LMFDB - Embedded newform 96.2.n.a.13.7

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			13.7
Character	$\chi$	$=$	96.13
Dual form			96.2.n.a.37.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34827 - 0.426820i) q^{2} +(0.382683 - 0.923880i) q^{3} +(1.63565 - 1.15093i) q^{4} +(-1.46213 + 0.605634i) q^{5} +(0.121630 - 1.40897i) q^{6} +(-3.54889 + 3.54889i) q^{7} +(1.71405 - 2.24989i) q^{8} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})$	\(q+(1.34827 - 0.426820i) q^{2} +(0.382683 - 0.923880i) q^{3} +(1.63565 - 1.15093i) q^{4} +(-1.46213 + 0.605634i) q^{5} +(0.121630 - 1.40897i) q^{6} +(-3.54889 + 3.54889i) q^{7} +(1.71405 - 2.24989i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(-1.71285 + 1.44062i) q^{10} +(-0.471165 - 1.13749i) q^{11} +(-0.437388 - 1.95159i) q^{12} +(4.97028 + 2.05876i) q^{13} +(-3.27012 + 6.29959i) q^{14} +1.58260i q^{15} +(1.35070 - 3.76505i) q^{16} -0.419142i q^{17} +(-1.25518 - 0.651562i) q^{18} +(-0.721541 - 0.298872i) q^{19} +(-1.69449 + 2.67342i) q^{20} +(1.92065 + 4.63685i) q^{21} +(-1.12076 - 1.33254i) q^{22} +(-5.76431 - 5.76431i) q^{23} +(-1.42269 - 2.44458i) q^{24} +(-1.76450 + 1.76450i) q^{25} +(7.57998 + 0.654342i) q^{26} +(-0.923880 + 0.382683i) q^{27} +(-1.72020 + 9.88929i) q^{28} +(1.26426 - 3.05219i) q^{29} +(0.675484 + 2.13377i) q^{30} +0.702664 q^{31} +(0.214109 - 5.65280i) q^{32} -1.23121 q^{33} +(-0.178898 - 0.565116i) q^{34} +(3.03961 - 7.33827i) q^{35} +(-1.97041 - 0.342746i) q^{36} +(1.86641 - 0.773092i) q^{37} +(-1.10039 - 0.0949916i) q^{38} +(3.80408 - 3.80408i) q^{39} +(-1.14355 + 4.32773i) q^{40} +(1.76678 + 1.76678i) q^{41} +(4.56865 + 5.43195i) q^{42} +(1.70666 + 4.12024i) q^{43} +(-2.07984 - 1.31826i) q^{44} +(1.46213 + 0.605634i) q^{45} +(-10.2322 - 5.31151i) q^{46} +9.64136i q^{47} +(-2.96156 - 2.68871i) q^{48} -18.1893i q^{49} +(-1.62590 + 3.13215i) q^{50} +(-0.387237 - 0.160399i) q^{51} +(10.4991 - 2.35306i) q^{52} +(-0.729689 - 1.76163i) q^{53} +(-1.08230 + 0.910290i) q^{54} +(1.37781 + 1.37781i) q^{55} +(1.90165 + 14.0676i) q^{56} +(-0.552244 + 0.552244i) q^{57} +(0.401824 - 4.65478i) q^{58} +(9.04676 - 3.74729i) q^{59} +(1.82147 + 2.58858i) q^{60} +(0.0348835 - 0.0842161i) q^{61} +(0.947379 - 0.299911i) q^{62} +5.01889 q^{63} +(-2.12405 - 7.71287i) q^{64} -8.51404 q^{65} +(-1.66001 + 0.525506i) q^{66} +(1.84116 - 4.44495i) q^{67} +(-0.482405 - 0.685570i) q^{68} +(-7.53144 + 3.11962i) q^{69} +(0.966091 - 11.1913i) q^{70} +(-4.81608 + 4.81608i) q^{71} +(-2.80293 + 0.378898i) q^{72} +(4.70238 + 4.70238i) q^{73} +(2.18645 - 1.83896i) q^{74} +(0.954942 + 2.30543i) q^{75} +(-1.52417 + 0.341596i) q^{76} +(5.70896 + 2.36473i) q^{77} +(3.50526 - 6.75258i) q^{78} -2.83705i q^{79} +(0.305342 + 6.32302i) q^{80} +1.00000i q^{81} +(3.13619 + 1.62800i) q^{82} +(8.15085 + 3.37619i) q^{83} +(8.47822 + 5.37373i) q^{84} +(0.253847 + 0.612841i) q^{85} +(4.05963 + 4.82675i) q^{86} +(-2.33605 - 2.33605i) q^{87} +(-3.36684 - 0.889651i) q^{88} +(-5.34580 + 5.34580i) q^{89} +(2.22984 + 0.192491i) q^{90} +(-24.9453 + 10.3327i) q^{91} +(-16.0627 - 2.79405i) q^{92} +(0.268898 - 0.649177i) q^{93} +(4.11512 + 12.9991i) q^{94} +1.23599 q^{95} +(-5.14057 - 2.36104i) q^{96} -10.5490 q^{97} +(-7.76354 - 24.5240i) q^{98} +(-0.471165 + 1.13749i) 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 $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$	$1$

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 $

$2$	1.34827	−	0.426820i	0.953369	−	0.301807i
$2$	1.34827	−	0.426820i	0.953369	−	0.301807i
$3$	0.382683	−	0.923880i	0.220942	−	0.533402i
$3$	0.382683	−	0.923880i	0.220942	−	0.533402i
$4$	1.63565	−	1.15093i	0.817825	−	0.575467i
$5$	−1.46213	+	0.605634i	−0.653884	+	0.270848i	−0.684863	−	0.728672i	$-0.740138\pi$
$5$	−1.46213	+	0.605634i	−0.653884	+	0.270848i	0.0309782	+	0.999520i	$0.490138\pi$
$6$	0.121630	−	1.40897i	0.0496551	−	0.575211i
$7$	−3.54889	+	3.54889i	−1.34136	+	1.34136i	−0.446643	+	0.894712i	$0.647381\pi$
$7$	−3.54889	+	3.54889i	−1.34136	+	1.34136i	−0.894712	+	0.446643i	$0.852619\pi$
$8$	1.71405	−	2.24989i	0.606009	−	0.795458i
$9$	−0.707107	−	0.707107i	−0.235702	−	0.235702i
$10$	−1.71285	+	1.44062i	−0.541649	+	0.455565i
$11$	−0.471165	−	1.13749i	−0.142062	−	0.342967i	0.836794	−	0.547517i	$-0.184427\pi$
$11$	−0.471165	−	1.13749i	−0.142062	−	0.342967i	−0.978856	+	0.204550i	$0.934427\pi$
$12$	−0.437388	−	1.95159i	−0.126263	−	0.563375i
$13$	4.97028	+	2.05876i	1.37851	+	0.570996i	0.944082	−	0.329712i	$-0.106952\pi$
$13$	4.97028	+	2.05876i	1.37851	+	0.570996i	0.434425	+	0.900708i	$0.356952\pi$
$14$	−3.27012	+	6.29959i	−0.873976	+	1.68364i
$15$			1.58260i			0.408625i
$16$	1.35070	−	3.76505i	0.337675	−	0.941263i
$17$		−	0.419142i		−	0.101657i	−0.998707	−	0.0508285i	$-0.983814\pi$
$17$		−	0.419142i		−	0.101657i	0.998707	−	0.0508285i	$-0.0161862\pi$
$18$	−1.25518	−	0.651562i	−0.295848	−	0.153575i
$19$	−0.721541	−	0.298872i	−0.165533	−	0.0685660i	0.298378	−	0.954448i	$-0.403554\pi$
$19$	−0.721541	−	0.298872i	−0.165533	−	0.0685660i	−0.463911	+	0.885882i	$0.653554\pi$
$20$	−1.69449	+	2.67342i	−0.378899	+	0.597795i
$21$	1.92065	+	4.63685i	0.419120	+	1.01184i
$22$	−1.12076	−	1.33254i	−0.238947	−	0.284099i
$23$	−5.76431	−	5.76431i	−1.20194	−	1.20194i	−0.973575	−	0.228367i	$-0.926661\pi$
$23$	−5.76431	−	5.76431i	−1.20194	−	1.20194i	−0.228367	−	0.973575i	$-0.573339\pi$
$24$	−1.42269	−	2.44458i	−0.290406	−	0.498997i
$25$	−1.76450	+	1.76450i	−0.352901	+	0.352901i
$26$	7.57998	+	0.654342i	1.48656	+	0.128327i
$27$	−0.923880	+	0.382683i	−0.177801	+	0.0736475i
$28$	−1.72020	+	9.88929i	−0.325088	+	1.86890i
$29$	1.26426	−	3.05219i	0.234767	−	0.566778i	−0.761959	−	0.647625i	$-0.775762\pi$
$29$	1.26426	−	3.05219i	0.234767	−	0.566778i	0.996727	+	0.0808468i	$0.0257625\pi$
$30$	0.675484	+	2.13377i	0.123326	+	0.389570i
$31$	0.702664			0.126202			0.0631011	−	0.998007i	$-0.479901\pi$
$31$	0.702664			0.126202			0.0631011	+	0.998007i	$0.479901\pi$
$32$	0.214109	−	5.65280i	0.0378495	−	0.999283i
$33$	−1.23121			−0.214327
$34$	−0.178898	−	0.565116i	−0.0306808	−	0.0969166i
$35$	3.03961	−	7.33827i	0.513788	−	1.24039i
$36$	−1.97041	−	0.342746i	−0.328402	−	0.0571243i
$37$	1.86641	−	0.773092i	0.306836	−	0.127096i	−0.223952	−	0.974600i	$-0.571896\pi$
