+	0.365608i	0.952054	−	0.305930i	$-0.0989673\pi$
$541$	4.90969	+	8.50383i	0.211084	+	0.365608i	−0.740970	+	0.671538i	$0.765634\pi$
$542$	−7.22087	−	1.55337i	−0.310163	−	0.0667228i
$543$		0			0
$544$	−7.94499	−	14.1594i	−0.340638	−	0.607080i
$545$		−	7.18976i		−	0.307975i
$546$		0			0
$547$		−	2.27148i		−	0.0971213i	−0.998820	−	0.0485606i	$-0.984537\pi$
$547$		−	2.27148i		−	0.0971213i	0.998820	−	0.0485606i	$-0.0154634\pi$
$548$	16.0584	−	35.5967i	0.685981	−	1.52062i
$549$		0			0
$550$	−8.28794	+	38.5267i	−0.353399	+	1.64278i
$551$	8.21094	+	14.2218i	0.349798	+	0.605867i
$552$		0			0
$553$	−15.7442	+	2.30639i	−0.669513	+	0.0980778i
$554$	13.7222	−	4.42143i	0.583001	−	0.187849i
$555$		0			0
$556$	32.4702	−	3.25176i	1.37704	−	0.137905i
$557$	−24.7675	−	14.2995i	−1.04943	−	0.605890i	−0.126942	−	0.991910i	$-0.540516\pi$
$557$	−24.7675	−	14.2995i	−1.04943	−	0.605890i	−0.922490	+	0.386020i	$0.873849\pi$
$558$		0			0
$559$			26.6289i			1.12628i
$560$	5.51775	−	1.98345i	0.233168	−	0.0838159i
$561$		0			0
$562$	26.8622	−	29.6867i	1.13311	−	1.25226i
$563$	−16.7025	+	28.9296i	−0.703926	+	1.21924i	0.263152	+	0.964754i	$0.415238\pi$
$563$	−16.7025	+	28.9296i	−0.703926	+	1.21924i	−0.967078	+	0.254481i	$0.918095\pi$
$564$		0			0
$565$	−3.34452	−	5.79287i	−0.140705	−	0.243708i
$566$	−3.59998	−	11.1728i	−0.151318	−	0.469627i
$567$		0			0
$568$	11.7703	−	15.9522i	0.493870	−	0.669338i
$569$	2.83434	−	1.63641i	0.118822	−	0.0686018i	−0.439411	−	0.898286i	$-0.644813\pi$
$569$	2.83434	−	1.63641i	0.118822	−	0.0686018i	0.558233	+	0.829684i	$0.311480\pi$
$570$		0			0
$571$	14.4191	+	8.32487i	0.603420	+	0.348385i	0.770386	−	0.637578i	$-0.220064\pi$
$571$	14.4191	+	8.32487i	0.603420	+	0.348385i	−0.166966	+	0.985963i	$0.553397\pi$
$572$	−34.6638	−	15.6375i	−1.44937	−	0.653839i
$573$		0			0
$574$	7.64870	−	3.76255i	0.319251	−	0.157046i
$575$	−1.36553			−0.0569466
$576$		0			0
$577$	−3.61179	+	6.25581i	−0.150361	+	0.260433i	−0.931360	−	0.364099i	$-0.881377\pi$
$577$	−3.61179	+	6.25581i	−0.150361	+	0.260433i	0.780999	+	0.624532i	$0.214710\pi$
$578$	−2.60607	+	12.1144i	−0.108398	+	0.503891i
$579$		0			0
$580$	−3.72051	+	2.67532i	−0.154486	+	0.111087i
$581$	−1.66075	−	0.659751i	−0.0688996	−	0.0273711i
$582$		0			0
$583$	25.0237	−	14.4474i	1.03638	−	0.598352i
$584$	−14.2326	−	32.6109i	−0.588951	−	1.34945i
$585$		0			0
$586$	17.4574	−	19.2931i	0.721160	−	0.796989i
$587$	−25.0736			−1.03490			−0.517448	−	0.855714i	$-0.673118\pi$
$587$	−25.0736			−1.03490			−0.517448	+	0.855714i	$0.673118\pi$
$588$		0			0
$589$	27.3300			1.12611
$590$	−6.56789	+	7.25849i	−0.270396	+	0.298827i
$591$		0			0
$592$	−6.36674	−	7.21206i	−0.261671	−	0.296414i
$593$	−10.8437	+	6.26064i	−0.445299	+	0.257094i	−0.705843	−	0.708368i	$-0.749432\pi$
$593$	−10.8437	+	6.26064i	−0.445299	+	0.257094i	0.260544	+	0.965462i	$0.416098\pi$
$594$		0			0
$595$	3.91002	+	1.55329i	0.160295	+	0.0636788i
$596$	−15.3679	−	21.3719i	−0.629495	−	0.875426i
$597$		0			0
$598$	0.277127	−	1.28823i	0.0113326	−	0.0526797i
$599$	−9.23709	+	15.9991i	−0.377417	+	0.653706i	−0.990686	−	0.136169i	$-0.956521\pi$
$599$	−9.23709	+	15.9991i	−0.377417	+	0.653706i	0.613268	+	0.789875i	$0.289854\pi$
$600$		0			0
$601$	1.51523			0.0618074			0.0309037	−	0.999522i	$-0.490161\pi$
$601$	1.51523			0.0618074			0.0309037	+	0.999522i	$0.490161\pi$
$602$	27.9193	−	13.7340i	1.13790	−	0.559758i
