LMFDB - Embedded newform 735.2.s.k.656.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(521,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("735.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.s (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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			656.1
Root			$-2.33086i$ of defining polynomial
Character	$\chi$	$=$	735.656
Dual form			735.2.s.k.521.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.01859 - 1.16543i) q^{2} +(1.21646 - 1.23297i) q^{3} +(1.71646 + 2.97300i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-3.89248 + 1.07116i) q^{6} -3.33995i q^{8} +(-0.0404447 - 2.99973i) q^{9} +O(q^{10})$	\(q+(-2.01859 - 1.16543i) q^{2} +(1.21646 - 1.23297i) q^{3} +(1.71646 + 2.97300i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-3.89248 + 1.07116i) q^{6} -3.33995i q^{8} +(-0.0404447 - 2.99973i) q^{9} +(2.01859 - 1.16543i) q^{10} +(2.42019 - 1.39730i) q^{11} +(5.75363 + 1.50019i) q^{12} +3.20486i q^{13} +(0.459555 + 1.66997i) q^{15} +(-0.459555 + 0.795973i) q^{16} +(0.440969 + 0.763780i) q^{17} +(-3.41434 + 6.10234i) q^{18} +(-1.90160 - 1.09789i) q^{19} -3.43292 q^{20} -6.51381 q^{22} +(6.53240 + 3.77148i) q^{23} +(-4.11806 - 4.06291i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(3.73505 - 6.46929i) q^{26} +(-3.74778 - 3.59918i) q^{27} -8.15270i q^{29} +(1.01859 - 3.90656i) q^{30} +(7.62645 - 4.40313i) q^{31} +(-3.92965 + 2.26878i) q^{32} +(1.22124 - 4.68378i) q^{33} -2.05568i q^{34} +(8.84876 - 5.26916i) q^{36} +(-0.203727 + 0.352865i) q^{37} +(2.55903 + 4.43237i) q^{38} +(3.95151 + 3.89859i) q^{39} +(2.89248 + 1.66997i) q^{40} +8.55098 q^{41} -0.118062 q^{43} +(8.30832 + 4.79681i) q^{44} +(2.61806 + 1.46484i) q^{45} +(-8.79081 - 15.2261i) q^{46} +(1.31486 - 2.27740i) q^{47} +(0.422382 + 1.53489i) q^{48} +2.33086i q^{50} +(1.47814 + 0.385407i) q^{51} +(-9.52805 + 5.50102i) q^{52} +(6.46794 - 3.73427i) q^{53} +(3.37062 + 11.6330i) q^{54} +2.79459i q^{55} +(-3.66689 + 1.00908i) q^{57} +(-9.50142 + 16.4569i) q^{58} +(-2.04991 - 3.55054i) q^{59} +(-4.17602 + 4.23270i) q^{60} +(-10.7004 - 6.17786i) q^{61} -20.5262 q^{62} +12.4147 q^{64} +(-2.77549 - 1.60243i) q^{65} +(-7.92380 + 8.03135i) q^{66} +(0.802125 + 1.38932i) q^{67} +(-1.51381 + 2.62200i) q^{68} +(12.5965 - 3.46641i) q^{69} +6.25869i q^{71} +(-10.0189 + 0.135083i) q^{72} +(-0.192022 + 0.110864i) q^{73} +(0.822480 - 0.474859i) q^{74} +(-1.67602 - 0.437000i) q^{75} -7.53794i q^{76} +(-3.43292 - 12.4749i) q^{78} +(1.56849 - 2.71671i) q^{79} +(-0.459555 - 0.795973i) q^{80} +(-8.99673 + 0.242646i) q^{81} +(-17.2609 - 9.96559i) q^{82} +0.666893 q^{83} -0.881938 q^{85} +(0.238319 + 0.137594i) q^{86} +(-10.0521 - 9.91745i) q^{87} +(-4.66689 - 8.08330i) q^{88} +(0.437271 - 0.757376i) q^{89} +(-3.57762 - 6.00807i) q^{90} +25.8944i q^{92} +(3.84834 - 14.7594i) q^{93} +(-5.30832 + 3.06476i) q^{94} +(1.90160 - 1.09789i) q^{95} +(-1.98292 + 7.60504i) q^{96} -6.37221i q^{97} +(-4.28939 - 7.20339i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} - q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} - 5 q^{9}+O(q^{10}) $ 8 * q - 3 * q^2 - q^3 + 3 * q^4 - 4 * q^5 - 5 * q^6 - 5 * q^9	$ 8 q - 3 q^{2} - q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} - 5 q^{9} + 3 q^{10} + 9 q^{12} - q^{15} + q^{16} + 12 q^{17} - 19 q^{18} - 9 q^{19} - 6 q^{20} - 40 q^{22} + 27 q^{23} - 16 q^{24} - 4 q^{25} + 6 q^{26} - 4 q^{27} - 5 q^{30} + 21 q^{31} + 21 q^{32} - 2 q^{33} + 9 q^{36} + 7 q^{37} + 12 q^{38} - 3 q^{39} - 3 q^{40} + 30 q^{41} + 16 q^{43} + 4 q^{45} - 7 q^{46} + 6 q^{47} + 25 q^{48} - 6 q^{51} - 30 q^{52} + 24 q^{53} - 17 q^{54} + 6 q^{57} - 13 q^{58} + 12 q^{59} - 18 q^{60} - 15 q^{61} - 24 q^{62} + 38 q^{64} - 3 q^{65} - 22 q^{66} + 4 q^{67} + 13 q^{69} - 14 q^{72} - 15 q^{73} + 54 q^{74} + 2 q^{75} - 6 q^{78} - 29 q^{79} + q^{80} - 41 q^{81} - 27 q^{82} - 30 q^{83} - 24 q^{85} + 9 q^{86} - 32 q^{87} - 2 q^{88} + 3 q^{89} - 7 q^{90} - 9 q^{93} + 24 q^{94} + 9 q^{95} + 3 q^{96} - 34 q^{99}+O(q^{100}) $ 8 * q - 3 * q^2 - q^3 + 3 * q^4 - 4 * q^5 - 5 * q^6 - 5 * q^9 + 3 * q^10 + 9 * q^12 - q^15 + q^16 + 12 * q^17 - 19 * q^18 - 9 * q^19 - 6 * q^20 - 40 * q^22 + 27 * q^23 - 16 * q^24 - 4 * q^25 + 6 * q^26 - 4 * q^27 - 5 * q^30 + 21 * q^31 + 21 * q^32 - 2 * q^33 + 9 * q^36 + 7 * q^37 + 12 * q^38 - 3 * q^39 - 3 * q^40 + 30 * q^41 + 16 * q^43 + 4 * q^45 - 7 * q^46 + 6 * q^47 + 25 * q^48 - 6 * q^51 - 30 * q^52 + 24 * q^53 - 17 * q^54 + 6 * q^57 - 13 * q^58 + 12 * q^59 - 18 * q^60 - 15 * q^61 - 24 * q^62 + 38 * q^64 - 3 * q^65 - 22 * q^66 + 4 * q^67 + 13 * q^69 - 14 * q^72 - 15 * q^73 + 54 * q^74 + 2 * q^75 - 6 * q^78 - 29 * q^79 + q^80 - 41 * q^81 - 27 * q^82 - 30 * q^83 - 24 * q^85 + 9 * q^86 - 32 * q^87 - 2 * q^88 + 3 * q^89 - 7 * q^90 - 9 * q^93 + 24 * q^94 + 9 * q^95 + 3 * q^96 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	−2.01859	−	1.16543i	−1.42736	−	0.824085i	−0.430445	−	0.902617i	$-0.641643\pi$
$2$	−2.01859	−	1.16543i	−1.42736	−	0.824085i	−0.996912	+	0.0785324i	$0.974977\pi$
$3$	1.21646	−	1.23297i	0.702324	−	0.711857i
$3$	1.21646	−	1.23297i	0.702324	−	0.711857i
$4$	1.71646	+	2.97300i	0.858231	+	1.48650i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−3.89248	+	1.07116i	−1.58910	+	0.437299i
$7$		0			0
$7$		0			0
$8$		−	3.33995i		−	1.18085i
$9$	−0.0404447	−	2.99973i	−0.0134816	−	0.999909i
$10$	2.01859	−	1.16543i	0.638333	−	0.368542i
$11$	2.42019	−	1.39730i	0.729714	−	0.421301i	−0.0886035	−	0.996067i	$-0.528240\pi$
$11$	2.42019	−	1.39730i	0.729714	−	0.421301i	0.818318	+	0.574766i	$0.194907\pi$
$12$	5.75363	+	1.50019i	1.66093	+	0.433066i
$13$			3.20486i			0.888869i	0.895811	+	0.444434i	$0.146595\pi$
$13$			3.20486i			0.888869i	−0.895811	+	0.444434i	$0.853405\pi$
$14$		0			0
$15$	0.459555	+	1.66997i	0.118657	+	0.431185i
$16$	−0.459555	+	0.795973i	−0.114889	+	0.198993i
$17$	0.440969	+	0.763780i	0.106951	+	0.185244i	0.914533	−	0.404510i	$-0.132558\pi$
$17$	0.440969	+	0.763780i	0.106951	+	0.185244i	−0.807583	+	0.589754i	$0.799225\pi$
$18$	−3.41434	+	6.10234i	−0.804767	+	1.43834i
$19$	−1.90160	−	1.09789i	−0.436257	−	0.251873i	0.265751	−	0.964042i	$-0.414380\pi$
$19$	−1.90160	−	1.09789i	−0.436257	−	0.251873i	−0.702009	+	0.712168i	$0.747713\pi$
$20$	−3.43292			−0.767625
$21$		0			0
$22$	−6.51381			−1.38875
$23$	6.53240	+	3.77148i	1.36210	+	0.786408i	0.989903	−	0.141746i	$-0.0452716\pi$
$23$	6.53240	+	3.77148i	1.36210	+	0.786408i	0.372196	+	0.928154i	$0.378605\pi$
$24$	−4.11806	−	4.06291i	−0.840596	−	0.829339i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	3.73505	−	6.46929i	0.732503	−	1.26873i
$27$	−3.74778	−	3.59918i	−0.721261	−	0.692663i
$28$		0			0
$29$		−	8.15270i		−	1.51392i	−0.653462	−	0.756959i	$-0.726684\pi$
$29$		−	8.15270i		−	1.51392i	0.653462	−	0.756959i	$-0.273316\pi$
$30$	1.01859	−	3.90656i	0.185968	−	0.713238i
$31$	7.62645	−	4.40313i	1.36975	−	0.790826i	0.378855	−	0.925456i	$-0.376318\pi$
$31$	7.62645	−	4.40313i	1.36975	−	0.790826i	0.990896	+	0.134630i	$0.0429847\pi$
$32$	−3.92965	+	2.26878i	−0.694671	+	0.401068i
$33$	1.22124	−	4.68378i	0.212590	−	0.815342i
$34$		−	2.05568i		−	0.352545i
$35$		0			0
$36$	8.84876	−	5.26916i	1.47479	−	0.878193i
$37$	−0.203727	+	0.352865i	−0.0334925	+	0.0580107i	−0.882286	−	0.470714i	$-0.843996\pi$
$37$	−0.203727	+	0.352865i	−0.0334925	+	0.0580107i	0.848793	+	0.528725i	$0.177330\pi$
$38$	2.55903	+	4.43237i	0.415130	+	0.719026i
$39$	3.95151	+	3.89859i	0.632748	+	0.624274i
$40$	2.89248	+	1.66997i	0.457341	+	0.264046i
$41$	8.55098			1.33544			0.667720	−	0.744413i	$-0.267270\pi$
$41$	8.55098			1.33544			0.667720	+	0.744413i	$0.267270\pi$
$42$		0			0
$43$	−0.118062			−0.0180044			−0.00900218	−	0.999959i	$-0.502866\pi$
$43$	−0.118062			−0.0180044			−0.00900218	+	0.999959i	$0.502866\pi$
$44$	8.30832	+	4.79681i	1.25253	+	0.723146i
$45$	2.61806	+	1.46484i	0.390278	+	0.218365i
$46$	−8.79081	−	15.2261i	−1.29613	−	2.24497i
$47$	1.31486	−	2.27740i	0.191792	−	0.332194i	−0.754052	−	0.656815i	$-0.771903\pi$
$47$	1.31486	−	2.27740i	0.191792	−	0.332194i	0.945844	+	0.324621i	$0.105237\pi$
$48$	0.422382	+	1.53489i	0.0609656	+	0.221542i
$49$		0			0
$50$			2.33086i			0.329634i
$51$	1.47814	+	0.385407i	0.206981	+	0.0539677i
$52$	−9.52805	+	5.50102i	−1.32130	+	0.762854i
$53$	6.46794	−	3.73427i	0.888440	−	0.512941i	0.0150081	−	0.999887i	$-0.495223\pi$
$53$	6.46794	−	3.73427i	0.888440	−	0.512941i	0.873432	+	0.486946i	$0.161889\pi$
$54$	3.37062	+	11.6330i	0.458683	+	1.58306i
$55$			2.79459i			0.376823i
$56$		0			0
$57$	−3.66689	+	1.00908i	−0.485692	+	0.133656i
$58$	−9.50142	+	16.4569i	−1.24760	+	2.16090i