$37$	1.86641	−	0.773092i	0.306836	−	0.127096i	0.530788	+	0.847505i	$0.321896\pi$
$38$	−1.10039	−	0.0949916i	−0.178508	−	0.0154097i
$39$	3.80408	−	3.80408i	0.609141	−	0.609141i
$40$	−1.14355	+	4.32773i	−0.180812	+	0.684274i
$41$	1.76678	+	1.76678i	0.275925	+	0.275925i	0.831480	−	0.555555i	$-0.187494\pi$
$41$	1.76678	+	1.76678i	0.275925	+	0.275925i	−0.555555	+	0.831480i	$0.687494\pi$
$42$	4.56865	+	5.43195i	0.704957	+	0.838168i
$43$	1.70666	+	4.12024i	0.260263	+	0.628330i	0.998955	−	0.0457131i	$-0.0145560\pi$
$43$	1.70666	+	4.12024i	0.260263	+	0.628330i	−0.738692	+	0.674044i	$0.764556\pi$
$44$	−2.07984	−	1.31826i	−0.313548	−	0.198735i
$45$	1.46213	+	0.605634i	0.217961	+	0.0902826i
$46$	−10.2322	−	5.31151i	−1.50865	−	0.783140i
$47$			9.64136i			1.40634i	0.711023	+	0.703169i	$0.248232\pi$
$47$			9.64136i			1.40634i	−0.711023	+	0.703169i	$0.751768\pi$
$48$	−2.96156	−	2.68871i	−0.427465	−	0.388082i
$49$		−	18.1893i		−	2.59847i
$50$	−1.62590	+	3.13215i	−0.229937	+	0.442952i
$51$	−0.387237	−	0.160399i	−0.0542240	−	0.0224603i
$52$	10.4991	−	2.35306i	1.45597	−	0.326310i
$53$	−0.729689	−	1.76163i	−0.100230	−	0.241978i	0.865808	−	0.500377i	$-0.166805\pi$
$53$	−0.729689	−	1.76163i	−0.100230	−	0.241978i	−0.966038	+	0.258399i	$0.916805\pi$
$54$	−1.08230	+	0.910290i	−0.147282	+	0.123875i
$55$	1.37781	+	1.37781i	0.185784	+	0.185784i
$56$	1.90165	+	14.0676i	0.254118	+	1.87987i
$57$	−0.552244	+	0.552244i	−0.0731464	+	0.0731464i
$58$	0.401824	−	4.65478i	0.0527621	−	0.611203i
$59$	9.04676	−	3.74729i	1.17779	−	0.487856i	0.294028	−	0.955797i	$-0.405004\pi$
$59$	9.04676	−	3.74729i	1.17779	−	0.487856i	0.883760	+	0.467941i	$0.155004\pi$
$60$	1.82147	+	2.58858i	0.235150	+	0.334184i
$61$	0.0348835	−	0.0842161i	0.00446637	−	0.0107828i	−0.921631	−	0.388068i	$-0.873142\pi$
$61$	0.0348835	−	0.0842161i	0.00446637	−	0.0107828i	0.926097	+	0.377286i	$0.123142\pi$
$62$	0.947379	−	0.299911i	0.120317	−	0.0380887i
$63$	5.01889			0.632321
$64$	−2.12405	−	7.71287i	−0.265506	−	0.964109i
$65$	−8.51404			−1.05604
$66$	−1.66001	+	0.525506i	−0.204333	+	0.0646854i
$67$	1.84116	−	4.44495i	0.224933	−	0.543037i	−0.770614	−	0.637303i	$-0.780050\pi$
$67$	1.84116	−	4.44495i	0.224933	−	0.543037i	0.995547	+	0.0942652i	$0.0300502\pi$
$68$	−0.482405	−	0.685570i	−0.0585002	−	0.0831376i
$69$	−7.53144	+	3.11962i	−0.906679	+	0.375559i
$70$	0.966091	−	11.1913i	0.115470	−	1.33762i
$71$	−4.81608	+	4.81608i	−0.571564	+	0.571564i	−0.932565	−	0.361001i	$-0.882435\pi$
$71$	−4.81608	+	4.81608i	−0.571564	+	0.571564i	0.361001	+	0.932565i	$0.382435\pi$
$72$	−2.80293	+	0.378898i	−0.330329	+	0.0446535i
$73$	4.70238	+	4.70238i	0.550372	+	0.550372i	0.926548	−	0.376176i	$-0.122761\pi$
$73$	4.70238	+	4.70238i	0.550372	+	0.550372i	−0.376176	+	0.926548i	$0.622761\pi$
$74$	2.18645	−	1.83896i	0.254169	−	0.213774i
$75$	0.954942	+	2.30543i	0.110267	+	0.266209i
$76$	−1.52417	+	0.341596i	−0.174834	+	0.0391838i
$77$	5.70896	+	2.36473i	0.650596	+	0.269486i
$78$	3.50526	−	6.75258i	0.396893	−	0.764579i
$79$		−	2.83705i		−	0.319193i	−0.987182	−	0.159597i	$-0.948981\pi$
$79$		−	2.83705i		−	0.319193i	0.987182	−	0.159597i	$-0.0510194\pi$
$80$	0.305342	+	6.32302i	0.0341382	+	0.706936i
$81$			1.00000i			0.111111i
$82$	3.13619	+	1.62800i	0.346334	+	0.179782i
$83$	8.15085	+	3.37619i	0.894672	+	0.370585i	0.782169	−	0.623066i	$-0.214113\pi$
$83$	8.15085	+	3.37619i	0.894672	+	0.370585i	0.112503	+	0.993651i	$0.464113\pi$
$84$	8.47822	+	5.37373i	0.925049	+	0.586322i
$85$	0.253847	+	0.612841i	0.0275336	+	0.0664719i
$86$	4.05963	+	4.82675i	0.437761	+	0.520481i
$87$	−2.33605	−	2.33605i	−0.250451	−	0.250451i
$88$	−3.36684	−	0.889651i	−0.358907	−	0.0948371i
$89$	−5.34580	+	5.34580i	−0.566654	+	0.566654i	−0.931189	−	0.364536i	$-0.881228\pi$
$89$	−5.34580	+	5.34580i	−0.566654	+	0.566654i	0.364536	+	0.931189i	$0.381228\pi$
$90$	2.22984	+	0.192491i	0.235046	+	0.0202903i
$91$	−24.9453	+	10.3327i	−2.61498	+	1.08316i
$92$	−16.0627	−	2.79405i	−1.67466	−	0.291300i
$93$	0.268898	−	0.649177i	0.0278834	−	0.0673165i
$94$	4.11512	+	12.9991i	0.424443	+	1.34076i
$95$	1.23599			0.126810
$96$	−5.14057	−	2.36104i	−0.524657	−	0.240973i
$97$	−10.5490			−1.07109			−0.535544	−	0.844507i	$-0.679893\pi$
$97$	−10.5490			−1.07109			−0.535544	+	0.844507i	$0.679893\pi$
$98$	−7.76354	−	24.5240i	−0.784236	−	2.47730i
$99$	−0.471165	+	1.13749i	−0.0473539	+	0.114322i
$100$	−0.855282	+	4.91693i	−0.0855282	+	0.491693i
$101$	−14.7491	+	6.10929i	−1.46759	+	0.607897i	−0.966309	−	0.257385i	$-0.917139\pi$
$101$	−14.7491	+	6.10929i	−1.46759	+	0.607897i	−0.501285	+	0.865282i	$0.667139\pi$
$102$	−0.590561	−	0.0509801i	−0.0584742	−	0.00504779i
$103$	−0.180630	+	0.180630i	−0.0177980	+	0.0177980i	−0.715950	−	0.698152i	$-0.754006\pi$
$103$	−0.180630	+	0.180630i	−0.0177980	+	0.0177980i	0.698152	+	0.715950i	$0.254006\pi$
$104$	13.1513	−	7.65378i	1.28959	−	0.750515i
$105$	−5.61647	−	5.61647i	−0.548111	−	0.548111i
$106$	−1.73571	−	2.06370i	−0.168587	−	0.200444i
$107$	3.57306	+	8.62613i	0.345421	+	0.833919i	0.997148	+	0.0754662i	$0.0240445\pi$
$107$	3.57306	+	8.62613i	0.345421	+	0.833919i	−0.651728	+	0.758453i	$0.725956\pi$
$108$	−1.07070	+	1.68926i	−0.103028	+	0.162549i
$109$	−7.71934	−	3.19745i	−0.739378	−	0.306261i	−0.0189789	−	0.999820i	$-0.506042\pi$
$109$	−7.71934	−	3.19745i	−0.739378	−	0.306261i	−0.720400	+	0.693559i	$0.756042\pi$
$110$	2.44573	+	1.26958i	0.233191	+	0.121050i
$111$		−	2.02019i		−	0.191748i
$112$	8.56827	+	18.1553i	0.809625	+	1.71551i
$113$			12.8803i			1.21168i	0.795587	+	0.605839i	$0.207162\pi$
$113$			12.8803i			1.21168i	−0.795587	+	0.605839i	$0.792838\pi$
$114$	−0.508864	+	0.980280i	−0.0476594	+	0.0918117i
$115$	11.9192	+	4.93711i	1.11147	+	0.460388i
$116$	−1.44499	−	6.44740i	−0.134164	−	0.598626i
$117$	−2.05876	−	4.97028i	−0.190332	−	0.459502i
$118$	10.5980	−	8.91368i	0.975628	−	0.820571i
$119$	1.48749	+	1.48749i	0.136358	+	0.136358i
$120$	3.56068	+	2.71266i	0.325044	+	0.247630i
$121$	6.70628	−	6.70628i	0.609662	−	0.609662i
$122$	0.0110871	−	0.128435i	0.00100378	−	0.0116279i
$123$	2.30841	−	0.956175i	0.208142	−	0.0862154i
$124$	1.14931	−	0.808720i	0.103211	−	0.0726252i
$125$	4.53946	−	10.9592i	0.406022	−	0.980223i
$126$	6.76681	−	2.14216i	0.602835	−	0.190839i
