LMFDB - Embedded newform 756.2.bf.c.271.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(271,756)]

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, 0, 5]))

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

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

chi := DirichletCharacter("756.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bf (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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.5
Character	$\chi$	$=$	756.271
Dual form			756.2.bf.c.703.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.996999 + 1.00299i) q^{2} +(-0.0119854 - 1.99996i) q^{4} +(-3.53919 - 2.04335i) q^{5} +(-2.14499 - 1.54888i) q^{7} +(2.01790 + 1.98194i) q^{8} +O(q^{10})$	\(q+(-0.996999 + 1.00299i) q^{2} +(-0.0119854 - 1.99996i) q^{4} +(-3.53919 - 2.04335i) q^{5} +(-2.14499 - 1.54888i) q^{7} +(2.01790 + 1.98194i) q^{8} +(5.57803 - 1.51256i) q^{10} +(-2.02019 + 1.16636i) q^{11} +0.570108i q^{13} +(3.69207 - 0.607169i) q^{14} +(-3.99971 + 0.0479407i) q^{16} +(-1.25927 + 0.727038i) q^{17} +(3.88353 - 6.72648i) q^{19} +(-4.04421 + 7.10274i) q^{20} +(0.844282 - 3.18910i) q^{22} +(2.14767 + 1.23996i) q^{23} +(5.85057 + 10.1335i) q^{25} +(-0.571814 - 0.568397i) q^{26} +(-3.07200 + 4.30846i) q^{28} -4.52320 q^{29} +(3.30992 + 5.73294i) q^{31} +(3.93963 - 4.05948i) q^{32} +(0.526275 - 1.98789i) q^{34} +(4.42660 + 9.86475i) q^{35} +(-2.68257 + 4.64635i) q^{37} +(2.87472 + 10.6014i) q^{38} +(-3.09192 - 11.1377i) q^{40} +10.3487i q^{41} +5.76038i q^{43} +(2.35689 + 4.02633i) q^{44} +(-3.38489 + 0.917857i) q^{46} +(4.40000 - 7.62102i) q^{47} +(2.20193 + 6.64466i) q^{49} +(-15.9968 - 4.23500i) q^{50} +(1.14020 - 0.00683297i) q^{52} +(4.16429 + 7.21277i) q^{53} +9.53312 q^{55} +(-1.25857 - 7.37672i) q^{56} +(4.50963 - 4.53674i) q^{58} +(-2.17732 - 3.77122i) q^{59} +(-6.64766 - 3.83803i) q^{61} +(-9.05008 - 2.39592i) q^{62} +(0.143818 + 7.99871i) q^{64} +(1.16493 - 2.01772i) q^{65} +(-4.12447 + 2.38127i) q^{67} +(1.46914 + 2.50977i) q^{68} +(-14.3076 - 5.39530i) q^{70} -9.60408i q^{71} +(1.90017 - 1.09707i) q^{73} +(-1.98573 - 7.32301i) q^{74} +(-13.4993 - 7.68631i) q^{76} +(6.13984 + 0.627217i) q^{77} +(-8.75786 - 5.05635i) q^{79} +(14.2537 + 8.00315i) q^{80} +(-10.3796 - 10.3176i) q^{82} +14.1953 q^{83} +5.94238 q^{85} +(-5.77761 - 5.74309i) q^{86} +(-6.38820 - 1.65031i) q^{88} +(3.41069 + 1.96916i) q^{89} +(0.883030 - 1.22287i) q^{91} +(2.45413 - 4.31012i) q^{92} +(3.25703 + 12.0113i) q^{94} +(-27.4891 + 15.8708i) q^{95} +14.3215i q^{97} +(-8.85986 - 4.41620i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 6 q^{11} + 17 q^{14} - 4 q^{16} - 8 q^{20} + 2 q^{22} + 14 q^{25} - 15 q^{26} - 13 q^{28} - 15 q^{32} - 6 q^{35} + 4 q^{37} + q^{38} - 15 q^{40} + 42 q^{44} - 9 q^{46} + 4 q^{47} + 14 q^{49} - 9 q^{52} - 45 q^{56} + 10 q^{58} + 16 q^{59} - 42 q^{64} + 49 q^{68} - 33 q^{70} + 36 q^{73} + 54 q^{74} + 15 q^{80} - 51 q^{82} - 20 q^{83} + 16 q^{85} - 78 q^{86} - 2 q^{88} - 27 q^{94} - 24 q^{95} + 46 q^{98}+O(q^{100}) $ 32 * q + 6 * q^11 + 17 * q^14 - 4 * q^16 - 8 * q^20 + 2 * q^22 + 14 * q^25 - 15 * q^26 - 13 * q^28 - 15 * q^32 - 6 * q^35 + 4 * q^37 + q^38 - 15 * q^40 + 42 * q^44 - 9 * q^46 + 4 * q^47 + 14 * q^49 - 9 * q^52 - 45 * q^56 + 10 * q^58 + 16 * q^59 - 42 * q^64 + 49 * q^68 - 33 * q^70 + 36 * q^73 + 54 * q^74 + 15 * q^80 - 51 * q^82 - 20 * q^83 + 16 * q^85 - 78 * q^86 - 2 * q^88 - 27 * q^94 - 24 * q^95 + 46 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.996999	+	1.00299i	−0.704985	+	0.709222i
$2$	−0.996999	+	1.00299i	−0.704985	+	0.709222i
$3$		0			0
$3$		0			0
$4$	−0.0119854	−	1.99996i	−0.00599270	−	0.999982i
$5$	−3.53919	−	2.04335i	−1.58277	−	0.913815i	−0.994452	−	0.105187i	$-0.966456\pi$
$5$	−3.53919	−	2.04335i	−1.58277	−	0.913815i	−0.588321	−	0.808628i	$-0.700211\pi$
$6$		0			0
$7$	−2.14499	−	1.54888i	−0.810728	−	0.585422i
$7$	−2.14499	−	1.54888i	−0.810728	−	0.585422i
$8$	2.01790	+	1.98194i	0.713434	+	0.700722i
$9$		0			0
$10$	5.57803	−	1.51256i	1.76393	−	0.478313i
$11$	−2.02019	+	1.16636i	−0.609111	+	0.351670i	−0.772617	−	0.634872i	$-0.781053\pi$
$11$	−2.02019	+	1.16636i	−0.609111	+	0.351670i	0.163506	+	0.986542i	$0.447720\pi$
$12$		0			0
$13$			0.570108i			0.158120i	0.996870	+	0.0790598i	$0.0251918\pi$
$13$			0.570108i			0.158120i	−0.996870	+	0.0790598i	$0.974808\pi$
$14$	3.69207	−	0.607169i	0.986746	−	0.162273i
$15$		0			0
$16$	−3.99971	+	0.0479407i	−0.999928	+	0.0119852i
$17$	−1.25927	+	0.727038i	−0.305417	+	0.176333i	−0.644874	−	0.764289i	$-0.723090\pi$
$17$	−1.25927	+	0.727038i	−0.305417	+	0.176333i	0.339457	+	0.940622i	$0.389757\pi$
$18$		0			0
$19$	3.88353	−	6.72648i	0.890943	−	1.54316i	0.0521972	−	0.998637i	$-0.483378\pi$
$19$	3.88353	−	6.72648i	0.890943	−	1.54316i	0.838746	−	0.544522i	$-0.183289\pi$
$20$	−4.04421	+	7.10274i	−0.904313	+	1.58822i
$21$		0			0
$22$	0.844282	−	3.18910i	0.180002	−	0.679917i
$23$	2.14767	+	1.23996i	0.447820	+	0.258549i	0.706909	−	0.707305i	$-0.250089\pi$
$23$	2.14767	+	1.23996i	0.447820	+	0.258549i	−0.259089	+	0.965853i	$0.583422\pi$
$24$		0			0
$25$	5.85057	+	10.1335i	1.17011	+	2.02670i
$26$	−0.571814	−	0.568397i	−0.112142	−	0.111472i
$27$		0			0
$28$	−3.07200	+	4.30846i	−0.580553	+	0.814222i
$29$	−4.52320			−0.839938			−0.419969	−	0.907538i	$-0.637959\pi$
$29$	−4.52320			−0.839938			−0.419969	+	0.907538i	$0.637959\pi$
$30$		0			0
$31$	3.30992	+	5.73294i	0.594479	+	1.02967i	0.993620	+	0.112778i	$0.0359749\pi$
$31$	3.30992	+	5.73294i	0.594479	+	1.02967i	−0.399142	+	0.916889i	$0.630692\pi$
$32$	3.93963	−	4.05948i	0.696434	−	0.717621i
$33$		0			0
$34$	0.526275	−	1.98789i	0.0902553	−	0.340920i
$35$	4.42660	+	9.86475i	0.748232	+	1.66745i
$36$		0			0
$37$	−2.68257	+	4.64635i	−0.441012	+	0.763856i	−0.997765	−	0.0668225i	$-0.978714\pi$
$37$	−2.68257	+	4.64635i	−0.441012	+	0.763856i	0.556752	+	0.830678i	$0.312047\pi$
$38$	2.87472	+	10.6014i	0.466341	+	1.71978i
$39$		0			0
$40$	−3.09192	−	11.1377i	−0.488875	−	1.76103i
$41$			10.3487i			1.61619i	0.589053	+	0.808094i	$0.299501\pi$
$41$			10.3487i			1.61619i	−0.589053	+	0.808094i	$0.700499\pi$
$42$		0			0
$43$			5.76038i			0.878450i	0.898377	+	0.439225i	$0.144747\pi$
$43$			5.76038i			0.878450i	−0.898377	+	0.439225i	$0.855253\pi$
$44$	2.35689	+	4.02633i	0.355314	+	0.606993i
$45$		0			0
$46$	−3.38489	+	0.917857i	−0.499075	+	0.135331i
$47$	4.40000	−	7.62102i	0.641806	−	1.11164i	−0.343224	−	0.939254i	$-0.611519\pi$
$47$	4.40000	−	7.62102i	0.641806	−	1.11164i	0.985029	−	0.172386i	$-0.0551477\pi$
$48$		0			0
$49$	2.20193	+	6.64466i	0.314561	+	0.949237i
$50$	−15.9968	−	4.23500i	−2.26229	−	0.598920i
$51$		0			0
$52$	1.14020	−	0.00683297i	0.158117	−	0.000947562i
$53$	4.16429	+	7.21277i	0.572010	+	0.990750i	0.996359	+	0.0852516i	$0.0271694\pi$
$53$	4.16429	+	7.21277i	0.572010	+	0.990750i	−0.424350	+	0.905498i	$0.639497\pi$
$54$		0			0
$55$	9.53312			1.28545
$56$	−1.25857	−	7.37672i	−0.168183	−	0.985756i
$57$		0			0
$58$	4.50963	−	4.53674i	0.592144	−	0.595703i
$59$	−2.17732	−	3.77122i	−0.283462	−	0.490971i	0.688773	−	0.724977i	$-0.258150\pi$
$59$	−2.17732	−	3.77122i	−0.283462	−	0.490971i	−0.972235	+	0.234006i	$0.924816\pi$
$60$		0			0
$61$	−6.64766	−	3.83803i	−0.851146	−	0.491409i	0.00989122	−	0.999951i	$-0.496851\pi$
$61$	−6.64766	−	3.83803i	−0.851146	−	0.491409i	−0.861037	+	0.508542i	$0.830185\pi$
$62$	−9.05008	−	2.39592i	−1.14936	−	0.304282i
$63$		0			0
$64$	0.143818	+	7.99871i	0.0179772	+	0.999838i
$65$	1.16493	−	2.01772i	0.144492	−	0.250267i
$66$		0			0
