LMFDB - Embedded newform 845.2.m.g.361.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(316,845)]

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, 1]))

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

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

chi := DirichletCharacter("845.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.m (of order $6$, 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 $\Q(\zeta_{6})$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.4
Root			$1.20036 - 0.747754i$ of defining polynomial
Character	$\chi$	$=$	845.361
Dual form			845.2.m.g.316.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	2.16117	−	1.24775i	1.52818	−	0.882295i	0.528742	−	0.848783i	$-0.322664\pi$
$2$	2.16117	−	1.24775i	1.52818	−	0.882295i	0.999438	−	0.0335125i	$-0.0106693\pi$
$3$	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
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	6.10929	+	3.52720i	2.49411	+	1.43997i
$7$	1.64996	+	0.952606i	0.623627	+	0.360051i	0.778280	−	0.627918i	$-0.216093\pi$
$7$	1.64996	+	0.952606i	0.623627	+	0.360051i	−0.154653	+	0.987969i	$0.549426\pi$
$8$		−	5.55889i		−	1.96536i
$9$	−2.49551	+	4.32235i	−0.831836	+	1.44078i
$10$	−1.24775	−	2.16117i	−0.394574	−	0.683423i
$11$	−0.926118	+	0.534695i	−0.279235	+	0.161217i	−0.633077	−	0.774089i	$-0.718208\pi$
$11$	−0.926118	+	0.534695i	−0.279235	+	0.161217i	0.353842	+	0.935305i	$0.384875\pi$
$12$	11.9506			3.44985
$13$		0			0
$13$		0			0
$14$	4.75447			1.27069
$15$	2.44811	−	1.41342i	0.632100	−	0.364943i
$16$	−2.70857	−	4.69138i	−0.677142	−	1.17284i
$17$	0.318632	−	0.551886i	0.0772795	−	0.133852i	−0.824796	−	0.565431i	$-0.808710\pi$
$17$	0.318632	−	0.551886i	0.0772795	−	0.133852i	0.902075	+	0.431579i	$0.142043\pi$
$18$			12.4551i			2.93570i
$19$	−4.96410	−	2.86603i	−1.13884	−	0.657511i	−0.192699	−	0.981258i	$-0.561724\pi$
$19$	−4.96410	−	2.86603i	−1.13884	−	0.657511i	−0.946144	+	0.323747i	$0.895057\pi$
$20$	−3.66117	−	2.11378i	−0.818663	−	0.472655i
$21$			5.38573i			1.17526i
$22$	−1.33433	+	2.31114i	−0.284481	+	0.492736i
$23$	1.90893	+	3.30636i	0.398039	+	0.689423i	0.993484	−	0.113973i	$-0.0363576\pi$
$23$	1.90893	+	3.30636i	0.398039	+	0.689423i	−0.595445	+	0.803396i	$0.703024\pi$
$24$	13.6088	−	7.85704i	2.77788	−	1.60381i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−5.62828			−1.08316
$28$	6.97531	−	4.02720i	1.31821	−	0.761069i
$29$	−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
$31$		−	1.46410i		−	0.262960i	−0.991319	−	0.131480i	$-0.958027\pi$
$31$		−	1.46410i		−	0.262960i	0.991319	−	0.131480i	$-0.0419730\pi$
$32$	−2.07908	−	1.20036i	−0.367534	−	0.212196i
$33$	−2.61799	−	1.51150i	−0.455733	−	0.263118i
$34$		−	1.59030i		−	0.272733i
$35$	0.952606	−	1.64996i	0.161020	−	0.278895i
$36$	10.5499	+	18.2730i	1.75832	+	3.04550i
$37$	−0.655970	+	0.378725i	−0.107841	+	0.0622619i	−0.552950	−	0.833214i	$-0.686498\pi$
$37$	−0.655970	+	0.378725i	−0.107841	+	0.0622619i	0.445110	+	0.895476i	$0.353165\pi$
$38$	−14.3044			−2.32048
$39$		0			0
$40$	−5.55889			−0.878938
$41$	0.232051	−	0.133975i	0.0362402	−	0.0209233i	−0.481770	−	0.876297i	$-0.660006\pi$
$41$	0.232051	−	0.133975i	0.0362402	−	0.0209233i	0.518011	+	0.855374i	$0.326673\pi$
$42$	6.72006	+	11.6395i	1.03693	+	1.79601i
$43$	0.318632	−	0.551886i	0.0485909	−	0.0841618i	−0.840707	−	0.541490i	$-0.817860\pi$
$43$	0.318632	−	0.551886i	0.0485909	−	0.0841618i	0.889298	+	0.457328i	$0.151194\pi$
$44$			4.52091i			0.681552i
$45$	4.32235	+	2.49551i	0.644337	+	0.372008i
$46$	8.25104	+	4.76374i	1.21655	+	0.702375i
$47$			9.44613i			1.37786i	0.724828	+	0.688930i	$0.241919\pi$
$47$			9.44613i			1.37786i	−0.724828	+	0.688930i	$0.758081\pi$
$48$	7.65668	−	13.2618i	1.10515	−	1.91417i
$49$	−1.68508	−	2.91865i	−0.240726	−	0.416950i
$50$	−2.16117	+	1.24775i	−0.305636	+	0.176459i
$51$	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	$0.659416\pi$
$54$	−12.1637	+	7.02271i	−1.65527	+	0.955669i
$55$	0.534695	+	0.926118i	0.0720982	+	0.124878i
$56$	5.29543	−	9.17196i	0.707632	−	1.22565i
$57$		−	16.2036i		−	2.14622i
$58$	−20.4341	−	11.7977i	−2.68313	−	1.54911i
$59$	0.641756	+	0.370518i	0.0835495	+	0.0482373i	0.541193	−	0.840899i	$-0.317973\pi$
$59$	0.641756	+	0.370518i	0.0835495	+	0.0482373i	−0.457643	+	0.889136i	$0.651306\pi$
$60$		−	11.9506i		−	1.54282i
$61$	−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
$63$	−8.23499	+	4.75447i	−1.03751	+	0.599007i
$64$	4.84325			0.605406
$65$		0			0
$66$	−7.54390			−0.928589
$67$	7.01029	−	4.04739i	0.856443	−	0.494468i	−0.00637624	−	0.999980i	$-0.502030\pi$
$67$	7.01029	−	4.04739i	0.856443	−	0.494468i	0.862820	+	0.505512i	$0.168696\pi$
$68$	−1.34703	−	2.33313i	−0.163352	−	0.282934i
$69$	−5.39623	+	9.34654i	−0.649629	+	1.12519i
$70$		−	4.75447i		−	0.568268i
$71$	−8.45663	−	4.88244i	−1.00362	−	0.579439i	−0.0943010	−	0.995544i	$-0.530062\pi$
$71$	−8.45663	−	4.88244i	−1.00362	−	0.579439i	−0.909317	+	0.416105i	$0.863395\pi$
$72$	24.0274	+	13.8723i	2.83166	+	1.63486i
$73$			3.71649i			0.434982i	0.976062	+	0.217491i	$0.0697873\pi$
$73$			3.71649i			0.434982i	−0.976062	+	0.217491i	$0.930213\pi$
$74$	−0.945110	+	1.63698i	−0.109867	+	0.190295i
$75$	−1.41342	−	2.44811i	−0.163208	−	0.282684i
$76$	−20.9860	+	12.1163i	−2.40726	+	1.38983i
$77$	−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	$0.675656\pi$
$80$	−4.69138	+	2.70857i	−0.524512	+	0.302827i
$81$	−0.468594	−	0.811629i	−0.0520660	−	0.0901809i
$82$	0.334335	−	0.579085i	0.0369211	−	0.0639492i
$83$			5.11778i			0.561749i	0.959744	+	0.280875i	$0.0906245\pi$
$83$			5.11778i			0.561749i	−0.959744	+	0.280875i	$0.909376\pi$
$84$	19.7181	+	11.3842i	2.15142	+	1.24212i
$85$	−0.551886	−	0.318632i	−0.0598605	−	0.0345605i
$86$		−	1.59030i		−	0.171486i
$87$	13.3640	−	23.1472i	1.43278	−	2.48164i
$88$	2.97231	+	5.14819i	0.316849	+	0.548799i
$89$	10.8932	−	6.28917i	1.15467	−	0.666650i	0.204651	−	0.978835i	$-0.434394\pi$
$89$	10.8932	−	6.28917i	1.15467	−	0.666650i	0.950021	+	0.312185i	$0.101061\pi$
$90$	12.4551			1.31288
$91$		0			0
$92$	16.1402			1.68273
$93$	3.58429	−	2.06939i	0.371673	−	0.214586i
$94$	11.7864	+	20.4147i	1.21568	+	2.10562i
$95$	−2.86603	+	4.96410i	−0.294048	+	0.509306i
$96$		−	6.78645i		−	0.692639i
$97$	3.65597	+	2.11078i	0.371208	+	0.214317i	0.673986	−	0.738744i	$-0.264581\pi$
$97$	3.65597	+	2.11078i	0.371208	+	0.214317i	−0.302778	+	0.953061i	$0.597914\pi$
$98$	−7.28351	−	4.20514i	−0.735746	−	0.424783i
$99$		−	5.33734i		−	0.536423i
$100$	−2.11378	+	3.66117i	−0.211378	+	0.366117i
$101$	−7.62379	−	13.2048i	−0.758595	−	1.31393i	−0.943567	−	0.331181i	$-0.892553\pi$
$101$	−7.62379	−	13.2048i	−0.758595	−	1.31393i	0.184972	−	0.982744i	$-0.440781\pi$
$102$	3.89322	−	2.24775i	0.385487	−	0.222561i
$103$	13.5269			1.33285			0.666423	−	0.745574i	$-0.267824\pi$
$103$	13.5269			1.33285			0.666423	+	0.745574i	$0.267824\pi$
$104$		0			0
$105$	5.38573			0.525593
$106$	−15.1088	+	8.72307i	−1.46750	+	0.847259i