$603$		0			0
$604$	−11.2149	+	24.8602i	−0.456330	+	1.01155i
$605$	11.6383	+	6.71939i	0.473165	+	0.273182i
$606$		0			0
$607$	−37.1840	+	21.4682i	−1.50925	+	0.871366i	−0.509309	+	0.860584i	$0.670099\pi$
$607$	−37.1840	+	21.4682i	−1.50925	+	0.871366i	−0.999942	+	0.0107826i	$0.996568\pi$
$608$	−22.4611	−	0.275527i	−0.910919	−	0.0111741i
$609$		0			0
$610$	−0.146948	−	0.456064i	−0.00594976	−	0.0184655i
$611$	19.8310	+	34.3483i	0.802276	+	1.38958i
$612$		0			0
$613$	−6.06912	+	10.5120i	−0.245130	+	0.424577i	−0.962168	−	0.272457i	$-0.912164\pi$
$613$	−6.06912	+	10.5120i	−0.245130	+	0.424577i	0.717039	+	0.697034i	$0.245497\pi$
$614$	−5.66393	+	6.25948i	−0.228578	+	0.252612i
$615$		0			0
$616$	1.48279	+	44.4087i	0.0597433	+	1.78928i
$617$			16.9417i			0.682049i	0.940054	+	0.341024i	$0.110774\pi$
$617$			16.9417i			0.682049i	−0.940054	+	0.341024i	$0.889226\pi$
$618$		0			0
$619$	9.94601	+	5.74233i	0.399764	+	0.230804i	0.686382	−	0.727241i	$-0.259198\pi$
$619$	9.94601	+	5.74233i	0.399764	+	0.230804i	−0.286618	+	0.958045i	$0.592531\pi$
$620$	0.759957	+	7.58849i	0.0305206	+	0.304761i
$621$		0			0
$622$	−40.2151	+	12.9577i	−1.61248	+	0.519556i
$623$	33.7177	−	4.93934i	1.35087	−	0.197891i
$624$		0			0
$625$	−10.2449	−	17.7447i	−0.409796	−	0.709788i
$626$	−0.513051	+	2.38493i	−0.0205056	+	0.0953209i
$627$		0			0
$628$	−20.5542	−	9.27244i	−0.820203	−	0.370011i
$629$		−	6.90294i		−	0.275238i
$630$		0			0
$631$		−	24.5485i		−	0.977262i	−0.872491	−	0.488631i	$-0.837497\pi$
$631$		−	24.5485i		−	0.977262i	0.872491	−	0.488631i	$-0.162503\pi$
$632$	−1.90259	+	16.9042i	−0.0756808	+	0.672413i
$633$		0			0
$634$	1.98051	+	0.426051i	0.0786561	+	0.0169207i
$635$	5.28199	+	9.14868i	0.209609	+	0.363054i
$636$		0			0
$637$	16.3050	+	15.3822i	0.646027	+	0.609464i
$638$	−10.6501	−	33.0534i	−0.421642	−	1.30860i
$639$		0			0
$640$	−0.548067	−	6.24425i	−0.0216642	−	0.246826i
$641$	−5.19237	−	2.99782i	−0.205086	−	0.118407i	0.393939	−	0.919136i	$-0.371112\pi$
$641$	−5.19237	−	2.99782i	−0.205086	−	0.118407i	−0.599026	+	0.800730i	$0.704445\pi$
$642$		0			0
$643$		−	34.2008i		−	1.34875i	−0.738390	−	0.674374i	$-0.764413\pi$
$643$		−	34.2008i		−	1.34875i	0.738390	−	0.674374i	$-0.235587\pi$
$644$	−1.49359	+	0.373859i	−0.0588556	+	0.0147321i
$645$		0			0
$646$	−11.9515	−	10.8144i	−0.470227	−	0.425488i
$647$	−15.1478	+	26.2367i	−0.595520	+	1.03147i	0.397954	+	0.917406i	$0.369721\pi$
$647$	−15.1478	+	26.2367i	−0.595520	+	1.03147i	−0.993473	+	0.114065i	$0.963613\pi$
$648$		0			0
$649$	−37.0906	−	64.2428i	−1.45593	−	2.52175i
$650$	20.2290	−	6.51798i	0.793447	−	0.255656i
$651$		0			0
$652$	−16.7850	−	23.3426i	−0.657351	−	0.914165i
$653$	19.9310	−	11.5072i	0.779959	−	0.450310i	−0.0564565	−	0.998405i	$-0.517980\pi$
$653$	19.9310	−	11.5072i	0.779959	−	0.450310i	0.836416	+	0.548095i	$0.184647\pi$
$654$		0			0
$655$	−0.907057	−	0.523690i	−0.0354417	−	0.0204623i
$656$	−1.80706	−	8.93162i	−0.0705537	−	0.348721i
$657$		0			0
$658$	25.7848	−	38.5074i	1.00519	−	1.50117i
$659$	−44.6195			−1.73813			−0.869065	−	0.494698i	$-0.835279\pi$
$659$	−44.6195			−1.73813			−0.869065	+	0.494698i	$0.835279\pi$
$660$		0			0
$661$	12.1633	−	21.0674i	0.473097	−	0.819428i	−0.526429	−	0.850219i	$-0.676469\pi$
$661$	12.1633	−	21.0674i	0.473097	−	0.819428i	0.999526	+	0.0307915i	$0.00980277\pi$
$662$	27.2785	+	5.86820i	1.06021	+	0.228074i
