LMFDB - Embedded newform 91.2.i.a.83.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(34,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("91.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.i (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:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 35x^{8} + 295x^{4} + 169 $ x^12 + 35x^8 + 295x^4 + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			83.6
Root			$1.33026 + 1.33026i$ of defining polynomial
Character	$\chi$	$=$	91.83
Dual form			91.2.i.a.34.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.854638 - 0.854638i) q^{2} +2.27378i q^{3} +0.539189i q^{4} +(-0.612999 - 0.612999i) q^{5} +(1.94326 + 1.94326i) q^{6} +(0.0148122 - 2.64571i) q^{7} +(2.17009 + 2.17009i) q^{8} -2.17009 q^{9} +O(q^{10})$	\(q+(0.854638 - 0.854638i) q^{2} +2.27378i q^{3} +0.539189i q^{4} +(-0.612999 - 0.612999i) q^{5} +(1.94326 + 1.94326i) q^{6} +(0.0148122 - 2.64571i) q^{7} +(2.17009 + 2.17009i) q^{8} -2.17009 q^{9} -1.04778 q^{10} +(-1.85464 - 1.85464i) q^{11} -1.22600 q^{12} +(-0.104263 - 3.60404i) q^{13} +(-2.24846 - 2.27378i) q^{14} +(1.39383 - 1.39383i) q^{15} +2.63090 q^{16} -3.04726 q^{17} +(-1.85464 + 1.85464i) q^{18} +(0.104263 + 0.104263i) q^{19} +(0.330522 - 0.330522i) q^{20} +(6.01577 + 0.0336798i) q^{21} -3.17009 q^{22} +6.51026i q^{23} +(-4.93430 + 4.93430i) q^{24} -4.24846i q^{25} +(-3.16926 - 2.99104i) q^{26} +1.88704i q^{27} +(1.42654 + 0.00798659i) q^{28} -3.78765 q^{29} -2.38243i q^{30} +(6.77330 + 6.77330i) q^{31} +(-2.09171 + 2.09171i) q^{32} +(4.21704 - 4.21704i) q^{33} +(-2.60430 + 2.60430i) q^{34} +(-1.63090 + 1.61274i) q^{35} -1.17009i q^{36} +(-2.02472 - 2.02472i) q^{37} +0.178214 q^{38} +(8.19481 - 0.237071i) q^{39} -2.66052i q^{40} +(-2.27378 - 2.27378i) q^{41} +(5.17009 - 5.11252i) q^{42} -3.18342i q^{43} +(1.00000 - 1.00000i) q^{44} +(1.33026 + 1.33026i) q^{45} +(5.56391 + 5.56391i) q^{46} +(5.21678 - 5.21678i) q^{47} +5.98209i q^{48} +(-6.99956 - 0.0783777i) q^{49} +(-3.63090 - 3.63090i) q^{50} -6.92881i q^{51} +(1.94326 - 0.0562174i) q^{52} +3.43188 q^{53} +(1.61274 + 1.61274i) q^{54} +2.27378i q^{55} +(5.77356 - 5.70928i) q^{56} +(-0.237071 + 0.237071i) q^{57} +(-3.23707 + 3.23707i) q^{58} +(-9.15135 + 9.15135i) q^{59} +(0.751536 + 0.751536i) q^{60} +9.20756i q^{61} +11.5774 q^{62} +(-0.0321438 + 5.74142i) q^{63} +8.83710i q^{64} +(-2.14536 + 2.27319i) q^{65} -7.20809i q^{66} +(-1.04945 + 1.04945i) q^{67} -1.64305i q^{68} -14.8029 q^{69} +(-0.0155200 + 2.77213i) q^{70} +(-4.10310 + 4.10310i) q^{71} +(-4.70928 - 4.70928i) q^{72} +(6.92561 - 6.92561i) q^{73} -3.46081 q^{74} +9.66008 q^{75} +(-0.0562174 + 0.0562174i) q^{76} +(-4.93430 + 4.87936i) q^{77} +(6.80098 - 7.20620i) q^{78} +17.5958 q^{79} +(-1.61274 - 1.61274i) q^{80} -10.8010 q^{81} -3.88652 q^{82} +(-10.5474 - 10.5474i) q^{83} +(-0.0181598 + 3.24364i) q^{84} +(1.86797 + 1.86797i) q^{85} +(-2.72067 - 2.72067i) q^{86} -8.61230i q^{87} -8.04945i q^{88} +(3.39552 - 3.39552i) q^{89} +2.27378 q^{90} +(-9.53680 + 0.222465i) q^{91} -3.51026 q^{92} +(-15.4010 + 15.4010i) q^{93} -8.91692i q^{94} -0.127826i q^{95} +(-4.75609 - 4.75609i) q^{96} +(4.44330 + 4.44330i) q^{97} +(-6.04907 + 5.91510i) q^{98} +(4.02472 + 4.02472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 8 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 - 8 * q^7 + 4 * q^8 - 4 * q^9	$ 12 q - 4 q^{2} - 8 q^{7} + 4 q^{8} - 4 q^{9} - 8 q^{11} + 8 q^{14} - 4 q^{15} + 16 q^{16} - 8 q^{18} - 16 q^{22} - 20 q^{28} - 4 q^{29} - 16 q^{32} - 4 q^{35} + 12 q^{37} + 40 q^{39} + 40 q^{42} + 12 q^{44} + 24 q^{46} - 28 q^{50} - 12 q^{53} - 8 q^{57} - 44 q^{58} + 44 q^{60} + 20 q^{63} - 40 q^{65} + 60 q^{67} + 4 q^{70} - 28 q^{72} - 48 q^{74} + 44 q^{78} - 4 q^{79} - 92 q^{81} - 4 q^{84} + 12 q^{85} + 36 q^{86} - 32 q^{91} + 24 q^{92} - 28 q^{93} - 28 q^{98} + 12 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 - 8 * q^7 + 4 * q^8 - 4 * q^9 - 8 * q^11 + 8 * q^14 - 4 * q^15 + 16 * q^16 - 8 * q^18 - 16 * q^22 - 20 * q^28 - 4 * q^29 - 16 * q^32 - 4 * q^35 + 12 * q^37 + 40 * q^39 + 40 * q^42 + 12 * q^44 + 24 * q^46 - 28 * q^50 - 12 * q^53 - 8 * q^57 - 44 * q^58 + 44 * q^60 + 20 * q^63 - 40 * q^65 + 60 * q^67 + 4 * q^70 - 28 * q^72 - 48 * q^74 + 44 * q^78 - 4 * q^79 - 92 * q^81 - 4 * q^84 + 12 * q^85 + 36 * q^86 - 32 * q^91 + 24 * q^92 - 28 * q^93 - 28 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.854638	−	0.854638i	0.604320	−	0.604320i	−0.337136	−	0.941456i	$-0.609458\pi$
$2$	0.854638	−	0.854638i	0.604320	−	0.604320i	0.941456	+	0.337136i	$0.109458\pi$
$3$			2.27378i			1.31277i	0.754427	+	0.656384i	$0.227915\pi$
$3$			2.27378i			1.31277i	−0.754427	+	0.656384i	$0.772085\pi$
$4$			0.539189i			0.269594i
$5$	−0.612999	−	0.612999i	−0.274142	−	0.274142i	0.556623	−	0.830765i	$-0.312097\pi$
$5$	−0.612999	−	0.612999i	−0.274142	−	0.274142i	−0.830765	+	0.556623i	$0.812097\pi$
$6$	1.94326	+	1.94326i	0.793333	+	0.793333i
$7$	0.0148122	−	2.64571i	0.00559850	−	0.999984i
$7$	0.0148122	−	2.64571i	0.00559850	−	0.999984i
$8$	2.17009	+	2.17009i	0.767241	+	0.767241i
$9$	−2.17009			−0.723362
$10$	−1.04778			−0.331338
$11$	−1.85464	−	1.85464i	−0.559194	−	0.559194i	0.369884	−	0.929078i	$-0.379398\pi$
$11$	−1.85464	−	1.85464i	−0.559194	−	0.559194i	−0.929078	+	0.369884i	$0.879398\pi$
$12$	−1.22600			−0.353915
$13$	−0.104263	−	3.60404i	−0.0289173	−	0.999582i
$13$	−0.104263	−	3.60404i	−0.0289173	−	0.999582i
$14$	−2.24846	−	2.27378i	−0.600927	−	0.607694i
$15$	1.39383	−	1.39383i	0.359884	−	0.359884i
$16$	2.63090			0.657724
$17$	−3.04726			−0.739070			−0.369535	−	0.929217i	$-0.620483\pi$
$17$	−3.04726			−0.739070			−0.369535	+	0.929217i	$0.620483\pi$
$18$	−1.85464	+	1.85464i	−0.437142	+	0.437142i
$19$	0.104263	+	0.104263i	0.0239195	+	0.0239195i	0.718965	−	0.695046i	$-0.244616\pi$
$19$	0.104263	+	0.104263i	0.0239195	+	0.0239195i	−0.695046	+	0.718965i	$0.744616\pi$
$20$	0.330522	−	0.330522i	0.0739070	−	0.0739070i
$21$	6.01577	+	0.0336798i	1.31275	+	0.00734953i
$22$	−3.17009			−0.675865
$23$			6.51026i			1.35748i	0.734377	+	0.678741i	$0.237474\pi$
$23$			6.51026i			1.35748i	−0.734377	+	0.678741i	$0.762526\pi$
$24$	−4.93430	+	4.93430i	−1.00721	+	1.00721i
$25$		−	4.24846i		−	0.849693i
$26$	−3.16926	−	2.99104i	−0.621543	−	0.586592i
$27$			1.88704i			0.363162i
$28$	1.42654	+	0.00798659i	0.269590	+	0.00150932i
$29$	−3.78765			−0.703350			−0.351675	−	0.936122i	$-0.614388\pi$
$29$	−3.78765			−0.703350			−0.351675	+	0.936122i	$0.614388\pi$
$30$		−	2.38243i		−	0.434971i
$31$	6.77330	+	6.77330i	1.21652	+	1.21652i	0.968842	+	0.247679i	$0.0796677\pi$
$31$	6.77330	+	6.77330i	1.21652	+	1.21652i	0.247679	+	0.968842i	$0.420332\pi$
$32$	−2.09171	+	2.09171i	−0.369765	+	0.369765i
$33$	4.21704	−	4.21704i	0.734093	−	0.734093i
$34$	−2.60430	+	2.60430i	−0.446635	+	0.446635i
$35$	−1.63090	+	1.61274i	−0.275672	+	0.272602i
$36$		−	1.17009i		−	0.195014i
$37$	−2.02472	−	2.02472i	−0.332863	−	0.332863i	0.520810	−	0.853673i	$-0.325630\pi$
$37$	−2.02472	−	2.02472i	−0.332863	−	0.332863i	−0.853673	+	0.520810i	$0.825630\pi$
$38$	0.178214			0.0289101
$39$	8.19481	−	0.237071i	1.31222	−	0.0379618i
$40$		−	2.66052i		−	0.420665i
$41$	−2.27378	−	2.27378i	−0.355105	−	0.355105i	0.506900	−	0.862005i	$-0.330791\pi$
$41$	−2.27378	−	2.27378i	−0.355105	−	0.355105i	−0.862005	+	0.506900i	$0.830791\pi$
$42$	5.17009	−	5.11252i	0.797762	−	0.788879i
$43$		−	3.18342i		−	0.485467i	−0.970093	−	0.242733i	$-0.921956\pi$
$43$		−	3.18342i		−	0.485467i	0.970093	−	0.242733i	$-0.0780440\pi$
$44$	1.00000	−	1.00000i	0.150756	−	0.150756i
$45$	1.33026	+	1.33026i	0.198304	+	0.198304i
$46$	5.56391	+	5.56391i	0.820354	+	0.820354i
$47$	5.21678	−	5.21678i	0.760946	−	0.760946i	−0.215548	−	0.976493i	$-0.569154\pi$
$47$	5.21678	−	5.21678i	0.760946	−	0.760946i	0.976493	+	0.215548i	$0.0691536\pi$
$48$			5.98209i			0.863440i
$49$	−6.99956	−	0.0783777i	−0.999937	−	0.0111968i
$50$	−3.63090	−	3.63090i	−0.513486	−	0.513486i
$51$		−	6.92881i		−	0.970227i
$52$	1.94326	−	0.0562174i	0.269482	−	0.00779595i
$53$	3.43188			0.471405			0.235703	−	0.971825i	$-0.424261\pi$
$53$	3.43188			0.471405			0.235703	+	0.971825i	$0.424261\pi$
$54$	1.61274	+	1.61274i	0.219466	+	0.219466i
$55$			2.27378i			0.306597i
$56$	5.77356	−	5.70928i	0.771525	−	0.762934i
$57$	−0.237071	+	0.237071i	−0.0314008	+	0.0314008i
$58$	−3.23707	+	3.23707i	−0.425048	+	0.425048i
$59$	−9.15135	+	9.15135i	−1.19140	+	1.19140i	−0.214731	+	0.976673i	$0.568887\pi$
$59$	−9.15135	+	9.15135i	−1.19140	+	1.19140i	−0.976673	+	0.214731i	$0.931113\pi$
