LMFDB - Embedded newform 253.3.c.a.208.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [253,3,Mod(208,253)] 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("253.208"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(253, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 253 = 11 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	253.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.89375068832$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			208.13
Character	$\chi$	$=$	253.208
Dual form			253.3.c.a.208.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.11822i q^{2} -0.499687 q^{3} -0.486856 q^{4} -0.611405 q^{5} +1.05845i q^{6} +3.26188i q^{7} -7.44161i q^{8} -8.75031 q^{9} +1.29509i q^{10} +(-10.9328 - 1.21414i) q^{11} +0.243276 q^{12} -21.2612i q^{13} +6.90937 q^{14} +0.305511 q^{15} -17.7104 q^{16} +1.07517i q^{17} +18.5351i q^{18} -28.1608i q^{19} +0.297666 q^{20} -1.62992i q^{21} +(-2.57182 + 23.1581i) q^{22} +4.79583 q^{23} +3.71848i q^{24} -24.6262 q^{25} -45.0358 q^{26} +8.86960 q^{27} -1.58806i q^{28} +27.8324i q^{29} -0.647140i q^{30} -6.55859 q^{31} +7.74806i q^{32} +(5.46297 + 0.606691i) q^{33} +2.27744 q^{34} -1.99433i q^{35} +4.26014 q^{36} +30.1465 q^{37} -59.6508 q^{38} +10.6239i q^{39} +4.54984i q^{40} +58.5480i q^{41} -3.45253 q^{42} -33.3823i q^{43} +(5.32269 + 0.591112i) q^{44} +5.34998 q^{45} -10.1586i q^{46} +28.9005 q^{47} +8.84966 q^{48} +38.3602 q^{49} +52.1637i q^{50} -0.537248i q^{51} +10.3511i q^{52} +36.5963 q^{53} -18.7878i q^{54} +(6.68436 + 0.742331i) q^{55} +24.2736 q^{56} +14.0716i q^{57} +58.9551 q^{58} -83.1044 q^{59} -0.148740 q^{60} -88.8156i q^{61} +13.8925i q^{62} -28.5424i q^{63} -54.4295 q^{64} +12.9992i q^{65} +(1.28510 - 11.5718i) q^{66} -42.3460 q^{67} -0.523452i q^{68} -2.39642 q^{69} -4.22442 q^{70} +117.091 q^{71} +65.1164i q^{72} -23.2535i q^{73} -63.8569i q^{74} +12.3054 q^{75} +13.7103i q^{76} +(3.96038 - 35.6614i) q^{77} +22.5038 q^{78} -38.1352i q^{79} +10.8282 q^{80} +74.3208 q^{81} +124.018 q^{82} +12.0032i q^{83} +0.793535i q^{84} -0.657363i q^{85} -70.7111 q^{86} -13.9075i q^{87} +(-9.03517 + 81.3576i) q^{88} +61.3905 q^{89} -11.3324i q^{90} +69.3513 q^{91} -2.33488 q^{92} +3.27725 q^{93} -61.2177i q^{94} +17.2176i q^{95} -3.87161i q^{96} -105.559 q^{97} -81.2552i q^{98} +(95.6653 + 10.6241i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 8 q^{3} - 88 q^{4} + 100 q^{9} + 8 q^{14} - 8 q^{15} + 72 q^{16} - 40 q^{20} - 76 q^{22} + 268 q^{25} - 40 q^{26} + 32 q^{27} + 72 q^{31} - 90 q^{33} + 60 q^{34} - 312 q^{36} + 4 q^{37} + 40 q^{38}+ \cdots + 494 q^{99}+O(q^{100}) $ 44 * q + 8 * q^3 - 88 * q^4 + 100 * q^9 + 8 * q^14 - 8 * q^15 + 72 * q^16 - 40 * q^20 - 76 * q^22 + 268 * q^25 - 40 * q^26 + 32 * q^27 + 72 * q^31 - 90 * q^33 + 60 * q^34 - 312 * q^36 + 4 * q^37 + 40 * q^38 + 12 * q^42 + 186 * q^44 - 180 * q^45 - 72 * q^47 + 252 * q^48 - 464 * q^49 + 100 * q^53 - 48 * q^55 + 208 * q^56 - 148 * q^58 - 144 * q^59 - 324 * q^60 - 416 * q^64 - 238 * q^66 + 292 * q^67 + 540 * q^70 + 544 * q^71 - 236 * q^75 + 64 * q^77 - 344 * q^78 + 156 * q^80 - 404 * q^81 + 72 * q^82 - 136 * q^86 + 608 * q^88 - 80 * q^89 - 4 * q^91 - 372 * q^93 + 68 * q^97 + 494 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/253\mathbb{Z}\right)^\times$.

$n$	$24$	$166$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	2.11822i		−	1.05911i	−0.848276	−	0.529555i	$-0.822359\pi$
$2$		−	2.11822i		−	1.05911i	0.848276	−	0.529555i	$-0.177641\pi$
$3$	−0.499687			−0.166562			−0.0832812	−	0.996526i	$-0.526540\pi$
$3$	−0.499687			−0.166562			−0.0832812	+	0.996526i	$0.526540\pi$
$4$	−0.486856			−0.121714
$5$	−0.611405			−0.122281			−0.0611405	−	0.998129i	$-0.519474\pi$
$5$	−0.611405			−0.122281			−0.0611405	+	0.998129i	$0.519474\pi$
$6$			1.05845i			0.176408i
$7$			3.26188i			0.465982i	0.972479	+	0.232991i	$0.0748513\pi$
$7$			3.26188i			0.465982i	−0.972479	+	0.232991i	$0.925149\pi$
$8$		−	7.44161i		−	0.930202i
$9$	−8.75031			−0.972257
$10$			1.29509i			0.129509i
$11$	−10.9328	−	1.21414i	−0.993890	−	0.110376i
$11$	−10.9328	−	1.21414i	−0.993890	−	0.110376i
$12$	0.243276			0.0202730
$13$		−	21.2612i		−	1.63547i	−0.575592	−	0.817737i	$-0.695228\pi$
$13$		−	21.2612i		−	1.63547i	0.575592	−	0.817737i	$-0.304772\pi$
$14$	6.90937			0.493527
$15$	0.305511			0.0203674
$16$	−17.7104			−1.10690
$17$			1.07517i			0.0632452i	0.999500	+	0.0316226i	$0.0100675\pi$
$17$			1.07517i			0.0632452i	−0.999500	+	0.0316226i	$0.989933\pi$
$18$			18.5351i			1.02973i
$19$		−	28.1608i		−	1.48215i	−0.671423	−	0.741074i	$-0.734317\pi$
$19$		−	28.1608i		−	1.48215i	0.671423	−	0.741074i	$-0.265683\pi$
$20$	0.297666			0.0148833
$21$		−	1.62992i		−	0.0776152i
$22$	−2.57182	+	23.1581i	−0.116901	+	1.05264i
$23$	4.79583			0.208514
$23$	4.79583			0.208514
$24$			3.71848i			0.154937i
$25$	−24.6262			−0.985047
$26$	−45.0358			−1.73215
$27$	8.86960			0.328504
$28$		−	1.58806i		−	0.0567166i
$29$			27.8324i			0.959736i	0.877341	+	0.479868i	$0.159316\pi$
$29$			27.8324i			0.959736i	−0.877341	+	0.479868i	$0.840684\pi$
$30$		−	0.647140i		−	0.0215713i
$31$	−6.55859			−0.211568			−0.105784	−	0.994389i	$-0.533735\pi$
$31$	−6.55859			−0.211568			−0.105784	+	0.994389i	$0.533735\pi$
$32$			7.74806i			0.242127i
$33$	5.46297	+	0.606691i	0.165545	+	0.0183846i
$34$	2.27744			0.0669837
$35$		−	1.99433i		−	0.0569808i
$36$	4.26014			0.118337
$37$	30.1465			0.814770			0.407385	−	0.913256i	$-0.366441\pi$
$37$	30.1465			0.814770			0.407385	+	0.913256i	$0.366441\pi$
$38$	−59.6508			−1.56976
$39$			10.6239i			0.272409i
$40$			4.54984i			0.113746i
$41$			58.5480i			1.42800i	0.700145	+	0.714001i	$0.253119\pi$
$41$			58.5480i			1.42800i	−0.700145	+	0.714001i	$0.746881\pi$
$42$	−3.45253			−0.0822030
$43$		−	33.3823i		−	0.776333i	−0.921589	−	0.388167i	$-0.873108\pi$
$43$		−	33.3823i		−	0.776333i	0.921589	−	0.388167i	$-0.126892\pi$
$44$	5.32269	+	0.591112i	0.120970	+	0.0134344i
$45$	5.34998			0.118888
$46$		−	10.1586i		−	0.220840i
$47$	28.9005			0.614905			0.307453	−	0.951563i	$-0.400523\pi$
$47$	28.9005			0.614905			0.307453	+	0.951563i	$0.400523\pi$
$48$	8.84966			0.184368
$49$	38.3602			0.782860
$50$			52.1637i			1.04327i
$51$		−	0.537248i		−	0.0105343i
$52$			10.3511i			0.199060i
$53$	36.5963			0.690497			0.345248	−	0.938511i	$-0.387795\pi$
$53$	36.5963			0.690497			0.345248	+	0.938511i	$0.387795\pi$
$54$		−	18.7878i		−	0.347922i
$55$	6.68436	+	0.742331i	0.121534	+	0.0134969i
$56$	24.2736			0.433458
$57$			14.0716i			0.246870i
$58$	58.9551			1.01647
$59$	−83.1044			−1.40855			−0.704274	−	0.709928i	$-0.748727\pi$
$59$	−83.1044			−1.40855			−0.704274	+	0.709928i	$0.748727\pi$
$60$	−0.148740			−0.00247900
$61$		−	88.8156i		−	1.45599i	−0.685581	−	0.727996i	$-0.740452\pi$