$663$		0			0
$664$	−1.13424	+	1.53723i	−0.0440170	+	0.0596560i
$665$	4.56585	−	3.61030i	0.177056	−	0.140001i
$666$		0			0
$667$	1.04211	−	0.601660i	0.0403505	−	0.0232964i
$668$	−1.48506	−	14.8289i	−0.0574586	−	0.573748i
$669$		0			0
$670$	2.48346	+	2.24718i	0.0959445	+	0.0868160i
$671$	3.63107			0.140176
$672$		0			0
$673$	−2.06192			−0.0794813			−0.0397406	−	0.999210i	$-0.512653\pi$
$673$	−2.06192			−0.0794813			−0.0397406	+	0.999210i	$0.512653\pi$
$674$	−3.62060	−	3.27612i	−0.139460	−	0.126192i
$675$		0			0
$676$	−0.547192	−	5.46394i	−0.0210458	−	0.210151i
$677$	−38.1309	+	22.0149i	−1.46549	+	0.846101i	−0.999256	−	0.0385604i	$-0.987723\pi$
$677$	−38.1309	+	22.0149i	−1.46549	+	0.846101i	−0.466234	+	0.884662i	$0.654389\pi$
$678$		0			0
$679$	−7.39626	−	2.93824i	−0.283842	−	0.112759i
$680$	2.67041	−	3.61919i	0.102406	−	0.138790i
$681$		0			0
$682$	−56.5013	−	12.1547i	−2.16355	−	0.465426i
$683$	8.85834	−	15.3431i	0.338955	−	0.587087i	−0.645282	−	0.763945i	$-0.723260\pi$
$683$	8.85834	−	15.3431i	0.338955	−	0.587087i	0.984236	+	0.176858i	$0.0565933\pi$
$684$		0			0
$685$	10.8180			0.413334
$686$	7.71816	−	25.0286i	0.294681	−	0.955596i
$687$		0			0
$688$	−6.59611	−	32.6022i	−0.251474	−	1.24295i
$689$	−13.4955	−	7.79164i	−0.514138	−	0.296838i
$690$		0			0
$691$	−6.82540	+	3.94065i	−0.259651	+	0.149909i	−0.624175	−	0.781284i	$-0.714565\pi$
$691$	−6.82540	+	3.94065i	−0.259651	+	0.149909i	0.364525	+	0.931194i	$0.381232\pi$
$692$	17.5203	+	24.3651i	0.666020	+	0.926221i
$693$		0			0
$694$	−20.7155	+	6.67475i	−0.786351	+	0.253370i
$695$	4.51995	+	7.82878i	0.171451	+	0.296962i
$696$		0			0
$697$	3.26934	−	5.66266i	0.123835	−	0.214488i
$698$	−37.1640	−	33.6281i	−1.40668	−	1.27284i
$699$		0			0
$700$	−17.2671	−	17.8476i	−0.652635	−	0.674575i
$701$			42.2417i			1.59545i	0.603025	+	0.797723i	$0.293962\pi$
$701$			42.2417i			1.59545i	−0.603025	+	0.797723i	$0.706038\pi$
$702$		0			0
$703$	−8.27078	−	4.77514i	−0.311938	−	0.180098i
$704$	46.3130	+	10.5589i	1.74549	+	0.397954i
$705$		0			0
$706$	−4.99108	−	15.4902i	−0.187842	−	0.582980i
$707$	29.0440	+	36.7312i	1.09231	+	1.38142i
$708$		0			0
$709$	−7.75030	−	13.4239i	−0.291069	−	0.504146i	0.682994	−	0.730424i	$-0.260678\pi$
$709$	−7.75030	−	13.4239i	−0.291069	−	0.504146i	−0.974063	+	0.226278i	$0.927344\pi$
$710$	5.36896	+	1.15498i	0.201494	+	0.0433457i
$711$		0			0
$712$	4.07456	−	36.2018i	0.152701	−	1.35672i
$713$		−	2.00262i		−	0.0749987i
$714$		0			0
$715$		−	10.5345i		−	0.393966i
$716$	12.2337	+	5.51885i	0.457193	+	0.206249i
$717$		0			0
$718$	−4.26392	+	19.8209i	−0.159128	+	0.739711i
$719$	−19.9952	−	34.6327i	−0.745695	−	1.29158i	−0.949869	−	0.312647i	$-0.898784\pi$
$719$	−19.9952	−	34.6327i	−0.745695	−	1.29158i	0.204174	−	0.978935i	$-0.434549\pi$
$720$		0			0
$721$	12.1407	−	1.77851i	0.452143	−	0.0662350i
$722$	4.35039	−	1.40174i	0.161905	−	0.0521672i
$723$		0			0
$724$	1.13553	+	11.3388i	0.0422017	+	0.421401i
$725$	16.8081	+	9.70415i	0.624237	+	0.360403i
$726$		0			0
$727$			4.48716i			0.166420i	0.996532	+	0.0832098i	$0.0265172\pi$
$727$			4.48716i			0.166420i	−0.996532	+	0.0832098i	$0.973483\pi$
$728$	20.3415	−	12.6676i	0.753907	−	0.469491i
$729$		0			0
$730$	6.61342	−	7.30881i	0.244774	−	0.270511i
$731$	11.9337	−	20.6698i	0.441385	−	0.764500i
$732$		0			0
$733$	15.0072	+	25.9933i	0.554305	+	0.960084i	0.997957	+	0.0638849i	$0.0203490\pi$
