LMFDB - Embedded newform 784.2.m.j.589.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [784,2,Mod(197,784)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("784.197"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(784, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,4,0,4,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			589.5
Character	$\chi$	$=$	784.589
Dual form			784.2.m.j.197.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.604218 - 1.27864i) q^{2} +(-0.853080 - 0.853080i) q^{3} +(-1.26984 + 1.54515i) q^{4} +(-0.718099 + 0.718099i) q^{5} +(-0.575337 + 1.60623i) q^{6} +(2.74296 + 0.690063i) q^{8} -1.54451i q^{9} +(1.35208 + 0.484303i) q^{10} +(1.73491 - 1.73491i) q^{11} +(2.40142 - 0.234863i) q^{12} +(-2.65786 - 2.65786i) q^{13} +1.22519 q^{15} +(-0.775001 - 3.92420i) q^{16} +1.01826 q^{17} +(-1.97487 + 0.933219i) q^{18} +(-0.0685610 - 0.0685610i) q^{19} +(-0.197701 - 2.02145i) q^{20} +(-3.26658 - 1.17006i) q^{22} +1.93110i q^{23} +(-1.75128 - 2.92864i) q^{24} +3.96867i q^{25} +(-1.79252 + 5.00437i) q^{26} +(-3.87683 + 3.87683i) q^{27} +(-5.05325 - 5.05325i) q^{29} +(-0.740283 - 1.56658i) q^{30} -8.56498 q^{31} +(-4.54938 + 3.36202i) q^{32} -2.96003 q^{33} +(-0.615248 - 1.30198i) q^{34} +(2.38650 + 1.96128i) q^{36} +(5.64724 - 5.64724i) q^{37} +(-0.0462391 + 0.129091i) q^{38} +4.53473i q^{39} +(-2.46525 + 1.47418i) q^{40} +8.51782i q^{41} +(-4.47950 + 4.47950i) q^{43} +(0.477640 + 4.88375i) q^{44} +(1.10911 + 1.10911i) q^{45} +(2.46918 - 1.16681i) q^{46} -12.0599 q^{47} +(-2.68652 + 4.00880i) q^{48} +(5.07450 - 2.39794i) q^{50} +(-0.868654 - 0.868654i) q^{51} +(7.48186 - 0.731739i) q^{52} +(1.04091 - 1.04091i) q^{53} +(7.29952 + 2.61462i) q^{54} +2.49167i q^{55} +0.116976i q^{57} +(-3.40803 + 9.51455i) q^{58} +(-5.09623 + 5.09623i) q^{59} +(-1.55580 + 1.89311i) q^{60} +(-3.24045 - 3.24045i) q^{61} +(5.17511 + 10.9515i) q^{62} +(7.04763 + 3.78563i) q^{64} +3.81721 q^{65} +(1.78850 + 3.78481i) q^{66} +(2.47945 + 2.47945i) q^{67} +(-1.29302 + 1.57336i) q^{68} +(1.64738 - 1.64738i) q^{69} -5.43131i q^{71} +(1.06581 - 4.23652i) q^{72} -8.47900i q^{73} +(-10.6330 - 3.80863i) q^{74} +(3.38559 - 3.38559i) q^{75} +(0.192999 - 0.0188756i) q^{76} +(5.79829 - 2.73996i) q^{78} +0.867190 q^{79} +(3.37450 + 2.26144i) q^{80} +1.98097 q^{81} +(10.8912 - 5.14661i) q^{82} +(-5.44318 - 5.44318i) q^{83} +(-0.731209 + 0.731209i) q^{85} +(8.43425 + 3.02107i) q^{86} +8.62165i q^{87} +(5.95597 - 3.56158i) q^{88} +4.53977i q^{89} +(0.748010 - 2.08830i) q^{90} +(-2.98385 - 2.45219i) q^{92} +(7.30661 + 7.30661i) q^{93} +(7.28680 + 15.4203i) q^{94} +0.0984673 q^{95} +(6.74905 + 1.01291i) q^{96} +16.4025 q^{97} +(-2.67958 - 2.67958i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 4 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{10} + 4 q^{11} - 2 q^{12} - 12 q^{13} - 20 q^{15} - 16 q^{16} - 8 q^{17} - 18 q^{18} + 4 q^{19} - 8 q^{20} - 18 q^{24} + 10 q^{26} - 12 q^{27}+ \cdots - 12 q^{99}+O(q^{100}) $ 24 * q + 4 * q^2 + 4 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^10 + 4 * q^11 - 2 * q^12 - 12 * q^13 - 20 * q^15 - 16 * q^16 - 8 * q^17 - 18 * q^18 + 4 * q^19 - 8 * q^20 - 18 * q^24 + 10 * q^26 - 12 * q^27 + 12 * q^29 + 4 * q^30 - 28 * q^31 - 16 * q^32 - 16 * q^33 - 22 * q^34 - 36 * q^36 + 24 * q^37 - 20 * q^38 - 26 * q^40 - 20 * q^43 - 6 * q^44 + 28 * q^45 + 14 * q^46 + 20 * q^47 + 28 * q^48 + 28 * q^50 - 24 * q^51 + 16 * q^52 + 16 * q^53 - 64 * q^54 + 6 * q^58 + 20 * q^59 - 46 * q^60 - 8 * q^61 + 12 * q^62 + 40 * q^64 - 8 * q^65 + 20 * q^66 - 48 * q^67 - 20 * q^69 + 32 * q^72 + 8 * q^74 + 4 * q^75 - 18 * q^76 + 58 * q^78 + 36 * q^79 + 28 * q^80 - 2 * q^82 - 4 * q^83 + 20 * q^86 + 42 * q^88 - 10 * q^90 + 38 * q^92 - 8 * q^93 + 72 * q^94 + 4 * q^95 + 120 * q^96 - 24 * q^97 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	−0.604218	−	1.27864i	−0.427246	−	0.904135i
$2$	−0.604218	−	1.27864i	−0.427246	−	0.904135i
$3$	−0.853080	−	0.853080i	−0.492526	−	0.492526i	0.416575	−	0.909101i	$-0.363230\pi$
$3$	−0.853080	−	0.853080i	−0.492526	−	0.492526i	−0.909101	+	0.416575i	$0.863230\pi$
$4$	−1.26984	+	1.54515i	−0.634921	+	0.772577i
$5$	−0.718099	+	0.718099i	−0.321144	+	0.321144i	−0.849206	−	0.528062i	$-0.822919\pi$
$5$	−0.718099	+	0.718099i	−0.321144	+	0.321144i	0.528062	+	0.849206i	$0.322919\pi$
$6$	−0.575337	+	1.60623i	−0.234880	+	0.655740i
$7$		0			0
$7$		0			0
$8$	2.74296	+	0.690063i	0.969782	+	0.243974i
$9$		−	1.54451i		−	0.514836i
$10$	1.35208	+	0.484303i	0.427565	+	0.153150i
$11$	1.73491	−	1.73491i	0.523094	−	0.523094i	−0.395411	−	0.918504i	$-0.629398\pi$
$11$	1.73491	−	1.73491i	0.523094	−	0.523094i	0.918504	+	0.395411i	$0.129398\pi$
$12$	2.40142	−	0.234863i	0.693229	−	0.0677990i
$13$	−2.65786	−	2.65786i	−0.737157	−	0.737157i	0.234870	−	0.972027i	$-0.424534\pi$
$13$	−2.65786	−	2.65786i	−0.737157	−	0.737157i	−0.972027	+	0.234870i	$0.924534\pi$
$14$		0			0
$15$	1.22519			0.316343
$16$	−0.775001	−	3.92420i	−0.193750	−	0.981051i
$17$	1.01826			0.246963			0.123482	−	0.992347i	$-0.460594\pi$
$17$	1.01826			0.246963			0.123482	+	0.992347i	$0.460594\pi$
$18$	−1.97487	+	0.933219i	−0.465482	+	0.219962i
$19$	−0.0685610	−	0.0685610i	−0.0157290	−	0.0157290i	0.699199	−	0.714928i	$-0.253540\pi$
$19$	−0.0685610	−	0.0685610i	−0.0157290	−	0.0157290i	−0.714928	+	0.699199i	$0.753540\pi$
$20$	−0.197701	−	2.02145i	−0.0442073	−	0.452009i
$21$		0			0
$22$	−3.26658	−	1.17006i	−0.696438	−	0.249458i
$23$			1.93110i			0.402662i	0.979523	+	0.201331i	$0.0645268\pi$
$23$			1.93110i			0.402662i	−0.979523	+	0.201331i	$0.935473\pi$
$24$	−1.75128	−	2.92864i	−0.357479	−	0.597806i
$25$			3.96867i			0.793733i
$26$	−1.79252	+	5.00437i	−0.351542	+	0.981438i
$27$	−3.87683	+	3.87683i	−0.746096	+	0.746096i
$28$		0			0
$29$	−5.05325	−	5.05325i	−0.938365	−	0.938365i	0.0598432	−	0.998208i	$-0.480940\pi$
$29$	−5.05325	−	5.05325i	−0.938365	−	0.938365i	−0.998208	+	0.0598432i	$0.980940\pi$
$30$	−0.740283	−	1.56658i	−0.135157	−	0.286017i
$31$	−8.56498			−1.53832			−0.769158	−	0.639059i	$-0.779324\pi$
$31$	−8.56498			−1.53832			−0.769158	+	0.639059i	$0.779324\pi$
$32$	−4.54938	+	3.36202i	−0.804224	+	0.594327i
$33$	−2.96003			−0.515275
$34$	−0.615248	−	1.30198i	−0.105514	−	0.223288i
$35$		0			0
$36$	2.38650	+	1.96128i	0.397751	+	0.326880i
$37$	5.64724	−	5.64724i	0.928401	−	0.928401i	−0.0692014	−	0.997603i	$-0.522045\pi$
$37$	5.64724	−	5.64724i	0.928401	−	0.928401i	0.997603	+	0.0692014i	$0.0220451\pi$
$38$	−0.0462391	+	0.129091i	−0.00750098	+	0.0209413i
$39$			4.53473i			0.726138i
$40$	−2.46525	+	1.47418i	−0.389790	+	0.233089i
$41$			8.51782i			1.33026i	0.746728	+	0.665130i	$0.231624\pi$
$41$			8.51782i			1.33026i	−0.746728	+	0.665130i	$0.768376\pi$
$42$		0			0
$43$	−4.47950	+	4.47950i	−0.683117	+	0.683117i	−0.960701	−	0.277584i	$-0.910466\pi$
$43$	−4.47950	+	4.47950i	−0.683117	+	0.683117i	0.277584	+	0.960701i	$0.410466\pi$
$44$	0.477640	+	4.88375i	0.0720069	+	0.736254i
$45$	1.10911	+	1.10911i	0.165336	+	0.165336i
$46$	2.46918	−	1.16681i	0.364061	−	0.172036i
$47$	−12.0599			−1.75912			−0.879559	−	0.475791i	$-0.842162\pi$
$47$	−12.0599			−1.75912			−0.879559	+	0.475791i	$0.842162\pi$
$48$	−2.68652	+	4.00880i	−0.387766	+	0.578620i
$49$		0			0
$50$	5.07450	−	2.39794i	0.717642	−	0.339120i
$51$	−0.868654	−	0.868654i	−0.121636	−	0.121636i
$52$	7.48186	−	0.731739i	1.03755	−	0.101474i
$53$	1.04091	−	1.04091i	0.142980	−	0.142980i	−0.631993	−	0.774974i	$-0.717763\pi$
$53$	1.04091	−	1.04091i	0.142980	−	0.142980i	0.774974	+	0.631993i	$0.217763\pi$
$54$	7.29952	+	2.61462i	0.993339	+	0.355805i
$55$			2.49167i			0.335977i
$56$		0			0
$57$			0.116976i			0.0154939i
$58$	−3.40803	+	9.51455i	−0.447496	+	1.24932i
$59$	−5.09623	+	5.09623i	−0.663472	+	0.663472i	−0.956197	−	0.292724i	$-0.905438\pi$
$59$	−5.09623	+	5.09623i	−0.663472	+	0.663472i	0.292724	+	0.956197i	$0.405438\pi$
$60$	−1.55580	+	1.89311i	−0.200853	+	0.244400i
$61$	−3.24045	−	3.24045i	−0.414897	−	0.414897i	0.468543	−	0.883441i	$-0.344779\pi$
$61$	−3.24045	−	3.24045i	−0.414897	−	0.414897i	−0.883441	+	0.468543i	$0.844779\pi$
$62$	5.17511	+	10.9515i	0.657240	+	1.39085i
$63$		0			0
$64$	7.04763	+	3.78563i	0.880953	+	0.473203i
$65$	3.81721			0.473467
$66$	1.78850	+	3.78481i	0.220149	+	0.465878i
$67$	2.47945	+	2.47945i	0.302913	+	0.302913i	0.842153	−	0.539239i	$-0.181288\pi$
