LMFDB - Embedded newform 210.3.c.a.29.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(29,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("210.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.20
Character	$\chi$	$=$	210.29
Dual form			210.3.c.a.29.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +(1.70910 + 2.46556i) q^{3} +2.00000 q^{4} +(4.99890 - 0.104764i) q^{5} +(2.41703 + 3.48683i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(-3.15796 + 8.42777i) q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +(1.70910 + 2.46556i) q^{3} +2.00000 q^{4} +(4.99890 - 0.104764i) q^{5} +(2.41703 + 3.48683i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(-3.15796 + 8.42777i) q^{9} +(7.06952 - 0.148158i) q^{10} -2.66621i q^{11} +(3.41820 + 4.93112i) q^{12} -5.56242i q^{13} -3.74166i q^{14} +(8.80192 + 12.1460i) q^{15} +4.00000 q^{16} -18.5525 q^{17} +(-4.46603 + 11.9187i) q^{18} +0.634999 q^{19} +(9.99780 - 0.209527i) q^{20} +(6.52326 - 4.52185i) q^{21} -3.77058i q^{22} -15.6144 q^{23} +(4.83406 + 6.97365i) q^{24} +(24.9780 - 1.04741i) q^{25} -7.86645i q^{26} +(-26.1764 + 6.61774i) q^{27} -5.29150i q^{28} +43.3517i q^{29} +(12.4478 + 17.1771i) q^{30} +13.5411 q^{31} +5.65685 q^{32} +(6.57369 - 4.55681i) q^{33} -26.2372 q^{34} +(-0.277179 - 13.2259i) q^{35} +(-6.31593 + 16.8555i) q^{36} -35.0014i q^{37} +0.898024 q^{38} +(13.7145 - 9.50672i) q^{39} +(14.1390 - 0.296316i) q^{40} -15.6116i q^{41} +(9.22528 - 6.39486i) q^{42} -64.4699i q^{43} -5.33241i q^{44} +(-14.9034 + 42.4604i) q^{45} -22.0820 q^{46} -52.5576 q^{47} +(6.83639 + 9.86224i) q^{48} -7.00000 q^{49} +(35.3243 - 1.48126i) q^{50} +(-31.7081 - 45.7423i) q^{51} -11.1248i q^{52} +51.6056 q^{53} +(-37.0191 + 9.35890i) q^{54} +(-0.279321 - 13.3281i) q^{55} -7.48331i q^{56} +(1.08528 + 1.56563i) q^{57} +61.3086i q^{58} -32.9384i q^{59} +(17.6038 + 24.2921i) q^{60} -104.197 q^{61} +19.1501 q^{62} +(22.2978 + 8.35519i) q^{63} +8.00000 q^{64} +(-0.582739 - 27.8060i) q^{65} +(9.29660 - 6.44430i) q^{66} -113.588i q^{67} -37.1050 q^{68} +(-26.6865 - 38.4981i) q^{69} +(-0.391990 - 18.7042i) q^{70} +36.8746i q^{71} +(-8.93207 + 23.8373i) q^{72} +144.926i q^{73} -49.4995i q^{74} +(45.2724 + 59.7947i) q^{75} +1.27000 q^{76} -7.05412 q^{77} +(19.3952 - 13.4445i) q^{78} +57.9487 q^{79} +(19.9956 - 0.419055i) q^{80} +(-61.0545 - 53.2292i) q^{81} -22.0781i q^{82} +45.0936 q^{83} +(13.0465 - 9.04370i) q^{84} +(-92.7422 + 1.94363i) q^{85} -91.1742i q^{86} +(-106.886 + 74.0924i) q^{87} -7.54117i q^{88} +80.9733i q^{89} +(-21.0766 + 60.0481i) q^{90} -14.7168 q^{91} -31.2287 q^{92} +(23.1432 + 33.3865i) q^{93} -74.3277 q^{94} +(3.17430 - 0.0665248i) q^{95} +(9.66812 + 13.9473i) q^{96} -96.2255i q^{97} -9.89949 q^{98} +(22.4702 + 8.41978i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 48 q^{4} + 44 q^{9}+O(q^{10}) $ 24 * q + 48 * q^4 + 44 * q^9	$ 24 q + 48 q^{4} + 44 q^{9} + 16 q^{10} + 4 q^{15} + 96 q^{16} - 80 q^{19} - 28 q^{21} + 48 q^{25} - 56 q^{30} + 224 q^{31} + 128 q^{34} + 88 q^{36} - 92 q^{39} + 32 q^{40} - 72 q^{45} - 144 q^{46} - 168 q^{49} - 284 q^{51} - 144 q^{54} - 320 q^{55} + 8 q^{60} + 192 q^{64} + 224 q^{66} - 152 q^{69} - 56 q^{70} + 48 q^{75} - 160 q^{76} - 72 q^{79} - 212 q^{81} - 56 q^{84} - 64 q^{85} - 240 q^{90} + 168 q^{91} - 128 q^{94} - 876 q^{99}+O(q^{100}) $ 24 * q + 48 * q^4 + 44 * q^9 + 16 * q^10 + 4 * q^15 + 96 * q^16 - 80 * q^19 - 28 * q^21 + 48 * q^25 - 56 * q^30 + 224 * q^31 + 128 * q^34 + 88 * q^36 - 92 * q^39 + 32 * q^40 - 72 * q^45 - 144 * q^46 - 168 * q^49 - 284 * q^51 - 144 * q^54 - 320 * q^55 + 8 * q^60 + 192 * q^64 + 224 * q^66 - 152 * q^69 - 56 * q^70 + 48 * q^75 - 160 * q^76 - 72 * q^79 - 212 * q^81 - 56 * q^84 - 64 * q^85 - 240 * q^90 + 168 * q^91 - 128 * q^94 - 876 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.41421			0.707107
$2$	1.41421			0.707107
$3$	1.70910	+	2.46556i	0.569700	+	0.821853i
$3$	1.70910	+	2.46556i	0.569700	+	0.821853i
$4$	2.00000			0.500000
$5$	4.99890	−	0.104764i	0.999780	−	0.0209527i
$5$	4.99890	−	0.104764i	0.999780	−	0.0209527i
$6$	2.41703	+	3.48683i	0.402838	+	0.581138i
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	2.82843			0.353553
$9$	−3.15796	+	8.42777i	−0.350885	+	0.936419i
$10$	7.06952	−	0.148158i	0.706952	−	0.0148158i
$11$		−	2.66621i		−	0.242382i	−0.992629	−	0.121191i	$-0.961329\pi$
$11$		−	2.66621i		−	0.242382i	0.992629	−	0.121191i	$-0.0386714\pi$
$12$	3.41820	+	4.93112i	0.284850	+	0.410927i
$13$		−	5.56242i		−	0.427878i	−0.976847	−	0.213939i	$-0.931371\pi$
$13$		−	5.56242i		−	0.427878i	0.976847	−	0.213939i	$-0.0686294\pi$
$14$		−	3.74166i		−	0.267261i
$15$	8.80192	+	12.1460i	0.586795	+	0.809736i
$16$	4.00000			0.250000
$17$	−18.5525			−1.09132			−0.545662	−	0.838005i	$-0.683722\pi$
$17$	−18.5525			−1.09132			−0.545662	+	0.838005i	$0.683722\pi$
$18$	−4.46603	+	11.9187i	−0.248113	+	0.662148i
$19$	0.634999			0.0334210			0.0167105	−	0.999860i	$-0.494681\pi$
$19$	0.634999			0.0334210			0.0167105	+	0.999860i	$0.494681\pi$
$20$	9.99780	−	0.209527i	0.499890	−	0.0104764i
$21$	6.52326	−	4.52185i	0.310631	−	0.215326i
$22$		−	3.77058i		−	0.171390i
$23$	−15.6144			−0.678885			−0.339442	−	0.940627i	$-0.610238\pi$
$23$	−15.6144			−0.678885			−0.339442	+	0.940627i	$0.610238\pi$
$24$	4.83406	+	6.97365i	0.201419	+	0.290569i
$25$	24.9780	−	1.04741i	0.999122	−	0.0418963i
$26$		−	7.86645i		−	0.302556i
$27$	−26.1764	+	6.61774i	−0.969497	+	0.245101i
$28$		−	5.29150i		−	0.188982i
$29$			43.3517i			1.49489i	0.664325	+	0.747444i	$0.268719\pi$
$29$			43.3517i			1.49489i	−0.664325	+	0.747444i	$0.731281\pi$
$30$	12.4478	+	17.1771i	0.414926	+	0.572570i
$31$	13.5411			0.436811			0.218406	−	0.975858i	$-0.429914\pi$
$31$	13.5411			0.436811			0.218406	+	0.975858i	$0.429914\pi$
$32$	5.65685			0.176777
$33$	6.57369	−	4.55681i	0.199203	−	0.138085i
$34$	−26.2372			−0.771683
$35$	−0.277179	−	13.2259i	−0.00791939	−	0.377881i
$36$	−6.31593	+	16.8555i	−0.175442	+	0.468209i
$37$		−	35.0014i		−	0.945984i	−0.881067	−	0.472992i	$-0.843174\pi$
$37$		−	35.0014i		−	0.945984i	0.881067	−	0.472992i	$-0.156826\pi$
$38$	0.898024			0.0236322
$39$	13.7145	−	9.50672i	0.351653	−	0.243762i
$40$	14.1390	−	0.296316i	0.353476	−	0.00740791i
$41$		−	15.6116i		−	0.380770i	−0.981710	−	0.190385i	$-0.939026\pi$
$41$		−	15.6116i		−	0.380770i	0.981710	−	0.190385i	$-0.0609736\pi$
$42$	9.22528	−	6.39486i	0.219649	−	0.152259i
$43$		−	64.4699i		−	1.49930i	−0.661835	−	0.749650i	$-0.730222\pi$
$43$		−	64.4699i		−	1.49930i	0.661835	−	0.749650i	$-0.269778\pi$
$44$		−	5.33241i		−	0.121191i
$45$	−14.9034	+	42.4604i	−0.331187	+	0.943565i
$46$	−22.0820			−0.480044
$47$	−52.5576			−1.11825			−0.559124	−	0.829084i	$-0.688862\pi$
$47$	−52.5576			−1.11825			−0.559124	+	0.829084i	$0.688862\pi$
$48$	6.83639	+	9.86224i	0.142425	+	0.205463i
$49$	−7.00000			−0.142857
$50$	35.3243	−	1.48126i	0.706486	−	0.0296251i
$51$	−31.7081	−	45.7423i	−0.621727	−	0.896908i
$52$		−	11.1248i		−	0.213939i
$53$	51.6056			0.973691			0.486846	−	0.873488i	$-0.338147\pi$
$53$	51.6056			0.973691			0.486846	+	0.873488i	$0.338147\pi$
$54$	−37.0191	+	9.35890i	−0.685538	+	0.173313i
$55$	−0.279321	−	13.3281i	−0.00507857	−	0.242329i
$56$		−	7.48331i		−	0.133631i
$57$	1.08528	+	1.56563i	0.0190399	+	0.0274672i
$58$			61.3086i			1.05705i
$59$		−	32.9384i		−	0.558277i	−0.960251	−	0.279139i	$-0.909951\pi$
$59$		−	32.9384i		−	0.558277i	0.960251	−	0.279139i	$-0.0900489\pi$
$60$	17.6038	+	24.2921i	0.293397	+	0.404868i
$61$	−104.197			−1.70815			−0.854077	−	0.520147i	$-0.825877\pi$
$61$	−104.197			−1.70815			−0.854077	+	0.520147i	$0.825877\pi$
$62$	19.1501			0.308872
$63$	22.2978	+	8.35519i	0.353933	+	0.132622i
$64$	8.00000			0.125000
$65$	−0.582739	−	27.8060i	−0.00896522	−	0.427784i
$66$	9.29660	−	6.44430i	0.140858	−	0.0976409i
