LMFDB - Embedded newform 845.2.e.n.146.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(146,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("845.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.e (of order $3$, degree $2$, not 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			146.4
Root			$1.20036 + 0.747754i$ of defining polynomial
Character	$\chi$	$=$	845.146
Dual form			845.2.e.n.191.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24775 + 2.16117i) q^{2} +(1.41342 + 2.44811i) q^{3} +(-2.11378 + 3.66117i) q^{4} +1.00000 q^{5} +(-3.52720 + 6.10929i) q^{6} +(0.952606 - 1.64996i) q^{7} -5.55889 q^{8} +(-2.49551 + 4.32235i) q^{9} +O(q^{10})$	\(q+(1.24775 + 2.16117i) q^{2} +(1.41342 + 2.44811i) q^{3} +(-2.11378 + 3.66117i) q^{4} +1.00000 q^{5} +(-3.52720 + 6.10929i) q^{6} +(0.952606 - 1.64996i) q^{7} -5.55889 q^{8} +(-2.49551 + 4.32235i) q^{9} +(1.24775 + 2.16117i) q^{10} +(0.534695 + 0.926118i) q^{11} -11.9506 q^{12} +4.75447 q^{14} +(1.41342 + 2.44811i) q^{15} +(-2.70857 - 4.69138i) q^{16} +(-0.318632 + 0.551886i) q^{17} -12.4551 q^{18} +(2.86603 - 4.96410i) q^{19} +(-2.11378 + 3.66117i) q^{20} +5.38573 q^{21} +(-1.33433 + 2.31114i) q^{22} +(-1.90893 - 3.30636i) q^{23} +(-7.85704 - 13.6088i) q^{24} +1.00000 q^{25} -5.62828 q^{27} +(4.02720 + 6.97531i) q^{28} +(-4.72756 - 8.18837i) q^{29} +(-3.52720 + 6.10929i) q^{30} +1.46410 q^{31} +(1.20036 - 2.07908i) q^{32} +(-1.51150 + 2.61799i) q^{33} -1.59030 q^{34} +(0.952606 - 1.64996i) q^{35} +(-10.5499 - 18.2730i) q^{36} +(0.378725 + 0.655970i) q^{37} +14.3044 q^{38} -5.55889 q^{40} +(0.133975 + 0.232051i) q^{41} +(6.72006 + 11.6395i) q^{42} +(-0.318632 + 0.551886i) q^{43} -4.52091 q^{44} +(-2.49551 + 4.32235i) q^{45} +(4.76374 - 8.25104i) q^{46} +9.44613 q^{47} +(7.65668 - 13.2618i) q^{48} +(1.68508 + 2.91865i) q^{49} +(1.24775 + 2.16117i) q^{50} -1.80144 q^{51} -6.99102 q^{53} +(-7.02271 - 12.1637i) q^{54} +(0.534695 + 0.926118i) q^{55} +(-5.29543 + 9.17196i) q^{56} +16.2036 q^{57} +(11.7977 - 20.4341i) q^{58} +(0.370518 - 0.641756i) q^{59} -11.9506 q^{60} +(-2.09928 + 3.63606i) q^{61} +(1.82684 + 3.16418i) q^{62} +(4.75447 + 8.23499i) q^{63} -4.84325 q^{64} -7.54390 q^{66} +(4.04739 + 7.01029i) q^{67} +(-1.34703 - 2.33313i) q^{68} +(5.39623 - 9.34654i) q^{69} +4.75447 q^{70} +(4.88244 - 8.45663i) q^{71} +(13.8723 - 24.0274i) q^{72} +3.71649 q^{73} +(-0.945110 + 1.63698i) q^{74} +(1.41342 + 2.44811i) q^{75} +(12.1163 + 20.9860i) q^{76} +2.03741 q^{77} -9.31937 q^{79} +(-2.70857 - 4.69138i) q^{80} +(-0.468594 - 0.811629i) q^{81} +(-0.334335 + 0.579085i) q^{82} -5.11778 q^{83} +(-11.3842 + 19.7181i) q^{84} +(-0.318632 + 0.551886i) q^{85} -1.59030 q^{86} +(13.3640 - 23.1472i) q^{87} +(-2.97231 - 5.14819i) q^{88} +(-6.28917 - 10.8932i) q^{89} -12.4551 q^{90} +16.1402 q^{92} +(2.06939 + 3.58429i) q^{93} +(11.7864 + 20.4147i) q^{94} +(2.86603 - 4.96410i) q^{95} +6.78645 q^{96} +(-2.11078 + 3.65597i) q^{97} +(-4.20514 + 7.28351i) q^{98} -5.33734 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} - 4 q^{6} + 10 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 - 4 * q^6 + 10 * q^7 - 12 * q^8 - 4 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} - 4 q^{6} + 10 q^{7} - 12 q^{8} - 4 q^{9} + 2 q^{10} - 20 q^{12} + 4 q^{14} + 2 q^{15} - 2 q^{16} + 2 q^{17} - 40 q^{18} + 16 q^{19} - 2 q^{20} - 8 q^{21} - 12 q^{22} + 10 q^{23} - 24 q^{24} + 8 q^{25} - 4 q^{27} + 8 q^{28} - 8 q^{29} - 4 q^{30} - 16 q^{31} + 4 q^{32} + 18 q^{33} + 8 q^{34} + 10 q^{35} - 20 q^{36} - 2 q^{37} + 16 q^{38} - 12 q^{40} + 8 q^{41} + 4 q^{42} + 2 q^{43} - 24 q^{44} - 4 q^{45} + 16 q^{46} - 16 q^{47} + 28 q^{48} - 12 q^{49} + 2 q^{50} + 8 q^{51} - 24 q^{53} - 16 q^{54} - 12 q^{56} + 28 q^{57} + 22 q^{58} + 12 q^{59} - 20 q^{60} - 28 q^{61} - 4 q^{62} + 4 q^{63} + 8 q^{64} + 12 q^{66} + 30 q^{67} - 14 q^{68} + 16 q^{69} + 4 q^{70} + 4 q^{71} + 12 q^{72} + 16 q^{73} + 10 q^{74} + 2 q^{75} + 20 q^{76} + 36 q^{77} - 16 q^{79} - 2 q^{80} + 8 q^{81} - 4 q^{82} + 24 q^{83} - 28 q^{84} + 2 q^{85} + 8 q^{86} + 22 q^{87} + 18 q^{88} - 12 q^{89} - 40 q^{90} + 44 q^{92} + 8 q^{93} + 32 q^{94} + 16 q^{95} - 8 q^{96} + 2 q^{97} - 24 q^{98} - 48 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 - 4 * q^6 + 10 * q^7 - 12 * q^8 - 4 * q^9 + 2 * q^10 - 20 * q^12 + 4 * q^14 + 2 * q^15 - 2 * q^16 + 2 * q^17 - 40 * q^18 + 16 * q^19 - 2 * q^20 - 8 * q^21 - 12 * q^22 + 10 * q^23 - 24 * q^24 + 8 * q^25 - 4 * q^27 + 8 * q^28 - 8 * q^29 - 4 * q^30 - 16 * q^31 + 4 * q^32 + 18 * q^33 + 8 * q^34 + 10 * q^35 - 20 * q^36 - 2 * q^37 + 16 * q^38 - 12 * q^40 + 8 * q^41 + 4 * q^42 + 2 * q^43 - 24 * q^44 - 4 * q^45 + 16 * q^46 - 16 * q^47 + 28 * q^48 - 12 * q^49 + 2 * q^50 + 8 * q^51 - 24 * q^53 - 16 * q^54 - 12 * q^56 + 28 * q^57 + 22 * q^58 + 12 * q^59 - 20 * q^60 - 28 * q^61 - 4 * q^62 + 4 * q^63 + 8 * q^64 + 12 * q^66 + 30 * q^67 - 14 * q^68 + 16 * q^69 + 4 * q^70 + 4 * q^71 + 12 * q^72 + 16 * q^73 + 10 * q^74 + 2 * q^75 + 20 * q^76 + 36 * q^77 - 16 * q^79 - 2 * q^80 + 8 * q^81 - 4 * q^82 + 24 * q^83 - 28 * q^84 + 2 * q^85 + 8 * q^86 + 22 * q^87 + 18 * q^88 - 12 * q^89 - 40 * q^90 + 44 * q^92 + 8 * q^93 + 32 * q^94 + 16 * q^95 - 8 * q^96 + 2 * q^97 - 24 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.24775	+	2.16117i	0.882295	+	1.52818i	0.848783	+	0.528742i	$0.177336\pi$
$2$	1.24775	+	2.16117i	0.882295	+	1.52818i	0.0335125	+	0.999438i	$0.489331\pi$
$3$	1.41342	+	2.44811i	0.816038	+	1.41342i	0.908580	+	0.417710i	$0.137167\pi$
$3$	1.41342	+	2.44811i	0.816038	+	1.41342i	−0.0925423	+	0.995709i	$0.529499\pi$
$4$	−2.11378	+	3.66117i	−1.05689	+	1.83059i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−3.52720	+	6.10929i	−1.43997	+	2.49411i
$7$	0.952606	−	1.64996i	0.360051	−	0.623627i	−0.627918	−	0.778280i	$-0.716093\pi$
$7$	0.952606	−	1.64996i	0.360051	−	0.623627i	0.987969	+	0.154653i	$0.0494259\pi$
$8$	−5.55889			−1.96536
$9$	−2.49551	+	4.32235i	−0.831836	+	1.44078i
$10$	1.24775	+	2.16117i	0.394574	+	0.683423i
$11$	0.534695	+	0.926118i	0.161217	+	0.279235i	0.935305	−	0.353842i	$-0.115125\pi$
$11$	0.534695	+	0.926118i	0.161217	+	0.279235i	−0.774089	+	0.633077i	$0.781792\pi$
$12$	−11.9506			−3.44985
$13$		0			0
$13$		0			0
$14$	4.75447			1.27069
$15$	1.41342	+	2.44811i	0.364943	+	0.632100i
$16$	−2.70857	−	4.69138i	−0.677142	−	1.17284i
$17$	−0.318632	+	0.551886i	−0.0772795	+	0.133852i	−0.902075	−	0.431579i	$-0.857957\pi$
$17$	−0.318632	+	0.551886i	−0.0772795	+	0.133852i	0.824796	+	0.565431i	$0.191290\pi$
$18$	−12.4551			−2.93570
$19$	2.86603	−	4.96410i	0.657511	−	1.13884i	−0.323747	−	0.946144i	$-0.604943\pi$
$19$	2.86603	−	4.96410i	0.657511	−	1.13884i	0.981258	−	0.192699i	$-0.0617242\pi$
$20$	−2.11378	+	3.66117i	−0.472655	+	0.818663i
$21$	5.38573			1.17526
$22$	−1.33433	+	2.31114i	−0.284481	+	0.492736i
$23$	−1.90893	−	3.30636i	−0.398039	−	0.689423i	0.595445	−	0.803396i	$-0.296976\pi$
$23$	−1.90893	−	3.30636i	−0.398039	−	0.689423i	−0.993484	+	0.113973i	$0.963642\pi$
$24$	−7.85704	−	13.6088i	−1.60381	−	2.77788i
$25$	1.00000			0.200000
$26$		0			0
$27$	−5.62828			−1.08316
$28$	4.02720	+	6.97531i	0.761069	+	1.31821i
$29$	−4.72756	−	8.18837i	−0.877886	−	1.52054i	−0.853657	−	0.520836i	$-0.825620\pi$
$29$	−4.72756	−	8.18837i	−0.877886	−	1.52054i	−0.0242288	−	0.999706i	$-0.507713\pi$
$30$	−3.52720	+	6.10929i	−0.643975	+	1.11540i
$31$	1.46410			0.262960			0.131480	−	0.991319i	$-0.458027\pi$
$31$	1.46410			0.262960			0.131480	+	0.991319i	$0.458027\pi$
$32$	1.20036	−	2.07908i	0.212196	−	0.367534i
$33$	−1.51150	+	2.61799i	−0.263118	+	0.455733i
$34$	−1.59030			−0.272733
$35$	0.952606	−	1.64996i	0.161020	−	0.278895i
$36$	−10.5499	−	18.2730i	−1.75832	−	3.04550i
$37$	0.378725	+	0.655970i	0.0622619	+	0.107841i	0.895476	−	0.445110i	$-0.146835\pi$
$37$	0.378725	+	0.655970i	0.0622619	+	0.107841i	−0.833214	+	0.552950i	$0.813502\pi$
$38$	14.3044			2.32048
$39$		0			0
$40$	−5.55889			−0.878938
$41$	0.133975	+	0.232051i	0.0209233	+	0.0362402i	0.876297	−	0.481770i	$-0.160006\pi$
$41$	0.133975	+	0.232051i	0.0209233	+	0.0362402i	−0.855374	+	0.518011i	$0.826673\pi$
$42$	6.72006	+	11.6395i	1.03693	+	1.79601i
$43$	−0.318632	+	0.551886i	−0.0485909	+	0.0841618i	−0.889298	−	0.457328i	$-0.848806\pi$
$43$	−0.318632	+	0.551886i	−0.0485909	+	0.0841618i	0.840707	+	0.541490i	$0.182140\pi$
$44$	−4.52091			−0.681552
$45$	−2.49551	+	4.32235i	−0.372008	+	0.644337i
$46$	4.76374	−	8.25104i	0.702375	−	1.21655i
$47$	9.44613			1.37786			0.688930	−	0.724828i	$-0.258081\pi$
$47$	9.44613			1.37786			0.688930	+	0.724828i	$0.258081\pi$
$48$	7.65668	−	13.2618i	1.10515	−	1.91417i
$49$	1.68508	+	2.91865i	0.240726	+	0.416950i