$67$	−4.12447	+	2.38127i	−0.503885	+	0.290918i	−0.730316	−	0.683109i	$-0.760627\pi$
$67$	−4.12447	+	2.38127i	−0.503885	+	0.290918i	0.226432	+	0.974027i	$0.427294\pi$
$68$	1.46914	+	2.50977i	0.178160	+	0.304355i
$69$		0			0
$70$	−14.3076	−	5.39530i	−1.71008	−	0.644862i
$71$		−	9.60408i		−	1.13979i	−0.821716	−	0.569897i	$-0.806983\pi$
$71$		−	9.60408i		−	1.13979i	0.821716	−	0.569897i	$-0.193017\pi$
$72$		0			0
$73$	1.90017	−	1.09707i	0.222399	−	0.128402i	−0.384662	−	0.923058i	$-0.625682\pi$
$73$	1.90017	−	1.09707i	0.222399	−	0.128402i	0.607060	+	0.794656i	$0.292349\pi$
$74$	−1.98573	−	7.32301i	−0.230837	−	0.851283i
$75$		0			0
$76$	−13.4993	−	7.68631i	−1.54847	−	0.881680i
$77$	6.13984	+	0.627217i	0.699699	+	0.0714780i
$78$		0			0
$79$	−8.75786	−	5.05635i	−0.985336	−	0.568884i	−0.0814591	−	0.996677i	$-0.525958\pi$
$79$	−8.75786	−	5.05635i	−0.985336	−	0.568884i	−0.903877	+	0.427793i	$0.859291\pi$
$80$	14.2537	+	8.00315i	1.59361	+	0.894779i
$81$		0			0
$82$	−10.3796	−	10.3176i	−1.14624	−	1.13939i
$83$	14.1953			1.55814			0.779068	−	0.626940i	$-0.215693\pi$
$83$	14.1953			1.55814			0.779068	+	0.626940i	$0.215693\pi$
$84$		0			0
$85$	5.94238			0.644541
$86$	−5.77761	−	5.74309i	−0.623016	−	0.619294i
$87$		0			0
$88$	−6.38820	−	1.65031i	−0.680984	−	0.175924i
$89$	3.41069	+	1.96916i	0.361532	+	0.208731i	0.669753	−	0.742584i	$-0.266400\pi$
$89$	3.41069	+	1.96916i	0.361532	+	0.208731i	−0.308220	+	0.951315i	$0.599733\pi$
$90$		0			0
$91$	0.883030	−	1.22287i	0.0925667	−	0.128192i
$92$	2.45413	−	4.31012i	0.255860	−	0.449361i
$93$		0			0
$94$	3.25703	+	12.0113i	0.335937	+	1.23887i
$95$	−27.4891	+	15.8708i	−2.82032	+	1.62831i
$96$		0			0
$97$			14.3215i			1.45413i	0.686569	+	0.727065i	$0.259116\pi$
$97$			14.3215i			1.45413i	−0.686569	+	0.727065i	$0.740884\pi$
$98$	−8.85986	−	4.41620i	−0.894981	−	0.446104i
$99$		0			0
$100$	20.1965	−	11.8224i	2.01965	−	1.18224i
$101$	2.61579	−	1.51023i	0.260281	−	0.150273i	−0.364182	−	0.931328i	$-0.618651\pi$
$101$	2.61579	−	1.51023i	0.260281	−	0.150273i	0.624463	+	0.781055i	$0.285318\pi$
$102$		0			0
$103$	−0.709482	+	1.22886i	−0.0699073	+	0.121083i	−0.898860	−	0.438235i	$-0.855604\pi$
$103$	−0.709482	+	1.22886i	−0.0699073	+	0.121083i	0.828953	+	0.559318i	$0.188937\pi$
$104$	−1.12992	+	1.15042i	−0.110798	+	0.112808i
$105$		0			0
$106$	−11.3861	−	3.01437i	−1.10592	−	0.292782i
$107$	−0.244446	−	0.141131i	−0.0236315	−	0.0136436i	0.488138	−	0.872767i	$-0.337676\pi$
$107$	−0.244446	−	0.141131i	−0.0236315	−	0.0136436i	−0.511769	+	0.859123i	$0.671010\pi$
$108$		0			0
$109$	−3.08275	−	5.33948i	−0.295274	−	0.511429i	0.679775	−	0.733421i	$-0.262078\pi$
$109$	−3.08275	−	5.33948i	−0.295274	−	0.511429i	−0.975049	+	0.221992i	$0.928744\pi$
$110$	−9.50452	+	9.56165i	−0.906220	+	0.911667i
$111$		0			0
$112$	8.65358	+	6.09225i	0.817687	+	0.575664i
$113$	−8.41504			−0.791620			−0.395810	−	0.918332i	$-0.629536\pi$
$113$	−8.41504			−0.791620			−0.395810	+	0.918332i	$0.629536\pi$
$114$		0			0
$115$	−5.06733	−	8.77688i	−0.472531	−	0.818448i
$116$	0.0542124	+	9.04625i	0.00503349	+	0.839923i
$117$		0			0
$118$	5.95329	+	1.57608i	0.548045	+	0.145089i
$119$	3.82720	+	0.390969i	0.350839	+	0.0358401i
$120$		0			0
$121$	−2.77921	+	4.81374i	−0.252656	+	0.437613i
$122$	10.4772	−	2.84104i	0.948564	−	0.257216i
$123$		0			0
$124$	11.4260	−	6.68843i	1.02609	−	0.600638i
$125$		−	27.3856i		−	2.44944i
$126$		0			0
$127$			15.0124i			1.33214i	0.745890	+	0.666069i	$0.232024\pi$
$127$			15.0124i			1.33214i	−0.745890	+	0.666069i	$0.767976\pi$
$128$	−8.16602	−	7.83046i	−0.721781	−	0.692121i
$129$		0			0
$130$	0.862321	+	3.18008i	0.0756306	+	0.278912i
$131$	−2.87353	+	4.97710i	−0.251062	+	0.434852i	−0.963818	−	0.266560i	$-0.914113\pi$
$131$	−2.87353	+	4.97710i	−0.251062	+	0.434852i	0.712757	+	0.701411i	$0.247446\pi$
$132$		0			0
$133$	−18.7486	+	8.41306i	−1.62571	+	0.729505i
$134$	1.72371	−	6.51093i	0.148906	−	0.562459i
$135$		0			0
$136$	−3.98202	−	1.02870i	−0.341455	−	0.0882107i
$137$	0.712721	+	1.23447i	0.0608919	+	0.105468i	0.894864	−	0.446338i	$-0.147272\pi$
$137$	0.712721	+	1.23447i	0.0608919	+	0.105468i	−0.833972	+	0.551806i	$0.813939\pi$
$138$		0			0
$139$	9.20213			0.780514			0.390257	−	0.920706i	$-0.372386\pi$
$139$	9.20213			0.780514			0.390257	+	0.920706i	$0.372386\pi$
$140$	19.6761	−	8.97127i	1.66293	−	0.758211i
$141$		0			0
$142$	9.63281	+	9.57526i	0.808368	+	0.803538i
$143$	−0.664950	−	1.15173i	−0.0556060	−	0.0963123i
$144$		0			0
$145$	16.0085	+	9.24250i	1.32943	+	0.767548i
$146$	−0.794124	+	2.99963i	−0.0657222	+	0.248251i
$147$		0			0
$148$	9.32469	+	5.30936i	0.766485	+	0.436427i
$149$	3.65750	−	6.33498i	0.299634	−	0.518981i	−0.676418	−	0.736518i	$-0.736469\pi$
$149$	3.65750	−	6.33498i	0.299634	−	0.518981i	0.976052	+	0.217536i	$0.0698021\pi$
$150$		0			0
$151$	−1.61266	+	0.931070i	−0.131236	+	0.0757694i	−0.564181	−	0.825651i	$-0.690808\pi$
$151$	−1.61266	+	0.931070i	−0.131236	+	0.0757694i	0.432944	+	0.901421i	$0.357475\pi$
$152$	21.1680	−	5.87640i	1.71696	−	0.476639i
$153$		0			0
$154$	−6.75051	+	5.53287i	−0.543971	+	0.445852i
$155$		−	27.0533i		−	2.17297i
$156$		0			0
$157$	−1.78446	+	1.03026i	−0.142415	+	0.0822236i	−0.569515	−	0.821981i	$-0.692869\pi$
$157$	−1.78446	+	1.03026i	−0.142415	+	0.0822236i	0.427099	+	0.904205i	$0.359535\pi$
$158$	13.8031	−	3.74288i	1.09811	−	0.297768i
$159$		0			0
$160$	−22.2380	+	6.31721i	−1.75807	+	0.499419i
$161$	−2.68617	−	5.98617i	−0.211700	−	0.471776i
$162$		0			0
$163$	13.0448	+	7.53143i	1.02175	+	0.589907i	0.914610	−	0.404337i	$-0.132498\pi$
$163$	13.0448	+	7.53143i	1.02175	+	0.589907i	0.107139	+	0.994244i	$0.465831\pi$
$164$	20.6969	−	0.124033i	1.61616	−	0.00968533i
$165$		0			0
$166$	−14.1527	+	14.2378i	−1.09846	+	1.10506i
$167$	−3.78773			−0.293103			−0.146552	−	0.989203i	$-0.546817\pi$
$167$	−3.78773			−0.293103			−0.146552	+	0.989203i	$0.546817\pi$
$168$		0			0
$169$	12.6750			0.974998
$170$	−5.92454	+	5.96015i	−0.454392	+	0.457123i
$171$		0			0
$172$	11.5206	−	0.0690404i	0.878434	−	0.00526428i
$173$	−11.8138	−	6.82071i	−0.898187	−	0.518569i	−0.0215758	−	0.999767i	$-0.506868\pi$
$173$	−11.8138	−	6.82071i	−0.898187	−	0.518569i	−0.876612	+	0.481198i	$0.840202\pi$
$174$		0			0
$175$	3.14618	−	30.7980i	0.237829	−	2.32811i
$176$	8.02427	−	4.76195i	0.604852	−	0.358945i
$177$		0			0
$178$	−5.37551	+	1.45764i	−0.402911	+	0.109255i
$179$	−5.92682	+	3.42185i	−0.442991	+	0.255761i	−0.704866	−	0.709341i	$-0.748993\pi$
$179$	−5.92682	+	3.42185i	−0.442991	+	0.255761i	0.261874	+	0.965102i	$0.415659\pi$
$180$		0			0
$181$		−	4.91328i		−	0.365201i	−0.983187	−	0.182600i	$-0.941549\pi$
$181$		−	4.91328i		−	0.365201i	0.983187	−	0.182600i	$-0.0584515\pi$
$182$	0.346152	+	2.10488i	0.0256585	+	0.156024i
$183$		0			0
$184$	1.87625	+	6.75865i	0.138319	+	0.498255i
$185$	18.9883	−	10.9629i	1.39605	−	0.806007i
$186$		0			0
$187$	1.69597	−	2.93751i	0.124022	−	0.214812i
$188$	−15.2945	−	8.70849i	−1.11547	−	0.635132i
$189$		0			0
$190$	11.4883	−	43.3946i	0.833448	−	3.14817i
$191$	−0.792896	−	0.457779i	−0.0573719	−	0.0331237i	0.471040	−	0.882112i	$-0.343879\pi$
$191$	−0.792896	−	0.457779i	−0.0573719	−	0.0331237i	−0.528412	+	0.848988i	$0.677212\pi$
$192$		0			0
$193$	2.88082	+	4.98973i	0.207366	+	0.359168i	0.950884	−	0.309548i	$-0.100178\pi$
$193$	2.88082	+	4.98973i	0.207366	+	0.359168i	−0.743518	+	0.668716i	$0.766844\pi$
$194$	−14.3644	−	14.2785i	−1.03130	−	1.02514i
$195$		0			0
$196$	13.2627	−	4.48342i	0.947335	−	0.320244i
$197$	−0.570257			−0.0406292			−0.0203146	−	0.999794i	$-0.506467\pi$
$197$	−0.570257			−0.0406292			−0.0203146	+	0.999794i	$0.506467\pi$
