LMFDB - Embedded newform 805.2.i.e.576.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(116,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("805.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			576.4
Character	$\chi$	$=$	805.576
Dual form			805.2.i.e.116.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13720 + 1.96969i) q^{2} +(-1.33307 - 2.30894i) q^{3} +(-1.58644 - 2.74779i) q^{4} +(0.500000 - 0.866025i) q^{5} +6.06385 q^{6} +(-0.155013 + 2.64121i) q^{7} +2.66759 q^{8} +(-2.05414 + 3.55788i) q^{9} +O(q^{10})$	\(q+(-1.13720 + 1.96969i) q^{2} +(-1.33307 - 2.30894i) q^{3} +(-1.58644 - 2.74779i) q^{4} +(0.500000 - 0.866025i) q^{5} +6.06385 q^{6} +(-0.155013 + 2.64121i) q^{7} +2.66759 q^{8} +(-2.05414 + 3.55788i) q^{9} +(1.13720 + 1.96969i) q^{10} +(-1.89757 - 3.28669i) q^{11} +(-4.22966 + 7.32599i) q^{12} -1.88978 q^{13} +(-5.02606 - 3.30890i) q^{14} -2.66614 q^{15} +(0.139299 - 0.241273i) q^{16} +(-0.0121412 - 0.0210291i) q^{17} +(-4.67193 - 8.09203i) q^{18} +(-1.42925 + 2.47553i) q^{19} -3.17288 q^{20} +(6.30504 - 3.16299i) q^{21} +8.63167 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-3.55608 - 6.15931i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.14905 - 3.72226i) q^{26} +2.95484 q^{27} +(7.50341 - 3.76417i) q^{28} +7.76047 q^{29} +(3.03193 - 5.25145i) q^{30} +(-0.153221 - 0.265386i) q^{31} +(2.98441 + 5.16915i) q^{32} +(-5.05919 + 8.76278i) q^{33} +0.0552276 q^{34} +(2.20985 + 1.45485i) q^{35} +13.0351 q^{36} +(-2.33727 + 4.04828i) q^{37} +(-3.25068 - 5.63034i) q^{38} +(2.51920 + 4.36338i) q^{39} +(1.33380 - 2.31020i) q^{40} -0.826650 q^{41} +(-0.939975 + 16.0159i) q^{42} +7.31713 q^{43} +(-6.02077 + 10.4283i) q^{44} +(2.05414 + 3.55788i) q^{45} +(-1.13720 - 1.96969i) q^{46} +(-5.16852 + 8.95214i) q^{47} -0.742780 q^{48} +(-6.95194 - 0.818842i) q^{49} +2.27440 q^{50} +(-0.0323700 + 0.0560665i) q^{51} +(2.99801 + 5.19271i) q^{52} +(4.69463 + 8.13134i) q^{53} +(-3.36024 + 5.82010i) q^{54} -3.79515 q^{55} +(-0.413511 + 7.04566i) q^{56} +7.62115 q^{57} +(-8.82520 + 15.2857i) q^{58} +(-0.376828 - 0.652686i) q^{59} +(4.22966 + 7.32599i) q^{60} +(-2.50079 + 4.33149i) q^{61} +0.696970 q^{62} +(-9.07868 - 5.97693i) q^{63} -13.0183 q^{64} +(-0.944888 + 1.63659i) q^{65} +(-11.5066 - 19.9300i) q^{66} +(1.40773 + 2.43826i) q^{67} +(-0.0385224 + 0.0667228i) q^{68} +2.66614 q^{69} +(-5.37862 + 2.69825i) q^{70} +6.26190 q^{71} +(-5.47961 + 9.49097i) q^{72} +(7.43843 + 12.8837i) q^{73} +(-5.31589 - 9.20739i) q^{74} +(-1.33307 + 2.30894i) q^{75} +9.06967 q^{76} +(8.97499 - 4.50240i) q^{77} -11.4593 q^{78} +(-5.59086 + 9.68365i) q^{79} +(-0.139299 - 0.241273i) q^{80} +(2.22342 + 3.85108i) q^{81} +(0.940065 - 1.62824i) q^{82} -4.82136 q^{83} +(-18.6938 - 12.3070i) q^{84} -0.0242823 q^{85} +(-8.32103 + 14.4124i) q^{86} +(-10.3452 - 17.9185i) q^{87} +(-5.06195 - 8.76756i) q^{88} +(7.65437 - 13.2578i) q^{89} -9.34387 q^{90} +(0.292940 - 4.99129i) q^{91} +3.17288 q^{92} +(-0.408508 + 0.707556i) q^{93} +(-11.7553 - 20.3607i) q^{94} +(1.42925 + 2.47553i) q^{95} +(7.95685 - 13.7817i) q^{96} -7.44696 q^{97} +(9.51860 - 12.7620i) q^{98} +15.5916 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 5 q^{2} - 19 q^{4} + 15 q^{5} - 16 q^{6} - 3 q^{7} + 30 q^{8} - 27 q^{9}+O(q^{10}) $ 30 * q - 5 * q^2 - 19 * q^4 + 15 * q^5 - 16 * q^6 - 3 * q^7 + 30 * q^8 - 27 * q^9	\( 30 q - 5 q^{2} - 19 q^{4} + 15 q^{5} - 16 q^{6} - 3 q^{7} + 30 q^{8} - 27 q^{9} + 5 q^{10} - 11 q^{11} + 6 q^{13} - 5 q^{14} - 43 q^{16} + q^{17} + 13 q^{18} + 17 q^{19} - 38 q^{20} - 3 q^{21} + 50 q^{22} - 15 q^{23} + 4 q^{24} - 15 q^{25} + 14 q^{26} - 6 q^{27} - q^{28} + 62 q^{29} - 8 q^{30} + 23 q^{31} - 30 q^{32} - 28 q^{33} - 20 q^{34} + 6 q^{35} + 30 q^{36} - 20 q^{37} - 12 q^{38} - 4 q^{39} + 15 q^{40} - 16 q^{42} + 8 q^{43} - 33 q^{44} + 27 q^{45} - 5 q^{46} + q^{47} + 52 q^{48} + 33 q^{49} + 10 q^{50} - 27 q^{51} - 11 q^{52} - 36 q^{53} - 12 q^{54} - 22 q^{55} + 18 q^{56} + 56 q^{57} - 14 q^{58} + 10 q^{59} + 10 q^{61} + 28 q^{62} - 51 q^{63} + 18 q^{64} + 3 q^{65} + 17 q^{66} - 13 q^{67} - 3 q^{68} - q^{70} - 14 q^{71} - 35 q^{72} - 9 q^{73} - 62 q^{74} + 10 q^{76} - 26 q^{77} - 34 q^{78} - 4 q^{79} + 43 q^{80} - 43 q^{81} - 32 q^{82} + 58 q^{83} - 78 q^{84} + 2 q^{85} - 100 q^{86} + 22 q^{87} - 24 q^{88} + 6 q^{89} + 26 q^{90} - 6 q^{91} + 38 q^{92} - q^{93} + 62 q^{94} - 17 q^{95} + 63 q^{96} + 72 q^{97} + q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q - 5 * q^2 - 19 * q^4 + 15 * q^5 - 16 * q^6 - 3 * q^7 + 30 * q^8 - 27 * q^9 + 5 * q^10 - 11 * q^11 + 6 * q^13 - 5 * q^14 - 43 * q^16 + q^17 + 13 * q^18 + 17 * q^19 - 38 * q^20 - 3 * q^21 + 50 * q^22 - 15 * q^23 + 4 * q^24 - 15 * q^25 + 14 * q^26 - 6 * q^27 - q^28 + 62 * q^29 - 8 * q^30 + 23 * q^31 - 30 * q^32 - 28 * q^33 - 20 * q^34 + 6 * q^35 + 30 * q^36 - 20 * q^37 - 12 * q^38 - 4 * q^39 + 15 * q^40 - 16 * q^42 + 8 * q^43 - 33 * q^44 + 27 * q^45 - 5 * q^46 + q^47 + 52 * q^48 + 33 * q^49 + 10 * q^50 - 27 * q^51 - 11 * q^52 - 36 * q^53 - 12 * q^54 - 22 * q^55 + 18 * q^56 + 56 * q^57 - 14 * q^58 + 10 * q^59 + 10 * q^61 + 28 * q^62 - 51 * q^63 + 18 * q^64 + 3 * q^65 + 17 * q^66 - 13 * q^67 - 3 * q^68 - q^70 - 14 * q^71 - 35 * q^72 - 9 * q^73 - 62 * q^74 + 10 * q^76 - 26 * q^77 - 34 * q^78 - 4 * q^79 + 43 * q^80 - 43 * q^81 - 32 * q^82 + 58 * q^83 - 78 * q^84 + 2 * q^85 - 100 * q^86 + 22 * q^87 - 24 * q^88 + 6 * q^89 + 26 * q^90 - 6 * q^91 + 38 * q^92 - q^93 + 62 * q^94 - 17 * q^95 + 63 * q^96 + 72 * q^97 + q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

$n$	$162$	$281$	$346$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.13720	+	1.96969i	−0.804121	+	1.39278i	0.112763	+	0.993622i	$0.464030\pi$
$2$	−1.13720	+	1.96969i	−0.804121	+	1.39278i	−0.916883	+	0.399156i	$0.869303\pi$
$3$	−1.33307	−	2.30894i	−0.769647	−	1.33307i	−0.937754	−	0.347300i	$-0.887099\pi$
$3$	−1.33307	−	2.30894i	−0.769647	−	1.33307i	0.168107	−	0.985769i	$-0.446235\pi$
$4$	−1.58644	−	2.74779i	−0.793220	−	1.37390i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	6.06385			2.47556
$7$	−0.155013	+	2.64121i	−0.0585894	+	0.998282i
$7$	−0.155013	+	2.64121i	−0.0585894	+	0.998282i
$8$	2.66759			0.943136
$9$	−2.05414	+	3.55788i	−0.684714	+	1.18596i
$10$	1.13720	+	1.96969i	0.359614	+	0.622869i
$11$	−1.89757	−	3.28669i	−0.572140	−	0.990976i	−0.996346	−	0.0854099i	$-0.972780\pi$
$11$	−1.89757	−	3.28669i	−0.572140	−	0.990976i	0.424206	−	0.905566i	$-0.360553\pi$
$12$	−4.22966	+	7.32599i	−1.22100	+	2.11483i
$13$	−1.88978			−0.524129			−0.262065	−	0.965050i	$-0.584403\pi$
$13$	−1.88978			−0.524129			−0.262065	+	0.965050i	$0.584403\pi$
$14$	−5.02606	−	3.30890i	−1.34327	−	0.884341i
$15$	−2.66614			−0.688394
$16$	0.139299	−	0.241273i	0.0348247	−	0.0603182i
$17$	−0.0121412	−	0.0210291i	−0.00294466	−	0.00510031i	0.864549	−	0.502548i	$-0.167604\pi$
$17$	−0.0121412	−	0.0210291i	−0.00294466	−	0.00510031i	−0.867494	+	0.497448i	$0.834271\pi$
$18$	−4.67193	−	8.09203i	−1.10119	−	1.90731i
$19$	−1.42925	+	2.47553i	−0.327892	+	0.567926i	−0.982093	−	0.188395i	$-0.939672\pi$
$19$	−1.42925	+	2.47553i	−0.327892	+	0.567926i	0.654201	+	0.756321i	$0.273005\pi$
$20$	−3.17288			−0.709477
$21$	6.30504	−	3.16299i	1.37587	−	0.690222i
$22$	8.63167			1.84028
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$24$	−3.55608	−	6.15931i	−0.725882	−	1.25726i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.14905	−	3.72226i	0.421463	−	0.729996i
$27$	2.95484			0.568659
$28$	7.50341	−	3.76417i	1.41801	−	0.711361i
$29$	7.76047			1.44108			0.720542	−	0.693411i	$-0.243893\pi$
$29$	7.76047			1.44108			0.720542	+	0.693411i	$0.243893\pi$
$30$	3.03193	−	5.25145i	0.553551	−	0.958779i
$31$	−0.153221	−	0.265386i	−0.0275193	−	0.0476648i	0.851938	−	0.523643i	$-0.175427\pi$
$31$	−0.153221	−	0.265386i	−0.0275193	−	0.0476648i	−0.879457	+	0.475978i	$0.842094\pi$
$32$	2.98441	+	5.16915i	0.527575	+	0.913786i
$33$	−5.05919	+	8.76278i	−0.880692	+	1.52540i
$34$	0.0552276			0.00947146
$35$	2.20985	+	1.45485i	0.373532	+	0.245914i
$36$	13.0351			2.17252
$37$	−2.33727	+	4.04828i	−0.384246	+	0.665533i	−0.991664	−	0.128849i	$-0.958872\pi$
$37$	−2.33727	+	4.04828i	−0.384246	+	0.665533i	0.607419	+	0.794382i	$0.292205\pi$
$38$	−3.25068	−	5.63034i	−0.527330	−	0.913362i
$39$	2.51920	+	4.36338i	0.403395	+	0.698700i
$40$	1.33380	−	2.31020i	0.210892	−	0.365275i
$41$	−0.826650			−0.129101			−0.0645505	−	0.997914i	$-0.520561\pi$
$41$	−0.826650			−0.129101			−0.0645505	+	0.997914i	$0.520561\pi$
$42$	−0.939975	+	16.0159i	−0.145041	+	2.47130i
$43$	7.31713			1.11585			0.557926	−	0.829891i	$-0.311597\pi$
$43$	7.31713			1.11585			0.557926	+	0.829891i	$0.311597\pi$
$44$	−6.02077	+	10.4283i	−0.907666	+	1.57212i
$45$	2.05414	+	3.55788i	0.306214	+	0.530377i
$46$	−1.13720	−	1.96969i	−0.167671	−	0.290414i
$47$	−5.16852	+	8.95214i	−0.753906	+	1.30580i	0.192010	+	0.981393i	$0.438499\pi$
$47$	−5.16852	+	8.95214i	−0.753906	+	1.30580i	−0.945916	+	0.324411i	$0.894834\pi$
$48$	−0.742780			−0.107211
