LMFDB - Embedded newform 201.3.k.a.14.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(14,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 8]))

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

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

chi := DirichletCharacter("201.14");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.k (of order $22$, degree $10$, 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:	$440$
Relative dimension:	$44$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			14.10
Character	$\chi$	$=$	201.14
Dual form			201.3.k.a.158.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.43065 + 1.11004i) q^{2} +(-2.55478 + 1.57260i) q^{3} +(2.05643 - 2.37324i) q^{4} +(-5.58064 + 0.802375i) q^{5} +(4.46414 - 6.65836i) q^{6} +(-1.45327 - 3.18223i) q^{7} +(0.647241 - 2.20430i) q^{8} +(4.05385 - 8.03532i) q^{9} +O(q^{10})$	\(q+(-2.43065 + 1.11004i) q^{2} +(-2.55478 + 1.57260i) q^{3} +(2.05643 - 2.37324i) q^{4} +(-5.58064 + 0.802375i) q^{5} +(4.46414 - 6.65836i) q^{6} +(-1.45327 - 3.18223i) q^{7} +(0.647241 - 2.20430i) q^{8} +(4.05385 - 8.03532i) q^{9} +(12.6739 - 8.14504i) q^{10} +(-8.16310 + 1.17368i) q^{11} +(-1.52156 + 9.29706i) q^{12} +(-3.67030 + 1.07770i) q^{13} +(7.06480 + 6.12168i) q^{14} +(12.9955 - 10.8260i) q^{15} +(2.66126 + 18.5095i) q^{16} +(-0.191379 + 0.165831i) q^{17} +(-0.933966 + 24.0310i) q^{18} +(-2.41799 + 5.29466i) q^{19} +(-9.57195 + 14.8942i) q^{20} +(8.71717 + 5.84448i) q^{21} +(18.5388 - 11.9142i) q^{22} +(12.0733 - 18.7865i) q^{23} +(1.81292 + 6.64937i) q^{24} +(6.51245 - 1.91223i) q^{25} +(7.72492 - 6.69368i) q^{26} +(2.27963 + 26.9036i) q^{27} +(-10.5407 - 3.09504i) q^{28} +46.4857i q^{29} +(-19.5703 + 40.7398i) q^{30} +(27.5546 + 8.09077i) q^{31} +(-22.0467 - 34.3053i) q^{32} +(19.0092 - 15.8358i) q^{33} +(0.281097 - 0.615516i) q^{34} +(10.6635 + 16.5928i) q^{35} +(-10.7333 - 26.1448i) q^{36} +21.2857 q^{37} -15.5535i q^{38} +(7.68203 - 8.52519i) q^{39} +(-1.84335 + 12.8207i) q^{40} +(16.3466 - 14.1644i) q^{41} +(-27.6760 - 4.52947i) q^{42} +(20.0276 + 23.1130i) q^{43} +(-14.0014 + 21.7866i) q^{44} +(-16.1758 + 48.0949i) q^{45} +(-8.49229 + 59.0652i) q^{46} +(23.9239 - 37.2263i) q^{47} +(-35.9070 - 43.1027i) q^{48} +(24.0736 - 27.7824i) q^{49} +(-13.7068 + 11.8770i) q^{50} +(0.228147 - 0.724626i) q^{51} +(-4.99006 + 10.9267i) q^{52} +(-66.2659 - 57.4198i) q^{53} +(-35.4051 - 62.8627i) q^{54} +(44.6136 - 13.0997i) q^{55} +(-7.95520 + 1.14379i) q^{56} +(-2.14894 - 17.3292i) q^{57} +(-51.6011 - 112.991i) q^{58} +(16.0048 - 54.5074i) q^{59} +(1.03157 - 53.1045i) q^{60} +(-3.43629 + 23.9000i) q^{61} +(-75.9567 + 10.9209i) q^{62} +(-31.4615 - 1.22276i) q^{63} +(28.7429 + 18.4720i) q^{64} +(19.6179 - 8.95919i) q^{65} +(-28.6264 + 59.5923i) q^{66} +(-45.1527 - 49.4999i) q^{67} +0.795209i q^{68} +(-1.30114 + 66.9819i) q^{69} +(-44.3380 - 28.4943i) q^{70} +(70.9353 + 61.4658i) q^{71} +(-15.0884 - 14.1367i) q^{72} +(8.93059 - 62.1136i) q^{73} +(-51.7380 + 23.6280i) q^{74} +(-13.6307 + 15.1268i) q^{75} +(7.59309 + 16.6265i) q^{76} +(15.5981 + 24.2711i) q^{77} +(-9.20901 + 29.2491i) q^{78} +(14.5315 - 4.26683i) q^{79} +(-29.7031 - 101.160i) q^{80} +(-48.1326 - 65.1479i) q^{81} +(-24.0098 + 52.5741i) q^{82} +(109.948 - 15.8082i) q^{83} +(31.7966 - 8.66922i) q^{84} +(0.934961 - 1.07900i) q^{85} +(-74.3364 - 33.9483i) q^{86} +(-73.1035 - 118.761i) q^{87} +(-2.69636 + 18.7536i) q^{88} +(81.1915 + 126.337i) q^{89} +(-14.0697 - 134.858i) q^{90} +(8.76342 + 10.1135i) q^{91} +(-19.7569 - 67.2859i) q^{92} +(-83.1197 + 22.6623i) q^{93} +(-16.8279 + 117.041i) q^{94} +(9.24563 - 31.4877i) q^{95} +(110.273 + 52.9721i) q^{96} +65.8520 q^{97} +(-27.6749 + 94.2521i) q^{98} +(-23.6611 + 70.3510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 11 q^{3} + 70 q^{4} - 17 q^{6} - 30 q^{7} - 15 q^{9}+O(q^{10}) $ 440 * q - 11 * q^3 + 70 * q^4 - 17 * q^6 - 30 * q^7 - 15 * q^9	$ 440 q - 11 q^{3} + 70 q^{4} - 17 q^{6} - 30 q^{7} - 15 q^{9} - 34 q^{10} - 123 q^{12} + 10 q^{13} + 19 q^{15} - 226 q^{16} - 33 q^{18} - 100 q^{19} + 85 q^{21} - 454 q^{22} - 251 q^{24} + 142 q^{25} - 53 q^{27} + 642 q^{28} - 80 q^{30} - 130 q^{31} + 104 q^{33} + 26 q^{34} + 67 q^{36} - 144 q^{37} + 117 q^{39} - 182 q^{40} + 193 q^{42} - 156 q^{43} + 341 q^{45} - 746 q^{46} - 485 q^{48} - 354 q^{49} - 125 q^{51} + 1130 q^{52} + 272 q^{54} - 590 q^{55} + 15 q^{57} - 274 q^{58} - 217 q^{60} - 1134 q^{61} + 279 q^{63} + 58 q^{64} + 1288 q^{66} - 87 q^{69} + 1038 q^{70} - 977 q^{72} + 1208 q^{73} - 751 q^{75} + 1126 q^{76} - 11 q^{78} + 678 q^{79} + 125 q^{81} + 510 q^{82} + 191 q^{84} + 166 q^{85} + 1080 q^{87} + 62 q^{88} - 105 q^{90} + 550 q^{91} + 635 q^{93} + 986 q^{94} - 1632 q^{96} - 112 q^{97} - 500 q^{99}+O(q^{100}) $ 440 * q - 11 * q^3 + 70 * q^4 - 17 * q^6 - 30 * q^7 - 15 * q^9 - 34 * q^10 - 123 * q^12 + 10 * q^13 + 19 * q^15 - 226 * q^16 - 33 * q^18 - 100 * q^19 + 85 * q^21 - 454 * q^22 - 251 * q^24 + 142 * q^25 - 53 * q^27 + 642 * q^28 - 80 * q^30 - 130 * q^31 + 104 * q^33 + 26 * q^34 + 67 * q^36 - 144 * q^37 + 117 * q^39 - 182 * q^40 + 193 * q^42 - 156 * q^43 + 341 * q^45 - 746 * q^46 - 485 * q^48 - 354 * q^49 - 125 * q^51 + 1130 * q^52 + 272 * q^54 - 590 * q^55 + 15 * q^57 - 274 * q^58 - 217 * q^60 - 1134 * q^61 + 279 * q^63 + 58 * q^64 + 1288 * q^66 - 87 * q^69 + 1038 * q^70 - 977 * q^72 + 1208 * q^73 - 751 * q^75 + 1126 * q^76 - 11 * q^78 + 678 * q^79 + 125 * q^81 + 510 * q^82 + 191 * q^84 + 166 * q^85 + 1080 * q^87 + 62 * q^88 - 105 * q^90 + 550 * q^91 + 635 * q^93 + 986 * q^94 - 1632 * q^96 - 112 * q^97 - 500 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$68$	$136$
$\chi(n)$	$-1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−2.43065	+	1.11004i	−1.21532	+	0.555020i	−0.916787	−	0.399377i	$-0.869226\pi$
$2$	−2.43065	+	1.11004i	−1.21532	+	0.555020i	−0.298538	+	0.954398i	$0.596499\pi$
$3$	−2.55478	+	1.57260i	−0.851595	+	0.524200i
$3$	−2.55478	+	1.57260i	−0.851595	+	0.524200i
$4$	2.05643	−	2.37324i	0.514107	−	0.593311i
$5$	−5.58064	+	0.802375i	−1.11613	+	0.160475i	−0.675604	−	0.737265i	$-0.736117\pi$
$5$	−5.58064	+	0.802375i	−1.11613	+	0.160475i	−0.440525	+	0.897740i	$0.645208\pi$
$6$	4.46414	−	6.65836i	0.744023	−	1.10973i
$7$	−1.45327	−	3.18223i	−0.207611	−	0.454604i	0.776970	−	0.629538i	$-0.216756\pi$
$7$	−1.45327	−	3.18223i	−0.207611	−	0.454604i	−0.984580	+	0.174935i	$0.944029\pi$
$8$	0.647241	−	2.20430i	0.0809051	−	0.275538i
$9$	4.05385	−	8.03532i	0.450428	−	0.892813i
$10$	12.6739	−	8.14504i	1.26739	−	0.814504i
$11$	−8.16310	+	1.17368i	−0.742100	+	0.106698i	−0.502987	−	0.864294i	$-0.667766\pi$
$11$	−8.16310	+	1.17368i	−0.742100	+	0.106698i	−0.239113	+	0.970992i	$0.576857\pi$
$12$	−1.52156	+	9.29706i	−0.126797	+	0.774755i
$13$	−3.67030	+	1.07770i	−0.282330	+	0.0828997i	−0.419832	−	0.907602i	$-0.637911\pi$
$13$	−3.67030	+	1.07770i	−0.282330	+	0.0828997i	0.137502	+	0.990502i	$0.456093\pi$
$14$	7.06480	+	6.12168i	0.504629	+	0.437263i
$15$	12.9955	−	10.8260i	0.866369	−	0.721735i
$16$	2.66126	+	18.5095i	0.166329	+	1.15684i
$17$	−0.191379	+	0.165831i	−0.0112576	+	0.00975477i	−0.660471	−	0.750851i	$-0.729644\pi$
$17$	−0.191379	+	0.165831i	−0.0112576	+	0.00975477i	0.649214	+	0.760606i	$0.275098\pi$
$18$	−0.933966	+	24.0310i	−0.0518870	+	1.33505i
$19$	−2.41799	+	5.29466i	−0.127263	+	0.278666i	−0.962529	−	0.271180i	$-0.912586\pi$
$19$	−2.41799	+	5.29466i	−0.127263	+	0.278666i	0.835266	+	0.549846i	$0.185314\pi$
$20$	−9.57195	+	14.8942i	−0.478598	+	0.744712i
$21$	8.71717	+	5.84448i	0.415103	+	0.278309i
$22$	18.5388	−	11.9142i	0.842673	−	0.541553i
$23$	12.0733	−	18.7865i	0.524927	−	0.816803i	−0.473006	−	0.881059i	$-0.656831\pi$
$23$	12.0733	−	18.7865i	0.524927	−	0.816803i	0.997933	+	0.0642564i	$0.0204676\pi$
$24$	1.81292	+	6.64937i	0.0755385	+	0.277057i
$25$	6.51245	−	1.91223i	0.260498	−	0.0764892i
$26$	7.72492	−	6.69368i	0.297112	−	0.257449i
$27$	2.27963	+	26.9036i	0.0844307	+	0.996429i
$28$	−10.5407	−	3.09504i	−0.376455	−	0.110537i
$29$			46.4857i			1.60296i	0.598024	+	0.801478i	$0.295953\pi$
$29$			46.4857i			1.60296i	−0.598024	+	0.801478i	$0.704047\pi$
$30$	−19.5703	+	40.7398i	−0.652342	+	1.35799i
$31$	27.5546	+	8.09077i	0.888859	+	0.260992i	0.694117	−	0.719862i	$-0.255795\pi$
$31$	27.5546	+	8.09077i	0.888859	+	0.260992i	0.194742	+	0.980855i	$0.437613\pi$
$32$	−22.0467	−	34.3053i	−0.688959	−	1.07204i
$33$	19.0092	−	15.8358i	0.576037	−	0.479872i
$34$	0.281097	−	0.615516i	0.00826756	−	0.0181034i
$35$	10.6635	+	16.5928i	0.304673	+	0.474080i
$36$	−10.7333	−	26.1448i	−0.298147	−	0.726245i
$37$	21.2857			0.575288			0.287644	−	0.957737i	$-0.407128\pi$
$37$	21.2857			0.575288			0.287644	+	0.957737i	$0.407128\pi$
$38$		−	15.5535i		−	0.409303i
$39$	7.68203	−	8.52519i	0.196975	−	0.218595i
$40$	−1.84335	+	12.8207i	−0.0460836	+	0.320519i
$41$	16.3466	−	14.1644i	0.398697	−	0.345473i	−0.432320	−	0.901720i	$-0.642305\pi$
$41$	16.3466	−	14.1644i	0.398697	−	0.345473i	0.831017	+	0.556247i	$0.187759\pi$
$42$	−27.6760	−	4.52947i	−0.658953	−	0.107845i
$43$	20.0276	+	23.1130i	0.465757	+	0.537512i	0.939227	−	0.343298i	$-0.111544\pi$
$43$	20.0276	+	23.1130i	0.465757	+	0.537512i	−0.473470	+	0.880810i	$0.656999\pi$
$44$	−14.0014	+	21.7866i	−0.318213	+	0.495150i
$45$	−16.1758	+	48.0949i	−0.359461	+	1.06878i
$46$	−8.49229	+	59.0652i	−0.184615	+	1.28403i
$47$	23.9239	−	37.2263i	0.509020	−	0.792050i	−0.487698	−	0.873013i	$-0.662163\pi$
$47$	23.9239	−	37.2263i	0.509020	−	0.792050i	0.996717	+	0.0809627i	$0.0257995\pi$
$48$	−35.9070	−	43.1027i	−0.748063	−	0.897972i
$49$	24.0736	−	27.7824i	0.491298	−	0.566989i
$50$	−13.7068	+	11.8770i	−0.274137	+	0.237541i
$51$	0.228147	−	0.724626i	0.00447347	−	0.0142084i
