LMFDB - Embedded newform 175.5.j.b.124.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,5,Mod(24,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("175.24");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	175.j (of order $6$, degree $2$, not 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:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			124.14
Character	$\chi$	$=$	175.124
Dual form			175.5.j.b.24.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.04601 + 1.18127i) q^{2} +(4.41391 + 7.64511i) q^{3} +(-5.20922 - 9.02264i) q^{4} +20.8560i q^{6} +(-48.9708 + 1.69012i) q^{7} -62.4144i q^{8} +(1.53484 - 2.65843i) q^{9} +(56.4068 + 97.6995i) q^{11} +(45.9861 - 79.6502i) q^{12} -313.449 q^{13} +(-102.191 - 54.3896i) q^{14} +(-9.61965 + 16.6617i) q^{16} +(-203.517 - 352.502i) q^{17} +(6.28061 - 3.62611i) q^{18} +(-106.640 - 61.5688i) q^{19} +(-229.074 - 366.928i) q^{21} +266.526i q^{22} +(-499.612 - 288.451i) q^{23} +(477.165 - 275.491i) q^{24} +(-641.320 - 370.266i) q^{26} +742.152 q^{27} +(270.349 + 433.042i) q^{28} -741.613 q^{29} +(1263.78 - 729.642i) q^{31} +(-904.203 + 522.042i) q^{32} +(-497.949 + 862.473i) q^{33} -961.629i q^{34} -31.9814 q^{36} +(466.972 + 269.606i) q^{37} +(-145.458 - 251.941i) q^{38} +(-1383.53 - 2396.35i) q^{39} +1444.11i q^{41} +(-35.2491 - 1021.33i) q^{42} -1017.68i q^{43} +(587.672 - 1017.88i) q^{44} +(-681.475 - 1180.35i) q^{46} +(476.972 - 826.140i) q^{47} -169.841 q^{48} +(2395.29 - 165.533i) q^{49} +(1796.61 - 3111.82i) q^{51} +(1632.82 + 2828.14i) q^{52} +(-2734.35 + 1578.68i) q^{53} +(1518.45 + 876.678i) q^{54} +(105.488 + 3056.49i) q^{56} -1087.04i q^{57} +(-1517.35 - 876.041i) q^{58} +(790.264 - 456.259i) q^{59} +(-1476.15 - 852.257i) q^{61} +3447.60 q^{62} +(-70.6695 + 132.779i) q^{63} -2158.85 q^{64} +(-2037.62 + 1176.42i) q^{66} +(-4642.17 + 2680.16i) q^{67} +(-2120.33 + 3672.52i) q^{68} -5092.79i q^{69} -4952.36 q^{71} +(-165.924 - 95.7963i) q^{72} +(-696.902 - 1207.07i) q^{73} +(636.953 + 1103.24i) q^{74} +1282.90i q^{76} +(-2927.41 - 4689.09i) q^{77} -6537.28i q^{78} +(-5068.88 + 8779.55i) q^{79} +(3151.47 + 5458.50i) q^{81} +(-1705.88 + 2954.66i) q^{82} +6357.92 q^{83} +(-2117.36 + 3978.26i) q^{84} +(1202.15 - 2082.19i) q^{86} +(-3273.41 - 5669.71i) q^{87} +(6097.85 - 3520.60i) q^{88} +(156.641 + 90.4366i) q^{89} +(15349.8 - 529.765i) q^{91} +6010.43i q^{92} +(11156.4 + 6441.14i) q^{93} +(1951.78 - 1126.86i) q^{94} +(-7982.14 - 4608.49i) q^{96} +5069.26 q^{97} +(5096.32 + 2490.79i) q^{98} +346.303 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 116 q^{4} - 532 q^{9} + 180 q^{11} + 1380 q^{14} - 252 q^{16} + 3324 q^{19} + 3360 q^{21} - 3816 q^{24} - 2700 q^{26} - 1680 q^{29} - 7272 q^{31} - 8328 q^{36} - 5952 q^{39} + 7236 q^{44} + 4076 q^{46}+ \cdots + 73432 q^{99}+O(q^{100}) $ 40 * q + 116 * q^4 - 532 * q^9 + 180 * q^11 + 1380 * q^14 - 252 * q^16 + 3324 * q^19 + 3360 * q^21 - 3816 * q^24 - 2700 * q^26 - 1680 * q^29 - 7272 * q^31 - 8328 * q^36 - 5952 * q^39 + 7236 * q^44 + 4076 * q^46 - 832 * q^49 + 12648 * q^51 - 66360 * q^54 + 27000 * q^56 - 432 * q^59 - 11712 * q^61 + 51576 * q^64 - 32496 * q^66 + 20976 * q^71 - 5076 * q^74 - 41576 * q^79 + 8308 * q^81 + 40632 * q^84 + 3960 * q^86 + 26352 * q^89 + 35952 * q^91 + 101220 * q^94 - 34920 * q^96 + 73432 * q^99

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	2.04601	+	1.18127i	0.511503	+	0.295316i	0.733451	−	0.679742i	$-0.237908\pi$
$2$	2.04601	+	1.18127i	0.511503	+	0.295316i	−0.221948	+	0.975058i	$0.571242\pi$
$3$	4.41391	+	7.64511i	0.490434	+	0.849457i	0.999939	−	0.0110107i	$-0.00350488\pi$
$3$	4.41391	+	7.64511i	0.490434	+	0.849457i	−0.509505	+	0.860468i	$0.670172\pi$
$4$	−5.20922	−	9.02264i	−0.325577	−	0.563915i
$5$		0			0
$5$		0			0
$6$			20.8560i			0.579333i
$7$	−48.9708	+	1.69012i	−0.999405	+	0.0344922i
$7$	−48.9708	+	1.69012i	−0.999405	+	0.0344922i
$8$		−	62.4144i		−	0.975225i
$9$	1.53484	−	2.65843i	0.0189487	−	0.0328201i
$10$		0			0
$11$	56.4068	+	97.6995i	0.466172	+	0.807434i	0.999254	−	0.0386302i	$-0.0122994\pi$
$11$	56.4068	+	97.6995i	0.466172	+	0.807434i	−0.533081	+	0.846064i	$0.678966\pi$
$12$	45.9861	−	79.6502i	0.319348	−	0.553126i
$13$	−313.449			−1.85473			−0.927363	−	0.374163i	$-0.877930\pi$
$13$	−313.449			−1.85473			−0.927363	+	0.374163i	$0.877930\pi$
$14$	−102.191	−	54.3896i	−0.521385	−	0.277498i
$15$		0			0
$16$	−9.61965	+	16.6617i	−0.0375767	+	0.0650848i
$17$	−203.517	−	352.502i	−0.704211	−	1.21973i	−0.966976	−	0.254869i	$-0.917968\pi$
$17$	−203.517	−	352.502i	−0.704211	−	1.21973i	0.262765	−	0.964860i	$-0.415366\pi$
$18$	6.28061	−	3.62611i	0.0193846	−	0.0111917i
$19$	−106.640	−	61.5688i	−0.295403	−	0.170551i	0.344973	−	0.938613i	$-0.387888\pi$
$19$	−106.640	−	61.5688i	−0.295403	−	0.170551i	−0.640376	+	0.768062i	$0.721221\pi$
$20$		0			0
$21$	−229.074	−	366.928i	−0.519442	−	0.832035i
$22$			266.526i			0.550673i
$23$	−499.612	−	288.451i	−0.944446	−	0.545276i	−0.0530948	−	0.998589i	$-0.516909\pi$
$23$	−499.612	−	288.451i	−0.944446	−	0.545276i	−0.891351	+	0.453313i	$0.850242\pi$
$24$	477.165	−	275.491i	0.828411	−	0.478284i
$25$		0			0
$26$	−641.320	−	370.266i	−0.948698	−	0.547731i
$27$	742.152			1.01804
$28$	270.349	+	433.042i	0.344834	+	0.552350i
$29$	−741.613			−0.881822			−0.440911	−	0.897551i	$-0.645345\pi$
$29$	−741.613			−0.881822			−0.440911	+	0.897551i	$0.645345\pi$
$30$		0			0
$31$	1263.78	−	729.642i	1.31506	−	0.759252i	0.332134	−	0.943232i	$-0.392231\pi$
$31$	1263.78	−	729.642i	1.31506	−	0.759252i	0.982930	+	0.183980i	$0.0588981\pi$
$32$	−904.203	+	522.042i	−0.883011	+	0.509806i
$33$	−497.949	+	862.473i	−0.457253	+	0.791986i
$34$		−	961.629i		−	0.831859i
$35$		0			0
$36$	−31.9814			−0.0246770
$37$	466.972	+	269.606i	0.341104	+	0.196937i	0.660760	−	0.750597i	$-0.270234\pi$
$37$	466.972	+	269.606i	0.341104	+	0.196937i	−0.319656	+	0.947534i	$0.603567\pi$
$38$	−145.458	−	251.941i	−0.100733	−	0.174474i
$39$	−1383.53	−	2396.35i	−0.909621	−	1.57551i
$40$		0			0
$41$			1444.11i			0.859077i	0.903049	+	0.429538i	$0.141324\pi$
$41$			1444.11i			0.859077i	−0.903049	+	0.429538i	$0.858676\pi$
$42$	−35.2491	−	1021.33i	−0.0199825	−	0.578988i
$43$		−	1017.68i		−	0.550396i	−0.961388	−	0.275198i	$-0.911257\pi$
$43$		−	1017.68i		−	0.550396i	0.961388	−	0.275198i	$-0.0887434\pi$
$44$	587.672	−	1017.88i	0.303549	−	0.525763i
$45$		0			0
$46$	−681.475	−	1180.35i	−0.322058	−	0.557821i
$47$	476.972	−	826.140i	0.215922	−	0.373988i	−0.737635	−	0.675199i	$-0.764058\pi$
$47$	476.972	−	826.140i	0.215922	−	0.373988i	0.953557	+	0.301211i	$0.0973909\pi$
$48$	−169.841			−0.0737157
$49$	2395.29	−	165.533i	0.997621	−	0.0689434i
$50$		0			0
$51$	1796.61	−	3111.82i	0.690738	−	1.19639i
$52$	1632.82	+	2828.14i	0.603855	+	1.04591i
$53$	−2734.35	+	1578.68i	−0.973425	+	0.562007i	−0.900279	−	0.435314i	$-0.856637\pi$
$53$	−2734.35	+	1578.68i	−0.973425	+	0.562007i	−0.0731463	+	0.997321i	$0.523304\pi$
$54$	1518.45	+	876.678i	0.520731	+	0.300644i
$55$		0			0
$56$	105.488	+	3056.49i	0.0336377	+	0.974645i
$57$		−	1087.04i		−	0.334576i
$58$	−1517.35	−	876.041i	−0.451055	−	0.260417i
$59$	790.264	−	456.259i	0.227022	−	0.131071i	−0.382175	−	0.924090i	$-0.624825\pi$
$59$	790.264	−	456.259i	0.227022	−	0.131071i	0.609198	+	0.793018i	$0.291492\pi$
$60$		0			0
$61$	−1476.15	−	852.257i	−0.396709	−	0.229040i	0.288354	−	0.957524i	$-0.406892\pi$
$61$	−1476.15	−	852.257i	−0.396709	−	0.229040i	−0.685063	+	0.728484i	$0.740225\pi$
$62$	3447.60			0.896878
$63$	−70.6695	+	132.779i	−0.0178054	+	0.0334541i
$64$	−2158.85			−0.527063
$65$		0			0
$66$	−2037.62	+	1176.42i	−0.467773	+	0.270069i
$67$	−4642.17	+	2680.16i	−1.03412	+	0.597051i	−0.918163	−	0.396203i	$-0.870328\pi$
$67$	−4642.17	+	2680.16i	−1.03412	+	0.597051i	−0.115959	+	0.993254i	$0.536994\pi$
$68$	−2120.33	+	3672.52i	−0.458549	+	0.794230i
$69$		−	5092.79i		−	1.06969i
