LMFDB - Embedded newform 175.5.g.c.43.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,5,Mod(43,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, 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("175.43");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	175.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:	$18.0897435397$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.9
Character	$\chi$	$=$	175.43
Dual form			175.5.g.c.57.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.97419 - 2.97419i) q^{2} +(1.22954 + 1.22954i) q^{3} -1.69164i q^{4} +7.31376 q^{6} +(-13.0958 + 13.0958i) q^{7} +(42.5558 + 42.5558i) q^{8} -77.9765i q^{9} +O(q^{10})$	\(q+(2.97419 - 2.97419i) q^{2} +(1.22954 + 1.22954i) q^{3} -1.69164i q^{4} +7.31376 q^{6} +(-13.0958 + 13.0958i) q^{7} +(42.5558 + 42.5558i) q^{8} -77.9765i q^{9} +17.6226 q^{11} +(2.07994 - 2.07994i) q^{12} +(160.405 + 160.405i) q^{13} +77.8989i q^{14} +280.205 q^{16} +(324.451 - 324.451i) q^{17} +(-231.917 - 231.917i) q^{18} +468.403i q^{19} -32.2036 q^{21} +(52.4131 - 52.4131i) q^{22} +(625.505 + 625.505i) q^{23} +104.648i q^{24} +954.152 q^{26} +(195.468 - 195.468i) q^{27} +(22.1534 + 22.1534i) q^{28} -755.645i q^{29} +553.934 q^{31} +(152.489 - 152.489i) q^{32} +(21.6677 + 21.6677i) q^{33} -1929.96i q^{34} -131.908 q^{36} +(-555.586 + 555.586i) q^{37} +(1393.12 + 1393.12i) q^{38} +394.449i q^{39} -1685.09 q^{41} +(-95.7796 + 95.7796i) q^{42} +(416.902 + 416.902i) q^{43} -29.8112i q^{44} +3720.74 q^{46} +(319.293 - 319.293i) q^{47} +(344.522 + 344.522i) q^{48} -343.000i q^{49} +797.849 q^{51} +(271.348 - 271.348i) q^{52} +(-3352.34 - 3352.34i) q^{53} -1162.72i q^{54} -1114.60 q^{56} +(-575.920 + 575.920i) q^{57} +(-2247.43 - 2247.43i) q^{58} -4679.64i q^{59} +848.263 q^{61} +(1647.51 - 1647.51i) q^{62} +(1021.16 + 1021.16i) q^{63} +3576.21i q^{64} +128.888 q^{66} +(-2472.93 + 2472.93i) q^{67} +(-548.854 - 548.854i) q^{68} +1538.16i q^{69} -2453.67 q^{71} +(3318.35 - 3318.35i) q^{72} +(2349.08 + 2349.08i) q^{73} +3304.84i q^{74} +792.371 q^{76} +(-230.782 + 230.782i) q^{77} +(1173.17 + 1173.17i) q^{78} -1766.38i q^{79} -5835.43 q^{81} +(-5011.77 + 5011.77i) q^{82} +(885.758 + 885.758i) q^{83} +54.4769i q^{84} +2479.89 q^{86} +(929.094 - 929.094i) q^{87} +(749.945 + 749.945i) q^{88} +3514.86i q^{89} -4201.27 q^{91} +(1058.13 - 1058.13i) q^{92} +(681.083 + 681.083i) q^{93} -1899.28i q^{94} +374.983 q^{96} +(-421.287 + 421.287i) q^{97} +(-1020.15 - 1020.15i) q^{98} -1374.15i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{3} + 72 q^{6}+O(q^{10}) $ 24 * q - 20 * q^3 + 72 * q^6	$ 24 q - 20 q^{3} + 72 q^{6} + 156 q^{11} + 80 q^{12} + 560 q^{13} - 1480 q^{16} - 1320 q^{17} - 340 q^{18} + 196 q^{21} + 2020 q^{22} - 1920 q^{23} + 2208 q^{26} + 340 q^{27} - 2112 q^{31} + 1200 q^{32} + 6140 q^{33} + 3904 q^{36} - 3980 q^{37} - 9120 q^{38} + 6384 q^{41} - 4900 q^{42} + 12220 q^{43} - 8080 q^{46} + 11820 q^{47} + 4040 q^{48} - 5900 q^{51} - 3600 q^{52} - 24240 q^{53} - 10584 q^{56} - 6460 q^{57} - 6100 q^{58} + 440 q^{61} + 16680 q^{62} - 7840 q^{63} + 4832 q^{66} + 5940 q^{67} + 47040 q^{68} + 8928 q^{71} - 46720 q^{72} + 2500 q^{73} + 47816 q^{76} - 5880 q^{77} + 17940 q^{78} - 11360 q^{81} + 32120 q^{82} - 15120 q^{83} - 41208 q^{86} + 25460 q^{87} - 52920 q^{88} - 11172 q^{91} - 19800 q^{92} - 1460 q^{93} + 20568 q^{96} + 33840 q^{97}+O(q^{100}) $ 24 * q - 20 * q^3 + 72 * q^6 + 156 * q^11 + 80 * q^12 + 560 * q^13 - 1480 * q^16 - 1320 * q^17 - 340 * q^18 + 196 * q^21 + 2020 * q^22 - 1920 * q^23 + 2208 * q^26 + 340 * q^27 - 2112 * q^31 + 1200 * q^32 + 6140 * q^33 + 3904 * q^36 - 3980 * q^37 - 9120 * q^38 + 6384 * q^41 - 4900 * q^42 + 12220 * q^43 - 8080 * q^46 + 11820 * q^47 + 4040 * q^48 - 5900 * q^51 - 3600 * q^52 - 24240 * q^53 - 10584 * q^56 - 6460 * q^57 - 6100 * q^58 + 440 * q^61 + 16680 * q^62 - 7840 * q^63 + 4832 * q^66 + 5940 * q^67 + 47040 * q^68 + 8928 * q^71 - 46720 * q^72 + 2500 * q^73 + 47816 * q^76 - 5880 * q^77 + 17940 * q^78 - 11360 * q^81 + 32120 * q^82 - 15120 * q^83 - 41208 * q^86 + 25460 * q^87 - 52920 * q^88 - 11172 * q^91 - 19800 * q^92 - 1460 * q^93 + 20568 * q^96 + 33840 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.97419	−	2.97419i	0.743548	−	0.743548i	−0.229711	−	0.973259i	$-0.573778\pi$
$2$	2.97419	−	2.97419i	0.743548	−	0.743548i	0.973259	+	0.229711i	$0.0737780\pi$
$3$	1.22954	+	1.22954i	0.136615	+	0.136615i	0.772107	−	0.635492i	$-0.219203\pi$
$3$	1.22954	+	1.22954i	0.136615	+	0.136615i	−0.635492	+	0.772107i	$0.719203\pi$
$4$		−	1.69164i		−	0.105728i
$5$		0			0
$5$		0			0
$6$	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
$10$		0			0
$11$	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	$-0.0158024\pi$
$13$	160.405	+	160.405i	0.949144	+	0.949144i	−0.0496243	+	0.998768i	$0.515802\pi$
$14$			77.8989i			0.397443i
$15$		0			0
$16$	280.205			1.09455
$17$	324.451	−	324.451i	1.12267	−	1.12267i	0.131328	−	0.991339i	$-0.458076\pi$
$17$	324.451	−	324.451i	1.12267	−	1.12267i	0.991339	−	0.131328i	$-0.0419242\pi$
$18$	−231.917	−	231.917i	−0.715793	−	0.715793i
$19$			468.403i			1.29752i	0.760995	+	0.648758i	$0.224711\pi$
$19$			468.403i			1.29752i	−0.760995	+	0.648758i	$0.775289\pi$
$20$		0			0
$21$	−32.2036			−0.0730239
$22$	52.4131	−	52.4131i	0.108291	−	0.108291i
$23$	625.505	+	625.505i	1.18243	+	1.18243i	0.979113	+	0.203315i	$0.0651717\pi$
