LMFDB - Embedded newform 825.2.p.a.196.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(181,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("825.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.p (of order $5$, degree $4$, 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:	$6.58765816676$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			196.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	825.196
Dual form			825.2.p.a.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80902 - 1.31433i) q^{2} +1.00000 q^{3} +(0.927051 + 2.85317i) q^{4} +(-0.690983 + 2.12663i) q^{5} +(-1.80902 - 1.31433i) q^{6} +(-0.309017 - 0.224514i) q^{7} +(0.690983 - 2.12663i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.80902 - 1.31433i) q^{2} +1.00000 q^{3} +(0.927051 + 2.85317i) q^{4} +(-0.690983 + 2.12663i) q^{5} +(-1.80902 - 1.31433i) q^{6} +(-0.309017 - 0.224514i) q^{7} +(0.690983 - 2.12663i) q^{8} +1.00000 q^{9} +(4.04508 - 2.93893i) q^{10} +(-0.309017 + 3.30220i) q^{11} +(0.927051 + 2.85317i) q^{12} -6.00000 q^{13} +(0.263932 + 0.812299i) q^{14} +(-0.690983 + 2.12663i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-1.42705 - 1.03681i) q^{17} +(-1.80902 - 1.31433i) q^{18} +(1.35410 - 4.16750i) q^{19} -6.70820 q^{20} +(-0.309017 - 0.224514i) q^{21} +(4.89919 - 5.56758i) q^{22} +(-1.07295 + 3.30220i) q^{23} +(0.690983 - 2.12663i) q^{24} +(-4.04508 - 2.93893i) q^{25} +(10.8541 + 7.88597i) q^{26} +1.00000 q^{27} +(0.354102 - 1.08981i) q^{28} +(-1.26393 - 3.88998i) q^{29} +(4.04508 - 2.93893i) q^{30} +(-0.454915 - 1.40008i) q^{31} -6.70820 q^{32} +(-0.309017 + 3.30220i) q^{33} +(1.21885 + 3.75123i) q^{34} +(0.690983 - 0.502029i) q^{35} +(0.927051 + 2.85317i) q^{36} +(2.42705 - 7.46969i) q^{37} +(-7.92705 + 5.75934i) q^{38} -6.00000 q^{39} +(4.04508 + 2.93893i) q^{40} +(-5.04508 - 3.66547i) q^{41} +(0.263932 + 0.812299i) q^{42} -9.94427 q^{43} +(-9.70820 + 2.17963i) q^{44} +(-0.690983 + 2.12663i) q^{45} +(6.28115 - 4.56352i) q^{46} -3.09017 q^{47} +(0.809017 - 0.587785i) q^{48} +(-2.11803 - 6.51864i) q^{49} +(3.45492 + 10.6331i) q^{50} +(-1.42705 - 1.03681i) q^{51} +(-5.56231 - 17.1190i) q^{52} +(0.809017 - 0.587785i) q^{53} +(-1.80902 - 1.31433i) q^{54} +(-6.80902 - 2.93893i) q^{55} +(-0.690983 + 0.502029i) q^{56} +(1.35410 - 4.16750i) q^{57} +(-2.82624 + 8.69827i) q^{58} +(-0.527864 + 1.62460i) q^{59} -6.70820 q^{60} +10.3262 q^{61} +(-1.01722 + 3.13068i) q^{62} +(-0.309017 - 0.224514i) q^{63} +(10.5172 + 7.64121i) q^{64} +(4.14590 - 12.7598i) q^{65} +(4.89919 - 5.56758i) q^{66} +(-0.690983 + 0.502029i) q^{67} +(1.63525 - 5.03280i) q^{68} +(-1.07295 + 3.30220i) q^{69} -1.90983 q^{70} +(-0.454915 + 1.40008i) q^{71} +(0.690983 - 2.12663i) q^{72} +(-1.00000 + 0.726543i) q^{73} +(-14.2082 + 10.3229i) q^{74} +(-4.04508 - 2.93893i) q^{75} +13.1459 q^{76} +(0.836881 - 0.951057i) q^{77} +(10.8541 + 7.88597i) q^{78} +(-4.00000 + 2.90617i) q^{79} +(0.690983 + 2.12663i) q^{80} +1.00000 q^{81} +(4.30902 + 13.2618i) q^{82} +(-9.35410 - 6.79615i) q^{83} +(0.354102 - 1.08981i) q^{84} +(3.19098 - 2.31838i) q^{85} +(17.9894 + 13.0700i) q^{86} +(-1.26393 - 3.88998i) q^{87} +(6.80902 + 2.93893i) q^{88} +(-5.11803 + 15.7517i) q^{89} +(4.04508 - 2.93893i) q^{90} +(1.85410 + 1.34708i) q^{91} -10.4164 q^{92} +(-0.454915 - 1.40008i) q^{93} +(5.59017 + 4.06150i) q^{94} +(7.92705 + 5.75934i) q^{95} -6.70820 q^{96} +(-9.28115 + 6.74315i) q^{97} +(-4.73607 + 14.5761i) q^{98} +(-0.309017 + 3.30220i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{2} + 4 q^{3} - 3 q^{4} - 5 q^{5} - 5 q^{6} + q^{7} + 5 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 5 * q^2 + 4 * q^3 - 3 * q^4 - 5 * q^5 - 5 * q^6 + q^7 + 5 * q^8 + 4 * q^9	\( 4 q - 5 q^{2} + 4 q^{3} - 3 q^{4} - 5 q^{5} - 5 q^{6} + q^{7} + 5 q^{8} + 4 q^{9} + 5 q^{10} + q^{11} - 3 q^{12} - 24 q^{13} + 10 q^{14} - 5 q^{15} + q^{16} + q^{17} - 5 q^{18} - 8 q^{19} + q^{21} - 5 q^{22} - 11 q^{23} + 5 q^{24} - 5 q^{25} + 30 q^{26} + 4 q^{27} - 12 q^{28} - 14 q^{29} + 5 q^{30} - 13 q^{31} + q^{33} + 25 q^{34} + 5 q^{35} - 3 q^{36} + 3 q^{37} - 25 q^{38} - 24 q^{39} + 5 q^{40} - 9 q^{41} + 10 q^{42} - 4 q^{43} - 12 q^{44} - 5 q^{45} + 5 q^{46} + 10 q^{47} + q^{48} - 4 q^{49} + 25 q^{50} + q^{51} + 18 q^{52} + q^{53} - 5 q^{54} - 25 q^{55} - 5 q^{56} - 8 q^{57} + 20 q^{58} - 20 q^{59} + 10 q^{61} + 25 q^{62} + q^{63} + 13 q^{64} + 30 q^{65} - 5 q^{66} - 5 q^{67} - 27 q^{68} - 11 q^{69} - 30 q^{70} - 13 q^{71} + 5 q^{72} - 4 q^{73} - 30 q^{74} - 5 q^{75} + 66 q^{76} + 19 q^{77} + 30 q^{78} - 16 q^{79} + 5 q^{80} + 4 q^{81} + 15 q^{82} - 24 q^{83} - 12 q^{84} + 15 q^{85} + 25 q^{86} - 14 q^{87} + 25 q^{88} - 16 q^{89} + 5 q^{90} - 6 q^{91} + 12 q^{92} - 13 q^{93} + 25 q^{95} - 17 q^{97} - 10 q^{98} + q^{99}+O(q^{100}) \) 4 * q - 5 * q^2 + 4 * q^3 - 3 * q^4 - 5 * q^5 - 5 * q^6 + q^7 + 5 * q^8 + 4 * q^9 + 5 * q^10 + q^11 - 3 * q^12 - 24 * q^13 + 10 * q^14 - 5 * q^15 + q^16 + q^17 - 5 * q^18 - 8 * q^19 + q^21 - 5 * q^22 - 11 * q^23 + 5 * q^24 - 5 * q^25 + 30 * q^26 + 4 * q^27 - 12 * q^28 - 14 * q^29 + 5 * q^30 - 13 * q^31 + q^33 + 25 * q^34 + 5 * q^35 - 3 * q^36 + 3 * q^37 - 25 * q^38 - 24 * q^39 + 5 * q^40 - 9 * q^41 + 10 * q^42 - 4 * q^43 - 12 * q^44 - 5 * q^45 + 5 * q^46 + 10 * q^47 + q^48 - 4 * q^49 + 25 * q^50 + q^51 + 18 * q^52 + q^53 - 5 * q^54 - 25 * q^55 - 5 * q^56 - 8 * q^57 + 20 * q^58 - 20 * q^59 + 10 * q^61 + 25 * q^62 + q^63 + 13 * q^64 + 30 * q^65 - 5 * q^66 - 5 * q^67 - 27 * q^68 - 11 * q^69 - 30 * q^70 - 13 * q^71 + 5 * q^72 - 4 * q^73 - 30 * q^74 - 5 * q^75 + 66 * q^76 + 19 * q^77 + 30 * q^78 - 16 * q^79 + 5 * q^80 + 4 * q^81 + 15 * q^82 - 24 * q^83 - 12 * q^84 + 15 * q^85 + 25 * q^86 - 14 * q^87 + 25 * q^88 - 16 * q^89 + 5 * q^90 - 6 * q^91 + 12 * q^92 - 13 * q^93 + 25 * q^95 - 17 * q^97 - 10 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.80902	−	1.31433i	−1.27917	−	0.929370i	−0.279641	−	0.960105i	$-0.590215\pi$
$2$	−1.80902	−	1.31433i	−1.27917	−	0.929370i	−0.999528	+	0.0307347i	$0.990215\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.927051	+	2.85317i	0.463525	+	1.42658i
$5$	−0.690983	+	2.12663i	−0.309017	+	0.951057i
$5$	−0.690983	+	2.12663i	−0.309017	+	0.951057i
$6$	−1.80902	−	1.31433i	−0.738528	−	0.536572i
$7$	−0.309017	−	0.224514i	−0.116797	−	0.0848583i	0.527853	−	0.849336i	$-0.322997\pi$
$7$	−0.309017	−	0.224514i	−0.116797	−	0.0848583i	−0.644651	+	0.764477i	$0.722997\pi$
$8$	0.690983	−	2.12663i	0.244299	−	0.751876i
$9$	1.00000			0.333333
$10$	4.04508	−	2.93893i	1.27917	−	0.929370i
$11$	−0.309017	+	3.30220i	−0.0931721	+	0.995650i
$11$	−0.309017	+	3.30220i	−0.0931721	+	0.995650i
$12$	0.927051	+	2.85317i	0.267617	+	0.823639i
$13$	−6.00000			−1.66410			−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000			−1.66410			−0.832050	+	0.554700i	$0.812833\pi$
$14$	0.263932	+	0.812299i	0.0705388	+	0.217096i
$15$	−0.690983	+	2.12663i	−0.178411	+	0.549093i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−1.42705	−	1.03681i	−0.346111	−	0.251464i	0.401125	−	0.916023i	$-0.368619\pi$
$17$	−1.42705	−	1.03681i	−0.346111	−	0.251464i	−0.747236	+	0.664559i	$0.768619\pi$
$18$	−1.80902	−	1.31433i	−0.426389	−	0.309790i
$19$	1.35410	−	4.16750i	0.310652	−	0.956089i	−0.666855	−	0.745188i	$-0.732360\pi$
$19$	1.35410	−	4.16750i	0.310652	−	0.956089i	0.977507	−	0.210902i	$-0.0676401\pi$
$20$	−6.70820			−1.50000
$21$	−0.309017	−	0.224514i	−0.0674330	−	0.0489930i
$22$	4.89919	−	5.56758i	1.04451	−	1.18701i
$23$	−1.07295	+	3.30220i	−0.223725	+	0.688556i	0.774693	+	0.632337i	$0.217904\pi$
$23$	−1.07295	+	3.30220i	−0.223725	+	0.688556i	−0.998418	+	0.0562184i	$0.982096\pi$
$24$	0.690983	−	2.12663i	0.141046	−	0.434096i
$25$	−4.04508	−	2.93893i	−0.809017	−	0.587785i
$26$	10.8541	+	7.88597i	2.12866	+	1.54657i
$27$	1.00000			0.192450
$28$	0.354102	−	1.08981i	0.0669190	−	0.205955i
$29$	−1.26393	−	3.88998i	−0.234706	−	0.722352i	−0.997160	−	0.0753092i	$-0.976006\pi$
$29$	−1.26393	−	3.88998i	−0.234706	−	0.722352i	0.762454	−	0.647042i	$-0.223994\pi$
$30$	4.04508	−	2.93893i	0.738528	−	0.536572i
$31$	−0.454915	−	1.40008i	−0.0817052	−	0.251463i	0.901856	−	0.432036i	$-0.142205\pi$
$31$	−0.454915	−	1.40008i	−0.0817052	−	0.251463i	−0.983562	+	0.180573i	$0.942205\pi$
$32$	−6.70820			−1.18585
$33$	−0.309017	+	3.30220i	−0.0537930	+	0.574839i
$34$	1.21885	+	3.75123i	0.209031	+	0.643330i
$35$	0.690983	−	0.502029i	0.116797	−	0.0848583i
$36$	0.927051	+	2.85317i	0.154508	+	0.475528i
$37$	2.42705	−	7.46969i	0.399005	−	1.22801i	−0.526794	−	0.849993i	$-0.676606\pi$
$37$	2.42705	−	7.46969i	0.399005	−	1.22801i	0.925799	−	0.378017i	$-0.123394\pi$
$38$	−7.92705	+	5.75934i	−1.28594	+	0.934288i
$39$	−6.00000			−0.960769
$40$	4.04508	+	2.93893i	0.639584	+	0.464685i
$41$	−5.04508	−	3.66547i	−0.787910	−	0.572450i	0.119433	−	0.992842i	$-0.461892\pi$
$41$	−5.04508	−	3.66547i	−0.787910	−	0.572450i	−0.907342	+	0.420392i	$0.861892\pi$
$42$	0.263932	+	0.812299i	0.0407256	+	0.125340i
$43$	−9.94427			−1.51649			−0.758244	−	0.651971i	$-0.773942\pi$
$43$	−9.94427			−1.51649			−0.758244	+	0.651971i	$0.773942\pi$
$44$	−9.70820	+	2.17963i	−1.46357	+	0.328591i
$45$	−0.690983	+	2.12663i	−0.103006	+	0.317019i
$46$	6.28115	−	4.56352i	0.926105	−	0.672855i
$47$	−3.09017			−0.450748			−0.225374	−	0.974272i	$-0.572360\pi$
$47$	−3.09017			−0.450748			−0.225374	+	0.974272i	$0.572360\pi$