$50$	1.24775	+	2.16117i	0.176459	+	0.305636i
$51$	−1.80144			−0.252252
$52$		0			0
$53$	−6.99102			−0.960290			−0.480145	−	0.877189i	$-0.659416\pi$
$53$	−6.99102			−0.960290			−0.480145	+	0.877189i	$0.659416\pi$
$54$	−7.02271	−	12.1637i	−0.955669	−	1.65527i
$55$	0.534695	+	0.926118i	0.0720982	+	0.124878i
$56$	−5.29543	+	9.17196i	−0.707632	+	1.22565i
$57$	16.2036			2.14622
$58$	11.7977	−	20.4341i	1.54911	−	2.68313i
$59$	0.370518	−	0.641756i	0.0482373	−	0.0835495i	−0.840899	−	0.541193i	$-0.817973\pi$
$59$	0.370518	−	0.641756i	0.0482373	−	0.0835495i	0.889136	+	0.457643i	$0.151306\pi$
$60$	−11.9506			−1.54282
$61$	−2.09928	+	3.63606i	−0.268785	+	0.465550i	−0.968548	−	0.248825i	$-0.919956\pi$
$61$	−2.09928	+	3.63606i	−0.268785	+	0.465550i	0.699763	+	0.714375i	$0.253289\pi$
$62$	1.82684	+	3.16418i	0.232009	+	0.401851i
$63$	4.75447	+	8.23499i	0.599007	+	1.03751i
$64$	−4.84325			−0.605406
$65$		0			0
$66$	−7.54390			−0.928589
$67$	4.04739	+	7.01029i	0.494468	+	0.856443i	0.999980	−	0.00637624i	$-0.00202963\pi$
$67$	4.04739	+	7.01029i	0.494468	+	0.856443i	−0.505512	+	0.862820i	$0.668696\pi$
$68$	−1.34703	−	2.33313i	−0.163352	−	0.282934i
$69$	5.39623	−	9.34654i	0.649629	−	1.12519i
$70$	4.75447			0.568268
$71$	4.88244	−	8.45663i	0.579439	−	1.00362i	−0.416105	−	0.909317i	$-0.636605\pi$
$71$	4.88244	−	8.45663i	0.579439	−	1.00362i	0.995544	−	0.0943010i	$-0.0300616\pi$
$72$	13.8723	−	24.0274i	1.63486	−	2.83166i
$73$	3.71649			0.434982			0.217491	−	0.976062i	$-0.430213\pi$
$73$	3.71649			0.434982			0.217491	+	0.976062i	$0.430213\pi$
$74$	−0.945110	+	1.63698i	−0.109867	+	0.190295i
$75$	1.41342	+	2.44811i	0.163208	+	0.282684i
$76$	12.1163	+	20.9860i	1.38983	+	2.40726i
$77$	2.03741			0.232185
$78$		0			0
$79$	−9.31937			−1.04851			−0.524255	−	0.851561i	$-0.675656\pi$
$79$	−9.31937			−1.04851			−0.524255	+	0.851561i	$0.675656\pi$
$80$	−2.70857	−	4.69138i	−0.302827	−	0.524512i
$81$	−0.468594	−	0.811629i	−0.0520660	−	0.0901809i
$82$	−0.334335	+	0.579085i	−0.0369211	+	0.0639492i
$83$	−5.11778			−0.561749			−0.280875	−	0.959744i	$-0.590624\pi$
$83$	−5.11778			−0.561749			−0.280875	+	0.959744i	$0.590624\pi$
$84$	−11.3842	+	19.7181i	−1.24212	+	2.15142i
$85$	−0.318632	+	0.551886i	−0.0345605	+	0.0598605i
$86$	−1.59030			−0.171486
$87$	13.3640	−	23.1472i	1.43278	−	2.48164i
$88$	−2.97231	−	5.14819i	−0.316849	−	0.548799i
$89$	−6.28917	−	10.8932i	−0.666650	−	1.15467i	−0.978835	−	0.204651i	$-0.934394\pi$
$89$	−6.28917	−	10.8932i	−0.666650	−	1.15467i	0.312185	−	0.950021i	$-0.398939\pi$
$90$	−12.4551			−1.31288
$91$		0			0
$92$	16.1402			1.68273
$93$	2.06939	+	3.58429i	0.214586	+	0.371673i
$94$	11.7864	+	20.4147i	1.21568	+	2.10562i
$95$	2.86603	−	4.96410i	0.294048	−	0.509306i
$96$	6.78645			0.692639
$97$	−2.11078	+	3.65597i	−0.214317	+	0.371208i	−0.953061	−	0.302778i	$-0.902086\pi$
$97$	−2.11078	+	3.65597i	−0.214317	+	0.371208i	0.738744	+	0.673986i	$0.235419\pi$
$98$	−4.20514	+	7.28351i	−0.424783	+	0.735746i
$99$	−5.33734			−0.536423
$100$	−2.11378	+	3.66117i	−0.211378	+	0.366117i
$101$	7.62379	+	13.2048i	0.758595	+	1.31393i	0.943567	+	0.331181i	$0.107447\pi$
$101$	7.62379	+	13.2048i	0.758595	+	1.31393i	−0.184972	+	0.982744i	$0.559219\pi$
$102$	−2.24775	−	3.89322i	−0.222561	−	0.385487i
$103$	−13.5269			−1.33285			−0.666423	−	0.745574i	$-0.732176\pi$
$103$	−13.5269			−1.33285			−0.666423	+	0.745574i	$0.732176\pi$
$104$		0			0
$105$	5.38573			0.525593
$106$	−8.72307	−	15.1088i	−0.847259	−	1.46750i
$107$	3.68137	+	6.37632i	0.355891	+	0.616422i	0.987270	−	0.159053i	$-0.0508440\pi$
$107$	3.68137	+	6.37632i	0.355891	+	0.616422i	−0.631379	+	0.775475i	$0.717511\pi$
$108$	11.8969	−	20.6061i	1.14478	−	1.98282i
$109$	−10.0760			−0.965103			−0.482551	−	0.875868i	$-0.660290\pi$
$109$	−10.0760			−0.965103			−0.482551	+	0.875868i	$0.660290\pi$
$110$	−1.33433	+	2.31114i	−0.127224	+	0.220358i
$111$	−1.07059	+	1.85432i	−0.101616	+	0.176004i
$112$	−10.3208			−0.975223
$113$	3.34403	−	5.79203i	0.314580	−	0.544868i	−0.664768	−	0.747050i	$-0.731470\pi$
$113$	3.34403	−	5.79203i	0.314580	−	0.544868i	0.979348	+	0.202181i	$0.0648030\pi$
$114$	20.2181	+	35.0187i	1.89360	+	3.27981i
$115$	−1.90893	−	3.30636i	−0.178008	−	0.308320i
$116$	39.9721			3.71131
$117$		0			0
$118$	1.84926			0.170238
$119$	0.607061	+	1.05146i	0.0556492	+	0.0963872i
$120$	−7.85704	−	13.6088i	−0.717246	−	1.24231i
$121$	4.92820	−	8.53590i	0.448018	−	0.775991i
$122$	−10.4775			−0.948592
$123$	−0.378725	+	0.655970i	−0.0341484	+	0.0591468i
$124$	−3.09479	+	5.36033i	−0.277920	+	0.481372i
$125$	1.00000			0.0894427
$126$	−11.8648	+	20.5505i	−1.05700	+	1.83078i
$127$	−0.744750	−	1.28994i	−0.0660859	−	0.114464i	0.831089	−	0.556139i	$-0.187718\pi$
$127$	−0.744750	−	1.28994i	−0.0660859	−	0.114464i	−0.897175	+	0.441675i	$0.854384\pi$
$128$	−8.44391	−	14.6253i	−0.746343	−	1.29270i
$129$	−1.80144			−0.158608
$130$		0			0
$131$	4.12676			0.360557			0.180278	−	0.983616i	$-0.442300\pi$
$131$	4.12676			0.360557			0.180278	+	0.983616i	$0.442300\pi$
$132$	−6.38994	−	11.0677i	−0.556172	−	0.963319i
$133$	−5.46039	−	9.45767i	−0.473476	−	0.820084i
$134$	−10.1003	+	17.4942i	−0.872533	+	1.51127i
$135$	−5.62828			−0.484405
$136$	1.77124	−	3.06787i	0.151882	−	0.263068i
$137$	−10.0548	+	17.4155i	−0.859041	+	1.48790i	0.0138029	+	0.999905i	$0.495606\pi$
$137$	−10.0548	+	17.4155i	−0.859041	+	1.48790i	−0.872844	+	0.487999i	$0.837727\pi$
$138$	26.9327			2.29266
$139$	−10.4126	+	18.0352i	−0.883189	+	1.52973i	−0.0354130	+	0.999373i	$0.511275\pi$
$139$	−10.4126	+	18.0352i	−0.883189	+	1.52973i	−0.847776	+	0.530355i	$0.822059\pi$
$140$	4.02720	+	6.97531i	0.340360	+	0.589521i
$141$	13.3513	+	23.1252i	1.12439	+	1.94749i
$142$	24.3683			2.04494
$143$		0			0
$144$	27.0370			2.25308
$145$	−4.72756	−	8.18837i	−0.392602	−	0.680007i
$146$	4.63726	+	8.03198i	0.383783	+	0.664731i
$147$	−4.76346	+	8.25055i	−0.392883	+	0.680494i
$148$	−3.20216			−0.263216
$149$	6.68388	−	11.5768i	0.547565	−	0.948410i	−0.450876	−	0.892587i	$-0.648888\pi$
$149$	6.68388	−	11.5768i	0.547565	−	0.948410i	0.998441	−	0.0558233i	$-0.0177783\pi$
$150$	−3.52720	+	6.10929i	−0.287995	+	0.498821i
$151$	−18.2984			−1.48910			−0.744550	−	0.667567i	$-0.767336\pi$
$151$	−18.2984			−1.48910			−0.744550	+	0.667567i	$0.767336\pi$
$152$	−15.9319	+	27.5949i	−1.29225	+	2.23824i
$153$	−1.59030	−	2.75447i	−0.128568	−	0.222686i
$154$	2.54219	+	4.40320i	0.204856	+	0.354820i
$155$	1.46410			0.117599
$156$		0			0
$157$	2.42229			0.193320			0.0966599	−	0.995317i	$-0.469184\pi$
$157$	2.42229			0.193320			0.0966599	+	0.995317i	$0.469184\pi$
$158$	−11.6283	−	20.1408i	−0.925096	−	1.60231i
$159$	−9.88124	−	17.1148i	−0.783633	−	1.35729i
$160$	1.20036	−	2.07908i	0.0948968	−	0.164366i
$161$	−7.27382			−0.573258
$162$	1.16938	−	2.02543i	0.0918752	−	0.159132i
$163$	7.99144	−	13.8416i	0.625938	−	1.08416i	−0.362421	−	0.932015i	$-0.618050\pi$
$163$	7.99144	−	13.8416i	0.625938	−	1.08416i	0.988359	−	0.152142i	$-0.0486170\pi$
$164$	−1.13277			−0.0884545
$165$	−1.51150	+	2.61799i	−0.117670	+	0.203810i
$166$	−6.38573	−	11.0604i	−0.495629	−	0.858454i
$167$	−7.19658	−	12.4648i	−0.556888	−	0.964558i	−0.997754	−	0.0669853i	$-0.978662\pi$
$167$	−7.19658	−	12.4648i	−0.556888	−	0.964558i	0.440866	−	0.897573i	$-0.354671\pi$
$168$	−29.9387			−2.30982
$169$		0			0
$170$	−1.59030			−0.121970
$171$	14.3044	+	24.7759i	1.09388	+	1.89466i
$172$	−1.34703	−	2.33313i	−0.102710	−	0.177900i
$173$	12.1745	−	21.0868i	0.925608	−	1.60320i	0.135027	−	0.990842i	$-0.456888\pi$
$173$	12.1745	−	21.0868i	0.925608	−	1.60320i	0.790581	−	0.612358i	$-0.209779\pi$
$174$	66.7001			5.05653
$175$	0.952606	−	1.64996i	0.0720103	−	0.124725i
$176$	2.89651	−	5.01691i	0.218333	−	0.378164i
$177$	2.09479			0.157454
$178$	15.6947	−	27.1840i	1.17636	−	2.03752i
$179$	−1.89414	−	3.28075i	−0.141575	−	0.245215i	0.786515	−	0.617571i	$-0.211883\pi$
$179$	−1.89414	−	3.28075i	−0.141575	−	0.245215i	−0.928090	+	0.372356i	$0.878550\pi$
$180$	−10.5499	−	18.2730i	−0.786343	−	1.36199i
$181$	−8.48794			−0.630904			−0.315452	−	0.948942i	$-0.602156\pi$
$181$	−8.48794			−0.630904			−0.315452	+	0.948942i	$0.602156\pi$
$182$		0			0
$183$	−11.8687			−0.877356
$184$	10.6115	+	18.3797i	0.782291	+	1.35497i
$185$	0.378725	+	0.655970i	0.0278444	+	0.0482279i
$186$	−5.16418	+	8.94462i	−0.378656	+	0.655851i
$187$	−0.681482			−0.0498349
$188$	−19.9670	+	34.5839i	−1.45625	+	2.52229i
$189$	−5.36153	+	9.28645i	−0.389994	+	0.675490i
$190$	14.3044			1.03775
$191$	2.72155	−	4.71386i	0.196924	−	0.341083i	−0.750605	−	0.660751i	$-0.770238\pi$
$191$	2.72155	−	4.71386i	0.196924	−	0.341083i	0.947530	+	0.319668i	$0.103571\pi$
$192$	−6.84555	−	11.8568i	−0.494035	−	0.855693i
