LMFDB - Embedded newform 250.3.f.f.243.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,3,Mod(7,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([17]))

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

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

chi := DirichletCharacter("250.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	250.f (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.81200660901$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			243.2
Character	$\chi$	$=$	250.243
Dual form			250.3.f.f.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642040 + 1.26007i) q^{2} +(0.0294182 + 0.185739i) q^{3} +(-1.17557 + 1.61803i) q^{4} +(-0.215157 + 0.156321i) q^{6} +(7.34278 - 7.34278i) q^{7} +(-2.79360 - 0.442463i) q^{8} +(8.52588 - 2.77022i) q^{9} +O(q^{10})$	\(q+(0.642040 + 1.26007i) q^{2} +(0.0294182 + 0.185739i) q^{3} +(-1.17557 + 1.61803i) q^{4} +(-0.215157 + 0.156321i) q^{6} +(7.34278 - 7.34278i) q^{7} +(-2.79360 - 0.442463i) q^{8} +(8.52588 - 2.77022i) q^{9} +(5.47552 - 16.8519i) q^{11} +(-0.335116 - 0.170750i) q^{12} +(-3.81236 + 7.48219i) q^{13} +(13.9668 + 4.53808i) q^{14} +(-1.23607 - 3.80423i) q^{16} +(-4.66258 + 29.4384i) q^{17} +(8.96464 + 8.96464i) q^{18} +(9.36667 + 12.8921i) q^{19} +(1.57985 + 1.14783i) q^{21} +(24.7502 - 3.92004i) q^{22} +(6.17981 - 3.14877i) q^{23} -0.531898i q^{24} -11.8758 q^{26} +(1.53373 + 3.01011i) q^{27} +(3.24891 + 20.5128i) q^{28} +(13.3163 - 18.3284i) q^{29} +(13.0736 - 9.49852i) q^{31} +(4.00000 - 4.00000i) q^{32} +(3.29114 + 0.521266i) q^{33} +(-40.0881 + 13.0254i) q^{34} +(-5.54045 + 17.0518i) q^{36} +(-0.991031 - 0.504956i) q^{37} +(-10.2312 + 20.0799i) q^{38} +(-1.50189 - 0.487993i) q^{39} +(-14.4667 - 44.5241i) q^{41} +(-0.432022 + 2.72768i) q^{42} +(8.20366 + 8.20366i) q^{43} +(20.8301 + 28.6702i) q^{44} +(7.93537 + 5.76538i) q^{46} +(-34.2382 + 5.42280i) q^{47} +(0.670231 - 0.341500i) q^{48} -58.8327i q^{49} -5.60502 q^{51} +(-7.62473 - 14.9644i) q^{52} +(-4.94745 - 31.2370i) q^{53} +(-2.80825 + 3.86522i) q^{54} +(-23.7617 + 17.2639i) q^{56} +(-2.11902 + 2.11902i) q^{57} +(31.6447 + 5.01203i) q^{58} +(-58.9939 + 19.1683i) q^{59} +(-19.9613 + 61.4346i) q^{61} +(20.3626 + 10.3753i) q^{62} +(42.2624 - 82.9447i) q^{63} +(7.60845 + 2.47214i) q^{64} +(1.45621 + 4.48176i) q^{66} +(-9.47690 + 59.8348i) q^{67} +(-42.1511 - 42.1511i) q^{68} +(0.766649 + 1.05520i) q^{69} +(66.2647 + 48.1441i) q^{71} +(-25.0436 + 3.96652i) q^{72} +(-46.6049 + 23.7464i) q^{73} -1.57297i q^{74} -31.8711 q^{76} +(-83.5344 - 163.945i) q^{77} +(-0.349364 - 2.20580i) q^{78} +(-1.37219 + 1.88866i) q^{79} +(64.7589 - 47.0501i) q^{81} +(46.8154 - 46.8154i) q^{82} +(-96.8447 - 15.3387i) q^{83} +(-3.71446 + 1.20690i) q^{84} +(-5.07014 + 15.6043i) q^{86} +(3.79604 + 1.93418i) q^{87} +(-22.7528 + 44.6549i) q^{88} +(6.69713 + 2.17603i) q^{89} +(26.9467 + 82.9333i) q^{91} +(-2.16999 + 13.7008i) q^{92} +(2.14885 + 2.14885i) q^{93} +(-28.8154 - 39.6610i) q^{94} +(0.860630 + 0.625284i) q^{96} +(-6.63322 + 1.05060i) q^{97} +(74.1335 - 37.7729i) q^{98} -158.846i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} - 40 q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 - 2 * q^7 - 12 * q^8 - 40 * q^9	$ 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} - 40 q^{9} - 32 q^{11} - 16 q^{12} + 2 q^{13} - 30 q^{14} + 24 q^{16} - 22 q^{17} - 136 q^{18} + 230 q^{19} + 68 q^{21} - 8 q^{22} + 42 q^{23} + 36 q^{26} - 340 q^{27} + 4 q^{28} - 100 q^{29} - 132 q^{31} + 96 q^{32} - 266 q^{33} - 150 q^{34} - 108 q^{36} + 38 q^{37} + 20 q^{38} + 80 q^{39} + 168 q^{41} - 128 q^{42} - 78 q^{43} + 40 q^{44} + 26 q^{46} + 168 q^{47} + 32 q^{48} + 168 q^{51} + 4 q^{52} + 42 q^{53} + 80 q^{54} - 48 q^{56} + 280 q^{57} - 160 q^{58} - 450 q^{59} - 492 q^{61} + 142 q^{62} + 762 q^{63} + 202 q^{66} + 498 q^{67} - 136 q^{68} + 670 q^{69} - 2 q^{71} - 72 q^{72} + 62 q^{73} - 40 q^{76} - 624 q^{77} + 658 q^{78} + 360 q^{79} - 46 q^{81} + 272 q^{82} - 128 q^{83} - 620 q^{84} - 264 q^{86} + 400 q^{87} - 44 q^{88} - 900 q^{89} + 798 q^{91} - 36 q^{92} + 294 q^{93} + 190 q^{94} + 16 q^{96} - 312 q^{97} + 66 q^{98}+O(q^{100}) $ 24 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 - 2 * q^7 - 12 * q^8 - 40 * q^9 - 32 * q^11 - 16 * q^12 + 2 * q^13 - 30 * q^14 + 24 * q^16 - 22 * q^17 - 136 * q^18 + 230 * q^19 + 68 * q^21 - 8 * q^22 + 42 * q^23 + 36 * q^26 - 340 * q^27 + 4 * q^28 - 100 * q^29 - 132 * q^31 + 96 * q^32 - 266 * q^33 - 150 * q^34 - 108 * q^36 + 38 * q^37 + 20 * q^38 + 80 * q^39 + 168 * q^41 - 128 * q^42 - 78 * q^43 + 40 * q^44 + 26 * q^46 + 168 * q^47 + 32 * q^48 + 168 * q^51 + 4 * q^52 + 42 * q^53 + 80 * q^54 - 48 * q^56 + 280 * q^57 - 160 * q^58 - 450 * q^59 - 492 * q^61 + 142 * q^62 + 762 * q^63 + 202 * q^66 + 498 * q^67 - 136 * q^68 + 670 * q^69 - 2 * q^71 - 72 * q^72 + 62 * q^73 - 40 * q^76 - 624 * q^77 + 658 * q^78 + 360 * q^79 - 46 * q^81 + 272 * q^82 - 128 * q^83 - 620 * q^84 - 264 * q^86 + 400 * q^87 - 44 * q^88 - 900 * q^89 + 798 * q^91 - 36 * q^92 + 294 * q^93 + 190 * q^94 + 16 * q^96 - 312 * q^97 + 66 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	0.642040	+	1.26007i	0.321020	+	0.630037i
$2$	0.642040	+	1.26007i	0.321020	+	0.630037i
$3$	0.0294182	+	0.185739i	0.00980607	+	0.0619131i	0.992106	−	0.125401i	$-0.0400218\pi$
$3$	0.0294182	+	0.185739i	0.00980607	+	0.0619131i	−0.982300	+	0.187314i	$0.940022\pi$
$4$	−1.17557	+	1.61803i	−0.293893	+	0.404508i
$5$		0			0
$5$		0			0
$6$	−0.215157	+	0.156321i	−0.0358596	+	0.0260535i
$7$	7.34278	−	7.34278i	1.04897	−	1.04897i	0.0502302	−	0.998738i	$-0.484004\pi$
$7$	7.34278	−	7.34278i	1.04897	−	1.04897i	0.998738	−	0.0502302i	$-0.0159955\pi$
$8$	−2.79360	−	0.442463i	−0.349201	−	0.0553079i
$9$	8.52588	−	2.77022i	0.947319	−	0.307803i
$10$		0			0
$11$	5.47552	−	16.8519i	0.497775	−	1.53199i	−0.314812	−	0.949154i	$-0.601942\pi$
$11$	5.47552	−	16.8519i	0.497775	−	1.53199i	0.812587	−	0.582840i	$-0.198058\pi$
$12$	−0.335116	−	0.170750i	−0.0279263	−	0.0142292i
$13$	−3.81236	+	7.48219i	−0.293259	+	0.575553i	−0.989883	−	0.141883i	$-0.954684\pi$
$13$	−3.81236	+	7.48219i	−0.293259	+	0.575553i	0.696625	+	0.717436i	$0.254684\pi$
$14$	13.9668	+	4.53808i	0.997628	+	0.324149i
$15$		0			0
$16$	−1.23607	−	3.80423i	−0.0772542	−	0.237764i
$17$	−4.66258	+	29.4384i	−0.274269	+	1.73167i	0.338111	+	0.941106i	$0.390212\pi$
$17$	−4.66258	+	29.4384i	−0.274269	+	1.73167i	−0.612381	+	0.790563i	$0.709788\pi$
$18$	8.96464	+	8.96464i	0.498035	+	0.498035i
$19$	9.36667	+	12.8921i	0.492983	+	0.678532i	0.980935	−	0.194338i	$-0.0622559\pi$
$19$	9.36667	+	12.8921i	0.492983	+	0.678532i	−0.487952	+	0.872870i	$0.662256\pi$
$20$		0			0
$21$	1.57985	+	1.14783i	0.0752311	+	0.0546586i
$22$	24.7502	−	3.92004i	1.12501	−	0.178184i
$23$	6.17981	−	3.14877i	0.268688	−	0.136903i	−0.314457	−	0.949272i	$-0.601822\pi$
$23$	6.17981	−	3.14877i	0.268688	−	0.136903i	0.583144	+	0.812369i	$0.301822\pi$
$24$		−	0.531898i		−	0.0221624i
$25$		0			0
$26$	−11.8758			−0.456761
$27$	1.53373	+	3.01011i	0.0568048	+	0.111486i
$28$	3.24891	+	20.5128i	0.116032	+	0.732600i
$29$	13.3163	−	18.3284i	0.459184	−	0.632012i	−0.515155	−	0.857097i	$-0.672266\pi$
$29$	13.3163	−	18.3284i	0.459184	−	0.632012i	0.974339	+	0.225084i	$0.0722658\pi$
$30$		0			0
$31$	13.0736	−	9.49852i	0.421729	−	0.306404i	−0.356604	−	0.934256i	$-0.616066\pi$
$31$	13.0736	−	9.49852i	0.421729	−	0.306404i	0.778333	+	0.627852i	$0.216066\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	3.29114	+	0.521266i	0.0997316	+	0.0157959i
$34$	−40.0881	+	13.0254i	−1.17906	+	0.383100i
$35$		0			0
$36$	−5.54045	+	17.0518i	−0.153901	+	0.473660i
$37$	−0.991031	−	0.504956i	−0.0267846	−	0.0136474i	0.440547	−	0.897730i	$-0.354785\pi$
$37$	−0.991031	−	0.504956i	−0.0267846	−	0.0136474i	−0.467332	+	0.884082i	$0.654785\pi$
$38$	−10.2312	+	20.0799i	−0.269243	+	0.528419i
$39$	−1.50189	−	0.487993i	−0.0385099	−	0.0125126i
$40$		0			0
$41$	−14.4667	−	44.5241i	−0.352847	−	1.08595i	−0.957247	−	0.289271i	$-0.906587\pi$
$41$	−14.4667	−	44.5241i	−0.352847	−	1.08595i	0.604400	−	0.796681i	$-0.293413\pi$
$42$	−0.432022	+	2.72768i	−0.0102862	+	0.0649448i
$43$	8.20366	+	8.20366i	0.190783	+	0.190783i	0.796034	−	0.605252i	$-0.206927\pi$
$43$	8.20366	+	8.20366i	0.190783	+	0.190783i	−0.605252	+	0.796034i	$0.706927\pi$
$44$	20.8301	+	28.6702i	0.473412	+	0.651596i
$45$		0			0
$46$	7.93537	+	5.76538i	0.172508	+	0.125334i
$47$	−34.2382	+	5.42280i	−0.728472	+	0.115379i	−0.509645	−	0.860385i	$-0.670223\pi$
$47$	−34.2382	+	5.42280i	−0.728472	+	0.115379i	−0.218827	+	0.975764i	$0.570223\pi$
$48$	0.670231	−	0.341500i	0.0139631	−	0.00711458i
$49$		−	58.8327i		−	1.20067i
$50$		0			0
$51$	−5.60502			−0.109902
$52$	−7.62473	−	14.9644i	−0.146629	−	0.287776i
