LMFDB - Embedded newform 414.2.j.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(17,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 7]))

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

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

chi := DirichletCharacter("414.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.j (of order $22$, degree $10$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			17.5
Character	$\chi$	$=$	414.17
Dual form			414.2.j.a.341.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.909632 + 0.415415i) q^{2} +(0.654861 + 0.755750i) q^{4} +(-2.68552 + 1.72588i) q^{5} +(-3.23801 - 0.465555i) q^{7} +(0.281733 + 0.959493i) q^{8} +O(q^{10})$	\(q+(0.909632 + 0.415415i) q^{2} +(0.654861 + 0.755750i) q^{4} +(-2.68552 + 1.72588i) q^{5} +(-3.23801 - 0.465555i) q^{7} +(0.281733 + 0.959493i) q^{8} +(-3.15979 + 0.454310i) q^{10} +(1.96239 + 4.29703i) q^{11} +(-0.154050 - 1.07144i) q^{13} +(-2.75200 - 1.76860i) q^{14} +(-0.142315 + 0.989821i) q^{16} +(-3.45571 + 3.98810i) q^{17} +(-3.14602 + 2.72604i) q^{19} +(-3.06298 - 0.899371i) q^{20} +4.72392i q^{22} +(-2.09132 - 4.31583i) q^{23} +(2.15629 - 4.72161i) q^{25} +(0.304964 - 1.03861i) q^{26} +(-1.76860 - 2.75200i) q^{28} +(5.66626 + 4.90984i) q^{29} +(3.52714 - 1.03566i) q^{31} +(-0.540641 + 0.841254i) q^{32} +(-4.80014 + 2.19215i) q^{34} +(9.49923 - 4.33816i) q^{35} +(5.70376 - 8.87523i) q^{37} +(-3.99416 + 1.17279i) q^{38} +(-2.41257 - 2.09050i) q^{40} +(1.30727 + 2.03415i) q^{41} +(0.210901 - 0.718263i) q^{43} +(-1.96239 + 4.29703i) q^{44} +(-0.109472 - 4.79458i) q^{46} +10.8153i q^{47} +(3.55151 + 1.04282i) q^{49} +(3.92286 - 3.39918i) q^{50} +(0.708859 - 0.818067i) q^{52} +(1.13317 - 7.88137i) q^{53} +(-12.6862 - 8.15291i) q^{55} +(-0.465555 - 3.23801i) q^{56} +(3.11459 + 6.81999i) q^{58} +(2.54689 - 0.366188i) q^{59} +(3.75802 + 12.7987i) q^{61} +(3.63863 + 0.523156i) q^{62} +(-0.841254 + 0.540641i) q^{64} +(2.26288 + 2.61150i) q^{65} +(7.20290 + 3.28945i) q^{67} -5.27701 q^{68} +10.4429 q^{70} +(-4.29582 - 1.96183i) q^{71} +(2.51510 + 2.90258i) q^{73} +(8.87523 - 5.70376i) q^{74} +(-4.12041 - 0.592426i) q^{76} +(-4.35372 - 14.8274i) q^{77} +(-9.45375 + 1.35924i) q^{79} +(-1.32612 - 2.90380i) q^{80} +(0.344116 + 2.39338i) q^{82} +(-11.8581 - 7.62072i) q^{83} +(2.39740 - 16.6743i) q^{85} +(0.490220 - 0.565744i) q^{86} +(-3.57010 + 3.09351i) q^{88} +(3.83372 + 1.12568i) q^{89} +3.54105i q^{91} +(1.89216 - 4.40678i) q^{92} +(-4.49284 + 9.83794i) q^{94} +(3.74388 - 12.7505i) q^{95} +(8.94718 + 13.9221i) q^{97} +(2.79737 + 2.42393i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 8 q^{4}+O(q^{10}) $ 80 * q + 8 * q^4	$ 80 q + 8 q^{4} - 16 q^{13} - 8 q^{16} + 24 q^{25} - 16 q^{31} + 88 q^{37} + 88 q^{43} + 8 q^{46} + 8 q^{49} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 176 q^{61} + 8 q^{64} - 88 q^{67} - 176 q^{70} - 56 q^{73} - 176 q^{79} - 88 q^{82} - 88 q^{85} + 16 q^{94}+O(q^{100}) $ 80 * q + 8 * q^4 - 16 * q^13 - 8 * q^16 + 24 * q^25 - 16 * q^31 + 88 * q^37 + 88 * q^43 + 8 * q^46 + 8 * q^49 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 176 * q^61 + 8 * q^64 - 88 * q^67 - 176 * q^70 - 56 * q^73 - 176 * q^79 - 88 * q^82 - 88 * q^85 + 16 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{7}{22}\right)$

Coefficient data

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

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

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

$2$	0.909632	+	0.415415i	0.643207	+	0.293743i
$2$	0.909632	+	0.415415i	0.643207	+	0.293743i
$3$		0			0
$3$		0			0
$4$	0.654861	+	0.755750i	0.327430	+	0.377875i
$5$	−2.68552	+	1.72588i	−1.20100	+	0.771837i	−0.979129	−	0.203239i	$-0.934853\pi$
$5$	−2.68552	+	1.72588i	−1.20100	+	0.771837i	−0.221872	+	0.975076i	$0.571217\pi$
$6$		0			0
$7$	−3.23801	−	0.465555i	−1.22385	−	0.175963i	−0.500066	−	0.865987i	$-0.666691\pi$
$7$	−3.23801	−	0.465555i	−1.22385	−	0.175963i	−0.723787	+	0.690024i	$0.757600\pi$
$8$	0.281733	+	0.959493i	0.0996075	+	0.339232i
$9$		0			0
$10$	−3.15979	+	0.454310i	−0.999214	+	0.143665i
$11$	1.96239	+	4.29703i	0.591682	+	1.29560i	0.934421	+	0.356172i	$0.115918\pi$
$11$	1.96239	+	4.29703i	0.591682	+	1.29560i	−0.342739	+	0.939431i	$0.611355\pi$
$12$		0			0
$13$	−0.154050	−	1.07144i	−0.0427257	−	0.297164i	−0.999969	−	0.00787965i	$-0.997492\pi$
$13$	−0.154050	−	1.07144i	−0.0427257	−	0.297164i	0.957243	−	0.289284i	$-0.0934173\pi$
$14$	−2.75200	−	1.76860i	−0.735502	−	0.472679i
$15$		0			0
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−3.45571	+	3.98810i	−0.838133	+	0.967257i	−0.999808	−	0.0195872i	$-0.993765\pi$
$17$	−3.45571	+	3.98810i	−0.838133	+	0.967257i	0.161675	+	0.986844i	$0.448310\pi$
$18$		0			0
$19$	−3.14602	+	2.72604i	−0.721747	+	0.625397i	−0.936253	−	0.351325i	$-0.885731\pi$
$19$	−3.14602	+	2.72604i	−0.721747	+	0.625397i	0.214507	+	0.976723i	$0.431186\pi$
$20$	−3.06298	−	0.899371i	−0.684902	−	0.201105i
$21$		0			0
$22$			4.72392i			1.00714i
$23$	−2.09132	−	4.31583i	−0.436070	−	0.899913i
$23$	−2.09132	−	4.31583i	−0.436070	−	0.899913i
$24$		0			0
$25$	2.15629	−	4.72161i	0.431258	−	0.944323i
$26$	0.304964	−	1.03861i	0.0598083	−	0.203688i
$27$		0			0
$28$	−1.76860	−	2.75200i	−0.334234	−	0.520079i
$29$	5.66626	+	4.90984i	1.05220	+	0.911734i	0.996235	−	0.0866988i	$-0.0276318\pi$
$29$	5.66626	+	4.90984i	1.05220	+	0.911734i	0.0559627	+	0.998433i	$0.482177\pi$
$30$		0			0
$31$	3.52714	−	1.03566i	0.633493	−	0.186010i	0.0508081	−	0.998708i	$-0.483820\pi$
$31$	3.52714	−	1.03566i	0.633493	−	0.186010i	0.582685	+	0.812698i	$0.302002\pi$
$32$	−0.540641	+	0.841254i	−0.0955727	+	0.148714i
$33$		0			0
$34$	−4.80014	+	2.19215i	−0.823217	+	0.375951i
$35$	9.49923	−	4.33816i	1.60566	−	0.733282i
$36$		0			0
$37$	5.70376	−	8.87523i	0.937693	−	1.45908i	0.0499432	−	0.998752i	$-0.484096\pi$
$37$	5.70376	−	8.87523i	0.937693	−	1.45908i	0.887750	−	0.460327i	$-0.152268\pi$
$38$	−3.99416	+	1.17279i	−0.647938	+	0.190252i
$39$		0			0
$40$	−2.41257	−	2.09050i	−0.381461	−	0.330537i
$41$	1.30727	+	2.03415i	0.204161	+	0.317680i	0.928202	−	0.372076i	$-0.121354\pi$
$41$	1.30727	+	2.03415i	0.204161	+	0.317680i	−0.724042	+	0.689756i	$0.757718\pi$
$42$		0			0
$43$	0.210901	−	0.718263i	0.0321621	−	0.109534i	−0.941848	−	0.336040i	$-0.890912\pi$
$43$	0.210901	−	0.718263i	0.0321621	−	0.109534i	0.974010	+	0.226506i	$0.0727303\pi$
$44$	−1.96239	+	4.29703i	−0.295841	+	0.647801i
$45$		0			0
$46$	−0.109472	−	4.79458i	−0.0161408	−	0.706923i
$47$			10.8153i			1.57757i	0.614667	+	0.788787i	$0.289290\pi$
$47$			10.8153i			1.57757i	−0.614667	+	0.788787i	$0.710710\pi$
$48$		0			0
$49$	3.55151	+	1.04282i	0.507359	+	0.148974i
$50$	3.92286	−	3.39918i	0.554776	−	0.480716i
$51$		0			0
$52$	0.708859	−	0.818067i	0.0983011	−	0.113445i
$53$	1.13317	−	7.88137i	0.155653	−	1.08259i	−0.750875	−	0.660444i	$-0.770368\pi$
$53$	1.13317	−	7.88137i	0.155653	−	1.08259i	0.906528	−	0.422146i	$-0.138723\pi$
$54$		0			0
$55$	−12.6862	−	8.15291i	−1.71060	−	1.09934i
$56$	−0.465555	−	3.23801i	−0.0622125	−	0.432697i
$57$		0			0
$58$	3.11459	+	6.81999i	0.408965	+	0.895509i
$59$	2.54689	−	0.366188i	0.331577	−	0.0476736i	0.0254842	−	0.999675i	$-0.491887\pi$
$59$	2.54689	−	0.366188i	0.331577	−	0.0476736i	0.306093	+	0.952002i	$0.400978\pi$
$60$		0			0
$61$	3.75802	+	12.7987i	0.481166	+	1.63870i	0.739875	+	0.672744i	$0.234885\pi$
$61$	3.75802	+	12.7987i	0.481166	+	1.63870i	−0.258709	+	0.965955i	$0.583297\pi$
$62$	3.63863	+	0.523156i	0.462106	+	0.0664409i
$63$		0			0
$64$	−0.841254	+	0.540641i	−0.105157	+	0.0675801i
$65$	2.26288	+	2.61150i	0.280676	+	0.323917i
$66$		0			0
$67$	7.20290	+	3.28945i	0.879974	+	0.401871i	0.803573	−	0.595206i	$-0.202930\pi$