$198$		0			0
$199$	−3.27802	−	5.67770i	−0.232373	−	0.402482i	0.726133	−	0.687554i	$-0.241316\pi$
$199$	−3.27802	−	5.67770i	−0.232373	−	0.402482i	−0.958506	+	0.285072i	$0.907982\pi$
$200$	−8.27813	+	32.0438i	−0.585352	+	2.26584i
$201$		0			0
$202$	−1.09320	+	4.12932i	−0.0769170	+	0.290538i
$203$	9.70221	+	7.00591i	0.680962	+	0.491718i
$204$		0			0
$205$	21.1459	−	36.6258i	1.47690	−	2.55806i
$206$	−0.525183	−	1.93678i	−0.0365912	−	0.134942i
$207$		0			0
$208$	−0.0273314	−	2.28027i	−0.00189509	−	0.158108i
$209$			18.1184i			1.25327i
$210$		0			0
$211$			8.94785i			0.615996i	0.951387	+	0.307998i	$0.0996590\pi$
$211$			8.94785i			0.615996i	−0.951387	+	0.307998i	$0.900341\pi$
$212$	14.3754	−	8.41489i	0.987304	−	0.577937i
$213$		0			0
$214$	0.385266	−	0.104470i	0.0263362	−	0.00714142i
$215$	11.7705	−	20.3871i	0.802740	−	1.39039i
$216$		0			0
$217$	1.77993	−	17.4238i	0.120829	−	1.18280i
$218$	8.42895	+	2.23148i	0.570881	+	0.151135i
$219$		0			0
$220$	−0.114258	−	19.0659i	−0.00770329	−	1.28542i
$221$	−0.414490	−	0.717918i	−0.0278816	−	0.0482924i
$222$		0			0
$223$	−1.66200			−0.111296			−0.0556480	−	0.998450i	$-0.517722\pi$
$223$	−1.66200			−0.111296			−0.0556480	+	0.998450i	$0.517722\pi$
$224$	−14.7381	+	2.60550i	−0.984730	+	0.174088i
$225$		0			0
$226$	8.38979	−	8.44022i	0.558080	−	0.561435i
$227$	4.79285	+	8.30147i	0.318113	+	0.550988i	0.980094	−	0.198533i	$-0.0636176\pi$
$227$	4.79285	+	8.30147i	0.318113	+	0.550988i	−0.661981	+	0.749520i	$0.730284\pi$
$228$		0			0
$229$	−15.5803	−	8.99532i	−1.02958	−	0.594427i	−0.112714	−	0.993627i	$-0.535954\pi$
$229$	−15.5803	−	8.99532i	−1.02958	−	0.594427i	−0.916864	+	0.399200i	$0.869288\pi$
$230$	13.8553	+	3.66805i	0.913589	+	0.241864i
$231$		0			0
$232$	−9.12736	−	8.96472i	−0.599241	−	0.588563i
$233$	−10.0323	+	17.3764i	−0.657237	+	1.13837i	0.324091	+	0.946026i	$0.394942\pi$
$233$	−10.0323	+	17.3764i	−0.657237	+	1.13837i	−0.981328	+	0.192342i	$0.938392\pi$
$234$		0			0
$235$	−31.1448	+	17.9815i	−2.03167	+	1.17298i
$236$	−7.51621	+	4.39975i	−0.489264	+	0.286400i
$237$		0			0
$238$	−4.20786	+	3.44886i	−0.272755	+	0.223556i
$239$			22.1177i			1.43068i	0.698778	+	0.715338i	$0.253727\pi$
$239$			22.1177i			1.43068i	−0.698778	+	0.715338i	$0.746273\pi$
$240$		0			0
$241$	−10.9406	+	6.31657i	−0.704747	+	0.406886i	−0.809113	−	0.587653i	$-0.800052\pi$
$241$	−10.9406	+	6.31657i	−0.704747	+	0.406886i	0.104366	+	0.994539i	$0.466719\pi$
$242$	−2.05727	−	7.58682i	−0.132246	−	0.487700i
$243$		0			0
$244$	−7.59625	+	13.3411i	−0.486300	+	0.854076i
$245$	5.78433	−	28.0160i	0.369548	−	1.78988i
$246$		0			0
$247$	3.83482	+	2.21403i	0.244004	+	0.140876i
$248$	−4.68329	+	18.1286i	−0.297389	+	1.15116i
$249$		0			0
$250$	27.4675	+	27.3034i	1.73720	+	1.72682i
$251$	−21.7686			−1.37402			−0.687010	−	0.726648i	$-0.741077\pi$
$251$	−21.7686			−1.37402			−0.687010	+	0.726648i	$0.741077\pi$
$252$		0			0
$253$	−5.78494			−0.363696
$254$	−15.0574	−	14.9674i	−0.944782	−	0.939137i
$255$		0			0
$256$	15.9954	−	0.383498i	0.999713	−	0.0239686i
$257$	24.7446	+	14.2863i	1.54353	+	0.891155i	0.998612	+	0.0526625i	$0.0167707\pi$
$257$	24.7446	+	14.2863i	1.54353	+	0.891155i	0.544913	+	0.838492i	$0.316563\pi$
$258$		0			0
$259$	12.9507	−	5.81137i	0.804720	−	0.361101i
$260$	−4.04933	−	2.30564i	−0.251129	−	0.142990i
$261$		0			0
$262$	−2.12709	−	7.84430i	−0.131412	−	0.484622i
$263$	−1.88202	+	1.08659i	−0.116051	+	0.0670018i	−0.556902	−	0.830578i	$-0.688010\pi$
$263$	−1.88202	+	1.08659i	−0.116051	+	0.0670018i	0.440851	+	0.897580i	$0.354677\pi$
$264$		0			0
$265$		−	34.0365i		−	2.09084i
$266$	10.2541	−	27.1925i	0.628722	−	1.66728i
$267$		0			0
$268$	4.81188	+	8.22026i	0.293932	+	0.502132i
$269$	−10.3874	+	5.99718i	−0.633332	+	0.365654i	−0.782041	−	0.623227i	$-0.785821\pi$
$269$	−10.3874	+	5.99718i	−0.633332	+	0.365654i	0.148709	+	0.988881i	$0.452488\pi$
$270$		0			0
$271$	−5.07774	+	8.79490i	−0.308451	+	0.534252i	−0.978024	−	0.208494i	$-0.933144\pi$
$271$	−5.07774	+	8.79490i	−0.308451	+	0.534252i	0.669573	+	0.742746i	$0.266477\pi$
$272$	5.00185	−	2.96831i	0.303282	−	0.179980i
$273$		0			0
$274$	−1.94874	−	0.515911i	−0.117728	−	0.0311673i
$275$	−23.6386	−	13.6477i	−1.42546	−	0.822989i
$276$		0			0
$277$	10.1302	+	17.5461i	0.608667	+	1.05424i	0.991460	+	0.130409i	$0.0416289\pi$
$277$	10.1302	+	17.5461i	0.608667	+	1.05424i	−0.382793	+	0.923834i	$0.625038\pi$
$278$	−9.17452	+	9.22966i	−0.550251	+	0.553558i
$279$		0			0
$280$	−10.6189	+	28.6793i	−0.634602	+	1.71392i
$281$	22.6913			1.35365			0.676825	−	0.736144i	$-0.263356\pi$
$281$	22.6913			1.35365			0.676825	+	0.736144i	$0.263356\pi$
$282$		0			0
$283$	−12.9463	−	22.4236i	−0.769577	−	1.33295i	−0.937792	−	0.347197i	$-0.887134\pi$
$283$	−12.9463	−	22.4236i	−0.769577	−	1.33295i	0.168215	−	0.985750i	$-0.446200\pi$
$284$	−19.2078	+	0.115109i	−1.13977	+	0.00683044i
$285$		0			0
$286$	1.81813	+	0.481332i	0.107508	+	0.0284618i
$287$	16.0288	−	22.1977i	0.946153	−	1.31029i
$288$		0			0
$289$	−7.44283	+	12.8914i	−0.437814	+	0.758315i
$290$	−25.2306	+	6.84161i	−1.48159	+	0.401753i
$291$		0			0
$292$	−2.21687	−	3.78713i	−0.129732	−	0.221625i
$293$		−	0.749896i		−	0.0438094i	−0.999760	−	0.0219047i	$-0.993027\pi$
$293$		−	0.749896i		−	0.0438094i	0.999760	−	0.0219047i	$-0.00697304\pi$
$294$		0			0
$295$			17.7961i			1.03613i
$296$	−14.6220	+	4.05916i	−0.849884	+	0.235934i
$297$		0			0
$298$	2.70740	+	9.98441i	0.156836	+	0.578381i
$299$	−0.706909	+	1.22440i	−0.0408816	+	0.0708090i
$300$		0			0
$301$	8.92215	−	12.3559i	0.514264	−	0.712184i
$302$	0.673965	−	2.54576i	0.0387823	−	0.146492i
$303$		0			0
$304$	−15.2105	+	27.0901i	−0.872384	+	1.55373i
$305$	15.6849	+	27.1670i	0.898114	+	1.55558i
$306$		0			0
$307$	17.9467			1.02427			0.512136	−	0.858904i	$-0.328854\pi$
$307$	17.9467			1.02427			0.512136	+	0.858904i	$0.328854\pi$
$308$	1.18082	−	12.2870i	0.0672836	−	0.700115i
$309$		0			0
$310$	27.1342	+	26.9721i	1.54112	+	1.53191i
$311$	13.7455	+	23.8080i	0.779437	+	1.35003i	0.932266	+	0.361773i	$0.117828\pi$
$311$	13.7455	+	23.8080i	0.779437	+	1.35003i	−0.152829	+	0.988253i	$0.548838\pi$
$312$		0			0
$313$	−18.4592	−	10.6574i	−1.04337	−	0.602392i	−0.122587	−	0.992458i	$-0.539119\pi$
$313$	−18.4592	−	10.6574i	−1.04337	−	0.602392i	−0.920787	+	0.390066i	$0.872452\pi$
$314$	0.745764	−	2.81697i	0.0420859	−	0.158971i
$315$		0			0
$316$	−10.0076	+	17.5760i	−0.562969	+	0.988727i
$317$	−8.03749	+	13.9213i	−0.451430	+	0.781900i	−0.998475	−	0.0552031i	$-0.982419\pi$
$317$	−8.03749	+	13.9213i	−0.451430	+	0.781900i	0.547045	+	0.837103i	$0.315753\pi$
$318$		0			0
$319$	9.13774	−	5.27568i	0.511615	−	0.295381i
$320$	15.8352	−	28.6028i	0.885213	−	1.59895i
$321$		0			0
$322$	8.68219	+	3.27400i	0.483840	+	0.182453i
$323$			11.2939i			0.628409i
$324$		0			0
$325$	−5.77718	+	3.33546i	−0.320460	+	0.185018i
$326$	−20.5596	+	5.57502i	−1.13869	+	0.308772i
$327$		0			0
$328$	−20.5104	+	20.8825i	−1.13250	+	1.15304i
$329$	−21.2420	+	9.53190i	−1.17111	+	0.525511i
$330$		0			0
$331$	−28.1855	−	16.2729i	−1.54921	−	0.894439i	−0.998202	−	0.0599423i	$-0.980908\pi$
$331$	−28.1855	−	16.2729i	−1.54921	−	0.894439i	−0.551012	−	0.834497i	$-0.685758\pi$
$332$	−0.170136	−	28.3901i	−0.00933743	−	1.55811i
$333$		0			0
$334$	3.77636	−	3.79906i	0.206633	−	0.207875i
$335$	19.4631			1.06338
$336$		0			0
$337$	−14.8826			−0.810705			−0.405353	−	0.914160i	$-0.632851\pi$
$337$	−14.8826			−0.810705			−0.405353	+	0.914160i	$0.632851\pi$
$338$	−12.6369	+	12.7129i	−0.687359	+	0.691491i
$339$		0			0
$340$	−0.0712217	−	11.8845i	−0.00386254	−	0.644530i