$53$	−4.94745	−	31.2370i	−0.0933481	−	0.589377i	−0.989376	−	0.145379i	$-0.953560\pi$
$53$	−4.94745	−	31.2370i	−0.0933481	−	0.589377i	0.896028	−	0.443998i	$-0.146440\pi$
$54$	−2.80825	+	3.86522i	−0.0520046	+	0.0715782i
$55$		0			0
$56$	−23.7617	+	17.2639i	−0.424316	+	0.308284i
$57$	−2.11902	+	2.11902i	−0.0371758	+	0.0371758i
$58$	31.6447	+	5.01203i	0.545598	+	0.0864143i
$59$	−58.9939	+	19.1683i	−0.999897	+	0.324886i	−0.762825	−	0.646605i	$-0.776188\pi$
$59$	−58.9939	+	19.1683i	−0.999897	+	0.324886i	−0.237073	+	0.971492i	$0.576188\pi$
$60$		0			0
$61$	−19.9613	+	61.4346i	−0.327234	+	1.00712i	0.643188	+	0.765709i	$0.277612\pi$
$61$	−19.9613	+	61.4346i	−0.327234	+	1.00712i	−0.970422	+	0.241415i	$0.922388\pi$
$62$	20.3626	+	10.3753i	0.328429	+	0.167343i
$63$	42.2624	−	82.9447i	0.670832	−	1.31658i
$64$	7.60845	+	2.47214i	0.118882	+	0.0386271i
$65$		0			0
$66$	1.45621	+	4.48176i	0.0220638	+	0.0679054i
$67$	−9.47690	+	59.8348i	−0.141446	+	0.893057i	0.810265	+	0.586063i	$0.199323\pi$
$67$	−9.47690	+	59.8348i	−0.141446	+	0.893057i	−0.951712	+	0.306993i	$0.900677\pi$
$68$	−42.1511	−	42.1511i	−0.619869	−	0.619869i
$69$	0.766649	+	1.05520i	0.0111109	+	0.0152928i
$70$		0			0
$71$	66.2647	+	48.1441i	0.933306	+	0.678086i	0.946800	−	0.321823i	$-0.104295\pi$
$71$	66.2647	+	48.1441i	0.933306	+	0.678086i	−0.0134942	+	0.999909i	$0.504295\pi$
$72$	−25.0436	+	3.96652i	−0.347828	+	0.0550906i
$73$	−46.6049	+	23.7464i	−0.638423	+	0.325293i	−0.743067	−	0.669217i	$-0.766630\pi$
$73$	−46.6049	+	23.7464i	−0.638423	+	0.325293i	0.104644	+	0.994510i	$0.466630\pi$
$74$		−	1.57297i		−	0.0212564i
$75$		0			0
$76$	−31.8711			−0.419356
$77$	−83.5344	−	163.945i	−1.08486	−	2.12916i
$78$	−0.349364	−	2.20580i	−0.00447903	−	0.0282795i
$79$	−1.37219	+	1.88866i	−0.0173695	+	0.0239071i	−0.817613	−	0.575768i	$-0.804703\pi$
$79$	−1.37219	+	1.88866i	−0.0173695	+	0.0239071i	0.800244	+	0.599675i	$0.204703\pi$
$80$		0			0
$81$	64.7589	−	47.0501i	0.799493	−	0.580865i
$82$	46.8154	−	46.8154i	0.570919	−	0.570919i
$83$	−96.8447	−	15.3387i	−1.16680	−	0.184804i	−0.457174	−	0.889378i	$-0.651138\pi$
$83$	−96.8447	−	15.3387i	−1.16680	−	0.184804i	−0.709631	+	0.704574i	$0.751138\pi$
$84$	−3.71446	+	1.20690i	−0.0442197	+	0.0143679i
$85$		0			0
$86$	−5.07014	+	15.6043i	−0.0589551	+	0.181445i
$87$	3.79604	+	1.93418i	0.0436326	+	0.0222319i
$88$	−22.7528	+	44.6549i	−0.258555	+	0.507442i
$89$	6.69713	+	2.17603i	0.0752486	+	0.0244498i	0.346399	−	0.938087i	$-0.387404\pi$
$89$	6.69713	+	2.17603i	0.0752486	+	0.0244498i	−0.271151	+	0.962537i	$0.587404\pi$
$90$		0			0
$91$	26.9467	+	82.9333i	0.296117	+	0.911355i
$92$	−2.16999	+	13.7008i	−0.0235868	+	0.148921i
$93$	2.14885	+	2.14885i	0.0231059	+	0.0231059i
$94$	−28.8154	−	39.6610i	−0.306547	−	0.421925i
$95$		0			0
$96$	0.860630	+	0.625284i	0.00896489	+	0.00651338i
$97$	−6.63322	+	1.05060i	−0.0683837	+	0.0108309i	−0.190533	−	0.981681i	$-0.561021\pi$
$97$	−6.63322	+	1.05060i	−0.0683837	+	0.0108309i	0.122149	+	0.992512i	$0.461021\pi$
$98$	74.1335	−	37.7729i	0.756465	−	0.385438i
$99$		−	158.846i		−	1.60450i
$100$		0			0
$101$	−40.1366			−0.397392			−0.198696	−	0.980061i	$-0.563671\pi$
$101$	−40.1366			−0.397392			−0.198696	+	0.980061i	$0.563671\pi$
$102$	−3.59865	−	7.06274i	−0.0352809	−	0.0692426i
$103$	−11.4230	−	72.1217i	−0.110903	−	0.700211i	−0.979007	−	0.203829i	$-0.934661\pi$
$103$	−11.4230	−	72.1217i	−0.110903	−	0.700211i	0.868104	−	0.496382i	$-0.165339\pi$
$104$	13.9608	−	19.2154i	0.134239	−	0.184764i
$105$		0			0
$106$	36.1844	−	26.2895i	0.341363	−	0.248014i
$107$	85.6650	−	85.6650i	0.800608	−	0.800608i	−0.182583	−	0.983190i	$-0.558446\pi$
$107$	85.6650	−	85.6650i	0.800608	−	0.800608i	0.983190	+	0.182583i	$0.0584457\pi$
$108$	−6.67347	−	1.05697i	−0.0617914	−	0.00978680i
$109$	−181.039	+	58.8232i	−1.66091	+	0.539662i	−0.981062	−	0.193692i	$-0.937954\pi$
$109$	−181.039	+	58.8232i	−1.66091	+	0.539662i	−0.679847	+	0.733354i	$0.737954\pi$
$110$		0			0
$111$	0.0646357	−	0.198928i	0.000582304	−	0.00179215i
$112$	−37.0097	−	18.8574i	−0.330444	−	0.168370i
$113$	1.74347	−	3.42176i	0.0154290	−	0.0302811i	−0.883163	−	0.469065i	$-0.844591\pi$
$113$	1.74347	−	3.42176i	0.0154290	−	0.0302811i	0.898592	+	0.438784i	$0.144591\pi$
$114$	−4.03062	−	1.30963i	−0.0353563	−	0.0114880i
$115$		0			0
$116$	14.0016	+	43.0926i	0.120704	+	0.371488i
$117$	−11.7764	+	74.3533i	−0.100653	+	0.635498i
$118$	−62.0299	−	62.0299i	−0.525677	−	0.525677i
$119$	181.923	+	250.396i	1.52877	+	2.10416i
$120$		0			0
$121$	−156.115	−	113.424i	−1.29021	−	0.937391i
$122$	−90.2280	+	14.2907i	−0.739574	+	0.117137i
$123$	7.84428	−	3.99686i	0.0637746	−	0.0324948i
$124$			32.3197i			0.260643i
$125$		0			0
$126$	131.651			1.04485
$127$	73.2331	+	143.728i	0.576638	+	1.13172i	0.976576	+	0.215174i	$0.0690318\pi$
$127$	73.2331	+	143.728i	0.576638	+	1.13172i	−0.399937	+	0.916542i	$0.630968\pi$
$128$	1.76985	+	11.1744i	0.0138270	+	0.0873001i
$129$	−1.28240	+	1.76508i	−0.00994112	+	0.0136828i
$130$		0			0
$131$	−150.705	+	109.494i	−1.15042	+	0.835828i	−0.988537	−	0.150982i	$-0.951757\pi$
$131$	−150.705	+	109.494i	−1.15042	+	0.835828i	−0.161882	+	0.986810i	$0.551757\pi$
$132$	−4.71240	+	4.71240i	−0.0357000	+	0.0357000i
$133$	163.441	+	25.8865i	1.22888	+	0.194636i
$134$	−81.4808	+	26.4747i	−0.608065	+	0.197572i
$135$		0			0
$136$	26.0508	−	80.1761i	0.191550	−	0.589530i
$137$	−13.2633	−	6.75798i	−0.0968122	−	0.0493283i	0.404914	−	0.914355i	$-0.367301\pi$
$137$	−13.2633	−	6.75798i	−0.0968122	−	0.0493283i	−0.501726	+	0.865027i	$0.667301\pi$
$138$	−0.837413	+	1.64352i	−0.00606821	+	0.0119095i
$139$	47.7855	+	15.5264i	0.343780	+	0.111701i	0.475818	−	0.879544i	$-0.342152\pi$
$139$	47.7855	+	15.5264i	0.343780	+	0.111701i	−0.132038	+	0.991245i	$0.542152\pi$
$140$		0			0
$141$	−2.01445	−	6.19985i	−0.0142869	−	0.0439705i
$142$	−18.1206	+	114.409i	−0.127610	+	0.805696i
$143$	105.215	+	105.215i	0.735766	+	0.735766i
$144$	−21.0771	−	29.0102i	−0.146369	−	0.201460i
$145$		0			0
$146$	−59.8444	−	43.4795i	−0.409893	−	0.297805i
$147$	10.9275	−	1.73075i	0.0743370	−	0.0117738i
$148$	1.98206	−	1.00991i	0.0133923	−	0.00682372i
$149$		−	188.734i		−	1.26667i	−0.773877	−	0.633335i	$-0.781685\pi$
$149$		−	188.734i		−	1.26667i	0.773877	−	0.633335i	$-0.218315\pi$
$150$		0			0
$151$	68.5434			0.453930			0.226965	−	0.973903i	$-0.427120\pi$
$151$	68.5434			0.453930			0.226965	+	0.973903i	$0.427120\pi$
$152$	−20.4625	−	40.1599i	−0.134622	−	0.264210i
$153$	41.7983	+	263.904i	0.273192	+	1.72486i
$154$	152.951	−	210.519i	0.993188	−	1.36701i
$155$		0			0
$156$	2.55516	−	1.85644i	0.0163793	−	0.0119002i
$157$	10.9153	−	10.9153i	0.0695245	−	0.0695245i	−0.671490	−	0.741014i	$-0.734345\pi$
$157$	10.9153	−	10.9153i	0.0695245	−	0.0695245i	0.741014	+	0.671490i	$0.234345\pi$
$158$	−3.26085	−	0.516468i	−0.0206383	−	0.00326879i
$159$	5.65639	−	1.83787i	0.0355748	−	0.0115589i
$160$		0			0
$161$	22.2563	−	68.4977i	0.138238	−	0.425452i
$162$	100.864	+	51.3930i	0.622620	+	0.317240i
$163$	−21.6766	+	42.5428i	−0.132986	+	0.260999i	−0.947891	−	0.318595i	$-0.896789\pi$
$163$	−21.6766	+	42.5428i	−0.132986	+	0.260999i	0.814905	+	0.579594i	$0.196789\pi$
$164$	89.0481	+	28.9335i	0.542976	+	0.176424i
$165$		0			0
$166$	−42.8503	−	131.880i	−0.258134	−	0.794455i
$167$	18.8593	−	119.073i	0.112930	−	0.713012i	−0.864639	−	0.502394i	$-0.832453\pi$
$167$	18.8593	−	119.073i	0.112930	−	0.713012i	0.977569	−	0.210618i	$-0.0675475\pi$
$168$	−3.90561	−	3.90561i	−0.0232477	−	0.0232477i
$169$	57.8867	+	79.6742i	0.342525	+	0.471445i
$170$		0			0
$171$	115.573	+	83.9688i	0.675866	+	0.491045i
$172$	−22.9178	+	3.62982i	−0.133243	+	0.0211036i
$173$	−295.510	+	150.570i	−1.70815	+	0.870347i	−0.724727	+	0.689036i	$0.758034\pi$
$173$	−295.510	+	150.570i	−1.70815	+	0.870347i	−0.983426	+	0.181312i	$0.941966\pi$
$174$			6.02510i			0.0346270i
$175$		0			0
$176$	−70.8767			−0.402708
$177$	−5.29580	−	10.3936i	−0.0299198	−	0.0587209i
$178$	1.55786	+	9.83597i	0.00875205	+	0.0552583i
$179$	−166.183	+	228.732i	−0.928398	+	1.27783i	0.0320838	+	0.999485i	$0.489786\pi$
$179$	−166.183	+	228.732i	−0.928398	+	1.27783i	−0.960481	+	0.278344i	$0.910214\pi$
$180$		0			0
$181$	22.1737	−	16.1101i	0.122506	−	0.0890061i	−0.524845	−	0.851198i	$-0.675877\pi$
$181$	22.1737	−	16.1101i	0.122506	−	0.0890061i	0.647351	+	0.762192i	$0.275877\pi$
$182$	−87.2013	+	87.2013i	−0.479128	+	0.479128i
$183$	−11.9980	−	1.90030i	−0.0655630	−	0.0103842i
$184$	−18.6572	+	6.06208i	−0.101398	+	0.0329461i
$185$		0			0
$186$	−1.32806	+	4.08735i	−0.00714012	+	0.0219750i
$187$	470.563	+	239.764i	2.51638	+	1.28216i
$188$	31.4751	−	61.7735i	0.167421	−	0.328582i
$189$	33.3644	+	10.8408i	0.176531	+	0.0573585i
$190$		0			0
$191$	−49.7113	−	152.996i	−0.260269	−	0.801025i	−0.992746	−	0.120233i	$-0.961636\pi$