$67$	2.47945	+	2.47945i	0.302913	+	0.302913i	−0.539239	+	0.842153i	$0.681288\pi$
$68$	−1.29302	+	1.57336i	−0.156802	+	0.190798i
$69$	1.64738	−	1.64738i	0.198322	−	0.198322i
$70$		0			0
$71$		−	5.43131i		−	0.644578i	−0.946641	−	0.322289i	$-0.895548\pi$
$71$		−	5.43131i		−	0.644578i	0.946641	−	0.322289i	$-0.104452\pi$
$72$	1.06581	−	4.23652i	0.125607	−	0.499279i
$73$		−	8.47900i		−	0.992392i	−0.868211	−	0.496196i	$-0.834730\pi$
$73$		−	8.47900i		−	0.992392i	0.868211	−	0.496196i	$-0.165270\pi$
$74$	−10.6330	−	3.80863i	−1.23606	−	0.442744i
$75$	3.38559	−	3.38559i	0.390934	−	0.390934i
$76$	0.192999	−	0.0188756i	0.0221385	−	0.00216518i
$77$		0			0
$78$	5.79829	−	2.73996i	0.656527	−	0.310240i
$79$	0.867190			0.0975665			0.0487832	−	0.998809i	$-0.484466\pi$
$79$	0.867190			0.0975665			0.0487832	+	0.998809i	$0.484466\pi$
$80$	3.37450	+	2.26144i	0.377280	+	0.252837i
$81$	1.98097			0.220107
$82$	10.8912	−	5.14661i	1.20273	−	0.568349i
$83$	−5.44318	−	5.44318i	−0.597466	−	0.597466i	0.342171	−	0.939638i	$-0.388838\pi$
$83$	−5.44318	−	5.44318i	−0.597466	−	0.597466i	−0.939638	+	0.342171i	$0.888838\pi$
$84$		0			0
$85$	−0.731209	+	0.731209i	−0.0793108	+	0.0793108i
$86$	8.43425	+	3.02107i	0.909489	+	0.325771i
$87$			8.62165i			0.924338i
$88$	5.95597	−	3.56158i	0.634908	−	0.379666i
$89$			4.53977i			0.481214i	0.970623	+	0.240607i	$0.0773465\pi$
$89$			4.53977i			0.481214i	−0.970623	+	0.240607i	$0.922653\pi$
$90$	0.748010	−	2.08830i	0.0788471	−	0.220126i
$91$		0			0
$92$	−2.98385	−	2.45219i	−0.311088	−	0.255659i
$93$	7.30661	+	7.30661i	0.757660	+	0.757660i
$94$	7.28680	+	15.4203i	0.751576	+	1.59048i
$95$	0.0984673			0.0101025
$96$	6.74905	+	1.01291i	0.688822	+	0.103380i
$97$	16.4025			1.66542			0.832712	−	0.553706i	$-0.186787\pi$
$97$	16.4025			1.66542			0.832712	+	0.553706i	$0.186787\pi$
$98$		0			0
$99$	−2.67958	−	2.67958i	−0.269308	−	0.269308i
$100$	−6.13220	−	5.03958i	−0.613220	−	0.503958i
$101$	6.50363	−	6.50363i	0.647135	−	0.647135i	−0.305164	−	0.952300i	$-0.598711\pi$
$101$	6.50363	−	6.50363i	0.647135	−	0.647135i	0.952300	+	0.305164i	$0.0987114\pi$
$102$	−0.585840	+	1.63555i	−0.0580068	+	0.161944i
$103$			7.73036i			0.761695i	0.924638	+	0.380848i	$0.124368\pi$
$103$			7.73036i			0.761695i	−0.924638	+	0.380848i	$0.875632\pi$
$104$	−5.45630	−	9.12448i	−0.535034	−	0.894729i
$105$		0			0
$106$	−1.95989	−	0.702015i	−0.190361	−	0.0681857i
$107$	−13.3639	+	13.3639i	−1.29194	+	1.29194i	−0.358354	+	0.933586i	$0.616662\pi$
$107$	−13.3639	+	13.3639i	−1.29194	+	1.29194i	−0.933586	+	0.358354i	$0.883338\pi$
$108$	−1.06734	−	10.9133i	−0.102704	−	1.05013i
$109$	−11.5683	−	11.5683i	−1.10804	−	1.10804i	−0.993408	−	0.114634i	$-0.963430\pi$
$109$	−11.5683	−	11.5683i	−1.10804	−	1.10804i	−0.114634	−	0.993408i	$-0.536570\pi$
$110$	3.18595	−	1.50551i	0.303768	−	0.143545i
$111$	−9.63510			−0.914524
$112$		0			0
$113$	−20.1152			−1.89228			−0.946138	−	0.323765i	$-0.895051\pi$
$113$	−20.1152			−1.89228			−0.946138	+	0.323765i	$0.895051\pi$
$114$	0.149570	−	0.0706790i	0.0140085	−	0.00661970i
$115$	−1.38672	−	1.38672i	−0.129313	−	0.129313i
$116$	14.2249	−	1.39122i	1.32075	−	0.129171i
$117$	−4.10509	+	4.10509i	−0.379515	+	0.379515i
$118$	9.59547	+	3.43701i	0.883335	+	0.316403i
$119$		0			0
$120$	3.36065	+	0.845460i	0.306784	+	0.0771796i
$121$			4.98020i			0.452745i
$122$	−2.18544	+	6.10131i	−0.197860	+	0.552387i
$123$	7.26638	−	7.26638i	0.655187	−	0.655187i
$124$	10.8762	−	13.2342i	0.976709	−	1.18847i
$125$	−6.44039	−	6.44039i	−0.576046	−	0.576046i
$126$		0			0
$127$	−0.988901			−0.0877508			−0.0438754	−	0.999037i	$-0.513970\pi$
$127$	−0.988901			−0.0877508			−0.0438754	+	0.999037i	$0.513970\pi$
$128$	0.582154	−	11.2987i	0.0514556	−	0.998675i
$129$	7.64274			0.672905
$130$	−2.30643	−	4.88084i	−0.202287	−	0.428078i
$131$	−5.57005	−	5.57005i	−0.486657	−	0.486657i	0.420592	−	0.907250i	$-0.361822\pi$
$131$	−5.57005	−	5.57005i	−0.486657	−	0.486657i	−0.907250	+	0.420592i	$0.861822\pi$
$132$	3.75877	−	4.57370i	0.327159	−	0.398089i
$133$		0			0
$134$	1.67220	−	4.66846i	0.144456	−	0.403293i
$135$		−	5.56790i		−	0.479208i
$136$	2.79303	+	0.702661i	0.239501	+	0.0602527i
$137$			11.0608i			0.944988i	0.881334	+	0.472494i	$0.156646\pi$
$137$			11.0608i			0.944988i	−0.881334	+	0.472494i	$0.843354\pi$
$138$	−3.10179	−	1.11103i	−0.264042	−	0.0945774i
$139$	12.4154	−	12.4154i	1.05306	−	1.05306i	0.0545473	−	0.998511i	$-0.482628\pi$
$139$	12.4154	−	12.4154i	1.05306	−	1.05306i	0.998511	−	0.0545473i	$-0.0173716\pi$
$140$		0			0
$141$	10.2881	+	10.2881i	0.866411	+	0.866411i
$142$	−6.94470	+	3.28170i	−0.582786	+	0.275394i
$143$	−9.22227			−0.771205
$144$	−6.06097	+	1.19700i	−0.505081	+	0.0997496i
$145$	7.25747			0.602700
$146$	−10.8416	+	5.12316i	−0.897256	+	0.423996i
$147$		0			0
$148$	1.55475	+	15.8970i	0.127800	+	1.30672i
$149$	3.70525	−	3.70525i	0.303546	−	0.303546i	−0.538853	−	0.842400i	$-0.681142\pi$
$149$	3.70525	−	3.70525i	0.303546	−	0.303546i	0.842400	+	0.538853i	$0.181142\pi$
$150$	−6.37459	−	2.28332i	−0.520483	−	0.186432i
$151$		−	1.36339i		−	0.110951i	−0.998460	−	0.0554754i	$-0.982333\pi$
$151$		−	1.36339i		−	0.110951i	0.998460	−	0.0554754i	$-0.0176674\pi$
$152$	−0.140749	−	0.235371i	−0.0114162	−	0.0190911i
$153$		−	1.57271i		−	0.127146i
$154$		0			0
$155$	6.15051	−	6.15051i	0.494021	−	0.494021i
$156$	−7.00686	−	5.75840i	−0.560998	−	0.461041i
$157$	−0.224718	−	0.224718i	−0.0179344	−	0.0179344i	0.698083	−	0.716017i	$-0.254037\pi$
$157$	−0.224718	−	0.224718i	−0.0179344	−	0.0179344i	−0.716017	+	0.698083i	$0.754037\pi$
$158$	−0.523971	−	1.10882i	−0.0416849	−	0.0882133i
$159$	−1.77596			−0.140843
$160$	0.852640	−	5.68117i	0.0674071	−	0.449136i
$161$		0			0
$162$	−1.19693	−	2.53294i	−0.0940400	−	0.199007i
$163$	−10.4959	−	10.4959i	−0.822098	−	0.822098i	0.164310	−	0.986409i	$-0.447460\pi$
$163$	−10.4959	−	10.4959i	−0.822098	−	0.822098i	−0.986409	+	0.164310i	$0.947460\pi$
$164$	−13.1613	−	10.8163i	−1.02773	−	0.844610i
$165$	2.12559	−	2.12559i	0.165477	−	0.165477i
$166$	−3.67100	+	10.2487i	−0.284925	+	0.795455i
$167$			14.5986i			1.12967i	0.825204	+	0.564836i	$0.191060\pi$
$167$			14.5986i			1.12967i	−0.825204	+	0.564836i	$0.808940\pi$
$168$		0			0
$169$			1.12842i			0.0868018i
$170$	1.37676	+	0.493144i	0.105593	+	0.0378224i
$171$	−0.105893	+	0.105893i	−0.00809785	+	0.00809785i
$172$	−1.23326	−	12.6098i	−0.0940349	−	0.961485i
$173$	−8.73327	−	8.73327i	−0.663978	−	0.663978i	0.292337	−	0.956315i	$-0.405567\pi$
$173$	−8.73327	−	8.73327i	−0.663978	−	0.663978i	−0.956315	+	0.292337i	$0.905567\pi$
$174$	11.0240	−	5.20935i	0.835727	−	0.394920i
$175$		0			0
$176$	−8.15268	−	5.46357i	−0.614531	−	0.411832i
$177$	8.69498			0.653555
$178$	5.80473	−	2.74301i	0.435083	−	0.205597i
$179$	−0.333536	−	0.333536i	−0.0249297	−	0.0249297i	0.694532	−	0.719462i	$-0.255611\pi$
$179$	−0.333536	−	0.333536i	−0.0249297	−	0.0249297i	−0.719462	+	0.694532i	$0.755611\pi$
$180$	−3.12214	+	0.305351i	−0.232711	+	0.0227595i
$181$	15.4654	−	15.4654i	1.14953	−	1.14953i	0.162887	−	0.986645i	$-0.447919\pi$
$181$	15.4654	−	15.4654i	1.14953	−	1.14953i	0.986645	−	0.162887i	$-0.0520807\pi$
$182$		0			0
$183$			5.52873i			0.408696i
$184$	−1.33258	+	5.29693i	−0.0982392	+	0.390495i
$185$			8.11057i			0.596301i
$186$	4.92775	−	13.7573i	0.361320	−	1.00874i
$187$	1.76658	−	1.76658i	0.129185	−	0.129185i
$188$	15.3142	−	18.6344i	1.11690	−	1.35905i
$189$		0			0
$190$	−0.0594956	−	0.125904i	−0.00431627	−	0.00913405i
$191$	6.08216			0.440090			0.220045	−	0.975490i	$-0.429380\pi$
$191$	6.08216			0.440090			0.220045	+	0.975490i	$0.429380\pi$
$192$	−2.78275	−	9.24163i	−0.200828	−	0.666957i
$193$	10.0618			0.724262			0.362131	−	0.932127i	$-0.382049\pi$
$193$	10.0618			0.724262			0.362131	+	0.932127i	$0.382049\pi$
$194$	−9.91069	−	20.9729i	−0.711546	−	1.50577i
$195$	−3.25639	−	3.25639i	−0.233195	−	0.233195i
$196$		0			0
$197$	−10.0837	+	10.0837i	−0.718432	+	0.718432i	−0.968284	−	0.249852i	$-0.919618\pi$
$197$	−10.0837	+	10.0837i	−0.718432	+	0.718432i	0.249852	+	0.968284i	$0.419618\pi$
$198$	−1.80717	+	5.04527i	−0.128430	+	0.358551i
$199$		−	11.6601i		−	0.826563i	−0.910603	−	0.413282i	$-0.864383\pi$
$199$		−	11.6601i		−	0.826563i	0.910603	−	0.413282i	$-0.135617\pi$
$200$	−2.73863	+	10.8859i	−0.193650	+	0.769748i
$201$		−	4.23034i		−	0.298386i
$202$	−12.2454	−	4.38620i	−0.861584	−	0.308612i
$203$		0			0
