LMFDB - Embedded newform 756.2.bf.b.271.12

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			271.12
Character	$\chi$	$=$	756.271
Dual form			756.2.bf.b.703.12

$q$-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	$0.0335442\pi$
$5$	3.53919	+	2.04335i	1.58277	+	0.913815i	0.588321	+	0.808628i	$0.299789\pi$
$6$		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	−0.163506	−	0.986542i	$-0.552280\pi$
$11$	2.02019	−	1.16636i	0.609111	−	0.351670i	0.772617	+	0.634872i	$0.218947\pi$
$12$		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	−0.339457	−	0.940622i	$-0.610243\pi$
$17$	1.25927	−	0.727038i	0.305417	−	0.176333i	0.644874	+	0.764289i	$0.276910\pi$
$18$		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	0.259089	−	0.965853i	$-0.416578\pi$
$23$	−2.14767	−	1.23996i	−0.447820	−	0.258549i	−0.706909	+	0.707305i	$0.749911\pi$
$24$		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	$-0.362041\pi$
$29$	4.52320			0.839938			0.419969	+	0.907538i	$0.362041\pi$
$30$		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	$-0.700499\pi$
$41$		−	10.3487i		−	1.61619i	0.589053	−	0.808094i	$-0.299501\pi$
$42$		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	$0.388481\pi$
$47$	−4.40000	+	7.62102i	−0.641806	+	1.11164i	−0.985029	+	0.172386i	$0.944852\pi$
$48$		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	$-0.972831\pi$
$53$	−4.16429	−	7.21277i	−0.572010	−	0.990750i	0.424350	−	0.905498i	$-0.360503\pi$
$54$		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	0.972235	−	0.234006i	$-0.0751835\pi$
$59$	2.17732	+	3.77122i	0.283462	+	0.490971i	−0.688773	+	0.724977i	$0.741850\pi$
$60$		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	$0.193017\pi$
$71$			9.60408i			1.13979i	−0.821716	+	0.569897i	$0.806983\pi$
$72$		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	$-0.784307\pi$
$83$	−14.1953			−1.55814			−0.779068	+	0.626940i	$0.784307\pi$
$84$		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	0.308220	−	0.951315i	$-0.400267\pi$
$89$	−3.41069	−	1.96916i	−0.361532	−	0.208731i	−0.669753	+	0.742584i	$0.733600\pi$
$90$		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	−0.624463	−	0.781055i	$-0.714682\pi$
$101$	−2.61579	+	1.51023i	−0.260281	+	0.150273i	0.364182	+	0.931328i	$0.381349\pi$
$102$		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	0.511769	−	0.859123i	$-0.328990\pi$
$107$	0.244446	+	0.141131i	0.0236315	+	0.0136436i	−0.488138	+	0.872767i	$0.662324\pi$
$108$		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	$-0.370464\pi$
$113$	8.41504			0.791620			0.395810	+	0.918332i	$0.370464\pi$
$114$		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	−0.712757	−	0.701411i	$-0.752554\pi$
$131$	2.87353	−	4.97710i	0.251062	−	0.434852i	0.963818	+	0.266560i	$0.0858870\pi$
$132$		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	0.833972	−	0.551806i	$-0.186061\pi$
$137$	−0.712721	−	1.23447i	−0.0608919	−	0.105468i	−0.894864	+	0.446338i	$0.852728\pi$
$138$		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	−0.976052	−	0.217536i	$-0.930198\pi$
$149$	−3.65750	+	6.33498i	−0.299634	+	0.518981i	0.676418	+	0.736518i	$0.263531\pi$
$150$		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	$-0.453183\pi$
$167$	3.78773			0.293103			0.146552	+	0.989203i	$0.453183\pi$
$168$		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	0.876612	−	0.481198i	$-0.159798\pi$
$173$	11.8138	+	6.82071i	0.898187	+	0.518569i	0.0215758	+	0.999767i	$0.493132\pi$
$174$		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	−0.261874	−	0.965102i	$-0.584341\pi$
$179$	5.92682	−	3.42185i	0.442991	−	0.255761i	0.704866	+	0.709341i	$0.251007\pi$
$180$		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	0.528412	−	0.848988i	$-0.322788\pi$
