LMFDB - Embedded newform 935.2.s.a.89.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [935,2,Mod(89,935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(935, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("935.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 935 = 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	935.s (of order $4$, degree $2$, 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:	$7.46601258899$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$88$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			89.12
Character	$\chi$	$=$	935.89
Dual form			935.2.s.a.914.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23685 q^{2} +(-1.31033 - 1.31033i) q^{3} +3.00350 q^{4} +(-1.16908 - 1.90611i) q^{5} +(2.93101 + 2.93101i) q^{6} +(-0.128790 + 0.128790i) q^{7} -2.24467 q^{8} +0.433933i q^{9} +O(q^{10})$	\(q-2.23685 q^{2} +(-1.31033 - 1.31033i) q^{3} +3.00350 q^{4} +(-1.16908 - 1.90611i) q^{5} +(2.93101 + 2.93101i) q^{6} +(-0.128790 + 0.128790i) q^{7} -2.24467 q^{8} +0.433933i q^{9} +(2.61505 + 4.26368i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(-3.93558 - 3.93558i) q^{12} +1.78747i q^{13} +(0.288083 - 0.288083i) q^{14} +(-0.965758 + 4.02951i) q^{15} -0.985995 q^{16} +(4.06390 + 0.696193i) q^{17} -0.970644i q^{18} +0.474997i q^{19} +(-3.51132 - 5.72500i) q^{20} +0.337514 q^{21} +(1.58169 + 1.58169i) q^{22} +(-2.23332 + 2.23332i) q^{23} +(2.94127 + 2.94127i) q^{24} +(-2.26652 + 4.45678i) q^{25} -3.99831i q^{26} +(-3.36240 + 3.36240i) q^{27} +(-0.386820 + 0.386820i) q^{28} +(-2.04072 + 2.04072i) q^{29} +(2.16026 - 9.01342i) q^{30} +(-3.18709 + 3.18709i) q^{31} +6.69487 q^{32} +1.85309i q^{33} +(-9.09034 - 1.55728i) q^{34} +(0.396052 + 0.0949224i) q^{35} +1.30332i q^{36} +(4.16671 + 4.16671i) q^{37} -1.06250i q^{38} +(2.34218 - 2.34218i) q^{39} +(2.62420 + 4.27860i) q^{40} +(-7.37662 - 7.37662i) q^{41} -0.754968 q^{42} -1.11549 q^{43} +(-2.12379 - 2.12379i) q^{44} +(0.827125 - 0.507301i) q^{45} +(4.99561 - 4.99561i) q^{46} -5.29894i q^{47} +(1.29198 + 1.29198i) q^{48} +6.96683i q^{49} +(5.06986 - 9.96915i) q^{50} +(-4.41281 - 6.23730i) q^{51} +5.36867i q^{52} -4.02530 q^{53} +(7.52118 - 7.52118i) q^{54} +(-0.521162 + 2.17449i) q^{55} +(0.289091 - 0.289091i) q^{56} +(0.622403 - 0.622403i) q^{57} +(4.56478 - 4.56478i) q^{58} +6.93926i q^{59} +(-2.90065 + 12.1026i) q^{60} +(7.77238 + 7.77238i) q^{61} +(7.12905 - 7.12905i) q^{62} +(-0.0558861 - 0.0558861i) q^{63} -13.0034 q^{64} +(3.40712 - 2.08969i) q^{65} -4.14508i q^{66} +2.52383i q^{67} +(12.2059 + 2.09102i) q^{68} +5.85279 q^{69} +(-0.885910 - 0.212327i) q^{70} +(10.1369 - 10.1369i) q^{71} -0.974039i q^{72} +(3.66883 + 3.66883i) q^{73} +(-9.32031 - 9.32031i) q^{74} +(8.80975 - 2.86997i) q^{75} +1.42665i q^{76} +0.182136 q^{77} +(-5.23910 + 5.23910i) q^{78} +(-1.04462 - 1.04462i) q^{79} +(1.15270 + 1.87942i) q^{80} +10.1135 q^{81} +(16.5004 + 16.5004i) q^{82} +0.965875 q^{83} +1.01372 q^{84} +(-3.42399 - 8.56016i) q^{85} +2.49518 q^{86} +5.34803 q^{87} +(1.58722 + 1.58722i) q^{88} +11.1193 q^{89} +(-1.85015 + 1.13476i) q^{90} +(-0.230208 - 0.230208i) q^{91} +(-6.70779 + 6.70779i) q^{92} +8.35229 q^{93} +11.8529i q^{94} +(0.905397 - 0.555308i) q^{95} +(-8.77250 - 8.77250i) q^{96} +(-2.97838 - 2.97838i) q^{97} -15.5837i q^{98} +(0.306837 - 0.306837i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 168 q^{4} + 4 q^{5} + 8 q^{6}+O(q^{10}) $ 176 * q + 168 * q^4 + 4 * q^5 + 8 * q^6	$ 176 q + 168 q^{4} + 4 q^{5} + 8 q^{6} - 8 q^{10} - 8 q^{14} + 136 q^{16} + 8 q^{20} - 48 q^{21} + 8 q^{24} - 104 q^{30} - 24 q^{31} - 24 q^{34} - 64 q^{35} - 16 q^{39} - 56 q^{40} - 16 q^{41} - 8 q^{44} + 12 q^{45} + 40 q^{46} + 24 q^{50} - 136 q^{54} - 24 q^{56} + 72 q^{61} + 88 q^{64} - 16 q^{65} + 160 q^{69} + 32 q^{71} + 32 q^{74} - 120 q^{75} + 32 q^{79} - 4 q^{80} - 112 q^{81} - 192 q^{84} + 84 q^{85} - 144 q^{86} - 48 q^{89} + 108 q^{90} + 16 q^{91} + 100 q^{95} - 72 q^{96}+O(q^{100}) $ 176 * q + 168 * q^4 + 4 * q^5 + 8 * q^6 - 8 * q^10 - 8 * q^14 + 136 * q^16 + 8 * q^20 - 48 * q^21 + 8 * q^24 - 104 * q^30 - 24 * q^31 - 24 * q^34 - 64 * q^35 - 16 * q^39 - 56 * q^40 - 16 * q^41 - 8 * q^44 + 12 * q^45 + 40 * q^46 + 24 * q^50 - 136 * q^54 - 24 * q^56 + 72 * q^61 + 88 * q^64 - 16 * q^65 + 160 * q^69 + 32 * q^71 + 32 * q^74 - 120 * q^75 + 32 * q^79 - 4 * q^80 - 112 * q^81 - 192 * q^84 + 84 * q^85 - 144 * q^86 - 48 * q^89 + 108 * q^90 + 16 * q^91 + 100 * q^95 - 72 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/935\mathbb{Z}\right)^\times$.

$n$	$496$	$562$	$596$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−2.23685			−1.58169			−0.790846	−	0.612015i	$-0.790359\pi$
$2$	−2.23685			−1.58169			−0.790846	+	0.612015i	$0.790359\pi$
$3$	−1.31033	−	1.31033i	−0.756520	−	0.756520i	0.219167	−	0.975687i	$-0.429666\pi$
$3$	−1.31033	−	1.31033i	−0.756520	−	0.756520i	−0.975687	+	0.219167i	$0.929666\pi$
$4$	3.00350			1.50175
$5$	−1.16908	−	1.90611i	−0.522827	−	0.852439i
$5$	−1.16908	−	1.90611i	−0.522827	−	0.852439i
$6$	2.93101	+	2.93101i	1.19658	+	1.19658i
$7$	−0.128790	+	0.128790i	−0.0486779	+	0.0486779i	−0.731027	−	0.682349i	$-0.760959\pi$
$7$	−0.128790	+	0.128790i	−0.0486779	+	0.0486779i	0.682349	+	0.731027i	$0.260959\pi$
$8$	−2.24467			−0.793612
$9$			0.433933i			0.144644i
$10$	2.61505	+	4.26368i	0.826951	+	1.34830i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$11$	−0.707107	−	0.707107i	−0.213201	−	0.213201i
$12$	−3.93558	−	3.93558i	−1.13610	−	1.13610i
$13$			1.78747i			0.495755i	0.968791	+	0.247878i	$0.0797331\pi$
$13$			1.78747i			0.495755i	−0.968791	+	0.247878i	$0.920267\pi$
$14$	0.288083	−	0.288083i	0.0769935	−	0.0769935i
$15$	−0.965758	+	4.02951i	−0.249358	+	1.04042i
$16$	−0.985995			−0.246499
$17$	4.06390	+	0.696193i	0.985641	+	0.168852i
$17$	4.06390	+	0.696193i	0.985641	+	0.168852i
$18$		−	0.970644i		−	0.228783i
$19$			0.474997i			0.108972i	0.998515	+	0.0544859i	$0.0173520\pi$
$19$			0.474997i			0.108972i	−0.998515	+	0.0544859i	$0.982648\pi$
$20$	−3.51132	−	5.72500i	−0.785155	−	1.28015i
$21$	0.337514			0.0736516
$22$	1.58169	+	1.58169i	0.337218	+	0.337218i
$23$	−2.23332	+	2.23332i	−0.465680	+	0.465680i	−0.900512	−	0.434831i	$-0.856808\pi$
$23$	−2.23332	+	2.23332i	−0.465680	+	0.465680i	0.434831	+	0.900512i	$0.356808\pi$
$24$	2.94127	+	2.94127i	0.600384	+	0.600384i
$25$	−2.26652	+	4.45678i	−0.453304	+	0.891356i
$26$		−	3.99831i		−	0.784132i
$27$	−3.36240	+	3.36240i	−0.647093	+	0.647093i
$28$	−0.386820	+	0.386820i	−0.0731020	+	0.0731020i
$29$	−2.04072	+	2.04072i	−0.378952	+	0.378952i	−0.870724	−	0.491772i	$-0.836349\pi$
$29$	−2.04072	+	2.04072i	−0.378952	+	0.378952i	0.491772	+	0.870724i	$0.336349\pi$
$30$	2.16026	−	9.01342i	0.394407	−	1.64562i
$31$	−3.18709	+	3.18709i	−0.572419	+	0.572419i	−0.932804	−	0.360385i	$-0.882645\pi$
$31$	−3.18709	+	3.18709i	−0.572419	+	0.572419i	0.360385	+	0.932804i	$0.382645\pi$
$32$	6.69487			1.18350
$33$			1.85309i			0.322581i
$34$	−9.09034	−	1.55728i	−1.55898	−	0.267071i
$35$	0.396052	+	0.0949224i	0.0669451	+	0.0160448i
$36$			1.30332i			0.217220i
$37$	4.16671	+	4.16671i	0.685004	+	0.685004i	0.961123	−	0.276120i	$-0.0890486\pi$
$37$	4.16671	+	4.16671i	0.685004	+	0.685004i	−0.276120	+	0.961123i	$0.589049\pi$
$38$		−	1.06250i		−	0.172360i
$39$	2.34218	−	2.34218i	0.375049	−	0.375049i
$40$	2.62420	+	4.27860i	0.414922	+	0.676506i
$41$	−7.37662	−	7.37662i	−1.15204	−	1.15204i	−0.986144	−	0.165891i	$-0.946950\pi$
$41$	−7.37662	−	7.37662i	−1.15204	−	1.15204i	−0.165891	−	0.986144i	$-0.553050\pi$
$42$	−0.754968			−0.116494
$43$	−1.11549			−0.170110			−0.0850550	−	0.996376i	$-0.527107\pi$
$43$	−1.11549			−0.170110			−0.0850550	+	0.996376i	$0.527107\pi$
$44$	−2.12379	−	2.12379i	−0.320174	−	0.320174i
$45$	0.827125	−	0.507301i	0.123300	−	0.0756240i
$46$	4.99561	−	4.99561i	0.736563	−	0.736563i
$47$		−	5.29894i		−	0.772930i	−0.922304	−	0.386465i	$-0.873696\pi$
$47$		−	5.29894i		−	0.772930i	0.922304	−	0.386465i	$-0.126304\pi$
$48$	1.29198	+	1.29198i	0.186481	+	0.186481i
$49$			6.96683i			0.995261i
$50$	5.06986	−	9.96915i	0.716987	−	1.40985i
$51$	−4.41281	−	6.23730i	−0.617918	−	0.873397i
$52$			5.36867i			0.744500i
$53$	−4.02530			−0.552918			−0.276459	−	0.961026i	$-0.589161\pi$
$53$	−4.02530			−0.552918			−0.276459	+	0.961026i	$0.589161\pi$
$54$	7.52118	−	7.52118i	1.02350	−	1.02350i
$55$	−0.521162	+	2.17449i	−0.0702734	+	0.293208i
$56$	0.289091	−	0.289091i	0.0386314	−	0.0386314i
$57$	0.622403	−	0.622403i	0.0824393	−	0.0824393i
$58$	4.56478	−	4.56478i	0.599385	−	0.599385i