$204$	2.44526	−	0.239150i	0.171202	−	0.0167439i
$205$	−6.11664	−	6.11664i	−0.427205	−	0.427205i
$206$	9.88435	−	4.67082i	0.688676	−	0.325431i
$207$	2.98260			0.207305
$208$	−8.37014	+	12.4898i	−0.580365	+	0.866013i
$209$	−0.237894			−0.0164555
$210$		0			0
$211$	6.53423	+	6.53423i	0.449835	+	0.449835i	0.895300	−	0.445465i	$-0.146962\pi$
$211$	6.53423	+	6.53423i	0.449835	+	0.449835i	−0.445465	+	0.895300i	$0.646962\pi$
$212$	0.286575	+	2.93016i	0.0196821	+	0.201244i
$213$	−4.63335	+	4.63335i	−0.317472	+	0.317472i
$214$	25.1624	+	9.01294i	1.72007	+	0.616112i
$215$		−	6.43345i		−	0.438757i
$216$	−13.3092	+	7.95872i	−0.905579	+	0.541522i
$217$		0			0
$218$	−7.80192	+	21.7815i	−0.528413	+	1.47523i
$219$	−7.23326	+	7.23326i	−0.488779	+	0.488779i
$220$	−3.85001	−	3.16403i	−0.259568	−	0.213319i
$221$	−2.70638	−	2.70638i	−0.182051	−	0.182051i
$222$	5.82170	+	12.3198i	0.390727	+	0.826853i
$223$	−23.3350			−1.56263			−0.781315	−	0.624137i	$-0.785451\pi$
$223$	−23.3350			−1.56263			−0.781315	+	0.624137i	$0.785451\pi$
$224$		0			0
$225$	6.12964			0.408643
$226$	12.1539	+	25.7201i	0.808468	+	1.71087i
$227$	−11.0658	−	11.0658i	−0.734461	−	0.734461i	0.237039	−	0.971500i	$-0.423823\pi$
$227$	−11.0658	−	11.0658i	−0.734461	−	0.734461i	−0.971500	+	0.237039i	$0.923823\pi$
$228$	−0.180746	−	0.148541i	−0.0119702	−	0.00983738i
$229$	18.9083	−	18.9083i	1.24950	−	1.24950i	0.293553	−	0.955943i	$-0.405162\pi$
$229$	18.9083	−	18.9083i	1.24950	−	1.24950i	0.955943	−	0.293553i	$-0.0948377\pi$
$230$	−0.935237	+	2.61100i	−0.0616677	+	0.172164i
$231$		0			0
$232$	−10.3738	−	17.3479i	−0.681072	−	1.13895i
$233$		−	12.7481i		−	0.835156i	−0.908641	−	0.417578i	$-0.862879\pi$
$233$		−	12.7481i		−	0.835156i	0.908641	−	0.417578i	$-0.137121\pi$
$234$	7.72929	+	2.76856i	0.505280	+	0.180987i
$235$	8.66021	−	8.66021i	0.564930	−	0.564930i
$236$	−1.40305	−	14.3459i	−0.0913308	−	0.933836i
$237$	−0.739782	−	0.739782i	−0.0480540	−	0.0480540i
$238$		0			0
$239$	14.9688			0.968253			0.484127	−	0.874998i	$-0.339137\pi$
$239$	14.9688			0.968253			0.484127	+	0.874998i	$0.339137\pi$
$240$	−0.949525	−	4.80791i	−0.0612916	−	0.310349i
$241$	19.8105			1.27611			0.638054	−	0.769992i	$-0.279740\pi$
$241$	19.8105			1.27611			0.638054	+	0.769992i	$0.279740\pi$
$242$	6.36788	−	3.00912i	0.409343	−	0.193434i
$243$	9.94057	+	9.94057i	0.637688	+	0.637688i
$244$	9.12186	−	0.892134i	0.583967	−	0.0571130i
$245$		0			0
$246$	−13.6816	−	4.90061i	−0.872305	−	0.312452i
$247$			0.364451i			0.0231895i
$248$	−23.4934	−	5.91037i	−1.49183	−	0.375309i
$249$			9.28693i			0.588535i
$250$	−4.34355	+	12.1263i	−0.274710	+	0.766938i
$251$	9.23966	−	9.23966i	0.583202	−	0.583202i	−0.352580	−	0.935782i	$-0.614695\pi$
$251$	9.23966	−	9.23966i	0.583202	−	0.583202i	0.935782	+	0.352580i	$0.114695\pi$
$252$		0			0
$253$	3.35028	+	3.35028i	0.210630	+	0.210630i
$254$	0.597511	+	1.26445i	0.0374912	+	0.0793386i
$255$	1.24756			0.0781252
$256$	−14.7987	+	6.08252i	−0.924922	+	0.380158i
$257$	23.2219			1.44854			0.724271	−	0.689516i	$-0.242177\pi$
$257$	23.2219			1.44854			0.724271	+	0.689516i	$0.242177\pi$
$258$	−4.61788	−	9.77231i	−0.287496	−	0.608398i
$259$		0			0
$260$	−4.84726	+	5.89818i	−0.300614	+	0.365790i
$261$	−7.80479	+	7.80479i	−0.483104	+	0.483104i
$262$	−3.75657	+	10.4876i	−0.232081	+	0.647926i
$263$			4.52013i			0.278723i	0.990242	+	0.139361i	$0.0445050\pi$
$263$			4.52013i			0.278723i	−0.990242	+	0.139361i	$0.955495\pi$
$264$	−8.11923	−	2.04261i	−0.499704	−	0.125714i
$265$			1.49496i			0.0918345i
$266$		0			0
$267$	3.87278	−	3.87278i	0.237011	−	0.237011i
$268$	−6.97965	+	0.682622i	−0.426350	+	0.0416978i
$269$	0.282106	+	0.282106i	0.0172003	+	0.0172003i	0.715655	−	0.698454i	$-0.246128\pi$
$269$	0.282106	+	0.282106i	0.0172003	+	0.0172003i	−0.698454	+	0.715655i	$0.746128\pi$
$270$	−7.11934	+	3.36422i	−0.433269	+	0.204740i
$271$	10.6217			0.645221			0.322611	−	0.946532i	$-0.395440\pi$
$271$	10.6217			0.645221			0.322611	+	0.946532i	$0.395440\pi$
$272$	−0.789149	−	3.99584i	−0.0478492	−	0.242284i
$273$		0			0
$274$	14.1428	−	6.68313i	0.854397	−	0.403742i
$275$	6.88526	+	6.88526i	0.415197	+	0.415197i
$276$	0.453544	+	4.63738i	0.0273001	+	0.279137i
$277$	−8.14182	+	8.14182i	−0.489195	+	0.489195i	−0.908052	−	0.418857i	$-0.862431\pi$
$277$	−8.14182	+	8.14182i	−0.489195	+	0.489195i	0.418857	+	0.908052i	$0.362431\pi$
$278$	−23.3764	−	8.37321i	−1.40202	−	0.502192i
$279$			13.2287i			0.791981i
$280$		0			0
$281$		−	18.6360i		−	1.11173i	−0.831272	−	0.555866i	$-0.812387\pi$
$281$		−	18.6360i		−	1.11173i	0.831272	−	0.555866i	$-0.187613\pi$
$282$	6.93850	−	19.3710i	0.413182	−	1.15352i
$283$	6.42639	−	6.42639i	0.382009	−	0.382009i	−0.489817	−	0.871826i	$-0.662936\pi$
$283$	6.42639	−	6.42639i	0.382009	−	0.382009i	0.871826	+	0.489817i	$0.162936\pi$
$284$	8.39222	+	6.89691i	0.497986	+	0.409257i
$285$	−0.0840005	−	0.0840005i	−0.00497576	−	0.00497576i
$286$	5.57226	+	11.7920i	0.329495	+	0.697274i
$287$		0			0
$288$	5.19267	+	7.02655i	0.305981	+	0.414044i
$289$	−15.9632			−0.939009
$290$	−4.38509	−	9.27969i	−0.257501	−	0.544922i
$291$	−13.9927	−	13.9927i	−0.820265	−	0.820265i
$292$	13.1014	+	10.7670i	0.766699	+	0.630091i
$293$	−12.0193	+	12.0193i	−0.702174	+	0.702174i	−0.964877	−	0.262703i	$-0.915386\pi$
$293$	−12.0193	+	12.0193i	−0.702174	+	0.702174i	0.262703	+	0.964877i	$0.415386\pi$
$294$		0			0
$295$		−	7.31920i		−	0.426140i
$296$	19.3871	−	11.5932i	1.12685	−	0.673841i
$297$			13.4519i			0.780557i
$298$	−6.97646	−	2.49891i	−0.404136	−	0.144758i
$299$	5.13259	−	5.13259i	0.296826	−	0.296826i
$300$	0.932092	+	9.53042i	0.0538143	+	0.550239i
$301$		0			0
$302$	−1.74328	+	0.823782i	−0.100315	+	0.0474033i
$303$	−11.0962			−0.637462
$304$	−0.215913	+	0.322182i	−0.0123834	+	0.0184784i
$305$	4.65393			0.266483
$306$	−2.01092	+	0.950256i	−0.114957	+	0.0543225i
$307$	17.8339	+	17.8339i	1.01784	+	1.01784i	0.999838	+	0.0179975i	$0.00572909\pi$
$307$	17.8339	+	17.8339i	1.01784	+	1.01784i	0.0179975	+	0.999838i	$0.494271\pi$
$308$		0			0
$309$	6.59462	−	6.59462i	0.375155	−	0.375155i
$310$	−11.5805	−	4.14804i	−0.657730	−	0.235593i
$311$			6.54459i			0.371109i	0.982634	+	0.185555i	$0.0594082\pi$
$311$			6.54459i			0.371109i	−0.982634	+	0.185555i	$0.940592\pi$
$312$	−3.12925	+	12.4386i	−0.177159	+	0.704196i
$313$			19.1734i			1.08375i	0.840461	+	0.541873i	$0.182285\pi$
$313$			19.1734i			1.08375i	−0.840461	+	0.541873i	$0.817715\pi$
$314$	−0.151555	+	0.423112i	−0.00855274	+	0.0238776i
$315$		0			0
$316$	−1.10119	+	1.33994i	−0.0619470	+	0.0753776i
$317$	13.3082	+	13.3082i	0.747464	+	0.747464i	0.974002	−	0.226538i	$-0.0727407\pi$
$317$	13.3082	+	13.3082i	0.747464	+	0.747464i	−0.226538	+	0.974002i	$0.572741\pi$
$318$	1.07307	+	2.27082i	0.0601747	+	0.127341i
$319$	−17.5338			−0.981706
$320$	−7.77935	+	2.34244i	−0.434879	+	0.130946i
$321$	22.8010			1.27263
$322$		0			0
$323$	−0.0698127	−	0.0698127i	−0.00388448	−	0.00388448i
$324$	−2.51551	+	3.06090i	−0.139751	+	0.170050i
$325$	10.5482	−	10.5482i	0.585106	−	0.585106i
$326$	−7.07864	+	19.7622i	−0.392050	+	1.09453i
$327$			19.7374i			1.09148i
$328$	−5.87783	+	23.3640i	−0.324549	+	1.29006i
$329$		0			0
$330$	−4.00219	−	1.43355i	−0.220313	−	0.0789143i
$331$	6.92509	−	6.92509i	0.380637	−	0.380637i	−0.490694	−	0.871332i	$-0.663257\pi$
$331$	6.92509	−	6.92509i	0.380637	−	0.380637i	0.871332	+	0.490694i	$0.163257\pi$
$332$	15.3225	−	1.49857i	0.840932	−	0.0822446i
$333$	−8.72222	−	8.72222i	−0.477975	−	0.477975i
$334$	18.6663	−	8.82071i	1.02138	−	0.482648i
$335$	−3.56099			−0.194558
$336$		0			0
$337$	4.91600			0.267792			0.133896	−	0.990995i	$-0.457251\pi$
$337$	4.91600			0.267792			0.133896	+	0.990995i	$0.457251\pi$
$338$	1.44285	−	0.681813i	0.0784806	−	0.0370857i
$339$	17.1598	+	17.1598i	0.931995	+	0.931995i
$340$	−0.201310	−	2.05835i	−0.0109176	−	0.111630i
$341$	−14.8594	+	14.8594i	−0.804684	+	0.804684i
$342$	0.199382	+	0.0714167i	0.0107813	+	0.00386178i
$343$		0			0
$344$	−15.3782	+	9.19593i	−0.829137	+	0.495811i
$345$			2.36597i			0.127380i
$346$	−5.88992	+	16.4435i	−0.316644	+	0.884008i
$347$	6.61363	−	6.61363i	0.355038	−	0.355038i	−0.506942	−	0.861980i	$-0.669224\pi$
$347$	6.61363	−	6.61363i	0.355038	−	0.355038i	0.861980	+	0.506942i	$0.169224\pi$
$348$	−13.3218	−	10.9481i	−0.714122	−	0.586882i
$349$	−17.2061	−	17.2061i	−0.921021	−	0.921021i	0.0760810	−	0.997102i	$-0.475759\pi$
