LMFDB - Embedded newform 756.2.bo.b.169.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(85,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("756.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bo (of order $9$, degree $6$, 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:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			169.7
Character	$\chi$	$=$	756.169
Dual form			756.2.bo.b.85.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.794215 + 1.53923i) q^{3} +(0.457658 + 2.59551i) q^{5} +(-0.766044 - 0.642788i) q^{7} +(-1.73845 + 2.44496i) q^{9} +O(q^{10})$	\(q+(0.794215 + 1.53923i) q^{3} +(0.457658 + 2.59551i) q^{5} +(-0.766044 - 0.642788i) q^{7} +(-1.73845 + 2.44496i) q^{9} +(0.324099 - 1.83806i) q^{11} +(0.713514 + 0.259698i) q^{13} +(-3.63160 + 2.76583i) q^{15} +(2.60634 + 4.51431i) q^{17} +(-4.33485 + 7.50819i) q^{19} +(0.380993 - 1.68963i) q^{21} +(5.46279 - 4.58383i) q^{23} +(-1.82874 + 0.665607i) q^{25} +(-5.14404 - 0.734045i) q^{27} +(-3.26578 + 1.18865i) q^{29} +(-5.21553 + 4.37635i) q^{31} +(3.08659 - 0.960949i) q^{33} +(1.31777 - 2.28245i) q^{35} +(-0.737364 - 1.27715i) q^{37} +(0.166949 + 1.30452i) q^{39} +(-8.70703 - 3.16910i) q^{41} +(1.35560 - 7.68798i) q^{43} +(-7.14151 - 3.39319i) q^{45} +(-0.138653 - 0.116344i) q^{47} +(0.173648 + 0.984808i) q^{49} +(-4.87856 + 7.59709i) q^{51} +7.64355 q^{53} +4.91901 q^{55} +(-14.9996 - 0.709216i) q^{57} +(-1.41891 - 8.04704i) q^{59} +(9.53852 + 8.00376i) q^{61} +(2.90331 - 0.755493i) q^{63} +(-0.347502 + 1.97078i) q^{65} +(2.25635 + 0.821244i) q^{67} +(11.3942 + 4.76794i) q^{69} +(1.62391 + 2.81270i) q^{71} +(-5.26329 + 9.11628i) q^{73} +(-2.47693 - 2.28621i) q^{75} +(-1.42975 + 1.19971i) q^{77} +(11.5282 - 4.19594i) q^{79} +(-2.95561 - 8.50084i) q^{81} +(16.4595 - 5.99076i) q^{83} +(-10.5241 + 8.83078i) q^{85} +(-4.42334 - 4.08274i) q^{87} +(1.19780 - 2.07465i) q^{89} +(-0.379653 - 0.657578i) q^{91} +(-10.8784 - 4.55213i) q^{93} +(-21.4714 - 7.81496i) q^{95} +(-1.94652 + 11.0393i) q^{97} +(3.93054 + 3.98777i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9}+O(q^{10}) $ 54 * q + 3 * q^3 - 3 * q^5 - 9 * q^9	$ 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9} + 9 q^{13} + 3 q^{15} + 3 q^{21} + 12 q^{23} + 27 q^{25} + 39 q^{27} + 30 q^{29} - 9 q^{31} - 6 q^{33} + 6 q^{35} - 18 q^{39} - 27 q^{41} + 9 q^{43} - 81 q^{45} + 9 q^{47} + 12 q^{53} - 21 q^{57} - 24 q^{59} - 3 q^{63} - 78 q^{65} - 9 q^{67} + 6 q^{69} - 30 q^{71} + 57 q^{75} + 9 q^{77} + 99 q^{81} + 78 q^{83} + 18 q^{85} + 21 q^{87} + 12 q^{89} - 51 q^{93} - 36 q^{95} + 36 q^{97} + 15 q^{99}+O(q^{100}) $ 54 * q + 3 * q^3 - 3 * q^5 - 9 * q^9 + 9 * q^13 + 3 * q^15 + 3 * q^21 + 12 * q^23 + 27 * q^25 + 39 * q^27 + 30 * q^29 - 9 * q^31 - 6 * q^33 + 6 * q^35 - 18 * q^39 - 27 * q^41 + 9 * q^43 - 81 * q^45 + 9 * q^47 + 12 * q^53 - 21 * q^57 - 24 * q^59 - 3 * q^63 - 78 * q^65 - 9 * q^67 + 6 * q^69 - 30 * q^71 + 57 * q^75 + 9 * q^77 + 99 * q^81 + 78 * q^83 + 18 * q^85 + 21 * q^87 + 12 * q^89 - 51 * q^93 - 36 * q^95 + 36 * q^97 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	0.794215	+	1.53923i	0.458540	+	0.888674i
$3$	0.794215	+	1.53923i	0.458540	+	0.888674i
$4$		0			0
$5$	0.457658	+	2.59551i	0.204671	+	1.16075i	0.897957	+	0.440083i	$0.145051\pi$
$5$	0.457658	+	2.59551i	0.204671	+	1.16075i	−0.693286	+	0.720662i	$0.743838\pi$
$6$		0			0
$7$	−0.766044	−	0.642788i	−0.289538	−	0.242951i
$7$	−0.766044	−	0.642788i	−0.289538	−	0.242951i
$8$		0			0
$9$	−1.73845	+	2.44496i	−0.579482	+	0.814985i
$10$		0			0
$11$	0.324099	−	1.83806i	0.0977195	−	0.554195i	−0.896161	−	0.443730i	$-0.853655\pi$
$11$	0.324099	−	1.83806i	0.0977195	−	0.554195i	0.993880	−	0.110465i	$-0.0352340\pi$
$12$		0			0
$13$	0.713514	+	0.259698i	0.197893	+	0.0720272i	0.439065	−	0.898455i	$-0.355310\pi$
$13$	0.713514	+	0.259698i	0.197893	+	0.0720272i	−0.241172	+	0.970482i	$0.577532\pi$
$14$		0			0
$15$	−3.63160	+	2.76583i	−0.937674	+	0.714134i
$16$		0			0
$17$	2.60634	+	4.51431i	0.632130	+	1.09488i	0.987115	+	0.160010i	$0.0511526\pi$
$17$	2.60634	+	4.51431i	0.632130	+	1.09488i	−0.354985	+	0.934872i	$0.615514\pi$
$18$		0			0
$19$	−4.33485	+	7.50819i	−0.994484	+	1.72250i	−0.406405	+	0.913693i	$0.633218\pi$
$19$	−4.33485	+	7.50819i	−0.994484	+	1.72250i	−0.588079	+	0.808804i	$0.700115\pi$
$20$		0			0
$21$	0.380993	−	1.68963i	0.0831395	−	0.368707i
$22$		0			0
$23$	5.46279	−	4.58383i	1.13907	−	0.955794i	0.139663	−	0.990199i	$-0.455398\pi$
$23$	5.46279	−	4.58383i	1.13907	−	0.955794i	0.999408	+	0.0344053i	$0.0109537\pi$
$24$		0			0
$25$	−1.82874	+	0.665607i	−0.365748	+	0.133121i
$26$		0			0
$27$	−5.14404	−	0.734045i	−0.989972	−	0.141267i
$28$		0			0
$29$	−3.26578	+	1.18865i	−0.606441	+	0.220726i	−0.626945	−	0.779063i	$-0.715695\pi$
$29$	−3.26578	+	1.18865i	−0.606441	+	0.220726i	0.0205043	+	0.999790i	$0.493473\pi$
$30$		0			0
$31$	−5.21553	+	4.37635i	−0.936737	+	0.786015i	−0.977014	−	0.213173i	$-0.931620\pi$
$31$	−5.21553	+	4.37635i	−0.936737	+	0.786015i	0.0402779	+	0.999189i	$0.487176\pi$
$32$		0			0
$33$	3.08659	−	0.960949i	0.537307	−	0.167280i
$34$		0			0
$35$	1.31777	−	2.28245i	0.222744	−	0.385804i
$36$		0			0
$37$	−0.737364	−	1.27715i	−0.121222	−	0.209962i	0.799028	−	0.601294i	$-0.205348\pi$
$37$	−0.737364	−	1.27715i	−0.121222	−	0.209962i	−0.920250	+	0.391331i	$0.872015\pi$
$38$		0			0
$39$	0.166949	+	1.30452i	0.0267333	+	0.208890i
$40$		0			0
$41$	−8.70703	−	3.16910i	−1.35981	−	0.494930i	−0.443814	−	0.896119i	$-0.646375\pi$
$41$	−8.70703	−	3.16910i	−1.35981	−	0.494930i	−0.915996	+	0.401188i	$0.868597\pi$
$42$		0			0
$43$	1.35560	−	7.68798i	0.206727	−	1.17241i	−0.687972	−	0.725737i	$-0.741499\pi$
$43$	1.35560	−	7.68798i	0.206727	−	1.17241i	0.894699	−	0.446669i	$-0.147390\pi$
$44$		0			0
$45$	−7.14151	−	3.39319i	−1.06459	−	0.505828i
$46$		0			0
$47$	−0.138653	−	0.116344i	−0.0202247	−	0.0169705i	0.632619	−	0.774463i	$-0.281980\pi$
$47$	−0.138653	−	0.116344i	−0.0202247	−	0.0169705i	−0.652844	+	0.757492i	$0.726424\pi$
$48$		0			0
$49$	0.173648	+	0.984808i	0.0248069	+	0.140687i
$50$		0			0
$51$	−4.87856	+	7.59709i	−0.683136	+	1.06380i
$52$		0			0
$53$	7.64355			1.04992			0.524961	−	0.851126i	$-0.324080\pi$
$53$	7.64355			1.04992			0.524961	+	0.851126i	$0.324080\pi$
$54$		0			0
$55$	4.91901			0.663280
$56$		0			0
$57$	−14.9996	−	0.709216i	−1.98675	−	0.0939379i
$58$		0			0
$59$	−1.41891	−	8.04704i	−0.184726	−	1.04764i	−0.926307	−	0.376771i	$-0.877034\pi$
$59$	−1.41891	−	8.04704i	−0.184726	−	1.04764i	0.741580	−	0.670864i	$-0.234077\pi$
$60$		0			0
$61$	9.53852	+	8.00376i	1.22128	+	1.02478i	0.998757	+	0.0498501i	$0.0158744\pi$
$61$	9.53852	+	8.00376i	1.22128	+	1.02478i	0.222525	+	0.974927i	$0.428570\pi$
$62$		0			0
$63$	2.90331	−	0.755493i	0.365783	−	0.0951832i
$64$		0			0
$65$	−0.347502	+	1.97078i	−0.0431023	+	0.244445i
$66$		0			0
$67$	2.25635	+	0.821244i	0.275657	+	0.100331i	0.476150	−	0.879364i	$-0.342032\pi$
