LMFDB - Embedded newform 756.2.be.d.431.4

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			431.4
Character	$\chi$	$=$	756.431
Dual form			756.2.be.d.107.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.943439 + 1.05353i) q^{2} +(-0.219845 - 1.98788i) q^{4} +(2.75822 - 1.59246i) q^{5} +(0.944233 + 2.47152i) q^{7} +(2.30170 + 1.64383i) q^{8} +O(q^{10})$	\(q+(-0.943439 + 1.05353i) q^{2} +(-0.219845 - 1.98788i) q^{4} +(2.75822 - 1.59246i) q^{5} +(0.944233 + 2.47152i) q^{7} +(2.30170 + 1.64383i) q^{8} +(-0.924512 + 4.40826i) q^{10} +(1.24831 - 2.16213i) q^{11} +6.61093 q^{13} +(-3.49465 - 1.33695i) q^{14} +(-3.90334 + 0.874051i) q^{16} +(-2.67612 - 1.54506i) q^{17} +(-4.40292 + 2.54203i) q^{19} +(-3.77200 - 5.13292i) q^{20} +(1.10017 + 3.35497i) q^{22} +(-2.53877 - 4.39728i) q^{23} +(2.57186 - 4.45459i) q^{25} +(-6.23701 + 6.96480i) q^{26} +(4.70551 - 2.42037i) q^{28} +1.59554i q^{29} +(7.31098 + 4.22099i) q^{31} +(2.76172 - 4.93689i) q^{32} +(4.15252 - 1.36170i) q^{34} +(6.54021 + 5.31335i) q^{35} +(-0.357491 - 0.619192i) q^{37} +(1.47579 - 7.03685i) q^{38} +(8.96633 + 0.868686i) q^{40} -12.2607i q^{41} -3.72407i q^{43} +(-4.57249 - 2.00615i) q^{44} +(7.02784 + 1.47390i) q^{46} +(2.51371 + 4.35388i) q^{47} +(-5.21685 + 4.66739i) q^{49} +(2.26665 + 6.91216i) q^{50} +(-1.45338 - 13.1417i) q^{52} +(7.21991 + 4.16842i) q^{53} -7.95152i q^{55} +(-1.88942 + 7.24086i) q^{56} +(-1.68095 - 1.50530i) q^{58} +(-5.36835 + 9.29825i) q^{59} +(0.997571 + 1.72784i) q^{61} +(-11.3444 + 3.72007i) q^{62} +(2.59564 + 7.56721i) q^{64} +(18.2344 - 10.5276i) q^{65} +(0.00277185 + 0.00160033i) q^{67} +(-2.48306 + 5.65947i) q^{68} +(-11.7681 + 1.87747i) q^{70} +12.4088 q^{71} +(0.957657 - 1.65871i) q^{73} +(0.989607 + 0.207543i) q^{74} +(6.02120 + 8.19362i) q^{76} +(6.52245 + 1.04366i) q^{77} +(-6.11304 + 3.52937i) q^{79} +(-9.37438 + 8.62674i) q^{80} +(12.9170 + 11.5672i) q^{82} -7.93317 q^{83} -9.84177 q^{85} +(3.92341 + 3.51343i) q^{86} +(6.42741 - 2.92457i) q^{88} +(0.482940 - 0.278825i) q^{89} +(6.24226 + 16.3391i) q^{91} +(-8.18314 + 6.01350i) q^{92} +(-6.95847 - 1.45935i) q^{94} +(-8.09615 + 14.0229i) q^{95} +0.127151 q^{97} +(0.00455176 - 9.89949i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.943439	+	1.05353i	−0.667112	+	0.744957i
$2$	−0.943439	+	1.05353i	−0.667112	+	0.744957i
$3$		0			0
$3$		0			0
$4$	−0.219845	−	1.98788i	−0.109923	−	0.993940i
$5$	2.75822	−	1.59246i	1.23351	−	0.712170i	0.265754	−	0.964041i	$-0.414379\pi$
$5$	2.75822	−	1.59246i	1.23351	−	0.712170i	0.967761	+	0.251871i	$0.0810459\pi$
$6$		0			0
$7$	0.944233	+	2.47152i	0.356887	+	0.934148i
$7$	0.944233	+	2.47152i	0.356887	+	0.934148i
$8$	2.30170	+	1.64383i	0.813774	+	0.581182i
$9$		0			0
$10$	−0.924512	+	4.40826i	−0.292356	+	1.39401i
$11$	1.24831	−	2.16213i	0.376379	−	0.651907i	−0.614153	−	0.789187i	$-0.710502\pi$
$11$	1.24831	−	2.16213i	0.376379	−	0.651907i	0.990532	+	0.137279i	$0.0438357\pi$
$12$		0			0
$13$	6.61093			1.83354			0.916771	−	0.399414i	$-0.130786\pi$
$13$	6.61093			1.83354			0.916771	+	0.399414i	$0.130786\pi$
$14$	−3.49465	−	1.33695i	−0.933984	−	0.357316i
$15$		0			0
$16$	−3.90334	+	0.874051i	−0.975834	+	0.218513i
$17$	−2.67612	−	1.54506i	−0.649054	−	0.374731i	0.139040	−	0.990287i	$-0.455598\pi$
$17$	−2.67612	−	1.54506i	−0.649054	−	0.374731i	−0.788094	+	0.615555i	$0.788932\pi$
$18$		0			0
$19$	−4.40292	+	2.54203i	−1.01010	+	0.583181i	−0.911220	−	0.411919i	$-0.864859\pi$
$19$	−4.40292	+	2.54203i	−1.01010	+	0.583181i	−0.0988779	+	0.995100i	$0.531525\pi$
$20$	−3.77200	−	5.13292i	−0.843445	−	1.14776i
$21$		0			0
$22$	1.10017	+	3.35497i	0.234556	+	0.715282i
$23$	−2.53877	−	4.39728i	−0.529371	−	0.916897i	−0.999413	−	0.0342533i	$-0.989095\pi$
$23$	−2.53877	−	4.39728i	−0.529371	−	0.916897i	0.470042	−	0.882644i	$-0.344239\pi$
$24$		0			0
$25$	2.57186	−	4.45459i	0.514372	−	0.890918i
$26$	−6.23701	+	6.96480i	−1.22318	+	1.36591i
$27$		0			0
$28$	4.70551	−	2.42037i	0.889257	−	0.457408i
$29$			1.59554i			0.296285i	0.988966	+	0.148143i	$0.0473294\pi$
$29$			1.59554i			0.296285i	−0.988966	+	0.148143i	$0.952671\pi$
$30$		0			0
$31$	7.31098	+	4.22099i	1.31309	+	0.758113i	0.982607	−	0.185699i	$-0.0594549\pi$
$31$	7.31098	+	4.22099i	1.31309	+	0.758113i	0.330483	+	0.943812i	$0.392788\pi$
$32$	2.76172	−	4.93689i	0.488208	−	0.872727i
$33$		0			0
$34$	4.15252	−	1.36170i	0.712151	−	0.233529i
$35$	6.54021	+	5.31335i	1.10550	+	0.898121i
$36$		0			0
$37$	−0.357491	−	0.619192i	−0.0587711	−	0.101795i	0.835143	−	0.550033i	$-0.185385\pi$
$37$	−0.357491	−	0.619192i	−0.0587711	−	0.101795i	−0.893914	+	0.448238i	$0.852052\pi$
$38$	1.47579	−	7.03685i	0.239404	−	1.14153i
$39$		0			0
$40$	8.96633	+	0.868686i	1.41770	+	0.137351i
$41$		−	12.2607i		−	1.91480i	−0.288763	−	0.957401i	$-0.593244\pi$
$41$		−	12.2607i		−	1.91480i	0.288763	−	0.957401i	$-0.406756\pi$
$42$		0			0
$43$		−	3.72407i		−	0.567915i	−0.958837	−	0.283958i	$-0.908352\pi$
$43$		−	3.72407i		−	0.567915i	0.958837	−	0.283958i	$-0.0916475\pi$
$44$	−4.57249	−	2.00615i	−0.689330	−	0.302439i
$45$		0			0
$46$	7.02784	+	1.47390i	1.03620	+	0.217315i
$47$	2.51371	+	4.35388i	0.366663	+	0.635078i	0.989041	−	0.147638i	$-0.0471670\pi$
$47$	2.51371	+	4.35388i	0.366663	+	0.635078i	−0.622379	+	0.782716i	$0.713834\pi$
$48$		0			0
$49$	−5.21685	+	4.66739i	−0.745264	+	0.666770i
$50$	2.26665	+	6.91216i	0.320552	+	0.977527i
$51$		0			0
$52$	−1.45338	−	13.1417i	−0.201548	−	1.82243i
$53$	7.21991	+	4.16842i	0.991732	+	0.572576i	0.905791	−	0.423724i	$-0.139277\pi$
$53$	7.21991	+	4.16842i	0.991732	+	0.572576i	0.0859401	+	0.996300i	$0.472611\pi$
$54$		0			0
$55$		−	7.95152i		−	1.07218i
$56$	−1.88942	+	7.24086i	−0.252485	+	0.967601i
$57$		0			0
$58$	−1.68095	−	1.50530i	−0.220720	−	0.197655i
$59$	−5.36835	+	9.29825i	−0.698899	+	1.21053i	0.269949	+	0.962875i	$0.412993\pi$
$59$	−5.36835	+	9.29825i	−0.698899	+	1.21053i	−0.968848	+	0.247654i	$0.920340\pi$
$60$		0			0
$61$	0.997571	+	1.72784i	0.127726	+	0.221228i	0.922795	−	0.385291i	$-0.125899\pi$
$61$	0.997571	+	1.72784i	0.127726	+	0.221228i	−0.795069	+	0.606519i	$0.792566\pi$
$62$	−11.3444	+	3.72007i	−1.44074	+	0.472450i
$63$		0			0
$64$	2.59564	+	7.56721i	0.324455	+	0.945901i
$65$	18.2344	−	10.5276i	2.26170	−	1.30579i
$66$		0			0
$67$	0.00277185	+	0.00160033i	0.000338635	+	0.000195511i	0.500169	−	0.865928i	$-0.333271\pi$
$67$	0.00277185	+	0.00160033i	0.000338635	+	0.000195511i	−0.499831	+	0.866123i	$0.666604\pi$
$68$	−2.48306	+	5.65947i	−0.301115	+	0.686312i
$69$		0			0
$70$	−11.7681	+	1.87747i	−1.40655	+	0.224400i
$71$	12.4088			1.47265			0.736324	−	0.676629i	$-0.236560\pi$
$71$	12.4088			1.47265			0.736324	+	0.676629i	$0.236560\pi$
$72$		0			0
$73$	0.957657	−	1.65871i	0.112085	−	0.194137i	−0.804526	−	0.593918i	$-0.797580\pi$
$73$	0.957657	−	1.65871i	0.112085	−	0.194137i	0.916611	+	0.399781i	$0.130914\pi$
$74$	0.989607	+	0.207543i	0.115040	+	0.0241264i
$75$		0			0
$76$	6.02120	+	8.19362i	0.690679	+	0.939873i
$77$	6.52245	+	1.04366i	0.743302	+	0.118936i
$78$		0			0
$79$	−6.11304	+	3.52937i	−0.687771	+	0.397085i	−0.802776	−	0.596280i	$-0.796645\pi$
$79$	−6.11304	+	3.52937i	−0.687771	+	0.397085i	0.115005	+	0.993365i	$0.463311\pi$
$80$	−9.37438	+	8.62674i	−1.04809	+	0.964498i
$81$		0			0
$82$	12.9170	+	11.5672i	1.42645	+	1.27739i