$70$		0			0
$71$	−4952.36			−0.982416			−0.491208	−	0.871042i	$-0.663445\pi$
$71$	−4952.36			−0.982416			−0.491208	+	0.871042i	$0.663445\pi$
$72$	−165.924	−	95.7963i	−0.0320070	−	0.0184792i
$73$	−696.902	−	1207.07i	−0.130775	−	0.226510i	0.793200	−	0.608961i	$-0.208413\pi$
$73$	−696.902	−	1207.07i	−0.130775	−	0.226510i	−0.923976	+	0.382451i	$0.875080\pi$
$74$	636.953	+	1103.24i	0.116317	+	0.201467i
$75$		0			0
$76$			1282.90i			0.222109i
$77$	−2927.41	−	4689.09i	−0.493745	−	0.790874i
$78$		−	6537.28i		−	1.07450i
$79$	−5068.88	+	8779.55i	−0.812190	+	1.40675i	0.0991386	+	0.995074i	$0.468391\pi$
$79$	−5068.88	+	8779.55i	−0.812190	+	1.40675i	−0.911328	+	0.411680i	$0.864942\pi$
$80$		0			0
$81$	3151.47	+	5458.50i	0.480333	+	0.831962i
$82$	−1705.88	+	2954.66i	−0.253699	+	0.439420i
$83$	6357.92			0.922909			0.461455	−	0.887164i	$-0.347328\pi$
$83$	6357.92			0.922909			0.461455	+	0.887164i	$0.347328\pi$
$84$	−2117.36	+	3978.26i	−0.300079	+	0.563812i
$85$		0			0
$86$	1202.15	−	2082.19i	0.162541	−	0.281529i
$87$	−3273.41	−	5669.71i	−0.432476	−	0.749070i
$88$	6097.85	−	3520.60i	0.787429	−	0.454623i
$89$	156.641	+	90.4366i	0.0197754	+	0.0114173i	0.509855	−	0.860260i	$-0.329699\pi$
$89$	156.641	+	90.4366i	0.0197754	+	0.0114173i	−0.490080	+	0.871678i	$0.663032\pi$
$90$		0			0
$91$	15349.8	−	529.765i	1.85362	−	0.0639736i
$92$			6010.43i			0.710117i
$93$	11156.4	+	6441.14i	1.28990	+	0.744727i
$94$	1951.78	−	1126.86i	0.220890	−	0.127531i
$95$		0			0
$96$	−7982.14	−	4608.49i	−0.866117	−	0.500053i
$97$	5069.26			0.538768			0.269384	−	0.963033i	$-0.413180\pi$
$97$	5069.26			0.538768			0.269384	+	0.963033i	$0.413180\pi$
$98$	5096.32	+	2490.79i	0.530646	+	0.259349i
$99$	346.303			0.0353334
$100$		0			0
$101$	3450.13	−	1991.93i	0.338215	−	0.195269i	−0.321267	−	0.946989i	$-0.604109\pi$
$101$	3450.13	−	1991.93i	0.338215	−	0.195269i	0.659482	+	0.751720i	$0.270775\pi$
$102$	7351.76	−	4244.54i	0.706629	−	0.407972i
$103$	2457.15	−	4255.91i	0.231610	−	0.401161i	−0.726672	−	0.686985i	$-0.758934\pi$
$103$	2457.15	−	4255.91i	0.231610	−	0.401161i	0.958282	+	0.285824i	$0.0922673\pi$
$104$			19563.7i			1.80877i
$105$		0			0
$106$	−7459.35			−0.663880
$107$	−7404.44	−	4274.95i	−0.646732	−	0.373391i	0.140471	−	0.990085i	$-0.455138\pi$
$107$	−7404.44	−	4274.95i	−0.646732	−	0.373391i	−0.787203	+	0.616694i	$0.788472\pi$
$108$	−3866.03	−	6696.17i	−0.331450	−	0.574089i
$109$	4551.17	+	7882.86i	0.383063	+	0.663484i	0.991498	−	0.130119i	$-0.0415359\pi$
$109$	4551.17	+	7882.86i	0.383063	+	0.663484i	−0.608436	+	0.793603i	$0.708203\pi$
$110$		0			0
$111$			4760.07i			0.386338i
$112$	442.922	−	832.197i	0.0353095	−	0.0663422i
$113$			10497.8i			0.822135i	0.911605	+	0.411068i	$0.134844\pi$
$113$			10497.8i			0.822135i	−0.911605	+	0.411068i	$0.865156\pi$
$114$	1284.08	−	2224.09i	0.0988057	−	0.171136i
$115$		0			0
$116$	3863.23	+	6691.31i	0.287101	+	0.497273i
$117$	−481.095	+	833.280i	−0.0351446	+	0.0608722i
$118$	2155.85			0.154830
$119$	10562.2	+	16918.3i	0.745863	+	1.19471i
$120$		0			0
$121$	957.041	−	1657.64i	0.0653672	−	0.113219i
$122$	−2013.48	−	3487.46i	−0.135278	−	0.234309i
$123$	−11040.4	+	6374.16i	−0.729749	+	0.421321i
$124$	−13166.6	−	7601.73i	−0.856308	−	0.494390i
$125$		0			0
$126$	−301.438	+	188.189i	−0.0189870	+	0.0118537i
$127$			3934.73i			0.243954i	0.992533	+	0.121977i	$0.0389234\pi$
$127$			3934.73i			0.243954i	−0.992533	+	0.121977i	$0.961077\pi$
$128$	10050.2	+	5802.49i	0.613416	+	0.354156i
$129$	7780.30	−	4491.96i	0.467538	−	0.269933i
$130$		0			0
$131$	6358.23	+	3670.93i	0.370505	+	0.213911i	0.673679	−	0.739024i	$-0.264713\pi$
$131$	6358.23	+	3670.93i	0.370505	+	0.213911i	−0.303174	+	0.952935i	$0.598046\pi$
$132$	10375.7			0.595484
$133$	5326.33	+	2834.84i	0.301110	+	0.160260i
$134$	−12663.9			−0.705275
$135$		0			0
$136$	−22001.2	+	12702.4i	−1.18951	+	0.686764i
$137$	−8323.71	+	4805.69i	−0.443482	+	0.256044i	−0.705073	−	0.709134i	$-0.749086\pi$
$137$	−8323.71	+	4805.69i	−0.443482	+	0.256044i	0.261592	+	0.965179i	$0.415753\pi$
$138$	6015.93	−	10419.9i	0.315896	−	0.547149i
$139$		−	6348.86i		−	0.328599i	−0.986410	−	0.164300i	$-0.947464\pi$
$139$		−	6348.86i		−	0.328599i	0.986410	−	0.164300i	$-0.0525364\pi$
$140$		0			0
$141$	8421.25			0.423583
$142$	−10132.6	−	5850.05i	−0.502509	−	0.290124i
$143$	−17680.6	−	30623.8i	−0.864621	−	1.49757i
$144$	29.5293	+	51.1462i	0.00142406	+	0.00246654i
$145$		0			0
$146$		−	3292.90i		−	0.154480i
$147$	11838.1	+	17581.6i	0.547832	+	0.813623i
$148$		−	5617.76i		−	0.256472i
$149$	5996.35	−	10386.0i	0.270094	−	0.467816i	−0.698792	−	0.715325i	$-0.746279\pi$
$149$	5996.35	−	10386.0i	0.270094	−	0.467816i	0.968886	+	0.247509i	$0.0796120\pi$
$150$		0			0
$151$	−19255.3	−	33351.1i	−0.844493	−	1.46271i	−0.886061	−	0.463569i	$-0.846568\pi$
$151$	−19255.3	−	33351.1i	−0.844493	−	1.46271i	0.0415675	−	0.999136i	$-0.486765\pi$
$152$	−3842.78	+	6655.89i	−0.166325	+	0.288084i
$153$	−1249.47			−0.0533754
$154$	−450.460	−	13052.0i	−0.0189939	−	0.550345i
$155$		0			0
$156$	−14414.3	+	24966.3i	−0.592302	+	1.02590i
$157$	−2170.22	−	3758.93i	−0.0880450	−	0.152498i	0.818640	−	0.574307i	$-0.194729\pi$
$157$	−2170.22	−	3758.93i	−0.0880450	−	0.152498i	−0.906685	+	0.421809i	$0.861395\pi$
$158$	−20742.0	+	11975.4i	−0.830875	+	0.479706i
$159$	−24138.3	−	13936.3i	−0.954802	−	0.551255i
$160$		0			0
$161$	24953.9	+	13281.3i	0.962692	+	0.512376i
$162$			14890.9i			0.567401i
$163$	23180.5	+	13383.3i	0.872464	+	0.503718i	0.868166	−	0.496273i	$-0.165299\pi$
$163$	23180.5	+	13383.3i	0.872464	+	0.503718i	0.00429800	+	0.999991i	$0.498632\pi$
$164$	13029.7	−	7522.69i	0.484447	−	0.279695i
$165$		0			0
$166$	13008.4	+	7510.39i	0.472071	+	0.272550i
$167$	−2791.76			−0.100103			−0.0500513	−	0.998747i	$-0.515938\pi$
$167$	−2791.76			−0.100103			−0.0500513	+	0.998747i	$0.515938\pi$
$168$	−22901.6	+	14297.5i	−0.811421	+	0.506573i
$169$	69689.1			2.44001
$170$		0			0
$171$	−327.352	+	188.997i	−0.0111950	+	0.00646343i
$172$	−9182.19	+	5301.34i	−0.310377	+	0.179196i
$173$	−3552.47	+	6153.06i	−0.118697	+	0.205589i	−0.919251	−	0.393671i	$-0.871205\pi$
$173$	−3552.47	+	6153.06i	−0.118697	+	0.205589i	0.800555	+	0.599260i	$0.204538\pi$
$174$		−	15467.1i		−	0.510869i
$175$		0			0
$176$	−2170.45			−0.0700689
$177$	6976.31	+	4027.77i	0.222679	+	0.128564i
$178$	213.659	+	370.068i	0.00674344	+	0.0116800i
$179$	−22495.5	−	38963.4i	−0.702085	−	1.21605i	−0.967733	−	0.251977i	$-0.918919\pi$
$179$	−22495.5	−	38963.4i	−0.702085	−	1.21605i	0.265648	−	0.964070i	$-0.414414\pi$
$180$		0			0
$181$		−	61782.2i		−	1.88584i	−0.333013	−	0.942922i	$-0.608065\pi$
$181$		−	61782.2i		−	1.88584i	0.333013	−	0.942922i	$-0.391935\pi$
$182$	32031.8	+	17048.3i	0.967025	+	0.514682i
$183$		−	15047.1i		−	0.449316i
$184$	−18003.5	+	31183.0i	−0.531767	+	0.921047i
$185$		0			0
$186$	15217.4	+	26357.3i	0.439860	+	0.761860i
$187$	22959.5	−	39767.0i	0.656567	−	1.13721i
$188$	−9938.63			−0.281197
$189$	−36343.8	+	1254.32i	−1.01743	+	0.0351145i
$190$		0			0
$191$	19870.9	−	34417.3i	0.544690	−	0.943432i	−0.453936	−	0.891034i	$-0.649980\pi$
$191$	19870.9	−	34417.3i	0.544690	−	0.943432i	0.998626	−	0.0523972i	$-0.0166862\pi$
$192$	−9528.97	−	16504.7i	−0.258490	−	0.447717i
$193$	−63511.3	+	36668.3i	−1.70505	+	0.984409i	−0.764577	+	0.644533i	$0.777052\pi$
$193$	−63511.3	+	36668.3i	−1.70505	+	0.984409i	−0.940470	+	0.339877i	$0.889615\pi$
$194$	10371.8	+	5988.15i	0.275581	+	0.159107i
$195$		0			0
$196$	−13971.1	−	20749.5i	−0.363680	−	0.540127i
$197$		−	70971.8i		−	1.82875i	−0.404872	−	0.914373i	$-0.632684\pi$
$197$		−	70971.8i		−	1.82875i	0.404872	−	0.914373i	$-0.367316\pi$
$198$	708.539	+	409.075i	0.0180731	+	0.0104345i
$199$	2968.18	−	1713.68i	0.0749521	−	0.0432736i	−0.462056	−	0.886851i	$-0.652888\pi$
$199$	2968.18	−	1713.68i	0.0749521	−	0.0432736i	0.537008	+	0.843577i	$0.319555\pi$
