LMFDB - Embedded newform 151.3.i.a.23.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [151,3,Mod(23,151)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("151.23"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(151, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([23])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 151 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	151.i (of order $30$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.11445199184$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$24$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			23.7
Character	$\chi$	$=$	151.23
Dual form			151.3.i.a.46.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.07636 + 1.86432i) q^{2} +(-3.53417 - 1.14832i) q^{3} +(-0.317116 - 0.549260i) q^{4} +(3.75572 - 1.67215i) q^{5} +(5.94489 - 5.35281i) q^{6} +(5.17823 + 11.6305i) q^{7} -7.24558 q^{8} +(3.89059 + 2.82668i) q^{9} +(-0.925096 + 8.80170i) q^{10} +(-11.5471 - 2.45441i) q^{11} +(0.490014 + 2.30533i) q^{12} +(-0.257314 - 1.21057i) q^{13} +(-27.2566 - 2.86478i) q^{14} +(-15.1935 + 1.59691i) q^{15} +(9.06734 - 15.7051i) q^{16} +(1.06212 + 10.1054i) q^{17} +(-9.45752 + 4.21076i) q^{18} -32.5891 q^{19} +(-2.10945 - 1.53260i) q^{20} +(-4.94520 - 47.0504i) q^{21} +(17.0046 - 18.8856i) q^{22} +(-19.6368 - 11.3373i) q^{23} +(25.6071 + 8.32027i) q^{24} +(-5.41892 + 6.01833i) q^{25} +(2.53384 + 0.823294i) q^{26} +(9.15407 + 12.5995i) q^{27} +(4.74607 - 6.53240i) q^{28} +(1.42469 + 4.38475i) q^{29} +(13.3766 - 30.0444i) q^{30} +(3.02798 + 28.8093i) q^{31} +(5.02834 + 8.70934i) q^{32} +(37.9909 + 21.9341i) q^{33} +(-19.9828 - 8.89691i) q^{34} +(38.8959 + 35.0221i) q^{35} +(0.318816 - 3.03333i) q^{36} +(5.65955 + 6.28557i) q^{37} +(35.0777 - 60.7564i) q^{38} +(-0.480729 + 4.57383i) q^{39} +(-27.2124 + 12.1157i) q^{40} +(-31.6572 - 10.2860i) q^{41} +(93.0397 + 41.4240i) q^{42} +(-6.98561 - 3.11019i) q^{43} +(2.31365 + 7.12068i) q^{44} +(19.3386 + 4.11055i) q^{45} +(42.2726 - 24.4061i) q^{46} +(-27.1605 + 5.77314i) q^{47} +(-50.0801 + 45.0923i) q^{48} +(-75.6668 + 84.0365i) q^{49} +(-5.38733 - 16.5805i) q^{50} +(7.85051 - 36.9337i) q^{51} +(-0.583317 + 0.525221i) q^{52} +(90.4935 - 29.4031i) q^{53} +(-33.3425 + 3.50444i) q^{54} +(-47.4717 + 10.0904i) q^{55} +(-37.5192 - 84.2696i) q^{56} +(115.176 + 37.4228i) q^{57} +(-9.70806 - 2.06351i) q^{58} +88.7697 q^{59} +(5.69523 + 7.83881i) q^{60} +(21.4787 + 19.3395i) q^{61} +(-56.9689 - 25.3642i) q^{62} +(-12.7293 + 59.8867i) q^{63} +50.8894 q^{64} +(-2.99065 - 4.11628i) q^{65} +(-81.7841 + 47.2181i) q^{66} +(51.8869 + 71.4162i) q^{67} +(5.21366 - 3.78794i) q^{68} +(56.3809 + 62.6173i) q^{69} +(-107.158 + 34.8179i) q^{70} +(-27.3594 - 2.87559i) q^{71} +(-28.1896 - 20.4809i) q^{72} +(55.5258 - 76.4247i) q^{73} +(-17.8100 + 3.78564i) q^{74} +(26.0624 - 15.0471i) q^{75} +(10.3345 + 17.8999i) q^{76} +(-31.2474 - 147.008i) q^{77} +(-8.00962 - 5.81933i) q^{78} +(-72.5209 + 99.8164i) q^{79} +(7.79305 - 74.1459i) q^{80} +(-31.2585 - 96.2036i) q^{81} +(53.2510 - 47.9474i) q^{82} +(-3.30268 - 4.54575i) q^{83} +(-24.2747 + 17.6366i) q^{84} +(20.8867 + 36.1769i) q^{85} +(13.3174 - 9.67568i) q^{86} -17.1325i q^{87} +(83.6653 + 17.7836i) q^{88} +(-21.0468 + 47.2719i) q^{89} +(-28.4788 + 31.6289i) q^{90} +(12.7470 - 9.26126i) q^{91} +14.3809i q^{92} +(22.3810 - 105.294i) q^{93} +(18.4716 - 56.8497i) q^{94} +(-122.396 + 54.4940i) q^{95} +(-7.76990 - 36.5545i) q^{96} +(-8.83203 - 84.0311i) q^{97} +(-75.2256 - 231.521i) q^{98} +(-37.9871 - 42.1890i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 5 q^{2} - 10 q^{3} - 181 q^{4} - 9 q^{5} + 13 q^{6} - 31 q^{7} + 80 q^{8} + 124 q^{9} + 41 q^{10} + 25 q^{11} + 55 q^{12} - 28 q^{13} + 7 q^{14} - 34 q^{15} - 321 q^{16} - 82 q^{17} - 194 q^{18}+ \cdots - 1441 q^{99}+O(q^{100}) $ 192 * q - 5 * q^2 - 10 * q^3 - 181 * q^4 - 9 * q^5 + 13 * q^6 - 31 * q^7 + 80 * q^8 + 124 * q^9 + 41 * q^10 + 25 * q^11 + 55 * q^12 - 28 * q^13 + 7 * q^14 - 34 * q^15 - 321 * q^16 - 82 * q^17 - 194 * q^18 - 72 * q^19 + 127 * q^20 - 38 * q^21 - 114 * q^22 + 165 * q^23 - 55 * q^24 + 203 * q^25 - 125 * q^26 + 155 * q^27 + 50 * q^28 + 55 * q^29 + 253 * q^30 + 108 * q^31 - 40 * q^32 + 117 * q^33 - 123 * q^34 + 186 * q^35 - 503 * q^36 - 377 * q^37 - 128 * q^38 + 261 * q^39 - 650 * q^40 + 60 * q^41 + 1000 * q^42 + 150 * q^43 - 274 * q^44 - 41 * q^45 + 93 * q^46 - 135 * q^47 - 644 * q^48 - 293 * q^49 + 350 * q^50 - 166 * q^51 + 606 * q^52 + 225 * q^53 + 382 * q^54 + 458 * q^55 - 713 * q^56 + 20 * q^57 + 216 * q^58 + 368 * q^59 - 120 * q^60 - 128 * q^61 - 522 * q^62 - 717 * q^63 + 788 * q^64 + 445 * q^65 + 759 * q^66 + 130 * q^67 + 218 * q^68 - 127 * q^69 - 1025 * q^70 - 247 * q^71 + 396 * q^72 + 350 * q^73 + 86 * q^74 - 882 * q^75 + 145 * q^76 - 260 * q^77 + 564 * q^78 - 1030 * q^79 + 151 * q^80 - 506 * q^81 + 268 * q^82 + 250 * q^83 - 320 * q^84 - 466 * q^85 - 294 * q^86 - 253 * q^88 - 479 * q^89 + 1861 * q^90 + 1252 * q^91 - 863 * q^93 + 7 * q^94 - 583 * q^95 + 1067 * q^96 - 278 * q^97 + 554 * q^98 - 1441 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/151\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{23}{30}\right)$

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 $

$2$	−1.07636	+	1.86432i	−0.538182	+	0.932158i	0.460820	+	0.887493i	$0.347555\pi$
$2$	−1.07636	+	1.86432i	−0.538182	+	0.932158i	−0.999002	+	0.0446645i	$0.985778\pi$
$3$	−3.53417	−	1.14832i	−1.17806	−	0.382774i	−0.346413	−	0.938082i	$-0.612601\pi$
$3$	−3.53417	−	1.14832i	−1.17806	−	0.382774i	−0.831645	+	0.555308i	$0.812601\pi$
$4$	−0.317116	−	0.549260i	−0.0792789	−	0.137315i
$5$	3.75572	−	1.67215i	0.751144	−	0.334431i	0.00479771	−	0.999988i	$-0.498473\pi$
$5$	3.75572	−	1.67215i	0.751144	−	0.334431i	0.746347	+	0.665558i	$0.231806\pi$
$6$	5.94489	−	5.35281i	0.990815	−	0.892134i
$7$	5.17823	+	11.6305i	0.739747	+	1.66150i	0.749901	+	0.661550i	$0.230101\pi$
$7$	5.17823	+	11.6305i	0.739747	+	1.66150i	−0.0101549	+	0.999948i	$0.503232\pi$
$8$	−7.24558			−0.905697
$9$	3.89059	+	2.82668i	0.432288	+	0.314076i
$10$	−0.925096	+	8.80170i	−0.0925096	+	0.880170i
$11$	−11.5471	−	2.45441i	−1.04973	−	0.223128i	−0.349423	−	0.936965i	$-0.613622\pi$
$11$	−11.5471	−	2.45441i	−1.04973	−	0.223128i	−0.700312	+	0.713837i	$0.746956\pi$
$12$	0.490014	+	2.30533i	0.0408345	+	0.192111i
$13$	−0.257314	−	1.21057i	−0.0197933	−	0.0931204i	0.967142	−	0.254236i	$-0.0818241\pi$
$13$	−0.257314	−	1.21057i	−0.0197933	−	0.0931204i	−0.986936	+	0.161116i	$0.948491\pi$
$14$	−27.2566	−	2.86478i	−1.94690	−	0.204627i
$15$	−15.1935	+	1.59691i	−1.01290	+	0.106460i
$16$	9.06734	−	15.7051i	0.566709	−	0.981568i
$17$	1.06212	+	10.1054i	0.0624774	+	0.594433i	0.980310	+	0.197465i	$0.0632709\pi$
$17$	1.06212	+	10.1054i	0.0624774	+	0.594433i	−0.917833	+	0.396968i	$0.870062\pi$
$18$	−9.45752	+	4.21076i	−0.525418	+	0.233931i
$19$	−32.5891			−1.71522			−0.857608	−	0.514304i	$-0.828050\pi$
$19$	−32.5891			−1.71522			−0.857608	+	0.514304i	$0.828050\pi$
$20$	−2.10945	−	1.53260i	−0.105472	−	0.0766301i
$21$	−4.94520	−	47.0504i	−0.235486	−	2.24050i
$22$	17.0046	−	18.8856i	0.772938	−	0.858435i
$23$	−19.6368	−	11.3373i	−0.853772	−	0.492926i	0.00814959	−	0.999967i	$-0.497406\pi$
$23$	−19.6368	−	11.3373i	−0.853772	−	0.492926i	−0.861922	+	0.507041i	$0.830739\pi$
$24$	25.6071	+	8.32027i	1.06696	+	0.346678i
$25$	−5.41892	+	6.01833i	−0.216757	+	0.240733i
$26$	2.53384	+	0.823294i	0.0974553	+	0.0316652i
$27$	9.15407	+	12.5995i	0.339040	+	0.466648i
$28$	4.74607	−	6.53240i	0.169502	−	0.233300i
$29$	1.42469	+	4.38475i	0.0491274	+	0.151198i	0.972611	−	0.232440i	$-0.0746709\pi$
$29$	1.42469	+	4.38475i	0.0491274	+	0.151198i	−0.923483	+	0.383638i	$0.874671\pi$
$30$	13.3766	−	30.0444i	0.445888	−	1.00148i
$31$	3.02798	+	28.8093i	0.0976768	+	0.929333i	0.928133	+	0.372249i	$0.121413\pi$
$31$	3.02798	+	28.8093i	0.0976768	+	0.929333i	−0.830456	+	0.557084i	$0.811920\pi$
$32$	5.02834	+	8.70934i	0.157136	+	0.272167i
$33$	37.9909	+	21.9341i	1.15124	+	0.664669i
$34$	−19.9828	−	8.89691i	−0.587729	−	0.261674i
$35$	38.8959	+	35.0221i	1.11131	+	1.00063i
$36$	0.318816	−	3.03333i	0.00885601	−	0.0842593i
$37$	5.65955	+	6.28557i	0.152961	+	0.169880i	0.814755	−	0.579805i	$-0.196871\pi$
$37$	5.65955	+	6.28557i	0.152961	+	0.169880i	−0.661794	+	0.749686i	$0.730205\pi$
$38$	35.0777	−	60.7564i	0.923098	−	1.59885i
$39$	−0.480729	+	4.57383i	−0.0123264	+	0.117278i
$40$	−27.2124	+	12.1157i	−0.680309	+	0.302893i
$41$	−31.6572	−	10.2860i	−0.772126	−	0.250879i	−0.103651	−	0.994614i	$-0.533052\pi$
$41$	−31.6572	−	10.2860i	−0.772126	−	0.250879i	−0.668475	+	0.743735i	$0.733052\pi$
$42$	93.0397	+	41.4240i	2.21523	+	0.986285i
$43$	−6.98561	−	3.11019i	−0.162456	−	0.0723300i	0.323898	−	0.946092i	$-0.395007\pi$
$43$	−6.98561	−	3.11019i	−0.162456	−	0.0723300i	−0.486354	+	0.873762i	$0.661673\pi$
$44$	2.31365	+	7.12068i	0.0525830	+	0.161834i
$45$	19.3386	+	4.11055i	0.429747	+	0.0913456i
$46$	42.2726	−	24.4061i	0.918969	−	0.530567i
$47$	−27.1605	+	5.77314i	−0.577882	+	0.122833i	−0.487575	−	0.873081i	$-0.662118\pi$
$47$	−27.1605	+	5.77314i	−0.577882	+	0.122833i	−0.0903075	+	0.995914i	$0.528785\pi$
$48$	−50.0801	+	45.0923i	−1.04333	+	0.939423i
$49$	−75.6668	+	84.0365i	−1.54422	+	1.71503i
$50$	−5.38733	−	16.5805i	−0.107747	−	0.331610i
$51$	7.85051	−	36.9337i	0.153932	−	0.724191i
$52$	−0.583317	+	0.525221i	−0.0112176	+	0.0101004i
$53$	90.4935	−	29.4031i	1.70742	−	0.554776i	0.717523	−	0.696535i	$-0.245276\pi$
$53$	90.4935	−	29.4031i	1.70742	−	0.554776i	0.989901	+	0.141759i	$0.0452758\pi$