$67$	2.25635	+	0.821244i	0.275657	+	0.100331i	−0.200493	+	0.979695i	$0.564254\pi$
$68$		0			0
$69$	11.3942	+	4.76794i	1.37170	+	0.573992i
$70$		0			0
$71$	1.62391	+	2.81270i	0.192723	+	0.333806i	0.946152	−	0.323723i	$-0.104935\pi$
$71$	1.62391	+	2.81270i	0.192723	+	0.333806i	−0.753429	+	0.657530i	$0.771601\pi$
$72$		0			0
$73$	−5.26329	+	9.11628i	−0.616021	+	1.06698i	0.374183	+	0.927355i	$0.377923\pi$
$73$	−5.26329	+	9.11628i	−0.616021	+	1.06698i	−0.990204	+	0.139625i	$0.955410\pi$
$74$		0			0
$75$	−2.47693	−	2.28621i	−0.286012	−	0.263989i
$76$		0			0
$77$	−1.42975	+	1.19971i	−0.162936	+	0.136719i
$78$		0			0
$79$	11.5282	−	4.19594i	1.29703	−	0.472080i	0.401001	−	0.916078i	$-0.368663\pi$
$79$	11.5282	−	4.19594i	1.29703	−	0.472080i	0.896028	+	0.443998i	$0.146440\pi$
$80$		0			0
$81$	−2.95561	−	8.50084i	−0.328401	−	0.944538i
$82$		0			0
$83$	16.4595	−	5.99076i	1.80666	−	0.657572i	0.809110	−	0.587657i	$-0.199950\pi$
$83$	16.4595	−	5.99076i	1.80666	−	0.657572i	0.997553	−	0.0699143i	$-0.0222726\pi$
$84$		0			0
$85$	−10.5241	+	8.83078i	−1.14150	+	0.957833i
$86$		0			0
$87$	−4.42334	−	4.08274i	−0.474231	−	0.437716i
$88$		0			0
$89$	1.19780	−	2.07465i	0.126967	−	0.219913i	−0.795533	−	0.605910i	$-0.792809\pi$
$89$	1.19780	−	2.07465i	0.126967	−	0.219913i	0.922500	+	0.385997i	$0.126143\pi$
$90$		0			0
$91$	−0.379653	−	0.657578i	−0.0397984	−	0.0689329i
$92$		0			0
$93$	−10.8784	−	4.55213i	−1.12804	−	0.472034i
$94$		0			0
$95$	−21.4714	−	7.81496i	−2.20292	−	0.801798i
$96$		0			0
$97$	−1.94652	+	11.0393i	−0.197640	+	1.12087i	0.710970	+	0.703223i	$0.248256\pi$
$97$	−1.94652	+	11.0393i	−0.197640	+	1.12087i	−0.908609	+	0.417647i	$0.862855\pi$
$98$		0			0
$99$	3.93054	+	3.98777i	0.395034	+	0.400786i
$100$		0			0
$101$	−3.01444	−	2.52942i	−0.299948	−	0.251686i	0.480375	−	0.877063i	$-0.340501\pi$
$101$	−3.01444	−	2.52942i	−0.299948	−	0.251686i	−0.780323	+	0.625377i	$0.784945\pi$
$102$		0			0
$103$	1.31144	+	7.43752i	0.129220	+	0.732841i	0.978712	+	0.205240i	$0.0657974\pi$
$103$	1.31144	+	7.43752i	0.129220	+	0.732841i	−0.849492	+	0.527601i	$0.823092\pi$
$104$		0			0
$105$	4.55981	+	0.215598i	0.444991	+	0.0210402i
$106$		0			0
$107$	10.7581			1.04002			0.520011	−	0.854160i	$-0.325928\pi$
$107$	10.7581			1.04002			0.520011	+	0.854160i	$0.325928\pi$
$108$		0			0
$109$	2.87392			0.275272			0.137636	−	0.990483i	$-0.456050\pi$
$109$	2.87392			0.275272			0.137636	+	0.990483i	$0.456050\pi$
$110$		0			0
$111$	1.38020	−	2.14930i	0.131003	−	0.204003i
$112$		0			0
$113$	0.410339	+	2.32715i	0.0386015	+	0.218920i	0.998006	−	0.0631123i	$-0.0201026\pi$
$113$	0.410339	+	2.32715i	0.0386015	+	0.218920i	−0.959405	+	0.282032i	$0.908992\pi$
$114$		0			0
$115$	14.3974	+	12.0809i	1.34257	+	1.12655i
$116$		0			0
$117$	−1.87535	+	1.29304i	−0.173377	+	0.119541i
$118$		0			0
$119$	0.905172	−	5.13349i	0.0829770	−	0.470586i
$120$		0			0
$121$	7.06321	+	2.57080i	0.642110	+	0.233709i
$122$		0			0
$123$	−2.03729	−	15.9191i	−0.183696	−	1.43537i
$124$		0			0
$125$	4.02434	+	6.97036i	0.359948	+	0.623448i
$126$		0			0
$127$	−2.53676	+	4.39380i	−0.225101	+	0.389887i	−0.956350	−	0.292224i	$-0.905605\pi$
$127$	−2.53676	+	4.39380i	−0.225101	+	0.389887i	0.731248	+	0.682111i	$0.238938\pi$
$128$		0			0
$129$	12.9102	−	4.01933i	1.13668	−	0.353883i
$130$		0			0
$131$	3.84012	−	3.22224i	0.335513	−	0.281529i	−0.459429	−	0.888215i	$-0.651946\pi$
$131$	3.84012	−	3.22224i	0.335513	−	0.281529i	0.794942	+	0.606686i	$0.207501\pi$
$132$		0			0
$133$	8.14686	−	2.96522i	0.706423	−	0.257117i
$134$		0			0
$135$	−0.448993	−	13.6873i	−0.0386432	−	1.17802i
$136$		0			0
$137$	2.56254	−	0.932690i	0.218933	−	0.0796851i	−0.230225	−	0.973137i	$-0.573946\pi$
$137$	2.56254	−	0.932690i	0.218933	−	0.0796851i	0.449158	+	0.893452i	$0.351724\pi$
$138$		0			0
$139$	11.9480	−	10.0256i	1.01342	−	0.850357i	0.0246297	−	0.999697i	$-0.492159\pi$
$139$	11.9480	−	10.0256i	1.01342	−	0.850357i	0.988786	+	0.149340i	$0.0477149\pi$
$140$		0			0
$141$	0.0689593	−	0.305821i	0.00580742	−	0.0257548i
$142$		0			0
$143$	0.708588	−	1.22731i	0.0592551	−	0.102633i
$144$		0			0
$145$	−4.57976	−	7.93237i	−0.380328	−	0.658747i
$146$		0			0
$147$	−1.37793	+	1.04943i	−0.113650	+	0.0865558i
$148$		0			0
$149$	19.1593	+	6.97340i	1.56959	+	0.571283i	0.972907	−	0.231196i	$-0.0742639\pi$
$149$	19.1593	+	6.97340i	1.56959	+	0.571283i	0.596680	+	0.802479i	$0.296486\pi$
$150$		0			0
$151$	−0.202741	+	1.14980i	−0.0164988	+	0.0935694i	−0.991945	−	0.126667i	$-0.959572\pi$
$151$	−0.202741	+	1.14980i	−0.0164988	+	0.0935694i	0.975446	+	0.220237i	$0.0706830\pi$
$152$		0			0
$153$	−15.5683	−	1.47550i	−1.25862	−	0.119287i
$154$		0			0
$155$	−13.7458	−	11.5341i	−1.10409	−	0.926439i
$156$		0			0
$157$	1.78909	+	10.1464i	0.142785	+	0.809774i	0.969119	+	0.246593i	$0.0793112\pi$
$157$	1.78909	+	10.1464i	0.142785	+	0.809774i	−0.826334	+	0.563180i	$0.809578\pi$
$158$		0			0
$159$	6.07062	+	11.7652i	0.481431	+	0.933038i
$160$		0			0
$161$	−7.13117			−0.562015
$162$		0			0
$163$	−20.5089			−1.60638			−0.803191	−	0.595721i	$-0.796866\pi$
$163$	−20.5089			−1.60638			−0.803191	+	0.595721i	$0.796866\pi$
$164$		0			0
$165$	3.90675	+	7.57148i	0.304140	+	0.589439i
$166$		0			0
$167$	1.26327	+	7.16436i	0.0977547	+	0.554395i	0.993868	+	0.110570i	$0.0352676\pi$
$167$	1.26327	+	7.16436i	0.0977547	+	0.554395i	−0.896114	+	0.443825i	$0.853621\pi$
$168$		0			0
$169$	−9.51692	−	7.98564i	−0.732071	−	0.614280i
$170$		0			0
$171$	−10.8213	−	23.6511i	−0.827524	−	1.80865i
$172$		0			0
$173$	2.75198	−	15.6072i	0.209229	−	1.18660i	−0.681416	−	0.731896i	$-0.738635\pi$
$173$	2.75198	−	15.6072i	0.209229	−	1.18660i	0.890645	−	0.454700i	$-0.150253\pi$
$174$		0			0
$175$	1.82874	+	0.665607i	0.138240	+	0.0503151i
$176$		0			0
$177$	11.2593	−	8.57510i	0.846301	−	0.644544i
$178$		0			0
$179$	−7.87321	−	13.6368i	−0.588471	−	1.01926i	−0.994433	−	0.105372i	$-0.966397\pi$
$179$	−7.87321	−	13.6368i	−0.588471	−	1.01926i	0.405961	−	0.913890i	$-0.366937\pi$
$180$		0			0
$181$	8.78554	−	15.2170i	0.653024	−	1.13107i	−0.329362	−	0.944204i	$-0.606834\pi$
$181$	8.78554	−	15.2170i	0.653024	−	1.13107i	0.982385	−	0.186866i	$-0.0598331\pi$
$182$		0			0
$183$	−4.74399	+	21.0387i	−0.350686	+	1.55522i
$184$		0			0
$185$	2.97740	−	2.49833i	0.218902	−	0.183681i
$186$		0			0
$187$	9.14228	−	3.32752i	0.668549	−	0.243332i
$188$		0			0
$189$	3.46873	+	3.86884i	0.252313	+	0.281417i
$190$		0			0
$191$	15.5399	−	5.65608i	1.12443	−	0.409259i	0.288163	−	0.957581i	$-0.406955\pi$
$191$	15.5399	−	5.65608i	1.12443	−	0.409259i	0.836267	+	0.548322i	$0.184733\pi$
$192$		0			0
$193$	0.0365053	−	0.0306316i	0.00262771	−	0.00220491i	−0.641473	−	0.767146i	$-0.721676\pi$
$193$	0.0365053	−	0.0306316i	0.00262771	−	0.00220491i	0.644101	+	0.764941i	$0.277232\pi$
$194$		0			0
$195$	−3.30947	+	1.03034i	−0.236996	+	0.0737841i
$196$		0			0
$197$	−3.57770	+	6.19677i	−0.254901	+	0.441501i	−0.964869	−	0.262733i	$-0.915376\pi$