$191$	0.792896	+	0.457779i	0.0573719	+	0.0331237i	−0.471040	+	0.882112i	$0.656121\pi$
$192$		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	$-0.493533\pi$
$197$	0.570257			0.0406292			0.0203146	+	0.999794i	$0.493533\pi$
$198$		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	0.661981	−	0.749520i	$-0.269716\pi$
$227$	−4.79285	−	8.30147i	−0.318113	−	0.550988i	−0.980094	+	0.198533i	$0.936382\pi$
$228$		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	$-0.605058\pi$
$233$	10.0323	−	17.3764i	0.657237	−	1.13837i	0.981328	−	0.192342i	$-0.0616083\pi$
$234$		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	$-0.746273\pi$
$239$		−	22.1177i		−	1.43068i	0.698778	−	0.715338i	$-0.253727\pi$
$240$		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	$-0.258923\pi$
$251$	21.7686			1.37402			0.687010	+	0.726648i	$0.258923\pi$
$252$		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	$-0.983229\pi$
$257$	−24.7446	−	14.2863i	−1.54353	−	0.891155i	−0.544913	−	0.838492i	$-0.683437\pi$
$258$		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	−0.440851	−	0.897580i	$-0.645323\pi$
$263$	1.88202	−	1.08659i	0.116051	−	0.0670018i	0.556902	+	0.830578i	$0.311990\pi$
$264$		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	−0.148709	−	0.988881i	$-0.547512\pi$
$269$	10.3874	−	5.99718i	0.633332	−	0.365654i	0.782041	+	0.623227i	$0.214179\pi$
$270$		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	$-0.736644\pi$
$281$	−22.6913			−1.35365			−0.676825	+	0.736144i	$0.736644\pi$
$282$		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	$0.00697304\pi$
$293$			0.749896i			0.0438094i	−0.999760	+	0.0219047i	$0.993027\pi$
$294$		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	$-0.882172\pi$
$311$	−13.7455	−	23.8080i	−0.779437	−	1.35003i	0.152829	−	0.988253i	$-0.451162\pi$
$312$		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	−0.547045	−	0.837103i	$-0.684247\pi$
$317$	8.03749	−	13.9213i	0.451430	−	0.781900i	0.998475	+	0.0552031i	$0.0175806\pi$
$318$		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	−0.692099	−	0.721803i	$-0.743314\pi$
$347$	−7.69425	+	4.44228i	−0.413049	+	0.238474i	0.279050	+	0.960277i	$0.409980\pi$
$348$		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	−0.321786	−	0.946813i	$-0.604283\pi$
$353$	6.33702	−	3.65868i	0.337285	−	0.194732i	0.659071	+	0.752081i	$0.270950\pi$
$354$		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	0.635252	−	0.772305i	$-0.280896\pi$
$359$	5.38184	+	3.10721i	0.284043	+	0.163992i	−0.351209	+	0.936297i	$0.614229\pi$
$360$		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	$-0.612181\pi$
$383$	12.5291	−	21.7011i	0.640208	−	1.10887i	0.985386	−	0.170336i	$-0.0544852\pi$
$384$		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	$0.0289421\pi$
$389$	11.3717	+	19.6964i	0.576569	+	0.998647i	−0.419300	+	0.907848i	$0.637725\pi$
$390$		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	$-0.552384\pi$
$401$	15.4675	−	26.7905i	0.772411	−	1.33785i	0.936238	−	0.351366i	$-0.114283\pi$
$402$		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	$-0.338089\pi$
$419$	19.9375			0.974013			0.487007	+	0.873398i	$0.338089\pi$
$420$		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	−0.919313	−	0.393528i	$-0.871255\pi$
$431$	−21.5529	+	12.4435i	−1.03816	+	0.599384i	−0.118851	+	0.992912i	$0.537921\pi$
$432$		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	0.138543	−	0.990356i	$-0.455758\pi$
$443$	−13.6780	−	7.89697i	−0.649859	−	0.375196i	−0.788402	+	0.615160i	$0.789091\pi$
$444$		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	$-0.201493\pi$
$449$	34.1683			1.61250			0.806251	+	0.591574i	$0.201493\pi$
$450$		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	$-0.992151\pi$