$48$	0.809017	−	0.587785i	0.116772	−	0.0848395i
$49$	−2.11803	−	6.51864i	−0.302576	−	0.931234i
$50$	3.45492	+	10.6331i	0.488599	+	1.50375i
$51$	−1.42705	−	1.03681i	−0.199827	−	0.145183i
$52$	−5.56231	−	17.1190i	−0.771353	−	2.37398i
$53$	0.809017	−	0.587785i	0.111127	−	0.0807385i	−0.530834	−	0.847476i	$-0.678121\pi$
$53$	0.809017	−	0.587785i	0.111127	−	0.0807385i	0.641961	+	0.766737i	$0.278121\pi$
$54$	−1.80902	−	1.31433i	−0.246176	−	0.178857i
$55$	−6.80902	−	2.93893i	−0.918128	−	0.396285i
$56$	−0.690983	+	0.502029i	−0.0923365	+	0.0670864i
$57$	1.35410	−	4.16750i	0.179355	−	0.551999i
$58$	−2.82624	+	8.69827i	−0.371103	+	1.14214i
$59$	−0.527864	+	1.62460i	−0.0687220	+	0.211505i	−0.979520	−	0.201348i	$-0.935468\pi$
$59$	−0.527864	+	1.62460i	−0.0687220	+	0.211505i	0.910798	+	0.412853i	$0.135468\pi$
$60$	−6.70820			−0.866025
$61$	10.3262			1.32214			0.661070	−	0.750325i	$-0.270103\pi$
$61$	10.3262			1.32214			0.661070	+	0.750325i	$0.270103\pi$
$62$	−1.01722	+	3.13068i	−0.129187	+	0.397597i
$63$	−0.309017	−	0.224514i	−0.0389325	−	0.0282861i
$64$	10.5172	+	7.64121i	1.31465	+	0.955151i
$65$	4.14590	−	12.7598i	0.514235	−	1.58265i
$66$	4.89919	−	5.56758i	0.603048	−	0.685322i
$67$	−0.690983	+	0.502029i	−0.0844170	+	0.0613325i	−0.629193	−	0.777249i	$-0.716615\pi$
$67$	−0.690983	+	0.502029i	−0.0844170	+	0.0613325i	0.544776	+	0.838581i	$0.316615\pi$
$68$	1.63525	−	5.03280i	0.198304	−	0.610316i
$69$	−1.07295	+	3.30220i	−0.129168	+	0.397538i
$70$	−1.90983			−0.228268
$71$	−0.454915	+	1.40008i	−0.0539885	+	0.166159i	−0.974415	−	0.224756i	$-0.927842\pi$
$71$	−0.454915	+	1.40008i	−0.0539885	+	0.166159i	0.920427	+	0.390915i	$0.127842\pi$
$72$	0.690983	−	2.12663i	0.0814331	−	0.250625i
$73$	−1.00000	+	0.726543i	−0.117041	+	0.0850354i	−0.644766	−	0.764380i	$-0.723045\pi$
$73$	−1.00000	+	0.726543i	−0.117041	+	0.0850354i	0.527725	+	0.849415i	$0.323045\pi$
$74$	−14.2082	+	10.3229i	−1.65167	+	1.20001i
$75$	−4.04508	−	2.93893i	−0.467086	−	0.339358i
$76$	13.1459			1.50794
$77$	0.836881	−	0.951057i	0.0953714	−	0.108383i
$78$	10.8541	+	7.88597i	1.22899	+	0.892910i
$79$	−4.00000	+	2.90617i	−0.450035	+	0.326970i	−0.789610	−	0.613609i	$-0.789717\pi$
$79$	−4.00000	+	2.90617i	−0.450035	+	0.326970i	0.339574	+	0.940579i	$0.389717\pi$
$80$	0.690983	+	2.12663i	0.0772542	+	0.237764i
$81$	1.00000			0.111111
$82$	4.30902	+	13.2618i	0.475851	+	1.46452i
$83$	−9.35410	−	6.79615i	−1.02675	−	0.745975i	−0.0590913	−	0.998253i	$-0.518820\pi$
$83$	−9.35410	−	6.79615i	−1.02675	−	0.745975i	−0.967655	+	0.252278i	$0.918820\pi$
$84$	0.354102	−	1.08981i	0.0386357	−	0.118908i
$85$	3.19098	−	2.31838i	0.346111	−	0.251464i
$86$	17.9894	+	13.0700i	1.93984	+	1.40938i
$87$	−1.26393	−	3.88998i	−0.135508	−	0.417050i
$88$	6.80902	+	2.93893i	0.725844	+	0.313291i
$89$	−5.11803	+	15.7517i	−0.542511	+	1.66968i	0.184326	+	0.982865i	$0.440990\pi$
$89$	−5.11803	+	15.7517i	−0.542511	+	1.66968i	−0.726837	+	0.686811i	$0.759010\pi$
$90$	4.04508	−	2.93893i	0.426389	−	0.309790i
$91$	1.85410	+	1.34708i	0.194363	+	0.141213i
$92$	−10.4164			−1.08599
$93$	−0.454915	−	1.40008i	−0.0471725	−	0.145182i
$94$	5.59017	+	4.06150i	0.576582	+	0.418911i
$95$	7.92705	+	5.75934i	0.813298	+	0.590896i
$96$	−6.70820			−0.684653
$97$	−9.28115	+	6.74315i	−0.942358	+	0.684663i	−0.948987	−	0.315315i	$-0.897890\pi$
$97$	−9.28115	+	6.74315i	−0.942358	+	0.684663i	0.00662888	+	0.999978i	$0.497890\pi$
$98$	−4.73607	+	14.5761i	−0.478415	+	1.47241i
$99$	−0.309017	+	3.30220i	−0.0310574	+	0.331883i
$100$	4.63525	−	14.2658i	0.463525	−	1.42658i
$101$	−5.16312	+	15.8904i	−0.513750	+	1.58116i	0.271796	+	0.962355i	$0.412382\pi$
$101$	−5.16312	+	15.8904i	−0.513750	+	1.58116i	−0.785546	+	0.618804i	$0.787618\pi$
$102$	1.21885	+	3.75123i	0.120684	+	0.371427i
$103$	1.45492	+	4.47777i	0.143357	+	0.441208i	0.996796	−	0.0799851i	$-0.0254873\pi$
$103$	1.45492	+	4.47777i	0.143357	+	0.441208i	−0.853439	+	0.521193i	$0.825487\pi$
$104$	−4.14590	+	12.7598i	−0.406539	+	1.25120i
$105$	0.690983	−	0.502029i	0.0674330	−	0.0489930i
$106$	−2.23607			−0.217186
$107$	11.6631	−	8.47375i	1.12752	−	0.819189i	0.142185	−	0.989840i	$-0.454587\pi$
$107$	11.6631	−	8.47375i	1.12752	−	0.819189i	0.985331	+	0.170652i	$0.0545873\pi$
$108$	0.927051	+	2.85317i	0.0892055	+	0.274546i
$109$	5.47214	+	16.8415i	0.524136	+	1.61312i	0.766019	+	0.642818i	$0.222235\pi$
$109$	5.47214	+	16.8415i	0.524136	+	1.61312i	−0.241883	+	0.970305i	$0.577765\pi$
$110$	8.45492	+	14.2658i	0.806145	+	1.36020i
$111$	2.42705	−	7.46969i	0.230365	−	0.708992i
$112$	−0.381966			−0.0360924
$113$	−1.19098	−	0.865300i	−0.112038	−	0.0814006i	0.530355	−	0.847775i	$-0.322059\pi$
$113$	−1.19098	−	0.865300i	−0.112038	−	0.0814006i	−0.642394	+	0.766375i	$0.722059\pi$
$114$	−7.92705	+	5.75934i	−0.742436	+	0.539412i
$115$	−6.28115	−	4.56352i	−0.585721	−	0.425551i
$116$	9.92705	−	7.21242i	0.921704	−	0.669657i
$117$	−6.00000			−0.554700
$118$	3.09017	−	2.24514i	0.284473	−	0.206682i
$119$	0.208204	+	0.640786i	0.0190860	+	0.0587407i
$120$	4.04508	+	2.93893i	0.369264	+	0.268286i
$121$	−10.8090	−	2.04087i	−0.982638	−	0.185534i
$122$	−18.6803	−	13.5721i	−1.69124	−	1.22876i
$123$	−5.04508	−	3.66547i	−0.454900	−	0.330504i
$124$	3.57295	−	2.59590i	0.320860	−	0.233119i
$125$	9.04508	−	6.57164i	0.809017	−	0.587785i
$126$	0.263932	+	0.812299i	0.0235129	+	0.0723654i
$127$	13.8541			1.22935			0.614676	−	0.788779i	$-0.289287\pi$
$127$	13.8541			1.22935			0.614676	+	0.788779i	$0.289287\pi$
$128$	−4.83688	−	14.8864i	−0.427524	−	1.31578i
$129$	−9.94427			−0.875544
$130$	−24.2705	+	17.6336i	−2.12866	+	1.54657i
$131$	1.35410	−	0.983813i	0.118308	−	0.0859561i	−0.527058	−	0.849830i	$-0.676705\pi$
$131$	1.35410	−	0.983813i	0.118308	−	0.0859561i	0.645366	+	0.763873i	$0.276705\pi$
$132$	−9.70820	+	2.17963i	−0.844991	+	0.189712i
$133$	−1.35410	+	0.983813i	−0.117416	+	0.0853074i
$134$	1.90983			0.164984
$135$	−0.690983	+	2.12663i	−0.0594703	+	0.183031i
$136$	−3.19098	+	2.31838i	−0.273625	+	0.198800i
$137$	−6.70820	+	4.87380i	−0.573121	+	0.416396i	−0.836237	−	0.548368i	$-0.815250\pi$
$137$	−6.70820	+	4.87380i	−0.573121	+	0.416396i	0.263117	+	0.964764i	$0.415250\pi$
$138$	6.28115	−	4.56352i	0.534687	−	0.388473i
$139$	−9.59017	+	6.96767i	−0.813428	+	0.590990i	−0.914822	−	0.403857i	$-0.867669\pi$
$139$	−9.59017	+	6.96767i	−0.813428	+	0.590990i	0.101395	+	0.994846i	$0.467669\pi$
$140$	2.07295	+	1.50609i	0.175196	+	0.127287i
$141$	−3.09017			−0.260239
$142$	2.66312	−	1.93487i	0.223484	−	0.162371i
$143$	1.85410	−	19.8132i	0.155048	−	1.65686i
$144$	0.809017	−	0.587785i	0.0674181	−	0.0489821i
$145$	9.14590			0.759525
$146$	2.76393			0.228745
$147$	−2.11803	−	6.51864i	−0.174692	−	0.537648i
$148$	23.5623			1.93681
$149$	−5.04508	−	15.5272i	−0.413309	−	1.27204i	−0.913754	−	0.406267i	$-0.866830\pi$
$149$	−5.04508	−	15.5272i	−0.413309	−	1.27204i	0.500445	−	0.865768i	$-0.333170\pi$
$150$	3.45492	+	10.6331i	0.282093	+	0.868192i
$151$	0.500000	−	0.363271i	0.0406894	−	0.0295626i	−0.567255	−	0.823542i	$-0.691994\pi$
$151$	0.500000	−	0.363271i	0.0406894	−	0.0295626i	0.607944	+	0.793980i	$0.291994\pi$
$152$	−7.92705	−	5.75934i	−0.642969	−	0.467144i
$153$	−1.42705	−	1.03681i	−0.115370	−	0.0838214i
$154$	−2.76393	+	0.620541i	−0.222724	+	0.0500047i
$155$	3.29180			0.264403
$156$	−5.56231	−	17.1190i	−0.445341	−	1.37062i
$157$	−3.80902	+	2.76741i	−0.303993	+	0.220864i	−0.729315	−	0.684179i	$-0.760161\pi$
$157$	−3.80902	+	2.76741i	−0.303993	+	0.220864i	0.425322	+	0.905042i	$0.360161\pi$
$158$	11.0557			0.879547
$159$	0.809017	−	0.587785i	0.0641592	−	0.0466144i
$160$	4.63525	−	14.2658i	0.366449	−	1.12781i
$161$	1.07295	−	0.779543i	0.0845602	−	0.0614366i
$162$	−1.80902	−	1.31433i	−0.142130	−	0.103263i
$163$	−13.0000			−1.01824			−0.509119	−	0.860696i	$-0.670029\pi$
$163$	−13.0000			−1.01824			−0.509119	+	0.860696i	$0.670029\pi$
$164$	5.78115	−	17.7926i	0.451432	−	1.38937i
$165$	−6.80902	−	2.93893i	−0.530081	−	0.228795i
$166$	7.98936	+	24.5887i	0.620094	+	1.90845i
$167$	2.98936	+	9.20029i	0.231323	+	0.711940i	0.997588	+	0.0694149i	$0.0221132\pi$
$167$	2.98936	+	9.20029i	0.231323	+	0.711940i	−0.766264	+	0.642525i	$0.777887\pi$
$168$	−0.690983	+	0.502029i	−0.0533105	+	0.0387323i
$169$	23.0000			1.76923
$170$	−8.81966			−0.676437
$171$	1.35410	−	4.16750i	0.103551	−	0.318696i
$172$	−9.21885	−	28.3727i	−0.702930	−	2.16340i
$173$	−4.10081	−	12.6210i	−0.311779	−	0.959557i	−0.977060	−	0.212964i	$-0.931688\pi$
$173$	−4.10081	−	12.6210i	−0.311779	−	0.959557i	0.665281	−	0.746593i	$-0.268312\pi$
$174$	−2.82624	+	8.69827i	−0.214257	+	0.659414i
$175$	0.590170	+	1.81636i	0.0446127	+	0.137304i
$176$	1.69098	+	2.85317i	0.127463	+	0.215066i
$177$	−0.527864	+	1.62460i	−0.0396767	+	0.122112i
$178$	29.9615	−	21.7683i	2.24571	−	1.63160i
$179$	−22.6525			−1.69313			−0.846563	−	0.532289i	$-0.821332\pi$
$179$	−22.6525			−1.69313			−0.846563	+	0.532289i	$0.821332\pi$
$180$	−6.70820			−0.500000
$181$	11.0172	+	8.00448i	0.818904	+	0.594968i	0.916398	−	0.400268i	$-0.131083\pi$
$181$	11.0172	+	8.00448i	0.818904	+	0.594968i	−0.0974946	+	0.995236i	$0.531083\pi$
$182$	−1.58359	−	4.87380i	−0.117384	−	0.361270i
$183$	10.3262			0.763337
$184$	6.28115	+	4.56352i	0.463053	+	0.336428i
$185$	14.2082	+	10.3229i	1.04461	+	0.758952i
$186$	−1.01722	+	3.13068i	−0.0745863	+	0.229553i
$187$	3.86475	−	4.39201i	0.282618	−	0.321176i
$188$	−2.86475	−	8.81678i	−0.208933	−	0.643030i
$189$	−0.309017	−	0.224514i	−0.0224777	−	0.0163310i
