LMFDB - Embedded newform 756.2.be.d.107.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(107,756)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			107.8
Character	$\chi$	$=$	756.107
Dual form			756.2.be.d.431.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.297424 - 1.38258i) q^{2} +(-1.82308 - 0.822428i) q^{4} +(-0.479813 - 0.277020i) q^{5} +(-2.45883 + 0.976797i) q^{7} +(-1.67930 + 2.27595i) q^{8} +O(q^{10})$	\(q+(0.297424 - 1.38258i) q^{2} +(-1.82308 - 0.822428i) q^{4} +(-0.479813 - 0.277020i) q^{5} +(-2.45883 + 0.976797i) q^{7} +(-1.67930 + 2.27595i) q^{8} +(-0.525712 + 0.580990i) q^{10} +(2.96884 + 5.14218i) q^{11} +3.20224 q^{13} +(0.619187 + 3.69007i) q^{14} +(2.64722 + 2.99870i) q^{16} +(-2.48564 + 1.43509i) q^{17} +(3.43890 + 1.98545i) q^{19} +(0.646908 + 0.899641i) q^{20} +(7.99249 - 2.57526i) q^{22} +(-0.145485 + 0.251987i) q^{23} +(-2.34652 - 4.06429i) q^{25} +(0.952425 - 4.42737i) q^{26} +(5.28599 + 0.241438i) q^{28} +4.13555i q^{29} +(5.96048 - 3.44128i) q^{31} +(4.93330 - 2.76812i) q^{32} +(1.24484 + 3.86344i) q^{34} +(1.45037 + 0.212467i) q^{35} +(1.20253 - 2.08285i) q^{37} +(3.76787 - 4.16405i) q^{38} +(1.43624 - 0.626829i) q^{40} -2.27815i q^{41} +8.31569i q^{43} +(-1.18335 - 11.8162i) q^{44} +(0.305123 + 0.276092i) q^{46} +(-6.19284 + 10.7263i) q^{47} +(5.09174 - 4.80356i) q^{49} +(-6.31714 + 2.03544i) q^{50} +(-5.83794 - 2.63362i) q^{52} +(-4.21439 + 2.43318i) q^{53} -3.28971i q^{55} +(1.90599 - 7.23652i) q^{56} +(5.71775 + 1.23001i) q^{58} +(6.24666 + 10.8195i) q^{59} +(-0.305765 + 0.529601i) q^{61} +(-2.98507 - 9.26438i) q^{62} +(-2.35988 - 7.64402i) q^{64} +(-1.53648 - 0.887087i) q^{65} +(-3.70186 + 2.13727i) q^{67} +(5.71177 - 0.572011i) q^{68} +(0.725130 - 1.94207i) q^{70} -7.00902 q^{71} +(6.28996 + 10.8945i) q^{73} +(-2.52205 - 2.28209i) q^{74} +(-4.63650 - 6.44788i) q^{76} +(-12.3227 - 9.74381i) q^{77} +(5.20851 + 3.00714i) q^{79} +(-0.439472 - 2.17215i) q^{80} +(-3.14973 - 0.677576i) q^{82} +0.675423 q^{83} +1.59019 q^{85} +(11.4971 + 2.47329i) q^{86} +(-16.6889 - 1.87836i) q^{88} +(11.1545 + 6.44005i) q^{89} +(-7.87379 + 3.12794i) q^{91} +(0.472472 - 0.339741i) q^{92} +(12.9881 + 11.7524i) q^{94} +(-1.10002 - 1.90529i) q^{95} -3.00803 q^{97} +(-5.12692 - 8.46845i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{4} + 2 q^{7}+O(q^{10}) $ 28 * q - 4 * q^4 + 2 * q^7	$ 28 q - 4 q^{4} + 2 q^{7} + 4 q^{10} + 8 q^{13} + 12 q^{16} - 42 q^{19} + 4 q^{22} + 6 q^{25} + 24 q^{28} + 30 q^{31} + 24 q^{34} + 12 q^{37} + 24 q^{46} - 14 q^{49} - 24 q^{52} - 44 q^{58} + 6 q^{61} + 8 q^{64} + 24 q^{67} - 32 q^{70} - 22 q^{73} + 48 q^{79} + 36 q^{82} - 24 q^{85} - 4 q^{88} + 16 q^{91} + 60 q^{94} - 4 q^{97}+O(q^{100}) $ 28 * q - 4 * q^4 + 2 * q^7 + 4 * q^10 + 8 * q^13 + 12 * q^16 - 42 * q^19 + 4 * q^22 + 6 * q^25 + 24 * q^28 + 30 * q^31 + 24 * q^34 + 12 * q^37 + 24 * q^46 - 14 * q^49 - 24 * q^52 - 44 * q^58 + 6 * q^61 + 8 * q^64 + 24 * q^67 - 32 * q^70 - 22 * q^73 + 48 * q^79 + 36 * q^82 - 24 * q^85 - 4 * q^88 + 16 * q^91 + 60 * q^94 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.297424	−	1.38258i	0.210311	−	0.977635i
$2$	0.297424	−	1.38258i	0.210311	−	0.977635i
$3$		0			0
$3$		0			0
$4$	−1.82308	−	0.822428i	−0.911539	−	0.411214i
$5$	−0.479813	−	0.277020i	−0.214579	−	0.123887i	0.388859	−	0.921297i	$-0.372869\pi$
$5$	−0.479813	−	0.277020i	−0.214579	−	0.123887i	−0.603438	+	0.797410i	$0.706203\pi$
$6$		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
$10$	−0.525712	+	0.580990i	−0.166245	+	0.183725i
$11$	2.96884	+	5.14218i	0.895138	+	1.55042i	0.833634	+	0.552317i	$0.186256\pi$
$11$	2.96884	+	5.14218i	0.895138	+	1.55042i	0.0615040	+	0.998107i	$0.480410\pi$
$12$		0			0
$13$	3.20224			0.888143			0.444071	−	0.895991i	$-0.353534\pi$
$13$	3.20224			0.888143			0.444071	+	0.895991i	$0.353534\pi$
$14$	0.619187	+	3.69007i	0.165485	+	0.986212i
$15$		0			0
$16$	2.64722	+	2.99870i	0.661806	+	0.749675i
$17$	−2.48564	+	1.43509i	−0.602856	+	0.348059i	−0.770164	−	0.637845i	$-0.779826\pi$
$17$	−2.48564	+	1.43509i	−0.602856	+	0.348059i	0.167308	+	0.985905i	$0.446493\pi$
$18$		0			0
$19$	3.43890	+	1.98545i	0.788938	+	0.455494i	0.839589	−	0.543223i	$-0.182796\pi$
$19$	3.43890	+	1.98545i	0.788938	+	0.455494i	−0.0506503	+	0.998716i	$0.516129\pi$
$20$	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	$-0.842991\pi$
$23$	−0.145485	+	0.251987i	−0.0303357	+	0.0525430i	0.850459	+	0.526041i	$0.176324\pi$
$24$		0			0
$25$	−2.34652	−	4.06429i	−0.469304	−	0.812858i
$26$	0.952425	−	4.42737i	0.186786	−	0.868279i
$27$		0			0
$28$	5.28599	+	0.241438i	0.998959	+	0.0456276i
$29$			4.13555i			0.767953i	0.923343	+	0.383976i	$0.125446\pi$
$29$			4.13555i			0.767953i	−0.923343	+	0.383976i	$0.874554\pi$
$30$		0			0
$31$	5.96048	−	3.44128i	1.07053	−	0.618073i	0.142206	−	0.989837i	$-0.454580\pi$
$31$	5.96048	−	3.44128i	1.07053	−	0.618073i	0.928327	+	0.371764i	$0.121247\pi$
$32$	4.93330	−	2.76812i	0.872093	−	0.489340i
$33$		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	−0.750086	−	0.661341i	$-0.769988\pi$
$37$	1.20253	−	2.08285i	0.197695	−	0.342418i	0.947781	+	0.318923i	$0.103321\pi$
$38$	3.76787	−	4.16405i	0.611229	−	0.675498i
$39$		0			0
$40$	1.43624	−	0.626829i	0.227089	−	0.0991104i
$41$		−	2.27815i		−	0.355787i	−0.984050	−	0.177893i	$-0.943072\pi$
$41$		−	2.27815i		−	0.355787i	0.984050	−	0.177893i	$-0.0569282\pi$
$42$		0			0
$43$			8.31569i			1.26813i	0.773280	+	0.634065i	$0.218615\pi$
$43$			8.31569i			1.26813i	−0.773280	+	0.634065i	$0.781385\pi$
$44$	−1.18335	−	11.8162i	−0.178397	−	1.78137i
$45$		0			0
$46$	0.305123	+	0.276092i	0.0449879	+	0.0407076i
$47$	−6.19284	+	10.7263i	−0.903318	+	1.56459i	−0.0801597	+	0.996782i	$0.525543\pi$
$47$	−6.19284	+	10.7263i	−0.903318	+	1.56459i	−0.823159	+	0.567811i	$0.807790\pi$
$48$		0			0
$49$	5.09174	−	4.80356i	0.727391	−	0.686223i
$50$	−6.31714	+	2.03544i	−0.893378	+	0.287855i
$51$		0			0
$52$	−5.83794	−	2.63362i	−0.809576	−	0.365217i
$53$	−4.21439	+	2.43318i	−0.578892	+	0.334223i	−0.760693	−	0.649112i	$-0.775141\pi$
$53$	−4.21439	+	2.43318i	−0.578892	+	0.334223i	0.181801	+	0.983335i	$0.441807\pi$
$54$		0			0
$55$		−	3.28971i		−	0.443585i
$56$	1.90599	−	7.23652i	0.254699	−	0.967020i
$57$		0			0
$58$	5.71775	+	1.23001i	0.750777	+	0.161509i
