LMFDB - Embedded newform 201.3.h.a.172.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(97,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("201.97");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			172.9
Character	$\chi$	$=$	201.172
Dual form			201.3.h.a.97.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.08753 + 1.20524i) q^{2} +1.73205i q^{3} +(0.905201 + 1.56785i) q^{4} +5.75683i q^{5} +(-2.08753 + 3.61572i) q^{6} +(-7.36527 + 4.25234i) q^{7} -5.27798i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(2.08753 + 1.20524i) q^{2} +1.73205i q^{3} +(0.905201 + 1.56785i) q^{4} +5.75683i q^{5} +(-2.08753 + 3.61572i) q^{6} +(-7.36527 + 4.25234i) q^{7} -5.27798i q^{8} -3.00000 q^{9} +(-6.93836 + 12.0176i) q^{10} +(-5.44938 + 3.14620i) q^{11} +(-2.71560 + 1.56785i) q^{12} +(20.4435 + 11.8030i) q^{13} -20.5003 q^{14} -9.97113 q^{15} +(9.98203 - 17.2894i) q^{16} +(-4.16525 + 7.21442i) q^{17} +(-6.26260 - 3.61572i) q^{18} +(7.70601 - 13.3472i) q^{19} +(-9.02587 + 5.21109i) q^{20} +(-7.36527 - 12.7570i) q^{21} -15.1677 q^{22} +(0.929844 - 1.61054i) q^{23} +9.14173 q^{24} -8.14112 q^{25} +(28.4510 + 49.2785i) q^{26} -5.19615i q^{27} +(-13.3341 - 7.69844i) q^{28} +(21.2167 + 36.7484i) q^{29} +(-20.8151 - 12.0176i) q^{30} +(28.0565 - 16.1984i) q^{31} +(23.3922 - 13.5055i) q^{32} +(-5.44938 - 9.43861i) q^{33} +(-17.3902 + 10.0402i) q^{34} +(-24.4800 - 42.4006i) q^{35} +(-2.71560 - 4.70356i) q^{36} +(-18.3017 + 31.6995i) q^{37} +(32.1731 - 18.5752i) q^{38} +(-20.4435 + 35.4091i) q^{39} +30.3844 q^{40} +(-3.69839 + 2.13527i) q^{41} -35.5076i q^{42} -38.4286i q^{43} +(-9.86557 - 5.69589i) q^{44} -17.2705i q^{45} +(3.88216 - 2.24137i) q^{46} +(-7.77202 - 13.4615i) q^{47} +(29.9461 + 17.2894i) q^{48} +(11.6648 - 20.2040i) q^{49} +(-16.9949 - 9.81199i) q^{50} +(-12.4957 - 7.21442i) q^{51} +42.7365i q^{52} -72.6301i q^{53} +(6.26260 - 10.8471i) q^{54} +(-18.1122 - 31.3712i) q^{55} +(22.4438 + 38.8737i) q^{56} +(23.1180 + 13.3472i) q^{57} +102.285i q^{58} +66.3229 q^{59} +(-9.02587 - 15.6333i) q^{60} +(26.5583 + 15.3334i) q^{61} +78.0918 q^{62} +(22.0958 - 12.7570i) q^{63} -14.7468 q^{64} +(-67.9481 + 117.690i) q^{65} -26.2712i q^{66} +(-2.18548 - 66.9643i) q^{67} -15.0815 q^{68} +(2.78953 + 1.61054i) q^{69} -118.017i q^{70} +(53.9794 + 93.4950i) q^{71} +15.8339i q^{72} +(45.0475 - 78.0245i) q^{73} +(-76.4108 + 44.1158i) q^{74} -14.1008i q^{75} +27.9019 q^{76} +(26.7575 - 46.3453i) q^{77} +(-85.3529 + 49.2785i) q^{78} +(-66.2599 + 38.2552i) q^{79} +(99.5320 + 57.4649i) q^{80} +9.00000 q^{81} -10.2940 q^{82} +(-0.274543 + 0.475522i) q^{83} +(13.3341 - 23.0953i) q^{84} +(-41.5322 - 23.9786i) q^{85} +(46.3157 - 80.2211i) q^{86} +(-63.6501 + 36.7484i) q^{87} +(16.6056 + 28.7617i) q^{88} -45.6941 q^{89} +(20.8151 - 36.0528i) q^{90} -200.762 q^{91} +3.36678 q^{92} +(28.0565 + 48.5952i) q^{93} -37.4686i q^{94} +(76.8376 + 44.3622i) q^{95} +(23.3922 + 40.5165i) q^{96} +(-65.4880 - 37.8095i) q^{97} +(48.7014 - 28.1177i) q^{98} +(16.3482 - 9.43861i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9}+O(q^{10}) $ 22 * q + 26 * q^4 - 15 * q^7 - 66 * q^9	$ 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9} + 6 q^{10} + 30 q^{11} - 78 q^{12} - 27 q^{13} + 6 q^{14} - 6 q^{15} - 58 q^{16} - 8 q^{17} + q^{19} - 12 q^{20} - 15 q^{21} + 14 q^{22} - q^{23} - 56 q^{25} + 71 q^{26} - 75 q^{28} + 42 q^{29} + 18 q^{30} + 120 q^{31} - 105 q^{32} + 30 q^{33} - 24 q^{34} + 3 q^{35} - 78 q^{36} + 13 q^{37} + 108 q^{38} + 27 q^{39} + 82 q^{40} - 159 q^{41} + 189 q^{44} + 372 q^{46} - 35 q^{47} - 174 q^{48} - 40 q^{49} + 285 q^{50} - 24 q^{51} - 212 q^{55} - 113 q^{56} + 3 q^{57} + 136 q^{59} - 12 q^{60} + 63 q^{61} - 150 q^{62} + 45 q^{63} - 284 q^{64} - 20 q^{65} + 94 q^{67} + 154 q^{68} - 3 q^{69} - 41 q^{71} - 16 q^{73} + 441 q^{74} - 390 q^{76} - 84 q^{77} - 213 q^{78} - 615 q^{79} + 267 q^{80} + 198 q^{81} - 302 q^{82} - 154 q^{83} + 75 q^{84} + 633 q^{85} + 221 q^{86} - 126 q^{87} + 410 q^{88} + 56 q^{89} - 18 q^{90} + 272 q^{91} + 636 q^{92} + 120 q^{93} + 588 q^{95} - 105 q^{96} - 441 q^{97} + 780 q^{98} - 90 q^{99}+O(q^{100}) $ 22 * q + 26 * q^4 - 15 * q^7 - 66 * q^9 + 6 * q^10 + 30 * q^11 - 78 * q^12 - 27 * q^13 + 6 * q^14 - 6 * q^15 - 58 * q^16 - 8 * q^17 + q^19 - 12 * q^20 - 15 * q^21 + 14 * q^22 - q^23 - 56 * q^25 + 71 * q^26 - 75 * q^28 + 42 * q^29 + 18 * q^30 + 120 * q^31 - 105 * q^32 + 30 * q^33 - 24 * q^34 + 3 * q^35 - 78 * q^36 + 13 * q^37 + 108 * q^38 + 27 * q^39 + 82 * q^40 - 159 * q^41 + 189 * q^44 + 372 * q^46 - 35 * q^47 - 174 * q^48 - 40 * q^49 + 285 * q^50 - 24 * q^51 - 212 * q^55 - 113 * q^56 + 3 * q^57 + 136 * q^59 - 12 * q^60 + 63 * q^61 - 150 * q^62 + 45 * q^63 - 284 * q^64 - 20 * q^65 + 94 * q^67 + 154 * q^68 - 3 * q^69 - 41 * q^71 - 16 * q^73 + 441 * q^74 - 390 * q^76 - 84 * q^77 - 213 * q^78 - 615 * q^79 + 267 * q^80 + 198 * q^81 - 302 * q^82 - 154 * q^83 + 75 * q^84 + 633 * q^85 + 221 * q^86 - 126 * q^87 + 410 * q^88 + 56 * q^89 - 18 * q^90 + 272 * q^91 + 636 * q^92 + 120 * q^93 + 588 * q^95 - 105 * q^96 - 441 * q^97 + 780 * q^98 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	2.08753	+	1.20524i	1.04377	+	0.602619i	0.920898	−	0.389804i	$-0.127457\pi$
$2$	2.08753	+	1.20524i	1.04377	+	0.602619i	0.122869	+	0.992423i	$0.460790\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	0.905201	+	1.56785i	0.226300	+	0.391963i
$5$			5.75683i			1.15137i	0.817673	+	0.575683i	$0.195264\pi$
$5$			5.75683i			1.15137i	−0.817673	+	0.575683i	$0.804736\pi$
$6$	−2.08753	+	3.61572i	−0.347922	+	0.602619i
$7$	−7.36527	+	4.25234i	−1.05218	+	0.607477i	−0.923259	−	0.384177i	$-0.874485\pi$
$7$	−7.36527	+	4.25234i	−1.05218	+	0.607477i	−0.128922	+	0.991655i	$0.541152\pi$
$8$		−	5.27798i		−	0.659747i
$9$	−3.00000			−0.333333
$10$	−6.93836	+	12.0176i	−0.693836	+	1.20176i
$11$	−5.44938	+	3.14620i	−0.495399	+	0.286018i	−0.726811	−	0.686837i	$-0.758999\pi$
$11$	−5.44938	+	3.14620i	−0.495399	+	0.286018i	0.231413	+	0.972856i	$0.425665\pi$
$12$	−2.71560	+	1.56785i	−0.226300	+	0.130654i
$13$	20.4435	+	11.8030i	1.57257	+	0.907926i	0.995852	+	0.0909864i	$0.0290020\pi$
$13$	20.4435	+	11.8030i	1.57257	+	0.907926i	0.576723	+	0.816940i	$0.304331\pi$
$14$	−20.5003			−1.46431
$15$	−9.97113			−0.664742
$16$	9.98203	−	17.2894i	0.623877	−	1.08059i
$17$	−4.16525	+	7.21442i	−0.245015	+	0.424378i	−0.962136	−	0.272571i	$-0.912126\pi$
$17$	−4.16525	+	7.21442i	−0.245015	+	0.424378i	0.717121	+	0.696949i	$0.245459\pi$
$18$	−6.26260	−	3.61572i	−0.347922	−	0.200873i
$19$	7.70601	−	13.3472i	0.405580	−	0.702484i	−0.588809	−	0.808272i	$-0.700403\pi$
$19$	7.70601	−	13.3472i	0.405580	−	0.702484i	0.994389	+	0.105788i	$0.0337364\pi$
$20$	−9.02587	+	5.21109i	−0.451294	+	0.260554i
$21$	−7.36527	−	12.7570i	−0.350727	−	0.607477i
$22$	−15.1677			−0.689441
$23$	0.929844	−	1.61054i	0.0404280	−	0.0700234i	−0.845103	−	0.534603i	$-0.820461\pi$
$23$	0.929844	−	1.61054i	0.0404280	−	0.0700234i	0.885531	+	0.464580i	$0.153795\pi$
$24$	9.14173			0.380905
$25$	−8.14112			−0.325645
$26$	28.4510	+	49.2785i	1.09427	+	1.89533i
$27$		−	5.19615i		−	0.192450i
$28$	−13.3341	−	7.69844i	−0.476218	−	0.274944i
$29$	21.2167	+	36.7484i	0.731610	+	1.26719i	0.956195	+	0.292731i	$0.0945641\pi$
$29$	21.2167	+	36.7484i	0.731610	+	1.26719i	−0.224585	+	0.974455i	$0.572103\pi$
$30$	−20.8151	−	12.0176i	−0.693836	−	0.400586i
$31$	28.0565	−	16.1984i	0.905047	−	0.522529i	0.0262128	−	0.999656i	$-0.491655\pi$
$31$	28.0565	−	16.1984i	0.905047	−	0.522529i	0.878834	+	0.477127i	$0.158322\pi$
$32$	23.3922	−	13.5055i	0.731006	−	0.422047i
$33$	−5.44938	−	9.43861i	−0.165133	−	0.286018i
$34$	−17.3902	+	10.0402i	−0.511476	+	0.295301i
$35$	−24.4800	−	42.4006i	−0.699429	−	1.21145i
$36$	−2.71560	−	4.70356i	−0.0754334	−	0.130654i
$37$	−18.3017	+	31.6995i	−0.494640	+	0.856742i	−0.999981	−	0.00617772i	$-0.998034\pi$
$37$	−18.3017	+	31.6995i	−0.494640	+	0.856742i	0.505341	+	0.862920i	$0.331367\pi$
$38$	32.1731	−	18.5752i	0.846661	−	0.488820i
$39$	−20.4435	+	35.4091i	−0.524192	+	0.907926i
$40$	30.3844			0.759611
$41$	−3.69839	+	2.13527i	−0.0902047	+	0.0520797i	−0.544424	−	0.838810i	$-0.683252\pi$
$41$	−3.69839	+	2.13527i	−0.0902047	+	0.0520797i	0.454219	+	0.890890i	$0.349918\pi$
$42$		−	35.5076i		−	0.845420i
$43$		−	38.4286i		−	0.893689i	−0.894612	−	0.446845i	$-0.852548\pi$
$43$		−	38.4286i		−	0.893689i	0.894612	−	0.446845i	$-0.147452\pi$
$44$	−9.86557	−	5.69589i	−0.224218	−	0.129452i
$45$		−	17.2705i		−	0.383789i
$46$	3.88216	−	2.24137i	0.0843949	−	0.0487254i
$47$	−7.77202	−	13.4615i	−0.165362	−	0.286416i	0.771422	−	0.636324i	$-0.219546\pi$
$47$	−7.77202	−	13.4615i	−0.165362	−	0.286416i	−0.936784	+	0.349909i	$0.886213\pi$
$48$	29.9461	+	17.2894i	0.623877	+	0.360195i
$49$	11.6648	−	20.2040i	0.238057	−	0.412327i
$50$	−16.9949	−	9.81199i	−0.339897	−	0.196240i