$190$	−6.77051	−	20.8375i	−0.491184	−	1.51171i
$191$	5.13525	−	15.8047i	0.371574	−	1.14359i	−0.574187	−	0.818724i	$-0.694682\pi$
$191$	5.13525	−	15.8047i	0.371574	−	1.14359i	0.945761	−	0.324863i	$-0.105318\pi$
$192$	10.5172	+	7.64121i	0.759015	+	0.551457i
$193$	−1.73607	−	5.34307i	−0.124965	−	0.384602i	0.868930	−	0.494935i	$-0.164808\pi$
$193$	−1.73607	−	5.34307i	−0.124965	−	0.384602i	−0.993895	+	0.110333i	$0.964808\pi$
$194$	25.6525			1.84174
$195$	4.14590	−	12.7598i	0.296894	−	0.913746i
$196$	16.6353	−	12.0862i	1.18823	−	0.863301i
$197$	12.5172	+	9.09429i	0.891815	+	0.647942i	0.936351	−	0.351066i	$-0.114181\pi$
$197$	12.5172	+	9.09429i	0.891815	+	0.647942i	−0.0445356	+	0.999008i	$0.514181\pi$
$198$	4.89919	−	5.56758i	0.348170	−	0.395671i
$199$	10.7984			0.765476			0.382738	−	0.923857i	$-0.374981\pi$
$199$	10.7984			0.765476			0.382738	+	0.923857i	$0.374981\pi$
$200$	−9.04508	+	6.57164i	−0.639584	+	0.464685i
$201$	−0.690983	+	0.502029i	−0.0487382	+	0.0354104i
$202$	30.2254	−	21.9601i	2.12665	−	1.54510i
$203$	−0.482779	+	1.48584i	−0.0338844	+	0.104286i
$204$	1.63525	−	5.03280i	0.114491	−	0.352366i
$205$	11.2812	−	8.19624i	0.787910	−	0.572450i
$206$	3.25329	−	10.0126i	0.226667	−	0.697610i
$207$	−1.07295	+	3.30220i	−0.0745751	+	0.229519i
$208$	−4.85410	+	3.52671i	−0.336571	+	0.244533i
$209$	13.3435	+	5.75934i	0.922986	+	0.398382i
$210$	−1.90983			−0.131791
$211$	−1.38197	−	1.00406i	−0.0951385	−	0.0691221i	0.539199	−	0.842178i	$-0.318727\pi$
$211$	−1.38197	−	1.00406i	−0.0951385	−	0.0691221i	−0.634338	+	0.773056i	$0.718727\pi$
$212$	2.42705	+	1.76336i	0.166691	+	0.121108i
$213$	−0.454915	+	1.40008i	−0.0311703	+	0.0959322i
$214$	−32.2361			−2.20361
$215$	6.87132	−	21.1478i	0.468620	−	1.44227i
$216$	0.690983	−	2.12663i	0.0470154	−	0.144699i
$217$	−0.173762	+	0.534785i	−0.0117957	+	0.0363036i
$218$	12.2361	−	37.6587i	0.828731	−	2.55057i
$219$	−1.00000	+	0.726543i	−0.0675737	+	0.0490952i
$220$	2.07295	−	22.1518i	0.139758	−	1.49348i
$221$	8.56231	+	6.22088i	0.575963	+	0.418462i
$222$	−14.2082	+	10.3229i	−0.953592	+	0.692825i
$223$	0.427051	+	1.31433i	0.0285974	+	0.0880139i	0.964337	−	0.264679i	$-0.0852660\pi$
$223$	0.427051	+	1.31433i	0.0285974	+	0.0880139i	−0.935739	+	0.352693i	$0.885266\pi$
$224$	2.07295	+	1.50609i	0.138505	+	0.100630i
$225$	−4.04508	−	2.93893i	−0.269672	−	0.195928i
$226$	1.01722	+	3.13068i	0.0676645	+	0.208250i
$227$	−18.3713	+	13.3475i	−1.21935	+	0.885908i	−0.996046	−	0.0888415i	$-0.971684\pi$
$227$	−18.3713	+	13.3475i	−1.21935	+	0.885908i	−0.223302	+	0.974749i	$0.571684\pi$
$228$	13.1459			0.870608
$229$	−13.7533	+	9.99235i	−0.908843	+	0.660313i	−0.940722	−	0.339179i	$-0.889851\pi$
$229$	−13.7533	+	9.99235i	−0.908843	+	0.660313i	0.0318790	+	0.999492i	$0.489851\pi$
$230$	5.36475	+	16.5110i	0.353741	+	1.08870i
$231$	0.836881	−	0.951057i	0.0550627	−	0.0625749i
$232$	−9.14590			−0.600458
$233$	−6.29180	−	19.3642i	−0.412189	−	1.26859i	−0.914741	−	0.404041i	$-0.867605\pi$
$233$	−6.29180	−	19.3642i	−0.412189	−	1.26859i	0.502552	−	0.864547i	$-0.332395\pi$
$234$	10.8541	+	7.88597i	0.709555	+	0.515522i
$235$	2.13525	−	6.57164i	0.139289	−	0.428686i
$236$	−5.12461			−0.333584
$237$	−4.00000	+	2.90617i	−0.259828	+	0.188776i
$238$	0.465558	−	1.43284i	0.0301777	−	0.0928773i
$239$	−0.590170	−	1.81636i	−0.0381749	−	0.117490i	0.930153	−	0.367172i	$-0.119674\pi$
$239$	−0.590170	−	1.81636i	−0.0381749	−	0.117490i	−0.968328	+	0.249682i	$0.919674\pi$
$240$	0.690983	+	2.12663i	0.0446028	+	0.137273i
$241$	3.44427	+	10.6004i	0.221865	+	0.682830i	0.998595	+	0.0529963i	$0.0168771\pi$
$241$	3.44427	+	10.6004i	0.221865	+	0.682830i	−0.776730	+	0.629834i	$0.783123\pi$
$242$	16.8713	+	17.8986i	1.08453	+	1.15056i
$243$	1.00000			0.0641500
$244$	9.57295	+	29.4625i	0.612845	+	1.88614i
$245$	15.3262			0.979157
$246$	4.30902	+	13.2618i	0.274733	+	0.845541i
$247$	−8.12461	+	25.0050i	−0.516957	+	1.59103i
$248$	−3.29180			−0.209029
$249$	−9.35410	−	6.79615i	−0.592792	−	0.430689i
$250$	−25.0000			−1.58114
$251$	8.97214	−	27.6134i	0.566316	−	1.74294i	−0.0976919	−	0.995217i	$-0.531146\pi$
$251$	8.97214	−	27.6134i	0.566316	−	1.74294i	0.664008	−	0.747725i	$-0.268854\pi$
$252$	0.354102	−	1.08981i	0.0223063	−	0.0686518i
$253$	−10.5729	−	4.56352i	−0.664716	−	0.286906i
$254$	−25.0623	−	18.2088i	−1.57255	−	1.14252i
$255$	3.19098	−	2.31838i	0.199827	−	0.145183i
$256$	−2.78115	+	8.55951i	−0.173822	+	0.534969i
$257$	−9.51722	−	6.91467i	−0.593668	−	0.431325i	0.249958	−	0.968257i	$-0.419583\pi$
$257$	−9.51722	−	6.91467i	−0.593668	−	0.431325i	−0.843626	+	0.536932i	$0.819583\pi$
$258$	17.9894	+	13.0700i	1.11997	+	0.813705i
$259$	−2.42705	+	1.76336i	−0.150810	+	0.109570i
$260$	40.2492			2.49615
$261$	−1.26393	−	3.88998i	−0.0782354	−	0.240784i
$262$	−3.74265			−0.231221
$263$	5.29180	+	16.2865i	0.326306	+	1.00427i	0.970848	+	0.239698i	$0.0770483\pi$
$263$	5.29180	+	16.2865i	0.326306	+	1.00427i	−0.644541	+	0.764569i	$0.722952\pi$
$264$	6.80902	+	2.93893i	0.419066	+	0.180878i
$265$	0.690983	+	2.12663i	0.0424467	+	0.130638i
$266$	3.74265			0.229476
$267$	−5.11803	+	15.7517i	−0.313219	+	0.963988i
$268$	−2.07295	−	1.50609i	−0.126626	−	0.0919988i
$269$	−11.0451	−	8.02472i	−0.673431	−	0.489276i	0.197741	−	0.980254i	$-0.436639\pi$
$269$	−11.0451	−	8.02472i	−0.673431	−	0.489276i	−0.871172	+	0.490978i	$0.836639\pi$
$270$	4.04508	−	2.93893i	0.246176	−	0.178857i
$271$	−6.42705	−	19.7804i	−0.390416	−	1.20158i	−0.932475	−	0.361235i	$-0.882355\pi$
$271$	−6.42705	−	19.7804i	−0.390416	−	1.20158i	0.542059	−	0.840340i	$-0.317645\pi$
$272$	−1.76393			−0.106954
$273$	1.85410	+	1.34708i	0.112215	+	0.0815292i
$274$	18.5410			1.12010
$275$	10.9549	−	12.4495i	0.660606	−	0.750733i
$276$	−10.4164			−0.626994
$277$	−14.8713	−	10.8046i	−0.893531	−	0.649188i	0.0432651	−	0.999064i	$-0.486224\pi$
$277$	−14.8713	−	10.8046i	−0.893531	−	0.649188i	−0.936796	+	0.349875i	$0.886224\pi$
$278$	26.5066			1.58976
$279$	−0.454915	−	1.40008i	−0.0272351	−	0.0838209i
$280$	−0.590170	−	1.81636i	−0.0352694	−	0.108548i
$281$	−7.89919	−	5.73910i	−0.471226	−	0.342366i	0.326693	−	0.945131i	$-0.394066\pi$
$281$	−7.89919	−	5.73910i	−0.471226	−	0.342366i	−0.797919	+	0.602765i	$0.794066\pi$
$282$	5.59017	+	4.06150i	0.332890	+	0.241859i
$283$	5.21885	−	16.0620i	0.310228	−	0.954784i	−0.667446	−	0.744658i	$-0.732613\pi$
$283$	5.21885	−	16.0620i	0.310228	−	0.954784i	0.977674	−	0.210126i	$-0.0673875\pi$
$284$	−4.41641			−0.262066
$285$	7.92705	+	5.75934i	0.469558	+	0.341154i
$286$	−29.3951	+	33.4055i	−1.73817	+	1.97531i
$287$	0.736068	+	2.26538i	0.0434487	+	0.133721i
$288$	−6.70820			−0.395285
$289$	−4.29180	−	13.2088i	−0.252459	−	0.776988i
$290$	−16.5451	−	12.0207i	−0.971561	−	0.705880i
$291$	−9.28115	+	6.74315i	−0.544071	+	0.395291i
$292$	−3.00000	−	2.17963i	−0.175562	−	0.127553i
$293$	20.0344	+	14.5559i	1.17042	+	0.850363i	0.991060	−	0.133419i	$-0.0425957\pi$
$293$	20.0344	+	14.5559i	1.17042	+	0.850363i	0.179365	+	0.983783i	$0.442596\pi$
$294$	−4.73607	+	14.5761i	−0.276213	+	0.850096i
$295$	−3.09017	−	2.24514i	−0.179917	−	0.130717i
$296$	−14.2082	−	10.3229i	−0.825835	−	0.600004i
$297$	−0.309017	+	3.30220i	−0.0179310	+	0.191613i
$298$	−11.2812	+	34.7198i	−0.653500	+	2.01127i
$299$	6.43769	−	19.8132i	0.372301	−	1.14583i
$300$	4.63525	−	14.2658i	0.267617	−	0.823639i
$301$	3.07295	+	2.23263i	0.177122	+	0.128687i
$302$	−1.38197			−0.0795232
$303$	−5.16312	+	15.8904i	−0.296613	+	0.912882i
$304$	−1.35410	−	4.16750i	−0.0776631	−	0.239022i
$305$	−7.13525	+	21.9601i	−0.408564	+	1.25743i
$306$	1.21885	+	3.75123i	0.0696768	+	0.214443i
$307$	28.4164			1.62181			0.810905	−	0.585178i	$-0.198975\pi$
$307$	28.4164			1.62181			0.810905	+	0.585178i	$0.198975\pi$
$308$	3.48936	+	1.50609i	0.198825	+	0.0858172i
$309$	1.45492	+	4.47777i	0.0827672	+	0.254731i
$310$	−5.95492	−	4.32650i	−0.338216	−	0.245729i
$311$	1.12868	+	3.47371i	0.0640014	+	0.196976i	0.977944	−	0.208868i	$-0.0669778\pi$
$311$	1.12868	+	3.47371i	0.0640014	+	0.196976i	−0.913943	+	0.405844i	$0.866978\pi$
$312$	−4.14590	+	12.7598i	−0.234715	+	0.722379i
$313$	−0.336881	+	0.244758i	−0.0190416	+	0.0138346i	−0.597265	−	0.802044i	$-0.703746\pi$
$313$	−0.336881	+	0.244758i	−0.0190416	+	0.0138346i	0.578224	+	0.815878i	$0.303746\pi$
$314$	10.5279			0.594122
$315$	0.690983	−	0.502029i	0.0389325	−	0.0282861i
$316$	−12.0000	−	8.71851i	−0.675053	−	0.490455i
$317$	−3.09017	−	9.51057i	−0.173561	−	0.534167i	0.826004	−	0.563665i	$-0.190609\pi$
$317$	−3.09017	−	9.51057i	−0.173561	−	0.534167i	−0.999565	+	0.0294983i	$0.990609\pi$
$318$	−2.23607			−0.125392
$319$	13.2361	−	2.97168i	0.741078	−	0.166382i
$320$	−23.5172	+	17.0863i	−1.31465	+	0.955151i
$321$	11.6631	−	8.47375i	0.650972	−	0.472959i
$322$	−2.96556			−0.165264
$323$	−6.25329	+	4.54328i	−0.347942	+	0.252795i
$324$	0.927051	+	2.85317i	0.0515028	+	0.158509i
$325$	24.2705	+	17.6336i	1.34629	+	0.978134i
$326$	23.5172	+	17.0863i	1.30250	+	0.946320i
$327$	5.47214	+	16.8415i	0.302610	+	0.931337i
$328$	−11.2812	+	8.19624i	−0.622897	+	0.452562i
$329$	0.954915	+	0.693786i	0.0526462	+	0.0382497i
$330$	8.45492	+	14.2658i	0.465428	+	0.785309i
$331$	−20.1803	+	14.6619i	−1.10921	+	0.805890i	−0.982539	−	0.186055i	$-0.940430\pi$
$331$	−20.1803	+	14.6619i	−1.10921	+	0.805890i	−0.126672	+	0.991945i	$0.540430\pi$
$332$	10.7188	−	32.9892i	0.588273	−	1.81052i
$333$	2.42705	−	7.46969i	0.133002	−	0.409337i