$193$	6.07880	+	10.5288i	0.437562	+	0.757879i	0.997501	−	0.0706548i	$-0.0225089\pi$
$193$	6.07880	+	10.5288i	0.437562	+	0.757879i	−0.559939	+	0.828534i	$0.689176\pi$
$194$	−10.5349			−0.756363
$195$		0			0
$196$	−14.2476			−1.01768
$197$	−2.18915	−	3.79172i	−0.155970	−	0.270149i	0.777442	−	0.628955i	$-0.216517\pi$
$197$	−2.18915	−	3.79172i	−0.155970	−	0.270149i	−0.933412	+	0.358807i	$0.883184\pi$
$198$	−6.65968	−	11.5349i	−0.473283	−	0.819751i
$199$	−10.4186	+	18.0456i	−0.738558	+	1.27922i	0.214586	+	0.976705i	$0.431160\pi$
$199$	−10.4186	+	18.0456i	−0.738558	+	1.27922i	−0.953144	+	0.302516i	$0.902174\pi$
$200$	−5.55889			−0.393073
$201$	−11.4413	+	19.8170i	−0.807009	+	1.39778i
$202$	−19.0252	+	32.9526i	−1.33861	+	2.31854i
$203$	−18.0140			−1.26434
$204$	3.80785	−	6.59538i	0.266603	−	0.461769i
$205$	0.133975	+	0.232051i	0.00935719	+	0.0162071i
$206$	−16.8783	−	29.2340i	−1.17596	−	2.03683i
$207$	19.0550			1.32441
$208$		0			0
$209$	6.12979			0.424007
$210$	6.72006	+	11.6395i	0.463728	+	0.803201i
$211$	5.32684	+	9.22635i	0.366715	+	0.635168i	0.989050	−	0.147583i	$-0.0471492\pi$
$211$	5.32684	+	9.22635i	0.366715	+	0.635168i	−0.622335	+	0.782751i	$0.713816\pi$
$212$	14.7775	−	25.5953i	1.01492	−	1.75789i
$213$	27.6037			1.89138
$214$	−9.18688	+	15.9121i	−0.628002	+	1.08773i
$215$	−0.318632	+	0.551886i	−0.0217305	+	0.0376383i
$216$	31.2870			2.12881
$217$	1.39471	−	2.41571i	0.0946792	−	0.163989i
$218$	−12.5723	−	21.7759i	−0.851505	−	1.47485i
$219$	5.25296	+	9.09839i	0.354962	+	0.614812i
$220$	−4.52091			−0.304799
$221$		0			0
$222$	−5.34335			−0.358622
$223$	10.6697	+	18.4804i	0.714494	+	1.23754i	0.963155	+	0.268949i	$0.0866762\pi$
$223$	10.6697	+	18.4804i	0.714494	+	1.23754i	−0.248661	+	0.968591i	$0.579990\pi$
$224$	−2.28694	−	3.96110i	−0.152803	−	0.264662i
$225$	−2.49551	+	4.32235i	−0.166367	+	0.288156i
$226$	16.6901			1.11021
$227$	7.84283	−	13.5842i	0.520547	−	0.901613i	−0.479168	−	0.877723i	$-0.659062\pi$
$227$	7.84283	−	13.5842i	0.520547	−	0.901613i	0.999715	−	0.0238900i	$-0.00760515\pi$
$228$	−34.2508	+	59.3241i	−2.26831	+	3.92884i
$229$	7.62085			0.503600			0.251800	−	0.967779i	$-0.418977\pi$
$229$	7.62085			0.503600			0.251800	+	0.967779i	$0.418977\pi$
$230$	4.76374	−	8.25104i	0.314112	−	0.544058i
$231$	2.87972	+	4.98782i	0.189472	+	0.328175i
$232$	26.2800	+	45.5182i	1.72536	+	2.98842i
$233$	−19.0550			−1.24833			−0.624166	−	0.781292i	$-0.714561\pi$
$233$	−19.0550			−1.24833			−0.624166	+	0.781292i	$0.714561\pi$
$234$		0			0
$235$	9.44613			0.616198
$236$	1.56639	+	2.71306i	0.101963	+	0.176605i
$237$	−13.1722	−	22.8149i	−0.855625	−	1.48199i
$238$	−1.51493	+	2.62393i	−0.0981980	+	0.170084i
$239$	−12.7535			−0.824954			−0.412477	−	0.910968i	$-0.635336\pi$
$239$	−12.7535			−0.824954			−0.412477	+	0.910968i	$0.635336\pi$
$240$	7.65668	−	13.2618i	0.494237	−	0.856043i
$241$	12.9644	−	22.4550i	0.835111	−	1.44646i	−0.0588285	−	0.998268i	$-0.518737\pi$
$241$	12.9644	−	22.4550i	0.835111	−	1.44646i	0.893940	−	0.448187i	$-0.147930\pi$
$242$	24.5967			1.58114
$243$	−7.11778	+	12.3284i	−0.456606	+	0.790864i
$244$	−8.87483	−	15.3717i	−0.568153	−	0.984069i
$245$	1.68508	+	2.91865i	0.107656	+	0.186466i
$246$	−1.89022			−0.120516
$247$		0			0
$248$	−8.13878			−0.516813
$249$	−7.23357	−	12.5289i	−0.458409	−	0.793987i
$250$	1.24775	+	2.16117i	0.0789149	+	0.136685i
$251$	−3.80593	+	6.59207i	−0.240228	+	0.416088i	−0.960779	−	0.277314i	$-0.910556\pi$
$251$	−3.80593	+	6.59207i	−0.240228	+	0.416088i	0.720551	+	0.693402i	$0.243889\pi$
$252$	−40.1996			−2.53234
$253$	2.04139	−	3.53578i	0.128341	−	0.222293i
$254$	1.85853	−	3.21907i	0.116614	−	0.201982i
$255$	−1.80144			−0.112811
$256$	16.2286	−	28.1087i	1.01429	−	1.75680i
$257$	−0.167891	−	0.290796i	−0.0104728	−	0.0181394i	0.860742	−	0.509042i	$-0.170000\pi$
$257$	−0.167891	−	0.290796i	−0.0104728	−	0.0181394i	−0.871214	+	0.490903i	$0.836667\pi$
$258$	−2.24775	−	3.89322i	−0.139939	−	0.242382i
$259$	1.44310			0.0896700
$260$		0			0
$261$	47.1906			2.92103
$262$	5.14918	+	8.91865i	0.318118	+	0.550996i
$263$	2.68795	+	4.65566i	0.165746	+	0.287080i	0.936920	−	0.349544i	$-0.113664\pi$
$263$	2.68795	+	4.65566i	0.165746	+	0.287080i	−0.771174	+	0.636624i	$0.780330\pi$
$264$	8.40224	−	14.5531i	0.517122	−	0.895681i
$265$	−6.99102			−0.429455
$266$	13.6264	−	23.6017i	0.835491	−	1.44711i
$267$	17.7785	−	30.7932i	1.08802	−	1.88451i
$268$	−34.2212			−2.09039
$269$	0.655192	−	1.13483i	0.0399478	−	0.0691916i	−0.845360	−	0.534197i	$-0.820614\pi$
$269$	0.655192	−	1.13483i	0.0399478	−	0.0691916i	0.885308	+	0.465005i	$0.153948\pi$
$270$	−7.02271	−	12.1637i	−0.427388	−	0.740258i
$271$	−5.82266	−	10.0851i	−0.353701	−	0.612629i	0.633194	−	0.773994i	$-0.281744\pi$
$271$	−5.82266	−	10.0851i	−0.353701	−	0.612629i	−0.986895	+	0.161365i	$0.948410\pi$
$272$	3.45214			0.209317
$273$		0			0
$274$	−50.1838			−3.03171
$275$	0.534695	+	0.926118i	0.0322433	+	0.0558470i
$276$	22.8129	+	39.5130i	1.37317	+	2.37841i
$277$	10.1581	−	17.5943i	0.610338	−	1.05714i	−0.380845	−	0.924639i	$-0.624367\pi$
$277$	10.1581	−	17.5943i	0.610338	−	1.05714i	0.991183	−	0.132498i	$-0.0422999\pi$
$278$	−51.9697			−3.11693
$279$	−3.65368	+	6.32835i	−0.218740	+	0.378869i
$280$	−5.29543	+	9.17196i	−0.316463	+	0.548129i
$281$	11.8744			0.708366			0.354183	−	0.935176i	$-0.384759\pi$
$281$	11.8744			0.708366			0.354183	+	0.935176i	$0.384759\pi$
$282$	−33.3184	+	57.7091i	−1.98408	+	3.43653i
$283$	11.3261	+	19.6173i	0.673264	+	1.16613i	0.976973	+	0.213363i	$0.0684418\pi$
$283$	11.3261	+	19.6173i	0.673264	+	1.16613i	−0.303709	+	0.952765i	$0.598225\pi$
$284$	20.6408	+	35.7509i	1.22481	+	2.12143i
$285$	16.2036			0.959817
$286$		0			0
$287$	0.510500			0.0301339
$288$	5.99102	+	10.3767i	0.353024	+	0.611455i
$289$	8.29695	+	14.3707i	0.488056	+	0.845337i
$290$	11.7977	−	20.4341i	0.692782	−	1.19993i
$291$	−11.9336			−0.699562
$292$	−7.85584	+	13.6067i	−0.459728	+	0.796272i
$293$	9.30636	−	16.1191i	0.543683	−	0.941687i	−0.455005	−	0.890489i	$-0.650363\pi$
$293$	9.30636	−	16.1191i	0.543683	−	0.941687i	0.998689	−	0.0511983i	$-0.0163040\pi$
$294$	−23.7745			−1.38656
$295$	0.370518	−	0.641756i	0.0215724	−	0.0373645i
$296$	−2.10529	−	3.64647i	−0.122367	−	0.211946i
$297$	−3.00941	−	5.21245i	−0.174624	−	0.302457i
$298$	33.3593			1.93245
$299$		0			0
$300$	−11.9506			−0.689970
$301$	0.607061	+	1.05146i	0.0349904	+	0.0606052i
$302$	−22.8319	−	39.5459i	−1.31383	−	2.27561i
$303$	−21.5512	+	37.3278i	−1.23808	+	2.14443i
$304$	−31.0513			−1.78091
$305$	−2.09928	+	3.63606i	−0.120204	+	0.208200i
$306$	3.96859	−	6.87381i	0.226869	−	0.392949i
$307$	−3.14776			−0.179652			−0.0898262	−	0.995957i	$-0.528631\pi$
$307$	−3.14776			−0.179652			−0.0898262	+	0.995957i	$0.528631\pi$
$308$	−4.30664	+	7.45932i	−0.245394	+	0.425034i
$309$	−19.1192	−	33.1154i	−1.08765	−	1.88387i
$310$	1.82684	+	3.16418i	0.103757	+	0.179713i
$311$	−3.18059			−0.180355			−0.0901774	−	0.995926i	$-0.528743\pi$
$311$	−3.18059			−0.180355			−0.0901774	+	0.995926i	$0.528743\pi$
$312$		0			0
$313$	35.3533			1.99829			0.999144	−	0.0413596i	$-0.0131689\pi$
$313$	35.3533			1.99829			0.999144	+	0.0413596i	$0.0131689\pi$
$314$	3.02242	+	5.23499i	0.170565	+	0.295427i
$315$	4.75447	+	8.23499i	0.267884	+	0.463989i
$316$	19.6991	−	34.1198i	1.10816	−	1.91939i
$317$	13.6357			0.765858			0.382929	−	0.923778i	$-0.374915\pi$
$317$	13.6357			0.765858			0.382929	+	0.923778i	$0.374915\pi$
$318$	24.6587	−	42.7101i	1.38279	−	2.39506i
$319$	5.05560	−	8.75656i	0.283059	−	0.490273i
$320$	−4.84325			−0.270746
$321$	−10.4066	+	18.0248i	−0.580842	+	1.00605i
$322$	−9.07594	−	15.7200i	−0.505782	−	0.876041i
$323$	1.82641	+	3.16344i	0.101624	+	0.176018i
$324$	3.96202			0.220112
$325$		0			0
$326$	39.8854			2.20905
$327$	−14.2416	−	24.6671i	−0.787560	−	1.36409i
$328$	−0.744750	−	1.28994i	−0.0411219	−	0.0712253i
$329$	8.99844	−	15.5858i	0.496100	−	0.859271i
$330$	−7.54390			−0.415278
$331$	−14.3980	+	24.9380i	−0.791383	+	1.37072i	0.133727	+	0.991018i	$0.457305\pi$
$331$	−14.3980	+	24.9380i	−0.791383	+	1.37072i	−0.925110	+	0.379698i	$0.876028\pi$
$332$	10.8179	−	18.7371i	0.593707	−	1.02833i
$333$	−3.78044			−0.207167
$334$	17.9591	−	31.1061i	0.982679	−	1.70205i
$335$	4.04739	+	7.01029i	0.221133	+	0.383013i
$336$	−14.5876	−	25.2665i	−0.795819	−	1.37840i
$337$	11.7493			0.640026			0.320013	−	0.947413i	$-0.396313\pi$
$337$	11.7493			0.640026			0.320013	+	0.947413i	$0.396313\pi$
$338$		0			0
$339$	18.9061			1.02684
$340$	−1.34703	−	2.33313i	−0.0730532	−	0.126532i
$341$	0.782847	+	1.35593i	0.0423936	+	0.0734278i
$342$	−35.6967	+	61.8285i	−1.93026	+	3.34330i
$343$	19.7574			1.06680
$344$	1.77124	−	3.06787i	0.0954987	−	0.165409i
$345$	5.39623	−	9.34654i	0.290523	−	0.503201i
$346$	60.7630			3.26664