$59$	−2.04991	−	3.55054i	−0.266875	−	0.462241i	0.701178	−	0.712986i	$-0.252658\pi$
$59$	−2.04991	−	3.55054i	−0.266875	−	0.462241i	−0.968053	+	0.250745i	$0.919324\pi$
$60$	−4.17602	+	4.23270i	−0.539121	+	0.546439i
$61$	−10.7004	−	6.17786i	−1.37004	−	0.790994i	−0.379109	−	0.925352i	$-0.623769\pi$
$61$	−10.7004	−	6.17786i	−1.37004	−	0.790994i	−0.990933	+	0.134358i	$0.957103\pi$
$62$	−20.5262			−2.60683
$63$		0			0
$64$	12.4147			1.55183
$65$	−2.77549	−	1.60243i	−0.344257	−	0.198757i
$66$	−7.92380	+	8.03135i	−0.975352	+	0.988591i
$67$	0.802125	+	1.38932i	0.0979952	+	0.169733i	0.910855	−	0.412727i	$-0.135424\pi$
$67$	0.802125	+	1.38932i	0.0979952	+	0.169733i	−0.812860	+	0.582460i	$0.802090\pi$
$68$	−1.51381	+	2.62200i	−0.183577	+	0.317964i
$69$	12.5965	−	3.46641i	1.51645	−	0.417307i
$70$		0			0
$71$			6.25869i			0.742770i	0.928479	+	0.371385i	$0.121117\pi$
$71$			6.25869i			0.742770i	−0.928479	+	0.371385i	$0.878883\pi$
$72$	−10.0189	+	0.135083i	−1.18074	+	0.0159197i
$73$	−0.192022	+	0.110864i	−0.0224745	+	0.0129757i	−0.511195	−	0.859465i	$-0.670797\pi$
$73$	−0.192022	+	0.110864i	−0.0224745	+	0.0129757i	0.488721	+	0.872440i	$0.337464\pi$
$74$	0.822480	−	0.474859i	0.0956114	−	0.0552012i
$75$	−1.67602	−	0.437000i	−0.193530	−	0.0504604i
$76$		−	7.53794i		−	0.864661i
$77$		0			0
$78$	−3.43292	−	12.4749i	−0.388702	−	1.41250i
$79$	1.56849	−	2.71671i	0.176469	−	0.305654i	−0.764199	−	0.644980i	$-0.776866\pi$
$79$	1.56849	−	2.71671i	0.176469	−	0.305654i	0.940669	+	0.339326i	$0.110199\pi$
$80$	−0.459555	−	0.795973i	−0.0513798	−	0.0889925i
$81$	−8.99673	+	0.242646i	−0.999636	+	0.0269607i
$82$	−17.2609	−	9.96559i	−1.90615	−	1.10051i
$83$	0.666893			0.0732010			0.0366005	−	0.999330i	$-0.488347\pi$
$83$	0.666893			0.0732010			0.0366005	+	0.999330i	$0.488347\pi$
$84$		0			0
$85$	−0.881938			−0.0956596
$86$	0.238319	+	0.137594i	0.0256986	+	0.0148371i
$87$	−10.0521	−	9.91745i	−1.07769	−	1.06326i
$88$	−4.66689	−	8.08330i	−0.497492	−	0.861682i
$89$	0.437271	−	0.757376i	0.0463506	−	0.0802816i	−0.841919	−	0.539603i	$-0.818574\pi$
$89$	0.437271	−	0.757376i	0.0463506	−	0.0802816i	0.888270	+	0.459322i	$0.151908\pi$
$90$	−3.57762	−	6.00807i	−0.377114	−	0.633307i
$91$		0			0
$92$			25.8944i			2.69968i
$93$	3.84834	−	14.7594i	0.399054	−	1.53048i
$94$	−5.30832	+	3.06476i	−0.547511	+	0.316106i
$95$	1.90160	−	1.09789i	0.195100	−	0.112641i
$96$	−1.98292	+	7.60504i	−0.202381	+	0.776186i
$97$		−	6.37221i		−	0.647000i	−0.946228	−	0.323500i	$-0.895140\pi$
$97$		−	6.37221i		−	0.647000i	0.946228	−	0.323500i	$-0.104860\pi$
$98$		0			0
$99$	−4.28939	−	7.20339i	−0.431100	−	0.723968i
$100$	1.71646	−	2.97300i	0.171646	−	0.297300i
$101$	−5.31267	−	9.20181i	−0.528630	−	0.915614i	−0.999443	−	0.0333808i	$-0.989373\pi$
$101$	−5.31267	−	9.20181i	−0.528630	−	0.915614i	0.470813	−	0.882233i	$-0.343961\pi$
$102$	−2.53459	−	2.50065i	−0.250962	−	0.247601i
$103$	0.868777	+	0.501589i	0.0856031	+	0.0494230i	0.542191	−	0.840256i	$-0.317595\pi$
$103$	0.868777	+	0.501589i	0.0856031	+	0.0494230i	−0.456587	+	0.889679i	$0.650928\pi$
$104$	10.7041			1.04962
$105$		0			0
$106$	−17.4081			−1.69083
$107$	−11.0651	−	6.38846i	−1.06971	−	0.617596i	−0.141606	−	0.989923i	$-0.545226\pi$
$107$	−11.0651	−	6.38846i	−1.06971	−	0.617596i	−0.928101	+	0.372328i	$0.878560\pi$
$108$	4.26745	−	17.3200i	0.410635	−	1.66662i
$109$	−0.00912370	−	0.0158027i	−0.000873892	−	0.00151363i	0.865588	−	0.500757i	$-0.166945\pi$
$109$	−0.00912370	−	0.0158027i	−0.000873892	−	0.00151363i	−0.866462	+	0.499243i	$0.833612\pi$
$110$	3.25691	−	5.64113i	0.310534	−	0.537860i
$111$	0.187247	+	0.680436i	0.0177727	+	0.0645841i
$112$		0			0
$113$			7.23027i			0.680166i	0.940395	+	0.340083i	$0.110455\pi$
$113$			7.23027i			0.680166i	−0.940395	+	0.340083i	$0.889545\pi$
$114$	8.57796	+	2.23659i	0.803399	+	0.209476i
$115$	−6.53240	+	3.77148i	−0.609149	+	0.351692i
$116$	24.2380	−	13.9938i	2.25044	−	1.29929i
$117$	9.61371	−	0.129620i	0.888788	−	0.0119833i
$118$			9.55611i			0.879711i
$119$		0			0
$120$	5.57762	−	1.53489i	0.509165	−	0.140116i
$121$	−1.59513	+	2.76284i	−0.145012	+	0.251167i
$122$	14.3997	+	24.9411i	1.30369	+	2.25806i
$123$	10.4019	−	10.5431i	0.937911	−	0.950642i
$124$	26.1810	+	15.1156i	2.35112	+	1.35742i
$125$	1.00000			0.0894427
$126$		0			0
$127$	6.99561			0.620760			0.310380	−	0.950613i	$-0.399544\pi$
$127$	6.99561			0.620760			0.310380	+	0.950613i	$0.399544\pi$
$128$	−17.2008	−	9.93088i	−1.52035	−	0.877774i
$129$	−0.143618	+	0.145568i	−0.0126449	+	0.0128165i
$130$	3.73505	+	6.46929i	0.327585	+	0.567394i
$131$	−4.94673	+	8.56799i	−0.432198	+	0.748589i	−0.997062	−	0.0765948i	$-0.975595\pi$
$131$	−4.94673	+	8.56799i	−0.432198	+	0.748589i	0.564864	+	0.825184i	$0.308929\pi$
$132$	16.0211	−	4.40880i	1.39446	−	0.383737i
$133$		0			0
$134$		−	3.73929i		−	0.323025i
$135$	4.99088	−	1.44608i	0.429546	−	0.124459i
$136$	2.55098	−	1.47281i	0.218745	−	0.126293i
$137$	−10.9111	+	6.29951i	−0.932195	+	0.538203i	−0.887505	−	0.460798i	$-0.847563\pi$
$137$	−10.9111	+	6.29951i	−0.932195	+	0.538203i	−0.0446900	+	0.999001i	$0.514230\pi$
$138$	−29.4671	−	7.68316i	−2.50840	−	0.654034i
$139$			0.988113i			0.0838106i	0.999122	+	0.0419053i	$0.0133428\pi$
$139$			0.988113i			0.0838106i	−0.999122	+	0.0419053i	$0.986657\pi$
$140$		0			0
$141$	−1.20850	−	4.39156i	−0.101774	−	0.369836i
$142$	7.29408	−	12.6337i	0.612106	−	1.06020i
$143$	4.47814	+	7.75637i	0.374481	+	0.648620i
$144$	2.40629	+	1.34635i	0.200524	+	0.112196i
$145$	7.06045	+	4.07635i	0.586338	+	0.338523i
$146$	0.516818			0.0427722
$147$		0			0
$148$	−1.39876			−0.114977
$149$	15.3604	+	8.86834i	1.25837	+	0.726523i	0.972758	−	0.231821i	$-0.0744684\pi$
$149$	15.3604	+	8.86834i	1.25837	+	0.726523i	0.285616	+	0.958344i	$0.407802\pi$
$150$	2.87389	+	2.83540i	0.234652	+	0.231510i
$151$	11.2504	+	19.4862i	0.915542	+	1.58576i	0.806106	+	0.591771i	$0.201571\pi$
$151$	11.2504	+	19.4862i	0.915542	+	1.58576i	0.109435	+	0.993994i	$0.465096\pi$
$152$	−3.66689	+	6.35124i	−0.297424	+	0.515154i
$153$	2.27330	−	1.35368i	0.183785	−	0.109438i
$154$		0			0
$155$			8.80626i			0.707336i
$156$	−4.80789	+	18.4396i	−0.384939	+	1.47635i
$157$	10.2988	−	5.94600i	0.821931	−	0.474542i	−0.0291509	−	0.999575i	$-0.509280\pi$
$157$	10.2988	−	5.94600i	0.821931	−	0.474542i	0.851082	+	0.525033i	$0.175947\pi$
$158$	−6.33228	+	3.65594i	−0.503769	+	0.290851i
$159$	3.26375	−	12.5174i	0.258832	−	0.992693i
$160$		−	4.53757i		−	0.358726i
$161$		0			0
$162$	18.4435	+	9.99527i	1.44906	+	0.785302i
$163$	−4.26159	+	7.38130i	−0.333794	+	0.578148i	−0.983252	−	0.182249i	$-0.941662\pi$
$163$	−4.26159	+	7.38130i	−0.333794	+	0.578148i	0.649459	+	0.760397i	$0.274996\pi$
$164$	14.6774	+	25.4221i	1.14611	+	1.98513i
$165$	3.44566	+	3.39951i	0.268244	+	0.264652i
$166$	−1.34618	−	0.777218i	−0.104484	−	0.0603238i
$167$	−3.56923			−0.276195			−0.138098	−	0.990419i	$-0.544099\pi$
$167$	−3.56923			−0.276195			−0.138098	+	0.990419i	$0.544099\pi$
$168$		0			0
$169$	2.72886			0.209912
$170$	1.78027	+	1.02784i	0.136540	+	0.0788316i
$171$	−3.21646	+	5.74869i	−0.245969	+	0.439613i
$172$	−0.202650	−	0.350999i	−0.0154519	−	0.0267634i
$173$	4.27114	−	7.39784i	0.324729	−	0.562447i	−0.656728	−	0.754127i	$-0.728060\pi$
$173$	4.27114	−	7.39784i	0.324729	−	0.562447i	0.981457	+	0.191680i	$0.0613936\pi$
$174$	8.73285	+	31.7342i	0.662036	+	2.40576i
$175$		0			0
$176$			2.56854i			0.193611i
$177$	−6.87136	−	1.79162i	−0.516483	−	0.134666i
$178$	−1.76534	+	1.01922i	−0.132318	+	0.0763937i
$179$	1.06480	−	0.614760i	0.0795866	−	0.0459493i	−0.459679	−	0.888085i	$-0.652035\pi$
$179$	1.06480	−	0.614760i	0.0795866	−	0.0459493i	0.539265	+	0.842136i	$0.318702\pi$
$180$	0.138843	+	10.2978i	0.0103488	+	0.767555i
$181$			15.3995i			1.14464i	0.820032	+	0.572318i	$0.193956\pi$
$181$			15.3995i			1.14464i	−0.820032	+	0.572318i	$0.806044\pi$
$182$		0			0
$183$	−20.6337	+	5.67814i	−1.52529	+	0.419740i
$184$	12.5965	−	21.8179i	0.928630	−	1.60843i
$185$	−0.203727	−	0.352865i	−0.0149783	−	0.0259432i
$186$	−24.9693	+	25.3082i	−1.83084	+	1.85569i
$187$	2.13445	+	1.23233i	0.156087	+	0.0901167i
$188$	9.02762			0.658407
$189$		0			0
$190$	−5.11806			−0.371303
$191$	−12.5795	−	7.26275i	−0.910218	−	0.525514i	−0.0297166	−	0.999558i	$-0.509460\pi$
$191$	−12.5795	−	7.26275i	−0.910218	−	0.525514i	−0.880501	+	0.474044i	$0.842794\pi$
$192$	15.1020	−	15.3070i	1.08989	−	1.10468i
$193$	0.201572	+	0.349134i	0.0145095	+	0.0251312i	0.873189	−	0.487382i	$-0.162048\pi$
$193$	0.201572	+	0.349134i	0.0145095	+	0.0251312i	−0.858679	+	0.512513i	$0.828715\pi$
$194$	−7.42638	+	12.8629i	−0.533183	+	0.923500i
$195$	−5.35203	+	1.47281i	−0.383267	+	0.105470i
$196$		0			0
$197$		−	11.6716i		−	0.831564i	−0.909464	−	0.415782i	$-0.863508\pi$