$334$	6.68441	−	20.5725i	0.365754	−	1.12568i
$335$	−0.590170	−	1.81636i	−0.0322444	−	0.0992381i
$336$	−0.381966			−0.0208380
$337$	−8.69098	+	26.7481i	−0.473428	+	1.45706i	0.374638	+	0.927171i	$0.377767\pi$
$337$	−8.69098	+	26.7481i	−0.473428	+	1.45706i	−0.848066	+	0.529890i	$0.822233\pi$
$338$	−41.6074	−	30.2295i	−2.26314	−	1.64427i
$339$	−1.19098	−	0.865300i	−0.0646853	−	0.0469966i
$340$	9.57295	+	6.95515i	0.519166	+	0.377196i
$341$	4.76393	−	1.06957i	0.257981	−	0.0579204i
$342$	−7.92705	+	5.75934i	−0.428646	+	0.311429i
$343$	−1.63525	+	5.03280i	−0.0882955	+	0.271746i
$344$	−6.87132	+	21.1478i	−0.370477	+	1.14021i
$345$	−6.28115	−	4.56352i	−0.338166	−	0.245692i
$346$	−9.16970	+	28.2214i	−0.492966	+	1.51719i
$347$	0.0172209	−	0.0530006i	0.000924468	−	0.00284522i	−0.950593	−	0.310439i	$-0.899524\pi$
$347$	0.0172209	−	0.0530006i	0.000924468	−	0.00284522i	0.951518	+	0.307594i	$0.0995239\pi$
$348$	9.92705	−	7.21242i	0.532146	−	0.386627i
$349$	−12.3992	+	9.00854i	−0.663713	+	0.482216i	−0.867915	−	0.496713i	$-0.834540\pi$
$349$	−12.3992	+	9.00854i	−0.663713	+	0.482216i	0.204202	+	0.978929i	$0.434540\pi$
$350$	1.31966	−	4.06150i	0.0705388	−	0.217096i
$351$	−6.00000			−0.320256
$352$	2.07295	−	22.1518i	0.110489	−	1.18070i
$353$	4.50000	+	3.26944i	0.239511	+	0.174015i	0.701065	−	0.713097i	$-0.252708\pi$
$353$	4.50000	+	3.26944i	0.239511	+	0.174015i	−0.461554	+	0.887112i	$0.652708\pi$
$354$	3.09017	−	2.24514i	0.164241	−	0.119328i
$355$	−2.66312	−	1.93487i	−0.141344	−	0.102692i
$356$	−49.6869			−2.63340
$357$	0.208204	+	0.640786i	0.0110193	+	0.0339140i
$358$	40.9787	+	29.7728i	2.16579	+	1.57354i
$359$	−11.5623	+	35.5851i	−0.610235	+	1.87811i	−0.154507	+	0.987992i	$0.549379\pi$
$359$	−11.5623	+	35.5851i	−0.610235	+	1.87811i	−0.455728	+	0.890119i	$0.650621\pi$
$360$	4.04508	+	2.93893i	0.213195	+	0.154895i
$361$	−0.163119	−	0.118513i	−0.00858521	−	0.00623752i
$362$	−9.40983	−	28.9605i	−0.494570	−	1.52213i
$363$	−10.8090	−	2.04087i	−0.567326	−	0.107118i
$364$	−2.12461	+	6.53888i	−0.111360	+	0.342731i
$365$	−0.854102	−	2.62866i	−0.0447057	−	0.137590i
$366$	−18.6803	−	13.5721i	−0.976437	−	0.709423i
$367$	31.7426			1.65695			0.828476	−	0.560024i	$-0.189208\pi$
$367$	31.7426			1.65695			0.828476	+	0.560024i	$0.189208\pi$
$368$	1.07295	+	3.30220i	0.0559313	+	0.172139i
$369$	−5.04508	−	3.66547i	−0.262637	−	0.190817i
$370$	−12.1353	−	37.3485i	−0.630882	−	1.94165i
$371$	−0.381966			−0.0198307
$372$	3.57295	−	2.59590i	0.185249	−	0.134591i
$373$	−10.2082	+	31.4176i	−0.528561	+	1.62674i	0.228604	+	0.973519i	$0.426584\pi$
$373$	−10.2082	+	31.4176i	−0.528561	+	1.62674i	−0.757165	+	0.653223i	$0.773416\pi$
$374$	−12.7639	+	2.86568i	−0.660007	+	0.148181i
$375$	9.04508	−	6.57164i	0.467086	−	0.339358i
$376$	−2.13525	+	6.57164i	−0.110117	+	0.338906i
$377$	7.58359	+	23.3399i	0.390575	+	1.20207i
$378$	0.263932	+	0.812299i	0.0135752	+	0.0417802i
$379$	6.22542	−	19.1599i	0.319779	−	0.984177i	−0.653964	−	0.756526i	$-0.726895\pi$
$379$	6.22542	−	19.1599i	0.319779	−	0.984177i	0.973743	−	0.227652i	$-0.0731048\pi$
$380$	−9.08359	+	27.9564i	−0.465978	+	1.43413i
$381$	13.8541			0.709767
$382$	−30.0623	+	21.8415i	−1.53812	+	1.11751i
$383$	11.7639	+	36.2057i	0.601109	+	1.85002i	0.521603	+	0.853188i	$0.325334\pi$
$383$	11.7639	+	36.2057i	0.601109	+	1.85002i	0.0795060	+	0.996834i	$0.474666\pi$
$384$	−4.83688	−	14.8864i	−0.246831	−	0.759668i
$385$	1.44427	+	2.43690i	0.0736069	+	0.124196i
$386$	−3.88197	+	11.9475i	−0.197587	+	0.608110i
$387$	−9.94427			−0.505496
$388$	−27.8435	−	20.2295i	−1.41354	−	1.02700i
$389$	16.0172	−	11.6372i	0.812105	−	0.590029i	−0.102335	−	0.994750i	$-0.532631\pi$
$389$	16.0172	−	11.6372i	0.812105	−	0.590029i	0.914440	+	0.404721i	$0.132631\pi$
$390$	−24.2705	+	17.6336i	−1.22899	+	0.892910i
$391$	4.95492	−	3.59996i	0.250581	−	0.182058i
$392$	−15.3262			−0.774092
$393$	1.35410	−	0.983813i	0.0683054	−	0.0496268i
$394$	−10.6910	−	32.9035i	−0.538604	−	1.65765i
$395$	−3.41641	−	10.5146i	−0.171898	−	0.529048i
$396$	−9.70820	+	2.17963i	−0.487856	+	0.109530i
$397$	−19.1074	−	13.8823i	−0.958972	−	0.696734i	−0.00606059	−	0.999982i	$-0.501929\pi$
$397$	−19.1074	−	13.8823i	−0.958972	−	0.696734i	−0.952912	+	0.303247i	$0.901929\pi$
$398$	−19.5344	−	14.1926i	−0.979173	−	0.711411i
$399$	−1.35410	+	0.983813i	−0.0677899	+	0.0492522i
$400$	−5.00000			−0.250000
$401$	3.21885	+	9.90659i	0.160742	+	0.494712i	0.998697	−	0.0510266i	$-0.0162493\pi$
$401$	3.21885	+	9.90659i	0.160742	+	0.494712i	−0.837956	+	0.545738i	$0.816249\pi$
$402$	1.90983			0.0952537
$403$	2.72949	+	8.40051i	0.135966	+	0.418459i
$404$	−50.1246			−2.49379
$405$	−0.690983	+	2.12663i	−0.0343352	+	0.105673i
$406$	2.82624	−	2.05338i	0.140264	−	0.101908i
$407$	23.9164	+	10.3229i	1.18549	+	0.511685i
$408$	−3.19098	+	2.31838i	−0.157977	+	0.114777i
$409$	15.9443			0.788394			0.394197	−	0.919026i	$-0.371023\pi$
$409$	15.9443			0.788394			0.394197	+	0.919026i	$0.371023\pi$
$410$	−31.1803			−1.53989
$411$	−6.70820	+	4.87380i	−0.330891	+	0.240407i
$412$	−11.4271	+	8.30224i	−0.562970	+	0.409022i
$413$	0.527864	−	0.383516i	0.0259745	−	0.0188716i
$414$	6.28115	−	4.56352i	0.308702	−	0.224285i
$415$	20.9164	−	15.1967i	1.02675	−	0.745975i
$416$	40.2492			1.97338
$417$	−9.59017	+	6.96767i	−0.469633	+	0.341208i
$418$	−16.5689	−	27.9564i	−0.810411	−	1.36739i
$419$	−24.9443	+	18.1231i	−1.21861	+	0.885370i	−0.995984	−	0.0895343i	$-0.971462\pi$
$419$	−24.9443	+	18.1231i	−1.21861	+	0.885370i	−0.222624	+	0.974904i	$0.571462\pi$
$420$	2.07295	+	1.50609i	0.101150	+	0.0734895i
$421$	−20.9787			−1.02244			−0.511220	−	0.859450i	$-0.670806\pi$
$421$	−20.9787			−1.02244			−0.511220	+	0.859450i	$0.670806\pi$
$422$	1.18034	+	3.63271i	0.0574580	+	0.176838i
$423$	−3.09017			−0.150249
$424$	−0.690983	−	2.12663i	−0.0335571	−	0.103278i
$425$	2.72542	+	8.38800i	0.132203	+	0.406878i
$426$	2.66312	−	1.93487i	0.129029	−	0.0937447i
$427$	−3.19098	−	2.31838i	−0.154422	−	0.112195i
$428$	34.9894	+	25.4213i	1.69127	+	1.22878i
$429$	1.85410	−	19.8132i	0.0895169	−	0.956590i
$430$	−40.2254	+	29.2255i	−1.93984	+	1.40938i
$431$	1.54508	+	4.75528i	0.0744241	+	0.229054i	0.981348	−	0.192241i	$-0.0615756\pi$
$431$	1.54508	+	4.75528i	0.0744241	+	0.229054i	−0.906924	+	0.421295i	$0.861576\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	7.05573			0.339077			0.169538	−	0.985524i	$-0.445772\pi$
$433$	7.05573			0.339077			0.169538	+	0.985524i	$0.445772\pi$
$434$	1.01722	−	0.739054i	0.0488282	−	0.0354757i
$435$	9.14590			0.438512
$436$	−42.9787	+	31.2259i	−2.05831	+	1.49545i
$437$	12.3090	+	8.94302i	0.588820	+	0.427803i
$438$	2.76393			0.132066
$439$	6.11803	−	18.8294i	0.291998	−	0.898677i	−0.692216	−	0.721691i	$-0.743365\pi$
$439$	6.11803	−	18.8294i	0.291998	−	0.898677i	0.984213	−	0.176986i	$-0.0566348\pi$
$440$	−10.9549	+	12.4495i	−0.522255	+	0.593506i
$441$	−2.11803	−	6.51864i	−0.100859	−	0.310411i
$442$	−7.31308	−	22.5074i	−0.347848	−	1.07057i
$443$	9.37132	−	6.80866i	0.445245	−	0.323489i	−0.342471	−	0.939529i	$-0.611264\pi$
$443$	9.37132	−	6.80866i	0.445245	−	0.323489i	0.787716	+	0.616039i	$0.211264\pi$
$444$	23.5623			1.11822
$445$	−29.9615	−	21.7683i	−1.42031	−	1.03192i
$446$	0.954915	−	2.93893i	0.0452165	−	0.139162i
$447$	−5.04508	−	15.5272i	−0.238624	−	0.734410i
$448$	−1.53444	−	4.72253i	−0.0724956	−	0.223118i
$449$	0.281153	−	0.865300i	0.0132684	−	0.0408360i	−0.944203	−	0.329364i	$-0.893166\pi$
$449$	0.281153	−	0.865300i	0.0132684	−	0.0408360i	0.957472	+	0.288528i	$0.0931658\pi$
$450$	3.45492	+	10.6331i	0.162866	+	0.501251i
$451$	13.6631	−	15.5272i	0.643371	−	0.731146i
$452$	1.36475	−	4.20025i	0.0641922	−	0.197563i
$453$	0.500000	−	0.363271i	0.0234920	−	0.0170680i
$454$	50.7771			2.38309
$455$	−4.14590	+	3.01217i	−0.194363	+	0.141213i
$456$	−7.92705	−	5.75934i	−0.371218	−	0.269706i
$457$	9.94427	+	30.6053i	0.465173	+	1.43166i	0.858764	+	0.512371i	$0.171233\pi$
$457$	9.94427	+	30.6053i	0.465173	+	1.43166i	−0.393591	+	0.919286i	$0.628767\pi$
$458$	38.0132			1.77624
$459$	−1.42705	−	1.03681i	−0.0666090	−	0.0483943i
$460$	7.19756	−	22.1518i	0.335588	−	1.03283i
$461$	−4.62868	+	14.2456i	−0.215579	+	0.663484i	0.783533	+	0.621350i	$0.213416\pi$
$461$	−4.62868	+	14.2456i	−0.215579	+	0.663484i	−0.999112	+	0.0421337i	$0.986584\pi$
$462$	−2.76393	+	0.620541i	−0.128590	+	0.0288702i
$463$	1.89261	+	5.82485i	0.0879570	+	0.270704i	0.985354	−	0.170520i	$-0.0545446\pi$
$463$	1.89261	+	5.82485i	0.0879570	+	0.270704i	−0.897397	+	0.441223i	$0.854545\pi$
$464$	−3.30902	−	2.40414i	−0.153617	−	0.111609i
$465$	3.29180			0.152653
$466$	−14.0689	+	43.2996i	−0.651728	+	2.00581i
$467$	−3.69098	−	2.68166i	−0.170798	−	0.124092i	0.499102	−	0.866543i	$-0.333663\pi$
$467$	−3.69098	−	2.68166i	−0.170798	−	0.124092i	−0.669900	+	0.742451i	$0.733663\pi$
$468$	−5.56231	−	17.1190i	−0.257118	−	0.791327i
$469$	0.326238			0.0150643
$470$	−12.5000	+	9.08178i	−0.576582	+	0.418911i
$471$	−3.80902	+	2.76741i	−0.175510	+	0.127516i
$472$	3.09017	+	2.24514i	0.142237	+	0.103341i
$473$	3.07295	−	32.8380i	0.141294	−	1.50989i
$474$	11.0557			0.507806
$475$	−17.7254	+	12.8783i	−0.813298	+	0.590896i
$476$	−1.63525	+	1.18808i	−0.0749518	+	0.0544557i
$477$	0.809017	−	0.587785i	0.0370423	−	0.0269128i
$478$	−1.31966	+	4.06150i	−0.0603598	+	0.185769i
$479$	−8.07295	+	24.8460i	−0.368862	+	1.13524i	0.578664	+	0.815566i	$0.303574\pi$
$479$	−8.07295	+	24.8460i	−0.368862	+	1.13524i	−0.947527	+	0.319676i	$0.896426\pi$