$341$	−13.3733	−	7.72110i	−0.724207	−	0.418121i
$342$		0			0
$343$	5.56869	−	17.6632i	0.300681	−	0.953725i
$344$	−11.4167	+	11.6239i	−0.615549	+	0.626716i
$345$		0			0
$346$	18.6195	−	5.04892i	1.00099	−	0.271431i
$347$	7.69425	−	4.44228i	0.413049	−	0.238474i	−0.279050	−	0.960277i	$-0.590020\pi$
$347$	7.69425	−	4.44228i	0.413049	−	0.238474i	0.692099	+	0.721803i	$0.256686\pi$
$348$		0			0
$349$		−	18.1821i		−	0.973265i	−0.873607	−	0.486633i	$-0.838225\pi$
$349$		−	18.1821i		−	0.973265i	0.873607	−	0.486633i	$-0.161775\pi$
$350$	27.7534	+	33.8612i	1.48348	+	1.80996i
$351$		0			0
$352$	−3.22400	+	12.7959i	−0.171840	+	0.682026i
$353$	−6.33702	+	3.65868i	−0.337285	+	0.194732i	−0.659071	−	0.752081i	$-0.729050\pi$
$353$	−6.33702	+	3.65868i	−0.337285	+	0.194732i	0.321786	+	0.946813i	$0.395717\pi$
$354$		0			0
$355$	−19.6245	+	33.9906i	−1.04156	+	1.80404i
$356$	3.89738	−	6.84486i	0.206560	−	0.362777i
$357$		0			0
$358$	2.47694	−	9.35613i	0.130911	−	0.494487i
$359$	−5.38184	−	3.10721i	−0.284043	−	0.163992i	0.351209	−	0.936297i	$-0.385771\pi$
$359$	−5.38184	−	3.10721i	−0.284043	−	0.163992i	−0.635252	+	0.772305i	$0.719104\pi$
$360$		0			0
$361$	−20.6636	−	35.7905i	−1.08756	−	1.88371i
$362$	4.92798	+	4.89853i	0.259009	+	0.257461i
$363$		0			0
$364$	−2.45629	−	1.75137i	−0.128744	−	0.0917968i
$365$	−8.96677			−0.469342
$366$		0			0
$367$	15.0497	+	26.0668i	0.785587	+	1.36068i	0.928648	+	0.370962i	$0.120972\pi$
$367$	15.0497	+	26.0668i	0.785587	+	1.36068i	−0.143061	+	0.989714i	$0.545695\pi$
$368$	−8.64950	−	4.85651i	−0.450886	−	0.253163i
$369$		0			0
$370$	−7.93561	+	29.9751i	−0.412553	+	1.55833i
$371$	2.23938	−	21.9213i	0.116263	−	1.13810i
$372$		0			0
$373$	−15.5830	+	26.9905i	−0.806857	+	1.39752i	0.108174	+	0.994132i	$0.465500\pi$
$373$	−15.5830	+	26.9905i	−0.806857	+	1.39752i	−0.915031	+	0.403385i	$0.867834\pi$
$374$	1.25542	+	4.62975i	0.0649161	+	0.239398i
$375$		0			0
$376$	23.9832	−	6.65790i	1.23684	−	0.343355i
$377$		−	2.57871i		−	0.132811i
$378$		0			0
$379$			6.02988i			0.309734i	0.987935	+	0.154867i	$0.0494949\pi$
$379$			6.02988i			0.309734i	−0.987935	+	0.154867i	$0.950505\pi$
$380$	32.0706	+	54.7870i	1.64519	+	2.81051i
$381$		0			0
$382$	1.24966	−	0.338863i	0.0639384	−	0.0173377i
$383$	−12.5291	+	21.7011i	−0.640208	+	1.10887i	0.345178	+	0.938537i	$0.387819\pi$
$383$	−12.5291	+	21.7011i	−0.640208	+	1.10887i	−0.985386	+	0.170336i	$0.945515\pi$
$384$		0			0
$385$	−20.4484	−	14.7657i	−1.04215	−	0.752529i
$386$	−7.87683	−	2.08531i	−0.400920	−	0.106140i
$387$		0			0
$388$	28.6425	−	0.171649i	1.45410	−	0.00871416i
$389$	−11.3717	−	19.6964i	−0.576569	−	0.998647i	−0.995869	−	0.0907991i	$-0.971058\pi$
$389$	−11.3717	−	19.6964i	−0.576569	−	0.998647i	0.419300	−	0.907848i	$-0.362275\pi$
$390$		0			0
$391$	−3.60598			−0.182362
$392$	−8.72606	+	17.7723i	−0.440733	+	0.897638i
$393$		0			0
$394$	0.568546	−	0.571964i	0.0286429	−	0.0288151i
$395$	20.6638	+	35.7908i	1.03971	+	1.80083i
$396$		0			0
$397$	17.9160	+	10.3438i	0.899178	+	0.519140i	0.876933	−	0.480612i	$-0.159586\pi$
$397$	17.9160	+	10.3438i	0.899178	+	0.519140i	0.0222443	+	0.999753i	$0.492919\pi$
$398$	8.96288	+	2.37283i	0.449269	+	0.118939i
$399$		0			0
$400$	−23.8864	−	40.2506i	−1.19432	−	2.01253i
$401$	−15.4675	+	26.7905i	−0.772411	+	1.33785i	0.163827	+	0.986489i	$0.447616\pi$
$401$	−15.4675	+	26.7905i	−0.772411	+	1.33785i	−0.936238	+	0.351366i	$0.885717\pi$
$402$		0			0
$403$	−3.26840	+	1.88701i	−0.162810	+	0.0939987i
$404$	−3.05175	−	5.21339i	−0.151830	−	0.259376i
$405$		0			0
$406$	−16.7000	+	2.74635i	−0.828805	+	0.136299i
$407$		−	12.5154i		−	0.620364i
$408$		0			0
$409$	30.1432	−	17.4032i	1.49049	−	0.860533i	0.490546	−	0.871415i	$-0.336797\pi$
$409$	30.1432	−	17.4032i	1.49049	−	0.860533i	0.999941	+	0.0108826i	$0.00346409\pi$
$410$	15.6529	+	57.7251i	0.773044	+	2.85084i
$411$		0			0
$412$	2.46618	+	1.40421i	0.121500	+	0.0691805i
$413$	−1.17087	+	11.4616i	−0.0576145	+	0.563990i
$414$		0			0
$415$	−50.2398	−	29.0060i	−2.46618	−	1.42385i
$416$	2.31434	+	2.24601i	0.113470	+	0.110120i
$417$		0			0
$418$	−18.1726	−	18.0640i	−0.888850	−	0.883539i
$419$	−19.9375			−0.974013			−0.487007	−	0.873398i	$-0.661911\pi$
$419$	−19.9375			−0.974013			−0.487007	+	0.873398i	$0.661911\pi$
$420$		0			0
$421$	5.18858			0.252876			0.126438	−	0.991975i	$-0.459646\pi$
$421$	5.18858			0.252876			0.126438	+	0.991975i	$0.459646\pi$
$422$	−8.97463	−	8.92100i	−0.436878	−	0.434268i
$423$		0			0
$424$	−5.89217	+	22.8080i	−0.286149	+	1.10765i
$425$	−14.7349	−	8.50717i	−0.714746	−	0.412659i
$426$		0			0
$427$	8.31449	+	18.5290i	0.402366	+	0.896680i
$428$	−0.279327	+	0.490575i	−0.0135018	+	0.0237128i
$429$		0			0
$430$	8.71291	+	32.1316i	0.420174	+	1.54952i
$431$	21.5529	−	12.4435i	1.03816	−	0.599384i	0.118851	−	0.992912i	$-0.462079\pi$
$431$	21.5529	−	12.4435i	1.03816	−	0.599384i	0.919313	+	0.393528i	$0.128745\pi$
$432$		0			0
$433$		−	10.7080i		−	0.514595i	−0.966332	−	0.257297i	$-0.917168\pi$
$433$		−	10.7080i		−	0.514595i	0.966332	−	0.257297i	$-0.0828320\pi$
$434$	15.7013	+	19.1567i	0.753686	+	0.919552i
$435$		0			0
$436$	−10.6418	+	6.22938i	−0.509650	+	0.298333i
$437$	16.6811	−	9.63082i	0.797964	−	0.460705i
$438$		0			0
$439$	−7.34136	+	12.7156i	−0.350384	+	0.606883i	−0.986317	−	0.164861i	$-0.947282\pi$
$439$	−7.34136	+	12.7156i	−0.350384	+	0.606883i	0.635933	+	0.771745i	$0.280616\pi$
$440$	19.2369	+	18.8941i	0.917082	+	0.900741i
$441$		0			0
$442$	1.13331	+	0.300033i	0.0539062	+	0.0142711i
$443$	13.6780	+	7.89697i	0.649859	+	0.375196i	0.788402	−	0.615160i	$-0.210909\pi$
$443$	13.6780	+	7.89697i	0.649859	+	0.375196i	−0.138543	+	0.990356i	$0.544242\pi$
$444$		0			0
$445$	−8.04738	−	13.9385i	−0.381483	−	0.660747i
$446$	1.65702	−	1.66698i	0.0784620	−	0.0789336i
$447$		0			0
$448$	12.0806	−	17.3799i	0.570753	−	0.821122i
$449$	−34.1683			−1.61250			−0.806251	−	0.591574i	$-0.798507\pi$
$449$	−34.1683			−1.61250			−0.806251	+	0.591574i	$0.798507\pi$
$450$		0			0
$451$	−12.0702	−	20.9063i	−0.568366	−	0.984438i
$452$	0.100858	+	16.8298i	0.00474394	+	0.791606i
$453$		0			0
$454$	−13.1048	−	3.46936i	−0.615037	−	0.162825i
$455$	−5.62397	+	2.52364i	−0.263656	+	0.118310i
$456$		0			0
$457$	13.2076	−	22.8763i	0.617827	−	1.07011i	−0.372054	−	0.928211i	$-0.621347\pi$
$457$	13.2076	−	22.8763i	0.617827	−	1.07011i	0.989881	−	0.141897i	$-0.0453201\pi$
$458$	24.5558	−	6.65864i	1.14742	−	0.311138i
$459$		0			0
$460$	−17.4927	+	10.2397i	−0.815602	+	0.477428i
$461$			1.05880i			0.0493132i	0.999696	+	0.0246566i	$0.00784924\pi$
$461$			1.05880i			0.0493132i	−0.999696	+	0.0246566i	$0.992151\pi$
$462$		0			0
$463$			30.7224i			1.42779i	0.700252	+	0.713895i	$0.253071\pi$
$463$			30.7224i			1.42779i	−0.700252	+	0.713895i	$0.746929\pi$
$464$	18.0915	−	0.216846i	0.839878	−	0.0100668i
$465$		0			0
$466$	−7.42624	−	27.3866i	−0.344014	−	1.26866i
$467$	−6.18825	+	10.7184i	−0.286358	+	0.495987i	−0.972938	−	0.231068i	$-0.925778\pi$
$467$	−6.18825	+	10.7184i	−0.286358	+	0.495987i	0.686580	+	0.727055i	$0.259111\pi$
$468$		0			0
$469$	12.5352	+	1.28054i	0.578824	+	0.0591299i
$470$	13.0161	−	49.1655i	0.600388	−	2.26784i
$471$		0			0
$472$	3.08074	−	11.9253i	0.141803	−	0.548904i
$473$	−6.71867	−	11.6371i	−0.308925	−	0.535073i
$474$		0			0
$475$	90.8835			4.17002
$476$	0.736054	−	7.65896i	0.0337370	−	0.351048i
$477$		0			0
$478$	−22.1839	−	22.0514i	−1.01467	−	1.00861i
$479$	9.93069	+	17.2005i	0.453745	+	0.785909i	0.998615	−	0.0526112i	$-0.0167544\pi$
$479$	9.93069	+	17.2005i	0.453745	+	0.785909i	−0.544870	+	0.838520i	$0.683421\pi$
$480$		0			0
