LMFDB - Embedded newform 96.2.n.a.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [96,2,Mod(13,96)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(96, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("96.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 96 = 2^{5} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	96.n (of order $8$, degree $4$, 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:	$0.766563859404$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			37.2
Character	$\chi$	$=$	96.37
Dual form			96.2.n.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26685 + 0.628571i) q^{2} +(-0.382683 - 0.923880i) q^{3} +(1.20980 - 1.59260i) q^{4} +(-3.09318 - 1.28124i) q^{5} +(1.06552 + 0.929869i) q^{6} +(-1.73503 - 1.73503i) q^{7} +(-0.531562 + 2.77803i) q^{8} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(-1.26685 + 0.628571i) q^{2} +(-0.382683 - 0.923880i) q^{3} +(1.20980 - 1.59260i) q^{4} +(-3.09318 - 1.28124i) q^{5} +(1.06552 + 0.929869i) q^{6} +(-1.73503 - 1.73503i) q^{7} +(-0.531562 + 2.77803i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(4.72394 - 0.321153i) q^{10} +(2.39923 - 5.79225i) q^{11} +(-1.93434 - 0.508244i) q^{12} +(0.0173304 - 0.00717850i) q^{13} +(3.28860 + 1.10742i) q^{14} +3.34804i q^{15} +(-1.07278 - 3.85346i) q^{16} +5.57978i q^{17} +(0.451329 - 1.34026i) q^{18} +(-1.03052 + 0.426856i) q^{19} +(-5.78263 + 3.37618i) q^{20} +(-0.938989 + 2.26692i) q^{21} +(0.601386 + 8.84597i) q^{22} +(2.01868 - 2.01868i) q^{23} +(2.76998 - 0.572006i) q^{24} +(4.39068 + 4.39068i) q^{25} +(-0.0174428 + 0.0199875i) q^{26} +(0.923880 + 0.382683i) q^{27} +(-4.86224 + 0.664180i) q^{28} +(-0.706079 - 1.70463i) q^{29} +(-2.10448 - 4.24145i) q^{30} +1.38048 q^{31} +(3.78122 + 4.20742i) q^{32} -6.26948 q^{33} +(-3.50729 - 7.06872i) q^{34} +(3.14377 + 7.58973i) q^{35} +(0.270686 + 1.98160i) q^{36} +(-2.87315 - 1.19010i) q^{37} +(1.03720 - 1.18852i) q^{38} +(-0.0132641 - 0.0132641i) q^{39} +(5.20354 - 7.91189i) q^{40} +(6.97897 - 6.97897i) q^{41} +(-0.235365 - 3.46206i) q^{42} +(1.67010 - 4.03197i) q^{43} +(-6.32218 - 10.8285i) q^{44} +(3.09318 - 1.28124i) q^{45} +(-1.28847 + 3.82623i) q^{46} -1.15993i q^{47} +(-3.14960 + 2.46577i) q^{48} -0.979375i q^{49} +(-8.32217 - 2.80246i) q^{50} +(5.15504 - 2.13529i) q^{51} +(0.00953380 - 0.0362851i) q^{52} +(2.56680 - 6.19681i) q^{53} +(-1.41096 + 0.0959227i) q^{54} +(-14.8425 + 14.8425i) q^{55} +(5.74222 - 3.89767i) q^{56} +(0.788727 + 0.788727i) q^{57} +(1.96597 + 1.71568i) q^{58} +(-0.735935 - 0.304834i) q^{59} +(5.33210 + 4.05045i) q^{60} +(4.82262 + 11.6428i) q^{61} +(-1.74885 + 0.867729i) q^{62} +2.45370 q^{63} +(-7.43488 - 2.95339i) q^{64} -0.0628036 q^{65} +(7.94247 - 3.94081i) q^{66} +(-2.05899 - 4.97085i) q^{67} +(8.88638 + 6.75040i) q^{68} +(-2.63753 - 1.09250i) q^{69} +(-8.75336 - 7.63894i) q^{70} +(-1.78298 - 1.78298i) q^{71} +(-1.58849 - 2.34023i) q^{72} +(1.67500 - 1.67500i) q^{73} +(4.38789 - 0.298307i) q^{74} +(2.37622 - 5.73670i) q^{75} +(-0.566909 + 2.15762i) q^{76} +(-14.2124 + 5.88697i) q^{77} +(0.0251411 + 0.00846617i) q^{78} +2.67236i q^{79} +(-1.61890 + 13.2939i) q^{80} -1.00000i q^{81} +(-4.45450 + 13.2281i) q^{82} +(-6.91877 + 2.86585i) q^{83} +(2.47432 + 4.23795i) q^{84} +(7.14903 - 17.2593i) q^{85} +(0.418623 + 6.15766i) q^{86} +(-1.30466 + 1.30466i) q^{87} +(14.8157 + 9.74406i) q^{88} +(6.73869 + 6.73869i) q^{89} +(-3.11324 + 3.56742i) q^{90} +(-0.0425236 - 0.0176139i) q^{91} +(-0.772764 - 5.65714i) q^{92} +(-0.528286 - 1.27540i) q^{93} +(0.729098 + 1.46945i) q^{94} +3.73450 q^{95} +(2.44014 - 5.10350i) q^{96} -1.75001 q^{97} +(0.615607 + 1.24072i) q^{98} +(2.39923 + 5.79225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} - 16 q^{12} - 32 q^{14} - 8 q^{16} - 8 q^{18} - 32 q^{20} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 40 q^{26} + 40 q^{28} - 48 q^{31} + 40 q^{32} + 40 q^{34} - 48 q^{35} + 40 q^{38} + 8 q^{40} - 16 q^{43} + 8 q^{44} - 32 q^{46} + 24 q^{50} + 16 q^{51} - 8 q^{52} - 32 q^{53} + 8 q^{54} + 32 q^{55} + 56 q^{56} - 32 q^{58} + 64 q^{59} + 48 q^{60} - 32 q^{61} + 48 q^{62} + 16 q^{63} + 24 q^{64} + 48 q^{66} + 16 q^{67} - 8 q^{68} - 32 q^{69} - 24 q^{70} + 64 q^{71} - 32 q^{74} + 32 q^{75} - 56 q^{76} - 32 q^{77} + 24 q^{78} - 56 q^{80} - 40 q^{82} - 64 q^{86} - 48 q^{88} - 48 q^{91} - 80 q^{92} - 32 q^{94} - 40 q^{96} - 80 q^{98}+O(q^{100}) $ 32 * q - 8 * q^10 - 16 * q^12 - 32 * q^14 - 8 * q^16 - 8 * q^18 - 32 * q^20 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 40 * q^26 + 40 * q^28 - 48 * q^31 + 40 * q^32 + 40 * q^34 - 48 * q^35 + 40 * q^38 + 8 * q^40 - 16 * q^43 + 8 * q^44 - 32 * q^46 + 24 * q^50 + 16 * q^51 - 8 * q^52 - 32 * q^53 + 8 * q^54 + 32 * q^55 + 56 * q^56 - 32 * q^58 + 64 * q^59 + 48 * q^60 - 32 * q^61 + 48 * q^62 + 16 * q^63 + 24 * q^64 + 48 * q^66 + 16 * q^67 - 8 * q^68 - 32 * q^69 - 24 * q^70 + 64 * q^71 - 32 * q^74 + 32 * q^75 - 56 * q^76 - 32 * q^77 + 24 * q^78 - 56 * q^80 - 40 * q^82 - 64 * q^86 - 48 * q^88 - 48 * q^91 - 80 * q^92 - 32 * q^94 - 40 * q^96 - 80 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$	$1$

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 $

$2$	−1.26685	+	0.628571i	−0.895795	+	0.444467i
$2$	−1.26685	+	0.628571i	−0.895795	+	0.444467i
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$4$	1.20980	−	1.59260i	0.604899	−	0.796302i
$5$	−3.09318	−	1.28124i	−1.38331	−	0.572987i	−0.437949	−	0.899000i	$-0.644295\pi$
$5$	−3.09318	−	1.28124i	−1.38331	−	0.572987i	−0.945365	+	0.326013i	$0.894295\pi$
$6$	1.06552	+	0.929869i	0.434999	+	0.379618i
$7$	−1.73503	−	1.73503i	−0.655778	−	0.655778i	0.298600	−	0.954378i	$-0.403480\pi$
$7$	−1.73503	−	1.73503i	−0.655778	−	0.655778i	−0.954378	+	0.298600i	$0.903480\pi$
$8$	−0.531562	+	2.77803i	−0.187936	+	0.982181i
$9$	−0.707107	+	0.707107i	−0.235702	+	0.235702i
$10$	4.72394	−	0.321153i	1.49384	−	0.101557i
$11$	2.39923	−	5.79225i	0.723394	−	1.74643i	0.0599515	−	0.998201i	$-0.480905\pi$
$11$	2.39923	−	5.79225i	0.723394	−	1.74643i	0.663443	−	0.748227i	$-0.269095\pi$
$12$	−1.93434	−	0.508244i	−0.558397	−	0.146717i
$13$	0.0173304	−	0.00717850i	0.00480660	−	0.00199096i	−0.380279	−	0.924872i	$-0.624172\pi$
$13$	0.0173304	−	0.00717850i	0.00480660	−	0.00199096i	0.385085	+	0.922881i	$0.374172\pi$
$14$	3.28860	+	1.10742i	0.878914	+	0.295971i
$15$			3.34804i			0.864460i
$16$	−1.07278	−	3.85346i	−0.268195	−	0.963365i
$17$			5.57978i			1.35329i	0.736307	+	0.676647i	$0.236568\pi$
$17$			5.57978i			1.35329i	−0.736307	+	0.676647i	$0.763432\pi$
$18$	0.451329	−	1.34026i	0.106379	−	0.315903i
$19$	−1.03052	+	0.426856i	−0.236418	+	0.0979274i	−0.497747	−	0.867322i	$-0.665839\pi$
$19$	−1.03052	+	0.426856i	−0.236418	+	0.0979274i	0.261329	+	0.965250i	$0.415839\pi$
$20$	−5.78263	+	3.37618i	−1.29304	+	0.754937i
$21$	−0.938989	+	2.26692i	−0.204904	+	0.494682i
$22$	0.601386	+	8.84597i	0.128216	+	1.88597i
$23$	2.01868	−	2.01868i	0.420923	−	0.420923i	−0.464598	−	0.885522i	$-0.653801\pi$
$23$	2.01868	−	2.01868i	0.420923	−	0.420923i	0.885522	+	0.464598i	$0.153801\pi$
$24$	2.76998	−	0.572006i	0.565421	−	0.116760i
$25$	4.39068	+	4.39068i	0.878136	+	0.878136i
$26$	−0.0174428	+	0.0199875i	−0.00342081	+	0.00391986i
$27$	0.923880	+	0.382683i	0.177801	+	0.0736475i
$28$	−4.86224	+	0.664180i	−0.918877	+	0.125518i
$29$	−0.706079	−	1.70463i	−0.131116	−	0.316541i	0.844664	−	0.535297i	$-0.179800\pi$
$29$	−0.706079	−	1.70463i	−0.131116	−	0.316541i	−0.975780	+	0.218756i	$0.929800\pi$
$30$	−2.10448	−	4.24145i	−0.384224	−	0.774379i
$31$	1.38048			0.247941			0.123971	−	0.992286i	$-0.460437\pi$
$31$	1.38048			0.247941			0.123971	+	0.992286i	$0.460437\pi$
$32$	3.78122	+	4.20742i	0.668431	+	0.743774i
$33$	−6.26948			−1.09138
$34$	−3.50729	−	7.06872i	−0.601495	−	1.21228i
$35$	3.14377	+	7.58973i	0.531394	+	1.28290i
$36$	0.270686	+	1.98160i	0.0451143	+	0.330266i
$37$	−2.87315	−	1.19010i	−0.472342	−	0.195651i	0.133797	−	0.991009i	$-0.457283\pi$
$37$	−2.87315	−	1.19010i	−0.472342	−	0.195651i	−0.606140	+	0.795358i	$0.707283\pi$
$38$	1.03720	−	1.18852i	0.168256	−	0.192803i
$39$	−0.0132641	−	0.0132641i	−0.00212396	−	0.00212396i
$40$	5.20354	−	7.91189i	0.822752	−	1.25098i
$41$	6.97897	−	6.97897i	1.08993	−	1.08993i	0.0943974	−	0.995535i	$-0.469908\pi$
$41$	6.97897	−	6.97897i	1.08993	−	1.08993i	0.995535	−	0.0943974i	$-0.0300924\pi$
$42$	−0.235365	−	3.46206i	−0.0363176	−	0.534207i
$43$	1.67010	−	4.03197i	0.254687	−	0.614869i	−0.743884	−	0.668309i	$-0.767018\pi$
$43$	1.67010	−	4.03197i	0.254687	−	0.614869i	0.998571	+	0.0534396i	$0.0170184\pi$
$44$	−6.32218	−	10.8285i	−0.953105	−	1.63245i
$45$	3.09318	−	1.28124i	0.461105	−	0.190996i
$46$	−1.28847	+	3.82623i	−0.189975	+	0.564147i
$47$		−	1.15993i		−	0.169193i	−0.996415	−	0.0845966i	$-0.973040\pi$
$47$		−	1.15993i		−	0.169193i	0.996415	−	0.0845966i	$-0.0269601\pi$
$48$	−3.14960	+	2.46577i	−0.454605	+	0.355904i
$49$		−	0.979375i		−	0.139911i
$50$	−8.32217	−	2.80246i	−1.17693	−	0.396328i
$51$	5.15504	−	2.13529i	0.721850	−	0.299000i
$52$	0.00953380	−	0.0362851i	0.00132210	−	0.00503183i
$53$	2.56680	−	6.19681i	0.352577	−	0.851197i	−0.643723	−	0.765258i	$-0.722611\pi$
$53$	2.56680	−	6.19681i	0.352577	−	0.851197i	0.996300	−	0.0859383i	$-0.0273888\pi$
$54$	−1.41096	+	0.0959227i	−0.192007	+	0.0130534i
$55$	−14.8425	+	14.8425i	−2.00136	+	2.00136i
$56$	5.74222	−	3.89767i	0.767337	−	0.520849i
$57$	0.788727	+	0.788727i	0.104469	+	0.104469i
$58$	1.96597	+	1.71568i	0.258145	+	0.225280i