$480$	4.63525	−	14.2658i	0.211569	−	0.651144i
$481$	−14.5623	+	44.8182i	−0.663984	+	2.04353i
$482$	7.70163	−	23.7032i	0.350799	−	1.07965i
$483$	1.07295	−	0.779543i	0.0488209	−	0.0354704i
$484$	−4.19756	−	32.7319i	−0.190798	−	1.48782i
$485$	−7.92705	−	24.3970i	−0.359949	−	1.10781i
$486$	−1.80902	−	1.31433i	−0.0820587	−	0.0596191i
$487$	−3.16312	−	2.29814i	−0.143335	−	0.104139i	0.513807	−	0.857906i	$-0.328235\pi$
$487$	−3.16312	−	2.29814i	−0.143335	−	0.104139i	−0.657142	+	0.753767i	$0.728235\pi$
$488$	7.13525	−	21.9601i	0.322998	−	0.994085i
$489$	−13.0000			−0.587880
$490$	−27.7254	−	20.1437i	−1.25251	−	0.910000i
$491$	12.8369	−	39.5079i	0.579320	−	1.78296i	−0.0416520	−	0.999132i	$-0.513262\pi$
$491$	12.8369	−	39.5079i	0.579320	−	1.78296i	0.620972	−	0.783832i	$-0.286738\pi$
$492$	5.78115	−	17.7926i	0.260635	−	0.802151i
$493$	−2.22949	+	6.86167i	−0.100411	+	0.309034i
$494$	47.5623	−	34.5560i	2.13993	−	1.55475i
$495$	−6.80902	−	2.93893i	−0.306043	−	0.132095i
$496$	−1.19098	−	0.865300i	−0.0534767	−	0.0388531i
$497$	0.454915	−	0.330515i	0.0204057	−	0.0148256i
$498$	7.98936	+	24.5887i	0.358012	+	1.10185i
$499$	−10.6631	−	7.74721i	−0.477347	−	0.346813i	0.322951	−	0.946416i	$-0.395325\pi$
$499$	−10.6631	−	7.74721i	−0.477347	−	0.346813i	−0.800298	+	0.599603i	$0.795325\pi$
$500$	27.1353	+	19.7149i	1.21353	+	0.881678i
$501$	2.98936	+	9.20029i	0.133555	+	0.411039i
$502$	−52.5238	+	38.1608i	−2.34425	+	1.70320i
$503$	6.00000			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$504$	−0.690983	+	0.502029i	−0.0307788	+	0.0223621i
$505$	−30.2254	−	21.9601i	−1.34501	−	0.977210i
$506$	13.1287	+	22.1518i	0.583641	+	0.984768i
$507$	23.0000			1.02147
$508$	12.8435	+	39.5281i	0.569836	+	1.75378i
$509$	14.0902	+	10.2371i	0.624536	+	0.453752i	0.854503	−	0.519447i	$-0.173862\pi$
$509$	14.0902	+	10.2371i	0.624536	+	0.453752i	−0.229967	+	0.973198i	$0.573862\pi$
$510$	−8.81966			−0.390541
$511$	0.472136			0.0208861
$512$	−9.04508	+	6.57164i	−0.399740	+	0.290428i
$513$	1.35410	−	4.16750i	0.0597851	−	0.184000i
$514$	8.12868	+	25.0175i	0.358541	+	1.10347i
$515$	−10.5279			−0.463913
$516$	−9.21885	−	28.3727i	−0.405837	−	1.24904i
$517$	0.954915	−	10.2044i	0.0419971	−	0.448787i
$518$	6.70820			0.294742
$519$	−4.10081	−	12.6210i	−0.180006	−	0.554001i
$520$	−24.2705	−	17.6336i	−1.06433	−	0.773283i
$521$	0.763932	+	2.35114i	0.0334685	+	0.103005i	0.966395	−	0.257061i	$-0.0827541\pi$
$521$	0.763932	+	2.35114i	0.0334685	+	0.103005i	−0.932927	+	0.360066i	$0.882754\pi$
$522$	−2.82624	+	8.69827i	−0.123701	+	0.380713i
$523$	7.20163			0.314905			0.157453	−	0.987527i	$-0.449672\pi$
$523$	7.20163			0.314905			0.157453	+	0.987527i	$0.449672\pi$
$524$	4.06231	+	2.95144i	0.177463	+	0.128934i
$525$	0.590170	+	1.81636i	0.0257571	+	0.0792723i
$526$	11.8328	−	36.4177i	0.515935	−	1.58789i
$527$	−0.802439	+	2.46965i	−0.0349548	+	0.107580i
$528$	1.69098	+	2.85317i	0.0735906	+	0.124168i
$529$	8.85410	+	6.43288i	0.384961	+	0.279691i
$530$	1.54508	−	4.75528i	0.0671142	−	0.206556i
$531$	−0.527864	+	1.62460i	−0.0229073	+	0.0705016i
$532$	−4.06231	−	2.95144i	−0.176123	−	0.127961i
$533$	30.2705	+	21.9928i	1.31116	+	0.952614i
$534$	29.9615	−	21.7683i	1.29656	−	0.942006i
$535$	9.96149	+	30.6583i	0.430673	+	1.32547i
$536$	0.590170	+	1.81636i	0.0254915	+	0.0784546i
$537$	−22.6525			−0.977526
$538$	9.43363	+	29.0337i	0.406713	+	1.25173i
$539$	22.1803	−	4.97980i	0.955375	−	0.214495i
$540$	−6.70820			−0.288675
$541$	−2.00000			−0.0859867			−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000			−0.0859867			−0.0429934	+	0.999075i	$0.513689\pi$
$542$	−14.3713	+	44.2304i	−0.617301	+	1.89986i
$543$	11.0172	+	8.00448i	0.472794	+	0.343505i
$544$	9.57295	+	6.95515i	0.410437	+	0.298200i
$545$	−39.5967			−1.69614
$546$	−1.58359	−	4.87380i	−0.0677715	−	0.208579i
$547$	44.2361			1.89140			0.945699	−	0.325044i	$-0.105379\pi$
$547$	44.2361			1.89140			0.945699	+	0.325044i	$0.105379\pi$
$548$	−20.1246	−	14.6214i	−0.859681	−	0.624595i
$549$	10.3262			0.440713
$550$	−36.1803	+	8.12299i	−1.54273	+	0.346366i
$551$	−17.9230			−0.763545
$552$	6.28115	+	4.56352i	0.267344	+	0.194237i
$553$	1.88854			0.0803091
$554$	12.7016	+	39.0916i	0.539640	+	1.66084i
$555$	14.2082	+	10.3229i	0.603105	+	0.438181i
$556$	−28.7705	−	20.9030i	−1.22014	−	0.886485i
$557$	−14.7254	−	10.6986i	−0.623936	−	0.453316i	0.230358	−	0.973106i	$-0.426010\pi$
$557$	−14.7254	−	10.6986i	−0.623936	−	0.453316i	−0.854294	+	0.519790i	$0.826010\pi$
$558$	−1.01722	+	3.13068i	−0.0430624	+	0.132532i
$559$	59.6656			2.52359
$560$	0.263932	−	0.812299i	0.0111532	−	0.0343259i
$561$	3.86475	−	4.39201i	0.163170	−	0.185431i
$562$	6.74671	+	20.7642i	0.284593	+	0.875887i
$563$	−42.5623			−1.79379			−0.896894	−	0.442246i	$-0.854182\pi$
$563$	−42.5623			−1.79379			−0.896894	+	0.442246i	$0.854182\pi$
$564$	−2.86475	−	8.81678i	−0.120628	−	0.371253i
$565$	2.66312	−	1.93487i	0.112038	−	0.0814006i
$566$	−30.5517	+	22.1971i	−1.28418	+	0.933013i
$567$	−0.309017	−	0.224514i	−0.0129775	−	0.00942870i
$568$	2.66312	+	1.93487i	0.111742	+	0.0811853i
$569$	−10.4271	+	32.0912i	−0.437125	+	1.34533i	0.453769	+	0.891119i	$0.350079\pi$
$569$	−10.4271	+	32.0912i	−0.437125	+	1.34533i	−0.890894	+	0.454212i	$0.849921\pi$
$570$	−6.77051	−	20.8375i	−0.283585	−	0.872786i
$571$	−10.6353	−	7.72696i	−0.445072	−	0.323363i	0.342575	−	0.939490i	$-0.388701\pi$
$571$	−10.6353	−	7.72696i	−0.445072	−	0.323363i	−0.787647	+	0.616127i	$0.788701\pi$
$572$	58.2492	−	13.0778i	2.43552	−	0.546809i
$573$	5.13525	−	15.8047i	0.214528	−	0.660250i
$574$	1.64590	−	5.06555i	0.0686985	−	0.211432i
$575$	14.0451	−	10.2044i	0.585721	−	0.425551i
$576$	10.5172	+	7.64121i	0.438218	+	0.318384i
$577$	−13.2361			−0.551025			−0.275512	−	0.961298i	$-0.588847\pi$
$577$	−13.2361			−0.551025			−0.275512	+	0.961298i	$0.588847\pi$
$578$	−9.59675	+	29.5358i	−0.399172	+	1.22853i
$579$	−1.73607	−	5.34307i	−0.0721485	−	0.222050i
$580$	8.47871	+	26.0948i	0.352059	+	1.08353i
$581$	1.36475	+	4.20025i	0.0566192	+	0.174256i
$582$	25.6525			1.06333
$583$	1.69098	+	2.85317i	0.0700334	+	0.118166i
$584$	0.854102	+	2.62866i	0.0353430	+	0.108775i
$585$	4.14590	−	12.7598i	0.171412	−	0.527551i
$586$	−17.1115	−	52.6636i	−0.706868	−	2.17552i
$587$	−0.500000	+	1.53884i	−0.0206372	+	0.0635148i	−0.960845	−	0.277087i	$-0.910631\pi$
$587$	−0.500000	+	1.53884i	−0.0206372	+	0.0635148i	0.940208	+	0.340602i	$0.110631\pi$
$588$	16.6353	−	12.0862i	0.686026	−	0.498427i
$589$	−6.45085			−0.265803
$590$	2.63932	+	8.12299i	0.108659	+	0.334418i
$591$	12.5172	+	9.09429i	0.514890	+	0.374089i
$592$	−2.42705	−	7.46969i	−0.0997512	−	0.307003i
$593$	−7.29180			−0.299438			−0.149719	−	0.988729i	$-0.547837\pi$
$593$	−7.29180			−0.299438			−0.149719	+	0.988729i	$0.547837\pi$
$594$	4.89919	−	5.56758i	0.201016	−	0.228441i
$595$	−1.50658			−0.0617637
$596$	39.6246	−	28.7890i	1.62309	−	1.17924i
$597$	10.7984			0.441948
$598$	−37.6869	+	27.3811i	−1.54113	+	1.11970i
$599$	−13.3262	−	41.0139i	−0.544495	−	1.67578i	−0.722187	−	0.691698i	$-0.756863\pi$
$599$	−13.3262	−	41.0139i	−0.544495	−	1.67578i	0.177692	−	0.984086i	$-0.443137\pi$
$600$	−9.04508	+	6.57164i	−0.369264	+	0.268286i
$601$	5.35410	+	3.88998i	0.218398	+	0.158676i	0.691605	−	0.722276i	$-0.256904\pi$
$601$	5.35410	+	3.88998i	0.218398	+	0.158676i	−0.473207	+	0.880951i	$0.656904\pi$
$602$	−2.62461	−	8.07772i	−0.106971	−	0.329223i
$603$	−0.690983	+	0.502029i	−0.0281390	+	0.0204442i
$604$	1.50000	+	1.08981i	0.0610341	+	0.0443439i
$605$	11.8090	−	21.5765i	0.480105	−	0.877211i
$606$	30.2254	−	21.9601i	1.22782	−	0.892066i
$607$	6.54508	−	20.1437i	0.265657	−	0.817608i	−0.725885	−	0.687817i	$-0.758569\pi$
$607$	6.54508	−	20.1437i	0.265657	−	0.817608i	0.991541	−	0.129791i	$-0.0414306\pi$
$608$	−9.08359	+	27.9564i	−0.368388	+	1.13378i
$609$	−0.482779	+	1.48584i	−0.0195632	+	0.0602093i
$610$	41.7705	−	30.3481i	1.69124	−	1.22876i
$611$	18.5410			0.750089
$612$	1.63525	−	5.03280i	0.0661013	−	0.203439i
$613$	−31.3885	−	22.8051i	−1.26777	−	0.921090i	−0.268660	−	0.963235i	$-0.586581\pi$
$613$	−31.3885	−	22.8051i	−1.26777	−	0.921090i	−0.999111	+	0.0421453i	$0.986581\pi$
$614$	−51.4058	−	37.3485i	−2.07457	−	1.50726i
$615$	11.2812	−	8.19624i	0.454900	−	0.330504i
$616$	−1.44427	−	2.43690i	−0.0581914	−	0.0981854i
$617$	34.4615	−	25.0377i	1.38737	−	1.00798i	0.391219	−	0.920298i	$-0.372053\pi$
$617$	34.4615	−	25.0377i	1.38737	−	1.00798i	0.996148	−	0.0876839i	$-0.0279465\pi$
$618$	3.25329	−	10.0126i	0.130866	−	0.402766i
$619$	7.16312	−	22.0458i	0.287910	−	0.886096i	−0.697601	−	0.716486i	$-0.745749\pi$
$619$	7.16312	−	22.0458i	0.287910	−	0.886096i	0.985511	−	0.169610i	$-0.0542507\pi$
$620$	3.05166	+	9.39205i	0.122558	+	0.377194i
$621$	−1.07295	+	3.30220i	−0.0430560	+	0.132513i
$622$	2.52380	−	7.76745i	0.101195	−	0.311447i
$623$	5.11803	−	3.71847i	0.205050	−	0.148977i
$624$	−4.85410	+	3.52671i	−0.194320	+	0.141181i
$625$	7.72542	+	23.7764i	0.309017	+	0.951057i
$626$	0.931116			0.0372149
$627$	13.3435	+	5.75934i	0.532886	+	0.230006i
$628$	−11.4271	−	8.30224i	−0.455989	−	0.331295i
$629$	−11.2082	+	8.14324i	−0.446900	+	0.324692i
$630$	−1.90983			−0.0760895
$631$	27.7082			1.10305			0.551523	−	0.834160i	$-0.314047\pi$
$631$	27.7082			1.10305			0.551523	+	0.834160i	$0.314047\pi$
$632$	3.41641	+	10.5146i	0.135897	+	0.418249i
$633$	−1.38197	−	1.00406i	−0.0549282	−	0.0399077i