$67$		−	113.588i		−	1.69535i	−0.530519	−	0.847673i	$-0.678003\pi$
$67$		−	113.588i		−	1.69535i	0.530519	−	0.847673i	$-0.321997\pi$
$68$	−37.1050			−0.545662
$69$	−26.6865	−	38.4981i	−0.386760	−	0.557944i
$70$	−0.391990	−	18.7042i	−0.00559985	−	0.267203i
$71$			36.8746i			0.519361i	0.965695	+	0.259680i	$0.0836172\pi$
$71$			36.8746i			0.519361i	−0.965695	+	0.259680i	$0.916383\pi$
$72$	−8.93207	+	23.8373i	−0.124057	+	0.331074i
$73$			144.926i			1.98529i	0.121058	+	0.992645i	$0.461371\pi$
$73$			144.926i			1.98529i	−0.121058	+	0.992645i	$0.538629\pi$
$74$		−	49.4995i		−	0.668912i
$75$	45.2724	+	59.7947i	0.603632	+	0.797263i
$76$	1.27000			0.0167105
$77$	−7.05412			−0.0916119
$78$	19.3952	−	13.4445i	0.248656	−	0.172366i
$79$	57.9487			0.733528			0.366764	−	0.930314i	$-0.380466\pi$
$79$	57.9487			0.733528			0.366764	+	0.930314i	$0.380466\pi$
$80$	19.9956	−	0.419055i	0.249945	−	0.00523818i
$81$	−61.0545	−	53.2292i	−0.753760	−	0.657150i
$82$		−	22.0781i		−	0.269245i
$83$	45.0936			0.543296			0.271648	−	0.962397i	$-0.412431\pi$
$83$	45.0936			0.543296			0.271648	+	0.962397i	$0.412431\pi$
$84$	13.0465	−	9.04370i	0.155316	−	0.107663i
$85$	−92.7422	+	1.94363i	−1.09109	+	0.0228662i
$86$		−	91.1742i		−	1.06016i
$87$	−106.886	+	74.0924i	−1.22858	+	0.851637i
$88$		−	7.54117i		−	0.0856951i
$89$			80.9733i			0.909813i	0.890539	+	0.454906i	$0.150327\pi$
$89$			80.9733i			0.909813i	−0.890539	+	0.454906i	$0.849673\pi$
$90$	−21.0766	+	60.0481i	−0.234185	+	0.667201i
$91$	−14.7168			−0.161723
$92$	−31.2287			−0.339442
$93$	23.1432	+	33.3865i	0.248851	+	0.358995i
$94$	−74.3277			−0.790720
$95$	3.17430	−	0.0665248i	0.0334137	−	0.000700261i
$96$	9.66812	+	13.9473i	0.100710	+	0.145284i
$97$		−	96.2255i		−	0.992016i	−0.868318	−	0.496008i	$-0.834799\pi$
$97$		−	96.2255i		−	0.992016i	0.868318	−	0.496008i	$-0.165201\pi$
$98$	−9.89949			−0.101015
$99$	22.4702	+	8.41978i	0.226971	+	0.0850483i
$100$	49.9561	−	2.09481i	0.499561	−	0.0209481i
$101$			91.9696i			0.910590i	0.890341	+	0.455295i	$0.150466\pi$
$101$			91.9696i			0.910590i	−0.890341	+	0.455295i	$0.849534\pi$
$102$	−44.8420	−	64.6894i	−0.439627	−	0.634210i
$103$		−	30.6043i		−	0.297129i	−0.988903	−	0.148565i	$-0.952535\pi$
$103$		−	30.6043i		−	0.297129i	0.988903	−	0.148565i	$-0.0474653\pi$
$104$		−	15.7329i		−	0.151278i
$105$	32.1354	−	23.2877i	0.306051	−	0.221787i
$106$	72.9814			0.688504
$107$	−190.645			−1.78173			−0.890864	−	0.454270i	$-0.849900\pi$
$107$	−190.645			−1.78173			−0.890864	+	0.454270i	$0.849900\pi$
$108$	−52.3529	+	13.2355i	−0.484749	+	0.122551i
$109$	73.9965			0.678867			0.339433	−	0.940630i	$-0.389765\pi$
$109$	73.9965			0.678867			0.339433	+	0.940630i	$0.389765\pi$
$110$	−0.395020	−	18.8488i	−0.00359109	−	0.171353i
$111$	86.2980	−	59.8208i	0.777460	−	0.538927i
$112$		−	10.5830i		−	0.0944911i
$113$	128.861			1.14037			0.570183	−	0.821518i	$-0.306872\pi$
$113$	128.861			1.14037			0.570183	+	0.821518i	$0.306872\pi$
$114$	1.53481	+	2.21413i	0.0134633	+	0.0194222i
$115$	−78.0546	+	1.63582i	−0.678736	+	0.0142245i
$116$			86.7035i			0.747444i
$117$	46.8788	+	17.5659i	0.400673	+	0.150136i
$118$		−	46.5819i		−	0.394762i
$119$			49.0853i			0.412482i
$120$	24.8956	+	34.3542i	0.207463	+	0.286285i
$121$	113.891			0.941251
$122$	−147.357			−1.20785
$123$	38.4912	−	26.6817i	0.312937	−	0.216924i
$124$	27.0823			0.218406
$125$	124.753	−	7.85267i	0.998025	−	0.0628214i
$126$	31.5338	+	11.8160i	0.250268	+	0.0937779i
$127$		−	95.8035i		−	0.754358i	−0.926140	−	0.377179i	$-0.876894\pi$
$127$		−	95.8035i		−	0.754358i	0.926140	−	0.377179i	$-0.123106\pi$
$128$	11.3137			0.0883883
$129$	158.954	−	110.185i	1.23220	−	0.854150i
$130$	−0.824118	−	39.3236i	−0.00633937	−	0.302489i
$131$			148.465i			1.13332i	0.823952	+	0.566660i	$0.191765\pi$
$131$			148.465i			1.13332i	−0.823952	+	0.566660i	$0.808235\pi$
$132$	13.1474	−	9.11361i	0.0996013	−	0.0690425i
$133$		−	1.68005i		−	0.0126320i
$134$		−	160.638i		−	1.19879i
$135$	−130.160	+	35.8238i	−0.964149	+	0.265361i
$136$	−52.4744			−0.385842
$137$	115.295			0.841572			0.420786	−	0.907160i	$-0.361754\pi$
$137$	115.295			0.841572			0.420786	+	0.907160i	$0.361754\pi$
$138$	−37.7404	−	54.4445i	−0.273481	−	0.394526i
$139$	95.1005			0.684176			0.342088	−	0.939668i	$-0.388866\pi$
$139$	95.1005			0.684176			0.342088	+	0.939668i	$0.388866\pi$
$140$	−0.554357	−	26.4517i	−0.00395969	−	0.188941i
$141$	−89.8262	−	129.584i	−0.637065	−	0.919035i
$142$			52.1486i			0.367244i
$143$	−14.8305			−0.103710
$144$	−12.6319	+	33.7111i	−0.0877212	+	0.234105i
$145$	4.54169	+	216.711i	0.0313220	+	1.49456i
$146$			204.957i			1.40381i
$147$	−11.9637	−	17.2589i	−0.0813857	−	0.117408i
$148$		−	70.0028i		−	0.472992i
$149$			179.342i			1.20364i	0.798632	+	0.601820i	$0.205558\pi$
$149$			179.342i			1.20364i	−0.798632	+	0.601820i	$0.794442\pi$
$150$	64.0248	+	84.5625i	0.426832	+	0.563750i
$151$	45.6621			0.302398			0.151199	−	0.988503i	$-0.451687\pi$
$151$	45.6621			0.302398			0.151199	+	0.988503i	$0.451687\pi$
$152$	1.79605			0.0118161
$153$	58.5882	−	156.356i	0.382929	−	1.02194i
$154$	−9.97603			−0.0647794
$155$	67.6909	−	1.41862i	0.436715	−	0.00915238i
$156$	27.4289	−	19.0134i	0.175827	−	0.121881i
$157$			223.977i			1.42661i	0.700856	+	0.713303i	$0.252802\pi$
$157$			223.977i			1.42661i	−0.700856	+	0.713303i	$0.747198\pi$
$158$	81.9518			0.518683
$159$	88.1991	+	127.237i	0.554711	+	0.800231i
$160$	28.2781	−	0.592633i	0.176738	−	0.00370395i
$161$			41.3117i			0.256594i
$162$	−86.3441	−	75.2774i	−0.532989	−	0.464675i
$163$			300.309i			1.84239i	0.389102	+	0.921195i	$0.372785\pi$
$163$			300.309i			1.84239i	−0.389102	+	0.921195i	$0.627215\pi$
$164$		−	31.2231i		−	0.190385i
$165$	32.3838	−	23.4677i	0.196266	−	0.142229i
$166$	63.7719			0.384168
$167$	−125.443			−0.751158			−0.375579	−	0.926790i	$-0.622556\pi$
$167$	−125.443			−0.751158			−0.375579	+	0.926790i	$0.622556\pi$
$168$	18.4506	−	12.7897i	0.109825	−	0.0761293i
$169$	138.060			0.816920
$170$	−131.157	+	2.74871i	−0.771514	+	0.0161689i
$171$	−2.00530	+	5.35163i	−0.0117269	+	0.0312961i
$172$		−	128.940i		−	0.749650i
$173$	−195.635			−1.13084			−0.565419	−	0.824804i	$-0.691286\pi$
$173$	−195.635			−1.13084			−0.565419	+	0.824804i	$0.691286\pi$
$174$	−151.160	+	104.782i	−0.868736	+	0.602198i
$175$	−2.77118	−	66.0857i	−0.0158353	−	0.377633i
$176$		−	10.6648i		−	0.0605956i
$177$	81.2115	−	56.2949i	0.458822	−	0.318050i
$178$			114.514i			0.643335i
$179$		−	164.110i		−	0.916815i	−0.888742	−	0.458408i	$-0.848420\pi$
$179$		−	164.110i		−	0.916815i	0.888742	−	0.458408i	$-0.151580\pi$
$180$	−29.8069	+	84.9209i	−0.165594	+	0.471783i
$181$	113.029			0.624468			0.312234	−	0.950005i	$-0.398923\pi$
$181$	113.029			0.624468			0.312234	+	0.950005i	$0.398923\pi$
$182$	−20.8127			−0.114355
$183$	−178.084	−	256.905i	−0.973135	−	1.40385i
$184$	−44.1641			−0.240022
$185$	−3.66687	−	174.969i	−0.0198209	−	0.945776i
$186$	32.7294	+	47.2156i	0.175964	+	0.253847i
$187$			49.4648i			0.264518i
$188$	−105.115			−0.559124
$189$	17.5089	+	69.2563i	0.0926397	+	0.366436i
$190$	4.48914	−	0.0940803i	0.0236270	−	0.000495160i
$191$			196.398i			1.02826i	0.857711	+	0.514132i	$0.171886\pi$
$191$			196.398i			1.02826i	−0.857711	+	0.514132i	$0.828114\pi$
$192$	13.6728	+	19.7245i	0.0712124	+	0.102732i
$193$			282.304i			1.46272i	0.681994	+	0.731358i	$0.261113\pi$
$193$			282.304i			1.46272i	−0.681994	+	0.731358i	$0.738887\pi$
$194$		−	136.083i		−	0.701461i
$195$	67.5613	−	48.9599i	0.346468	−	0.251077i
$196$	−14.0000			−0.0714286
$197$	286.761			1.45564			0.727821	−	0.685767i	$-0.240533\pi$
$197$	286.761			1.45564			0.727821	+	0.685767i	$0.240533\pi$
$198$	31.7776	+	11.9074i	0.160493	+	0.0601382i
$199$	−74.9133			−0.376449			−0.188224	−	0.982126i	$-0.560273\pi$
$199$	−74.9133			−0.376449			−0.188224	+	0.982126i	$0.560273\pi$
$200$	70.6486	−	2.96251i	0.353243	−	0.0148126i
