LMFDB - Embedded newform 845.2.e.m.146.1

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			146.1
Root			$1.20036 + 0.747754i$ of defining polynomial
Character	$\chi$	$=$	845.146
Dual form			845.2.e.m.191.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24775 - 2.16117i) q^{2} +(1.41342 + 2.44811i) q^{3} +(-2.11378 + 3.66117i) q^{4} -1.00000 q^{5} +(3.52720 - 6.10929i) q^{6} +(-0.952606 + 1.64996i) q^{7} +5.55889 q^{8} +(-2.49551 + 4.32235i) q^{9} +O(q^{10})$	\(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	$-0.822664\pi$
$2$	−1.24775	−	2.16117i	−0.882295	−	1.52818i	−0.0335125	−	0.999438i	$-0.510669\pi$
$3$	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	−0.987969	−	0.154653i	$-0.950574\pi$
$7$	−0.952606	+	1.64996i	−0.360051	+	0.623627i	0.627918	+	0.778280i	$0.283907\pi$
$8$	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	0.774089	−	0.633077i	$-0.218208\pi$
$11$	−0.534695	−	0.926118i	−0.161217	−	0.279235i	−0.935305	+	0.353842i	$0.884875\pi$
$12$	−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	$0.395057\pi$
$19$	−2.86603	+	4.96410i	−0.657511	+	1.13884i	−0.981258	+	0.192699i	$0.938276\pi$
$20$	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	$-0.541973\pi$
$31$	−1.46410			−0.262960			−0.131480	+	0.991319i	$0.541973\pi$
$32$	−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	0.833214	−	0.552950i	$-0.186498\pi$
$37$	−0.378725	−	0.655970i	−0.0622619	−	0.107841i	−0.895476	+	0.445110i	$0.853165\pi$
$38$	14.3044			2.32048
$39$		0			0
$40$	−5.55889			−0.878938
$41$	−0.133975	−	0.232051i	−0.0209233	−	0.0362402i	0.855374	−	0.518011i	$-0.173327\pi$
$41$	−0.133975	−	0.232051i	−0.0209233	−	0.0362402i	−0.876297	+	0.481770i	$0.839994\pi$
$42$	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	$-0.741919\pi$
$47$	−9.44613			−1.37786			−0.688930	+	0.724828i	$0.741919\pi$
$48$	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	−0.889136	−	0.457643i	$-0.848694\pi$
$59$	−0.370518	+	0.641756i	−0.0482373	+	0.0835495i	0.840899	+	0.541193i	$0.182027\pi$
$60$	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	0.505512	−	0.862820i	$-0.331304\pi$
$67$	−4.04739	−	7.01029i	−0.494468	−	0.856443i	−0.999980	+	0.00637624i	$0.997970\pi$
$68$	−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	$0.363395\pi$
$71$	−4.88244	+	8.45663i	−0.579439	+	1.00362i	−0.995544	+	0.0943010i	$0.969938\pi$
$72$	−13.8723	+	24.0274i	−1.63486	+	2.83166i
$73$	−3.71649			−0.434982			−0.217491	−	0.976062i	$-0.569787\pi$
$73$	−3.71649			−0.434982			−0.217491	+	0.976062i	$0.569787\pi$
$74$	−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	$-0.409376\pi$
$83$	5.11778			0.561749			0.280875	+	0.959744i	$0.409376\pi$
$84$	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	$0.0656059\pi$
$89$	6.28917	+	10.8932i	0.666650	+	1.15467i	−0.312185	+	0.950021i	$0.601061\pi$
$90$	−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	−0.738744	−	0.673986i	$-0.764581\pi$
$97$	2.11078	−	3.65597i	0.214317	−	0.371208i	0.953061	+	0.302778i	$0.0979142\pi$
$98$	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	$-0.339710\pi$
$109$	10.0760			0.965103			0.482551	+	0.875868i	$0.339710\pi$
$110$	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	$-0.504394\pi$
$137$	10.0548	−	17.4155i	0.859041	−	1.48790i	0.872844	−	0.487999i	$-0.162273\pi$
$138$	−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	$0.351112\pi$