$54$	−33.3425	+	3.50444i	−0.617454	+	0.0648971i
$55$	−47.4717	+	10.0904i	−0.863123	+	0.183462i
$56$	−37.5192	−	84.2696i	−0.669987	−	1.50481i
$57$	115.176	+	37.4228i	2.02062	+	0.656541i
$58$	−9.70806	−	2.06351i	−0.167380	−	0.0355778i
$59$	88.7697			1.50457			0.752286	−	0.658837i	$-0.228951\pi$
$59$	88.7697			1.50457			0.752286	+	0.658837i	$0.228951\pi$
$60$	5.69523	+	7.83881i	0.0949205	+	0.130647i
$61$	21.4787	+	19.3395i	0.352111	+	0.317042i	0.826138	−	0.563469i	$-0.190533\pi$
$61$	21.4787	+	19.3395i	0.352111	+	0.317042i	−0.474027	+	0.880510i	$0.657200\pi$
$62$	−56.9689	−	25.3642i	−0.918853	−	0.409100i
$63$	−12.7293	+	59.8867i	−0.202052	+	0.950582i
$64$	50.8894			0.795147
$65$	−2.99065	−	4.11628i	−0.0460100	−	0.0633273i
$66$	−81.7841	+	47.2181i	−1.23915	+	0.715425i
$67$	51.8869	+	71.4162i	0.774432	+	1.06591i	0.995875	+	0.0907405i	$0.0289234\pi$
$67$	51.8869	+	71.4162i	0.774432	+	1.06591i	−0.221443	+	0.975173i	$0.571077\pi$
$68$	5.21366	−	3.78794i	0.0766715	−	0.0557051i
$69$	56.3809	+	62.6173i	0.817114	+	0.907497i
$70$	−107.158	+	34.8179i	−1.53083	+	0.497398i
$71$	−27.3594	−	2.87559i	−0.385344	−	0.0405013i	−0.0901240	−	0.995931i	$-0.528726\pi$
$71$	−27.3594	−	2.87559i	−0.385344	−	0.0405013i	−0.295220	+	0.955429i	$0.595393\pi$
$72$	−28.1896	−	20.4809i	−0.391522	−	0.284458i
$73$	55.5258	−	76.4247i	0.760628	−	1.04691i	−0.236534	−	0.971623i	$-0.576011\pi$
$73$	55.5258	−	76.4247i	0.760628	−	1.04691i	0.997162	−	0.0752909i	$-0.0239885\pi$
$74$	−17.8100	+	3.78564i	−0.240676	+	0.0511573i
$75$	26.0624	−	15.0471i	0.347499	−	0.200628i
$76$	10.3345	+	17.8999i	0.135980	+	0.235525i
$77$	−31.2474	−	147.008i	−0.405811	−	1.90919i
$78$	−8.00962	−	5.81933i	−0.102687	−	0.0746068i
$79$	−72.5209	+	99.8164i	−0.917986	+	1.26350i	0.0463790	+	0.998924i	$0.485232\pi$
$79$	−72.5209	+	99.8164i	−0.917986	+	1.26350i	−0.964365	+	0.264575i	$0.914768\pi$
$80$	7.79305	−	74.1459i	0.0974131	−	0.926824i
$81$	−31.2585	−	96.2036i	−0.385907	−	1.18770i
$82$	53.2510	−	47.9474i	0.649402	−	0.584725i
$83$	−3.30268	−	4.54575i	−0.0397914	−	0.0547681i	0.788658	−	0.614832i	$-0.210776\pi$
$83$	−3.30268	−	4.54575i	−0.0397914	−	0.0547681i	−0.828449	+	0.560064i	$0.810776\pi$
$84$	−24.2747	+	17.6366i	−0.288985	+	0.209960i
$85$	20.8867	+	36.1769i	0.245726	+	0.425610i
$86$	13.3174	−	9.67568i	0.154854	−	0.112508i
$87$		−	17.1325i		−	0.196925i
$88$	83.6653	+	17.7836i	0.950742	+	0.202086i
$89$	−21.0468	+	47.2719i	−0.236481	+	0.531144i	−0.992332	−	0.123599i	$-0.960556\pi$
$89$	−21.0468	+	47.2719i	−0.236481	+	0.531144i	0.755852	+	0.654743i	$0.227223\pi$
$90$	−28.4788	+	31.6289i	−0.316431	+	0.351432i
$91$	12.7470	−	9.26126i	0.140077	−	0.101772i
$92$			14.3809i			0.156314i
$93$	22.3810	−	105.294i	0.240656	−	1.13220i
$94$	18.4716	−	56.8497i	0.196506	−	0.604784i
$95$	−122.396	+	54.4940i	−1.28837	+	0.573621i
$96$	−7.76990	−	36.5545i	−0.0809364	−	0.380776i
$97$	−8.83203	−	84.0311i	−0.0910518	−	0.866300i	−0.940766	−	0.339057i	$-0.889892\pi$
$97$	−8.83203	−	84.0311i	−0.0910518	−	0.866300i	0.849714	−	0.527244i	$-0.176775\pi$
$98$	−75.2256	−	231.521i	−0.767608	−	2.36245i
$99$	−37.9871	−	42.1890i	−0.383709	−	0.426152i
$100$	5.02405	+	1.06790i	0.0502405	+	0.0106790i
$101$	−152.979	+	49.7060i	−1.51465	+	0.492139i	−0.944250	−	0.329230i	$-0.893211\pi$
$101$	−152.979	+	49.7060i	−1.51465	+	0.492139i	−0.570398	+	0.821369i	$0.693211\pi$
$102$	60.4062	+	54.3900i	0.592217	+	0.533235i
$103$	69.7556	+	77.4715i	0.677239	+	0.752150i	0.979581	−	0.201049i	$-0.0644351\pi$
$103$	69.7556	+	77.4715i	0.677239	+	0.752150i	−0.302342	+	0.953200i	$0.597768\pi$
$104$	1.86439	+	8.77124i	0.0179268	+	0.0843389i
$105$	−97.2484	−	168.439i	−0.926176	−	1.60418i
$106$	−42.5872	+	200.357i	−0.401766	+	1.89016i
$107$	−30.5809	+	9.93634i	−0.285803	+	0.0928630i	−0.448410	−	0.893828i	$-0.648010\pi$
$107$	−30.5809	+	9.93634i	−0.285803	+	0.0928630i	0.162607	+	0.986691i	$0.448010\pi$
$108$	4.01751	−	9.02347i	0.0371991	−	0.0835506i
$109$	30.7918	−	69.1596i	0.282494	−	0.634492i	−0.715445	−	0.698669i	$-0.753776\pi$
$109$	30.7918	−	69.1596i	0.282494	−	0.634492i	0.997938	+	0.0641778i	$0.0204425\pi$
$110$	32.2851	−	99.3633i	0.293501	−	0.903303i
$111$	−12.7840	−	28.7133i	−0.115171	−	0.258678i
$112$	229.611	+	24.1330i	2.05009	+	0.215474i
$113$	157.591	+	90.9854i	1.39461	+	0.805180i	0.993822	−	0.110989i	$-0.0354019\pi$
$113$	157.591	+	90.9854i	1.39461	+	0.805180i	0.400791	+	0.916169i	$0.368735\pi$
$114$	−193.739	+	174.443i	−1.69946	+	1.53020i
$115$	−92.7079	−	9.74399i	−0.806156	−	0.0847304i
$116$	1.95658	−	2.17300i	0.0168671	−	0.0187328i
$117$	2.42078	−	5.43716i	0.0206904	−	0.0464714i
$118$	−95.5485	+	165.495i	−0.809733	+	1.40250i
$119$	−112.030	+	64.6807i	−0.941431	+	0.543536i
$120$	110.086	−	11.5705i	0.917384	−	0.0964209i
$121$	16.7718	+	7.46731i	0.138610	+	0.0617133i
$122$	−59.1740	+	19.2268i	−0.485032	+	0.157597i
$123$	100.070	+	72.7053i	0.813579	+	0.591100i
$124$	14.8636	−	10.7990i	0.119868	−	0.0870890i
$125$	−42.0488	+	129.413i	−0.336390	+	1.03530i
$126$	−97.9463	−	88.1913i	−0.777352	−	0.699931i
$127$	−57.7254	+	177.661i	−0.454531	+	1.39890i	0.417154	+	0.908836i	$0.363028\pi$
$127$	−57.7254	+	177.661i	−0.454531	+	1.39890i	−0.871685	+	0.490067i	$0.836972\pi$
$128$	−74.8889	+	129.711i	−0.585069	+	1.01337i
$129$	21.1168	+	19.0137i	0.163696	+	0.147393i
$130$	10.8931	−	1.14491i	0.0837928	−	0.00880698i
$131$	89.2118	−	122.789i	0.681006	−	0.937324i	−0.318940	−	0.947775i	$-0.603327\pi$
$131$	89.2118	−	122.789i	0.681006	−	0.937324i	0.999945	+	0.0104510i	$0.00332670\pi$
$132$		−	27.8226i		−	0.210777i
$133$	−168.754	−	379.027i	−1.26883	−	2.84983i
$134$	−188.992	+	19.8638i	−1.41038	+	0.148237i
$135$	55.4484	+	32.0132i	0.410729	+	0.237135i
$136$	−7.69564	−	73.2192i	−0.0565856	−	0.538376i
$137$	0.501114	−	4.76778i	0.00365776	−	0.0348013i	−0.992541	−	0.121913i	$-0.961097\pi$
$137$	0.501114	−	4.76778i	0.00365776	−	0.0348013i	0.996199	+	0.0871118i	$0.0277637\pi$
$138$	−177.425	+	37.7128i	−1.28569	+	0.273281i
$139$	−130.521	+	27.7430i	−0.938998	+	0.199590i	−0.651895	−	0.758310i	$-0.726026\pi$
$139$	−130.521	+	27.7430i	−0.938998	+	0.199590i	−0.287103	+	0.957900i	$0.592692\pi$
$140$	6.90172	−	32.4701i	0.0492980	−	0.231929i
$141$	102.619	+	10.7857i	0.727796	+	0.0764945i
$142$	34.8097	−	47.9115i	0.245139	−	0.337405i
$143$			14.6100i			0.102168i
$144$	79.6706	−	35.4716i	0.553268	−	0.246331i
$145$	12.6827	+	14.0856i	0.0874672	+	0.0971421i
$146$	82.7139	+	185.778i	0.566533	+	1.27246i
$147$	363.921	−	210.110i	2.47565	−	1.42932i
$148$	1.65768	−	5.10182i	0.0112006	−	0.0344718i
$149$	8.87550	+	5.12427i	0.0595671	+	0.0343911i	0.529488	−	0.848318i	$-0.322384\pi$
$149$	8.87550	+	5.12427i	0.0595671	+	0.0343911i	−0.469921	+	0.882709i	$0.655717\pi$
$150$			64.7847i			0.431898i
$151$	122.543	+	88.2276i	0.811546	+	0.584289i
$151$	122.543	+	88.2276i	0.811546	+	0.584289i
$152$	236.127			1.55347
$153$	−24.4324	+	42.3181i	−0.159689	+	0.276589i
$154$	307.702	+	99.9785i	1.99807	+	0.649211i
$155$	59.5459	+	103.136i	0.384167	+	0.665397i
$156$	2.66467	−	1.18639i	0.0170812	−	0.00760505i
$157$	27.5245	−	24.7832i	0.175315	−	0.157855i	−0.576802	−	0.816884i	$-0.695699\pi$
$157$	27.5245	−	24.7832i	0.175315	−	0.157855i	0.752117	+	0.659029i	$0.229033\pi$
$158$	−108.031	−	242.641i	−0.683738	−	1.53570i
$159$	−353.584			−2.22380
$160$	33.4484	+	24.3017i	0.209053	+	0.151886i
$161$	30.1746	−	287.092i	0.187420	−	1.78318i
$162$	212.999	+	45.2744i	1.31481	+	0.279472i
$163$	58.0826	+	273.257i	0.356335	+	1.67642i	0.682323	+	0.731051i	$0.260970\pi$
$163$	58.0826	+	273.257i	0.356335	+	1.67642i	−0.325988	+	0.945374i	$0.605697\pi$
$164$	4.38927	+	20.6499i	0.0267638	+	0.125914i
$165$	179.361	+	18.8516i	1.08703	+	0.114252i
$166$	12.0296	−	1.26436i	0.0724675	−	0.00761664i
$167$	29.0029	−	50.2345i	0.173670	−	0.300806i	−0.766030	−	0.642805i	$-0.777771\pi$
$167$	29.0029	−	50.2345i	0.173670	−	0.300806i	0.939700	+	0.341999i	$0.111104\pi$
$168$	35.8308	+	340.908i	0.213279	+	2.02921i
$169$	152.990	−	68.1155i	0.905266	−	0.403050i
$170$	−89.9268			−0.528981
$171$	−126.791	−	92.1190i	−0.741467	−	0.538708i
$172$	0.506940	+	4.82321i	0.00294732	+	0.0280419i
$173$	−88.6089	+	98.4101i	−0.512190	+	0.568845i	−0.942658	−	0.333761i	$-0.891682\pi$
$173$	−88.6089	+	98.4101i	−0.512190	+	0.568845i	0.430468	+	0.902606i	$0.358349\pi$
$174$	31.9404	+	18.4408i	0.183565	+	0.105982i
$175$	−98.0565	−	31.8605i	−0.560323	−	0.182060i
$176$	−143.248	+	159.093i	−0.813909	+	0.903937i
$177$	−313.728	−	101.936i	−1.77247	−	0.575911i
$178$	−65.4757	−	90.1195i	−0.367841	−	0.506290i
$179$	207.001	−	284.913i	1.15643	−	1.59169i	0.432829	−	0.901476i	$-0.357515\pi$
$179$	207.001	−	284.913i	1.15643	−	1.59169i	0.723603	−	0.690216i	$-0.242485\pi$
$180$	−3.87482	−	11.9255i	−0.0215268	−	0.0662526i
$181$	−10.8397	+	24.3463i	−0.0598876	+	0.134510i	−0.941010	−	0.338378i	$-0.890122\pi$
$181$	−10.8397	+	24.3463i	−0.0598876	+	0.134510i	0.881123	+	0.472888i	$0.156788\pi$
$182$	3.54548	+	33.7330i	0.0194806	+	0.185346i
$183$	−53.7016	−	93.0139i	−0.293451	−	0.508273i
$184$	142.280	+	82.1452i	0.773259	+	0.446441i
$185$	31.7662	+	14.1432i	0.171709	+	0.0764498i
$186$	172.212	+	155.060i	0.925869	+	0.833656i
$187$	12.5383	−	119.294i	0.0670499	−	0.637937i
$188$	11.7840	+	13.0874i	0.0626807	+	0.0696139i
$189$	−99.1364	+	171.709i	−0.524531	+	0.908515i
$190$	30.1480	−	286.839i	0.158674	−	1.50968i
$191$	−33.6432	+	14.9789i	−0.176142	+	0.0784235i	−0.492913	−	0.870078i	$-0.664068\pi$
$191$	−33.6432	+	14.9789i	−0.176142	+	0.0784235i	0.316771	+	0.948502i	$0.397401\pi$
$192$	−179.852	−	58.4375i	−0.936730	−	0.304362i