$23$	625.505	+	625.505i	1.18243	+	1.18243i	0.203315	+	0.979113i	$0.434828\pi$
$24$			104.648i			0.181680i
$25$		0			0
$26$	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	$-0.851690\pi$
$29$		−	755.645i		−	0.898508i	0.893404	−	0.449254i	$-0.148310\pi$
$30$		0			0
$31$	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
$35$		0			0
$36$	−131.908			−0.101781
$37$	−555.586	+	555.586i	−0.405834	+	0.405834i	−0.880283	−	0.474449i	$-0.842647\pi$
$37$	−555.586	+	555.586i	−0.405834	+	0.405834i	0.474449	+	0.880283i	$0.342647\pi$
$38$	1393.12	+	1393.12i	0.964766	+	0.964766i
$39$			394.449i			0.259335i
$40$		0			0
$41$	−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	$-0.199033\pi$
$43$	416.902	+	416.902i	0.225474	+	0.225474i	−0.585325	+	0.810799i	$0.699033\pi$
$44$		−	29.8112i		−	0.0153983i
$45$		0			0
$46$	3720.74			1.75839
$47$	319.293	−	319.293i	0.144542	−	0.144542i	−0.631133	−	0.775675i	$-0.717410\pi$
$47$	319.293	−	319.293i	0.144542	−	0.144542i	0.775675	+	0.631133i	$0.217410\pi$
$48$	344.522	+	344.522i	0.149532	+	0.149532i
$49$		−	343.000i		−	0.142857i
$50$		0			0
$51$	797.849			0.306747
$52$	271.348	−	271.348i	0.100351	−	0.100351i
$53$	−3352.34	−	3352.34i	−1.19343	−	1.19343i	−0.976098	−	0.217329i	$-0.930266\pi$
$53$	−3352.34	−	3352.34i	−1.19343	−	1.19343i	−0.217329	−	0.976098i	$-0.569734\pi$
$54$		−	1162.72i		−	0.398737i
$55$		0			0
$56$	−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	$-0.765363\pi$
$59$		−	4679.64i		−	1.34434i	0.740398	−	0.672168i	$-0.234637\pi$
$60$		0			0
$61$	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
$65$		0			0
$66$	128.888			0.0295885
$67$	−2472.93	+	2472.93i	−0.550886	+	0.550886i	−0.926696	−	0.375811i	$-0.877364\pi$
$67$	−2472.93	+	2472.93i	−0.550886	+	0.550886i	0.375811	+	0.926696i	$0.377364\pi$
$68$	−548.854	−	548.854i	−0.118697	−	0.118697i
$69$			1538.16i			0.323076i
$70$		0			0
$71$	−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	$-0.149102\pi$
$73$	2349.08	+	2349.08i	0.440811	+	0.440811i	−0.451474	+	0.892284i	$0.649102\pi$
$74$			3304.84i			0.603514i
$75$		0			0
$76$	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	$-0.954803\pi$
$79$		−	1766.38i		−	0.283028i	0.989936	−	0.141514i	$-0.0451970\pi$
$80$		0			0
$81$	−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	$-0.221020\pi$
$83$	885.758	+	885.758i	0.128576	+	0.128576i	−0.639890	+	0.768466i	$0.721020\pi$
$84$			54.4769i			0.00772065i
$85$		0			0
$86$	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	$0.0712160\pi$
$89$			3514.86i			0.443740i	−0.975076	+	0.221870i	$0.928784\pi$
$90$		0			0
$91$	−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
$95$		0			0
$96$	374.983			0.0406883
$97$	−421.287	+	421.287i	−0.0447748	+	0.0447748i	−0.729140	−	0.684365i	$-0.760080\pi$
$97$	−421.287	+	421.287i	−0.0447748	+	0.0447748i	0.684365	+	0.729140i	$0.260080\pi$
$98$	−1020.15	−	1020.15i	−0.106221	−	0.106221i
$99$		−	1374.15i		−	0.140205i
$100$		0			0
$101$	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	$-0.173868\pi$
$103$	3554.31	+	3554.31i	0.335028	+	0.335028i	−0.519464	+	0.854492i	$0.673868\pi$
$104$			13652.4i			1.26224i
$105$		0			0
$106$	−19941.0			−1.77474
$107$	−5312.92	+	5312.92i	−0.464051	+	0.464051i	−0.899981	−	0.435930i	$-0.856420\pi$
$107$	−5312.92	+	5312.92i	−0.464051	+	0.464051i	0.435930	+	0.899981i	$0.356420\pi$
$108$	−330.661	−	330.661i	−0.0283489	−	0.0283489i
$109$			9313.69i			0.783915i	0.919983	+	0.391957i	$0.128202\pi$
$109$			9313.69i			0.783915i	−0.919983	+	0.391957i	$0.871798\pi$
$110$		0			0
$111$	−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	$-0.456952\pi$
$113$	−10930.8	−	10930.8i	−0.856043	−	0.856043i	−0.990869	+	0.134826i	$0.956952\pi$
$114$			3425.79i			0.263604i
$115$		0			0
$116$	−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
$120$		0			0
$121$	−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
$125$		0			0
$126$	6074.28			0.382608
$127$	−14279.3	+	14279.3i	−0.885318	+	0.885318i	−0.994069	−	0.108751i	$-0.965315\pi$
$127$	−14279.3	+	14279.3i	−0.885318	+	0.885318i	0.108751	+	0.994069i	$0.465315\pi$
$128$	13076.2	+	13076.2i	0.798106	+	0.798106i
$129$			1025.19i			0.0616064i
$130$		0			0
$131$	−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
$135$		0			0
$136$	27614.5			1.49300
$137$	2649.32	−	2649.32i	0.141154	−	0.141154i	−0.632999	−	0.774153i	$-0.718176\pi$
$137$	2649.32	−	2649.32i	0.141154	−	0.141154i	0.774153	+	0.632999i	$0.218176\pi$
$138$	4574.79	+	4574.79i	0.240222	+	0.240222i
$139$		−	29935.3i		−	1.54937i	−0.632349	−	0.774684i	$-0.717909\pi$
$139$		−	29935.3i		−	1.54937i	0.632349	−	0.774684i	$-0.282091\pi$
$140$		0			0
$141$	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
$145$		0			0
$146$	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	$-0.701874\pi$
$149$		−	35767.7i		−	1.61108i	0.592538	−	0.805542i	$-0.298126\pi$
$150$		0			0
$151$	−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
$155$		0			0
$156$	667.266			0.0274189
$157$	20305.2	−	20305.2i	0.823774	−	0.823774i	−0.162873	−	0.986647i	$-0.552076\pi$
$157$	20305.2	−	20305.2i	0.823774	−	0.823774i	0.986647	+	0.162873i	$0.0520762\pi$
$158$	−5253.55	−	5253.55i	−0.210445	−	0.210445i
$159$		−	8243.65i		−	0.326081i
$160$		0			0
$161$	−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	$-0.0267397\pi$
$163$	24246.0	+	24246.0i	0.912567	+	0.912567i	−0.0839065	+	0.996474i	$0.526740\pi$
