LMFDB - Embedded newform 201.3.h.a.97.9

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			97.9
Character	$\chi$	$=$	201.97
Dual form			201.3.h.a.172.9

$q$-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 $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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	0.122869	−	0.992423i	$-0.460790\pi$
$2$	2.08753	−	1.20524i	1.04377	−	0.602619i	0.920898	+	0.389804i	$0.127457\pi$
$3$		−	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	$-0.804736\pi$
$5$		−	5.75683i		−	1.15137i	0.817673	−	0.575683i	$-0.195264\pi$
$6$	−2.08753	−	3.61572i	−0.347922	−	0.602619i
$7$	−7.36527	−	4.25234i	−1.05218	−	0.607477i	−0.128922	−	0.991655i	$-0.541152\pi$
$7$	−7.36527	−	4.25234i	−1.05218	−	0.607477i	−0.923259	+	0.384177i	$0.874485\pi$
$8$			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	0.231413	−	0.972856i	$-0.425665\pi$
$11$	−5.44938	−	3.14620i	−0.495399	−	0.286018i	−0.726811	+	0.686837i	$0.758999\pi$
$12$	−2.71560	−	1.56785i	−0.226300	−	0.130654i
$13$	20.4435	−	11.8030i	1.57257	−	0.907926i	0.576723	−	0.816940i	$-0.304331\pi$
$13$	20.4435	−	11.8030i	1.57257	−	0.907926i	0.995852	−	0.0909864i	$-0.0290020\pi$
$14$	−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	0.717121	−	0.696949i	$-0.245459\pi$
$17$	−4.16525	−	7.21442i	−0.245015	−	0.424378i	−0.962136	+	0.272571i	$0.912126\pi$
$18$	−6.26260	+	3.61572i	−0.347922	+	0.200873i
$19$	7.70601	+	13.3472i	0.405580	+	0.702484i	0.994389	−	0.105788i	$-0.0337364\pi$
$19$	7.70601	+	13.3472i	0.405580	+	0.702484i	−0.588809	+	0.808272i	$0.700403\pi$
$20$	−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	0.885531	−	0.464580i	$-0.153795\pi$
$23$	0.929844	+	1.61054i	0.0404280	+	0.0700234i	−0.845103	+	0.534603i	$0.820461\pi$
$24$	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	−0.224585	−	0.974455i	$-0.572103\pi$
$29$	21.2167	−	36.7484i	0.731610	−	1.26719i	0.956195	−	0.292731i	$-0.0945641\pi$
$30$	−20.8151	+	12.0176i	−0.693836	+	0.400586i
$31$	28.0565	+	16.1984i	0.905047	+	0.522529i	0.878834	−	0.477127i	$-0.158322\pi$
$31$	28.0565	+	16.1984i	0.905047	+	0.522529i	0.0262128	+	0.999656i	$0.491655\pi$
$32$	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	0.505341	−	0.862920i	$-0.331367\pi$
$37$	−18.3017	−	31.6995i	−0.494640	−	0.856742i	−0.999981	+	0.00617772i	$0.998034\pi$
$38$	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	0.454219	−	0.890890i	$-0.349918\pi$
$41$	−3.69839	−	2.13527i	−0.0902047	−	0.0520797i	−0.544424	+	0.838810i	$0.683252\pi$
$42$			35.5076i			0.845420i
$43$			38.4286i			0.893689i	0.894612	+	0.446845i	$0.147452\pi$
$43$			38.4286i			0.893689i	−0.894612	+	0.446845i	$0.852548\pi$
$44$	−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	−0.936784	−	0.349909i	$-0.886213\pi$
$47$	−7.77202	+	13.4615i	−0.165362	+	0.286416i	0.771422	+	0.636324i	$0.219546\pi$
$48$	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	$0.240281\pi$
$53$			72.6301i			1.37038i	−0.728365	+	0.685189i	$0.759719\pi$
$54$	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	−0.266255	−	0.963903i	$-0.585786\pi$
$61$	26.5583	−	15.3334i	0.435382	−	0.251368i	0.701637	+	0.712535i	$0.252453\pi$