$733$	15.0072	+	25.9933i	0.554305	+	0.960084i	−0.443653	+	0.896199i	$0.646318\pi$
$734$	13.3260	+	41.3581i	0.491871	+	1.52656i
$735$		0			0
$736$	−0.0201893	+	1.64585i	−0.000744189	+	0.0606668i
$737$	−21.9804	+	12.6904i	−0.809659	+	0.467457i
$738$		0			0
$739$	−7.53183	−	4.34850i	−0.277063	−	0.159962i	0.355030	−	0.934855i	$-0.384471\pi$
$739$	−7.53183	−	4.34850i	−0.277063	−	0.159962i	−0.632093	+	0.774893i	$0.717804\pi$
$740$	1.09589	−	2.42926i	0.0402856	−	0.0893012i
$741$		0			0
$742$	−1.20880	+	18.1681i	−0.0443763	+	0.666972i
$743$	9.85512			0.361549			0.180775	−	0.983525i	$-0.442140\pi$
$743$	9.85512			0.361549			0.180775	+	0.983525i	$0.442140\pi$
$744$		0			0
$745$	3.64608	−	6.31520i	0.133582	−	0.231371i
$746$	4.72878	−	21.9818i	0.173133	−	0.804812i
$747$		0			0
$748$	19.8987	+	27.6727i	0.727568	+	1.01181i
$749$	2.60374	+	17.7740i	0.0951387	+	0.649450i
$750$		0			0
$751$	2.10524	−	1.21546i	0.0768214	−	0.0443528i	−0.461097	−	0.887350i	$-0.652544\pi$
$751$	2.10524	−	1.21546i	0.0768214	−	0.0443528i	0.537919	+	0.842997i	$0.319211\pi$
$752$	−32.7877	−	37.1409i	−1.19564	−	1.35439i
$753$		0			0
$754$	−12.5659	+	13.8872i	−0.457624	+	0.505742i
$755$	−7.55511			−0.274959
$756$		0			0
$757$	−36.0235			−1.30929			−0.654647	−	0.755934i	$-0.727183\pi$
$757$	−36.0235			−1.30929			−0.654647	+	0.755934i	$0.727183\pi$
$758$	22.6191	−	24.9974i	0.821562	−	0.907948i
$759$		0			0
$760$	−2.48908	−	5.70315i	−0.0902883	−	0.206875i
$761$	24.3003	−	14.0298i	0.880884	−	0.508578i	0.00993401	−	0.999951i	$-0.496838\pi$
$761$	24.3003	−	14.0298i	0.880884	−	0.508578i	0.870950	+	0.491372i	$0.163505\pi$
$762$		0			0
$763$	−26.9317	+	21.2954i	−0.974993	+	0.770944i
$764$	6.55511	−	4.71360i	0.237156	−	0.170532i
$765$		0			0
$766$	2.16271	−	10.0534i	0.0781418	−	0.363244i
$767$	−20.0033	+	34.6468i	−0.722278	+	1.25102i
$768$		0			0
$769$	−29.3367			−1.05791			−0.528955	−	0.848650i	$-0.677416\pi$
$769$	−29.3367			−1.05791			−0.528955	+	0.848650i	$0.677416\pi$
$770$	−11.0449	+	5.43323i	−0.398032	+	0.195800i
$771$		0			0
$772$	33.6917	+	15.1990i	1.21259	+	0.547025i
$773$	2.54413	+	1.46885i	0.0915059	+	0.0528310i	0.545055	−	0.838400i	$-0.316509\pi$
$773$	2.54413	+	1.46885i	0.0915059	+	0.0528310i	−0.453549	+	0.891231i	$0.649842\pi$
$774$		0			0
$775$	27.9728	−	16.1501i	1.00481	−	0.580128i
$776$	−5.05140	+	6.84613i	−0.181335	+	0.245762i
$777$		0			0
$778$	6.82830	+	21.1921i	0.244806	+	0.759773i
$779$	−4.52315	−	7.83433i	−0.162059	−	0.280694i
$780$		0			0
$781$	−20.8086	+	36.0416i	−0.744592	+	1.28967i
$782$	−0.792432	+	0.875754i	−0.0283373	+	0.0313169i
$783$		0			0
$784$	−23.7727	−	14.7938i	−0.849026	−	0.528351i
$785$		−	6.24652i		−	0.222948i
$786$		0			0
$787$	34.7966	+	20.0898i	1.24037	+	0.716125i	0.969169	−	0.246399i	$-0.0792472\pi$
$787$	34.7966	+	20.0898i	1.24037	+	0.716125i	0.271197	+	0.962524i	$0.412581\pi$
$788$	17.7433	−	1.77692i	0.632077	−	0.0633001i
$789$		0			0
$790$	−4.48529	+	1.44520i	−0.159580	+	0.0514181i
$791$	−11.7930	+	29.6859i	−0.419312	+	1.05551i
$792$		0			0
$793$	−0.979135	−	1.69591i	−0.0347701	−	0.0602236i
$794$	2.93355	−	13.6367i	0.104108	−	0.483948i
$795$		0			0
$796$	−5.77789	+	12.8079i	−0.204792	+	0.453962i
$797$		−	37.9519i		−	1.34433i	−0.740403	−	0.672164i	$-0.765365\pi$
$797$		−	37.9519i		−	1.34433i	0.740403	−	0.672164i	$-0.234635\pi$
$798$		0			0
$799$		−	35.5490i		−	1.25763i