$200$		0			0
$201$	−40980.3	−	23660.0i	−1.01434	−	0.585628i
$202$	9412.01			0.230664
$203$	36317.4	−	1253.41i	0.881298	−	0.0304160i
$204$	−37435.8			−0.899552
$205$		0			0
$206$	10054.7	−	5805.10i	0.236938	−	0.136796i
$207$	−1533.65	+	885.454i	−0.0357920	+	0.0206645i
$208$	3015.27	−	5222.59i	0.0696946	−	0.120715i
$209$		−	13891.6i		−	0.318024i
$210$		0			0
$211$	−8102.71			−0.181998			−0.0909988	−	0.995851i	$-0.529006\pi$
$211$	−8102.71			−0.181998			−0.0909988	+	0.995851i	$0.529006\pi$
$212$	28487.7	+	16447.4i	0.633849	+	0.365953i
$213$	−21859.3	−	37861.4i	−0.481811	−	0.834520i
$214$	−10099.7	−	17493.2i	−0.220537	−	0.381981i
$215$		0			0
$216$		−	46320.9i		−	0.992819i
$217$	−60655.0	+	37867.1i	−1.28809	+	0.804160i
$218$			21504.6i			0.452499i
$219$	6152.12	−	10655.8i	0.128273	−	0.222176i
$220$		0			0
$221$	63792.1	+	110491.i	1.30612	+	2.26226i
$222$	−5622.90	+	9739.16i	−0.114092	+	0.197613i
$223$	74216.1			1.49241			0.746205	−	0.665716i	$-0.231874\pi$
$223$	74216.1			1.49241			0.746205	+	0.665716i	$0.231874\pi$
$224$	43397.3	−	27093.0i	0.864901	−	0.539960i
$225$		0			0
$226$	−12400.7	+	21478.7i	−0.242790	+	0.420524i
$227$	−11947.1	−	20693.0i	−0.231852	−	0.401580i	0.726501	−	0.687166i	$-0.241145\pi$
$227$	−11947.1	−	20693.0i	−0.231852	−	0.401580i	−0.958353	+	0.285585i	$0.907812\pi$
$228$	−9807.94	+	5662.62i	−0.188672	+	0.108930i
$229$	−33123.8	−	19124.1i	−0.631640	−	0.364678i	0.149747	−	0.988724i	$-0.452154\pi$
$229$	−33123.8	−	19124.1i	−0.631640	−	0.364678i	−0.781387	+	0.624047i	$0.785487\pi$
$230$		0			0
$231$	22927.3	−	43077.6i	0.429664	−	0.807287i
$232$			46287.3i			0.859975i
$233$	−75396.1	−	43530.0i	−1.38879	−	0.801820i	−0.395613	−	0.918417i	$-0.629468\pi$
$233$	−75396.1	−	43530.0i	−1.38879	−	0.801820i	−0.993179	+	0.116598i	$0.962801\pi$
$234$	−1968.65	+	1136.60i	−0.0359531	+	0.0207576i
$235$		0			0
$236$	−8233.33	−	4753.51i	−0.147826	−	0.0853475i
$237$	−89494.2			−1.59330
$238$	1625.27	+	47091.8i	0.0286927	+	0.831364i
$239$	7221.47			0.126424			0.0632121	−	0.998000i	$-0.479866\pi$
$239$	7221.47			0.126424			0.0632121	+	0.998000i	$0.479866\pi$
$240$		0			0
$241$	−70163.0	+	40508.6i	−1.20802	+	0.697451i	−0.962326	−	0.271897i	$-0.912349\pi$
$241$	−70163.0	+	40508.6i	−1.20802	+	0.697451i	−0.245694	+	0.969347i	$0.579016\pi$
$242$	3916.23	−	2261.04i	0.0668710	−	0.0386080i
$243$	2236.58	−	3873.87i	0.0378767	−	0.0656043i
$244$			17758.4i			0.298280i
$245$		0			0
$246$	−30118.3			−0.497691
$247$	33426.3	+	19298.7i	0.547891	+	0.316325i
$248$	−45540.1	−	78877.8i	−0.740442	−	1.28248i
$249$	28063.3	+	48607.0i	0.452626	+	0.783971i
$250$		0			0
$251$			9872.20i			0.156699i	0.996926	+	0.0783496i	$0.0249650\pi$
$251$			9872.20i			0.156699i	−0.996926	+	0.0783496i	$0.975035\pi$
$252$	1566.15	−	54.0523i	0.0246623	−	0.000851164i
$253$		−	65082.4i		−	1.01677i
$254$	−4647.96	+	8050.50i	−0.0720435	+	0.124783i
$255$		0			0
$256$	30979.4	+	53657.9i	0.472708	+	0.818754i
$257$	29846.8	−	51696.2i	0.451889	−	0.782694i	−0.546615	−	0.837384i	$-0.684084\pi$
$257$	29846.8	−	51696.2i	0.451889	−	0.782694i	0.998503	+	0.0546901i	$0.0174171\pi$
$258$	21224.8			0.318863
$259$	−23323.7	−	12413.6i	−0.347694	−	0.185054i
$260$		0			0
$261$	−1138.26	+	1971.52i	−0.0167094	+	0.0289415i
$262$	8672.68	+	15021.5i	0.126343	+	0.218832i
$263$	−48773.6	+	28159.4i	−0.705136	+	0.407110i	−0.809257	−	0.587454i	$-0.800130\pi$
$263$	−48773.6	+	28159.4i	−0.705136	+	0.407110i	0.104121	+	0.994565i	$0.466797\pi$
$264$	53830.7	+	31079.2i	0.772365	+	0.445925i
$265$		0			0
$266$	7549.02	+	12091.9i	0.106691	+	0.170896i
$267$			1596.71i			0.0223978i
$268$	48364.3	+	27923.1i	0.673372	+	0.388771i
$269$	−34003.8	+	19632.1i	−0.469919	+	0.271308i	−0.716206	−	0.697889i	$-0.754123\pi$
$269$	−34003.8	+	19632.1i	−0.469919	+	0.271308i	0.246287	+	0.969197i	$0.420789\pi$
$270$		0			0
$271$	−71447.6	−	41250.3i	−0.972857	−	0.561679i	−0.0727506	−	0.997350i	$-0.523178\pi$
$271$	−71447.6	−	41250.3i	−0.972857	−	0.561679i	−0.900106	+	0.435671i	$0.856511\pi$
$272$	7831.04			0.105848
$273$	71802.9	+	115013.i	0.963422	+	1.54320i
$274$	−22707.2			−0.302456
$275$		0			0
$276$	−45950.4	+	26529.5i	−0.603213	+	0.348265i
$277$	15424.4	−	8905.27i	0.201024	−	0.116061i	−0.396109	−	0.918204i	$-0.629640\pi$
$277$	15424.4	−	8905.27i	0.201024	−	0.116061i	0.597133	+	0.802142i	$0.296306\pi$
$278$	7499.69	−	12989.8i	0.0970407	−	0.168079i
$279$		−	4479.54i		−	0.0575473i
$280$		0			0
$281$	141355.			1.79019			0.895095	−	0.445876i	$-0.147108\pi$
$281$	141355.			1.79019			0.895095	+	0.445876i	$0.147108\pi$
$282$	17230.0	+	9947.73i	0.216664	+	0.125091i
$283$	15127.4	+	26201.4i	0.188882	+	0.327154i	0.944878	−	0.327423i	$-0.106180\pi$
$283$	15127.4	+	26201.4i	0.188882	+	0.327154i	−0.755996	+	0.654577i	$0.772847\pi$
$284$	25798.0	+	44683.4i	0.319852	+	0.553999i
$285$		0			0
$286$		−	83542.1i		−	1.02135i
$287$	−2440.71	−	70719.2i	−0.0296315	−	0.858566i
$288$			3205.01i			0.0386406i
$289$	−41077.7	+	71148.7i	−0.491825	+	0.851866i
$290$		0			0
$291$	22375.3	+	38755.1i	0.264230	+	0.457660i
$292$	−7260.64	+	12575.8i	−0.0851548	+	0.147492i
$293$	126488.			1.47337			0.736687	−	0.676233i	$-0.236389\pi$
$293$	126488.			1.47337			0.736687	+	0.676233i	$0.236389\pi$
$294$	3452.35	+	49956.1i	0.0399412	+	0.577954i
$295$		0			0
$296$	16827.3	−	29145.8i	0.192058	−	0.332653i
$297$	41862.4	+	72507.8i	0.474582	+	0.822000i
$298$	24537.2	−	14166.6i	0.276307	−	0.159526i
$299$	156603.	+	90414.6i	1.75169	+	1.01134i
$300$		0			0
$301$	1720.00	+	49836.8i	0.0189844	+	0.550069i
$302$		−	90982.4i		−	0.997570i
$303$	30457.1	+	17584.4i	0.331744	+	0.191533i
$304$	2051.68	−	1184.54i	0.0222005	−	0.0128175i
$305$		0			0
$306$	−2556.42	−	1475.95i	−0.0273017	−	0.0157626i
$307$	100711.			1.06856			0.534282	−	0.845306i	$-0.320582\pi$
$307$	100711.			1.06856			0.534282	+	0.845306i	$0.320582\pi$
$308$	−27058.4	+	50839.5i	−0.285234	+	0.535920i
$309$	43382.6			0.454358
$310$		0			0
$311$	−137912.	+	79623.3i	−1.42587	+	0.823226i	−0.996792	−	0.0800410i	$-0.974495\pi$
$311$	−137912.	+	79623.3i	−1.42587	+	0.823226i	−0.429078	+	0.903267i	$0.641162\pi$
$312$	−149567.	+	86352.4i	−1.53648	+	0.887085i
$313$	86242.1	−	149376.i	0.880300	−	1.52472i	0.0292920	−	0.999571i	$-0.490675\pi$
$313$	86242.1	−	149376.i	0.880300	−	1.52472i	0.851008	−	0.525153i	$-0.175992\pi$
$314$		−	10254.4i		−	0.104004i
$315$		0			0
$316$	105620.			1.05772
$317$	63763.3	+	36813.7i	0.634530	+	0.366346i	0.782504	−	0.622645i	$-0.213942\pi$
$317$	63763.3	+	36813.7i	0.634530	+	0.366346i	−0.147974	+	0.988991i	$0.547275\pi$
$318$	−32924.9	−	57027.6i	−0.325589	−	0.563937i
$319$	−41832.0	−	72455.2i	−0.411081	−	0.712013i
$320$		0			0
$321$		−	75477.0i		−	0.732495i
$322$	35367.3	+	56650.9i	0.341107	+	0.546380i
$323$			50121.2i			0.480415i
$324$	32833.4	−	56869.1i	0.312770	−	0.541734i
$325$		0			0
$326$	31618.4	+	54764.7i	0.297512	+	0.515306i
$327$	−40176.9	+	69588.4i	−0.375734	+	0.650791i
$328$	90133.2			0.837793
$329$	−21961.5	+	41262.9i	−0.202894	+	0.381214i
$330$		0			0
$331$	25791.2	−	44671.7i	0.235405	−	0.407734i	−0.723985	−	0.689816i	$-0.757692\pi$
$331$	25791.2	−	44671.7i	0.235405	−	0.407734i	0.959390	+	0.282082i	$0.0910249\pi$
$332$	−33119.8	−	57365.2i	−0.300478	−	0.520442i
$333$	1433.46	−	827.607i	0.0129270	−	0.00746338i
$334$	−5711.97	−	3297.81i	−0.0512028	−	0.0295619i
$335$		0			0
$336$	8317.25	−	287.051i	0.0736718	−	0.00254262i
$337$			26290.2i			0.231491i	0.993279	+	0.115746i	$0.0369258\pi$
$337$			26290.2i			0.231491i	−0.993279	+	0.115746i	$0.963074\pi$
$338$	142585.	+	82321.3i	1.24807	+	0.720574i
$339$	−80257.2	+	46336.5i	−0.698368	+	0.403203i
$340$		0			0
$341$	142571.	+	82313.5i	1.22609	+	0.707885i
$342$	−893.022			−0.00763502
$343$	−117019.	+	12154.6i	−0.994649	+	0.103312i
$344$	−63518.0			−0.536760
$345$		0			0
$346$	−14536.8	+	8392.82i	−0.121427	+	0.0701061i