$83$	−7.93317			−0.870778			−0.435389	−	0.900242i	$-0.643389\pi$
$83$	−7.93317			−0.870778			−0.435389	+	0.900242i	$0.643389\pi$
$84$		0			0
$85$	−9.84177			−1.06749
$86$	3.92341	+	3.51343i	0.423073	+	0.378863i
$87$		0			0
$88$	6.42741	−	2.92457i	0.685164	−	0.311760i
$89$	0.482940	−	0.278825i	0.0511915	−	0.0295554i	−0.474186	−	0.880425i	$-0.657258\pi$
$89$	0.482940	−	0.278825i	0.0511915	−	0.0295554i	0.525377	+	0.850869i	$0.323924\pi$
$90$		0			0
$91$	6.24226	+	16.3391i	0.654366	+	1.71280i
$92$	−8.18314	+	6.01350i	−0.853151	+	0.626951i
$93$		0			0
$94$	−6.95847	−	1.45935i	−0.717711	−	0.150520i
$95$	−8.09615	+	14.0229i	−0.830647	+	1.43872i
$96$		0			0
$97$	0.127151			0.0129103			0.00645513	−	0.999979i	$-0.497945\pi$
$97$	0.127151			0.0129103			0.00645513	+	0.999979i	$0.497945\pi$
$98$	0.00455176	−	9.89949i	0.000459797	−	1.00000i
$99$		0			0
$100$	−9.42060	−	4.13323i	−0.942060	−	0.413323i
$101$	2.78771	+	1.60949i	0.277388	+	0.160150i	0.632240	−	0.774772i	$-0.282136\pi$
$101$	2.78771	+	1.60949i	0.277388	+	0.160150i	−0.354852	+	0.934922i	$0.615469\pi$
$102$		0			0
$103$	1.60433	−	0.926260i	0.158079	−	0.0912671i	−0.418874	−	0.908045i	$-0.637575\pi$
$103$	1.60433	−	0.926260i	0.158079	−	0.0912671i	0.576953	+	0.816777i	$0.304242\pi$
$104$	15.2164	+	10.8672i	1.49209	+	1.06562i
$105$		0			0
$106$	−11.2031	+	3.67374i	−1.08814	+	0.356825i
$107$	−1.34472	−	2.32912i	−0.129999	−	0.225165i	0.793677	−	0.608340i	$-0.208164\pi$
$107$	−1.34472	−	2.32912i	−0.129999	−	0.225165i	−0.923676	+	0.383175i	$0.874831\pi$
$108$		0			0
$109$	−1.16374	+	2.01566i	−0.111466	+	0.193065i	−0.916362	−	0.400352i	$-0.868888\pi$
$109$	−1.16374	+	2.01566i	−0.111466	+	0.193065i	0.804895	+	0.593417i	$0.202221\pi$
$110$	8.37716	+	7.50178i	0.798730	+	0.715266i
$111$		0			0
$112$	−5.84590	−	8.82188i	−0.552385	−	0.833589i
$113$			3.19262i			0.300336i	0.988660	+	0.150168i	$0.0479815\pi$
$113$			3.19262i			0.300336i	−0.988660	+	0.150168i	$0.952019\pi$
$114$		0			0
$115$	−14.0050	−	8.08579i	−1.30597	−	0.754004i
$116$	3.17175	−	0.350773i	0.294490	−	0.0325684i
$117$		0			0
$118$	−4.73126	−	14.4280i	−0.435548	−	1.32821i
$119$	1.29176	−	8.07298i	0.118416	−	0.740049i
$120$		0			0
$121$	2.38346	+	4.12827i	0.216678	+	0.375297i
$122$	−2.76148	−	0.579146i	−0.250013	−	0.0524334i
$123$		0			0
$124$	6.78355	−	15.4613i	0.609181	−	1.38847i
$125$		−	0.457730i		−	0.0409406i
$126$		0			0
$127$		−	16.3682i		−	1.45244i	−0.687463	−	0.726220i	$-0.741275\pi$
$127$		−	16.3682i		−	1.45244i	0.687463	−	0.726220i	$-0.258725\pi$
$128$	−10.4211	−	4.40462i	−0.921104	−	0.389317i
$129$		0			0
$130$	−6.11188	+	29.1427i	−0.536048	+	2.55598i
$131$	−6.73046	−	11.6575i	−0.588043	−	1.01852i	−0.994489	−	0.104845i	$-0.966565\pi$
$131$	−6.73046	−	11.6575i	−0.588043	−	1.01852i	0.406445	−	0.913675i	$-0.366768\pi$
$132$		0			0
$133$	−10.4401	−	8.48164i	−0.905267	−	0.735452i
$134$	−0.00430106	+	0.00141041i	−0.000371555	+	0.000121841i
$135$		0			0
$136$	−3.61980	−	7.95534i	−0.310396	−	0.682165i
$137$	−17.8601	−	10.3115i	−1.52589	−	0.880974i	−0.999528	−	0.0307143i	$-0.990222\pi$
$137$	−17.8601	−	10.3115i	−1.52589	−	0.880974i	−0.526363	−	0.850260i	$-0.676445\pi$
$138$		0			0
$139$		−	1.68786i		−	0.143163i	−0.997435	−	0.0715813i	$-0.977195\pi$
$139$		−	1.68786i		−	0.143163i	0.997435	−	0.0715813i	$-0.0228045\pi$
$140$	9.12448	−	14.1693i	0.771159	−	1.19752i
$141$		0			0
$142$	−11.7069	+	13.0730i	−0.982422	+	1.09706i
$143$	8.25247	−	14.2937i	0.690106	−	1.19530i
$144$		0			0
$145$	2.54084	+	4.40086i	0.211005	+	0.365472i
$146$	0.844008	+	2.57381i	0.0698506	+	0.213010i
$147$		0			0
$148$	−1.15229	+	0.846775i	−0.0947174	+	0.0696045i
$149$	−1.78690	+	1.03167i	−0.146389	+	0.0845175i	−0.571405	−	0.820668i	$-0.693602\pi$
$149$	−1.78690	+	1.03167i	−0.146389	+	0.0845175i	0.425017	+	0.905186i	$0.360268\pi$
$150$		0			0
$151$	−3.42476	−	1.97728i	−0.278703	−	0.160909i	0.354133	−	0.935195i	$-0.384776\pi$
$151$	−3.42476	−	1.97728i	−0.278703	−	0.160909i	−0.632836	+	0.774286i	$0.718109\pi$
$152$	−14.3129	−	1.38667i	−1.16093	−	0.112474i
$153$		0			0
$154$	−7.25307	+	5.88696i	−0.584469	+	0.474385i
$155$	26.8871			2.15962
$156$		0			0
$157$	0.964497	−	1.67056i	0.0769753	−	0.133325i	−0.824968	−	0.565179i	$-0.808807\pi$
$157$	0.964497	−	1.67056i	0.0769753	−	0.133325i	0.901944	+	0.431854i	$0.142140\pi$
$158$	2.04899	−	9.77001i	0.163009	−	0.777260i
$159$		0			0
$160$	−0.244360	−	18.0150i	−0.0193183	−	1.42421i
$161$	8.47079	−	10.4267i	0.667592	−	0.821739i
$162$		0			0
$163$	3.87357	−	2.23640i	0.303401	−	0.175169i	−0.340569	−	0.940220i	$-0.610620\pi$
$163$	3.87357	−	2.23640i	0.303401	−	0.175169i	0.643970	+	0.765051i	$0.277286\pi$
$164$	−24.3728	+	2.69546i	−1.90320	+	0.210480i
$165$		0			0
$166$	7.48446	−	8.35782i	0.580907	−	0.648692i
$167$	−10.5654			−0.817573			−0.408787	−	0.912630i	$-0.634048\pi$
$167$	−10.5654			−0.817573			−0.408787	+	0.912630i	$0.634048\pi$
$168$		0			0
$169$	30.7044			2.36187
$170$	9.28511	−	10.3686i	0.712135	−	0.795234i
$171$		0			0
$172$	−7.40300	+	0.818718i	−0.564474	+	0.0624267i
$173$	−0.942299	+	0.544036i	−0.0716417	+	0.0413623i	−0.535393	−	0.844603i	$-0.679836\pi$
$173$	−0.942299	+	0.544036i	−0.0716417	+	0.0413623i	0.463751	+	0.885965i	$0.346503\pi$
$174$		0			0
$175$	13.4381	+	2.15023i	1.01582	+	0.162542i
$176$	−2.98275	+	9.53061i	−0.224833	+	0.718397i
$177$		0			0
$178$	−0.161874	+	0.771845i	−0.0121329	+	0.0578522i
$179$	−7.75422	+	13.4307i	−0.579578	+	1.00386i	0.415950	+	0.909388i	$0.363449\pi$
$179$	−7.75422	+	13.4307i	−0.579578	+	1.00386i	−0.995528	+	0.0944707i	$0.969884\pi$
$180$		0			0
$181$	−6.30027			−0.468295			−0.234148	−	0.972201i	$-0.575230\pi$
$181$	−6.30027			−0.468295			−0.234148	+	0.972201i	$0.575230\pi$
$182$	−23.1029	−	8.83851i	−1.71250	−	0.655154i
$183$		0			0
$184$	1.38490	−	14.2945i	0.102096	−	1.05381i
$185$	−1.97208	−	1.13858i	−0.144990	−	0.0837100i
$186$		0			0
$187$	−6.68124	+	3.85741i	−0.488580	+	0.282082i
$188$	8.10236	−	5.95414i	0.590925	−	0.434250i
$189$		0			0
$190$	−7.13535	−	21.7593i	−0.517652	−	1.57859i
$191$	7.84498	+	13.5879i	0.567643	+	0.983186i	0.996798	+	0.0799556i	$0.0254779\pi$
$191$	7.84498	+	13.5879i	0.567643	+	0.983186i	−0.429156	+	0.903231i	$0.641189\pi$
$192$		0			0
$193$	−9.09152	+	15.7470i	−0.654422	+	1.13349i	0.327617	+	0.944811i	$0.393755\pi$
$193$	−9.09152	+	15.7470i	−0.654422	+	1.13349i	−0.982038	+	0.188681i	$0.939579\pi$
$194$	−0.119960	+	0.133958i	−0.00861260	+	0.00961759i
$195$		0			0
$196$	10.4251	+	9.34437i	0.744650	+	0.667455i
$197$			15.1305i			1.07801i	0.842304	+	0.539003i	$0.181199\pi$
$197$			15.1305i			1.07801i	−0.842304	+	0.539003i	$0.818801\pi$
$198$		0			0
$199$	12.7163	+	7.34175i	0.901434	+	0.520443i	0.877665	−	0.479275i	$-0.159100\pi$
$199$	12.7163	+	7.34175i	0.901434	+	0.520443i	0.0237685	+	0.999717i	$0.492434\pi$
$200$	13.2422	−	6.02543i	0.936368	−	0.426062i
$201$		0			0
$202$	−4.32568	+	1.41848i	−0.304354	+	0.0998041i
$203$	−3.94342	+	1.50657i	−0.276774	+	0.105740i
$204$		0			0
$205$	−19.5247	−	33.8178i	−1.36366	−	2.36193i
$206$	−0.537746	+	2.56408i	−0.0374665	+	0.178648i
$207$		0			0
$208$	−25.8047	+	5.77829i	−1.78923	+	0.400652i
$209$			12.6929i			0.877988i
$210$		0			0
$211$		−	12.6913i		−	0.873707i	−0.899533	−	0.436853i	$-0.856093\pi$
$211$		−	12.6913i		−	0.873707i	0.899533	−	0.436853i	$-0.143907\pi$
$212$	6.69906	−	15.2687i	0.460093	−	1.04866i