$60$	0.751536	+	0.751536i	0.0970229	+	0.0970229i
$61$			9.20756i			1.17891i	0.807802	+	0.589454i	$0.200657\pi$
$61$			9.20756i			1.17891i	−0.807802	+	0.589454i	$0.799343\pi$
$62$	11.5774			1.47034
$63$	−0.0321438	+	5.74142i	−0.00404974	+	0.723351i
$64$			8.83710i			1.10464i
$65$	−2.14536	+	2.27319i	−0.266099	+	0.281954i
$66$		−	7.20809i		−	0.887254i
$67$	−1.04945	+	1.04945i	−0.128211	+	0.128211i	−0.768300	−	0.640090i	$-0.778897\pi$
$67$	−1.04945	+	1.04945i	−0.128211	+	0.128211i	0.640090	+	0.768300i	$0.278897\pi$
$68$		−	1.64305i		−	0.199249i
$69$	−14.8029			−1.78206
$70$	−0.0155200	+	2.77213i	−0.00185500	+	0.331333i
$71$	−4.10310	+	4.10310i	−0.486949	+	0.486949i	−0.907342	−	0.420393i	$-0.861892\pi$
$71$	−4.10310	+	4.10310i	−0.486949	+	0.486949i	0.420393	+	0.907342i	$0.361892\pi$
$72$	−4.70928	−	4.70928i	−0.554993	−	0.554993i
$73$	6.92561	−	6.92561i	0.810581	−	0.810581i	−0.174140	−	0.984721i	$-0.555714\pi$
$73$	6.92561	−	6.92561i	0.810581	−	0.810581i	0.984721	+	0.174140i	$0.0557144\pi$
$74$	−3.46081			−0.402311
$75$	9.66008			1.11545
$76$	−0.0562174	+	0.0562174i	−0.00644858	+	0.00644858i
$77$	−4.93430	+	4.87936i	−0.562316	+	0.556055i
$78$	6.80098	−	7.20620i	0.770060	−	0.815942i
$79$	17.5958			1.97968			0.989842	−	0.142168i	$-0.0454074\pi$
$79$	17.5958			1.97968			0.989842	+	0.142168i	$0.0454074\pi$
$80$	−1.61274	−	1.61274i	−0.180310	−	0.180310i
$81$	−10.8010			−1.20011
$82$	−3.88652			−0.429194
$83$	−10.5474	−	10.5474i	−1.15773	−	1.15773i	−0.984963	−	0.172763i	$-0.944731\pi$
$83$	−10.5474	−	10.5474i	−1.15773	−	1.15773i	−0.172763	−	0.984963i	$-0.555269\pi$
$84$	−0.0181598	+	3.24364i	−0.00198139	+	0.353910i
$85$	1.86797	+	1.86797i	0.202610	+	0.202610i
$86$	−2.72067	−	2.72067i	−0.293377	−	0.293377i
$87$		−	8.61230i		−	0.923335i
$88$		−	8.04945i		−	0.858074i
$89$	3.39552	−	3.39552i	0.359924	−	0.359924i	−0.503861	−	0.863785i	$-0.668088\pi$
$89$	3.39552	−	3.39552i	0.359924	−	0.359924i	0.863785	+	0.503861i	$0.168088\pi$
$90$	2.27378			0.239678
$91$	−9.53680	+	0.222465i	−0.999728	+	0.0233207i
$92$	−3.51026			−0.365970
$93$	−15.4010	+	15.4010i	−1.59701	+	1.59701i
$94$		−	8.91692i		−	0.919710i
$95$		−	0.127826i		−	0.0131147i
$96$	−4.75609	−	4.75609i	−0.485416	−	0.485416i
$97$	4.44330	+	4.44330i	0.451149	+	0.451149i	0.895736	−	0.444587i	$-0.146649\pi$
$97$	4.44330	+	4.44330i	0.451149	+	0.451149i	−0.444587	+	0.895736i	$0.646649\pi$
$98$	−6.04907	+	5.91510i	−0.611049	+	0.597516i
$99$	4.02472	+	4.02472i	0.404500	+	0.404500i
$100$	2.29072			0.229072
$101$	1.16022			0.115446			0.0577231	−	0.998333i	$-0.481616\pi$
$101$	1.16022			0.115446			0.0577231	+	0.998333i	$0.481616\pi$
$102$	−5.92162	−	5.92162i	−0.586328	−	0.586328i
$103$	−5.32104			−0.524298			−0.262149	−	0.965027i	$-0.584431\pi$
$103$	−5.32104			−0.524298			−0.262149	+	0.965027i	$0.584431\pi$
$104$	7.59483	−	8.04735i	0.744734	−	0.789107i
$105$	−3.66701	−	3.70831i	−0.357864	−	0.361894i
$106$	2.93302	−	2.93302i	0.284880	−	0.284880i
$107$	10.2485			0.990756			0.495378	−	0.868677i	$-0.335029\pi$
$107$	10.2485			0.990756			0.495378	+	0.868677i	$0.335029\pi$
$108$	−1.01747			−0.0979063
$109$	−5.85464	+	5.85464i	−0.560773	+	0.560773i	−0.929527	−	0.368754i	$-0.879784\pi$
$109$	−5.85464	+	5.85464i	−0.560773	+	0.560773i	0.368754	+	0.929527i	$0.379784\pi$
$110$	1.94326	+	1.94326i	0.185283	+	0.185283i
$111$	4.60378	−	4.60378i	0.436972	−	0.436972i
$112$	0.0389695	−	6.96059i	0.00368227	−	0.657714i
$113$	5.74539			0.540481			0.270241	−	0.962793i	$-0.412897\pi$
$113$	5.74539			0.540481			0.270241	+	0.962793i	$0.412897\pi$
$114$			0.405220i			0.0379523i
$115$	3.99078	−	3.99078i	0.372142	−	0.372142i
$116$		−	2.04226i		−	0.189619i
$117$	0.226259	+	7.82109i	0.0209177	+	0.723060i
$118$			15.6422i			1.43998i
$119$	−0.0451368	+	8.06217i	−0.00413768	+	0.739058i
$120$	6.04945			0.552237
$121$		−	4.12064i		−	0.374603i
$122$	7.86913	+	7.86913i	0.712438	+	0.712438i
$123$	5.17009	−	5.17009i	0.466171	−	0.466171i
$124$	−3.65209	+	3.65209i	−0.327967	+	0.327967i
$125$	−5.66930	+	5.66930i	−0.507078	+	0.507078i
$126$	4.87936	+	4.93430i	0.434688	+	0.439583i
$127$		−	7.37629i		−	0.654540i	−0.944931	−	0.327270i	$-0.893871\pi$
$127$		−	7.37629i		−	0.654540i	0.944931	−	0.327270i	$-0.106129\pi$
$128$	3.36910	+	3.36910i	0.297789	+	0.297789i
$129$	7.23840			0.637305
$130$	0.109245	+	3.77626i	0.00958142	+	0.331200i
$131$			11.9642i			1.04532i	0.852543	+	0.522658i	$0.175059\pi$
$131$			11.9642i			1.04532i	−0.852543	+	0.522658i	$0.824941\pi$
$132$	2.27378	+	2.27378i	0.197907	+	0.197907i
$133$	0.277394	−	0.274305i	0.0240531	−	0.0237853i
$134$			1.79380i			0.154960i
$135$	1.15676	−	1.15676i	0.0995577	−	0.0995577i
$136$	−6.61282	−	6.61282i	−0.567045	−	0.567045i
$137$	1.88357	+	1.88357i	0.160924	+	0.160924i	0.782976	−	0.622052i	$-0.213701\pi$
$137$	1.88357	+	1.88357i	0.160924	+	0.160924i	−0.622052	+	0.782976i	$0.713701\pi$
$138$	−12.6511	+	12.6511i	−1.07694	+	1.07694i
$139$		−	6.36883i		−	0.540197i	−0.962833	−	0.270098i	$-0.912944\pi$
$139$		−	6.36883i		−	0.540197i	0.962833	−	0.270098i	$-0.0870563\pi$
$140$	−0.869570	−	0.879362i	−0.0734921	−	0.0743196i
$141$	11.8618	+	11.8618i	0.998946	+	0.998946i
$142$			7.01333i			0.588546i
$143$	−6.49082	+	6.87756i	−0.542790	+	0.575131i
$144$	−5.70928			−0.475773
$145$	2.32183	+	2.32183i	0.192817	+	0.192817i
$146$		−	11.8378i		−	0.979701i
$147$	0.178214	−	15.9155i	0.0146988	−	1.31269i
$148$	1.09171	−	1.09171i	0.0897379	−	0.0897379i
$149$	13.3360	−	13.3360i	1.09253	−	1.09253i	0.0972667	−	0.995258i	$-0.468990\pi$
$149$	13.3360	−	13.3360i	1.09253	−	1.09253i	0.995258	−	0.0972667i	$-0.0310100\pi$
$150$	8.25587	−	8.25587i	0.674089	−	0.674089i
$151$	7.64229	+	7.64229i	0.621921	+	0.621921i	0.946022	−	0.324102i	$-0.105062\pi$
$151$	7.64229	+	7.64229i	0.621921	+	0.621921i	−0.324102	+	0.946022i	$0.605062\pi$
$152$			0.452519i			0.0367041i
$153$	6.61282			0.534615
$154$	−0.0469561	+	8.38713i	−0.00378383	+	0.675854i
$155$		−	8.30406i		−	0.666998i
$156$	0.127826	+	4.41855i	0.0102343	+	0.353767i
$157$		−	21.0290i		−	1.67830i	−0.543903	−	0.839148i	$-0.683054\pi$
$157$		−	21.0290i		−	1.67830i	0.543903	−	0.839148i	$-0.316946\pi$
$158$	15.0381	−	15.0381i	1.19636	−	1.19636i
$159$			7.80335i			0.618846i
$160$	2.56443			0.202736
$161$	17.2243	+	0.0964315i	1.35746	+	0.00759987i
$162$	−9.23093	+	9.23093i	−0.725250	+	0.725250i
$163$	−7.03612	−	7.03612i	−0.551111	−	0.551111i	0.375650	−	0.926762i	$-0.377419\pi$
$163$	−7.03612	−	7.03612i	−0.551111	−	0.551111i	−0.926762	+	0.375650i	$0.877419\pi$
$164$	1.22600	−	1.22600i	0.0957344	−	0.0957344i
$165$	−5.17009			−0.402491
$166$	−18.0284			−1.39927
$167$	12.0684	−	12.0684i	0.933884	−	0.933884i	−0.0640620	−	0.997946i	$-0.520406\pi$
$167$	12.0684	−	12.0684i	0.933884	−	0.933884i	0.997946	+	0.0640620i	$0.0204055\pi$
$168$	12.9816	+	13.1278i	1.00156	+	1.01283i
$169$	−12.9783	+	0.751536i	−0.998328	+	0.0578104i
$170$	3.19287			0.244882
$171$	−0.226259	−	0.226259i	−0.0173025	−	0.0173025i
$172$	1.71646			0.130879
$173$	−7.48239			−0.568876			−0.284438	−	0.958694i	$-0.591807\pi$
$173$	−7.48239			−0.568876			−0.284438	+	0.958694i	$0.591807\pi$
$174$	−7.36040	−	7.36040i	−0.557990	−	0.557990i
$175$	−11.2402	−	0.0629292i	−0.849680	−	0.00475700i
$176$	−4.87936	−	4.87936i	−0.367796	−	0.367796i
$177$	−20.8082	−	20.8082i	−1.56404	−	1.56404i
$178$		−	5.80387i		−	0.435019i
$179$			22.7009i			1.69674i	0.529402	+	0.848371i	$0.322416\pi$
$179$			22.7009i			1.69674i	−0.529402	+	0.848371i	$0.677584\pi$
$180$	−0.717262	+	0.717262i	−0.0534615	+	0.0534615i
$181$	−1.91735			−0.142516			−0.0712579	−	0.997458i	$-0.522701\pi$
$181$	−1.91735			−0.142516			−0.0712579	+	0.997458i	$0.522701\pi$
$182$	−7.96038	+	8.34063i	−0.590063	+	0.618249i
$183$	−20.9360			−1.54763
$184$	−14.1278	+	14.1278i	−1.04152	+	1.04152i
$185$			2.48231i			0.182503i
$186$			26.3246i			1.93021i
$187$	5.65157	+	5.65157i	0.413283	+	0.413283i
$188$	2.81283	+	2.81283i	0.205147	+	0.205147i
$189$	4.99257	+	0.0279513i	0.363156	+	0.00203316i
$190$	−0.109245	−	0.109245i	−0.00792546	−	0.00792546i
$191$	−10.0072			−0.724095			−0.362047	−	0.932160i	$-0.617922\pi$
$191$	−10.0072			−0.724095			−0.362047	+	0.932160i	$0.617922\pi$
$192$	−20.0936			−1.45013
$193$	−10.2351	−	10.2351i	−0.736741	−	0.736741i	0.235205	−	0.971946i	$-0.424424\pi$
$193$	−10.2351	−	10.2351i	−0.736741	−	0.736741i	−0.971946	+	0.235205i	$0.924424\pi$
$194$	7.59483			0.545277
$195$	−5.16874	−	4.87809i	−0.370141	−	0.349327i
$196$	0.0422604	−	3.77409i	0.00301860	−	0.269578i
$197$	15.2690	−	15.2690i	1.08787	−	1.08787i	0.0921223	−	0.995748i	$-0.470635\pi$