$347$	−48507.3	+	28005.7i	−0.402854	+	0.232588i	−0.687715	−	0.725981i	$-0.741386\pi$
$347$	−48507.3	+	28005.7i	−0.402854	+	0.232588i	0.284860	+	0.958569i	$0.408053\pi$
$348$	−34103.9	+	59069.6i	−0.281608	+	0.487759i
$349$			97457.4i			0.800136i	0.916485	+	0.400068i	$0.131014\pi$
$349$			97457.4i			0.800136i	−0.916485	+	0.400068i	$0.868986\pi$
$350$		0			0
$351$	−232626.			−1.88819
$352$	−102006.	−	58893.4i	−0.823270	−	0.475315i
$353$	−7762.53	−	13445.1i	−0.0622951	−	0.107898i	0.833196	−	0.552978i	$-0.186509\pi$
$353$	−7762.53	−	13445.1i	−0.0622951	−	0.107898i	−0.895491	+	0.445080i	$0.853175\pi$
$354$	9515.73	+	16481.7i	0.0759339	+	0.131521i
$355$		0			0
$356$		−	1884.42i		−	0.0148688i
$357$	−82722.1	+	155425.i	−0.649061	+	1.21951i
$358$		−	106293.i		−	0.829349i
$359$	−271.507	+	470.263i	−0.00210665	+	0.00364882i	−0.867077	−	0.498174i	$-0.834004\pi$
$359$	−271.507	+	470.263i	−0.00210665	+	0.00364882i	0.864970	+	0.501823i	$0.167337\pi$
$360$		0			0
$361$	−57579.1	−	99729.8i	−0.441825	−	0.765263i
$362$	72981.1	−	126407.i	0.556921	−	0.964615i
$363$	16897.2			0.128233
$364$	−84740.7	−	135736.i	−0.639572	−	1.02446i
$365$		0			0
$366$	17774.7	−	30786.6i	0.132690	−	0.229826i
$367$	−88682.9	−	153603.i	−0.658427	−	1.14043i	−0.981023	−	0.193893i	$-0.937889\pi$
$367$	−88682.9	−	153603.i	−0.658427	−	1.14043i	0.322595	−	0.946537i	$-0.395445\pi$
$368$	9612.18	−	5549.59i	0.0709784	−	0.0409794i
$369$	3839.06	+	2216.48i	0.0281950	+	0.0162784i
$370$		0			0
$371$	131235.	−	81930.6i	0.953461	−	0.595248i
$372$		−	134213.i		−	0.969862i
$373$	−166006.	−	95843.8i	−1.19318	−	0.688884i	−0.234156	−	0.972199i	$-0.575232\pi$
$373$	−166006.	−	95843.8i	−1.19318	−	0.688884i	−0.959027	+	0.283315i	$0.908566\pi$
$374$	93950.7	−	54242.5i	0.671671	−	0.387790i
$375$		0			0
$376$	−51563.1	−	29769.9i	−0.364723	−	0.210573i
$377$	232457.			1.63554
$378$	−75841.5	−	40365.3i	−0.530791	−	0.282504i
$379$	−150128.			−1.04516			−0.522582	−	0.852589i	$-0.675031\pi$
$379$	−150128.			−1.04516			−0.522582	+	0.852589i	$0.675031\pi$
$380$		0			0
$381$	−30081.4	+	17367.5i	−0.207228	+	0.119643i
$382$	81312.0	−	46945.5i	0.557221	−	0.321712i
$383$	958.064	−	1659.42i	0.00653126	−	0.0113125i	−0.862741	−	0.505646i	$-0.831254\pi$
$383$	958.064	−	1659.42i	0.00653126	−	0.0113125i	0.869273	+	0.494333i	$0.164588\pi$
$384$			102447.i			0.694761i
$385$		0			0
$386$	−173260.			−1.16285
$387$	−2705.43	−	1561.98i	−0.0180640	−	0.0104293i
$388$	−26406.9	−	45738.2i	−0.175410	−	0.303819i
$389$	−18629.1	−	32266.5i	−0.123110	−	0.213232i	0.797883	−	0.602813i	$-0.205953\pi$
$389$	−18629.1	−	32266.5i	−0.123110	−	0.213232i	−0.920992	+	0.389580i	$0.872620\pi$
$390$		0			0
$391$			234819.i			1.53596i
$392$	−10331.6	−	149500.i	−0.0672353	−	0.972904i
$393$			64812.6i			0.419637i
$394$	83836.6	−	145209.i	0.540059	−	0.935409i
$395$		0			0
$396$	−1803.97	−	3124.56i	−0.0115037	−	0.0199250i
$397$	−127391.	+	220648.i	−0.808274	+	1.39997i	0.105785	+	0.994389i	$0.466265\pi$
$397$	−127391.	+	220648.i	−0.808274	+	1.39997i	−0.914059	+	0.405582i	$0.867069\pi$
$398$	8097.23			0.0511176
$399$	1837.22	+	53233.1i	0.0115403	+	0.334377i
$400$		0			0
$401$	−10345.4	+	17918.8i	−0.0643368	+	0.111435i	−0.896400	−	0.443247i	$-0.853827\pi$
$401$	−10345.4	+	17918.8i	−0.0643368	+	0.111435i	0.832063	+	0.554681i	$0.187160\pi$
$402$	−55897.4	−	96817.1i	−0.345891	−	0.599101i
$403$	−396129.	+	228705.i	−2.43908	+	1.40820i
$404$	−35945.0	−	20752.9i	−0.220230	−	0.127150i
$405$		0			0
$406$	75786.4	+	40336.0i	0.459769	+	0.244704i
$407$			60830.5i			0.367226i
$408$	−194222.	−	112134.i	−1.16675	−	0.673625i
$409$	76648.2	−	44252.9i	0.458200	−	0.264542i	−0.253087	−	0.967444i	$-0.581446\pi$
$409$	76648.2	−	44252.9i	0.458200	−	0.264542i	0.711287	+	0.702901i	$0.248113\pi$
$410$		0			0
$411$	−73480.1	−	42423.8i	−0.434997	−	0.251146i
$412$	−51199.4			−0.301627
$413$	−37928.8	+	23679.0i	−0.222366	+	0.138824i
$414$	−4183.83			−0.0244103
$415$		0			0
$416$	283421.	−	163633.i	1.63774	−	0.945551i
$417$	48537.8	−	28023.3i	0.279131	−	0.161156i
$418$	16409.7	−	28422.4i	0.0939177	−	0.162670i
$419$		−	208106.i		−	1.18538i	−0.805432	−	0.592688i	$-0.798067\pi$
$419$		−	208106.i		−	1.18538i	0.805432	−	0.592688i	$-0.201933\pi$
$420$		0			0
$421$	−20020.3			−0.112956			−0.0564778	−	0.998404i	$-0.517987\pi$
$421$	−20020.3			−0.112956			−0.0564778	+	0.998404i	$0.517987\pi$
$422$	−16578.2	−	9571.45i	−0.0930923	−	0.0537468i
$423$	−1464.16	−	2535.99i	−0.00818289	−	0.0141732i
$424$	98532.2	+	170663.i	0.548083	+	0.949308i
$425$		0			0
$426$		−	103286.i		−	0.569146i
$427$	73728.9	+	39240.9i	0.404373	+	0.215220i
$428$			89076.8i			0.486270i
$429$	156081.	−	270341.i	0.848080	−	1.46892i
$430$		0			0
$431$	12223.5	+	21171.8i	0.0658025	+	0.113973i	0.897050	−	0.441930i	$-0.145706\pi$
$431$	12223.5	+	21171.8i	0.0658025	+	0.113973i	−0.831247	+	0.555903i	$0.812373\pi$
$432$	−7139.24	+	12365.5i	−0.0382546	+	0.0662590i
$433$	−62356.0			−0.332585			−0.166292	−	0.986076i	$-0.553180\pi$
$433$	−62356.0			−0.332585			−0.166292	+	0.986076i	$0.553180\pi$
$434$	−168832.	+	5826.85i	−0.896345	+	0.0309353i
$435$		0			0
$436$	47416.1	−	82127.1i	0.249433	−	0.432030i
$437$	35519.2	+	61521.1i	0.185995	+	0.322152i
$438$	25174.6	−	14534.6i	0.131224	−	0.0757625i
$439$	−163500.	−	94396.7i	−0.848376	−	0.489810i	0.0117263	−	0.999931i	$-0.496267\pi$
$439$	−163500.	−	94396.7i	−0.848376	−	0.489810i	−0.860103	+	0.510121i	$0.829601\pi$
$440$		0			0
$441$	3236.33	−	6621.76i	0.0166409	−	0.0340484i
$442$			301421.i			1.54287i
$443$	250560.	+	144661.i	1.27674	+	0.737129i	0.976248	−	0.216654i	$-0.0695144\pi$
$443$	250560.	+	144661.i	1.27674	+	0.737129i	0.300496	+	0.953783i	$0.402848\pi$
$444$	42948.4	−	24796.3i	0.217862	−	0.125783i
$445$		0			0
$446$	151847.	+	87668.9i	0.763372	+	0.440733i
$447$	105869.			0.529852
$448$	105721.	−	3648.71i	0.526750	−	0.0181796i
$449$	236914.			1.17516			0.587581	−	0.809165i	$-0.300080\pi$
$449$	236914.			1.17516			0.587581	+	0.809165i	$0.300080\pi$
$450$		0			0
$451$	−141089.	+	81457.6i	−0.693648	+	0.400478i
$452$	94718.3	−	54685.6i	0.463614	−	0.267668i
$453$	169982.	−	294418.i	0.828337	−	1.43472i
$454$		−	56450.9i		−	0.273879i
$455$		0			0
$456$	−67846.7			−0.326287
$457$	−107036.	−	61797.0i	−0.512502	−	0.295893i	0.221359	−	0.975192i	$-0.428951\pi$
$457$	−107036.	−	61797.0i	−0.512502	−	0.295893i	−0.733862	+	0.679299i	$0.762284\pi$
$458$	−45181.2	−	78256.1i	−0.215390	−	0.373067i
$459$	−151040.	−	261610.i	−0.716915	−	1.24173i
$460$		0			0
$461$			74323.1i			0.349721i	0.984593	+	0.174861i	$0.0559475\pi$
$461$			74323.1i			0.349721i	−0.984593	+	0.174861i	$0.944053\pi$
$462$	97795.6	−	61054.1i	0.458179	−	0.286043i
$463$		−	24703.3i		−	0.115237i	−0.998339	−	0.0576186i	$-0.981649\pi$
$463$		−	24703.3i		−	0.115237i	0.998339	−	0.0576186i	$-0.0183507\pi$
$464$	7134.05	−	12356.5i	0.0331360	−	0.0573933i
$465$		0			0
$466$	−102841.	−	178126.i	−0.473581	−	0.820266i
$467$	33003.7	−	57164.2i	0.151332	−	0.262114i	−0.780386	−	0.625298i	$-0.784977\pi$
$467$	33003.7	−	57164.2i	0.151332	−	0.262114i	0.931717	+	0.363185i	$0.118311\pi$
$468$	10024.5			0.0457690
$469$	222801.	−	139096.i	1.01291	−	0.632365i
$470$		0			0
$471$	19158.3	−	33183.2i	0.0863605	−	0.149581i
$472$	−28477.1	−	49323.9i	−0.127824	−	0.221398i
$473$	99427.1	−	57404.2i	0.444408	−	0.256579i
$474$	−183106.	−	105716.i	−0.814979	−	0.470528i
$475$		0			0
$476$	97627.4	−	183430.i	0.430881	−	0.809574i
$477$			9692.09i			0.0425972i
$478$	14775.2	+	8530.48i	0.0646663	+	0.0373351i
$479$	−299681.	+	173021.i	−1.30613	+	0.754096i	−0.981449	−	0.191726i	$-0.938592\pi$
$479$	−299681.	+	173021.i	−1.30613	+	0.754096i	−0.324685	+	0.945822i	$0.605258\pi$
$480$		0			0
$481$	−146372.	−	84507.7i	−0.632655	−	0.365264i
$482$	−191406.			−0.823874
$483$	8607.41	+	249398.i	0.0368959	+	1.06905i
$484$	−19941.8			−0.0851281
$485$		0			0
$486$	9152.14	−	5283.99i	0.0387481	−	0.0223712i