$201$	280.058	−	194.133i	1.39333	−	0.965838i
$202$			130.065i			0.643884i
$203$	114.698			0.565014
$204$	−63.4162	−	91.4847i	−0.310864	−	0.448454i
$205$	−1.63552	−	78.0406i	−0.00797816	−	0.380686i
$206$		−	43.2810i		−	0.210102i
$207$	49.3096	−	131.594i	0.238210	−	0.635720i
$208$		−	22.2497i		−	0.106970i
$209$		−	1.69304i		−	0.00810066i
$210$	45.4463	−	32.9338i	0.216411	−	0.156827i
$211$	−136.746			−0.648083			−0.324042	−	0.946043i	$-0.605042\pi$
$211$	−136.746			−0.648083			−0.324042	+	0.946043i	$0.605042\pi$
$212$	103.211			0.486846
$213$	−90.9166	+	63.0224i	−0.426838	+	0.295880i
$214$	−269.613			−1.25987
$215$	−6.75410	−	322.279i	−0.0314144	−	1.49897i
$216$	−74.0381	+	18.7178i	−0.342769	+	0.0866565i
$217$		−	35.8265i		−	0.165099i
$218$	104.647			0.480031
$219$	−357.324	+	247.693i	−1.63162	+	1.13102i
$220$	−0.558643	−	26.6562i	−0.00253929	−	0.121165i
$221$			103.197i			0.466954i
$222$	122.044	−	84.5994i	0.549747	−	0.381079i
$223$		−	25.8662i		−	0.115992i	−0.998317	−	0.0579959i	$-0.981529\pi$
$223$		−	25.8662i		−	0.115992i	0.998317	−	0.0579959i	$-0.0184710\pi$
$224$		−	14.9666i		−	0.0668153i
$225$	−70.0525	+	213.817i	−0.311344	+	0.950297i
$226$	182.238			0.806361
$227$	−24.3393			−0.107222			−0.0536109	−	0.998562i	$-0.517073\pi$
$227$	−24.3393			−0.107222			−0.0536109	+	0.998562i	$0.517073\pi$
$228$	2.17055	+	3.13126i	0.00951997	+	0.0137336i
$229$	−241.018			−1.05248			−0.526239	−	0.850336i	$-0.676398\pi$
$229$	−241.018			−1.05248			−0.526239	+	0.850336i	$0.676398\pi$
$230$	−110.386	+	2.31339i	−0.479939	+	0.0100582i
$231$	−12.0562	−	17.3923i	−0.0521913	−	0.0752915i
$232$			122.617i			0.528523i
$233$	−24.9582			−0.107117			−0.0535584	−	0.998565i	$-0.517056\pi$
$233$	−24.9582			−0.107117			−0.0535584	+	0.998565i	$0.517056\pi$
$234$	66.2966	+	24.8420i	0.283319	+	0.106162i
$235$	−262.731	+	5.50613i	−1.11800	+	0.0234303i
$236$		−	65.8767i		−	0.279139i
$237$	99.0401	+	142.876i	0.417891	+	0.602852i
$238$			69.4172i			0.291669i
$239$		−	240.780i		−	1.00745i	−0.863864	−	0.503725i	$-0.831963\pi$
$239$		−	240.780i		−	1.00745i	0.863864	−	0.503725i	$-0.168037\pi$
$240$	35.2077	+	48.5842i	0.146699	+	0.202434i
$241$	−147.382			−0.611543			−0.305771	−	0.952105i	$-0.598914\pi$
$241$	−147.382			−0.611543			−0.305771	+	0.952105i	$0.598914\pi$
$242$	161.067			0.665565
$243$	26.8914	−	241.507i	0.110664	−	0.993858i
$244$	−208.395			−0.854077
$245$	−34.9923	+	0.733345i	−0.142826	+	0.00299325i
$246$	54.4348	−	37.7336i	0.221280	−	0.153389i
$247$		−	3.53213i		−	0.0143001i
$248$	38.3001			0.154436
$249$	77.0693	+	111.181i	0.309515	+	0.446509i
$250$	176.428	−	11.1054i	0.705710	−	0.0444214i
$251$		−	387.525i		−	1.54393i	−0.635668	−	0.771963i	$-0.719275\pi$
$251$		−	387.525i		−	1.54393i	0.635668	−	0.771963i	$-0.280725\pi$
$252$	44.5956	+	16.7104i	0.176966	+	0.0663110i
$253$			41.6311i			0.164550i
$254$		−	135.487i		−	0.533412i
$255$	−163.298	−	225.340i	−0.640383	−	0.883685i
$256$	16.0000			0.0625000
$257$	11.2525			0.0437839			0.0218919	−	0.999760i	$-0.493031\pi$
$257$	11.2525			0.0437839			0.0218919	+	0.999760i	$0.493031\pi$
$258$	224.795	−	155.826i	0.871300	−	0.603975i
$259$	−92.6050			−0.357548
$260$	−1.16548	−	55.6120i	−0.00448261	−	0.213892i
$261$	−365.358	−	136.903i	−1.39984	−	0.524533i
$262$			209.961i			0.801378i
$263$	−308.658			−1.17361			−0.586803	−	0.809730i	$-0.699614\pi$
$263$	−308.658			−1.17361			−0.586803	+	0.809730i	$0.699614\pi$
$264$	18.5932	−	12.8886i	0.0704288	−	0.0488204i
$265$	257.971	−	5.40639i	0.973477	−	0.0204015i
$266$		−	2.37595i		−	0.00893214i
$267$	−199.644	+	138.391i	−0.747732	+	0.518320i
$268$		−	227.176i		−	0.847673i
$269$		−	198.926i		−	0.739503i	−0.929131	−	0.369751i	$-0.879443\pi$
$269$		−	198.926i		−	0.739503i	0.929131	−	0.369751i	$-0.120557\pi$
$270$	−184.074	+	50.6625i	−0.681756	+	0.187639i
$271$	−176.341			−0.650706			−0.325353	−	0.945593i	$-0.605483\pi$
$271$	−176.341			−0.650706			−0.325353	+	0.945593i	$0.605483\pi$
$272$	−74.2101			−0.272831
$273$	−25.1524	−	36.2851i	−0.0921334	−	0.132912i
$274$	163.052			0.595082
$275$	−2.79260	−	66.5966i	−0.0101549	−	0.242169i
$276$	−53.3729	−	76.9962i	−0.193380	−	0.278972i
$277$		−	433.093i		−	1.56351i	−0.623583	−	0.781757i	$-0.714324\pi$
$277$		−	433.093i		−	1.56351i	0.623583	−	0.781757i	$-0.285676\pi$
$278$	134.492			0.483786
$279$	−42.7624	+	114.122i	−0.153270	+	0.409038i
$280$	−0.783979	−	37.4084i	−0.00279993	−	0.133601i
$281$			281.134i			1.00048i	0.865887	+	0.500239i	$0.166754\pi$
$281$			281.134i			1.00048i	−0.865887	+	0.500239i	$0.833246\pi$
$282$	−127.033	−	183.259i	−0.450473	−	0.649856i
$283$		−	113.795i		−	0.402101i	−0.979581	−	0.201050i	$-0.935565\pi$
$283$		−	113.795i		−	0.402101i	0.979581	−	0.201050i	$-0.0644355\pi$
$284$			73.7492i			0.259680i
$285$	5.58921	+	7.71272i	0.0196113	+	0.0270622i
$286$	−20.9736			−0.0733341
$287$	−41.3043			−0.143917
$288$	−17.8641	+	47.6747i	−0.0620283	+	0.165537i
$289$	55.1959			0.190989
$290$	6.42291	+	306.476i	0.0221480	+	1.05681i
$291$	237.250	−	164.459i	0.815291	−	0.565151i
$292$			289.852i			0.992645i
$293$	−355.330			−1.21273			−0.606365	−	0.795187i	$-0.707373\pi$
$293$	−355.330			−1.21273			−0.606365	+	0.795187i	$0.707373\pi$
$294$	−16.9192	−	24.4078i	−0.0575483	−	0.0830197i
$295$	−3.45074	−	164.656i	−0.0116974	−	0.558155i
$296$		−	98.9989i		−	0.334456i
$297$	17.6443	+	69.7917i	0.0594083	+	0.234989i
$298$			253.628i			0.851102i
$299$			86.8535i			0.290480i
$300$	90.5448	+	119.589i	0.301816	+	0.398632i
$301$	−170.571			−0.566682
$302$	64.5759			0.213828
$303$	−226.756	+	157.185i	−0.748371	+	0.518763i
$304$	2.54000			0.00835525
$305$	−520.873	+	10.9161i	−1.70778	+	0.0357905i
$306$	82.8562	−	221.121i	0.270772	−	0.722618i
$307$			404.490i			1.31756i	0.752337	+	0.658778i	$0.228926\pi$
$307$			404.490i			1.31756i	−0.752337	+	0.658778i	$0.771074\pi$
$308$	−14.1082			−0.0458059
$309$	75.4567	−	52.3058i	0.244196	−	0.169274i
$310$	95.7293	−	2.00623i	0.308804	−	0.00647171i
$311$			530.330i			1.70524i	0.522530	+	0.852621i	$0.324988\pi$
$311$			530.330i			1.70524i	−0.522530	+	0.852621i	$0.675012\pi$
$312$	38.7904	−	26.8891i	0.124328	−	0.0861829i
$313$		−	561.172i		−	1.79288i	−0.443165	−	0.896440i	$-0.646144\pi$
$313$		−	561.172i		−	1.79288i	0.443165	−	0.896440i	$-0.353856\pi$
$314$			316.751i			1.00876i
$315$	112.340	+	39.4308i	0.356634	+	0.125177i
$316$	115.897			0.366764
$317$	264.560			0.834574			0.417287	−	0.908775i	$-0.362981\pi$
$317$	264.560			0.834574			0.417287	+	0.908775i	$0.362981\pi$
$318$	124.732	+	179.940i	0.392240	+	0.565849i
$319$	115.585			0.362334
$320$	39.9912	−	0.838109i	0.124973	−	0.00261909i
$321$	−325.831	−	470.046i	−1.01505	−	1.46432i
$322$			58.4236i			0.181440i
$323$	−11.7808			−0.0364732
$324$	−122.109	−	106.458i	−0.376880	−	0.328575i
$325$	−5.82611	−	138.938i	−0.0179265	−	0.427503i
$326$			424.702i			1.30277i
$327$	126.467	+	182.443i	0.386750	+	0.557929i
$328$		−	44.1561i		−	0.134622i
$329$			139.054i			0.422658i
$330$	45.7976	−	33.1884i	0.138781	−	0.100571i
$331$	540.436			1.63274			0.816369	−	0.577530i	$-0.195984\pi$
$331$	540.436			1.63274			0.816369	+	0.577530i	$0.195984\pi$
$332$	90.1871			0.271648
$333$	294.984	+	110.533i	0.885837	+	0.331931i
$334$	−177.404			−0.531149
$335$	−11.8999	−	567.816i	−0.0355221	−	1.69497i
$336$	26.0930	−	18.0874i	0.0776578	−	0.0538315i
$337$			444.323i			1.31847i	0.751939	+	0.659233i	$0.229119\pi$
$337$			444.323i			1.31847i	−0.751939	+	0.659233i	$0.770881\pi$
$338$	195.246			0.577650
$339$	220.237	+	317.715i	0.649666	+	0.937214i
$340$	−185.484	+	3.88726i	−0.545543	+	0.0114331i
$341$		−	36.1035i		−	0.105875i
$342$	−2.83593	+	7.56834i	−0.00829219	+	0.0221297i
$343$			18.5203i			0.0539949i
$344$		−	182.348i		−	0.530082i
$345$	−137.436	−	189.653i	−0.398366	−	0.549717i
$346$	−276.670			−0.799624
$347$	253.956			0.731861			0.365931	−	0.930642i	$-0.380751\pi$