$62$	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	−0.182437	−	0.983218i	$-0.558399\pi$
$71$	53.9794	−	93.4950i	0.760273	−	1.31683i	0.942710	−	0.333613i	$-0.108268\pi$
$72$		−	15.8339i		−	0.219916i
$73$	45.0475	+	78.0245i	0.617089	+	1.06883i	0.990014	+	0.140968i	$0.0450214\pi$
$73$	45.0475	+	78.0245i	0.617089	+	1.06883i	−0.372925	+	0.927861i	$0.621645\pi$
$74$	−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	0.0181000	−	0.999836i	$-0.494238\pi$
$79$	−66.2599	−	38.2552i	−0.838733	−	0.484243i	−0.856834	+	0.515593i	$0.827572\pi$
$80$	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	0.864367	−	0.502862i	$-0.167720\pi$
$83$	−0.274543	−	0.475522i	−0.00330774	−	0.00572918i	−0.867675	+	0.497133i	$0.834386\pi$
$84$	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	−0.798019	−	0.602632i	$-0.794119\pi$
$97$	−65.4880	+	37.8095i	−0.675134	+	0.389789i	0.122885	+	0.992421i	$0.460785\pi$
$98$	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	0.0231109	−	0.999733i	$-0.492643\pi$
$101$	−83.9439	−	48.4650i	−0.831128	−	0.479852i	−0.854239	+	0.519881i	$0.825976\pi$
$102$	−17.3902	+	30.1207i	−0.170492	+	0.295301i
$103$	36.0840	−	62.4993i	0.350330	−	0.606789i	−0.635977	−	0.771708i	$-0.719403\pi$
$103$	36.0840	−	62.4993i	0.350330	−	0.606789i	0.986307	+	0.164919i	$0.0527361\pi$
$104$	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	$0.272374\pi$
$109$			164.595i			1.51004i	−0.655700	+	0.755021i	$0.727626\pi$
$110$			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	−0.282039	−	0.959403i	$-0.591011\pi$
$113$	−141.694	−	81.8068i	−1.25393	−	0.723954i	−0.971887	+	0.235449i	$0.924344\pi$
$114$	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	0.183066	+	0.983101i	$0.441398\pi$
$127$	−96.5019	+	167.146i	−0.759857	+	1.31611i	−0.942923	+	0.333011i	$0.891936\pi$
$128$	−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	$-0.963397\pi$
$137$		−	31.4381i		−	0.229475i	0.993396	−	0.114738i	$-0.0366028\pi$
$138$	3.88216	−	6.72411i	0.0281316	−	0.0487254i
$139$			228.763i			1.64578i	0.568204	+	0.822888i	$0.307639\pi$
$139$			228.763i			1.64578i	−0.568204	+	0.822888i	$0.692361\pi$
$140$	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	−0.994410	−	0.105583i	$-0.966329\pi$
$151$	−88.8851	−	153.953i	−0.588643	−	1.01956i	0.405767	−	0.913976i	$-0.367004\pi$
$152$	−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	0.893584	+	0.448895i	$0.148182\pi$
$157$	131.181	+	227.212i	0.835547	+	1.44721i	−0.0580373	+	0.998314i	$0.518484\pi$
$158$	−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	−0.973819	−	0.227325i	$-0.927002\pi$
$163$	−47.2765	+	81.8853i	−0.290040	+	0.502364i	0.683779	+	0.729689i	$0.260335\pi$
$164$	−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	−0.828701	−	0.559692i	$-0.810919\pi$
$167$	11.7497	−	20.3511i	0.0703575	−	0.121863i	0.899058	+	0.437830i	$0.144253\pi$
$168$	−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	0.631943	−	0.775015i	$-0.282258\pi$
$173$	−61.4515	−	106.437i	−0.355211	−	0.615243i	−0.987154	+	0.159772i	$0.948924\pi$
$174$	−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	$-0.822922\pi$