$213$		0			0
$214$	3.72246	+	0.780686i	0.254462	+	0.0533666i
$215$	−5.93043	−	10.2718i	−0.404452	−	0.700532i
$216$		0			0
$217$	−3.52901	+	22.0548i	−0.239565	+	1.49718i
$218$	−1.02564	−	3.12769i	−0.0694648	−	0.211834i
$219$		0			0
$220$	−15.8067	+	1.74810i	−1.06569	+	0.117857i
$221$	−17.6916	−	10.2143i	−1.19007	−	0.687086i
$222$		0			0
$223$		−	26.9731i		−	1.80625i	−0.429377	−	0.903125i	$-0.641267\pi$
$223$		−	26.9731i		−	1.80625i	0.429377	−	0.903125i	$-0.358733\pi$
$224$	14.8093	+	2.16408i	0.989491	+	0.144594i
$225$		0			0
$226$	−3.36351	−	3.01204i	−0.223738	−	0.200358i
$227$	10.4418	−	18.0857i	0.693045	−	1.20039i	−0.277790	−	0.960642i	$-0.589602\pi$
$227$	10.4418	−	18.0857i	0.693045	−	1.20039i	0.970835	−	0.239748i	$-0.0770648\pi$
$228$		0			0
$229$	−10.3698	−	17.9611i	−0.685258	−	1.18690i	−0.973356	−	0.229301i	$-0.926356\pi$
$229$	−10.3698	−	17.9611i	−0.685258	−	1.18690i	0.288097	−	0.957601i	$-0.406977\pi$
$230$	21.7315	−	7.12622i	1.43293	−	0.469889i
$231$		0			0
$232$	−2.62280	+	3.67246i	−0.172196	+	0.241109i
$233$	−14.4007	+	8.31426i	−0.943422	+	0.544685i	−0.891031	−	0.453942i	$-0.850017\pi$
$233$	−14.4007	+	8.31426i	−0.943422	+	0.544685i	−0.0523907	+	0.998627i	$0.516684\pi$
$234$		0			0
$235$	13.8668	+	8.00597i	0.904567	+	0.522252i
$236$	19.6640	+	8.62746i	1.28002	+	0.561600i
$237$		0			0
$238$	7.28641	+	8.97727i	0.472308	+	0.581910i
$239$	−20.5645			−1.33021			−0.665104	−	0.746751i	$-0.731613\pi$
$239$	−20.5645			−1.33021			−0.665104	+	0.746751i	$0.731613\pi$
$240$		0			0
$241$	−11.2591	+	19.5013i	−0.725262	+	1.25619i	0.233604	+	0.972332i	$0.424948\pi$
$241$	−11.2591	+	19.5013i	−0.725262	+	1.25619i	−0.958866	+	0.283859i	$0.908385\pi$
$242$	−6.59789	−	1.38373i	−0.424129	−	0.0889495i
$243$		0			0
$244$	3.21544	−	2.36291i	0.205847	−	0.151270i
$245$	−6.95659	+	21.1813i	−0.444440	+	1.35322i
$246$		0			0
$247$	−29.1074	+	16.8051i	−1.85206	+	1.06929i
$248$	9.88907	+	21.7335i	0.627956	+	1.38008i
$249$		0			0
$250$	0.482231	+	0.431840i	0.0304990	+	0.0273120i
$251$	5.03762			0.317972			0.158986	−	0.987281i	$-0.449178\pi$
$251$	5.03762			0.317972			0.158986	+	0.987281i	$0.449178\pi$
$252$		0			0
$253$	−12.6767			−0.796976
$254$	17.2443	+	15.4424i	1.08201	+	0.968940i
$255$		0			0
$256$	14.4721	−	6.82343i	0.904504	−	0.426465i
$257$	−2.41622	+	1.39501i	−0.150720	+	0.0870182i	−0.573463	−	0.819231i	$-0.694400\pi$
$257$	−2.41622	+	1.39501i	−0.150720	+	0.0870182i	0.422743	+	0.906249i	$0.361067\pi$
$258$		0			0
$259$	1.19279	−	1.46821i	0.0741165	−	0.0912300i
$260$	−24.9364	−	33.9334i	−1.54649	−	2.10446i
$261$		0			0
$262$	18.6313	+	3.90741i	1.15105	+	0.241401i
$263$	−14.2092	+	24.6110i	−0.876176	+	1.51758i	−0.0206722	+	0.999786i	$0.506581\pi$
$263$	−14.2092	+	24.6110i	−0.876176	+	1.51758i	−0.855504	+	0.517796i	$0.826753\pi$
$264$		0			0
$265$	26.5522			1.63109
$266$	18.7852	−	2.99698i	1.15180	−	0.183757i
$267$		0			0
$268$	0.00257188	−	0.00586193i	0.000157103	−	0.000358074i
$269$	−6.30707	−	3.64139i	−0.384549	−	0.222019i	0.295247	−	0.955421i	$-0.404598\pi$
$269$	−6.30707	−	3.64139i	−0.384549	−	0.222019i	−0.679796	+	0.733402i	$0.737932\pi$
$270$		0			0
$271$	−3.46120	+	1.99832i	−0.210253	+	0.121390i	−0.601429	−	0.798926i	$-0.705402\pi$
$271$	−3.46120	+	1.99832i	−0.210253	+	0.121390i	0.391176	+	0.920316i	$0.372068\pi$
$272$	11.7962	+	3.69181i	0.715252	+	0.223849i
$273$		0			0
$274$	27.7134	−	9.08782i	1.67423	−	0.549016i
$275$	−6.42094	−	11.1214i	−0.387197	−	0.670646i
$276$		0			0
$277$	−9.96864	+	17.2662i	−0.598958	+	1.03743i	0.394018	+	0.919103i	$0.371085\pi$
$277$	−9.96864	+	17.2662i	−0.598958	+	1.03743i	−0.992975	+	0.118322i	$0.962248\pi$
$278$	1.77821	+	1.59240i	0.106650	+	0.0955056i
$279$		0			0
$280$	6.31933	+	22.9807i	0.377652	+	1.37336i
$281$			13.3615i			0.797082i	0.917150	+	0.398541i	$0.130483\pi$
$281$			13.3615i			0.797082i	−0.917150	+	0.398541i	$0.869517\pi$
$282$		0			0
$283$	−18.4457	−	10.6496i	−1.09648	−	0.633054i	−0.161187	−	0.986924i	$-0.551532\pi$
$283$	−18.4457	−	10.6496i	−1.09648	−	0.633054i	−0.935295	+	0.353870i	$0.884866\pi$
$284$	−2.72800	−	24.6671i	−0.161877	−	1.46372i
$285$		0			0
$286$	7.27312	+	22.1795i	0.430068	+	1.31150i
$287$	30.3026	−	11.5770i	1.78871	−	0.683367i
$288$		0			0
$289$	−3.72560	−	6.45293i	−0.219153	−	0.379584i
$290$	−7.03357	−	1.47510i	−0.413025	−	0.0866209i
$291$		0			0
$292$	−3.50785	−	1.53905i	−0.205282	−	0.0900659i
$293$		−	0.551006i		−	0.0321901i	−0.999870	−	0.0160951i	$-0.994877\pi$
$293$		−	0.551006i		−	0.0321901i	0.999870	−	0.0160951i	$-0.00512344\pi$
$294$		0			0
$295$			34.1955i			1.99094i
$296$	0.195011	−	2.01285i	0.0113348	−	0.116994i
$297$		0			0
$298$	0.598941	−	2.85587i	0.0346957	−	0.165436i
$299$	−16.7836	−	29.0701i	−0.970623	−	1.68117i
$300$		0			0
$301$	9.20412	−	3.51639i	0.530517	−	0.202681i
$302$	5.31417	−	1.74263i	0.305796	−	0.100277i
$303$		0			0
$304$	14.9642	−	13.7708i	0.858256	−	0.789807i
$305$	5.50305	+	3.17719i	0.315104	+	0.181925i
$306$		0			0
$307$		−	3.49188i		−	0.199292i	−0.995023	−	0.0996460i	$-0.968229\pi$
$307$		−	3.49188i		−	0.199292i	0.995023	−	0.0996460i	$-0.0317710\pi$
$308$	0.640749	−	13.1953i	0.0365100	−	0.751872i
$309$		0			0
$310$	−25.3663	+	28.3263i	−1.44071	+	1.60882i
$311$	−6.52568	+	11.3028i	−0.370037	+	0.640924i	−0.989571	−	0.144047i	$-0.953988\pi$
$311$	−6.52568	+	11.3028i	−0.370037	+	0.640924i	0.619533	+	0.784970i	$0.287322\pi$
$312$		0			0
$313$	10.0472	+	17.4022i	0.567899	+	0.983630i	0.996774	+	0.0802656i	$0.0255768\pi$
$313$	10.0472	+	17.4022i	0.567899	+	0.983630i	−0.428875	+	0.903364i	$0.641090\pi$
$314$	0.850036	+	2.59220i	0.0479703	+	0.146286i
$315$		0			0
$316$	8.35988	+	11.3761i	0.470280	+	0.639955i
$317$	−18.4393	+	10.6459i	−1.03565	+	0.597935i	−0.918599	−	0.395190i	$-0.870679\pi$
$317$	−18.4393	+	10.6459i	−1.03565	+	0.597935i	−0.117055	+	0.993125i	$0.537345\pi$
$318$		0			0
$319$	3.44978	+	1.99173i	0.193150	+	0.111515i
$320$	19.2098	+	16.7386i	1.07386	+	0.935716i
$321$		0			0
$322$	2.99315	+	18.7612i	0.166802	+	1.04552i
$323$	15.7103			0.874144
$324$		0			0
$325$	17.0024	−	29.4490i	0.943122	−	1.63354i
$326$	−1.29836	+	6.19083i	−0.0719094	+	0.342878i
$327$		0			0
$328$	20.1545	−	28.2205i	1.11285	−	1.55821i
$329$	−8.38717	+	10.3238i	−0.462400	+	0.569168i
$330$		0			0
$331$	4.03493	−	2.32957i	0.221780	−	0.128045i	−0.384994	−	0.922919i	$-0.625797\pi$
$331$	4.03493	−	2.32957i	0.221780	−	0.128045i	0.606774	+	0.794874i	$0.292463\pi$
$332$	1.74407	+	15.7702i	0.0957181	+	0.865501i
$333$		0			0
$334$	9.96779	−	11.1309i	0.545413	−	0.609057i
$335$	0.0101938			0.000556948
$336$		0			0
$337$	−7.41763			−0.404064			−0.202032	−	0.979379i	$-0.564754\pi$
$337$	−7.41763			−0.404064			−0.202032	+	0.979379i	$0.564754\pi$
$338$	−28.9677	+	32.3479i	−1.57564	+	1.75950i
$339$		0			0
$340$	2.16366	+	19.5643i	0.117341	+	1.06102i
$341$	18.2527	−	10.5382i	0.988439	−	0.570675i
$342$		0			0
$343$	−16.4615	−	8.48645i	−0.888836	−	0.458225i
$344$	6.12174	−	8.57169i	0.330062	−	0.462154i
$345$		0			0
$346$	0.315844	−	1.50600i	0.0169799	−	0.0809633i
$347$	−6.28113	+	10.8792i	−0.337188	+	0.584028i	−0.983903	−	0.178705i	$-0.942809\pi$
$347$	−6.28113	+	10.8792i	−0.337188	+	0.584028i	0.646714	+	0.762732i	$0.276143\pi$
$348$		0			0
$349$	−16.6865			−0.893208			−0.446604	−	0.894732i	$-0.647367\pi$