$127$	14.5951			1.29510			0.647552	−	0.762021i	$-0.275793\pi$
$127$	14.5951			1.29510			0.647552	+	0.762021i	$0.275793\pi$
$128$	−6.15579	−	9.49243i	−0.544100	−	0.839020i
$129$	4.45971			0.392656
$130$	−11.4792	+	3.63396i	−1.00679	+	0.318719i
$131$	1.05197	−	2.53967i	0.0919108	−	0.221892i	−0.871238	−	0.490860i	$-0.836683\pi$
$131$	1.05197	−	2.53967i	0.0919108	−	0.221892i	0.963149	+	0.268968i	$0.0866826\pi$
$132$	−2.01384	+	1.41705i	−0.175282	+	0.123338i
$133$	3.62134	−	1.50001i	0.314010	−	0.130067i
$134$	0.585182	−	6.77883i	0.0505521	−	0.585602i
$135$	1.11907	−	1.11907i	0.0963139	−	0.0963139i
$136$	−0.943026	−	0.718432i	−0.0808638	−	0.0616050i
$137$	10.5319	+	10.5319i	0.899805	+	0.899805i	0.995419	−	0.0956134i	$-0.0304812\pi$
$137$	10.5319	+	10.5319i	0.899805	+	0.899805i	−0.0956134	+	0.995419i	$0.530481\pi$
$138$	−8.82288	+	7.42065i	−0.751053	+	0.631688i
$139$	−4.34181	−	10.4820i	−0.368267	−	0.889076i	−0.994035	−	0.109066i	$-0.965214\pi$
$139$	−4.34181	−	10.4820i	−0.368267	−	0.889076i	0.625767	−	0.780010i	$-0.284786\pi$
$140$	−3.47413	−	15.5012i	−0.293617	−	1.31009i
$141$	8.90746	+	3.68959i	0.750143	+	0.310719i
$142$	−4.43777	+	8.54896i	−0.372409	+	0.717413i
$143$		−	6.62367i		−	0.553899i
$144$	−3.61738	+	1.70720i	−0.301449	+	0.142267i
$145$			5.22838i			0.434193i
$146$	8.34713	+	4.33300i	0.690814	+	0.358601i
$147$	−16.8047	−	6.96074i	−1.38603	−	0.574112i
$148$	2.16301	−	3.41262i	0.177799	−	0.280516i
$149$	−7.35637	−	17.7598i	−0.602657	−	1.45494i	−0.870836	−	0.491574i	$-0.836422\pi$
$149$	−7.35637	−	17.7598i	−0.602657	−	1.45494i	0.268179	−	0.963369i	$-0.413578\pi$
$150$	2.27152	+	2.70075i	0.185469	+	0.220516i
$151$	1.67484	+	1.67484i	0.136297	+	0.136297i	0.771964	−	0.635667i	$-0.219275\pi$
$151$	1.67484	+	1.67484i	0.136297	+	0.136297i	−0.635667	+	0.771964i	$0.719275\pi$
$152$	−1.90919	+	1.11111i	−0.154856	+	0.0901228i
$153$	−0.296378	+	0.296378i	−0.0239608	+	0.0239608i
$154$	8.70651	+	0.751590i	0.701591	+	0.0605648i
$155$	−1.02739	+	0.425557i	−0.0825216	+	0.0341816i
$156$	1.84390	−	10.6004i	0.147630	−	0.848711i
$157$	−5.88393	+	14.2051i	−0.469589	+	1.13369i	0.494755	+	0.869033i	$0.335258\pi$
$157$	−5.88393	+	14.2051i	−0.469589	+	1.13369i	−0.964343	+	0.264654i	$0.914742\pi$
$158$	−1.21091	−	3.82510i	−0.0963348	−	0.304309i
$159$	−1.90677			−0.151217
$160$	3.11047	+	8.39480i	0.245905	+	0.663667i
$161$	40.9139			3.22446
$162$	0.426820	+	1.34827i	0.0335341	+	0.105930i
$163$	−0.0308652	+	0.0745152i	−0.00241755	+	0.00583648i	−0.925084	−	0.379763i	$-0.876005\pi$
$163$	−0.0308652	+	0.0745152i	−0.00241755	+	0.00583648i	0.922666	+	0.385600i	$0.126005\pi$
$164$	4.92328	+	0.856387i	0.384444	+	0.0668726i
$165$	1.80020	−	0.745665i	0.140145	−	0.0580500i
$166$	12.4306	+	1.07307i	0.964798	+	0.0832862i
$167$	3.70781	−	3.70781i	0.286919	−	0.286919i	−0.548942	−	0.835861i	$-0.684969\pi$
$167$	3.70781	−	3.70781i	0.286919	−	0.286919i	0.835861	+	0.548942i	$0.184969\pi$
$168$	13.7245	+	3.62655i	1.05887	+	0.279795i
$169$	11.2728	+	11.2728i	0.867136	+	0.867136i
$170$	0.603826	+	0.717926i	0.0463113	+	0.0550624i
$171$	0.298872	+	0.721541i	0.0228553	+	0.0551776i
$172$	7.53362	+	4.77502i	0.574433	+	0.364091i
$173$	−14.4940	−	6.00361i	−1.10196	−	0.456446i	−0.243797	−	0.969826i	$-0.578393\pi$
$173$	−14.4940	−	6.00361i	−1.10196	−	0.456446i	−0.858161	+	0.513380i	$0.828393\pi$
$174$	−4.14669	−	2.15255i	−0.314360	−	0.163184i
$175$		−	12.5241i		−	0.946730i
$176$	−4.91912	+	0.237547i	−0.370793	+	0.0179058i
$177$		−	9.79214i		−	0.736022i
$178$	−4.92588	+	9.48926i	−0.369210	+	0.711250i
$179$	−21.2978	−	8.82184i	−1.59187	−	0.659376i	−0.601637	−	0.798770i	$-0.705484\pi$
$179$	−21.2978	−	8.82184i	−1.59187	−	0.659376i	−0.990237	+	0.139394i	$0.955484\pi$
$180$	3.08858	−	0.692210i	0.230209	−	0.0515943i
$181$	−0.843844	−	2.03722i	−0.0627224	−	0.151425i	0.889411	−	0.457109i	$-0.151115\pi$
$181$	−0.843844	−	2.03722i	−0.0627224	−	0.151425i	−0.952133	+	0.305684i	$0.901115\pi$
$182$	−29.2227	+	24.5783i	−2.16613	+	1.82187i
$183$	−0.0644562	−	0.0644562i	−0.00476474	−	0.00476474i
$184$	−22.8494	+	3.08876i	−1.68448	+	0.227707i
$185$	−2.26072	+	2.26072i	−0.166212	+	0.166212i
$186$	0.0854648	−	0.990035i	0.00626658	−	0.0725929i
$187$	−0.476772	+	0.197485i	−0.0348650	+	0.0144416i
$188$	11.0966	+	15.7699i	0.809301	+	1.15014i
$189$	1.92065	−	4.63685i	0.139707	−	0.337281i
$190$	1.66645	−	0.527546i	0.120897	−	0.0382722i
$191$	−10.5263			−0.761656			−0.380828	−	0.924646i	$-0.624361\pi$
$191$	−10.5263			−0.761656			−0.380828	+	0.924646i	$0.624361\pi$
$192$	−7.93860	−	0.989222i	−0.572919	−	0.0713910i
$193$	−14.4005			−1.03657			−0.518285	−	0.855208i	$-0.673429\pi$
$193$	−14.4005			−1.03657			−0.518285	+	0.855208i	$0.673429\pi$
$194$	−14.2229	+	4.50252i	−1.02114	+	0.323262i
$195$	−3.25818	+	7.86595i	−0.233323	+	0.563292i
$196$	−20.9347	−	29.7513i	−1.49533	−	2.12509i
$197$	15.2594	−	6.32063i	1.08718	−	0.450326i	0.234160	−	0.972198i	$-0.424766\pi$
$197$	15.2594	−	6.32063i	1.08718	−	0.450326i	0.853024	+	0.521872i	$0.174766\pi$
$198$	−0.149752	+	1.73475i	−0.0106424	+	0.123283i
$199$	4.42484	−	4.42484i	0.313668	−	0.313668i	−0.532661	−	0.846329i	$-0.678808\pi$
$199$	4.42484	−	4.42484i	0.313668	−	0.313668i	0.846329	+	0.532661i	$0.178808\pi$
$200$	0.945495	+	6.99439i	0.0668566	+	0.494578i
$201$	−3.40202	−	3.40202i	−0.239960	−	0.239960i
$202$	−17.2782	+	14.5322i	−1.21569	+	1.02248i
$203$	6.34518	+	15.3186i	0.445345	+	1.07516i
$204$	−0.817993	+	0.183328i	−0.0572710	+	0.0128355i
$205$	−3.65329	−	1.51324i	−0.255157	−	0.105689i
$206$	−0.166441	+	0.320634i	−0.0115965	+	0.0223396i
$207$			8.15197i			0.566601i
$208$	14.4647	−	15.9326i	1.00294	−	1.10473i
$209$			0.961566i			0.0665129i
$210$	−9.96973	−	5.17528i	−0.687976	−	0.357129i
$211$	5.03490	+	2.08552i	0.346617	+	0.143573i	0.549198	−	0.835692i	$-0.314933\pi$
$211$	5.03490	+	2.08552i	0.346617	+	0.143573i	−0.202582	+	0.979265i	$0.564933\pi$
$212$	−3.22103	−	2.04158i	−0.221221	−	0.140216i
$213$	2.60644	+	6.29251i	0.178591	+	0.431156i
$214$	8.49924	+	10.1053i	0.580996	+	0.690782i
$215$	−4.99071	−	4.99071i	−0.340364	−	0.340364i
$216$	−0.722580	+	2.73457i	−0.0491654	+	0.186064i
$217$	−2.49368	+	2.49368i	−0.169282	+	0.169282i
$218$	−11.7725	−	1.01626i	−0.797332	−	0.0688297i