$347$	253.956			0.731861			0.365931	+	0.930642i	$0.380751\pi$
$348$	−213.773	+	148.185i	−0.614289	+	0.425818i
$349$	415.627			1.19091			0.595454	−	0.803389i	$-0.296972\pi$
$349$	415.627			1.19091			0.595454	+	0.803389i	$0.296972\pi$
$350$	−3.91904	−	93.4593i	−0.0111972	−	0.267027i
$351$	36.8106	+	145.604i	0.104874	+	0.414827i
$352$		−	15.0823i		−	0.0428475i
$353$	278.041			0.787652			0.393826	−	0.919185i	$-0.371151\pi$
$353$	278.041			0.787652			0.393826	+	0.919185i	$0.371151\pi$
$354$	114.850	−	79.6130i	0.324436	−	0.224895i
$355$	3.86312	+	184.333i	0.0108820	+	0.519247i
$356$			161.947i			0.454906i
$357$	−121.023	+	83.8917i	−0.339000	+	0.234991i
$358$		−	232.086i		−	0.648286i
$359$		−	81.6150i		−	0.227340i	−0.993519	−	0.113670i	$-0.963739\pi$
$359$		−	81.6150i		−	0.227340i	0.993519	−	0.113670i	$-0.0362606\pi$
$360$	−42.1533	+	120.096i	−0.117092	+	0.333601i
$361$	−360.597			−0.998883
$362$	159.847			0.441565
$363$	194.652	+	280.806i	0.536230	+	0.773570i
$364$	−29.4335			−0.0808614
$365$	15.1830	+	724.472i	0.0415973	+	1.98485i
$366$	−251.848	−	363.318i	−0.688110	−	0.992673i
$367$		−	514.501i		−	1.40191i	−0.713206	−	0.700955i	$-0.752758\pi$
$367$		−	514.501i		−	1.40191i	0.713206	−	0.700955i	$-0.247242\pi$
$368$	−62.4574			−0.169721
$369$	131.571	+	49.3007i	0.356560	+	0.133606i
$370$	−5.18574	−	247.443i	−0.0140155	−	0.668765i
$371$		−	136.536i		−	0.368021i
$372$	46.2863	+	66.7730i	0.124426	+	0.179497i
$373$			80.1359i			0.214842i	0.994214	+	0.107421i	$0.0342592\pi$
$373$			80.1359i			0.214842i	−0.994214	+	0.107421i	$0.965741\pi$
$374$			69.9538i			0.187042i
$375$	232.577	+	294.165i	0.620204	+	0.784440i
$376$	−148.655			−0.395360
$377$	241.140			0.639630
$378$	24.7613	+	97.9432i	0.0655061	+	0.259109i
$379$	706.877			1.86511			0.932556	−	0.361026i	$-0.117573\pi$
$379$	706.877			1.86511			0.932556	+	0.361026i	$0.117573\pi$
$380$	6.34860	−	0.133050i	0.0167068	−	0.000350131i
$381$	236.209	−	163.738i	0.619972	−	0.429758i
$382$			277.749i			0.727092i
$383$	−49.2802			−0.128669			−0.0643345	−	0.997928i	$-0.520492\pi$
$383$	−49.2802			−0.128669			−0.0643345	+	0.997928i	$0.520492\pi$
$384$	19.3362	+	27.8946i	0.0503548	+	0.0726422i
$385$	−35.2628	+	0.739015i	−0.0915918	+	0.00191952i
$386$			399.238i			1.03430i
$387$	543.337	+	203.594i	1.40397	+	0.526081i
$388$		−	192.451i		−	0.496008i
$389$			2.68340i			0.00689821i	0.999994	+	0.00344911i	$0.00109789\pi$
$389$			2.68340i			0.00689821i	−0.999994	+	0.00344911i	$0.998902\pi$
$390$	95.5462	−	69.2398i	0.244990	−	0.177538i
$391$	289.686			0.740884
$392$	−19.7990			−0.0505076
$393$	−366.049	+	253.741i	−0.931423	+	0.645652i
$394$	405.542			1.02929
$395$	289.680	−	6.07092i	0.733367	−	0.0153694i
$396$	44.9403	+	16.8396i	0.113486	+	0.0425241i
$397$		−	372.015i		−	0.937065i	−0.883446	−	0.468532i	$-0.844783\pi$
$397$		−	372.015i		−	0.937065i	0.883446	−	0.468532i	$-0.155217\pi$
$398$	−105.943			−0.266190
$399$	4.14226	−	2.87137i	0.0103816	−	0.00719642i
$400$	99.9122	−	4.18963i	0.249780	−	0.0104741i
$401$			119.122i			0.297062i	0.988908	+	0.148531i	$0.0474545\pi$
$401$			119.122i			0.297062i	−0.988908	+	0.148531i	$0.952545\pi$
$402$	396.062	−	274.546i	0.985230	−	0.682950i
$403$		−	75.3215i		−	0.186902i
$404$			183.939i			0.455295i
$405$	−310.782	−	259.691i	−0.767363	−	0.641213i
$406$	162.207			0.399525
$407$	−93.3209			−0.229290
$408$	−89.6840	−	129.379i	−0.219814	−	0.317105i
$409$	198.033			0.484189			0.242095	−	0.970253i	$-0.422166\pi$
$409$	198.033			0.484189			0.242095	+	0.970253i	$0.422166\pi$
$410$	−2.31298	−	110.366i	−0.00564141	−	0.269186i
$411$	197.051	+	284.268i	0.479443	+	0.691649i
$412$		−	61.2086i		−	0.148565i
$413$	−87.1467			−0.211009
$414$	69.7342	−	186.102i	0.168440	−	0.449522i
$415$	225.418	−	4.72416i	0.543177	−	0.0113835i
$416$		−	31.4658i		−	0.0756389i
$417$	162.536	+	234.476i	0.389775	+	0.562292i
$418$		−	2.39432i		−	0.00572803i
$419$			229.736i			0.548295i	0.961688	+	0.274148i	$0.0883957\pi$
$419$			229.736i			0.548295i	−0.961688	+	0.274148i	$0.911604\pi$
$420$	64.2708	−	46.5754i	0.153026	−	0.110894i
$421$	−590.500			−1.40261			−0.701306	−	0.712860i	$-0.747399\pi$
$421$	−590.500			−1.40261			−0.701306	+	0.712860i	$0.747399\pi$
$422$	−193.387			−0.458264
$423$	165.975	−	442.944i	0.392376	−	1.04715i
$424$	145.963			0.344252
$425$	−463.406	+	19.4320i	−1.09037	+	0.0457224i
$426$	−128.575	+	89.1271i	−0.301820	+	0.209219i
$427$			275.680i			0.645622i
$428$	−381.290			−0.890864
$429$	−25.3469	−	36.5656i	−0.0590836	−	0.0852345i
$430$	−9.55174	−	455.771i	−0.0222133	−	1.05993i
$431$		−	414.879i		−	0.962597i	−0.876557	−	0.481298i	$-0.840165\pi$
$431$		−	414.879i		−	0.962597i	0.876557	−	0.481298i	$-0.159835\pi$
$432$	−104.706	+	26.4710i	−0.242374	+	0.0612754i
$433$		−	219.764i		−	0.507538i	−0.967265	−	0.253769i	$-0.918330\pi$
$433$		−	219.764i		−	0.507538i	0.967265	−	0.253769i	$-0.0816703\pi$
$434$		−	50.6663i		−	0.116743i
$435$	−526.552	+	381.578i	−1.21046	+	0.877192i
$436$	147.993			0.339433
$437$	−9.91510			−0.0226890
$438$	−505.333	+	350.291i	−1.15373	+	0.799751i
$439$	−638.375			−1.45416			−0.727079	−	0.686554i	$-0.759123\pi$
$439$	−638.375			−1.45416			−0.727079	+	0.686554i	$0.759123\pi$
$440$	−0.790040	−	37.6976i	−0.00179555	−	0.0856763i
$441$	22.1057	−	58.9944i	0.0501264	−	0.133774i
$442$			145.942i			0.330186i
$443$	299.160			0.675305			0.337652	−	0.941271i	$-0.390367\pi$
$443$	299.160			0.675305			0.337652	+	0.941271i	$0.390367\pi$
$444$	172.596	−	119.642i	0.388730	−	0.269463i
$445$	8.48306	+	404.778i	0.0190631	+	0.909613i
$446$		−	36.5803i		−	0.0820185i
$447$	−442.179	+	306.514i	−0.989216	+	0.685713i
$448$		−	21.1660i		−	0.0472456i
$449$		−	580.653i		−	1.29321i	−0.762823	−	0.646607i	$-0.776187\pi$
$449$		−	580.653i		−	1.29321i	0.762823	−	0.646607i	$-0.223813\pi$
$450$	−99.0692	+	302.383i	−0.220154	+	0.671962i
$451$	−41.6236			−0.0922918
$452$	257.723			0.570183
$453$	78.0410	+	112.583i	0.172276	+	0.248527i
$454$	−34.4210			−0.0758172
$455$	−73.5677	+	1.54178i	−0.161687	+	0.00338853i
$456$	3.06962	+	4.42826i	0.00673163	+	0.00971111i
$457$		−	563.314i		−	1.23264i	−0.787498	−	0.616318i	$-0.788624\pi$
$457$		−	563.314i		−	1.23264i	0.787498	−	0.616318i	$-0.211376\pi$
$458$	−340.850			−0.744215
$459$	485.639	−	122.776i	1.05804	−	0.267485i
$460$	−156.109	+	3.27163i	−0.339368	+	0.00711224i
$461$			138.227i			0.299842i	0.988698	+	0.149921i	$0.0479020\pi$
$461$			138.227i			0.299842i	−0.988698	+	0.149921i	$0.952098\pi$
$462$	−17.0500	−	24.5965i	−0.0369048	−	0.0532391i
$463$			154.802i			0.334346i	0.985928	+	0.167173i	$0.0534638\pi$
$463$			154.802i			0.334346i	−0.985928	+	0.167173i	$0.946536\pi$
$464$			173.407i			0.373722i
$465$	119.188	+	164.471i	0.256318	+	0.353702i
$466$	−35.2963			−0.0757431
$467$	462.873			0.991162			0.495581	−	0.868562i	$-0.334955\pi$
$467$	462.873			0.991162			0.495581	+	0.868562i	$0.334955\pi$
$468$	93.7575	+	35.1318i	0.200337	+	0.0750680i
$469$	−300.526			−0.640781
$470$	−371.557	+	7.78684i	−0.790547	+	0.0165678i
$471$	−552.229	+	382.799i	−1.17246	+	0.812737i
$472$		−	93.1637i		−	0.197381i
$473$	−171.890			−0.363404
$474$	140.064	+	202.057i	0.295493	+	0.426281i
$475$	15.8610	−	0.665102i	0.0333917	−	0.00140022i
$476$			98.1707i			0.206241i
$477$	−162.969	+	434.920i	−0.341653	+	0.911782i
$478$		−	340.515i		−	0.712374i
$479$		−	836.942i		−	1.74727i	−0.486582	−	0.873635i	$-0.661757\pi$
$479$		−	836.942i		−	1.74727i	0.486582	−	0.873635i	$-0.338243\pi$
$480$	49.7912	+	68.7084i	0.103732	+	0.143142i
$481$	−194.692			−0.404766
$482$	−208.429			−0.432426
$483$	−101.856	+	70.6058i	−0.210883	+	0.146182i
$484$	227.783			0.470625
$485$	−10.0809	−	481.022i	−0.0207854	−	0.991798i
$486$	38.0302	−	341.543i	0.0782515	−	0.702764i
$487$			212.042i			0.435405i	0.976015	+	0.217703i	$0.0698563\pi$