$487$	−180193.	+	104034.i	−0.759766	+	0.438651i	−0.829212	−	0.558935i	$-0.811210\pi$
$487$	−180193.	+	104034.i	−0.759766	+	0.438651i	0.0694459	+	0.997586i	$0.477877\pi$
$488$	−53193.1	+	92133.2i	−0.223365	+	0.386880i
$489$			236290.i			0.988161i
$490$		0			0
$491$	31227.4			0.129531			0.0647653	−	0.997901i	$-0.479370\pi$
$491$	31227.4			0.129531			0.0647653	+	0.997901i	$0.479370\pi$
$492$	115024.	+	66408.9i	0.475178	+	0.274344i
$493$	150931.	+	261420.i	0.620989	+	1.07558i
$494$	45593.7	+	78970.6i	0.186832	+	0.323602i
$495$		0			0
$496$			28075.6i			0.114121i
$497$	242521.	−	8370.08i	0.981832	−	0.0338857i
$498$			132601.i			0.534672i
$499$	−46479.8	+	80505.4i	−0.186665	+	0.323314i	−0.944136	−	0.329555i	$-0.893101\pi$
$499$	−46479.8	+	80505.4i	−0.186665	+	0.323314i	0.757471	+	0.652869i	$0.226435\pi$
$500$		0			0
$501$	−12322.6	−	21343.3i	−0.0490937	−	0.0850328i
$502$	−11661.7	+	20198.6i	−0.0462758	+	0.0801521i
$503$	−401841.			−1.58825			−0.794123	−	0.607757i	$-0.792069\pi$
$503$	−401841.			−1.58825			−0.794123	+	0.607757i	$0.792069\pi$
$504$	8287.35	+	4410.79i	0.0326253	+	0.0173642i
$505$		0			0
$506$	76879.6	−	133159.i	0.300269	−	0.520081i
$507$	307601.	+	532781.i	1.19666	+	2.07268i
$508$	35501.7	−	20496.9i	0.137569	−	0.0794256i
$509$	241739.	+	139568.i	0.933064	+	0.538704i	0.887779	−	0.460270i	$-0.152247\pi$
$509$	241739.	+	139568.i	0.933064	+	0.538704i	0.0452844	+	0.998974i	$0.485581\pi$
$510$		0			0
$511$	36168.0	+	57933.4i	0.138510	+	0.221864i
$512$		−	39300.4i		−	0.149919i
$513$	−79143.3	−	45693.4i	−0.300732	−	0.173628i
$514$	122134.	−	70514.0i	0.462285	−	0.266900i
$515$		0			0
$516$	−81058.6	−	46799.2i	−0.304439	−	0.175768i
$517$	107618.			0.402628
$518$	−33056.7	−	52949.8i	−0.123197	−	0.197335i
$519$	−62721.1			−0.232851
$520$		0			0
$521$	−213004.	+	122978.i	−0.784715	+	0.453056i	−0.838099	−	0.545518i	$-0.816333\pi$
$521$	−213004.	+	122978.i	−0.784715	+	0.453056i	0.0533834	+	0.998574i	$0.482999\pi$
$522$	−4657.78	+	2689.17i	−0.0170938	+	0.00986910i
$523$	−140056.	+	242584.i	−0.512034	+	0.886869i	0.487869	+	0.872917i	$0.337774\pi$
$523$	−140056.	+	242584.i	−0.512034	+	0.886869i	−0.999903	+	0.0139516i	$0.995559\pi$
$524$		−	76490.8i		−	0.278578i
$525$		0			0
$526$	−133055.			−0.480905
$527$	−514399.	−	296989.i	−1.85216	−	1.06935i
$528$	−9580.19	−	16593.4i	−0.0343642	−	0.0595205i
$529$	26487.6	+	45877.8i	0.0946522	+	0.163942i
$530$		0			0
$531$		−	2801.15i		−	0.00993451i
$532$	−2168.26	−	62824.9i	−0.00766104	−	0.221977i
$533$		−	452654.i		−	1.59335i
$534$	−1886.14	+	3266.90i	−0.00661443	+	0.0114565i
$535$		0			0
$536$	167281.	+	289739.i	0.582259	+	1.00850i
$537$	198586.	−	343961.i	0.688653	−	1.19278i
$538$	−92762.8			−0.320486
$539$	151283.	+	224681.i	0.520730	+	0.773373i
$540$		0			0
$541$	−96042.2	+	166350.i	−0.328146	+	0.568366i	−0.982144	−	0.188130i	$-0.939757\pi$
$541$	−96042.2	+	166350.i	−0.328146	+	0.568366i	0.653998	+	0.756496i	$0.273091\pi$
$542$	−97455.0	−	168797.i	−0.331746	−	0.574601i
$543$	472331.	−	272701.i	1.60194	−	0.924883i
$544$	368041.	+	212489.i	1.24365	+	0.718022i
$545$		0			0
$546$	11048.8	+	320136.i	0.0370620	+	1.07386i
$547$			103731.i			0.346685i	0.984862	+	0.173342i	$0.0554567\pi$
$547$			103731.i			0.346685i	−0.984862	+	0.173342i	$0.944543\pi$
$548$	86720.1	+	50067.9i	0.288774	+	0.166724i
$549$	−4531.33	+	2616.16i	−0.0150342	+	0.00868001i
$550$		0			0
$551$	79085.8	+	45660.2i	0.260493	+	0.150396i
$552$	−317863.			−1.04319
$553$	233389.	−	438509.i	0.763184	−	1.43393i
$554$	42078.0			0.137099
$555$		0			0
$556$	−57283.5	+	33072.6i	−0.185302	+	0.106984i
$557$	46316.6	−	26740.9i	0.149289	−	0.0861918i	−0.423495	−	0.905898i	$-0.639197\pi$
$557$	46316.6	−	26740.9i	0.149289	−	0.0861918i	0.572784	+	0.819707i	$0.305864\pi$
$558$	5291.53	−	9165.19i	0.0169947	−	0.0294356i
$559$			318991.i			1.02083i
$560$		0			0
$561$	405364.			1.28801
$562$	289214.	+	166978.i	0.915687	+	0.528672i
$563$	1221.39	+	2115.51i	0.00385334	+	0.00667417i	0.867946	−	0.496659i	$-0.165440\pi$
$563$	1221.39	+	2115.51i	0.00385334	+	0.00667417i	−0.864092	+	0.503333i	$0.832107\pi$
$564$	−43868.2	−	75981.9i	−0.137909	−	0.238865i
$565$		0			0
$566$			71477.9i			0.223120i
$567$	−163555.	−	261981.i	−0.508744	−	0.814899i
$568$			309099.i			0.958077i
$569$	−312029.	+	540450.i	−0.963763	+	1.66929i	−0.250860	+	0.968023i	$0.580714\pi$
$569$	−312029.	+	540450.i	−0.963763	+	1.66929i	−0.712903	+	0.701263i	$0.752620\pi$
$570$		0			0
$571$	−38637.1	−	66921.3i	−0.118504	−	0.205254i	0.800671	−	0.599104i	$-0.204476\pi$
$571$	−38637.1	−	66921.3i	−0.118504	−	0.205254i	−0.919175	+	0.393850i	$0.871143\pi$
$572$	−184205.	+	319052.i	−0.563001	+	0.975146i
$573$	350832.			1.06854
$574$	78544.4	−	147575.i	0.238392	−	0.447910i
$575$		0			0
$576$	−3313.50	+	5739.15i	−0.00998715	+	0.0172983i
$577$	−275875.	−	477830.i	−0.828631	−	1.43523i	−0.899112	−	0.437718i	$-0.855787\pi$
$577$	−275875.	−	477830.i	−0.828631	−	1.43523i	0.0704812	−	0.997513i	$-0.477547\pi$
$578$	−168091.	+	97047.3i	−0.503140	+	0.290488i
$579$	−560666.	−	323701.i	−1.67243	−	0.965576i
$580$		0			0
$581$	−311353.	+	10745.6i	−0.922360	+	0.0318332i
$582$			105724.i			0.312126i
$583$	−308472.	−	178096.i	−0.907567	−	0.523984i
$584$	−75338.5	+	43496.7i	−0.220898	+	0.127535i
$585$		0			0
$586$	258795.	+	149416.i	0.753635	+	0.435112i
$587$	45284.3			0.131423			0.0657115	−	0.997839i	$-0.479068\pi$
$587$	45284.3			0.131423			0.0657115	+	0.997839i	$0.479068\pi$
$588$	96965.1	−	198397.i	0.280453	−	0.573827i
$589$	−179693.			−0.517964
$590$		0			0
$591$	542588.	−	313263.i	1.55344	−	0.896880i
$592$	−8984.21	+	5187.03i	−0.0256352	+	0.0148005i
$593$	−17416.4	+	30166.0i	−0.0495277	+	0.0857844i	−0.889726	−	0.456494i	$-0.849105\pi$
$593$	−17416.4	+	30166.0i	−0.0495277	+	0.0857844i	0.840199	+	0.542279i	$0.182438\pi$
$594$			197802.i			0.560607i
$595$		0			0
$596$	−124945.			−0.351745
$597$	26202.5	+	15128.0i	0.0735181	+	0.0424457i
$598$	213607.	+	369979.i	0.597329	+	1.03460i
$599$	−53294.7	−	92309.1i	−0.148535	−	0.257271i	0.782151	−	0.623089i	$-0.214123\pi$
$599$	−53294.7	−	92309.1i	−0.148535	−	0.257271i	−0.930686	+	0.365818i	$0.880789\pi$
$600$		0			0
$601$			112464.i			0.311362i	0.987807	+	0.155681i	$0.0497573\pi$
$601$			112464.i			0.311362i	−0.987807	+	0.155681i	$0.950243\pi$
$602$	−55351.3	+	103998.i	−0.152734	+	0.286968i
$603$			16454.5i			0.0452533i
$604$	−200610.	+	347467.i	−0.549894	+	0.952445i
$605$		0			0
$606$	41543.8	+	71955.9i	0.113125	+	0.195939i
$607$	166739.	−	288800.i	0.452542	−	0.783826i	−0.546001	−	0.837784i	$-0.683851\pi$
$607$	166739.	−	288800.i	0.452542	−	0.783826i	0.998543	+	0.0539585i	$0.0171839\pi$
$608$	128566.			0.347792
$609$	169884.	+	272118.i	0.458056	+	0.733707i
$610$		0			0
$611$	−149506.	+	258953.i	−0.400477	+	0.693646i
$612$	6508.75	+	11273.5i	0.0173778	+	0.0300992i
$613$	281175.	−	162337.i	0.748266	−	0.432012i	−0.0768010	−	0.997046i	$-0.524471\pi$
$613$	281175.	−	162337.i	0.748266	−	0.432012i	0.825067	+	0.565035i	$0.191137\pi$
$614$	206056.	+	118967.i	0.546574	+	0.315564i
$615$		0			0
$616$	−292667.	+	182713.i	−0.771280	+	0.481512i
$617$			54190.8i			0.142349i	0.997464	+	0.0711747i	$0.0226748\pi$
$617$			54190.8i			0.142349i	−0.997464	+	0.0711747i	$0.977325\pi$
$618$	88761.2	+	51246.3i	0.232405	+	0.134179i
$619$	27588.2	−	15928.1i	0.0720016	−	0.0415702i	−0.463567	−	0.886062i	$-0.653431\pi$
$619$	27588.2	−	15928.1i	0.0720016	−	0.0415702i	0.535569	+	0.844492i	$0.320097\pi$
$620$		0			0
$621$	−370788.	−	214074.i	−0.961484	−	0.555113i
$622$	−376225.			−0.972449
$623$	−7823.68	−	4164.01i	−0.0201574	−	0.0107284i
$624$	53236.4			0.136722
$625$		0			0
$626$	352905.	−	203750.i	0.900552	−	0.519934i
$627$	106203.	−	61316.3i	0.270148	−	0.155970i
$628$	−22610.3	+	39162.3i	−0.0573308	+	0.0992998i
$629$		−	219478.i		−	0.554740i
$630$		0			0