$219$	6.14396	−	2.54491i	0.415170	−	0.171969i
$220$	3.83938	+	0.667846i	0.258851	+	0.0450262i
$221$	0.862912	−	2.08325i	0.0580457	−	0.140135i
$222$	−0.862256	−	2.72375i	−0.0578708	−	0.182806i
$223$	−6.55302			−0.438823			−0.219411	−	0.975632i	$-0.570414\pi$
$223$	−6.55302			−0.438823			−0.219411	+	0.975632i	$0.570414\pi$
$224$	19.3013	+	20.8210i	1.28962	+	1.39116i
$225$	2.49538			0.166359
$226$	5.49757	+	17.3661i	0.365693	+	1.15518i
$227$	−7.13682	+	17.2298i	−0.473687	+	1.14358i	0.488834	+	0.872377i	$0.337422\pi$
$227$	−7.13682	+	17.2298i	−0.473687	+	1.14358i	−0.962521	+	0.271206i	$0.912578\pi$
$228$	−0.267681	+	1.53887i	−0.0177276	+	0.101914i
$229$	19.5161	−	8.08385i	1.28966	−	0.534196i	0.370778	−	0.928721i	$-0.379091\pi$
$229$	19.5161	−	8.08385i	1.28966	−	0.534196i	0.918885	+	0.394526i	$0.129091\pi$
$230$	18.1776	+	1.56918i	1.19859	+	0.103469i
$231$	4.36945	−	4.36945i	0.287489	−	0.287489i
$232$	−4.70010	−	8.07607i	−0.308577	−	0.530220i
$233$	−12.3229	−	12.3229i	−0.807303	−	0.807303i	0.176922	−	0.984225i	$-0.443386\pi$
$233$	−12.3229	−	12.3229i	−0.807303	−	0.807303i	−0.984225	+	0.176922i	$0.943386\pi$
$234$	−4.89716	−	5.82254i	−0.320138	−	0.380632i
$235$	−5.83914	−	14.0969i	−0.380903	−	0.919582i
$236$	10.4844	−	16.5415i	0.682479	−	1.07676i
$237$	−2.62109	−	1.08569i	−0.170258	−	0.0705233i
$238$	2.64043	+	1.37065i	0.171153	+	0.0888458i
$239$			9.89811i			0.640256i	0.947374	+	0.320128i	$0.103726\pi$
$239$			9.89811i			0.640256i	−0.947374	+	0.320128i	$0.896274\pi$
$240$	5.95856	+	2.13762i	0.384624	+	0.137983i
$241$			4.48193i			0.288706i	0.989526	+	0.144353i	$0.0461101\pi$
$241$			4.48193i			0.288706i	−0.989526	+	0.144353i	$0.953890\pi$
$242$	6.17949	−	11.9042i	0.397232	−	0.765233i
$243$	0.923880	+	0.382683i	0.0592669	+	0.0245492i
$244$	−0.0398701	−	0.177897i	−0.00255242	−	0.0113887i
$245$	11.0160	+	26.5951i	0.703790	+	1.69910i
$246$	2.70424	−	2.27445i	0.172416	−	0.145014i
$247$	−2.97095	−	2.97095i	−0.189037	−	0.189037i
$248$	1.20440	−	1.58092i	0.0764797	−	0.100389i
$249$	6.23839	−	6.23839i	0.395342	−	0.395342i
$250$	1.44279	−	16.7135i	0.0912502	−	1.05705i
$251$	−4.74357	+	1.96485i	−0.299412	+	0.124020i	−0.527332	−	0.849659i	$-0.676808\pi$
$251$	−4.74357	+	1.96485i	−0.299412	+	0.124020i	0.227920	+	0.973680i	$0.426808\pi$
$252$	8.20915	−	5.77641i	0.517128	−	0.363880i
$253$	−3.84093	+	9.27281i	−0.241477	+	0.582977i
$254$	19.6781	−	6.22947i	1.23471	−	0.390871i
$255$	0.663334			0.0415396
$256$	−12.3512	−	10.1709i	−0.771951	−	0.635682i
$257$	−21.8091			−1.36042			−0.680208	−	0.733019i	$-0.738111\pi$
$257$	−21.8091			−1.36042			−0.680208	+	0.733019i	$0.738111\pi$
$258$	6.01289	−	1.90349i	0.374346	−	0.118506i
$259$	−3.88007	+	9.36731i	−0.241096	+	0.582056i
$260$	−13.9260	+	9.79910i	−0.863653	+	0.607714i
$261$	−3.05219	+	1.26426i	−0.188926	+	0.0782557i
$262$	0.334351	−	3.87316i	0.0206562	−	0.239285i
$263$	12.6621	−	12.6621i	0.780776	−	0.780776i	−0.199186	−	0.979962i	$-0.563830\pi$
$263$	12.6621	−	12.6621i	0.780776	−	0.780776i	0.979962	+	0.199186i	$0.0638296\pi$
$264$	−2.11037	+	2.77010i	−0.129884	+	0.170488i
$265$	2.13380	+	2.13380i	0.131078	+	0.131078i
$266$	4.24230	−	3.56807i	0.260112	−	0.218772i
$267$	2.89313	+	6.98463i	0.177056	+	0.427452i
$268$	−2.10435	−	9.38944i	−0.128544	−	0.573551i
$269$	11.0354	+	4.57101i	0.672840	+	0.278699i	0.692830	−	0.721101i	$-0.256364\pi$
$269$	11.0354	+	4.57101i	0.672840	+	0.278699i	−0.0199903	+	0.999800i	$0.506364\pi$
$270$	1.03116	−	1.98644i	0.0627544	−	0.120891i
$271$		−	24.7890i		−	1.50582i	−0.658121	−	0.752912i	$-0.728648\pi$
$271$		−	24.7890i		−	1.50582i	0.658121	−	0.752912i	$-0.271352\pi$
$272$	−1.57809	−	0.566136i	−0.0956859	−	0.0343271i
$273$			27.0006i			1.63415i
$274$	18.6951	+	9.70464i	1.12941	+	0.586279i
$275$	2.83848	+	1.17574i	0.171167	+	0.0708997i
$276$	−8.72832	+	13.7708i	−0.525383	+	0.828905i
$277$	0.490227	+	1.18351i	0.0294549	+	0.0711104i	0.937923	−	0.346845i	$-0.112747\pi$
$277$	0.490227	+	1.18351i	0.0294549	+	0.0711104i	−0.908468	+	0.417955i	$0.862747\pi$
$278$	−10.3279	−	12.2794i	−0.619424	−	0.736471i
$279$	−0.496859	−	0.496859i	−0.0297461	−	0.0297461i
$280$	−11.3003	−	19.4170i	−0.675321	−	1.16039i
$281$	11.2732	−	11.2732i	0.672504	−	0.672504i	−0.285789	−	0.958293i	$-0.592256\pi$
$281$	11.2732	−	11.2732i	0.672504	−	0.672504i	0.958293	+	0.285789i	$0.0922556\pi$
$282$	13.5844	+	1.17268i	0.808941	+	0.0698318i
$283$	19.6457	−	8.13751i	1.16782	−	0.483725i	0.287345	−	0.957827i	$-0.407227\pi$
$283$	19.6457	−	8.13751i	1.16782	−	0.483725i	0.880470	+	0.474102i	$0.157227\pi$
$284$	−2.33443	+	13.4204i	−0.138523	+	0.796355i
$285$	0.472994	−	1.14191i	0.0280178	−	0.0676409i
$286$	−2.82711	−	8.93048i	−0.167171	−	0.528070i
$287$	−12.5402			−0.740227
$288$	−4.14853	+	3.84574i	−0.244455	+	0.226612i
$289$	16.8243			0.989666
$290$	2.23158	+	7.04926i	0.131043	+	0.413947i
$291$	−4.03693	+	9.74600i	−0.236649	+	0.571321i
$292$	13.1036	+	2.27932i	0.766829	+	0.133387i
$293$	−12.9966	+	5.38336i	−0.759269	+	0.314499i	−0.728517	−	0.685028i	$-0.759790\pi$
$293$	−12.9966	+	5.38336i	−0.759269	+	0.314499i	−0.0307516	+	0.999527i	$0.509790\pi$
$294$	−25.6282	−	2.21236i	−1.49467	−	0.129027i
$295$	−10.9581	+	10.9581i	−0.638002	+	0.638002i
$296$	1.45975	−	5.52434i	0.0848461	−	0.321096i
$297$	0.870600	+	0.870600i	0.0505173	+	0.0505173i
$298$	−17.4986	−	20.8052i	−1.01367	−	1.20521i
$299$	−16.7829	−	40.5175i	−0.970581	−	2.34319i
$300$	4.21535	+	2.67181i	0.243374	+	0.154257i
$301$	−20.6790	−	8.56553i	−1.19192	−	0.493709i
$302$	2.97299	+	1.54328i	0.171077	+	0.0888059i
$303$			15.9644i			0.917128i
$304$	−2.09985	+	2.31295i	−0.120435	+	0.132657i
$305$			0.144262i			0.00826039i
$306$	−0.273097	+	0.526098i	−0.0156119	+	0.0300750i
$307$	5.44024	+	2.25342i	0.310491	+	0.128609i	0.532487	−	0.846438i	$-0.321257\pi$
$307$	5.44024	+	2.25342i	0.310491	+	0.128609i	−0.221997	+	0.975047i	$0.571257\pi$
$308$	12.0595	−	2.70277i	0.687154	−	0.154004i
$309$	0.0977562	+	0.236004i	0.00556116	+	0.0134258i
$310$	−1.20356	+	1.01227i	−0.0683573	+	0.0574933i
$311$	12.0286	+	12.0286i	0.682077	+	0.682077i	0.960468	−	0.278391i	$-0.0898010\pi$
$311$	12.0286	+	12.0286i	0.682077	+	0.682077i	−0.278391	+	0.960468i	$0.589801\pi$
$312$	−2.03839	−	15.0792i	−0.115401	−	0.853691i
