LMFDB - Embedded newform 784.2.m.k.589.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(197,784)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.26027151847$
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.k.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	0.909101	−	0.416575i	$-0.136770\pi$
$3$	0.853080	+	0.853080i	0.492526	+	0.492526i	−0.416575	+	0.909101i	$0.636770\pi$
$4$	−1.26984	+	1.54515i	−0.634921	+	0.772577i
$5$	0.718099	−	0.718099i	0.321144	−	0.321144i	−0.528062	−	0.849206i	$-0.677081\pi$
$5$	0.718099	−	0.718099i	0.321144	−	0.321144i	0.849206	+	0.528062i	$0.177081\pi$
$6$	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	0.972027	−	0.234870i	$-0.0754663\pi$
$13$	2.65786	+	2.65786i	0.737157	+	0.737157i	−0.234870	+	0.972027i	$0.575466\pi$
$14$		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	$-0.539406\pi$
$17$	−1.01826			−0.246963			−0.123482	+	0.992347i	$0.539406\pi$
$18$	−1.97487	+	0.933219i	−0.465482	+	0.219962i
$19$	0.0685610	+	0.0685610i	0.0157290	+	0.0157290i	0.714928	−	0.699199i	$-0.246460\pi$
$19$	0.0685610	+	0.0685610i	0.0157290	+	0.0157290i	−0.699199	+	0.714928i	$0.746460\pi$
$20$	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	$-0.220676\pi$
$31$	8.56498			1.53832			0.769158	+	0.639059i	$0.220676\pi$
$32$	−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	$-0.768376\pi$
$41$		−	8.51782i		−	1.33026i	0.746728	−	0.665130i	$-0.231624\pi$
$42$		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	$-0.157838\pi$
$47$	12.0599			1.75912			0.879559	+	0.475791i	$0.157838\pi$
$48$	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	−0.292724	−	0.956197i	$-0.594562\pi$
$59$	5.09623	−	5.09623i	0.663472	−	0.663472i	0.956197	+	0.292724i	$0.0945618\pi$
$60$	−1.55580	+	1.89311i	−0.200853	+	0.244400i
$61$	3.24045	+	3.24045i	0.414897	+	0.414897i	0.883441	−	0.468543i	$-0.155221\pi$
$61$	3.24045	+	3.24045i	0.414897	+	0.414897i	−0.468543	+	0.883441i	$0.655221\pi$
$62$	−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	$0.165270\pi$
$73$			8.47900i			0.992392i	−0.868211	+	0.496196i	$0.834730\pi$
$74$	−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	0.939638	−	0.342171i	$-0.111162\pi$
$83$	5.44318	+	5.44318i	0.597466	+	0.597466i	−0.342171	+	0.939638i	$0.611162\pi$
$84$		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	$-0.922653\pi$
$89$		−	4.53977i		−	0.481214i	0.970623	−	0.240607i	$-0.0773465\pi$
$90$	−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	$-0.813213\pi$
$97$	−16.4025			−1.66542			−0.832712	+	0.553706i	$0.813213\pi$
$98$		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	−0.952300	−	0.305164i	$-0.901289\pi$
$101$	−6.50363	+	6.50363i	−0.647135	+	0.647135i	0.305164	+	0.952300i	$0.401289\pi$
$102$	−0.585840	+	1.63555i	−0.0580068	+	0.161944i
$103$		−	7.73036i		−	0.761695i	−0.924638	−	0.380848i	$-0.875632\pi$
$103$		−	7.73036i		−	0.761695i	0.924638	−	0.380848i	$-0.124368\pi$
$104$	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	0.907250	−	0.420592i	$-0.138178\pi$
$131$	5.57005	+	5.57005i	0.486657	+	0.486657i	−0.420592	+	0.907250i	$0.638178\pi$
$132$	−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	$0.517372\pi$
$139$	−12.4154	+	12.4154i	−1.05306	+	1.05306i	−0.998511	+	0.0545473i	$0.982628\pi$