$51$	−12.4957	−	7.21442i	−0.245015	−	0.141459i
$52$			42.7365i			0.821856i
$53$		−	72.6301i		−	1.37038i	−0.728365	−	0.685189i	$-0.759719\pi$
$53$		−	72.6301i		−	1.37038i	0.728365	−	0.685189i	$-0.240281\pi$
$54$	6.26260	−	10.8471i	0.115974	−	0.200873i
$55$	−18.1122	−	31.3712i	−0.329312	−	0.570385i
$56$	22.4438	+	38.8737i	0.400781	+	0.694174i
$57$	23.1180	+	13.3472i	0.405580	+	0.234161i
$58$			102.285i			1.76353i
$59$	66.3229			1.12412			0.562058	−	0.827098i	$-0.310010\pi$
$59$	66.3229			1.12412			0.562058	+	0.827098i	$0.310010\pi$
$60$	−9.02587	−	15.6333i	−0.150431	−	0.260554i
$61$	26.5583	+	15.3334i	0.435382	+	0.251368i	0.701637	−	0.712535i	$-0.252453\pi$
$61$	26.5583	+	15.3334i	0.435382	+	0.251368i	−0.266255	+	0.963903i	$0.585786\pi$
$62$	78.0918			1.25954
$63$	22.0958	−	12.7570i	0.350727	−	0.202492i
$64$	−14.7468			−0.230419
$65$	−67.9481	+	117.690i	−1.04536	+	1.81061i
$66$		−	26.2712i		−	0.398049i
$67$	−2.18548	−	66.9643i	−0.0326191	−	0.999468i
$67$	−2.18548	−	66.9643i	−0.0326191	−	0.999468i
$68$	−15.0815			−0.221787
$69$	2.78953	+	1.61054i	0.0404280	+	0.0233411i
$70$		−	118.017i		−	1.68596i
$71$	53.9794	+	93.4950i	0.760273	+	1.31683i	0.942710	+	0.333613i	$0.108268\pi$
$71$	53.9794	+	93.4950i	0.760273	+	1.31683i	−0.182437	+	0.983218i	$0.558399\pi$
$72$			15.8339i			0.219916i
$73$	45.0475	−	78.0245i	0.617089	−	1.06883i	−0.372925	−	0.927861i	$-0.621645\pi$
$73$	45.0475	−	78.0245i	0.617089	−	1.06883i	0.990014	−	0.140968i	$-0.0450214\pi$
$74$	−76.4108	+	44.1158i	−1.03258	+	0.596160i
$75$		−	14.1008i		−	0.188011i
$76$	27.9019			0.367131
$77$	26.7575	−	46.3453i	0.347499	−	0.601887i
$78$	−85.3529	+	49.2785i	−1.09427	+	0.631776i
$79$	−66.2599	+	38.2552i	−0.838733	+	0.484243i	−0.856834	−	0.515593i	$-0.827572\pi$
$79$	−66.2599	+	38.2552i	−0.838733	+	0.484243i	0.0181000	+	0.999836i	$0.494238\pi$
$80$	99.5320	+	57.4649i	1.24415	+	0.718311i
$81$	9.00000			0.111111
$82$	−10.2940			−0.125537
$83$	−0.274543	+	0.475522i	−0.00330774	+	0.00572918i	−0.867675	−	0.497133i	$-0.834386\pi$
$83$	−0.274543	+	0.475522i	−0.00330774	+	0.00572918i	0.864367	+	0.502862i	$0.167720\pi$
$84$	13.3341	−	23.0953i	0.158739	−	0.274944i
$85$	−41.5322	−	23.9786i	−0.488614	−	0.282102i
$86$	46.3157	−	80.2211i	0.538555	−	0.932804i
$87$	−63.6501	+	36.7484i	−0.731610	+	0.422395i
$88$	16.6056	+	28.7617i	0.188700	+	0.326838i
$89$	−45.6941			−0.513417			−0.256708	−	0.966489i	$-0.582638\pi$
$89$	−45.6941			−0.513417			−0.256708	+	0.966489i	$0.582638\pi$
$90$	20.8151	−	36.0528i	0.231279	−	0.400586i
$91$	−200.762			−2.20618
$92$	3.36678			0.0365955
$93$	28.0565	+	48.5952i	0.301682	+	0.522529i
$94$		−	37.4686i		−	0.398602i
$95$	76.8376	+	44.3622i	0.808817	+	0.466971i
$96$	23.3922	+	40.5165i	0.243669	+	0.422047i
$97$	−65.4880	−	37.8095i	−0.675134	−	0.389789i	0.122885	−	0.992421i	$-0.460785\pi$
$97$	−65.4880	−	37.8095i	−0.675134	−	0.389789i	−0.798019	+	0.602632i	$0.794119\pi$
$98$	48.7014	−	28.1177i	0.496953	−	0.286916i
$99$	16.3482	−	9.43861i	0.165133	−	0.0953395i
$100$	−7.36935	−	12.7641i	−0.0736935	−	0.127641i
$101$	−83.9439	+	48.4650i	−0.831128	+	0.479852i	−0.854239	−	0.519881i	$-0.825976\pi$
$101$	−83.9439	+	48.4650i	−0.831128	+	0.479852i	0.0231109	+	0.999733i	$0.492643\pi$
$102$	−17.3902	−	30.1207i	−0.170492	−	0.295301i
$103$	36.0840	+	62.4993i	0.350330	+	0.606789i	0.986307	−	0.164919i	$-0.0527361\pi$
$103$	36.0840	+	62.4993i	0.350330	+	0.606789i	−0.635977	+	0.771708i	$0.719403\pi$
$104$	62.2962	−	107.900i	0.599002	−	1.03750i
$105$	73.4400	−	42.4006i	0.699429	−	0.403815i
$106$	87.5366	−	151.618i	0.825817	−	1.43036i
$107$	165.599			1.54765			0.773825	−	0.633399i	$-0.218341\pi$
$107$	165.599			1.54765			0.773825	+	0.633399i	$0.218341\pi$
$108$	8.14681	−	4.70356i	0.0754334	−	0.0435515i
$109$		−	164.595i		−	1.51004i	−0.655700	−	0.755021i	$-0.727626\pi$
$109$		−	164.595i		−	1.51004i	0.655700	−	0.755021i	$-0.272374\pi$
$110$		−	87.3179i		−	0.793799i
$111$	−54.9051	−	31.6995i	−0.494640	−	0.285581i
$112$			169.788i			1.51596i
$113$	−141.694	+	81.8068i	−1.25393	+	0.723954i	−0.971887	−	0.235449i	$-0.924344\pi$
$113$	−141.694	+	81.8068i	−1.25393	+	0.723954i	−0.282039	+	0.959403i	$0.591011\pi$
$114$	32.1731	+	55.7255i	0.282220	+	0.488820i
$115$	9.27159	+	5.35296i	0.0806226	+	0.0465475i
$116$	−38.4107	+	66.5293i	−0.331127	+	0.573529i
$117$	−61.3304	−	35.4091i	−0.524192	−	0.302642i
$118$	138.451	+	79.9349i	1.17332	+	0.677414i
$119$		−	70.8482i		−	0.595363i
$120$			52.6274i			0.438562i
$121$	−40.7028	+	70.4993i	−0.336387	+	0.582639i
$122$	36.9609	+	64.0182i	0.302958	+	0.524739i
$123$	−3.69839	−	6.40580i	−0.0300682	−	0.0520797i
$124$	50.7934	+	29.3256i	0.409625	+	0.236497i
$125$			97.0537i			0.776430i
$126$	61.5010			0.488103
$127$	−96.5019	−	167.146i	−0.759857	−	1.31611i	−0.942923	−	0.333011i	$-0.891936\pi$
$127$	−96.5019	−	167.146i	−0.759857	−	1.31611i	0.183066	−	0.983101i	$-0.441398\pi$
$128$	−124.353	−	71.7954i	−0.971510	−	0.560902i
$129$	66.5604			0.515972
$130$	−283.688	+	163.787i	−2.18222	+	1.25990i
$131$	−179.000			−1.36641			−0.683204	−	0.730227i	$-0.739414\pi$
$131$	−179.000			−1.36641			−0.683204	+	0.730227i	$0.739414\pi$
$132$	9.86557	−	17.0877i	0.0747392	−	0.129452i
$133$			131.074i			0.985521i
$134$	76.1458	−	142.424i	0.568252	−	1.06287i
$135$	29.9134			0.221581
$136$	38.0775	+	21.9841i	0.279982	+	0.161648i
$137$			31.4381i			0.229475i	0.993396	+	0.114738i	$0.0366028\pi$
$137$			31.4381i			0.229475i	−0.993396	+	0.114738i	$0.963397\pi$
$138$	3.88216	+	6.72411i	0.0281316	+	0.0487254i
$139$		−	228.763i		−	1.64578i	−0.568204	−	0.822888i	$-0.692361\pi$
$139$		−	228.763i		−	1.64578i	0.568204	−	0.822888i	$-0.307639\pi$
$140$	44.3187	−	76.7622i	0.316562	−	0.548301i
$141$	23.3161	−	13.4615i	0.165362	−	0.0954719i
$142$			260.232i			1.83262i
$143$	−148.539			−1.03874
$144$	−29.9461	+	51.8681i	−0.207959	+	0.360195i
$145$	−211.554	+	122.141i	−1.45900	+	0.842351i
$146$	188.076	−	108.586i	1.28819	−	0.743739i
$147$	34.9944	+	20.2040i	0.238057	+	0.137442i
$148$	−66.2668			−0.447749
$149$	25.5097			0.171206			0.0856032	−	0.996329i	$-0.472718\pi$
$149$	25.5097			0.171206			0.0856032	+	0.996329i	$0.472718\pi$
$150$	16.9949	−	29.4360i	0.113299	−	0.196240i
$151$	−88.8851	+	153.953i	−0.588643	+	1.01956i	0.405767	+	0.913976i	$0.367004\pi$
$151$	−88.8851	+	153.953i	−0.588643	+	1.01956i	−0.994410	+	0.105583i	$0.966329\pi$
$152$	−70.4462	−	40.6722i	−0.463462	−	0.267580i
$153$	12.4957	−	21.6433i	0.0816715	−	0.141459i
$154$	111.714	−	64.4982i	0.725417	−	0.418820i
$155$	93.2515	+	161.516i	0.601623	+	1.04204i
$156$	−74.0218			−0.474499
$157$	131.181	−	227.212i	0.835547	−	1.44721i	−0.0580373	−	0.998314i	$-0.518484\pi$
$157$	131.181	−	227.212i	0.835547	−	1.44721i	0.893584	−	0.448895i	$-0.148182\pi$
$158$	−184.427			−1.16726
$159$	125.799			0.791189
$160$	77.7489	+	134.665i	0.485930	+	0.841656i
$161$			15.8161i			0.0982364i
$162$	18.7878	+	10.8471i	0.115974	+	0.0669577i
$163$	−47.2765	−	81.8853i	−0.290040	−	0.502364i	0.683779	−	0.729689i	$-0.260335\pi$
$163$	−47.2765	−	81.8853i	−0.290040	−	0.502364i	−0.973819	+	0.227325i	$0.927002\pi$
$164$	−6.69558	−	3.86569i	−0.0408267	−	0.0235713i
$165$	54.3365	−	31.3712i	0.329312	−	0.190128i
$166$	−1.14623	+	0.661779i	−0.00690503	+	0.00398662i
$167$	11.7497	+	20.3511i	0.0703575	+	0.121863i	0.899058	−	0.437830i	$-0.144253\pi$
$167$	11.7497	+	20.3511i	0.0703575	+	0.121863i	−0.828701	+	0.559692i	$0.810919\pi$
$168$	−67.3313	+	38.8737i	−0.400781	+	0.231391i
$169$	194.124	+	336.232i	1.14866	+	1.98954i
$170$	−57.7999	−	100.112i	−0.340000	−	0.588897i
$171$	−23.1180	+	40.0416i	−0.135193	+	0.234161i
$172$	60.2505	−	34.7856i	0.350294	−	0.202242i
$173$	−61.4515	+	106.437i	−0.355211	+	0.615243i	−0.987154	−	0.159772i	$-0.948924\pi$
$173$	−61.4515	+	106.437i	−0.355211	+	0.615243i	0.631943	+	0.775015i	$0.282258\pi$
$174$	−177.162			−1.01817
$175$	59.9616	−	34.6188i	0.342637	−	0.197822i
$176$			125.622i			0.713761i
$177$			114.875i			0.649009i
$178$	−95.3880	−	55.0723i	−0.535887	−	0.309395i
$179$			189.043i			1.05611i	0.849211	+	0.528053i	$0.177078\pi$
$179$			189.043i			1.05611i	−0.849211	+	0.528053i	$0.822922\pi$
$180$	27.0776	−	15.6333i	0.150431	−	0.0868515i
$181$	87.1187	+	150.894i	0.481319	+	0.833669i	0.999770	−	0.0214382i	$-0.00682452\pi$
$181$	87.1187	+	150.894i	0.481319	+	0.833669i	−0.518451	+	0.855107i	$0.673491\pi$
$182$	−419.098	−	241.966i	−2.30274	−	1.32949i
$183$	−26.5583	+	46.0003i	−0.145127	+	0.251368i
$184$	−8.50038	−	4.90770i	−0.0461977	−	0.0266723i
$185$	−182.489	−	105.360i	−0.986424	−	0.569512i
$186$			135.259i			0.727198i
$187$		−	52.4189i		−	0.280315i
$188$	14.0705	−	24.3708i	0.0748430	−	0.129632i
$189$	22.0958	+	38.2711i	0.116909	+	0.202492i
$190$	106.934	+	185.215i	0.562811	+	0.974817i
$191$	−80.3766	−	46.4055i	−0.420820	−	0.242961i	0.274608	−	0.961556i	$-0.411452\pi$
