LMFDB - Embedded newform 91.2.i.a.83.5

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			83.5
Root			$-1.33026 - 1.33026i$ of defining polynomial
Character	$\chi$	$=$	91.83
Dual form			91.2.i.a.34.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.854638 - 0.854638i) q^{2} -2.27378i q^{3} +0.539189i q^{4} +(0.612999 + 0.612999i) q^{5} +(-1.94326 - 1.94326i) q^{6} +(-2.64571 + 0.0148122i) q^{7} +(2.17009 + 2.17009i) q^{8} -2.17009 q^{9} +O(q^{10})$	\(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} +(-2.64571 + 0.0148122i) 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} +(0.0336798 + 6.01577i) 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} +(-0.00798659 - 1.42654i) 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} +(5.74142 - 0.0321438i) 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} +(-2.77213 + 0.0155200i) 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} +(-3.24364 + 0.0181598i) 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} +(-0.329233 - 9.53371i) 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} +(5.91510 - 6.04907i) 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	$-0.772085\pi$
$3$		−	2.27378i		−	1.31277i	0.754427	−	0.656384i	$-0.227915\pi$
$4$			0.539189i			0.269594i
$5$	0.612999	+	0.612999i	0.274142	+	0.274142i	0.830765	−	0.556623i	$-0.187903\pi$
$5$	0.612999	+	0.612999i	0.274142	+	0.274142i	−0.556623	+	0.830765i	$0.687903\pi$
$6$	−1.94326	−	1.94326i	−0.793333	−	0.793333i
$7$	−2.64571	+	0.0148122i	−0.999984	+	0.00559850i
$7$	−2.64571	+	0.0148122i	−0.999984	+	0.00559850i
$8$	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	$-0.379517\pi$
$17$	3.04726			0.739070			0.369535	+	0.929217i	$0.379517\pi$
$18$	−1.85464	+	1.85464i	−0.437142	+	0.437142i
$19$	−0.104263	−	0.104263i	−0.0239195	−	0.0239195i	0.695046	−	0.718965i	$-0.255384\pi$
$19$	−0.104263	−	0.104263i	−0.0239195	−	0.0239195i	−0.718965	+	0.695046i	$0.755384\pi$
$20$	−0.330522	+	0.330522i	−0.0739070	+	0.0739070i
$21$	0.0336798	+	6.01577i	0.00734953	+	1.31275i
$22$	−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
$28$	−0.00798659	−	1.42654i	−0.00150932	−	0.269590i
$29$	−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	$-0.920332\pi$
$31$	−6.77330	−	6.77330i	−1.21652	−	1.21652i	−0.247679	−	0.968842i	$-0.579668\pi$
$32$	−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	0.862005	−	0.506900i	$-0.169209\pi$
$41$	2.27378	+	2.27378i	0.355105	+	0.355105i	−0.506900	+	0.862005i	$0.669209\pi$
$42$	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	−0.976493	−	0.215548i	$-0.930846\pi$
$47$	−5.21678	+	5.21678i	−0.760946	+	0.760946i	0.215548	+	0.976493i	$0.430846\pi$
$48$		−	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	$-0.431113\pi$
$59$	9.15135	−	9.15135i	1.19140	−	1.19140i	0.976673	−	0.214731i	$-0.0688873\pi$
$60$	0.751536	+	0.751536i	0.0970229	+	0.0970229i
$61$		−	9.20756i		−	1.17891i	−0.807802	−	0.589454i	$-0.799343\pi$
$61$		−	9.20756i		−	1.17891i	0.807802	−	0.589454i	$-0.200657\pi$
$62$	−11.5774			−1.47034
$63$	5.74142	−	0.0321438i	0.723351	−	0.00404974i
$64$			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
$70$	−2.77213	+	0.0155200i	−0.331333	+	0.00185500i
$71$	−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	−0.984721	−	0.174140i	$-0.944286\pi$
$73$	−6.92561	+	6.92561i	−0.810581	+	0.810581i	0.174140	+	0.984721i	$0.444286\pi$
$74$	−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	$0.0552694\pi$
$83$	10.5474	+	10.5474i	1.15773	+	1.15773i	0.172763	+	0.984963i	$0.444731\pi$