$193$	300.638	+	133.852i	1.55771	+	0.693536i	0.991425	−	0.130675i	$-0.0417145\pi$
$193$	300.638	+	133.852i	1.55771	+	0.693536i	0.566282	+	0.824211i	$0.308381\pi$
$194$	166.167	+	73.9823i	0.856531	+	0.381352i
$195$	5.84267	+	17.9819i	0.0299624	+	0.0922147i
$196$	70.1530	+	14.9115i	0.357924	+	0.0760790i
$197$	−32.2669	+	18.6293i	−0.163791	+	0.0945648i	−0.579655	−	0.814862i	$-0.696813\pi$
$197$	−32.2669	+	18.6293i	−0.163791	+	0.0945648i	0.415864	+	0.909427i	$0.363479\pi$
$198$	119.542	−	25.4093i	0.603745	−	0.128330i
$199$	150.673	−	135.666i	0.757149	−	0.681740i	−0.197223	−	0.980359i	$-0.563192\pi$
$199$	150.673	−	135.666i	0.757149	−	0.681740i	0.954373	+	0.298618i	$0.0965258\pi$
$200$	39.2632	−	43.6063i	0.196316	−	0.218031i
$201$	−101.369	−	311.980i	−0.504321	−	1.55214i
$202$	71.9937	−	338.704i	0.356404	−	1.67675i
$203$	−43.6194	+	39.2751i	−0.214874	+	0.193474i
$204$	−22.7758	+	7.40030i	−0.111646	+	0.0362760i
$205$	−136.095	+	14.3042i	−0.663879	+	0.0697765i
$206$	−219.514	+	46.6591i	−1.06560	+	0.226500i
$207$	−44.3517	−	99.6156i	−0.214260	−	0.481235i
$208$	−21.3452	−	6.93547i	−0.102621	−	0.0333436i
$209$	376.309	+	79.9869i	1.80052	+	0.382712i
$210$	418.699			1.99380
$211$	−168.590	−	232.044i	−0.799003	−	1.09973i	−0.992928	−	0.118717i	$-0.962122\pi$
$211$	−168.590	−	232.044i	−0.799003	−	1.09973i	0.193925	−	0.981016i	$-0.437878\pi$
$212$	−44.8469	−	40.3803i	−0.211542	−	0.190473i
$213$	93.3909	+	41.5803i	0.438455	+	0.195213i
$214$	14.3917	−	67.7076i	0.0672509	−	0.316390i
$215$	−31.4367			−0.146217
$216$	−66.3265	−	91.2906i	−0.307067	−	0.422642i
$217$	−319.387	+	184.398i	−1.47183	+	0.849760i
$218$	95.7921	+	131.847i	0.439413	+	0.604801i
$219$	−283.998	+	206.337i	−1.29680	+	0.942177i
$220$	20.5963	+	22.8745i	0.0936196	+	0.103975i
$221$	11.9599	−	3.88600i	0.0541172	−	0.0175837i
$222$	67.2909	+	7.07256i	0.303112	+	0.0318584i
$223$	−213.293	−	154.967i	−0.956472	−	0.694918i	−0.00414333	−	0.999991i	$-0.501319\pi$
$223$	−213.293	−	154.967i	−0.956472	−	0.694918i	−0.952329	+	0.305074i	$0.901319\pi$
$224$	−75.2560	+	103.581i	−0.335964	+	0.462415i
$225$	−38.0947	+	8.09728i	−0.169310	+	0.0359879i
$226$	−339.251	+	195.867i	−1.50111	+	0.866666i
$227$	−35.1180	−	60.8262i	−0.154705	−	0.267957i	0.778247	−	0.627959i	$-0.216109\pi$
$227$	−35.1180	−	60.8262i	−0.154705	−	0.267957i	−0.932952	+	0.360002i	$0.882776\pi$
$228$	−15.9691	−	75.1288i	−0.0700400	−	0.329512i
$229$	86.7690	+	63.0413i	0.378904	+	0.275290i	0.760893	−	0.648877i	$-0.224761\pi$
$229$	86.7690	+	63.0413i	0.378904	+	0.275290i	−0.381990	+	0.924167i	$0.624761\pi$
$230$	117.953	−	162.349i	0.512840	−	0.705864i
$231$	−58.3783	+	555.433i	−0.252720	+	2.40447i
$232$	−10.3227	−	31.7701i	−0.0444945	−	0.136940i
$233$	−202.110	+	181.981i	−0.867425	+	0.781033i	−0.977066	−	0.212938i	$-0.931697\pi$
$233$	−202.110	+	181.981i	−0.867425	+	0.781033i	0.109641	+	0.993971i	$0.465030\pi$
$234$	7.53094	+	10.3655i	0.0321835	+	0.0442968i
$235$	−92.3536	+	67.0988i	−0.392994	+	0.285527i
$236$	−28.1503	−	48.7577i	−0.119281	−	0.206600i
$237$	370.923	−	269.491i	1.56508	−	1.13709i
$238$		−	278.480i		−	1.17008i
$239$	−70.4221	−	14.9687i	−0.294653	−	0.0626305i	0.0582132	−	0.998304i	$-0.481460\pi$
$239$	−70.4221	−	14.9687i	−0.294653	−	0.0626305i	−0.352866	+	0.935674i	$0.614793\pi$
$240$	−112.685	+	253.096i	−0.469523	+	1.05457i
$241$	−79.6762	+	88.4894i	−0.330607	+	0.367176i	−0.885414	−	0.464803i	$-0.846125\pi$
$241$	−79.6762	+	88.4894i	−0.330607	+	0.367176i	0.554808	+	0.831979i	$0.312792\pi$
$242$	−31.9740	+	23.2305i	−0.132124	+	0.0959937i
$243$			235.731i			0.970086i
$244$	3.81120	−	17.9303i	0.0156197	−	0.0734848i
$245$	−143.661	+	442.144i	−0.586373	+	1.80467i
$246$	−243.257	+	108.305i	−0.988852	+	0.440265i
$247$	8.38562	+	39.4512i	0.0339499	+	0.159722i
$248$	−21.9395	−	208.740i	−0.0884656	−	0.841694i
$249$	6.45227	+	19.8580i	0.0259127	+	0.0797512i
$250$	−196.007	−	217.687i	−0.784026	−	0.870749i
$251$	259.729	+	55.2071i	1.03478	+	0.219948i	0.693833	−	0.720136i	$-0.255920\pi$
$251$	259.729	+	55.2071i	1.03478	+	0.219948i	0.340943	+	0.940084i	$0.389254\pi$
$252$	36.9300	−	11.9993i	0.146548	−	0.0476163i
$253$	198.921	+	179.109i	0.786248	+	0.707941i
$254$	−269.082	−	298.846i	−1.05938	−	1.17656i
$255$	−32.2746	−	151.840i	−0.126567	−	0.595451i
$256$	−59.4364	−	102.947i	−0.232173	−	0.402136i
$257$	−85.8021	+	403.667i	−0.333860	+	1.57069i	0.416170	+	0.909287i	$0.363372\pi$
$257$	−85.8021	+	403.667i	−0.333860	+	1.57069i	−0.750031	+	0.661403i	$0.769961\pi$
$258$	−58.1769	+	18.9028i	−0.225492	+	0.0732668i
$259$	−43.7978	+	98.3715i	−0.169103	+	0.379813i
$260$	−1.31253	+	2.94798i	−0.00504818	+	0.0113384i
$261$	−6.85140	+	21.0864i	−0.0262506	+	0.0807910i
$262$	132.894	+	298.485i	0.507229	+	1.13926i
$263$	−145.262	−	15.2676i	−0.552327	−	0.0580519i	−0.175746	−	0.984436i	$-0.556234\pi$
$263$	−145.262	−	15.2676i	−0.552327	−	0.0580519i	−0.376581	+	0.926384i	$0.622900\pi$
$264$	−275.266	−	158.925i	−1.04268	−	0.601989i
$265$	290.702	−	261.749i	1.09699	−	0.987732i
$266$	888.267	+	93.3606i	3.33935	+	0.350980i
$267$	128.666	−	142.898i	0.481897	−	0.535200i
$268$	22.7720	−	51.1466i	0.0849700	−	0.190846i
$269$	79.8460	−	138.297i	0.296825	−	0.514116i	−0.678583	−	0.734524i	$-0.737405\pi$
$269$	79.8460	−	138.297i	0.296825	−	0.514116i	0.975408	+	0.220408i	$0.0707388\pi$
$270$	−119.365	+	68.9156i	−0.442094	+	0.255243i
$271$	−26.4593	+	2.78099i	−0.0976360	+	0.0102620i	−0.153220	−	0.988192i	$-0.548964\pi$
$271$	−26.4593	+	2.78099i	−0.0976360	+	0.0102620i	0.0555845	+	0.998454i	$0.482298\pi$
$272$	168.336	+	74.9481i	0.618883	+	0.275544i
$273$	−55.6852	+	18.0932i	−0.203975	+	0.0662755i
$274$	8.34927	+	6.06610i	0.0304718	+	0.0221390i
$275$	77.3441	−	56.1938i	0.281251	−	0.204341i
$276$	16.5140	−	50.8247i	0.0598332	−	0.184148i
$277$	−136.307	−	122.732i	−0.492084	−	0.443075i	0.385351	−	0.922770i	$-0.374080\pi$
$277$	−136.307	−	122.732i	−0.492084	−	0.443075i	−0.877435	+	0.479695i	$0.840747\pi$
$278$	88.7659	−	273.193i	0.319302	−	0.982710i
$279$	−69.6541	+	120.644i	−0.249656	+	0.432417i
$280$	−281.824	−	253.755i	−1.00651	−	0.906268i
$281$	−425.847	+	44.7583i	−1.51547	+	0.159282i	−0.825436	−	0.564495i	$-0.809071\pi$
$281$	−425.847	+	44.7583i	−1.51547	+	0.159282i	−0.690033	+	0.723778i	$0.742404\pi$
$282$	−130.564	+	179.705i	−0.462991	+	0.637253i
$283$		−	433.089i		−	1.53035i	−0.643823	−	0.765175i	$-0.722653\pi$
$283$		−	433.089i		−	1.53035i	0.643823	−	0.765175i	$-0.277347\pi$
$284$	7.09666	+	15.9394i	0.0249882	+	0.0561245i
$285$	495.144	−	52.0417i	1.73735	−	0.182603i
$286$	−27.2377	−	15.7257i	−0.0952368	−	0.0549850i
$287$	−44.2963	−	421.451i	−0.154343	−	1.46847i
$288$	−5.05530	+	48.0980i	−0.0175531	+	0.167007i
$289$	181.695	−	38.6204i	0.628701	−	0.133634i
$290$	−39.9113	+	8.48340i	−0.137625	+	0.0292531i
$291$	−65.2810	+	307.123i	−0.224333	+	1.05540i
$292$	−59.5852	−	6.26266i	−0.204059	−	0.0214475i
$293$	10.1676	−	13.9945i	0.0347018	−	0.0477630i	−0.791314	−	0.611411i	$-0.790602\pi$
$293$	10.1676	−	13.9945i	0.0347018	−	0.0477630i	0.826015	+	0.563648i	$0.190602\pi$
$294$			904.617i			3.07693i
$295$	333.394	−	148.437i	1.13015	−	0.503175i
$296$	−41.0068	−	45.5426i	−0.138536	−	0.153860i
$297$	−74.7784	−	167.955i	−0.251779	−	0.565505i
$298$	−19.1065	+	11.0312i	−0.0641159	+	0.0370173i
$299$	−8.67172	+	26.6888i	−0.0290024	+	0.0892603i
$300$	−16.5296	−	9.54337i	−0.0550987	−	0.0318112i
$301$		−	97.3513i		−	0.323426i
$302$	−296.385	+	133.495i	−0.981409	+	0.442035i
$303$	597.735			1.97272
$304$	−295.496	+	511.815i	−0.972028	+	1.68360i
$305$	113.007	+	36.7182i	0.370514	+	0.120387i
$306$	−52.5962	−	91.0993i	−0.171883	−	0.297710i
$307$	−11.3312	+	5.04498i	−0.0369095	+	0.0164331i	−0.425108	−	0.905142i	$-0.639764\pi$
$307$	−11.3312	+	5.04498i	−0.0369095	+	0.0164331i	0.388199	+	0.921576i	$0.373097\pi$
$308$	−70.8364	+	63.7814i	−0.229988	+	0.207082i
$309$	−157.566	−	353.900i	−0.509923	−	1.14531i
$310$	−256.372			−0.827006
$311$	−371.454	−	269.877i	−1.19439	−	0.867773i	−0.200666	−	0.979660i	$-0.564311\pi$
$311$	−371.454	−	269.877i	−1.19439	−	0.867773i	−0.993721	+	0.111887i	$0.964311\pi$
$312$	3.48316	−	33.1400i	0.0111640	−	0.106218i
$313$	−315.686	−	67.1012i	−1.00858	−	0.214381i	−0.326141	−	0.945321i	$-0.605748\pi$
$313$	−315.686	−	67.1012i	−1.00858	−	0.214381i	−0.682441	+	0.730941i	$0.739082\pi$
$314$	16.5773	+	77.9901i	0.0527940	+	0.248376i
$315$	52.3321	+	246.203i	0.166134	+	0.781597i
$316$	77.8227	+	8.17950i	0.246274	+	0.0258845i
$317$	−381.845	+	40.1336i	−1.20456	+	0.126604i	−0.685461	−	0.728110i	$-0.740399\pi$
$317$	−381.845	+	40.1336i	−1.20456	+	0.126604i	−0.519099	+	0.854714i	$0.673732\pi$
$318$	380.585	−	659.192i	1.19681	−	2.07293i
$319$	−5.68907	−	54.1279i	−0.0178341	−	0.169680i
$320$	191.126	−	85.0950i	0.597270	−	0.265922i
$321$	119.488			0.372238
$322$	502.752	+	365.270i	1.56134	+	1.13438i
$323$	−34.6134	−	329.324i	−0.107162	−	1.01958i
$324$	−42.9283	+	47.6767i	−0.132495	+	0.147150i
$325$	8.67994	+	5.01136i	0.0267075	+	0.0154196i
$326$	−571.956	−	185.840i	−1.75447	−	0.570060i
$327$	−188.241	+	209.063i	−0.575661	+	0.639337i
$328$	229.374	+	74.5283i	0.699312	+	0.227220i
$329$	−207.787	−	285.995i	−0.631573	−	0.869285i
$330$	−228.202	+	314.094i	−0.691522	+	0.951799i
$331$	50.0254	+	153.962i	0.151134	+	0.465143i	0.997749	−	0.0670635i	$-0.0213630\pi$
$331$	50.0254	+	153.962i	0.151134	+	0.465143i	−0.846615	+	0.532206i	$0.821363\pi$
$332$	−1.44947	+	3.25556i	−0.00436587	+	0.00980591i
$333$	4.25171	+	40.4524i	0.0127679	+	0.121479i
$334$	62.4354	+	108.141i	0.186932	+	0.323776i
$335$	314.292	+	181.456i	0.938185	+	0.541661i