$52$	−4.99006	+	10.9267i	−0.0959626	+	0.210129i
$53$	−66.2659	−	57.4198i	−1.25030	−	1.08339i	−0.993129	−	0.117026i	$-0.962664\pi$
$53$	−66.2659	−	57.4198i	−1.25030	−	1.08339i	−0.257172	−	0.966366i	$-0.582791\pi$
$54$	−35.4051	−	62.8627i	−0.655649	−	1.16412i
$55$	44.6136	−	13.0997i	0.811156	−	0.238177i
$56$	−7.95520	+	1.14379i	−0.142057	+	0.0204247i
$57$	−2.14894	−	17.3292i	−0.0377007	−	0.304022i
$58$	−51.6011	−	112.991i	−0.889674	−	1.94811i
$59$	16.0048	−	54.5074i	0.271268	−	0.923855i	−0.705347	−	0.708862i	$-0.749209\pi$
$59$	16.0048	−	54.5074i	0.271268	−	0.923855i	0.976616	−	0.214993i	$-0.0689729\pi$
$60$	1.03157	−	53.1045i	0.0171928	−	0.885074i
$61$	−3.43629	+	23.9000i	−0.0563327	+	0.391803i	0.942075	+	0.335401i	$0.108872\pi$
$61$	−3.43629	+	23.9000i	−0.0563327	+	0.391803i	−0.998408	+	0.0564016i	$0.982037\pi$
$62$	−75.9567	+	10.9209i	−1.22511	+	0.176144i
$63$	−31.4615	−	1.22276i	−0.499390	−	0.0194088i
$64$	28.7429	+	18.4720i	0.449109	+	0.288625i
$65$	19.6179	−	8.95919i	0.301814	−	0.137834i
$66$	−28.6264	+	59.5923i	−0.433734	+	0.902913i
$67$	−45.1527	−	49.4999i	−0.673920	−	0.738804i
$67$	−45.1527	−	49.4999i	−0.673920	−	0.738804i
$68$			0.795209i			0.0116943i
$69$	−1.30114	+	66.9819i	−0.0188571	+	0.970752i
$70$	−44.3380	−	28.4943i	−0.633400	−	0.407062i
$71$	70.9353	+	61.4658i	0.999089	+	0.865716i	0.990947	−	0.134251i	$-0.0428629\pi$
$71$	70.9353	+	61.4658i	0.999089	+	0.865716i	0.00814184	+	0.999967i	$0.497408\pi$
$72$	−15.0884	−	14.1367i	−0.209562	−	0.196343i
$73$	8.93059	−	62.1136i	0.122337	−	0.850872i	−0.832560	−	0.553935i	$-0.813126\pi$
$73$	8.93059	−	62.1136i	0.122337	−	0.850872i	0.954897	−	0.296937i	$-0.0959652\pi$
$74$	−51.7380	+	23.6280i	−0.699162	+	0.319297i
$75$	−13.6307	+	15.1268i	−0.181743	+	0.201691i
$76$	7.59309	+	16.6265i	0.0999090	+	0.218770i
$77$	15.5981	+	24.2711i	0.202573	+	0.315210i
$78$	−9.20901	+	29.2491i	−0.118064	+	0.374989i
$79$	14.5315	−	4.26683i	0.183943	−	0.0540105i	−0.188464	−	0.982080i	$-0.560351\pi$
$79$	14.5315	−	4.26683i	0.183943	−	0.0540105i	0.372407	+	0.928070i	$0.378533\pi$
$80$	−29.7031	−	101.160i	−0.371289	−	1.26449i
$81$	−48.1326	−	65.1479i	−0.594229	−	0.804296i
$82$	−24.0098	+	52.5741i	−0.292802	+	0.641147i
$83$	109.948	−	15.8082i	1.32468	−	0.190460i	0.556580	−	0.830794i	$-0.312113\pi$
$83$	109.948	−	15.8082i	1.32468	−	0.190460i	0.768097	+	0.640334i	$0.221204\pi$
$84$	31.7966	−	8.66922i	0.378531	−	0.103205i
$85$	0.934961	−	1.07900i	0.0109995	−	0.0126942i
$86$	−74.3364	−	33.9483i	−0.864376	−	0.394747i
$87$	−73.1035	−	118.761i	−0.840271	−	1.36507i
$88$	−2.69636	+	18.7536i	−0.0306404	+	0.213109i
$89$	81.1915	+	126.337i	0.912265	+	1.41951i	0.907745	+	0.419522i	$0.137802\pi$
$89$	81.1915	+	126.337i	0.912265	+	1.41951i	0.00451922	+	0.999990i	$0.498561\pi$
$90$	−14.0697	−	134.858i	−0.156330	−	1.49842i
$91$	8.76342	+	10.1135i	0.0963013	+	0.111138i
$92$	−19.7569	−	67.2859i	−0.214749	−	0.731368i
$93$	−83.1197	+	22.6623i	−0.893760	+	0.243680i
$94$	−16.8279	+	117.041i	−0.179020	+	1.24511i
$95$	9.24563	−	31.4877i	0.0973224	−	0.331450i
$96$	110.273	+	52.9721i	1.14868	+	0.551793i
$97$	65.8520			0.678887			0.339443	−	0.940627i	$-0.389761\pi$
$97$	65.8520			0.678887			0.339443	+	0.940627i	$0.389761\pi$
$98$	−27.6749	+	94.2521i	−0.282397	+	0.961756i
$99$	−23.6611	+	70.3510i	−0.239001	+	0.710616i
$100$	8.85420	−	19.3880i	0.0885420	−	0.193880i
$101$	27.0400	+	12.3488i	0.267723	+	0.122265i	0.544754	−	0.838596i	$-0.316623\pi$
$101$	27.0400	+	12.3488i	0.267723	+	0.122265i	−0.277031	+	0.960861i	$0.589350\pi$
$102$	0.249820	+	2.01457i	0.00244921	+	0.0197506i
$103$	28.3172	+	8.31469i	0.274925	+	0.0807251i	0.416289	−	0.909233i	$-0.363331\pi$
$103$	28.3172	+	8.31469i	0.274925	+	0.0807251i	−0.141364	+	0.989958i	$0.545149\pi$
$104$			8.78796i			0.0844997i
$105$	−53.3369	−	25.6215i	−0.507971	−	0.244015i
$106$	224.808	+	66.0095i	2.12083	+	0.622731i
$107$	39.2350	+	5.64114i	0.366682	+	0.0527209i	0.323193	−	0.946333i	$-0.395244\pi$
$107$	39.2350	+	5.64114i	0.366682	+	0.0527209i	0.0434888	+	0.999054i	$0.486153\pi$
$108$	68.5366	+	49.9151i	0.634598	+	0.462177i
$109$	−13.6315	+	4.00256i	−0.125059	+	0.0367208i	−0.343663	−	0.939093i	$-0.611668\pi$
$109$	−13.6315	+	4.00256i	−0.125059	+	0.0367208i	0.218604	+	0.975814i	$0.429850\pi$
$110$	−93.8988	+	81.3638i	−0.853625	+	0.739671i
$111$	−54.3803	+	33.4739i	−0.489913	+	0.301566i
$112$	55.0338	−	35.3681i	0.491374	−	0.315787i
$113$	14.6750	+	2.10995i	0.129867	+	0.0186721i	0.206942	−	0.978353i	$-0.433649\pi$
$113$	14.6750	+	2.10995i	0.129867	+	0.0186721i	−0.0770747	+	0.997025i	$0.524558\pi$
$114$	24.4595	+	39.7359i	0.214557	+	0.348560i
$115$	−52.3031	+	114.528i	−0.454810	+	0.995895i
$116$	110.322	+	95.5945i	0.951051	+	0.824091i
$117$	−6.21920	+	33.8608i	−0.0531556	+	0.289409i
$118$	21.6033	+	150.255i	0.183079	+	1.27334i
$119$	0.805839	+	0.368014i	0.00677175	+	0.00309256i
$120$	−15.4526	−	35.6531i	−0.128771	−	0.297109i
$121$	−50.8400	+	14.9280i	−0.420166	+	0.123372i
$122$	−18.1775	−	61.9069i	−0.148996	−	0.507433i
$123$	−19.4871	+	61.8937i	−0.158431	+	0.503200i
$124$	75.8654	−	48.7557i	0.611818	−	0.393191i
$125$	93.4040	−	42.6562i	0.747232	−	0.341249i
$126$	77.8293	−	31.9515i	0.617693	−	0.253583i
$127$	−84.0596	−	184.065i	−0.661886	−	1.44933i	−0.880754	−	0.473574i	$-0.842963\pi$
$127$	−84.0596	−	184.065i	−0.661886	−	1.44933i	0.218867	−	0.975755i	$-0.429764\pi$
$128$	71.0864	+	10.2207i	0.555362	+	0.0798491i
$129$	−87.5137	−	27.5535i	−0.678400	−	0.213593i
$130$	−37.7392	+	43.5533i	−0.290301	+	0.335026i
$131$	100.654	−	156.621i	0.768355	−	1.19558i	−0.207728	−	0.978187i	$-0.566607\pi$
$131$	100.654	−	156.621i	0.768355	−	1.19558i	0.976083	−	0.217397i	$-0.0697566\pi$
$132$	1.50892	−	77.6786i	0.0114312	−	0.588474i
$133$	20.3628			0.153104
$134$	164.697	+	70.1956i	1.22908	+	0.523848i
$135$	−34.3086	−	148.310i	−0.254138	−	1.09859i
$136$	0.241673	+	0.529190i	0.00177701	+	0.00389111i
$137$	−121.807	+	189.535i	−0.889100	+	1.38347i	0.0342112	+	0.999415i	$0.489108\pi$
$137$	−121.807	+	189.535i	−0.889100	+	1.38347i	−0.923311	+	0.384052i	$0.874528\pi$
$138$	−71.1900	−	164.254i	−0.515870	−	1.19025i
$139$	2.37709	+	16.5330i	0.0171013	+	0.118943i	0.996584	−	0.0825865i	$-0.0263181\pi$
$139$	2.37709	+	16.5330i	0.0171013	+	0.118943i	−0.979483	+	0.201529i	$0.935409\pi$
$140$	61.3075	+	8.81469i	0.437911	+	0.0629621i
$141$	−2.57827	+	132.728i	−0.0182856	+	0.941334i
$142$	−240.649	−	70.6608i	−1.69471	−	0.497611i
$143$	28.6961	−	13.1051i	0.200672	−	0.0916439i
$144$	159.518	+	53.6506i	1.10776	+	0.372574i
$145$	−37.2990	−	259.420i	−0.257235	−	1.78911i
$146$	47.2415	+	160.890i	0.323572	+	1.10199i
$147$	−17.8122	+	108.836i	−0.121172	+	0.740383i
$148$	43.7724	−	50.5161i	0.295760	−	0.341325i
$149$	145.961	+	66.6580i	0.979601	+	0.447369i	0.839851	−	0.542818i	$-0.182643\pi$
$149$	145.961	+	66.6580i	0.979601	+	0.447369i	0.139751	+	0.990187i	$0.455370\pi$
$150$	16.3402	−	51.8987i	0.108935	−	0.345991i
$151$	−4.95959	−	5.72367i	−0.0328450	−	0.0379051i	0.739089	−	0.673607i	$-0.235256\pi$
$151$	−4.95959	−	5.72367i	−0.0328450	−	0.0379051i	−0.771934	+	0.635702i	$0.780711\pi$
$152$	10.1060	+	8.75689i	0.0664868	+	0.0576111i
$153$	0.556682	+	2.21005i	0.00363845	+	0.0144448i
$154$	−64.8555	−	41.6801i	−0.421140	−	0.270650i
$155$	−160.264	−	23.0425i	−1.03396	−	0.148662i
$156$	−4.43482	−	35.7627i	−0.0284283	−	0.229248i
$157$	−160.967	−	103.447i	−1.02527	−	0.658900i	−0.0839672	−	0.996469i	$-0.526759\pi$
$157$	−160.967	−	103.447i	−1.02527	−	0.658900i	−0.941301	+	0.337569i	$0.890395\pi$
$158$	−30.5846	+	26.5017i	−0.193573	+	0.167732i
$159$	259.594	+	42.4852i	1.63266	+	0.267203i
$160$	150.561	+	173.756i	0.941004	+	1.08598i
$161$	−77.3286	−	11.1182i	−0.480302	−	0.0690570i
$162$	189.310	+	104.923i	1.16858	+	0.647671i
$163$	245.026			1.50323			0.751614	−	0.659603i	$-0.229276\pi$
$163$	245.026			1.50323			0.751614	+	0.659603i	$0.229276\pi$
$164$		−	67.9224i		−	0.414161i
$165$	−93.3775	+	103.626i	−0.565924	+	0.628039i
$166$	−249.698	+	160.471i	−1.50420	+	0.966693i
$167$	22.1358	+	10.1091i	0.132549	+	0.0605333i	0.480586	−	0.876948i	$-0.340424\pi$
$167$	22.1358	+	10.1091i	0.132549	+	0.0605333i	−0.348036	+	0.937481i	$0.613151\pi$
$168$	18.5251	−	15.4325i	0.110269	−	0.0918600i
$169$	−129.862	+	83.4574i	−0.768415	+	0.493831i
$170$	−1.07483	+	3.66052i	−0.00632251	+	0.0215325i
$171$	32.7421	+	40.8930i	0.191474	+	0.239141i
$172$	96.0380			0.558360
$173$	−65.2195	+	222.117i	−0.376991	+	1.28391i	0.524608	+	0.851344i	$0.324212\pi$
$173$	−65.2195	+	222.117i	−0.376991	+	1.28391i	−0.901600	+	0.432571i	$0.857606\pi$
$174$	309.519	+	207.519i	1.77884	+	1.19264i
$175$	−15.5495	−	17.9451i	−0.0888544	−	0.102543i
$176$	−43.4483	−	147.971i	−0.246865	−	0.840746i
$177$	44.8296	+	164.424i	0.253274	+	0.928949i
$178$	−337.587	−	216.954i	−1.89656	−	1.21884i
$179$	−44.0494	−	68.5422i	−0.246086	−	0.382917i	0.696134	−	0.717912i	$-0.254902\pi$
$179$	−44.0494	−	68.5422i	−0.246086	−	0.382917i	−0.942220	+	0.334995i	$0.891266\pi$
$180$	80.8767	+	137.293i	0.449315	+	0.762737i
$181$	122.507	+	78.7304i	0.676834	+	0.434975i	0.833383	−	0.552695i	$-0.186401\pi$
$181$	122.507	+	78.7304i	0.676834	+	0.434975i	−0.156550	+	0.987670i	$0.550037\pi$
$182$	−32.5272	−	14.8547i	−0.178721	−	0.0816191i
$183$	−28.8061	−	66.4632i	−0.157410	−	0.363187i
$184$	−33.5967	−	38.7726i	−0.182591	−	0.210721i
$185$	−118.788	+	17.0791i	−0.642096	+	0.0923195i
$186$	176.879	−	147.350i	0.950961	−	0.792206i
$187$	1.36762	−	1.57831i	0.00731345	−	0.00844018i
$188$	−39.1494	−	133.330i	−0.208241	−	0.709205i
$189$	82.3004	−	46.3526i	0.435452	−	0.245252i
$190$	12.4798	+	86.7986i	0.0656830	+	0.456835i
$191$	−1.07119	−	1.66680i	−0.00560831	−	0.00872671i	0.838438	−	0.544997i	$-0.183469\pi$