$84$	−3.24364	+	0.0181598i	−0.353910	+	0.00198139i
$85$	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	−0.863785	−	0.503861i	$-0.831912\pi$
$89$	−3.39552	+	3.39552i	−0.359924	+	0.359924i	0.503861	+	0.863785i	$0.331912\pi$
$90$	−2.27378			−0.239678
$91$	−0.329233	−	9.53371i	−0.0345130	−	0.999404i
$92$	−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	0.444587	−	0.895736i	$-0.353351\pi$
$97$	−4.44330	−	4.44330i	−0.451149	−	0.451149i	−0.895736	+	0.444587i	$0.853351\pi$
$98$	5.91510	−	6.04907i	0.597516	−	0.611049i
$99$	4.02472	+	4.02472i	0.404500	+	0.404500i
$100$	2.29072			0.229072
$101$	−1.16022			−0.115446			−0.0577231	−	0.998333i	$-0.518384\pi$
$101$	−1.16022			−0.115446			−0.0577231	+	0.998333i	$0.518384\pi$
$102$	−5.92162	−	5.92162i	−0.586328	−	0.586328i
$103$	5.32104			0.524298			0.262149	−	0.965027i	$-0.415569\pi$
$103$	5.32104			0.524298			0.262149	+	0.965027i	$0.415569\pi$
$104$	−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
$112$	−6.96059	+	0.0389695i	−0.657714	+	0.00368227i
$113$	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
$119$	−8.06217	+	0.0451368i	−0.739058	+	0.00413768i
$120$	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	$-0.824941\pi$
$131$		−	11.9642i		−	1.04532i	0.852543	−	0.522658i	$-0.175059\pi$
$132$	−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	$0.0870563\pi$
$139$			6.36883i			0.540197i	−0.962833	+	0.270098i	$0.912944\pi$
$140$	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
$154$	8.38713	−	0.0469561i	0.675854	−	0.00378383i
$155$		−	8.30406i		−	0.666998i
$156$	0.127826	+	4.41855i	0.0102343	+	0.353767i
$157$			21.0290i			1.67830i	0.543903	+	0.839148i	$0.316946\pi$
$157$			21.0290i			1.67830i	−0.543903	+	0.839148i	$0.683054\pi$
$158$	15.0381	−	15.0381i	1.19636	−	1.19636i
$159$		−	7.80335i		−	0.618846i
$160$	−2.56443			−0.202736
$161$	−0.0964315	−	17.2243i	−0.00759987	−	1.35746i
$162$	−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	−0.997946	−	0.0640620i	$-0.979594\pi$
$167$	−12.0684	+	12.0684i	−0.933884	+	0.933884i	0.0640620	+	0.997946i	$0.479594\pi$
$168$	−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	$-0.408193\pi$
$173$	7.48239			0.568876			0.284438	+	0.958694i	$0.408193\pi$
$174$	7.36040	+	7.36040i	0.557990	+	0.557990i
$175$	0.0629292	+	11.2402i	0.00475700	+	0.849680i
$176$	−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	$-0.477299\pi$
$181$	1.91735			0.142516			0.0712579	+	0.997458i	$0.477299\pi$
$182$	−8.42924	−	7.86649i	−0.624817	−	0.583103i
$183$	−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
$189$	0.0279513	+	4.99257i	0.00203316	+	0.363156i
$190$	−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	$-0.793159\pi$
$199$	−22.4635			−1.59240			−0.796198	+	0.605036i	$0.793159\pi$
$200$	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
$203$	10.0210	−	0.0561036i	0.703339	−	0.00393770i
$204$	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
$210$	0.0352892	+	6.30323i	0.00243518	+	0.434964i
$211$	−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	0.547457	−	0.836833i	$-0.315596\pi$
$223$	−4.32131	−	4.32131i	−0.289376	−	0.289376i	−0.836833	+	0.547457i	$0.815596\pi$
$224$	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	0.845416	−	0.534109i	$-0.179353\pi$
$227$	4.69031	+	4.69031i	0.311307	+	0.311307i	−0.534109	+	0.845416i	$0.679353\pi$
$228$	−0.127826	−	0.127826i	−0.00846549	−	0.00846549i
$229$	0.264743	−	0.264743i	0.0174947	−	0.0174947i	−0.698305	−	0.715800i	$-0.746062\pi$
$229$	0.264743	−	0.264743i	0.0174947	−	0.0174947i	0.715800	+	0.698305i	$0.246062\pi$