$67$	7.20290	+	3.28945i	0.879974	+	0.401871i	0.0764013	+	0.997077i	$0.475657\pi$
$68$	−5.27701			−0.639932
$69$		0			0
$70$	10.4429			1.24817
$71$	−4.29582	−	1.96183i	−0.509820	−	0.232827i	0.143860	−	0.989598i	$-0.454048\pi$
$71$	−4.29582	−	1.96183i	−0.509820	−	0.232827i	−0.653680	+	0.756771i	$0.726776\pi$
$72$		0			0
$73$	2.51510	+	2.90258i	0.294370	+	0.339721i	0.883598	−	0.468245i	$-0.155114\pi$
$73$	2.51510	+	2.90258i	0.294370	+	0.339721i	−0.589228	+	0.807966i	$0.700568\pi$
$74$	8.87523	−	5.70376i	1.03172	−	0.663049i
$75$		0			0
$76$	−4.12041	−	0.592426i	−0.472644	−	0.0679559i
$77$	−4.35372	−	14.8274i	−0.496153	−	1.68974i
$78$		0			0
$79$	−9.45375	+	1.35924i	−1.06363	+	0.152927i	−0.651843	−	0.758354i	$-0.726004\pi$
$79$	−9.45375	+	1.35924i	−1.06363	+	0.152927i	−0.411786	+	0.911280i	$0.635095\pi$
$80$	−1.32612	−	2.90380i	−0.148265	−	0.324655i
$81$		0			0
$82$	0.344116	+	2.39338i	0.0380013	+	0.264305i
$83$	−11.8581	−	7.62072i	−1.30159	−	0.836482i	−0.308208	−	0.951319i	$-0.599729\pi$
$83$	−11.8581	−	7.62072i	−1.30159	−	0.836482i	−0.993384	+	0.114837i	$0.963365\pi$
$84$		0			0
$85$	2.39740	−	16.6743i	0.260034	−	1.80858i
$86$	0.490220	−	0.565744i	0.0528618	−	0.0610057i
$87$		0			0
$88$	−3.57010	+	3.09351i	−0.380574	+	0.329769i
$89$	3.83372	+	1.12568i	0.406373	+	0.119322i	0.478530	−	0.878071i	$-0.341170\pi$
$89$	3.83372	+	1.12568i	0.406373	+	0.119322i	−0.0721565	+	0.997393i	$0.522988\pi$
$90$		0			0
$91$			3.54105i			0.371203i
$92$	1.89216	−	4.40678i	0.197272	−	0.459439i
$93$		0			0
$94$	−4.49284	+	9.83794i	−0.463401	+	1.01471i
$95$	3.74388	−	12.7505i	0.384114	−	1.30817i
$96$		0			0
$97$	8.94718	+	13.9221i	0.908448	+	1.41357i	0.910470	+	0.413575i	$0.135720\pi$
$97$	8.94718	+	13.9221i	0.908448	+	1.41357i	−0.00202210	+	0.999998i	$0.500644\pi$
$98$	2.79737	+	2.42393i	0.282577	+	0.244854i
$99$		0			0
$100$	4.98043	−	1.46238i	0.498043	−	0.146238i
$101$	−0.750538	+	1.16786i	−0.0746814	+	0.116206i	−0.876585	−	0.481247i	$-0.840184\pi$
$101$	−0.750538	+	1.16786i	−0.0746814	+	0.116206i	0.801904	+	0.597453i	$0.203821\pi$
$102$		0			0
$103$	9.87197	−	4.50838i	0.972714	−	0.444224i	0.135307	−	0.990804i	$-0.456798\pi$
$103$	9.87197	−	4.50838i	0.972714	−	0.444224i	0.837407	+	0.546580i	$0.184071\pi$
$104$	0.984638	−	0.449669i	0.0965517	−	0.0440937i
$105$		0			0
$106$	4.30481	−	6.69841i	0.418120	−	0.650607i
$107$	−5.44399	+	1.59850i	−0.526291	+	0.154533i	−0.534075	−	0.845437i	$-0.679340\pi$
$107$	−5.44399	+	1.59850i	−0.526291	+	0.154533i	0.00778479	+	0.999970i	$0.497522\pi$
$108$		0			0
$109$	5.10528	+	4.42375i	0.488997	+	0.423719i	0.864142	−	0.503248i	$-0.167862\pi$
$109$	5.10528	+	4.42375i	0.488997	+	0.423719i	−0.375145	+	0.926966i	$0.622407\pi$
$110$	−8.15291	−	12.6862i	−0.777350	−	1.20958i
$111$		0			0
$112$	0.921633	−	3.13880i	0.0870862	−	0.296588i
$113$	−6.71202	+	14.6973i	−0.631414	+	1.38260i	0.275506	+	0.961299i	$0.411155\pi$
$113$	−6.71202	+	14.6973i	−0.631414	+	1.38260i	−0.906920	+	0.421304i	$0.861573\pi$
$114$		0			0
$115$	13.0649	+	7.98088i	1.21831	+	0.744221i
$116$			7.49753i			0.696128i
$117$		0			0
$118$	2.46885	+	0.724921i	0.227276	+	0.0667344i
$119$	13.0463	−	11.3047i	1.19595	−	1.03630i
$120$		0			0
$121$	−7.41001	+	8.55161i	−0.673638	+	0.777419i
$122$	−1.89833	+	13.2032i	−0.171867	+	1.19536i
$123$		0			0
$124$	3.09249	+	1.98742i	0.277714	+	0.178476i
$125$	0.0866298	+	0.602524i	0.00774841	+	0.0538914i
$126$		0			0
$127$	−6.28722	−	13.7671i	−0.557901	−	1.22163i	−0.952993	−	0.302991i	$-0.902015\pi$
$127$	−6.28722	−	13.7671i	−0.557901	−	1.22163i	0.395093	−	0.918641i	$-0.370712\pi$
$128$	−0.989821	+	0.142315i	−0.0874887	+	0.0125790i
$129$		0			0
$130$	0.973531	+	3.31554i	0.0853843	+	0.290792i
$131$	−1.89434	−	0.272365i	−0.165509	−	0.0237967i	0.0590619	−	0.998254i	$-0.481189\pi$
$131$	−1.89434	−	0.272365i	−0.165509	−	0.0237967i	−0.224571	+	0.974458i	$0.572098\pi$
$132$		0			0
$133$	11.4560	−	7.36230i	0.993358	−	0.638393i
$134$	5.18550	+	5.98438i	0.447959	+	0.516972i
$135$		0			0
$136$	−4.80014	−	2.19215i	−0.411609	−	0.187975i
$137$	5.52182			0.471761			0.235880	−	0.971782i	$-0.424203\pi$
$137$	5.52182			0.471761			0.235880	+	0.971782i	$0.424203\pi$
$138$		0			0
$139$	−11.3925			−0.966299			−0.483149	−	0.875538i	$-0.660507\pi$
$139$	−11.3925			−0.966299			−0.483149	+	0.875538i	$0.660507\pi$
$140$	9.49923	+	4.33816i	0.802832	+	0.366641i
$141$		0			0
$142$	−3.09264	−	3.56909i	−0.259528	−	0.299512i
$143$	4.30170	−	2.76454i	0.359726	−	0.231182i
$144$		0			0
$145$	−23.6906	−	3.40620i	−1.96740	−	0.282869i
$146$	1.08204	+	3.68509i	0.0895502	+	0.304980i
$147$		0			0
$148$	10.4426	−	1.50142i	0.858378	−	0.123416i
$149$	−2.12871	−	4.66122i	−0.174391	−	0.381862i	0.802173	−	0.597092i	$-0.203677\pi$
$149$	−2.12871	−	4.66122i	−0.174391	−	0.381862i	−0.976563	+	0.215230i	$0.930950\pi$
$150$		0			0
$151$	2.21999	+	15.4404i	0.180660	+	1.25652i	0.855207	+	0.518287i	$0.173430\pi$
$151$	2.21999	+	15.4404i	0.180660	+	1.25652i	−0.674547	+	0.738232i	$0.735661\pi$
$152$	−3.50196	−	2.25057i	−0.284046	−	0.182545i
$153$		0			0
$154$	2.19925	−	15.2961i	0.177220	−	1.23259i
$155$	−7.68478	+	8.86871i	−0.617257	+	0.712352i
$156$		0			0
$157$	−12.7886	+	11.0814i	−1.02064	+	0.884393i	−0.993338	−	0.115235i	$-0.963238\pi$
$157$	−12.7886	+	11.0814i	−1.02064	+	0.884393i	−0.0273052	+	0.999627i	$0.508693\pi$
$158$	−9.16408	−	2.69082i	−0.729055	−	0.214070i
$159$		0			0
$160$		−	3.19229i		−	0.252372i
$161$	4.76246	+	14.9483i	0.375334	+	1.17809i
$162$		0			0
$163$	0.468501	−	1.02587i	0.0366958	−	0.0803526i	−0.890396	−	0.455186i	$-0.849573\pi$
$163$	0.468501	−	1.02587i	0.0366958	−	0.0803526i	0.927092	+	0.374833i	$0.122300\pi$
$164$	−0.681228	+	2.32005i	−0.0531949	+	0.181165i
$165$		0			0
$166$	−7.62072	−	11.8581i	−0.591482	−	0.920364i
$167$	−12.2788	−	10.6396i	−0.950159	−	0.823318i	0.0342137	−	0.999415i	$-0.489107\pi$
$167$	−12.2788	−	10.6396i	−0.950159	−	0.823318i	−0.984373	+	0.176097i	$0.943653\pi$
$168$		0			0
$169$	11.3492	−	3.33241i	0.873012	−	0.256339i
$170$	9.10749	−	14.1715i	0.698513	−	1.08691i
$171$		0			0
$172$	0.680938	−	0.310974i	0.0519211	−	0.0237116i
$173$	8.99441	−	4.10761i	0.683832	−	0.312296i	−0.0430353	−	0.999074i	$-0.513703\pi$
$173$	8.99441	−	4.10761i	0.683832	−	0.312296i	0.726867	+	0.686778i	$0.240976\pi$
$174$		0			0
$175$	−9.18025	+	14.2848i	−0.693962	+	1.07983i
$176$	−4.53257	+	1.33088i	−0.341655	+	0.100319i
$177$		0			0
$178$	3.01965	+	2.61654i	0.226332	+	0.196118i
$179$	−4.95212	−	7.70564i	−0.370139	−	0.575947i	0.605360	−	0.795952i	$-0.293029\pi$
$179$	−4.95212	−	7.70564i	−0.370139	−	0.575947i	−0.975499	+	0.220005i	$0.929393\pi$
$180$		0			0
$181$	−4.49976	+	15.3248i	−0.334465	+	1.13908i	0.604940	+	0.796271i	$0.293197\pi$
$181$	−4.49976	+	15.3248i	−0.334465	+	1.13908i	−0.939404	+	0.342811i	$0.888621\pi$
$182$	−1.47101	+	3.22105i	−0.109038	+	0.238760i
$183$		0			0
$184$	3.55181	−	3.22252i	0.261843	−	0.237567i
$185$			33.6786i			2.47610i
$186$		0			0
$187$	−23.9184	−	7.02308i	−1.74909	−	0.513579i
$188$	−8.17366	+	7.08251i	−0.596125	+	0.516545i
$189$		0			0
$190$	8.70231	−	10.0430i	0.631332	−	0.728595i
$191$	1.08965	−	7.57868i	0.0788443	−	0.548374i	−0.911666	−	0.410933i	$-0.865203\pi$
$191$	1.08965	−	7.57868i	0.0788443	−	0.548374i	0.990510	−	0.137441i	$-0.0438878\pi$
$192$		0			0
$193$	8.55701	+	5.49926i	0.615947	+	0.395845i	0.811083	−	0.584931i	$-0.198878\pi$
$193$	8.55701	+	5.49926i	0.615947	+	0.395845i	−0.195136	+	0.980776i	$0.562515\pi$
$194$	2.35520	+	16.3808i	0.169093	+	1.17607i
$195$		0			0
$196$	1.53764	+	3.36695i	0.109831	+	0.240497i
$197$	11.9411	−	1.71687i	0.850768	−	0.122322i	0.296881	−	0.954914i	$-0.404053\pi$