$59$	−0.735935	−	0.304834i	−0.0958106	−	0.0396860i	0.334263	−	0.942480i	$-0.391513\pi$
$59$	−0.735935	−	0.304834i	−0.0958106	−	0.0396860i	−0.430074	+	0.902794i	$0.641513\pi$
$60$	5.33210	+	4.05045i	0.688371	+	0.522911i
$61$	4.82262	+	11.6428i	0.617473	+	1.49071i	0.854629	+	0.519240i	$0.173785\pi$
$61$	4.82262	+	11.6428i	0.617473	+	1.49071i	−0.237156	+	0.971472i	$0.576215\pi$
$62$	−1.74885	+	0.867729i	−0.222105	+	0.110202i
$63$	2.45370			0.309137
$64$	−7.43488	−	2.95339i	−0.929360	−	0.369174i
$65$	−0.0628036			−0.00778983
$66$	7.94247	−	3.94081i	0.977650	−	0.485081i
$67$	−2.05899	−	4.97085i	−0.251546	−	0.607286i	0.746783	−	0.665068i	$-0.231597\pi$
$67$	−2.05899	−	4.97085i	−0.251546	−	0.607286i	−0.998329	+	0.0577816i	$0.981597\pi$
$68$	8.88638	+	6.75040i	1.07763	+	0.818606i
$69$	−2.63753	−	1.09250i	−0.317521	−	0.131522i
$70$	−8.75336	−	7.63894i	−1.04623	−	0.913028i
$71$	−1.78298	−	1.78298i	−0.211600	−	0.211600i	0.593347	−	0.804947i	$-0.297806\pi$
$71$	−1.78298	−	1.78298i	−0.211600	−	0.211600i	−0.804947	+	0.593347i	$0.797806\pi$
$72$	−1.58849	−	2.34023i	−0.187205	−	0.275799i
$73$	1.67500	−	1.67500i	0.196044	−	0.196044i	−0.602258	−	0.798302i	$-0.705732\pi$
$73$	1.67500	−	1.67500i	0.196044	−	0.196044i	0.798302	+	0.602258i	$0.205732\pi$
$74$	4.38789	−	0.298307i	0.510082	−	0.0346775i
$75$	2.37622	−	5.73670i	0.274382	−	0.662417i
$76$	−0.566909	+	2.15762i	−0.0650290	+	0.247496i
$77$	−14.2124	+	5.88697i	−1.61965	+	0.670883i
$78$	0.0251411	+	0.00846617i	0.00284667	+	0.000958605i
$79$			2.67236i			0.300664i	0.988636	+	0.150332i	$0.0480343\pi$
$79$			2.67236i			0.300664i	−0.988636	+	0.150332i	$0.951966\pi$
$80$	−1.61890	+	13.2939i	−0.180998	+	1.48631i
$81$		−	1.00000i		−	0.111111i
$82$	−4.45450	+	13.2281i	−0.491918	+	1.46079i
$83$	−6.91877	+	2.86585i	−0.759433	+	0.314568i	−0.728584	−	0.684956i	$-0.759821\pi$
$83$	−6.91877	+	2.86585i	−0.759433	+	0.314568i	−0.0308494	+	0.999524i	$0.509821\pi$
$84$	2.47432	+	4.23795i	0.269971	+	0.462398i
$85$	7.14903	−	17.2593i	0.775421	−	1.87203i
$86$	0.418623	+	6.15766i	0.0451413	+	0.663997i
$87$	−1.30466	+	1.30466i	−0.139875	+	0.139875i
$88$	14.8157	+	9.74406i	1.57936	+	1.03872i
$89$	6.73869	+	6.73869i	0.714300	+	0.714300i	0.967432	−	0.253132i	$-0.0814607\pi$
$89$	6.73869	+	6.73869i	0.714300	+	0.714300i	−0.253132	+	0.967432i	$0.581461\pi$
$90$	−3.11324	+	3.56742i	−0.328164	+	0.376039i
$91$	−0.0425236	−	0.0176139i	−0.00445769	−	0.00184643i
$92$	−0.772764	−	5.65714i	−0.0805662	−	0.589798i
$93$	−0.528286	−	1.27540i	−0.0547807	−	0.132252i
$94$	0.729098	+	1.46945i	0.0752007	+	0.151562i
$95$	3.73450			0.383151
$96$	2.44014	−	5.10350i	0.249046	−	0.520874i
$97$	−1.75001			−0.177686			−0.0888431	−	0.996046i	$-0.528317\pi$
$97$	−1.75001			−0.177686			−0.0888431	+	0.996046i	$0.528317\pi$
$98$	0.615607	+	1.24072i	0.0621857	+	0.125331i
$99$	2.39923	+	5.79225i	0.241131	+	0.582143i
$100$	12.3045	−	1.68078i	1.23045	−	0.168078i
$101$	−7.71200	−	3.19442i	−0.767373	−	0.317856i	−0.0355651	−	0.999367i	$-0.511323\pi$
$101$	−7.71200	−	3.19442i	−0.767373	−	0.317856i	−0.731808	+	0.681511i	$0.761323\pi$
$102$	−5.18847	+	5.94539i	−0.513735	+	0.588681i
$103$	−3.90293	−	3.90293i	−0.384567	−	0.384567i	0.488177	−	0.872744i	$-0.337662\pi$
$103$	−3.90293	−	3.90293i	−0.384567	−	0.384567i	−0.872744	+	0.488177i	$0.837662\pi$
$104$	0.0107299	+	0.0519602i	0.00105215	+	0.00509512i
$105$	5.80893	−	5.80893i	0.566894	−	0.566894i
$106$	0.643389	+	9.46381i	0.0624915	+	0.919207i
$107$	−5.55747	+	13.4169i	−0.537261	+	1.29706i	0.389366	+	0.921083i	$0.372694\pi$
$107$	−5.55747	+	13.4169i	−0.537261	+	1.29706i	−0.926628	+	0.375981i	$0.877306\pi$
$108$	1.72717	−	1.00841i	0.166197	−	0.0970339i
$109$	14.8488	−	6.15056i	1.42225	−	0.589117i	0.466828	−	0.884348i	$-0.345397\pi$
$109$	14.8488	−	6.15056i	1.42225	−	0.589117i	0.955426	+	0.295231i	$0.0953967\pi$
$110$	9.47360	−	28.1327i	0.903273	−	2.68235i
$111$			3.10987i			0.295176i
$112$	−4.82455	+	8.54715i	−0.455877	+	0.807630i
$113$		−	2.72924i		−	0.256745i	−0.991726	−	0.128373i	$-0.959025\pi$
$113$		−	2.72924i		−	0.256745i	0.991726	−	0.128373i	$-0.0409753\pi$
$114$	−1.49497	−	0.503425i	−0.140016	−	0.0471500i
$115$	−8.83055	+	3.65773i	−0.823453	+	0.341085i
$116$	−3.56901	−	0.937747i	−0.331374	−	0.0870677i
$117$	−0.00717850	+	0.0173304i	−0.000663652	+	0.00160220i
$118$	1.12393	−	0.0764092i	0.103466	−	0.00703403i
$119$	9.68106	−	9.68106i	0.887461	−	0.887461i
$120$	−9.30095	−	1.77969i	−0.849056	−	0.162463i
$121$	−20.0157	−	20.0157i	−1.81961	−	1.81961i
$122$	−13.4279	−	11.7183i	−1.21570	−	1.06093i
$123$	−9.11846	−	3.77699i	−0.822184	−	0.340560i
$124$	1.67010	−	2.19856i	0.149979	−	0.197436i
$125$	−1.54948	−	3.74078i	−0.138590	−	0.334585i
$126$	−3.10846	+	1.54232i	−0.276923	+	0.137401i
$127$	15.3336			1.36064			0.680319	−	0.732916i	$-0.261841\pi$
$127$	15.3336			1.36064			0.680319	+	0.732916i	$0.261841\pi$
$128$	11.2753	−	0.931859i	0.996602	−	0.0823655i
$129$	−4.36417			−0.384244
$130$	0.0795625	−	0.0394765i	0.00697809	−	0.00346232i
$131$	5.70595	+	13.7754i	0.498531	+	1.20356i	0.950275	+	0.311412i	$0.100802\pi$
$131$	5.70595	+	13.7754i	0.498531	+	1.20356i	−0.451744	+	0.892148i	$0.649198\pi$
$132$	−7.58481	+	9.98481i	−0.660173	+	0.869066i
$133$	2.52859	+	1.04737i	0.219256	+	0.0908189i
$134$	5.73296	+	5.00308i	0.495252	+	0.432200i
$135$	−2.36742	−	2.36742i	−0.203755	−	0.203755i
$136$	−15.5008	−	2.96600i	−1.32918	−	0.254332i
$137$	−3.06155	+	3.06155i	−0.261566	+	0.261566i	−0.825690	−	0.564124i	$-0.809214\pi$
$137$	−3.06155	+	3.06155i	−0.261566	+	0.261566i	0.564124	+	0.825690i	$0.309214\pi$
$138$	4.02806	−	0.273844i	0.342891	−	0.0233111i
$139$	0.621401	−	1.50020i	0.0527066	−	0.127245i	−0.895333	−	0.445397i	$-0.853062\pi$
$139$	0.621401	−	1.50020i	0.0527066	−	0.127245i	0.948040	+	0.318152i	$0.103062\pi$
$140$	15.8908	+	4.17526i	1.34302	+	0.352874i
$141$	−1.07164	+	0.443886i	−0.0902480	+	0.0373819i
$142$	3.37948	+	1.13803i	0.283600	+	0.0955013i
$143$		−	0.117605i		−	0.00983462i
$144$	3.48338	+	1.96624i	0.290281	+	0.163853i
$145$			6.17738i			0.513003i
$146$	−1.06911	+	3.17483i	−0.0884804	+	0.262751i
$147$	−0.904825	+	0.374791i	−0.0746287	+	0.0309122i
$148$	−5.37128	+	3.13601i	−0.441516	+	0.257779i
$149$	−8.53959	+	20.6164i	−0.699591	+	1.68896i	0.0249118	+	0.999690i	$0.492070\pi$
$149$	−8.53959	+	20.6164i	−0.699591	+	1.68896i	−0.724503	+	0.689272i	$0.757930\pi$
$150$	0.595619	+	8.76114i	0.0486321	+	0.715344i
$151$	9.42348	−	9.42348i	0.766872	−	0.766872i	−0.210683	−	0.977555i	$-0.567569\pi$
$151$	9.42348	−	9.42348i	0.766872	−	0.766872i	0.977555	+	0.210683i	$0.0675687\pi$
$152$	−0.638031	−	3.08972i	−0.0517512	−	0.250609i
$153$	−3.94550	−	3.94550i	−0.318975	−	0.318975i
$154$	14.3046	−	16.3914i	1.15269	−	1.32086i
$155$	−4.27007	−	1.76872i	−0.342981	−	0.142067i
$156$	−0.0371714	+	0.00507761i	−0.00297610	+	0.000406534i
$157$	7.53965	+	18.2023i	0.601729	+	1.45270i	0.871800	+	0.489863i	$0.162953\pi$
$157$	7.53965	+	18.2023i	0.601729	+	1.45270i	−0.270070	+	0.962841i	$0.587047\pi$
$158$	−1.67977	−	3.38547i	−0.133635	−	0.269334i
$159$	−6.70737			−0.531929
$160$	−6.30529	−	17.8590i	−0.498477	−	1.41188i
$161$	−7.00491			−0.552064
$162$	0.628571	+	1.26685i	0.0493852	+	0.0995328i
$163$	−6.01448	−	14.5202i	−0.471090	−	1.13731i	−0.963682	−	0.267052i	$-0.913950\pi$
$163$	−6.01448	−	14.5202i	−0.471090	−	1.13731i	0.492592	−	0.870260i	$-0.336050\pi$
$164$	−2.67160	−	19.5579i	−0.208617	−	1.52721i
$165$	19.3927	+	8.03271i	1.50972	+	0.625345i
$166$	6.96363	−	7.97952i	0.540482	−	0.619331i
$167$	−11.8392	−	11.8392i	−0.916142	−	0.916142i	0.0806038	−	0.996746i	$-0.474315\pi$
$167$	−11.8392	−	11.8392i	−0.916142	−	0.916142i	−0.996746	+	0.0806038i	$0.974315\pi$
$168$	−5.79844	−	3.81355i	−0.447359	−	0.294222i
$169$	−9.19214	+	9.19214i	−0.707088	+	0.707088i
$170$	1.79196	+	26.3585i	0.137437	+	2.02161i
$171$	0.426856	−	1.03052i	0.0326425	−	0.0788059i
$172$	−4.40085	−	7.53767i	−0.335562	−	0.574742i
$173$	21.0615	−	8.72397i	1.60128	−	0.663271i	0.609683	−	0.792645i	$-0.291297\pi$
$173$	21.0615	−	8.72397i	1.60128	−	0.663271i	0.991596	+	0.129374i	$0.0412968\pi$
$174$	0.832735	−	2.47288i	0.0631295	−	0.187469i
$175$		−	15.2359i		−	1.15172i
$176$	−24.8940	−	3.03152i	−1.87646	−	0.228509i
$177$			0.796570i			0.0598739i
$178$	−12.7726	−	4.30114i	−0.957349	−	0.322384i
$179$	−4.75826	+	1.97094i	−0.355649	+	0.147315i	−0.553353	−	0.832947i	$-0.686652\pi$
$179$	−4.75826	+	1.97094i	−0.355649	+	0.147315i	0.197703	+	0.980262i	$0.436652\pi$
$180$	1.70162	−	6.47626i	0.126831	−	0.482712i
$181$	−3.71100	+	8.95914i	−0.275836	+	0.665928i	−0.999712	−	0.0240027i	$-0.992359\pi$
$181$	−3.71100	+	8.95914i	−0.275836	+	0.665928i	0.723876	+	0.689931i	$0.242359\pi$
$182$	0.0649424	−	0.00441506i	0.00481385	−	0.000327266i
$183$	8.91104	−	8.91104i	0.658723	−	0.658723i
$184$	4.53489	+	6.68099i	0.334316	+	0.492529i
$185$	7.36237	+	7.36237i	0.541293	+	0.541293i
$186$	1.47093	+	1.28366i	0.107854	+	0.0941229i
$187$	32.3195	+	13.3872i	2.36343	+	0.978966i
$188$	−1.84731	−	1.40328i	−0.134729	−	0.102345i
$189$	−0.938989	−	2.26692i	−0.0683014	−	0.164894i
$190$	−4.73103	+	2.34739i	−0.343225	+	0.170298i
$191$	11.4844			0.830980			0.415490	−	0.909598i	$-0.363610\pi$
$191$	11.4844			0.830980			0.415490	+	0.909598i	$0.363610\pi$
$192$	0.116629	+	7.99915i	0.00841700	+	0.577289i
$193$	19.2681			1.38695			0.693474	−	0.720482i	$-0.256079\pi$
$193$	19.2681			1.38695			0.693474	+	0.720482i	$0.256079\pi$
$194$	2.21699	−	1.10000i	0.159170	−	0.0789756i
$195$	0.0240339	+	0.0580229i	0.00172110	+	0.00415511i