$179$		−	189.043i		−	1.05611i	0.849211	−	0.528053i	$-0.177078\pi$
$180$	27.0776	+	15.6333i	0.150431	+	0.0868515i
$181$	87.1187	−	150.894i	0.481319	−	0.833669i	−0.518451	−	0.855107i	$-0.673491\pi$
$181$	87.1187	−	150.894i	0.481319	−	0.833669i	0.999770	+	0.0214382i	$0.00682452\pi$
$182$	−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	−0.695428	−	0.718596i	$-0.744785\pi$
$191$	−80.3766	+	46.4055i	−0.420820	+	0.242961i	0.274608	+	0.961556i	$0.411452\pi$
$192$			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	0.585563	−	0.810627i	$-0.300874\pi$
$197$	34.7351	+	20.0543i	0.176320	+	0.101799i	−0.409242	+	0.912426i	$0.634207\pi$
$198$	45.5031			0.229814
$199$	125.129	+	216.729i	0.628787	+	1.08909i	0.987796	+	0.155756i	$0.0497815\pi$
$199$	125.129	+	216.729i	0.628787	+	1.08909i	−0.359009	+	0.933334i	$0.616885\pi$
$200$		−	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	0.997208	+	0.0746795i	$0.0237934\pi$
$211$	118.852	+	205.857i	0.563278	+	0.975626i	−0.433929	+	0.900947i	$0.642873\pi$
$212$	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	−0.866343	−	0.499450i	$-0.833536\pi$
$227$	−0.144222	+	0.249800i	−0.000635340	+	0.00110044i	0.865708	+	0.500550i	$0.166869\pi$
$228$		−	48.3276i		−	0.211963i
$229$	119.801	−	69.1674i	0.523150	−	0.302041i	−0.215072	−	0.976598i	$-0.568999\pi$
$229$	119.801	−	69.1674i	0.523150	−	0.302041i	0.738223	+	0.674557i	$0.235665\pi$
$230$	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	0.987342	−	0.158606i	$-0.0507000\pi$
$233$	313.072	+	180.752i	1.34366	+	0.775760i	0.356314	+	0.934366i	$0.384033\pi$
$234$	−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	0.969474	−	0.245194i	$-0.0788515\pi$
$239$	296.806	+	171.361i	1.24187	+	0.716992i	0.272393	+	0.962186i	$0.412185\pi$
$240$	−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	−0.413036	−	0.910715i	$-0.635532\pi$
$251$	42.4560	−	24.5120i	0.169148	−	0.0976574i	0.582184	+	0.813057i	$0.302198\pi$
$252$	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	−0.165820	+	0.986156i	$0.553027\pi$
$257$	−240.795	+	417.070i	−0.936946	+	1.62284i	−0.771126	+	0.636683i	$0.780306\pi$
$258$	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	$-0.846515\pi$
$271$		−	251.335i		−	0.927437i	0.885983	−	0.463718i	$-0.153485\pi$
$272$	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	−0.349945	−	0.936770i	$-0.613800\pi$
$281$	80.4644	−	46.4562i	0.286350	−	0.165324i	0.636295	+	0.771446i	$0.280466\pi$
$282$	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	0.716730	−	0.697351i	$-0.245638\pi$
$307$	−75.3865	−	130.573i	−0.245559	−	0.425320i	−0.962289	+	0.272031i	$0.912305\pi$
$308$	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	$0.0719946\pi$
$311$			139.486i			0.448509i	−0.974531	+	0.224254i	$0.928005\pi$
$312$	186.889	−	107.900i	0.599002	−	0.345834i
$313$			162.925i			0.520528i	0.965537	+	0.260264i	$0.0838096\pi$
$313$			162.925i			0.520528i	−0.965537	+	0.260264i	$0.916190\pi$
$314$	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	0.802127	−	0.597153i	$-0.203702\pi$
$317$	−36.7993	−	63.7382i	−0.116086	−	0.201067i	−0.918213	+	0.396086i	$0.870368\pi$
$318$	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	0.517298	−	0.855805i	$-0.326938\pi$