$631$	83642.3			0.210071			0.105036	−	0.994468i	$-0.466504\pi$
$631$	83642.3			0.210071			0.105036	+	0.994468i	$0.466504\pi$
$632$	547970.	+	316371.i	1.37190	+	0.792068i
$633$	−35764.6	−	61946.1i	−0.0892578	−	0.154599i
$634$	86973.6	+	150643.i	0.216376	+	0.374774i
$635$		0			0
$636$			290389.i			0.717903i
$637$	−750799.	+	51886.1i	−1.85031	+	0.127871i
$638$		−	197659.i		−	0.485596i
$639$	−7601.10	+	13165.5i	−0.0186155	+	0.0322430i
$640$		0			0
$641$	−142082.	−	246094.i	−0.345799	−	0.598942i	0.639699	−	0.768625i	$-0.279059\pi$
$641$	−142082.	−	246094.i	−0.345799	−	0.598942i	−0.985499	+	0.169683i	$0.945726\pi$
$642$	89158.4	−	154427.i	0.216318	−	0.374673i
$643$	−121681.			−0.294307			−0.147153	−	0.989114i	$-0.547011\pi$
$643$	−121681.			−0.294307			−0.147153	+	0.989114i	$0.547011\pi$
$644$	−10158.3	−	294336.i	−0.0244935	−	0.709694i
$645$		0			0
$646$	−59206.4	+	102549.i	−0.141874	+	0.245733i
$647$	288279.	+	499313.i	0.688659	+	1.19279i	0.972272	+	0.233853i	$0.0751335\pi$
$647$	288279.	+	499313.i	0.688659	+	1.19279i	−0.283613	+	0.958939i	$0.591533\pi$
$648$	340689.	−	196697.i	0.811350	−	0.468433i
$649$	89152.6	+	51472.3i	0.211663	+	0.122204i
$650$		0			0
$651$	−557224.	−	296572.i	−1.31482	−	0.699792i
$652$		−	278866.i		−	0.655995i
$653$	377668.	+	218047.i	0.885694	+	0.511355i	0.872531	−	0.488558i	$-0.162477\pi$
$653$	377668.	+	218047.i	0.885694	+	0.511355i	0.0131622	+	0.999913i	$0.495810\pi$
$654$	−164405.	+	94919.1i	−0.384378	+	0.221921i
$655$		0			0
$656$	−24061.3	−	13891.8i	−0.0559129	−	0.0322813i
$657$	−4278.54			−0.00991208
$658$	−93675.9	+	58482.1i	−0.216359	+	0.135074i
$659$	378597.			0.871779			0.435890	−	0.900000i	$-0.356434\pi$
$659$	378597.			0.871779			0.435890	+	0.900000i	$0.356434\pi$
$660$		0			0
$661$	651728.	−	376275.i	1.49164	−	0.861197i	0.491684	−	0.870774i	$-0.336382\pi$
$661$	651728.	−	376275.i	1.49164	−	0.861197i	0.999954	+	0.00957646i	$0.00304833\pi$
$662$	105538.	−	60932.6i	0.240821	−	0.139038i
$663$	−563145.	+	975395.i	−1.28113	+	2.21898i
$664$		−	396826.i		−	0.900044i
$665$		0			0
$666$	3910.49			0.00881623
$667$	370519.	+	213919.i	0.832834	+	0.480837i
$668$	14542.9	+	25189.1i	0.0325911	+	0.0564494i
$669$	327583.	+	567390.i	0.731929	+	1.26774i
$670$		0			0
$671$		−	192293.i		−	0.427088i
$672$	398681.	+	212191.i	0.882850	+	0.469881i
$673$			97686.9i			0.215678i	0.994168	+	0.107839i	$0.0343931\pi$
$673$			97686.9i			0.215678i	−0.994168	+	0.107839i	$0.965607\pi$
$674$	−31055.8	+	53790.1i	−0.0683632	+	0.118408i
$675$		0			0
$676$	−363026.	−	628779.i	−0.794409	−	1.37596i
$677$	−207216.	+	358909.i	−0.452112	+	0.783082i	−0.998517	−	0.0544397i	$-0.982663\pi$
$677$	−207216.	+	358909.i	−0.452112	+	0.783082i	0.546405	+	0.837521i	$0.315996\pi$
$678$	−218943.			−0.476290
$679$	−248246.	+	8567.66i	−0.538447	+	0.0185833i
$680$		0			0
$681$	105467.	−	182674.i	0.227417	−	0.393897i
$682$	194468.	+	336829.i	0.418100	+	0.724170i
$683$	555211.	−	320551.i	1.19019	−	0.687157i	0.231840	−	0.972754i	$-0.425525\pi$
$683$	555211.	−	320551.i	1.19019	−	0.687157i	0.958350	+	0.285597i	$0.0921919\pi$
$684$	3410.51	+	1969.06i	0.00728965	+	0.00420868i
$685$		0			0
$686$	−253781.	−	113363.i	−0.539276	−	0.240891i
$687$		−	337647.i		−	0.715401i
$688$	16956.3	+	9789.75i	0.0358224	+	0.0206821i
$689$	857079.	−	494835.i	1.80544	−	1.04237i
$690$		0			0
$691$	510907.	+	294973.i	1.07001	+	0.617768i	0.928183	−	0.372124i	$-0.121370\pi$
$691$	510907.	+	294973.i	1.07001	+	0.617768i	0.141823	+	0.989892i	$0.454704\pi$
$692$	74022.5			0.154579
$693$	−16958.7	+	585.292i	−0.0353124	+	0.00121873i
$694$	−132329.			−0.274748
$695$		0			0
$696$	−353872.	+	204308.i	−0.730512	+	0.421761i
$697$	509050.	−	293900.i	1.04784	−	0.604971i
$698$	−115123.	+	199399.i	−0.236293	+	0.409272i
$699$		−	768549.i		−	1.57296i
$700$		0			0
$701$	726881.			1.47920			0.739601	−	0.673046i	$-0.235014\pi$
$701$	726881.			1.47920			0.739601	+	0.673046i	$0.235014\pi$
$702$	−475956.	−	274794.i	−0.965813	−	0.557612i
$703$	−33198.7	−	57501.8i	−0.0671754	−	0.116351i
$704$	−121774.	−	210919.i	−0.245702	−	0.425569i
$705$		0			0
$706$		−	36678.4i		−	0.0735870i
$707$	−165589.	+	103378.i	−0.331279	+	0.206818i
$708$		−	83926.3i		−	0.167429i
$709$	−27376.8	+	47418.0i	−0.0544616	+	0.0943302i	−0.891971	−	0.452093i	$-0.850678\pi$
$709$	−27376.8	+	47418.0i	−0.0544616	+	0.0943302i	0.837509	+	0.546423i	$0.184011\pi$
$710$		0			0
$711$	15559.9	+	26950.5i	0.0307798	+	0.0533123i
$712$	5644.54	−	9776.63i	0.0111344	−	0.0192854i
$713$	−841864.			−1.65601
$714$	−352848.	+	220284.i	−0.692136	+	0.432103i
$715$		0			0
$716$	−234368.	+	405938.i	−0.457165	+	0.791833i
$717$	31874.9	+	55209.0i	0.0620027	+	0.107392i
$718$	−1111.01	+	641.443i	−0.00215511	+	0.00124425i
$719$	−729749.	−	421321.i	−1.41161	−	0.814996i	−0.416073	−	0.909331i	$-0.636594\pi$
$719$	−729749.	−	421321.i	−1.41161	−	0.814996i	−0.995540	+	0.0943355i	$0.969927\pi$
$720$		0			0
$721$	−113136.	+	212568.i	−0.217635	+	0.408911i
$722$		−	272065.i		−	0.521912i
$723$	−619386.	−	357603.i	−1.18491	−	0.684107i
$724$	−557438.	+	321837.i	−1.06346	+	0.613987i
$725$		0			0
$726$	34571.8	+	19960.0i	0.0655916	+	0.0378693i
$727$	−163904.			−0.310113			−0.155057	−	0.987906i	$-0.549556\pi$
$727$	−163904.			−0.310113			−0.155057	+	0.987906i	$0.549556\pi$
$728$	−33065.0	−	958051.i	−0.0623886	−	1.80770i
$729$	550026.			1.03497
$730$		0			0
$731$	−358735.	+	207116.i	−0.671334	+	0.387595i
$732$	−135765.	+	78383.9i	−0.253376	+	0.146287i
$733$	285664.	−	494785.i	0.531677	−	0.920892i	−0.467639	−	0.883920i	$-0.654895\pi$
$733$	285664.	−	494785.i	0.531677	−	0.920892i	0.999316	−	0.0369727i	$-0.0117715\pi$
$734$		−	419032.i		−	0.777777i
$735$		0			0
$736$	602334.			1.11194
$737$	−523701.	−	302359.i	−0.964158	−	0.556657i
$738$	5236.50	+	9069.89i	0.00961454	+	0.0166529i
$739$	−443959.	−	768959.i	−0.812931	−	1.40804i	−0.910804	−	0.412839i	$-0.864537\pi$
$739$	−443959.	−	768959.i	−0.812931	−	1.40804i	0.0978725	−	0.995199i	$-0.468796\pi$
$740$		0			0
$741$			340730.i			0.620546i
$742$	365291.	−	12607.2i	0.663485	−	0.0228987i
$743$			1.05528e6i			1.91157i	0.294074	+	0.955783i	$0.404989\pi$
$743$			1.05528e6i			1.91157i	−0.294074	+	0.955783i	$0.595011\pi$
$744$	402020.	−	696319.i	0.726276	−	1.25795i
$745$		0			0
$746$	−226434.	−	392195.i	−0.406877	−	0.704732i
$747$	9758.41	−	16902.1i	0.0174879	−	0.0302899i
$748$	−478404.			−0.855051
$749$	369827.	+	196834.i	0.659227	+	0.350862i
$750$		0			0
$751$	−323750.	+	560751.i	−0.574023	+	0.994237i	0.422124	+	0.906538i	$0.361285\pi$
$751$	−323750.	+	560751.i	−0.574023	+	0.994237i	−0.996147	+	0.0876993i	$0.972049\pi$
$752$	9176.61	+	15894.4i	0.0162273	+	0.0281065i
$753$	−75474.1	+	43575.0i	−0.133109	+	0.0768506i
$754$	475611.	+	274594.i	0.836583	+	0.483001i
$755$		0			0
$756$	200640.	+	321383.i	0.351055	+	0.562314i
$757$			131510.i			0.229491i	0.993395	+	0.114745i	$0.0366052\pi$
$757$			131510.i			0.229491i	−0.993395	+	0.114745i	$0.963395\pi$
$758$	−307165.	−	177342.i	−0.534605	−	0.308654i
$759$	497563.	−	287268.i	0.863702	−	0.498659i
$760$		0			0
$761$	21820.4	+	12598.0i	0.0376784	+	0.0217536i	0.518721	−	0.854944i	$-0.326408\pi$
$761$	21820.4	+	12598.0i	0.0376784	+	0.0217536i	−0.481042	+	0.876697i	$0.659742\pi$
$762$	−82062.6			−0.141330
$763$	−236198.	−	378338.i	−0.405720	−	0.649877i
$764$	−414047.			−0.709354
$765$		0			0
$766$	3920.42	−	2263.46i	0.00668152	−	0.00385758i
$767$	−247707.	+	143014.i	−0.421064	+	0.243101i
$768$	−273480.	+	473682.i	−0.463664	+	0.803090i
$769$		−	319994.i		−	0.541115i	−0.962704	−	0.270557i	$-0.912792\pi$
$769$		−	319994.i		−	0.541115i	0.962704	−	0.270557i	$-0.0872080\pi$
$770$		0			0
$771$	526964.			0.886487
$772$	661689.	+	382026.i	1.11025	+	0.641001i
$773$	413601.	+	716378.i	0.692186	+	1.19890i	0.971120	+	0.238591i	$0.0766856\pi$
$773$	413601.	+	716378.i	0.692186	+	1.19890i	−0.278934	+	0.960310i	$0.589981\pi$