$349$	−16.6865			−0.893208			−0.446604	+	0.894732i	$0.647367\pi$
$350$	−14.9433	+	12.1288i	−0.798754	+	0.648309i
$351$		0			0
$352$	−7.22673	−	12.1340i	−0.385186	−	0.646743i
$353$	−9.31826	−	5.37990i	−0.495961	−	0.286343i	0.231083	−	0.972934i	$-0.425773\pi$
$353$	−9.31826	−	5.37990i	−0.495961	−	0.286343i	−0.727044	+	0.686591i	$0.759106\pi$
$354$		0			0
$355$	34.2261	−	19.7605i	1.81653	−	1.04878i
$356$	−0.660443	−	0.898728i	−0.0350034	−	0.0476325i
$357$		0			0
$358$	−6.83400	−	20.8404i	−0.361188	−	1.10145i
$359$	−13.8374	−	23.9670i	−0.730309	−	1.26493i	−0.956751	−	0.290908i	$-0.906043\pi$
$359$	−13.8374	−	23.9670i	−0.730309	−	1.26493i	0.226442	−	0.974025i	$-0.427291\pi$
$360$		0			0
$361$	3.42378	−	5.93017i	0.180199	−	0.312114i
$362$	5.94392	−	6.63752i	0.312406	−	0.348860i
$363$		0			0
$364$	31.1078	−	16.0009i	1.63049	−	0.838676i
$365$		−	6.10012i		−	0.319295i
$366$		0			0
$367$	−2.00186	−	1.15577i	−0.104496	−	0.0603308i	0.446841	−	0.894613i	$-0.352549\pi$
$367$	−2.00186	−	1.15577i	−0.104496	−	0.0603308i	−0.551337	+	0.834282i	$0.685882\pi$
$368$	13.7531	+	14.9451i	0.716932	+	0.779065i
$369$		0			0
$370$	3.06006	−	1.00346i	0.159085	−	0.0521674i
$371$	−3.48506	+	21.7801i	−0.180935	+	1.13077i
$372$		0			0
$373$	4.61557	+	7.99441i	0.238985	+	0.413935i	0.960423	−	0.278544i	$-0.0898519\pi$
$373$	4.61557	+	7.99441i	0.238985	+	0.413935i	−0.721438	+	0.692479i	$0.756519\pi$
$374$	2.23944	−	10.6781i	0.115799	−	0.552152i
$375$		0			0
$376$	−1.37123	+	14.1534i	−0.0707157	+	0.729908i
$377$			10.5480i			0.543251i
$378$		0			0
$379$			9.38441i			0.482045i	0.970520	+	0.241022i	$0.0774827\pi$
$379$			9.38441i			0.482045i	−0.970520	+	0.241022i	$0.922517\pi$
$380$	29.6558	+	13.0113i	1.52131	+	0.667466i
$381$		0			0
$382$	−21.7165	−	4.55445i	−1.11111	−	0.233026i
$383$	−5.31186	−	9.20042i	−0.271424	−	0.470119i	0.697803	−	0.716290i	$-0.254161\pi$
$383$	−5.31186	−	9.20042i	−0.271424	−	0.470119i	−0.969227	+	0.246170i	$0.920828\pi$
$384$		0			0
$385$	19.6524	−	7.50809i	1.00158	−	0.382648i
$386$	−8.01259	−	24.4345i	−0.407830	−	1.24368i
$387$		0			0
$388$	−0.0279536	−	0.252762i	−0.00141913	−	0.0128320i
$389$	15.4666	+	8.92965i	0.784188	+	0.452751i	0.837912	−	0.545805i	$-0.183776\pi$
$389$	15.4666	+	8.92965i	0.784188	+	0.452751i	−0.0537245	+	0.998556i	$0.517109\pi$
$390$		0			0
$391$			15.6902i			0.793487i
$392$	−19.6800	+	2.16731i	−0.993991	+	0.109466i
$393$		0			0
$394$	−15.9404	−	14.2747i	−0.803068	−	0.719150i
$395$	−11.2408	+	19.4696i	−0.565584	+	0.979620i
$396$		0			0
$397$	3.96912	+	6.87472i	0.199204	+	0.345032i	0.948271	−	0.317463i	$-0.102831\pi$
$397$	3.96912	+	6.87472i	0.199204	+	0.345032i	−0.749066	+	0.662495i	$0.769498\pi$
$398$	−19.7318	+	6.47047i	−0.989065	+	0.324336i
$399$		0			0
$400$	−6.14529	+	19.6357i	−0.307264	+	0.981785i
$401$	−5.23636	+	3.02322i	−0.261491	+	0.150972i	−0.625015	−	0.780613i	$-0.714907\pi$
$401$	−5.23636	+	3.02322i	−0.261491	+	0.150972i	0.363523	+	0.931585i	$0.381574\pi$
$402$		0			0
$403$	48.3323	+	27.9047i	2.40761	+	1.39003i
$404$	2.58660	−	5.89548i	0.128688	−	0.293311i
$405$		0			0
$406$	2.13317	−	5.57586i	0.105867	−	0.276725i
$407$	−1.78503			−0.0884808
$408$		0			0
$409$	14.4850	−	25.0887i	0.716237	−	1.24056i	−0.246244	−	0.969208i	$-0.579196\pi$
$409$	14.4850	−	25.0887i	0.716237	−	1.24056i	0.962481	−	0.271351i	$-0.0874703\pi$
$410$	54.0483	+	11.3352i	2.66926	+	0.559805i
$411$		0			0
$412$	−2.19400	−	2.98558i	−0.108091	−	0.147089i
$413$	−28.0498	−	4.48827i	−1.38024	−	0.220854i
$414$		0			0
$415$	−21.8814	+	12.6333i	−1.07412	+	0.620142i
$416$	18.2575	−	32.6374i	0.895150	−	1.60018i
$417$		0			0
$418$	−13.3724	−	11.9750i	−0.654063	−	0.585716i
$419$	−23.3784			−1.14211			−0.571054	−	0.820913i	$-0.693465\pi$
$419$	−23.3784			−1.14211			−0.571054	+	0.820913i	$0.693465\pi$
$420$		0			0
$421$	19.0596			0.928910			0.464455	−	0.885597i	$-0.346250\pi$
$421$	19.0596			0.928910			0.464455	+	0.885597i	$0.346250\pi$
$422$	13.3707	+	11.9735i	0.650874	+	0.582860i
$423$		0			0
$424$	9.76589	+	21.4628i	0.474274	+	1.04232i
$425$	−13.7652	+	7.94734i	−0.667710	+	0.385502i
$426$		0			0
$427$	−3.32847	+	4.09701i	−0.161076	+	0.198268i
$428$	−4.33439	+	3.18519i	−0.209511	+	0.153962i
$429$		0			0
$430$	16.4166	+	3.44295i	0.791681	+	0.166034i
$431$	−6.24488	+	10.8164i	−0.300805	+	0.521010i	−0.976319	−	0.216338i	$-0.930589\pi$
$431$	−6.24488	+	10.8164i	−0.300805	+	0.521010i	0.675513	+	0.737348i	$0.263922\pi$
$432$		0			0
$433$	21.0419			1.01121			0.505604	−	0.862766i	$-0.331270\pi$
$433$	21.0419			1.01121			0.505604	+	0.862766i	$0.331270\pi$
$434$	−19.9060	−	24.5253i	−0.955518	−	1.17725i
$435$		0			0
$436$	4.26273	+	1.87025i	0.204148	+	0.0895685i
$437$	22.3560	+	12.9073i	1.06943	+	0.617438i
$438$		0			0
$439$	27.9142	−	16.1163i	1.33227	−	0.769189i	0.346626	−	0.938003i	$-0.387327\pi$
$439$	27.9142	−	16.1163i	1.33227	−	0.769189i	0.985648	+	0.168815i	$0.0539939\pi$
$440$	13.0710	−	18.3020i	0.623133	−	0.872514i
$441$		0			0
$442$	27.4520	−	9.00209i	1.30576	−	0.428186i
$443$	1.90658	+	3.30230i	0.0905844	+	0.156897i	0.907757	−	0.419496i	$-0.137793\pi$
$443$	1.90658	+	3.30230i	0.0905844	+	0.156897i	−0.817173	+	0.576393i	$0.804460\pi$
$444$		0			0
$445$	0.888036	−	1.53812i	0.0420970	−	0.0729141i
$446$	28.4169	+	25.4474i	1.34558	+	1.20497i
$447$		0			0
$448$	−16.2516	+	13.5604i	−0.767818	+	0.640668i
$449$			33.6975i			1.59028i	0.606425	+	0.795141i	$0.292603\pi$
$449$			33.6975i			1.59028i	−0.606425	+	0.795141i	$0.707397\pi$
$450$		0			0
$451$	−26.5093	−	15.3051i	−1.24827	−	0.720691i
$452$	6.34654	−	0.701881i	0.298516	−	0.0330137i
$453$		0			0
$454$	9.20261	+	28.0635i	0.431900	+	1.31708i
$455$	43.2368	+	35.1262i	2.02697	+	1.64674i
$456$		0			0
$457$	12.8270	+	22.2171i	0.600023	+	1.03927i	0.992817	+	0.119644i	$0.0381752\pi$
$457$	12.8270	+	22.2171i	0.600023	+	1.03927i	−0.392794	+	0.919626i	$0.628491\pi$
$458$	28.7058	+	6.02027i	1.34134	+	0.281309i
$459$		0			0
$460$	−12.9947	+	29.6179i	−0.605879	+	1.38094i
$461$		−	12.8586i		−	0.598884i	−0.954115	−	0.299442i	$-0.903200\pi$
$461$		−	12.8586i		−	0.598884i	0.954115	−	0.299442i	$-0.0968005\pi$
$462$		0			0
$463$			15.0540i			0.699619i	0.936821	+	0.349809i	$0.113754\pi$
$463$			15.0540i			0.699619i	−0.936821	+	0.349809i	$0.886246\pi$
$464$	−1.39459	−	6.22795i	−0.0647421	−	0.289125i
$465$		0			0
$466$	4.82689	−	23.0156i	0.223601	−	1.06618i
$467$	−5.85210	−	10.1361i	−0.270803	−	0.469044i	0.698265	−	0.715840i	$-0.253956\pi$
$467$	−5.85210	−	10.1361i	−0.270803	−	0.469044i	−0.969068	+	0.246795i	$0.920622\pi$
$468$		0			0
$469$	−0.00133797	+	0.00836177i	−6.17819e−5	+	0.000386111i
$470$	−21.5170	+	7.05587i	−0.992503	+	0.325463i
$471$		0			0
$472$	−27.6411	+	12.5771i	−1.27228	+	0.578909i
$473$	−8.05193	−	4.64878i	−0.370228	−	0.213751i
$474$		0			0
$475$			26.1509i			1.19989i
$476$	−16.3321	−	0.793068i	−0.748581	−	0.0363502i
$477$		0			0
$478$	19.4014	−	21.6653i	0.887398	−	0.990948i
$479$	15.5454	−	26.9254i	0.710287	−	1.23025i	−0.254462	−	0.967083i	$-0.581898\pi$
$479$	15.5454	−	26.9254i	0.710287	−	1.23025i	0.964749	−	0.263170i	$-0.0847682\pi$
$480$		0			0
$481$	−2.36335	−	4.09343i	−0.107759	−	0.186645i
$482$	−9.92293	−	30.2601i	−0.451977	−	1.37831i
$483$		0			0
$484$	7.68251	−	5.64560i	0.349205	−	0.256618i
$485$	0.350712	−	0.202483i	0.0159250	−	0.00919430i
$486$		0			0