$487$			212.042i			0.435405i	−0.976015	+	0.217703i	$0.930144\pi$
$488$	−294.715			−0.603924
$489$	−740.431	+	513.258i	−1.51417	+	1.04961i
$490$	−49.4866	+	1.03711i	−0.100993	+	0.00211655i
$491$		−	79.1998i		−	0.161303i	−0.996742	−	0.0806516i	$-0.974300\pi$
$491$		−	79.1998i		−	0.161303i	0.996742	−	0.0806516i	$-0.0257001\pi$
$492$	76.9824	−	53.3634i	0.156468	−	0.108462i
$493$		−	804.284i		−	1.63141i
$494$		−	4.99519i		−	0.0101117i
$495$	113.208	+	39.7356i	0.228703	+	0.0802739i
$496$	54.1646			0.109203
$497$	97.5611			0.196300
$498$	108.992	+	157.233i	0.218860	+	0.315730i
$499$	−259.432			−0.519905			−0.259952	−	0.965621i	$-0.583707\pi$
$499$	−259.432			−0.519905			−0.259952	+	0.965621i	$0.583707\pi$
$500$	249.506	−	15.7053i	0.499012	−	0.0314107i
$501$	−214.395	−	309.288i	−0.427934	−	0.617341i
$502$		−	548.044i		−	1.09172i
$503$	175.890			0.349683			0.174841	−	0.984597i	$-0.444059\pi$
$503$	175.890			0.349683			0.174841	+	0.984597i	$0.444059\pi$
$504$	63.0676	+	23.6320i	0.125134	+	0.0468890i
$505$	9.63507	+	459.747i	0.0190793	+	0.910390i
$506$			58.8752i			0.116354i
$507$	235.957	+	340.394i	0.465399	+	0.671388i
$508$		−	191.607i		−	0.377179i
$509$			577.094i			1.13378i	0.823794	+	0.566890i	$0.191853\pi$
$509$			577.094i			1.13378i	−0.823794	+	0.566890i	$0.808147\pi$
$510$	−230.938	−	318.678i	−0.452819	−	0.624859i
$511$	383.439			0.750369
$512$	22.6274			0.0441942
$513$	−16.6220	+	4.20226i	−0.0324016	+	0.00819154i
$514$	15.9134			0.0309599
$515$	−3.20622	−	152.988i	−0.00622566	−	0.297064i
$516$	317.909	−	220.371i	0.616102	−	0.427075i
$517$			140.129i			0.271043i
$518$	−130.963			−0.252825
$519$	−334.360	−	482.350i	−0.644238	−	0.929383i
$520$	−1.64824	−	78.6472i	−0.00316968	−	0.151245i
$521$		−	198.309i		−	0.380631i	−0.981723	−	0.190316i	$-0.939049\pi$
$521$		−	198.309i		−	0.380631i	0.981723	−	0.190316i	$-0.0609512\pi$
$522$	−516.695	−	193.610i	−0.989837	−	0.370901i
$523$			307.722i			0.588378i	0.955747	+	0.294189i	$0.0950495\pi$
$523$			307.722i			0.588378i	−0.955747	+	0.294189i	$0.904951\pi$
$524$			296.930i			0.566660i
$525$	158.202	−	119.779i	0.301337	−	0.228151i
$526$	−436.509			−0.829864
$527$	−251.222			−0.476703
$528$	26.2947	−	18.2272i	0.0498007	−	0.0345213i
$529$	−285.192			−0.539115
$530$	364.827	−	7.64579i	0.688352	−	0.0144260i
$531$	277.597	+	104.018i	0.522781	+	0.195891i
$532$		−	3.36010i		−	0.00631598i
$533$	−86.8380			−0.162923
$534$	−282.340	+	195.715i	−0.528726	+	0.366507i
$535$	−953.015	+	19.9727i	−1.78134	+	0.0373321i
$536$		−	321.276i		−	0.599395i
$537$	404.623	−	280.480i	0.753487	−	0.522309i
$538$		−	281.324i		−	0.522907i
$539$			18.6634i			0.0346260i
$540$	−260.320	+	71.6476i	−0.482075	+	0.132681i
$541$	229.692			0.424569			0.212284	−	0.977208i	$-0.431910\pi$
$541$	229.692			0.424569			0.212284	+	0.977208i	$0.431910\pi$
$542$	−249.384			−0.460118
$543$	193.177	+	278.679i	0.355759	+	0.513221i
$544$	−104.949			−0.192921
$545$	369.901	−	7.75214i	0.678718	−	0.0142241i
$546$	−35.5709	−	51.3148i	−0.0651482	−	0.0939832i
$547$		−	296.031i		−	0.541191i	−0.962693	−	0.270596i	$-0.912779\pi$
$547$		−	296.031i		−	0.541191i	0.962693	−	0.270596i	$-0.0872206\pi$
$548$	230.591			0.420786
$549$	329.052	−	878.151i	0.599365	−	1.59955i
$550$	−3.94933	−	94.1818i	−0.00718061	−	0.171240i
$551$			27.5283i			0.0499606i
$552$	−75.4807	−	108.889i	−0.136740	−	0.197263i
$553$		−	153.318i		−	0.277247i
$554$		−	612.487i		−	1.10557i
$555$	425.128	−	308.079i	0.765997	−	0.555098i
$556$	190.201			0.342088
$557$	−659.047			−1.18321			−0.591604	−	0.806228i	$-0.701505\pi$
$557$	−659.047			−1.18321			−0.591604	+	0.806228i	$0.701505\pi$
$558$	−60.4752	+	161.392i	−0.108379	+	0.289234i
$559$	−358.608			−0.641518
$560$	−1.10871	−	52.9034i	−0.00197985	−	0.0944704i
$561$	−121.958	+	84.5403i	−0.217395	+	0.150696i
$562$			397.584i			0.707444i
$563$	1041.64			1.85016			0.925079	−	0.379774i	$-0.123998\pi$
$563$	1041.64			1.85016			0.925079	+	0.379774i	$0.123998\pi$
$564$	−179.652	−	259.168i	−0.318533	−	0.459518i
$565$	644.166	−	13.5000i	1.14012	−	0.0238938i
$566$		−	160.930i		−	0.284328i
$567$	−140.831	+	161.535i	−0.248379	+	0.284894i
$568$			104.297i			0.183622i
$569$			143.782i			0.252692i	0.991986	+	0.126346i	$0.0403250\pi$
$569$			143.782i			0.252692i	−0.991986	+	0.126346i	$0.959675\pi$
$570$	7.90434	+	10.9074i	0.0138673	+	0.0191359i
$571$	198.901			0.348337			0.174169	−	0.984716i	$-0.444276\pi$
$571$	198.901			0.348337			0.174169	+	0.984716i	$0.444276\pi$
$572$	−29.6611			−0.0518551
$573$	−484.232	+	335.664i	−0.845082	+	0.585801i
$574$	−58.4131			−0.101765
$575$	−390.016	+	16.3546i	−0.678289	+	0.0284427i
$576$	−25.2637	+	67.4221i	−0.0438606	+	0.117052i
$577$		−	55.7825i		−	0.0966767i	−0.998831	−	0.0483384i	$-0.984607\pi$
$577$		−	55.7825i		−	0.0966767i	0.998831	−	0.0483384i	$-0.0153926\pi$
$578$	78.0588			0.135050
$579$	−696.037	+	482.486i	−1.20214	+	0.833308i
$580$	9.08337	+	433.422i	0.0156610	+	0.747280i
$581$		−	119.306i		−	0.205347i
$582$	335.522	−	232.580i	0.576498	−	0.399622i
$583$		−	137.591i		−	0.236005i
$584$			409.913i			0.701906i
$585$	236.183	+	82.8991i	0.403731	+	0.141708i
$586$	−502.512			−0.857529
$587$	679.045			1.15681			0.578403	−	0.815751i	$-0.303676\pi$
$587$	679.045			1.15681			0.578403	+	0.815751i	$0.303676\pi$
$588$	−23.9274	−	34.5178i	−0.0406928	−	0.0587038i
$589$	8.59862			0.0145987
$590$	−4.88009	−	232.858i	−0.00827133	−	0.394675i
$591$	490.104	+	707.027i	0.829278	+	1.19632i
$592$		−	140.006i		−	0.236496i
$593$	794.933			1.34053			0.670264	−	0.742123i	$-0.266181\pi$
$593$	794.933			1.34053			0.670264	+	0.742123i	$0.266181\pi$
$594$	24.9527	+	98.7004i	0.0420080	+	0.166162i
$595$	5.14236	+	245.373i	0.00864262	+	0.412391i
$596$			358.685i			0.601820i
$597$	−128.034	−	184.703i	−0.214463	−	0.309386i
$598$			122.829i			0.205400i
$599$		−	525.925i		−	0.878004i	−0.898486	−	0.439002i	$-0.855332\pi$
$599$		−	525.925i		−	0.878004i	0.898486	−	0.439002i	$-0.144668\pi$
$600$	128.050	+	169.125i	0.213416	+	0.281875i
$601$	169.552			0.282116			0.141058	−	0.990001i	$-0.454950\pi$
$601$	169.552			0.282116			0.141058	+	0.990001i	$0.454950\pi$
$602$	−241.224			−0.400705
$603$	957.295	+	358.707i	1.58755	+	0.594871i
$604$	91.3242			0.151199
$605$	569.332	−	11.9317i	0.941044	−	0.0197218i
$606$	−320.682	+	222.293i	−0.529178	+	0.366821i
$607$		−	29.1399i		−	0.0480064i	−0.999712	−	0.0240032i	$-0.992359\pi$
$607$		−	29.1399i		−	0.0480064i	0.999712	−	0.0240032i	$-0.00764119\pi$
$608$	3.59210			0.00590806
$609$	196.030	+	282.794i	0.321888	+	0.464359i
$610$	−736.625	+	15.4377i	−1.20758	+	0.0253077i
$611$			292.348i			0.478474i
$612$	117.176	−	312.713i	0.191465	−	0.510968i
$613$		−	167.118i		−	0.272623i	−0.990666	−	0.136311i	$-0.956475\pi$
$613$		−	167.118i		−	0.272623i	0.990666	−	0.136311i	$-0.0435247\pi$
$614$			572.035i			0.931653i
$615$	189.618	−	137.412i	0.308323	−	0.223433i
$616$	−19.9521			−0.0323897
$617$	−872.471			−1.41405			−0.707027	−	0.707187i	$-0.749964\pi$
$617$	−872.471			−1.41405			−0.707027	+	0.707187i	$0.749964\pi$
$618$	106.712	−	73.9715i	0.172673	−	0.119695i
$619$	−852.170			−1.37669			−0.688344	−	0.725384i	$-0.741662\pi$
$619$	−852.170			−1.37669			−0.688344	+	0.725384i	$0.741662\pi$
$620$	135.382	−	2.83724i	0.218358	−	0.00457619i
$621$	408.728	−	103.332i	0.658177	−	0.166396i
$622$			750.000i			1.20579i
$623$	214.235			0.343877
$624$	54.8579	−	38.0269i	0.0879133	−	0.0609405i
$625$	622.806	−	52.3243i	0.996489	−	0.0837189i
$626$		−	793.616i		−	1.26776i
$627$	4.17429	−	2.89357i	0.00665755	−	0.00461494i
$628$			447.954i			0.713303i
$629$			649.364i			1.03238i
$630$	158.872	+	55.7635i	0.252178	+	0.0885135i
$631$	550.448			0.872343			0.436171	−	0.899864i	$-0.356334\pi$
$631$	550.448			0.872343			0.436171	+	0.899864i	$0.356334\pi$
$632$	163.904			0.259341
$633$	−233.712	−	337.154i	−0.369213	−	0.532629i
$634$	374.144			0.590133