$230$			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	−0.742020	−	0.670378i	$-0.766132\pi$
$241$	−1.11217	+	1.11217i	−0.0716414	+	0.0716414i	0.670378	+	0.742020i	$0.266132\pi$
$242$	−3.52165	−	3.52165i	−0.226380	−	0.226380i
$243$			18.8980i			1.21230i
$244$	4.96462			0.317827
$245$	4.33877	+	4.24268i	0.277194	+	0.271055i
$246$		−	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	$-0.624796\pi$
$251$	−12.1069			−0.764182			−0.382091	+	0.924125i	$0.624796\pi$
$252$	0.0173316	+	3.09571i	0.00109179	+	0.195011i
$253$	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	$-0.684678\pi$
$257$	−17.5759			−1.09635			−0.548176	+	0.836363i	$0.684678\pi$
$258$	−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
$266$	0.471502	−	0.00263975i	0.0289097	−	0.000161853i
$267$	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	$-0.746961\pi$
$269$		−	23.4152i		−	1.42765i	0.700324	−	0.713825i	$-0.253039\pi$
$270$		−	1.97721i		−	0.120329i
$271$	−2.41653	+	2.41653i	−0.146794	+	0.146794i	−0.776684	−	0.629890i	$-0.783100\pi$
$271$	−2.41653	+	2.41653i	−0.146794	+	0.146794i	0.629890	+	0.776684i	$0.283100\pi$
$272$	8.01703			0.486104
$273$	−21.6776	+	0.748605i	−1.31199	+	0.0453076i
$274$	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
$280$	−0.0394083	−	7.03897i	−0.00235509	−	0.420659i
$281$	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	$-0.459173\pi$
$283$	4.30357			0.255821			0.127910	+	0.991786i	$0.459173\pi$
$284$	−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	−0.803749	−	0.594969i	$-0.797164\pi$
$293$	−3.57373	+	3.57373i	−0.208780	+	0.208780i	0.594969	+	0.803749i	$0.297164\pi$
$294$	−13.7543	−	13.4497i	−0.802166	−	0.784400i
$295$	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
$301$	0.0471535	+	8.42240i	0.00271788	+	0.485459i
$302$	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	−0.417952	−	0.908469i	$-0.637252\pi$
$307$	8.59457	−	8.59457i	0.490518	−	0.490518i	0.908469	+	0.417952i	$0.137252\pi$
$308$	−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	$-0.279317\pi$
$311$	22.5405			1.27815			0.639077	+	0.769143i	$0.279317\pi$
$312$	18.2979	+	17.2690i	1.03592	+	0.977664i
$313$		−	4.30873i		−	0.243544i	−0.992558	−	0.121772i	$-0.961142\pi$
$313$		−	4.30873i		−	0.243544i	0.992558	−	0.121772i	$-0.0388576\pi$
$314$	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
$336$	0.0886081	+	15.8269i	0.00483397	+	0.863427i
$337$			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
$343$	−18.5176	+	0.311044i	−0.999859	+	0.0167948i
$344$	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	$-0.493345\pi$
$349$	19.0680	−	19.0680i	1.02069	−	1.02069i	0.999781	−	0.0209053i	$-0.00665484\pi$
$350$	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	0.823479	−	0.567346i	$-0.192030\pi$
$353$	4.81231	+	4.81231i	0.256133	+	0.256133i	−0.567346	+	0.823479i	$0.692030\pi$
$354$	−35.5669			−1.89036
$355$	−5.03040			−0.266986
$356$	−1.83083	−	1.83083i	−0.0970336	−	0.0970336i
$357$	0.102631	+	18.3316i	0.00543182	+	0.970212i
$358$	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
$364$	5.14047	−	0.177519i	0.269434	−	0.00930452i
$365$	−8.49079			−0.444428
$366$	−17.8927	+	17.8927i	−0.935266	+	0.935266i
$367$		−	22.8806i		−	1.19436i	−0.802109	−	0.597178i	$-0.796289\pi$
$367$		−	22.8806i		−	1.19436i	0.802109	−	0.597178i	$-0.203711\pi$
$368$			17.1278i			0.892850i
$369$	−4.93430	−	4.93430i	−0.256870	−	0.256870i
$370$	−2.12147	−	2.12147i	−0.110290	−	0.110290i
$371$	−9.07976	+	0.0508338i	−0.471398	+	0.00263916i
$372$	−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	$0.0974603\pi$