$140$		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	0.716017	−	0.698083i	$-0.245963\pi$
$157$	0.224718	+	0.224718i	0.0179344	+	0.0179344i	−0.698083	+	0.716017i	$0.745963\pi$
$158$	−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	$-0.808940\pi$
$167$		−	14.5986i		−	1.12967i	0.825204	−	0.564836i	$-0.191060\pi$
$168$		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	0.956315	−	0.292337i	$-0.0944330\pi$
$173$	8.73327	+	8.73327i	0.663978	+	0.663978i	−0.292337	+	0.956315i	$0.594433\pi$
$174$	−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	$0.552081\pi$
$181$	−15.4654	+	15.4654i	−1.14953	+	1.14953i	−0.986645	+	0.162887i	$0.947919\pi$
$182$		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	$0.135617\pi$
$199$			11.6601i			0.826563i	−0.910603	+	0.413282i	$0.864383\pi$
$200$	−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	$-0.214549\pi$
$223$	23.3350			1.56263			0.781315	+	0.624137i	$0.214549\pi$
$224$		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	0.971500	−	0.237039i	$-0.0761769\pi$
$227$	11.0658	+	11.0658i	0.734461	+	0.734461i	−0.237039	+	0.971500i	$0.576177\pi$
$228$	−0.180746	−	0.148541i	−0.0119702	−	0.00983738i
$229$	−18.9083	+	18.9083i	−1.24950	+	1.24950i	−0.293553	+	0.955943i	$0.594838\pi$
$229$	−18.9083	+	18.9083i	−1.24950	+	1.24950i	−0.955943	+	0.293553i	$0.905162\pi$
$230$	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	$-0.720260\pi$
$241$	−19.8105			−1.27611			−0.638054	+	0.769992i	$0.720260\pi$
$242$	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	−0.935782	−	0.352580i	$-0.885305\pi$
$251$	−9.23966	+	9.23966i	−0.583202	+	0.583202i	0.352580	+	0.935782i	$0.385305\pi$
$252$		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	$-0.757823\pi$
$257$	−23.2219			−1.44854			−0.724271	+	0.689516i	$0.757823\pi$
$258$	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	0.698454	−	0.715655i	$-0.253872\pi$
$269$	−0.282106	−	0.282106i	−0.0172003	−	0.0172003i	−0.715655	+	0.698454i	$0.753872\pi$
$270$	−7.11934	+	3.36422i	−0.433269	+	0.204740i
$271$	−10.6217			−0.645221			−0.322611	−	0.946532i	$-0.604560\pi$
$271$	−10.6217			−0.645221			−0.322611	+	0.946532i	$0.604560\pi$
$272$	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	−0.871826	−	0.489817i	$-0.837064\pi$
$283$	−6.42639	+	6.42639i	−0.382009	+	0.382009i	0.489817	+	0.871826i	$0.337064\pi$
$284$	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	−0.262703	−	0.964877i	$-0.584614\pi$
$293$	12.0193	−	12.0193i	0.702174	−	0.702174i	0.964877	+	0.262703i	$0.0846138\pi$
$294$		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	$-0.994271\pi$
$307$	−17.8339	−	17.8339i	−1.01784	−	1.01784i	−0.0179975	−	0.999838i	$-0.505729\pi$
$308$		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	$-0.940592\pi$
$311$		−	6.54459i		−	0.371109i	0.982634	−	0.185555i	$-0.0594082\pi$
$312$	−3.12925	+	12.4386i	−0.177159	+	0.704196i
$313$		−	19.1734i		−	1.08375i	−0.840461	−	0.541873i	$-0.817715\pi$
$313$		−	19.1734i		−	1.08375i	0.840461	−	0.541873i	$-0.182285\pi$
$314$	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	0.997102	−	0.0760810i	$-0.0242407\pi$
$349$	17.2061	+	17.2061i	0.921021	+	0.921021i	−0.0760810	+	0.997102i	$0.524241\pi$