$59$			6.93926i			0.903415i	0.892166	+	0.451708i	$0.149185\pi$
$59$			6.93926i			0.903415i	−0.892166	+	0.451708i	$0.850815\pi$
$60$	−2.90065	+	12.1026i	−0.374473	+	1.56244i
$61$	7.77238	+	7.77238i	0.995151	+	0.995151i	0.999988	−	0.00483696i	$-0.00153966\pi$
$61$	7.77238	+	7.77238i	0.995151	+	0.995151i	−0.00483696	+	0.999988i	$0.501540\pi$
$62$	7.12905	−	7.12905i	0.905390	−	0.905390i
$63$	−0.0558861	−	0.0558861i	−0.00704099	−	0.00704099i
$64$	−13.0034			−1.62543
$65$	3.40712	−	2.08969i	0.422601	−	0.259194i
$66$		−	4.14508i		−	0.510224i
$67$			2.52383i			0.308334i	0.988045	+	0.154167i	$0.0492694\pi$
$67$			2.52383i			0.308334i	−0.988045	+	0.154167i	$0.950731\pi$
$68$	12.2059	+	2.09102i	1.48019	+	0.253573i
$69$	5.85279			0.704593
$70$	−0.885910	−	0.212327i	−0.105886	−	0.0253779i
$71$	10.1369	−	10.1369i	1.20303	−	1.20303i	0.229786	−	0.973241i	$-0.426197\pi$
$71$	10.1369	−	10.1369i	1.20303	−	1.20303i	0.973241	−	0.229786i	$-0.0738027\pi$
$72$		−	0.974039i		−	0.114792i
$73$	3.66883	+	3.66883i	0.429405	+	0.429405i	0.888425	−	0.459021i	$-0.151800\pi$
$73$	3.66883	+	3.66883i	0.429405	+	0.429405i	−0.459021	+	0.888425i	$0.651800\pi$
$74$	−9.32031	−	9.32031i	−1.08346	−	1.08346i
$75$	8.80975	−	2.86997i	1.01726	−	0.331395i
$76$			1.42665i			0.163648i
$77$	0.182136			0.0207563
$78$	−5.23910	+	5.23910i	−0.593212	+	0.593212i
$79$	−1.04462	−	1.04462i	−0.117529	−	0.117529i	0.645896	−	0.763425i	$-0.276484\pi$
$79$	−1.04462	−	1.04462i	−0.117529	−	0.117529i	−0.763425	+	0.645896i	$0.776484\pi$
$80$	1.15270	+	1.87942i	0.128876	+	0.210125i
$81$	10.1135			1.12372
$82$	16.5004	+	16.5004i	1.82216	+	1.82216i
$83$	0.965875			0.106019			0.0530093	−	0.998594i	$-0.483119\pi$
$83$	0.965875			0.106019			0.0530093	+	0.998594i	$0.483119\pi$
$84$	1.01372			0.110606
$85$	−3.42399	−	8.56016i	−0.371384	−	0.928479i
$86$	2.49518			0.269062
$87$	5.34803			0.573369
$88$	1.58722	+	1.58722i	0.169199	+	0.169199i
$89$	11.1193			1.17864			0.589322	−	0.807898i	$-0.299395\pi$
$89$	11.1193			1.17864			0.589322	+	0.807898i	$0.299395\pi$
$90$	−1.85015	+	1.13476i	−0.195023	+	0.119614i
$91$	−0.230208	−	0.230208i	−0.0241323	−	0.0241323i
$92$	−6.70779	+	6.70779i	−0.699335	+	0.699335i
$93$	8.35229			0.866092
$94$			11.8529i			1.22254i
$95$	0.905397	−	0.555308i	0.0928918	−	0.0569734i
$96$	−8.77250	−	8.77250i	−0.895339	−	0.895339i
$97$	−2.97838	−	2.97838i	−0.302409	−	0.302409i	0.539547	−	0.841956i	$-0.318596\pi$
$97$	−2.97838	−	2.97838i	−0.302409	−	0.302409i	−0.841956	+	0.539547i	$0.818596\pi$
$98$		−	15.5837i		−	1.57420i
$99$	0.306837	−	0.306837i	0.0308383	−	0.0308383i
$100$	−6.80748	+	13.3859i	−0.680748	+	1.33859i
$101$	6.04228			0.601229			0.300615	−	0.953746i	$-0.402808\pi$
$101$	6.04228			0.601229			0.300615	+	0.953746i	$0.402808\pi$
$102$	9.87081	+	13.9519i	0.977355	+	1.38144i
$103$			9.95101i			0.980503i	0.871581	+	0.490251i	$0.163095\pi$
$103$			9.95101i			0.980503i	−0.871581	+	0.490251i	$0.836905\pi$
$104$		−	4.01229i		−	0.393438i
$105$	−0.394580	−	0.643339i	−0.0385071	−	0.0627835i
$106$	9.00400			0.874546
$107$	0.211222	+	0.211222i	0.0204196	+	0.0204196i	0.717243	−	0.696823i	$-0.245404\pi$
$107$	0.211222	+	0.211222i	0.0204196	+	0.0204196i	−0.696823	+	0.717243i	$0.745404\pi$
$108$	−10.0990	+	10.0990i	−0.971772	+	0.971772i
$109$	5.73541	+	5.73541i	0.549353	+	0.549353i	0.926254	−	0.376901i	$-0.123010\pi$
$109$	5.73541	+	5.73541i	0.549353	+	0.549353i	−0.376901	+	0.926254i	$0.623010\pi$
$110$	1.16576	−	4.86400i	0.111151	−	0.463764i
$111$		−	10.9195i		−	1.03644i
$112$	0.126986	−	0.126986i	0.0119990	−	0.0119990i
$113$	7.27181	−	7.27181i	0.684074	−	0.684074i	−0.276841	−	0.960916i	$-0.589288\pi$
$113$	7.27181	−	7.27181i	0.684074	−	0.684074i	0.960916	+	0.276841i	$0.0892877\pi$
$114$	−1.39222	+	1.39222i	−0.130394	+	0.130394i
$115$	6.86789	+	1.64604i	0.640434	+	0.153494i
$116$	−6.12930	+	6.12930i	−0.569091	+	0.569091i
$117$	−0.775643			−0.0717082
$118$		−	15.5221i		−	1.42892i
$119$	−0.613051	+	0.433726i	−0.0561983	+	0.0397596i
$120$	2.16781	−	9.04495i	0.197893	−	0.825687i
$121$			1.00000i			0.0909091i
$122$	−17.3856	−	17.3856i	−1.57402	−	1.57402i
$123$			19.3316i			1.74307i
$124$	−9.57242	+	9.57242i	−0.859629	+	0.859629i
$125$	11.1449	−	0.890085i	0.996826	−	0.0796116i
$126$	0.125009	+	0.125009i	0.0111367	+	0.0111367i
$127$	7.30621			0.648321			0.324160	−	0.946002i	$-0.394918\pi$
$127$	7.30621			0.648321			0.324160	+	0.946002i	$0.394918\pi$
$128$	15.6970			1.38743
$129$	1.46166	+	1.46166i	0.128692	+	0.128692i
$130$	−7.62121	+	4.67433i	−0.668425	+	0.409966i
$131$	−0.326277	+	0.326277i	−0.0285070	+	0.0285070i	−0.721217	−	0.692710i	$-0.756417\pi$
$131$	−0.326277	+	0.326277i	−0.0285070	+	0.0285070i	0.692710	+	0.721217i	$0.256417\pi$
$132$			5.56574i			0.484436i
$133$	−0.0611747	−	0.0611747i	−0.00530452	−	0.00530452i
$134$		−	5.64542i		−	0.487690i
$135$	10.3400	+	2.47820i	0.889926	+	0.213290i
$136$	−9.12214	−	1.56273i	−0.782217	−	0.134003i
$137$			17.3349i			1.48102i	0.672043	+	0.740512i	$0.265417\pi$
$137$			17.3349i			1.48102i	−0.672043	+	0.740512i	$0.734583\pi$
$138$	−13.0918			−1.11445
$139$	−6.25098	+	6.25098i	−0.530201	+	0.530201i	−0.920632	−	0.390431i	$-0.872326\pi$
$139$	−6.25098	+	6.25098i	−0.530201	+	0.530201i	0.390431	+	0.920632i	$0.372326\pi$
$140$	1.18954	+	0.285099i	0.100535	+	0.0240953i
$141$	−6.94336	+	6.94336i	−0.584736	+	0.584736i
$142$	−22.6747	+	22.6747i	−1.90282	+	1.90282i
$143$	1.26393	−	1.26393i	0.105695	−	0.105695i
$144$		−	0.427856i		−	0.0356547i
$145$	6.27560	+	1.50408i	0.521160	+	0.124907i
$146$	−8.20663	−	8.20663i	−0.679186	−	0.679186i
$147$	9.12885	−	9.12885i	0.752935	−	0.752935i
$148$	12.5147	+	12.5147i	1.02870	+	1.02870i
$149$	7.21058			0.590713			0.295357	−	0.955387i	$-0.404562\pi$
$149$	7.21058			0.590713			0.295357	+	0.955387i	$0.404562\pi$
$150$	−19.7061	+	6.41969i	−1.60899	+	0.524165i
$151$		−	11.8089i		−	0.960992i	−0.876997	−	0.480496i	$-0.840457\pi$
$151$		−	11.8089i		−	0.960992i	0.876997	−	0.480496i	$-0.159543\pi$
$152$		−	1.06621i		−	0.0864814i
$153$	−0.302101	+	1.76346i	−0.0244234	+	0.142568i
$154$	−0.407411			−0.0328301
$155$	9.80091	+	2.34899i	0.787228	+	0.188676i
$156$	7.03473	−	7.03473i	0.563229	−	0.563229i
$157$		−	10.9517i		−	0.874038i	−0.899452	−	0.437019i	$-0.856034\pi$
$157$		−	10.9517i		−	0.874038i	0.899452	−	0.437019i	$-0.143966\pi$
$158$	2.33666	+	2.33666i	0.185894	+	0.185894i
$159$	5.27448	+	5.27448i	0.418293	+	0.418293i
$160$	−7.82682	−	12.7612i	−0.618765	−	1.00886i
$161$		−	0.575258i		−	0.0453367i
$162$	−22.6224			−1.77738
$163$	−3.67401	+	3.67401i	−0.287771	+	0.287771i	−0.836198	−	0.548427i	$-0.815227\pi$
$163$	−3.67401	+	3.67401i	−0.287771	+	0.287771i	0.548427	+	0.836198i	$0.315227\pi$
$164$	−22.1557	−	22.1557i	−1.73007	−	1.73007i
$165$	3.53219	−	2.16640i	0.274981	−	0.168654i
$166$	−2.16052			−0.167689
$167$	4.48598	+	4.48598i	0.347136	+	0.347136i	0.859042	−	0.511906i	$-0.171060\pi$
$167$	4.48598	+	4.48598i	0.347136	+	0.347136i	−0.511906	+	0.859042i	$0.671060\pi$
$168$	−0.757610			−0.0584508
$169$	9.80495			0.754227
$170$	7.65896	+	19.1478i	0.587416	+	1.46857i
$171$	−0.206117			−0.0157622
$172$	−3.35036			−0.255463
$173$	−14.6052	−	14.6052i	−1.11041	−	1.11041i	−0.993095	−	0.117315i	$-0.962571\pi$
$173$	−14.6052	−	14.6052i	−1.11041	−	1.11041i	−0.117315	−	0.993095i	$-0.537429\pi$
$174$	−11.9628			−0.906894
$175$	−0.282083	−	0.865891i	−0.0213235	−	0.0654552i
$176$	0.697204	+	0.697204i	0.0525537	+	0.0525537i
$177$	9.09273	−	9.09273i	0.683451	−	0.683451i
$178$	−24.8722			−1.86425
$179$			25.0877i			1.87514i	0.347793	+	0.937571i	$0.386931\pi$
$179$			25.0877i			1.87514i	−0.347793	+	0.937571i	$0.613069\pi$
$180$	2.48427	−	1.52368i	0.185166	−	0.113568i
$181$	−15.3978	−	15.3978i	−1.14451	−	1.14451i	−0.987615	−	0.156896i	$-0.949851\pi$
$181$	−15.3978	−	15.3978i	−1.14451	−	1.14451i	−0.156896	−	0.987615i	$-0.550149\pi$
$182$	0.514940	+	0.514940i	0.0381699	+	0.0381699i
$183$		−	20.3688i		−	1.50570i
$184$	5.01309	−	5.01309i	0.369570	−	0.369570i
$185$	3.07101	−	12.8134i	0.225785	−	0.942062i
$186$	−18.6828			−1.36989
$187$	−2.38133	−	3.36590i	−0.174140	−	0.246139i
$188$		−	15.9154i		−	1.16075i
$189$		−	0.866084i		−	0.0629983i
$190$	−2.02524	+	1.24214i	−0.146926	+	0.0901144i
$191$	−24.0425			−1.73966			−0.869828	−	0.493354i	$-0.835771\pi$
$191$	−24.0425			−1.73966			−0.869828	+	0.493354i	$0.835771\pi$
$192$	17.0388	+	17.0388i	1.22967	+	1.22967i
$193$	13.6382	−	13.6382i	0.981701	−	0.981701i	−0.0181346	−	0.999836i	$-0.505773\pi$
$193$	13.6382	−	13.6382i	0.981701	−	0.981701i	0.999836	+	0.0181346i	$0.00577273\pi$