$191$	−1.07119	−	1.66680i	−0.00560831	−	0.00872671i	−0.844046	+	0.536270i	$0.819833\pi$
$192$	−102.481	−	1.99072i	−0.533756	−	0.0103683i
$193$	173.604	+	50.9746i	0.899500	+	0.264117i	0.698615	−	0.715498i	$-0.253800\pi$
$193$	173.604	+	50.9746i	0.899500	+	0.264117i	0.200885	+	0.979615i	$0.435618\pi$
$194$	−160.063	+	73.0984i	−0.825068	+	0.376796i
$195$	−36.0303	+	53.7399i	−0.184771	+	0.275589i
$196$	−16.4288	−	114.265i	−0.0838206	−	0.582985i
$197$	−265.601	−	230.144i	−1.34823	−	1.16824i	−0.970160	−	0.242466i	$-0.922044\pi$
$197$	−265.601	−	230.144i	−1.34823	−	1.16824i	−0.378066	−	0.925779i	$-0.623411\pi$
$198$	−20.5805	−	197.263i	−0.103942	−	0.996279i
$199$	−127.260	−	278.661i	−0.639498	−	1.40030i	−0.900453	−	0.434954i	$-0.856765\pi$
$199$	−127.260	−	278.661i	−0.639498	−	1.40030i	0.260955	−	0.965351i	$-0.415963\pi$
$200$		−	15.5931i		−	0.0779654i
$201$	193.199	+	55.4544i	0.961188	+	0.275893i
$202$	−79.4324			−0.393230
$203$	147.928	−	67.5565i	0.728710	−	0.332791i
$204$	−1.25055	−	2.03159i	−0.00613013	−	0.00995877i
$205$	−79.8593	+	92.1626i	−0.389558	+	0.449573i
$206$	−78.0589	+	11.2232i	−0.378927	+	0.0544814i
$207$	−102.012	−	173.170i	−0.492810	−	0.836572i
$208$	−29.7152	−	65.0673i	−0.142862	−	0.312823i
$209$	13.5241	−	46.0587i	0.0647084	−	0.220377i
$210$	158.084	+	3.07082i	0.752782	+	0.0146230i
$211$	25.1544	−	16.1657i	0.119215	−	0.0766148i	−0.479674	−	0.877447i	$-0.659245\pi$
$211$	25.1544	−	16.1657i	0.119215	−	0.0766148i	0.598889	+	0.800832i	$0.295609\pi$
$212$	−272.542	+	39.1856i	−1.28558	+	0.184838i
$213$	−277.886	−	45.4789i	−1.30463	−	0.213516i
$214$	−101.628	+	29.8408i	−0.474899	+	0.139443i
$215$	−130.312	−	112.916i	−0.606102	−	0.525190i
$216$	60.7791	+	12.3881i	0.281385	+	0.0573524i
$217$	−14.2978	−	99.4431i	−0.0658883	−	0.458263i
$218$	28.6903	−	24.8603i	0.131607	−	0.114038i
$219$	74.8642	+	172.731i	0.341846	+	0.788727i
$220$	60.6557	−	132.818i	0.275708	−	0.603716i
$221$	0.523703	−	0.814898i	0.00236970	−	0.00368732i
$222$	95.0221	−	141.728i	0.428028	−	0.638413i
$223$	147.808	−	94.9904i	0.662816	−	0.425966i	−0.165513	−	0.986208i	$-0.552928\pi$
$223$	147.808	−	94.9904i	0.662816	−	0.425966i	0.828329	+	0.560242i	$0.189292\pi$
$224$	−77.1274	+	120.013i	−0.344319	+	0.535771i
$225$	11.0352	−	60.0815i	0.0490451	−	0.267029i
$226$	−38.0119	+	11.1613i	−0.168194	+	0.0493863i
$227$	33.5147	−	29.0406i	0.147642	−	0.127932i	−0.577908	−	0.816102i	$-0.696131\pi$
$227$	33.5147	−	29.0406i	0.147642	−	0.127932i	0.725550	+	0.688169i	$0.241585\pi$
$228$	−45.5456	−	30.5363i	−0.199761	−	0.133931i
$229$	−290.192	−	85.2082i	−1.26722	−	0.372088i	−0.422040	−	0.906577i	$-0.638686\pi$
$229$	−290.192	−	85.2082i	−1.26722	−	0.372088i	−0.845176	+	0.534489i	$0.820504\pi$
$230$		−	336.436i		−	1.46276i
$231$	−78.0186	−	37.4779i	−0.337743	−	0.162242i
$232$	102.469	+	30.0875i	0.441675	+	0.129687i
$233$	−135.064	−	210.163i	−0.579673	−	0.901988i	0.420313	−	0.907379i	$-0.361920\pi$
$233$	−135.064	−	210.163i	−0.579673	−	0.901988i	−0.999985	+	0.00539085i	$0.998284\pi$
$234$	−22.4702	−	89.2073i	−0.0960263	−	0.381228i
$235$	−103.641	+	226.943i	−0.441027	+	0.965715i
$236$	−96.4466	−	150.074i	−0.408672	−	0.635906i
$237$	−30.4148	+	33.7531i	−0.128332	+	0.142418i
$238$	−2.36722			−0.00994631
$239$		−	389.974i		−	1.63169i	−0.578272	−	0.815844i	$-0.696273\pi$
$239$		−	389.974i		−	1.63169i	0.578272	−	0.815844i	$-0.303727\pi$
$240$	234.969	+	211.730i	0.979036	+	0.882207i
$241$	−26.5077	+	184.365i	−0.109990	+	0.764999i	0.857935	+	0.513759i	$0.171747\pi$
$241$	−26.5077	+	184.365i	−0.109990	+	0.764999i	−0.967925	+	0.251240i	$0.919162\pi$
$242$	107.004	−	92.7192i	0.442164	−	0.383137i
$243$	225.420	+	90.7456i	0.927655	+	0.373439i
$244$	49.6539	+	57.3037i	0.203500	+	0.234851i
$245$	−112.054	+	174.360i	−0.457365	+	0.711673i
$246$	−21.3382	−	172.073i	−0.0867408	−	0.699485i
$247$	3.16870	−	22.0388i	0.0128288	−	0.0892259i
$248$	35.6690	−	55.5020i	0.143826	−	0.223798i
$249$	−256.034	+	213.291i	−1.02825	+	0.856591i
$250$	−179.682	+	207.364i	−0.718729	+	0.829458i
$251$	156.547	−	135.648i	0.623692	−	0.540432i	−0.284665	−	0.958627i	$-0.591883\pi$
$251$	156.547	−	135.648i	0.623692	−	0.540432i	0.908357	+	0.418195i	$0.137337\pi$
$252$	−67.6002	+	72.1514i	−0.268255	+	0.286315i
$253$	−76.5065	+	167.526i	−0.302397	+	0.662157i
$254$	408.639	+	354.088i	1.60881	+	1.39405i
$255$	−0.691784	+	4.22694i	−0.00271288	+	0.0165762i
$256$	−315.263	+	92.5695i	−1.23150	+	0.361600i
$257$	−315.068	+	45.2999i	−1.22594	+	0.176264i	−0.724714	−	0.689050i	$-0.758028\pi$
$257$	−315.068	+	45.2999i	−1.22594	+	0.176264i	−0.501231	+	0.865314i	$0.667119\pi$
$258$	243.301	−	30.1709i	0.943025	−	0.116941i
$259$	−30.9339	−	67.7358i	−0.119436	−	0.261528i
$260$	19.0804	−	64.9819i	0.0733862	−	0.249931i
$261$	373.528	+	188.446i	1.43114	+	0.722016i
$262$	−70.7997	+	492.422i	−0.270228	+	1.87948i
$263$	−73.6731	+	10.5926i	−0.280126	+	0.0402760i	−0.280946	−	0.959724i	$-0.590648\pi$
$263$	−73.6731	+	10.5926i	−0.280126	+	0.0402760i	0.000819925		1.00000i	$0.499739\pi$
$264$	−22.6033	−	52.1516i	−0.0856185	−	0.197544i
$265$	415.879	+	267.269i	1.56935	+	1.00856i
$266$	−49.4948	+	22.6035i	−0.186071	+	0.0849756i
$267$	−406.104	−	195.081i	−1.52099	−	0.730639i
$268$	−210.328	+	5.36536i	−0.784807	+	0.0200200i
$269$			8.00011i			0.0297402i	0.999889	+	0.0148701i	$0.00473347\pi$
$269$			8.00011i			0.0297402i	−0.999889	+	0.0148701i	$0.995267\pi$
$270$	248.023	+	322.406i	0.918602	+	1.19410i
$271$	420.043	+	269.945i	1.54997	+	0.996107i	0.985308	+	0.170787i	$0.0546311\pi$
$271$	420.043	+	269.945i	1.54997	+	0.996107i	0.564665	+	0.825320i	$0.309005\pi$
$272$	−3.57876	−	3.10101i	−0.0131572	−	0.0114008i
$273$	−38.2932	−	12.0565i	−0.140268	−	0.0441630i
$274$	85.6780	−	595.904i	0.312693	−	2.17483i
$275$	−50.9175	+	23.2532i	−0.185154	+	0.0845572i
$276$	156.289	+	140.831i	0.566263	+	0.510258i
$277$	−3.11706	−	6.82541i	−0.0112529	−	0.0246405i	0.903922	−	0.427697i	$-0.140675\pi$
$277$	−3.11706	−	6.82541i	−0.0112529	−	0.0246405i	−0.915175	+	0.403057i	$0.867948\pi$
$278$	−24.1302	−	37.5473i	−0.0867992	−	0.135062i
$279$	176.714	−	188.611i	0.633384	−	0.676026i
$280$	43.4774	−	12.7661i	0.155276	−	0.0455933i
$281$	75.7357	+	257.932i	0.269522	+	0.917907i	0.977369	+	0.211542i	$0.0678484\pi$
$281$	75.7357	+	257.932i	0.269522	+	0.917907i	−0.707847	+	0.706366i	$0.750333\pi$
$282$	−141.067	−	325.478i	−0.500237	−	1.15418i
$283$	20.1996	−	44.2310i	0.0713768	−	0.156293i	−0.870581	−	0.492026i	$-0.836257\pi$
$283$	20.1996	−	44.2310i	0.0713768	−	0.156293i	0.941957	+	0.335733i	$0.108984\pi$
$284$	291.747	−	41.9468i	1.02728	−	0.147700i
$285$	25.8970	+	94.9840i	0.0908668	+	0.333277i
$286$	−55.2030	+	63.7077i	−0.193018	+	0.222754i
$287$	−68.8304	−	31.4338i	−0.239827	−	0.109525i
$288$	−365.028	+	38.0835i	−1.26746	+	0.132234i
$289$	−41.1199	+	285.995i	−0.142283	+	0.989602i
$290$	378.628	+	589.157i	1.30561	+	2.03157i
$291$	−168.238	+	103.559i	−0.578136	+	0.355873i
$292$	−129.046	−	148.927i	−0.441937	−	0.510023i
$293$	148.758	+	506.623i	0.507707	+	1.72909i	0.670013	+	0.742350i	$0.266289\pi$
$293$	148.758	+	506.623i	0.507707	+	1.72909i	−0.162306	+	0.986740i	$0.551893\pi$
$294$	−77.5175	−	284.315i	−0.263665	−	0.967059i
$295$	−45.5818	+	317.029i	−0.154515	+	1.07467i
$296$	13.7770	−	46.9200i	0.0465438	−	0.158514i
$297$	−50.1849	−	216.941i	−0.168973	−	0.730441i
$298$	−428.772			−1.43883
$299$	−24.0666	+	81.9632i	−0.0804902	+	0.274125i
$300$	7.86901	+	63.4563i	0.0262300	+	0.211521i
$301$	44.4453	−	97.3217i	0.147659	−	0.323328i
$302$	18.4085	+	8.40690i	0.0609554	+	0.0278374i
$303$	−88.5010	+	10.9747i	−0.292083	+	0.0362202i
$304$	−104.436	−	30.6653i	−0.343540	−	0.100873i
$305$		−	136.134i		−	0.446342i
$306$	−3.80634	−	4.75391i	−0.0124390	−	0.0155357i
$307$	258.264	+	75.8331i	0.841251	+	0.247013i	0.673843	−	0.738874i	$-0.264642\pi$
$307$	258.264	+	75.8331i	0.841251	+	0.247013i	0.167407	+	0.985888i	$0.446460\pi$
$308$	89.6777	+	12.8937i	0.291161	+	0.0418627i
$309$	−85.4201	+	23.2895i	−0.276440	+	0.0753704i
$310$	415.125	−	121.892i	1.33911	−	0.393199i
$311$	323.899	−	280.660i	1.04148	−	0.902445i	0.0461426	−	0.998935i	$-0.485307\pi$
$311$	323.899	−	280.660i	1.04148	−	0.902445i	0.995334	+	0.0964903i	$0.0307617\pi$
$312$	−13.8200	−	22.4514i	−0.0442948	−	0.0719595i
$313$	514.116	−	330.402i	1.64254	−	1.05560i	0.704139	−	0.710063i	$-0.251333\pi$
$313$	514.116	−	330.402i	1.64254	−	1.05560i	0.938405	−	0.345536i	$-0.112303\pi$
$314$	506.085	+	72.7641i	1.61174	+	0.231733i
$315$	176.557	−	18.4202i	0.560498	−	0.0584768i
$316$	19.7567	−	43.2611i	0.0625212	−	0.136902i
$317$	−310.120	−	268.720i	−0.978296	−	0.847698i	0.0100460	−	0.999950i	$-0.496802\pi$
$317$	−310.120	−	268.720i	−0.978296	−	0.847698i	−0.988342	+	0.152251i	$0.951348\pi$
$318$	−678.142	+	184.893i	−2.13252	+	0.581424i
$319$	−54.5592	−	379.468i	−0.171032	−	1.18955i
$320$	−175.226	−	80.0228i	−0.547580	−	0.250071i
$321$	−109.108	+	47.2891i	−0.339901	+	0.147318i
$322$	200.300	−	58.8135i	0.622051	−	0.182651i
$323$	−0.415266	−	1.41427i	−0.00128565	−	0.00437853i
$324$	−253.593	−	19.7416i	−0.782694	−	0.0609310i
$325$	−21.8418	+	14.0369i	−0.0672056	+	0.0431904i
$326$	−595.573	+	271.989i	−1.82691	+	0.834322i
$327$	28.5311	−	31.6626i	0.0872509	−	0.0968274i
$328$	−20.6424	−	45.2006i	−0.0629342	−	0.137807i
$329$	−153.231	−	22.0312i	−0.465747	−	0.0669643i
$330$	111.938	−	355.532i	0.339207	−	1.07737i
$331$	−163.691	+	188.909i	−0.494534	+	0.570723i	−0.947072	−	0.321022i	$-0.895973\pi$
$331$	−163.691	+	188.909i	−0.494534	+	0.570723i	0.452537	+	0.891745i	$0.350519\pi$
$332$	188.584	−	293.442i	0.568023	−	0.883862i
$333$	86.2889	−	171.037i	0.259126	−	0.513625i
$334$	−65.0258			−0.194688
$335$	291.698	+	240.012i	0.870741	+	0.716453i
$336$	−84.9797	+	176.904i	−0.252916	+	0.526501i