$196$	−1.55976	−	1.18485i	−0.111411	−	0.0846319i
$197$	6.48659	+	2.68683i	0.462151	+	0.191429i	0.601596	−	0.798801i	$-0.294532\pi$
$197$	6.48659	+	2.68683i	0.462151	+	0.191429i	−0.139445	+	0.990230i	$0.544532\pi$
$198$	−6.68029	−	5.82980i	−0.474747	−	0.414306i
$199$	14.6525	+	14.6525i	1.03868	+	1.03868i	0.999221	+	0.0394638i	$0.0125650\pi$
$199$	14.6525	+	14.6525i	1.03868	+	1.03868i	0.0394638	+	0.999221i	$0.487435\pi$
$200$	−14.5314	+	9.86352i	−1.02752	+	0.697456i
$201$	−3.80452	+	3.80452i	−0.268350	+	0.268350i
$202$	11.7778	−	0.800706i	0.828686	−	0.0563375i
$203$	−1.73250	+	4.18263i	−0.121598	+	0.293563i
$204$	2.83589	−	10.7932i	0.198552	−	0.755676i
$205$	−30.5290	+	12.6455i	−2.13224	+	0.883201i
$206$	7.39768	+	2.49114i	0.515421	+	0.173566i
$207$			2.85484i			0.198425i
$208$	−0.0462538	−	0.0590811i	−0.00320712	−	0.00409654i
$209$			6.99316i			0.483727i
$210$	−3.70770	+	11.0103i	−0.255855	+	0.759786i
$211$	−2.80379	+	1.16137i	−0.193021	+	0.0799519i	−0.477100	−	0.878849i	$-0.658312\pi$
$211$	−2.80379	+	1.16137i	−0.193021	+	0.0799519i	0.284079	+	0.958801i	$0.408312\pi$
$212$	−6.76375	−	11.5848i	−0.464536	−	0.795646i
$213$	−0.964940	+	2.32957i	−0.0661166	+	0.159620i
$214$	−1.39303	−	20.4905i	−0.0952253	−	1.40070i
$215$	−10.3318	+	10.3318i	−0.704625	+	0.704625i
$216$	−1.55421	+	2.36314i	−0.105750	+	0.160792i
$217$	−2.39517	−	2.39517i	−0.162594	−	0.162594i
$218$	−14.9450	+	17.1253i	−1.01221	+	1.15987i
$219$	−2.18850	−	0.906505i	−0.147885	−	0.0612559i
$220$	5.68182	+	41.5947i	0.383068	+	2.80431i
$221$	0.0400544	+	0.0966999i	0.00269435	+	0.00650474i
$222$	−1.95477	−	3.93973i	−0.131196	−	0.264417i
$223$	−6.12103			−0.409894			−0.204947	−	0.978773i	$-0.565702\pi$
$223$	−6.12103			−0.409894			−0.204947	+	0.978773i	$0.565702\pi$
$224$	0.739472	−	13.8605i	0.0494080	−	0.926093i
$225$	−6.20936			−0.413957
$226$	1.71552	+	3.45752i	0.114115	+	0.229991i
$227$	−6.52469	−	15.7520i	−0.433059	−	1.04550i	−0.978296	−	0.207214i	$-0.933560\pi$
$227$	−6.52469	−	15.7520i	−0.433059	−	1.04550i	0.545237	−	0.838282i	$-0.316440\pi$
$228$	2.21033	−	0.301930i	0.146383	−	0.0199958i
$229$	−8.60895	−	3.56595i	−0.568896	−	0.235644i	0.0796463	−	0.996823i	$-0.474621\pi$
$229$	−8.60895	−	3.56595i	−0.568896	−	0.235644i	−0.648542	+	0.761179i	$0.724621\pi$
$230$	8.88780	−	10.1844i	0.586044	−	0.671540i
$231$	10.8777	+	10.8777i	0.715701	+	0.715701i
$232$	5.11083	−	1.05539i	0.335542	−	0.0692900i
$233$	7.99720	−	7.99720i	0.523914	−	0.523914i	−0.394837	−	0.918751i	$-0.629199\pi$
$233$	7.99720	−	7.99720i	0.523914	−	0.523914i	0.918751	+	0.394837i	$0.129199\pi$
$234$	−0.00179935	−	0.0264672i	−0.000117627	−	0.00173021i
$235$	−1.48615	+	3.58788i	−0.0969456	+	0.234047i
$236$	−1.37581	+	0.803266i	−0.0895578	+	0.0522881i
$237$	2.46894	−	1.02267i	0.160375	−	0.0664295i
$238$	−6.17918	+	18.3496i	−0.400537	+	1.18943i
$239$		−	6.26707i		−	0.405383i	−0.979243	−	0.202692i	$-0.935031\pi$
$239$		−	6.26707i		−	0.405383i	0.979243	−	0.202692i	$-0.0649689\pi$
$240$	12.9015	−	3.59171i	0.832790	−	0.231844i
$241$		−	15.7602i		−	1.01520i	−0.861592	−	0.507601i	$-0.830532\pi$
$241$		−	15.7602i		−	1.01520i	0.861592	−	0.507601i	$-0.169468\pi$
$242$	37.9380	+	12.7755i	2.43875	+	0.821240i
$243$	−0.923880	+	0.382683i	−0.0592669	+	0.0245492i
$244$	24.3768	+	6.40494i	1.56057	+	0.410034i
$245$	−1.25481	+	3.02939i	−0.0801671	+	0.193541i
$246$	13.9258	−	0.946734i	0.887876	−	0.0603615i
$247$	−0.0147952	+	0.0147952i	−0.000941395	+	0.000941395i
$248$	−0.733811	+	3.83501i	−0.0465970	+	0.243523i
$249$	5.29540	+	5.29540i	0.335582	+	0.335582i
$250$	4.31430	+	3.76503i	0.272860	+	0.238121i
$251$	−19.0196	−	7.87816i	−1.20050	−	0.497265i	−0.309342	−	0.950951i	$-0.600109\pi$
$251$	−19.0196	−	7.87816i	−1.20050	−	0.497265i	−0.891162	+	0.453686i	$0.850109\pi$
$252$	2.96848	−	3.90777i	0.186996	−	0.246166i
$253$	−6.84941	−	16.5359i	−0.430619	−	1.03961i
$254$	−19.4253	+	9.63826i	−1.21885	+	0.604758i
$255$	−18.6813			−1.16987
$256$	−13.6983	+	8.26783i	−0.856143	+	0.516739i
$257$	−5.22771			−0.326096			−0.163048	−	0.986618i	$-0.552132\pi$
$257$	−5.22771			−0.326096			−0.163048	+	0.986618i	$0.552132\pi$
$258$	5.52873	−	2.74319i	0.344204	−	0.170784i
$259$	2.92013	+	7.04983i	0.181448	+	0.438055i
$260$	−0.0759796	+	0.100021i	−0.00471206	+	0.00620306i
$261$	1.70463	+	0.706079i	0.105514	+	0.0437052i
$262$	−15.8874	−	13.8647i	−0.981524	−	0.856563i
$263$	5.59065	+	5.59065i	0.344734	+	0.344734i	0.858144	−	0.513410i	$-0.171618\pi$
$263$	5.59065	+	5.59065i	0.344734	+	0.344734i	−0.513410	+	0.858144i	$0.671618\pi$
$264$	3.33262	−	17.4168i	0.205109	−	1.07193i
$265$	−15.8792	+	15.8792i	−0.975450	+	0.975450i
$266$	−3.86168	+	0.262533i	−0.236775	+	0.0160969i
$267$	3.64695	−	8.80452i	0.223190	−	0.538828i
$268$	−10.4076	−	2.73456i	−0.635743	−	0.167040i
$269$	9.92617	−	4.11155i	0.605209	−	0.250686i	−0.0589693	−	0.998260i	$-0.518781\pi$
$269$	9.92617	−	4.11155i	0.605209	−	0.250686i	0.664179	+	0.747574i	$0.268781\pi$
$270$	4.48725	+	1.51107i	0.273085	+	0.0919605i
$271$		−	15.4368i		−	0.937717i	−0.883273	−	0.468858i	$-0.844665\pi$
$271$		−	15.4368i		−	0.937717i	0.883273	−	0.468858i	$-0.155335\pi$
$272$	21.5014	−	5.98587i	1.30372	−	0.362947i
$273$			0.0460272i			0.00278569i
$274$	1.95411	−	5.80292i	0.118052	−	0.350567i
$275$	35.9662	−	14.8977i	2.16884	−	0.898363i
$276$	−4.93080	+	2.87884i	−0.296799	+	0.173286i
$277$	1.79136	−	4.32473i	0.107633	−	0.259848i	−0.860882	−	0.508804i	$-0.830088\pi$
$277$	1.79136	−	4.32473i	0.107633	−	0.259848i	0.968515	+	0.248956i	$0.0800876\pi$
$278$	0.155759	+	2.29111i	0.00934182	+	0.137412i
$279$	−0.976146	+	0.976146i	−0.0584403	+	0.0584403i
$280$	−22.7556	+	4.69907i	−1.35991	+	0.280823i
$281$	−3.70347	−	3.70347i	−0.220931	−	0.220931i	0.587960	−	0.808890i	$-0.299931\pi$
$281$	−3.70347	−	3.70347i	−0.220931	−	0.220931i	−0.808890	+	0.587960i	$0.799931\pi$
$282$	1.07858	−	1.23593i	0.0642287	−	0.0735988i
$283$	−16.1605	−	6.69389i	−0.960641	−	0.397910i	−0.153421	−	0.988161i	$-0.549029\pi$
$283$	−16.1605	−	6.69389i	−0.960641	−	0.397910i	−0.807220	+	0.590250i	$0.799029\pi$
$284$	−4.99662	+	0.682536i	−0.296495	+	0.0405011i
$285$	−1.42913	−	3.45022i	−0.0846543	−	0.204374i
$286$	0.0739231	+	0.148987i	0.00437116	+	0.00880981i
$287$	−24.2174			−1.42951
$288$	−5.64882	−	0.301371i	−0.332860	−	0.0177584i
$289$	−14.1339			−0.831407
$290$	−3.88292	−	7.82579i	−0.228013	−	0.459546i
$291$	0.669698	+	1.61679i	0.0392584	+	0.0947782i
$292$	−0.641203	−	4.69403i	−0.0375236	−	0.274697i
$293$	13.5656	+	5.61904i	0.792509	+	0.328268i	0.741952	−	0.670453i	$-0.233900\pi$
$293$	13.5656	+	5.61904i	0.792509	+	0.328268i	0.0505573	+	0.998721i	$0.483900\pi$
$294$	0.910691	−	1.04355i	0.0531126	−	0.0608610i
$295$	1.88582	+	1.88582i	0.109796	+	0.109796i
$296$	4.83338	−	7.34907i	0.280934	−	0.427156i
$297$	4.43319	−	4.43319i	0.257240	−	0.257240i
$298$	−2.14052	−	31.4855i	−0.123997	−	1.82391i
$299$	0.0204935	−	0.0494756i	0.00118517	−	0.00286125i
$300$	−6.26155	−	10.7246i	−0.361511	−	0.619187i
$301$	−9.89322	+	4.09791i	−0.570236	+	0.236199i
$302$	−6.01477	+	17.8614i	−0.346111	+	1.02781i
$303$			8.34741i			0.479546i
$304$	2.75039	+	3.51315i	0.157746	+	0.201493i
$305$		−	42.1923i		−	2.41593i
$306$	7.47836	+	2.51831i	0.427510	+	0.143962i
$307$	15.6321	−	6.47504i	0.892173	−	0.369550i	0.110968	−	0.993824i	$-0.464605\pi$
$307$	15.6321	−	6.47504i	0.892173	−	0.369550i	0.781206	+	0.624274i	$0.214605\pi$
$308$	−7.81852	+	29.7568i	−0.445502	+	1.69555i
$309$	−2.11225	+	5.09942i	−0.120162	+	0.290096i
$310$	6.52129	−	0.443345i	0.370385	−	0.0251803i
$311$	22.8167	−	22.8167i	1.29381	−	1.29381i	0.361407	−	0.932408i	$-0.382297\pi$
$311$	22.8167	−	22.8167i	1.29381	−	1.29381i	0.932408	−	0.361407i	$-0.117703\pi$
$312$	0.0438989	−	0.0297974i	0.00248528	−	0.00168695i
$313$	7.52178	+	7.52178i	0.425156	+	0.425156i	0.886974	−	0.461819i	$-0.152803\pi$
$313$	7.52178	+	7.52178i	0.425156	+	0.425156i	−0.461819	+	0.886974i	$0.652803\pi$
$314$	−20.9930	−	18.3203i	−1.18470	−	1.03388i
$315$	−7.58973	−	3.14377i	−0.427633	−	0.177131i
$316$	4.25602	+	3.23302i	0.239420	+	0.181872i
$317$	−9.98241	−	24.0997i	−0.560668	−	1.35357i	−0.909233	−	0.416288i	$-0.863331\pi$
$317$	−9.98241	−	24.0997i	−0.560668	−	1.35357i	0.348565	−	0.937285i	$-0.386669\pi$
$318$	8.49721	−	4.21606i	0.476500	−	0.236425i
$319$	−11.5677			−0.647665
$320$	19.2135	+	18.6612i	1.07407	+	1.04320i
$321$	14.5224			0.810560
$322$	8.87414	−	4.40308i	0.494537	−	0.245374i
$323$	−2.38176	−	5.75008i	−0.132525	−	0.319943i
$324$	−1.59260	−	1.20980i	−0.0884780	−	0.0672110i
$325$	0.107611	+	0.0445739i	0.00596918	+	0.00247251i
$326$	16.7464	+	14.6144i	0.927498	+	0.809415i
$327$	−11.3648	−	11.3648i	−0.628472	−	0.628472i
$328$	15.6780	+	23.0975i	0.865674	+	1.27535i
$329$	−2.01251	+	2.01251i	−0.110953	+	0.110953i
$330$	−29.6166	+	2.01346i	−1.63034	+	0.110837i
$331$	−12.9034	+	31.1516i	−0.709235	+	1.71225i	−0.00733222	+	0.999973i	$0.502334\pi$
$331$	−12.9034	+	31.1516i	−0.709235	+	1.71225i	−0.701903	+	0.712272i	$0.747666\pi$
$332$	−3.80615	+	14.4860i	−0.208889	+	0.795020i
$333$	2.87315	−	1.19010i	0.157447	−	0.0652169i
$334$	22.4402	+	7.55665i	1.22787	+	0.413481i
$335$			18.0138i			0.984200i
$336$	9.74281	+	1.18645i	0.531514	+	0.0647261i
$337$			0.925243i			0.0504012i	0.999682	+	0.0252006i	$0.00802245\pi$
$337$			0.925243i			0.0504012i	−0.999682	+	0.0252006i	$0.991978\pi$
$338$	5.86711	−	17.4229i	0.319129	−	0.947683i
$339$	−2.52149	+	1.04443i	−0.136948	+	0.0567259i
$340$	−18.8383	−	32.2658i	−1.02165	−	1.74986i
$341$	3.31208	−	7.99607i	0.179359	−	0.433012i