$164$			2850.56i			0.105985i
$165$		0			0
$166$	5268.83			0.191204
$167$	29647.0	−	29647.0i	1.06303	−	1.06303i	0.0651591	−	0.997875i	$-0.479245\pi$
$167$	29647.0	−	29647.0i	1.06303	−	1.06303i	0.997875	−	0.0651591i	$-0.0207555\pi$
$168$	−1370.45	−	1370.45i	−0.0485561	−	0.0485561i
$169$			22898.7i			0.801747i
$170$		0			0
$171$	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	$-0.219265\pi$
$173$	4080.56	+	4080.56i	0.136341	+	0.136341i	−0.635642	+	0.771984i	$0.719265\pi$
$174$		−	5526.61i		−	0.182541i
$175$		0			0
$176$	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	$-0.893737\pi$
$179$		−	20997.6i		−	0.655335i	0.944793	−	0.327668i	$-0.106263\pi$
$180$		0			0
$181$	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
$185$		0			0
$186$	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
$190$		0			0
$191$	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	$-0.187612\pi$
$193$	10258.8	+	10258.8i	0.275412	+	0.275412i	−0.555863	+	0.831274i	$0.687612\pi$
$194$			2505.97i			0.0665845i
$195$		0			0
$196$	−580.233			−0.0151039
$197$	−14590.3	+	14590.3i	−0.375951	+	0.375951i	−0.869639	−	0.493688i	$-0.835649\pi$
$197$	−14590.3	+	14590.3i	−0.375951	+	0.375951i	0.493688	+	0.869639i	$0.335649\pi$
$198$	−4086.99	−	4086.99i	−0.104249	−	0.104249i
$199$		−	50015.5i		−	1.26299i	−0.775381	−	0.631493i	$-0.782442\pi$
$199$		−	50015.5i		−	1.26299i	0.775381	−	0.631493i	$-0.217558\pi$
$200$		0			0
$201$	−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
$205$		0			0
$206$	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
$210$		0			0
$211$	−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
$215$		0			0
$216$	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
$220$		0			0
$221$	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	$-0.291278\pi$
$223$	−9094.35	−	9094.35i	−0.182878	−	0.182878i	−0.792609	+	0.609731i	$0.791278\pi$
$224$			3993.94i			0.0795987i
$225$		0			0
$226$	−65020.7			−1.27302
$227$	30816.0	−	30816.0i	0.598032	−	0.598032i	−0.341757	−	0.939789i	$-0.611022\pi$
$227$	30816.0	−	30816.0i	0.598032	−	0.598032i	0.939789	+	0.341757i	$0.111022\pi$
$228$	974.250	+	974.250i	0.0187413	+	0.0187413i
$229$		−	13976.7i		−	0.266522i	−0.991081	−	0.133261i	$-0.957455\pi$
$229$		−	13976.7i		−	0.266522i	0.991081	−	0.133261i	$-0.0425448\pi$
$230$		0			0
$231$	−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	$-0.277647\pi$
$233$	−6660.07	−	6660.07i	−0.122678	−	0.122678i	−0.765780	+	0.643102i	$0.777647\pi$
$234$		−	74401.4i		−	1.35878i
$235$		0			0
$236$	−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	$-0.978137\pi$
$239$		−	7840.64i		−	0.137264i	0.997642	−	0.0686318i	$-0.0218634\pi$
$240$		0			0
$241$	−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
$245$		0			0
$246$	−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
$250$		0			0
$251$	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
$255$		0			0
$256$	20562.7			0.313762
$257$	−53468.3	+	53468.3i	−0.809525	+	0.809525i	−0.984562	−	0.175037i	$-0.943995\pi$
$257$	−53468.3	+	53468.3i	−0.809525	+	0.809525i	0.175037	+	0.984562i	$0.443995\pi$
$258$	3049.12	+	3049.12i	0.0458073	+	0.0458073i
$259$		−	14551.7i		−	0.216927i
$260$		0			0
$261$	−58922.6			−0.864969
$262$	−27326.0	+	27326.0i	−0.398083	+	0.398083i
$263$	−78703.8	−	78703.8i	−1.13785	−	1.13785i	−0.988835	−	0.149013i	$-0.952390\pi$
$263$	−78703.8	−	78703.8i	−1.13785	−	1.13785i	−0.149013	−	0.988835i	$-0.547610\pi$
$264$			1844.17i			0.0264602i
$265$		0			0
$266$	−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	$0.195986\pi$
$269$			83582.2i			1.15507i	−0.816365	+	0.577536i	$0.804014\pi$
$270$		0			0
$271$	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
$275$		0			0
$276$	2602.02			0.0341580
$277$	58656.0	−	58656.0i	0.764456	−	0.764456i	−0.212668	−	0.977124i	$-0.568215\pi$
$277$	58656.0	−	58656.0i	0.764456	−	0.764456i	0.977124	+	0.212668i	$0.0682154\pi$
$278$	−89033.5	−	89033.5i	−1.15203	−	1.15203i
$279$		−	43193.8i		−	0.554898i
$280$		0			0
$281$	−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	$-0.471351\pi$
$283$	−72566.2	−	72566.2i	−0.906070	−	0.906070i	−0.995952	+	0.0898824i	$0.971351\pi$
$284$			4150.73i			0.0514622i
$285$		0			0
$286$	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
$290$		0			0
$291$	−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	$-0.209526\pi$
$293$	15395.9	+	15395.9i	0.179336	+	0.179336i	−0.611730	+	0.791067i	$0.709526\pi$
$294$		−	2508.62i		−	0.0290229i
$295$		0			0
$296$	−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
$300$		0			0
$301$	−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
$305$		0			0
$306$	−150491.			−1.60720
$307$	−40854.0	+	40854.0i	−0.433469	+	0.433469i	−0.889807	−	0.456338i	$-0.849161\pi$
$307$	−40854.0	+	40854.0i	−0.433469	+	0.433469i	0.456338	+	0.889807i	$0.349161\pi$
$308$	390.401	+	390.401i	0.00411538	+	0.00411538i
$309$			8740.32i			0.0915399i
$310$		0			0
$311$	−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	$-0.185698\pi$
$313$	27798.6	+	27798.6i	0.283749	+	0.283749i	−0.550853	+	0.834602i	$0.685698\pi$
$314$		−	120783.i		−	1.22503i
$315$		0			0
$316$	−2988.08			−0.0299239
$317$	−83808.0	+	83808.0i	−0.834002	+	0.834002i	−0.988062	−	0.154060i	$-0.950765\pi$
$317$	−83808.0	+	83808.0i	−0.834002	+	0.834002i	0.154060	+	0.988062i	$0.450765\pi$
$318$	−24518.2	−	24518.2i	−0.242457	−	0.242457i
$319$		−	13316.5i		−	0.130860i