$149$	−6.68388	+	11.5768i	−0.547565	+	0.948410i	−0.998441	+	0.0558233i	$0.982222\pi$
$150$	3.52720	−	6.10929i	0.287995	−	0.498821i
$151$	18.2984			1.48910			0.744550	−	0.667567i	$-0.232664\pi$
$151$	18.2984			1.48910			0.744550	+	0.667567i	$0.232664\pi$
$152$	−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	$0.381950\pi$
$163$	−7.99144	+	13.8416i	−0.625938	+	1.08416i	−0.988359	+	0.152142i	$0.951383\pi$
$164$	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	$0.0213381\pi$
$167$	7.19658	+	12.4648i	0.556888	+	0.964558i	−0.440866	+	0.897573i	$0.645329\pi$
$168$	−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	0.559939	−	0.828534i	$-0.310824\pi$
$193$	−6.07880	−	10.5288i	−0.437562	−	0.757879i	−0.997501	+	0.0706548i	$0.977491\pi$
$194$	−10.5349			−0.756363
$195$		0			0
$196$	−14.2476			−1.01768
$197$	2.18915	+	3.79172i	0.155970	+	0.270149i	0.933412	−	0.358807i	$-0.116816\pi$
$197$	2.18915	+	3.79172i	0.155970	+	0.270149i	−0.777442	+	0.628955i	$0.783483\pi$
$198$	−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	$-0.913324\pi$
$223$	−10.6697	−	18.4804i	−0.714494	−	1.23754i	0.248661	−	0.968591i	$-0.420010\pi$
$224$	−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	$0.340938\pi$
$227$	−7.84283	+	13.5842i	−0.520547	+	0.901613i	−0.999715	+	0.0238900i	$0.992395\pi$
$228$	34.2508	−	59.3241i	2.26831	−	3.92884i
$229$	−7.62085			−0.503600			−0.251800	−	0.967779i	$-0.581023\pi$
$229$	−7.62085			−0.503600			−0.251800	+	0.967779i	$0.581023\pi$
$230$	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	$-0.364664\pi$
$239$	12.7535			0.824954			0.412477	+	0.910968i	$0.364664\pi$
$240$	−7.65668	+	13.2618i	−0.494237	+	0.856043i
$241$	−12.9644	+	22.4550i	−0.835111	+	1.44646i	0.0588285	+	0.998268i	$0.481263\pi$
$241$	−12.9644	+	22.4550i	−0.835111	+	1.44646i	−0.893940	+	0.448187i	$0.852070\pi$
$242$	−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	0.986895	−	0.161365i	$-0.0515896\pi$
$271$	5.82266	+	10.0851i	0.353701	+	0.612629i	−0.633194	+	0.773994i	$0.718256\pi$
$272$	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	$-0.615241\pi$
$281$	−11.8744			−0.708366			−0.354183	+	0.935176i	$0.615241\pi$
$282$	−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	$0.349637\pi$
$293$	−9.30636	+	16.1191i	−0.543683	+	0.941687i	−0.998689	+	0.0511983i	$0.983696\pi$
$294$	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	$-0.471369\pi$
$307$	3.14776			0.179652			0.0898262	+	0.995957i	$0.471369\pi$
$308$	−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	$-0.625085\pi$
$317$	−13.6357			−0.765858			−0.382929	+	0.923778i	$0.625085\pi$
$318$	−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	$-0.542695\pi$
$331$	14.3980	−	24.9380i	0.791383	−	1.37072i	0.925110	−	0.379698i	$-0.123972\pi$
$332$	−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	0.970096	−	0.242721i	$-0.0780398\pi$
$349$	5.13454	+	8.89329i	0.274846	+	0.476047i	−0.695250	+	0.718768i	$0.744707\pi$
$350$	4.75447			0.254137
$351$		0			0
$352$	2.56730			0.136838
$353$	−0.400294	−	0.693330i	−0.0213055	−	0.0369022i	0.855176	−	0.518338i	$-0.173449\pi$
$353$	−0.400294	−	0.693330i	−0.0213055	−	0.0369022i	−0.876482	+	0.481435i	$0.840116\pi$
$354$	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	$-0.431151\pi$
$359$	8.13272			0.429228			0.214614	+	0.976699i	$0.431151\pi$