$49$	−6.95194	−	0.818842i	−0.993135	−	0.116977i
$50$	2.27440			0.321648
$51$	−0.0323700	+	0.0560665i	−0.00453271	+	0.00785088i
$52$	2.99801	+	5.19271i	0.415750	+	0.720100i
$53$	4.69463	+	8.13134i	0.644857	+	1.11693i	0.984334	+	0.176311i	$0.0564166\pi$
$53$	4.69463	+	8.13134i	0.644857	+	1.11693i	−0.339477	+	0.940614i	$0.610250\pi$
$54$	−3.36024	+	5.82010i	−0.457271	+	0.792016i
$55$	−3.79515			−0.511738
$56$	−0.413511	+	7.04566i	−0.0552577	+	0.941516i
$57$	7.62115			1.00945
$58$	−8.82520	+	15.2857i	−1.15881	+	2.00711i
$59$	−0.376828	−	0.652686i	−0.0490589	−	0.0849724i	0.840453	−	0.541884i	$-0.182289\pi$
$59$	−0.376828	−	0.652686i	−0.0490589	−	0.0849724i	−0.889512	+	0.456912i	$0.848956\pi$
$60$	4.22966	+	7.32599i	0.546047	+	0.945782i
$61$	−2.50079	+	4.33149i	−0.320193	+	0.554591i	−0.980528	−	0.196381i	$-0.937081\pi$
$61$	−2.50079	+	4.33149i	−0.320193	+	0.554591i	0.660335	+	0.750971i	$0.270414\pi$
$62$	0.696970			0.0885152
$63$	−9.07868	−	5.97693i	−1.14381	−	0.753023i
$64$	−13.0183			−1.62728
$65$	−0.944888	+	1.63659i	−0.117199	+	0.202994i
$66$	−11.5066	−	19.9300i	−1.41637	−	2.45322i
$67$	1.40773	+	2.43826i	0.171982	+	0.297881i	0.939113	−	0.343610i	$-0.111650\pi$
$67$	1.40773	+	2.43826i	0.171982	+	0.297881i	−0.767131	+	0.641491i	$0.778316\pi$
$68$	−0.0385224	+	0.0667228i	−0.00467153	+	0.00809133i
$69$	2.66614			0.320965
$70$	−5.37862	+	2.69825i	−0.642869	+	0.322502i
$71$	6.26190			0.743151			0.371575	−	0.928403i	$-0.378818\pi$
$71$	6.26190			0.743151			0.371575	+	0.928403i	$0.378818\pi$
$72$	−5.47961	+	9.49097i	−0.645779	+	1.11852i
$73$	7.43843	+	12.8837i	0.870602	+	1.50793i	0.861375	+	0.507969i	$0.169604\pi$
$73$	7.43843	+	12.8837i	0.870602	+	1.50793i	0.00922651	+	0.999957i	$0.497063\pi$
$74$	−5.31589	−	9.20739i	−0.617959	−	1.07034i
$75$	−1.33307	+	2.30894i	−0.153929	+	0.266614i
$76$	9.06967			1.04036
$77$	8.97499	−	4.50240i	1.02279	−	0.513097i
$78$	−11.4593			−1.29751
$79$	−5.59086	+	9.68365i	−0.629021	+	1.08950i	0.358728	+	0.933442i	$0.383211\pi$
$79$	−5.59086	+	9.68365i	−0.629021	+	1.08950i	−0.987749	+	0.156053i	$0.950123\pi$
$80$	−0.139299	−	0.241273i	−0.0155741	−	0.0269751i
$81$	2.22342	+	3.85108i	0.247047	+	0.427898i
$82$	0.940065	−	1.62824i	0.103813	−	0.179809i
$83$	−4.82136			−0.529213			−0.264606	−	0.964357i	$-0.585242\pi$
$83$	−4.82136			−0.529213			−0.264606	+	0.964357i	$0.585242\pi$
$84$	−18.6938	−	12.3070i	−2.03966	−	1.34281i
$85$	−0.0242823			−0.00263379
$86$	−8.32103	+	14.4124i	−0.897280	+	1.55413i
$87$	−10.3452	−	17.9185i	−1.10913	−	1.92106i
$88$	−5.06195	−	8.76756i	−0.539606	−	0.934625i
$89$	7.65437	−	13.2578i	0.811362	−	1.40532i	−0.100550	−	0.994932i	$-0.532060\pi$
$89$	7.65437	−	13.2578i	0.811362	−	1.40532i	0.911911	−	0.410388i	$-0.134607\pi$
$90$	−9.34387			−0.984930
$91$	0.292940	−	4.99129i	0.0307084	−	0.523229i
$92$	3.17288			0.330795
$93$	−0.408508	+	0.707556i	−0.0423603	+	0.0733701i
$94$	−11.7553	−	20.3607i	−1.21246	−	2.10005i
$95$	1.42925	+	2.47553i	0.146638	+	0.253984i
$96$	7.95685	−	13.7817i	0.812093	−	1.40659i
$97$	−7.44696			−0.756124			−0.378062	−	0.925780i	$-0.623409\pi$
$97$	−7.44696			−0.756124			−0.378062	+	0.925780i	$0.623409\pi$
$98$	9.51860	−	12.7620i	0.961523	−	1.28915i
$99$	15.5916			1.56701
$100$	−1.58644	+	2.74779i	−0.158644	+	0.274779i
$101$	7.29675	+	12.6383i	0.726054	+	1.25756i	0.958539	+	0.284962i	$0.0919811\pi$
$101$	7.29675	+	12.6383i	0.726054	+	1.25756i	−0.232485	+	0.972600i	$0.574686\pi$
$102$	−0.0736222	−	0.127517i	−0.00728968	−	0.0126261i
$103$	−5.36761	+	9.29698i	−0.528887	+	0.916058i	0.470546	+	0.882375i	$0.344057\pi$
$103$	−5.36761	+	9.29698i	−0.528887	+	0.916058i	−0.999433	+	0.0336829i	$0.989276\pi$
$104$	−5.04115			−0.494325
$105$	0.413286	−	7.04182i	0.0403325	−	0.687211i
$106$	−21.3549			−2.07417
$107$	3.53925	−	6.13017i	0.342153	−	0.592626i	−0.642680	−	0.766135i	$-0.722177\pi$
$107$	3.53925	−	6.13017i	0.342153	−	0.592626i	0.984832	+	0.173509i	$0.0555107\pi$
$108$	−4.68768	−	8.11929i	−0.451072	−	0.781279i
$109$	3.37881	+	5.85227i	0.323631	+	0.560545i	0.981234	−	0.192819i	$-0.0617630\pi$
$109$	3.37881	+	5.85227i	0.323631	+	0.560545i	−0.657603	+	0.753364i	$0.728430\pi$
$110$	4.31584	−	7.47525i	0.411499	−	0.712737i
$111$	12.4630			1.18293
$112$	0.615658	+	0.405317i	0.0581742	+	0.0382989i
$113$	16.1764			1.52175			0.760876	−	0.648897i	$-0.224769\pi$
$113$	16.1764			1.52175			0.760876	+	0.648897i	$0.224769\pi$
$114$	−8.66676	+	15.0113i	−0.811716	+	1.40593i
$115$	0.500000	+	0.866025i	0.0466252	+	0.0807573i
$116$	−12.3115	−	21.3242i	−1.14310	−	1.97990i
$117$	3.88187	−	6.72359i	0.358879	−	0.621596i
$118$	1.71411			0.157797
$119$	0.0574242	−	0.0288075i	0.00526407	−	0.00264078i
$120$	−7.11216			−0.649249
$121$	−1.70157	+	2.94721i	−0.154689	+	0.267928i
$122$	−5.68778	−	9.85153i	−0.514948	−	0.891915i
$123$	1.10198	+	1.90869i	0.0993623	+	0.172100i
$124$	−0.486151	+	0.842038i	−0.0436577	+	0.0756173i
$125$	−1.00000			−0.0894427
$126$	22.0969	−	11.0852i	1.96855	−	0.987546i
$127$	−22.2468			−1.97409			−0.987043	−	0.160454i	$-0.948704\pi$
$127$	−22.2468			−1.97409			−0.987043	+	0.160454i	$0.948704\pi$
$128$	8.83554	−	15.3036i	0.780958	−	1.35266i
$129$	−9.75424	−	16.8948i	−0.858813	−	1.48751i
$130$	−2.14905	−	3.72226i	−0.188484	−	0.326464i
$131$	6.65789	−	11.5318i	0.581702	−	1.00754i	−0.413576	−	0.910470i	$-0.635720\pi$
$131$	6.65789	−	11.5318i	0.581702	−	1.00754i	0.995278	−	0.0970679i	$-0.0309464\pi$
$132$	32.1044			2.79433
$133$	−6.31684	−	4.15868i	−0.547739	−	0.360603i
$134$	−6.40348			−0.553176
$135$	1.47742	−	2.55897i	0.127156	−	0.220241i
$136$	−0.0323876	−	0.0560971i	−0.00277722	−	0.00481028i
$137$	0.205066	+	0.355184i	0.0175199	+	0.0303454i	0.874652	−	0.484751i	$-0.161090\pi$
$137$	0.205066	+	0.355184i	0.0175199	+	0.0303454i	−0.857133	+	0.515096i	$0.827756\pi$
$138$	−3.03193	+	5.25145i	−0.258095	+	0.447033i
$139$	−6.36508			−0.539879			−0.269940	−	0.962877i	$-0.587004\pi$
$139$	−6.36508			−0.539879			−0.269940	+	0.962877i	$0.587004\pi$
$140$	0.491837	−	8.38023i	0.0415678	−	0.708259i
$141$	27.5600			2.32097
$142$	−7.12102	+	12.3340i	−0.597583	+	1.03504i
$143$	3.58599	+	6.21112i	0.299875	+	0.519400i
$144$	0.572280	+	0.991217i	0.0476900	+	0.0826014i
$145$	3.88024	−	6.72077i	0.322236	−	0.558129i
$146$	−33.8359			−2.80028
$147$	7.37676	+	17.1432i	0.608425	+	1.41395i
$148$	14.8318			1.21916
$149$	1.09527	−	1.89706i	0.0897279	−	0.155413i	−0.817668	−	0.575690i	$-0.804734\pi$
$149$	1.09527	−	1.89706i	0.0897279	−	0.155413i	0.907396	+	0.420276i	$0.138067\pi$
$150$	−3.03193	−	5.25145i	−0.247556	−	0.428779i
$151$	0.324320	+	0.561739i	0.0263928	+	0.0457137i	0.878920	−	0.476969i	$-0.158265\pi$
$151$	0.324320	+	0.561739i	0.0263928	+	0.0457137i	−0.852527	+	0.522683i	$0.824931\pi$
$152$	−3.81265	+	6.60371i	−0.309247	+	0.535631i
$153$	0.0997587			0.00806501
$154$	−1.33802	+	22.7980i	−0.107821	+	1.83712i
$155$	−0.306442			−0.0246140
$156$	7.99312	−	13.8445i	0.639962	−	1.10845i
$157$	5.39433	+	9.34325i	0.430514	+	0.745672i	0.996918	−	0.0784557i	$-0.0249989\pi$
$157$	5.39433	+	9.34325i	0.430514	+	0.745672i	−0.566403	+	0.824128i	$0.691666\pi$
$158$	−12.7158	−	22.0245i	−1.01162	−	1.75217i
$159$	12.5165	−	21.6793i	0.992626	−	1.71928i
$160$	5.96882			0.471877
$161$	−2.20985	−	1.45485i	−0.174160	−	0.114658i
$162$	−10.1139			−0.794623
$163$	−2.31040	+	4.00173i	−0.180965	+	0.313440i	−0.942209	−	0.335025i	$-0.891255\pi$
$163$	−2.31040	+	4.00173i	−0.180965	+	0.313440i	0.761245	+	0.648465i	$0.224589\pi$
$164$	1.31143	+	2.27146i	0.102405	+	0.177371i
$165$	5.05919	+	8.76278i	0.393858	+	0.682181i
$166$	5.48284	−	9.49655i	0.425551	−	0.737075i
$167$	−15.4877			−1.19847			−0.599237	−	0.800572i	$-0.704529\pi$
$167$	−15.4877			−1.19847			−0.599237	+	0.800572i	$0.704529\pi$
$168$	16.8193	−	8.43757i	1.29763	−	0.650973i
$169$	−9.42875			−0.725288
$170$	0.0276138	−	0.0478285i	0.00211788	−	0.00366828i
$171$	−5.87176	−	10.1702i	−0.449025	−	0.777734i
$172$	−11.6082	−	20.1060i	−0.885116	−	1.53307i
$173$	−1.95391	+	3.38428i	−0.148553	+	0.257302i	−0.930693	−	0.365801i	$-0.880795\pi$
$173$	−1.95391	+	3.38428i	−0.148553	+	0.257302i	0.782140	+	0.623103i	$0.214128\pi$
$174$	47.0584			3.56749
$175$	2.36486	−	1.18636i	0.178766	−	0.0896802i
$176$	−1.05732			−0.0796985
$177$	−1.00468	+	1.74015i	−0.0755160	+	0.130798i
$178$	17.4091	+	30.1534i	1.30487	+	2.26009i
$179$	7.80255	+	13.5144i	0.583190	+	1.01012i	0.995098	+	0.0988897i	$0.0315291\pi$
$179$	7.80255	+	13.5144i	0.583190	+	1.01012i	−0.411908	+	0.911225i	$0.635138\pi$
$180$	6.51755	−	11.2887i	0.485789	−	0.841412i
$181$	−6.51091			−0.483952			−0.241976	−	0.970282i	$-0.577796\pi$
$181$	−6.51091			−0.483952			−0.241976	+	0.970282i	$0.577796\pi$
$182$	9.49813	+	6.25308i	0.704049	+	0.463509i
$183$	13.3349			0.985743
$184$	−1.33380	+	2.31020i	−0.0983287	+	0.170310i
$185$	2.33727	+	4.04828i	0.171840	+	0.297635i
$186$	−0.929108	−	1.60926i	−0.0681255	−	0.117997i
$187$	−0.0460775	+	0.0798086i	−0.00336952	+	0.00583618i
$188$	32.7982			2.39205
$189$	−0.458038	+	7.80434i	−0.0333174	+	0.567682i