$191$	−80.3766	−	46.4055i	−0.420820	−	0.242961i	−0.695428	+	0.718596i	$0.744785\pi$
$192$		−	25.5423i		−	0.133033i
$193$	216.421			1.12135			0.560676	−	0.828035i	$-0.310541\pi$
$193$	216.421			1.12135			0.560676	+	0.828035i	$0.310541\pi$
$194$	−91.1390	−	157.857i	−0.469789	−	0.813698i
$195$	−203.844	−	117.690i	−1.04536	−	0.603537i
$196$	42.2360			0.215490
$197$	34.7351	−	20.0543i	0.176320	−	0.101799i	−0.409242	−	0.912426i	$-0.634207\pi$
$197$	34.7351	−	20.0543i	0.176320	−	0.101799i	0.585563	+	0.810627i	$0.300874\pi$
$198$	45.5031			0.229814
$199$	125.129	−	216.729i	0.628787	−	1.08909i	−0.359009	−	0.933334i	$-0.616885\pi$
$199$	125.129	−	216.729i	0.628787	−	1.08909i	0.987796	−	0.155756i	$-0.0497815\pi$
$200$			42.9687i			0.214843i
$201$	115.986	−	3.78536i	0.577043	−	0.0188326i
$202$	−233.648			−1.15667
$203$	−312.533	−	180.441i	−1.53957	−	0.888873i
$204$		−	26.1220i		−	0.128049i
$205$	−12.2924	−	21.2910i	−0.0599628	−	0.103859i
$206$			173.959i			0.844462i
$207$	−2.78953	+	4.83161i	−0.0134760	+	0.0233411i
$208$	408.135	−	235.637i	1.96219	−	1.13287i
$209$			96.9787i			0.464013i
$210$	204.412			0.973388
$211$	118.852	−	205.857i	0.563278	−	0.975626i	−0.433929	−	0.900947i	$-0.642873\pi$
$211$	118.852	−	205.857i	0.563278	−	0.975626i	0.997208	−	0.0746795i	$-0.0237934\pi$
$212$	113.873	−	65.7448i	0.537138	−	0.310117i
$213$	−161.938	+	93.4950i	−0.760273	+	0.438944i
$214$	345.693	+	199.586i	1.61539	+	0.932644i
$215$	221.227			1.02896
$216$	−27.4252			−0.126968
$217$	−137.762	+	238.611i	−0.634849	+	1.09959i
$218$	198.376	−	343.597i	0.909981	−	1.57613i
$219$	135.142	+	78.0245i	0.617089	+	0.356276i
$220$	32.7903	−	56.7945i	0.149047	−	0.258157i
$221$	−170.304	+	98.3252i	−0.770607	+	0.444910i
$222$	−76.4108	−	132.347i	−0.344193	−	0.596160i
$223$	343.462			1.54019			0.770093	−	0.637931i	$-0.220210\pi$
$223$	343.462			1.54019			0.770093	+	0.637931i	$0.220210\pi$
$224$	−114.860	+	198.943i	−0.512767	+	0.888139i
$225$	24.4234			0.108548
$226$	−394.387			−1.74508
$227$	−0.144222	−	0.249800i	−0.000635340	−	0.00110044i	0.865708	−	0.500550i	$-0.166869\pi$
$227$	−0.144222	−	0.249800i	−0.000635340	−	0.00110044i	−0.866343	+	0.499450i	$0.833536\pi$
$228$			48.3276i			0.211963i
$229$	119.801	+	69.1674i	0.523150	+	0.302041i	0.738223	−	0.674557i	$-0.235665\pi$
$229$	119.801	+	69.1674i	0.523150	+	0.302041i	−0.215072	+	0.976598i	$0.568999\pi$
$230$	12.9032	+	22.3490i	0.0561008	+	0.0971694i
$231$	80.2724	+	46.3453i	0.347499	+	0.200629i
$232$	193.957	−	111.981i	0.836022	−	0.482678i
$233$	313.072	−	180.752i	1.34366	−	0.775760i	0.356314	−	0.934366i	$-0.384033\pi$
$233$	313.072	−	180.752i	1.34366	−	0.775760i	0.987342	+	0.158606i	$0.0507000\pi$
$234$	−85.3529	−	147.836i	−0.364756	−	0.631776i
$235$	77.4958	−	44.7422i	0.329770	−	0.190393i
$236$	60.0355	+	103.985i	0.254388	+	0.440612i
$237$	−66.2599	−	114.766i	−0.279578	−	0.484243i
$238$	85.3890	−	147.898i	0.358777	−	0.621420i
$239$	296.806	−	171.361i	1.24187	−	0.716992i	0.272393	−	0.962186i	$-0.412185\pi$
$239$	296.806	−	171.361i	1.24187	−	0.716992i	0.969474	+	0.245194i	$0.0788515\pi$
$240$	−99.5320	+	172.395i	−0.414717	+	0.718311i
$241$	−251.342			−1.04291			−0.521457	−	0.853277i	$-0.674611\pi$
$241$	−251.342			−1.04291			−0.521457	+	0.853277i	$0.674611\pi$
$242$	−169.937	+	98.1132i	−0.702219	+	0.405426i
$243$			15.5885i			0.0641500i
$244$			55.5194i			0.227539i
$245$	116.311	+	67.1523i	0.474740	+	0.274091i
$246$		−	17.8298i		−	0.0724788i
$247$	315.075	−	181.909i	1.27561	−	0.736473i
$248$	−85.4948	−	148.081i	−0.344737	−	0.597102i
$249$	−0.823628	−	0.475522i	−0.00330774	−	0.00190973i
$250$	−116.973	+	202.603i	−0.467892	+	0.810412i
$251$	42.4560	+	24.5120i	0.169148	+	0.0976574i	0.582184	−	0.813057i	$-0.302198\pi$
$251$	42.4560	+	24.5120i	0.169148	+	0.0976574i	−0.413036	+	0.910715i	$0.635532\pi$
$252$	40.0023	+	23.0953i	0.158739	+	0.0916481i
$253$			11.7019i			0.0462526i
$254$		−	465.231i		−	1.83162i
$255$	41.5322	−	71.9359i	0.162871	−	0.282102i
$256$	−143.568	−	248.666i	−0.560811	−	0.971353i
$257$	−240.795	−	417.070i	−0.936946	−	1.62284i	−0.771126	−	0.636683i	$-0.780306\pi$
$257$	−240.795	−	417.070i	−0.936946	−	1.62284i	−0.165820	−	0.986156i	$-0.553027\pi$
$258$	138.947	+	80.2211i	0.538555	+	0.310935i
$259$		−	311.300i		−	1.20193i
$260$	−246.027			−0.946257
$261$	−63.6501	−	110.245i	−0.243870	−	0.422395i
$262$	−373.668	−	215.737i	−1.42621	−	0.823424i
$263$	188.225			0.715684			0.357842	−	0.933782i	$-0.383513\pi$
$263$	188.225			0.715684			0.357842	+	0.933782i	$0.383513\pi$
$264$	−49.8168	+	28.7617i	−0.188700	+	0.108946i
$265$	418.119			1.57781
$266$	−157.976	+	273.622i	−0.593894	+	1.02865i
$267$		−	79.1445i		−	0.296421i
$268$	103.012	−	64.0427i	0.384373	−	0.238965i
$269$	525.008			1.95170			0.975851	−	0.218439i	$-0.0700965\pi$
$269$	525.008			1.95170			0.975851	+	0.218439i	$0.0700965\pi$
$270$	62.4452	+	36.0528i	0.231279	+	0.133529i
$271$			251.335i			0.927437i	0.885983	+	0.463718i	$0.153485\pi$
$271$			251.335i			0.927437i	−0.885983	+	0.463718i	$0.846515\pi$
$272$	83.1552	+	144.029i	0.305718	+	0.529519i
$273$		−	347.730i		−	1.27374i
$274$	−37.8905	+	65.6282i	−0.138286	+	0.239519i
$275$	44.3641	−	25.6136i	0.161324	−	0.0931405i
$276$			5.83144i			0.0211284i
$277$	77.1413			0.278488			0.139244	−	0.990258i	$-0.455533\pi$
$277$	77.1413			0.278488			0.139244	+	0.990258i	$0.455533\pi$
$278$	275.714	−	477.550i	0.991776	−	1.71781i
$279$	−84.1694	+	48.5952i	−0.301682	+	0.174176i
$280$	−223.790	+	129.205i	−0.799248	+	0.461446i
$281$	80.4644	+	46.4562i	0.286350	+	0.165324i	0.636295	−	0.771446i	$-0.280466\pi$
$281$	80.4644	+	46.4562i	0.286350	+	0.165324i	−0.349945	+	0.936770i	$0.613800\pi$
$282$	64.8975			0.230133
$283$	−491.167			−1.73557			−0.867787	−	0.496937i	$-0.834458\pi$
$283$	−491.167			−1.73557			−0.867787	+	0.496937i	$0.834458\pi$
$284$	−97.7243	+	169.263i	−0.344100	+	0.595998i
$285$	−76.8376	+	133.087i	−0.269606	+	0.466971i
$286$	−310.081	−	179.025i	−1.08420	−	0.625962i
$287$	18.1598	−	31.4537i	0.0632745	−	0.109595i
$288$	−70.1766	+	40.5165i	−0.243669	+	0.140682i
$289$	109.801	+	190.182i	0.379936	+	0.658068i
$290$	−588.836			−2.03047
$291$	65.4880	−	113.429i	0.225045	−	0.389789i
$292$	163.108			0.558589
$293$	−323.962			−1.10567			−0.552836	−	0.833290i	$-0.686454\pi$
$293$	−323.962			−1.10567			−0.552836	+	0.833290i	$0.686454\pi$
$294$	48.7014	+	84.3532i	0.165651	+	0.286916i
$295$			381.810i			1.29427i
$296$	167.309	+	96.5959i	0.565233	+	0.326338i
$297$	16.3482	+	28.3158i	0.0550443	+	0.0953395i
$298$	53.2525	+	30.7453i	0.178700	+	0.103172i
$299$	38.0185	−	21.9500i	0.127152	−	0.0734113i
$300$	22.1080	−	12.7641i	0.0736935	−	0.0425470i
$301$	163.412	+	283.037i	0.542896	+	0.940323i
$302$	−371.101	+	214.255i	−1.22881	+	0.709455i
$303$	−83.9439	−	145.395i	−0.277043	−	0.479852i
$304$	−153.843	−	266.464i	−0.506063	−	0.876527i
$305$	−88.2721	+	152.892i	−0.289417	+	0.501284i
$306$	52.1706	−	30.1207i	0.170492	−	0.0984337i
$307$	−75.3865	+	130.573i	−0.245559	+	0.425320i	−0.962289	−	0.272031i	$-0.912305\pi$
$307$	−75.3865	+	130.573i	−0.245559	+	0.425320i	0.716730	+	0.697351i	$0.245638\pi$
$308$	96.8835			0.314557
$309$	−108.252	+	62.4993i	−0.350330	+	0.202263i
$310$			449.561i			1.45020i
$311$		−	139.486i		−	0.448509i	−0.974531	−	0.224254i	$-0.928005\pi$
$311$		−	139.486i		−	0.448509i	0.974531	−	0.224254i	$-0.0719946\pi$
$312$	186.889	+	107.900i	0.599002	+	0.345834i
$313$		−	162.925i		−	0.520528i	−0.965537	−	0.260264i	$-0.916190\pi$
$313$		−	162.925i		−	0.520528i	0.965537	−	0.260264i	$-0.0838096\pi$
$314$	547.689	−	316.209i	1.74423	−	1.00703i
$315$	73.4400	+	127.202i	0.233143	+	0.403815i
$316$	−119.957	−	69.2573i	−0.379611	−	0.219169i
$317$	−36.7993	+	63.7382i	−0.116086	+	0.201067i	−0.918213	−	0.396086i	$-0.870368\pi$
$317$	−36.7993	+	63.7382i	−0.116086	+	0.201067i	0.802127	+	0.597153i	$0.203702\pi$
$318$	262.610	+	151.618i	0.825817	+	0.476786i
$319$	−231.236	−	133.504i	−0.724877	−	0.418508i
$320$		−	84.8951i		−	0.265297i
$321$			286.825i			0.893536i
$322$	−19.0621	+	33.0166i	−0.0591991	+	0.102536i
$323$	64.1949	+	111.189i	0.198746	+	0.344238i
$324$	8.14681	+	14.1107i	0.0251445	+	0.0435515i
$325$	−166.433	−	96.0900i	−0.512101	−	0.295662i
$326$		−	227.918i		−	0.699135i
$327$	285.086			0.871824
$328$	11.2699	+	19.5200i	0.0343594	+	0.0595123i
$329$	114.486	+	66.0986i	0.347982	+	0.200908i
$330$	151.239			0.458300
$331$	11.5179	−	6.64988i	0.0347974	−	0.0200903i	−0.482500	−	0.875896i	$-0.660271\pi$
$331$	11.5179	−	6.64988i	0.0347974	−	0.0200903i	0.517298	+	0.855805i	$0.326938\pi$
$332$	−0.994065			−0.00299417
$333$	54.9051	−	95.0984i	0.164880	−	0.285581i
$334$			56.6448i			0.169595i
$335$	385.503	−	12.5814i	1.15075	−	0.0375565i
$336$	−294.081			−0.875242
$337$	−12.6420	−	7.29885i	−0.0375133	−	0.0216583i	0.481126	−	0.876651i	$-0.340228\pi$
$337$	−12.6420	−	7.29885i	−0.0375133	−	0.0216583i	−0.518639	+	0.854993i	$0.673561\pi$
