LMFDB - Embedded newform 35.5.g.a.22.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(8,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("35.8");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			22.4
Character	$\chi$	$=$	35.22
Dual form			35.5.g.a.8.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.97419 - 2.97419i) q^{2} +(-1.22954 + 1.22954i) q^{3} +1.69164i q^{4} +(-22.1755 + 11.5432i) q^{5} +7.31376 q^{6} +(13.0958 + 13.0958i) q^{7} +(-42.5558 + 42.5558i) q^{8} +77.9765i q^{9} +O(q^{10})$	\(q+(-2.97419 - 2.97419i) q^{2} +(-1.22954 + 1.22954i) q^{3} +1.69164i q^{4} +(-22.1755 + 11.5432i) q^{5} +7.31376 q^{6} +(13.0958 + 13.0958i) q^{7} +(-42.5558 + 42.5558i) q^{8} +77.9765i q^{9} +(100.286 + 31.6225i) q^{10} +17.6226 q^{11} +(-2.07994 - 2.07994i) q^{12} +(-160.405 + 160.405i) q^{13} -77.8989i q^{14} +(13.0728 - 41.4585i) q^{15} +280.205 q^{16} +(-324.451 - 324.451i) q^{17} +(231.917 - 231.917i) q^{18} -468.403i q^{19} +(-19.5270 - 37.5130i) q^{20} -32.2036 q^{21} +(-52.4131 - 52.4131i) q^{22} +(-625.505 + 625.505i) q^{23} -104.648i q^{24} +(358.508 - 511.954i) q^{25} +954.152 q^{26} +(-195.468 - 195.468i) q^{27} +(-22.1534 + 22.1534i) q^{28} +755.645i q^{29} +(-162.187 + 84.4243i) q^{30} +553.934 q^{31} +(-152.489 - 152.489i) q^{32} +(-21.6677 + 21.6677i) q^{33} +1929.96i q^{34} +(-441.574 - 139.239i) q^{35} -131.908 q^{36} +(555.586 + 555.586i) q^{37} +(-1393.12 + 1393.12i) q^{38} -394.449i q^{39} +(452.467 - 1434.93i) q^{40} -1685.09 q^{41} +(95.7796 + 95.7796i) q^{42} +(-416.902 + 416.902i) q^{43} +29.8112i q^{44} +(-900.099 - 1729.17i) q^{45} +3720.74 q^{46} +(-319.293 - 319.293i) q^{47} +(-344.522 + 344.522i) q^{48} +343.000i q^{49} +(-2588.92 + 456.377i) q^{50} +797.849 q^{51} +(-271.348 - 271.348i) q^{52} +(3352.34 - 3352.34i) q^{53} +1162.72i q^{54} +(-390.791 + 203.422i) q^{55} -1114.60 q^{56} +(575.920 + 575.920i) q^{57} +(2247.43 - 2247.43i) q^{58} +4679.64i q^{59} +(70.1329 + 22.1145i) q^{60} +848.263 q^{61} +(-1647.51 - 1647.51i) q^{62} +(-1021.16 + 1021.16i) q^{63} -3576.21i q^{64} +(1705.48 - 5408.66i) q^{65} +128.888 q^{66} +(2472.93 + 2472.93i) q^{67} +(548.854 - 548.854i) q^{68} -1538.16i q^{69} +(899.203 + 1727.45i) q^{70} -2453.67 q^{71} +(-3318.35 - 3318.35i) q^{72} +(-2349.08 + 2349.08i) q^{73} -3304.84i q^{74} +(188.667 + 1070.27i) q^{75} +792.371 q^{76} +(230.782 + 230.782i) q^{77} +(-1173.17 + 1173.17i) q^{78} +1766.38i q^{79} +(-6213.69 + 3234.46i) q^{80} -5835.43 q^{81} +(5011.77 + 5011.77i) q^{82} +(-885.758 + 885.758i) q^{83} -54.4769i q^{84} +(10940.1 + 3449.66i) q^{85} +2479.89 q^{86} +(-929.094 - 929.094i) q^{87} +(-749.945 + 749.945i) q^{88} -3514.86i q^{89} +(-2465.81 + 7819.95i) q^{90} -4201.27 q^{91} +(-1058.13 - 1058.13i) q^{92} +(-681.083 + 681.083i) q^{93} +1899.28i q^{94} +(5406.88 + 10387.1i) q^{95} +374.983 q^{96} +(421.287 + 421.287i) q^{97} +(1020.15 - 1020.15i) q^{98} +1374.15i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6}+O(q^{10}) $ 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97}+O(q^{100}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6 - 112 * q^10 + 156 * q^11 - 80 * q^12 - 560 * q^13 + 896 * q^15 - 1480 * q^16 + 1320 * q^17 + 340 * q^18 + 180 * q^20 + 196 * q^21 - 2020 * q^22 + 1920 * q^23 - 676 * q^25 + 2208 * q^26 - 340 * q^27 - 5356 * q^30 - 2112 * q^31 - 1200 * q^32 - 6140 * q^33 + 3904 * q^36 + 3980 * q^37 + 9120 * q^38 + 14716 * q^40 + 6384 * q^41 + 4900 * q^42 - 12220 * q^43 - 10528 * q^45 - 8080 * q^46 - 11820 * q^47 - 4040 * q^48 + 10728 * q^50 - 5900 * q^51 + 3600 * q^52 + 24240 * q^53 + 4636 * q^55 - 10584 * q^56 + 6460 * q^57 + 6100 * q^58 - 30088 * q^60 + 440 * q^61 - 16680 * q^62 + 7840 * q^63 - 14652 * q^65 + 4832 * q^66 - 5940 * q^67 - 47040 * q^68 - 6272 * q^70 + 8928 * q^71 + 46720 * q^72 - 2500 * q^73 + 60708 * q^75 + 47816 * q^76 + 5880 * q^77 - 17940 * q^78 + 16140 * q^80 - 11360 * q^81 - 32120 * q^82 + 15120 * q^83 + 18816 * q^85 - 41208 * q^86 - 25460 * q^87 + 52920 * q^88 - 55680 * q^90 - 11172 * q^91 + 19800 * q^92 + 1460 * q^93 - 35508 * q^95 + 20568 * q^96 - 33840 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−2.97419	−	2.97419i	−0.743548	−	0.743548i	0.229711	−	0.973259i	$-0.426222\pi$
$2$	−2.97419	−	2.97419i	−0.743548	−	0.743548i	−0.973259	+	0.229711i	$0.926222\pi$
$3$	−1.22954	+	1.22954i	−0.136615	+	0.136615i	−0.772107	−	0.635492i	$-0.780797\pi$
$3$	−1.22954	+	1.22954i	−0.136615	+	0.136615i	0.635492	+	0.772107i	$0.280797\pi$
$4$			1.69164i			0.105728i
$5$	−22.1755	+	11.5432i	−0.887021	+	0.461729i
$5$	−22.1755	+	11.5432i	−0.887021	+	0.461729i
$6$	7.31376			0.203160
$7$	13.0958	+	13.0958i	0.267261	+	0.267261i
$7$	13.0958	+	13.0958i	0.267261	+	0.267261i
$8$	−42.5558	+	42.5558i	−0.664935	+	0.664935i
$9$			77.9765i			0.962673i
$10$	100.286	+	31.6225i	1.00286	+	0.316225i
$11$	17.6226			0.145642			0.0728208	−	0.997345i	$-0.476800\pi$
$11$	17.6226			0.145642			0.0728208	+	0.997345i	$0.476800\pi$
$12$	−2.07994	−	2.07994i	−0.0144440	−	0.0144440i
$13$	−160.405	+	160.405i	−0.949144	+	0.949144i	−0.998768	−	0.0496243i	$-0.984198\pi$
$13$	−160.405	+	160.405i	−0.949144	+	0.949144i	0.0496243	+	0.998768i	$0.484198\pi$
$14$		−	77.8989i		−	0.397443i
$15$	13.0728	−	41.4585i	0.0581015	−	0.184260i
$16$	280.205			1.09455
$17$	−324.451	−	324.451i	−1.12267	−	1.12267i	−0.991339	−	0.131328i	$-0.958076\pi$
$17$	−324.451	−	324.451i	−1.12267	−	1.12267i	−0.131328	−	0.991339i	$-0.541924\pi$
$18$	231.917	−	231.917i	0.715793	−	0.715793i
$19$		−	468.403i		−	1.29752i	−0.760995	−	0.648758i	$-0.775289\pi$
$19$		−	468.403i		−	1.29752i	0.760995	−	0.648758i	$-0.224711\pi$
$20$	−19.5270	−	37.5130i	−0.0488175	−	0.0937826i
$21$	−32.2036			−0.0730239
$22$	−52.4131	−	52.4131i	−0.108291	−	0.108291i
$23$	−625.505	+	625.505i	−1.18243	+	1.18243i	−0.203315	+	0.979113i	$0.565172\pi$
$23$	−625.505	+	625.505i	−1.18243	+	1.18243i	−0.979113	+	0.203315i	$0.934828\pi$
$24$		−	104.648i		−	0.181680i
$25$	358.508	−	511.954i	0.573613	−	0.819126i
$26$	954.152			1.41147
$27$	−195.468	−	195.468i	−0.268131	−	0.268131i
$28$	−22.1534	+	22.1534i	−0.0282569	+	0.0282569i
$29$			755.645i			0.898508i	0.893404	+	0.449254i	$0.148310\pi$
$29$			755.645i			0.898508i	−0.893404	+	0.449254i	$0.851690\pi$
$30$	−162.187	+	84.4243i	−0.180207	+	0.0938048i
$31$	553.934			0.576414			0.288207	−	0.957568i	$-0.406941\pi$
$31$	553.934			0.576414			0.288207	+	0.957568i	$0.406941\pi$
$32$	−152.489	−	152.489i	−0.148915	−	0.148915i
$33$	−21.6677	+	21.6677i	−0.0198969	+	0.0198969i
$34$			1929.96i			1.66951i
$35$	−441.574	−	139.239i	−0.360469	−	0.113664i
$36$	−131.908			−0.101781
$37$	555.586	+	555.586i	0.405834	+	0.405834i	0.880283	−	0.474449i	$-0.157353\pi$
$37$	555.586	+	555.586i	0.405834	+	0.405834i	−0.474449	+	0.880283i	$0.657353\pi$
$38$	−1393.12	+	1393.12i	−0.964766	+	0.964766i
$39$		−	394.449i		−	0.259335i
$40$	452.467	−	1434.93i	0.282792	−	0.896830i
$41$	−1685.09			−1.00243			−0.501215	−	0.865323i	$-0.667113\pi$
$41$	−1685.09			−1.00243			−0.501215	+	0.865323i	$0.667113\pi$
$42$	95.7796	+	95.7796i	0.0542968	+	0.0542968i
$43$	−416.902	+	416.902i	−0.225474	+	0.225474i	−0.810799	−	0.585325i	$-0.800967\pi$
$43$	−416.902	+	416.902i	−0.225474	+	0.225474i	0.585325	+	0.810799i	$0.300967\pi$
$44$			29.8112i			0.0153983i
$45$	−900.099	−	1729.17i	−0.444493	−	0.853911i
$46$	3720.74			1.75839
$47$	−319.293	−	319.293i	−0.144542	−	0.144542i	0.631133	−	0.775675i	$-0.282590\pi$
$47$	−319.293	−	319.293i	−0.144542	−	0.144542i	−0.775675	+	0.631133i	$0.782590\pi$
$48$	−344.522	+	344.522i	−0.149532	+	0.149532i
$49$			343.000i			0.142857i
$50$	−2588.92	+	456.377i	−1.03557	+	0.182551i
$51$	797.849			0.306747
$52$	−271.348	−	271.348i	−0.100351	−	0.100351i
$53$	3352.34	−	3352.34i	1.19343	−	1.19343i	0.217329	−	0.976098i	$-0.430266\pi$
$53$	3352.34	−	3352.34i	1.19343	−	1.19343i	0.976098	−	0.217329i	$-0.0697345\pi$
$54$			1162.72i			0.398737i
$55$	−390.791	+	203.422i	−0.129187	+	0.0672469i
$56$	−1114.60			−0.355422
$57$	575.920	+	575.920i	0.177261	+	0.177261i
$58$	2247.43	−	2247.43i	0.668084	−	0.668084i
$59$			4679.64i			1.34434i	0.740398	+	0.672168i	$0.234637\pi$
$59$			4679.64i			1.34434i	−0.740398	+	0.672168i	$0.765363\pi$
$60$	70.1329	+	22.1145i	0.0194813	+	0.00614293i
$61$	848.263			0.227966			0.113983	−	0.993483i	$-0.463639\pi$
$61$	848.263			0.227966			0.113983	+	0.993483i	$0.463639\pi$
$62$	−1647.51	−	1647.51i	−0.428592	−	0.428592i
