LMFDB - Embedded newform 115.4.b.a.24.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,4,Mod(24,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("115.24");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	115.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.78521965066$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.19
Character	$\chi$	$=$	115.24
Dual form			115.4.b.a.24.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.407036i q^{2} -3.62432i q^{3} +7.83432 q^{4} +(7.84032 - 7.97054i) q^{5} +1.47523 q^{6} +11.1245i q^{7} +6.44514i q^{8} +13.8643 q^{9} +O(q^{10})$	\(q+0.407036i q^{2} -3.62432i q^{3} +7.83432 q^{4} +(7.84032 - 7.97054i) q^{5} +1.47523 q^{6} +11.1245i q^{7} +6.44514i q^{8} +13.8643 q^{9} +(3.24429 + 3.19129i) q^{10} -36.0095 q^{11} -28.3941i q^{12} -72.7865i q^{13} -4.52808 q^{14} +(-28.8878 - 28.4158i) q^{15} +60.0512 q^{16} +57.7321i q^{17} +5.64327i q^{18} +58.5985 q^{19} +(61.4236 - 62.4437i) q^{20} +40.3188 q^{21} -14.6572i q^{22} +23.0000i q^{23} +23.3592 q^{24} +(-2.05886 - 124.983i) q^{25} +29.6267 q^{26} -148.105i q^{27} +87.1531i q^{28} +194.843 q^{29} +(11.5663 - 11.7584i) q^{30} -321.303 q^{31} +76.0041i q^{32} +130.510i q^{33} -23.4990 q^{34} +(88.6684 + 87.2198i) q^{35} +108.617 q^{36} +89.7344i q^{37} +23.8517i q^{38} -263.802 q^{39} +(51.3712 + 50.5319i) q^{40} -334.357 q^{41} +16.4112i q^{42} +177.970i q^{43} -282.110 q^{44} +(108.700 - 110.506i) q^{45} -9.36182 q^{46} +367.225i q^{47} -217.645i q^{48} +219.245 q^{49} +(50.8726 - 0.838032i) q^{50} +209.240 q^{51} -570.233i q^{52} +599.734i q^{53} +60.2842 q^{54} +(-282.326 + 287.015i) q^{55} -71.6991 q^{56} -212.380i q^{57} +79.3083i q^{58} -663.154 q^{59} +(-226.316 - 222.619i) q^{60} -96.6484 q^{61} -130.782i q^{62} +154.234i q^{63} +449.473 q^{64} +(-580.148 - 570.669i) q^{65} -53.1223 q^{66} -24.2898i q^{67} +452.292i q^{68} +83.3594 q^{69} +(-35.5016 + 36.0912i) q^{70} +362.040 q^{71} +89.3573i q^{72} +798.592i q^{73} -36.5251 q^{74} +(-452.979 + 7.46199i) q^{75} +459.079 q^{76} -400.589i q^{77} -107.377i q^{78} +825.651 q^{79} +(470.820 - 478.640i) q^{80} -162.445 q^{81} -136.095i q^{82} +1073.26i q^{83} +315.871 q^{84} +(460.156 + 452.638i) q^{85} -72.4401 q^{86} -706.175i q^{87} -232.086i q^{88} -794.808 q^{89} +(44.9798 + 44.2450i) q^{90} +809.715 q^{91} +180.189i q^{92} +1164.51i q^{93} -149.474 q^{94} +(459.431 - 467.061i) q^{95} +275.463 q^{96} -1700.70i q^{97} +89.2406i q^{98} -499.247 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9}+O(q^{10}) $ 34 * q - 144 * q^4 + 14 * q^5 + 24 * q^6 - 310 * q^9	$ 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9} + 14 q^{10} - 8 q^{11} + 236 q^{14} + 440 q^{16} + 144 q^{19} - 180 q^{20} - 32 q^{21} + 108 q^{24} + 134 q^{25} - 144 q^{26} + 56 q^{29} - 294 q^{30} - 80 q^{31} + 264 q^{34} + 116 q^{35} + 1864 q^{36} - 1200 q^{39} + 650 q^{40} + 268 q^{41} - 1612 q^{44} - 1346 q^{45} + 184 q^{46} - 1474 q^{49} + 120 q^{50} - 1104 q^{51} + 1564 q^{54} + 1160 q^{55} - 2300 q^{56} - 708 q^{59} - 516 q^{60} + 1100 q^{61} + 100 q^{64} + 1164 q^{65} - 1416 q^{66} - 552 q^{69} + 1144 q^{70} + 1360 q^{71} + 1588 q^{74} - 2064 q^{75} + 108 q^{76} + 3968 q^{79} + 2542 q^{80} + 4914 q^{81} - 1948 q^{84} + 124 q^{85} - 6148 q^{86} + 1196 q^{89} + 2760 q^{90} - 544 q^{91} - 2340 q^{94} + 3920 q^{95} + 2960 q^{96} - 3816 q^{99}+O(q^{100}) $ 34 * q - 144 * q^4 + 14 * q^5 + 24 * q^6 - 310 * q^9 + 14 * q^10 - 8 * q^11 + 236 * q^14 + 440 * q^16 + 144 * q^19 - 180 * q^20 - 32 * q^21 + 108 * q^24 + 134 * q^25 - 144 * q^26 + 56 * q^29 - 294 * q^30 - 80 * q^31 + 264 * q^34 + 116 * q^35 + 1864 * q^36 - 1200 * q^39 + 650 * q^40 + 268 * q^41 - 1612 * q^44 - 1346 * q^45 + 184 * q^46 - 1474 * q^49 + 120 * q^50 - 1104 * q^51 + 1564 * q^54 + 1160 * q^55 - 2300 * q^56 - 708 * q^59 - 516 * q^60 + 1100 * q^61 + 100 * q^64 + 1164 * q^65 - 1416 * q^66 - 552 * q^69 + 1144 * q^70 + 1360 * q^71 + 1588 * q^74 - 2064 * q^75 + 108 * q^76 + 3968 * q^79 + 2542 * q^80 + 4914 * q^81 - 1948 * q^84 + 124 * q^85 - 6148 * q^86 + 1196 * q^89 + 2760 * q^90 - 544 * q^91 - 2340 * q^94 + 3920 * q^95 + 2960 * q^96 - 3816 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$1$

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 $

$2$			0.407036i			0.143909i	0.997408	+	0.0719545i	$0.0229236\pi$
$2$			0.407036i			0.143909i	−0.997408	+	0.0719545i	$0.977076\pi$
$3$		−	3.62432i		−	0.697501i	−0.937216	−	0.348750i	$-0.886606\pi$
$3$		−	3.62432i		−	0.697501i	0.937216	−	0.348750i	$-0.113394\pi$
$4$	7.83432			0.979290
$5$	7.84032	−	7.97054i	0.701259	−	0.712906i
$5$	7.84032	−	7.97054i	0.701259	−	0.712906i
$6$	1.47523			0.100377
$7$			11.1245i			0.600668i	0.953834	+	0.300334i	$0.0970981\pi$
$7$			11.1245i			0.600668i	−0.953834	+	0.300334i	$0.902902\pi$
$8$			6.44514i			0.284837i
$9$	13.8643			0.513492
$10$	3.24429	+	3.19129i	0.102594	+	0.100917i
$11$	−36.0095			−0.987025			−0.493513	−	0.869739i	$-0.664287\pi$
$11$	−36.0095			−0.987025			−0.493513	+	0.869739i	$0.664287\pi$
$12$		−	28.3941i		−	0.683056i
$13$		−	72.7865i		−	1.55287i	−0.630196	−	0.776436i	$-0.717025\pi$
$13$		−	72.7865i		−	1.55287i	0.630196	−	0.776436i	$-0.282975\pi$
$14$	−4.52808			−0.0864414
$15$	−28.8878	−	28.4158i	−0.497253	−	0.489129i
$16$	60.0512			0.938300
$17$			57.7321i			0.823653i	0.911262	+	0.411826i	$0.135109\pi$
$17$			57.7321i			0.823653i	−0.911262	+	0.411826i	$0.864891\pi$
$18$			5.64327i			0.0738961i
$19$	58.5985			0.707548			0.353774	−	0.935331i	$-0.384898\pi$
$19$	58.5985			0.707548			0.353774	+	0.935331i	$0.384898\pi$
$20$	61.4236	−	62.4437i	0.686736	−	0.698142i
$21$	40.3188			0.418966
$22$		−	14.6572i		−	0.142042i
$23$			23.0000i			0.208514i
$23$			23.0000i			0.208514i
$24$	23.3592			0.198674
$25$	−2.05886	−	124.983i	−0.0164709	−	0.999864i
$26$	29.6267			0.223472
$27$		−	148.105i		−	1.05566i
$28$			87.1531i			0.588228i
$29$	194.843			1.24764			0.623819	−	0.781568i	$-0.285580\pi$
$29$	194.843			1.24764			0.623819	+	0.781568i	$0.285580\pi$
$30$	11.5663	−	11.7584i	0.0703900	−	0.0715591i
$31$	−321.303			−1.86154			−0.930771	−	0.365603i	$-0.880863\pi$
$31$	−321.303			−1.86154			−0.930771	+	0.365603i	$0.880863\pi$
$32$			76.0041i			0.419867i
$33$			130.510i			0.688451i
$34$	−23.4990			−0.118531
$35$	88.6684	+	87.2198i	0.428220	+	0.421224i
$36$	108.617			0.502858
$37$			89.7344i			0.398709i	0.979927	+	0.199355i	$0.0638846\pi$
$37$			89.7344i			0.398709i	−0.979927	+	0.199355i	$0.936115\pi$
$38$			23.8517i			0.101822i
$39$	−263.802			−1.08313
$40$	51.3712	+	50.5319i	0.203062	+	0.199745i
$41$	−334.357			−1.27360			−0.636801	−	0.771028i	$-0.719743\pi$
$41$	−334.357			−1.27360			−0.636801	+	0.771028i	$0.719743\pi$
$42$			16.4112i			0.0602930i
$43$			177.970i			0.631166i	0.948898	+	0.315583i	$0.102200\pi$
$43$			177.970i			0.631166i	−0.948898	+	0.315583i	$0.897800\pi$
$44$	−282.110			−0.966584
$45$	108.700	−	110.506i	0.360091	−	0.366072i
$46$	−9.36182			−0.0300071
$47$			367.225i			1.13969i	0.821753	+	0.569843i	$0.192996\pi$
$47$			367.225i			1.13969i	−0.821753	+	0.569843i	$0.807004\pi$
$48$		−	217.645i		−	0.654465i
$49$	219.245			0.639198
$50$	50.8726	−	0.838032i	0.143889	−	0.00237031i
$51$	209.240			0.574499
$52$		−	570.233i		−	1.52071i