$197$		−	11.6716i		−	0.831564i	0.909464	−	0.415782i	$-0.136492\pi$
$198$	0.263449	+	19.5397i	0.0187225	+	1.38862i
$199$	16.0886	−	9.28875i	1.14049	−	0.658462i	0.193938	−	0.981014i	$-0.437874\pi$
$199$	16.0886	−	9.28875i	1.14049	−	0.658462i	0.946552	+	0.322552i	$0.104541\pi$
$200$	−2.89248	+	1.66997i	−0.204529	+	0.118085i
$201$	2.68875	+	0.701057i	0.189650	+	0.0494488i
$202$			24.7662i			1.74254i
$203$		0			0
$204$	1.39136	+	5.05605i	0.0974147	+	0.353994i
$205$	−4.27549	+	7.40537i	−0.298613	+	0.517213i
$206$	−1.16913	−	2.02500i	−0.0814574	−	0.141088i
$207$	11.0492	−	19.7479i	0.767974	−	1.37258i
$208$	−2.55098	−	1.47281i	−0.176879	−	0.102121i
$209$	−6.13631			−0.424457
$210$		0			0
$211$	6.98175			0.480644			0.240322	−	0.970693i	$-0.422747\pi$
$211$	6.98175			0.480644			0.240322	+	0.970693i	$0.422747\pi$
$212$	22.2039	+	12.8194i	1.52497	+	0.880443i
$213$	7.71680	+	7.61346i	0.528746	+	0.521666i
$214$	14.8906	+	25.7913i	1.01790	+	1.76306i
$215$	0.0590312	−	0.102245i	0.00402590	−	0.00697306i
$216$	−12.0211	+	12.5174i	−0.817931	+	0.851700i
$217$		0			0
$218$			0.0425322i			0.00288064i
$219$	−0.0968952	+	0.371620i	−0.00654757	+	0.0251118i
$220$	−8.30832	+	4.79681i	−0.560147	+	0.323401i
$221$	−2.44781	+	1.41324i	−0.164658	+	0.0950651i
$222$	0.415027	−	1.59174i	0.0278548	−	0.106831i
$223$		−	1.44594i		−	0.0968271i	−0.998827	−	0.0484135i	$-0.984583\pi$
$223$		−	1.44594i		−	0.0968271i	0.998827	−	0.0484135i	$-0.0154165\pi$
$224$		0			0
$225$	−2.57762	+	1.53489i	−0.171841	+	0.102326i
$226$	8.42638	−	14.5949i	0.560514	−	0.970839i
$227$	0.533562	+	0.924157i	0.0354138	+	0.0613385i	0.883189	−	0.469017i	$-0.155392\pi$
$227$	0.533562	+	0.924157i	0.0354138	+	0.0613385i	−0.847775	+	0.530356i	$0.822058\pi$
$228$	−9.29408	−	9.16961i	−0.615515	−	0.607272i
$229$	6.58058	+	3.79930i	0.434857	+	0.251065i	0.701414	−	0.712755i	$-0.252553\pi$
$229$	6.58058	+	3.79930i	0.434857	+	0.251065i	−0.266557	+	0.963819i	$0.585886\pi$
$230$	17.5816			1.15930
$231$		0			0
$232$	−27.2296			−1.78771
$233$	15.5882	+	8.99983i	1.02121	+	0.589598i	0.914455	−	0.404687i	$-0.132619\pi$
$233$	15.5882	+	8.99983i	1.02121	+	0.589598i	0.106759	+	0.994285i	$0.465953\pi$
$234$	−19.5572	−	10.9425i	−1.27849	−	0.715332i
$235$	1.31486	+	2.27740i	0.0857720	+	0.148561i
$236$	7.03717	−	12.1887i	0.458081	−	0.793419i
$237$	−1.44162	−	5.23868i	−0.0936433	−	0.340289i
$238$		0			0
$239$			29.8816i			1.93288i	0.256892	+	0.966440i	$0.417302\pi$
$239$			29.8816i			1.93288i	−0.256892	+	0.966440i	$0.582698\pi$
$240$	−1.54044	−	0.401651i	−0.0994353	−	0.0259265i
$241$	−4.53760	+	2.61978i	−0.292292	+	0.168755i	−0.638975	−	0.769227i	$-0.720641\pi$
$241$	−4.53760	+	2.61978i	−0.292292	+	0.168755i	0.346683	+	0.937982i	$0.387308\pi$
$242$	6.43980	−	3.71802i	0.413966	−	0.239004i
$243$	−10.6450	+	11.3879i	−0.682877	+	0.730534i
$244$		−	42.4162i		−	2.71542i
$245$		0			0
$246$	−33.2845	+	9.15948i	−2.12214	+	0.583987i
$247$	3.51859	−	6.09437i	0.223882	−	0.387776i
$248$	−14.7062	−	25.4719i	−0.933846	−	1.61747i
$249$	0.811249	−	0.822261i	0.0514108	−	0.0521087i
$250$	−2.01859	−	1.16543i	−0.127667	−	0.0737084i
$251$	15.0765			0.951620			0.475810	−	0.879548i	$-0.342155\pi$
$251$	15.0765			0.951620			0.475810	+	0.879548i	$0.342155\pi$
$252$		0			0
$253$	21.0795			1.32526
$254$	−14.1212	−	8.15291i	−0.886046	−	0.511559i
$255$	−1.07284	+	1.08741i	−0.0671840	+	0.0680960i
$256$	10.7329	+	18.5898i	0.670803	+	1.16187i
$257$	−7.95478	+	13.7781i	−0.496206	+	0.859453i	−0.999990	−	0.00437591i	$-0.998607\pi$
$257$	−7.95478	+	13.7781i	−0.496206	+	0.859453i	0.503785	+	0.863829i	$0.331940\pi$
$258$	0.459555	−	0.126464i	0.0286107	−	0.00787329i
$259$		0			0
$260$		−	11.0020i		−	0.682318i
$261$	−24.4559	+	0.329733i	−1.51378	+	0.0204100i
$262$	19.9708	−	11.5302i	1.23380	−	0.712336i
$263$	7.19124	−	4.15187i	0.443431	−	0.256015i	−0.261621	−	0.965171i	$-0.584257\pi$
$263$	7.19124	−	4.15187i	0.443431	−	0.256015i	0.705052	+	0.709156i	$0.250924\pi$
$264$	−15.6436	−	4.07886i	−0.962796	−	0.251037i
$265$			7.46853i			0.458788i
$266$		0			0
$267$	−0.401900	−	1.46046i	−0.0245959	−	0.0893788i
$268$	−2.75363	+	4.76943i	−0.168205	+	0.291340i
$269$	−8.69353	−	15.0576i	−0.530054	−	0.918080i	−0.999385	−	0.0350578i	$-0.988838\pi$
$269$	−8.69353	−	15.0576i	−0.530054	−	0.918080i	0.469332	−	0.883022i	$-0.344495\pi$
$270$	−11.7598	−	2.89748i	−0.715680	−	0.176335i
$271$	8.82614	+	5.09577i	0.536150	+	0.309546i	0.743517	−	0.668717i	$-0.233156\pi$
$271$	8.82614	+	5.09577i	0.536150	+	0.309546i	−0.207367	+	0.978263i	$0.566490\pi$
$272$	−0.810598			−0.0491497
$273$		0			0
$274$	29.3666			1.77410
$275$	−2.42019	−	1.39730i	−0.145943	−	0.0842601i
$276$	31.9271	+	31.4995i	1.92179	+	1.89605i
$277$	−4.78018	−	8.27951i	−0.287213	−	0.497468i	0.685930	−	0.727667i	$-0.259395\pi$
$277$	−4.78018	−	8.27951i	−0.287213	−	0.497468i	−0.973143	+	0.230199i	$0.926062\pi$
$278$	1.15158	−	1.99459i	0.0690670	−	0.119628i
$279$	−13.5166	−	22.6992i	−0.809220	−	1.35896i
$280$		0			0
$281$		−	11.9239i		−	0.711320i	−0.934616	−	0.355660i	$-0.884256\pi$
$281$		−	11.9239i		−	0.711320i	0.934616	−	0.355660i	$-0.115744\pi$
$282$	−2.67860	+	10.2732i	−0.159508	+	0.611758i
$283$	−17.2940	+	9.98469i	−1.02802	+	0.593528i	−0.916417	−	0.400225i	$-0.868932\pi$
$283$	−17.2940	+	9.98469i	−1.02802	+	0.593528i	−0.111604	+	0.993753i	$0.535599\pi$
$284$	−18.6071	+	10.7428i	−1.10413	+	0.637468i
$285$	0.959555	−	3.68016i	0.0568392	−	0.217994i
$286$		−	20.8759i		−	1.23442i
$287$		0			0
$288$	6.96467	+	11.6961i	0.410397	+	0.689201i
$289$	8.11109	−	14.0488i	0.477123	−	0.826401i
$290$	−9.50142	−	16.4569i	−0.557942	−	0.966385i
$291$	−7.85677	−	7.75155i	−0.460572	−	0.454404i
$292$	−0.659198	−	0.380588i	−0.0385766	−	0.0222722i
$293$	−3.01023			−0.175859			−0.0879297	−	0.996127i	$-0.528025\pi$
$293$	−3.01023			−0.175859			−0.0879297	+	0.996127i	$0.528025\pi$
$294$		0			0
$295$	4.09982			0.238700
$296$	1.17855	+	0.680436i	0.0685018	+	0.0395495i
$297$	−14.0995	−	3.47394i	−0.818134	−	0.201579i
$298$	−20.6709	−	35.8030i	−1.19743	−	2.07401i
$299$	−12.0871	+	20.9354i	−0.699014	+	1.21073i
$300$	−1.57762	−	5.73289i	−0.0910838	−	0.330988i
$301$		0			0
$302$		−	52.4461i		−	3.01793i
$303$	−17.8082	−	4.64327i	−1.02306	−	0.266749i
$304$	1.74778	−	1.00908i	0.100242	−	0.0578748i
$305$	10.7004	−	6.17786i	0.612701	−	0.353743i
$306$	−6.16647	+	0.0831411i	−0.352513	+	0.00475286i
$307$			20.3794i			1.16311i	0.813507	+	0.581556i	$0.197556\pi$
$307$			20.3794i			1.16311i	−0.813507	+	0.581556i	$0.802444\pi$
$308$		0			0
$309$	1.67528	−	0.461015i	0.0953033	−	0.0262263i
$310$	10.2631	−	17.7762i	0.582905	−	1.00962i
$311$	−13.6359	−	23.6181i	−0.773222	−	1.33926i	−0.935789	−	0.352562i	$-0.885311\pi$
$311$	−13.6359	−	23.6181i	−0.773222	−	1.33926i	0.162567	−	0.986697i	$-0.448023\pi$
$312$	13.0211	−	13.1978i	0.737173	−	0.747180i
$313$	−0.546210	−	0.315354i	−0.0308736	−	0.0178249i	0.484484	−	0.874800i	$-0.339007\pi$
$313$	−0.546210	−	0.315354i	−0.0308736	−	0.0178249i	−0.515357	+	0.856975i	$0.672341\pi$
$314$	−27.7186			−1.56425
$315$		0			0
$316$	10.7690			0.605806
$317$	22.0233	+	12.7151i	1.23695	+	0.714153i	0.968470	−	0.249132i	$-0.0801453\pi$
$317$	22.0233	+	12.7151i	1.23695	+	0.714153i	0.268480	+	0.963285i	$0.413479\pi$
$318$	−21.1763	+	21.4638i	−1.18751	+	1.20363i
$319$	−11.3917	−	19.7311i	−0.637815	−	1.10473i
$320$	−6.20734	+	10.7514i	−0.347001	+	0.601023i
$321$	−21.3371	+	5.87170i	−1.19092	+	0.327726i
$322$		0			0
$323$		−	1.93654i		−	0.107752i
$324$	−16.1639	−	26.3308i	−0.897996	−	1.46282i
$325$	2.77549	−	1.60243i	0.153957	−	0.0888869i
$326$	17.2048	−	9.93319i	0.952885	−	0.550149i
$327$	−0.0305829	−	0.00797411i	−0.00169124	−	0.000440969i
$328$		−	28.5598i		−	1.57695i
$329$		0			0
$330$	−2.99346	−	10.8779i	−0.164784	−	0.598808i
$331$	−5.74666	+	9.95352i	−0.315865	+	0.547095i	−0.979621	−	0.200855i	$-0.935628\pi$
$331$	−5.74666	+	9.95352i	−0.315865	+	0.547095i	0.663756	+	0.747949i	$0.268961\pi$
$332$	1.14470	+	1.98267i	0.0628233	+	0.108813i
$333$	1.06674	+	0.596853i	0.0584569	+	0.0327074i
$334$	7.20480	+	4.15970i	0.394229	+	0.227608i
$335$	−1.60425			−0.0876496
$336$		0			0
$337$	−16.2041			−0.882694			−0.441347	−	0.897336i	$-0.645499\pi$
$337$	−16.2041			−0.882694			−0.441347	+	0.897336i	$0.645499\pi$
$338$	−5.50843	−	3.18030i	−0.299619	−	0.172985i
$339$	8.91472	+	8.79534i	0.484181	+	0.477697i
$340$	−1.51381	−	2.62200i	−0.0820980	−	0.142198i
$341$	12.3050	−	21.3128i	0.666351	−	1.15415i
$342$	13.1924	−	7.85566i	0.713364	−	0.424786i
$343$		0			0
$344$			0.394322i			0.0212604i
$345$	−3.29627	+	12.6421i	−0.177465	+	0.680629i
$346$	−17.2433	+	9.95545i	−0.927008	+	0.535208i
$347$	−15.5732	+	8.99121i	−0.836015	+	0.482673i	−0.855908	−	0.517129i	$-0.827001\pi$