$107$	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
$109$			10.0760i			0.965103i	0.875868	+	0.482551i	$0.160290\pi$
$109$			10.0760i			0.965103i	−0.875868	+	0.482551i	$0.839710\pi$
$110$	2.31114	+	1.33433i	0.220358	+	0.127224i
$111$	−1.85432	−	1.07059i	−0.176004	−	0.101616i
$112$		−	10.3208i		−	0.975223i
$113$	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
$115$	3.30636	−	1.90893i	0.308320	−	0.178008i
$116$	−39.9721			−3.71131
$117$		0			0
$118$	1.84926			0.170238
$119$	1.05146	−	0.607061i	0.0963872	−	0.0556492i
$120$	−7.85704	−	13.6088i	−0.717246	−	1.24231i
$121$	−4.92820	+	8.53590i	−0.448018	+	0.775991i
$122$			10.4775i			0.948592i
$123$	0.655970	+	0.378725i	0.0591468	+	0.0341484i
$124$	−5.36033	−	3.09479i	−0.481372	−	0.277920i
$125$			1.00000i			0.0894427i
$126$	−11.8648	+	20.5505i	−1.05700	+	1.83078i
$127$	0.744750	+	1.28994i	0.0660859	+	0.114464i	0.897175	−	0.441675i	$-0.145616\pi$
$127$	0.744750	+	1.28994i	0.0660859	+	0.114464i	−0.831089	+	0.556139i	$0.812282\pi$
$128$	14.6253	−	8.44391i	1.29270	−	0.746343i
$129$	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	$0.442300\pi$
$132$	−11.0677	+	6.38994i	−0.963319	+	0.556172i
$133$	−5.46039	−	9.45767i	−0.473476	−	0.820084i
$134$	10.1003	−	17.4942i	0.872533	−	1.51127i
$135$			5.62828i			0.484405i
$136$	−3.06787	−	1.77124i	−0.263068	−	0.151882i
$137$	−17.4155	−	10.0548i	−1.48790	−	0.859041i	−0.487999	−	0.872844i	$-0.662273\pi$
$137$	−17.4155	−	10.0548i	−1.48790	−	0.859041i	−0.999905	+	0.0138029i	$0.995606\pi$
$138$			26.9327i			2.29266i
$139$	−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
$141$	−23.1252	+	13.3513i	−1.94749	+	1.12439i
$142$	−24.3683			−2.04494
$143$		0			0
$144$	27.0370			2.25308
$145$	−8.18837	+	4.72756i	−0.680007	+	0.392602i
$146$	4.63726	+	8.03198i	0.383783	+	0.664731i
$147$	4.76346	−	8.25055i	0.392883	−	0.680494i
$148$			3.20216i			0.263216i
$149$	−11.5768	−	6.68388i	−0.948410	−	0.547565i	−0.0558233	−	0.998441i	$-0.517778\pi$
$149$	−11.5768	−	6.68388i	−0.948410	−	0.547565i	−0.892587	+	0.450876i	$0.851112\pi$
$150$	−6.10929	−	3.52720i	−0.498821	−	0.287995i
$151$		−	18.2984i		−	1.48910i	−0.667567	−	0.744550i	$-0.732664\pi$
$151$		−	18.2984i		−	1.48910i	0.667567	−	0.744550i	$-0.267336\pi$
$152$	−15.9319	+	27.5949i	−1.29225	+	2.23824i
$153$	1.59030	+	2.75447i	0.128568	+	0.222686i
$154$	−4.40320	+	2.54219i	−0.354820	+	0.204856i
$155$	−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	$0.469184\pi$
$158$	−20.1408	+	11.6283i	−1.60231	+	0.925096i
$159$	−9.88124	−	17.1148i	−0.783633	−	1.35729i
$160$	−1.20036	+	2.07908i	−0.0948968	+	0.164366i
$161$			7.27382i			0.573258i
$162$	−2.02543	−	1.16938i	−0.159132	−	0.0918752i
$163$	13.8416	+	7.99144i	1.08416	+	0.625938i	0.932015	−	0.362421i	$-0.118050\pi$
$163$	13.8416	+	7.99144i	1.08416	+	0.625938i	0.152142	+	0.988359i	$0.451383\pi$
$164$		−	1.13277i		−	0.0884545i
$165$	−1.51150	+	2.61799i	−0.117670	+	0.203810i
$166$	6.38573	+	11.0604i	0.495629	+	0.858454i
$167$	12.4648	−	7.19658i	0.964558	−	0.556888i	0.0669853	−	0.997754i	$-0.478662\pi$
$167$	12.4648	−	7.19658i	0.964558	−	0.556888i	0.897573	+	0.440866i	$0.145329\pi$
$168$	29.9387			2.30982
$169$		0			0
$170$	−1.59030			−0.121970
$171$	24.7759	−	14.3044i	1.89466	−	1.09388i
$172$	−1.34703	−	2.33313i	−0.102710	−	0.177900i
$173$	−12.1745	+	21.0868i	−0.925608	+	1.60320i	−0.135027	+	0.990842i	$0.543112\pi$
$173$	−12.1745	+	21.0868i	−0.925608	+	1.60320i	−0.790581	+	0.612358i	$0.790221\pi$
$174$		−	66.7001i		−	5.05653i
$175$	−1.64996	−	0.952606i	−0.124725	−	0.0720103i
$176$	5.01691	+	2.89651i	0.378164	+	0.218333i
$177$			2.09479i			0.157454i
$178$	15.6947	−	27.1840i	1.17636	−	2.03752i
$179$	1.89414	+	3.28075i	0.141575	+	0.245215i	0.928090	−	0.372356i	$-0.121450\pi$
$179$	1.89414	+	3.28075i	0.141575	+	0.245215i	−0.786515	+	0.617571i	$0.788117\pi$
$180$	18.2730	−	10.5499i	1.36199	−	0.786343i
$181$	8.48794			0.630904			0.315452	−	0.948942i	$-0.397844\pi$
$181$	8.48794			0.630904			0.315452	+	0.948942i	$0.397844\pi$
$182$		0			0
$183$	−11.8687			−0.877356
$184$	18.3797	−	10.6115i	1.35497	−	0.782291i
$185$	0.378725	+	0.655970i	0.0278444	+	0.0482279i
$186$	5.16418	−	8.94462i	0.378656	−	0.655851i
$187$			0.681482i			0.0498349i
$188$	34.5839	+	19.9670i	2.52229	+	1.45625i
$189$	−9.28645	−	5.36153i	−0.675490	−	0.389994i
$190$			14.3044i			1.03775i
$191$	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
$193$	−10.5288	+	6.07880i	−0.757879	+	0.437562i	−0.828534	−	0.559939i	$-0.810824\pi$
$193$	−10.5288	+	6.07880i	−0.757879	+	0.437562i	0.0706548	+	0.997501i	$0.477491\pi$
$194$	10.5349			0.756363
$195$		0			0
$196$	−14.2476			−1.01768
$197$	−3.79172	+	2.18915i	−0.270149	+	0.155970i	−0.628955	−	0.777442i	$-0.716517\pi$
$197$	−3.79172	+	2.18915i	−0.270149	+	0.155970i	0.358807	+	0.933412i	$0.383184\pi$
$198$	−6.65968	−	11.5349i	−0.473283	−	0.819751i
$199$	10.4186	−	18.0456i	0.738558	−	1.27922i	−0.214586	−	0.976705i	$-0.568840\pi$
$199$	10.4186	−	18.0456i	0.738558	−	1.27922i	0.953144	−	0.302516i	$-0.0978265\pi$
$200$			5.55889i			0.393073i
$201$	19.8170	+	11.4413i	1.39778	+	0.807009i
$202$	−32.9526	−	19.0252i	−2.31854	−	1.33861i
$203$		−	18.0140i		−	1.26434i
$204$	3.80785	−	6.59538i	0.266603	−	0.461769i
$205$	−0.133975	−	0.232051i	−0.00935719	−	0.0162071i
$206$	29.2340	−	16.8783i	2.03683	−	1.17596i
$207$	−19.0550			−1.32441
$208$		0			0
$209$	6.12979			0.424007
$210$	11.6395	−	6.72006i	0.803201	−	0.463728i
$211$	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
$213$		−	27.6037i		−	1.89138i
$214$	15.9121	+	9.18688i	1.08773	+	0.628002i
$215$	−0.551886	−	0.318632i	−0.0376383	−	0.0217305i
$216$			31.2870i			2.12881i
$217$	1.39471	−	2.41571i	0.0946792	−	0.163989i
$218$	12.5723	+	21.7759i	0.851505	+	1.47485i
$219$	−9.09839	+	5.25296i	−0.614812	+	0.354962i
$220$	4.52091			0.304799
$221$		0			0
$222$	−5.34335			−0.358622
$223$	18.4804	−	10.6697i	1.23754	−	0.714494i	0.268949	−	0.963155i	$-0.413324\pi$
$223$	18.4804	−	10.6697i	1.23754	−	0.714494i	0.968591	+	0.248661i	$0.0799905\pi$
$224$	−2.28694	−	3.96110i	−0.152803	−	0.264662i
$225$	2.49551	−	4.32235i	0.166367	−	0.288156i
$226$		−	16.6901i		−	1.11021i
$227$	−13.5842	−	7.84283i	−0.901613	−	0.520547i	−0.0238900	−	0.999715i	$-0.507605\pi$
$227$	−13.5842	−	7.84283i	−0.901613	−	0.520547i	−0.877723	+	0.479168i	$0.840938\pi$
$228$	−59.3241	−	34.2508i	−3.92884	−	2.26831i
$229$			7.62085i			0.503600i	0.967779	+	0.251800i	$0.0810225\pi$
$229$			7.62085i			0.503600i	−0.967779	+	0.251800i	$0.918977\pi$
$230$	4.76374	−	8.25104i	0.314112	−	0.544058i
$231$	−2.87972	−	4.98782i	−0.189472	−	0.328175i
$232$	−45.5182	+	26.2800i	−2.98842	+	1.72536i
$233$	19.0550			1.24833			0.624166	−	0.781292i	$-0.285439\pi$
$233$	19.0550			1.24833			0.624166	+	0.781292i	$0.285439\pi$
$234$		0			0
$235$	9.44613			0.616198
$236$	2.71306	−	1.56639i	0.176605	−	0.101963i
$237$	−13.1722	−	22.8149i	−0.855625	−	1.48199i