$487$	−4.79848	−	2.77040i	−0.217440	−	0.125539i	0.387324	−	0.921943i	$-0.373399\pi$
$487$	−4.79848	−	2.77040i	−0.217440	−	0.125539i	−0.604764	+	0.796405i	$0.706733\pi$
$488$	−0.544175	+	5.61682i	−0.0246336	+	0.254261i
$489$		0			0
$490$	−15.7520	−	27.3122i	−0.711603	−	1.23384i
$491$	30.3204			1.36834			0.684171	−	0.729321i	$-0.260164\pi$
$491$	30.3204			1.36834			0.684171	+	0.729321i	$0.260164\pi$
$492$		0			0
$493$	2.46521	−	4.26986i	0.111027	−	0.192305i
$494$	9.75633	−	46.5201i	0.438958	−	2.09304i
$495$		0			0
$496$	−32.2266	−	10.0858i	−1.44702	−	0.452865i
$497$	11.7168	+	30.6685i	0.525569	+	1.37567i
$498$		0			0
$499$	−11.9203	+	6.88217i	−0.533624	+	0.308088i	−0.742491	−	0.669856i	$-0.766356\pi$
$499$	−11.9203	+	6.88217i	−0.533624	+	0.308088i	0.208867	+	0.977944i	$0.433022\pi$
$500$	−0.909912	+	0.100630i	−0.0406925	+	0.00450029i
$501$		0			0
$502$	−4.75269	+	5.30727i	−0.212123	+	0.236875i
$503$	−5.66994			−0.252810			−0.126405	−	0.991979i	$-0.540344\pi$
$503$	−5.66994			−0.252810			−0.126405	+	0.991979i	$0.540344\pi$
$504$		0			0
$505$	10.2522			0.456216
$506$	11.9597	−	13.3552i	0.531673	−	0.593713i
$507$		0			0
$508$	−32.5379	+	3.59846i	−1.44364	+	0.159656i
$509$	−23.9698	+	13.8390i	−1.06244	+	0.613401i	−0.926107	−	0.377262i	$-0.876866\pi$
$509$	−23.9698	+	13.8390i	−1.06244	+	0.613401i	−0.136335	+	0.990663i	$0.543532\pi$
$510$		0			0
$511$	5.00379	+	0.800661i	0.221355	+	0.0354192i
$512$	−6.46483	+	21.6842i	−0.285708	+	0.958317i
$513$		0			0
$514$	0.809880	−	3.86166i	0.0357223	−	0.170331i
$515$	2.95006	−	5.10966i	0.129995	−	0.225159i
$516$		0			0
$517$	12.5515			0.552016
$518$	0.421472	+	2.64181i	0.0185184	+	0.116074i
$519$		0			0
$520$	59.2758	+	5.74282i	2.59942	+	0.251839i
$521$	4.14916	+	2.39552i	0.181778	+	0.104950i	0.588128	−	0.808768i	$-0.299865\pi$
$521$	4.14916	+	2.39552i	0.181778	+	0.104950i	−0.406350	+	0.913718i	$0.633199\pi$
$522$		0			0
$523$	−6.54438	+	3.77840i	−0.286166	+	0.165218i	−0.636211	−	0.771515i	$-0.719499\pi$
$523$	−6.54438	+	3.77840i	−0.286166	+	0.165218i	0.350046	+	0.936733i	$0.386166\pi$
$524$	−21.6941	+	15.9422i	−0.947709	+	0.696438i
$525$		0			0
$526$	−12.5229	−	38.1888i	−0.546026	−	1.66511i
$527$	−13.0434	−	22.5917i	−0.568177	−	0.984112i
$528$		0			0
$529$	−1.39074	+	2.40883i	−0.0604670	+	0.104732i
$530$	−25.0504	+	27.9735i	−1.08812	+	1.21509i
$531$		0			0
$532$	−14.5653	+	22.6182i	−0.631486	+	0.980624i
$533$		−	81.0547i		−	3.51087i
$534$		0			0
$535$	−7.41808	−	4.28283i	−0.320711	−	0.185163i
$536$	0.00374929	+	0.00823992i	0.000161945	+	0.000355910i
$537$		0			0
$538$	9.78665	−	3.20925i	0.421932	−	0.138361i
$539$	3.57928	+	17.1058i	0.154170	+	0.736801i
$540$		0			0
$541$	−10.7589	−	18.6349i	−0.462560	−	0.801177i	0.536528	−	0.843883i	$-0.319736\pi$
$541$	−10.7589	−	18.6349i	−0.462560	−	0.801177i	−0.999088	+	0.0427053i	$0.986402\pi$
$542$	1.16014	−	5.53177i	0.0498322	−	0.237610i
$543$		0			0
$544$	−15.0185	+	8.94468i	−0.643912	+	0.383500i
$545$			7.41285i			0.317532i
$546$		0			0
$547$		−	10.1856i		−	0.435505i	−0.976004	−	0.217752i	$-0.930128\pi$
$547$		−	10.1856i		−	0.435505i	0.976004	−	0.217752i	$-0.0698725\pi$
$548$	−16.5716	+	37.7707i	−0.707906	+	1.61348i
$549$		0			0
$550$	17.7745	+	3.72772i	0.757906	+	0.158950i
$551$	−4.05591	−	7.02505i	−0.172788	−	0.299277i
$552$		0			0
$553$	−14.4950	−	11.7760i	−0.616392	−	0.500765i
$554$	−8.78562	−	26.7919i	−0.373265	−	1.13828i
$555$		0			0
$556$	−3.35527	+	0.371068i	−0.142295	+	0.0157368i
$557$	−32.7379	−	18.9012i	−1.38715	−	0.800871i	−0.394156	−	0.919044i	$-0.628963\pi$
$557$	−32.7379	−	18.9012i	−1.38715	−	0.800871i	−0.992993	+	0.118173i	$0.962296\pi$
$558$		0			0
$559$		−	24.6196i		−	1.04130i
$560$	−30.1728	−	15.0233i	−1.27503	−	0.634852i
$561$		0			0
$562$	−14.0768	−	12.6058i	−0.593792	−	0.531743i
$563$	10.9769	−	19.0126i	0.462623	−	0.801286i	−0.536468	−	0.843921i	$-0.680242\pi$
$563$	10.9769	−	19.0126i	0.462623	−	0.801286i	0.999091	+	0.0426347i	$0.0135752\pi$
$564$		0			0
$565$	5.08412	+	8.80595i	0.213890	+	0.370469i
$566$	28.6221	−	9.38579i	1.20307	−	0.394514i
$567$		0			0
$568$	28.5612	+	20.3979i	1.19840	+	0.855877i
$569$	11.2711	−	6.50737i	0.472509	−	0.272803i	−0.244781	−	0.969578i	$-0.578716\pi$
$569$	11.2711	−	6.50737i	0.472509	−	0.272803i	0.717289	+	0.696775i	$0.245383\pi$
$570$		0			0
$571$	−24.3678	−	14.0688i	−1.01976	−	0.588760i	−0.105727	−	0.994395i	$-0.533717\pi$
$571$	−24.3678	−	14.0688i	−1.01976	−	0.588760i	−0.914035	+	0.405635i	$0.867050\pi$
$572$	−30.2284	−	13.2625i	−1.26391	−	0.554534i
$573$		0			0
$574$	−16.3920	+	42.8468i	−0.684189	+	1.78839i
$575$	−26.1175			−1.08917
$576$		0			0
$577$	−9.72878	+	16.8507i	−0.405014	+	0.701505i	−0.994323	−	0.106403i	$-0.966067\pi$
$577$	−9.72878	+	16.8507i	−0.405014	+	0.701505i	0.589309	+	0.807908i	$0.299400\pi$
$578$	10.3132	+	2.16292i	0.428973	+	0.0899655i
$579$		0			0
$580$	8.18980	−	6.01840i	0.340063	−	0.249900i
$581$	−7.49076	−	19.6070i	−0.310769	−	0.813435i
$582$		0			0
$583$	18.0253	−	10.4069i	0.746534	−	0.431011i
$584$	4.93088	−	2.24363i	0.204041	−	0.0928419i
$585$		0			0
$586$	0.580501	+	0.519841i	0.0239803	+	0.0214744i
$587$	−17.0416			−0.703384			−0.351692	−	0.936116i	$-0.614393\pi$
$587$	−17.0416			−0.703384			−0.351692	+	0.936116i	$0.614393\pi$
$588$		0			0
$589$	−42.9195			−1.76847
$590$	−36.0260	−	32.2614i	−1.48316	−	1.32818i
$591$		0			0
$592$	1.93661	+	2.10445i	0.0795943	+	0.0864923i
$593$	34.0062	−	19.6335i	1.39647	−	0.806251i	0.402448	−	0.915443i	$-0.368160\pi$
$593$	34.0062	−	19.6335i	1.39647	−	0.806251i	0.994021	+	0.109192i	$0.0348262\pi$
$594$		0			0
$595$	−9.29292	−	24.3241i	−0.380973	−	0.997193i
$596$	2.44367	+	3.32534i	0.100097	+	0.136211i
$597$		0			0
$598$	46.4606	+	9.74385i	1.89991	+	0.398456i
$599$	2.41297	−	4.17938i	0.0985912	−	0.170765i	−0.812511	−	0.582946i	$-0.801900\pi$
$599$	2.41297	−	4.17938i	0.0985912	−	0.170765i	0.911102	+	0.412182i	$0.135233\pi$
$600$		0			0
$601$	−17.5618			−0.716363			−0.358181	−	0.933652i	$-0.616603\pi$
$601$	−17.5618			−0.716363			−0.358181	+	0.933652i	$0.616603\pi$
$602$	−4.97891	+	13.0143i	−0.202925	+	0.530424i
$603$		0			0
$604$	−3.17769	+	7.24270i	−0.129298	+	0.294701i
$605$	13.1482	+	7.59112i	0.534550	+	0.308623i
$606$		0			0
$607$	−0.967882	+	0.558807i	−0.0392851	+	0.0226813i	−0.519514	−	0.854462i	$-0.673887\pi$
$607$	−0.967882	+	0.558807i	−0.0392851	+	0.0226813i	0.480229	+	0.877143i	$0.340554\pi$
$608$	0.390068	+	28.7571i	0.0158194	+	1.16625i
$609$		0			0
$610$	−8.53905	+	2.80014i	−0.345736	+	0.113374i
$611$	16.6180	+	28.7832i	0.672291	+	1.16444i
$612$		0			0
$613$	21.2827	−	36.8627i	0.859599	−	1.48887i	−0.0127126	−	0.999919i	$-0.504047\pi$
$613$	21.2827	−	36.8627i	0.859599	−	1.48887i	0.872312	−	0.488950i	$-0.162620\pi$
$614$	3.67879	+	3.29437i	0.148464	+	0.132950i
$615$		0			0
$616$	13.2971	+	13.1240i	0.535756	+	0.528781i
$617$		−	13.9753i		−	0.562625i	−0.959616	−	0.281313i	$-0.909230\pi$
$617$		−	13.9753i		−	0.562625i	0.959616	−	0.281313i	$-0.0907698\pi$
$618$		0			0
$619$	26.7181	+	15.4257i	1.07389	+	0.620012i	0.929242	−	0.369470i	$-0.120461\pi$
$619$	26.7181	+	15.4257i	1.07389	+	0.620012i	0.144650	+	0.989483i	$0.453794\pi$
$620$	−5.91099	−	53.4483i	−0.237391	−	2.14653i
$621$		0			0
$622$	−5.75125	−	17.5385i	−0.230604	−	0.703230i
$623$	1.14513	+	0.930320i	0.0458787	+	0.0372725i
$624$		0			0