$61$		−	88.8156i		−	1.45599i	0.685581	−	0.727996i	$-0.259548\pi$
$62$			13.8925i			0.224073i
$63$		−	28.5424i		−	0.453055i
$64$	−54.4295			−0.850461
$65$			12.9992i			0.199987i
$66$	1.28510	−	11.5718i	0.0194713	−	0.175330i
$67$	−42.3460			−0.632030			−0.316015	−	0.948754i	$-0.602345\pi$
$67$	−42.3460			−0.632030			−0.316015	+	0.948754i	$0.602345\pi$
$68$		−	0.523452i		−	0.00769783i
$69$	−2.39642			−0.0347307
$70$	−4.22442			−0.0603489
$71$	117.091			1.64917			0.824583	−	0.565742i	$-0.191410\pi$
$71$	117.091			1.64917			0.824583	+	0.565742i	$0.191410\pi$
$72$			65.1164i			0.904395i
$73$		−	23.2535i		−	0.318542i	−0.987235	−	0.159271i	$-0.949086\pi$
$73$		−	23.2535i		−	0.318542i	0.987235	−	0.159271i	$-0.0509143\pi$
$74$		−	63.8569i		−	0.862931i
$75$	12.3054			0.164072
$76$			13.7103i			0.180398i
$77$	3.96038	−	35.6614i	0.0514335	−	0.463135i
$78$	22.5038			0.288511
$79$		−	38.1352i		−	0.482723i	−0.970435	−	0.241362i	$-0.922406\pi$
$79$		−	38.1352i		−	0.482723i	0.970435	−	0.241362i	$-0.0775940\pi$
$80$	10.8282			0.135353
$81$	74.3208			0.917541
$82$	124.018			1.51241
$83$			12.0032i			0.144617i	0.997382	+	0.0723085i	$0.0230366\pi$
$83$			12.0032i			0.144617i	−0.997382	+	0.0723085i	$0.976963\pi$
$84$			0.793535i			0.00944685i
$85$		−	0.657363i		−	0.00773369i
$86$	−70.7111			−0.822222
$87$		−	13.9075i		−	0.159856i
$88$	−9.03517	+	81.3576i	−0.102672	+	0.924518i
$89$	61.3905			0.689780			0.344890	−	0.938643i	$-0.387916\pi$
$89$	61.3905			0.689780			0.344890	+	0.938643i	$0.387916\pi$
$90$		−	11.3324i		−	0.125916i
$91$	69.3513			0.762103
$92$	−2.33488			−0.0253791
$93$	3.27725			0.0352392
$94$		−	61.2177i		−	0.651252i
$95$			17.2176i			0.181238i
$96$		−	3.87161i		−	0.0403293i
$97$	−105.559			−1.08824			−0.544119	−	0.839008i	$-0.683136\pi$
$97$	−105.559			−1.08824			−0.544119	+	0.839008i	$0.683136\pi$
$98$		−	81.2552i		−	0.829135i
$99$	95.6653	+	10.6241i	0.966316	+	0.107314i
$100$	11.9894			0.119894
$101$		−	108.396i		−	1.07323i	−0.843829	−	0.536613i	$-0.819704\pi$
$101$		−	108.396i		−	1.07323i	0.843829	−	0.536613i	$-0.180296\pi$
$102$	−1.13801			−0.0111570
$103$	−17.8607			−0.173405			−0.0867025	−	0.996234i	$-0.527633\pi$
$103$	−17.8607			−0.173405			−0.0867025	+	0.996234i	$0.527633\pi$
$104$	−158.217			−1.52132
$105$			0.996540i			0.00949086i
$106$		−	77.5191i		−	0.731312i
$107$		−	45.8343i		−	0.428358i	−0.976794	−	0.214179i	$-0.931292\pi$
$107$		−	45.8343i		−	0.428358i	0.976794	−	0.214179i	$-0.0687075\pi$
$108$	−4.31822			−0.0399835
$109$		−	143.578i		−	1.31723i	−0.752479	−	0.658617i	$-0.771142\pi$
$109$		−	143.578i		−	1.31723i	0.752479	−	0.658617i	$-0.228858\pi$
$110$	1.57242	−	14.1589i	0.0142947	−	0.128718i
$111$	−15.0638			−0.135710
$112$		−	57.7691i		−	0.515796i
$113$	156.329			1.38345			0.691723	−	0.722163i	$-0.256852\pi$
$113$	156.329			1.38345			0.691723	+	0.722163i	$0.256852\pi$
$114$	29.8067			0.261463
$115$	−2.93219			−0.0254973
$116$		−	13.5503i		−	0.116813i
$117$			186.042i			1.59010i
$118$			176.033i			1.49181i
$119$	−3.50707			−0.0294712
$120$		−	2.27350i		−	0.0189458i
$121$	118.052	+	26.5479i	0.975634	+	0.219404i
$122$	−188.131			−1.54206
$123$		−	29.2557i		−	0.237851i
$124$	3.19309			0.0257507
$125$	30.3417			0.242733
$126$	−60.4592			−0.479835
$127$			218.705i			1.72209i	0.508532	+	0.861043i	$0.330188\pi$
$127$			218.705i			1.72209i	−0.508532	+	0.861043i	$0.669812\pi$
$128$			146.286i			1.14286i
$129$			16.6807i			0.129308i
$130$	27.5351			0.211809
$131$		−	59.0313i		−	0.450620i	−0.974287	−	0.225310i	$-0.927660\pi$
$131$		−	59.0313i		−	0.450620i	0.974287	−	0.225310i	$-0.0723395\pi$
$132$	−2.65968	−	0.295371i	−0.0201491	−	0.00223766i
$133$	91.8571			0.690655
$134$			89.6982i			0.669390i
$135$	−5.42292			−0.0401698
$136$	8.00099			0.0588308
$137$	−210.703			−1.53798			−0.768990	−	0.639261i	$-0.779241\pi$
$137$	−210.703			−1.53798			−0.768990	+	0.639261i	$0.779241\pi$
$138$			5.07614i			0.0367836i
$139$			64.9424i			0.467211i	0.972331	+	0.233606i	$0.0750525\pi$
$139$			64.9424i			0.467211i	−0.972331	+	0.233606i	$0.924947\pi$
$140$			0.970950i			0.00693535i
$141$	−14.4412			−0.102420
$142$		−	248.024i		−	1.74665i
$143$	−25.8141	+	232.444i	−0.180518	+	1.62548i
$144$	154.971			1.07619
$145$		−	17.0168i		−	0.117357i
$146$	−49.2561			−0.337371
$147$	−19.1681			−0.130395
$148$	−14.6770			−0.0991689
$149$			99.6338i			0.668683i	0.942452	+	0.334341i	$0.108514\pi$
$149$			99.6338i			0.668683i	−0.942452	+	0.334341i	$0.891486\pi$
$150$		−	26.0655i		−	0.173770i
$151$		−	6.57200i		−	0.0435232i	−0.999763	−	0.0217616i	$-0.993073\pi$
$151$		−	6.57200i		−	0.0435232i	0.999763	−	0.0217616i	$-0.00692748\pi$
$152$	−209.562			−1.37870
$153$		−	9.40806i		−	0.0614906i
$154$	−75.5387	−	8.38895i	−0.490511	−	0.0544737i
$155$	4.00995			0.0258707
$156$		−	5.17232i		−	0.0331559i
$157$	205.373			1.30811			0.654053	−	0.756448i	$-0.273067\pi$
$157$	205.373			1.30811			0.654053	+	0.756448i	$0.273067\pi$
$158$	−80.7786			−0.511257
$159$	−18.2867			−0.115011
$160$		−	4.73720i		−	0.0296075i
$161$			15.6434i			0.0971641i
$162$		−	157.428i		−	0.971776i
$163$	−184.127			−1.12961			−0.564806	−	0.825224i	$-0.691049\pi$
$163$	−184.127			−1.12961			−0.564806	+	0.825224i	$0.691049\pi$
$164$		−	28.5045i		−	0.173808i
$165$	−3.34009	−	0.370934i	−0.0202430	−	0.00224808i
$166$	25.4254			0.153165
$167$			35.3214i			0.211505i	0.994392	+	0.105753i	$0.0337252\pi$
$167$			35.3214i			0.211505i	−0.994392	+	0.105753i	$0.966275\pi$
$168$	−12.1292			−0.0721977
$169$	−283.037			−1.67478
$170$	−1.39244			−0.00819082
$171$			246.416i			1.44103i
$172$			16.2524i			0.0944906i
$173$			173.845i			1.00488i	0.864611	+	0.502442i	$0.167565\pi$
$173$			173.845i			1.00488i	−0.864611	+	0.502442i	$0.832435\pi$
$174$	−29.4591			−0.169305
$175$		−	80.3276i		−	0.459015i
$176$	193.624	+	21.5029i	1.10014	+	0.122176i
$177$	41.5262			0.234611
$178$		−	130.038i		−	0.730553i
$179$	−219.209			−1.22463			−0.612315	−	0.790614i	$-0.709762\pi$
$179$	−219.209			−1.22463			−0.612315	+	0.790614i	$0.709762\pi$
$180$	−2.60467			−0.0144704
$181$	331.346			1.83064			0.915321	−	0.402726i	$-0.131937\pi$
$181$	331.346			1.83064			0.915321	+	0.402726i	$0.131937\pi$
$182$		−	146.901i		−	0.807150i
$183$			44.3800i			0.242514i
$184$		−	35.6887i		−	0.193960i
$185$	−18.4317			−0.0996309
$186$		−	6.94193i		−	0.0373222i
$187$	1.30541	−	11.7546i	0.00698078	−	0.0628588i
$188$	−14.0704			−0.0748425
$189$			28.9316i			0.153077i
$190$	36.4708			0.191951
$191$	−353.382			−1.85017			−0.925083	−	0.379765i	$-0.876005\pi$
$191$	−353.382			−1.85017			−0.925083	+	0.379765i	$0.876005\pi$
$192$	27.1977			0.141655
$193$		−	160.977i		−	0.834079i	−0.908888	−	0.417039i	$-0.863068\pi$
$193$		−	160.977i		−	0.834079i	0.908888	−	0.417039i	$-0.136932\pi$
