LMFDB - Embedded newform 75.3.k.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(13,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19]))

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

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

chi := DirichletCharacter("75.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.k (of order $20$, degree $8$, 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:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.2
Character	$\chi$	$=$	75.13
Dual form			75.3.k.a.52.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.60745 + 0.412980i) q^{2} +(0.786335 - 1.54327i) q^{3} +(2.82402 - 0.917581i) q^{4} +(-1.42490 + 4.79267i) q^{5} +(-1.41299 + 4.34874i) q^{6} +(5.98338 - 5.98338i) q^{7} +(2.42430 - 1.23524i) q^{8} +(-1.76336 - 2.42705i) q^{9} +O(q^{10})$	\(q+(-2.60745 + 0.412980i) q^{2} +(0.786335 - 1.54327i) q^{3} +(2.82402 - 0.917581i) q^{4} +(-1.42490 + 4.79267i) q^{5} +(-1.41299 + 4.34874i) q^{6} +(5.98338 - 5.98338i) q^{7} +(2.42430 - 1.23524i) q^{8} +(-1.76336 - 2.42705i) q^{9} +(1.73607 - 13.0851i) q^{10} +(13.4856 + 9.79785i) q^{11} +(0.804553 - 5.07975i) q^{12} +(20.8493 + 3.30220i) q^{13} +(-13.1304 + 18.0724i) q^{14} +(6.27593 + 5.96764i) q^{15} +(-15.4202 + 11.2034i) q^{16} +(-10.4375 - 20.4848i) q^{17} +(5.60019 + 5.60019i) q^{18} +(8.88586 + 2.88719i) q^{19} +(0.373717 + 14.8421i) q^{20} +(-4.52902 - 13.9389i) q^{21} +(-39.2093 - 19.9781i) q^{22} +(0.840422 + 5.30621i) q^{23} -4.71267i q^{24} +(-20.9393 - 13.6581i) q^{25} -55.7272 q^{26} +(-5.13218 + 0.812857i) q^{27} +(11.4070 - 22.3874i) q^{28} +(-20.9015 + 6.79131i) q^{29} +(-18.8287 - 12.9685i) q^{30} +(-3.67506 + 11.3107i) q^{31} +(27.8848 - 27.8848i) q^{32} +(25.7249 - 13.1075i) q^{33} +(35.6752 + 49.1027i) q^{34} +(20.1506 + 37.2020i) q^{35} +(-7.20677 - 5.23603i) q^{36} +(-7.04822 + 44.5007i) q^{37} +(-24.3618 - 3.85853i) q^{38} +(21.4907 - 29.5794i) q^{39} +(2.46573 + 13.3790i) q^{40} +(49.1533 - 35.7120i) q^{41} +(17.5657 + 34.4746i) q^{42} +(-19.8888 - 19.8888i) q^{43} +(47.0739 + 15.2952i) q^{44} +(14.1447 - 4.99288i) q^{45} +(-4.38272 - 13.4886i) q^{46} +(-30.4015 - 15.4904i) q^{47} +(5.16445 + 32.6071i) q^{48} -22.6016i q^{49} +(60.2388 + 26.9654i) q^{50} -39.8210 q^{51} +(61.9088 - 9.80539i) q^{52} +(15.7315 - 30.8749i) q^{53} +(13.0462 - 4.23897i) q^{54} +(-66.1734 + 50.6710i) q^{55} +(7.11459 - 21.8965i) q^{56} +(11.4430 - 11.4430i) q^{57} +(51.6950 - 26.3399i) q^{58} +(8.53853 + 11.7523i) q^{59} +(23.1992 + 11.0941i) q^{60} +(11.7754 + 8.55534i) q^{61} +(4.91146 - 31.0097i) q^{62} +(-25.0728 - 3.97114i) q^{63} +(-16.3787 + 22.5434i) q^{64} +(-45.5344 + 95.2183i) q^{65} +(-61.6633 + 44.8010i) q^{66} +(6.67100 + 13.0926i) q^{67} +(-48.2723 - 48.2723i) q^{68} +(8.84977 + 2.87546i) q^{69} +(-67.9055 - 88.6807i) q^{70} +(-15.5502 - 47.8586i) q^{71} +(-7.27291 - 3.70573i) q^{72} +(-1.42052 - 8.96883i) q^{73} -118.944i q^{74} +(-37.5435 + 21.5752i) q^{75} +27.7431 q^{76} +(139.314 - 22.0651i) q^{77} +(-43.8202 + 86.0020i) q^{78} +(-30.1612 + 9.79997i) q^{79} +(-31.7220 - 89.8674i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(-113.416 + 113.416i) q^{82} +(-127.859 + 65.1473i) q^{83} +(-25.5801 - 35.2080i) q^{84} +(113.049 - 20.8349i) q^{85} +(60.0728 + 43.6454i) q^{86} +(-5.95476 + 37.5969i) q^{87} +(44.7959 + 7.09497i) q^{88} +(-56.4424 + 77.6863i) q^{89} +(-34.8195 + 18.8601i) q^{90} +(144.507 - 104.991i) q^{91} +(7.24225 + 14.2137i) q^{92} +(14.5656 + 14.5656i) q^{93} +(85.6677 + 27.8351i) q^{94} +(-26.4988 + 38.4730i) q^{95} +(-21.1069 - 64.9604i) q^{96} +(-157.426 - 80.2125i) q^{97} +(9.33402 + 58.9327i) q^{98} -50.0073i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$

Coefficient data

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

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

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

$2$	−2.60745	+	0.412980i	−1.30373	+	0.206490i	−0.769388	−	0.638782i	$-0.779439\pi$
$2$	−2.60745	+	0.412980i	−1.30373	+	0.206490i	−0.534337	+	0.845271i	$0.679439\pi$
$3$	0.786335	−	1.54327i	0.262112	−	0.514423i
$3$	0.786335	−	1.54327i	0.262112	−	0.514423i
$4$	2.82402	−	0.917581i	0.706006	−	0.229395i
$5$	−1.42490	+	4.79267i	−0.284979	+	0.958534i
$5$	−1.42490	+	4.79267i	−0.284979	+	0.958534i
$6$	−1.41299	+	4.34874i	−0.235498	+	0.724790i
$7$	5.98338	−	5.98338i	0.854768	−	0.854768i	−0.135948	−	0.990716i	$-0.543408\pi$
$7$	5.98338	−	5.98338i	0.854768	−	0.854768i	0.990716	+	0.135948i	$0.0434079\pi$
$8$	2.42430	−	1.23524i	0.303038	−	0.154406i
$9$	−1.76336	−	2.42705i	−0.195928	−	0.269672i
$10$	1.73607	−	13.0851i	0.173607	−	1.30851i
$11$	13.4856	+	9.79785i	1.22596	+	0.890714i	0.996581	−	0.0826231i	$-0.0263298\pi$
$11$	13.4856	+	9.79785i	1.22596	+	0.890714i	0.229381	+	0.973337i	$0.426330\pi$
$12$	0.804553	−	5.07975i	0.0670461	−	0.423313i
$13$	20.8493	+	3.30220i	1.60379	+	0.254015i	0.893223	−	0.449615i	$-0.148439\pi$
$13$	20.8493	+	3.30220i	1.60379	+	0.254015i	0.710566	+	0.703630i	$0.248439\pi$
$14$	−13.1304	+	18.0724i	−0.937882	+	1.29088i
$15$	6.27593	+	5.96764i	0.418395	+	0.397843i
$16$	−15.4202	+	11.2034i	−0.963759	+	0.700212i
$17$	−10.4375	−	20.4848i	−0.613973	−	1.20499i	−0.963411	−	0.268030i	$-0.913627\pi$
$17$	−10.4375	−	20.4848i	−0.613973	−	1.20499i	0.349438	−	0.936960i	$-0.386373\pi$
$18$	5.60019	+	5.60019i	0.311121	+	0.311121i
$19$	8.88586	+	2.88719i	0.467677	+	0.151957i	0.533369	−	0.845883i	$-0.320926\pi$
$19$	8.88586	+	2.88719i	0.467677	+	0.151957i	−0.0656925	+	0.997840i	$0.520926\pi$
$20$	0.373717	+	14.8421i	0.0186859	+	0.742103i
$21$	−4.52902	−	13.9389i	−0.215668	−	0.663757i
$22$	−39.2093	−	19.9781i	−1.78224	−	0.908097i
$23$	0.840422	+	5.30621i	0.0365401	+	0.230705i	0.999199	−	0.0400115i	$-0.0127394\pi$
$23$	0.840422	+	5.30621i	0.0365401	+	0.230705i	−0.962659	+	0.270716i	$0.912739\pi$
$24$		−	4.71267i		−	0.196361i
$25$	−20.9393	−	13.6581i	−0.837573	−	0.546325i
$26$	−55.7272			−2.14335
$27$	−5.13218	+	0.812857i	−0.190081	+	0.0301058i
$28$	11.4070	−	22.3874i	0.407392	−	0.799551i
$29$	−20.9015	+	6.79131i	−0.720742	+	0.234183i	−0.646345	−	0.763045i	$-0.723703\pi$
$29$	−20.9015	+	6.79131i	−0.720742	+	0.234183i	−0.0743971	+	0.997229i	$0.523703\pi$
$30$	−18.8287	−	12.9685i	−0.627623	−	0.432283i
$31$	−3.67506	+	11.3107i	−0.118550	+	0.364860i	−0.992671	−	0.120849i	$-0.961438\pi$
$31$	−3.67506	+	11.3107i	−0.118550	+	0.364860i	0.874121	+	0.485709i	$0.161438\pi$
$32$	27.8848	−	27.8848i	0.871399	−	0.871399i
$33$	25.7249	−	13.1075i	0.779542	−	0.397197i
$34$	35.6752	+	49.1027i	1.04927	+	1.44420i
$35$	20.1506	+	37.2020i	0.575733	+	1.06292i
$36$	−7.20677	−	5.23603i	−0.200188	−	0.145445i
$37$	−7.04822	+	44.5007i	−0.190492	+	1.20272i	0.688267	+	0.725457i	$0.258372\pi$
$37$	−7.04822	+	44.5007i	−0.190492	+	1.20272i	−0.878760	+	0.477264i	$0.841628\pi$
$38$	−24.3618	−	3.85853i	−0.641100	−	0.101540i
$39$	21.4907	−	29.5794i	0.551043	−	0.758445i
$40$	2.46573	+	13.3790i	0.0616433	+	0.334474i
$41$	49.1533	−	35.7120i	1.19886	−	0.871023i	0.204689	−	0.978827i	$-0.434382\pi$
$41$	49.1533	−	35.7120i	1.19886	−	0.871023i	0.994172	+	0.107804i	$0.0343819\pi$
$42$	17.5657	+	34.4746i	0.418231	+	0.820824i
$43$	−19.8888	−	19.8888i	−0.462531	−	0.462531i	0.436953	−	0.899484i	$-0.356057\pi$
$43$	−19.8888	−	19.8888i	−0.462531	−	0.462531i	−0.899484	+	0.436953i	$0.856057\pi$
$44$	47.0739	+	15.2952i	1.06986	+	0.347619i
$45$	14.1447	−	4.99288i	0.314326	−	0.110953i
$46$	−4.38272	−	13.4886i	−0.0952764	−	0.293231i
$47$	−30.4015	−	15.4904i	−0.646841	−	0.329582i	0.0996059	−	0.995027i	$-0.468242\pi$
$47$	−30.4015	−	15.4904i	−0.646841	−	0.329582i	−0.746447	+	0.665445i	$0.768242\pi$
$48$	5.16445	+	32.6071i	0.107593	+	0.679314i
$49$		−	22.6016i		−	0.461258i
$50$	60.2388	+	26.9654i	1.20478	+	0.539307i
$51$	−39.8210			−0.780803
$52$	61.9088	−	9.80539i	1.19055	−	0.188565i
$53$	15.7315	−	30.8749i	0.296821	−	0.582545i	−0.693642	−	0.720320i	$-0.743995\pi$
$53$	15.7315	−	30.8749i	0.296821	−	0.582545i	0.990464	+	0.137775i	$0.0439951\pi$
$54$	13.0462	−	4.23897i	0.241597	−	0.0784995i
$55$	−66.1734	+	50.6710i	−1.20315	+	0.921291i
$56$	7.11459	−	21.8965i	0.127046	−	0.391008i
$57$	11.4430	−	11.4430i	0.200754	−	0.200754i
$58$	51.6950	−	26.3399i	0.891293	−	0.454137i
$59$	8.53853	+	11.7523i	0.144721	+	0.199191i	0.875224	−	0.483719i	$-0.160714\pi$
$59$	8.53853	+	11.7523i	0.144721	+	0.199191i	−0.730503	+	0.682910i	$0.760714\pi$
$60$	23.1992	+	11.0941i	0.386653	+	0.184901i
$61$	11.7754	+	8.55534i	0.193040	+	0.140251i	0.680107	−	0.733113i	$-0.261933\pi$
$61$	11.7754	+	8.55534i	0.193040	+	0.140251i	−0.487067	+	0.873364i	$0.661933\pi$
$62$	4.91146	−	31.0097i	0.0792171	−	0.500157i
$63$	−25.0728	−	3.97114i	−0.397981	−	0.0630340i
$64$	−16.3787	+	22.5434i	−0.255918	+	0.352240i
$65$	−45.5344	+	95.2183i	−0.700529	+	1.46490i
$66$	−61.6633	+	44.8010i	−0.934292	+	0.678803i
$67$	6.67100	+	13.0926i	0.0995672	+	0.195412i	0.935417	−	0.353547i	$-0.115024\pi$
$67$	6.67100	+	13.0926i	0.0995672	+	0.195412i	−0.835850	+	0.548958i	$0.815024\pi$
$68$	−48.2723	−	48.2723i	−0.709887	−	0.709887i
$69$	8.84977	+	2.87546i	0.128257	+	0.0416734i
$70$	−67.9055	−	88.6807i	−0.970079	−	1.26687i
$71$	−15.5502	−	47.8586i	−0.219017	−	0.674065i	−0.998844	−	0.0480700i	$-0.984693\pi$