$342$	0.106995	+	1.57382i	0.00578562	+	0.0851025i
$343$	−13.8444	+	13.8444i	−0.747528	+	0.747528i
$344$	10.3132	+	6.78282i	0.556048	+	0.365705i
$345$	6.75861	+	6.75861i	0.363871	+	0.363871i
$346$	−21.1981	+	24.2906i	−1.13962	+	1.30587i
$347$	8.68292	+	3.59658i	0.466123	+	0.193075i	0.603369	−	0.797462i	$-0.293825\pi$
$347$	8.68292	+	3.59658i	0.466123	+	0.193075i	−0.137245	+	0.990537i	$0.543825\pi$
$348$	0.499435	+	3.65619i	0.0267725	+	0.195993i
$349$	0.586633	+	1.41626i	0.0314017	+	0.0758105i	0.938802	−	0.344456i	$-0.111937\pi$
$349$	0.586633	+	1.41626i	0.0314017	+	0.0758105i	−0.907401	+	0.420266i	$0.861937\pi$
$350$	9.57683	+	19.3015i	0.511903	+	1.03171i
$351$	0.0187583			0.00100125
$352$	33.4424	−	11.8072i	1.78249	−	0.629326i
$353$	10.8550			0.577751			0.288876	−	0.957367i	$-0.406719\pi$
$353$	10.8550			0.577751			0.288876	+	0.957367i	$0.406719\pi$
$354$	−0.500701	−	1.00913i	−0.0266119	−	0.0536347i
$355$	3.23066	+	7.79949i	0.171465	+	0.413954i
$356$	18.8845	−	2.57962i	1.00088	−	0.136720i
$357$	−12.6489	−	5.23935i	−0.669451	−	0.277296i
$358$	4.78911	−	5.48778i	0.253113	−	0.290038i
$359$	21.6767	+	21.6767i	1.14406	+	1.14406i	0.987701	+	0.156354i	$0.0499741\pi$
$359$	21.6767	+	21.6767i	1.14406	+	1.14406i	0.156354	+	0.987701i	$0.450026\pi$
$360$	1.91510	+	9.27401i	0.100935	+	0.488783i
$361$	−12.5553	+	12.5553i	−0.660803	+	0.660803i
$362$	−0.930192	−	13.6825i	−0.0488898	−	0.719135i
$363$	−10.8324	+	26.1517i	−0.568553	+	1.37261i
$364$	−0.0794969	+	0.0464141i	−0.00416677	+	0.00243276i
$365$	−7.32717	+	3.03501i	−0.383521	+	0.158860i
$366$	−5.68769	+	16.8901i	−0.297301	+	0.882861i
$367$			0.154514i			0.00806555i	0.999992	+	0.00403277i	$0.00128367\pi$
$367$			0.154514i			0.00806555i	−0.999992	+	0.00403277i	$0.998716\pi$
$368$	−9.94448	−	5.61329i	−0.518392	−	0.292613i
$369$			9.86975i			0.513799i
$370$	−13.9548	−	4.69922i	−0.725474	−	0.244301i
$371$	−15.2051	+	6.29815i	−0.789408	+	0.326984i
$372$	−2.67032	−	0.701620i	−0.138450	−	0.0363773i
$373$	5.40842	−	13.0571i	0.280037	−	0.676070i	−0.719799	−	0.694183i	$-0.755766\pi$
$373$	5.40842	−	13.0571i	0.280037	−	0.676070i	0.999836	+	0.0181131i	$0.00576589\pi$
$374$	−49.3585	+	3.35560i	−2.55227	+	0.173514i
$375$	−2.86307	+	2.86307i	−0.147848	+	0.147848i
$376$	3.22232	+	0.616575i	0.166178	+	0.0317974i
$377$	−0.0244733	−	0.0244733i	−0.00126044	−	0.00126044i
$378$	2.61447	+	2.28162i	0.134474	+	0.117354i
$379$	17.4888	+	7.24410i	0.898340	+	0.372105i	0.783582	−	0.621289i	$-0.213391\pi$
$379$	17.4888	+	7.24410i	0.898340	+	0.372105i	0.114758	+	0.993393i	$0.463391\pi$
$380$	4.51798	−	5.94758i	0.231768	−	0.305104i
$381$	−5.86792	−	14.1664i	−0.300623	−	0.725767i
$382$	−14.5489	+	7.21874i	−0.744388	+	0.369343i
$383$	−30.0898			−1.53752			−0.768759	−	0.639538i	$-0.779126\pi$
$383$	−30.0898			−1.53752			−0.768759	+	0.639538i	$0.779126\pi$
$384$	−5.17578	−	10.0604i	−0.264126	−	0.513392i
$385$	51.5042			2.62490
$386$	−24.4097	+	12.1114i	−1.24242	+	0.616452i
$387$	1.67010	+	4.03197i	0.0848957	+	0.204956i
$388$	−2.11715	+	2.78707i	−0.107482	+	0.141492i
$389$	11.7666	+	4.87387i	0.596589	+	0.247115i	0.660482	−	0.750842i	$-0.270352\pi$
$389$	11.7666	+	4.87387i	0.596589	+	0.247115i	−0.0638936	+	0.997957i	$0.520352\pi$
$390$	−0.0669188	−	0.0583991i	−0.00338856	−	0.00295715i
$391$	11.2638	+	11.2638i	0.569633	+	0.569633i
$392$	2.72073	+	0.520599i	0.137418	+	0.0262942i
$393$	10.5432	−	10.5432i	0.531835	−	0.531835i
$394$	−9.90638	+	0.673477i	−0.499076	+	0.0339293i
$395$	3.42394	−	8.26611i	0.172277	−	0.415913i
$396$	12.1273	+	3.18643i	0.609422	+	0.160124i
$397$	15.2331	−	6.30976i	0.764527	−	0.316678i	0.0338739	−	0.999426i	$-0.489216\pi$
$397$	15.2331	−	6.30976i	0.764527	−	0.316678i	0.730653	+	0.682749i	$0.239216\pi$
$398$	−27.7725	−	9.35230i	−1.39211	−	0.468788i
$399$		−	2.73692i		−	0.137017i
$400$	12.2091	−	21.6295i	0.610454	−	1.08148i
$401$			35.7766i			1.78660i	0.449463	+	0.893299i	$0.351615\pi$
$401$			35.7766i			1.78660i	−0.449463	+	0.893299i	$0.648385\pi$
$402$	2.42833	−	7.21116i	0.121114	−	0.359660i
$403$	0.0239243	−	0.00990976i	0.00119175	−	0.000493641i
$404$	−14.4174	+	8.41757i	−0.717293	+	0.418790i
$405$	−1.28124	+	3.09318i	−0.0636653	+	0.153702i
$406$	−0.434266	−	6.38776i	−0.0215523	−	0.317019i
$407$	−13.7867	+	13.7867i	−0.683380	+	0.683380i
$408$	3.19167	+	15.4559i	0.158011	+	0.765181i
$409$	−4.31657	−	4.31657i	−0.213440	−	0.213440i	0.592287	−	0.805727i	$-0.298225\pi$
$409$	−4.31657	−	4.31657i	−0.213440	−	0.213440i	−0.805727	+	0.592287i	$0.798225\pi$
$410$	30.7269	−	35.2095i	1.51749	−	1.73887i
$411$	4.00011	+	1.65690i	0.197311	+	0.0817289i
$412$	−10.9376	+	1.49407i	−0.538856	+	0.0736075i
$413$	0.747970	+	1.80576i	0.0368052	+	0.0888557i
$414$	−1.79447	−	3.61664i	−0.0881933	−	0.177748i
$415$	25.0729			1.23078
$416$	0.0957331	+	0.0457729i	0.00469370	+	0.00224420i
$417$	−1.62380			−0.0795178
$418$	−4.39569	−	8.85925i	−0.215000	−	0.433320i
$419$	−7.37576	−	17.8067i	−0.360330	−	0.869913i	−0.995252	−	0.0973364i	$-0.968968\pi$
$419$	−7.37576	−	17.8067i	−0.360330	−	0.869913i	0.634922	−	0.772576i	$-0.281032\pi$
$420$	−2.22370	−	16.2790i	−0.108505	−	0.794332i
$421$	−5.03356	−	2.08497i	−0.245321	−	0.101615i	0.256635	−	0.966508i	$-0.417386\pi$
$421$	−5.03356	−	2.08497i	−0.245321	−	0.101615i	−0.501956	+	0.864893i	$0.667386\pi$
$422$	2.82197	−	3.23365i	0.137371	−	0.157412i
$423$	0.820194	+	0.820194i	0.0398792	+	0.0398792i
$424$	15.8505	+	10.4246i	0.769768	+	0.506265i
$425$	−24.4990	+	24.4990i	−1.18838	+	1.18838i
$426$	−0.241870	−	3.55774i	−0.0117186	−	0.172373i
$427$	11.8332	−	28.5680i	0.572651	−	1.38250i
$428$	14.6444	+	25.0826i	0.707866	+	1.21241i
$429$	−0.108653	+	0.0450055i	−0.00524581	+	0.00217288i
$430$	6.59455	−	19.5831i	0.318017	−	0.944382i
$431$			18.4128i			0.886914i	0.896296	+	0.443457i	$0.146248\pi$
$431$			18.4128i			0.886914i	−0.896296	+	0.443457i	$0.853752\pi$
$432$	0.483535	−	3.97067i	0.0232641	−	0.191039i
$433$		−	0.227663i		−	0.0109408i	−0.999985	−	0.00547038i	$-0.998259\pi$
$433$		−	0.227663i		−	0.0109408i	0.999985	−	0.00547038i	$-0.00174129\pi$
$434$	4.53984	+	1.52877i	0.217919	+	0.0733835i
$435$	5.70715	−	2.36398i	0.273637	−	0.113344i
$436$	8.16859	−	31.0891i	0.391204	−	1.48890i
$437$	−1.21860	+	2.94197i	−0.0582938	+	0.140734i
$438$	3.34229	−	0.227223i	0.159701	−	0.0108571i
$439$	−19.0619	+	19.0619i	−0.909774	+	0.909774i	−0.996254	−	0.0864799i	$-0.972438\pi$
$439$	−19.0619	+	19.0619i	−0.909774	+	0.909774i	0.0864799	+	0.996254i	$0.472438\pi$
$440$	−33.3432	−	49.1226i	−1.58957	−	2.34183i
$441$	0.692523	+	0.692523i	0.0329773	+	0.0329773i
$442$	−0.111526	−	0.0973269i	−0.00530473	−	0.00462937i
$443$	28.0493	+	11.6184i	1.33266	+	0.552008i	0.931414	−	0.363961i	$-0.118576\pi$
$443$	28.0493	+	11.6184i	1.33266	+	0.552008i	0.401250	+	0.915968i	$0.368576\pi$
$444$	4.95280	+	3.76231i	0.235049	+	0.178552i
$445$	−12.2101	−	29.4779i	−0.578816	−	1.39739i
$446$	7.75440	−	3.84750i	0.367182	−	0.182184i
$447$	22.3150			1.05546
$448$	7.77550	+	18.0239i	0.367358	+	0.851550i
$449$	33.0005			1.55739			0.778696	−	0.627401i	$-0.215881\pi$
$449$	33.0005			1.55739			0.778696	+	0.627401i	$0.215881\pi$
$450$	7.86630	−	3.90302i	0.370821	−	0.183990i
$451$	−23.6798	−	57.1681i	−1.11504	−	2.69194i
$452$	−4.34660	−	3.30183i	−0.204447	−	0.155305i
$453$	−12.3124	−	5.09995i	−0.578486	−	0.239617i
$454$	18.1670	+	15.8541i	0.852620	+	0.744070i
$455$	0.108966	+	0.108966i	0.00510839	+	0.00510839i
$456$	−2.61036	+	1.77185i	−0.122241	+	0.0829744i
$457$	19.3344	−	19.3344i	0.904423	−	0.904423i	−0.0913920	−	0.995815i	$-0.529132\pi$
$457$	19.3344	−	19.3344i	0.904423	−	0.904423i	0.995815	+	0.0913920i	$0.0291316\pi$
$458$	13.1477	−	0.893833i	0.614350	−	0.0417661i
$459$	−2.13529	+	5.15504i	−0.0996667	+	0.240617i
$460$	−4.85785	+	18.4887i	−0.226498	+	0.862039i
$461$	−19.0532	+	7.89211i	−0.887398	+	0.367572i	−0.779361	−	0.626575i	$-0.784456\pi$
$461$	−19.0532	+	7.89211i	−0.887398	+	0.367572i	−0.108037	+	0.994147i	$0.534456\pi$
$462$	−20.6178	−	6.94297i	−0.959227	−	0.323016i
$463$			18.6664i			0.867499i	0.901034	+	0.433749i	$0.142810\pi$
$463$			18.6664i			0.867499i	−0.901034	+	0.433749i	$0.857190\pi$
$464$	−5.81124	+	4.54954i	−0.269780	+	0.211207i
$465$			4.62190i			0.214335i
$466$	−5.10441	+	15.1580i	−0.236457	+	0.702182i
$467$	−1.38748	+	0.574712i	−0.0642048	+	0.0265945i	−0.414555	−	0.910024i	$-0.636063\pi$
$467$	−1.38748	+	0.574712i	−0.0642048	+	0.0265945i	0.350350	+	0.936619i	$0.386063\pi$
$468$	0.0189160	+	0.0323988i	0.000874392	+	0.00149764i
$469$	−5.05214	+	12.1970i	−0.233286	+	0.563203i
$470$	−0.372515	−	5.47944i	−0.0171828	−	0.252748i
$471$	13.9315	−	13.9315i	0.641927	−	0.641927i
$472$	1.23803	−	1.88241i	0.0569851	−	0.0866449i
$473$	−19.3472	−	19.3472i	−0.889586	−	0.889586i
$474$	−2.48495	+	2.84747i	−0.114138	+	0.130789i
$475$	−6.39888	−	2.65050i	−0.293601	−	0.121613i
$476$	−3.70598	−	27.1302i	−0.169863	−	1.24351i
$477$	2.56680	+	6.19681i	0.117526	+	0.283732i
$478$	3.93930	+	7.93942i	0.180179	+	0.363140i
$479$	−20.1621			−0.921229			−0.460615	−	0.887600i	$-0.652371\pi$
$479$	−20.1621			−0.921229			−0.460615	+	0.887600i	$0.652371\pi$
$480$	−14.0866	+	12.6597i	−0.642963	+	0.577832i
$481$	−0.0583360			−0.00265989
$482$	9.90639	+	19.9657i	0.451224	+	0.909414i
$483$	2.68066	+	6.47169i	0.121974	+	0.294472i
$484$	−56.0919	+	7.66214i	−2.54963	+	0.348279i
$485$	5.41309	+	2.24218i	0.245796	+	0.101812i
$486$	0.929869	−	1.06552i	0.0421797	−	0.0483332i
$487$	−14.3589	−	14.3589i	−0.650665	−	0.650665i	0.302488	−	0.953153i	$-0.402183\pi$
