LMFDB - Embedded newform 650.3.k.g.551.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,3,Mod(151,650)] 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("650.151"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	650.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,4,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$17.7112171834$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			551.1
Root			$1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	650.551
Dual form			650.3.k.g.151.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.00000i) q^{2} -4.44949 q^{3} -2.00000i q^{4} +(-4.44949 + 4.44949i) q^{6} +(-0.674235 - 0.674235i) q^{7} +(-2.00000 - 2.00000i) q^{8} +10.7980 q^{9} +(12.0227 + 12.0227i) q^{11} +8.89898i q^{12} -13.0000i q^{13} -1.34847 q^{14} -4.00000 q^{16} +17.6969i q^{17} +(10.7980 - 10.7980i) q^{18} +(6.00000 - 6.00000i) q^{19} +(3.00000 + 3.00000i) q^{21} +24.0454 q^{22} -18.6515i q^{23} +(8.89898 + 8.89898i) q^{24} +(-13.0000 - 13.0000i) q^{26} -8.00000 q^{27} +(-1.34847 + 1.34847i) q^{28} -10.3939 q^{29} +(18.6742 - 18.6742i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-53.4949 - 53.4949i) q^{33} +(17.6969 + 17.6969i) q^{34} -21.5959i q^{36} +(-2.30306 - 2.30306i) q^{37} -12.0000i q^{38} +57.8434i q^{39} +(-13.3939 + 13.3939i) q^{41} +6.00000 q^{42} -60.0454i q^{43} +(24.0454 - 24.0454i) q^{44} +(-18.6515 - 18.6515i) q^{46} +(-65.4620 - 65.4620i) q^{47} +17.7980 q^{48} -48.0908i q^{49} -78.7423i q^{51} -26.0000 q^{52} -50.3031 q^{53} +(-8.00000 + 8.00000i) q^{54} +2.69694i q^{56} +(-26.6969 + 26.6969i) q^{57} +(-10.3939 + 10.3939i) q^{58} +(-27.4166 - 27.4166i) q^{59} +19.0908 q^{61} -37.3485i q^{62} +(-7.28036 - 7.28036i) q^{63} +8.00000i q^{64} -106.990 q^{66} +(36.7650 - 36.7650i) q^{67} +35.3939 q^{68} +82.9898i q^{69} +(72.7878 - 72.7878i) q^{71} +(-21.5959 - 21.5959i) q^{72} +(49.7878 + 49.7878i) q^{73} -4.60612 q^{74} +(-12.0000 - 12.0000i) q^{76} -16.2122i q^{77} +(57.8434 + 57.8434i) q^{78} +42.7878 q^{79} -61.5857 q^{81} +26.7878i q^{82} +(-75.4166 + 75.4166i) q^{83} +(6.00000 - 6.00000i) q^{84} +(-60.0454 - 60.0454i) q^{86} +46.2474 q^{87} -48.0908i q^{88} +(6.30306 + 6.30306i) q^{89} +(-8.76505 + 8.76505i) q^{91} -37.3031 q^{92} +(-83.0908 + 83.0908i) q^{93} -130.924 q^{94} +(17.7980 - 17.7980i) q^{96} +(2.60612 - 2.60612i) q^{97} +(-48.0908 - 48.0908i) q^{98} +(129.821 + 129.821i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{3} - 8 q^{6} + 12 q^{7} - 8 q^{8} + 4 q^{9} + 4 q^{11} + 24 q^{14} - 16 q^{16} + 4 q^{18} + 24 q^{19} + 12 q^{21} + 8 q^{22} + 16 q^{24} - 52 q^{26} - 32 q^{27} + 24 q^{28} + 76 q^{29}+ \cdots + 436 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^3 - 8 * q^6 + 12 * q^7 - 8 * q^8 + 4 * q^9 + 4 * q^11 + 24 * q^14 - 16 * q^16 + 4 * q^18 + 24 * q^19 + 12 * q^21 + 8 * q^22 + 16 * q^24 - 52 * q^26 - 32 * q^27 + 24 * q^28 + 76 * q^29 + 60 * q^31 - 16 * q^32 - 116 * q^33 + 12 * q^34 - 68 * q^37 + 64 * q^41 + 24 * q^42 + 8 * q^44 - 104 * q^46 - 12 * q^47 + 32 * q^48 - 104 * q^52 - 260 * q^53 - 32 * q^54 - 48 * q^57 + 76 * q^58 + 52 * q^59 - 100 * q^61 - 132 * q^63 - 232 * q^66 - 44 * q^67 + 24 * q^68 + 56 * q^71 - 8 * q^72 - 36 * q^73 - 136 * q^74 - 48 * q^76 + 104 * q^78 - 64 * q^79 + 28 * q^81 - 140 * q^83 + 24 * q^84 - 152 * q^86 + 136 * q^87 + 84 * q^89 + 156 * q^91 - 208 * q^92 - 156 * q^93 - 24 * q^94 + 32 * q^96 + 128 * q^97 - 16 * q^98 + 436 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$	−4.44949			−1.48316			−0.741582	−	0.670863i	$-0.765924\pi$
$3$	−4.44949			−1.48316			−0.741582	+	0.670863i	$0.765924\pi$
$4$		−	2.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	−4.44949	+	4.44949i	−0.741582	+	0.741582i
$7$	−0.674235	−	0.674235i	−0.0963192	−	0.0963192i	0.657305	−	0.753624i	$-0.271696\pi$
$7$	−0.674235	−	0.674235i	−0.0963192	−	0.0963192i	−0.753624	+	0.657305i	$0.771696\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$	10.7980			1.19977
$10$		0			0
$11$	12.0227	+	12.0227i	1.09297	+	1.09297i	0.995210	+	0.0977634i	$0.0311688\pi$
$11$	12.0227	+	12.0227i	1.09297	+	1.09297i	0.0977634	+	0.995210i	$0.468831\pi$
$12$			8.89898i			0.741582i
$13$		−	13.0000i		−	1.00000i
$13$		−	13.0000i		−	1.00000i
$14$	−1.34847			−0.0963192
$15$		0			0
$16$	−4.00000			−0.250000
$17$			17.6969i			1.04100i	0.853863	+	0.520498i	$0.174254\pi$
$17$			17.6969i			1.04100i	−0.853863	+	0.520498i	$0.825746\pi$
$18$	10.7980	−	10.7980i	0.599887	−	0.599887i
$19$	6.00000	−	6.00000i	0.315789	−	0.315789i	−0.531358	−	0.847147i	$-0.678318\pi$
$19$	6.00000	−	6.00000i	0.315789	−	0.315789i	0.847147	+	0.531358i	$0.178318\pi$
$20$		0			0
$21$	3.00000	+	3.00000i	0.142857	+	0.142857i
$22$	24.0454			1.09297
$23$		−	18.6515i		−	0.810936i	−0.914109	−	0.405468i	$-0.867109\pi$
$23$		−	18.6515i		−	0.810936i	0.914109	−	0.405468i	$-0.132891\pi$
$24$	8.89898	+	8.89898i	0.370791	+	0.370791i
$25$		0			0
$26$	−13.0000	−	13.0000i	−0.500000	−	0.500000i
$27$	−8.00000			−0.296296
$28$	−1.34847	+	1.34847i	−0.0481596	+	0.0481596i
$29$	−10.3939			−0.358410			−0.179205	−	0.983812i	$-0.557352\pi$
$29$	−10.3939			−0.358410			−0.179205	+	0.983812i	$0.557352\pi$
$30$		0			0
$31$	18.6742	−	18.6742i	0.602395	−	0.602395i	−0.338553	−	0.940947i	$-0.609937\pi$
$31$	18.6742	−	18.6742i	0.602395	−	0.602395i	0.940947	+	0.338553i	$0.109937\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	−53.4949	−	53.4949i	−1.62106	−	1.62106i
$34$	17.6969	+	17.6969i	0.520498	+	0.520498i
$35$		0			0
$36$		−	21.5959i		−	0.599887i
$37$	−2.30306	−	2.30306i	−0.0622449	−	0.0622449i	0.675299	−	0.737544i	$-0.264015\pi$
$37$	−2.30306	−	2.30306i	−0.0622449	−	0.0622449i	−0.737544	+	0.675299i	$0.764015\pi$
$38$		−	12.0000i		−	0.315789i
$39$			57.8434i			1.48316i
$40$		0			0
$41$	−13.3939	+	13.3939i	−0.326680	+	0.326680i	−0.851323	−	0.524643i	$-0.824199\pi$
$41$	−13.3939	+	13.3939i	−0.326680	+	0.326680i	0.524643	+	0.851323i	$0.324199\pi$
$42$	6.00000			0.142857
$43$		−	60.0454i		−	1.39640i	−0.715900	−	0.698202i	$-0.753984\pi$
$43$		−	60.0454i		−	1.39640i	0.715900	−	0.698202i	$-0.246016\pi$
$44$	24.0454	−	24.0454i	0.546487	−	0.546487i
$45$		0			0
$46$	−18.6515	−	18.6515i	−0.405468	−	0.405468i
$47$	−65.4620	−	65.4620i	−1.39281	−	1.39281i	−0.818965	−	0.573843i	$-0.805452\pi$
$47$	−65.4620	−	65.4620i	−1.39281	−	1.39281i	−0.573843	−	0.818965i	$-0.694548\pi$
$48$	17.7980			0.370791
$49$		−	48.0908i		−	0.981445i
$50$		0			0
$51$		−	78.7423i		−	1.54397i
$52$	−26.0000			−0.500000
$53$	−50.3031			−0.949114			−0.474557	−	0.880225i	$-0.657392\pi$
$53$	−50.3031			−0.949114			−0.474557	+	0.880225i	$0.657392\pi$
$54$	−8.00000	+	8.00000i	−0.148148	+	0.148148i
$55$		0			0
$56$			2.69694i			0.0481596i
$57$	−26.6969	+	26.6969i	−0.468367	+	0.468367i
$58$	−10.3939	+	10.3939i	−0.179205	+	0.179205i
$59$	−27.4166	−	27.4166i	−0.464688	−	0.464688i	0.435501	−	0.900188i	$-0.356571\pi$
$59$	−27.4166	−	27.4166i	−0.464688	−	0.464688i	−0.900188	+	0.435501i	$0.856571\pi$
$60$		0			0
$61$	19.0908			0.312964			0.156482	−	0.987681i	$-0.449985\pi$
$61$	19.0908			0.312964			0.156482	+	0.987681i	$0.449985\pi$
$62$		−	37.3485i		−	0.602395i
$63$	−7.28036	−	7.28036i	−0.115561	−	0.115561i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	−106.990			−1.62106
$67$	36.7650	−	36.7650i	0.548732	−	0.548732i	−0.377342	−	0.926074i	$-0.623162\pi$