$197$	11.9411	−	1.71687i	0.850768	−	0.122322i	0.553886	+	0.832592i	$0.313144\pi$
$198$		0			0
$199$	−2.69243	−	9.16956i	−0.190861	−	0.650013i	−0.998203	−	0.0599287i	$-0.980913\pi$
$199$	−2.69243	−	9.16956i	−0.190861	−	0.650013i	0.807342	−	0.590084i	$-0.200906\pi$
$200$	5.13785	+	0.738711i	0.363301	+	0.0522348i
$201$		0			0
$202$	−1.16786	+	0.750538i	−0.0821704	+	0.0528077i
$203$	−16.0616	−	18.5361i	−1.12730	−	1.30098i
$204$		0			0
$205$	−7.02138	−	3.20656i	−0.490395	−	0.223956i
$206$	10.8527			0.756144
$207$		0			0
$208$	1.08246			0.0750549
$209$	−17.8876	−	8.16899i	−1.23731	−	0.565061i
$210$		0			0
$211$	−2.26736	−	2.61667i	−0.156091	−	0.180139i	0.672318	−	0.740263i	$-0.265299\pi$
$211$	−2.26736	−	2.61667i	−0.156091	−	0.180139i	−0.828409	+	0.560124i	$0.810754\pi$
$212$	6.69841	−	4.30481i	0.460049	−	0.295655i
$213$		0			0
$214$	−5.61607	−	0.807469i	−0.383907	−	0.0551975i
$215$	0.673257	+	2.29290i	0.0459157	+	0.156375i
$216$		0			0
$217$	−11.9031	+	1.71140i	−0.808033	+	0.116178i
$218$	2.80624	+	6.14480i	0.190062	+	0.416178i
$219$		0			0
$220$	−2.14612	−	14.9266i	−0.144691	−	1.00635i
$221$	4.80536	+	3.08822i	0.323244	+	0.207736i
$222$		0			0
$223$	1.38738	−	9.64943i	0.0929057	−	0.646173i	−0.889155	−	0.457607i	$-0.848707\pi$
$223$	1.38738	−	9.64943i	0.0929057	−	0.646173i	0.982060	−	0.188567i	$-0.0603841\pi$
$224$	2.14225	−	2.47229i	0.143135	−	0.165187i
$225$		0			0
$226$	−12.2109	+	10.5808i	−0.812259	+	0.703827i
$227$	11.6008	+	3.40630i	0.769971	+	0.226084i	0.643045	−	0.765828i	$-0.277671\pi$
$227$	11.6008	+	3.40630i	0.769971	+	0.226084i	0.126926	+	0.991912i	$0.459489\pi$
$228$		0			0
$229$		−	19.1954i		−	1.26847i	−0.773141	−	0.634234i	$-0.781316\pi$
$229$		−	19.1954i		−	1.26847i	0.773141	−	0.634234i	$-0.218684\pi$
$230$	8.56886	+	12.6870i	0.565014	+	0.836557i
$231$		0			0
$232$	−3.11459	+	6.81999i	−0.204483	+	0.447755i
$233$	−4.95884	+	16.8883i	−0.324865	+	1.10639i	0.621534	+	0.783387i	$0.286510\pi$
$233$	−4.95884	+	16.8883i	−0.324865	+	1.10639i	−0.946399	+	0.323000i	$0.895309\pi$
$234$		0			0
$235$	−18.6659	−	29.0447i	−1.21763	−	1.89467i
$236$	1.94461	+	1.68501i	0.126583	+	0.109685i
$237$		0			0
$238$	16.5635	−	4.86347i	1.07365	−	0.315252i
$239$	−8.19549	+	12.7524i	−0.530122	+	0.824886i	−0.998272	−	0.0587629i	$-0.981284\pi$
$239$	−8.19549	+	12.7524i	−0.530122	+	0.824886i	0.468150	+	0.883649i	$0.344921\pi$
$240$		0			0
$241$	26.0722	−	11.9068i	1.67946	−	0.766982i	0.680027	−	0.733187i	$-0.261968\pi$
$241$	26.0722	−	11.9068i	1.67946	−	0.766982i	0.999429	−	0.0337950i	$-0.0107593\pi$
$242$	−10.2929	+	4.70059i	−0.661650	+	0.302165i
$243$		0			0
$244$	−7.21159	+	11.2215i	−0.461675	+	0.718380i
$245$	−11.3374	+	3.32897i	−0.724322	+	0.212680i
$246$		0			0
$247$	3.40543	+	2.95083i	0.216683	+	0.187757i
$248$	1.98742	+	3.09249i	0.126201	+	0.196373i
$249$		0			0
$250$	−0.171496	+	0.584062i	−0.0108464	+	0.0369393i
$251$	−7.34958	+	16.0933i	−0.463902	+	1.01580i	0.522679	+	0.852529i	$0.324933\pi$
$251$	−7.34958	+	16.0933i	−0.463902	+	1.01580i	−0.986581	+	0.163274i	$0.947795\pi$
$252$		0			0
$253$	14.4413	−	17.4558i	0.907914	−	1.09744i
$254$		−	15.1348i		−	0.949642i
$255$		0			0
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−4.14944	+	3.59551i	−0.258835	+	0.224282i	−0.774605	−	0.632445i	$-0.782051\pi$
$257$	−4.14944	+	3.59551i	−0.258835	+	0.224282i	0.515770	+	0.856727i	$0.327506\pi$
$258$		0			0
$259$	−22.6007	+	26.0827i	−1.40434	+	1.62070i
$260$	−0.491771	+	3.42034i	−0.0304983	+	0.212121i
$261$		0			0
$262$	−1.61001	−	1.03469i	−0.0994667	−	0.0639234i
$263$	3.23229	+	22.4811i	0.199312	+	1.38624i	0.806288	+	0.591523i	$0.201473\pi$
$263$	3.23229	+	22.4811i	0.199312	+	1.38624i	−0.606977	+	0.794720i	$0.707618\pi$
$264$		0			0
$265$	10.5591	+	23.1213i	0.648643	+	1.42033i
$266$	13.4791	−	1.93801i	0.826458	−	0.118827i
$267$		0			0
$268$	2.23089	+	7.59772i	0.136273	+	0.464105i
$269$	−9.09935	−	1.30829i	−0.554797	−	0.0797678i	−0.140787	−	0.990040i	$-0.544963\pi$
$269$	−9.09935	−	1.30829i	−0.554797	−	0.0797678i	−0.414010	+	0.910272i	$0.635872\pi$
$270$		0			0
$271$	−14.8363	+	9.53471i	−0.901241	+	0.579192i	−0.907158	−	0.420790i	$-0.861753\pi$
$271$	−14.8363	+	9.53471i	−0.901241	+	0.579192i	0.00591736	+	0.999982i	$0.498116\pi$
$272$	−3.45571	−	3.98810i	−0.209533	−	0.241814i
$273$		0			0
$274$	5.02282	+	2.29385i	0.303440	+	0.138576i
$275$	24.5204			1.47863
$276$		0			0
$277$	22.0016			1.32195			0.660973	−	0.750410i	$-0.270144\pi$
$277$	22.0016			1.32195			0.660973	+	0.750410i	$0.270144\pi$
$278$	−10.3630	−	4.73261i	−0.621530	−	0.283843i
$279$		0			0
$280$	6.83867	+	7.89225i	0.408689	+	0.471652i
$281$	−5.79828	+	3.72633i	−0.345896	+	0.222294i	−0.702041	−	0.712137i	$-0.747728\pi$
$281$	−5.79828	+	3.72633i	−0.345896	+	0.222294i	0.356144	+	0.934431i	$0.384091\pi$
$282$		0			0
$283$	6.47874	+	0.931503i	0.385121	+	0.0553721i	0.332157	−	0.943224i	$-0.392224\pi$
$283$	6.47874	+	0.931503i	0.385121	+	0.0553721i	0.0529648	+	0.998596i	$0.483133\pi$
$284$	−1.33051	−	4.53129i	−0.0789510	−	0.268883i
$285$		0			0
$286$	5.06139	−	0.727719i	0.299286	−	0.0430309i
$287$	−3.28593	−	7.19519i	−0.193962	−	0.424719i
$288$		0			0
$289$	−1.54367	−	10.7365i	−0.0908043	−	0.631558i
$290$	−20.1348	−	12.9398i	−1.18235	−	0.759853i
$291$		0			0
$292$	−0.546583	+	3.80157i	−0.0319864	+	0.222470i
$293$	15.9060	−	18.3566i	0.929241	−	1.07240i	−0.0679638	−	0.997688i	$-0.521650\pi$
$293$	15.9060	−	18.3566i	0.929241	−	1.07240i	0.997205	−	0.0747138i	$-0.0238043\pi$
$294$		0			0
$295$	−6.20774	+	5.37903i	−0.361428	+	0.313180i
$296$	10.1227	+	2.97228i	0.588367	+	0.172760i
$297$		0			0
$298$		−	5.12430i		−	0.296842i
$299$	−4.30198	+	2.90558i	−0.248790	+	0.168034i
$300$		0			0
$301$	−1.01729	+	2.22756i	−0.0586357	+	0.128394i
$302$	−4.39479	+	14.9673i	−0.252892	+	0.861270i
$303$		0			0
$304$	−2.25057	−	3.50196i	−0.129079	−	0.200851i
$305$	−32.1812	−	27.8852i	−1.84269	−	1.59670i
$306$		0			0
$307$	5.75288	−	1.68920i	0.328334	−	0.0964076i	−0.113411	−	0.993548i	$-0.536178\pi$
$307$	5.75288	−	1.68920i	0.328334	−	0.0964076i	0.441745	+	0.897141i	$0.354360\pi$
$308$	8.35473	−	13.0002i	0.476055	−	0.740756i
$309$		0			0
$310$	−10.6745	+	4.87489i	−0.606272	+	0.276875i
$311$	25.7896	−	11.7777i	1.46239	−	0.667852i	0.484087	−	0.875020i	$-0.339152\pi$
$311$	25.7896	−	11.7777i	1.46239	−	0.667852i	0.978305	+	0.207168i	$0.0664246\pi$
$312$		0			0
$313$	−4.73420	+	7.36656i	−0.267593	+	0.416383i	−0.948882	−	0.315632i	$-0.897783\pi$
$313$	−4.73420	+	7.36656i	−0.267593	+	0.416383i	0.681289	+	0.732015i	$0.261420\pi$
$314$	−16.2363	+	4.76742i	−0.916269	+	0.269041i
$315$		0			0
$316$	−7.21814	−	6.25455i	−0.406052	−	0.351846i
$317$	14.3203	+	22.2828i	0.804308	+	1.25153i	0.964406	+	0.264426i	$0.0851825\pi$
$317$	14.3203	+	22.2828i	0.804308	+	1.25153i	−0.160098	+	0.987101i	$0.551181\pi$
$318$		0			0
$319$	−9.97833	+	33.9831i	−0.558679	+	1.90269i
$320$	1.32612	−	2.90380i	0.0741325	−	0.162328i
$321$		0			0
$322$	−1.87767	+	15.5759i	−0.104639	+	0.868009i
$323$		−	21.9671i		−	1.22228i
$324$		0			0
$325$	−5.39110	−	1.58297i	−0.299044	−	0.0878074i
$326$	0.852327	−	0.738545i	0.0472060	−	0.0409042i
$327$		0			0
$328$	−1.58345	+	1.82740i	−0.0874314	+	0.100901i
$329$	5.03512	−	35.0200i	0.277595	−	1.93072i
$330$		0			0
$331$	4.69565	+	3.01771i	0.258096	+	0.165868i	0.663290	−	0.748362i	$-0.269160\pi$
$331$	4.69565	+	3.01771i	0.258096	+	0.165868i	−0.405194	+	0.914231i	$0.632796\pi$
$332$	−2.00603	−	13.9522i	−0.110095	−	0.765728i
$333$		0			0
$334$	−6.74930	−	14.7789i	−0.369305	−	0.808666i
$335$	−25.0207	+	3.59744i	−1.36703	+	0.196549i
$336$		0			0
$337$	8.36186	+	28.4779i	0.455499	+	1.55129i	0.792553	+	0.609803i	$0.208751\pi$