$197$	−3.57770	+	6.19677i	−0.254901	+	0.441501i	0.709968	+	0.704234i	$0.248710\pi$
$198$		0			0
$199$	−4.21314	−	7.29738i	−0.298662	−	0.517297i	0.677168	−	0.735828i	$-0.263207\pi$
$199$	−4.21314	−	7.29738i	−0.298662	−	0.517297i	−0.975830	+	0.218531i	$0.929874\pi$
$200$		0			0
$201$	0.527944	+	4.12528i	0.0372383	+	0.290975i
$202$		0			0
$203$	3.26578	+	1.18865i	0.229213	+	0.0834268i
$204$		0			0
$205$	4.24058	−	24.0495i	0.296175	−	1.67969i
$206$		0			0
$207$	1.71048	+	21.3250i	0.118887	+	1.48219i
$208$		0			0
$209$	12.3956	+	10.4011i	0.857418	+	0.719459i
$210$		0			0
$211$	2.12535	+	12.0534i	0.146315	+	0.829793i	0.966302	+	0.257411i	$0.0828694\pi$
$211$	2.12535	+	12.0534i	0.146315	+	0.829793i	−0.819987	+	0.572382i	$0.806019\pi$
$212$		0			0
$213$	−3.03965	+	4.73347i	−0.208274	+	0.324332i
$214$		0			0
$215$	20.5746			1.40318
$216$		0			0
$217$	6.80839			0.462184
$218$		0			0
$219$	−18.2122	−	0.861114i	−1.23067	−	0.0581887i
$220$		0			0
$221$	0.687302	+	3.89789i	0.0462330	+	0.262200i
$222$		0			0
$223$	−16.2277	−	13.6166i	−1.08668	−	0.911837i	−0.0902261	−	0.995921i	$-0.528759\pi$
$223$	−16.2277	−	13.6166i	−1.08668	−	0.911837i	−0.996459	+	0.0840846i	$0.973203\pi$
$224$		0			0
$225$	1.55179	−	5.62831i	0.103452	−	0.375221i
$226$		0			0
$227$	4.52933	−	25.6871i	0.300622	−	1.70491i	−0.342805	−	0.939407i	$-0.611377\pi$
$227$	4.52933	−	25.6871i	0.300622	−	1.70491i	0.643427	−	0.765507i	$-0.277512\pi$
$228$		0			0
$229$	−2.11904	−	0.771269i	−0.140030	−	0.0509669i	0.271054	−	0.962564i	$-0.412628\pi$
$229$	−2.11904	−	0.771269i	−0.140030	−	0.0509669i	−0.411085	+	0.911597i	$0.634850\pi$
$230$		0			0
$231$	−2.98215	−	1.24789i	−0.196211	−	0.0821054i
$232$		0			0
$233$	4.39597	+	7.61404i	0.287990	+	0.498812i	0.973330	−	0.229411i	$-0.0736798\pi$
$233$	4.39597	+	7.61404i	0.287990	+	0.498812i	−0.685340	+	0.728223i	$0.740346\pi$
$234$		0			0
$235$	0.238516	−	0.413121i	0.0155590	−	0.0269491i
$236$		0			0
$237$	15.6144	+	14.4121i	1.01426	+	0.936167i
$238$		0			0
$239$	−7.49187	+	6.28642i	−0.484609	+	0.406635i	−0.852089	−	0.523396i	$-0.824665\pi$
$239$	−7.49187	+	6.28642i	−0.484609	+	0.406635i	0.367481	+	0.930031i	$0.380220\pi$
$240$		0			0
$241$	−26.1085	+	9.50272i	−1.68180	+	0.612124i	−0.993554	−	0.113356i	$-0.963840\pi$
$241$	−26.1085	+	9.50272i	−1.68180	+	0.612124i	−0.688243	+	0.725481i	$0.741618\pi$
$242$		0			0
$243$	10.7373	−	11.3009i	0.688801	−	0.724950i
$244$		0			0
$245$	−2.47660	+	0.901410i	−0.158224	+	0.0575890i
$246$		0			0
$247$	−5.04284	+	4.23144i	−0.320868	+	0.269240i
$248$		0			0
$249$	22.2935	+	20.5769i	1.41279	+	1.30401i
$250$		0			0
$251$	9.61841	−	16.6596i	0.607109	−	1.05154i	−0.384606	−	0.923081i	$-0.625663\pi$
$251$	9.61841	−	16.6596i	0.607109	−	1.05154i	0.991714	−	0.128462i	$-0.0410041\pi$
$252$		0			0
$253$	−6.65485	−	11.5265i	−0.418387	−	0.724667i
$254$		0			0
$255$	−21.9510	−	9.18548i	−1.37462	−	0.575217i
$256$		0			0
$257$	−9.81684	−	3.57304i	−0.612358	−	0.222880i	0.0171767	−	0.999852i	$-0.494532\pi$
$257$	−9.81684	−	3.57304i	−0.612358	−	0.222880i	−0.629535	+	0.776972i	$0.716754\pi$
$258$		0			0
$259$	−0.256084	+	1.45232i	−0.0159123	+	0.0902430i
$260$		0			0
$261$	2.77120	−	10.0511i	0.171533	−	0.622147i
$262$		0			0
$263$	3.45634	+	2.90021i	0.213127	+	0.178835i	0.743101	−	0.669179i	$-0.233354\pi$
$263$	3.45634	+	2.90021i	0.213127	+	0.178835i	−0.529974	+	0.848014i	$0.677798\pi$
$264$		0			0
$265$	3.49813	+	19.8389i	0.214888	+	1.21869i
$266$		0			0
$267$	4.14468	+	0.195970i	0.253650	+	0.0119931i
$268$		0			0
$269$	7.06600			0.430821			0.215411	−	0.976524i	$-0.430891\pi$
$269$	7.06600			0.430821			0.215411	+	0.976524i	$0.430891\pi$
$270$		0			0
$271$	20.4133			1.24002			0.620010	−	0.784594i	$-0.287129\pi$
$271$	20.4133			1.24002			0.620010	+	0.784594i	$0.287129\pi$
$272$		0			0
$273$	0.710636	−	1.10663i	0.0430097	−	0.0669763i
$274$		0			0
$275$	0.630730	+	3.57705i	0.0380345	+	0.215704i
$276$		0			0
$277$	12.1234	+	10.1727i	0.728422	+	0.611218i	0.929701	−	0.368315i	$-0.120065\pi$
$277$	12.1234	+	10.1727i	0.728422	+	0.611218i	−0.201279	+	0.979534i	$0.564510\pi$
$278$		0			0
$279$	−1.63306	−	20.3598i	−0.0977688	−	1.21891i
$280$		0			0
$281$	−0.711219	+	4.03352i	−0.0424278	+	0.240620i	−0.998645	−	0.0520376i	$-0.983428\pi$
$281$	−0.711219	+	4.03352i	−0.0424278	+	0.240620i	0.956217	+	0.292657i	$0.0945395\pi$
$282$		0			0
$283$	−4.69564	−	1.70907i	−0.279127	−	0.101594i	0.198663	−	0.980068i	$-0.436340\pi$
$283$	−4.69564	−	1.70907i	−0.279127	−	0.101594i	−0.477790	+	0.878474i	$0.658562\pi$
$284$		0			0
$285$	−5.02392	−	39.2562i	−0.297591	−	2.32534i
$286$		0			0
$287$	4.63292	+	8.02444i	0.273472	+	0.473668i
$288$		0			0
$289$	−5.08602	+	8.80924i	−0.299178	+	0.518191i
$290$		0			0
$291$	−18.5379	+	5.77142i	−1.08671	+	0.338327i
$292$		0			0
$293$	−5.62069	+	4.71632i	−0.328364	+	0.275530i	−0.792033	−	0.610478i	$-0.790977\pi$
$293$	−5.62069	+	4.71632i	−0.328364	+	0.275530i	0.463669	+	0.886009i	$0.346533\pi$
$294$		0			0
$295$	20.2368	−	7.36558i	1.17823	−	0.428841i
$296$		0			0
$297$	−3.01639	+	9.21714i	−0.175029	+	0.534833i
$298$		0			0
$299$	5.08819	−	1.85195i	0.294257	−	0.107101i
$300$		0			0
$301$	−5.98019	+	5.01797i	−0.344692	+	0.289231i
$302$		0			0
$303$	1.49924	−	6.64881i	0.0861288	−	0.381964i
$304$		0			0
$305$	−16.4084	+	28.4203i	−0.939545	+	1.62734i
$306$		0			0
$307$	−14.8001	−	25.6345i	−0.844686	−	1.46304i	−0.885894	−	0.463888i	$-0.846454\pi$
$307$	−14.8001	−	25.6345i	−0.844686	−	1.46304i	0.0412076	−	0.999151i	$-0.486879\pi$
$308$		0			0
$309$	−10.4065	+	7.92559i	−0.592004	+	0.450871i
$310$		0			0
$311$	−19.7477	−	7.18757i	−1.11979	−	0.407570i	−0.285213	−	0.958464i	$-0.592064\pi$
$311$	−19.7477	−	7.18757i	−1.11979	−	0.407570i	−0.834575	+	0.550895i	$0.814287\pi$
$312$		0			0
$313$	0.0491409	−	0.278692i	0.00277761	−	0.0157526i	−0.983387	−	0.181519i	$-0.941899\pi$
$313$	0.0491409	−	0.278692i	0.00277761	−	0.0157526i	0.986165	+	0.165766i	$0.0530097\pi$
$314$		0			0
$315$	3.28961	+	7.18981i	0.185349	+	0.405100i
$316$		0			0
$317$	−7.54304	−	6.32936i	−0.423659	−	0.355492i	0.405894	−	0.913920i	$-0.366960\pi$
$317$	−7.54304	−	6.32936i	−0.423659	−	0.355492i	−0.829553	+	0.558428i	$0.811405\pi$
$318$		0			0
$319$	1.12637	+	6.38794i	0.0630644	+	0.357656i
$320$		0			0
$321$	8.54421	+	16.5591i	0.476891	+	0.924240i
$322$		0			0
$323$	−45.1924			−2.51457
$324$		0			0
$325$	−1.47769			−0.0819674
$326$		0			0
$327$	2.28251	+	4.42362i	0.126223	+	0.244627i
$328$		0			0
$329$	0.0314302	+	0.178249i	0.00173280	+	0.00982720i
$330$		0			0
$331$	8.75560	+	7.34682i	0.481251	+	0.403818i	0.850879	−	0.525362i	$-0.176070\pi$
$331$	8.75560	+	7.34682i	0.481251	+	0.403818i	−0.369627	+	0.929180i	$0.620515\pi$
$332$		0			0
$333$	4.40445	+	0.417437i	0.241362	+	0.0228754i
$334$		0			0
$335$	−1.09891	+	6.23222i	−0.0600398	+	0.340502i
$336$		0			0
$337$	−18.2666	−	6.64848i	−0.995042	−	0.362166i	−0.207372	−	0.978262i	$-0.566491\pi$
$337$	−18.2666	−	6.64848i	−0.995042	−	0.362166i	−0.787671	+	0.616096i	$0.788713\pi$