$53$			599.734i			1.55434i	0.629293	+	0.777168i	$0.283345\pi$
$53$			599.734i			1.55434i	−0.629293	+	0.777168i	$0.716655\pi$
$54$	60.2842			0.151919
$55$	−282.326	+	287.015i	−0.692161	+	0.703657i
$56$	−71.6991			−0.171093
$57$		−	212.380i		−	0.493516i
$58$			79.3083i			0.179546i
$59$	−663.154			−1.46331			−0.731655	−	0.681675i	$-0.761252\pi$
$59$	−663.154			−1.46331			−0.731655	+	0.681675i	$0.761252\pi$
$60$	−226.316	−	222.619i	−0.486955	−	0.478999i
$61$	−96.6484			−0.202862			−0.101431	−	0.994843i	$-0.532342\pi$
$61$	−96.6484			−0.202862			−0.101431	+	0.994843i	$0.532342\pi$
$62$		−	130.782i		−	0.267892i
$63$			154.234i			0.308438i
$64$	449.473			0.877877
$65$	−580.148	−	570.669i	−1.10705	−	1.08897i
$66$	−53.1223			−0.0990742
$67$		−	24.2898i		−	0.0442907i	−0.999755	−	0.0221453i	$-0.992950\pi$
$67$		−	24.2898i		−	0.0442907i	0.999755	−	0.0221453i	$-0.00704966\pi$
$68$			452.292i			0.806595i
$69$	83.3594			0.145439
$70$	−35.5016	+	36.0912i	−0.0606179	+	0.0616247i
$71$	362.040			0.605159			0.302579	−	0.953124i	$-0.402152\pi$
$71$	362.040			0.605159			0.302579	+	0.953124i	$0.402152\pi$
$72$			89.3573i			0.146262i
$73$			798.592i			1.28038i	0.768215	+	0.640192i	$0.221145\pi$
$73$			798.592i			1.28038i	−0.768215	+	0.640192i	$0.778855\pi$
$74$	−36.5251			−0.0573778
$75$	−452.979	+	7.46199i	−0.697406	+	0.0114885i
$76$	459.079			0.692895
$77$		−	400.589i		−	0.592874i
$78$		−	107.377i		−	0.155872i
$79$	825.651			1.17586			0.587930	−	0.808912i	$-0.299943\pi$
$79$	825.651			1.17586			0.587930	+	0.808912i	$0.299943\pi$
$80$	470.820	−	478.640i	0.657991	−	0.668920i
$81$	−162.445			−0.222833
$82$		−	136.095i		−	0.183283i
$83$			1073.26i			1.41934i	0.704533	+	0.709671i	$0.251156\pi$
$83$			1073.26i			1.41934i	−0.704533	+	0.709671i	$0.748844\pi$
$84$	315.871			0.410290
$85$	460.156	+	452.638i	0.587187	+	0.577594i
$86$	−72.4401			−0.0908305
$87$		−	706.175i		−	0.870229i
$88$		−	232.086i		−	0.281142i
$89$	−794.808			−0.946623			−0.473311	−	0.880895i	$-0.656941\pi$
$89$	−794.808			−0.946623			−0.473311	+	0.880895i	$0.656941\pi$
$90$	44.9798	+	44.2450i	0.0526810	+	0.0518203i
$91$	809.715			0.932761
$92$			180.189i			0.204196i
$93$			1164.51i			1.29843i
$94$	−149.474			−0.164011
$95$	459.431	−	467.061i	0.496175	−	0.504416i
$96$	275.463			0.292858
$97$		−	1700.70i		−	1.78020i	−0.455763	−	0.890101i	$-0.650633\pi$
$97$		−	1700.70i		−	1.78020i	0.455763	−	0.890101i	$-0.349367\pi$
$98$			89.2406i			0.0919863i
$99$	−499.247			−0.506830
$100$	−16.1298	−	979.157i	−0.0161298	−	0.979157i
$101$	−545.142			−0.537066			−0.268533	−	0.963270i	$-0.586539\pi$
$101$	−545.142			−0.537066			−0.268533	+	0.963270i	$0.586539\pi$
$102$			85.1681i			0.0826755i
$103$		−	994.869i		−	0.951722i	−0.879521	−	0.475861i	$-0.842137\pi$
$103$		−	994.869i		−	0.951722i	0.879521	−	0.475861i	$-0.157863\pi$
$104$	469.119			0.442316
$105$	316.113	−	321.363i	0.293804	−	0.298684i
$106$	−244.113			−0.223683
$107$			1063.23i			0.960618i	0.877099	+	0.480309i	$0.159475\pi$
$107$			1063.23i			0.960618i	−0.877099	+	0.480309i	$0.840525\pi$
$108$		−	1160.30i		−	1.03380i
$109$	927.429			0.814968			0.407484	−	0.913212i	$-0.366406\pi$
$109$	927.429			0.814968			0.407484	+	0.913212i	$0.366406\pi$
$110$	−116.825	−	114.917i	−0.101262	−	0.0996081i
$111$	325.226			0.278100
$112$			668.041i			0.563606i
$113$		−	1564.75i		−	1.30265i	−0.758799	−	0.651325i	$-0.774213\pi$
$113$		−	1564.75i		−	1.30265i	0.758799	−	0.651325i	$-0.225787\pi$
$114$	86.4462			0.0710213
$115$	183.322	+	180.327i	0.148651	+	0.146223i
$116$	1526.47			1.22180
$117$		−	1009.13i		−	0.797389i
$118$		−	269.927i		−	0.210583i
$119$	−642.242			−0.494742
$120$	183.144	−	186.186i	0.139322	−	0.141636i
$121$	−34.3149			−0.0257813
$122$		−	39.3394i		−	0.0291936i
$123$			1211.82i			0.888339i
$124$	−2517.19			−1.82299
$125$	−1012.32	−	963.496i	−0.724360	−	0.689422i
$126$	−62.7786			−0.0443870
$127$			1299.53i			0.907989i	0.891004	+	0.453995i	$0.150001\pi$
$127$			1299.53i			0.907989i	−0.891004	+	0.453995i	$0.849999\pi$
$128$			790.984i			0.546201i
$129$	645.020			0.440239
$130$	232.283	−	236.141i	0.156712	−	0.159315i
$131$	−321.197			−0.214222			−0.107111	−	0.994247i	$-0.534160\pi$
$131$	−321.197			−0.214222			−0.107111	+	0.994247i	$0.534160\pi$
$132$			1022.46i			0.674193i
$133$			651.880i			0.425001i
$134$	9.88683			0.00637382
$135$	−1180.48	−	1161.19i	−0.752588	−	0.740293i
$136$	−372.091			−0.234607
$137$			233.607i			0.145682i	0.997344	+	0.0728409i	$0.0232065\pi$
$137$			233.607i			0.145682i	−0.997344	+	0.0728409i	$0.976793\pi$
$138$			33.9303i			0.0209300i
$139$	980.052			0.598035			0.299018	−	0.954248i	$-0.403341\pi$
$139$	980.052			0.598035			0.299018	+	0.954248i	$0.403341\pi$
$140$	694.657	+	683.308i	0.419352	+	0.412500i
$141$	1330.94			0.794932
$142$			147.363i			0.0870877i
$143$			2621.01i			1.53272i
$144$	832.567			0.481810
$145$	1527.63	−	1553.01i	0.874918	−	0.889450i
$146$	−325.055			−0.184259
$147$		−	794.614i		−	0.445841i
$148$			703.008i			0.390452i
$149$	−125.696			−0.0691104			−0.0345552	−	0.999403i	$-0.511001\pi$
$149$	−125.696			−0.0691104			−0.0345552	+	0.999403i	$0.511001\pi$
$150$	−3.03730	−	184.379i	−0.00165329	−	0.100363i
$151$	−2280.11			−1.22883			−0.614414	−	0.788984i	$-0.710608\pi$
$151$	−2280.11			−1.22883			−0.614414	+	0.788984i	$0.710608\pi$
$152$			377.675i			0.201536i
$153$			800.415i			0.422940i
$154$	163.054			0.0853199
$155$	−2519.12	+	2560.96i	−1.30542	+	1.32711i
$156$	−2066.71			−1.06070
$157$			1261.53i			0.641283i	0.947201	+	0.320641i	$0.103898\pi$
$157$			1261.53i			0.641283i	−0.947201	+	0.320641i	$0.896102\pi$
$158$			336.069i			0.169217i
$159$	2173.63			1.08415
$160$	605.793	+	595.896i	0.299326	+	0.294436i
$161$	−255.864			−0.125248
$162$		−	66.1211i		−	0.0320677i
$163$		−	1888.54i		−	0.907496i	−0.891130	−	0.453748i	$-0.850087\pi$
$163$		−	1888.54i		−	0.907496i	0.891130	−	0.453748i	$-0.149913\pi$
$164$	−2619.46			−1.24723
$165$	1040.23	+	1023.24i	0.490801	+	0.482783i
$166$	−436.855			−0.204256
$167$		−	1633.99i		−	0.757138i	−0.925573	−	0.378569i	$-0.876416\pi$
$167$		−	1633.99i		−	0.757138i	0.925573	−	0.378569i	$-0.123584\pi$
$168$			259.860i			0.119337i
$169$	−3100.88			−1.41141
$170$	−184.240	+	187.300i	−0.0831209	+	0.0845015i
$171$	812.427			0.363321
$172$			1394.27i			0.618095i
$173$		−	2875.91i		−	1.26388i	−0.775018	−	0.631940i	$-0.782259\pi$
$173$		−	2875.91i		−	1.26388i	0.775018	−	0.631940i	$-0.217741\pi$
$174$	287.439			0.125234
$175$	1390.38	−	22.9039i	0.600586	−	0.00989355i
$176$	−2162.41			−0.926125
$177$			2403.48i			1.02066i
$178$		−	323.515i		−	0.136227i
$179$	1318.82			0.550688			0.275344	−	0.961346i	$-0.411208\pi$
$179$	1318.82			0.550688			0.275344	+	0.961346i	$0.411208\pi$
$180$	851.594	−	865.738i	0.352634	−	0.358491i
$181$	−177.164			−0.0727539			−0.0363770	−	0.999338i	$-0.511582\pi$
$181$	−177.164			−0.0727539			−0.0363770	+	0.999338i	$0.511582\pi$
$182$			329.583i			0.134233i
$183$			350.285i			0.141496i
$184$	−148.238			−0.0593927
$185$	715.231	+	703.546i	0.284242	+	0.279599i
$186$	−473.996			−0.186855
$187$		−	2078.91i		−	0.812966i
$188$			2876.96i			1.11608i
$189$	1647.60			0.634102
$190$	190.111	+	187.005i	0.0725899	+	0.0714040i