$71$	−15.5502	−	47.8586i	−0.219017	−	0.674065i	0.779827	−	0.625995i	$-0.215307\pi$
$72$	−7.27291	−	3.70573i	−0.101013	−	0.0514685i
$73$	−1.42052	−	8.96883i	−0.0194592	−	0.122861i	0.976047	−	0.217562i	$-0.0698104\pi$
$73$	−1.42052	−	8.96883i	−0.0194592	−	0.122861i	−0.995506	+	0.0947013i	$0.969810\pi$
$74$		−	118.944i		−	1.60735i
$75$	−37.5435	+	21.5752i	−0.500580	+	0.287669i
$76$	27.7431			0.365041
$77$	139.314	−	22.0651i	1.80927	−	0.286560i
$78$	−43.8202	+	86.0020i	−0.561797	+	1.10259i
$79$	−30.1612	+	9.79997i	−0.381787	+	0.124050i	−0.493622	−	0.869677i	$-0.664327\pi$
$79$	−30.1612	+	9.79997i	−0.381787	+	0.124050i	0.111834	+	0.993727i	$0.464327\pi$
$80$	−31.7220	−	89.8674i	−0.396525	−	1.12334i
$81$	−2.78115	+	8.55951i	−0.0343352	+	0.105673i
$82$	−113.416	+	113.416i	−1.38313	+	1.38313i
$83$	−127.859	+	65.1473i	−1.54047	+	0.784907i	−0.998461	−	0.0554667i	$-0.982335\pi$
$83$	−127.859	+	65.1473i	−1.54047	+	0.784907i	−0.542007	+	0.840374i	$0.682335\pi$
$84$	−25.5801	−	35.2080i	−0.304525	−	0.419143i
$85$	113.049	−	20.8349i	1.32999	−	0.245116i
$86$	60.0728	+	43.6454i	0.698521	+	0.507505i
$87$	−5.95476	+	37.5969i	−0.0684456	+	0.432148i
$88$	44.7959	+	7.09497i	0.509044	+	0.0806247i
$89$	−56.4424	+	77.6863i	−0.634184	+	0.872879i	−0.998289	−	0.0584786i	$-0.981375\pi$
$89$	−56.4424	+	77.6863i	−0.634184	+	0.872879i	0.364105	+	0.931358i	$0.381375\pi$
$90$	−34.8195	+	18.8601i	−0.386884	+	0.209557i
$91$	144.507	−	104.991i	1.58799	−	1.15374i
$92$	7.24225	+	14.2137i	0.0787201	+	0.154497i
$93$	14.5656	+	14.5656i	0.156619	+	0.156619i
$94$	85.6677	+	27.8351i	0.911358	+	0.296118i
$95$	−26.4988	+	38.4730i	−0.278934	+	0.404979i
$96$	−21.1069	−	64.9604i	−0.219864	−	0.676671i
$97$	−157.426	−	80.2125i	−1.62295	−	0.826933i	−0.998965	−	0.0454949i	$-0.985514\pi$
$97$	−157.426	−	80.2125i	−1.62295	−	0.826933i	−0.623983	−	0.781438i	$-0.714486\pi$
$98$	9.33402	+	58.9327i	0.0952451	+	0.601354i
$99$		−	50.0073i		−	0.505124i
$100$	−71.6656	−	19.3573i	−0.716656	−	0.193573i
$101$	5.66123			0.0560518			0.0280259	−	0.999607i	$-0.491078\pi$
$101$	5.66123			0.0560518			0.0280259	+	0.999607i	$0.491078\pi$
$102$	103.831	−	16.4453i	1.01795	−	0.161228i
$103$	8.25683	−	16.2049i	0.0801634	−	0.157330i	−0.847445	−	0.530882i	$-0.821861\pi$
$103$	8.25683	−	16.2049i	0.0801634	−	0.157330i	0.927609	+	0.373553i	$0.121861\pi$
$104$	54.6240	−	17.7484i	0.525230	−	0.170658i
$105$	73.2579	−	1.84461i	0.697694	−	0.0175677i
$106$	−28.2685	+	87.0015i	−0.266684	+	0.820769i
$107$	−23.7705	+	23.7705i	−0.222154	+	0.222154i	−0.809405	−	0.587251i	$-0.800210\pi$
$107$	−23.7705	+	23.7705i	−0.222154	+	0.222154i	0.587251	+	0.809405i	$0.300210\pi$
$108$	−13.7475	+	7.00472i	−0.127292	+	0.0648585i
$109$	−48.3468	−	66.5437i	−0.443549	−	0.610493i	0.527447	−	0.849588i	$-0.323149\pi$
$109$	−48.3468	−	66.5437i	−0.443549	−	0.610493i	−0.970996	+	0.239095i	$0.923149\pi$
$110$	151.618	−	159.450i	1.37834	−	1.44955i
$111$	63.1343	+	45.8697i	0.568777	+	0.413241i
$112$	−25.2304	+	159.299i	−0.225272	+	1.42231i
$113$	4.92541	+	0.780108i	0.0435877	+	0.00690361i	0.178190	−	0.983996i	$-0.442976\pi$
$113$	4.92541	+	0.780108i	0.0435877	+	0.00690361i	−0.134603	+	0.990900i	$0.542976\pi$
$114$	−25.1113	+	34.5627i	−0.220274	+	0.303181i
$115$	−26.6284	−	3.53295i	−0.231552	−	0.0307213i
$116$	−52.7948	+	38.3577i	−0.455127	+	0.330669i
$117$	−28.7501	−	56.4252i	−0.245727	−	0.482266i
$118$	−27.1173	−	27.1173i	−0.229807	−	0.229807i
$119$	−185.020	−	60.1167i	−1.55479	−	0.505182i
$120$	22.5863	+	6.71507i	0.188219	+	0.0559589i
$121$	48.4720	+	149.182i	0.400595	+	1.23291i
$122$	−34.2370	−	17.4446i	−0.280631	−	0.142989i
$123$	−16.4622	−	103.938i	−0.133839	−	0.845027i
$124$			35.3137i			0.284788i
$125$	95.2952	−	80.8939i	0.762362	−	0.647151i
$126$	67.0161			0.531874
$127$	−48.9427	+	7.75176i	−0.385376	+	0.0610375i	−0.346116	−	0.938192i	$-0.612500\pi$
$127$	−48.9427	+	7.75176i	−0.385376	+	0.0610375i	−0.0392591	+	0.999229i	$0.512500\pi$
$128$	−38.2157	+	75.0025i	−0.298560	+	0.585957i
$129$	−46.3331	+	15.0545i	−0.359171	+	0.116702i
$130$	79.4055	−	267.082i	0.610811	−	2.05448i
$131$	−24.1400	+	74.2952i	−0.184275	+	0.567139i	−0.999935	−	0.0113918i	$-0.996374\pi$
$131$	−24.1400	+	74.2952i	−0.184275	+	0.567139i	0.815660	+	0.578531i	$0.196374\pi$
$132$	60.6205	−	60.6205i	0.459246	−	0.459246i
$133$	70.4426	−	35.8923i	0.529644	−	0.269867i
$134$	−22.8013	−	31.3833i	−0.170159	−	0.234204i
$135$	3.41707	−	25.7551i	0.0253116	−	0.190778i
$136$	−50.6075	−	36.7685i	−0.372114	−	0.270357i
$137$	−0.183368	+	1.15774i	−0.00133845	+	0.00845067i	−0.988349	−	0.152208i	$-0.951362\pi$
$137$	−0.183368	+	1.15774i	−0.00133845	+	0.00845067i	0.987010	+	0.160658i	$0.0513617\pi$
$138$	−24.2628	−	3.84286i	−0.175818	−	0.0278468i
$139$	−98.7560	+	135.926i	−0.710475	+	0.977885i	0.289312	+	0.957235i	$0.406574\pi$
$139$	−98.7560	+	135.926i	−0.710475	+	0.977885i	−0.999787	+	0.0206501i	$0.993426\pi$
$140$	91.0418	+	86.5696i	0.650298	+	0.618354i
$141$	−47.8115	+	34.7371i	−0.339089	+	0.246363i
$142$	60.3111	+	118.367i	0.424726	+	0.833571i
$143$	248.810	+	248.810i	1.73993	+	1.73993i
$144$	54.3824	+	17.6699i	0.377656	+	0.122708i
$145$	−2.76601	−	109.851i	−0.0190759	−	0.757593i
$146$	7.40789	+	22.7991i	0.0507390	+	0.156158i
$147$	−34.8804	−	17.7724i	−0.237282	−	0.120901i
$148$	20.9286	+	132.138i	0.141410	+	0.892826i
$149$		−	110.913i		−	0.744385i	−0.928156	−	0.372193i	$-0.878606\pi$
$149$		−	110.913i		−	0.744385i	0.928156	−	0.372193i	$-0.121394\pi$
$150$	88.9827	−	71.7609i	0.593218	−	0.478406i
$151$	175.747			1.16389			0.581943	−	0.813230i	$-0.302293\pi$
$151$	175.747			1.16389			0.581943	+	0.813230i	$0.302293\pi$
$152$	25.1084	−	3.97678i	0.165187	−	0.0261630i
$153$	−31.3126	+	61.4545i	−0.204658	+	0.401663i
$154$	−354.141	+	115.067i	−2.29962	+	0.747191i
$155$	−48.9717	−	33.7299i	−0.315946	−	0.217612i
$156$	33.5487	−	103.252i	0.215056	−	0.661873i
$157$	170.397	−	170.397i	1.08533	−	1.08533i	0.0893292	−	0.996002i	$-0.471528\pi$
$157$	170.397	−	170.397i	1.08533	−	1.08533i	0.996002	−	0.0893292i	$-0.0284723\pi$
$158$	74.5967	−	38.0089i	0.472131	−	0.240563i
$159$	−35.2780	−	48.5560i	−0.221874	−	0.305383i
$160$	93.9095	+	173.375i	0.586934	+	1.08360i
$161$	36.7776	+	26.7205i	0.228433	+	0.165966i
$162$	3.71682	−	23.4671i	0.0229433	−	0.144858i
$163$	−143.354	−	22.7050i	−0.879470	−	0.139294i	−0.299660	−	0.954046i	$-0.596873\pi$
$163$	−143.354	−	22.7050i	−0.879470	−	0.139294i	−0.579810	+	0.814752i	$0.696873\pi$
$164$	106.041	−	145.953i	0.646594	−	0.889960i
$165$	26.1645	+	141.968i	0.158573	+	0.860410i
$166$	306.481	−	222.671i	1.84627	−	1.34139i
$167$	135.719	+	266.363i	0.812687	+	1.59499i	0.803705	+	0.595027i	$0.202859\pi$
$167$	135.719	+	266.363i	0.812687	+	1.59499i	0.00898118	+	0.999960i	$0.497141\pi$
$168$	−28.1977	−	28.1977i	−0.167843	−	0.167843i
$169$	263.058	+	85.4729i	1.55656	+	0.505757i
$170$	−286.166	+	101.013i	−1.68333	+	0.594194i
$171$	−8.66157	−	26.6576i	−0.0506525	−	0.155892i
$172$	−74.4161	−	37.9169i	−0.432652	−	0.220447i
$173$	−46.6024	−	294.236i	−0.269378	−	1.70078i	−0.637044	−	0.770827i	$-0.719843\pi$
$173$	−46.6024	−	294.236i	−0.269378	−	1.70078i	0.367666	−	0.929958i	$-0.380157\pi$
$174$		−	100.491i		−	0.577536i
$175$	−207.010	+	43.5663i	−1.18291	+	0.248950i
$176$	−317.719			−1.80522
$177$	24.8511	−	3.93602i	0.140402	−	0.0222374i
$178$	115.088	−	225.873i	0.646561	−	1.26895i
$179$	−191.792	+	62.3168i	−1.07146	+	0.348139i	−0.791056	−	0.611743i	$-0.790469\pi$
$179$	−191.792	+	62.3168i	−1.07146	+	0.348139i	−0.280404	+	0.959882i	$0.590469\pi$
$180$	35.3634	−	27.0789i	0.196464	−	0.150438i
$181$	−84.1687	+	259.045i	−0.465021	+	1.43119i	0.393936	+	0.919138i	$0.371113\pi$
$181$	−84.1687	+	259.045i	−0.465021	+	1.43119i	−0.858957	+	0.512048i	$0.828887\pi$
$182$	−333.437	+	333.437i	−1.83207	+	1.83207i
$183$	22.4626	−	11.4453i	0.122746	−	0.0625424i
$184$	8.59191	+	11.8257i	0.0466952	+	0.0642704i
$185$	−203.234	−	97.1887i	−1.09856	−	0.525344i
$186$	−43.9943	−	31.9637i	−0.236529	−	0.171848i
$187$	59.9509	−	378.515i	0.320593	−	2.02415i
$188$	−100.068	−	15.8493i	−0.532278	−	0.0843045i
$189$	−25.8441	+	35.5714i	−0.136741	+	0.188208i
$190$	53.2057	−	111.260i	0.280030	−	0.585579i
$191$	−73.6955	+	53.5429i	−0.385840	+	0.280329i	−0.763749	−	0.645514i	$-0.776643\pi$
$191$	−73.6955	+	53.5429i	−0.385840	+	0.280329i	0.377909	+	0.925843i	$0.376643\pi$
$192$	21.9113	+	43.0034i	0.114122	+	0.223976i
$193$	−225.833	−	225.833i	−1.17012	−	1.17012i	−0.982180	−	0.187941i	$-0.939818\pi$
$193$	−225.833	−	225.833i	−1.17012	−	1.17012i	−0.187941	−	0.982180i	$-0.560182\pi$
$194$	443.606	+	144.136i	2.28663	+	0.742972i
$195$	111.142	+	145.145i	0.569960	+	0.744334i
$196$	−20.7388	−	63.8275i	−0.105810	−	0.325651i
$197$	80.7981	+	41.1687i	0.410143	+	0.208978i	0.646874	−	0.762597i	$-0.276076\pi$
$197$	80.7981	+	41.1687i	0.410143	+	0.208978i	−0.236731	+	0.971575i	$0.576076\pi$
$198$	20.6520	+	130.392i	0.104303	+	0.658543i
$199$		−	186.812i		−	0.938753i	−0.882998	−	0.469377i	$-0.844479\pi$
$199$		−	186.812i		−	0.938753i	0.882998	−	0.469377i	$-0.155521\pi$
$200$	−67.6344	−	7.24623i	−0.338172	−	0.0362311i
$201$	25.4510			0.126622
$202$	−14.7614	+	2.33797i	−0.0730761	+	0.0115741i
$203$	−84.4267	+	165.697i	−0.415895	+	0.816240i