$313$	−18.0892	+	18.0892i	−1.02246	+	1.02246i	−0.0227184	+	0.999742i	$0.507232\pi$
$313$	−18.0892	+	18.0892i	−1.02246	+	1.02246i	−0.999742	+	0.0227184i	$0.992768\pi$
$314$	−1.87011	+	21.6636i	−0.105536	+	1.22255i
$315$	−7.33827	+	3.03961i	−0.413465	+	0.171263i
$316$	−3.26526	−	4.64042i	−0.183685	−	0.261044i
$317$	6.30035	−	15.2104i	0.353863	−	0.854300i	−0.642273	−	0.766476i	$-0.722009\pi$
$317$	6.30035	−	15.2104i	0.353863	−	0.854300i	0.996136	−	0.0878245i	$-0.0279915\pi$
$318$	−2.57083	+	0.813847i	−0.144165	+	0.0456383i
$319$	−4.06752			−0.227738
$320$	7.77682	+	9.99083i	0.434737	+	0.558504i
$321$	9.33685			0.521132
$322$	55.1628	−	17.4628i	3.07410	−	0.973166i
$323$	−0.125270	+	0.302428i	−0.00697021	+	0.0168276i
$324$	1.15093	+	1.63565i	0.0639408	+	0.0908694i
$325$	−12.4027	+	5.13738i	−0.687980	+	0.284971i
$326$	−0.00981000	+	0.113640i	−0.000543326	+	0.00629396i
$327$	−5.90812	+	5.90812i	−0.326720	+	0.326720i
$328$	7.00343	−	0.946716i	0.386700	−	0.0522736i
$329$	−34.2162	−	34.2162i	−1.88640	−	1.88640i
$330$	2.10888	−	1.77371i	0.116090	−	0.0976398i
$331$	3.57821	+	8.63857i	0.196676	+	0.474819i	0.991193	−	0.132423i	$-0.0422758\pi$
$331$	3.57821	+	8.63857i	0.196676	+	0.474819i	−0.794517	+	0.607242i	$0.792276\pi$
$332$	17.2177	−	3.85882i	0.944945	−	0.211780i
$333$	−1.86641	−	0.773092i	−0.102279	−	0.0423652i
$334$	3.41655	−	6.58168i	0.186945	−	0.360133i
$335$			7.61417i			0.416006i
$336$	20.0522	−	0.968330i	1.09394	−	0.0528267i
$337$			7.95561i			0.433370i	0.976242	+	0.216685i	$0.0695244\pi$
$337$			7.95561i			0.433370i	−0.976242	+	0.216685i	$0.930476\pi$
$338$	20.0102	+	10.3873i	1.08841	+	0.564993i
$339$	11.8999	+	4.92908i	0.646312	+	0.267711i
$340$	1.12054	+	0.710232i	0.0607700	+	0.0385177i
$341$	−0.331071	−	0.799276i	−0.0179285	−	0.0432832i
$342$	0.710927	+	0.845266i	0.0384425	+	0.0457067i
$343$	39.7096	+	39.7096i	2.14412	+	2.14412i
$344$	12.1954	+	3.22250i	0.657532	+	0.173746i
$345$	9.12259	−	9.12259i	0.491144	−	0.491144i
$346$	−22.1042	−	1.90815i	−1.18833	−	0.102583i
$347$	24.7595	−	10.2557i	1.32916	−	0.550557i	0.398745	−	0.917062i	$-0.369446\pi$
$347$	24.7595	−	10.2557i	1.32916	−	0.550557i	0.930416	+	0.366505i	$0.119446\pi$
$348$	−6.50959	−	1.13232i	−0.348951	−	0.0606987i
$349$	−9.76660	+	23.5787i	−0.522794	+	1.26214i	0.413366	+	0.910565i	$0.364353\pi$
$349$	−9.76660	+	23.5787i	−0.522794	+	1.26214i	−0.936161	+	0.351572i	$0.885647\pi$
$350$	−5.34552	−	16.8858i	−0.285730	−	0.902583i
$351$	−5.37979			−0.287152
$352$	−6.53091	+	2.41986i	−0.348098	+	0.128979i
$353$	−6.97022			−0.370987			−0.185494	−	0.982645i	$-0.559388\pi$
$353$	−6.97022			−0.370987			−0.185494	+	0.982645i	$0.559388\pi$
$354$	−4.17948	−	13.2024i	−0.222137	−	0.701701i
$355$	4.12495	−	9.95852i	0.218930	−	0.528543i
$356$	−2.59119	+	14.8965i	−0.137333	+	0.789514i
$357$	1.94350	−	0.805025i	0.102861	−	0.0426064i
$358$	−32.4805	−	2.80388i	−1.71665	−	0.148190i
$359$	−17.8636	+	17.8636i	−0.942805	+	0.942805i	−0.998451	−	0.0556457i	$-0.982278\pi$
$359$	−17.8636	+	17.8636i	−0.942805	+	0.942805i	0.0556457	+	0.998451i	$0.482278\pi$
$360$	3.86878	−	2.25155i	0.203903	−	0.118667i
$361$	−13.0037	−	13.0037i	−0.684407	−	0.684407i
$362$	−2.00725	−	2.38655i	−0.105499	−	0.125434i
$363$	−3.62941	−	8.76218i	−0.190495	−	0.459895i
$364$	−28.9095	+	45.6110i	−1.51527	+	2.39067i
$365$	−9.72341	−	4.02757i	−0.508947	−	0.210813i
$366$	−0.114415	−	0.0593931i	−0.00598059	−	0.00310452i
$367$		−	5.77401i		−	0.301401i	−0.988579	−	0.150700i	$-0.951847\pi$
$367$		−	5.77401i		−	0.301401i	0.988579	−	0.150700i	$-0.0481529\pi$
$368$	−29.4888	+	13.9171i	−1.53721	+	0.725477i
$369$		−	2.49861i		−	0.130072i
$370$	−2.08314	+	4.01298i	−0.108297	+	0.208625i
$371$	8.84141	+	3.66223i	0.459023	+	0.190134i
$372$	−0.307337	−	1.37131i	−0.0159347	−	0.0710991i
$373$	−6.93394	−	16.7400i	−0.359026	−	0.866766i	−0.995438	−	0.0954158i	$-0.969582\pi$
$373$	−6.93394	−	16.7400i	−0.359026	−	0.866766i	0.636411	−	0.771350i	$-0.280418\pi$
$374$	−0.558525	+	0.469759i	−0.0288807	+	0.0242906i
$375$	−8.38783	−	8.38783i	−0.433146	−	0.433146i
$376$	21.6920	+	16.5258i	1.11868	+	0.852253i
$377$	12.5674	−	12.5674i	0.647256	−	0.647256i
$378$	0.610446	−	7.07149i	0.0313980	−	0.363718i
$379$	17.3937	−	7.20472i	0.893456	−	0.370082i	0.111755	−	0.993736i	$-0.464353\pi$
$379$	17.3937	−	7.20472i	0.893456	−	0.370082i	0.781700	+	0.623654i	$0.214353\pi$
$380$	2.02165	−	1.42255i	0.103709	−	0.0729751i
$381$	5.58529	−	13.4841i	0.286143	−	0.690811i
$382$	−14.1923	+	4.49283i	−0.726139	+	0.229873i
$383$	7.76327			0.396685			0.198342	−	0.980133i	$-0.436444\pi$
$383$	7.76327			0.396685			0.198342	+	0.980133i	$0.436444\pi$
$384$	−11.1256	+	2.05462i	−0.567750	+	0.104849i
$385$	−9.77940			−0.498404
$386$	−19.4157	+	6.14642i	−0.988234	+	0.312844i
$387$	1.70666	−	4.12024i	0.0867543	−	0.209443i
$388$	−17.2545	+	12.1412i	−0.875963	+	0.616376i
$389$	22.1262	−	9.16496i	1.12184	−	0.464682i	0.256841	−	0.966454i	$-0.417318\pi$
$389$	22.1262	−	9.16496i	1.12184	−	0.464682i	0.865000	+	0.501772i	$0.167318\pi$
$390$	−1.03556	+	11.9961i	−0.0524376	+	0.607444i
$391$	−2.41607	+	2.41607i	−0.122186	+	0.122186i
$392$	−40.9240	−	31.1774i	−2.06697	−	1.57470i
$393$	−1.94378	−	1.94378i	−0.0980508	−	0.0980508i
$394$	17.8759	−	15.0349i	0.900576	−	0.757447i
$395$	1.71822	+	4.14814i	0.0864528	+	0.208715i
$396$	0.538519	+	2.40282i	0.0270616	+	0.120746i
$397$	17.1908	+	7.12064i	0.862779	+	0.357375i	0.769794	−	0.638293i	$-0.220359\pi$
$397$	17.1908	+	7.12064i	0.862779	+	0.357375i	0.0929854	+	0.995667i	$0.470359\pi$
$398$	4.07725	−	7.85447i	0.204374	−	0.393709i
$399$		−	3.91971i		−	0.196231i
$400$	4.26013	+	9.02676i	0.213006	+	0.451338i
$401$			13.4861i			0.673466i	0.941600	+	0.336733i	$0.109322\pi$
$401$			13.4861i			0.673466i	−0.941600	+	0.336733i	$0.890678\pi$
$402$	−6.03888	−	3.13478i	−0.301192	−	0.156349i
$403$	3.49243	+	1.44661i	0.173971	+	0.0720610i
$404$	−17.0930	+	26.9680i	−0.850410	+	1.34171i
$405$	−0.605634	−	1.46213i	−0.0300942	−	0.0726538i
$406$	15.0933	+	17.9454i	0.749068	+	0.890613i
$407$	−1.75877	−	1.75877i	−0.0871792	−	0.0871792i
$408$	−1.02463	+	0.596311i	−0.0507265	+	0.0295218i
$409$	2.39993	−	2.39993i	0.118669	−	0.118669i	−0.645278	−	0.763948i	$-0.723259\pi$
$409$	2.39993	−	2.39993i	0.118669	−	0.118669i	0.763948	+	0.645278i	$0.223259\pi$