$338$			935.861i			2.76882i
$339$	−141.694	−	245.421i	−0.417975	−	0.723954i
$340$		−	86.8219i		−	0.255359i
$341$	−101.927	+	176.543i	−0.298906	+	0.517720i
$342$	−96.5194	+	55.7255i	−0.282220	+	0.162940i
$343$		−	218.319i		−	0.636497i
$344$	−202.826			−0.589609
$345$	−9.27159	+	16.0589i	−0.0268742	+	0.0465475i
$346$	−256.564	+	148.127i	−0.741515	+	0.428114i
$347$	−262.715	+	151.679i	−0.757104	+	0.437114i	−0.828255	−	0.560351i	$-0.810666\pi$
$347$	−262.715	+	151.679i	−0.757104	+	0.437114i	0.0711509	+	0.997466i	$0.477333\pi$
$348$	−115.232	−	66.5293i	−0.331127	−	0.191176i
$349$	−29.0333			−0.0831899			−0.0415949	−	0.999135i	$-0.513244\pi$
$349$	−29.0333			−0.0831899			−0.0415949	+	0.999135i	$0.513244\pi$
$350$	166.896			0.476845
$351$	61.3304	−	106.227i	0.174731	−	0.302642i
$352$	−84.9821	+	147.193i	−0.241426	+	0.418163i
$353$	154.131	+	88.9877i	0.436632	+	0.252090i	0.702168	−	0.712011i	$-0.252216\pi$
$353$	154.131	+	88.9877i	0.436632	+	0.252090i	−0.265536	+	0.964101i	$0.585549\pi$
$354$	−138.451	+	239.805i	−0.391105	+	0.677414i
$355$	−538.235	+	310.750i	−1.51616	+	0.875353i
$356$	−41.3623	−	71.6416i	−0.116186	−	0.201241i
$357$	122.713			0.343733
$358$	−227.842	+	394.634i	−0.636430	+	1.10233i
$359$	−173.459			−0.483173			−0.241587	−	0.970379i	$-0.577668\pi$
$359$	−173.459			−0.483173			−0.241587	+	0.970379i	$0.577668\pi$
$360$	−91.1533			−0.253204
$361$	61.7348	+	106.928i	0.171011	+	0.296199i
$362$			419.996i			1.16021i
$363$	−122.108	−	70.4993i	−0.336387	−	0.194213i
$364$	−181.730	−	314.766i	−0.499259	−	0.864741i
$365$	449.174	+	259.331i	1.23061	+	0.710495i
$366$	−110.883	+	64.0182i	−0.302958	+	0.174913i
$367$	−73.2924	+	42.3154i	−0.199707	+	0.115301i	−0.596519	−	0.802599i	$-0.703450\pi$
$367$	−73.2924	+	42.3154i	−0.199707	+	0.115301i	0.396812	+	0.917900i	$0.370117\pi$
$368$	−18.5635	−	32.1529i	−0.0504442	−	0.0873719i
$369$	11.0952	−	6.40580i	0.0300682	−	0.0173599i
$370$	−253.967	−	439.884i	−0.686398	−	1.18888i
$371$	308.848	+	534.940i	0.832474	+	1.44189i
$372$	−50.7934	+	87.9768i	−0.136542	+	0.236497i
$373$	−159.388	+	92.0229i	−0.427315	+	0.246710i	−0.698202	−	0.715901i	$-0.746016\pi$
$373$	−159.388	+	92.0229i	−0.427315	+	0.246710i	0.270887	+	0.962611i	$0.412683\pi$
$374$	63.1772	−	109.426i	0.168923	−	0.292583i
$375$	−168.102			−0.448272
$376$	−71.0497	+	41.0206i	−0.188962	+	0.109097i
$377$			1001.69i			2.65699i
$378$			106.523i			0.281807i
$379$	−153.180	−	88.4383i	−0.404168	−	0.233346i	0.284113	−	0.958791i	$-0.408301\pi$
$379$	−153.180	−	88.4383i	−0.404168	−	0.233346i	−0.688281	+	0.725444i	$0.741634\pi$
$380$			160.627i			0.422702i
$381$	289.506	−	167.146i	0.759857	−	0.438704i
$382$	−111.859	−	193.746i	−0.292825	−	0.507189i
$383$	−613.620	−	354.274i	−1.60214	−	0.924997i	−0.991058	−	0.133431i	$-0.957400\pi$
$383$	−613.620	−	354.274i	−1.60214	−	0.924997i	−0.611084	−	0.791566i	$-0.709266\pi$
$384$	124.353	−	215.386i	0.323837	−	0.560902i
$385$	266.802	+	154.038i	0.692992	+	0.400099i
$386$	451.786	+	260.839i	1.17043	+	0.675748i
$387$			115.286i			0.297896i
$388$		−	136.901i		−	0.352837i
$389$	194.763	−	337.340i	0.500677	−	0.867198i	−0.499323	−	0.866416i	$-0.666418\pi$
$389$	194.763	−	337.340i	0.500677	−	0.867198i	1.00000		0.000782130i	$-0.000248960\pi$
$390$	−283.688	−	491.362i	−0.727406	−	1.25990i
$391$	7.74606	+	13.4166i	0.0198109	+	0.0343135i
$392$	−106.636	−	61.5666i	−0.272032	−	0.157058i
$393$		−	310.036i		−	0.788896i
$394$	96.6810			0.245383
$395$	−220.229	−	381.447i	−0.557541	−	0.965690i
$396$	29.5967	+	17.0877i	0.0747392	+	0.0431507i
$397$	−184.614			−0.465022			−0.232511	−	0.972594i	$-0.574694\pi$
$397$	−184.614			−0.465022			−0.232511	+	0.972594i	$0.574694\pi$
$398$	522.420	−	301.620i	1.31261	−	0.757838i
$399$	−227.027			−0.568991
$400$	−81.2649	+	140.755i	−0.203162	+	0.351887i
$401$			666.355i			1.66173i	0.556471	+	0.830867i	$0.312155\pi$
$401$			666.355i			1.66173i	−0.556471	+	0.830867i	$0.687845\pi$
$402$	246.686	+	131.888i	0.613648	+	0.328080i
$403$	764.762			1.89767
$404$	−151.972	−	87.7412i	−0.376169	−	0.217181i
$405$			51.8115i			0.127930i
$406$	−434.949	−	753.355i	−1.07130	−	1.85555i
$407$		−	230.323i		−	0.565905i
$408$	−38.0775	+	65.9523i	−0.0933273	+	0.161648i
$409$	419.518	−	242.209i	1.02572	−	0.592198i	0.109962	−	0.993936i	$-0.464927\pi$
$409$	419.518	−	242.209i	1.02572	−	0.592198i	0.915755	+	0.401738i	$0.131594\pi$
$410$		−	59.2610i		−	0.144539i
$411$	−54.4525			−0.132488
$412$	−65.3265	+	113.149i	−0.158559	+	0.274633i
$413$	−488.486	+	282.027i	−1.18277	+	0.682875i
$414$	−11.6465	+	6.72411i	−0.0281316	+	0.0162418i
$415$	−2.73750	−	1.58050i	−0.00659638	−	0.00380842i
$416$	637.624			1.53275
$417$	396.229			0.950189
$418$	−116.882	+	202.446i	−0.279623	+	0.484322i
$419$	−275.141	+	476.558i	−0.656661	+	1.13737i	0.324814	+	0.945778i	$0.394698\pi$
$419$	−275.141	+	476.558i	−0.656661	+	1.13737i	−0.981475	+	0.191592i	$0.938635\pi$
$420$	132.956	+	76.7622i	0.316562	+	0.182767i
$421$	333.111	−	576.966i	0.791238	−	1.37046i	−0.133962	−	0.990986i	$-0.542770\pi$
$421$	333.111	−	576.966i	0.791238	−	1.37046i	0.925201	−	0.379479i	$-0.123897\pi$
$422$	496.214	−	286.489i	1.17586	−	0.678885i
$423$	23.3161	+	40.3846i	0.0551207	+	0.0954719i
$424$	−383.340			−0.904104
$425$	33.9098	−	58.7335i	0.0797877	−	0.138196i
$426$	−450.735			−1.05806
$427$	−260.812			−0.610801
$428$	149.900	+	259.634i	0.350234	+	0.606622i
$429$		−	257.277i		−	0.599714i
$430$	461.820	+	266.632i	1.07400	+	0.620074i
$431$	−277.495	−	480.635i	−0.643839	−	1.11516i	−0.984568	−	0.175000i	$-0.944007\pi$
$431$	−277.495	−	480.635i	−0.643839	−	1.11516i	0.340730	−	0.940161i	$-0.389326\pi$
$432$	−89.8382	−	51.8681i	−0.207959	−	0.120065i
$433$	317.159	−	183.112i	0.732468	−	0.422890i	−0.0868566	−	0.996221i	$-0.527682\pi$
$433$	317.159	−	183.112i	0.732468	−	0.422890i	0.819324	+	0.573330i	$0.194349\pi$
$434$	−575.167	+	332.073i	−1.32527	+	0.765145i
$435$	−211.554	−	366.423i	−0.486332	−	0.842351i
$436$	258.060	−	148.991i	0.591882	−	0.341723i
$437$	−14.3308	−	24.8216i	−0.0327935	−	0.0568001i
$438$	188.076	+	325.758i	0.429398	+	0.743739i
$439$	155.388	−	269.140i	0.353958	−	0.613074i	−0.632981	−	0.774168i	$-0.718169\pi$
$439$	155.388	−	269.140i	0.353958	−	0.613074i	0.986939	+	0.161094i	$0.0515021\pi$
$440$	−165.576	+	95.5956i	−0.376310	+	0.217263i
$441$	−34.9944	+	60.6121i	−0.0793524	+	0.137442i
$442$	−474.021			−1.07245
$443$	−442.947	+	255.735i	−0.999880	+	0.577281i	−0.908213	−	0.418509i	$-0.862553\pi$
$443$	−442.947	+	255.735i	−0.999880	+	0.577281i	−0.0916672	+	0.995790i	$0.529220\pi$
$444$		−	114.778i		−	0.258508i
$445$		−	263.053i		−	0.591131i
$446$	716.988	+	413.953i	1.60760	+	0.928146i
$447$			44.1842i			0.0988460i
$448$	108.614	−	62.7086i	0.242443	−	0.139975i
$449$	−256.222	−	443.789i	−0.570650	−	0.988394i	−0.996499	−	0.0836002i	$-0.973358\pi$
$449$	−256.222	−	443.789i	−0.570650	−	0.988394i	0.425850	−	0.904794i	$-0.359975\pi$
$450$	50.9846	+	29.4360i	0.113299	+	0.0654133i
$451$	13.4360	−	23.2718i	0.0297915	−	0.0516004i
$452$	−256.522	−	148.103i	−0.567527	−	0.327662i
$453$	−266.655	−	153.953i	−0.588643	−	0.339853i
$454$		−	0.695289i		−	0.00153147i
$455$		−	1155.75i		−	2.54012i
$456$	70.4462	−	122.016i	0.154487	−	0.267580i
$457$	151.457	+	262.331i	0.331416	+	0.574029i	0.982790	−	0.184728i	$-0.0591405\pi$
$457$	151.457	+	262.331i	0.331416	+	0.574029i	−0.651374	+	0.758757i	$0.725807\pi$
$458$	166.726	+	288.779i	0.364031	+	0.630521i
$459$	37.4872	+	21.6433i	0.0816715	+	0.0471531i
$460$			19.3820i			0.0421348i
$461$	−162.724			−0.352980			−0.176490	−	0.984302i	$-0.556474\pi$
$461$	−162.724			−0.352980			−0.176490	+	0.984302i	$0.556474\pi$
$462$	111.714	+	193.495i	0.241806	+	0.418820i
$463$	−706.584	−	407.946i	−1.52610	−	0.881094i	−0.999520	−	0.0309673i	$-0.990141\pi$
$463$	−706.584	−	407.946i	−1.52610	−	0.881094i	−0.526579	−	0.850126i	$-0.676525\pi$
$464$	847.142			1.82574
$465$	−279.754	+	161.516i	−0.601623	+	0.347347i
$466$	871.398			1.86995
$467$	156.025	−	270.244i	0.334101	−	0.578680i	−0.649211	−	0.760609i	$-0.724901\pi$
$467$	156.025	−	270.244i	0.334101	−	0.578680i	0.983312	+	0.181929i	$0.0582340\pi$
$468$		−	128.209i		−	0.273952i
$469$	300.852	+	483.917i	0.641475	+	1.03181i
$470$	215.700			0.458937
$471$	393.543	+	227.212i	0.835547	+	0.482403i
$472$		−	350.051i		−	0.741633i
$473$	120.904	+	209.412i	0.255612	+	0.442732i
$474$		−	319.436i		−	0.673916i
$475$	−62.7356	+	108.661i	−0.132075	+	0.228760i
$476$	111.080	−	64.1318i	0.233361	−	0.134731i
$477$			217.890i			0.456793i
$478$	826.125			1.72829
$479$	291.980	−	505.724i	0.609562	−	1.05579i	−0.381751	−	0.924265i	$-0.624679\pi$
$479$	291.980	−	505.724i	0.609562	−	1.05579i	0.991313	−	0.131527i	$-0.0419879\pi$
$480$	−233.247	+	134.665i	−0.485930	+	0.280552i
$481$	−748.300	+	432.031i	−1.55572	+	0.898194i
$482$	−524.686	−	302.928i	−1.08856	−	0.628481i