$634$	−6.90983	+	21.2663i	−0.274424	+	0.844591i
$635$	−9.57295	+	29.4625i	−0.379891	+	1.16918i
$636$	2.42705	+	1.76336i	0.0962388	+	0.0699216i
$637$	12.7082	+	39.1118i	0.503517	+	1.54967i
$638$	−27.8500	−	12.0207i	−1.10259	−	0.475904i
$639$	−0.454915	+	1.40008i	−0.0179962	+	0.0553865i
$640$	35.0000			1.38350
$641$	2.42705	+	1.76336i	0.0958628	+	0.0696484i	0.634684	−	0.772772i	$-0.281130\pi$
$641$	2.42705	+	1.76336i	0.0958628	+	0.0696484i	−0.538821	+	0.842420i	$0.681130\pi$
$642$	−32.2361			−1.27226
$643$	−4.38197	−	13.4863i	−0.172808	−	0.531848i	0.826719	−	0.562615i	$-0.190205\pi$
$643$	−4.38197	−	13.4863i	−0.172808	−	0.531848i	−0.999527	+	0.0307676i	$0.990205\pi$
$644$	3.21885	+	2.33863i	0.126840	+	0.0921549i
$645$	6.87132	−	21.1478i	0.270558	−	0.832692i
$646$	17.2837			0.680017
$647$	−30.1803	+	21.9273i	−1.18651	+	0.862051i	−0.992891	−	0.119025i	$-0.962023\pi$
$647$	−30.1803	+	21.9273i	−1.18651	+	0.862051i	−0.193620	+	0.981077i	$0.562023\pi$
$648$	0.690983	−	2.12663i	0.0271444	−	0.0835418i
$649$	−5.20163	−	2.24514i	−0.204182	−	0.0881294i
$650$	−20.7295	−	63.7988i	−0.813077	−	2.50240i
$651$	−0.173762	+	0.534785i	−0.00681027	+	0.0209599i
$652$	−12.0517	−	37.0912i	−0.471980	−	1.45260i
$653$	−6.50000	−	20.0049i	−0.254365	−	0.782854i	−0.993954	−	0.109796i	$-0.964980\pi$
$653$	−6.50000	−	20.0049i	−0.254365	−	0.782854i	0.739590	−	0.673058i	$-0.235020\pi$
$654$	12.2361	−	37.6587i	0.478468	−	1.47257i
$655$	1.15654	+	3.55947i	0.0451898	+	0.139080i
$656$	−6.23607			−0.243478
$657$	−1.00000	+	0.726543i	−0.0390137	+	0.0283451i
$658$	−0.815595	−	2.51014i	−0.0317952	−	0.0978556i
$659$	−8.40983	−	25.8828i	−0.327600	−	1.00825i	−0.970253	−	0.242093i	$-0.922166\pi$
$659$	−8.40983	−	25.8828i	−0.327600	−	1.00825i	0.642653	−	0.766158i	$-0.277834\pi$
$660$	2.07295	−	22.1518i	0.0806894	−	0.862258i
$661$	4.94427	−	15.2169i	0.192310	−	0.591869i	−0.807688	−	0.589611i	$-0.799281\pi$
$661$	4.94427	−	15.2169i	0.192310	−	0.591869i	0.999997	−	0.00225826i	$-0.000718826\pi$
$662$	55.7771			2.16784
$663$	8.56231	+	6.22088i	0.332532	+	0.241599i
$664$	−20.9164	+	15.1967i	−0.811714	+	0.589745i
$665$	−1.15654	−	3.55947i	−0.0448487	−	0.138030i
$666$	−14.2082	+	10.3229i	−0.550557	+	0.400003i
$667$	14.2016			0.549889
$668$	−23.4787	+	17.0583i	−0.908419	+	0.660005i
$669$	0.427051	+	1.31433i	0.0165107	+	0.0508148i
$670$	−1.31966	+	4.06150i	−0.0509829	+	0.156909i
$671$	−3.19098	+	34.0993i	−0.123187	+	1.31639i
$672$	2.07295	+	1.50609i	0.0799657	+	0.0580985i
$673$	11.2533	+	8.17599i	0.433782	+	0.315161i	0.783160	−	0.621821i	$-0.213607\pi$
$673$	11.2533	+	8.17599i	0.433782	+	0.315161i	−0.349377	+	0.936982i	$0.613607\pi$
$674$	50.8779	−	36.9650i	1.95974	−	1.42384i
$675$	−4.04508	−	2.93893i	−0.155695	−	0.113119i
$676$	21.3222	+	65.6229i	0.820084	+	2.52396i
$677$	5.00000			0.192166			0.0960828	−	0.995373i	$-0.469369\pi$
$677$	5.00000			0.192166			0.0960828	+	0.995373i	$0.469369\pi$
$678$	1.01722	+	3.13068i	0.0390661	+	0.120233i
$679$	4.38197			0.168164
$680$	−2.72542	−	8.38800i	−0.104515	−	0.321665i
$681$	−18.3713	+	13.3475i	−0.703991	+	0.511479i
$682$	−10.0238	−	4.32650i	−0.383831	−	0.165670i
$683$	13.2533	−	9.62908i	0.507123	−	0.368446i	−0.304608	−	0.952478i	$-0.598525\pi$
$683$	13.2533	−	9.62908i	0.507123	−	0.368446i	0.811731	+	0.584031i	$0.198525\pi$
$684$	13.1459			0.502646
$685$	−5.72949	−	17.6336i	−0.218913	−	0.673744i
$686$	9.57295	−	6.95515i	0.365497	−	0.265549i
$687$	−13.7533	+	9.99235i	−0.524721	+	0.381232i
$688$	−8.04508	+	5.84510i	−0.306716	+	0.222842i
$689$	−4.85410	+	3.52671i	−0.184927	+	0.134357i
$690$	5.36475	+	16.5110i	0.204232	+	0.628563i
$691$	39.4164			1.49947			0.749735	−	0.661738i	$-0.230181\pi$
$691$	39.4164			1.49947			0.749735	+	0.661738i	$0.230181\pi$
$692$	32.2082	−	23.4006i	1.22437	−	0.889558i
$693$	0.836881	−	0.951057i	0.0317905	−	0.0361276i
$694$	−0.100813	+	0.0732450i	−0.00382681	+	0.00278034i
$695$	−8.19098	−	25.2093i	−0.310702	−	0.956241i
$696$	−9.14590			−0.346674
$697$	3.39919	+	10.4616i	0.128753	+	0.396262i
$698$	34.2705			1.29716
$699$	−6.29180	−	19.3642i	−0.237978	−	0.732420i
$700$	−4.63525	+	3.36771i	−0.175196	+	0.127287i
$701$	−16.5902	+	12.0535i	−0.626602	+	0.455253i	−0.855221	−	0.518263i	$-0.826579\pi$
$701$	−16.5902	+	12.0535i	−0.626602	+	0.455253i	0.228619	+	0.973516i	$0.426579\pi$
$702$	10.8541	+	7.88597i	0.409662	+	0.297637i
$703$	−27.8435	−	20.2295i	−1.05014	−	0.762968i
$704$	−28.4828	+	32.3687i	−1.07349	+	1.21994i
$705$	2.13525	−	6.57164i	0.0804184	−	0.247502i
$706$	−3.84346	−	11.8290i	−0.144650	−	0.445188i
$707$	5.16312	−	3.75123i	0.194179	−	0.141079i
$708$	−5.12461			−0.192595
$709$	22.2254	−	16.1477i	0.834693	−	0.606440i	−0.0861899	−	0.996279i	$-0.527469\pi$
$709$	22.2254	−	16.1477i	0.834693	−	0.606440i	0.920883	+	0.389839i	$0.127469\pi$
$710$	2.27458	+	7.00042i	0.0853633	+	0.262721i
$711$	−4.00000	+	2.90617i	−0.150012	+	0.108990i
$712$	29.9615	+	21.7683i	1.12285	+	0.815801i
$713$	5.11146			0.191426
$714$	0.465558	−	1.43284i	0.0174231	−	0.0536227i
$715$	40.8541	+	17.6336i	1.52786	+	0.659458i
$716$	−21.0000	−	64.6314i	−0.784807	−	2.41539i
$717$	−0.590170	−	1.81636i	−0.0220403	−	0.0678331i
$718$	67.6869	−	49.1774i	2.52605	−	1.83529i
$719$	−10.1459			−0.378378			−0.189189	−	0.981941i	$-0.560586\pi$
$719$	−10.1459			−0.378378			−0.189189	+	0.981941i	$0.560586\pi$
$720$	0.690983	+	2.12663i	0.0257514	+	0.0792547i
$721$	0.555728	−	1.71036i	0.0206964	−	0.0636970i
$722$	0.139320	+	0.428784i	0.00518496	+	0.0159577i
$723$	3.44427	+	10.6004i	0.128094	+	0.394232i
$724$	−12.6246	+	38.8546i	−0.469190	+	1.44402i
$725$	−6.31966	+	19.4499i	−0.234706	+	0.722352i
$726$	16.8713	+	17.8986i	0.626154	+	0.664278i
$727$	1.31966	−	4.06150i	0.0489435	−	0.150633i	−0.923598	−	0.383363i	$-0.874766\pi$
$727$	1.31966	−	4.06150i	0.0489435	−	0.150633i	0.972541	+	0.232730i	$0.0747659\pi$
$728$	4.14590	−	3.01217i	0.153657	−	0.111638i
$729$	1.00000			0.0370370
$730$	−1.90983	+	5.87785i	−0.0706860	+	0.217549i
$731$	14.1910	+	10.3104i	0.524872	+	0.381342i
$732$	9.57295	+	29.4625i	0.353826	+	1.08897i
$733$	−33.5623			−1.23965			−0.619826	−	0.784739i	$-0.712797\pi$
$733$	−33.5623			−1.23965			−0.619826	+	0.784739i	$0.712797\pi$
$734$	−57.4230	−	41.7202i	−2.11952	−	1.53992i
$735$	15.3262			0.565317
$736$	7.19756	−	22.1518i	0.265306	−	0.816527i
$737$	−1.44427	−	2.43690i	−0.0532004	−	0.0897643i
$738$	4.30902	+	13.2618i	0.158617	+	0.488173i
$739$	2.95492	+	2.14687i	0.108698	+	0.0789739i	0.640807	−	0.767702i	$-0.278600\pi$
$739$	2.95492	+	2.14687i	0.108698	+	0.0789739i	−0.532108	+	0.846676i	$0.678600\pi$
$740$	−16.2812	+	50.1082i	−0.598507	+	1.84202i
$741$	−8.12461	+	25.0050i	−0.298465	+	0.918581i
$742$	0.690983	+	0.502029i	0.0253668	+	0.0184300i
$743$	−3.01064	−	9.26581i	−0.110450	−	0.339929i	0.880521	−	0.474007i	$-0.157193\pi$
$743$	−3.01064	−	9.26581i	−0.110450	−	0.339929i	−0.990971	+	0.134078i	$0.957193\pi$
$744$	−3.29180			−0.120683
$745$	36.5066			1.33750
$746$	59.7599	−	43.4181i	2.18796	−	1.58965i
$747$	−9.35410	−	6.79615i	−0.342249	−	0.248658i
$748$	16.1140	+	6.95515i	0.589185	+	0.254306i
$749$	−5.50658			−0.201206
$750$	−25.0000			−0.912871
$751$	3.28115	−	2.38390i	0.119731	−	0.0869896i	−0.526308	−	0.850294i	$-0.676424\pi$
$751$	3.28115	−	2.38390i	0.119731	−	0.0869896i	0.646039	+	0.763304i	$0.276424\pi$
$752$	−2.50000	+	1.81636i	−0.0911656	+	0.0662357i
$753$	8.97214	−	27.6134i	0.326963	−	1.00629i
$754$	16.9574	−	52.1896i	0.617553	−	1.90063i
$755$	0.427051	+	1.31433i	0.0155420	+	0.0478333i
$756$	0.354102	−	1.08981i	0.0128786	−	0.0396361i
$757$	−13.0106	+	40.0426i	−0.472880	+	1.45537i	0.375916	+	0.926654i	$0.377328\pi$
$757$	−13.0106	+	40.0426i	−0.472880	+	1.45537i	−0.848796	+	0.528721i	$0.822672\pi$
$758$	−36.4443	+	26.4783i	−1.32372	+	0.961736i
$759$	−10.5729	−	4.56352i	−0.383774	−	0.165645i
$760$	17.7254	−	12.8783i	0.642969	−	0.467144i
$761$	−27.1976	−	19.7602i	−0.985911	−	0.716306i	−0.0268890	−	0.999638i	$-0.508560\pi$
$761$	−27.1976	−	19.7602i	−0.985911	−	0.716306i	−0.959022	+	0.283332i	$0.908560\pi$
$762$	−25.0623	−	18.2088i	−0.907912	−	0.659636i
$763$	2.09017	−	6.43288i	0.0756692	−	0.232886i
$764$	49.8541			1.80366
$765$	3.19098	−	2.31838i	0.115370	−	0.0838214i
$766$	26.3050	−	80.9583i	0.950437	−	2.92514i
$767$	3.16718	−	9.74759i	0.114360	−	0.351965i
$768$	−2.78115	+	8.55951i	−0.100356	+	0.308865i
$769$	−27.1803	+	19.7477i	−0.980148	+	0.712119i	−0.957742	−	0.287630i	$-0.907133\pi$
$769$	−27.1803	+	19.7477i	−0.980148	+	0.712119i	−0.0224064	+	0.999749i	$0.507133\pi$
$770$	0.590170	−	6.30664i	0.0212682	−	0.227275i
$771$	−9.51722	−	6.91467i	−0.342754	−	0.249026i
$772$	13.6353	−	9.90659i	0.490744	−	0.356546i
$773$	8.93363	+	27.4949i	0.321320	+	0.988922i	0.973074	+	0.230492i	$0.0740335\pi$
$773$	8.93363	+	27.4949i	0.321320	+	0.988922i	−0.651754	+	0.758430i	$0.725967\pi$
$774$	17.9894	+	13.0700i	0.646614	+	0.469793i
$775$	−2.27458	+	7.00042i	−0.0817052	+	0.251463i
$776$	7.92705	+	24.3970i	0.284565	+	0.875800i
$777$	−2.42705	+	1.76336i	−0.0870700	+	0.0632600i
$778$	−44.2705			−1.58717
$779$	−22.1074	+	16.0620i	−0.792079	+	0.575479i
$780$	40.2492			1.44115
$781$	−4.48278	−	1.93487i	−0.160406	−	0.0692351i
$782$	−13.6950			−0.489734
$783$	−1.26393	−	3.88998i	−0.0451692	−	0.139017i
$784$	−5.54508	−	4.02874i	−0.198039	−	0.143884i
$785$	−3.25329	−	10.0126i	−0.116115	−	0.357365i
$786$	−3.74265			−0.133496