$197$	15.2690	−	15.2690i	1.08787	−	1.08787i	0.995748	−	0.0921223i	$-0.0293651\pi$
$198$	6.87936			0.488895
$199$	22.4635			1.59240			0.796198	−	0.605036i	$-0.206841\pi$
$199$	22.4635			1.59240			0.796198	+	0.605036i	$0.206841\pi$
$200$	9.21953	−	9.21953i	0.651920	−	0.651920i
$201$	−2.38622	−	2.38622i	−0.168311	−	0.168311i
$202$	0.991567	−	0.991567i	0.0697664	−	0.0697664i
$203$	−0.0561036	+	10.0210i	−0.00393770	+	0.703339i
$204$	3.73594			0.261568
$205$			2.78765i			0.194698i
$206$	−4.54756	+	4.54756i	−0.316844	+	0.316844i
$207$		−	14.1278i		−	0.981952i
$208$	−0.274305	−	9.48187i	−0.0190196	−	0.657449i
$209$		−	0.386740i		−	0.0267513i
$210$	−6.30323	−	0.0352892i	−0.434964	−	0.00243518i
$211$	−18.8504			−1.29772			−0.648859	−	0.760909i	$-0.724753\pi$
$211$	−18.8504			−1.29772			−0.648859	+	0.760909i	$0.724753\pi$
$212$			1.85043i			0.127088i
$213$	−9.32956	−	9.32956i	−0.639251	−	0.639251i
$214$	8.75872	−	8.75872i	0.598734	−	0.598734i
$215$	−1.95143	+	1.95143i	−0.133087	+	0.133087i
$216$	−4.09505	+	4.09505i	−0.278633	+	0.278633i
$217$	18.0205	−	17.8199i	1.22331	−	1.20969i
$218$			10.0072i			0.677772i
$219$	15.7473	+	15.7473i	1.06411	+	1.06411i
$220$	−1.22600			−0.0826568
$221$	0.317716	+	10.9825i	0.0213719	+	0.738760i
$222$		−	7.86913i		−	0.528142i
$223$	4.32131	+	4.32131i	0.289376	+	0.289376i	0.836833	−	0.547457i	$-0.184404\pi$
$223$	4.32131	+	4.32131i	0.289376	+	0.289376i	−0.547457	+	0.836833i	$0.684404\pi$
$224$	5.50307	+	5.56504i	0.367689	+	0.371830i
$225$			9.21953i			0.614636i
$226$	4.91023	−	4.91023i	0.326624	−	0.326624i
$227$	−4.69031	−	4.69031i	−0.311307	−	0.311307i	0.534109	−	0.845416i	$-0.320647\pi$
$227$	−4.69031	−	4.69031i	−0.311307	−	0.311307i	−0.845416	+	0.534109i	$0.820647\pi$
$228$	−0.127826	−	0.127826i	−0.00846549	−	0.00846549i
$229$	−0.264743	+	0.264743i	−0.0174947	+	0.0174947i	−0.715800	−	0.698305i	$-0.753938\pi$
$229$	−0.264743	+	0.264743i	−0.0174947	+	0.0174947i	0.698305	+	0.715800i	$0.253938\pi$
$230$		−	6.82135i		−	0.449786i
$231$	−11.0946	−	11.2195i	−0.729972	−	0.738191i
$232$	−8.21953	−	8.21953i	−0.539639	−	0.539639i
$233$			6.16290i			0.403745i	0.979412	+	0.201872i	$0.0647026\pi$
$233$			6.16290i			0.403745i	−0.979412	+	0.201872i	$0.935297\pi$
$234$	6.87756	+	6.49082i	0.449600	+	0.424319i
$235$	−6.39576			−0.417214
$236$	−4.93430	−	4.93430i	−0.321196	−	0.321196i
$237$			40.0091i			2.59887i
$238$	6.85166	+	6.92881i	0.444127	+	0.449128i
$239$	−5.63090	+	5.63090i	−0.364232	+	0.364232i	−0.865369	−	0.501136i	$-0.832916\pi$
$239$	−5.63090	+	5.63090i	−0.364232	+	0.364232i	0.501136	+	0.865369i	$0.332916\pi$
$240$	3.66701	−	3.66701i	0.236705	−	0.236705i
$241$	1.11217	−	1.11217i	0.0716414	−	0.0716414i	−0.670378	−	0.742020i	$-0.733868\pi$
$241$	1.11217	−	1.11217i	0.0716414	−	0.0716414i	0.742020	+	0.670378i	$0.233868\pi$
$242$	−3.52165	−	3.52165i	−0.226380	−	0.226380i
$243$		−	18.8980i		−	1.21230i
$244$	−4.96462			−0.317827
$245$	4.24268	+	4.33877i	0.271055	+	0.277194i
$246$		−	8.83710i		−	0.563433i
$247$	0.364897	−	0.386639i	0.0232178	−	0.0246012i
$248$			29.3973i			1.86673i
$249$	23.9825	−	23.9825i	1.51983	−	1.51983i
$250$			9.69040i			0.612874i
$251$	12.1069			0.764182			0.382091	−	0.924125i	$-0.375204\pi$
$251$	12.1069			0.764182			0.382091	+	0.924125i	$0.375204\pi$
$252$	−3.09571	−	0.0173316i	−0.195011	−	0.00109179i
$253$	12.0742	−	12.0742i	0.759097	−	0.759097i
$254$	−6.30406	−	6.30406i	−0.395552	−	0.395552i
$255$	−4.24735	+	4.24735i	−0.265980	+	0.265980i
$256$	−11.9155			−0.744717
$257$	17.5759			1.09635			0.548176	−	0.836363i	$-0.315322\pi$
$257$	17.5759			1.09635			0.548176	+	0.836363i	$0.315322\pi$
$258$	6.18621	−	6.18621i	0.385137	−	0.385137i
$259$	−5.38682	+	5.32684i	−0.334721	+	0.330994i
$260$	−1.22568	−	1.15676i	−0.0760133	−	0.0717389i
$261$	8.21953			0.508776
$262$	10.2250	+	10.2250i	0.631705	+	0.631705i
$263$	−14.5259			−0.895703			−0.447851	−	0.894108i	$-0.647811\pi$
$263$	−14.5259			−0.895703			−0.447851	+	0.894108i	$0.647811\pi$
$264$	18.3027			1.12645
$265$	−2.10374	−	2.10374i	−0.129232	−	0.129232i
$266$	0.00263975	−	0.471502i	0.000161853	−	0.0289097i
$267$	7.72067	+	7.72067i	0.472497	+	0.472497i
$268$	−0.565851	−	0.565851i	−0.0345648	−	0.0345648i
$269$			23.4152i			1.42765i	0.700324	+	0.713825i	$0.253039\pi$
$269$			23.4152i			1.42765i	−0.700324	+	0.713825i	$0.746961\pi$
$270$		−	1.97721i		−	0.120329i
$271$	2.41653	−	2.41653i	0.146794	−	0.146794i	−0.629890	−	0.776684i	$-0.716900\pi$
$271$	2.41653	−	2.41653i	0.146794	−	0.146794i	0.776684	+	0.629890i	$0.216900\pi$
$272$	−8.01703			−0.486104
$273$	−0.505838	−	21.6846i	−0.0306147	−	1.31241i
$274$	3.21953			0.194499
$275$	−7.87936	+	7.87936i	−0.475143	+	0.475143i
$276$		−	7.98157i		−	0.480434i
$277$			29.0722i			1.74678i	0.487020	+	0.873391i	$0.338084\pi$
$277$			29.0722i			1.74678i	−0.487020	+	0.873391i	$0.661916\pi$
$278$	−5.44304	−	5.44304i	−0.326452	−	0.326452i
$279$	−14.6987	−	14.6987i	−0.879985	−	0.879985i
$280$	−7.03897	−	0.0394083i	−0.420659	−	0.00235509i
$281$	9.68455	+	9.68455i	0.577732	+	0.577732i	0.934278	−	0.356546i	$-0.116046\pi$
$281$	9.68455	+	9.68455i	0.577732	+	0.577732i	−0.356546	+	0.934278i	$0.616046\pi$
$282$	20.2751			1.20737
$283$	−4.30357			−0.255821			−0.127910	−	0.991786i	$-0.540827\pi$
$283$	−4.30357			−0.255821			−0.127910	+	0.991786i	$0.540827\pi$
$284$	−2.21235	−	2.21235i	−0.131279	−	0.131279i
$285$	0.290649			0.0172165
$286$	0.330522	+	11.4251i	0.0195442	+	0.675582i
$287$	−6.04945	+	5.98209i	−0.357088	+	0.353112i
$288$	4.53919	−	4.53919i	0.267474	−	0.267474i
$289$	−7.71420			−0.453776
$290$	3.96864			0.233047
$291$	−10.1031	+	10.1031i	−0.592254	+	0.592254i
$292$	3.73421	+	3.73421i	0.218528	+	0.218528i
$293$	3.57373	−	3.57373i	0.208780	−	0.208780i	−0.594969	−	0.803749i	$-0.702836\pi$
$293$	3.57373	−	3.57373i	0.208780	−	0.208780i	0.803749	+	0.594969i	$0.202836\pi$
$294$	−13.4497	−	13.7543i	−0.784400	−	0.802166i
$295$	11.2195			0.653227
$296$		−	8.78765i		−	0.510772i
$297$	3.49978	−	3.49978i	0.203078	−	0.203078i
$298$		−	22.7948i		−	1.32047i
$299$	23.4633	−	0.678778i	1.35692	−	0.0392548i
$300$			5.20861i			0.300719i
$301$	−8.42240	−	0.0471535i	−0.485459	−	0.00271788i
$302$	13.0628			0.751678
$303$			2.63809i			0.151554i
$304$	0.274305	+	0.274305i	0.0157325	+	0.0157325i
$305$	5.64423	−	5.64423i	0.323188	−	0.323188i
$306$	5.65157	−	5.65157i	0.323079	−	0.323079i
$307$	−8.59457	+	8.59457i	−0.490518	+	0.490518i	−0.908469	−	0.417952i	$-0.862748\pi$
$307$	−8.59457	+	8.59457i	−0.490518	+	0.490518i	0.417952	+	0.908469i	$0.362748\pi$
$308$	−2.63090	−	2.66052i	−0.149909	−	0.151597i
$309$		−	12.0989i		−	0.688282i
$310$	−7.09696	−	7.09696i	−0.403080	−	0.403080i
$311$	−22.5405			−1.27815			−0.639077	−	0.769143i	$-0.720683\pi$
$311$	−22.5405			−1.27815			−0.639077	+	0.769143i	$0.720683\pi$
$312$	18.2979	+	17.2690i	1.03592	+	0.977664i
$313$			4.30873i			0.243544i	0.992558	+	0.121772i	$0.0388576\pi$
$313$			4.30873i			0.243544i	−0.992558	+	0.121772i	$0.961142\pi$
$314$	−17.9722	−	17.9722i	−1.01423	−	1.01423i
$315$	3.53919	−	3.49978i	0.199411	−	0.197190i
$316$			9.48747i			0.533712i
$317$	3.97107	−	3.97107i	0.223038	−	0.223038i	−0.586739	−	0.809776i	$-0.699588\pi$
$317$	3.97107	−	3.97107i	0.223038	−	0.223038i	0.809776	+	0.586739i	$0.199588\pi$
$318$	6.66904	+	6.66904i	0.373981	+	0.373981i
$319$	7.02472	+	7.02472i	0.393309	+	0.393309i
$320$	5.41714	−	5.41714i	0.302827	−	0.302827i
$321$			23.3028i			1.30063i
$322$	14.8029	−	14.6381i	0.824934	−	0.815749i
$323$	−0.317716	−	0.317716i	−0.0176782	−	0.0176782i
$324$		−	5.82377i		−	0.323543i
$325$	−15.3116	+	0.442957i	−0.849338	+	0.0245708i
$326$	−12.0267			−0.666095
$327$	−13.3122	−	13.3122i	−0.736165	−	0.736165i
$328$		−	9.86861i		−	0.544903i
$329$	−13.7248	−	13.8794i	−0.756674	−	0.765194i
$330$	−4.41855	+	4.41855i	−0.243233	+	0.243233i
$331$	1.70928	−	1.70928i	0.0939503	−	0.0939503i	−0.658570	−	0.752520i	$-0.728838\pi$
$331$	1.70928	−	1.70928i	0.0939503	−	0.0939503i	0.752520	+	0.658570i	$0.228838\pi$
$332$	5.68703	−	5.68703i	0.312117	−	0.312117i
$333$	4.39383	+	4.39383i	0.240780	+	0.240780i
$334$		−	20.6283i		−	1.12873i
$335$	1.28662			0.0702957
$336$	15.8269	+	0.0886081i	0.863427	+	0.00483397i
$337$			23.1327i			1.26012i	0.776546	+	0.630061i	$0.216970\pi$
$337$			23.1327i			1.26012i	−0.776546	+	0.630061i	$0.783030\pi$
$338$	−10.4494	+	11.7340i	−0.568373	+	0.638245i
$339$			13.0638i			0.709527i
$340$	−1.00719	+	1.00719i	−0.0546224	+	0.0546224i
$341$		−	25.1240i		−	1.36054i
$342$	−0.386740			−0.0209125
$343$	−0.311044	+	18.5176i	−0.0167948	+	0.999859i
$344$	6.90829	−	6.90829i	0.372470	−	0.372470i