$331$	11.5179	+	6.64988i	0.0347974	+	0.0200903i	−0.482500	+	0.875896i	$0.660271\pi$
$332$	−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	−0.518639	−	0.854993i	$-0.673561\pi$
$337$	−12.6420	+	7.29885i	−0.0375133	+	0.0216583i	0.481126	+	0.876651i	$0.340228\pi$
$338$		−	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	0.0711509	−	0.997466i	$-0.477333\pi$
$347$	−262.715	−	151.679i	−0.757104	−	0.437114i	−0.828255	+	0.560351i	$0.810666\pi$
$348$	−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	−0.265536	−	0.964101i	$-0.585549\pi$
$353$	154.131	−	88.9877i	0.436632	−	0.252090i	0.702168	+	0.712011i	$0.252216\pi$
$354$	−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	0.396812	−	0.917900i	$-0.370117\pi$
$367$	−73.2924	−	42.3154i	−0.199707	−	0.115301i	−0.596519	+	0.802599i	$0.703450\pi$
$368$	−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	0.270887	−	0.962611i	$-0.412683\pi$
$373$	−159.388	−	92.0229i	−0.427315	−	0.246710i	−0.698202	+	0.715901i	$0.746016\pi$
$374$	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	−0.688281	−	0.725444i	$-0.741634\pi$
$379$	−153.180	+	88.4383i	−0.404168	+	0.233346i	0.284113	+	0.958791i	$0.408301\pi$
$380$		−	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	−0.611084	+	0.791566i	$0.709266\pi$
$383$	−613.620	+	354.274i	−1.60214	+	0.924997i	−0.991058	+	0.133431i	$0.957400\pi$
$384$	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	1.00000		0.000782130i	$0.000248960\pi$
$389$	194.763	+	337.340i	0.500677	+	0.867198i	−0.499323	+	0.866416i	$0.666418\pi$
$390$	−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	$-0.687845\pi$
$401$		−	666.355i		−	1.66173i	0.556471	−	0.830867i	$-0.312155\pi$
$402$	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	0.915755	−	0.401738i	$-0.131594\pi$
$409$	419.518	+	242.209i	1.02572	+	0.592198i	0.109962	+	0.993936i	$0.464927\pi$
$410$			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	−0.981475	−	0.191592i	$-0.938635\pi$
$419$	−275.141	−	476.558i	−0.656661	−	1.13737i	0.324814	−	0.945778i	$-0.394698\pi$
$420$	132.956	−	76.7622i	0.316562	−	0.182767i
$421$	333.111	+	576.966i	0.791238	+	1.37046i	0.925201	+	0.379479i	$0.123897\pi$
$421$	333.111	+	576.966i	0.791238	+	1.37046i	−0.133962	+	0.990986i	$0.542770\pi$
$422$	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	0.340730	+	0.940161i	$0.389326\pi$
$431$	−277.495	+	480.635i	−0.643839	+	1.11516i	−0.984568	+	0.175000i	$0.944007\pi$
$432$	−89.8382	+	51.8681i	−0.207959	+	0.120065i
$433$	317.159	+	183.112i	0.732468	+	0.422890i	0.819324	−	0.573330i	$-0.194349\pi$
$433$	317.159	+	183.112i	0.732468	+	0.422890i	−0.0868566	+	0.996221i	$0.527682\pi$
$434$	−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	0.986939	−	0.161094i	$-0.0515021\pi$
$439$	155.388	+	269.140i	0.353958	+	0.613074i	−0.632981	+	0.774168i	$0.718169\pi$
$440$	−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	−0.0916672	−	0.995790i	$-0.529220\pi$
$443$	−442.947	−	255.735i	−0.999880	−	0.577281i	−0.908213	+	0.418509i	$0.862553\pi$
$444$			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	0.425850	+	0.904794i	$0.359975\pi$