$336$	−783.771	−	348.957i	−2.33265	−	1.03856i
$337$	449.262	+	404.518i	1.33312	+	1.20035i	0.962410	+	0.271602i	$0.0875534\pi$
$337$	449.262	+	404.518i	1.33312	+	1.20035i	0.370713	+	0.928747i	$0.379113\pi$
$338$	−37.6839	+	358.539i	−0.111491	+	1.06076i
$339$	−452.474	−	502.524i	−1.33473	−	1.48237i
$340$	13.2470	−	22.9445i	0.0389618	−	0.0674839i
$341$	35.7454	−	340.095i	0.104825	−	0.997347i
$342$	308.212	−	137.225i	0.901205	−	0.401242i
$343$	−775.910	−	252.109i	−2.26213	−	0.735010i
$344$	50.6148	+	22.5351i	0.147136	+	0.0655091i
$345$	316.457	+	140.896i	0.917266	+	0.408393i
$346$	−88.0922	−	271.120i	−0.254602	−	0.783584i
$347$	330.245	+	70.1958i	0.951715	+	0.202293i	0.657507	−	0.753448i	$-0.271611\pi$
$347$	330.245	+	70.1958i	0.951715	+	0.202293i	0.294208	+	0.955741i	$0.404944\pi$
$348$	−9.41020	+	5.43298i	−0.0270408	+	0.0156120i
$349$	−388.978	+	82.6798i	−1.11455	+	0.236905i	−0.728144	−	0.685424i	$-0.759617\pi$
$349$	−388.978	+	82.6798i	−1.11455	+	0.236905i	−0.386406	+	0.922329i	$0.626284\pi$
$350$	164.942	−	148.515i	0.471264	−	0.424328i
$351$	12.8970	−	14.3236i	0.0367437	−	0.0408080i
$352$	−36.6864	−	112.909i	−0.104223	−	0.320764i
$353$	−100.434	+	472.503i	−0.284514	+	1.33853i	0.571083	+	0.820892i	$0.306523\pi$
$353$	−100.434	+	472.503i	−0.284514	+	1.33853i	−0.855597	+	0.517642i	$0.826810\pi$
$354$	527.726	−	475.167i	1.49075	−	1.34228i
$355$	−107.563	+	34.9493i	−0.302994	+	0.0984487i
$356$	32.6388	−	3.43048i	0.0916821	−	0.00963618i
$357$	470.209	−	99.9460i	1.31711	−	0.279961i
$358$	308.359	+	692.586i	0.861338	+	1.93460i
$359$	−521.465	−	169.434i	−1.45255	−	0.471962i	−0.526763	−	0.850012i	$-0.676595\pi$
$359$	−521.465	−	169.434i	−1.45255	−	0.471962i	−0.925785	+	0.378050i	$0.876595\pi$
$360$	−140.120	−	29.7833i	−0.389221	−	0.0827315i
$361$	701.050			1.94197
$362$	−33.7217	−	46.4140i	−0.0931540	−	0.128215i
$363$	−50.6997	−	45.6503i	−0.139669	−	0.125758i
$364$	−9.12913	−	4.06455i	−0.0250800	−	0.0111663i
$365$	80.7455	−	379.878i	0.221221	−	1.04076i
$366$	231.210			0.631720
$367$	83.7701	+	115.300i	0.228256	+	0.314168i	0.907748	−	0.419515i	$-0.137800\pi$
$367$	83.7701	+	115.300i	0.228256	+	0.314168i	−0.679492	+	0.733683i	$0.737800\pi$
$368$	−356.106	+	205.598i	−0.967680	+	0.558690i
$369$	−94.0898	−	129.503i	−0.254986	−	0.350958i
$370$	−60.5593	+	43.9989i	−0.163674	+	0.118916i
$371$	810.568	+	900.227i	2.18482	+	2.42649i
$372$	−64.9313	+	21.0975i	−0.174547	+	0.0567136i
$373$	−168.810	−	17.7427i	−0.452575	−	0.0475675i	−0.124501	−	0.992220i	$-0.539733\pi$
$373$	−168.810	−	17.7427i	−0.452575	−	0.0475675i	−0.328074	+	0.944652i	$0.606400\pi$
$374$	208.906	+	151.779i	0.558573	+	0.405827i
$375$	297.215	−	409.082i	0.792574	−	1.09089i
$376$	196.793	−	41.8297i	0.523386	−	0.111249i
$377$	4.94144	−	2.85294i	0.0131073	−	0.00756748i
$378$	−213.414	−	369.643i	−0.564586	−	0.977892i
$379$	−16.9731	−	79.8522i	−0.0447839	−	0.210692i	0.950066	−	0.312048i	$-0.101015\pi$
$379$	−16.9731	−	79.8522i	−0.0447839	−	0.210692i	−0.994850	+	0.101356i	$0.967682\pi$
$380$	68.7450	+	49.9461i	0.180908	+	0.131437i
$381$	408.024	−	561.596i	1.07093	−	1.47401i
$382$	8.28686	−	78.8442i	0.0216933	−	0.206398i
$383$	81.3657	+	250.418i	0.212443	+	0.653833i	0.999325	+	0.0367294i	$0.0116939\pi$
$383$	81.3657	+	250.418i	0.212443	+	0.653833i	−0.786882	+	0.617103i	$0.788306\pi$
$384$	413.621	−	372.426i	1.07714	−	0.969859i
$385$	−363.176	−	499.869i	−0.943314	−	1.29836i
$386$	−573.138	+	416.409i	−1.48481	+	1.07878i
$387$	−18.3866	−	31.8466i	−0.0475107	−	0.0822909i
$388$	−43.3542	+	31.4987i	−0.111738	+	0.0811822i
$389$			126.264i			0.324587i	0.986743	+	0.162294i	$0.0518891\pi$
$389$			126.264i			0.324587i	−0.986743	+	0.162294i	$0.948111\pi$
$390$	−39.8127	−	8.46246i	−0.102084	−	0.0216986i
$391$	93.7108	−	210.478i	0.239670	−	0.538307i
$392$	548.250	−	608.893i	1.39860	−	1.55330i
$393$	−456.292	+	331.515i	−1.16105	+	0.843551i
$394$		−	80.2075i		−	0.203572i
$395$	−105.460	+	496.149i	−0.266987	+	1.25607i
$396$	−11.1264	+	34.2436i	−0.0280970	+	0.0864738i
$397$	390.544	−	173.882i	0.983739	−	0.437989i	0.149122	−	0.988819i	$-0.452355\pi$
$397$	390.544	−	173.882i	0.983739	−	0.437989i	0.834617	+	0.550830i	$0.185689\pi$
$398$	90.7463	+	426.928i	0.228006	+	1.07268i
$399$	161.160	+	1533.33i	0.403909	+	3.84294i
$400$	45.3831	+	139.675i	0.113458	+	0.349187i
$401$	35.5267	+	39.4564i	0.0885953	+	0.0983950i	0.785812	−	0.618465i	$-0.212245\pi$
$401$	35.5267	+	39.4564i	0.0885953	+	0.0983950i	−0.697217	+	0.716860i	$0.745579\pi$
$402$	690.739	+	146.821i	1.71826	+	0.365227i
$403$	34.0964	−	11.0786i	0.0846065	−	0.0274903i
$404$	75.8137	+	68.2630i	0.187658	+	0.168968i
$405$	−278.265	−	309.045i	−0.687075	−	0.763074i
$406$	−26.2709	−	123.595i	−0.0647066	−	0.304420i
$407$	−49.9240	−	86.4708i	−0.122663	−	0.212459i
$408$	−56.8815	+	267.606i	−0.139415	+	0.655898i
$409$	113.072	−	36.7395i	0.276461	−	0.0898276i	−0.167505	−	0.985871i	$-0.553571\pi$
$409$	113.072	−	36.7395i	0.276461	−	0.0898276i	0.443966	+	0.896044i	$0.353571\pi$
$410$	119.820	−	269.121i	0.292245	−	0.656393i
$411$	−7.24597	+	16.2747i	−0.0176301	+	0.0395979i
$412$	20.4314	−	62.8814i	0.0495908	−	0.152625i
$413$	459.670	+	1032.44i	1.11300	+	2.49984i
$414$	233.454	+	24.5370i	0.563898	+	0.0592680i
$415$	−20.0052	−	11.5500i	−0.0482052	−	0.0278313i
$416$	9.24936	−	8.32816i	0.0222340	−	0.0200196i
$417$	493.141	+	51.8312i	1.18259	+	0.124295i
$418$	−554.166	+	615.464i	−1.32576	+	1.47240i
$419$	−39.6994	+	89.1664i	−0.0947481	+	0.212808i	−0.954702	−	0.297564i	$-0.903826\pi$
$419$	−39.6994	+	89.1664i	−0.0947481	+	0.212808i	0.859954	+	0.510372i	$0.170492\pi$
$420$	−61.6780	+	106.829i	−0.146852	+	0.254356i
$421$	−77.9682	+	45.0150i	−0.185198	+	0.106924i	−0.589732	−	0.807599i	$-0.700767\pi$
$421$	−77.9682	+	45.0150i	−0.185198	+	0.106924i	0.404535	+	0.914523i	$0.367433\pi$
$422$	614.066	−	64.5410i	1.45513	−	0.152941i
$423$	−121.989	−	54.3131i	−0.288390	−	0.128400i
$424$	−655.678	+	213.043i	−1.54641	+	0.502459i
$425$	−66.5728	−	48.3680i	−0.156642	−	0.113807i
$426$	−178.041	+	129.355i	−0.417938	+	0.303649i
$427$	−113.707	+	349.953i	−0.266292	+	0.819562i
$428$	15.1553	+	13.6459i	0.0354096	+	0.0318830i
$429$	16.7770	−	51.6344i	0.0391073	−	0.120360i
$430$	33.8373	−	58.6080i	0.0786914	−	0.136298i
$431$	319.389	+	287.579i	0.741042	+	0.667238i	0.950551	−	0.310569i	$-0.100520\pi$
$431$	319.389	+	287.579i	0.741042	+	0.667238i	−0.209508	+	0.977807i	$0.567186\pi$
$432$	280.879	−	29.5216i	0.650183	−	0.0683370i
$433$	104.086	−	143.262i	0.240383	−	0.330859i	−0.671731	−	0.740795i	$-0.734449\pi$
$433$	104.086	−	143.262i	0.240383	−	0.330859i	0.912114	+	0.409936i	$0.134449\pi$
$434$		−	793.917i		−	1.82930i
$435$	−28.6482	−	64.3449i	−0.0658579	−	0.147919i
$436$	−47.7512	+	5.01885i	−0.109521	+	0.0115111i
$437$	639.944	+	369.472i	1.46440	+	0.845474i
$438$	−78.9917	−	751.556i	−0.180346	−	1.71588i
$439$	54.9266	−	522.592i	0.125118	−	1.19041i	−0.734186	−	0.678949i	$-0.762436\pi$
$439$	54.9266	−	522.592i	0.125118	−	1.19041i	0.859303	−	0.511466i	$-0.170897\pi$
$440$	343.960	−	73.1110i	0.781728	−	0.166161i
$441$	−531.933	+	113.066i	−1.20620	+	0.256385i
$442$	−5.62845	+	26.4798i	−0.0127340	+	0.0599090i
$443$	−168.778	−	17.7392i	−0.380988	−	0.0400434i	−0.0879009	−	0.996129i	$-0.528016\pi$
$443$	−168.778	−	17.7392i	−0.380988	−	0.0400434i	−0.293087	+	0.956086i	$0.594683\pi$
$444$	−11.7171	+	16.1272i	−0.0263898	+	0.0363225i
$445$			212.733i			0.478053i
$446$	518.488	−	230.846i	1.16253	−	0.517591i
$447$	−25.4832	−	28.3020i	−0.0570095	−	0.0633155i
$448$	263.517	+	591.869i	0.588207	+	1.32114i
$449$	−99.7221	+	57.5746i	−0.222098	+	0.128228i	−0.606921	−	0.794762i	$-0.707596\pi$
$449$	−99.7221	+	57.5746i	−0.222098	+	0.128228i	0.384823	+	0.922990i	$0.374262\pi$
$450$	25.9079	−	79.7362i	0.0575730	−	0.177192i
$451$	340.301	+	196.473i	0.754549	+	0.435639i
$452$		−	115.412i		−	0.255335i
$453$	−331.776	−	452.531i	−0.732397	−	0.998965i
$454$	151.199			0.333037
$455$	32.3880	−	56.0977i	0.0711825	−	0.123292i
$456$	−834.514	−	271.150i	−1.83007	−	0.594627i
$457$	−427.132	−	739.814i	−0.934643	−	1.61885i	−0.775268	−	0.631632i	$-0.782385\pi$
$457$	−427.132	−	739.814i	−0.934643	−	1.61885i	−0.159375	−	0.987218i	$-0.550948\pi$
$458$	−210.924	+	93.9094i	−0.460533	+	0.205042i
$459$	−117.600	+	105.887i	−0.256208	+	0.230691i
$460$	24.0471	+	54.0108i	0.0522764	+	0.117415i
$461$	186.526			0.404611			0.202305	−	0.979322i	$-0.435157\pi$
$461$	186.526			0.404611			0.202305	+	0.979322i	$0.435157\pi$
$462$	−972.665	−	706.683i	−2.10534	−	1.52962i
$463$	7.19292	−	68.4361i	0.0155355	−	0.147810i	−0.984004	−	0.178145i	$-0.942991\pi$
$463$	7.19292	−	68.4361i	0.0155355	−	0.147810i	0.999540	+	0.0303344i	$0.00965721\pi$
$464$	81.7811	+	17.3831i	0.176252	+	0.0374636i
$465$	−92.0116	−	432.880i	−0.197874	−	0.930925i
$466$	−121.726	−	572.674i	−0.261214	−	1.22891i
$467$	428.828	+	45.0717i	0.918262	+	0.0965132i	0.551854	−	0.833941i	$-0.313921\pi$
$467$	428.828	+	45.0717i	0.918262	+	0.0965132i	0.366408	+	0.930454i	$0.380587\pi$
$468$	−3.75408	+	0.394570i	−0.00802155	+	0.000843098i
$469$	−561.923	+	973.279i	−1.19813	+	2.07522i
$470$	−25.6874	−	244.399i	−0.0546540	−	0.519998i
$471$	−125.736	+	55.9811i	−0.266955	+	0.118856i
$472$	−643.188			−1.36269
$473$	73.0296	+	53.0591i	0.154397	+	0.112176i
$474$	103.169	+	981.588i	0.217656	+	2.07086i
$475$	176.598	−	196.132i	0.371785	−	0.412909i
$476$	71.0531	+	41.0226i	0.149271	+	0.0861818i
$477$	435.187	+	141.401i	0.912341	+	0.296437i
$478$	103.706	−	115.177i	0.216958	−	0.240957i
$479$	−788.995	−	256.360i	−1.64717	−	0.535198i	−0.669047	−	0.743220i	$-0.733297\pi$