$800$	−23.1522	+	12.9909i	−0.818553	+	0.459298i
$801$		0			0
$802$	−36.3223	−	7.81373i	−1.28259	−	0.275912i
$803$	37.3477	+	64.6882i	1.31797	+	2.28280i
$804$		0			0
$805$	−0.264547	−	0.334565i	−0.00932404	−	0.0117919i
$806$	9.55893	+	29.6668i	0.336699	+	1.04497i
$807$		0			0
$808$	45.8805	−	20.0240i	1.61407	−	0.704442i
$809$	−19.6636	−	11.3528i	−0.691337	−	0.399144i	0.112776	−	0.993620i	$-0.464026\pi$
$809$	−19.6636	−	11.3528i	−0.691337	−	0.399144i	−0.804113	+	0.594477i	$0.797359\pi$
$810$		0			0
$811$			49.7833i			1.74813i	0.485810	+	0.874064i	$0.338525\pi$
$811$			49.7833i			1.74813i	−0.485810	+	0.874064i	$0.661475\pi$
$812$	21.0411	+	6.01241i	0.738399	+	0.210994i
$813$		0			0
$814$	14.9751	+	13.5503i	0.524877	+	0.474938i
$815$	3.98228	−	6.89752i	0.139493	−	0.241609i
$816$		0			0
$817$	−16.5104	−	28.5968i	−0.577626	−	1.00048i
$818$	−33.1153	+	10.6701i	−1.15785	+	0.373070i
$819$		0			0
$820$	2.04952	−	1.47375i	0.0715722	−	0.0514656i
$821$	−18.0237	+	10.4060i	−0.629033	+	0.363172i	−0.780377	−	0.625309i	$-0.784973\pi$
$821$	−18.0237	+	10.4060i	−0.629033	+	0.363172i	0.151345	+	0.988481i	$0.451640\pi$
$822$		0			0
$823$	−6.19964	−	3.57936i	−0.216106	−	0.124769i	0.388040	−	0.921643i	$-0.373152\pi$
$823$	−6.19964	−	3.57936i	−0.216106	−	0.124769i	−0.604146	+	0.796874i	$0.706486\pi$
$824$	1.46712	−	13.0352i	0.0511096	−	0.454102i
$825$		0			0
$826$	46.6426	+	3.10332i	1.62290	+	0.107978i
$827$	41.7124			1.45048			0.725241	−	0.688495i	$-0.241728\pi$
$827$	41.7124			1.45048			0.725241	+	0.688495i	$0.241728\pi$
$828$		0			0
$829$	−16.5508	+	28.6668i	−0.574832	+	0.995638i	0.421228	+	0.906955i	$0.361599\pi$
$829$	−16.5508	+	28.6668i	−0.574832	+	0.995638i	−0.996060	+	0.0886830i	$0.971734\pi$
$830$	−0.517379	−	0.111300i	−0.0179585	−	0.00386327i
$831$		0			0
$832$	−7.55691	−	24.4780i	−0.261989	−	0.848622i
$833$	−5.76270	−	19.2470i	−0.199666	−	0.666869i
$834$		0			0
$835$	3.57535	−	2.06423i	0.123730	−	0.0714356i
$836$	46.9211	−	4.69897i	1.62280	−	0.162517i
$837$		0			0
$838$	−23.2142	−	21.0055i	−0.801921	−	0.725623i
$839$	−2.73750			−0.0945091			−0.0472545	−	0.998883i	$-0.515047\pi$
$839$	−2.73750			−0.0945091			−0.0472545	+	0.998883i	$0.515047\pi$
$840$		0			0
$841$	11.8972			0.410249
$842$	−6.73821	−	6.09711i	−0.232214	−	0.210120i
$843$		0			0
$844$	21.1987	−	2.12297i	0.729689	−	0.0730755i
$845$	1.31739	−	0.760597i	0.0453197	−	0.0261653i
$846$		0			0
$847$	−9.30184	−	63.4975i	−0.319615	−	2.18180i
$848$	18.4528	+	6.19653i	0.633673	+	0.212790i
$849$		0			0
$850$	−18.6232	−	4.00625i	−0.638769	−	0.137413i
$851$	−0.349900	+	0.606045i	−0.0119944	+	0.0207750i
$852$		0			0
$853$	−20.9013			−0.715647			−0.357824	−	0.933789i	$-0.616481\pi$
$853$	−20.9013			−0.715647			−0.357824	+	0.933789i	$0.616481\pi$
$854$	−1.27310	+	1.90126i	−0.0435645	+	0.0650599i
$855$		0			0
$856$	19.0836	+	2.14788i	0.652263	+	0.0734129i
$857$	29.1110	+	16.8073i	0.994413	+	0.574125i	0.906591	−	0.422011i	$-0.138676\pi$
$857$	29.1110	+	16.8073i	0.994413	+	0.574125i	0.0878229	+	0.996136i	$0.472009\pi$
$858$		0			0
$859$	38.3404	−	22.1358i	1.30816	−	0.755265i	0.326369	−	0.945243i	$-0.394175\pi$
$859$	38.3404	−	22.1358i	1.30816	−	0.755265i	0.981788	+	0.189978i	$0.0608416\pi$
$860$	7.48114	−	5.37948i	0.255105	−	0.183439i
$861$		0			0
$862$	−40.3693	+	13.0074i	−1.37499	+	0.443033i
$863$	7.62621	+	13.2090i	0.259599	+	0.449639i	0.966135	−	0.258039i	$-0.0830763\pi$