$238$	1.51493	−	2.62393i	0.0981980	−	0.170084i
$239$			12.7535i			0.824954i	0.910968	+	0.412477i	$0.135336\pi$
$239$			12.7535i			0.824954i	−0.910968	+	0.412477i	$0.864664\pi$
$240$	−13.2618	−	7.65668i	−0.856043	−	0.494237i
$241$	22.4550	+	12.9644i	1.44646	+	0.835111i	0.998268	−	0.0588285i	$-0.0187365\pi$
$241$	22.4550	+	12.9644i	1.44646	+	0.835111i	0.448187	+	0.893940i	$0.352070\pi$
$242$			24.5967i			1.58114i
$243$	−7.11778	+	12.3284i	−0.456606	+	0.790864i
$244$	8.87483	+	15.3717i	0.568153	+	0.984069i
$245$	−2.91865	+	1.68508i	−0.186466	+	0.107656i
$246$	1.89022			0.120516
$247$		0			0
$248$	−8.13878			−0.516813
$249$	−12.5289	+	7.23357i	−0.793987	+	0.458409i
$250$	1.24775	+	2.16117i	0.0789149	+	0.136685i
$251$	3.80593	−	6.59207i	0.240228	−	0.416088i	−0.720551	−	0.693402i	$-0.756111\pi$
$251$	3.80593	−	6.59207i	0.240228	−	0.416088i	0.960779	+	0.277314i	$0.0894444\pi$
$252$			40.1996i			2.53234i
$253$	−3.53578	−	2.04139i	−0.222293	−	0.128341i
$254$	3.21907	+	1.85853i	0.201982	+	0.116614i
$255$		−	1.80144i		−	0.112811i
$256$	16.2286	−	28.1087i	1.01429	−	1.75680i
$257$	0.167891	+	0.290796i	0.0104728	+	0.0181394i	0.871214	−	0.490903i	$-0.163333\pi$
$257$	0.167891	+	0.290796i	0.0104728	+	0.0181394i	−0.860742	+	0.509042i	$0.830000\pi$
$258$	3.89322	−	2.24775i	0.242382	−	0.139939i
$259$	−1.44310			−0.0896700
$260$		0			0
$261$	47.1906			2.92103
$262$	8.91865	−	5.14918i	0.550996	−	0.318118i
$263$	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
$265$			6.99102i			0.429455i
$266$	−23.6017	−	13.6264i	−1.44711	−	0.835491i
$267$	30.7932	+	17.7785i	1.88451	+	1.08802i
$268$		−	34.2212i		−	2.09039i
$269$	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
$271$	10.0851	−	5.82266i	0.612629	−	0.353701i	−0.161365	−	0.986895i	$-0.551590\pi$
$271$	10.0851	−	5.82266i	0.612629	−	0.353701i	0.773994	+	0.633194i	$0.218256\pi$
$272$	−3.45214			−0.209317
$273$		0			0
$274$	−50.1838			−3.03171
$275$	0.926118	−	0.534695i	0.0558470	−	0.0322433i
$276$	22.8129	+	39.5130i	1.37317	+	2.37841i
$277$	−10.1581	+	17.5943i	−0.610338	+	1.05714i	0.380845	+	0.924639i	$0.375633\pi$
$277$	−10.1581	+	17.5943i	−0.610338	+	1.05714i	−0.991183	+	0.132498i	$0.957700\pi$
$278$			51.9697i			3.11693i
$279$	6.32835	+	3.65368i	0.378869	+	0.218740i
$280$	−9.17196	−	5.29543i	−0.548129	−	0.316463i
$281$			11.8744i			0.708366i	0.935176	+	0.354183i	$0.115241\pi$
$281$			11.8744i			0.708366i	−0.935176	+	0.354183i	$0.884759\pi$
$282$	−33.3184	+	57.7091i	−1.98408	+	3.43653i
$283$	−11.3261	−	19.6173i	−0.673264	−	1.16613i	−0.976973	−	0.213363i	$-0.931558\pi$
$283$	−11.3261	−	19.6173i	−0.673264	−	1.16613i	0.303709	−	0.952765i	$-0.401775\pi$
$284$	−35.7509	+	20.6408i	−2.12143	+	1.22481i
$285$	−16.2036			−0.959817
$286$		0			0
$287$	0.510500			0.0301339
$288$	10.3767	−	5.99102i	0.611455	−	0.353024i
$289$	8.29695	+	14.3707i	0.488056	+	0.845337i
$290$	−11.7977	+	20.4341i	−0.692782	+	1.19993i
$291$			11.9336i			0.699562i
$292$	13.6067	+	7.85584i	0.796272	+	0.459728i
$293$	16.1191	+	9.30636i	0.941687	+	0.543683i	0.890489	−	0.455005i	$-0.150363\pi$
$293$	16.1191	+	9.30636i	0.941687	+	0.543683i	0.0511983	+	0.998689i	$0.483696\pi$
$294$		−	23.7745i		−	1.38656i
$295$	0.370518	−	0.641756i	0.0215724	−	0.0373645i
$296$	2.10529	+	3.64647i	0.122367	+	0.211946i
$297$	5.21245	−	3.00941i	0.302457	−	0.174624i
$298$	−33.3593			−1.93245
$299$		0			0
$300$	−11.9506			−0.689970
$301$	1.05146	−	0.607061i	0.0606052	−	0.0349904i
$302$	−22.8319	−	39.5459i	−1.31383	−	2.27561i
$303$	21.5512	−	37.3278i	1.23808	−	2.14443i
$304$			31.0513i			1.78091i
$305$	3.63606	+	2.09928i	0.208200	+	0.120204i
$306$	6.87381	+	3.96859i	0.392949	+	0.226869i
$307$		−	3.14776i		−	0.179652i	−0.995957	−	0.0898262i	$-0.971369\pi$
$307$		−	3.14776i		−	0.179652i	0.995957	−	0.0898262i	$-0.0286311\pi$
$308$	−4.30664	+	7.45932i	−0.245394	+	0.425034i
$309$	19.1192	+	33.1154i	1.08765	+	1.88387i
$310$	−3.16418	+	1.82684i	−0.179713	+	0.103757i
$311$	3.18059			0.180355			0.0901774	−	0.995926i	$-0.471257\pi$
$311$	3.18059			0.180355			0.0901774	+	0.995926i	$0.471257\pi$
$312$		0			0
$313$	35.3533			1.99829			0.999144	−	0.0413596i	$-0.0131689\pi$
$313$	35.3533			1.99829			0.999144	+	0.0413596i	$0.0131689\pi$
$314$	5.23499	−	3.02242i	0.295427	−	0.170565i
$315$	4.75447	+	8.23499i	0.267884	+	0.463989i
$316$	−19.6991	+	34.1198i	−1.10816	+	1.91939i
$317$		−	13.6357i		−	0.765858i	−0.923778	−	0.382929i	$-0.874915\pi$
$317$		−	13.6357i		−	0.765858i	0.923778	−	0.382929i	$-0.125085\pi$
$318$	−42.7101	−	24.6587i	−2.39506	−	1.38279i
$319$	8.75656	+	5.05560i	0.490273	+	0.283059i
$320$		−	4.84325i		−	0.270746i
$321$	−10.4066	+	18.0248i	−0.580842	+	1.00605i
$322$	9.07594	+	15.7200i	0.505782	+	0.876041i
$323$	−3.16344	+	1.82641i	−0.176018	+	0.101624i
$324$	−3.96202			−0.220112
$325$		0			0
$326$	39.8854			2.20905
$327$	−24.6671	+	14.2416i	−1.36409	+	0.787560i
$328$	−0.744750	−	1.28994i	−0.0411219	−	0.0712253i
$329$	−8.99844	+	15.5858i	−0.496100	+	0.859271i
$330$			7.54390i			0.415278i
$331$	24.9380	+	14.3980i	1.37072	+	0.791383i	0.991018	−	0.133727i	$-0.0426945\pi$
$331$	24.9380	+	14.3980i	1.37072	+	0.791383i	0.379698	+	0.925110i	$0.376028\pi$
$332$	18.7371	+	10.8179i	1.02833	+	0.593707i
$333$		−	3.78044i		−	0.207167i
$334$	17.9591	−	31.1061i	0.982679	−	1.70205i
$335$	−4.04739	−	7.01029i	−0.221133	−	0.383013i
$336$	25.2665	−	14.5876i	1.37840	−	0.795819i
$337$	−11.7493			−0.640026			−0.320013	−	0.947413i	$-0.603687\pi$
$337$	−11.7493			−0.640026			−0.320013	+	0.947413i	$0.603687\pi$
$338$		0			0
$339$	18.9061			1.02684
$340$	−2.33313	+	1.34703i	−0.126532	+	0.0730532i
$341$	0.782847	+	1.35593i	0.0423936	+	0.0734278i
$342$	35.6967	−	61.8285i	1.93026	−	3.34330i
$343$		−	19.7574i		−	1.06680i
$344$	−3.06787	−	1.77124i	−0.165409	−	0.0954987i
$345$	9.34654	+	5.39623i	0.503201	+	0.290523i
$346$			60.7630i			3.26664i
$347$	−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
$349$	8.89329	−	5.13454i	0.476047	−	0.274846i	−0.242721	−	0.970096i	$-0.578040\pi$
$349$	8.89329	−	5.13454i	0.476047	−	0.274846i	0.718768	+	0.695250i	$0.244707\pi$
$350$	−4.75447			−0.254137
$351$		0			0
$352$	2.56730			0.136838
$353$	0.693330	−	0.400294i	0.0369022	−	0.0213055i	−0.481435	−	0.876482i	$-0.659884\pi$
$353$	0.693330	−	0.400294i	0.0369022	−	0.0213055i	0.518338	+	0.855176i	$0.326551\pi$
$354$	2.61378	+	4.52720i	0.138921	+	0.240618i
$355$	−4.88244	+	8.45663i	−0.259133	+	0.448831i
$356$		−	53.1756i		−	2.81830i
$357$	2.97231	+	1.71606i	0.157311	+	0.0908237i
$358$	8.18714	+	4.72685i	0.432704	+	0.249822i
$359$		−	8.13272i		−	0.429228i	−0.976699	−	0.214614i	$-0.931151\pi$
$359$		−	8.13272i		−	0.429228i	0.976699	−	0.214614i	$-0.0688494\pi$
$360$	13.8723	−	24.0274i	0.731132	−	1.26636i
$361$	6.92820	+	12.0000i	0.364642	+	0.631579i
$362$	18.3439	−	10.5909i	0.964135	−	0.556643i
$363$	−27.8625			−1.46240
$364$		0			0
$365$	3.71649			0.194530
$366$	−25.6502	+	14.8092i	−1.34076	+	0.774087i