$191$	−49.7113	−	152.996i	−0.260269	−	0.801025i	0.732477	−	0.680792i	$-0.238364\pi$
$192$	−0.235346	+	1.48591i	−0.00122576	+	0.00773913i
$193$	190.941	+	190.941i	0.989331	+	0.989331i	0.999944	−	0.0106129i	$-0.00337827\pi$
$193$	190.941	+	190.941i	0.989331	+	0.989331i	−0.0106129	+	0.999944i	$0.503378\pi$
$194$	−5.58262	−	7.68382i	−0.0287764	−	0.0396073i
$195$		0			0
$196$	95.1933	+	69.1620i	0.485680	+	0.352867i
$197$	−155.407	+	24.6140i	−0.788868	+	0.124944i	−0.537853	−	0.843039i	$-0.680764\pi$
$197$	−155.407	+	24.6140i	−0.788868	+	0.124944i	−0.251015	+	0.967983i	$0.580764\pi$
$198$	200.158	−	101.985i	1.01090	−	0.515077i
$199$			213.484i			1.07279i	0.843968	+	0.536393i	$0.180213\pi$
$199$			213.484i			1.07279i	−0.843968	+	0.536393i	$0.819787\pi$
$200$		0			0
$201$	−11.3925			−0.0566789
$202$	−25.7693	−	50.5751i	−0.127571	−	0.250372i
$203$	−36.8022	−	232.360i	−0.181292	−	1.14463i
$204$	6.58910	−	9.06912i	0.0322995	−	0.0444565i
$205$		0			0
$206$	83.5447	−	60.6988i	0.405557	−	0.294654i
$207$	43.9655	−	43.9655i	0.212394	−	0.212394i
$208$	33.1763	+	5.25460i	0.159501	+	0.0252625i
$209$	268.544	−	87.2554i	1.28490	−	0.417490i
$210$		0			0
$211$	8.19988	−	25.2366i	0.0388620	−	0.119605i	−0.929743	−	0.368208i	$-0.879971\pi$
$211$	8.19988	−	25.2366i	0.0388620	−	0.119605i	0.968605	+	0.248603i	$0.0799714\pi$
$212$	56.3586	+	28.7161i	0.265842	+	0.135453i
$213$	−6.99286	+	13.7243i	−0.0328303	+	0.0644332i
$214$	162.945	+	52.9439i	0.761423	+	0.247401i
$215$		0			0
$216$	−2.95277	−	9.08769i	−0.0136702	−	0.0420726i
$217$	26.2509	−	165.742i	0.120972	−	0.763788i
$218$	−190.356	−	190.356i	−0.873192	−	0.873192i
$219$	−5.78166	−	7.95778i	−0.0264003	−	0.0363369i
$220$		0			0
$221$	−202.488	−	147.116i	−0.916235	−	0.665684i
$222$	0.292163	−	0.0462741i	0.00131605	−	0.000208442i
$223$	167.891	−	85.5448i	0.752875	−	0.383609i	−0.0350456	−	0.999386i	$-0.511158\pi$
$223$	167.891	−	85.5448i	0.752875	−	0.383609i	0.787921	+	0.615777i	$0.211158\pi$
$224$		−	58.7422i		−	0.262242i
$225$		0			0
$226$	5.43105			0.0240312
$227$	−33.3966	−	65.5445i	−0.147122	−	0.288742i	0.805672	−	0.592362i	$-0.201805\pi$
$227$	−33.3966	−	65.5445i	−0.147122	−	0.288742i	−0.952793	+	0.303620i	$0.901805\pi$
$228$	−0.937589	−	5.91970i	−0.00411223	−	0.0259636i
$229$	115.180	−	158.531i	0.502969	−	0.692277i	−0.479745	−	0.877408i	$-0.659271\pi$
$229$	115.180	−	158.531i	0.502969	−	0.692277i	0.982714	+	0.185131i	$0.0592709\pi$
$230$		0			0
$231$	27.9937	−	20.3386i	0.121185	−	0.0880459i
$232$	−45.3102	+	45.3102i	−0.195303	+	0.195303i
$233$	−268.492	−	42.5249i	−1.15233	−	0.182510i	−0.449103	−	0.893480i	$-0.648256\pi$
$233$	−268.492	−	42.5249i	−1.15233	−	0.182510i	−0.703223	+	0.710970i	$0.748256\pi$
$234$	−101.252	+	32.8986i	−0.432699	+	0.140592i
$235$		0			0
$236$	38.3366	−	117.988i	0.162443	−	0.499949i
$237$	−0.391166	−	0.199309i	−0.00165049	−	0.000840965i
$238$	−198.715	+	390.000i	−0.834937	+	1.63866i
$239$	−113.170	−	36.7711i	−0.473514	−	0.153854i	0.0625316	−	0.998043i	$-0.480083\pi$
$239$	−113.170	−	36.7711i	−0.473514	−	0.153854i	−0.536046	+	0.844189i	$0.680083\pi$
$240$		0			0
$241$	104.021	+	320.142i	0.431621	+	1.32839i	0.896510	+	0.443023i	$0.146094\pi$
$241$	104.021	+	320.142i	0.431621	+	1.32839i	−0.464890	+	0.885369i	$0.653906\pi$
$242$	42.6909	−	269.539i	0.176409	−	1.11380i
$243$	32.1437	+	32.1437i	0.132279	+	0.132279i
$244$	−75.9373	−	104.519i	−0.311218	−	0.428355i
$245$		0			0
$246$	10.0727	+	7.31823i	0.0409458	+	0.0297489i
$247$	−132.170	+	20.9337i	−0.535102	+	0.0847519i
$248$	−40.7252	+	20.7505i	−0.164215	+	0.0836715i
$249$		−	18.4391i		−	0.0740526i
$250$		0			0
$251$	−24.6454			−0.0981890			−0.0490945	−	0.998794i	$-0.515634\pi$
$251$	−24.6454			−0.0981890			−0.0490945	+	0.998794i	$0.515634\pi$
$252$	84.5249	+	165.889i	0.335416	+	0.658291i
$253$	−19.2252	−	121.383i	−0.0759888	−	0.479775i
$254$	−134.089	+	184.558i	−0.527911	+	0.726607i
$255$		0			0
$256$	−12.9443	+	9.40456i	−0.0505636	+	0.0367366i
$257$	−20.8782	+	20.8782i	−0.0812381	+	0.0812381i	−0.746558	−	0.665320i	$-0.768295\pi$
$257$	−20.8782	+	20.8782i	−0.0812381	+	0.0812381i	0.665320	+	0.746558i	$0.268295\pi$
$258$	−3.04748	−	0.482674i	−0.0118119	−	0.00187083i
$259$	−10.9847	+	3.56914i	−0.0424120	+	0.0137805i
$260$		0			0
$261$	62.7597	−	193.155i	0.240459	−	0.740056i
$262$	−234.728	−	119.600i	−0.895910	−	0.456489i
$263$	138.804	−	272.419i	0.527774	−	1.03581i	−0.461141	−	0.887327i	$-0.652560\pi$
$263$	138.804	−	272.419i	0.527774	−	1.03581i	0.988914	−	0.148487i	$-0.0474403\pi$
$264$	−8.96351	−	2.91242i	−0.0339527	−	0.0110319i
$265$		0			0
$266$	72.3168	+	222.568i	0.271868	+	0.836722i
$267$	−0.207156	+	1.30793i	−0.000775867	+	0.00489863i
$268$	−85.6740	−	85.6740i	−0.319679	−	0.319679i
$269$	−28.2649	−	38.9033i	−0.105074	−	0.144622i	0.753242	−	0.657744i	$-0.228489\pi$
$269$	−28.2649	−	38.9033i	−0.105074	−	0.144622i	−0.858316	+	0.513122i	$0.828489\pi$
$270$		0			0
$271$	265.655	+	193.010i	0.980276	+	0.712212i	0.957770	−	0.287535i	$-0.0928356\pi$
$271$	265.655	+	193.010i	0.980276	+	0.712212i	0.0225057	+	0.999747i	$0.492836\pi$
$272$	117.753	−	18.6503i	0.432917	−	0.0685674i
$273$	−14.6112	+	7.44480i	−0.0535211	+	0.0272703i
$274$		−	21.0516i		−	0.0768306i
$275$		0			0
$276$	−2.60860			−0.00945146
$277$	−1.57507	−	3.09125i	−0.00568617	−	0.0111597i	0.888146	−	0.459561i	$-0.151993\pi$
$277$	−1.57507	−	3.09125i	−0.00568617	−	0.0111597i	−0.893832	+	0.448402i	$0.851993\pi$
$278$	11.1157	+	70.1818i	0.0399845	+	0.252452i
$279$	85.1508	−	117.200i	0.305200	−	0.420072i
$280$		0			0
$281$	−333.008	+	241.945i	−1.18508	+	0.861013i	−0.992736	−	0.120314i	$-0.961610\pi$
$281$	−333.008	+	241.945i	−1.18508	+	0.861013i	−0.192347	+	0.981327i	$0.561610\pi$
$282$	6.51890	−	6.51890i	0.0231167	−	0.0231167i
$283$	−98.5216	−	15.6043i	−0.348133	−	0.0551388i	−0.0200805	−	0.999798i	$-0.506392\pi$
$283$	−98.5216	−	15.6043i	−0.348133	−	0.0551388i	−0.328052	+	0.944660i	$0.606392\pi$
$284$	−155.798	+	50.6217i	−0.548583	+	0.178246i
$285$		0			0
$286$	−65.0262	+	200.130i	−0.227364	+	0.699755i
$287$	−433.156	−	220.704i	−1.50926	−	0.769004i
$288$	23.0226	−	45.1844i	0.0799396	−	0.156890i
$289$	−570.023	−	185.212i	−1.97240	−	0.640871i
$290$		0			0
$291$	−0.390275	−	1.20114i	−0.00134115	−	0.00412764i
$292$	16.3649	−	103.324i	0.0560441	−	0.353849i
$293$	−34.4622	−	34.4622i	−0.117618	−	0.117618i	0.645848	−	0.763466i	$-0.276504\pi$
$293$	−34.4622	−	34.4622i	−0.117618	−	0.117618i	−0.763466	+	0.645848i	$0.776504\pi$
$294$	9.19679	+	12.6583i	0.0312816	+	0.0430554i
$295$		0			0
$296$	2.54512	+	1.84914i	0.00859839	+	0.00624710i
$297$	59.1242	−	9.36435i	0.199071	−	0.0315298i
$298$	237.819	−	121.175i	0.798049	−	0.406626i
$299$			58.2428i			0.194792i
$300$		0			0
$301$	120.475			0.400250
$302$	44.0076	+	86.3697i	0.145720	+	0.285993i
$303$	−1.18075	−	7.45494i	−0.00389685	−	0.0246038i
$304$	37.4667	−	51.5684i	0.123246	−	0.169633i
$305$		0			0
$306$	−305.703	+	222.106i	−0.999028	+	0.725836i
$307$	−270.723	+	270.723i	−0.881835	+	0.881835i	−0.993721	−	0.111886i	$-0.964311\pi$
$307$	−270.723	+	270.723i	−0.881835	+	0.881835i	0.111886	+	0.993721i	$0.464311\pi$
$308$	363.470	+	57.5680i	1.18010	+	0.186909i
$309$	13.0598	−	4.24338i	0.0422647	−	0.0137326i
$310$		0			0
$311$	−131.481	+	404.658i	−0.422769	+	1.30115i	0.482345	+	0.875981i	$0.339785\pi$
$311$	−131.481	+	404.658i	−0.422769	+	1.30115i	−0.905114	+	0.425169i	$0.860215\pi$
$312$	3.97976	+	2.02779i	0.0127556	+	0.00649933i
$313$	220.198	−	432.163i	0.703507	−	1.38071i	−0.211542	−	0.977369i	$-0.567849\pi$
$313$	220.198	−	432.163i	0.703507	−	1.38071i	0.915049	−	0.403342i	$-0.132151\pi$
$314$	20.7622	+	6.74606i	0.0661217	+	0.0214843i
$315$		0			0
$316$	−1.44281	−	4.44051i	−0.00456585	−	0.0140522i
$317$	−29.3958	+	185.598i	−0.0927312	+	0.585482i	0.896943	+	0.442146i	$0.145783\pi$
$317$	−29.3958	+	185.598i	−0.0927312	+	0.585482i	−0.989674	+	0.143336i	$0.954217\pi$
$318$	5.94748	+	5.94748i	0.0187028	+	0.0187028i
$319$	−235.954	−	324.763i	−0.739669	−	1.01807i
$320$		0			0
$321$	18.4315	+	13.3912i	0.0574189	+	0.0417173i
$322$	100.602	−	15.9337i	0.312427	−	0.0494836i
$323$	−423.196	+	215.629i	−1.31020	+	0.667582i
$324$			160.093i			0.494114i
$325$		0			0
$326$	−67.5243			−0.207130
$327$	−16.2516	−	31.8956i	−0.0496991	−	0.0975400i
$328$	20.7141	+	130.784i	0.0631527	+	0.398731i
$329$	−211.585	+	291.222i	−0.643116	+	0.885173i
$330$		0			0
$331$	437.596	−	317.932i	1.32204	−	0.960519i	0.322137	−	0.946693i	$-0.395599\pi$
$331$	437.596	−	317.932i	1.32204	−	0.960519i	0.999904	−	0.0138259i	$-0.00440105\pi$
$332$	138.666	−	138.666i	0.417670	−	0.417670i
$333$	−9.84825	−	1.55981i	−0.0295743	−	0.00468411i
$334$	162.149	−	52.6855i	0.485476	−	0.157741i
$335$		0			0
$336$	2.41380	−	7.42891i	0.00718393	−	0.0221099i
$337$	−566.865	−	288.832i	−1.68209	−	0.857068i	−0.990932	−	0.134365i	$-0.957101\pi$