$194$	6.66219	+	6.66219i	0.478318	+	0.478318i
$195$	−7.20264	−	1.72627i	−0.515792	−	0.123620i
$196$			20.9249i			1.49463i
$197$	−4.78854	+	4.78854i	−0.341170	+	0.341170i	−0.856807	−	0.515637i	$-0.827555\pi$
$197$	−4.78854	+	4.78854i	−0.341170	+	0.341170i	0.515637	+	0.856807i	$0.327555\pi$
$198$	−0.686349	+	0.686349i	−0.0487767	+	0.0487767i
$199$	5.57266	−	5.57266i	0.395036	−	0.395036i	−0.481442	−	0.876478i	$-0.659887\pi$
$199$	5.57266	−	5.57266i	0.395036	−	0.395036i	0.876478	+	0.481442i	$0.159887\pi$
$200$	5.08760	−	10.0040i	0.359747	−	0.707391i
$201$	3.30705	−	3.30705i	0.233261	−	0.233261i
$202$	−13.5157			−0.950960
$203$		−	0.525647i		−	0.0368932i
$204$	−13.2539	−	18.7337i	−0.927957	−	1.31162i
$205$	−5.43682	+	22.6845i	−0.379724	+	1.58435i
$206$		−	22.2589i		−	1.55085i
$207$	−0.969114	−	0.969114i	−0.0673581	−	0.0673581i
$208$		−	1.76244i		−	0.122203i
$209$	0.335874	−	0.335874i	0.0232329	−	0.0232329i
$210$	0.882616	+	1.43905i	0.0609063	+	0.0993041i
$211$	−19.7325	−	19.7325i	−1.35844	−	1.35844i	−0.875837	−	0.482606i	$-0.839690\pi$
$211$	−19.7325	−	19.7325i	−1.35844	−	1.35844i	−0.482606	−	0.875837i	$-0.660310\pi$
$212$	−12.0900			−0.830344
$213$	−26.5654			−1.82023
$214$	−0.472472	−	0.472472i	−0.0322975	−	0.0322975i
$215$	1.30409	+	2.12624i	0.0889381	+	0.145008i
$216$	7.54749	−	7.54749i	0.513541	−	0.513541i
$217$		−	0.820929i		−	0.0557283i
$218$	−12.8293	−	12.8293i	−0.868907	−	0.868907i
$219$		−	9.61477i		−	0.649706i
$220$	−1.56531	+	6.53107i	−0.105533	+	0.440324i
$221$	−1.24443	+	7.26411i	−0.0837091	+	0.488637i
$222$			24.4254i			1.63932i
$223$	−15.8083			−1.05860			−0.529300	−	0.848435i	$-0.677545\pi$
$223$	−15.8083			−1.05860			−0.529300	+	0.848435i	$0.677545\pi$
$224$	−0.862230	+	0.862230i	−0.0576102	+	0.0576102i
$225$	−1.93395	−	0.983518i	−0.128930	−	0.0655678i
$226$	−16.2659	+	16.2659i	−1.08199	+	1.08199i
$227$	−7.24823	+	7.24823i	−0.481082	+	0.481082i	−0.905477	−	0.424395i	$-0.860487\pi$
$227$	−7.24823	+	7.24823i	−0.481082	+	0.481082i	0.424395	+	0.905477i	$0.360487\pi$
$228$	1.86939	−	1.86939i	0.123803	−	0.123803i
$229$			18.4060i			1.21630i	0.793822	+	0.608151i	$0.208088\pi$
$229$			18.4060i			1.21630i	−0.793822	+	0.608151i	$0.791912\pi$
$230$	−15.3624	−	3.68194i	−1.01297	−	0.242780i
$231$	−0.238659	−	0.238659i	−0.0157026	−	0.0157026i
$232$	4.58075	−	4.58075i	0.300741	−	0.300741i
$233$	2.95687	+	2.95687i	0.193711	+	0.193711i	0.797298	−	0.603586i	$-0.206262\pi$
$233$	2.95687	+	2.95687i	0.193711	+	0.193711i	−0.603586	+	0.797298i	$0.706262\pi$
$234$	1.73500			0.113420
$235$	−10.1004	+	6.19487i	−0.658875	+	0.404109i
$236$			20.8421i			1.35670i
$237$			2.73759i			0.177826i
$238$	1.37130	−	0.970181i	0.0888884	−	0.0628875i
$239$	−5.75403			−0.372197			−0.186099	−	0.982531i	$-0.559584\pi$
$239$	−5.75403			−0.372197			−0.186099	+	0.982531i	$0.559584\pi$
$240$	0.952233	−	3.97308i	0.0614664	−	0.256461i
$241$	−2.56785	+	2.56785i	−0.165410	+	0.165410i	−0.784958	−	0.619549i	$-0.787316\pi$
$241$	−2.56785	+	2.56785i	−0.165410	+	0.165410i	0.619549	+	0.784958i	$0.287316\pi$
$242$		−	2.23685i		−	0.143790i
$243$	−3.16484	−	3.16484i	−0.203025	−	0.203025i
$244$	23.3443	+	23.3443i	1.49447	+	1.49447i
$245$	13.2795	−	8.14476i	0.848399	−	0.520349i
$246$		−	43.2420i		−	2.75701i
$247$	−0.849044			−0.0540234
$248$	7.15398	−	7.15398i	0.454278	−	0.454278i
$249$	−1.26562	−	1.26562i	−0.0802051	−	0.0802051i
$250$	−24.9294	+	1.99099i	−1.57667	+	0.125921i
$251$	20.0039			1.26263			0.631316	−	0.775526i	$-0.282515\pi$
$251$	20.0039			1.26263			0.631316	+	0.775526i	$0.282515\pi$
$252$	−0.167854	−	0.167854i	−0.0105738	−	0.0105738i
$253$	3.15840			0.198567
$254$	−16.3429			−1.02544
$255$	−6.73007	+	15.7032i	−0.421453	+	0.983373i
$256$	−9.10495			−0.569059
$257$	−16.3020			−1.01689			−0.508445	−	0.861094i	$-0.669780\pi$
$257$	−16.3020			−1.01689			−0.508445	+	0.861094i	$0.669780\pi$
$258$	−3.26950	−	3.26950i	−0.203550	−	0.203550i
$259$	−1.07326			−0.0666891
$260$	10.2333	−	6.27639i	0.634641	−	0.389245i
$261$	−0.885536	−	0.885536i	−0.0548133	−	0.0548133i
$262$	0.729833	−	0.729833i	0.0450892	−	0.0450892i
$263$	13.1621			0.811611			0.405806	−	0.913959i	$-0.366991\pi$
$263$	13.1621			0.811611			0.405806	+	0.913959i	$0.366991\pi$
$264$		−	4.15958i		−	0.256004i
$265$	4.70589	+	7.67268i	0.289081	+	0.471329i
$266$	0.136839	+	0.136839i	0.00839012	+	0.00839012i
$267$	−14.5700	−	14.5700i	−0.891668	−	0.891668i
$268$			7.58031i			0.463041i
$269$	−7.13523	+	7.13523i	−0.435043	+	0.435043i	−0.890340	−	0.455297i	$-0.849533\pi$
$269$	−7.13523	+	7.13523i	−0.435043	+	0.435043i	0.455297	+	0.890340i	$0.349533\pi$
$270$	−23.1290	−	5.54336i	−1.40759	−	0.337358i
$271$	5.71842			0.347369			0.173685	−	0.984801i	$-0.444433\pi$
$271$	5.71842			0.347369			0.173685	+	0.984801i	$0.444433\pi$
$272$	−4.00699	−	0.686443i	−0.242959	−	0.0416217i
$273$			0.603297i			0.0365132i
$274$		−	38.7757i		−	2.34252i
$275$	4.75409	−	1.54875i	0.286682	−	0.0933931i
$276$	17.5788			1.05812
$277$	17.4185	+	17.4185i	1.04658	+	1.04658i	0.998861	+	0.0477141i	$0.0151936\pi$
$277$	17.4185	+	17.4185i	1.04658	+	1.04658i	0.0477141	+	0.998861i	$0.484806\pi$
$278$	13.9825	−	13.9825i	0.838615	−	0.838615i
$279$	−1.38298	−	1.38298i	−0.0827971	−	0.0827971i
$280$	−0.889009	−	0.213070i	−0.0531285	−	0.0127334i
$281$			8.32211i			0.496456i	0.968702	+	0.248228i	$0.0798482\pi$
$281$			8.32211i			0.496456i	−0.968702	+	0.248228i	$0.920152\pi$
$282$	15.5313	−	15.5313i	0.924873	−	0.924873i
$283$	5.70770	−	5.70770i	0.339287	−	0.339287i	−0.516812	−	0.856099i	$-0.672881\pi$
$283$	5.70770	−	5.70770i	0.339287	−	0.339287i	0.856099	+	0.516812i	$0.172881\pi$
$284$	30.4461	−	30.4461i	1.80665	−	1.80665i
$285$	−1.91401	−	0.458732i	−0.113376	−	0.0271730i
$286$	−2.82723	+	2.82723i	−0.167178	+	0.167178i
$287$	1.90007			0.112157
$288$			2.90513i			0.171186i
$289$	16.0306	+	5.65852i	0.942978	+	0.332854i
$290$	−14.0376	−	3.36440i	−0.824314	−	0.197564i
$291$			7.80533i			0.457557i
$292$	11.0193	+	11.0193i	0.644858	+	0.644858i
$293$		−	16.4113i		−	0.958758i	−0.877608	−	0.479379i	$-0.840862\pi$
$293$		−	16.4113i		−	0.958758i	0.877608	−	0.479379i	$-0.159138\pi$
$294$	−20.4199	+	20.4199i	−1.19091	+	1.19091i
$295$	13.2270	−	8.11253i	0.770106	−	0.472330i
$296$	−9.35292	−	9.35292i	−0.543627	−	0.543627i
$297$	4.75515			0.275922
$298$	−16.1290			−0.934327
$299$	−3.99200	−	3.99200i	−0.230864	−	0.230864i
$300$	26.4601	−	8.61995i	1.52767	−	0.497673i
$301$	0.143663	−	0.143663i	0.00828060	−	0.00828060i
$302$			26.4147i			1.51999i
$303$	−7.91739	−	7.91739i	−0.454842	−	0.454842i
$304$		−	0.468345i		−	0.0268614i
$305$	5.72851	−	23.9015i	0.328013	−	1.36860i
$306$	0.675755	−	3.94460i	0.0386304	−	0.225498i
$307$			25.0172i			1.42780i	0.700245	+	0.713902i	$0.253074\pi$
$307$			25.0172i			1.42780i	−0.700245	+	0.713902i	$0.746926\pi$
$308$	0.547045			0.0311708
$309$	13.0391	−	13.0391i	0.741770	−	0.741770i
$310$	−21.9232	−	5.25435i	−1.24515	−	0.298427i
$311$	−15.2141	+	15.2141i	−0.862712	+	0.862712i	−0.991652	−	0.128940i	$-0.958843\pi$
$311$	−15.2141	+	15.2141i	−0.862712	+	0.862712i	0.128940	+	0.991652i	$0.458843\pi$
$312$	−5.25743	+	5.25743i	−0.297643	+	0.297643i
$313$	13.5838	−	13.5838i	0.767802	−	0.767802i	−0.209917	−	0.977719i	$-0.567319\pi$
$313$	13.5838	−	13.5838i	0.767802	−	0.767802i	0.977719	+	0.209917i	$0.0673193\pi$
$314$			24.4972i			1.38246i
$315$	−0.0411900	+	0.171860i	−0.00232079	+	0.00968323i
$316$	−3.13751	−	3.13751i	−0.176499	−	0.176499i
$317$	−1.36701	+	1.36701i	−0.0767791	+	0.0767791i	−0.744453	−	0.667674i	$-0.767290\pi$
$317$	−1.36701	+	1.36701i	−0.0767791	+	0.0767791i	0.667674	+	0.744453i	$0.267290\pi$
$318$	−11.7982	−	11.7982i	−0.661611	−	0.661611i
$319$	2.88601			0.161586
$320$	15.2020	+	24.7860i	0.849819	+	1.38558i
$321$		−	0.553541i		−	0.0308957i
$322$			1.28677i			0.0717087i
$323$	−0.330690	+	1.93034i	−0.0184001	+	0.107407i
$324$	30.3759			1.68755
$325$	−7.96637	−	4.05134i	−0.441895	−	0.224728i
$326$	8.21821	−	8.21821i	0.455165	−	0.455165i
$327$		−	15.0306i		−	0.831193i
$328$	16.5581	+	16.5581i	0.914269	+	0.914269i
$329$	0.682448	+	0.682448i	0.0376246	+	0.0376246i
$330$	−7.90098	+	4.84592i	−0.434935	+	0.266759i
$331$			29.3728i			1.61448i	0.590225	+	0.807239i	$0.299039\pi$
$331$			29.3728i			1.61448i	−0.590225	+	0.807239i	$0.700961\pi$
$332$	2.90100			0.159213
$333$	−1.80808	+	1.80808i	−0.0990819	+	0.0990819i
$334$	−10.0345	−	10.0345i	−0.549062	−	0.549062i
$335$	4.81069	−	2.95055i	0.262836	−	0.161206i
$336$	−0.332787			−0.0181550
$337$	−4.14302	−	4.14302i	−0.225685	−	0.225685i	0.585202	−	0.810887i	$-0.301015\pi$