$367$	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
$369$			1.33734i			0.0696191i
$370$	1.63698	+	0.945110i	0.0851025	+	0.0491339i
$371$	−11.5349	−	6.65968i	−0.598863	−	0.345754i
$372$		−	17.4969i		−	0.907173i
$373$	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
$375$	−2.44811	+	1.41342i	−0.126420	+	0.0729887i
$376$	52.5100			2.70800
$377$		0			0
$378$	−26.7595			−1.37636
$379$	1.77150	−	1.02277i	0.0909956	−	0.0525363i	−0.453812	−	0.891098i	$-0.649936\pi$
$379$	1.77150	−	1.02277i	0.0909956	−	0.0525363i	0.544807	+	0.838561i	$0.316603\pi$
$380$	12.1163	+	20.9860i	0.621553	+	1.07656i
$381$	−2.10529	+	3.64647i	−0.107857	+	0.186814i
$382$		−	13.5833i		−	0.694982i
$383$	6.84611	+	3.95261i	0.349820	+	0.201969i	0.664606	−	0.747194i	$-0.268599\pi$
$383$	6.84611	+	3.95261i	0.349820	+	0.201969i	−0.314786	+	0.949163i	$0.601933\pi$
$384$	41.3433	+	23.8696i	2.10979	+	1.21809i
$385$			2.03741i			0.103836i
$386$	−15.1697	+	26.2747i	−0.772117	+	1.33735i
$387$	1.59030	+	2.75447i	0.0808393	+	0.140018i
$388$	15.4558	−	8.92343i	0.784651	−	0.453018i
$389$	9.21171			0.467052			0.233526	−	0.972351i	$-0.424974\pi$
$389$	9.21171			0.467052			0.233526	+	0.972351i	$0.424974\pi$
$390$		0			0
$391$	2.43298			0.123041
$392$	−16.2244	+	9.36719i	−0.819458	+	0.473114i
$393$	5.83285	+	10.1028i	0.294228	+	0.509618i
$394$	−5.46304	+	9.46226i	−0.275224	+	0.476702i
$395$			9.31937i			0.468908i
$396$	−19.5409	−	11.2820i	−0.981968	−	0.566940i
$397$	−5.50305	−	3.17719i	−0.276190	−	0.159458i	0.355507	−	0.934674i	$-0.384308\pi$
$397$	−5.50305	−	3.17719i	−0.276190	−	0.159458i	−0.631697	+	0.775215i	$0.717641\pi$
$398$		−	51.9996i		−	2.60651i
$399$	15.4356	−	26.7353i	0.772748	−	1.33844i
$400$	2.70857	+	4.69138i	0.135428	+	0.234569i
$401$	−3.61063	+	2.08460i	−0.180306	+	0.104100i	−0.587437	−	0.809270i	$-0.699863\pi$
$401$	−3.61063	+	2.08460i	−0.180306	+	0.104100i	0.407130	+	0.913370i	$0.366530\pi$
$402$	57.1038			2.84808
$403$		0			0
$404$	−64.4600			−3.20701
$405$	−0.811629	+	0.468594i	−0.0403301	+	0.0232846i
$406$	−22.4770	−	38.9314i	−1.11552	−	1.93213i
$407$	0.405004	−	0.701487i	0.0200753	−	0.0347714i
$408$		−	10.0140i		−	0.495767i
$409$	−8.80580	−	5.08403i	−0.435419	−	0.251389i	0.266234	−	0.963909i	$-0.414221\pi$
$409$	−8.80580	−	5.08403i	−0.435419	−	0.251389i	−0.701652	+	0.712519i	$0.747554\pi$
$410$	−0.579085	−	0.334335i	−0.0285989	−	0.0165116i
$411$		−	56.8467i		−	2.80404i
$412$	28.5929	−	49.5244i	1.40867	−	2.43989i
$413$	0.705915	+	1.22268i	0.0347358	+	0.0601642i
$414$	−41.1811	+	23.7759i	−2.02394	+	1.16852i
$415$	5.11778			0.251222
$416$		0			0
$417$	−58.8697			−2.88286
$418$	13.2475	−	7.64847i	0.647959	−	0.374099i
$419$	−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
$421$			2.01797i			0.0983498i	0.998790	+	0.0491749i	$0.0156592\pi$
$421$			2.01797i			0.0983498i	−0.998790	+	0.0491749i	$0.984341\pi$
$422$	23.0244	+	13.2932i	1.12081	+	0.647101i
$423$	−40.8295	−	23.5729i	−1.98520	−	1.14615i
$424$			38.8623i			1.88732i
$425$	−0.318632	+	0.551886i	−0.0154559	+	0.0267704i
$426$	−34.4427	−	59.6564i	−1.66875	−	2.89036i
$427$	−6.92747	+	3.99957i	−0.335244	+	0.193553i
$428$	31.1264			1.50455
$429$		0			0
$430$	−1.59030			−0.0766908
$431$	−17.8508	+	10.3061i	−0.859842	+	0.496430i	−0.863959	−	0.503562i	$-0.832023\pi$
$431$	−17.8508	+	10.3061i	−0.859842	+	0.496430i	0.00411765	+	0.999992i	$0.498689\pi$
$432$	15.2446	+	26.4044i	0.733455	+	1.27038i
$433$	14.7178	−	25.4920i	0.707292	−	1.22507i	−0.258566	−	0.965994i	$-0.583250\pi$
$433$	14.7178	−	25.4920i	0.707292	−	1.22507i	0.965858	−	0.259072i	$-0.0834168\pi$
$434$		−	6.96103i		−	0.334140i
$435$	−23.1472	−	13.3640i	−1.10982	−	0.640757i
$436$	36.8899	+	21.2984i	1.76670	+	1.02001i
$437$		−	21.8841i		−	1.04686i
$438$	−13.1088	+	22.7051i	−0.626362	+	1.08489i
$439$	8.47602	+	14.6809i	0.404538	+	0.700681i	0.994268	−	0.106920i	$-0.0340988\pi$
$439$	8.47602	+	14.6809i	0.404538	+	0.700681i	−0.589729	+	0.807601i	$0.700765\pi$
$440$	5.14819	−	2.97231i	0.245430	−	0.141699i
$441$	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	$0.694400\pi$
$444$	−7.83925	+	4.52599i	−0.372034	+	0.214794i
$445$	−6.28917	−	10.8932i	−0.298135	−	0.516385i
$446$	26.6262	−	46.1180i	1.26079	−	2.18375i
$447$		−	37.7885i		−	1.78733i
$448$	7.99118	+	4.61371i	0.377548	+	0.217977i
$449$	−18.0679	−	10.4315i	−0.852676	−	0.492293i	0.00887706	−	0.999961i	$-0.497174\pi$
$449$	−18.0679	−	10.4315i	−0.852676	−	0.492293i	−0.861553	+	0.507668i	$0.830508\pi$
$450$		−	12.4551i		−	0.587140i
$451$	−0.143271	+	0.248153i	−0.00674637	+	0.0116851i
$452$	−14.1371	−	24.4861i	−0.664952	−	1.15173i
$453$	44.7965	−	25.8633i	2.10472	−	1.21516i
$454$	−39.1437			−1.83710
$455$		0			0
$456$	−90.0739			−4.21810
$457$	−26.4708	+	15.2830i	−1.23825	+	0.714906i	−0.968737	−	0.248089i	$-0.920197\pi$
$457$	−26.4708	+	15.2830i	−1.23825	+	0.714906i	−0.269517	+	0.962996i	$0.586864\pi$
$458$	9.50894	+	16.4700i	0.444324	+	0.769591i
$459$	−1.79335	+	3.10617i	−0.0837063	+	0.144984i
$460$		−	16.1402i		−	0.752541i
$461$	−4.05146	−	2.33911i	−0.188695	−	0.108943i	0.402676	−	0.915342i	$-0.368080\pi$
$461$	−4.05146	−	2.33911i	−0.188695	−	0.108943i	−0.591372	+	0.806399i	$0.701413\pi$
$462$	−12.4471	−	7.18636i	−0.579094	−	0.334340i
$463$			14.0011i			0.650688i	0.945596	+	0.325344i	$0.105480\pi$
$463$			14.0011i			0.650688i	−0.945596	+	0.325344i	$0.894520\pi$
$464$	−25.6098	+	44.3575i	−1.18891	+	2.05925i
$465$	−2.06939	−	3.58429i	−0.0959656	−	0.166217i
$466$	41.1811	−	23.7759i	1.90768	−	1.10140i
$467$	6.98506			0.323230			0.161615	−	0.986854i	$-0.448330\pi$
$467$	6.98506			0.323230			0.161615	+	0.986854i	$0.448330\pi$
$468$		0			0
$469$	15.4223			0.712135
$470$	20.4147	−	11.7864i	0.941661	−	0.543668i
$471$	3.42371	+	5.93004i	0.157756	+	0.273242i
$472$	2.05967	−	3.56745i	0.0948039	−	0.164205i
$473$			0.681482i			0.0313346i
$474$	−56.9347	−	32.8713i	−2.61510	−	1.50983i
$475$	4.96410	+	2.86603i	0.227769	+	0.131502i
$476$		−	5.13277i		−	0.235260i
$477$	17.4461	−	30.2176i	0.798804	−	1.38357i
$478$	15.9132	+	27.5625i	0.727853	+	1.26068i
$479$	14.1065	−	8.14438i	0.644542	−	0.372126i	−0.141820	−	0.989892i	$-0.545296\pi$
$479$	14.1065	−	8.14438i	0.644542	−	0.372126i	0.786362	+	0.617766i	$0.211962\pi$
$480$	−6.78645			−0.309758
$481$		0			0
$482$	64.7056			2.94726
$483$	−17.8071	+	10.2810i	−0.810253	+	0.467800i
$484$	20.8343	+	36.0860i	0.947012	+	1.64027i
$485$	2.11078	−	3.65597i	0.0958454	−	0.166009i
$486$			35.5249i			1.61144i
$487$	−17.3559	−	10.0204i	−0.786471	−	0.454069i	0.0522474	−	0.998634i	$-0.483362\pi$
$487$	−17.3559	−	10.0204i	−0.786471	−	0.454069i	−0.838719	+	0.544565i	$0.816695\pi$
$488$	20.2125	+	11.6697i	0.914975	+	0.528261i
$489$			45.1810i			2.04316i
$490$	−4.20514	+	7.28351i	−0.189969	+	0.329035i
$491$	−7.89916	−	13.6818i	−0.356484	−	0.617449i	0.630887	−	0.775875i	$-0.282691\pi$
$491$	−7.89916	−	13.6818i	−0.356484	−	0.617449i	−0.987371	+	0.158426i	$0.949358\pi$
$492$	2.77315	−	1.60108i	0.125023	−	0.0721823i