$863$	7.62621	+	13.2090i	0.259599	+	0.449639i	−0.706535	+	0.707678i	$0.749743\pi$
$864$		0			0
$865$	−4.15673	+	7.19966i	−0.141333	+	0.244796i
$866$	−35.2395	−	31.8867i	−1.19749	−	1.08355i
$867$		0			0
$868$	26.1743	−	25.3230i	0.888415	−	0.859520i
$869$		−	35.7108i		−	1.21141i
$870$		0			0
$871$	11.8543	+	6.84406i	0.401666	+	0.231902i
$872$	14.6818	+	33.6401i	0.497189	+	1.13920i
$873$		0			0
$874$	0.501120	+	1.55526i	0.0169506	+	0.0526075i
$875$	5.24573	−	13.2048i	0.177338	−	0.446403i
$876$		0			0
$877$	17.3837	+	30.1095i	0.587006	+	1.01672i	0.994622	+	0.103571i	$0.0330269\pi$
$877$	17.3837	+	30.1095i	0.587006	+	1.01672i	−0.407616	+	0.913153i	$0.633640\pi$
$878$	15.7015	+	3.37773i	0.529899	+	0.113993i
$879$		0			0
$880$	2.60944	+	12.8975i	0.0879643	+	0.434775i
$881$			32.5275i			1.09588i	0.836518	+	0.547940i	$0.184588\pi$
$881$			32.5275i			1.09588i	−0.836518	+	0.547940i	$0.815412\pi$
$882$		0			0
$883$			15.6505i			0.526682i	0.964703	+	0.263341i	$0.0848244\pi$
$883$			15.6505i			0.526682i	−0.964703	+	0.263341i	$0.915176\pi$
$884$	7.55892	−	16.7559i	0.254234	−	0.563561i
$885$		0			0
$886$	8.41517	−	39.1181i	0.282713	−	1.31420i
$887$	24.5362	+	42.4979i	0.823844	+	1.42694i	0.902800	+	0.430061i	$0.141508\pi$
$887$	24.5362	+	42.4979i	0.823844	+	1.42694i	−0.0789562	+	0.996878i	$0.525159\pi$
$888$		0			0
$889$	18.6247	−	46.8830i	0.624654	−	1.57241i
$890$	9.60565	−	3.09503i	0.321982	−	0.103746i
$891$		0			0
$892$	−0.965600	+	0.0967010i	−0.0323307	+	0.00323779i
$893$	−42.5931	−	24.5912i	−1.42533	−	0.822912i
$894$		0			0
$895$			3.71786i			0.124274i
$896$	−21.7666	+	20.5478i	−0.727172	+	0.686455i
$897$		0			0
$898$	27.9912	−	30.9345i	0.934080	−	1.03230i
$899$	−14.2316	+	24.6499i	−0.474651	+	0.822119i
$900$		0			0
$901$	6.98365	+	12.0960i	0.232659	+	0.402977i
$902$	5.86682	+	18.2081i	0.195344	+	0.606263i
$903$		0			0
$904$	27.4779	+	20.2745i	0.913902	+	0.674321i
$905$	−2.73385	+	1.57839i	−0.0908762	+	0.0524674i
$906$		0			0
$907$	−21.3280	−	12.3137i	−0.708184	−	0.408870i	0.102204	−	0.994763i	$-0.467411\pi$
$907$	−21.3280	−	12.3137i	−0.708184	−	0.408870i	−0.810388	+	0.585893i	$0.800744\pi$
$908$	29.3603	+	13.2450i	0.974355	+	0.439552i
$909$		0			0
$910$	5.51595	+	3.69351i	0.182852	+	0.122439i
$911$	−35.3866			−1.17241			−0.586205	−	0.810163i	$-0.699379\pi$
$911$	−35.3866			−1.17241			−0.586205	+	0.810163i	$0.699379\pi$
$912$		0			0
$913$	2.00522	−	3.47314i	0.0663631	−	0.114944i
$914$	0.851905	−	3.96010i	0.0281785	−	0.130989i
$915$		0			0
$916$	−22.6825	+	16.3104i	−0.749450	+	0.538909i
$917$	0.724958	+	4.94881i	0.0239402	+	0.163424i
$918$		0			0
$919$	−10.4726	+	6.04637i	−0.345460	+	0.199451i	−0.662684	−	0.748899i	$-0.730583\pi$
$919$	−10.4726	+	6.04637i	−0.345460	+	0.199451i	0.317224	+	0.948351i	$0.397249\pi$
$920$	−0.417901	+	0.182388i	−0.0137778	+	0.00601316i
$921$		0			0
$922$	−20.0569	+	22.1659i	−0.660540	+	0.729994i
$923$	22.4446			0.738773
$924$		0			0
$925$	−11.2871			−0.371116
$926$	37.2387	−	41.1543i	1.22374	−	1.35241i
$927$		0			0
$928$	11.9447	−	20.1150i	0.392105	−	0.660307i
$929$	11.1624	−	6.44460i	0.366226	−	0.211441i	−0.305583	−	0.952166i	$-0.598851\pi$
$929$	11.1624	−	6.44460i	0.366226	−	0.211441i	0.671808	+	0.740725i	$0.265518\pi$
$930$		0			0
$931$	−27.0472	−	6.40959i	−0.886437	−	0.210066i
$932$	24.8253	+	34.5241i	0.813181	+	1.13087i