$481$	−2.64892	−	1.52936i	−0.120781	−	0.0697327i
$482$	4.57232	−	17.2710i	0.208263	−	0.786671i
$483$		0			0
$484$	9.66062	+	5.50063i	0.439119	+	0.250029i
$485$	29.2639	−	50.6865i	1.32880	−	2.30156i
$486$		0			0
$487$	22.5673	−	13.0292i	1.02262	−	0.590412i	0.107760	−	0.994177i	$-0.465632\pi$
$487$	22.5673	−	13.0292i	1.02262	−	0.590412i	0.914863	+	0.403765i	$0.132299\pi$
$488$	−5.80755	−	20.9200i	−0.262896	−	0.947005i
$489$		0			0
$490$	22.3329	+	33.7336i	1.00890	+	1.52393i
$491$		−	31.0731i		−	1.40231i	−0.713008	−	0.701156i	$-0.752668\pi$
$491$		−	31.0731i		−	1.40231i	0.713008	−	0.701156i	$-0.247332\pi$
$492$		0			0
$493$	5.69592	−	3.28854i	0.256531	−	0.148108i
$494$	−6.04397	+	1.63890i	−0.271931	+	0.0737377i
$495$		0			0
$496$	−13.5136	−	22.7715i	−0.606777	−	1.02247i
$497$	−14.8756	+	20.6006i	−0.667261	+	0.924064i
$498$		0			0
$499$	−18.0827	−	10.4400i	−0.809491	−	0.467360i	0.0372880	−	0.999305i	$-0.488128\pi$
$499$	−18.0827	−	10.4400i	−0.809491	−	0.467360i	−0.846779	+	0.531945i	$0.821461\pi$
$500$	−54.7702	+	0.328227i	−2.44940	+	0.0146788i
$501$		0			0
$502$	21.7032	−	21.8337i	0.968663	−	0.974486i
$503$	−19.0163			−0.847896			−0.423948	−	0.905687i	$-0.639356\pi$
$503$	−19.0163			−0.847896			−0.423948	+	0.905687i	$0.639356\pi$
$504$		0			0
$505$	−12.3437			−0.549288
$506$	5.76758	−	5.80224i	0.256400	−	0.257941i
$507$		0			0
$508$	30.0243	−	0.179930i	1.33211	−	0.00798310i
$509$	−8.98062	−	5.18497i	−0.398059	−	0.229820i	0.287587	−	0.957755i	$-0.407147\pi$
$509$	−8.98062	−	5.18497i	−0.398059	−	0.229820i	−0.685646	+	0.727935i	$0.740480\pi$
$510$		0			0
$511$	−5.77507	−	0.589954i	−0.255474	−	0.0260980i
$512$	−15.5628	+	16.4256i	−0.687783	+	0.725916i
$513$		0			0
$514$	−38.9994	+	10.5752i	−1.72019	+	0.466452i
$515$	5.02198	−	2.89944i	0.221295	−	0.127765i
$516$		0			0
$517$			20.5279i			0.902816i
$518$	−7.08311	+	18.7834i	−0.311214	+	0.825296i
$519$		0			0
$520$	6.34971	−	1.76273i	0.278453	−	0.0773007i
$521$	1.39578	−	0.805852i	0.0611500	−	0.0353050i	−0.469113	−	0.883138i	$-0.655426\pi$
$521$	1.39578	−	0.805852i	0.0611500	−	0.0353050i	0.530263	+	0.847833i	$0.322093\pi$
$522$		0			0
$523$	17.7201	−	30.6922i	0.774847	−	1.34207i	−0.160033	−	0.987112i	$-0.551160\pi$
$523$	17.7201	−	30.6922i	0.774847	−	1.34207i	0.934880	−	0.354963i	$-0.115507\pi$
$524$	9.98847	+	5.68731i	0.436348	+	0.248451i
$525$		0			0
$526$	0.786538	−	2.97098i	0.0342947	−	0.129541i
$527$	−8.33613	−	4.81287i	−0.363128	−	0.209652i
$528$		0			0
$529$	−8.42502	−	14.5926i	−0.366305	−	0.634459i
$530$	34.1383	+	33.9343i	1.48287	+	1.47401i
$531$		0			0
$532$	17.0505	+	37.3958i	0.739234	+	1.62131i
$533$	−5.89985			−0.255551
$534$		0			0
$535$	0.576761	+	0.998979i	0.0249355	+	0.0431896i
$536$	−13.0423	−	3.36932i	−0.563341	−	0.145532i
$537$		0			0
$538$	4.34112	−	16.3977i	0.187159	−	0.706954i
$539$	−12.1984	−	10.8553i	−0.525421	−	0.467569i
$540$		0			0
$541$	−14.0626	+	24.3572i	−0.604599	+	1.04720i	0.387516	+	0.921863i	$0.373333\pi$
$541$	−14.0626	+	24.3572i	−0.604599	+	1.04720i	−0.992115	+	0.125333i	$0.960000\pi$
$542$	−3.75871	−	13.8614i	−0.161450	−	0.595400i
$543$		0			0
$544$	−2.00965	+	7.97622i	−0.0861629	+	0.341978i
$545$			25.1966i			1.07930i
$546$		0			0
$547$			4.80974i			0.205650i	0.994699	+	0.102825i	$0.0327881\pi$
$547$			4.80974i			0.205650i	−0.994699	+	0.102825i	$0.967212\pi$
$548$	2.46035	−	1.44021i	0.105101	−	0.0615228i
$549$		0			0
$550$	37.2562	−	10.1025i	1.58861	−	0.430773i
$551$	−17.5660	+	30.4252i	−0.748337	+	1.29616i
$552$		0			0
$553$	10.9538	+	24.4107i	0.465803	+	1.03805i
$554$	−27.6984	−	7.33289i	−1.17679	−	0.311545i
$555$		0			0
$556$	−0.110291	−	18.4039i	−0.00467739	−	0.780500i
$557$	5.22481	+	9.04964i	0.221382	+	0.383446i	0.955228	−	0.295871i	$-0.0956098\pi$
$557$	5.22481	+	9.04964i	0.221382	+	0.383446i	−0.733846	+	0.679316i	$0.762276\pi$
$558$		0			0
$559$	−3.28404			−0.138900
$560$	−18.1781	−	39.2439i	−0.768163	−	1.65836i
$561$		0			0
$562$	−22.6232	+	22.7592i	−0.954302	+	0.960038i
$563$	2.54332	+	4.40516i	0.107188	+	0.185655i	0.914630	−	0.404292i	$-0.132482\pi$
$563$	2.54332	+	4.40516i	0.107188	+	0.185655i	−0.807442	+	0.589947i	$0.799149\pi$
$564$		0			0
$565$	29.7824	+	17.1949i	1.25296	+	0.723394i
$566$	35.3982	+	9.37132i	1.48790	+	0.393906i
$567$		0			0
$568$	19.0347	−	19.3800i	0.798679	−	0.813168i
$569$	0.928415	−	1.60806i	0.0389212	−	0.0674135i	−0.845909	−	0.533328i	$-0.820941\pi$
$569$	0.928415	−	1.60806i	0.0389212	−	0.0674135i	0.884830	+	0.465914i	$0.154275\pi$
$570$		0			0
$571$	−37.3252	+	21.5497i	−1.56201	+	0.901827i	−0.564957	+	0.825120i	$0.691107\pi$
$571$	−37.3252	+	21.5497i	−1.56201	+	0.901827i	−0.997054	+	0.0767070i	$0.975559\pi$
$572$	−2.29545	+	1.34368i	−0.0959774	+	0.0561821i
$573$		0			0
$574$	6.28339	+	38.2079i	0.262264	+	1.59477i
$575$			29.0178i			1.21013i
$576$		0			0
$577$	−21.8842	+	12.6349i	−0.911052	+	0.525996i	−0.880769	−	0.473546i	$-0.842974\pi$
$577$	−21.8842	+	12.6349i	−0.911052	+	0.525996i	−0.0302822	+	0.999541i	$0.509641\pi$
$578$	−5.50944	−	20.3178i	−0.229162	−	0.845108i
$579$		0			0
$580$	18.2928	−	32.1271i	0.759567	−	1.33401i
$581$	−30.4487	−	21.9868i	−1.26322	−	0.912167i
$582$		0			0
$583$	−16.8254	−	9.71412i	−0.696835	−	0.402318i
$584$	6.00868	+	1.55227i	0.248641	+	0.0642333i
$585$		0			0
$586$	0.752140	+	0.747646i	0.0310706	+	0.0308850i
$587$	−33.9636			−1.40183			−0.700913	−	0.713247i	$-0.747224\pi$
$587$	−33.9636			−1.40183			−0.700913	+	0.713247i	$0.747224\pi$
$588$		0			0
$589$	51.4167			2.11859
$590$	−17.8493	−	17.7427i	−0.734846	−	0.730455i
$591$		0			0
$592$	10.5068	−	18.7127i	0.431826	−	0.769087i
$593$	15.9907	+	9.23225i	0.656661	+	0.379123i	0.791003	−	0.611812i	$-0.209559\pi$
$593$	15.9907	+	9.23225i	0.656661	+	0.379123i	−0.134343	+	0.990935i	$0.542892\pi$
$594$		0			0
$595$	−12.7463	−	9.20404i	−0.522548	−	0.377329i
$596$	−12.7136	−	7.23894i	−0.520768	−	0.296519i
$597$		0			0
$598$	−0.523278	−	1.92975i	−0.0213984	−	0.0789134i
$599$	29.0104	−	16.7492i	1.18533	−	0.684352i	0.228091	−	0.973640i	$-0.426752\pi$
$599$	29.0104	−	16.7492i	1.18533	−	0.684352i	0.957242	+	0.289287i	$0.0934183\pi$
$600$		0			0
$601$			8.02683i			0.327421i	0.986508	+	0.163711i	$0.0523463\pi$
$601$			8.02683i			0.327421i	−0.986508	+	0.163711i	$0.947654\pi$
$602$	3.49753	+	21.2677i	0.142549	+	0.866807i
$603$		0			0
$604$	1.88143	+	3.21410i	0.0765545	+	0.130780i
$605$	19.6723	−	11.3578i	0.799794	−	0.461761i
$606$		0			0
$607$	14.0948	−	24.4129i	0.572090	−	0.990890i	−0.424261	−	0.905540i	$-0.639466\pi$
$607$	14.0948	−	24.4129i	0.572090	−	0.990890i	0.996351	−	0.0853496i	$-0.0272007\pi$
$608$	−12.0063	−	42.2649i	−0.486920	−	1.71407i
$609$		0			0
$610$	−42.8861	−	11.3537i	−1.73641	−	0.459697i
$611$	4.34480	+	2.50847i	0.175772	+	0.101482i
$612$		0			0
$613$	18.6002	+	32.2164i	0.751254	+	1.30121i	0.947215	+	0.320598i	$0.103884\pi$
$613$	18.6002	+	32.2164i	0.751254	+	1.30121i	−0.195962	+	0.980612i	$0.562783\pi$
$614$	−17.8928	+	18.0004i	−0.722096	+	0.726436i
$615$		0			0
$616$	11.1465	+	13.4345i	0.449103	+	0.541290i
$617$	45.7253			1.84083			0.920415	−	0.390942i	$-0.127851\pi$
$617$	45.7253			1.84083			0.920415	+	0.390942i	$0.127851\pi$
$618$		0			0
$619$	−3.92199	−	6.79309i	−0.157638	−	0.273037i	0.776378	−	0.630267i	$-0.217055\pi$
$619$	−3.92199	−	6.79309i	−0.157638	−	0.273037i	−0.934016	+	0.357230i	$0.883721\pi$
$620$	−54.1056	+	0.324244i	−2.17293	+	0.0130220i
$621$		0			0
$622$	−37.5835	−	9.94986i	−1.50696	−	0.398953i
$623$	−4.26588	−	9.50658i	−0.170909	−	0.380873i
$624$		0			0
$625$	−26.7055	+	46.2553i	−1.06822	+	1.85021i