$337$	−4.14302	−	4.14302i	−0.225685	−	0.225685i	−0.810887	+	0.585202i	$0.801015\pi$
$338$	−21.9322			−1.19295
$339$	−19.0570			−1.03503
$340$	−10.2840	−	25.7104i	−0.557726	−	1.39434i
$341$	4.50723			0.244080
$342$	0.461053			0.0249309
$343$	−1.79878	−	1.79878i	−0.0971252	−	0.0971252i
$344$	2.50390			0.135001
$345$	−6.84236	−	11.1561i	−0.368380	−	0.600622i
$346$	32.6696	+	32.6696i	1.75633	+	1.75633i
$347$	−7.54910	+	7.54910i	−0.405257	+	0.405257i	−0.880081	−	0.474824i	$-0.842512\pi$
$347$	−7.54910	+	7.54910i	−0.405257	+	0.405257i	0.474824	+	0.880081i	$0.342512\pi$
$348$	16.0628			0.861057
$349$			26.8570i			1.43762i	0.695205	+	0.718811i	$0.255314\pi$
$349$			26.8570i			1.43762i	−0.695205	+	0.718811i	$0.744686\pi$
$350$	0.630978	+	1.93687i	0.0337272	+	0.103530i
$351$	−6.01019	−	6.01019i	−0.320800	−	0.320800i
$352$	−4.73399	−	4.73399i	−0.252323	−	0.252323i
$353$			34.1178i			1.81591i	0.419071	+	0.907953i	$0.362356\pi$
$353$			34.1178i			1.81591i	−0.419071	+	0.907953i	$0.637644\pi$
$354$	−20.3391	+	20.3391i	−1.08101	+	1.08101i
$355$	−31.1728	−	7.47123i	−1.65448	−	0.396532i
$356$	33.3968			1.77003
$357$	1.37162	+	0.234975i	0.0725941	+	0.0124362i
$358$		−	56.1174i		−	2.96590i
$359$		−	14.3149i		−	0.755512i	−0.925905	−	0.377756i	$-0.876696\pi$
$359$		−	14.3149i		−	0.755512i	0.925905	−	0.377756i	$-0.123304\pi$
$360$	−1.85663	+	1.13873i	−0.0978528	+	0.0600162i
$361$	18.7744			0.988125
$362$	34.4426	+	34.4426i	1.81026	+	1.81026i
$363$	1.31033	−	1.31033i	0.0687745	−	0.0687745i
$364$	−0.691429	−	0.691429i	−0.0362407	−	0.0362407i
$365$	2.70406	−	11.2824i	0.141537	−	0.590545i
$366$			45.5619i			2.38156i
$367$	4.85784	−	4.85784i	0.253577	−	0.253577i	−0.568858	−	0.822436i	$-0.692615\pi$
$367$	4.85784	−	4.85784i	0.253577	−	0.253577i	0.822436	+	0.568858i	$0.192615\pi$
$368$	2.20205	−	2.20205i	0.114790	−	0.114790i
$369$	3.20096	−	3.20096i	0.166635	−	0.166635i
$370$	−6.86939	+	28.6617i	−0.357123	+	1.49005i
$371$	0.518418	−	0.518418i	0.0269149	−	0.0269149i
$372$	25.0861			1.30065
$373$			9.52614i			0.493245i	0.969112	+	0.246622i	$0.0793208\pi$
$373$			9.52614i			0.493245i	−0.969112	+	0.246622i	$0.920679\pi$
$374$	5.32668	+	7.52901i	0.275436	+	0.389316i
$375$	−15.7697	−	13.4371i	−0.814346	−	0.693891i
$376$			11.8944i			0.613407i
$377$	−3.64773	−	3.64773i	−0.187868	−	0.187868i
$378$			1.93730i			0.0996439i
$379$	−8.63986	+	8.63986i	−0.443800	+	0.443800i	−0.893287	−	0.449487i	$-0.851607\pi$
$379$	−8.63986	+	8.63986i	−0.443800	+	0.443800i	0.449487	+	0.893287i	$0.351607\pi$
$380$	2.71936	−	1.66787i	0.139500	−	0.0855598i
$381$	−9.57355	−	9.57355i	−0.490468	−	0.490468i
$382$	53.7795			2.75160
$383$	−4.42255			−0.225982			−0.112991	−	0.993596i	$-0.536043\pi$
$383$	−4.42255			−0.225982			−0.112991	+	0.993596i	$0.536043\pi$
$384$	−20.5683	−	20.5683i	−1.04962	−	1.04962i
$385$	−0.212931	−	0.347172i	−0.0108520	−	0.0176935i
$386$	−30.5067	+	30.5067i	−1.55275	+	1.55275i
$387$		−	0.484047i		−	0.0246055i
$388$	−8.94557	−	8.94557i	−0.454142	−	0.454142i
$389$			8.31436i			0.421555i	0.977534	+	0.210777i	$0.0675995\pi$
$389$			8.31436i			0.421555i	−0.977534	+	0.210777i	$0.932400\pi$
$390$	16.1112	+	3.86140i	0.815824	+	0.195529i
$391$	−10.6308	+	7.52119i	−0.537625	+	0.380363i
$392$		−	15.6383i		−	0.789851i
$393$	0.855062			0.0431322
$394$	10.7113	−	10.7113i	0.539625	−	0.539625i
$395$	−0.769920	+	3.21240i	−0.0387389	+	0.161633i
$396$	0.921585	−	0.921585i	0.0463114	−	0.0463114i
$397$	6.85832	−	6.85832i	0.344209	−	0.344209i	−0.513738	−	0.857947i	$-0.671740\pi$
$397$	6.85832	−	6.85832i	0.344209	−	0.344209i	0.857947	+	0.513738i	$0.171740\pi$
$398$	−12.4652	+	12.4652i	−0.624825	+	0.624825i
$399$			0.160318i			0.00802595i
$400$	2.23478	−	4.39436i	0.111739	−	0.219718i
$401$	10.7810	+	10.7810i	0.538379	+	0.538379i	0.923053	−	0.384674i	$-0.125686\pi$
$401$	10.7810	+	10.7810i	0.538379	+	0.538379i	−0.384674	+	0.923053i	$0.625686\pi$
$402$	−7.39737	+	7.39737i	−0.368947	+	0.368947i
$403$	−5.69684	−	5.69684i	−0.283780	−	0.283780i
$404$	18.1480			0.902896
$405$	−11.8235	−	19.2775i	−0.587513	−	0.957905i
$406$			1.17579i			0.0583537i
$407$		−	5.89262i		−	0.292086i
$408$	9.90534	+	14.0007i	0.490387	+	0.693139i
$409$	22.6813			1.12152			0.560758	−	0.827980i	$-0.310510\pi$
$409$	22.6813			1.12152			0.560758	+	0.827980i	$0.310510\pi$
$410$	12.1614	−	50.7418i	0.600607	−	2.50596i
$411$	22.7145	−	22.7145i	1.12042	−	1.12042i
$412$			29.8879i			1.47247i
$413$	−0.893705	−	0.893705i	−0.0439764	−	0.0439764i
$414$	2.16776	+	2.16776i	0.106540	+	0.106540i
$415$	−1.12918	−	1.84107i	−0.0554294	−	0.0903743i
$416$			11.9669i			0.586725i
$417$	16.3817			0.802216
$418$	−0.751299	+	0.751299i	−0.0367472	+	0.0367472i
$419$	−4.25383	−	4.25383i	−0.207813	−	0.207813i	0.595524	−	0.803337i	$-0.296944\pi$
$419$	−4.25383	−	4.25383i	−0.207813	−	0.207813i	−0.803337	+	0.595524i	$0.796944\pi$
$420$	−1.18512	−	1.93227i	−0.0578279	−	0.0942851i
$421$	1.53674			0.0748963			0.0374482	−	0.999299i	$-0.488077\pi$
$421$	1.53674			0.0748963			0.0374482	+	0.999299i	$0.488077\pi$
$422$	44.1387	+	44.1387i	2.14864	+	2.14864i
$423$	2.29939			0.111800
$424$	9.03550			0.438803
$425$	−12.3137	+	16.5340i	−0.597302	+	0.802017i
$426$	59.4227			2.87904
$427$	−2.00200			−0.0968838
$428$	0.634405	+	0.634405i	0.0306651	+	0.0306651i
$429$	−3.31234			−0.159921
$430$	−2.91705	−	4.75608i	−0.140673	−	0.229359i
$431$	3.76126	+	3.76126i	0.181174	+	0.181174i	0.791867	−	0.610693i	$-0.209109\pi$
$431$	3.76126	+	3.76126i	0.181174	+	0.181174i	−0.610693	+	0.791867i	$0.709109\pi$
$432$	3.31531	−	3.31531i	0.159508	−	0.159508i
$433$	32.3877			1.55645			0.778227	−	0.627983i	$-0.216119\pi$
$433$	32.3877			1.55645			0.778227	+	0.627983i	$0.216119\pi$
$434$			1.83629i			0.0881450i
$435$	−6.25226	−	10.1939i	−0.299773	−	0.488762i
$436$	17.2263	+	17.2263i	0.824990	+	0.824990i
$437$	−1.06082	−	1.06082i	−0.0507460	−	0.0507460i
$438$			21.5068i			1.02763i
$439$	24.2993	−	24.2993i	1.15974	−	1.15974i	0.175211	−	0.984531i	$-0.443939\pi$
$439$	24.2993	−	24.2993i	1.15974	−	1.15974i	0.984531	−	0.175211i	$-0.0560609\pi$
$440$	1.16984	−	4.88101i	0.0557699	−	0.232693i
$441$	−3.02314			−0.143959
$442$	2.78359	−	16.2487i	0.132402	−	0.772873i
$443$			15.4198i			0.732615i	0.930494	+	0.366307i	$0.119378\pi$
$443$			15.4198i			0.732615i	−0.930494	+	0.366307i	$0.880622\pi$
$444$		−	32.7968i		−	1.55647i
$445$	−12.9993	−	21.1946i	−0.616228	−	1.00472i
$446$	35.3607			1.67438
$447$	−9.44824	−	9.44824i	−0.446886	−	0.446886i
$448$	1.67471	−	1.67471i	0.0791225	−	0.0791225i
$449$	18.6590	+	18.6590i	0.880574	+	0.880574i	0.993593	−	0.113019i	$-0.0360520\pi$
$449$	18.6590	+	18.6590i	0.880574	+	0.880574i	−0.113019	+	0.993593i	$0.536052\pi$
$450$	4.32595	+	2.19998i	0.203927	+	0.103708i
$451$			10.4321i			0.491229i
$452$	21.8409	−	21.8409i	1.02731	−	1.02731i
$453$	−15.4735	+	15.4735i	−0.727009	+	0.727009i
$454$	16.2132	−	16.2132i	0.760923	−	0.760923i
$455$	−0.169671	+	0.707932i	−0.00795430	+	0.0331884i
$456$	−1.39709	+	1.39709i	−0.0654249	+	0.0654249i
$457$	20.8813			0.976786			0.488393	−	0.872624i	$-0.337583\pi$
$457$	20.8813			0.976786			0.488393	+	0.872624i	$0.337583\pi$
$458$		−	41.1714i		−	1.92381i
$459$	−16.0053	+	11.3236i	−0.747065	+	0.528539i
$460$	20.6277	+	4.94387i	0.961772	+	0.230509i
$461$			10.5590i			0.491784i	0.969297	+	0.245892i	$0.0790808\pi$
$461$			10.5590i			0.491784i	−0.969297	+	0.245892i	$0.920919\pi$
$462$	0.533843	+	0.533843i	0.0248366	+	0.0248366i
$463$			19.9148i			0.925518i	0.886484	+	0.462759i	$0.153140\pi$
$463$			19.9148i			0.925518i	−0.886484	+	0.462759i	$0.846860\pi$
$464$	2.01214	−	2.01214i	0.0934112	−	0.0934112i
$465$	−9.76447	−	15.9204i	−0.452816	−	0.738290i
$466$	−6.61408	−	6.61408i	−0.306391	−	0.306391i
$467$	−33.8181			−1.56492			−0.782458	−	0.622703i	$-0.786035\pi$
$467$	−33.8181			−1.56492			−0.782458	+	0.622703i	$0.786035\pi$
$468$	−2.32964			−0.107688
$469$	−0.325043	−	0.325043i	−0.0150091	−	0.0150091i
$470$	22.5930	−	13.8570i	1.04214	−	0.639175i
$471$	−14.3503	+	14.3503i	−0.661227	+	0.661227i
$472$		−	15.5764i		−	0.716961i
$473$	0.788768	+	0.788768i	0.0362676	+	0.0362676i
$474$		−	6.12359i		−	0.281266i
$475$	−2.11696	−	1.07659i	−0.0971327	−	0.0493973i
$476$	−1.84130	+	1.30270i	−0.0843958	+	0.0597090i
$477$		−	1.74671i		−	0.0799765i
$478$	12.8709			0.588702
$479$	−4.55790	+	4.55790i	−0.208256	+	0.208256i	−0.803526	−	0.595270i	$-0.797045\pi$
$479$	−4.55790	+	4.55790i	−0.208256	+	0.208256i	0.595270	+	0.803526i	$0.297045\pi$
$480$	−6.46563	+	26.9771i	−0.295114	+	1.23133i
$481$	−7.44788	+	7.44788i	−0.339594	+	0.339594i