$194$			223.598i			1.15256i
$195$		−	6.49552i		−	0.0333104i
$196$	−18.6759			−0.0952850
$197$		−	282.614i		−	1.43459i	−0.696770	−	0.717295i	$-0.745380\pi$
$197$		−	282.614i		−	1.43459i	0.696770	−	0.717295i	$-0.254620\pi$
$198$	22.5042	−	202.640i	0.113658	−	1.02344i
$199$	−49.8399			−0.250452			−0.125226	−	0.992128i	$-0.539966\pi$
$199$	−49.8399			−0.250452			−0.125226	+	0.992128i	$0.539966\pi$
$200$			183.259i			0.916293i
$201$	21.1598			0.105273
$202$	−229.606			−1.13666
$203$	−90.7857			−0.447220
$204$			0.261562i			0.00128217i
$205$		−	35.7965i		−	0.174617i
$206$			37.8329i			0.183655i
$207$	−41.9650			−0.202730
$208$			376.544i			1.81031i
$209$	−34.1912	+	307.876i	−0.163594	+	1.47309i
$210$	2.11089			0.0100519
$211$		−	330.637i		−	1.56700i	−0.621391	−	0.783500i	$-0.713432\pi$
$211$		−	330.637i		−	1.56700i	0.621391	−	0.783500i	$-0.286568\pi$
$212$	−17.8171			−0.0840431
$213$	−58.5087			−0.274689
$214$	−97.0871			−0.453678
$215$			20.4101i			0.0949308i
$216$		−	66.0042i		−	0.305575i
$217$		−	21.3933i		−	0.0985868i
$218$	−304.131			−1.39509
$219$			11.6195i			0.0530571i
$220$	−3.25432	−	0.361408i	−0.0147924	−	0.00164277i
$221$	22.8594			0.103436
$222$			31.9085i			0.143732i
$223$	246.837			1.10689			0.553446	−	0.832885i	$-0.313313\pi$
$223$	246.837			1.10689			0.553446	+	0.832885i	$0.313313\pi$
$224$	−25.2732			−0.112827
$225$	215.487			0.957719
$226$		−	331.140i		−	1.46522i
$227$		−	339.183i		−	1.49420i	−0.664714	−	0.747098i	$-0.731446\pi$
$227$		−	339.183i		−	1.49420i	0.664714	−	0.747098i	$-0.268554\pi$
$228$		−	6.85084i		−	0.0300475i
$229$	243.049			1.06135			0.530676	−	0.847575i	$-0.321938\pi$
$229$	243.049			1.06135			0.530676	+	0.847575i	$0.321938\pi$
$230$			6.21103i			0.0270045i
$231$	−1.97895	+	17.8196i	−0.00856689	+	0.0771409i
$232$	207.118			0.892748
$233$			67.3715i			0.289148i	0.989494	+	0.144574i	$0.0461812\pi$
$233$			67.3715i			0.289148i	−0.989494	+	0.144574i	$0.953819\pi$
$234$	394.078			1.68409
$235$	−17.6699			−0.0751912
$236$	40.4598			0.171440
$237$			19.0557i			0.0804036i
$238$			7.42874i			0.0312132i
$239$		−	329.032i		−	1.37670i	−0.725377	−	0.688352i	$-0.758334\pi$
$239$		−	329.032i		−	1.37670i	0.725377	−	0.688352i	$-0.241666\pi$
$240$	−5.41072			−0.0225447
$241$			88.6880i			0.368000i	0.982926	+	0.184000i	$0.0589047\pi$
$241$			88.6880i			0.368000i	−0.982926	+	0.184000i	$0.941095\pi$
$242$	56.2343	−	250.060i	0.232373	−	1.03330i
$243$	−116.964			−0.481332
$244$			43.2404i			0.177215i
$245$	−23.4536			−0.0957289
$246$	−61.9700			−0.251911
$247$	−598.732			−2.42402
$248$			48.8065i			0.196800i
$249$		−	5.99785i		−	0.0240878i
$250$		−	64.2704i		−	0.257081i
$251$	−26.8660			−0.107036			−0.0535178	−	0.998567i	$-0.517043\pi$
$251$	−26.8660			−0.107036			−0.0535178	+	0.998567i	$0.517043\pi$
$252$			13.8961i			0.0551431i
$253$	−52.4318	−	5.82281i	−0.207240	−	0.0230151i
$254$	463.265			1.82388
$255$			0.328476i			0.00128814i
$256$	92.1477			0.359952
$257$	204.281			0.794867			0.397433	−	0.917631i	$-0.369901\pi$
$257$	204.281			0.794867			0.397433	+	0.917631i	$0.369901\pi$
$258$	35.3334			0.136951
$259$			98.3342i			0.379669i
$260$		−	6.32873i		−	0.0243413i
$261$		−	243.542i		−	0.933110i
$262$	−125.041			−0.477256
$263$			359.755i			1.36789i	0.729533	+	0.683946i	$0.239738\pi$
$263$			359.755i			1.36789i	−0.729533	+	0.683946i	$0.760262\pi$
$264$	4.51476	−	40.6533i	0.0171014	−	0.153990i
$265$	−22.3752			−0.0844346
$266$		−	194.574i		−	0.731479i
$267$	−30.6760			−0.114891
$268$	20.6164			0.0769269
$269$	−160.244			−0.595703			−0.297852	−	0.954612i	$-0.596270\pi$
$269$	−160.244			−0.595703			−0.297852	+	0.954612i	$0.596270\pi$
$270$			11.4869i			0.0425442i
$271$		−	148.817i		−	0.549142i	−0.961567	−	0.274571i	$-0.911464\pi$
$271$		−	148.817i		−	0.549142i	0.961567	−	0.274571i	$-0.0885358\pi$
$272$		−	19.0417i		−	0.0700061i
$273$	−34.6540			−0.126938
$274$			446.316i			1.62889i
$275$	269.233	+	29.8997i	0.979029	+	0.108726i
$276$	1.16671			0.00422721
$277$			258.524i			0.933300i	0.884442	+	0.466650i	$0.154539\pi$
$277$			258.524i			0.933300i	−0.884442	+	0.466650i	$0.845461\pi$
$278$	137.562			0.494828
$279$	57.3897			0.205698
$280$	−14.8410			−0.0530036
$281$		−	223.525i		−	0.795463i	−0.917502	−	0.397731i	$-0.869798\pi$
$281$		−	223.525i		−	0.795463i	0.917502	−	0.397731i	$-0.130202\pi$
$282$			30.5897i			0.108474i
$283$			16.5565i			0.0585034i	0.999572	+	0.0292517i	$0.00931244\pi$
$283$			16.5565i			0.0585034i	−0.999572	+	0.0292517i	$0.990688\pi$
$284$	−57.0063			−0.200726
$285$		−	8.60344i		−	0.0301875i
$286$	492.367	+	54.6798i	1.72156	+	0.191188i
$287$	−190.977			−0.665424
$288$		−	67.7980i		−	0.235410i
$289$	287.844			0.996000
$290$	−36.0454			−0.124294
$291$	52.7466			0.181260
$292$			11.3211i			0.0387710i
$293$			35.7607i			0.122050i	0.998136	+	0.0610251i	$0.0194370\pi$
$293$			35.7607i			0.122050i	−0.998136	+	0.0610251i	$0.980563\pi$
$294$			40.6022i			0.138103i
$295$	50.8104			0.172239
$296$		−	224.339i		−	0.757900i
$297$	−96.9695	−	10.7689i	−0.326497	−	0.0362591i
$298$	211.046			0.708209
$299$		−	101.965i		−	0.341020i
$300$	−5.99095			−0.0199698
$301$	108.889			0.361758
$302$	−13.9209			−0.0460959
$303$			54.1640i			0.178759i
$304$			498.739i			1.64059i
$305$			54.3023i			0.178040i
$306$	−19.9284			−0.0651253
$307$			514.466i			1.67578i	0.545836	+	0.837892i	$0.316212\pi$
$307$			514.466i			1.67578i	−0.545836	+	0.837892i	$0.683788\pi$
$308$	−1.92813	+	17.3620i	−0.00626017	+	0.0563700i
$309$	8.92478			0.0288828
$310$		−	8.49397i		−	0.0273999i
$311$	314.121			1.01003			0.505017	−	0.863109i	$-0.331486\pi$
$311$	314.121			1.01003			0.505017	+	0.863109i	$0.331486\pi$
$312$	79.0592			0.253395
$313$	313.193			1.00062			0.500309	−	0.865847i	$-0.333220\pi$
$313$	313.193			1.00062			0.500309	+	0.865847i	$0.333220\pi$
$314$		−	435.025i		−	1.38543i
$315$			17.4510i			0.0554000i
$316$			18.5663i			0.0587542i
$317$	−444.166			−1.40116			−0.700578	−	0.713576i	$-0.747074\pi$
$317$	−444.166			−1.40116			−0.700578	+	0.713576i	$0.747074\pi$
$318$			38.7353i			0.121809i
$319$	33.7924	−	304.285i	0.105932	−	0.953872i
$320$	33.2784			0.103995
$321$			22.9028i			0.0713483i
$322$	33.1362			0.102907
$323$	30.2776			0.0937388
$324$	−36.1835			−0.111677
$325$			523.581i			1.61102i
$326$			390.021i			1.19638i
$327$			71.7443i			0.219402i
$328$	435.692			1.32833
$329$			94.2700i			0.286535i
$330$	−0.785719	+	7.07504i	−0.00238097	+	0.0214395i
$331$	45.3969			0.137151			0.0685753	−	0.997646i	$-0.478155\pi$
$331$	45.3969			0.137151			0.0685753	+	0.997646i	$0.478155\pi$
$332$		−	5.84383i		−	0.0176019i
$333$	−263.791			−0.792166
$334$	74.8185			0.224007
$335$	25.8906			0.0772853
$336$			28.8665i			0.0859122i
$337$		−	612.935i		−	1.81880i	−0.415924	−	0.909399i	$-0.636542\pi$