$59$	6.24666	+	10.8195i	0.813246	+	1.40858i	0.910581	+	0.413331i	$0.135635\pi$
$59$	6.24666	+	10.8195i	0.813246	+	1.40858i	−0.0973349	+	0.995252i	$0.531032\pi$
$60$		0			0
$61$	−0.305765	+	0.529601i	−0.0391492	+	0.0678085i	−0.884936	−	0.465712i	$-0.845798\pi$
$61$	−0.305765	+	0.529601i	−0.0391492	+	0.0678085i	0.845787	+	0.533521i	$0.179131\pi$
$62$	−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	$-0.750755\pi$
$67$	−3.70186	+	2.13727i	−0.452254	+	0.261109i	0.256528	+	0.966537i	$0.417422\pi$
$68$	5.71177	−	0.572011i	0.692654	−	0.0693666i
$69$		0			0
$70$	0.725130	−	1.94207i	0.0866696	−	0.232122i
$71$	−7.00902			−0.831818			−0.415909	−	0.909406i	$-0.636536\pi$
$71$	−7.00902			−0.831818			−0.415909	+	0.909406i	$0.636536\pi$
$72$		0			0
$73$	6.28996	+	10.8945i	0.736184	+	1.27511i	0.954202	+	0.299164i	$0.0967078\pi$
$73$	6.28996	+	10.8945i	0.736184	+	1.27511i	−0.218017	+	0.975945i	$0.569959\pi$
$74$	−2.52205	−	2.28209i	−0.293182	−	0.265288i
$75$		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	$-0.223472\pi$
$79$	5.20851	+	3.00714i	0.586003	+	0.338329i	−0.177512	+	0.984119i	$0.556805\pi$
$80$	−0.439472	−	2.17215i	−0.0491345	−	0.242854i
$81$		0			0
$82$	−3.14973	−	0.677576i	−0.347830	−	0.0748258i
$83$	0.675423			0.0741373			0.0370686	−	0.999313i	$-0.488198\pi$
$83$	0.675423			0.0741373			0.0370686	+	0.999313i	$0.488198\pi$
$84$		0			0
$85$	1.59019			0.172480
$86$	11.4971	+	2.47329i	1.23977	+	0.266701i
$87$		0			0
$88$	−16.6889	−	1.87836i	−1.77904	−	0.200233i
$89$	11.1545	+	6.44005i	1.18237	+	0.682644i	0.956562	−	0.291527i	$-0.0941635\pi$
$89$	11.1545	+	6.44005i	1.18237	+	0.682644i	0.225811	+	0.974171i	$0.427497\pi$
$90$		0			0
$91$	−7.87379	+	3.12794i	−0.825397	+	0.327897i
$92$	0.472472	−	0.339741i	0.0492586	−	0.0354205i
$93$		0			0
$94$	12.9881	+	11.7524i	1.33962	+	1.21217i
$95$	−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	$0.548800\pi$
$98$	−5.12692	−	8.46845i	−0.517898	−	0.855443i
$99$		0			0
$100$	0.935300	+	9.33936i	0.0935300	+	0.933936i
$101$	15.3276	−	8.84940i	1.52515	−	0.880548i	0.525598	−	0.850733i	$-0.323842\pi$
$101$	15.3276	−	8.84940i	1.52515	−	0.880548i	0.999555	−	0.0298150i	$-0.00949180\pi$
$102$		0			0
$103$	−4.01639	−	2.31886i	−0.395746	−	0.228484i	0.288901	−	0.957359i	$-0.406710\pi$
$103$	−4.01639	−	2.31886i	−0.395746	−	0.228484i	−0.684647	+	0.728875i	$0.740044\pi$
$104$	−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	$-0.939772\pi$
$107$	−3.39483	+	5.88002i	−0.328191	+	0.568443i	0.653962	+	0.756527i	$0.273105\pi$
$108$		0			0
$109$	−6.48848	−	11.2384i	−0.621483	−	1.07644i	−0.989210	−	0.146507i	$-0.953197\pi$
$109$	−6.48848	−	11.2384i	−0.621483	−	1.07644i	0.367726	−	0.929934i	$-0.380136\pi$
$110$	−4.54830	−	0.978440i	−0.433664	−	0.0932906i
$111$		0			0
$112$	−9.43821	−	4.78751i	−0.891827	−	0.452377i
$113$		−	12.0732i		−	1.13575i	−0.823115	−	0.567875i	$-0.807766\pi$
$113$		−	12.0732i		−	1.13575i	0.823115	−	0.567875i	$-0.192234\pi$
$114$		0			0
$115$	0.139611	−	0.0806045i	0.0130188	−	0.00751641i
$116$	3.40119	−	7.53943i	0.315793	−	0.700019i
$117$		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
$122$	0.641276	+	0.580263i	0.0580584	+	0.0525345i
$123$		0			0
$124$	−13.6966	+	1.37166i	−1.22999	+	0.123179i
$125$			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	$-0.320977\pi$
$128$	−11.2704	+	0.989217i	−0.996170	+	0.0874353i
$129$		0			0
$130$	−1.68346	+	1.86047i	−0.147649	+	0.163174i
$131$	−0.945219	+	1.63717i	−0.0825842	+	0.143040i	−0.904359	−	0.426772i	$-0.859651\pi$
$131$	−0.945219	+	1.63717i	−0.0825842	+	0.143040i	0.821775	+	0.569812i	$0.192984\pi$
$132$		0			0
$133$	−10.3951	−	1.52279i	−0.901367	−	0.132042i
$134$	1.85393	+	5.75381i	0.160155	+	0.497053i
$135$		0			0
$136$	0.907965	−	8.06713i	0.0778574	−	0.691751i
$137$	−16.9097	+	9.76280i	−1.44469	+	0.834092i	−0.998158	−	0.0606749i	$-0.980675\pi$
$137$	−16.9097	+	9.76280i	−1.44469	+	0.834092i	−0.446533	+	0.894767i	$0.647341\pi$
$138$		0			0
$139$		−	16.3163i		−	1.38393i	−0.721931	−	0.691965i	$-0.756745\pi$
$139$		−	16.3163i		−	1.38393i	0.721931	−	0.691965i	$-0.243255\pi$
$140$	−2.46941	−	1.58017i	−0.208703	−	0.133549i
$141$		0			0
$142$	−2.08465	+	9.69056i	−0.174940	+	0.813214i
$143$	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	−0.0457864	−	0.998951i	$-0.514579\pi$
$149$	−11.3984	−	6.58089i	−0.933797	−	0.539128i	−0.888010	+	0.459823i	$0.847913\pi$
$150$		0			0
$151$	−11.8095	+	6.81819i	−0.961040	+	0.554856i	−0.896493	−	0.443058i	$-0.853894\pi$
$151$	−11.8095	+	6.81819i	−0.961040	+	0.554856i	−0.0645468	+	0.997915i	$0.520560\pi$
$152$	−10.2937	+	4.49259i	−0.834933	+	0.364397i
$153$		0			0
$154$	−17.1367	+	14.1392i	−1.38092	+	1.13937i
$155$	−3.81322			−0.306285
$156$		0			0
$157$	−5.63724	−	9.76398i	−0.449900	−	0.779250i	0.548479	−	0.836165i	$-0.315207\pi$
$157$	−5.63724	−	9.76398i	−0.449900	−	0.779250i	−0.998379	+	0.0569142i	$0.981874\pi$
$158$	5.70676	−	6.30681i	0.454005	−	0.501743i
$159$		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	$-0.142986\pi$
$163$	12.4495	+	7.18771i	0.975118	+	0.562985i	0.0743256	+	0.997234i	$0.476320\pi$
$164$	−1.87361	+	4.15324i	−0.146305	+	0.324314i
$165$		0			0
$166$	0.200887	−	0.933829i	0.0155919	−	0.0724792i
$167$	7.45155			0.576618			0.288309	−	0.957537i	$-0.406907\pi$
$167$	7.45155			0.576618			0.288309	+	0.957537i	$0.406907\pi$
$168$		0			0
$169$	−2.74563			−0.211203
$170$	0.472961	−	2.19857i	0.0362745	−	0.168623i
$171$		0			0
$172$	6.83905	−	15.1601i	0.521473	−	1.15595i
$173$	12.9948	+	7.50257i	0.987978	+	0.570410i	0.904669	−	0.426114i	$-0.140118\pi$
$173$	12.9948	+	7.50257i	0.987978	+	0.570410i	0.0833090	+	0.996524i	$0.473451\pi$
$174$		0			0
$175$	9.73969	+	7.70135i	0.736251	+	0.582167i
$176$	−7.56067	+	22.5151i	−0.569907	+	1.69714i
$177$		0			0
$178$	12.2215	−	13.5066i	0.916042	−	1.01236i
$179$	−3.35522	−	5.81141i	−0.250781	−	0.434365i	0.712960	−	0.701205i	$-0.247354\pi$
$179$	−3.35522	−	5.81141i	−0.250781	−	0.434365i	−0.963741	+	0.266839i	$0.914021\pi$
$180$		0			0
$181$	5.69773			0.423509			0.211755	−	0.977323i	$-0.432082\pi$
$181$	5.69773			0.423509			0.211755	+	0.977323i	$0.432082\pi$
$182$	1.98279	+	11.8165i	0.146974	+	0.875897i
$183$		0			0
$184$	−0.329197	−	0.754279i	−0.0242687	−	0.0556062i
$185$	−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	$-0.786677\pi$