$349$	−17.2061	−	17.2061i	−0.921021	−	0.921021i	−0.997102	+	0.0760810i	$0.975759\pi$
$350$		0			0
$351$	20.6081			1.09998
$352$	−2.05995	+	13.7255i	−0.109796	+	0.731573i
$353$	−8.16944			−0.434815			−0.217408	−	0.976081i	$-0.569760\pi$
$353$	−8.16944			−0.434815			−0.217408	+	0.976081i	$0.569760\pi$
$354$	−5.25366	−	11.1178i	−0.279229	−	0.590902i
$355$	3.90022	+	3.90022i	0.207002	+	0.207002i
$356$	−7.01464	−	5.76479i	−0.371775	−	0.305533i
$357$		0			0
$358$	−0.224944	+	0.628001i	−0.0118887	+	0.0331909i
$359$		−	11.5693i		−	0.610604i	−0.952256	−	0.305302i	$-0.901243\pi$
$359$		−	11.5693i		−	0.610604i	0.952256	−	0.305302i	$-0.0987574\pi$
$360$	2.27689	+	3.80760i	0.120003	+	0.200678i
$361$		−	18.9906i		−	0.999505i
$362$	−29.1191	−	10.4302i	−1.53047	−	0.548199i
$363$	4.24851	−	4.24851i	0.222989	−	0.222989i
$364$		0			0
$365$	6.08876	+	6.08876i	0.318700	+	0.318700i
$366$	7.06926	−	3.34056i	0.369516	−	0.174614i
$367$	8.50712			0.444068			0.222034	−	0.975039i	$-0.428730\pi$
$367$	8.50712			0.444068			0.222034	+	0.975039i	$0.428730\pi$
$368$	7.57803	−	1.49660i	0.395032	−	0.0780159i
$369$	13.1558			0.684866
$370$	10.3705	−	4.90055i	0.539136	−	0.254767i
$371$		0			0
$372$	−20.5681	+	2.01159i	−1.06641	+	0.104296i
$373$	3.70893	−	3.70893i	0.192041	−	0.192041i	−0.604536	−	0.796577i	$-0.706642\pi$
$373$	3.70893	−	3.70893i	0.192041	−	0.192041i	0.796577	+	0.604536i	$0.206642\pi$
$374$	−3.32622	−	1.19142i	−0.171995	−	0.0616069i
$375$			10.9883i			0.567436i
$376$	−33.0798	−	8.32209i	−1.70596	−	0.429179i
$377$			26.8616i			1.38344i
$378$		0			0
$379$	−3.62966	+	3.62966i	−0.186443	+	0.186443i	−0.794156	−	0.607713i	$-0.792087\pi$
$379$	−3.62966	+	3.62966i	−0.186443	+	0.186443i	0.607713	+	0.794156i	$0.292087\pi$
$380$	−0.125038	+	0.152147i	−0.00641431	+	0.00780498i
$381$	0.843612	+	0.843612i	0.0432195	+	0.0432195i
$382$	−3.67495	−	7.77690i	−0.188027	−	0.397901i
$383$	−6.96253			−0.355769			−0.177884	−	0.984051i	$-0.556925\pi$
$383$	−6.96253			−0.355769			−0.177884	+	0.984051i	$0.556925\pi$
$384$	−10.1353	+	9.14209i	−0.517217	+	0.466530i
$385$		0			0
$386$	−6.07950	−	12.8654i	−0.309438	−	0.654831i
$387$	6.91862	+	6.91862i	0.351693	+	0.351693i
$388$	−20.8286	+	25.3444i	−1.05741	+	1.28667i
$389$	−9.32025	+	9.32025i	−0.472555	+	0.472555i	−0.902741	−	0.430185i	$-0.858448\pi$
$389$	−9.32025	+	9.32025i	−0.472555	+	0.472555i	0.430185	+	0.902741i	$0.358448\pi$
$390$	−2.19618	+	6.13132i	−0.111208	+	0.310471i
$391$			1.96636i			0.0994429i
$392$		0			0
$393$			9.50339i			0.479383i
$394$	18.9861	+	6.80066i	0.956507	+	0.342612i
$395$	−0.622728	+	0.622728i	−0.0313329	+	0.0313329i
$396$	7.54300	−	0.737718i	0.379050	−	0.0370717i
$397$	4.41374	+	4.41374i	0.221519	+	0.221519i	0.809138	−	0.587619i	$-0.199934\pi$
$397$	4.41374	+	4.41374i	0.221519	+	0.221519i	−0.587619	+	0.809138i	$0.699934\pi$
$398$	−14.9091	+	7.04524i	−0.747325	+	0.353146i
$399$		0			0
$400$	15.5739	−	3.07572i	0.778693	−	0.153786i
$401$	−15.9015			−0.794085			−0.397042	−	0.917800i	$-0.629963\pi$
$401$	−15.9015			−0.794085			−0.397042	+	0.917800i	$0.629963\pi$
$402$	−5.40909	+	2.55605i	−0.269781	+	0.127484i
$403$	22.7645	+	22.7645i	1.13398	+	1.13398i
$404$	1.79052	+	18.3077i	0.0890819	+	0.910842i
$405$	−1.42253	+	1.42253i	−0.0706861	+	0.0706861i
$406$		0			0
$407$		−	19.5949i		−	0.971282i
$408$	−1.78325	−	2.98211i	−0.0882843	−	0.147636i
$409$		−	5.70265i		−	0.281978i	−0.990011	−	0.140989i	$-0.954972\pi$
$409$		−	5.70265i		−	0.281978i	0.990011	−	0.140989i	$-0.0450282\pi$
$410$	−4.12520	+	11.5168i	−0.203729	+	0.568772i
$411$	9.43575	−	9.43575i	0.465431	−	0.465431i
$412$	−11.9446	−	9.81634i	−0.588468	−	0.483616i
$413$		0			0
$414$	−1.80214	−	3.81368i	−0.0885704	−	0.187432i
$415$	7.81748			0.383745
$416$	21.0274	+	3.15583i	1.03095	+	0.154727i
$417$	−21.1826			−1.03732
$418$	0.143740	+	0.304181i	0.00703054	+	0.0148780i
$419$	−4.57142	−	4.57142i	−0.223328	−	0.223328i	0.586570	−	0.809898i	$-0.300478\pi$
$419$	−4.57142	−	4.57142i	−0.223328	−	0.223328i	−0.809898	+	0.586570i	$0.800478\pi$
$420$		0			0
$421$	0.421252	−	0.421252i	0.0205306	−	0.0205306i	−0.696767	−	0.717298i	$-0.745379\pi$
$421$	0.421252	−	0.421252i	0.0205306	−	0.0205306i	0.717298	+	0.696767i	$0.245379\pi$
$422$	4.40683	−	12.3030i	0.214521	−	0.598902i
$423$			18.6266i			0.905657i
$424$	3.57347	−	2.13688i	0.173543	−	0.103776i
$425$			4.04112i			0.196023i
$426$	8.72393	+	3.12483i	0.422676	+	0.151399i
$427$		0			0
$428$	−3.67924	−	37.6194i	−0.177843	−	1.81840i
$429$	7.86734	+	7.86734i	0.379839	+	0.379839i
$430$	−8.22606	+	3.88720i	−0.396696	+	0.187457i
$431$	−21.1036			−1.01652			−0.508262	−	0.861202i	$-0.669712\pi$
$431$	−21.1036			−1.01652			−0.508262	+	0.861202i	$0.669712\pi$
$432$	18.2180	+	12.2089i	0.876515	+	0.587402i
$433$	−13.9717			−0.671436			−0.335718	−	0.941962i	$-0.608979\pi$
$433$	−13.9717			−0.671436			−0.335718	+	0.941962i	$0.608979\pi$
$434$		0			0
$435$	−6.19120	−	6.19120i	−0.296845	−	0.296845i
$436$	32.5647	−	3.18488i	1.55957	−	0.152528i
$437$	0.132398	−	0.132398i	0.00633347	−	0.00633347i
$438$	13.6192	+	4.87828i	0.650751	+	0.233093i
$439$			5.41926i			0.258647i	0.991602	+	0.129324i	$0.0412806\pi$
$439$			5.41926i			0.258647i	−0.991602	+	0.129324i	$0.958719\pi$
$440$	−1.71941	+	6.83455i	−0.0819696	+	0.325824i
$441$		0			0
$442$	−1.82525	+	5.09573i	−0.0868181	+	0.242379i
$443$	4.27297	−	4.27297i	0.203015	−	0.203015i	−0.598276	−	0.801290i	$-0.704147\pi$
$443$	4.27297	−	4.27297i	0.203015	−	0.203015i	0.801290	+	0.598276i	$0.204147\pi$
$444$	12.2351	−	14.8877i	0.580650	−	0.706540i
$445$	−3.26000	−	3.26000i	−0.154539	−	0.154539i
$446$	14.0994	+	29.8371i	0.667628	+	1.41283i
$447$	−6.32175			−0.299009
$448$		0			0
$449$	18.4262			0.869587			0.434794	−	0.900530i	$-0.356821\pi$
$449$	18.4262			0.869587			0.434794	+	0.900530i	$0.356821\pi$
$450$	−3.70364	−	7.83761i	−0.174591	−	0.369468i
$451$	14.7776	+	14.7776i	0.695851	+	0.695851i
$452$	25.5431	−	31.0810i	1.20145	−	1.46193i
$453$	−1.16308	+	1.16308i	−0.0546462	+	0.0546462i
$454$	−7.46301	+	20.8353i	−0.350257	+	0.977848i
$455$		0			0
$456$	−0.0807208	+	0.320860i	−0.00378010	+	0.0150257i
$457$		−	35.9724i		−	1.68272i	−0.540478	−	0.841358i	$-0.681757\pi$
$457$		−	35.9724i		−	1.68272i	0.540478	−	0.841358i	$-0.318243\pi$
$458$	−35.6016	−	12.7522i	−1.66356	−	0.595871i
$459$	−3.94761	+	3.94761i	−0.184258	+	0.184258i
$460$	3.90362	−	0.381781i	0.182007	−	0.0178006i
$461$	−0.903879	−	0.903879i	−0.0420978	−	0.0420978i	0.685745	−	0.727842i	$-0.259477\pi$
$461$	−0.903879	−	0.903879i	−0.0420978	−	0.0420978i	−0.727842	+	0.685745i	$0.759477\pi$
$462$		0			0
$463$	−12.5999			−0.585565			−0.292782	−	0.956179i	$-0.594581\pi$
$463$	−12.5999			−0.585565			−0.292782	+	0.956179i	$0.594581\pi$
$464$	−15.9137	+	23.7462i	−0.738775	+	1.10239i
$465$	−10.4937			−0.486636
$466$	−16.3002	+	7.70263i	−0.755094	+	0.356817i
$467$	−5.86130	−	5.86130i	−0.271228	−	0.271228i	0.558366	−	0.829595i	$-0.311428\pi$
$467$	−5.86130	−	5.86130i	−0.271228	−	0.271228i	−0.829595	+	0.558366i	$0.811428\pi$
$468$	−1.13018	−	11.5558i	−0.0522424	−	0.534167i
$469$		0			0
$470$	−16.3059	−	5.84064i	−0.752137	−	0.269409i
$471$			0.383405i			0.0176664i
$472$	−17.4955	+	10.4620i	−0.805294	+	0.481553i
$473$			15.5430i			0.714668i
$474$	−0.498926	+	1.39290i	−0.0229164	+	0.0639782i
$475$	0.272096	−	0.272096i	0.0124846	−	0.0124846i
$476$		0			0
$477$	−1.60770	−	1.60770i	−0.0736114	−	0.0736114i
$478$	−9.04443	−	19.1397i	−0.413683	−	0.875432i
$479$	9.27836			0.423939			0.211969	−	0.977276i	$-0.432012\pi$
$479$	9.27836			0.423939			0.211969	+	0.977276i	$0.432012\pi$
$480$	−5.57386	+	4.11912i	−0.254411	+	0.188011i
$481$	−30.0192			−1.36876
$482$	−11.9699	−	25.3305i	−0.545212	−	1.15377i
$483$		0			0
$484$	−7.69517	−	6.32407i	−0.349781	−	0.287458i
$485$	−11.7786	+	11.7786i	−0.534841	+	0.534841i
$486$	6.70415	−	18.7167i	0.304106	−	0.849006i
$487$			38.6868i			1.75307i	0.481342	+	0.876533i	$0.340149\pi$
$487$			38.6868i			1.75307i	−0.481342	+	0.876533i	$0.659851\pi$
$488$	−6.65231	−	11.1245i	−0.301136	−	0.503584i
$489$			17.9076i			0.809810i
$490$		0			0
$491$	−29.8086	+	29.8086i	−1.34524	+	1.34524i	−0.454494	+	0.890750i	$0.650180\pi$
$491$	−29.8086	+	29.8086i	−1.34524	+	1.34524i	−0.890750	+	0.454494i	$0.849820\pi$
$492$	2.00052	+	20.4548i	0.0901903	+	0.922175i
$493$	−5.14550	−	5.14550i	−0.231742	−	0.231742i