$337$		−	612.935i		−	1.81880i	0.415924	−	0.909399i	$-0.363458\pi$
$338$			599.535i			1.77377i
$339$	−78.1158			−0.230430
$340$			0.320041i			0.000941298i
$341$	71.7037	+	7.96306i	0.210275	+	0.0233521i
$342$	521.963			1.52621
$343$			284.958i			0.830782i
$344$	−248.418			−0.722146
$345$	1.46518			0.00424690
$346$	368.242			1.06428
$347$			364.149i			1.04942i	0.851281	+	0.524710i	$0.175826\pi$
$347$			364.149i			1.04942i	−0.851281	+	0.524710i	$0.824174\pi$
$348$			6.77093i			0.0194567i
$349$		−	322.845i		−	0.925058i	−0.886604	−	0.462529i	$-0.846942\pi$
$349$		−	322.845i		−	0.925058i	0.886604	−	0.462529i	$-0.153058\pi$
$350$	−170.152			−0.486147
$351$		−	188.578i		−	0.537260i
$352$	9.40724	−	84.7079i	0.0267251	−	0.240648i
$353$	−154.512			−0.437711			−0.218856	−	0.975757i	$-0.570232\pi$
$353$	−154.512			−0.437711			−0.218856	+	0.975757i	$0.570232\pi$
$354$		−	87.9616i		−	0.248479i
$355$	−71.5898			−0.201661
$356$	−29.8883			−0.0839559
$357$	1.75244			0.00490879
$358$			464.333i			1.29702i
$359$		−	660.474i		−	1.83976i	−0.392199	−	0.919880i	$-0.628285\pi$
$359$		−	660.474i		−	1.83976i	0.392199	−	0.919880i	$-0.371715\pi$
$360$		−	39.8125i		−	0.110590i
$361$	−432.031			−1.19676
$362$		−	701.864i		−	1.93885i
$363$	−58.9889	−	13.2656i	−0.162504	−	0.0365445i
$364$	−33.7641			−0.0927585
$365$			14.2173i			0.0389516i
$366$	94.0066			0.256849
$367$	−505.697			−1.37792			−0.688961	−	0.724798i	$-0.741933\pi$
$367$	−505.697			−1.37792			−0.688961	+	0.724798i	$0.741933\pi$
$368$	−84.9361			−0.230805
$369$		−	512.314i		−	1.38838i
$370$			39.0424i			0.105520i
$371$			119.373i			0.321759i
$372$	−1.59555			−0.00428910
$373$		−	200.489i		−	0.537504i	−0.963209	−	0.268752i	$-0.913389\pi$
$373$		−	200.489i		−	0.537504i	0.963209	−	0.268752i	$-0.0866112\pi$
$374$	−24.8988	−	2.76514i	−0.0665744	−	0.00739342i
$375$	−15.1614			−0.0404303
$376$		−	215.067i		−	0.571986i
$377$	591.748			1.56962
$378$	61.2834			0.162125
$379$	−328.794			−0.867529			−0.433765	−	0.901026i	$-0.642815\pi$
$379$	−328.794			−0.867529			−0.433765	+	0.901026i	$0.642815\pi$
$380$		−	8.38251i		−	0.0220592i
$381$		−	109.284i		−	0.286835i
$382$			748.540i			1.95953i
$383$	−512.859			−1.33906			−0.669529	−	0.742786i	$-0.733504\pi$
$383$	−512.859			−1.33906			−0.669529	+	0.742786i	$0.733504\pi$
$384$		−	73.0972i		−	0.190357i
$385$	−2.42139	+	21.8036i	−0.00628933	+	0.0566326i
$386$	−340.985			−0.883381
$387$			292.106i			0.754796i
$388$	51.3921			0.132454
$389$	442.677			1.13799			0.568993	−	0.822342i	$-0.307333\pi$
$389$	442.677			1.13799			0.568993	+	0.822342i	$0.307333\pi$
$390$	−13.7589			−0.0352794
$391$			5.15633i			0.0131875i
$392$		−	285.461i		−	0.728218i
$393$			29.4972i			0.0750564i
$394$	−598.639			−1.51939
$395$			23.3160i			0.0590279i
$396$	−46.5752	−	5.17241i	−0.117614	−	0.0130616i
$397$	309.841			0.780455			0.390228	−	0.920718i	$-0.372396\pi$
$397$	309.841			0.780455			0.390228	+	0.920718i	$0.372396\pi$
$398$			105.572i			0.265256i
$399$	−45.8998			−0.115037
$400$	436.139			1.09035
$401$	217.187			0.541614			0.270807	−	0.962634i	$-0.412710\pi$
$401$	217.187			0.541614			0.270807	+	0.962634i	$0.412710\pi$
$402$		−	44.8211i		−	0.111495i
$403$			139.443i			0.346013i
$404$			52.7731i			0.130626i
$405$	−45.4401			−0.112198
$406$			192.304i			0.473656i
$407$	−329.585	−	36.6021i	−0.809792	−	0.0899314i
$408$	−3.99799			−0.00979900
$409$			565.456i			1.38253i	0.722600	+	0.691266i	$0.242947\pi$
$409$			565.456i			1.38253i	−0.722600	+	0.691266i	$0.757053\pi$
$410$	−75.8250			−0.184939
$411$	105.286			0.256170
$412$	8.69560			0.0211058
$413$		−	271.076i		−	0.656359i
$414$			88.8912i			0.214713i
$415$		−	7.33882i		−	0.0176839i
$416$	164.733			0.395993
$417$		−	32.4509i		−	0.0778199i
$418$	652.149	+	72.4245i	1.56017	+	0.173264i
$419$	−629.101			−1.50143			−0.750717	−	0.660624i	$-0.770292\pi$
$419$	−629.101			−1.50143			−0.750717	+	0.660624i	$0.770292\pi$
$420$		−	0.485171i		−	0.00115517i
$421$	−323.129			−0.767528			−0.383764	−	0.923431i	$-0.625372\pi$
$421$	−323.129			−0.767528			−0.383764	+	0.923431i	$0.625372\pi$
$422$	−700.362			−1.65963
$423$	−252.889			−0.597846
$424$		−	272.336i		−	0.642301i
$425$		−	26.4773i		−	0.0622996i
$426$			123.934i			0.290926i
$427$	289.705			0.678467
$428$			22.3147i			0.0521371i
$429$	12.8990	−	116.149i	0.0300675	−	0.270744i
$430$	43.2331			0.100542
$431$		−	49.8931i		−	0.115761i	−0.998324	−	0.0578806i	$-0.981566\pi$
$431$		−	49.8931i		−	0.115761i	0.998324	−	0.0578806i	$-0.0184343\pi$
$432$	−157.084			−0.363621
$433$	−590.727			−1.36427			−0.682133	−	0.731228i	$-0.738947\pi$
$433$	−590.727			−1.36427			−0.682133	+	0.731228i	$0.738947\pi$
$434$	−45.3158			−0.104414
$435$			8.50309i			0.0195473i
$436$			69.9020i			0.160326i
$437$		−	135.054i		−	0.309049i
$438$	24.6126			0.0561933
$439$		−	403.320i		−	0.918724i	−0.888249	−	0.459362i	$-0.848078\pi$
$439$		−	403.320i		−	0.918724i	0.888249	−	0.459362i	$-0.151922\pi$
$440$	5.52414	−	49.7424i	0.0125549	−	0.113051i
$441$	−335.663			−0.761141
$442$		−	48.4211i		−	0.109550i
$443$	741.896			1.67471			0.837355	−	0.546660i	$-0.184101\pi$
$443$	741.896			1.67471			0.837355	+	0.546660i	$0.184101\pi$
$444$	7.33391			0.0165178
$445$	−37.5344			−0.0843470
$446$		−	522.855i		−	1.17232i
$447$		−	49.7857i		−	0.111377i
$448$		−	177.542i		−	0.396300i
$449$	233.596			0.520259			0.260130	−	0.965574i	$-0.416235\pi$
$449$	233.596			0.520259			0.260130	+	0.965574i	$0.416235\pi$
$450$		−	456.448i		−	1.01433i
$451$	71.0856	−	640.093i	0.157618	−	1.41928i
$452$	−76.1098			−0.168385
$453$			3.28395i			0.00724933i
$454$	−718.463			−1.58252
$455$	−42.4017			−0.0931906
$456$	104.715			0.229639
$457$		−	152.527i		−	0.333757i	−0.985977	−	0.166879i	$-0.946631\pi$
$457$		−	152.527i		−	0.333757i	0.985977	−	0.166879i	$-0.0533688\pi$
$458$		−	514.832i		−	1.12409i
$459$			9.53632i			0.0207763i
$460$	1.42756			0.00310338
$461$			611.144i			1.32569i	0.748756	+	0.662846i	$0.230652\pi$
$461$			611.144i			1.32569i	−0.748756	+	0.662846i	$0.769348\pi$
$462$	37.7457	+	4.19185i	0.0817007	+	0.00907327i
$463$	15.9892			0.0345338			0.0172669	−	0.999851i	$-0.494503\pi$
$463$	15.9892			0.0345338			0.0172669	+	0.999851i	$0.494503\pi$
$464$		−	492.922i		−	1.06233i
$465$	−2.00372			−0.00430908
$466$	142.708			0.306239
$467$	−4.89271			−0.0104769			−0.00523845	−	0.999986i	$-0.501667\pi$
$467$	−4.89271			−0.0104769			−0.00523845	+	0.999986i	$0.501667\pi$
$468$		−	90.5756i		−	0.193538i
$469$		−	138.128i		−	0.294515i
$470$			37.4288i			0.0796357i
$471$	−102.622			−0.217881
$472$			618.430i			1.31023i
$473$	−40.5309	+	364.962i	−0.0856889	+	0.771590i
$474$	40.3641			0.0851562
$475$			693.493i			1.45999i
$476$	1.70744			0.00358705
$477$	−320.229			−0.671340