$191$	2.01847	−	3.49609i	0.146051	−	0.252968i	0.929765	+	0.368154i	$0.120010\pi$
$192$		0			0
$193$	9.24035	+	16.0047i	0.665135	+	1.15205i	0.979249	+	0.202662i	$0.0649592\pi$
$193$	9.24035	+	16.0047i	0.665135	+	1.15205i	−0.314114	+	0.949385i	$0.601707\pi$
$194$	−0.894662	+	4.15886i	−0.0642330	+	0.298589i
$195$		0			0
$196$	−13.2332	+	4.56968i	−0.945230	+	0.326406i
$197$			8.91601i			0.635239i	0.948218	+	0.317620i	$0.102883\pi$
$197$			8.91601i			0.635239i	−0.948218	+	0.317620i	$0.897117\pi$
$198$		0			0
$199$	−6.08418	+	3.51270i	−0.431296	+	0.249009i	−0.699898	−	0.714242i	$-0.746771\pi$
$199$	−6.08418	+	3.51270i	−0.431296	+	0.249009i	0.268603	+	0.963251i	$0.413438\pi$
$200$	13.1906	+	1.48462i	0.932719	+	0.104979i
$201$		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
$206$	−4.40059	+	4.86331i	−0.306604	+	0.338843i
$207$		0			0
$208$	8.47706	+	9.60257i	0.587778	+	0.665818i
$209$			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	$-0.119502\pi$
$212$	9.68428	−	0.969843i	0.665119	−	0.0666091i
$213$		0			0
$214$	7.11991	+	6.44250i	0.486707	+	0.440400i
$215$	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
$220$	−2.70555	+	5.99740i	−0.182408	+	0.404345i
$221$	−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	$0.994828\pi$
$224$	−9.42629	+	11.6252i	−0.629820	+	0.776741i
$225$		0			0
$226$	−16.6922	−	3.59086i	−1.11035	−	0.238860i
$227$	−8.05240	−	13.9472i	−0.534456	−	0.925705i	−0.999189	−	0.0402546i	$-0.987183\pi$
$227$	−8.05240	−	13.9472i	−0.534456	−	0.925705i	0.464733	−	0.885451i	$-0.346150\pi$
$228$		0			0
$229$	6.98446	−	12.0974i	0.461546	−	0.799421i	−0.537492	−	0.843269i	$-0.680628\pi$
$229$	6.98446	−	12.0974i	0.461546	−	0.799421i	0.999038	+	0.0438475i	$0.0139616\pi$
$230$	−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	0.961944	−	0.273247i	$-0.0880975\pi$
$233$	18.4130	+	10.6308i	1.20628	+	0.696445i	0.244333	+	0.969691i	$0.421431\pi$
$234$		0			0
$235$	5.94281	−	3.43108i	0.387666	−	0.223819i
$236$	−2.48986	−	24.8623i	−0.162076	−	1.61840i
$237$		0			0
$238$	−6.83464	−	8.28360i	−0.443024	−	0.536946i
$239$	13.8556			0.896247			0.448123	−	0.893972i	$-0.352093\pi$
$239$	13.8556			0.896247			0.448123	+	0.893972i	$0.352093\pi$
$240$		0			0
$241$	4.31224	+	7.46902i	0.277776	+	0.481122i	0.970832	−	0.239762i	$-0.0770694\pi$
$241$	4.31224	+	7.46902i	0.277776	+	0.481122i	−0.693056	+	0.720884i	$0.743736\pi$
$242$	25.4358	+	23.0157i	1.63507	+	1.47951i
$243$		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
$248$	−2.17727	+	19.3447i	−0.138257	+	1.22839i
$249$		0			0
$250$	7.42494	+	1.59727i	0.469595	+	0.101020i
$251$	−10.0174			−0.632293			−0.316147	−	0.948710i	$-0.602389\pi$
$251$	−10.0174			−0.632293			−0.316147	+	0.948710i	$0.602389\pi$
$252$		0			0
$253$	−1.72768			−0.108619
$254$	−26.3620	−	5.67104i	−1.65410	−	0.355832i
$255$		0			0
$256$	−1.98441	+	15.8765i	−0.124025	+	0.992279i
$257$	−8.40598	−	4.85319i	−0.524351	−	0.302734i	0.214362	−	0.976754i	$-0.431233\pi$
$257$	−8.40598	−	4.85319i	−0.524351	−	0.302734i	−0.738713	+	0.674020i	$0.764566\pi$
$258$		0			0
$259$	−0.922309	+	6.29600i	−0.0573095	+	0.391215i
$260$	2.07156	+	2.88087i	0.128472	+	0.178664i
$261$		0			0
$262$	1.98239	+	1.79378i	0.122472	+	0.110820i
$263$	−5.83530	−	10.1070i	−0.359820	−	0.623226i	0.628111	−	0.778124i	$-0.283829\pi$
$263$	−5.83530	−	10.1070i	−0.359820	−	0.623226i	−0.987931	+	0.154898i	$0.950495\pi$
$264$		0			0
$265$	2.69616			0.165624
$266$	−5.19713	+	13.9192i	−0.318656	+	0.853438i
$267$		0			0
$268$	8.50653	−	0.851895i	0.519619	−	0.0520378i
$269$	12.2044	−	7.04622i	0.744116	−	0.429616i	−0.0794480	−	0.996839i	$-0.525316\pi$
$269$	12.2044	−	7.04622i	0.744116	−	0.429616i	0.823564	+	0.567223i	$0.191982\pi$
$270$		0			0
$271$	−4.52302	−	2.61137i	−0.274754	−	0.158629i	0.356292	−	0.934375i	$-0.384041\pi$
$271$	−4.52302	−	2.61137i	−0.274754	−	0.158629i	−0.631046	+	0.775745i	$0.717374\pi$
$272$	−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	0.671282	−	0.741202i	$-0.265744\pi$
$277$	−5.09716	−	8.82854i	−0.306259	−	0.530456i	−0.977541	+	0.210746i	$0.932411\pi$
$278$	−22.5587	−	4.85286i	−1.35298	−	0.291055i
$279$		0			0
$280$	−2.91918	+	2.94418i	−0.174455	+	0.175948i
$281$		−	28.3097i		−	1.68881i	−0.535702	−	0.844407i	$-0.679953\pi$
$281$		−	28.3097i		−	1.68881i	0.535702	−	0.844407i	$-0.320047\pi$
$282$		0			0
$283$	−7.18829	+	4.15016i	−0.427300	+	0.246702i	−0.698196	−	0.715907i	$-0.746013\pi$
$283$	−7.18829	+	4.15016i	−0.427300	+	0.246702i	0.270896	+	0.962609i	$0.412680\pi$
$284$	12.7780	+	5.76442i	0.758234	+	0.342055i
$285$		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
$290$	−2.40271	−	2.17411i	−0.141092	−	0.127668i
$291$		0			0
$292$	−2.50712	−	25.0346i	−0.146718	−	1.46504i
$293$		−	18.3982i		−	1.07483i	−0.843317	−	0.537416i	$-0.819401\pi$
$293$		−	18.3982i		−	1.07483i	0.843317	−	0.537416i	$-0.180599\pi$
$294$		0			0
$295$		−	6.92181i		−	0.403003i
$296$	2.72103	+	6.23463i	0.158157	+	0.362380i
$297$		0			0
$298$	−12.4888	+	13.8020i	−0.723458	+	0.799528i
$299$	−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
$304$	3.14977	+	15.5682i	0.180652	+	0.892896i
$305$	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	$-0.0544861\pi$
$308$	14.4517	+	27.8983i	0.823464	+	1.58965i
$309$		0			0
$310$	−1.13414	+	5.27210i	−0.0644151	+	0.299435i
$311$	−14.9380	−	25.8734i	−0.847058	−	1.46715i	−0.883822	−	0.467823i	$-0.845038\pi$
$311$	−14.9380	−	25.8734i	−0.847058	−	1.46715i	0.0367643	−	0.999324i	$-0.488295\pi$
$312$		0			0
$313$	−0.862490	+	1.49388i	−0.0487508	+	0.0844389i	−0.889371	−	0.457186i	$-0.848857\pi$
$313$	−0.862490	+	1.49388i	−0.0487508	+	0.0844389i	0.840620	+	0.541625i	$0.182191\pi$
$314$	−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	0.464757	−	0.885438i	$-0.346142\pi$
$317$	−1.24055	−	0.716235i	−0.0696765	−	0.0402277i	−0.534434	+	0.845211i	$0.679475\pi$
$318$		0			0
$319$	−21.2657	+	12.2778i	−1.19065	+	0.687423i
$320$	−0.985246	+	4.32143i	−0.0550769	+	0.241576i
$321$		0			0
$322$	−1.01993	−	0.380822i	−0.0568386	−	0.0212224i
$323$	−11.3972			−0.634155
$324$		0			0
$325$	−7.51413	−	13.0149i	−0.416809	−	0.721934i
$326$	13.6404	−	15.0747i	0.755471	−	0.834908i
$327$		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	$-0.150913\pi$
$331$	17.0867	+	9.86503i	0.939172	+	0.542231i	0.0494711	+	0.998776i	$0.484246\pi$