$483$	−27.3942			−0.0567168
$484$	−147.377			−0.304498
$485$	217.663	−	377.004i	0.448790	−	0.777327i
$486$	−18.7878	+	32.5414i	−0.0386580	+	0.0669577i
$487$	−246.853	−	142.521i	−0.506885	−	0.292650i	0.224667	−	0.974436i	$-0.427870\pi$
$487$	−246.853	−	142.521i	−0.506885	−	0.292650i	−0.731552	+	0.681785i	$0.761204\pi$
$488$	80.9296	−	140.174i	0.165839	−	0.287242i
$489$	141.830	−	81.8853i	0.290040	−	0.167455i
$490$	161.869	+	280.366i	0.330345	+	0.572175i
$491$	625.843			1.27463			0.637315	−	0.770604i	$-0.280045\pi$
$491$	625.843			1.27463			0.637315	+	0.770604i	$0.280045\pi$
$492$	6.69558	−	11.5971i	0.0136089	−	0.0235713i
$493$	−353.491			−0.717020
$494$	876.974			1.77525
$495$	54.3365	+	94.1136i	0.109771	+	0.190128i
$496$		−	646.772i		−	1.30397i
$497$	−795.145	−	459.077i	−1.59989	−	0.923697i
$498$	−1.14623	−	1.98534i	−0.00230168	−	0.00398662i
$499$	−249.745	−	144.190i	−0.500491	−	0.288958i	0.228426	−	0.973561i	$-0.426642\pi$
$499$	−249.745	−	144.190i	−0.500491	−	0.288958i	−0.728916	+	0.684603i	$0.759976\pi$
$500$	−152.166	+	87.8531i	−0.304332	+	0.175706i
$501$	−35.2491	+	20.3511i	−0.0703575	+	0.0406209i
$502$	59.0856	+	102.339i	0.117700	+	0.203863i
$503$	−166.887	+	96.3522i	−0.331783	+	0.191555i	−0.656633	−	0.754211i	$-0.728020\pi$
$503$	−166.887	+	96.3522i	−0.331783	+	0.191555i	0.324849	+	0.945766i	$0.394686\pi$
$504$	−67.3313	−	116.621i	−0.133594	−	0.231391i
$505$	−279.005	−	483.251i	−0.552485	−	0.956933i
$506$	−14.1036	+	24.4282i	−0.0278727	+	0.0482770i
$507$	−582.371	+	336.232i	−1.14866	+	0.663180i
$508$	174.707	−	302.602i	0.343912	−	0.595672i
$509$	−340.806			−0.669559			−0.334780	−	0.942296i	$-0.608662\pi$
$509$	−340.806			−0.669559			−0.334780	+	0.942296i	$0.608662\pi$
$510$	173.400	−	100.112i	0.340000	−	0.196299i
$511$			766.229i			1.49947i
$512$		−	117.769i		−	0.230018i
$513$	−69.3541	−	40.0416i	−0.135193	−	0.0780538i
$514$		−	1160.86i		−	2.25849i
$515$	−359.798	+	207.729i	−0.698637	+	0.403358i
$516$	60.2505	+	104.357i	0.116765	+	0.202242i
$517$	84.7055	+	48.9047i	0.163840	+	0.0945933i
$518$	375.191	−	649.850i	0.724307	−	1.25454i
$519$	−184.354	−	106.437i	−0.355211	−	0.205081i
$520$	621.163	+	358.629i	1.19454	+	0.689671i
$521$		−	63.1363i		−	0.121183i	−0.998163	−	0.0605915i	$-0.980701\pi$
$521$		−	63.1363i		−	0.121183i	0.998163	−	0.0605915i	$-0.0192987\pi$
$522$		−	306.854i		−	0.587843i
$523$	−260.394	+	451.016i	−0.497886	+	0.862363i	−0.999997	−	0.00243984i	$-0.999223\pi$
$523$	−260.394	+	451.016i	−0.497886	+	0.862363i	0.502111	+	0.864803i	$0.332557\pi$
$524$	−162.030	−	280.645i	−0.309218	−	0.535582i
$525$	59.9616	+	103.856i	0.114212	+	0.197822i
$526$	392.926	+	226.856i	0.747007	+	0.431285i
$527$			269.881i			0.512109i
$528$	−217.584			−0.412090
$529$	262.771	+	455.132i	0.496731	+	0.860364i
$530$	872.838	+	503.933i	1.64686	+	0.950818i
$531$	−198.969			−0.374705
$532$	−205.505	+	118.649i	−0.386288	+	0.223024i
$533$	−100.811			−0.189138
$534$	95.3880	−	165.217i	0.178629	−	0.309395i
$535$			953.323i			1.78191i
$536$	−353.436	+	11.5349i	−0.659396	+	0.0215203i
$537$	−327.432			−0.609743
$538$	1095.97	+	632.760i	2.03712	+	1.17613i
$539$			146.799i			0.272355i
$540$	27.0776	+	46.8998i	0.0501437	+	0.0868515i
$541$			649.822i			1.20115i	0.799569	+	0.600575i	$0.205061\pi$
$541$			649.822i			1.20115i	−0.799569	+	0.600575i	$0.794939\pi$
$542$	−302.919	+	524.671i	−0.558891	+	0.968028i
$543$	−261.356	+	150.894i	−0.481319	+	0.277890i
$544$			225.015i			0.413630i
$545$	947.544			1.73861
$546$	419.098	−	725.899i	0.767579	−	1.32949i
$547$	−572.089	+	330.295i	−1.04587	+	0.603831i	−0.921489	−	0.388404i	$-0.873026\pi$
$547$	−572.089	+	330.295i	−1.04587	+	0.603831i	−0.124377	+	0.992235i	$0.539693\pi$
$548$	−49.2904	+	28.4578i	−0.0899460	+	0.0519303i
$549$	−79.6749	−	46.0003i	−0.145127	−	0.0837893i
$550$	123.482			0.224513
$551$	653.984			1.18690
$552$	8.50038	−	14.7231i	0.0153992	−	0.0266723i
$553$	325.348	−	563.520i	0.588333	−	1.01902i
$554$	161.035	+	92.9736i	0.290677	+	0.167822i
$555$	182.489	−	316.079i	0.328808	−	0.569512i
$556$	358.667	−	207.076i	0.645084	−	0.372439i
$557$	401.277	+	695.032i	0.720425	+	1.24781i	0.960829	+	0.277141i	$0.0893867\pi$
$557$	401.277	+	695.032i	0.720425	+	1.24781i	−0.240404	+	0.970673i	$0.577280\pi$
$558$	−234.275			−0.419848
$559$	453.575	−	785.615i	0.811404	−	1.40539i
$560$	−977.441			−1.74543
$561$	90.7921			0.161840
$562$	111.982	+	193.958i	0.199255	+	0.345120i
$563$			347.110i			0.616537i	0.951299	+	0.308268i	$0.0997495\pi$
$563$			347.110i			0.616537i	−0.951299	+	0.308268i	$0.900250\pi$
$564$	42.2115	+	24.3708i	0.0748430	+	0.0432106i
$565$	−470.948	−	815.706i	−0.833537	−	1.44373i
$566$	−1025.33	−	591.974i	−1.81153	−	1.04589i
$567$	−66.2874	+	38.2711i	−0.116909	+	0.0674975i
$568$	493.465	−	284.902i	0.868776	−	0.501588i
$569$	254.773	+	441.279i	0.447755	+	0.775535i	0.998240	−	0.0593108i	$-0.0188903\pi$
$569$	254.773	+	441.279i	0.447755	+	0.775535i	−0.550484	+	0.834845i	$0.685557\pi$
$570$	−320.802	+	185.215i	−0.562811	+	0.324939i
$571$	181.090	+	313.657i	0.317145	+	0.549311i	0.979891	−	0.199533i	$-0.0639425\pi$
$571$	181.090	+	313.657i	0.317145	+	0.549311i	−0.662746	+	0.748844i	$0.730609\pi$
$572$	−134.458	−	232.888i	−0.235066	−	0.407146i
$573$	80.3766	−	139.216i	0.140273	−	0.242961i
$574$	75.8183	−	43.7737i	0.132088	−	0.0762609i
$575$	−7.56997	+	13.1116i	−0.0131652	+	0.0228027i
$576$	44.2405			0.0768065
$577$	−153.447	+	88.5925i	−0.265939	+	0.153540i	−0.627041	−	0.778987i	$-0.715734\pi$
$577$	−153.447	+	88.5925i	−0.265939	+	0.153540i	0.361102	+	0.932526i	$0.382401\pi$
$578$			529.348i			0.915827i
$579$			374.852i			0.647413i
$580$	−382.998	−	221.124i	−0.660342	−	0.381248i
$581$		−	4.66979i		−	0.00803751i
$582$	273.417	−	157.857i	0.469789	−	0.271233i
$583$	228.509	+	395.789i	0.391954	+	0.678884i
$584$	−411.812	−	237.760i	−0.705157	−	0.407123i
$585$	203.844	−	353.069i	0.348452	−	0.603537i
$586$	−676.282	−	390.452i	−1.15406	−	0.666300i
$587$	147.166	+	84.9662i	0.250708	+	0.144746i	0.620088	−	0.784532i	$-0.287097\pi$
$587$	147.166	+	84.9662i	0.250708	+	0.144746i	−0.369380	+	0.929278i	$0.620430\pi$
$588$			73.1548i			0.124413i
$589$		−	499.300i		−	0.847708i
$590$	−460.172	+	797.041i	−0.779952	+	1.35092i
$591$	34.7351	+	60.1630i	0.0587734	+	0.101799i
$592$	365.376	+	632.850i	0.617189	+	1.06900i
$593$	−243.928	−	140.832i	−0.411346	−	0.237491i	0.280022	−	0.959994i	$-0.409658\pi$
$593$	−243.928	−	140.832i	−0.411346	−	0.237491i	−0.691368	+	0.722503i	$0.742992\pi$
$594$			78.8137i			0.132683i
$595$	407.861			0.685481
$596$	23.0914	+	39.9956i	0.0387440	+	0.0671066i
$597$	375.386	+	216.729i	0.628787	+	0.363030i
$598$	105.820			0.176956
$599$	−223.460	+	129.015i	−0.373055	+	0.215383i	−0.674792	−	0.738008i	$-0.735767\pi$
$599$	−223.460	+	129.015i	−0.373055	+	0.215383i	0.301737	+	0.953391i	$0.402433\pi$
$600$	−74.4239			−0.124040
$601$	−95.2833	+	165.036i	−0.158541	+	0.274602i	−0.934343	−	0.356375i	$-0.884012\pi$
$601$	−95.2833	+	165.036i	−0.158541	+	0.274602i	0.775802	+	0.630977i	$0.217346\pi$
$602$			787.800i			1.30864i
$603$	6.55643	+	200.893i	0.0108730	+	0.333156i
$604$	−321.835			−0.532840
$605$	−405.853	−	234.319i	−0.670831	−	0.387305i
$606$		−	404.690i		−	0.667805i
$607$	574.304	+	994.724i	0.946136	+	1.63876i	0.753461	+	0.657493i	$0.228383\pi$
$607$	574.304	+	994.724i	0.946136	+	1.63876i	0.192675	+	0.981263i	$0.438284\pi$
$608$		−	416.294i		−	0.684694i
$609$	312.533	−	541.324i	0.513191	−	0.888873i
$610$	−368.542	+	212.778i	−0.604167	+	0.348816i
$611$		−	366.934i		−	0.600547i
$612$	45.2446			0.0739291
$613$	−36.6647	+	63.5051i	−0.0598119	+	0.103597i	−0.894381	−	0.447306i	$-0.852383\pi$
$613$	−36.6647	+	63.5051i	−0.0598119	+	0.103597i	0.834569	+	0.550903i	$0.185717\pi$
$614$	−314.744	+	181.717i	−0.512612	+	0.295957i
$615$	36.8771	−	21.2910i	0.0599628	−	0.0346196i
$616$	−244.609	−	141.225i	−0.397093	−	0.229262i
$617$	−957.423			−1.55174			−0.775870	−	0.630893i	$-0.782689\pi$
$617$	−957.423			−1.55174			−0.775870	+	0.630893i	$0.782689\pi$
$618$	−301.306			−0.487551
$619$	−531.324	+	920.281i	−0.858359	+	1.48672i	0.0151336	+	0.999885i	$0.495183\pi$
$619$	−531.324	+	920.281i	−0.858359	+	1.48672i	−0.873493	+	0.486837i	$0.838151\pi$
$620$	−168.823	+	292.409i	−0.272295	+	0.471628i
$621$	−8.36860	−	4.83161i	−0.0134760	−	0.00778037i
$622$	168.114	−	291.182i	0.270280	−	0.468139i
$623$	336.549	−	194.307i	0.540207	−	0.311889i
$624$	408.135	+	706.910i	0.654062	+	1.13287i
$625$	−762.250			−1.21960
$626$	196.364	−	340.112i	0.313680	−	0.543310i
$627$	−167.972			−0.267898
$628$	474.980			0.756338
$629$	−152.462	−	264.072i	−0.242388	−	0.419829i
$630$			354.051i			0.561986i
$631$	−748.468	−	432.128i	−1.18616	−	0.684831i	−0.228730	−	0.973490i	$-0.573457\pi$
$631$	−748.468	−	432.128i	−1.18616	−	0.684831i	−0.957432	+	0.288659i	$0.906791\pi$