$625$	12.1304	+	21.0104i	0.485215	+	0.840417i
$626$	−27.8126	−	5.83294i	−1.11161	−	0.233131i
$627$		0			0
$628$	−3.53291	−	1.55004i	−0.140978	−	0.0618534i
$629$			2.20937i			0.0880935i
$630$		0			0
$631$			27.5528i			1.09686i	0.836197	+	0.548429i	$0.184774\pi$
$631$			27.5528i			1.09686i	−0.836197	+	0.548429i	$0.815226\pi$
$632$	−19.8721	−	1.92527i	−0.790468	−	0.0765831i
$633$		0			0
$634$	6.18056	−	29.4701i	0.245461	−	1.17041i
$635$	−26.0656	−	45.1470i	−1.03438	−	1.79161i
$636$		0			0
$637$	−34.4882	+	30.8558i	−1.36647	+	1.22255i
$638$	−5.35300	+	1.75536i	−0.211927	+	0.0694955i
$639$		0			0
$640$	−35.7579	+	4.44626i	−1.41345	+	0.175754i
$641$	15.1145	+	8.72634i	0.596986	+	0.344670i	0.767855	−	0.640624i	$-0.221324\pi$
$641$	15.1145	+	8.72634i	0.596986	+	0.344670i	−0.170869	+	0.985294i	$0.554658\pi$
$642$		0			0
$643$			18.1663i			0.716409i	0.933643	+	0.358205i	$0.116611\pi$
$643$			18.1663i			0.716409i	−0.933643	+	0.358205i	$0.883389\pi$
$644$	−22.5893	−	14.5467i	−0.890143	−	0.573219i
$645$		0			0
$646$	−14.8217	+	16.5512i	−0.583152	+	0.651200i
$647$	23.0188	−	39.8697i	0.904961	−	1.56744i	0.0839921	−	0.996466i	$-0.473233\pi$
$647$	23.0188	−	39.8697i	0.904961	−	1.56744i	0.820969	−	0.570973i	$-0.193434\pi$
$648$		0			0
$649$	13.4027	+	23.2142i	0.526102	+	0.911235i
$650$	14.9846	+	45.6958i	0.587746	+	1.79234i
$651$		0			0
$652$	−5.29729	−	7.20852i	−0.207458	−	0.282308i
$653$	26.5274	−	15.3156i	1.03810	−	0.599345i	0.118803	−	0.992918i	$-0.462094\pi$
$653$	26.5274	−	15.3156i	1.03810	−	0.599345i	0.919293	+	0.393573i	$0.128761\pi$
$654$		0			0
$655$	−37.1282	−	21.4360i	−1.45072	−	0.837573i
$656$	10.7165	+	47.8577i	0.418409	+	1.86853i
$657$		0			0
$658$	−2.96360	−	18.5760i	−0.115533	−	0.724167i
$659$	23.5790			0.918508			0.459254	−	0.888305i	$-0.348117\pi$
$659$	23.5790			0.918508			0.459254	+	0.888305i	$0.348117\pi$
$660$		0			0
$661$	−8.01914	+	13.8896i	−0.311908	+	0.540241i	−0.978775	−	0.204936i	$-0.934302\pi$
$661$	−8.01914	+	13.8896i	−0.311908	+	0.540241i	0.666867	+	0.745177i	$0.267635\pi$
$662$	−1.35245	+	6.44873i	−0.0525643	+	0.250637i
$663$		0			0
$664$	−18.2598	−	13.0408i	−0.708616	−	0.506081i
$665$	−42.3027	−	6.76889i	−1.64043	−	0.262486i
$666$		0			0
$667$	7.01606	−	4.05072i	0.271663	−	0.156845i
$668$	2.32275	+	21.0027i	0.0898697	+	0.812619i
$669$		0			0
$670$	−0.00961726	+	0.0107395i	−0.000371547	+	0.000414903i
$671$	4.98110			0.192293
$672$		0			0
$673$	−44.4724			−1.71429			−0.857143	−	0.515079i	$-0.827763\pi$
$673$	−44.4724			−1.71429			−0.857143	+	0.515079i	$0.827763\pi$
$674$	6.99808	−	7.81468i	0.269556	−	0.301010i
$675$		0			0
$676$	−6.75021	−	61.0366i	−0.259623	−	2.34756i
$677$	9.48306	−	5.47505i	0.364464	−	0.210423i	−0.306573	−	0.951847i	$-0.599182\pi$
$677$	9.48306	−	5.47505i	0.364464	−	0.210423i	0.671037	+	0.741424i	$0.265849\pi$
$678$		0			0
$679$	0.120061	+	0.314257i	0.00460750	+	0.0120601i
$680$	−22.6528	−	16.1782i	−0.868695	−	0.620406i
$681$		0			0
$682$	−6.11801	+	29.1719i	−0.234271	+	1.11705i
$683$	−4.06412	+	7.03927i	−0.155509	+	0.269350i	−0.933244	−	0.359242i	$-0.883035\pi$
$683$	−4.06412	+	7.03927i	−0.155509	+	0.269350i	0.777735	+	0.628592i	$0.216369\pi$
$684$		0			0
$685$	−65.6828			−2.50961
$686$	24.4711	−	9.33618i	0.934312	−	0.356457i
$687$		0			0
$688$	3.25503	+	14.5363i	0.124097	+	0.554191i
$689$	47.7303	+	27.5571i	1.81838	+	1.04984i
$690$		0			0
$691$	−8.95759	+	5.17166i	−0.340763	+	0.196739i	−0.660609	−	0.750730i	$-0.729702\pi$
$691$	−8.95759	+	5.17166i	−0.340763	+	0.196739i	0.319847	+	0.947469i	$0.396369\pi$
$692$	1.28864	+	1.75357i	0.0489867	+	0.0666609i
$693$		0			0
$694$	−5.53572	−	16.8812i	−0.210133	−	0.640803i
$695$	−2.68785	−	4.65550i	−0.101956	−	0.176593i
$696$		0			0
$697$	−18.9435	+	32.8111i	−0.717536	+	1.24281i
$698$	15.7427	−	17.5797i	0.595870	−	0.665402i
$699$		0			0
$700$	1.32012	−	27.1860i	0.0498958	−	1.02753i
$701$			36.9229i			1.39456i	0.716800	+	0.697279i	$0.245606\pi$
$701$			36.9229i			1.39456i	−0.716800	+	0.697279i	$0.754394\pi$
$702$		0			0
$703$	3.14800	+	1.81750i	0.118729	+	0.0685483i
$704$	19.6015	+	3.83409i	0.738758	+	0.144503i
$705$		0			0
$706$	14.4591	−	4.74145i	0.544175	−	0.178447i
$707$	−1.34563	+	8.40963i	−0.0506077	+	0.316277i
$708$		0			0
$709$	−15.4835	−	26.8182i	−0.581494	−	1.00718i	−0.995303	−	0.0968137i	$-0.969135\pi$
$709$	−15.4835	−	26.8182i	−0.581494	−	1.00718i	0.413808	−	0.910364i	$-0.364198\pi$
$710$	−11.4721	+	54.7010i	−0.430538	+	2.05289i
$711$		0			0
$712$	1.56992	+	0.152099i	0.0588354	+	0.00570015i
$713$		−	42.8646i		−	1.60529i
$714$		0			0
$715$		−	52.5669i		−	1.96589i
$716$	28.4034	+	12.4618i	1.06148	+	0.465719i
$717$		0			0
$718$	38.3047	+	8.03337i	1.42952	+	0.299803i
$719$	23.5411	+	40.7744i	0.877936	+	1.52063i	0.853602	+	0.520925i	$0.174413\pi$
$719$	23.5411	+	40.7744i	0.877936	+	1.52063i	0.0243332	+	0.999704i	$0.492254\pi$
$720$		0			0
$721$	3.80413	+	3.09053i	0.141673	+	0.115097i
$722$	3.01747	+	9.20181i	0.112299	+	0.342456i
$723$		0			0
$724$	1.38508	+	12.5242i	0.0514762	+	0.465458i
$725$	7.10750	+	4.10351i	0.263966	+	0.152401i
$726$		0			0
$727$		−	23.8977i		−	0.886317i	−0.896443	−	0.443158i	$-0.853858\pi$
$727$		−	23.8977i		−	0.886317i	0.896443	−	0.443158i	$-0.146142\pi$
$728$	−12.4908	+	47.8688i	−0.462942	+	1.77414i
$729$		0			0
$730$	6.42665	+	5.75509i	0.237861	+	0.213006i
$731$	−5.75390	+	9.96605i	−0.212816	+	0.368608i
$732$		0			0
$733$	−19.4989	−	33.7731i	−0.720210	−	1.24744i	−0.960916	−	0.276842i	$-0.910712\pi$
$733$	−19.4989	−	33.7731i	−0.720210	−	1.24744i	0.240706	−	0.970598i	$-0.422621\pi$
$734$	3.10627	−	1.01861i	0.114654	−	0.0375977i
$735$		0			0
$736$	−28.7203	+	0.389569i	−1.05864	+	0.0143597i
$737$	0.00692024	−	0.00399540i	0.000254910	−	0.000147173i
$738$		0			0
$739$	19.5445	+	11.2840i	0.718957	+	0.415090i	0.814369	−	0.580348i	$-0.197083\pi$
$739$	19.5445	+	11.2840i	0.718957	+	0.415090i	−0.0954118	+	0.995438i	$0.530417\pi$
$740$	−1.82981	+	4.17056i	−0.0672651	+	0.153313i
$741$		0			0
$742$	−19.6581	−	24.2198i	−0.721670	−	0.889139i
$743$	25.8493			0.948319			0.474159	−	0.880439i	$-0.342752\pi$
$743$	25.8493			0.948319			0.474159	+	0.880439i	$0.342752\pi$
$744$		0			0
$745$	−3.28578	+	5.69114i	−0.120382	+	0.208507i
$746$	−12.7769	−	2.67960i	−0.467794	−	0.0981071i
$747$		0			0
$748$	9.13691	+	12.4335i	0.334079	+	0.454612i
$749$	4.48675	−	5.52274i	0.163942	−	0.201797i
$750$		0			0
$751$	37.3627	−	21.5714i	1.36339	−	0.787151i	0.373313	−	0.927706i	$-0.378222\pi$
$751$	37.3627	−	21.5714i	1.36339	−	0.787151i	0.990073	+	0.140555i	$0.0448885\pi$
$752$	−13.6174	−	14.7975i	−0.496575	−	0.539610i
$753$		0			0
$754$	−11.1126	−	9.95142i	−0.404699	−	0.362409i
$755$	−12.5950			−0.458378
$756$		0			0
$757$	0.176821			0.00642668			0.00321334	−	0.999995i	$-0.498977\pi$
$757$	0.176821			0.00642668			0.00321334	+	0.999995i	$0.498977\pi$
$758$	−9.88675	−	8.85362i	−0.359103	−	0.321578i
$759$		0			0
$760$	−41.6862	+	18.9679i	−1.51212	+	0.688038i
$761$	26.2278	−	15.1426i	0.950758	−	0.548920i	0.0574416	−	0.998349i	$-0.481706\pi$
$761$	26.2278	−	15.1426i	0.950758	−	0.548920i	0.893316	+	0.449429i	$0.148372\pi$
$762$		0			0
$763$	−6.08059	−	0.972961i	−0.220132	−	0.0352235i
$764$	25.2864	−	18.5821i	0.914832	−	0.672277i
$765$		0			0
$766$	14.7043	+	3.08383i	0.531289	+	0.111423i
$767$	−35.4898	+	61.4701i	−1.28146	+	2.21956i