$190$	−6.50136			−0.471658
$191$	−9.15552	+	15.8578i	−0.662470	+	1.14743i	0.317494	+	0.948260i	$0.397159\pi$
$191$	−9.15552	+	15.8578i	−0.662470	+	1.14743i	−0.979965	+	0.199172i	$0.936175\pi$
$192$	17.3543	+	30.0584i	1.25244	+	2.16928i
$193$	−7.52603	−	13.0355i	−0.541736	−	0.938314i	−0.998805	−	0.0488823i	$-0.984434\pi$
$193$	−7.52603	−	13.0355i	−0.541736	−	0.938314i	0.457069	−	0.889431i	$-0.348899\pi$
$194$	8.46867	−	14.6682i	0.608015	−	1.05311i
$195$	5.03840			0.360807
$196$	8.77883	+	20.4015i	0.627059	+	1.45725i
$197$	7.94784			0.566260			0.283130	−	0.959082i	$-0.408627\pi$
$197$	7.94784			0.566260			0.283130	+	0.959082i	$0.408627\pi$
$198$	−17.7307	+	30.7104i	−1.26006	+	2.18250i
$199$	8.18743	+	14.1810i	0.580391	+	1.00527i	0.995433	+	0.0954650i	$0.0304338\pi$
$199$	8.18743	+	14.1810i	0.580391	+	1.00527i	−0.415041	+	0.909803i	$0.636233\pi$
$200$	−1.33380	−	2.31020i	−0.0943136	−	0.163356i
$201$	3.75320	−	6.50074i	0.264731	−	0.458527i
$202$	−33.1914			−2.33534
$203$	−1.20297	+	20.4970i	−0.0844322	+	1.43861i
$204$	0.205412			0.0143817
$205$	−0.413325	+	0.715900i	−0.0288679	+	0.0500006i
$206$	−12.2081	−	21.1450i	−0.850577	−	1.47324i
$207$	−2.05414	−	3.55788i	−0.142773	−	0.247290i
$208$	−0.263244	+	0.455951i	−0.0182527	+	0.0316145i
$209$	10.8484			0.750401
$210$	13.4002	+	8.82198i	0.924700	+	0.608775i
$211$	16.4120			1.12985			0.564925	−	0.825142i	$-0.308905\pi$
$211$	16.4120			1.12985			0.564925	+	0.825142i	$0.308905\pi$
$212$	14.8955	−	25.7998i	1.02303	−	1.77194i
$213$	−8.34754	−	14.4584i	−0.571964	−	0.990671i
$214$	8.04967	+	13.9424i	0.550264	+	0.953085i
$215$	3.65857	−	6.33682i	0.249512	−	0.432168i
$216$	7.88231			0.536323
$217$	0.724691	−	0.363550i	0.0491952	−	0.0246793i
$218$	−15.3695			−1.04095
$219$	19.8319	−	34.3498i	1.34011	−	2.32114i
$220$	6.02077	+	10.4283i	0.405920	+	0.703075i
$221$	0.0229441	+	0.0397403i	0.00154338	+	0.00267322i
$222$	−14.1729	+	24.5482i	−0.951222	+	1.64756i
$223$	−17.8928			−1.19819			−0.599094	−	0.800679i	$-0.704472\pi$
$223$	−17.8928			−1.19819			−0.599094	+	0.800679i	$0.704472\pi$
$224$	−14.1154	+	7.08116i	−0.943126	+	0.473130i
$225$	4.10829			0.273886
$226$	−18.3958	+	31.8625i	−1.22367	+	2.11946i
$227$	−13.2635	−	22.9731i	−0.880332	−	1.52478i	−0.850972	−	0.525211i	$-0.823986\pi$
$227$	−13.2635	−	22.9731i	−0.880332	−	1.52478i	−0.0293602	−	0.999569i	$-0.509347\pi$
$228$	−12.0905	−	20.9413i	−0.800712	−	1.38687i
$229$	−3.96257	+	6.86337i	−0.261854	+	0.453544i	−0.966735	−	0.255782i	$-0.917667\pi$
$229$	−3.96257	+	6.86337i	−0.261854	+	0.453544i	0.704881	+	0.709326i	$0.251001\pi$
$230$	−2.27440			−0.149969
$231$	−22.3601	−	14.7207i	−1.47118	−	0.968552i
$232$	20.7018			1.35914
$233$	8.18768	−	14.1815i	0.536393	−	0.929060i	−0.462702	−	0.886514i	$-0.653120\pi$
$233$	8.18768	−	14.1815i	0.536393	−	0.929060i	0.999095	−	0.0425457i	$-0.0135468\pi$
$234$	8.82891	+	15.2921i	0.577164	+	0.999677i
$235$	5.16852	+	8.95214i	0.337157	+	0.583973i
$236$	−1.19563	+	2.07089i	−0.0778289	+	0.134804i
$237$	29.8120			1.93650
$238$	−0.00856099	+	0.145868i	−0.000554927	+	0.00945519i
$239$	1.65650			0.107150			0.0535750	−	0.998564i	$-0.482938\pi$
$239$	1.65650			0.107150			0.0535750	+	0.998564i	$0.482938\pi$
$240$	−0.371390	+	0.643266i	−0.0239731	+	0.0415226i
$241$	3.39649	+	5.88289i	0.218787	+	0.378950i	0.954437	−	0.298411i	$-0.0964566\pi$
$241$	3.39649	+	5.88289i	0.218787	+	0.378950i	−0.735650	+	0.677362i	$0.763123\pi$
$242$	−3.87005	−	6.70313i	−0.248777	−	0.430894i
$243$	10.3602	−	17.9444i	0.664608	−	1.15113i
$244$	15.8694			1.01593
$245$	−4.18511	+	5.61114i	−0.267377	+	0.358482i
$246$	−5.01268			−0.319597
$247$	2.70096	−	4.67820i	0.171858	−	0.297667i
$248$	−0.408731	−	0.707942i	−0.0259544	−	0.0449544i
$249$	6.42720	+	11.1322i	0.407307	+	0.705476i
$250$	1.13720	−	1.96969i	0.0719227	−	0.124574i
$251$	−16.7788			−1.05907			−0.529536	−	0.848288i	$-0.677634\pi$
$251$	−16.7788			−1.05907			−0.529536	+	0.848288i	$0.677634\pi$
$252$	−2.02061	+	34.4284i	−0.127286	+	2.16878i
$253$	3.79515			0.238599
$254$	25.2991	−	43.8192i	1.58740	−	2.74946i
$255$	0.0323700	+	0.0560665i	0.00202709	+	0.00351102i
$256$	7.07723	+	12.2581i	0.442327	+	0.766133i
$257$	8.27774	−	14.3375i	0.516351	−	0.894347i	−0.483468	−	0.875362i	$-0.660623\pi$
$257$	8.27774	−	14.3375i	0.516351	−	0.894347i	0.999820	−	0.0189851i	$-0.00604351\pi$
$258$	44.3700			2.76236
$259$	−10.3300	−	6.80076i	−0.641877	−	0.422579i
$260$	5.99603			0.371858
$261$	−15.9411	+	27.6108i	−0.986731	+	1.70907i
$262$	15.1427	+	26.2279i	0.935517	+	1.62036i
$263$	−12.5762	−	21.7825i	−0.775479	−	1.34317i	−0.934525	−	0.355898i	$-0.884175\pi$
$263$	−12.5762	−	21.7825i	−0.775479	−	1.34317i	0.159046	−	0.987271i	$-0.449158\pi$
$264$	−13.4959	+	23.3755i	−0.830613	+	1.43866i
$265$	9.38927			0.576778
$266$	15.3748	−	7.71294i	0.942689	−	0.472911i
$267$	−40.8152			−2.49785
$268$	4.46656	−	7.73631i	0.272839	−	0.472570i
$269$	4.26565	+	7.38832i	0.260081	+	0.450474i	0.966263	−	0.257556i	$-0.0829173\pi$
$269$	4.26565	+	7.38832i	0.260081	+	0.450474i	−0.706182	+	0.708030i	$0.749584\pi$
$270$	3.36024	+	5.82010i	0.204498	+	0.354200i
$271$	15.2508	−	26.4152i	0.926421	−	1.60461i	0.137161	−	0.990549i	$-0.456202\pi$
$271$	15.2508	−	26.4152i	0.926421	−	1.60461i	0.789260	−	0.614060i	$-0.210465\pi$
$272$	−0.00676500			−0.000410188
$273$	−11.9151	+	5.97735i	−0.721135	+	0.361766i
$274$	−0.932801			−0.0563525
$275$	−1.89757	+	3.28669i	−0.114428	+	0.198195i
$276$	−4.22966	−	7.32599i	−0.254596	−	0.440973i
$277$	−4.69156	−	8.12602i	−0.281889	−	0.488245i	0.689961	−	0.723846i	$-0.257628\pi$
$277$	−4.69156	−	8.12602i	−0.281889	−	0.488245i	−0.971850	+	0.235601i	$0.924294\pi$
$278$	7.23836	−	12.5372i	0.434128	−	0.751932i
$279$	1.25895			0.0753713
$280$	5.89496	+	3.88094i	0.352291	+	0.231931i
$281$	−23.6922			−1.41336			−0.706679	−	0.707534i	$-0.749808\pi$
$281$	−23.6922			−1.41336			−0.706679	+	0.707534i	$0.749808\pi$
$282$	−31.3411	+	54.2844i	−1.86634	+	3.23259i
$283$	−11.2121	−	19.4199i	−0.666491	−	1.15440i	−0.978879	−	0.204441i	$-0.934462\pi$
$283$	−11.2121	−	19.4199i	−0.666491	−	1.15440i	0.312388	−	0.949955i	$-0.398871\pi$
$284$	−9.93413	−	17.2064i	−0.589482	−	1.02101i
$285$	3.81057	−	6.60011i	0.225719	−	0.390957i
$286$	−16.3119			−0.964544
$287$	0.128141	−	2.18335i	0.00756395	−	0.128879i
$288$	−24.5216			−1.44495
$289$	8.49971	−	14.7219i	0.499983	−	0.865995i
$290$	8.82520	+	15.2857i	0.518233	+	0.897607i
$291$	9.92730	+	17.1946i	0.581949	+	1.00796i
$292$	23.6012	−	40.8785i	1.38116	−	2.39223i
$293$	14.0496			0.820785			0.410393	−	0.911909i	$-0.365392\pi$
$293$	14.0496			0.820785			0.410393	+	0.911909i	$0.365392\pi$
$294$	−42.1555	−	4.96534i	−2.45856	−	0.289584i
$295$	−0.753656			−0.0438796
$296$	−6.23489	+	10.7992i	−0.362396	+	0.627688i
$297$	−5.60703	−	9.71166i	−0.325353	−	0.563528i
$298$	2.49108	+	4.31467i	0.144304	+	0.249942i
$299$	0.944888	−	1.63659i	0.0546443	−	0.0946467i
$300$	8.45933			0.488400
$301$	−1.13425	+	19.3261i	−0.0653771	+	1.11394i
$302$	−1.47527			−0.0848920
$303$	19.4541	−	33.6956i	1.11761	−	1.93576i
$304$	0.398186	+	0.689678i	0.0228375	+	0.0395557i
$305$	2.50079	+	4.33149i	0.143195	+	0.248020i
$306$	−0.113445	+	0.196493i	−0.00648524	+	0.0112328i
$307$	30.3350			1.73131			0.865654	−	0.500644i	$-0.166903\pi$
$307$	30.3350			1.73131			0.865654	+	0.500644i	$0.166903\pi$
$308$	−26.6100	−	17.5186i	−1.51624	−	0.998216i
$309$	28.6216			1.62822
$310$	0.348485	−	0.603594i	0.0197926	−	0.0342818i
$311$	−13.0873	−	22.6679i	−0.742115	−	1.28538i	−0.951531	−	0.307554i	$-0.900490\pi$
$311$	−13.0873	−	22.6679i	−0.742115	−	1.28538i	0.209416	−	0.977827i	$-0.432844\pi$
$312$	6.72020	+	11.6397i	0.380456	+	0.658969i
$313$	−6.91560	+	11.9782i	−0.390893	+	0.677046i	−0.992568	−	0.121695i	$-0.961167\pi$
$313$	−6.91560	+	11.9782i	−0.390893	+	0.677046i	0.601675	+	0.798741i	$0.294500\pi$
$314$	−24.5377			−1.38474
$315$	−9.71551	+	4.87390i	−0.547407	+	0.274613i
$316$	35.4782			1.99581
$317$	−5.42483	+	9.39608i	−0.304689	+	0.527736i	−0.977192	−	0.212358i	$-0.931886\pi$
$317$	−5.42483	+	9.39608i	−0.304689	+	0.527736i	0.672503	+	0.740094i	$0.265219\pi$
$318$	28.4676	+	49.3073i	1.59638	+	2.76501i
$319$	−14.7261	−	25.5063i	−0.824502	−	1.42808i
$320$	−6.50914	+	11.2742i	−0.363872	+	0.630245i
$321$	−18.8723			−1.05335
$322$	5.37862	−	2.69825i	0.299739	−	0.150368i
$323$	0.0694110			0.00386213
$324$	7.05465	−	12.2190i	0.391925	−	0.678834i
$325$	0.944888	+	1.63659i	0.0524129	+	0.0907819i
$326$	−5.25477	−	9.10153i	−0.291035	−	0.504087i
$327$	9.00836	−	15.6029i	0.498164	−	0.862845i
$328$	−2.20516			−0.121760
$329$	−22.8433	−	15.0388i	−1.25939	−	0.829117i
$330$	−23.0132			−1.26684
$331$	−15.1970	+	26.3219i	−0.835301	+	1.44678i	0.0584847	+	0.998288i	$0.481373\pi$
$331$	−15.1970	+	26.3219i	−0.835301	+	1.44678i	−0.893785	+	0.448495i	$0.851960\pi$
$332$	7.64879	+	13.2481i	0.419782	+	0.727083i
$333$	−9.60219	−	16.6315i	−0.526197	−	0.911400i
$334$	17.6126	−	30.5059i	0.963717	−	1.66921i
$335$	2.81546			0.153825
$336$	0.115140	−	1.96183i	0.00628143	−	0.107027i