$337$	−80.4809	−	176.228i	−0.238816	−	0.522933i	0.751836	−	0.659350i	$-0.229169\pi$
$337$	−80.4809	−	176.228i	−0.238816	−	0.522933i	−0.990651	+	0.136417i	$0.956441\pi$
$338$	223.008	−	347.008i	0.659788	−	1.02665i
$339$	−40.8096	+	17.6875i	−0.120382	+	0.0521754i
$340$	−0.638056	−	4.43778i	−0.00187664	−	0.0130523i
$341$	−234.427	−	33.7055i	−0.687469	−	0.0988431i
$342$	−124.977	−	63.0516i	−0.365431	−	0.184362i
$343$	−287.872	−	84.5268i	−0.839276	−	0.246434i
$344$	63.9107	−	29.1870i	0.185787	−	0.0848461i
$345$	−46.4834	−	374.846i	−0.134735	−	1.08651i
$346$	−88.0334	−	612.286i	−0.254432	−	1.76961i
$347$	67.6393	+	230.358i	0.194926	+	0.663857i	0.997713	+	0.0675913i	$0.0215314\pi$
$347$	67.6393	+	230.358i	0.194926	+	0.663857i	−0.802787	+	0.596266i	$0.796650\pi$
$348$	−432.181	−	70.7310i	−1.24190	−	0.203250i
$349$	407.663	−	470.468i	1.16809	−	1.34805i	0.242211	−	0.970223i	$-0.422127\pi$
$349$	407.663	−	470.468i	1.16809	−	1.34805i	0.925878	−	0.377823i	$-0.123327\pi$
$350$	57.7152	+	26.3577i	0.164901	+	0.0753076i
$351$	−37.3608	−	96.2874i	−0.106441	−	0.274323i
$352$	220.233	+	254.162i	0.625661	+	0.722051i
$353$	445.377	+	385.921i	1.26169	+	1.09326i	0.991453	+	0.130467i	$0.0416478\pi$
$353$	445.377	+	385.921i	1.26169	+	1.09326i	0.270238	+	0.962794i	$0.412898\pi$
$354$	−291.482	−	349.895i	−0.823396	−	0.988403i
$355$	−445.183	−	286.102i	−1.25404	−	0.805921i
$356$	466.792	+	67.1145i	1.31121	+	0.188524i
$357$	−2.63748	+	0.327066i	−0.00738791	+	0.000916151i
$358$	183.153	+	117.705i	0.511601	+	0.328786i
$359$	−260.251	+	225.509i	−0.724933	+	0.628158i	−0.937094	−	0.349077i	$-0.886495\pi$
$359$	−260.251	+	225.509i	−0.724933	+	0.628158i	0.212161	+	0.977235i	$0.431950\pi$
$360$	95.5461	+	66.7853i	0.265406	+	0.185515i
$361$	214.218	+	247.221i	0.593402	+	0.684822i
$362$	−385.165	−	55.3784i	−1.06399	−	0.152979i
$363$	106.410	−	118.089i	0.293139	−	0.325314i
$364$	42.0232			0.115448
$365$			353.800i			0.969315i
$366$	143.794	+	129.573i	0.392881	+	0.354024i
$367$	−141.385	+	90.8623i	−0.385244	+	0.247581i	−0.718900	−	0.695114i	$-0.755354\pi$
$367$	−141.385	+	90.8623i	−0.385244	+	0.247581i	0.333656	+	0.942695i	$0.391718\pi$
$368$	379.858	+	173.475i	1.03222	+	0.471401i
$369$	−47.5488	−	188.770i	−0.128858	−	0.511573i
$370$	269.773	−	173.373i	0.729116	−	0.468574i
$371$	−86.4201	+	294.320i	−0.232938	+	0.793315i
$372$	−117.146	+	243.866i	−0.314910	+	0.655555i
$373$	629.760			1.68837			0.844183	−	0.536055i	$-0.180086\pi$
$373$	629.760			1.68837			0.844183	+	0.536055i	$0.180086\pi$
$374$	−1.57220	+	5.35444i	−0.00420375	+	0.0143167i
$375$	−171.546	+	255.865i	−0.457456	+	0.682305i
$376$	−66.5735	−	76.8300i	−0.177057	−	0.204335i
$377$	−50.0975	−	170.616i	−0.132885	−	0.452563i
$378$	−148.590	+	204.024i	−0.393096	+	0.539745i
$379$	214.288	+	137.715i	0.565404	+	0.363363i	0.791902	−	0.610649i	$-0.209091\pi$
$379$	214.288	+	137.715i	0.565404	+	0.363363i	−0.226498	+	0.974012i	$0.572728\pi$
$380$	−55.7150	−	86.6943i	−0.146619	−	0.228143i
$381$	504.215	+	338.054i	1.32340	+	0.887280i
$382$	4.45390	+	2.86235i	0.0116594	+	0.00749306i
$383$	129.081	+	58.9493i	0.337026	+	0.153915i	0.576738	−	0.816930i	$-0.304326\pi$
$383$	129.081	+	58.9493i	0.337026	+	0.153915i	−0.239711	+	0.970844i	$0.577053\pi$
$384$	−197.683	+	85.6789i	−0.514801	+	0.223122i
$385$	−106.522	−	122.933i	−0.276681	−	0.319307i
$386$	−478.553	+	68.8056i	−1.23978	+	0.178253i
$387$	266.909	−	67.2309i	0.689688	−	0.173723i
$388$	135.420	−	156.283i	0.349020	−	0.402791i
$389$	30.9347	+	105.354i	0.0795237	+	0.270833i	0.989651	−	0.143496i	$-0.0458345\pi$
$389$	30.9347	+	105.354i	0.0795237	+	0.270833i	−0.910127	+	0.414329i	$0.864016\pi$
$390$	27.9234	−	170.618i	0.0715986	−	0.437482i
$391$	0.804795	+	5.59747i	0.00205830	+	0.0143158i
$392$	−45.6594	−	71.0474i	−0.116478	−	0.181243i
$393$	−10.8475	+	558.423i	−0.0276018	+	1.42092i
$394$	901.051	+	264.573i	2.28693	+	0.671504i
$395$	−77.6714	+	35.4714i	−0.196637	+	0.0898009i
$396$	118.303	+	200.825i	0.298744	+	0.507134i
$397$	−5.78557	−	40.2395i	−0.0145732	−	0.101359i	0.981237	−	0.192808i	$-0.0617593\pi$
$397$	−5.78557	−	40.2395i	−0.0145732	−	0.101359i	−0.995810	+	0.0914487i	$0.970850\pi$
$398$	618.649	+	536.063i	1.55440	+	1.34689i
$399$	−52.0225	+	32.0225i	−0.130382	+	0.0802570i
$400$	52.7258	+	115.453i	0.131814	+	0.288633i
$401$		−	280.097i		−	0.698497i	−0.937030	−	0.349249i	$-0.886437\pi$
$401$		−	280.097i		−	0.698497i	0.937030	−	0.349249i	$-0.113563\pi$
$402$	−531.156	+	79.6684i	−1.32128	+	0.198180i
$403$	−109.853			−0.272588
$404$	84.9123	−	38.7782i	0.210179	−	0.0959856i
$405$	320.884	+	324.947i	0.792306	+	0.802338i
$406$	−284.571	+	328.412i	−0.700914	+	0.808898i
$407$	−173.757	+	24.9825i	−0.426921	+	0.0613820i
$408$	−1.44963	−	0.971912i	−0.00355301	−	0.00238214i
$409$	−167.540	−	366.861i	−0.409632	−	0.896970i	−0.996202	−	0.0870711i	$-0.972249\pi$
$409$	−167.540	−	366.861i	−0.409632	−	0.896970i	0.586570	−	0.809899i	$-0.300478\pi$
$410$	91.8058	−	312.662i	0.223917	−	0.762590i
$411$	13.1271	−	675.774i	0.0319393	−	1.64422i
$412$	77.9651	−	50.1051i	0.189236	−	0.121614i
$413$	−196.714	+	28.2833i	−0.476306	+	0.0684825i
$414$	440.181	+	307.680i	1.06324	+	0.743188i
$415$	−600.898	+	176.439i	−1.44795	+	0.425155i
$416$	117.889	+	102.151i	0.283386	+	0.245555i
$417$	−32.0728	−	38.5001i	−0.0769131	−	0.0923263i
$418$	18.2548	+	126.965i	0.0436717	+	0.303744i
$419$	−90.0951	+	78.0678i	−0.215024	+	0.186319i	−0.755713	−	0.654904i	$-0.772709\pi$
$419$	−90.0951	+	78.0678i	−0.215024	+	0.186319i	0.540688	+	0.841223i	$0.318164\pi$
$420$	−170.489	+	73.8926i	−0.405927	+	0.175935i
$421$	−113.937	+	249.488i	−0.270635	+	0.592607i	−0.995337	−	0.0964543i	$-0.969250\pi$
$421$	−113.937	+	249.488i	−0.270635	+	0.592607i	0.724703	+	0.689062i	$0.241977\pi$
$422$	−43.1968	+	67.2156i	−0.102362	+	0.159279i
$423$	−202.141	−	343.146i	−0.477876	−	0.811221i
$424$	−169.460	+	108.906i	−0.399671	+	0.256853i
$425$	−0.929242	+	1.44593i	−0.00218645	+	0.00340219i
$426$	725.926	−	197.921i	1.70405	−	0.464603i
$427$	81.0489	−	23.7981i	0.189810	−	0.0557333i
$428$	94.0716	−	81.5135i	0.219793	−	0.190452i
$429$	−52.7033	+	78.6082i	−0.122852	+	0.183236i
$430$	442.084	+	129.808i	1.02810	+	0.301878i
$431$		−	760.506i		−	1.76451i	−0.470767	−	0.882257i	$-0.656023\pi$
$431$		−	760.506i		−	1.76451i	0.470767	−	0.882257i	$-0.343977\pi$
$432$	−491.905	+	113.792i	−1.13867	+	0.263408i
$433$	525.825	+	154.396i	1.21438	+	0.356573i	0.825333	−	0.564646i	$-0.190987\pi$
$433$	525.825	+	154.396i	1.21438	+	0.356573i	0.389044	+	0.921219i	$0.372805\pi$
$434$	145.139	+	225.840i	0.334421	+	0.520369i
$435$	503.256	+	604.107i	1.15691	+	1.38875i
$436$	−18.5331	+	40.5818i	−0.0425071	+	0.0930775i
$437$	70.2747	+	109.350i	0.160812	+	0.250228i
$438$	−373.707	−	336.747i	−0.853213	−	0.768828i
$439$	−518.437			−1.18095			−0.590475	−	0.807056i	$-0.701059\pi$
$439$	−518.437			−1.18095			−0.590475	+	0.807056i	$0.701059\pi$
$440$		−	106.820i		−	0.242774i
$441$	−125.650	−	306.065i	−0.284920	−	0.694025i
$442$	−0.368369	+	2.56206i	−0.000833414	+	0.00579652i
$443$	−527.234	+	456.851i	−1.19014	+	1.03127i	−0.191382	+	0.981516i	$0.561297\pi$
$443$	−527.234	+	456.851i	−1.19014	+	1.03127i	−0.998762	+	0.0497502i	$0.984157\pi$
$444$	−32.3875	+	197.894i	−0.0729448	+	0.445708i
$445$	−554.470	−	639.893i	−1.24600	−	1.43796i
$446$	−253.826	+	394.961i	−0.569117	+	0.885563i
$447$	−477.724	+	59.2410i	−1.06873	+	0.132530i
$448$	17.0106	−	118.311i	0.0379701	−	0.264088i
$449$	126.060	−	196.153i	0.280756	−	0.436866i	−0.672022	−	0.740531i	$-0.734574\pi$
$449$	126.060	−	196.153i	0.280756	−	0.436866i	0.952779	+	0.303665i	$0.0982105\pi$
$450$	39.8703	+	158.287i	0.0886007	+	0.351748i
$451$	−116.814	+	134.811i	−0.259012	+	0.298916i
$452$	35.1855	−	30.4884i	0.0778440	−	0.0674522i
$453$	21.6717	+	6.82329i	0.0478405	+	0.0150625i
$454$	−49.2261	+	107.790i	−0.108428	+	0.237423i
$455$	−57.0203	−	49.4084i	−0.125319	−	0.108590i
$456$	−39.5897	−	6.47928i	−0.0868196	−	0.0142089i
$457$	475.920	−	139.743i	1.04140	−	0.305783i	0.284063	−	0.958806i	$-0.408318\pi$
$457$	475.920	−	139.743i	1.04140	−	0.305783i	0.757338	+	0.653023i	$0.226499\pi$
$458$	799.941	−	115.014i	1.74660	−	0.251123i
$459$	−4.89773	−	4.77076i	−0.0106704	−	0.0103938i
$460$	164.245	+	359.646i	0.357054	+	0.781839i
$461$	153.076	−	521.329i	0.332052	−	1.13087i	−0.609159	−	0.793048i	$-0.708493\pi$
$461$	153.076	−	521.329i	0.332052	−	1.13087i	0.941211	−	0.337818i	$-0.109689\pi$
$462$	231.238	+	4.49185i	0.500515	+	0.00972261i
$463$	−5.68880	+	39.5665i	−0.0122868	+	0.0854568i	−0.995042	−	0.0994538i	$-0.968290\pi$
$463$	−5.68880	+	39.5665i	−0.0122868	+	0.0854568i	0.982755	+	0.184911i	$0.0591995\pi$
$464$	−860.428	+	123.711i	−1.85437	+	0.266618i
$465$	445.678	−	193.163i	0.958446	−	0.415405i
$466$	561.583	+	360.907i	1.20511	+	0.774479i
$467$	104.661	−	47.7972i	0.224114	−	0.102349i	−0.300194	−	0.953878i	$-0.597051\pi$
$467$	104.661	−	47.7972i	0.224114	−	0.102349i	0.524308	+	0.851529i	$0.324324\pi$
$468$	67.5705	+	84.3919i	0.144382	+	0.180325i
$469$	−91.9006	+	215.623i	−0.195950	+	0.459750i
$470$		−	666.665i		−	1.41844i
$471$	573.918	+	11.1485i	1.21851	+	0.0236698i
$472$	−109.792	−	70.5589i	−0.232610	−	0.149489i
$473$	−190.614	−	165.168i	−0.402989	−	0.349192i
$474$	36.4604	−	115.804i	0.0769208	−	0.244311i
$475$	−5.62244	+	39.1049i	−0.0118367	+	0.0823262i
$476$	2.53053	−	1.15566i	0.00531625	−	0.00242785i
$477$	−730.018	+	299.697i	−1.53044	+	0.628295i
$478$	432.886	+	947.889i	0.905620	+	1.98303i
$479$	187.148	+	291.208i	0.390706	+	0.607950i	0.979768	−	0.200138i	$-0.0641390\pi$
$479$	187.148	+	291.208i	0.390706	+	0.607950i	−0.589062	+	0.808088i	$0.700503\pi$
$480$	−657.899	−	207.138i	−1.37062	−	0.431537i
$481$	−78.1247	+	22.9395i	−0.162421	+	0.0476912i