$787$	−4.73607	+	3.44095i	−0.168823	+	0.122657i	−0.668988	−	0.743273i	$-0.733272\pi$
$787$	−4.73607	+	3.44095i	−0.168823	+	0.122657i	0.500166	+	0.865930i	$0.333272\pi$
$788$	−14.3435	+	44.1446i	−0.510965	+	1.57259i
$789$	5.29180	+	16.2865i	0.188393	+	0.579814i
$790$	−7.63932	+	23.5114i	−0.271795	+	0.836498i
$791$	0.173762	+	0.534785i	0.00617827	+	0.0190148i
$792$	6.80902	+	2.93893i	0.241948	+	0.104430i
$793$	−61.9574			−2.20017
$794$	16.3197	+	50.2267i	0.579163	+	1.78248i
$795$	0.690983	+	2.12663i	0.0245066	+	0.0754237i
$796$	10.0106	+	30.8096i	0.354818	+	1.09202i
$797$	9.79837	−	30.1563i	0.347076	−	1.06819i	−0.613387	−	0.789783i	$-0.710193\pi$
$797$	9.79837	−	30.1563i	0.347076	−	1.06819i	0.960463	−	0.278408i	$-0.0898067\pi$
$798$	3.74265			0.132488
$799$	4.40983	+	3.20393i	0.156009	+	0.113347i
$800$	27.1353	+	19.7149i	0.959376	+	0.697028i
$801$	−5.11803	+	15.7517i	−0.180837	+	0.556559i
$802$	7.19756	−	22.1518i	0.254155	−	0.782208i
$803$	−2.09017	−	3.52671i	−0.0737605	−	0.124455i
$804$	−2.07295	−	1.50609i	−0.0731073	−	0.0531155i
$805$	0.916408	+	2.82041i	0.0322991	+	0.0994065i
$806$	6.10333	−	18.7841i	0.214980	−	0.661642i
$807$	−11.0451	−	8.02472i	−0.388805	−	0.282484i
$808$	30.2254	+	21.9601i	1.06333	+	0.772552i
$809$	−31.3156	+	22.7521i	−1.10100	+	0.799922i	−0.981222	−	0.192879i	$-0.938217\pi$
$809$	−31.3156	+	22.7521i	−1.10100	+	0.799922i	−0.119775	+	0.992801i	$0.538217\pi$
$810$	4.04508	−	2.93893i	0.142130	−	0.103263i
$811$	−3.74671	−	11.5312i	−0.131565	−	0.404915i	0.863475	−	0.504392i	$-0.168283\pi$
$811$	−3.74671	−	11.5312i	−0.131565	−	0.404915i	−0.995040	+	0.0994766i	$0.968283\pi$
$812$	−4.68692			−0.164479
$813$	−6.42705	−	19.7804i	−0.225407	−	0.693730i
$814$	−29.6976	−	50.1082i	−1.04090	−	1.75629i
$815$	8.98278	−	27.6462i	0.314653	−	0.968402i
$816$	−1.76393			−0.0617500
$817$	−13.4656	+	41.4427i	−0.471100	+	1.44990i
$818$	−28.8435	−	20.9560i	−1.00849	−	0.732709i
$819$	1.85410	+	1.34708i	0.0647876	+	0.0470709i
$820$	33.8435	+	24.5887i	1.18186	+	0.858675i
$821$	−11.2188	−	34.5281i	−0.391540	−	1.20504i	−0.931623	−	0.363426i	$-0.881607\pi$
$821$	−11.2188	−	34.5281i	−0.391540	−	1.20504i	0.540083	−	0.841612i	$-0.318393\pi$
$822$	18.5410			0.646692
$823$	−24.3156	−	17.6663i	−0.847588	−	0.615809i	0.0768917	−	0.997039i	$-0.475500\pi$
$823$	−24.3156	−	17.6663i	−0.847588	−	0.615809i	−0.924480	+	0.381230i	$0.875500\pi$
$824$	10.5279			0.366756
$825$	10.9549	−	12.4495i	0.381401	−	0.433436i
$826$	−1.45898			−0.0507644
$827$	1.57295	+	1.14281i	0.0546968	+	0.0397395i	0.614798	−	0.788685i	$-0.289238\pi$
$827$	1.57295	+	1.14281i	0.0546968	+	0.0397395i	−0.560101	+	0.828424i	$0.689238\pi$
$828$	−10.4164			−0.361995
$829$	12.5795	+	38.7158i	0.436905	+	1.34466i	0.891122	+	0.453764i	$0.149919\pi$
$829$	12.5795	+	38.7158i	0.436905	+	1.34466i	−0.454217	+	0.890891i	$0.650081\pi$
$830$	−57.8115			−2.00667
$831$	−14.8713	−	10.8046i	−0.515880	−	0.374809i
$832$	−63.1033	−	45.8472i	−2.18771	−	1.58947i
$833$	−3.73607	+	11.4984i	−0.129447	+	0.398397i
$834$	26.5066			0.917848
$835$	−21.6312			−0.748578
$836$	−4.06231	+	43.4104i	−0.140498	+	1.50138i
$837$	−0.454915	−	1.40008i	−0.0157242	−	0.0483940i
$838$	68.9443			2.38164
$839$	10.2639	+	31.5891i	0.354350	+	1.09058i	0.956385	+	0.292108i	$0.0943568\pi$
$839$	10.2639	+	31.5891i	0.354350	+	1.09058i	−0.602035	+	0.798470i	$0.705643\pi$
$840$	−0.590170	−	1.81636i	−0.0203628	−	0.0626702i
$841$	9.92705	−	7.21242i	0.342312	−	0.248704i
$842$	37.9508	+	27.5729i	1.30787	+	0.950225i
$843$	−7.89919	−	5.73910i	−0.272062	−	0.197665i
$844$	1.58359	−	4.87380i	0.0545095	−	0.167763i
$845$	−15.8926	+	48.9124i	−0.546722	+	1.68264i
$846$	5.59017	+	4.06150i	0.192194	+	0.139637i
$847$	2.88197	+	3.05744i	0.0990255	+	0.105055i
$848$	0.309017	−	0.951057i	0.0106117	−	0.0326594i
$849$	5.21885	−	16.0620i	0.179110	−	0.551245i
$850$	6.09424	−	18.7561i	0.209031	−	0.643330i
$851$	22.0623	+	16.0292i	0.756286	+	0.549474i
$852$	−4.41641			−0.151304
$853$	−1.56231	+	4.80828i	−0.0534923	+	0.164632i	−0.974234	−	0.225541i	$-0.927585\pi$
$853$	−1.56231	+	4.80828i	−0.0534923	+	0.164632i	0.920741	+	0.390174i	$0.127585\pi$
$854$	2.72542	+	8.38800i	0.0932621	+	0.287031i
$855$	7.92705	+	5.75934i	0.271099	+	0.196965i
$856$	−9.96149	−	30.6583i	−0.340477	−	1.04788i
$857$	−34.2705			−1.17066			−0.585329	−	0.810796i	$-0.699035\pi$
$857$	−34.2705			−1.17066			−0.585329	+	0.810796i	$0.699035\pi$
$858$	−29.3951	+	33.4055i	−1.00353	+	1.14044i
$859$	−7.78115	−	23.9479i	−0.265490	−	0.817093i	−0.991580	−	0.129494i	$-0.958665\pi$
$859$	−7.78115	−	23.9479i	−0.265490	−	0.817093i	0.726091	−	0.687599i	$-0.241335\pi$
$860$	66.7082			2.27473
$861$	0.736068	+	2.26538i	0.0250851	+	0.0772041i
$862$	3.45492	−	10.6331i	0.117675	−	0.362166i
$863$	25.7254	−	18.6906i	0.875704	−	0.636236i	−0.0564077	−	0.998408i	$-0.517965\pi$
$863$	25.7254	−	18.6906i	0.875704	−	0.636236i	0.932111	+	0.362172i	$0.117965\pi$
$864$	−6.70820			−0.228218
$865$	29.6738			1.00894
$866$	−12.7639	−	9.27354i	−0.433736	−	0.315128i
$867$	−4.29180	−	13.2088i	−0.145757	−	0.448594i
$868$	−1.68692			−0.0572577
$869$	−8.36068	−	14.1068i	−0.283617	−	0.478542i
$870$	−16.5451	−	12.0207i	−0.560931	−	0.407540i
$871$	4.14590	−	3.01217i	0.140478	−	0.102064i
$872$	39.5967			1.34092
$873$	−9.28115	+	6.74315i	−0.314119	+	0.228221i
$874$	−10.5132	−	32.3562i	−0.355613	−	1.09446i
$875$	−4.27051			−0.144370
$876$	−3.00000	−	2.17963i	−0.101361	−	0.0736428i
$877$	12.7361	+	39.1976i	0.430066	+	1.32361i	0.898059	+	0.439876i	$0.144978\pi$
$877$	12.7361	+	39.1976i	0.430066	+	1.32361i	−0.467992	+	0.883733i	$0.655022\pi$
$878$	−35.8156	+	26.0216i	−1.20872	+	0.878185i
$879$	20.0344	+	14.5559i	0.675745	+	0.490957i
$880$	−7.23607	+	1.62460i	−0.243928	+	0.0547652i
$881$	4.73607	−	3.44095i	0.159562	−	0.115929i	−0.505139	−	0.863038i	$-0.668559\pi$
$881$	4.73607	−	3.44095i	0.159562	−	0.115929i	0.664701	+	0.747109i	$0.268559\pi$
$882$	−4.73607	+	14.5761i	−0.159472	+	0.490803i
$883$	−12.0000	+	36.9322i	−0.403832	+	1.24287i	0.518034	+	0.855360i	$0.326664\pi$
$883$	−12.0000	+	36.9322i	−0.403832	+	1.24287i	−0.921866	+	0.387508i	$0.873336\pi$
$884$	−9.81153	+	30.1968i	−0.329997	+	1.01563i
$885$	−3.09017	−	2.24514i	−0.103875	−	0.0754696i
$886$	−25.9017			−0.870185
$887$	11.5238	−	35.4666i	0.386931	−	1.19085i	−0.548138	−	0.836388i	$-0.684663\pi$
$887$	11.5238	−	35.4666i	0.386931	−	1.19085i	0.935070	−	0.354464i	$-0.115337\pi$
$888$	−14.2082	−	10.3229i	−0.476796	−	0.346413i
$889$	−4.28115	−	3.11044i	−0.143585	−	0.104321i
$890$	25.5902	+	78.7584i	0.857784	+	2.63999i
$891$	−0.309017	+	3.30220i	−0.0103525	+	0.110628i
$892$	−3.35410	+	2.43690i	−0.112304	+	0.0815934i
$893$	−4.18441	+	12.8783i	−0.140026	+	0.430955i
$894$	−11.2812	+	34.7198i	−0.377298	+	1.16120i
$895$	15.6525	−	48.1734i	0.523205	−	1.61026i
$896$	−1.84752	+	5.68609i	−0.0617215	+	0.189959i
$897$	6.43769	−	19.8132i	0.214948	−	0.661543i
$898$	−1.64590	+	1.19581i	−0.0549243	+	0.0399049i
$899$	−4.87132	+	3.53922i	−0.162468	+	0.118040i
$900$	4.63525	−	14.2658i	0.154508	−	0.475528i
$901$	−1.76393			−0.0587651
$902$	−45.1246	+	10.1311i	−1.50249	+	0.337329i
$903$	3.07295	+	2.23263i	0.102261	+	0.0742972i
$904$	−2.66312	+	1.93487i	−0.0885740	+	0.0643528i
$905$	−24.6353	+	17.8986i	−0.818904	+	0.594968i
$906$	−1.38197			−0.0459127
$907$	14.2467	+	43.8469i	0.473054	+	1.45591i	0.848564	+	0.529093i	$0.177468\pi$
$907$	14.2467	+	43.8469i	0.473054	+	1.45591i	−0.375510	+	0.926818i	$0.622532\pi$
$908$	−55.1140	−	40.0426i	−1.82902	−	1.32886i
$909$	−5.16312	+	15.8904i	−0.171250	+	0.527053i
$910$	11.4590			0.379861
$911$	−15.4271	−	11.2084i	−0.511121	−	0.371351i	0.302128	−	0.953267i	$-0.402303\pi$
$911$	−15.4271	−	11.2084i	−0.511121	−	0.371351i	−0.813249	+	0.581916i	$0.802303\pi$
$912$	−1.35410	−	4.16750i	−0.0448388	−	0.138000i
$913$	25.3328	−	28.7890i	0.838394	−	0.952776i
$914$	22.2361	−	68.4356i	0.735504	−	2.26365i
$915$	−7.13525	+	21.9601i	−0.235884	+	0.725977i
$916$	−41.2599	−	29.9770i	−1.36326	−	0.990470i
$917$	−0.639320			−0.0211122
$918$	1.21885	+	3.75123i	0.0402279	+	0.123809i
$919$	−14.2812	−	10.3759i	−0.471092	−	0.342268i	0.326775	−	0.945102i	$-0.394038\pi$
$919$	−14.2812	−	10.3759i	−0.471092	−	0.342268i	−0.797867	+	0.602834i	$0.794038\pi$
$920$	−14.0451	+	10.2044i	−0.463053	+	0.336428i
$921$	28.4164			0.936352
$922$	27.0967	−	19.6869i	0.892384	−	0.648355i
$923$	2.72949	−	8.40051i	0.0898423	−	0.276506i
$924$	3.48936	+	1.50609i	0.114791	+	0.0495466i
$925$	−31.7705	+	23.0826i	−1.04461	+	0.758952i
$926$	4.23200	−	13.0248i	0.139072	−	0.428020i
$927$	1.45492	+	4.47777i	0.0477857	+	0.147069i
$928$	8.47871	+	26.0948i	0.278327	+	0.856604i
$929$	−15.5066	+	47.7243i	−0.508754	+	1.56578i	0.285612	+	0.958345i	$0.407803\pi$
$929$	−15.5066	+	47.7243i	−0.508754	+	1.56578i	−0.794366	+	0.607439i	$0.792197\pi$
$930$	−5.95492	−	4.32650i	−0.195269	−	0.141871i
$931$	−30.0344			−0.984339
$932$	49.4164	−	35.9031i	1.61869	−	1.17605i
$933$	1.12868	+	3.47371i	0.0369512	+	0.113724i
$934$	3.15248	+	9.70232i	0.103152	+	0.317470i
$935$	6.66970	+	11.2537i	0.218122	+	0.368035i
$936$	−4.14590	+	12.7598i	−0.135513	+	0.417066i
$937$	18.4508			0.602763			0.301381	−	0.953504i	$-0.402552\pi$
$937$	18.4508			0.602763			0.301381	+	0.953504i	$0.402552\pi$
$938$	−0.590170	−	0.428784i	−0.0192697	−	0.0140003i
$939$	−0.336881	+	0.244758i	−0.0109937	+	0.00798739i
$940$	20.7295			0.676121
$941$	5.04508	−	3.66547i	0.164465	−	0.119491i	−0.502508	−	0.864572i	$-0.667589\pi$