$635$	−10.0367	−	478.912i	−0.0158059	−	0.754193i
$636$	176.398	+	254.473i	0.277356	+	0.400115i
$637$			38.9369i			0.0611255i
$638$	163.461			0.256209
$639$	−310.771	−	116.449i	−0.486339	−	0.182236i
$640$	56.5561	−	1.18527i	0.0883689	−	0.00185198i
$641$			56.3780i			0.0879532i	0.999033	+	0.0439766i	$0.0140027\pi$
$641$			56.3780i			0.0879532i	−0.999033	+	0.0439766i	$0.985997\pi$
$642$	−460.795	−	664.746i	−0.717749	−	1.03543i
$643$			934.856i			1.45390i	0.686692	+	0.726948i	$0.259062\pi$
$643$			934.856i			1.45390i	−0.686692	+	0.726948i	$0.740938\pi$
$644$			82.6234i			0.128297i
$645$	783.054	−	567.459i	1.21404	−	0.879781i
$646$	−16.6606			−0.0257904
$647$	−523.120			−0.808532			−0.404266	−	0.914641i	$-0.632473\pi$
$647$	−523.120			−0.808532			−0.404266	+	0.914641i	$0.632473\pi$
$648$	−172.688	−	150.555i	−0.266494	−	0.232338i
$649$	−87.8204			−0.135316
$650$	−8.23937	−	196.488i	−0.0126759	−	0.302290i
$651$	88.3324	−	61.2310i	0.135687	−	0.0940569i
$652$			600.619i			0.921195i
$653$	−629.201			−0.963554			−0.481777	−	0.876294i	$-0.660008\pi$
$653$	−629.201			−0.963554			−0.481777	+	0.876294i	$0.660008\pi$
$654$	178.852	+	258.013i	0.273474	+	0.394515i
$655$	15.5537	+	742.162i	0.0237461	+	1.13307i
$656$		−	62.4462i		−	0.0951924i
$657$	−1221.40	−	457.672i	−1.85906	−	0.696608i
$658$			196.653i			0.298864i
$659$		−	1205.86i		−	1.82983i	−0.403644	−	0.914916i	$-0.632257\pi$
$659$		−	1205.86i		−	1.82983i	0.403644	−	0.914916i	$-0.367743\pi$
$660$	64.7677	−	46.9354i	0.0981328	−	0.0711143i
$661$	421.451			0.637596			0.318798	−	0.947823i	$-0.396721\pi$
$661$	421.451			0.637596			0.318798	+	0.947823i	$0.396721\pi$
$662$	764.292			1.15452
$663$	−254.438	+	176.374i	−0.383768	+	0.266024i
$664$	127.544			0.192084
$665$	−0.176008	−	8.39840i	−0.000264674	−	0.0126292i
$666$	417.170	+	156.317i	0.626381	+	0.234711i
$667$		−	676.909i		−	1.01486i
$668$	−250.887			−0.375579
$669$	63.7745	−	44.2078i	0.0953281	−	0.0660804i
$670$	−16.8290	−	803.013i	−0.0251179	−	1.19853i
$671$			277.812i			0.414026i
$672$	36.9011	−	25.5794i	0.0549124	−	0.0380647i
$673$			208.482i			0.309779i	0.987932	+	0.154890i	$0.0495022\pi$
$673$			208.482i			0.309779i	−0.987932	+	0.154890i	$0.950498\pi$
$674$			628.368i			0.932297i
$675$	−646.905	+	192.716i	−0.958377	+	0.285505i
$676$	276.119			0.408460
$677$	−1253.11			−1.85097			−0.925485	−	0.378784i	$-0.876342\pi$
$677$	−1253.11			−1.85097			−0.925485	+	0.378784i	$0.876342\pi$
$678$	311.462	+	449.317i	0.459383	+	0.662710i
$679$	−254.589			−0.374947
$680$	−262.315	+	5.49741i	−0.385757	+	0.00808443i
$681$	−41.5983	−	60.0101i	−0.0610842	−	0.0881205i
$682$		−	51.0580i		−	0.0748651i
$683$	−982.114			−1.43794			−0.718971	−	0.695041i	$-0.755386\pi$
$683$	−982.114			−1.43794			−0.718971	+	0.695041i	$0.755386\pi$
$684$	−4.01061	+	10.7033i	−0.00586346	+	0.0156480i
$685$	576.350	−	12.0788i	0.841388	−	0.0176332i
$686$			26.1916i			0.0381802i
$687$	−411.923	−	594.243i	−0.599597	−	0.864983i
$688$		−	257.880i		−	0.374825i
$689$		−	287.052i		−	0.416621i
$690$	−194.364	−	268.209i	−0.281687	−	0.388709i
$691$	204.605			0.296099			0.148050	−	0.988980i	$-0.452700\pi$
$691$	204.605			0.296099			0.148050	+	0.988980i	$0.452700\pi$
$692$	−391.270			−0.565419
$693$	22.2766	−	59.4504i	0.0321452	−	0.0857871i
$694$	359.148			0.517504
$695$	475.398	−	9.96307i	0.684026	−	0.0143354i
$696$	−302.320	+	209.565i	−0.434368	+	0.301099i
$697$			289.634i			0.415543i
$698$	587.785			0.842099
$699$	−42.6561	−	61.5360i	−0.0610244	−	0.0880343i
$700$	−5.54235	−	132.171i	−0.00791765	−	0.188816i
$701$			330.503i			0.471473i	0.971817	+	0.235736i	$0.0757502\pi$
$701$			330.503i			0.471473i	−0.971817	+	0.235736i	$0.924250\pi$
$702$	52.0581	+	205.915i	0.0741568	+	0.293327i
$703$		−	22.2259i		−	0.0316157i
$704$		−	21.3296i		−	0.0302978i
$705$	−462.608	−	638.367i	−0.656182	−	0.905485i
$706$	393.210			0.556954
$707$	243.329			0.344171
$708$	162.423	−	112.590i	0.229411	−	0.159025i
$709$	265.328			0.374229			0.187114	−	0.982338i	$-0.440086\pi$
$709$	265.328			0.374229			0.187114	+	0.982338i	$0.440086\pi$
$710$	5.46328	+	260.686i	0.00769476	+	0.367163i
$711$	−183.000	+	488.378i	−0.257384	+	0.686889i
$712$			229.027i			0.321667i
$713$	−211.436			−0.296544
$714$	−171.152	+	118.641i	−0.239709	+	0.166164i
$715$	−74.1364	+	1.55370i	−0.103687	+	0.00217301i
$716$		−	328.220i		−	0.458408i
$717$	593.658	−	411.517i	0.827975	−	0.573943i
$718$		−	115.421i		−	0.160754i
$719$			994.084i			1.38259i	0.722572	+	0.691296i	$0.242960\pi$
$719$			994.084i			1.38259i	−0.722572	+	0.691296i	$0.757040\pi$
$720$	−59.6137	+	169.842i	−0.0827968	+	0.235891i
$721$	−80.9713			−0.112304
$722$	−509.961			−0.706317
$723$	−251.890	−	363.379i	−0.348396	−	0.502598i
$724$	226.057			0.312234
$725$	45.4069	+	1082.84i	0.0626302	+	1.49357i
$726$	275.279	+	397.119i	0.379172	+	0.546996i
$727$		−	1244.89i		−	1.71236i	−0.516674	−	0.856182i	$-0.672830\pi$
$727$		−	1244.89i		−	1.71236i	0.516674	−	0.856182i	$-0.327170\pi$
$728$	−41.6253			−0.0571776
$729$	641.411	−	346.458i	0.879851	−	0.475251i
$730$	21.4720	+	1024.56i	0.0294137	+	1.40350i
$731$			1196.08i			1.63622i
$732$	−356.167	−	513.810i	−0.486567	−	0.701926i
$733$			822.707i			1.12238i	0.827686	+	0.561192i	$0.189657\pi$
$733$			822.707i			1.12238i	−0.827686	+	0.561192i	$0.810343\pi$
$734$		−	727.614i		−	0.991300i
$735$	−61.6134	−	85.0223i	−0.0838278	−	0.115677i
$736$	−88.3281			−0.120011
$737$	−302.849			−0.410922
$738$	186.069	+	69.7217i	0.252126	+	0.0944739i
$739$	−550.154			−0.744458			−0.372229	−	0.928141i	$-0.621406\pi$
$739$	−550.154			−0.744458			−0.372229	+	0.928141i	$0.621406\pi$
$740$	−7.33375	−	349.937i	−0.00991047	−	0.472888i
$741$	8.70868	−	6.03676i	0.0117526	−	0.00814677i
$742$		−	193.091i		−	0.260230i
$743$	−356.858			−0.480293			−0.240147	−	0.970737i	$-0.577195\pi$
$743$	−356.858			−0.480293			−0.240147	+	0.970737i	$0.577195\pi$
$744$	65.4587	+	94.4313i	0.0879821	+	0.126924i
$745$	18.7886	+	896.515i	0.0252196	+	1.20338i
$746$			113.329i			0.151916i
$747$	−142.404	+	380.038i	−0.190634	+	0.508752i
$748$			98.9296i			0.132259i
$749$			504.399i			0.673430i
$750$	328.913	+	416.012i	0.438551	+	0.554683i
$751$	1027.14			1.36770			0.683850	−	0.729623i	$-0.260304\pi$
$751$	1027.14			1.36770			0.683850	+	0.729623i	$0.260304\pi$
$752$	−210.231			−0.279562
$753$	955.467	−	662.319i	1.26888	−	0.879574i
$754$	341.024			0.452287
$755$	228.260	−	4.78373i	0.302332	−	0.00633606i
$756$	35.0178	+	138.513i	0.0463198	+	0.183218i
$757$		−	799.336i		−	1.05593i	−0.849267	−	0.527963i	$-0.822956\pi$
$757$		−	799.336i		−	1.05593i	0.849267	−	0.527963i	$-0.177044\pi$
$758$	999.675			1.31883
$759$	−102.644	+	71.1516i	−0.135236	+	0.0937439i
$760$	8.97827	−	0.188161i	0.0118135	−	0.000247580i
$761$		−	799.993i		−	1.05124i	−0.850720	−	0.525619i	$-0.823834\pi$
$761$		−	799.993i		−	1.05124i	0.850720	−	0.525619i	$-0.176166\pi$
$762$	334.050	−	231.560i	0.438386	−	0.303884i
$763$		−	195.776i		−	0.256588i
$764$			392.797i			0.514132i
$765$	276.496	−	787.748i	0.361433	−	1.02974i
$766$	−69.6927			−0.0909827
$767$	−183.217			−0.238875
$768$	27.3456	+	39.4489i	0.0356062	+	0.0513658i
$769$	−1066.44			−1.38679			−0.693393	−	0.720560i	$-0.743885\pi$
$769$	−1066.44			−1.38679			−0.693393	+	0.720560i	$0.743885\pi$
$770$	−49.8692	+	1.04512i	−0.0647652	+	0.00135730i
$771$	19.2315	+	27.7436i	0.0249436	+	0.0359839i
$772$			564.608i			0.731358i
$773$	10.9234			0.0141311			0.00706557	−	0.999975i	$-0.497751\pi$
$773$	10.9234			0.0141311			0.00706557	+	0.999975i	$0.497751\pi$
$774$	768.395	+	287.925i	0.992758	+	0.371996i
$775$	338.231	−	14.1831i	0.436428	−	0.0183008i
$776$		−	272.167i		−	0.350731i
$777$	−158.271	−	228.323i	−0.203695	−	0.293852i
$778$			3.79491i			0.00487777i
$779$		−	9.91332i		−	0.0127257i
$780$	135.123	−	97.9199i	0.173234	−	0.125538i
$781$	98.3153			0.125884