$494$	0.466002	−	0.220208i	0.0209664	−	0.00990761i
$495$	3.84841			0.172973
$496$	6.63786	+	33.6107i	0.298049	+	1.50917i
$497$		0			0
$498$	11.8746	−	5.61132i	0.532115	−	0.251449i
$499$	−7.90565	−	7.90565i	−0.353905	−	0.353905i	0.507655	−	0.861560i	$-0.330512\pi$
$499$	−7.90565	−	7.90565i	−0.353905	−	0.353905i	−0.861560	+	0.507655i	$0.830512\pi$
$500$	18.1297	−	1.77311i	0.810784	−	0.0792961i
$501$	12.4537	−	12.4537i	0.556392	−	0.556392i
$502$	−17.3970	−	6.23144i	−0.776464	−	0.278123i
$503$		−	18.1532i		−	0.809409i	−0.914448	−	0.404704i	$-0.867374\pi$
$503$		−	18.1532i		−	0.809409i	0.914448	−	0.404704i	$-0.132626\pi$
$504$		0			0
$505$			9.34050i			0.415647i
$506$	2.25951	−	6.30810i	0.100447	−	0.280429i
$507$	0.962635	−	0.962635i	0.0427521	−	0.0427521i
$508$	1.25575	−	1.52800i	0.0557148	−	0.0677942i
$509$	1.44869	+	1.44869i	0.0642121	+	0.0642121i	0.738484	−	0.674271i	$-0.235542\pi$
$509$	1.44869	+	1.44869i	0.0642121	+	0.0642121i	−0.674271	+	0.738484i	$0.735542\pi$
$510$	−0.753798	−	1.59518i	−0.0333787	−	0.0706358i
$511$		0			0
$512$	16.7190	+	15.2471i	0.738883	+	0.673834i
$513$	0.531599			0.0234707
$514$	−14.0311	−	29.6924i	−0.618884	−	1.30968i
$515$	−5.55117	−	5.55117i	−0.244614	−	0.244614i
$516$	−9.70507	+	11.8092i	−0.427242	+	0.519871i
$517$	−20.9228	+	20.9228i	−0.920183	+	0.920183i
$518$		0			0
$519$			14.9004i			0.654053i
$520$	10.4705	+	2.63412i	0.459160	+	0.115514i
$521$			2.90874i			0.127434i	0.997968	+	0.0637172i	$0.0202956\pi$
$521$			2.90874i			0.127434i	−0.997968	+	0.0637172i	$0.979704\pi$
$522$	14.6953	+	5.26373i	0.643196	+	0.230387i
$523$	11.7145	−	11.7145i	0.512240	−	0.512240i	−0.402972	−	0.915212i	$-0.632023\pi$
$523$	11.7145	−	11.7145i	0.512240	−	0.512240i	0.915212	+	0.402972i	$0.132023\pi$
$524$	15.6797	−	1.53350i	0.684969	−	0.0669911i
$525$		0			0
$526$	5.77962	−	2.73114i	0.252003	−	0.119083i
$527$	−8.72134			−0.379908
$528$	2.29402	+	11.6158i	0.0998346	+	0.505511i
$529$	19.2708			0.837863
$530$	1.91151	−	0.903279i	0.0830308	−	0.0392359i
$531$	7.87117	+	7.87117i	0.341580	+	0.341580i
$532$		0			0
$533$	22.6392	−	22.6392i	0.980611	−	0.980611i
$534$	−7.29190	−	2.61189i	−0.315552	−	0.113028i
$535$		−	19.1933i		−	0.829797i
$536$	5.09006	+	8.51201i	0.219857	+	0.367663i
$537$			0.569066i			0.0245570i
$538$	0.190258	−	0.531165i	0.00820262	−	0.0229001i
$539$		0			0
$540$	8.60326	+	7.07035i	0.370225	+	0.304260i
$541$	5.13565	+	5.13565i	0.220799	+	0.220799i	0.808835	−	0.588036i	$-0.200099\pi$
$541$	5.13565	+	5.13565i	0.220799	+	0.220799i	−0.588036	+	0.808835i	$0.700099\pi$
$542$	−6.41780	−	13.5813i	−0.275668	−	0.583367i
$543$	−26.3864			−1.13235
$544$	−4.63243	+	3.42340i	−0.198614	+	0.146777i
$545$	16.6144			0.711682
$546$		0			0
$547$	18.2712	+	18.2712i	0.781218	+	0.781218i	0.980036	−	0.198818i	$-0.0637103\pi$
$547$	18.2712	+	18.2712i	0.781218	+	0.781218i	−0.198818	+	0.980036i	$0.563710\pi$
$548$	−17.0906	−	14.0455i	−0.730076	−	0.599993i
$549$	−5.00491	+	5.00491i	−0.213604	+	0.213604i
$550$	4.64358	−	12.9640i	0.198003	−	0.552786i
$551$			0.692912i			0.0295190i
$552$	5.65550	−	3.38190i	0.240714	−	0.143943i
$553$		0			0
$554$	15.3299	+	5.49103i	0.651305	+	0.233291i
$555$	6.91896	−	6.91896i	0.293694	−	0.293694i
$556$	3.41809	+	34.9492i	0.144960	+	1.48218i
$557$	3.50389	+	3.50389i	0.148465	+	0.148465i	0.777432	−	0.628967i	$-0.216522\pi$
$557$	3.50389	+	3.50389i	0.148465	+	0.148465i	−0.628967	+	0.777432i	$0.716522\pi$
$558$	16.9147	−	7.99300i	0.716058	−	0.338371i
$559$	23.8117			1.00713
$560$		0			0
$561$	−3.01407			−0.127254
$562$	−23.8288	+	11.2602i	−1.00516	+	0.474983i
$563$	−17.1928	−	17.1928i	−0.724591	−	0.724591i	0.244946	−	0.969537i	$-0.421230\pi$
$563$	−17.1928	−	17.1928i	−0.724591	−	0.724591i	−0.969537	+	0.244946i	$0.921230\pi$
$564$	−28.9608	+	2.83242i	−1.21947	+	0.119266i
$565$	14.4447	−	14.4447i	0.607693	−	0.607693i
$566$	−12.1000	−	4.33410i	−0.508600	−	0.182176i
$567$		0			0
$568$	3.74795	−	14.8979i	0.157260	−	0.625100i
$569$			2.70044i			0.113208i	0.998397	+	0.0566041i	$0.0180273\pi$
$569$			2.70044i			0.113208i	−0.998397	+	0.0566041i	$0.981973\pi$
$570$	−0.0566518	+	0.158161i	−0.00237288	+	0.00662463i
$571$	−9.38460	+	9.38460i	−0.392733	+	0.392733i	−0.875660	−	0.482927i	$-0.839574\pi$
$571$	−9.38460	+	9.38460i	−0.392733	+	0.392733i	0.482927	+	0.875660i	$0.339574\pi$
$572$	11.7108	−	14.2498i	0.489654	−	0.595815i
$573$	−5.18857	−	5.18857i	−0.216756	−	0.216756i
$574$		0			0
$575$	−7.66390			−0.319607
$576$	5.84693	−	10.8851i	0.243622	−	0.453547i
$577$	−24.8922			−1.03627			−0.518137	−	0.855298i	$-0.673374\pi$
$577$	−24.8922			−1.03627			−0.518137	+	0.855298i	$0.673374\pi$
$578$	9.64522	+	20.4111i	0.401188	+	0.848991i
$579$	−8.58350	−	8.58350i	−0.356718	−	0.356718i
$580$	−9.21584	+	11.2139i	−0.382667	+	0.465632i
$581$		0			0
$582$	−9.43697	+	26.3462i	−0.391175	+	1.09209i
$583$		−	3.61177i		−	0.149584i
$584$	5.85104	−	23.2575i	0.242118	−	0.962403i
$585$		−	5.89572i		−	0.243758i
$586$	22.6306	+	8.10608i	0.934862	+	0.334859i
$587$	23.9315	−	23.9315i	0.987758	−	0.987758i	−0.0121684	−	0.999926i	$-0.503873\pi$
$587$	23.9315	−	23.9315i	0.987758	−	0.987758i	0.999926	+	0.0121684i	$0.00387340\pi$
$588$		0			0
$589$	0.587224	+	0.587224i	0.0241961	+	0.0241961i
$590$	−9.35862	+	4.42239i	−0.385288	+	0.182067i
$591$	17.2044			0.707692
$592$	−26.5376	−	17.7843i	−1.09069	−	0.730931i
$593$	1.79017			0.0735134			0.0367567	−	0.999324i	$-0.488297\pi$
$593$	1.79017			0.0735134			0.0367567	+	0.999324i	$0.488297\pi$
$594$	17.2001	−	8.12786i	0.705729	−	0.333490i
$595$		0			0
$596$	1.02010	+	10.4303i	0.0417849	+	0.427241i
$597$	−9.94701	+	9.94701i	−0.407104	+	0.407104i
$598$	−9.66394	−	3.46154i	−0.395188	−	0.141553i
$599$		−	43.1613i		−	1.76352i	−0.471696	−	0.881761i	$-0.656358\pi$
$599$		−	43.1613i		−	1.76352i	0.471696	−	0.881761i	$-0.343642\pi$
$600$	11.6228	−	6.95026i	0.474499	−	0.283743i
$601$		−	27.6564i		−	1.12813i	−0.825730	−	0.564065i	$-0.809237\pi$
$601$		−	27.6564i		−	1.12813i	0.825730	−	0.564065i	$-0.190763\pi$
$602$		0			0
$603$	3.82954	−	3.82954i	0.155951	−	0.155951i
$604$	2.10664	+	1.73129i	0.0857180	+	0.0704450i
$605$	−3.57628	−	3.57628i	−0.145396	−	0.145396i
$606$	6.70454	+	14.1881i	0.272353	+	0.576352i
$607$	−21.5936			−0.876455			−0.438228	−	0.898864i	$-0.644394\pi$
$607$	−21.5936			−0.876455			−0.438228	+	0.898864i	$0.644394\pi$
$608$	0.542413	+	0.0814064i	0.0219978	+	0.00330147i
$609$		0			0
$610$	−2.81199	−	5.95071i	−0.113854	−	0.240937i
$611$	32.0535	+	32.0535i	1.29675	+	1.29675i
$612$	2.43007	+	1.99709i	0.0982298	+	0.0807275i
$613$	−7.01823	+	7.01823i	−0.283464	+	0.283464i	−0.834489	−	0.551025i	$-0.814237\pi$
$613$	−7.01823	+	7.01823i	−0.283464	+	0.283464i	0.551025	+	0.834489i	$0.314237\pi$
$614$	12.0276	−	33.5787i	0.485395	−	1.35513i
$615$			10.4360i			0.420819i
$616$		0			0
$617$		−	14.2458i		−	0.573515i	−0.958003	−	0.286758i	$-0.907423\pi$
$617$		−	14.2458i		−	0.573515i	0.958003	−	0.286758i	$-0.0925774\pi$
$618$	−12.4167	−	4.44756i	−0.499474	−	0.178907i
$619$	25.8337	−	25.8337i	1.03834	−	1.03834i	0.0391090	−	0.999235i	$-0.487548\pi$
$619$	25.8337	−	25.8337i	1.03834	−	1.03834i	0.999235	−	0.0391090i	$-0.0124519\pi$
$620$	1.69330	+	17.3137i	0.0680048	+	0.695333i
$621$	−7.48655	−	7.48655i	−0.300425	−	0.300425i
$622$	8.36817	−	3.95435i	0.335533	−	0.158555i
$623$		0			0
$624$	17.7952	−	3.51442i	0.712379	−	0.140689i
$625$	−10.5936			−0.423746
$626$	24.5159	−	11.5849i	0.979853	−	0.463026i
$627$	0.202943	+	0.202943i	0.00810475	+	0.00810475i
$628$	0.632580	−	0.0618674i	0.0252427	−	0.00246878i
$629$	5.75034	−	5.75034i	0.229281	−	0.229281i
$630$		0			0
$631$			4.87006i			0.193874i	0.995291	+	0.0969370i	$0.0309045\pi$
$631$			4.87006i			0.193874i	−0.995291	+	0.0969370i	$0.969095\pi$
$632$	2.37866	+	0.598415i	0.0946182	+	0.0238037i
$633$		−	11.1484i		−	0.443111i
$634$	8.97537	−	25.0575i	0.356458	−	0.995160i
$635$	0.710129	−	0.710129i	0.0281806	−	0.0281806i
$636$	2.25519	−	2.74414i	0.0894242	−	0.108812i
$637$		0			0
$638$	10.5942	+	22.4195i	0.419430	+	0.887595i
$639$	−8.38871			−0.331852
$640$	7.69556	+	8.53165i	0.304194	+	0.337243i
$641$	34.3879			1.35824			0.679120	−	0.734027i	$-0.262362\pi$
$641$	34.3879			1.35824			0.679120	+	0.734027i	$0.262362\pi$
$642$	−13.7768	−	29.1543i	−0.543726	−	1.15063i
$643$	−11.9018	−	11.9018i	−0.469361	−	0.469361i	0.432346	−	0.901708i	$-0.357686\pi$