$410$	−5.57149	−	0.480959i	−0.275156	−	0.0237529i
$411$	13.7607	−	5.69985i	0.678763	−	0.281153i
$412$	−0.0875542	+	0.503341i	−0.00431349	+	0.0247978i
$413$	−18.8072	+	45.4047i	−0.925444	+	2.23422i
$414$	3.47942	+	10.9910i	0.171004	+	0.540180i
$415$	−13.9623			−0.685384
$416$	12.7019	−	27.6552i	0.622763	−	1.35591i
$417$	−11.3457			−0.555601
$418$	0.410415	+	1.29645i	0.0200741	+	0.0634114i
$419$	−3.43963	+	8.30401i	−0.168037	+	0.405677i	−0.985356	−	0.170508i	$-0.945459\pi$
$419$	−3.43963	+	8.30401i	−0.168037	+	0.405677i	0.817319	+	0.576185i	$0.195459\pi$
$420$	−15.6508	−	2.72239i	−0.763679	−	0.132839i
$421$	27.1820	−	11.2592i	1.32477	−	0.548738i	0.395612	−	0.918418i	$-0.370533\pi$
$421$	27.1820	−	11.2592i	1.32477	−	0.548738i	0.929159	+	0.369680i	$0.120533\pi$
$422$	7.67853	+	0.662849i	0.373785	+	0.0322670i
$423$	6.81747	−	6.81747i	0.331477	−	0.331477i
$424$	−5.21420	−	1.37779i	−0.253224	−	0.0669116i
$425$	0.739578	+	0.739578i	0.0358748	+	0.0358748i
$426$	6.19995	+	7.37151i	0.300389	+	0.357151i
$427$	0.175076	+	0.422672i	0.00847254	+	0.0204545i
$428$	15.7724	+	9.99697i	0.762387	+	0.483222i
$429$	−6.11947	−	2.53477i	−0.295451	−	0.122380i
$430$	−8.85895	−	4.59868i	−0.427216	−	0.221768i
$431$		−	11.2962i		−	0.544119i	−0.962280	−	0.272060i	$-0.912295\pi$
$431$		−	11.2962i		−	0.544119i	0.962280	−	0.272060i	$-0.0877048\pi$
$432$	0.192937	+	3.99534i	0.00928269	+	0.192226i
$433$		−	38.7244i		−	1.86098i	−0.366323	−	0.930488i	$-0.619383\pi$
$433$		−	38.7244i		−	1.86098i	0.366323	−	0.930488i	$-0.380617\pi$
$434$	−2.29780	+	4.42650i	−0.110298	+	0.212479i
$435$	4.83039	+	2.00081i	0.231600	+	0.0959317i
$436$	−16.3062	+	3.65453i	−0.780925	+	0.175020i
$437$	2.43640	+	5.88198i	0.116549	+	0.281373i
$438$	7.19748	−	6.05358i	0.343909	−	0.289251i
$439$	−12.1768	−	12.1768i	−0.581166	−	0.581166i	0.354058	−	0.935223i	$-0.384802\pi$
$439$	−12.1768	−	12.1768i	−0.581166	−	0.581166i	−0.935223	+	0.354058i	$0.884802\pi$
$440$	5.46156	−	0.738289i	0.260370	−	0.0351965i
$441$	−12.8618	+	12.8618i	−0.612465	+	0.612465i
$442$	0.274262	−	3.17709i	0.0130453	−	0.151119i
$443$	−5.56969	+	2.30704i	−0.264624	+	0.109611i	−0.511051	−	0.859551i	$-0.670744\pi$
$443$	−5.56969	+	2.30704i	−0.264624	+	0.109611i	0.246427	+	0.969161i	$0.420744\pi$
$444$	−2.32510	−	3.30432i	−0.110344	−	0.156816i
$445$	4.57866	−	11.0539i	0.217049	−	0.524003i
$446$	−8.83522	+	2.79696i	−0.418360	+	0.132440i
$447$	−19.2231			−0.909222
$448$	34.9102	+	19.8341i	1.64935	+	0.937075i
$449$	−13.4725			−0.635805			−0.317903	−	0.948123i	$-0.602978\pi$
$449$	−13.4725			−0.635805			−0.317903	+	0.948123i	$0.602978\pi$
$450$	3.36444	−	1.06508i	0.158601	−	0.0502083i
$451$	1.17726	−	2.84215i	0.0554348	−	0.133832i
$452$	14.8244	+	21.0677i	0.697281	+	0.990940i
$453$	2.18829	−	0.906419i	0.102815	−	0.0425873i
$454$	−2.26832	+	26.2765i	−0.106458	+	1.23322i
$455$	30.2154	−	30.2154i	1.41652	−	1.41652i
$456$	0.295915	+	2.18906i	0.0138575	+	0.102512i
$457$	−0.807356	−	0.807356i	−0.0377665	−	0.0377665i	0.687971	−	0.725738i	$-0.258501\pi$
$457$	−0.807356	−	0.807356i	−0.0377665	−	0.0377665i	−0.725738	+	0.687971i	$0.758501\pi$
$458$	22.8626	−	19.2291i	1.06830	−	0.898515i
$459$	0.160399	+	0.387237i	0.00748678	+	0.0180747i
$460$	25.1780	−	5.64287i	1.17393	−	0.263100i
$461$	4.82041	+	1.99668i	0.224509	+	0.0929945i	0.492102	−	0.870537i	$-0.336229\pi$
$461$	4.82041	+	1.99668i	0.224509	+	0.0929945i	−0.267594	+	0.963532i	$0.586229\pi$
$462$	4.02622	−	7.75615i	0.187317	−	0.360849i
$463$			15.0849i			0.701053i	0.936553	+	0.350526i	$0.113997\pi$
$463$			15.0849i			0.701053i	−0.936553	+	0.350526i	$0.886003\pi$
$464$	−9.78402	−	8.88260i	−0.454212	−	0.412364i
$465$			1.11203i			0.0515694i
$466$	−21.8743	−	11.3549i	−1.01331	−	0.526008i
$467$	−17.1432	−	7.10095i	−0.793294	−	0.328593i	−0.0510266	−	0.998697i	$-0.516249\pi$
$467$	−17.1432	−	7.10095i	−0.793294	−	0.328593i	−0.742267	+	0.670104i	$0.766249\pi$
$468$	−9.08786	−	5.76014i	−0.420087	−	0.266262i
$469$	9.24058	+	22.3087i	0.426690	+	1.03012i
$470$	−13.8896	−	16.5142i	−0.640678	−	0.761742i
$471$	10.8721	+	10.8721i	0.500959	+	0.500959i
$472$	7.07561	−	26.7773i	0.325681	−	1.23253i
$473$	3.88263	−	3.88263i	0.178523	−	0.178523i
$474$	−3.99733	−	0.345070i	−0.183603	−	0.0158496i
$475$	1.80052	−	0.745800i	0.0826136	−	0.0342197i
$476$	4.14502	+	0.721011i	0.189987	+	0.0330475i
$477$	−0.729689	+	1.76163i	−0.0334102	+	0.0806593i
$478$	4.22471	+	13.3453i	0.193234	+	0.610400i
$479$	13.4984			0.616757			0.308379	−	0.951264i	$-0.400214\pi$
$479$	13.4984			0.616757			0.308379	+	0.951264i	$0.400214\pi$
$480$	8.94611	+	0.338849i	0.408332	+	0.0154663i
$481$	10.8682			0.495546
$482$	1.91297	+	6.04283i	0.0871336	+	0.275244i
$483$	15.6571	−	37.7995i	0.712421	−	1.71994i
$484$	3.25064	−	18.6876i	0.147756	−	0.849437i
$485$	15.4240	−	6.38883i	0.700368	−	0.290102i
$486$	1.40897	+	0.121630i	0.0639123	+	0.00551723i
$487$	−18.9270	+	18.9270i	−0.857666	+	0.857666i	−0.991063	−	0.133397i	$-0.957412\pi$
$487$	−18.9270	+	18.9270i	−0.857666	+	0.857666i	0.133397	+	0.991063i	$0.457412\pi$
$488$	−0.129685	−	0.222835i	−0.00587058	−	0.0100873i
$489$	0.0570315	+	0.0570315i	0.00257905	+	0.00257905i
$490$	26.2039	+	31.1554i	1.18377	+	1.40746i
$491$	11.5298	+	27.8355i	0.520335	+	1.25620i	0.937695	+	0.347458i	$0.112955\pi$
$491$	11.5298	+	27.8355i	0.520335	+	1.25620i	−0.417361	+	0.908741i	$0.637045\pi$
$492$	2.67526	−	4.22080i	0.120610	−	0.190288i
$493$	−1.27930	−	0.529905i	−0.0576169	−	0.0238657i
$494$	−5.27370	−	2.73758i	−0.237275	−	0.123169i
$495$		−	1.94852i		−	0.0875793i
$496$	0.949089	−	2.64557i	0.0426154	−	0.118789i
$497$		−	34.1835i		−	1.53334i
$498$	5.74835	−	11.0737i	0.257590	−	0.496224i
$499$	−4.77450	−	1.97766i	−0.213736	−	0.0885323i	0.273247	−	0.961944i	$-0.411902\pi$
$499$	−4.77450	−	1.97766i	−0.213736	−	0.0885323i	−0.486983	+	0.873412i	$0.661902\pi$
$500$	−5.18838	−	23.1501i	−0.232031	−	1.03530i
$501$	−2.00665	−	4.84448i	−0.0896505	−	0.216435i
$502$	−5.55697	+	4.67380i	−0.248020	+	0.208602i
$503$	0.935522	+	0.935522i	0.0417129	+	0.0417129i	0.727656	−	0.685943i	$-0.240610\pi$
$503$	0.935522	+	0.935522i	0.0417129	+	0.0417129i	−0.685943	+	0.727656i	$0.740610\pi$
$504$	8.60264	−	11.2920i	0.383192	−	0.502985i