$345$	9.07417	+	9.07417i	0.488537	+	0.488537i
$346$	−6.39473	+	6.39473i	−0.343783	+	0.343783i
$347$	−8.60424			−0.461900			−0.230950	−	0.972966i	$-0.574183\pi$
$347$	−8.60424			−0.461900			−0.230950	+	0.972966i	$0.574183\pi$
$348$	4.64366			0.248926
$349$	−19.0680	+	19.0680i	−1.02069	+	1.02069i	−0.0209053	+	0.999781i	$0.506655\pi$
$349$	−19.0680	+	19.0680i	−1.02069	+	1.02069i	−0.999781	+	0.0209053i	$0.993345\pi$
$350$	−9.66008	+	9.55252i	−0.516353	+	0.510604i
$351$	6.80098	−	0.196748i	0.363010	−	0.0105017i
$352$	7.75872			0.413541
$353$	−4.81231	−	4.81231i	−0.256133	−	0.256133i	0.567346	−	0.823479i	$-0.307970\pi$
$353$	−4.81231	−	4.81231i	−0.256133	−	0.256133i	−0.823479	+	0.567346i	$0.807970\pi$
$354$	−35.5669			−1.89036
$355$	5.03040			0.266986
$356$	1.83083	+	1.83083i	0.0970336	+	0.0970336i
$357$	−18.3316	−	0.102631i	−0.970212	−	0.00543182i
$358$	19.4010	+	19.4010i	1.02538	+	1.02538i
$359$	−12.5506	−	12.5506i	−0.662394	−	0.662394i	0.293549	−	0.955944i	$-0.405163\pi$
$359$	−12.5506	−	12.5506i	−0.662394	−	0.662394i	−0.955944	+	0.293549i	$0.905163\pi$
$360$			5.77356i			0.304293i
$361$		−	18.9783i		−	0.998856i
$362$	−1.63864	+	1.63864i	−0.0861252	+	0.0861252i
$363$	9.36943			0.491768
$364$	−0.119951	−	5.14214i	−0.00628713	−	0.269521i
$365$	−8.49079			−0.444428
$366$	−17.8927	+	17.8927i	−0.935266	+	0.935266i
$367$			22.8806i			1.19436i	0.802109	+	0.597178i	$0.203711\pi$
$367$			22.8806i			1.19436i	−0.802109	+	0.597178i	$0.796289\pi$
$368$			17.1278i			0.892850i
$369$	4.93430	+	4.93430i	0.256870	+	0.256870i
$370$	2.12147	+	2.12147i	0.110290	+	0.110290i
$371$	0.0508338	−	9.07976i	0.00263916	−	0.471398i
$372$	−8.30406	−	8.30406i	−0.430545	−	0.430545i
$373$	10.5041			0.543883			0.271941	−	0.962314i	$-0.412334\pi$
$373$	10.5041			0.543883			0.271941	+	0.962314i	$0.412334\pi$
$374$	9.66008			0.499511
$375$	−12.8908	−	12.8908i	−0.665676	−	0.665676i
$376$	22.6417			1.16766
$377$	0.394912	+	13.6509i	0.0203390	+	0.703055i
$378$	4.29072	−	4.24295i	0.220691	−	0.218234i
$379$	3.64229	−	3.64229i	0.187092	−	0.187092i	−0.607346	−	0.794438i	$-0.707766\pi$
$379$	3.64229	−	3.64229i	0.187092	−	0.187092i	0.794438	+	0.607346i	$0.207766\pi$
$380$	0.0689224			0.00353564
$381$	16.7721			0.859260
$382$	−8.55252	+	8.55252i	−0.437585	+	0.437585i
$383$	−24.5591	−	24.5591i	−1.25491	−	1.25491i	−0.953492	−	0.301419i	$-0.902540\pi$
$383$	−24.5591	−	24.5591i	−1.25491	−	1.25491i	−0.301419	−	0.953492i	$-0.597460\pi$
$384$	−7.66061	+	7.66061i	−0.390929	+	0.390929i
$385$	6.01577	+	0.0336798i	0.306592	+	0.00171648i
$386$	−17.4947			−0.890455
$387$			6.90829i			0.351168i
$388$	−2.39578	+	2.39578i	−0.121627	+	0.121627i
$389$		−	6.48974i		−	0.329043i	−0.986374	−	0.164521i	$-0.947392\pi$
$389$		−	6.48974i		−	0.329043i	0.986374	−	0.164521i	$-0.0526080\pi$
$390$	−8.58639	+	0.248399i	−0.434789	+	0.0125782i
$391$		−	19.8385i		−	1.00327i
$392$	−15.0196	−	15.3597i	−0.758603	−	0.775784i
$393$	−27.2039			−1.37226
$394$		−	26.0989i		−	1.31484i
$395$	−10.7862	−	10.7862i	−0.542714	−	0.542714i
$396$	−2.17009	+	2.17009i	−0.109051	+	0.109051i
$397$	−6.89530	+	6.89530i	−0.346065	+	0.346065i	−0.858642	−	0.512576i	$-0.828691\pi$
$397$	−6.89530	+	6.89530i	−0.346065	+	0.346065i	0.512576	+	0.858642i	$0.328691\pi$
$398$	19.1982	−	19.1982i	0.962317	−	0.962317i
$399$	0.623710	+	0.630733i	0.0312245	+	0.0315761i
$400$		−	11.1773i		−	0.558864i
$401$	9.02279	+	9.02279i	0.450576	+	0.450576i	0.895546	−	0.444969i	$-0.146785\pi$
$401$	9.02279	+	9.02279i	0.450576	+	0.450576i	−0.444969	+	0.895546i	$0.646785\pi$
$402$	−4.07870			−0.203427
$403$	23.7051	−	25.1175i	1.18083	−	1.25119i
$404$			0.625577i			0.0311236i
$405$	6.62099	+	6.62099i	0.329000	+	0.329000i
$406$	8.51640	+	8.61230i	0.422662	+	0.427421i
$407$			7.51026i			0.372270i
$408$	15.0361	−	15.0361i	0.744399	−	0.744399i
$409$	2.86088	+	2.86088i	0.141461	+	0.141461i	0.774291	−	0.632830i	$-0.218107\pi$
$409$	2.86088	+	2.86088i	0.141461	+	0.141461i	−0.632830	+	0.774291i	$0.718107\pi$
$410$	2.38243	+	2.38243i	0.117660	+	0.117660i
$411$	−4.28282	+	4.28282i	−0.211256	+	0.211256i
$412$		−	2.86905i		−	0.141348i
$413$	24.0763	+	24.3474i	1.18472	+	1.19806i
$414$	−12.0742	−	12.0742i	−0.593413	−	0.593413i
$415$			12.9311i			0.634762i
$416$	7.75670	+	7.32052i	0.380303	+	0.358918i
$417$	14.4813			0.709154
$418$	−0.330522	−	0.330522i	−0.0161664	−	0.0161664i
$419$		−	35.4097i		−	1.72988i	−0.501878	−	0.864939i	$-0.667357\pi$
$419$		−	35.4097i		−	1.72988i	0.501878	−	0.864939i	$-0.332643\pi$
$420$	1.99948	−	1.97721i	0.0975645	−	0.0964781i
$421$	18.9307	−	18.9307i	0.922628	−	0.922628i	−0.0745864	−	0.997215i	$-0.523764\pi$
$421$	18.9307	−	18.9307i	0.922628	−	0.922628i	0.997215	+	0.0745864i	$0.0237636\pi$
$422$	−16.1103	+	16.1103i	−0.784237	+	0.784237i
$423$	−11.3209	+	11.3209i	−0.550439	+	0.550439i
$424$	7.44748	+	7.44748i	0.361682	+	0.361682i
$425$			12.9462i			0.627982i
$426$	−15.9468			−0.772624
$427$	24.3605	+	0.136385i	1.17889	+	0.00660011i
$428$			5.52586i			0.267102i
$429$	−15.6381	−	14.7587i	−0.755014	−	0.712558i
$430$			3.33553i			0.160854i
$431$	12.6042	−	12.6042i	0.607125	−	0.607125i	−0.335069	−	0.942194i	$-0.608760\pi$
$431$	12.6042	−	12.6042i	0.607125	−	0.607125i	0.942194	+	0.335069i	$0.108760\pi$
$432$			4.96462i			0.238860i
$433$	14.3392			0.689098			0.344549	−	0.938768i	$-0.388032\pi$
$433$	14.3392			0.689098			0.344549	+	0.938768i	$0.388032\pi$
$434$	0.171488	−	30.6305i	0.00823167	−	1.47031i
$435$	−5.27933	+	5.27933i	−0.253125	+	0.253125i
$436$	−3.15676	−	3.15676i	−0.151181	−	0.151181i
$437$	−0.678778	+	0.678778i	−0.0324704	+	0.0324704i
$438$	26.9165			1.28612
$439$	−19.9812			−0.953651			−0.476826	−	0.878998i	$-0.658213\pi$
$439$	−19.9812			−0.953651			−0.476826	+	0.878998i	$0.658213\pi$
$440$	−4.93430	+	4.93430i	−0.235234	+	0.235234i
$441$	15.1897	+	0.170086i	0.723317	+	0.00809936i
$442$	9.65756	+	9.11450i	0.459363	+	0.433532i
$443$	−5.63809			−0.267874			−0.133937	−	0.990990i	$-0.542762\pi$
$443$	−5.63809			−0.267874			−0.133937	+	0.990990i	$0.542762\pi$
$444$	2.48231	+	2.48231i	0.117805	+	0.117805i
$445$	−4.16290			−0.197340
$446$	7.38630			0.349751
$447$	30.3231	+	30.3231i	1.43423	+	1.43423i
$448$	23.3804	+	0.130897i	1.10462	+	0.00618431i
$449$	−12.9060	−	12.9060i	−0.609073	−	0.609073i	0.333631	−	0.942704i	$-0.391726\pi$
$449$	−12.9060	−	12.9060i	−0.609073	−	0.609073i	−0.942704	+	0.333631i	$0.891726\pi$
$450$	7.87936	+	7.87936i	0.371437	+	0.371437i
$451$			8.43409i			0.397146i
$452$			3.09785i			0.145711i
$453$	−17.3769	+	17.3769i	−0.816438	+	0.816438i
$454$	−8.01703			−0.376258
$455$	5.98242	+	5.70968i	0.280460	+	0.267674i
$456$	−1.02893			−0.0481840
$457$	6.96687	−	6.96687i	0.325896	−	0.325896i	−0.525127	−	0.851024i	$-0.675982\pi$
$457$	6.96687	−	6.96687i	0.325896	−	0.325896i	0.851024	+	0.525127i	$0.175982\pi$
$458$			0.452519i			0.0211448i
$459$		−	5.75031i		−	0.268402i
$460$	2.15179	+	2.15179i	0.100328	+	0.100328i
$461$	7.20809	+	7.20809i	0.335714	+	0.335714i	0.854752	−	0.519037i	$-0.173709\pi$
$461$	7.20809	+	7.20809i	0.335714	+	0.335714i	−0.519037	+	0.854752i	$0.673709\pi$
$462$	−19.0705	−	0.106768i	−0.887240	−	0.00496729i
$463$	−4.06084	−	4.06084i	−0.188723	−	0.188723i	0.606421	−	0.795144i	$-0.292605\pi$
$463$	−4.06084	−	4.06084i	−0.188723	−	0.188723i	−0.795144	+	0.606421i	$0.792605\pi$
$464$	−9.96493			−0.462610
$465$	18.8816			0.875614
$466$	5.26705	+	5.26705i	0.243991	+	0.243991i
$467$	−17.3673			−0.803665			−0.401832	−	0.915713i	$-0.631627\pi$
$467$	−17.3673			−0.803665			−0.401832	+	0.915713i	$0.631627\pi$
$468$	−4.21704	+	0.121997i	−0.194933	+	0.00563929i
$469$	2.76099	+	2.79208i	0.127491	+	0.128926i
$470$	−5.46606	+	5.46606i	−0.252131	+	0.252131i
$471$	47.8154			2.20322
$472$	−39.7184			−1.82819
$473$	−5.90409	+	5.90409i	−0.271470	+	0.271470i
$474$	34.1933	+	34.1933i	1.57055	+	1.57055i
$475$	0.442957	−	0.442957i	0.0203243	−	0.0203243i
$476$	−4.34703	−	0.0243372i	−0.199246	−	0.00111550i
$477$	−7.44748			−0.340997
$478$			9.62475i			0.440226i
$479$	9.88634	−	9.88634i	0.451719	−	0.451719i	−0.444206	−	0.895925i	$-0.646514\pi$
$479$	9.88634	−	9.88634i	0.451719	−	0.451719i	0.895925	+	0.444206i	$0.146514\pi$
$480$			5.83096i			0.266146i
$481$	−7.08609	+	7.50830i	−0.323098	+	0.342349i
$482$		−	1.90101i		−	0.0865887i
$483$	−0.219264	+	39.1642i	−0.00997687	+	1.78203i
$484$	2.22180			0.100991
$485$		−	5.44748i		−	0.247357i
$486$	−16.1509	−	16.1509i	−0.732620	−	0.732620i
$487$	−12.6092	+	12.6092i	−0.571375	+	0.571375i	−0.932513	−	0.361137i	$-0.882389\pi$
$487$	−12.6092	+	12.6092i	−0.571375	+	0.571375i	0.361137	+	0.932513i	$0.382389\pi$