$933$		0			0
$934$	−8.74378	+	40.6457i	−0.286105	+	1.32997i
$935$	−4.72102	+	8.17704i	−0.154394	+	0.267418i
$936$		0			0
$937$	−9.49179			−0.310083			−0.155042	−	0.987908i	$-0.549551\pi$
$937$	−9.49179			−0.310083			−0.155042	+	0.987908i	$0.549551\pi$
$938$	1.06179	−	15.9586i	0.0346686	−	0.521066i
$939$		0			0
$940$	5.64364	−	12.5103i	0.184075	−	0.408040i
$941$	22.6714	+	13.0893i	0.739067	+	0.426700i	0.821730	−	0.569877i	$-0.193009\pi$
$941$	22.6714	+	13.0893i	0.739067	+	0.426700i	−0.0826632	+	0.996578i	$0.526343\pi$
$942$		0			0
$943$	−0.574064	+	0.331436i	−0.0186941	+	0.0107930i
$944$	15.9082	−	47.3736i	0.517769	−	1.54188i
$945$		0			0
$946$	21.4150	+	66.4631i	0.696263	+	2.16090i
$947$	−16.4945	−	28.5693i	−0.536000	−	0.928379i	−0.999114	−	0.0420801i	$-0.986602\pi$
$947$	−16.4945	−	28.5693i	−0.536000	−	0.928379i	0.463115	−	0.886298i	$-0.346732\pi$
$948$		0			0
$949$	20.1420	−	34.8870i	0.653837	−	1.13248i
$950$	−17.6827	+	19.5421i	−0.573704	+	0.634028i
$951$		0			0
$952$	−21.4664	+	0.716756i	−0.695731	+	0.0232302i
$953$			35.8953i			1.16276i	0.813631	+	0.581382i	$0.197488\pi$
$953$			35.8953i			1.16276i	−0.813631	+	0.581382i	$0.802512\pi$
$954$		0			0
$955$	1.93698	+	1.11831i	0.0626791	+	0.0361878i
$956$	−2.76136	−	27.5733i	−0.0893088	−	0.891786i
$957$		0			0
$958$	−26.4295	+	8.51584i	−0.853898	+	0.275134i
$959$	−32.0418	−	40.5224i	−1.03468	−	1.30854i
$960$		0			0
$961$	8.18487	+	14.1766i	0.264028	+	0.457310i
$962$	2.29064	−	10.6481i	0.0738533	−	0.343309i
$963$		0			0
$964$	15.7231	+	7.09302i	0.506407	+	0.228451i
$965$			10.2391i			0.329607i
$966$		0			0
$967$		−	16.1841i		−	0.520444i	−0.965549	−	0.260222i	$-0.916204\pi$
$967$		−	16.1841i		−	0.520444i	0.965549	−	0.260222i	$-0.0837958\pi$
$968$	−68.1758	−	7.67326i	−2.19125	−	0.246628i
$969$		0			0
$970$	−2.30418	−	0.495679i	−0.0739827	−	0.0159153i
$971$	−10.2868	−	17.8172i	−0.330118	−	0.571781i	0.652417	−	0.757861i	$-0.273755\pi$
$971$	−10.2868	−	17.8172i	−0.330118	−	0.571781i	−0.982535	+	0.186079i	$0.940422\pi$
$972$		0			0
$973$	15.9377	−	40.1191i	0.510939	−	1.28616i
$974$	0.399801	+	1.24081i	0.0128105	+	0.0397581i
$975$		0			0
$976$	1.61886	+	1.83380i	0.0518184	+	0.0586984i
$977$	21.0179	+	12.1347i	0.672421	+	0.388222i	0.796993	−	0.603988i	$-0.206423\pi$
$977$	21.0179	+	12.1347i	0.672421	+	0.388222i	−0.124572	+	0.992211i	$0.539756\pi$
$978$		0			0
$979$			76.4778i			2.44424i
$980$	1.02760	−	7.68820i	0.0328255	−	0.245591i
$981$		0			0
$982$	32.7575	+	29.6409i	1.04534	+	0.945878i
$983$	−7.34094	+	12.7149i	−0.234140	+	0.405542i	−0.959022	−	0.283331i	$-0.908561\pi$
$983$	−7.34094	+	12.7149i	−0.234140	+	0.405542i	0.724883	+	0.688872i	$0.241894\pi$
$984$		0			0
$985$	2.46992	+	4.27802i	0.0786980	+	0.136309i
$986$	15.9774	−	5.14808i	0.508825	−	0.163948i
$987$		0			0
$988$	−14.8472	−	20.6477i	−0.472352	−	0.656891i
$989$	−2.09545	+	1.20981i	−0.0666313	+	0.0384696i
$990$		0			0
$991$	23.6167	+	13.6351i	0.750209	+	0.433133i	0.825769	−	0.564008i	$-0.190741\pi$
$991$	23.6167	+	13.6351i	0.750209	+	0.433133i	−0.0755605	+	0.997141i	$0.524075\pi$
$992$	−19.0518	−	33.9538i	−0.604895	−	1.07803i
$993$		0			0
$994$	−11.5760	−	23.5322i	−0.367168	−	0.746397i
$995$	−3.89236			−0.123396
$996$		0			0
$997$	−13.4820	+	23.3515i	−0.426979	+	0.739550i	−0.996603	−	0.0823557i	$-0.973756\pi$
$997$	−13.4820	+	23.3515i	−0.426979	+	0.739550i	0.569624	+	0.821906i	$0.307089\pi$