$626$	29.0931	−	7.88897i	1.16279	−	0.315307i
$627$		0			0
$628$	2.08187	+	3.55651i	0.0830756	+	0.141920i
$629$		−	7.80133i		−	0.311059i
$630$		0			0
$631$			14.9251i			0.594159i	0.954853	+	0.297079i	$0.0960126\pi$
$631$			14.9251i			0.594159i	−0.954853	+	0.297079i	$0.903987\pi$
$632$	−7.65106	−	27.5608i	−0.304343	−	1.09631i
$633$		0			0
$634$	−5.94962	−	21.9411i	−0.236290	−	0.871392i
$635$	30.6757	−	53.1318i	1.21733	−	2.10847i
$636$		0			0
$637$	−3.78817	+	1.25534i	−0.150093	+	0.0497383i
$638$	−3.81886	+	14.4249i	−0.151190	+	0.571088i
$639$		0			0
$640$	12.9007	+	44.3995i	0.509946	+	1.75505i
$641$	14.7462	+	25.5412i	0.582440	+	1.00882i	0.995189	+	0.0979713i	$0.0312354\pi$
$641$	14.7462	+	25.5412i	0.582440	+	1.00882i	−0.412749	+	0.910845i	$0.635431\pi$
$642$		0			0
$643$	20.9682			0.826905			0.413453	−	0.910526i	$-0.364323\pi$
$643$	20.9682			0.826905			0.413453	+	0.910526i	$0.364323\pi$
$644$	−11.9399	+	5.44399i	−0.470499	+	0.214523i
$645$		0			0
$646$	−11.3277	−	11.2600i	−0.445682	−	0.443019i
$647$	−10.6102	−	18.3773i	−0.417128	−	0.722487i	0.578521	−	0.815667i	$-0.303630\pi$
$647$	−10.6102	−	18.3773i	−0.417128	−	0.722487i	−0.995649	+	0.0931801i	$0.970297\pi$
$648$		0			0
$649$	8.79720	+	5.07906i	0.345320	+	0.199371i
$650$	2.41441	−	9.11992i	0.0947009	−	0.357713i
$651$		0			0
$652$	14.9062	−	26.1794i	0.583773	−	1.02527i
$653$	3.27331	−	5.66954i	0.128095	−	0.221866i	−0.794844	−	0.606814i	$-0.792447\pi$
$653$	3.27331	−	5.66954i	0.128095	−	0.221866i	0.922938	+	0.384948i	$0.125781\pi$
$654$		0			0
$655$	20.3399	−	11.7433i	0.794747	−	0.458848i
$656$	−0.496122	−	41.3917i	−0.0193703	−	1.61607i
$657$		0			0
$658$	11.6178	−	30.8088i	0.452910	−	1.20105i
$659$			7.63411i			0.297383i	0.988884	+	0.148691i	$0.0475061\pi$
$659$			7.63411i			0.297383i	−0.988884	+	0.148691i	$0.952494\pi$
$660$		0			0
$661$	4.86154	−	2.80681i	0.189092	−	0.109172i	−0.402465	−	0.915435i	$-0.631847\pi$
$661$	4.86154	−	2.80681i	0.189092	−	0.109172i	0.591557	+	0.806263i	$0.298513\pi$
$662$	44.4225	−	12.0457i	1.72653	−	0.468171i
$663$		0			0
$664$	28.6446	+	28.1342i	1.11163	+	1.09182i
$665$	83.5458	+	8.53465i	3.23977	+	0.330959i
$666$		0			0
$667$	−9.71434	−	5.60858i	−0.376141	−	0.217165i
$668$	0.0453974	+	7.57532i	0.00175648	+	0.293098i
$669$		0			0
$670$	−19.4047	+	19.5213i	−0.749667	+	0.754173i
$671$	17.9061			0.691257
$672$		0			0
$673$	5.35197			0.206303			0.103152	−	0.994666i	$-0.467107\pi$
$673$	5.35197			0.206303			0.103152	+	0.994666i	$0.467107\pi$
$674$	14.8379	−	14.9271i	0.571535	−	0.574970i
$675$		0			0
$676$	−0.151915	−	25.3495i	−0.00584287	−	0.974981i
$677$	38.8597	+	22.4357i	1.49350	+	0.862273i	0.999972	−	0.00745575i	$-0.00237326\pi$
$677$	38.8597	+	22.4357i	1.49350	+	0.862273i	0.493529	+	0.869729i	$0.335707\pi$
$678$		0			0
$679$	22.1823	−	30.7194i	0.851280	−	1.17890i
$680$	11.9911	+	11.7774i	0.459838	+	0.451644i
$681$		0			0
$682$	21.0774	−	5.71542i	0.807096	−	0.218855i
$683$	3.54984	−	2.04950i	0.135831	−	0.0784219i	−0.430545	−	0.902569i	$-0.641679\pi$
$683$	3.54984	−	2.04950i	0.135831	−	0.0784219i	0.566376	+	0.824147i	$0.308345\pi$
$684$		0			0
$685$		−	5.82536i		−	0.222576i
$686$	12.1641	+	23.1956i	0.464428	+	0.885611i
$687$		0			0
$688$	−0.276157	−	23.0399i	−0.0105284	−	0.878386i
$689$	−4.11206	+	2.37410i	−0.156657	+	0.0904459i
$690$		0			0
$691$	9.00736	−	15.6012i	0.342656	−	0.593498i	−0.642269	−	0.766479i	$-0.722007\pi$
$691$	9.00736	−	15.6012i	0.342656	−	0.593498i	0.984925	+	0.172982i	$0.0553401\pi$
$692$	−13.4996	+	23.7089i	−0.513177	+	0.901279i
$693$		0			0
$694$	−3.21559	+	12.1462i	−0.122062	+	0.461064i
$695$	−32.5681	−	18.8032i	−1.23538	−	0.713246i
$696$		0			0
$697$	−7.52386	−	13.0317i	−0.284987	−	0.493611i
$698$	18.2365	+	18.1275i	0.690262	+	0.686137i
$699$		0			0
$700$	−61.6327	−	5.92312i	−2.32950	−	0.223873i
$701$	−22.9585			−0.867131			−0.433565	−	0.901122i	$-0.642745\pi$
$701$	−22.9585			−0.867131			−0.433565	+	0.901122i	$0.642745\pi$
$702$		0			0
$703$	20.8357	+	36.0885i	0.785834	+	1.36110i
$704$	−9.61990	−	15.9912i	−0.362564	−	0.602691i
$705$		0			0
$706$	2.64838	−	10.0037i	0.0996730	−	0.376493i
$707$	−7.95001	−	0.812135i	−0.298991	−	0.0305435i
$708$		0			0
$709$	−9.00913	+	15.6043i	−0.338345	+	0.586031i	−0.984122	−	0.177496i	$-0.943200\pi$
$709$	−9.00913	+	15.6043i	−0.338345	+	0.586031i	0.645777	+	0.763526i	$0.276534\pi$
$710$	−14.5267	−	53.5719i	−0.545178	−	2.01052i
$711$		0			0
$712$	2.97966	+	10.7334i	0.111667	+	0.402249i
$713$			16.4166i			0.614807i
$714$		0			0
$715$			5.43491i			0.203254i
$716$	6.91461	+	11.8124i	0.258411	+	0.441450i
$717$		0			0
$718$	8.48220	−	2.30006i	0.316553	−	0.0858375i
$719$	−11.2030	+	19.4042i	−0.417801	+	0.723653i	−0.995718	−	0.0924426i	$-0.970533\pi$
$719$	−11.2030	+	19.4042i	−0.417801	+	0.723653i	0.577917	+	0.816096i	$0.303866\pi$
$720$		0			0
$721$	3.42519	−	1.53698i	0.127561	−	0.0572402i
$722$	56.4992	+	14.9576i	2.10268	+	0.556665i
$723$		0			0
$724$	−9.82638	+	0.0588876i	−0.365194	+	0.00218854i
$725$	−26.4633	−	45.8358i	−0.982823	−	1.70230i
$726$		0			0
$727$	−22.0274			−0.816950			−0.408475	−	0.912770i	$-0.633939\pi$
$727$	−22.0274			−0.816950			−0.408475	+	0.912770i	$0.633939\pi$
$728$	4.20553	−	0.717520i	0.155867	−	0.0265930i
$729$		0			0
$730$	8.93986	−	8.99360i	0.330879	−	0.332868i
$731$	−4.18801	−	7.25385i	−0.154899	−	0.268293i
$732$		0			0
$733$	−16.3515	−	9.44057i	−0.603958	−	0.348695i	0.166639	−	0.986018i	$-0.446709\pi$
$733$	−16.3515	−	9.44057i	−0.603958	−	0.348695i	−0.770597	+	0.637323i	$0.780042\pi$
$734$	−41.1493	−	10.8939i	−1.51885	−	0.402100i
$735$		0			0
$736$	13.4946	−	3.83344i	0.497417	−	0.141302i
$737$	5.55482	−	9.62123i	0.204615	−	0.354403i
$738$		0			0
$739$	−6.79199	+	3.92136i	−0.249847	+	0.144250i	−0.619694	−	0.784843i	$-0.712743\pi$
$739$	−6.79199	+	3.92136i	−0.249847	+	0.144250i	0.369847	+	0.929093i	$0.379410\pi$
$740$	−22.1530	−	37.8445i	−0.814359	−	1.39119i
$741$		0			0
$742$	19.7542	+	24.1016i	0.725200	+	0.884797i
$743$		−	24.2015i		−	0.887867i	−0.896060	−	0.443934i	$-0.853583\pi$
$743$		−	24.2015i		−	0.887867i	0.896060	−	0.443934i	$-0.146417\pi$
$744$		0			0
$745$	−25.8892	+	14.9471i	−0.948506	+	0.547620i
$746$	−11.5351	−	42.5391i	−0.422328	−	1.55747i
$747$		0			0
$748$	−5.89525	−	3.35668i	−0.215552	−	0.122732i
$749$	0.305738	+	0.681342i	0.0111714	+	0.0248957i
$750$		0			0
$751$	0.110458	+	0.0637727i	0.00403066	+	0.00232710i	0.502014	−	0.864860i	$-0.332593\pi$
$751$	0.110458	+	0.0637727i	0.00403066	+	0.00232710i	−0.497983	+	0.867187i	$0.665926\pi$
$752$	−17.2334	+	30.6928i	−0.628436	+	1.11925i
$753$		0			0
$754$	2.58643	+	2.57098i	0.0941922	+	0.0936294i
$755$	7.61001			0.276957
$756$		0			0
$757$	2.03533			0.0739752			0.0369876	−	0.999316i	$-0.488224\pi$
$757$	2.03533			0.0739752			0.0369876	+	0.999316i	$0.488224\pi$
$758$	−6.04792	−	6.01179i	−0.219670	−	0.218358i
$759$		0			0
$760$	−86.9253	−	22.4561i	−3.15311	−	0.814567i
$761$	−7.21754	−	4.16705i	−0.261636	−	0.151055i	0.363445	−	0.931616i	$-0.381601\pi$
$761$	−7.21754	−	4.16705i	−0.261636	−	0.151055i	−0.625081	+	0.780560i	$0.714934\pi$
$762$		0			0
$763$	−1.65777	+	16.2279i	−0.0600152	+	0.587490i
$764$	−0.906037	+	1.59125i	−0.0327793	+	0.0575694i
$765$		0			0
$766$	−9.27448	−	34.2026i	−0.335101	−	1.23579i
$767$	2.15000	−	1.24131i	0.0776322	−	0.0448210i
$768$		0			0
$769$		−	29.5981i		−	1.06733i	−0.845695	−	0.533667i	$-0.820814\pi$
$769$		−	29.5981i		−	1.06733i	0.845695	−	0.533667i	$-0.179186\pi$
$770$	35.1969	−	5.78822i	1.26841	−	0.208593i
$771$		0			0
$772$	9.94474	−	5.82134i	0.357919	−	0.209515i