$482$	5.74390	−	5.74390i	0.261627	−	0.261627i
$483$	−0.753779	+	0.753779i	−0.0342981	+	0.0342981i
$484$			3.00350i			0.136523i
$485$	−2.19517	+	9.15909i	−0.0996775	+	0.415893i
$486$	7.07928	+	7.07928i	0.321123	+	0.321123i
$487$	−1.30811	+	1.30811i	−0.0592761	+	0.0592761i	−0.736123	−	0.676847i	$-0.763346\pi$
$487$	−1.30811	+	1.30811i	−0.0592761	+	0.0592761i	0.676847	+	0.736123i	$0.263346\pi$
$488$	−17.4465	−	17.4465i	−0.789765	−	0.789765i
$489$	9.62834			0.435408
$490$	−29.7043	+	18.2186i	−1.34191	+	0.823032i
$491$		−	42.1560i		−	1.90247i	−0.308464	−	0.951236i	$-0.599815\pi$
$491$		−	42.1560i		−	1.90247i	0.308464	−	0.951236i	$-0.400185\pi$
$492$			58.0625i			2.61766i
$493$	−9.71402	+	6.87255i	−0.437498	+	0.309524i
$494$	1.89918			0.0854483
$495$	−0.943582	−	0.226149i	−0.0424108	−	0.0101647i
$496$	3.14246	−	3.14246i	0.141100	−	0.141100i
$497$			2.61105i			0.117122i
$498$	2.83099	+	2.83099i	0.126860	+	0.126860i
$499$	−2.23845	−	2.23845i	−0.100207	−	0.100207i	0.655226	−	0.755433i	$-0.272573\pi$
$499$	−2.23845	−	2.23845i	−0.100207	−	0.100207i	−0.755433	+	0.655226i	$0.772573\pi$
$500$	33.4735	−	2.67337i	1.49698	−	0.119557i
$501$		−	11.7562i		−	0.525230i
$502$	−44.7456			−1.99709
$503$	0.188530	−	0.188530i	0.00840615	−	0.00840615i	−0.702891	−	0.711297i	$-0.748108\pi$
$503$	0.188530	−	0.188530i	0.00840615	−	0.00840615i	0.711297	+	0.702891i	$0.248108\pi$
$504$	0.125446	+	0.125446i	0.00558782	+	0.00558782i
$505$	−7.06389	−	11.5173i	−0.314339	−	0.512511i
$506$	−7.06486			−0.314071
$507$	−12.8477	−	12.8477i	−0.570587	−	0.570587i
$508$	21.9442			0.973615
$509$	1.70409			0.0755325			0.0377663	−	0.999287i	$-0.487976\pi$
$509$	1.70409			0.0755325			0.0377663	+	0.999287i	$0.487976\pi$
$510$	15.0542	−	35.1257i	0.666609	−	1.55539i
$511$	−0.945016			−0.0418050
$512$	−11.0276			−0.487355
$513$	−1.59713	−	1.59713i	−0.0705150	−	0.0705150i
$514$	36.4651			1.60841
$515$	18.9677	−	11.6335i	0.835818	−	0.512633i
$516$	4.39008	+	4.39008i	0.193263	+	0.193263i
$517$	−3.74691	+	3.74691i	−0.164789	+	0.164789i
$518$	2.40072			0.105482
$519$			38.2752i			1.68009i
$520$	−7.64787	+	4.69068i	−0.335381	+	0.205700i
$521$	−19.4746	−	19.4746i	−0.853199	−	0.853199i	0.137327	−	0.990526i	$-0.456149\pi$
$521$	−19.4746	−	19.4746i	−0.853199	−	0.853199i	−0.990526	+	0.137327i	$0.956149\pi$
$522$	1.98081	+	1.98081i	0.0866977	+	0.0866977i
$523$			29.6493i			1.29647i	0.761440	+	0.648236i	$0.224493\pi$
$523$			29.6493i			1.29647i	−0.761440	+	0.648236i	$0.775507\pi$
$524$	−0.979973	+	0.979973i	−0.0428103	+	0.0428103i
$525$	−0.764982	+	1.50423i	−0.0333865	+	0.0656498i
$526$	−29.4417			−1.28372
$527$	−15.1709	+	10.7332i	−0.660853	+	0.467546i
$528$		−	1.82713i		−	0.0795158i
$529$			13.0245i			0.566284i
$530$	−10.5264	−	17.1626i	−0.457236	−	0.745497i
$531$	−3.01118			−0.130674
$532$	−0.183738	−	0.183738i	−0.00796606	−	0.00796606i
$533$	13.1855	−	13.1855i	0.571128	−	0.571128i
$534$	32.5909	+	32.5909i	1.41034	+	1.41034i
$535$	0.155678	−	0.649547i	0.00673054	−	0.0280824i
$536$		−	5.66517i		−	0.244698i
$537$	32.8732	−	32.8732i	1.41858	−	1.41858i
$538$	15.9604	−	15.9604i	0.688104	−	0.688104i
$539$	4.92629	−	4.92629i	0.212190	−	0.212190i
$540$	31.0562	+	7.44327i	1.33644	+	0.320307i
$541$	−16.0888	+	16.0888i	−0.691710	+	0.691710i	−0.962608	−	0.270898i	$-0.912679\pi$
$541$	−16.0888	+	16.0888i	−0.691710	+	0.691710i	0.270898	+	0.962608i	$0.412679\pi$
$542$	−12.7912			−0.549431
$543$			40.3525i			1.73169i
$544$	27.2073	+	4.66093i	1.16650	+	0.199836i
$545$	4.22720	−	17.6375i	0.181073	−	0.755506i
$546$		−	1.34948i		−	0.0577526i
$547$	−6.51978	−	6.51978i	−0.278766	−	0.278766i	0.553850	−	0.832616i	$-0.313158\pi$
$547$	−6.51978	−	6.51978i	−0.278766	−	0.278766i	−0.832616	+	0.553850i	$0.813158\pi$
$548$			52.0654i			2.22413i
$549$	−3.37269	+	3.37269i	−0.143943	+	0.143943i
$550$	−10.6342	+	3.46432i	−0.453443	+	0.147719i
$551$	−0.969336	−	0.969336i	−0.0412951	−	0.0412951i
$552$	−13.1376			−0.559174
$553$	0.269072			0.0114421
$554$	−38.9625	−	38.9625i	−1.65536	−	1.65536i
$555$	−20.8139	+	12.7658i	−0.883499	+	0.541878i
$556$	−18.7748	+	18.7748i	−0.796230	+	0.796230i
$557$		−	15.1532i		−	0.642063i	−0.947069	−	0.321031i	$-0.895971\pi$
$557$		−	15.1532i		−	0.642063i	0.947069	−	0.321031i	$-0.104029\pi$
$558$	3.09353	+	3.09353i	0.130960	+	0.130960i
$559$		−	1.99390i		−	0.0843330i
$560$	−0.390506	−	0.0935930i	−0.0165019	−	0.00395503i
$561$	−1.29011	+	7.53077i	−0.0544684	+	0.317949i
$562$		−	18.6153i		−	0.785240i
$563$	2.79421			0.117762			0.0588810	−	0.998265i	$-0.481247\pi$
$563$	2.79421			0.117762			0.0588810	+	0.998265i	$0.481247\pi$
$564$	−20.8544	+	20.8544i	−0.878128	+	0.878128i
$565$	−22.3622	−	5.35957i	−0.940784	−	0.225479i
$566$	−12.7673	+	12.7673i	−0.536648	+	0.536648i
$567$	−1.30251	+	1.30251i	−0.0547005	+	0.0547005i
$568$	−22.7540	+	22.7540i	−0.954737	+	0.954737i
$569$			18.4135i			0.771935i	0.922512	+	0.385968i	$0.126132\pi$
$569$			18.4135i			0.771935i	−0.922512	+	0.385968i	$0.873868\pi$
$570$	4.28135	+	1.02612i	0.179326	+	0.0429793i
$571$	14.9966	+	14.9966i	0.627589	+	0.627589i	0.947461	−	0.319872i	$-0.103640\pi$
$571$	14.9966	+	14.9966i	0.627589	+	0.627589i	−0.319872	+	0.947461i	$0.603640\pi$
$572$	3.79622	−	3.79622i	0.158728	−	0.158728i
$573$	31.5037	+	31.5037i	1.31608	+	1.31608i
$574$	−4.25016			−0.177398
$575$	−4.89157	−	15.0153i	−0.203992	−	0.626182i
$576$		−	5.64262i		−	0.235109i
$577$			20.7279i			0.862913i	0.902134	+	0.431457i	$0.142000\pi$
$577$			20.7279i			0.862913i	−0.902134	+	0.431457i	$0.858000\pi$
$578$	−35.8581	−	12.6573i	−1.49150	−	0.526473i
$579$	−35.7412			−1.48535
$580$	18.8487	+	4.51750i	0.782651	+	0.187579i
$581$	−0.124395	+	0.124395i	−0.00516076	+	0.00516076i
$582$		−	17.4594i		−	0.723714i
$583$	2.84632	+	2.84632i	0.117883	+	0.117883i
$584$	−8.23534	−	8.23534i	−0.340781	−	0.340781i
$585$	0.906787	+	1.47846i	0.0374910	+	0.0611269i
$586$			36.7096i			1.51646i
$587$	−35.8008			−1.47766			−0.738829	−	0.673893i	$-0.764621\pi$
$587$	−35.8008			−1.47766			−0.738829	+	0.673893i	$0.764621\pi$
$588$	27.4185	−	27.4185i	1.13072	−	1.13072i
$589$	−1.51386	−	1.51386i	−0.0623775	−	0.0623775i
$590$	−29.5868	+	18.1465i	−1.21807	+	0.747080i
$591$	12.5492			0.516203
$592$	−4.10836	−	4.10836i	−0.168853	−	0.168853i
$593$	−6.03820			−0.247959			−0.123980	−	0.992285i	$-0.539566\pi$
$593$	−6.03820			−0.247959			−0.123980	+	0.992285i	$0.539566\pi$
$594$	−10.6365			−0.436423
$595$	1.54343	+	0.661484i	0.0632747	+	0.0271182i
$596$	21.6570			0.887103
$597$	−14.6041			−0.597704
$598$	8.92951	+	8.92951i	0.365155	+	0.365155i
$599$	−42.4648			−1.73506			−0.867532	−	0.497381i	$-0.834295\pi$
$599$	−42.4648			−1.73506			−0.867532	+	0.497381i	$0.834295\pi$
$600$	−19.7750	+	6.44215i	−0.807312	+	0.263000i
$601$	−24.7522	−	24.7522i	−1.00966	−	1.00966i	−0.999953	−	0.00971030i	$-0.996909\pi$
$601$	−24.7522	−	24.7522i	−1.00966	−	1.00966i	−0.00971030	−	0.999953i	$-0.503091\pi$
$602$	−0.321353	+	0.321353i	−0.0130974	+	0.0130974i
$603$	−1.09517			−0.0445989
$604$		−	35.4679i		−	1.44317i
$605$	1.90611	−	1.16908i	0.0774944	−	0.0475297i
$606$	17.7100	+	17.7100i	0.719420	+	0.719420i
$607$	−18.8240	−	18.8240i	−0.764042	−	0.764042i	0.213008	−	0.977050i	$-0.431674\pi$
$607$	−18.8240	−	18.8240i	−0.764042	−	0.764042i	−0.977050	+	0.213008i	$0.931674\pi$
$608$			3.18005i			0.128968i
$609$	−0.688772	+	0.688772i	−0.0279104	+	0.0279104i
$610$	−12.8138	+	53.4641i	−0.518816	+	2.16470i
$611$	9.47170			0.383184
$612$	−0.907361	+	5.29656i	−0.0366779	+	0.214101i
$613$		−	24.3934i		−	0.985239i	−0.870245	−	0.492620i	$-0.836039\pi$
$613$		−	24.3934i		−	0.985239i	0.870245	−	0.492620i	$-0.163961\pi$
$614$		−	55.9596i		−	2.25835i
$615$	36.8482	−	22.6002i	1.48586	−	0.911327i
$616$	−0.408836			−0.0164725
$617$	−5.37406	−	5.37406i	−0.216351	−	0.216351i	0.590608	−	0.806959i	$-0.298888\pi$
$617$	−5.37406	−	5.37406i	−0.216351	−	0.216351i	−0.806959	+	0.590608i	$0.798888\pi$
$618$	−29.1666	+	29.1666i	−1.17325	+	1.17325i
$619$	9.75599	+	9.75599i	0.392126	+	0.392126i	0.875445	−	0.483318i	$-0.160569\pi$
$619$	9.75599	+	9.75599i	0.392126	+	0.392126i	−0.483318	+	0.875445i	$0.660569\pi$
$620$	29.4370	+	7.05520i	1.18222	+	0.283344i
$621$		−	15.0186i		−	0.602677i
$622$	34.0317	−	34.0317i	1.36455	−	1.36455i
$623$	−1.43205	+	1.43205i	−0.0573740	+	0.0573740i
$624$	−2.30938	+	2.30938i	−0.0924491	+	0.0924491i
$625$	−14.7258	−	20.2027i	−0.589032	−	0.808110i
$626$	−30.3849	+	30.3849i	−1.21443	+	1.21443i
$627$	−0.880211			−0.0351523
$628$		−	32.8933i		−	1.31259i
$629$	14.0323	+	19.8340i	0.559504	+	0.790832i