$493$	−6.02540			−0.271370
$494$		0			0
$495$	−5.33734			−0.239896
$496$	−6.86865	+	3.96562i	−0.308411	+	0.178061i
$497$	−9.30208	−	16.1117i	−0.417255	−	0.722708i
$498$	−18.0514	+	31.2660i	−0.808903	+	1.40106i
$499$			1.24651i			0.0558016i	0.999611	+	0.0279008i	$0.00888226\pi$
$499$			1.24651i			0.0558016i	−0.999611	+	0.0279008i	$0.991118\pi$
$500$	3.66117	+	2.11378i	0.163733	+	0.0945311i
$501$	35.2361	+	20.3436i	1.57423	+	0.908883i
$502$		−	18.9955i		−	0.847809i
$503$	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
$505$	−13.2048	+	7.62379i	−0.587605	+	0.339254i
$506$	−10.1886			−0.452938
$507$		0			0
$508$	6.29695			0.279382
$509$	22.2777	−	12.8621i	0.987444	−	0.570101i	0.0829345	−	0.996555i	$-0.473571\pi$
$509$	22.2777	−	12.8621i	0.987444	−	0.570101i	0.904509	+	0.426454i	$0.140237\pi$
$510$	−2.24775	−	3.89322i	−0.0995322	−	0.172395i
$511$	−3.54035	+	6.13207i	−0.156616	+	0.271267i
$512$		−	47.2215i		−	2.08691i
$513$	27.9393	+	16.1308i	1.23355	+	0.712192i
$514$	0.725685	+	0.418974i	0.0320086	+	0.0184802i
$515$		−	13.5269i		−	0.596067i
$516$	3.80785	−	6.59538i	0.167631	−	0.290346i
$517$	−5.05080	−	8.74824i	−0.222134	−	0.384747i
$518$	−3.11879	+	1.80064i	−0.137032	+	0.0791154i
$519$	−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	$0.729651\pi$
$522$	101.987	−	58.8823i	4.46386	−	2.57721i
$523$	−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
$525$		−	5.38573i		−	0.235052i
$526$	11.6182	+	6.70779i	0.506579	+	0.292473i
$527$	−0.808017	−	0.466509i	−0.0351978	−	0.0203215i
$528$			16.3759i			0.712672i
$529$	4.21200	−	7.29539i	0.183130	−	0.317191i
$530$	8.72307	+	15.1088i	0.378906	+	0.656284i
$531$	−3.20301	+	1.84926i	−0.138999	+	0.0802510i
$532$	−46.1682			−2.00165
$533$		0			0
$534$	88.7326			3.83983
$535$	6.37632	−	3.68137i	0.275672	−	0.159159i
$536$	−22.4990	−	38.9694i	−0.971809	−	1.68322i
$537$	−5.35444	+	9.27415i	−0.231061	+	0.400209i
$538$		−	3.27007i		−	0.140983i
$539$	3.12117	+	1.80201i	0.134438	+	0.0776180i
$540$	20.6061	+	11.8969i	0.886745	+	0.511963i
$541$			15.8881i			0.683083i	0.939867	+	0.341541i	$0.110949\pi$
$541$			15.8881i			0.683083i	−0.939867	+	0.341541i	$0.889051\pi$
$542$	14.5305	−	25.1675i	0.624138	−	1.08104i
$543$	11.9970	+	20.7795i	0.514842	+	0.891732i
$544$	−1.32492	+	0.764945i	−0.0568057	+	0.0327968i
$545$	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	$0.544796\pi$
$548$	−73.6249	+	42.5074i	−3.14510	+	1.81582i
$549$	−10.4775	−	18.1476i	−0.447170	−	0.774522i
$550$	1.33433	−	2.31114i	0.0568962	−	0.0985471i
$551$			54.1972i			2.30888i
$552$	51.9564	+	29.9970i	2.21141	+	1.27676i
$553$	−15.3766	−	8.87769i	−0.653880	−	0.377518i
$554$			50.6990i			2.15399i
$555$	−1.07059	+	1.85432i	−0.0454441	+	0.0787116i
$556$	44.0200	+	76.2450i	1.86687	+	3.23351i
$557$	−6.79835	+	3.92503i	−0.288055	+	0.166309i	−0.637065	−	0.770810i	$-0.719852\pi$
$557$	−6.79835	+	3.92503i	−0.288055	+	0.166309i	0.349009	+	0.937119i	$0.386518\pi$
$558$	18.2356			0.771973
$559$		0			0
$560$	−10.3208			−0.436133
$561$	−1.66835	+	0.963220i	−0.0704377	+	0.0406672i
$562$	14.8163	+	25.6626i	0.624988	+	1.08251i
$563$	−7.77976	+	13.4749i	−0.327878	+	0.567901i	−0.982091	−	0.188410i	$-0.939667\pi$
$563$	−7.77976	+	13.4749i	−0.327878	+	0.567901i	0.654213	+	0.756310i	$0.273000\pi$
$564$			112.887i			4.75341i
$565$	−5.79203	−	3.34403i	−0.243673	−	0.140684i
$566$	−48.9552	−	28.2643i	−2.05774	−	1.18804i
$567$		−	1.78554i		−	0.0749857i
$568$	−27.1409	+	47.0095i	−1.13881	+	1.97247i
$569$	1.73957	+	3.01303i	0.0729267	+	0.126313i	0.900183	−	0.435512i	$-0.143433\pi$
$569$	1.73957	+	3.01303i	0.0729267	+	0.126313i	−0.827256	+	0.561825i	$0.810099\pi$
$570$	−35.0187	+	20.2181i	−1.46677	+	0.846842i
$571$	21.5118			0.900240			0.450120	−	0.892968i	$-0.351381\pi$
$571$	21.5118			0.900240			0.450120	+	0.892968i	$0.351381\pi$
$572$		0			0
$573$	15.3868			0.642791
$574$	1.10328	−	0.636978i	0.0460500	−	0.0265870i
$575$	−1.90893	−	3.30636i	−0.0796078	−	0.137885i
$576$	−12.0864	+	20.9342i	−0.503599	+	0.872259i
$577$			9.97608i			0.415310i	0.978202	+	0.207655i	$0.0665831\pi$
$577$			9.97608i			0.415310i	−0.978202	+	0.207655i	$0.933417\pi$
$578$	35.8623	+	20.7051i	1.49167	+	0.861218i
$579$	−29.7632	−	17.1838i	−1.23692	−	0.714134i
$580$			39.9721i			1.65975i
$581$	−4.87523	+	8.44414i	−0.202259	+	0.350322i
$582$	14.8902	+	25.7907i	0.617221	+	1.06906i
$583$	6.47451	−	3.73806i	0.268147	−	0.154815i
$584$	20.6595			0.854898
$585$		0			0
$586$	46.4482			1.91876
$587$	−20.8341	+	12.0286i	−0.859915	+	0.496472i	−0.863984	−	0.503519i	$-0.832038\pi$
$587$	−20.8341	+	12.0286i	−0.859915	+	0.496472i	0.00406862	+	0.999992i	$0.498705\pi$
$588$	−20.1378	−	34.8797i	−0.830469	−	1.43841i
$589$	−4.19615	+	7.26795i	−0.172899	+	0.299471i
$590$		−	1.84926i		−	0.0761328i
$591$	−10.7186	−	6.18837i	−0.440903	−	0.254556i
$592$	3.55348	+	2.05160i	0.146047	+	0.0843203i
$593$		−	0.940219i		−	0.0386102i	−0.999814	−	0.0193051i	$-0.993855\pi$
$593$		−	0.940219i		−	0.0386102i	0.999814	−	0.0193051i	$-0.00614538\pi$
$594$	7.51001	−	13.0077i	0.308139	−	0.533713i
$595$	−0.607061	−	1.05146i	−0.0248871	−	0.0431057i
$596$	−48.9417	+	28.2565i	−2.00473	+	1.15743i
$597$	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	$0.575001\pi$
$600$	−13.6088	+	7.85704i	−0.555577	+	0.320762i
$601$	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
$603$			40.4012i			1.64526i
$604$	−66.9935	−	38.6787i	−2.72593	−	1.57381i
$605$	8.53590	+	4.92820i	0.347034	+	0.200360i
$606$		−	107.562i		−	4.36942i
$607$	−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
$609$	44.1003	−	25.4613i	1.78704	−	1.03175i
$610$	10.4775			0.424223
$611$		0			0
$612$	13.4461			0.543528
$613$	−0.299187	+	0.172736i	−0.0120841	+	0.00697673i	−0.506030	−	0.862516i	$-0.668887\pi$
$613$	−0.299187	+	0.172736i	−0.0120841	+	0.00697673i	0.493946	+	0.869493i	$0.335554\pi$
$614$	−3.92763	−	6.80286i	−0.158506	−	0.274541i
$615$	0.378725	−	0.655970i	0.0152716	−	0.0264513i
$616$			11.3258i			0.456328i
$617$	−33.5022	−	19.3425i	−1.34875	−	0.778700i	−0.360676	−	0.932691i	$-0.617454\pi$
$617$	−33.5022	−	19.3425i	−1.34875	−	0.778700i	−0.988072	+	0.153991i	$0.950787\pi$
$618$	82.6398	+	47.7121i	3.32426	+	1.91926i
$619$		−	14.8971i		−	0.598764i	−0.954133	−	0.299382i	$-0.903219\pi$
$619$		−	14.8971i		−	0.598764i	0.954133	−	0.299382i	$-0.0967805\pi$
$620$	−3.09479	+	5.36033i	−0.124290	+	0.215276i
$621$	−10.7440	−	18.6091i	−0.431141	−	0.746758i
$622$	6.87381	−	3.96859i	0.275615	−	0.159126i
$623$	23.9644			0.960113
$624$		0			0
$625$	1.00000			0.0400000
$626$	76.4047	−	44.1123i	3.05374	−	1.76308i
$627$	8.66397	+	15.0064i	0.346006	+	0.599299i
$628$	5.12019	−	8.86842i	0.204318	−	0.353889i
$629$			0.482694i			0.0192463i
$630$	20.5505	+	11.8648i	0.818750	+	0.472706i
$631$	−33.6408	−	19.4225i	−1.33922	−	0.773198i	−0.352526	−	0.935802i	$-0.614677\pi$
$631$	−33.6408	−	19.4225i	−1.33922	−	0.773198i	−0.986691	+	0.162604i	$0.948011\pi$