$360$	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	0.838561	−	0.544807i	$-0.183397\pi$
$379$	−1.02277	−	1.77150i	−0.0525363	−	0.0909956i	−0.891098	+	0.453812i	$0.850064\pi$
$380$	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	−0.747194	−	0.664606i	$-0.768599\pi$
$383$	3.95261	−	6.84611i	0.201969	−	0.349820i	0.949163	+	0.314786i	$0.101933\pi$
$384$	−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	−0.775215	−	0.631697i	$-0.782359\pi$
$397$	3.17719	−	5.50305i	0.159458	−	0.276190i	0.934674	+	0.355507i	$0.115692\pi$
$398$	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	0.809270	−	0.587437i	$-0.199863\pi$
$401$	−2.08460	−	3.61063i	−0.104100	−	0.180306i	−0.913370	+	0.407130i	$0.866530\pi$
$402$	−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	−0.963909	−	0.266234i	$-0.914221\pi$
$409$	−5.08403	+	8.80580i	−0.251389	+	0.435419i	0.712519	+	0.701652i	$0.247554\pi$
$410$	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	$-0.484341\pi$
$421$	2.01797			0.0983498			0.0491749	+	0.998790i	$0.484341\pi$
$422$	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	0.999992	−	0.00411765i	$-0.00131069\pi$
$431$	10.3061	+	17.8508i	0.496430	+	0.859842i	−0.503562	+	0.863959i	$0.667977\pi$
$432$	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	−0.507668	−	0.861553i	$-0.669492\pi$
$449$	10.4315	−	18.0679i	0.492293	−	0.852676i	0.999961	+	0.00887706i	$0.00282569\pi$
$450$	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	$0.0868640\pi$
$457$	15.2830	+	26.4708i	0.714906	+	1.23825i	−0.248089	+	0.968737i	$0.579803\pi$
$458$	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	−0.915342	−	0.402676i	$-0.868080\pi$
$461$	−2.33911	+	4.05146i	−0.108943	+	0.188695i	0.806399	+	0.591372i	$0.201413\pi$
$462$	7.18636	−	12.4471i	0.334340	−	0.579094i
$463$	−14.0011			−0.650688			−0.325344	−	0.945596i	$-0.605480\pi$
$463$	−14.0011			−0.650688			−0.325344	+	0.945596i	$0.605480\pi$
$464$	−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	0.989892	−	0.141820i	$-0.0452955\pi$
$479$	8.14438	+	14.1065i	0.372126	+	0.644542i	−0.617766	+	0.786362i	$0.711962\pi$
$480$	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	−0.998634	−	0.0522474i	$-0.983362\pi$
$487$	−10.0204	+	17.3559i	−0.454069	+	0.786471i	0.544565	+	0.838719i	$0.316695\pi$
$488$	−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	$-0.491118\pi$
$499$	1.24651			0.0558016			0.0279008	+	0.999611i	$0.491118\pi$
$500$	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	$-0.973571\pi$
$509$	−12.8621	−	22.2777i	−0.570101	−	0.987444i	0.426454	−	0.904509i	$-0.359763\pi$
$510$	−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	$-0.610949\pi$
$541$	−15.8881			−0.683083			−0.341541	+	0.939867i	$0.610949\pi$
$542$	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	0.770810	−	0.637065i	$-0.219852\pi$
$557$	−3.92503	−	6.79835i	−0.166309	−	0.288055i	−0.937119	+	0.349009i	$0.886518\pi$
$558$	−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	$-0.433417\pi$
$577$	9.97608			0.415310			0.207655	+	0.978202i	$0.433417\pi$
$578$	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	0.999992	−	0.00406862i	$-0.00129509\pi$
$587$	12.0286	+	20.8341i	0.496472	+	0.859915i	−0.503519	+	0.863984i	$0.667962\pi$
$588$	−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	$-0.493855\pi$