$630$	0.0921358	−	0.384426i	0.00367078	−	0.0153159i
$631$		−	1.96921i		−	0.0783931i	−0.999232	−	0.0391966i	$-0.987520\pi$
$631$		−	1.96921i		−	0.0783931i	0.999232	−	0.0391966i	$-0.0124799\pi$
$632$	2.34483	+	2.34483i	0.0932724	+	0.0932724i
$633$			51.7123i			2.05538i
$634$	3.05780	−	3.05780i	0.121441	−	0.121441i
$635$	−8.54152	−	13.9264i	−0.338960	−	0.552654i
$636$	15.8419	+	15.8419i	0.628172	+	0.628172i
$637$	−12.4530			−0.493406
$638$	−6.45558			−0.255579
$639$	4.39873	+	4.39873i	0.174011	+	0.174011i
$640$	−18.3510	−	29.9202i	−0.725387	−	1.18270i
$641$	−17.8966	+	17.8966i	−0.706874	+	0.706874i	−0.965877	−	0.259002i	$-0.916606\pi$
$641$	−17.8966	+	17.8966i	−0.706874	+	0.706874i	0.259002	+	0.965877i	$0.416606\pi$
$642$			1.23819i			0.0488674i
$643$	−13.0827	−	13.0827i	−0.515930	−	0.515930i	0.400407	−	0.916337i	$-0.368869\pi$
$643$	−13.0827	−	13.0827i	−0.515930	−	0.515930i	−0.916337	+	0.400407i	$0.868869\pi$
$644$		−	1.72779i		−	0.0680844i
$645$	1.07729	−	4.49487i	0.0424183	−	0.176985i
$646$	0.739704	−	4.31789i	0.0291032	−	0.169885i
$647$		−	4.31276i		−	0.169552i	−0.996400	−	0.0847761i	$-0.972982\pi$
$647$		−	4.31276i		−	0.169552i	0.996400	−	0.0847761i	$-0.0270175\pi$
$648$	−22.7015			−0.891800
$649$	4.90680	−	4.90680i	0.192609	−	0.192609i
$650$	17.8196	+	9.06223i	0.698941	+	0.355450i
$651$	−1.07569	+	1.07569i	−0.0421596	+	0.0421596i
$652$	−11.0349	+	11.0349i	−0.432159	+	0.432159i
$653$	−34.3045	+	34.3045i	−1.34244	+	1.34244i	−0.448812	+	0.893626i	$0.648153\pi$
$653$	−34.3045	+	34.3045i	−1.34244	+	1.34244i	−0.893626	+	0.448812i	$0.851847\pi$
$654$			33.6212i			1.31469i
$655$	1.00336	+	0.240477i	0.0392047	+	0.00939623i
$656$	7.27331	+	7.27331i	0.283975	+	0.283975i
$657$	−1.59203	+	1.59203i	−0.0621110	+	0.0621110i
$658$	−1.52653	−	1.52653i	−0.0595105	−	0.0595105i
$659$	−13.6353			−0.531155			−0.265577	−	0.964090i	$-0.585563\pi$
$659$	−13.6353			−0.531155			−0.265577	+	0.964090i	$0.585563\pi$
$660$	10.6089	−	6.50678i	0.412952	−	0.253276i
$661$			10.0570i			0.391171i	0.980687	+	0.195585i	$0.0626607\pi$
$661$			10.0570i			0.391171i	−0.980687	+	0.195585i	$0.937339\pi$
$662$		−	65.7027i		−	2.55361i
$663$	11.1490	−	7.88778i	0.432991	−	0.306336i
$664$	−2.16808			−0.0841377
$665$	−0.0450879	+	0.188124i	−0.00174843	+	0.00729513i
$666$	4.04439	−	4.04439i	0.156717	−	0.156717i
$667$		−	9.11518i		−	0.352941i
$668$	13.4736	+	13.4736i	0.521311	+	0.521311i
$669$	20.7141	+	20.7141i	0.800852	+	0.800852i
$670$	−10.7608	+	6.59993i	−0.415726	+	0.254978i
$671$		−	10.9918i		−	0.424334i
$672$	2.25961			0.0871665
$673$	25.4348	−	25.4348i	0.980439	−	0.980439i	−0.0193730	−	0.999812i	$-0.506167\pi$
$673$	25.4348	−	25.4348i	0.980439	−	0.980439i	0.999812	+	0.0193730i	$0.00616700\pi$
$674$	9.26732	+	9.26732i	0.356964	+	0.356964i
$675$	−7.36453	−	22.6064i	−0.283461	−	0.870121i
$676$	29.4491			1.13266
$677$	9.68162	+	9.68162i	0.372095	+	0.372095i	0.868240	−	0.496145i	$-0.165252\pi$
$677$	9.68162	+	9.68162i	0.372095	+	0.372095i	−0.496145	+	0.868240i	$0.665252\pi$
$678$	42.6275			1.63710
$679$	0.767170			0.0294413
$680$	7.68576	+	19.2148i	0.294735	+	0.736853i
$681$	18.9952			0.727896
$682$	−10.0820			−0.386059
$683$	23.1752	+	23.1752i	0.886773	+	0.886773i	0.994212	−	0.107438i	$-0.0342648\pi$
$683$	23.1752	+	23.1752i	0.886773	+	0.886773i	−0.107438	+	0.994212i	$0.534265\pi$
$684$	−0.619072			−0.0236708
$685$	33.0423	−	20.2659i	1.26248	−	0.774319i
$686$	4.02361	+	4.02361i	0.153622	+	0.153622i
$687$	24.1179	−	24.1179i	0.920156	−	0.920156i
$688$	1.09986			0.0419319
$689$		−	7.19512i		−	0.274112i
$690$	15.3053	+	24.9544i	0.582664	+	0.949999i
$691$	−18.9479	−	18.9479i	−0.720811	−	0.720811i	0.247960	−	0.968770i	$-0.420240\pi$
$691$	−18.9479	−	18.9479i	−0.720811	−	0.720811i	−0.968770	+	0.247960i	$0.920240\pi$
$692$	−43.8666	−	43.8666i	−1.66756	−	1.66756i
$693$			0.0790349i			0.00300229i
$694$	16.8862	−	16.8862i	0.640992	−	0.640992i
$695$	19.2229	+	4.60719i	0.729168	+	0.174761i
$696$	−12.0046			−0.455033
$697$	−24.8423	−	35.1134i	−0.940971	−	1.33002i
$698$		−	60.0751i		−	2.27388i
$699$		−	7.74896i		−	0.293093i
$700$	−0.847236	−	2.60070i	−0.0320225	−	0.0982974i
$701$	47.6955			1.80143			0.900716	−	0.434408i	$-0.143042\pi$
$701$	47.6955			1.80143			0.900716	+	0.434408i	$0.143042\pi$
$702$	13.4439	+	13.4439i	0.507407	+	0.507407i
$703$	−1.97918	+	1.97918i	−0.0746461	+	0.0746461i
$704$	9.19482	+	9.19482i	0.346543	+	0.346543i
$705$	21.3521	+	5.11749i	0.804168	+	0.192736i
$706$		−	76.3164i		−	2.87221i
$707$	−0.778183	+	0.778183i	−0.0292666	+	0.0292666i
$708$	27.3100	−	27.3100i	1.02637	−	1.02637i
$709$	21.4846	−	21.4846i	0.806870	−	0.806870i	−0.177289	−	0.984159i	$-0.556733\pi$
$709$	21.4846	−	21.4846i	0.806870	−	0.806870i	0.984159	+	0.177289i	$0.0567327\pi$
$710$	69.7290	+	16.7120i	2.61688	+	0.627191i
$711$	0.453295	−	0.453295i	0.0169999	−	0.0169999i
$712$	−24.9592			−0.935387
$713$		−	14.2356i		−	0.533128i
$714$	−3.06812	−	0.525604i	−0.114821	−	0.0196702i
$715$	−3.88683	−	0.931562i	−0.145359	−	0.0348384i
$716$			75.3509i			2.81599i
$717$	7.53969	+	7.53969i	0.281575	+	0.281575i
$718$			32.0203i			1.19499i
$719$	7.48729	−	7.48729i	0.279229	−	0.279229i	−0.553572	−	0.832801i	$-0.686736\pi$
$719$	7.48729	−	7.48729i	0.279229	−	0.279229i	0.832801	+	0.553572i	$0.186736\pi$
$720$	−0.815541	+	0.500197i	−0.0303934	+	0.0186412i
$721$	−1.28159	−	1.28159i	−0.0477288	−	0.0477288i
$722$	−41.9955			−1.56291
$723$	6.72947			0.250272
$724$	−46.2473	−	46.2473i	−1.71877	−	1.71877i
$725$	−4.46971	−	13.7204i	−0.166001	−	0.509562i
$726$	−2.93101	+	2.93101i	−0.108780	+	0.108780i
$727$			23.8371i			0.884070i	0.896998	+	0.442035i	$0.145743\pi$
$727$			23.8371i			0.884070i	−0.896998	+	0.442035i	$0.854257\pi$
$728$	0.516742	+	0.516742i	0.0191517	+	0.0191517i
$729$		−	22.0465i		−	0.816538i
$730$	−6.04857	+	25.2369i	−0.223868	+	0.934061i
$731$	−4.53323	−	0.776594i	−0.167668	−	0.0287234i
$732$		−	61.1776i		−	2.26119i
$733$	4.22484			0.156048			0.0780240	−	0.996951i	$-0.475139\pi$
$733$	4.22484			0.156048			0.0780240	+	0.996951i	$0.475139\pi$
$734$	−10.8663	+	10.8663i	−0.401081	+	0.401081i
$735$	−28.0729	−	6.72827i	−1.03549	−	0.248176i
$736$	−14.9518	+	14.9518i	−0.551132	+	0.551132i
$737$	1.78461	−	1.78461i	0.0657371	−	0.0657371i
$738$	−7.16007	+	7.16007i	−0.263566	+	0.263566i
$739$			10.2720i			0.377862i	0.981990	+	0.188931i	$0.0605023\pi$
$739$			10.2720i			0.377862i	−0.981990	+	0.188931i	$0.939498\pi$
$740$	9.22377	−	38.4851i	0.339073	−	1.41474i
$741$	1.11253	+	1.11253i	0.0408697	+	0.0408697i
$742$	−1.15962	+	1.15962i	−0.0425711	+	0.0425711i
$743$	30.7685	+	30.7685i	1.12879	+	1.12879i	0.990375	+	0.138413i	$0.0442002\pi$
$743$	30.7685	+	30.7685i	1.12879	+	1.12879i	0.138413	+	0.990375i	$0.455800\pi$
$744$	−18.7482			−0.687341
$745$	−8.42972	−	13.7442i	−0.308841	−	0.503547i
$746$		−	21.3086i		−	0.780162i
$747$			0.419125i			0.0153350i
$748$	−7.15232	−	10.1095i	−0.261515	−	0.369639i
$749$	−0.0544064			−0.00198797
$750$	35.2746	+	30.0569i	1.28804	+	1.09752i
$751$	−27.8118	+	27.8118i	−1.01487	+	1.01487i	−0.0149787	+	0.999888i	$0.504768\pi$
$751$	−27.8118	+	27.8118i	−1.01487	+	1.01487i	−0.999888	+	0.0149787i	$0.995232\pi$
$752$			5.22473i			0.190526i
$753$	−26.2117	−	26.2117i	−0.955206	−	0.955206i
$754$	8.15942	+	8.15942i	0.297149	+	0.297149i
$755$	−22.5090	+	13.8055i	−0.819186	+	0.502432i
$756$		−	2.60128i		−	0.0946077i
$757$	25.9161			0.941935			0.470967	−	0.882151i	$-0.343905\pi$
$757$	25.9161			0.941935			0.470967	+	0.882151i	$0.343905\pi$
$758$	19.3261	−	19.3261i	0.701954	−	0.701954i
$759$	−4.13855	−	4.13855i	−0.150220	−	0.150220i
$760$	−2.03232	+	1.24649i	−0.0737201	+	0.0452148i
$761$	51.7561			1.87616			0.938079	−	0.346421i	$-0.112603\pi$
$761$	51.7561			1.87616			0.938079	+	0.346421i	$0.112603\pi$
$762$	21.4146	+	21.4146i	0.775769	+	0.775769i
$763$	−1.47732			−0.0534827
$764$	−72.2117			−2.61253
$765$	3.71454	−	1.48579i	0.134299	−	0.0537187i
$766$	9.89258			0.357433
$767$	−12.4037			−0.447873
$768$	11.9305	+	11.9305i	0.430504	+	0.430504i
$769$	3.60748			0.130089			0.0650445	−	0.997882i	$-0.479281\pi$
$769$	3.60748			0.130089			0.0650445	+	0.997882i	$0.479281\pi$
$770$	0.476295	+	0.776571i	0.0171645	+	0.0279857i
$771$	21.3610	+	21.3610i	0.769298	+	0.769298i
$772$	40.9624	−	40.9624i	1.47427	−	1.47427i
$773$	6.43377			0.231407			0.115703	−	0.993284i	$-0.463088\pi$
$773$	6.43377			0.231407			0.115703	+	0.993284i	$0.463088\pi$
$774$			1.08274i			0.0389183i
$775$	−6.98057	−	21.4278i	−0.250749	−	0.769708i
$776$	6.68550	+	6.68550i	0.239995	+	0.239995i
$777$	1.40632	+	1.40632i	0.0504516	+	0.0504516i