$479$	−788.995	−	256.360i	−1.64717	−	0.535198i	−0.978124	+	0.208022i	$0.933297\pi$
$480$	−90.3063	−	124.296i	−0.188138	−	0.258950i
$481$	6.15281	−	8.46862i	0.0127917	−	0.0176063i
$482$	−79.2116	−	243.788i	−0.164339	−	0.505785i
$483$	−436.317	+	979.984i	−0.903347	+	2.02895i
$484$	−1.21712	−	11.5801i	−0.00251471	−	0.0239258i
$485$	−173.684	−	300.829i	−0.358111	−	0.620266i
$486$	−439.477	−	253.732i	−0.904273	−	0.522082i
$487$	255.954	+	113.958i	0.525573	+	0.234000i	0.652332	−	0.757933i	$-0.273791\pi$
$487$	255.954	+	113.958i	0.525573	+	0.234000i	−0.126759	+	0.991934i	$0.540457\pi$
$488$	−155.626	−	140.126i	−0.318906	−	0.287144i
$489$	108.513	−	1032.44i	0.221909	−	2.11132i
$490$	−669.664	−	743.738i	−1.36666	−	1.51783i
$491$	−165.948	+	287.430i	−0.337980	+	0.585398i	−0.984053	−	0.177878i	$-0.943077\pi$
$491$	−165.948	+	287.430i	−0.337980	+	0.585398i	0.646073	+	0.763276i	$0.276410\pi$
$492$	8.20029	−	78.0206i	0.0166673	−	0.158578i
$493$	−42.7963	+	19.0541i	−0.0868079	+	0.0386494i
$494$	−82.5755	−	26.8304i	−0.167157	−	0.0543126i
$495$	−213.216	−	94.9297i	−0.430739	−	0.191777i
$496$	479.909	+	213.669i	0.967558	+	0.430784i
$497$	−108.229	−	333.094i	−0.217764	−	0.670209i
$498$	−43.9666	−	9.34540i	−0.0882864	−	0.0187659i
$499$	−645.232	+	372.525i	−1.29305	+	0.746543i	−0.979194	−	0.202928i	$-0.934954\pi$
$499$	−645.232	+	372.525i	−1.29305	+	0.746543i	−0.313856	+	0.949471i	$0.601621\pi$
$500$	84.4157	−	17.9431i	0.168831	−	0.0358862i
$501$	−160.187	+	144.233i	−0.319734	+	0.287890i
$502$	−382.486	+	424.794i	−0.761924	+	0.846203i
$503$	83.8256	+	257.989i	0.166651	+	0.512900i	0.999154	−	0.0411209i	$-0.0130929\pi$
$503$	83.8256	+	257.989i	0.166651	+	0.512900i	−0.832503	+	0.554021i	$0.813093\pi$
$504$	92.2312	−	433.914i	0.182998	−	0.860940i
$505$	−491.432	+	442.487i	−0.973132	+	0.876212i
$506$	−548.027	+	178.065i	−1.08306	+	0.351907i
$507$	−618.912	+	65.0502i	−1.22073	+	0.128304i
$508$	115.888	−	24.6327i	0.228125	−	0.0484895i
$509$	154.008	+	345.907i	0.302569	+	0.679581i	0.999287	−	0.0377645i	$-0.0120237\pi$
$509$	154.008	+	345.907i	0.302569	+	0.679581i	−0.696718	+	0.717345i	$0.745357\pi$
$510$	317.817	+	103.265i	0.623171	+	0.202481i
$511$	1176.38	+	250.048i	2.30212	+	0.489330i
$512$	−343.210			−0.670333
$513$	−298.323	−	410.606i	−0.581526	−	0.800402i
$514$	−660.209	−	594.455i	−1.28445	−	1.15653i
$515$	391.527	+	174.319i	0.760247	+	0.338484i
$516$	3.74699	−	17.6282i	0.00726160	−	0.0341632i
$517$	327.794			0.634030
$518$	−136.253	−	187.536i	−0.263037	−	0.362039i
$519$	426.166	−	246.047i	0.821129	−	0.474079i
$520$	21.6690	+	29.8248i	0.0416711	+	0.0573554i
$521$	−124.661	+	90.5712i	−0.239272	+	0.173841i	−0.700959	−	0.713202i	$-0.747244\pi$
$521$	−124.661	+	90.5712i	−0.239272	+	0.173841i	0.461687	+	0.887043i	$0.347244\pi$
$522$	−31.9372	−	35.4699i	−0.0611824	−	0.0679499i
$523$	−13.9303	+	4.52622i	−0.0266353	+	0.00865434i	−0.322304	−	0.946636i	$-0.604457\pi$
$523$	−13.9303	+	4.52622i	−0.0266353	+	0.00865434i	0.295669	+	0.955290i	$0.404457\pi$
$524$	−95.7338	−	10.0620i	−0.182698	−	0.0192024i
$525$	309.963	+	225.201i	0.590405	+	0.428954i
$526$	184.818	−	254.381i	0.351366	−	0.483613i
$527$	−287.912	+	61.1976i	−0.546323	+	0.116125i
$528$	688.953	−	397.767i	1.30484	−	0.753347i
$529$	−7.43172	−	12.8721i	−0.0140486	−	0.0243329i
$530$	175.082	+	823.697i	0.330344	+	1.55415i
$531$	345.367	+	250.924i	0.650408	+	0.472549i
$532$	−154.670	+	212.885i	−0.290733	+	0.400160i
$533$	−4.30610	+	40.9698i	−0.00807898	+	0.0768664i
$534$	127.916	+	393.685i	0.239543	+	0.737239i
$535$	−98.2382	+	88.4541i	−0.183623	+	0.165335i
$536$	−375.951	−	517.452i	−0.701401	−	0.965395i
$537$	−1058.75	+	769.228i	−1.97160	+	1.43245i
$538$	171.887	+	297.716i	0.319492	+	0.553376i
$539$	1079.99	−	784.658i	2.00369	−	1.45577i
$540$		−	40.6075i		−	0.0751991i
$541$	83.6716	+	17.7849i	0.154661	+	0.0328742i	0.284591	−	0.958649i	$-0.408142\pi$
$541$	83.6716	+	17.7849i	0.154661	+	0.0328742i	−0.129930	+	0.991523i	$0.541475\pi$
$542$	23.2952	−	52.3219i	0.0429801	−	0.0965349i
$543$	66.2667	−	73.5966i	0.122038	−	0.135537i
$544$	−82.6703	+	60.0635i	−0.151967	+	0.110411i
$545$		−	311.233i		−	0.571069i
$546$	26.2060	−	123.290i	0.0479964	−	0.225805i
$547$	167.175	−	514.511i	0.305621	−	0.940605i	−0.673824	−	0.738892i	$-0.735349\pi$
$547$	167.175	−	514.511i	0.305621	−	0.940605i	0.979445	−	0.201713i	$-0.0646508\pi$
$548$	−2.77766	+	1.23670i	−0.00506873	+	0.00225674i
$549$	28.8983	+	135.956i	0.0526381	+	0.247643i
$550$	21.5126	+	204.679i	0.0391138	+	0.372143i
$551$	−46.4295	−	142.895i	−0.0842640	−	0.259338i
$552$	−408.512	−	453.699i	−0.740058	−	0.821918i
$553$	−1536.44	−	326.581i	−2.77838	−	0.590563i
$554$	375.527	−	122.016i	0.677846	−	0.220246i
$555$	−96.0262	−	86.4624i	−0.173020	−	0.155788i
$556$	56.6283	+	62.8921i	0.101849	+	0.113115i
$557$	178.209	+	838.406i	0.319944	+	1.50522i	0.784754	+	0.619807i	$0.212789\pi$
$557$	178.209	+	838.406i	0.319944	+	1.50522i	−0.464811	+	0.885410i	$0.653878\pi$
$558$	−149.946	−	259.714i	−0.268721	−	0.465438i
$559$	−1.96760	+	9.25682i	−0.00351985	+	0.0165596i
$560$	902.707	−	293.307i	1.61198	−	0.523763i
$561$	−181.301	+	407.208i	−0.323174	+	0.725862i
$562$	374.922	−	842.089i	0.667122	−	1.49838i
$563$	283.011	−	871.019i	0.502684	−	1.54710i	−0.301945	−	0.953325i	$-0.597636\pi$
$563$	283.011	−	871.019i	0.502684	−	1.54710i	0.804629	−	0.593778i	$-0.202364\pi$
$564$	−26.6180	−	59.7850i	−0.0471950	−	0.106002i
$565$	744.010	+	78.1987i	1.31683	+	0.138405i
$566$	807.414	+	466.161i	1.42653	+	0.823606i
$567$	957.032	−	861.715i	1.68789	−	1.51978i
$568$	198.235	+	20.8353i	0.349005	+	0.0366819i
$569$	468.898	−	520.764i	0.824074	−	0.915227i	−0.173500	−	0.984834i	$-0.555508\pi$
$569$	468.898	−	520.764i	0.824074	−	0.915227i	0.997575	+	0.0696069i	$0.0221745\pi$
$570$	−435.933	+	979.121i	−0.764794	+	1.71776i
$571$	79.4259	−	137.570i	0.139100	−	0.240928i	−0.788056	−	0.615603i	$-0.788913\pi$
$571$	79.4259	−	137.570i	0.139100	−	0.240928i	0.927156	+	0.374675i	$0.122246\pi$
$572$	8.02472	−	4.63307i	0.0140292	−	0.00809978i
$573$	136.101	−	14.3048i	0.237524	−	0.0249648i
$574$	833.398	+	371.052i	1.45191	+	0.646433i
$575$	174.642	−	56.7445i	0.303725	−	0.0986861i
$576$	197.990	+	143.848i	0.343733	+	0.249736i
$577$	159.694	−	116.024i	0.276765	−	0.201082i	−0.440740	−	0.897635i	$-0.645284\pi$
$577$	159.694	−	116.024i	0.276765	−	0.201082i	0.717505	+	0.696553i	$0.245284\pi$
$578$	−123.569	+	380.306i	−0.213787	+	0.657968i
$579$	−908.800	−	818.287i	−1.56960	−	1.41328i
$580$	3.71477	−	11.4329i	0.00640478	−	0.0197119i
$581$	35.7673	−	61.9508i	0.0615616	−	0.106628i
$582$	−502.308	−	452.280i	−0.863072	−	0.777113i
$583$	−1117.10	+	117.412i	−1.91613	+	0.201393i
$584$	−402.317	+	553.741i	−0.688898	+	0.948187i
$585$		−	24.4684i		−	0.0418263i
$586$	15.1462	+	34.0189i	0.0258467	+	0.0580527i
$587$	−864.085	+	90.8190i	−1.47204	+	0.154717i	−0.806316	−	0.591485i	$-0.798542\pi$
$587$	−864.085	+	90.8190i	−1.47204	+	0.154717i	−0.665719	+	0.746202i	$0.731875\pi$
$588$	−230.810	−	133.258i	−0.392534	−	0.226629i
$589$	−98.6792	−	938.870i	−0.167537	−	1.59401i
$590$	−82.1205	+	781.324i	−0.139187	+	1.32428i
$591$	135.429	−	28.7863i	0.229152	−	0.0487079i
$592$	150.033	−	31.8904i	0.253433	−	0.0538689i
$593$	51.1944	−	240.851i	0.0863312	−	0.406156i	−0.913669	−	0.406460i	$-0.866763\pi$
$593$	51.1944	−	240.851i	0.0863312	−	0.406156i	1.00000		0.000303251i	$9.65280e-5\pi$
$594$	393.610	+	41.3701i	0.662643	+	0.0696466i
$595$	−312.598	+	430.255i	−0.525376	+	0.723117i
$596$		−	6.49995i		−	0.0109060i
$597$	−688.292	+	306.447i	−1.15292	+	0.513312i
$598$	−40.4225	−	44.8937i	−0.0675961	−	0.0750731i
$599$	109.459	+	245.848i	0.182736	+	0.410431i	0.981566	−	0.191126i	$-0.0612139\pi$
$599$	109.459	+	245.848i	0.182736	+	0.410431i	−0.798830	+	0.601557i	$0.794547\pi$
$600$	−188.837	+	109.025i	−0.314729	+	0.181709i
$601$	−100.089	+	308.043i	−0.166538	+	0.512551i	−0.999146	−	0.0413112i	$-0.986847\pi$
$601$	−100.089	+	308.043i	−0.166538	+	0.512551i	0.832608	+	0.553862i	$0.186847\pi$
$602$	181.493	+	104.785i	0.301484	+	0.174062i
$603$			424.519i			0.704012i
$604$	9.59952	−	95.2866i	0.0158932	−	0.157759i
$605$	75.4769			0.124755
$606$	−643.380	+	1114.37i	−1.06168	+	1.83889i
$607$	−594.869	−	193.285i	−0.980015	−	0.318426i	−0.225163	−	0.974321i	$-0.572291\pi$
$607$	−594.869	−	193.285i	−0.980015	−	0.318426i	−0.754852	+	0.655895i	$0.772291\pi$
$608$	−163.869	−	283.830i	−0.269522	−	0.466825i
$609$	199.259	−	88.7159i	0.327191	−	0.145675i
$610$	−190.091	+	171.158i	−0.311624	+	0.280588i
$611$	13.9775	+	31.3940i	0.0228764	+	0.0513813i
$612$	30.9915			0.0506398
$613$	831.053	+	603.795i	1.35571	+	0.984984i	0.998705	+	0.0508840i	$0.0162039\pi$
$613$	831.053	+	603.795i	1.35571	+	0.984984i	0.357010	+	0.934100i	$0.383796\pi$
$614$	2.79106	−	26.5552i	0.00454570	−	0.0432495i
$615$	497.410	+	105.728i	0.808797	+	0.171915i
$616$	226.406	+	1065.16i	0.367542	+	1.72915i
$617$	247.334	+	1163.61i	0.400865	+	1.88592i	0.460430	+	0.887696i	$0.347695\pi$
$617$	247.334	+	1163.61i	0.400865	+	1.88592i	−0.0595653	+	0.998224i	$0.518971\pi$
$618$	829.380	+	87.1713i	1.34204	+	0.141054i
$619$	321.619	−	33.8035i	0.519578	−	0.0546098i	0.158890	−	0.987296i	$-0.449209\pi$
$619$	321.619	−	33.8035i	0.519578	−	0.0546098i	0.360688	+	0.932687i	$0.382542\pi$
$620$	37.7659	−	65.4124i	0.0609127	−	0.105504i
$621$	−36.9121	−	351.196i	−0.0594398	−	0.565532i
$622$	902.956	−	402.022i	1.45170	−	0.646338i
$623$	−658.780			−1.05743
$624$	67.4734	+	49.0223i	0.108131	+	0.0785614i
$625$	37.3118	+	354.998i	0.0596989	+	0.567997i