$768$		0			0
$769$	48.5276			1.74995			0.874974	−	0.484169i	$-0.160878\pi$
$769$	48.5276			1.74995			0.874974	+	0.484169i	$0.160878\pi$
$770$	−10.6308	+	27.7878i	−0.383108	+	1.00140i
$771$		0			0
$772$	33.3018	+	14.6110i	1.19856	+	0.525860i
$773$	−3.70357	−	2.13826i	−0.133208	−	0.0769078i	0.431915	−	0.901914i	$-0.357838\pi$
$773$	−3.70357	−	2.13826i	−0.133208	−	0.0769078i	−0.565123	+	0.825007i	$0.691171\pi$
$774$		0			0
$775$	37.6056	−	21.7116i	1.35083	−	0.779904i
$776$	0.292664	+	0.209015i	0.0105060	+	0.00750321i
$777$		0			0
$778$	−23.9994	+	7.86993i	−0.860422	+	0.282151i
$779$	31.1670	+	53.9829i	1.11667	+	1.93414i
$780$		0			0
$781$	15.4900	−	26.8294i	0.554274	−	0.960031i
$782$	−16.5301	−	14.8027i	−0.591114	−	0.529345i
$783$		0			0
$784$	16.2836	−	22.7782i	0.581556	−	0.813506i
$785$		−	6.14369i		−	0.219278i
$786$		0			0
$787$	−11.2769	−	6.51073i	−0.401979	−	0.232083i	0.285359	−	0.958421i	$-0.407887\pi$
$787$	−11.2769	−	6.51073i	−0.401979	−	0.232083i	−0.687337	+	0.726338i	$0.741221\pi$
$788$	30.0777	−	3.32637i	1.07147	−	0.118497i
$789$		0			0
$790$	−9.90677	−	30.2108i	−0.352467	−	1.07485i
$791$	−7.89063	+	3.01458i	−0.280558	+	0.107186i
$792$		0			0
$793$	6.59487	+	11.4227i	0.234191	+	0.405630i
$794$	−10.9873	−	2.30430i	−0.389926	−	0.0817764i
$795$		0			0
$796$	11.7989	−	26.8925i	0.418201	−	0.953179i
$797$		−	14.3145i		−	0.507044i	−0.967330	−	0.253522i	$-0.918411\pi$
$797$		−	14.3145i		−	0.507044i	0.967330	−	0.253522i	$-0.0815891\pi$
$798$		0			0
$799$		−	15.5353i		−	0.549600i
$800$	−14.8891	−	24.9993i	−0.526408	−	0.883860i
$801$		0			0
$802$	1.75515	−	8.36888i	0.0619763	−	0.295515i
$803$	−2.39090	−	4.14116i	−0.0843730	−	0.146138i
$804$		0			0
$805$	6.76023	−	42.2485i	0.238267	−	1.48907i
$806$	−74.9970	+	24.5931i	−2.64166	+	0.866256i
$807$		0			0
$808$	3.77075	+	8.28708i	0.132655	+	0.291539i
$809$	27.1605	+	15.6811i	0.954911	+	0.551318i	0.894603	−	0.446862i	$-0.147458\pi$
$809$	27.1605	+	15.6811i	0.954911	+	0.551318i	0.0603080	+	0.998180i	$0.480792\pi$
$810$		0			0
$811$		−	6.06315i		−	0.212906i	−0.994318	−	0.106453i	$-0.966051\pi$
$811$		−	6.06315i		−	0.212906i	0.994318	−	0.106453i	$-0.0339493\pi$
$812$	3.86181	+	7.50784i	0.135523	+	0.263474i
$813$		0			0
$814$	1.68407	−	1.88058i	0.0590266	−	0.0659144i
$815$	7.12277	−	12.3370i	0.249500	−	0.432146i
$816$		0			0
$817$	9.46668	+	16.3968i	0.331197	+	0.573650i
$818$	12.7660	+	38.9301i	0.446353	+	1.36116i
$819$		0			0
$820$	−62.9333	+	46.2474i	−2.19772	+	1.61503i
$821$	14.9421	−	8.62681i	0.521482	−	0.301078i	−0.216059	−	0.976380i	$-0.569320\pi$
$821$	14.9421	−	8.62681i	0.521482	−	0.301078i	0.737541	+	0.675303i	$0.235987\pi$
$822$		0			0
$823$	−15.6910	−	9.05923i	−0.546955	−	0.315785i	0.200938	−	0.979604i	$-0.435601\pi$
$823$	−15.6910	−	9.05923i	−0.546955	−	0.315785i	−0.747893	+	0.663819i	$0.768934\pi$
$824$	5.21530	+	0.505274i	0.181684	+	0.0176021i
$825$		0			0
$826$	31.1918	−	25.3169i	1.08530	−	0.880886i
$827$	−30.9864			−1.07750			−0.538751	−	0.842465i	$-0.681104\pi$
$827$	−30.9864			−1.07750			−0.538751	+	0.842465i	$0.681104\pi$
$828$		0			0
$829$	−21.8585	+	37.8601i	−0.759178	+	1.31493i	0.184092	+	0.982909i	$0.441065\pi$
$829$	−21.8585	+	37.8601i	−0.759178	+	1.31493i	−0.943270	+	0.332026i	$0.892268\pi$
$830$	7.33431	−	34.9714i	0.254578	−	1.21388i
$831$		0			0
$832$	17.1596	+	50.0263i	0.594901	+	1.73435i
$833$	21.1723	−	4.43015i	0.733576	−	0.153496i
$834$		0			0
$835$	−29.1416	+	16.8249i	−1.00849	+	0.582251i
$836$	25.2320	−	2.79048i	0.872667	−	0.0965106i
$837$		0			0
$838$	22.0561	−	24.6298i	0.761914	−	0.850821i
$839$	−35.4628			−1.22431			−0.612156	−	0.790737i	$-0.709698\pi$
$839$	−35.4628			−1.22431			−0.612156	+	0.790737i	$0.709698\pi$
$840$		0			0
$841$	26.4542			0.912215
$842$	−17.9816	+	20.0799i	−0.619687	+	0.691998i
$843$		0			0
$844$	−25.2288	+	2.79013i	−0.868412	+	0.0960401i
$845$	84.6895	−	48.8955i	2.91341	−	1.68206i
$846$		0			0
$847$	−7.95257	+	9.78881i	−0.273253	+	0.336348i
$848$	−31.8252	−	9.96017i	−1.09288	−	0.342034i
$849$		0			0
$850$	4.61387	−	21.9999i	0.158255	−	0.754589i
$851$	−1.81518	+	3.14398i	−0.0622234	+	0.107774i
$852$		0			0
$853$	31.1730			1.06734			0.533672	−	0.845692i	$-0.320812\pi$
$853$	31.1730			1.06734			0.533672	+	0.845692i	$0.320812\pi$
$854$	−1.17611	−	7.37191i	−0.0402457	−	0.252262i
$855$		0			0
$856$	0.733545	−	7.57144i	0.0250720	−	0.258786i
$857$	6.55908	+	3.78689i	0.224054	+	0.129358i	0.607826	−	0.794070i	$-0.292042\pi$
$857$	6.55908	+	3.78689i	0.224054	+	0.129358i	−0.383772	+	0.923428i	$0.625375\pi$
$858$		0			0
$859$	−35.8209	+	20.6812i	−1.22219	+	0.705633i	−0.965385	−	0.260830i	$-0.916004\pi$
$859$	−35.8209	+	20.6812i	−1.22219	+	0.705633i	−0.256807	+	0.966463i	$0.582670\pi$
$860$	−19.1154	+	14.0472i	−0.651828	+	0.479005i
$861$		0			0
$862$	−5.50377	−	16.7838i	−0.187459	−	0.571659i
$863$	5.01544	+	8.68700i	0.170728	+	0.295709i	0.938674	−	0.344805i	$-0.112055\pi$
$863$	5.01544	+	8.68700i	0.170728	+	0.295709i	−0.767947	+	0.640514i	$0.778721\pi$
$864$		0			0
$865$	−1.73271	+	3.00115i	−0.0589140	+	0.102042i
$866$	−19.8517	+	22.1682i	−0.674589	+	0.753306i
$867$		0			0
$868$	44.6182	+	2.16661i	1.51444	+	0.0735395i
$869$			17.6229i			0.597817i
$870$		0			0
$871$	0.0183245	+	0.0105796i	0.000620902	+	0.000358478i
$872$	−5.99199	+	2.72645i	−0.202914	+	0.0923292i
$873$		0			0
$874$	−34.6897	+	11.3755i	−1.17340	+	0.384782i
$875$	1.13129	−	0.432204i	0.0382446	−	0.0146111i
$876$		0			0
$877$	−2.63052	−	4.55619i	−0.0888263	−	0.153852i	0.818189	−	0.574949i	$-0.194978\pi$
$877$	−2.63052	−	4.55619i	−0.0888263	−	0.153852i	−0.907015	+	0.421098i	$0.861645\pi$
$878$	−9.35641	+	44.6132i	−0.315764	+	1.50562i
$879$		0			0
$880$	6.95004	+	31.0375i	0.234286	+	1.04627i
$881$		−	29.4366i		−	0.991746i	−0.868395	−	0.495873i	$-0.834848\pi$
$881$		−	29.4366i		−	0.991746i	0.868395	−	0.495873i	$-0.165152\pi$
$882$		0			0
$883$			46.4470i			1.56307i	0.623864	+	0.781533i	$0.285562\pi$
$883$			46.4470i			1.56307i	−0.623864	+	0.781533i	$0.714438\pi$
$884$	−16.4153	+	37.4144i	−0.552107	+	1.25838i
$885$		0			0
$886$	−5.27781	−	1.10688i	−0.177311	−	0.0371863i
$887$	21.0703	+	36.4948i	0.707471	+	1.22538i	0.965792	+	0.259316i	$0.0834972\pi$
$887$	21.0703	+	36.4948i	0.707471	+	1.22538i	−0.258322	+	0.966059i	$0.583169\pi$
$888$		0			0
$889$	40.4543	−	15.4554i	1.35679	−	0.518356i
$890$	0.782649	+	2.38670i	0.0262345	+	0.0800023i
$891$		0			0
$892$	−53.6192	+	5.92990i	−1.79530	+	0.198548i
$893$	−22.1353	−	12.7798i	−0.740731	−	0.427661i
$894$		0			0
$895$			49.3932i			1.65103i
$896$	1.04617	−	29.9150i	0.0349502	−	0.999389i
$897$		0			0
$898$	−35.5012	−	31.7915i	−1.18469	−	1.06090i
$899$	−6.73478	+	11.6650i	−0.224618	+	0.389049i
$900$		0			0
$901$	−12.8809	−	22.3104i	−0.429125	−	0.743266i
$902$	41.1343	−	13.4888i	1.36962	−	0.449128i
$903$		0			0
$904$	−5.24812	+	7.34845i	−0.174550	+	0.244406i
$905$	−17.3775	+	10.0329i	−0.577649	+	0.333506i
$906$		0			0
$907$	−23.5846	−	13.6166i	−0.783115	−	0.452132i	0.0544183	−	0.998518i	$-0.482670\pi$
$907$	−23.5846	−	13.6166i	−0.783115	−	0.452132i	−0.837533	+	0.546387i	$0.816003\pi$
$908$	−38.2478	−	16.7810i	−1.26930	−	0.556896i
$909$		0			0
$910$	−77.7978	+	12.4118i	−2.57897	+	0.411447i
$911$	34.1346			1.13093			0.565466	−	0.824772i	$-0.308697\pi$
$911$	34.1346			1.13093			0.565466	+	0.824772i	$0.308697\pi$