$337$	8.36186	+	28.4779i	0.455499	+	1.55129i	−0.337054	+	0.941485i	$0.609430\pi$
$338$	11.7079	+	1.68334i	0.636825	+	0.0915617i
$339$		0			0
$340$	14.1715	−	9.10749i	0.768559	−	0.493923i
$341$	11.3719	+	13.1239i	0.615822	+	0.710696i
$342$		0			0
$343$	9.81546	+	4.48257i	0.529985	+	0.242036i
$344$	0.748587			0.0403611
$345$		0			0
$346$	9.88796			0.531580
$347$	9.19943	+	4.20124i	0.493851	+	0.225534i	0.646742	−	0.762709i	$-0.276131\pi$
$347$	9.19943	+	4.20124i	0.493851	+	0.225534i	−0.152891	+	0.988243i	$0.548858\pi$
$348$		0			0
$349$	−20.3393	−	23.4728i	−1.08874	−	1.25647i	−0.964462	−	0.264223i	$-0.914885\pi$
$349$	−20.3393	−	23.4728i	−1.08874	−	1.25647i	−0.124276	−	0.992248i	$-0.539661\pi$
$350$	−14.2848	+	9.18025i	−0.763552	+	0.490705i
$351$		0			0
$352$	−4.67584	−	0.672284i	−0.249223	−	0.0358328i
$353$	0.370038	+	1.26023i	0.0196951	+	0.0670754i	0.968754	−	0.248023i	$-0.0797808\pi$
$353$	0.370038	+	1.26023i	0.0196951	+	0.0670754i	−0.949059	+	0.315098i	$0.897963\pi$
$354$		0			0
$355$	14.9224	−	2.14552i	0.791999	−	0.113872i
$356$	1.65982	+	3.63449i	0.0879702	+	0.192628i
$357$		0			0
$358$	−1.30356	−	9.06648i	−0.0688955	−	0.479179i
$359$	12.1285	+	7.79451i	0.640117	+	0.411378i	0.820043	−	0.572302i	$-0.193949\pi$
$359$	12.1285	+	7.79451i	0.640117	+	0.411378i	−0.179926	+	0.983680i	$0.557586\pi$
$360$		0			0
$361$	−0.237843	+	1.65423i	−0.0125181	+	0.0870650i
$362$	−10.4593	+	12.0706i	−0.549727	+	0.634419i
$363$		0			0
$364$	−2.67615	+	2.31889i	−0.140268	+	0.121543i
$365$	−11.7639	−	3.45418i	−0.615748	−	0.180800i
$366$		0			0
$367$		−	14.2006i		−	0.741265i	−0.928780	−	0.370633i	$-0.879141\pi$
$367$		−	14.2006i		−	0.741265i	0.928780	−	0.370633i	$-0.120859\pi$
$368$	4.56953	−	1.45583i	0.238203	−	0.0758903i
$369$		0			0
$370$	−13.9906	+	30.6352i	−0.727337	+	1.59265i
$371$	−7.33843	+	24.9924i	−0.380992	+	1.29754i
$372$		0			0
$373$	−16.2595	−	25.3003i	−0.841885	−	1.31000i	−0.948847	−	0.315736i	$-0.897749\pi$
$373$	−16.2595	−	25.3003i	−0.841885	−	1.31000i	0.106962	−	0.994263i	$-0.465888\pi$
$374$	−18.8395	−	16.3245i	−0.974166	−	0.844119i
$375$		0			0
$376$	−10.3772	+	3.04702i	−0.535163	+	0.157138i
$377$	4.38771	−	6.82741i	0.225979	−	0.351630i
$378$		0			0
$379$	25.3298	−	11.5678i	1.30111	−	0.594196i	0.360204	−	0.932873i	$-0.382707\pi$
$379$	25.3298	−	11.5678i	1.30111	−	0.594196i	0.940902	+	0.338678i	$0.109980\pi$
$380$	12.0879	−	5.52036i	0.620097	−	0.283189i
$381$		0			0
$382$	4.13948	−	6.44115i	0.211794	−	0.329558i
$383$	−30.3204	+	8.90286i	−1.54930	+	0.454915i	−0.940891	−	0.338710i	$-0.890009\pi$
$383$	−30.3204	+	8.90286i	−1.54930	+	0.454915i	−0.608407	+	0.793625i	$0.708191\pi$
$384$		0			0
$385$	37.2823	+	32.3053i	1.90008	+	1.64643i
$386$	5.49926	+	8.55701i	0.279905	+	0.435540i
$387$		0			0
$388$	−4.66245	+	15.8788i	−0.236700	+	0.806126i
$389$	14.7044	−	32.1982i	0.745543	−	1.63251i	−0.0286708	−	0.999589i	$-0.509127\pi$
$389$	14.7044	−	32.1982i	0.745543	−	1.63251i	0.774214	−	0.632924i	$-0.218145\pi$
$390$		0			0
$391$	24.4390	+	6.57385i	1.23593	+	0.332454i
$392$			3.70144i			0.186951i
$393$		0			0
$394$	11.5752	+	3.39879i	0.583151	+	0.171229i
$395$	23.0423	−	19.9663i	1.15939	−	1.00461i
$396$		0			0
$397$	3.52863	−	4.07225i	0.177097	−	0.204381i	−0.660260	−	0.751037i	$-0.729554\pi$
$397$	3.52863	−	4.07225i	0.177097	−	0.204381i	0.837357	+	0.546656i	$0.184100\pi$
$398$	1.36006	−	9.45940i	0.0681735	−	0.474157i
$399$		0			0
$400$	4.36668	+	2.80630i	0.218334	+	0.140315i
$401$	−3.13847	−	21.8285i	−0.156728	−	1.09006i	−0.904612	−	0.426235i	$-0.859840\pi$
$401$	−3.13847	−	21.8285i	−0.156728	−	1.09006i	0.747885	−	0.663829i	$-0.231070\pi$
$402$		0			0
$403$	−1.65300	−	3.61958i	−0.0823420	−	0.180304i
$404$	−1.37411	+	0.197567i	−0.0683644	+	0.00982932i
$405$		0			0
$406$	−6.90998	−	23.5332i	−0.342936	−	1.16793i
$407$	49.3301	+	7.09260i	2.44520	+	0.351567i
$408$		0			0
$409$	14.2200	−	9.13866i	0.703135	−	0.451878i	−0.139599	−	0.990208i	$-0.544581\pi$
$409$	14.2200	−	9.13866i	0.703135	−	0.451878i	0.842734	+	0.538331i	$0.180945\pi$
$410$	−5.05482	−	5.83358i	−0.249640	−	0.288100i
$411$		0			0
$412$	9.87197	+	4.50838i	0.486357	+	0.222112i
$413$	−8.41734			−0.414190
$414$		0			0
$415$	44.9975			2.20884
$416$	0.984638	+	0.449669i	0.0482759	+	0.0220468i
$417$		0			0
$418$	−12.8776	−	14.8615i	−0.629864	−	0.726902i
$419$	24.3907	−	15.6750i	1.19156	−	0.765772i	0.214087	−	0.976815i	$-0.431322\pi$
$419$	24.3907	−	15.6750i	1.19156	−	0.765772i	0.977477	+	0.211043i	$0.0676860\pi$
$420$		0			0
$421$	−11.9365	−	1.71621i	−0.581749	−	0.0836429i	−0.154843	−	0.987939i	$-0.549487\pi$
$421$	−11.9365	−	1.71621i	−0.581749	−	0.0836429i	−0.426906	+	0.904296i	$0.640396\pi$
$422$	−0.975457	−	3.32210i	−0.0474845	−	0.161717i
$423$		0			0
$424$	7.88137	−	1.13317i	0.382753	−	0.0550316i
$425$	11.3788	+	24.9160i	0.551951	+	1.20860i
$426$		0			0
$427$	−6.21003	−	43.1917i	−0.300525	−	2.09019i
$428$	−4.77312	−	3.06750i	−0.230718	−	0.148273i
$429$		0			0
$430$	−0.340090	+	2.36538i	−0.0164006	+	0.114069i
$431$	6.46200	−	7.45755i	0.311264	−	0.359217i	−0.578465	−	0.815707i	$-0.696348\pi$
$431$	6.46200	−	7.45755i	0.311264	−	0.359217i	0.889729	+	0.456490i	$0.150893\pi$
$432$		0			0
$433$	14.7674	−	12.7960i	0.709675	−	0.614937i	−0.223354	−	0.974737i	$-0.571701\pi$
$433$	14.7674	−	12.7960i	0.709675	−	0.614937i	0.933029	+	0.359800i	$0.117155\pi$
$434$	−11.5384	−	3.38797i	−0.553859	−	0.162628i
$435$		0			0
$436$			6.75526i			0.323518i
$437$	18.3445	+	7.87666i	0.877535	+	0.376792i
$438$		0			0
$439$	5.65584	−	12.3846i	0.269938	−	0.591083i	−0.725313	−	0.688419i	$-0.758305\pi$
$439$	5.65584	−	12.3846i	0.269938	−	0.591083i	0.995252	+	0.0973364i	$0.0310323\pi$
$440$	4.24855	−	14.4692i	0.202542	−	0.689794i
$441$		0			0
$442$	3.08822	+	4.80536i	0.146892	+	0.228568i
$443$	−17.5268	−	15.1870i	−0.832722	−	0.721558i	0.130156	−	0.991493i	$-0.458452\pi$
$443$	−17.5268	−	15.1870i	−0.832722	−	0.721558i	−0.962878	+	0.269936i	$0.912998\pi$
$444$		0			0
$445$	−12.2383	+	3.59349i	−0.580152	+	0.170348i
$446$	5.27052	−	8.20109i	0.249566	−	0.388333i
$447$		0			0
$448$	2.97568	−	1.35895i	0.140588	−	0.0642043i
$449$	0.780664	−	0.356517i	0.0368418	−	0.0168251i	−0.396909	−	0.917858i	$-0.629917\pi$
$449$	0.780664	−	0.356517i	0.0368418	−	0.0168251i	0.433751	+	0.901033i	$0.357190\pi$
$450$		0			0
$451$	−6.17542	+	9.60914i	−0.290789	+	0.452477i
$452$	−15.5029	+	4.55206i	−0.729195	+	0.214111i
$453$		0			0
$454$	9.13741	+	7.91761i	0.428840	+	0.371592i
$455$	−6.11143	−	9.50957i	−0.286508	−	0.445815i
$456$		0			0
$457$	9.85506	−	33.5632i	0.461000	−	1.57002i	−0.321210	−	0.947008i	$-0.604090\pi$
$457$	9.85506	−	33.5632i	0.461000	−	1.57002i	0.782210	−	0.623015i	$-0.214092\pi$
$458$	7.97405	−	17.4607i	0.372603	−	0.815887i
$459$		0			0
$460$	2.52413	+	15.1001i	0.117688	+	0.704048i
$461$			14.5940i			0.679712i	0.940477	+	0.339856i	$0.110378\pi$
$461$			14.5940i			0.679712i	−0.940477	+	0.339856i	$0.889622\pi$
$462$		0			0
$463$	−6.16018	−	1.80879i	−0.286288	−	0.0840617i	0.135436	−	0.990786i	$-0.456757\pi$
$463$	−6.16018	−	1.80879i	−0.286288	−	0.0840617i	−0.421724	+	0.906724i	$0.638575\pi$
$464$	−5.66626	+	4.90984i	−0.263049	+	0.227934i
$465$		0			0
$466$	−11.5264	+	13.3021i	−0.533948	+	0.616209i
$467$	2.06239	−	14.3442i	0.0954359	−	0.663772i	−0.884805	−	0.465962i	$-0.845708\pi$
$467$	2.06239	−	14.3442i	0.0954359	−	0.663772i	0.980241	−	0.197809i	$-0.0633827\pi$
$468$		0			0
$469$	−21.7916	−	14.0046i	−1.00624	−	0.646674i
$470$	−4.91349	−	34.1741i	−0.226643	−	1.57633i
$471$		0			0
$472$	1.06890	+	2.34056i	0.0492000	+	0.107733i
$473$	3.50027	−	0.503262i	0.160942	−	0.0231400i
$474$		0			0
$475$	6.08759	+	20.7324i	0.279318	+	0.951269i
$476$	17.0870	+	2.45674i	0.783182	+	0.112605i
$477$		0			0