$487$	−14.3589	−	14.3589i	−0.650665	−	0.650665i	−0.953153	+	0.302488i	$0.902183\pi$
$488$	−34.9076	+	7.20848i	−1.58019	+	0.326313i
$489$	−11.1133	+	11.1133i	−0.502561	+	0.502561i
$490$	−0.314529	−	4.62651i	−0.0142090	−	0.209004i
$491$	7.84066	−	18.9290i	0.353844	−	0.854255i	−0.642294	−	0.766458i	$-0.722017\pi$
$491$	7.84066	−	18.9290i	0.353844	−	0.854255i	0.996138	−	0.0877968i	$-0.0279826\pi$
$492$	−17.0467	+	9.95271i	−0.768527	+	0.448703i
$493$	9.51144	−	3.93977i	0.428374	−	0.177438i
$494$	0.00944340	−	0.0280430i	0.000424879	−	0.00126172i
$495$		−	20.9905i		−	0.943452i
$496$	−1.48095	−	5.31962i	−0.0664966	−	0.238858i
$497$			6.18702i			0.277526i
$498$	−10.0370	−	3.37992i	−0.449768	−	0.151458i
$499$	11.1249	−	4.60809i	0.498020	−	0.206286i	−0.119512	−	0.992833i	$-0.538133\pi$
$499$	11.1249	−	4.60809i	0.498020	−	0.206286i	0.617531	+	0.786546i	$0.288133\pi$
$500$	−7.83214	−	2.05787i	−0.350264	−	0.0920308i
$501$	−6.40731	+	15.4686i	−0.286258	+	0.691087i
$502$	29.0468	−	1.97472i	1.29642	−	0.0881363i
$503$	−10.7388	+	10.7388i	−0.478820	+	0.478820i	−0.904754	−	0.425934i	$-0.859946\pi$
$503$	−10.7388	+	10.7388i	−0.478820	+	0.478820i	0.425934	+	0.904754i	$0.359946\pi$
$504$	−1.30429	+	6.81644i	−0.0580978	+	0.303628i
$505$	19.7618	+	19.7618i	0.879390	+	0.879390i
$506$	19.0712	+	16.6431i	0.847816	+	0.739878i
$507$	12.0101	+	4.97475i	0.533388	+	0.220936i
$508$	18.5506	−	24.4204i	0.823048	−	1.08348i
$509$	−7.73386	−	18.6712i	−0.342797	−	0.827586i	−0.997431	−	0.0716392i	$-0.977177\pi$
$509$	−7.73386	−	18.6712i	−0.342797	−	0.827586i	0.654633	−	0.755947i	$-0.272823\pi$
$510$	23.6663	−	11.7425i	1.04796	−	0.519968i
$511$	−5.81234			−0.257123
$512$	12.1567	−	19.0844i	0.537256	−	0.843419i
$513$	−1.11543			−0.0492473
$514$	6.62270	−	3.28599i	0.292115	−	0.144939i
$515$	7.07189	+	17.0731i	0.311625	+	0.752329i
$516$	−5.27976	+	6.95040i	−0.232429	+	0.305974i
$517$	−6.71860	−	2.78294i	−0.295484	−	0.122393i
$518$	−8.13068	−	7.09554i	−0.357241	−	0.311760i
$519$	−16.1198	−	16.1198i	−0.707581	−	0.707581i
$520$	0.0333840	−	0.174470i	0.00146399	−	0.00765102i
$521$	13.6485	−	13.6485i	0.597953	−	0.597953i	−0.341815	−	0.939767i	$-0.611042\pi$
$521$	13.6485	−	13.6485i	0.597953	−	0.597953i	0.939767	+	0.341815i	$0.111042\pi$
$522$	−2.60332	+	0.176985i	−0.113944	+	0.00774640i
$523$	−6.91544	+	16.6954i	−0.302391	+	0.730037i	0.697518	+	0.716567i	$0.254288\pi$
$523$	−6.91544	+	16.6954i	−0.302391	+	0.730037i	−0.999909	+	0.0134697i	$0.995712\pi$
$524$	28.8418	+	7.57809i	1.25996	+	0.331051i
$525$	−14.0761	+	5.83052i	−0.614332	+	0.254465i
$526$	−10.5966	−	3.56837i	−0.462034	−	0.155588i
$527$			7.70276i			0.335538i
$528$	6.72578	+	24.1592i	0.292702	+	1.05139i
$529$			14.8499i			0.645647i
$530$	10.1353	−	30.0977i	0.440249	−	1.30736i
$531$	0.735935	−	0.304834i	0.0319369	−	0.0132287i
$532$	4.72713	−	2.75993i	0.204947	−	0.119658i
$533$	0.0708500	−	0.171047i	0.00306885	−	0.00740887i
$534$	0.914138	+	13.4463i	0.0395586	+	0.581880i
$535$	34.3806	−	34.3806i	1.48640	−	1.48640i
$536$	14.9036	−	3.07763i	0.643740	−	0.132933i
$537$	3.64182	+	3.64182i	0.157156	+	0.157156i
$538$	−9.99053	+	11.4480i	−0.430722	+	0.493559i
$539$	−5.67279	−	2.34974i	−0.244344	−	0.101211i
$540$	−6.63447	+	0.906266i	−0.285502	+	0.0389995i
$541$	9.51555	+	22.9726i	0.409106	+	0.987668i	0.985374	+	0.170407i	$0.0545084\pi$
$541$	9.51555	+	22.9726i	0.409106	+	0.987668i	−0.576268	+	0.817261i	$0.695492\pi$
$542$	9.70310	+	19.5560i	0.416784	+	0.840002i
$543$	9.69731			0.416151
$544$	−23.4765	+	21.0984i	−1.00655	+	0.904585i
$545$	−53.8103			−2.30498
$546$	−0.0289314	−	0.0583094i	−0.00123815	−	0.00249541i
$547$	11.3958	+	27.5119i	0.487250	+	1.17633i	0.956098	+	0.293046i	$0.0946690\pi$
$547$	11.3958	+	27.5119i	0.487250	+	1.17633i	−0.468848	+	0.883279i	$0.655331\pi$
$548$	1.17198	+	8.57971i	0.0500647	+	0.366507i
$549$	−11.6428	−	4.82262i	−0.496904	−	0.205824i
$550$	−36.1993	+	41.4803i	−1.54355	+	1.76873i
$551$	1.45526	+	1.45526i	0.0619961	+	0.0619961i
$552$	4.43701	−	6.74640i	0.188852	−	0.287146i
$553$	4.63662	−	4.63662i	0.197169	−	0.197169i
$554$	0.449020	+	6.60477i	0.0190770	+	0.280610i
$555$	3.98449	−	9.61941i	0.169132	−	0.408321i
$556$	−1.63745	−	2.80458i	−0.0694433	−	0.118941i
$557$	1.70939	−	0.708053i	0.0724292	−	0.0300012i	−0.346175	−	0.938170i	$-0.612520\pi$
$557$	1.70939	−	0.708053i	0.0724292	−	0.0300012i	0.418604	+	0.908169i	$0.362520\pi$
$558$	0.623050	−	1.85020i	0.0263758	−	0.0783253i
$559$		−	0.0818645i		−	0.00346250i
$560$	25.8742	−	20.2565i	1.09338	−	0.855994i
$561$		−	34.9823i		−	1.47695i
$562$	7.01962	+	2.36383i	0.296105	+	0.0997123i
$563$	19.1605	−	7.93652i	0.807517	−	0.334485i	0.0595542	−	0.998225i	$-0.481032\pi$
$563$	19.1605	−	7.93652i	0.807517	−	0.334485i	0.747963	+	0.663741i	$0.231032\pi$
$564$	−0.589527	+	2.24370i	−0.0248236	+	0.0944770i
$565$	−3.49681	+	8.44204i	−0.147112	+	0.355159i
$566$	24.6804	−	1.67788i	1.03740	−	0.0705265i
$567$	−1.73503	+	1.73503i	−0.0728642	+	0.0728642i
$568$	5.90092	−	4.00540i	0.247597	−	0.168063i
$569$	−15.1289	−	15.1289i	−0.634235	−	0.634235i	0.314892	−	0.949127i	$-0.398032\pi$
$569$	−15.1289	−	15.1289i	−0.634235	−	0.634235i	−0.949127	+	0.314892i	$0.898032\pi$
$570$	3.97920	+	3.47259i	0.166670	+	0.145451i
$571$	−12.1094	−	5.01587i	−0.506761	−	0.209907i	0.114629	−	0.993408i	$-0.463432\pi$
$571$	−12.1094	−	5.01587i	−0.506761	−	0.209907i	−0.621391	+	0.783501i	$0.713432\pi$
$572$	−0.187298	−	0.142278i	−0.00783133	−	0.00594895i
$573$	−4.39488	−	10.6102i	−0.183599	−	0.443246i
$574$	30.6797	−	15.2223i	1.28055	−	0.635368i
$575$	17.7267			0.739256
$576$	7.34562	−	3.16889i	0.306067	−	0.132037i
$577$	−35.7790			−1.48950			−0.744749	−	0.667344i	$-0.767431\pi$
$577$	−35.7790			−1.48950			−0.744749	+	0.667344i	$0.767431\pi$
$578$	17.9055	−	8.88417i	0.744771	−	0.369533i
$579$	−7.37358	−	17.8014i	−0.306435	−	0.739801i
$580$	9.83812	+	7.47338i	0.408506	+	0.310315i
$581$	16.9766	+	7.03192i	0.704306	+	0.291733i
$582$	−1.86467	−	1.62728i	−0.0772932	−	0.0674528i
$583$	−29.7351	−	29.7351i	−1.23150	−	1.23150i
$584$	3.76283	+	5.54357i	0.155707	+	0.229395i
$585$	0.0444088	−	0.0444088i	0.00183608	−	0.00183608i
$586$	−20.7175	+	1.40846i	−0.855830	+	0.0581829i
$587$	10.9958	−	26.5462i	0.453845	−	1.09568i	−0.517003	−	0.855984i	$-0.672952\pi$
$587$	10.9958	−	26.5462i	0.453845	−	1.09568i	0.970848	−	0.239696i	$-0.0770477\pi$
$588$	−0.497761	+	1.89445i	−0.0205273	+	0.0781258i
$589$	−1.42261	+	0.589265i	−0.0586177	+	0.0242803i
$590$	−3.57441	−	1.20367i	−0.147156	−	0.0495543i
$591$		−	7.02104i		−	0.288807i
$592$	−1.50373	+	12.3483i	−0.0618031	+	0.507510i
$593$			13.4778i			0.553469i	0.960946	+	0.276734i	$0.0892522\pi$
$593$			13.4778i			0.553469i	−0.960946	+	0.276734i	$0.910748\pi$
$594$	−2.82960	+	8.40275i	−0.116100	+	0.344769i
$595$	−42.3490	+	17.5415i	−1.73614	+	0.719133i
$596$	22.5026	+	38.5419i	0.921743	+	1.57874i
$597$	7.92985	−	19.1444i	0.324547	−	0.783526i
$598$	0.00513685	+	0.0755596i	0.000210062	+	0.00308986i
$599$	−11.7247	+	11.7247i	−0.479059	+	0.479059i	−0.904831	−	0.425771i	$-0.860003\pi$
$599$	−11.7247	+	11.7247i	−0.479059	+	0.479059i	0.425771	+	0.904831i	$0.360003\pi$
$600$	14.6736	+	9.65062i	0.599048	+	0.393985i
$601$	−14.2752	−	14.2752i	−0.582299	−	0.582299i	0.353235	−	0.935535i	$-0.385082\pi$
$601$	−14.2752	−	14.2752i	−0.582299	−	0.582299i	−0.935535	+	0.353235i	$0.885082\pi$
$602$	9.95737	−	11.4100i	0.405832	−	0.465037i
$603$	4.97085	+	2.05899i	0.202429	+	0.0838487i
$604$	−3.60738	−	26.4084i	−0.146782	−	1.07454i
$605$	36.2673	+	87.5570i	1.47447	+	3.55970i
$606$	−5.24694	−	10.5749i	−0.213142	−	0.429575i
$607$	−30.9234			−1.25514			−0.627571	−	0.778559i	$-0.715951\pi$
$607$	−30.9234			−1.25514			−0.627571	+	0.778559i	$0.715951\pi$
$608$	−5.69259	−	2.72180i	−0.230865	−	0.110384i
$609$	4.52725			0.183453
$610$	26.5209	+	53.4512i	1.07380	+	2.16418i
$611$	−0.00832655	−	0.0201021i	−0.000336856	−	0.000813243i
$612$	−11.0569	+	1.51037i	−0.446948	+	0.0610529i
$613$	34.3535	+	14.2297i	1.38753	+	0.574732i	0.946483	−	0.322754i	$-0.104609\pi$
$613$	34.3535	+	14.2297i	1.38753	+	0.574732i	0.441043	+	0.897486i	$0.354609\pi$
$614$	−15.7335	+	18.0288i	−0.634952	+	0.727583i
$615$	23.3659	+	23.3659i	0.942202	+	0.942202i
$616$	−8.79940	−	42.6118i	−0.354538	−	1.71688i
$617$	−10.2583	+	10.2583i	−0.412985	+	0.412985i	−0.882777	−	0.469792i	$-0.844329\pi$
$617$	−10.2583	+	10.2583i	−0.412985	+	0.412985i	0.469792	+	0.882777i	$0.344329\pi$
$618$	−0.529453	−	7.78788i	−0.0212977	−	0.313274i
$619$	−8.23548	+	19.8822i	−0.331012	+	0.799133i	0.667501	+	0.744609i	$0.267364\pi$
$619$	−8.23548	+	19.8822i	−0.331012	+	0.799133i	−0.998512	+	0.0545238i	$0.982636\pi$
$620$	−7.98280	+	4.66074i	−0.320597	+	0.187180i
$621$	2.63753	−	1.09250i	0.105840	−	0.0438405i
$622$	−14.5633	+	43.2471i	−0.583936	+	1.73405i
$623$		−	23.3836i		−	0.936844i
$624$	−0.0368833	+	0.0653423i	−0.00147651	+	0.00261579i
$625$		−	17.4906i		−	0.699626i
$626$	−14.2569	−	4.80096i	−0.569820	−	0.191885i
$627$	6.46083	−	2.67617i	0.258021	−	0.106876i
$628$	38.1105	+	10.0134i	1.52078	+	0.399580i
$629$	6.64047	−	16.0315i	0.264773	−	0.639219i
$630$	11.5911	−	0.788012i	0.461801	−	0.0313951i
$631$	10.2772	−	10.2772i	0.409128	−	0.409128i	−0.472307	−	0.881434i	$-0.656579\pi$
$631$	10.2772	−	10.2772i	0.409128	−	0.409128i	0.881434	+	0.472307i	$0.156579\pi$
$632$	−7.42390	−	1.42053i	−0.295307	−	0.0565056i
$633$	2.14593	+	2.14593i	0.0852930	+	0.0852930i
$634$	27.7945	+	24.2559i	1.10386	+	0.963326i
$635$	−47.4297	−	19.6460i	−1.88219	−	0.779629i