$998$	−19.4767	−	4.18987i	−0.616525	−	0.132628i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.be.c.431.3	yes	28
3.2	odd	2	inner	756.2.be.c.431.12	yes	28
4.3	odd	2		756.2.be.d.431.8	yes	28
7.2	even	3		756.2.be.d.107.7	yes	28
12.11	even	2		756.2.be.d.431.7	yes	28
21.2	odd	6		756.2.be.d.107.8	yes	28
28.23	odd	6	inner	756.2.be.c.107.12	yes	28
84.23	even	6	inner	756.2.be.c.107.3	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.c.107.3	✓	28	84.23	even	6	inner
756.2.be.c.107.12	yes	28	28.23	odd	6	inner
756.2.be.c.431.3	yes	28	1.1	even	1	trivial
756.2.be.c.431.12	yes	28	3.2	odd	2	inner
756.2.be.d.107.7	yes	28	7.2	even	3
756.2.be.d.107.8	yes	28	21.2	odd	6
756.2.be.d.431.7	yes	28	12.11	even	2
756.2.be.d.431.8	yes	28	4.3	odd	2

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04864 - 0.948869i) q^{2} +(0.199295 + 1.99005i) q^{4} +(-0.479813 + 0.277020i) q^{5} +(2.45883 + 0.976797i) q^{7} +(1.67930 - 2.27595i) q^{8} +(0.766008 + 0.164785i) q^{10} +(-2.96884 + 5.14218i) q^{11} +3.20224 q^{13} +(-1.65158 - 3.35742i) q^{14} +(-3.92056 + 0.793213i) q^{16} +(-2.48564 - 1.43509i) q^{17} +(-3.43890 + 1.98545i) q^{19} +(-0.646908 - 0.899641i) q^{20} +(7.99249 - 2.57526i) q^{22} +(0.145485 + 0.251987i) q^{23} +(-2.34652 + 4.06429i) q^{25} +(-3.35800 - 3.03851i) q^{26} +(-1.45384 + 5.08786i) q^{28} -4.13555i q^{29} +(-5.96048 - 3.44128i) q^{31} +(4.86392 + 2.88830i) q^{32} +(1.24484 + 3.86344i) q^{34} +(-1.45037 + 0.212467i) q^{35} +(1.20253 + 2.08285i) q^{37} +(5.49011 + 1.18104i) q^{38} +(-0.175268 + 1.55723i) q^{40} +2.27815i q^{41} +8.31569i q^{43} +(-10.8248 - 4.88331i) q^{44} +(0.0865415 - 0.402290i) q^{46} +(6.19284 + 10.7263i) q^{47} +(5.09174 + 4.80356i) q^{49} +(6.31714 - 2.03544i) q^{50} +(0.638192 + 6.37261i) q^{52} +(-4.21439 - 2.43318i) q^{53} -3.28971i q^{55} +(6.35227 - 3.95584i) q^{56} +(-3.92410 + 4.33671i) q^{58} +(-6.24666 + 10.8195i) q^{59} +(-0.305765 - 0.529601i) q^{61} +(2.98507 + 9.26438i) q^{62} +(-2.35988 - 7.64402i) q^{64} +(-1.53648 + 0.887087i) q^{65} +(3.70186 + 2.13727i) q^{67} +(2.36051 - 5.23254i) q^{68} +(1.72253 + 1.15341i) q^{70} +7.00902 q^{71} +(6.28996 - 10.8945i) q^{73} +(0.715324 - 3.32520i) q^{74} +(-4.63650 - 6.44788i) q^{76} +(-12.3227 + 9.74381i) q^{77} +(-5.20851 + 3.00714i) q^{79} +(1.66140 - 1.46667i) q^{80} +(2.16166 - 2.38896i) q^{82} -0.675423 q^{83} +1.59019 q^{85} +(7.89050 - 8.72017i) q^{86} +(6.71775 + 15.3922i) q^{88} +(11.1545 - 6.44005i) q^{89} +(7.87379 + 3.12794i) q^{91} +(-0.472472 + 0.339741i) q^{92} +(3.68380 - 17.1242i) q^{94} +(1.10002 - 1.90529i) q^{95} -3.00803 q^{97} +(-0.781450 - 9.86860i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{4} - 2 q^{7} - 20 q^{10} + 8 q^{13} + 12 q^{16} + 42 q^{19} + 4 q^{22} + 6 q^{25} - 28 q^{28} - 30 q^{31} + 24 q^{34} + 12 q^{37} + 36 q^{40} - 12 q^{46} - 14 q^{49} + 84 q^{52} + 28 q^{58}+ \cdots - 4 q^{97}+O(q^{100}) \) 28 * q - 4 * q^4 - 2 * q^7 - 20 * q^10 + 8 * q^13 + 12 * q^16 + 42 * q^19 + 4 * q^22 + 6 * q^25 - 28 * q^28 - 30 * q^31 + 24 * q^34 + 12 * q^37 + 36 * q^40 - 12 * q^46 - 14 * q^49 + 84 * q^52 + 28 * q^58 + 6 * q^61 + 8 * q^64 - 24 * q^67 + 128 * q^70 - 22 * q^73 - 48 * q^79 - 36 * q^82 - 24 * q^85 - 16 * q^88 - 16 * q^91 - 12 * q^94 - 4 * q^97

Introduction

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