$332$	−1.23135	−	0.555486i	−0.0675790	−	0.0304863i
$333$		0			0
$334$	2.21627	−	10.3024i	0.121269	−	0.563722i
$335$	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	$0.470022\pi$
$338$	−0.816618	+	3.79607i	−0.0444182	+	0.206479i
$339$		0			0
$340$	−2.89904	−	1.30782i	−0.157223	−	0.0709264i
$341$	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
$346$	14.2379	−	15.7350i	0.765435	−	0.845919i
$347$	−7.69485	−	13.3279i	−0.413081	−	0.715478i	0.582144	−	0.813086i	$-0.302214\pi$
$347$	−7.69485	−	13.3279i	−0.413081	−	0.715478i	−0.995225	+	0.0976081i	$0.968881\pi$
$348$		0			0
$349$	35.4402			1.89707			0.948534	−	0.316676i	$-0.102567\pi$
$349$	35.4402			1.89707			0.948534	+	0.316676i	$0.102567\pi$
$350$	13.5446	−	11.1754i	0.723988	−	0.597349i
$351$		0			0
$352$	28.8804	+	17.1498i	1.53933	+	0.914088i
$353$	9.96600	−	5.75387i	0.530436	−	0.306248i	−0.210758	−	0.977538i	$-0.567593\pi$
$353$	9.96600	−	5.75387i	0.530436	−	0.306248i	0.741194	+	0.671291i	$0.234260\pi$
$354$		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	$-0.709836\pi$
$359$	7.16808	−	12.4155i	0.378317	−	0.655264i	0.990817	+	0.135206i	$0.0431697\pi$
$360$		0			0
$361$	−1.61596	−	2.79893i	−0.0850508	−	0.147312i
$362$	1.69464	−	7.87760i	0.0890685	−	0.414037i
$363$		0			0
$364$	16.9270	+	0.773145i	0.887218	+	0.0405238i
$365$		−	6.96979i		−	0.364815i
$366$		0			0
$367$	26.6088	−	15.3626i	1.38897	−	0.801921i	0.395770	−	0.918350i	$-0.370478\pi$
$367$	26.6088	−	15.3626i	1.38897	−	0.801921i	0.993199	+	0.116428i	$0.0371445\pi$
$368$	−1.14077	+	0.230801i	−0.0594665	+	0.0120313i
$369$		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	−0.583454	−	0.812146i	$-0.698299\pi$
$373$	7.94955	−	13.7690i	0.411612	−	0.712933i	0.995066	+	0.0992132i	$0.0316326\pi$
$374$	−16.1708	+	17.8711i	−0.836170	+	0.924091i
$375$		0			0
$376$	−14.0129	−	32.1073i	−0.722659	−	1.65581i
$377$			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	$0.790270\pi$
$380$	0.438458	+	4.37818i	0.0224924	+	0.224596i
$381$		0			0
$382$	−4.23330	−	3.83053i	−0.216594	−	0.195987i
$383$	−3.63573	+	6.29726i	−0.185777	+	0.321775i	−0.943838	−	0.330408i	$-0.892814\pi$
$383$	−3.63573	+	6.29726i	−0.185777	+	0.321775i	0.758061	+	0.652184i	$0.226147\pi$
$384$		0			0
$385$	3.21338	+	8.08886i	0.163769	+	0.412246i
$386$	24.8762	−	8.01536i	1.26617	−	0.407971i
$387$		0			0
$388$	5.48388	+	2.47389i	0.278402	+	0.125593i
$389$	−13.6345	+	7.87187i	−0.691295	+	0.399120i	−0.804097	−	0.594498i	$-0.797351\pi$
$389$	−13.6345	+	7.87187i	−0.691295	+	0.399120i	0.112802	+	0.993618i	$0.464017\pi$
$390$		0			0
$391$		−	0.835133i		−	0.0422345i
$392$	2.38209	+	19.6552i	0.120314	+	0.992736i
$393$		0			0
$394$	12.3271	+	2.65184i	0.621032	+	0.133598i
$395$	−1.66608	−	2.88573i	−0.0838293	−	0.145197i
$396$		0			0
$397$	4.93160	−	8.54177i	0.247510	−	0.428699i	−0.715325	−	0.698792i	$-0.753721\pi$
$397$	4.93160	−	8.54177i	0.247510	−	0.428699i	0.962834	+	0.270093i	$0.0870545\pi$
$398$	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	0.945477	−	0.325688i	$-0.105596\pi$
$401$	22.7516	+	13.1357i	1.13616	+	0.655964i	0.190685	+	0.981651i	$0.438929\pi$
$402$		0			0
$403$	19.0869	−	11.0198i	0.950786	−	0.548937i
$404$	−35.2214	+	3.52729i	−1.75233	+	0.175489i
$405$		0			0
$406$	−15.2605	+	2.56068i	−0.757364	+	0.127084i
$407$	14.2805			0.707857
$408$		0			0
$409$	12.3008	+	21.3056i	0.608234	+	1.05349i	0.991531	+	0.129867i	$0.0414551\pi$
$409$	12.3008	+	21.3056i	0.608234	+	1.05349i	−0.383298	+	0.923625i	$0.625212\pi$
$410$	1.32358	+	1.19765i	0.0653670	+	0.0591477i
$411$		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
$416$	15.7976	−	8.86421i	0.774543	−	0.434604i
$417$		0			0
$418$	32.5985	+	7.01265i	1.59444	+	0.343000i
$419$	−22.1374			−1.08148			−0.540742	−	0.841189i	$-0.681856\pi$
$419$	−22.1374			−1.08148			−0.540742	+	0.841189i	$0.681856\pi$
$420$		0			0
$421$	6.42567			0.313168			0.156584	−	0.987665i	$-0.449952\pi$
$421$	6.42567			0.313168			0.156584	+	0.987665i	$0.449952\pi$
$422$	−14.7278	−	3.16827i	−0.716937	−	0.154229i
$423$		0			0
$424$	1.53945	−	13.6778i	0.0747624	−	0.664252i
$425$	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
$430$	−4.83133	−	4.37166i	−0.232987	−	0.210820i
$431$	−14.9953	−	25.9727i	−0.722299	−	1.25106i	−0.960076	−	0.279739i	$-0.909752\pi$
$431$	−14.9953	−	25.9727i	−0.722299	−	1.25106i	0.237777	−	0.971320i	$-0.423581\pi$
$432$		0			0
$433$	33.6049			1.61495			0.807475	−	0.589902i	$-0.200833\pi$
$433$	33.6049			1.61495			0.807475	+	0.589902i	$0.200833\pi$
$434$	16.3892	+	19.8638i	0.786708	+	0.953492i
$435$		0			0
$436$	2.58625	+	25.8247i	0.123859	+	1.23678i
$437$	−1.00062	+	0.577706i	−0.0478660	+	0.0276354i
$438$		0			0
$439$	9.83511	+	5.67831i	0.469404	+	0.271011i	0.715990	−	0.698110i	$-0.245975\pi$
$439$	9.83511	+	5.67831i	0.469404	+	0.271011i	−0.246586	+	0.969121i	$0.579309\pi$
$440$	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	0.305166	+	0.952299i	$0.401288\pi$
$443$	−14.1468	+	24.5029i	−0.672132	+	1.16417i	−0.977298	+	0.211868i	$0.932045\pi$
$444$		0			0
$445$	−3.56805	−	6.18004i	−0.169142	−	0.292962i
$446$	0.670851	+	0.144315i	0.0317657	+	0.00683350i
$447$		0			0
$448$	13.2692	+	16.4902i	0.626911	+	0.779091i
$449$		−	29.4996i		−	1.39217i	−0.717959	−	0.696086i	$-0.754923\pi$
$449$		−	29.4996i		−	1.39217i	0.717959	−	0.696086i	$-0.245077\pi$
$450$		0			0
$451$	11.7146	−	6.76345i	0.551621	−	0.318478i
$452$	−9.92932	+	22.0103i	−0.467036	+	1.03528i
$453$		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	−0.830584	−	0.556894i	$-0.811993\pi$
$457$	1.43214	−	2.48054i	0.0669926	−	0.116035i	0.897576	+	0.440859i	$0.145326\pi$
$458$	−14.6484	−	13.2547i	−0.684474	−	0.619350i
$459$		0			0
$460$	−0.320813	+	0.0321282i	−0.0149580	+	0.00149799i
$461$			21.1377i			0.984482i	0.870459	+	0.492241i	$0.163822\pi$
$461$			21.1377i			0.984482i	−0.870459	+	0.492241i	$0.836178\pi$
$462$		0			0
$463$			39.2453i			1.82389i	0.410317	+	0.911943i	$0.365418\pi$
$463$			39.2453i			1.82389i	−0.410317	+	0.911943i	$0.634582\pi$
$464$	−12.4013	+	10.9477i	−0.575715	+	0.508236i
$465$		0			0
$466$	20.1744	−	22.2957i	0.934561	−	1.03283i
$467$	14.6992	−	25.4597i	0.680196	−	1.17813i	−0.294725	−	0.955582i	$-0.595228\pi$
$467$	14.6992	−	25.4597i	0.680196	−	1.17813i	0.974921	−	0.222552i	$-0.0714387\pi$