$204$	−112.455	+	36.5390i	−0.551252	+	0.179113i
$205$	101.117	+	286.461i	0.493254	+	1.39737i
$206$	−14.8370	+	45.6635i	−0.0720241	+	0.221667i
$207$	11.3965	−	11.3965i	0.0550555	−	0.0550555i
$208$	−358.495	+	182.662i	−1.72353	+	0.878183i
$209$	91.5427	+	125.998i	0.438003	+	0.602860i
$210$	−190.255	+	35.0637i	−0.905974	+	0.166970i
$211$	−127.903	−	92.9271i	−0.606176	−	0.440413i	0.241890	−	0.970304i	$-0.422233\pi$
$211$	−127.903	−	92.9271i	−0.606176	−	0.440413i	−0.848066	+	0.529891i	$0.822233\pi$
$212$	16.0960	−	101.626i	0.0759246	−	0.479369i
$213$	−86.0864	−	13.6347i	−0.404161	−	0.0640129i
$214$	52.1636	−	71.7970i	0.243755	−	0.335500i
$215$	123.660	−	66.9810i	0.575163	−	0.311539i
$216$	−11.4379	+	8.31011i	−0.0529532	+	0.0384727i
$217$	45.6867	+	89.6653i	0.210538	+	0.413204i
$218$	153.543	+	153.543i	0.704327	+	0.704327i
$219$	−14.9583	−	4.86025i	−0.0683028	−	0.0221929i
$220$	−140.380	+	203.815i	−0.638093	+	0.926434i
$221$	−149.970	−	461.560i	−0.678597	−	2.08851i
$222$	−183.563	−	93.5299i	−0.826859	−	0.421306i
$223$	−15.5513	−	98.1871i	−0.0697368	−	0.440301i	−0.997709	−	0.0676515i	$-0.978449\pi$
$223$	−15.5513	−	98.1871i	−0.0697368	−	0.440301i	0.927972	−	0.372649i	$-0.121551\pi$
$224$		−	333.690i		−	1.48969i
$225$	3.77455	+	74.9050i	0.0167758	+	0.332911i
$226$	−13.1649			−0.0582519
$227$	123.888	−	19.6219i	0.545762	−	0.0864403i	0.122536	−	0.992464i	$-0.460897\pi$
$227$	123.888	−	19.6219i	0.545762	−	0.0864403i	0.423227	+	0.906024i	$0.360897\pi$
$228$	21.8154	−	42.8150i	0.0956814	−	0.187785i
$229$	320.874	−	104.258i	1.40120	−	0.455276i	0.491618	−	0.870811i	$-0.336405\pi$
$229$	320.874	−	104.258i	1.40120	−	0.455276i	0.909577	+	0.415535i	$0.136405\pi$
$230$	70.8914	−	1.78502i	0.308223	−	0.00776095i
$231$	75.4947	−	232.349i	0.326817	−	1.00584i
$232$	−42.2827	+	42.2827i	−0.182253	+	0.182253i
$233$	113.261	−	57.7093i	0.486098	−	0.247679i	−0.193724	−	0.981056i	$-0.562057\pi$
$233$	113.261	−	57.7093i	0.486098	−	0.247679i	0.679823	+	0.733377i	$0.262057\pi$
$234$	98.2668	+	135.253i	0.419944	+	0.578003i
$235$	117.559	−	123.632i	0.500252	−	0.526095i
$236$	34.8967	+	25.3539i	0.147867	+	0.107432i
$237$	−8.59282	+	54.2529i	−0.0362566	+	0.228915i
$238$	507.258	+	80.3418i	2.13134	+	0.337571i
$239$	1.39387	−	1.91850i	0.00583211	−	0.00802721i	−0.806091	−	0.591792i	$-0.798421\pi$
$239$	1.39387	−	1.91850i	0.00583211	−	0.00802721i	0.811923	+	0.583764i	$0.198421\pi$
$240$	−163.634	−	21.7102i	−0.681807	−	0.0904592i
$241$	−254.702	+	185.052i	−1.05686	+	0.767851i	−0.973504	−	0.228669i	$-0.926563\pi$
$241$	−254.702	+	185.052i	−1.05686	+	0.767851i	−0.0833518	+	0.996520i	$0.526563\pi$
$242$	−187.997	−	368.966i	−0.776849	−	1.52465i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$	41.1042	+	13.3556i	0.168460	+	0.0547360i
$245$	108.322	+	32.2050i	0.442131	+	0.131449i
$246$	85.8488	+	264.215i	0.348979	+	1.07405i
$247$	175.729	+	89.5386i	0.711455	+	0.362505i
$248$	5.06198	+	31.9601i	0.0204112	+	0.128871i
$249$			248.548i			0.998185i
$250$	−215.070	+	250.282i	−0.860280	+	1.00113i
$251$	215.221			0.857453			0.428726	−	0.903434i	$-0.358962\pi$
$251$	215.221			0.857453			0.428726	+	0.903434i	$0.358962\pi$
$252$	−74.4500	+	11.7917i	−0.295436	+	0.0467925i
$253$	−40.6559	+	79.7917i	−0.160695	+	0.315382i
$254$	124.414	−	40.4247i	0.489820	−	0.159152i
$255$	56.7408	−	190.849i	0.222513	−	0.748426i
$256$	103.114	−	317.353i	0.402790	−	1.23966i
$257$	24.9463	−	24.9463i	0.0970674	−	0.0970674i	−0.656906	−	0.753973i	$-0.728135\pi$
$257$	24.9463	−	24.9463i	0.0970674	−	0.0970674i	0.753973	+	0.656906i	$0.228135\pi$
$258$	114.594	−	58.3885i	0.444163	−	0.226312i
$259$	224.092	+	308.437i	0.865221	+	1.19088i
$260$	−41.2197	+	310.680i	−0.158537	+	1.19492i
$261$	53.3397	+	38.7535i	0.204367	+	0.148481i
$262$	32.2614	−	203.690i	0.123135	−	0.777445i
$263$	286.840	+	45.4310i	1.09065	+	0.172742i	0.675753	−	0.737128i	$-0.263819\pi$
$263$	286.840	+	45.4310i	1.09065	+	0.172742i	0.414894	+	0.909870i	$0.363819\pi$
$264$	46.1740	−	63.5531i	0.174902	−	0.240731i
$265$	125.557	+	119.390i	0.473801	+	0.450527i
$266$	−168.853	+	122.679i	−0.634785	+	0.461198i
$267$	75.5082	+	148.193i	0.282802	+	0.555031i
$268$	30.8526	+	30.8526i	0.115122	+	0.115122i
$269$	201.306	+	65.4082i	0.748349	+	0.243153i	0.658270	−	0.752782i	$-0.271288\pi$
$269$	201.306	+	65.4082i	0.748349	+	0.243153i	0.0900781	+	0.995935i	$0.471288\pi$
$270$	1.72647	+	68.5663i	0.00639434	+	0.253949i
$271$	117.659	+	362.118i	0.434167	+	1.33623i	0.893938	+	0.448191i	$0.147932\pi$
$271$	117.659	+	362.118i	0.434167	+	1.33623i	−0.459770	+	0.888038i	$0.652068\pi$
$272$	390.448	+	198.943i	1.43547	+	0.731409i
$273$	−48.3978	−	305.571i	−0.177281	−	1.11931i
$274$		−	3.09448i		−	0.0112937i
$275$	−148.559	−	389.348i	−0.540214	−	1.41581i
$276$	27.6304			0.100110
$277$	−118.299	+	18.7367i	−0.427073	+	0.0676417i	−0.366271	−	0.930508i	$-0.619366\pi$
$277$	−118.299	+	18.7367i	−0.427073	+	0.0676417i	−0.0608016	+	0.998150i	$0.519366\pi$
$278$	201.367	−	395.205i	0.724341	−	1.42160i
$279$	33.9320	−	11.0252i	0.121620	−	0.0395168i
$280$	94.8049	+	65.2981i	0.338589	+	0.233207i
$281$	47.5379	−	146.307i	0.169174	−	0.520664i	−0.830146	−	0.557547i	$-0.811743\pi$
$281$	47.5379	−	146.307i	0.169174	−	0.520664i	0.999320	+	0.0368828i	$0.0117428\pi$
$282$	110.321	−	110.321i	0.391208	−	0.391208i
$283$	−376.766	+	191.972i	−1.33133	+	0.678346i	−0.967441	−	0.253096i	$-0.918551\pi$
$283$	−376.766	+	191.972i	−1.33133	+	0.678346i	−0.363889	+	0.931442i	$0.618551\pi$
$284$	−87.8283	−	120.885i	−0.309255	−	0.425652i
$285$	38.5373	+	71.1474i	0.135219	+	0.249640i
$286$	−751.513	−	546.006i	−2.62767	−	1.90911i
$287$	80.4246	−	507.781i	0.280225	−	1.76927i
$288$	−116.848	−	18.5070i	−0.405724	−	0.0642604i
$289$	−140.816	+	193.816i	−0.487252	+	0.670645i
$290$	52.5784	+	285.289i	0.181305	+	0.983754i
$291$	−247.579	+	179.877i	−0.850786	+	0.618133i
$292$	−12.2412	−	24.0247i	−0.0419220	−	0.0822765i
$293$	−251.177	−	251.177i	−0.857258	−	0.857258i	0.133756	−	0.991014i	$-0.457296\pi$
$293$	−251.177	−	251.177i	−0.857258	−	0.857258i	−0.991014	+	0.133756i	$0.957296\pi$
$294$	98.2886	+	31.9359i	0.334315	+	0.108626i
$295$	−68.4913	+	24.1766i	−0.232174	+	0.0819545i
$296$	37.8822	+	116.589i	0.127980	+	0.393883i
$297$	−77.1747	−	39.3225i	−0.259847	−	0.132399i
$298$	45.8050	+	289.201i	0.153708	+	0.970474i
$299$			113.406i			0.379284i
$300$	−86.2266	+	95.3779i	−0.287422	+	0.317926i
$301$	−238.005			−0.790713
$302$	−458.251	+	72.5798i	−1.51739	+	0.240331i
$303$	4.45162	−	8.73680i	0.0146918	−	0.0288343i
$304$	−169.368	+	55.0309i	−0.557130	+	0.181023i
$305$	−57.7816	+	44.2452i	−0.189448	+	0.145066i
$306$	56.2667	−	173.171i	0.183878	−	0.565918i
$307$	−112.500	+	112.500i	−0.366451	+	0.366451i	−0.866181	−	0.499730i	$-0.833432\pi$
$307$	−112.500	+	112.500i	−0.366451	+	0.366451i	0.499730	+	0.866181i	$0.333432\pi$
$308$	373.178	−	190.144i	1.21162	−	0.617350i
$309$	−18.5159	−	25.4850i	−0.0599222	−	0.0824758i
$310$	141.621	+	67.7247i	0.456842	+	0.218467i
$311$	222.772	+	161.853i	0.716308	+	0.520428i	0.885202	−	0.465206i	$-0.154020\pi$
$311$	222.772	+	161.853i	0.716308	+	0.520428i	−0.168895	+	0.985634i	$0.554020\pi$
$312$	15.5622	−	98.2556i	0.0498787	−	0.314922i
$313$	395.294	+	62.6085i	1.26292	+	0.200027i	0.751748	−	0.659450i	$-0.229211\pi$
$313$	395.294	+	62.6085i	1.26292	+	0.200027i	0.511173	+	0.859478i	$0.329211\pi$
$314$	−373.931	+	514.672i	−1.19086	+	1.63908i
$315$	54.7585	−	114.507i	0.173837	−	0.363515i
$316$	−76.1837	+	55.3507i	−0.241088	+	0.175160i
$317$	−158.738	−	311.541i	−0.500751	−	0.982778i	−0.993631	−	0.112681i	$-0.964056\pi$
$317$	−158.738	−	311.541i	−0.500751	−	0.982778i	0.492881	−	0.870097i	$-0.335944\pi$
$318$	112.038	+	112.038i	0.352321	+	0.352321i
$319$	−348.409	−	113.205i	−1.09219	−	0.354875i
$320$	−84.7049	−	110.620i	−0.264703	−	0.345687i
$321$	17.9927	+	55.3757i	0.0560519	+	0.172510i
$322$	−106.931	−	54.4840i	−0.332084	−	0.169205i
$323$	−33.6029	−	212.160i	−0.104034	−	0.656843i
$324$			26.7242i			0.0824820i
$325$	−391.468	−	353.907i	−1.20452	−	1.08895i
$326$	383.164			1.17535
$327$	−140.712	+	22.2865i	−0.430311	+	0.0681545i
$328$	75.0495	−	147.293i	0.228809	−	0.449064i
$329$	−274.588	+	89.2192i	−0.834615	+	0.271183i
$330$	−126.852	−	359.368i	−0.384401	−	1.08900i
$331$	−0.706047	+	2.17299i	−0.00213307	+	0.00656493i	−0.952117	−	0.305733i	$-0.901099\pi$
$331$	−0.706047	+	2.17299i	−0.00213307	+	0.00656493i	0.949984	+	0.312298i	$0.101099\pi$
$332$	−301.298	+	301.298i	−0.907525	+	0.907525i
$333$	120.434	−	61.3642i	0.361664	−	0.184277i
$334$	−463.882	−	638.479i	−1.38887	−	1.91161i
$335$	−72.2539	+	13.3163i	−0.215683	+	0.0397502i
$336$	226.001	+	164.199i	0.672623	+	0.488689i
$337$	−48.5152	+	306.313i	−0.143962	+	0.908940i	0.804937	+	0.593360i	$0.202199\pi$
$337$	−48.5152	+	306.313i	−0.143962	+	0.908940i	−0.948899	+	0.315580i	$0.897801\pi$
$338$	−721.211	−	114.229i	−2.13376	−	0.337954i
$339$	5.07693	−	6.98780i	0.0149762	−	0.0206130i
$340$	300.136	−	162.570i	0.882754	−	0.478147i
$341$	−160.381	+	116.523i	−0.470324	+	0.341710i
$342$	33.5937	+	65.9313i	0.0982271	+	0.192781i
$343$	157.951	+	157.951i	0.460500	+	0.460500i
$344$	−72.7841	−	23.6490i	−0.211582	−	0.0687470i
$345$	−26.3911	+	38.3167i	−0.0764961	+	0.111063i