$320$		0			0
$321$	−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
$325$		0			0
$326$	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
$330$		0			0
$331$	−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
$335$		0			0
$336$	−9023.59			−0.0799283
$337$	7169.19	−	7169.19i	0.0631263	−	0.0631263i	−0.674839	−	0.737965i	$-0.735787\pi$
$337$	7169.19	−	7169.19i	0.0631263	−	0.0631263i	0.737965	+	0.674839i	$0.235787\pi$
$338$	68105.1	+	68105.1i	0.596138	+	0.596138i
$339$		−	26879.7i		−	0.233897i
$340$		0			0
$341$	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
$345$		0			0
$346$	24272.7			0.202753
$347$	−9680.63	+	9680.63i	−0.0803979	+	0.0803979i	−0.746162	−	0.665764i	$-0.768106\pi$
$347$	−9680.63	+	9680.63i	−0.0803979	+	0.0803979i	0.665764	+	0.746162i	$0.268106\pi$
$348$	−1571.69	−	1571.69i	−0.0129781	−	0.0129781i
$349$		−	72057.7i		−	0.591602i	−0.955250	−	0.295801i	$-0.904413\pi$
$349$		−	72057.7i		−	0.591602i	0.955250	−	0.295801i	$-0.0955866\pi$
$350$		0			0
$351$	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	$-0.346679\pi$
$353$	−52704.4	−	52704.4i	−0.422958	−	0.422958i	−0.886221	+	0.463263i	$0.846679\pi$
$354$		−	34225.7i		−	0.273115i
$355$		0			0
$356$	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	$0.358497\pi$
$359$			232709.i			1.80561i	−0.430046	+	0.902807i	$0.641503\pi$
$360$		0			0
$361$	−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
$365$		0			0
$366$	6203.99			0.0463137
$367$	44132.8	−	44132.8i	0.327664	−	0.327664i	−0.524033	−	0.851698i	$-0.675573\pi$
$367$	44132.8	−	44132.8i	0.327664	−	0.327664i	0.851698	+	0.524033i	$0.175573\pi$
$368$	175269.	+	175269.i	1.29423	+	1.29423i
$369$			131397.i			0.965012i
$370$		0			0
$371$	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	$-0.402897\pi$
$373$	−90918.1	−	90918.1i	−0.653480	−	0.653480i	−0.953829	+	0.300349i	$0.902897\pi$
$374$		−	34010.9i		−	0.243151i
$375$		0			0
$376$	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	$0.102143\pi$
$379$			90612.2i			0.630824i	−0.948955	+	0.315412i	$0.897857\pi$
$380$		0			0
$381$	−35113.8			−0.241896
$382$	171869.	−	171869.i	1.17780	−	1.17780i
$383$	178249.	+	178249.i	1.21515	+	1.21515i	0.969310	+	0.245840i	$0.0790639\pi$
$383$	178249.	+	178249.i	1.21515	+	1.21515i	0.245840	+	0.969310i	$0.420936\pi$
$384$			32155.3i			0.218067i
$385$		0			0
$386$	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	$-0.864033\pi$
$389$		−	125379.i		−	0.828564i	0.910149	−	0.414282i	$-0.135967\pi$
$390$		0			0
$391$	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
$395$		0			0
$396$	−2324.57			−0.0148235
$397$	−187283.	+	187283.i	−1.18828	+	1.18828i	−0.210735	+	0.977543i	$0.567586\pi$
$397$	−187283.	+	187283.i	−1.18828	+	1.18828i	−0.977543	+	0.210735i	$0.932414\pi$
$398$	−148756.	−	148756.i	−0.939091	−	0.939091i
$399$		−	15084.3i		−	0.0947498i
$400$		0			0
$401$	−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
$405$		0			0
$406$	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	$0.0960105\pi$
$409$			99389.4i			0.594146i	−0.954855	+	0.297073i	$0.903989\pi$
$410$		0			0
$411$	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
$415$		0			0
$416$	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	$0.146391\pi$
$419$			155849.i			0.887721i	−0.896096	+	0.443860i	$0.853609\pi$
$420$		0			0
$421$	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
$425$		0			0
$426$	−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
$430$		0			0
$431$	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	$-0.0828584\pi$
$433$	132917.	+	132917.i	0.708933	+	0.708933i	−0.257378	+	0.966311i	$0.582858\pi$
$434$			43150.8i			0.229092i
$435$		0			0
$436$	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	$-0.860252\pi$
$439$		−	163837.i		−	0.850124i	0.905164	−	0.425062i	$-0.139748\pi$
$440$		0			0
$441$	−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	$-0.281404\pi$
$443$	−27337.1	−	27337.1i	−0.139298	−	0.139298i	−0.773317	+	0.634019i	$0.781404\pi$
$444$			2311.17i			0.0117237i
$445$		0			0
$446$	−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	$0.130056\pi$
$449$			160196.i			0.794617i	−0.917685	+	0.397308i	$0.869944\pi$
$450$		0			0
$451$	−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
$455$		0			0
$456$	−49017.5			−0.235733
$457$	106963.	−	106963.i	0.512153	−	0.512153i	−0.403033	−	0.915186i	$-0.632044\pi$
$457$	106963.	−	106963.i	0.512153	−	0.512153i	0.915186	+	0.403033i	$0.132044\pi$
$458$	−41569.3	−	41569.3i	−0.198172	−	0.198172i
$459$		−	126839.i		−	0.602044i
$460$		0			0
$461$	−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	$-0.117668\pi$
$463$	122436.	+	122436.i	0.571147	+	0.571147i	−0.361302	+	0.932449i	$0.617668\pi$
$464$		−	211735.i		−	0.983462i
$465$		0			0
$466$	−39616.7			−0.182434
$467$	−37772.5	+	37772.5i	−0.173198	+	0.173198i	−0.788383	−	0.615185i	$-0.789081\pi$
$467$	−37772.5	+	37772.5i	−0.173198	+	0.173198i	0.615185	+	0.788383i	$0.289081\pi$
$468$	−21158.8	−	21158.8i	−0.0966048	−	0.0966048i
$469$		−	64769.9i		−	0.294461i
$470$		0			0
$471$	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
$475$		0			0
$476$	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	$-0.870782\pi$
$479$		−	181209.i		−	0.789787i	0.918727	−	0.394893i	$-0.129218\pi$
$480$		0			0
$481$	−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
$485$		0			0
$486$	−136859.			−0.579429