$488$	−19.9812	+	19.9812i	−0.904507	+	0.904507i
$489$	15.9986	−	15.9986i	0.723482	−	0.723482i
$490$	7.33403	+	0.0821230i	0.331318	+	0.00370994i
$491$		−	1.72487i		−	0.0778425i	−0.999242	−	0.0389212i	$-0.987608\pi$
$491$		−	1.72487i		−	0.0778425i	0.999242	−	0.0389212i	$-0.0123921\pi$
$492$	2.78765	+	2.78765i	0.125677	+	0.125677i
$493$	11.5420			0.519824
$494$	−0.0185811	−	0.642291i	−0.000836003	−	0.0288980i
$495$		−	4.93430i		−	0.221780i
$496$	17.8199	+	17.8199i	0.800135	+	0.800135i
$497$	10.7948	+	10.9164i	0.484215	+	0.489667i
$498$		−	40.9926i		−	1.83692i
$499$	−27.5555	+	27.5555i	−1.23355	+	1.23355i	−0.270964	+	0.962589i	$0.587343\pi$
$499$	−27.5555	+	27.5555i	−1.23355	+	1.23355i	−0.962589	+	0.270964i	$0.912657\pi$
$500$	−3.05682	−	3.05682i	−0.136705	−	0.136705i
$501$	27.4410	+	27.4410i	1.22597	+	1.22597i
$502$	10.3470	−	10.3470i	0.461811	−	0.461811i
$503$		−	20.8862i		−	0.931272i	−0.884976	−	0.465636i	$-0.845826\pi$
$503$		−	20.8862i		−	0.931272i	0.884976	−	0.465636i	$-0.154174\pi$
$504$	−12.5291	+	12.3896i	−0.558092	+	0.551878i
$505$	−0.711213	−	0.711213i	−0.0316486	−	0.0316486i
$506$		−	20.6381i		−	0.917475i
$507$	−1.70883	−	29.5097i	−0.0758918	−	1.31057i
$508$	3.97721			0.176460
$509$	15.2473	+	15.2473i	0.675823	+	0.675823i	0.959052	−	0.283229i	$-0.0914057\pi$
$509$	15.2473	+	15.2473i	0.675823	+	0.675823i	−0.283229	+	0.959052i	$0.591406\pi$
$510$			7.25990i			0.321474i
$511$	−18.2206	−	18.4257i	−0.806031	−	0.815107i
$512$	−16.9216	+	16.9216i	−0.747837	+	0.747837i
$513$	−0.196748	+	0.196748i	−0.00868666	+	0.00868666i
$514$	15.0210	−	15.0210i	0.662548	−	0.662548i
$515$	3.26180	+	3.26180i	0.143732	+	0.143732i
$516$			3.90286i			0.171814i
$517$	−19.3505			−0.851033
$518$	−0.0512623	+	9.15630i	−0.00225234	+	0.402305i
$519$		−	17.0133i		−	0.746802i
$520$	−9.58864	+	0.277394i	−0.420490	+	0.0121645i
$521$		−	20.1543i		−	0.882975i	−0.897268	−	0.441487i	$-0.854451\pi$
$521$		−	20.1543i		−	0.882975i	0.897268	−	0.441487i	$-0.145549\pi$
$522$	7.02472	−	7.02472i	0.307464	−	0.307464i
$523$		−	11.3031i		−	0.494251i	−0.968983	−	0.247126i	$-0.920514\pi$
$523$		−	11.3031i		−	0.494251i	0.968983	−	0.247126i	$-0.0794861\pi$
$524$	−6.45095			−0.281811
$525$	0.143087	−	25.5578i	0.00624485	−	1.11543i
$526$	−12.4143	+	12.4143i	−0.541291	+	0.541291i
$527$	−20.6400	−	20.6400i	−0.899094	−	0.899094i
$528$	11.0946	−	11.0946i	0.482831	−	0.482831i
$529$	−19.3835			−0.842760
$530$	−3.59587			−0.156195
$531$	19.8592	−	19.8592i	0.861817	−	0.861817i
$532$	0.147902	+	0.149568i	0.00641237	+	0.00648458i
$533$	−7.95774	+	8.43188i	−0.344688	+	0.365225i
$534$	13.1967			0.571079
$535$	−6.28230	−	6.28230i	−0.271607	−	0.271607i
$536$	−4.55479			−0.196737
$537$	−51.6168			−2.22743
$538$	20.0115	+	20.0115i	0.862758	+	0.862758i
$539$	12.8363	+	13.1270i	0.552898	+	0.565420i
$540$	0.623710	+	0.623710i	0.0268402	+	0.0268402i
$541$	−9.28879	−	9.28879i	−0.399356	−	0.399356i	0.478650	−	0.878006i	$-0.341126\pi$
$541$	−9.28879	−	9.28879i	−0.399356	−	0.399356i	−0.878006	+	0.478650i	$0.841126\pi$
$542$		−	4.13051i		−	0.177421i
$543$		−	4.35965i		−	0.187090i
$544$	6.37398	−	6.37398i	0.273282	−	0.273282i
$545$	7.17778			0.307462
$546$	−18.9648	−	18.1002i	−0.811618	−	0.774616i
$547$	12.8999			0.551559			0.275780	−	0.961221i	$-0.411064\pi$
$547$	12.8999			0.551559			0.275780	+	0.961221i	$0.411064\pi$
$548$	−1.01560	+	1.01560i	−0.0433842	+	0.0433842i
$549$		−	19.9812i		−	0.852777i
$550$			13.4680i			0.574277i
$551$	−0.394912	−	0.394912i	−0.0168238	−	0.0168238i
$552$	−32.1236	−	32.1236i	−1.36727	−	1.36727i
$553$	0.260633	−	46.5534i	0.0110833	−	1.97965i
$554$	24.8462	+	24.8462i	1.05562	+	1.05562i
$555$	−5.64423			−0.239584
$556$	3.43400			0.145634
$557$	−16.6153	−	16.6153i	−0.704013	−	0.704013i	0.261257	−	0.965269i	$-0.415863\pi$
$557$	−16.6153	−	16.6153i	−0.704013	−	0.704013i	−0.965269	+	0.261257i	$0.915863\pi$
$558$	−25.1240			−1.06359
$559$	−11.4732	+	0.331912i	−0.485264	+	0.0140384i
$560$	−4.29072	+	4.24295i	−0.181316	+	0.179297i
$561$	−12.8504	+	12.8504i	−0.542546	+	0.542546i
$562$	16.5536			0.698270
$563$	−21.6761			−0.913538			−0.456769	−	0.889585i	$-0.650993\pi$
$563$	−21.6761			−0.913538			−0.456769	+	0.889585i	$0.650993\pi$
$564$	−6.39576	+	6.39576i	−0.269310	+	0.269310i
$565$	−3.52192	−	3.52192i	−0.148168	−	0.148168i
$566$	−3.67799	+	3.67799i	−0.154598	+	0.154598i
$567$	−0.159987	+	28.5763i	−0.00671881	+	1.20009i
$568$	−17.8082			−0.747214
$569$			18.0738i			0.757695i	0.925459	+	0.378847i	$0.123679\pi$
$569$			18.0738i			0.757695i	−0.925459	+	0.378847i	$0.876321\pi$
$570$	0.248399	−	0.248399i	0.0104043	−	0.0104043i
$571$		−	8.53692i		−	0.357259i	−0.983916	−	0.178630i	$-0.942834\pi$
$571$		−	8.53692i		−	0.357259i	0.983916	−	0.178630i	$-0.0571664\pi$
$572$	−3.70831	−	3.49978i	−0.155052	−	0.146333i
$573$		−	22.7542i		−	0.950569i
$574$	−0.0575680	+	10.2826i	−0.00240284	+	0.429188i
$575$	27.6586			1.15344
$576$		−	19.1773i		−	0.799053i
$577$	−8.56564	−	8.56564i	−0.356592	−	0.356592i	0.505963	−	0.862555i	$-0.331137\pi$
$577$	−8.56564	−	8.56564i	−0.356592	−	0.356592i	−0.862555	+	0.505963i	$0.831137\pi$
$578$	−6.59284	+	6.59284i	−0.274226	+	0.274226i
$579$	23.2725	−	23.2725i	0.967171	−	0.967171i
$580$	−1.25190	+	1.25190i	−0.0519825	+	0.0519825i
$581$	−28.0616	+	27.7491i	−1.16419	+	1.15123i
$582$			17.2690i			0.715822i
$583$	−6.36490	−	6.36490i	−0.263607	−	0.263607i
$584$	30.0583			1.24382
$585$	4.65562	−	4.93302i	0.192486	−	0.203955i
$586$		−	6.10849i		−	0.252339i
$587$	−0.308382	−	0.308382i	−0.0127283	−	0.0127283i	0.700714	−	0.713442i	$-0.252865\pi$
$587$	−0.308382	−	0.308382i	−0.0127283	−	0.0127283i	−0.713442	+	0.700714i	$0.752865\pi$
$588$	8.58145	+	0.0960910i	0.353893	+	0.00396272i
$589$			1.41241i			0.0581972i
$590$	9.58864	−	9.58864i	0.394758	−	0.394758i
$591$	34.7183	+	34.7183i	1.42812	+	1.42812i
$592$	−5.32684	−	5.32684i	−0.218932	−	0.218932i
$593$	−4.95204	+	4.95204i	−0.203356	+	0.203356i	−0.801436	−	0.598080i	$-0.795930\pi$
$593$	−4.95204	+	4.95204i	−0.203356	+	0.203356i	0.598080	+	0.801436i	$0.295930\pi$
$594$		−	5.98209i		−	0.245448i
$595$	4.96977	−	4.91443i	0.203741	−	0.201472i
$596$	7.19061	+	7.19061i	0.294539	+	0.294539i
$597$			51.0772i			2.09045i
$598$	19.4725	−	20.6327i	0.796289	−	0.843734i
$599$	−17.6309			−0.720379			−0.360189	−	0.932879i	$-0.617288\pi$
$599$	−17.6309			−0.720379			−0.360189	+	0.932879i	$0.617288\pi$
$600$	20.9632	+	20.9632i	0.855820	+	0.855820i
$601$		−	7.14746i		−	0.291551i	−0.989318	−	0.145776i	$-0.953432\pi$
$601$		−	7.14746i		−	0.291551i	0.989318	−	0.145776i	$-0.0465677\pi$
$602$	−7.23840	+	7.15780i	−0.295015	+	0.291730i
$603$	2.27739	−	2.27739i	0.0927426	−	0.0927426i
$604$	−4.12064	+	4.12064i	−0.167666	+	0.167666i
$605$	−2.52595	+	2.52595i	−0.102694	+	0.102694i
$606$	2.25461	+	2.25461i	0.0915872	+	0.0915872i
$607$			29.8550i			1.21178i	0.795550	+	0.605888i	$0.207182\pi$
$607$			29.8550i			1.21178i	−0.795550	+	0.605888i	$0.792818\pi$
$608$	−0.436175			−0.0176892
$609$	−22.7856	−	0.127567i	−0.923321	−	0.00516929i
$610$		−	9.64754i		−	0.390618i
$611$	−19.3454	−	18.2576i	−0.782632	−	0.738623i
$612$			3.56556i			0.144129i
$613$	−6.43907	+	6.43907i	−0.260072	+	0.260072i	−0.825083	−	0.565011i	$-0.808872\pi$
$613$	−6.43907	+	6.43907i	−0.260072	+	0.260072i	0.565011	+	0.825083i	$0.308872\pi$
$614$			14.6905i			0.592859i
$615$	−6.33852			−0.255594
$616$	−21.2965	−	0.119230i	−0.858061	−	0.00480393i
$617$	16.4908	−	16.4908i	0.663894	−	0.663894i	−0.292402	−	0.956296i	$-0.594454\pi$
$617$	16.4908	−	16.4908i	0.663894	−	0.663894i	0.956296	+	0.292402i	$0.0944544\pi$
$618$	−10.3402	−	10.3402i	−0.415943	−	0.415943i
$619$	−22.3208	+	22.3208i	−0.897148	+	0.897148i	−0.995183	−	0.0980353i	$-0.968744\pi$
$619$	−22.3208	+	22.3208i	−0.897148	+	0.897148i	0.0980353	+	0.995183i	$0.468744\pi$
$620$	4.47745			0.179819
$621$	−12.2851			−0.492986
$622$	−19.2639	+	19.2639i	−0.772414	+	0.772414i
$623$	−8.93326	−	9.03385i	−0.357903	−	0.361934i
$624$	21.5597	−	0.623710i	0.863079	−	0.0249684i
$625$	−14.2918			−0.571671
$626$	3.68240	+	3.68240i	0.147178	+	0.147178i
$627$	0.879362			0.0351183
$628$	11.3386			0.452459
$629$	6.16986	+	6.16986i	0.246009	+	0.246009i
$630$	0.0336798	−	6.01577i	0.00134184	−	0.239674i
$631$	3.75154	+	3.75154i	0.149346	+	0.149346i	0.777826	−	0.628480i	$-0.216322\pi$
$631$	3.75154	+	3.75154i	0.149346	+	0.149346i	−0.628480	+	0.777826i	$0.716322\pi$
$632$	38.1845	+	38.1845i	1.51890	+	1.51890i
$633$		−	42.8618i		−	1.70360i
$634$		−	6.78765i		−	0.269572i
$635$	−4.52166	+	4.52166i	−0.179437	+	0.179437i