$626$	464.891	−	516.313i	0.742637	−	0.824782i
$627$	−1238.09	−	714.812i	−1.97463	−	1.14005i
$628$	−22.3409	−	7.25900i	−0.0355747	−	0.0115589i
$629$	−57.5068	+	63.8678i	−0.0914258	+	0.101539i
$630$	−515.329	−	167.440i	−0.817982	−	0.265778i
$631$	573.448	+	789.284i	0.908793	+	1.25085i	0.967577	+	0.252575i	$0.0812776\pi$
$631$	573.448	+	789.284i	0.908793	+	1.25085i	−0.0587842	+	0.998271i	$0.518722\pi$
$632$	525.456	−	723.228i	0.831418	−	1.14435i
$633$	329.364	+	1013.68i	0.520322	+	1.60139i
$634$	336.183	−	755.079i	0.530257	−	1.19098i
$635$	80.2754	+	763.770i	0.126418	+	1.20279i
$636$	112.127	+	194.210i	0.176300	+	0.305361i
$637$	121.202	+	69.9758i	0.190270	+	0.109852i
$638$	107.035	+	47.6550i	0.167766	+	0.0746944i
$639$	−98.3161	−	88.5242i	−0.153859	−	0.138536i
$640$	−64.3643	+	612.385i	−0.100569	+	0.956852i
$641$	578.412	+	642.392i	0.902360	+	1.00217i	0.999976	+	0.00694768i	$0.00221153\pi$
$641$	578.412	+	642.392i	0.902360	+	1.00217i	−0.0976163	+	0.995224i	$0.531122\pi$
$642$	−128.613	+	222.764i	−0.200332	+	0.346984i
$643$	52.5457	−	499.939i	0.0817195	−	0.777509i	−0.874533	−	0.484966i	$-0.838832\pi$
$643$	52.5457	−	499.939i	0.0817195	−	0.777509i	0.956252	−	0.292543i	$-0.0945015\pi$
$644$	−167.257	+	74.4677i	−0.259716	+	0.115633i
$645$	111.103	+	36.0995i	0.172252	+	0.0559682i
$646$	651.221	+	289.942i	1.00808	+	0.448827i
$647$	−7.82779	−	3.48516i	−0.0120986	−	0.00538664i	0.400678	−	0.916219i	$-0.368774\pi$
$647$	−7.82779	−	3.48516i	−0.0120986	−	0.00538664i	−0.412777	+	0.910832i	$0.635441\pi$
$648$	226.486	+	697.051i	0.349515	+	1.07570i
$649$	−1025.03	−	217.877i	−1.57940	−	0.335712i
$650$	−18.6855	+	10.7881i	−0.0287470	+	0.0165971i
$651$	1340.52	−	284.936i	2.05917	−	0.437689i
$652$	131.670	−	118.557i	0.201949	−	0.181835i
$653$	365.478	−	405.905i	0.559691	−	0.621600i	−0.395186	−	0.918601i	$-0.629320\pi$
$653$	365.478	−	405.905i	0.559691	−	0.621600i	0.954877	+	0.297001i	$0.0959865\pi$
$654$	−187.144	−	575.969i	−0.286152	−	0.880687i
$655$	129.732	−	610.339i	0.198063	−	0.931815i
$656$	−448.589	+	403.911i	−0.683825	+	0.615719i
$657$	432.057	−	140.384i	0.657621	−	0.213674i
$658$	756.839	−	79.5470i	1.15021	−	0.120892i
$659$	233.047	−	49.5356i	0.353637	−	0.0751678i	−0.0276681	−	0.999617i	$-0.508808\pi$
$659$	233.047	−	49.5356i	0.353637	−	0.0751678i	0.381305	+	0.924449i	$0.375475\pi$
$660$	−46.5236	−	104.494i	−0.0704903	−	0.158324i
$661$	−43.1724	−	14.0276i	−0.0653138	−	0.0212217i	0.276178	−	0.961107i	$-0.410932\pi$
$661$	−43.1724	−	14.0276i	−0.0653138	−	0.0212217i	−0.341492	+	0.939885i	$0.610932\pi$
$662$	−340.880	−	72.4562i	−0.514924	−	0.109451i
$663$	−46.7307			−0.0704838
$664$	23.9299	+	32.9366i	0.0360389	+	0.0496033i
$665$	−1267.58	−	1141.34i	−1.90614	−	1.71630i
$666$	−79.9924	−	35.6149i	−0.120109	−	0.0534758i
$667$	21.7349	−	102.255i	0.0325860	−	0.153305i
$668$	−36.7891			−0.0550736
$669$	575.864	+	792.609i	0.860783	+	1.18477i
$670$	−676.584	+	390.626i	−1.00983	+	0.583024i
$671$	−200.550	−	276.033i	−0.298882	−	0.411375i
$672$	384.912	−	279.655i	0.572786	−	0.416153i
$673$	−9.13967	−	10.1506i	−0.0135805	−	0.0150827i	0.736316	−	0.676637i	$-0.236564\pi$
$673$	−9.13967	−	10.1506i	−0.0135805	−	0.0150827i	−0.749897	+	0.661555i	$0.769897\pi$
$674$	−1237.72	+	402.159i	−1.83638	+	0.596675i
$675$	−125.433	−	13.1835i	−0.185827	−	0.0195312i
$676$	−85.9287	−	62.4308i	−0.127113	−	0.0923533i
$677$	−595.970	+	820.282i	−0.880310	+	1.21164i	0.0960256	+	0.995379i	$0.469387\pi$
$677$	−595.970	+	820.282i	−0.880310	+	1.21164i	−0.976335	+	0.216263i	$0.930613\pi$
$678$	1423.89	−	302.657i	2.10013	−	0.446397i
$679$	931.589	−	537.853i	1.37200	−	0.792125i
$680$	−151.336	−	262.122i	−0.222554	−	0.385474i
$681$	54.2651	+	255.297i	0.0796845	+	0.374886i
$682$	595.570	+	432.707i	0.873270	+	0.634467i
$683$	−518.660	+	713.874i	−0.759385	+	1.04520i	0.237880	+	0.971294i	$0.423547\pi$
$683$	−518.660	+	713.874i	−0.759385	+	1.04520i	−0.997265	+	0.0739089i	$0.976453\pi$
$684$	−10.3899	+	98.8536i	−0.0151900	+	0.144523i
$685$	−6.09042	−	18.7444i	−0.00889113	−	0.0273641i
$686$	1305.17	−	1175.18i	1.90258	−	1.71309i
$687$	−234.265	−	322.438i	−0.340997	−	0.469342i
$688$	−112.187	+	81.5084i	−0.163062	+	0.118472i
$689$	−58.8796	−	101.982i	−0.0854566	−	0.148015i
$690$	−603.296	+	438.320i	−0.874342	+	0.635247i
$691$		−	19.2272i		−	0.0278252i	−0.999903	−	0.0139126i	$-0.995571\pi$
$691$		−	19.2272i		−	0.0278252i	0.999903	−	0.0139126i	$-0.00442867\pi$
$692$	82.1521	+	17.4620i	0.118717	+	0.0252340i
$693$	293.973	−	660.273i	0.424203	−	0.952775i
$694$	−486.331	+	540.125i	−0.700765	+	0.778278i
$695$	−443.809	+	322.446i	−0.638574	+	0.463951i
$696$			124.135i			0.178355i
$697$	70.3205	−	330.832i	0.100890	−	0.474651i
$698$	264.540	−	814.171i	0.378998	−	1.16643i
$699$	923.265	−	411.064i	1.32084	−	0.588074i
$700$	13.5955	+	63.9620i	0.0194222	+	0.0913743i
$701$	26.0922	+	248.250i	0.0372214	+	0.354138i	0.997243	+	0.0742104i	$0.0236437\pi$
$701$	26.0922	+	248.250i	0.0372214	+	0.354138i	−0.960021	+	0.279927i	$0.909690\pi$
$702$	12.8218	+	39.4616i	0.0182647	+	0.0562131i
$703$	−184.440	−	204.841i	−0.262361	−	0.291381i
$704$	−587.624	−	124.903i	−0.834693	−	0.177420i
$705$	403.445	−	131.087i	0.572262	−	0.185939i
$706$	−772.791	−	695.824i	−1.09460	−	0.985587i
$707$	−1370.27	−	1521.84i	−1.93814	−	2.15253i
$708$	43.4984	+	204.644i	0.0614384	+	0.289045i
$709$	−160.407	−	277.833i	−0.226244	−	0.391865i	0.730448	−	0.682968i	$-0.239311\pi$
$709$	−160.407	−	277.833i	−0.226244	−	0.391865i	−0.956692	+	0.291103i	$0.905978\pi$
$710$	50.6202	−	238.149i	0.0712961	−	0.335422i
$711$	−564.299	+	183.352i	−0.793669	+	0.257879i
$712$	152.496	−	342.512i	0.214180	−	0.481056i
$713$	267.160	−	600.051i	0.374698	−	0.841586i
$714$	−319.785	+	984.197i	−0.447878	+	1.37843i
$715$	24.4302	+	54.8712i	0.0341682	+	0.0767430i
$716$	−222.135	−	23.3473i	−0.310244	−	0.0326080i
$717$	231.695	+	133.769i	0.323145	+	0.186568i
$718$	877.165	−	789.802i	1.22168	−	1.10000i
$719$	502.612	+	52.8266i	0.699043	+	0.0734723i	0.447382	−	0.894343i	$-0.352357\pi$
$719$	502.612	+	52.8266i	0.699043	+	0.0734723i	0.251661	+	0.967815i	$0.419023\pi$
$720$	239.907	−	266.443i	0.333203	−	0.370060i
$721$	−539.821	+	1212.46i	−0.748711	+	1.68163i
$722$	−754.584	+	1306.98i	−1.04513	+	1.81022i
$723$	383.204	−	221.243i	0.530019	−	0.306007i
$724$	16.8099	−	1.76679i	0.0232181	−	0.00244032i
$725$	−34.1092	−	15.1864i	−0.0470472	−	0.0209467i
$726$	139.678	−	45.3841i	0.192394	−	0.0625125i
$727$	−589.866	−	428.563i	−0.811371	−	0.589495i	0.102857	−	0.994696i	$-0.467202\pi$
$727$	−589.866	−	428.563i	−0.811371	−	0.589495i	−0.914228	+	0.405201i	$0.867202\pi$
$728$	−92.3596	+	67.1032i	−0.126868	+	0.0921747i
$729$	−10.6310	+	32.7189i	−0.0145830	+	0.0448819i
$730$	621.301	+	559.422i	0.851097	+	0.766331i
$731$	24.0101	−	73.8954i	0.0328455	−	0.101088i
$732$	−34.0592	+	58.9923i	−0.0465290	+	0.0805906i
$733$	−73.9440	−	66.5794i	−0.100879	−	0.0908314i	0.617148	−	0.786847i	$-0.288288\pi$
$733$	−73.9440	−	66.5794i	−0.100879	−	0.0908314i	−0.718027	+	0.696015i	$0.754955\pi$
$734$	−305.122	+	32.0696i	−0.415697	+	0.0436916i
$735$	1015.45	−	1397.64i	1.38156	−	1.90156i
$736$		−	228.031i		−	0.309825i
$737$	−423.858	−	952.000i	−0.575112	−	1.29172i
$738$	342.710	−	36.0203i	0.464377	−	0.0488080i
$739$	740.114	+	427.305i	1.00151	+	0.578221i	0.908694	−	0.417463i	$-0.137081\pi$
$739$	740.114	+	427.305i	1.00151	+	0.578221i	0.0928137	+	0.995683i	$0.470414\pi$
$740$	−2.30524	−	21.9329i	−0.00311519	−	0.0296391i
$741$	15.6665	−	149.057i	0.0211424	−	0.201156i
$742$	−2550.77	+	542.184i	−3.43770	+	0.730706i
$743$	336.122	−	71.4450i	0.452385	−	0.0961575i	0.0239164	−	0.999714i	$-0.492386\pi$
$743$	336.122	−	71.4450i	0.452385	−	0.0961575i	0.428469	+	0.903556i	$0.359053\pi$
$744$	−162.163	+	762.918i	−0.217961	+	1.02543i
$745$	41.9025	+	4.40413i	0.0562449	+	0.00591158i
$746$	214.779	−	295.618i	0.287908	−	0.396271i
$747$		−	27.0213i		−	0.0361731i
$748$	−69.4997	+	30.9432i	−0.0929140	+	0.0413680i
$749$	−273.919	−	304.218i	−0.365713	−	0.406166i
$750$	442.746	+	994.424i	0.590328	+	1.32590i
$751$	533.222	−	307.856i	0.710015	−	0.409928i	−0.101051	−	0.994881i	$-0.532221\pi$
$751$	533.222	−	307.856i	0.710015	−	0.409928i	0.811067	+	0.584954i	$0.198887\pi$
$752$	−155.606	+	478.905i	−0.206922	+	0.636841i
$753$	−854.532	−	493.364i	−1.13484	−	0.655198i
$754$			12.2832i			0.0162907i
$755$	607.769	+	126.447i	0.804992	+	0.167479i
$756$	125.751			0.166337
$757$	590.759	−	1023.23i	0.780395	−	1.35168i	−0.151316	−	0.988485i	$-0.548351\pi$
$757$	590.759	−	1023.23i	0.780395	−	1.35168i	0.931712	−	0.363199i	$-0.118316\pi$
$758$	167.139	+	54.3067i	0.220500	+	0.0716447i
$759$	−497.346	−	861.428i	−0.655265	−	1.13495i
$760$	886.827	−	394.841i	1.16688	−	0.519527i
$761$	314.342	−	283.035i	0.413064	−	0.371924i	−0.436238	−	0.899831i	$-0.643690\pi$
$761$	314.342	−	283.035i	0.413064	−	0.371924i	0.849302	+	0.527907i	$0.177023\pi$
$762$	607.811	+	1365.17i	0.797653	+	1.79156i
$763$	963.807			1.26318
$764$	18.8961	+	13.7288i	0.0247331	+	0.0179696i
$765$	−20.9987	+	199.790i	−0.0274493	+	0.261163i
$766$	−554.437	−	117.849i	−0.723808	−	0.153850i
$767$	−22.8417	−	107.462i	−0.0297805	−	0.140106i
$768$	91.8424	+	432.084i	0.119586	+	0.562610i
$769$	−954.394	−	100.311i	−1.24108	−	0.130443i	−0.538858	−	0.842397i	$-0.681144\pi$
$769$	−954.394	−	100.311i	−1.24108	−	0.130443i	−0.702227	+	0.711954i	$0.747811\pi$
$770$	1322.82	−	139.034i	1.71795	−	0.180564i
$771$	766.780	−	1328.10i	0.994527	−	1.72257i
$772$	−21.8170	−	207.575i	−0.0282604	−	0.268880i
$773$	−793.631	+	353.347i	−1.02669	+	0.457112i	−0.849792	−	0.527118i	$-0.823273\pi$