$191$	−3430.85			−1.29973			−0.649864	−	0.760051i	$-0.725174\pi$
$191$	−3430.85			−1.29973			−0.649864	+	0.760051i	$0.725174\pi$
$192$		−	1629.03i		−	0.612320i
$193$		−	2662.93i		−	0.993170i	−0.867988	−	0.496585i	$-0.834587\pi$
$193$		−	2662.93i		−	0.993170i	0.867988	−	0.496585i	$-0.165413\pi$
$194$	692.245			0.256187
$195$	−2068.29	+	2102.64i	−0.759555	+	0.772170i
$196$	1717.64			0.625961
$197$		−	3712.53i		−	1.34267i	−0.741152	−	0.671337i	$-0.765720\pi$
$197$		−	3712.53i		−	1.34267i	0.741152	−	0.671337i	$-0.234280\pi$
$198$		−	203.211i		−	0.0729373i
$199$	−1460.41			−0.520228			−0.260114	−	0.965578i	$-0.583760\pi$
$199$	−1460.41			−0.520228			−0.260114	+	0.965578i	$0.583760\pi$
$200$	805.533	−	13.2697i	0.284799	−	0.00469153i
$201$	−88.0342			−0.0308928
$202$		−	221.892i		−	0.0772886i
$203$			2167.54i			0.749417i
$204$	1639.25			0.562601
$205$	−2621.46	+	2665.00i	−0.893126	+	0.907960i
$206$	404.947			0.136961
$207$			318.879i			0.107071i
$208$		−	4370.92i		−	1.45706i
$209$	−2110.10			−0.698368
$210$	130.806	+	128.669i	0.0429833	+	0.0422810i
$211$	2541.93			0.829355			0.414677	−	0.909968i	$-0.363894\pi$
$211$	2541.93			0.829355			0.414677	+	0.909968i	$0.363894\pi$
$212$			4698.51i			1.52215i
$213$		−	1312.15i		−	0.422099i
$214$	−432.772			−0.138241
$215$	1418.52	+	1395.34i	0.449962	+	0.442611i
$216$	954.559			0.300692
$217$		−	3574.35i		−	1.11817i
$218$			377.497i			0.117281i
$219$	2894.35			0.893069
$220$	−2211.83	+	2248.57i	−0.677826	+	0.689084i
$221$	4202.12			1.27903
$222$			132.379i			0.0400211i
$223$		−	2427.33i		−	0.728905i	−0.931222	−	0.364452i	$-0.881256\pi$
$223$		−	2427.33i		−	0.728905i	0.931222	−	0.364452i	$-0.118744\pi$
$224$	−845.509			−0.252201
$225$	−28.5447	−	1732.80i	−0.00845769	−	0.513423i
$226$	636.910			0.187463
$227$			2206.66i			0.645204i	0.946535	+	0.322602i	$0.104558\pi$
$227$			2206.66i			0.645204i	−0.946535	+	0.322602i	$0.895442\pi$
$228$		−	1663.85i		−	0.483295i
$229$	2055.59			0.593177			0.296588	−	0.955005i	$-0.404151\pi$
$229$	2055.59			0.593177			0.296588	+	0.955005i	$0.404151\pi$
$230$	−73.3997	+	74.6188i	−0.0210427	+	0.0213922i
$231$	−1451.86			−0.413530
$232$			1255.79i			0.355374i
$233$			1513.90i			0.425659i	0.977089	+	0.212830i	$0.0682679\pi$
$233$			1513.90i			0.425659i	−0.977089	+	0.212830i	$0.931732\pi$
$234$	410.754			0.114751
$235$	2926.98	+	2879.16i	0.812490	+	0.799216i
$236$	−5195.36			−1.43300
$237$		−	2992.42i		−	0.820164i
$238$		−	261.416i		−	0.0711977i
$239$	−1445.68			−0.391268			−0.195634	−	0.980677i	$-0.562676\pi$
$239$	−1445.68			−0.391268			−0.195634	+	0.980677i	$0.562676\pi$
$240$	−1734.75	−	1706.40i	−0.466572	−	0.458950i
$241$	5787.91			1.54702			0.773510	−	0.633784i	$-0.218499\pi$
$241$	5787.91			1.54702			0.773510	+	0.633784i	$0.218499\pi$
$242$		−	13.9674i		−	0.00371016i
$243$		−	3410.09i		−	0.900236i
$244$	−757.175			−0.198660
$245$	1718.95	−	1747.50i	0.448244	−	0.455688i
$246$	−493.252			−0.127840
$247$		−	4265.18i		−	1.09873i
$248$		−	2070.84i		−	0.530237i
$249$	3889.83			0.989992
$250$	392.178	−	412.052i	0.0992140	−	0.104242i
$251$	994.398			0.250063			0.125032	−	0.992153i	$-0.460097\pi$
$251$	994.398			0.250063			0.125032	+	0.992153i	$0.460097\pi$
$252$			1208.32i			0.302051i
$253$		−	828.219i		−	0.205809i
$254$	−528.955			−0.130668
$255$	1640.51	−	1667.75i	0.402872	−	0.409564i
$256$	3273.83			0.799274
$257$			2039.32i			0.494977i	0.968891	+	0.247489i	$0.0796053\pi$
$257$			2039.32i			0.494977i	−0.968891	+	0.247489i	$0.920395\pi$
$258$			262.546i			0.0633543i
$259$	−998.252			−0.239492
$260$	−4545.06	−	4470.81i	−1.08413	−	1.06641i
$261$	2701.37			0.640653
$262$		−	130.739i		−	0.0308285i
$263$		−	2638.43i		−	0.618603i	−0.950964	−	0.309302i	$-0.899905\pi$
$263$		−	2638.43i		−	0.618603i	0.950964	−	0.309302i	$-0.100095\pi$
$264$	−841.155			−0.196097
$265$	4780.20	+	4702.11i	1.10810	+	1.08999i
$266$	−265.339			−0.0611615
$267$			2880.64i			0.660270i
$268$		−	190.294i		−	0.0433734i
$269$	420.669			0.0953480			0.0476740	−	0.998863i	$-0.484819\pi$
$269$	420.669			0.0953480			0.0476740	+	0.998863i	$0.484819\pi$
$270$	472.647	−	480.497i	0.106535	−	0.108304i
$271$	−1776.58			−0.398228			−0.199114	−	0.979976i	$-0.563806\pi$
$271$	−1776.58			−0.398228			−0.199114	+	0.979976i	$0.563806\pi$
$272$			3466.88i			0.772833i
$273$		−	2934.67i		−	0.650602i
$274$	−95.0864			−0.0209649
$275$	74.1387	+	4500.58i	0.0162572	+	0.986891i
$276$	653.064			0.142427
$277$		−	804.678i		−	0.174543i	−0.996185	−	0.0872715i	$-0.972185\pi$
$277$		−	804.678i		−	0.174543i	0.996185	−	0.0872715i	$-0.0278148\pi$
$278$			398.916i			0.0860626i
$279$	−4454.65			−0.955888
$280$	−562.143	+	571.480i	−0.119980	+	0.121973i
$281$	4420.61			0.938475			0.469237	−	0.883072i	$-0.344529\pi$
$281$	4420.61			0.938475			0.469237	+	0.883072i	$0.344529\pi$
$282$			541.741i			0.114398i
$283$		−	8746.31i		−	1.83715i	−0.395244	−	0.918576i	$-0.629340\pi$
$283$		−	8746.31i		−	1.83715i	0.395244	−	0.918576i	$-0.370660\pi$
$284$	2836.34			0.592626
$285$	−1692.78	−	1665.12i	−0.351830	−	0.346082i
$286$	−1066.84			−0.220573
$287$		−	3719.56i		−	0.765012i
$288$			1053.74i			0.215599i
$289$	1580.00			0.321596
$290$	632.129	+	621.802i	0.128000	+	0.125909i
$291$	−6163.87			−1.24169
$292$			6256.42i			1.25387i
$293$		−	4546.93i		−	0.906602i	−0.891357	−	0.453301i	$-0.850246\pi$
$293$		−	4546.93i		−	0.906602i	0.891357	−	0.453301i	$-0.149754\pi$
$294$	323.436			0.0641605
$295$	−5199.34	+	5285.69i	−1.02616	+	1.04320i
$296$	−578.350			−0.113567
$297$			5333.20i			1.04197i
$298$		−	51.1629i		−	0.00994560i
$299$	1674.09			0.323796
$300$	−3548.78	+	58.4596i	−0.682963	+	0.0112506i
$301$	−1979.83			−0.379121
$302$		−	928.089i		−	0.176839i
$303$			1975.77i			0.374604i
$304$	3518.91			0.663892
$305$	−757.754	+	770.340i	−0.142259	+	0.144621i
$306$	−325.798			−0.0608648
$307$			3539.50i			0.658012i	0.944328	+	0.329006i	$0.106714\pi$
$307$			3539.50i			0.658012i	−0.944328	+	0.329006i	$0.893286\pi$
$308$		−	3138.34i		−	0.580596i
$309$	−3605.72			−0.663827
$310$	−1042.40	−	1025.37i	−0.190982	−	0.187862i
$311$	−5941.05			−1.08324			−0.541618	−	0.840625i	$-0.682188\pi$
$311$	−5941.05			−1.08324			−0.541618	+	0.840625i	$0.682188\pi$
$312$		−	1700.24i		−	0.308516i
$313$			7762.86i			1.40186i	0.713229	+	0.700931i	$0.247232\pi$
$313$			7762.86i			1.40186i	−0.713229	+	0.700931i	$0.752768\pi$
$314$	−513.489			−0.0922863
$315$	1229.33	+	1209.24i	0.219888	+	0.216295i
$316$	6468.41			1.15151
$317$			6178.48i			1.09469i	0.836906	+	0.547347i	$0.184362\pi$
$317$			6178.48i			1.09469i	−0.836906	+	0.547347i	$0.815638\pi$
$318$			884.745i			0.156019i
$319$	−7016.22			−1.23145
$320$	3524.01	−	3582.54i	0.615619	−	0.625844i
$321$	3853.48			0.670032
$322$		−	104.146i		−	0.0180243i
$323$			3383.02i			0.582774i
$324$	−1272.65			−0.218218
$325$	−9097.08	+	149.858i	−1.55266	+	0.0255772i
$326$	768.703			0.130597
$327$		−	3361.30i		−	0.568441i
$328$		−	2154.97i		−	0.362770i
$329$	−4085.20			−0.684573
$330$	−416.495	+	423.413i	−0.0694767	+	0.0706306i
$331$	−5281.13			−0.876970			−0.438485	−	0.898739i	$-0.644485\pi$
$331$	−5281.13			−0.876970			−0.438485	+	0.898739i	$0.644485\pi$
$332$			8408.25i			1.38995i
$333$			1244.10i			0.204734i
$334$	665.093			0.108959
$335$	−193.603	−	190.440i	−0.0315751	−	0.0310593i