$782$	409.677			0.523884
$783$	−286.891	−	1134.79i	−0.366399	−	1.44929i
$784$	−28.0000			−0.0357143
$785$	23.4647	+	1119.64i	0.0298913	+	1.42629i
$786$	−517.672	+	358.844i	−0.658615	+	0.456545i
$787$			741.962i			0.942772i	0.881927	+	0.471386i	$0.156246\pi$
$787$			741.962i			0.942772i	−0.881927	+	0.471386i	$0.843754\pi$
$788$	573.523			0.727821
$789$	−527.527	−	761.015i	−0.668602	−	0.964531i
$790$	409.669	−	8.58557i	0.518569	−	0.0108678i
$791$		−	340.935i		−	0.431018i
$792$	63.5552	+	23.8147i	0.0802465	+	0.0300691i
$793$			579.589i			0.730882i
$794$		−	526.108i		−	0.662605i
$795$	454.228	+	626.804i	0.571357	+	0.788433i
$796$	−149.827			−0.188224
$797$	805.498			1.01066			0.505331	−	0.862925i	$-0.331370\pi$
$797$	805.498			1.01066			0.505331	+	0.862925i	$0.331370\pi$
$798$	5.85804	−	4.06073i	0.00734091	−	0.00508864i
$799$	975.077			1.22037
$800$	141.297	−	5.92503i	0.176621	−	0.00740628i
$801$	−682.424	−	255.711i	−0.851965	−	0.319239i
$802$			168.464i			0.210055i
$803$	386.403			0.481199
$804$	560.117	−	388.267i	0.696663	−	0.482919i
$805$	4.32796	+	206.513i	0.00537635	+	0.256538i
$806$		−	106.521i		−	0.132160i
$807$	490.464	−	339.985i	0.607762	−	0.421294i
$808$			260.129i			0.321942i
$809$			968.340i			1.19696i	0.801138	+	0.598480i	$0.204228\pi$
$809$			968.340i			1.19696i	−0.801138	+	0.598480i	$0.795772\pi$
$810$	−439.512	−	367.259i	−0.542608	−	0.453406i
$811$	−542.257			−0.668627			−0.334314	−	0.942462i	$-0.608504\pi$
$811$	−542.257			−0.668627			−0.334314	+	0.942462i	$0.608504\pi$
$812$	229.396			0.282507
$813$	−301.385	−	434.780i	−0.370707	−	0.534784i
$814$	−131.976			−0.162132
$815$	31.4615	+	1501.22i	0.0386031	+	1.84198i
$816$	−126.832	−	182.969i	−0.155432	−	0.224227i
$817$		−	40.9383i		−	0.0501081i
$818$	280.062			0.342374
$819$	46.4750	−	124.030i	0.0567461	−	0.151440i
$820$	−3.27105	−	156.081i	−0.00398908	−	0.190343i
$821$		−	1034.06i		−	1.25951i	−0.776793	−	0.629756i	$-0.783155\pi$
$821$		−	1034.06i		−	1.25951i	0.776793	−	0.629756i	$-0.216845\pi$
$822$	278.673	+	402.015i	0.339018	+	0.489070i
$823$		−	352.261i		−	0.428021i	−0.976831	−	0.214010i	$-0.931347\pi$
$823$		−	352.261i		−	0.428021i	0.976831	−	0.214010i	$-0.0686527\pi$
$824$		−	86.5620i		−	0.105051i
$825$	159.425	−	120.705i	0.193242	−	0.146310i
$826$	−123.244			−0.149206
$827$	1125.16			1.36054			0.680268	−	0.732964i	$-0.261864\pi$
$827$	1125.16			1.36054			0.680268	+	0.732964i	$0.261864\pi$
$828$	98.6191	−	263.188i	0.119105	−	0.317860i
$829$	1107.76			1.33626			0.668128	−	0.744046i	$-0.267096\pi$
$829$	1107.76			1.33626			0.668128	+	0.744046i	$0.267096\pi$
$830$	318.790	−	6.68098i	0.384084	−	0.00804937i
$831$	1067.82	−	740.200i	1.28498	−	0.890733i
$832$		−	44.4993i		−	0.0534848i
$833$	129.868			0.155904
$834$	229.861	+	331.599i	0.275612	+	0.397601i
$835$	−627.079	+	13.1419i	−0.750993	+	0.0157388i
$836$		−	3.38608i		−	0.00405033i
$837$	−354.459	+	89.6118i	−0.423487	+	0.107063i
$838$			324.895i			0.387703i
$839$		−	13.3680i		−	0.0159333i	−0.999968	−	0.00796664i	$-0.997464\pi$
$839$		−	13.3680i		−	0.0159333i	0.999968	−	0.00796664i	$-0.00253589\pi$
$840$	90.8926	−	65.8675i	0.108206	−	0.0784137i
$841$	−1038.37			−1.23469
$842$	−835.093			−0.991797
$843$	−693.153	+	480.486i	−0.822246	+	0.569972i
$844$	−273.491			−0.324042
$845$	690.146	−	14.4636i	0.816741	−	0.0171167i
$846$	234.724	−	626.417i	0.277452	−	0.740445i
$847$		−	301.328i		−	0.355759i
$848$	206.423			0.243423
$849$	280.567	−	194.486i	0.330468	−	0.229077i
$850$	−655.355	+	27.4810i	−0.771005	+	0.0323306i
$851$			546.524i			0.642214i
$852$	−181.833	+	126.045i	−0.213419	+	0.147940i
$853$			498.127i			0.583971i	0.956423	+	0.291985i	$0.0943158\pi$
$853$			498.127i			0.583971i	−0.956423	+	0.291985i	$0.905684\pi$
$854$			389.871i			0.456523i
$855$	−9.46366	+	26.9623i	−0.0110686	+	0.0315349i
$856$	−539.225			−0.629936
$857$	−1519.40			−1.77293			−0.886463	−	0.462799i	$-0.846845\pi$
$857$	−1519.40			−1.77293			−0.886463	+	0.462799i	$0.846845\pi$
$858$	−35.8459	−	51.7115i	−0.0417784	−	0.0602699i
$859$	964.144			1.12240			0.561201	−	0.827679i	$-0.310339\pi$
$859$	964.144			1.12240			0.561201	+	0.827679i	$0.310339\pi$
$860$	−13.5082	−	644.557i	−0.0157072	−	0.749485i
$861$	−70.5931	−	101.838i	−0.0819897	−	0.118279i
$862$		−	586.728i		−	0.680659i
$863$	−1169.35			−1.35498			−0.677490	−	0.735532i	$-0.736932\pi$
$863$	−1169.35			−1.35498			−0.677490	+	0.735532i	$0.736932\pi$
$864$	−148.076	+	37.4356i	−0.171385	+	0.0433282i
$865$	−977.961	+	20.4954i	−1.13059	+	0.0236942i
$866$		−	310.793i		−	0.358884i
$867$	94.3353	+	136.089i	0.108807	+	0.156965i
$868$		−	71.6530i		−	0.0825495i
$869$		−	154.503i		−	0.177794i
$870$	−744.657	+	539.633i	−0.855927	+	0.620268i
$871$	−631.825			−0.725402
$872$	209.294			0.240016
$873$	810.966	+	303.877i	0.928942	+	0.348083i
$874$	−14.0221			−0.0160436
$875$	−20.7762	−	330.066i	−0.0237443	−	0.377218i
$876$	−714.648	+	495.386i	−0.815809	+	0.565510i
$877$			937.994i			1.06955i	0.844995	+	0.534774i	$0.179603\pi$
$877$			937.994i			1.06955i	−0.844995	+	0.534774i	$0.820397\pi$
$878$	−902.799			−1.02824
$879$	−607.294	−	876.087i	−0.690892	−	0.996686i
$880$	−1.11729	−	53.3124i	−0.00126964	−	0.0605823i
$881$		−	274.915i		−	0.312049i	−0.987753	−	0.156024i	$-0.950132\pi$
$881$		−	274.915i		−	0.312049i	0.987753	−	0.156024i	$-0.0498679\pi$
$882$	31.2622	−	83.4306i	0.0354447	−	0.0945926i
$883$			1155.73i			1.30886i	0.756121	+	0.654432i	$0.227092\pi$
$883$			1155.73i			1.30886i	−0.756121	+	0.654432i	$0.772908\pi$
$884$			206.394i			0.233477i
$885$	400.070	−	289.921i	0.452057	−	0.327594i
$886$	423.076			0.477512
$887$	−887.696			−1.00079			−0.500393	−	0.865799i	$-0.666811\pi$
$887$	−887.696			−1.00079			−0.500393	+	0.865799i	$0.666811\pi$
$888$	244.088	−	169.199i	0.274873	−	0.190539i
$889$	−253.472			−0.285121
$890$	11.9969	+	572.442i	0.0134796	+	0.643193i
$891$	−141.920	+	162.784i	−0.159282	+	0.182698i
$892$		−	51.7323i		−	0.0579959i
$893$	−33.3741			−0.0373730
$894$	−625.336	+	433.476i	−0.699481	+	0.484873i
$895$	−17.1928	−	820.369i	−0.0192098	−	0.916614i
$896$		−	29.9333i		−	0.0334077i
$897$	−214.143	+	148.441i	−0.238732	+	0.165486i
$898$		−	821.168i		−	0.914441i
$899$			587.032i			0.652983i
$900$	−140.105	+	427.634i	−0.155672	+	0.475149i
$901$	−957.414			−1.06261
$902$	−58.8647			−0.0652601
$903$	−291.523	−	420.554i	−0.322838	−	0.465729i
$904$	364.475			0.403180
$905$	565.019	−	11.8413i	0.624331	−	0.0130843i
$906$	110.367	+	159.216i	0.121818	+	0.175735i
$907$		−	326.166i		−	0.359610i	−0.983702	−	0.179805i	$-0.942453\pi$
$907$		−	326.166i		−	0.359610i	0.983702	−	0.179805i	$-0.0575466\pi$
$908$	−48.6787			−0.0536109
$909$	−775.098	−	290.437i	−0.852693	−	0.319512i
$910$	−104.040	+	2.18041i	−0.114330	+	0.00239606i
$911$		−	455.102i		−	0.499563i	−0.968302	−	0.249782i	$-0.919641\pi$
$911$		−	455.102i		−	0.499563i	0.968302	−	0.249782i	$-0.0803588\pi$
$912$	4.34110	+	6.26251i	0.00475998	+	0.00686679i
$913$		−	120.229i		−	0.131685i
$914$		−	796.647i		−	0.871605i
$915$	−917.137	−	1265.59i	−1.00234	−	1.38315i
$916$	−482.035			−0.526239
$917$	392.801			0.428355
$918$	686.797	−	173.631i	0.748145	−	0.189141i
$919$	−1354.04			−1.47338			−0.736690	−	0.676230i	$-0.763612\pi$
$919$	−1354.04			−1.47338			−0.736690	+	0.676230i	$0.763612\pi$
$920$	−220.772	+	4.62679i	−0.239969	+	0.00502912i
$921$	−997.294	+	691.313i	−1.08284	+	0.750611i
$922$			195.483i			0.212021i
$923$	205.112			0.222223
$924$	−24.1124	−	34.7847i	−0.0260956	−	0.0376458i
$925$	−36.6607	−	874.267i	−0.0396332	−	0.945153i
$926$			218.923i			0.236418i
$927$	257.926	+	96.6472i	0.278237	+	0.104258i
$928$			245.234i			0.264261i
$929$		−	1705.50i		−	1.83585i	−0.396759	−	0.917923i	$-0.629865\pi$
$929$		−	1705.50i		−	1.83585i	0.396759	−	0.917923i	$-0.370135\pi$
$930$	168.557	+	232.597i	0.181244	+	0.250105i
$931$	−4.44499			−0.00477443