$67$	36.7650	−	36.7650i	0.548732	−	0.548732i	0.926074	+	0.377342i	$0.123162\pi$
$68$	35.3939			0.520498
$69$			82.9898i			1.20275i
$70$		0			0
$71$	72.7878	−	72.7878i	1.02518	−	1.02518i	0.0255049	−	0.999675i	$-0.491881\pi$
$71$	72.7878	−	72.7878i	1.02518	−	1.02518i	0.999675	−	0.0255049i	$-0.00811935\pi$
$72$	−21.5959	−	21.5959i	−0.299943	−	0.299943i
$73$	49.7878	+	49.7878i	0.682024	+	0.682024i	0.960456	−	0.278432i	$-0.0898147\pi$
$73$	49.7878	+	49.7878i	0.682024	+	0.682024i	−0.278432	+	0.960456i	$0.589815\pi$
$74$	−4.60612			−0.0622449
$75$		0			0
$76$	−12.0000	−	12.0000i	−0.157895	−	0.157895i
$77$		−	16.2122i		−	0.210549i
$78$	57.8434	+	57.8434i	0.741582	+	0.741582i
$79$	42.7878			0.541617			0.270809	−	0.962633i	$-0.412709\pi$
$79$	42.7878			0.541617			0.270809	+	0.962633i	$0.412709\pi$
$80$		0			0
$81$	−61.5857			−0.760317
$82$			26.7878i			0.326680i
$83$	−75.4166	+	75.4166i	−0.908634	+	0.908634i	−0.996162	−	0.0875285i	$-0.972103\pi$
$83$	−75.4166	+	75.4166i	−0.908634	+	0.908634i	0.0875285	+	0.996162i	$0.472103\pi$
$84$	6.00000	−	6.00000i	0.0714286	−	0.0714286i
$85$		0			0
$86$	−60.0454	−	60.0454i	−0.698202	−	0.698202i
$87$	46.2474			0.531580
$88$		−	48.0908i		−	0.546487i
$89$	6.30306	+	6.30306i	0.0708209	+	0.0708209i	0.741630	−	0.670809i	$-0.234053\pi$
$89$	6.30306	+	6.30306i	0.0708209	+	0.0708209i	−0.670809	+	0.741630i	$0.734053\pi$
$90$		0			0
$91$	−8.76505	+	8.76505i	−0.0963192	+	0.0963192i
$92$	−37.3031			−0.405468
$93$	−83.0908	+	83.0908i	−0.893450	+	0.893450i
$94$	−130.924			−1.39281
$95$		0			0
$96$	17.7980	−	17.7980i	0.185395	−	0.185395i
$97$	2.60612	−	2.60612i	0.0268672	−	0.0268672i	−0.693546	−	0.720413i	$-0.743952\pi$
$97$	2.60612	−	2.60612i	0.0268672	−	0.0268672i	0.720413	+	0.693546i	$0.243952\pi$
$98$	−48.0908	−	48.0908i	−0.490723	−	0.490723i
$99$	129.821	+	129.821i	1.31132	+	1.31132i
$100$		0			0
$101$		−	50.4847i		−	0.499848i	−0.968265	−	0.249924i	$-0.919594\pi$
$101$		−	50.4847i		−	0.499848i	0.968265	−	0.249924i	$-0.0804057\pi$
$102$	−78.7423	−	78.7423i	−0.771984	−	0.771984i
$103$		−	185.576i		−	1.80170i	−0.434126	−	0.900852i	$-0.642943\pi$
$103$		−	185.576i		−	1.80170i	0.434126	−	0.900852i	$-0.357057\pi$
$104$	−26.0000	+	26.0000i	−0.250000	+	0.250000i
$105$		0			0
$106$	−50.3031	+	50.3031i	−0.474557	+	0.474557i
$107$	158.742			1.48357			0.741787	−	0.670636i	$-0.233979\pi$
$107$	158.742			1.48357			0.741787	+	0.670636i	$0.233979\pi$
$108$			16.0000i			0.148148i
$109$	69.1816	−	69.1816i	0.634694	−	0.634694i	−0.314548	−	0.949242i	$-0.601853\pi$
$109$	69.1816	−	69.1816i	0.634694	−	0.634694i	0.949242	+	0.314548i	$0.101853\pi$
$110$		0			0
$111$	10.2474	+	10.2474i	0.0923194	+	0.0923194i
$112$	2.69694	+	2.69694i	0.0240798	+	0.0240798i
$113$	−13.3939			−0.118530			−0.0592649	−	0.998242i	$-0.518876\pi$
$113$	−13.3939			−0.118530			−0.0592649	+	0.998242i	$0.518876\pi$
$114$			53.3939i			0.468367i
$115$		0			0
$116$			20.7878i			0.179205i
$117$		−	140.373i		−	1.19977i
$118$	−54.8332			−0.464688
$119$	11.9319	−	11.9319i	0.100268	−	0.100268i
$120$		0			0
$121$			168.091i			1.38918i
$122$	19.0908	−	19.0908i	0.156482	−	0.156482i
$123$	59.5959	−	59.5959i	0.484520	−	0.484520i
$124$	−37.3485	−	37.3485i	−0.301197	−	0.301197i
$125$		0			0
$126$	−14.5607			−0.115561
$127$		−	53.2122i		−	0.418994i	−0.977809	−	0.209497i	$-0.932817\pi$
$127$		−	53.2122i		−	0.418994i	0.977809	−	0.209497i	$-0.0671827\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$			267.171i			2.07110i
$130$		0			0
$131$	−97.5301			−0.744505			−0.372252	−	0.928132i	$-0.621414\pi$
$131$	−97.5301			−0.744505			−0.372252	+	0.928132i	$0.621414\pi$
$132$	−106.990	+	106.990i	−0.810529	+	0.810529i
$133$	−8.09082			−0.0608332
$134$		−	73.5301i		−	0.548732i
$135$		0			0
$136$	35.3939	−	35.3939i	0.260249	−	0.260249i
$137$	115.697	+	115.697i	0.844503	+	0.844503i	0.989441	−	0.144938i	$-0.0462981\pi$
$137$	115.697	+	115.697i	0.844503	+	0.844503i	−0.144938	+	0.989441i	$0.546298\pi$
$138$	82.9898	+	82.9898i	0.601375	+	0.601375i
$139$	−257.621			−1.85339			−0.926694	−	0.375817i	$-0.877362\pi$
$139$	−257.621			−1.85339			−0.926694	+	0.375817i	$0.877362\pi$
$140$		0			0
$141$	291.272	+	291.272i	2.06576	+	2.06576i
$142$		−	145.576i		−	1.02518i
$143$	156.295	−	156.295i	1.09297	−	1.09297i
$144$	−43.1918			−0.299943
$145$		0			0
$146$	99.5755			0.682024
$147$			213.980i			1.45564i
$148$	−4.60612	+	4.60612i	−0.0311225	+	0.0311225i
$149$	144.091	−	144.091i	0.967052	−	0.967052i	−0.0324218	−	0.999474i	$-0.510322\pi$
$149$	144.091	−	144.091i	0.967052	−	0.967052i	0.999474	+	0.0324218i	$0.0103220\pi$
$150$		0			0
$151$	80.6742	+	80.6742i	0.534266	+	0.534266i	0.921839	−	0.387573i	$-0.126686\pi$
$151$	80.6742	+	80.6742i	0.534266	+	0.534266i	−0.387573	+	0.921839i	$0.626686\pi$
$152$	−24.0000			−0.157895
$153$			191.091i			1.24896i
$154$	−16.2122	−	16.2122i	−0.105274	−	0.105274i
$155$		0			0
$156$	115.687			0.741582
$157$	176.394			1.12353			0.561764	−	0.827298i	$-0.310123\pi$
$157$	176.394			1.12353			0.561764	+	0.827298i	$0.310123\pi$
$158$	42.7878	−	42.7878i	0.270809	−	0.270809i
$159$	223.823			1.40769
$160$		0			0
$161$	−12.5755	+	12.5755i	−0.0781087	+	0.0781087i
$162$	−61.5857	+	61.5857i	−0.380159	+	0.380159i
$163$	−196.742	−	196.742i	−1.20701	−	1.20701i	−0.971991	−	0.235017i	$-0.924485\pi$
$163$	−196.742	−	196.742i	−1.20701	−	1.20701i	−0.235017	−	0.971991i	$-0.575515\pi$
$164$	26.7878	+	26.7878i	0.163340	+	0.163340i
$165$		0			0
$166$			150.833i			0.908634i
$167$	191.576	+	191.576i	1.14716	+	1.14716i	0.987109	+	0.160050i	$0.0511655\pi$
$167$	191.576	+	191.576i	1.14716	+	1.14716i	0.160050	+	0.987109i	$0.448835\pi$
$168$		−	12.0000i		−	0.0714286i
$169$	−169.000			−1.00000
$170$		0			0
$171$	64.7878	−	64.7878i	0.378876	−	0.378876i
$172$	−120.091			−0.698202
$173$			317.272i			1.83394i	0.398951	+	0.916972i	$0.369374\pi$
$173$			317.272i			1.83394i	−0.398951	+	0.916972i	$0.630626\pi$
$174$	46.2474	−	46.2474i	0.265790	−	0.265790i
$175$		0			0
$176$	−48.0908	−	48.0908i	−0.273243	−	0.273243i
$177$	121.990	+	121.990i	0.689208	+	0.689208i
$178$	12.6061			0.0708209
$179$		−	140.000i		−	0.782123i	−0.920365	−	0.391061i	$-0.872108\pi$
$179$		−	140.000i		−	0.782123i	0.920365	−	0.391061i	$-0.127892\pi$
$180$		0			0
$181$		−	107.363i		−	0.593167i	−0.955007	−	0.296584i	$-0.904153\pi$
$181$		−	107.363i		−	0.593167i	0.955007	−	0.296584i	$-0.0958473\pi$
$182$			17.5301i			0.0963192i
$183$	−84.9444			−0.464177
$184$	−37.3031	+	37.3031i	−0.202734	+	0.202734i
$185$		0			0
$186$			166.182i			0.893450i
$187$	−212.765	+	212.765i	−1.13778	+	1.13778i
$188$	−130.924	+	130.924i	−0.696404	+	0.696404i
$189$	5.39388	+	5.39388i	0.0285390	+	0.0285390i
$190$		0			0
$191$	−74.7878			−0.391559			−0.195779	−	0.980648i	$-0.562724\pi$
$191$	−74.7878			−0.391559			−0.195779	+	0.980648i	$0.562724\pi$
$192$		−	35.5959i		−	0.185395i
$193$	258.879	+	258.879i	1.34134	+	1.34134i	0.894728	+	0.446612i	$0.147370\pi$
$193$	258.879	+	258.879i	1.34134	+	1.34134i	0.446612	+	0.894728i	$0.352630\pi$
$194$		−	5.21225i		−	0.0268672i
$195$		0			0
$196$	−96.1816			−0.490723
$197$	−53.2122	+	53.2122i	−0.270113	+	0.270113i	−0.829146	−	0.559033i	$-0.811173\pi$
$197$	−53.2122	+	53.2122i	−0.270113	+	0.270113i	0.559033	+	0.829146i	$0.311173\pi$
$198$	259.641			1.31132