$461$		−	1.05880i		−	0.0493132i	0.999696	−	0.0246566i	$-0.00784924\pi$
$462$		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	−0.686580	−	0.727055i	$-0.740889\pi$
$467$	6.18825	−	10.7184i	0.286358	−	0.495987i	0.972938	+	0.231068i	$0.0742220\pi$
$468$		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	0.544870	−	0.838520i	$-0.316579\pi$
$479$	−9.93069	−	17.2005i	−0.453745	−	0.785909i	−0.998615	+	0.0526112i	$0.983246\pi$
$480$		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	$0.247332\pi$
$491$			31.0731i			1.40231i	−0.713008	+	0.701156i	$0.752668\pi$
$492$		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	$-0.360644\pi$
$503$	19.0163			0.847896			0.423948	+	0.905687i	$0.360644\pi$
$504$		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	0.685646	−	0.727935i	$-0.259520\pi$
$509$	8.98062	+	5.18497i	0.398059	+	0.229820i	−0.287587	+	0.957755i	$0.592853\pi$
$510$		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	−0.530263	−	0.847833i	$-0.677907\pi$
$521$	−1.39578	+	0.805852i	−0.0611500	+	0.0353050i	0.469113	+	0.883138i	$0.344574\pi$
$522$		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	0.733846	−	0.679316i	$-0.237724\pi$
$557$	−5.22481	−	9.04964i	−0.221382	−	0.383446i	−0.955228	+	0.295871i	$0.904390\pi$
$558$		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	0.807442	−	0.589947i	$-0.200851\pi$
$563$	−2.54332	−	4.40516i	−0.107188	−	0.185655i	−0.914630	+	0.404292i	$0.867518\pi$
$564$		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	−0.884830	−	0.465914i	$-0.845725\pi$
$569$	−0.928415	+	1.60806i	−0.0389212	+	0.0674135i	0.845909	+	0.533328i	$0.179059\pi$
$570$		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	$-0.252776\pi$
$587$	33.9636			1.40183			0.700913	+	0.713247i	$0.252776\pi$
$588$		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	0.134343	−	0.990935i	$-0.457108\pi$
$593$	−15.9907	−	9.23225i	−0.656661	−	0.379123i	−0.791003	+	0.611812i	$0.790441\pi$
$594$		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	−0.957242	−	0.289287i	$-0.906582\pi$
$599$	−29.0104	+	16.7492i	−1.18533	+	0.684352i	−0.228091	+	0.973640i	$0.573248\pi$
$600$		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	$-0.872149\pi$
$617$	−45.7253			−1.84083			−0.920415	+	0.390942i	$0.872149\pi$
$618$		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	$-0.968765\pi$
$641$	−14.7462	−	25.5412i	−0.582440	−	1.00882i	0.412749	−	0.910845i	$-0.364569\pi$
$642$		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	0.995649	−	0.0931801i	$-0.0297033\pi$
$647$	10.6102	+	18.3773i	0.417128	+	0.722487i	−0.578521	+	0.815667i	$0.696370\pi$
$648$		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	−0.922938	−	0.384948i	$-0.874219\pi$
$653$	−3.27331	+	5.66954i	−0.128095	+	0.221866i	0.794844	+	0.606814i	$0.207553\pi$
$654$		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	$-0.952494\pi$
$659$		−	7.63411i		−	0.297383i	0.988884	−	0.148691i	$-0.0475061\pi$
$660$		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	−0.493529	−	0.869729i	$-0.664293\pi$
$677$	−38.8597	−	22.4357i	−1.49350	−	0.862273i	−0.999972	+	0.00745575i	$0.997627\pi$
$678$		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	−0.566376	−	0.824147i	$-0.691655\pi$
$683$	−3.54984	+	2.04950i	−0.135831	+	0.0784219i	0.430545	+	0.902569i	$0.358321\pi$
$684$		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	$-0.357255\pi$
$701$	22.9585			0.867131			0.433565	+	0.901122i	$0.357255\pi$
$702$		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	−0.577917	−	0.816096i	$-0.696134\pi$
$719$	11.2030	−	19.4042i	0.417801	−	0.723653i	0.995718	+	0.0924426i	$0.0294675\pi$
$720$		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	$0.146417\pi$
$743$			24.2015i			0.887867i	−0.896060	+	0.443934i	$0.853583\pi$