$482$	−140.222	−	477.551i	−0.290916	−	0.990769i
$483$	215.042	−	93.2025i	0.445222	−	0.192966i
$484$	−69.1211	+	151.354i	−0.142812	+	0.312715i
$485$	−367.497	+	52.8380i	−0.757725	+	0.108944i
$486$	−648.649	+	29.6547i	−1.33467	+	0.0610179i
$487$	−190.881	+	220.288i	−0.391952	+	0.452337i	−0.917090	−	0.398680i	$-0.869468\pi$
$487$	−190.881	+	220.288i	−0.391952	+	0.452337i	0.525138	+	0.851017i	$0.324014\pi$
$488$	50.4586	+	23.0437i	0.103399	+	0.0472206i
$489$	−625.989	+	385.328i	−1.28014	+	0.787993i
$490$	78.8183	−	548.193i	0.160854	−	1.11876i
$491$	148.087	+	230.427i	0.301602	+	0.469302i	0.958666	−	0.284532i	$-0.0918383\pi$
$491$	148.087	+	230.427i	0.301602	+	0.469302i	−0.657064	+	0.753835i	$0.728202\pi$
$492$	106.815	+	173.527i	0.217104	+	0.352698i
$493$	−7.70879	−	8.89641i	−0.0156365	−	0.0180455i
$494$	16.7620	+	57.0860i	0.0339311	+	0.115559i
$495$	75.5964	−	411.589i	0.152720	−	0.831492i
$496$	−76.4259	+	531.554i	−0.154084	+	1.07168i
$497$	92.5096	−	315.059i	0.186136	−	0.633921i
$498$	385.567	−	802.644i	0.774232	−	1.61174i
$499$	625.129			1.25276			0.626382	−	0.779517i	$-0.284535\pi$
$499$	625.129			1.25276			0.626382	+	0.779517i	$0.284535\pi$
$500$	90.8450	−	309.389i	0.181690	−	0.618779i
$501$	−72.4496	+	8.98424i	−0.144610	+	0.0179326i
$502$	−229.935	+	503.487i	−0.458038	+	1.00296i
$503$	178.435	+	81.4884i	0.354741	+	0.162005i	0.584812	−	0.811169i	$-0.301168\pi$
$503$	178.435	+	81.4884i	0.354741	+	0.162005i	−0.230071	+	0.973174i	$0.573896\pi$
$504$	−23.0585	+	68.5593i	−0.0457510	+	0.136030i
$505$	−160.809	−	47.2178i	−0.318433	−	0.0935005i
$506$		−	492.122i		−	0.972573i
$507$	200.525	−	417.437i	0.395512	−	0.823347i
$508$	−609.693	−	179.022i	−1.20018	−	0.352405i
$509$	15.4547	+	2.22205i	0.0303629	+	0.00436552i	0.157480	−	0.987522i	$-0.449663\pi$
$509$	15.4547	+	2.22205i	0.0303629	+	0.00436552i	−0.127117	+	0.991888i	$0.540572\pi$
$510$	−3.01059	−	11.0421i	−0.00590312	−	0.0216512i
$511$	−210.638	+	61.8490i	−0.412208	+	0.121035i
$512$	446.434	−	386.837i	0.871941	−	0.755541i
$513$	−147.957	−	52.9827i	−0.288416	−	0.103280i
$514$	715.535	−	459.846i	1.39209	−	0.894643i
$515$	−164.700	−	23.6803i	−0.319806	−	0.0459811i
$516$	−245.356	+	151.029i	−0.475497	+	0.292693i
$517$	−151.602	+	331.961i	−0.293233	+	0.642091i
$518$	150.379	+	130.304i	0.290307	+	0.251552i
$519$	−182.680	−	670.026i	−0.351985	−	1.29099i
$520$	−7.05125	−	49.0425i	−0.0135601	−	0.0943125i
$521$	−251.565	−	114.886i	−0.482850	−	0.220510i	0.159092	−	0.987264i	$-0.449143\pi$
$521$	−251.565	−	114.886i	−0.482850	−	0.220510i	−0.641941	+	0.766754i	$0.721871\pi$
$522$	−1117.10	−	43.4161i	−2.14003	−	0.0831726i
$523$	148.985	−	43.7461i	0.284867	−	0.0836445i	−0.136178	−	0.990684i	$-0.543482\pi$
$523$	148.985	−	43.7461i	0.284867	−	0.0836445i	0.421045	+	0.907040i	$0.361664\pi$
$524$	−164.712	−	560.958i	−0.314336	−	1.07053i
$525$	67.9462	+	21.3927i	0.129421	+	0.0407480i
$526$	167.315	−	107.527i	0.318090	−	0.204424i
$527$	−6.61509	+	3.02101i	−0.0125523	+	0.00573246i
$528$	343.701	+	309.708i	0.650949	+	0.586568i
$529$	12.5886	+	27.5652i	0.0237970	+	0.0521081i
$530$	−1307.54	−	187.995i	−2.46705	−	0.354708i
$531$	−373.103	−	349.569i	−0.702643	−	0.658322i
$532$	41.8746	−	48.3258i	0.0787116	−	0.0908380i
$533$	−44.7319	+	69.6042i	−0.0839247	+	0.130589i
$534$	1203.64	+	23.3810i	2.25401	+	0.0437847i
$535$	−223.483			−0.417725
$536$	−138.337	+	67.4917i	−0.258092	+	0.125917i
$537$	220.326	+	105.838i	0.410291	+	0.197092i
$538$	−8.88045	−	19.4455i	−0.0165064	−	0.0361440i
$539$	−163.908	+	255.045i	−0.304096	+	0.473182i
$540$	−422.529	−	223.566i	−0.782462	−	0.414012i
$541$	−75.4848	−	525.008i	−0.139528	−	0.970440i	−0.932497	−	0.361178i	$-0.882375\pi$
$541$	−75.4848	−	525.008i	−0.139528	−	0.970440i	0.792969	−	0.609262i	$-0.208534\pi$
$542$	−1320.63	−	189.877i	−2.43658	−	0.350327i
$543$	−436.790	−	8.48474i	−0.804402	−	0.0156257i
$544$	9.90818	+	2.90930i	0.0182136	+	0.00534798i
$545$	72.8609	−	33.2744i	0.133690	−	0.0610540i
$546$	106.461	−	13.2018i	0.194983	−	0.0241792i
$547$	−100.796	−	701.053i	−0.184271	−	1.28163i	−0.846524	−	0.532351i	$-0.821309\pi$
$547$	−100.796	−	701.053i	−0.184271	−	1.28163i	0.662253	−	0.749281i	$-0.269601\pi$
$548$	199.326	+	678.842i	0.363733	+	1.23876i
$549$	178.113	+	124.499i	0.324433	+	0.226773i
$550$	97.9505	−	113.041i	0.178092	−	0.205529i
$551$	−246.126	−	112.402i	−0.446690	−	0.203996i
$552$	146.806	+	46.2215i	0.265953	+	0.0837347i
$553$	−34.6962	−	40.0416i	−0.0627418	−	0.0724079i
$554$	15.1530	+	13.1301i	0.0273519	+	0.0237006i
$555$	276.619	−	230.439i	0.498412	−	0.415206i
$556$	44.1251	+	28.3575i	0.0793618	+	0.0510027i
$557$	−271.076	−	38.9748i	−0.486671	−	0.0699727i	−0.105388	−	0.994431i	$-0.533608\pi$
$557$	−271.076	−	38.9748i	−0.486671	−	0.0699727i	−0.381283	+	0.924458i	$0.624518\pi$
$558$	−220.164	+	654.608i	−0.394559	+	1.17313i
$559$	−98.4158	−	63.2480i	−0.176057	−	0.113145i
$560$	−278.746	+	241.535i	−0.497760	+	0.431312i
$561$	−1.01191	+	6.18296i	−0.00180376	+	0.0110213i
$562$	−470.402	−	542.873i	−0.837014	−	0.965966i
$563$	476.291	+	68.4804i	0.845988	+	0.121635i	0.551659	−	0.834070i	$-0.313995\pi$
$563$	476.291	+	68.4804i	0.845988	+	0.121635i	0.294329	+	0.955704i	$0.404904\pi$
$564$	309.694	+	279.064i	0.549103	+	0.494795i
$565$	−83.5889			−0.147945
$566$			129.933i			0.229563i
$567$	−137.366	+	247.847i	−0.242267	+	0.437119i
$568$	181.401	−	116.580i	0.319369	−	0.205246i
$569$	385.178	+	175.905i	0.676939	+	0.309148i	0.724055	−	0.689742i	$-0.242276\pi$
$569$	385.178	+	175.905i	0.676939	+	0.309148i	−0.0471166	+	0.998889i	$0.515003\pi$
$570$	−168.383	−	202.126i	−0.295408	−	0.354607i
$571$	874.473	−	561.990i	1.53148	−	0.984220i	0.541864	−	0.840466i	$-0.317719\pi$
$571$	874.473	−	561.990i	1.53148	−	0.984220i	0.989613	−	0.143754i	$-0.0459174\pi$
$572$	27.9099	−	95.0524i	0.0487935	−	0.166176i
$573$	5.35787	+	2.57377i	0.00935055	+	0.00449174i
$574$	202.195			0.352257
$575$	42.7030	−	145.433i	0.0742660	−	0.252927i
$576$	264.948	−	156.076i	0.459979	−	0.270965i
$577$	−161.634	−	186.535i	−0.280128	−	0.323285i	0.598197	−	0.801349i	$-0.295884\pi$
$577$	−161.634	−	186.535i	−0.280128	−	0.323285i	−0.878325	+	0.478064i	$0.841339\pi$
$578$	−217.518	−	740.798i	−0.376329	−	1.28166i
$579$	−523.682	+	142.780i	−0.904460	+	0.246598i
$580$	−692.370	−	444.959i	−1.19374	−	0.767171i
$581$	−210.090	−	326.906i	−0.361601	−	0.562662i
$582$	293.972	−	438.466i	0.505107	−	0.753378i
$583$	608.327	+	390.948i	1.04344	+	0.670580i
$584$	−131.137	−	59.8882i	−0.224550	−	0.102548i
$585$	7.53809	−	193.955i	0.0128856	−	0.331547i
$586$	−923.951	−	1066.30i	−1.57671	−	1.81962i
$587$	−112.892	+	16.2314i	−0.192321	+	0.0276515i	−0.237802	−	0.971314i	$-0.576427\pi$
$587$	−112.892	+	16.2314i	−0.192321	+	0.0276515i	0.0454813	+	0.998965i	$0.485518\pi$
$588$	221.666	+	266.087i	0.376982	+	0.452528i
$589$	−109.465	+	126.329i	−0.185848	+	0.214480i
$590$	−241.121	−	821.183i	−0.408680	−	1.39184i
$591$	1040.48	+	170.285i	1.76054	+	0.288130i
$592$	56.6468	+	393.987i	0.0956871	+	0.665519i
$593$	361.134	+	561.936i	0.608995	+	0.947615i	0.999634	+	0.0270708i	$0.00861795\pi$
$593$	361.134	+	561.936i	0.608995	+	0.947615i	−0.390638	+	0.920544i	$0.627746\pi$
$594$	362.795	+	471.600i	0.610767	+	0.793940i
$595$	−4.79238	−	1.40717i	−0.00805443	−	0.00236499i
$596$	458.353	−	209.323i	0.769048	−	0.351213i
$597$	763.344	+	511.789i	1.27863	+	0.857267i
$598$	−32.4851	−	225.939i	−0.0543229	−	0.377824i
$599$	478.352	+	414.495i	0.798585	+	0.691978i	0.955291	−	0.295668i	$-0.0955421\pi$
$599$	478.352	+	414.495i	0.798585	+	0.691978i	−0.156706	+	0.987645i	$0.550088\pi$
$600$	24.5217	+	39.8370i	0.0408695	+	0.0663950i
$601$	−417.771	−	914.791i	−0.695126	−	1.52211i	−0.845782	−	0.533528i	$-0.820866\pi$
$601$	−417.771	−	914.791i	−0.695126	−	1.52211i	0.150656	−	0.988586i	$-0.451861\pi$
$602$			285.891i			0.474902i
$603$	−580.789	+	162.151i	−0.963166	+	0.268907i
$604$	−23.7827			−0.0393753
$605$	271.742	−	124.101i	0.449161	−	0.205125i
$606$	202.933	−	124.915i	0.334872	−	0.206131i
$607$	−183.070	+	211.274i	−0.301598	+	0.348063i	−0.886238	−	0.463230i	$-0.846690\pi$
$607$	−183.070	+	211.274i	−0.301598	+	0.348063i	0.584640	+	0.811293i	$0.301236\pi$
$608$	234.944	−	33.7798i	0.386420	−	0.0555589i
$609$	−271.685	+	405.224i	−0.446117	+	0.665393i
$610$	151.115	+	330.895i	0.247729	+	0.542451i
$611$	−47.6892	+	162.414i	−0.0780510	+	0.265817i
$612$	6.38976	+	3.22366i	0.0104408	+	0.00526742i
$613$	−533.753	+	343.022i	−0.870723	+	0.559580i	−0.897974	−	0.440049i	$-0.854961\pi$
$613$	−533.753	+	343.022i	−0.870723	+	0.559580i	0.0272506	+	0.999629i	$0.491325\pi$
$614$	−711.927	+	102.360i	−1.15949	+	0.166710i
$615$	59.0884	−	361.042i	0.0960787	−	0.587061i
$616$	63.5966	−	18.6737i	0.103241	−	0.0303144i
$617$	−283.243	−	245.431i	−0.459065	−	0.397782i	0.394395	−	0.918941i	$-0.370954\pi$
$617$	−283.243	−	245.431i	−0.459065	−	0.397782i	−0.853459	+	0.521159i	$0.825500\pi$
$618$	181.774	−	151.428i	0.294133	−	0.245030i
$619$	−152.801	−	1062.76i	−0.246852	−	1.71689i	−0.616192	−	0.787596i	$-0.711325\pi$
$619$	−152.801	−	1062.76i	−0.246852	−	1.71689i	0.369340	−	0.929294i	$-0.379584\pi$
$620$	−384.257	+	332.961i	−0.619770	+	0.537034i
$621$	532.946	+	281.990i	0.858206	+	0.454090i
$622$	−475.741	+	1041.73i	−0.764857	+	1.67480i
$623$	284.038	−	441.971i	0.455919	−	0.709424i
$624$	178.241	+	119.503i	0.285642	+	0.191511i
$625$	−629.776	+	404.732i	−1.00764	+	0.647572i
$626$	−882.877	+	1373.78i	−1.41035	+	2.19454i
$627$	37.8809	+	138.938i	0.0604161	+	0.221592i
$628$	−576.522	+	169.282i	−0.918029	+	0.269558i
$629$	−4.07364	+	3.52983i	−0.00647637	+	0.00561181i
$630$	−408.701	+	240.758i	−0.648731	+	0.382156i
$631$	635.172	+	186.503i	1.00661	+	0.295568i	0.743166	−	0.669107i	$-0.233323\pi$