$478$	−696.963			−1.45808
$479$		−	59.2560i		−	0.123708i	−0.998085	−	0.0618538i	$-0.980299\pi$
$479$		−	59.2560i		−	0.123708i	0.998085	−	0.0618538i	$-0.0197013\pi$
$480$			2.36712i			0.00493150i
$481$		−	640.950i		−	1.33254i
$482$	187.861			0.389753
$483$		−	7.81681i		−	0.0161839i
$484$	−57.4742	−	12.9250i	−0.118748	−	0.0267045i
$485$	64.5394			0.133071
$486$			247.755i			0.509783i
$487$	−582.522			−1.19614			−0.598072	−	0.801442i	$-0.704066\pi$
$487$	−582.522			−1.19614			−0.598072	+	0.801442i	$0.704066\pi$
$488$	−660.931			−1.35437
$489$	92.0058			0.188151
$490$			49.6798i			0.101387i
$491$		−	234.231i		−	0.477048i	−0.971137	−	0.238524i	$-0.923336\pi$
$491$		−	234.231i		−	0.477048i	0.971137	−	0.238524i	$-0.0766636\pi$
$492$			14.2433i			0.0289498i
$493$	−29.9245			−0.0606988
$494$			1268.25i			2.56730i
$495$	−58.4902	−	6.49563i	−0.118162	−	0.0131225i
$496$	116.155			0.234184
$497$			381.936i			0.768482i
$498$	−12.7048			−0.0255116
$499$	−270.816			−0.542717			−0.271358	−	0.962478i	$-0.587473\pi$
$499$	−270.816			−0.542717			−0.271358	+	0.962478i	$0.587473\pi$
$500$	−14.7720			−0.0295440
$501$		−	17.6496i		−	0.0352288i
$502$			56.9080i			0.113363i
$503$			192.186i			0.382080i	0.981582	+	0.191040i	$0.0611861\pi$
$503$			192.186i			0.382080i	−0.981582	+	0.191040i	$0.938814\pi$
$504$	−212.402			−0.421432
$505$			66.2737i			0.131235i
$506$	−12.3340	+	111.062i	−0.0243755	+	0.219490i
$507$	141.430			0.278955
$508$		−	106.478i		−	0.209602i
$509$	20.0308			0.0393532			0.0196766	−	0.999806i	$-0.493736\pi$
$509$	20.0308			0.0393532			0.0196766	+	0.999806i	$0.493736\pi$
$510$	0.695785			0.00136428
$511$	75.8502			0.148435
$512$			389.954i			0.761629i
$513$		−	249.775i		−	0.486891i
$514$		−	432.712i		−	0.841852i
$515$	10.9201			0.0212041
$516$		−	8.12111i		−	0.0157386i
$517$	−315.964	−	35.0893i	−0.611148	−	0.0678710i
$518$	208.293			0.402111
$519$		−	86.8681i		−	0.167376i
$520$	96.7348			0.186029
$521$	732.700			1.40633			0.703167	−	0.711025i	$-0.251769\pi$
$521$	732.700			1.40633			0.703167	+	0.711025i	$0.251769\pi$
$522$	−515.875			−0.988267
$523$			242.201i			0.463100i	0.972823	+	0.231550i	$0.0743797\pi$
$523$			242.201i			0.463100i	−0.972823	+	0.231550i	$0.925620\pi$
$524$			28.7397i			0.0548468i
$525$			40.1387i			0.0764546i
$526$	762.041			1.44875
$527$		−	7.05160i		−	0.0133806i
$528$	−96.7514	−	10.7447i	−0.183241	−	0.0203499i
$529$	23.0000			0.0434783
$530$			47.3955i			0.0894255i
$531$	727.189			1.36947
$532$	−44.7212			−0.0840623
$533$	1244.80			2.33546
$534$			64.9786i			0.121683i
$535$			28.0233i			0.0523800i
$536$			315.123i			0.587916i
$537$	109.536			0.203977
$538$			339.432i			0.630915i
$539$	−419.383	−	46.5746i	−0.778077	−	0.0864093i
$540$	2.64018			0.00488922
$541$			471.642i			0.871797i	0.899996	+	0.435899i	$0.143569\pi$
$541$			471.642i			0.871797i	−0.899996	+	0.435899i	$0.856431\pi$
$542$	−315.228			−0.581602
$543$	−165.569			−0.304916
$544$	−8.33048			−0.0153134
$545$			87.7845i			0.161073i
$546$			73.4047i			0.134441i
$547$		−	150.848i		−	0.275773i	−0.990448	−	0.137886i	$-0.955969\pi$
$547$		−	150.848i		−	0.275773i	0.990448	−	0.137886i	$-0.0440309\pi$
$548$	102.582			0.187194
$549$			777.164i			1.41560i
$550$	63.3340	−	570.294i	0.115153	−	1.03690i
$551$	783.782			1.42247
$552$			17.8332i			0.0323065i
$553$	124.392			0.224941
$554$	547.611			0.988467
$555$	9.21009			0.0165948
$556$		−	31.6176i		−	0.0568662i
$557$		−	225.525i		−	0.404893i	−0.979293	−	0.202446i	$-0.935111\pi$
$557$		−	225.525i		−	0.404893i	0.979293	−	0.202446i	$-0.0648892\pi$
$558$		−	121.564i		−	0.217857i
$559$	−709.747			−1.26967
$560$			35.3203i			0.0630720i
$561$	−0.652295	+	5.87362i	−0.00116274	+	0.0104699i
$562$	−473.475			−0.842483
$563$		−	360.017i		−	0.639463i	−0.947508	−	0.319731i	$-0.896407\pi$
$563$		−	360.017i		−	0.639463i	0.947508	−	0.319731i	$-0.103593\pi$
$564$	7.03080			0.0124660
$565$	−95.5805			−0.169169
$566$	35.0703			0.0619616
$567$			242.425i			0.427558i
$568$		−	871.344i		−	1.53406i
$569$			756.606i			1.32971i	0.746971	+	0.664856i	$0.231507\pi$
$569$			756.606i			1.32971i	−0.746971	+	0.664856i	$0.768493\pi$
$570$	−18.2240			−0.0319719
$571$			208.680i			0.365464i	0.983163	+	0.182732i	$0.0584940\pi$
$571$			208.680i			0.365464i	−0.983163	+	0.182732i	$0.941506\pi$
$572$	12.5677	−	113.167i	0.0219715	−	0.197844i
$573$	176.580			0.308168
$574$			404.530i			0.704757i
$575$	−118.103			−0.205397
$576$	476.275			0.826866
$577$	61.4553			0.106508			0.0532542	−	0.998581i	$-0.483041\pi$
$577$	61.4553			0.106508			0.0532542	+	0.998581i	$0.483041\pi$
$578$		−	609.717i		−	1.05487i
$579$			80.4383i			0.138926i
$580$			8.28474i			0.0142840i
$581$	−39.1530			−0.0673890
$582$		−	111.729i		−	0.191974i
$583$	−400.100	−	44.4331i	−0.686278	−	0.0762146i
$584$	−173.044			−0.296308
$585$		−	113.747i		−	0.194439i
$586$	75.7490			0.129265
$587$	205.302			0.349747			0.174874	−	0.984591i	$-0.444048\pi$
$587$	205.302			0.349747			0.174874	+	0.984591i	$0.444048\pi$
$588$	9.33209			0.0158709
$589$			184.695i			0.313574i
$590$		−	107.628i		−	0.182420i
$591$			141.219i			0.238949i
$592$	−533.906			−0.901869
$593$			751.185i			1.26675i	0.773844	+	0.633377i	$0.218332\pi$
$593$			751.185i			1.26675i	−0.773844	+	0.633377i	$0.781668\pi$
$594$	−22.8110	+	205.403i	−0.0384024	+	0.345796i
$595$	2.14424			0.00360376
$596$		−	48.5073i		−	0.0813880i
$597$	24.9043			0.0417158
$598$	−215.984			−0.361178
$599$	−445.534			−0.743797			−0.371898	−	0.928273i	$-0.621293\pi$
$599$	−445.534			−0.743797			−0.371898	+	0.928273i	$0.621293\pi$
$600$		−	91.5719i		−	0.152620i
$601$			497.121i			0.827157i	0.910469	+	0.413578i	$0.135721\pi$
$601$			497.121i			0.827157i	−0.910469	+	0.413578i	$0.864279\pi$
$602$		−	230.651i		−	0.383141i
$603$	370.541			0.614496
$604$			3.19962i			0.00529738i
$605$	−72.1774	−	16.2315i	−0.119301	−	0.0268289i
$606$	114.731			0.189325
$607$			493.272i			0.812639i	0.913731	+	0.406320i	$0.133188\pi$
$607$			493.272i			0.812639i	−0.913731	+	0.406320i	$0.866812\pi$
$608$	218.192			0.358868
$609$	45.3645			0.0744901
$610$	115.024			0.188564
$611$		−	614.459i		−	1.00566i
$612$			4.58037i			0.00748427i
$613$		−	45.9183i		−	0.0749075i	−0.999298	−	0.0374537i	$-0.988075\pi$
$613$		−	45.9183i		−	0.0749075i	0.999298	−	0.0374537i	$-0.0119247\pi$
$614$	1089.75			1.77484
$615$			17.8871i			0.0290847i
$616$	−265.378	−	29.4716i	−0.430809	−	0.0478435i
$617$	−114.129			−0.184974			−0.0924870	−	0.995714i	$-0.529482\pi$
$617$	−114.129			−0.184974			−0.0924870	+	0.995714i	$0.529482\pi$
$618$		−	18.9046i		−	0.0305900i
$619$	−5.04916			−0.00815697			−0.00407848	−	0.999992i	$-0.501298\pi$
$619$	−5.04916			−0.00815697			−0.00407848	+	0.999992i	$0.501298\pi$
$620$	−1.95227			−0.00314882
$621$	42.5371			0.0684978