$643$	−11.9018	−	11.9018i	−0.469361	−	0.469361i	−0.901708	+	0.432346i	$0.857686\pi$
$644$		0			0
$645$	−5.48825	+	5.48825i	−0.216099	+	0.216099i
$646$	−0.0470833	+	0.131447i	−0.00185247	+	0.00517173i
$647$			5.26762i			0.207092i	0.994625	+	0.103546i	$0.0330188\pi$
$647$			5.26762i			0.207092i	−0.994625	+	0.103546i	$0.966981\pi$
$648$	5.43370	+	1.36699i	0.213456	+	0.0537005i
$649$			17.6830i			0.694117i
$650$	−19.8607	−	7.11392i	−0.779000	−	0.279031i
$651$		0			0
$652$	29.5458	−	2.88963i	1.15710	−	0.113167i
$653$	−24.2555	−	24.2555i	−0.949190	−	0.949190i	0.0495806	−	0.998770i	$-0.484212\pi$
$653$	−24.2555	−	24.2555i	−0.949190	−	0.949190i	−0.998770	+	0.0495806i	$0.984212\pi$
$654$	25.2370	−	11.9257i	0.986845	−	0.466330i
$655$	7.99969			0.312574
$656$	33.4257	−	6.60131i	1.30505	−	0.257738i
$657$	−13.0959			−0.510919
$658$		0			0
$659$	−14.4817	−	14.4817i	−0.564126	−	0.564126i	0.366351	−	0.930477i	$-0.380607\pi$
$659$	−14.4817	−	14.4817i	−0.564126	−	0.564126i	−0.930477	+	0.366351i	$0.880607\pi$
$660$	0.585200	+	5.98354i	0.0227789	+	0.232909i
$661$	−11.2258	+	11.2258i	−0.436633	+	0.436633i	−0.890877	−	0.454244i	$-0.849909\pi$
$661$	−11.2258	+	11.2258i	−0.436633	+	0.436633i	0.454244	+	0.890877i	$0.349909\pi$
$662$	−13.0390	−	4.67044i	−0.506774	−	0.181522i
$663$			4.61752i			0.179330i
$664$	−11.1743	−	18.6865i	−0.433646	−	0.725178i
$665$		0			0
$666$	−5.88246	+	16.4227i	−0.227941	+	0.636367i
$667$	9.75833	−	9.75833i	0.377844	−	0.377844i
$668$	−22.5570	−	18.5379i	−0.872758	−	0.717252i
$669$	19.9067	+	19.9067i	0.769636	+	0.769636i
$670$	2.15161	+	4.55322i	0.0831240	+	0.175906i
$671$	−11.2438			−0.434061
$672$		0			0
$673$	−8.09831			−0.312167			−0.156083	−	0.987744i	$-0.549887\pi$
$673$	−8.09831			−0.312167			−0.156083	+	0.987744i	$0.549887\pi$
$674$	−2.97033	−	6.28580i	−0.114413	−	0.242120i
$675$	−15.3858	−	15.3858i	−0.592201	−	0.592201i
$676$	−1.74359	−	1.43292i	−0.0670611	−	0.0551123i
$677$	−16.0136	+	16.0136i	−0.615452	+	0.615452i	−0.944362	−	0.328909i	$-0.893319\pi$
$677$	−16.0136	+	16.0136i	−0.615452	+	0.615452i	0.328909	+	0.944362i	$0.393319\pi$
$678$	11.5730	−	32.3095i	0.444458	−	1.24084i
$679$		0			0
$680$	−2.51026	+	1.50110i	−0.0962639	+	0.0575644i
$681$			18.8800i			0.723483i
$682$	27.9782	+	10.0215i	1.07134	+	0.383745i
$683$	26.9423	−	26.9423i	1.03092	−	1.03092i	0.0314113	−	0.999507i	$-0.490000\pi$
$683$	26.9423	−	26.9423i	1.03092	−	1.03092i	0.999507	−	0.0314113i	$-0.0100002\pi$
$684$	−0.0291536	−	0.298089i	−0.00111472	−	0.0113977i
$685$	−7.94275	−	7.94275i	−0.303477	−	0.303477i
$686$		0			0
$687$	−32.2606			−1.23082
$688$	21.0501	+	14.1068i	0.802526	+	0.537818i
$689$	−5.53319			−0.210798
$690$	3.02523	−	1.42956i	0.115168	−	0.0544225i
$691$	17.4925	+	17.4925i	0.665447	+	0.665447i	0.956659	−	0.291211i	$-0.0940583\pi$
$691$	17.4925	+	17.4925i	0.665447	+	0.665447i	−0.291211	+	0.956659i	$0.594058\pi$
$692$	24.5841	−	2.40437i	0.934548	−	0.0914004i
$693$		0			0
$694$	−12.4525	−	4.46038i	−0.472691	−	0.169314i
$695$			17.8309i			0.676366i
$696$	−5.94948	+	23.6488i	−0.225514	+	0.896406i
$697$			8.67332i			0.328525i
$698$	−11.6042	+	32.3966i	−0.439225	+	1.22623i
$699$	−10.8752	+	10.8752i	−0.411336	+	0.411336i
$700$		0			0
$701$	−10.6300	−	10.6300i	−0.401489	−	0.401489i	0.477269	−	0.878757i	$-0.341627\pi$
$701$	−10.6300	−	10.6300i	−0.401489	−	0.401489i	−0.878757	+	0.477269i	$0.841627\pi$
$702$	−12.4518	−	26.3504i	−0.469963	−	0.994531i
$703$	−0.774362			−0.0292056
$704$	18.7947	−	5.65927i	0.708351	−	0.213292i
$705$	−14.7757			−0.556485
$706$	4.93612	+	10.4458i	0.185773	+	0.393132i
$707$		0			0
$708$	−11.0413	+	13.4351i	−0.414956	+	0.504921i
$709$	−2.50496	+	2.50496i	−0.0940757	+	0.0940757i	−0.752578	−	0.658503i	$-0.771190\pi$
$709$	−2.50496	+	2.50496i	−0.0940757	+	0.0940757i	0.658503	+	0.752578i	$0.271190\pi$
$710$	2.63040	−	7.34357i	0.0987172	−	0.275599i
$711$		−	1.33938i		−	0.0502308i
$712$	−3.13272	+	12.4524i	−0.117404	+	0.466673i
$713$		−	16.5398i		−	0.619422i
$714$		0			0
$715$	6.62251	−	6.62251i	0.247668	−	0.247668i
$716$	0.938903	−	0.0918263i	0.0350884	−	0.00343171i
$717$	−12.7696	−	12.7696i	−0.476890	−	0.476890i
$718$	−14.7930	+	6.99037i	−0.552069	+	0.260878i
$719$	16.2120			0.604604			0.302302	−	0.953212i	$-0.402245\pi$
$719$	16.2120			0.604604			0.302302	+	0.953212i	$0.402245\pi$
$720$	3.49282	−	5.21194i	0.130170	−	0.194237i
$721$		0			0
$722$	−24.2821	+	11.4745i	−0.903688	+	0.427035i
$723$	−16.9000	−	16.9000i	−0.628516	−	0.628516i
$724$	4.25779	+	43.5350i	0.158240	+	1.61796i
$725$	20.0547	−	20.0547i	0.744811	−	0.744811i
$726$	−7.99934	−	2.86529i	−0.296883	−	0.106341i
$727$		−	14.2822i		−	0.529699i	−0.964290	−	0.264849i	$-0.914678\pi$
$727$		−	14.2822i		−	0.529699i	0.964290	−	0.264849i	$-0.0853223\pi$
$728$		0			0
$729$		−	22.9031i		−	0.848263i
$730$	4.10640	−	11.4643i	0.151985	−	0.424312i
$731$	−4.56127	+	4.56127i	−0.168705	+	0.168705i
$732$	−8.54274	−	7.02062i	−0.315749	−	0.259489i
$733$	−24.3482	−	24.3482i	−0.899322	−	0.899322i	0.0960545	−	0.995376i	$-0.469378\pi$
$733$	−24.3482	−	24.3482i	−0.899322	−	0.899322i	−0.995376	+	0.0960545i	$0.969378\pi$
$734$	−5.14015	−	10.8775i	−0.189726	−	0.401497i
$735$		0			0
$736$	−6.49240	−	8.78531i	−0.239313	−	0.323831i
$737$	8.60324			0.316904
$738$	−7.94899	−	16.8216i	−0.292606	−	0.619211i
$739$	−14.7533	−	14.7533i	−0.542710	−	0.542710i	0.381612	−	0.924322i	$-0.375369\pi$
$739$	−14.7533	−	14.7533i	−0.542710	−	0.542710i	−0.924322	+	0.381612i	$0.875369\pi$
$740$	−12.5321	−	10.2991i	−0.460688	−	0.378604i
$741$	0.310906	−	0.310906i	0.0114214	−	0.0114214i
$742$		0			0
$743$			30.1201i			1.10500i	0.833513	+	0.552500i	$0.186326\pi$
$743$			30.1201i			1.10500i	−0.833513	+	0.552500i	$0.813674\pi$
$744$	14.9997	+	25.0837i	0.549916	+	0.919615i
$745$			5.32148i			0.194964i
$746$	−6.98339	−	2.50139i	−0.255680	−	0.0915823i
$747$	−8.40703	+	8.40703i	−0.307597	+	0.307597i
$748$	0.486359	+	4.97291i	0.0177831	+	0.181828i
$749$		0			0
$750$	14.0501	−	6.63935i	0.513039	−	0.242435i
$751$	45.2186			1.65005			0.825026	−	0.565095i	$-0.191161\pi$
$751$	45.2186			1.65005			0.825026	+	0.565095i	$0.191161\pi$
$752$	9.34643	+	47.3255i	0.340829	+	1.72578i
$753$	−15.7643			−0.574484
$754$	34.3464	−	16.2303i	1.25082	−	0.591072i
$755$	0.979047	+	0.979047i	0.0356312	+	0.0356312i
$756$		0			0
$757$	−10.1353	+	10.1353i	−0.368375	+	0.368375i	−0.866884	−	0.498509i	$-0.833881\pi$
$757$	−10.1353	+	10.1353i	−0.368375	+	0.368375i	0.498509	+	0.866884i	$0.333881\pi$
$758$	6.83414	+	2.44793i	0.248227	+	0.0889127i
$759$		−	5.71611i		−	0.207482i
$760$	0.270091	+	0.0679486i	0.00979725	+	0.00246475i
$761$		−	19.7273i		−	0.715113i	−0.933892	−	0.357556i	$-0.883610\pi$
$761$		−	19.7273i		−	0.715113i	0.933892	−	0.357556i	$-0.116390\pi$
$762$	0.568951	−	1.58840i	0.0206109	−	0.0575417i
$763$		0			0
$764$	−7.72339	+	9.39788i	−0.279422	+	0.340003i
$765$	1.12936	+	1.12936i	0.0408321	+	0.0408321i
$766$	4.20688	+	8.90257i	0.152001	+	0.321663i
$767$	27.0901			0.978167
$768$	17.8134	+	7.43564i	0.642785	+	0.268311i
$769$	−41.2736			−1.48837			−0.744183	−	0.667976i	$-0.767161\pi$
$769$	−41.2736			−1.48837			−0.744183	+	0.667976i	$0.767161\pi$
$770$		0			0
$771$	−19.8101	−	19.8101i	−0.713444	−	0.713444i
$772$	−12.7769	+	15.5470i	−0.459849	+	0.559548i
$773$	−37.7572	+	37.7572i	−1.35803	+	1.35803i	−0.481689	+	0.876342i	$0.659977\pi$
$773$	−37.7572	+	37.7572i	−1.35803	+	1.35803i	−0.876342	+	0.481689i	$0.840023\pi$
$774$	4.66608	−	13.0268i	0.167719	−	0.468238i
$775$		−	33.9915i		−	1.22101i
$776$	44.9914	+	11.3188i	1.61510	+	0.406320i
$777$		0			0
$778$	17.5487	+	6.28579i	0.629152	+	0.225356i
$779$	0.583990	−	0.583990i	0.0209236	−	0.0209236i
$780$	9.16672	−	0.896521i	0.328221	−	0.0321006i
$781$	−9.42282	−	9.42282i	−0.337175	−	0.337175i
$782$	2.51426	−	1.18811i	0.0899098	−	0.0424866i
$783$	39.1812			1.40022
$784$		0			0
$785$	0.322740			0.0115191
$786$	12.1514	−	5.74212i	0.433427	−	0.204814i
$787$	−0.361908	−	0.361908i	−0.0129006	−	0.0129006i	0.700627	−	0.713528i	$-0.252904\pi$
$787$	−0.361908	−	0.361908i	−0.0129006	−	0.0129006i	−0.713528	+	0.700627i	$0.752904\pi$
$788$	−2.77615	−	28.3855i	−0.0988962	−	1.01119i
$789$	3.85603	−	3.85603i	0.137278	−	0.137278i
$790$	1.17251	+	0.419982i	0.0417160	+	0.0149423i
$791$		0			0
$792$	−5.50089	−	9.19905i	−0.195466	−	0.326874i
$793$			17.2253i			0.611689i