$631$	635.172	+	186.503i	1.00661	+	0.295568i	0.263445	+	0.964674i	$0.415141\pi$
$632$		−	34.7934i		−	0.0550529i
$633$	−38.8417	+	80.8577i	−0.0613614	+	0.127737i
$634$	1052.08	+	308.919i	1.65944	+	0.487255i
$635$	616.796	+	959.753i	0.971332	+	1.51142i
$636$	634.663	−	528.711i	0.997898	−	0.831306i
$637$	−58.4163	+	127.914i	−0.0917053	+	0.200807i
$638$	553.839	+	861.790i	0.868086	+	1.35077i
$639$	781.458	−	320.815i	1.22294	−	0.502057i
$640$	−404.909			−0.632670
$641$		−	590.504i		−	0.921223i	−0.887602	−	0.460612i	$-0.847630\pi$
$641$		−	590.504i		−	0.921223i	0.887602	−	0.460612i	$-0.152370\pi$
$642$	212.711	−	236.058i	0.331325	−	0.367691i
$643$	−160.597	+	1116.98i	−0.249762	+	1.73714i	0.349815	+	0.936819i	$0.386245\pi$
$643$	−160.597	+	1116.98i	−0.249762	+	1.73714i	−0.599577	+	0.800317i	$0.704665\pi$
$644$	−185.407	+	160.656i	−0.287899	+	0.249466i
$645$	510.491	+	83.5472i	0.791459	+	0.129531i
$646$	2.57926	+	2.97662i	0.00399266	+	0.00460777i
$647$	84.2788	−	131.140i	0.130261	−	0.202690i	−0.769996	−	0.638048i	$-0.779742\pi$
$647$	84.2788	−	131.140i	0.130261	−	0.202690i	0.900257	+	0.435358i	$0.143378\pi$
$648$	−174.759	+	63.9323i	−0.269690	+	0.0986609i
$649$	−66.6749	+	463.734i	−0.102735	+	0.714536i
$650$	37.5083	−	58.3641i	0.0577051	−	0.0897909i
$651$	192.912	+	231.571i	0.296332	+	0.355716i
$652$	503.878	−	581.506i	0.772819	−	0.891881i
$653$	50.8905	−	44.0968i	0.0779333	−	0.0675296i	−0.615023	−	0.788509i	$-0.710853\pi$
$653$	50.8905	−	44.0968i	0.0779333	−	0.0675296i	0.692956	+	0.720980i	$0.256308\pi$
$654$	−34.2023	+	108.631i	−0.0522971	+	0.166103i
$655$	−436.048	+	954.811i	−0.665722	+	1.45773i
$656$	305.678	+	264.872i	0.465973	+	0.403768i
$657$	−462.899	−	323.560i	−0.704565	−	0.492480i
$658$	396.906	−	116.542i	0.603200	−	0.177116i
$659$	706.111	−	101.523i	1.07149	−	0.154057i	0.416077	−	0.909329i	$-0.363405\pi$
$659$	706.111	−	101.523i	1.07149	−	0.154057i	0.655411	+	0.755273i	$0.272495\pi$
$660$	53.9067	+	434.707i	0.0816767	+	0.658648i
$661$	392.988	+	860.523i	0.594535	+	1.30185i	0.932663	+	0.360750i	$0.117479\pi$
$661$	392.988	+	860.523i	0.594535	+	1.30185i	−0.338128	+	0.941100i	$0.609794\pi$
$662$	188.178	−	640.876i	0.284257	−	0.968091i
$663$	−0.0564393	+	2.90547i	−8.51271e−5	+	0.00438230i
$664$	36.3170	−	252.591i	0.0546944	−	0.380408i
$665$	−113.637	+	16.3386i	−0.170883	+	0.0245693i
$666$	−19.8801	+	511.516i	−0.0298500	+	0.768041i
$667$	873.303	+	561.238i	1.30930	+	0.841436i
$668$	69.5118	−	31.7450i	0.104060	−	0.0475224i
$669$	−228.235	+	475.123i	−0.341159	+	0.710199i
$670$	−975.439	−	259.588i	−1.45588	−	0.387444i
$671$		−	199.131i		−	0.296767i
$672$	8.31199	−	427.897i	0.0123690	−	0.636752i
$673$	398.400	+	256.036i	0.591976	+	0.380440i	0.802060	−	0.597243i	$-0.203737\pi$
$673$	398.400	+	256.036i	0.591976	+	0.380440i	−0.210084	+	0.977683i	$0.567374\pi$
$674$	391.242	+	339.013i	0.580477	+	0.502986i
$675$	66.2918	+	170.849i	0.0982101	+	0.253110i
$676$	−68.9875	+	479.818i	−0.102052	+	0.709791i
$677$	836.917	−	382.207i	1.23621	−	0.564560i	0.313332	−	0.949644i	$-0.398555\pi$
$677$	836.917	−	382.207i	1.23621	−	0.564560i	0.922882	+	0.385084i	$0.125827\pi$
$678$	79.5600	−	88.2923i	0.117345	−	0.130225i
$679$	−95.7010	−	209.556i	−0.140944	−	0.308624i
$680$	−1.77330	−	2.75931i	−0.00260780	−	0.00405781i
$681$	−39.9534	+	126.898i	−0.0586688	+	0.186340i
$682$	607.224	−	178.297i	0.890358	−	0.261433i
$683$	−238.198	−	811.228i	−0.348753	−	1.18774i	−0.927997	−	0.372589i	$-0.878470\pi$
$683$	−238.198	−	811.228i	−0.348753	−	1.18774i	0.579244	−	0.815154i	$-0.303348\pi$
$684$	164.381	+	6.38867i	0.240323	+	0.00934016i
$685$	527.682	−	1155.46i	0.770338	−	1.68681i
$686$	793.544	−	114.094i	1.15677	−	0.166318i
$687$	875.378	−	238.668i	1.27420	−	0.347407i
$688$	−374.512	+	432.210i	−0.544349	+	0.628212i
$689$	305.097	+	139.333i	0.442811	+	0.202225i
$690$	529.079	+	859.521i	0.766782	+	1.24568i
$691$	−71.2418	+	495.498i	−0.103100	+	0.717073i	0.871054	+	0.491187i	$0.163437\pi$
$691$	−71.2418	+	495.498i	−0.103100	+	0.717073i	−0.974154	+	0.225886i	$0.927472\pi$
$692$	393.019	+	611.549i	0.567947	+	0.883742i
$693$	258.259	−	26.9442i	0.372668	−	0.0388805i
$694$	−420.115	−	484.838i	−0.605353	−	0.698614i
$695$	−26.5314	−	90.3575i	−0.0381746	−	0.130011i
$696$	−309.101	+	84.2751i	−0.444110	+	0.121085i
$697$	−0.779501	+	5.42155i	−0.00111837	+	0.00777840i
$698$	−468.647	+	1596.07i	−0.671415	+	2.28663i
$699$	675.562	+	324.521i	0.966469	+	0.464264i
$700$	−74.5645			−0.106521
$701$	−282.246	+	961.241i	−0.402633	+	1.37124i	0.469914	+	0.882712i	$0.344285\pi$
$701$	−282.246	+	961.241i	−0.402633	+	1.37124i	−0.872547	+	0.488530i	$0.837533\pi$
$702$	197.694	+	192.569i	0.281615	+	0.274315i
$703$	−51.4685	+	112.700i	−0.0732127	+	0.160313i
$704$	−256.312	−	117.054i	−0.364079	−	0.166269i
$705$	−92.1094	−	742.777i	−0.130652	−	1.05358i
$706$	−1510.94	−	443.653i	−2.14015	−	0.628404i
$707$		−	103.993i		−	0.147091i
$708$	482.407	+	231.734i	0.681365	+	0.327308i
$709$	−405.170	−	118.969i	−0.571467	−	0.167798i	−0.0167832	−	0.999859i	$-0.505343\pi$
$709$	−405.170	−	118.969i	−0.571467	−	0.167798i	−0.554684	+	0.832061i	$0.687161\pi$
$710$	1399.67	+	201.242i	1.97137	+	0.283440i
$711$	24.6232	−	134.062i	0.0346317	−	0.188554i
$712$	331.034	−	97.2004i	0.464936	−	0.136517i
$713$	484.673	−	419.971i	0.679765	−	0.589020i
$714$	6.04774	−	3.72270i	0.00847023	−	0.00521386i
$715$	−149.628	+	96.1598i	−0.209269	+	0.134489i
$716$	−253.252	−	36.4121i	−0.353703	−	0.0508549i
$717$	613.273	+	996.298i	0.855332	+	1.38954i
$718$	382.255	−	837.022i	0.532389	−	1.16577i
$719$	−704.109	−	610.114i	−0.979289	−	0.848559i	0.00918338	−	0.999958i	$-0.497077\pi$
$719$	−704.109	−	610.114i	−0.979289	−	0.848559i	−0.988473	+	0.151399i	$0.951622\pi$
$720$	−933.261	−	171.412i	−1.29620	−	0.238072i
$721$	−14.6935	−	102.195i	−0.0203793	−	0.141741i
$722$	−795.114	−	363.116i	−1.10127	−	0.502931i
$723$	−222.211	−	512.698i	−0.307346	−	0.709126i
$724$	438.773	−	128.835i	0.606040	−	0.177949i
$725$	88.8914	+	302.736i	0.122609	+	0.417567i
$726$	−127.561	+	405.152i	−0.175704	+	0.558060i
$727$	−418.925	+	269.226i	−0.576237	+	0.370325i	−0.796063	−	0.605214i	$-0.793088\pi$
$727$	−418.925	+	269.226i	−0.576237	+	0.370325i	0.219825	+	0.975539i	$0.429451\pi$
$728$	27.9653	−	12.7713i	0.0384139	−	0.0175430i
$729$	−718.607	+	122.660i	−0.985743	+	0.168259i
$730$	−392.732	−	859.963i	−0.537989	−	1.17803i
$731$	−7.66572	−	1.10216i	−0.0104866	−	0.00150775i
$732$	−216.971	−	68.3127i	−0.296408	−	0.0933234i
$733$	198.067	−	228.582i	0.270214	−	0.311844i	−0.604383	−	0.796694i	$-0.706580\pi$
$733$	198.067	−	228.582i	0.270214	−	0.311844i	0.874597	+	0.484850i	$0.161126\pi$
$734$	242.795	−	377.797i	0.330784	−	0.514710i
$735$	12.0761	−	621.669i	0.0164300	−	0.845808i
$736$	−910.653			−1.23730
$737$	426.682	+	351.078i	0.578945	+	0.476360i
$738$	325.117	+	406.054i	0.440538	+	0.550208i
$739$	531.838	+	1164.56i	0.719673	+	1.57586i	0.814362	+	0.580357i	$0.197087\pi$
$739$	531.838	+	1164.56i	0.719673	+	1.57586i	−0.0946892	+	0.995507i	$0.530186\pi$
$740$	−203.745	+	317.034i	−0.275332	+	0.428424i
$741$	26.5629	+	61.2875i	0.0358474	+	0.0827092i
$742$	−116.650	−	811.318i	−0.157210	−	1.09342i
$743$	1198.93	+	172.380i	1.61363	+	0.232005i	0.889260	−	0.457402i	$-0.151220\pi$
$743$	1198.93	+	172.380i	1.61363	+	0.232005i	0.724374	+	0.689408i	$0.242129\pi$
$744$	−3.84403	+	197.889i	−0.00516671	+	0.265979i
$745$	−868.039	−	254.879i	−1.16515	−	0.342120i
$746$	−1530.73	+	699.060i	−2.05191	+	0.937077i
$747$	318.690	−	947.552i	0.426627	−	1.26848i
$748$	−0.933318	−	6.49137i	−0.00124775	−	0.00867830i
$749$	−39.0678	−	133.053i	−0.0521599	−	0.177640i
$750$	132.948	−	812.340i	0.177264	−	1.08312i
$751$	2.19078	−	2.52830i	0.00291716	−	0.00336658i	−0.754289	−	0.656542i	$-0.772018\pi$
$751$	2.19078	−	2.52830i	0.00291716	−	0.00336658i	0.757206	+	0.653176i	$0.226564\pi$
$752$	752.709	+	343.751i	1.00094	+	0.457115i
$753$	−186.622	+	592.738i	−0.247838	+	0.787169i
$754$	311.161	+	359.099i	0.412680	+	0.476258i
$755$	32.2702	+	27.9623i	0.0427420	+	0.0370362i
$756$	59.2387	−	290.639i	0.0783581	−	0.384444i
$757$	−159.421	−	102.454i	−0.210596	−	0.135342i	0.431091	−	0.902309i	$-0.358129\pi$
$757$	−159.421	−	102.454i	−0.210596	−	0.135342i	−0.641687	+	0.766967i	$0.721765\pi$
$758$	−673.728	−	96.8675i	−0.888824	−	0.127794i
$759$	−67.9937	−	548.307i	−0.0895833	−	0.722407i
$760$	−63.4243	−	40.7603i	−0.0834530	−	0.0536320i
$761$	−645.035	+	558.926i	−0.847616	+	0.734463i	−0.966010	−	0.258504i	$-0.916771\pi$
$761$	−645.035	+	558.926i	−0.847616	+	0.734463i	0.118395	+	0.992967i	$0.462225\pi$
$762$	−1600.82	−	261.992i	−2.10082	−	0.343821i
$763$	32.5473	+	37.5616i	0.0426570	+	0.0492289i
$764$	−6.15854	−	0.885465i	−0.00806092	−	0.00115899i
$765$	−4.87993	−	11.8868i	−0.00637900	−	0.0155383i
$766$	−379.187			−0.495022
$767$			217.307i			0.283320i
$768$	659.854	−	732.278i	0.859184	−	0.953487i
$769$	1112.82	−	715.168i	1.44710	−	0.929997i	0.447746	−	0.894161i	$-0.352227\pi$
$769$	1112.82	−	715.168i	1.44710	−	0.929997i	0.999358	−	0.0358361i	$-0.0114094\pi$
$770$	395.379	+	180.563i	0.513479	+	0.234498i
$771$	733.692	−	611.208i	0.951611	−	0.792746i
$772$	477.978	−	307.178i	0.619142	−	0.397899i
$773$	302.403	−	1029.89i	0.391207	−	1.33233i	−0.494940	−	0.868927i	$-0.664810\pi$
$773$	302.403	−	1029.89i	0.391207	−	1.33233i	0.886148	−	0.463403i	$-0.153372\pi$
$774$	−574.134	+	459.695i	−0.741775	+	0.593921i
$775$	194.920			0.251509
$776$	42.6221	−	145.158i	0.0549254	−	0.187059i
$777$	185.551	+	124.404i	0.238804	+	0.160108i
$778$	−192.139	−	221.740i	−0.246965	−	0.285013i
$779$	35.4698	+	120.799i	0.0455324	+	0.155069i
$780$	53.4443	+	196.021i	0.0685183	+	0.251309i
$781$	−651.193	−	418.496i	−0.833794	−	0.535847i