$773$	−793.631	+	353.347i	−1.02669	+	0.457112i	−0.176897	+	0.984229i	$0.556606\pi$
$774$	79.1628			0.102277
$775$	−189.792	−	137.892i	−0.244893	−	0.177925i
$776$	63.9932	+	608.854i	0.0824654	+	0.784606i
$777$	267.751	−	297.368i	0.344596	−	0.382713i
$778$	−235.397	−	135.906i	−0.302566	−	0.174687i
$779$	1031.68	+	335.213i	1.32436	+	0.430311i
$780$	8.02393	−	8.91148i	0.0102871	−	0.0114250i
$781$	308.864	+	100.356i	0.395472	+	0.128497i
$782$	291.531	+	401.257i	0.372801	+	0.513117i
$783$	−42.2040	+	58.0888i	−0.0539003	+	0.0741874i
$784$	633.704	+	1950.34i	0.808296	+	2.48768i
$785$	61.9331	−	139.104i	0.0788957	−	0.177203i
$786$	−126.914	−	1207.50i	−0.161468	−	1.53626i
$787$	550.027	+	952.676i	0.698891	+	1.21052i	0.968851	+	0.247644i	$0.0796562\pi$
$787$	550.027	+	952.676i	0.698891	+	1.21052i	−0.269960	+	0.962872i	$0.587010\pi$
$788$	20.4646	+	11.8153i	0.0259704	+	0.0149940i
$789$	495.849	+	220.766i	0.628452	+	0.279805i
$790$	−811.465	−	730.647i	−1.02717	−	0.924869i
$791$	−242.161	+	2304.01i	−0.306145	+	2.91278i
$792$	275.239	+	305.684i	0.347524	+	0.385964i
$793$	17.8850	−	30.9777i	0.0225536	−	0.0390640i
$794$	−96.1975	+	915.258i	−0.121156	+	1.15272i
$795$	−1327.96	+	591.247i	−1.67039	+	0.743707i
$796$	−122.297	−	39.7366i	−0.153639	−	0.0499204i
$797$	−700.049	−	311.682i	−0.878355	−	0.391069i	−0.0825250	−	0.996589i	$-0.526298\pi$
$797$	−700.049	−	311.682i	−0.878355	−	0.391069i	−0.795830	+	0.605520i	$0.792965\pi$
$798$	−3032.08	−	1349.97i	−3.79960	−	1.69169i
$799$	−87.1871	−	268.334i	−0.109120	−	0.335838i
$800$	−79.6638	−	16.9331i	−0.0995798	−	0.0211663i
$801$	−215.507	+	124.423i	−0.269047	+	0.155335i
$802$	−111.799	+	23.7636i	−0.139400	+	0.0296304i
$803$	−828.738	+	746.199i	−1.03205	+	0.929264i
$804$	−139.213	+	154.612i	−0.173150	+	0.192303i
$805$	−366.735	−	1128.69i	−0.455572	−	1.40211i
$806$	−16.0461	+	75.4911i	−0.0199083	+	0.0936614i
$807$	−441.000	+	397.078i	−0.546468	+	0.492042i
$808$	1108.42	−	360.149i	1.37181	−	0.445729i
$809$	−630.756	+	66.2951i	−0.779674	+	0.0819470i	−0.486000	−	0.873959i	$-0.661545\pi$
$809$	−630.756	+	66.2951i	−0.779674	+	0.0819470i	−0.293674	+	0.955906i	$0.594878\pi$
$810$	875.672	−	186.130i	1.08108	−	0.229790i
$811$	−634.766	−	1425.71i	−0.782695	−	1.75796i	−0.640260	−	0.768158i	$-0.721173\pi$
$811$	−634.766	−	1425.71i	−0.782695	−	1.75796i	−0.142435	−	0.989804i	$-0.545493\pi$
$812$	35.4047	+	11.5037i	0.0436018	+	0.0141671i
$813$	96.7054	+	20.5554i	0.118949	+	0.0252834i
$814$	214.945			0.264060
$815$	675.071	+	929.155i	0.828307	+	1.14007i
$816$	−508.865	−	458.184i	−0.623609	−	0.561500i
$817$	227.655	+	101.358i	0.278647	+	0.124062i
$818$	−53.2131	+	250.348i	−0.0650527	+	0.306049i
$819$	75.7721			0.0925179
$820$	51.0147	+	70.2157i	0.0622130	+	0.0856289i
$821$	−362.548	+	209.317i	−0.441593	+	0.254954i	−0.704273	−	0.709929i	$-0.748727\pi$
$821$	−362.548	+	209.317i	−0.441593	+	0.254954i	0.262680	+	0.964883i	$0.415394\pi$
$822$	−22.5419	−	31.0263i	−0.0274233	−	0.0377449i
$823$	337.135	−	244.943i	0.409641	−	0.297622i	−0.363815	−	0.931471i	$-0.618526\pi$
$823$	337.135	−	244.943i	0.409641	−	0.297622i	0.773456	+	0.633849i	$0.218526\pi$
$824$	−505.420	−	561.326i	−0.613374	−	0.681221i
$825$	−337.876	+	109.783i	−0.409547	+	0.133070i
$826$	−2419.56	−	254.306i	−2.92925	−	0.307876i
$827$	−428.368	−	311.227i	−0.517978	−	0.376333i	0.297864	−	0.954608i	$-0.403726\pi$
$827$	−428.368	−	311.227i	−0.517978	−	0.376333i	−0.815842	+	0.578275i	$0.803726\pi$
$828$	−40.6503	+	55.9503i	−0.0490946	+	0.0675729i
$829$	1379.73	−	293.270i	1.66433	−	0.353764i	0.722894	−	0.690959i	$-0.242811\pi$
$829$	1379.73	−	293.270i	1.66433	−	0.353764i	0.941435	+	0.337195i	$0.109478\pi$
$830$	43.0656	−	24.8640i	0.0518863	−	0.0299566i
$831$	340.798	+	590.280i	0.410106	+	0.710325i
$832$	−13.0945	−	61.6050i	−0.0157386	−	0.0740444i
$833$	−929.585	−	675.383i	−1.11595	−	0.810784i
$834$	−627.428	+	863.581i	−0.752312	+	1.03547i
$835$	24.9270	−	237.164i	0.0298527	−	0.284029i
$836$	−75.3998	−	232.057i	−0.0901911	−	0.277580i
$837$	−335.264	+	301.873i	−0.400555	+	0.360661i
$838$	−123.503	−	169.988i	−0.147379	−	0.202849i
$839$	−678.243	+	492.772i	−0.808395	+	0.587333i	−0.913365	−	0.407142i	$-0.866525\pi$
$839$	−678.243	+	492.772i	−0.808395	+	0.587333i	0.104970	+	0.994475i	$0.466525\pi$
$840$	704.621	+	1220.44i	0.838835	+	1.45290i
$841$	663.187	−	481.834i	0.788570	−	0.572929i
$842$		−	193.810i		−	0.230178i
$843$	1556.41	+	330.826i	1.84628	+	0.392439i
$844$	−73.9900	+	166.184i	−0.0876659	+	0.196901i
$845$	460.688	−	511.646i	0.545193	−	0.605498i
$846$	232.561	−	168.966i	0.274895	−	0.199723i
$847$			233.732i			0.275953i
$848$	358.756	−	1687.82i	0.423062	−	1.99035i
$849$	−497.326	+	1530.61i	−0.585778	+	1.80284i
$850$	161.830	−	72.0513i	0.190388	−	0.0847662i
$851$	−39.8740	−	187.592i	−0.0468554	−	0.220437i
$852$	−6.77730	−	64.4817i	−0.00795458	−	0.0756828i
$853$	208.966	+	643.132i	0.244978	+	0.753965i	0.995640	+	0.0932785i	$0.0297347\pi$
$853$	208.966	+	643.132i	0.244978	+	0.753965i	−0.750662	+	0.660686i	$0.770265\pi$
$854$	−530.033	−	588.661i	−0.620647	−	0.689299i
$855$	−630.229	−	133.959i	−0.737110	−	0.156677i
$856$	221.576	−	71.9945i	0.258851	−	0.0841057i
$857$	−250.222	−	225.301i	−0.291975	−	0.262895i	0.510105	−	0.860112i	$-0.329607\pi$
$857$	−250.222	−	225.301i	−0.291975	−	0.262895i	−0.802080	+	0.597217i	$0.796273\pi$
$858$	78.2047	+	86.8551i	0.0911477	+	0.101230i
$859$	−93.9501	−	442.000i	−0.109371	−	0.514552i	−0.998392	−	0.0566851i	$-0.981947\pi$
$859$	−93.9501	−	442.000i	−0.109371	−	0.514552i	0.889021	−	0.457867i	$-0.151386\pi$
$860$	9.96907	+	17.2669i	0.0115919	+	0.0200778i
$861$	−327.411	+	1540.35i	−0.380269	+	1.78902i
$862$	−879.918	+	285.903i	−1.02079	+	0.331674i
$863$	365.528	−	820.989i	0.423555	−	0.951320i	−0.568167	−	0.822913i	$-0.692347\pi$
$863$	365.528	−	820.989i	0.423555	−	0.951320i	0.991722	−	0.128406i	$-0.0409862\pi$
$864$	−63.7035	+	143.080i	−0.0737309	+	0.165602i
$865$	−168.233	+	517.769i	−0.194489	+	0.598577i
$866$	155.051	+	348.251i	0.179043	+	0.402137i
$867$	−686.489	−	72.1529i	−0.791798	−	0.0832213i
$868$	202.565	+	116.951i	0.233370	+	0.134736i
$869$	1082.39	−	974.592i	1.24556	−	1.12151i
$870$	150.795	+	15.8492i	0.173328	+	0.0182175i
$871$	73.1028	−	81.1889i	0.0839297	−	0.0932134i
$872$	−223.105	+	501.101i	−0.255854	+	0.574657i
$873$	203.167	−	351.896i	0.232723	−	0.403089i
$874$	−1377.63	+	795.372i	−1.57623	+	0.910037i
$875$	−1722.87	+	181.081i	−1.96900	+	0.206950i
$876$	203.393	+	90.5564i	0.232184	+	0.103375i
$877$	225.992	−	73.4294i	0.257688	−	0.0837279i	−0.177324	−	0.984153i	$-0.556744\pi$
$877$	225.992	−	73.4294i	0.257688	−	0.0837279i	0.435012	+	0.900425i	$0.356744\pi$
$878$	915.156	+	664.900i	1.04232	+	0.757289i
$879$	−52.0044	+	37.7834i	−0.0591632	+	0.0429846i
$880$	−271.971	+	837.041i	−0.309058	+	0.951183i
$881$	−204.342	−	183.990i	−0.231943	−	0.208843i	0.544961	−	0.838461i	$-0.316544\pi$
$881$	−204.342	−	183.990i	−0.231943	−	0.208843i	−0.776904	+	0.629619i	$0.783211\pi$
$882$	361.763	−	1113.39i	0.410162	−	1.26235i
$883$	−663.242	+	1148.77i	−0.751123	+	1.30098i	0.196155	+	0.980573i	$0.437154\pi$
$883$	−663.242	+	1148.77i	−0.751123	+	1.30098i	−0.947279	+	0.320411i	$0.896179\pi$
$884$	−5.92710	−	5.33678i	−0.00670486	−	0.00603709i
$885$	−1348.73	+	141.757i	−1.52399	+	0.160177i
$886$	214.738	−	295.561i	0.242368	−	0.333590i
$887$		−	1087.11i		−	1.22560i	−0.790238	−	0.612801i	$-0.790043\pi$
$887$		−	1087.11i		−	1.22560i	0.790238	−	0.612801i	$-0.209957\pi$
$888$	92.6274	+	208.045i	0.104310	+	0.234284i
$889$	−2365.20	+	248.592i	−2.66051	+	0.279631i
$890$	−396.602	−	228.978i	−0.445621	−	0.257279i
$891$	124.821	+	1187.59i	0.140091	+	1.33288i
$892$	−17.4784	+	166.296i	−0.0195946	+	0.186430i
$893$	885.135	−	188.141i	0.991193	−	0.210685i
$894$	80.1931	−	17.0456i	0.0897015	−	0.0190666i
$895$	301.021	−	1416.19i	0.336336	−	1.58234i
$896$	−1896.40	−	199.319i	−2.11651	−	0.222455i
$897$	61.2948	−	84.3650i	0.0683331	−	0.0940524i
$898$		−	247.885i		−	0.276041i
$899$	−122.008	+	54.3214i	−0.135715	+	0.0604242i
$900$	16.5279	+	18.3561i	0.0183644	+	0.0203957i
$901$	393.243	+	883.239i	0.436452	+	0.980288i
$902$	−732.576	+	422.953i	−0.812168	+	0.468906i
$903$	−111.791	+	344.056i	−0.123799	+	0.381015i
$904$	−1141.84	−	659.242i	−1.26310	−	0.729250i
$905$			109.563i			0.121065i
$906$	1200.77	−	131.447i	1.32536	−	0.145085i
$907$	401.300			0.442448			0.221224	−	0.975223i	$-0.428995\pi$
$907$	401.300			0.442448			0.221224	+	0.975223i	$0.428995\pi$
$908$	−22.2730	+	38.5779i	−0.0245297	+	0.0424867i
$909$	−735.684	−	239.038i	−0.809333	−	0.262968i
$910$	69.7226	+	120.763i	0.0766182	+	0.132707i
$911$	1015.61	−	452.180i	1.11483	−	0.496355i	0.235170	−	0.971954i	$-0.424435\pi$
$911$	1015.61	−	452.180i	1.11483	−	0.496355i	0.879662	+	0.475599i	$0.157769\pi$
$912$	1632.06	−	1469.52i	1.78954	−	1.61131i
$913$	26.9792	+	60.5963i	0.0295501	+	0.0663705i
$914$	1839.00			2.01203
$915$	−357.222	−	259.537i	−0.390406	−	0.283647i
$916$	7.11032	−	67.6502i	0.00776236	−	0.0738539i
$917$	1890.06	+	401.745i	2.06113	+	0.438108i
$918$	−70.8273	−	333.216i	−0.0771539	−	0.362981i
$919$	0.963838	+	4.53450i	0.00104879	+	0.00493417i	0.978669	−	0.205444i	$-0.0658638\pi$
$919$	0.963838	+	4.53450i	0.00104879	+	0.00493417i	−0.977620	+	0.210378i	$0.932530\pi$
$920$	671.723	+	70.6009i	0.730133	+	0.0767401i
$921$	45.8397	−	4.81795i	0.0497717	−	0.00523121i
$922$	−200.769	+	347.743i	−0.217754	+	0.377161i
$923$	3.55886	+	33.8603i	0.00385576	+	0.0366851i
$924$	323.590	−	144.071i	0.350205	−	0.155922i
$925$	−68.4973			−0.0740511