$336$	2421.19			0.393116
$337$		−	7454.94i		−	1.20503i	−0.798106	−	0.602517i	$-0.794165\pi$
$337$		−	7454.94i		−	1.20503i	0.798106	−	0.602517i	$-0.205835\pi$
$338$		−	1262.17i		−	0.203115i
$339$	−5671.16			−0.908600
$340$	3605.01	+	3546.11i	0.575027	+	0.565632i
$341$	11570.0			1.83739
$342$			330.687i			0.0522851i
$343$			6254.71i			0.984614i
$344$	−1147.04			−0.179780
$345$	653.564	−	664.419i	0.101990	−	0.103684i
$346$	1170.60			0.181883
$347$		−	1416.63i		−	0.219160i	−0.993978	−	0.109580i	$-0.965049\pi$
$347$		−	1416.63i		−	0.219160i	0.993978	−	0.109580i	$-0.0349506\pi$
$348$		−	5532.41i		−	0.852207i
$349$	9885.44			1.51620			0.758102	−	0.652136i	$-0.226127\pi$
$349$	9885.44			1.51620			0.758102	+	0.652136i	$0.226127\pi$
$350$	9.32270	+	565.933i	0.00142377	+	0.0864297i
$351$	−10780.1			−1.63931
$352$		−	2736.87i		−	0.414419i
$353$		−	6540.93i		−	0.986229i	−0.869964	−	0.493114i	$-0.835858\pi$
$353$		−	6540.93i		−	0.986229i	0.869964	−	0.493114i	$-0.164142\pi$
$354$	−978.303			−0.146882
$355$	2838.51	−	2885.65i	0.424373	−	0.431422i
$356$	−6226.78			−0.927019
$357$			2327.69i			0.345083i
$358$			536.806i			0.0792488i
$359$	9371.08			1.37768			0.688839	−	0.724914i	$-0.258121\pi$
$359$	9371.08			1.37768			0.688839	+	0.724914i	$0.258121\pi$
$360$	712.225	+	700.589i	0.104271	+	0.102568i
$361$	−3425.22			−0.499376
$362$		−	72.1119i		−	0.0104699i
$363$			124.368i			0.0179825i
$364$	6343.57			0.913444
$365$	6365.20	+	6261.21i	0.912794	+	0.897882i
$366$	−142.579			−0.0203626
$367$			9957.94i			1.41635i	0.706037	+	0.708175i	$0.250481\pi$
$367$			9957.94i			1.41635i	−0.706037	+	0.708175i	$0.749519\pi$
$368$			1381.18i			0.195649i
$369$	−4635.62			−0.653985
$370$	−286.368	+	291.125i	−0.0402367	+	0.0409050i
$371$	−6671.76			−0.933640
$372$			9123.12i			1.27154i
$373$			9516.93i			1.32109i	0.750785	+	0.660547i	$0.229676\pi$
$373$			9516.93i			1.32109i	−0.750785	+	0.660547i	$0.770324\pi$
$374$	846.189			0.116993
$375$	−3492.02	+	3668.99i	−0.480872	+	0.505242i
$376$	−2366.81			−0.324625
$377$		−	14182.0i		−	1.93742i
$378$			670.633i			0.0912530i
$379$	−7057.35			−0.956495			−0.478247	−	0.878225i	$-0.658728\pi$
$379$	−7057.35			−0.956495			−0.478247	+	0.878225i	$0.658728\pi$
$380$	3599.33	−	3659.11i	0.485899	−	0.493969i
$381$	4709.91			0.633323
$382$		−	1396.48i		−	0.187042i
$383$			1483.21i			0.197881i	0.995093	+	0.0989403i	$0.0315453\pi$
$383$			1483.21i			0.197881i	−0.995093	+	0.0989403i	$0.968455\pi$
$384$	2866.78			0.380976
$385$	−3192.91	−	3140.74i	−0.422664	−	0.415759i
$386$	1083.91			0.142926
$387$			2467.43i			0.324099i
$388$		−	13323.8i		−	1.74334i
$389$	−3532.86			−0.460471			−0.230235	−	0.973135i	$-0.573950\pi$
$389$	−3532.86			−0.460471			−0.230235	+	0.973135i	$0.573950\pi$
$390$	−855.850	−	841.868i	−0.111122	−	0.109307i
$391$	−1327.84			−0.171743
$392$			1413.06i			0.182068i
$393$			1164.12i			0.149420i
$394$	1511.13			0.193223
$395$	6473.36	−	6580.88i	0.824583	−	0.838278i
$396$	−3911.26			−0.496334
$397$		−	12950.7i		−	1.63722i	−0.574349	−	0.818610i	$-0.694745\pi$
$397$		−	12950.7i		−	1.63722i	0.574349	−	0.818610i	$-0.305255\pi$
$398$		−	594.437i		−	0.0748655i
$399$	2362.62			0.296439
$400$	−123.637	−	7505.38i	−0.0154547	−	0.938172i
$401$	−4322.59			−0.538303			−0.269152	−	0.963098i	$-0.586743\pi$
$401$	−4322.59			−0.538303			−0.269152	+	0.963098i	$0.586743\pi$
$402$		−	35.8331i		−	0.00444575i
$403$			23386.6i			2.89074i
$404$	−4270.82			−0.525943
$405$	−1273.62	+	1294.78i	−0.156264	+	0.158859i
$406$	−882.267			−0.107848
$407$		−	3231.29i		−	0.393536i
$408$			1348.58i			0.163639i
$409$	−13823.7			−1.67124			−0.835621	−	0.549306i	$-0.814892\pi$
$409$	−13823.7			−1.67124			−0.835621	+	0.549306i	$0.814892\pi$
$410$	−1084.75	−	1067.03i	−0.130663	−	0.128529i
$411$	846.667			0.101613
$412$		−	7794.12i		−	0.932012i
$413$		−	7377.27i		−	0.878963i
$414$	−129.795			−0.0154084
$415$	8554.44	+	8414.68i	1.01186	+	0.995327i
$416$	5532.07			0.652000
$417$		−	3552.02i		−	0.417130i
$418$		−	858.888i		−	0.100501i
$419$	6217.56			0.724935			0.362467	−	0.931996i	$-0.381934\pi$
$419$	6217.56			0.724935			0.362467	+	0.931996i	$0.381934\pi$
$420$	2476.53	−	2517.66i	0.287719	−	0.292498i
$421$	−14645.4			−1.69542			−0.847711	−	0.530458i	$-0.822020\pi$
$421$	−14645.4			−1.69542			−0.847711	+	0.530458i	$0.822020\pi$
$422$			1034.66i			0.119352i
$423$			5091.31i			0.585220i
$424$	−3865.37			−0.442733
$425$	7215.54	−	118.863i	0.823541	−	0.0135663i
$426$	534.092			0.0607438
$427$		−	1075.17i		−	0.121852i
$428$			8329.67i			0.940724i
$429$	9499.37			1.06908
$430$	−567.954	+	577.387i	−0.0636957	+	0.0647536i
$431$	14229.5			1.59028			0.795139	−	0.606427i	$-0.207398\pi$
$431$	14229.5			1.59028			0.795139	+	0.606427i	$0.207398\pi$
$432$		−	8893.90i		−	0.990528i
$433$			1319.06i			0.146397i	0.997317	+	0.0731984i	$0.0233206\pi$
$433$			1319.06i			0.146397i	−0.997317	+	0.0731984i	$0.976679\pi$
$434$	1454.89			0.160914
$435$	−5628.60	−	5536.64i	−0.620392	−	0.610256i
$436$	7265.77			0.798090
$437$			1347.77i			0.147534i
$438$			1178.11i			0.128521i
$439$	−6012.78			−0.653700			−0.326850	−	0.945076i	$-0.605987\pi$
$439$	−6012.78			−0.653700			−0.326850	+	0.945076i	$0.605987\pi$
$440$	−1849.85	−	1819.63i	−0.200428	−	0.197153i
$441$	3039.68			0.328223
$442$			1710.41i			0.184064i
$443$		−	15873.2i		−	1.70239i	−0.524851	−	0.851194i	$-0.675879\pi$
$443$		−	15873.2i		−	1.70239i	0.524851	−	0.851194i	$-0.324121\pi$
$444$	2547.93			0.272341
$445$	−6231.54	+	6335.04i	−0.663828	+	0.674854i
$446$	988.009			0.104896
$447$			455.564i			0.0482045i
$448$			5000.17i			0.527312i
$449$	9155.31			0.962285			0.481142	−	0.876642i	$-0.340222\pi$
$449$	9155.31			0.962285			0.481142	+	0.876642i	$0.340222\pi$
$450$	705.313	−	11.6187i	0.0738861	−	0.00121714i
$451$	12040.0			1.25708
$452$		−	12258.8i		−	1.27567i
$453$			8263.87i			0.857109i
$454$	−898.191			−0.0928506
$455$	6348.42	−	6453.86i	0.654107	−	0.664971i
$456$	1368.82			0.140572
$457$		−	13077.8i		−	1.33863i	−0.742977	−	0.669317i	$-0.766587\pi$
$457$		−	13077.8i		−	1.33863i	0.742977	−	0.669317i	$-0.233413\pi$
$458$			836.700i			0.0853634i
$459$	8550.44			0.869499
$460$	1436.21	+	1412.74i	0.145573	+	0.143194i
$461$	9359.48			0.945585			0.472792	−	0.881174i	$-0.343246\pi$
$461$	9359.48			0.945585			0.472792	+	0.881174i	$0.343246\pi$
$462$		−	590.960i		−	0.0595107i
$463$			6240.32i			0.626377i	0.949691	+	0.313188i	$0.101397\pi$
$463$			6240.32i			0.626377i	−0.949691	+	0.313188i	$0.898603\pi$
$464$	11700.6			1.17066
$465$	9281.74	+	9130.10i	0.925657	+	0.910534i
$466$	−616.210			−0.0612562
$467$			5368.43i			0.531951i	0.963980	+	0.265976i	$0.0856941\pi$
$467$			5368.43i			0.531951i	−0.963980	+	0.265976i	$0.914306\pi$
$468$		−	7905.88i		−	0.780875i
$469$	270.213			0.0266040
$470$	−1171.92	+	1191.39i	−0.115014	+	0.116924i
$471$	4572.20			0.447295
$472$		−	4274.12i		−	0.416805i
$473$		−	6408.61i		−	0.622977i
$474$	1218.02			0.118029
$475$	−120.646	−	7323.82i	−0.0116540	−	0.707452i
$476$	−5031.53			−0.484496
$477$			8314.89i			0.798140i
$478$		−	588.442i		−	0.0563070i
$479$	−12394.4			−1.18229			−0.591143	−	0.806567i	$-0.701323\pi$
$479$	−12394.4			−1.18229			−0.591143	+	0.806567i	$0.701323\pi$