$63$	−1021.16	+	1021.16i	−0.257285	+	0.257285i
$64$		−	3576.21i		−	0.873098i
$65$	1705.48	−	5408.66i	0.403664	−	1.28016i
$66$	128.888			0.0295885
$67$	2472.93	+	2472.93i	0.550886	+	0.550886i	0.926696	−	0.375811i	$-0.122636\pi$
$67$	2472.93	+	2472.93i	0.550886	+	0.550886i	−0.375811	+	0.926696i	$0.622636\pi$
$68$	548.854	−	548.854i	0.118697	−	0.118697i
$69$		−	1538.16i		−	0.323076i
$70$	899.203	+	1727.45i	0.183511	+	0.352541i
$71$	−2453.67			−0.486743			−0.243371	−	0.969933i	$-0.578253\pi$
$71$	−2453.67			−0.486743			−0.243371	+	0.969933i	$0.578253\pi$
$72$	−3318.35	−	3318.35i	−0.640114	−	0.640114i
$73$	−2349.08	+	2349.08i	−0.440811	+	0.440811i	−0.892284	−	0.451474i	$-0.850898\pi$
$73$	−2349.08	+	2349.08i	−0.440811	+	0.440811i	0.451474	+	0.892284i	$0.350898\pi$
$74$		−	3304.84i		−	0.603514i
$75$	188.667	+	1070.27i	0.0335408	+	0.190270i
$76$	792.371			0.137183
$77$	230.782	+	230.782i	0.0389243	+	0.0389243i
$78$	−1173.17	+	1173.17i	−0.192828	+	0.192828i
$79$			1766.38i			0.283028i	0.989936	+	0.141514i	$0.0451970\pi$
$79$			1766.38i			0.283028i	−0.989936	+	0.141514i	$0.954803\pi$
$80$	−6213.69	+	3234.46i	−0.970888	+	0.505385i
$81$	−5835.43			−0.889411
$82$	5011.77	+	5011.77i	0.745355	+	0.745355i
$83$	−885.758	+	885.758i	−0.128576	+	0.128576i	−0.768466	−	0.639890i	$-0.778980\pi$
$83$	−885.758	+	885.758i	−0.128576	+	0.128576i	0.639890	+	0.768466i	$0.278980\pi$
$84$		−	54.4769i		−	0.00772065i
$85$	10940.1	+	3449.66i	1.51420	+	0.477462i
$86$	2479.89			0.335302
$87$	−929.094	−	929.094i	−0.122750	−	0.122750i
$88$	−749.945	+	749.945i	−0.0968421	+	0.0968421i
$89$		−	3514.86i		−	0.443740i	−0.975076	−	0.221870i	$-0.928784\pi$
$89$		−	3514.86i		−	0.443740i	0.975076	−	0.221870i	$-0.0712160\pi$
$90$	−2465.81	+	7819.95i	−0.304422	+	0.965426i
$91$	−4201.27			−0.507339
$92$	−1058.13	−	1058.13i	−0.125015	−	0.125015i
$93$	−681.083	+	681.083i	−0.0787470	+	0.0787470i
$94$			1899.28i			0.214948i
$95$	5406.88	+	10387.1i	0.599101	+	1.15092i
$96$	374.983			0.0406883
$97$	421.287	+	421.287i	0.0447748	+	0.0447748i	0.729140	−	0.684365i	$-0.239920\pi$
$97$	421.287	+	421.287i	0.0447748	+	0.0447748i	−0.684365	+	0.729140i	$0.739920\pi$
$98$	1020.15	−	1020.15i	0.106221	−	0.106221i
$99$			1374.15i			0.140205i
$100$	866.042	+	606.468i	0.0866042	+	0.0606468i
$101$	9326.25			0.914249			0.457124	−	0.889403i	$-0.348879\pi$
$101$	9326.25			0.914249			0.457124	+	0.889403i	$0.348879\pi$
$102$	−2372.96	−	2372.96i	−0.228081	−	0.228081i
$103$	−3554.31	+	3554.31i	−0.335028	+	0.335028i	−0.854492	−	0.519464i	$-0.826132\pi$
$103$	−3554.31	+	3554.31i	−0.335028	+	0.335028i	0.519464	+	0.854492i	$0.326132\pi$
$104$		−	13652.4i		−	1.26224i
$105$	714.131	−	371.733i	0.0647738	−	0.0337172i
$106$	−19941.0			−1.77474
$107$	5312.92	+	5312.92i	0.464051	+	0.464051i	0.899981	−	0.435930i	$-0.143580\pi$
$107$	5312.92	+	5312.92i	0.464051	+	0.464051i	−0.435930	+	0.899981i	$0.643580\pi$
$108$	330.661	−	330.661i	0.0283489	−	0.0283489i
$109$		−	9313.69i		−	0.783915i	−0.919983	−	0.391957i	$-0.871798\pi$
$109$		−	9313.69i		−	0.783915i	0.919983	−	0.391957i	$-0.128202\pi$
$110$	1767.30	+	557.272i	0.146058	+	0.0460556i
$111$	−1366.23			−0.110886
$112$	3669.50	+	3669.50i	0.292531	+	0.292531i
$113$	10930.8	−	10930.8i	0.856043	−	0.856043i	−0.134826	−	0.990869i	$-0.543048\pi$
$113$	10930.8	−	10930.8i	0.856043	−	0.856043i	0.990869	+	0.134826i	$0.0430477\pi$
$114$		−	3425.79i		−	0.263604i
$115$	6650.56	−	21091.2i	0.502878	−	1.59480i
$116$	−1278.28			−0.0949971
$117$	−12507.8	−	12507.8i	−0.913714	−	0.913714i
$118$	13918.1	−	13918.1i	0.999579	−	0.999579i
$119$		−	8497.89i		−	0.600091i
$120$	1207.97	+	2320.62i	0.0838871	+	0.161154i
$121$	−14330.4			−0.978789
$122$	−2522.90	−	2522.90i	−0.169504	−	0.169504i
$123$	2071.88	−	2071.88i	0.136947	−	0.136947i
$124$			937.058i			0.0609429i
$125$	−2040.52	+	15491.2i	−0.130593	+	0.991436i
$126$	6074.28			0.382608
$127$	14279.3	+	14279.3i	0.885318	+	0.885318i	0.994069	−	0.108751i	$-0.0346852\pi$
$127$	14279.3	+	14279.3i	0.885318	+	0.885318i	−0.108751	+	0.994069i	$0.534685\pi$
$128$	−13076.2	+	13076.2i	−0.798106	+	0.798106i
$129$		−	1025.19i		−	0.0616064i
$130$	−21158.8	+	11014.0i	−1.25200	+	0.651715i
$131$	−9187.71			−0.535383			−0.267692	−	0.963505i	$-0.586261\pi$
$131$	−9187.71			−0.535383			−0.267692	+	0.963505i	$0.586261\pi$
$132$	−36.6539	−	36.6539i	−0.00210365	−	0.00210365i
$133$	6134.12	−	6134.12i	0.346776	−	0.346776i
$134$		−	14709.9i		−	0.819220i
$135$	6590.92	+	2078.27i	0.361642	+	0.114034i
$136$	27614.5			1.49300
$137$	−2649.32	−	2649.32i	−0.141154	−	0.141154i	0.632999	−	0.774153i	$-0.281824\pi$
$137$	−2649.32	−	2649.32i	−0.141154	−	0.141154i	−0.774153	+	0.632999i	$0.781824\pi$
$138$	−4574.79	+	4574.79i	−0.240222	+	0.240222i
$139$			29935.3i			1.54937i	0.632349	+	0.774684i	$0.282091\pi$
$139$			29935.3i			1.54937i	−0.632349	+	0.774684i	$0.717909\pi$
$140$	235.542	−	746.985i	0.0120174	−	0.0381115i
$141$	785.166			0.0394933
$142$	7297.69	+	7297.69i	0.361917	+	0.361917i
$143$	−2826.76	+	2826.76i	−0.138235	+	0.138235i
$144$			21849.4i			1.05369i
$145$	−8722.58	−	16756.8i	−0.414867	−	0.796996i
$146$	13973.2			0.655528
$147$	−421.731	−	421.731i	−0.0195165	−	0.0195165i
$148$	−939.853	+	939.853i	−0.0429078	+	0.0429078i
$149$			35767.7i			1.61108i	0.592538	+	0.805542i	$0.298126\pi$
$149$			35767.7i			1.61108i	−0.592538	+	0.805542i	$0.701874\pi$
$150$	2622.04	−	3744.31i	0.116535	−	0.166414i
$151$	−41532.5			−1.82152			−0.910760	−	0.412936i	$-0.864503\pi$
$151$	−41532.5			−1.82152			−0.910760	+	0.412936i	$0.864503\pi$
$152$	19933.3	+	19933.3i	0.862764	+	0.862764i
$153$	25299.5	−	25299.5i	1.08076	−	1.08076i
$154$		−	1372.78i		−	0.0578842i
$155$	−12283.8	+	6394.18i	−0.511291	+	0.266147i
$156$	667.266			0.0274189
$157$	−20305.2	−	20305.2i	−0.823774	−	0.823774i	0.162873	−	0.986647i	$-0.447924\pi$
$157$	−20305.2	−	20305.2i	−0.823774	−	0.823774i	−0.986647	+	0.162873i	$0.947924\pi$
$158$	5253.55	−	5253.55i	0.210445	−	0.210445i
$159$			8243.65i			0.326081i
$160$	5141.75	+	1621.32i	0.200850	+	0.0633326i
$161$	−16383.0			−0.632035
$162$	17355.7	+	17355.7i	0.661320	+	0.661320i
$163$	−24246.0	+	24246.0i	−0.912567	+	0.912567i	−0.996474	−	0.0839065i	$-0.973260\pi$
$163$	−24246.0	+	24246.0i	−0.912567	+	0.912567i	0.0839065	+	0.996474i	$0.473260\pi$
$164$		−	2850.56i		−	0.105985i
$165$	230.378	−	730.607i	0.00846199	−	0.0268359i
$166$	5268.83			0.191204
$167$	−29647.0	−	29647.0i	−1.06303	−	1.06303i	−0.997875	−	0.0651591i	$-0.979245\pi$
$167$	−29647.0	−	29647.0i	−1.06303	−	1.06303i	−0.0651591	−	0.997875i	$-0.520755\pi$
$168$	1370.45	−	1370.45i	0.0485561	−	0.0485561i
$169$		−	22898.7i		−	0.801747i
$170$	−22277.9	−	42797.9i	−0.770863	−	1.48089i
$171$	36524.4			1.24908
$172$	−705.248	−	705.248i	−0.0238388	−	0.0238388i
$173$	−4080.56	+	4080.56i	−0.136341	+	0.136341i	−0.771984	−	0.635642i	$-0.780735\pi$
$173$	−4080.56	+	4080.56i	−0.136341	+	0.136341i	0.635642	+	0.771984i	$0.280735\pi$
$174$			5526.61i			0.182541i
$175$	11399.4	−	2009.49i	0.372225	−	0.0656161i
$176$	4937.94			0.159412
$177$	−5753.79	−	5753.79i	−0.183657	−	0.183657i
$178$	−10453.9	+	10453.9i	−0.329942	+	0.329942i
$179$			20997.6i			0.655335i	0.944793	+	0.327668i	$0.106263\pi$
$179$			20997.6i			0.655335i	−0.944793	+	0.327668i	$0.893737\pi$
$180$	2925.14	−	1522.65i	0.0902819	−	0.0469952i
$181$	22890.3			0.698705			0.349352	−	0.936991i	$-0.386402\pi$
$181$	22890.3			0.698705			0.349352	+	0.936991i	$0.386402\pi$
$182$	12495.4	+	12495.4i	0.377231	+	0.377231i
$183$	−1042.97	+	1042.97i	−0.0311437	+	0.0311437i
$184$		−	53237.7i		−	1.57248i
$185$	−18733.7	−	5907.17i	−0.547368	−	0.172598i
$186$	4051.34			0.117104
$187$	−5717.68	−	5717.68i	−0.163507	−	0.163507i
$188$	540.130	−	540.130i	0.0152821	−	0.0152821i
$189$		−	5119.61i		−	0.143322i
$190$	14812.1	−	46974.3i	0.410308	−	1.30123i
$191$	57786.8			1.58402			0.792012	−	0.610506i	$-0.209034\pi$
$191$	57786.8			1.58402			0.792012	+	0.610506i	$0.209034\pi$
$192$	4397.08	+	4397.08i	0.119278	+	0.119278i
$193$	−10258.8	+	10258.8i	−0.275412	+	0.275412i	−0.831274	−	0.555863i	$-0.812388\pi$
$193$	−10258.8	+	10258.8i	−0.275412	+	0.275412i	0.555863	+	0.831274i	$0.312388\pi$
$194$		−	2505.97i		−	0.0665845i
$195$	4553.21	+	8747.11i	0.119742	+	0.230036i
$196$	−580.233			−0.0151039
$197$	14590.3	+	14590.3i	0.375951	+	0.375951i	0.869639	−	0.493688i	$-0.164351\pi$
$197$	14590.3	+	14590.3i	0.375951	+	0.375951i	−0.493688	+	0.869639i	$0.664351\pi$