$347$	−15.5732	+	8.99121i	−0.836015	+	0.482673i	0.0198929	+	0.999802i	$0.493667\pi$
$348$	12.2306	−	46.9077i	0.655627	−	2.51451i
$349$			6.15422i			0.329428i	0.986341	+	0.164714i	$0.0526701\pi$
$349$			6.15422i			0.329428i	−0.986341	+	0.164714i	$0.947330\pi$
$350$		0			0
$351$	11.5349	−	12.0111i	0.615687	−	0.641106i
$352$	−6.34033	+	10.9818i	−0.337941	+	0.585330i
$353$	14.7332	+	25.5186i	0.784169	+	1.35822i	0.929494	+	0.368836i	$0.120244\pi$
$353$	14.7332	+	25.5186i	0.784169	+	1.35822i	−0.145326	+	0.989384i	$0.546423\pi$
$354$	11.7824	+	11.6246i	0.626229	+	0.617842i
$355$	−5.42019	−	3.12935i	−0.287674	−	0.166088i
$356$	3.00223			0.159118
$357$		0			0
$358$	−2.86584			−0.151465
$359$	−30.5228	−	17.6224i	−1.61093	−	0.930073i	−0.989154	−	0.146881i	$-0.953077\pi$
$359$	−30.5228	−	17.6224i	−1.61093	−	0.930073i	−0.621779	−	0.783192i	$-0.713590\pi$
$360$	4.89248	−	8.74419i	0.257856	−	0.460859i
$361$	−7.08928	−	12.2790i	−0.373120	−	0.646262i
$362$	17.9471	−	31.0852i	0.943277	−	1.63380i
$363$	1.46610	+	5.32764i	0.0769502	+	0.279628i
$364$		0			0
$365$		−	0.221728i		−	0.0116058i
$366$	48.2684	+	12.5854i	2.52303	+	0.657848i
$367$	−30.1613	+	17.4136i	−1.57441	+	0.908984i	−0.578788	+	0.815478i	$0.696474\pi$
$367$	−30.1613	+	17.4136i	−1.57441	+	0.908984i	−0.995619	+	0.0935065i	$0.970192\pi$
$368$	−6.00400	+	3.46641i	−0.312980	+	0.180699i
$369$	−0.345842	−	25.6506i	−0.0180038	−	1.33532i
$370$			0.949718i			0.0493735i
$371$		0			0
$372$	50.4853	−	13.8929i	2.61754	−	0.720314i
$373$	−10.1371	+	17.5579i	−0.524878	+	0.909115i	0.474702	+	0.880146i	$0.342556\pi$
$373$	−10.1371	+	17.5579i	−0.524878	+	0.909115i	−0.999580	+	0.0289688i	$0.990778\pi$
$374$	−2.87239	−	4.97512i	−0.148528	−	0.257257i
$375$	1.21646	−	1.23297i	0.0628178	−	0.0636705i
$376$	−7.60641	−	4.39156i	−0.392270	−	0.226477i
$377$	26.1283			1.34568
$378$		0			0
$379$	−9.07202			−0.465998			−0.232999	−	0.972477i	$-0.574854\pi$
$379$	−9.07202			−0.465998			−0.232999	+	0.972477i	$0.574854\pi$
$380$	6.52805	+	3.76897i	0.334882	+	0.193344i
$381$	8.50989	−	8.62540i	0.435975	−	0.441893i
$382$	16.9285	+	29.3210i	0.866137	+	1.50019i
$383$	13.8881	−	24.0549i	0.709648	−	1.22915i	−0.255339	−	0.966851i	$-0.582187\pi$
$383$	13.8881	−	24.0549i	0.709648	−	1.22915i	0.964988	−	0.262295i	$-0.0844794\pi$
$384$	−33.1686	+	9.12758i	−1.69263	+	0.465790i
$385$		0			0
$386$		−	0.939675i		−	0.0478282i
$387$	0.00477499	+	0.354155i	0.000242727	+	0.0180027i
$388$	18.9446	−	10.9377i	0.961765	−	0.555275i
$389$	−13.4945	+	7.79107i	−0.684200	+	0.395023i	−0.801436	−	0.598081i	$-0.795930\pi$
$389$	−13.4945	+	7.79107i	−0.684200	+	0.395023i	0.117236	+	0.993104i	$0.462597\pi$
$390$	12.5200	+	3.26443i	0.633975	+	0.165301i
$391$			6.65242i			0.336427i
$392$		0			0
$393$	4.54660	+	16.5218i	0.229345	+	0.833416i
$394$	−13.6024	+	23.5600i	−0.685279	+	1.18694i
$395$	1.56849	+	2.71671i	0.0789195	+	0.136693i
$396$	14.0531	−	25.1167i	0.706194	−	1.26216i
$397$	16.3596	+	9.44524i	0.821067	+	0.474043i	0.850784	−	0.525515i	$-0.176127\pi$
$397$	16.3596	+	9.44524i	0.821067	+	0.474043i	−0.0297174	+	0.999558i	$0.509461\pi$
$398$	−43.3016			−2.17051
$399$		0			0
$400$	0.919111			0.0459555
$401$	18.0127	+	10.3996i	0.899511	+	0.519333i	0.877042	−	0.480415i	$-0.159514\pi$
$401$	18.0127	+	10.3996i	0.899511	+	0.519333i	0.0224695	+	0.999748i	$0.492847\pi$
$402$	−4.61044	−	4.54870i	−0.229948	−	0.226869i
$403$	14.1114	+	24.4417i	0.702941	+	1.21753i
$404$	18.2380	−	31.5891i	0.907373	−	1.57162i
$405$	4.28823	−	7.91272i	0.213084	−	0.393186i
$406$		0			0
$407$			1.13867i			0.0564416i
$408$	1.28724	−	4.93691i	0.0637277	−	0.244414i
$409$	−24.9664	+	14.4143i	−1.23451	+	0.712744i	−0.967966	−	0.251080i	$-0.919214\pi$
$409$	−24.9664	+	14.4143i	−1.23451	+	0.712744i	−0.266542	+	0.963823i	$0.585881\pi$
$410$	17.2609	−	9.96559i	0.852455	−	0.492165i
$411$	−5.50577	+	21.1162i	−0.271579	+	1.04158i
$412$			3.44383i			0.169665i
$413$		0			0
$414$	−45.3187	+	26.9858i	−2.22729	+	1.32628i
$415$	−0.333446	+	0.577546i	−0.0163682	+	0.0283506i
$416$	−7.27114	−	12.5940i	−0.356497	−	0.617471i
$417$	1.21832	+	1.20200i	0.0596612	+	0.0588622i
$418$	12.3867	+	7.15145i	0.605852	+	0.349789i
$419$	3.24500			0.158528			0.0792642	−	0.996854i	$-0.474743\pi$
$419$	3.24500			0.158528			0.0792642	+	0.996854i	$0.474743\pi$
$420$		0			0
$421$	27.9322			1.36133			0.680665	−	0.732594i	$-0.261691\pi$
$421$	27.9322			1.36133			0.680665	+	0.732594i	$0.261691\pi$
$422$	−14.0933	−	8.13675i	−0.686050	−	0.396091i
$423$	−6.88477	−	3.85211i	−0.334749	−	0.187296i
$424$	−12.4722	−	21.6026i	−0.605706	−	1.04911i
$425$	0.440969	−	0.763780i	0.0213901	−	0.0370488i
$426$	−6.70407	−	24.3618i	−0.324813	−	1.18033i
$427$		0			0
$428$		−	43.8622i		−	2.12016i
$429$	15.0109	+	3.91389i	0.724732	+	0.188965i
$430$	−0.238319	+	0.137594i	−0.0114928	+	0.00663536i
$431$	−33.1792	+	19.1560i	−1.59819	+	0.922714i	−0.606351	+	0.795197i	$0.707367\pi$
$431$	−33.1792	+	19.1560i	−1.59819	+	0.922714i	−0.991836	+	0.127516i	$0.959299\pi$
$432$	4.58717	−	1.32911i	0.220700	−	0.0639468i
$433$		−	28.9533i		−	1.39140i	−0.718330	−	0.695702i	$-0.755093\pi$
$433$		−	28.9533i		−	1.39140i	0.718330	−	0.695702i	$-0.244907\pi$
$434$		0			0
$435$	13.6148	−	3.74662i	0.652779	−	0.179637i
$436$	0.0313210	−	0.0542495i	0.00150000	−	0.00259808i
$437$	−8.28134	−	14.3437i	−0.396150	−	0.686153i
$438$	0.628690	−	0.637223i	0.0300400	−	0.0304477i
$439$	13.2197	+	7.63242i	0.630943	+	0.364275i	0.781117	−	0.624384i	$-0.214650\pi$
$439$	13.2197	+	7.63242i	0.630943	+	0.364275i	−0.150174	+	0.988660i	$0.547983\pi$
$440$	9.33379			0.444971
$441$		0			0
$442$	6.58816			0.313367
$443$	−1.97776	−	1.14186i	−0.0939660	−	0.0542513i	0.452281	−	0.891876i	$-0.350611\pi$
$443$	−1.97776	−	1.14186i	−0.0939660	−	0.0542513i	−0.546247	+	0.837624i	$0.683944\pi$
$444$	−1.70153	+	1.72463i	−0.0807512	+	0.0818472i
$445$	0.437271	+	0.757376i	0.0207286	+	0.0359030i
$446$	−1.68514	+	2.91875i	−0.0797937	+	0.138207i
$447$	29.6198	−	8.15099i	1.40097	−	0.385528i
$448$		0			0
$449$		−	10.3113i		−	0.486619i	−0.969949	−	0.243310i	$-0.921767\pi$
$449$		−	10.3113i		−	0.486619i	0.969949	−	0.243310i	$-0.0782331\pi$
$450$	6.99195	−	0.0942709i	0.329604	−	0.00444398i
$451$	20.6950	−	11.9483i	0.974489	−	0.562621i
$452$	−21.4956	+	12.4105i	−1.01107	+	0.583739i
$453$	37.7116	+	9.83281i	1.77184	+	0.461986i
$454$		−	2.48732i		−	0.116736i
$455$		0			0
$456$	3.37028	+	12.2472i	0.157828	+	0.573529i
$457$	−16.3987	+	28.4033i	−0.767097	+	1.32865i	0.172033	+	0.985091i	$0.444966\pi$
$457$	−16.3987	+	28.4033i	−0.767097	+	1.32865i	−0.939131	+	0.343560i	$0.888367\pi$
$458$	−8.85564	−	15.3384i	−0.413797	−	0.716718i
$459$	1.09633	−	4.44961i	0.0511724	−	0.207690i
$460$	−22.4252	−	12.9472i	−1.04558	−	0.603666i
$461$	−16.5678			−0.771637			−0.385819	−	0.922575i	$-0.626081\pi$
$461$	−16.5678			−0.771637			−0.385819	+	0.922575i	$0.626081\pi$
$462$		0			0
$463$	−36.5866			−1.70032			−0.850162	−	0.526522i	$-0.823496\pi$
$463$	−36.5866			−1.70032			−0.850162	+	0.526522i	$0.823496\pi$
$464$	6.48933	+	3.74662i	0.301260	+	0.173932i
$465$	10.8579	+	10.7125i	0.503522	+	0.496779i
$466$	−20.9774	−	36.3339i	−0.971758	−	1.68313i
$467$	−20.5550	+	35.6023i	−0.951171	+	1.64748i	−0.208275	+	0.978070i	$0.566785\pi$
$467$	−20.5550	+	35.6023i	−0.951171	+	1.64748i	−0.742896	+	0.669406i	$0.766549\pi$
$468$	16.8869	+	28.3591i	0.780598	+	1.31090i
$469$		0			0
$470$		−	6.12952i		−	0.282733i
$471$	5.19680	−	19.9312i	0.239456	−	0.918380i
$472$	−11.8586	+	6.84658i	−0.545837	+	0.315139i
$473$	−0.285733	+	0.164968i	−0.0131380	+	0.00758524i
$474$	−3.19529	+	12.2548i	−0.146765	+	0.562884i
$475$			2.19578i			0.100749i
$476$		0			0
$477$	−11.4634	−	19.2510i	−0.524872	−	0.881444i
$478$	34.8250	−	60.3186i	1.59286	−	2.75891i
$479$	8.25944	+	14.3058i	0.377383	+	0.653647i	0.990681	−	0.136205i	$-0.0434906\pi$
$479$	8.25944	+	14.3058i	0.377383	+	0.653647i	−0.613297	+	0.789852i	$0.710157\pi$
$480$	−5.59470	−	5.51978i	−0.255362	−	0.251942i
$481$	−1.13088	−	0.652916i	−0.0515639	−	0.0297704i
$482$	12.2127			0.556274
$483$		0			0
$484$	−10.9519			−0.497813
$485$	5.51850	+	3.18611i	0.250582	+	0.144674i
$486$	34.7597	−	10.5814i	1.57673	−	0.479984i
$487$	1.01601	+	1.75977i	0.0460396	+	0.0797430i	0.888127	−	0.459598i	$-0.152007\pi$
$487$	1.01601	+	1.75977i	0.0460396	+	0.0797430i	−0.842087	+	0.539341i	$0.818673\pi$
$488$	−20.6337	+	35.7386i	−0.934044	+	1.61781i
$489$	3.91688	+	14.2335i	0.177127	+	0.643661i
$490$		0			0
$491$		−	5.97889i		−	0.269824i	−0.990858	−	0.134912i	$-0.956925\pi$
$491$		−	5.97889i		−	0.269824i	0.990858	−	0.134912i	$-0.0430751\pi$
$492$	49.1992	+	12.8281i	2.21807	+	0.578334i