$199$		−	149.212i		−	0.749810i	−0.927063	−	0.374905i	$-0.877675\pi$
$199$		−	149.212i		−	0.749810i	0.927063	−	0.374905i	$-0.122325\pi$
$200$		0			0
$201$	−163.586	+	163.586i	−0.813859	+	0.813859i
$202$	−50.4847	−	50.4847i	−0.249924	−	0.249924i
$203$	7.00791	+	7.00791i	0.0345217	+	0.0345217i
$204$	−157.485			−0.771984
$205$		0			0
$206$	−185.576	−	185.576i	−0.900852	−	0.900852i
$207$		−	201.398i		−	0.972939i
$208$			52.0000i			0.250000i
$209$	144.272			0.690299
$210$		0			0
$211$	257.530			1.22052			0.610261	−	0.792201i	$-0.291065\pi$
$211$	257.530			1.22052			0.610261	+	0.792201i	$0.291065\pi$
$212$			100.606i			0.474557i
$213$	−323.868	+	323.868i	−1.52051	+	1.52051i
$214$	158.742	−	158.742i	0.741787	−	0.741787i
$215$		0			0
$216$	16.0000	+	16.0000i	0.0740741	+	0.0740741i
$217$	−25.1816			−0.116044
$218$		−	138.363i		−	0.634694i
$219$	−221.530	−	221.530i	−1.01155	−	1.01155i
$220$		0			0
$221$	230.060			1.04100
$222$	20.4949			0.0923194
$223$	108.561	−	108.561i	0.486819	−	0.486819i	−0.420482	−	0.907301i	$-0.638139\pi$
$223$	108.561	−	108.561i	0.486819	−	0.486819i	0.907301	+	0.420482i	$0.138139\pi$
$224$	5.39388			0.0240798
$225$		0			0
$226$	−13.3939	+	13.3939i	−0.0592649	+	0.0592649i
$227$	−80.0227	+	80.0227i	−0.352523	+	0.352523i	−0.861047	−	0.508525i	$-0.830191\pi$
$227$	−80.0227	+	80.0227i	−0.352523	+	0.352523i	0.508525	+	0.861047i	$0.330191\pi$
$228$	53.3939	+	53.3939i	0.234184	+	0.234184i
$229$	−211.151	−	211.151i	−0.922057	−	0.922057i	0.0751178	−	0.997175i	$-0.476067\pi$
$229$	−211.151	−	211.151i	−0.922057	−	0.922057i	−0.997175	+	0.0751178i	$0.976067\pi$
$230$		0			0
$231$			72.1362i			0.312278i
$232$	20.7878	+	20.7878i	0.0896024	+	0.0896024i
$233$			94.0000i			0.403433i	0.979444	+	0.201717i	$0.0646520\pi$
$233$			94.0000i			0.403433i	−0.979444	+	0.201717i	$0.935348\pi$
$234$	−140.373	−	140.373i	−0.599887	−	0.599887i
$235$		0			0
$236$	−54.8332	+	54.8332i	−0.232344	+	0.232344i
$237$	−190.384			−0.803307
$238$		−	23.8638i		−	0.100268i
$239$	−21.6436	+	21.6436i	−0.0905591	+	0.0905591i	−0.750935	−	0.660376i	$-0.770397\pi$
$239$	−21.6436	+	21.6436i	−0.0905591	+	0.0905591i	0.660376	+	0.750935i	$0.270397\pi$
$240$		0			0
$241$	−123.060	−	123.060i	−0.510623	−	0.510623i	0.404094	−	0.914717i	$-0.367587\pi$
$241$	−123.060	−	123.060i	−0.510623	−	0.510623i	−0.914717	+	0.404094i	$0.867587\pi$
$242$	168.091	+	168.091i	0.694590	+	0.694590i
$243$	346.025			1.42397
$244$		−	38.1816i		−	0.156482i
$245$		0			0
$246$		−	119.192i		−	0.484520i
$247$	−78.0000	−	78.0000i	−0.315789	−	0.315789i
$248$	−74.6969			−0.301197
$249$	335.565	−	335.565i	1.34765	−	1.34765i
$250$		0			0
$251$		−	403.151i		−	1.60618i	−0.595858	−	0.803090i	$-0.703188\pi$
$251$		−	403.151i		−	1.60618i	0.595858	−	0.803090i	$-0.296812\pi$
$252$	−14.5607	+	14.5607i	−0.0577806	+	0.0577806i
$253$	224.242	−	224.242i	0.886331	−	0.886331i
$254$	−53.2122	−	53.2122i	−0.209497	−	0.209497i
$255$		0			0
$256$	16.0000			0.0625000
$257$		−	435.788i		−	1.69567i	−0.530258	−	0.847836i	$-0.677905\pi$
$257$		−	435.788i		−	1.69567i	0.530258	−	0.847836i	$-0.322095\pi$
$258$	267.171	+	267.171i	1.03555	+	1.03555i
$259$			3.10561i			0.0119908i
$260$		0			0
$261$	−112.233			−0.430010
$262$	−97.5301	+	97.5301i	−0.372252	+	0.372252i
$263$	404.499			1.53802			0.769010	−	0.639236i	$-0.220749\pi$
$263$	404.499			1.53802			0.769010	+	0.639236i	$0.220749\pi$
$264$			213.980i			0.810529i
$265$		0			0
$266$	−8.09082	+	8.09082i	−0.0304166	+	0.0304166i
$267$	−28.0454	−	28.0454i	−0.105039	−	0.105039i
$268$	−73.5301	−	73.5301i	−0.274366	−	0.274366i
$269$	−456.757			−1.69798			−0.848991	−	0.528407i	$-0.822789\pi$
$269$	−456.757			−1.69798			−0.848991	+	0.528407i	$0.822789\pi$
$270$		0			0
$271$	240.674	+	240.674i	0.888097	+	0.888097i	0.994340	−	0.106243i	$-0.0338823\pi$
$271$	240.674	+	240.674i	0.888097	+	0.888097i	−0.106243	+	0.994340i	$0.533882\pi$
$272$		−	70.7878i		−	0.260249i
$273$	39.0000	−	39.0000i	0.142857	−	0.142857i
$274$	231.394			0.844503
$275$		0			0
$276$	165.980			0.601375
$277$		−	173.151i		−	0.625094i	−0.949902	−	0.312547i	$-0.898818\pi$
$277$		−	173.151i		−	0.625094i	0.949902	−	0.312547i	$-0.101182\pi$
$278$	−257.621	+	257.621i	−0.926694	+	0.926694i
$279$	201.644	−	201.644i	0.722737	−	0.722737i
$280$		0			0
$281$	−31.8184	−	31.8184i	−0.113233	−	0.113233i	0.648220	−	0.761453i	$-0.275514\pi$
$281$	−31.8184	−	31.8184i	−0.113233	−	0.113233i	−0.761453	+	0.648220i	$0.775514\pi$
$282$	582.545			2.06576
$283$			195.106i			0.689419i	0.938709	+	0.344710i	$0.112023\pi$
$283$			195.106i			0.689419i	−0.938709	+	0.344710i	$0.887977\pi$
$284$	−145.576	−	145.576i	−0.512590	−	0.512590i
$285$		0			0
$286$		−	312.590i		−	1.09297i
$287$	18.0612			0.0629311
$288$	−43.1918	+	43.1918i	−0.149972	+	0.149972i
$289$	−24.1816			−0.0836735
$290$		0			0
$291$	−11.5959	+	11.5959i	−0.0398485	+	0.0398485i
$292$	99.5755	−	99.5755i	0.341012	−	0.341012i
$293$	−146.788	−	146.788i	−0.500982	−	0.500982i	0.410761	−	0.911743i	$-0.365263\pi$
$293$	−146.788	−	146.788i	−0.500982	−	0.500982i	−0.911743	+	0.410761i	$0.865263\pi$
$294$	213.980	+	213.980i	0.727822	+	0.727822i
$295$		0			0
$296$			9.21225i			0.0311225i
$297$	−96.1816	−	96.1816i	−0.323844	−	0.323844i
$298$		−	288.182i		−	0.967052i
$299$	−242.470			−0.810936
$300$		0			0
$301$	−40.4847	+	40.4847i	−0.134501	+	0.134501i
$302$	161.348			0.534266
$303$			224.631i			0.741357i
$304$	−24.0000	+	24.0000i	−0.0789474	+	0.0789474i
$305$		0			0
$306$	191.091	+	191.091i	0.624480	+	0.624480i
$307$	−27.2122	−	27.2122i	−0.0886392	−	0.0886392i	0.661397	−	0.750036i	$-0.269964\pi$
$307$	−27.2122	−	27.2122i	−0.0886392	−	0.0886392i	−0.750036	+	0.661397i	$0.769964\pi$
$308$	−32.4245			−0.105274
$309$			825.716i			2.67222i
$310$		0			0
$311$		−	532.227i		−	1.71134i	−0.517521	−	0.855670i	$-0.673145\pi$
$311$		−	532.227i		−	1.71134i	0.517521	−	0.855670i	$-0.326855\pi$
$312$	115.687	−	115.687i	0.370791	−	0.370791i
$313$	−580.605			−1.85497			−0.927484	−	0.373862i	$-0.878033\pi$
$313$	−580.605			−1.85497			−0.927484	+	0.373862i	$0.878033\pi$
$314$	176.394	−	176.394i	0.561764	−	0.561764i
$315$		0			0
$316$		−	85.5755i		−	0.270809i
$317$	−248.272	+	248.272i	−0.783194	+	0.783194i	−0.980368	−	0.197175i	$-0.936823\pi$
$317$	−248.272	+	248.272i	−0.783194	+	0.783194i	0.197175	+	0.980368i	$0.436823\pi$
$318$	223.823	−	223.823i	0.703846	−	0.703846i
$319$	−124.963	−	124.963i	−0.391732	−	0.391732i
$320$		0			0
$321$	−706.322			−2.20038
$322$			25.1510i			0.0781087i
$323$	106.182	+	106.182i	0.328736	+	0.328736i
$324$			123.171i			0.380159i
$325$		0			0
$326$	−393.485			−1.20701
$327$	−307.823	+	307.823i	−0.941355	+	0.941355i
$328$	53.5755			0.163340
$329$			88.2735i			0.268308i
$330$		0			0
$331$	−445.151	+	445.151i	−1.34487	+	1.34487i	−0.453726	+	0.891141i	$0.649905\pi$
$331$	−445.151	+	445.151i	−1.34487	+	1.34487i	−0.891141	+	0.453726i	$0.850095\pi$
$332$	150.833	+	150.833i	0.454317	+	0.454317i
$333$	−24.8684	−	24.8684i	−0.0746798	−	0.0746798i
$334$	383.151			1.14716
$335$		0			0
$336$	−12.0000	−	12.0000i	−0.0357143	−	0.0357143i
$337$			95.4541i			0.283247i	0.989921	+	0.141623i	$0.0452322\pi$
$337$			95.4541i			0.283247i	−0.989921	+	0.141623i	$0.954768\pi$
$338$	−169.000	+	169.000i	−0.500000	+	0.500000i
$339$	59.5959			0.175799
$340$		0			0
$341$	449.030			1.31680
$342$		−	129.576i		−	0.378876i