$383$	24.5591	+	24.5591i	1.25491	+	1.25491i	0.301419	+	0.953492i	$0.402540\pi$
$384$	7.66061	−	7.66061i	0.390929	−	0.390929i
$385$	0.0336798	+	6.01577i	0.00171648	+	0.306592i
$386$	−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
$392$	15.3597	+	15.0196i	0.775784	+	0.758603i
$393$	−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	−0.512576	−	0.858642i	$-0.671309\pi$
$397$	6.89530	−	6.89530i	0.346065	−	0.346065i	0.858642	+	0.512576i	$0.171309\pi$
$398$	−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	0.632830	−	0.774291i	$-0.281893\pi$
$409$	−2.86088	−	2.86088i	−0.141461	−	0.141461i	−0.774291	+	0.632830i	$0.781893\pi$
$410$	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	$0.332643\pi$
$419$			35.4097i			1.72988i	−0.501878	+	0.864939i	$0.667357\pi$
$420$	−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
$427$	0.136385	+	24.3605i	0.00660011	+	1.17889i
$428$			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	$-0.611968\pi$
$433$	−14.3392			−0.689098			−0.344549	+	0.938768i	$0.611968\pi$
$434$	30.6305	−	0.171488i	1.47031	−	0.00823167i
$435$	−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	$-0.341787\pi$
$439$	19.9812			0.953651			0.476826	+	0.878998i	$0.341787\pi$
$440$	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
$448$	−0.130897	−	23.3804i	−0.00618431	−	1.10462i
$449$	−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
$455$	5.64234	−	6.04597i	0.264517	−	0.283440i
$456$	−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	0.519037	−	0.854752i	$-0.326291\pi$
$461$	−7.20809	−	7.20809i	−0.335714	−	0.335714i	−0.854752	+	0.519037i	$0.826291\pi$
$462$	−0.106768	−	19.0705i	−0.00496729	−	0.887240i
$463$	−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	$-0.368373\pi$
$467$	17.3673			0.803665			0.401832	+	0.915713i	$0.368373\pi$
$468$	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
$476$	−0.0243372	−	4.34703i	−0.00111550	−	0.199246i
$477$	−7.44748			−0.340997
$478$			9.62475i			0.440226i
$479$	−9.88634	+	9.88634i	−0.451719	+	0.451719i	−0.895925	−	0.444206i	$-0.853486\pi$
$479$	−9.88634	+	9.88634i	−0.451719	+	0.451719i	0.444206	+	0.895925i	$0.353486\pi$
$480$			5.83096i			0.266146i
$481$	7.08609	−	7.50830i	0.323098	−	0.342349i
$482$			1.90101i			0.0865887i
$483$	−39.1642	+	0.219264i	−1.78203	+	0.00997687i
$484$	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	$0.154174\pi$
$503$			20.8862i			0.931272i	−0.884976	+	0.465636i	$0.845826\pi$
$504$	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	0.283229	−	0.959052i	$-0.408594\pi$
$509$	−15.2473	−	15.2473i	−0.675823	−	0.675823i	−0.959052	+	0.283229i	$0.908594\pi$
$510$		−	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
$518$	9.15630	−	0.0512623i	0.402305	−	0.00225234i
$519$		−	17.0133i		−	0.746802i
$520$	−9.58864	+	0.277394i	−0.420490	+	0.0121645i
$521$			20.1543i			0.882975i	0.897268	+	0.441487i	$0.145549\pi$
$521$			20.1543i			0.882975i	−0.897268	+	0.441487i	$0.854451\pi$
$522$	7.02472	−	7.02472i	0.307464	−	0.307464i
$523$			11.3031i			0.494251i	0.968983	+	0.247126i	$0.0794861\pi$
$523$			11.3031i			0.494251i	−0.968983	+	0.247126i	$0.920514\pi$
$524$	6.45095			0.281811
$525$	25.5578	−	0.143087i	1.11543	−	0.00624485i
$526$	−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
$539$	−13.1270	−	12.8363i	−0.565420	−	0.552898i
$540$	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
$546$	−17.8867	+	19.1663i	−0.765480	+	0.820240i
$547$	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
$553$	−46.5534	+	0.260633i	−1.97965	+	0.0110833i