$487$	−38680.6	+	38680.6i	−0.163093	+	0.163093i	−0.783935	−	0.620842i	$-0.786791\pi$
$487$	−38680.6	+	38680.6i	−0.163093	+	0.163093i	0.620842	+	0.783935i	$0.286791\pi$
$488$	36098.5	+	36098.5i	0.151583	+	0.151583i
$489$			59622.7i			0.249341i
$490$		0			0
$491$	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
$495$		0			0
$496$	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	$-0.624260\pi$
$499$		−	460535.i		−	1.84953i	0.380536	−	0.924766i	$-0.375740\pi$
$500$		0			0
$501$	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	$-0.296007\pi$
$503$	−51536.3	−	51536.3i	−0.203694	−	0.203694i	−0.801580	+	0.597887i	$0.796007\pi$
$504$			86913.0i			0.342155i
$505$		0			0
$506$	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	$0.0993912\pi$
$509$			159178.i			0.614395i	−0.951646	+	0.307198i	$0.900609\pi$
$510$		0			0
$511$	−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
$515$		0			0
$516$	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
$520$		0			0
$521$	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	−0.998878	−	0.0473640i	$-0.984918\pi$
$523$	−286177.	−	286177.i	−1.04624	−	1.04624i	−0.0473640	−	0.998878i	$-0.515082\pi$
$524$			15542.3i			0.0566048i
$525$		0			0
$526$	−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
$530$		0			0
$531$	−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
$535$		0			0
$536$	−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
$540$		0			0
$541$	−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
$545$		0			0
$546$	−30727.1			−0.103071
$547$	243105.	−	243105.i	0.812492	−	0.812492i	−0.172515	−	0.985007i	$-0.555189\pi$
$547$	243105.	−	243105.i	0.812492	−	0.812492i	0.985007	+	0.172515i	$0.0551892\pi$
$548$	−4481.71	−	4481.71i	−0.0149239	−	0.0149239i
$549$		−	66144.5i		−	0.219457i
$550$		0			0
$551$	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
$555$		0			0
$556$	−50639.9			−0.163811
$557$	22586.2	−	22586.2i	0.0728003	−	0.0728003i	−0.669769	−	0.742569i	$-0.733607\pi$
$557$	22586.2	−	22586.2i	0.0728003	−	0.0728003i	0.742569	+	0.669769i	$0.233607\pi$
$558$	−128467.	−	128467.i	−0.412593	−	0.412593i
$559$			133746.i			0.428015i
$560$		0			0
$561$	14060.2			0.0446751
$562$	−179716.	+	179716.i	−0.569003	+	0.569003i
$563$	422208.	+	422208.i	1.33202	+	1.33202i	0.903565	+	0.428451i	$0.140941\pi$
$563$	422208.	+	422208.i	1.33202	+	1.33202i	0.428451	+	0.903565i	$0.359059\pi$
$564$		−	1328.22i		−	0.00417553i
$565$		0			0
$566$	−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	$0.212213\pi$
$569$			400419.i			1.23677i	−0.785874	+	0.618387i	$0.787787\pi$
$570$		0			0
$571$	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
$575$		0			0
$576$	278860.			0.840507
$577$	112269.	−	112269.i	0.337215	−	0.337215i	−0.518103	−	0.855318i	$-0.673362\pi$
$577$	112269.	−	112269.i	0.337215	−	0.337215i	0.855318	+	0.518103i	$0.173362\pi$
$578$	−377769.	−	377769.i	−1.13076	−	1.13076i
$579$			25227.2i			0.0752509i
$580$		0			0
$581$	−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
$585$		0			0
$586$	91580.5			0.266691
$587$	−154399.	+	154399.i	−0.448094	+	0.448094i	−0.894720	−	0.446627i	$-0.852625\pi$
$587$	−154399.	+	154399.i	−0.448094	+	0.448094i	0.446627	+	0.894720i	$0.352625\pi$
$588$	−713.418	−	713.418i	−0.00206343	−	0.00206343i
$589$			259465.i			0.747907i
$590$		0			0
$591$	−35878.6			−0.102721
$592$	−155678.	+	155678.i	−0.444205	+	0.444205i
$593$	202843.	+	202843.i	0.576835	+	0.576835i	0.934030	−	0.357195i	$-0.116267\pi$
$593$	202843.	+	202843.i	0.576835	+	0.576835i	−0.357195	+	0.934030i	$0.616267\pi$
$594$		−	20490.1i		−	0.0580726i
$595$		0			0
$596$	−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	$-0.757201\pi$
$599$		−	495814.i		−	1.38186i	0.722921	−	0.690931i	$-0.242799\pi$
$600$		0			0
$601$	−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
$605$		0			0
$606$	68210.0			0.185739
$607$	−60231.6	+	60231.6i	−0.163473	+	0.163473i	−0.784103	−	0.620630i	$-0.786877\pi$
$607$	−60231.6	+	60231.6i	−0.163473	+	0.163473i	0.620630	+	0.784103i	$0.286877\pi$
$608$	71426.6	+	71426.6i	0.193220	+	0.193220i
$609$			24334.5i			0.0656126i
$610$		0			0
$611$	102433.			0.274382
$612$	−42797.7	+	42797.7i	−0.114266	+	0.114266i
$613$	−376210.	−	376210.i	−1.00117	−	1.00117i	−0.999999	−	0.00117501i	$-0.999626\pi$
$613$	−376210.	−	376210.i	−1.00117	−	1.00117i	−0.00117501	−	0.999999i	$-0.500374\pi$
$614$			243016.i			0.644610i
$615$		0			0
$616$	−19642.3			−0.0517643
$617$	127411.	−	127411.i	0.334685	−	0.334685i	−0.519677	−	0.854363i	$-0.673948\pi$
$617$	127411.	−	127411.i	0.334685	−	0.334685i	0.854363	+	0.519677i	$0.173948\pi$
$618$	25995.4	+	25995.4i	0.0680643	+	0.0680643i
$619$		−	527739.i		−	1.37733i	−0.725080	−	0.688665i	$-0.758197\pi$
$619$		−	527739.i		−	1.37733i	0.725080	−	0.688665i	$-0.241803\pi$
$620$		0			0
$621$	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
$625$		0			0
$626$	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
$630$		0			0
$631$	−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
$635$		0			0
$636$	−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
$640$		0			0
$641$	−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	$-0.262155\pi$
$643$	−22321.8	−	22321.8i	−0.0539892	−	0.0539892i	−0.733586	+	0.679597i	$0.762155\pi$
$644$			27714.1i			0.0668235i
$645$		0			0
$646$	903999.			2.16622
$647$	−61507.7	+	61507.7i	−0.146934	+	0.146934i	−0.776747	−	0.629813i	$-0.783131\pi$