$632$	201.910	+	349.719i	0.319478	+	0.553352i
$633$	356.555	+	205.857i	0.563278	+	0.325209i
$634$	−153.640	+	88.7038i	−0.242334	+	0.139911i
$635$	962.232	−	555.545i	1.51533	−	0.874874i
$636$	113.873	+	197.234i	0.179046	+	0.310117i
$637$	476.938	−	275.360i	0.748725	−	0.432277i
$638$	−321.809	−	557.389i	−0.504402	−	0.873650i
$639$	−161.938	−	280.485i	−0.253424	−	0.438944i
$640$	413.314	−	715.881i	0.645804	−	1.11856i
$641$	655.791	−	378.621i	1.02307	−	0.590672i	0.108081	−	0.994142i	$-0.465529\pi$
$641$	655.791	−	378.621i	1.02307	−	0.590672i	0.914993	+	0.403470i	$0.132196\pi$
$642$	−345.693	+	598.757i	−0.538462	+	0.932644i
$643$	667.633			1.03831			0.519154	−	0.854680i	$-0.326247\pi$
$643$	667.633			1.03831			0.519154	+	0.854680i	$0.326247\pi$
$644$	−24.7973	+	14.3167i	−0.0385051	+	0.0222309i
$645$			383.177i			0.594073i
$646$			309.481i			0.479072i
$647$	−585.138	−	337.829i	−0.904386	−	0.522147i	−0.0257653	−	0.999668i	$-0.508202\pi$
$647$	−585.138	−	337.829i	−0.904386	−	0.522147i	−0.878621	+	0.477521i	$0.841536\pi$
$648$		−	47.5018i		−	0.0733053i
$649$	−361.419	+	208.665i	−0.556886	+	0.321518i
$650$	−231.623	−	401.182i	−0.356343	−	0.617204i
$651$	−413.287	−	238.611i	−0.634849	−	0.366530i
$652$	85.5894	−	148.245i	0.131272	−	0.227370i
$653$	−958.172	−	553.201i	−1.46734	−	0.847168i	−0.468007	−	0.883725i	$-0.655028\pi$
$653$	−958.172	−	553.201i	−1.46734	−	0.847168i	−0.999332	+	0.0365566i	$0.988361\pi$
$654$	595.128	+	343.597i	0.909981	+	0.525378i
$655$		−	1030.47i		−	1.57324i
$656$			85.2572i			0.129965i
$657$	−135.142	+	234.074i	−0.205696	+	0.356276i
$658$	159.329	+	275.966i	0.242142	+	0.419402i
$659$	−220.314	−	381.595i	−0.334316	−	0.579052i	0.649037	−	0.760757i	$-0.275172\pi$
$659$	−220.314	−	381.595i	−0.334316	−	0.579052i	−0.983353	+	0.181705i	$0.941839\pi$
$660$	98.3709	+	56.7945i	0.149047	+	0.0860522i
$661$		−	896.356i		−	1.35606i	−0.735034	−	0.678031i	$-0.762834\pi$
$661$		−	896.356i		−	1.35606i	0.735034	−	0.678031i	$-0.237166\pi$
$662$	32.0588			0.0484272
$663$	−170.304	−	294.976i	−0.256869	−	0.444910i
$664$	2.50979	+	1.44903i	0.00377981	+	0.00218227i
$665$	−754.573			−1.13470
$666$	229.233	−	132.347i	0.344193	−	0.198720i
$667$	78.9129			0.118310
$668$	−21.2717	+	36.8436i	−0.0318438	+	0.0551551i
$669$			594.893i			0.889227i
$670$	819.914	+	438.358i	1.22375	+	0.654266i
$671$	−192.969			−0.287584
$672$	−344.580	−	198.943i	−0.512767	−	0.296046i
$673$		−	584.956i		−	0.869177i	−0.900629	−	0.434588i	$-0.856894\pi$
$673$		−	584.956i		−	0.869177i	0.900629	−	0.434588i	$-0.143106\pi$
$674$	−17.5937	−	30.4732i	−0.0261034	−	0.0452125i
$675$			42.3025i			0.0626704i
$676$	−351.442	+	608.715i	−0.519884	+	0.900466i
$677$	−532.151	+	307.237i	−0.786042	+	0.453822i	−0.838567	−	0.544798i	$-0.816606\pi$
$677$	−532.151	+	307.237i	−0.786042	+	0.453822i	0.0525252	+	0.998620i	$0.483273\pi$
$678$		−	683.098i		−	1.00752i
$679$	643.116			0.947152
$680$	−126.559	+	219.206i	−0.186116	+	0.322362i
$681$	0.432667	−	0.249800i	0.000635340	−	0.000366814i
$682$	−425.552	+	245.693i	−0.623977	+	0.360253i
$683$	403.405	+	232.906i	0.590637	+	0.341004i	0.765349	−	0.643615i	$-0.222566\pi$
$683$	403.405	+	232.906i	0.590637	+	0.341004i	−0.174712	+	0.984620i	$0.555900\pi$
$684$	−83.7058			−0.122377
$685$	−180.984			−0.264210
$686$	263.126	−	455.747i	0.383566	−	0.664355i
$687$	−119.801	+	207.502i	−0.174383	+	0.302041i
$688$	−664.407	−	383.596i	−0.965708	−	0.557552i
$689$	857.256	−	1484.81i	1.24420	−	2.15502i
$690$	−38.7095	+	22.3490i	−0.0561008	+	0.0323898i
$691$	−285.473	−	494.454i	−0.413130	−	0.715563i	0.582100	−	0.813117i	$-0.302231\pi$
$691$	−285.473	−	494.454i	−0.413130	−	0.715563i	−0.995230	+	0.0975544i	$0.968898\pi$
$692$	−222.504			−0.321537
$693$	−80.2724	+	139.036i	−0.115833	+	0.200629i
$694$	−731.236			−1.05365
$695$	1316.95			1.89489
$696$	193.957	+	335.944i	0.278674	+	0.482678i
$697$		−	35.5757i		−	0.0510411i
$698$	−60.6080	−	34.9920i	−0.0868309	−	0.0501318i
$699$	313.072	+	542.256i	0.447885	+	0.775760i
$700$	108.554	+	62.6740i	0.155078	+	0.0895342i
$701$	−411.726	+	237.710i	−0.587341	+	0.339102i	−0.764046	−	0.645162i	$-0.776790\pi$
$701$	−411.726	+	237.710i	−0.587341	+	0.339102i	0.176704	+	0.984264i	$0.443456\pi$
$702$	256.059	−	147.836i	0.364756	−	0.210592i
$703$	282.066	+	488.553i	0.401232	+	0.694954i
$704$	80.3612	−	46.3966i	0.114149	−	0.0659042i
$705$	77.4958	+	134.227i	0.109923	+	0.190393i
$706$	214.503	+	371.530i	0.303828	+	0.526246i
$707$	412.180	−	713.916i	0.582998	−	1.00978i
$708$	−180.106	+	103.985i	−0.254388	+	0.146871i
$709$	−224.194	+	388.316i	−0.316212	+	0.547695i	−0.979694	−	0.200497i	$-0.935744\pi$
$709$	−224.194	+	388.316i	−0.316212	+	0.547695i	0.663482	+	0.748192i	$0.269078\pi$
$710$	−1498.11			−2.11002
$711$	198.780	−	114.766i	0.279578	−	0.161414i
$712$			241.172i			0.338725i
$713$		−	60.2480i		−	0.0844992i
$714$	256.167	+	147.898i	0.358777	+	0.207140i
$715$		−	855.115i		−	1.19596i
$716$	−296.392	+	171.122i	−0.413955	+	0.238997i
$717$	296.806	+	514.084i	0.413956	+	0.716992i
$718$	−362.102	−	209.060i	−0.504320	−	0.291170i
$719$	−207.823	+	359.959i	−0.289044	+	0.500639i	−0.973582	−	0.228339i	$-0.926671\pi$
$719$	−207.823	+	359.959i	−0.289044	+	0.500639i	0.684538	+	0.728977i	$0.260004\pi$
$720$	−298.596	−	172.395i	−0.414717	−	0.239437i
$721$	−531.537	−	306.883i	−0.737221	−	0.425635i
$722$			297.621i			0.412217i
$723$		−	435.338i		−	0.602127i
$724$	−157.720	+	273.179i	−0.217845	+	0.377319i
$725$	−172.728	−	299.173i	−0.238245	−	0.412653i
$726$	−169.937	−	294.340i	−0.234073	−	0.405426i
$727$	55.6822	+	32.1482i	0.0765918	+	0.0442203i	0.537807	−	0.843068i	$-0.319253\pi$
$727$	55.6822	+	32.1482i	0.0765918	+	0.0442203i	−0.461215	+	0.887288i	$0.652586\pi$
$728$			1059.62i			1.45552i
$729$	−27.0000			−0.0370370
$730$	625.111	+	1082.72i	0.856317	+	1.48318i
$731$	277.240	+	160.065i	0.379262	+	0.218967i
$732$	−96.1624			−0.131369
$733$	262.655	−	151.644i	0.358328	−	0.206881i	−0.310019	−	0.950730i	$-0.600335\pi$
$733$	262.655	−	151.644i	0.358328	−	0.206881i	0.668347	+	0.743849i	$0.267002\pi$
$734$	−204.001			−0.277930
$735$	−116.311	+	201.457i	−0.158247	+	0.274091i
$736$		−	50.2320i		−	0.0682500i
$737$	222.593	+	358.038i	0.302026	+	0.485805i
$738$	30.8821			0.0418457
$739$	−114.147	−	65.9028i	−0.154462	−	0.0891784i	0.420777	−	0.907164i	$-0.361757\pi$
$739$	−114.147	−	65.9028i	−0.154462	−	0.0891784i	−0.575239	+	0.817986i	$0.695091\pi$
$740$		−	381.487i		−	0.515523i
$741$	315.075	+	545.726i	0.425203	+	0.736473i
$742$			1488.94i			2.00666i
$743$	−224.880	+	389.503i	−0.302664	+	0.524230i	−0.976739	−	0.214434i	$-0.931209\pi$
$743$	−224.880	+	389.503i	−0.302664	+	0.524230i	0.674074	+	0.738664i	$0.264543\pi$
$744$	256.484	−	148.081i	0.344737	−	0.199034i
$745$			146.855i			0.197121i
$746$	−443.638			−0.594689
$747$	0.823628	−	1.42657i	0.00110258	−	0.00190973i
$748$	82.1851	−	47.4496i	0.109873	−	0.0634353i
$749$	−1219.68	+	704.182i	−1.62841	+	0.940162i
$750$	−350.919	−	202.603i	−0.467892	−	0.270137i
$751$	−156.876			−0.208890			−0.104445	−	0.994531i	$-0.533307\pi$
$751$	−156.876			−0.208890			−0.104445	+	0.994531i	$0.533307\pi$
$752$	−310.322			−0.412663
$753$	−42.4560	+	73.5360i	−0.0563825	+	0.0976574i
$754$	−1207.27	+	2091.05i	−1.60116	+	2.77328i
$755$	−886.284	−	511.697i	−1.17389	−	0.677744i
$756$	−40.0023	+	69.2860i	−0.0529131	+	0.0916481i
$757$	717.002	−	413.961i	0.947162	−	0.546844i	0.0549641	−	0.998488i	$-0.482496\pi$
$757$	717.002	−	413.961i	0.947162	−	0.546844i	0.892198	+	0.451644i	$0.149162\pi$
$758$	−213.179	−	369.236i	−0.281238	−	0.487119i
$759$	−20.2683			−0.0267040
$760$	234.143	−	405.547i	0.308083	−	0.533615i
$761$	1051.60			1.38187			0.690934	−	0.722918i	$-0.257199\pi$
$761$	1051.60			1.38187			0.690934	+	0.722918i	$0.257199\pi$
$762$	805.804			1.05749
$763$	699.913	+	1212.28i	0.917317	+	1.58884i
$764$		−	168.025i		−	0.219928i
$765$	124.597	+	71.9359i	0.162871	+	0.0940338i
$766$	−853.969	−	1479.12i	−1.11484	−	1.93096i
$767$	1355.87	+	782.812i	1.76776	+	1.02061i
$768$	430.703	−	248.666i	0.560811	−	0.323784i
$769$	202.411	−	116.862i	0.263213	−	0.151966i	−0.362586	−	0.931950i	$-0.618106\pi$
$769$	202.411	−	116.862i	0.263213	−	0.151966i	0.625799	+	0.779984i	$0.284773\pi$
$770$	371.306	+	643.120i	0.482215	+	0.835221i
$771$	722.386	−	417.070i	0.936946	−	0.540946i
$772$	195.904	+	339.316i	0.253762	+	0.439529i
$773$	−606.286	−	1050.12i	−0.784328	−	1.35850i	−0.929400	−	0.369075i	$-0.879675\pi$
$773$	−606.286	−	1050.12i	−0.784328	−	1.35850i	0.145071	−	0.989421i	$-0.453659\pi$
$774$	−138.947	+	240.663i	−0.179518	+	0.310935i
$775$	−228.411	+	131.873i	−0.294724	+	0.170159i
$776$	−199.558	+	345.644i	−0.257162	+	0.445418i
$777$	539.188			0.693935
$778$	813.151	−	469.473i	1.04518	−	0.603436i
$779$			65.8176i			0.0844899i
$780$		−	426.131i		−	0.546322i
$781$	−588.309	−	339.660i	−0.753276	−	0.434904i
$782$			37.3434i			0.0477537i