$773$	−9.04127	+	5.21998i	−0.325192	+	0.187750i	−0.653704	−	0.756750i	$-0.726786\pi$
$773$	−9.04127	+	5.21998i	−0.325192	+	0.187750i	0.328513	+	0.944500i	$0.393453\pi$
$774$		0			0
$775$	−38.7298	+	67.0820i	−1.39122	+	2.40966i
$776$	−28.3844	+	28.8993i	−1.01894	+	1.03743i
$777$		0			0
$778$	31.0929	+	8.23155i	1.11473	+	0.295115i
$779$	69.6100	+	40.1893i	2.49404	+	1.43993i
$780$		0			0
$781$	11.2018	+	19.4021i	0.400832	+	0.694261i
$782$	3.59516	−	3.61677i	0.128563	−	0.129335i
$783$		0			0
$784$	−9.12563	−	26.4712i	−0.325916	−	0.945399i
$785$	8.42072			0.300548
$786$		0			0
$787$	−23.1132	−	40.0333i	−0.823897	−	1.42703i	−0.902759	−	0.430146i	$-0.858462\pi$
$787$	−23.1132	−	40.0333i	−0.823897	−	1.42703i	0.0788620	−	0.996886i	$-0.474871\pi$
$788$	0.00683476	+	1.14049i	0.000243478	+	0.0406284i
$789$		0			0
$790$	−56.4996	−	14.9577i	−2.01017	−	0.532172i
$791$	18.0501	+	13.0339i	0.641789	+	0.463432i
$792$		0			0
$793$	2.18809	−	3.78989i	0.0777014	−	0.134583i
$794$	−28.2370	+	7.65683i	−1.00209	+	0.271731i
$795$		0			0
$796$	−11.3159	+	6.62398i	−0.401082	+	0.234781i
$797$			2.88962i			0.102356i	0.998690	+	0.0511778i	$0.0162975\pi$
$797$			2.88962i			0.102356i	−0.998690	+	0.0511778i	$0.983702\pi$
$798$		0			0
$799$			12.7959i			0.452685i
$800$	64.1857	+	16.1719i	2.26931	+	0.571763i
$801$		0			0
$802$	−11.4496	−	42.2239i	−0.404299	−	1.49098i
$803$	−2.55915	+	4.43257i	−0.0903103	+	0.156422i
$804$		0			0
$805$	−2.72499	+	26.6750i	−0.0960433	+	0.940170i
$806$	1.36593	−	5.15952i	0.0481130	−	0.181736i
$807$		0			0
$808$	8.27159	+	2.13686i	0.290993	+	0.0751745i
$809$	2.29714	+	3.97876i	0.0807631	+	0.139886i	0.903578	−	0.428424i	$-0.140931\pi$
$809$	2.29714	+	3.97876i	0.0807631	+	0.139886i	−0.822815	+	0.568310i	$0.807598\pi$
$810$		0			0
$811$	17.8171			0.625644			0.312822	−	0.949812i	$-0.398726\pi$
$811$	17.8171			0.625644			0.312822	+	0.949812i	$0.398726\pi$
$812$	13.8953	−	19.4880i	0.487629	−	0.683896i
$813$		0			0
$814$	12.5528	+	12.4778i	0.439976	+	0.437347i
$815$	−30.7787	−	53.3103i	−1.07813	−	1.86738i
$816$		0			0
$817$	38.7470	+	22.3706i	1.35559	+	0.782649i
$818$	−12.5975	+	47.5844i	−0.440461	+	1.66375i
$819$		0			0
$820$	−73.5038	−	41.8522i	−2.56686	−	1.46154i
$821$	3.97884	−	6.89156i	0.138863	−	0.240517i	−0.788204	−	0.615414i	$-0.788989\pi$
$821$	3.97884	−	6.89156i	0.138863	−	0.240517i	0.927066	+	0.374897i	$0.122322\pi$
$822$		0			0
$823$	27.3701	−	15.8021i	0.954062	−	0.550828i	0.0597216	−	0.998215i	$-0.480979\pi$
$823$	27.3701	−	15.8021i	0.954062	−	0.550828i	0.894340	+	0.447387i	$0.147645\pi$
$824$	−3.86719	+	1.07356i	−0.134720	+	0.0373992i
$825$		0			0
$826$	−10.3286	−	12.6016i	−0.359377	−	0.438466i
$827$			3.26564i			0.113557i	0.998387	+	0.0567787i	$0.0180830\pi$
$827$			3.26564i			0.113557i	−0.998387	+	0.0567787i	$0.981917\pi$
$828$		0			0
$829$	3.27611	−	1.89146i	0.113784	−	0.0656931i	−0.442028	−	0.897001i	$-0.645741\pi$
$829$	3.27611	−	1.89146i	0.113784	−	0.0656931i	0.555812	+	0.831308i	$0.312407\pi$
$830$	79.1818	−	21.4712i	2.74844	−	0.745276i
$831$		0			0
$832$	−4.56013	+	0.0819917i	−0.158094	+	0.00284255i
$833$	−7.60373	−	6.76651i	−0.263454	−	0.234446i
$834$		0			0
$835$	13.4055	+	7.73966i	0.463916	+	0.267842i
$836$	36.2361	−	0.217156i	1.25325	−	0.00751049i
$837$		0			0
$838$	19.8777	−	19.9972i	0.686664	−	0.690792i
$839$	−12.5506			−0.433296			−0.216648	−	0.976250i	$-0.569512\pi$
$839$	−12.5506			−0.433296			−0.216648	+	0.976250i	$0.569512\pi$
$840$		0			0
$841$	−8.54062			−0.294504
$842$	−5.17301	+	5.20411i	−0.178274	+	0.179345i
$843$		0			0
$844$	17.8954	−	0.107244i	0.615985	−	0.00369148i
$845$	−44.8591	−	25.8994i	−1.54320	−	0.890968i
$846$		0			0
$847$	13.4173	−	6.02073i	0.461024	−	0.206875i
$848$	−17.0018	−	28.6494i	−0.583843	−	0.983823i
$849$		0			0
$850$	23.2233	−	6.29730i	0.796551	−	0.215996i
$851$	−11.5226	+	6.65255i	−0.394988	+	0.228046i
$852$		0			0
$853$			25.4776i			0.872336i	0.899865	+	0.436168i	$0.143665\pi$
$853$			25.4776i			0.872336i	−0.899865	+	0.436168i	$0.856335\pi$
$854$	−26.8739	−	10.1340i	−0.919607	−	0.346778i
$855$		0			0
$856$	−0.213554	−	0.769266i	−0.00729911	−	0.0262930i
$857$	−4.00303	+	2.31115i	−0.136741	+	0.0789473i	−0.566810	−	0.823849i	$-0.691823\pi$
$857$	−4.00303	+	2.31115i	−0.136741	+	0.0789473i	0.430069	+	0.902796i	$0.358489\pi$
$858$		0			0
$859$	−9.56988	+	16.5755i	−0.326520	+	0.565549i	−0.981819	−	0.189821i	$-0.939209\pi$
$859$	−9.56988	+	16.5755i	−0.326520	+	0.565549i	0.655299	+	0.755370i	$0.272543\pi$
$860$	−40.9145	−	23.2962i	−1.39517	−	0.794393i
$861$		0			0
$862$	−9.00740	+	34.0235i	−0.306793	+	1.15885i
$863$	−40.5681	−	23.4220i	−1.38096	−	0.797295i	−0.388683	−	0.921372i	$-0.627070\pi$
$863$	−40.5681	−	23.4220i	−1.38096	−	0.797295i	−0.992273	+	0.124077i	$0.960403\pi$
$864$		0			0
$865$	27.8742	+	48.2795i	0.947751	+	1.64155i
$866$	10.7401	+	10.6759i	0.364962	+	0.362782i
$867$		0			0
$868$	−34.8682	−	3.35096i	−1.18350	−	0.113739i
$869$	23.5901			0.800239
$870$		0			0
$871$	−1.35758	−	2.35140i	−0.0459998	−	0.0796740i
$872$	4.36186	−	16.8843i	0.147711	−	0.571776i
$873$		0			0
$874$	−6.97138	+	26.3329i	−0.235810	+	0.890724i
$875$	−42.4170	+	58.7417i	−1.43396	+	1.98583i
$876$		0			0
$877$	−1.97585	+	3.42227i	−0.0667197	+	0.115562i	−0.897456	−	0.441105i	$-0.854587\pi$
$877$	−1.97585	+	3.42227i	−0.0667197	+	0.115562i	0.830736	+	0.556667i	$0.187920\pi$
$878$	−5.43433	−	20.0408i	−0.183400	−	0.676344i
$879$		0			0
$880$	−38.1298	+	0.457025i	−1.28535	+	0.0154063i
$881$		−	20.6665i		−	0.696273i	−0.937444	−	0.348137i	$-0.886815\pi$
$881$		−	20.6665i		−	0.696273i	0.937444	−	0.348137i	$-0.113185\pi$
$882$		0			0
$883$			31.9650i			1.07571i	0.843038	+	0.537854i	$0.180765\pi$
$883$			31.9650i			1.07571i	−0.843038	+	0.537854i	$0.819235\pi$
$884$	−1.43084	+	0.837570i	−0.0481244	+	0.0281705i
$885$		0			0
$886$	−21.5575	+	5.84560i	−0.724238	+	0.196387i
$887$	7.46072	−	12.9223i	0.250506	−	0.433890i	−0.713159	−	0.701002i	$-0.752736\pi$
$887$	7.46072	−	12.9223i	0.250506	−	0.433890i	0.963665	+	0.267113i	$0.0860696\pi$
$888$		0			0
$889$	23.2525	−	32.2015i	0.779864	−	1.08000i
$890$	22.0034	+	5.82519i	0.737556	+	0.195261i
$891$		0			0
$892$	0.0199198	+	3.32395i	0.000666964	+	0.111294i
$893$	−34.1751	−	59.1929i	−1.14362	−	1.98082i
$894$		0			0
$895$	27.9682			0.934873
$896$	5.38756	+	29.4444i	0.179986	+	0.983669i
$897$		0			0
$898$	34.0658	−	34.2705i	1.13679	−	1.14362i
$899$	−14.9714	−	25.9313i	−0.499325	−	0.864857i
$900$		0			0
$901$	−10.4879	−	6.05520i	−0.349403	−	0.201728i
$902$	33.0029	+	8.73718i	1.09887	+	0.290916i
$903$		0			0
$904$	−16.9807	−	16.6781i	−0.564769	−	0.554706i
$905$	−10.0396	+	17.3890i	−0.333726	+	0.578030i
$906$		0			0
$907$	−5.11465	+	2.95295i	−0.169829	+	0.0980510i	−0.582505	−	0.812827i	$-0.697927\pi$
$907$	−5.11465	+	2.95295i	−0.169829	+	0.0980510i	0.412676	+	0.910878i	$0.364594\pi$
$908$	16.5452	−	9.68503i	0.549071	−	0.321409i
$909$		0			0
$910$	3.07590	−	8.15686i	0.101965	−	0.270397i
$911$			49.6596i			1.64529i	0.568552	+	0.822647i	$0.307504\pi$
$911$			49.6596i			1.64529i	−0.568552	+	0.822647i	$0.692496\pi$
$912$		0			0
$913$	−28.6772	+	16.5568i	−0.949077	+	0.547950i
$914$	9.77674	+	36.0548i	0.323386	+	1.19259i
$915$		0			0
$916$	−17.8036	+	31.2679i	−0.588247	+	1.03312i
$917$	13.8726	−	6.22506i	0.458115	−	0.205569i
$918$		0			0
$919$	2.93574	+	1.69495i	0.0968412	+	0.0559113i	0.547638	−	0.836715i	$-0.315527\pi$
$919$	2.93574	+	1.69495i	0.0968412	+	0.0559113i	−0.450797	+	0.892626i	$0.648860\pi$
$920$	7.16990	−	27.7540i	0.236385	−	0.915022i
$921$		0			0
$922$	−1.06197	−	1.05562i	−0.0349740	−	0.0347651i