$346$	243.027	+	747.960i	0.702390	+	2.16173i
$347$	437.018	+	222.672i	1.25942	+	0.641705i	0.950895	−	0.309512i	$-0.100166\pi$
$347$	437.018	+	222.672i	1.25942	+	0.641705i	0.308521	+	0.951217i	$0.400166\pi$
$348$	17.6818	+	111.638i	0.0508098	+	0.320800i
$349$		−	298.967i		−	0.856639i	−0.903627	−	0.428320i	$-0.859106\pi$
$349$		−	298.967i		−	0.856639i	0.903627	−	0.428320i	$-0.140894\pi$
$350$	521.776	−	199.088i	1.49079	−	0.568822i
$351$	−109.686			−0.312497
$352$	649.253	−	102.832i	1.84447	−	0.292135i
$353$	−182.786	+	358.739i	−0.517809	+	1.01626i	0.473010	+	0.881057i	$0.343167\pi$
$353$	−182.786	+	358.739i	−0.517809	+	1.01626i	−0.990818	+	0.135199i	$0.956833\pi$
$354$	−63.1725	+	20.5260i	−0.178453	+	0.0579830i
$355$	251.528	−	6.33338i	0.708529	−	0.0178405i
$356$	−88.1111	+	271.178i	−0.247503	+	0.761737i
$357$	−238.264	+	238.264i	−0.667406	+	0.667406i
$358$	474.351	−	241.694i	1.32500	−	0.675123i
$359$	98.8049	+	135.993i	0.275223	+	0.378812i	0.924144	−	0.382044i	$-0.124780\pi$
$359$	98.8049	+	135.993i	0.275223	+	0.378812i	−0.648922	+	0.760855i	$0.724780\pi$
$360$	28.1235	−	29.5764i	0.0781208	−	0.0821566i
$361$	−221.433	−	160.880i	−0.613387	−	0.445651i
$362$	112.486	−	710.206i	0.310734	−	1.96190i
$363$	268.342	+	42.5013i	0.739235	+	0.117083i
$364$	311.754	−	429.093i	0.856468	−	1.17883i
$365$	45.0087	+	5.97156i	0.123312	+	0.0163604i
$366$	−53.8435	+	39.1196i	−0.147113	+	0.106884i
$367$	−167.472	−	328.682i	−0.456327	−	0.895592i	−0.998469	−	0.0553054i	$-0.982387\pi$
$367$	−167.472	−	328.682i	−0.456327	−	0.895592i	0.542143	−	0.840286i	$-0.317613\pi$
$368$	−72.4070	−	72.4070i	−0.196758	−	0.196758i
$369$	−173.349	−	56.3247i	−0.469782	−	0.152641i
$370$	570.060	+	169.483i	1.54070	+	0.458063i
$371$	−90.6083	−	278.864i	−0.244227	−	0.751654i
$372$	54.4986	+	27.7684i	0.146502	+	0.0746463i
$373$	62.6859	+	395.783i	0.168059	+	1.06108i	0.917129	+	0.398590i	$0.130501\pi$
$373$	62.6859	+	395.783i	0.168059	+	1.06108i	−0.749070	+	0.662491i	$0.769499\pi$
$374$			1011.72i			2.70513i
$375$	−49.9070	−	210.676i	−0.133085	−	0.561802i
$376$	−92.8369			−0.246907
$377$	−458.207	+	72.5729i	−1.21540	+	0.192501i
$378$	52.6971	−	103.424i	0.139410	−	0.273608i
$379$	464.377	−	150.885i	1.22527	−	0.398114i	0.376271	−	0.926510i	$-0.377206\pi$
$379$	464.377	−	150.885i	1.22527	−	0.398114i	0.848998	+	0.528395i	$0.177206\pi$
$380$	−39.5311	+	132.963i	−0.104029	+	0.349904i
$381$	−26.5223	+	81.6272i	−0.0696123	+	0.214245i
$382$	170.045	−	170.045i	0.445145	−	0.445145i
$383$	2.17326	−	1.10733i	0.00567431	−	0.00289121i	−0.451151	−	0.892448i	$-0.648986\pi$
$383$	2.17326	−	1.10733i	0.00567431	−	0.00289121i	0.456825	+	0.889556i	$0.348986\pi$
$384$	85.6987	+	117.954i	0.223174	+	0.307172i
$385$	−92.7568	+	699.124i	−0.240927	+	1.81591i
$386$	682.114	+	495.585i	1.76714	+	1.28390i
$387$	−13.2001	+	83.3422i	−0.0341088	+	0.215355i
$388$	−518.176	−	82.0710i	−1.33550	−	0.211523i
$389$	45.1598	−	62.1571i	0.116092	−	0.159787i	−0.747016	−	0.664806i	$-0.768514\pi$
$389$	45.1598	−	62.1571i	0.116092	−	0.159787i	0.863108	+	0.505019i	$0.168514\pi$
$390$	−349.740	−	332.560i	−0.896768	−	0.852717i
$391$	99.9249	−	72.5997i	0.255562	−	0.185677i
$392$	−27.9185	−	54.7932i	−0.0712208	−	0.139779i
$393$	95.6754	+	95.6754i	0.243449	+	0.243449i
$394$	−227.679	−	73.9773i	−0.577865	−	0.187760i
$395$	−3.99139	−	158.517i	−0.0101048	−	0.401308i
$396$	−45.8857	−	141.222i	−0.115873	−	0.356620i
$397$	−22.4390	−	11.4332i	−0.0565214	−	0.0287991i	0.425501	−	0.904958i	$-0.360098\pi$
$397$	−22.4390	−	11.4332i	−0.0565214	−	0.0287991i	−0.482023	+	0.876159i	$0.660098\pi$
$398$	77.1495	+	487.103i	0.193843	+	1.22388i
$399$		−	136.935i		−	0.343196i
$400$	475.905	−	23.9814i	1.18976	−	0.0599536i
$401$	−100.069			−0.249548			−0.124774	−	0.992185i	$-0.539821\pi$
$401$	−100.069			−0.249548			−0.124774	+	0.992185i	$0.539821\pi$
$402$	−66.3623	+	10.5107i	−0.165080	+	0.0261461i
$403$	−113.972	+	223.683i	−0.282810	+	0.555045i
$404$	15.9874	−	5.19463i	0.0395729	−	0.0128580i
$405$	−37.0600	−	25.5256i	−0.0915062	−	0.0630261i
$406$	151.709	−	466.913i	0.373668	−	1.15003i
$407$	−531.060	+	531.060i	−1.30482	+	1.30482i
$408$	−96.5381	+	49.1886i	−0.236613	+	0.120560i
$409$	9.49312	+	13.0662i	0.0232106	+	0.0319466i	0.820465	−	0.571697i	$-0.193715\pi$
$409$	9.49312	+	13.0662i	0.0232106	+	0.0319466i	−0.797254	+	0.603644i	$0.793715\pi$
$410$	−381.961	−	705.174i	−0.931612	−	1.71994i
$411$	1.64252	+	1.19336i	0.00399639	+	0.00290355i
$412$	8.44814	−	53.3394i	0.0205052	−	0.129465i
$413$	121.408	+	19.2291i	0.293965	+	0.0465595i
$414$	−25.0093	+	34.4223i	−0.0604089	+	0.0831457i
$415$	−130.044	−	705.613i	−0.313359	−	1.70027i
$416$	673.458	−	489.296i	1.61889	−	1.17619i
$417$	132.115	+	259.290i	0.316823	+	0.621800i
$418$	−290.728	−	290.728i	−0.695521	−	0.695521i
$419$	−427.717	−	138.974i	−1.02081	−	0.331680i	−0.249656	−	0.968335i	$-0.580318\pi$
$419$	−427.717	−	138.974i	−1.02081	−	0.331680i	−0.771149	+	0.636655i	$0.780318\pi$
$420$	205.189	−	72.4292i	0.488546	−	0.172451i
$421$	−135.222	−	416.171i	−0.321193	−	0.988530i	−0.973130	−	0.230257i	$-0.926043\pi$
$421$	−135.222	−	416.171i	−0.321193	−	0.988530i	0.651937	−	0.758273i	$-0.273957\pi$
$422$	371.878	+	189.481i	0.881228	+	0.449008i
$423$	16.0128	+	101.101i	0.0378554	+	0.239010i
$424$		−	94.2824i		−	0.222364i
$425$	−61.2290	+	571.496i	−0.144068	+	1.34470i
$426$	230.097			0.540134
$427$	121.647	−	19.2669i	0.284887	−	0.0451216i
$428$	−45.3170	+	88.9396i	−0.105881	+	0.207803i
$429$	579.628	−	188.333i	1.35112	−	0.439004i
$430$	−294.776	+	225.719i	−0.685525	+	0.524927i
$431$	131.878	−	405.880i	0.305983	−	0.941717i	−0.673326	−	0.739346i	$-0.735135\pi$
$431$	131.878	−	405.880i	0.305983	−	0.941717i	0.979309	−	0.202372i	$-0.0648650\pi$
$432$	70.0322	−	70.0322i	0.162112	−	0.162112i
$433$	−588.392	+	299.801i	−1.35887	+	0.692381i	−0.973137	−	0.230228i	$-0.926053\pi$
$433$	−588.392	+	299.801i	−1.35887	+	0.692381i	−0.385737	+	0.922609i	$0.626053\pi$
$434$	−156.156	−	214.930i	−0.359806	−	0.495231i
$435$	−171.705	−	82.1109i	−0.394723	−	0.188761i
$436$	−197.592	−	143.559i	−0.453192	−	0.329263i
$437$	−7.85218	+	49.5767i	−0.0179684	+	0.113448i
$438$	41.0103	+	6.49539i	0.0936308	+	0.0148297i
$439$	184.043	−	253.313i	0.419232	−	0.577023i	−0.546208	−	0.837650i	$-0.683929\pi$
$439$	184.043	−	253.313i	0.419232	−	0.577023i	0.965440	+	0.260627i	$0.0839292\pi$
$440$	−97.8334	+	204.582i	−0.222349	+	0.464960i
$441$	−54.8553	+	39.8547i	−0.124388	+	0.0903735i
$442$	581.654	+	1141.56i	1.31596	+	2.58272i
$443$	−97.3339	−	97.3339i	−0.219715	−	0.219715i	0.588663	−	0.808378i	$-0.299654\pi$
$443$	−97.3339	−	97.3339i	−0.219715	−	0.219715i	−0.808378	+	0.588663i	$0.799654\pi$
$444$	220.382	+	71.6064i	0.496355	+	0.161276i
$445$	−291.900	−	381.205i	−0.655955	−	0.856639i
$446$	81.0986	+	249.596i	0.181835	+	0.559632i
$447$	−171.169	−	87.2150i	−0.382929	−	0.195112i
$448$	36.8855	+	232.886i	0.0823336	+	0.519834i
$449$		−	446.795i		−	0.995089i	−0.867438	−	0.497545i	$-0.834235\pi$
$449$		−	446.795i		−	0.995089i	0.867438	−	0.497545i	$-0.165765\pi$
$450$	−40.7762	−	193.752i	−0.0906137	−	0.430560i
$451$	1012.76			2.24559
$452$	14.6253	−	2.31642i	0.0323568	−	0.00512481i
$453$	138.196	−	271.224i	0.305068	−	0.598729i
$454$	−314.929	+	102.327i	−0.693675	+	0.225389i
$455$	297.278	+	842.176i	0.653357	+	1.85094i
$456$	13.6064	−	41.8761i	0.0298385	−	0.0918335i
$457$	563.369	−	563.369i	1.23275	−	1.23275i	0.269853	−	0.962901i	$-0.413025\pi$
$457$	563.369	−	563.369i	1.23275	−	1.23275i	0.962901	−	0.269853i	$-0.0869752\pi$
$458$	−793.606	+	404.363i	−1.73276	+	0.882888i
$459$	70.2186	+	96.6475i	0.152982	+	0.210561i
$460$	−78.4411	+	14.4566i	−0.170524	+	0.0314274i
$461$	107.064	+	77.7863i	0.232242	+	0.168734i	0.697820	−	0.716273i	$-0.254153\pi$
$461$	107.064	+	77.7863i	0.232242	+	0.168734i	−0.465578	+	0.885007i	$0.654153\pi$
$462$	−100.893	+	637.016i	−0.218384	+	1.37882i
$463$	−356.188	−	56.4146i	−0.769305	−	0.121846i	−0.240569	−	0.970632i	$-0.577334\pi$
$463$	−356.188	−	56.4146i	−0.769305	−	0.121846i	−0.528736	+	0.848786i	$0.677334\pi$
$464$	246.219	−	338.891i	0.530644	−	0.730369i
$465$	−90.5624	+	49.0535i	−0.194758	+	0.105491i
$466$	−271.489	+	197.249i	−0.582595	+	0.423280i
$467$	319.076	+	626.222i	0.683247	+	1.34095i	0.928444	+	0.371474i	$0.121147\pi$
$467$	319.076	+	626.222i	0.683247	+	1.34095i	−0.245197	+	0.969473i	$0.578853\pi$
$468$	−132.965	−	132.965i	−0.284114	−	0.284114i
$469$	118.253	+	38.4227i	0.252139	+	0.0819248i
$470$	−255.472	+	370.915i	−0.543558	+	0.789180i
$471$	−128.979	−	396.957i	−0.273841	−	0.842797i
$472$	35.2169	+	17.9439i	0.0746122	+	0.0380168i
$473$	−73.3447	−	463.080i	−0.155063	−	0.979027i
$474$		−	145.010i		−	0.305929i
$475$	−146.630	−	181.820i	−0.308696	−	0.382779i
$476$	−577.663			−1.21358
$477$	−102.675	+	16.2622i	−0.215252	+	0.0340926i
$478$	−2.84216	+	5.57804i	−0.00594593	+	0.0116695i
$479$	−21.6392	+	7.03099i	−0.0451757	+	0.0146785i	−0.331518	−	0.943449i	$-0.607561\pi$
$479$	−21.6392	+	7.03099i	−0.0451757	+	0.0146785i	0.286342	+	0.958127i	$0.407561\pi$
$480$	341.409	−	8.59655i	0.711269	−	0.0179095i
$481$	−293.900	+	904.532i	−0.611019	+	1.88052i
$482$	587.701	−	587.701i	1.21930	−	1.21930i
$483$	70.1565	−	35.7465i	0.145252	−	0.0740093i
$484$	273.772	+	376.815i	0.565645	+	0.778544i