$647$	−61507.7	+	61507.7i	−0.146934	+	0.146934i	0.629813	+	0.776747i	$0.283131\pi$
$648$	−248331.	−	248331.i	−0.591400	−	0.591400i
$649$		−	82467.5i		−	0.195791i
$650$		0			0
$651$	−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	$-0.485390\pi$
$653$	−406395.	−	406395.i	−0.953064	−	0.953064i	−0.998947	+	0.0458828i	$0.985390\pi$
$654$			68118.1i			0.159260i
$655$		0			0
$656$	−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	$-0.952884\pi$
$659$		−	128094.i		−	0.294956i	0.989065	−	0.147478i	$-0.0471156\pi$
$660$		0			0
$661$	−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
$665$		0			0
$666$	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
$670$		0			0
$671$	14948.6			0.0332014
$672$	−4910.70	+	4910.70i	−0.0108744	+	0.0108744i
$673$	−595757.	−	595757.i	−1.31534	−	1.31534i	−0.917417	−	0.397927i	$-0.869730\pi$
$673$	−595757.	−	595757.i	−1.31534	−	1.31534i	−0.397927	−	0.917417i	$-0.630270\pi$
$674$		−	42645.1i		−	0.0938749i
$675$		0			0
$676$	38736.4			0.0847668
$677$	249719.	−	249719.i	0.544846	−	0.544846i	−0.380099	−	0.924946i	$-0.624110\pi$
$677$	249719.	−	249719.i	0.544846	−	0.544846i	0.924946	+	0.380099i	$0.124110\pi$
$678$	−79945.4	−	79945.4i	−0.173914	−	0.173914i
$679$		−	11034.2i		−	0.0239332i
$680$		0			0
$681$	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	$-0.0474166\pi$
$683$	392090.	+	392090.i	0.840512	+	0.840512i	−0.148413	+	0.988925i	$0.547417\pi$
$684$		−	61786.3i		−	0.132063i
$685$		0			0
$686$	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
$690$		0			0
$691$	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
$695$		0			0
$696$	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
$700$		0			0
$701$	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
$705$		0			0
$706$	−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	$-0.761471\pi$
$709$		−	684824.i		−	1.36234i	0.732124	−	0.681172i	$-0.238529\pi$
$710$		0			0
$711$	−137736.			−0.272463
$712$	−149578.	+	149578.i	−0.295058	+	0.295058i
$713$	346488.	+	346488.i	0.681569	+	0.681569i
$714$			62151.5i			0.121915i
$715$		0			0
$716$	−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	$-0.844368\pi$
$719$		−	485616.i		−	0.939367i	0.882835	−	0.469683i	$-0.155632\pi$
$720$		0			0
$721$	−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
$725$		0			0
$726$	−104809.			−0.198851
$727$	−650933.	+	650933.i	−1.23159	+	1.23159i	−0.268243	+	0.963351i	$0.586443\pi$
$727$	−650933.	+	650933.i	−1.23159	+	1.23159i	−0.963351	+	0.268243i	$0.913557\pi$
$728$	−178788.	−	178788.i	−0.337347	−	0.337347i
$729$			416092.i			0.782950i
$730$		0			0
$731$	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	$-0.264491\pi$
$733$	−34579.8	−	34579.8i	−0.0643599	−	0.0643599i	−0.738554	+	0.674194i	$0.764491\pi$
$734$		−	262519.i		−	0.487268i
$735$		0			0
$736$	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	$0.0605150\pi$
$739$			206401.i			0.377941i	−0.981983	+	0.188970i	$0.939485\pi$
$740$		0			0
$741$	−184761.			−0.336491
$742$	261143.	−	261143.i	0.474320	−	0.474320i
$743$	601192.	+	601192.i	1.08902	+	1.08902i	0.995630	+	0.0933899i	$0.0297703\pi$
$743$	601192.	+	601192.i	1.08902	+	1.08902i	0.0933899	+	0.995630i	$0.470230\pi$
$744$			57968.0i			0.104723i
$745$		0			0
$746$	−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
$750$		0			0
$751$	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
$755$		0			0
$756$	8660.54			0.0151531
$757$	282485.	−	282485.i	0.492951	−	0.492951i	−0.416284	−	0.909235i	$-0.636668\pi$
$757$	282485.	−	282485.i	0.492951	−	0.492951i	0.909235	+	0.416284i	$0.136668\pi$
$758$	269498.	+	269498.i	0.469048	+	0.469048i
$759$			27106.5i			0.0470532i
$760$		0			0
$761$	−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
$765$		0			0
$766$	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	$0.236969\pi$
$769$			801382.i			1.35515i	−0.735455	+	0.677574i	$0.763031\pi$
$770$		0			0
$771$	−131483.			−0.221187
$772$	17354.2	−	17354.2i	0.0291186	−	0.0291186i
$773$	−407066.	−	407066.i	−0.681249	−	0.681249i	0.279033	−	0.960282i	$-0.409986\pi$
$773$	−407066.	−	407066.i	−0.681249	−	0.681249i	−0.960282	+	0.279033i	$0.909986\pi$
$774$		−	193373.i		−	0.322786i
$775$		0			0
$776$	−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
$780$		0			0
$781$	−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
$785$		0			0
$786$	−67196.7			−0.108768
$787$	−384677.	+	384677.i	−0.621079	+	0.621079i	−0.945807	−	0.324728i	$-0.894727\pi$
$787$	−384677.	+	384677.i	−0.621079	+	0.621079i	0.324728	+	0.945807i	$0.394727\pi$
$788$	24681.6	+	24681.6i	0.0397484	+	0.0397484i
$789$		−	193539.i		−	0.310895i
$790$		0			0
$791$	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
$795$		0			0
$796$	−84608.3			−0.133533
$797$	−168513.	+	168513.i	−0.265287	+	0.265287i	−0.827198	−	0.561911i	$-0.810067\pi$
$797$	−168513.	+	168513.i	−0.265287	+	0.265287i	0.561911	+	0.827198i	$0.310067\pi$
$798$	−44863.5	−	44863.5i	−0.0704510	−	0.0704510i
$799$		−	207190.i		−	0.324545i
$800$		0			0
$801$	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
$805$		0			0
$806$	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	$-0.962381\pi$
$809$		−	154337.i		−	0.235816i	0.993025	−	0.117908i	$-0.0376188\pi$
$810$		0			0
$811$	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
$815$		0			0
$816$	223561.			0.335750
$817$	−195278.	+	195278.i	−0.292556	+	0.292556i