$480$	2159.72	−	2195.59i	0.205369	−	0.208780i
$481$	6531.45			0.619145
$482$			2355.89i			0.222630i
$483$			927.333i			0.0873605i
$484$	−268.834			−0.0252474
$485$	−13555.5	−	13334.0i	−1.26912	−	1.24838i
$486$	1388.03			0.129552
$487$		−	2257.68i		−	0.210073i	−0.994468	−	0.105036i	$-0.966504\pi$
$487$		−	2257.68i		−	0.210073i	0.994468	−	0.105036i	$-0.0334959\pi$
$488$		−	622.912i		−	0.0577826i
$489$	−6844.68			−0.632979
$490$	711.295	+	699.674i	0.0655776	+	0.0645063i
$491$	−5578.86			−0.512770			−0.256385	−	0.966575i	$-0.582532\pi$
$491$	−5578.86			−0.512770			−0.256385	+	0.966575i	$0.582532\pi$
$492$			9493.75i			0.869942i
$493$			11248.7i			1.02762i
$494$	1736.08			0.158117
$495$	−3914.25	+	3979.26i	−0.355419	+	0.361322i
$496$	−19294.6			−1.74668
$497$			4027.53i			0.363499i
$498$			1583.30i			0.142469i
$499$	11909.2			1.06839			0.534197	−	0.845360i	$-0.320614\pi$
$499$	11909.2			1.06839			0.534197	+	0.845360i	$0.320614\pi$
$500$	−7930.87	−	7548.34i	−0.709359	−	0.675144i
$501$	−5922.11			−0.528104
$502$			404.756i			0.0359863i
$503$		−	486.345i		−	0.0431114i	−0.999768	−	0.0215557i	$-0.993138\pi$
$503$		−	486.345i		−	0.0431114i	0.999768	−	0.0215557i	$-0.00686192\pi$
$504$	−994.057			−0.0878548
$505$	−4274.09	+	4345.07i	−0.376622	+	0.382878i
$506$	337.115			0.0296177
$507$			11238.6i			0.984463i
$508$			10180.9i			0.889185i
$509$	−2745.98			−0.239123			−0.119561	−	0.992827i	$-0.538149\pi$
$509$	−2745.98			−0.239123			−0.119561	+	0.992827i	$0.538149\pi$
$510$	678.835	+	667.745i	0.0589399	+	0.0579769i
$511$	−8883.95			−0.769086
$512$			7660.44i			0.661224i
$513$		−	8678.75i		−	0.746932i
$514$	−830.076			−0.0712316
$515$	−7929.64	−	7800.09i	−0.678488	−	0.667404i
$516$	5053.29			0.431122
$517$		−	13223.6i		−	1.12490i
$518$		−	406.325i		−	0.0344650i
$519$	−10423.2			−0.881557
$520$	3678.04	−	3739.13i	0.310178	−	0.315330i
$521$	−5980.35			−0.502886			−0.251443	−	0.967872i	$-0.580905\pi$
$521$	−5980.35			−0.502886			−0.251443	+	0.967872i	$0.580905\pi$
$522$			1099.55i			0.0921957i
$523$			7512.46i			0.628102i	0.949406	+	0.314051i	$0.101686\pi$
$523$			7512.46i			0.628102i	−0.949406	+	0.314051i	$0.898314\pi$
$524$	−2516.36			−0.209786
$525$	−83.0110	−	5039.17i	−0.00690076	−	0.418910i
$526$	1073.94			0.0890225
$527$		−	18549.5i		−	1.53326i
$528$			7837.28i			0.645973i
$529$	−529.000			−0.0434783
$530$	−1913.93	+	1945.71i	−0.156860	+	0.159465i
$531$	−9194.16			−0.751398
$532$			5107.04i			0.416200i
$533$			24336.6i			1.97774i
$534$	−1172.52			−0.0950188
$535$	8474.49	+	8336.04i	0.684831	+	0.673642i
$536$	156.551			0.0126156
$537$		−	4779.82i		−	0.384105i
$538$			171.227i			0.0137214i
$539$	−7894.90			−0.630905
$540$	−9248.25	−	9097.16i	−0.737002	−	0.724962i
$541$	−5901.75			−0.469013			−0.234506	−	0.972115i	$-0.575347\pi$
$541$	−5901.75			−0.469013			−0.234506	+	0.972115i	$0.575347\pi$
$542$		−	723.133i		−	0.0573086i
$543$			642.097i			0.0507459i
$544$	−4387.88			−0.345825
$545$	7271.33	−	7392.10i	0.571504	−	0.580996i
$546$	1194.52			0.0936274
$547$		−	4632.59i		−	0.362112i	−0.983473	−	0.181056i	$-0.942049\pi$
$547$		−	4632.59i		−	0.362112i	0.983473	−	0.181056i	$-0.0579515\pi$
$548$			1830.15i			0.142665i
$549$	−1339.96			−0.104168
$550$	−1831.90	+	30.1771i	−0.142022	+	0.00233956i
$551$	11417.5			0.882765
$552$			537.263i			0.0414265i
$553$			9184.97i			0.706301i
$554$	327.533			0.0251183
$555$	2549.88	−	2592.23i	0.195020	−	0.198259i
$556$	7678.04			0.585650
$557$			13974.4i			1.06304i	0.847045	+	0.531522i	$0.178380\pi$
$557$			13974.4i			1.06304i	−0.847045	+	0.531522i	$0.821620\pi$
$558$		−	1813.20i		−	0.137561i
$559$	12953.8			0.980121
$560$	5324.64	+	5237.65i	0.401799	+	0.395234i
$561$	−7534.62			−0.567045
$562$			1799.35i			0.135055i
$563$			4891.88i			0.366196i	0.983095	+	0.183098i	$0.0586125\pi$
$563$			4891.88i			0.366196i	−0.983095	+	0.183098i	$0.941387\pi$
$564$	10427.0			0.778469
$565$	−12471.9	−	12268.1i	−0.928667	−	0.913495i
$566$	3560.06			0.264383
$567$		−	1807.13i		−	0.133849i
$568$			2333.40i			0.172372i
$569$	6953.36			0.512302			0.256151	−	0.966637i	$-0.417546\pi$
$569$	6953.36			0.512302			0.256151	+	0.966637i	$0.417546\pi$
$570$	677.765	−	689.022i	0.0498043	−	0.0506315i
$571$	6421.00			0.470596			0.235298	−	0.971923i	$-0.424393\pi$
$571$	6421.00			0.470596			0.235298	+	0.971923i	$0.424393\pi$
$572$			20533.8i			1.50098i
$573$			12434.5i			0.906561i
$574$	1513.99			0.110092
$575$	2874.61	−	47.3539i	0.208486	−	0.00343442i
$576$	6231.63			0.450783
$577$			7752.32i			0.559330i	0.960098	+	0.279665i	$0.0902234\pi$
$577$			7752.32i			0.559330i	−0.960098	+	0.279665i	$0.909777\pi$
$578$			643.117i			0.0462805i
$579$	−9651.30			−0.692737
$580$	11968.0	−	12166.8i	0.856799	−	0.871029i
$581$	−11939.5			−0.852553
$582$		−	2508.92i		−	0.178691i
$583$		−	21596.1i		−	1.53417i
$584$	−5147.03			−0.364702
$585$	−8043.34	−	7911.93i	−0.568463	−	0.559176i
$586$	1850.76			0.130468
$587$			15435.4i			1.08533i	0.839949	+	0.542665i	$0.182585\pi$
$587$			15435.4i			1.08533i	−0.839949	+	0.542665i	$0.817415\pi$
$588$		−	6225.26i		−	0.436608i
$589$	−18827.9			−1.31713
$590$	−2151.47	−	2116.32i	−0.150126	−	0.147673i
$591$	−13455.4			−0.936517
$592$			5388.66i			0.374109i
$593$		−	3628.86i		−	0.251298i	−0.992075	−	0.125649i	$-0.959899\pi$
$593$		−	3628.86i		−	0.251298i	0.992075	−	0.125649i	$-0.0401013\pi$
$594$	−2170.80			−0.149948
$595$	−5035.38	+	5119.02i	−0.346942	+	0.352705i
$596$	−984.745			−0.0676791
$597$			5292.98i			0.362860i
$598$			681.415i			0.0465972i
$599$	2281.33			0.155614			0.0778070	−	0.996968i	$-0.475208\pi$
$599$	2281.33			0.155614			0.0778070	+	0.996968i	$0.475208\pi$
$600$	−48.0935	−	2919.51i	−0.00327235	−	0.198647i
$601$	26992.6			1.83203			0.916017	−	0.401139i	$-0.131386\pi$
$601$	26992.6			1.83203			0.916017	+	0.401139i	$0.131386\pi$
$602$		−	805.862i		−	0.0545589i
$603$		−	336.761i		−	0.0227429i
$604$	−17863.2			−1.20338
$605$	−269.040	+	273.509i	−0.0180794	+	0.0183797i
$606$	−804.209			−0.0539089
$607$		−	19796.5i		−	1.32375i	−0.749614	−	0.661875i	$-0.769761\pi$
$607$		−	19796.5i		−	1.32375i	0.749614	−	0.661875i	$-0.230239\pi$
$608$			4453.72i			0.297076i
$609$	7855.86			0.522719
$610$	−313.556	−	308.433i	−0.0208123	−	0.0204723i
$611$	26729.0			1.76979
$612$			6270.71i			0.414181i
$613$			24783.3i			1.63293i	0.577395	+	0.816465i	$0.304069\pi$
$613$			24783.3i			1.63293i	−0.577395	+	0.816465i	$0.695931\pi$
$614$	−1440.70			−0.0946938
$615$	9658.82	+	9501.02i	0.633303	+	0.622956i
$616$	2581.85			0.168873
$617$		−	7076.87i		−	0.461757i	−0.972983	−	0.230879i	$-0.925840\pi$
$617$		−	7076.87i		−	0.461757i	0.972983	−	0.230879i	$-0.0741600\pi$
$618$		−	1467.66i		−	0.0955306i
$619$	−1086.22			−0.0705313			−0.0352656	−	0.999378i	$-0.511228\pi$
$619$	−1086.22			−0.0705313			−0.0352656	+	0.999378i	$0.511228\pi$
$620$	−19735.6	+	20063.4i	−1.27839	+	1.29962i
$621$	3406.42			0.220121
$622$		−	2418.22i		−	0.155887i
$623$		−	8841.86i		−	0.568606i
$624$	−15841.6			−1.01630
$625$	−15616.5	+	514.646i	−0.999457	+	0.0329374i
$626$	−3159.76			−0.201740
$627$			7647.69i			0.487112i
$628$			9883.26i			0.628002i
$629$	−5180.56			−0.328398
$630$	−492.204	+	500.379i	−0.0311268	+	0.0316438i
$631$	9419.46			0.594267			0.297134	−	0.954836i	$-0.403969\pi$