$485$	608.748	−	640.196i	1.25515	−	1.31999i
$486$	−33.2933	−	24.1890i	−0.0685048	−	0.0497716i
$487$	−126.686	+	799.865i	−0.260136	+	1.64243i	0.418686	+	0.908131i	$0.362491\pi$
$487$	−126.686	+	799.865i	−0.260136	+	1.64243i	−0.678822	+	0.734303i	$0.737509\pi$
$488$	39.1151	+	6.19522i	0.0801539	+	0.0126951i
$489$	−147.764	+	203.380i	−0.302176	+	0.415909i
$490$	−295.745	−	39.2381i	−0.603561	−	0.0800778i
$491$	238.356	−	173.176i	0.485451	−	0.352701i	−0.317981	−	0.948097i	$-0.603005\pi$
$491$	238.356	−	173.176i	0.485451	−	0.352701i	0.803432	+	0.595396i	$0.203005\pi$
$492$	−141.861	−	278.419i	−0.288336	−	0.565892i
$493$	357.279	+	357.279i	0.724704	+	0.724704i
$494$	−495.184	−	160.895i	−1.00240	−	0.325698i
$495$	239.668	+	71.2552i	0.484178	+	0.143950i
$496$	−70.0479	−	215.585i	−0.141226	−	0.434648i
$497$	−379.399	−	193.313i	−0.763378	−	0.388961i
$498$	−102.645	−	648.077i	−0.206115	−	1.30136i
$499$		−	312.828i		−	0.626909i	−0.949603	−	0.313454i	$-0.898514\pi$
$499$		−	312.828i		−	0.626909i	0.949603	−	0.313454i	$-0.101486\pi$
$500$	194.889	−	315.887i	0.389778	−	0.631774i
$501$	517.790			1.03351
$502$	−561.177	+	88.8818i	−1.11788	+	0.177055i
$503$	−211.257	+	414.616i	−0.419994	+	0.824285i	0.579959	+	0.814646i	$0.303069\pi$
$503$	−211.257	+	414.616i	−0.419994	+	0.824285i	−0.999954	+	0.00963984i	$0.996931\pi$
$504$	−65.6894	+	21.3438i	−0.130336	+	0.0423488i
$505$	−8.06667	+	27.1324i	−0.0159736	+	0.0537275i
$506$	73.0559	−	224.843i	0.144379	−	0.444354i
$507$	338.760	−	338.760i	0.668165	−	0.668165i
$508$	−131.102	+	66.8000i	−0.258076	+	0.131496i
$509$	206.048	+	283.601i	0.404810	+	0.557173i	0.961943	−	0.273250i	$-0.0880987\pi$
$509$	206.048	+	283.601i	0.404810	+	0.557173i	−0.557133	+	0.830423i	$0.688099\pi$
$510$	−69.1322	+	521.062i	−0.135553	+	1.02169i
$511$	−62.1634	−	45.1644i	−0.121651	−	0.0883843i
$512$	−85.1321	+	537.503i	−0.166274	+	1.04981i
$513$	−47.9507	−	7.59464i	−0.0934711	−	0.0148044i
$514$	−54.7440	+	75.3486i	−0.106506	+	0.146593i
$515$	65.8998	+	62.6626i	0.127961	+	0.121675i
$516$	−117.032	+	85.0286i	−0.226806	+	0.164784i
$517$	−258.210	−	506.766i	−0.499439	−	0.980205i
$518$	−711.688	−	711.688i	−1.37391	−	1.37391i
$519$	−490.730	−	159.448i	−0.945530	−	0.307221i
$520$	7.22867	+	287.084i	0.0139013	+	0.552085i
$521$	−33.8730	−	104.250i	−0.0650153	−	0.200096i	0.913272	−	0.407351i	$-0.133547\pi$
$521$	−33.8730	−	104.250i	−0.0650153	−	0.200096i	−0.978287	+	0.207254i	$0.933547\pi$
$522$	−155.085	−	79.0198i	−0.297098	−	0.151379i
$523$	−10.5961	−	66.9010i	−0.0202602	−	0.127918i	0.975485	−	0.220065i	$-0.0706270\pi$
$523$	−10.5961	−	66.9010i	−0.0202602	−	0.127918i	−0.995745	+	0.0921472i	$0.970627\pi$
$524$			231.962i			0.442675i
$525$	−95.5444	+	353.729i	−0.181989	+	0.673770i
$526$	−766.684			−1.45757
$527$	270.056	−	42.7726i	0.512439	−	0.0811624i
$528$	−249.833	+	490.326i	−0.473169	+	0.928647i
$529$	475.659	−	154.551i	0.899167	−	0.292157i
$530$	−376.690	−	259.450i	−0.710735	−	0.489528i
$531$	13.4669	−	41.4469i	0.0253614	−	0.0780545i
$532$	165.997	−	165.997i	0.312025	−	0.312025i
$533$	1142.74	−	582.254i	2.14397	−	1.09241i
$534$	−258.085	−	355.223i	−0.483305	−	0.665212i
$535$	−80.0535	−	147.794i	−0.149633	−	0.276251i
$536$	32.3451	+	23.5001i	0.0603453	+	0.0438434i
$537$	−54.6407	+	344.988i	−0.101752	+	0.642435i
$538$	−551.907	−	87.4135i	−1.02585	−	0.162479i
$539$	221.447	−	304.796i	0.410849	−	0.565485i
$540$	−13.9825	−	75.8683i	−0.0258934	−	0.140497i
$541$	178.704	−	129.836i	0.330321	−	0.239992i	−0.410246	−	0.911975i	$-0.634557\pi$
$541$	178.704	−	129.836i	0.330321	−	0.239992i	0.740567	+	0.671983i	$0.234557\pi$
$542$	−456.338	−	895.614i	−0.841953	−	1.65242i
$543$	333.591	+	333.591i	0.614348	+	0.614348i
$544$	−862.263	−	280.166i	−1.58504	−	0.515011i
$545$	387.811	−	136.892i	0.711580	−	0.251179i
$546$	252.390	+	776.775i	0.462252	+	1.42267i
$547$	393.337	+	200.415i	0.719080	+	0.366390i	0.774928	−	0.632050i	$-0.217786\pi$
$547$	393.337	+	200.415i	0.719080	+	0.366390i	−0.0558479	+	0.998439i	$0.517786\pi$
$548$	0.544485	+	3.43774i	0.000993586	+	0.00627325i
$549$		−	43.6656i		−	0.0795366i
$550$	548.153	+	953.854i	0.996642	+	1.73428i
$551$	−205.336			−0.372660
$552$	25.0064	−	3.96063i	0.0453015	−	0.00717505i
$553$	−121.829	+	239.103i	−0.220306	+	0.432374i
$554$	300.721	−	97.7103i	0.542818	−	0.176372i
$555$	−309.798	+	237.222i	−0.558195	+	0.427427i
$556$	−154.166	+	474.475i	−0.277277	+	0.853372i
$557$	−442.862	+	442.862i	−0.795084	+	0.795084i	−0.982316	−	0.187232i	$-0.940048\pi$
$557$	−442.862	+	442.862i	−0.795084	+	0.795084i	0.187232	+	0.982316i	$0.440048\pi$
$558$	−83.9229	+	42.7608i	−0.150399	+	0.0766323i
$559$	−348.990	−	480.344i	−0.624312	−	0.859291i
$560$	−727.515	−	347.905i	−1.29913	−	0.621260i
$561$	−537.009	−	390.160i	−0.957235	−	0.695472i
$562$	−63.5311	+	401.119i	−0.113045	+	0.713735i
$563$	258.974	+	41.0175i	0.459990	+	0.0728552i	0.382129	−	0.924109i	$-0.375191\pi$
$563$	258.974	+	41.0175i	0.459990	+	0.0728552i	0.0778608	+	0.996964i	$0.475191\pi$
$564$	−103.147	+	141.969i	−0.182884	+	0.251719i
$565$	−10.7570	+	22.4943i	−0.0190389	+	0.0398129i
$566$	903.119	−	656.154i	1.59562	−	1.15928i
$567$	34.5741	+	67.8555i	0.0609772	+	0.119675i
$568$	−96.8155	−	96.8155i	−0.170450	−	0.170450i
$569$	−158.371	−	51.4579i	−0.278332	−	0.0904357i	0.166525	−	0.986037i	$-0.446746\pi$
$569$	−158.371	−	51.4579i	−0.278332	−	0.0904357i	−0.444857	+	0.895602i	$0.646746\pi$
$570$	−129.867	−	169.598i	−0.227836	−	0.297541i
$571$	−270.856	−	833.609i	−0.474354	−	1.45991i	−0.846827	−	0.531868i	$-0.821490\pi$
$571$	−270.856	−	833.609i	−0.474354	−	1.45991i	0.372474	−	0.928043i	$-0.378510\pi$
$572$	930.948	+	474.342i	1.62753	+	0.829269i
$573$	24.6818	+	155.835i	0.0430747	+	0.271963i
$574$			1357.23i			2.36451i
$575$	54.8750	−	122.587i	0.0954348	−	0.213195i
$576$	83.5955			0.145131
$577$	−286.670	+	45.4041i	−0.496828	+	0.0786899i	−0.399820	−	0.916594i	$-0.630927\pi$
$577$	−286.670	+	45.4041i	−0.496828	+	0.0786899i	−0.0970084	+	0.995284i	$0.530927\pi$
$578$	287.128	−	563.521i	0.496761	−	0.974949i
$579$	−526.102	+	170.941i	−0.908640	+	0.295235i
$580$	−108.608	−	307.684i	−0.187256	−	0.530489i
$581$	−375.227	+	1154.83i	−0.645829	+	1.98766i
$582$	571.264	−	571.264i	0.981554	−	0.981554i
$583$	514.656	−	262.230i	0.882772	−	0.449795i
$584$	−14.5225	−	19.9885i	−0.0248673	−	0.0342268i
$585$	311.393	−	57.3894i	0.532296	−	0.0981016i
$586$	758.662	+	551.200i	1.29464	+	0.940615i
$587$	−85.7162	+	541.191i	−0.146024	+	0.921961i	0.800501	+	0.599331i	$0.204567\pi$
$587$	−85.7162	+	541.191i	−0.146024	+	0.921961i	−0.946525	+	0.322629i	$0.895433\pi$
$588$	−114.811	−	18.1842i	−0.195256	−	0.0309256i
$589$	−65.3121	+	89.8944i	−0.110886	+	0.152622i
$590$	168.603	−	91.3247i	0.285768	−	0.154788i
$591$	127.069	−	92.3208i	0.215006	−	0.156211i
$592$	−389.874	−	765.171i	−0.658571	−	1.29252i
$593$	456.741	+	456.741i	0.770220	+	0.770220i	0.978145	−	0.207924i	$-0.0666708\pi$
$593$	456.741	+	456.741i	0.770220	+	0.770220i	−0.207924	+	0.978145i	$0.566671\pi$
$594$	217.469	+	70.6598i	0.366109	+	0.118956i
$595$	551.754	−	801.080i	0.927318	−	1.34635i
$596$	−101.772	−	313.222i	−0.170758	−	0.525540i
$597$	−288.301	−	146.897i	−0.482916	−	0.246058i
$598$	−46.8343	−	295.700i	−0.0783182	−	0.494482i
$599$			1123.94i			1.87637i	0.346138	+	0.938183i	$0.387493\pi$
$599$			1123.94i			1.87637i	−0.346138	+	0.938183i	$0.612507\pi$
$600$	−64.3662	+	98.6801i	−0.107277	+	0.164467i
$601$	−288.110			−0.479385			−0.239692	−	0.970849i	$-0.577047\pi$
$601$	−288.110			−0.479385			−0.239692	+	0.970849i	$0.577047\pi$
$602$	620.585	−	98.2911i	1.03087	−	0.163274i
$603$	20.0130	−	39.2777i	0.0331891	−	0.0651372i
$604$	496.313	−	161.262i	0.821710	−	0.266990i
$605$	−784.045	+	19.7420i	−1.29594	+	0.0326313i
$606$	−7.99926	+	24.6192i	−0.0132001	+	0.0406257i
$607$	225.529	−	225.529i	0.371546	−	0.371546i	−0.496494	−	0.868040i	$-0.665380\pi$
$607$	225.529	−	225.529i	0.371546	−	0.371546i	0.868040	+	0.496494i	$0.165380\pi$
$608$	328.289	−	167.271i	0.539948	−	0.275117i
$609$	189.327	+	260.586i	0.310882	+	0.427892i
$610$	132.390	−	139.230i	0.217033	−	0.228245i
$611$	−582.697	−	423.354i	−0.953678	−	0.692887i
$612$	−32.0381	+	202.281i	−0.0523498	+	0.330524i
$613$	651.628	+	103.208i	1.06301	+	0.168365i	0.663360	−	0.748301i	$-0.269130\pi$
$613$	651.628	+	103.208i	1.06301	+	0.168365i	0.399655	+	0.916666i	$0.369130\pi$
$614$	246.879	−	339.800i	0.402083	−	0.553420i
$615$	521.599	+	69.2035i	0.848128	+	0.112526i
$616$	310.483	−	225.579i	0.504030	−	0.366199i
$617$	−421.696	−	827.626i	−0.683462	−	1.34137i	−0.928309	−	0.371809i	$-0.878738\pi$
$617$	−421.696	−	827.626i	−0.683462	−	1.34137i	0.244847	−	0.969562i	$-0.421262\pi$
$618$	58.8042	+	58.8042i	0.0951524	+	0.0951524i
$619$	1111.58	+	361.176i	1.79578	+	0.583483i	0.999762	−	0.0217970i	$-0.00693874\pi$
$619$	1111.58	+	361.176i	1.79578	+	0.583483i	0.796013	+	0.605280i	$0.206939\pi$
$620$	−169.247	−	50.3185i	−0.272979	−	0.0811588i
$621$	−8.62639	−	26.5493i	−0.0138911	−	0.0427525i
$622$	−647.708	−	330.024i	−1.04133	−	0.530585i
$623$	127.110	+	802.542i	0.204029	+	1.28819i
$624$			696.887i			1.11681i
$625$	251.912	+	571.984i	0.403059	+	0.915174i
$626$	−1056.57			−1.68781
$627$	266.432	−	42.1986i	0.424931	−	0.0673024i