$774$	−3690.23	−	6391.67i	−0.00615987	−	0.0106692i
$775$		0			0
$776$		−	316395.i		−	0.525420i
$777$	−8045.08	−	233105.i	−0.0133257	−	0.386108i
$778$		−	88023.6i		−	0.145425i
$779$	88912.1	−	154000.i	0.146516	−	0.253774i
$780$		0			0
$781$	−279347.	−	483843.i	−0.457975	−	0.793236i
$782$	−277383.	+	480442.i	−0.453593	+	0.785646i
$783$	−550389.			−0.897731
$784$	−20283.7	+	41502.0i	−0.0330002	+	0.0675206i
$785$		0			0
$786$	−76560.8	+	132607.i	−0.123926	+	0.214646i
$787$	73573.4	+	127433.i	0.118788	+	0.205746i	0.919287	−	0.393587i	$-0.128766\pi$
$787$	73573.4	+	127433.i	0.118788	+	0.205746i	−0.800500	+	0.599333i	$0.795433\pi$
$788$	−640354.	+	369708.i	−1.03126	+	0.595397i
$789$	−430564.	−	248586.i	−0.691646	−	0.399322i
$790$		0			0
$791$	−17742.6	−	514088.i	−0.0283573	−	0.821646i
$792$		−	21614.3i		−	0.0344580i
$793$	462698.	+	267139.i	0.735786	+	0.424806i
$794$	−521288.	+	300966.i	−0.826869	+	0.477393i
$795$		0			0
$796$	−30923.8	−	17853.9i	−0.0488053	−	0.0281777i
$797$	−85804.0			−0.135080			−0.0675400	−	0.997717i	$-0.521515\pi$
$797$	−85804.0			−0.135080			−0.0675400	+	0.997717i	$0.521515\pi$
$798$	−59123.4	+	111086.i	−0.0928440	+	0.174443i
$799$	−388288.			−0.608219
$800$		0			0
$801$	480.838	−	277.612i	0.000749434	−	0.000432686i
$802$	−42333.7	+	24441.4i	−0.0658169	+	0.0379994i
$803$	78620.1	−	136174.i	0.121928	−	0.211185i
$804$			493000.i			0.762667i
$805$		0			0
$806$	−1.08065e6			−1.66346
$807$	−300179.	−	173308.i	−0.460928	−	0.266117i
$808$	−124325.	−	215338.i	−0.190431	−	0.329836i
$809$	189747.	+	328652.i	0.289920	+	0.502156i	0.973790	−	0.227447i	$-0.0730379\pi$
$809$	189747.	+	328652.i	0.289920	+	0.502156i	−0.683870	+	0.729604i	$0.739705\pi$
$810$		0			0
$811$		−	686920.i		−	1.04439i	−0.852825	−	0.522197i	$-0.825112\pi$
$811$		−	686920.i		−	1.04439i	0.852825	−	0.522197i	$-0.174888\pi$
$812$	−200495.	−	321150.i	−0.304082	−	0.487074i
$813$		−	728299.i		−	1.10187i
$814$	−71857.0	+	124460.i	−0.108448	+	0.187837i
$815$		0			0
$816$	34565.5	+	59869.2i	0.0519113	+	0.0899131i
$817$	−62657.5	+	108526.i	−0.0938705	+	0.162589i
$818$	209097.			0.312494
$819$	22151.3	−	41619.5i	0.0330241	−	0.0620482i
$820$		0			0
$821$	407240.	−	705361.i	0.604177	−	1.04647i	−0.388004	−	0.921658i	$-0.626835\pi$
$821$	407240.	−	705361.i	0.604177	−	1.04647i	0.992181	−	0.124808i	$-0.0398314\pi$
$822$	−100227.	−	173599.i	−0.148335	−	0.256923i
$823$	158119.	−	91290.1i	0.233445	−	0.134780i	−0.378715	−	0.925513i	$-0.623634\pi$
$823$	158119.	−	91290.1i	0.233445	−	0.134780i	0.612160	+	0.790734i	$0.290301\pi$
$824$	−265630.	−	153362.i	−0.391222	−	0.225872i
$825$		0			0
$826$	−105574.	+	3643.65i	−0.154738	+	0.00534043i
$827$		−	1.07962e6i		−	1.57855i	−0.614040	−	0.789275i	$-0.710457\pi$
$827$		−	1.07962e6i		−	1.57855i	0.614040	−	0.789275i	$-0.289543\pi$
$828$	15978.3	+	9225.06i	0.0233061	+	0.0134558i
$829$	1.00399e6	−	579653.i	1.46090	−	0.843450i	0.461845	−	0.886961i	$-0.347188\pi$
$829$	1.00399e6	−	579653.i	1.46090	−	0.843450i	0.999053	+	0.0435111i	$0.0138544\pi$
$830$		0			0
$831$	136164.	+	78614.1i	0.197178	+	0.113841i
$832$	676689.			0.977558
$833$	−545832.	−	810654.i	−0.786627	−	1.16828i
$834$	132412.			0.190368
$835$		0			0
$836$	−125339.	+	72364.5i	−0.179339	+	0.103541i
$837$	937914.	−	541505.i	1.33879	−	0.772950i
$838$	245828.	−	425787.i	0.350061	−	0.606324i
$839$			652032.i			0.926286i	0.886284	+	0.463143i	$0.153278\pi$
$839$			652032.i			0.926286i	−0.886284	+	0.463143i	$0.846722\pi$
$840$		0			0
$841$	−157292.			−0.222389
$842$	−40961.9	−	23649.3i	−0.0577771	−	0.0333576i
$843$	623929.	+	1.08068e6i	0.877970	+	1.52069i
$844$	42208.9	+	73107.9i	0.0592541	+	0.102631i
$845$		0			0
$846$		−	6918.22i		−	0.00966616i
$847$	−44065.5	+	82793.7i	−0.0614231	+	0.115407i
$848$		−	60745.3i		−	0.0844736i
$849$	−133542.	+	231301.i	−0.185269	+	0.320895i
$850$		0			0
$851$	−155536.	−	269397.i	−0.214770	−	0.371992i
$852$	−227740.	+	394457.i	−0.313732	+	0.543400i
$853$	−440903.			−0.605962			−0.302981	−	0.952997i	$-0.597982\pi$
$853$	−440903.			−0.605962			−0.302981	+	0.952997i	$0.597982\pi$
$854$	104496.	+	167381.i	0.143280	+	0.229504i
$855$		0			0
$856$	−266819.	+	462144.i	−0.364140	+	0.630710i
$857$	572878.	+	992254.i	0.780011	+	1.35102i	0.931935	+	0.362626i	$0.118120\pi$
$857$	572878.	+	992254.i	0.780011	+	1.35102i	−0.151924	+	0.988392i	$0.548547\pi$
$858$	638689.	−	368747.i	0.867590	−	0.500904i
$859$	−66164.8	−	38200.3i	−0.0896687	−	0.0517703i	0.454495	−	0.890749i	$-0.349820\pi$
$859$	−66164.8	−	38200.3i	−0.0896687	−	0.0517703i	−0.544164	+	0.838979i	$0.683153\pi$
$860$		0			0
$861$	529883.	−	330808.i	0.714782	−	0.446241i
$862$			57756.9i			0.0777301i
$863$	483775.	+	279307.i	0.649563	+	0.375026i	0.788289	−	0.615305i	$-0.210967\pi$
$863$	483775.	+	279307.i	0.649563	+	0.375026i	−0.138725	+	0.990331i	$0.544301\pi$
$864$	−671056.	+	387434.i	−0.898941	+	0.519004i
$865$		0			0
$866$	−127581.	−	73658.9i	−0.170118	−	0.0982177i
$867$	−725253.			−0.964831
$868$	657627.	+	350010.i	0.872851	+	0.464559i
$869$	−1.14368e6			−1.51448
$870$		0			0
$871$	1.45508e6	−	840093.i	1.91801	−	1.10737i
$872$	492004.	−	284058.i	0.647046	−	0.373572i
$873$	7780.53	−	13476.3i	0.0102089	−	0.0176824i
$874$			167830.i			0.219709i
$875$		0			0
$876$	−128191.			−0.167051
$877$	−1.32839e6	−	766947.i	−1.72714	−	0.997163i	−0.901202	−	0.433399i	$-0.857314\pi$
$877$	−1.32839e6	−	766947.i	−1.72714	−	0.997163i	−0.825936	−	0.563764i	$-0.809353\pi$
$878$	−223015.	−	386274.i	−0.289298	−	0.501079i
$879$	558305.	+	967013.i	0.722593	+	1.25157i
$880$		0			0
$881$			1.04666e6i			1.34851i	0.738498	+	0.674256i	$0.235536\pi$
$881$			1.04666e6i			1.34851i	−0.738498	+	0.674256i	$0.764464\pi$
$882$	14443.6	−	9725.23i	0.0185669	−	0.0125015i
$883$			554282.i			0.710901i	0.934695	+	0.355450i	$0.115673\pi$
$883$			554282.i			0.710901i	−0.934695	+	0.355450i	$0.884327\pi$
$884$	664615.	−	1.15115e6i	0.850482	−	1.47308i
$885$		0			0
$886$	341766.	+	591955.i	0.435372	+	0.754087i
$887$	82488.6	−	142874.i	0.104845	−	0.181596i	−0.808830	−	0.588043i	$-0.799899\pi$
$887$	82488.6	−	142874.i	0.104845	−	0.181596i	0.913675	+	0.406446i	$0.133232\pi$
$888$	297097.			0.376766
$889$	−6650.16	−	192687.i	−0.00841450	−	0.243809i
$890$		0			0
$891$	−355528.	+	615793.i	−0.447836	+	0.775674i
$892$	−386608.	−	669625.i	−0.485894	−	0.841593i
$893$	−101729.	+	58733.3i	−0.127568	+	0.0736514i
$894$	216610.	+	125060.i	0.271021	+	0.156474i
$895$		0			0
$896$	−501974.	−	267167.i	−0.625267	−	0.332787i
$897$			1.59633e6i			1.98398i
$898$	484729.	+	279858.i	0.601099	+	0.347045i
$899$	−937232.	+	541111.i	−1.15965	+	0.669526i
$900$		0			0
$901$	1.11297e6	+	642575.i	1.37099	+	0.791543i
$902$	−384892.			−0.473070
$903$	−373416.	+	233125.i	−0.457949	+	0.285899i
$904$	655217.			0.801767
$905$		0			0
$906$	695571.	−	401588.i	0.847393	−	0.489243i
$907$	−168830.	+	97474.0i	−0.205227	+	0.118488i	−0.599091	−	0.800681i	$-0.704471\pi$
$907$	−168830.	+	97474.0i	−0.205227	+	0.118488i	0.393864	+	0.919169i	$0.371138\pi$
$908$	−124471.	+	215589.i	−0.150971	+	0.261490i
$909$		−	12229.2i		−	0.0148003i
$910$		0			0
$911$	−1.42407e6			−1.71591			−0.857955	−	0.513726i	$-0.828265\pi$
$911$	−1.42407e6			−1.71591			−0.857955	+	0.513726i	$0.828265\pi$
$912$	18111.9	+	10456.9i	0.0217758	+	0.0125723i
$913$	358630.	+	621166.i	0.430234	+	0.745188i
$914$	−145997.	−	252875.i	−0.174764	−	0.302701i
$915$		0			0
$916$			398486.i			0.474922i
$917$	−317572.	−	169022.i	−0.377663	−	0.201004i
$918$		−	713675.i		−	0.846867i
$919$	−616265.	+	1.06740e6i	−0.729687	+	1.26385i	0.227329	+	0.973818i	$0.427001\pi$
$919$	−616265.	+	1.06740e6i	−0.729687	+	1.26385i	−0.957016	+	0.290037i	$0.906333\pi$
$920$		0			0
$921$	444529.	+	769948.i	0.524060	+	0.907699i
$922$	−87795.3	+	152066.i	−0.103278	+	0.178883i
$923$	1.55231e6			1.82211
$924$	−508107.	+	17536.2i	−0.595130	+	0.0205396i