$622$		−	665.376i		−	1.06974i
$623$			200.248i			0.321426i
$624$		−	188.154i		−	0.301529i
$625$	597.104			0.955366
$626$		−	663.412i		−	1.05976i
$627$	17.0849	−	153.842i	0.0272486	−	0.245362i
$628$	−99.9869			−0.159215
$629$			32.4126i			0.0515303i
$630$	36.9650			0.0586746
$631$	471.546			0.747300			0.373650	−	0.927570i	$-0.378106\pi$
$631$	471.546			0.747300			0.373650	+	0.927570i	$0.378106\pi$
$632$	−283.787			−0.449030
$633$			165.215i			0.261003i
$634$			940.842i			1.48398i
$635$		−	133.717i		−	0.210578i
$636$	8.90300			0.0139984
$637$		−	815.582i		−	1.28035i
$638$	−644.543	−	71.5797i	−1.01026	−	0.112194i
$639$	−1024.58			−1.60341
$640$		−	89.4399i		−	0.139750i
$641$	656.705			1.02450			0.512250	−	0.858836i	$-0.328812\pi$
$641$	656.705			1.02450			0.512250	+	0.858836i	$0.328812\pi$
$642$	48.5132			0.0755657
$643$	1010.86			1.57210			0.786050	−	0.618162i	$-0.212123\pi$
$643$	1010.86			1.57210			0.786050	+	0.618162i	$0.212123\pi$
$644$		−	7.61609i		−	0.0118262i
$645$		−	10.1987i		−	0.0158119i
$646$		−	64.1347i		−	0.0992797i
$647$	641.187			0.991015			0.495508	−	0.868604i	$-0.334982\pi$
$647$	641.187			0.991015			0.495508	+	0.868604i	$0.334982\pi$
$648$		−	553.066i		−	0.853498i
$649$	908.562	+	100.900i	1.39994	+	0.155471i
$650$	1109.06			1.70625
$651$			10.6900i			0.0164208i
$652$	89.6432			0.137490
$653$	325.626			0.498661			0.249330	−	0.968418i	$-0.419789\pi$
$653$	325.626			0.498661			0.249330	+	0.968418i	$0.419789\pi$
$654$	151.970			0.232370
$655$			36.0920i			0.0551023i
$656$		−	1036.91i		−	1.58065i
$657$			203.476i			0.309704i
$658$	199.685			0.303472
$659$			344.536i			0.522816i	0.965228	+	0.261408i	$0.0841868\pi$
$659$			344.536i			0.522816i	−0.965228	+	0.261408i	$0.915813\pi$
$660$	1.62614	+	0.180591i	0.00246385	+	0.000273623i
$661$	−88.5609			−0.133980			−0.0669901	−	0.997754i	$-0.521340\pi$
$661$	−88.5609			−0.133980			−0.0669901	+	0.997754i	$0.521340\pi$
$662$		−	96.1606i		−	0.145258i
$663$	−11.4225			−0.0172285
$664$	89.3232			0.134523
$665$	−56.1619			−0.0844539
$666$			558.768i			0.838991i
$667$			133.479i			0.200119i
$668$		−	17.1964i		−	0.0257431i
$669$	−123.341			−0.184367
$670$		−	54.8419i		−	0.0818536i
$671$	−107.835	+	971.002i	−0.160707	+	1.44710i
$672$	12.6287			0.0187927
$673$		−	801.545i		−	1.19100i	−0.803354	−	0.595501i	$-0.796953\pi$
$673$		−	801.545i		−	1.19100i	0.803354	−	0.595501i	$-0.203047\pi$
$674$	−1298.33			−1.92631
$675$	−218.425			−0.323592
$676$	137.798			0.203844
$677$		−	278.657i		−	0.411606i	−0.978593	−	0.205803i	$-0.934019\pi$
$677$		−	278.657i		−	0.411606i	0.978593	−	0.205803i	$-0.0659806\pi$
$678$			165.466i			0.244051i
$679$		−	344.321i		−	0.507100i
$680$	−4.89184			−0.00719389
$681$			169.485i			0.248877i
$682$	16.8675	−	151.884i	0.0247324	−	0.222704i
$683$	89.2038			0.130606			0.0653029	−	0.997865i	$-0.479199\pi$
$683$	89.2038			0.130606			0.0653029	+	0.997865i	$0.479199\pi$
$684$		−	119.969i		−	0.175393i
$685$	128.825			0.188066
$686$	603.604			0.879889
$687$	−121.449			−0.176781
$688$			591.214i			0.859323i
$689$		−	778.081i		−	1.12929i
$690$		−	3.10357i		−	0.00449793i
$691$	880.358			1.27403			0.637017	−	0.770850i	$-0.280168\pi$
$691$	880.358			1.27403			0.637017	+	0.770850i	$0.280168\pi$
$692$		−	84.6374i		−	0.122308i
$693$	−34.6545	+	312.049i	−0.0500066	+	0.450286i
$694$	771.347			1.11145
$695$		−	39.7061i		−	0.0571311i
$696$	−103.494			−0.148698
$697$	−62.9490			−0.0903143
$698$	−683.857			−0.979738
$699$		−	33.6647i		−	0.0481612i
$700$			39.1080i			0.0558685i
$701$		−	1110.02i		−	1.58348i	−0.610860	−	0.791738i	$-0.709176\pi$
$701$		−	1110.02i		−	1.58348i	0.610860	−	0.791738i	$-0.290824\pi$
$702$	−399.450			−0.569017
$703$		−	848.950i		−	1.20761i
$704$	595.066	+	66.0850i	0.845264	+	0.0938708i
$705$	8.82944			0.0125240
$706$			327.290i			0.463584i
$707$	353.574			0.500104
$708$	−20.2173			−0.0285555
$709$	553.629			0.780860			0.390430	−	0.920633i	$-0.372326\pi$
$709$	553.629			0.780860			0.390430	+	0.920633i	$0.372326\pi$
$710$			151.643i			0.213582i
$711$			333.695i			0.469331i
$712$		−	456.844i		−	0.641635i
$713$	−31.4539			−0.0441149
$714$		−	3.71205i		−	0.00519895i
$715$	15.7828	−	142.117i	0.0220739	−	0.198765i
$716$	106.723			0.149055
$717$			164.413i			0.229307i
$718$	−1399.03			−1.94851
$719$	−90.1655			−0.125404			−0.0627020	−	0.998032i	$-0.519972\pi$
$719$	−90.1655			−0.125404			−0.0627020	+	0.998032i	$0.519972\pi$
$720$	−94.7503			−0.131598
$721$		−	58.2595i		−	0.0808037i
$722$			915.137i			1.26750i
$723$		−	44.3163i		−	0.0612950i
$724$	−161.318			−0.222815
$725$		−	685.405i		−	0.945386i
$726$	−28.0995	+	124.952i	−0.0387046	+	0.172110i
$727$	−1277.14			−1.75673			−0.878365	−	0.477990i	$-0.841365\pi$
$727$	−1277.14			−1.75673			−0.878365	+	0.477990i	$0.841365\pi$
$728$		−	516.086i		−	0.708909i
$729$	−610.442			−0.837369
$730$	30.1154			0.0412540
$731$	35.8917			0.0490994
$732$		−	21.6067i		−	0.0295173i
$733$		−	128.376i		−	0.175138i	−0.996158	−	0.0875690i	$-0.972090\pi$
$733$		−	128.376i		−	0.175138i	0.996158	−	0.0875690i	$-0.0279098\pi$
$734$			1071.18i			1.45937i
$735$	11.7195			0.0159448
$736$			37.1584i			0.0504870i
$737$	462.960	+	51.4140i	0.628169	+	0.0697613i
$738$	−1085.19			−1.47045
$739$		−	984.333i		−	1.33198i	−0.745961	−	0.665990i	$-0.768009\pi$
$739$		−	984.333i		−	1.33198i	0.745961	−	0.665990i	$-0.231991\pi$
$740$	8.97358			0.0121265
$741$	299.179			0.403750
$742$	252.858			0.340779
$743$			4.86703i			0.00655051i	0.999995	+	0.00327525i	$0.00104255\pi$
$743$			4.86703i			0.00655051i	−0.999995	+	0.00327525i	$0.998957\pi$
$744$		−	24.3880i		−	0.0327796i
$745$		−	60.9165i		−	0.0817672i
$746$	−424.680			−0.569276
$747$		−	105.032i		−	0.140605i
$748$	−0.635545	+	5.72279i	−0.000849659	+	0.00765079i
$749$	149.506			0.199607
$750$			32.1151i			0.0428201i
$751$	−113.224			−0.150764			−0.0753819	−	0.997155i	$-0.524018\pi$
$751$	−113.224			−0.150764			−0.0753819	+	0.997155i	$0.524018\pi$
$752$	−511.840			−0.680638
$753$	13.4246			0.0178281
$754$		−	1253.45i		−	1.66241i
$755$			4.01815i			0.00532206i
$756$		−	14.0855i		−	0.0186316i
$757$	787.825			1.04072			0.520360	−	0.853947i	$-0.325798\pi$
$757$	787.825			1.04072			0.520360	+	0.853947i	$0.325798\pi$
$758$			696.457i			0.918809i
$759$	26.1995	+	2.90959i	0.0345185	+	0.00383345i
$760$	128.127			0.168588
$761$		−	1257.62i		−	1.65259i	−0.563239	−	0.826294i	$-0.690445\pi$
$761$		−	1257.62i		−	1.65259i	0.563239	−	0.826294i	$-0.309555\pi$
$762$	−231.488			−0.303790
$763$	468.335			0.613808
$764$	172.046			0.225191
$765$			5.75213i			0.00751913i
$766$			1086.35i			1.41821i
$767$			1766.90i			2.30365i
$768$	−46.0450			−0.0599545
$769$		−	1245.32i		−	1.61940i	−0.586846	−	0.809698i	$-0.699631\pi$