$636$	−4.20748			−0.166837
$637$	0.447317	+	25.2349i	0.0177234	+	0.999843i
$638$	12.0072			0.475369
$639$	8.90409	−	8.90409i	0.352240	−	0.352240i
$640$		−	4.13051i		−	0.163273i
$641$		−	25.6947i		−	1.01488i	−0.861687	−	0.507440i	$-0.830592\pi$
$641$		−	25.6947i		−	1.01488i	0.861687	−	0.507440i	$-0.169408\pi$
$642$	19.9154	+	19.9154i	0.785999	+	0.785999i
$643$	22.1537	+	22.1537i	0.873658	+	0.873658i	0.992869	−	0.119211i	$-0.0380363\pi$
$643$	22.1537	+	22.1537i	0.873658	+	0.873658i	−0.119211	+	0.992869i	$0.538036\pi$
$644$	−0.0519948	+	9.28713i	−0.00204888	+	0.365964i
$645$	−4.43713	−	4.43713i	−0.174712	−	0.174712i
$646$	−0.543065			−0.0213666
$647$	32.4446			1.27553			0.637764	−	0.770232i	$-0.279860\pi$
$647$	32.4446			1.27553			0.637764	+	0.770232i	$0.279860\pi$
$648$	−23.4391	−	23.4391i	−0.920774	−	0.920774i
$649$	33.9449			1.33245
$650$	−12.7073	+	13.4645i	−0.498423	+	0.528120i
$651$	40.5185	+	40.9747i	1.58804	+	1.60593i
$652$	3.79380	−	3.79380i	0.148577	−	0.148577i
$653$	31.6514			1.23862			0.619308	−	0.785148i	$-0.287413\pi$
$653$	31.6514			1.23862			0.619308	+	0.785148i	$0.287413\pi$
$654$	−22.7542			−0.889758
$655$	7.33403	−	7.33403i	0.286564	−	0.286564i
$656$	−5.98209	−	5.98209i	−0.233561	−	0.233561i
$657$	−15.0292	+	15.0292i	−0.586344	+	0.586344i
$658$	−23.5916	−	0.132079i	−0.919695	−	0.00514899i
$659$	30.5330			1.18940			0.594699	−	0.803948i	$-0.297271\pi$
$659$	30.5330			1.18940			0.594699	+	0.803948i	$0.297271\pi$
$660$		−	2.78765i		−	0.108509i
$661$	9.20895	−	9.20895i	0.358187	−	0.358187i	−0.504957	−	0.863144i	$-0.668492\pi$
$661$	9.20895	−	9.20895i	0.358187	−	0.358187i	0.863144	+	0.504957i	$0.168492\pi$
$662$		−	2.92162i		−	0.113552i
$663$	−24.9717	+	0.722418i	−0.969822	+	0.0280564i
$664$		−	45.7775i		−	1.77651i
$665$	−0.338191	−	0.00189339i	−0.0131145	−	7.34225e-5i
$666$	7.51026			0.291017
$667$		−	24.6586i		−	0.954785i
$668$	6.50717	+	6.50717i	0.251770	+	0.251770i
$669$	−9.82571	+	9.82571i	−0.379884	+	0.379884i
$670$	1.09960	−	1.09960i	0.0424811	−	0.0424811i
$671$	17.0767	−	17.0767i	0.659239	−	0.659239i
$672$	−12.6537	+	12.5128i	−0.488126	+	0.482691i
$673$			22.6319i			0.872397i	0.899850	+	0.436199i	$0.143675\pi$
$673$			22.6319i			0.872397i	−0.899850	+	0.436199i	$0.856325\pi$
$674$	19.7701	+	19.7701i	0.761516	+	0.761516i
$675$	8.01703			0.308576
$676$	−0.405220	−	6.99773i	−0.0155854	−	0.269144i
$677$		−	10.7242i		−	0.412165i	−0.978535	−	0.206082i	$-0.933928\pi$
$677$		−	10.7242i		−	0.412165i	0.978535	−	0.206082i	$-0.0660715\pi$
$678$	11.1648	+	11.1648i	0.428781	+	0.428781i
$679$	11.8215	−	11.6899i	0.453668	−	0.448616i
$680$			8.10731i			0.310901i
$681$	10.6647	−	10.6647i	0.408674	−	0.408674i
$682$	−21.4720	−	21.4720i	−0.822204	−	0.822204i
$683$	−3.70701	−	3.70701i	−0.141845	−	0.141845i	0.632619	−	0.774463i	$-0.281980\pi$
$683$	−3.70701	−	3.70701i	−0.141845	−	0.141845i	−0.774463	+	0.632619i	$0.781980\pi$
$684$	0.121997	−	0.121997i	0.00466466	−	0.00466466i
$685$		−	2.30925i		−	0.0882319i
$686$	15.5600	+	16.0917i	0.594085	+	0.614384i
$687$	−0.601968	−	0.601968i	−0.0229665	−	0.0229665i
$688$		−	8.37525i		−	0.319303i
$689$	−0.357818	−	12.3687i	−0.0136318	−	0.471208i
$690$	15.5103			0.590465
$691$	−0.266133	−	0.266133i	−0.0101242	−	0.0101242i	0.702027	−	0.712151i	$-0.252279\pi$
$691$	−0.266133	−	0.266133i	−0.0101242	−	0.0101242i	−0.712151	+	0.702027i	$0.752279\pi$
$692$		−	4.03442i		−	0.153366i
$693$	10.7079	−	10.5886i	0.406758	−	0.402229i
$694$	−7.35350	+	7.35350i	−0.279135	+	0.279135i
$695$	−3.90409	+	3.90409i	−0.148090	+	0.148090i
$696$	18.6894	−	18.6894i	0.708421	−	0.708421i
$697$	6.92881	+	6.92881i	0.262447	+	0.262447i
$698$			32.5925i			1.23364i
$699$	−14.0131			−0.530024
$700$	0.0339307	−	6.06059i	0.00128246	−	0.229069i
$701$		−	34.0349i		−	1.28548i	−0.766084	−	0.642740i	$-0.777798\pi$
$701$		−	34.0349i		−	1.28548i	0.766084	−	0.642740i	$-0.222202\pi$
$702$	5.64423	−	5.98053i	0.213028	−	0.225720i
$703$		−	0.422207i		−	0.0159238i
$704$	16.3896	−	16.3896i	0.617707	−	0.617707i
$705$		−	14.5426i		−	0.547705i
$706$	−8.22556			−0.309573
$707$	0.0171854	−	3.06960i	0.000646325	−	0.115444i
$708$	11.2195	−	11.2195i	0.421656	−	0.421656i
$709$	11.4989	+	11.4989i	0.431849	+	0.431849i	0.889257	−	0.457408i	$-0.151222\pi$
$709$	11.4989	+	11.4989i	0.431849	+	0.431849i	−0.457408	+	0.889257i	$0.651222\pi$
$710$	4.29917	−	4.29917i	0.161345	−	0.161345i
$711$	−38.1845			−1.43203
$712$	14.7371			0.552297
$713$	−44.0960	+	44.0960i	−1.65141	+	1.65141i
$714$	−15.7546	+	15.5792i	−0.589601	+	0.583036i
$715$	8.19481	−	0.237071i	0.306469	−	0.00886596i
$716$	−12.2401			−0.457432
$717$	−12.8034	−	12.8034i	−0.478153	−	0.478153i
$718$	−21.4524			−0.800596
$719$	35.0445			1.30694			0.653469	−	0.756953i	$-0.273313\pi$
$719$	35.0445			1.30694			0.653469	+	0.756953i	$0.273313\pi$
$720$	3.49978	+	3.49978i	0.130429	+	0.130429i
$721$	−0.0788166	+	14.0779i	−0.00293528	+	0.524290i
$722$	−16.2195	−	16.2195i	−0.603629	−	0.603629i
$723$	2.52884	+	2.52884i	0.0940486	+	0.0940486i
$724$		−	1.03382i		−	0.0384215i
$725$			16.0917i			0.597631i
$726$	8.00747	−	8.00747i	0.297185	−	0.297185i
$727$	15.0936			0.559789			0.279895	−	0.960031i	$-0.409700\pi$
$727$	15.0936			0.559789			0.279895	+	0.960031i	$0.409700\pi$
$728$	−21.1784	−	20.2129i	−0.784925	−	0.749140i
$729$	10.5669			0.391367
$730$	−7.25655	+	7.25655i	−0.268577	+	0.268577i
$731$			9.70071i			0.358794i
$732$		−	11.2885i		−	0.417233i
$733$	−14.8155	−	14.8155i	−0.547223	−	0.547223i	0.378414	−	0.925637i	$-0.376470\pi$
$733$	−14.8155	−	14.8155i	−0.547223	−	0.547223i	−0.925637	+	0.378414i	$0.876470\pi$
$734$	19.5546	+	19.5546i	0.721773	+	0.721773i
$735$	−9.86542	+	9.64693i	−0.363891	+	0.355832i
$736$	−13.6176	−	13.6176i	−0.501950	−	0.501950i
$737$	3.89269			0.143389
$738$	8.43409			0.310463
$739$	16.1370	+	16.1370i	0.593607	+	0.593607i	0.938604	−	0.344997i	$-0.112120\pi$
$739$	16.1370	+	16.1370i	0.593607	+	0.593607i	−0.344997	+	0.938604i	$0.612120\pi$
$740$	−1.33843			−0.0492018
$741$	0.879132	+	0.829697i	0.0322957	+	0.0304797i
$742$	−7.71646	−	7.80335i	−0.283280	−	0.286470i
$743$	−24.1350	+	24.1350i	−0.885428	+	0.885428i	−0.994080	−	0.108652i	$-0.965347\pi$
$743$	−24.1350	+	24.1350i	−0.885428	+	0.885428i	0.108652	+	0.994080i	$0.465347\pi$
$744$	−66.8431			−2.45059
$745$	−16.3499			−0.599013
$746$	8.97721	−	8.97721i	0.328679	−	0.328679i
$747$	22.8887	+	22.8887i	0.837455	+	0.837455i
$748$	−3.04726	+	3.04726i	−0.111419	+	0.111419i
$749$	0.151803	−	27.1145i	0.00554675	−	0.990741i
$750$	−22.0338			−0.804562
$751$		−	16.7770i		−	0.612201i	−0.951999	−	0.306100i	$-0.900976\pi$
$751$		−	16.7770i		−	0.612201i	0.951999	−	0.306100i	$-0.0990243\pi$
$752$	13.7248	−	13.7248i	0.500493	−	0.500493i
$753$			27.5285i			1.00319i
$754$	12.0041	+	11.3290i	0.437162	+	0.412579i
$755$		−	9.36943i		−	0.340989i
$756$	−0.0150710	+	2.69194i	−0.000548128	+	0.0979048i
$757$	−20.7321			−0.753520			−0.376760	−	0.926311i	$-0.622962\pi$
$757$	−20.7321			−0.753520			−0.376760	+	0.926311i	$0.622962\pi$
$758$		−	6.22568i		−	0.226127i
$759$	27.4540	+	27.4540i	0.996519	+	0.996519i
$760$	0.277394	−	0.277394i	0.0100621	−	0.0100621i
$761$	−2.11330	+	2.11330i	−0.0766071	+	0.0766071i	−0.744372	−	0.667765i	$-0.767251\pi$
$761$	−2.11330	+	2.11330i	−0.0766071	+	0.0766071i	0.667765	+	0.744372i	$0.267251\pi$
$762$	14.3341	−	14.3341i	0.519268	−	0.519268i
$763$	15.4030	+	15.5764i	0.557624	+	0.563903i
$764$		−	5.39576i		−	0.195212i
$765$	−4.05365	−	4.05365i	−0.146560	−	0.146560i
$766$	−41.9782			−1.51674
$767$	33.9360	+	32.0277i	1.22536	+	1.15645i
$768$		−	27.0932i		−	0.977642i
$769$	−25.9456	−	25.9456i	−0.935621	−	0.935621i	0.0624284	−	0.998049i	$-0.480115\pi$
$769$	−25.9456	−	25.9456i	−0.935621	−	0.935621i	−0.998049	+	0.0624284i	$0.980115\pi$
$770$	5.17009	−	5.11252i	0.186317	−	0.184242i
$771$			39.9637i			1.43926i
$772$	5.51867	−	5.51867i	0.198621	−	0.198621i
$773$	−0.951693	−	0.951693i	−0.0342300	−	0.0342300i	0.689785	−	0.724015i	$-0.257705\pi$
$773$	−0.951693	−	0.951693i	−0.0342300	−	0.0342300i	−0.724015	+	0.689785i	$0.757705\pi$
$774$	5.90409	+	5.90409i	0.212218	+	0.212218i
$775$	28.7761	−	28.7761i	1.03367	−	1.03367i
$776$			19.2847i			0.692280i
$777$	−12.1121	−	12.2485i	−0.434518	−	0.439411i
$778$	−5.54638	−	5.54638i	−0.198847	−	0.198847i
$779$		−	0.474142i		−	0.0169879i
$780$	2.63021	−	2.78692i	0.0941766	−	0.0997879i
$781$	15.2195			0.544598
$782$	−16.9547	−	16.9547i	−0.606299	−	0.606299i
$783$		−	7.14746i		−	0.255430i
$784$	−18.4151	−	0.206204i	−0.657683	−	0.00736442i
$785$	−12.8908	+	12.8908i	−0.460091	+	0.460091i