$343$	−65.4620	+	65.4620i	−0.190851	+	0.190851i
$344$	−120.091	+	120.091i	−0.349101	+	0.349101i
$345$		0			0
$346$	317.272	+	317.272i	0.916972	+	0.916972i
$347$	41.6209			0.119945			0.0599725	−	0.998200i	$-0.480899\pi$
$347$	41.6209			0.119945			0.0599725	+	0.998200i	$0.480899\pi$
$348$		−	92.4949i		−	0.265790i
$349$	−186.879	−	186.879i	−0.535469	−	0.535469i	0.386726	−	0.922195i	$-0.373606\pi$
$349$	−186.879	−	186.879i	−0.535469	−	0.535469i	−0.922195	+	0.386726i	$0.873606\pi$
$350$		0			0
$351$			104.000i			0.296296i
$352$	−96.1816			−0.273243
$353$	49.5153	−	49.5153i	0.140270	−	0.140270i	−0.633485	−	0.773755i	$-0.718376\pi$
$353$	49.5153	−	49.5153i	0.140270	−	0.140270i	0.773755	+	0.633485i	$0.218376\pi$
$354$	243.980			0.689208
$355$		0			0
$356$	12.6061	−	12.6061i	0.0354105	−	0.0354105i
$357$	−53.0908	+	53.0908i	−0.148714	+	0.148714i
$358$	−140.000	−	140.000i	−0.391061	−	0.391061i
$359$	234.538	+	234.538i	0.653309	+	0.653309i	0.953788	−	0.300479i	$-0.0971466\pi$
$359$	234.538	+	234.538i	0.653309	+	0.653309i	−0.300479	+	0.953788i	$0.597147\pi$
$360$		0			0
$361$			289.000i			0.800554i
$362$	−107.363	−	107.363i	−0.296584	−	0.296584i
$363$		−	747.918i		−	2.06038i
$364$	17.5301	+	17.5301i	0.0481596	+	0.0481596i
$365$		0			0
$366$	−84.9444	+	84.9444i	−0.232088	+	0.232088i
$367$	111.287			0.303235			0.151617	−	0.988439i	$-0.451552\pi$
$367$	111.287			0.303235			0.151617	+	0.988439i	$0.451552\pi$
$368$			74.6061i			0.202734i
$369$	−144.627	+	144.627i	−0.391942	+	0.391942i
$370$		0			0
$371$	33.9161	+	33.9161i	0.0914180	+	0.0914180i
$372$	166.182	+	166.182i	0.446725	+	0.446725i
$373$	58.9388			0.158013			0.0790064	−	0.996874i	$-0.474825\pi$
$373$	58.9388			0.158013			0.0790064	+	0.996874i	$0.474825\pi$
$374$			425.530i			1.13778i
$375$		0			0
$376$			261.848i			0.696404i
$377$			135.120i			0.358410i
$378$	10.7878			0.0285390
$379$	151.235	−	151.235i	0.399037	−	0.399037i	−0.478856	−	0.877893i	$-0.658949\pi$
$379$	151.235	−	151.235i	0.399037	−	0.399037i	0.877893	+	0.478856i	$0.158949\pi$
$380$		0			0
$381$			236.767i			0.621437i
$382$	−74.7878	+	74.7878i	−0.195779	+	0.195779i
$383$	−510.954	+	510.954i	−1.33408	+	1.33408i	−0.432401	+	0.901681i	$0.642333\pi$
$383$	−510.954	+	510.954i	−1.33408	+	1.33408i	−0.901681	+	0.432401i	$0.857667\pi$
$384$	−35.5959	−	35.5959i	−0.0926977	−	0.0926977i
$385$		0			0
$386$	517.757			1.34134
$387$		−	648.368i		−	1.67537i
$388$	−5.21225	−	5.21225i	−0.0134336	−	0.0134336i
$389$			10.0612i			0.0258643i	0.999916	+	0.0129322i	$0.00411655\pi$
$389$			10.0612i			0.0258643i	−0.999916	+	0.0129322i	$0.995883\pi$
$390$		0			0
$391$	330.075			0.844182
$392$	−96.1816	+	96.1816i	−0.245361	+	0.245361i
$393$	433.959			1.10422
$394$			106.424i			0.270113i
$395$		0			0
$396$	259.641	−	259.641i	0.655660	−	0.655660i
$397$	−485.091	−	485.091i	−1.22189	−	1.22189i	−0.966959	−	0.254932i	$-0.917947\pi$
$397$	−485.091	−	485.091i	−1.22189	−	1.22189i	−0.254932	−	0.966959i	$-0.582053\pi$
$398$	−149.212	−	149.212i	−0.374905	−	0.374905i
$399$	36.0000			0.0902256
$400$		0			0
$401$	224.363	+	224.363i	0.559509	+	0.559509i	0.929168	−	0.369658i	$-0.120525\pi$
$401$	224.363	+	224.363i	0.559509	+	0.559509i	−0.369658	+	0.929168i	$0.620525\pi$
$402$			327.171i			0.813859i
$403$	−242.765	−	242.765i	−0.602395	−	0.602395i
$404$	−100.969			−0.249924
$405$		0			0
$406$	14.0158			0.0345217
$407$		−	55.3781i		−	0.136064i
$408$	−157.485	+	157.485i	−0.385992	+	0.385992i
$409$	−463.727	+	463.727i	−1.13381	+	1.13381i	−0.144267	+	0.989539i	$0.546082\pi$
$409$	−463.727	+	463.727i	−1.13381	+	1.13381i	−0.989539	+	0.144267i	$0.953918\pi$
$410$		0			0
$411$	−514.792	−	514.792i	−1.25254	−	1.25254i
$412$	−371.151			−0.900852
$413$			36.9704i			0.0895167i
$414$	−201.398	−	201.398i	−0.486470	−	0.486470i
$415$		0			0
$416$	52.0000	+	52.0000i	0.125000	+	0.125000i
$417$	1146.28			2.74888
$418$	144.272	−	144.272i	0.345149	−	0.345149i
$419$	517.167			1.23429			0.617144	−	0.786850i	$-0.288290\pi$
$419$	517.167			1.23429			0.617144	+	0.786850i	$0.288290\pi$
$420$		0			0
$421$	−45.3031	+	45.3031i	−0.107608	+	0.107608i	−0.758861	−	0.651253i	$-0.774244\pi$
$421$	−45.3031	+	45.3031i	−0.107608	+	0.107608i	0.651253	+	0.758861i	$0.274244\pi$
$422$	257.530	−	257.530i	0.610261	−	0.610261i
$423$	−706.856	−	706.856i	−1.67105	−	1.67105i
$424$	100.606	+	100.606i	0.237279	+	0.237279i
$425$		0			0
$426$			647.737i			1.52051i
$427$	−12.8717	−	12.8717i	−0.0301445	−	0.0301445i
$428$		−	317.485i		−	0.741787i
$429$	−695.434	+	695.434i	−1.62106	+	1.62106i
$430$		0			0
$431$	295.348	−	295.348i	0.685263	−	0.685263i	−0.275918	−	0.961181i	$-0.588982\pi$
$431$	295.348	−	295.348i	0.685263	−	0.685263i	0.961181	+	0.275918i	$0.0889818\pi$
$432$	32.0000			0.0740741
$433$			74.6061i			0.172301i	0.996282	+	0.0861503i	$0.0274565\pi$
$433$			74.6061i			0.172301i	−0.996282	+	0.0861503i	$0.972543\pi$
$434$	−25.1816	+	25.1816i	−0.0580222	+	0.0580222i
$435$		0			0
$436$	−138.363	−	138.363i	−0.317347	−	0.317347i
$437$	−111.909	−	111.909i	−0.256085	−	0.256085i
$438$	−443.060			−1.01155
$439$		−	158.302i		−	0.360597i	−0.983612	−	0.180298i	$-0.942294\pi$
$439$		−	158.302i		−	0.360597i	0.983612	−	0.180298i	$-0.0577064\pi$
$440$		0			0
$441$		−	519.283i		−	1.17751i
$442$	230.060	−	230.060i	0.520498	−	0.520498i
$443$	281.258			0.634893			0.317447	−	0.948276i	$-0.397175\pi$
$443$	281.258			0.634893			0.317447	+	0.948276i	$0.397175\pi$
$444$	20.4949	−	20.4949i	0.0461597	−	0.0461597i
$445$		0			0
$446$		−	217.121i		−	0.486819i
$447$	−641.131	+	641.131i	−1.43430	+	1.43430i
$448$	5.39388	−	5.39388i	0.0120399	−	0.0120399i
$449$	404.333	+	404.333i	0.900518	+	0.900518i	0.995481	−	0.0949627i	$-0.0302732\pi$
$449$	404.333	+	404.333i	0.900518	+	0.900518i	−0.0949627	+	0.995481i	$0.530273\pi$
$450$		0			0
$451$	−322.061			−0.714105
$452$			26.7878i			0.0592649i
$453$	−358.959	−	358.959i	−0.792404	−	0.792404i
$454$			160.045i			0.352523i
$455$		0			0
$456$	106.788			0.234184
$457$	318.576	−	318.576i	0.697102	−	0.697102i	−0.266683	−	0.963784i	$-0.585928\pi$
$457$	318.576	−	318.576i	0.697102	−	0.697102i	0.963784	+	0.266683i	$0.0859276\pi$
$458$	−422.302			−0.922057
$459$		−	141.576i		−	0.308443i
$460$		0			0
$461$	−216.454	+	216.454i	−0.469532	+	0.469532i	−0.901763	−	0.432231i	$-0.857726\pi$
$461$	−216.454	+	216.454i	−0.469532	+	0.469532i	0.432231	+	0.901763i	$0.357726\pi$
$462$	72.1362	+	72.1362i	0.156139	+	0.156139i
$463$	187.401	+	187.401i	0.404753	+	0.404753i	0.879904	−	0.475151i	$-0.157607\pi$
$463$	187.401	+	187.401i	0.404753	+	0.404753i	−0.475151	+	0.879904i	$0.657607\pi$
$464$	41.5755			0.0896024
$465$		0			0
$466$	94.0000	+	94.0000i	0.201717	+	0.201717i
$467$			78.1066i			0.167252i	0.996497	+	0.0836260i	$0.0266501\pi$
$467$			78.1066i			0.167252i	−0.996497	+	0.0836260i	$0.973350\pi$
$468$	−280.747			−0.599887
$469$	−49.5765			−0.105707
$470$		0			0
$471$	−784.863			−1.66638
$472$			109.666i			0.232344i
$473$	721.908	−	721.908i	1.52623	−	1.52623i
$474$	−190.384	+	190.384i	−0.401653	+	0.401653i
$475$		0			0
$476$	−23.8638	−	23.8638i	−0.0501340	−	0.0501340i
$477$	−543.170			−1.13872
$478$			43.2872i			0.0905591i
$479$	296.007	+	296.007i	0.617968	+	0.617968i	0.945010	−	0.327042i	$-0.106052\pi$
$479$	296.007	+	296.007i	0.617968	+	0.617968i	−0.327042	+	0.945010i	$0.606052\pi$