$783$	190.950	−	110.245i	0.243870	−	0.140798i
$784$	−232.877	−	403.354i	−0.297037	−	0.514483i
$785$	1308.02	+	755.186i	1.66627	+	0.962021i
$786$	373.668	−	647.211i	0.475404	−	0.823424i
$787$	−735.683	−	424.747i	−0.934795	−	0.539704i	−0.0464699	−	0.998920i	$-0.514797\pi$
$787$	−735.683	−	424.747i	−0.934795	−	0.539704i	−0.888325	+	0.459216i	$0.848131\pi$
$788$	62.8845	+	36.3064i	0.0798026	+	0.0460741i
$789$			326.015i			0.413200i
$790$		−	1061.71i		−	1.34394i
$791$	695.741	−	1205.06i	0.879572	−	1.52346i
$792$	−49.8168	−	86.2852i	−0.0629000	−	0.108946i
$793$	361.963	+	626.938i	0.456447	+	0.790590i
$794$	−385.388	−	222.504i	−0.485375	−	0.280231i
$795$			724.204i			0.910948i
$796$	453.066			0.569178
$797$	−485.596	−	841.077i	−0.609280	−	1.05530i	−0.991359	−	0.131174i	$-0.958125\pi$
$797$	−485.596	−	841.077i	−0.609280	−	1.05530i	0.382080	−	0.924129i	$-0.375208\pi$
$798$	−473.928	−	273.622i	−0.593894	−	0.342885i
$799$	129.490			0.162065
$800$	−190.439	+	109.950i	−0.238048	+	0.137437i
$801$	137.082			0.171139
$802$	−803.117	+	1391.04i	−1.00139	+	1.73446i
$803$			566.914i			0.705995i
$804$	110.925	+	178.422i	0.137967	+	0.221918i
$805$	−91.0504			−0.113106
$806$	1596.47	+	921.721i	1.98073	+	1.14357i
$807$			909.340i			1.12682i
$808$	255.797	+	443.054i	0.316581	+	0.548334i
$809$			1328.46i			1.64210i	0.570854	+	0.821052i	$0.306612\pi$
$809$			1328.46i			1.64210i	−0.570854	+	0.821052i	$0.693388\pi$
$810$	−62.4452	+	108.158i	−0.0770929	+	0.133529i
$811$	399.452	−	230.624i	0.492543	−	0.284370i	−0.233086	−	0.972456i	$-0.574882\pi$
$811$	399.452	−	230.624i	0.492543	−	0.284370i	0.725629	+	0.688086i	$0.241549\pi$
$812$		−	653.342i		−	0.804608i
$813$	−435.326			−0.535456
$814$	277.595	−	480.808i	0.341025	−	0.590673i
$815$	471.400	−	272.163i	0.578405	−	0.333942i
$816$	−249.466	+	144.029i	−0.305718	+	0.176506i
$817$	−512.915	−	296.132i	−0.627803	−	0.362462i
$818$	1167.68			1.42748
$819$	602.287			0.735393
$820$	22.2541	−	38.5453i	0.0271392	−	0.0470065i
$821$	−529.015	+	916.282i	−0.644355	+	1.11606i	0.340095	+	0.940391i	$0.389541\pi$
$821$	−529.015	+	916.282i	−0.644355	+	1.11606i	−0.984450	+	0.175664i	$0.943793\pi$
$822$	−113.671	−	65.6282i	−0.138286	−	0.0798397i
$823$	−90.3360	+	156.467i	−0.109764	+	0.190117i	−0.915675	−	0.401920i	$-0.868343\pi$
$823$	−90.3360	+	156.467i	−0.109764	+	0.190117i	0.805910	+	0.592038i	$0.201676\pi$
$824$	329.870	−	190.450i	0.400328	−	0.231129i
$825$	44.3641	+	76.8409i	0.0537747	+	0.0931405i
$826$	−1359.64			−1.64605
$827$	444.146	−	769.283i	0.537057	−	0.930210i	−0.462004	−	0.886878i	$-0.652869\pi$
$827$	444.146	−	769.283i	0.537057	−	0.930210i	0.999061	−	0.0433318i	$-0.0137972\pi$
$828$	−10.1003			−0.0121985
$829$	415.673			0.501415			0.250708	−	0.968063i	$-0.419337\pi$
$829$	415.673			0.501415			0.250708	+	0.968063i	$0.419337\pi$
$830$	−3.80975	−	6.59868i	−0.00459006	−	0.00795022i
$831$			133.613i			0.160785i
$832$	−301.477	−	174.058i	−0.362352	−	0.209204i
$833$	97.1736	+	168.310i	0.116655	+	0.202052i
$834$	827.141	+	477.550i	0.991776	+	0.572602i
$835$	−117.158	+	67.6410i	−0.140309	+	0.0810072i
$836$	−152.048	+	87.7852i	−0.181876	+	0.105006i
$837$	−84.1694	−	145.786i	−0.100561	−	0.174176i
$838$	−1148.73	+	663.221i	−1.37080	+	0.791433i
$839$	−92.9496	−	160.993i	−0.110786	−	0.191887i	0.805301	−	0.592866i	$-0.202004\pi$
$839$	−92.9496	−	160.993i	−0.110786	−	0.191887i	−0.916087	+	0.400979i	$0.868670\pi$
$840$	−223.790	−	387.615i	−0.266416	−	0.461446i
$841$	−479.796	+	831.031i	−0.570506	+	0.988146i
$842$	1390.76	−	802.957i	1.65174	−	0.953631i
$843$	−80.4644	+	139.368i	−0.0954501	+	0.165324i
$844$	430.339			0.509880
$845$	−1935.63	+	1117.54i	−2.29069	+	1.32253i
$846$			112.406i			0.132867i
$847$		−	692.329i		−	0.817389i
$848$	−1255.73	−	724.995i	−1.48081	−	0.854947i
$849$		−	850.727i		−	1.00203i
$850$	141.576	−	81.7388i	0.166560	−	0.0961633i
$851$	34.0354	+	58.9511i	0.0399947	+	0.0692728i
$852$	−293.173	−	169.263i	−0.344100	−	0.198666i
$853$	175.365	−	303.741i	0.205586	−	0.356085i	−0.744733	−	0.667362i	$-0.767423\pi$
$853$	175.365	−	303.741i	0.205586	−	0.356085i	0.950319	+	0.311277i	$0.100757\pi$
$854$	−544.455	−	314.341i	−0.637535	−	0.368081i
$855$	−230.513	−	133.087i	−0.269606	−	0.155657i
$856$		−	874.026i		−	1.02106i
$857$		−	428.556i		−	0.500065i	−0.968237	−	0.250033i	$-0.919559\pi$
$857$		−	428.556i		−	0.500065i	0.968237	−	0.250033i	$-0.0804414\pi$
$858$	310.081	−	537.075i	0.361399	−	0.625962i
$859$	133.217	+	230.739i	0.155084	+	0.268613i	0.933090	−	0.359644i	$-0.117102\pi$
$859$	133.217	+	230.739i	0.155084	+	0.268613i	−0.778006	+	0.628257i	$0.783769\pi$
$860$	200.255	+	346.852i	0.232855	+	0.403316i
$861$	54.4793	+	31.4537i	0.0632745	+	0.0365315i
$862$		−	1337.79i		−	1.55196i
$863$	233.726			0.270830			0.135415	−	0.990789i	$-0.456763\pi$
$863$	233.726			0.270830			0.135415	+	0.990789i	$0.456763\pi$
$864$	−70.1766	−	121.549i	−0.0812229	−	0.140682i
$865$	−612.740	−	353.766i	−0.708370	−	0.408978i
$866$	882.773			1.01937
$867$	−329.404	+	190.182i	−0.379936	+	0.219356i
$868$	−498.810			−0.574666
$869$	240.717	−	416.935i	0.277005	−	0.479787i
$870$		−	1019.89i		−	1.17229i
$871$	745.704	−	1394.78i	0.856147	−	1.60135i
$872$	−868.727			−0.996247
$873$	196.464	+	113.429i	0.225045	+	0.129930i
$874$		−	69.0880i		−	0.0790481i
$875$	−412.706	−	714.827i	−0.471664	−	0.816945i
$876$			282.511i			0.322502i
$877$	−6.23058	+	10.7917i	−0.00710442	+	0.0123052i	−0.869556	−	0.493835i	$-0.835595\pi$
$877$	−6.23058	+	10.7917i	−0.00710442	+	0.0123052i	0.862451	+	0.506140i	$0.168928\pi$
$878$	648.755	−	374.559i	0.738901	−	0.426604i
$879$		−	561.119i		−	0.638360i
$880$	−723.184			−0.821801
$881$	434.203	−	752.061i	0.492852	−	0.853645i	−0.507114	−	0.861879i	$-0.669288\pi$
$881$	434.203	−	752.061i	0.492852	−	0.853645i	0.999966	+	0.00823388i	$0.00262095\pi$
$882$	−146.104	+	84.3532i	−0.165651	+	0.0956386i
$883$	−1424.01	+	822.155i	−1.61270	+	0.931093i	−0.623960	+	0.781456i	$0.714477\pi$
$883$	−1424.01	+	822.155i	−1.61270	+	0.931093i	−0.988741	+	0.149637i	$0.952190\pi$
$884$	−308.319	−	178.008i	−0.348777	−	0.201367i
$885$	−661.314			−0.747247
$886$	−1232.89			−1.39152
$887$	454.484	−	787.190i	0.512384	−	0.887475i	−0.487513	−	0.873116i	$-0.662096\pi$
$887$	454.484	−	787.190i	0.512384	−	0.887475i	0.999897	−	0.0143590i	$-0.00457078\pi$
$888$	−167.309	+	289.788i	−0.188411	+	0.326338i
$889$	1421.52	+	820.718i	1.59902	+	0.923192i
$890$	317.042	−	549.133i	0.356227	−	0.617003i
$891$	−49.0445	+	28.3158i	−0.0550443	+	0.0317798i
$892$	310.902	+	538.497i	0.348544	+	0.603697i
$893$	−239.565			−0.268270
$894$	−53.2525	+	92.2360i	−0.0595665	+	0.103172i
$895$	−1088.29			−1.21597
$896$	1221.19			1.36294
$897$	38.0185	+	65.8499i	0.0423840	+	0.0734113i
$898$		−	1235.23i		−	1.37554i
$899$	1190.53	+	687.353i	1.32428	+	0.764575i
$900$	22.1080	+	38.2923i	0.0245645	+	0.0425470i
$901$	523.984	+	302.522i	0.581558	+	0.335763i
$902$	56.0961	−	32.3871i	0.0621908	−	0.0359059i
$903$	−490.235	+	283.037i	−0.542896	+	0.313441i
$904$	431.775	+	747.856i	0.477627	+	0.827274i
$905$	−868.672	+	501.528i	−0.959859	+	0.554175i
$906$	−371.101	−	642.766i	−0.409604	−	0.709455i
$907$	888.214	+	1538.43i	0.979288	+	1.69618i	0.664989	+	0.746853i	$0.268436\pi$
$907$	888.214	+	1538.43i	0.979288	+	1.69618i	0.314299	+	0.949324i	$0.398230\pi$
$908$	0.261100	−	0.452239i	0.000287555	−	0.000498060i
$909$	251.832	−	145.395i	0.277043	−	0.159951i
$910$	1392.96	−	2412.68i	1.53073	−	2.65129i
$911$	−1408.56			−1.54617			−0.773083	−	0.634304i	$-0.781287\pi$
$911$	−1408.56			−1.54617			−0.773083	+	0.634304i	$0.781287\pi$
$912$	461.530	−	266.464i	0.506063	−	0.292176i
$913$		−	3.45507i		−	0.00378430i
$914$			730.167i			0.798870i
$915$	−264.816	−	152.892i	−0.289417	−	0.167095i
$916$			250.441i			0.273408i
$917$	1318.38	−	761.167i	1.43771	−	0.830062i
$918$	52.1706	+	90.3621i	0.0568307	+	0.0984337i
$919$	1290.35	+	744.982i	1.40408	+	0.810644i	0.994808	−	0.101770i	$-0.0324506\pi$
$919$	1290.35	+	744.982i	1.40408	+	0.810644i	0.409269	+	0.912414i	$0.365784\pi$
$920$	28.2528	−	48.9353i	0.0307096	−	0.0531905i
$921$	−226.159	−	130.573i	−0.245559	−	0.141773i
$922$	−339.692	−	196.121i	−0.368429	−	0.212713i
$923$			2548.48i			2.76109i
$924$			167.807i			0.181609i
$925$	148.996	−	258.069i	0.161077	−	0.278994i
$926$	−983.346	−	1703.20i	−1.06193	−	1.83931i
$927$	−108.252	−	187.498i	−0.116777	−	0.202263i
$928$	992.610	+	573.084i	1.06962	+	0.617547i
$929$		−	1059.16i		−	1.14011i	−0.821608	−	0.570053i	$-0.806923\pi$
$929$		−	1059.16i		−	1.14011i	0.821608	−	0.570053i	$-0.193077\pi$
$930$	−778.663			−0.837272
$931$	−179.778	−	311.385i	−0.193102	−	0.334463i
$932$	566.786	+	327.234i	0.608139	+	0.351109i
$933$	241.597			0.258947
$934$	651.416	−	376.095i	0.697448	−	0.402672i
$935$	301.767			0.322745
$936$	−186.889	+	323.701i	−0.199667	+	0.345834i