$337$	−566.865	−	288.832i	−1.68209	−	0.857068i	−0.691159	−	0.722703i	$-0.742899\pi$
$338$	−63.2298	+	124.096i	−0.187071	+	0.367147i
$339$	0.686845	+	0.223169i	0.00202609	+	0.000658317i
$340$		0			0
$341$	−88.4837	−	272.325i	−0.259483	−	0.798606i
$342$	−31.6043	+	199.542i	−0.0924103	+	0.583456i
$343$	−72.1993	−	72.1993i	−0.210494	−	0.210494i
$344$	−19.2880	−	26.5476i	−0.0560696	−	0.0771732i
$345$		0			0
$346$	−379.459	−	275.693i	−1.09670	−	0.796800i
$347$	175.289	−	27.7630i	0.505154	−	0.0800086i	0.101344	−	0.994851i	$-0.467686\pi$
$347$	175.289	−	27.7630i	0.505154	−	0.0800086i	0.403810	+	0.914843i	$0.367686\pi$
$348$	−7.59207	+	3.86836i	−0.0218163	+	0.0111160i
$349$		−	43.7714i		−	0.125420i	−0.998032	−	0.0627098i	$-0.980026\pi$
$349$		−	43.7714i		−	0.125420i	0.998032	−	0.0627098i	$-0.0199743\pi$
$350$		0			0
$351$	−28.3694			−0.0808244
$352$	−45.5056	−	89.3098i	−0.129277	−	0.253721i
$353$	−30.6578	−	193.566i	−0.0868492	−	0.548344i	−0.992296	−	0.123886i	$-0.960464\pi$
$353$	−30.6578	−	193.566i	−0.0868492	−	0.548344i	0.905447	−	0.424459i	$-0.139536\pi$
$354$	9.69658	−	13.3462i	0.0273915	−	0.0377011i
$355$		0			0
$356$	−11.3938	+	8.27810i	−0.0320051	+	0.0232531i
$357$	−41.1564	+	41.1564i	−0.115284	+	0.115284i
$358$	−394.915	−	62.5483i	−1.10311	−	0.174716i
$359$	539.276	−	175.221i	1.50216	−	0.488082i	0.561513	−	0.827468i	$-0.310219\pi$
$359$	539.276	−	175.221i	1.50216	−	0.488082i	0.940647	+	0.339386i	$0.110219\pi$
$360$		0			0
$361$	33.0830	−	101.819i	0.0916428	−	0.282047i
$362$	34.5363	+	17.5971i	0.0954041	+	0.0486108i
$363$	16.4747	−	32.3334i	0.0453849	−	0.0890729i
$364$	−165.867	−	53.8933i	−0.455678	−	0.148059i
$365$		0			0
$366$	−5.30869	−	16.3385i	−0.0145046	−	0.0446406i
$367$	18.2199	−	115.036i	0.0496455	−	0.313449i	−0.950352	−	0.311177i	$-0.899277\pi$
$367$	18.2199	−	115.036i	0.0496455	−	0.313449i	0.999997	−	0.00227212i	$-0.000723238\pi$
$368$	−19.6173	−	19.6173i	−0.0533079	−	0.0533079i
$369$	−246.683	−	339.530i	−0.668518	−	0.920137i
$370$		0			0
$371$	−265.694	−	193.038i	−0.716157	−	0.520318i
$372$	−6.00304	+	0.950787i	−0.0161372	+	0.00255588i
$373$	338.361	−	172.404i	0.907134	−	0.462208i	0.0628006	−	0.998026i	$-0.479997\pi$
$373$	338.361	−	172.404i	0.907134	−	0.462208i	0.844333	+	0.535818i	$0.179997\pi$
$374$			746.882i			1.99701i
$375$		0			0
$376$	98.0474			0.260764
$377$	86.3695	+	169.510i	0.229097	+	0.449628i
$378$	7.76113	+	49.0018i	0.0205321	+	0.129634i
$379$	−164.027	+	225.764i	−0.432790	+	0.595684i	−0.968591	−	0.248660i	$-0.920010\pi$
$379$	−164.027	+	225.764i	−0.432790	+	0.595684i	0.535801	+	0.844344i	$0.320010\pi$
$380$		0			0
$381$	−24.5415	+	17.8305i	−0.0644135	+	0.0467991i
$382$	160.869	−	160.869i	0.421124	−	0.421124i
$383$	592.759	+	93.8837i	1.54767	+	0.245127i	0.871047	−	0.491200i	$-0.163442\pi$
$383$	592.759	+	93.8837i	1.54767	+	0.245127i	0.676626	+	0.736327i	$0.263442\pi$
$384$	−2.02346	+	0.657463i	−0.00526943	+	0.00171214i
$385$		0			0
$386$	−118.008	+	363.191i	−0.305720	+	0.940909i
$387$	92.6693	+	47.2174i	0.239456	+	0.122009i
$388$	6.09792	−	11.9678i	0.0157163	−	0.0308449i
$389$	268.657	+	87.2921i	0.690636	+	0.224401i	0.633246	−	0.773951i	$-0.281722\pi$
$389$	268.657	+	87.2921i	0.690636	+	0.224401i	0.0573901	+	0.998352i	$0.481722\pi$
$390$		0			0
$391$	63.8809	+	196.605i	0.163378	+	0.502826i
$392$	−26.0313	+	164.355i	−0.0664064	+	0.419274i
$393$	−24.7707	−	24.7707i	−0.0630298	−	0.0630298i
$394$	−130.793	−	180.021i	−0.331962	−	0.456906i
$395$		0			0
$396$	257.018	+	186.735i	0.649035	+	0.471552i
$397$	587.229	−	93.0080i	1.47917	−	0.234277i	0.635900	−	0.771772i	$-0.280629\pi$
$397$	587.229	−	93.0080i	1.47917	−	0.234277i	0.843267	+	0.537495i	$0.180629\pi$
$398$	−269.006	+	137.065i	−0.675895	+	0.344385i
$399$			31.1190i			0.0779924i
$400$		0			0
$401$	338.722			0.844693			0.422346	−	0.906435i	$-0.361207\pi$
$401$	338.722			0.844693			0.422346	+	0.906435i	$0.361207\pi$
$402$	−7.31441	−	14.3553i	−0.0181950	−	0.0357098i
$403$	21.2284	+	134.031i	0.0526759	+	0.332583i
$404$	47.1834	−	64.9424i	0.116791	−	0.160748i
$405$		0			0
$406$	269.162	−	195.558i	0.662961	−	0.481669i
$407$	−13.9359	+	13.9359i	−0.0342405	+	0.0342405i
$408$	15.6582	+	2.48002i	0.0383780	+	0.00607848i
$409$	771.108	−	250.548i	1.88535	−	0.612587i	0.901739	−	0.432281i	$-0.142291\pi$
$409$	771.108	−	250.548i	1.88535	−	0.612587i	0.983611	−	0.180306i	$-0.0577087\pi$
$410$		0			0
$411$	0.865040	−	2.66232i	0.00210472	−	0.00647766i
$412$	130.124	+	66.3014i	0.315835	+	0.160926i
$413$	−292.431	+	573.928i	−0.708065	+	1.38966i
$414$	83.6274	+	27.1722i	0.201998	+	0.0656333i
$415$		0			0
$416$	14.6793	+	45.1782i	0.0352867	+	0.108601i
$417$	−1.47811	+	9.33239i	−0.00354462	+	0.0223798i
$418$	282.364	+	282.364i	0.675513	+	0.675513i
$419$	−23.3449	−	32.1315i	−0.0557158	−	0.0766862i	0.780250	−	0.625468i	$-0.215092\pi$
$419$	−23.3449	−	32.1315i	−0.0557158	−	0.0766862i	−0.835966	+	0.548782i	$0.815092\pi$
$420$		0			0
$421$	201.243	+	146.212i	0.478012	+	0.347296i	0.800556	−	0.599258i	$-0.204538\pi$
$421$	201.243	+	146.212i	0.478012	+	0.347296i	−0.322543	+	0.946555i	$0.604538\pi$
$422$	37.0647	−	5.87047i	0.0878310	−	0.0139111i
$423$	−276.888	+	141.082i	−0.654582	+	0.333526i
$424$			89.4528i			0.210974i
$425$		0			0
$426$	−21.7833			−0.0511345
$427$	304.529	+	597.671i	0.713182	+	1.39970i
$428$	37.9036	+	239.314i	0.0885599	+	0.559145i
$429$	−16.4472	+	22.6377i	−0.0383386	+	0.0527685i
$430$		0			0
$431$	553.004	−	401.781i	1.28307	−	0.932206i	0.283430	−	0.958993i	$-0.408528\pi$
$431$	553.004	−	401.781i	1.28307	−	0.932206i	0.999641	+	0.0267868i	$0.00852751\pi$
$432$	9.55536	−	9.55536i	0.0221189	−	0.0221189i
$433$	−464.218	−	73.5249i	−1.07210	−	0.169803i	−0.404658	−	0.914468i	$-0.632609\pi$
$433$	−464.218	−	73.5249i	−1.07210	−	0.169803i	−0.667439	+	0.744665i	$0.732609\pi$
$434$	225.701	−	73.3348i	0.520049	−	0.168974i
$435$		0			0
$436$	117.646	−	362.078i	0.269831	−	0.830455i
$437$	98.4786	+	50.1773i	0.225351	+	0.114822i
$438$	6.31533	−	12.3945i	0.0144186	−	0.0282980i
$439$	342.493	+	111.283i	0.780166	+	0.253491i	0.671911	−	0.740632i	$-0.265474\pi$
$439$	342.493	+	111.283i	0.780166	+	0.253491i	0.108255	+	0.994123i	$0.465474\pi$
$440$		0			0
$441$	−162.980	−	501.600i	−0.369569	−	1.13742i
$442$	55.3718	−	349.604i	0.125276	−	0.790959i
$443$	−111.700	−	111.700i	−0.252144	−	0.252144i	0.569705	−	0.821849i	$-0.307057\pi$
$443$	−111.700	−	111.700i	−0.252144	−	0.252144i	−0.821849	+	0.569705i	$0.807057\pi$
$444$	0.245889	+	0.338437i	0.000553804	+	0.000762245i
$445$		0			0
$446$	215.586	+	156.632i	0.483376	+	0.351193i
$447$	35.0553	−	5.55221i	0.0784235	−	0.0124211i
$448$	74.0195	−	37.7148i	0.165222	−	0.0841849i
$449$			289.169i			0.644029i	0.946735	+	0.322014i	$0.104360\pi$
$449$			289.169i			0.644029i	−0.946735	+	0.322014i	$0.895640\pi$
$450$		0			0
$451$	−829.529			−1.83931
$452$	3.48695	+	6.84352i	0.00771448	+	0.0151405i
$453$	2.01642	+	12.7312i	0.00445127	+	0.0281042i
$454$	61.1490	−	84.1644i	0.134689	−	0.185384i
$455$		0			0
$456$	6.85729	−	4.98212i	0.0150379	−	0.0109257i
$457$	−383.361	+	383.361i	−0.838864	+	0.838864i	−0.988709	−	0.149845i	$-0.952122\pi$
$457$	−383.361	+	383.361i	−0.838864	+	0.838864i	0.149845	+	0.988709i	$0.452122\pi$
$458$	273.711	+	43.3516i	0.597623	+	0.0946542i
$459$	−95.7640	+	31.1156i	−0.208636	+	0.0677900i
$460$		0			0
$461$	133.417	−	410.614i	0.289407	−	0.890703i	−0.695636	−	0.718395i	$-0.744877\pi$
$461$	133.417	−	410.614i	0.289407	−	0.890703i	0.985043	−	0.172309i	$-0.0551227\pi$
$462$	43.6012	+	22.2159i	0.0943748	+	0.0480864i
$463$	44.5748	−	87.4829i	0.0962738	−	0.188948i	−0.837847	−	0.545905i	$-0.816186\pi$
$463$	44.5748	−	87.4829i	0.0962738	−	0.188948i	0.934121	+	0.356957i	$0.116186\pi$
$464$	−86.1851	−	28.0032i	−0.185744	−	0.0603518i
$465$		0			0
$466$	−118.798	−	365.622i	−0.254931	−	0.784597i
$467$	66.0461	−	416.998i	0.141426	−	0.892930i	−0.810307	−	0.586005i	$-0.800700\pi$
$467$	66.0461	−	416.998i	0.141426	−	0.892930i	0.951734	−	0.306925i	$-0.0993001\pi$
$468$	−106.462	−	106.462i	−0.227483	−	0.227483i
$469$	369.767	+	508.940i	0.788415	+	1.08516i
$470$		0			0
$471$	2.34852	+	1.70630i	0.00498624	+	0.00362271i
$472$	173.287	−	27.4460i	0.367134	−	0.0581482i
$473$	183.167	−	93.3282i	0.387245	−	0.197311i
$474$		−	0.620862i		−	0.00130983i
$475$		0			0
$476$	−619.012			−1.30045
$477$	−128.715	−	252.617i	−0.269842	−	0.529595i
$478$	−26.3252	−	166.211i	−0.0550737	−	0.347722i
$479$	331.632	−	456.452i	0.692343	−	0.952928i	−0.307656	−	0.951498i	$-0.599545\pi$
$479$	331.632	−	456.452i	0.692343	−	0.952928i	0.999999	−	0.00143028i	$-0.000455271\pi$
$480$		0			0
$481$	7.55634	−	5.49000i	0.0157097	−	0.0114137i
$482$	−336.618	+	336.618i	−0.698377	+	0.698377i
$483$	13.3774	+	2.11878i	0.0276966	+	0.00438671i