$449$	−256.222	+	443.789i	−0.570650	+	0.988394i	−0.996499	+	0.0836002i	$0.973358\pi$
$450$	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	−0.651374	−	0.758757i	$-0.725807\pi$
$457$	151.457	−	262.331i	0.331416	−	0.574029i	0.982790	+	0.184728i	$0.0591405\pi$
$458$	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	−0.526579	+	0.850126i	$0.676525\pi$
$463$	−706.584	+	407.946i	−1.52610	+	0.881094i	−0.999520	+	0.0309673i	$0.990141\pi$
$464$	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	0.983312	−	0.181929i	$-0.0582340\pi$
$467$	156.025	+	270.244i	0.334101	+	0.578680i	−0.649211	+	0.760609i	$0.724901\pi$
$468$			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	0.991313	+	0.131527i	$0.0419879\pi$
$479$	291.980	+	505.724i	0.609562	+	1.05579i	−0.381751	+	0.924265i	$0.624679\pi$
$480$	−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	−0.731552	−	0.681785i	$-0.761204\pi$
$487$	−246.853	+	142.521i	−0.506885	+	0.292650i	0.224667	+	0.974436i	$0.427870\pi$
$488$	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	−0.728916	−	0.684603i	$-0.759976\pi$
$499$	−249.745	+	144.190i	−0.500491	+	0.288958i	0.228426	+	0.973561i	$0.426642\pi$
$500$	−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	0.324849	−	0.945766i	$-0.394686\pi$
$503$	−166.887	−	96.3522i	−0.331783	−	0.191555i	−0.656633	+	0.754211i	$0.728020\pi$
$504$	−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	$0.0192987\pi$
$521$			63.1363i			0.121183i	−0.998163	+	0.0605915i	$0.980701\pi$
$522$			306.854i			0.587843i
$523$	−260.394	−	451.016i	−0.497886	−	0.862363i	0.502111	−	0.864803i	$-0.332557\pi$
$523$	−260.394	−	451.016i	−0.497886	−	0.862363i	−0.999997	+	0.00243984i	$0.999223\pi$
$524$	−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	$-0.794939\pi$
$541$		−	649.822i		−	1.20115i	0.799569	−	0.600575i	$-0.205061\pi$
$542$	−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	−0.124377	−	0.992235i	$-0.539693\pi$
$547$	−572.089	−	330.295i	−1.04587	−	0.603831i	−0.921489	+	0.388404i	$0.873026\pi$
$548$	−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	−0.240404	−	0.970673i	$-0.577280\pi$
$557$	401.277	−	695.032i	0.720425	−	1.24781i	0.960829	−	0.277141i	$-0.0893867\pi$
$558$	−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	$-0.900250\pi$
$563$		−	347.110i		−	0.616537i	0.951299	−	0.308268i	$-0.0997495\pi$
$564$	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	−0.550484	−	0.834845i	$-0.685557\pi$
$569$	254.773	−	441.279i	0.447755	−	0.775535i	0.998240	+	0.0593108i	$0.0188903\pi$
$570$	−320.802	−	185.215i	−0.562811	−	0.324939i
$571$	181.090	−	313.657i	0.317145	−	0.549311i	−0.662746	−	0.748844i	$-0.730609\pi$
$571$	181.090	−	313.657i	0.317145	−	0.549311i	0.979891	+	0.199533i	$0.0639425\pi$
$572$	−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	0.361102	−	0.932526i	$-0.382401\pi$
$577$	−153.447	−	88.5925i	−0.265939	−	0.153540i	−0.627041	+	0.778987i	$0.715734\pi$
$578$		−	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	−0.369380	−	0.929278i	$-0.620430\pi$
$587$	147.166	−	84.9662i	0.250708	−	0.144746i	0.620088	+	0.784532i	$0.287097\pi$