$480$		0			0
$481$	−29.9398	+	29.9398i	−0.0622449	+	0.0622449i
$482$	−246.120			−0.510623
$483$	55.9546	−	55.9546i	0.115848	−	0.115848i
$484$	336.182			0.694590
$485$		0			0
$486$	346.025	−	346.025i	0.711986	−	0.711986i
$487$	−340.250	+	340.250i	−0.698665	+	0.698665i	−0.964122	−	0.265458i	$-0.914477\pi$
$487$	−340.250	+	340.250i	−0.698665	+	0.698665i	0.265458	+	0.964122i	$0.414477\pi$
$488$	−38.1816	−	38.1816i	−0.0782410	−	0.0782410i
$489$	875.403	+	875.403i	1.79019	+	1.79019i
$490$		0			0
$491$		−	551.923i		−	1.12408i	−0.827110	−	0.562040i	$-0.810017\pi$
$491$		−	551.923i		−	1.12408i	0.827110	−	0.562040i	$-0.189983\pi$
$492$	−119.192	−	119.192i	−0.242260	−	0.242260i
$493$		−	183.940i		−	0.373103i
$494$	−156.000			−0.315789
$495$		0			0
$496$	−74.6969	+	74.6969i	−0.150599	+	0.150599i
$497$	−98.1520			−0.197489
$498$		−	671.131i		−	1.34765i
$499$	116.023	−	116.023i	0.232510	−	0.232510i	−0.581229	−	0.813740i	$-0.697428\pi$
$499$	116.023	−	116.023i	0.232510	−	0.232510i	0.813740	+	0.581229i	$0.197428\pi$
$500$		0			0
$501$	−852.413	−	852.413i	−1.70142	−	1.70142i
$502$	−403.151	−	403.151i	−0.803090	−	0.803090i
$503$	636.727			1.26586			0.632929	−	0.774210i	$-0.281853\pi$
$503$	636.727			1.26586			0.632929	+	0.774210i	$0.281853\pi$
$504$			29.1214i			0.0577806i
$505$		0			0
$506$		−	448.484i		−	0.886331i
$507$	751.964			1.48316
$508$	−106.424			−0.209497
$509$	−40.5449	+	40.5449i	−0.0796560	+	0.0796560i	−0.745812	−	0.666156i	$-0.767938\pi$
$509$	−40.5449	+	40.5449i	−0.0796560	+	0.0796560i	0.666156	+	0.745812i	$0.267938\pi$
$510$		0			0
$511$		−	67.1373i		−	0.131384i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	−48.0000	+	48.0000i	−0.0935673	+	0.0935673i
$514$	−435.788	−	435.788i	−0.847836	−	0.847836i
$515$		0			0
$516$	534.343			1.03555
$517$		−	1574.06i		−	3.04460i
$518$	3.10561	+	3.10561i	0.00599538	+	0.00599538i
$519$		−	1411.70i		−	2.72004i
$520$		0			0
$521$	−760.908			−1.46048			−0.730238	−	0.683193i	$-0.760591\pi$
$521$	−760.908			−1.46048			−0.730238	+	0.683193i	$0.760591\pi$
$522$	−112.233	+	112.233i	−0.215005	+	0.215005i
$523$	160.000			0.305927			0.152964	−	0.988232i	$-0.451118\pi$
$523$	160.000			0.305927			0.152964	+	0.988232i	$0.451118\pi$
$524$			195.060i			0.372252i
$525$		0			0
$526$	404.499	−	404.499i	0.769010	−	0.769010i
$527$	330.477	+	330.477i	0.627091	+	0.627091i
$528$	213.980	+	213.980i	0.405264	+	0.405264i
$529$	181.120			0.342383
$530$		0			0
$531$	−296.043	−	296.043i	−0.557520	−	0.557520i
$532$			16.1816i			0.0304166i
$533$	174.120	+	174.120i	0.326680	+	0.326680i
$534$	−56.0908			−0.105039
$535$		0			0
$536$	−147.060			−0.274366
$537$			622.929i			1.16002i
$538$	−456.757	+	456.757i	−0.848991	+	0.848991i
$539$	578.182	−	578.182i	1.07269	−	1.07269i
$540$		0			0
$541$	−184.091	−	184.091i	−0.340279	−	0.340279i	0.516193	−	0.856472i	$-0.327349\pi$
$541$	−184.091	−	184.091i	−0.340279	−	0.340279i	−0.856472	+	0.516193i	$0.827349\pi$
$542$	481.348			0.888097
$543$			477.712i			0.879764i
$544$	−70.7878	−	70.7878i	−0.130125	−	0.130125i
$545$		0			0
$546$		−	78.0000i		−	0.142857i
$547$	−758.983			−1.38754			−0.693769	−	0.720198i	$-0.744051\pi$
$547$	−758.983			−1.38754			−0.693769	+	0.720198i	$0.744051\pi$
$548$	231.394	−	231.394i	0.422252	−	0.422252i
$549$	206.142			0.375486
$550$		0			0
$551$	−62.3633	+	62.3633i	−0.113182	+	0.113182i
$552$	165.980	−	165.980i	0.300688	−	0.300688i
$553$	−28.8490	−	28.8490i	−0.0521681	−	0.0521681i
$554$	−173.151	−	173.151i	−0.312547	−	0.312547i
$555$		0			0
$556$			515.242i			0.926694i
$557$	−165.666	−	165.666i	−0.297426	−	0.297426i	0.542579	−	0.840005i	$-0.317448\pi$
$557$	−165.666	−	165.666i	−0.297426	−	0.297426i	−0.840005	+	0.542579i	$0.817448\pi$
$558$		−	403.287i		−	0.722737i
$559$	−780.590			−1.39640
$560$		0			0
$561$	946.696	−	946.696i	1.68751	−	1.68751i
$562$	−63.6367			−0.113233
$563$			923.514i			1.64035i	0.572116	+	0.820173i	$0.306123\pi$
$563$			923.514i			1.64035i	−0.572116	+	0.820173i	$0.693877\pi$
$564$	582.545	−	582.545i	1.03288	−	1.03288i
$565$		0			0
$566$	195.106	+	195.106i	0.344710	+	0.344710i
$567$	41.5232	+	41.5232i	0.0732332	+	0.0732332i
$568$	−291.151			−0.512590
$569$			809.788i			1.42318i	0.702596	+	0.711589i	$0.252024\pi$
$569$			809.788i			1.42318i	−0.702596	+	0.711589i	$0.747976\pi$
$570$		0			0
$571$			596.363i			1.04442i	0.852817	+	0.522210i	$0.174892\pi$
$571$			596.363i			1.04442i	−0.852817	+	0.522210i	$0.825108\pi$
$572$	−312.590	−	312.590i	−0.546487	−	0.546487i
$573$	332.767			0.580746
$574$	18.0612	−	18.0612i	0.0314656	−	0.0314656i
$575$		0			0
$576$			86.3837i			0.149972i
$577$	649.453	−	649.453i	1.12557	−	1.12557i	0.134679	−	0.990889i	$-0.457000\pi$
$577$	649.453	−	649.453i	1.12557	−	1.12557i	0.990889	−	0.134679i	$-0.0430004\pi$
$578$	−24.1816	+	24.1816i	−0.0418367	+	0.0418367i
$579$	−1151.88	−	1151.88i	−1.98943	−	1.98943i
$580$		0			0
$581$	101.697			0.175038
$582$			23.1918i			0.0398485i
$583$	−604.779	−	604.779i	−1.03736	−	1.03736i
$584$		−	199.151i		−	0.341012i
$585$		0			0
$586$	−293.576			−0.500982
$587$	−462.765	+	462.765i	−0.788356	+	0.788356i	−0.981225	−	0.192868i	$-0.938221\pi$
$587$	−462.765	+	462.765i	−0.788356	+	0.788356i	0.192868	+	0.981225i	$0.438221\pi$
$588$	427.959			0.727822
$589$		−	224.091i		−	0.380460i
$590$		0			0
$591$	236.767	−	236.767i	0.400622	−	0.400622i
$592$	9.21225	+	9.21225i	0.0155612	+	0.0155612i
$593$	662.666	+	662.666i	1.11748	+	1.11748i	0.992110	+	0.125371i	$0.0400122\pi$
$593$	662.666	+	662.666i	1.11748	+	1.11748i	0.125371	+	0.992110i	$0.459988\pi$
$594$	−192.363			−0.323844
$595$		0			0
$596$	−288.182	−	288.182i	−0.483526	−	0.483526i
$597$			663.918i			1.11209i
$598$	−242.470	+	242.470i	−0.405468	+	0.405468i
$599$	−111.741			−0.186546			−0.0932732	−	0.995641i	$-0.529733\pi$
$599$	−111.741			−0.186546			−0.0932732	+	0.995641i	$0.529733\pi$
$600$		0			0
$601$	−268.303			−0.446428			−0.223214	−	0.974769i	$-0.571655\pi$
$601$	−268.303			−0.446428			−0.223214	+	0.974769i	$0.571655\pi$
$602$			80.9694i			0.134501i
$603$	396.988	−	396.988i	0.658354	−	0.658354i
$604$	161.348	−	161.348i	0.267133	−	0.267133i
$605$		0			0
$606$	224.631	+	224.631i	0.370678	+	0.370678i
$607$	735.650			1.21194			0.605972	−	0.795486i	$-0.292784\pi$
$607$	735.650			1.21194			0.605972	+	0.795486i	$0.292784\pi$
$608$			48.0000i			0.0789474i
$609$	−31.1816	−	31.1816i	−0.0512014	−	0.0512014i
$610$		0			0
$611$	−851.006	+	851.006i	−1.39281	+	1.39281i
$612$	382.182			0.624480
$613$	39.6367	−	39.6367i	0.0646603	−	0.0646603i	−0.674037	−	0.738697i	$-0.735441\pi$
$613$	39.6367	−	39.6367i	0.0646603	−	0.0646603i	0.738697	+	0.674037i	$0.235441\pi$
$614$	−54.4245			−0.0886392
$615$		0			0
$616$	−32.4245	+	32.4245i	−0.0526372	+	0.0526372i
$617$	474.605	−	474.605i	0.769214	−	0.769214i	−0.208754	−	0.977968i	$-0.566941\pi$
$617$	474.605	−	474.605i	0.769214	−	0.769214i	0.977968	+	0.208754i	$0.0669408\pi$
$618$	825.716	+	825.716i	1.33611	+	1.33611i
$619$	70.3633	+	70.3633i	0.113672	+	0.113672i	0.761655	−	0.647983i	$-0.224387\pi$
$619$	70.3633	+	70.3633i	0.113672	+	0.113672i	−0.647983	+	0.761655i	$0.724387\pi$
$620$		0			0
$621$			149.212i			0.240277i
$622$	−532.227	−	532.227i	−0.855670	−	0.855670i
$623$		−	8.49948i		−	0.0136428i
$624$		−	231.373i		−	0.370791i
$625$		0			0
$626$	−580.605	+	580.605i	−0.927484	+	0.927484i