$631$	9419.46			0.594267			0.297134	+	0.954836i	$0.403969\pi$
$632$			5321.43i			0.334929i
$633$		−	9212.78i		−	0.578476i
$634$	−2514.86			−0.157536
$635$	10357.9	+	10188.7i	0.647311	+	0.636736i
$636$	17028.9			1.06170
$637$		−	15958.1i		−	0.992594i
$638$		−	2855.85i		−	0.177217i
$639$	5019.43			0.310744
$640$	6304.57	+	6201.57i	0.389390	+	0.383029i
$641$	−12081.2			−0.744431			−0.372216	−	0.928146i	$-0.621402\pi$
$641$	−12081.2			−0.744431			−0.372216	+	0.928146i	$0.621402\pi$
$642$			1568.50i			0.0964235i
$643$		−	6784.03i		−	0.416075i	−0.978121	−	0.208037i	$-0.933292\pi$
$643$		−	6784.03i		−	0.416075i	0.978121	−	0.208037i	$-0.0667075\pi$
$644$	−2004.52			−0.122654
$645$	5057.16	−	5141.15i	0.308722	−	0.313849i
$646$	−1377.01			−0.0838664
$647$		−	8895.99i		−	0.540553i	−0.962783	−	0.270276i	$-0.912885\pi$
$647$		−	8895.99i		−	0.540553i	0.962783	−	0.270276i	$-0.0871150\pi$
$648$		−	1046.98i		−	0.0634712i
$649$	23879.8			1.44432
$650$	−60.9974	−	3702.84i	−0.00368079	−	0.223442i
$651$	−12954.6			−0.779923
$652$		−	14795.4i		−	0.888702i
$653$		−	931.063i		−	0.0557968i	−0.999611	−	0.0278984i	$-0.991119\pi$
$653$		−	931.063i		−	0.0557968i	0.999611	−	0.0278984i	$-0.00888149\pi$
$654$	1368.17			0.0818037
$655$	−2518.29	+	2560.11i	−0.150225	+	0.152720i
$656$	−20078.5			−1.19502
$657$			11071.9i			0.657468i
$658$		−	1662.82i		−	0.0985161i
$659$	16439.6			0.971770			0.485885	−	0.874023i	$-0.338497\pi$
$659$	16439.6			0.971770			0.485885	+	0.874023i	$0.338497\pi$
$660$	8149.53	+	8016.39i	0.480637	+	0.472784i
$661$	−17730.1			−1.04330			−0.521648	−	0.853161i	$-0.674683\pi$
$661$	−17730.1			−1.04330			−0.521648	+	0.853161i	$0.674683\pi$
$662$		−	2149.61i		−	0.126204i
$663$		−	15229.8i		−	0.892123i
$664$	−6917.30			−0.404282
$665$	5195.84	+	5110.95i	0.302986	+	0.298036i
$666$	−506.395			−0.0294631
$667$			4481.40i			0.260151i
$668$		−	12801.2i		−	0.741458i
$669$	−8797.41			−0.508412
$670$	77.5159	−	78.8034i	0.00446970	−	0.00454394i
$671$	3480.26			0.200230
$672$			3064.40i			0.175910i
$673$			8409.83i			0.481687i	0.970564	+	0.240843i	$0.0774240\pi$
$673$			8409.83i			0.481687i	−0.970564	+	0.240843i	$0.922576\pi$
$674$	3034.43			0.173415
$675$	−18510.7	+	304.929i	−1.05552	+	0.0173877i
$676$	−24293.3			−1.38218
$677$		−	23967.0i		−	1.36060i	−0.732933	−	0.680301i	$-0.761849\pi$
$677$		−	23967.0i		−	1.36060i	0.732933	−	0.680301i	$-0.238151\pi$
$678$		−	2308.37i		−	0.130756i
$679$	18919.4			1.06931
$680$	−2917.32	+	2965.77i	−0.164520	+	0.167253i
$681$	7997.66			0.450031
$682$			4709.40i			0.264417i
$683$		−	33541.6i		−	1.87911i	−0.342395	−	0.939556i	$-0.611238\pi$
$683$		−	33541.6i		−	1.87911i	0.342395	−	0.939556i	$-0.388762\pi$
$684$	6364.81			0.355796
$685$	1861.97	+	1831.55i	0.103857	+	0.102161i
$686$	−2545.89			−0.141695
$687$		−	7450.13i		−	0.413741i
$688$			10687.3i			0.592223i
$689$	43652.6			2.41369
$690$	270.442	+	266.024i	0.0149211	+	0.0146773i
$691$	10191.1			0.561050			0.280525	−	0.959847i	$-0.409491\pi$
$691$	10191.1			0.561050			0.280525	+	0.959847i	$0.409491\pi$
$692$		−	22530.8i		−	1.23770i
$693$		−	5553.88i		−	0.304436i
$694$	576.618			0.0315391
$695$	7683.92	−	7811.54i	0.419378	−	0.426343i
$696$	4551.40			0.247874
$697$		−	19303.1i		−	1.04901i
$698$			4023.73i			0.218195i
$699$	5486.85			0.296898
$700$	10892.7	−	179.436i	0.588148	−	0.00968866i
$701$	−18403.2			−0.991555			−0.495777	−	0.868450i	$-0.665117\pi$
$701$	−18403.2			−0.991555			−0.495777	+	0.868450i	$0.665117\pi$
$702$		−	4387.88i		−	0.235911i
$703$			5258.30i			0.282106i
$704$	−16185.3			−0.866487
$705$	10435.0	−	10608.3i	0.557454	−	0.566712i
$706$	2662.39			0.141927
$707$		−	6064.45i		−	0.322598i
$708$			18829.7i			0.999522i
$709$	8570.78			0.453995			0.226997	−	0.973895i	$-0.427109\pi$
$709$	8570.78			0.453995			0.226997	+	0.973895i	$0.427109\pi$
$710$	1174.56	+	1155.38i	0.0620854	+	0.0610711i
$711$	11447.1			0.603795
$712$		−	5122.64i		−	0.269634i
$713$		−	7389.98i		−	0.388158i
$714$	−947.454			−0.0496605
$715$	20890.8	+	20549.5i	1.09269	+	1.07484i
$716$	10332.0			0.539283
$717$			5239.60i			0.272910i
$718$			3814.36i			0.198260i
$719$	30115.4			1.56205			0.781026	−	0.624499i	$-0.214697\pi$
$719$	30115.4			1.56205			0.781026	+	0.624499i	$0.214697\pi$
$720$	6527.59	−	6636.01i	0.337874	−	0.343485i
$721$	11067.4			0.571669
$722$		−	1394.19i		−	0.0718646i
$723$		−	20977.2i		−	1.07905i
$724$	−1387.96			−0.0712472
$725$	−401.156	−	24352.1i	−0.0205498	−	1.24747i
$726$	−50.6224			−0.00258784
$727$		−	11255.0i		−	0.574174i	−0.957904	−	0.287087i	$-0.907313\pi$
$727$		−	11255.0i		−	0.574174i	0.957904	−	0.287087i	$-0.0926869\pi$
$728$			5218.73i			0.265685i
$729$	−16745.3			−0.850749
$730$	−2548.54	+	2590.87i	−0.129213	+	0.131359i
$731$	−10274.6			−0.519862
$732$			2744.25i			0.138566i
$733$		−	10481.0i		−	0.528136i	−0.964504	−	0.264068i	$-0.914936\pi$
$733$		−	10481.0i		−	0.528136i	0.964504	−	0.264068i	$-0.0850643\pi$
$734$	−4053.24			−0.203825
$735$	−6333.50	−	6230.03i	−0.317843	−	0.312650i
$736$	−1748.09			−0.0875484
$737$			874.665i			0.0437160i
$738$		−	1886.86i		−	0.0941143i
$739$	−5789.11			−0.288168			−0.144084	−	0.989565i	$-0.546023\pi$
$739$	−5789.11			−0.288168			−0.144084	+	0.989565i	$0.546023\pi$
$740$	5603.35	+	5511.81i	0.278356	+	0.273808i
$741$	−15458.4			−0.766367
$742$		−	2715.64i		−	0.134359i
$743$			14360.7i			0.709074i	0.935042	+	0.354537i	$0.115362\pi$
$743$			14360.7i			0.709074i	−0.935042	+	0.354537i	$0.884638\pi$
$744$	−7505.41			−0.369841
$745$	−985.499	+	1001.87i	−0.0484643	+	0.0492692i
$746$	−3873.73			−0.190117
$747$			14880.0i			0.728821i
$748$		−	16286.8i		−	0.796130i
$749$	−11827.9			−0.577012
$750$	−1493.41	−	1421.38i	−0.0727088	−	0.0692018i
$751$	−33974.4			−1.65079			−0.825396	−	0.564555i	$-0.809048\pi$
$751$	−33974.4			−1.65079			−0.825396	+	0.564555i	$0.809048\pi$
$752$			22052.3i			1.06937i
$753$		−	3604.02i		−	0.174419i
$754$	5772.57			0.278813
$755$	−17876.8	+	18173.7i	−0.861727	+	0.876040i
$756$	12907.8			0.620970
$757$			16482.2i			0.791355i	0.918390	+	0.395677i	$0.129490\pi$
$757$			16482.2i			0.791355i	−0.918390	+	0.395677i	$0.870510\pi$
$758$		−	2872.59i		−	0.137648i
$759$	−3001.73			−0.143552
$760$	3010.27	+	2961.09i	0.143676	+	0.141329i
$761$	29912.0			1.42485			0.712423	−	0.701750i	$-0.247598\pi$
$761$	29912.0			1.42485			0.712423	+	0.701750i	$0.247598\pi$
$762$			1917.10i			0.0911409i
$763$			10317.2i			0.489525i
$764$	−26878.4			−1.27281
$765$	6379.74	+	6275.51i	0.301516	+	0.296590i
$766$	−603.718			−0.0284768
$767$			48268.7i			2.27233i
$768$		−	11865.4i		−	0.557494i
$769$	23459.8			1.10011			0.550054	−	0.835129i	$-0.314607\pi$
$769$	23459.8			1.10011			0.550054	+	0.835129i	$0.314607\pi$
$770$	1278.39	−	1299.63i	0.0598314	−	0.0608251i
$771$	7391.14			0.345247
$772$		−	20862.2i		−	0.972601i
$773$			14071.4i			0.654739i	0.944896	+	0.327370i	$0.106162\pi$
$773$			14071.4i			0.654739i	−0.944896	+	0.327370i	$0.893838\pi$
$774$	−1004.33			−0.0466408
$775$	661.520	+	40157.5i	0.0306613	+	1.86129i
$776$	10961.2			0.507068
$777$			3617.99i			0.167046i
$778$		−	1438.00i		−	0.0662659i
$779$	−19592.8			−0.901135
$780$	−16203.6	+	16472.8i	−0.743825	+	0.756179i
$781$	−13036.9			−0.597307
$782$		−	540.478i		−	0.0247154i