$588$		−	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	−0.691368	−	0.722503i	$-0.742992\pi$
$593$	−243.928	+	140.832i	−0.411346	+	0.237491i	0.280022	+	0.959994i	$0.409658\pi$
$594$		−	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	0.301737	−	0.953391i	$-0.402433\pi$
$599$	−223.460	−	129.015i	−0.373055	−	0.215383i	−0.674792	+	0.738008i	$0.735767\pi$
$600$	−74.4239			−0.124040
$601$	−95.2833	−	165.036i	−0.158541	−	0.274602i	0.775802	−	0.630977i	$-0.217346\pi$
$601$	−95.2833	−	165.036i	−0.158541	−	0.274602i	−0.934343	+	0.356375i	$0.884012\pi$
$602$		−	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	0.192675	−	0.981263i	$-0.438284\pi$
$607$	574.304	−	994.724i	0.946136	−	1.63876i	0.753461	−	0.657493i	$-0.228383\pi$
$608$			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	0.834569	−	0.550903i	$-0.185717\pi$
$613$	−36.6647	−	63.5051i	−0.0598119	−	0.103597i	−0.894381	+	0.447306i	$0.852383\pi$
$614$	−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	−0.873493	−	0.486837i	$-0.838151\pi$
$619$	−531.324	−	920.281i	−0.858359	−	1.48672i	0.0151336	−	0.999885i	$-0.495183\pi$
$620$	−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	−0.957432	−	0.288659i	$-0.906791\pi$
$631$	−748.468	+	432.128i	−1.18616	+	0.684831i	−0.228730	+	0.973490i	$0.573457\pi$
$632$	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	0.914993	−	0.403470i	$-0.132196\pi$
$641$	655.791	+	378.621i	1.02307	+	0.590672i	0.108081	+	0.994142i	$0.465529\pi$
$642$	−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	−0.878621	−	0.477521i	$-0.841536\pi$
$647$	−585.138	+	337.829i	−0.904386	+	0.522147i	−0.0257653	+	0.999668i	$0.508202\pi$
$648$			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	−0.999332	−	0.0365566i	$-0.988361\pi$
$653$	−958.172	+	553.201i	−1.46734	+	0.847168i	−0.468007	+	0.883725i	$0.655028\pi$
$654$	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	−0.983353	−	0.181705i	$-0.941839\pi$
$659$	−220.314	+	381.595i	−0.334316	+	0.579052i	0.649037	+	0.760757i	$0.275172\pi$
$660$	98.3709	−	56.7945i	0.149047	−	0.0860522i
$661$			896.356i			1.35606i	0.735034	+	0.678031i	$0.237166\pi$
$661$			896.356i			1.35606i	−0.735034	+	0.678031i	$0.762834\pi$
$662$	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	$0.143106\pi$
$673$			584.956i			0.869177i	−0.900629	+	0.434588i	$0.856894\pi$
$674$	−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	0.0525252	−	0.998620i	$-0.483273\pi$
$677$	−532.151	−	307.237i	−0.786042	−	0.453822i	−0.838567	+	0.544798i	$0.816606\pi$
$678$			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	−0.174712	−	0.984620i	$-0.555900\pi$
$683$	403.405	−	232.906i	0.590637	−	0.341004i	0.765349	+	0.643615i	$0.222566\pi$
$684$	−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	−0.995230	−	0.0975544i	$-0.968898\pi$
$691$	−285.473	+	494.454i	−0.413130	+	0.715563i	0.582100	+	0.813117i	$0.302231\pi$
$692$	−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	0.176704	−	0.984264i	$-0.443456\pi$
$701$	−411.726	−	237.710i	−0.587341	−	0.339102i	−0.764046	+	0.645162i	$0.776790\pi$
$702$	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	0.663482	−	0.748192i	$-0.269078\pi$