$786$	−23.2495	+	23.2495i	−0.829283	+	0.829283i
$787$	−24.8017	+	24.8017i	−0.884085	+	0.884085i	−0.993947	−	0.109862i	$-0.964959\pi$
$787$	−24.8017	+	24.8017i	−0.884085	+	0.884085i	0.109862	+	0.993947i	$0.464959\pi$
$788$	8.23287	+	8.23287i	0.293284	+	0.293284i
$789$		−	33.0286i		−	1.17585i
$790$	−18.4366			−0.655946
$791$	0.0851021	−	15.2006i	0.00302588	−	0.540473i
$792$			17.4680i			0.620698i
$793$	33.1845	−	0.960007i	1.17841	−	0.0340908i
$794$			11.7860i			0.418268i
$795$	4.78345	−	4.78345i	0.169651	−	0.169651i
$796$			12.1121i			0.429301i
$797$	34.9017			1.23628			0.618141	−	0.786067i	$-0.287886\pi$
$797$	34.9017			1.23628			0.618141	+	0.786067i	$0.287886\pi$
$798$	1.07209	+	0.00600221i	0.0379517	+	0.000212476i
$799$	−15.8969	+	15.8969i	−0.562392	+	0.562392i
$800$	8.88655	+	8.88655i	0.314187	+	0.314187i
$801$	−7.36857	+	7.36857i	−0.260356	+	0.260356i
$802$	15.4224			0.544585
$803$	−25.6890			−0.906545
$804$	1.28662	−	1.28662i	0.0453757	−	0.0453757i
$805$	−10.4993	−	10.6176i	−0.370053	−	0.374220i
$806$	−1.20710	−	41.7256i	−0.0425182	−	1.46972i
$807$	−53.2411			−1.87418
$808$	2.51778	+	2.51778i	0.0885750	+	0.0885750i
$809$	10.2618			0.360786			0.180393	−	0.983595i	$-0.442263\pi$
$809$	10.2618			0.360786			0.180393	+	0.983595i	$0.442263\pi$
$810$	11.3171			0.397642
$811$	−13.3684	−	13.3684i	−0.469428	−	0.469428i	0.432301	−	0.901729i	$-0.357702\pi$
$811$	−13.3684	−	13.3684i	−0.469428	−	0.469428i	−0.901729	+	0.432301i	$0.857702\pi$
$812$	−5.40323	−	0.0302504i	−0.189616	−	0.00106158i
$813$	5.49466	+	5.49466i	0.192706	+	0.192706i
$814$	6.41855	+	6.41855i	0.224970	+	0.224970i
$815$			8.62627i			0.302165i
$816$		−	18.2290i		−	0.638142i
$817$	0.331912	−	0.331912i	0.0116121	−	0.0116121i
$818$	4.89002			0.170976
$819$	20.6957	−	0.482769i	0.723165	−	0.0168693i
$820$	−1.50307			−0.0524895
$821$	17.3074	−	17.3074i	0.604031	−	0.604031i	−0.337349	−	0.941380i	$-0.609530\pi$
$821$	17.3074	−	17.3074i	0.604031	−	0.604031i	0.941380	+	0.337349i	$0.109530\pi$
$822$			7.32052i			0.255333i
$823$			35.0772i			1.22271i	0.791355	+	0.611356i	$0.209376\pi$
$823$			35.0772i			1.22271i	−0.791355	+	0.611356i	$0.790624\pi$
$824$	−11.5471	−	11.5471i	−0.402263	−	0.402263i
$825$	−17.9160	−	17.9160i	−0.623753	−	0.623753i
$826$	41.3846	+	0.231696i	1.43996	+	0.00806172i
$827$	−19.4173	−	19.4173i	−0.675207	−	0.675207i	0.283705	−	0.958912i	$-0.408436\pi$
$827$	−19.4173	−	19.4173i	−0.675207	−	0.675207i	−0.958912	+	0.283705i	$0.908436\pi$
$828$	7.61757			0.264729
$829$	9.16091			0.318172			0.159086	−	0.987265i	$-0.449145\pi$
$829$	9.16091			0.318172			0.159086	+	0.987265i	$0.449145\pi$
$830$	11.0514	+	11.0514i	0.383599	+	0.383599i
$831$	−66.1039			−2.29312
$832$	31.8493	−	0.921381i	1.10418	−	0.0319432i
$833$	21.3295	+	0.238838i	0.739023	+	0.00827523i
$834$	12.3763	−	12.3763i	0.428556	−	0.428556i
$835$	−14.7959			−0.512033
$836$	0.208526			0.00721201
$837$	−12.7815	+	12.7815i	−0.441794	+	0.441794i
$838$	−30.2625	−	30.2625i	−1.04540	−	1.04540i
$839$	−26.1882	+	26.1882i	−0.904116	+	0.904116i	−0.995789	−	0.0916731i	$-0.970779\pi$
$839$	−26.1882	+	26.1882i	−0.904116	+	0.904116i	0.0916731	+	0.995789i	$0.470779\pi$
$840$	0.0896058	−	16.0051i	0.00309170	−	0.552228i
$841$	−14.6537			−0.505299
$842$		−	32.3579i		−	1.11513i
$843$	−22.0206	+	22.0206i	−0.758428	+	0.758428i
$844$		−	10.1639i		−	0.349857i
$845$	8.41635	+	7.49497i	0.289531	+	0.257835i
$846$			19.3505i			0.665283i
$847$	−10.9020	−	0.0610359i	−0.374598	−	0.00209722i
$848$	9.02893			0.310055
$849$		−	9.78539i		−	0.335834i
$850$	11.0643	+	11.0643i	0.379502	+	0.379502i
$851$	13.1815	−	13.1815i	0.451855	−	0.451855i
$852$	5.03040	−	5.03040i	0.172339	−	0.172339i
$853$	7.70865	−	7.70865i	0.263939	−	0.263939i	−0.562713	−	0.826652i	$-0.690242\pi$
$853$	7.70865	−	7.70865i	0.263939	−	0.263939i	0.826652	+	0.562713i	$0.190242\pi$
$854$	20.9360	−	20.7029i	0.716415	−	0.708438i
$855$			0.277394i			0.00948666i
$856$	22.2401	+	22.2401i	0.760149	+	0.760149i
$857$	22.4141			0.765651			0.382825	−	0.923821i	$-0.374951\pi$
$857$	22.4141			0.765651			0.382825	+	0.923821i	$0.374951\pi$
$858$	−25.9783	+	0.751536i	−0.886883	+	0.0256570i
$859$			43.5695i			1.48657i	0.668974	+	0.743286i	$0.266734\pi$
$859$			43.5695i			1.48657i	−0.668974	+	0.743286i	$0.733266\pi$
$860$	−1.05219	−	1.05219i	−0.0358794	−	0.0358794i
$861$	−13.6020	−	13.7551i	−0.463554	−	0.468774i
$862$		−	21.5441i		−	0.733795i
$863$	−9.02893	+	9.02893i	−0.307348	+	0.307348i	−0.843880	−	0.536532i	$-0.819734\pi$
$863$	−9.02893	+	9.02893i	−0.307348	+	0.307348i	0.536532	+	0.843880i	$0.319734\pi$
$864$	−3.94714	−	3.94714i	−0.134285	−	0.134285i
$865$	4.58670	+	4.58670i	0.155952	+	0.155952i
$866$	12.2548	−	12.2548i	0.416436	−	0.416436i
$867$		−	17.5404i		−	0.595703i
$868$	9.60827	+	9.71646i	0.326126	+	0.329798i
$869$	−32.6339	−	32.6339i	−1.10703	−	1.10703i
$870$			9.02383i			0.305937i
$871$	3.89168	+	3.67284i	0.131864	+	0.124449i
$872$	−25.4101			−0.860496
$873$	−9.64235	−	9.64235i	−0.326344	−	0.326344i
$874$			1.16022i			0.0392450i
$875$	14.9153	+	15.0833i	0.504231	+	0.509909i
$876$	−8.49079	+	8.49079i	−0.286877	+	0.286877i
$877$	−4.81957	+	4.81957i	−0.162745	+	0.162745i	−0.783782	−	0.621036i	$-0.786712\pi$
$877$	−4.81957	+	4.81957i	−0.162745	+	0.162745i	0.621036	+	0.783782i	$0.286712\pi$
$878$	−17.0767	+	17.0767i	−0.576311	+	0.576311i
$879$	8.12589	+	8.12589i	0.274079	+	0.274079i
$880$			5.98209i			0.201656i
$881$	3.46947			0.116889			0.0584447	−	0.998291i	$-0.481386\pi$
$881$	3.46947			0.116889			0.0584447	+	0.998291i	$0.481386\pi$
$882$	13.1270	−	12.8363i	0.442009	−	0.432220i
$883$		−	47.0772i		−	1.58427i	−0.610344	−	0.792136i	$-0.708969\pi$
$883$		−	47.0772i		−	1.58427i	0.610344	−	0.792136i	$-0.291031\pi$
$884$	−5.92162	+	0.171309i	−0.199166	+	0.00576175i
$885$			25.5108i			0.857536i
$886$	−4.81852	+	4.81852i	−0.161881	+	0.161881i
$887$			5.75722i			0.193309i	0.995318	+	0.0966543i	$0.0308141\pi$
$887$			5.75722i			0.193309i	−0.995318	+	0.0966543i	$0.969186\pi$
$888$	19.9812			0.670526
$889$	−19.5155	−	0.109259i	−0.654530	−	0.00366444i
$890$	−3.55777	+	3.55777i	−0.119257	+	0.119257i
$891$	20.0319	+	20.0319i	0.671094	+	0.671094i
$892$	−2.33000	+	2.33000i	−0.0780142	+	0.0780142i
$893$	1.08783			0.0364029
$894$	51.8305			1.73347
$895$	13.9156	−	13.9156i	0.465148	−	0.465148i
$896$	8.96357	−	8.86376i	0.299452	−	0.296118i
$897$	1.54339	+	53.3503i	0.0515324	+	1.78132i
$898$	−22.0599			−0.736150
$899$	−25.6549	−	25.6549i	−0.855639	−	0.855639i
$900$	−4.97107			−0.165702
$901$	−10.4578			−0.348401
$902$	7.20809	+	7.20809i	0.240003	+	0.240003i
$903$	0.107217	−	19.1507i	0.00356795	−	0.637295i
$904$	12.4680	+	12.4680i	0.414679	+	0.414679i
$905$	1.17534	+	1.17534i	0.0390695	+	0.0390695i
$906$			29.7019i			0.986780i
$907$		−	13.1412i		−	0.436345i	−0.975910	−	0.218172i	$-0.929990\pi$
$907$		−	13.1412i		−	0.436345i	0.975910	−	0.218172i	$-0.0700095\pi$
$908$	2.52896	−	2.52896i	0.0839266	−	0.0839266i
$909$	−2.51778			−0.0835093
$910$	9.99251	−	0.233096i	0.331248	−	0.00772705i
$911$	22.8394			0.756702			0.378351	−	0.925662i	$-0.376491\pi$
$911$	22.8394			0.756702			0.378351	+	0.925662i	$0.376491\pi$
$912$	−0.623710	+	0.623710i	−0.0206531	+	0.0206531i
$913$			39.1232i			1.29479i
$914$		−	11.9083i		−	0.393891i
$915$	12.8337	+	12.8337i	0.424271	+	0.424271i
$916$	−0.142747	−	0.142747i	−0.00471648	−	0.00471648i
$917$	31.6537	+	0.177216i	1.04530	+	0.00585219i
$918$	−4.91443	−	4.91443i	−0.162201	−	0.162201i
$919$	35.0265			1.15542			0.577709	−	0.816243i	$-0.303947\pi$
$919$	35.0265			1.15542			0.577709	+	0.816243i	$0.303947\pi$
$920$	17.3207			0.571046
$921$	−19.5422	−	19.5422i	−0.643936	−	0.643936i
$922$	12.3206			0.405758
$923$	15.2156	+	14.3600i	0.500826	+	0.472664i
$924$	6.04945	−	5.98209i	0.199012	−	0.196796i
$925$	−8.60197	+	8.60197i	−0.282831	+	0.282831i
$926$	−6.94110			−0.228099
$927$	11.5471			0.379257
$928$	7.92267	−	7.92267i	0.260074	−	0.260074i
$929$	−16.0163	−	16.0163i	−0.525479	−	0.525479i	0.393742	−	0.919221i	$-0.371180\pi$
$929$	−16.0163	−	16.0163i	−0.525479	−	0.525479i	−0.919221	+	0.393742i	$0.871180\pi$
$930$	16.1369	−	16.1369i	0.529151	−	0.529151i
$931$	−0.721622	−	0.737966i	−0.0236502	−	0.0241859i
$932$	−3.32297			−0.108847
$933$		−	51.2522i		−	1.67792i
$934$	−14.8428	+	14.8428i	−0.485671	+	0.485671i
$935$		−	6.92881i		−	0.226596i
$936$	−16.4814	+	17.4634i	−0.538712	+	0.570810i
$937$			39.2356i			1.28177i	0.767636	+	0.640886i	$0.221433\pi$
$937$			39.2356i			1.28177i	−0.767636	+	0.640886i	$0.778567\pi$
$938$	4.74586	+	0.0265701i	0.154958	+	0.000867545i