$347$	−0.949887	+	1.64525i	−0.0509926	+	0.0883218i	−0.890395	−	0.455189i	$-0.849572\pi$
$347$	−0.949887	+	1.64525i	−0.0509926	+	0.0883218i	0.839402	+	0.543510i	$0.182905\pi$
$348$	56.4973	+	97.8562i	3.02857	+	5.24564i
$349$	−5.13454	−	8.89329i	−0.274846	−	0.476047i	0.695250	−	0.718768i	$-0.255293\pi$
$349$	−5.13454	−	8.89329i	−0.274846	−	0.476047i	−0.970096	+	0.242721i	$0.921960\pi$
$350$	4.75447			0.254137
$351$		0			0
$352$	2.56730			0.136838
$353$	0.400294	+	0.693330i	0.0213055	+	0.0369022i	0.876482	−	0.481435i	$-0.159884\pi$
$353$	0.400294	+	0.693330i	0.0213055	+	0.0369022i	−0.855176	+	0.518338i	$0.826551\pi$
$354$	2.61378	+	4.52720i	0.138921	+	0.240618i
$355$	4.88244	−	8.45663i	0.259133	−	0.448831i
$356$	53.1756			2.81830
$357$	−1.71606	+	2.97231i	−0.0908237	+	0.157311i
$358$	4.72685	−	8.18714i	0.249822	−	0.432704i
$359$	−8.13272			−0.429228			−0.214614	−	0.976699i	$-0.568849\pi$
$359$	−8.13272			−0.429228			−0.214614	+	0.976699i	$0.568849\pi$
$360$	13.8723	−	24.0274i	0.731132	−	1.26636i
$361$	−6.92820	−	12.0000i	−0.364642	−	0.631579i
$362$	−10.5909	−	18.3439i	−0.556643	−	0.964135i
$363$	27.8625			1.46240
$364$		0			0
$365$	3.71649			0.194530
$366$	−14.8092	−	25.6502i	−0.774087	−	1.34076i
$367$	10.2632	+	17.7765i	0.535737	+	0.927924i	0.999127	+	0.0417696i	$0.0132996\pi$
$367$	10.2632	+	17.7765i	0.535737	+	0.927924i	−0.463390	+	0.886154i	$0.653367\pi$
$368$	−10.3409	+	17.9110i	−0.539057	+	0.933675i
$369$	−1.33734			−0.0696191
$370$	−0.945110	+	1.63698i	−0.0491339	+	0.0851025i
$371$	−6.65968	+	11.5349i	−0.345754	+	0.598863i
$372$	−17.4969			−0.907173
$373$	8.90292	−	15.4203i	0.460976	−	0.798433i	−0.538034	−	0.842923i	$-0.680833\pi$
$373$	8.90292	−	15.4203i	0.460976	−	0.798433i	0.999010	+	0.0444897i	$0.0141662\pi$
$374$	−0.850322	−	1.47280i	−0.0439691	−	0.0761568i
$375$	1.41342	+	2.44811i	0.0729887	+	0.126420i
$376$	−52.5100			−2.70800
$377$		0			0
$378$	−26.7595			−1.37636
$379$	1.02277	+	1.77150i	0.0525363	+	0.0909956i	0.891098	−	0.453812i	$-0.149936\pi$
$379$	1.02277	+	1.77150i	0.0525363	+	0.0909956i	−0.838561	+	0.544807i	$0.816603\pi$
$380$	12.1163	+	20.9860i	0.621553	+	1.07656i
$381$	2.10529	−	3.64647i	0.107857	−	0.186814i
$382$	13.5833			0.694982
$383$	−3.95261	+	6.84611i	−0.201969	+	0.349820i	−0.949163	−	0.314786i	$-0.898067\pi$
$383$	−3.95261	+	6.84611i	−0.201969	+	0.349820i	0.747194	+	0.664606i	$0.231401\pi$
$384$	23.8696	−	41.3433i	1.21809	−	2.10979i
$385$	2.03741			0.103836
$386$	−15.1697	+	26.2747i	−0.772117	+	1.33735i
$387$	−1.59030	−	2.75447i	−0.0808393	−	0.140018i
$388$	−8.92343	−	15.4558i	−0.453018	−	0.784651i
$389$	−9.21171			−0.467052			−0.233526	−	0.972351i	$-0.575026\pi$
$389$	−9.21171			−0.467052			−0.233526	+	0.972351i	$0.575026\pi$
$390$		0			0
$391$	2.43298			0.123041
$392$	−9.36719	−	16.2244i	−0.473114	−	0.819458i
$393$	5.83285	+	10.1028i	0.294228	+	0.509618i
$394$	5.46304	−	9.46226i	0.275224	−	0.476702i
$395$	−9.31937			−0.468908
$396$	11.2820	−	19.5409i	0.566940	−	0.981968i
$397$	−3.17719	+	5.50305i	−0.159458	+	0.276190i	−0.934674	−	0.355507i	$-0.884308\pi$
$397$	−3.17719	+	5.50305i	−0.159458	+	0.276190i	0.775215	+	0.631697i	$0.217641\pi$
$398$	−51.9996			−2.60651
$399$	15.4356	−	26.7353i	0.772748	−	1.33844i
$400$	−2.70857	−	4.69138i	−0.135428	−	0.234569i
$401$	2.08460	+	3.61063i	0.104100	+	0.180306i	0.913370	−	0.407130i	$-0.133470\pi$
$401$	2.08460	+	3.61063i	0.104100	+	0.180306i	−0.809270	+	0.587437i	$0.800137\pi$
$402$	−57.1038			−2.84808
$403$		0			0
$404$	−64.4600			−3.20701
$405$	−0.468594	−	0.811629i	−0.0232846	−	0.0403301i
$406$	−22.4770	−	38.9314i	−1.11552	−	1.93213i
$407$	−0.405004	+	0.701487i	−0.0200753	+	0.0347714i
$408$	10.0140			0.495767
$409$	5.08403	−	8.80580i	0.251389	−	0.435419i	−0.712519	−	0.701652i	$-0.752446\pi$
$409$	5.08403	−	8.80580i	0.251389	−	0.435419i	0.963909	+	0.266234i	$0.0857793\pi$
$410$	−0.334335	+	0.579085i	−0.0165116	+	0.0285989i
$411$	−56.8467			−2.80404
$412$	28.5929	−	49.5244i	1.40867	−	2.43989i
$413$	−0.705915	−	1.22268i	−0.0347358	−	0.0601642i
$414$	23.7759	+	41.1811i	1.16852	+	2.02394i
$415$	−5.11778			−0.251222
$416$		0			0
$417$	−58.8697			−2.88286
$418$	7.64847	+	13.2475i	0.374099	+	0.647959i
$419$	−14.2954	−	24.7604i	−0.698378	−	1.20963i	−0.969029	−	0.246948i	$-0.920572\pi$
$419$	−14.2954	−	24.7604i	−0.698378	−	1.20963i	0.270651	−	0.962677i	$-0.412761\pi$
$420$	−11.3842	+	19.7181i	−0.555494	+	0.962144i
$421$	−2.01797			−0.0983498			−0.0491749	−	0.998790i	$-0.515659\pi$
$421$	−2.01797			−0.0983498			−0.0491749	+	0.998790i	$0.515659\pi$
$422$	−13.2932	+	23.0244i	−0.647101	+	1.12081i
$423$	−23.5729	+	40.8295i	−1.14615	+	1.98520i
$424$	38.8623			1.88732
$425$	−0.318632	+	0.551886i	−0.0154559	+	0.0267704i
$426$	34.4427	+	59.6564i	1.66875	+	2.89036i
$427$	3.99957	+	6.92747i	0.193553	+	0.335244i
$428$	−31.1264			−1.50455
$429$		0			0
$430$	−1.59030			−0.0766908
$431$	−10.3061	−	17.8508i	−0.496430	−	0.859842i	0.503562	−	0.863959i	$-0.332023\pi$
$431$	−10.3061	−	17.8508i	−0.496430	−	0.859842i	−0.999992	+	0.00411765i	$0.998689\pi$
$432$	15.2446	+	26.4044i	0.733455	+	1.27038i
$433$	−14.7178	+	25.4920i	−0.707292	+	1.22507i	0.258566	+	0.965994i	$0.416750\pi$
$433$	−14.7178	+	25.4920i	−0.707292	+	1.22507i	−0.965858	+	0.259072i	$0.916583\pi$
$434$	6.96103			0.334140
$435$	13.3640	−	23.1472i	0.640757	−	1.10982i
$436$	21.2984	−	36.8899i	1.02001	−	1.76670i
$437$	−21.8841			−1.04686
$438$	−13.1088	+	22.7051i	−0.626362	+	1.08489i
$439$	−8.47602	−	14.6809i	−0.404538	−	0.700681i	0.589729	−	0.807601i	$-0.299235\pi$
$439$	−8.47602	−	14.6809i	−0.404538	−	0.700681i	−0.994268	+	0.106920i	$0.965901\pi$
$440$	−2.97231	−	5.14819i	−0.141699	−	0.245430i
$441$	−16.8205			−0.800978
$442$		0			0
$443$	−24.1399			−1.14692			−0.573461	−	0.819233i	$-0.694400\pi$
$443$	−24.1399			−1.14692			−0.573461	+	0.819233i	$0.694400\pi$
$444$	−4.52599	−	7.83925i	−0.214794	−	0.372034i
$445$	−6.28917	−	10.8932i	−0.298135	−	0.516385i
$446$	−26.6262	+	46.1180i	−1.26079	+	2.18375i
$447$	37.7885			1.78733
$448$	−4.61371	+	7.99118i	−0.217977	+	0.377548i
$449$	−10.4315	+	18.0679i	−0.492293	+	0.852676i	−0.999961	−	0.00887706i	$-0.997174\pi$
$449$	−10.4315	+	18.0679i	−0.492293	+	0.852676i	0.507668	+	0.861553i	$0.330508\pi$
$450$	−12.4551			−0.587140
$451$	−0.143271	+	0.248153i	−0.00674637	+	0.0116851i
$452$	14.1371	+	24.4861i	0.664952	+	1.15173i
$453$	−25.8633	−	44.7965i	−1.21516	−	2.10472i
$454$	39.1437			1.83710
$455$		0			0
$456$	−90.0739			−4.21810
$457$	−15.2830	−	26.4708i	−0.714906	−	1.23825i	−0.962996	−	0.269517i	$-0.913136\pi$
$457$	−15.2830	−	26.4708i	−0.714906	−	1.23825i	0.248089	−	0.968737i	$-0.420197\pi$
$458$	9.50894	+	16.4700i	0.444324	+	0.769591i
$459$	1.79335	−	3.10617i	0.0837063	−	0.144984i
$460$	16.1402			0.752541
$461$	2.33911	−	4.05146i	0.108943	−	0.188695i	−0.806399	−	0.591372i	$-0.798587\pi$
$461$	2.33911	−	4.05146i	0.108943	−	0.188695i	0.915342	+	0.402676i	$0.131920\pi$
$462$	−7.18636	+	12.4471i	−0.334340	+	0.579094i
$463$	14.0011			0.650688			0.325344	−	0.945596i	$-0.394520\pi$
$463$	14.0011			0.650688			0.325344	+	0.945596i	$0.394520\pi$
$464$	−25.6098	+	44.3575i	−1.18891	+	2.05925i
$465$	2.06939	+	3.58429i	0.0959656	+	0.166217i
$466$	−23.7759	−	41.1811i	−1.10140	−	1.90768i
$467$	−6.98506			−0.323230			−0.161615	−	0.986854i	$-0.551670\pi$
$467$	−6.98506			−0.323230			−0.161615	+	0.986854i	$0.551670\pi$
$468$		0			0
$469$	15.4223			0.712135
$470$	11.7864	+	20.4147i	0.543668	+	0.941661i
$471$	3.42371	+	5.93004i	0.157756	+	0.273242i
$472$	−2.05967	+	3.56745i	−0.0948039	+	0.164205i
$473$	−0.681482			−0.0313346
$474$	32.8713	−	56.9347i	1.50983	−	2.61510i
$475$	2.86603	−	4.96410i	0.131502	−	0.227769i
$476$	−5.13277			−0.235260
$477$	17.4461	−	30.2176i	0.798804	−	1.38357i
$478$	−15.9132	−	27.5625i	−0.727853	−	1.26068i
$479$	−8.14438	−	14.1065i	−0.372126	−	0.644542i	0.617766	−	0.786362i	$-0.288038\pi$
$479$	−8.14438	−	14.1065i	−0.372126	−	0.644542i	−0.989892	+	0.141820i	$0.954704\pi$
$480$	6.78645			0.309758
$481$		0			0
$482$	64.7056			2.94726
$483$	−10.2810	−	17.8071i	−0.467800	−	0.810253i
$484$	20.8343	+	36.0860i	0.947012	+	1.64027i
$485$	−2.11078	+	3.65597i	−0.0958454	+	0.166009i
$486$	−35.5249			−1.61144
$487$	10.0204	−	17.3559i	0.454069	−	0.786471i	−0.544565	−	0.838719i	$-0.683305\pi$
$487$	10.0204	−	17.3559i	0.454069	−	0.786471i	0.998634	+	0.0522474i	$0.0166385\pi$
$488$	11.6697	−	20.2125i	0.528261	−	0.914975i
$489$	45.1810			2.04316
$490$	−4.20514	+	7.28351i	−0.189969	+	0.329035i
$491$	7.89916	+	13.6818i	0.356484	+	0.617449i	0.987371	−	0.158426i	$-0.0506420\pi$
$491$	7.89916	+	13.6818i	0.356484	+	0.617449i	−0.630887	+	0.775875i	$0.717309\pi$