$468$		0			0
$469$	7.01458	−	8.87115i	0.323903	−	0.409632i
$470$	−2.97623	−	9.23693i	−0.137283	−	0.426068i
$471$		0			0
$472$	−35.1147	−	3.95220i	−1.61629	−	0.181915i
$473$	−42.7607	+	24.6879i	−1.96614	+	1.13515i
$474$		0			0
$475$		−	18.6356i		−	0.855060i
$476$	−13.4856	+	6.98572i	−0.618110	+	0.320190i
$477$		0			0
$478$	4.12100	−	19.1566i	0.188490	−	0.876202i
$479$	−9.81732	−	17.0041i	−0.448565	−	0.776937i	0.549728	−	0.835344i	$-0.314731\pi$
$479$	−9.81732	−	17.0041i	−0.448565	−	0.776937i	−0.998293	+	0.0584067i	$0.981398\pi$
$480$		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	$-0.660018\pi$
$487$	0.798307	−	0.460903i	0.0361748	−	0.0208855i	0.517978	+	0.855394i	$0.326685\pi$
$488$	−0.691872	−	1.58527i	−0.0313196	−	0.0717617i
$489$		0			0
$490$	0.114034	+	5.48354i	0.00515152	+	0.247721i
$491$	31.2381			1.40976			0.704878	−	0.709329i	$-0.251002\pi$
$491$	31.2381			1.40976			0.704878	+	0.709329i	$0.251002\pi$
$492$		0			0
$493$	−5.93487	−	10.2795i	−0.267293	−	0.462965i
$494$	12.0656	−	13.3343i	0.542858	−	0.599939i
$495$		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	$-0.435443\pi$
$499$	−12.1999	−	7.04359i	−0.546141	−	0.315314i	−0.747564	+	0.664190i	$0.768777\pi$
$500$	4.41672	−	9.79054i	0.197522	−	0.437846i
$501$		0			0
$502$	−2.97942	+	13.8499i	−0.132978	+	0.618152i
$503$	−21.4391			−0.955922			−0.477961	−	0.878381i	$-0.658624\pi$
$503$	−21.4391			−0.955922			−0.477961	+	0.878381i	$0.658624\pi$
$504$		0			0
$505$	−9.80585			−0.436355
$506$	−0.513855	+	2.38867i	−0.0228436	+	0.106189i
$507$		0			0
$508$	−15.6814	+	34.7609i	−0.695748	+	1.54227i
$509$	32.8654	+	18.9749i	1.45673	+	0.841046i	0.998849	−	0.0479657i	$-0.0152738\pi$
$509$	32.8654	+	18.9749i	1.45673	+	0.841046i	0.457885	+	0.889011i	$0.348607\pi$
$510$		0			0
$511$	−26.1077	−	20.6438i	−1.15494	−	0.913230i
$512$	21.3603	+	7.46566i	0.944002	+	0.329938i
$513$		0			0
$514$	−9.21009	+	10.1785i	−0.406240	+	0.448955i
$515$	1.28474	+	2.22524i	0.0566126	+	0.0980559i
$516$		0			0
$517$	−73.5421			−3.23438
$518$	8.43043	+	3.14775i	0.370412	+	0.138304i
$519$		0			0
$520$	4.59918	−	2.00726i	0.201687	−	0.0880241i
$521$	−24.5753	+	14.1886i	−1.07666	+	0.621613i	−0.929995	−	0.367573i	$-0.880189\pi$
$521$	−24.5753	+	14.1886i	−1.07666	+	0.621613i	−0.146670	+	0.989185i	$0.546856\pi$
$522$		0			0
$523$	−13.2425	−	7.64559i	−0.579056	−	0.334318i	0.181702	−	0.983354i	$-0.441839\pi$
$523$	−13.2425	−	7.64559i	−0.579056	−	0.334318i	−0.760758	+	0.649035i	$0.775173\pi$
$524$	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
$530$	0.801904	−	3.72767i	0.0348325	−	0.161920i
$531$		0			0
$532$	17.6986	+	11.3254i	0.767334	+	0.491017i
$533$		−	7.29518i		−	0.315990i
$534$		0			0
$535$	3.25777	−	1.88087i	0.140846	−	0.0813172i
$536$	1.35223	−	12.0144i	0.0584074	−	0.518941i
$537$		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	−0.740970	−	0.671538i	$-0.765634\pi$
$541$	4.90969	−	8.50383i	0.211084	−	0.365608i	0.952054	+	0.305930i	$0.0989673\pi$
$542$	−4.95569	+	5.47677i	−0.212865	+	0.235247i
$543$		0			0
$544$	−8.28993	+	13.9603i	−0.355428	+	0.598542i
$545$			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	$-0.0154634\pi$
$548$	38.8568	−	3.89136i	1.65988	−	0.166231i
$549$		0			0
$550$	−29.2211	−	26.4409i	−1.24599	−	1.12744i
$551$	−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
$556$	−13.4190	+	29.7459i	−0.569092	+	1.26151i
$557$	−24.7675	+	14.2995i	−1.04943	+	0.605890i	−0.922490	−	0.386020i	$-0.873849\pi$
$557$	−24.7675	+	14.2995i	−1.04943	+	0.605890i	−0.126942	+	0.991910i	$0.540516\pi$
$558$		0			0
$559$			26.6289i			1.12628i
$560$	3.20234	+	4.91169i	0.135324	+	0.207557i
$561$		0			0
$562$	−39.1405	−	8.41999i	−1.65104	−	0.355176i
$563$	16.7025	+	28.9296i	0.703926	+	1.21924i	0.967078	+	0.254481i	$0.0819046\pi$
$563$	16.7025	+	28.9296i	0.703926	+	1.21924i	−0.263152	+	0.964754i	$0.584762\pi$
$564$		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	0.558233	−	0.829684i	$-0.311480\pi$
$569$	2.83434	+	1.63641i	0.118822	+	0.0686018i	−0.439411	+	0.898286i	$0.644813\pi$
$570$		0			0
$571$	−14.4191	+	8.32487i	−0.603420	+	0.348385i	−0.770386	−	0.637578i	$-0.779936\pi$
$571$	−14.4191	+	8.32487i	−0.603420	+	0.348385i	0.166966	+	0.985963i	$0.446603\pi$
$572$	−3.78938	−	37.8385i	−0.158442	−	1.58211i
$573$		0			0
$574$	8.40652	−	1.41060i	0.350881	−	0.0588772i
$575$	1.36553			0.0569466
$576$		0			0
$577$	−3.61179	−	6.25581i	−0.150361	−	0.260433i	0.780999	−	0.624532i	$-0.214710\pi$
$577$	−3.61179	−	6.25581i	−0.150361	−	0.260433i	−0.931360	+	0.364099i	$0.881377\pi$
$578$	9.18832	+	8.31411i	0.382184	+	0.345821i
$579$		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
$584$	−35.3582	−	3.97960i	−1.46313	−	0.164677i
$585$		0			0
$586$	−25.4370	−	5.47206i	−1.05079	−	0.226049i
$587$	25.0736			1.03490			0.517448	−	0.855714i	$-0.326882\pi$
$587$	25.0736			1.03490			0.517448	+	0.855714i	$0.326882\pi$
$588$		0			0
$589$	27.3300			1.12611
$590$	−9.56998	−	2.05871i	−0.393990	−	0.0847559i
$591$		0			0
$592$	9.42920	−	1.90773i	0.387538	−	0.0784071i
$593$	−10.8437	−	6.26064i	−0.445299	−	0.257094i	0.260544	−	0.965462i	$-0.416098\pi$
$593$	−10.8437	−	6.26064i	−0.445299	−	0.257094i	−0.705843	+	0.708368i	$0.749432\pi$
$594$		0			0
$595$	−3.91002	+	1.55329i	−0.160295	+	0.0636788i
$596$	15.3679	+	21.3719i	0.629495	+	0.875426i
$597$		0			0
$598$	0.977078	+	0.884115i	0.0399557	+	0.0361541i
$599$	9.23709	+	15.9991i	0.377417	+	0.653706i	0.990686	−	0.136169i	$-0.0434789\pi$
$599$	9.23709	+	15.9991i	0.377417	+	0.653706i	−0.613268	+	0.789875i	$0.710146\pi$
$600$		0			0
$601$	1.51523			0.0618074			0.0309037	−	0.999522i	$-0.490161\pi$
$601$	1.51523			0.0618074			0.0309037	+	0.999522i	$0.490161\pi$
$602$	−30.6855	+	5.14896i	−1.25065	+	0.209856i
$603$		0			0
$604$	27.1370	−	2.71767i	1.10419	−	0.110580i
$605$	11.6383	−	6.71939i	0.473165	−	0.273182i
$606$		0			0
$607$	37.1840	+	21.4682i	1.50925	+	0.871366i	0.999942	+	0.0107826i	$0.00343226\pi$
$607$	37.1840	+	21.4682i	1.50925	+	0.871366i	0.509309	+	0.860584i	$0.329901\pi$
$608$	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	0.717039	−	0.697034i	$-0.245497\pi$
$613$	−6.06912	−	10.5120i	−0.245130	−	0.424577i	−0.962168	+	0.272457i	$0.912164\pi$
$614$	−8.25284	−	1.77537i	−0.333057	−	0.0716480i
$615$		0			0
$616$	42.8700	−	11.6831i	1.72728	−	0.470726i