$632$			51.8053i			2.06071i
$633$	−15.0581	+	26.0814i	−0.598506	+	1.03664i
$634$	−17.0140	−	29.4691i	−0.675713	−	1.17037i
$635$	1.28994	−	0.744750i	0.0511899	−	0.0295545i
$636$	−83.5470			−3.31285
$637$		0			0
$638$	25.2326			0.998967
$639$	42.2072	−	24.3683i	1.66969	−	0.963996i
$640$	−8.44391	−	14.6253i	−0.333775	−	0.578115i
$641$	18.5908	−	32.2003i	0.734293	−	1.27183i	−0.220739	−	0.975333i	$-0.570847\pi$
$641$	18.5908	−	32.2003i	0.734293	−	1.27183i	0.955033	−	0.296501i	$-0.0958197\pi$
$642$			51.9397i			2.04990i
$643$	−7.88410	−	4.55189i	−0.310918	−	0.179509i	0.336419	−	0.941712i	$-0.390784\pi$
$643$	−7.88410	−	4.55189i	−0.310918	−	0.179509i	−0.647337	+	0.762204i	$0.724118\pi$
$644$	26.6307	+	15.3753i	1.04940	+	0.605870i
$645$		−	1.80144i		−	0.0709316i
$646$	−4.55783	+	7.89439i	−0.179325	+	0.310601i
$647$	−9.56118	−	16.5605i	−0.375889	−	0.651059i	0.614571	−	0.788862i	$-0.289329\pi$
$647$	−9.56118	−	16.5605i	−0.375889	−	0.651059i	−0.990460	+	0.137803i	$0.955996\pi$
$648$	−4.51175	+	2.60486i	−0.177238	+	0.102329i
$649$	−0.792455			−0.0311066
$650$		0			0
$651$	7.88525			0.309047
$652$	58.5161	−	33.7843i	2.29167	−	1.32309i
$653$	−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
$655$		−	4.12676i		−	0.161246i
$656$	−1.25705	−	0.725758i	−0.0490796	−	0.0283361i
$657$	−16.0640	−	9.27453i	−0.626714	−	0.361834i
$658$			44.9114i			1.75083i
$659$	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
$661$	−5.22004	+	3.01379i	−0.203036	+	0.117223i	−0.598071	−	0.801443i	$-0.704066\pi$
$661$	−5.22004	+	3.01379i	−0.203036	+	0.117223i	0.395035	+	0.918666i	$0.370732\pi$
$662$	71.8604			2.79294
$663$		0			0
$664$	28.4492			1.10404
$665$	−9.45767	+	5.46039i	−0.366753	+	0.211745i
$666$	−4.71706	−	8.17018i	−0.182782	−	0.316588i
$667$	18.0491	−	31.2620i	0.698865	−	1.21047i
$668$		−	60.8479i		−	2.35428i
$669$	52.2411	+	30.1614i	2.01976	+	1.16611i
$670$	−17.4942	−	10.1003i	−0.675861	−	0.390209i
$671$		−	4.48990i		−	0.173330i
$672$	6.46481	−	11.1974i	0.249386	−	0.431948i
$673$	11.6784	+	20.2276i	0.450169	+	0.779715i	0.998396	−	0.0566140i	$-0.0180304\pi$
$673$	11.6784	+	20.2276i	0.450169	+	0.779715i	−0.548227	+	0.836329i	$0.684697\pi$
$674$	−25.3923	+	14.6603i	−0.978075	+	0.564692i
$675$	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	$0.837511\pi$
$678$	40.8593	−	23.5901i	1.56919	−	0.905973i
$679$	4.02148	+	6.96540i	0.154330	+	0.267308i
$680$	−1.77124	+	3.06787i	−0.0679239	+	0.117648i
$681$		−	44.3408i		−	1.69914i
$682$	3.38374	+	1.95360i	0.129570	+	0.0748073i
$683$	−22.0817	−	12.7489i	−0.844934	−	0.487823i	0.0140045	−	0.999902i	$-0.495542\pi$
$683$	−22.0817	−	12.7489i	−0.844934	−	0.487823i	−0.858938	+	0.512079i	$0.828875\pi$
$684$		−	120.945i		−	4.62445i
$685$	−10.0548	+	17.4155i	−0.384175	+	0.665411i
$686$	−24.6523	−	42.6991i	−0.941230	−	1.63026i
$687$	−18.6567	+	10.7715i	−0.711798	+	0.410957i
$688$	−3.45214			−0.131612
$689$		0			0
$690$	26.9327			1.02531
$691$	−5.71257	+	3.29815i	−0.217316	+	0.125468i	−0.604707	−	0.796448i	$-0.706710\pi$
$691$	−5.71257	+	3.29815i	−0.217316	+	0.125468i	0.387391	+	0.921916i	$0.373376\pi$
$692$	51.4683	+	89.1457i	1.95653	+	3.38881i
$693$	5.08438	−	8.80641i	0.193140	−	0.334528i
$694$			4.74090i			0.179962i
$695$	18.0352	+	10.4126i	0.684115	+	0.394974i
$696$	−128.673	−	74.2892i	−4.87733	−	2.81593i
$697$		−	0.170754i		−	0.00646778i
$698$	12.8133	−	22.1933i	0.484990	−	0.840028i
$699$	26.9327	+	46.6487i	1.01869	+	1.76442i
$700$	−6.97531	+	4.02720i	−0.263642	+	0.152214i
$701$	−29.2474			−1.10466			−0.552329	−	0.833626i	$-0.686261\pi$
$701$	−29.2474			−1.10466			−0.552329	+	0.833626i	$0.686261\pi$
$702$		0			0
$703$	4.34174			0.163752
$704$	−4.48542	+	2.58966i	−0.169051	+	0.0976015i
$705$	13.3513	+	23.1252i	0.502841	+	0.870946i
$706$	0.998937	−	1.73021i	0.0375955	−	0.0651173i
$707$		−	29.0499i		−	1.09253i
$708$	7.66938	+	4.42792i	0.288233	+	0.166411i
$709$	9.46865	+	5.46673i	0.355603	+	0.205307i	0.667150	−	0.744923i	$-0.267514\pi$
$709$	9.46865	+	5.46673i	0.355603	+	0.205307i	−0.311548	+	0.950231i	$0.600847\pi$
$710$			24.3683i			0.914527i
$711$	23.2566	−	40.2815i	0.872189	−	1.51068i
$712$	−34.9608	−	60.5538i	−1.31021	−	2.26935i
$713$	4.84084	−	2.79486i	0.181291	−	0.104668i
$714$	8.56490			0.320533
$715$		0			0
$716$	16.0152			0.598516
$717$	−31.2220	+	18.0260i	−1.16601	+	0.673194i
$718$	−10.1476	−	17.5762i	−0.378706	−	0.655938i
$719$	8.02989	−	13.9082i	0.299464	−	0.518688i	−0.676549	−	0.736398i	$-0.736525\pi$
$719$	8.02989	−	13.9082i	0.299464	−	0.518688i	0.976014	+	0.217710i	$0.0698587\pi$
$720$		−	27.0370i		−	1.00761i
$721$	22.3189	+	12.8858i	0.831199	+	0.479893i
$722$	29.9461	+	17.2894i	1.11448	+	0.643444i
$723$			73.2966i			2.72593i
$724$	17.9416	−	31.0758i	0.666796	−	1.15492i
$725$	4.72756	+	8.18837i	0.175577	+	0.304108i
$726$	−60.2156	+	34.7655i	−2.23481	+	1.29027i
$727$	−51.3754			−1.90541			−0.952704	−	0.303900i	$-0.901711\pi$
$727$	−51.3754			−1.90541			−0.952704	+	0.303900i	$0.901711\pi$
$728$		0			0
$729$	−43.0532			−1.59456
$730$	8.03198	−	4.63726i	0.297277	−	0.171633i
$731$	−0.203052	−	0.351697i	−0.00751016	−	0.0130080i
$732$	−25.0877	+	43.4532i	−0.927268	+	1.60608i
$733$		−	9.82358i		−	0.362842i	−0.983406	−	0.181421i	$-0.941930\pi$
$733$		−	9.82358i		−	0.362842i	0.983406	−	0.181421i	$-0.0580697\pi$
$734$	44.3613	+	25.6120i	1.63741	+	0.945357i
$735$	−8.25055	−	4.76346i	−0.304326	−	0.175703i
$736$		−	9.16560i		−	0.337848i
$737$	−4.32824	+	7.49673i	−0.159433	+	0.276146i
$738$	1.66867	+	2.89022i	0.0614246	+	0.106390i
$739$	−42.5082	+	24.5421i	−1.56369	+	0.902797i	−0.566811	+	0.823848i	$0.691823\pi$
$739$	−42.5082	+	24.5421i	−1.56369	+	0.902797i	−0.996879	+	0.0789487i	$0.974844\pi$
$740$	3.20216			0.117714
$741$		0			0
$742$	−33.2386			−1.22023
$743$	35.3663	−	20.4188i	1.29746	−	0.749091i	0.317499	−	0.948259i	$-0.397157\pi$
$743$	35.3663	−	20.4188i	1.29746	−	0.749091i	0.979966	+	0.199167i	$0.0638237\pi$
$744$	−11.5035	−	19.9247i	−0.421739	−	0.730473i
$745$	−6.68388	+	11.5768i	−0.244878	+	0.424142i
$746$		−	44.4346i		−	1.62687i
$747$	−22.1208	−	12.7715i	−0.809358	−	0.467283i
$748$	2.49503	+	1.44050i	0.0912272	+	0.0526700i
$749$			14.0276i			0.512557i
$750$	−3.52720	+	6.10929i	−0.128795	+	0.223080i
$751$	−1.36340	−	2.36148i	−0.0497512	−	0.0861716i	0.840077	−	0.542467i	$-0.182510\pi$
$751$	−1.36340	−	2.36148i	−0.0497512	−	0.0861716i	−0.889829	+	0.456295i	$0.849176\pi$
$752$	44.3154	−	25.5855i	1.61601	−	0.933006i
$753$	21.5175			0.784142
$754$		0			0
$755$	−18.2984			−0.665946
$756$	−39.2590	+	22.6662i	−1.42784	+	0.824362i
$757$	−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
$759$		−	11.5413i		−	0.418924i
$760$	27.5949	+	15.9319i	1.00097	+	0.577911i
$761$	−9.84575	−	5.68445i	−0.356908	−	0.206061i	0.310815	−	0.950470i	$-0.399398\pi$
$761$	−9.84575	−	5.68445i	−0.356908	−	0.206061i	−0.667724	+	0.744409i	$0.732731\pi$
$762$			10.5075i			0.380647i
$763$	−9.59843	+	16.6250i	−0.347486	+	0.601864i