$338$		0			0
$339$	−3.25612	+	2.47986i	−0.176848	+	0.134688i
$340$		0			0
$341$	6.35363	+	11.0048i	0.344068	+	0.595944i
$342$		0			0
$343$	0.500000	−	0.866025i	0.0269975	−	0.0467610i
$344$		0			0
$345$	−7.16058	+	31.7558i	−0.385513	+	1.70967i
$346$		0			0
$347$	−24.5233	+	20.5775i	−1.31648	+	1.10466i	−0.329440	+	0.944177i	$0.606860\pi$
$347$	−24.5233	+	20.5775i	−1.31648	+	1.10466i	−0.987039	+	0.160480i	$0.948696\pi$
$348$		0			0
$349$	26.5858	−	9.67645i	1.42311	−	0.517969i	0.488159	−	0.872755i	$-0.337668\pi$
$349$	26.5858	−	9.67645i	1.42311	−	0.517969i	0.934948	+	0.354786i	$0.115446\pi$
$350$		0			0
$351$	−3.47972	−	1.85965i	−0.185733	−	0.0992607i
$352$		0			0
$353$	19.4588	−	7.08243i	1.03569	−	0.376960i	0.232445	−	0.972610i	$-0.425328\pi$
$353$	19.4588	−	7.08243i	1.03569	−	0.376960i	0.803244	+	0.595650i	$0.203105\pi$
$354$		0			0
$355$	−6.55719	+	5.50214i	−0.348020	+	0.292023i
$356$		0			0
$357$	8.62051	−	2.68383i	0.456246	−	0.142043i
$358$		0			0
$359$	−5.82037	+	10.0812i	−0.307188	+	0.532065i	−0.977746	−	0.209792i	$-0.932721\pi$
$359$	−5.82037	+	10.0812i	−0.307188	+	0.532065i	0.670558	+	0.741857i	$0.266055\pi$
$360$		0			0
$361$	−28.0819	−	48.6393i	−1.47800	−	2.55997i
$362$		0			0
$363$	1.65266	+	12.9137i	0.0867422	+	0.677791i
$364$		0			0
$365$	−26.0701	−	9.48876i	−1.36457	−	0.496664i
$366$		0			0
$367$	−3.39615	+	19.2605i	−0.177278	+	1.00539i	0.758204	+	0.652017i	$0.226077\pi$
$367$	−3.39615	+	19.2605i	−0.177278	+	1.00539i	−0.935482	+	0.353375i	$0.885034\pi$
$368$		0			0
$369$	22.8850	−	15.7790i	1.19135	−	0.821422i
$370$		0			0
$371$	−5.85530	−	4.91318i	−0.303992	−	0.255079i
$372$		0			0
$373$	0.699886	+	3.96925i	0.0362387	+	0.205520i	0.997551	−	0.0699403i	$-0.0222809\pi$
$373$	0.699886	+	3.96925i	0.0362387	+	0.205520i	−0.961312	+	0.275460i	$0.911170\pi$
$374$		0			0
$375$	−7.53279	+	11.7303i	−0.388992	+	0.605752i
$376$		0			0
$377$	−2.63887			−0.135909
$378$		0			0
$379$	−17.8788			−0.918370			−0.459185	−	0.888341i	$-0.651859\pi$
$379$	−17.8788			−0.918370			−0.459185	+	0.888341i	$0.651859\pi$
$380$		0			0
$381$	−8.77780	−	0.415034i	−0.449700	−	0.0212628i
$382$		0			0
$383$	1.14900	+	6.51628i	0.0587109	+	0.332966i	0.999989	−	0.00466582i	$-0.00148518\pi$
$383$	1.14900	+	6.51628i	0.0587109	+	0.332966i	−0.941278	+	0.337632i	$0.890374\pi$
$384$		0			0
$385$	−3.76818	−	3.16188i	−0.192044	−	0.161144i
$386$		0			0
$387$	16.4401	+	16.6795i	0.835699	+	0.847867i
$388$		0			0
$389$	−0.664051	+	3.76602i	−0.0336687	+	0.190945i	−0.997003	−	0.0773579i	$-0.975352\pi$
$389$	−0.664051	+	3.76602i	−0.0336687	+	0.190945i	0.963335	+	0.268303i	$0.0864627\pi$
$390$		0			0
$391$	34.9307	+	12.7137i	1.76652	+	0.642962i
$392$		0			0
$393$	8.00965	+	3.35167i	0.404033	+	0.169069i
$394$		0			0
$395$	16.1666	+	28.0013i	0.813428	+	1.40890i
$396$		0			0
$397$	3.45551	−	5.98511i	0.173427	−	0.300384i	−0.766189	−	0.642615i	$-0.777849\pi$
$397$	3.45551	−	5.98511i	0.173427	−	0.300384i	0.939616	+	0.342231i	$0.111183\pi$
$398$		0			0
$399$	11.0345	+	10.1849i	0.552416	+	0.509881i
$400$		0			0
$401$	16.5769	−	13.9096i	0.827809	−	0.694614i	−0.126978	−	0.991906i	$-0.540528\pi$
$401$	16.5769	−	13.9096i	0.827809	−	0.694614i	0.954787	+	0.297291i	$0.0960833\pi$
$402$		0			0
$403$	−4.85788	+	1.76812i	−0.241988	+	0.0880765i
$404$		0			0
$405$	20.7113	−	11.5618i	1.02915	−	0.574510i
$406$		0			0
$407$	−2.58646	+	0.941393i	−0.128206	+	0.0466631i
$408$		0			0
$409$	−20.3505	+	17.0761i	−1.00627	+	0.844358i	−0.987840	−	0.155472i	$-0.950310\pi$
$409$	−20.3505	+	17.0761i	−1.00627	+	0.844358i	−0.0184265	+	0.999830i	$0.505866\pi$
$410$		0			0
$411$	3.47083	+	3.20358i	0.171204	+	0.158021i
$412$		0			0
$413$	−4.08559	+	7.07645i	−0.201039	+	0.348209i
$414$		0			0
$415$	23.0819	+	39.9790i	1.13304	+	1.96249i
$416$		0			0
$417$	24.9209	+	10.4282i	1.22038	+	0.510673i
$418$		0			0
$419$	−23.7081	−	8.62906i	−1.15822	−	0.421557i	−0.309758	−	0.950816i	$-0.600248\pi$
$419$	−23.7081	−	8.62906i	−1.15822	−	0.421557i	−0.848461	+	0.529259i	$0.822470\pi$
$420$		0			0
$421$	−0.147205	+	0.834841i	−0.00717433	+	0.0406877i	−0.988185	−	0.153267i	$-0.951020\pi$
$421$	−0.147205	+	0.834841i	−0.00717433	+	0.0406877i	0.981010	+	0.193955i	$0.0621316\pi$
$422$		0			0
$423$	0.525497	−	0.136744i	0.0255505	−	0.00664870i
$424$		0			0
$425$	−7.77108	−	6.52071i	−0.376953	−	0.316301i
$426$		0			0
$427$	−2.16221	−	12.2625i	−0.104636	−	0.593423i
$428$		0			0
$429$	2.45188	+	0.115930i	0.118378	+	0.00559718i
$430$		0			0
$431$	30.4708			1.46773			0.733864	−	0.679296i	$-0.237715\pi$
$431$	30.4708			1.46773			0.733864	+	0.679296i	$0.237715\pi$
$432$		0			0
$433$	−29.0175			−1.39449			−0.697247	−	0.716831i	$-0.745592\pi$
$433$	−29.0175			−1.39449			−0.697247	+	0.716831i	$0.745592\pi$
$434$		0			0
$435$	8.57242	−	13.3493i	0.411016	−	0.640050i
$436$		0			0
$437$	10.7358	+	60.8859i	0.513564	+	2.91257i
$438$		0			0
$439$	−2.17828	−	1.82779i	−0.103964	−	0.0872359i	0.589324	−	0.807897i	$-0.299394\pi$
$439$	−2.17828	−	1.82779i	−0.103964	−	0.0872359i	−0.693288	+	0.720661i	$0.743839\pi$
$440$		0			0
$441$	−2.70969	−	1.28747i	−0.129033	−	0.0613082i
$442$		0			0
$443$	−0.275132	+	1.56035i	−0.0130719	+	0.0741345i	−0.990646	−	0.136458i	$-0.956428\pi$
$443$	−0.275132	+	1.56035i	−0.0130719	+	0.0741345i	0.977574	+	0.210592i	$0.0675393\pi$
$444$		0			0
$445$	5.93296	+	2.15942i	0.281249	+	0.102366i
$446$		0			0
$447$	4.48291	+	35.0288i	0.212034	+	1.65681i
$448$		0			0
$449$	8.00618	+	13.8671i	0.377835	+	0.654429i	0.990747	−	0.135722i	$-0.0433354\pi$
$449$	8.00618	+	13.8671i	0.377835	+	0.654429i	−0.612912	+	0.790151i	$0.710002\pi$
$450$		0			0
$451$	−8.64693	+	14.9769i	−0.407168	+	0.705235i
$452$		0			0
$453$	−1.93083	+	0.601124i	−0.0907181	+	0.0282433i
$454$		0			0
$455$	1.53300	−	1.28634i	0.0718680	−	0.0603044i
$456$		0			0
$457$	−18.6022	+	6.77064i	−0.870174	+	0.316717i	−0.738238	−	0.674541i	$-0.764342\pi$
$457$	−18.6022	+	6.77064i	−0.870174	+	0.316717i	−0.131936	+	0.991258i	$0.542119\pi$
$458$		0			0
$459$	−10.0934	−	25.1350i	−0.471120	−	1.17320i
$460$		0			0
$461$	−33.9529	+	12.3579i	−1.58135	+	0.575563i	−0.975496	−	0.220016i	$-0.929389\pi$
$461$	−33.9529	+	12.3579i	−1.58135	+	0.575563i	−0.605850	+	0.795579i	$0.707167\pi$
$462$		0			0
$463$	29.0947	−	24.4133i	1.35214	−	1.13458i	0.373822	−	0.927501i	$-0.378047\pi$
$463$	29.0947	−	24.4133i	1.35214	−	1.13458i	0.978323	−	0.207084i	$-0.0663973\pi$
$464$		0			0
$465$	6.83647	−	30.3184i	0.317034	−	1.40598i
$466$		0			0
$467$	−17.9474	+	31.0859i	−0.830509	+	1.43848i	0.0671263	+	0.997744i	$0.478617\pi$
$467$	−17.9474	+	31.0859i	−0.830509	+	1.43848i	−0.897635	+	0.440739i	$0.854716\pi$
$468$		0			0
$469$	−1.20058	−	2.07946i	−0.0554376	−	0.0960207i
$470$		0			0
$471$	−14.1968	+	10.8123i	−0.654152	+	0.498203i
$472$		0			0
$473$	−13.6916	−	4.98333i	−0.629540	−	0.229134i
$474$		0			0
$475$	2.92982	−	16.6158i	0.134429	−	0.762387i
$476$		0			0
$477$	−13.2879	+	18.6881i	−0.608411	+	0.855671i