$350$		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	$-0.430240\pi$
$353$	8.16944			0.434815			0.217408	+	0.976081i	$0.430240\pi$
$354$	−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	$-0.571270\pi$
$367$	−8.50712			−0.444068			−0.222034	+	0.975039i	$0.571270\pi$
$368$	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	$-0.443075\pi$
$383$	6.96253			0.355769			0.177884	+	0.984051i	$0.443075\pi$
$384$	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	0.587619	−	0.809138i	$-0.300066\pi$
$397$	−4.41374	−	4.41374i	−0.221519	−	0.221519i	−0.809138	+	0.587619i	$0.800066\pi$
$398$	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	$0.0450282\pi$
$409$			5.70265i			0.281978i	−0.990011	+	0.140989i	$0.954972\pi$
$410$	−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	0.809898	−	0.586570i	$-0.199522\pi$
$419$	4.57142	+	4.57142i	0.223328	+	0.223328i	−0.586570	+	0.809898i	$0.699522\pi$
$420$		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	$-0.391021\pi$
$433$	13.9717			0.671436			0.335718	+	0.941962i	$0.391021\pi$
$434$		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	$-0.958719\pi$
$439$		−	5.41926i		−	0.258647i	0.991602	−	0.129324i	$-0.0412806\pi$
$440$	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	0.727842	−	0.685745i	$-0.240523\pi$
$461$	0.903879	+	0.903879i	0.0420978	+	0.0420978i	−0.685745	+	0.727842i	$0.740523\pi$
$462$		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	0.829595	−	0.558366i	$-0.188572\pi$
$467$	5.86130	+	5.86130i	0.271228	+	0.271228i	−0.558366	+	0.829595i	$0.688572\pi$
$468$	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	$-0.567988\pi$
$479$	−9.27836			−0.423939			−0.211969	+	0.977276i	$0.567988\pi$
$480$	−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	$0.132626\pi$
$503$			18.1532i			0.809409i	−0.914448	+	0.404704i	$0.867374\pi$
$504$		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	0.674271	−	0.738484i	$-0.264458\pi$
$509$	−1.44869	−	1.44869i	−0.0642121	−	0.0642121i	−0.738484	+	0.674271i	$0.764458\pi$
$510$	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	$-0.979704\pi$
$521$		−	2.90874i		−	0.127434i	0.997968	−	0.0637172i	$-0.0202956\pi$
$522$	14.6953	+	5.26373i	0.643196	+	0.230387i
$523$	−11.7145	+	11.7145i	−0.512240	+	0.512240i	−0.915212	−	0.402972i	$-0.867977\pi$
$523$	−11.7145	+	11.7145i	−0.512240	+	0.512240i	0.402972	+	0.915212i	$0.367977\pi$
$524$	−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	0.969537	−	0.244946i	$-0.0787703\pi$
$563$	17.1928	+	17.1928i	0.724591	+	0.724591i	−0.244946	+	0.969537i	$0.578770\pi$
$564$	−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	$-0.326626\pi$
$577$	24.8922			1.03627			0.518137	+	0.855298i	$0.326626\pi$
$578$	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	−0.999926	−	0.0121684i	$-0.996127\pi$
$587$	−23.9315	+	23.9315i	−0.987758	+	0.987758i	0.0121684	+	0.999926i	$0.496127\pi$
$588$		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	$-0.511703\pi$
$593$	−1.79017			−0.0735134			−0.0367567	+	0.999324i	$0.511703\pi$
$594$	−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	$0.190763\pi$
$601$			27.6564i			1.12813i	−0.825730	+	0.564065i	$0.809237\pi$
$602$		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	$-0.355606\pi$