$818$	295603.	+	295603.i	0.441776	+	0.441776i
$819$			327600.i			0.488401i
$820$		0			0
$821$	−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	$-0.151321\pi$
$823$	292221.	+	292221.i	0.431432	+	0.431432i	−0.457683	+	0.889115i	$0.651321\pi$
$824$			302513.i			0.445543i
$825$		0			0
$826$	364538.			0.534297
$827$	652551.	−	652551.i	0.954122	−	0.954122i	−0.0448712	−	0.998993i	$-0.514288\pi$
$827$	652551.	−	652551.i	0.954122	−	0.954122i	0.998993	+	0.0448712i	$0.0142878\pi$
$828$	−82509.2	−	82509.2i	−0.120349	−	0.120349i
$829$			604523.i			0.879637i	0.898087	+	0.439819i	$0.144957\pi$
$829$			604523.i			0.879637i	−0.898087	+	0.439819i	$0.855043\pi$
$830$		0			0
$831$	144239.			0.208873
$832$	−573643.	+	573643.i	−0.828695	+	0.828695i
$833$	−111287.	−	111287.i	−0.160381	−	0.160381i
$834$		−	218940.i		−	0.314770i
$835$		0			0
$836$	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	$0.0138437\pi$
$839$			61209.4i			0.0869549i	−0.999054	+	0.0434775i	$0.986156\pi$
$840$		0			0
$841$	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
$845$		0			0
$846$	−148099.			−0.206924
$847$	187669.	−	187669.i	0.261592	−	0.261592i
$848$	−939341.	−	939341.i	−1.30627	−	1.30627i
$849$		−	178446.i		−	0.247566i
$850$		0			0
$851$	−695044.			−0.959739
$852$	−5103.48	+	5103.48i	−0.00703052	+	0.00703052i
$853$	587656.	+	587656.i	0.807654	+	0.807654i	0.984278	−	0.176625i	$-0.0565178\pi$
$853$	587656.	+	587656.i	0.807654	+	0.807654i	−0.176625	+	0.984278i	$0.556518\pi$
$854$			66078.7i			0.0906037i
$855$		0			0
$856$	−452191.			−0.617127
$857$	162064.	−	162064.i	0.220661	−	0.220661i	−0.588116	−	0.808777i	$-0.700130\pi$
$857$	162064.	−	162064.i	0.220661	−	0.220661i	0.808777	+	0.588116i	$0.200130\pi$
$858$	20674.3	+	20674.3i	0.0280838	+	0.0280838i
$859$			1.21163e6i			1.64204i	0.570897	+	0.821022i	$0.306596\pi$
$859$			1.21163e6i			1.64204i	−0.570897	+	0.821022i	$0.693404\pi$
$860$		0			0
$861$	54265.7			0.0732014
$862$	116560.	−	116560.i	0.156868	−	0.156868i
$863$	−199163.	−	199163.i	−0.267416	−	0.267416i	0.560642	−	0.828058i	$-0.310554\pi$
$863$	−199163.	−	199163.i	−0.267416	−	0.267416i	−0.828058	+	0.560642i	$0.810554\pi$
$864$		−	59613.5i		−	0.0798577i
$865$		0			0
$866$	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
$870$		0			0
$871$	−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
$875$		0			0
$876$	9771.88			0.0127341
$877$	67773.5	−	67773.5i	0.0881172	−	0.0881172i	−0.661674	−	0.749791i	$-0.730154\pi$
$877$	67773.5	−	67773.5i	0.0881172	−	0.0881172i	0.749791	+	0.661674i	$0.230154\pi$
$878$	−487282.	−	487282.i	−0.632108	−	0.632108i
$879$			37859.6i			0.0490002i
$880$		0			0
$881$	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	$-0.0456811\pi$
$883$	660163.	+	660163.i	0.846701	+	0.846701i	−0.143019	+	0.989720i	$0.545681\pi$
$884$		−	176078.i		−	0.225321i
$885$		0			0
$886$	−162612.			−0.207150
$887$	−846037.	+	846037.i	−1.07533	+	1.07533i	−0.0784092	+	0.996921i	$0.524984\pi$
$887$	−846037.	+	846037.i	−1.07533	+	1.07533i	−0.996921	+	0.0784092i	$0.975016\pi$
$888$	−58141.0	−	58141.0i	−0.0737320	−	0.0737320i
$889$		−	373997.i		−	0.473222i
$890$		0			0
$891$	−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
$895$		0			0
$896$	−342486.			−0.426605
$897$	−246730.	+	246730.i	−0.306645	+	0.306645i
$898$	476452.	+	476452.i	0.590836	+	0.590836i
$899$		−	418578.i		−	0.517913i
$900$		0			0
$901$	−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
$905$		0			0
$906$	−303759.			−0.370060
$907$	67185.8	−	67185.8i	0.0816701	−	0.0816701i	−0.665092	−	0.746762i	$-0.731608\pi$
$907$	67185.8	−	67185.8i	0.0816701	−	0.0816701i	0.746762	+	0.665092i	$0.231608\pi$
$908$	−52129.6	−	52129.6i	−0.0632285	−	0.0632285i
$909$		−	727228.i		−	0.880122i
$910$		0			0
$911$	−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
$915$		0			0
$916$	−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	$-0.965181\pi$
$919$		−	184400.i		−	0.218339i	0.994023	−	0.109169i	$-0.0348191\pi$
$920$		0			0
$921$	−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
$925$		0			0
$926$	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	$-0.958680\pi$
$929$		−	223434.i		−	0.258891i	0.991587	−	0.129446i	$-0.0413198\pi$
$930$		0			0
$931$	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
$935$		0			0
$936$	1.06456e6			1.21512
$937$	−799998.	+	799998.i	−0.911192	+	0.911192i	−0.996366	−	0.0851740i	$-0.972855\pi$
$937$	−799998.	+	799998.i	−0.911192	+	0.911192i	0.0851740	+	0.996366i	$0.472855\pi$
$938$	−192638.	−	192638.i	−0.218946	−	0.218946i
$939$			68358.9i			0.0775289i
$940$		0			0
$941$	−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
$945$		0			0
$946$	43702.2			0.0488339
$947$	−45066.2	+	45066.2i	−0.0502517	+	0.0502517i	−0.731786	−	0.681534i	$-0.761313\pi$
$947$	−45066.2	+	45066.2i	−0.0502517	+	0.0502517i	0.681534	+	0.731786i	$0.261313\pi$
$948$	−3673.96	−	3673.96i	−0.00408806	−	0.00408806i
$949$			753610.i			0.836785i
$950$		0			0
$951$	−206090.			−0.227875
$952$	−361634.	+	361634.i	−0.399021	+	0.399021i
$953$	−148966.	−	148966.i	−0.164022	−	0.164022i	0.620324	−	0.784346i	$-0.287001\pi$
$953$	−148966.	−	148966.i	−0.164022	−	0.164022i	−0.784346	+	0.620324i	$0.787001\pi$
$954$			1.55493e6i			1.70849i
$955$		0			0
$956$	−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
$960$		0			0
$961$	−616678.			−0.667747
$962$	−530114.	+	530114.i	−0.572821	+	0.572821i