$492$	−1.60108	−	2.77315i	−0.0721823	−	0.125023i
$493$	6.02540			0.271370
$494$		0			0
$495$	−5.33734			−0.239896
$496$	−3.96562	−	6.86865i	−0.178061	−	0.308411i
$497$	−9.30208	−	16.1117i	−0.417255	−	0.722708i
$498$	18.0514	−	31.2660i	0.808903	−	1.40106i
$499$	−1.24651			−0.0558016			−0.0279008	−	0.999611i	$-0.508882\pi$
$499$	−1.24651			−0.0558016			−0.0279008	+	0.999611i	$0.508882\pi$
$500$	−2.11378	+	3.66117i	−0.0945311	+	0.163733i
$501$	20.3436	−	35.2361i	0.908883	−	1.57423i
$502$	−18.9955			−0.847809
$503$	3.82672	−	6.62808i	0.170625	−	0.295532i	−0.768013	−	0.640434i	$-0.778755\pi$
$503$	3.82672	−	6.62808i	0.170625	−	0.295532i	0.938639	+	0.344902i	$0.112088\pi$
$504$	−26.4296	−	45.7774i	−1.17727	−	2.03909i
$505$	7.62379	+	13.2048i	0.339254	+	0.587605i
$506$	10.1886			0.452938
$507$		0			0
$508$	6.29695			0.279382
$509$	12.8621	+	22.2777i	0.570101	+	0.987444i	0.996555	+	0.0829345i	$0.0264292\pi$
$509$	12.8621	+	22.2777i	0.570101	+	0.987444i	−0.426454	+	0.904509i	$0.640237\pi$
$510$	−2.24775	−	3.89322i	−0.0995322	−	0.172395i
$511$	3.54035	−	6.13207i	0.156616	−	0.271267i
$512$	47.2215			2.08691
$513$	−16.1308	+	27.9393i	−0.712192	+	1.23355i
$514$	0.418974	−	0.725685i	0.0184802	−	0.0320086i
$515$	−13.5269			−0.596067
$516$	3.80785	−	6.59538i	0.167631	−	0.290346i
$517$	5.05080	+	8.74824i	0.222134	+	0.384747i
$518$	1.80064	+	3.11879i	0.0791154	+	0.137032i
$519$	68.8305			3.02132
$520$		0			0
$521$	−30.1519			−1.32098			−0.660490	−	0.750835i	$-0.729651\pi$
$521$	−30.1519			−1.32098			−0.660490	+	0.750835i	$0.729651\pi$
$522$	58.8823	+	101.987i	2.57721	+	4.46386i
$523$	−1.96876	−	3.41000i	−0.0860880	−	0.149109i	0.819766	−	0.572698i	$-0.194103\pi$
$523$	−1.96876	−	3.41000i	−0.0860880	−	0.149109i	−0.905854	+	0.423589i	$0.860770\pi$
$524$	−8.72307	+	15.1088i	−0.381069	+	0.660031i
$525$	5.38573			0.235052
$526$	−6.70779	+	11.6182i	−0.292473	+	0.506579i
$527$	−0.466509	+	0.808017i	−0.0203215	+	0.0351978i
$528$	16.3759			0.712672
$529$	4.21200	−	7.29539i	0.183130	−	0.317191i
$530$	−8.72307	−	15.1088i	−0.378906	−	0.656284i
$531$	1.84926	+	3.20301i	0.0802510	+	0.138999i
$532$	46.1682			2.00165
$533$		0			0
$534$	88.7326			3.83983
$535$	3.68137	+	6.37632i	0.159159	+	0.275672i
$536$	−22.4990	−	38.9694i	−0.971809	−	1.68322i
$537$	5.35444	−	9.27415i	0.231061	−	0.400209i
$538$	3.27007			0.140983
$539$	−1.80201	+	3.12117i	−0.0776180	+	0.134438i
$540$	11.8969	−	20.6061i	0.511963	−	0.886745i
$541$	15.8881			0.683083			0.341541	−	0.939867i	$-0.389051\pi$
$541$	15.8881			0.683083			0.341541	+	0.939867i	$0.389051\pi$
$542$	14.5305	−	25.1675i	0.624138	−	1.08104i
$543$	−11.9970	−	20.7795i	−0.514842	−	0.891732i
$544$	0.764945	+	1.32492i	0.0327968	+	0.0568057i
$545$	−10.0760			−0.431607
$546$		0			0
$547$	−6.56107			−0.280531			−0.140266	−	0.990114i	$-0.544796\pi$
$547$	−6.56107			−0.280531			−0.140266	+	0.990114i	$0.544796\pi$
$548$	−42.5074	−	73.6249i	−1.81582	−	3.14510i
$549$	−10.4775	−	18.1476i	−0.447170	−	0.774522i
$550$	−1.33433	+	2.31114i	−0.0568962	+	0.0985471i
$551$	−54.1972			−2.30888
$552$	−29.9970	+	51.9564i	−1.27676	+	2.21141i
$553$	−8.87769	+	15.3766i	−0.377518	+	0.653880i
$554$	50.6990			2.15399
$555$	−1.07059	+	1.85432i	−0.0454441	+	0.0787116i
$556$	−44.0200	−	76.2450i	−1.86687	−	3.23351i
$557$	3.92503	+	6.79835i	0.166309	+	0.288055i	0.937119	−	0.349009i	$-0.113482\pi$
$557$	3.92503	+	6.79835i	0.166309	+	0.288055i	−0.770810	+	0.637065i	$0.780148\pi$
$558$	−18.2356			−0.771973
$559$		0			0
$560$	−10.3208			−0.436133
$561$	−0.963220	−	1.66835i	−0.0406672	−	0.0704377i
$562$	14.8163	+	25.6626i	0.624988	+	1.08251i
$563$	7.77976	−	13.4749i	0.327878	−	0.567901i	−0.654213	−	0.756310i	$-0.727000\pi$
$563$	7.77976	−	13.4749i	0.327878	−	0.567901i	0.982091	+	0.188410i	$0.0603333\pi$
$564$	−112.887			−4.75341
$565$	3.34403	−	5.79203i	0.140684	−	0.243673i
$566$	−28.2643	+	48.9552i	−1.18804	+	2.05774i
$567$	−1.78554			−0.0749857
$568$	−27.1409	+	47.0095i	−1.13881	+	1.97247i
$569$	−1.73957	−	3.01303i	−0.0729267	−	0.126313i	0.827256	−	0.561825i	$-0.189901\pi$
$569$	−1.73957	−	3.01303i	−0.0729267	−	0.126313i	−0.900183	+	0.435512i	$0.856567\pi$
$570$	20.2181	+	35.0187i	0.846842	+	1.46677i
$571$	−21.5118			−0.900240			−0.450120	−	0.892968i	$-0.648619\pi$
$571$	−21.5118			−0.900240			−0.450120	+	0.892968i	$0.648619\pi$
$572$		0			0
$573$	15.3868			0.642791
$574$	0.636978	+	1.10328i	0.0265870	+	0.0460500i
$575$	−1.90893	−	3.30636i	−0.0796078	−	0.137885i
$576$	12.0864	−	20.9342i	0.503599	−	0.872259i
$577$	−9.97608			−0.415310			−0.207655	−	0.978202i	$-0.566583\pi$
$577$	−9.97608			−0.415310			−0.207655	+	0.978202i	$0.566583\pi$
$578$	−20.7051	+	35.8623i	−0.861218	+	1.49167i
$579$	−17.1838	+	29.7632i	−0.714134	+	1.23692i
$580$	39.9721			1.65975
$581$	−4.87523	+	8.44414i	−0.202259	+	0.350322i
$582$	−14.8902	−	25.7907i	−0.617221	−	1.06906i
$583$	−3.73806	−	6.47451i	−0.154815	−	0.268147i
$584$	−20.6595			−0.854898
$585$		0			0
$586$	46.4482			1.91876
$587$	−12.0286	−	20.8341i	−0.496472	−	0.859915i	0.503519	−	0.863984i	$-0.332038\pi$
$587$	−12.0286	−	20.8341i	−0.496472	−	0.859915i	−0.999992	+	0.00406862i	$0.998705\pi$
$588$	−20.1378	−	34.8797i	−0.830469	−	1.43841i
$589$	4.19615	−	7.26795i	0.172899	−	0.299471i
$590$	1.84926			0.0761328
$591$	6.18837	−	10.7186i	0.254556	−	0.440903i
$592$	2.05160	−	3.55348i	0.0843203	−	0.146047i
$593$	−0.940219			−0.0386102			−0.0193051	−	0.999814i	$-0.506145\pi$
$593$	−0.940219			−0.0386102			−0.0193051	+	0.999814i	$0.506145\pi$
$594$	7.51001	−	13.0077i	0.308139	−	0.533713i
$595$	0.607061	+	1.05146i	0.0248871	+	0.0431057i
$596$	28.2565	+	48.9417i	1.15743	+	2.00473i
$597$	−58.9037			−2.41077
$598$		0			0
$599$	−11.4270			−0.466896			−0.233448	−	0.972369i	$-0.575001\pi$
$599$	−11.4270			−0.466896			−0.233448	+	0.972369i	$0.575001\pi$
$600$	−7.85704	−	13.6088i	−0.320762	−	0.555577i
$601$	18.0215	+	31.2142i	0.735114	+	1.27325i	0.954674	+	0.297655i	$0.0962045\pi$
$601$	18.0215	+	31.2142i	0.735114	+	1.27325i	−0.219560	+	0.975599i	$0.570462\pi$
$602$	−1.51493	+	2.62393i	−0.0617437	+	0.106943i
$603$	−40.4012			−1.64526
$604$	38.6787	−	66.9935i	1.57381	−	2.72593i
$605$	4.92820	−	8.53590i	0.200360	−	0.347034i
$606$	−107.562			−4.36942
$607$	−19.9454	+	34.5464i	−0.809557	+	1.40219i	0.103614	+	0.994618i	$0.466959\pi$
$607$	−19.9454	+	34.5464i	−0.809557	+	1.40219i	−0.913171	+	0.407576i	$0.866374\pi$
$608$	−6.88052	−	11.9174i	−0.279042	−	0.483315i
$609$	−25.4613	−	44.1003i	−1.03175	−	1.78704i
$610$	−10.4775			−0.424223
$611$		0			0
$612$	13.4461			0.543528
$613$	−0.172736	−	0.299187i	−0.00697673	−	0.0120841i	0.862516	−	0.506030i	$-0.168887\pi$
$613$	−0.172736	−	0.299187i	−0.00697673	−	0.0120841i	−0.869493	+	0.493946i	$0.835554\pi$
$614$	−3.92763	−	6.80286i	−0.158506	−	0.274541i
$615$	−0.378725	+	0.655970i	−0.0152716	+	0.0264513i
$616$	−11.3258			−0.456328
$617$	19.3425	−	33.5022i	0.778700	−	1.34875i	−0.153991	−	0.988072i	$-0.549213\pi$
$617$	19.3425	−	33.5022i	0.778700	−	1.34875i	0.932691	−	0.360676i	$-0.117454\pi$
$618$	47.7121	−	82.6398i	1.91926	−	3.32426i
$619$	−14.8971			−0.598764			−0.299382	−	0.954133i	$-0.596781\pi$
$619$	−14.8971			−0.598764			−0.299382	+	0.954133i	$0.596781\pi$
$620$	−3.09479	+	5.36033i	−0.124290	+	0.215276i
$621$	10.7440	+	18.6091i	0.431141	+	0.746758i
$622$	−3.96859	−	6.87381i	−0.159126	−	0.275615i
$623$	−23.9644			−0.960113
$624$		0			0
$625$	1.00000			0.0400000
$626$	44.1123	+	76.4047i	1.76308	+	3.05374i
$627$	8.66397	+	15.0064i	0.346006	+	0.599299i
$628$	−5.12019	+	8.86842i	−0.204318	+	0.353889i
$629$	−0.482694			−0.0192463
$630$	−11.8648	+	20.5505i	−0.472706	+	0.818750i
$631$	−19.4225	+	33.6408i	−0.773198	+	1.33922i	0.162604	+	0.986691i	$0.448011\pi$
$631$	−19.4225	+	33.6408i	−0.773198	+	1.33922i	−0.935802	+	0.352526i	$0.885323\pi$
$632$	51.8053			2.06071
$633$	−15.0581	+	26.0814i	−0.598506	+	1.03664i
$634$	17.0140	+	29.4691i	0.675713	+	1.17037i
$635$	−0.744750	−	1.28994i	−0.0295545	−	0.0511899i
$636$	83.5470			3.31285
$637$		0			0
$638$	25.2326			0.998967
$639$	24.3683	+	42.2072i	0.963996	+	1.66969i
$640$	−8.44391	−	14.6253i	−0.333775	−	0.578115i
$641$	−18.5908	+	32.2003i	−0.734293	+	1.27183i	0.220739	+	0.975333i	$0.429153\pi$
$641$	−18.5908	+	32.2003i	−0.734293	+	1.27183i	−0.955033	+	0.296501i	$0.904180\pi$
$642$	−51.9397			−2.04990
$643$	4.55189	−	7.88410i	0.179509	−	0.310918i	−0.762204	−	0.647337i	$-0.775882\pi$
$643$	4.55189	−	7.88410i	0.179509	−	0.310918i	0.941712	+	0.336419i	$0.109216\pi$
$644$	15.3753	−	26.6307i	0.605870	−	1.04940i
$645$	−1.80144			−0.0709316
$646$	−4.55783	+	7.89439i	−0.179325	+	0.310601i
$647$	9.56118	+	16.5605i	0.375889	+	0.651059i	0.990460	−	0.137803i	$-0.0440041\pi$