$198$	4086.99	−	4086.99i	0.104249	−	0.104249i
$199$			50015.5i			1.26299i	0.775381	+	0.631493i	$0.217558\pi$
$199$			50015.5i			1.26299i	−0.775381	+	0.631493i	$0.782442\pi$
$200$	6530.00	+	37043.2i	0.163250	+	0.926081i
$201$	−6081.11			−0.150519
$202$	−27738.1	−	27738.1i	−0.679788	−	0.679788i
$203$	−9895.78	+	9895.78i	−0.240136	+	0.240136i
$204$			1349.67i			0.0324316i
$205$	37367.7	−	19451.3i	0.889177	−	0.462851i
$206$	21142.4			0.498219
$207$	−48774.7	−	48774.7i	−1.13829	−	1.13829i
$208$	−44946.3	+	44946.3i	−1.03888	+	1.03888i
$209$		−	8254.50i		−	0.188972i
$210$	−3229.57	−	1018.36i	−0.0732328	−	0.0230920i
$211$	−37327.4			−0.838422			−0.419211	−	0.907889i	$-0.637693\pi$
$211$	−37327.4			−0.838422			−0.419211	+	0.907889i	$0.637693\pi$
$212$	5670.95	+	5670.95i	0.126178	+	0.126178i
$213$	3016.88	−	3016.88i	0.0664965	−	0.0664965i
$214$		−	31603.3i		−	0.690089i
$215$	4432.63	−	14057.4i	0.0958925	−	0.304108i
$216$	16636.6			0.356579
$217$	7254.21	+	7254.21i	0.154053	+	0.154053i
$218$	−27700.7	+	27700.7i	−0.582878	+	0.582878i
$219$		−	5776.57i		−	0.120443i
$220$	−344.117	−	661.078i	−0.00710985	−	0.0136586i
$221$	104087.			2.13114
$222$	4063.43	+	4063.43i	0.0824492	+	0.0824492i
$223$	9094.35	−	9094.35i	0.182878	−	0.182878i	−0.609731	−	0.792609i	$-0.708722\pi$
$223$	9094.35	−	9094.35i	0.182878	−	0.182878i	0.792609	+	0.609731i	$0.208722\pi$
$224$		−	3993.94i		−	0.0795987i
$225$	39920.4	+	27955.2i	0.788550	+	0.552202i
$226$	−65020.7			−1.27302
$227$	−30816.0	−	30816.0i	−0.598032	−	0.598032i	0.341757	−	0.939789i	$-0.388978\pi$
$227$	−30816.0	−	30816.0i	−0.598032	−	0.598032i	−0.939789	+	0.341757i	$0.888978\pi$
$228$	−974.250	+	974.250i	−0.0187413	+	0.0187413i
$229$			13976.7i			0.266522i	0.991081	+	0.133261i	$0.0425448\pi$
$229$			13976.7i			0.266522i	−0.991081	+	0.133261i	$0.957455\pi$
$230$	−82509.5	+	42949.3i	−1.55973	+	0.811897i
$231$	−567.511			−0.0106353
$232$	−32157.1	−	32157.1i	−0.597449	−	0.597449i
$233$	6660.07	−	6660.07i	0.122678	−	0.122678i	−0.643102	−	0.765780i	$-0.722353\pi$
$233$	6660.07	−	6660.07i	0.122678	−	0.122678i	0.765780	+	0.643102i	$0.222353\pi$
$234$			74401.4i			1.35878i
$235$	10766.2	+	3394.83i	0.194951	+	0.0614727i
$236$	−7916.26			−0.142133
$237$	−2171.83	−	2171.83i	−0.0386660	−	0.0386660i
$238$	−25274.4	+	25274.4i	−0.446196	+	0.446196i
$239$			7840.64i			0.137264i	0.997642	+	0.0686318i	$0.0218634\pi$
$239$			7840.64i			0.137264i	−0.997642	+	0.0686318i	$0.978137\pi$
$240$	3663.07	−	11616.9i	0.0635949	−	0.201681i
$241$	−79730.7			−1.37275			−0.686375	−	0.727247i	$-0.740799\pi$
$241$	−79730.7			−1.37275			−0.686375	+	0.727247i	$0.740799\pi$
$242$	42621.5	+	42621.5i	0.727776	+	0.727776i
$243$	23007.7	−	23007.7i	0.389638	−	0.389638i
$244$			1434.96i			0.0241023i
$245$	−3959.32	−	7606.21i	−0.0659612	−	0.126717i
$246$	−12324.3			−0.203654
$247$	75134.4	+	75134.4i	1.23153	+	1.23153i
$248$	−23573.1	+	23573.1i	−0.383278	+	0.383278i
$249$		−	2178.15i		−	0.0351308i
$250$	52142.7	−	40004.9i	0.834283	−	0.640078i
$251$	55697.0			0.884065			0.442032	−	0.896999i	$-0.354258\pi$
$251$	55697.0			0.884065			0.442032	+	0.896999i	$0.354258\pi$
$252$	−1727.44	−	1727.44i	−0.0272021	−	0.0272021i
$253$	−11023.0	+	11023.0i	−0.172211	+	0.172211i
$254$		−	84938.7i		−	1.31655i
$255$	−17692.7	+	9209.74i	−0.272091	+	0.141634i
$256$	20562.7			0.313762
$257$	53468.3	+	53468.3i	0.809525	+	0.809525i	0.984562	−	0.175037i	$-0.0560046\pi$
$257$	53468.3	+	53468.3i	0.809525	+	0.809525i	−0.175037	+	0.984562i	$0.556005\pi$
$258$	−3049.12	+	3049.12i	−0.0458073	+	0.0458073i
$259$			14551.7i			0.216927i
$260$	9149.52	+	2885.06i	0.135348	+	0.0426784i
$261$	−58922.6			−0.864969
$262$	27326.0	+	27326.0i	0.398083	+	0.398083i
$263$	78703.8	−	78703.8i	1.13785	−	1.13785i	0.149013	−	0.988835i	$-0.452390\pi$
$263$	78703.8	−	78703.8i	1.13785	−	1.13785i	0.988835	−	0.149013i	$-0.0476097\pi$
$264$		−	1844.17i		−	0.0264602i
$265$	−35643.1	+	113037.i	−0.507556	+	1.60964i
$266$	−36488.1			−0.515689
$267$	4321.66	+	4321.66i	0.0606216	+	0.0606216i
$268$	−4183.31	+	4183.31i	−0.0582438	+	0.0582438i
$269$		−	83582.2i		−	1.15507i	−0.816365	−	0.577536i	$-0.804014\pi$
$269$		−	83582.2i		−	1.15507i	0.816365	−	0.577536i	$-0.195986\pi$
$270$	−13421.5	−	25783.8i	−0.184108	−	0.353688i
$271$	32293.6			0.439721			0.219861	−	0.975531i	$-0.429440\pi$
$271$	32293.6			0.439721			0.219861	+	0.975531i	$0.429440\pi$
$272$	−90912.6	−	90912.6i	−1.22881	−	1.22881i
$273$	5165.62	−	5165.62i	0.0693102	−	0.0693102i
$274$			15759.2i			0.209910i
$275$	6317.86	−	9021.97i	0.0835419	−	0.119299i
$276$	2602.02			0.0341580
$277$	−58656.0	−	58656.0i	−0.764456	−	0.764456i	0.212668	−	0.977124i	$-0.431785\pi$
$277$	−58656.0	−	58656.0i	−0.764456	−	0.764456i	−0.977124	+	0.212668i	$0.931785\pi$
$278$	89033.5	−	89033.5i	1.15203	−	1.15203i
$279$			43193.8i			0.554898i
$280$	24717.0	−	12866.1i	0.315267	−	0.164109i
$281$	−60425.2			−0.765254			−0.382627	−	0.923903i	$-0.624980\pi$
$281$	−60425.2			−0.765254			−0.382627	+	0.923903i	$0.624980\pi$
$282$	−2335.24	−	2335.24i	−0.0293652	−	0.0293652i
$283$	72566.2	−	72566.2i	0.906070	−	0.906070i	−0.0898824	−	0.995952i	$-0.528649\pi$
$283$	72566.2	−	72566.2i	0.906070	−	0.906070i	0.995952	+	0.0898824i	$0.0286491\pi$
$284$		−	4150.73i		−	0.0514622i
$285$	−19419.3	−	6123.36i	−0.239080	−	0.0753876i
$286$	16814.7			0.205568
$287$	−22067.5	−	22067.5i	−0.267911	−	0.267911i
$288$	11890.6	−	11890.6i	0.143357	−	0.143357i
$289$			127016.i			1.52076i
$290$	−23895.4	+	75780.7i	−0.284131	+	0.901078i
$291$	−1035.98			−0.0122339
$292$	−3973.80	−	3973.80i	−0.0466059	−	0.0466059i
$293$	−15395.9	+	15395.9i	−0.179336	+	0.179336i	−0.791067	−	0.611730i	$-0.790474\pi$
$293$	−15395.9	+	15395.9i	−0.179336	+	0.179336i	0.611730	+	0.791067i	$0.290474\pi$
$294$			2508.62i			0.0290229i
$295$	−54018.0	−	103773.i	−0.620719	−	1.19245i
$296$	−47286.8			−0.539706
$297$	−3444.65	−	3444.65i	−0.0390510	−	0.0390510i
$298$	106380.	−	106380.i	1.19792	−	1.19792i
$299$		−	200669.i		−	2.24459i
$300$	−1810.51	+	319.157i	−0.0201167	+	0.00354619i
$301$	−10919.3			−0.120521
$302$	123526.	+	123526.i	1.35439	+	1.35439i
$303$	−11467.0	+	11467.0i	−0.124900	+	0.124900i
$304$		−	131249.i		−	1.42020i
$305$	−18810.7	+	9791.68i	−0.202211	+	0.105259i
$306$	−150491.			−1.60720
$307$	40854.0	+	40854.0i	0.433469	+	0.433469i	0.889807	−	0.456338i	$-0.150839\pi$
$307$	40854.0	+	40854.0i	0.433469	+	0.433469i	−0.456338	+	0.889807i	$0.650839\pi$
$308$	−390.401	+	390.401i	−0.00411538	+	0.00411538i
$309$		−	8740.32i		−	0.0915399i
$310$	55551.8	+	17516.8i	0.578063	+	0.182277i
$311$	−124994.			−1.29231			−0.646157	−	0.763205i	$-0.723625\pi$
$311$	−124994.			−1.29231			−0.646157	+	0.763205i	$0.723625\pi$
$312$	16786.1	+	16786.1i	0.172441	+	0.172441i
$313$	−27798.6	+	27798.6i	−0.283749	+	0.283749i	−0.834602	−	0.550853i	$-0.814302\pi$
$313$	−27798.6	+	27798.6i	−0.283749	+	0.283749i	0.550853	+	0.834602i	$0.314302\pi$
$314$			120783.i			1.22503i
$315$	10857.3	−	34432.4i	0.109421	−	0.347013i
$316$	−2988.08			−0.0299239
$317$	83808.0	+	83808.0i	0.834002	+	0.834002i	0.988062	−	0.154060i	$-0.0492348\pi$
$317$	83808.0	+	83808.0i	0.834002	+	0.834002i	−0.154060	+	0.988062i	$0.549235\pi$
$318$	24518.2	−	24518.2i	0.242457	−	0.242457i
$319$			13316.5i			0.130860i
$320$	41280.9	+	79304.3i	0.403134	+	0.774456i
$321$	−13064.9			−0.126793
$322$	48726.1	+	48726.1i	0.469948	+	0.469948i
$323$	−151974.	+	151974.i	−1.45668	+	1.45668i
$324$		−	9871.45i		−	0.0940353i
$325$	24613.5	+	139627.i	0.233027	+	1.32191i
$326$	144225.			1.35708
$327$	11451.5	+	11451.5i	0.107095	+	0.107095i
$328$	71710.2	−	71710.2i	0.666551	−	0.666551i
$329$		−	8362.81i		−	0.0772610i
$330$	−2858.15	+	1487.78i	−0.0262457	+	0.0136619i
$331$	−37373.1			−0.341117			−0.170558	−	0.985348i	$-0.554557\pi$
$331$	−37373.1			−0.341117			−0.170558	+	0.985348i	$0.554557\pi$
$332$	−1498.38	−	1498.38i	−0.0135940	−	0.0135940i
$333$	−43322.7	+	43322.7i	−0.390685	+	0.390685i
$334$			176352.i			1.58083i
$335$	−83384.0	−	26292.9i	−0.743007	−	0.234288i
$336$	−9023.59			−0.0799283
$337$	−7169.19	−	7169.19i	−0.0631263	−	0.0631263i	0.674839	−	0.737965i	$-0.264213\pi$
$337$	−7169.19	−	7169.19i	−0.0631263	−	0.0631263i	−0.737965	+	0.674839i	$0.764213\pi$
$338$	−68105.1	+	68105.1i	−0.596138	+	0.596138i
$339$			26879.7i			0.233897i
$340$	−5835.59	+	18506.7i	−0.0504809	+	0.160092i
$341$	9761.77			0.0839498