$709$	−224.194	−	388.316i	−0.316212	−	0.547695i	−0.979694	+	0.200497i	$0.935744\pi$
$710$	−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	0.684538	−	0.728977i	$-0.260004\pi$
$719$	−207.823	−	359.959i	−0.289044	−	0.500639i	−0.973582	+	0.228339i	$0.926671\pi$
$720$	−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	−0.461215	−	0.887288i	$-0.652586\pi$
$727$	55.6822	−	32.1482i	0.0765918	−	0.0442203i	0.537807	+	0.843068i	$0.319253\pi$
$728$		−	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	0.668347	−	0.743849i	$-0.267002\pi$
$733$	262.655	+	151.644i	0.358328	+	0.206881i	−0.310019	+	0.950730i	$0.600335\pi$
$734$	−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	−0.575239	−	0.817986i	$-0.695091\pi$
$739$	−114.147	+	65.9028i	−0.154462	+	0.0891784i	0.420777	+	0.907164i	$0.361757\pi$
$740$			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	0.674074	−	0.738664i	$-0.264543\pi$
$743$	−224.880	−	389.503i	−0.302664	−	0.524230i	−0.976739	+	0.214434i	$0.931209\pi$
$744$	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	0.892198	−	0.451644i	$-0.149162\pi$
$757$	717.002	+	413.961i	0.947162	+	0.546844i	0.0549641	+	0.998488i	$0.482496\pi$
$758$	−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	0.625799	−	0.779984i	$-0.284773\pi$
$769$	202.411	+	116.862i	0.263213	+	0.151966i	−0.362586	+	0.931950i	$0.618106\pi$
$770$	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	0.145071	+	0.989421i	$0.453659\pi$
$773$	−606.286	+	1050.12i	−0.784328	+	1.35850i	−0.929400	+	0.369075i	$0.879675\pi$
$774$	−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	−0.888325	−	0.459216i	$-0.848131\pi$
$787$	−735.683	+	424.747i	−0.934795	+	0.539704i	−0.0464699	+	0.998920i	$0.514797\pi$
$788$	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	0.382080	+	0.924129i	$0.375208\pi$
$797$	−485.596	+	841.077i	−0.609280	+	1.05530i	−0.991359	+	0.131174i	$0.958125\pi$
$798$	−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	$-0.693388\pi$
$809$		−	1328.46i		−	1.64210i	0.570854	−	0.821052i	$-0.306612\pi$
$810$	−62.4452	−	108.158i	−0.0770929	−	0.133529i
$811$	399.452	+	230.624i	0.492543	+	0.284370i	0.725629	−	0.688086i	$-0.241549\pi$
$811$	399.452	+	230.624i	0.492543	+	0.284370i	−0.233086	+	0.972456i	$0.574882\pi$
$812$			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	−0.984450	−	0.175664i	$-0.943793\pi$
$821$	−529.015	−	916.282i	−0.644355	−	1.11606i	0.340095	−	0.940391i	$-0.389541\pi$
$822$	−113.671	+	65.6282i	−0.138286	+	0.0798397i
$823$	−90.3360	−	156.467i	−0.109764	−	0.190117i	0.805910	−	0.592038i	$-0.201676\pi$
$823$	−90.3360	−	156.467i	−0.109764	−	0.190117i	−0.915675	+	0.401920i	$0.868343\pi$
$824$	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	0.999061	+	0.0433318i	$0.0137972\pi$
$827$	444.146	+	769.283i	0.537057	+	0.930210i	−0.462004	+	0.886878i	$0.652869\pi$
$828$	−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	−0.916087	−	0.400979i	$-0.868670\pi$
$839$	−92.9496	+	160.993i	−0.110786	+	0.191887i	0.805301	+	0.592866i	$0.202004\pi$
$840$	−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	0.950319	−	0.311277i	$-0.100757\pi$
$853$	175.365	+	303.741i	0.205586	+	0.356085i	−0.744733	+	0.667362i	$0.767423\pi$