$628$	324.852	−	637.558i	0.517280	−	1.01522i
$629$	985.155	−	320.096i	1.56622	−	0.508897i
$630$	−95.4910	+	321.186i	−0.151573	+	0.509819i
$631$	169.941	−	523.023i	0.269319	−	0.828880i	−0.721347	−	0.692574i	$-0.756477\pi$
$631$	169.941	−	523.023i	0.269319	−	0.828880i	0.990667	−	0.136307i	$-0.0435232\pi$
$632$	−61.0146	+	61.0146i	−0.0965421	+	0.0965421i
$633$	−243.986	+	124.317i	−0.385444	+	0.196394i
$634$	542.561	+	746.772i	0.855775	+	1.17787i
$635$	32.5867	−	245.612i	0.0513176	−	0.386790i
$636$	−144.180	−	104.753i	−0.226698	−	0.164706i
$637$	74.6351	−	471.227i	0.117167	−	0.739760i
$638$	955.212	+	151.291i	1.49720	+	0.237133i
$639$	−88.7348	+	122.133i	−0.138865	+	0.191131i
$640$	−305.009	−	290.026i	−0.476576	−	0.453166i
$641$	−394.480	+	286.607i	−0.615414	+	0.447124i	−0.851316	−	0.524653i	$-0.824195\pi$
$641$	−394.480	+	286.607i	−0.615414	+	0.447124i	0.235903	+	0.971777i	$0.424195\pi$
$642$	−69.7840	−	136.959i	−0.108698	−	0.213332i
$643$	421.612	+	421.612i	0.655695	+	0.655695i	0.954358	−	0.298664i	$-0.0965409\pi$
$643$	421.612	+	421.612i	0.655695	+	0.655695i	−0.298664	+	0.954358i	$0.596541\pi$
$644$	128.379	+	41.7129i	0.199346	+	0.0647716i
$645$	−6.13149	−	243.510i	−0.00950619	−	0.377535i
$646$	175.236	+	539.320i	0.271263	+	0.834861i
$647$	−473.989	−	241.509i	−0.732594	−	0.373276i	0.0475550	−	0.998869i	$-0.484857\pi$
$647$	−473.989	−	241.509i	−0.732594	−	0.373276i	−0.780150	+	0.625593i	$0.784857\pi$
$648$	3.83073	+	24.1863i	0.00591161	+	0.0373245i
$649$			242.146i			0.373106i
$650$	1166.89	+	761.128i	1.79521	+	1.17097i
$651$	174.303			0.267746
$652$	−425.668	+	67.4191i	−0.652865	+	0.103404i
$653$	55.6185	−	109.157i	0.0851738	−	0.167163i	−0.844491	−	0.535570i	$-0.820097\pi$
$653$	55.6185	−	109.157i	0.0851738	−	0.167163i	0.929665	+	0.368407i	$0.120097\pi$
$654$	357.695	−	116.222i	0.546934	−	0.177710i
$655$	−321.675	−	221.558i	−0.491107	−	0.338256i
$656$	−357.856	+	1101.37i	−0.545512	+	1.67891i
$657$	−19.2629	+	19.2629i	−0.0293195	+	0.0293195i
$658$	679.130	−	346.034i	1.03211	−	0.525888i
$659$	−705.047	−	970.413i	−1.06987	−	1.47255i	−0.870204	−	0.492691i	$-0.836013\pi$
$659$	−705.047	−	970.413i	−1.06987	−	1.47255i	−0.199669	−	0.979863i	$-0.563987\pi$
$660$	204.156	+	376.912i	0.309327	+	0.571079i
$661$	868.786	+	631.210i	1.31435	+	0.954932i	0.999984	+	0.00563078i	$0.00179234\pi$
$661$	868.786	+	631.210i	1.31435	+	0.954932i	0.314367	+	0.949301i	$0.398208\pi$
$662$	0.943583	−	5.95755i	0.00142535	−	0.00899932i
$663$	−830.238	−	131.497i	−1.25224	−	0.198336i
$664$	−229.496	+	315.874i	−0.345626	+	0.475713i
$665$	71.6464	+	388.751i	0.107739	+	0.584588i
$666$	−288.684	+	209.741i	−0.433459	+	0.314926i
$667$	−53.6023	−	105.200i	−0.0803632	−	0.157722i
$668$	627.682	+	627.682i	0.939644	+	0.939644i
$669$	−163.758	−	53.2081i	−0.244780	−	0.0795337i
$670$	182.899	−	64.5611i	0.272984	−	0.0963598i
$671$	74.9744	+	230.747i	0.111735	+	0.343886i
$672$	−514.974	−	262.392i	−0.766330	−	0.390464i
$673$	−177.594	−	1121.29i	−0.263885	−	1.66610i	−0.662559	−	0.749009i	$-0.730530\pi$
$673$	−177.594	−	1121.29i	−0.263885	−	1.66610i	0.398675	−	0.917092i	$-0.369470\pi$
$674$		−	818.731i		−	1.21473i
$675$	118.567	+	53.0752i	0.175654	+	0.0786300i
$676$	821.311			1.21496
$677$	−705.000	+	111.661i	−1.04136	+	0.164935i	−0.653611	−	0.756830i	$-0.726747\pi$
$677$	−705.000	+	111.661i	−1.04136	+	0.164935i	−0.387748	+	0.921766i	$0.626747\pi$
$678$	−10.3520	+	20.3170i	−0.0152685	+	0.0299661i
$679$	−1421.88	+	461.997i	−2.09408	+	0.680408i
$680$	248.330	−	190.154i	0.365191	−	0.279638i
$681$	67.1356	−	206.622i	0.0985838	−	0.303410i
$682$	370.063	−	370.063i	0.542614	−	0.542614i
$683$	−597.915	+	304.653i	−0.875424	+	0.446051i	−0.833145	−	0.553055i	$-0.813462\pi$
$683$	−597.915	+	304.653i	−0.875424	+	0.446051i	−0.0422794	+	0.999106i	$0.513462\pi$
$684$	−48.9209	−	67.3339i	−0.0715218	−	0.0984414i
$685$	−5.28739	−	2.52848i	−0.00771882	−	0.00369122i
$686$	−477.081	−	346.620i	−0.695454	−	0.505277i
$687$	91.4158	−	577.176i	0.133065	−	0.840140i
$688$	529.511	+	83.8663i	0.769638	+	0.121899i
$689$	429.946	−	591.770i	0.624014	−	0.858882i
$690$	52.9896	−	110.808i	0.0767965	−	0.160591i
$691$	−962.809	+	699.521i	−1.39336	+	1.01233i	−0.397867	+	0.917443i	$0.630250\pi$
$691$	−962.809	+	699.521i	−1.39336	+	1.01233i	−0.995488	+	0.0948890i	$0.969750\pi$
$692$	−401.591	−	788.167i	−0.580334	−	1.13897i
$693$	−299.213	−	299.213i	−0.431764	−	0.431764i
$694$	−1231.46	−	400.126i	−1.77444	−	0.576550i
$695$	−510.731	−	666.985i	−0.734865	−	0.959691i
$696$	32.0052	+	98.5019i	0.0459845	+	0.141526i
$697$	−1244.59	−	634.151i	−1.78564	−	0.909830i
$698$	123.467	+	779.542i	0.176887	+	1.11682i
$699$		−	220.171i		−	0.314980i
$700$	−544.624	+	312.980i	−0.778035	+	0.447115i
$701$	−580.715			−0.828410			−0.414205	−	0.910184i	$-0.635940\pi$
$701$	−580.715			−0.828410			−0.414205	+	0.910184i	$0.635940\pi$
$702$	286.002	−	45.2982i	0.407410	−	0.0645274i
$703$	−191.111	+	375.077i	−0.271851	+	0.533538i
$704$	−441.753	+	143.534i	−0.627490	+	0.203884i
$705$	−98.3570	−	278.642i	−0.139513	−	0.395236i
$706$	328.455	−	1010.88i	0.465234	−	1.43184i
$707$	33.8733	−	33.8733i	0.0479113	−	0.0479113i
$708$	66.5684	−	33.9183i	0.0940231	−	0.0479072i
$709$	−100.578	−	138.434i	−0.141859	−	0.195253i	0.732175	−	0.681116i	$-0.238505\pi$
$709$	−100.578	−	138.434i	−0.141859	−	0.195253i	−0.874035	+	0.485864i	$0.838505\pi$
$710$	−653.231	+	120.390i	−0.920044	+	0.169563i
$711$	76.9700	+	55.9220i	0.108256	+	0.0786525i
$712$	−40.8719	+	258.055i	−0.0574044	+	0.362437i
$713$	−63.1054	−	9.99492i	−0.0885069	−	0.0140181i
$714$	522.863	−	719.660i	0.732302	−	1.00793i
$715$	−1546.99	+	837.935i	−2.16363	+	1.17194i
$716$	−484.443	+	351.968i	−0.676596	+	0.491576i
$717$	−1.86471	−	3.65971i	−0.00260072	−	0.00510419i
$718$	−313.792	−	313.792i	−0.437036	−	0.437036i
$719$	406.190	+	131.979i	0.564938	+	0.183559i	0.577542	−	0.816361i	$-0.304012\pi$
$719$	406.190	+	131.979i	0.564938	+	0.183559i	−0.0126040	+	0.999921i	$0.504012\pi$
$720$	−162.175	+	235.459i	−0.225244	+	0.327027i
$721$	−47.5566	−	146.364i	−0.0659592	−	0.203001i
$722$	643.815	+	328.040i	0.891710	+	0.454349i
$723$	85.3038	+	538.587i	0.117986	+	0.744933i
$724$			808.780i			1.11710i
$725$	530.421	+	143.270i	0.731614	+	0.197613i
$726$	−717.242			−0.987937
$727$	41.6531	−	6.59720i	0.0572945	−	0.00907456i	−0.127721	−	0.991810i	$-0.540766\pi$
$727$	41.6531	−	6.59720i	0.0572945	−	0.00907456i	0.185016	+	0.982736i	$0.440766\pi$
$728$	220.640	−	433.031i	0.303077	−	0.594823i
$729$	25.6785	−	8.34346i	0.0352243	−	0.0114451i
$730$	−119.824	+	3.01713i	−0.164143	+	0.00413305i
$731$	−199.829	+	615.009i	−0.273363	+	0.841326i
$732$	52.9329	−	52.9329i	0.0723127	−	0.0723127i
$733$	−37.2836	+	18.9969i	−0.0508644	+	0.0259167i	−0.479238	−	0.877685i	$-0.659087\pi$
$733$	−37.2836	+	18.9969i	−0.0508644	+	0.0259167i	0.428373	+	0.903602i	$0.359087\pi$
$734$	572.414	+	787.860i	0.779856	+	1.07338i
$735$	134.878	−	141.846i	0.183508	−	0.192988i
$736$	171.397	+	124.528i	0.232877	+	0.169195i
$737$	−38.3168	+	241.923i	−0.0519902	+	0.328253i
$738$	475.261	+	75.2740i	0.643985	+	0.101997i
$739$	−436.188	+	600.362i	−0.590241	+	0.812397i	−0.994771	−	0.102127i	$-0.967435\pi$
$739$	−436.188	+	600.362i	−0.590241	+	0.812397i	0.404530	+	0.914525i	$0.367435\pi$
$740$	−663.116	−	87.9794i	−0.896103	−	0.118891i
$741$	276.364	−	200.790i	0.372961	−	0.270972i
$742$	351.422	+	689.704i	0.473614	+	0.929521i
$743$	−146.685	−	146.685i	−0.197423	−	0.197423i	0.601472	−	0.798894i	$-0.294581\pi$
$743$	−146.685	−	146.685i	−0.197423	−	0.197423i	−0.798894	+	0.601472i	$0.794581\pi$
$744$	53.3034	+	17.3193i	0.0716444	+	0.0232787i
$745$	531.571	+	158.040i	0.713518	+	0.212134i
$746$	−326.901	−	1006.10i	−0.438205	−	1.34866i
$747$	383.576	+	195.442i	0.513489	+	0.261636i
$748$	−178.015	−	1123.95i	−0.237989	−	1.50260i
$749$			284.455i			0.379780i
$750$	217.135	+	528.716i	0.289513	+	0.704955i
$751$	747.440			0.995260			0.497630	−	0.867389i	$-0.334204\pi$
$751$	747.440			0.995260			0.497630	+	0.867389i	$0.334204\pi$
$752$	642.341	−	101.737i	0.854176	−	0.135288i
$753$	169.235	−	332.143i	0.224748	−	0.441093i
$754$	1164.78	−	378.461i	1.54480	−	0.501937i
$755$	−250.421	+	842.296i	−0.331683	+	1.11562i
$756$	−40.3448	+	124.169i	−0.0533661	+	0.164244i
$757$	183.668	−	183.668i	0.242627	−	0.242627i	−0.575309	−	0.817936i	$-0.695118\pi$
$757$	183.668	−	183.668i	0.242627	−	0.242627i	0.817936	+	0.575309i	$0.195118\pi$
$758$	−1148.53	+	585.204i	−1.51521	+	0.772037i
$759$	91.1709	+	125.486i	0.120120	+	0.165331i
$760$	−16.7175	+	126.003i	−0.0219967	+	0.165793i
$761$	481.968	+	350.171i	0.633336	+	0.460145i	0.857554	−	0.514394i	$-0.171983\pi$
$761$	481.968	+	350.171i	0.633336	+	0.460145i	−0.224219	+	0.974539i	$0.571983\pi$
$762$	35.4452	−	223.792i	0.0465160	−	0.293690i
$763$	−687.434	−	108.879i	−0.900961	−	0.142698i
$764$	−158.988	+	218.828i	−0.208099	+	0.286424i
$765$	−249.914	−	237.637i	−0.326684	−	0.310637i
$766$	−5.20937	+	3.78483i	−0.00680074	+	0.00494103i
$767$	139.214	+	273.222i	0.181504	+	0.356222i
$768$	−408.679	−	408.679i	−0.532134	−	0.532134i
$769$	−235.461	−	76.5059i	−0.306191	−	0.0994875i	0.151891	−	0.988397i	$-0.451464\pi$
$769$	−235.461	−	76.5059i	−0.306191	−	0.0994875i	−0.458083	+	0.888910i	$0.651464\pi$