$342$	−108631.	−	108631.i	−0.928754	−	0.928754i
$343$	−4491.86	+	4491.86i	−0.0381802	+	0.0381802i
$344$		−	35483.2i		−	0.299851i
$345$	17755.4	+	34109.6i	0.149173	+	0.286575i
$346$	24272.7			0.202753
$347$	9680.63	+	9680.63i	0.0803979	+	0.0803979i	0.746162	−	0.665764i	$-0.231894\pi$
$347$	9680.63	+	9680.63i	0.0803979	+	0.0803979i	−0.665764	+	0.746162i	$0.731894\pi$
$348$	1571.69	−	1571.69i	0.0129781	−	0.0129781i
$349$			72057.7i			0.591602i	0.955250	+	0.295801i	$0.0955866\pi$
$349$			72057.7i			0.591602i	−0.955250	+	0.295801i	$0.904413\pi$
$350$	−39880.6	−	27927.4i	−0.325556	−	0.227979i
$351$	62708.0			0.508990
$352$	−2687.26	−	2687.26i	−0.0216883	−	0.0216883i
$353$	52704.4	−	52704.4i	0.422958	−	0.422958i	−0.463263	−	0.886221i	$-0.653321\pi$
$353$	52704.4	−	52704.4i	0.422958	−	0.422958i	0.886221	+	0.463263i	$0.153321\pi$
$354$			34225.7i			0.273115i
$355$	54411.5	−	28323.3i	0.431751	−	0.224743i
$356$	5945.89			0.0469155
$357$	10448.5	+	10448.5i	0.0819816	+	0.0819816i
$358$	62450.9	−	62450.9i	0.487273	−	0.487273i
$359$		−	232709.i		−	1.80561i	−0.430046	−	0.902807i	$-0.641503\pi$
$359$		−	232709.i		−	1.80561i	0.430046	−	0.902807i	$-0.358497\pi$
$360$	111891.	+	35281.8i	0.863354	+	0.272236i
$361$	−89080.8			−0.683549
$362$	−68080.0	−	68080.0i	−0.519520	−	0.519520i
$363$	17619.8	−	17619.8i	0.133717	−	0.133717i
$364$		−	7107.04i		−	0.0536397i
$365$	24976.2	−	79208.1i	0.187474	−	0.594543i
$366$	6203.99			0.0463137
$367$	−44132.8	−	44132.8i	−0.327664	−	0.327664i	0.524033	−	0.851698i	$-0.324427\pi$
$367$	−44132.8	−	44132.8i	−0.327664	−	0.327664i	−0.851698	+	0.524033i	$0.824427\pi$
$368$	−175269.	+	175269.i	−1.29423	+	1.29423i
$369$		−	131397.i		−	0.965012i
$370$	38148.5	+	73286.6i	0.278660	+	0.535329i
$371$	87803.1			0.637914
$372$	−1152.15	−	1152.15i	−0.00832573	−	0.00832573i
$373$	90918.1	−	90918.1i	0.653480	−	0.653480i	−0.300349	−	0.953829i	$-0.597103\pi$
$373$	90918.1	−	90918.1i	0.653480	−	0.653480i	0.953829	+	0.300349i	$0.0971031\pi$
$374$			34010.9i			0.243151i
$375$	−16538.1	−	21555.9i	−0.117604	−	0.153286i
$376$	27175.6			0.192222
$377$	−121210.	−	121210.i	−0.852813	−	0.852813i
$378$	−15226.7	+	15226.7i	−0.106567	+	0.106567i
$379$		−	90612.2i		−	0.630824i	−0.948955	−	0.315412i	$-0.897857\pi$
$379$		−	90612.2i		−	0.630824i	0.948955	−	0.315412i	$-0.102143\pi$
$380$	−17571.2	+	9146.51i	−0.121684	+	0.0633415i
$381$	−35113.8			−0.241896
$382$	−171869.	−	171869.i	−1.17780	−	1.17780i
$383$	−178249.	+	178249.i	−1.21515	+	1.21515i	−0.245840	+	0.969310i	$0.579064\pi$
$383$	−178249.	+	178249.i	−1.21515	+	1.21515i	−0.969310	+	0.245840i	$0.920936\pi$
$384$		−	32155.3i		−	0.218067i
$385$	−7781.69	−	2453.75i	−0.0524992	−	0.0165542i
$386$	61023.4			0.409564
$387$	−32508.5	−	32508.5i	−0.217058	−	0.217058i
$388$	−712.666	+	712.666i	−0.00473394	+	0.00473394i
$389$			125379.i			0.828564i	0.910149	+	0.414282i	$0.135967\pi$
$389$			125379.i			0.828564i	−0.910149	+	0.414282i	$0.864033\pi$
$390$	12473.5	−	39557.7i	0.0820084	−	0.260077i
$391$	405891.			2.65495
$392$	−14596.6	−	14596.6i	−0.0949907	−	0.0949907i
$393$	11296.6	−	11296.6i	0.0731415	−	0.0731415i
$394$		−	86788.7i		−	0.559076i
$395$	−20389.7	−	39170.4i	−0.130682	−	0.251052i
$396$	−2324.57			−0.0148235
$397$	187283.	+	187283.i	1.18828	+	1.18828i	0.977543	+	0.210735i	$0.0675858\pi$
$397$	187283.	+	187283.i	1.18828	+	1.18828i	0.210735	+	0.977543i	$0.432414\pi$
$398$	148756.	−	148756.i	0.939091	−	0.939091i
$399$			15084.3i			0.0947498i
$400$	100456.	−	143452.i	0.627848	−	0.896574i
$401$	−159884.			−0.994296			−0.497148	−	0.867666i	$-0.665619\pi$
$401$	−159884.			−0.994296			−0.497148	+	0.867666i	$0.665619\pi$
$402$	18086.4	+	18086.4i	0.111918	+	0.111918i
$403$	−88853.9	+	88853.9i	−0.547100	+	0.547100i
$404$			15776.7i			0.0966613i
$405$	129404.	−	67359.6i	0.788926	−	0.410667i
$406$	58863.9			0.357106
$407$	9790.89	+	9790.89i	0.0591062	+	0.0591062i
$408$	−33953.1	+	33953.1i	−0.203967	+	0.203967i
$409$		−	99389.4i		−	0.594146i	−0.954855	−	0.297073i	$-0.903989\pi$
$409$		−	99389.4i		−	0.594146i	0.954855	−	0.297073i	$-0.0960105\pi$
$410$	−168991.	−	53286.7i	−1.00530	−	0.316994i
$411$	6514.89			0.0385676
$412$	−6012.62	−	6012.62i	−0.0354217	−	0.0354217i
$413$	−61283.6	+	61283.6i	−0.359289	+	0.359289i
$414$			290130.i			1.69275i
$415$	9417.66	−	29866.6i	0.0546823	−	0.173416i
$416$	48920.2			0.282684
$417$	−36806.6	−	36806.6i	−0.211667	−	0.211667i
$418$	−24550.5	+	24550.5i	−0.140510	+	0.140510i
$419$		−	155849.i		−	0.887721i	−0.896096	−	0.443860i	$-0.853609\pi$
$419$		−	155849.i		−	0.887721i	0.896096	−	0.443860i	$-0.146391\pi$
$420$	628.838	+	1208.05i	0.00356484	+	0.00684838i
$421$	150890.			0.851325			0.425663	−	0.904882i	$-0.360041\pi$
$421$	150890.			0.851325			0.425663	+	0.904882i	$0.360041\pi$
$422$	111019.	+	111019.i	0.623407	+	0.623407i
$423$	24897.4	−	24897.4i	0.139147	−	0.139147i
$424$			285323.i			1.58710i
$425$	−282422.	+	49785.5i	−1.56358	+	0.275629i
$426$	−17945.6			−0.0988867
$427$	11108.7	+	11108.7i	0.0609266	+	0.0609266i
$428$	−8987.56	+	8987.56i	−0.0490630	+	0.0490630i
$429$		−	6951.22i		−	0.0377700i
$430$	−54992.9	+	28625.9i	−0.297420	+	0.154818i
$431$	39190.3			0.210972			0.105486	−	0.994421i	$-0.466360\pi$
$431$	39190.3			0.210972			0.105486	+	0.994421i	$0.466360\pi$
$432$	−54770.9	−	54770.9i	−0.293483	−	0.293483i
$433$	−132917.	+	132917.i	−0.708933	+	0.708933i	−0.966311	−	0.257378i	$-0.917142\pi$
$433$	−132917.	+	132917.i	−0.708933	+	0.708933i	0.257378	+	0.966311i	$0.417142\pi$
$434$		−	43150.8i		−	0.229092i
$435$	31327.9	+	9878.42i	0.165559	+	0.0522046i
$436$	15755.4			0.0828814
$437$	292989.	+	292989.i	1.53422	+	1.53422i
$438$	−17180.6	+	17180.6i	−0.0895551	+	0.0895551i
$439$			163837.i			0.850124i	0.905164	+	0.425062i	$0.139748\pi$
$439$			163837.i			0.850124i	−0.905164	+	0.425062i	$0.860252\pi$
$440$	7973.65	−	25287.2i	0.0411862	−	0.130616i
$441$	−26745.9			−0.137525
$442$	−309575.	−	309575.i	−1.58461	−	1.58461i
$443$	27337.1	−	27337.1i	0.139298	−	0.139298i	−0.634019	−	0.773317i	$-0.718596\pi$
$443$	27337.1	−	27337.1i	0.139298	−	0.139298i	0.773317	+	0.634019i	$0.218596\pi$
$444$		−	2311.17i		−	0.0117237i
$445$	40572.8	+	77943.9i	0.204887	+	0.393607i
$446$	−54096.7			−0.271957
$447$	−43977.7	−	43977.7i	−0.220099	−	0.220099i
$448$	46833.3	−	46833.3i	0.233345	−	0.233345i
$449$		−	160196.i		−	0.794617i	−0.917685	−	0.397308i	$-0.869944\pi$
$449$		−	160196.i		−	0.794617i	0.917685	−	0.397308i	$-0.130056\pi$
$450$	−35586.6	−	201875.i	−0.175737	−	0.996914i
$451$	−29695.6			−0.145995
$452$	18491.0	+	18491.0i	0.0905073	+	0.0905073i
$453$	51065.7	−	51065.7i	0.248847	−	0.248847i
$454$			183305.i			0.889331i
$455$	93165.4	−	48496.2i	0.450020	−	0.234253i
$456$	−49017.5			−0.235733
$457$	−106963.	−	106963.i	−0.512153	−	0.512153i	0.403033	−	0.915186i	$-0.367956\pi$
$457$	−106963.	−	106963.i	−0.512153	−	0.512153i	−0.915186	+	0.403033i	$0.867956\pi$
$458$	41569.3	−	41569.3i	0.198172	−	0.198172i
$459$			126839.i			0.602044i
$460$	35678.8	+	11250.4i	0.168614	+	0.0531681i
$461$	−23815.9			−0.112064			−0.0560318	−	0.998429i	$-0.517845\pi$
$461$	−23815.9			−0.112064			−0.0560318	+	0.998429i	$0.517845\pi$
$462$	1687.89	+	1687.89i	0.00790787	+	0.00790787i
$463$	−122436.	+	122436.i	−0.571147	+	0.571147i	−0.932449	−	0.361302i	$-0.882332\pi$
$463$	−122436.	+	122436.i	−0.571147	+	0.571147i	0.361302	+	0.932449i	$0.382332\pi$
$464$			211735.i			0.983462i
$465$	7241.48	−	22965.2i	0.0334905	−	0.106210i
$466$	−39616.7			−0.182434
$467$	37772.5	+	37772.5i	0.173198	+	0.173198i	0.788383	−	0.615185i	$-0.210919\pi$
$467$	37772.5	+	37772.5i	0.173198	+	0.173198i	−0.615185	+	0.788383i	$0.710919\pi$
$468$	21158.8	−	21158.8i	0.0966048	−	0.0966048i
$469$			64769.9i			0.294461i
$470$	−21923.8	−	42117.5i	−0.0992476	−	0.190663i
$471$	49932.0			0.225080
$472$	−199146.	−	199146.i	−0.893896	−	0.893896i
$473$	−7346.90	+	7346.90i	−0.0328384	+	0.0328384i
$474$			12918.9i			0.0575000i
$475$	−239801.	−	167927.i	−1.06283	−	0.744273i
$476$	14375.4			0.0634462
$477$	261403.	+	261403.i	1.14888	+	1.14888i
$478$	23319.6	−	23319.6i	0.102062	−	0.102062i
$479$			181209.i			0.789787i	0.918727	+	0.394893i	$0.129218\pi$
$479$			181209.i			0.789787i	−0.918727	+	0.394893i	$0.870782\pi$
$480$	−8315.45	+	4328.51i	−0.0360914	+	0.0187869i
$481$	−178238.			−0.770389
$482$	237135.	+	237135.i	1.02071	+	1.02071i
$483$	20143.5	−	20143.5i	0.0863456	−	0.0863456i
$484$		−	24242.0i		−	0.103485i