$939$	−9.79711			−0.319717
$940$		−	3.44852i		−	0.112478i
$941$	−31.6697	−	31.6697i	−1.03240	−	1.03240i	−0.999457	−	0.0329454i	$-0.989511\pi$
$941$	−31.6697	−	31.6697i	−1.03240	−	1.03240i	−0.0329454	−	0.999457i	$-0.510489\pi$
$942$	40.8648	−	40.8648i	1.33145	−	1.33145i
$943$	14.8029	−	14.8029i	0.482049	−	0.482049i
$944$	−24.0763	+	24.0763i	−0.783615	+	0.783615i
$945$	−3.04331	−	3.07757i	−0.0989987	−	0.100113i
$946$			10.0917i			0.328110i
$947$	−11.5948	−	11.5948i	−0.376780	−	0.376780i	0.493159	−	0.869939i	$-0.335842\pi$
$947$	−11.5948	−	11.5948i	−0.376780	−	0.376780i	−0.869939	+	0.493159i	$0.835842\pi$
$948$	−21.5724			−0.700641
$949$	−25.6823	−	24.2381i	−0.833682	−	0.786803i
$950$		−	0.757136i		−	0.0245647i
$951$	9.02935	+	9.02935i	0.292797	+	0.292797i
$952$	−17.5936	+	17.3977i	−0.570210	+	0.563861i
$953$			37.1939i			1.20483i	0.798183	+	0.602415i	$0.205795\pi$
$953$			37.1939i			1.20483i	−0.798183	+	0.602415i	$0.794205\pi$
$954$	−6.36490	+	6.36490i	−0.206071	+	0.206071i
$955$	6.13440	+	6.13440i	0.198504	+	0.198504i
$956$	−3.03612	−	3.03612i	−0.0981951	−	0.0981951i
$957$	−15.9727	+	15.9727i	−0.516324	+	0.516324i
$958$		−	16.8985i		−	0.545965i
$959$	5.01127	−	4.95547i	0.161822	−	0.160021i
$960$	12.3174	+	12.3174i	0.397542	+	0.397542i
$961$			60.7552i			1.95985i
$962$	0.360834	+	12.4729i	0.0116338	+	0.402143i
$963$	−22.2401			−0.716676
$964$	0.599672	+	0.599672i	0.0193141	+	0.0193141i
$965$			12.5483i			0.403943i
$966$	33.2838	+	33.6586i	1.07089	+	1.08295i
$967$	34.8785	−	34.8785i	1.12162	−	1.12162i	0.130117	−	0.991499i	$-0.458465\pi$
$967$	34.8785	−	34.8785i	1.12162	−	1.12162i	0.991499	−	0.130117i	$-0.0415354\pi$
$968$	8.94214	−	8.94214i	0.287411	−	0.287411i
$969$	0.722418	−	0.722418i	0.0232074	−	0.0232074i
$970$	−4.65562	−	4.65562i	−0.149483	−	0.149483i
$971$			13.7033i			0.439760i	0.975527	+	0.219880i	$0.0705666\pi$
$971$			13.7033i			0.439760i	−0.975527	+	0.219880i	$0.929433\pi$
$972$	10.1896			0.326831
$973$	−16.8501	−	0.0943366i	−0.540189	−	0.00302429i
$974$			21.5525i			0.690587i
$975$	−1.00719	−	34.8154i	−0.0322558	−	1.11498i
$976$			24.2242i			0.775396i
$977$	5.81011	−	5.81011i	0.185882	−	0.185882i	−0.608031	−	0.793913i	$-0.708040\pi$
$977$	5.81011	−	5.81011i	0.185882	−	0.185882i	0.793913	+	0.608031i	$0.208040\pi$
$978$		−	27.3460i		−	0.874429i
$979$	−12.5949			−0.402535
$980$	−2.33942	+	2.28761i	−0.0747299	+	0.0730749i
$981$	12.7051	−	12.7051i	0.405642	−	0.405642i
$982$	−1.47414	−	1.47414i	−0.0470418	−	0.0470418i
$983$	12.2658	−	12.2658i	0.391218	−	0.391218i	−0.483904	−	0.875121i	$-0.660782\pi$
$983$	12.2658	−	12.2658i	0.391218	−	0.391218i	0.875121	+	0.483904i	$0.160782\pi$
$984$	22.4391			0.715331
$985$	−18.7197			−0.596461
$986$	9.86420	−	9.86420i	0.314140	−	0.314140i
$987$	31.5586	−	31.2072i	1.00452	−	0.993338i
$988$	0.208471	+	0.196748i	0.00663235	+	0.00625940i
$989$	20.7249			0.659013
$990$	−4.21704	−	4.21704i	−0.134026	−	0.134026i
$991$	40.5574			1.28835			0.644175	−	0.764878i	$-0.277201\pi$
$991$	40.5574			1.28835			0.644175	+	0.764878i	$0.277201\pi$
$992$	−28.3355			−0.899655
$993$	3.88652	+	3.88652i	0.123335	+	0.123335i
$994$	18.5552	+	0.103883i	0.588536	+	0.00329497i
$995$	−13.7701	−	13.7701i	−0.436542	−	0.436542i
$996$	12.9311	+	12.9311i	0.409737	+	0.409737i
$997$			17.4686i			0.553236i	0.960980	+	0.276618i	$0.0892136\pi$
$997$			17.4686i			0.553236i	−0.960980	+	0.276618i	$0.910786\pi$
$998$			47.0999i			1.49092i
$999$	3.82074	−	3.82074i	0.120883	−	0.120883i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.i.a.83.6	yes	12
3.2	odd	2		819.2.y.h.811.2		12
7.2	even	3		637.2.bc.a.31.1		24
7.3	odd	6		637.2.bc.a.460.5		24
7.4	even	3		637.2.bc.a.460.6		24
7.5	odd	6		637.2.bc.a.31.2		24
7.6	odd	2	inner	91.2.i.a.83.5	yes	12
13.8	odd	4	inner	91.2.i.a.34.6	yes	12
21.20	even	2		819.2.y.h.811.1		12
39.8	even	4		819.2.y.h.307.1		12
91.34	even	4	inner	91.2.i.a.34.5	✓	12
91.47	even	12		637.2.bc.a.619.6		24
91.60	odd	12		637.2.bc.a.411.2		24
91.73	even	12		637.2.bc.a.411.1		24
91.86	odd	12		637.2.bc.a.619.5		24
273.125	odd	4		819.2.y.h.307.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.i.a.34.5	✓	12	91.34	even	4	inner
91.2.i.a.34.6	yes	12	13.8	odd	4	inner
91.2.i.a.83.5	yes	12	7.6	odd	2	inner
91.2.i.a.83.6	yes	12	1.1	even	1	trivial
637.2.bc.a.31.1		24	7.2	even	3
637.2.bc.a.31.2		24	7.5	odd	6
637.2.bc.a.411.1		24	91.73	even	12
637.2.bc.a.411.2		24	91.60	odd	12
637.2.bc.a.460.5		24	7.3	odd	6
637.2.bc.a.460.6		24	7.4	even	3
637.2.bc.a.619.5		24	91.86	odd	12
637.2.bc.a.619.6		24	91.47	even	12
819.2.y.h.307.1		12	39.8	even	4
819.2.y.h.307.2		12	273.125	odd	4
819.2.y.h.811.1		12	21.20	even	2
819.2.y.h.811.2		12	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.854638 - 0.854638i) q^{2} +2.27378i q^{3} +0.539189i q^{4} +(-0.612999 - 0.612999i) q^{5} +(1.94326 + 1.94326i) q^{6} +(0.0148122 - 2.64571i) q^{7} +(2.17009 + 2.17009i) q^{8} -2.17009 q^{9} +O(q^{10})\)	\(q+(0.854638 - 0.854638i) q^{2} +2.27378i q^{3} +0.539189i q^{4} +(-0.612999 - 0.612999i) q^{5} +(1.94326 + 1.94326i) q^{6} +(0.0148122 - 2.64571i) q^{7} +(2.17009 + 2.17009i) q^{8} -2.17009 q^{9} -1.04778 q^{10} +(-1.85464 - 1.85464i) q^{11} -1.22600 q^{12} +(-0.104263 - 3.60404i) q^{13} +(-2.24846 - 2.27378i) q^{14} +(1.39383 - 1.39383i) q^{15} +2.63090 q^{16} -3.04726 q^{17} +(-1.85464 + 1.85464i) q^{18} +(0.104263 + 0.104263i) q^{19} +(0.330522 - 0.330522i) q^{20} +(6.01577 + 0.0336798i) q^{21} -3.17009 q^{22} +6.51026i q^{23} +(-4.93430 + 4.93430i) q^{24} -4.24846i q^{25} +(-3.16926 - 2.99104i) q^{26} +1.88704i q^{27} +(1.42654 + 0.00798659i) q^{28} -3.78765 q^{29} -2.38243i q^{30} +(6.77330 + 6.77330i) q^{31} +(-2.09171 + 2.09171i) q^{32} +(4.21704 - 4.21704i) q^{33} +(-2.60430 + 2.60430i) q^{34} +(-1.63090 + 1.61274i) q^{35} -1.17009i q^{36} +(-2.02472 - 2.02472i) q^{37} +0.178214 q^{38} +(8.19481 - 0.237071i) q^{39} -2.66052i q^{40} +(-2.27378 - 2.27378i) q^{41} +(5.17009 - 5.11252i) q^{42} -3.18342i q^{43} +(1.00000 - 1.00000i) q^{44} +(1.33026 + 1.33026i) q^{45} +(5.56391 + 5.56391i) q^{46} +(5.21678 - 5.21678i) q^{47} +5.98209i q^{48} +(-6.99956 - 0.0783777i) q^{49} +(-3.63090 - 3.63090i) q^{50} -6.92881i q^{51} +(1.94326 - 0.0562174i) q^{52} +3.43188 q^{53} +(1.61274 + 1.61274i) q^{54} +2.27378i q^{55} +(5.77356 - 5.70928i) q^{56} +(-0.237071 + 0.237071i) q^{57} +(-3.23707 + 3.23707i) q^{58} +(-9.15135 + 9.15135i) q^{59} +(0.751536 + 0.751536i) q^{60} +9.20756i q^{61} +11.5774 q^{62} +(-0.0321438 + 5.74142i) q^{63} +8.83710i q^{64} +(-2.14536 + 2.27319i) q^{65} -7.20809i q^{66} +(-1.04945 + 1.04945i) q^{67} -1.64305i q^{68} -14.8029 q^{69} +(-0.0155200 + 2.77213i) q^{70} +(-4.10310 + 4.10310i) q^{71} +(-4.70928 - 4.70928i) q^{72} +(6.92561 - 6.92561i) q^{73} -3.46081 q^{74} +9.66008 q^{75} +(-0.0562174 + 0.0562174i) q^{76} +(-4.93430 + 4.87936i) q^{77} +(6.80098 - 7.20620i) q^{78} +17.5958 q^{79} +(-1.61274 - 1.61274i) q^{80} -10.8010 q^{81} -3.88652 q^{82} +(-10.5474 - 10.5474i) q^{83} +(-0.0181598 + 3.24364i) q^{84} +(1.86797 + 1.86797i) q^{85} +(-2.72067 - 2.72067i) q^{86} -8.61230i q^{87} -8.04945i q^{88} +(3.39552 - 3.39552i) q^{89} +2.27378 q^{90} +(-9.53680 + 0.222465i) q^{91} -3.51026 q^{92} +(-15.4010 + 15.4010i) q^{93} -8.91692i q^{94} -0.127826i q^{95} +(-4.75609 - 4.75609i) q^{96} +(4.44330 + 4.44330i) q^{97} +(-6.04907 + 5.91510i) q^{98} +(4.02472 + 4.02472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 8 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 - 8 * q^7 + 4 * q^8 - 4 * q^9	\( 12 q - 4 q^{2} - 8 q^{7} + 4 q^{8} - 4 q^{9} - 8 q^{11} + 8 q^{14} - 4 q^{15} + 16 q^{16} - 8 q^{18} - 16 q^{22} - 20 q^{28} - 4 q^{29} - 16 q^{32} - 4 q^{35} + 12 q^{37} + 40 q^{39} + 40 q^{42} + 12 q^{44} + 24 q^{46} - 28 q^{50} - 12 q^{53} - 8 q^{57} - 44 q^{58} + 44 q^{60} + 20 q^{63} - 40 q^{65} + 60 q^{67} + 4 q^{70} - 28 q^{72} - 48 q^{74} + 44 q^{78} - 4 q^{79} - 92 q^{81} - 4 q^{84} + 12 q^{85} + 36 q^{86} - 32 q^{91} + 24 q^{92} - 28 q^{93} - 28 q^{98} + 12 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 8 * q^7 + 4 * q^8 - 4 * q^9 - 8 * q^11 + 8 * q^14 - 4 * q^15 + 16 * q^16 - 8 * q^18 - 16 * q^22 - 20 * q^28 - 4 * q^29 - 16 * q^32 - 4 * q^35 + 12 * q^37 + 40 * q^39 + 40 * q^42 + 12 * q^44 + 24 * q^46 - 28 * q^50 - 12 * q^53 - 8 * q^57 - 44 * q^58 + 44 * q^60 + 20 * q^63 - 40 * q^65 + 60 * q^67 + 4 * q^70 - 28 * q^72 - 48 * q^74 + 44 * q^78 - 4 * q^79 - 92 * q^81 - 4 * q^84 + 12 * q^85 + 36 * q^86 - 32 * q^91 + 24 * q^92 - 28 * q^93 - 28 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more