$607$	21.5936			0.876455			0.438228	+	0.898864i	$0.355606\pi$
$608$	−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	$0.512452\pi$
$619$	−25.8337	+	25.8337i	−1.03834	+	1.03834i	−0.999235	+	0.0391090i	$0.987548\pi$
$620$	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	0.901708	−	0.432346i	$-0.142314\pi$
$643$	11.9018	+	11.9018i	0.469361	+	0.469361i	−0.432346	+	0.901708i	$0.642314\pi$
$644$		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	$-0.966981\pi$
$647$		−	5.26762i		−	0.207092i	0.994625	−	0.103546i	$-0.0330188\pi$
$648$	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	−0.454244	−	0.890877i	$-0.650091\pi$
$661$	11.2258	−	11.2258i	0.436633	−	0.436633i	0.890877	+	0.454244i	$0.150091\pi$
$662$	−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	−0.328909	−	0.944362i	$-0.606681\pi$
$677$	16.0136	−	16.0136i	0.615452	−	0.615452i	0.944362	+	0.328909i	$0.106681\pi$
$678$	−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	0.291211	−	0.956659i	$-0.405942\pi$
$691$	−17.4925	−	17.4925i	−0.665447	−	0.665447i	−0.956659	+	0.291211i	$0.905942\pi$
$692$	−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	$-0.597755\pi$
$719$	−16.2120			−0.604604			−0.302302	+	0.953212i	$0.597755\pi$
$720$	−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	$0.0853223\pi$
$727$			14.2822i			0.529699i	−0.964290	+	0.264849i	$0.914678\pi$
$728$		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	0.995376	−	0.0960545i	$-0.0306223\pi$
$733$	24.3482	+	24.3482i	0.899322	+	0.899322i	−0.0960545	+	0.995376i	$0.530622\pi$
$734$	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	$0.116390\pi$
$761$			19.7273i			0.715113i	−0.933892	+	0.357556i	$0.883610\pi$
$762$	−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	$-0.232839\pi$
$769$	41.2736			1.48837			0.744183	+	0.667976i	$0.232839\pi$
$770$		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	$-0.340023\pi$
$773$	37.7572	−	37.7572i	1.35803	−	1.35803i	0.876342	−	0.481689i	$-0.159977\pi$
$774$	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	0.713528	−	0.700627i	$-0.247096\pi$
$787$	0.361908	+	0.361908i	0.0129006	+	0.0129006i	−0.700627	+	0.713528i	$0.747096\pi$
$788$	−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	$-0.900226\pi$
$797$	−35.5605	−	35.5605i	−1.25962	−	1.25962i	−0.308341	−	0.951276i	$-0.599774\pi$
$798$		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	−0.890907	−	0.454186i	$-0.849930\pi$
$811$	−12.4370	+	12.4370i	−0.436722	+	0.436722i	0.454186	+	0.890907i	$0.349930\pi$
$812$		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	0.955050	−	0.296446i	$-0.0958015\pi$
$829$	18.9628	+	18.9628i	0.658604	+	0.658604i	−0.296446	+	0.955050i	$0.595801\pi$
$830$	−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	$-0.970609\pi$
$839$		−	5.34140i		−	0.184406i	0.995740	−	0.0922028i	$-0.0293908\pi$
$840$		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	−0.731138	−	0.682230i	$-0.761010\pi$
$853$	−1.42841	+	1.42841i	−0.0489078	+	0.0489078i	0.682230	+	0.731138i	$0.261010\pi$
$854$		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	$-0.856067\pi$
$857$		−	25.5816i		−	0.873852i	0.899498	−	0.436926i	$-0.143933\pi$
$858$	5.30591	−	14.8131i	0.181141	−	0.505710i
$859$	32.2295	−	32.2295i	1.09966	−	1.09966i	0.105207	−	0.994450i	$-0.466449\pi$