$912$		0			0
$913$	−9.90303	+	17.1526i	−0.327743	+	0.567667i
$914$	−35.5078	−	7.44681i	−1.17449	−	0.246318i
$915$		0			0
$916$	−33.4247	+	24.5627i	−1.10438	+	0.811573i
$917$	22.4567	−	27.6419i	0.741584	−	0.912815i
$918$		0			0
$919$	33.2306	−	19.1857i	1.09618	−	0.632878i	0.160962	−	0.986961i	$-0.448540\pi$
$919$	33.2306	−	19.1857i	1.09618	−	0.632878i	0.935214	+	0.354083i	$0.115207\pi$
$920$	−18.9436	−	41.6329i	−0.624553	−	1.37260i
$921$		0			0
$922$	13.5469	+	12.1313i	0.446143	+	0.399523i
$923$	82.0334			2.70016
$924$		0			0
$925$	−3.67766			−0.120921
$926$	−15.8598	−	14.2025i	−0.521186	−	0.466724i
$927$		0			0
$928$	7.87703	+	4.40645i	0.258576	+	0.144649i
$929$	−39.0507	+	22.5459i	−1.28121	+	0.739708i	−0.977070	−	0.212919i	$-0.931703\pi$
$929$	−39.0507	+	22.5459i	−1.28121	+	0.739708i	−0.304142	+	0.952627i	$0.598370\pi$
$930$		0			0
$931$	11.1047	−	33.8115i	0.363943	−	1.10813i
$932$	19.6937	+	26.7990i	0.645088	+	0.877832i
$933$		0			0
$934$	16.1998	+	3.39747i	0.530074	+	0.111169i
$935$	−12.2856	+	21.2792i	−0.401781	+	0.695904i
$936$		0			0
$937$	−14.4277			−0.471333			−0.235667	−	0.971834i	$-0.575727\pi$
$937$	−14.4277			−0.471333			−0.235667	+	0.971834i	$0.575727\pi$
$938$	−0.00754706	−	0.00929841i	−0.000246420	−	0.000303604i
$939$		0			0
$940$	12.8664	−	29.3255i	0.419655	−	0.956493i
$941$	−35.1619	−	20.3007i	−1.14624	−	0.661784i	−0.198275	−	0.980147i	$-0.563534\pi$
$941$	−35.1619	−	20.3007i	−1.14624	−	0.661784i	−0.947969	+	0.318362i	$0.896867\pi$
$942$		0			0
$943$	−53.9138	+	31.1272i	−1.75568	+	1.01364i
$944$	12.8273	−	40.9864i	0.417494	−	1.33399i
$945$		0			0
$946$	12.4941	−	4.09709i	0.406219	−	0.133208i
$947$	−7.38792	−	12.7963i	−0.240075	−	0.415822i	0.720660	−	0.693288i	$-0.243839\pi$
$947$	−7.38792	−	12.7963i	−0.240075	−	0.415822i	−0.960735	+	0.277466i	$0.910505\pi$
$948$		0			0
$949$	6.33100	−	10.9656i	0.205513	−	0.355959i
$950$	−27.5507	−	24.6718i	−0.893864	−	0.800459i
$951$		0			0
$952$	16.2439	−	16.4581i	0.526467	−	0.533411i
$953$		−	31.2092i		−	1.01097i	−0.862836	−	0.505483i	$-0.831314\pi$
$953$		−	31.2092i		−	1.01097i	0.862836	−	0.505483i	$-0.168686\pi$
$954$		0			0
$955$	43.2764	+	24.9856i	1.40039	+	0.808516i
$956$	4.52101	+	40.8798i	0.146220	+	1.32215i
$957$		0			0
$958$	13.7006	+	41.7800i	0.442645	+	1.34985i
$959$	8.62109	−	53.8781i	0.278390	−	1.73982i
$960$		0			0
$961$	20.1336	+	34.8724i	0.649470	+	1.12492i
$962$	6.54222	+	1.37205i	0.210930	+	0.0442368i
$963$		0			0
$964$	41.2416	+	18.0945i	1.32830	+	0.582783i
$965$			57.9115i			1.86424i
$966$		0			0
$967$			39.3749i			1.26621i	0.774065	+	0.633106i	$0.218220\pi$
$967$			39.3749i			1.26621i	−0.774065	+	0.633106i	$0.781780\pi$
$968$	−1.30017	+	13.4200i	−0.0417892	+	0.431336i
$969$		0			0
$970$	−0.117553	+	0.560516i	−0.00377440	+	0.0179971i
$971$	−30.0829	−	52.1052i	−0.965407	−	1.67213i	−0.708517	−	0.705694i	$-0.750635\pi$
$971$	−30.0829	−	52.1052i	−0.965407	−	1.67213i	−0.256890	−	0.966441i	$-0.582698\pi$
$972$		0			0
$973$	4.17159	−	1.59374i	0.133735	−	0.0510928i
$974$	7.44577	−	2.44163i	0.238578	−	0.0782348i
$975$		0			0
$976$	−5.40408	−	5.87243i	−0.172980	−	0.187972i
$977$	−12.5257	−	7.23172i	−0.400733	−	0.231363i	0.286067	−	0.958209i	$-0.407652\pi$
$977$	−12.5257	−	7.23172i	−0.400733	−	0.231363i	−0.686800	+	0.726846i	$0.740985\pi$
$978$		0			0
$979$		−	1.39224i		−	0.0444961i
$980$	43.6353	+	9.17227i	1.39388	+	0.292997i
$981$		0			0
$982$	−28.6055	+	31.9435i	−0.912838	+	1.01936i
$983$	−0.291450	+	0.504806i	−0.00929582	+	0.0161008i	−0.870636	−	0.491928i	$-0.836292\pi$
$983$	−0.291450	+	0.504806i	−0.00929582	+	0.0161008i	0.861340	+	0.508029i	$0.169626\pi$
$984$		0			0
$985$	24.0948	+	41.7333i	0.767723	+	1.32973i
$986$	2.17265	+	6.62552i	0.0691913	+	0.211000i
$987$		0			0
$988$	39.8057	+	54.1674i	1.26639	+	1.72330i
$989$	−16.3758	+	9.45457i	−0.520720	+	0.300638i
$990$		0			0
$991$	6.69703	+	3.86653i	0.212738	+	0.122824i	0.602583	−	0.798056i	$-0.294138\pi$
$991$	6.69703	+	3.86653i	0.212738	+	0.122824i	−0.389845	+	0.920880i	$0.627471\pi$
$992$	41.0295	−	24.4363i	1.30269	−	0.775853i
$993$		0			0
$994$	−43.3642	−	16.5899i	−1.37543	−	0.526201i
$995$	46.7658			1.48257
$996$		0			0
$997$	12.6526	−	21.9150i	0.400713	−	0.694055i	−0.593099	−	0.805130i	$-0.702096\pi$
$997$	12.6526	−	21.9150i	0.400713	−	0.694055i	0.993812	+	0.111074i	$0.0354291\pi$
$998$	3.99548	−	19.0512i	0.126475	−	0.603056i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.be.d.431.4	yes	28
3.2	odd	2	inner	756.2.be.d.431.11	yes	28
4.3	odd	2		756.2.be.c.431.2	yes	28
7.2	even	3		756.2.be.c.107.13	yes	28
12.11	even	2		756.2.be.c.431.13	yes	28
21.2	odd	6		756.2.be.c.107.2	✓	28
28.23	odd	6	inner	756.2.be.d.107.11	yes	28
84.23	even	6	inner	756.2.be.d.107.4	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.c.107.2	✓	28	21.2	odd	6
756.2.be.c.107.13	yes	28	7.2	even	3
756.2.be.c.431.2	yes	28	4.3	odd	2
756.2.be.c.431.13	yes	28	12.11	even	2
756.2.be.d.107.4	yes	28	84.23	even	6	inner
756.2.be.d.107.11	yes	28	28.23	odd	6	inner
756.2.be.d.431.4	yes	28	1.1	even	1	trivial
756.2.be.d.431.11	yes	28	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-0.943439 + 1.05353i) q^{2} +(-0.219845 - 1.98788i) q^{4} +(2.75822 - 1.59246i) q^{5} +(0.944233 + 2.47152i) q^{7} +(2.30170 + 1.64383i) q^{8} +O(q^{10})\)	\(q+(-0.943439 + 1.05353i) q^{2} +(-0.219845 - 1.98788i) q^{4} +(2.75822 - 1.59246i) q^{5} +(0.944233 + 2.47152i) q^{7} +(2.30170 + 1.64383i) q^{8} +(-0.924512 + 4.40826i) q^{10} +(1.24831 - 2.16213i) q^{11} +6.61093 q^{13} +(-3.49465 - 1.33695i) q^{14} +(-3.90334 + 0.874051i) q^{16} +(-2.67612 - 1.54506i) q^{17} +(-4.40292 + 2.54203i) q^{19} +(-3.77200 - 5.13292i) q^{20} +(1.10017 + 3.35497i) q^{22} +(-2.53877 - 4.39728i) q^{23} +(2.57186 - 4.45459i) q^{25} +(-6.23701 + 6.96480i) q^{26} +(4.70551 - 2.42037i) q^{28} +1.59554i q^{29} +(7.31098 + 4.22099i) q^{31} +(2.76172 - 4.93689i) q^{32} +(4.15252 - 1.36170i) q^{34} +(6.54021 + 5.31335i) q^{35} +(-0.357491 - 0.619192i) q^{37} +(1.47579 - 7.03685i) q^{38} +(8.96633 + 0.868686i) q^{40} -12.2607i q^{41} -3.72407i q^{43} +(-4.57249 - 2.00615i) q^{44} +(7.02784 + 1.47390i) q^{46} +(2.51371 + 4.35388i) q^{47} +(-5.21685 + 4.66739i) q^{49} +(2.26665 + 6.91216i) q^{50} +(-1.45338 - 13.1417i) q^{52} +(7.21991 + 4.16842i) q^{53} -7.95152i q^{55} +(-1.88942 + 7.24086i) q^{56} +(-1.68095 - 1.50530i) q^{58} +(-5.36835 + 9.29825i) q^{59} +(0.997571 + 1.72784i) q^{61} +(-11.3444 + 3.72007i) q^{62} +(2.59564 + 7.56721i) q^{64} +(18.2344 - 10.5276i) q^{65} +(0.00277185 + 0.00160033i) q^{67} +(-2.48306 + 5.65947i) q^{68} +(-11.7681 + 1.87747i) q^{70} +12.4088 q^{71} +(0.957657 - 1.65871i) q^{73} +(0.989607 + 0.207543i) q^{74} +(6.02120 + 8.19362i) q^{76} +(6.52245 + 1.04366i) q^{77} +(-6.11304 + 3.52937i) q^{79} +(-9.37438 + 8.62674i) q^{80} +(12.9170 + 11.5672i) q^{82} -7.93317 q^{83} -9.84177 q^{85} +(3.92341 + 3.51343i) q^{86} +(6.42741 - 2.92457i) q^{88} +(0.482940 - 0.278825i) q^{89} +(6.24226 + 16.3391i) q^{91} +(-8.18314 + 6.01350i) q^{92} +(-6.95847 - 1.45935i) q^{94} +(-8.09615 + 14.0229i) q^{95} +0.127151 q^{97} +(0.00455176 - 9.89949i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{4} + 2 q^{7}+O(q^{10}) \) 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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