$478$		0			0
$479$	20.4859	+	17.1897i	0.936026	+	0.785419i	0.976889	−	0.213745i	$-0.0685663\pi$
$479$	20.4859	+	17.1897i	0.936026	+	0.785419i	−0.0408631	+	0.999165i	$0.513011\pi$
$480$		0			0
$481$	−0.194446	−	1.10276i	−0.00886597	−	0.0502814i
$482$		0			0
$483$	−5.66368	−	10.9765i	−0.257706	−	0.499448i
$484$		0			0
$485$	−29.5434			−1.34150
$486$		0			0
$487$	−13.1761			−0.597067			−0.298533	−	0.954399i	$-0.596497\pi$
$487$	−13.1761			−0.597067			−0.298533	+	0.954399i	$0.596497\pi$
$488$		0			0
$489$	−16.2885	−	31.5679i	−0.736591	−	1.42755i
$490$		0			0
$491$	4.26708	+	24.1998i	0.192571	+	1.09212i	0.915836	+	0.401553i	$0.131529\pi$
$491$	4.26708	+	24.1998i	0.192571	+	1.09212i	−0.723265	+	0.690570i	$0.757360\pi$
$492$		0			0
$493$	−13.8777	−	11.6448i	−0.625019	−	0.524453i
$494$		0			0
$495$	−8.55144	+	12.0268i	−0.384359	+	0.540563i
$496$		0			0
$497$	0.563980	−	3.19849i	0.0252979	−	0.143472i
$498$		0			0
$499$	7.22843	+	2.63093i	0.323589	+	0.117777i	0.498707	−	0.866771i	$-0.333808\pi$
$499$	7.22843	+	2.63093i	0.323589	+	0.117777i	−0.175118	+	0.984547i	$0.556031\pi$
$500$		0			0
$501$	−10.0243	+	7.63450i	−0.447852	+	0.341084i
$502$		0			0
$503$	−15.1711	−	26.2772i	−0.676447	−	1.17164i	−0.976044	−	0.217574i	$-0.930185\pi$
$503$	−15.1711	−	26.2772i	−0.676447	−	1.17164i	0.299597	−	0.954066i	$-0.403148\pi$
$504$		0			0
$505$	5.18554	−	8.98161i	0.230753	−	0.399676i
$506$		0			0
$507$	4.73325	−	20.9910i	0.210211	−	0.932244i
$508$		0			0
$509$	12.7913	−	10.7332i	0.566963	−	0.475739i	−0.313673	−	0.949531i	$-0.601560\pi$
$509$	12.7913	−	10.7332i	0.566963	−	0.475739i	0.880637	+	0.473792i	$0.157115\pi$
$510$		0			0
$511$	9.89174	−	3.60030i	0.437585	−	0.159268i
$512$		0			0
$513$	27.8100	−	35.4405i	1.22784	−	1.56473i
$514$		0			0
$515$	−18.7039	+	6.80768i	−0.824195	+	0.299982i
$516$		0			0
$517$	−0.258784	+	0.217146i	−0.0113813	+	0.00955006i
$518$		0			0
$519$	26.2088	−	8.15958i	1.15044	−	0.358166i
$520$		0			0
$521$	16.2182	−	28.0907i	0.710532	−	1.23068i	−0.254126	−	0.967171i	$-0.581788\pi$
$521$	16.2182	−	28.0907i	0.710532	−	1.23068i	0.964658	−	0.263506i	$-0.0848789\pi$
$522$		0			0
$523$	−0.583445	−	1.01056i	−0.0255123	−	0.0441885i	0.852987	−	0.521932i	$-0.174788\pi$
$523$	−0.583445	−	1.01056i	−0.0255123	−	0.0441885i	−0.878500	+	0.477743i	$0.841455\pi$
$524$		0			0
$525$	0.427891	+	3.34348i	0.0186747	+	0.145922i
$526$		0			0
$527$	−33.3496	−	12.1383i	−1.45273	−	0.528752i
$528$		0			0
$529$	4.83672	−	27.4304i	0.210292	−	1.19263i
$530$		0			0
$531$	22.1413	+	10.5202i	0.960853	+	0.456536i
$532$		0			0
$533$	−5.38958	−	4.52239i	−0.233449	−	0.195887i
$534$		0			0
$535$	4.92351	+	27.9226i	0.212862	+	1.20720i
$536$		0			0
$537$	14.7371	−	22.9492i	0.635954	−	0.990332i
$538$		0			0
$539$	1.86641			0.0803920
$540$		0			0
$541$	1.25882			0.0541211			0.0270606	−	0.999634i	$-0.491385\pi$
$541$	1.25882			0.0541211			0.0270606	+	0.999634i	$0.491385\pi$
$542$		0			0
$543$	30.4000	+	1.43738i	1.30459	+	0.0616839i
$544$		0			0
$545$	1.31527	+	7.45929i	0.0563401	+	0.319521i
$546$		0			0
$547$	−12.6962	−	10.6534i	−0.542851	−	0.455506i	0.329661	−	0.944099i	$-0.393066\pi$
$547$	−12.6962	−	10.6534i	−0.542851	−	0.455506i	−0.872512	+	0.488594i	$0.837510\pi$
$548$		0			0
$549$	−36.1510	+	9.40713i	−1.54289	+	0.401487i
$550$		0			0
$551$	5.23211	−	29.6727i	0.222895	−	1.26410i
$552$		0			0
$553$	−11.5282	−	4.19594i	−0.490231	−	0.178429i
$554$		0			0
$555$	6.21019	+	2.59868i	0.263608	+	0.110308i
$556$		0			0
$557$	−8.49517	−	14.7141i	−0.359952	−	0.623455i	0.628000	−	0.778213i	$-0.283874\pi$
$557$	−8.49517	−	14.7141i	−0.359952	−	0.623455i	−0.987952	+	0.154758i	$0.950540\pi$
$558$		0			0
$559$	2.96379	−	5.13343i	0.125355	−	0.217121i
$560$		0			0
$561$	12.3827	+	11.4293i	0.522800	+	0.482545i
$562$		0			0
$563$	−6.23274	+	5.22989i	−0.262679	+	0.220414i	−0.764609	−	0.644494i	$-0.777068\pi$
$563$	−6.23274	+	5.22989i	−0.262679	+	0.220414i	0.501930	+	0.864908i	$0.332623\pi$
$564$		0			0
$565$	−5.85234	+	2.13008i	−0.246210	+	0.0896130i
$566$		0			0
$567$	−3.20011	+	8.41186i	−0.134392	+	0.353265i
$568$		0			0
$569$	−8.37987	+	3.05002i	−0.351302	+	0.127864i	−0.511643	−	0.859198i	$-0.670963\pi$
$569$	−8.37987	+	3.05002i	−0.351302	+	0.127864i	0.160341	+	0.987062i	$0.448741\pi$
$570$		0			0
$571$	3.71804	−	3.11980i	0.155595	−	0.130560i	−0.561667	−	0.827364i	$-0.689840\pi$
$571$	3.71804	−	3.11980i	0.155595	−	0.130560i	0.717262	+	0.696804i	$0.245395\pi$
$572$		0			0
$573$	21.0480	+	19.4274i	0.879294	+	0.811590i
$574$		0			0
$575$	−6.93900	+	12.0187i	−0.289376	+	0.501214i
$576$		0			0
$577$	−12.1742	−	21.0863i	−0.506818	−	0.877834i	−0.999969	−	0.00789044i	$-0.997488\pi$
$577$	−12.1742	−	21.0863i	−0.506818	−	0.877834i	0.493151	−	0.869944i	$-0.335845\pi$
$578$		0			0
$579$	0.0761420	+	0.0318619i	0.00316435	+	0.00132414i
$580$		0			0
$581$	−16.4595	−	5.99076i	−0.682854	−	0.248539i
$582$		0			0
$583$	2.47727	−	14.0493i	0.102598	−	0.581861i
$584$		0			0
$585$	−4.21436	−	4.27573i	−0.174242	−	0.176779i
$586$		0			0
$587$	−2.47191	−	2.07418i	−0.102027	−	0.0856107i	0.590347	−	0.807149i	$-0.298991\pi$
$587$	−2.47191	−	2.07418i	−0.102027	−	0.0856107i	−0.692374	+	0.721539i	$0.743435\pi$
$588$		0			0
$589$	−10.2499	−	58.1300i	−0.422339	−	2.39521i
$590$		0			0
$591$	−12.3797	−	0.585340i	−0.509233	−	0.0240777i
$592$		0			0
$593$	21.5011			0.882945			0.441472	−	0.897275i	$-0.354456\pi$
$593$	21.5011			0.882945			0.441472	+	0.897275i	$0.354456\pi$
$594$		0			0
$595$	13.7383			0.563214
$596$		0			0
$597$	7.88619	−	12.2807i	0.322760	−	0.502614i
$598$		0			0
$599$	1.02914	+	5.83654i	0.0420495	+	0.238475i	0.998587	−	0.0531334i	$-0.0169209\pi$
$599$	1.02914	+	5.83654i	0.0420495	+	0.238475i	−0.956538	+	0.291608i	$0.905810\pi$
$600$		0			0
$601$	−4.45291	−	3.73643i	−0.181638	−	0.152412i	0.547435	−	0.836848i	$-0.315604\pi$
$601$	−4.45291	−	3.73643i	−0.181638	−	0.152412i	−0.729073	+	0.684436i	$0.760049\pi$
$602$		0			0
$603$	−5.93045	+	4.08899i	−0.241506	+	0.166516i
$604$		0			0
$605$	−3.43999	+	19.5091i	−0.139855	+	0.793160i
$606$		0			0
$607$	−42.7509	−	15.5600i	−1.73520	−	0.631563i	−0.736226	−	0.676736i	$-0.763394\pi$
$607$	−42.7509	−	15.5600i	−1.73520	−	0.631563i	−0.998979	+	0.0451734i	$0.985616\pi$
$608$		0			0
$609$	0.764133	+	5.97083i	0.0309642	+	0.241950i
$610$		0			0
$611$	−0.0687168	−	0.119021i	−0.00277998	−	0.00481507i
$612$		0			0
$613$	14.1140	−	24.4462i	0.570059	−	0.987371i	−0.426500	−	0.904487i	$-0.640254\pi$
$613$	14.1140	−	24.4462i	0.570059	−	0.987371i	0.996559	−	0.0828837i	$-0.0264130\pi$
$614$		0			0
$615$	40.3856	−	12.5733i	1.62851	−	0.507003i
$616$		0			0
$617$	22.8988	−	19.2144i	0.921870	−	0.773541i	−0.0524696	−	0.998623i	$-0.516709\pi$
$617$	22.8988	−	19.2144i	0.921870	−	0.773541i	0.974340	+	0.225081i	$0.0722648\pi$
$618$		0			0
$619$	30.6847	−	11.1683i	1.23332	−	0.448893i	0.358588	−	0.933496i	$-0.383258\pi$
$619$	30.6847	−	11.1683i	1.23332	−	0.448893i	0.874734	+	0.484603i	$0.161036\pi$