$769$		−	1245.32i		−	1.61940i	0.586846	−	0.809698i	$-0.300369\pi$
$770$	46.1847	+	5.12904i	0.0599802	+	0.00666110i
$771$	−102.077			−0.132395
$772$			78.3727i			0.101519i
$773$	469.468			0.607332			0.303666	−	0.952778i	$-0.401789\pi$
$773$	469.468			0.607332			0.303666	+	0.952778i	$0.401789\pi$
$774$	618.744			0.799411
$775$	161.513			0.208404
$776$			785.530i			1.01228i
$777$		−	49.1363i		−	0.0632385i
$778$		−	937.687i		−	1.20525i
$779$	1648.76			2.11651
$780$			3.16238i			0.00405434i
$781$	−1280.13	−	142.165i	−1.63909	−	0.182029i
$782$	10.9222			0.0139671
$783$			246.862i			0.315277i
$784$	−679.374			−0.866548
$785$	−125.566			−0.159957
$786$	62.4815			0.0794930
$787$			1220.73i			1.55112i	0.631275	+	0.775559i	$0.282532\pi$
$787$			1220.73i			1.55112i	−0.631275	+	0.775559i	$0.717468\pi$
$788$			137.592i			0.174610i
$789$		−	179.765i		−	0.227839i
$790$	49.3884			0.0625170
$791$			509.927i			0.644661i
$792$	79.0605	−	711.904i	0.0998239	−	0.898869i
$793$	−1888.32			−2.38124
$794$		−	656.311i		−	0.826588i
$795$	11.1806			0.0140636
$796$	24.2648			0.0304834
$797$	532.395			0.667998			0.333999	−	0.942573i	$-0.391602\pi$
$797$	532.395			0.667998			0.333999	+	0.942573i	$0.391602\pi$
$798$			97.2259i			0.121837i
$799$			31.0730i			0.0388898i
$800$		−	190.805i		−	0.238507i
$801$	−537.186			−0.670644
$802$		−	460.050i		−	0.573629i
$803$	−28.2331	+	254.226i	−0.0351595	+	0.316595i
$804$	−10.3018			−0.0128131
$805$		−	9.56446i		−	0.0118813i
$806$	295.372			0.366466
$807$	80.0720			0.0992218
$808$	−806.639			−0.998316
$809$			905.238i			1.11896i	0.828844	+	0.559479i	$0.188999\pi$
$809$			905.238i			1.11896i	−0.828844	+	0.559479i	$0.811001\pi$
$810$			96.2521i			0.118830i
$811$		−	529.844i		−	0.653321i	−0.945142	−	0.326661i	$-0.894077\pi$
$811$		−	529.844i		−	0.653321i	0.945142	−	0.326661i	$-0.105923\pi$
$812$	44.1996			0.0544330
$813$			74.3622i			0.0914664i
$814$	−77.5313	+	698.134i	−0.0952473	+	0.857659i
$815$	112.576			0.138130
$816$			9.51488i			0.0116604i
$817$	−940.073			−1.15064
$818$	1197.76			1.46425
$819$	−606.846			−0.740959
$820$			17.4278i			0.0212534i
$821$			970.619i			1.18224i	0.806584	+	0.591120i	$0.201314\pi$
$821$			970.619i			1.18224i	−0.806584	+	0.591120i	$0.798686\pi$
$822$		−	223.018i		−	0.271312i
$823$	584.559			0.710278			0.355139	−	0.934813i	$-0.384433\pi$
$823$	584.559			0.710278			0.355139	+	0.934813i	$0.384433\pi$
$824$			132.913i			0.161302i
$825$	−134.532	−	14.9405i	−0.163069	−	0.0181097i
$826$	−574.199			−0.695156
$827$		−	711.039i		−	0.859781i	−0.902881	−	0.429891i	$-0.858552\pi$
$827$		−	711.039i		−	0.859781i	0.902881	−	0.429891i	$-0.141448\pi$
$828$	20.4309			0.0246750
$829$	−1293.52			−1.56033			−0.780166	−	0.625572i	$-0.784866\pi$
$829$	−1293.52			−1.56033			−0.780166	+	0.625572i	$0.784866\pi$
$830$	−15.5452			−0.0187292
$831$		−	129.181i		−	0.155453i
$832$			1157.23i			1.39091i
$833$			41.2437i			0.0495122i
$834$	−68.7381			−0.0824198
$835$		−	21.5957i		−	0.0258631i
$836$	16.6462	−	149.891i	0.0199117	−	0.179296i
$837$	−58.1721			−0.0695008
$838$			1332.57i			1.59018i
$839$	−811.091			−0.966735			−0.483368	−	0.875417i	$-0.660587\pi$
$839$	−811.091			−0.966735			−0.483368	+	0.875417i	$0.660587\pi$
$840$	7.41586			0.00882841
$841$	66.3600			0.0789060
$842$			684.459i			0.812897i
$843$			111.693i			0.132494i
$844$			160.973i			0.190726i
$845$	173.050			0.204793
$846$			535.674i			0.633185i
$847$	−86.5960	+	385.070i	−0.102238	+	0.454628i
$848$	−648.135			−0.764311
$849$		−	8.27306i		−	0.00974447i
$850$	−56.0848			−0.0659821
$851$	144.578			0.169891
$852$	28.4853			0.0334335
$853$			662.420i			0.776577i	0.921538	+	0.388288i	$0.126934\pi$
$853$			662.420i			0.776577i	−0.921538	+	0.388288i	$0.873066\pi$
$854$		−	613.660i		−	0.718571i
$855$		−	150.660i		−	0.176210i
$856$	−341.081			−0.398459
$857$			538.833i			0.628744i	0.949300	+	0.314372i	$0.101794\pi$
$857$			538.833i			0.628744i	−0.949300	+	0.314372i	$0.898206\pi$
$858$	−246.030	−	27.3228i	−0.286748	−	0.0318448i
$859$	678.546			0.789926			0.394963	−	0.918697i	$-0.370757\pi$
$859$	678.546			0.789926			0.394963	+	0.918697i	$0.370757\pi$
$860$		−	9.93678i		−	0.0115544i
$861$	95.4285			0.110835
$862$	−105.685			−0.122604
$863$	661.355			0.766344			0.383172	−	0.923677i	$-0.374832\pi$
$863$	661.355			0.766344			0.383172	+	0.923677i	$0.374832\pi$
$864$			68.7223i			0.0795396i
$865$		−	106.290i		−	0.122878i
$866$			1251.29i			1.44491i
$867$	−143.832			−0.165896
$868$			10.4155i			0.0119994i
$869$	−46.3014	+	416.924i	−0.0532813	+	0.479774i
$870$	18.0114			0.0207028
$871$			900.326i			1.03367i
$872$	−1068.45			−1.22529
$873$	923.676			1.05805
$874$	−286.075			−0.327317
$875$			98.9708i			0.113110i
$876$		−	5.65702i		−	0.00645778i
$877$		−	377.585i		−	0.430542i	−0.976554	−	0.215271i	$-0.930937\pi$
$877$		−	377.585i		−	0.430542i	0.976554	−	0.215271i	$-0.0690634\pi$
$878$	−854.320			−0.973030
$879$		−	17.8692i		−	0.0203290i
$880$	−118.383	−	13.1470i	−0.134526	−	0.0149398i
$881$	−67.1935			−0.0762696			−0.0381348	−	0.999273i	$-0.512142\pi$
$881$	−67.1935			−0.0762696			−0.0381348	+	0.999273i	$0.512142\pi$
$882$			711.009i			0.806132i
$883$	322.940			0.365731			0.182865	−	0.983138i	$-0.441463\pi$
$883$	322.940			0.365731			0.182865	+	0.983138i	$0.441463\pi$
$884$	−11.1292			−0.0125896
$885$	−25.3893			−0.0286885
$886$		−	1571.50i		−	1.77370i
$887$			478.863i			0.539868i	0.962879	+	0.269934i	$0.0870019\pi$
$887$			478.863i			0.539868i	−0.962879	+	0.269934i	$0.912998\pi$
$888$			112.099i			0.126238i
$889$	−713.389			−0.802462
$890$			79.5061i			0.0893327i
$891$	−812.533	−	90.2359i	−0.911934	−	0.101275i
$892$	−120.174			−0.134724
$893$		−	813.863i		−	0.911380i
$894$	−105.457			−0.117961
$895$	134.025			0.149749
$896$	−477.167			−0.532552
$897$			50.9506i			0.0568011i
$898$		−	494.808i		−	0.551012i
$899$		−	182.541i		−	0.203049i
$900$	−104.911			−0.116568
$901$			39.3472i			0.0436706i
$902$	−1355.86	−	150.575i	−1.50317	−	0.166934i
$903$	−54.4105			−0.0602552
$904$		−	1163.34i		−	1.28688i
$905$	−202.587			−0.223853
$906$	6.95612			0.00767784
$907$	736.925			0.812486			0.406243	−	0.913765i	$-0.366839\pi$
$907$	736.925			0.812486			0.406243	+	0.913765i	$0.366839\pi$
$908$			165.133i			0.181865i
$909$			948.497i			1.04345i
$910$			89.8162i			0.0986991i
$911$	−140.994			−0.154769			−0.0773844	−	0.997001i	$-0.524657\pi$
$911$	−140.994			−0.154769			−0.0773844	+	0.997001i	$0.524657\pi$
$912$		−	249.214i		−	0.273260i
$913$	14.5736	−	131.229i	0.0159623	−	0.143733i
$914$	−323.086			−0.353486
$915$		−	27.1341i		−	0.0296548i
$916$	−118.330			−0.129181
$917$	192.553			0.209981
$918$	20.2000			0.0220044
$919$		−	1334.18i		−	1.45177i	−0.687815	−	0.725886i	$-0.741430\pi$
$919$		−	1334.18i		−	1.45177i	0.687815	−	0.725886i	$-0.258570\pi$