$782$	−8.16960	−	12.7121i	−0.0104471	−	0.0162559i
$783$	−1250.63	+	105.970i	−1.59723	+	0.135339i
$784$	578.305	+	371.654i	0.737634	+	0.474049i
$785$	981.304	+	448.146i	1.25007	+	0.570887i
$786$	−593.506	−	1369.37i	−0.755097	−	1.74220i
$787$	423.688	+	488.962i	0.538358	+	0.621298i	0.958131	−	0.286331i	$-0.0924357\pi$
$787$	423.688	+	488.962i	0.538358	+	0.621298i	−0.419773	+	0.907629i	$0.637890\pi$
$788$	−1092.38	+	157.060i	−1.38626	+	0.199315i
$789$	171.561	−	142.920i	0.217441	−	0.181141i
$790$	149.417	−	172.437i	0.189136	−	0.218275i
$791$	−14.6125	−	49.7655i	−0.0184734	−	0.0629146i
$792$	139.760	+	97.6903i	0.176465	+	0.123346i
$793$	−13.1447	−	91.4232i	−0.0165759	−	0.115288i
$794$	58.7302	+	91.3860i	0.0739675	+	0.115096i
$795$	−1482.79	−	28.8035i	−1.86514	−	0.0362308i
$796$	−923.030	−	271.026i	−1.15959	−	0.340485i
$797$	357.737	−	163.373i	0.448854	−	0.204985i	−0.178146	−	0.984004i	$-0.557010\pi$
$797$	357.737	−	163.373i	0.448854	−	0.204985i	0.627000	+	0.779019i	$0.284283\pi$
$798$	90.9023	−	135.583i	0.113913	−	0.169903i
$799$	1.59474	+	11.0917i	0.00199592	+	0.0138820i
$800$	−209.178	−	181.254i	−0.261472	−	0.226567i
$801$	1344.29	−	140.250i	1.67827	−	0.175094i
$802$	310.919	+	680.819i	0.387680	+	0.848901i
$803$			517.521i			0.644485i
$804$	528.906	−	344.470i	0.657843	−	0.428445i
$805$	440.464			0.547161
$806$	267.014	−	121.941i	0.331283	−	0.151292i
$807$	−12.5810	−	20.4386i	−0.0155898	−	0.0253266i
$808$	44.7218	−	51.6117i	0.0553487	−	0.0638758i
$809$	−349.355	+	50.2297i	−0.431836	+	0.0620886i	−0.354806	−	0.934940i	$-0.615453\pi$
$809$	−349.355	+	50.2297i	−0.431836	+	0.0620886i	−0.0770304	+	0.997029i	$0.524544\pi$
$810$	−1140.66	−	433.638i	−1.40822	−	0.535356i
$811$	−260.005	−	569.332i	−0.320598	−	0.702013i	0.678882	−	0.734247i	$-0.262465\pi$
$811$	−260.005	−	569.332i	−0.320598	−	0.702013i	−0.999480	+	0.0322349i	$0.989738\pi$
$812$	143.875	−	489.994i	0.177186	−	0.603441i
$813$	−1497.63	−	29.0919i	−1.84211	−	0.0357834i
$814$	394.611	−	253.601i	0.484780	−	0.311549i
$815$	−1367.40	+	196.603i	−1.67780	+	0.241231i
$816$	14.0196	+	2.29446i	0.0171809	+	0.00281184i
$817$	−170.802	+	50.1520i	−0.209060	+	0.0613855i
$818$	814.461	+	705.734i	0.995673	+	0.862756i
$819$	116.791	−	29.4181i	0.142602	−	0.0359195i
$820$	54.4993	+	379.051i	0.0664626	+	0.462257i
$821$	250.267	−	216.857i	0.304832	−	0.264138i	−0.488989	−	0.872290i	$-0.662634\pi$
$821$	250.267	−	216.857i	0.304832	−	0.264138i	0.793821	+	0.608152i	$0.208089\pi$
$822$	718.230	+	1657.14i	0.873759	+	2.01599i
$823$	−106.276	+	232.712i	−0.129133	+	0.282761i	−0.963144	−	0.268986i	$-0.913311\pi$
$823$	−106.276	+	232.712i	−0.129133	+	0.282761i	0.834011	+	0.551747i	$0.186039\pi$
$824$	36.6562	−	57.0381i	0.0444856	−	0.0692210i
$825$	93.5151	−	139.480i	0.113352	−	0.169066i
$826$	446.748	−	287.108i	0.540857	−	0.347588i
$827$	−852.410	+	1326.38i	−1.03073	+	1.60384i	−0.261136	+	0.965302i	$0.584097\pi$
$827$	−852.410	+	1326.38i	−1.03073	+	1.60384i	−0.769590	+	0.638538i	$0.779539\pi$
$828$	−620.755	−	114.014i	−0.749704	−	0.137698i
$829$	−1527.55	+	448.530i	−1.84265	+	0.541050i	−0.842649	+	0.538463i	$0.819005\pi$
$829$	−1527.55	+	448.530i	−1.84265	+	0.541050i	−0.999997	+	0.00258668i	$0.999177\pi$
$830$	1264.72	−	1095.88i	1.52376	−	1.32034i
$831$	18.6971	+	12.5356i	0.0224995	+	0.0150849i
$832$	−125.402	−	36.8214i	−0.150724	−	0.0442565i
$833$			9.30914i			0.0111754i
$834$	120.694	+	57.9781i	0.144717	+	0.0695181i
$835$	−131.643	−	38.6539i	−0.157656	−	0.0462921i
$836$	−81.4972	−	126.812i	−0.0974847	−	0.151689i
$837$	−154.856	+	759.762i	−0.185014	+	0.907721i
$838$	132.331	−	289.765i	0.157913	−	0.345781i
$839$	−453.660	−	705.908i	−0.540715	−	0.841369i	0.458156	−	0.888872i	$-0.348510\pi$
$839$	−453.660	−	705.908i	−0.540715	−	0.841369i	−0.998871	+	0.0475030i	$0.984874\pi$
$840$	−90.9994	+	100.987i	−0.108333	+	0.120223i
$841$	−1319.92			−1.56947
$842$		−	732.892i		−	0.870418i
$843$	−599.112	−	539.859i	−0.710691	−	0.640402i
$844$	13.3629	−	92.9410i	0.0158328	−	0.110120i
$845$	657.751	−	569.944i	0.778403	−	0.674490i
$846$	872.241	+	609.683i	1.03102	+	0.720666i
$847$	121.389	+	140.090i	0.143316	+	0.165396i
$848$	886.460	−	1379.36i	1.04535	−	1.62660i
$849$	17.9520	+	144.767i	0.0211449	+	0.170514i
$850$	0.653623	−	4.54604i	0.000768968	−	0.00534829i
$851$	256.989	−	399.882i	0.301985	−	0.469897i
$852$	−679.384	+	565.966i	−0.797399	+	0.664279i
$853$	−356.156	+	411.026i	−0.417533	+	0.481859i	−0.925084	−	0.379763i	$-0.876006\pi$
$853$	−356.156	+	411.026i	−0.417533	+	0.481859i	0.507551	+	0.861622i	$0.330551\pi$
$854$	−170.585	+	147.812i	−0.199748	+	0.173083i
$855$	−215.533	−	201.938i	−0.252086	−	0.236185i
$856$	37.8292	−	82.8345i	0.0441930	−	0.0967693i
$857$	233.305	+	202.160i	0.272235	+	0.235893i	0.780269	−	0.625444i	$-0.215082\pi$
$857$	233.305	+	202.160i	0.272235	+	0.235893i	−0.508034	+	0.861337i	$0.669628\pi$
$858$	40.8451	−	249.572i	0.0476050	−	0.290876i
$859$	−697.517	+	204.809i	−0.812010	+	0.238428i	−0.661272	−	0.750146i	$-0.729983\pi$
$859$	−697.517	+	204.809i	−0.812010	+	0.238428i	−0.150738	+	0.988574i	$0.548165\pi$
$860$	−535.954	+	77.0585i	−0.623202	+	0.0896029i
$861$	225.280	−	27.9362i	0.261649	−	0.0324462i
$862$	844.192	+	1848.52i	0.979342	+	2.14446i
$863$	422.627	−	1439.34i	0.489719	−	1.66783i	−0.229708	−	0.973260i	$-0.573777\pi$
$863$	422.627	−	1439.34i	0.489719	−	1.66783i	0.719427	−	0.694569i	$-0.244405\pi$
$864$	872.679	−	671.339i	1.01004	−	0.777013i
$865$	185.745	−	1291.89i	0.214735	−	1.49351i
$866$	−1449.48	+	208.404i	−1.67377	+	0.240652i
$867$	−344.704	−	795.321i	−0.397582	−	0.917325i
$868$	−265.405	−	170.565i	−0.305766	−	0.196504i
$869$	−113.614	+	51.8858i	−0.130741	+	0.0597074i
$870$	−1893.82	−	909.738i	−2.17681	−	1.04568i
$871$	219.069	+	133.018i	0.251515	+	0.152719i
$872$			32.6385i			0.0374295i
$873$	266.954	−	529.142i	0.305789	−	0.606119i
$874$	−292.196	−	187.783i	−0.334320	−	0.214854i
$875$	−271.483	−	235.241i	−0.310266	−	0.268847i
$876$	563.886	+	177.538i	0.643705	+	0.202669i
$877$	113.342	−	788.309i	0.129238	−	0.898870i	−0.817285	−	0.576234i	$-0.804522\pi$
$877$	113.342	−	788.309i	0.129238	−	0.898870i	0.946523	−	0.322636i	$-0.104569\pi$
$878$	1260.14	−	575.486i	1.43524	−	0.655451i
$879$	−1176.76	−	1060.38i	−1.33875	−	1.20634i
$880$	361.198	+	790.913i	0.410452	+	0.898765i
$881$	124.965	+	194.449i	0.141844	+	0.220714i	0.904906	−	0.425612i	$-0.139941\pi$
$881$	124.965	+	194.449i	0.141844	+	0.220714i	−0.763062	+	0.646326i	$0.776305\pi$
$882$	645.155	+	604.461i	0.731469	+	0.685329i
$883$	−517.714	+	152.014i	−0.586312	+	0.172157i	−0.561417	−	0.827533i	$-0.689744\pi$
$883$	−517.714	+	152.014i	−0.586312	+	0.172157i	−0.0248956	+	0.999690i	$0.507925\pi$
$884$	−0.856994	−	2.91865i	−0.000969450	−	0.00330164i
$885$	−382.108	−	881.622i	−0.431760	−	0.996183i
$886$	774.398	−	1695.70i	0.874038	−	1.91388i
$887$	−491.523	+	70.6704i	−0.554141	+	0.0796735i	−0.413696	−	0.910415i	$-0.635762\pi$
$887$	−491.523	+	70.6704i	−0.554141	+	0.0796735i	−0.140445	+	0.990088i	$0.544853\pi$
$888$	38.5893	+	141.536i	0.0434564	+	0.159388i
$889$	−463.574	+	534.993i	−0.521456	+	0.601792i
$890$	2058.03	+	939.871i	2.31239	+	1.05603i
$891$	469.373	+	475.317i	0.526794	+	0.533464i
$892$	78.5209	−	546.125i	0.0880279	−	0.612247i
$893$	139.253	+	216.682i	0.155938	+	0.242645i
$894$	1095.42	−	674.288i	1.22530	−	0.754237i
$895$	300.821	+	347.165i	0.336112	+	0.387894i
$896$	−70.7835	−	241.066i	−0.0789994	−	0.269047i
$897$	−67.4106	−	247.246i	−0.0751511	−	0.275636i
$898$	−88.6695	+	616.710i	−0.0987411	+	0.686759i
$899$	−376.105	+	1280.90i	−0.418360	+	1.42480i
$900$	−119.895	−	149.742i	−0.133217	−	0.166380i
$901$	22.2039			0.0246436
$902$	134.289	−	457.347i	0.148879	−	0.507036i
$903$	39.5000	+	318.531i	0.0437431	+	0.352747i
$904$	14.1492	−	30.9825i	0.0156518	−	0.0342726i
$905$	−746.839	−	341.070i	−0.825236	−	0.376873i
$906$	−60.2505	+	7.47147i	−0.0665017	+	0.00824666i
$907$	1271.97	+	373.485i	1.40240	+	0.411780i	0.893506	−	0.449051i	$-0.148238\pi$
$907$	1271.97	+	373.485i	1.40240	+	0.411780i	0.508889	+	0.860832i	$0.330056\pi$
$908$		−	139.258i		−	0.153368i
$909$	208.842	−	167.215i	0.229749	−	0.183955i
$910$	193.442	+	56.7996i	0.212573	+	0.0624172i
$911$	115.931	+	16.6684i	0.127257	+	0.0182968i	0.205649	−	0.978626i	$-0.434069\pi$
$911$	115.931	+	16.6684i	0.127257	+	0.0182968i	−0.0783918	+	0.996923i	$0.524979\pi$
$912$	315.036	−	85.8935i	0.345435	−	0.0941815i
$913$	−878.964	+	258.087i	−0.962721	+	0.282680i
$914$	−1001.68	+	867.957i	−1.09593	+	0.949625i
$915$	214.085	+	347.794i	0.233973	+	0.380103i
$916$	−798.979	+	513.473i	−0.872248	+	0.560560i
$917$	−644.683	−	92.6915i	−0.703035	−	0.101081i
$918$	17.2004	+	6.15937i	0.0187368	+	0.00670955i
$919$	−610.860	+	1337.60i	−0.664701	+	1.45549i	0.213375	+	0.976970i	$0.431554\pi$
$919$	−610.860	+	1337.60i	−0.664701	+	1.45549i	−0.878076	+	0.478521i	$0.841173\pi$
$920$	218.601	+	189.419i	0.237610	+	0.205890i
$921$	−779.064	+	212.409i	−0.845889	+	0.230628i
$922$	206.622	+	1437.09i	0.224102	+	1.55867i
$923$	−326.595	−	149.151i	−0.353841	−	0.161594i
$924$	−249.384	+	108.087i	−0.269896	+	0.116977i
$925$	138.622	−	40.7031i	0.149862	−	0.0440033i
$926$	−30.0929	−	102.487i	−0.0324978	−	0.110677i
$927$	181.605	−	193.831i	0.195906	−	0.209095i
$928$	1594.71	−	1024.86i	1.71844	−	1.10437i
$929$	38.8765	−	17.7543i	0.0418477	−	0.0191112i	−0.394381	−	0.918947i	$-0.629041\pi$
$929$	38.8765	−	17.7543i	0.0418477	−	0.0191112i	0.436229	+	0.899836i	$0.356314\pi$
$930$	−868.867	+	964.232i	−0.934266	+	1.03681i
$931$	88.8887	+	194.639i	0.0954766	+	0.209065i
$932$	−776.517	−	111.646i	−0.833173	−	0.119792i
$933$	−386.126	+	1226.39i	−0.413854	+	1.31446i
$934$	−201.338	+	232.356i	−0.215565	+	0.248775i
$935$	−6.36578	+	9.90534i	−0.00680832	+	0.0105940i