$926$	119.844	+	87.0720i	0.129421	+	0.0940302i
$927$	52.4036	+	498.587i	0.0565303	+	0.537850i
$928$	−31.0245	+	34.4562i	−0.0334316	+	0.0371295i
$929$	71.9243	+	41.5255i	0.0774212	+	0.0446991i	0.538211	−	0.842810i	$-0.319100\pi$
$929$	71.9243	+	41.5255i	0.0774212	+	0.0446991i	−0.460790	+	0.887509i	$0.652434\pi$
$930$	906.063	+	294.398i	0.974262	+	0.316557i
$931$	2465.91	−	2738.67i	2.64867	−	2.94165i
$932$	164.047	+	53.3021i	0.176016	+	0.0571911i
$933$	1002.88	+	1380.34i	1.07490	+	1.47947i
$934$	−545.603	+	750.958i	−0.584157	+	0.804023i
$935$	−152.388	−	469.002i	−0.162982	−	0.501606i
$936$	−17.5399	+	39.3954i	−0.0187393	+	0.0420891i
$937$	167.468	+	1593.35i	0.178728	+	1.70048i	0.605274	+	0.796017i	$0.293064\pi$
$937$	167.468	+	1593.35i	0.178728	+	1.70048i	−0.426546	+	0.904466i	$0.640270\pi$
$938$	−1209.67	−	2095.20i	−1.28962	−	2.23369i
$939$	1038.64	+	599.657i	1.10611	+	0.638612i
$940$	66.1415	+	29.4481i	0.0703633	+	0.0313277i
$941$	209.919	+	189.011i	0.223080	+	0.200862i	0.773091	−	0.634295i	$-0.218710\pi$
$941$	209.919	+	189.011i	0.223080	+	0.200862i	−0.550011	+	0.835158i	$0.685376\pi$
$942$	30.9707	−	294.667i	0.0328776	−	0.312810i
$943$	505.028	+	560.891i	0.535555	+	0.594794i
$944$	804.905	−	1394.14i	0.852654	−	1.47684i
$945$	−85.2042	+	810.664i	−0.0901632	+	0.857845i
$946$	−177.525	+	79.0394i	−0.187659	+	0.0835512i
$947$	−559.269	−	181.718i	−0.590569	−	0.191888i	−0.00153928	−	0.999999i	$-0.500490\pi$
$947$	−559.269	−	181.718i	−0.590569	−	0.191888i	−0.589030	+	0.808111i	$0.700490\pi$
$948$	−265.646	−	118.273i	−0.280218	−	0.124761i
$949$	−106.805	−	47.5525i	−0.112544	−	0.0501080i
$950$	175.568	+	540.343i	0.184809	+	0.568782i
$951$	1395.59	+	296.643i	1.46750	+	0.311927i
$952$	811.725	−	468.649i	0.852652	−	0.492279i
$953$	−1292.69	+	274.770i	−1.35645	+	0.288321i	−0.828039	−	0.560670i	$-0.810544\pi$
$953$	−1292.69	+	274.770i	−1.35645	+	0.288321i	−0.528406	+	0.848992i	$0.677210\pi$
$954$	−732.034	+	659.127i	−0.767332	+	0.690908i
$955$	−101.307	+	112.513i	−0.106081	+	0.117815i
$956$	14.1103	+	43.4269i	0.0147597	+	0.0454256i
$957$	−42.0501	+	197.830i	−0.0439395	+	0.206719i
$958$	1327.18	−	1195.00i	1.38537	−	1.24739i
$959$	58.0465	−	18.8604i	0.0605281	−	0.0196668i
$960$	−773.191	+	81.2656i	−0.805407	+	0.0846517i
$961$	119.192	−	25.3350i	0.124029	−	0.0263632i
$962$	9.16552	+	20.5861i	0.00952757	+	0.0213993i
$963$	−147.065	−	47.7842i	−0.152715	−	0.0496202i
$964$	73.8703	+	15.7016i	0.0766289	+	0.0162880i
$965$	1352.93			1.40200
$966$	−1357.36	−	1868.25i	−1.40514	−	1.93401i
$967$	1323.45	+	1191.64i	1.36862	+	1.23231i	0.945249	+	0.326349i	$0.105818\pi$
$967$	1323.45	+	1191.64i	1.36862	+	1.23231i	0.423367	+	0.905958i	$0.360848\pi$
$968$	−121.522	−	54.1050i	−0.125539	−	0.0558936i
$969$	−255.841	+	1203.64i	−0.264026	+	1.24214i
$970$	747.787			0.770914
$971$	−1008.75	−	1388.42i	−1.03888	−	1.42989i	−0.898071	−	0.439851i	$-0.855031\pi$
$971$	−1008.75	−	1388.42i	−1.03888	−	1.42989i	−0.140805	−	0.990037i	$-0.544969\pi$
$972$	129.478	−	74.7539i	0.133207	−	0.0769073i
$973$	−998.531	−	1374.36i	−1.02624	−	1.41250i
$974$	−487.954	+	354.519i	−0.500979	+	0.363983i
$975$	−24.9217	−	27.6784i	−0.0255608	−	0.0283881i
$976$	498.484	−	161.967i	0.510742	−	0.165950i
$977$	146.338	+	15.3807i	0.149783	+	0.0157428i	0.179123	−	0.983827i	$-0.442674\pi$
$977$	146.338	+	15.3807i	0.149783	+	0.0157428i	−0.0293402	+	0.999569i	$0.509341\pi$
$978$	1807.99	+	1313.58i	1.84866	+	1.34313i
$979$	359.053	−	494.194i	0.366755	−	0.504795i
$980$	288.410	−	61.3033i	0.294295	−	0.0625544i
$981$	315.291	−	182.033i	0.321397	−	0.185559i
$982$	−357.241	−	618.759i	−0.363789	−	0.630101i
$983$	183.990	+	865.606i	0.187172	+	0.880575i	0.967039	+	0.254630i	$0.0819535\pi$
$983$	183.990	+	865.606i	0.187172	+	0.880575i	−0.779867	+	0.625946i	$0.784713\pi$
$984$	−725.067	−	526.792i	−0.736856	−	0.535358i
$985$	−90.0343	+	123.922i	−0.0914053	+	0.125809i
$986$	10.5414	−	100.295i	0.0106911	−	0.101719i
$987$	405.943	+	1249.36i	0.411289	+	1.26582i
$988$	19.0098	−	17.1165i	0.0192407	−	0.0173244i
$989$	101.914	+	140.272i	0.103047	+	0.141832i
$990$	406.477	−	295.322i	0.410582	−	0.298306i
$991$	384.149	+	665.365i	0.387637	+	0.671408i	0.992131	−	0.125202i	$-0.0399579\pi$
$991$	384.149	+	665.365i	0.387637	+	0.671408i	−0.604494	+	0.796610i	$0.706625\pi$
$992$	−235.684	+	171.235i	−0.237585	+	0.172616i
$993$		−	601.575i		−	0.605816i
$994$	737.486	+	156.758i	0.741938	+	0.157704i
$995$	339.030	−	761.473i	0.340733	−	0.765299i
$996$	8.86112	−	9.84127i	0.00889671	−	0.00988079i
$997$	−1024.71	+	744.495i	−1.02779	+	0.746735i	−0.967866	−	0.251468i	$-0.919087\pi$
$997$	−1024.71	+	744.495i	−1.02779	+	0.746735i	−0.0599268	+	0.998203i	$0.519087\pi$
$998$		−	1603.89i		−	1.60710i
$999$	−27.3871	+	128.846i	−0.0274145	+	0.128975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.3.i.a.23.7	✓	192
151.46	odd	30	inner	151.3.i.a.46.7	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.3.i.a.23.7	✓	192	1.1	even	1	trivial
151.3.i.a.46.7	yes	192	151.46	odd	30	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	151.i (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07636 + 1.86432i) q^{2} +(-3.53417 - 1.14832i) q^{3} +(-0.317116 - 0.549260i) q^{4} +(3.75572 - 1.67215i) q^{5} +(5.94489 - 5.35281i) q^{6} +(5.17823 + 11.6305i) q^{7} -7.24558 q^{8} +(3.89059 + 2.82668i) q^{9} +(-0.925096 + 8.80170i) q^{10} +(-11.5471 - 2.45441i) q^{11} +(0.490014 + 2.30533i) q^{12} +(-0.257314 - 1.21057i) q^{13} +(-27.2566 - 2.86478i) q^{14} +(-15.1935 + 1.59691i) q^{15} +(9.06734 - 15.7051i) q^{16} +(1.06212 + 10.1054i) q^{17} +(-9.45752 + 4.21076i) q^{18} -32.5891 q^{19} +(-2.10945 - 1.53260i) q^{20} +(-4.94520 - 47.0504i) q^{21} +(17.0046 - 18.8856i) q^{22} +(-19.6368 - 11.3373i) q^{23} +(25.6071 + 8.32027i) q^{24} +(-5.41892 + 6.01833i) q^{25} +(2.53384 + 0.823294i) q^{26} +(9.15407 + 12.5995i) q^{27} +(4.74607 - 6.53240i) q^{28} +(1.42469 + 4.38475i) q^{29} +(13.3766 - 30.0444i) q^{30} +(3.02798 + 28.8093i) q^{31} +(5.02834 + 8.70934i) q^{32} +(37.9909 + 21.9341i) q^{33} +(-19.9828 - 8.89691i) q^{34} +(38.8959 + 35.0221i) q^{35} +(0.318816 - 3.03333i) q^{36} +(5.65955 + 6.28557i) q^{37} +(35.0777 - 60.7564i) q^{38} +(-0.480729 + 4.57383i) q^{39} +(-27.2124 + 12.1157i) q^{40} +(-31.6572 - 10.2860i) q^{41} +(93.0397 + 41.4240i) q^{42} +(-6.98561 - 3.11019i) q^{43} +(2.31365 + 7.12068i) q^{44} +(19.3386 + 4.11055i) q^{45} +(42.2726 - 24.4061i) q^{46} +(-27.1605 + 5.77314i) q^{47} +(-50.0801 + 45.0923i) q^{48} +(-75.6668 + 84.0365i) q^{49} +(-5.38733 - 16.5805i) q^{50} +(7.85051 - 36.9337i) q^{51} +(-0.583317 + 0.525221i) q^{52} +(90.4935 - 29.4031i) q^{53} +(-33.3425 + 3.50444i) q^{54} +(-47.4717 + 10.0904i) q^{55} +(-37.5192 - 84.2696i) q^{56} +(115.176 + 37.4228i) q^{57} +(-9.70806 - 2.06351i) q^{58} +88.7697 q^{59} +(5.69523 + 7.83881i) q^{60} +(21.4787 + 19.3395i) q^{61} +(-56.9689 - 25.3642i) q^{62} +(-12.7293 + 59.8867i) q^{63} +50.8894 q^{64} +(-2.99065 - 4.11628i) q^{65} +(-81.7841 + 47.2181i) q^{66} +(51.8869 + 71.4162i) q^{67} +(5.21366 - 3.78794i) q^{68} +(56.3809 + 62.6173i) q^{69} +(-107.158 + 34.8179i) q^{70} +(-27.3594 - 2.87559i) q^{71} +(-28.1896 - 20.4809i) q^{72} +(55.5258 - 76.4247i) q^{73} +(-17.8100 + 3.78564i) q^{74} +(26.0624 - 15.0471i) q^{75} +(10.3345 + 17.8999i) q^{76} +(-31.2474 - 147.008i) q^{77} +(-8.00962 - 5.81933i) q^{78} +(-72.5209 + 99.8164i) q^{79} +(7.79305 - 74.1459i) q^{80} +(-31.2585 - 96.2036i) q^{81} +(53.2510 - 47.9474i) q^{82} +(-3.30268 - 4.54575i) q^{83} +(-24.2747 + 17.6366i) q^{84} +(20.8867 + 36.1769i) q^{85} +(13.3174 - 9.67568i) q^{86} -17.1325i q^{87} +(83.6653 + 17.7836i) q^{88} +(-21.0468 + 47.2719i) q^{89} +(-28.4788 + 31.6289i) q^{90} +(12.7470 - 9.26126i) q^{91} +14.3809i q^{92} +(22.3810 - 105.294i) q^{93} +(18.4716 - 56.8497i) q^{94} +(-122.396 + 54.4940i) q^{95} +(-7.76990 - 36.5545i) q^{96} +(-8.83203 - 84.0311i) q^{97} +(-75.2256 - 231.521i) q^{98} +(-37.9871 - 42.1890i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 5 q^{2} - 10 q^{3} - 181 q^{4} - 9 q^{5} + 13 q^{6} - 31 q^{7} + 80 q^{8} + 124 q^{9} + 41 q^{10} + 25 q^{11} + 55 q^{12} - 28 q^{13} + 7 q^{14} - 34 q^{15} - 321 q^{16} - 82 q^{17} - 194 q^{18}+ \cdots - 1441 q^{99}+O(q^{100}) \) 192 * q - 5 * q^2 - 10 * q^3 - 181 * q^4 - 9 * q^5 + 13 * q^6 - 31 * q^7 + 80 * q^8 + 124 * q^9 + 41 * q^10 + 25 * q^11 + 55 * q^12 - 28 * q^13 + 7 * q^14 - 34 * q^15 - 321 * q^16 - 82 * q^17 - 194 * q^18 - 72 * q^19 + 127 * q^20 - 38 * q^21 - 114 * q^22 + 165 * q^23 - 55 * q^24 + 203 * q^25 - 125 * q^26 + 155 * q^27 + 50 * q^28 + 55 * q^29 + 253 * q^30 + 108 * q^31 - 40 * q^32 + 117 * q^33 - 123 * q^34 + 186 * q^35 - 503 * q^36 - 377 * q^37 - 128 * q^38 + 261 * q^39 - 650 * q^40 + 60 * q^41 + 1000 * q^42 + 150 * q^43 - 274 * q^44 - 41 * q^45 + 93 * q^46 - 135 * q^47 - 644 * q^48 - 293 * q^49 + 350 * q^50 - 166 * q^51 + 606 * q^52 + 225 * q^53 + 382 * q^54 + 458 * q^55 - 713 * q^56 + 20 * q^57 + 216 * q^58 + 368 * q^59 - 120 * q^60 - 128 * q^61 - 522 * q^62 - 717 * q^63 + 788 * q^64 + 445 * q^65 + 759 * q^66 + 130 * q^67 + 218 * q^68 - 127 * q^69 - 1025 * q^70 - 247 * q^71 + 396 * q^72 + 350 * q^73 + 86 * q^74 - 882 * q^75 + 145 * q^76 - 260 * q^77 + 564 * q^78 - 1030 * q^79 + 151 * q^80 - 506 * q^81 + 268 * q^82 + 250 * q^83 - 320 * q^84 - 466 * q^85 - 294 * q^86 - 253 * q^88 - 479 * q^89 + 1861 * q^90 + 1252 * q^91 - 863 * q^93 + 7 * q^94 - 583 * q^95 + 1067 * q^96 - 278 * q^97 + 554 * q^98 - 1441 * q^99

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