$783$		−	28857.4i		−	1.31709i
$784$	13165.9			0.599759
$785$	10055.1	+	9890.82i	0.457174	+	0.449705i
$786$	−473.839			−0.0215029
$787$		−	16228.1i		−	0.735029i	−0.930018	−	0.367514i	$-0.880209\pi$
$787$		−	16228.1i		−	0.735029i	0.930018	−	0.367514i	$-0.119791\pi$
$788$		−	29085.2i		−	1.31487i
$789$	−9562.52			−0.431476
$790$	2678.65	+	2634.89i	0.120636	+	0.118665i
$791$	17407.1			0.782460
$792$		−	3217.71i		−	0.144364i
$793$			7034.70i			0.315018i
$794$	5271.40			0.235611
$795$	17041.9	−	17325.0i	0.760271	−	0.772898i
$796$	−11441.3			−0.509454
$797$			39546.3i			1.75759i	0.477198	+	0.878796i	$0.341652\pi$
$797$			39546.3i			1.75759i	−0.477198	+	0.878796i	$0.658348\pi$
$798$			961.673i			0.0426602i
$799$	−21200.7			−0.938706
$800$	9499.22	−	156.482i	0.419810	−	0.00691560i
$801$	−11019.4			−0.486084
$802$		−	1759.45i		−	0.0774666i
$803$		−	28756.9i		−	1.26377i
$804$	−689.688			−0.0302530
$805$	−2006.06	+	2039.37i	−0.0878312	+	0.0892900i
$806$	−9519.17			−0.416003
$807$		−	1524.64i		−	0.0665053i
$808$		−	3513.51i		−	0.152977i
$809$	1628.28			0.0707629			0.0353814	−	0.999374i	$-0.488735\pi$
$809$	1628.28			0.0707629			0.0353814	+	0.999374i	$0.488735\pi$
$810$	−527.020	−	518.410i	−0.0228612	−	0.0224877i
$811$	−8124.92			−0.351793			−0.175897	−	0.984409i	$-0.556282\pi$
$811$	−8124.92			−0.351793			−0.175897	+	0.984409i	$0.556282\pi$
$812$			16981.2i			0.733896i
$813$			6438.91i			0.277764i
$814$	1315.25			0.0566333
$815$	−15052.7	−	14806.8i	−0.646960	−	0.636390i
$816$	12565.1			0.539052
$817$			10428.8i			0.446581i
$818$		−	5626.74i		−	0.240507i
$819$	11226.1			0.478966
$820$	−20537.4	+	20878.5i	−0.874629	+	0.889156i
$821$	5217.62			0.221798			0.110899	−	0.993832i	$-0.464627\pi$
$821$	5217.62			0.221798			0.110899	+	0.993832i	$0.464627\pi$
$822$			344.624i			0.0146230i
$823$		−	9884.38i		−	0.418649i	−0.977846	−	0.209324i	$-0.932874\pi$
$823$		−	9884.38i		−	0.418649i	0.977846	−	0.209324i	$-0.0671265\pi$
$824$	6412.07			0.271086
$825$	16311.5	−	268.703i	0.688358	−	0.0113394i
$826$	3002.81			0.126491
$827$		−	3440.59i		−	0.144669i	−0.997380	−	0.0723343i	$-0.976955\pi$
$827$		−	3440.59i		−	0.144669i	0.997380	−	0.0723343i	$-0.0230449\pi$
$828$			2498.20i			0.104853i
$829$	−28116.7			−1.17796			−0.588982	−	0.808146i	$-0.700471\pi$
$829$	−28116.7			−1.17796			−0.588982	+	0.808146i	$0.700471\pi$
$830$	−3425.08	+	3481.96i	−0.143236	+	0.145615i
$831$	−2916.41			−0.121744
$832$		−	32715.6i		−	1.36323i
$833$			12657.5i			0.526477i
$834$	1445.80			0.0600287
$835$	−13023.8	−	12811.0i	−0.539768	−	0.530950i
$836$	−16531.2			−0.683905
$837$			47586.8i			1.96516i
$838$			2530.77i			0.104325i
$839$	−3336.30			−0.137285			−0.0686424	−	0.997641i	$-0.521867\pi$
$839$	−3336.30			−0.137285			−0.0686424	+	0.997641i	$0.521867\pi$
$840$	2071.23	+	2037.39i	0.0850763	+	0.0836864i
$841$	13575.0			0.556603
$842$		−	5961.20i		−	0.243986i
$843$		−	16021.7i		−	0.654587i
$844$	19914.3			0.812179
$845$	−24311.9	+	24715.7i	−0.989767	+	1.00621i
$846$	−2072.35			−0.0842184
$847$		−	381.737i		−	0.0154860i
$848$			36014.7i			1.45843i
$849$	−31699.4			−1.28142
$850$	48.3814	+	2936.98i	0.00195231	+	0.118515i
$851$	−2063.89			−0.0831366
$852$		−	10279.8i		−	0.413357i
$853$			4036.71i			0.162033i	0.996713	+	0.0810166i	$0.0258167\pi$
$853$			4036.71i			0.162033i	−0.996713	+	0.0810166i	$0.974183\pi$
$854$	437.632			0.0175357
$855$	6369.68	−	6475.48i	0.254782	−	0.259014i
$856$	−6852.65			−0.273620
$857$			28484.0i			1.13535i	0.823252	+	0.567676i	$0.192157\pi$
$857$			28484.0i			1.13535i	−0.823252	+	0.567676i	$0.807843\pi$
$858$			3866.58i			0.153850i
$859$	35885.3			1.42537			0.712684	−	0.701486i	$-0.247480\pi$
$859$	35885.3			1.42537			0.712684	+	0.701486i	$0.247480\pi$
$860$	11113.1	+	10931.5i	0.440644	+	0.433445i
$861$	−13480.9			−0.533597
$862$			5791.91i			0.228855i
$863$		−	35932.4i		−	1.41733i	−0.705547	−	0.708663i	$-0.749299\pi$
$863$		−	35932.4i		−	1.41733i	0.705547	−	0.708663i	$-0.250701\pi$
$864$	11256.6			0.443238
$865$	−22922.5	−	22548.0i	−0.901027	−	0.886307i
$866$	−536.903			−0.0210678
$867$		−	5726.43i		−	0.224313i
$868$		−	28002.6i		−	1.09501i
$869$	−29731.3			−1.16060
$870$	2253.61	−	2291.04i	0.0878213	−	0.0892799i
$871$	−1767.97			−0.0687778
$872$			5977.40i			0.232134i
$873$		−	23579.0i		−	0.914121i
$874$	−548.589			−0.0212315
$875$	10718.4	−	11261.6i	0.414114	−	0.435100i
$876$	22675.3			0.874574
$877$			11084.7i			0.426800i	0.976965	+	0.213400i	$0.0684538\pi$
$877$			11084.7i			0.426800i	−0.976965	+	0.213400i	$0.931546\pi$
$878$		−	2447.42i		−	0.0940733i
$879$	−16479.5			−0.632356
$880$	−16954.0	+	17235.6i	−0.649454	+	0.660241i
$881$	−4285.25			−0.163875			−0.0819373	−	0.996637i	$-0.526111\pi$
$881$	−4285.25			−0.163875			−0.0819373	+	0.996637i	$0.526111\pi$
$882$			1237.26i			0.0472343i
$883$		−	3945.76i		−	0.150380i	−0.997169	−	0.0751899i	$-0.976044\pi$
$883$		−	3945.76i		−	0.150380i	0.997169	−	0.0751899i	$-0.0239563\pi$
$884$	32920.8			1.25254
$885$	19157.0	+	18844.1i	0.727635	+	0.715747i
$886$	6460.96			0.244989
$887$			41828.1i			1.58337i	0.610929	+	0.791685i	$0.290796\pi$
$887$			41828.1i			1.58337i	−0.610929	+	0.791685i	$0.709204\pi$
$888$			2096.13i			0.0792133i
$889$	−14456.7			−0.545400
$890$	−2578.59	−	2536.46i	−0.0971174	−	0.0955308i
$891$	5849.58			0.219942
$892$		−	19016.5i		−	0.713809i
$893$			21518.8i			0.806383i
$894$	−185.431			−0.00693706
$895$	10340.0	−	10511.7i	0.386175	−	0.392589i
$896$	−8799.32			−0.328086
$897$		−	6067.44i		−	0.225848i
$898$			3726.54i			0.138481i
$899$	−62603.9			−2.32253
$900$	−223.628	−	13575.3i	−0.00828253	−	0.502790i
$901$	−34623.9			−1.28023
$902$			4900.72i			0.180905i
$903$			7175.54i			0.264437i
$904$	10085.0			0.371044
$905$	−1389.02	+	1412.09i	−0.0510194	+	0.0518667i
$906$	−3363.69			−0.123346
$907$		−	9810.78i		−	0.359164i	−0.983743	−	0.179582i	$-0.942525\pi$
$907$		−	9810.78i		−	0.359164i	0.983743	−	0.179582i	$-0.0574745\pi$
$908$			17287.7i			0.631842i
$909$	−7558.01			−0.275779
$910$	2626.95	+	2584.04i	0.0956953	+	0.0941318i
$911$	−16679.6			−0.606609			−0.303305	−	0.952894i	$-0.598090\pi$
$911$	−16679.6			−0.606609			−0.303305	+	0.952894i	$0.598090\pi$
$912$		−	12753.7i		−	0.463065i
$913$		−	38647.5i		−	1.40093i
$914$	5323.15			0.192641
$915$	2791.96	+	2746.34i	0.100874	+	0.0992255i
$916$	16104.2			0.580892
$917$		−	3573.16i		−	0.128676i
$918$			3480.33i			0.125129i
$919$	−37422.1			−1.34325			−0.671623	−	0.740893i	$-0.734402\pi$
$919$	−37422.1			−1.34325			−0.671623	+	0.740893i	$0.734402\pi$
$920$	−1162.23	+	1181.54i	−0.0416497	+	0.0423414i
$921$	12828.3			0.458964
$922$			3809.65i			0.136078i
$923$		−	26351.7i		−	0.939735i
$924$	−11374.4			−0.404966
$925$	11215.3	−	184.751i	0.398655	−	0.00656711i
$926$	−2540.04			−0.0901412
$927$		−	13793.2i		−	0.488702i
$928$			14808.9i			0.523843i
$929$	8532.76			0.301346			0.150673	−	0.988584i	$-0.451856\pi$
$929$	8532.76			0.301346			0.150673	+	0.988584i	$0.451856\pi$
$930$	−3716.28	+	3778.00i	−0.131034	+	0.133210i
$931$	12847.4			0.452264
$932$			11860.3i			0.416844i
$933$			21532.3i			0.755558i
$934$	−2185.14			−0.0765525
$935$	−16570.0	−	16299.3i	−0.579569	−	0.570100i
$936$	6504.01			0.227126
$937$			16978.6i			0.591961i	0.955194	+	0.295981i	$0.0956464\pi$