$932$	−49.9165			−0.0535584
$933$	−1307.56	+	906.386i	−1.40146	+	0.971475i
$934$	654.601			0.700857
$935$	5.18211	+	247.270i	0.00554237	+	0.264460i
$936$	132.593	+	49.6839i	0.141659	+	0.0530811i
$937$		−	445.015i		−	0.474936i	−0.971395	−	0.237468i	$-0.923683\pi$
$937$		−	445.015i		−	0.474936i	0.971395	−	0.237468i	$-0.0763174\pi$
$938$	−425.008			−0.453100
$939$	1383.60	−	959.098i	1.47348	−	1.02140i
$940$	−525.461	+	11.0123i	−0.559001	+	0.0117152i
$941$		−	1110.66i		−	1.18030i	−0.807294	−	0.590150i	$-0.799069\pi$
$941$		−	1110.66i		−	1.18030i	0.807294	−	0.590150i	$-0.200931\pi$
$942$	−780.969	+	541.359i	−0.829054	+	0.574692i
$943$			243.764i			0.258499i
$944$		−	131.753i		−	0.139569i
$945$	94.7808	+	344.371i	0.100297	+	0.364414i
$946$	−243.089			−0.256965
$947$	32.4631			0.0342799			0.0171400	−	0.999853i	$-0.494544\pi$
$947$	32.4631			0.0342799			0.0171400	+	0.999853i	$0.494544\pi$
$948$	198.080	+	285.752i	0.208945	+	0.301426i
$949$	806.140			0.849463
$950$	22.4309	−	0.940597i	0.0236115	−	0.000990102i
$951$	452.159	+	652.288i	0.475456	+	0.685897i
$952$			138.834i			0.145834i
$953$	458.990			0.481626			0.240813	−	0.970572i	$-0.422586\pi$
$953$	458.990			0.481626			0.240813	+	0.970572i	$0.422586\pi$
$954$	−230.473	+	615.070i	−0.241585	+	0.644728i
$955$	20.5754	+	981.776i	0.0215449	+	1.02804i
$956$		−	481.561i		−	0.503725i
$957$	197.546	+	284.981i	0.206422	+	0.297785i
$958$		−	1183.61i		−	1.23551i
$959$		−	305.043i		−	0.318084i
$960$	70.4153	+	97.1683i	0.0733493	+	0.101217i
$961$	−777.637			−0.809196
$962$	−275.337			−0.286213
$963$	602.050	−	1606.71i	0.625182	−	1.66844i
$964$	−294.764			−0.305771
$965$	29.5752	+	1411.21i	0.0306479	+	1.46239i
$966$	−144.047	+	99.8516i	−0.149117	+	0.103366i
$967$		−	899.118i		−	0.929802i	−0.885363	−	0.464901i	$-0.846090\pi$
$967$		−	899.118i		−	0.929802i	0.885363	−	0.464901i	$-0.153910\pi$
$968$	322.133			0.332782
$969$	−20.1346	−	29.0463i	−0.0207787	−	0.0299756i
$970$	−14.2566	−	680.268i	−0.0146975	−	0.701307i
$971$		−	1201.62i		−	1.23750i	−0.785587	−	0.618752i	$-0.787639\pi$
$971$		−	1201.62i		−	1.23750i	0.785587	−	0.618752i	$-0.212361\pi$
$972$	53.7829	−	483.015i	0.0553322	−	0.496929i
$973$		−	251.612i		−	0.258594i
$974$			299.873i			0.307878i
$975$	332.603	−	251.824i	0.341132	−	0.258281i
$976$	−416.790			−0.427039
$977$	227.188			0.232536			0.116268	−	0.993218i	$-0.462907\pi$
$977$	227.188			0.232536			0.116268	+	0.993218i	$0.462907\pi$
$978$	−1047.13	+	725.857i	−1.07068	+	0.742185i
$979$	215.891			0.220522
$980$	−69.9846	+	1.46669i	−0.0714129	+	0.00149662i
$981$	−233.678	+	623.625i	−0.238204	+	0.635704i
$982$		−	112.005i		−	0.114059i
$983$	−510.695			−0.519527			−0.259763	−	0.965672i	$-0.583645\pi$
$983$	−510.695			−0.519527			−0.259763	+	0.965672i	$0.583645\pi$
$984$	108.870	−	75.4672i	0.110640	−	0.0766943i
$985$	1433.49	−	30.0422i	1.45532	−	0.0304997i
$986$		−	1137.43i		−	1.15358i
$987$	−342.847	+	237.658i	−0.347363	+	0.240788i
$988$		−	7.06426i		−	0.00715006i
$989$			1006.66i			1.01785i
$990$	160.101	+	56.1946i	0.161718	+	0.0567622i
$991$	1161.49			1.17204			0.586019	−	0.810297i	$-0.300694\pi$
$991$	1161.49			1.17204			0.586019	+	0.810297i	$0.300694\pi$
$992$	76.6003			0.0772180
$993$	923.659	+	1332.48i	0.930170	+	1.34187i
$994$	137.972			0.138805
$995$	−374.484	+	7.84819i	−0.376366	+	0.00788763i
$996$	154.139	+	222.362i	0.154758	+	0.223255i
$997$			506.932i			0.508457i	0.967144	+	0.254229i	$0.0818216\pi$
$997$			506.932i			0.508457i	−0.967144	+	0.254229i	$0.918178\pi$
$998$	−366.893			−0.367628
$999$	231.630	+	916.212i	0.231862	+	0.917129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.c.a.29.20	yes	24
3.2	odd	2	inner	210.3.c.a.29.6	yes	24
5.2	odd	4		1050.3.e.e.701.12		24
5.3	odd	4		1050.3.e.e.701.9		24
5.4	even	2	inner	210.3.c.a.29.5	✓	24
15.2	even	4		1050.3.e.e.701.10		24
15.8	even	4		1050.3.e.e.701.11		24
15.14	odd	2	inner	210.3.c.a.29.19	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.c.a.29.5	✓	24	5.4	even	2	inner
210.3.c.a.29.6	yes	24	3.2	odd	2	inner
210.3.c.a.29.19	yes	24	15.14	odd	2	inner
210.3.c.a.29.20	yes	24	1.1	even	1	trivial
1050.3.e.e.701.9		24	5.3	odd	4
1050.3.e.e.701.10		24	15.2	even	4
1050.3.e.e.701.11		24	15.8	even	4
1050.3.e.e.701.12		24	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +(1.70910 + 2.46556i) q^{3} +2.00000 q^{4} +(4.99890 - 0.104764i) q^{5} +(2.41703 + 3.48683i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(-3.15796 + 8.42777i) q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +(1.70910 + 2.46556i) q^{3} +2.00000 q^{4} +(4.99890 - 0.104764i) q^{5} +(2.41703 + 3.48683i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(-3.15796 + 8.42777i) q^{9} +(7.06952 - 0.148158i) q^{10} -2.66621i q^{11} +(3.41820 + 4.93112i) q^{12} -5.56242i q^{13} -3.74166i q^{14} +(8.80192 + 12.1460i) q^{15} +4.00000 q^{16} -18.5525 q^{17} +(-4.46603 + 11.9187i) q^{18} +0.634999 q^{19} +(9.99780 - 0.209527i) q^{20} +(6.52326 - 4.52185i) q^{21} -3.77058i q^{22} -15.6144 q^{23} +(4.83406 + 6.97365i) q^{24} +(24.9780 - 1.04741i) q^{25} -7.86645i q^{26} +(-26.1764 + 6.61774i) q^{27} -5.29150i q^{28} +43.3517i q^{29} +(12.4478 + 17.1771i) q^{30} +13.5411 q^{31} +5.65685 q^{32} +(6.57369 - 4.55681i) q^{33} -26.2372 q^{34} +(-0.277179 - 13.2259i) q^{35} +(-6.31593 + 16.8555i) q^{36} -35.0014i q^{37} +0.898024 q^{38} +(13.7145 - 9.50672i) q^{39} +(14.1390 - 0.296316i) q^{40} -15.6116i q^{41} +(9.22528 - 6.39486i) q^{42} -64.4699i q^{43} -5.33241i q^{44} +(-14.9034 + 42.4604i) q^{45} -22.0820 q^{46} -52.5576 q^{47} +(6.83639 + 9.86224i) q^{48} -7.00000 q^{49} +(35.3243 - 1.48126i) q^{50} +(-31.7081 - 45.7423i) q^{51} -11.1248i q^{52} +51.6056 q^{53} +(-37.0191 + 9.35890i) q^{54} +(-0.279321 - 13.3281i) q^{55} -7.48331i q^{56} +(1.08528 + 1.56563i) q^{57} +61.3086i q^{58} -32.9384i q^{59} +(17.6038 + 24.2921i) q^{60} -104.197 q^{61} +19.1501 q^{62} +(22.2978 + 8.35519i) q^{63} +8.00000 q^{64} +(-0.582739 - 27.8060i) q^{65} +(9.29660 - 6.44430i) q^{66} -113.588i q^{67} -37.1050 q^{68} +(-26.6865 - 38.4981i) q^{69} +(-0.391990 - 18.7042i) q^{70} +36.8746i q^{71} +(-8.93207 + 23.8373i) q^{72} +144.926i q^{73} -49.4995i q^{74} +(45.2724 + 59.7947i) q^{75} +1.27000 q^{76} -7.05412 q^{77} +(19.3952 - 13.4445i) q^{78} +57.9487 q^{79} +(19.9956 - 0.419055i) q^{80} +(-61.0545 - 53.2292i) q^{81} -22.0781i q^{82} +45.0936 q^{83} +(13.0465 - 9.04370i) q^{84} +(-92.7422 + 1.94363i) q^{85} -91.1742i q^{86} +(-106.886 + 74.0924i) q^{87} -7.54117i q^{88} +80.9733i q^{89} +(-21.0766 + 60.0481i) q^{90} -14.7168 q^{91} -31.2287 q^{92} +(23.1432 + 33.3865i) q^{93} -74.3277 q^{94} +(3.17430 - 0.0665248i) q^{95} +(9.66812 + 13.9473i) q^{96} -96.2255i q^{97} -9.89949 q^{98} +(22.4702 + 8.41978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 48 q^{4} + 44 q^{9}+O(q^{10}) \) 24 * q + 48 * q^4 + 44 * q^9	\( 24 q + 48 q^{4} + 44 q^{9} + 16 q^{10} + 4 q^{15} + 96 q^{16} - 80 q^{19} - 28 q^{21} + 48 q^{25} - 56 q^{30} + 224 q^{31} + 128 q^{34} + 88 q^{36} - 92 q^{39} + 32 q^{40} - 72 q^{45} - 144 q^{46} - 168 q^{49} - 284 q^{51} - 144 q^{54} - 320 q^{55} + 8 q^{60} + 192 q^{64} + 224 q^{66} - 152 q^{69} - 56 q^{70} + 48 q^{75} - 160 q^{76} - 72 q^{79} - 212 q^{81} - 56 q^{84} - 64 q^{85} - 240 q^{90} + 168 q^{91} - 128 q^{94} - 876 q^{99}+O(q^{100}) \) 24 * q + 48 * q^4 + 44 * q^9 + 16 * q^10 + 4 * q^15 + 96 * q^16 - 80 * q^19 - 28 * q^21 + 48 * q^25 - 56 * q^30 + 224 * q^31 + 128 * q^34 + 88 * q^36 - 92 * q^39 + 32 * q^40 - 72 * q^45 - 144 * q^46 - 168 * q^49 - 284 * q^51 - 144 * q^54 - 320 * q^55 + 8 * q^60 + 192 * q^64 + 224 * q^66 - 152 * q^69 - 56 * q^70 + 48 * q^75 - 160 * q^76 - 72 * q^79 - 212 * q^81 - 56 * q^84 - 64 * q^85 - 240 * q^90 + 168 * q^91 - 128 * q^94 - 876 * q^99

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