$493$	6.22687	−	3.59509i	0.280444	−	0.161915i
$494$	−14.2051	+	8.20134i	−0.639120	+	0.368996i
$495$	8.38301	−	0.113026i	0.376788	−	0.00508016i
$496$			8.09393i			0.363428i
$497$		0			0
$498$	−2.59587	+	0.714349i	−0.116323	+	0.0320108i
$499$	−4.24155	+	7.34658i	−0.189878	+	0.328878i	−0.945209	−	0.326465i	$-0.894143\pi$
$499$	−4.24155	+	7.34658i	−0.189878	+	0.328878i	0.755331	+	0.655343i	$0.227476\pi$
$500$	1.71646	+	2.97300i	0.0767625	+	0.132957i
$501$	−4.34183	+	4.40077i	−0.193979	+	0.196612i
$502$	−30.4332	−	17.5706i	−1.35830	−	0.784216i
$503$	−17.0296			−0.759312			−0.379656	−	0.925128i	$-0.623958\pi$
$503$	−17.0296			−0.759312			−0.379656	+	0.925128i	$0.623958\pi$
$504$		0			0
$505$	10.6253			0.472821
$506$	−42.5508	−	24.5667i	−1.89161	−	1.09212i
$507$	3.31955	−	3.36461i	0.147426	−	0.149427i
$508$	12.0077	+	20.7979i	0.532755	+	0.922759i
$509$	−6.43409	+	11.1442i	−0.285186	+	0.493956i	−0.972654	−	0.232258i	$-0.925389\pi$
$509$	−6.43409	+	11.1442i	−0.285186	+	0.493956i	0.687468	+	0.726214i	$0.258722\pi$
$510$	3.43292	−	0.944697i	0.152012	−	0.0418319i
$511$		0			0
$512$		−	10.3101i		−	0.455646i
$513$	3.17528	+	10.9589i	0.140192	+	0.483846i
$514$	32.1148	−	18.5415i	1.41652	−	0.817831i
$515$	−0.868777	+	0.501589i	−0.0382829	+	0.0221026i
$516$	−0.679288	−	0.177116i	−0.0299040	−	0.00779708i
$517$		−	7.34899i		−	0.323208i
$518$		0			0
$519$	−3.92565	−	14.2654i	−0.172317	−	0.626181i
$520$	−5.35203	+	9.26999i	−0.234702	+	0.406516i
$521$	8.32724	+	14.4232i	0.364823	+	0.631892i	0.988748	−	0.149592i	$-0.0477961\pi$
$521$	8.32724	+	14.4232i	0.364823	+	0.631892i	−0.623925	+	0.781485i	$0.714463\pi$
$522$	49.7506	+	27.8361i	2.17752	+	1.21835i
$523$	−31.4934	−	18.1827i	−1.37711	−	0.795075i	−0.385300	−	0.922791i	$-0.625902\pi$
$523$	−31.4934	−	18.1827i	−1.37711	−	0.795075i	−0.991811	+	0.127716i	$0.959235\pi$
$524$	−33.9635			−1.48370
$525$		0			0
$526$	−19.3549			−0.843912
$527$	6.72605	+	3.88329i	0.292991	+	0.169159i
$528$	3.16694	+	3.12453i	0.137823	+	0.135978i
$529$	16.9482	+	29.3551i	0.736876	+	1.27631i
$530$	8.70407	−	15.0759i	0.378080	−	0.654855i
$531$	−10.5678	+	6.29276i	−0.458602	+	0.273083i
$532$		0			0
$533$			27.4047i			1.18703i
$534$	−0.890797	+	3.41645i	−0.0385485	+	0.147844i
$535$	11.0651	−	6.38846i	0.478388	−	0.276197i
$536$	4.64026	−	2.67906i	0.200429	−	0.115718i
$537$	0.537300	−	2.06070i	0.0231862	−	0.0889256i
$538$			40.5268i			1.74724i
$539$		0			0
$540$	12.8658	+	12.3557i	0.553658	+	0.531706i
$541$	−1.89575	+	3.28353i	−0.0815046	+	0.141170i	−0.903896	−	0.427751i	$-0.859306\pi$
$541$	−1.89575	+	3.28353i	−0.0815046	+	0.141170i	0.822392	+	0.568922i	$0.192639\pi$
$542$	−11.8775	−	20.5725i	−0.510184	−	0.883665i
$543$	18.9872	+	18.7329i	0.814818	+	0.803906i
$544$	−3.46571	−	2.00093i	−0.148591	−	0.0857890i
$545$	0.0182474			0.000781633
$546$		0			0
$547$	−10.9382			−0.467684			−0.233842	−	0.972275i	$-0.575130\pi$
$547$	−10.9382			−0.467684			−0.233842	+	0.972275i	$0.575130\pi$
$548$	−37.4568	−	21.6257i	−1.60008	−	0.923805i
$549$	−18.0991	+	32.3480i	−0.772452	+	1.38058i
$550$	3.25691	+	5.64113i	0.138875	+	0.240538i
$551$	−8.95077	+	15.5032i	−0.381316	+	0.660458i
$552$	−11.5776	−	42.0718i	−0.492776	−	1.79069i
$553$		0			0
$554$			22.2839i			0.946752i
$555$	−0.682899	−	0.178057i	−0.0289874	−	0.00755810i
$556$	−2.93766	+	1.69606i	−0.124584	+	0.0719288i
$557$	8.42853	−	4.86622i	0.357128	−	0.206188i	−0.310692	−	0.950511i	$-0.600561\pi$
$557$	8.42853	−	4.86622i	0.357128	−	0.206188i	0.667820	+	0.744322i	$0.267227\pi$
$558$	0.830175	+	61.5730i	0.0351441	+	2.60659i
$559$		−	0.378374i		−	0.0160035i
$560$		0			0
$561$	4.11591	−	1.13265i	0.173774	−	0.0478203i
$562$	−13.8965	+	24.0694i	−0.586187	+	1.01531i
$563$	−0.235135	−	0.407265i	−0.00990975	−	0.0171642i	0.861028	−	0.508558i	$-0.169821\pi$
$563$	−0.235135	−	0.407265i	−0.00990975	−	0.0171642i	−0.870938	+	0.491393i	$0.836488\pi$
$564$	10.9818	−	11.1308i	0.462415	−	0.468692i
$565$	−6.26159	−	3.61513i	−0.263427	−	0.152090i
$566$	46.5459			1.95647
$567$		0			0
$568$	20.9037			0.877100
$569$	−5.38387	−	3.10838i	−0.225703	−	0.130310i	0.382885	−	0.923796i	$-0.374931\pi$
$569$	−5.38387	−	3.10838i	−0.225703	−	0.130310i	−0.608588	+	0.793486i	$0.708264\pi$
$570$	−6.22592	+	6.31043i	−0.260775	+	0.264315i
$571$	−5.31121	−	9.19928i	−0.222267	−	0.384978i	0.733229	−	0.679982i	$-0.238012\pi$
$571$	−5.31121	−	9.19928i	−0.222267	−	0.384978i	−0.955496	+	0.295004i	$0.904679\pi$
$572$	−15.3731	+	26.6270i	−0.642782	+	1.11333i
$573$	−24.2572	+	6.67528i	−1.01336	+	0.278864i
$574$		0			0
$575$		−	7.54296i		−	0.314563i
$576$	−0.502107	−	37.2406i	−0.0209211	−	1.55169i
$577$	2.56914	−	1.48330i	0.106955	−	0.0617504i	−0.445568	−	0.895248i	$-0.646998\pi$
$577$	2.56914	−	1.48330i	0.106955	−	0.0617504i	0.552523	+	0.833497i	$0.313665\pi$
$578$	−32.7459	+	18.9058i	−1.36205	+	0.786380i
$579$	0.675677	+	0.176174i	0.0280802	+	0.00732155i
$580$			27.9876i			1.16212i
$581$		0			0
$582$	6.82566	+	24.8037i	0.282933	+	1.02815i
$583$	10.4358	−	18.0753i	0.432205	−	0.748601i
$584$	0.370280	+	0.641344i	0.0153223	+	0.0265390i
$585$	−4.69460	+	8.39053i	−0.194098	+	0.346906i
$586$	6.07641	+	3.50821i	0.251014	+	0.144923i
$587$	−18.8819			−0.779341			−0.389670	−	0.920954i	$-0.627411\pi$
$587$	−18.8819			−0.779341			−0.389670	+	0.920954i	$0.627411\pi$
$588$		0			0
$589$	−19.3366			−0.796751
$590$	−8.27583	−	4.77805i	−0.340711	−	0.196709i
$591$	−14.3907	−	14.1980i	−0.591955	−	0.584027i
$592$	−0.187247	−	0.324322i	−0.00769582	−	0.0133296i
$593$	−15.1472	+	26.2357i	−0.622020	+	1.07737i	0.367088	+	0.930186i	$0.380355\pi$
$593$	−15.1472	+	26.2357i	−0.622020	+	1.07737i	−0.989109	+	0.147185i	$0.952979\pi$
$594$	24.4123	+	23.4444i	1.00165	+	0.961936i
$595$		0			0
$596$			60.8887i			2.49410i
$597$	8.11836	−	31.1362i	0.332262	−	1.27432i
$598$	48.7976	−	28.1733i	1.99548	−	1.15209i
$599$	6.29024	−	3.63167i	0.257012	−	0.148386i	−0.365959	−	0.930631i	$-0.619259\pi$
$599$	6.29024	−	3.63167i	0.257012	−	0.148386i	0.622971	+	0.782245i	$0.285925\pi$
$600$	−1.45956	+	5.59780i	−0.0595861	+	0.228529i
$601$			45.3302i			1.84906i	0.381110	+	0.924530i	$0.375542\pi$
$601$			45.3302i			1.84906i	−0.381110	+	0.924530i	$0.624458\pi$
$602$		0			0
$603$	4.13515	−	2.46235i	0.168396	−	0.100275i
$604$	−38.6216	+	66.8946i	−1.57149	+	2.72190i
$605$	−1.59513	−	2.76284i	−0.0648511	−	0.112325i
$606$	30.5360	+	30.1271i	1.24044	+	1.22383i
$607$	−22.5370	−	13.0117i	−0.914748	−	0.528130i	−0.0327925	−	0.999462i	$-0.510440\pi$
$607$	−22.5370	−	13.0117i	−0.914748	−	0.528130i	−0.881956	+	0.471332i	$0.843773\pi$
$608$	9.96351			0.404073
$609$		0			0
$610$	−28.7995			−1.16606
$611$	7.29877	+	4.21394i	0.295276	+	0.170478i
$612$	7.92651	+	4.43498i	0.320410	+	0.179273i
$613$	−12.8525	−	22.2611i	−0.519106	−	0.899118i	−0.999753	−	0.0222040i	$-0.992932\pi$
$613$	−12.8525	−	22.2611i	−0.519106	−	0.899118i	0.480648	−	0.876914i	$-0.340402\pi$
$614$	23.7507	−	41.1375i	0.958502	−	1.66017i
$615$	3.92965	+	14.2799i	0.158459	+	0.575822i
$616$		0			0
$617$		−	8.88258i		−	0.357599i	−0.983886	−	0.178800i	$-0.942779\pi$
$617$		−	8.88258i		−	0.357599i	0.983886	−	0.178800i	$-0.0572213\pi$
$618$	−3.91898	−	1.02182i	−0.157644	−	0.0411037i
$619$	26.4112	−	15.2485i	1.06156	−	0.612890i	0.135694	−	0.990751i	$-0.456673\pi$
$619$	26.4112	−	15.2485i	1.06156	−	0.612890i	0.925863	+	0.377861i	$0.123340\pi$
$620$	−26.1810	+	15.1156i	−1.05145	+	0.607057i
$621$	−10.9077	−	37.6460i	−0.437713	−	1.51068i
$622$			63.5669i			2.54880i
$623$		0			0
$624$	−4.91911	+	1.35368i	−0.196922	+	0.0541904i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	0.735048	+	1.27314i	0.0293784	+	0.0508849i
$627$	−7.46458	+	7.56590i	−0.298107	+	0.302153i
$628$	35.3549	+	20.4121i	1.41081	+	0.814533i
$629$	−0.359349			−0.0143282
$630$		0			0
$631$	44.3335			1.76489			0.882445	−	0.470416i	$-0.155896\pi$
$631$	44.3335			1.76489			0.882445	+	0.470416i	$0.155896\pi$
$632$	−9.07367	−	5.23868i	−0.360931	−	0.208384i
$633$	8.49303	−	8.60831i	0.337568	−	0.342150i
$634$	−29.6372	−	51.3332i	−1.17705	−	2.03870i
$635$	−3.49781	+	6.05838i	−0.138806	+	0.240419i
$636$	42.8163	−	11.7825i	1.69778	−	0.467206i
$637$		0			0
$638$			53.1052i			2.10245i
$639$	18.7744	−	0.253131i	0.742703	−	0.0100137i
$640$	17.2008	−	9.93088i	0.679921	−	0.392553i
$641$	6.03197	−	3.48256i	0.238249	−	0.137553i	−0.376123	−	0.926570i	$-0.622743\pi$
$641$	6.03197	−	3.48256i	0.238249	−	0.137553i	0.614371	+	0.789017i	$0.289410\pi$
$642$	49.9139	+	13.0144i	1.96994	+	0.513637i
$643$		−	25.8907i		−	1.02103i	−0.859869	−	0.510514i	$-0.829455\pi$
$643$		−	25.8907i		−	1.02103i	0.859869	−	0.510514i	$-0.170545\pi$
$644$		0			0
$645$	−0.0542562	−	0.197161i	−0.00213634	−	0.00776321i