$937$			16978.6i			0.591961i	−0.955194	+	0.295981i	$0.904354\pi$
$938$			109.986i			0.00382855i
$939$	28135.1			0.977800
$940$	22930.9	+	22556.3i	0.795663	+	0.782664i
$941$	−13563.0			−0.469865			−0.234932	−	0.972012i	$-0.575487\pi$
$941$	−13563.0			−0.469865			−0.234932	+	0.972012i	$0.575487\pi$
$942$			1861.05i			0.0643698i
$943$		−	7690.20i		−	0.265565i
$944$	−39823.2			−1.37302
$945$	12917.7	−	13132.3i	0.444670	−	0.452056i
$946$	2608.53			0.0896519
$947$		−	20866.2i		−	0.716007i	−0.933720	−	0.358004i	$-0.883458\pi$
$947$		−	20866.2i		−	0.716007i	0.933720	−	0.358004i	$-0.116542\pi$
$948$		−	23443.6i		−	0.803178i
$949$	58126.7			1.98827
$950$	2981.06	−	49.1074i	0.101809	−	0.00167711i
$951$	22392.8			0.763550
$952$		−	4139.34i		−	0.140921i
$953$			56041.8i			1.90490i	0.304693	+	0.952451i	$0.401446\pi$
$953$			56041.8i			1.90490i	−0.304693	+	0.952451i	$0.598554\pi$
$954$	−3384.46			−0.114859
$955$	−26899.0	+	27345.7i	−0.911446	+	0.926584i
$956$	−11325.9			−0.383165
$957$			25429.0i			0.858938i
$958$		−	5044.97i		−	0.170141i
$959$	−2598.77			−0.0875063
$960$	−12984.3	−	12772.1i	−0.436527	−	0.429395i
$961$	73444.9			2.46534
$962$			2658.54i			0.0891005i
$963$			14740.9i			0.493270i
$964$	45344.3			1.51498
$965$	−21225.0	−	20878.2i	−0.708037	−	0.696469i
$966$	−377.458			−0.0125720
$967$			42155.3i			1.40188i	0.713218	+	0.700942i	$0.247237\pi$
$967$			42155.3i			1.40188i	−0.713218	+	0.700942i	$0.752763\pi$
$968$		−	221.165i		−	0.00734349i
$969$	12261.1			0.406485
$970$	5427.42	−	5517.56i	0.179654	−	0.182637i
$971$	49005.8			1.61964			0.809820	−	0.586678i	$-0.199565\pi$
$971$	49005.8			1.61964			0.809820	+	0.586678i	$0.199565\pi$
$972$		−	26715.7i		−	0.881592i
$973$			10902.6i			0.359221i
$974$	918.957			0.0302313
$975$	543.132	+	32970.7i	0.0178401	+	1.08298i
$976$	−5803.85			−0.190345
$977$		−	25974.7i		−	0.850567i	−0.905060	−	0.425284i	$-0.860174\pi$
$977$		−	25974.7i		−	0.850567i	0.905060	−	0.425284i	$-0.139826\pi$
$978$		−	2786.03i		−	0.0910914i
$979$	28620.6			0.934341
$980$	13466.8	−	13690.5i	0.438961	−	0.446251i
$981$	12858.1			0.418480
$982$		−	2270.79i		−	0.0737922i
$983$		−	11480.7i		−	0.372509i	−0.982502	−	0.186254i	$-0.940365\pi$
$983$		−	11480.7i		−	0.372509i	0.982502	−	0.186254i	$-0.0596349\pi$
$984$	−7810.32			−0.253032
$985$	−29590.9	−	29107.4i	−0.957201	−	0.941563i
$986$	−4578.64			−0.147884
$987$			14806.1i			0.477490i
$988$		−	33414.8i		−	1.07598i
$989$	−4093.31			−0.131607
$990$	−1619.70	−	1593.24i	−0.0519975	−	0.0511480i
$991$	5005.14			0.160437			0.0802187	−	0.996777i	$-0.474438\pi$
$991$	5005.14			0.160437			0.0802187	+	0.996777i	$0.474438\pi$
$992$		−	24420.4i		−	0.781600i
$993$			19140.5i			0.611687i
$994$	−1639.35			−0.0523108
$995$	−11450.0	+	11640.2i	−0.364815	+	0.370874i
$996$	30474.2			0.969490
$997$		−	27405.9i		−	0.870565i	−0.900294	−	0.435282i	$-0.856649\pi$
$997$		−	27405.9i		−	0.870565i	0.900294	−	0.435282i	$-0.143351\pi$
$998$			4847.47i			0.153751i
$999$	13290.1			0.420902

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.4.b.a.24.19	yes	34
5.2	odd	4		575.4.a.r.1.8		17
5.3	odd	4		575.4.a.q.1.10		17
5.4	even	2	inner	115.4.b.a.24.16	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.4.b.a.24.16	✓	34	5.4	even	2	inner
115.4.b.a.24.19	yes	34	1.1	even	1	trivial
575.4.a.q.1.10		17	5.3	odd	4
575.4.a.r.1.8		17	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	115.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.407036i q^{2} -3.62432i q^{3} +7.83432 q^{4} +(7.84032 - 7.97054i) q^{5} +1.47523 q^{6} +11.1245i q^{7} +6.44514i q^{8} +13.8643 q^{9} +O(q^{10})\)	\(q+0.407036i q^{2} -3.62432i q^{3} +7.83432 q^{4} +(7.84032 - 7.97054i) q^{5} +1.47523 q^{6} +11.1245i q^{7} +6.44514i q^{8} +13.8643 q^{9} +(3.24429 + 3.19129i) q^{10} -36.0095 q^{11} -28.3941i q^{12} -72.7865i q^{13} -4.52808 q^{14} +(-28.8878 - 28.4158i) q^{15} +60.0512 q^{16} +57.7321i q^{17} +5.64327i q^{18} +58.5985 q^{19} +(61.4236 - 62.4437i) q^{20} +40.3188 q^{21} -14.6572i q^{22} +23.0000i q^{23} +23.3592 q^{24} +(-2.05886 - 124.983i) q^{25} +29.6267 q^{26} -148.105i q^{27} +87.1531i q^{28} +194.843 q^{29} +(11.5663 - 11.7584i) q^{30} -321.303 q^{31} +76.0041i q^{32} +130.510i q^{33} -23.4990 q^{34} +(88.6684 + 87.2198i) q^{35} +108.617 q^{36} +89.7344i q^{37} +23.8517i q^{38} -263.802 q^{39} +(51.3712 + 50.5319i) q^{40} -334.357 q^{41} +16.4112i q^{42} +177.970i q^{43} -282.110 q^{44} +(108.700 - 110.506i) q^{45} -9.36182 q^{46} +367.225i q^{47} -217.645i q^{48} +219.245 q^{49} +(50.8726 - 0.838032i) q^{50} +209.240 q^{51} -570.233i q^{52} +599.734i q^{53} +60.2842 q^{54} +(-282.326 + 287.015i) q^{55} -71.6991 q^{56} -212.380i q^{57} +79.3083i q^{58} -663.154 q^{59} +(-226.316 - 222.619i) q^{60} -96.6484 q^{61} -130.782i q^{62} +154.234i q^{63} +449.473 q^{64} +(-580.148 - 570.669i) q^{65} -53.1223 q^{66} -24.2898i q^{67} +452.292i q^{68} +83.3594 q^{69} +(-35.5016 + 36.0912i) q^{70} +362.040 q^{71} +89.3573i q^{72} +798.592i q^{73} -36.5251 q^{74} +(-452.979 + 7.46199i) q^{75} +459.079 q^{76} -400.589i q^{77} -107.377i q^{78} +825.651 q^{79} +(470.820 - 478.640i) q^{80} -162.445 q^{81} -136.095i q^{82} +1073.26i q^{83} +315.871 q^{84} +(460.156 + 452.638i) q^{85} -72.4401 q^{86} -706.175i q^{87} -232.086i q^{88} -794.808 q^{89} +(44.9798 + 44.2450i) q^{90} +809.715 q^{91} +180.189i q^{92} +1164.51i q^{93} -149.474 q^{94} +(459.431 - 467.061i) q^{95} +275.463 q^{96} -1700.70i q^{97} +89.2406i q^{98} -499.247 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9}+O(q^{10}) \) 34 * q - 144 * q^4 + 14 * q^5 + 24 * q^6 - 310 * q^9	\( 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9} + 14 q^{10} - 8 q^{11} + 236 q^{14} + 440 q^{16} + 144 q^{19} - 180 q^{20} - 32 q^{21} + 108 q^{24} + 134 q^{25} - 144 q^{26} + 56 q^{29} - 294 q^{30} - 80 q^{31} + 264 q^{34} + 116 q^{35} + 1864 q^{36} - 1200 q^{39} + 650 q^{40} + 268 q^{41} - 1612 q^{44} - 1346 q^{45} + 184 q^{46} - 1474 q^{49} + 120 q^{50} - 1104 q^{51} + 1564 q^{54} + 1160 q^{55} - 2300 q^{56} - 708 q^{59} - 516 q^{60} + 1100 q^{61} + 100 q^{64} + 1164 q^{65} - 1416 q^{66} - 552 q^{69} + 1144 q^{70} + 1360 q^{71} + 1588 q^{74} - 2064 q^{75} + 108 q^{76} + 3968 q^{79} + 2542 q^{80} + 4914 q^{81} - 1948 q^{84} + 124 q^{85} - 6148 q^{86} + 1196 q^{89} + 2760 q^{90} - 544 q^{91} - 2340 q^{94} + 3920 q^{95} + 2960 q^{96} - 3816 q^{99}+O(q^{100}) \) 34 * q - 144 * q^4 + 14 * q^5 + 24 * q^6 - 310 * q^9 + 14 * q^10 - 8 * q^11 + 236 * q^14 + 440 * q^16 + 144 * q^19 - 180 * q^20 - 32 * q^21 + 108 * q^24 + 134 * q^25 - 144 * q^26 + 56 * q^29 - 294 * q^30 - 80 * q^31 + 264 * q^34 + 116 * q^35 + 1864 * q^36 - 1200 * q^39 + 650 * q^40 + 268 * q^41 - 1612 * q^44 - 1346 * q^45 + 184 * q^46 - 1474 * q^49 + 120 * q^50 - 1104 * q^51 + 1564 * q^54 + 1160 * q^55 - 2300 * q^56 - 708 * q^59 - 516 * q^60 + 1100 * q^61 + 100 * q^64 + 1164 * q^65 - 1416 * q^66 - 552 * q^69 + 1144 * q^70 + 1360 * q^71 + 1588 * q^74 - 2064 * q^75 + 108 * q^76 + 3968 * q^79 + 2542 * q^80 + 4914 * q^81 - 1948 * q^84 + 124 * q^85 - 6148 * q^86 + 1196 * q^89 + 2760 * q^90 - 544 * q^91 - 2340 * q^94 + 3920 * q^95 + 2960 * q^96 - 3816 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more