$478$	−12.7524	+	8.19549i	−0.583283	+	0.374853i
$479$	17.9024	+	20.6605i	0.817981	+	0.944000i	0.999222	−	0.0394384i	$-0.0125569\pi$
$479$	17.9024	+	20.6605i	0.817981	+	0.944000i	−0.181241	+	0.983439i	$0.558011\pi$
$480$		0			0
$481$	−10.3879	−	4.74401i	−0.473649	−	0.216308i
$482$	28.6623			1.30553
$483$		0			0
$484$	−11.3154			−0.514336
$485$	−48.0557	−	21.9463i	−2.18210	−	0.996529i
$486$		0			0
$487$	22.1371	+	25.5476i	1.00313	+	1.15767i	0.987472	+	0.157794i	$0.0504383\pi$
$487$	22.1371	+	25.5476i	1.00313	+	1.15767i	0.0156562	+	0.999877i	$0.495016\pi$
$488$	−11.2215	+	7.21159i	−0.507972	+	0.326454i
$489$		0			0
$490$	−11.6958	−	1.68160i	−0.528362	−	0.0759670i
$491$	10.2982	+	35.0724i	0.464751	+	1.58280i	0.774884	+	0.632103i	$0.217808\pi$
$491$	10.2982	+	35.0724i	0.464751	+	1.58280i	−0.310133	+	0.950693i	$0.600374\pi$
$492$		0			0
$493$	−39.1619	+	5.63063i	−1.76376	+	0.253591i
$494$	1.87187	+	4.09883i	0.0842196	+	0.184415i
$495$		0			0
$496$	0.523156	+	3.63863i	0.0234904	+	0.163379i
$497$	12.9966	+	8.35238i	0.582975	+	0.374655i
$498$		0			0
$499$	5.44390	−	37.8631i	0.243702	−	1.69499i	−0.389521	−	0.921018i	$-0.627359\pi$
$499$	5.44390	−	37.8631i	0.243702	−	1.69499i	0.633223	−	0.773969i	$-0.281732\pi$
$500$	−0.398627	+	0.460040i	−0.0178271	+	0.0205736i
$501$		0			0
$502$	−13.3708	+	11.5859i	−0.596770	+	0.517104i
$503$	−15.5862	−	4.57651i	−0.694953	−	0.204057i	−0.0848675	−	0.996392i	$-0.527047\pi$
$503$	−15.5862	−	4.57651i	−0.694953	−	0.204057i	−0.610085	+	0.792336i	$0.708865\pi$
$504$		0			0
$505$		−	4.43165i		−	0.197206i
$506$	20.3876	−	9.87923i	0.906340	−	0.439185i
$507$		0			0
$508$	6.28722	−	13.7671i	0.278950	−	0.610816i
$509$	−7.00992	+	23.8736i	−0.310709	+	1.05818i	0.645078	+	0.764117i	$0.276825\pi$
$509$	−7.00992	+	23.8736i	−0.310709	+	1.05818i	−0.955787	+	0.294061i	$0.904993\pi$
$510$		0			0
$511$	−6.79260	−	10.5695i	−0.300487	−	0.467567i
$512$	−0.755750	−	0.654861i	−0.0333997	−	0.0289410i
$513$		0			0
$514$	−5.26809	+	1.54685i	−0.232365	+	0.0682286i
$515$	−18.7305	+	29.1452i	−0.825363	+	1.28429i
$516$		0			0
$517$	−46.4736	+	21.2238i	−2.04391	+	0.933421i
$518$	−31.3935	+	14.3369i	−1.37935	+	0.629928i
$519$		0			0
$520$	−1.86819	+	2.90696i	−0.0819256	+	0.127479i
$521$	12.3392	−	3.62310i	0.540588	−	0.158731i	−2.85397e−5	−	1.00000i	$-0.500009\pi$
$521$	12.3392	−	3.62310i	0.540588	−	0.158731i	0.540617	+	0.841269i	$0.318191\pi$
$522$		0			0
$523$	8.64680	+	7.49250i	0.378098	+	0.327624i	0.823090	−	0.567911i	$-0.192248\pi$
$523$	8.64680	+	7.49250i	0.378098	+	0.327624i	−0.444992	+	0.895535i	$0.646794\pi$
$524$	−1.03469	−	1.61001i	−0.0452006	−	0.0703336i
$525$		0			0
$526$	−6.39878	+	21.7922i	−0.279000	+	0.950187i
$527$	−8.05845	+	17.6455i	−0.351032	+	0.768652i
$528$		0			0
$529$	−14.2528	+	18.0516i	−0.619685	+	0.784851i
$530$			25.4183i			1.10410i
$531$		0			0
$532$	13.0661	+	3.83656i	0.566488	+	0.166336i
$533$	1.97808	−	1.71402i	0.0856802	−	0.0742423i
$534$		0			0
$535$	11.8611	−	13.6885i	0.512802	−	0.591805i
$536$	−1.12692	+	7.83788i	−0.0486754	+	0.338545i
$537$		0			0
$538$	−7.73358	−	4.97007i	−0.333418	−	0.214275i
$539$	2.48842	+	17.3073i	0.107184	+	0.745480i
$540$		0			0
$541$	8.29874	+	18.1717i	0.356791	+	0.781262i	0.999880	+	0.0154715i	$0.00492492\pi$
$541$	8.29874	+	18.1717i	0.356791	+	0.781262i	−0.643090	+	0.765791i	$0.722348\pi$
$542$	−17.4564	+	2.50986i	−0.749818	+	0.107808i
$543$		0			0
$544$	−1.48671	−	5.06326i	−0.0637420	−	0.217085i
$545$	−21.3452	−	3.06898i	−0.914328	−	0.131461i
$546$		0			0
$547$	−12.6685	+	8.14152i	−0.541664	+	0.348106i	−0.782689	−	0.622412i	$-0.786153\pi$
$547$	−12.6685	+	8.14152i	−0.541664	+	0.348106i	0.241025	+	0.970519i	$0.422516\pi$
$548$	3.61602	+	4.17311i	0.154469	+	0.178266i
$549$		0			0
$550$	22.3045	+	10.1861i	0.951068	+	0.434338i
$551$	−31.2106			−1.32962
$552$		0			0
$553$	31.2441			1.32864
$554$	20.0133	+	9.13978i	0.850285	+	0.388312i
$555$		0			0
$556$	−7.46050	−	8.60987i	−0.316396	−	0.365140i
$557$	20.8117	−	13.3749i	0.881819	−	0.566711i	−0.0195273	−	0.999809i	$-0.506216\pi$
$557$	20.8117	−	13.3749i	0.881819	−	0.566711i	0.901347	+	0.433099i	$0.142580\pi$
$558$		0			0
$559$	−0.802065	−	0.115320i	−0.0339238	−	0.00487750i
$560$	2.94212	+	10.0199i	0.124327	+	0.423419i
$561$		0			0
$562$	−6.82227	+	0.980895i	−0.287780	+	0.0413765i
$563$	−13.1435	−	28.7803i	−0.553933	−	1.21294i	−0.954921	−	0.296861i	$-0.904060\pi$
$563$	−13.1435	−	28.7803i	−0.553933	−	1.21294i	0.400987	−	0.916084i	$-0.368667\pi$
$564$		0			0
$565$	−7.34045	−	51.0540i	−0.308815	−	2.14786i
$566$	5.50631	+	3.53869i	0.231448	+	0.148742i
$567$		0			0
$568$	0.672094	−	4.67452i	0.0282005	−	0.196138i
$569$	6.75217	−	7.79242i	0.283066	−	0.326675i	−0.596355	−	0.802721i	$-0.703385\pi$
$569$	6.75217	−	7.79242i	0.283066	−	0.326675i	0.879421	+	0.476046i	$0.157930\pi$
$570$		0			0
$571$	−1.29723	+	1.12406i	−0.0542874	+	0.0470403i	−0.681582	−	0.731742i	$-0.738708\pi$
$571$	−1.29723	+	1.12406i	−0.0542874	+	0.0470403i	0.627295	+	0.778782i	$0.284162\pi$
$572$	4.90631	+	1.44062i	0.205143	+	0.0602355i
$573$		0			0
$574$		−	7.91000i		−	0.330157i
$575$	−24.8872	+	0.568235i	−1.03787	+	0.0236970i
$576$		0			0
$577$	−8.82431	+	19.3225i	−0.367361	+	0.804408i	0.632201	+	0.774805i	$0.282152\pi$
$577$	−8.82431	+	19.3225i	−0.367361	+	0.804408i	−0.999562	+	0.0296035i	$0.990576\pi$
$578$	3.05592	−	10.4075i	0.127110	−	0.432895i
$579$		0			0
$580$	−12.9398	−	20.1348i	−0.537297	−	0.836051i
$581$	34.8487	+	30.1965i	1.44577	+	1.25276i
$582$		0			0
$583$	36.0902	−	10.5970i	1.49470	−	0.438884i
$584$	−2.07642	+	3.23097i	−0.0859228	+	0.133699i
$585$		0			0
$586$	22.0942	−	10.0901i	0.912705	−	0.416818i
$587$	−5.09175	+	2.32533i	−0.210159	+	0.0959765i	−0.517714	−	0.855554i	$-0.673217\pi$
$587$	−5.09175	+	2.32533i	−0.210159	+	0.0959765i	0.307554	+	0.951531i	$0.400489\pi$
$588$		0			0
$589$	−8.27320	+	12.8734i	−0.340891	+	0.530437i
$590$	−7.88129	+	2.31415i	−0.324467	+	0.0952722i
$591$		0			0
$592$	7.97316	+	6.90878i	0.327695	+	0.283949i
$593$	3.34993	+	5.21259i	0.137565	+	0.214055i	0.903200	−	0.429220i	$-0.141211\pi$
$593$	3.34993	+	5.21259i	0.137565	+	0.214055i	−0.765635	+	0.643275i	$0.777575\pi$
$594$		0			0
$595$	−15.5256	+	52.8753i	−0.636487	+	2.16768i
$596$	2.12871	−	4.66122i	0.0871953	−	0.190931i
$597$		0			0
$598$	−5.12024	+	0.855897i	−0.209382	+	0.0350002i
$599$			11.9823i			0.489585i	0.969576	+	0.244792i	$0.0787198\pi$
$599$			11.9823i			0.489585i	−0.969576	+	0.244792i	$0.921280\pi$
$600$		0			0
$601$	−17.1803	−	5.04460i	−0.700800	−	0.205773i	−0.0881260	−	0.996109i	$-0.528088\pi$
$601$	−17.1803	−	5.04460i	−0.700800	−	0.205773i	−0.612674	+	0.790336i	$0.709906\pi$
$602$	−1.85072	+	1.60366i	−0.0754298	+	0.0653603i
$603$		0			0
$604$	−10.2153	+	11.7890i	−0.415653	+	0.479690i
$605$	5.14070	−	35.7543i	0.208999	−	1.45362i
$606$		0			0
$607$	−29.6599	−	19.0613i	−1.20386	−	0.773673i	−0.224238	−	0.974534i	$-0.571989\pi$
$607$	−29.6599	−	19.0613i	−1.20386	−	0.773673i	−0.979620	+	0.200862i	$0.935626\pi$
$608$	−0.592426	−	4.12041i	−0.0240260	−	0.167105i
$609$		0			0
$610$	−17.6891	−	38.7338i	−0.716212	−	1.56828i
$611$	11.5879	−	1.66609i	0.468798	−	0.0674030i
$612$		0			0
$613$	3.60039	+	12.2618i	0.145418	+	0.495249i	0.999698	−	0.0245639i	$-0.00781973\pi$
$613$	3.60039	+	12.2618i	0.145418	+	0.495249i	−0.854280	+	0.519813i	$0.826002\pi$
$614$	5.93472	+	0.853284i	0.239506	+	0.0344357i
$615$		0			0
$616$	13.0002	−	8.35473i	0.523794	−	0.336622i
$617$	−25.8095	−	29.7858i	−1.03905	−	1.19913i	−0.979612	−	0.200898i	$-0.935614\pi$
$617$	−25.8095	−	29.7858i	−1.03905	−	1.19913i	−0.0594403	−	0.998232i	$-0.518932\pi$
$618$		0			0
$619$	12.7389	+	5.81766i	0.512020	+	0.233832i	0.654633	−	0.755947i	$-0.272823\pi$