$646$	−2.25691	+	3.90908i	−0.0887968	+	0.153801i
$647$	−5.01859	−	8.69245i	−0.197301	−	0.341735i	0.750351	−	0.661039i	$-0.229884\pi$
$647$	−5.01859	−	8.69245i	−0.197301	−	0.341735i	−0.947652	+	0.319304i	$0.896551\pi$
$648$	0.810424	+	30.0486i	0.0318365	+	1.18042i
$649$	−9.92232	−	5.72866i	−0.389485	−	0.224869i
$650$	−7.47010			−0.293001
$651$		0			0
$652$	−29.2594			−1.14589
$653$	34.2946	+	19.8000i	1.34205	+	0.774833i	0.987108	−	0.160055i	$-0.0511671\pi$
$653$	34.2946	+	19.8000i	1.34205	+	0.774833i	0.354942	+	0.934888i	$0.384500\pi$
$654$	0.0524410	+	0.0517388i	0.00205061	+	0.00202315i
$655$	−4.94673	−	8.56799i	−0.193285	−	0.334779i
$656$	−3.92965	+	6.80635i	−0.153427	+	0.265744i
$657$	0.340329	+	0.571531i	0.0132775	+	0.0222975i
$658$		0			0
$659$		−	17.9364i		−	0.698705i	−0.936991	−	0.349352i	$-0.886402\pi$
$659$		−	17.9364i		−	0.698705i	0.936991	−	0.349352i	$-0.113598\pi$
$660$	−4.19241	+	16.0791i	−0.163189	+	0.625877i
$661$	3.31012	−	1.91110i	0.128749	−	0.0743332i	−0.434242	−	0.900796i	$-0.642984\pi$
$661$	3.31012	−	1.91110i	0.128749	−	0.0743332i	0.562991	+	0.826463i	$0.309650\pi$
$662$	23.2003	−	13.3947i	0.901705	−	0.520599i
$663$	−1.23517	+	4.73724i	−0.0479702	+	0.183979i
$664$		−	2.22739i		−	0.0864393i
$665$		0			0
$666$	−1.45771	−	2.44801i	−0.0564852	−	0.0948585i
$667$	30.7478	−	53.2567i	1.19056	−	2.06211i
$668$	−6.12645	−	10.6113i	−0.237039	−	0.410564i
$669$	−1.78280	−	1.75893i	−0.0689271	−	0.0680040i
$670$	3.23832	+	1.86964i	0.125107	+	0.0722307i
$671$	−34.5292			−1.33299
$672$		0			0
$673$	1.08304			0.0417483			0.0208741	−	0.999782i	$-0.493355\pi$
$673$	1.08304			0.0417483			0.0208741	+	0.999782i	$0.493355\pi$
$674$	32.7094	+	18.8848i	1.25992	+	0.727415i
$675$	−1.24309	+	5.04527i	−0.0478467	+	0.194192i
$676$	4.68398	+	8.11288i	0.180153	+	0.312034i
$677$	15.5014	−	26.8492i	0.595766	−	1.03190i	−0.397672	−	0.917528i	$-0.630182\pi$
$677$	15.5014	−	26.8492i	0.595766	−	1.03190i	0.993438	−	0.114370i	$-0.0364849\pi$
$678$	−7.74478	−	28.1436i	−0.297436	−	1.08085i
$679$		0			0
$680$			2.94562i			0.112960i
$681$	1.78852	+	0.466333i	0.0685362	+	0.0178699i
$682$	−49.6772	+	28.6812i	−1.90224	+	1.09826i
$683$	−16.5419	+	9.55050i	−0.632960	+	0.365440i	−0.781898	−	0.623407i	$-0.785748\pi$
$683$	−16.5419	+	9.55050i	−0.632960	+	0.365440i	0.148937	+	0.988847i	$0.452415\pi$
$684$	−22.6118	+	0.304869i	−0.864583	+	0.0116570i
$685$		−	12.5990i		−	0.481383i
$686$		0			0
$687$	12.6894	−	3.49198i	0.484133	−	0.133227i
$688$	0.0542562	−	0.0939745i	0.00206850	−	0.00358275i
$689$	11.9678	+	20.7289i	0.455937	+	0.789707i
$690$	21.3874	−	21.6777i	0.814203	−	0.825254i
$691$	14.5775	+	8.41632i	0.554554	+	0.320172i	0.750957	−	0.660351i	$-0.229593\pi$
$691$	14.5775	+	8.41632i	0.554554	+	0.320172i	−0.196403	+	0.980523i	$0.562926\pi$
$692$	29.3250			1.11477
$693$		0			0
$694$	41.9145			1.59105
$695$	−0.855731	−	0.494056i	−0.0324597	−	0.0187406i
$696$	−33.1237	+	33.5733i	−1.25555	+	1.27259i
$697$	3.77072	+	6.53107i	0.142826	+	0.247382i
$698$	7.17232	−	12.4228i	0.271476	−	0.470211i
$699$	30.0589	−	8.27184i	1.13693	−	0.312870i
$700$		0			0
$701$		−	21.8878i		−	0.826691i	−0.910574	−	0.413345i	$-0.864360\pi$
$701$		−	21.8878i		−	0.826691i	0.910574	−	0.413345i	$-0.135640\pi$
$702$	−37.2823	+	10.8024i	−1.40713	+	0.407709i
$703$	0.774814	−	0.447339i	0.0292227	−	0.0168717i
$704$	30.0458	−	17.3470i	1.13240	−	0.653789i
$705$	4.40745	+	1.14919i	0.165994	+	0.0432809i
$706$		−	68.6821i		−	2.58489i
$707$		0			0
$708$	−6.46794	−	23.5038i	−0.243080	−	0.883326i
$709$	5.41030	−	9.37091i	0.203188	−	0.351932i	−0.746366	−	0.665536i	$-0.768203\pi$
$709$	5.41030	−	9.37091i	0.203188	−	0.351932i	0.949554	+	0.313604i	$0.101536\pi$
$710$	7.29408	+	12.6337i	0.273742	+	0.474135i
$711$	−8.21283	−	4.59518i	−0.308005	−	0.172333i
$712$	−2.52959	−	1.46046i	−0.0948005	−	0.0547331i
$713$	66.4253			2.48765
$714$		0			0
$715$	−8.95628			−0.334946
$716$	3.65536	+	2.11042i	0.136607	+	0.0788703i
$717$	36.8432	+	36.3498i	1.37593	+	1.35751i
$718$	41.0753	+	71.1445i	1.53292	+	2.65509i
$719$	−11.1296	+	19.2770i	−0.415064	+	0.718912i	−0.995435	−	0.0954404i	$-0.969574\pi$
$719$	−11.1296	+	19.2770i	−0.415064	+	0.718912i	0.580371	+	0.814352i	$0.302907\pi$
$720$	−2.36912	+	1.41073i	−0.0882917	+	0.0525749i
$721$		0			0
$722$			33.0483i			1.22993i
$723$	−2.28969	+	8.78160i	−0.0851545	+	0.326591i
$724$	−45.7827	+	26.4327i	−1.70150	+	0.982362i
$725$	−7.06045	+	4.07635i	−0.262218	+	0.151392i
$726$	3.24955	−	12.4629i	0.120602	−	0.462543i
$727$		−	43.7899i		−	1.62408i	−0.583604	−	0.812038i	$-0.698358\pi$
$727$		−	43.7899i		−	1.62408i	0.583604	−	0.812038i	$-0.301642\pi$
$728$		0			0
$729$	1.09174	+	26.9779i	0.0404349	+	0.999182i
$730$	−0.258409	+	0.447578i	−0.00956415	+	0.0165656i
$731$	−0.0520618	−	0.0901738i	−0.00192558	−	0.00333520i
$732$	−52.2981	−	51.5977i	−1.93299	−	1.90711i
$733$	−22.6647	−	13.0854i	−0.837138	−	0.483322i	0.0191524	−	0.999817i	$-0.493903\pi$
$733$	−22.6647	−	13.0854i	−0.837138	−	0.483322i	−0.856290	+	0.516495i	$0.827237\pi$
$734$	81.1776			2.99632
$735$		0			0
$736$	−34.2267			−1.26161
$737$	3.88259	+	2.24161i	0.143017	+	0.0825709i
$738$	−29.1959	+	52.1811i	−1.07472	+	1.92081i
$739$	−20.1777	−	34.9489i	−0.742250	−	1.28561i	−0.951469	−	0.307746i	$-0.900425\pi$
$739$	−20.1777	−	34.9489i	−0.742250	−	1.28561i	0.209219	−	0.977869i	$-0.432908\pi$
$740$	0.699378	−	1.21136i	0.0257096	−	0.0445304i
$741$	−3.23397	−	11.7519i	−0.118803	−	0.431716i
$742$		0			0
$743$		−	8.82565i		−	0.323782i	−0.986809	−	0.161891i	$-0.948241\pi$
$743$		−	8.82565i		−	0.323782i	0.986809	−	0.161891i	$-0.0517593\pi$
$744$	−49.2957	−	12.8532i	−1.80727	−	0.471222i
$745$	−15.3604	+	8.86834i	−0.562762	+	0.324911i
$746$	40.9251	−	23.6281i	1.49838	−	0.865087i
$747$	−0.0269722	−	2.00050i	−0.000986863	−	0.0731943i
$748$			8.46097i			0.309364i
$749$		0			0
$750$	−3.89248	+	1.07116i	−0.142133	+	0.0391133i
$751$	−18.9165	+	32.7644i	−0.690274	+	1.19559i	0.281475	+	0.959569i	$0.409176\pi$
$751$	−18.9165	+	32.7644i	−0.690274	+	1.19559i	−0.971748	+	0.236020i	$0.924157\pi$
$752$	1.20850	+	2.09319i	0.0440695	+	0.0763307i
$753$	18.3400	−	18.5889i	0.668346	−	0.677418i
$754$	−52.7422	−	30.4507i	−1.92076	−	1.10895i
$755$	−22.5007			−0.818885
$756$		0			0
$757$	−34.7636			−1.26351			−0.631753	−	0.775170i	$-0.717664\pi$
$757$	−34.7636			−1.26351			−0.631753	+	0.775170i	$0.717664\pi$
$758$	18.3127	+	10.5728i	0.665146	+	0.384022i
$759$	25.6424	−	25.9905i	0.930760	−	0.943394i
$760$	−3.66689	−	6.35124i	−0.133012	−	0.230384i
$761$	0.915074	−	1.58495i	0.0331714	−	0.0574545i	−0.848963	−	0.528452i	$-0.822773\pi$
$761$	0.915074	−	1.58495i	0.0331714	−	0.0574545i	0.882135	+	0.470998i	$0.156106\pi$
$762$	−27.2303	+	7.49342i	−0.986448	+	0.271458i
$763$		0			0
$764$		−	49.8649i		−	1.80405i
$765$	0.0356697	+	2.64557i	0.00128964	+	0.0956509i
$766$	−56.0686	+	32.3712i	−2.02584	+	1.16962i
$767$	11.3790	−	6.56967i	0.410872	−	0.237217i
$768$	35.9769	+	9.38051i	1.29820	+	0.338490i
$769$		−	23.5601i		−	0.849598i	−0.905288	−	0.424799i	$-0.860345\pi$
$769$		−	23.5601i		−	0.849598i	0.905288	−	0.424799i	$-0.139655\pi$
$770$		0			0
$771$	7.31132	+	26.5685i	0.263311	+	0.956842i
$772$	−0.691982	+	1.19855i	−0.0249050	+	0.0431367i
$773$	24.0437	+	41.6448i	0.864790	+	1.49786i	0.867255	+	0.497864i	$0.165882\pi$
$773$	24.0437	+	41.6448i	0.864790	+	1.49786i	−0.00246461	+	0.999997i	$0.500785\pi$
$774$	0.403105	−	0.720458i	0.0144893	−	0.0258963i
$775$	−7.62645	−	4.40313i	−0.273950	−	0.158165i
$776$	−21.2828			−0.764010
$777$		0			0
$778$	36.3198			1.30213
$779$	−16.2606	−	9.38804i	−0.582595	−	0.336361i
$780$	−13.5652	−	13.3836i	−0.485713	−	0.479208i
$781$	8.74525	+	15.1472i	0.312930	+	0.542010i
$782$	7.75294	−	13.4285i	0.277245	−	0.480202i
$783$	−29.3431	+	30.5546i	−1.04864	+	1.09193i
$784$		0			0
$785$			11.8920i			0.424443i
$786$	10.0774	−	38.6495i	0.359447	−	1.37858i
$787$	26.1234	−	15.0823i	0.931197	−	0.537627i	0.0440072	−	0.999031i	$-0.485988\pi$
$787$	26.1234	−	15.0823i	0.931197	−	0.537627i	0.887190	+	0.461404i	$0.152654\pi$
$788$	34.6995	−	20.0338i	1.23612	−	0.713673i
$789$	3.62873	−	13.9172i	0.129186	−	0.495465i
$790$		−	7.31189i		−	0.260145i
$791$		0			0
$792$	−24.0589	+	14.3263i	−0.854897	+	0.509064i
$793$	19.7992	−	34.2932i	0.703090	−	1.21779i
$794$	−22.0156	−	38.1321i	−0.781303	−	1.35326i
$795$	9.20850	+	9.08518i	0.326592	+	0.322218i
$796$	55.2309	+	31.8876i	1.95761	+	1.13022i
$797$	−3.60475			−0.127687			−0.0638435	−	0.997960i	$-0.520336\pi$
$797$	−3.60475			−0.127687			−0.0638435	+	0.997960i	$0.520336\pi$
$798$		0			0
$799$	2.31925			0.0820491
$800$	3.92965	+	2.26878i	0.138934	+	0.0802137i
$801$	−2.28961	−	1.28106i	−0.0808992	−	0.0452641i