$617$		−	16.9417i		−	0.682049i	−0.940054	−	0.341024i	$-0.889226\pi$
$617$		−	16.9417i		−	0.682049i	0.940054	−	0.341024i	$-0.110774\pi$
$618$		0			0
$619$	−9.94601	+	5.74233i	−0.399764	+	0.230804i	−0.686382	−	0.727241i	$-0.740802\pi$
$619$	−9.94601	+	5.74233i	−0.399764	+	0.230804i	0.286618	+	0.958045i	$0.407469\pi$
$620$	6.95180	+	3.13610i	0.279191	+	0.125949i
$621$		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
$626$	1.80888	+	1.63678i	0.0722975	+	0.0654189i
$627$		0			0
$628$	2.24695	+	22.4367i	0.0896630	+	0.895322i
$629$			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	$-0.162503\pi$
$632$	−15.5908	+	6.80441i	−0.620167	+	0.270665i
$633$		0			0
$634$	−1.35923	+	1.50215i	−0.0539818	+	0.0596578i
$635$	−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
$640$	5.68171	+	2.64748i	0.224589	+	0.104651i
$641$	−5.19237	+	2.99782i	−0.205086	+	0.118407i	−0.599026	−	0.800730i	$-0.704445\pi$
$641$	−5.19237	+	2.99782i	−0.205086	+	0.118407i	0.393939	+	0.919136i	$0.371112\pi$
$642$		0			0
$643$		−	34.2008i		−	1.34875i	−0.738390	−	0.674374i	$-0.764413\pi$
$643$		−	34.2008i		−	1.34875i	0.738390	−	0.674374i	$-0.235587\pi$
$644$	−0.829871	+	1.29688i	−0.0327015	+	0.0511041i
$645$		0			0
$646$	−3.38979	+	15.7575i	−0.133370	+	0.619972i
$647$	15.1478	+	26.2367i	0.595520	+	1.03147i	0.993473	+	0.114065i	$0.0363872\pi$
$647$	15.1478	+	26.2367i	0.595520	+	1.03147i	−0.397954	+	0.917406i	$0.630279\pi$
$648$		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	0.836416	−	0.548095i	$-0.184647\pi$
$653$	19.9310	+	11.5072i	0.779959	+	0.450310i	−0.0564565	+	0.998405i	$0.517980\pi$
$654$		0			0
$655$	0.907057	−	0.523690i	0.0354417	−	0.0204623i
$656$	6.83148	−	6.03077i	0.266725	−	0.235462i
$657$		0			0
$658$	−43.4154	−	16.2104i	−1.69251	−	0.631948i
$659$	44.6195			1.73813			0.869065	−	0.494698i	$-0.164721\pi$
$659$	44.6195			1.73813			0.869065	+	0.494698i	$0.164721\pi$
$660$		0			0
$661$	12.1633	+	21.0674i	0.473097	+	0.819428i	0.999526	−	0.0307915i	$-0.00980277\pi$
$661$	12.1633	+	21.0674i	0.473097	+	0.819428i	−0.526429	+	0.850219i	$0.676469\pi$
$662$	18.7212	−	20.6897i	0.727622	−	0.804130i
$663$		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
$668$	−13.5848	−	6.12836i	−0.525610	−	0.237113i
$669$		0			0
$670$	0.704380	−	3.27433i	0.0272126	−	0.126498i
$671$	−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	$0.512653\pi$
$674$	1.02691	−	4.77360i	0.0395549	−	0.183872i
$675$		0			0
$676$	5.00551	+	2.25809i	0.192519	+	0.0868495i
$677$	−38.1309	−	22.0149i	−1.46549	−	0.846101i	−0.466234	−	0.884662i	$-0.654389\pi$
$677$	−38.1309	−	22.0149i	−1.46549	−	0.846101i	−0.999256	+	0.0385604i	$0.987723\pi$
$678$		0			0
$679$	7.39626	−	2.93824i	0.283842	−	0.112759i
$680$	−2.67041	+	3.61919i	−0.102406	+	0.138790i
$681$		0			0
$682$	38.7769	−	42.8542i	1.48484	−	1.64097i
$683$	−8.85834	−	15.3431i	−0.338955	−	0.587087i	0.645282	−	0.763945i	$-0.276740\pi$
$683$	−8.85834	−	15.3431i	−0.338955	−	0.587087i	−0.984236	+	0.176858i	$0.943407\pi$
$684$		0			0
$685$	10.8180			0.413334
$686$	20.8782	+	15.8146i	0.797134	+	0.603803i
$687$		0			0
$688$	−24.9363	+	22.0135i	−0.950686	+	0.839256i
$689$	−13.4955	+	7.79164i	−0.514138	+	0.296838i
$690$		0			0
$691$	6.82540	+	3.94065i	0.259651	+	0.149909i	0.624175	−	0.781284i	$-0.285435\pi$
$691$	6.82540	+	3.94065i	0.259651	+	0.149909i	−0.364525	+	0.931194i	$0.618768\pi$
$692$	−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
$698$	10.5408	−	48.9990i	0.398974	−	1.85464i
$699$		0			0
$700$	−11.4224	−	22.0503i	−0.431726	−	0.833425i
$701$		−	42.2417i		−	1.59545i	−0.603025	−	0.797723i	$-0.706038\pi$
$701$		−	42.2417i		−	1.59545i	0.603025	−	0.797723i	$-0.293962\pi$
$702$		0			0
$703$	8.27078	−	4.77514i	0.311938	−	0.180098i
$704$	32.3008	−	34.8287i	1.21738	−	1.31266i
$705$		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	−0.974063	−	0.226278i	$-0.927344\pi$
$709$	−7.75030	+	13.4239i	−0.291069	+	0.504146i	0.682994	+	0.730424i	$0.260678\pi$
$710$	3.68473	−	4.07217i	0.138285	−	0.152826i
$711$		0			0
$712$	−33.3890	+	14.5722i	−1.25131	+	0.546118i
$713$			2.00262i			0.0749987i
$714$		0			0
$715$		−	10.5345i		−	0.393966i
$716$	1.33736	+	13.3541i	0.0499794	+	0.499065i
$717$		0			0
$718$	−15.0335	−	13.6031i	−0.561044	−	0.507664i
$719$	19.9952	−	34.6327i	0.745695	−	1.29158i	−0.204174	−	0.978935i	$-0.565451\pi$
$719$	19.9952	−	34.6327i	0.745695	−	1.29158i	0.949869	−	0.312647i	$-0.101216\pi$
$720$		0			0
$721$	12.1407	+	1.77851i	0.452143	+	0.0662350i
$722$	−4.35039	+	1.40174i	−0.161905	+	0.0521672i
$723$		0			0
$724$	−10.3874	−	4.68598i	−0.386045	−	0.174153i
$725$	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	$0.973483\pi$
$728$	6.10345	−	23.1731i	0.226209	−	0.858852i
$729$		0			0
$730$	−9.63632	−	2.07298i	−0.356656	−	0.0767246i
$731$	−11.9337	−	20.6698i	−0.441385	−	0.764500i
$732$		0			0
$733$	15.0072	−	25.9933i	0.554305	−	0.960084i	−0.443653	−	0.896199i	$-0.646318\pi$
$733$	15.0072	−	25.9933i	0.554305	−	0.960084i	0.997957	−	0.0638849i	$-0.0203490\pi$
$734$	−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	$-0.615529\pi$
$739$	7.53183	−	4.34850i	0.277063	−	0.159962i	0.632093	+	0.774893i	$0.282196\pi$
$740$	2.65174	−	0.265561i	0.0974799	−	0.00976223i
$741$		0			0
$742$	−11.5881	−	14.0448i	−0.425413	−	0.515601i
$743$	−9.85512			−0.361549			−0.180775	−	0.983525i	$-0.557860\pi$
$743$	−9.85512			−0.361549			−0.180775	+	0.983525i	$0.557860\pi$
$744$		0			0
$745$	3.64608	+	6.31520i	0.133582	+	0.231371i
$746$	−16.6724	−	15.0862i	−0.610421	−	0.552343i
$747$		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	$-0.347456\pi$
$751$	−2.10524	−	1.21546i	−0.0768214	−	0.0443528i	−0.537919	+	0.842997i	$0.680789\pi$
$752$	−48.5588	+	9.82448i	−1.77076	+	0.358262i
$753$		0			0
$754$	18.3096	+	3.93880i	0.666797	+	0.143443i
$755$	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	$0.727183\pi$
$758$	32.9580	+	7.08998i	1.19709	+	0.257520i
$759$		0			0
$760$	6.18361	+	0.695973i	0.224303	+	0.0252456i
$761$	24.3003	+	14.0298i	0.880884	+	0.508578i	0.870950	−	0.491372i	$-0.163505\pi$
$761$	24.3003	+	14.0298i	0.880884	+	0.508578i	0.00993401	+	0.999951i	$0.496838\pi$
$762$		0			0
$763$	26.9317	+	21.2954i	0.974993	+	0.770944i
$764$	−6.55511	+	4.71360i	−0.237156	+	0.170532i
$765$		0			0