$505$	17.8652	−	17.8652i	0.794989	−	0.794989i
$506$	−1.22077	+	14.1416i	−0.0542701	+	0.628671i
$507$	14.7286	−	6.10078i	0.654120	−	0.270945i
$508$	23.8724	−	16.7980i	1.05917	−	0.745289i
$509$	−3.46080	+	8.35510i	−0.153397	+	0.370333i	−0.981832	−	0.189752i	$-0.939232\pi$
$509$	−3.46080	+	8.35510i	−0.153397	+	0.370333i	0.828435	+	0.560085i	$0.189232\pi$
$510$	0.894352	−	0.283124i	0.0396026	−	0.0125369i
$511$	−33.3765			−1.47649
$512$	−20.9939	−	8.44138i	−0.927807	−	0.373060i
$513$	0.780990			0.0344816
$514$	−29.4046	+	9.30857i	−1.29698	+	0.410583i
$515$	0.154709	−	0.373500i	0.00681729	−	0.0164584i
$516$	7.29453	−	5.13284i	0.321124	−	0.225960i
$517$	10.9670	−	4.54267i	0.482328	−	0.199787i
$518$	−1.23322	+	14.2857i	−0.0541844	+	0.627679i
$519$	−11.0932	+	11.0932i	−0.486938	+	0.486938i
$520$	−14.5935	+	19.1557i	−0.639968	+	0.840033i
$521$	18.6279	+	18.6279i	0.816103	+	0.816103i	0.985541	−	0.169438i	$-0.0541953\pi$
$521$	18.6279	+	18.6279i	0.816103	+	0.816103i	−0.169438	+	0.985541i	$0.554195\pi$
$522$	−3.57556	+	3.00730i	−0.156498	+	0.131626i
$523$	−6.71157	−	16.2032i	−0.293476	−	0.708514i	−1.00000		0.000824669i	$-0.999737\pi$
$523$	−6.71157	−	16.2032i	−0.293476	−	0.708514i	0.706523	−	0.707690i	$-0.250263\pi$
$524$	−1.20235	−	5.36476i	−0.0525248	−	0.234361i
$525$	−11.5707	−	4.79275i	−0.504988	−	0.209173i
$526$	11.6674	−	22.4763i	0.508724	−	0.980012i
$527$		−	0.294516i		−	0.0128293i
$528$	−1.66300	+	4.63558i	−0.0723729	+	0.201738i
$529$			43.4546i			1.88933i
$530$	3.78768	+	1.96619i	0.164526	+	0.0854056i
$531$	−9.04676	−	3.74729i	−0.392596	−	0.162619i
$532$	4.19683	−	6.62141i	0.181956	−	0.287074i
$533$	5.14402	+	12.4188i	0.222812	+	0.537916i
$534$	6.88188	+	8.18230i	0.297808	+	0.354083i
$535$	−10.4486	−	10.4486i	−0.451730	−	0.451730i
$536$	−6.84483	−	11.7613i	−0.295652	−	0.508011i
$537$	−16.3006	+	16.3006i	−0.703425	+	0.703425i
$538$	16.8297	+	1.45282i	0.725578	+	0.0626355i
$539$	−20.6902	+	8.57016i	−0.891190	+	0.369143i
$540$	0.542429	−	3.11837i	0.0233424	−	0.134193i
$541$	−1.92568	+	4.64901i	−0.0827916	+	0.199877i	−0.959854	−	0.280500i	$-0.909500\pi$
$541$	−1.92568	+	4.64901i	−0.0827916	+	0.199877i	0.877063	+	0.480376i	$0.159500\pi$
$542$	−10.5804	−	33.4222i	−0.454468	−	1.43561i
$543$	−2.20507			−0.0946286
$544$	−2.36933	−	0.0897422i	−0.101584	−	0.00384767i
$545$	13.2232			0.566418
$546$	11.5244	+	36.4040i	0.493198	+	1.55795i
$547$	3.16571	−	7.64271i	0.135356	−	0.326779i	−0.841639	−	0.540041i	$-0.818409\pi$
$547$	3.16571	−	7.64271i	0.135356	−	0.326779i	0.976995	+	0.213262i	$0.0684088\pi$
$548$	29.3482	+	5.10500i	1.25369	+	0.218075i
$549$	−0.0842161	+	0.0348835i	−0.00359426	+	0.00148879i
$550$	4.32886	+	0.373689i	0.184583	+	0.0159342i
$551$	−1.82443	+	1.82443i	−0.0777233	+	0.0777233i
$552$	−5.89045	+	22.2921i	−0.250714	+	0.948816i
$553$	10.0684	+	10.0684i	0.428152	+	0.428152i
$554$	1.16610	+	1.38645i	0.0495430	+	0.0589048i
$555$	1.22349	+	2.95378i	0.0519344	+	0.125381i
$556$	−19.1658	−	12.1478i	−0.812812	−	0.515183i
$557$	27.6378	+	11.4479i	1.17105	+	0.485065i	0.881540	−	0.472110i	$-0.156507\pi$
$557$	27.6378	+	11.4479i	1.17105	+	0.485065i	0.289511	+	0.957175i	$0.406507\pi$
$558$	−0.881967	−	0.457829i	−0.0373366	−	0.0193815i
$559$			23.9923i			1.01477i
$560$	−23.5234	−	21.3561i	−0.994043	−	0.902460i
$561$			0.516054i			0.0217878i
$562$	10.3877	−	20.0109i	0.438178	−	0.844110i
$563$	−23.2024	−	9.61075i	−0.977865	−	0.405045i	−0.164231	−	0.986422i	$-0.552514\pi$
$563$	−23.2024	−	9.61075i	−0.977865	−	0.405045i	−0.813634	+	0.581377i	$0.802514\pi$
$564$	18.8160	−	4.21702i	0.792295	−	0.177569i
$565$	−7.80076	−	18.8327i	−0.328180	−	0.792297i
$566$	23.0144	−	19.3567i	0.967367	−	0.813623i
$567$	−3.54889	−	3.54889i	−0.149039	−	0.149039i
$568$	2.58066	+	19.0907i	0.108282	+	0.801028i
$569$	−17.3917	+	17.3917i	−0.729097	+	0.729097i	−0.970440	−	0.241343i	$-0.922412\pi$
$569$	−17.3917	+	17.3917i	−0.729097	+	0.729097i	0.241343	+	0.970440i	$0.422412\pi$
$570$	0.150333	−	1.74148i	0.00629678	−	0.0729427i
$571$	−37.7837	+	15.6505i	−1.58120	+	0.654954i	−0.988603	−	0.150546i	$-0.951897\pi$
$571$	−37.7837	+	15.6505i	−1.58120	+	0.654954i	−0.592596	+	0.805500i	$0.701897\pi$
$572$	−7.62341	−	10.8340i	−0.318751	−	0.452993i
$573$	−4.02824	+	9.72503i	−0.168282	+	0.406269i
$574$	−16.9076	+	5.35242i	−0.705709	+	0.223406i
$575$	20.3423			0.848332
$576$	−3.95189	+	6.95576i	−0.164662	+	0.289823i
$577$	−13.8026			−0.574610			−0.287305	−	0.957839i	$-0.592759\pi$
$577$	−13.8026			−0.574610			−0.287305	+	0.957839i	$0.592759\pi$
$578$	22.6837	−	7.18095i	0.943517	−	0.298688i
$579$	−5.51083	+	13.3043i	−0.229022	+	0.552909i
$580$	6.01752	+	8.55180i	0.249864	+	0.355094i
$581$	−40.9082	+	16.9447i	−1.69716	+	0.702987i
$582$	−1.28307	+	14.8633i	−0.0531850	+	0.616102i
$583$	−1.66003	+	1.66003i	−0.0687515	+	0.0687515i
$584$	18.6400	−	2.51973i	0.771328	−	0.104267i
$585$	6.02034	+	6.02034i	0.248910	+	0.248910i
$586$	−15.2251	+	12.8054i	−0.628945	+	0.528987i
$587$	−3.50667	−	8.46586i	−0.144736	−	0.349423i	0.834842	−	0.550490i	$-0.185559\pi$
$587$	−3.50667	−	8.46586i	−0.144736	−	0.349423i	−0.979578	+	0.201067i	$0.935559\pi$
$588$	−35.4980	+	7.95578i	−1.46391	+	0.328091i
$589$	−0.507001	−	0.210007i	−0.0208906	−	0.00865317i
$590$	−10.0973	+	19.4515i	−0.415698	+	0.800805i
$591$		−	16.5166i		−	0.679403i
$592$	−0.389769	−	8.07134i	−0.0160194	−	0.331730i
$593$			9.94303i			0.408311i	0.978938	+	0.204156i	$0.0654449\pi$
$593$			9.94303i			0.408311i	−0.978938	+	0.204156i	$0.934555\pi$
$594$	1.54539	+	0.802212i	0.0634081	+	0.0329152i
$595$	−3.07578	−	1.27403i	−0.126095	−	0.0522302i
$596$	−32.4729	−	20.5822i	−1.33014	−	0.843079i
$597$	−2.39470	−	5.78133i	−0.0980087	−	0.236614i
$598$	−39.9215	−	47.4652i	−1.63251	−	1.94100i
$599$	7.33034	+	7.33034i	0.299510	+	0.299510i	0.840822	−	0.541312i	$-0.182072\pi$
$599$	7.33034	+	7.33034i	0.299510	+	0.299510i	−0.541312	+	0.840822i	$0.682072\pi$
$600$	6.82380	+	1.80312i	0.278581	+	0.0736119i
$601$	13.1690	−	13.1690i	0.537174	−	0.537174i	−0.385524	−	0.922698i	$-0.625979\pi$
$601$	13.1690	−	13.1690i	0.537174	−	0.537174i	0.922698	+	0.385524i	$0.125979\pi$
$602$	−31.5368	−	2.72241i	−1.28534	−	0.110957i
$603$	−4.44495	+	1.84116i	−0.181012	+	0.0749778i
$604$	4.66709	+	0.811824i	0.189901	+	0.0330326i