$593$	0.940219			0.0386102			0.0193051	+	0.999814i	$0.493855\pi$
$594$	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	0.869493	−	0.493946i	$-0.164446\pi$
$613$	0.172736	+	0.299187i	0.00697673	+	0.0120841i	−0.862516	+	0.506030i	$0.831113\pi$
$614$	−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	$0.450787\pi$
$617$	−19.3425	+	33.5022i	−0.778700	+	1.34875i	−0.932691	+	0.360676i	$0.882546\pi$
$618$	−47.7121	+	82.6398i	−1.91926	+	3.32426i
$619$	14.8971			0.598764			0.299382	−	0.954133i	$-0.403219\pi$
$619$	14.8971			0.598764			0.299382	+	0.954133i	$0.403219\pi$
$620$	−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	$-0.551989\pi$
$631$	19.4225	−	33.6408i	0.773198	−	1.33922i	0.935802	−	0.352526i	$-0.114677\pi$
$632$	−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	−0.941712	−	0.336419i	$-0.890784\pi$
$643$	−4.55189	+	7.88410i	−0.179509	+	0.310918i	0.762204	+	0.647337i	$0.224118\pi$
$644$	−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	0.801443	−	0.598071i	$-0.204066\pi$
$661$	−3.01379	−	5.22004i	−0.117223	−	0.203036i	−0.918666	+	0.395035i	$0.870732\pi$
$662$	−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	−0.512079	−	0.858938i	$-0.671125\pi$
$683$	12.7489	−	22.0817i	0.487823	−	0.844934i	0.999902	+	0.0140045i	$0.00445791\pi$
$684$	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	0.921916	−	0.387391i	$-0.126624\pi$
$691$	3.29815	+	5.71257i	0.125468	+	0.217316i	−0.796448	+	0.604707i	$0.793290\pi$
$692$	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	−0.950231	−	0.311548i	$-0.899153\pi$
$709$	−5.46673	+	9.46865i	−0.205307	+	0.355603i	0.744923	+	0.667150i	$0.232486\pi$
$710$	−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	$-0.558070\pi$
$733$	−9.82358			−0.362842			−0.181421	+	0.983406i	$0.558070\pi$
$734$	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	$-0.808177\pi$
$739$	−24.5421	−	42.5082i	−0.902797	−	1.56369i	−0.0789487	−	0.996879i	$-0.525156\pi$
$740$	−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	$-0.897157\pi$
$743$	−20.4188	−	35.3663i	−0.749091	−	1.29746i	0.199167	−	0.979966i	$-0.436176\pi$
$744$	−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	−0.744409	−	0.667724i	$-0.767269\pi$
$761$	5.68445	−	9.84575i	0.206061	−	0.356908i	0.950470	+	0.310815i	$0.100602\pi$
$762$	−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	0.991012	−	0.133775i	$-0.0427098\pi$
$769$	10.5281	+	18.2352i	0.379654	+	0.657579i	−0.611358	+	0.791354i	$0.709377\pi$
$770$	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	−0.964422	−	0.264367i	$-0.914837\pi$
$773$	−7.04144	+	12.1961i	−0.253263	+	0.438664i	0.711159	+	0.703031i	$0.248170\pi$
$774$	−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	$0.366985\pi$
$787$	−16.5121	+	28.5998i	−0.588593	+	1.01947i	−0.994417	+	0.105522i	$0.966349\pi$
$788$	−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	$-0.369696\pi$
$811$	22.6699			0.796047			0.398023	+	0.917375i	$0.369696\pi$
$812$	−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	$-0.999936\pi$
$821$	−14.3315	−	24.8230i	−0.500174	−	0.866328i	0.499826	−	0.866126i	$-0.333397\pi$
$822$	−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	$-0.590206\pi$
$827$	−16.0820			−0.559227			−0.279613	+	0.960113i	$0.590206\pi$
$828$	−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	−0.669908	−	0.742444i	$-0.733667\pi$