$554$	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	$-0.349007\pi$
$563$	21.6761			0.913538			0.456769	+	0.889585i	$0.349007\pi$
$564$	−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
$567$	28.5763	−	0.159987i	1.20009	−	0.00671881i
$568$	−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
$574$	−10.2826	+	0.0575680i	−0.429188	+	0.00240284i
$575$	27.6586			1.15344
$576$		−	19.1773i		−	0.799053i
$577$	8.56564	+	8.56564i	0.356592	+	0.356592i	0.862555	−	0.505963i	$-0.168863\pi$
$577$	8.56564	+	8.56564i	0.356592	+	0.356592i	−0.505963	+	0.862555i	$0.668863\pi$
$578$	−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	0.713442	−	0.700714i	$-0.247135\pi$
$587$	0.308382	+	0.308382i	0.0127283	+	0.0127283i	−0.700714	+	0.713442i	$0.747135\pi$
$588$	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	−0.598080	−	0.801436i	$-0.704070\pi$
$593$	4.95204	−	4.95204i	0.203356	−	0.203356i	0.801436	+	0.598080i	$0.204070\pi$
$594$			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	$0.0465677\pi$
$601$			7.14746i			0.291551i	−0.989318	+	0.145776i	$0.953432\pi$
$602$	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	$-0.792818\pi$
$607$		−	29.8550i		−	1.21178i	0.795550	−	0.605888i	$-0.207182\pi$
$608$	0.436175			0.0176892
$609$	−0.127567	−	22.7856i	−0.00516929	−	0.923321i
$610$		−	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
$616$	0.119230	+	21.2965i	0.00480393	+	0.858061i
$617$	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	−0.0980353	−	0.995183i	$-0.531256\pi$
$619$	22.3208	−	22.3208i	0.897148	−	0.897148i	0.995183	+	0.0980353i	$0.0312558\pi$
$620$	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
$630$	6.01577	−	0.0336798i	0.239674	−	0.00134184i
$631$	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
$637$	1.01227	+	25.2186i	0.0401076	+	0.999195i
$638$	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	0.119211	−	0.992869i	$-0.461964\pi$
$643$	−22.1537	−	22.1537i	−0.873658	−	0.873658i	−0.992869	+	0.119211i	$0.961964\pi$
$644$	9.28713	−	0.0519948i	0.365964	−	0.00204888i
$645$	−4.43713	−	4.43713i	−0.174712	−	0.174712i
$646$	−0.543065			−0.0213666
$647$	−32.4446			−1.27553			−0.637764	−	0.770232i	$-0.720140\pi$
$647$	−32.4446			−1.27553			−0.637764	+	0.770232i	$0.720140\pi$
$648$	−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
$658$	−0.132079	−	23.5916i	−0.00514899	−	0.919695i
$659$	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	−0.863144	−	0.504957i	$-0.831508\pi$
$661$	−9.20895	+	9.20895i	−0.358187	+	0.358187i	0.504957	+	0.863144i	$0.331508\pi$
$662$		−	2.92162i		−	0.113552i
$663$	24.9717	−	0.722418i	0.969822	−	0.0280564i
$664$			45.7775i			1.77651i
$665$	0.00189339	+	0.338191i	7.34225e−5	+	0.0131145i
$666$	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	$0.0660715\pi$
$677$			10.7242i			0.412165i	−0.978535	+	0.206082i	$0.933928\pi$
$678$	−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	0.712151	−	0.702027i	$-0.247721\pi$
$691$	0.266133	+	0.266133i	0.0101242	+	0.0101242i	−0.702027	+	0.712151i	$0.747721\pi$
$692$			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
$700$	−6.06059	+	0.0339307i	−0.229069	+	0.00128246i
$701$		−	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
$707$	3.06960	−	0.0171854i	0.115444	−	0.000646325i
$708$	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	$-0.726687\pi$
$719$	−35.0445			−1.30694			−0.653469	+	0.756953i	$0.726687\pi$
$720$	−3.49978	−	3.49978i	−0.130429	−	0.130429i
$721$	−14.0779	+	0.0788166i	−0.524290	+	0.00293528i
$722$	−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	$-0.590300\pi$