$859$	32.2295	−	32.2295i	1.09966	−	1.09966i	0.994450	−	0.105207i	$-0.0335506\pi$
$860$	−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	$-0.416232\pi$
$881$	15.4426			0.520274			0.260137	+	0.965572i	$0.416232\pi$
$882$		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	$0.262707\pi$
$887$			43.7662i			1.46953i	−0.678324	+	0.734763i	$0.737293\pi$
$888$	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	$-0.520746\pi$
$929$	−3.97030			−0.130261			−0.0651306	+	0.997877i	$0.520746\pi$
$930$	−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	$0.0968031\pi$
$937$			18.3326i			0.598899i	−0.954112	+	0.299450i	$0.903197\pi$
$938$		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	0.274470	−	0.961596i	$-0.411498\pi$
$941$	−21.0781	−	21.0781i	−0.687126	−	0.687126i	−0.961596	+	0.274470i	$0.911498\pi$
$942$	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	−0.771461	−	0.636277i	$-0.780474\pi$
$971$	−4.21246	+	4.21246i	−0.135184	+	0.135184i	0.636277	+	0.771461i	$0.280474\pi$
$972$	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	$0.0820543\pi$
$983$			15.9859i			0.509871i	−0.966958	+	0.254936i	$0.917946\pi$
$984$	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	$0.538521\pi$
$997$	−35.1562	+	35.1562i	−1.11341	+	1.11341i	−0.992687	+	0.120721i	$0.961479\pi$
$998$	−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.k.589.5		24
7.2	even	3		784.2.x.o.557.5		48
7.3	odd	6		112.2.w.c.93.12	yes	48
7.4	even	3		784.2.x.o.765.12		48
7.5	odd	6		112.2.w.c.109.5	yes	48
7.6	odd	2		784.2.m.j.589.5		24
16.5	even	4	inner	784.2.m.k.197.5		24
28.3	even	6		448.2.ba.c.401.9		48
28.19	even	6		448.2.ba.c.81.4		48
56.3	even	6		896.2.ba.e.289.4		48
56.5	odd	6		896.2.ba.f.417.4		48
56.19	even	6		896.2.ba.e.417.9		48
56.45	odd	6		896.2.ba.f.289.9		48
112.3	even	12		896.2.ba.e.737.9		48
112.5	odd	12		112.2.w.c.53.12	yes	48
112.19	even	12		896.2.ba.e.865.4		48
112.37	even	12		784.2.x.o.165.12		48
112.45	odd	12		896.2.ba.f.737.4		48
112.53	even	12		784.2.x.o.373.5		48
112.59	even	12		448.2.ba.c.177.4		48
112.61	odd	12		896.2.ba.f.865.9		48
112.69	odd	4		784.2.m.j.197.5		24
112.75	even	12		448.2.ba.c.305.9		48
112.101	odd	12		112.2.w.c.37.5	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.5	✓	48	112.101	odd	12
112.2.w.c.53.12	yes	48	112.5	odd	12
112.2.w.c.93.12	yes	48	7.3	odd	6
112.2.w.c.109.5	yes	48	7.5	odd	6
448.2.ba.c.81.4		48	28.19	even	6
448.2.ba.c.177.4		48	112.59	even	12
448.2.ba.c.305.9		48	112.75	even	12
448.2.ba.c.401.9		48	28.3	even	6
784.2.m.j.197.5		24	112.69	odd	4
784.2.m.j.589.5		24	7.6	odd	2
784.2.m.k.197.5		24	16.5	even	4	inner
784.2.m.k.589.5		24	1.1	even	1	trivial
784.2.x.o.165.12		48	112.37	even	12
784.2.x.o.373.5		48	112.53	even	12
784.2.x.o.557.5		48	7.2	even	3
784.2.x.o.765.12		48	7.4	even	3
896.2.ba.e.289.4		48	56.3	even	6
896.2.ba.e.417.9		48	56.19	even	6
896.2.ba.e.737.9		48	112.3	even	12
896.2.ba.e.865.4		48	112.19	even	12
896.2.ba.f.289.9		48	56.45	odd	6
896.2.ba.f.417.4		48	56.5	odd	6
896.2.ba.f.737.4		48	112.45	odd	12
896.2.ba.f.865.9		48	112.61	odd	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 $\F_{q}$

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

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