$627$	−641.939			−1.02383
$628$		−	352.788i		−	0.561764i
$629$	40.7571	−	40.7571i	0.0647967	−	0.0647967i
$630$		0			0
$631$	323.803	+	323.803i	0.513158	+	0.513158i	0.915493	−	0.402335i	$-0.131801\pi$
$631$	323.803	+	323.803i	0.513158	+	0.513158i	−0.402335	+	0.915493i	$0.631801\pi$
$632$	−85.5755	−	85.5755i	−0.135404	−	0.135404i
$633$	−1145.88			−1.81023
$634$			496.545i			0.783194i
$635$		0			0
$636$		−	447.646i		−	0.703846i
$637$	−625.181			−0.981445
$638$	−249.925			−0.391732
$639$	785.959	−	785.959i	1.22998	−	1.22998i
$640$		0			0
$641$		−	645.938i		−	1.00770i	−0.863790	−	0.503852i	$-0.831916\pi$
$641$		−	645.938i		−	1.00770i	0.863790	−	0.503852i	$-0.168084\pi$
$642$	−706.322	+	706.322i	−1.10019	+	1.10019i
$643$	201.637	−	201.637i	0.313587	−	0.313587i	−0.532710	−	0.846298i	$-0.678826\pi$
$643$	201.637	−	201.637i	0.313587	−	0.313587i	0.846298	+	0.532710i	$0.178826\pi$
$644$	25.1510	+	25.1510i	0.0390544	+	0.0390544i
$645$		0			0
$646$	212.363			0.328736
$647$			104.136i			0.160952i	0.996757	+	0.0804762i	$0.0256441\pi$
$647$			104.136i			0.160952i	−0.996757	+	0.0804762i	$0.974356\pi$
$648$	123.171	+	123.171i	0.190079	+	0.190079i
$649$		−	659.243i		−	1.01578i
$650$		0			0
$651$	112.045			0.172113
$652$	−393.485	+	393.485i	−0.603504	+	0.603504i
$653$	−155.908			−0.238757			−0.119378	−	0.992849i	$-0.538090\pi$
$653$	−155.908			−0.238757			−0.119378	+	0.992849i	$0.538090\pi$
$654$			615.646i			0.941355i
$655$		0			0
$656$	53.5755	−	53.5755i	0.0816700	−	0.0816700i
$657$	537.606	+	537.606i	0.818274	+	0.818274i
$658$	88.2735	+	88.2735i	0.134154	+	0.134154i
$659$	525.816			0.797900			0.398950	−	0.916973i	$-0.369375\pi$
$659$	525.816			0.797900			0.398950	+	0.916973i	$0.369375\pi$
$660$		0			0
$661$	767.879	+	767.879i	1.16169	+	1.16169i	0.984105	+	0.177587i	$0.0568292\pi$
$661$	767.879	+	767.879i	1.16169	+	1.16169i	0.177587	+	0.984105i	$0.443171\pi$
$662$			890.302i			1.34487i
$663$	−1023.65			−1.54397
$664$	301.666			0.454317
$665$		0			0
$666$	−49.7367			−0.0746798
$667$			193.862i			0.290647i
$668$	383.151	−	383.151i	0.573579	−	0.573579i
$669$	−483.040	+	483.040i	−0.722033	+	0.722033i
$670$		0			0
$671$	229.523	+	229.523i	0.342061	+	0.342061i
$672$	−24.0000			−0.0357143
$673$			446.728i			0.663785i	0.943317	+	0.331893i	$0.107687\pi$
$673$			446.728i			0.663785i	−0.943317	+	0.331893i	$0.892313\pi$
$674$	95.4541	+	95.4541i	0.141623	+	0.141623i
$675$		0			0
$676$			338.000i			0.500000i
$677$	45.1510			0.0666928			0.0333464	−	0.999444i	$-0.489384\pi$
$677$	45.1510			0.0666928			0.0333464	+	0.999444i	$0.489384\pi$
$678$	59.5959	−	59.5959i	0.0878996	−	0.0878996i
$679$	−3.51428			−0.00517567
$680$		0			0
$681$	356.060	−	356.060i	0.522849	−	0.522849i
$682$	449.030	−	449.030i	0.658401	−	0.658401i
$683$	92.0227	+	92.0227i	0.134733	+	0.134733i	0.771257	−	0.636524i	$-0.219628\pi$
$683$	92.0227	+	92.0227i	0.134733	+	0.134733i	−0.636524	+	0.771257i	$0.719628\pi$
$684$	−129.576	−	129.576i	−0.189438	−	0.189438i
$685$		0			0
$686$			130.924i			0.190851i
$687$	939.514	+	939.514i	1.36756	+	1.36756i
$688$			240.182i			0.349101i
$689$			653.940i			0.949114i
$690$		0			0
$691$	672.386	−	672.386i	0.973062	−	0.973062i	−0.0265844	−	0.999647i	$-0.508463\pi$
$691$	672.386	−	672.386i	0.973062	−	0.973062i	0.999647	+	0.0265844i	$0.00846307\pi$
$692$	634.545			0.916972
$693$		−	175.059i		−	0.252611i
$694$	41.6209	−	41.6209i	0.0599725	−	0.0599725i
$695$		0			0
$696$	−92.4949	−	92.4949i	−0.132895	−	0.132895i
$697$	−237.031	−	237.031i	−0.340073	−	0.340073i
$698$	−373.757			−0.535469
$699$		−	418.252i		−	0.598358i
$700$		0			0
$701$			1188.09i			1.69485i	0.530915	+	0.847425i	$0.321848\pi$
$701$			1188.09i			1.69485i	−0.530915	+	0.847425i	$0.678152\pi$
$702$	104.000	+	104.000i	0.148148	+	0.148148i
$703$	−27.6367			−0.0393126
$704$	−96.1816	+	96.1816i	−0.136622	+	0.136622i
$705$		0			0
$706$		−	99.0306i		−	0.140270i
$707$	−34.0385	+	34.0385i	−0.0481450	+	0.0481450i
$708$	243.980	−	243.980i	0.344604	−	0.344604i
$709$	−309.031	−	309.031i	−0.435868	−	0.435868i	0.454751	−	0.890619i	$-0.349728\pi$
$709$	−309.031	−	309.031i	−0.435868	−	0.435868i	−0.890619	+	0.454751i	$0.849728\pi$
$710$		0			0
$711$	462.020			0.649818
$712$		−	25.2122i		−	0.0354105i
$713$	−348.303	−	348.303i	−0.488504	−	0.488504i
$714$			106.182i			0.148714i
$715$		0			0
$716$	−280.000			−0.391061
$717$	96.3031	−	96.3031i	0.134314	−	0.134314i
$718$	469.076			0.653309
$719$			793.589i			1.10374i	0.833930	+	0.551870i	$0.186086\pi$
$719$			793.589i			1.10374i	−0.833930	+	0.551870i	$0.813914\pi$
$720$		0			0
$721$	−125.121	+	125.121i	−0.173539	+	0.173539i
$722$	289.000	+	289.000i	0.400277	+	0.400277i
$723$	547.555	+	547.555i	0.757338	+	0.757338i
$724$	−214.727			−0.296584
$725$		0			0
$726$	−747.918	−	747.918i	−1.03019	−	1.03019i
$727$		−	173.090i		−	0.238088i	−0.992889	−	0.119044i	$-0.962017\pi$
$727$		−	173.090i		−	0.238088i	0.992889	−	0.119044i	$-0.0379829\pi$
$728$	35.0602			0.0481596
$729$	−985.363			−1.35166
$730$		0			0
$731$	1062.62			1.45365
$732$			169.889i			0.232088i
$733$	451.727	−	451.727i	0.616271	−	0.616271i	−0.328302	−	0.944573i	$-0.606476\pi$
$733$	451.727	−	451.727i	0.616271	−	0.616271i	0.944573	+	0.328302i	$0.106476\pi$
$734$	111.287	−	111.287i	0.151617	−	0.151617i
$735$		0			0
$736$	74.6061	+	74.6061i	0.101367	+	0.101367i
$737$	884.031			1.19950
$738$			289.253i			0.391942i
$739$	452.643	+	452.643i	0.612507	+	0.612507i	0.943599	−	0.331092i	$-0.107417\pi$
$739$	452.643	+	452.643i	0.612507	+	0.612507i	−0.331092	+	0.943599i	$0.607417\pi$
$740$		0			0
$741$	347.060	+	347.060i	0.468367	+	0.468367i
$742$	67.8321			0.0914180
$743$	510.295	−	510.295i	0.686804	−	0.686804i	−0.274720	−	0.961524i	$-0.588585\pi$
$743$	510.295	−	510.295i	0.686804	−	0.686804i	0.961524	+	0.274720i	$0.0885853\pi$
$744$	332.363			0.446725
$745$		0			0
$746$	58.9388	−	58.9388i	0.0790064	−	0.0790064i
$747$	−814.345	+	814.345i	−1.09015	+	1.09015i
$748$	425.530	+	425.530i	0.568891	+	0.568891i
$749$	−107.030	−	107.030i	−0.142897	−	0.142897i
$750$		0			0
$751$			1224.50i			1.63049i	0.579115	+	0.815246i	$0.303398\pi$
$751$			1224.50i			1.63049i	−0.579115	+	0.815246i	$0.696602\pi$
$752$	261.848	+	261.848i	0.348202	+	0.348202i
$753$			1793.82i			2.38223i
$754$	135.120	+	135.120i	0.179205	+	0.179205i
$755$		0			0
$756$	10.7878	−	10.7878i	0.0142695	−	0.0142695i
$757$	−1440.06			−1.90232			−0.951161	−	0.308694i	$-0.900108\pi$
$757$	−1440.06			−1.90232			−0.951161	+	0.308694i	$0.900108\pi$
$758$		−	302.470i		−	0.399037i
$759$	−997.762	+	997.762i	−1.31457	+	1.31457i
$760$		0			0
$761$	390.393	+	390.393i	0.513000	+	0.513000i	0.915444	−	0.402445i	$-0.131839\pi$
$761$	390.393	+	390.393i	0.513000	+	0.513000i	−0.402445	+	0.915444i	$0.631839\pi$
$762$	236.767	+	236.767i	0.310718	+	0.310718i
$763$	−93.2893			−0.122266
$764$			149.576i			0.195779i
$765$		0			0
$766$			1021.91i			1.33408i
$767$	−356.416	+	356.416i	−0.464688	+	0.464688i
$768$	−71.1918			−0.0926977
$769$	409.090	−	409.090i	0.531976	−	0.531976i	−0.389184	−	0.921160i	$-0.627243\pi$
$769$	409.090	−	409.090i	0.531976	−	0.531976i	0.921160	+	0.389184i	$0.127243\pi$
$770$		0			0
$771$			1939.03i			2.51496i
$772$	517.757	−	517.757i	0.670670	−	0.670670i
$773$	−18.0612	+	18.0612i	−0.0233651	+	0.0233651i	−0.718693	−	0.695328i	$-0.755259\pi$