$770$	−46.8653	−	1861.24i	−0.0608640	−	2.41719i
$771$	−18.8827	−	58.1150i	−0.0244912	−	0.0753762i
$772$	−844.979	−	430.538i	−1.09453	−	0.557692i
$773$	−158.200	−	998.838i	−0.204658	−	1.29216i	−0.849397	−	0.527755i	$-0.823034\pi$
$773$	−158.200	−	998.838i	−0.204658	−	1.29216i	0.644739	−	0.764403i	$-0.276966\pi$
$774$		−	222.762i		−	0.287806i
$775$	231.436	−	186.643i	0.298627	−	0.240830i
$776$	−480.730			−0.619498
$777$	652.212	−	103.300i	0.839398	−	0.132948i
$778$	−92.0823	+	180.722i	−0.118358	+	0.232290i
$779$	539.876	−	175.416i	0.693038	−	0.225182i
$780$	447.050	+	307.912i	0.573141	+	0.394758i
$781$	259.208	−	797.760i	0.331892	−	1.02146i
$782$	−230.567	+	230.567i	−0.294843	+	0.294843i
$783$	101.750	−	51.8442i	0.129949	−	0.0662123i
$784$	253.215	+	348.521i	0.322978	+	0.444542i
$785$	573.858	+	1059.45i	0.731030	+	1.34962i
$786$	−288.981	−	209.957i	−0.367660	−	0.267121i
$787$	−199.293	+	1258.29i	−0.253231	+	1.59884i	0.453434	+	0.891290i	$0.350199\pi$
$787$	−199.293	+	1258.29i	−0.253231	+	1.59884i	−0.706665	+	0.707548i	$0.749801\pi$
$788$	265.951	+	42.1225i	0.337501	+	0.0534550i
$789$	295.665	−	406.947i	0.374733	−	0.515776i
$790$	75.8715	+	411.676i	0.0960399	+	0.521109i
$791$	34.1383	−	24.8029i	0.0431584	−	0.0313564i
$792$	−61.7712	−	121.233i	−0.0779940	−	0.153072i
$793$	217.257	+	217.257i	0.273969	+	0.273969i
$794$	63.2302	+	20.5447i	0.0796351	+	0.0258750i
$795$	282.980	−	99.8884i	0.355950	−	0.125646i
$796$	−171.415	−	527.561i	−0.215345	−	0.662765i
$797$	1069.10	+	544.734i	1.34141	+	0.683481i	0.969569	−	0.244817i	$-0.0787279\pi$
$797$	1069.10	+	544.734i	1.34141	+	0.683481i	0.371837	+	0.928298i	$0.378728\pi$
$798$	56.5515	+	357.052i	0.0708665	+	0.447433i
$799$			784.451i			0.981791i
$800$	−964.742	+	203.035i	−1.20593	+	0.253794i
$801$	288.077			0.359646
$802$	260.925	−	41.3264i	0.325343	−	0.0515292i
$803$	68.7187	−	134.868i	0.0855774	−	0.167955i
$804$	71.8742	−	23.3534i	0.0893958	−	0.0290465i
$805$	−180.467	+	138.189i	−0.224183	+	0.171663i
$806$	204.801	−	630.311i	0.254095	−	0.782024i
$807$	259.236	−	259.236i	0.321234	−	0.321234i
$808$	13.7245	−	6.99300i	0.0169858	−	0.00865471i
$809$	21.4245	+	29.4884i	0.0264827	+	0.0364504i	0.822053	−	0.569411i	$-0.192829\pi$
$809$	21.4245	+	29.4884i	0.0264827	+	0.0364504i	−0.795570	+	0.605861i	$0.792829\pi$
$810$	107.174	+	51.2516i	0.132313	+	0.0632736i
$811$	300.778	+	218.528i	0.370872	+	0.269455i	0.757573	−	0.652751i	$-0.226385\pi$
$811$	300.778	+	218.528i	0.370872	+	0.269455i	−0.386700	+	0.922205i	$0.626385\pi$
$812$	−86.3828	+	545.400i	−0.106383	+	0.671674i
$813$	651.365	+	103.166i	0.801187	+	0.126896i
$814$	1165.40	−	1604.03i	1.43169	−	1.97055i
$815$	313.082	−	654.694i	0.384149	−	0.803306i
$816$	614.045	−	446.130i	0.752507	−	0.546728i
$817$	−119.306	−	234.152i	−0.146030	−	0.286600i
$818$	−30.1489	−	30.1489i	−0.0368569	−	0.0368569i
$819$	−509.636	−	165.591i	−0.622266	−	0.202186i
$820$	548.408	+	716.190i	0.668791	+	0.873402i
$821$	−109.666	−	337.518i	−0.133576	−	0.411105i	0.861790	−	0.507266i	$-0.169344\pi$
$821$	−109.666	−	337.518i	−0.133576	−	0.411105i	−0.995366	+	0.0961605i	$0.969344\pi$
$822$	−4.77561	−	2.43330i	−0.00580975	−	0.00296022i
$823$	−157.996	−	997.548i	−0.191976	−	1.21209i	−0.875885	−	0.482520i	$-0.839722\pi$
$823$	−157.996	−	997.548i	−0.191976	−	1.21209i	0.683909	−	0.729567i	$-0.260278\pi$
$824$		−	49.4849i		−	0.0600545i
$825$	−717.686	−	76.8915i	−0.869922	−	0.0932019i
$826$	−324.506			−0.392864
$827$	736.208	−	116.604i	0.890215	−	0.140996i	0.305459	−	0.952205i	$-0.401190\pi$
$827$	736.208	−	116.604i	0.890215	−	0.140996i	0.584756	+	0.811209i	$0.301190\pi$
$828$	21.7267	−	42.6411i	0.0262400	−	0.0514990i
$829$	766.047	−	248.904i	0.924061	−	0.300246i	0.191929	−	0.981409i	$-0.438526\pi$
$829$	766.047	−	248.904i	0.924061	−	0.300246i	0.732132	+	0.681163i	$0.238526\pi$
$830$	630.487	+	1786.15i	0.759622	+	2.15198i
$831$	−64.1069	+	197.301i	−0.0771443	+	0.237426i
$832$	−415.927	+	415.927i	−0.499912	+	0.499912i
$833$	−462.991	+	235.905i	−0.555811	+	0.283200i
$834$	−451.565	−	621.526i	−0.541445	−	0.745235i
$835$	−1469.97	+	270.915i	−1.76045	+	0.324449i
$836$	374.132	+	271.823i	0.447526	+	0.325147i
$837$	9.66710	−	61.0357i	0.0115497	−	0.0729220i
$838$	1172.65	+	185.729i	1.39934	+	0.221633i
$839$	167.846	−	231.020i	0.200054	−	0.275351i	−0.697189	−	0.716887i	$-0.745566\pi$
$839$	167.846	−	231.020i	0.200054	−	0.275351i	0.897244	+	0.441536i	$0.145566\pi$
$840$	175.321	−	94.9633i	0.208715	−	0.113052i
$841$	−289.632	+	210.430i	−0.344390	+	0.250214i
$842$	524.456	+	1029.30i	0.622869	+	1.22245i
$843$	−188.410	−	188.410i	−0.223499	−	0.223499i
$844$	−446.470	−	145.067i	−0.528992	−	0.171880i
$845$	−784.474	+	1138.96i	−0.928372	+	1.34788i
$846$	−83.5054	−	257.003i	−0.0987061	−	0.303786i
$847$	1182.64	+	602.583i	1.39626	+	0.711432i
$848$	103.321	+	652.342i	0.121841	+	0.769271i
$849$			732.406i			0.862669i
$850$	−76.3645	−	1515.43i	−0.0898406	−	1.78286i
$851$	−242.054			−0.284434
$852$	−255.621	+	40.4864i	−0.300024	+	0.0475192i
$853$	222.805	−	437.280i	0.261202	−	0.512637i	−0.722742	−	0.691118i	$-0.757118\pi$
$853$	222.805	−	437.280i	0.261202	−	0.512637i	0.983943	+	0.178481i	$0.0571183\pi$
$854$	−309.231	+	100.475i	−0.362097	+	0.117652i
$855$	140.103	−	3.52773i	0.163863	−	0.00412600i
$856$	−28.2645	+	86.9891i	−0.0330193	+	0.101623i
$857$	461.781	−	461.781i	0.538834	−	0.538834i	−0.384353	−	0.923186i	$-0.625575\pi$
$857$	461.781	−	461.781i	0.538834	−	0.538834i	0.923186	+	0.384353i	$0.125575\pi$
$858$	−1433.58	+	730.443i	−1.67083	+	0.851332i
$859$	460.233	+	633.457i	0.535778	+	0.737435i	0.987997	−	0.154472i	$-0.0493676\pi$
$859$	460.233	+	633.457i	0.535778	+	0.737435i	−0.452219	+	0.891907i	$0.649368\pi$
$860$	287.758	−	302.624i	0.334603	−	0.351888i
$861$	−720.402	−	523.402i	−0.836703	−	0.607901i
$862$	−176.246	+	1112.78i	−0.204462	+	1.29092i
$863$	−1228.46	−	194.569i	−1.42348	−	0.225457i	−0.603276	−	0.797532i	$-0.706138\pi$
$863$	−1228.46	−	194.569i	−1.42348	−	0.225457i	−0.820201	+	0.572076i	$0.806138\pi$
$864$	−120.443	+	165.776i	−0.139402	+	0.191870i
$865$	1476.58	+	195.906i	1.70703	+	0.226481i
$866$	1410.39	−	1024.71i	1.62863	−	1.18327i
$867$	188.382	+	369.721i	0.217281	+	0.426437i
$868$	211.296	+	211.296i	0.243428	+	0.243428i
$869$	−502.760	−	163.357i	−0.578550	−	0.187982i
$870$	481.621	+	143.190i	0.553588	+	0.164586i
$871$	95.8512	+	295.000i	0.110047	+	0.338691i
$872$	−199.405	−	101.602i	−0.228676	−	0.116516i
$873$	82.9180	+	523.524i	0.0949806	+	0.599684i
$874$		−	132.512i		−	0.151615i
$875$	86.1687	−	1054.21i	0.0984786	−	1.20481i
$876$	−46.7023			−0.0533131
$877$	464.910	−	73.6344i	0.530114	−	0.0839617i	0.114361	−	0.993439i	$-0.463518\pi$
$877$	464.910	−	73.6344i	0.530114	−	0.0839617i	0.415753	+	0.909478i	$0.363518\pi$
$878$	−375.269	+	736.507i	−0.427414	+	0.838846i
$879$	−585.142	+	190.124i	−0.665691	+	0.216296i
$880$	452.717	−	1522.72i	0.514451	−	1.73037i
$881$	319.472	−	983.234i	0.362625	−	1.11604i	−0.588831	−	0.808256i	$-0.700412\pi$
$881$	319.472	−	983.234i	0.362625	−	1.11604i	0.951455	−	0.307787i	$-0.0995885\pi$
$882$	126.573	−	126.573i	0.143507	−	0.143507i
$883$	274.564	−	139.897i	0.310944	−	0.158434i	−0.291554	−	0.956554i	$-0.594172\pi$
$883$	274.564	−	139.897i	0.310944	−	0.158434i	0.602498	+	0.798121i	$0.294172\pi$
$884$	−847.037	−	1165.85i	−0.958187	−	1.31883i
$885$	−16.5462	+	124.711i	−0.0186962	+	0.140917i
$886$	293.990	+	213.596i	0.331817	+	0.241080i
$887$	143.797	−	907.899i	0.162116	−	1.02356i	−0.763695	−	0.645577i	$-0.776617\pi$
$887$	143.797	−	907.899i	0.162116	−	1.02356i	0.925812	−	0.377985i	$-0.123383\pi$
$888$	209.717	+	33.2159i	0.236168	+	0.0374053i
$889$	−246.461	+	339.224i	−0.277234	+	0.381580i
$890$	918.544	+	873.423i	1.03207	+	0.981375i
$891$	−121.370	+	88.1806i	−0.136218	+	0.0989682i
$892$	−134.012	−	263.013i	−0.150237	−	0.294858i
$893$	−225.420	−	225.420i	−0.252430	−	0.252430i
$894$	482.333	+	156.720i	0.539523	+	0.175302i
$895$	−25.3808	−	1007.99i	−0.0283584	−	1.12624i
$896$	220.110	+	677.428i	0.245658	+	0.756058i
$897$	175.016	+	89.1749i	0.195112	+	0.0994146i
$898$	184.517	+	1165.00i	0.205476	+	1.29732i
$899$		−	261.369i		−	0.290733i
$900$	79.3907	+	208.070i	0.0882119	+	0.231189i
$901$	−796.665			−0.884201
$902$	−2640.72	+	418.250i	−2.92763	+	0.463691i
$903$	−187.151	+	367.305i	−0.207255	+	0.406761i
$904$	12.9043	−	4.19286i	0.0142747	−	0.00463812i
$905$	−1121.58	−	772.505i	−1.23932	−	0.853596i
$906$	−248.328	+	764.276i	−0.274093	+	0.843572i
$907$	−782.445	+	782.445i	−0.862674	+	0.862674i	−0.991648	−	0.128974i	$-0.958832\pi$
$907$	−782.445	+	782.445i	−0.862674	+	0.862674i	0.128974	+	0.991648i	$0.458832\pi$
$908$	331.858	−	169.090i	0.365482	−	0.186223i
$909$	−9.98276	−	13.7401i	−0.0109821	−	0.0151156i
$910$	−1122.94	−	2073.16i	−1.23400	−	2.27820i
$911$	310.582	+	225.651i	0.340924	+	0.247696i	0.745052	−	0.667007i	$-0.232425\pi$
$911$	310.582	+	225.651i	0.340924	+	0.247696i	−0.404127	+	0.914703i	$0.632425\pi$
$912$	−48.2522	+	304.652i	−0.0529081	+	0.334049i
$913$	−2362.55	−	374.192i	−2.58768	−	0.409849i
$914$	−1236.30	+	1701.62i	−1.35262	+	1.86173i
$915$	22.8465	+	123.964i	0.0249688	+	0.135480i
$916$	810.490	−	588.855i	0.884814	−	0.642855i
$917$	300.098	+	588.975i	0.327260	+	0.642285i