$636$	−8.11456	+	10.6822i	−0.321763	+	0.423577i
$637$	−0.00703045	−	0.0169730i	−0.000278556	−	0.000672495i
$638$	14.6544	−	7.27109i	0.580175	−	0.287865i
$639$	2.52151			0.0997494
$640$	−36.0704	−	11.5639i	−1.42581	−	0.457103i
$641$	−14.5702			−0.575489			−0.287745	−	0.957707i	$-0.592905\pi$
$641$	−14.5702			−0.575489			−0.287745	+	0.957707i	$0.592905\pi$
$642$	−18.3976	+	9.12834i	−0.726096	+	0.360267i
$643$	7.72635	+	18.6531i	0.304698	+	0.735605i	0.999860	+	0.0167519i	$0.00533255\pi$
$643$	7.72635	+	18.6531i	0.304698	+	0.735605i	−0.695162	+	0.718853i	$0.744667\pi$
$644$	−8.47452	+	11.1561i	−0.333943	+	0.439610i
$645$	13.4992	+	5.59154i	0.531530	+	0.220167i
$646$	6.63166	+	5.78736i	0.260919	+	0.227701i
$647$	5.45944	+	5.45944i	0.214633	+	0.214633i	0.806232	−	0.591599i	$-0.201503\pi$
$647$	5.45944	+	5.45944i	0.214633	+	0.214633i	−0.591599	+	0.806232i	$0.701503\pi$
$648$	2.77803	+	0.531562i	0.109131	+	0.0208817i
$649$	−3.53135	+	3.53135i	−0.138618	+	0.138618i
$650$	−0.164344	+	0.0111728i	−0.00644611	+	0.000438234i
$651$	−1.29625	+	3.12943i	−0.0508042	+	0.122652i
$652$	−30.4013	−	7.98786i	−1.19061	−	0.312829i
$653$	−8.05307	+	3.33569i	−0.315141	+	0.130536i	−0.534647	−	0.845075i	$-0.679555\pi$
$653$	−8.05307	+	3.33569i	−0.315141	+	0.130536i	0.219506	+	0.975611i	$0.429555\pi$
$654$	21.5409	+	7.25384i	0.842318	+	0.283648i
$655$		−	49.9204i		−	1.95055i
$656$	−34.3801	−	19.4063i	−1.34232	−	0.757688i
$657$			2.36881i			0.0924161i
$658$	1.28453	−	3.81454i	0.0500763	−	0.148706i
$659$	11.5755	−	4.79474i	0.450919	−	0.186777i	−0.145654	−	0.989336i	$-0.546529\pi$
$659$	11.5755	−	4.79474i	0.450919	−	0.186777i	0.596573	+	0.802559i	$0.296529\pi$
$660$	36.2541	−	21.1669i	1.41119	−	0.823921i
$661$	−4.73190	+	11.4238i	−0.184049	+	0.444335i	−0.988794	−	0.149287i	$-0.952302\pi$
$661$	−4.73190	+	11.4238i	−0.184049	+	0.444335i	0.804745	+	0.593621i	$0.202302\pi$
$662$	−3.23434	−	47.5750i	−0.125706	−	1.84905i
$663$	0.0740109	−	0.0740109i	0.00287435	−	0.00287435i
$664$	−4.28365	−	20.7439i	−0.166238	−	0.805020i
$665$	−6.47944	−	6.47944i	−0.251262	−	0.251262i
$666$	−2.89177	+	3.31364i	−0.112054	+	0.128401i
$667$	−4.86643	−	2.01574i	−0.188429	−	0.0780499i
$668$	−33.1781	+	4.53212i	−1.28370	+	0.175353i
$669$	2.34242	+	5.65509i	0.0905631	+	0.218639i
$670$	−11.3230	−	22.8207i	−0.437444	−	0.881642i
$671$	79.0087			3.05010
$672$	−13.0884	+	4.62100i	−0.504896	+	0.178259i
$673$	11.7838			0.454233			0.227117	−	0.973868i	$-0.427070\pi$
$673$	11.7838			0.454233			0.227117	+	0.973868i	$0.427070\pi$
$674$	−0.581581	−	1.17214i	−0.0224017	−	0.0451492i
$675$	2.37622	+	5.73670i	0.0914607	+	0.220806i
$676$	3.51882	+	25.7601i	0.135339	+	0.990772i
$677$	−31.1449	−	12.9006i	−1.19700	−	0.495812i	−0.306969	−	0.951719i	$-0.599315\pi$
$677$	−31.1449	−	12.9006i	−1.19700	−	0.495812i	−0.890027	+	0.455907i	$0.849315\pi$
$678$	2.53784	−	2.90807i	0.0974650	−	0.111684i
$679$	3.03630	+	3.03630i	0.116523	+	0.116523i
$680$	44.1466	+	29.0346i	1.69295	+	1.11343i
$681$	−12.0560	+	12.0560i	−0.461989	+	0.461989i
$682$	0.830200	+	12.2117i	0.0317900	+	0.467609i
$683$	−2.44866	+	5.91159i	−0.0936954	+	0.226201i	−0.963778	−	0.266705i	$-0.914065\pi$
$683$	−2.44866	+	5.91159i	−0.0936954	+	0.226201i	0.870083	+	0.492905i	$0.164065\pi$
$684$	−1.12480	−	1.92653i	−0.0430079	−	0.0736629i
$685$	13.3925	−	5.54737i	0.511702	−	0.211954i
$686$	8.83655	−	26.2409i	0.337381	−	1.00188i
$687$			9.31826i			0.355514i
$688$	−17.3287	−	2.11023i	−0.660649	−	0.0804518i
$689$		−	0.125819i		−	0.00479333i
$690$	−12.8104	−	4.31385i	−0.487683	−	0.164226i
$691$	6.81893	−	2.82449i	0.259404	−	0.107449i	−0.249191	−	0.968454i	$-0.580165\pi$
$691$	6.81893	−	2.82449i	0.259404	−	0.107449i	0.508596	+	0.861005i	$0.330165\pi$
$692$	11.5864	−	44.0969i	0.440447	−	1.67631i
$693$	5.88697	−	14.2124i	0.223628	−	0.539885i
$694$	−13.2606	+	0.901513i	−0.503367	+	0.0342210i
$695$	−3.84422	+	3.84422i	−0.145819	+	0.145819i
$696$	−2.93088	−	4.31791i	−0.111095	−	0.163670i
$697$	38.9411	+	38.9411i	1.47500	+	1.47500i
$698$	−1.63339	−	1.42544i	−0.0618248	−	0.0539537i
$699$	−10.4488	−	4.32805i	−0.395212	−	0.163702i
$700$	−24.2647	−	18.4323i	−0.917121	−	0.696677i
$701$	2.75369	+	6.64799i	0.104005	+	0.251091i	0.967312	−	0.253588i	$-0.0816108\pi$
$701$	2.75369	+	6.64799i	0.104005	+	0.251091i	−0.863307	+	0.504679i	$0.831611\pi$
$702$	−0.0237639	+	0.0117909i	−0.000896911	+	0.000445020i
$703$	3.46884			0.130830
$704$	−34.9447	+	35.9788i	−1.31703	+	1.35600i
$705$	3.88349			0.146261
$706$	−13.7516	+	6.82311i	−0.517547	+	0.256791i
$707$	7.83813	+	18.9229i	0.294783	+	0.711669i
$708$	1.26862	+	0.963689i	0.0476777	+	0.0362176i
$709$	−46.0951	−	19.0932i	−1.73114	−	0.717061i	−0.999369	−	0.0355098i	$-0.988695\pi$
$709$	−46.0951	−	19.0932i	−1.73114	−	0.717061i	−0.731770	−	0.681552i	$-0.761305\pi$
$710$	−8.99528	−	7.85006i	−0.337587	−	0.294607i
$711$	−1.88965	−	1.88965i	−0.0708673	−	0.0708673i
$712$	−22.3023	+	15.1382i	−0.835814	+	0.567329i
$713$	2.78674	−	2.78674i	0.104364	−	0.104364i
$714$	19.3175	−	1.31329i	0.722940	−	0.0491485i
$715$	−0.150680	+	0.363774i	−0.00563512	+	0.0136044i
$716$	−2.61761	+	9.96247i	−0.0978247	+	0.372315i
$717$	−5.79002	+	2.39830i	−0.216232	+	0.0895663i
$718$	−41.0865	−	13.8357i	−1.53333	−	0.516345i
$719$		−	22.0801i		−	0.823447i	−0.911309	−	0.411724i	$-0.864927\pi$
$719$		−	22.0801i		−	0.823447i	0.911309	−	0.411724i	$-0.135073\pi$
$720$	−8.25551	−	10.5450i	−0.307665	−	0.392988i
$721$			13.5434i			0.504381i
$722$	8.01371	−	23.7975i	0.298239	−	0.885649i
$723$	−14.5605	+	6.03116i	−0.541511	+	0.224301i
$724$	9.77882	+	16.7489i	0.363427	+	0.622468i
$725$	4.38430	−	10.5846i	0.162829	−	0.393104i
$726$	−2.71523	−	39.9391i	−0.100772	−	1.48228i
$727$	12.2216	−	12.2216i	0.453274	−	0.453274i	−0.443166	−	0.896440i	$-0.646145\pi$
$727$	12.2216	−	12.2216i	0.453274	−	0.453274i	0.896440	+	0.443166i	$0.146145\pi$
$728$	0.0715357	−	0.108769i	0.00265129	−	0.00403124i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	7.37467	−	8.45054i	0.272949	−	0.312768i
$731$	22.4975	+	9.31876i	0.832100	+	0.344667i
$732$	−3.41121	−	24.9723i	−0.126082	−	0.923003i
$733$	10.2112	+	24.6520i	0.377159	+	0.910541i	0.992496	+	0.122278i	$0.0390198\pi$
$733$	10.2112	+	24.6520i	0.377159	+	0.910541i	−0.615337	+	0.788264i	$0.710980\pi$
$734$	−0.0971227	−	0.195745i	−0.00358487	−	0.00722508i
$735$	3.27899			0.120947
$736$	16.1265	+	0.860365i	0.594430	+	0.0317135i
$737$	−33.7324			−1.24255
$738$	−6.20384	−	12.5035i	−0.228366	−	0.460259i
$739$	12.9929	+	31.3677i	0.477953	+	1.15388i	0.960567	+	0.278048i	$0.0896874\pi$
$739$	12.9929	+	31.3677i	0.477953	+	1.15388i	−0.482614	+	0.875833i	$0.660313\pi$
$740$	20.6323	−	2.81837i	0.758460	−	0.103605i
$741$	0.0193308	+	0.00800710i	0.000710136	+	0.000294148i
$742$	15.3037	−	17.5363i	0.561815	−	0.643776i
$743$	−14.2568	−	14.2568i	−0.523030	−	0.523030i	0.395455	−	0.918485i	$-0.370587\pi$
$743$	−14.2568	−	14.2568i	−0.523030	−	0.523030i	−0.918485	+	0.395455i	$0.870587\pi$
$744$	3.82390	−	0.789642i	0.140191	−	0.0289497i
$745$	52.8291	−	52.8291i	1.93551	−	1.93551i
$746$	1.35566	+	19.9409i	0.0496344	+	0.730087i
$747$	2.86585	−	6.91877i	0.104856	−	0.253144i
$748$	60.4204	−	35.2764i	2.20919	−	1.28983i
$749$	32.9211	−	13.6364i	1.20291	−	0.498262i
$750$	1.82742	−	5.42670i	0.0667281	−	0.198155i
$751$			37.4275i			1.36575i	0.730536	+	0.682874i	$0.239270\pi$
$751$			37.4275i			1.36575i	−0.730536	+	0.682874i	$0.760730\pi$
$752$	−4.46974	+	1.24435i	−0.162995	+	0.0453768i
$753$			20.5866i			0.750218i
$754$	0.0463871	+	0.0156207i	0.00168932	+	0.000568873i
$755$	−41.2223	+	17.0748i	−1.50023	+	0.621417i
$756$	−4.74629	−	1.24708i	−0.172621	−	0.0453557i
$757$	14.2534	−	34.4107i	0.518048	−	1.25068i	−0.421052	−	0.907036i	$-0.638339\pi$
$757$	14.2534	−	34.4107i	0.518048	−	1.25068i	0.939100	−	0.343643i	$-0.111661\pi$
$758$	−26.7091	+	1.81579i	−0.970117	+	0.0659526i
$759$	−12.6561	+	12.6561i	−0.459386	+	0.459386i
$760$	−1.98512	+	10.3745i	−0.0720078	+	0.376324i
$761$	4.71958	+	4.71958i	0.171085	+	0.171085i	0.787456	−	0.616371i	$-0.211398\pi$
$761$	4.71958	+	4.71958i	0.171085	+	0.171085i	−0.616371	+	0.787456i	$0.711398\pi$
$762$	16.3383	+	14.2583i	0.591876	+	0.516522i
$763$	−36.4344	−	15.0916i	−1.31901	−	0.546353i
$764$	13.8938	−	18.2901i	0.502659	−	0.661711i
$765$	7.14903	+	17.2593i	0.258474	+	0.624011i
$766$	38.1192	−	18.9136i	1.37730	−	0.683376i
$767$	−0.0149423			−0.000539536
$768$	12.8806	+	9.49161i	0.464788	+	0.342499i
$769$	−0.848264			−0.0305892			−0.0152946	−	0.999883i	$-0.504869\pi$
$769$	−0.848264			−0.0305892			−0.0152946	+	0.999883i	$0.504869\pi$
$770$	−65.2479	+	32.3741i	−2.35137	+	1.16668i
$771$	2.00056	+	4.82977i	0.0720483	+	0.173940i
$772$	23.3105	−	30.6864i	0.838963	−	1.10443i
$773$	−7.34212	−	3.04121i	−0.264078	−	0.109385i	0.246716	−	0.969088i	$-0.420648\pi$
$773$	−7.34212	−	3.04121i	−0.264078	−	0.109385i	−0.510794	+	0.859703i	$0.670648\pi$
$774$	−4.65013	−	4.05811i	−0.167146	−	0.145866i
$775$	6.06124	+	6.06124i	0.217726	+	0.217726i
$776$	0.930237	−	4.86157i	0.0333936	−	0.174520i
$777$	5.39571	−	5.39571i	0.193570	−	0.193570i
$778$	−17.9700	+	1.22168i	−0.644256	+	0.0437992i
$779$	−4.21296	+	10.1710i	−0.150945	+	0.364413i
$780$	0.121484	+	0.0319195i	0.00434982	+	0.00114290i
$781$	−14.6052	+	6.04967i	−0.522615	+	0.216474i
$782$	−21.3495	−	7.18938i	−0.763458	−	0.257092i
$783$		−	1.84507i		−	0.0659376i
$784$	−3.77398	+	1.05065i	−0.134785	+	0.0375234i
$785$		−	65.9632i		−	2.35433i
$786$	−6.72947	+	19.9838i	−0.240032	+	0.712798i