$773$	−18.0612	+	18.0612i	−0.0233651	+	0.0233651i	0.695328	+	0.718693i	$0.255259\pi$
$774$	−648.368	−	648.368i	−0.837685	−	0.837685i
$775$		0			0
$776$	−10.4245			−0.0134336
$777$		−	13.8184i		−	0.0177843i
$778$	10.0612	+	10.0612i	0.0129322	+	0.0129322i
$779$			160.727i			0.206324i
$780$		0			0
$781$	1750.21			2.24099
$782$	330.075	−	330.075i	0.422091	−	0.422091i
$783$	83.1510			0.106195
$784$			192.363i			0.245361i
$785$		0			0
$786$	433.959	−	433.959i	0.552111	−	0.552111i
$787$	−148.461	−	148.461i	−0.188642	−	0.188642i	0.606467	−	0.795109i	$-0.292586\pi$
$787$	−148.461	−	148.461i	−0.188642	−	0.188642i	−0.795109	+	0.606467i	$0.792586\pi$
$788$	106.424	+	106.424i	0.135056	+	0.135056i
$789$	−1799.82			−2.28114
$790$		0			0
$791$	9.03062	+	9.03062i	0.0114167	+	0.0114167i
$792$		−	519.283i		−	0.655660i
$793$		−	248.181i		−	0.312964i
$794$	−970.182			−1.22189
$795$		0			0
$796$	−298.424			−0.374905
$797$		−	342.878i		−	0.430210i	−0.976591	−	0.215105i	$-0.930991\pi$
$797$		−	342.878i		−	0.430210i	0.976591	−	0.215105i	$-0.0690094\pi$
$798$	36.0000	−	36.0000i	0.0451128	−	0.0451128i
$799$	1158.48	−	1158.48i	1.44991	−	1.44991i
$800$		0			0
$801$	68.0602	+	68.0602i	0.0849690	+	0.0849690i
$802$	448.727			0.559509
$803$			1197.17i			1.49087i
$804$	327.171	+	327.171i	0.406930	+	0.406930i
$805$		0			0
$806$	−485.530			−0.602395
$807$	2032.34			2.51838
$808$	−100.969	+	100.969i	−0.124962	+	0.124962i
$809$	1194.00			1.47590			0.737948	−	0.674857i	$-0.235795\pi$
$809$	1194.00			1.47590			0.737948	+	0.674857i	$0.235795\pi$
$810$		0			0
$811$	441.734	−	441.734i	0.544679	−	0.544679i	−0.380218	−	0.924897i	$-0.624151\pi$
$811$	441.734	−	441.734i	0.544679	−	0.544679i	0.924897	+	0.380218i	$0.124151\pi$
$812$	14.0158	−	14.0158i	0.0172609	−	0.0172609i
$813$	−1070.88	−	1070.88i	−1.31719	−	1.31719i
$814$	−55.3781	−	55.3781i	−0.0680320	−	0.0680320i
$815$		0			0
$816$			314.969i			0.385992i
$817$	−360.272	−	360.272i	−0.440970	−	0.440970i
$818$			927.453i			1.13381i
$819$	−94.6447	+	94.6447i	−0.115561	+	0.115561i
$820$		0			0
$821$	−397.485	+	397.485i	−0.484147	+	0.484147i	−0.906453	−	0.422306i	$-0.861221\pi$
$821$	−397.485	+	397.485i	−0.484147	+	0.484147i	0.422306	+	0.906453i	$0.361221\pi$
$822$	−1029.58			−1.25254
$823$			478.061i			0.580876i	0.956894	+	0.290438i	$0.0938011\pi$
$823$			478.061i			0.580876i	−0.956894	+	0.290438i	$0.906199\pi$
$824$	−371.151	+	371.151i	−0.450426	+	0.450426i
$825$		0			0
$826$	36.9704	+	36.9704i	0.0447584	+	0.0447584i
$827$	−743.310	−	743.310i	−0.898803	−	0.898803i	0.0965275	−	0.995330i	$-0.469226\pi$
$827$	−743.310	−	743.310i	−0.898803	−	0.898803i	−0.995330	+	0.0965275i	$0.969226\pi$
$828$	−402.797			−0.486470
$829$			1039.94i			1.25445i	0.778838	+	0.627225i	$0.215810\pi$
$829$			1039.94i			1.25445i	−0.778838	+	0.627225i	$0.784190\pi$
$830$		0			0
$831$			770.434i			0.927116i
$832$	104.000			0.125000
$833$	851.060			1.02168
$834$	1146.28	−	1146.28i	1.37444	−	1.37444i
$835$		0			0
$836$		−	288.545i		−	0.345149i
$837$	−149.394	+	149.394i	−0.178487	+	0.178487i
$838$	517.167	−	517.167i	0.617144	−	0.617144i
$839$	−579.939	−	579.939i	−0.691226	−	0.691226i	0.271276	−	0.962502i	$-0.412555\pi$
$839$	−579.939	−	579.939i	−0.691226	−	0.691226i	−0.962502	+	0.271276i	$0.912555\pi$
$840$		0			0
$841$	−732.967			−0.871543
$842$			90.6061i			0.107608i
$843$	141.576	+	141.576i	0.167942	+	0.167942i
$844$		−	515.060i		−	0.610261i
$845$		0			0
$846$	−1413.71			−1.67105
$847$	113.333	−	113.333i	0.133805	−	0.133805i
$848$	201.212			0.237279
$849$		−	868.120i		−	1.02252i
$850$		0			0
$851$	−42.9556	+	42.9556i	−0.0504766	+	0.0504766i
$852$	647.737	+	647.737i	0.760254	+	0.760254i
$853$	256.212	+	256.212i	0.300366	+	0.300366i	0.841157	−	0.540791i	$-0.181875\pi$
$853$	256.212	+	256.212i	0.300366	+	0.300366i	−0.540791	+	0.841157i	$0.681875\pi$
$854$	−25.7434			−0.0301445
$855$		0			0
$856$	−317.485	−	317.485i	−0.370893	−	0.370893i
$857$			474.969i			0.554223i	0.960838	+	0.277112i	$0.0893772\pi$
$857$			474.969i			0.554223i	−0.960838	+	0.277112i	$0.910623\pi$
$858$			1390.87i			1.62106i
$859$	−1241.53			−1.44532			−0.722660	−	0.691204i	$-0.757081\pi$
$859$	−1241.53			−1.44532			−0.722660	+	0.691204i	$0.757081\pi$
$860$		0			0
$861$	−80.3633			−0.0933371
$862$		−	590.697i		−	0.685263i
$863$	−146.976	+	146.976i	−0.170309	+	0.170309i	−0.787115	−	0.616806i	$-0.788426\pi$
$863$	−146.976	+	146.976i	−0.170309	+	0.170309i	0.616806	+	0.787115i	$0.288426\pi$
$864$	32.0000	−	32.0000i	0.0370370	−	0.0370370i
$865$		0			0
$866$	74.6061	+	74.6061i	0.0861503	+	0.0861503i
$867$	107.596			0.124101
$868$			50.3633i			0.0580222i
$869$	514.424	+	514.424i	0.591973	+	0.591973i
$870$		0			0
$871$	−477.946	−	477.946i	−0.548732	−	0.548732i
$872$	−276.727			−0.317347
$873$	28.1408	−	28.1408i	0.0322346	−	0.0322346i
$874$	−223.818			−0.256085
$875$		0			0
$876$	−443.060	+	443.060i	−0.505776	+	0.505776i
$877$	−99.8173	+	99.8173i	−0.113817	+	0.113817i	−0.761721	−	0.647905i	$-0.775646\pi$
$877$	−99.8173	+	99.8173i	−0.113817	+	0.113817i	0.647905	+	0.761721i	$0.275646\pi$
$878$	−158.302	−	158.302i	−0.180298	−	0.180298i
$879$	653.131	+	653.131i	0.743038	+	0.743038i
$880$		0			0
$881$			318.273i			0.361264i	0.983551	+	0.180632i	$0.0578143\pi$
$881$			318.273i			0.361264i	−0.983551	+	0.180632i	$0.942186\pi$
$882$	−519.283	−	519.283i	−0.588756	−	0.588756i
$883$			1458.54i			1.65180i	0.563814	+	0.825902i	$0.309334\pi$
$883$			1458.54i			1.65180i	−0.563814	+	0.825902i	$0.690666\pi$
$884$		−	460.120i		−	0.520498i
$885$		0			0
$886$	281.258	−	281.258i	0.317447	−	0.317447i
$887$	−573.576			−0.646647			−0.323323	−	0.946289i	$-0.604800\pi$
$887$	−573.576			−0.646647			−0.323323	+	0.946289i	$0.604800\pi$
$888$		−	40.9898i		−	0.0461597i
$889$	−35.8775	+	35.8775i	−0.0403572	+	0.0403572i
$890$		0			0
$891$	−740.427	−	740.427i	−0.831006	−	0.831006i
$892$	−217.121	−	217.121i	−0.243410	−	0.243410i
$893$	−785.544			−0.879668
$894$			1282.26i			1.43430i
$895$		0			0
$896$		−	10.7878i		−	0.0120399i
$897$	1078.87			1.20275
$898$	808.665			0.900518
$899$	−194.098	+	194.098i	−0.215904	+	0.215904i
$900$		0			0
$901$		−	890.210i		−	0.988025i
$902$	−322.061	+	322.061i	−0.357052	+	0.357052i
$903$	180.136	−	180.136i	0.199486	−	0.199486i
$904$	26.7878	+	26.7878i	0.0296325	+	0.0296325i
$905$		0			0
$906$	−717.918			−0.792404
$907$			743.392i			0.819616i	0.912172	+	0.409808i	$0.134404\pi$
$907$			743.392i			0.819616i	−0.912172	+	0.409808i	$0.865596\pi$
$908$	160.045	+	160.045i	0.176261	+	0.176261i
$909$		−	545.132i		−	0.599705i
$910$		0			0
$911$	1593.21			1.74886			0.874430	−	0.485151i	$-0.161235\pi$
$911$	1593.21			1.74886			0.874430	+	0.485151i	$0.161235\pi$
$912$	106.788	−	106.788i	0.117092	−	0.117092i
$913$	−1813.42			−1.98622
$914$		−	637.151i		−	0.697102i
$915$		0			0
$916$	−422.302	+	422.302i	−0.461028	+	0.461028i
$917$	65.7582	+	65.7582i	0.0717101	+	0.0717101i
$918$	−141.576	−	141.576i	−0.154222	−	0.154222i
$919$	−1111.03			−1.20895			−0.604477	−	0.796623i	$-0.706618\pi$
$919$	−1111.03			−1.20895			−0.604477	+	0.796623i	$0.706618\pi$
$920$		0			0
$921$	121.081	+	121.081i	0.131466	+	0.131466i
$922$			432.908i			0.469532i
$923$	−946.241	−	946.241i	−1.02518	−	1.02518i
$924$	144.272			0.156139
$925$		0			0
$926$	374.802			0.404753
$927$		−	2003.84i		−	2.16164i