$839$	8.92198	−	15.4533i	0.308021	−	0.533508i	0.977929	+	0.208936i	$0.0670000\pi$
$840$	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	$-0.389959\pi$
$853$	19.7936			0.677720			0.338860	+	0.940837i	$0.389959\pi$
$854$	−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	$-0.641842\pi$
$863$	−25.3234			−0.862017			−0.431008	+	0.902348i	$0.641842\pi$
$864$	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	−0.986134	−	0.165949i	$-0.946931\pi$
$877$	−10.3458	+	17.9194i	−0.349352	+	0.605095i	0.636783	+	0.771043i	$0.280265\pi$
$878$	−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	−0.713744	−	0.700406i	$-0.753002\pi$
$929$	7.61066	−	13.1821i	0.249698	−	0.432489i	0.963442	+	0.267917i	$0.0863354\pi$
$930$	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	$-0.500258\pi$
$941$	−0.0496576			−0.00161879			−0.000809396		1.00000i	$0.500258\pi$
$942$	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	0.976849	−	0.213932i	$-0.0686270\pi$
$947$	9.32907	+	16.1584i	0.303154	+	0.525078i	−0.673695	+	0.739010i	$0.735294\pi$
$948$	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	$-0.326943\pi$
$967$	32.1716			1.03457			0.517285	+	0.855813i	$0.326943\pi$
$968$	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	0.712432	−	0.701741i	$-0.247593\pi$
$977$	−7.86142	−	13.6164i	−0.251509	−	0.435626i	−0.963942	+	0.266114i	$0.914260\pi$
$978$	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	$-0.289338\pi$
$983$	38.5356			1.22910			0.614548	+	0.788880i	$0.289338\pi$
$984$	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.m.146.1		8
13.2	odd	12		845.2.c.g.506.1		8
13.3	even	3		845.2.a.m.1.4		4
13.4	even	6		845.2.e.n.191.4		8
13.5	odd	4		65.2.m.a.36.1	✓	8
13.6	odd	12		845.2.m.g.316.4		8
13.7	odd	12		65.2.m.a.56.1	yes	8
13.8	odd	4		845.2.m.g.361.4		8
13.9	even	3	inner	845.2.e.m.191.1		8
13.10	even	6		845.2.a.l.1.1		4
13.11	odd	12		845.2.c.g.506.8		8
13.12	even	2		845.2.e.n.146.4		8
39.5	even	4		585.2.bu.c.361.4		8
39.20	even	12		585.2.bu.c.316.4		8
39.23	odd	6		7605.2.a.cj.1.4		4
39.29	odd	6		7605.2.a.cf.1.1		4
52.7	even	12		1040.2.da.b.641.1		8
52.31	even	4		1040.2.da.b.881.1		8
65.7	even	12		325.2.m.c.199.4		8
65.18	even	4		325.2.m.c.49.4		8
65.29	even	6		4225.2.a.bi.1.1		4
65.33	even	12		325.2.m.b.199.1		8
65.44	odd	4		325.2.n.d.101.4		8
65.49	even	6		4225.2.a.bl.1.4		4
65.57	even	4		325.2.m.b.49.1		8
65.59	odd	12		325.2.n.d.251.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.1	✓	8	13.5	odd	4
65.2.m.a.56.1	yes	8	13.7	odd	12
325.2.m.b.49.1		8	65.57	even	4
325.2.m.b.199.1		8	65.33	even	12
325.2.m.c.49.4		8	65.18	even	4
325.2.m.c.199.4		8	65.7	even	12
325.2.n.d.101.4		8	65.44	odd	4
325.2.n.d.251.4		8	65.59	odd	12
585.2.bu.c.316.4		8	39.20	even	12
585.2.bu.c.361.4		8	39.5	even	4
845.2.a.l.1.1		4	13.10	even	6
845.2.a.m.1.4		4	13.3	even	3
845.2.c.g.506.1		8	13.2	odd	12
845.2.c.g.506.8		8	13.11	odd	12
845.2.e.m.146.1		8	1.1	even	1	trivial
845.2.e.m.191.1		8	13.9	even	3	inner
845.2.e.n.146.4		8	13.12	even	2
845.2.e.n.191.4		8	13.4	even	6
845.2.m.g.316.4		8	13.6	odd	12
845.2.m.g.361.4		8	13.8	odd	4
1040.2.da.b.641.1		8	52.7	even	12
1040.2.da.b.881.1		8	52.31	even	4
4225.2.a.bi.1.1		4	65.29	even	6
4225.2.a.bl.1.4		4	65.49	even	6
7605.2.a.cf.1.1		4	39.29	odd	6
7605.2.a.cj.1.4		4	39.23	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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