$337$	22.4384			1.22230			0.611149	−	0.791515i	$-0.290707\pi$
$337$	22.4384			1.22230			0.611149	+	0.791515i	$0.290707\pi$
$338$	10.7224	−	18.5717i	0.583219	−	1.01017i
$339$	−21.5643	−	37.3505i	−1.17121	−	2.02860i
$340$	0.0385224	+	0.0667228i	0.00208917	+	0.00361855i
$341$	−0.581496	+	1.00718i	−0.0314898	+	0.0545419i
$342$	26.7094			1.44428
$343$	3.24037	−	18.2346i	0.174964	−	0.984575i
$344$	19.5191			1.05240
$345$	1.33307	−	2.30894i	0.0717700	−	0.124309i
$346$	−4.44397	−	7.69719i	−0.238909	−	0.413803i
$347$	17.8632	+	30.9400i	0.958949	+	1.66095i	0.725061	+	0.688685i	$0.241812\pi$
$347$	17.8632	+	30.9400i	0.958949	+	1.66095i	0.233888	+	0.972263i	$0.424855\pi$
$348$	−32.8242	+	56.8532i	−1.75956	+	3.04765i
$349$	−9.97898			−0.534163			−0.267081	−	0.963674i	$-0.586059\pi$
$349$	−9.97898			−0.534163			−0.267081	+	0.963674i	$0.586059\pi$
$350$	−0.352561	+	6.00715i	−0.0188452	+	0.321096i
$351$	−5.58399			−0.298051
$352$	11.3263	−	19.6177i	0.603693	−	1.04563i
$353$	−5.74027	−	9.94244i	−0.305524	−	0.529183i	0.671854	−	0.740683i	$-0.265498\pi$
$353$	−5.74027	−	9.94244i	−0.305524	−	0.529183i	−0.977378	+	0.211501i	$0.932165\pi$
$354$	−2.28503	−	3.95779i	−0.121448	−	0.210354i
$355$	3.13095	−	5.42296i	0.166174	−	0.287821i
$356$	−48.5728			−2.57435
$357$	−0.143065	−	0.0941868i	−0.00757182	−	0.00498490i
$358$	−35.4922			−1.87582
$359$	−8.84140	+	15.3137i	−0.466631	+	0.808229i	−0.999273	−	0.0381116i	$-0.987866\pi$
$359$	−8.84140	+	15.3137i	−0.466631	+	0.808229i	0.532642	+	0.846340i	$0.321199\pi$
$360$	5.47961	+	9.49097i	0.288801	+	0.500218i
$361$	5.41449	+	9.37818i	0.284973	+	0.493588i
$362$	7.40419	−	12.8244i	0.389156	−	0.674038i
$363$	9.07326			0.476223
$364$	−14.1798	+	7.11344i	−0.743221	+	0.372845i
$365$	14.8769			0.778690
$366$	−15.1644	+	26.2655i	−0.792656	+	1.37292i
$367$	−9.35967	−	16.2114i	−0.488571	−	0.846229i	0.511343	−	0.859377i	$-0.329148\pi$
$367$	−9.35967	−	16.2114i	−0.488571	−	0.846229i	−0.999914	+	0.0131474i	$0.995815\pi$
$368$	0.139299	+	0.241273i	0.00726146	+	0.0125772i
$369$	1.69806	−	2.94112i	0.0883973	−	0.153109i
$370$	−10.6318			−0.552720
$371$	−22.2043	+	11.1390i	−1.15279	+	0.578310i
$372$	2.59229			0.134404
$373$	−7.35898	+	12.7461i	−0.381034	+	0.659970i	−0.991210	−	0.132296i	$-0.957765\pi$
$373$	−7.35898	+	12.7461i	−0.381034	+	0.659970i	0.610177	+	0.792265i	$0.291099\pi$
$374$	−0.104798	−	0.181516i	−0.00541900	−	0.00938598i
$375$	1.33307	+	2.30894i	0.0688394	+	0.119233i
$376$	−13.7875	+	23.8806i	−0.711036	+	1.23155i
$377$	−14.6656			−0.755315
$378$	−14.8512	−	9.77728i	−0.763864	−	0.502889i
$379$	−12.4260			−0.638280			−0.319140	−	0.947708i	$-0.603394\pi$
$379$	−12.4260			−0.638280			−0.319140	+	0.947708i	$0.603394\pi$
$380$	4.53483	−	7.85456i	0.232632	−	0.402931i
$381$	29.6565	+	51.3666i	1.51935	+	2.63159i
$382$	−20.8233	−	36.0670i	−1.06541	−	1.84535i
$383$	−15.6643	+	27.1313i	−0.800408	+	1.38635i	0.118940	+	0.992901i	$0.462050\pi$
$383$	−15.6643	+	27.1313i	−0.800408	+	1.38635i	−0.919348	+	0.393445i	$0.871283\pi$
$384$	−47.1135			−2.40425
$385$	0.588297	−	10.0238i	0.0299824	−	0.510859i
$386$	34.2344			1.74248
$387$	−15.0304	+	26.0335i	−0.764040	+	1.32336i
$388$	11.8141	+	20.4627i	0.599772	+	1.03884i
$389$	12.0879	+	20.9369i	0.612882	+	1.06154i	0.990752	+	0.135684i	$0.0433233\pi$
$389$	12.0879	+	20.9369i	0.612882	+	1.06154i	−0.377870	+	0.925859i	$0.623343\pi$
$390$	−5.72966	+	9.92406i	−0.290133	+	0.502524i
$391$	0.0242823			0.00122801
$392$	−18.5449	−	2.18434i	−0.936661	−	0.110326i
$393$	−35.5017			−1.79082
$394$	−9.03827	+	15.6547i	−0.455341	+	0.788674i
$395$	5.59086	+	9.68365i	0.281307	+	0.487237i
$396$	−24.7351	−	42.8424i	−1.24298	−	2.15291i
$397$	−8.94305	+	15.4898i	−0.448839	+	0.777411i	−0.998311	−	0.0581007i	$-0.981496\pi$
$397$	−8.94305	+	15.4898i	−0.448839	+	0.777411i	0.549472	+	0.835512i	$0.314829\pi$
$398$	−37.2429			−1.86682
$399$	−1.18138	+	20.1290i	−0.0591428	+	1.00771i
$400$	−0.278598			−0.0139299
$401$	−14.3604	+	24.8730i	−0.717125	+	1.24210i	0.245010	+	0.969521i	$0.421209\pi$
$401$	−14.3604	+	24.8730i	−0.717125	+	1.24210i	−0.962134	+	0.272576i	$0.912124\pi$
$402$	8.53627	+	14.7853i	0.425751	+	0.737422i
$403$	0.289553	+	0.501520i	0.0144237	+	0.0249825i
$404$	23.1517	−	40.0999i	1.15184	−	1.99505i
$405$	4.44685			0.220966
$406$	−39.0046	−	25.6786i	−1.93577	−	1.27441i
$407$	17.7406			0.879369
$408$	−0.0863499	+	0.149562i	−0.00427496	+	0.00740444i
$409$	10.8985	+	18.8768i	0.538897	+	0.933398i	0.998964	+	0.0455132i	$0.0144923\pi$
$409$	10.8985	+	18.8768i	0.538897	+	0.933398i	−0.460066	+	0.887885i	$0.652174\pi$
$410$	−0.940065	−	1.62824i	−0.0464265	−	0.0804130i
$411$	0.546733	−	0.946969i	0.0269683	−	0.0467105i
$412$	34.0616			1.67809
$413$	1.78229	−	0.894106i	0.0877008	−	0.0439961i
$414$	9.34387			0.459226
$415$	−2.41068	+	4.17542i	−0.118336	+	0.204963i
$416$	−5.63987	−	9.76854i	−0.276517	−	0.478942i
$417$	8.48509	+	14.6966i	0.415517	+	0.719696i
$418$	−12.3368	+	21.3680i	−0.603413	+	1.04514i
$419$	4.61281			0.225351			0.112675	−	0.993632i	$-0.464058\pi$
$419$	4.61281			0.225351			0.112675	+	0.993632i	$0.464058\pi$
$420$	−20.0051	+	10.0358i	−0.976150	+	0.489697i
$421$	1.66325			0.0810618			0.0405309	−	0.999178i	$-0.487095\pi$
$421$	1.66325			0.0810618			0.0405309	+	0.999178i	$0.487095\pi$
$422$	−18.6637	+	32.3265i	−0.908536	+	1.57363i
$423$	−21.2338	−	36.7779i	−1.03242	−	1.78820i
$424$	12.5234	+	21.6911i	0.608188	+	1.05341i
$425$	−0.0121412	+	0.0210291i	−0.000588933	+	0.00102006i
$426$	37.9712			1.83971
$427$	−11.0527	−	7.27653i	−0.534878	−	0.352136i
$428$	−22.4592			−1.08561
$429$	9.56074	−	16.5597i	0.461597	−	0.799509i
$430$	8.32103	+	14.4124i	0.401276	+	0.695030i
$431$	8.38766	+	14.5278i	0.404019	+	0.699782i	0.994207	−	0.107484i	$-0.0342796\pi$
$431$	8.38766	+	14.5278i	0.404019	+	0.699782i	−0.590188	+	0.807266i	$0.700946\pi$
$432$	0.411606	−	0.712922i	0.0198034	−	0.0343005i
$433$	−17.5471			−0.843261			−0.421631	−	0.906768i	$-0.638542\pi$
$433$	−17.5471			−0.843261			−0.421631	+	0.906768i	$0.638542\pi$
$434$	−0.108039	+	1.84084i	−0.00518605	+	0.0883632i
$435$	−20.6905			−0.992033
$436$	10.7205	−	18.5685i	0.513421	−	0.889271i
$437$	−1.42925	−	2.47553i	−0.0683703	−	0.118421i
$438$	45.1055	+	78.1250i	2.15522	+	3.73296i
$439$	−14.9847	+	25.9542i	−0.715179	+	1.23873i	0.247712	+	0.968834i	$0.420321\pi$
$439$	−14.9847	+	25.9542i	−0.715179	+	1.23873i	−0.962890	+	0.269892i	$0.913012\pi$
$440$	−10.1239			−0.482638
$441$	17.1936	−	23.0522i	0.818744	−	1.09772i
$442$	−0.104368			−0.00496427
$443$	8.92813	−	15.4640i	0.424188	−	0.734715i	−0.572156	−	0.820145i	$-0.693893\pi$
$443$	8.92813	−	15.4640i	0.424188	−	0.734715i	0.996344	+	0.0854294i	$0.0272262\pi$
$444$	−19.7718	−	34.2457i	−0.938327	−	1.62523i
$445$	−7.65437	−	13.2578i	−0.362852	−	0.628478i
$446$	20.3476	−	35.2431i	0.963487	−	1.66881i
$447$	−5.84028			−0.276236
$448$	2.01800	−	34.3840i	0.0953416	−	1.62449i
$449$	12.4814			0.589032			0.294516	−	0.955646i	$-0.404842\pi$
$449$	12.4814			0.589032			0.294516	+	0.955646i	$0.404842\pi$
$450$	−4.67193	+	8.09203i	−0.220237	+	0.381462i
$451$	1.56863	+	2.71695i	0.0738639	+	0.127936i
$452$	−25.6630	−	44.4495i	−1.20708	−	2.09073i
$453$	0.864682	−	1.49767i	0.0406263	−	0.0703668i
$454$	60.3331			2.83157
$455$	−4.17611	−	2.74934i	−0.195779	−	0.128891i
$456$	20.3301			0.952045
$457$	−1.29059	+	2.23536i	−0.0603712	+	0.104566i	−0.894631	−	0.446805i	$-0.852562\pi$
$457$	−1.29059	+	2.23536i	−0.0603712	+	0.104566i	0.834260	+	0.551371i	$0.185895\pi$
$458$	−9.01245	−	15.6100i	−0.421124	−	0.729408i
$459$	−0.0358752	−	0.0621376i	−0.00167451	−	0.00290034i
$460$	1.58644	−	2.74779i	0.0739681	−	0.128117i
$461$	−30.0705			−1.40052			−0.700261	−	0.713887i	$-0.746933\pi$
$461$	−30.0705			−1.40052			−0.700261	+	0.713887i	$0.746933\pi$
$462$	54.4230	−	27.3019i	2.53199	−	1.27020i
$463$	19.2562			0.894912			0.447456	−	0.894306i	$-0.352330\pi$
$463$	19.2562			0.894912			0.447456	+	0.894306i	$0.352330\pi$
$464$	1.08103	−	1.87239i	0.0501853	−	0.0869236i
$465$	0.408508	+	0.707556i	0.0189441	+	0.0328121i
$466$	18.6220	+	32.2543i	0.862649	+	1.49415i
$467$	−1.04726	+	1.81391i	−0.0484614	+	0.0839376i	−0.889239	−	0.457444i	$-0.848765\pi$
$467$	−1.04726	+	1.81391i	−0.0484614	+	0.0839376i	0.840777	+	0.541381i	$0.182098\pi$
$468$	−24.6334			−1.13868
$469$	−6.65817	+	3.34015i	−0.307446	+	0.154234i
$470$	−23.5105			−1.08446
$471$	14.3820	−	24.9104i	0.662688	−	1.14781i
$472$	−1.00522	−	1.74110i	−0.0462692	−	0.0801406i
$473$	−13.8848	−	24.0492i	−0.638424	−	1.10578i
$474$	−33.9021	+	58.7202i	−1.55718	+	2.69711i
$475$	2.85850			0.131157
$476$	−0.170257	−	0.112089i	−0.00780373	−	0.00513757i
$477$	−38.5738			−1.76617
$478$	−1.88377	+	3.26278i	−0.0861615	+	0.149236i
$479$	1.71169	+	2.96473i	0.0782090	+	0.135462i	0.902477	−	0.430738i	$-0.141747\pi$
$479$	1.71169	+	2.96473i	0.0782090	+	0.135462i	−0.824268	+	0.566199i	$0.808413\pi$
$480$	−7.95685	−	13.7817i	−0.363179	−	0.629044i
$481$	4.41692	−	7.65034i	0.201394	−	0.348825i
$482$	−15.4499			−0.703725
$483$	−0.413286	+	7.04182i	−0.0188051	+	0.320414i