$794$	2.97673	−	8.31045i	0.105640	−	0.294927i
$795$	1.27532	−	1.27532i	0.0452309	−	0.0452309i
$796$	18.0167	+	14.8065i	0.638584	+	0.524803i
$797$	35.5605	+	35.5605i	1.25962	+	1.25962i	0.951276	+	0.308341i	$0.0997736\pi$
$797$	35.5605	+	35.5605i	1.25962	+	1.25962i	0.308341	+	0.951276i	$0.400226\pi$
$798$		0			0
$799$	−12.2801			−0.434438
$800$	−13.3427	−	18.0550i	−0.471737	−	0.638339i
$801$	7.01171			0.247747
$802$	9.60798	+	20.3323i	0.339270	+	0.717960i
$803$	−14.7103	−	14.7103i	−0.519114	−	0.519114i
$804$	6.53653	+	5.37187i	0.230526	+	0.189451i
$805$		0			0
$806$	15.3529	−	42.8623i	0.540783	−	1.50976i
$807$		−	0.481317i		−	0.0169432i
$808$	22.3271	−	13.3513i	0.785464	−	0.469696i
$809$			1.36026i			0.0478243i	0.999714	+	0.0239121i	$0.00761220\pi$
$809$			1.36026i			0.0478243i	−0.999714	+	0.0239121i	$0.992388\pi$
$810$	2.67842	+	0.959387i	0.0941102	+	0.0337094i
$811$	12.4370	−	12.4370i	0.436722	−	0.436722i	−0.454186	−	0.890907i	$-0.650070\pi$
$811$	12.4370	−	12.4370i	0.436722	−	0.436722i	0.890907	+	0.454186i	$0.150070\pi$
$812$		0			0
$813$	−9.06114	−	9.06114i	−0.317788	−	0.317788i
$814$	−25.0548	+	11.8396i	−0.878171	+	0.414977i
$815$	15.0741			0.528024
$816$	−2.73557	+	4.08198i	−0.0957640	+	0.142898i
$817$	0.614238			0.0214895
$818$	−7.29164	+	3.44564i	−0.254946	+	0.120474i
$819$		0			0
$820$	17.2183	−	1.68398i	0.601290	−	0.0588072i
$821$	−3.90598	+	3.90598i	−0.136320	+	0.136320i	−0.771974	−	0.635654i	$-0.780730\pi$
$821$	−3.90598	+	3.90598i	−0.136320	+	0.136320i	0.635654	+	0.771974i	$0.280730\pi$
$822$	−17.7662	−	6.36368i	−0.619666	−	0.221959i
$823$		−	19.0620i		−	0.664460i	−0.943198	−	0.332230i	$-0.892199\pi$
$823$		−	19.0620i		−	0.664460i	0.943198	−	0.332230i	$-0.107801\pi$
$824$	−5.33444	+	21.2041i	−0.185834	+	0.738678i
$825$		−	11.7474i		−	0.408991i
$826$		0			0
$827$	3.94521	−	3.94521i	0.137188	−	0.137188i	−0.635178	−	0.772366i	$-0.719073\pi$
$827$	3.94521	−	3.94521i	0.137188	−	0.137188i	0.772366	+	0.635178i	$0.219073\pi$
$828$	−3.78744	+	4.60858i	−0.131622	+	0.160159i
$829$	−18.9628	−	18.9628i	−0.658604	−	0.658604i	0.296446	−	0.955050i	$-0.404199\pi$
$829$	−18.9628	−	18.9628i	−0.658604	−	0.658604i	−0.955050	+	0.296446i	$0.904199\pi$
$830$	−4.72346	−	9.99575i	−0.163954	−	0.346957i
$831$	13.8912			0.481882
$832$	−8.66994	−	28.7932i	−0.300576	−	0.998226i
$833$		0			0
$834$	12.7989	+	27.0850i	0.443190	+	0.937875i
$835$	−10.4832	−	10.4832i	−0.362787	−	0.362787i
$836$	0.302088	−	0.367583i	0.0104479	−	0.0127131i
$837$	33.2050	−	33.2050i	1.14773	−	1.14773i
$838$	−3.08307	+	8.60733i	−0.106503	+	0.297335i
$839$			5.34140i			0.184406i	0.995740	+	0.0922028i	$0.0293908\pi$
$839$			5.34140i			0.184406i	−0.995740	+	0.0922028i	$0.970609\pi$
$840$		0			0
$841$			22.0706i			0.761056i
$842$	−0.793158	−	0.284102i	−0.0273340	−	0.00979081i
$843$	−15.8980	+	15.8980i	−0.547557	+	0.547557i
$844$	−18.3938	+	1.79895i	−0.633142	+	0.0619223i
$845$	−0.810320	−	0.810320i	−0.0278759	−	0.0278759i
$846$	23.8167	−	11.2545i	0.818837	−	0.386939i
$847$		0			0
$848$	−4.89146	−	3.27804i	−0.167973	−	0.112568i
$849$	−10.9644			−0.376299
$850$	5.16714	−	2.44171i	0.177231	−	0.0837501i
$851$	10.9054	+	10.9054i	0.373832	+	0.373832i
$852$	−1.27561	−	13.0429i	−0.0437018	−	0.446841i
$853$	1.42841	−	1.42841i	0.0489078	−	0.0489078i	−0.682230	−	0.731138i	$-0.738990\pi$
$853$	1.42841	−	1.42841i	0.0489078	−	0.0489078i	0.731138	+	0.682230i	$0.238990\pi$
$854$		0			0
$855$		−	0.152084i		−	0.00520115i
$856$	−45.8786	+	27.4347i	−1.56810	+	0.937700i
$857$			25.5816i			0.873852i	0.899498	+	0.436926i	$0.143933\pi$
$857$			25.5816i			0.873852i	−0.899498	+	0.436926i	$0.856067\pi$
$858$	5.30591	−	14.8131i	0.181141	−	0.505710i
$859$	−32.2295	+	32.2295i	−1.09966	+	1.09966i	−0.105207	+	0.994450i	$0.533551\pi$
$859$	−32.2295	+	32.2295i	−1.09966	+	1.09966i	−0.994450	+	0.105207i	$0.966449\pi$
$860$	9.94066	+	8.16946i	0.338974	+	0.278576i
$861$		0			0
$862$	12.7512	+	26.9839i	0.434306	+	0.919075i
$863$	39.4446			1.34271			0.671356	−	0.741135i	$-0.265712\pi$
$863$	39.4446			1.34271			0.671356	+	0.741135i	$0.265712\pi$
$864$	4.60318	−	30.6711i	0.156603	−	1.04345i
$865$	12.5427			0.426465
$866$	8.44194	+	17.8648i	0.286869	+	0.607069i
$867$	13.6178	+	13.6178i	0.462486	+	0.462486i
$868$		0			0
$869$	1.50449	−	1.50449i	0.0510364	−	0.0510364i
$870$	−4.17549	+	11.6572i	−0.141562	+	0.395215i
$871$		−	13.1801i		−	0.446590i
$872$	−23.7485	−	39.7142i	−0.804225	−	1.34489i
$873$		−	25.3338i		−	0.857421i
$874$	−0.249287	−	0.0892924i	−0.00843226	−	0.00302036i
$875$		0			0
$876$	−1.99140	−	20.3616i	−0.0672832	−	0.687955i
$877$	−7.45394	−	7.45394i	−0.251702	−	0.251702i	0.569966	−	0.821668i	$-0.306956\pi$
$877$	−7.45394	−	7.45394i	−0.251702	−	0.251702i	−0.821668	+	0.569966i	$0.806956\pi$
$878$	6.92928	−	3.27441i	0.233852	−	0.110506i
$879$	20.5068			0.691678
$880$	9.77782	−	1.93105i	0.329610	−	0.0650955i
$881$	−15.4426			−0.520274			−0.260137	−	0.965572i	$-0.583768\pi$
$881$	−15.4426			−0.520274			−0.260137	+	0.965572i	$0.583768\pi$
$882$		0			0
$883$	10.0224	+	10.0224i	0.337280	+	0.337280i	0.855343	−	0.518063i	$-0.173347\pi$
$883$	10.0224	+	10.0224i	0.337280	+	0.337280i	−0.518063	+	0.855343i	$0.673347\pi$
$884$	7.61845	−	0.745098i	0.256236	−	0.0250603i
$885$	−6.24386	+	6.24386i	−0.209885	+	0.209885i
$886$	−8.04539	−	2.88179i	−0.270290	−	0.0968155i
$887$		−	43.7662i		−	1.46953i	−0.678324	−	0.734763i	$-0.737293\pi$
$887$		−	43.7662i		−	1.46953i	0.678324	−	0.734763i	$-0.262707\pi$
$888$	−26.4287	−	6.64883i	−0.886888	−	0.223120i
$889$		0			0
$890$	−2.19862	+	6.13812i	−0.0736979	+	0.205750i
$891$	3.43679	−	3.43679i	0.115137	−	0.115137i
$892$	29.6318	−	36.0562i	0.992147	−	1.20725i
$893$	0.826839	+	0.826839i	0.0276691	+	0.0276691i
$894$	3.81971	+	8.08325i	0.127750	+	0.270344i
$895$	0.479024			0.0160120
$896$		0			0
$897$	−8.75703			−0.292389
$898$	−11.1334	−	23.5605i	−0.371528	−	0.786225i
$899$	43.2810	+	43.2810i	1.44350	+	1.44350i
$900$	−7.78368	+	9.47124i	−0.259456	+	0.315708i
$901$	1.05992	−	1.05992i	0.0353109	−	0.0353109i
$902$	9.96636	−	27.8242i	0.331844	−	0.926443i
$903$		0			0
$904$	−55.1750	−	13.8807i	−1.83509	−	0.461666i
$905$			22.2113i			0.738330i
$906$	2.18991	+	0.784406i	0.0727549	+	0.0260602i
$907$	−34.3143	+	34.3143i	−1.13939	+	1.13939i	−0.150829	+	0.988560i	$0.548194\pi$
$907$	−34.3143	+	34.3143i	−1.13939	+	1.13939i	−0.988560	+	0.150829i	$0.951806\pi$
$908$	31.1501	−	3.04653i	1.03375	−	0.101103i
$909$	−10.0449	−	10.0449i	−0.333169	−	0.333169i
$910$		0			0
$911$	−35.2525			−1.16797			−0.583983	−	0.811766i	$-0.698507\pi$
$911$	−35.2525			−1.16797			−0.583983	+	0.811766i	$0.698507\pi$
$912$	0.459038	−	0.0906565i	0.0152003	−	0.00300194i
$913$	−18.8868			−0.625062
$914$	−45.9957	+	21.7351i	−1.52140	+	0.718934i
$915$	−3.97018	−	3.97018i	−0.131250	−	0.131250i
$916$	5.20567	+	53.2268i	0.172000	+	1.75866i
$917$		0			0
$918$	7.43278	+	2.66236i	0.245318	+	0.0878708i
$919$		−	25.5452i		−	0.842657i	−0.906908	−	0.421329i	$-0.861564\pi$
$919$		−	25.5452i		−	0.842657i	0.906908	−	0.421329i	$-0.138436\pi$
$920$	−2.84679	−	4.76065i	−0.0938560	−	0.156954i
$921$		−	30.4275i		−	1.00262i
$922$	−0.609597	+	1.70188i	−0.0200760	+	0.0560483i
$923$	−14.4357	+	14.4357i	−0.475156	+	0.475156i
$924$		0			0
$925$	22.4120	+	22.4120i	0.736903	+	0.736903i
$926$	7.61305	+	16.1107i	0.250180	+	0.529430i
$927$	11.9396			0.392148
$928$	39.9782	+	6.00001i	1.31235	+	0.196960i
$929$	3.97030			0.130261			0.0651306	−	0.997877i	$-0.479254\pi$
$929$	3.97030			0.130261			0.0651306	+	0.997877i	$0.479254\pi$
$930$	6.34051	+	13.4177i	0.207913	+	0.439985i
$931$		0			0
$932$	19.6978	+	16.1881i	0.645222	+	0.530258i
$933$	5.58306	−	5.58306i	0.182781	−	0.182781i
$934$	−3.95299	+	11.0360i	−0.129346	+	0.361109i
$935$			2.53716i			0.0829740i
$936$	−14.0928	+	8.42731i	−0.460639	+	0.275455i
$937$		−	18.3326i		−	0.598899i	−0.954112	−	0.299450i	$-0.903197\pi$
$937$		−	18.3326i		−	0.598899i	0.954112	−	0.299450i	$-0.0968031\pi$
$938$		0			0
$939$	16.3565	−	16.3565i	0.533773	−	0.533773i
$940$	2.38425	+	24.3784i	0.0777658	+	0.795137i
$941$	21.0781	+	21.0781i	0.687126	+	0.687126i	0.961596	−	0.274470i	$-0.0885023\pi$
$941$	21.0781	+	21.0781i	0.687126	+	0.687126i	−0.274470	+	0.961596i	$0.588502\pi$
$942$	0.490237	−	0.231660i	0.0159728	−	0.00754788i
$943$	−16.4488			−0.535646
$944$	23.9482	+	16.0491i	0.779448	+	0.522352i