$920$			21.8202i			0.0237177i
$921$		−	257.072i		−	0.279123i
$922$	1294.54			1.40405
$923$		−	2489.49i		−	2.69717i
$924$	0.963464	−	8.67555i	0.00104271	−	0.00938913i
$925$	−742.393			−0.802587
$926$		−	33.8686i		−	0.0365751i
$927$	156.287			0.168594
$928$	−215.647			−0.232378
$929$	922.321			0.992811			0.496405	−	0.868091i	$-0.334653\pi$
$929$	922.321			0.992811			0.496405	+	0.868091i	$0.334653\pi$
$930$			4.24433i			0.00456379i
$931$		−	1080.25i		−	1.16031i
$932$		−	32.8002i		−	0.0351933i
$933$	−156.962			−0.168234
$934$			10.3638i			0.0110962i
$935$	−0.798132	+	7.18681i	−0.000853617	+	0.00768643i
$936$	1384.45			1.47911
$937$			1556.45i			1.66110i	0.556945	+	0.830549i	$0.311973\pi$
$937$			1556.45i			1.66110i	−0.556945	+	0.830549i	$0.688027\pi$
$938$	−292.585			−0.311924
$939$	−156.499			−0.166665
$940$	8.60271			0.00915182
$941$			788.312i			0.837738i	0.908047	+	0.418869i	$0.137573\pi$
$941$			788.312i			0.837738i	−0.908047	+	0.418869i	$0.862427\pi$
$942$			217.376i			0.230760i
$943$			280.787i			0.297759i
$944$	1471.81			1.55912
$945$		−	17.6889i		−	0.0187184i
$946$	773.070	+	85.8533i	0.817199	+	0.0907540i
$947$	−426.391			−0.450255			−0.225127	−	0.974329i	$-0.572280\pi$
$947$	−426.391			−0.450255			−0.225127	+	0.974329i	$0.572280\pi$
$948$		−	9.27735i		−	0.00978624i
$949$	−494.397			−0.520967
$950$	1468.97			1.54629
$951$	221.944			0.233380
$952$			26.0982i			0.0274141i
$953$		−	1844.38i		−	1.93534i	−0.252222	−	0.967669i	$-0.581161\pi$
$953$		−	1844.38i		−	1.93534i	0.252222	−	0.967669i	$-0.418839\pi$
$954$			678.316i			0.711023i
$955$	216.059			0.226240
$956$			160.191i			0.167564i
$957$	−16.8856	+	152.047i	−0.0176443	+	0.158879i
$958$	−125.517			−0.131020
$959$		−	687.288i		−	0.716672i
$960$	−16.6288			−0.0173217
$961$	−917.985			−0.955239
$962$	−1357.67			−1.41130
$963$			401.064i			0.416474i
$964$		−	43.1783i		−	0.0447908i
$965$			98.4222i			0.101992i
$966$	−16.5577			−0.0171405
$967$		−	1190.35i		−	1.23097i	−0.788149	−	0.615484i	$-0.788960\pi$
$967$		−	1190.35i		−	1.23097i	0.788149	−	0.615484i	$-0.211040\pi$
$968$	197.559	−	878.495i	0.204090	−	0.907536i
$969$	−15.1293			−0.0156134
$970$		−	136.709i		−	0.140937i
$971$	1428.10			1.47075			0.735377	−	0.677658i	$-0.237005\pi$
$971$	1428.10			1.47075			0.735377	+	0.677658i	$0.237005\pi$
$972$	56.9444			0.0585848
$973$	−211.834			−0.217712
$974$			1233.91i			1.26685i
$975$		−	261.627i		−	0.268335i
$976$			1572.96i			1.61164i
$977$	870.246			0.890733			0.445367	−	0.895348i	$-0.353073\pi$
$977$	870.246			0.890733			0.445367	+	0.895348i	$0.353073\pi$
$978$		−	194.889i		−	0.199273i
$979$	−671.169	−	74.5367i	−0.685566	−	0.0761355i
$980$	11.4185			0.0116515
$981$			1256.36i			1.28069i
$982$	−496.152			−0.505247
$983$	−670.436			−0.682030			−0.341015	−	0.940058i	$-0.610771\pi$
$983$	−670.436			−0.682030			−0.341015	+	0.940058i	$0.610771\pi$
$984$	−217.710			−0.221250
$985$			172.792i			0.175423i
$986$			63.3866i			0.0642867i
$987$		−	47.1055i		−	0.0477260i
$988$	291.496			0.295036
$989$		−	160.096i		−	0.161877i
$990$	−13.7592	+	123.895i	−0.0138982	+	0.125147i
$991$	448.647			0.452722			0.226361	−	0.974044i	$-0.427317\pi$
$991$	448.647			0.452722			0.226361	+	0.974044i	$0.427317\pi$
$992$		−	50.8164i		−	0.0512262i
$993$	−22.6842			−0.0228442
$994$	809.024			0.813907
$995$	30.4723			0.0306254
$996$			2.92009i			0.00293182i
$997$			761.729i			0.764021i	0.924158	+	0.382010i	$0.124768\pi$
$997$			761.729i			0.764021i	−0.924158	+	0.382010i	$0.875232\pi$
$998$			573.647i			0.574796i
$999$	267.387			0.267655

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	253.3.c.a.208.13	✓	44
11.10	odd	2	inner	253.3.c.a.208.32	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.3.c.a.208.13	✓	44	1.1	even	1	trivial
253.3.c.a.208.32	yes	44	11.10	odd	2	inner

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:	\( N \)	\(=\)	\( 253 = 11 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	253.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.11822i q^{2} -0.499687 q^{3} -0.486856 q^{4} -0.611405 q^{5} +1.05845i q^{6} +3.26188i q^{7} -7.44161i q^{8} -8.75031 q^{9} +1.29509i q^{10} +(-10.9328 - 1.21414i) q^{11} +0.243276 q^{12} -21.2612i q^{13} +6.90937 q^{14} +0.305511 q^{15} -17.7104 q^{16} +1.07517i q^{17} +18.5351i q^{18} -28.1608i q^{19} +0.297666 q^{20} -1.62992i q^{21} +(-2.57182 + 23.1581i) q^{22} +4.79583 q^{23} +3.71848i q^{24} -24.6262 q^{25} -45.0358 q^{26} +8.86960 q^{27} -1.58806i q^{28} +27.8324i q^{29} -0.647140i q^{30} -6.55859 q^{31} +7.74806i q^{32} +(5.46297 + 0.606691i) q^{33} +2.27744 q^{34} -1.99433i q^{35} +4.26014 q^{36} +30.1465 q^{37} -59.6508 q^{38} +10.6239i q^{39} +4.54984i q^{40} +58.5480i q^{41} -3.45253 q^{42} -33.3823i q^{43} +(5.32269 + 0.591112i) q^{44} +5.34998 q^{45} -10.1586i q^{46} +28.9005 q^{47} +8.84966 q^{48} +38.3602 q^{49} +52.1637i q^{50} -0.537248i q^{51} +10.3511i q^{52} +36.5963 q^{53} -18.7878i q^{54} +(6.68436 + 0.742331i) q^{55} +24.2736 q^{56} +14.0716i q^{57} +58.9551 q^{58} -83.1044 q^{59} -0.148740 q^{60} -88.8156i q^{61} +13.8925i q^{62} -28.5424i q^{63} -54.4295 q^{64} +12.9992i q^{65} +(1.28510 - 11.5718i) q^{66} -42.3460 q^{67} -0.523452i q^{68} -2.39642 q^{69} -4.22442 q^{70} +117.091 q^{71} +65.1164i q^{72} -23.2535i q^{73} -63.8569i q^{74} +12.3054 q^{75} +13.7103i q^{76} +(3.96038 - 35.6614i) q^{77} +22.5038 q^{78} -38.1352i q^{79} +10.8282 q^{80} +74.3208 q^{81} +124.018 q^{82} +12.0032i q^{83} +0.793535i q^{84} -0.657363i q^{85} -70.7111 q^{86} -13.9075i q^{87} +(-9.03517 + 81.3576i) q^{88} +61.3905 q^{89} -11.3324i q^{90} +69.3513 q^{91} -2.33488 q^{92} +3.27725 q^{93} -61.2177i q^{94} +17.2176i q^{95} -3.87161i q^{96} -105.559 q^{97} -81.2552i q^{98} +(95.6653 + 10.6241i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 8 q^{3} - 88 q^{4} + 100 q^{9} + 8 q^{14} - 8 q^{15} + 72 q^{16} - 40 q^{20} - 76 q^{22} + 268 q^{25} - 40 q^{26} + 32 q^{27} + 72 q^{31} - 90 q^{33} + 60 q^{34} - 312 q^{36} + 4 q^{37} + 40 q^{38}+ \cdots + 494 q^{99}+O(q^{100}) \) 44 * q + 8 * q^3 - 88 * q^4 + 100 * q^9 + 8 * q^14 - 8 * q^15 + 72 * q^16 - 40 * q^20 - 76 * q^22 + 268 * q^25 - 40 * q^26 + 32 * q^27 + 72 * q^31 - 90 * q^33 + 60 * q^34 - 312 * q^36 + 4 * q^37 + 40 * q^38 + 12 * q^42 + 186 * q^44 - 180 * q^45 - 72 * q^47 + 252 * q^48 - 464 * q^49 + 100 * q^53 - 48 * q^55 + 208 * q^56 - 148 * q^58 - 144 * q^59 - 324 * q^60 - 416 * q^64 - 238 * q^66 + 292 * q^67 + 540 * q^70 + 544 * q^71 - 236 * q^75 + 64 * q^77 - 344 * q^78 + 156 * q^80 - 404 * q^81 + 72 * q^82 - 136 * q^86 + 608 * q^88 - 80 * q^89 - 4 * q^91 - 372 * q^93 + 68 * q^97 + 494 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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