$484$	10.7978			0.490808
$485$	−3.72348	+	6.44925i	−0.169074	+	0.292846i
$486$	23.5632	+	40.8127i	1.06885	+	1.85130i
$487$	−1.18663	−	2.05531i	−0.0537714	−	0.0931348i	0.837887	−	0.545844i	$-0.183791\pi$
$487$	−1.18663	−	2.05531i	−0.0537714	−	0.0931348i	−0.891658	+	0.452709i	$0.850458\pi$
$488$	−6.67108	+	11.5546i	−0.301986	+	0.523054i
$489$	12.3197			0.557116
$490$	−6.29287	−	14.6243i	−0.284283	−	0.660660i
$491$	−13.6725			−0.617031			−0.308516	−	0.951219i	$-0.599832\pi$
$491$	−13.6725			−0.617031			−0.308516	+	0.951219i	$0.599832\pi$
$492$	3.49645	−	6.05603i	0.157632	−	0.273027i
$493$	−0.0942212	−	0.163196i	−0.00424351	−	0.00734997i
$494$	6.14305	+	10.6401i	0.276389	+	0.478720i
$495$	7.79578	−	13.5027i	0.350394	−	0.606900i
$496$	−0.0853740			−0.00383340
$497$	−0.970675	+	16.5390i	−0.0435407	+	0.741874i
$498$	−29.2360			−1.31010
$499$	13.9554	−	24.1714i	0.624729	−	1.08206i	−0.363865	−	0.931452i	$-0.618543\pi$
$499$	13.9554	−	24.1714i	0.624729	−	1.08206i	0.988593	−	0.150610i	$-0.0481237\pi$
$500$	1.58644	+	2.74779i	0.0709477	+	0.122885i
$501$	20.6462	+	35.7602i	0.922402	+	1.59765i
$502$	19.0809	−	33.0490i	0.851621	−	1.47505i
$503$	18.0895			0.806569			0.403285	−	0.915075i	$-0.367868\pi$
$503$	18.0895			0.806569			0.403285	+	0.915075i	$0.367868\pi$
$504$	−24.2182	−	15.9440i	−1.07876	−	0.710203i
$505$	14.5935			0.649402
$506$	−4.31584	+	7.47525i	−0.191862	+	0.332315i
$507$	12.5692	+	21.7704i	0.558216	+	0.966859i
$508$	35.2932	+	61.1297i	1.56588	+	2.71219i
$509$	−2.98195	+	5.16489i	−0.132173	+	0.228930i	−0.924514	−	0.381149i	$-0.875529\pi$
$509$	−2.98195	+	5.16489i	−0.132173	+	0.228930i	0.792341	+	0.610078i	$0.208862\pi$
$510$	−0.147244			−0.00652009
$511$	−35.1816	+	17.6493i	−1.55634	+	0.780758i
$512$	3.14927			0.139179
$513$	−4.22320	+	7.31480i	−0.186459	+	0.322956i
$514$	18.8269	+	32.6091i	0.830418	+	1.43833i
$515$	5.36761	+	9.29698i	0.236525	+	0.409674i
$516$	−30.9490	+	53.6053i	−1.36245	+	2.35984i
$517$	39.2306			1.72536
$518$	25.1426	−	12.6131i	1.10470	−	0.554188i
$519$	10.4188			0.457335
$520$	−2.52057	+	4.36576i	−0.110535	+	0.191451i
$521$	5.78325	+	10.0169i	0.253369	+	0.438848i	0.964451	−	0.264261i	$-0.0851280\pi$
$521$	5.78325	+	10.0169i	0.253369	+	0.438848i	−0.711082	+	0.703109i	$0.751795\pi$
$522$	−36.2564	−	62.7980i	−1.58690	−	2.74859i
$523$	−15.8328	+	27.4232i	−0.692320	+	1.19913i	0.278756	+	0.960362i	$0.410078\pi$
$523$	−15.8328	+	27.4232i	−0.692320	+	1.19913i	−0.971076	+	0.238771i	$0.923255\pi$
$524$	−42.2493			−1.84567
$525$	−5.89175	−	3.87882i	−0.257137	−	0.169286i
$526$	57.2063			2.49431
$527$	−0.00372056	+	0.00644419i	−0.000162070	+	0.000280713i
$528$	1.40948	+	2.44129i	0.0613397	+	0.106244i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−10.6775	+	18.4939i	−0.463799	+	0.803324i
$531$	3.09624			0.134365
$532$	−1.40592	+	23.9549i	−0.0609542	+	1.03858i
$533$	1.56218			0.0676656
$534$	46.4150	−	80.3931i	2.00857	−	3.47895i
$535$	−3.53925	−	6.13017i	−0.153015	−	0.265030i
$536$	3.75525	+	6.50429i	0.162202	+	0.280942i
$537$	20.8027	−	36.0313i	0.897702	−	1.55486i
$538$	−19.4036			−0.836547
$539$	10.5005	+	24.4027i	0.452290	+	1.05110i
$540$	−9.37535			−0.403451
$541$	1.76759	−	3.06156i	0.0759948	−	0.131627i	−0.825524	−	0.564368i	$-0.809120\pi$
$541$	1.76759	−	3.06156i	0.0759948	−	0.131627i	0.901518	+	0.432741i	$0.142453\pi$
$542$	34.6864	+	60.0786i	1.48991	+	2.58060i
$543$	8.67949	+	15.0333i	0.372472	+	0.645141i
$544$	0.0724684	−	0.125519i	0.00310706	−	0.00538158i
$545$	6.75761			0.289464
$546$	1.77634	−	30.2664i	0.0760204	−	1.29528i
$547$	−13.1555			−0.562490			−0.281245	−	0.959636i	$-0.590747\pi$
$547$	−13.1555			−0.562490			−0.281245	+	0.959636i	$0.590747\pi$
$548$	0.650648	−	1.12696i	0.0277943	−	0.0481412i
$549$	−10.2739	−	17.7950i	−0.438481	−	0.759472i
$550$	−4.31584	−	7.47525i	−0.184028	−	0.318746i
$551$	−11.0917	+	19.2113i	−0.472520	+	0.818429i
$552$	7.11216			0.302714
$553$	−24.7099	−	16.2677i	−1.05077	−	0.691773i
$554$	21.3409			0.906690
$555$	6.23149	−	10.7933i	0.264512	−	0.458149i
$556$	10.0978	+	17.4899i	0.428243	+	0.741739i
$557$	8.65907	+	14.9979i	0.366896	+	0.635483i	0.989079	−	0.147389i	$-0.0470870\pi$
$557$	8.65907	+	14.9979i	0.366896	+	0.635483i	−0.622182	+	0.782873i	$0.713754\pi$
$558$	−1.43168	+	2.47973i	−0.0606076	+	0.104976i
$559$	−13.8277			−0.584851
$560$	0.658844	−	0.330517i	0.0278412	−	0.0139669i
$561$	0.245698			0.0103734
$562$	26.9427	−	46.6662i	1.13651	−	1.96849i
$563$	−16.1352	−	27.9470i	−0.680017	−	1.17782i	−0.974975	−	0.222314i	$-0.928639\pi$
$563$	−16.1352	−	27.9470i	−0.680017	−	1.17782i	0.294958	−	0.955510i	$-0.404694\pi$
$564$	−43.7222	−	75.7291i	−1.84104	−	3.18877i
$565$	8.08822	−	14.0092i	0.340274	−	0.589372i
$566$	51.0016			2.14376
$567$	−10.5162	+	5.27555i	−0.441637	+	0.221552i
$568$	16.7042			0.700892
$569$	21.7661	−	37.7001i	0.912484	−	1.58047i	0.101941	−	0.994790i	$-0.467495\pi$
$569$	21.7661	−	37.7001i	0.912484	−	1.58047i	0.810543	−	0.585679i	$-0.199172\pi$
$570$	8.66676	+	15.0113i	0.363010	+	0.628753i
$571$	−18.3636	−	31.8068i	−0.768495	−	1.33107i	−0.938379	−	0.345608i	$-0.887673\pi$
$571$	−18.3636	−	31.8068i	−0.768495	−	1.33107i	0.169885	−	0.985464i	$-0.445661\pi$
$572$	11.3779	−	19.7071i	0.475734	−	0.823996i
$573$	48.8198			2.03947
$574$	4.15479	+	2.73530i	0.173418	+	0.114169i
$575$	1.00000			0.0417029
$576$	26.7414	−	46.3175i	1.11422	−	1.92989i
$577$	−3.07944	−	5.33374i	−0.128199	−	0.222047i	0.794780	−	0.606898i	$-0.207586\pi$
$577$	−3.07944	−	5.33374i	−0.128199	−	0.222047i	−0.922979	+	0.384851i	$0.874253\pi$
$578$	19.3317	+	33.4835i	0.804093	+	1.39273i
$579$	−20.0654	+	34.7543i	−0.833891	+	1.44434i
$580$	−24.6230			−1.02242
$581$	0.747372	−	12.7342i	0.0310062	−	0.528303i
$582$	−45.1572			−1.87183
$583$	17.8168	−	30.8597i	0.737898	−	1.27808i
$584$	19.8427	+	34.3685i	0.821096	+	1.42218i
$585$	−3.88187	−	6.72359i	−0.160496	−	0.277986i
$586$	−15.9772	+	27.6733i	−0.660010	+	1.14317i
$587$	−20.8578			−0.860895			−0.430448	−	0.902616i	$-0.641644\pi$
$587$	−20.8578			−0.860895			−0.430448	+	0.902616i	$0.641644\pi$
$588$	35.4032	−	47.4665i	1.46000	−	1.95748i
$589$	0.875963			0.0360934
$590$	0.857057	−	1.48447i	0.0352845	−	0.0611145i
$591$	−10.5950	−	18.3511i	−0.435821	−	0.754863i
$592$	0.651159	+	1.12784i	0.0267625	+	0.0463540i
$593$	2.57106	−	4.45321i	0.105581	−	0.182872i	−0.808394	−	0.588641i	$-0.799663\pi$
$593$	2.57106	−	4.45321i	0.105581	−	0.182872i	0.913975	+	0.405770i	$0.132996\pi$
$594$	25.5052			1.04649
$595$	0.00376407	−	0.0641346i	0.000154312	−	0.00262926i
$596$	−6.95031			−0.284696
$597$	21.8288	−	37.8086i	0.893394	−	1.54740i
$598$	2.14905	+	3.72226i	0.0878812	+	0.152215i
$599$	23.1069	+	40.0224i	0.944123	+	1.63527i	0.757498	+	0.652838i	$0.226422\pi$
$599$	23.1069	+	40.0224i	0.944123	+	1.63527i	0.186625	+	0.982431i	$0.440245\pi$
$600$	−3.55608	+	6.15931i	−0.145176	+	0.251453i
$601$	−11.8299			−0.482553			−0.241276	−	0.970456i	$-0.577566\pi$
$601$	−11.8299			−0.482553			−0.241276	+	0.970456i	$0.577566\pi$
$602$	−36.7764	−	24.2117i	−1.49889	−	0.986794i
$603$	−11.5667			−0.471033
$604$	1.02903	−	1.78233i	0.0418706	−	0.0725220i
$605$	1.70157	+	2.94721i	0.0691788	+	0.119821i
$606$	44.2464	+	76.6371i	1.79739	+	3.11317i
$607$	−5.80340	+	10.0518i	−0.235553	+	0.407990i	−0.959433	−	0.281936i	$-0.909023\pi$
$607$	−5.80340	+	10.0518i	−0.235553	+	0.407990i	0.723880	+	0.689926i	$0.242357\pi$
$608$	−17.0619			−0.691950
$609$	48.9301	−	24.5463i	1.98275	−	0.994667i
$610$	−11.3756			−0.460583
$611$	9.76734	−	16.9175i	0.395144	−	0.684410i
$612$	−0.158261	−	0.274116i	−0.00639733	−	0.0110805i
$613$	15.3533	+	26.5927i	0.620114	+	1.07407i	0.989464	+	0.144779i	$0.0462470\pi$
$613$	15.3533	+	26.5927i	0.620114	+	1.07407i	−0.369350	+	0.929290i	$0.620420\pi$
$614$	−34.4969	+	59.7503i	−1.39218	+	2.41133i
$615$	2.20396			0.0888723
$616$	23.9416	−	12.0106i	0.964634	−	0.483920i
$617$	−46.6074			−1.87634			−0.938171	−	0.346173i	$-0.887481\pi$
$617$	−46.6074			−1.87634			−0.938171	+	0.346173i	$0.887481\pi$
$618$	−32.5484	+	56.3755i	−1.30929	+	2.26775i
$619$	13.5677	+	23.4999i	0.545331	+	0.944540i	0.998586	+	0.0531596i	$0.0169292\pi$
$619$	13.5677	+	23.4999i	0.545331	+	0.944540i	−0.453255	+	0.891381i	$0.649737\pi$
$620$	0.486151	+	0.842038i	0.0195243	+	0.0338171i
$621$	−1.47742	+	2.55897i	−0.0592868	+	0.102688i
$622$	59.5316			2.38700
$623$	33.8300	+	22.2719i	1.35537	+	0.892305i
$624$	1.40369			0.0561925
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−15.7288	−	27.2431i	−0.628650	−	1.08885i
$627$	−14.4617	−	25.0484i	−0.577544	−	1.00034i
$628$	17.1155	−	29.6450i	0.682985	−	1.18296i
$629$	0.113509			0.00452590
$630$	1.44842	−	24.6791i	0.0577064	−	0.983238i
$631$	−36.2764			−1.44414			−0.722071	−	0.691819i	$-0.756809\pi$
$631$	−36.2764			−1.44414			−0.722071	+	0.691819i	$0.756809\pi$
$632$	−14.9141	+	25.8320i	−0.593252	+	1.02754i
$633$	−21.8784	−	37.8944i	−0.869587	−	1.50617i
$634$	−12.3382	−	21.3704i	−0.490013	−	0.848727i
$635$	−11.1234	+	19.2663i	−0.441419	+	0.764561i