$647$	9.56118	+	16.5605i	0.375889	+	0.651059i	−0.614571	+	0.788862i	$0.710671\pi$
$648$	2.60486	+	4.51175i	0.102329	+	0.177238i
$649$	0.792455			0.0311066
$650$		0			0
$651$	7.88525			0.309047
$652$	33.7843	+	58.5161i	1.32309	+	2.29167i
$653$	−17.3162	−	29.9926i	−0.677636	−	1.17370i	−0.975691	−	0.219152i	$-0.929671\pi$
$653$	−17.3162	−	29.9926i	−0.677636	−	1.17370i	0.298055	−	0.954549i	$-0.403662\pi$
$654$	35.5399	−	61.5570i	1.38972	−	2.40707i
$655$	4.12676			0.161246
$656$	0.725758	−	1.25705i	0.0283361	−	0.0490796i
$657$	−9.27453	+	16.0640i	−0.361834	+	0.626714i
$658$	44.9114			1.75083
$659$	3.34926	−	5.80109i	0.130469	−	0.225978i	−0.793389	−	0.608715i	$-0.791685\pi$
$659$	3.34926	−	5.80109i	0.130469	−	0.225978i	0.923857	+	0.382737i	$0.125018\pi$
$660$	−6.38994	−	11.0677i	−0.248728	−	0.430809i
$661$	3.01379	+	5.22004i	0.117223	+	0.203036i	0.918666	−	0.395035i	$-0.129268\pi$
$661$	3.01379	+	5.22004i	0.117223	+	0.203036i	−0.801443	+	0.598071i	$0.795934\pi$
$662$	−71.8604			−2.79294
$663$		0			0
$664$	28.4492			1.10404
$665$	−5.46039	−	9.45767i	−0.211745	−	0.366753i
$666$	−4.71706	−	8.17018i	−0.182782	−	0.316588i
$667$	−18.0491	+	31.2620i	−0.698865	+	1.21047i
$668$	60.8479			2.35428
$669$	−30.1614	+	52.2411i	−1.16611	+	2.01976i
$670$	−10.1003	+	17.4942i	−0.390209	+	0.675861i
$671$	−4.48990			−0.173330
$672$	6.46481	−	11.1974i	0.249386	−	0.431948i
$673$	−11.6784	−	20.2276i	−0.450169	−	0.779715i	0.548227	−	0.836329i	$-0.315303\pi$
$673$	−11.6784	−	20.2276i	−0.450169	−	0.779715i	−0.998396	+	0.0566140i	$0.981970\pi$
$674$	14.6603	+	25.3923i	0.564692	+	0.978075i
$675$	−5.62828			−0.216633
$676$		0			0
$677$	−45.4042			−1.74503			−0.872513	−	0.488590i	$-0.837511\pi$
$677$	−45.4042			−1.74503			−0.872513	+	0.488590i	$0.837511\pi$
$678$	23.5901	+	40.8593i	0.905973	+	1.56919i
$679$	4.02148	+	6.96540i	0.154330	+	0.267308i
$680$	1.77124	−	3.06787i	0.0679239	−	0.117648i
$681$	44.3408			1.69914
$682$	−1.95360	+	3.38374i	−0.0748073	+	0.129570i
$683$	−12.7489	+	22.0817i	−0.487823	+	0.844934i	−0.999902	−	0.0140045i	$-0.995542\pi$
$683$	−12.7489	+	22.0817i	−0.487823	+	0.844934i	0.512079	+	0.858938i	$0.328875\pi$
$684$	−120.945			−4.62445
$685$	−10.0548	+	17.4155i	−0.384175	+	0.665411i
$686$	24.6523	+	42.6991i	0.941230	+	1.63026i
$687$	10.7715	+	18.6567i	0.410957	+	0.711798i
$688$	3.45214			0.131612
$689$		0			0
$690$	26.9327			1.02531
$691$	−3.29815	−	5.71257i	−0.125468	−	0.217316i	0.796448	−	0.604707i	$-0.206710\pi$
$691$	−3.29815	−	5.71257i	−0.125468	−	0.217316i	−0.921916	+	0.387391i	$0.873376\pi$
$692$	51.4683	+	89.1457i	1.95653	+	3.38881i
$693$	−5.08438	+	8.80641i	−0.193140	+	0.334528i
$694$	−4.74090			−0.179962
$695$	−10.4126	+	18.0352i	−0.394974	+	0.684115i
$696$	−74.2892	+	128.673i	−2.81593	+	4.87733i
$697$	−0.170754			−0.00646778
$698$	12.8133	−	22.1933i	0.484990	−	0.840028i
$699$	−26.9327	−	46.6487i	−1.01869	−	1.76442i
$700$	4.02720	+	6.97531i	0.152214	+	0.263642i
$701$	29.2474			1.10466			0.552329	−	0.833626i	$-0.313739\pi$
$701$	29.2474			1.10466			0.552329	+	0.833626i	$0.313739\pi$
$702$		0			0
$703$	4.34174			0.163752
$704$	−2.58966	−	4.48542i	−0.0976015	−	0.169051i
$705$	13.3513	+	23.1252i	0.502841	+	0.870946i
$706$	−0.998937	+	1.73021i	−0.0375955	+	0.0651173i
$707$	29.0499			1.09253
$708$	−4.42792	+	7.66938i	−0.166411	+	0.288233i
$709$	5.46673	−	9.46865i	0.205307	−	0.355603i	−0.744923	−	0.667150i	$-0.767514\pi$
$709$	5.46673	−	9.46865i	0.205307	−	0.355603i	0.950231	+	0.311548i	$0.100847\pi$
$710$	24.3683			0.914527
$711$	23.2566	−	40.2815i	0.872189	−	1.51068i
$712$	34.9608	+	60.5538i	1.31021	+	2.26935i
$713$	−2.79486	−	4.84084i	−0.104668	−	0.181291i
$714$	−8.56490			−0.320533
$715$		0			0
$716$	16.0152			0.598516
$717$	−18.0260	−	31.2220i	−0.673194	−	1.16601i
$718$	−10.1476	−	17.5762i	−0.378706	−	0.655938i
$719$	−8.02989	+	13.9082i	−0.299464	+	0.518688i	−0.976014	−	0.217710i	$-0.930141\pi$
$719$	−8.02989	+	13.9082i	−0.299464	+	0.518688i	0.676549	+	0.736398i	$0.263475\pi$
$720$	27.0370			1.00761
$721$	−12.8858	+	22.3189i	−0.479893	+	0.831199i
$722$	17.2894	−	29.9461i	0.643444	−	1.11448i
$723$	73.2966			2.72593
$724$	17.9416	−	31.0758i	0.666796	−	1.15492i
$725$	−4.72756	−	8.18837i	−0.175577	−	0.304108i
$726$	34.7655	+	60.2156i	1.29027	+	2.23481i
$727$	51.3754			1.90541			0.952704	−	0.303900i	$-0.0982889\pi$
$727$	51.3754			1.90541			0.952704	+	0.303900i	$0.0982889\pi$
$728$		0			0
$729$	−43.0532			−1.59456
$730$	4.63726	+	8.03198i	0.171633	+	0.297277i
$731$	−0.203052	−	0.351697i	−0.00751016	−	0.0130080i
$732$	25.0877	−	43.4532i	0.927268	−	1.60608i
$733$	9.82358			0.362842			0.181421	−	0.983406i	$-0.441930\pi$
$733$	9.82358			0.362842			0.181421	+	0.983406i	$0.441930\pi$
$734$	−25.6120	+	44.3613i	−0.945357	+	1.63741i
$735$	−4.76346	+	8.25055i	−0.175703	+	0.304326i
$736$	−9.16560			−0.337848
$737$	−4.32824	+	7.49673i	−0.159433	+	0.276146i
$738$	−1.66867	−	2.89022i	−0.0614246	−	0.106390i
$739$	24.5421	+	42.5082i	0.902797	+	1.56369i	0.823848	+	0.566811i	$0.191823\pi$
$739$	24.5421	+	42.5082i	0.902797	+	1.56369i	0.0789487	+	0.996879i	$0.474844\pi$
$740$	−3.20216			−0.117714
$741$		0			0
$742$	−33.2386			−1.22023
$743$	20.4188	+	35.3663i	0.749091	+	1.29746i	0.948259	+	0.317499i	$0.102843\pi$
$743$	20.4188	+	35.3663i	0.749091	+	1.29746i	−0.199167	+	0.979966i	$0.563824\pi$
$744$	−11.5035	−	19.9247i	−0.421739	−	0.730473i
$745$	6.68388	−	11.5768i	0.244878	−	0.424142i
$746$	44.4346			1.62687
$747$	12.7715	−	22.1208i	0.467283	−	0.809358i
$748$	1.44050	−	2.49503i	0.0526700	−	0.0912272i
$749$	14.0276			0.512557
$750$	−3.52720	+	6.10929i	−0.128795	+	0.223080i
$751$	1.36340	+	2.36148i	0.0497512	+	0.0861716i	0.889829	−	0.456295i	$-0.150824\pi$
$751$	1.36340	+	2.36148i	0.0497512	+	0.0861716i	−0.840077	+	0.542467i	$0.817490\pi$
$752$	−25.5855	−	44.3154i	−0.933006	−	1.61601i
$753$	−21.5175			−0.784142
$754$		0			0
$755$	−18.2984			−0.665946
$756$	−22.6662	−	39.2590i	−0.824362	−	1.42784i
$757$	−7.40301	−	12.8224i	−0.269067	−	0.466038i	0.699554	−	0.714580i	$-0.253382\pi$
$757$	−7.40301	−	12.8224i	−0.269067	−	0.466038i	−0.968621	+	0.248542i	$0.920049\pi$
$758$	−2.55234	+	4.42078i	−0.0927051	+	0.160570i
$759$	11.5413			0.418924
$760$	−15.9319	+	27.5949i	−0.577911	+	1.00097i
$761$	−5.68445	+	9.84575i	−0.206061	+	0.356908i	−0.950470	−	0.310815i	$-0.899398\pi$
$761$	−5.68445	+	9.84575i	−0.206061	+	0.356908i	0.744409	+	0.667724i	$0.232731\pi$
$762$	10.5075			0.380647
$763$	−9.59843	+	16.6250i	−0.347486	+	0.601864i
$764$	11.5055	+	19.9281i	0.416255	+	0.720975i
$765$	−1.59030	−	2.75447i	−0.0574972	−	0.0995882i
$766$	−19.7275			−0.712784
$767$		0			0
$768$	91.7512			3.31078
$769$	−10.5281	−	18.2352i	−0.379654	−	0.657579i	0.611358	−	0.791354i	$-0.290623\pi$
$769$	−10.5281	−	18.2352i	−0.379654	−	0.657579i	−0.991012	+	0.133775i	$0.957290\pi$
$770$	2.54219	+	4.40320i	0.0916142	+	0.158680i
$771$	0.474602	−	0.822034i	0.0170924	−	0.0296048i
$772$	−51.3970			−1.84982
$773$	7.04144	−	12.1961i	0.253263	−	0.438664i	−0.711159	−	0.703031i	$-0.751830\pi$
$773$	7.04144	−	12.1961i	0.253263	−	0.438664i	0.964422	+	0.264367i	$0.0851629\pi$
$774$	3.96859	−	6.87381i	0.142648	−	0.247074i
$775$	1.46410			0.0525921
$776$	11.7336	−	20.3231i	0.421210	−	0.729558i
$777$	2.03971	+	3.53288i	0.0731741	+	0.126741i
$778$	−11.4940	−	19.9081i	−0.412078	−	0.713740i
$779$	1.53590			0.0550293
$780$		0			0
$781$	10.4425			0.373660
$782$	3.03576	+	5.25809i	0.108558	+	0.188029i
$783$	26.6080	+	46.0864i	0.950893	+	1.64699i
$784$	9.12832	−	15.8107i	0.326011	−	0.564668i
$785$	2.42229			0.0864552
$786$	−14.5559	+	25.2116i	−0.519192	+	0.899267i
$787$	16.5121	−	28.5998i	0.588593	−	1.01947i	−0.405823	−	0.913951i	$-0.633015\pi$
$787$	16.5121	−	28.5998i	0.588593	−	1.01947i	0.994417	−	0.105522i	$-0.0336514\pi$
$788$	18.5095			0.659374
$789$	−7.59839	+	13.1608i	−0.270510	+	0.468537i
$790$	−11.6283	−	20.1408i	−0.413716	−	0.716576i
$791$	−6.37109	−	11.0350i	−0.226530	−	0.392361i
$792$	29.6697			1.05427
$793$		0			0
$794$	−15.8574			−0.562758
$795$	−9.88124	−	17.1148i	−0.350451	−	0.606999i
$796$	−44.0454	−	76.2890i	−1.56115	−	2.70399i
$797$	8.47079	−	14.6718i	0.300051	−	0.519703i	−0.676096	−	0.736813i	$-0.736330\pi$
$797$	8.47079	−	14.6718i	0.300051	−	0.519703i	0.976147	+	0.217110i	$0.0696630\pi$
$798$	77.0395			2.72717
$799$	−3.00984	+	5.21319i	−0.106480	+	0.184429i
$800$	1.20036	−	2.07908i	0.0424391	−	0.0735067i
$801$	62.7787			2.21817
$802$	−5.20213	+	9.01036i	−0.183694	+	0.318167i
$803$	1.98719	+	3.44191i	0.0701263	+	0.121462i
$804$	−48.3689	−	83.7774i	−1.70584	−	2.95460i
$805$	−7.27382			−0.256369
$806$		0			0
$807$	3.70425			0.130396
$808$	−42.3798	−	73.4039i	−1.49092	−	2.58234i