$937$			804.298i			0.858376i	0.903215	+	0.429188i	$0.141200\pi$
$937$			804.298i			0.858376i	−0.903215	+	0.429188i	$0.858800\pi$
$938$	44.8030	+	1372.79i	0.0477644	+	1.46353i
$939$	282.195			0.300527
$940$	140.299	+	81.0014i	0.149254	+	0.0861717i
$941$		−	939.916i		−	0.998848i	−0.866358	−	0.499424i	$-0.833545\pi$
$941$		−	939.916i		−	0.998848i	0.866358	−	0.499424i	$-0.166455\pi$
$942$	547.689	+	948.626i	0.581411	+	1.00703i
$943$			7.94187i			0.00842192i
$944$	662.036	−	1146.68i	0.701310	−	1.21470i
$945$	−220.320	+	127.202i	−0.233143	+	0.134605i
$946$			582.874i			0.616146i
$947$	750.189			0.792174			0.396087	−	0.918213i	$-0.370368\pi$
$947$	750.189			0.792174			0.396087	+	0.918213i	$0.370368\pi$
$948$	119.957	−	207.772i	0.126537	−	0.219169i
$949$	1841.85	−	1063.39i	1.94084	−	1.12054i
$950$	−261.925	+	151.223i	−0.275711	+	0.159182i
$951$	−110.398	−	63.7382i	−0.116086	−	0.0670223i
$952$	−373.935			−0.392789
$953$	−877.081			−0.920337			−0.460169	−	0.887832i	$-0.652211\pi$
$953$	−877.081			−0.920337			−0.460169	+	0.887832i	$0.652211\pi$
$954$	−262.610	+	454.853i	−0.275272	+	0.476786i
$955$	267.149	−	462.715i	0.279737	−	0.484518i
$956$	537.339	+	310.233i	0.562070	+	0.324511i
$957$	231.236	−	400.512i	0.241626	−	0.418508i
$958$	1219.04	−	703.811i	1.27248	−	0.734667i
$959$	−133.686	−	231.550i	−0.139401	−	0.241450i
$960$	147.043			0.153169
$961$	44.2765	−	76.6891i	0.0460733	−	0.0798014i
$962$	−2082.80			−2.16508
$963$	−496.796			−0.515883
$964$	−227.515	−	394.068i	−0.236012	−	0.408784i
$965$			1245.90i			1.29109i
$966$	−57.1864	−	33.0166i	−0.0591991	−	0.0341786i
$967$	305.177	+	528.581i	0.315591	+	0.546620i	0.979563	−	0.201138i	$-0.0644639\pi$
$967$	305.177	+	528.581i	0.315591	+	0.546620i	−0.663972	+	0.747758i	$0.731131\pi$
$968$	372.094	+	214.829i	0.384395	+	0.221930i
$969$	−192.585	+	111.189i	−0.198746	+	0.114746i
$970$	908.759	−	524.672i	0.936865	−	0.540899i
$971$	171.151	+	296.442i	0.176262	+	0.305295i	0.940597	−	0.339524i	$-0.110266\pi$
$971$	171.151	+	296.442i	0.176262	+	0.305295i	−0.764335	+	0.644819i	$0.776933\pi$
$972$	−24.4404	+	14.1107i	−0.0251445	+	0.0145172i
$973$	972.777	+	1684.90i	0.999771	+	1.73165i
$974$	−343.543	−	595.034i	−0.352713	−	0.610917i
$975$	166.433	−	288.270i	0.170700	−	0.295662i
$976$	530.212	−	306.118i	0.543250	−	0.313645i
$977$	−320.302	+	554.779i	−0.327842	+	0.567840i	−0.982083	−	0.188446i	$-0.939655\pi$
$977$	−320.302	+	554.779i	−0.327842	+	0.567840i	0.654241	+	0.756286i	$0.272988\pi$
$978$	394.765			0.403646
$979$	249.005	−	143.763i	0.254346	−	0.146847i
$980$			243.145i			0.248107i
$981$			493.784i			0.503348i
$982$	1306.47	+	754.290i	1.33042	+	0.768116i
$983$			560.681i			0.570377i	0.958471	+	0.285189i	$0.0920563\pi$
$983$			560.681i			0.570377i	−0.958471	+	0.285189i	$0.907944\pi$
$984$	−33.8097	+	19.5200i	−0.0343594	+	0.0198374i
$985$	115.449	+	199.964i	0.117207	+	0.203009i
$986$	−737.925	−	426.041i	−0.748402	−	0.432090i
$987$	−114.486	+	198.296i	−0.115994	+	0.200908i
$988$	570.413	+	329.328i	0.577341	+	0.333328i
$989$	−61.8908	−	35.7327i	−0.0625791	−	0.0361301i
$990$			261.954i			0.264600i
$991$		−	55.1813i		−	0.0556825i	−0.999612	−	0.0278412i	$-0.991137\pi$
$991$		−	55.1813i		−	0.0556825i	0.999612	−	0.0278412i	$-0.00886329\pi$
$992$	437.535	−	757.833i	0.441063	−	0.763944i
$993$	11.5179	+	19.9496i	0.0115991	+	0.0200903i
$994$	−1106.60	−	1916.68i	−1.11328	−	1.92825i
$995$	1247.67	+	720.344i	1.25394	+	0.723964i
$996$		−	1.72177i		−	0.00172869i
$997$	−465.062			−0.466461			−0.233231	−	0.972421i	$-0.574930\pi$
$997$	−465.062			−0.466461			−0.233231	+	0.972421i	$0.574930\pi$
$998$	−347.567	−	602.004i	−0.348264	−	0.603211i
$999$	164.715	+	95.0984i	0.164880	+	0.0951936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.h.a.172.9	yes	22
67.30	odd	6	inner	201.3.h.a.97.9	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.h.a.97.9	✓	22	67.30	odd	6	inner
201.3.h.a.172.9	yes	22	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.08753 + 1.20524i) q^{2} +1.73205i q^{3} +(0.905201 + 1.56785i) q^{4} +5.75683i q^{5} +(-2.08753 + 3.61572i) q^{6} +(-7.36527 + 4.25234i) q^{7} -5.27798i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(2.08753 + 1.20524i) q^{2} +1.73205i q^{3} +(0.905201 + 1.56785i) q^{4} +5.75683i q^{5} +(-2.08753 + 3.61572i) q^{6} +(-7.36527 + 4.25234i) q^{7} -5.27798i q^{8} -3.00000 q^{9} +(-6.93836 + 12.0176i) q^{10} +(-5.44938 + 3.14620i) q^{11} +(-2.71560 + 1.56785i) q^{12} +(20.4435 + 11.8030i) q^{13} -20.5003 q^{14} -9.97113 q^{15} +(9.98203 - 17.2894i) q^{16} +(-4.16525 + 7.21442i) q^{17} +(-6.26260 - 3.61572i) q^{18} +(7.70601 - 13.3472i) q^{19} +(-9.02587 + 5.21109i) q^{20} +(-7.36527 - 12.7570i) q^{21} -15.1677 q^{22} +(0.929844 - 1.61054i) q^{23} +9.14173 q^{24} -8.14112 q^{25} +(28.4510 + 49.2785i) q^{26} -5.19615i q^{27} +(-13.3341 - 7.69844i) q^{28} +(21.2167 + 36.7484i) q^{29} +(-20.8151 - 12.0176i) q^{30} +(28.0565 - 16.1984i) q^{31} +(23.3922 - 13.5055i) q^{32} +(-5.44938 - 9.43861i) q^{33} +(-17.3902 + 10.0402i) q^{34} +(-24.4800 - 42.4006i) q^{35} +(-2.71560 - 4.70356i) q^{36} +(-18.3017 + 31.6995i) q^{37} +(32.1731 - 18.5752i) q^{38} +(-20.4435 + 35.4091i) q^{39} +30.3844 q^{40} +(-3.69839 + 2.13527i) q^{41} -35.5076i q^{42} -38.4286i q^{43} +(-9.86557 - 5.69589i) q^{44} -17.2705i q^{45} +(3.88216 - 2.24137i) q^{46} +(-7.77202 - 13.4615i) q^{47} +(29.9461 + 17.2894i) q^{48} +(11.6648 - 20.2040i) q^{49} +(-16.9949 - 9.81199i) q^{50} +(-12.4957 - 7.21442i) q^{51} +42.7365i q^{52} -72.6301i q^{53} +(6.26260 - 10.8471i) q^{54} +(-18.1122 - 31.3712i) q^{55} +(22.4438 + 38.8737i) q^{56} +(23.1180 + 13.3472i) q^{57} +102.285i q^{58} +66.3229 q^{59} +(-9.02587 - 15.6333i) q^{60} +(26.5583 + 15.3334i) q^{61} +78.0918 q^{62} +(22.0958 - 12.7570i) q^{63} -14.7468 q^{64} +(-67.9481 + 117.690i) q^{65} -26.2712i q^{66} +(-2.18548 - 66.9643i) q^{67} -15.0815 q^{68} +(2.78953 + 1.61054i) q^{69} -118.017i q^{70} +(53.9794 + 93.4950i) q^{71} +15.8339i q^{72} +(45.0475 - 78.0245i) q^{73} +(-76.4108 + 44.1158i) q^{74} -14.1008i q^{75} +27.9019 q^{76} +(26.7575 - 46.3453i) q^{77} +(-85.3529 + 49.2785i) q^{78} +(-66.2599 + 38.2552i) q^{79} +(99.5320 + 57.4649i) q^{80} +9.00000 q^{81} -10.2940 q^{82} +(-0.274543 + 0.475522i) q^{83} +(13.3341 - 23.0953i) q^{84} +(-41.5322 - 23.9786i) q^{85} +(46.3157 - 80.2211i) q^{86} +(-63.6501 + 36.7484i) q^{87} +(16.6056 + 28.7617i) q^{88} -45.6941 q^{89} +(20.8151 - 36.0528i) q^{90} -200.762 q^{91} +3.36678 q^{92} +(28.0565 + 48.5952i) q^{93} -37.4686i q^{94} +(76.8376 + 44.3622i) q^{95} +(23.3922 + 40.5165i) q^{96} +(-65.4880 - 37.8095i) q^{97} +(48.7014 - 28.1177i) q^{98} +(16.3482 - 9.43861i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9}+O(q^{10}) \) 22 * q + 26 * q^4 - 15 * q^7 - 66 * q^9	\( 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9} + 6 q^{10} + 30 q^{11} - 78 q^{12} - 27 q^{13} + 6 q^{14} - 6 q^{15} - 58 q^{16} - 8 q^{17} + q^{19} - 12 q^{20} - 15 q^{21} + 14 q^{22} - q^{23} - 56 q^{25} + 71 q^{26} - 75 q^{28} + 42 q^{29} + 18 q^{30} + 120 q^{31} - 105 q^{32} + 30 q^{33} - 24 q^{34} + 3 q^{35} - 78 q^{36} + 13 q^{37} + 108 q^{38} + 27 q^{39} + 82 q^{40} - 159 q^{41} + 189 q^{44} + 372 q^{46} - 35 q^{47} - 174 q^{48} - 40 q^{49} + 285 q^{50} - 24 q^{51} - 212 q^{55} - 113 q^{56} + 3 q^{57} + 136 q^{59} - 12 q^{60} + 63 q^{61} - 150 q^{62} + 45 q^{63} - 284 q^{64} - 20 q^{65} + 94 q^{67} + 154 q^{68} - 3 q^{69} - 41 q^{71} - 16 q^{73} + 441 q^{74} - 390 q^{76} - 84 q^{77} - 213 q^{78} - 615 q^{79} + 267 q^{80} + 198 q^{81} - 302 q^{82} - 154 q^{83} + 75 q^{84} + 633 q^{85} + 221 q^{86} - 126 q^{87} + 410 q^{88} + 56 q^{89} - 18 q^{90} + 272 q^{91} + 636 q^{92} + 120 q^{93} + 588 q^{95} - 105 q^{96} - 441 q^{97} + 780 q^{98} - 90 q^{99}+O(q^{100}) \) 22 * q + 26 * q^4 - 15 * q^7 - 66 * q^9 + 6 * q^10 + 30 * q^11 - 78 * q^12 - 27 * q^13 + 6 * q^14 - 6 * q^15 - 58 * q^16 - 8 * q^17 + q^19 - 12 * q^20 - 15 * q^21 + 14 * q^22 - q^23 - 56 * q^25 + 71 * q^26 - 75 * q^28 + 42 * q^29 + 18 * q^30 + 120 * q^31 - 105 * q^32 + 30 * q^33 - 24 * q^34 + 3 * q^35 - 78 * q^36 + 13 * q^37 + 108 * q^38 + 27 * q^39 + 82 * q^40 - 159 * q^41 + 189 * q^44 + 372 * q^46 - 35 * q^47 - 174 * q^48 - 40 * q^49 + 285 * q^50 - 24 * q^51 - 212 * q^55 - 113 * q^56 + 3 * q^57 + 136 * q^59 - 12 * q^60 + 63 * q^61 - 150 * q^62 + 45 * q^63 - 284 * q^64 - 20 * q^65 + 94 * q^67 + 154 * q^68 - 3 * q^69 - 41 * q^71 - 16 * q^73 + 441 * q^74 - 390 * q^76 - 84 * q^77 - 213 * q^78 - 615 * q^79 + 267 * q^80 + 198 * q^81 - 302 * q^82 - 154 * q^83 + 75 * q^84 + 633 * q^85 + 221 * q^86 - 126 * q^87 + 410 * q^88 + 56 * q^89 - 18 * q^90 + 272 * q^91 + 636 * q^92 + 120 * q^93 + 588 * q^95 - 105 * q^96 - 441 * q^97 + 780 * q^98 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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