$764$	−11.5055	−	19.9281i	−0.416255	−	0.720975i
$765$	2.75447	−	1.59030i	0.0995882	−	0.0574972i
$766$	19.7275			0.712784
$767$		0			0
$768$	91.7512			3.31078
$769$	−18.2352	+	10.5281i	−0.657579	+	0.379654i	−0.791354	−	0.611358i	$-0.790623\pi$
$769$	−18.2352	+	10.5281i	−0.657579	+	0.379654i	0.133775	+	0.991012i	$0.457290\pi$
$770$	2.54219	+	4.40320i	0.0916142	+	0.158680i
$771$	−0.474602	+	0.822034i	−0.0170924	+	0.0296048i
$772$			51.3970i			1.84982i
$773$	−12.1961	−	7.04144i	−0.438664	−	0.253263i	0.264367	−	0.964422i	$-0.414837\pi$
$773$	−12.1961	−	7.04144i	−0.438664	−	0.253263i	−0.703031	+	0.711159i	$0.748170\pi$
$774$	6.87381	+	3.96859i	0.247074	+	0.142648i
$775$			1.46410i			0.0525921i
$776$	11.7336	−	20.3231i	0.421210	−	0.729558i
$777$	−2.03971	−	3.53288i	−0.0731741	−	0.126741i
$778$	19.9081	−	11.4940i	0.713740	−	0.412078i
$779$	−1.53590			−0.0550293
$780$		0			0
$781$	10.4425			0.373660
$782$	5.25809	−	3.03576i	0.188029	−	0.108558i
$783$	26.6080	+	46.0864i	0.950893	+	1.64699i
$784$	−9.12832	+	15.8107i	−0.326011	+	0.564668i
$785$		−	2.42229i		−	0.0864552i
$786$	25.2116	+	14.5559i	0.899267	+	0.519192i
$787$	28.5998	+	16.5121i	1.01947	+	0.588593i	0.913951	−	0.405823i	$-0.133015\pi$
$787$	28.5998	+	16.5121i	1.01947	+	0.588593i	0.105522	+	0.994417i	$0.466349\pi$
$788$			18.5095i			0.659374i
$789$	−7.59839	+	13.1608i	−0.270510	+	0.468537i
$790$	11.6283	+	20.1408i	0.413716	+	0.716576i
$791$	11.0350	−	6.37109i	0.392361	−	0.226530i
$792$	−29.6697			−1.05427
$793$		0			0
$794$	−15.8574			−0.562758
$795$	−17.1148	+	9.88124i	−0.606999	+	0.350451i
$796$	−44.0454	−	76.2890i	−1.56115	−	2.70399i
$797$	−8.47079	+	14.6718i	−0.300051	+	0.519703i	−0.976147	−	0.217110i	$-0.930337\pi$
$797$	−8.47079	+	14.6718i	−0.300051	+	0.519703i	0.676096	+	0.736813i	$0.263670\pi$
$798$		−	77.0395i		−	2.72717i
$799$	5.21319	+	3.00984i	0.184429	+	0.106480i
$800$	2.07908	+	1.20036i	0.0735067	+	0.0424391i
$801$			62.7787i			2.21817i
$802$	−5.20213	+	9.01036i	−0.183694	+	0.318167i
$803$	−1.98719	−	3.44191i	−0.0701263	−	0.121462i
$804$	83.7774	−	48.3689i	2.95460	−	1.70584i
$805$	7.27382			0.256369
$806$		0			0
$807$	3.70425			0.130396
$808$	−73.4039	+	42.3798i	−2.58234	+	1.49092i
$809$	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
$811$			22.6699i			0.796047i	0.917375	+	0.398023i	$0.130304\pi$
$811$			22.6699i			0.796047i	−0.917375	+	0.398023i	$0.869696\pi$
$812$	−65.9524	−	38.0776i	−2.31448	−	1.33626i
$813$	28.5091	+	16.4597i	0.999856	+	0.577267i
$814$		−	2.02138i		−	0.0708494i
$815$	7.99144	−	13.8416i	0.279928	−	0.484849i
$816$	−4.87932	−	8.45123i	−0.170810	−	0.295852i
$817$	−3.16344	+	1.82641i	−0.110675	+	0.0638981i
$818$	−25.3745			−0.887198
$819$		0			0
$820$	−1.13277			−0.0395581
$821$	24.8230	−	14.3315i	0.866328	−	0.500174i	0.000201482	−	1.00000i	$-0.499936\pi$
$821$	24.8230	−	14.3315i	0.866328	−	0.500174i	0.866126	+	0.499826i	$0.166603\pi$
$822$	−70.9307	−	122.856i	−2.47399	−	4.28508i
$823$	−12.9164	+	22.3718i	−0.450236	+	0.779831i	−0.998400	−	0.0565391i	$-0.981993\pi$
$823$	−12.9164	+	22.3718i	−0.450236	+	0.779831i	0.548165	+	0.836371i	$0.315327\pi$
$824$		−	75.1946i		−	2.61953i
$825$	2.61799	+	1.51150i	0.0911466	+	0.0526235i
$826$	3.05121	+	1.76162i	0.106165	+	0.0612945i
$827$			16.0820i			0.559227i	0.960113	+	0.279613i	$0.0902063\pi$
$827$			16.0820i			0.559227i	−0.960113	+	0.279613i	$0.909794\pi$
$828$	−40.2780	+	69.7635i	−1.39976	+	2.42445i
$829$	−11.2909	−	19.5564i	−0.392149	−	0.679222i	0.600584	−	0.799562i	$-0.294935\pi$
$829$	−11.2909	−	19.5564i	−0.392149	−	0.679222i	−0.992733	+	0.120340i	$0.961602\pi$
$830$	11.0604	−	6.38573i	0.383912	−	0.221652i
$831$	−57.4304			−1.99224
$832$		0			0
$833$	−2.14768			−0.0744128
$834$	−127.228	+	73.4549i	−4.40553	+	2.54354i
$835$	−7.19658	−	12.4648i	−0.249048	−	0.431364i
$836$	12.9570	−	22.4422i	0.448128	−	0.776181i
$837$			8.24037i			0.284829i
$838$	−61.7898	−	35.6744i	−2.13449	−	1.23235i
$839$	−15.4533	−	8.92198i	−0.533508	−	0.308021i	0.208936	−	0.977929i	$-0.433000\pi$
$839$	−15.4533	−	8.92198i	−0.533508	−	0.308021i	−0.742444	+	0.669908i	$0.766333\pi$
$840$		−	29.9387i		−	1.03298i
$841$	−30.1996	+	52.3073i	−1.04137	+	1.80370i
$842$	2.51793	+	4.36118i	0.0867736	+	0.150296i
$843$	−29.0698	+	16.7835i	−1.00122	+	0.578053i
$844$	45.0390			1.55031
$845$		0			0
$846$	−117.653			−4.04498
$847$	−16.2627	+	9.38927i	−0.558793	+	0.322619i
$848$	18.9356	+	32.7975i	0.650252	+	1.12627i
$849$	32.0169	−	55.4550i	1.09882	−	1.90321i
$850$			1.59030i			0.0545467i
$851$	−2.50440	−	1.44591i	−0.0858497	−	0.0495653i
$852$	−101.062	−	58.3482i	−3.46233	−	1.99898i
$853$		−	19.7936i		−	0.677720i	−0.940837	−	0.338860i	$-0.889959\pi$
$853$		−	19.7936i		−	0.677720i	0.940837	−	0.338860i	$-0.110041\pi$
$854$	−9.98097	+	17.2875i	−0.341542	+	0.591568i
$855$	−14.3044	−	24.7759i	−0.489199	−	0.847318i
$856$	35.4452	−	20.4643i	1.21149	−	0.699456i
$857$	11.7302			0.400696			0.200348	−	0.979725i	$-0.435793\pi$
$857$	11.7302			0.400696			0.200348	+	0.979725i	$0.435793\pi$
$858$		0			0
$859$	5.37452			0.183376			0.0916882	−	0.995788i	$-0.470774\pi$
$859$	5.37452			0.183376			0.0916882	+	0.995788i	$0.470774\pi$
$860$	−2.33313	+	1.34703i	−0.0795591	+	0.0459335i
$861$	0.721551	+	1.24976i	0.0245904	+	0.0425918i
$862$	−25.7191	+	44.5467i	−0.875995	+	1.51727i
$863$		−	25.3234i		−	0.862017i	−0.902348	−	0.431008i	$-0.858158\pi$
$863$		−	25.3234i		−	0.862017i	0.902348	−	0.431008i	$-0.141842\pi$
$864$	11.7017	+	6.75596i	0.398099	+	0.229842i
$865$	21.0868	+	12.1745i	0.716973	+	0.413944i
$866$		−	73.4567i		−	2.49616i
$867$	−23.4541	+	40.6237i	−0.796544	+	1.37965i
$868$	−5.89623	−	10.2126i	−0.200131	−	0.346637i
$869$	8.63084	−	4.98302i	0.292781	−	0.169037i
$870$	−66.7001			−2.26135
$871$		0			0
$872$	56.0112			1.89678
$873$	−18.2470	+	10.5349i	−0.617567	+	0.356553i
$874$	−27.3060	−	47.2954i	−0.923640	−	1.59979i
$875$	−0.952606	+	1.64996i	−0.0322040	+	0.0557789i
$876$			44.4144i			1.50062i
$877$	−17.9194	−	10.3458i	−0.605095	−	0.349352i	0.165949	−	0.986134i	$-0.446931\pi$
$877$	−17.9194	−	10.3458i	−0.605095	−	0.349352i	−0.771043	+	0.636783i	$0.780265\pi$
$878$	36.6363	+	21.1520i	1.23642	+	0.713845i
$879$			52.6151i			1.77466i
$880$	2.89651	−	5.01691i	0.0976414	−	0.169120i
$881$	24.1997	+	41.9150i	0.815307	+	1.41215i	0.909107	+	0.416562i	$0.136765\pi$
$881$	24.1997	+	41.9150i	0.815307	+	1.41215i	−0.0937999	+	0.995591i	$0.529901\pi$
$882$	36.3521	−	20.9879i	1.22404	−	0.706699i
$883$	−45.8550			−1.54314			−0.771572	−	0.636142i	$-0.780529\pi$
$883$	−45.8550			−1.54314			−0.771572	+	0.636142i	$0.780529\pi$
$884$		0			0
$885$	2.09479			0.0704155
$886$	−52.1705	+	30.1207i	−1.75270	+	1.01192i
$887$	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
$889$			2.83781i			0.0951772i
$890$	−27.1840	−	15.6947i	−0.911208	−	0.526086i
$891$	0.867947	+	0.501109i	0.0290773	+	0.0167878i
$892$		−	90.2133i		−	3.02056i
$893$	27.0729	−	46.8916i	0.905959	−	1.56917i