$766$	7.62514	+	6.89966i	0.275508	+	0.249295i
$767$	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	$0.677416\pi$
$770$	12.1393	−	2.03695i	0.437469	−	0.0734064i
$771$		0			0
$772$	−3.68311	−	36.7774i	−0.132558	−	1.32365i
$773$	2.54413	−	1.46885i	0.0915059	−	0.0528310i	−0.453549	−	0.891231i	$-0.649842\pi$
$773$	2.54413	−	1.46885i	0.0915059	−	0.0528310i	0.545055	+	0.838400i	$0.316509\pi$
$774$		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
$782$	−1.15464	−	0.248389i	−0.0412899	−	0.00888236i
$783$		0			0
$784$	27.8834	+	2.55248i	0.995836	+	0.0911601i
$785$			6.24652i			0.222948i
$786$		0			0
$787$	−34.7966	+	20.0898i	−1.24037	+	0.716125i	−0.969169	−	0.246399i	$-0.920753\pi$
$787$	−34.7966	+	20.0898i	−1.24037	+	0.716125i	−0.271197	+	0.962524i	$0.587419\pi$
$788$	7.33277	−	16.2546i	0.261219	−	0.579045i
$789$		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
$794$	−10.3429	−	9.35888i	−0.367057	−	0.332134i
$795$		0			0
$796$	13.9809	−	1.40013i	0.495539	−	0.0496263i
$797$			37.9519i			1.34433i	0.740403	+	0.672164i	$0.234635\pi$
$797$			37.9519i			1.34433i	−0.740403	+	0.672164i	$0.765365\pi$
$798$		0			0
$799$		−	35.5490i		−	1.25763i
$800$	−22.8266	−	13.5549i	−0.807041	−	0.479239i
$801$		0			0
$802$	24.9280	−	27.5492i	0.880240	−	0.972795i
$803$	−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
$808$	−5.59893	+	49.7457i	−0.196970	+	1.75005i
$809$	−19.6636	+	11.3528i	−0.691337	+	0.399144i	−0.804113	−	0.594477i	$-0.797359\pi$
$809$	−19.6636	+	11.3528i	−0.691337	+	0.399144i	0.112776	+	0.993620i	$0.464026\pi$
$810$		0			0
$811$			49.7833i			1.74813i	0.485810	+	0.874064i	$0.338525\pi$
$811$			49.7833i			1.74813i	−0.485810	+	0.874064i	$0.661475\pi$
$812$	−0.998481	+	21.8605i	−0.0350398	+	0.767153i
$813$		0			0
$814$	4.24736	−	19.7440i	0.148870	−	0.692025i
$815$	−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	0.151345	−	0.988481i	$-0.451640\pi$
$821$	−18.0237	−	10.4060i	−0.629033	−	0.363172i	−0.780377	+	0.625309i	$0.784973\pi$
$822$		0			0
$823$	6.19964	−	3.57936i	0.216106	−	0.124769i	−0.388040	−	0.921643i	$-0.626848\pi$
$823$	6.19964	−	3.57936i	0.216106	−	0.124769i	0.604146	+	0.796874i	$0.293514\pi$
$824$	12.0223	−	5.24702i	0.418818	−	0.182789i
$825$		0			0
$826$	−36.0570	+	29.7499i	−1.25458	+	1.03513i
$827$	−41.7124			−1.45048			−0.725241	−	0.688495i	$-0.758272\pi$
$827$	−41.7124			−1.45048			−0.725241	+	0.688495i	$0.758272\pi$
$828$		0			0
$829$	−16.5508	−	28.6668i	−0.574832	−	0.995638i	−0.996060	−	0.0886830i	$-0.971734\pi$
$829$	−16.5508	−	28.6668i	−0.574832	−	0.995638i	0.421228	−	0.906955i	$-0.361599\pi$
$830$	−0.355078	+	0.392414i	−0.0123249	+	0.0136209i
$831$		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
$836$	19.3911	−	42.9844i	0.670657	−	1.48665i
$837$		0			0
$838$	−6.58420	+	30.6068i	−0.227448	+	1.05730i
$839$	2.73750			0.0945091			0.0472545	−	0.998883i	$-0.484953\pi$
$839$	2.73750			0.0945091			0.0472545	+	0.998883i	$0.484953\pi$
$840$		0			0
$841$	11.8972			0.410249
$842$	1.91115	−	8.88402i	0.0658625	−	0.306164i
$843$		0			0
$844$	−8.76080	+	19.4201i	−0.301559	+	0.668467i
$845$	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
$850$	12.7811	−	14.1250i	0.438388	−	0.484484i
$851$	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	$0.616481\pi$
$854$	−2.14359	−	0.800373i	−0.0733522	−	0.0273882i
$855$		0			0
$856$	−7.68166	−	17.6008i	−0.262554	−	0.601583i
$857$	29.1110	−	16.8073i	0.994413	−	0.574125i	0.0878229	−	0.996136i	$-0.472009\pi$
$857$	29.1110	−	16.8073i	0.994413	−	0.574125i	0.906591	+	0.422011i	$0.138676\pi$
$858$		0			0
$859$	−38.3404	−	22.1358i	−1.30816	−	0.755265i	−0.326369	−	0.945243i	$-0.605825\pi$
$859$	−38.3404	−	22.1358i	−1.30816	−	0.755265i	−0.981788	+	0.189978i	$0.939158\pi$
$860$	−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	$-0.916924\pi$
$863$	−7.62621	+	13.2090i	−0.259599	+	0.449639i	0.706535	+	0.707678i	$0.250257\pi$
$864$		0			0
$865$	−4.15673	−	7.19966i	−0.141333	−	0.244796i
$866$	9.99492	−	46.4617i	0.339641	−	1.57883i
$867$		0			0
$868$	32.3379	−	16.7515i	1.09762	−	0.568583i
$869$			35.7108i			1.21141i
$870$		0			0
$871$	−11.8543	+	6.84406i	−0.401666	+	0.231902i
$872$	36.4741	+	4.10520i	1.23517	+	0.139020i
$873$		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	−0.407616	−	0.913153i	$-0.633640\pi$
$877$	17.3837	−	30.1095i	0.587006	−	1.01672i	0.994622	−	0.103571i	$-0.0330269\pi$
$878$	10.7759	−	11.9090i	0.363670	−	0.401909i
$879$		0			0
$880$	9.86486	−	8.70861i	0.332544	−	0.293567i
$881$		−	32.5275i		−	1.09588i	−0.836518	−	0.547940i	$-0.815412\pi$
$881$		−	32.5275i		−	1.09588i	0.836518	−	0.547940i	$-0.184588\pi$
$882$		0			0
$883$			15.6505i			0.526682i	0.964703	+	0.263341i	$0.0848244\pi$
$883$			15.6505i			0.526682i	−0.964703	+	0.263341i	$0.915176\pi$
$884$	18.2905	−	1.83172i	0.615175	−	0.0616074i
$885$		0			0
$886$	29.6697	+	26.8468i	0.996774	+	0.901937i
$887$	−24.5362	+	42.4979i	−0.823844	+	1.42694i	0.0789562	+	0.996878i	$0.474841\pi$
$887$	−24.5362	+	42.4979i	−0.823844	+	1.42694i	−0.902800	+	0.430061i	$0.858492\pi$
$888$		0			0
$889$	18.6247	+	46.8830i	0.624654	+	1.57241i
$890$	−9.60565	+	3.09503i	−0.321982	+	0.103746i
$891$		0			0
$892$	0.399054	−	0.884585i	0.0133613	−	0.0296181i
$893$	−42.5931	+	24.5912i	−1.42533	+	0.822912i
$894$		0			0
$895$			3.71786i			0.124274i
$896$	26.7457	−	13.4412i	0.893512	−	0.449039i
$897$		0			0
$898$	−40.7857	−	8.77389i	−1.36103	−	0.292789i
$899$	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	$-0.532589\pi$
$907$	21.3280	−	12.3137i	0.708184	−	0.408870i	0.810388	+	0.585893i	$0.199256\pi$
$908$	3.20961	+	32.0493i	0.106515	+	1.06359i
$909$		0			0
$910$	2.32204	−	6.21899i	0.0769750	−	0.206157i
$911$	35.3866			1.17241			0.586205	−	0.810163i	$-0.300621\pi$
$911$	35.3866			1.17241			0.586205	+	0.810163i	$0.300621\pi$
$912$		0			0
$913$	2.00522	+	3.47314i	0.0663631	+	0.114944i
$914$	−3.00360	−	2.71782i	−0.0993501	−	0.0898976i
$915$		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	$-0.269417\pi$
$919$	10.4726	+	6.04637i	0.345460	+	0.199451i	−0.317224	+	0.948351i	$0.602751\pi$
$920$	−0.0509977	+	0.453107i	−0.00168135	+	0.0149385i
$921$		0			0
$922$	29.2247	+	6.28687i	0.962463	+	0.207047i
$923$	−22.4446			−0.738773
$924$		0			0
$925$	−11.2871			−0.371116
$926$	54.2600	+	11.6725i	1.78309	+	0.383583i