$936$	70.6141	+	35.6251i	0.0754424	+	0.0380610i
$937$	792.248			0.845515			0.422758	−	0.906243i	$-0.361062\pi$
$937$	792.248			0.845515			0.422758	+	0.906243i	$0.361062\pi$
$938$	−15.9719	−	626.117i	−0.0170276	−	0.667502i
$939$	−793.865	+	1652.61i	−0.845437	+	1.75996i
$940$	325.460	+	712.658i	0.346234	+	0.758146i
$941$	−221.435	+	344.560i	−0.235319	+	0.366163i	−0.938749	−	0.344601i	$-0.888014\pi$
$941$	−221.435	+	344.560i	−0.235319	+	0.366163i	0.703430	+	0.710764i	$0.251651\pi$
$942$	−1407.37	+	609.974i	−1.49402	+	0.647531i
$943$	−68.7413	−	478.106i	−0.0728963	−	0.507005i
$944$	1051.50	+	151.183i	1.11388	+	0.160151i
$945$	−422.097	+	324.713i	−0.446663	+	0.343612i
$946$	646.659	+	189.876i	0.683572	+	0.200715i
$947$	−1207.66	+	551.522i	−1.27525	+	0.582388i	−0.933896	−	0.357545i	$-0.883614\pi$
$947$	−1207.66	+	551.522i	−1.27525	+	0.582388i	−0.341357	+	0.939934i	$0.610887\pi$
$948$	17.5584	+	141.592i	0.0185215	+	0.149359i
$949$	34.1617	+	237.600i	0.0359976	+	0.250369i
$950$	−29.7419	−	101.292i	−0.0313073	−	0.106623i
$951$	1214.88	+	198.828i	1.27748	+	0.209072i
$952$	1.33279	−	1.53812i	0.00139999	−	0.00161567i
$953$	−524.318	−	239.448i	−0.550177	−	0.251257i	0.120875	−	0.992668i	$-0.461430\pi$
$953$	−524.318	−	239.448i	−0.550177	−	0.251257i	−0.671052	+	0.741410i	$0.734157\pi$
$954$	1441.74	−	1538.81i	1.51126	−	1.61301i
$955$	7.31532	+	8.44233i	0.00766002	+	0.00884013i
$956$	−925.502	−	801.952i	−0.968098	−	0.838862i
$957$	736.138	+	883.658i	0.769214	+	0.923363i
$958$	−778.144	−	500.083i	−0.812259	−	0.522007i
$959$	780.162	+	112.170i	0.813516	+	0.116966i
$960$	573.508	−	71.1188i	0.597404	−	0.0740821i
$961$	−114.648	−	73.6799i	−0.119301	−	0.0766700i
$962$	164.430	−	142.479i	0.170925	−	0.148108i
$963$	204.381	−	292.397i	0.212234	−	0.303631i
$964$	383.031	+	442.042i	0.397335	+	0.458549i
$965$	−1009.72	−	145.176i	−1.04634	−	0.150441i
$966$	−419.234	+	465.248i	−0.433990	+	0.481624i
$967$	308.777			0.319315			0.159657	−	0.987173i	$-0.448961\pi$
$967$	308.777			0.319315			0.159657	+	0.987173i	$0.448961\pi$
$968$			121.729i			0.125753i
$969$	3.28499	+	2.96010i	0.00339008	+	0.00305480i
$970$	834.603	−	536.367i	0.860416	−	0.552956i
$971$	−1643.70	−	750.652i	−1.69279	−	0.773071i	−0.998579	−	0.0532982i	$-0.983027\pi$
$971$	−1643.70	−	750.652i	−1.69279	−	0.773071i	−0.694210	−	0.719772i	$-0.744246\pi$
$972$	678.921	−	348.365i	0.698479	−	0.358400i
$973$	49.1572	−	31.5914i	0.0505213	−	0.0324681i
$974$	219.435	−	747.328i	0.225293	−	0.767278i
$975$	33.7267	−	70.2097i	0.0345915	−	0.0720100i
$976$	−451.521			−0.462624
$977$	−295.098	+	1005.01i	−0.302045	+	1.02867i	0.658969	+	0.752170i	$0.270993\pi$
$977$	−295.098	+	1005.01i	−0.302045	+	1.02867i	−0.961014	+	0.276500i	$0.910825\pi$
$978$	1093.83	−	1631.47i	1.11844	−	1.66817i
$979$	−811.052	−	936.004i	−0.828450	−	0.956082i
$980$	183.367	+	624.491i	0.187109	+	0.637235i
$981$	−23.0981	+	125.759i	−0.0235455	+	0.128195i
$982$	−615.731	−	395.706i	−0.627017	−	0.402959i
$983$	−740.801	−	1152.71i	−0.753613	−	1.17264i	−0.980076	−	0.198624i	$-0.936353\pi$
$983$	−740.801	−	1152.71i	−0.753613	−	1.17264i	0.226463	−	0.974020i	$-0.427284\pi$
$984$	123.819	+	83.0155i	0.125833	+	0.0843653i
$985$	1666.88	+	1071.24i	1.69227	+	1.08755i
$986$	28.6127	+	13.0670i	0.0290190	+	0.0132525i
$987$	426.118	−	184.686i	0.431730	−	0.187118i
$988$	−45.7872	−	52.8413i	−0.0463433	−	0.0534831i
$989$	676.011	−	97.1957i	0.683530	−	0.0982768i
$990$	273.132	+	1084.34i	0.275891	+	1.09530i
$991$	91.6052	−	105.718i	0.0924371	−	0.106678i	−0.707646	−	0.706567i	$-0.750243\pi$
$991$	91.6052	−	105.718i	0.0924371	−	0.106678i	0.800084	+	0.599889i	$0.204788\pi$
$992$	−329.932	−	1123.65i	−0.332593	−	1.13271i
$993$	121.116	−	740.043i	0.121970	−	0.745260i
$994$	124.870	+	868.487i	0.125623	+	0.873730i
$995$	933.783	+	1453.00i	0.938476	+	1.46030i
$996$	−20.3236	+	1046.25i	−0.0204052	+	1.05045i
$997$	−622.104	−	182.666i	−0.623976	−	0.183216i	−0.0455651	−	0.998961i	$-0.514509\pi$
$997$	−622.104	−	182.666i	−0.623976	−	0.183216i	−0.578411	+	0.815745i	$0.696327\pi$
$998$	−1519.47	+	693.918i	−1.52251	+	0.695309i
$999$	48.5234	+	572.661i	0.0485720	+	0.573234i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.k.a.14.10	✓	440
3.2	odd	2	inner	201.3.k.a.14.35	yes	440
67.24	even	11	inner	201.3.k.a.158.35	yes	440
201.158	odd	22	inner	201.3.k.a.158.10	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.k.a.14.10	✓	440	1.1	even	1	trivial
201.3.k.a.14.35	yes	440	3.2	odd	2	inner
201.3.k.a.158.10	yes	440	201.158	odd	22	inner
201.3.k.a.158.35	yes	440	67.24	even	11	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.k (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.43065 + 1.11004i) q^{2} +(-2.55478 + 1.57260i) q^{3} +(2.05643 - 2.37324i) q^{4} +(-5.58064 + 0.802375i) q^{5} +(4.46414 - 6.65836i) q^{6} +(-1.45327 - 3.18223i) q^{7} +(0.647241 - 2.20430i) q^{8} +(4.05385 - 8.03532i) q^{9} +O(q^{10})\)	\(q+(-2.43065 + 1.11004i) q^{2} +(-2.55478 + 1.57260i) q^{3} +(2.05643 - 2.37324i) q^{4} +(-5.58064 + 0.802375i) q^{5} +(4.46414 - 6.65836i) q^{6} +(-1.45327 - 3.18223i) q^{7} +(0.647241 - 2.20430i) q^{8} +(4.05385 - 8.03532i) q^{9} +(12.6739 - 8.14504i) q^{10} +(-8.16310 + 1.17368i) q^{11} +(-1.52156 + 9.29706i) q^{12} +(-3.67030 + 1.07770i) q^{13} +(7.06480 + 6.12168i) q^{14} +(12.9955 - 10.8260i) q^{15} +(2.66126 + 18.5095i) q^{16} +(-0.191379 + 0.165831i) q^{17} +(-0.933966 + 24.0310i) q^{18} +(-2.41799 + 5.29466i) q^{19} +(-9.57195 + 14.8942i) q^{20} +(8.71717 + 5.84448i) q^{21} +(18.5388 - 11.9142i) q^{22} +(12.0733 - 18.7865i) q^{23} +(1.81292 + 6.64937i) q^{24} +(6.51245 - 1.91223i) q^{25} +(7.72492 - 6.69368i) q^{26} +(2.27963 + 26.9036i) q^{27} +(-10.5407 - 3.09504i) q^{28} +46.4857i q^{29} +(-19.5703 + 40.7398i) q^{30} +(27.5546 + 8.09077i) q^{31} +(-22.0467 - 34.3053i) q^{32} +(19.0092 - 15.8358i) q^{33} +(0.281097 - 0.615516i) q^{34} +(10.6635 + 16.5928i) q^{35} +(-10.7333 - 26.1448i) q^{36} +21.2857 q^{37} -15.5535i q^{38} +(7.68203 - 8.52519i) q^{39} +(-1.84335 + 12.8207i) q^{40} +(16.3466 - 14.1644i) q^{41} +(-27.6760 - 4.52947i) q^{42} +(20.0276 + 23.1130i) q^{43} +(-14.0014 + 21.7866i) q^{44} +(-16.1758 + 48.0949i) q^{45} +(-8.49229 + 59.0652i) q^{46} +(23.9239 - 37.2263i) q^{47} +(-35.9070 - 43.1027i) q^{48} +(24.0736 - 27.7824i) q^{49} +(-13.7068 + 11.8770i) q^{50} +(0.228147 - 0.724626i) q^{51} +(-4.99006 + 10.9267i) q^{52} +(-66.2659 - 57.4198i) q^{53} +(-35.4051 - 62.8627i) q^{54} +(44.6136 - 13.0997i) q^{55} +(-7.95520 + 1.14379i) q^{56} +(-2.14894 - 17.3292i) q^{57} +(-51.6011 - 112.991i) q^{58} +(16.0048 - 54.5074i) q^{59} +(1.03157 - 53.1045i) q^{60} +(-3.43629 + 23.9000i) q^{61} +(-75.9567 + 10.9209i) q^{62} +(-31.4615 - 1.22276i) q^{63} +(28.7429 + 18.4720i) q^{64} +(19.6179 - 8.95919i) q^{65} +(-28.6264 + 59.5923i) q^{66} +(-45.1527 - 49.4999i) q^{67} +0.795209i q^{68} +(-1.30114 + 66.9819i) q^{69} +(-44.3380 - 28.4943i) q^{70} +(70.9353 + 61.4658i) q^{71} +(-15.0884 - 14.1367i) q^{72} +(8.93059 - 62.1136i) q^{73} +(-51.7380 + 23.6280i) q^{74} +(-13.6307 + 15.1268i) q^{75} +(7.59309 + 16.6265i) q^{76} +(15.5981 + 24.2711i) q^{77} +(-9.20901 + 29.2491i) q^{78} +(14.5315 - 4.26683i) q^{79} +(-29.7031 - 101.160i) q^{80} +(-48.1326 - 65.1479i) q^{81} +(-24.0098 + 52.5741i) q^{82} +(109.948 - 15.8082i) q^{83} +(31.7966 - 8.66922i) q^{84} +(0.934961 - 1.07900i) q^{85} +(-74.3364 - 33.9483i) q^{86} +(-73.1035 - 118.761i) q^{87} +(-2.69636 + 18.7536i) q^{88} +(81.1915 + 126.337i) q^{89} +(-14.0697 - 134.858i) q^{90} +(8.76342 + 10.1135i) q^{91} +(-19.7569 - 67.2859i) q^{92} +(-83.1197 + 22.6623i) q^{93} +(-16.8279 + 117.041i) q^{94} +(9.24563 - 31.4877i) q^{95} +(110.273 + 52.9721i) q^{96} +65.8520 q^{97} +(-27.6749 + 94.2521i) q^{98} +(-23.6611 + 70.3510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 11 q^{3} + 70 q^{4} - 17 q^{6} - 30 q^{7} - 15 q^{9}+O(q^{10}) \) 440 * q - 11 * q^3 + 70 * q^4 - 17 * q^6 - 30 * q^7 - 15 * q^9	\( 440 q - 11 q^{3} + 70 q^{4} - 17 q^{6} - 30 q^{7} - 15 q^{9} - 34 q^{10} - 123 q^{12} + 10 q^{13} + 19 q^{15} - 226 q^{16} - 33 q^{18} - 100 q^{19} + 85 q^{21} - 454 q^{22} - 251 q^{24} + 142 q^{25} - 53 q^{27} + 642 q^{28} - 80 q^{30} - 130 q^{31} + 104 q^{33} + 26 q^{34} + 67 q^{36} - 144 q^{37} + 117 q^{39} - 182 q^{40} + 193 q^{42} - 156 q^{43} + 341 q^{45} - 746 q^{46} - 485 q^{48} - 354 q^{49} - 125 q^{51} + 1130 q^{52} + 272 q^{54} - 590 q^{55} + 15 q^{57} - 274 q^{58} - 217 q^{60} - 1134 q^{61} + 279 q^{63} + 58 q^{64} + 1288 q^{66} - 87 q^{69} + 1038 q^{70} - 977 q^{72} + 1208 q^{73} - 751 q^{75} + 1126 q^{76} - 11 q^{78} + 678 q^{79} + 125 q^{81} + 510 q^{82} + 191 q^{84} + 166 q^{85} + 1080 q^{87} + 62 q^{88} - 105 q^{90} + 550 q^{91} + 635 q^{93} + 986 q^{94} - 1632 q^{96} - 112 q^{97} - 500 q^{99}+O(q^{100}) \) 440 * q - 11 * q^3 + 70 * q^4 - 17 * q^6 - 30 * q^7 - 15 * q^9 - 34 * q^10 - 123 * q^12 + 10 * q^13 + 19 * q^15 - 226 * q^16 - 33 * q^18 - 100 * q^19 + 85 * q^21 - 454 * q^22 - 251 * q^24 + 142 * q^25 - 53 * q^27 + 642 * q^28 - 80 * q^30 - 130 * q^31 + 104 * q^33 + 26 * q^34 + 67 * q^36 - 144 * q^37 + 117 * q^39 - 182 * q^40 + 193 * q^42 - 156 * q^43 + 341 * q^45 - 746 * q^46 - 485 * q^48 - 354 * q^49 - 125 * q^51 + 1130 * q^52 + 272 * q^54 - 590 * q^55 + 15 * q^57 - 274 * q^58 - 217 * q^60 - 1134 * q^61 + 279 * q^63 + 58 * q^64 + 1288 * q^66 - 87 * q^69 + 1038 * q^70 - 977 * q^72 + 1208 * q^73 - 751 * q^75 + 1126 * q^76 - 11 * q^78 + 678 * q^79 + 125 * q^81 + 510 * q^82 + 191 * q^84 + 166 * q^85 + 1080 * q^87 + 62 * q^88 - 105 * q^90 + 550 * q^91 + 635 * q^93 + 986 * q^94 - 1632 * q^96 - 112 * q^97 - 500 * q^99

Introduction

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