$620$		0			0
$621$	−31.4656	+	19.5695i	−1.26267	+	0.785296i
$622$		0			0
$623$	−2.25113	+	0.819345i	−0.0901897	+	0.0328264i
$624$		0			0
$625$	−23.7039	+	19.8899i	−0.948155	+	0.795596i
$626$		0			0
$627$	−6.16494	+	27.3403i	−0.246204	+	1.09187i
$628$		0			0
$629$	3.84364	−	6.65739i	0.153256	−	0.265447i
$630$		0			0
$631$	10.2522	+	17.7574i	0.408135	+	0.706910i	0.994681	−	0.103006i	$-0.0328461\pi$
$631$	10.2522	+	17.7574i	0.408135	+	0.706910i	−0.586546	+	0.809916i	$0.699513\pi$
$632$		0			0
$633$	−16.8650	+	12.8444i	−0.670324	+	0.510519i
$634$		0			0
$635$	−12.5651	−	4.57333i	−0.498631	−	0.181487i
$636$		0			0
$637$	−0.131852	+	0.747770i	−0.00522417	+	0.0296277i
$638$		0			0
$639$	−9.70002	−	0.919333i	−0.383727	−	0.0363682i
$640$		0			0
$641$	−15.2232	−	12.7738i	−0.601282	−	0.504535i	0.290576	−	0.956852i	$-0.406153\pi$
$641$	−15.2232	−	12.7738i	−0.601282	−	0.504535i	−0.891857	+	0.452317i	$0.850598\pi$
$642$		0			0
$643$	−0.0922428	−	0.523135i	−0.00363770	−	0.0206304i	0.982935	−	0.183954i	$-0.0588897\pi$
$643$	−0.0922428	−	0.523135i	−0.00363770	−	0.0206304i	−0.986573	+	0.163323i	$0.947779\pi$
$644$		0			0
$645$	16.3407	+	31.6690i	0.643413	+	1.24697i
$646$		0			0
$647$	46.9034			1.84396			0.921982	−	0.387233i	$-0.126569\pi$
$647$	46.9034			1.84396			0.921982	+	0.387233i	$0.126569\pi$
$648$		0			0
$649$	−15.2508			−0.598645
$650$		0			0
$651$	5.40732	+	10.4797i	0.211930	+	0.410730i
$652$		0			0
$653$	0.514238	+	2.91639i	0.0201237	+	0.114127i	0.993215	−	0.116293i	$-0.0371011\pi$
$653$	0.514238	+	2.91639i	0.0201237	+	0.114127i	−0.973091	+	0.230420i	$0.925990\pi$
$654$		0			0
$655$	10.1208	+	8.49237i	0.395453	+	0.331825i
$656$		0			0
$657$	−13.1390	−	28.7167i	−0.512599	−	1.12034i
$658$		0			0
$659$	4.33344	−	24.5761i	0.168807	−	0.957350i	−0.776245	−	0.630431i	$-0.782878\pi$
$659$	4.33344	−	24.5761i	0.168807	−	0.957350i	0.945052	−	0.326920i	$-0.106011\pi$
$660$		0			0
$661$	6.56182	+	2.38831i	0.255225	+	0.0928944i	0.466464	−	0.884540i	$-0.345528\pi$
$661$	6.56182	+	2.38831i	0.255225	+	0.0928944i	−0.211239	+	0.977434i	$0.567750\pi$
$662$		0			0
$663$	−5.45387	+	4.15367i	−0.211811	+	0.161315i
$664$		0			0
$665$	11.4247	+	19.7882i	0.443031	+	0.767353i
$666$		0			0
$667$	−12.3917	+	21.4631i	−0.479810	+	0.831056i
$668$		0			0
$669$	8.07084	−	35.7926i	0.312037	−	1.38382i
$670$		0			0
$671$	17.8028	−	14.9383i	0.687269	−	0.576687i
$672$		0			0
$673$	42.0396	−	15.3012i	1.62051	−	0.589817i	0.637029	−	0.770840i	$-0.280163\pi$
$673$	42.0396	−	15.3012i	1.62051	−	0.589817i	0.983479	+	0.181023i	$0.0579410\pi$
$674$		0			0
$675$	9.89570	−	2.08153i	0.380886	−	0.0801182i
$676$		0			0
$677$	25.7313	−	9.36541i	0.988933	−	0.359942i	0.203626	−	0.979049i	$-0.434727\pi$
$677$	25.7313	−	9.36541i	0.988933	−	0.359942i	0.785307	+	0.619107i	$0.212505\pi$
$678$		0			0
$679$	8.58704	−	7.20538i	0.329540	−	0.276517i
$680$		0			0
$681$	43.1356	−	13.4294i	1.65296	−	0.514616i
$682$		0			0
$683$	−3.71682	+	6.43773i	−0.142220	+	0.246333i	−0.928332	−	0.371751i	$-0.878757\pi$
$683$	−3.71682	+	6.43773i	−0.142220	+	0.246333i	0.786112	+	0.618084i	$0.212091\pi$
$684$		0			0
$685$	3.59357	+	6.22425i	0.137303	+	0.237816i
$686$		0			0
$687$	−0.495817	−	3.87424i	−0.0189166	−	0.147812i
$688$		0			0
$689$	5.45378	+	1.98501i	0.207772	+	0.0756229i
$690$		0			0
$691$	7.64892	−	43.3792i	0.290979	−	1.65022i	−0.392133	−	0.919908i	$-0.628263\pi$
$691$	7.64892	−	43.3792i	0.290979	−	1.65022i	0.683112	−	0.730314i	$-0.260626\pi$
$692$		0			0
$693$	−0.447678	−	5.58131i	−0.0170059	−	0.212016i
$694$		0			0
$695$	31.4895	+	26.4228i	1.19446	+	1.00227i
$696$		0			0
$697$	−8.38717	−	47.5660i	−0.317687	−	1.80169i
$698$		0			0
$699$	−8.22840	+	12.8136i	−0.311227	+	0.484654i
$700$		0			0
$701$	−6.29438			−0.237736			−0.118868	−	0.992910i	$-0.537926\pi$
$701$	−6.29438			−0.237736			−0.118868	+	0.992910i	$0.537926\pi$
$702$		0			0
$703$	12.7855			0.482213
$704$		0			0
$705$	0.825321	+	0.0390230i	0.0310834	+	0.00146969i
$706$		0			0
$707$	0.683319	+	3.87529i	0.0256988	+	0.145745i
$708$		0			0
$709$	−13.8554	−	11.6260i	−0.520350	−	0.436625i	0.344404	−	0.938822i	$-0.388081\pi$
$709$	−13.8554	−	11.6260i	−0.520350	−	0.436625i	−0.864754	+	0.502196i	$0.832526\pi$
$710$		0			0
$711$	−9.78234	+	35.4804i	−0.366867	+	1.33062i
$712$		0			0
$713$	−8.43092	+	47.8142i	−0.315741	+	1.79065i
$714$		0			0
$715$	3.50978	+	1.27746i	0.131258	+	0.0477742i
$716$		0			0
$717$	−15.6264	−	6.53892i	−0.583578	−	0.244201i
$718$		0			0
$719$	15.0761	+	26.1126i	0.562244	+	0.973835i	0.997300	+	0.0734319i	$0.0233952\pi$
$719$	15.0761	+	26.1126i	0.562244	+	0.973835i	−0.435056	+	0.900403i	$0.643271\pi$
$720$		0			0
$721$	3.77613	−	6.54045i	0.140630	−	0.243579i
$722$		0			0
$723$	−35.3626	−	32.6398i	−1.31515	−	1.21389i
$724$		0			0
$725$	5.18110	−	4.34746i	0.192421	−	0.161460i
$726$		0			0
$727$	−12.1647	+	4.42759i	−0.451164	+	0.164210i	−0.557601	−	0.830109i	$-0.688278\pi$
$727$	−12.1647	+	4.42759i	−0.451164	+	0.164210i	0.106437	+	0.994319i	$0.466056\pi$
$728$		0			0
$729$	25.9224	+	7.55192i	0.960087	+	0.279701i
$730$		0			0
$731$	38.2391	−	13.9179i	1.41432	−	0.514772i
$732$		0			0
$733$	−1.05236	+	0.883032i	−0.0388697	+	0.0326155i	−0.662016	−	0.749490i	$-0.730299\pi$
$733$	−1.05236	+	0.883032i	−0.0388697	+	0.0326155i	0.623146	+	0.782106i	$0.285854\pi$
$734$		0			0
$735$	−3.35443	−	3.09614i	−0.123730	−	0.114203i
$736$		0			0
$737$	2.24077	−	3.88113i	0.0825400	−	0.142963i
$738$		0			0
$739$	14.4286	+	24.9910i	0.530763	+	0.919309i	0.999356	+	0.0358946i	$0.0114281\pi$
$739$	14.4286	+	24.9910i	0.530763	+	0.919309i	−0.468592	+	0.883415i	$0.655239\pi$
$740$		0			0
$741$	−10.5183	−	4.40140i	−0.386398	−	0.161690i
$742$		0			0
$743$	−28.7141	−	10.4511i	−1.05342	−	0.383413i	−0.243467	−	0.969909i	$-0.578285\pi$
$743$	−28.7141	−	10.4511i	−1.05342	−	0.383413i	−0.809952	+	0.586496i	$0.800507\pi$
$744$		0			0
$745$	−9.33112	+	52.9194i	−0.341866	+	1.93882i
$746$		0			0
$747$	−13.9668	+	50.6573i	−0.511018	+	1.85345i
$748$		0			0
$749$	−8.24115	−	6.91515i	−0.301125	−	0.252674i
$750$		0			0
$751$	4.89220	+	27.7450i	0.178519	+	1.01243i	0.934003	+	0.357264i	$0.116290\pi$
$751$	4.89220	+	27.7450i	0.178519	+	1.01243i	−0.755485	+	0.655166i	$0.772599\pi$
$752$		0			0
$753$	33.2820	+	1.57365i	1.21286	+	0.0573469i
$754$		0			0
$755$	−3.07710			−0.111987
$756$		0			0
$757$	−12.7549			−0.463585			−0.231792	−	0.972765i	$-0.574459\pi$
$757$	−12.7549			−0.463585			−0.231792	+	0.972765i	$0.574459\pi$
$758$		0			0
$759$	12.4566	−	19.3979i	0.452145	−	0.704098i
$760$		0			0
$761$	5.45806	+	30.9542i	0.197854	+	1.12209i	0.908295	+	0.418331i	$0.137385\pi$
$761$	5.45806	+	30.9542i	0.197854	+	1.12209i	−0.710440	+	0.703757i	$0.751504\pi$
$762$		0			0
$763$	−2.20155	−	1.84732i	−0.0797016	−	0.0668776i
$764$		0			0
$765$	−3.29526	−	41.0828i	−0.119140	−	1.48535i
$766$		0			0
$767$	1.07739	−	6.11016i	0.0389022	−	0.220625i
$768$		0			0