$925$		0			0
$926$	29181.1	−	50543.2i	0.0340314	−	0.0589442i
$927$	−7542.69	−	13064.3i	−0.00877741	−	0.0152029i
$928$	670568.	−	387153.i	0.778659	−	0.449559i
$929$	310706.	+	179386.i	0.360013	+	0.207854i	0.669087	−	0.743184i	$-0.266685\pi$
$929$	310706.	+	179386.i	0.360013	+	0.207854i	−0.309073	+	0.951038i	$0.600019\pi$
$930$		0			0
$931$	−265626.	−	129823.i	−0.306458	−	0.149779i
$932$			907030.i			1.04421i
$933$	−1.21746e6	−	702900.i	−1.39859	−	0.807477i
$934$	135052.	−	77972.4i	0.154813	−	0.0893813i
$935$		0			0
$936$	52008.7	+	30027.2i	0.0593641	+	0.0342739i
$937$	941678.			1.07256			0.536282	−	0.844039i	$-0.319828\pi$
$937$	941678.			1.07256			0.536282	+	0.844039i	$0.319828\pi$
$938$	620163.	−	21403.5i	0.704856	−	0.0243265i
$939$	1.52266e6			1.72692
$940$		0			0
$941$	−700931.	+	404683.i	−0.791583	+	0.457020i	−0.840519	−	0.541781i	$-0.817750\pi$
$941$	−700931.	+	404683.i	−0.791583	+	0.457020i	0.0489369	+	0.998802i	$0.484417\pi$
$942$	78396.2	−	45262.1i	0.0883473	−	0.0510074i
$943$	416555.	−	721494.i	0.468434	−	0.811352i
$944$			17556.2i			0.0197009i
$945$		0			0
$946$	271239.			0.303088
$947$	982974.	+	567520.i	1.09608	+	0.632822i	0.935188	−	0.354150i	$-0.115230\pi$
$947$	982974.	+	567520.i	1.09608	+	0.632822i	0.160891	+	0.986972i	$0.448563\pi$
$948$	466195.	+	807474.i	0.518742	+	0.898487i
$949$	218443.	+	378354.i	0.242552	+	0.420113i
$950$		0			0
$951$			649970.i			0.718674i
$952$	1.05595e6	−	659231.i	1.16511	−	0.727384i
$953$		−	175576.i		−	0.193322i	−0.995317	−	0.0966608i	$-0.969184\pi$
$953$		−	175576.i		−	0.193322i	0.995317	−	0.0966608i	$-0.0308162\pi$
$954$	−11448.9	+	19830.1i	−0.0125796	+	0.0217886i
$955$		0			0
$956$	−37618.3	−	65156.8i	−0.0411607	−	0.0712925i
$957$	369285.	−	639621.i	0.403216	−	0.698391i
$958$	−817533.			−0.890788
$959$	399497.	−	249407.i	0.434386	−	0.271189i
$960$		0			0
$961$	602993.	−	1.04441e6i	0.652928	−	1.13091i
$962$	−199652.	−	345808.i	−0.215737	−	0.373667i
$963$	−22729.3	+	13122.8i	−0.0245095	+	0.0141505i
$964$	730990.	+	422037.i	0.786606	+	0.454147i
$965$		0			0
$966$	−276994.	+	520439.i	−0.296836	+	0.557719i
$967$		−	406655.i		−	0.434884i	−0.976073	−	0.217442i	$-0.930229\pi$
$967$		−	406655.i		−	0.434884i	0.976073	−	0.217442i	$-0.0697712\pi$
$968$	−103461.	−	59733.1i	−0.110414	−	0.0637477i
$969$	−383182.	+	221230.i	−0.408092	+	0.235612i
$970$		0			0
$971$	−593480.	−	342646.i	−0.629459	−	0.363418i	0.151084	−	0.988521i	$-0.451724\pi$
$971$	−593480.	−	342646.i	−0.629459	−	0.363418i	−0.780543	+	0.625103i	$0.785057\pi$
$972$	−46603.4			−0.0493270
$973$	10730.3	+	310909.i	0.0113341	+	0.328404i
$974$	−491569.			−0.518163
$975$		0			0
$976$	28400.1	−	16396.8i	0.0298140	−	0.0172131i
$977$	−1.15497e6	+	666825.i	−1.20999	+	0.698590i	−0.962758	−	0.270365i	$-0.912856\pi$
$977$	−1.15497e6	+	666825.i	−1.20999	+	0.698590i	−0.247236	+	0.968955i	$0.579522\pi$
$978$	−279121.	+	483452.i	−0.291820	+	0.505447i
$979$			20405.0i			0.0212897i
$980$		0			0
$981$	27941.3			0.0290341
$982$	63891.5	+	36887.8i	0.0662553	+	0.0382525i
$983$	−511263.	−	885533.i	−0.529099	−	0.916427i	−0.999424	−	0.0339336i	$-0.989197\pi$
$983$	−511263.	−	885533.i	−0.529099	−	0.916427i	0.470325	−	0.882493i	$-0.344137\pi$
$984$	397839.	+	689078.i	0.410882	+	0.711669i
$985$		0			0
$986$			713157.i			0.733552i
$987$	−412396.	+	14232.9i	−0.423331	+	0.0146103i
$988$		−	402124.i		−	0.411952i
$989$	−293552.	+	508446.i	−0.300118	+	0.519820i
$990$		0			0
$991$	−683213.	−	1.18336e6i	−0.695679	−	1.20495i	−0.969951	−	0.243300i	$-0.921770\pi$
$991$	−683213.	−	1.18336e6i	−0.695679	−	1.20495i	0.274272	−	0.961652i	$-0.411563\pi$
$992$	−761807.	+	1.31949e6i	−0.774144	+	1.34086i
$993$	455361.			0.461803
$994$	506089.	+	269357.i	0.512217	+	0.272618i
$995$		0			0
$996$	292376.	−	506410.i	0.294729	−	0.510485i
$997$	−190668.	−	330246.i	−0.191817	−	0.332237i	0.754035	−	0.656834i	$-0.228105\pi$
$997$	−190668.	−	330246.i	−0.191817	−	0.332237i	−0.945852	+	0.324597i	$0.894771\pi$
$998$	−190196.	+	109810.i	−0.190960	+	0.110251i
$999$	346564.	+	200089.i	0.347258	+	0.200490i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.5.j.b.124.14		40
5.2	odd	4		175.5.i.b.26.4		20
5.3	odd	4		35.5.h.a.26.7	✓	20
5.4	even	2	inner	175.5.j.b.124.7		40
7.3	odd	6	inner	175.5.j.b.24.7		40
35.3	even	12		35.5.h.a.31.7	yes	20
35.17	even	12		175.5.i.b.101.4		20
35.23	odd	12		245.5.d.a.146.7		20
35.24	odd	6	inner	175.5.j.b.24.14		40
35.33	even	12		245.5.d.a.146.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.h.a.26.7	✓	20	5.3	odd	4
35.5.h.a.31.7	yes	20	35.3	even	12
175.5.i.b.26.4		20	5.2	odd	4
175.5.i.b.101.4		20	35.17	even	12
175.5.j.b.24.7		40	7.3	odd	6	inner
175.5.j.b.24.14		40	35.24	odd	6	inner
175.5.j.b.124.7		40	5.4	even	2	inner
175.5.j.b.124.14		40	1.1	even	1	trivial
245.5.d.a.146.7		20	35.23	odd	12
245.5.d.a.146.8		20	35.33	even	12

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.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.04601 + 1.18127i) q^{2} +(4.41391 + 7.64511i) q^{3} +(-5.20922 - 9.02264i) q^{4} +20.8560i q^{6} +(-48.9708 + 1.69012i) q^{7} -62.4144i q^{8} +(1.53484 - 2.65843i) q^{9} +(56.4068 + 97.6995i) q^{11} +(45.9861 - 79.6502i) q^{12} -313.449 q^{13} +(-102.191 - 54.3896i) q^{14} +(-9.61965 + 16.6617i) q^{16} +(-203.517 - 352.502i) q^{17} +(6.28061 - 3.62611i) q^{18} +(-106.640 - 61.5688i) q^{19} +(-229.074 - 366.928i) q^{21} +266.526i q^{22} +(-499.612 - 288.451i) q^{23} +(477.165 - 275.491i) q^{24} +(-641.320 - 370.266i) q^{26} +742.152 q^{27} +(270.349 + 433.042i) q^{28} -741.613 q^{29} +(1263.78 - 729.642i) q^{31} +(-904.203 + 522.042i) q^{32} +(-497.949 + 862.473i) q^{33} -961.629i q^{34} -31.9814 q^{36} +(466.972 + 269.606i) q^{37} +(-145.458 - 251.941i) q^{38} +(-1383.53 - 2396.35i) q^{39} +1444.11i q^{41} +(-35.2491 - 1021.33i) q^{42} -1017.68i q^{43} +(587.672 - 1017.88i) q^{44} +(-681.475 - 1180.35i) q^{46} +(476.972 - 826.140i) q^{47} -169.841 q^{48} +(2395.29 - 165.533i) q^{49} +(1796.61 - 3111.82i) q^{51} +(1632.82 + 2828.14i) q^{52} +(-2734.35 + 1578.68i) q^{53} +(1518.45 + 876.678i) q^{54} +(105.488 + 3056.49i) q^{56} -1087.04i q^{57} +(-1517.35 - 876.041i) q^{58} +(790.264 - 456.259i) q^{59} +(-1476.15 - 852.257i) q^{61} +3447.60 q^{62} +(-70.6695 + 132.779i) q^{63} -2158.85 q^{64} +(-2037.62 + 1176.42i) q^{66} +(-4642.17 + 2680.16i) q^{67} +(-2120.33 + 3672.52i) q^{68} -5092.79i q^{69} -4952.36 q^{71} +(-165.924 - 95.7963i) q^{72} +(-696.902 - 1207.07i) q^{73} +(636.953 + 1103.24i) q^{74} +1282.90i q^{76} +(-2927.41 - 4689.09i) q^{77} -6537.28i q^{78} +(-5068.88 + 8779.55i) q^{79} +(3151.47 + 5458.50i) q^{81} +(-1705.88 + 2954.66i) q^{82} +6357.92 q^{83} +(-2117.36 + 3978.26i) q^{84} +(1202.15 - 2082.19i) q^{86} +(-3273.41 - 5669.71i) q^{87} +(6097.85 - 3520.60i) q^{88} +(156.641 + 90.4366i) q^{89} +(15349.8 - 529.765i) q^{91} +6010.43i q^{92} +(11156.4 + 6441.14i) q^{93} +(1951.78 - 1126.86i) q^{94} +(-7982.14 - 4608.49i) q^{96} +5069.26 q^{97} +(5096.32 + 2490.79i) q^{98} +346.303 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 116 q^{4} - 532 q^{9} + 180 q^{11} + 1380 q^{14} - 252 q^{16} + 3324 q^{19} + 3360 q^{21} - 3816 q^{24} - 2700 q^{26} - 1680 q^{29} - 7272 q^{31} - 8328 q^{36} - 5952 q^{39} + 7236 q^{44} + 4076 q^{46}+ \cdots + 73432 q^{99}+O(q^{100}) \) 40 * q + 116 * q^4 - 532 * q^9 + 180 * q^11 + 1380 * q^14 - 252 * q^16 + 3324 * q^19 + 3360 * q^21 - 3816 * q^24 - 2700 * q^26 - 1680 * q^29 - 7272 * q^31 - 8328 * q^36 - 5952 * q^39 + 7236 * q^44 + 4076 * q^46 - 832 * q^49 + 12648 * q^51 - 66360 * q^54 + 27000 * q^56 - 432 * q^59 - 11712 * q^61 + 51576 * q^64 - 32496 * q^66 + 20976 * q^71 - 5076 * q^74 - 41576 * q^79 + 8308 * q^81 + 40632 * q^84 + 3960 * q^86 + 26352 * q^89 + 35952 * q^91 + 101220 * q^94 - 34920 * q^96 + 73432 * q^99

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