$778$		−	18.5980i		−	0.666770i
$779$	3.50388	−	3.50388i	0.125539	−	0.125539i
$780$	−21.6331	−	5.18484i	−0.774590	−	0.185647i
$781$	−14.3357			−0.512973
$782$	23.7796	−	16.8238i	0.850357	−	0.601617i
$783$		−	13.7234i		−	0.490435i
$784$		−	6.86926i		−	0.245331i
$785$	−20.8751	+	12.8033i	−0.745063	+	0.456971i
$786$	−1.91265			−0.0682218
$787$	6.63959	+	6.63959i	0.236676	+	0.236676i	0.815472	−	0.578796i	$-0.196477\pi$
$787$	6.63959	+	6.63959i	0.236676	+	0.236676i	−0.578796	+	0.815472i	$0.696477\pi$
$788$	−14.3824	+	14.3824i	−0.512351	+	0.512351i
$789$	−17.2467	−	17.2467i	−0.614000	−	0.614000i
$790$	1.72220	−	7.18566i	0.0612730	−	0.255654i
$791$			1.87307i			0.0665986i
$792$	−0.688750	+	0.688750i	−0.0244737	+	0.0244737i
$793$	−13.8929	+	13.8929i	−0.493352	+	0.493352i
$794$	−15.3410	+	15.3410i	−0.544433	+	0.544433i
$795$	3.88747	−	16.2200i	0.137874	−	0.575265i
$796$	16.7375	−	16.7375i	0.593244	−	0.593244i
$797$	−44.3902			−1.57238			−0.786191	−	0.617984i	$-0.787950\pi$
$797$	−44.3902			−1.57238			−0.786191	+	0.617984i	$0.787950\pi$
$798$		−	0.358608i		−	0.0126946i
$799$	3.68908	−	21.5344i	0.130510	−	0.761831i
$800$	−15.1741	+	29.8376i	−0.536484	+	1.05492i
$801$			4.82504i			0.170484i
$802$	−24.1156	−	24.1156i	−0.851550	−	0.851550i
$803$		−	5.18852i		−	0.183099i
$804$	9.93271	−	9.93271i	0.350300	−	0.350300i
$805$	−1.09651	+	0.672521i	−0.0386468	+	0.0237033i
$806$	12.7430	+	12.7430i	0.448852	+	0.448852i
$807$	18.6990			0.658237
$808$	−13.5630			−0.477143
$809$	19.9870	+	19.9870i	0.702704	+	0.702704i	0.964990	−	0.262286i	$-0.0844765\pi$
$809$	19.9870	+	19.9870i	0.702704	+	0.702704i	−0.262286	+	0.964990i	$0.584476\pi$
$810$	26.4473	+	43.1208i	0.929264	+	1.51511i
$811$	−33.8671	+	33.8671i	−1.18924	+	1.18924i	−0.211957	+	0.977279i	$0.567984\pi$
$811$	−33.8671	+	33.8671i	−1.18924	+	1.18924i	−0.977279	+	0.211957i	$0.932016\pi$
$812$		−	1.57878i		−	0.0554043i
$813$	−7.49302	−	7.49302i	−0.262792	−	0.262792i
$814$			13.1809i			0.461991i
$815$	11.2983	+	2.70787i	0.395761	+	0.0948526i
$816$	4.35101	+	6.14995i	0.152316	+	0.215291i
$817$		−	0.529853i		−	0.0185372i
$818$	−50.7346			−1.77389
$819$	0.0998948	−	0.0998948i	0.00349061	−	0.00349061i
$820$	−16.3295	+	68.1329i	−0.570250	+	2.37930i
$821$	17.4823	−	17.4823i	0.610136	−	0.610136i	−0.332845	−	0.942981i	$-0.608009\pi$
$821$	17.4823	−	17.4823i	0.610136	−	0.610136i	0.942981	+	0.332845i	$0.108009\pi$
$822$	−50.8089	+	50.8089i	−1.77216	+	1.77216i
$823$	−17.8633	+	17.8633i	−0.622676	+	0.622676i	−0.946215	−	0.323539i	$-0.895127\pi$
$823$	−17.8633	+	17.8633i	−0.622676	+	0.622676i	0.323539	+	0.946215i	$0.395127\pi$
$824$		−	22.3368i		−	0.778139i
$825$	−8.25880	−	4.20006i	−0.287535	−	0.146227i
$826$	1.99908	+	1.99908i	0.0695571	+	0.0695571i
$827$	−25.8541	+	25.8541i	−0.899036	+	0.899036i	−0.995351	−	0.0963145i	$-0.969295\pi$
$827$	−25.8541	+	25.8541i	−0.899036	+	0.899036i	0.0963145	+	0.995351i	$0.469295\pi$
$828$	−2.91073	−	2.91073i	−0.101155	−	0.101155i
$829$	4.34066			0.150757			0.0753786	−	0.997155i	$-0.475983\pi$
$829$	4.34066			0.150757			0.0753786	+	0.997155i	$0.475983\pi$
$830$	2.52581	+	4.11819i	0.0876722	+	0.142944i
$831$		−	45.6479i		−	1.58351i
$832$		−	23.2433i		−	0.805815i
$833$	−4.85026	+	28.3125i	−0.168051	+	0.980970i
$834$	−36.6434			−1.26886
$835$	3.30632	−	13.7952i	0.114420	−	0.477404i
$836$	1.00880	−	1.00880i	0.0348899	−	0.0348899i
$837$		−	21.4325i		−	0.740817i
$838$	9.51518	+	9.51518i	0.328696	+	0.328696i
$839$	−27.7231	−	27.7231i	−0.957108	−	0.957108i	0.0420094	−	0.999117i	$-0.486624\pi$
$839$	−27.7231	−	27.7231i	−0.957108	−	0.957108i	−0.999117	+	0.0420094i	$0.986624\pi$
$840$	0.885704	+	1.44409i	0.0305597	+	0.0498258i
$841$			20.6709i			0.712791i
$842$	−3.43747			−0.118463
$843$	10.9047	−	10.9047i	0.375579	−	0.375579i
$844$	−59.2666	−	59.2666i	−2.04004	−	2.04004i
$845$	−11.4627	−	18.6893i	−0.394330	−	0.642932i
$846$	−5.14338			−0.176833
$847$	−0.128790	−	0.128790i	−0.00442527	−	0.00442527i
$848$	3.96893			0.136294
$849$	−14.9579			−0.513355
$850$	27.5439	−	36.9841i	0.944747	−	1.26854i
$851$	−18.6112			−0.637985
$852$	−79.7890			−2.73353
$853$	32.1207	+	32.1207i	1.09979	+	1.09979i	0.994434	+	0.105357i	$0.0335984\pi$
$853$	32.1207	+	32.1207i	1.09979	+	1.09979i	0.105357	+	0.994434i	$0.466402\pi$
$854$	4.47818			0.153240
$855$	0.240967	+	0.392882i	0.00824089	+	0.0134363i
$856$	−0.474125	−	0.474125i	−0.0162052	−	0.0162052i
$857$	−30.5999	+	30.5999i	−1.04527	+	1.04527i	−0.0463469	+	0.998925i	$0.514758\pi$
$857$	−30.5999	+	30.5999i	−1.04527	+	1.04527i	−0.998925	+	0.0463469i	$0.985242\pi$
$858$	7.40921			0.252946
$859$		−	19.3281i		−	0.659467i	−0.944074	−	0.329734i	$-0.893041\pi$
$859$		−	19.3281i		−	0.659467i	0.944074	−	0.329734i	$-0.106959\pi$
$860$	3.91683	+	6.38616i	0.133563	+	0.217766i
$861$	−2.48971	−	2.48971i	−0.0848493	−	0.0848493i
$862$	−8.41338	−	8.41338i	−0.286561	−	0.286561i
$863$			40.5781i			1.38129i	0.723192	+	0.690647i	$0.242674\pi$
$863$			40.5781i			1.38129i	−0.723192	+	0.690647i	$0.757326\pi$
$864$	−22.5108	+	22.5108i	−0.765833	+	0.765833i
$865$	−10.7645	+	44.9136i	−0.366004	+	1.52711i
$866$	−72.4464			−2.46183
$867$	−13.5909	−	28.4200i	−0.461571	−	0.965193i
$868$		−	2.46566i		−	0.0836899i
$869$			1.47731i			0.0501145i
$870$	13.9854	+	22.8023i	0.474149	+	0.773071i
$871$	−4.51127			−0.152858
$872$	−12.8741	−	12.8741i	−0.435973	−	0.435973i
$873$	1.29242	−	1.29242i	0.0437418	−	0.0437418i
$874$	2.37290	+	2.37290i	0.0802646	+	0.0802646i
$875$	−1.32071	+	1.54998i	−0.0446481	+	0.0523987i
$876$		−	28.8780i		−	0.975696i
$877$	1.31899	−	1.31899i	0.0445391	−	0.0445391i	−0.684486	−	0.729026i	$-0.739974\pi$
$877$	1.31899	−	1.31899i	0.0445391	−	0.0445391i	0.729026	+	0.684486i	$0.239974\pi$
$878$	−54.3539	+	54.3539i	−1.83435	+	1.83435i
$879$	−21.5042	+	21.5042i	−0.725319	+	0.725319i
$880$	0.513863	−	2.14403i	0.0173223	−	0.0722753i
$881$	23.0269	−	23.0269i	0.775795	−	0.775795i	−0.203317	−	0.979113i	$-0.565172\pi$
$881$	23.0269	−	23.0269i	0.775795	−	0.775795i	0.979113	+	0.203317i	$0.0651723\pi$
$882$	6.76231			0.227699
$883$		−	19.8368i		−	0.667560i	−0.942651	−	0.333780i	$-0.891676\pi$
$883$		−	19.8368i		−	0.667560i	0.942651	−	0.333780i	$-0.108324\pi$
$884$	−3.73763	+	21.8177i	−0.125710	+	0.733810i
$885$	−27.9619	−	6.70165i	−0.939927	−	0.225274i
$886$		−	34.4917i		−	1.15877i
$887$	21.7757	+	21.7757i	0.731156	+	0.731156i	0.970849	−	0.239693i	$-0.0770468\pi$
$887$	21.7757	+	21.7757i	0.731156	+	0.731156i	−0.239693	+	0.970849i	$0.577047\pi$
$888$			24.5108i			0.822530i
$889$	−0.940964	+	0.940964i	−0.0315589	+	0.0315589i
$890$	29.0776	+	47.4092i	0.974682	+	1.58916i
$891$	−7.15133	−	7.15133i	−0.239578	−	0.239578i
$892$	−47.4801			−1.58975
$893$	2.51698			0.0842275
$894$	21.1343	+	21.1343i	0.706837	+	0.706837i
$895$	47.8199	−	29.3295i	1.59844	−	0.980376i
$896$	−2.02161	+	2.02161i	−0.0675373	+	0.0675373i
$897$			10.4617i			0.349306i
$898$	−41.7375	−	41.7375i	−1.39280	−	1.39280i
$899$		−	13.0079i		−	0.433838i
$900$	−5.80860	−	2.95399i	−0.193620	−	0.0984664i
$901$	−16.3584	−	2.80239i	−0.544979	−	0.0933611i
$902$		−	23.3351i		−	0.776974i
$903$	−0.376492			−0.0125289
$904$	−16.3228	+	16.3228i	−0.542890	+	0.542890i
$905$	−11.3487	+	47.3512i	−0.377244	+	1.57401i
$906$	34.6119	−	34.6119i	1.14990	−	1.14990i
$907$	35.4552	−	35.4552i	1.17727	−	1.17727i	0.196834	−	0.980437i	$-0.436934\pi$
$907$	35.4552	−	35.4552i	1.17727	−	1.17727i	0.980437	−	0.196834i	$-0.0630660\pi$
$908$	−21.7700	+	21.7700i	−0.722464	+	0.722464i
$909$			2.62195i			0.0869645i
$910$	0.379529	−	1.58354i	0.0125813	−	0.0524938i
$911$	−16.6662	−	16.6662i	−0.552177	−	0.552177i	0.374891	−	0.927069i	$-0.377680\pi$
$911$	−16.6662	−	16.6662i	−0.552177	−	0.552177i	−0.927069	+	0.374891i	$0.877680\pi$
$912$	−0.613687	+	0.613687i	−0.0203212	+	0.0203212i
$913$	−0.682977	−	0.682977i	−0.0226032	−	0.0226032i
$914$	−46.7083			−1.54497
$915$	−38.8252	+	23.8127i	−1.28352	+	0.787223i
$916$			55.2823i			1.82658i
$917$		−	0.0840423i		−	0.00277532i
$918$	35.8015	−	25.3291i	1.18163	−	0.835986i
$919$	−49.9512			−1.64774			−0.823869	−	0.566780i	$-0.808189\pi$
$919$	−49.9512			−1.64774			−0.823869	+	0.566780i	$0.808189\pi$
$920$	−15.4162	−	3.69482i	−0.508257	−	0.121814i
$921$	32.7808	−	32.7808i	1.08016	−	1.08016i
$922$		−	23.6190i		−	0.777850i
$923$	18.1194	+	18.1194i	0.596407	+	0.596407i
$924$	−0.716810	−	0.716810i	−0.0235813	−	0.0235813i
$925$	−28.0141	+	9.12620i	−0.921097	+	0.300068i
$926$		−	44.5463i		−	1.46388i
$927$	−4.31808			−0.141824
$928$	−13.6624	+	13.6624i	−0.448489	+	0.448489i