$769$	2.37283	+	0.863641i	0.0855666	+	0.0311437i	0.384449	−	0.923146i	$-0.374392\pi$
$769$	2.37283	+	0.863641i	0.0855666	+	0.0311437i	−0.298882	+	0.954290i	$0.596614\pi$
$770$		0			0
$771$	−2.29696	−	17.9481i	−0.0827230	−	0.646386i
$772$		0			0
$773$	−9.42324	−	16.3215i	−0.338931	−	0.587045i	0.645301	−	0.763928i	$-0.276732\pi$
$773$	−9.42324	−	16.3215i	−0.338931	−	0.587045i	−0.984232	+	0.176883i	$0.943399\pi$
$774$		0			0
$775$	6.62492	−	11.4747i	0.237974	−	0.412183i
$776$		0			0
$777$	−2.43884	+	0.759285i	−0.0874930	+	0.0272392i
$778$		0			0
$779$	61.5379	−	51.6365i	2.20483	−	1.85007i
$780$		0			0
$781$	5.69622	−	2.07325i	0.203827	−	0.0741868i
$782$		0			0
$783$	17.6719	−	3.71723i	0.631541	−	0.132843i
$784$		0			0
$785$	−25.5163	+	9.28719i	−0.910718	+	0.331474i
$786$		0			0
$787$	−17.5995	+	14.7677i	−0.627353	+	0.526411i	−0.900105	−	0.435673i	$-0.856510\pi$
$787$	−17.5995	+	14.7677i	−0.627353	+	0.526411i	0.272752	+	0.962084i	$0.412066\pi$
$788$		0			0
$789$	−1.71901	+	7.62348i	−0.0611985	+	0.271403i
$790$		0			0
$791$	1.18152	−	2.04646i	0.0420102	−	0.0727638i
$792$		0			0
$793$	4.72730	+	8.18793i	0.167871	+	0.290762i
$794$		0			0
$795$	−27.7583	+	21.1407i	−0.984485	+	0.749785i
$796$		0			0
$797$	−12.8131	−	4.66357i	−0.453862	−	0.165192i	0.104966	−	0.994476i	$-0.466527\pi$
$797$	−12.8131	−	4.66357i	−0.453862	−	0.165192i	−0.558828	+	0.829284i	$0.688749\pi$
$798$		0			0
$799$	0.163835	−	0.929156i	0.00579608	−	0.0328712i
$800$		0			0
$801$	2.99012	+	6.53525i	0.105651	+	0.230912i
$802$		0			0
$803$	15.0504	+	12.6288i	0.531117	+	0.445660i
$804$		0			0
$805$	−3.26363	−	18.5090i	−0.115028	−	0.652356i
$806$		0			0
$807$	5.61192	+	10.8762i	0.197549	+	0.382860i
$808$		0			0
$809$	1.67639			0.0589387			0.0294694	−	0.999566i	$-0.490618\pi$
$809$	1.67639			0.0589387			0.0294694	+	0.999566i	$0.490618\pi$
$810$		0			0
$811$	−40.2511			−1.41341			−0.706703	−	0.707510i	$-0.749818\pi$
$811$	−40.2511			−1.41341			−0.706703	+	0.707510i	$0.749818\pi$
$812$		0			0
$813$	16.2125	+	31.4207i	0.568599	+	1.10197i
$814$		0			0
$815$	−9.38607	−	53.2310i	−0.328780	−	1.86460i
$816$		0			0
$817$	51.8465	+	43.5044i	1.81388	+	1.52203i
$818$		0			0
$819$	2.26775	+	0.214929i	0.0792417	+	0.00751024i
$820$		0			0
$821$	−0.913242	+	5.17925i	−0.0318724	+	0.180757i	−0.996588	−	0.0825368i	$-0.973698\pi$
$821$	−0.913242	+	5.17925i	−0.0318724	+	0.180757i	0.964716	+	0.263294i	$0.0848089\pi$
$822$		0			0
$823$	8.02112	+	2.91945i	0.279599	+	0.101766i	0.478013	−	0.878353i	$-0.341357\pi$
$823$	8.02112	+	2.91945i	0.279599	+	0.101766i	−0.198415	+	0.980118i	$0.563579\pi$
$824$		0			0
$825$	−5.00496	+	3.81178i	−0.174250	+	0.132709i
$826$		0			0
$827$	13.9517	+	24.1650i	0.485147	+	0.840299i	0.999854	−	0.0170671i	$-0.00543288\pi$
$827$	13.9517	+	24.1650i	0.485147	+	0.840299i	−0.514708	+	0.857366i	$0.672100\pi$
$828$		0			0
$829$	22.1986	−	38.4490i	0.770988	−	1.33539i	−0.166034	−	0.986120i	$-0.553096\pi$
$829$	22.1986	−	38.4490i	0.770988	−	1.33539i	0.937022	−	0.349271i	$-0.113571\pi$
$830$		0			0
$831$	−6.02956	+	26.7399i	−0.209163	+	0.927597i
$832$		0			0
$833$	−3.99314	+	3.35065i	−0.138354	+	0.116093i
$834$		0			0
$835$	−18.0170	+	6.55765i	−0.623504	+	0.226937i
$836$		0			0
$837$	30.0413	−	18.6837i	1.03838	−	0.645803i
$838$		0			0
$839$	−23.1498	+	8.42583i	−0.799219	+	0.290892i	−0.709163	−	0.705045i	$-0.750927\pi$
$839$	−23.1498	+	8.42583i	−0.799219	+	0.290892i	−0.0900563	+	0.995937i	$0.528705\pi$
$840$		0			0
$841$	−12.9628	+	10.8771i	−0.446994	+	0.375072i
$842$		0			0
$843$	−6.77337	+	2.10875i	−0.233287	+	0.0726294i
$844$		0			0
$845$	16.3713	−	28.3559i	0.563190	−	0.975473i
$846$		0			0
$847$	−3.75825	−	6.50949i	−0.129135	−	0.223669i
$848$		0			0
$849$	−1.09869	−	8.58504i	−0.0377071	−	0.294638i
$850$		0			0
$851$	−9.88231	−	3.59687i	−0.338761	−	0.123299i
$852$		0			0
$853$	−3.59158	+	20.3689i	−0.122973	+	0.697417i	0.859517	+	0.511107i	$0.170764\pi$
$853$	−3.59158	+	20.3689i	−0.122973	+	0.697417i	−0.982491	+	0.186311i	$0.940347\pi$
$854$		0			0
$855$	56.4342	−	38.9108i	1.93001	−	1.33072i
$856$		0			0
$857$	0.420846	+	0.353132i	0.0143758	+	0.0120627i	0.649947	−	0.759979i	$-0.274791\pi$
$857$	0.420846	+	0.353132i	0.0143758	+	0.0120627i	−0.635571	+	0.772042i	$0.719235\pi$
$858$		0			0
$859$	0.0857922	+	0.486552i	0.00292719	+	0.0166009i	0.986236	−	0.165342i	$-0.0528726\pi$
$859$	0.0857922	+	0.486552i	0.00292719	+	0.0166009i	−0.983309	+	0.181942i	$0.941762\pi$
$860$		0			0
$861$	−8.67192	+	13.5042i	−0.295538	+	0.460223i
$862$		0			0
$863$	−22.3325			−0.760208			−0.380104	−	0.924944i	$-0.624112\pi$
$863$	−22.3325			−0.760208			−0.380104	+	0.924944i	$0.624112\pi$
$864$		0			0
$865$	41.7681			1.42016
$866$		0			0
$867$	−17.5988	−	0.832112i	−0.597687	−	0.0282600i
$868$		0			0
$869$	−3.97608	−	22.5495i	−0.134879	−	0.764938i
$870$		0			0
$871$	1.39666	+	1.17194i	0.0473241	+	0.0397096i
$872$		0			0
$873$	−23.6066	−	23.9504i	−0.798964	−	0.810597i
$874$		0			0
$875$	1.39764	−	7.92641i	0.0472488	−	0.267961i
$876$		0			0
$877$	19.4572	+	7.08185i	0.657023	+	0.239137i	0.648951	−	0.760830i	$-0.275208\pi$
$877$	19.4572	+	7.08185i	0.657023	+	0.239137i	0.00807267	+	0.999967i	$0.497430\pi$
$878$		0			0
$879$	−11.7235	−	4.90575i	−0.395424	−	0.165467i
$880$		0			0
$881$	−21.6157	−	37.4394i	−0.728250	−	1.26137i	−0.957622	−	0.288028i	$-0.907001\pi$
$881$	−21.6157	−	37.4394i	−0.728250	−	1.26137i	0.229372	−	0.973339i	$-0.426333\pi$
$882$		0			0
$883$	5.14138	−	8.90513i	0.173021	−	0.299681i	−0.766454	−	0.642300i	$-0.777980\pi$
$883$	5.14138	−	8.90513i	0.173021	−	0.299681i	0.939475	+	0.342618i	$0.111314\pi$
$884$		0			0
$885$	27.4096	+	25.2991i	0.921365	+	0.850421i
$886$		0			0
$887$	−20.3306	+	17.0594i	−0.682636	+	0.572800i	−0.916775	−	0.399403i	$-0.869217\pi$
$887$	−20.3306	+	17.0594i	−0.682636	+	0.572800i	0.234139	+	0.972203i	$0.424773\pi$
$888$		0			0
$889$	4.76756	−	1.73525i	0.159899	−	0.0581984i
$890$		0			0
$891$	−16.5829	+	2.67747i	−0.555550	+	0.0896986i
$892$		0			0
$893$	1.47457	−	0.536701i	0.0493447	−	0.0179600i
$894$		0			0
$895$	31.7912	−	26.6760i	1.06266	−	0.891679i
$896$		0			0
$897$	6.89168	+	6.36103i	0.230107	+	0.212389i
$898$		0			0
$899$	11.8309	−	20.4916i	0.394581	−	0.683434i
$900$		0			0
$901$	19.9217	+	34.5054i	0.663688	+	1.14954i
$902$		0			0
$903$	−12.4734	−	5.21952i	−0.415087	−	0.173695i
$904$		0			0
$905$	43.5166	+	15.8387i	1.44654	+	0.526497i
$906$		0			0
$907$	5.07449	−	28.7789i	0.168496	−	0.955587i	−0.776891	−	0.629635i	$-0.783204\pi$
$907$	5.07449	−	28.7789i	0.168496	−	0.955587i	0.945387	−	0.325951i	$-0.105685\pi$
$908$		0			0
$909$	11.4248	−	2.97292i	0.378935	−	0.0986056i
$910$		0			0
$911$	−8.56239	−	7.18470i	−0.283685	−	0.238040i	0.489830	−	0.871818i	$-0.337059\pi$
$911$	−8.56239	−	7.18470i	−0.283685	−	0.238040i	−0.773515	+	0.633778i	$0.781503\pi$
$912$		0			0
$913$	−5.67686	−	32.1951i	−0.187877	−	1.06550i
$914$		0			0
$915$	−56.7771	−	2.68455i	−1.87699	−	0.0887484i