$485$	−14205.3	−	4479.25i	−0.0603901	−	0.0190424i
$486$	−136859.			−0.579429
$487$	38680.6	+	38680.6i	0.163093	+	0.163093i	0.783935	−	0.620842i	$-0.213209\pi$
$487$	38680.6	+	38680.6i	0.163093	+	0.163093i	−0.620842	+	0.783935i	$0.713209\pi$
$488$	−36098.5	+	36098.5i	−0.151583	+	0.151583i
$489$		−	59622.7i		−	0.249341i
$490$	−10846.5	+	34398.1i	−0.0451751	+	0.143266i
$491$	281643.			1.16825			0.584126	−	0.811663i	$-0.301437\pi$
$491$	281643.			1.16825			0.584126	+	0.811663i	$0.301437\pi$
$492$	3504.87	+	3504.87i	0.0144791	+	0.0144791i
$493$	245170.	−	245170.i	1.00873	−	1.00873i
$494$		−	446928.i		−	1.83140i
$495$	−15862.1	−	30472.5i	−0.0647367	−	0.124365i
$496$	155215.			0.630914
$497$	−32132.8	−	32132.8i	−0.130088	−	0.130088i
$498$	−6478.22	+	6478.22i	−0.0261214	+	0.0261214i
$499$			460535.i			1.84953i	0.380536	+	0.924766i	$0.375740\pi$
$499$			460535.i			1.84953i	−0.380536	+	0.924766i	$0.624260\pi$
$500$	−26205.5	−	3451.82i	−0.104822	−	0.0138073i
$501$	72904.1			0.290453
$502$	−165653.	−	165653.i	−0.657345	−	0.657345i
$503$	51536.3	−	51536.3i	0.203694	−	0.203694i	−0.597887	−	0.801580i	$-0.703993\pi$
$503$	51536.3	−	51536.3i	0.203694	−	0.203694i	0.801580	+	0.597887i	$0.203993\pi$
$504$		−	86913.0i		−	0.342155i
$505$	−206815.	+	107655.i	−0.810958	+	0.422135i
$506$	65569.3			0.256094
$507$	28154.8	+	28154.8i	0.109531	+	0.109531i
$508$	−24155.4	+	24155.4i	−0.0936025	+	0.0936025i
$509$		−	159178.i		−	0.614395i	−0.951646	−	0.307198i	$-0.900609\pi$
$509$		−	159178.i		−	0.614395i	0.951646	−	0.307198i	$-0.0993912\pi$
$510$	80013.1	+	25230.0i	0.307624	+	0.0970012i
$511$	−61526.2			−0.235623
$512$	148061.	+	148061.i	0.564808	+	0.564808i
$513$	−91557.7	+	91557.7i	−0.347904	+	0.347904i
$514$		−	318050.i		−	1.20384i
$515$	37790.6	−	119847.i	0.142485	−	0.451869i
$516$	1734.26			0.00651350
$517$	−5626.79	−	5626.79i	−0.0210513	−	0.0210513i
$518$	43279.5	−	43279.5i	0.161296	−	0.161296i
$519$		−	10034.4i		−	0.0372526i
$520$	157592.	+	302748.i	0.582811	+	1.11963i
$521$	302546.			1.11459			0.557295	−	0.830314i	$-0.311839\pi$
$521$	302546.			1.11459			0.557295	+	0.830314i	$0.311839\pi$
$522$	175247.	+	175247.i	0.643146	+	0.643146i
$523$	286177.	−	286177.i	1.04624	−	1.04624i	0.0473640	−	0.998878i	$-0.484918\pi$
$523$	286177.	−	286177.i	1.04624	−	1.04624i	0.998878	−	0.0473640i	$-0.0150821\pi$
$524$		−	15542.3i		−	0.0566048i
$525$	−11545.2	+	16486.7i	−0.0418875	+	0.0598158i
$526$	−468161.			−1.69209
$527$	−179724.	−	179724.i	−0.647121	−	0.647121i
$528$	−6071.38	+	6071.38i	−0.0217781	+	0.0217781i
$529$		−	502672.i		−	1.79628i
$530$	442202.	−	230183.i	1.57423	−	0.819449i
$531$	−364901.			−1.29416
$532$	10376.7	+	10376.7i	0.0366638	+	0.0366638i
$533$	270297.	−	270297.i	0.951450	−	0.951450i
$534$		−	25706.9i		−	0.0901502i
$535$	−179145.	−	56488.6i	−0.625889	−	0.197357i
$536$	−210475.			−0.732606
$537$	−25817.3	−	25817.3i	−0.0895288	−	0.0895288i
$538$	−248589.	+	248589.i	−0.858852	+	0.858852i
$539$			6044.56i			0.0208059i
$540$	−3515.69	+	11149.5i	−0.0120566	+	0.0382355i
$541$	−266396.			−0.910192			−0.455096	−	0.890442i	$-0.650395\pi$
$541$	−266396.			−0.910192			−0.455096	+	0.890442i	$0.650395\pi$
$542$	−96047.3	−	96047.3i	−0.326954	−	0.326954i
$543$	−28144.4	+	28144.4i	−0.0954537	+	0.0954537i
$544$			98950.7i			0.334365i
$545$	107510.	+	206536.i	0.361956	+	0.695349i
$546$	−30727.1			−0.103071
$547$	−243105.	−	243105.i	−0.812492	−	0.812492i	0.172515	−	0.985007i	$-0.444811\pi$
$547$	−243105.	−	243105.i	−0.812492	−	0.812492i	−0.985007	+	0.172515i	$0.944811\pi$
$548$	4481.71	−	4481.71i	0.0149239	−	0.0149239i
$549$			66144.5i			0.219457i
$550$	−45623.6	+	8042.56i	−0.150822	+	0.0265870i
$551$	353947.			1.16583
$552$	65457.8	+	65457.8i	0.214824	+	0.214824i
$553$	−23132.1	+	23132.1i	−0.0756425	+	0.0756425i
$554$			348908.i			1.13682i
$555$	30296.8	−	15770.7i	0.0983584	−	0.0511993i
$556$	−50639.9			−0.163811
$557$	−22586.2	−	22586.2i	−0.0728003	−	0.0728003i	0.669769	−	0.742569i	$-0.266393\pi$
$557$	−22586.2	−	22586.2i	−0.0728003	−	0.0728003i	−0.742569	+	0.669769i	$0.766393\pi$
$558$	128467.	−	128467.i	0.412593	−	0.412593i
$559$		−	133746.i		−	0.428015i
$560$	−123731.	−	39015.3i	−0.394551	−	0.124411i
$561$	14060.2			0.0446751
$562$	179716.	+	179716.i	0.569003	+	0.569003i
$563$	−422208.	+	422208.i	−1.33202	+	1.33202i	−0.428451	+	0.903565i	$0.640941\pi$
$563$	−422208.	+	422208.i	−1.33202	+	1.33202i	−0.903565	+	0.428451i	$0.859059\pi$
$564$			1328.22i			0.00417553i
$565$	−116220.	+	368573.i	−0.364069	+	1.15459i
$566$	−431652.			−1.34741
$567$	−76419.6	−	76419.6i	−0.237705	−	0.237705i
$568$	104418.	−	104418.i	0.323652	−	0.323652i
$569$		−	400419.i		−	1.23677i	−0.785874	−	0.618387i	$-0.787787\pi$
$569$		−	400419.i		−	1.23677i	0.785874	−	0.618387i	$-0.212213\pi$
$570$	39544.7	+	75968.7i	0.121713	+	0.233822i
$571$	281832.			0.864406			0.432203	−	0.901776i	$-0.357736\pi$
$571$	281832.			0.864406			0.432203	+	0.901776i	$0.357736\pi$
$572$	−4781.87	−	4781.87i	−0.0146152	−	0.0146152i
$573$	−71051.0	+	71051.0i	−0.216402	+	0.216402i
$574$			131266.i			0.398409i
$575$	95980.9	+	544478.i	0.290302	+	1.64682i
$576$	278860.			0.840507
$577$	−112269.	−	112269.i	−0.337215	−	0.337215i	0.518103	−	0.855318i	$-0.326638\pi$
$577$	−112269.	−	112269.i	−0.337215	−	0.337215i	−0.855318	+	0.518103i	$0.826638\pi$
$578$	377769.	−	377769.i	1.13076	−	1.13076i
$579$		−	25227.2i		−	0.0752509i
$580$	28346.6	−	14755.5i	0.0842645	−	0.0438629i
$581$	−23199.4			−0.0687266
$582$	3081.19	+	3081.19i	0.00909646	+	0.00909646i
$583$	59077.0	−	59077.0i	0.173813	−	0.173813i
$584$		−	199934.i		−	0.586221i
$585$	421749.	+	132987.i	1.23237	+	0.388596i
$586$	91580.5			0.266691
$587$	154399.	+	154399.i	0.448094	+	0.448094i	0.894720	−	0.446627i	$-0.147375\pi$
$587$	154399.	+	154399.i	0.448094	+	0.448094i	−0.446627	+	0.894720i	$0.647375\pi$
$588$	713.418	−	713.418i	0.00206343	−	0.00206343i
$589$		−	259465.i		−	0.747907i
$590$	−147982.	+	469302.i	−0.425113	+	1.34818i
$591$	−35878.6			−0.102721
$592$	155678.	+	155678.i	0.444205	+	0.444205i
$593$	−202843.	+	202843.i	−0.576835	+	0.576835i	−0.934030	−	0.357195i	$-0.883733\pi$
$593$	−202843.	+	202843.i	−0.576835	+	0.576835i	0.357195	+	0.934030i	$0.383733\pi$
$594$			20490.1i			0.0580726i
$595$	98092.9	+	188445.i	0.277079	+	0.532293i
$596$	−60506.1			−0.170336
$597$	−61496.0	−	61496.0i	−0.172543	−	0.172543i
$598$	−596827.	+	596827.i	−1.66896	+	1.66896i
$599$			495814.i			1.38186i	0.722921	+	0.690931i	$0.242799\pi$
$599$			495814.i			1.38186i	−0.722921	+	0.690931i	$0.757201\pi$
$600$	−53574.9	−	37517.2i	−0.148819	−	0.104214i
$601$	−552708.			−1.53020			−0.765098	−	0.643914i	$-0.777309\pi$
$601$	−552708.			−1.53020			−0.765098	+	0.643914i	$0.777309\pi$
$602$	32476.2	+	32476.2i	0.0896132	+	0.0896132i
$603$	−192830.	+	192830.i	−0.530323	+	0.530323i
$604$		−	70258.0i		−	0.192585i
$605$	317785.	−	165419.i	0.868206	−	0.451935i
$606$	68210.0			0.185739
$607$	60231.6	+	60231.6i	0.163473	+	0.163473i	0.784103	−	0.620630i	$-0.213123\pi$
$607$	60231.6	+	60231.6i	0.163473	+	0.163473i	−0.620630	+	0.784103i	$0.713123\pi$
$608$	−71426.6	+	71426.6i	−0.193220	+	0.193220i
$609$		−	24334.5i		−	0.0656126i
$610$	85068.9	+	26824.2i	0.228618	+	0.0720888i
$611$	102433.			0.274382
$612$	42797.7	+	42797.7i	0.114266	+	0.114266i
$613$	376210.	−	376210.i	1.00117	−	1.00117i	0.00117501	−	0.999999i	$-0.499626\pi$
$613$	376210.	−	376210.i	1.00117	−	1.00117i	0.999999	−	0.00117501i	$-0.000374018\pi$
$614$		−	243016.i		−	0.644610i
$615$	−22028.8	+	69861.1i	−0.0582427	+	0.184708i
$616$	−19642.3			−0.0517643
$617$	−127411.	−	127411.i	−0.334685	−	0.334685i	0.519677	−	0.854363i	$-0.326052\pi$
$617$	−127411.	−	127411.i	−0.334685	−	0.334685i	−0.854363	+	0.519677i	$0.826052\pi$
$618$	−25995.4	+	25995.4i	−0.0680643	+	0.0680643i
$619$			527739.i			1.37733i	0.725080	+	0.688665i	$0.241803\pi$
$619$			527739.i			1.37733i	−0.725080	+	0.688665i	$0.758197\pi$
$620$	−10816.7	−	20779.7i	−0.0281391	−	0.0540576i
$621$	244532.			0.634092
$622$	371756.	+	371756.i	0.960898	+	0.960898i
$623$	46029.9	−	46029.9i	0.118594	−	0.118594i
$624$		−	110526.i		−	0.283855i
$625$	−133569.	−	367079.i	−0.341936	−	0.939723i
$626$	165357.			0.421962
$627$	10149.2	+	10149.2i	0.0258165	+	0.0258165i
$628$	34349.1	−	34349.1i	0.0870956	−	0.0870956i
$629$		−	360521.i		−	0.911232i
$630$	−134700.	+	70116.7i	−0.339381	+	0.176661i
$631$	−594356.			−1.49275			−0.746376	−	0.665524i	$-0.768208\pi$