$636$	−79.4269			−3.14948
$637$	13.1376	+	1.54743i	0.520531	+	0.0613113i
$638$	66.9859			2.65200
$639$	−12.8628	+	22.2791i	−0.508846	+	0.881347i
$640$	−8.83554	−	15.3036i	−0.349255	−	0.604928i
$641$	14.6710	+	25.4109i	0.579469	+	1.00367i	0.995540	+	0.0943383i	$0.0300735\pi$
$641$	14.6710	+	25.4109i	0.579469	+	1.00367i	−0.416071	+	0.909332i	$0.636593\pi$
$642$	21.4615	−	37.1724i	0.847018	−	1.46708i
$643$	20.7358			0.817740			0.408870	−	0.912593i	$-0.365923\pi$
$643$	20.7358			0.817740			0.408870	+	0.912593i	$0.365923\pi$
$644$	−0.491837	+	8.38023i	−0.0193811	+	0.330227i
$645$	−19.5085			−0.768146
$646$	−0.0789340	+	0.136718i	−0.00310562	+	0.00537909i
$647$	−8.67253	−	15.0213i	−0.340952	−	0.590547i	0.643658	−	0.765314i	$-0.277416\pi$
$647$	−8.67253	−	15.0213i	−0.340952	−	0.590547i	−0.984610	+	0.174767i	$0.944083\pi$
$648$	5.93119	+	10.2731i	0.232999	+	0.403566i
$649$	−1.43012	+	2.47704i	−0.0561371	+	0.0972323i
$650$	−4.29810			−0.168585
$651$	−1.80548	−	1.18863i	−0.0707622	−	0.0465862i
$652$	14.6613			0.574179
$653$	2.82804	−	4.89832i	0.110670	−	0.191686i	−0.805371	−	0.592772i	$-0.798034\pi$
$653$	2.82804	−	4.89832i	0.110670	−	0.191686i	0.916041	+	0.401086i	$0.131367\pi$
$654$	20.4886	+	35.4873i	0.801167	+	1.38766i
$655$	−6.65789	−	11.5318i	−0.260145	−	0.450585i
$656$	−0.115151	+	0.199448i	−0.00449591	+	0.00778714i
$657$	−61.1183			−2.38445
$658$	55.5991	−	27.8919i	2.16748	−	1.08734i
$659$	35.4551			1.38113			0.690567	−	0.723268i	$-0.257361\pi$
$659$	35.4551			1.38113			0.690567	+	0.723268i	$0.257361\pi$
$660$	16.0522	−	27.8032i	0.624831	−	1.08224i
$661$	15.2277	+	26.3752i	0.592289	+	1.02588i	0.993923	+	0.110075i	$0.0351091\pi$
$661$	15.2277	+	26.3752i	0.592289	+	1.02588i	−0.401634	+	0.915800i	$0.631558\pi$
$662$	−34.5639	−	59.8665i	−1.34336	−	2.32678i
$663$	0.0611720	−	0.105953i	0.00237572	−	0.00411488i
$664$	−12.8614			−0.499119
$665$	−6.75994	+	3.39120i	−0.262139	+	0.131505i
$666$	43.6784			1.69250
$667$	−3.88024	+	6.72077i	−0.150243	+	0.260229i
$668$	24.5703	+	42.5570i	0.950653	+	1.64658i
$669$	23.8523	+	41.3133i	0.922182	+	1.59727i
$670$	−3.20174	+	5.54557i	−0.123694	+	0.214244i
$671$	18.9817			0.732781
$672$	35.1668	+	23.1520i	1.35659	+	0.893109i
$673$	−9.35173			−0.360483			−0.180241	−	0.983622i	$-0.557688\pi$
$673$	−9.35173			−0.360483			−0.180241	+	0.983622i	$0.557688\pi$
$674$	−25.5169	+	44.1966i	−0.982875	+	1.70239i
$675$	−1.47742	−	2.55897i	−0.0568659	−	0.0984947i
$676$	14.9581	+	25.9083i	0.575313	+	0.996471i
$677$	17.7940	−	30.8201i	0.683879	−	1.18451i	−0.289909	−	0.957054i	$-0.593625\pi$
$677$	17.7940	−	30.8201i	0.683879	−	1.18451i	0.973788	−	0.227459i	$-0.0730417\pi$
$678$	98.0916			3.76719
$679$	1.15437	−	19.6690i	0.0443008	−	0.754825i
$680$	−0.0647753			−0.00248402
$681$	−35.3624	+	61.2495i	−1.35509	+	2.34709i
$682$	−1.32255	−	2.29073i	−0.0506431	−	0.0877165i
$683$	−8.27017	−	14.3244i	−0.316449	−	0.548106i	0.663295	−	0.748358i	$-0.269157\pi$
$683$	−8.27017	−	14.3244i	−0.316449	−	0.548106i	−0.979745	+	0.200252i	$0.935824\pi$
$684$	−18.6304	+	32.2688i	−0.712351	+	1.23383i
$685$	0.410131			0.0156703
$686$	32.2314	+	27.1188i	1.23060	+	1.03540i
$687$	21.1295			0.806141
$688$	1.01927	−	1.76542i	0.0388592	−	0.0673062i
$689$	−8.87180	−	15.3664i	−0.337989	−	0.585414i
$690$	3.03193	+	5.25145i	0.115423	+	0.199919i
$691$	−14.8902	+	25.7906i	−0.566450	+	0.981120i	0.430463	+	0.902608i	$0.358350\pi$
$691$	−14.8902	+	25.7906i	−0.566450	+	0.981120i	−0.996913	+	0.0785120i	$0.974983\pi$
$692$	12.3991			0.471342
$693$	−2.41689	+	41.1805i	−0.0918101	+	1.56432i
$694$	−81.2562			−3.08444
$695$	−3.18254	+	5.51232i	−0.120721	+	0.209094i
$696$	−27.5969	−	47.7992i	−1.04606	−	1.81182i
$697$	0.0100365	+	0.0173837i	0.000380159	+	0.000658455i
$698$	11.3481	−	19.6555i	0.429531	−	0.743970i
$699$	−43.6590			−1.65133
$700$	−7.01157	−	4.61606i	−0.265012	−	0.174471i
$701$	16.1252			0.609040			0.304520	−	0.952506i	$-0.401504\pi$
$701$	16.1252			0.609040			0.304520	+	0.952506i	$0.401504\pi$
$702$	6.35010	−	10.9987i	0.239669	−	0.415119i
$703$	−6.68110	−	11.5720i	−0.251982	−	0.436446i
$704$	24.7031	+	42.7871i	0.931035	+	1.61260i
$705$	13.7800	−	23.8676i	0.518984	−	0.898907i
$706$	26.1113			0.982711
$707$	−34.5116	+	17.3131i	−1.29794	+	0.651127i
$708$	6.37543			0.239603
$709$	8.61525	−	14.9221i	0.323553	−	0.560409i	−0.657666	−	0.753310i	$-0.728456\pi$
$709$	8.61525	−	14.9221i	0.323553	−	0.560409i	0.981218	+	0.192900i	$0.0617894\pi$
$710$	7.12102	+	12.3340i	0.267247	+	0.462886i
$711$	−22.9688	−	39.7832i	−0.861399	−	1.49199i
$712$	20.4187	−	35.3663i	0.765224	−	1.32541i
$713$	0.306442			0.0114763
$714$	0.348212	−	0.174685i	0.0130315	−	0.00653741i
$715$	7.17198			0.268217
$716$	24.7566	−	42.8796i	0.925196	−	1.60249i
$717$	−2.20823	−	3.82476i	−0.0824677	−	0.142838i
$718$	−20.1088	−	34.8295i	−0.750455	−	1.29983i
$719$	−19.9391	+	34.5355i	−0.743602	+	1.28796i	0.207243	+	0.978290i	$0.433551\pi$
$719$	−19.9391	+	34.5355i	−0.743602	+	1.28796i	−0.950845	+	0.309667i	$0.899782\pi$
$720$	1.14456			0.0426552
$721$	−23.7232	−	15.6181i	−0.883498	−	0.581649i
$722$	−24.6294			−0.916612
$723$	9.05551	−	15.6846i	0.336778	−	0.583316i
$724$	10.3292	+	17.8906i	0.383880	+	0.664900i
$725$	−3.88024	−	6.72077i	−0.144108	−	0.249603i
$726$	−10.3181	+	17.8715i	−0.382940	+	0.663272i
$727$	48.3332			1.79258			0.896290	−	0.443468i	$-0.146252\pi$
$727$	48.3332			1.79258			0.896290	+	0.443468i	$0.146252\pi$
$728$	0.781443	−	13.3147i	0.0289622	−	0.493476i
$729$	−41.9029			−1.55196
$730$	−16.9179	+	29.3027i	−0.626161	+	1.08454i
$731$	−0.0888385	−	0.153873i	−0.00328581	−	0.00569119i
$732$	−21.1550	−	36.6415i	−0.781911	−	1.35431i
$733$	−3.32076	+	5.75172i	−0.122655	+	0.212445i	−0.920814	−	0.390002i	$-0.872474\pi$
$733$	−3.32076	+	5.75172i	−0.122655	+	0.212445i	0.798159	+	0.602447i	$0.205808\pi$
$734$	42.5752			1.57148
$735$	18.5348	+	2.18314i	0.683667	+	0.0805265i
$736$	−5.96882			−0.220014
$737$	5.34255	−	9.25357i	0.196795	−	0.340859i
$738$	3.86205	+	6.68927i	0.142164	+	0.246236i
$739$	7.85739	+	13.6094i	0.289039	+	0.500630i	0.973581	−	0.228344i	$-0.0733311\pi$
$739$	7.85739	+	13.6094i	0.289039	+	0.500630i	−0.684542	+	0.728974i	$0.739998\pi$
$740$	7.41589	−	12.8447i	0.272613	−	0.472180i
$741$	−14.4023			−0.529080
$742$	3.31029	−	56.4027i	0.121524	−	2.07061i
$743$	−31.6283			−1.16033			−0.580164	−	0.814499i	$-0.697012\pi$
$743$	−31.6283			−1.16033			−0.580164	+	0.814499i	$0.697012\pi$
$744$	−1.08973	+	1.88747i	−0.0399515	+	0.0691980i
$745$	−1.09527	−	1.89706i	−0.0401276	−	0.0695030i
$746$	−16.7372	−	28.9898i	−0.612794	−	1.06139i
$747$	9.90375	−	17.1538i	0.362359	−	0.627625i
$748$	0.292397			0.0106911
$749$	15.6424	+	10.2982i	0.571561	+	0.376286i
$750$	−6.06385			−0.221421
$751$	6.08966	−	10.5476i	0.222215	−	0.384887i	−0.733265	−	0.679942i	$-0.762005\pi$
$751$	6.08966	−	10.5476i	0.222215	−	0.384887i	0.955480	+	0.295055i	$0.0953381\pi$
$752$	1.43994	+	2.49405i	0.0525091	+	0.0909485i
$753$	22.3673	+	38.7414i	0.815112	+	1.41181i
$754$	16.6776	−	28.8865i	0.607364	−	1.05199i
$755$	0.648640			0.0236064
$756$	22.1714	−	11.1225i	0.806365	−	0.404522i
$757$	18.8755			0.686043			0.343022	−	0.939328i	$-0.388550\pi$
$757$	18.8755			0.686043			0.343022	+	0.939328i	$0.388550\pi$
$758$	14.1308	−	24.4753i	0.513254	−	0.888982i
$759$	−5.05919	−	8.76278i	−0.183637	−	0.318069i
$760$	3.81265	+	6.60371i	0.138299	+	0.239542i
$761$	−18.2534	+	31.6158i	−0.661685	+	1.14607i	0.318487	+	0.947927i	$0.396825\pi$
$761$	−18.2534	+	31.6158i	−0.661685	+	1.14607i	−0.980173	+	0.198145i	$0.936508\pi$
$762$	−134.901			−4.88696
$763$	−15.9808	+	8.01695i	−0.578544	+	0.290233i
$764$	58.0987			2.10194
$765$	0.0498793	−	0.0863936i	0.00180339	−	0.00312357i
$766$	−35.6268	−	61.7074i	−1.28725	−	2.22958i
$767$	0.712121	+	1.23343i	0.0257132	+	0.0445366i
$768$	18.8689	−	32.6819i	0.680872	−	1.17930i
$769$	22.9989			0.829362			0.414681	−	0.909967i	$-0.363893\pi$
$769$	22.9989			0.829362			0.414681	+	0.909967i	$0.363893\pi$
$770$	19.0747	+	12.5578i	0.687403	+	0.452551i
$771$	−44.1392			−1.58963
$772$	−23.8792	+	41.3600i	−0.859431	+	1.48858i
$773$	1.57427	+	2.72672i	0.0566227	+	0.0980733i	0.892947	−	0.450161i	$-0.148633\pi$
$773$	1.57427	+	2.72672i	0.0566227	+	0.0980733i	−0.836325	+	0.548234i	$0.815300\pi$
$774$	−34.1852	−	59.2105i	−1.22876	−	2.12828i
$775$	−0.153221	+	0.265386i	−0.00550385	+	0.00953296i
$776$	−19.8654			−0.713128
$777$	−1.93192	+	32.9173i	−0.0693074	+	1.18090i
$778$	−54.9855			−1.97132
$779$	1.18149	−	2.04640i	0.0423312	−	0.0733198i
$780$	−7.99312	−	13.8445i	−0.286199	−	0.495712i
$781$	−11.8824	−	20.5810i	−0.425186	−	0.736444i
$782$	−0.0276138	+	0.0478285i	−0.000987468	+	0.00171034i
$783$	22.9310			0.819486
$784$	−1.16596	+	1.56325i	−0.0416415	+	0.0558304i
$785$	10.7887			0.385064
$786$	40.3724	−	69.9271i	1.44004	−	2.49422i
$787$	14.0008	+	24.2500i	0.499073	+	0.864421i	0.999999	−	0.00106952i	$-0.000340438\pi$
$787$	14.0008	+	24.2500i	0.499073	+	0.864421i	−0.500926	+	0.865490i	$0.667007\pi$
$788$	−12.6088	−	21.8390i	−0.449169	−	0.777983i