$945$		0			0
$946$	19.8739	−	9.39136i	0.646157	−	0.305339i
$947$	19.9001	+	19.9001i	0.646666	+	0.646666i	0.952186	−	0.305520i	$-0.0988302\pi$
$947$	19.9001	+	19.9001i	0.646666	+	0.646666i	−0.305520	+	0.952186i	$0.598830\pi$
$948$	2.08248	−	0.203671i	0.0676360	−	0.00661491i
$949$	−22.5360	+	22.5360i	−0.731549	+	0.731549i
$950$	−0.512318	−	0.183508i	−0.0166218	−	0.00595378i
$951$		−	22.7060i		−	0.736291i
$952$		0			0
$953$			9.54510i			0.309196i	0.987977	+	0.154598i	$0.0494083\pi$
$953$			9.54510i			0.309196i	−0.987977	+	0.154598i	$0.950592\pi$
$954$	−1.08427	+	3.02707i	−0.0351045	+	0.0980049i
$955$	−4.36760	+	4.36760i	−0.141332	+	0.141332i
$956$	−19.0081	+	23.1291i	−0.614764	+	0.748050i
$957$	14.9578	+	14.9578i	0.483516	+	0.483516i
$958$	−5.60615	−	11.8637i	−0.181126	−	0.383298i
$959$		0			0
$960$	8.63470	+	4.63812i	0.278684	+	0.149695i
$961$	42.3589			1.36642
$962$	18.1381	+	38.3837i	0.584796	+	1.23754i
$963$	20.6407	+	20.6407i	0.665138	+	0.665138i
$964$	−25.1562	+	30.6103i	−0.810228	+	0.985892i
$965$	−7.22535	+	7.22535i	−0.232592	+	0.232592i
$966$		0			0
$967$		−	54.0255i		−	1.73734i	−0.495388	−	0.868672i	$-0.664974\pi$
$967$		−	54.0255i		−	1.73734i	0.495388	−	0.868672i	$-0.335026\pi$
$968$	−3.43665	+	13.6605i	−0.110458	+	0.439064i
$969$			0.119112i			0.00382642i
$970$	22.1775	+	7.94379i	0.712077	+	0.255060i
$971$	4.21246	−	4.21246i	0.135184	−	0.135184i	−0.636277	−	0.771461i	$-0.719526\pi$
$971$	4.21246	−	4.21246i	0.135184	−	0.135184i	0.771461	+	0.636277i	$0.219526\pi$
$972$	−27.9827	+	2.73675i	−0.897544	+	0.0877813i
$973$		0			0
$974$	49.4665	−	23.3752i	1.58501	−	0.748991i
$975$	−17.9968			−0.576360
$976$	−10.2048	+	15.2275i	−0.326649	+	0.487422i
$977$	−29.2997			−0.937381			−0.468690	−	0.883363i	$-0.655274\pi$
$977$	−29.2997			−0.937381			−0.468690	+	0.883363i	$0.655274\pi$
$978$	22.8974	−	10.8201i	0.732178	−	0.345988i
$979$	7.87607	+	7.87607i	0.251720	+	0.251720i
$980$		0			0
$981$	−17.8673	+	17.8673i	−0.570460	+	0.570460i
$982$	56.1254	+	20.1036i	1.79103	+	0.641532i
$983$		−	15.9859i		−	0.509871i	−0.966958	−	0.254936i	$-0.917946\pi$
$983$		−	15.9859i		−	0.509871i	0.966958	−	0.254936i	$-0.0820543\pi$
$984$	24.9456	−	14.9171i	0.795238	−	0.475540i
$985$		−	14.4822i		−	0.461440i
$986$	−3.47024	+	9.68825i	−0.110515	+	0.308537i
$987$		0			0
$988$	−0.563133	−	0.462795i	−0.0179156	−	0.0147235i
$989$	−8.65036	−	8.65036i	−0.275065	−	0.275065i
$990$	−2.32527	−	4.92073i	−0.0739021	−	0.156391i
$991$	20.7652			0.659628			0.329814	−	0.944046i	$-0.393014\pi$
$991$	20.7652			0.659628			0.329814	+	0.944046i	$0.393014\pi$
$992$	38.9653	−	28.7956i	1.23715	−	0.914262i
$993$	−11.8153			−0.374948
$994$		0			0
$995$	8.37312	+	8.37312i	0.265446	+	0.265446i
$996$	−14.3497	−	11.7929i	−0.454689	−	0.373673i
$997$	35.1562	−	35.1562i	1.11341	−	1.11341i	0.120721	−	0.992687i	$-0.461479\pi$
$997$	35.1562	−	35.1562i	1.11341	−	1.11341i	0.992687	−	0.120721i	$-0.0385205\pi$
$998$	−5.33175	+	14.8852i	−0.168774	+	0.471183i
$999$			43.7868i			1.38535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.m.j.589.5		24
7.2	even	3		112.2.w.c.109.5	yes	48
7.3	odd	6		784.2.x.o.765.12		48
7.4	even	3		112.2.w.c.93.12	yes	48
7.5	odd	6		784.2.x.o.557.5		48
7.6	odd	2		784.2.m.k.589.5		24
16.5	even	4	inner	784.2.m.j.197.5		24
28.11	odd	6		448.2.ba.c.401.9		48
28.23	odd	6		448.2.ba.c.81.4		48
56.11	odd	6		896.2.ba.e.289.4		48
56.37	even	6		896.2.ba.f.417.4		48
56.51	odd	6		896.2.ba.e.417.9		48
56.53	even	6		896.2.ba.f.289.9		48
112.5	odd	12		784.2.x.o.165.12		48
112.11	odd	12		448.2.ba.c.177.4		48
112.37	even	12		112.2.w.c.53.12	yes	48
112.51	odd	12		896.2.ba.e.865.4		48
112.53	even	12		112.2.w.c.37.5	✓	48
112.67	odd	12		896.2.ba.e.737.9		48
112.69	odd	4		784.2.m.k.197.5		24
112.93	even	12		896.2.ba.f.865.9		48
112.101	odd	12		784.2.x.o.373.5		48
112.107	odd	12		448.2.ba.c.305.9		48
112.109	even	12		896.2.ba.f.737.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.5	✓	48	112.53	even	12
112.2.w.c.53.12	yes	48	112.37	even	12
112.2.w.c.93.12	yes	48	7.4	even	3
112.2.w.c.109.5	yes	48	7.2	even	3
448.2.ba.c.81.4		48	28.23	odd	6
448.2.ba.c.177.4		48	112.11	odd	12
448.2.ba.c.305.9		48	112.107	odd	12
448.2.ba.c.401.9		48	28.11	odd	6
784.2.m.j.197.5		24	16.5	even	4	inner
784.2.m.j.589.5		24	1.1	even	1	trivial
784.2.m.k.197.5		24	112.69	odd	4
784.2.m.k.589.5		24	7.6	odd	2
784.2.x.o.165.12		48	112.5	odd	12
784.2.x.o.373.5		48	112.101	odd	12
784.2.x.o.557.5		48	7.5	odd	6
784.2.x.o.765.12		48	7.3	odd	6
896.2.ba.e.289.4		48	56.11	odd	6
896.2.ba.e.417.9		48	56.51	odd	6
896.2.ba.e.737.9		48	112.67	odd	12
896.2.ba.e.865.4		48	112.51	odd	12
896.2.ba.f.289.9		48	56.53	even	6
896.2.ba.f.417.4		48	56.37	even	6
896.2.ba.f.737.4		48	112.109	even	12
896.2.ba.f.865.9		48	112.93	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.604218 - 1.27864i) q^{2} +(-0.853080 - 0.853080i) q^{3} +(-1.26984 + 1.54515i) q^{4} +(-0.718099 + 0.718099i) q^{5} +(-0.575337 + 1.60623i) q^{6} +(2.74296 + 0.690063i) q^{8} -1.54451i q^{9} +(1.35208 + 0.484303i) q^{10} +(1.73491 - 1.73491i) q^{11} +(2.40142 - 0.234863i) q^{12} +(-2.65786 - 2.65786i) q^{13} +1.22519 q^{15} +(-0.775001 - 3.92420i) q^{16} +1.01826 q^{17} +(-1.97487 + 0.933219i) q^{18} +(-0.0685610 - 0.0685610i) q^{19} +(-0.197701 - 2.02145i) q^{20} +(-3.26658 - 1.17006i) q^{22} +1.93110i q^{23} +(-1.75128 - 2.92864i) q^{24} +3.96867i q^{25} +(-1.79252 + 5.00437i) q^{26} +(-3.87683 + 3.87683i) q^{27} +(-5.05325 - 5.05325i) q^{29} +(-0.740283 - 1.56658i) q^{30} -8.56498 q^{31} +(-4.54938 + 3.36202i) q^{32} -2.96003 q^{33} +(-0.615248 - 1.30198i) q^{34} +(2.38650 + 1.96128i) q^{36} +(5.64724 - 5.64724i) q^{37} +(-0.0462391 + 0.129091i) q^{38} +4.53473i q^{39} +(-2.46525 + 1.47418i) q^{40} +8.51782i q^{41} +(-4.47950 + 4.47950i) q^{43} +(0.477640 + 4.88375i) q^{44} +(1.10911 + 1.10911i) q^{45} +(2.46918 - 1.16681i) q^{46} -12.0599 q^{47} +(-2.68652 + 4.00880i) q^{48} +(5.07450 - 2.39794i) q^{50} +(-0.868654 - 0.868654i) q^{51} +(7.48186 - 0.731739i) q^{52} +(1.04091 - 1.04091i) q^{53} +(7.29952 + 2.61462i) q^{54} +2.49167i q^{55} +0.116976i q^{57} +(-3.40803 + 9.51455i) q^{58} +(-5.09623 + 5.09623i) q^{59} +(-1.55580 + 1.89311i) q^{60} +(-3.24045 - 3.24045i) q^{61} +(5.17511 + 10.9515i) q^{62} +(7.04763 + 3.78563i) q^{64} +3.81721 q^{65} +(1.78850 + 3.78481i) q^{66} +(2.47945 + 2.47945i) q^{67} +(-1.29302 + 1.57336i) q^{68} +(1.64738 - 1.64738i) q^{69} -5.43131i q^{71} +(1.06581 - 4.23652i) q^{72} -8.47900i q^{73} +(-10.6330 - 3.80863i) q^{74} +(3.38559 - 3.38559i) q^{75} +(0.192999 - 0.0188756i) q^{76} +(5.79829 - 2.73996i) q^{78} +0.867190 q^{79} +(3.37450 + 2.26144i) q^{80} +1.98097 q^{81} +(10.8912 - 5.14661i) q^{82} +(-5.44318 - 5.44318i) q^{83} +(-0.731209 + 0.731209i) q^{85} +(8.43425 + 3.02107i) q^{86} +8.62165i q^{87} +(5.95597 - 3.56158i) q^{88} +4.53977i q^{89} +(0.748010 - 2.08830i) q^{90} +(-2.98385 - 2.45219i) q^{92} +(7.30661 + 7.30661i) q^{93} +(7.28680 + 15.4203i) q^{94} +0.0984673 q^{95} +(6.74905 + 1.01291i) q^{96} +16.4025 q^{97} +(-2.67958 - 2.67958i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 4 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{10} + 4 q^{11} - 2 q^{12} - 12 q^{13} - 20 q^{15} - 16 q^{16} - 8 q^{17} - 18 q^{18} + 4 q^{19} - 8 q^{20} - 18 q^{24} + 10 q^{26} - 12 q^{27}+ \cdots - 12 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 4 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^10 + 4 * q^11 - 2 * q^12 - 12 * q^13 - 20 * q^15 - 16 * q^16 - 8 * q^17 - 18 * q^18 + 4 * q^19 - 8 * q^20 - 18 * q^24 + 10 * q^26 - 12 * q^27 + 12 * q^29 + 4 * q^30 - 28 * q^31 - 16 * q^32 - 16 * q^33 - 22 * q^34 - 36 * q^36 + 24 * q^37 - 20 * q^38 - 26 * q^40 - 20 * q^43 - 6 * q^44 + 28 * q^45 + 14 * q^46 + 20 * q^47 + 28 * q^48 + 28 * q^50 - 24 * q^51 + 16 * q^52 + 16 * q^53 - 64 * q^54 + 6 * q^58 + 20 * q^59 - 46 * q^60 - 8 * q^61 + 12 * q^62 + 40 * q^64 - 8 * q^65 + 20 * q^66 - 48 * q^67 - 20 * q^69 + 32 * q^72 + 8 * q^74 + 4 * q^75 - 18 * q^76 + 58 * q^78 + 36 * q^79 + 28 * q^80 - 2 * q^82 - 4 * q^83 + 20 * q^86 + 42 * q^88 - 10 * q^90 + 38 * q^92 - 8 * q^93 + 72 * q^94 + 4 * q^95 + 120 * q^96 - 24 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

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Database

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