$631$	−594356.			−1.49275			−0.746376	+	0.665524i	$0.768208\pi$
$632$	−75169.7	−	75169.7i	−0.188195	−	0.188195i
$633$	45895.4	−	45895.4i	0.114541	−	0.114541i
$634$		−	498522.i		−	1.24024i
$635$	−481480.	−	151822.i	−1.19407	−	0.376519i
$636$	−13945.3			−0.0344757
$637$	−55019.0	−	55019.0i	−0.135592	−	0.135592i
$638$	39605.7	−	39605.7i	0.0973008	−	0.0973008i
$639$		−	191329.i		−	0.468574i
$640$	139030.	−	440912.i	0.339428	−	1.07644i
$641$	−720768.			−1.75420			−0.877100	−	0.480307i	$-0.840525\pi$
$641$	−720768.			−1.75420			−0.877100	+	0.480307i	$0.840525\pi$
$642$	38857.4	+	38857.4i	0.0942767	+	0.0942767i
$643$	22321.8	−	22321.8i	0.0539892	−	0.0539892i	−0.679597	−	0.733586i	$-0.737845\pi$
$643$	22321.8	−	22321.8i	0.0539892	−	0.0539892i	0.733586	+	0.679597i	$0.237845\pi$
$644$		−	27714.1i		−	0.0668235i
$645$	11834.0	+	22734.2i	0.0284455	+	0.0546462i
$646$	903999.			2.16622
$647$	61507.7	+	61507.7i	0.146934	+	0.146934i	0.776747	−	0.629813i	$-0.216869\pi$
$647$	61507.7	+	61507.7i	0.146934	+	0.146934i	−0.629813	+	0.776747i	$0.716869\pi$
$648$	248331.	−	248331.i	0.591400	−	0.591400i
$649$			82467.5i			0.195791i
$650$	342072.	−	488482.i	0.809637	−	1.15617i
$651$	−17838.6			−0.0420920
$652$	−41015.5	−	41015.5i	−0.0964835	−	0.0964835i
$653$	406395.	−	406395.i	0.953064	−	0.953064i	−0.0458828	−	0.998947i	$-0.514610\pi$
$653$	406395.	−	406395.i	0.953064	−	0.953064i	0.998947	+	0.0458828i	$0.0146101\pi$
$654$		−	68118.1i		−	0.159260i
$655$	203742.	−	106056.i	0.474896	−	0.247202i
$656$	−472169.			−1.09721
$657$	−183173.	−	183173.i	−0.424356	−	0.424356i
$658$	−24872.6	+	24872.6i	−0.0574473	+	0.0574473i
$659$			128094.i			0.294956i	0.989065	+	0.147478i	$0.0471156\pi$
$659$			128094.i			0.294956i	−0.989065	+	0.147478i	$0.952884\pi$
$660$	1235.93	+	389.716i	0.00283729	+	0.000894665i
$661$	−328592.			−0.752062			−0.376031	−	0.926607i	$-0.622711\pi$
$661$	−328592.			−0.752062			−0.376031	+	0.926607i	$0.622711\pi$
$662$	111155.	+	111155.i	0.253637	+	0.253637i
$663$	−127979.	+	127979.i	−0.291147	+	0.291147i
$664$		−	75388.3i		−	0.170989i
$665$	−65219.9	+	206835.i	−0.147481	+	0.467714i
$666$	257700.			0.580986
$667$	−472660.	−	472660.i	−1.06242	−	1.06242i
$668$	50152.0	−	50152.0i	0.112392	−	0.112392i
$669$			22363.7i			0.0499679i
$670$	169800.	+	326200.i	0.378257	+	0.726666i
$671$	14948.6			0.0332014
$672$	4910.70	+	4910.70i	0.0108744	+	0.0108744i
$673$	595757.	−	595757.i	1.31534	−	1.31534i	0.397927	−	0.917417i	$-0.369730\pi$
$673$	595757.	−	595757.i	1.31534	−	1.31534i	0.917417	−	0.397927i	$-0.130270\pi$
$674$			42645.1i			0.0938749i
$675$	−170147.	+	29993.6i	−0.373437	+	0.0658296i
$676$	38736.4			0.0847668
$677$	−249719.	−	249719.i	−0.544846	−	0.544846i	0.380099	−	0.924946i	$-0.375890\pi$
$677$	−249719.	−	249719.i	−0.544846	−	0.544846i	−0.924946	+	0.380099i	$0.875890\pi$
$678$	79945.4	−	79945.4i	0.173914	−	0.173914i
$679$			11034.2i			0.0239332i
$680$	−612367.	+	318761.i	−1.32432	+	0.689361i
$681$	75778.8			0.163401
$682$	−29033.4	−	29033.4i	−0.0624207	−	0.0624207i
$683$	−392090.	+	392090.i	−0.840512	+	0.840512i	−0.988925	−	0.148413i	$-0.952583\pi$
$683$	−392090.	+	392090.i	−0.840512	+	0.840512i	0.148413	+	0.988925i	$0.452583\pi$
$684$			61786.3i			0.132063i
$685$	89331.9	+	28168.4i	0.190382	+	0.0600318i
$686$	26719.3			0.0567776
$687$	−17184.8	−	17184.8i	−0.0364109	−	0.0364109i
$688$	−116818.	+	116818.i	−0.246793	+	0.246793i
$689$			1.07547e6i			2.26547i
$690$	48640.6	−	154256.i	0.102165	−	0.324000i
$691$	905394.			1.89619			0.948094	−	0.317990i	$-0.103008\pi$
$691$	905394.			1.89619			0.948094	+	0.317990i	$0.103008\pi$
$692$	−6902.84	−	6902.84i	−0.0144150	−	0.0144150i
$693$	−17995.6	+	17995.6i	−0.0374714	+	0.0374714i
$694$		−	57584.1i		−	0.119559i
$695$	−345550.	−	663832.i	−0.715388	−	1.37432i
$696$	79076.7			0.163241
$697$	546727.	+	546727.i	1.12540	+	1.12540i
$698$	214314.	−	214314.i	0.439885	−	0.439885i
$699$			16377.6i			0.0335194i
$700$	3399.34	+	19283.7i	0.00693743	+	0.0393545i
$701$	528653.			1.07581			0.537904	−	0.843006i	$-0.319216\pi$
$701$	528653.			1.07581			0.537904	+	0.843006i	$0.319216\pi$
$702$	−186506.	−	186506.i	−0.378458	−	0.378458i
$703$	260239.	−	260239.i	0.526576	−	0.526576i
$704$		−	63022.2i		−	0.127159i
$705$	−17411.5	+	9063.35i	−0.0350314	+	0.0182352i
$706$	−313506.			−0.628980
$707$	122135.	+	122135.i	0.244343	+	0.244343i
$708$	9733.34	−	9733.34i	0.0194176	−	0.0194176i
$709$			684824.i			1.36234i	0.732124	+	0.681172i	$0.238529\pi$
$709$			684824.i			1.36234i	−0.732124	+	0.681172i	$0.761471\pi$
$710$	−246069.	−	77591.3i	−0.488135	−	0.153921i
$711$	−137736.			−0.272463
$712$	149578.	+	149578.i	0.295058	+	0.295058i
$713$	−346488.	+	346488.i	−0.681569	+	0.681569i
$714$		−	62151.5i		−	0.121915i
$715$	30055.0	−	95314.9i	0.0587902	−	0.186444i
$716$	−35520.4			−0.0692870
$717$	−9640.36	−	9640.36i	−0.0187523	−	0.0187523i
$718$	−692122.	+	692122.i	−1.34256	+	1.34256i
$719$			485616.i			0.939367i	0.882835	+	0.469683i	$0.155632\pi$
$719$			485616.i			0.939367i	−0.882835	+	0.469683i	$0.844368\pi$
$720$	−252212.	−	484521.i	−0.486520	−	0.934648i
$721$	−93093.1			−0.179080
$722$	264943.	+	264943.i	0.508252	+	0.508252i
$723$	98031.9	−	98031.9i	0.187539	−	0.187539i
$724$			38722.1i			0.0738724i
$725$	386856.	+	270905.i	0.735992	+	0.515396i
$726$	−104809.			−0.198851
$727$	650933.	+	650933.i	1.23159	+	1.23159i	0.963351	+	0.268243i	$0.0864428\pi$
$727$	650933.	+	650933.i	1.23159	+	1.23159i	0.268243	+	0.963351i	$0.413557\pi$
$728$	178788.	−	178788.i	0.337347	−	0.337347i
$729$		−	416092.i		−	0.782950i
$730$	−309864.	+	161296.i	−0.581467	+	0.302676i
$731$	270528.			0.506265
$732$	−1764.33	−	1764.33i	−0.00329275	−	0.00329275i
$733$	34579.8	−	34579.8i	0.0643599	−	0.0643599i	−0.674194	−	0.738554i	$-0.735509\pi$
$733$	34579.8	−	34579.8i	0.0643599	−	0.0643599i	0.738554	+	0.674194i	$0.235509\pi$
$734$			262519.i			0.487268i
$735$	14220.3	+	4483.98i	0.0263228	+	0.00830021i
$736$	190766.			0.352164
$737$	43579.5	+	43579.5i	0.0802319	+	0.0802319i
$738$	−390800.	+	390800.i	−0.717533	+	0.717533i
$739$		−	206401.i		−	0.377941i	−0.981983	−	0.188970i	$-0.939485\pi$
$739$		−	206401.i		−	0.377941i	0.981983	−	0.188970i	$-0.0605150\pi$
$740$	9992.81	−	31690.7i	0.0182484	−	0.0578719i
$741$	−184761.			−0.336491
$742$	−261143.	−	261143.i	−0.474320	−	0.474320i
$743$	−601192.	+	601192.i	−1.08902	+	1.08902i	−0.0933899	+	0.995630i	$0.529770\pi$
$743$	−601192.	+	601192.i	−1.08902	+	1.08902i	−0.995630	+	0.0933899i	$0.970230\pi$
$744$		−	57968.0i		−	0.104723i
$745$	−412874.	−	793167.i	−0.743884	−	1.42907i
$746$	−540816.			−0.971788
$747$	−69068.3	−	69068.3i	−0.123776	−	0.123776i
$748$	9672.26	−	9672.26i	0.0172872	−	0.0172872i
$749$			139154.i			0.248046i
$750$	−14923.9	+	113299.i	−0.0265313	+	0.201420i
$751$	565097.			1.00194			0.500972	−	0.865463i	$-0.332976\pi$
$751$	565097.			1.00194			0.500972	+	0.865463i	$0.332976\pi$
$752$	−89467.5	−	89467.5i	−0.158208	−	0.158208i
$753$	−68481.5	+	68481.5i	−0.120777	+	0.120777i
$754$			721001.i			1.26822i
$755$	921005.	−	479418.i	1.61573	−	0.841048i
$756$	8660.54			0.0151531
$757$	−282485.	−	282485.i	−0.492951	−	0.492951i	0.416284	−	0.909235i	$-0.363332\pi$
$757$	−282485.	−	282485.i	−0.492951	−	0.492951i	−0.909235	+	0.416284i	$0.863332\pi$
$758$	−269498.	+	269498.i	−0.469048	+	0.469048i
$759$		−	27106.5i		−	0.0470532i
$760$	−672126.	−	211937.i	−1.16365	−	0.366927i
$761$	−157487.			−0.271942			−0.135971	−	0.990713i	$-0.543415\pi$
$761$	−157487.			−0.271942			−0.135971	+	0.990713i	$0.543415\pi$
$762$	104435.	+	104435.i	0.179861	+	0.179861i
$763$	121970.	−	121970.i	0.209510	−	0.209510i
$764$			97754.5i			0.167475i
$765$	−268993.	+	853068.i	−0.459640	+	1.45768i
$766$	1.06030e6			1.80705
$767$	−750638.	−	750638.i	−1.27597	−	1.27597i
$768$	−25282.6	+	25282.6i	−0.0428647	+	0.0428647i
$769$		−	801382.i		−	1.35515i	−0.735455	−	0.677574i	$-0.763031\pi$
$769$		−	801382.i		−	1.35515i	0.735455	−	0.677574i	$-0.236969\pi$
$770$	15846.3	+	30442.2i	0.0267268	+	0.0513445i
$771$	−131483.			−0.221187
$772$	−17354.2	−	17354.2i	−0.0291186	−	0.0291186i
$773$	407066.	−	407066.i	0.681249	−	0.681249i	−0.279033	−	0.960282i	$-0.590014\pi$
$773$	407066.	−	407066.i	0.681249	−	0.681249i	0.960282	+	0.279033i	$0.0900139\pi$
$774$			193373.i			0.322786i
$775$	198590.	−	283589.i	0.330639	−	0.472156i
$776$	−35856.4			−0.0595447
$777$	−17891.9	−	17891.9i	−0.0296356	−	0.0296356i