$789$	−33.5298	+	58.0752i	−1.19369	+	2.06753i
$790$	−25.4316			−0.904817
$791$	−2.50756	+	42.7253i	−0.0891585	+	1.51914i
$792$	41.5919			1.47790
$793$	4.72593	−	8.18555i	0.167823	−	0.290677i
$794$	−20.3400	−	35.2300i	−0.721841	−	1.25026i
$795$	−12.5165	−	21.6793i	−0.443916	−	0.768885i
$796$	25.9777	−	44.9947i	0.920756	−	1.59480i
$797$	6.89806			0.244342			0.122171	−	0.992509i	$-0.461014\pi$
$797$	6.89806			0.244342			0.122171	+	0.992509i	$0.461014\pi$
$798$	−38.3044	−	25.2176i	−1.35596	−	0.892694i
$799$	0.251007			0.00888000
$800$	2.98441	−	5.16915i	0.105515	−	0.182757i
$801$	31.4463	+	54.4667i	1.11110	+	1.92448i
$802$	−32.6613	−	56.5710i	−1.15331	−	1.99759i
$803$	28.2299	−	48.8957i	0.996212	−	1.72549i
$804$	−23.8169			−0.839958
$805$	−2.36486	+	1.18636i	−0.0833503	+	0.0418136i
$806$	−1.31712			−0.0463934
$807$	11.3728	−	19.6983i	0.400342	−	0.693412i
$808$	19.4648	+	33.7139i	0.684768	+	1.18605i
$809$	−24.4058	−	42.2720i	−0.858061	−	1.48621i	−0.873776	−	0.486329i	$-0.838336\pi$
$809$	−24.4058	−	42.2720i	−0.858061	−	1.48621i	0.0157152	−	0.999877i	$-0.494998\pi$
$810$	−5.05695	+	8.75889i	−0.177683	+	0.307756i
$811$	39.4329			1.38468			0.692338	−	0.721573i	$-0.256581\pi$
$811$	39.4329			1.38468			0.692338	+	0.721573i	$0.256581\pi$
$812$	58.2300	−	29.2117i	2.04347	−	1.02513i
$813$	−81.3215			−2.85207
$814$	−20.1746	+	34.9434i	−0.707119	+	1.22477i
$815$	2.31040	+	4.00173i	0.0809299	+	0.140175i
$816$	0.00901821	+	0.0156200i	0.000315700	+	0.000546809i
$817$	−10.4580	+	18.1138i	−0.365879	+	0.633722i
$818$	−49.5751			−1.73335
$819$	17.1567	+	11.2951i	0.599502	+	0.394681i
$820$	2.62286			0.0915942
$821$	−1.76704	+	3.06061i	−0.0616702	+	0.106816i	−0.895212	−	0.445640i	$-0.852976\pi$
$821$	−1.76704	+	3.06061i	−0.0616702	+	0.106816i	0.833542	+	0.552456i	$0.186309\pi$
$822$	1.24349	+	2.15378i	0.0433716	+	0.0751218i
$823$	−12.6125	−	21.8455i	−0.439645	−	0.761488i	0.558017	−	0.829830i	$-0.311562\pi$
$823$	−12.6125	−	21.8455i	−0.439645	−	0.761488i	−0.997662	+	0.0683420i	$0.978229\pi$
$824$	−14.3186	+	24.8005i	−0.498812	+	0.863968i
$825$	10.1184			0.352277
$826$	−0.265710	+	4.52733i	−0.00924522	+	0.157526i
$827$	−7.47842			−0.260050			−0.130025	−	0.991511i	$-0.541506\pi$
$827$	−7.47842			−0.260050			−0.130025	+	0.991511i	$0.541506\pi$
$828$	−6.51755	+	11.2887i	−0.226500	+	0.392310i
$829$	−2.41416	−	4.18144i	−0.0838471	−	0.145228i	0.821052	−	0.570853i	$-0.193387\pi$
$829$	−2.41416	−	4.18144i	−0.0838471	−	0.145228i	−0.904899	+	0.425626i	$0.860054\pi$
$830$	−5.48284	−	9.49655i	−0.190312	−	0.329630i
$831$	−12.5083	+	21.6651i	−0.433910	+	0.751554i
$832$	24.6016			0.852908
$833$	0.0671851	+	0.156135i	0.00232783	+	0.00540975i
$834$	−38.5969			−1.33650
$835$	−7.74385	+	13.4127i	−0.267987	+	0.464167i
$836$	−17.2104	−	29.8092i	−0.595233	−	1.03097i
$837$	−0.452743	−	0.784174i	−0.0156491	−	0.0271050i
$838$	−5.24568	+	9.08578i	−0.181209	+	0.313863i
$839$	20.5636			0.709934			0.354967	−	0.934879i	$-0.384492\pi$
$839$	20.5636			0.709934			0.354967	+	0.934879i	$0.384492\pi$
$840$	1.10248	−	18.7847i	0.0380391	−	0.648133i
$841$	31.2250			1.07672
$842$	−1.89144	+	3.27608i	−0.0651835	+	0.112901i
$843$	31.5833	+	54.7039i	1.08779	+	1.88410i
$844$	−26.0367	−	45.0969i	−0.896220	−	1.55230i
$845$	−4.71437	+	8.16554i	−0.162179	+	0.280903i
$846$	96.5879			3.32076
$847$	−7.52043	−	4.95107i	−0.258405	−	0.170121i
$848$	2.61583			0.0898279
$849$	−29.8930	+	51.7762i	−1.02593	+	1.77696i
$850$	−0.0276138	−	0.0478285i	−0.000947146	−	0.00164050i
$851$	−2.33727	−	4.04828i	−0.0801207	−	0.138773i
$852$	−26.4857	+	45.8746i	−0.907386	+	1.57164i
$853$	−9.37477			−0.320986			−0.160493	−	0.987037i	$-0.551308\pi$
$853$	−9.37477			−0.320986			−0.160493	+	0.987037i	$0.551308\pi$
$854$	26.9016	−	13.4955i	0.920554	−	0.461806i
$855$	−11.7435			−0.401620
$856$	9.44128	−	16.3528i	0.322696	−	0.558927i
$857$	−14.5068	−	25.1265i	−0.495543	−	0.858305i	0.504444	−	0.863444i	$-0.331698\pi$
$857$	−14.5068	−	25.1265i	−0.495543	−	0.858305i	−0.999987	+	0.00513903i	$0.998364\pi$
$858$	21.7449	+	37.6633i	0.742359	+	1.28580i
$859$	28.0314	−	48.5518i	0.956419	−	1.65657i	0.225332	−	0.974282i	$-0.427653\pi$
$859$	28.0314	−	48.5518i	0.956419	−	1.65657i	0.731087	−	0.682285i	$-0.239013\pi$
$860$	−23.2164			−0.791672
$861$	−5.21206	+	2.61469i	−0.177626	+	0.0891083i
$862$	−38.1537			−1.29952
$863$	−5.00912	+	8.67605i	−0.170512	+	0.295336i	−0.938599	−	0.345010i	$-0.887876\pi$
$863$	−5.00912	+	8.67605i	−0.170512	+	0.295336i	0.768087	+	0.640346i	$0.221209\pi$
$864$	8.81846	+	15.2740i	0.300010	+	0.519633i
$865$	1.95391	+	3.38428i	0.0664350	+	0.115069i
$866$	19.9546	−	34.5623i	0.678084	−	1.17448i
$867$	−45.3228			−1.53924
$868$	−2.14864	−	1.41455i	−0.0729295	−	0.0480130i
$869$	42.4363			1.43955
$870$	23.5292	−	40.7537i	0.797714	−	1.38168i
$871$	−2.66030	−	4.60777i	−0.0901407	−	0.156128i
$872$	9.01328	+	15.6115i	0.305228	+	0.528670i
$873$	15.2971	−	26.4954i	0.517729	−	0.896733i
$874$	6.50136			0.219912
$875$	0.155013	−	2.64121i	0.00524039	−	0.0892891i
$876$	−125.848			−4.25202
$877$	−9.21976	+	15.9691i	−0.311329	+	0.539238i	−0.978650	−	0.205532i	$-0.934108\pi$
$877$	−9.21976	+	15.9691i	−0.311329	+	0.539238i	0.667321	+	0.744770i	$0.267441\pi$
$878$	−34.0811	−	59.0301i	−1.15018	−	1.99217i
$879$	−18.7291	−	32.4397i	−0.631715	−	1.09416i
$880$	−0.528660	+	0.915666i	−0.0178211	+	0.0308671i
$881$	−20.8971			−0.704040			−0.352020	−	0.935992i	$-0.614505\pi$
$881$	−20.8971			−0.704040			−0.352020	+	0.935992i	$0.614505\pi$
$882$	25.8529	+	60.0809i	0.870513	+	2.02303i
$883$	19.5470			0.657808			0.328904	−	0.944363i	$-0.393321\pi$
$883$	19.5470			0.657808			0.328904	+	0.944363i	$0.393321\pi$
$884$	0.0727987	−	0.126091i	0.00244849	−	0.00424090i
$885$	1.00468	+	1.74015i	0.0337718	+	0.0584945i
$886$	20.3061	+	35.1712i	0.682197	+	1.18160i
$887$	0.882838	−	1.52912i	0.0296428	−	0.0513428i	−0.850823	−	0.525452i	$-0.823896\pi$
$887$	0.882838	−	1.52912i	0.0296428	−	0.0513428i	0.880466	+	0.474109i	$0.157230\pi$
$888$	33.2462			1.11567
$889$	3.44855	−	58.7585i	0.115660	−	1.97070i
$890$	34.8181			1.16711
$891$	8.43822	−	14.6154i	0.282691	−	0.489635i
$892$	28.3858	+	49.1656i	0.950426	+	1.64619i
$893$	−14.7742	−	25.5897i	−0.494400	−	0.856326i
$894$	6.64155	−	11.5035i	0.222127	−	0.384735i
$895$	15.6051			0.521621
$896$	39.0503	+	25.7087i	1.30458	+	0.858868i
$897$	−5.03840			−0.168227
$898$	−14.1938	+	24.5844i	−0.473653	+	0.820391i
$899$	−1.18907	−	2.05952i	−0.0396576	−	0.0686889i
$900$	−6.51755	−	11.2887i	−0.217252	−	0.376291i
$901$	0.113997	−	0.197448i	0.00379778	−	0.00657794i
$902$	−7.13537			−0.237582
$903$	46.1348	−	23.1440i	1.53527	−	0.770186i
$904$	43.1522			1.43522
$905$	−3.25545	+	5.63861i	−0.108215	+	0.187434i
$906$	1.96663	+	3.40630i	0.0653369	+	0.113167i
$907$	20.9442	+	36.2765i	0.695441	+	1.20454i	0.970032	+	0.242979i	$0.0781245\pi$
$907$	20.9442	+	36.2765i	0.695441	+	1.20454i	−0.274590	+	0.961561i	$0.588542\pi$
$908$	−42.0836	+	72.8909i	−1.39659	+	2.41897i
$909$	−59.9543			−1.98856
$910$	10.1644	−	5.09908i	0.336946	−	0.169033i
$911$	59.8950			1.98441			0.992206	−	0.124611i	$-0.0397684\pi$
$911$	59.8950			1.98441			0.992206	+	0.124611i	$0.0397684\pi$
$912$	1.06162	−	1.83878i	0.0351537	−	0.0608879i
$913$	9.14888	+	15.8463i	0.302784	+	0.524437i
$914$	−2.93531	−	5.08411i	−0.0970914	−	0.168167i
$915$	6.66744	−	11.5483i	0.220419	−	0.381777i
$916$	25.1455			0.830831
$917$	29.4258	+	19.3724i	0.971725	+	0.639734i
$918$	0.163189			0.00538603
$919$	−6.91620	+	11.9792i	−0.228144	+	0.395158i	−0.957258	−	0.289235i	$-0.906599\pi$
$919$	−6.91620	+	11.9792i	−0.228144	+	0.395158i	0.729114	+	0.684392i	$0.239932\pi$
$920$	1.33380	+	2.31020i	0.0439739	+	0.0761651i
$921$	−40.4386	−	70.0416i	−1.33250	−	2.30795i
$922$	34.1961	−	59.2293i	1.12619	−	1.95061i
$923$	−11.8336			−0.389507
$924$	−4.97660	+	84.7944i	−0.163718	+	2.78953i
$925$	4.67455			0.153698
$926$	−21.8981	+	37.9287i	−0.719617	+	1.24641i
$927$	−22.0517	−	38.1946i	−0.724272	−	1.25448i
$928$	23.1605	+	40.1151i	0.760279	+	1.31684i
$929$	−9.44140	+	16.3530i	−0.309762	+	0.536524i	−0.978310	−	0.207145i	$-0.933583\pi$
$929$	−9.44140	+	16.3530i	−0.309762	+	0.536524i	0.668548	+	0.743669i	$0.266916\pi$
$930$	−1.85822			−0.0609333
$931$	11.9631	−	16.0394i	0.392076	−	0.525671i
$932$	−51.9570			−1.70191
$933$	−34.8926	+	60.4358i	−1.14233	+	1.97858i
$934$	−2.38188	−	4.12554i	−0.0779376	−	0.134992i
$935$	0.0460775	+	0.0798086i	0.00150690	+	0.00261002i
$936$	10.3552	−	17.9358i	0.338472	−	0.586250i
$937$	−46.9054			−1.53233			−0.766166	−	0.642643i	$-0.777838\pi$
$937$	−46.9054			−1.53233			−0.766166	+	0.642643i	$0.777838\pi$
$938$	0.992622	−	16.9129i	0.0324102	−	0.552226i
$939$	36.8759			1.20340
$940$	16.3991	−	28.4040i	0.534879	−	0.926438i
$941$	−15.2692	−	26.4471i	−0.497763	−	0.862150i	0.502234	−	0.864732i	$-0.332512\pi$
$941$	−15.2692	−	26.4471i	−0.497763	−	0.862150i	−0.999997	+	0.00258141i	$0.999178\pi$
$942$	32.7104	+	56.6561i	1.06576	+	1.84595i
$943$	0.413325	−	0.715900i	0.0134597	−	0.0233129i