$941$	5.04508	−	3.66547i	0.164465	−	0.119491i	0.666973	+	0.745081i	$0.267589\pi$
$942$	10.5279			0.343016
$943$	17.5172	−	12.7270i	0.570439	−	0.414448i
$944$	0.527864	+	1.62460i	0.0171805	+	0.0528762i
$945$	0.690983	−	0.502029i	0.0224777	−	0.0163310i
$946$	−48.7188	+	55.3655i	−1.58399	+	1.80009i
$947$	−17.5451	−	12.7473i	−0.570139	−	0.414230i	0.265017	−	0.964244i	$-0.414622\pi$
$947$	−17.5451	−	12.7473i	−0.570139	−	0.414230i	−0.835156	+	0.550014i	$0.814622\pi$
$948$	−12.0000	−	8.71851i	−0.389742	−	0.283164i
$949$	6.00000	−	4.35926i	0.194768	−	0.141507i
$950$	48.9919			1.58951
$951$	−3.09017	−	9.51057i	−0.100206	−	0.308401i
$952$	1.50658			0.0488285
$953$	5.02786	+	15.4742i	0.162868	+	0.501258i	0.998873	−	0.0474651i	$-0.0151143\pi$
$953$	5.02786	+	15.4742i	0.162868	+	0.501258i	−0.836004	+	0.548723i	$0.815114\pi$
$954$	−2.23607			−0.0723954
$955$	30.0623	+	21.8415i	0.972793	+	0.706776i
$956$	4.63525	−	3.36771i	0.149915	−	0.108920i
$957$	13.2361	−	2.97168i	0.427861	−	0.0960608i
$958$	47.2599	−	34.3363i	1.52690	−	1.10936i
$959$	3.16718			0.102274
$960$	−23.5172	+	17.0863i	−0.759015	+	0.551457i
$961$	23.3262	−	16.9475i	0.752459	−	0.546694i
$962$	85.2492	−	61.9372i	2.74855	−	1.99694i
$963$	11.6631	−	8.47375i	0.375839	−	0.273063i
$964$	−27.0517	+	19.6542i	−0.871275	+	0.633019i
$965$	12.5623			0.404395
$966$	−2.96556			−0.0954153
$967$	−6.57295	+	4.77553i	−0.211372	+	0.153571i	−0.688434	−	0.725299i	$-0.741702\pi$
$967$	−6.57295	+	4.77553i	−0.211372	+	0.153571i	0.477062	+	0.878869i	$0.341702\pi$
$968$	−11.8090	+	21.5765i	−0.379556	+	0.693496i
$969$	−6.25329	+	4.54328i	−0.200885	+	0.145951i
$970$	−17.7254	+	54.5532i	−0.569129	+	1.75160i
$971$	−36.1246			−1.15929			−0.579647	−	0.814868i	$-0.696810\pi$
$971$	−36.1246			−1.15929			−0.579647	+	0.814868i	$0.696810\pi$
$972$	0.927051	+	2.85317i	0.0297352	+	0.0915155i
$973$	4.52786			0.145157
$974$	2.70163	+	8.31475i	0.0865657	+	0.266422i
$975$	24.2705	+	17.6336i	0.777278	+	0.564726i
$976$	8.35410	−	6.06961i	0.267408	−	0.194283i
$977$	26.4164	+	19.1926i	0.845136	+	0.614027i	0.923801	−	0.382874i	$-0.125066\pi$
$977$	26.4164	+	19.1926i	0.845136	+	0.614027i	−0.0786648	+	0.996901i	$0.525066\pi$
$978$	23.5172	+	17.0863i	0.751998	+	0.546358i
$979$	−50.4336	−	21.7683i	−1.61187	−	0.695718i
$980$	14.2082	+	43.7284i	0.453864	+	1.39685i
$981$	5.47214	+	16.8415i	0.174712	+	0.537708i
$982$	−75.1484	+	54.5985i	−2.39808	+	1.74231i
$983$	8.94427			0.285278			0.142639	−	0.989775i	$-0.454441\pi$
$983$	8.94427			0.285278			0.142639	+	0.989775i	$0.454441\pi$
$984$	−11.2812	+	8.19624i	−0.359630	+	0.261287i
$985$	−27.9894	+	20.3355i	−0.891815	+	0.647942i
$986$	13.0517	−	9.48259i	0.415650	−	0.301987i
$987$	0.954915	+	0.693786i	0.0303953	+	0.0220835i
$988$	−78.8754			−2.50936
$989$	10.6697	−	32.8380i	0.339277	−	1.04419i
$990$	8.45492	+	14.2658i	0.268715	+	0.453398i
$991$	−4.43363	−	13.6453i	−0.140839	−	0.433457i	0.855614	−	0.517615i	$-0.173180\pi$
$991$	−4.43363	−	13.6453i	−0.140839	−	0.433457i	−0.996452	+	0.0841576i	$0.973180\pi$
$992$	3.05166	+	9.39205i	0.0968904	+	0.298198i
$993$	−20.1803	+	14.6619i	−0.640404	+	0.465281i
$994$	−1.25735			−0.0398809
$995$	−7.46149	+	22.9641i	−0.236545	+	0.728011i
$996$	10.7188	−	32.9892i	0.339640	−	1.04530i
$997$	8.15248	+	25.0907i	0.258192	+	0.794632i	0.993184	+	0.116557i	$0.0371856\pi$
$997$	8.15248	+	25.0907i	0.258192	+	0.794632i	−0.734993	+	0.678075i	$0.762814\pi$
$998$	9.10739	+	28.0297i	0.288289	+	0.887264i
$999$	2.42705	−	7.46969i	0.0767885	−	0.236331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.p.a.196.1	yes	4
11.5	even	5		825.2.r.a.346.1	yes	4
25.6	even	5		825.2.r.a.31.1	yes	4
275.181	even	5	inner	825.2.p.a.181.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.p.a.181.1	✓	4	275.181	even	5	inner
825.2.p.a.196.1	yes	4	1.1	even	1	trivial
825.2.r.a.31.1	yes	4	25.6	even	5
825.2.r.a.346.1	yes	4	11.5	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.p (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80902 - 1.31433i) q^{2} +1.00000 q^{3} +(0.927051 + 2.85317i) q^{4} +(-0.690983 + 2.12663i) q^{5} +(-1.80902 - 1.31433i) q^{6} +(-0.309017 - 0.224514i) q^{7} +(0.690983 - 2.12663i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.80902 - 1.31433i) q^{2} +1.00000 q^{3} +(0.927051 + 2.85317i) q^{4} +(-0.690983 + 2.12663i) q^{5} +(-1.80902 - 1.31433i) q^{6} +(-0.309017 - 0.224514i) q^{7} +(0.690983 - 2.12663i) q^{8} +1.00000 q^{9} +(4.04508 - 2.93893i) q^{10} +(-0.309017 + 3.30220i) q^{11} +(0.927051 + 2.85317i) q^{12} -6.00000 q^{13} +(0.263932 + 0.812299i) q^{14} +(-0.690983 + 2.12663i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-1.42705 - 1.03681i) q^{17} +(-1.80902 - 1.31433i) q^{18} +(1.35410 - 4.16750i) q^{19} -6.70820 q^{20} +(-0.309017 - 0.224514i) q^{21} +(4.89919 - 5.56758i) q^{22} +(-1.07295 + 3.30220i) q^{23} +(0.690983 - 2.12663i) q^{24} +(-4.04508 - 2.93893i) q^{25} +(10.8541 + 7.88597i) q^{26} +1.00000 q^{27} +(0.354102 - 1.08981i) q^{28} +(-1.26393 - 3.88998i) q^{29} +(4.04508 - 2.93893i) q^{30} +(-0.454915 - 1.40008i) q^{31} -6.70820 q^{32} +(-0.309017 + 3.30220i) q^{33} +(1.21885 + 3.75123i) q^{34} +(0.690983 - 0.502029i) q^{35} +(0.927051 + 2.85317i) q^{36} +(2.42705 - 7.46969i) q^{37} +(-7.92705 + 5.75934i) q^{38} -6.00000 q^{39} +(4.04508 + 2.93893i) q^{40} +(-5.04508 - 3.66547i) q^{41} +(0.263932 + 0.812299i) q^{42} -9.94427 q^{43} +(-9.70820 + 2.17963i) q^{44} +(-0.690983 + 2.12663i) q^{45} +(6.28115 - 4.56352i) q^{46} -3.09017 q^{47} +(0.809017 - 0.587785i) q^{48} +(-2.11803 - 6.51864i) q^{49} +(3.45492 + 10.6331i) q^{50} +(-1.42705 - 1.03681i) q^{51} +(-5.56231 - 17.1190i) q^{52} +(0.809017 - 0.587785i) q^{53} +(-1.80902 - 1.31433i) q^{54} +(-6.80902 - 2.93893i) q^{55} +(-0.690983 + 0.502029i) q^{56} +(1.35410 - 4.16750i) q^{57} +(-2.82624 + 8.69827i) q^{58} +(-0.527864 + 1.62460i) q^{59} -6.70820 q^{60} +10.3262 q^{61} +(-1.01722 + 3.13068i) q^{62} +(-0.309017 - 0.224514i) q^{63} +(10.5172 + 7.64121i) q^{64} +(4.14590 - 12.7598i) q^{65} +(4.89919 - 5.56758i) q^{66} +(-0.690983 + 0.502029i) q^{67} +(1.63525 - 5.03280i) q^{68} +(-1.07295 + 3.30220i) q^{69} -1.90983 q^{70} +(-0.454915 + 1.40008i) q^{71} +(0.690983 - 2.12663i) q^{72} +(-1.00000 + 0.726543i) q^{73} +(-14.2082 + 10.3229i) q^{74} +(-4.04508 - 2.93893i) q^{75} +13.1459 q^{76} +(0.836881 - 0.951057i) q^{77} +(10.8541 + 7.88597i) q^{78} +(-4.00000 + 2.90617i) q^{79} +(0.690983 + 2.12663i) q^{80} +1.00000 q^{81} +(4.30902 + 13.2618i) q^{82} +(-9.35410 - 6.79615i) q^{83} +(0.354102 - 1.08981i) q^{84} +(3.19098 - 2.31838i) q^{85} +(17.9894 + 13.0700i) q^{86} +(-1.26393 - 3.88998i) q^{87} +(6.80902 + 2.93893i) q^{88} +(-5.11803 + 15.7517i) q^{89} +(4.04508 - 2.93893i) q^{90} +(1.85410 + 1.34708i) q^{91} -10.4164 q^{92} +(-0.454915 - 1.40008i) q^{93} +(5.59017 + 4.06150i) q^{94} +(7.92705 + 5.75934i) q^{95} -6.70820 q^{96} +(-9.28115 + 6.74315i) q^{97} +(-4.73607 + 14.5761i) q^{98} +(-0.309017 + 3.30220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{2} + 4 q^{3} - 3 q^{4} - 5 q^{5} - 5 q^{6} + q^{7} + 5 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 5 * q^2 + 4 * q^3 - 3 * q^4 - 5 * q^5 - 5 * q^6 + q^7 + 5 * q^8 + 4 * q^9	\( 4 q - 5 q^{2} + 4 q^{3} - 3 q^{4} - 5 q^{5} - 5 q^{6} + q^{7} + 5 q^{8} + 4 q^{9} + 5 q^{10} + q^{11} - 3 q^{12} - 24 q^{13} + 10 q^{14} - 5 q^{15} + q^{16} + q^{17} - 5 q^{18} - 8 q^{19} + q^{21} - 5 q^{22} - 11 q^{23} + 5 q^{24} - 5 q^{25} + 30 q^{26} + 4 q^{27} - 12 q^{28} - 14 q^{29} + 5 q^{30} - 13 q^{31} + q^{33} + 25 q^{34} + 5 q^{35} - 3 q^{36} + 3 q^{37} - 25 q^{38} - 24 q^{39} + 5 q^{40} - 9 q^{41} + 10 q^{42} - 4 q^{43} - 12 q^{44} - 5 q^{45} + 5 q^{46} + 10 q^{47} + q^{48} - 4 q^{49} + 25 q^{50} + q^{51} + 18 q^{52} + q^{53} - 5 q^{54} - 25 q^{55} - 5 q^{56} - 8 q^{57} + 20 q^{58} - 20 q^{59} + 10 q^{61} + 25 q^{62} + q^{63} + 13 q^{64} + 30 q^{65} - 5 q^{66} - 5 q^{67} - 27 q^{68} - 11 q^{69} - 30 q^{70} - 13 q^{71} + 5 q^{72} - 4 q^{73} - 30 q^{74} - 5 q^{75} + 66 q^{76} + 19 q^{77} + 30 q^{78} - 16 q^{79} + 5 q^{80} + 4 q^{81} + 15 q^{82} - 24 q^{83} - 12 q^{84} + 15 q^{85} + 25 q^{86} - 14 q^{87} + 25 q^{88} - 16 q^{89} + 5 q^{90} - 6 q^{91} + 12 q^{92} - 13 q^{93} + 25 q^{95} - 17 q^{97} - 10 q^{98} + q^{99}+O(q^{100}) \) 4 * q - 5 * q^2 + 4 * q^3 - 3 * q^4 - 5 * q^5 - 5 * q^6 + q^7 + 5 * q^8 + 4 * q^9 + 5 * q^10 + q^11 - 3 * q^12 - 24 * q^13 + 10 * q^14 - 5 * q^15 + q^16 + q^17 - 5 * q^18 - 8 * q^19 + q^21 - 5 * q^22 - 11 * q^23 + 5 * q^24 - 5 * q^25 + 30 * q^26 + 4 * q^27 - 12 * q^28 - 14 * q^29 + 5 * q^30 - 13 * q^31 + q^33 + 25 * q^34 + 5 * q^35 - 3 * q^36 + 3 * q^37 - 25 * q^38 - 24 * q^39 + 5 * q^40 - 9 * q^41 + 10 * q^42 - 4 * q^43 - 12 * q^44 - 5 * q^45 + 5 * q^46 + 10 * q^47 + q^48 - 4 * q^49 + 25 * q^50 + q^51 + 18 * q^52 + q^53 - 5 * q^54 - 25 * q^55 - 5 * q^56 - 8 * q^57 + 20 * q^58 - 20 * q^59 + 10 * q^61 + 25 * q^62 + q^63 + 13 * q^64 + 30 * q^65 - 5 * q^66 - 5 * q^67 - 27 * q^68 - 11 * q^69 - 30 * q^70 - 13 * q^71 + 5 * q^72 - 4 * q^73 - 30 * q^74 - 5 * q^75 + 66 * q^76 + 19 * q^77 + 30 * q^78 - 16 * q^79 + 5 * q^80 + 4 * q^81 + 15 * q^82 - 24 * q^83 - 12 * q^84 + 15 * q^85 + 25 * q^86 - 14 * q^87 + 25 * q^88 - 16 * q^89 + 5 * q^90 - 6 * q^91 + 12 * q^92 - 13 * q^93 + 25 * q^95 - 17 * q^97 - 10 * q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more