$787$	−19.1514	+	7.93278i	−0.682674	+	0.282773i	−0.696944	−	0.717125i	$-0.745458\pi$
$787$	−19.1514	+	7.93278i	−0.682674	+	0.282773i	0.0142701	+	0.999898i	$0.495458\pi$
$788$	12.1265	−	7.08005i	0.431990	−	0.252216i
$789$	3.02564	−	7.30453i	0.107716	−	0.260048i
$790$	0.858237	+	12.6241i	0.0305347	+	0.449145i
$791$	−4.73530	+	4.73530i	−0.168368	+	0.168368i
$792$	−17.3664	+	3.58618i	−0.617087	+	0.127429i
$793$	0.167156	+	0.167156i	0.00593589	+	0.00593589i
$794$	−15.3319	+	17.5686i	−0.544107	+	0.623485i
$795$	20.7471	+	8.59375i	0.735825	+	0.304789i
$796$	41.0621	−	5.60906i	1.45541	−	0.198808i
$797$	−8.34929	−	20.1570i	−0.295747	−	0.713997i	−0.999992	−	0.00403944i	$-0.998714\pi$
$797$	−8.34929	−	20.1570i	−0.295747	−	0.713997i	0.704245	−	0.709957i	$-0.251286\pi$
$798$	1.72035	+	3.46726i	0.0608997	+	0.122740i
$799$	6.47215			0.228968
$800$	−1.87132	+	35.0756i	−0.0661611	+	1.24011i
$801$	−9.52995			−0.336724
$802$	−22.4881	−	45.3234i	−0.794083	−	1.60043i
$803$	−5.68331	−	13.7207i	−0.200560	−	0.484194i
$804$	1.45640	+	10.6618i	0.0513632	+	0.376013i
$805$	21.6675	+	8.97496i	0.763678	+	0.316326i
$806$	−0.0240794	+	0.0275923i	−0.000848161	+	0.000971896i
$807$	−7.59716	−	7.59716i	−0.267433	−	0.267433i
$808$	12.9736	−	19.7261i	0.456409	−	0.693963i
$809$	2.49506	−	2.49506i	0.0877217	−	0.0877217i	−0.661884	−	0.749606i	$-0.730243\pi$
$809$	2.49506	−	2.49506i	0.0877217	−	0.0877217i	0.749606	+	0.661884i	$0.230243\pi$
$810$	−0.321153	−	4.72394i	−0.0112842	−	0.165982i
$811$	11.3640	−	27.4351i	0.399044	−	0.963378i	−0.588849	−	0.808243i	$-0.700419\pi$
$811$	11.3640	−	27.4351i	0.399044	−	0.963378i	0.987893	−	0.155135i	$-0.0495812\pi$
$812$	4.56531	+	7.81934i	0.160211	+	0.274405i
$813$	−14.2617	+	5.90740i	−0.500180	+	0.207181i
$814$	8.79969	−	26.1315i	0.308429	−	0.915908i
$815$			52.6197i			1.84319i
$816$	−13.7585	−	17.5740i	−0.481643	−	0.615215i
$817$			4.86792i			0.170307i
$818$	8.18169	+	2.75516i	0.286066	+	0.0963318i
$819$	0.0425236	−	0.0176139i	0.00148590	−	0.000615478i
$820$	−16.7946	+	63.9191i	−0.586492	+	2.23215i
$821$	−11.7466	+	28.3588i	−0.409959	+	0.989728i	0.575189	+	0.818020i	$0.304928\pi$
$821$	−11.7466	+	28.3588i	−0.409959	+	0.989728i	−0.985148	+	0.171708i	$0.945072\pi$
$822$	−6.10901	+	0.415316i	−0.213076	+	0.0144858i
$823$	−13.6697	+	13.6697i	−0.476496	+	0.476496i	−0.904009	−	0.427513i	$-0.859390\pi$
$823$	−13.6697	+	13.6697i	−0.476496	+	0.476496i	0.427513	+	0.904009i	$0.359390\pi$
$824$	12.9171	−	8.76780i	0.449988	−	0.305441i
$825$	−27.5273	−	27.5273i	−0.958378	−	0.958378i
$826$	−2.08261	−	1.81747i	−0.0724633	−	0.0632378i
$827$	35.2612	+	14.6057i	1.22615	+	0.507889i	0.899361	−	0.437207i	$-0.144032\pi$
$827$	35.2612	+	14.6057i	1.22615	+	0.507889i	0.326792	+	0.945096i	$0.394032\pi$
$828$	4.54663	+	3.45378i	0.158006	+	0.120027i
$829$	−16.0030	−	38.6346i	−0.555806	−	1.34184i	−0.913059	−	0.407828i	$-0.866286\pi$
$829$	−16.0030	−	38.6346i	−0.555806	−	1.34184i	0.357253	−	0.934008i	$-0.383714\pi$
$830$	−31.7634	+	15.7601i	−1.10253	+	0.547040i
$831$	−4.68106			−0.162384
$832$	−0.150051	+	0.00218777i	−0.00520207	+	7.58473e-5i
$833$	5.46470			0.189341
$834$	2.05710	−	1.02067i	0.0712317	−	0.0353430i
$835$	21.4519	+	51.7895i	0.742375	+	1.79225i
$836$	11.1373	+	8.46030i	0.385193	+	0.292606i
$837$	1.27540	+	0.528286i	0.0440841	+	0.0182602i
$838$	20.5367	+	17.9221i	0.709429	+	0.619109i
$839$	14.1294	+	14.1294i	0.487800	+	0.487800i	0.907611	−	0.419811i	$-0.137904\pi$
$839$	14.1294	+	14.1294i	0.487800	+	0.487800i	−0.419811	+	0.907611i	$0.637904\pi$
$840$	13.0496	+	19.2252i	0.450253	+	0.663332i
$841$	18.0989	−	18.0989i	0.624100	−	0.624100i
$842$	7.68729	−	0.522614i	0.264922	−	0.0180105i
$843$	−2.00430	+	4.83882i	−0.0690319	+	0.166658i
$844$	−1.54242	+	5.87035i	−0.0530922	+	0.202066i
$845$	40.2103	−	16.6557i	1.38328	−	0.572972i
$846$	−1.55461	−	0.523510i	−0.0534486	−	0.0179986i
$847$			69.4554i			2.38651i
$848$	−26.6327	−	3.24325i	−0.914572	−	0.111374i
$849$			17.4920i			0.600323i
$850$	15.6371	−	46.4359i	0.536349	−	1.59274i
$851$	−8.20237	+	3.39753i	−0.281174	+	0.116466i
$852$	2.54270	+	4.35508i	0.0871116	+	0.149202i
$853$	−19.9078	+	48.0618i	−0.681631	+	1.64560i	0.0793634	+	0.996846i	$0.474711\pi$
$853$	−19.9078	+	48.0618i	−0.681631	+	1.64560i	−0.760995	+	0.648758i	$0.775289\pi$
$854$	2.96610	+	43.6292i	0.101498	+	1.49296i
$855$	−2.64069	+	2.64069i	−0.0903096	+	0.0903096i
$856$	−34.3185	−	22.5708i	−1.17298	−	0.771453i
$857$	34.0981	+	34.0981i	1.16477	+	1.16477i	0.983419	+	0.181349i	$0.0580463\pi$
$857$	34.0981	+	34.0981i	1.16477	+	1.16477i	0.181349	+	0.983419i	$0.441954\pi$
$858$	0.109357	−	0.125311i	0.00373340	−	0.00427805i
$859$	3.10766	+	1.28723i	0.106032	+	0.0439199i	0.435069	−	0.900397i	$-0.356724\pi$
$859$	3.10766	+	1.28723i	0.106032	+	0.0439199i	−0.329037	+	0.944317i	$0.606724\pi$
$860$	3.95510	+	28.9539i	0.134868	+	0.987321i
$861$	9.26759	+	22.3739i	0.315839	+	0.762502i
$862$	−11.5738	−	23.3262i	−0.394204	−	0.794493i
$863$	−10.0110			−0.340777			−0.170389	−	0.985377i	$-0.554502\pi$
$863$	−10.0110			−0.340777			−0.170389	+	0.985377i	$0.554502\pi$
$864$	1.88328	+	5.33416i	0.0640705	+	0.181472i
$865$	−76.3247			−2.59512
$866$	0.143102	+	0.288413i	0.00486281	+	0.00980069i
$867$	5.40882	+	13.0580i	0.183693	+	0.443474i
$868$	−6.71222	+	0.916887i	−0.227827	+	0.0311212i
$869$	15.4790	+	6.41161i	0.525089	+	0.217499i
$870$	−5.74416	+	6.58215i	−0.194745	+	0.223156i
$871$	−0.0713665	−	0.0713665i	−0.00241816	−	0.00241816i
$872$	9.19339	+	44.5197i	0.311327	+	1.50763i
$873$	1.23744	−	1.23744i	0.0418810	−	0.0418810i
$874$	−0.305453	−	4.49301i	−0.0103321	−	0.151978i
$875$	−3.80195	+	9.17873i	−0.128529	+	0.310298i
$876$	−4.09134	+	2.38872i	−0.138234	+	0.0807074i
$877$	22.1720	−	9.18393i	0.748694	−	0.310119i	0.0244855	−	0.999700i	$-0.492205\pi$
$877$	22.1720	−	9.18393i	0.748694	−	0.310119i	0.724209	+	0.689581i	$0.242205\pi$
$878$	12.1667	−	36.1302i	0.410607	−	1.21934i
$879$		−	14.6833i		−	0.495254i
$880$	73.1177	+	41.2722i	2.46480	+	1.39129i
$881$		−	16.0746i		−	0.541568i	−0.962640	−	0.270784i	$-0.912717\pi$
$881$		−	16.0746i		−	0.541568i	0.962640	−	0.270784i	$-0.0872829\pi$
$882$	−1.31262	−	0.442020i	−0.0441982	−	0.0148836i
$883$	−12.8293	+	5.31406i	−0.431740	+	0.178832i	−0.587960	−	0.808890i	$-0.700069\pi$
$883$	−12.8293	+	5.31406i	−0.431740	+	0.178832i	0.156221	+	0.987722i	$0.450069\pi$
$884$	0.202463	+	0.0531965i	0.00680955	+	0.00178919i
$885$	1.02060	−	2.46394i	0.0343070	−	0.0828244i
$886$	−42.8372	+	2.91225i	−1.43914	+	0.0978390i
$887$	29.2489	−	29.2489i	0.982081	−	0.982081i	−0.0177612	−	0.999842i	$-0.505654\pi$
$887$	29.2489	−	29.2489i	0.982081	−	0.982081i	0.999842	+	0.0177612i	$0.00565387\pi$
$888$	−8.63931	−	1.65309i	−0.289916	−	0.0554741i
$889$	−26.6042	−	26.6042i	−0.892276	−	0.892276i
$890$	33.9973	+	29.6690i	1.13959	+	0.994507i
$891$	−5.79225	−	2.39923i	−0.194048	−	0.0803771i
$892$	−7.40521	+	9.74838i	−0.247945	+	0.326400i
$893$	0.495123	+	1.19533i	0.0165687	+	0.0400003i
$894$	−28.2697	+	14.0266i	−0.945481	+	0.469119i
$895$	17.2434			0.576384
$896$	−21.1797	−	17.9461i	−0.707563	−	0.599536i
$897$	−0.0535520			−0.00178805
$898$	−41.8066	+	20.7432i	−1.39510	+	0.692209i
$899$	−0.974727	−	2.35320i	−0.0325090	−	0.0784836i
$900$	−7.51207	+	9.88906i	−0.250402	+	0.329635i
$901$	34.5768	+	14.3222i	1.15192	+	0.477141i
$902$	65.9328	+	57.5387i	2.19532	+	1.91583i
$903$	7.57195	+	7.57195i	0.251979	+	0.251979i
$904$	7.58190	+	1.45076i	0.252170	+	0.0482516i
$905$	22.9576	−	22.9576i	0.763137	−	0.763137i
$906$	18.8036	−	1.27834i	0.624706	−	0.0424701i
$907$	21.8942	−	52.8573i	0.726986	−	1.75510i	0.0745987	−	0.997214i	$-0.476232\pi$
$907$	21.8942	−	52.8573i	0.726986	−	1.75510i	0.652387	−	0.757886i	$-0.273768\pi$
$908$	−32.9802	−	8.66547i	−1.09449	−	0.287574i
$909$	7.71200	−	3.19442i	0.255791	−	0.105952i
$910$	−0.206536	−	0.0695502i	−0.00684659	−	0.00230557i
$911$		−	59.8222i		−	1.98200i	−0.133873	−	0.990999i	$-0.542741\pi$
$911$		−	59.8222i		−	1.98200i	0.133873	−	0.990999i	$-0.457259\pi$
$912$	2.19320	−	3.88546i	0.0726240	−	0.128660i
$913$			46.9510i			1.55385i
$914$	−12.3406	+	36.6467i	−0.408192	+	1.21216i
$915$	−38.9806	+	16.1463i	−1.28866	+	0.533781i
$916$	−16.0942	+	9.39659i	−0.531768	+	0.310472i
$917$	14.0007	−	33.8006i	0.462342	−	1.11619i
$918$	−0.535227	−	7.87283i	−0.0176651	−	0.259842i
$919$	17.5355	−	17.5355i	0.578444	−	0.578444i	−0.356030	−	0.934474i	$-0.615870\pi$
$919$	17.5355	−	17.5355i	0.578444	−	0.578444i	0.934474	+	0.356030i	$0.115870\pi$
$920$	−5.46730	−	26.4758i	−0.180251	−	0.872882i
$921$	−11.9643	−	11.9643i	−0.394238	−	0.394238i
$922$	19.1768	−	21.9744i	0.631553	−	0.723688i
$923$	−0.0436988	−	0.0181006i	−0.00143836	−	0.000595790i
$924$	30.4837	−	4.16407i	1.00284	−	0.136988i
$925$	−7.38974	−	17.8404i	−0.242973	−	0.586589i
$926$	−11.7331	−	23.6474i	−0.385574	−	0.777102i
$927$	5.51957			0.181287
$928$	4.50224	−	9.41634i	0.147793	−	0.309106i
$929$	47.3964			1.55502			0.777512	−	0.628868i	$-0.216481\pi$
$929$	47.3964			1.55502			0.777512	+	0.628868i	$0.216481\pi$
$930$	−2.90519	−	5.85523i	−0.0952649	−	0.192001i
$931$	0.418052	+	1.00927i	0.0137011	+	0.0330774i
$932$	−3.06139	−	22.4114i	−0.100279	−	0.734109i
$933$	−29.8114	−	12.3483i	−0.975982	−	0.404265i
$934$	1.39647	−	1.60020i	0.0456940	−	0.0523601i
$935$	−82.8179	−	82.8179i	−2.70843	−	2.70843i
$936$	−0.0443286	−	0.0291543i	−0.00144893	−	0.000952937i
$937$	−3.12631	+	3.12631i	−0.102132	+	0.102132i	−0.756326	−	0.654194i	$-0.773008\pi$
$937$	−3.12631	+	3.12631i	−0.102132	+	0.102132i	0.654194	+	0.756326i	$0.273008\pi$