$944$	−0.209967			−0.00683384
$945$	6.52974	+	4.29884i	0.212412	+	0.139841i
$946$	63.1591			2.05348
$947$	19.8676	−	34.4116i	0.645609	−	1.11823i	−0.338552	−	0.940948i	$-0.609937\pi$
$947$	19.8676	−	34.4116i	0.645609	−	1.11823i	0.984161	−	0.177280i	$-0.0567297\pi$
$948$	−47.2949	−	81.9172i	−1.53607	−	2.66055i
$949$	−14.0570	−	24.3474i	−0.456308	−	0.790349i
$950$	−3.25068	+	5.63034i	−0.105466	+	0.182672i
$951$	28.9267			0.938012
$952$	0.153184	−	0.0768467i	0.00496473	−	0.00249062i
$953$	12.4988			0.404875			0.202437	−	0.979295i	$-0.435114\pi$
$953$	12.4988			0.404875			0.202437	+	0.979295i	$0.435114\pi$
$954$	43.8660	−	75.9782i	1.42022	−	2.45989i
$955$	9.15552	+	15.8578i	0.296266	+	0.513147i
$956$	−2.62793	−	4.55172i	−0.0849935	−	0.147213i
$957$	−39.2617	+	68.0033i	−1.26915	+	2.19823i
$958$	−7.78611			−0.251558
$959$	−0.969902	+	0.486562i	−0.0313198	+	0.0157119i
$960$	34.7085			1.12021
$961$	15.4530	−	26.7655i	0.498485	−	0.863402i
$962$	10.0458	+	17.3999i	0.323891	+	0.560995i
$963$	14.5403	+	25.1845i	0.468553	+	0.811558i
$964$	10.7766	−	18.6657i	0.347092	−	0.601182i
$965$	−15.0521			−0.484543
$966$	−13.4002	−	8.82198i	−0.431144	−	0.283843i
$967$	−56.1061			−1.80425			−0.902126	−	0.431474i	$-0.857994\pi$
$967$	−56.1061			−1.80425			−0.902126	+	0.431474i	$0.857994\pi$
$968$	−4.53911	+	7.86196i	−0.145892	+	0.252693i
$969$	−0.0925296	−	0.160266i	−0.00297248	−	0.00514848i
$970$	−8.46867	−	14.6682i	−0.271912	−	0.470966i
$971$	21.8329	−	37.8157i	0.700652	−	1.21356i	−0.267586	−	0.963534i	$-0.586226\pi$
$971$	21.8329	−	37.8157i	0.700652	−	1.21356i	0.968238	−	0.250031i	$-0.0804407\pi$
$972$	−65.7434			−2.10872
$973$	0.986670	−	16.8115i	0.0316312	−	0.538952i
$974$	5.39774			0.172955
$975$	2.51920	−	4.36338i	0.0806790	−	0.139740i
$976$	0.696714	+	1.20674i	0.0223013	+	0.0386269i
$977$	29.3258	+	50.7937i	0.938214	+	1.62503i	0.768800	+	0.639490i	$0.220854\pi$
$977$	29.3258	+	50.7937i	0.938214	+	1.62503i	0.169414	+	0.985545i	$0.445812\pi$
$978$	−14.0099	+	24.2659i	−0.447988	+	0.775939i
$979$	−58.0989			−1.85685
$980$	22.0577	+	2.59809i	0.704606	+	0.0829928i
$981$	−27.7622			−0.886379
$982$	15.5483	−	26.9305i	0.496168	−	0.859388i
$983$	1.62808	+	2.81992i	0.0519277	+	0.0899414i	0.890821	−	0.454355i	$-0.150130\pi$
$983$	1.62808	+	2.81992i	0.0519277	+	0.0899414i	−0.838893	+	0.544296i	$0.816797\pi$
$984$	2.93963	+	5.09160i	0.0937121	+	0.162314i
$985$	3.97392	−	6.88303i	0.126620	−	0.219312i
$986$	0.428593			0.0136492
$987$	−4.27215	+	72.7915i	−0.135984	+	2.31698i
$988$	−17.1396			−0.545285
$989$	−3.65857	+	6.33682i	−0.116336	+	0.201499i
$990$	17.7307	+	30.7104i	0.563518	+	0.976042i
$991$	9.05618	+	15.6858i	0.287679	+	0.498275i	0.973255	−	0.229726i	$-0.0737831\pi$
$991$	9.05618	+	15.6858i	0.287679	+	0.498275i	−0.685576	+	0.728001i	$0.740450\pi$
$992$	0.914548	−	1.58404i	0.0290369	−	0.0502934i
$993$	81.0344			2.57155
$994$	−31.4727	−	20.7200i	−0.998254	−	0.657199i
$995$	16.3749			0.519118
$996$	20.3927	−	35.3212i	0.646168	−	1.11920i
$997$	4.94210	+	8.55996i	0.156518	+	0.271097i	0.933611	−	0.358289i	$-0.116640\pi$
$997$	4.94210	+	8.55996i	0.156518	+	0.271097i	−0.777093	+	0.629386i	$0.783306\pi$
$998$	31.7401	+	54.9754i	1.00471	+	1.74022i
$999$	−6.90627	+	11.9620i	−0.218505	+	0.378461i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.i.e.576.4	yes	30
7.2	even	3		5635.2.a.bi.1.12		15
7.4	even	3	inner	805.2.i.e.116.4	✓	30
7.5	odd	6		5635.2.a.bj.1.12		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.i.e.116.4	✓	30	7.4	even	3	inner
805.2.i.e.576.4	yes	30	1.1	even	1	trivial
5635.2.a.bi.1.12		15	7.2	even	3
5635.2.a.bj.1.12		15	7.5	odd	6

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:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13720 + 1.96969i) q^{2} +(-1.33307 - 2.30894i) q^{3} +(-1.58644 - 2.74779i) q^{4} +(0.500000 - 0.866025i) q^{5} +6.06385 q^{6} +(-0.155013 + 2.64121i) q^{7} +2.66759 q^{8} +(-2.05414 + 3.55788i) q^{9} +O(q^{10})\)	\(q+(-1.13720 + 1.96969i) q^{2} +(-1.33307 - 2.30894i) q^{3} +(-1.58644 - 2.74779i) q^{4} +(0.500000 - 0.866025i) q^{5} +6.06385 q^{6} +(-0.155013 + 2.64121i) q^{7} +2.66759 q^{8} +(-2.05414 + 3.55788i) q^{9} +(1.13720 + 1.96969i) q^{10} +(-1.89757 - 3.28669i) q^{11} +(-4.22966 + 7.32599i) q^{12} -1.88978 q^{13} +(-5.02606 - 3.30890i) q^{14} -2.66614 q^{15} +(0.139299 - 0.241273i) q^{16} +(-0.0121412 - 0.0210291i) q^{17} +(-4.67193 - 8.09203i) q^{18} +(-1.42925 + 2.47553i) q^{19} -3.17288 q^{20} +(6.30504 - 3.16299i) q^{21} +8.63167 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-3.55608 - 6.15931i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.14905 - 3.72226i) q^{26} +2.95484 q^{27} +(7.50341 - 3.76417i) q^{28} +7.76047 q^{29} +(3.03193 - 5.25145i) q^{30} +(-0.153221 - 0.265386i) q^{31} +(2.98441 + 5.16915i) q^{32} +(-5.05919 + 8.76278i) q^{33} +0.0552276 q^{34} +(2.20985 + 1.45485i) q^{35} +13.0351 q^{36} +(-2.33727 + 4.04828i) q^{37} +(-3.25068 - 5.63034i) q^{38} +(2.51920 + 4.36338i) q^{39} +(1.33380 - 2.31020i) q^{40} -0.826650 q^{41} +(-0.939975 + 16.0159i) q^{42} +7.31713 q^{43} +(-6.02077 + 10.4283i) q^{44} +(2.05414 + 3.55788i) q^{45} +(-1.13720 - 1.96969i) q^{46} +(-5.16852 + 8.95214i) q^{47} -0.742780 q^{48} +(-6.95194 - 0.818842i) q^{49} +2.27440 q^{50} +(-0.0323700 + 0.0560665i) q^{51} +(2.99801 + 5.19271i) q^{52} +(4.69463 + 8.13134i) q^{53} +(-3.36024 + 5.82010i) q^{54} -3.79515 q^{55} +(-0.413511 + 7.04566i) q^{56} +7.62115 q^{57} +(-8.82520 + 15.2857i) q^{58} +(-0.376828 - 0.652686i) q^{59} +(4.22966 + 7.32599i) q^{60} +(-2.50079 + 4.33149i) q^{61} +0.696970 q^{62} +(-9.07868 - 5.97693i) q^{63} -13.0183 q^{64} +(-0.944888 + 1.63659i) q^{65} +(-11.5066 - 19.9300i) q^{66} +(1.40773 + 2.43826i) q^{67} +(-0.0385224 + 0.0667228i) q^{68} +2.66614 q^{69} +(-5.37862 + 2.69825i) q^{70} +6.26190 q^{71} +(-5.47961 + 9.49097i) q^{72} +(7.43843 + 12.8837i) q^{73} +(-5.31589 - 9.20739i) q^{74} +(-1.33307 + 2.30894i) q^{75} +9.06967 q^{76} +(8.97499 - 4.50240i) q^{77} -11.4593 q^{78} +(-5.59086 + 9.68365i) q^{79} +(-0.139299 - 0.241273i) q^{80} +(2.22342 + 3.85108i) q^{81} +(0.940065 - 1.62824i) q^{82} -4.82136 q^{83} +(-18.6938 - 12.3070i) q^{84} -0.0242823 q^{85} +(-8.32103 + 14.4124i) q^{86} +(-10.3452 - 17.9185i) q^{87} +(-5.06195 - 8.76756i) q^{88} +(7.65437 - 13.2578i) q^{89} -9.34387 q^{90} +(0.292940 - 4.99129i) q^{91} +3.17288 q^{92} +(-0.408508 + 0.707556i) q^{93} +(-11.7553 - 20.3607i) q^{94} +(1.42925 + 2.47553i) q^{95} +(7.95685 - 13.7817i) q^{96} -7.44696 q^{97} +(9.51860 - 12.7620i) q^{98} +15.5916 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 5 q^{2} - 19 q^{4} + 15 q^{5} - 16 q^{6} - 3 q^{7} + 30 q^{8} - 27 q^{9}+O(q^{10}) \) 30 * q - 5 * q^2 - 19 * q^4 + 15 * q^5 - 16 * q^6 - 3 * q^7 + 30 * q^8 - 27 * q^9	\( 30 q - 5 q^{2} - 19 q^{4} + 15 q^{5} - 16 q^{6} - 3 q^{7} + 30 q^{8} - 27 q^{9} + 5 q^{10} - 11 q^{11} + 6 q^{13} - 5 q^{14} - 43 q^{16} + q^{17} + 13 q^{18} + 17 q^{19} - 38 q^{20} - 3 q^{21} + 50 q^{22} - 15 q^{23} + 4 q^{24} - 15 q^{25} + 14 q^{26} - 6 q^{27} - q^{28} + 62 q^{29} - 8 q^{30} + 23 q^{31} - 30 q^{32} - 28 q^{33} - 20 q^{34} + 6 q^{35} + 30 q^{36} - 20 q^{37} - 12 q^{38} - 4 q^{39} + 15 q^{40} - 16 q^{42} + 8 q^{43} - 33 q^{44} + 27 q^{45} - 5 q^{46} + q^{47} + 52 q^{48} + 33 q^{49} + 10 q^{50} - 27 q^{51} - 11 q^{52} - 36 q^{53} - 12 q^{54} - 22 q^{55} + 18 q^{56} + 56 q^{57} - 14 q^{58} + 10 q^{59} + 10 q^{61} + 28 q^{62} - 51 q^{63} + 18 q^{64} + 3 q^{65} + 17 q^{66} - 13 q^{67} - 3 q^{68} - q^{70} - 14 q^{71} - 35 q^{72} - 9 q^{73} - 62 q^{74} + 10 q^{76} - 26 q^{77} - 34 q^{78} - 4 q^{79} + 43 q^{80} - 43 q^{81} - 32 q^{82} + 58 q^{83} - 78 q^{84} + 2 q^{85} - 100 q^{86} + 22 q^{87} - 24 q^{88} + 6 q^{89} + 26 q^{90} - 6 q^{91} + 38 q^{92} - q^{93} + 62 q^{94} - 17 q^{95} + 63 q^{96} + 72 q^{97} + q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q - 5 * q^2 - 19 * q^4 + 15 * q^5 - 16 * q^6 - 3 * q^7 + 30 * q^8 - 27 * q^9 + 5 * q^10 - 11 * q^11 + 6 * q^13 - 5 * q^14 - 43 * q^16 + q^17 + 13 * q^18 + 17 * q^19 - 38 * q^20 - 3 * q^21 + 50 * q^22 - 15 * q^23 + 4 * q^24 - 15 * q^25 + 14 * q^26 - 6 * q^27 - q^28 + 62 * q^29 - 8 * q^30 + 23 * q^31 - 30 * q^32 - 28 * q^33 - 20 * q^34 + 6 * q^35 + 30 * q^36 - 20 * q^37 - 12 * q^38 - 4 * q^39 + 15 * q^40 - 16 * q^42 + 8 * q^43 - 33 * q^44 + 27 * q^45 - 5 * q^46 + q^47 + 52 * q^48 + 33 * q^49 + 10 * q^50 - 27 * q^51 - 11 * q^52 - 36 * q^53 - 12 * q^54 - 22 * q^55 + 18 * q^56 + 56 * q^57 - 14 * q^58 + 10 * q^59 + 10 * q^61 + 28 * q^62 - 51 * q^63 + 18 * q^64 + 3 * q^65 + 17 * q^66 - 13 * q^67 - 3 * q^68 - q^70 - 14 * q^71 - 35 * q^72 - 9 * q^73 - 62 * q^74 + 10 * q^76 - 26 * q^77 - 34 * q^78 - 4 * q^79 + 43 * q^80 - 43 * q^81 - 32 * q^82 + 58 * q^83 - 78 * q^84 + 2 * q^85 - 100 * q^86 + 22 * q^87 - 24 * q^88 + 6 * q^89 + 26 * q^90 - 6 * q^91 + 38 * q^92 - q^93 + 62 * q^94 - 17 * q^95 + 63 * q^96 + 72 * q^97 + q^98 + 26 * q^99

Introduction

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