$854$	−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	$0.0804414\pi$
$857$			428.556i			0.500065i	−0.968237	+	0.250033i	$0.919559\pi$
$858$	310.081	+	537.075i	0.361399	+	0.625962i
$859$	133.217	−	230.739i	0.155084	−	0.268613i	−0.778006	−	0.628257i	$-0.783769\pi$
$859$	133.217	−	230.739i	0.155084	−	0.268613i	0.933090	+	0.359644i	$0.117102\pi$
$860$	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	0.862451	−	0.506140i	$-0.168928\pi$
$877$	−6.23058	−	10.7917i	−0.00710442	−	0.0123052i	−0.869556	+	0.493835i	$0.835595\pi$
$878$	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	0.999966	−	0.00823388i	$-0.00262095\pi$
$881$	434.203	+	752.061i	0.492852	+	0.853645i	−0.507114	+	0.861879i	$0.669288\pi$
$882$	−146.104	−	84.3532i	−0.165651	−	0.0956386i
$883$	−1424.01	−	822.155i	−1.61270	−	0.931093i	−0.988741	−	0.149637i	$-0.952190\pi$
$883$	−1424.01	−	822.155i	−1.61270	−	0.931093i	−0.623960	−	0.781456i	$-0.714477\pi$
$884$	−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	0.999897	+	0.0143590i	$0.00457078\pi$
$887$	454.484	+	787.190i	0.512384	+	0.887475i	−0.487513	+	0.873116i	$0.662096\pi$
$888$	−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	0.314299	−	0.949324i	$-0.398230\pi$
$907$	888.214	−	1538.43i	0.979288	−	1.69618i	0.664989	−	0.746853i	$-0.268436\pi$
$908$	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	0.409269	−	0.912414i	$-0.365784\pi$
$919$	1290.35	−	744.982i	1.40408	−	0.810644i	0.994808	+	0.101770i	$0.0324506\pi$
$920$	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	$0.193077\pi$
$929$			1059.16i			1.14011i	−0.821608	+	0.570053i	$0.806923\pi$
$930$	−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	$-0.858800\pi$
$937$		−	804.298i		−	0.858376i	0.903215	−	0.429188i	$-0.141200\pi$
$938$	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	$0.166455\pi$
$941$			939.916i			0.998848i	−0.866358	+	0.499424i	$0.833545\pi$
$942$	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	−0.663972	−	0.747758i	$-0.731131\pi$
$967$	305.177	−	528.581i	0.315591	−	0.546620i	0.979563	+	0.201138i	$0.0644639\pi$
$968$	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	−0.764335	−	0.644819i	$-0.776933\pi$
$971$	171.151	−	296.442i	0.176262	−	0.305295i	0.940597	+	0.339524i	$0.110266\pi$
$972$	−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	0.654241	−	0.756286i	$-0.272988\pi$
$977$	−320.302	−	554.779i	−0.327842	−	0.567840i	−0.982083	+	0.188446i	$0.939655\pi$
$978$	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	$-0.907944\pi$
$983$		−	560.681i		−	0.570377i	0.958471	−	0.285189i	$-0.0920563\pi$
$984$	−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	$0.00886329\pi$
$991$			55.1813i			0.0556825i	−0.999612	+	0.0278412i	$0.991137\pi$
$992$	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.97.9	✓	22
67.38	odd	6	inner	201.3.h.a.172.9	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.h.a.97.9	✓	22	1.1	even	1	trivial
201.3.h.a.172.9	yes	22	67.38	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
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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