$484$	367.049	−	119.261i	0.758365	−	0.246408i
$485$		0			0
$486$	−19.8659	+	61.1409i	−0.0408763	+	0.125804i
$487$	−168.527	−	85.8690i	−0.346052	−	0.176322i	0.272322	−	0.962206i	$-0.412208\pi$
$487$	−168.527	−	85.8690i	−0.346052	−	0.176322i	−0.618374	+	0.785884i	$0.712208\pi$
$488$	82.9465	−	162.792i	0.169972	−	0.333590i
$489$	−8.53956	−	2.77467i	−0.0174633	−	0.00567417i
$490$		0			0
$491$	−182.614	−	562.028i	−0.371922	−	1.14466i	−0.945532	−	0.325530i	$-0.894457\pi$
$491$	−182.614	−	562.028i	−0.371922	−	1.14466i	0.573609	−	0.819129i	$-0.305543\pi$
$492$	−2.75445	+	17.3909i	−0.00559847	+	0.0353474i
$493$	477.469	+	477.469i	0.968496	+	0.968496i
$494$	−111.237	−	153.104i	−0.225175	−	0.309927i
$495$		0			0
$496$	−52.2944	−	37.9941i	−0.105432	−	0.0766010i
$497$	840.078	−	133.055i	1.69030	−	0.267717i
$498$	23.2346	−	11.8386i	0.0466559	−	0.0237724i
$499$			284.999i			0.571140i	0.958358	+	0.285570i	$0.0921829\pi$
$499$			284.999i			0.571140i	−0.958358	+	0.285570i	$0.907817\pi$
$500$		0			0
$501$	22.6713			0.0452522
$502$	−15.8233	−	31.0551i	−0.0315206	−	0.0618627i
$503$	34.1664	+	215.718i	0.0679252	+	0.428863i	0.998093	+	0.0617280i	$0.0196611\pi$
$503$	34.1664	+	215.718i	0.0679252	+	0.428863i	−0.930168	+	0.367135i	$0.880339\pi$
$504$	−154.765	+	213.015i	−0.307073	+	0.422649i
$505$		0			0
$506$	140.608	−	102.158i	0.277882	−	0.201893i
$507$	−13.0957	+	13.0957i	−0.0258298	+	0.0258298i
$508$	−318.647	−	50.4688i	−0.627259	−	0.0993480i
$509$	−324.255	+	105.357i	−0.637044	+	0.206988i	−0.609693	−	0.792638i	$-0.708707\pi$
$509$	−324.255	+	105.357i	−0.637044	+	0.206988i	−0.0273511	+	0.999626i	$0.508707\pi$
$510$		0			0
$511$	−167.845	+	516.573i	−0.328464	+	1.01091i
$512$	−20.1612	−	10.2726i	−0.0393773	−	0.0200637i
$513$	−24.4408	+	47.9678i	−0.0476429	+	0.0935044i
$514$	−39.7127	−	12.9034i	−0.0772620	−	0.0251039i
$515$		0			0
$516$	−1.34840	−	4.14995i	−0.00261318	−	0.00804253i
$517$	−96.0875	+	606.672i	−0.185856	+	1.17345i
$518$	−11.5500	−	11.5500i	−0.0222973	−	0.0222973i
$519$	−36.6602	−	50.4584i	−0.0706361	−	0.0972223i
$520$		0			0
$521$	528.326	+	383.851i	1.01406	+	0.736759i	0.965057	−	0.262040i	$-0.0843952\pi$
$521$	528.326	+	383.851i	1.01406	+	0.736759i	0.0490042	+	0.998799i	$0.484395\pi$
$522$	283.683	−	44.9310i	0.543454	−	0.0860747i
$523$	180.372	−	91.9041i	0.344880	−	0.175725i	−0.272967	−	0.962023i	$-0.588005\pi$
$523$	180.372	−	91.9041i	0.344880	−	0.175725i	0.617847	+	0.786298i	$0.288005\pi$
$524$		−	372.563i		−	0.710998i
$525$		0			0
$526$	432.386			0.822027
$527$	218.664	+	429.153i	0.414923	+	0.814332i
$528$	−2.08506	−	13.1646i	−0.00394899	−	0.0249329i
$529$	−282.663	+	389.052i	−0.534335	+	0.735449i
$530$		0			0
$531$	−449.875	+	326.853i	−0.847221	+	0.615542i
$532$	−234.022	+	234.022i	−0.439891	+	0.439891i
$533$	388.290	+	61.4991i	0.728499	+	0.115383i
$534$	−1.78110	+	0.578713i	−0.00333538	+	0.00108373i
$535$		0			0
$536$	52.9494	−	162.962i	0.0987862	−	0.304033i
$537$	−47.3732	−	24.1379i	−0.0882183	−	0.0449495i
$538$	30.8738	−	60.5933i	0.0573863	−	0.112627i
$539$	−991.445	−	322.140i	−1.83941	−	0.597662i
$540$		0			0
$541$	327.863	+	1009.06i	0.606031	+	1.86517i	0.489542	+	0.871980i	$0.337164\pi$
$541$	327.863	+	1009.06i	0.606031	+	1.86517i	0.116489	+	0.993192i	$0.462836\pi$
$542$	−72.6453	+	458.664i	−0.134032	+	0.846244i
$543$	3.64459	+	3.64459i	0.00671195	+	0.00671195i
$544$	99.1032	+	136.404i	0.182175	+	0.250742i
$545$		0			0
$546$	−18.7620	−	13.6314i	−0.0343626	−	0.0249659i
$547$	−620.075	+	98.2103i	−1.13359	+	0.179544i	−0.694909	−	0.719098i	$-0.744555\pi$
$547$	−620.075	+	98.2103i	−1.13359	+	0.179544i	−0.438684	+	0.898641i	$0.644555\pi$
$548$	26.5266	−	13.5160i	0.0484061	−	0.0246641i
$549$			579.081i			1.05479i
$550$		0			0
$551$	361.021			0.655210
$552$	−1.67483	−	3.28703i	−0.00303411	−	0.00595477i
$553$	3.79231	+	23.9437i	0.00685770	+	0.0432978i
$554$	2.88394	−	3.96941i	0.00520568	−	0.00716500i
$555$		0			0
$556$	−81.2975	+	59.0661i	−0.146218	+	0.106234i
$557$	410.470	−	410.470i	0.736930	−	0.736930i	−0.235053	−	0.971983i	$-0.575526\pi$
$557$	410.470	−	410.470i	0.736930	−	0.736930i	0.971983	+	0.235053i	$0.0755263\pi$
$558$	202.351	+	32.0492i	0.362636	+	0.0574359i
$559$	−92.6566	+	30.1060i	−0.165754	+	0.0538568i
$560$		0			0
$561$	−30.6904	+	94.4555i	−0.0547067	+	0.168370i
$562$	−518.673	−	264.277i	−0.922905	−	0.470244i
$563$	−296.043	+	581.018i	−0.525832	+	1.03200i	0.463469	+	0.886113i	$0.346605\pi$
$563$	−296.043	+	581.018i	−0.525832	+	1.03200i	−0.989301	+	0.145890i	$0.953395\pi$
$564$	12.3997	+	4.02890i	0.0219853	+	0.00714345i
$565$		0			0
$566$	−43.5922	−	134.163i	−0.0770181	−	0.237037i
$567$	130.032	−	820.988i	0.229333	−	1.44795i
$568$	−163.815	−	163.815i	−0.288407	−	0.288407i
$569$	−422.211	−	581.123i	−0.742022	−	1.02131i	−0.998500	−	0.0547557i	$-0.982562\pi$
$569$	−422.211	−	581.123i	−0.742022	−	1.02131i	0.256478	−	0.966550i	$-0.417438\pi$
$570$		0			0
$571$	−882.819	−	641.406i	−1.54609	−	1.12330i	−0.946365	−	0.323099i	$-0.895275\pi$
$571$	−882.819	−	641.406i	−1.54609	−	1.12330i	−0.599728	−	0.800204i	$-0.704725\pi$
$572$	−293.928	+	46.5536i	−0.513860	+	0.0813874i
$573$	26.9549	−	13.7342i	0.0470417	−	0.0239689i
$574$		−	687.509i		−	1.19775i
$575$		0			0
$576$	71.7171			0.124509
$577$	−194.120	−	380.981i	−0.336429	−	0.660279i	0.659373	−	0.751816i	$-0.270822\pi$
$577$	−194.120	−	380.981i	−0.336429	−	0.660279i	−0.995802	+	0.0915372i	$0.970822\pi$
$578$	−132.597	−	837.184i	−0.229406	−	1.44841i
$579$	−29.8481	+	41.0823i	−0.0515511	+	0.0709539i
$580$		0			0
$581$	−823.738	+	598.481i	−1.41779	+	1.03009i
$582$	1.26296	−	1.26296i	0.00217003	−	0.00217003i
$583$	−553.493	−	87.6647i	−0.949388	−	0.150368i
$584$	140.703	−	45.7170i	0.240929	−	0.0782826i
$585$		0			0
$586$	21.2988	−	65.5510i	0.0363461	−	0.111862i
$587$	−374.759	−	190.949i	−0.638430	−	0.325296i	0.104640	−	0.994510i	$-0.466631\pi$
$587$	−374.759	−	190.949i	−0.638430	−	0.325296i	−0.743070	+	0.669214i	$0.766631\pi$
$588$	−10.0457	+	19.7157i	−0.0170845	+	0.0335302i
$589$	244.912	+	79.5767i	0.415810	+	0.135105i
$590$		0			0
$591$	−9.14358	−	28.1411i	−0.0154714	−	0.0476160i
$592$	−0.695983	+	4.39427i	−0.00117565	+	0.00742275i
$593$	−80.9820	−	80.9820i	−0.136563	−	0.136563i	0.635521	−	0.772084i	$-0.280785\pi$
$593$	−80.9820	−	80.9820i	−0.136563	−	0.136563i	−0.772084	+	0.635521i	$0.780785\pi$
$594$	49.7599	+	68.4886i	0.0837708	+	0.115301i
$595$		0			0
$596$	305.378	+	221.870i	0.512379	+	0.372265i
$597$	−39.6524	+	6.28033i	−0.0664195	+	0.0105198i
$598$	−73.3902	+	37.3942i	−0.122726	+	0.0625321i
$599$		−	412.824i		−	0.689188i	−0.938752	−	0.344594i	$-0.888017\pi$
$599$		−	412.824i		−	0.689188i	0.938752	−	0.344594i	$-0.111983\pi$
$600$		0			0
$601$	−213.346			−0.354986			−0.177493	−	0.984122i	$-0.556799\pi$
$601$	−213.346			−0.354986			−0.177493	+	0.984122i	$0.556799\pi$
$602$	77.3499	+	151.808i	0.128488	+	0.252172i
$603$	84.9570	+	536.397i	0.140890	+	0.889547i
$604$	−80.5776	+	110.906i	−0.133407	+	0.183618i
$605$		0			0
$606$	8.63569	−	6.27419i	0.0142503	−	0.0103535i
$607$	769.147	−	769.147i	1.26713	−	1.26713i	0.319564	−	0.947565i	$-0.396464\pi$
$607$	769.147	−	769.147i	1.26713	−	1.26713i	0.947565	−	0.319564i	$-0.103536\pi$
$608$	89.0351	+	14.1018i	0.146439	+	0.0231937i
$609$	42.0757	−	13.6712i	0.0690898	−	0.0224486i
$610$		0			0
$611$	89.9541	−	276.850i	0.147224	−	0.453110i
$612$	−476.143	−	242.607i	−0.778011	−	0.396417i
$613$	257.477	−	505.327i	0.420028	−	0.824351i	−0.579926	−	0.814670i	$-0.696918\pi$
$613$	257.477	−	505.327i	0.420028	−	0.824351i	0.999953	−	0.00968113i	$-0.00308165\pi$
$614$	−514.946	−	167.316i	−0.838675	−	0.272502i
$615$		0			0
$616$	160.822	+	494.960i	0.261075	+	0.803506i
$617$	−92.4339	+	583.605i	−0.149812	+	0.945875i	0.792192	+	0.610272i	$0.208940\pi$
$617$	−92.4339	+	583.605i	−0.149812	+	0.945875i	−0.942004	+	0.335602i	$0.891060\pi$
$618$	13.7319	+	13.7319i	0.0222199	+	0.0222199i
$619$	−403.441	−	555.290i	−0.651763	−	0.897075i	0.347411	−	0.937713i	$-0.387061\pi$
$619$	−403.441	−	555.290i	−0.651763	−	0.897075i	−0.999174	+	0.0406379i	$0.987061\pi$
$620$		0			0
$621$	18.9563	+	13.7726i	0.0305255	+	0.0221781i
$622$	−594.315	+	94.1302i	−0.955490	+	0.151335i
$623$	65.1536	−	33.1974i	0.104580	−	0.0532864i
$624$			6.31671i			0.0101229i
$625$		0			0
$626$	685.932			1.09574
$627$	24.1068	+	47.3123i	0.0384479	+	0.0754583i
$628$	4.82964	+	30.4932i	0.00769051	+	0.0485560i
$629$	19.4858	−	26.8200i	0.0309791	−	0.0426390i
$630$		0			0
$631$	130.769	−	95.0090i	0.207240	−	0.150569i	−0.479324	−	0.877638i	$-0.659118\pi$
$631$	130.769	−	95.0090i	0.207240	−	0.150569i	0.686564	+	0.727069i	$0.259118\pi$
$632$	4.66902	−	4.66902i	0.00738770	−	0.00738770i
$633$	4.92866	+	0.780623i	0.00778619	+	0.00123321i
$634$	−252.740	+	82.1203i	−0.398644	+	0.129527i
$635$		0			0