$929$	−27.5885	−	27.5885i	−0.905149	−	0.905149i	0.0907270	−	0.995876i	$-0.471081\pi$
$929$	−27.5885	−	27.5885i	−0.905149	−	0.905149i	−0.995876	+	0.0907270i	$0.971081\pi$
$930$	21.8416	+	35.6115i	0.716216	+	1.16775i
$931$	−3.30922			−0.108455
$932$	8.88096	+	8.88096i	0.290906	+	0.290906i
$933$	39.8710			1.30532
$934$	75.6461			2.47522
$935$	−3.63181	+	8.47407i	−0.118773	+	0.277132i
$936$	1.74107			0.0569086
$937$	11.5737			0.378095			0.189048	−	0.981968i	$-0.439460\pi$
$937$	11.5737			0.378095			0.189048	+	0.981968i	$0.439460\pi$
$938$	0.727072	+	0.727072i	0.0237397	+	0.0237397i
$939$	−35.5986			−1.16172
$940$	−30.3364	+	18.6063i	−0.989465	+	0.606870i
$941$	−22.2013	−	22.2013i	−0.723743	−	0.723743i	0.245622	−	0.969366i	$-0.421008\pi$
$941$	−22.2013	−	22.2013i	−0.723743	−	0.723743i	−0.969366	+	0.245622i	$0.921008\pi$
$942$	32.0995	−	32.0995i	1.04586	−	1.04586i
$943$	32.9488			1.07296
$944$		−	6.84208i		−	0.222691i
$945$	−1.65085	+	1.01252i	−0.0537022	+	0.0329372i
$946$	−1.76436	−	1.76436i	−0.0573641	−	0.0573641i
$947$	23.2939	+	23.2939i	0.756949	+	0.756949i	0.975766	−	0.218817i	$-0.0702198\pi$
$947$	23.2939	+	23.2939i	0.756949	+	0.756949i	−0.218817	+	0.975766i	$0.570220\pi$
$948$			8.22236i			0.267050i
$949$	−6.55794	+	6.55794i	−0.212880	+	0.212880i
$950$	4.73532	+	2.40817i	0.153634	+	0.0781313i
$951$	3.58248			0.116170
$952$	1.37610	−	0.973575i	0.0445997	−	0.0315537i
$953$			6.48428i			0.210046i	0.994470	+	0.105023i	$0.0334917\pi$
$953$			6.48428i			0.210046i	−0.994470	+	0.105023i	$0.966508\pi$
$954$			3.90714i			0.126498i
$955$	28.1076	+	45.8277i	0.909540	+	1.48295i
$956$	−17.2822			−0.558947
$957$	−3.78163	−	3.78163i	−0.122243	−	0.122243i
$958$	10.1953	−	10.1953i	0.329397	−	0.329397i
$959$	−2.23256	−	2.23256i	−0.0720931	−	0.0720931i
$960$	12.5582	−	52.3975i	0.405313	−	1.69112i
$961$			10.6849i			0.344674i
$962$	16.6598	−	16.6598i	0.537133	−	0.537133i
$963$	−0.0916562	+	0.0916562i	−0.00295358	+	0.00295358i
$964$	−7.71253	+	7.71253i	−0.248404	+	0.248404i
$965$	−41.9401	−	10.0518i	−1.35010	−	0.323580i
$966$	1.68609	−	1.68609i	0.0542490	−	0.0542490i
$967$	54.0337			1.73761			0.868803	−	0.495157i	$-0.164890\pi$
$967$	54.0337			1.73761			0.868803	+	0.495157i	$0.164890\pi$
$968$		−	2.24467i		−	0.0721466i
$969$	2.96270	−	2.09607i	0.0951757	−	0.0673356i
$970$	4.91026	−	20.4875i	0.157659	−	0.657814i
$971$			29.6420i			0.951256i	0.879647	+	0.475628i	$0.157779\pi$
$971$			29.6420i			0.951256i	−0.879647	+	0.475628i	$0.842221\pi$
$972$	−9.50560	−	9.50560i	−0.304892	−	0.304892i
$973$		−	1.61012i		−	0.0516182i
$974$	2.92604	−	2.92604i	0.0937565	−	0.0937565i
$975$	5.12999	+	15.7472i	0.164291	+	0.504313i
$976$	−7.66353	−	7.66353i	−0.245304	−	0.245304i
$977$	−4.20696			−0.134593			−0.0672963	−	0.997733i	$-0.521437\pi$
$977$	−4.20696			−0.134593			−0.0672963	+	0.997733i	$0.521437\pi$
$978$	−21.5371			−0.688682
$979$	−7.86254	−	7.86254i	−0.251288	−	0.251288i
$980$	39.8851	−	24.4628i	1.27408	−	0.781434i
$981$	−2.48879	+	2.48879i	−0.0794608	+	0.0794608i
$982$			94.2966i			3.00912i
$983$	28.3749	+	28.3749i	0.905019	+	0.905019i	0.995865	−	0.0908457i	$-0.0289570\pi$
$983$	28.3749	+	28.3749i	0.905019	+	0.905019i	−0.0908457	+	0.995865i	$0.528957\pi$
$984$		−	43.3932i		−	1.38333i
$985$	14.7257	+	3.52932i	0.469199	+	0.112453i
$986$	21.7288	−	15.3729i	0.691986	−	0.489572i
$987$		−	1.78847i		−	0.0569275i
$988$	−2.55010			−0.0811295
$989$	2.49124	−	2.49124i	0.0792169	−	0.0792169i
$990$	2.11065	+	0.505862i	0.0670809	+	0.0160774i
$991$	−38.1502	+	38.1502i	−1.21188	+	1.21188i	−0.241473	+	0.970408i	$0.577630\pi$
$991$	−38.1502	+	38.1502i	−1.21188	+	1.21188i	−0.970408	+	0.241473i	$0.922370\pi$
$992$	−21.3372	+	21.3372i	−0.677456	+	0.677456i
$993$	38.4881	−	38.4881i	1.22138	−	1.22138i
$994$		−	5.84053i		−	0.185250i
$995$	−17.1370	−	4.10724i	−0.543279	−	0.130208i
$996$	−3.80127	−	3.80127i	−0.120448	−	0.120448i
$997$	−30.9336	+	30.9336i	−0.979677	+	0.979677i	−0.999798	−	0.0201203i	$-0.993595\pi$
$997$	−30.9336	+	30.9336i	−0.979677	+	0.979677i	0.0201203	+	0.999798i	$0.493595\pi$
$998$	5.00707	+	5.00707i	0.158496	+	0.158496i
$999$	−28.0203			−0.886523

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	935.2.s.a.89.12	✓	176
5.4	even	2	inner	935.2.s.a.89.77	yes	176
17.13	even	4	inner	935.2.s.a.914.77	yes	176
85.64	even	4	inner	935.2.s.a.914.12	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
935.2.s.a.89.12	✓	176	1.1	even	1	trivial
935.2.s.a.89.77	yes	176	5.4	even	2	inner
935.2.s.a.914.12	yes	176	85.64	even	4	inner
935.2.s.a.914.77	yes	176	17.13	even	4	inner

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:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.23685 q^{2} +(-1.31033 - 1.31033i) q^{3} +3.00350 q^{4} +(-1.16908 - 1.90611i) q^{5} +(2.93101 + 2.93101i) q^{6} +(-0.128790 + 0.128790i) q^{7} -2.24467 q^{8} +0.433933i q^{9} +O(q^{10})\)	\(q-2.23685 q^{2} +(-1.31033 - 1.31033i) q^{3} +3.00350 q^{4} +(-1.16908 - 1.90611i) q^{5} +(2.93101 + 2.93101i) q^{6} +(-0.128790 + 0.128790i) q^{7} -2.24467 q^{8} +0.433933i q^{9} +(2.61505 + 4.26368i) q^{10} +(-0.707107 - 0.707107i) q^{11} +(-3.93558 - 3.93558i) q^{12} +1.78747i q^{13} +(0.288083 - 0.288083i) q^{14} +(-0.965758 + 4.02951i) q^{15} -0.985995 q^{16} +(4.06390 + 0.696193i) q^{17} -0.970644i q^{18} +0.474997i q^{19} +(-3.51132 - 5.72500i) q^{20} +0.337514 q^{21} +(1.58169 + 1.58169i) q^{22} +(-2.23332 + 2.23332i) q^{23} +(2.94127 + 2.94127i) q^{24} +(-2.26652 + 4.45678i) q^{25} -3.99831i q^{26} +(-3.36240 + 3.36240i) q^{27} +(-0.386820 + 0.386820i) q^{28} +(-2.04072 + 2.04072i) q^{29} +(2.16026 - 9.01342i) q^{30} +(-3.18709 + 3.18709i) q^{31} +6.69487 q^{32} +1.85309i q^{33} +(-9.09034 - 1.55728i) q^{34} +(0.396052 + 0.0949224i) q^{35} +1.30332i q^{36} +(4.16671 + 4.16671i) q^{37} -1.06250i q^{38} +(2.34218 - 2.34218i) q^{39} +(2.62420 + 4.27860i) q^{40} +(-7.37662 - 7.37662i) q^{41} -0.754968 q^{42} -1.11549 q^{43} +(-2.12379 - 2.12379i) q^{44} +(0.827125 - 0.507301i) q^{45} +(4.99561 - 4.99561i) q^{46} -5.29894i q^{47} +(1.29198 + 1.29198i) q^{48} +6.96683i q^{49} +(5.06986 - 9.96915i) q^{50} +(-4.41281 - 6.23730i) q^{51} +5.36867i q^{52} -4.02530 q^{53} +(7.52118 - 7.52118i) q^{54} +(-0.521162 + 2.17449i) q^{55} +(0.289091 - 0.289091i) q^{56} +(0.622403 - 0.622403i) q^{57} +(4.56478 - 4.56478i) q^{58} +6.93926i q^{59} +(-2.90065 + 12.1026i) q^{60} +(7.77238 + 7.77238i) q^{61} +(7.12905 - 7.12905i) q^{62} +(-0.0558861 - 0.0558861i) q^{63} -13.0034 q^{64} +(3.40712 - 2.08969i) q^{65} -4.14508i q^{66} +2.52383i q^{67} +(12.2059 + 2.09102i) q^{68} +5.85279 q^{69} +(-0.885910 - 0.212327i) q^{70} +(10.1369 - 10.1369i) q^{71} -0.974039i q^{72} +(3.66883 + 3.66883i) q^{73} +(-9.32031 - 9.32031i) q^{74} +(8.80975 - 2.86997i) q^{75} +1.42665i q^{76} +0.182136 q^{77} +(-5.23910 + 5.23910i) q^{78} +(-1.04462 - 1.04462i) q^{79} +(1.15270 + 1.87942i) q^{80} +10.1135 q^{81} +(16.5004 + 16.5004i) q^{82} +0.965875 q^{83} +1.01372 q^{84} +(-3.42399 - 8.56016i) q^{85} +2.49518 q^{86} +5.34803 q^{87} +(1.58722 + 1.58722i) q^{88} +11.1193 q^{89} +(-1.85015 + 1.13476i) q^{90} +(-0.230208 - 0.230208i) q^{91} +(-6.70779 + 6.70779i) q^{92} +8.35229 q^{93} +11.8529i q^{94} +(0.905397 - 0.555308i) q^{95} +(-8.77250 - 8.77250i) q^{96} +(-2.97838 - 2.97838i) q^{97} -15.5837i q^{98} +(0.306837 - 0.306837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 168 q^{4} + 4 q^{5} + 8 q^{6}+O(q^{10}) \) 176 * q + 168 * q^4 + 4 * q^5 + 8 * q^6	\( 176 q + 168 q^{4} + 4 q^{5} + 8 q^{6} - 8 q^{10} - 8 q^{14} + 136 q^{16} + 8 q^{20} - 48 q^{21} + 8 q^{24} - 104 q^{30} - 24 q^{31} - 24 q^{34} - 64 q^{35} - 16 q^{39} - 56 q^{40} - 16 q^{41} - 8 q^{44} + 12 q^{45} + 40 q^{46} + 24 q^{50} - 136 q^{54} - 24 q^{56} + 72 q^{61} + 88 q^{64} - 16 q^{65} + 160 q^{69} + 32 q^{71} + 32 q^{74} - 120 q^{75} + 32 q^{79} - 4 q^{80} - 112 q^{81} - 192 q^{84} + 84 q^{85} - 144 q^{86} - 48 q^{89} + 108 q^{90} + 16 q^{91} + 100 q^{95} - 72 q^{96}+O(q^{100}) \) 176 * q + 168 * q^4 + 4 * q^5 + 8 * q^6 - 8 * q^10 - 8 * q^14 + 136 * q^16 + 8 * q^20 - 48 * q^21 + 8 * q^24 - 104 * q^30 - 24 * q^31 - 24 * q^34 - 64 * q^35 - 16 * q^39 - 56 * q^40 - 16 * q^41 - 8 * q^44 + 12 * q^45 + 40 * q^46 + 24 * q^50 - 136 * q^54 - 24 * q^56 + 72 * q^61 + 88 * q^64 - 16 * q^65 + 160 * q^69 + 32 * q^71 + 32 * q^74 - 120 * q^75 + 32 * q^79 - 4 * q^80 - 112 * q^81 - 192 * q^84 + 84 * q^85 - 144 * q^86 - 48 * q^89 + 108 * q^90 + 16 * q^91 + 100 * q^95 - 72 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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