$923$	5.47536			0.180224
$924$		0			0
$925$	−62.7784			−2.06414
$926$	−30.8143	−	30.6302i	−1.01262	−	1.00657i
$927$		0			0
$928$	−17.8197	+	18.3618i	−0.584961	+	0.602757i
$929$	−20.8249	−	12.0233i	−0.683243	−	0.394470i	0.117833	−	0.993033i	$-0.462405\pi$
$929$	−20.8249	−	12.0233i	−0.683243	−	0.394470i	−0.801076	+	0.598563i	$0.795739\pi$
$930$		0			0
$931$	53.2464	+	10.9935i	1.74508	+	0.360298i
$932$	34.8725	+	19.8559i	1.14229	+	0.650403i
$933$		0			0
$934$	−4.58075	−	16.8930i	−0.149887	−	0.552754i
$935$	−12.0047	+	6.93094i	−0.392597	+	0.226666i
$936$		0			0
$937$			42.0696i			1.37435i	0.726490	+	0.687177i	$0.241150\pi$
$937$			42.0696i			1.37435i	−0.726490	+	0.687177i	$0.758850\pi$
$938$	−13.7820	+	11.2960i	−0.449998	+	0.368829i
$939$		0			0
$940$	36.3356	+	62.0730i	1.18514	+	2.02460i
$941$	17.1062	−	9.87629i	0.557647	−	0.321958i	−0.194553	−	0.980892i	$-0.562326\pi$
$941$	17.1062	−	9.87629i	0.557647	−	0.321958i	0.752201	+	0.658934i	$0.228992\pi$
$942$		0			0
$943$	−12.8319	+	22.2255i	−0.417864	+	0.723761i
$944$	8.88944	+	14.9794i	0.289327	+	0.487539i
$945$		0			0
$946$	18.3704	+	4.86338i	0.597273	+	0.158122i
$947$	35.3729	+	20.4226i	1.14947	+	0.663644i	0.948757	−	0.316007i	$-0.102342\pi$
$947$	35.3729	+	20.4226i	1.14947	+	0.663644i	0.200709	+	0.979651i	$0.435676\pi$
$948$		0			0
$949$	0.625446	+	1.08330i	0.0203028	+	0.0351656i
$950$	−90.6108	+	91.1555i	−2.93980	+	2.95747i
$951$		0			0
$952$	6.94803	+	8.37423i	0.225187	+	0.271410i
$953$	−18.1050			−0.586478			−0.293239	−	0.956039i	$-0.594733\pi$
$953$	−18.1050			−0.586478			−0.293239	+	0.956039i	$0.594733\pi$
$954$		0			0
$955$	1.87080	+	3.24033i	0.0605378	+	0.104855i
$956$	44.2347	−	0.265090i	1.43065	−	0.00857361i
$957$		0			0
$958$	−27.1528	−	7.18844i	−0.877268	−	0.232248i
$959$	0.383270	−	3.75184i	0.0123764	−	0.121153i
$960$		0			0
$961$	−6.41110	+	11.1044i	−0.206810	+	0.358205i
$962$	4.17491	−	1.13208i	0.134604	−	0.0364998i
$963$		0			0
$964$	12.7640	+	21.8051i	0.411102	+	0.702296i
$965$		−	23.5461i		−	0.757976i
$966$		0			0
$967$		−	53.9924i		−	1.73628i	−0.496321	−	0.868139i	$-0.665316\pi$
$967$		−	53.9924i		−	1.73628i	0.496321	−	0.868139i	$-0.334684\pi$
$968$	−15.1487	+	4.20539i	−0.486898	+	0.135166i
$969$		0			0
$970$	21.6621	+	79.8859i	0.695529	+	2.56498i
$971$	2.31451	−	4.00884i	0.0742760	−	0.128650i	−0.826495	−	0.562944i	$-0.809669\pi$
$971$	2.31451	−	4.00884i	0.0742760	−	0.128650i	0.900771	+	0.434294i	$0.143002\pi$
$972$		0			0
$973$	−19.7384	−	14.2530i	−0.632785	−	0.456931i
$974$	−9.43137	+	35.6250i	−0.302201	+	1.14150i
$975$		0			0
$976$	26.7727	+	15.0323i	0.856975	+	0.481173i
$977$	−2.62817	−	4.55213i	−0.0840827	−	0.145636i	0.820917	−	0.571047i	$-0.193463\pi$
$977$	−2.62817	−	4.55213i	−0.0840827	−	0.145636i	−0.905000	+	0.425412i	$0.860129\pi$
$978$		0			0
$979$	−9.18700			−0.293618
$980$	−56.1004	−	11.2327i	−1.79206	−	0.358815i
$981$		0			0
$982$	31.1661	+	30.9799i	0.994550	+	0.988608i
$983$	−15.7410	−	27.2643i	−0.502061	−	0.869595i	−0.999997	−	0.00238162i	$-0.999242\pi$
$983$	−15.7410	−	27.2643i	−0.502061	−	0.869595i	0.497936	−	0.867214i	$-0.334091\pi$
$984$		0			0
$985$	2.01825	+	1.16524i	0.0643068	+	0.0371275i
$986$	−2.38045	+	8.99163i	−0.0758089	+	0.286352i
$987$		0			0
$988$	4.38202	−	7.69603i	0.139411	−	0.244843i
$989$	−7.14262	+	12.3714i	−0.227122	+	0.393387i
$990$		0			0
$991$	23.9337	−	13.8182i	0.760280	−	0.438948i	−0.0691160	−	0.997609i	$-0.522018\pi$
$991$	23.9337	−	13.8182i	0.760280	−	0.438948i	0.829396	+	0.558661i	$0.188685\pi$
$992$	36.3126	+	9.14913i	1.15293	+	0.290485i
$993$		0			0
$994$	−5.83130	−	35.4589i	−0.184958	−	1.12469i
$995$			26.7926i			0.849383i
$996$		0			0
$997$	−24.2866	+	14.0219i	−0.769163	+	0.444076i	−0.832576	−	0.553911i	$-0.813135\pi$
$997$	−24.2866	+	14.0219i	−0.769163	+	0.444076i	0.0634129	+	0.997987i	$0.479801\pi$
$998$	28.4997	−	7.72806i	0.902141	−	0.244628i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bf.c.271.5	yes	32
3.2	odd	2		756.2.bf.b.271.12	yes	32
4.3	odd	2		756.2.bf.b.271.7	✓	32
7.3	odd	6		756.2.bf.b.703.7	yes	32
12.11	even	2	inner	756.2.bf.c.271.10	yes	32
21.17	even	6	inner	756.2.bf.c.703.10	yes	32
28.3	even	6	inner	756.2.bf.c.703.5	yes	32
84.59	odd	6		756.2.bf.b.703.12	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bf.b.271.7	✓	32	4.3	odd	2
756.2.bf.b.271.12	yes	32	3.2	odd	2
756.2.bf.b.703.7	yes	32	7.3	odd	6
756.2.bf.b.703.12	yes	32	84.59	odd	6
756.2.bf.c.271.5	yes	32	1.1	even	1	trivial
756.2.bf.c.271.10	yes	32	12.11	even	2	inner
756.2.bf.c.703.5	yes	32	28.3	even	6	inner
756.2.bf.c.703.10	yes	32	21.17	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.996999 + 1.00299i) q^{2} +(-0.0119854 - 1.99996i) q^{4} +(-3.53919 - 2.04335i) q^{5} +(-2.14499 - 1.54888i) q^{7} +(2.01790 + 1.98194i) q^{8} +O(q^{10})\)	\(q+(-0.996999 + 1.00299i) q^{2} +(-0.0119854 - 1.99996i) q^{4} +(-3.53919 - 2.04335i) q^{5} +(-2.14499 - 1.54888i) q^{7} +(2.01790 + 1.98194i) q^{8} +(5.57803 - 1.51256i) q^{10} +(-2.02019 + 1.16636i) q^{11} +0.570108i q^{13} +(3.69207 - 0.607169i) q^{14} +(-3.99971 + 0.0479407i) q^{16} +(-1.25927 + 0.727038i) q^{17} +(3.88353 - 6.72648i) q^{19} +(-4.04421 + 7.10274i) q^{20} +(0.844282 - 3.18910i) q^{22} +(2.14767 + 1.23996i) q^{23} +(5.85057 + 10.1335i) q^{25} +(-0.571814 - 0.568397i) q^{26} +(-3.07200 + 4.30846i) q^{28} -4.52320 q^{29} +(3.30992 + 5.73294i) q^{31} +(3.93963 - 4.05948i) q^{32} +(0.526275 - 1.98789i) q^{34} +(4.42660 + 9.86475i) q^{35} +(-2.68257 + 4.64635i) q^{37} +(2.87472 + 10.6014i) q^{38} +(-3.09192 - 11.1377i) q^{40} +10.3487i q^{41} +5.76038i q^{43} +(2.35689 + 4.02633i) q^{44} +(-3.38489 + 0.917857i) q^{46} +(4.40000 - 7.62102i) q^{47} +(2.20193 + 6.64466i) q^{49} +(-15.9968 - 4.23500i) q^{50} +(1.14020 - 0.00683297i) q^{52} +(4.16429 + 7.21277i) q^{53} +9.53312 q^{55} +(-1.25857 - 7.37672i) q^{56} +(4.50963 - 4.53674i) q^{58} +(-2.17732 - 3.77122i) q^{59} +(-6.64766 - 3.83803i) q^{61} +(-9.05008 - 2.39592i) q^{62} +(0.143818 + 7.99871i) q^{64} +(1.16493 - 2.01772i) q^{65} +(-4.12447 + 2.38127i) q^{67} +(1.46914 + 2.50977i) q^{68} +(-14.3076 - 5.39530i) q^{70} -9.60408i q^{71} +(1.90017 - 1.09707i) q^{73} +(-1.98573 - 7.32301i) q^{74} +(-13.4993 - 7.68631i) q^{76} +(6.13984 + 0.627217i) q^{77} +(-8.75786 - 5.05635i) q^{79} +(14.2537 + 8.00315i) q^{80} +(-10.3796 - 10.3176i) q^{82} +14.1953 q^{83} +5.94238 q^{85} +(-5.77761 - 5.74309i) q^{86} +(-6.38820 - 1.65031i) q^{88} +(3.41069 + 1.96916i) q^{89} +(0.883030 - 1.22287i) q^{91} +(2.45413 - 4.31012i) q^{92} +(3.25703 + 12.0113i) q^{94} +(-27.4891 + 15.8708i) q^{95} +14.3215i q^{97} +(-8.85986 - 4.41620i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 6 q^{11} + 17 q^{14} - 4 q^{16} - 8 q^{20} + 2 q^{22} + 14 q^{25} - 15 q^{26} - 13 q^{28} - 15 q^{32} - 6 q^{35} + 4 q^{37} + q^{38} - 15 q^{40} + 42 q^{44} - 9 q^{46} + 4 q^{47} + 14 q^{49} - 9 q^{52} - 45 q^{56} + 10 q^{58} + 16 q^{59} - 42 q^{64} + 49 q^{68} - 33 q^{70} + 36 q^{73} + 54 q^{74} + 15 q^{80} - 51 q^{82} - 20 q^{83} + 16 q^{85} - 78 q^{86} - 2 q^{88} - 27 q^{94} - 24 q^{95} + 46 q^{98}+O(q^{100}) \) 32 * q + 6 * q^11 + 17 * q^14 - 4 * q^16 - 8 * q^20 + 2 * q^22 + 14 * q^25 - 15 * q^26 - 13 * q^28 - 15 * q^32 - 6 * q^35 + 4 * q^37 + q^38 - 15 * q^40 + 42 * q^44 - 9 * q^46 + 4 * q^47 + 14 * q^49 - 9 * q^52 - 45 * q^56 + 10 * q^58 + 16 * q^59 - 42 * q^64 + 49 * q^68 - 33 * q^70 + 36 * q^73 + 54 * q^74 + 15 * q^80 - 51 * q^82 - 20 * q^83 + 16 * q^85 - 78 * q^86 - 2 * q^88 - 27 * q^94 - 24 * q^95 + 46 * q^98

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