$938$	−1.26636	−	18.6273i	−0.0413482	−	0.608203i
$939$	4.07076	−	9.82767i	0.132844	−	0.320714i
$940$	3.91613	+	6.70745i	0.127730	+	0.218773i
$941$	6.78357	−	2.80985i	0.221138	−	0.0915984i	−0.269364	−	0.963038i	$-0.586813\pi$
$941$	6.78357	−	2.80985i	0.221138	−	0.0915984i	0.490502	+	0.871440i	$0.336813\pi$
$942$	−8.89210	+	26.4059i	−0.289720	+	0.860351i
$943$		−	28.1766i		−	0.917555i
$944$	−0.385170	+	3.16291i	−0.0125362	+	0.102944i
$945$			8.21507i			0.267236i
$946$	36.6710	+	12.3488i	1.19228	+	0.401496i
$947$	−48.2859	+	20.0007i	−1.56908	+	0.649935i	−0.986637	−	0.162936i	$-0.947904\pi$
$947$	−48.2859	+	20.0007i	−1.56908	+	0.649935i	−0.582444	+	0.812871i	$0.697904\pi$
$948$	1.35821	−	5.16927i	0.0441127	−	0.167890i
$949$	0.0170045	−	0.0410525i	0.000551990	−	0.00133262i
$950$	9.77242	−	0.664370i	0.317059	−	0.0215550i
$951$	−18.4451	+	18.4451i	−0.598123	+	0.598123i
$952$	21.7482	+	32.0403i	0.704862	+	1.03843i
$953$	−12.2493	−	12.2493i	−0.396794	−	0.396794i	0.480307	−	0.877101i	$-0.340525\pi$
$953$	−12.2493	−	12.2493i	−0.396794	−	0.396794i	−0.877101	+	0.480307i	$0.840525\pi$
$954$	−7.14687	−	6.23698i	−0.231389	−	0.201930i
$955$	−35.5233	−	14.7142i	−1.14951	−	0.476141i
$956$	−9.98097	−	7.58189i	−0.322808	−	0.245216i
$957$	4.42675	+	10.6871i	0.143097	+	0.345466i
$958$	25.5423	−	12.6733i	0.825233	−	0.409456i
$959$	10.6237			0.343059
$960$	9.88807	−	24.8923i	0.319136	−	0.803395i
$961$	−29.0943			−0.938525
$962$	0.0739027	−	0.0366683i	0.00238272	−	0.00118223i
$963$	−5.55747	−	13.4169i	−0.179087	−	0.432355i
$964$	−25.0997	−	19.0666i	−0.808408	−	0.614095i
$965$	−59.5997	−	24.6870i	−1.91858	−	0.794703i
$966$	−7.46390	−	6.51365i	−0.240147	−	0.209573i
$967$	−11.6821	−	11.6821i	−0.375671	−	0.375671i	0.493867	−	0.869538i	$-0.335583\pi$
$967$	−11.6821	−	11.6821i	−0.375671	−	0.375671i	−0.869538	+	0.493867i	$0.835583\pi$
$968$	66.2437	−	44.9645i	2.12915	−	1.44521i
$969$	−4.40092	+	4.40092i	−0.141378	+	0.141378i
$970$	−8.26692	+	0.562019i	−0.265435	+	0.0180454i
$971$	−12.0421	+	29.0723i	−0.386451	+	0.932975i	0.604235	+	0.796806i	$0.293479\pi$
$971$	−12.0421	+	29.0723i	−0.386451	+	0.932975i	−0.990686	+	0.136168i	$0.956521\pi$
$972$	−0.508244	+	1.93434i	−0.0163019	+	0.0620441i
$973$	−3.68102	+	1.52473i	−0.118008	+	0.0488806i
$974$	27.2161	+	9.16494i	0.872061	+	0.293664i
$975$		−	0.116477i		−	0.00373026i
$976$	39.6916	−	31.0740i	1.27050	−	0.994653i
$977$			46.2289i			1.47899i	0.673159	+	0.739497i	$0.264937\pi$
$977$			46.2289i			1.47899i	−0.673159	+	0.739497i	$0.735063\pi$
$978$	7.09335	−	21.0643i	0.226820	−	0.673563i
$979$	55.1998	−	22.8645i	1.76419	−	0.730753i
$980$	3.30655	+	5.66337i	0.105624	+	0.180910i
$981$	−6.15056	+	14.8488i	−0.196372	+	0.474085i
$982$	1.96532	+	28.9086i	0.0627160	+	0.922509i
$983$	−36.8328	+	36.8328i	−1.17478	+	1.17478i	−0.193729	+	0.981055i	$0.562058\pi$
$983$	−36.8328	+	36.8328i	−1.17478	+	1.17478i	−0.981055	+	0.193729i	$0.937942\pi$
$984$	15.3396	−	23.3236i	0.489009	−	0.743531i
$985$	−16.6217	−	16.6217i	−0.529613	−	0.529613i
$986$	−9.57310	+	10.9697i	−0.304870	+	0.349346i
$987$	2.62947	+	1.08916i	0.0836969	+	0.0346684i
$988$	0.00566370	+	0.0414621i	0.000180186	+	0.00131908i
$989$	−4.76786	−	11.5106i	−0.151609	−	0.366016i
$990$	13.1940	+	26.5917i	0.419333	+	0.845140i
$991$	−0.0778010			−0.00247143			−0.00123571	−	0.999999i	$-0.500393\pi$
$991$	−0.0778010			−0.00247143			−0.00123571	+	0.999999i	$0.500393\pi$
$992$	5.21989	+	5.80825i	0.165732	+	0.184412i
$993$	33.7182			1.07002
$994$	−3.88898	−	7.83800i	−0.123351	−	0.248606i
$995$	−26.5494	−	64.0960i	−0.841674	−	2.03198i
$996$	14.8398	−	2.02712i	0.470218	−	0.0642316i
$997$	−14.8961	−	6.17018i	−0.471765	−	0.195412i	0.134118	−	0.990965i	$-0.457180\pi$
$997$	−14.8961	−	6.17018i	−0.471765	−	0.195412i	−0.605883	+	0.795554i	$0.707180\pi$
$998$	−11.1970	+	12.8305i	−0.354436	+	0.406144i
$999$	−2.19901	−	2.19901i	−0.0695736	−	0.0695736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.2.n.a.37.2	yes	32
3.2	odd	2		288.2.v.d.37.7		32
4.3	odd	2		384.2.n.a.241.5		32
8.3	odd	2		768.2.n.b.481.4		32
8.5	even	2		768.2.n.a.481.8		32
12.11	even	2		1152.2.v.c.1009.8		32
32.3	odd	8		768.2.n.b.289.4		32
32.13	even	8	inner	96.2.n.a.13.2	✓	32
32.19	odd	8		384.2.n.a.145.5		32
32.29	even	8		768.2.n.a.289.8		32
96.77	odd	8		288.2.v.d.109.7		32
96.83	even	8		1152.2.v.c.145.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.13.2	✓	32	32.13	even	8	inner
96.2.n.a.37.2	yes	32	1.1	even	1	trivial
288.2.v.d.37.7		32	3.2	odd	2
288.2.v.d.109.7		32	96.77	odd	8
384.2.n.a.145.5		32	32.19	odd	8
384.2.n.a.241.5		32	4.3	odd	2
768.2.n.a.289.8		32	32.29	even	8
768.2.n.a.481.8		32	8.5	even	2
768.2.n.b.289.4		32	32.3	odd	8
768.2.n.b.481.4		32	8.3	odd	2
1152.2.v.c.145.8		32	96.83	even	8
1152.2.v.c.1009.8		32	12.11	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:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	96.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26685 + 0.628571i) q^{2} +(-0.382683 - 0.923880i) q^{3} +(1.20980 - 1.59260i) q^{4} +(-3.09318 - 1.28124i) q^{5} +(1.06552 + 0.929869i) q^{6} +(-1.73503 - 1.73503i) q^{7} +(-0.531562 + 2.77803i) q^{8} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(-1.26685 + 0.628571i) q^{2} +(-0.382683 - 0.923880i) q^{3} +(1.20980 - 1.59260i) q^{4} +(-3.09318 - 1.28124i) q^{5} +(1.06552 + 0.929869i) q^{6} +(-1.73503 - 1.73503i) q^{7} +(-0.531562 + 2.77803i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(4.72394 - 0.321153i) q^{10} +(2.39923 - 5.79225i) q^{11} +(-1.93434 - 0.508244i) q^{12} +(0.0173304 - 0.00717850i) q^{13} +(3.28860 + 1.10742i) q^{14} +3.34804i q^{15} +(-1.07278 - 3.85346i) q^{16} +5.57978i q^{17} +(0.451329 - 1.34026i) q^{18} +(-1.03052 + 0.426856i) q^{19} +(-5.78263 + 3.37618i) q^{20} +(-0.938989 + 2.26692i) q^{21} +(0.601386 + 8.84597i) q^{22} +(2.01868 - 2.01868i) q^{23} +(2.76998 - 0.572006i) q^{24} +(4.39068 + 4.39068i) q^{25} +(-0.0174428 + 0.0199875i) q^{26} +(0.923880 + 0.382683i) q^{27} +(-4.86224 + 0.664180i) q^{28} +(-0.706079 - 1.70463i) q^{29} +(-2.10448 - 4.24145i) q^{30} +1.38048 q^{31} +(3.78122 + 4.20742i) q^{32} -6.26948 q^{33} +(-3.50729 - 7.06872i) q^{34} +(3.14377 + 7.58973i) q^{35} +(0.270686 + 1.98160i) q^{36} +(-2.87315 - 1.19010i) q^{37} +(1.03720 - 1.18852i) q^{38} +(-0.0132641 - 0.0132641i) q^{39} +(5.20354 - 7.91189i) q^{40} +(6.97897 - 6.97897i) q^{41} +(-0.235365 - 3.46206i) q^{42} +(1.67010 - 4.03197i) q^{43} +(-6.32218 - 10.8285i) q^{44} +(3.09318 - 1.28124i) q^{45} +(-1.28847 + 3.82623i) q^{46} -1.15993i q^{47} +(-3.14960 + 2.46577i) q^{48} -0.979375i q^{49} +(-8.32217 - 2.80246i) q^{50} +(5.15504 - 2.13529i) q^{51} +(0.00953380 - 0.0362851i) q^{52} +(2.56680 - 6.19681i) q^{53} +(-1.41096 + 0.0959227i) q^{54} +(-14.8425 + 14.8425i) q^{55} +(5.74222 - 3.89767i) q^{56} +(0.788727 + 0.788727i) q^{57} +(1.96597 + 1.71568i) q^{58} +(-0.735935 - 0.304834i) q^{59} +(5.33210 + 4.05045i) q^{60} +(4.82262 + 11.6428i) q^{61} +(-1.74885 + 0.867729i) q^{62} +2.45370 q^{63} +(-7.43488 - 2.95339i) q^{64} -0.0628036 q^{65} +(7.94247 - 3.94081i) q^{66} +(-2.05899 - 4.97085i) q^{67} +(8.88638 + 6.75040i) q^{68} +(-2.63753 - 1.09250i) q^{69} +(-8.75336 - 7.63894i) q^{70} +(-1.78298 - 1.78298i) q^{71} +(-1.58849 - 2.34023i) q^{72} +(1.67500 - 1.67500i) q^{73} +(4.38789 - 0.298307i) q^{74} +(2.37622 - 5.73670i) q^{75} +(-0.566909 + 2.15762i) q^{76} +(-14.2124 + 5.88697i) q^{77} +(0.0251411 + 0.00846617i) q^{78} +2.67236i q^{79} +(-1.61890 + 13.2939i) q^{80} -1.00000i q^{81} +(-4.45450 + 13.2281i) q^{82} +(-6.91877 + 2.86585i) q^{83} +(2.47432 + 4.23795i) q^{84} +(7.14903 - 17.2593i) q^{85} +(0.418623 + 6.15766i) q^{86} +(-1.30466 + 1.30466i) q^{87} +(14.8157 + 9.74406i) q^{88} +(6.73869 + 6.73869i) q^{89} +(-3.11324 + 3.56742i) q^{90} +(-0.0425236 - 0.0176139i) q^{91} +(-0.772764 - 5.65714i) q^{92} +(-0.528286 - 1.27540i) q^{93} +(0.729098 + 1.46945i) q^{94} +3.73450 q^{95} +(2.44014 - 5.10350i) q^{96} -1.75001 q^{97} +(0.615607 + 1.24072i) q^{98} +(2.39923 + 5.79225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} - 16 q^{12} - 32 q^{14} - 8 q^{16} - 8 q^{18} - 32 q^{20} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 40 q^{26} + 40 q^{28} - 48 q^{31} + 40 q^{32} + 40 q^{34} - 48 q^{35} + 40 q^{38} + 8 q^{40} - 16 q^{43} + 8 q^{44} - 32 q^{46} + 24 q^{50} + 16 q^{51} - 8 q^{52} - 32 q^{53} + 8 q^{54} + 32 q^{55} + 56 q^{56} - 32 q^{58} + 64 q^{59} + 48 q^{60} - 32 q^{61} + 48 q^{62} + 16 q^{63} + 24 q^{64} + 48 q^{66} + 16 q^{67} - 8 q^{68} - 32 q^{69} - 24 q^{70} + 64 q^{71} - 32 q^{74} + 32 q^{75} - 56 q^{76} - 32 q^{77} + 24 q^{78} - 56 q^{80} - 40 q^{82} - 64 q^{86} - 48 q^{88} - 48 q^{91} - 80 q^{92} - 32 q^{94} - 40 q^{96} - 80 q^{98}+O(q^{100}) \) 32 * q - 8 * q^10 - 16 * q^12 - 32 * q^14 - 8 * q^16 - 8 * q^18 - 32 * q^20 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 40 * q^26 + 40 * q^28 - 48 * q^31 + 40 * q^32 + 40 * q^34 - 48 * q^35 + 40 * q^38 + 8 * q^40 - 16 * q^43 + 8 * q^44 - 32 * q^46 + 24 * q^50 + 16 * q^51 - 8 * q^52 - 32 * q^53 + 8 * q^54 + 32 * q^55 + 56 * q^56 - 32 * q^58 + 64 * q^59 + 48 * q^60 - 32 * q^61 + 48 * q^62 + 16 * q^63 + 24 * q^64 + 48 * q^66 + 16 * q^67 - 8 * q^68 - 32 * q^69 - 24 * q^70 + 64 * q^71 - 32 * q^74 + 32 * q^75 - 56 * q^76 - 32 * q^77 + 24 * q^78 - 56 * q^80 - 40 * q^82 - 64 * q^86 - 48 * q^88 - 48 * q^91 - 80 * q^92 - 32 * q^94 - 40 * q^96 - 80 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more