$802$	−24.2401	−	41.9851i	−0.855948	−	1.48255i
$803$	−0.309820	+	0.536624i	−0.0109333	+	0.0189371i
$804$	2.53089	+	9.19699i	0.0892578	+	0.324353i
$805$		0			0
$806$		−	65.7836i		−	2.31713i
$807$	−29.1410	−	7.59814i	−1.02581	−	0.267467i
$808$	−30.7335	+	17.7440i	−1.08120	+	0.624232i
$809$	−18.7612	+	10.8318i	−0.659607	+	0.380824i	−0.792127	−	0.610356i	$-0.791026\pi$
$809$	−18.7612	+	10.8318i	−0.659607	+	0.380824i	0.132520	+	0.991180i	$0.457693\pi$
$810$	−17.8779	+	10.9749i	−0.628165	+	0.385618i
$811$		−	27.6526i		−	0.971015i	−0.874232	−	0.485508i	$-0.838635\pi$
$811$		−	27.6526i		−	0.971015i	0.874232	−	0.485508i	$-0.161365\pi$
$812$		0			0
$813$	17.0196	−	4.68358i	0.596904	−	0.164260i
$814$	1.32704	−	2.29850i	0.0465126	−	0.0805623i
$815$	−4.26159	−	7.38130i	−0.149277	−	0.258556i
$816$	−0.986061	+	0.999446i	−0.0345190	+	0.0349876i
$817$	0.224508	+	0.129620i	0.00785453	+	0.00453481i
$818$	67.1957			2.34944
$819$		0			0
$820$	−29.3549			−1.02512
$821$	12.2722	+	7.08534i	0.428302	+	0.247280i	0.698623	−	0.715490i	$-0.253797\pi$
$821$	12.2722	+	7.08534i	0.428302	+	0.247280i	−0.270321	+	0.962770i	$0.587130\pi$
$822$	35.7233	−	36.2082i	1.24599	−	1.26291i
$823$	−11.6538	−	20.1850i	−0.406227	−	0.703605i	0.588237	−	0.808689i	$-0.299822\pi$
$823$	−11.6538	−	20.1850i	−0.406227	−	0.703605i	−0.994463	+	0.105084i	$0.966489\pi$
$824$	1.67528	−	2.90167i	0.0583611	−	0.101084i
$825$	−4.66689	+	1.28427i	−0.162480	+	0.0447125i
$826$		0			0
$827$			32.0877i			1.11580i	0.829908	+	0.557900i	$0.188393\pi$
$827$			32.0877i			1.11580i	−0.829908	+	0.557900i	$0.811607\pi$
$828$	77.6762	−	1.04729i	2.69943	−	0.0363959i
$829$	−25.9947	+	15.0080i	−0.902833	+	0.521251i	−0.878118	−	0.478444i	$-0.841201\pi$
$829$	−25.9947	+	15.0080i	−0.902833	+	0.521251i	−0.0247149	+	0.999695i	$0.507868\pi$
$830$	1.34618	−	0.777218i	0.0467266	−	0.0269776i
$831$	−16.0233	−	4.17788i	−0.555843	−	0.144929i
$832$			39.7873i			1.37938i
$833$		0			0
$834$	−1.05843	−	3.84621i	−0.0366503	−	0.133183i
$835$	1.78462	−	3.09105i	0.0617592	−	0.106970i
$836$	−10.5327	−	18.2432i	−0.364282	−	0.630956i
$837$	−44.4299	−	10.9470i	−1.53572	−	0.378384i
$838$	−6.55031	−	3.78182i	−0.226277	−	0.130641i
$839$	−28.6277			−0.988337			−0.494168	−	0.869366i	$-0.664527\pi$
$839$	−28.6277			−0.988337			−0.494168	+	0.869366i	$0.664527\pi$
$840$		0			0
$841$	−37.4666			−1.29195
$842$	−56.3835	−	32.5530i	−1.94310	−	1.12185i
$843$	−14.7018	−	14.5049i	−0.506358	−	0.499577i
$844$	11.9839	+	20.7567i	0.412503	+	0.714476i
$845$	−1.36443	+	2.36326i	−0.0469378	+	0.0812986i
$846$	9.40813	+	15.7995i	0.323458	+	0.543200i
$847$		0			0
$848$			6.86441i			0.235725i
$849$	−8.72661	+	33.4690i	−0.299497	+	1.14865i
$850$	−1.78027	+	1.02784i	−0.0610627	+	0.0352545i
$851$	−2.66165	+	1.53670i	−0.0912401	+	0.0526775i
$852$	−9.38921	+	36.0102i	−0.321669	+	1.23369i
$853$		−	17.3563i		−	0.594269i	−0.954836	−	0.297135i	$-0.903969\pi$
$853$		−	17.3563i		−	0.594269i	0.954836	−	0.297135i	$-0.0960310\pi$
$854$		0			0
$855$	−3.37028	−	5.65988i	−0.115261	−	0.193564i
$856$	−21.3371	+	36.9569i	−0.729287	+	1.26316i
$857$	23.2842	+	40.3294i	0.795372	+	1.37763i	0.922602	+	0.385752i	$0.126058\pi$
$857$	23.2842	+	40.3294i	0.795372	+	1.37763i	−0.127230	+	0.991873i	$0.540609\pi$
$858$	−25.7394	−	25.3947i	−0.878728	−	0.866960i
$859$	−31.5359	−	18.2072i	−1.07599	−	0.621223i	−0.146178	−	0.989258i	$-0.546697\pi$
$859$	−31.5359	−	18.2072i	−1.07599	−	0.621223i	−0.929812	+	0.368035i	$0.880031\pi$
$860$	0.405299			0.0138206
$861$		0			0
$862$	89.3002			3.04158
$863$	−2.05942	−	1.18901i	−0.0701034	−	0.0404742i	0.464539	−	0.885553i	$-0.346220\pi$
$863$	−2.05942	−	1.18901i	−0.0701034	−	0.0404742i	−0.534642	+	0.845079i	$0.679554\pi$
$864$	22.8933	+	5.64063i	0.778844	+	0.191898i
$865$	4.27114	+	7.39784i	0.145223	+	0.251534i
$866$	−33.7430	+	58.4447i	−1.14664	+	1.98603i
$867$	−7.45499	−	27.0906i	−0.253185	−	0.920045i
$868$		0			0
$869$		−	8.76660i		−	0.297387i
$870$	−31.8491	−	8.30423i	−1.07978	−	0.281540i
$871$	−4.45259	+	2.57070i	−0.150870	+	0.0871049i
$872$	−0.0527802	+	0.0304727i	−0.00178736	+	0.00103193i
$873$	−19.1149	+	0.257722i	−0.646942	+	0.00872257i
$874$			38.6054i			1.30585i
$875$		0			0
$876$	−1.27114	+	0.349803i	−0.0429480	+	0.0118187i
$877$	11.0465	−	19.1332i	0.373015	−	0.646082i	−0.617012	−	0.786953i	$-0.711657\pi$
$877$	11.0465	−	19.1332i	0.373015	−	0.646082i	0.990028	+	0.140872i	$0.0449905\pi$
$878$	−17.7901	−	30.8134i	−0.600387	−	1.03990i
$879$	−3.66183	+	3.71153i	−0.123510	+	0.125187i
$880$	−2.22442	−	1.28427i	−0.0749852	−	0.0432927i
$881$	33.5633			1.13078			0.565388	−	0.824825i	$-0.308727\pi$
$881$	33.5633			1.13078			0.565388	+	0.824825i	$0.308727\pi$
$882$		0			0
$883$	−3.74124			−0.125903			−0.0629514	−	0.998017i	$-0.520051\pi$
$883$	−3.74124			−0.125903			−0.0629514	+	0.998017i	$0.520051\pi$
$884$	−8.40314	−	4.85156i	−0.282628	−	0.163176i
$885$	4.98727	−	5.05496i	0.167645	−	0.169921i
$886$	2.66151	+	4.60988i	0.0894153	+	0.154872i
$887$	13.7685	−	23.8478i	0.462302	−	0.800730i	−0.536773	−	0.843726i	$-0.680357\pi$
$887$	13.7685	−	23.8478i	0.462302	−	0.800730i	0.999075	+	0.0429963i	$0.0136904\pi$
$888$	2.27262	−	0.625396i	0.0762641	−	0.0209869i
$889$		0			0
$890$		−	2.03844i		−	0.0683286i
$891$	−21.4347	+	13.1583i	−0.718090	+	0.440821i
$892$	4.29877	−	2.48189i	0.143933	−	0.0831000i
$893$	−5.00068	+	2.88714i	−0.167341	+	0.0966146i
$894$	−69.2895	−	18.0663i	−2.31739	−	0.604229i
$895$			1.22952i			0.0410983i
$896$		0			0
$897$	11.1094	+	40.3702i	0.370931	+	1.34792i
$898$	−12.0171	+	20.8142i	−0.401015	+	0.694579i
$899$	−35.8974	−	62.1762i	−1.19725	−	2.07369i
$900$	−8.98760	−	5.02867i	−0.299587	−	0.167622i
$901$	5.70432	+	3.29339i	0.190038	+	0.109719i
$902$	−55.6995			−1.85459
$903$		0			0
$904$	24.1487			0.803174
$905$	−13.3364	−	7.69975i	−0.443316	−	0.255949i
$906$	−64.6646	−	63.7987i	−2.14834	−	2.11957i
$907$	−19.3650	−	33.5412i	−0.643005	−	1.11372i	−0.984758	−	0.173928i	$-0.944354\pi$
$907$	−19.3650	−	33.5412i	−0.643005	−	1.11372i	0.341754	−	0.939790i	$-0.388979\pi$
$908$	−1.83168	+	3.17256i	−0.0607864	+	0.105285i
$909$	−27.3880	+	16.3087i	−0.908404	+	0.540926i
$910$		0			0
$911$			23.3967i			0.775167i	0.921835	+	0.387583i	$0.126690\pi$
$911$			23.3967i			0.775167i	−0.921835	+	0.387583i	$0.873310\pi$
$912$	0.881938	−	3.38248i	0.0292039	−	0.112005i
$913$	1.61401	−	0.931847i	0.0534158	−	0.0308396i
$914$	66.2043	−	38.2231i	2.18984	−	1.26431i
$915$	5.39945	−	20.7084i	0.178500	−	0.684598i
$916$			26.0854i			0.861886i
$917$		0			0
$918$	−7.39876	+	7.70422i	−0.244195	+	0.254277i
$919$	4.32329	−	7.48816i	0.142612	−	0.247012i	−0.785867	−	0.618395i	$-0.787783\pi$
$919$	4.32329	−	7.48816i	0.142612	−	0.247012i	0.928480	+	0.371383i	$0.121116\pi$
$920$	12.5965	+	21.8179i	0.415296	+	0.719313i
$921$	25.1272	+	24.7907i	0.827969	+	0.816881i
$922$	33.4434	+	19.3086i	1.10140	+	0.635894i
$923$	−20.0583			−0.660225
$924$		0			0
$925$	0.407453			0.0133970
$926$	73.8532	+	42.6392i	2.42697	+	1.40121i
$927$	1.46949	−	2.62638i	0.0482644	−	0.0862616i
$928$	18.4967	+	32.0373i	0.607185	+	1.05168i
$929$	−6.27980	+	10.8769i	−0.206034	+	0.356861i	−0.950462	−	0.310842i	$-0.899389\pi$
$929$	−6.27980	+	10.8769i	−0.206034	+	0.356861i	0.744428	+	0.667703i	$0.232722\pi$
$930$	−9.43292	−	34.2782i	−0.309318	−	1.12403i
$931$		0			0
$932$			61.7914i			2.02405i
$933$	−45.7080	−	11.9178i	−1.49641	−	0.390171i
$934$	82.9840	−	47.9108i	2.71532	−	1.56769i
$935$	−2.13445	+	1.23233i	−0.0698041	+	0.0403014i
$936$	−0.432922	−	32.1093i	−0.0141505	−	1.04952i
$937$		−	11.3901i		−	0.372097i	−0.982541	−	0.186048i	$-0.940432\pi$
$937$		−	11.3901i		−	0.372097i	0.982541	−	0.186048i	$-0.0595681\pi$
$938$		0			0
$939$	−1.05327	+	0.289846i	−0.0343720	+	0.00945875i
$940$	−4.51381	+	7.81815i	−0.147224	+	0.255000i
$941$	21.0434	+	36.4482i	0.685994	+	1.18818i	0.973123	+	0.230285i	$0.0739658\pi$
$941$	21.0434	+	36.4482i	0.685994	+	1.18818i	−0.287129	+	0.957892i	$0.592701\pi$
$942$	−33.7186	+	34.1763i	−1.09861	+	1.11352i
$943$	55.8584	+	32.2499i	1.81900	+	1.05020i
$944$	3.76818			0.122644
$945$		0			0
$946$	0.769036			0.0250035
$947$	12.6504	+	7.30370i	0.411082	+	0.237338i	0.691255	−	0.722611i	$-0.257058\pi$
$947$	12.6504	+	7.30370i	0.411082	+	0.237338i	−0.280172	+	0.959950i	$0.590392\pi$
$948$	13.1001	−	13.2779i	0.425472	−	0.431247i
$949$	−0.355304	−	0.615405i	−0.0115337	−	0.0199769i
$950$	2.55903	−	4.43237i	0.0830259	−	0.143805i
$951$	42.4679	−	11.6866i	1.37711	−	0.378965i
$952$		0			0
$953$		−	28.8817i		−	0.935570i	−0.883842	−	0.467785i	$-0.845052\pi$
$953$		−	28.8817i		−	0.935570i	0.883842	−	0.467785i	$-0.154948\pi$
$954$	0.704066	+	52.2196i	0.0227950	+	1.69067i
$955$	12.5795	−	7.26275i	0.407062	−	0.235017i