$927$		0			0
$928$	11.4477	+	20.4019i	0.375790	+	0.669726i
$929$	11.1624	+	6.44460i	0.366226	+	0.211441i	0.671808	−	0.740725i	$-0.265518\pi$
$929$	11.1624	+	6.44460i	0.366226	+	0.211441i	−0.305583	+	0.952166i	$0.598851\pi$
$930$		0			0
$931$	27.0472	−	6.40959i	0.886437	−	0.210066i
$932$	−24.8253	−	34.5241i	−0.813181	−	1.13087i
$933$		0			0
$934$	−30.8283	−	27.8952i	−1.00873	−	0.912758i
$935$	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	$0.549551\pi$
$938$	−10.1788	−	12.3367i	−0.332350	−	0.402809i
$939$		0			0
$940$	−13.6560	+	1.36760i	−0.445411	+	0.0446061i
$941$	22.6714	−	13.0893i	0.739067	−	0.426700i	−0.0826632	−	0.996578i	$-0.526343\pi$
$941$	22.6714	−	13.0893i	0.739067	−	0.426700i	0.821730	+	0.569877i	$0.193009\pi$
$942$		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	−0.463115	−	0.886298i	$-0.653268\pi$
$947$	16.4945	−	28.5693i	0.536000	−	0.928379i	0.999114	−	0.0420801i	$-0.0133985\pi$
$948$		0			0
$949$	20.1420	+	34.8870i	0.653837	+	1.13248i
$950$	−25.7653	−	5.54268i	−0.835936	−	0.179828i
$951$		0			0
$952$	5.64741	+	20.7226i	0.183034	+	0.671625i
$953$		−	35.8953i		−	1.16276i	−0.813631	−	0.581382i	$-0.802512\pi$
$953$		−	35.8953i		−	1.16276i	0.813631	−	0.581382i	$-0.197488\pi$
$954$		0			0
$955$	−1.93698	+	1.11831i	−0.0626791	+	0.0361878i
$956$	−25.2599	−	11.3953i	−0.816964	−	0.368549i
$957$		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
$962$	−8.07621	−	7.30781i	−0.260387	−	0.235613i
$963$		0			0
$964$	−1.71882	−	17.1631i	−0.0553594	−	0.552787i
$965$		−	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	$-0.0837958\pi$
$968$	−27.4426	−	62.8786i	−0.882040	−	2.02099i
$969$		0			0
$970$	1.58136	−	1.74764i	0.0507744	−	0.0561132i
$971$	10.2868	−	17.8172i	0.330118	−	0.571781i	−0.652417	−	0.757861i	$-0.726245\pi$
$971$	10.2868	−	17.8172i	0.330118	−	0.571781i	0.982535	+	0.186079i	$0.0595781\pi$
$972$		0			0
$973$	15.9377	+	40.1191i	0.510939	+	1.28616i
$974$	−0.399801	−	1.24081i	−0.0128105	−	0.0397581i
$975$		0			0
$976$	−2.39754	+	0.485074i	−0.0767435	+	0.0155268i
$977$	21.0179	−	12.1347i	0.672421	−	0.388222i	−0.124572	−	0.992211i	$-0.539756\pi$
$977$	21.0179	−	12.1347i	0.672421	−	0.388222i	0.796993	+	0.603988i	$0.206423\pi$
$978$		0			0
$979$			76.4778i			2.44424i
$980$	7.61537	+	1.47328i	0.243264	+	0.0470621i
$981$		0			0
$982$	9.29097	−	43.1893i	0.296487	−	1.37823i
$983$	7.34094	+	12.7149i	0.234140	+	0.405542i	0.959022	−	0.283331i	$-0.0914393\pi$
$983$	7.34094	+	12.7149i	0.234140	+	0.405542i	−0.724883	+	0.688872i	$0.758106\pi$
$984$		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	$-0.809259\pi$
$991$	−23.6167	+	13.6351i	−0.750209	+	0.433133i	0.0755605	+	0.997141i	$0.475925\pi$
$992$	19.8790	−	33.4762i	0.631157	−	1.06287i
$993$		0			0
$994$	−4.33989	−	25.8638i	−0.137653	−	0.820349i
$995$	3.89236			0.123396
$996$		0			0
$997$	−13.4820	−	23.3515i	−0.426979	−	0.739550i	0.569624	−	0.821906i	$-0.307089\pi$
$997$	−13.4820	−	23.3515i	−0.426979	−	0.739550i	−0.996603	+	0.0823557i	$0.973756\pi$
$998$	−13.3669	+	14.7724i	−0.423122	+	0.467612i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.c.107.3	✓	28	4.3	odd	2
756.2.be.c.107.12	yes	28	12.11	even	2
756.2.be.c.431.3	yes	28	21.11	odd	6
756.2.be.c.431.12	yes	28	7.4	even	3
756.2.be.d.107.7	yes	28	3.2	odd	2	inner
756.2.be.d.107.8	yes	28	1.1	even	1	trivial
756.2.be.d.431.7	yes	28	28.11	odd	6	inner
756.2.be.d.431.8	yes	28	84.11	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.297424 - 1.38258i) q^{2} +(-1.82308 - 0.822428i) q^{4} +(-0.479813 - 0.277020i) q^{5} +(-2.45883 + 0.976797i) q^{7} +(-1.67930 + 2.27595i) q^{8} +O(q^{10})\)	\(q+(0.297424 - 1.38258i) q^{2} +(-1.82308 - 0.822428i) q^{4} +(-0.479813 - 0.277020i) q^{5} +(-2.45883 + 0.976797i) q^{7} +(-1.67930 + 2.27595i) q^{8} +(-0.525712 + 0.580990i) q^{10} +(2.96884 + 5.14218i) q^{11} +3.20224 q^{13} +(0.619187 + 3.69007i) q^{14} +(2.64722 + 2.99870i) q^{16} +(-2.48564 + 1.43509i) q^{17} +(3.43890 + 1.98545i) q^{19} +(0.646908 + 0.899641i) q^{20} +(7.99249 - 2.57526i) q^{22} +(-0.145485 + 0.251987i) q^{23} +(-2.34652 - 4.06429i) q^{25} +(0.952425 - 4.42737i) q^{26} +(5.28599 + 0.241438i) q^{28} +4.13555i q^{29} +(5.96048 - 3.44128i) q^{31} +(4.93330 - 2.76812i) q^{32} +(1.24484 + 3.86344i) q^{34} +(1.45037 + 0.212467i) q^{35} +(1.20253 - 2.08285i) q^{37} +(3.76787 - 4.16405i) q^{38} +(1.43624 - 0.626829i) q^{40} -2.27815i q^{41} +8.31569i q^{43} +(-1.18335 - 11.8162i) q^{44} +(0.305123 + 0.276092i) q^{46} +(-6.19284 + 10.7263i) q^{47} +(5.09174 - 4.80356i) q^{49} +(-6.31714 + 2.03544i) q^{50} +(-5.83794 - 2.63362i) q^{52} +(-4.21439 + 2.43318i) q^{53} -3.28971i q^{55} +(1.90599 - 7.23652i) q^{56} +(5.71775 + 1.23001i) q^{58} +(6.24666 + 10.8195i) q^{59} +(-0.305765 + 0.529601i) q^{61} +(-2.98507 - 9.26438i) q^{62} +(-2.35988 - 7.64402i) q^{64} +(-1.53648 - 0.887087i) q^{65} +(-3.70186 + 2.13727i) q^{67} +(5.71177 - 0.572011i) q^{68} +(0.725130 - 1.94207i) q^{70} -7.00902 q^{71} +(6.28996 + 10.8945i) q^{73} +(-2.52205 - 2.28209i) q^{74} +(-4.63650 - 6.44788i) q^{76} +(-12.3227 - 9.74381i) q^{77} +(5.20851 + 3.00714i) q^{79} +(-0.439472 - 2.17215i) q^{80} +(-3.14973 - 0.677576i) q^{82} +0.675423 q^{83} +1.59019 q^{85} +(11.4971 + 2.47329i) q^{86} +(-16.6889 - 1.87836i) q^{88} +(11.1545 + 6.44005i) q^{89} +(-7.87379 + 3.12794i) q^{91} +(0.472472 - 0.339741i) q^{92} +(12.9881 + 11.7524i) q^{94} +(-1.10002 - 1.90529i) q^{95} -3.00803 q^{97} +(-5.12692 - 8.46845i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{4} + 2 q^{7}+O(q^{10}) \) 28 * q - 4 * q^4 + 2 * q^7	\( 28 q - 4 q^{4} + 2 q^{7} + 4 q^{10} + 8 q^{13} + 12 q^{16} - 42 q^{19} + 4 q^{22} + 6 q^{25} + 24 q^{28} + 30 q^{31} + 24 q^{34} + 12 q^{37} + 24 q^{46} - 14 q^{49} - 24 q^{52} - 44 q^{58} + 6 q^{61} + 8 q^{64} + 24 q^{67} - 32 q^{70} - 22 q^{73} + 48 q^{79} + 36 q^{82} - 24 q^{85} - 4 q^{88} + 16 q^{91} + 60 q^{94} - 4 q^{97}+O(q^{100}) \) 28 * q - 4 * q^4 + 2 * q^7 + 4 * q^10 + 8 * q^13 + 12 * q^16 - 42 * q^19 + 4 * q^22 + 6 * q^25 + 24 * q^28 + 30 * q^31 + 24 * q^34 + 12 * q^37 + 24 * q^46 - 14 * q^49 - 24 * q^52 - 44 * q^58 + 6 * q^61 + 8 * q^64 + 24 * q^67 - 32 * q^70 - 22 * q^73 + 48 * q^79 + 36 * q^82 - 24 * q^85 - 4 * q^88 + 16 * q^91 + 60 * q^94 - 4 * q^97

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