$916$		0			0
$917$	−5.01292			−0.165541
$918$		0			0
$919$	−56.7616			−1.87239			−0.936197	−	0.351476i	$-0.885680\pi$
$919$	−56.7616			−1.87239			−0.936197	+	0.351476i	$0.885680\pi$
$920$		0			0
$921$	27.7029	−	43.1400i	0.912842	−	1.42151i
$922$		0			0
$923$	0.428233	+	2.42863i	0.0140955	+	0.0799393i
$924$		0			0
$925$	2.19853	+	1.84478i	0.0722872	+	0.0606561i
$926$		0			0
$927$	−20.4643	−	9.72333i	−0.672135	−	0.319356i
$928$		0			0
$929$	−4.41528	+	25.0403i	−0.144861	+	0.821546i	0.822618	+	0.568594i	$0.192513\pi$
$929$	−4.41528	+	25.0403i	−0.144861	+	0.821546i	−0.967479	+	0.252952i	$0.918599\pi$
$930$		0			0
$931$	−8.14686	−	2.96522i	−0.267003	−	0.0971810i
$932$		0			0
$933$	−4.62059	−	36.1047i	−0.151271	−	1.18201i
$934$		0			0
$935$	12.8206	+	22.2060i	0.419279	+	0.726213i
$936$		0			0
$937$	−8.36076	+	14.4813i	−0.273134	+	0.473082i	−0.969663	−	0.244447i	$-0.921394\pi$
$937$	−8.36076	+	14.4813i	−0.273134	+	0.473082i	0.696529	+	0.717529i	$0.254727\pi$
$938$		0			0
$939$	0.467999	−	0.145702i	0.0152726	−	0.00475481i
$940$		0			0
$941$	28.0784	−	23.5606i	0.915331	−	0.768054i	−0.0577946	−	0.998328i	$-0.518407\pi$
$941$	28.0784	−	23.5606i	0.915331	−	0.768054i	0.973126	+	0.230275i	$0.0739624\pi$
$942$		0			0
$943$	−62.0913	+	22.5994i	−2.02197	+	0.735937i
$944$		0			0
$945$	−8.45410	+	10.7737i	−0.275012	+	0.350469i
$946$		0			0
$947$	−44.0554	+	16.0348i	−1.43161	+	0.521062i	−0.937392	−	0.348277i	$-0.886767\pi$
$947$	−44.0554	+	16.0348i	−1.43161	+	0.521062i	−0.494215	+	0.869340i	$0.664545\pi$
$948$		0			0
$949$	−6.12290	+	5.13773i	−0.198758	+	0.166778i
$950$		0			0
$951$	3.75154	−	16.6373i	0.121652	−	0.539502i
$952$		0			0
$953$	7.30463	−	12.6520i	0.236620	−	0.409838i	−0.723122	−	0.690720i	$-0.757294\pi$
$953$	7.30463	−	12.6520i	0.236620	−	0.409838i	0.959742	+	0.280882i	$0.0906270\pi$
$954$		0			0
$955$	21.7924	+	37.7455i	0.705184	+	1.22141i
$956$		0			0
$957$	−8.93791	+	6.80713i	−0.288922	+	0.220043i
$958$		0			0
$959$	−2.56254	−	0.932690i	−0.0827489	−	0.0301181i
$960$		0			0
$961$	2.66622	−	15.1209i	0.0860071	−	0.487771i
$962$		0			0
$963$	−18.7023	+	26.3030i	−0.602674	+	0.847602i
$964$		0			0
$965$	0.0962114	+	0.0807309i	0.00309715	+	0.00259882i
$966$		0			0
$967$	9.51416	+	53.9575i	0.305955	+	1.73516i	0.618977	+	0.785409i	$0.287548\pi$
$967$	9.51416	+	53.9575i	0.305955	+	1.73516i	−0.313022	+	0.949746i	$0.601341\pi$
$968$		0			0
$969$	−35.8925	−	69.5615i	−1.15303	−	2.23464i
$970$		0			0
$971$	−37.3825			−1.19966			−0.599831	−	0.800127i	$-0.704765\pi$
$971$	−37.3825			−1.19966			−0.599831	+	0.800127i	$0.704765\pi$
$972$		0			0
$973$	−15.5970			−0.500017
$974$		0			0
$975$	−1.17360	−	2.27450i	−0.0375853	−	0.0728422i
$976$		0			0
$977$	4.98156	+	28.2518i	0.159374	+	0.903855i	0.954677	+	0.297643i	$0.0962006\pi$
$977$	4.98156	+	28.2518i	0.159374	+	0.903855i	−0.795303	+	0.606212i	$0.792688\pi$
$978$		0			0
$979$	−3.42513	−	2.87402i	−0.109467	−	0.0918541i
$980$		0			0
$981$	−4.99616	+	7.02661i	−0.159515	+	0.224343i
$982$		0			0
$983$	5.21080	−	29.5519i	0.166199	−	0.942559i	−0.781621	−	0.623753i	$-0.785607\pi$
$983$	5.21080	−	29.5519i	0.166199	−	0.942559i	0.947820	−	0.318806i	$-0.103282\pi$
$984$		0			0
$985$	−17.7211	−	6.44996i	−0.564641	−	0.205513i
$986$		0			0
$987$	−0.249404	+	0.189946i	−0.00793862	+	0.00604606i
$988$		0			0
$989$	−27.8350	−	48.2117i	−0.885102	−	1.53304i
$990$		0			0
$991$	15.3004	−	26.5010i	0.486032	−	0.841833i	−0.513839	−	0.857887i	$-0.671777\pi$
$991$	15.3004	−	26.5010i	0.486032	−	0.841833i	0.999871	+	0.0160539i	$0.00511033\pi$
$992$		0			0
$993$	−4.35460	+	19.3118i	−0.138189	+	0.612842i
$994$		0			0
$995$	17.0122	−	14.2749i	0.539323	−	0.452546i
$996$		0			0
$997$	7.19220	−	2.61775i	0.227779	−	0.0829049i	−0.225609	−	0.974218i	$-0.572437\pi$
$997$	7.19220	−	2.61775i	0.227779	−	0.0829049i	0.453389	+	0.891313i	$0.350215\pi$
$998$		0			0
$999$	2.85555	+	7.11098i	0.0903455	+	0.224982i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bo.b.169.7	yes	54
27.4	even	9	inner	756.2.bo.b.85.7	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bo.b.85.7	✓	54	27.4	even	9	inner
756.2.bo.b.169.7	yes	54	1.1	even	1	trivial

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.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.794215 + 1.53923i) q^{3} +(0.457658 + 2.59551i) q^{5} +(-0.766044 - 0.642788i) q^{7} +(-1.73845 + 2.44496i) q^{9} +O(q^{10})\)	\(q+(0.794215 + 1.53923i) q^{3} +(0.457658 + 2.59551i) q^{5} +(-0.766044 - 0.642788i) q^{7} +(-1.73845 + 2.44496i) q^{9} +(0.324099 - 1.83806i) q^{11} +(0.713514 + 0.259698i) q^{13} +(-3.63160 + 2.76583i) q^{15} +(2.60634 + 4.51431i) q^{17} +(-4.33485 + 7.50819i) q^{19} +(0.380993 - 1.68963i) q^{21} +(5.46279 - 4.58383i) q^{23} +(-1.82874 + 0.665607i) q^{25} +(-5.14404 - 0.734045i) q^{27} +(-3.26578 + 1.18865i) q^{29} +(-5.21553 + 4.37635i) q^{31} +(3.08659 - 0.960949i) q^{33} +(1.31777 - 2.28245i) q^{35} +(-0.737364 - 1.27715i) q^{37} +(0.166949 + 1.30452i) q^{39} +(-8.70703 - 3.16910i) q^{41} +(1.35560 - 7.68798i) q^{43} +(-7.14151 - 3.39319i) q^{45} +(-0.138653 - 0.116344i) q^{47} +(0.173648 + 0.984808i) q^{49} +(-4.87856 + 7.59709i) q^{51} +7.64355 q^{53} +4.91901 q^{55} +(-14.9996 - 0.709216i) q^{57} +(-1.41891 - 8.04704i) q^{59} +(9.53852 + 8.00376i) q^{61} +(2.90331 - 0.755493i) q^{63} +(-0.347502 + 1.97078i) q^{65} +(2.25635 + 0.821244i) q^{67} +(11.3942 + 4.76794i) q^{69} +(1.62391 + 2.81270i) q^{71} +(-5.26329 + 9.11628i) q^{73} +(-2.47693 - 2.28621i) q^{75} +(-1.42975 + 1.19971i) q^{77} +(11.5282 - 4.19594i) q^{79} +(-2.95561 - 8.50084i) q^{81} +(16.4595 - 5.99076i) q^{83} +(-10.5241 + 8.83078i) q^{85} +(-4.42334 - 4.08274i) q^{87} +(1.19780 - 2.07465i) q^{89} +(-0.379653 - 0.657578i) q^{91} +(-10.8784 - 4.55213i) q^{93} +(-21.4714 - 7.81496i) q^{95} +(-1.94652 + 11.0393i) q^{97} +(3.93054 + 3.98777i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9}+O(q^{10}) \) 54 * q + 3 * q^3 - 3 * q^5 - 9 * q^9	\( 54 q + 3 q^{3} - 3 q^{5} - 9 q^{9} + 9 q^{13} + 3 q^{15} + 3 q^{21} + 12 q^{23} + 27 q^{25} + 39 q^{27} + 30 q^{29} - 9 q^{31} - 6 q^{33} + 6 q^{35} - 18 q^{39} - 27 q^{41} + 9 q^{43} - 81 q^{45} + 9 q^{47} + 12 q^{53} - 21 q^{57} - 24 q^{59} - 3 q^{63} - 78 q^{65} - 9 q^{67} + 6 q^{69} - 30 q^{71} + 57 q^{75} + 9 q^{77} + 99 q^{81} + 78 q^{83} + 18 q^{85} + 21 q^{87} + 12 q^{89} - 51 q^{93} - 36 q^{95} + 36 q^{97} + 15 q^{99}+O(q^{100}) \) 54 * q + 3 * q^3 - 3 * q^5 - 9 * q^9 + 9 * q^13 + 3 * q^15 + 3 * q^21 + 12 * q^23 + 27 * q^25 + 39 * q^27 + 30 * q^29 - 9 * q^31 - 6 * q^33 + 6 * q^35 - 18 * q^39 - 27 * q^41 + 9 * q^43 - 81 * q^45 + 9 * q^47 + 12 * q^53 - 21 * q^57 - 24 * q^59 - 3 * q^63 - 78 * q^65 - 9 * q^67 + 6 * q^69 - 30 * q^71 + 57 * q^75 + 9 * q^77 + 99 * q^81 + 78 * q^83 + 18 * q^85 + 21 * q^87 + 12 * q^89 - 51 * q^93 - 36 * q^95 + 36 * q^97 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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