$778$	372902.	−	372902.i	0.616077	−	0.616077i
$779$			789300.i			1.30067i
$780$	−14797.0	+	7702.39i	−0.0243211	+	0.0126601i
$781$	−43240.1			−0.0708900
$782$	−1.20720e6	−	1.20720e6i	−1.97408	−	1.97408i
$783$	147704.	−	147704.i	0.240918	−	0.240918i
$784$			96110.2i			0.156364i
$785$	684666.	+	215891.i	1.11106	+	0.350345i
$786$	−67196.7			−0.108768
$787$	384677.	+	384677.i	0.621079	+	0.621079i	0.945807	−	0.324728i	$-0.105273\pi$
$787$	384677.	+	384677.i	0.621079	+	0.621079i	−0.324728	+	0.945807i	$0.605273\pi$
$788$	−24681.6	+	24681.6i	−0.0397484	+	0.0397484i
$789$			193539.i			0.310895i
$790$	−55857.4	+	177143.i	−0.0895007	+	0.283838i
$791$	286295.			0.457574
$792$	−58478.1	−	58478.1i	−0.0932272	−	0.0932272i
$793$	−136066.	+	136066.i	−0.216373	+	0.216373i
$794$		−	1.11403e6i		−	1.76708i
$795$	−95158.2	−	182807.i	−0.150561	−	0.289241i
$796$	−84608.3			−0.133533
$797$	168513.	+	168513.i	0.265287	+	0.265287i	0.827198	−	0.561911i	$-0.189933\pi$
$797$	168513.	+	168513.i	0.265287	+	0.265287i	−0.561911	+	0.827198i	$0.689933\pi$
$798$	44863.5	−	44863.5i	0.0704510	−	0.0704510i
$799$			207190.i			0.324545i
$800$	−132736.	+	23398.8i	−0.207400	+	0.0365607i
$801$	274077.			0.427176
$802$	475525.	+	475525.i	0.739307	+	0.739307i
$803$	−41397.0	+	41397.0i	−0.0642004	+	0.0642004i
$804$		−	10287.1i		−	0.0159140i
$805$	363301.	−	189112.i	0.560628	−	0.291829i
$806$	528537.			0.813590
$807$	102767.	+	102767.i	0.157801	+	0.157801i
$808$	−396886.	+	396886.i	−0.607916	+	0.607916i
$809$			154337.i			0.235816i	0.993025	+	0.117908i	$0.0376188\pi$
$809$			154337.i			0.235816i	−0.993025	+	0.117908i	$0.962381\pi$
$810$	−585212.	−	184531.i	−0.891955	−	0.281254i
$811$	196780.			0.299185			0.149592	−	0.988748i	$-0.452204\pi$
$811$	196780.			0.299185			0.149592	+	0.988748i	$0.452204\pi$
$812$	−16740.1	−	16740.1i	−0.0253890	−	0.0253890i
$813$	−39706.1	+	39706.1i	−0.0600726	+	0.0600726i
$814$		−	58240.0i		−	0.0878967i
$815$	257791.	−	817545.i	0.388108	−	1.23082i
$816$	223561.			0.335750
$817$	195278.	+	195278.i	0.292556	+	0.292556i
$818$	−295603.	+	295603.i	−0.441776	+	0.441776i
$819$		−	327600.i		−	0.488401i
$820$	32904.6	+	63212.7i	0.0489361	+	0.0940105i
$821$	−392342.			−0.582074			−0.291037	−	0.956712i	$-0.594000\pi$
$821$	−392342.			−0.582074			−0.291037	+	0.956712i	$0.594000\pi$
$822$	−19376.5	−	19376.5i	−0.0286769	−	0.0286769i
$823$	−292221.	+	292221.i	−0.431432	+	0.431432i	−0.889115	−	0.457683i	$-0.848679\pi$
$823$	−292221.	+	292221.i	−0.431432	+	0.431432i	0.457683	+	0.889115i	$0.348679\pi$
$824$		−	302513.i		−	0.445543i
$825$	3324.81	+	18860.9i	0.00488494	+	0.0277111i
$826$	364538.			0.534297
$827$	−652551.	−	652551.i	−0.954122	−	0.954122i	0.0448712	−	0.998993i	$-0.485712\pi$
$827$	−652551.	−	652551.i	−0.954122	−	0.954122i	−0.998993	+	0.0448712i	$0.985712\pi$
$828$	82509.2	−	82509.2i	0.120349	−	0.120349i
$829$		−	604523.i		−	0.879637i	−0.898087	−	0.439819i	$-0.855043\pi$
$829$		−	604523.i		−	0.879637i	0.898087	−	0.439819i	$-0.144957\pi$
$830$	−116839.	+	60819.2i	−0.169602	+	0.0882846i
$831$	144239.			0.208873
$832$	573643.	+	573643.i	0.828695	+	0.828695i
$833$	111287.	−	111287.i	0.160381	−	0.160381i
$834$			218940.i			0.314770i
$835$	999658.	+	315216.i	1.43377	+	0.452100i
$836$	13963.7			0.0199796
$837$	−108276.	−	108276.i	−0.154555	−	0.154555i
$838$	−463525.	+	463525.i	−0.660063	+	0.660063i
$839$		−	61209.4i		−	0.0869549i	−0.999054	−	0.0434775i	$-0.986156\pi$
$839$		−	61209.4i		−	0.0869549i	0.999054	−	0.0434775i	$-0.0138437\pi$
$840$	−14571.0	+	46209.8i	−0.0206506	+	0.0654901i
$841$	136281.			0.192683
$842$	−448775.	−	448775.i	−0.633001	−	0.633001i
$843$	74295.0	−	74295.0i	0.104545	−	0.104545i
$844$		−	63144.5i		−	0.0886443i
$845$	264325.	+	507791.i	0.370190	+	0.711167i
$846$	−148099.			−0.206924
$847$	−187669.	−	187669.i	−0.261592	−	0.261592i
$848$	939341.	−	939341.i	1.30627	−	1.30627i
$849$			178446.i			0.247566i
$850$	988050.	+	691906.i	1.36754	+	0.957656i
$851$	−695044.			−0.959739
$852$	5103.48	+	5103.48i	0.00703052	+	0.00703052i
$853$	−587656.	+	587656.i	−0.807654	+	0.807654i	−0.984278	−	0.176625i	$-0.943482\pi$
$853$	−587656.	+	587656.i	−0.807654	+	0.807654i	0.176625	+	0.984278i	$0.443482\pi$
$854$		−	66078.7i		−	0.0906037i
$855$	−809949.	+	421610.i	−1.10796	+	0.576738i
$856$	−452191.			−0.617127
$857$	−162064.	−	162064.i	−0.220661	−	0.220661i	0.588116	−	0.808777i	$-0.299870\pi$
$857$	−162064.	−	162064.i	−0.220661	−	0.220661i	−0.808777	+	0.588116i	$0.799870\pi$
$858$	−20674.3	+	20674.3i	−0.0280838	+	0.0280838i
$859$		−	1.21163e6i		−	1.64204i	−0.570897	−	0.821022i	$-0.693404\pi$
$859$		−	1.21163e6i		−	1.64204i	0.570897	−	0.821022i	$-0.306596\pi$
$860$	23780.1	+	7498.42i	0.0321526	+	0.0101385i
$861$	54265.7			0.0732014
$862$	−116560.	−	116560.i	−0.156868	−	0.156868i
$863$	199163.	−	199163.i	0.267416	−	0.267416i	−0.560642	−	0.828058i	$-0.689446\pi$
$863$	199163.	−	199163.i	0.267416	−	0.267416i	0.828058	+	0.560642i	$0.189446\pi$
$864$			59613.5i			0.0798577i
$865$	43385.8	−	137591.i	0.0579849	−	0.183890i
$866$	790643.			1.05425
$867$	−156171.	−	156171.i	−0.207760	−	0.207760i
$868$	−12271.5	+	12271.5i	−0.0162877	+	0.0162877i
$869$			31128.2i			0.0412207i
$870$	−63794.9	−	122556.i	−0.0842844	−	0.161918i
$871$	−793341.			−1.04574
$872$	396352.	+	396352.i	0.521252	+	0.521252i
$873$	−32850.4	+	32850.4i	−0.0431035	+	0.0431035i
$874$		−	1.74281e6i		−	2.28153i
$875$	−229592.	+	176147.i	−0.299875	+	0.230070i
$876$	9771.88			0.0127341
$877$	−67773.5	−	67773.5i	−0.0881172	−	0.0881172i	0.661674	−	0.749791i	$-0.269846\pi$
$877$	−67773.5	−	67773.5i	−0.0881172	−	0.0881172i	−0.749791	+	0.661674i	$0.769846\pi$
$878$	487282.	−	487282.i	0.632108	−	0.632108i
$879$		−	37859.6i		−	0.0490002i
$880$	−109501.	+	56999.7i	−0.141402	+	0.0736050i
$881$	623471.			0.803276			0.401638	−	0.915799i	$-0.368441\pi$
$881$	623471.			0.803276			0.401638	+	0.915799i	$0.368441\pi$
$882$	79547.5	+	79547.5i	0.102256	+	0.102256i
$883$	−660163.	+	660163.i	−0.846701	+	0.846701i	−0.989720	−	0.143019i	$-0.954319\pi$
$883$	−660163.	+	660163.i	−0.846701	+	0.846701i	0.143019	+	0.989720i	$0.454319\pi$
$884$			176078.i			0.225321i
$885$	194010.	+	61176.1i	0.247707	+	0.0781079i
$886$	−162612.			−0.207150
$887$	846037.	+	846037.i	1.07533	+	1.07533i	0.996921	+	0.0784092i	$0.0249841\pi$
$887$	846037.	+	846037.i	1.07533	+	1.07533i	0.0784092	+	0.996921i	$0.475016\pi$
$888$	58141.0	−	58141.0i	0.0737320	−	0.0737320i
$889$			373997.i			0.473222i
$890$	111149.	−	352492.i	0.140322	−	0.445009i
$891$	−102836.			−0.129535
$892$	15384.4	+	15384.4i	0.0193353	+	0.0193353i
$893$	−149558.	+	149558.i	−0.187546	+	0.187546i
$894$			261596.i			0.327308i
$895$	−242380.	−	465633.i	−0.302587	−	0.581296i
$896$	−342486.			−0.426605
$897$	246730.	+	246730.i	0.306645	+	0.306645i
$898$	−476452.	+	476452.i	−0.590836	+	0.590836i
$899$			418578.i			0.517913i
$900$	−47290.2	+	67530.9i	−0.0583830	+	0.0833715i
$901$	−2.17534e6			−2.67964
$902$	88320.5	+	88320.5i	0.108555	+	0.108555i
$903$	13425.7	−	13425.7i	0.0164650	−	0.0164650i
$904$			930339.i			1.13842i
$905$	−507604.	+	264227.i	−0.619766	+	0.322612i
$906$	−303759.			−0.370060
$907$	−67185.8	−	67185.8i	−0.0816701	−	0.0816701i	0.665092	−	0.746762i	$-0.268392\pi$
$907$	−67185.8	−	67185.8i	−0.0816701	−	0.0816701i	−0.746762	+	0.665092i	$0.768392\pi$
$908$	52129.6	−	52129.6i	0.0632285	−	0.0632285i
$909$			727228.i			0.880122i
$910$	−421329.	−	132855.i	−0.508790	−	0.160433i
$911$	−286850.			−0.345635			−0.172818	−	0.984954i	$-0.555287\pi$
$911$	−286850.			−0.345635			−0.172818	+	0.984954i	$0.555287\pi$
$912$	161375.	+	161375.i	0.194020	+	0.194020i
$913$	−15609.4	+	15609.4i	−0.0187260	+	0.0187260i
$914$			636255.i			0.761621i
$915$	11089.2	−	35167.7i	0.0132452	−	0.0420050i
$916$	−23643.5			−0.0281787
$917$	−120320.	−	120320.i	−0.143087	−	0.143087i
$918$	377244.	−	377244.i	0.447649	−	0.447649i
$919$			184400.i			0.218339i	0.994023	+	0.109169i	$0.0348191\pi$
$919$			184400.i			0.218339i	−0.994023	+	0.109169i	$0.965181\pi$
$920$	614535.	+	1.18057e6i	0.726057	+	1.39482i
$921$	−100463.			−0.118437
$922$	70833.0	+	70833.0i	0.0833247	+	0.0833247i
$923$	393582.	−	393582.i	0.461989	−	0.461989i
$924$		−	960.026i		−	0.00112445i
$925$	483617.	−	85252.3i	0.565221	−	0.0996374i
$926$	728297.			0.849350
$927$	−277153.	−	277153.i	−0.322522	−	0.322522i
$928$	115228.	−	115228.i	0.133802	−	0.133802i