$636$	−3.67574	+	11.3128i	−0.00577947	+	0.0177874i
$637$	440.197	+	224.292i	0.691047	+	0.352106i
$638$	257.734	−	505.831i	0.403971	−	0.792838i
$639$	698.335	+	226.903i	1.09286	+	0.355090i
$640$		0			0
$641$	244.269	+	751.783i	0.381075	+	1.17283i	0.939288	+	0.343131i	$0.111487\pi$
$641$	244.269	+	751.783i	0.381075	+	1.17283i	−0.558212	+	0.829698i	$0.688513\pi$
$642$	−5.04022	+	31.8227i	−0.00785081	+	0.0495681i
$643$	−365.724	−	365.724i	−0.568778	−	0.568778i	0.363008	−	0.931786i	$-0.381750\pi$
$643$	−365.724	−	365.724i	−0.568778	−	0.568778i	−0.931786	+	0.363008i	$0.881750\pi$
$644$	84.6678	+	116.535i	0.131472	+	0.180955i
$645$		0			0
$646$	−543.417	−	394.815i	−0.841202	−	0.611169i
$647$	−1267.86	+	200.810i	−1.95960	+	0.310371i	−0.960071	+	0.279755i	$0.909747\pi$
$647$	−1267.86	+	200.810i	−1.95960	+	0.310371i	−0.999531	+	0.0306158i	$0.990253\pi$
$648$	−201.729	+	102.786i	−0.311310	+	0.158620i
$649$			1099.12i			1.69356i
$650$		0			0
$651$	31.5570			0.0484747
$652$	−43.3533	−	85.0856i	−0.0664928	−	0.130499i
$653$	−105.831	−	668.189i	−0.162069	−	1.02326i	−0.925879	−	0.377820i	$-0.876674\pi$
$653$	−105.831	−	668.189i	−0.162069	−	1.02326i	0.763811	−	0.645440i	$-0.223326\pi$
$654$	29.7566	−	40.9565i	0.0454994	−	0.0626246i
$655$		0			0
$656$	−151.498	+	110.070i	−0.230942	+	0.167789i
$657$	−331.565	+	331.565i	−0.504665	+	0.504665i
$658$	−502.807	−	79.6368i	−0.764144	−	0.121029i
$659$	−202.168	+	65.6882i	−0.306779	+	0.0996786i	−0.458361	−	0.888766i	$-0.651563\pi$
$659$	−202.168	+	65.6882i	−0.306779	+	0.0996786i	0.151582	+	0.988445i	$0.451563\pi$
$660$		0			0
$661$	−178.262	+	548.635i	−0.269686	+	0.830007i	0.720891	+	0.693048i	$0.243733\pi$
$661$	−178.262	+	548.635i	−0.269686	+	0.830007i	−0.990577	+	0.136959i	$0.956267\pi$
$662$	681.571	+	347.278i	1.02956	+	0.524589i
$663$	21.3684	−	41.9378i	0.0322299	−	0.0632546i
$664$	263.759	+	85.7005i	0.397228	+	0.129067i
$665$		0			0
$666$	−4.35749	−	13.4110i	−0.00654278	−	0.0201366i
$667$	24.5806	−	155.196i	0.0368525	−	0.232678i
$668$	170.494	+	170.494i	0.255230	+	0.255230i
$669$	20.8281	+	28.6674i	0.0311332	+	0.0428511i
$670$		0			0
$671$	925.992	+	672.773i	1.38002	+	1.00264i
$672$	10.9107	−	1.72809i	0.0162362	−	0.00257156i
$673$	306.458	−	156.148i	0.455361	−	0.232018i	−0.211238	−	0.977435i	$-0.567749\pi$
$673$	306.458	−	156.148i	0.455361	−	0.232018i	0.666599	+	0.745417i	$0.267749\pi$
$674$		−	899.732i		−	1.33491i
$675$		0			0
$676$	−196.966			−0.291369
$677$	−335.599	−	658.650i	−0.495715	−	0.972895i	−0.994357	−	0.106087i	$-0.966168\pi$
$677$	−335.599	−	658.650i	−0.495715	−	0.972895i	0.498642	−	0.866808i	$-0.333832\pi$
$678$	0.159772	+	1.00876i	0.000235651	+	0.00148784i
$679$	−40.9920	+	56.4206i	−0.0603711	+	0.0830936i
$680$		0			0
$681$	11.1917	−	8.13126i	0.0164342	−	0.0119402i
$682$	286.339	−	286.339i	0.419852	−	0.419852i
$683$	496.669	+	78.6646i	0.727187	+	0.115175i	0.509043	−	0.860741i	$-0.330000\pi$
$683$	496.669	+	78.6646i	0.727187	+	0.115175i	0.218144	+	0.975916i	$0.430000\pi$
$684$	−271.729	+	88.2900i	−0.397264	+	0.129079i
$685$		0			0
$686$	44.6216	−	137.331i	0.0650461	−	0.200191i
$687$	32.8339	+	16.7297i	0.0477931	+	0.0243518i
$688$	21.0683	−	41.3489i	0.0306225	−	0.0601001i
$689$	252.582	+	82.0690i	0.366593	+	0.119113i
$690$		0			0
$691$	−148.890	−	458.235i	−0.215470	−	0.663148i	−0.999120	−	0.0419455i	$-0.986644\pi$
$691$	−148.890	−	458.235i	−0.215470	−	0.663148i	0.783650	−	0.621203i	$-0.213356\pi$
$692$	103.766	−	655.152i	0.149951	−	0.946751i
$693$	−1166.37	−	1166.37i	−1.68307	−	1.68307i
$694$	147.526	+	203.052i	0.212573	+	0.292581i
$695$		0			0
$696$	−9.74882	−	7.08294i	−0.0140069	−	0.0101766i
$697$	1378.17	−	218.280i	1.97729	−	0.313171i
$698$	55.1552	−	28.1030i	0.0790189	−	0.0402622i
$699$		−	51.1205i		−	0.0731337i
$700$		0			0
$701$	462.142			0.659260			0.329630	−	0.944110i	$-0.393076\pi$
$701$	462.142			0.659260			0.329630	+	0.944110i	$0.393076\pi$
$702$	−18.2143	−	35.7475i	−0.0259462	−	0.0509223i
$703$	−2.77272	−	17.5062i	−0.00394412	−	0.0249022i
$704$	83.3205	−	114.681i	0.118353	−	0.162899i
$705$		0			0
$706$	224.223	−	162.908i	0.317597	−	0.230748i
$707$	−294.714	+	294.714i	−0.416851	+	0.416851i
$708$	23.0428	+	3.64962i	0.0325463	+	0.00515483i
$709$	−1195.01	+	388.281i	−1.68548	+	0.547647i	−0.985963	−	0.166966i	$-0.946603\pi$
$709$	−1195.01	+	388.281i	−1.68548	+	0.547647i	−0.699521	+	0.714613i	$0.746603\pi$
$710$		0			0
$711$	−6.46712	+	19.9038i	−0.00909581	+	0.0279940i
$712$	−17.7463	−	9.04220i	−0.0249246	−	0.0126997i
$713$	50.8837	−	99.8649i	0.0713656	−	0.140063i
$714$	−78.2842	−	25.4361i	−0.109642	−	0.0356248i
$715$		0			0
$716$	−174.735	−	537.780i	−0.244044	−	0.751089i
$717$	3.50059	−	22.1018i	0.00488227	−	0.0308254i
$718$	567.028	+	567.028i	0.789732	+	0.789732i
$719$	332.930	+	458.239i	0.463046	+	0.637328i	0.975137	−	0.221603i	$-0.0711289\pi$
$719$	332.930	+	458.239i	0.463046	+	0.637328i	−0.512091	+	0.858931i	$0.671129\pi$
$720$		0			0
$721$	−613.450	−	445.697i	−0.850832	−	0.618166i
$722$	149.540	−	23.6848i	0.207119	−	0.0328045i
$723$	−56.4029	+	28.7387i	−0.0780123	+	0.0397493i
$724$			54.8163i			0.0757131i
$725$		0			0
$726$	51.3199			0.0706886
$727$	−388.260	−	762.004i	−0.534058	−	1.04815i	−0.987611	−	0.156919i	$-0.949844\pi$
$727$	−388.260	−	762.004i	−0.534058	−	1.04815i	0.453553	−	0.891229i	$-0.350156\pi$
$728$	−38.5834	−	243.606i	−0.0529991	−	0.334623i
$729$	418.426	−	575.914i	0.573973	−	0.790006i
$730$		0			0
$731$	−279.753	+	203.252i	−0.382698	+	0.278047i
$732$	17.1793	−	17.1793i	0.0234690	−	0.0234690i
$733$	−236.849	−	37.5132i	−0.323123	−	0.0511777i	−0.00723420	−	0.999974i	$-0.502303\pi$
$733$	−236.849	−	37.5132i	−0.323123	−	0.0511777i	−0.315889	+	0.948796i	$0.602303\pi$
$734$	156.652	−	50.8992i	0.213422	−	0.0693449i
$735$		0			0
$736$	12.1242	−	37.3143i	0.0164731	−	0.0506988i
$737$	956.441	+	487.331i	1.29775	+	0.661236i
$738$	269.453	−	528.831i	0.365112	−	0.716573i
$739$	−510.511	−	165.875i	−0.690814	−	0.224459i	−0.0574900	−	0.998346i	$-0.518310\pi$
$739$	−510.511	−	165.875i	−0.690814	−	0.224459i	−0.633324	+	0.773887i	$0.718310\pi$
$740$		0			0
$741$	−7.77643	−	23.9334i	−0.0104945	−	0.0322988i
$742$	72.6561	−	458.732i	0.0979192	−	0.618238i
$743$	747.446	+	747.446i	1.00598	+	1.00598i	0.999982	+	0.00600177i	$0.00191043\pi$
$743$	747.446	+	747.446i	1.00598	+	1.00598i	0.00600177	+	0.999982i	$0.498090\pi$
$744$	−5.05225	−	6.95382i	−0.00679066	−	0.00934654i
$745$		0			0
$746$	434.482	+	315.670i	0.582416	+	0.423150i
$747$	−868.178	+	137.506i	−1.16222	+	0.184077i
$748$	−941.127	+	479.528i	−1.25819	+	0.641080i
$749$		−	1258.04i		−	1.67962i
$750$		0			0
$751$	−436.245			−0.580885			−0.290443	−	0.956892i	$-0.593803\pi$
$751$	−436.245			−0.580885			−0.290443	+	0.956892i	$0.593803\pi$
$752$	62.9503	+	123.547i	0.0837105	+	0.164291i
$753$	−0.725024	−	4.57762i	−0.000962848	−	0.00607918i
$754$	−158.142	+	217.664i	−0.209737	+	0.288679i
$755$		0			0
$756$	−56.7629	+	41.2407i	−0.0750833	+	0.0545512i
$757$	−160.414	+	160.414i	−0.211907	+	0.211907i	−0.805077	−	0.593170i	$-0.797876\pi$
$757$	−160.414	+	160.414i	−0.211907	+	0.211907i	0.593170	+	0.805077i	$0.297876\pi$
$758$	−389.792	−	61.7369i	−0.514237	−	0.0814471i
$759$	21.9800	−	7.14174i	0.0289592	−	0.00940940i
$760$		0			0
$761$	296.697	−	913.138i	0.389877	−	1.19992i	−0.543002	−	0.839731i	$-0.682713\pi$
$761$	296.697	−	913.138i	0.389877	−	1.19992i	0.932880	−	0.360188i	$-0.117287\pi$
$762$	−38.2243	−	19.4763i	−0.0501632	−	0.0255594i
$763$	−897.404	+	1761.26i	−1.17615	+	2.30833i
$764$	305.991	+	99.4226i	0.400512	+	0.130134i
$765$		0			0
$766$	262.274	+	807.196i	0.342394	+	1.05378i
$767$	81.4857	−	514.480i	0.106239	−	0.670769i
$768$	−2.12759	−	2.12759i	−0.00277030	−	0.00277030i
$769$	710.831	+	978.375i	0.924358	+	1.27227i	0.962020	+	0.272979i	$0.0880089\pi$
$769$	710.831	+	978.375i	0.924358	+	1.27227i	−0.0376621	+	0.999291i	$0.511991\pi$
$770$		0			0
$771$	−4.49210	−	3.26370i	−0.00582632	−	0.00423307i
$772$	−533.413	+	84.4843i	−0.690950	+	0.109436i
$773$	−12.6208	+	6.43059i	−0.0163270	+	0.00831901i	−0.462135	−	0.886810i	$-0.652916\pi$
$773$	−12.6208	+	6.43059i	−0.0163270	+	0.00831901i	0.445808	+	0.895129i	$0.352916\pi$
$774$			147.086i			0.190033i
$775$		0			0
$776$	18.9955			0.0244787
$777$	−0.986080	−	1.93529i	−0.00126909	−	0.00249072i
$778$	62.4942	+	394.573i	0.0803268	+	0.507163i
$779$	438.504	−	603.549i	0.562906	−	0.774774i
$780$		0			0
$781$	1174.16	−	853.074i	1.50340	−	1.09228i
$782$	−206.723	+	206.723i	−0.264351	+	0.264351i
$783$	75.5941	+	11.9729i	0.0965442	+	0.0152911i
$784$	−223.813	+	72.7212i	−0.285476	+	0.0927566i
$785$		0			0
$786$	15.3091	−	47.1167i	0.0194773	−	0.0599449i
$787$	1213.75	+	618.435i	1.54224	+	0.785813i	0.998569	−	0.0534821i	$-0.0170320\pi$
$787$	1213.75	+	618.435i	1.54224	+	0.785813i	0.543676	+	0.839295i	$0.317032\pi$