$956$	−88.8379	+	51.2906i	−2.87322	+	1.65886i
$957$	−38.1855	−	9.95637i	−1.23436	−	0.321844i
$958$		−	38.5032i		−	1.24398i
$959$		0			0
$960$	5.70523	+	20.7322i	0.184136	+	0.669128i
$961$	23.2751	−	40.3137i	0.750811	−	1.30044i
$962$	1.52186	+	2.63594i	0.0490667	+	0.0849860i
$963$	−18.7161	+	33.4508i	−0.603118	+	1.07794i
$964$	−15.5772	−	8.99352i	−0.501709	−	0.289662i
$965$	−0.403145			−0.0129777
$966$		0			0
$967$	0.409782			0.0131777			0.00658885	−	0.999978i	$-0.497903\pi$
$967$	0.409782			0.0131777			0.00658885	+	0.999978i	$0.497903\pi$
$968$	9.22774	+	5.32764i	0.296591	+	0.171237i
$969$	−2.38770	−	2.35573i	−0.0767041	−	0.0756768i
$970$	−7.42638	−	12.8629i	−0.238447	−	0.413002i
$971$	2.64865	−	4.58759i	0.0849991	−	0.147223i	−0.820392	−	0.571802i	$-0.806245\pi$
$971$	2.64865	−	4.58759i	0.0849991	−	0.147223i	0.905391	+	0.424579i	$0.139578\pi$
$972$	−52.1279	−	12.1007i	−1.67200	−	0.388129i
$973$		0			0
$974$		−	4.73634i		−	0.151762i
$975$	1.40052	−	5.37140i	0.0448527	−	0.172023i
$976$	9.83482	−	5.67814i	0.314805	−	0.181753i
$977$	24.1247	−	13.9284i	0.771818	−	0.445610i	−0.0617045	−	0.998094i	$-0.519654\pi$
$977$	24.1247	−	13.9284i	0.771818	−	0.445610i	0.833523	+	0.552485i	$0.186320\pi$
$978$	8.68160	−	33.2964i	0.277607	−	1.06470i
$979$		−	2.44399i		−	0.0781102i
$980$		0			0
$981$	−0.0470348	+	0.0280077i	−0.00150171	+	0.000894219i
$982$	−6.96799	+	12.0689i	−0.222357	+	0.385134i
$983$	0.330614	+	0.572640i	0.0105449	+	0.0182644i	0.871250	−	0.490840i	$-0.163310\pi$
$983$	0.330614	+	0.572640i	0.0105449	+	0.0182644i	−0.860705	+	0.509104i	$0.829977\pi$
$984$	−35.2135	−	34.7419i	−1.12257	−	1.10753i
$985$	10.1079	+	5.83578i	0.322063	+	0.185943i
$986$	−16.7593			−0.533725
$987$		0			0
$988$	24.1581			0.768571
$989$	−0.771231	−	0.445270i	−0.0245237	−	0.0141588i
$990$	−17.0536	−	9.54168i	−0.541998	−	0.303254i
$991$	25.3374	+	43.8856i	0.804868	+	1.39407i	0.916380	+	0.400309i	$0.131097\pi$
$991$	25.3374	+	43.8856i	0.804868	+	1.39407i	−0.111513	+	0.993763i	$0.535570\pi$
$992$	−19.9795	+	34.6055i	−0.634350	+	1.09873i
$993$	5.28182	+	19.1935i	0.167614	+	0.609089i
$994$		0			0
$995$			18.5775i			0.588946i
$996$	3.83706	+	1.00046i	0.121582	+	0.0317009i
$997$	−5.21879	+	3.01307i	−0.165281	+	0.0954249i	−0.580359	−	0.814361i	$-0.697088\pi$
$997$	−5.21879	+	3.01307i	−0.165281	+	0.0954249i	0.415078	+	0.909786i	$0.363754\pi$
$998$	17.1239	−	9.88647i	0.542047	−	0.312951i
$999$	2.03355	−	0.589211i	0.0643387	−	0.0186418i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.s.k.656.1		8
3.2	odd	2		735.2.s.l.656.4		8
7.2	even	3		735.2.b.c.146.8		8
7.3	odd	6		735.2.s.l.521.4		8
7.4	even	3		105.2.s.d.101.4	yes	8
7.5	odd	6		735.2.b.d.146.8		8
7.6	odd	2		105.2.s.c.26.1	✓	8
21.2	odd	6		735.2.b.d.146.1		8
21.5	even	6		735.2.b.c.146.1		8
21.11	odd	6		105.2.s.c.101.1	yes	8
21.17	even	6	inner	735.2.s.k.521.1		8
21.20	even	2		105.2.s.d.26.4	yes	8
35.4	even	6		525.2.t.f.101.1		8
35.13	even	4		525.2.q.f.299.1		16
35.18	odd	12		525.2.q.e.374.1		16
35.27	even	4		525.2.q.f.299.8		16
35.32	odd	12		525.2.q.e.374.8		16
35.34	odd	2		525.2.t.g.26.4		8
105.32	even	12		525.2.q.f.374.1		16
105.53	even	12		525.2.q.f.374.8		16
105.62	odd	4		525.2.q.e.299.1		16
105.74	odd	6		525.2.t.g.101.4		8
105.83	odd	4		525.2.q.e.299.8		16
105.104	even	2		525.2.t.f.26.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.1	✓	8	7.6	odd	2
105.2.s.c.101.1	yes	8	21.11	odd	6
105.2.s.d.26.4	yes	8	21.20	even	2
105.2.s.d.101.4	yes	8	7.4	even	3
525.2.q.e.299.1		16	105.62	odd	4
525.2.q.e.299.8		16	105.83	odd	4
525.2.q.e.374.1		16	35.18	odd	12
525.2.q.e.374.8		16	35.32	odd	12
525.2.q.f.299.1		16	35.13	even	4
525.2.q.f.299.8		16	35.27	even	4
525.2.q.f.374.1		16	105.32	even	12
525.2.q.f.374.8		16	105.53	even	12
525.2.t.f.26.1		8	105.104	even	2
525.2.t.f.101.1		8	35.4	even	6
525.2.t.g.26.4		8	35.34	odd	2
525.2.t.g.101.4		8	105.74	odd	6
735.2.b.c.146.1		8	21.5	even	6
735.2.b.c.146.8		8	7.2	even	3
735.2.b.d.146.1		8	21.2	odd	6
735.2.b.d.146.8		8	7.5	odd	6
735.2.s.k.521.1		8	21.17	even	6	inner
735.2.s.k.656.1		8	1.1	even	1	trivial
735.2.s.l.521.4		8	7.3	odd	6
735.2.s.l.656.4		8	3.2	odd	2

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.01859 - 1.16543i) q^{2} +(1.21646 - 1.23297i) q^{3} +(1.71646 + 2.97300i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-3.89248 + 1.07116i) q^{6} -3.33995i q^{8} +(-0.0404447 - 2.99973i) q^{9} +O(q^{10})\)	\(q+(-2.01859 - 1.16543i) q^{2} +(1.21646 - 1.23297i) q^{3} +(1.71646 + 2.97300i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-3.89248 + 1.07116i) q^{6} -3.33995i q^{8} +(-0.0404447 - 2.99973i) q^{9} +(2.01859 - 1.16543i) q^{10} +(2.42019 - 1.39730i) q^{11} +(5.75363 + 1.50019i) q^{12} +3.20486i q^{13} +(0.459555 + 1.66997i) q^{15} +(-0.459555 + 0.795973i) q^{16} +(0.440969 + 0.763780i) q^{17} +(-3.41434 + 6.10234i) q^{18} +(-1.90160 - 1.09789i) q^{19} -3.43292 q^{20} -6.51381 q^{22} +(6.53240 + 3.77148i) q^{23} +(-4.11806 - 4.06291i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(3.73505 - 6.46929i) q^{26} +(-3.74778 - 3.59918i) q^{27} -8.15270i q^{29} +(1.01859 - 3.90656i) q^{30} +(7.62645 - 4.40313i) q^{31} +(-3.92965 + 2.26878i) q^{32} +(1.22124 - 4.68378i) q^{33} -2.05568i q^{34} +(8.84876 - 5.26916i) q^{36} +(-0.203727 + 0.352865i) q^{37} +(2.55903 + 4.43237i) q^{38} +(3.95151 + 3.89859i) q^{39} +(2.89248 + 1.66997i) q^{40} +8.55098 q^{41} -0.118062 q^{43} +(8.30832 + 4.79681i) q^{44} +(2.61806 + 1.46484i) q^{45} +(-8.79081 - 15.2261i) q^{46} +(1.31486 - 2.27740i) q^{47} +(0.422382 + 1.53489i) q^{48} +2.33086i q^{50} +(1.47814 + 0.385407i) q^{51} +(-9.52805 + 5.50102i) q^{52} +(6.46794 - 3.73427i) q^{53} +(3.37062 + 11.6330i) q^{54} +2.79459i q^{55} +(-3.66689 + 1.00908i) q^{57} +(-9.50142 + 16.4569i) q^{58} +(-2.04991 - 3.55054i) q^{59} +(-4.17602 + 4.23270i) q^{60} +(-10.7004 - 6.17786i) q^{61} -20.5262 q^{62} +12.4147 q^{64} +(-2.77549 - 1.60243i) q^{65} +(-7.92380 + 8.03135i) q^{66} +(0.802125 + 1.38932i) q^{67} +(-1.51381 + 2.62200i) q^{68} +(12.5965 - 3.46641i) q^{69} +6.25869i q^{71} +(-10.0189 + 0.135083i) q^{72} +(-0.192022 + 0.110864i) q^{73} +(0.822480 - 0.474859i) q^{74} +(-1.67602 - 0.437000i) q^{75} -7.53794i q^{76} +(-3.43292 - 12.4749i) q^{78} +(1.56849 - 2.71671i) q^{79} +(-0.459555 - 0.795973i) q^{80} +(-8.99673 + 0.242646i) q^{81} +(-17.2609 - 9.96559i) q^{82} +0.666893 q^{83} -0.881938 q^{85} +(0.238319 + 0.137594i) q^{86} +(-10.0521 - 9.91745i) q^{87} +(-4.66689 - 8.08330i) q^{88} +(0.437271 - 0.757376i) q^{89} +(-3.57762 - 6.00807i) q^{90} +25.8944i q^{92} +(3.84834 - 14.7594i) q^{93} +(-5.30832 + 3.06476i) q^{94} +(1.90160 - 1.09789i) q^{95} +(-1.98292 + 7.60504i) q^{96} -6.37221i q^{97} +(-4.28939 - 7.20339i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} - q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} - 5 q^{9}+O(q^{10}) \) 8 * q - 3 * q^2 - q^3 + 3 * q^4 - 4 * q^5 - 5 * q^6 - 5 * q^9	\( 8 q - 3 q^{2} - q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} - 5 q^{9} + 3 q^{10} + 9 q^{12} - q^{15} + q^{16} + 12 q^{17} - 19 q^{18} - 9 q^{19} - 6 q^{20} - 40 q^{22} + 27 q^{23} - 16 q^{24} - 4 q^{25} + 6 q^{26} - 4 q^{27} - 5 q^{30} + 21 q^{31} + 21 q^{32} - 2 q^{33} + 9 q^{36} + 7 q^{37} + 12 q^{38} - 3 q^{39} - 3 q^{40} + 30 q^{41} + 16 q^{43} + 4 q^{45} - 7 q^{46} + 6 q^{47} + 25 q^{48} - 6 q^{51} - 30 q^{52} + 24 q^{53} - 17 q^{54} + 6 q^{57} - 13 q^{58} + 12 q^{59} - 18 q^{60} - 15 q^{61} - 24 q^{62} + 38 q^{64} - 3 q^{65} - 22 q^{66} + 4 q^{67} + 13 q^{69} - 14 q^{72} - 15 q^{73} + 54 q^{74} + 2 q^{75} - 6 q^{78} - 29 q^{79} + q^{80} - 41 q^{81} - 27 q^{82} - 30 q^{83} - 24 q^{85} + 9 q^{86} - 32 q^{87} - 2 q^{88} + 3 q^{89} - 7 q^{90} - 9 q^{93} + 24 q^{94} + 9 q^{95} + 3 q^{96} - 34 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 - q^3 + 3 * q^4 - 4 * q^5 - 5 * q^6 - 5 * q^9 + 3 * q^10 + 9 * q^12 - q^15 + q^16 + 12 * q^17 - 19 * q^18 - 9 * q^19 - 6 * q^20 - 40 * q^22 + 27 * q^23 - 16 * q^24 - 4 * q^25 + 6 * q^26 - 4 * q^27 - 5 * q^30 + 21 * q^31 + 21 * q^32 - 2 * q^33 + 9 * q^36 + 7 * q^37 + 12 * q^38 - 3 * q^39 - 3 * q^40 + 30 * q^41 + 16 * q^43 + 4 * q^45 - 7 * q^46 + 6 * q^47 + 25 * q^48 - 6 * q^51 - 30 * q^52 + 24 * q^53 - 17 * q^54 + 6 * q^57 - 13 * q^58 + 12 * q^59 - 18 * q^60 - 15 * q^61 - 24 * q^62 + 38 * q^64 - 3 * q^65 - 22 * q^66 + 4 * q^67 + 13 * q^69 - 14 * q^72 - 15 * q^73 + 54 * q^74 + 2 * q^75 - 6 * q^78 - 29 * q^79 + q^80 - 41 * q^81 - 27 * q^82 - 30 * q^83 - 24 * q^85 + 9 * q^86 - 32 * q^87 - 2 * q^88 + 3 * q^89 - 7 * q^90 - 9 * q^93 + 24 * q^94 + 9 * q^95 + 3 * q^96 - 34 * q^99

Introduction

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