$918$	−223.005	−	223.005i	−0.242925	−	0.242925i
$919$	1549.72	+	503.533i	1.68631	+	0.547914i	0.986118	−	0.166044i	$-0.0530994\pi$
$919$	1549.72	+	503.533i	1.68631	+	0.547914i	0.700188	+	0.713958i	$0.253099\pi$
$920$	−68.9195	+	24.3277i	−0.0749125	+	0.0264431i
$921$	85.1554	+	262.081i	0.0924597	+	0.284562i
$922$	−311.287	−	158.609i	−0.337622	−	0.172027i
$923$	−166.172	−	1049.17i	−0.180034	−	1.13669i
$924$		−	725.431i		−	0.785098i
$925$	755.381	−	835.550i	0.816628	−	0.903297i
$926$	952.041			1.02812
$927$	−53.8899	+	8.53533i	−0.0581337	+	0.00920747i
$928$	−393.460	+	772.208i	−0.423987	+	0.832121i
$929$	−106.182	+	34.5007i	−0.114297	+	0.0371375i	−0.365607	−	0.930769i	$-0.619139\pi$
$929$	−106.182	+	34.5007i	−0.114297	+	0.0371375i	0.251310	+	0.967907i	$0.419139\pi$
$930$	215.879	−	165.305i	0.232128	−	0.177747i
$931$	65.2552	−	200.835i	0.0700915	−	0.215720i
$932$	266.898	−	266.898i	0.286372	−	0.286372i
$933$	424.956	−	216.526i	0.455473	−	0.232075i
$934$	−1090.59	−	1501.07i	−1.16766	−	1.60714i
$935$	1728.67	+	826.670i	1.84885	+	0.884139i
$936$	−139.398	−	101.278i	−0.148929	−	0.108203i
$937$	124.614	−	786.782i	0.132993	−	0.839682i	−0.827518	−	0.561439i	$-0.810248\pi$
$937$	124.614	−	786.782i	0.132993	−	0.839682i	0.960511	−	0.278243i	$-0.0897520\pi$
$938$	−324.207	−	51.3493i	−0.345636	−	0.0547434i
$939$	407.455	−	560.814i	0.433925	−	0.597246i
$940$	218.547	−	457.010i	0.232497	−	0.486181i
$941$	−630.955	+	458.415i	−0.670515	+	0.487158i	−0.870198	−	0.492703i	$-0.836009\pi$
$941$	−630.955	+	458.415i	−0.670515	+	0.487158i	0.199682	+	0.979861i	$0.436009\pi$
$942$	500.243	+	981.781i	0.531043	+	1.04223i
$943$	230.805	+	230.805i	0.244756	+	0.244756i
$944$	−263.331	−	85.5614i	−0.278952	−	0.0906371i
$945$	−133.657	−	174.548i	−0.141436	−	0.184707i
$946$	382.485	+	1177.17i	0.404318	+	1.24436i
$947$	−551.381	−	280.943i	−0.582240	−	0.296666i	0.137954	−	0.990439i	$-0.455947\pi$
$947$	−551.381	−	280.943i	−0.582240	−	0.296666i	−0.720194	+	0.693773i	$0.755947\pi$
$948$	25.5151	+	161.096i	0.0269147	+	0.169933i
$949$		−	191.684i		−	0.201986i
$950$	457.419	+	413.531i	0.481494	+	0.435296i
$951$	−605.612			−0.636816
$952$	−522.804	+	82.8040i	−0.549164	+	0.0869790i
$953$	−76.6627	+	150.459i	−0.0804435	+	0.157879i	−0.927725	−	0.373266i	$-0.878238\pi$
$953$	−76.6627	+	150.459i	−0.0804435	+	0.157879i	0.847281	+	0.531145i	$0.178238\pi$
$954$	261.005	−	84.8055i	0.273590	−	0.0888947i
$955$	−151.605	−	429.491i	−0.158749	−	0.449729i
$956$	2.17595	−	6.69689i	0.00227610	−	0.00700511i
$957$	−448.672	+	448.672i	−0.468832	+	0.468832i
$958$	53.5194	−	27.2695i	0.0558658	−	0.0284650i
$959$	5.83004	+	8.02436i	0.00607929	+	0.00836743i
$960$	−237.322	+	43.7383i	−0.247211	+	0.0455607i
$961$	663.040	+	481.727i	0.689948	+	0.501277i
$962$	392.777	−	2479.90i	0.408292	−	2.57786i
$963$	99.6079	+	15.7763i	0.103435	+	0.0163825i
$964$	−549.485	+	756.301i	−0.570005	+	0.784545i
$965$	1404.13	−	760.555i	1.45506	−	0.788140i
$966$	−168.167	+	122.180i	−0.174086	+	0.126481i
$967$	33.1642	+	65.0884i	0.0342960	+	0.0673096i	0.907519	−	0.420012i	$-0.137974\pi$
$967$	33.1642	+	65.0884i	0.0342960	+	0.0673096i	−0.873223	+	0.487321i	$0.837974\pi$
$968$	301.787	+	301.787i	0.311763	+	0.311763i
$969$	−353.844	−	114.971i	−0.365164	−	0.118649i
$970$	−1322.89	+	1920.68i	−1.36381	+	1.98008i
$971$	5.93376	+	18.2622i	0.00611097	+	0.0188076i	0.954066	−	0.299598i	$-0.0968526\pi$
$971$	5.93376	+	18.2622i	0.00611097	+	0.0188076i	−0.947955	+	0.318406i	$0.896853\pi$
$972$	41.2426	+	21.0141i	0.0424306	+	0.0216195i
$973$	222.402	+	1404.19i	0.228574	+	1.44316i
$974$		−	2137.93i		−	2.19500i
$975$	−853.999	+	325.850i	−0.875896	+	0.334205i
$976$	−277.427			−0.284249
$977$	304.582	−	48.2410i	0.311752	−	0.0493766i	0.00140186	−	0.999999i	$-0.499554\pi$
$977$	304.582	−	48.2410i	0.311752	−	0.0493766i	0.310350	+	0.950622i	$0.399554\pi$
$978$	301.295	−	591.326i	0.308073	−	0.604627i
$979$	−1522.32	+	494.631i	−1.55497	+	0.505241i
$980$	335.455	−	8.44663i	0.342301	−	0.00861901i
$981$	−76.2523	+	234.680i	−0.0777292	+	0.239226i
$982$	−549.984	+	549.984i	−0.560065	+	0.560065i
$983$	−63.6431	+	32.4278i	−0.0647438	+	0.0329886i	−0.486063	−	0.873924i	$-0.661567\pi$
$983$	−63.6431	+	32.4278i	−0.0647438	+	0.0329886i	0.421319	+	0.906913i	$0.361567\pi$
$984$	−168.299	−	231.643i	−0.171035	−	0.235410i
$985$	−312.437	+	328.577i	−0.317195	+	0.333581i
$986$	−1079.14	−	784.039i	−1.09446	−	0.795171i
$987$	−78.2292	+	493.920i	−0.0792596	+	0.500425i
$988$	578.423	+	91.6132i	0.585448	+	0.0927259i
$989$	88.8193	−	122.249i	0.0898072	−	0.123609i
$990$	−654.350	−	86.8164i	−0.660960	−	0.0876933i
$991$	−671.273	+	487.708i	−0.677369	+	0.492137i	−0.872484	−	0.488643i	$-0.837492\pi$
$991$	−671.273	+	487.708i	−0.677369	+	0.492137i	0.195115	+	0.980780i	$0.437492\pi$
$992$	212.917	+	417.873i	0.214634	+	0.421243i
$993$	2.79832	+	2.79832i	0.00281805	+	0.00281805i
$994$	1069.10	+	347.371i	1.07555	+	0.349468i
$995$	895.327	+	266.188i	0.899826	+	0.267525i
$996$	228.063	+	701.905i	0.228979	+	0.704724i
$997$	1537.51	+	783.401i	1.54214	+	0.785758i	0.998562	−	0.0536022i	$-0.0170703\pi$
$997$	1537.51	+	783.401i	1.54214	+	0.785758i	0.543575	+	0.839360i	$0.317070\pi$
$998$	129.191	+	815.682i	0.129450	+	0.817317i
$999$		−	234.115i		−	0.234349i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.k.a.13.2	✓	80
3.2	odd	2		225.3.r.b.163.9		80
5.2	odd	4		375.3.k.c.82.2		80
5.3	odd	4		375.3.k.b.82.9		80
5.4	even	2		375.3.k.a.43.9		80
25.2	odd	20	inner	75.3.k.a.52.2	yes	80
25.11	even	5		375.3.k.c.343.2		80
25.14	even	10		375.3.k.b.343.9		80
25.23	odd	20		375.3.k.a.157.9		80
75.2	even	20		225.3.r.b.127.9		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.13.2	✓	80	1.1	even	1	trivial
75.3.k.a.52.2	yes	80	25.2	odd	20	inner
225.3.r.b.127.9		80	75.2	even	20
225.3.r.b.163.9		80	3.2	odd	2
375.3.k.a.43.9		80	5.4	even	2
375.3.k.a.157.9		80	25.23	odd	20
375.3.k.b.82.9		80	5.3	odd	4
375.3.k.b.343.9		80	25.14	even	10
375.3.k.c.82.2		80	5.2	odd	4
375.3.k.c.343.2		80	25.11	even	5

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.60745 + 0.412980i) q^{2} +(0.786335 - 1.54327i) q^{3} +(2.82402 - 0.917581i) q^{4} +(-1.42490 + 4.79267i) q^{5} +(-1.41299 + 4.34874i) q^{6} +(5.98338 - 5.98338i) q^{7} +(2.42430 - 1.23524i) q^{8} +(-1.76336 - 2.42705i) q^{9} +O(q^{10})\)	\(q+(-2.60745 + 0.412980i) q^{2} +(0.786335 - 1.54327i) q^{3} +(2.82402 - 0.917581i) q^{4} +(-1.42490 + 4.79267i) q^{5} +(-1.41299 + 4.34874i) q^{6} +(5.98338 - 5.98338i) q^{7} +(2.42430 - 1.23524i) q^{8} +(-1.76336 - 2.42705i) q^{9} +(1.73607 - 13.0851i) q^{10} +(13.4856 + 9.79785i) q^{11} +(0.804553 - 5.07975i) q^{12} +(20.8493 + 3.30220i) q^{13} +(-13.1304 + 18.0724i) q^{14} +(6.27593 + 5.96764i) q^{15} +(-15.4202 + 11.2034i) q^{16} +(-10.4375 - 20.4848i) q^{17} +(5.60019 + 5.60019i) q^{18} +(8.88586 + 2.88719i) q^{19} +(0.373717 + 14.8421i) q^{20} +(-4.52902 - 13.9389i) q^{21} +(-39.2093 - 19.9781i) q^{22} +(0.840422 + 5.30621i) q^{23} -4.71267i q^{24} +(-20.9393 - 13.6581i) q^{25} -55.7272 q^{26} +(-5.13218 + 0.812857i) q^{27} +(11.4070 - 22.3874i) q^{28} +(-20.9015 + 6.79131i) q^{29} +(-18.8287 - 12.9685i) q^{30} +(-3.67506 + 11.3107i) q^{31} +(27.8848 - 27.8848i) q^{32} +(25.7249 - 13.1075i) q^{33} +(35.6752 + 49.1027i) q^{34} +(20.1506 + 37.2020i) q^{35} +(-7.20677 - 5.23603i) q^{36} +(-7.04822 + 44.5007i) q^{37} +(-24.3618 - 3.85853i) q^{38} +(21.4907 - 29.5794i) q^{39} +(2.46573 + 13.3790i) q^{40} +(49.1533 - 35.7120i) q^{41} +(17.5657 + 34.4746i) q^{42} +(-19.8888 - 19.8888i) q^{43} +(47.0739 + 15.2952i) q^{44} +(14.1447 - 4.99288i) q^{45} +(-4.38272 - 13.4886i) q^{46} +(-30.4015 - 15.4904i) q^{47} +(5.16445 + 32.6071i) q^{48} -22.6016i q^{49} +(60.2388 + 26.9654i) q^{50} -39.8210 q^{51} +(61.9088 - 9.80539i) q^{52} +(15.7315 - 30.8749i) q^{53} +(13.0462 - 4.23897i) q^{54} +(-66.1734 + 50.6710i) q^{55} +(7.11459 - 21.8965i) q^{56} +(11.4430 - 11.4430i) q^{57} +(51.6950 - 26.3399i) q^{58} +(8.53853 + 11.7523i) q^{59} +(23.1992 + 11.0941i) q^{60} +(11.7754 + 8.55534i) q^{61} +(4.91146 - 31.0097i) q^{62} +(-25.0728 - 3.97114i) q^{63} +(-16.3787 + 22.5434i) q^{64} +(-45.5344 + 95.2183i) q^{65} +(-61.6633 + 44.8010i) q^{66} +(6.67100 + 13.0926i) q^{67} +(-48.2723 - 48.2723i) q^{68} +(8.84977 + 2.87546i) q^{69} +(-67.9055 - 88.6807i) q^{70} +(-15.5502 - 47.8586i) q^{71} +(-7.27291 - 3.70573i) q^{72} +(-1.42052 - 8.96883i) q^{73} -118.944i q^{74} +(-37.5435 + 21.5752i) q^{75} +27.7431 q^{76} +(139.314 - 22.0651i) q^{77} +(-43.8202 + 86.0020i) q^{78} +(-30.1612 + 9.79997i) q^{79} +(-31.7220 - 89.8674i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(-113.416 + 113.416i) q^{82} +(-127.859 + 65.1473i) q^{83} +(-25.5801 - 35.2080i) q^{84} +(113.049 - 20.8349i) q^{85} +(60.0728 + 43.6454i) q^{86} +(-5.95476 + 37.5969i) q^{87} +(44.7959 + 7.09497i) q^{88} +(-56.4424 + 77.6863i) q^{89} +(-34.8195 + 18.8601i) q^{90} +(144.507 - 104.991i) q^{91} +(7.24225 + 14.2137i) q^{92} +(14.5656 + 14.5656i) q^{93} +(85.6677 + 27.8351i) q^{94} +(-26.4988 + 38.4730i) q^{95} +(-21.1069 - 64.9604i) q^{96} +(-157.426 - 80.2125i) q^{97} +(9.33402 + 58.9327i) q^{98} -50.0073i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

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