$619$	12.7389	+	5.81766i	0.512020	+	0.233832i	−0.142613	+	0.989779i	$0.545550\pi$
$620$	−11.7350			−0.471289
$621$		0			0
$622$	28.3516			1.13680
$623$	−11.8895	−	5.42977i	−0.476344	−	0.217539i
$624$		0			0
$625$	15.7233	+	18.1457i	0.628934	+	0.725828i
$626$	−7.36656	+	4.73420i	−0.294427	+	0.189217i
$627$		0			0
$628$	−16.7495	−	2.40822i	−0.668379	−	0.0960984i
$629$	15.6848	+	53.4174i	0.625393	+	2.12989i
$630$		0			0
$631$	−19.6217	+	2.82117i	−0.781126	+	0.112309i	−0.521331	−	0.853355i	$-0.674564\pi$
$631$	−19.6217	+	2.82117i	−0.781126	+	0.112309i	−0.259795	+	0.965664i	$0.583655\pi$
$632$	−3.96761	−	8.68786i	−0.157823	−	0.345585i
$633$		0			0
$634$	3.76958	+	26.2180i	0.149709	+	1.04125i
$635$	40.6448	+	26.1208i	1.61294	+	1.03657i
$636$		0			0
$637$	0.570207	−	3.96588i	0.0225924	−	0.157134i
$638$	−23.1937	+	26.7669i	−0.918246	+	1.05971i
$639$		0			0
$640$	2.41257	−	2.09050i	0.0953651	−	0.0826344i
$641$	−15.8984	−	4.66818i	−0.627948	−	0.184382i	−0.0477522	−	0.998859i	$-0.515206\pi$
$641$	−15.8984	−	4.66818i	−0.627948	−	0.184382i	−0.580196	+	0.814477i	$0.697024\pi$
$642$		0			0
$643$			1.38423i			0.0545887i	0.999627	+	0.0272944i	$0.00868914\pi$
$643$			1.38423i			0.0545887i	−0.999627	+	0.0272944i	$0.991311\pi$
$644$	−8.17844	+	13.3883i	−0.322276	+	0.527573i
$645$		0			0
$646$	9.12545	−	19.9819i	0.359036	−	0.786179i
$647$	0.352387	−	1.20012i	0.0138538	−	0.0471816i	−0.952276	−	0.305238i	$-0.901264\pi$
$647$	0.352387	−	1.20012i	0.0138538	−	0.0471816i	0.966130	+	0.258057i	$0.0830821\pi$
$648$		0			0
$649$	6.57151	+	10.2255i	0.257954	+	0.401385i
$650$	−4.24633	−	3.67946i	−0.166555	−	0.144320i
$651$		0			0
$652$	1.08211	−	0.317735i	0.0423786	−	0.0124435i
$653$	14.6700	−	22.8269i	0.574080	−	0.893286i	−0.425854	−	0.904792i	$-0.640026\pi$
$653$	14.6700	−	22.8269i	0.574080	−	0.893286i	0.999934	+	0.0115063i	$0.00366265\pi$
$654$		0			0
$655$	5.55736	−	2.53796i	0.217144	−	0.0991664i
$656$	−2.19948	+	1.00447i	−0.0858754	+	0.0392180i
$657$		0			0
$658$	19.1280	−	29.7637i	0.745685	−	1.16031i
$659$	−28.4385	+	8.35029i	−1.10781	+	0.325281i	−0.783949	−	0.620825i	$-0.786798\pi$
$659$	−28.4385	+	8.35029i	−1.10781	+	0.325281i	−0.323856	+	0.946106i	$0.604979\pi$
$660$		0			0
$661$	16.6300	+	14.4099i	0.646830	+	0.560482i	0.915283	−	0.402811i	$-0.131967\pi$
$661$	16.6300	+	14.4099i	0.646830	+	0.560482i	−0.268453	+	0.963293i	$0.586512\pi$
$662$	3.01771	+	4.69565i	0.117287	+	0.182502i
$663$		0			0
$664$	3.97122	−	13.5247i	0.154113	−	0.524862i
$665$	−18.0588	+	39.5432i	−0.700290	+	1.53342i
$666$		0			0
$667$	9.34006	−	34.7226i	0.361649	−	1.34447i
$668$		−	16.2471i		−	0.628620i
$669$		0			0
$670$	−24.2541	−	7.12164i	−0.937017	−	0.275133i
$671$	−47.6215	+	41.2642i	−1.83841	+	1.59299i
$672$		0			0
$673$	−11.9810	+	13.8268i	−0.461832	+	0.532983i	−0.938122	−	0.346306i	$-0.887436\pi$
$673$	−11.9810	+	13.8268i	−0.461832	+	0.532983i	0.476289	+	0.879289i	$0.341981\pi$
$674$	−4.22392	+	29.3780i	−0.162699	+	1.13160i
$675$		0			0
$676$	9.95059	+	6.39485i	0.382715	+	0.245956i
$677$	1.18905	+	8.27000i	0.0456988	+	0.317842i	0.999830	+	0.0184524i	$0.00587391\pi$
$677$	1.18905	+	8.27000i	0.0456988	+	0.317842i	−0.954131	+	0.299390i	$0.903217\pi$
$678$		0			0
$679$	−22.4895	−	49.2452i	−0.863069	−	1.88986i
$680$	16.6743	−	2.39740i	0.639429	−	0.0919360i
$681$		0			0
$682$	4.89238	+	16.6619i	0.187339	+	0.638018i
$683$	3.57060	+	0.513375i	0.136625	+	0.0196438i	0.210288	−	0.977639i	$-0.432560\pi$
$683$	3.57060	+	0.513375i	0.136625	+	0.0196438i	−0.0736628	+	0.997283i	$0.523469\pi$
$684$		0			0
$685$	−14.8290	+	9.52999i	−0.566585	+	0.364122i
$686$	7.06633	+	8.15498i	0.269794	+	0.311359i
$687$		0			0
$688$	0.680938	+	0.310974i	0.0259605	+	0.0118558i
$689$	−8.61898			−0.328357
$690$		0			0
$691$	−12.4537			−0.473760			−0.236880	−	0.971539i	$-0.576125\pi$
$691$	−12.4537			−0.473760			−0.236880	+	0.971539i	$0.576125\pi$
$692$	8.99441	+	4.10761i	0.341916	+	0.156148i
$693$		0			0
$694$	6.62284	+	7.64317i	0.251400	+	0.290131i
$695$	30.5948	−	19.6621i	1.16053	−	0.745825i
$696$		0			0
$697$	−12.6299	−	1.81591i	−0.478392	−	0.0687824i
$698$	−8.75033	−	29.8009i	−0.331205	−	1.12798i
$699$		0			0
$700$	−16.8075	+	2.41655i	−0.635263	+	0.0913371i
$701$	−5.42942	−	11.8888i	−0.205066	−	0.449033i	0.778956	−	0.627079i	$-0.215750\pi$
$701$	−5.42942	−	11.8888i	−0.205066	−	0.449033i	−0.984022	+	0.178046i	$0.943022\pi$
$702$		0			0
$703$	6.25009	+	43.4704i	0.235727	+	1.63952i
$704$	−3.97401	−	2.55394i	−0.149776	−	0.0962553i
$705$		0			0
$706$	−0.186921	+	1.30007i	−0.00703488	+	0.0489287i
$707$	2.97395	−	3.43213i	0.111847	−	0.129078i
$708$		0			0
$709$	−32.7763	+	28.4008i	−1.23094	+	1.06661i	−0.235435	+	0.971890i	$0.575652\pi$
$709$	−32.7763	+	28.4008i	−1.23094	+	1.06661i	−0.995504	+	0.0947244i	$0.969803\pi$
$710$	14.4652	+	4.24736i	0.542868	+	0.159400i
$711$		0			0
$712$			3.99556i			0.149740i
$713$	−11.8461	−	13.0566i	−0.443641	−	0.488975i
$714$		0			0
$715$	−6.78105	+	14.8484i	−0.253597	+	0.555300i
$716$	2.58059	−	8.78868i	0.0964412	−	0.328449i
$717$		0			0
$718$	7.79451	+	12.1285i	0.290888	+	0.452631i
$719$	−2.73971	−	2.37397i	−0.102174	−	0.0885343i	0.602276	−	0.798288i	$-0.294261\pi$
$719$	−2.73971	−	2.37397i	−0.102174	−	0.0885343i	−0.704450	+	0.709754i	$0.748806\pi$
$720$		0			0
$721$	−34.0644	+	10.0022i	−1.26863	+	0.372502i
$722$	−0.903544	+	1.40594i	−0.0336264	+	0.0523237i
$723$		0			0
$724$	−14.5284	+	6.63490i	−0.539944	+	0.246584i
$725$	35.4004	−	16.1668i	1.31474	−	0.600421i
$726$		0			0
$727$	−3.54453	+	5.51540i	−0.131459	+	0.204555i	−0.900743	−	0.434353i	$-0.856977\pi$
$727$	−3.54453	+	5.51540i	−0.131459	+	0.204555i	0.769283	+	0.638908i	$0.220613\pi$
$728$	−3.39761	+	0.997629i	−0.125924	+	0.0369746i
$729$		0			0
$730$	−9.26586	−	8.02891i	−0.342945	−	0.297163i
$731$	2.13569	+	3.32321i	0.0789915	+	0.122913i
$732$		0			0
$733$	10.7161	−	36.4958i	0.395809	−	1.34800i	−0.484993	−	0.874518i	$-0.661178\pi$
$733$	10.7161	−	36.4958i	0.395809	−	1.34800i	0.880802	−	0.473485i	$-0.157004\pi$
$734$	5.89914	−	12.9173i	0.217741	−	0.476787i
$735$		0			0
$736$	4.76136	+	0.573982i	0.175506	+	0.0211573i
$737$			37.4062i			1.37788i
$738$		0			0
$739$	40.2841	+	11.8285i	1.48188	+	0.435118i	0.919939	−	0.392062i	$-0.128238\pi$
$739$	40.2841	+	11.8285i	1.48188	+	0.435118i	0.561937	+	0.827180i	$0.310056\pi$
$740$	−25.4526	+	22.0548i	−0.935656	+	0.810751i
$741$		0			0
$742$	−17.0575	+	19.6854i	−0.626200	+	0.722674i
$743$	−2.16178	+	15.0355i	−0.0793079	+	0.551599i	0.910968	+	0.412478i	$0.135337\pi$
$743$	−2.16178	+	15.0355i	−0.0793079	+	0.551599i	−0.990275	+	0.139121i	$0.955572\pi$
$744$		0			0
$745$	13.7614	+	8.84392i	0.504179	+	0.324016i
$746$	−4.28005	−	29.7684i	−0.156704	−	1.08990i
$747$		0			0
$748$	−10.3555	−	22.6755i	−0.378636	−	0.829098i
$749$	18.3719	−	2.64148i	0.671294	−	0.0965175i
$750$		0			0
$751$	6.87217	+	23.4045i	0.250769	+	0.854041i	0.984617	+	0.174727i	$0.0559044\pi$
$751$	6.87217	+	23.4045i	0.250769	+	0.854041i	−0.733848	+	0.679314i	$0.762277\pi$
$752$	−10.7052	−	1.53918i	−0.390379	−	0.0561280i
$753$		0			0
$754$	6.82741	−	4.38771i	0.248640	−	0.159791i
$755$	−32.6100	−	37.6340i	−1.18680	−	1.36964i
$756$		0			0
$757$	−39.0303	−	17.8245i	−1.41858	−	0.647844i	−0.449206	−	0.893428i	$-0.648293\pi$
$757$	−39.0303	−	17.8245i	−1.41858	−	0.647844i	−0.969375	+	0.245584i	$0.921020\pi$
$758$	27.8463			1.01142
$759$		0			0
$760$	13.2888			0.482035
$761$	−13.4311	−	6.13380i	−0.486879	−	0.222350i	0.156823	−	0.987627i	$-0.449875\pi$
$761$	−13.4311	−	6.13380i	−0.486879	−	0.222350i	−0.643701	+	0.765277i	$0.722602\pi$
$762$		0			0
$763$	−14.4714	−	16.7009i	−0.523902	−	0.604615i
$764$	6.44115	−	4.13948i	0.233033	−	0.149761i