$929$			223434.i			0.258891i	0.991587	+	0.129446i	$0.0413198\pi$
$929$			223434.i			0.258891i	−0.991587	+	0.129446i	$0.958680\pi$
$930$	−89840.6	+	46765.5i	−0.103874	+	0.0540704i
$931$	160662.			0.185359
$932$	11266.5	+	11266.5i	0.0129705	+	0.0129705i
$933$	153685.	−	153685.i	0.176550	−	0.176550i
$934$		−	224685.i		−	0.257562i
$935$	192793.	+	60792.1i	0.220530	+	0.0695383i
$936$	1.06456e6			1.21512
$937$	799998.	+	799998.i	0.911192	+	0.911192i	0.996366	−	0.0851740i	$-0.0271446\pi$
$937$	799998.	+	799998.i	0.911192	+	0.911192i	−0.0851740	+	0.996366i	$0.527145\pi$
$938$	192638.	−	192638.i	0.218946	−	0.218946i
$939$		−	68358.9i		−	0.0775289i
$940$	−5742.83	+	18212.5i	−0.00649936	+	0.0206117i
$941$	−1.67631e6			−1.89311			−0.946554	−	0.322545i	$-0.895462\pi$
$941$	−1.67631e6			−1.89311			−0.946554	+	0.322545i	$0.895462\pi$
$942$	−148507.	−	148507.i	−0.167358	−	0.167358i
$943$	1.05403e6	−	1.05403e6i	1.18530	−	1.18530i
$944$			1.31126e6i			1.47144i
$945$	59096.7	+	113530.i	0.0661759	+	0.127130i
$946$	43702.2			0.0488339
$947$	45066.2	+	45066.2i	0.0502517	+	0.0502517i	0.731786	−	0.681534i	$-0.238687\pi$
$947$	45066.2	+	45066.2i	0.0502517	+	0.0502517i	−0.681534	+	0.731786i	$0.738687\pi$
$948$	3673.96	−	3673.96i	0.00408806	−	0.00408806i
$949$		−	753610.i		−	0.836785i
$950$	213768.	+	1.21266e6i	0.236862	+	1.34367i
$951$	−206090.			−0.227875
$952$	361634.	+	361634.i	0.399021	+	0.399021i
$953$	148966.	−	148966.i	0.164022	−	0.164022i	−0.620324	−	0.784346i	$-0.712999\pi$
$953$	148966.	−	148966.i	0.164022	−	0.164022i	0.784346	+	0.620324i	$0.212999\pi$
$954$		−	1.55493e6i		−	1.70849i
$955$	−1.28145e6	+	667045.i	−1.40506	+	0.731389i
$956$	−13263.5			−0.0145126
$957$	−16373.1	−	16373.1i	−0.0178775	−	0.0178775i
$958$	538952.	−	538952.i	0.587245	−	0.587245i
$959$		−	69390.0i		−	0.0754501i
$960$	−148264.	−	46751.2i	−0.160877	−	0.0507283i
$961$	−616678.			−0.667747
$962$	530114.	+	530114.i	0.572821	+	0.572821i
$963$	−414283.	+	414283.i	−0.446729	+	0.446729i
$964$		−	134876.i		−	0.145138i
$965$	109075.	−	345914.i	0.117131	−	0.371462i
$966$	−119821.			−0.128404
$967$	205113.	+	205113.i	0.219352	+	0.219352i	0.808225	−	0.588874i	$-0.200428\pi$
$967$	205113.	+	205113.i	0.219352	+	0.219352i	−0.588874	+	0.808225i	$0.700428\pi$
$968$	609844.	−	609844.i	0.650830	−	0.650830i
$969$		−	373715.i		−	0.398009i
$970$	28927.0	+	55571.3i	0.0307440	+	0.0590619i
$971$	−57664.8			−0.0611606			−0.0305803	−	0.999532i	$-0.509736\pi$
$971$	−57664.8			−0.0611606			−0.0305803	+	0.999532i	$0.509736\pi$
$972$	38920.9	+	38920.9i	0.0411955	+	0.0411955i
$973$	−392027.	+	392027.i	−0.414086	+	0.414086i
$974$		−	230087.i		−	0.242535i
$975$	−201940.	−	141413.i	−0.212428	−	0.148758i
$976$	237687.			0.249520
$977$	161161.	+	161161.i	0.168838	+	0.168838i	0.786469	−	0.617630i	$-0.211907\pi$
$977$	161161.	+	161161.i	0.168838	+	0.168838i	−0.617630	+	0.786469i	$0.711907\pi$
$978$	−177329.	+	177329.i	−0.185397	+	0.185397i
$979$		−	61941.1i		−	0.0646269i
$980$	12867.0	−	6697.76i	0.0133975	−	0.00697392i
$981$	726249.			0.754653
$982$	−837662.	−	837662.i	−0.868652	−	0.868652i
$983$	392165.	−	392165.i	0.405847	−	0.405847i	−0.474441	−	0.880287i	$-0.657350\pi$
$983$	392165.	−	392165.i	0.405847	−	0.405847i	0.880287	+	0.474441i	$0.157350\pi$
$984$			176341.i			0.182122i
$985$	−491967.	−	155129.i	−0.507064	−	0.159889i
$986$	−1.45836e6			−1.50007
$987$	10282.4	+	10282.4i	0.0105550	+	0.0105550i
$988$	−127100.	+	127100.i	−0.130207	+	0.130207i
$989$		−	521548.i		−	0.533214i
$990$	−43454.1	+	137808.i	−0.0443364	+	0.140606i
$991$	988822.			1.00686			0.503432	−	0.864035i	$-0.332070\pi$
$991$	988822.			1.00686			0.503432	+	0.864035i	$0.332070\pi$
$992$	−84469.1	−	84469.1i	−0.0858370	−	0.0858370i
$993$	45951.6	−	45951.6i	0.0466018	−	0.0466018i
$994$			191138.i			0.193453i
$995$	−577340.	−	1.10912e6i	−0.583157	−	1.12030i
$996$	3684.64			0.00371430
$997$	952325.	+	952325.i	0.958064	+	0.958064i	0.999155	−	0.0410911i	$-0.0130834\pi$
$997$	952325.	+	952325.i	0.958064	+	0.958064i	−0.0410911	+	0.999155i	$0.513083\pi$
$998$	1.36972e6	−	1.36972e6i	1.37522	−	1.37522i
$999$		−	217198.i		−	0.217633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.g.a.22.4	yes	24
5.2	odd	4		175.5.g.c.43.9		24
5.3	odd	4	inner	35.5.g.a.8.4	✓	24
5.4	even	2		175.5.g.c.57.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.g.a.8.4	✓	24	5.3	odd	4	inner
35.5.g.a.22.4	yes	24	1.1	even	1	trivial
175.5.g.c.43.9		24	5.2	odd	4
175.5.g.c.57.9		24	5.4	even	2

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.97419 - 2.97419i) q^{2} +(-1.22954 + 1.22954i) q^{3} +1.69164i q^{4} +(-22.1755 + 11.5432i) q^{5} +7.31376 q^{6} +(13.0958 + 13.0958i) q^{7} +(-42.5558 + 42.5558i) q^{8} +77.9765i q^{9} +O(q^{10})\)	\(q+(-2.97419 - 2.97419i) q^{2} +(-1.22954 + 1.22954i) q^{3} +1.69164i q^{4} +(-22.1755 + 11.5432i) q^{5} +7.31376 q^{6} +(13.0958 + 13.0958i) q^{7} +(-42.5558 + 42.5558i) q^{8} +77.9765i q^{9} +(100.286 + 31.6225i) q^{10} +17.6226 q^{11} +(-2.07994 - 2.07994i) q^{12} +(-160.405 + 160.405i) q^{13} -77.8989i q^{14} +(13.0728 - 41.4585i) q^{15} +280.205 q^{16} +(-324.451 - 324.451i) q^{17} +(231.917 - 231.917i) q^{18} -468.403i q^{19} +(-19.5270 - 37.5130i) q^{20} -32.2036 q^{21} +(-52.4131 - 52.4131i) q^{22} +(-625.505 + 625.505i) q^{23} -104.648i q^{24} +(358.508 - 511.954i) q^{25} +954.152 q^{26} +(-195.468 - 195.468i) q^{27} +(-22.1534 + 22.1534i) q^{28} +755.645i q^{29} +(-162.187 + 84.4243i) q^{30} +553.934 q^{31} +(-152.489 - 152.489i) q^{32} +(-21.6677 + 21.6677i) q^{33} +1929.96i q^{34} +(-441.574 - 139.239i) q^{35} -131.908 q^{36} +(555.586 + 555.586i) q^{37} +(-1393.12 + 1393.12i) q^{38} -394.449i q^{39} +(452.467 - 1434.93i) q^{40} -1685.09 q^{41} +(95.7796 + 95.7796i) q^{42} +(-416.902 + 416.902i) q^{43} +29.8112i q^{44} +(-900.099 - 1729.17i) q^{45} +3720.74 q^{46} +(-319.293 - 319.293i) q^{47} +(-344.522 + 344.522i) q^{48} +343.000i q^{49} +(-2588.92 + 456.377i) q^{50} +797.849 q^{51} +(-271.348 - 271.348i) q^{52} +(3352.34 - 3352.34i) q^{53} +1162.72i q^{54} +(-390.791 + 203.422i) q^{55} -1114.60 q^{56} +(575.920 + 575.920i) q^{57} +(2247.43 - 2247.43i) q^{58} +4679.64i q^{59} +(70.1329 + 22.1145i) q^{60} +848.263 q^{61} +(-1647.51 - 1647.51i) q^{62} +(-1021.16 + 1021.16i) q^{63} -3576.21i q^{64} +(1705.48 - 5408.66i) q^{65} +128.888 q^{66} +(2472.93 + 2472.93i) q^{67} +(548.854 - 548.854i) q^{68} -1538.16i q^{69} +(899.203 + 1727.45i) q^{70} -2453.67 q^{71} +(-3318.35 - 3318.35i) q^{72} +(-2349.08 + 2349.08i) q^{73} -3304.84i q^{74} +(188.667 + 1070.27i) q^{75} +792.371 q^{76} +(230.782 + 230.782i) q^{77} +(-1173.17 + 1173.17i) q^{78} +1766.38i q^{79} +(-6213.69 + 3234.46i) q^{80} -5835.43 q^{81} +(5011.77 + 5011.77i) q^{82} +(-885.758 + 885.758i) q^{83} -54.4769i q^{84} +(10940.1 + 3449.66i) q^{85} +2479.89 q^{86} +(-929.094 - 929.094i) q^{87} +(-749.945 + 749.945i) q^{88} -3514.86i q^{89} +(-2465.81 + 7819.95i) q^{90} -4201.27 q^{91} +(-1058.13 - 1058.13i) q^{92} +(-681.083 + 681.083i) q^{93} +1899.28i q^{94} +(5406.88 + 10387.1i) q^{95} +374.983 q^{96} +(421.287 + 421.287i) q^{97} +(1020.15 - 1020.15i) q^{98} +1374.15i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6}+O(q^{10}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97}+O(q^{100}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6 - 112 * q^10 + 156 * q^11 - 80 * q^12 - 560 * q^13 + 896 * q^15 - 1480 * q^16 + 1320 * q^17 + 340 * q^18 + 180 * q^20 + 196 * q^21 - 2020 * q^22 + 1920 * q^23 - 676 * q^25 + 2208 * q^26 - 340 * q^27 - 5356 * q^30 - 2112 * q^31 - 1200 * q^32 - 6140 * q^33 + 3904 * q^36 + 3980 * q^37 + 9120 * q^38 + 14716 * q^40 + 6384 * q^41 + 4900 * q^42 - 12220 * q^43 - 10528 * q^45 - 8080 * q^46 - 11820 * q^47 - 4040 * q^48 + 10728 * q^50 - 5900 * q^51 + 3600 * q^52 + 24240 * q^53 + 4636 * q^55 - 10584 * q^56 + 6460 * q^57 + 6100 * q^58 - 30088 * q^60 + 440 * q^61 - 16680 * q^62 + 7840 * q^63 - 14652 * q^65 + 4832 * q^66 - 5940 * q^67 - 47040 * q^68 - 6272 * q^70 + 8928 * q^71 + 46720 * q^72 - 2500 * q^73 + 60708 * q^75 + 47816 * q^76 + 5880 * q^77 - 17940 * q^78 + 16140 * q^80 - 11360 * q^81 - 32120 * q^82 + 15120 * q^83 + 18816 * q^85 - 41208 * q^86 - 25460 * q^87 + 52920 * q^88 - 55680 * q^90 - 11172 * q^91 + 19800 * q^92 + 1460 * q^93 - 35508 * q^95 + 20568 * q^96 - 33840 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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