$744$		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	0.625081	−	0.780560i	$-0.285066\pi$
$761$	7.21754	+	4.16705i	0.261636	+	0.151055i	−0.363445	+	0.931616i	$0.618399\pi$
$762$		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	−0.328513	−	0.944500i	$-0.606547\pi$
$773$	9.04127	−	5.21998i	0.325192	−	0.187750i	0.653704	+	0.756750i	$0.273214\pi$
$774$		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	$-0.983702\pi$
$797$		−	2.88962i		−	0.102356i	0.998690	−	0.0511778i	$-0.0162975\pi$
$798$		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	0.822815	−	0.568310i	$-0.192402\pi$
$809$	−2.29714	−	3.97876i	−0.0807631	−	0.139886i	−0.903578	+	0.428424i	$0.859069\pi$
$810$		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	−0.927066	−	0.374897i	$-0.877678\pi$
$821$	−3.97884	+	6.89156i	−0.138863	+	0.240517i	0.788204	+	0.615414i	$0.211011\pi$
$822$		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	$-0.981917\pi$
$827$		−	3.26564i		−	0.113557i	0.998387	−	0.0567787i	$-0.0180830\pi$
$828$		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	$-0.430488\pi$
$839$	12.5506			0.433296			0.216648	+	0.976250i	$0.430488\pi$
$840$		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	−0.430069	−	0.902796i	$-0.641511\pi$
$857$	4.00303	−	2.31115i	0.136741	−	0.0789473i	0.566810	+	0.823849i	$0.308177\pi$
$858$		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	0.992273	−	0.124077i	$-0.0395969\pi$
$863$	40.5681	+	23.4220i	1.38096	+	0.797295i	0.388683	+	0.921372i	$0.372930\pi$
$864$		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	$0.113185\pi$
$881$			20.6665i			0.696273i	−0.937444	+	0.348137i	$0.886815\pi$
$882$		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	−0.963665	−	0.267113i	$-0.913930\pi$
$887$	−7.46072	+	12.9223i	−0.250506	+	0.433890i	0.713159	+	0.701002i	$0.247264\pi$
$888$		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	$-0.692496\pi$
$911$		−	49.6596i		−	1.64529i	0.568552	−	0.822647i	$-0.307504\pi$
$912$		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	0.801076	−	0.598563i	$-0.204261\pi$
$929$	20.8249	+	12.0233i	0.683243	+	0.394470i	−0.117833	+	0.993033i	$0.537595\pi$
$930$		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	−0.752201	−	0.658934i	$-0.771008\pi$
$941$	−17.1062	+	9.87629i	−0.557647	+	0.321958i	0.194553	+	0.980892i	$0.437674\pi$
$942$		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	−0.200709	−	0.979651i	$-0.564324\pi$
$947$	−35.3729	−	20.4226i	−1.14947	−	0.663644i	−0.948757	+	0.316007i	$0.897658\pi$
$948$		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	$-0.405267\pi$
$953$	18.1050			0.586478			0.293239	+	0.956039i	$0.405267\pi$
$954$		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	−0.900771	−	0.434294i	$-0.856998\pi$
$971$	−2.31451	+	4.00884i	−0.0742760	+	0.128650i	0.826495	+	0.562944i	$0.190331\pi$
$972$		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	0.905000	−	0.425412i	$-0.139871\pi$
$977$	2.62817	+	4.55213i	0.0840827	+	0.145636i	−0.820917	+	0.571047i	$0.806537\pi$
$978$		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	$0.000758093\pi$
$983$	15.7410	+	27.2643i	0.502061	+	0.869595i	−0.497936	+	0.867214i	$0.665909\pi$
$984$		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.b.271.12	yes	32
3.2	odd	2		756.2.bf.c.271.5	yes	32
4.3	odd	2		756.2.bf.c.271.10	yes	32
7.3	odd	6		756.2.bf.c.703.10	yes	32
12.11	even	2	inner	756.2.bf.b.271.7	✓	32
21.17	even	6	inner	756.2.bf.b.703.7	yes	32
28.3	even	6	inner	756.2.bf.b.703.12	yes	32
84.59	odd	6		756.2.bf.c.703.5	yes	32

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

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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