$765$		0			0
$766$	−31.2787	−	4.49721i	−1.13015	−	0.162491i
$767$	−0.784696	−	2.67243i	−0.0283337	−	0.0964959i
$768$		0			0
$769$	8.03989	−	1.15596i	0.289926	−	0.0416850i	0.00418253	−	0.999991i	$-0.498669\pi$
$769$	8.03989	−	1.15596i	0.289926	−	0.0416850i	0.285743	+	0.958306i	$0.407760\pi$
$770$	20.4931	+	44.8736i	0.738520	+	1.61713i
$771$		0			0
$772$	1.44759	+	10.0682i	0.0520999	+	0.362363i
$773$	−35.3861	−	22.7412i	−1.27275	−	0.817946i	−0.282773	−	0.959187i	$-0.591254\pi$
$773$	−35.3861	−	22.7412i	−1.27275	−	0.817946i	−0.989975	+	0.141241i	$0.954891\pi$
$774$		0			0
$775$	2.71554	−	18.8870i	0.0975450	−	0.678440i
$776$	−10.8374	+	12.5071i	−0.389041	+	0.448977i
$777$		0			0
$778$	26.7512	−	23.1801i	0.959078	−	0.831045i
$779$	−9.65786	−	2.83580i	−0.346029	−	0.101603i
$780$		0			0
$781$		−	22.3091i		−	0.798283i
$782$	19.4996	+	16.1321i	0.697304	+	0.576883i
$783$		0			0
$784$	−1.53764	+	3.36695i	−0.0549156	+	0.120248i
$785$	15.2190	−	51.8310i	0.543188	−	1.84993i
$786$		0			0
$787$	27.9200	+	43.4443i	0.995239	+	1.54862i	0.826480	+	0.562965i	$0.190340\pi$
$787$	27.9200	+	43.4443i	0.995239	+	1.54862i	0.168759	+	0.985657i	$0.446024\pi$
$788$	9.11728	+	7.90016i	0.324789	+	0.281432i
$789$		0			0
$790$	29.2544	−	8.58986i	1.04082	−	0.305613i
$791$	28.5760	−	44.4651i	1.01604	−	1.58100i
$792$		0			0
$793$	13.1341	−	5.99813i	0.466404	−	0.213000i
$794$	4.90143	−	2.23841i	0.173945	−	0.0794381i
$795$		0			0
$796$	5.16673	−	8.03959i	0.183130	−	0.284956i
$797$	26.6786	−	7.83356i	0.945006	−	0.277479i	0.227300	−	0.973825i	$-0.427010\pi$
$797$	26.6786	−	7.83356i	0.945006	−	0.277479i	0.717706	+	0.696346i	$0.245192\pi$
$798$		0			0
$799$	−43.1325	−	37.3745i	−1.52592	−	1.32222i
$800$	2.80630	+	4.36668i	0.0992175	+	0.154386i
$801$		0			0
$802$	6.21304	−	21.1597i	0.219390	−	0.747174i
$803$	−7.53686	+	16.5034i	−0.265970	+	0.582393i
$804$		0			0
$805$	−38.5887	−	31.9246i	−1.36007	−	1.12519i
$806$		−	3.97916i		−	0.140160i
$807$		0			0
$808$	−1.33201	−	0.391112i	−0.0468598	−	0.0137593i
$809$	10.0495	−	8.70798i	0.353323	−	0.306156i	−0.460056	−	0.887890i	$-0.652171\pi$
$809$	10.0495	−	8.70798i	0.353323	−	0.306156i	0.813379	+	0.581734i	$0.197625\pi$
$810$		0			0
$811$	−5.22861	+	6.03414i	−0.183601	+	0.211887i	−0.840088	−	0.542451i	$-0.817497\pi$
$811$	−5.22861	+	6.03414i	−0.183601	+	0.211887i	0.656486	+	0.754338i	$0.272042\pi$
$812$	3.49052	−	24.2771i	0.122493	−	0.851958i
$813$		0			0
$814$	41.9259	+	26.9441i	1.46950	+	0.944391i
$815$	0.512366	+	3.56358i	0.0179474	+	0.124827i
$816$		0			0
$817$	1.29452	+	2.83460i	0.0452894	+	0.0991700i
$818$	16.7313	−	2.40560i	0.584997	−	0.0841099i
$819$		0			0
$820$	−2.17467	−	7.40626i	−0.0759429	−	0.258638i
$821$	43.8244	+	6.30100i	1.52948	+	0.219906i	0.855095	−	0.518471i	$-0.173499\pi$
$821$	43.8244	+	6.30100i	1.52948	+	0.219906i	0.674388	+	0.738377i	$0.264408\pi$
$822$		0			0
$823$	−6.10450	+	3.92312i	−0.212789	+	0.136751i	−0.642694	−	0.766123i	$-0.722183\pi$
$823$	−6.10450	+	3.92312i	−0.212789	+	0.136751i	0.429905	+	0.902874i	$0.358547\pi$
$824$	7.10701	+	8.20193i	0.247585	+	0.285728i
$825$		0			0
$826$	−7.65668	−	3.49669i	−0.266410	−	0.121665i
$827$	20.4733			0.711928			0.355964	−	0.934500i	$-0.384153\pi$
$827$	20.4733			0.711928			0.355964	+	0.934500i	$0.384153\pi$
$828$		0			0
$829$	29.3904			1.02077			0.510385	−	0.859946i	$-0.329503\pi$
$829$	29.3904			1.02077			0.510385	+	0.859946i	$0.329503\pi$
$830$	40.9312	+	18.6926i	1.42074	+	0.648831i
$831$		0			0
$832$	0.708859	+	0.818067i	0.0245753	+	0.0283614i
$833$	−16.4319	+	10.5601i	−0.569330	+	0.365886i
$834$		0			0
$835$	51.3376	+	7.38123i	1.77661	+	0.255438i
$836$	−5.54017	−	18.8681i	−0.191611	−	0.652566i
$837$		0			0
$838$	28.6982	−	4.12617i	0.991362	−	0.142536i
$839$	−1.46516	−	3.20824i	−0.0505828	−	0.110761i	0.882653	−	0.470025i	$-0.155755\pi$
$839$	−1.46516	−	3.20824i	−0.0505828	−	0.110761i	−0.933236	+	0.359264i	$0.883028\pi$
$840$		0			0
$841$	3.87281	+	26.9360i	0.133545	+	0.928827i
$842$	−10.1449	−	6.51972i	−0.349615	−	0.224684i
$843$		0			0
$844$	0.492744	−	3.42711i	0.0169609	−	0.117966i
$845$	−24.7271	+	28.5365i	−0.850637	+	0.981687i
$846$		0			0
$847$	27.9749	−	24.2404i	0.961230	−	0.832911i
$848$	7.63989	+	2.24327i	0.262355	+	0.0770343i
$849$		0			0
$850$			27.3913i			0.939515i
$851$	−50.2324	−	6.05552i	−1.72194	−	0.207580i
$852$		0			0
$853$	2.89528	−	6.33977i	0.0991324	−	0.217070i	−0.853568	−	0.520982i	$-0.825566\pi$
$853$	2.89528	−	6.33977i	0.0991324	−	0.217070i	0.952700	+	0.303913i	$0.0982931\pi$
$854$	12.2936	−	41.8683i	0.420680	−	1.43270i
$855$		0			0
$856$	−3.06750	−	4.77312i	−0.104845	−	0.163142i
$857$	−3.38214	−	2.93064i	−0.115532	−	0.100109i	0.595179	−	0.803593i	$-0.297081\pi$
$857$	−3.38214	−	2.93064i	−0.115532	−	0.100109i	−0.710711	+	0.703484i	$0.751627\pi$
$858$		0			0
$859$	38.1809	−	11.2109i	1.30271	−	0.382511i	0.444489	−	0.895785i	$-0.353385\pi$
$859$	38.1809	−	11.2109i	1.30271	−	0.382511i	0.858225	+	0.513273i	$0.171567\pi$
$860$	−1.29197	+	2.01034i	−0.0440558	+	0.0685522i
$861$		0			0
$862$	8.97602	−	4.09921i	0.305725	−	0.139620i
$863$	−2.96098	+	1.35223i	−0.100793	+	0.0460306i	−0.465173	−	0.885220i	$-0.654008\pi$
$863$	−2.96098	+	1.35223i	−0.100793	+	0.0460306i	0.364380	+	0.931250i	$0.381281\pi$
$864$		0			0
$865$	−17.0654	+	26.5543i	−0.580242	+	0.902874i
$866$	18.7485	−	5.50507i	0.637102	−	0.187070i
$867$		0			0
$868$	−9.08825	−	7.87501i	−0.308475	−	0.267295i
$869$	−24.3926	−	37.9556i	−0.827463	−	1.28756i
$870$		0			0
$871$	2.41485	−	8.22421i	0.0818240	−	0.278667i
$872$	−2.80624	+	6.14480i	−0.0950311	+	0.208089i
$873$		0			0
$874$	13.4146	+	14.7854i	0.453757	+	0.500125i
$875$		−	1.99131i		−	0.0673185i
$876$		0			0
$877$	−10.6430	−	3.12508i	−0.359390	−	0.105527i	0.0970525	−	0.995279i	$-0.469059\pi$
$877$	−10.6430	−	3.12508i	−0.359390	−	0.105527i	−0.456443	+	0.889753i	$0.650877\pi$
$878$	10.2895	−	8.91587i	0.347253	−	0.300896i
$879$		0			0
$880$	9.87536	−	11.3968i	0.332898	−	0.384185i
$881$	−3.55530	+	24.7277i	−0.119781	+	0.833097i	0.838015	+	0.545648i	$0.183716\pi$
$881$	−3.55530	+	24.7277i	−0.119781	+	0.833097i	−0.957796	+	0.287449i	$0.907193\pi$
$882$		0			0
$883$	−21.7414	−	13.9723i	−0.731656	−	0.470207i	0.121018	−	0.992650i	$-0.461384\pi$
$883$	−21.7414	−	13.9723i	−0.731656	−	0.470207i	−0.852674	+	0.522444i	$0.825020\pi$
$884$	0.812923	+	5.65400i	0.0273416	+	0.190165i
$885$		0			0
$886$	−9.63399	−	21.0955i	−0.323660	−	0.708717i
$887$	14.3210	−	2.05906i	0.480854	−	0.0691363i	0.102374	−	0.994746i	$-0.467356\pi$
$887$	14.3210	−	2.05906i	0.480854	−	0.0691363i	0.378480	+	0.925610i	$0.376447\pi$
$888$		0			0
$889$	13.9487	+	47.5050i	0.467826	+	1.59327i
$890$	−12.6252	−	1.81522i	−0.423196	−	0.0608464i
$891$		0			0
$892$	8.20109	−	5.27052i	0.274593	−	0.176470i
$893$	−29.4830	−	34.0252i	−0.986610	−	1.13861i
$894$		0			0
$895$	26.5980	+	12.1469i	0.889074	+	0.406026i
$896$	3.27131			0.109287
$897$		0			0
$898$	0.858219			0.0286391
$899$	25.0706	+	11.4494i	0.836152	+	0.381858i
$900$		0			0
$901$	27.5158	+	31.7549i	0.916685	+	1.05791i
$902$	−9.60914	+	6.17542i	−0.319949	+	0.205619i
$903$		0			0
$904$	−15.9929	−	2.29944i	−0.531917	−	0.0764781i
$905$	−14.3645	−	48.9211i	−0.477493	−	1.62619i
$906$		0			0
$907$	−8.44817	+	1.21466i	−0.280517	+	0.0403322i	−0.281137	−	0.959668i	$-0.590712\pi$
$907$	−8.44817	+	1.21466i	−0.280517	+	0.0403322i	0.000620373		1.00000i	$0.499803\pi$
$908$	5.02259	+	10.9979i	0.166680	+	0.364979i
$909$		0			0
$910$	−1.60873	−	11.1890i	−0.0533290	−	0.370911i
$911$	11.2470	+	7.22802i	0.372630	+	0.239475i	0.713530	−	0.700625i	$-0.247095\pi$
$911$	11.2470	+	7.22802i	0.372630	+	0.239475i	−0.340900	+	0.940100i	$0.610732\pi$
$912$		0			0