$809$	25.8818	+	44.8285i	0.909954	+	1.57609i	0.814125	+	0.580689i	$0.197217\pi$
$809$	25.8818	+	44.8285i	0.909954	+	1.57609i	0.0958292	+	0.995398i	$0.469450\pi$
$810$	1.16938	−	2.02543i	0.0410878	−	0.0711662i
$811$	−22.6699			−0.796047			−0.398023	−	0.917375i	$-0.630304\pi$
$811$	−22.6699			−0.796047			−0.398023	+	0.917375i	$0.630304\pi$
$812$	38.0776	−	65.9524i	1.33626	−	2.31448i
$813$	16.4597	−	28.5091i	0.577267	−	0.999856i
$814$	−2.02138			−0.0708494
$815$	7.99144	−	13.8416i	0.279928	−	0.484849i
$816$	4.87932	+	8.45123i	0.170810	+	0.295852i
$817$	1.82641	+	3.16344i	0.0638981	+	0.110675i
$818$	25.3745			0.887198
$819$		0			0
$820$	−1.13277			−0.0395581
$821$	14.3315	+	24.8230i	0.500174	+	0.866328i	1.00000		0.000201482i	$6.41336e-5\pi$
$821$	14.3315	+	24.8230i	0.500174	+	0.866328i	−0.499826	+	0.866126i	$0.666603\pi$
$822$	−70.9307	−	122.856i	−2.47399	−	4.28508i
$823$	12.9164	−	22.3718i	0.450236	−	0.779831i	−0.548165	−	0.836371i	$-0.684673\pi$
$823$	12.9164	−	22.3718i	0.450236	−	0.779831i	0.998400	+	0.0565391i	$0.0180066\pi$
$824$	75.1946			2.61953
$825$	−1.51150	+	2.61799i	−0.0526235	+	0.0911466i
$826$	1.76162	−	3.05121i	0.0612945	−	0.106165i
$827$	16.0820			0.559227			0.279613	−	0.960113i	$-0.409794\pi$
$827$	16.0820			0.559227			0.279613	+	0.960113i	$0.409794\pi$
$828$	−40.2780	+	69.7635i	−1.39976	+	2.42445i
$829$	11.2909	+	19.5564i	0.392149	+	0.679222i	0.992733	−	0.120340i	$-0.0383984\pi$
$829$	11.2909	+	19.5564i	0.392149	+	0.679222i	−0.600584	+	0.799562i	$0.705065\pi$
$830$	−6.38573	−	11.0604i	−0.221652	−	0.383912i
$831$	57.4304			1.99224
$832$		0			0
$833$	−2.14768			−0.0744128
$834$	−73.4549	−	127.228i	−2.54354	−	4.40553i
$835$	−7.19658	−	12.4648i	−0.249048	−	0.431364i
$836$	−12.9570	+	22.4422i	−0.448128	+	0.776181i
$837$	−8.24037			−0.284829
$838$	35.6744	−	61.7898i	1.23235	−	2.13449i
$839$	−8.92198	+	15.4533i	−0.308021	+	0.533508i	−0.977929	−	0.208936i	$-0.933000\pi$
$839$	−8.92198	+	15.4533i	−0.308021	+	0.533508i	0.669908	+	0.742444i	$0.266333\pi$
$840$	−29.9387			−1.03298
$841$	−30.1996	+	52.3073i	−1.04137	+	1.80370i
$842$	−2.51793	−	4.36118i	−0.0867736	−	0.150296i
$843$	16.7835	+	29.0698i	0.578053	+	1.00122i
$844$	−45.0390			−1.55031
$845$		0			0
$846$	−117.653			−4.04498
$847$	−9.38927	−	16.2627i	−0.322619	−	0.558793i
$848$	18.9356	+	32.7975i	0.650252	+	1.12627i
$849$	−32.0169	+	55.4550i	−1.09882	+	1.90321i
$850$	−1.59030			−0.0545467
$851$	1.44591	−	2.50440i	0.0495653	−	0.0858497i
$852$	−58.3482	+	101.062i	−1.99898	+	3.46233i
$853$	−19.7936			−0.677720			−0.338860	−	0.940837i	$-0.610041\pi$
$853$	−19.7936			−0.677720			−0.338860	+	0.940837i	$0.610041\pi$
$854$	−9.98097	+	17.2875i	−0.341542	+	0.591568i
$855$	14.3044	+	24.7759i	0.489199	+	0.847318i
$856$	−20.4643	−	35.4452i	−0.699456	−	1.21149i
$857$	−11.7302			−0.400696			−0.200348	−	0.979725i	$-0.564207\pi$
$857$	−11.7302			−0.400696			−0.200348	+	0.979725i	$0.564207\pi$
$858$		0			0
$859$	5.37452			0.183376			0.0916882	−	0.995788i	$-0.470774\pi$
$859$	5.37452			0.183376			0.0916882	+	0.995788i	$0.470774\pi$
$860$	−1.34703	−	2.33313i	−0.0459335	−	0.0795591i
$861$	0.721551	+	1.24976i	0.0245904	+	0.0425918i
$862$	25.7191	−	44.5467i	0.875995	−	1.51727i
$863$	25.3234			0.862017			0.431008	−	0.902348i	$-0.358158\pi$
$863$	25.3234			0.862017			0.431008	+	0.902348i	$0.358158\pi$
$864$	−6.75596	+	11.7017i	−0.229842	+	0.398099i
$865$	12.1745	−	21.0868i	0.413944	−	0.716973i
$866$	−73.4567			−2.49616
$867$	−23.4541	+	40.6237i	−0.796544	+	1.37965i
$868$	5.89623	+	10.2126i	0.200131	+	0.346637i
$869$	−4.98302	−	8.63084i	−0.169037	−	0.292781i
$870$	66.7001			2.26135
$871$		0			0
$872$	56.0112			1.89678
$873$	−10.5349	−	18.2470i	−0.356553	−	0.617567i
$874$	−27.3060	−	47.2954i	−0.923640	−	1.59979i
$875$	0.952606	−	1.64996i	0.0322040	−	0.0557789i
$876$	−44.4144			−1.50062
$877$	10.3458	−	17.9194i	0.349352	−	0.605095i	−0.636783	−	0.771043i	$-0.719735\pi$
$877$	10.3458	−	17.9194i	0.349352	−	0.605095i	0.986134	+	0.165949i	$0.0530686\pi$
$878$	21.1520	−	36.6363i	0.713845	−	1.23642i
$879$	52.6151			1.77466
$880$	2.89651	−	5.01691i	0.0976414	−	0.169120i
$881$	−24.1997	−	41.9150i	−0.815307	−	1.41215i	−0.909107	−	0.416562i	$-0.863235\pi$
$881$	−24.1997	−	41.9150i	−0.815307	−	1.41215i	0.0937999	−	0.995591i	$-0.470099\pi$
$882$	−20.9879	−	36.3521i	−0.706699	−	1.22404i
$883$	45.8550			1.54314			0.771572	−	0.636142i	$-0.219471\pi$
$883$	45.8550			1.54314			0.771572	+	0.636142i	$0.219471\pi$
$884$		0			0
$885$	2.09479			0.0704155
$886$	−30.1207	−	52.1705i	−1.01192	−	1.75270i
$887$	0.541169	+	0.937332i	0.0181707	+	0.0314725i	0.874968	−	0.484181i	$-0.160882\pi$
$887$	0.541169	+	0.937332i	0.0181707	+	0.0314725i	−0.856797	+	0.515654i	$0.827549\pi$
$888$	5.95131	−	10.3080i	0.199713	−	0.345913i
$889$	−2.83781			−0.0951772
$890$	15.6947	−	27.1840i	0.526086	−	0.911208i
$891$	0.501109	−	0.867947i	0.0167878	−	0.0290773i
$892$	−90.2133			−3.02056
$893$	27.0729	−	46.8916i	0.905959	−	1.56917i
$894$	47.1507	+	81.6675i	1.57696	+	2.73137i
$895$	−1.89414	−	3.28075i	−0.0633142	−	0.109663i
$896$	−32.1749			−1.07489
$897$		0			0
$898$	−52.0637			−1.73739
$899$	−6.92163	−	11.9886i	−0.230849	−	0.399842i
$900$	−10.5499	−	18.2730i	−0.351663	−	0.609099i
$901$	2.22756	−	3.85824i	0.0742107	−	0.128537i
$902$	−0.715068			−0.0238092
$903$	−1.71606	+	2.97231i	−0.0571070	+	0.0989122i
$904$	−18.5891	+	32.1973i	−0.618264	+	1.07086i
$905$	−8.48794			−0.282149
$906$	64.5420	−	111.790i	2.14426	−	3.71397i
$907$	22.7653	+	39.4307i	0.755910	+	1.30928i	0.944920	+	0.327300i	$0.106139\pi$
$907$	22.7653	+	39.4307i	0.755910	+	1.30928i	−0.189010	+	0.981975i	$0.560528\pi$
$908$	33.1560	+	57.4279i	1.10032	+	1.90581i
$909$	−76.1009			−2.52411
$910$		0			0
$911$	39.7417			1.31670			0.658350	−	0.752712i	$-0.271255\pi$
$911$	39.7417			1.31670			0.658350	+	0.752712i	$0.271255\pi$
$912$	−43.8885	−	76.0171i	−1.45329	−	2.51718i
$913$	−2.73645	−	4.73967i	−0.0905632	−	0.156860i
$914$	38.1387	−	66.0582i	1.26152	−	2.18501i
$915$	−11.8687			−0.392365
$916$	−16.1088	+	27.9012i	−0.532250	+	0.921883i
$917$	3.93118	−	6.80900i	0.129819	−	0.224853i
$918$	8.95062			0.295415
$919$	−23.4969	+	40.6978i	−0.775091	+	1.34250i	0.159653	+	0.987173i	$0.448963\pi$
$919$	−23.4969	+	40.6978i	−0.775091	+	1.34250i	−0.934743	+	0.355323i	$0.884371\pi$
$920$	10.6115	+	18.3797i	0.349851	+	0.605960i
$921$	−4.44911	−	7.70608i	−0.146603	−	0.253924i
$922$	11.6745			0.384481
$923$		0			0
$924$	−24.3484			−0.801002
$925$	0.378725	+	0.655970i	0.0124524	+	0.0215682i
$926$	17.4700	+	30.2589i	0.574099	+	0.994369i
$927$	33.7565	−	58.4680i	1.10871	−	1.92034i
$928$	−22.6991			−0.745134
$929$	−7.61066	+	13.1821i	−0.249698	+	0.432489i	−0.963442	−	0.267917i	$-0.913665\pi$
$929$	−7.61066	+	13.1821i	−0.249698	+	0.432489i	0.713744	+	0.700406i	$0.246998\pi$
$930$	−5.16418	+	8.94462i	−0.169340	+	0.293306i
$931$	19.3180			0.633121
$932$	40.2780	−	69.7635i	1.31935	−	2.28518i
$933$	−4.49551	−	7.78645i	−0.147176	−	0.254917i
$934$	−8.71564	−	15.0959i	−0.285184	−	0.493954i
$935$	−0.681482			−0.0222869
$936$		0			0
$937$	6.07285			0.198392			0.0991958	−	0.995068i	$-0.468373\pi$
$937$	6.07285			0.198392			0.0991958	+	0.995068i	$0.468373\pi$
$938$	19.2432	+	33.3302i	0.628313	+	1.08827i
$939$	49.9691	+	86.5490i	1.63068	+	2.82442i
$940$	−19.9670	+	34.5839i	−0.651253	+	1.12800i
$941$	0.0496576			0.00161879			0.000809396	−	1.00000i	$-0.499742\pi$
$941$	0.0496576			0.00161879			0.000809396		1.00000i	$0.499742\pi$
$942$	−8.54390	+	14.7985i	−0.278375	+	0.482160i
$943$	0.511495	−	0.885936i	0.0166566	−	0.0288500i
$944$	−4.01429			−0.130654
$945$	−5.36153	+	9.28645i	−0.174411	+	0.302088i
$946$	−0.850322	−	1.47280i	−0.0276464	−	0.0478849i
$947$	−9.32907	−	16.1584i	−0.303154	−	0.525078i	0.673695	−	0.739010i	$-0.264706\pi$
$947$	−9.32907	−	16.1584i	−0.303154	−	0.525078i	−0.976849	+	0.213932i	$0.931373\pi$
$948$	111.372			3.61720
$949$		0			0
$950$	14.3044			0.464095
$951$	19.2730	+	33.3818i	0.624969	+	1.08248i
$952$	−3.37458	−	5.84495i	−0.109371	−	0.189436i
$953$	0.764764	−	1.32461i	0.0247731	−	0.0429083i	−0.853373	−	0.521301i	$-0.825447\pi$
$953$	0.764764	−	1.32461i	0.0247731	−	0.0429083i	0.878146	+	0.478392i	$0.158780\pi$
$954$	87.0739			2.81912
$955$	2.72155	−	4.71386i	0.0880673	−	0.152537i
$956$	26.9581	−	46.6927i	0.871886	−	1.51015i
$957$	28.5827			0.923948
$958$	20.3244	−	35.2028i	0.656650	−	1.13735i
$959$	19.1566	+	33.1802i	0.618598	+	1.07144i
$960$	−6.84555	−	11.8568i	−0.220939	−	0.382678i
$961$	−28.8564			−0.930852
$962$		0			0
$963$	−36.7475			−1.18417
$964$	54.8078	+	94.9299i	1.76524	+	3.05749i
$965$	6.07880	+	10.5288i	0.195683	+	0.338934i
$966$	25.6562	−	44.4379i	0.825475	−	1.42976i