$727$	−15.0936			−0.559789			−0.279895	+	0.960031i	$0.590300\pi$
$728$	19.9745	−	21.4034i	0.740305	−	0.793264i
$729$	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	0.925637	−	0.378414i	$-0.123530\pi$
$733$	14.8155	+	14.8155i	0.547223	+	0.547223i	−0.378414	+	0.925637i	$0.623530\pi$
$734$	−19.5546	−	19.5546i	−0.721773	−	0.721773i
$735$	9.64693	−	9.86542i	0.355832	−	0.363891i
$736$	−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
$749$	−27.1145	+	0.151803i	−0.990741	+	0.00554675i
$750$	−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
$756$	−2.69194	+	0.0150710i	−0.0979048	+	0.000548128i
$757$	−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	−0.667765	−	0.744372i	$-0.732749\pi$
$761$	2.11330	−	2.11330i	0.0766071	−	0.0766071i	0.744372	+	0.667765i	$0.232749\pi$
$762$	−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	0.998049	−	0.0624284i	$-0.0198845\pi$
$769$	25.9456	+	25.9456i	0.935621	+	0.935621i	−0.0624284	+	0.998049i	$0.519885\pi$
$770$	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	0.724015	−	0.689785i	$-0.242295\pi$
$773$	0.951693	+	0.951693i	0.0342300	+	0.0342300i	−0.689785	+	0.724015i	$0.742295\pi$
$774$	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	−0.109862	−	0.993947i	$-0.535041\pi$
$787$	24.8017	−	24.8017i	0.884085	−	0.884085i	0.993947	+	0.109862i	$0.0350409\pi$
$788$	8.23287	+	8.23287i	0.293284	+	0.293284i
$789$			33.0286i			1.17585i
$790$	18.4366			0.655946
$791$	−15.2006	+	0.0851021i	−0.540473	+	0.00302588i
$792$			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	$-0.712114\pi$
$797$	−34.9017			−1.23628			−0.618141	+	0.786067i	$0.712114\pi$
$798$	−0.00600221	−	1.07209i	−0.000212476	−	0.0379517i
$799$	−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	0.901729	−	0.432301i	$-0.142298\pi$
$811$	13.3684	+	13.3684i	0.469428	+	0.469428i	−0.432301	+	0.901729i	$0.642298\pi$
$812$	0.0302504	+	5.40323i	0.00106158	+	0.189616i
$813$	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
$819$	0.714465	+	20.6890i	0.0249654	+	0.722931i
$820$	−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
$826$	0.231696	+	41.3846i	0.00806172	+	1.43996i
$827$	−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	$-0.550855\pi$
$829$	−9.16091			−0.318172			−0.159086	+	0.987265i	$0.550855\pi$
$830$	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	−0.0916731	−	0.995789i	$-0.529221\pi$
$839$	26.1882	−	26.1882i	0.904116	−	0.904116i	0.995789	+	0.0916731i	$0.0292215\pi$
$840$	−16.0051	+	0.0896058i	−0.552228	+	0.00309170i
$841$	−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
$847$	0.0610359	+	10.9020i	0.00209722	+	0.374598i
$848$	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	−0.826652	−	0.562713i	$-0.809758\pi$
$853$	−7.70865	+	7.70865i	−0.263939	+	0.263939i	0.562713	+	0.826652i	$0.309758\pi$
$854$	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	$-0.625049\pi$
$857$	−22.4141			−0.765651			−0.382825	+	0.923821i	$0.625049\pi$
$858$	−25.9783	+	0.751536i	−0.886883	+	0.0256570i
$859$		−	43.5695i		−	1.48657i	−0.668974	−	0.743286i	$-0.733266\pi$
$859$		−	43.5695i		−	1.48657i	0.668974	−	0.743286i	$-0.266734\pi$
$860$	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	$-0.518614\pi$
$881$	−3.46947			−0.116889			−0.0584447	+	0.998291i	$0.518614\pi$
$882$	−12.8363	+	13.1270i	−0.432220	+	0.442009i
$883$		−	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	$-0.969186\pi$
$887$		−	5.75722i		−	0.193309i	0.995318	−	0.0966543i	$-0.0308141\pi$
$888$	−19.9812			−0.670526