$913$	9.47632	−	65.9092i	0.313620	−	2.18128i
$914$	22.9072	−	26.4363i	0.757701	−	0.874434i
$915$		0			0
$916$	14.5069	−	12.5703i	0.479322	−	0.415335i
$917$	6.00709	+	1.76384i	0.198372	+	0.0582472i
$918$		0			0
$919$			56.3098i			1.85749i	0.370721	+	0.928744i	$0.379110\pi$
$919$			56.3098i			1.85749i	−0.370721	+	0.928744i	$0.620890\pi$
$920$	−3.97680	+	14.7841i	−0.131111	+	0.487419i
$921$		0			0
$922$	−6.06258	+	13.2752i	−0.199661	+	0.437196i
$923$	−1.44022	+	4.90493i	−0.0474053	+	0.161448i
$924$		0			0
$925$	−29.6064	−	46.0685i	−0.973454	−	1.51472i
$926$	−4.85210	−	4.20437i	−0.159450	−	0.138164i
$927$		0			0
$928$	−7.19383	+	2.11230i	−0.236149	+	0.0693396i
$929$	−16.6314	+	25.8789i	−0.545657	+	0.849059i	−0.999108	−	0.0422218i	$-0.986556\pi$
$929$	−16.6314	+	25.8789i	−0.545657	+	0.849059i	0.453451	+	0.891281i	$0.350193\pi$
$930$		0			0
$931$	−14.0159	+	6.40084i	−0.459352	+	0.209779i
$932$	−16.0107	+	7.31182i	−0.524446	+	0.239507i
$933$		0			0
$934$	7.83482	−	12.1912i	0.256363	−	0.398909i
$935$	76.3544	−	22.4197i	2.49706	−	0.733202i
$936$		0			0
$937$	2.03686	+	1.76495i	0.0665413	+	0.0576584i	0.687497	−	0.726188i	$-0.258710\pi$
$937$	2.03686	+	1.76495i	0.0665413	+	0.0576584i	−0.620955	+	0.783846i	$0.713255\pi$
$938$	−14.0046	−	21.7916i	−0.457267	−	0.711522i
$939$		0			0
$940$	9.72696	−	33.1270i	0.317259	−	1.08048i
$941$	8.76617	−	19.1952i	0.285769	−	0.625747i	−0.711247	−	0.702942i	$-0.751869\pi$
$941$	8.76617	−	19.1952i	0.285769	−	0.625747i	0.997016	+	0.0771953i	$0.0245965\pi$
$942$		0			0
$943$	6.04511	−	9.89599i	0.196856	−	0.322258i
$944$			2.57308i			0.0837467i
$945$		0			0
$946$	3.39302	+	0.996280i	0.110317	+	0.0323919i
$947$	35.7132	−	30.9456i	1.16052	−	1.00560i	0.160695	−	0.987004i	$-0.448626\pi$
$947$	35.7132	−	30.9456i	1.16052	−	1.00560i	0.999827	−	0.0185944i	$-0.00591911\pi$
$948$		0			0
$949$	2.72249	−	3.14192i	0.0883757	−	0.101991i
$950$	−3.07509	+	21.3878i	−0.0997692	+	0.693910i
$951$		0			0
$952$	14.5223	+	9.33294i	0.470672	+	0.302482i
$953$	−0.890262	−	6.19191i	−0.0288384	−	0.200576i	0.970309	−	0.241870i	$-0.0777609\pi$
$953$	−0.890262	−	6.19191i	−0.0288384	−	0.200576i	−0.999147	+	0.0412947i	$0.986852\pi$
$954$		0			0
$955$	10.1536	+	22.2333i	0.328563	+	0.719453i
$956$	−15.0046	+	2.15733i	−0.485282	+	0.0697730i
$957$		0			0
$958$	7.70192	+	26.2303i	0.248838	+	0.847464i
$959$	−17.8797	−	2.57071i	−0.577365	−	0.0830126i
$960$		0			0
$961$	−14.7107	+	9.45401i	−0.474540	+	0.304968i
$962$	−7.47847	−	8.63061i	−0.241115	−	0.278262i
$963$		0			0
$964$	26.0722	+	11.9068i	0.839728	+	0.383491i
$965$	−32.4711			−1.04528
$966$		0			0
$967$	−31.1024			−1.00018			−0.500092	−	0.865972i	$-0.666701\pi$
$967$	−31.1024			−1.00018			−0.500092	+	0.865972i	$0.666701\pi$
$968$	−10.2929	−	4.70059i	−0.330825	−	0.151083i
$969$		0			0
$970$	−34.5961	−	39.9261i	−1.11082	−	1.28195i
$971$	25.3603	−	16.2981i	0.813850	−	0.523029i	−0.0662587	−	0.997802i	$-0.521106\pi$
$971$	25.3603	−	16.2981i	0.813850	−	0.523029i	0.880108	+	0.474773i	$0.157470\pi$
$972$		0			0
$973$	36.8890	+	5.30384i	1.18261	+	0.170033i
$974$	9.52377	+	32.4350i	0.305161	+	1.03928i
$975$		0			0
$976$	−13.2032	+	1.89833i	−0.422624	+	0.0607642i
$977$	−10.4138	−	22.8030i	−0.333167	−	0.729533i	0.666709	−	0.745318i	$-0.267703\pi$
$977$	−10.4138	−	22.8030i	−0.333167	−	0.729533i	−0.999875	+	0.0157851i	$0.994975\pi$
$978$		0			0
$979$	2.68615	+	18.6826i	0.0858498	+	0.597099i
$980$	−9.94031	−	6.38825i	−0.317531	−	0.204065i
$981$		0			0
$982$	−5.20205	+	36.1810i	−0.166004	+	1.15458i
$983$	−17.6297	+	20.3457i	−0.562300	+	0.648929i	−0.963704	−	0.266972i	$-0.913977\pi$
$983$	−17.6297	+	20.3457i	−0.562300	+	0.648929i	0.401404	+	0.915901i	$0.368522\pi$
$984$		0			0
$985$	−29.1049	+	25.2196i	−0.927361	+	0.803563i
$986$	−37.9619	−	11.1466i	−1.20895	−	0.354981i
$987$		0			0
$988$			4.50604i			0.143356i
$989$	−3.54096	+	0.591906i	−0.112596	+	0.0188215i
$990$		0			0
$991$	−14.8991	+	32.6245i	−0.473285	+	1.03635i	0.510970	+	0.859598i	$0.329286\pi$
$991$	−14.8991	+	32.6245i	−0.473285	+	1.03635i	−0.984255	+	0.176752i	$0.943441\pi$
$992$	−1.03566	+	3.52714i	−0.0328823	+	0.111987i
$993$		0			0
$994$	8.35238	+	12.9966i	0.264921	+	0.412226i
$995$	23.0561	+	19.9782i	0.730928	+	0.633353i
$996$		0			0
$997$	−23.6970	+	6.95807i	−0.750492	+	0.220364i	−0.634539	−	0.772890i	$-0.718810\pi$
$997$	−23.6970	+	6.95807i	−0.750492	+	0.220364i	−0.115952	+	0.993255i	$0.536992\pi$
$998$	20.6809	−	32.1800i	0.654641	−	1.01864i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.j.a.17.5	yes	80
3.2	odd	2	inner	414.2.j.a.17.4	✓	80
23.19	odd	22	inner	414.2.j.a.341.4	yes	80
69.65	even	22	inner	414.2.j.a.341.5	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.j.a.17.4	✓	80	3.2	odd	2	inner
414.2.j.a.17.5	yes	80	1.1	even	1	trivial
414.2.j.a.341.4	yes	80	23.19	odd	22	inner
414.2.j.a.341.5	yes	80	69.65	even	22	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.909632 + 0.415415i) q^{2} +(0.654861 + 0.755750i) q^{4} +(-2.68552 + 1.72588i) q^{5} +(-3.23801 - 0.465555i) q^{7} +(0.281733 + 0.959493i) q^{8} +O(q^{10})\)	\(q+(0.909632 + 0.415415i) q^{2} +(0.654861 + 0.755750i) q^{4} +(-2.68552 + 1.72588i) q^{5} +(-3.23801 - 0.465555i) q^{7} +(0.281733 + 0.959493i) q^{8} +(-3.15979 + 0.454310i) q^{10} +(1.96239 + 4.29703i) q^{11} +(-0.154050 - 1.07144i) q^{13} +(-2.75200 - 1.76860i) q^{14} +(-0.142315 + 0.989821i) q^{16} +(-3.45571 + 3.98810i) q^{17} +(-3.14602 + 2.72604i) q^{19} +(-3.06298 - 0.899371i) q^{20} +4.72392i q^{22} +(-2.09132 - 4.31583i) q^{23} +(2.15629 - 4.72161i) q^{25} +(0.304964 - 1.03861i) q^{26} +(-1.76860 - 2.75200i) q^{28} +(5.66626 + 4.90984i) q^{29} +(3.52714 - 1.03566i) q^{31} +(-0.540641 + 0.841254i) q^{32} +(-4.80014 + 2.19215i) q^{34} +(9.49923 - 4.33816i) q^{35} +(5.70376 - 8.87523i) q^{37} +(-3.99416 + 1.17279i) q^{38} +(-2.41257 - 2.09050i) q^{40} +(1.30727 + 2.03415i) q^{41} +(0.210901 - 0.718263i) q^{43} +(-1.96239 + 4.29703i) q^{44} +(-0.109472 - 4.79458i) q^{46} +10.8153i q^{47} +(3.55151 + 1.04282i) q^{49} +(3.92286 - 3.39918i) q^{50} +(0.708859 - 0.818067i) q^{52} +(1.13317 - 7.88137i) q^{53} +(-12.6862 - 8.15291i) q^{55} +(-0.465555 - 3.23801i) q^{56} +(3.11459 + 6.81999i) q^{58} +(2.54689 - 0.366188i) q^{59} +(3.75802 + 12.7987i) q^{61} +(3.63863 + 0.523156i) q^{62} +(-0.841254 + 0.540641i) q^{64} +(2.26288 + 2.61150i) q^{65} +(7.20290 + 3.28945i) q^{67} -5.27701 q^{68} +10.4429 q^{70} +(-4.29582 - 1.96183i) q^{71} +(2.51510 + 2.90258i) q^{73} +(8.87523 - 5.70376i) q^{74} +(-4.12041 - 0.592426i) q^{76} +(-4.35372 - 14.8274i) q^{77} +(-9.45375 + 1.35924i) q^{79} +(-1.32612 - 2.90380i) q^{80} +(0.344116 + 2.39338i) q^{82} +(-11.8581 - 7.62072i) q^{83} +(2.39740 - 16.6743i) q^{85} +(0.490220 - 0.565744i) q^{86} +(-3.57010 + 3.09351i) q^{88} +(3.83372 + 1.12568i) q^{89} +3.54105i q^{91} +(1.89216 - 4.40678i) q^{92} +(-4.49284 + 9.83794i) q^{94} +(3.74388 - 12.7505i) q^{95} +(8.94718 + 13.9221i) q^{97} +(2.79737 + 2.42393i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 8 q^{4}+O(q^{10}) \) 80 * q + 8 * q^4	\( 80 q + 8 q^{4} - 16 q^{13} - 8 q^{16} + 24 q^{25} - 16 q^{31} + 88 q^{37} + 88 q^{43} + 8 q^{46} + 8 q^{49} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 176 q^{61} + 8 q^{64} - 88 q^{67} - 176 q^{70} - 56 q^{73} - 176 q^{79} - 88 q^{82} - 88 q^{85} + 16 q^{94}+O(q^{100}) \) 80 * q + 8 * q^4 - 16 * q^13 - 8 * q^16 + 24 * q^25 - 16 * q^31 + 88 * q^37 + 88 * q^43 + 8 * q^46 + 8 * q^49 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 176 * q^61 + 8 * q^64 - 88 * q^67 - 176 * q^70 - 56 * q^73 - 176 * q^79 - 88 * q^82 - 88 * q^85 + 16 * q^94

Introduction

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