$894$	−47.1507	−	81.6675i	−1.57696	−	2.73137i
$895$	3.28075	−	1.89414i	0.109663	−	0.0633142i
$896$	32.1749			1.07489
$897$		0			0
$898$	−52.0637			−1.73739
$899$	−11.9886	+	6.92163i	−0.399842	+	0.230849i
$900$	−10.5499	−	18.2730i	−0.351663	−	0.609099i
$901$	−2.22756	+	3.85824i	−0.0742107	+	0.128537i
$902$			0.715068i			0.0238092i
$903$	2.97231	+	1.71606i	0.0989122	+	0.0571070i
$904$	−32.1973	−	18.5891i	−1.07086	−	0.618264i
$905$		−	8.48794i		−	0.282149i
$906$	64.5420	−	111.790i	2.14426	−	3.71397i
$907$	−22.7653	−	39.4307i	−0.755910	−	1.30928i	−0.944920	−	0.327300i	$-0.893861\pi$
$907$	−22.7653	−	39.4307i	−0.755910	−	1.30928i	0.189010	−	0.981975i	$-0.439472\pi$
$908$	−57.4279	+	33.1560i	−1.90581	+	1.10032i
$909$	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	$0.271255\pi$
$912$	−76.0171	+	43.8885i	−2.51718	+	1.45329i
$913$	−2.73645	−	4.73967i	−0.0905632	−	0.156860i
$914$	−38.1387	+	66.0582i	−1.26152	+	2.18501i
$915$			11.8687i			0.392365i
$916$	27.9012	+	16.1088i	0.921883	+	0.532250i
$917$	6.80900	+	3.93118i	0.224853	+	0.129819i
$918$			8.95062i			0.295415i
$919$	−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
$921$	7.70608	−	4.44911i	0.253924	−	0.146603i
$922$	−11.6745			−0.384481
$923$		0			0
$924$	−24.3484			−0.801002
$925$	0.655970	−	0.378725i	0.0215682	−	0.0124524i
$926$	17.4700	+	30.2589i	0.574099	+	0.994369i
$927$	−33.7565	+	58.4680i	−1.10871	+	1.92034i
$928$			22.6991i			0.745134i
$929$	13.1821	+	7.61066i	0.432489	+	0.249698i	0.700406	−	0.713744i	$-0.253002\pi$
$929$	13.1821	+	7.61066i	0.432489	+	0.249698i	−0.267917	+	0.963442i	$0.586335\pi$
$930$	−8.94462	−	5.16418i	−0.293306	−	0.169340i
$931$			19.3180i			0.633121i
$932$	40.2780	−	69.7635i	1.31935	−	2.28518i
$933$	4.49551	+	7.78645i	0.147176	+	0.254917i
$934$	15.0959	−	8.71564i	0.493954	−	0.285184i
$935$	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	$0.468373\pi$
$938$	33.3302	−	19.2432i	1.08827	−	0.628313i
$939$	49.9691	+	86.5490i	1.63068	+	2.82442i
$940$	19.9670	−	34.5839i	0.651253	−	1.12800i
$941$		−	0.0496576i		−	0.00161879i	−1.00000		0.000809396i	$-0.999742\pi$
$941$		−	0.0496576i		−	0.00161879i	1.00000		0.000809396i	$-0.000257639\pi$
$942$	14.7985	+	8.54390i	0.482160	+	0.278375i
$943$	0.885936	+	0.511495i	0.0288500	+	0.0166566i
$944$		−	4.01429i		−	0.130654i
$945$	−5.36153	+	9.28645i	−0.174411	+	0.302088i
$946$	0.850322	+	1.47280i	0.0276464	+	0.0478849i
$947$	16.1584	−	9.32907i	0.525078	−	0.303154i	−0.213932	−	0.976849i	$-0.568627\pi$
$947$	16.1584	−	9.32907i	0.525078	−	0.303154i	0.739010	+	0.673695i	$0.235294\pi$
$948$	−111.372			−3.61720
$949$		0			0
$950$	14.3044			0.464095
$951$	33.3818	−	19.2730i	1.08248	−	0.624969i
$952$	−3.37458	−	5.84495i	−0.109371	−	0.189436i
$953$	−0.764764	+	1.32461i	−0.0247731	+	0.0429083i	−0.878146	−	0.478392i	$-0.841220\pi$
$953$	−0.764764	+	1.32461i	−0.0247731	+	0.0429083i	0.853373	+	0.521301i	$0.174553\pi$
$954$		−	87.0739i		−	2.81912i
$955$	−4.71386	−	2.72155i	−0.152537	−	0.0880673i
$956$	46.6927	+	26.9581i	1.51015	+	0.871886i
$957$			28.5827i			0.923948i
$958$	20.3244	−	35.2028i	0.656650	−	1.13735i
$959$	−19.1566	−	33.1802i	−0.618598	−	1.07144i
$960$	11.8568	−	6.84555i	0.382678	−	0.220939i
$961$	28.8564			0.930852
$962$		0			0
$963$	−36.7475			−1.18417
$964$	94.9299	−	54.8078i	3.05749	−	1.76524i
$965$	6.07880	+	10.5288i	0.195683	+	0.338934i
$966$	−25.6562	+	44.4379i	−0.825475	+	1.42976i
$967$			32.1716i			1.03457i	0.855813	+	0.517285i	$0.173057\pi$
$967$			32.1716i			1.03457i	−0.855813	+	0.517285i	$0.826943\pi$
$968$	47.4501	+	27.3953i	1.52510	+	0.880519i
$969$	−8.94253	−	5.16297i	−0.287276	−	0.165859i
$970$		−	10.5349i		−	0.338256i
$971$	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
$973$	−34.3609	+	19.8383i	−1.10156	+	0.635986i
$974$	−50.0122			−1.60249
$975$		0			0
$976$	22.7442			0.728023
$977$	13.6164	−	7.86142i	0.435626	−	0.251509i	−0.266114	−	0.963942i	$-0.585740\pi$
$977$	13.6164	−	7.86142i	0.435626	−	0.251509i	0.701741	+	0.712432i	$0.252407\pi$
$978$	56.3748	+	97.6440i	1.80267	+	3.12231i
$979$	−6.72557	+	11.6490i	−0.214950	+	0.372304i
$980$			14.2476i			0.455122i
$981$	−43.5518	−	25.1447i	−1.39050	−	0.802807i
$982$	−34.1429	−	19.7124i	−1.08954	−	0.629049i
$983$		−	38.5356i		−	1.22910i	−0.788880	−	0.614548i	$-0.789338\pi$
$983$		−	38.5356i		−	1.22910i	0.788880	−	0.614548i	$-0.210662\pi$
$984$	2.10529	−	3.64647i	0.0671141	−	0.116245i
$985$	2.18915	+	3.79172i	0.0697521	+	0.120814i
$986$	−13.0219	+	7.51821i	−0.414703	+	0.239429i
$987$	−50.8743			−1.61935
$988$		0			0
$989$	2.43298			0.0773642
$990$	−11.5349	+	6.65968i	−0.366604	+	0.211659i
$991$	−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
$993$			81.4014i			2.58320i
$994$	−40.2068	−	23.2134i	−1.27528	−	0.736285i
$995$	−18.0456	−	10.4186i	−0.572085	−	0.330293i
$996$			61.1606i			1.93795i
$997$	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
$999$	3.69198	−	2.13157i	0.116809	−	0.0674398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.m.g.361.4		8
13.2	odd	12		845.2.a.m.1.4		4
13.3	even	3		845.2.c.g.506.8		8
13.4	even	6	inner	845.2.m.g.316.4		8
13.5	odd	4		845.2.e.m.146.1		8
13.6	odd	12		845.2.e.m.191.1		8
13.7	odd	12		845.2.e.n.191.4		8
13.8	odd	4		845.2.e.n.146.4		8
13.9	even	3		65.2.m.a.56.1	yes	8
13.10	even	6		845.2.c.g.506.1		8
13.11	odd	12		845.2.a.l.1.1		4
13.12	even	2		65.2.m.a.36.1	✓	8
39.2	even	12		7605.2.a.cf.1.1		4
39.11	even	12		7605.2.a.cj.1.4		4
39.35	odd	6		585.2.bu.c.316.4		8
39.38	odd	2		585.2.bu.c.361.4		8
52.35	odd	6		1040.2.da.b.641.1		8
52.51	odd	2		1040.2.da.b.881.1		8
65.9	even	6		325.2.n.d.251.4		8
65.12	odd	4		325.2.m.b.49.1		8
65.22	odd	12		325.2.m.c.199.4		8
65.24	odd	12		4225.2.a.bl.1.4		4
65.38	odd	4		325.2.m.c.49.4		8
65.48	odd	12		325.2.m.b.199.1		8
65.54	odd	12		4225.2.a.bi.1.1		4
65.64	even	2		325.2.n.d.101.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.1	✓	8	13.12	even	2
65.2.m.a.56.1	yes	8	13.9	even	3
325.2.m.b.49.1		8	65.12	odd	4
325.2.m.b.199.1		8	65.48	odd	12
325.2.m.c.49.4		8	65.38	odd	4
325.2.m.c.199.4		8	65.22	odd	12
325.2.n.d.101.4		8	65.64	even	2
325.2.n.d.251.4		8	65.9	even	6
585.2.bu.c.316.4		8	39.35	odd	6
585.2.bu.c.361.4		8	39.38	odd	2
845.2.a.l.1.1		4	13.11	odd	12
845.2.a.m.1.4		4	13.2	odd	12
845.2.c.g.506.1		8	13.10	even	6
845.2.c.g.506.8		8	13.3	even	3
845.2.e.m.146.1		8	13.5	odd	4
845.2.e.m.191.1		8	13.6	odd	12
845.2.e.n.146.4		8	13.8	odd	4
845.2.e.n.191.4		8	13.7	odd	12
845.2.m.g.316.4		8	13.4	even	6	inner
845.2.m.g.361.4		8	1.1	even	1	trivial
1040.2.da.b.641.1		8	52.35	odd	6
1040.2.da.b.881.1		8	52.51	odd	2
4225.2.a.bi.1.1		4	65.54	odd	12
4225.2.a.bl.1.4		4	65.24	odd	12
7605.2.a.cf.1.1		4	39.2	even	12
7605.2.a.cj.1.4		4	39.11	even	12

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.m (of order \(6\), degree \(2\), not minimal)

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

Introduction

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