$788$	142.865	−	280.389i	0.181301	−	0.355824i
$789$	54.6823	+	17.7674i	0.0693058	+	0.0225188i
$790$		0			0
$791$	−12.3233	−	37.9271i	−0.0155794	−	0.0479483i
$792$	−70.2835	+	443.753i	−0.0887418	+	0.560294i
$793$	−383.565	−	383.565i	−0.483689	−	0.483689i
$794$	494.221	+	680.237i	0.622445	+	0.856722i
$795$		0			0
$796$	−345.425	−	250.966i	−0.433951	−	0.315284i
$797$	−264.394	+	41.8758i	−0.331736	+	0.0525418i	−0.320081	−	0.947390i	$-0.603710\pi$
$797$	−264.394	+	41.8758i	−0.331736	+	0.0525418i	−0.0116553	+	0.999932i	$0.503710\pi$
$798$	−39.2122	+	19.9796i	−0.0491381	+	0.0250371i
$799$		−	1033.20i		−	1.29312i
$800$		0			0
$801$	63.1270			0.0788102
$802$	217.473	+	426.814i	0.271163	+	0.532187i
$803$	144.986	+	915.406i	0.180556	+	1.13998i
$804$	13.3926	−	18.4334i	0.0166575	−	0.0229271i
$805$		0			0
$806$	−155.259	+	112.802i	−0.192629	+	0.139953i
$807$	6.39436	−	6.39436i	0.00792362	−	0.00792362i
$808$	112.126	+	17.7590i	0.138770	+	0.0219789i
$809$	−459.152	+	149.188i	−0.567555	+	0.184410i	−0.578718	−	0.815528i	$-0.696447\pi$
$809$	−459.152	+	149.188i	−0.567555	+	0.184410i	0.0111627	+	0.999938i	$0.496447\pi$
$810$		0			0
$811$	−108.992	+	335.444i	−0.134393	+	0.413618i	−0.995495	−	0.0948136i	$-0.969774\pi$
$811$	−108.992	+	335.444i	−0.134393	+	0.413618i	0.861102	+	0.508431i	$0.169774\pi$
$812$	419.230	+	213.608i	0.516293	+	0.263064i
$813$	−28.0343	+	55.0205i	−0.0344826	+	0.0676759i
$814$	−26.5076	−	8.61286i	−0.0325647	−	0.0105809i
$815$		0			0
$816$	6.92819	+	21.3228i	0.00849043	+	0.0261309i
$817$	−28.9215	+	182.603i	−0.0353997	+	0.223505i
$818$	810.791	+	810.791i	0.991187	+	0.991187i
$819$	459.488	+	632.431i	0.561035	+	0.772199i
$820$		0			0
$821$	−499.761	−	363.098i	−0.608723	−	0.442263i	0.240242	−	0.970713i	$-0.422773\pi$
$821$	−499.761	−	363.098i	−0.608723	−	0.442263i	−0.848964	+	0.528450i	$0.822773\pi$
$822$	3.91011	−	0.619300i	0.00475682	−	0.000753406i
$823$	1381.69	−	704.006i	1.67885	−	0.855415i	0.687194	−	0.726474i	$-0.258842\pi$
$823$	1381.69	−	704.006i	1.67885	−	0.855415i	0.991652	−	0.128941i	$-0.0411578\pi$
$824$			206.534i			0.250648i
$825$		0			0
$826$	−910.943			−1.10284
$827$	678.366	+	1331.37i	0.820273	+	1.60988i	0.792192	+	0.610272i	$0.208940\pi$
$827$	678.366	+	1331.37i	0.820273	+	1.60988i	0.0280811	+	0.999606i	$0.491060\pi$
$828$	19.4531	+	122.822i	0.0234941	+	0.148336i
$829$	292.387	−	402.436i	0.352699	−	0.485448i	−0.595398	−	0.803431i	$-0.703006\pi$
$829$	292.387	−	402.436i	0.352699	−	0.485448i	0.948096	+	0.317983i	$0.103006\pi$
$830$		0			0
$831$	0.527831	−	0.383491i	0.000635175	−	0.000461482i
$832$	−47.5032	+	47.5032i	−0.0570952	+	0.0570952i
$833$	1731.94	+	274.312i	2.07916	+	0.329306i
$834$	−12.7085	+	4.12924i	−0.0152380	+	0.00495113i
$835$		0			0
$836$	−174.511	+	537.089i	−0.208745	+	0.642451i
$837$	48.6430	+	24.7848i	0.0581159	+	0.0296115i
$838$	25.4997	−	50.0460i	0.0304292	−	0.0597207i
$839$	877.533	+	285.128i	1.04593	+	0.339842i	0.781069	−	0.624445i	$-0.214675\pi$
$839$	877.533	+	285.128i	1.04593	+	0.339842i	0.264858	+	0.964287i	$0.414675\pi$
$840$		0			0
$841$	101.279	+	311.706i	0.120427	+	0.370637i
$842$	−55.0314	+	347.455i	−0.0653580	+	0.412654i
$843$	−54.7351	−	54.7351i	−0.0649290	−	0.0649290i
$844$	31.1942	+	42.9351i	0.0369600	+	0.0508710i
$845$		0			0
$846$	−355.546	−	258.320i	−0.420268	−	0.305342i
$847$	−1979.17	+	313.469i	−2.33668	+	0.370094i
$848$	−112.717	+	57.4323i	−0.132921	+	0.0677267i
$849$		−	18.7584i		−	0.0220947i
$850$		0			0
$851$	−7.71438			−0.00906508
$852$	−13.9857	−	27.4485i	−0.0164152	−	0.0322166i
$853$	32.2497	+	203.617i	0.0378074	+	0.238707i	0.999354	−	0.0359348i	$-0.0114409\pi$
$853$	32.2497	+	203.617i	0.0378074	+	0.238707i	−0.961547	+	0.274641i	$0.911441\pi$
$854$	−557.590	+	767.457i	−0.652916	+	0.898662i
$855$		0			0
$856$	−277.218	+	201.411i	−0.323853	+	0.235293i
$857$	71.7689	−	71.7689i	0.0837444	−	0.0837444i	−0.663994	−	0.747738i	$-0.731140\pi$
$857$	71.7689	−	71.7689i	0.0837444	−	0.0837444i	0.747738	+	0.663994i	$0.231140\pi$
$858$	−39.0849	−	6.19045i	−0.0455535	−	0.00721497i
$859$	−1025.56	+	333.225i	−1.19390	+	0.387922i	−0.837513	−	0.546417i	$-0.815991\pi$
$859$	−1025.56	+	333.225i	−1.19390	+	0.387922i	−0.356387	+	0.934339i	$0.615991\pi$
$860$		0			0
$861$	28.2507	−	86.9468i	0.0328115	−	0.100984i
$862$	861.324	+	438.866i	0.999215	+	0.509126i
$863$	561.612	−	1102.23i	0.650767	−	1.27720i	−0.295971	−	0.955197i	$-0.595643\pi$
$863$	561.612	−	1102.23i	0.650767	−	1.27720i	0.946738	−	0.322005i	$-0.104357\pi$
$864$	18.1754	+	5.90554i	0.0210363	+	0.00683511i
$865$		0			0
$866$	−205.399	−	632.154i	−0.237182	−	0.729970i
$867$	17.6320	−	111.324i	0.0203368	−	0.128402i
$868$	237.316	+	237.316i	0.273406	+	0.273406i
$869$	24.3141	+	33.4655i	0.0279794	+	0.0385103i
$870$		0			0
$871$	−411.566	−	299.020i	−0.472521	−	0.343306i
$872$	531.779	−	84.2255i	0.609838	−	0.0965889i
$873$	−53.6436	+	27.3328i	−0.0614475	+	0.0313090i
$874$			156.306i			0.178840i
$875$		0			0
$876$	19.6727			0.0224574
$877$	−55.7280	−	109.372i	−0.0635439	−	0.124712i	0.857050	−	0.515233i	$-0.172295\pi$
$877$	−55.7280	−	109.372i	−0.0635439	−	0.124712i	−0.920594	+	0.390521i	$0.872295\pi$
$878$	79.6696	+	503.014i	0.0907399	+	0.572909i
$879$	5.38717	−	7.41480i	0.00612874	−	0.00843549i
$880$		0			0
$881$	−44.4342	+	32.2833i	−0.0504361	+	0.0366440i	−0.612718	−	0.790302i	$-0.709924\pi$
$881$	−44.4342	+	32.2833i	−0.0504361	+	0.0366440i	0.562282	+	0.826946i	$0.309924\pi$
$882$	527.414	−	527.414i	0.597975	−	0.597975i
$883$	−1157.48	−	183.327i	−1.31085	−	0.207619i	−0.538399	−	0.842690i	$-0.680971\pi$
$883$	−1157.48	−	183.327i	−1.31085	−	0.207619i	−0.772454	+	0.635071i	$0.780971\pi$
$884$	476.078	−	154.687i	0.538549	−	0.174985i
$885$		0			0
$886$	69.0343	−	212.466i	0.0779168	−	0.239803i
$887$	89.9531	+	45.8334i	0.101413	+	0.0516724i	0.503961	−	0.863726i	$-0.331875\pi$
$887$	89.9531	+	45.8334i	0.101413	+	0.0516724i	−0.402548	+	0.915399i	$0.631875\pi$
$888$	−0.268585	+	0.527128i	−0.000302461	+	0.000593612i
$889$	1593.10	+	517.628i	1.79201	+	0.582259i
$890$		0			0
$891$	−438.296	−	1348.94i	−0.491915	−	1.51396i
$892$	−58.9535	+	372.218i	−0.0660913	+	0.417284i
$893$	−390.609	−	390.609i	−0.437412	−	0.437412i
$894$	29.5031	+	40.6075i	0.0330012	+	0.0454223i
$895$		0			0
$896$	95.0469	+	69.0556i	0.106079	+	0.0770710i
$897$	−10.8180	+	1.71340i	−0.0120602	+	0.00191014i
$898$	−364.374	+	185.658i	−0.405762	+	0.206746i
$899$		−	366.103i		−	0.407234i
$900$		0			0
$901$	942.634			1.04621
$902$	−532.591	−	1045.27i	−0.590455	−	1.15883i
$903$	3.54416	+	22.3770i	0.00392488	+	0.0247807i
$904$	−6.38458	+	8.78762i	−0.00706259	+	0.00972082i
$905$		0			0
$906$	−14.7476	+	10.7148i	−0.0162777	+	0.0118265i
$907$	394.165	−	394.165i	0.434581	−	0.434581i	−0.455602	−	0.890183i	$-0.650576\pi$
$907$	394.165	−	394.165i	0.434581	−	0.434581i	0.890183	+	0.455602i	$0.150576\pi$
$908$	145.313	+	23.0154i	0.160037	+	0.0253473i
$909$	−342.200	+	111.187i	−0.376457	+	0.122318i
$910$		0			0
$911$	337.243	−	1037.93i	0.370190	−	1.13933i	−0.576477	−	0.817114i	$-0.695573\pi$
$911$	337.243	−	1037.93i	0.370190	−	1.13933i	0.946667	−	0.322214i	$-0.104427\pi$
$912$	10.6805	+	5.44198i	0.0117111	+	0.00596708i
$913$	−788.762	+	1548.03i	−0.863924	+	1.69555i
$914$	−729.196	−	236.930i	−0.797807	−	0.259223i
$915$		0			0
$916$	121.107	+	372.730i	0.132213	+	0.406910i
$917$	−302.606	+	1910.58i	−0.329995	+	2.08351i
$918$	−100.692	−	100.692i	−0.109687	−	0.109687i
$919$	−650.818	−	895.775i	−0.708181	−	0.974728i	−0.999834	−	0.0182035i	$-0.994205\pi$
$919$	−650.818	−	895.775i	−0.708181	−	0.974728i	0.291653	−	0.956524i	$-0.405795\pi$
$920$		0			0
$921$	−58.2481	−	42.3197i	−0.0632444	−	0.0459498i
$922$	603.063	−	95.5158i	0.654081	−	0.103596i
$923$	−612.848	+	312.262i	−0.663975	+	0.338312i
$924$			69.2042i			0.0748963i
$925$		0			0
$926$	138.854			0.149950
$927$	−297.184	−	583.257i	−0.320587	−	0.629187i
$928$	−20.0481	−	126.579i	−0.0216036	−	0.136400i
$929$	30.4145	−	41.8620i	0.0327390	−	0.0450613i	−0.792334	−	0.610088i	$-0.791134\pi$
$929$	30.4145	−	41.8620i	0.0327390	−	0.0450613i	0.825073	+	0.565027i	$0.191134\pi$
$930$		0			0
$931$	758.478	−	551.066i	0.814691	−	0.591908i
$932$	384.438	−	384.438i	0.412487	−	0.412487i
$933$	−79.0287	−	12.5169i	−0.0847039	−	0.0134158i
$934$	567.853	−	184.507i	0.607979	−	0.197545i
$935$		0			0
$936$	65.7972	−	202.503i	0.0702962	−	0.216349i
$937$	−853.370	−	434.814i	−0.910747	−	0.464049i	−0.0651528	−	0.997875i	$-0.520753\pi$
$937$	−853.370	−	434.814i	−0.910747	−	0.464049i	−0.845594	+	0.533827i	$0.820753\pi$
$938$	−403.897	+	792.693i	−0.430594	+	0.845088i
$939$	86.7473	+	28.1859i	0.0923827	+	0.0300170i
$940$		0			0
$941$	168.148	+	517.505i	0.178690	+	0.549953i	0.999783	−	0.0208427i	$-0.00663493\pi$