$928$	41.5755	−	41.5755i	0.0448012	−	0.0448012i
$929$	670.757	−	670.757i	0.722021	−	0.722021i	−0.246996	−	0.969017i	$-0.579443\pi$
$929$	670.757	−	670.757i	0.722021	−	0.722021i	0.969017	+	0.246996i	$0.0794434\pi$
$930$		0			0
$931$	−288.545	−	288.545i	−0.309930	−	0.309930i
$932$	188.000			0.201717
$933$			2368.14i			2.53820i
$934$	78.1066	+	78.1066i	0.0836260	+	0.0836260i
$935$		0			0
$936$	−280.747	+	280.747i	−0.299943	+	0.299943i
$937$	1367.67			1.45962			0.729811	−	0.683649i	$-0.239608\pi$
$937$	1367.67			1.45962			0.729811	+	0.683649i	$0.239608\pi$
$938$	−49.5765	+	49.5765i	−0.0528535	+	0.0528535i
$939$	2583.40			2.75122
$940$		0			0
$941$	−171.574	+	171.574i	−0.182332	+	0.182332i	−0.792371	−	0.610039i	$-0.791154\pi$
$941$	−171.574	+	171.574i	−0.182332	+	0.182332i	0.610039	+	0.792371i	$0.291154\pi$
$942$	−784.863	+	784.863i	−0.833188	+	0.833188i
$943$	249.816	+	249.816i	0.264917	+	0.264917i
$944$	109.666	+	109.666i	0.116172	+	0.116172i
$945$		0			0
$946$		−	1443.82i		−	1.52623i
$947$	−77.5528	−	77.5528i	−0.0818931	−	0.0818931i	0.664974	−	0.746867i	$-0.268443\pi$
$947$	−77.5528	−	77.5528i	−0.0818931	−	0.0818931i	−0.746867	+	0.664974i	$0.768443\pi$
$948$			380.767i			0.401653i
$949$	647.241	−	647.241i	0.682024	−	0.682024i
$950$		0			0
$951$	1104.69	−	1104.69i	1.16160	−	1.16160i
$952$	−47.7276			−0.0501340
$953$			94.7571i			0.0994304i	0.998763	+	0.0497152i	$0.0158314\pi$
$953$			94.7571i			0.0994304i	−0.998763	+	0.0497152i	$0.984169\pi$
$954$	−543.170	+	543.170i	−0.569361	+	0.569361i
$955$		0			0
$956$	43.2872	+	43.2872i	0.0452795	+	0.0452795i
$957$	556.019	+	556.019i	0.581002	+	0.581002i
$958$	592.014			0.617968
$959$		−	156.014i		−	0.162684i
$960$		0			0
$961$			263.546i			0.274241i
$962$			59.8796i			0.0622449i
$963$	1714.09			1.77995
$964$	−246.120	+	246.120i	−0.255312	+	0.255312i
$965$		0			0
$966$		−	111.909i		−	0.115848i
$967$	936.917	−	936.917i	0.968890	−	0.968890i	−0.0306400	−	0.999530i	$-0.509755\pi$
$967$	936.917	−	936.917i	0.968890	−	0.968890i	0.999530	+	0.0306400i	$0.00975454\pi$
$968$	336.182	−	336.182i	0.347295	−	0.347295i
$969$	−472.454	−	472.454i	−0.487569	−	0.487569i
$970$		0			0
$971$	−1135.95			−1.16988			−0.584941	−	0.811076i	$-0.698882\pi$
$971$	−1135.95			−1.16988			−0.584941	+	0.811076i	$0.698882\pi$
$972$		−	692.050i		−	0.711986i
$973$	173.697	+	173.697i	0.178517	+	0.178517i
$974$			680.499i			0.698665i
$975$		0			0
$976$	−76.3633			−0.0782410
$977$	−481.817	+	481.817i	−0.493160	+	0.493160i	−0.909300	−	0.416140i	$-0.863382\pi$
$977$	−481.817	+	481.817i	−0.493160	+	0.493160i	0.416140	+	0.909300i	$0.363382\pi$
$978$	1750.81			1.79019
$979$			151.560i			0.154811i
$980$		0			0
$981$	747.020	−	747.020i	0.761489	−	0.761489i
$982$	−551.923	−	551.923i	−0.562040	−	0.562040i
$983$	−948.234	−	948.234i	−0.964633	−	0.964633i	0.0347629	−	0.999396i	$-0.488932\pi$
$983$	−948.234	−	948.234i	−0.964633	−	0.964633i	−0.999396	+	0.0347629i	$0.988932\pi$
$984$	−238.384			−0.242260
$985$		0			0
$986$	−183.940	−	183.940i	−0.186552	−	0.186552i
$987$		−	392.772i		−	0.397945i
$988$	−156.000	+	156.000i	−0.157895	+	0.157895i
$989$	−1119.94			−1.13240
$990$		0			0
$991$	120.350			0.121442			0.0607212	−	0.998155i	$-0.480660\pi$
$991$	120.350			0.121442			0.0607212	+	0.998155i	$0.480660\pi$
$992$			149.394i			0.150599i
$993$	1980.69	−	1980.69i	1.99466	−	1.99466i
$994$	−98.1520	+	98.1520i	−0.0987445	+	0.0987445i
$995$		0			0
$996$	−671.131	−	671.131i	−0.673826	−	0.673826i
$997$	660.362			0.662349			0.331175	−	0.943569i	$-0.392555\pi$
$997$	660.362			0.662349			0.331175	+	0.943569i	$0.392555\pi$
$998$		−	232.045i		−	0.232510i
$999$	18.4245	+	18.4245i	0.0184429	+	0.0184429i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.3.k.g.551.1	yes	4
5.2	odd	4		650.3.f.h.499.2		4
5.3	odd	4		650.3.f.g.499.1		4
5.4	even	2		650.3.k.f.551.2	yes	4
13.8	odd	4	inner	650.3.k.g.151.1	yes	4
65.8	even	4		650.3.f.h.99.1		4
65.34	odd	4		650.3.k.f.151.2	✓	4
65.47	even	4		650.3.f.g.99.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.3.f.g.99.2		4	65.47	even	4
650.3.f.g.499.1		4	5.3	odd	4
650.3.f.h.99.1		4	65.8	even	4
650.3.f.h.499.2		4	5.2	odd	4
650.3.k.f.151.2	✓	4	65.34	odd	4
650.3.k.f.551.2	yes	4	5.4	even	2
650.3.k.g.151.1	yes	4	13.8	odd	4	inner
650.3.k.g.551.1	yes	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	650.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} -4.44949 q^{3} -2.00000i q^{4} +(-4.44949 + 4.44949i) q^{6} +(-0.674235 - 0.674235i) q^{7} +(-2.00000 - 2.00000i) q^{8} +10.7980 q^{9} +(12.0227 + 12.0227i) q^{11} +8.89898i q^{12} -13.0000i q^{13} -1.34847 q^{14} -4.00000 q^{16} +17.6969i q^{17} +(10.7980 - 10.7980i) q^{18} +(6.00000 - 6.00000i) q^{19} +(3.00000 + 3.00000i) q^{21} +24.0454 q^{22} -18.6515i q^{23} +(8.89898 + 8.89898i) q^{24} +(-13.0000 - 13.0000i) q^{26} -8.00000 q^{27} +(-1.34847 + 1.34847i) q^{28} -10.3939 q^{29} +(18.6742 - 18.6742i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-53.4949 - 53.4949i) q^{33} +(17.6969 + 17.6969i) q^{34} -21.5959i q^{36} +(-2.30306 - 2.30306i) q^{37} -12.0000i q^{38} +57.8434i q^{39} +(-13.3939 + 13.3939i) q^{41} +6.00000 q^{42} -60.0454i q^{43} +(24.0454 - 24.0454i) q^{44} +(-18.6515 - 18.6515i) q^{46} +(-65.4620 - 65.4620i) q^{47} +17.7980 q^{48} -48.0908i q^{49} -78.7423i q^{51} -26.0000 q^{52} -50.3031 q^{53} +(-8.00000 + 8.00000i) q^{54} +2.69694i q^{56} +(-26.6969 + 26.6969i) q^{57} +(-10.3939 + 10.3939i) q^{58} +(-27.4166 - 27.4166i) q^{59} +19.0908 q^{61} -37.3485i q^{62} +(-7.28036 - 7.28036i) q^{63} +8.00000i q^{64} -106.990 q^{66} +(36.7650 - 36.7650i) q^{67} +35.3939 q^{68} +82.9898i q^{69} +(72.7878 - 72.7878i) q^{71} +(-21.5959 - 21.5959i) q^{72} +(49.7878 + 49.7878i) q^{73} -4.60612 q^{74} +(-12.0000 - 12.0000i) q^{76} -16.2122i q^{77} +(57.8434 + 57.8434i) q^{78} +42.7878 q^{79} -61.5857 q^{81} +26.7878i q^{82} +(-75.4166 + 75.4166i) q^{83} +(6.00000 - 6.00000i) q^{84} +(-60.0454 - 60.0454i) q^{86} +46.2474 q^{87} -48.0908i q^{88} +(6.30306 + 6.30306i) q^{89} +(-8.76505 + 8.76505i) q^{91} -37.3031 q^{92} +(-83.0908 + 83.0908i) q^{93} -130.924 q^{94} +(17.7980 - 17.7980i) q^{96} +(2.60612 - 2.60612i) q^{97} +(-48.0908 - 48.0908i) q^{98} +(129.821 + 129.821i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{3} - 8 q^{6} + 12 q^{7} - 8 q^{8} + 4 q^{9} + 4 q^{11} + 24 q^{14} - 16 q^{16} + 4 q^{18} + 24 q^{19} + 12 q^{21} + 8 q^{22} + 16 q^{24} - 52 q^{26} - 32 q^{27} + 24 q^{28} + 76 q^{29}+ \cdots + 436 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^3 - 8 * q^6 + 12 * q^7 - 8 * q^8 + 4 * q^9 + 4 * q^11 + 24 * q^14 - 16 * q^16 + 4 * q^18 + 24 * q^19 + 12 * q^21 + 8 * q^22 + 16 * q^24 - 52 * q^26 - 32 * q^27 + 24 * q^28 + 76 * q^29 + 60 * q^31 - 16 * q^32 - 116 * q^33 + 12 * q^34 - 68 * q^37 + 64 * q^41 + 24 * q^42 + 8 * q^44 - 104 * q^46 - 12 * q^47 + 32 * q^48 - 104 * q^52 - 260 * q^53 - 32 * q^54 - 48 * q^57 + 76 * q^58 + 52 * q^59 - 100 * q^61 - 132 * q^63 - 232 * q^66 - 44 * q^67 + 24 * q^68 + 56 * q^71 - 8 * q^72 - 36 * q^73 - 136 * q^74 - 48 * q^76 + 104 * q^78 - 64 * q^79 + 28 * q^81 - 140 * q^83 + 24 * q^84 - 152 * q^86 + 136 * q^87 + 84 * q^89 + 156 * q^91 - 208 * q^92 - 156 * q^93 - 24 * q^94 + 32 * q^96 + 128 * q^97 - 16 * q^98 + 436 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more