$963$	414283.	+	414283.i	0.446729	+	0.446729i
$964$			134876.i			0.145138i
$965$		0			0
$966$	−119821.			−0.128404
$967$	−205113.	+	205113.i	−0.219352	+	0.219352i	−0.808225	−	0.588874i	$-0.799572\pi$
$967$	−205113.	+	205113.i	−0.219352	+	0.219352i	0.588874	+	0.808225i	$0.299572\pi$
$968$	−609844.	−	609844.i	−0.650830	−	0.650830i
$969$			373715.i			0.398009i
$970$		0			0
$971$	−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
$975$		0			0
$976$	237687.			0.249520
$977$	−161161.	+	161161.i	−0.168838	+	0.168838i	−0.786469	−	0.617630i	$-0.788093\pi$
$977$	−161161.	+	161161.i	−0.168838	+	0.168838i	0.617630	+	0.786469i	$0.288093\pi$
$978$	177329.	+	177329.i	0.185397	+	0.185397i
$979$			61941.1i			0.0646269i
$980$		0			0
$981$	726249.			0.754653
$982$	837662.	−	837662.i	0.868652	−	0.868652i
$983$	−392165.	−	392165.i	−0.405847	−	0.405847i	0.474441	−	0.880287i	$-0.342650\pi$
$983$	−392165.	−	392165.i	−0.405847	−	0.405847i	−0.880287	+	0.474441i	$0.842650\pi$
$984$		−	176341.i		−	0.182122i
$985$		0			0
$986$	−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
$990$		0			0
$991$	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
$995$		0			0
$996$	3684.64			0.00371430
$997$	−952325.	+	952325.i	−0.958064	+	0.958064i	−0.999155	−	0.0410911i	$-0.986917\pi$
$997$	−952325.	+	952325.i	−0.958064	+	0.958064i	0.0410911	+	0.999155i	$0.486917\pi$
$998$	−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	175.5.g.c.43.9		24
5.2	odd	4	inner	175.5.g.c.57.9		24
5.3	odd	4		35.5.g.a.22.4	yes	24
5.4	even	2		35.5.g.a.8.4	✓	24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	175.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.97419 - 2.97419i) q^{2} +(1.22954 + 1.22954i) q^{3} -1.69164i q^{4} +7.31376 q^{6} +(-13.0958 + 13.0958i) q^{7} +(42.5558 + 42.5558i) q^{8} -77.9765i q^{9} +O(q^{10})\)	\(q+(2.97419 - 2.97419i) q^{2} +(1.22954 + 1.22954i) q^{3} -1.69164i q^{4} +7.31376 q^{6} +(-13.0958 + 13.0958i) q^{7} +(42.5558 + 42.5558i) q^{8} -77.9765i q^{9} +17.6226 q^{11} +(2.07994 - 2.07994i) q^{12} +(160.405 + 160.405i) q^{13} +77.8989i q^{14} +280.205 q^{16} +(324.451 - 324.451i) q^{17} +(-231.917 - 231.917i) q^{18} +468.403i q^{19} -32.2036 q^{21} +(52.4131 - 52.4131i) q^{22} +(625.505 + 625.505i) q^{23} +104.648i q^{24} +954.152 q^{26} +(195.468 - 195.468i) q^{27} +(22.1534 + 22.1534i) q^{28} -755.645i q^{29} +553.934 q^{31} +(152.489 - 152.489i) q^{32} +(21.6677 + 21.6677i) q^{33} -1929.96i q^{34} -131.908 q^{36} +(-555.586 + 555.586i) q^{37} +(1393.12 + 1393.12i) q^{38} +394.449i q^{39} -1685.09 q^{41} +(-95.7796 + 95.7796i) q^{42} +(416.902 + 416.902i) q^{43} -29.8112i q^{44} +3720.74 q^{46} +(319.293 - 319.293i) q^{47} +(344.522 + 344.522i) q^{48} -343.000i q^{49} +797.849 q^{51} +(271.348 - 271.348i) q^{52} +(-3352.34 - 3352.34i) q^{53} -1162.72i q^{54} -1114.60 q^{56} +(-575.920 + 575.920i) q^{57} +(-2247.43 - 2247.43i) q^{58} -4679.64i q^{59} +848.263 q^{61} +(1647.51 - 1647.51i) q^{62} +(1021.16 + 1021.16i) q^{63} +3576.21i q^{64} +128.888 q^{66} +(-2472.93 + 2472.93i) q^{67} +(-548.854 - 548.854i) q^{68} +1538.16i q^{69} -2453.67 q^{71} +(3318.35 - 3318.35i) q^{72} +(2349.08 + 2349.08i) q^{73} +3304.84i q^{74} +792.371 q^{76} +(-230.782 + 230.782i) q^{77} +(1173.17 + 1173.17i) q^{78} -1766.38i q^{79} -5835.43 q^{81} +(-5011.77 + 5011.77i) q^{82} +(885.758 + 885.758i) q^{83} +54.4769i q^{84} +2479.89 q^{86} +(929.094 - 929.094i) q^{87} +(749.945 + 749.945i) q^{88} +3514.86i q^{89} -4201.27 q^{91} +(1058.13 - 1058.13i) q^{92} +(681.083 + 681.083i) q^{93} -1899.28i q^{94} +374.983 q^{96} +(-421.287 + 421.287i) q^{97} +(-1020.15 - 1020.15i) q^{98} -1374.15i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{3} + 72 q^{6}+O(q^{10}) \) 24 * q - 20 * q^3 + 72 * q^6	\( 24 q - 20 q^{3} + 72 q^{6} + 156 q^{11} + 80 q^{12} + 560 q^{13} - 1480 q^{16} - 1320 q^{17} - 340 q^{18} + 196 q^{21} + 2020 q^{22} - 1920 q^{23} + 2208 q^{26} + 340 q^{27} - 2112 q^{31} + 1200 q^{32} + 6140 q^{33} + 3904 q^{36} - 3980 q^{37} - 9120 q^{38} + 6384 q^{41} - 4900 q^{42} + 12220 q^{43} - 8080 q^{46} + 11820 q^{47} + 4040 q^{48} - 5900 q^{51} - 3600 q^{52} - 24240 q^{53} - 10584 q^{56} - 6460 q^{57} - 6100 q^{58} + 440 q^{61} + 16680 q^{62} - 7840 q^{63} + 4832 q^{66} + 5940 q^{67} + 47040 q^{68} + 8928 q^{71} - 46720 q^{72} + 2500 q^{73} + 47816 q^{76} - 5880 q^{77} + 17940 q^{78} - 11360 q^{81} + 32120 q^{82} - 15120 q^{83} - 41208 q^{86} + 25460 q^{87} - 52920 q^{88} - 11172 q^{91} - 19800 q^{92} - 1460 q^{93} + 20568 q^{96} + 33840 q^{97}+O(q^{100}) \) 24 * q - 20 * q^3 + 72 * q^6 + 156 * q^11 + 80 * q^12 + 560 * q^13 - 1480 * q^16 - 1320 * q^17 - 340 * q^18 + 196 * q^21 + 2020 * q^22 - 1920 * q^23 + 2208 * q^26 + 340 * q^27 - 2112 * q^31 + 1200 * q^32 + 6140 * q^33 + 3904 * q^36 - 3980 * q^37 - 9120 * q^38 + 6384 * q^41 - 4900 * q^42 + 12220 * q^43 - 8080 * q^46 + 11820 * q^47 + 4040 * q^48 - 5900 * q^51 - 3600 * q^52 - 24240 * q^53 - 10584 * q^56 - 6460 * q^57 - 6100 * q^58 + 440 * q^61 + 16680 * q^62 - 7840 * q^63 + 4832 * q^66 + 5940 * q^67 + 47040 * q^68 + 8928 * q^71 - 46720 * q^72 + 2500 * q^73 + 47816 * q^76 - 5880 * q^77 + 17940 * q^78 - 11360 * q^81 + 32120 * q^82 - 15120 * q^83 - 41208 * q^86 + 25460 * q^87 - 52920 * q^88 - 11172 * q^91 - 19800 * q^92 - 1460 * q^93 + 20568 * q^96 + 33840 * q^97

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