$941$	168.148	+	517.505i	0.178690	+	0.549953i	−0.821092	+	0.570795i	$0.806635\pi$
$942$	−0.642220	+	4.05482i	−0.000681762	+	0.00430448i
$943$	−229.598	−	229.598i	−0.243476	−	0.243476i
$944$	145.841	+	200.733i	0.154493	+	0.212641i
$945$		0			0
$946$	235.201	+	170.883i	0.248627	+	0.180638i
$947$	1455.19	−	230.479i	1.53663	−	0.243378i	0.670010	−	0.742352i	$-0.266290\pi$
$947$	1455.19	−	230.479i	1.53663	−	0.243378i	0.866617	+	0.498974i	$0.166290\pi$
$948$	0.782331	−	0.398618i	0.000825244	−	0.000420483i
$949$		−	439.236i		−	0.462841i
$950$		0			0
$951$	−35.3376			−0.0371583
$952$	−397.430	−	780.001i	−0.417469	−	0.819328i
$953$	56.0150	+	353.665i	0.0587776	+	0.371107i	0.999491	+	0.0319045i	$0.0101572\pi$
$953$	56.0150	+	353.665i	0.0587776	+	0.371107i	−0.940713	+	0.339203i	$0.889843\pi$
$954$	235.676	−	324.380i	0.247040	−	0.340021i
$955$		0			0
$956$	192.536	−	139.886i	0.201398	−	0.146324i
$957$	53.3799	−	53.3799i	0.0557784	−	0.0557784i
$958$	788.085	+	124.820i	0.822635	+	0.130293i
$959$	−147.012	+	47.7670i	−0.153297	+	0.0498091i
$960$		0			0
$961$	−216.268	+	665.606i	−0.225045	+	0.692618i
$962$	11.7693	+	5.99675i	0.0122342	+	0.00623363i
$963$	493.058	−	967.681i	0.512002	−	1.00486i
$964$	−640.285	−	208.041i	−0.664196	−	0.215810i
$965$		0			0
$966$	5.91903	+	18.2169i	0.00612736	+	0.0188581i
$967$	−82.3645	+	520.029i	−0.0851753	+	0.537775i	0.907795	+	0.419414i	$0.137764\pi$
$967$	−82.3645	+	520.029i	−0.0851753	+	0.537775i	−0.992971	+	0.118362i	$0.962236\pi$
$968$	385.938	+	385.938i	0.398696	+	0.398696i
$969$	−52.5004	−	72.2606i	−0.0541800	−	0.0745723i
$970$		0			0
$971$	712.193	+	517.438i	0.733463	+	0.532892i	0.890657	−	0.454675i	$-0.150245\pi$
$971$	712.193	+	517.438i	0.733463	+	0.532892i	−0.157194	+	0.987568i	$0.550245\pi$
$972$	−89.7968	+	14.2224i	−0.0923835	+	0.0146321i
$973$	464.885	−	236.871i	0.477785	−	0.243444i
$974$		−	267.488i		−	0.274629i
$975$		0			0
$976$	258.384			0.264738
$977$	−68.4541	−	134.349i	−0.0700656	−	0.137512i	0.853317	−	0.521393i	$-0.174587\pi$
$977$	−68.4541	−	134.349i	−0.0700656	−	0.137512i	−0.923383	+	0.383881i	$0.874587\pi$
$978$	−1.98644	−	12.5419i	−0.00203113	−	0.0128240i
$979$	73.3406	−	100.945i	0.0749138	−	0.103110i
$980$		0			0
$981$	−1380.56	+	1003.04i	−1.40730	+	1.02247i
$982$	590.951	−	590.951i	0.601783	−	0.601783i
$983$	−310.650	−	49.2021i	−0.316022	−	0.0500530i	−0.00359144	−	0.999994i	$-0.501143\pi$
$983$	−310.650	−	49.2021i	−0.316022	−	0.0500530i	−0.312431	+	0.949941i	$0.601143\pi$
$984$	−23.6823	+	7.69484i	−0.0240674	+	0.00781996i
$985$		0			0
$986$	−295.092	+	908.199i	−0.299282	+	0.921095i
$987$	−60.3158	−	30.7324i	−0.0611102	−	0.0311372i
$988$	121.504	−	238.465i	0.122980	−	0.241361i
$989$	76.5285	+	24.8656i	0.0773797	+	0.0251422i
$990$		0			0
$991$	−81.9066	−	252.083i	−0.0826505	−	0.254372i	0.901189	−	0.433427i	$-0.142696\pi$
$991$	−81.9066	−	252.083i	−0.0826505	−	0.254372i	−0.983839	+	0.179055i	$0.942696\pi$
$992$	14.3003	−	90.2885i	0.0144156	−	0.0910166i
$993$	71.9257	+	71.9257i	0.0724327	+	0.0724327i
$994$	707.023	+	973.134i	0.711291	+	0.979008i
$995$		0			0
$996$	29.8351	+	21.6765i	0.0299549	+	0.0217635i
$997$	−108.016	+	17.1081i	−0.108342	+	0.0171596i	−0.210370	−	0.977622i	$-0.567467\pi$
$997$	−108.016	+	17.1081i	−0.108342	+	0.0171596i	0.102028	+	0.994782i	$0.467467\pi$
$998$	−359.120	+	182.981i	−0.359839	+	0.183347i
$999$		−	3.75758i		−	0.00376134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.3.f.f.243.2		24
5.2	odd	4		50.3.f.b.47.2	yes	24
5.3	odd	4		250.3.f.e.7.2		24
5.4	even	2		250.3.f.d.243.2		24
20.7	even	4		400.3.bg.b.97.2		24
25.6	even	5		50.3.f.b.33.2	✓	24
25.8	odd	20		250.3.f.d.107.2		24
25.17	odd	20	inner	250.3.f.f.107.2		24
25.19	even	10		250.3.f.e.143.2		24
100.31	odd	10		400.3.bg.b.33.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.b.33.2	✓	24	25.6	even	5
50.3.f.b.47.2	yes	24	5.2	odd	4
250.3.f.d.107.2		24	25.8	odd	20
250.3.f.d.243.2		24	5.4	even	2
250.3.f.e.7.2		24	5.3	odd	4
250.3.f.e.143.2		24	25.19	even	10
250.3.f.f.107.2		24	25.17	odd	20	inner
250.3.f.f.243.2		24	1.1	even	1	trivial
400.3.bg.b.33.2		24	100.31	odd	10
400.3.bg.b.97.2		24	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	250.f (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.642040 + 1.26007i) q^{2} +(0.0294182 + 0.185739i) q^{3} +(-1.17557 + 1.61803i) q^{4} +(-0.215157 + 0.156321i) q^{6} +(7.34278 - 7.34278i) q^{7} +(-2.79360 - 0.442463i) q^{8} +(8.52588 - 2.77022i) q^{9} +O(q^{10})\)	\(q+(0.642040 + 1.26007i) q^{2} +(0.0294182 + 0.185739i) q^{3} +(-1.17557 + 1.61803i) q^{4} +(-0.215157 + 0.156321i) q^{6} +(7.34278 - 7.34278i) q^{7} +(-2.79360 - 0.442463i) q^{8} +(8.52588 - 2.77022i) q^{9} +(5.47552 - 16.8519i) q^{11} +(-0.335116 - 0.170750i) q^{12} +(-3.81236 + 7.48219i) q^{13} +(13.9668 + 4.53808i) q^{14} +(-1.23607 - 3.80423i) q^{16} +(-4.66258 + 29.4384i) q^{17} +(8.96464 + 8.96464i) q^{18} +(9.36667 + 12.8921i) q^{19} +(1.57985 + 1.14783i) q^{21} +(24.7502 - 3.92004i) q^{22} +(6.17981 - 3.14877i) q^{23} -0.531898i q^{24} -11.8758 q^{26} +(1.53373 + 3.01011i) q^{27} +(3.24891 + 20.5128i) q^{28} +(13.3163 - 18.3284i) q^{29} +(13.0736 - 9.49852i) q^{31} +(4.00000 - 4.00000i) q^{32} +(3.29114 + 0.521266i) q^{33} +(-40.0881 + 13.0254i) q^{34} +(-5.54045 + 17.0518i) q^{36} +(-0.991031 - 0.504956i) q^{37} +(-10.2312 + 20.0799i) q^{38} +(-1.50189 - 0.487993i) q^{39} +(-14.4667 - 44.5241i) q^{41} +(-0.432022 + 2.72768i) q^{42} +(8.20366 + 8.20366i) q^{43} +(20.8301 + 28.6702i) q^{44} +(7.93537 + 5.76538i) q^{46} +(-34.2382 + 5.42280i) q^{47} +(0.670231 - 0.341500i) q^{48} -58.8327i q^{49} -5.60502 q^{51} +(-7.62473 - 14.9644i) q^{52} +(-4.94745 - 31.2370i) q^{53} +(-2.80825 + 3.86522i) q^{54} +(-23.7617 + 17.2639i) q^{56} +(-2.11902 + 2.11902i) q^{57} +(31.6447 + 5.01203i) q^{58} +(-58.9939 + 19.1683i) q^{59} +(-19.9613 + 61.4346i) q^{61} +(20.3626 + 10.3753i) q^{62} +(42.2624 - 82.9447i) q^{63} +(7.60845 + 2.47214i) q^{64} +(1.45621 + 4.48176i) q^{66} +(-9.47690 + 59.8348i) q^{67} +(-42.1511 - 42.1511i) q^{68} +(0.766649 + 1.05520i) q^{69} +(66.2647 + 48.1441i) q^{71} +(-25.0436 + 3.96652i) q^{72} +(-46.6049 + 23.7464i) q^{73} -1.57297i q^{74} -31.8711 q^{76} +(-83.5344 - 163.945i) q^{77} +(-0.349364 - 2.20580i) q^{78} +(-1.37219 + 1.88866i) q^{79} +(64.7589 - 47.0501i) q^{81} +(46.8154 - 46.8154i) q^{82} +(-96.8447 - 15.3387i) q^{83} +(-3.71446 + 1.20690i) q^{84} +(-5.07014 + 15.6043i) q^{86} +(3.79604 + 1.93418i) q^{87} +(-22.7528 + 44.6549i) q^{88} +(6.69713 + 2.17603i) q^{89} +(26.9467 + 82.9333i) q^{91} +(-2.16999 + 13.7008i) q^{92} +(2.14885 + 2.14885i) q^{93} +(-28.8154 - 39.6610i) q^{94} +(0.860630 + 0.625284i) q^{96} +(-6.63322 + 1.05060i) q^{97} +(74.1335 - 37.7729i) q^{98} -158.846i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} - 40 q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 - 2 * q^7 - 12 * q^8 - 40 * q^9	\( 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} - 40 q^{9} - 32 q^{11} - 16 q^{12} + 2 q^{13} - 30 q^{14} + 24 q^{16} - 22 q^{17} - 136 q^{18} + 230 q^{19} + 68 q^{21} - 8 q^{22} + 42 q^{23} + 36 q^{26} - 340 q^{27} + 4 q^{28} - 100 q^{29} - 132 q^{31} + 96 q^{32} - 266 q^{33} - 150 q^{34} - 108 q^{36} + 38 q^{37} + 20 q^{38} + 80 q^{39} + 168 q^{41} - 128 q^{42} - 78 q^{43} + 40 q^{44} + 26 q^{46} + 168 q^{47} + 32 q^{48} + 168 q^{51} + 4 q^{52} + 42 q^{53} + 80 q^{54} - 48 q^{56} + 280 q^{57} - 160 q^{58} - 450 q^{59} - 492 q^{61} + 142 q^{62} + 762 q^{63} + 202 q^{66} + 498 q^{67} - 136 q^{68} + 670 q^{69} - 2 q^{71} - 72 q^{72} + 62 q^{73} - 40 q^{76} - 624 q^{77} + 658 q^{78} + 360 q^{79} - 46 q^{81} + 272 q^{82} - 128 q^{83} - 620 q^{84} - 264 q^{86} + 400 q^{87} - 44 q^{88} - 900 q^{89} + 798 q^{91} - 36 q^{92} + 294 q^{93} + 190 q^{94} + 16 q^{96} - 312 q^{97} + 66 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 - 2 * q^7 - 12 * q^8 - 40 * q^9 - 32 * q^11 - 16 * q^12 + 2 * q^13 - 30 * q^14 + 24 * q^16 - 22 * q^17 - 136 * q^18 + 230 * q^19 + 68 * q^21 - 8 * q^22 + 42 * q^23 + 36 * q^26 - 340 * q^27 + 4 * q^28 - 100 * q^29 - 132 * q^31 + 96 * q^32 - 266 * q^33 - 150 * q^34 - 108 * q^36 + 38 * q^37 + 20 * q^38 + 80 * q^39 + 168 * q^41 - 128 * q^42 - 78 * q^43 + 40 * q^44 + 26 * q^46 + 168 * q^47 + 32 * q^48 + 168 * q^51 + 4 * q^52 + 42 * q^53 + 80 * q^54 - 48 * q^56 + 280 * q^57 - 160 * q^58 - 450 * q^59 - 492 * q^61 + 142 * q^62 + 762 * q^63 + 202 * q^66 + 498 * q^67 - 136 * q^68 + 670 * q^69 - 2 * q^71 - 72 * q^72 + 62 * q^73 - 40 * q^76 - 624 * q^77 + 658 * q^78 + 360 * q^79 - 46 * q^81 + 272 * q^82 - 128 * q^83 - 620 * q^84 - 264 * q^86 + 400 * q^87 - 44 * q^88 - 900 * q^89 + 798 * q^91 - 36 * q^92 + 294 * q^93 + 190 * q^94 + 16 * q^96 - 312 * q^97 + 66 * q^98

Introduction

L-functions

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