$889$	0.109259	+	19.5155i	0.00366444	+	0.654530i
$890$	−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
$903$	19.1507	−	0.107217i	0.637295	−	0.00356795i
$904$	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
$910$	−0.344965	−	9.98927i	−0.0114355	−	0.331141i
$911$	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
$917$	0.177216	+	31.6537i	0.00585219	+	1.04530i
$918$	−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	0.919221	−	0.393742i	$-0.128820\pi$
$929$	16.0163	+	16.0163i	0.525479	+	0.525479i	−0.393742	+	0.919221i	$0.628820\pi$
$930$	−16.1369	+	16.1369i	−0.529151	+	0.529151i
$931$	−0.737966	−	0.721622i	−0.0241859	−	0.0236502i
$932$	−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	$-0.778567\pi$
$937$		−	39.2356i		−	1.28177i	0.767636	−	0.640886i	$-0.221433\pi$
$938$	−0.0265701	−	4.74586i	−0.000867545	−	0.154958i
$939$	−9.79711			−0.319717
$940$		−	3.44852i		−	0.112478i
$941$	31.6697	+	31.6697i	1.03240	+	1.03240i	0.999457	+	0.0329454i	$0.0104887\pi$
$941$	31.6697	+	31.6697i	1.03240	+	1.03240i	0.0329454	+	0.999457i	$0.489511\pi$
$942$	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	$-0.929433\pi$
$971$		−	13.7033i		−	0.439760i	0.975527	−	0.219880i	$-0.0705666\pi$
$972$	−10.1896			−0.326831
$973$	−0.0943366	−	16.8501i	−0.00302429	−	0.540189i
$974$			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
$980$	−2.28761	+	2.33942i	−0.0730749	+	0.0747299i
$981$	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	−0.875121	−	0.483904i	$-0.839218\pi$
$983$	−12.2658	+	12.2658i	−0.391218	+	0.391218i	0.483904	+	0.875121i	$0.339218\pi$
$984$	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
$994$	−0.103883	−	18.5552i	−0.00329497	−	0.588536i
$995$	−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	$-0.910786\pi$
$997$		−	17.4686i		−	0.553236i	0.960980	−	0.276618i	$-0.0892136\pi$
$998$			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.83.5	yes	12
3.2	odd	2		819.2.y.h.811.1		12
7.2	even	3		637.2.bc.a.31.2		24
7.3	odd	6		637.2.bc.a.460.6		24
7.4	even	3		637.2.bc.a.460.5		24
7.5	odd	6		637.2.bc.a.31.1		24
7.6	odd	2	inner	91.2.i.a.83.6	yes	12
13.8	odd	4	inner	91.2.i.a.34.5	✓	12
21.20	even	2		819.2.y.h.811.2		12
39.8	even	4		819.2.y.h.307.2		12
91.34	even	4	inner	91.2.i.a.34.6	yes	12
91.47	even	12		637.2.bc.a.619.5		24
91.60	odd	12		637.2.bc.a.411.1		24
91.73	even	12		637.2.bc.a.411.2		24
91.86	odd	12		637.2.bc.a.619.6		24
273.125	odd	4		819.2.y.h.307.1		12

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

\(f(q)\)	\(=\)	\(q+(0.854638 - 0.854638i) q^{2} -2.27378i q^{3} +0.539189i q^{4} +(0.612999 + 0.612999i) q^{5} +(-1.94326 - 1.94326i) q^{6} +(-2.64571 + 0.0148122i) q^{7} +(2.17009 + 2.17009i) q^{8} -2.17009 q^{9} +O(q^{10})\)	\(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} +(-2.64571 + 0.0148122i) 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} +(0.0336798 + 6.01577i) 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} +(-0.00798659 - 1.42654i) 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} +(5.74142 - 0.0321438i) 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} +(-2.77213 + 0.0155200i) 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} +(-3.24364 + 0.0181598i) 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} +(-0.329233 - 9.53371i) 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} +(5.91510 - 6.04907i) 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

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Representations

Groups

Database

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