$967$	−32.1716			−1.03457			−0.517285	−	0.855813i	$-0.673057\pi$
$967$	−32.1716			−1.03457			−0.517285	+	0.855813i	$0.673057\pi$
$968$	−27.3953	+	47.4501i	−0.880519	+	1.52510i
$969$	−5.16297	+	8.94253i	−0.165859	+	0.287276i
$970$	−10.5349			−0.338256
$971$	8.62705	−	14.9425i	0.276855	−	0.479527i	−0.693746	−	0.720219i	$-0.744041\pi$
$971$	8.62705	−	14.9425i	0.276855	−	0.479527i	0.970601	+	0.240692i	$0.0773745\pi$
$972$	−30.0908	−	52.1188i	−0.965164	−	1.67171i
$973$	19.8383	+	34.3609i	0.635986	+	1.10156i
$974$	50.0122			1.60249
$975$		0			0
$976$	22.7442			0.728023
$977$	7.86142	+	13.6164i	0.251509	+	0.435626i	0.963942	−	0.266114i	$-0.0857398\pi$
$977$	7.86142	+	13.6164i	0.251509	+	0.435626i	−0.712432	+	0.701741i	$0.752407\pi$
$978$	56.3748	+	97.6440i	1.80267	+	3.12231i
$979$	6.72557	−	11.6490i	0.214950	−	0.372304i
$980$	−14.2476			−0.455122
$981$	25.1447	−	43.5518i	0.802807	−	1.39050i
$982$	−19.7124	+	34.1429i	−0.629049	+	1.08954i
$983$	−38.5356			−1.22910			−0.614548	−	0.788880i	$-0.710662\pi$
$983$	−38.5356			−1.22910			−0.614548	+	0.788880i	$0.710662\pi$
$984$	2.10529	−	3.64647i	0.0671141	−	0.116245i
$985$	−2.18915	−	3.79172i	−0.0697521	−	0.120814i
$986$	7.51821	+	13.0219i	0.239429	+	0.414703i
$987$	50.8743			1.61935
$988$		0			0
$989$	2.43298			0.0773642
$990$	−6.65968	−	11.5349i	−0.211659	−	0.366604i
$991$	−4.29571	−	7.44040i	−0.136458	−	0.236352i	0.789696	−	0.613499i	$-0.210238\pi$
$991$	−4.29571	−	7.44040i	−0.136458	−	0.236352i	−0.926153	+	0.377147i	$0.876905\pi$
$992$	1.75745	−	3.04399i	0.0557991	−	0.0966468i
$993$	−81.4014			−2.58320
$994$	23.2134	−	40.2068i	0.736285	−	1.27528i
$995$	−10.4186	+	18.0456i	−0.330293	+	0.572085i
$996$	61.1606			1.93795
$997$	10.2687	−	17.7859i	0.325213	−	0.563285i	−0.656343	−	0.754463i	$-0.727897\pi$
$997$	10.2687	−	17.7859i	0.325213	−	0.563285i	0.981555	+	0.191178i	$0.0612308\pi$
$998$	−1.55534	−	2.69393i	−0.0492335	−	0.0852750i
$999$	−2.13157	−	3.69198i	−0.0674398	−	0.116809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.e.n.146.4		8
13.2	odd	12		845.2.c.g.506.8		8
13.3	even	3		845.2.a.l.1.1		4
13.4	even	6		845.2.e.m.191.1		8
13.5	odd	4		845.2.m.g.361.4		8
13.6	odd	12		65.2.m.a.56.1	yes	8
13.7	odd	12		845.2.m.g.316.4		8
13.8	odd	4		65.2.m.a.36.1	✓	8
13.9	even	3	inner	845.2.e.n.191.4		8
13.10	even	6		845.2.a.m.1.4		4
13.11	odd	12		845.2.c.g.506.1		8
13.12	even	2		845.2.e.m.146.1		8
39.8	even	4		585.2.bu.c.361.4		8
39.23	odd	6		7605.2.a.cf.1.1		4
39.29	odd	6		7605.2.a.cj.1.4		4
39.32	even	12		585.2.bu.c.316.4		8
52.19	even	12		1040.2.da.b.641.1		8
52.47	even	4		1040.2.da.b.881.1		8
65.8	even	4		325.2.m.c.49.4		8
65.19	odd	12		325.2.n.d.251.4		8
65.29	even	6		4225.2.a.bl.1.4		4
65.32	even	12		325.2.m.c.199.4		8
65.34	odd	4		325.2.n.d.101.4		8
65.47	even	4		325.2.m.b.49.1		8
65.49	even	6		4225.2.a.bi.1.1		4
65.58	even	12		325.2.m.b.199.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.1	✓	8	13.8	odd	4
65.2.m.a.56.1	yes	8	13.6	odd	12
325.2.m.b.49.1		8	65.47	even	4
325.2.m.b.199.1		8	65.58	even	12
325.2.m.c.49.4		8	65.8	even	4
325.2.m.c.199.4		8	65.32	even	12
325.2.n.d.101.4		8	65.34	odd	4
325.2.n.d.251.4		8	65.19	odd	12
585.2.bu.c.316.4		8	39.32	even	12
585.2.bu.c.361.4		8	39.8	even	4
845.2.a.l.1.1		4	13.3	even	3
845.2.a.m.1.4		4	13.10	even	6
845.2.c.g.506.1		8	13.11	odd	12
845.2.c.g.506.8		8	13.2	odd	12
845.2.e.m.146.1		8	13.12	even	2
845.2.e.m.191.1		8	13.4	even	6
845.2.e.n.146.4		8	1.1	even	1	trivial
845.2.e.n.191.4		8	13.9	even	3	inner
845.2.m.g.316.4		8	13.7	odd	12
845.2.m.g.361.4		8	13.5	odd	4
1040.2.da.b.641.1		8	52.19	even	12
1040.2.da.b.881.1		8	52.47	even	4
4225.2.a.bi.1.1		4	65.49	even	6
4225.2.a.bl.1.4		4	65.29	even	6
7605.2.a.cf.1.1		4	39.23	odd	6
7605.2.a.cj.1.4		4	39.29	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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.24775 + 2.16117i) q^{2} +(1.41342 + 2.44811i) q^{3} +(-2.11378 + 3.66117i) q^{4} +1.00000 q^{5} +(-3.52720 + 6.10929i) q^{6} +(0.952606 - 1.64996i) q^{7} -5.55889 q^{8} +(-2.49551 + 4.32235i) q^{9} +O(q^{10})\)	\(q+(1.24775 + 2.16117i) q^{2} +(1.41342 + 2.44811i) q^{3} +(-2.11378 + 3.66117i) q^{4} +1.00000 q^{5} +(-3.52720 + 6.10929i) q^{6} +(0.952606 - 1.64996i) q^{7} -5.55889 q^{8} +(-2.49551 + 4.32235i) q^{9} +(1.24775 + 2.16117i) q^{10} +(0.534695 + 0.926118i) q^{11} -11.9506 q^{12} +4.75447 q^{14} +(1.41342 + 2.44811i) q^{15} +(-2.70857 - 4.69138i) q^{16} +(-0.318632 + 0.551886i) q^{17} -12.4551 q^{18} +(2.86603 - 4.96410i) q^{19} +(-2.11378 + 3.66117i) q^{20} +5.38573 q^{21} +(-1.33433 + 2.31114i) q^{22} +(-1.90893 - 3.30636i) q^{23} +(-7.85704 - 13.6088i) q^{24} +1.00000 q^{25} -5.62828 q^{27} +(4.02720 + 6.97531i) q^{28} +(-4.72756 - 8.18837i) q^{29} +(-3.52720 + 6.10929i) q^{30} +1.46410 q^{31} +(1.20036 - 2.07908i) q^{32} +(-1.51150 + 2.61799i) q^{33} -1.59030 q^{34} +(0.952606 - 1.64996i) q^{35} +(-10.5499 - 18.2730i) q^{36} +(0.378725 + 0.655970i) q^{37} +14.3044 q^{38} -5.55889 q^{40} +(0.133975 + 0.232051i) q^{41} +(6.72006 + 11.6395i) q^{42} +(-0.318632 + 0.551886i) q^{43} -4.52091 q^{44} +(-2.49551 + 4.32235i) q^{45} +(4.76374 - 8.25104i) q^{46} +9.44613 q^{47} +(7.65668 - 13.2618i) q^{48} +(1.68508 + 2.91865i) q^{49} +(1.24775 + 2.16117i) q^{50} -1.80144 q^{51} -6.99102 q^{53} +(-7.02271 - 12.1637i) q^{54} +(0.534695 + 0.926118i) q^{55} +(-5.29543 + 9.17196i) q^{56} +16.2036 q^{57} +(11.7977 - 20.4341i) q^{58} +(0.370518 - 0.641756i) q^{59} -11.9506 q^{60} +(-2.09928 + 3.63606i) q^{61} +(1.82684 + 3.16418i) q^{62} +(4.75447 + 8.23499i) q^{63} -4.84325 q^{64} -7.54390 q^{66} +(4.04739 + 7.01029i) q^{67} +(-1.34703 - 2.33313i) q^{68} +(5.39623 - 9.34654i) q^{69} +4.75447 q^{70} +(4.88244 - 8.45663i) q^{71} +(13.8723 - 24.0274i) q^{72} +3.71649 q^{73} +(-0.945110 + 1.63698i) q^{74} +(1.41342 + 2.44811i) q^{75} +(12.1163 + 20.9860i) q^{76} +2.03741 q^{77} -9.31937 q^{79} +(-2.70857 - 4.69138i) q^{80} +(-0.468594 - 0.811629i) q^{81} +(-0.334335 + 0.579085i) q^{82} -5.11778 q^{83} +(-11.3842 + 19.7181i) q^{84} +(-0.318632 + 0.551886i) q^{85} -1.59030 q^{86} +(13.3640 - 23.1472i) q^{87} +(-2.97231 - 5.14819i) q^{88} +(-6.28917 - 10.8932i) q^{89} -12.4551 q^{90} +16.1402 q^{92} +(2.06939 + 3.58429i) q^{93} +(11.7864 + 20.4147i) q^{94} +(2.86603 - 4.96410i) q^{95} +6.78645 q^{96} +(-2.11078 + 3.65597i) q^{97} +(-4.20514 + 7.28351i) q^{98} -5.33734 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} - 4 q^{6} + 10 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 - 4 * q^6 + 10 * q^7 - 12 * q^8 - 4 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} - 4 q^{6} + 10 q^{7} - 12 q^{8} - 4 q^{9} + 2 q^{10} - 20 q^{12} + 4 q^{14} + 2 q^{15} - 2 q^{16} + 2 q^{17} - 40 q^{18} + 16 q^{19} - 2 q^{20} - 8 q^{21} - 12 q^{22} + 10 q^{23} - 24 q^{24} + 8 q^{25} - 4 q^{27} + 8 q^{28} - 8 q^{29} - 4 q^{30} - 16 q^{31} + 4 q^{32} + 18 q^{33} + 8 q^{34} + 10 q^{35} - 20 q^{36} - 2 q^{37} + 16 q^{38} - 12 q^{40} + 8 q^{41} + 4 q^{42} + 2 q^{43} - 24 q^{44} - 4 q^{45} + 16 q^{46} - 16 q^{47} + 28 q^{48} - 12 q^{49} + 2 q^{50} + 8 q^{51} - 24 q^{53} - 16 q^{54} - 12 q^{56} + 28 q^{57} + 22 q^{58} + 12 q^{59} - 20 q^{60} - 28 q^{61} - 4 q^{62} + 4 q^{63} + 8 q^{64} + 12 q^{66} + 30 q^{67} - 14 q^{68} + 16 q^{69} + 4 q^{70} + 4 q^{71} + 12 q^{72} + 16 q^{73} + 10 q^{74} + 2 q^{75} + 20 q^{76} + 36 q^{77} - 16 q^{79} - 2 q^{80} + 8 q^{81} - 4 q^{82} + 24 q^{83} - 28 q^{84} + 2 q^{85} + 8 q^{86} + 22 q^{87} + 18 q^{88} - 12 q^{89} - 40 q^{90} + 44 q^{92} + 8 q^{93} + 32 q^{94} + 16 q^{95} - 8 q^{96} + 2 q^{97} - 24 q^{98} - 48 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 - 4 * q^6 + 10 * q^7 - 12 * q^8 - 4 * q^9 + 2 * q^10 - 20 * q^12 + 4 * q^14 + 2 * q^15 - 2 * q^16 + 2 * q^17 - 40 * q^18 + 16 * q^19 - 2 * q^20 - 8 * q^21 - 12 * q^22 + 10 * q^23 - 24 * q^24 + 8 * q^25 - 4 * q^27 + 8 * q^28 - 8 * q^29 - 4 * q^30 - 16 * q^31 + 4 * q^32 + 18 * q^33 + 8 * q^34 + 10 * q^35 - 20 * q^36 - 2 * q^37 + 16 * q^38 - 12 * q^40 + 8 * q^41 + 4 * q^42 + 2 * q^43 - 24 * q^44 - 4 * q^45 + 16 * q^46 - 16 * q^47 + 28 * q^48 - 12 * q^49 + 2 * q^50 + 8 * q^51 - 24 * q^53 - 16 * q^54 - 12 * q^56 + 28 * q^57 + 22 * q^58 + 12 * q^59 - 20 * q^60 - 28 * q^61 - 4 * q^62 + 4 * q^63 + 8 * q^64 + 12 * q^66 + 30 * q^67 - 14 * q^68 + 16 * q^69 + 4 * q^70 + 4 * q^71 + 12 * q^72 + 16 * q^73 + 10 * q^74 + 2 * q^75 + 20 * q^76 + 36 * q^77 - 16 * q^79 - 2 * q^80 + 8 * q^81 - 4 * q^82 + 24 * q^83 - 28 * q^84 + 2 * q^85 + 8 * q^86 + 22 * q^87 + 18 * q^88 - 12 * q^89 - 40 * q^90 + 44 * q^92 + 8 * q^93 + 32 * q^94 + 16 * q^95 - 8 * q^96 + 2 * q^97 - 24 * q^98 - 48 * q^99

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