$605$	−5.74390	+	13.8670i	−0.233523	+	0.563774i
$606$	6.81390	+	21.5242i	0.276796	+	0.874362i
$607$	26.6851			1.08312			0.541558	−	0.840663i	$-0.317835\pi$
$607$	26.6851			1.08312			0.541558	+	0.840663i	$0.317835\pi$
$608$	−1.84395	+	4.01474i	−0.0747822	+	0.162819i
$609$	16.5808			0.671886
$610$	0.0615737	+	0.194503i	0.00249304	+	0.00787520i
$611$	−19.8492	+	47.9202i	−0.803013	+	1.93864i
$612$	−0.143659	+	0.825883i	−0.00580708	+	0.0333844i
$613$	−32.3066	+	13.3818i	−1.30485	+	0.540487i	−0.923378	−	0.383893i	$-0.874583\pi$
$613$	−32.3066	+	13.3818i	−1.30485	+	0.540487i	−0.381473	+	0.924380i	$0.624583\pi$
$614$	8.29670	+	0.716212i	0.334827	+	0.0289040i
$615$	−2.79610	+	2.79610i	−0.112750	+	0.112750i
$616$	15.1058	−	8.79129i	0.608632	−	0.354211i
$617$	8.69424	+	8.69424i	0.350017	+	0.350017i	0.860116	−	0.510099i	$-0.170391\pi$
$617$	8.69424	+	8.69424i	0.350017	+	0.350017i	−0.510099	+	0.860116i	$0.670391\pi$
$618$	0.232533	+	0.276473i	0.00935384	+	0.0111214i
$619$	4.36939	+	10.5486i	0.175621	+	0.423986i	0.987039	−	0.160480i	$-0.0513041\pi$
$619$	4.36939	+	10.5486i	0.175621	+	0.423986i	−0.811418	+	0.584466i	$0.801304\pi$
$620$	−1.19066	+	1.87852i	−0.0478179	+	0.0754430i
$621$	7.53144	+	3.11962i	0.302226	+	0.125186i
$622$	21.3517	+	11.0837i	0.856127	+	0.444415i
$623$		−	37.9434i		−	1.52017i
$624$	−9.18439	−	19.4608i	−0.367670	−	0.779053i
$625$			6.29614i			0.251846i
$626$	−16.6682	+	32.1099i	−0.666196	+	1.28337i
$627$	0.888371	+	0.367976i	0.0354781	+	0.0146955i
$628$	6.72504	+	30.0065i	0.268358	+	1.19739i
$629$	−0.324036	−	0.782291i	−0.0129201	−	0.0311920i
$630$	−8.59659	+	7.23033i	−0.342496	+	0.288063i
$631$	−25.2614	−	25.2614i	−1.00564	−	1.00564i	−0.999984	−	0.00565528i	$-0.998200\pi$
$631$	−25.2614	−	25.2614i	−1.00564	−	1.00564i	−0.00565528	−	0.999984i	$-0.501800\pi$
$632$	−6.38307	−	4.86285i	−0.253905	−	0.193434i
$633$	3.85355	−	3.85355i	0.153165	−	0.153165i
$634$	2.00246	−	23.1968i	0.0795279	−	0.921262i
$635$	−21.3399	+	8.83928i	−0.846848	+	0.350776i
$636$	−3.11881	+	2.19457i	−0.123669	+	0.0870202i
$637$	37.4473	−	90.4057i	1.48372	−	3.58201i
$638$	−5.48411	+	1.73610i	−0.217118	+	0.0687328i
$639$	6.81097			0.269438
$640$	14.7495	+	10.1510i	0.583026	+	0.401254i
$641$	−5.16034			−0.203821			−0.101911	−	0.994794i	$-0.532496\pi$
$641$	−5.16034			−0.203821			−0.101911	+	0.994794i	$0.532496\pi$
$642$	12.5886	−	3.98515i	0.496831	−	0.157281i
$643$	−11.5208	+	27.8137i	−0.454336	+	1.09686i	0.516321	+	0.856395i	$0.327301\pi$
$643$	−11.5208	+	27.8137i	−0.454336	+	1.09686i	−0.970657	+	0.240469i	$0.922699\pi$
$644$	66.9208	−	47.0892i	2.63705	−	1.85557i
$645$	−6.52068	+	2.70095i	−0.256752	+	0.106350i
$646$	−0.0398150	+	0.461222i	−0.00156650	+	0.0181465i
$647$	−10.2546	+	10.2546i	−0.403152	+	0.403152i	−0.879342	−	0.476190i	$-0.842017\pi$
$647$	−10.2546	+	10.2546i	−0.403152	+	0.403152i	0.476190	+	0.879342i	$0.342017\pi$
$648$	2.24989	+	1.71405i	0.0883842	+	0.0673343i
$649$	−8.52504	−	8.52504i	−0.334637	−	0.334637i
$650$	−14.5295	+	12.2203i	−0.569893	+	0.479320i
$651$	1.34957	+	3.25815i	0.0528938	+	0.127697i
$652$	0.0352774	+	0.157405i	0.00138157	+	0.00616444i
$653$	33.9760	+	14.0733i	1.32958	+	0.550732i	0.930537	−	0.366198i	$-0.119341\pi$
$653$	33.9760	+	14.0733i	1.32958	+	0.550732i	0.399048	+	0.916930i	$0.369341\pi$
$654$	−5.44403	+	10.4874i	−0.212878	+	0.410091i
$655$			4.35044i			0.169986i
$656$	9.03841	−	4.26563i	0.352891	−	0.166545i
$657$		−	6.65017i		−	0.259448i
$658$	−60.7367	−	31.5284i	−2.36776	−	1.22911i
$659$	37.0134	+	15.3315i	1.44184	+	0.597229i	0.960243	−	0.279164i	$-0.0900573\pi$
$659$	37.0134	+	15.3315i	1.44184	+	0.597229i	0.481596	+	0.876393i	$0.340057\pi$
$660$	2.08628	−	3.29155i	0.0812082	−	0.128124i
$661$	−5.34519	−	12.9044i	−0.207904	−	0.501924i	0.785189	−	0.619256i	$-0.212566\pi$
$661$	−5.34519	−	12.9044i	−0.207904	−	0.501924i	−0.993093	+	0.117332i	$0.962566\pi$
$662$	8.51150	+	10.1198i	0.330809	+	0.393319i
$663$	−1.59445	−	1.59445i	−0.0619234	−	0.0619234i
$664$	21.5671	−	12.5516i	0.836964	−	0.487096i
$665$	−4.38641	+	4.38641i	−0.170098	+	0.170098i
$666$	−2.84639	−	0.245715i	−0.110295	−	0.00952125i
$667$	−24.8814	+	10.3062i	−0.963411	+	0.399058i
$668$	1.79723	−	10.3321i	0.0695370	−	0.399761i
$669$	−2.50773	+	6.05420i	−0.0969545	+	0.234069i
$670$	3.24988	+	10.2659i	0.125554	+	0.396608i
$671$	−0.112231			−0.00433264
$672$	26.6224	−	9.86424i	1.02698	−	0.380521i
$673$	22.7067			0.875278			0.437639	−	0.899151i	$-0.355815\pi$
$673$	22.7067			0.875278			0.437639	+	0.899151i	$0.355815\pi$
$674$	3.39561	+	10.7263i	0.130794	+	0.413161i
$675$	0.954942	−	2.30543i	0.0367557	−	0.0887362i
$676$	31.4125	+	5.46409i	1.20817	+	0.210157i
$677$	2.47043	−	1.02328i	0.0949462	−	0.0393280i	−0.334705	−	0.942323i	$-0.608637\pi$
$677$	2.47043	−	1.02328i	0.0949462	−	0.0393280i	0.429651	+	0.902995i	$0.358637\pi$
$678$	18.1480	+	1.56663i	0.696970	+	0.0601660i
$679$	37.4373	−	37.4373i	1.43671	−	1.43671i
$680$	1.81393	+	0.479312i	0.0695612	+	0.0183808i
$681$	13.1871	+	13.1871i	0.505332	+	0.505332i
$682$	−0.787519	−	0.936330i	−0.0301557	−	0.0358539i
$683$	−7.12261	−	17.1955i	−0.272539	−	0.657967i	0.727052	−	0.686583i	$-0.240890\pi$
$683$	−7.12261	−	17.1955i	−0.272539	−	0.657967i	−0.999590	+	0.0286156i	$0.990890\pi$
$684$	1.31930	+	0.836206i	0.0504446	+	0.0319732i
$685$	−21.7776	−	9.02057i	−0.832079	−	0.344658i
$686$	70.4879	+	36.5903i	2.69124	+	1.39702i
$687$		−	21.1241i		−	0.805936i
$688$	17.8181	−	0.860444i	0.679308	−	0.0328041i
$689$		−	10.2580i		−	0.390799i
$690$	8.40599	−	16.1934i	0.320011	−	0.616472i
$691$	27.2224	+	11.2759i	1.03559	+	0.428956i	0.834727	−	0.550664i	$-0.185625\pi$
$691$	27.2224	+	11.2759i	1.03559	+	0.428956i	0.200863	+	0.979619i	$0.435625\pi$
$692$	−30.6169	+	6.86183i	−1.16388	+	0.260848i
$693$	−2.36473	−	5.70896i	−0.0898286	−	0.216865i
$694$	29.0051	−	24.3953i	1.10102	−	0.926034i
$695$	12.6966	+	12.6966i	0.481608	+	0.481608i
$696$	−9.25997	+	1.25175i	−0.350998	+	0.0474476i
$697$	0.740533	−	0.740533i	0.0280497	−	0.0280497i
$698$	−3.10415	+	35.9589i	−0.117494	+	1.36107i
$699$	−16.1007	+	6.66913i	−0.608984	+	0.252250i
$700$	−14.4144	−	20.4850i	−0.544812	−	0.774259i
$701$	10.0320	−	24.2193i	0.378902	−	0.914750i	−0.613271	−	0.789873i	$-0.710146\pi$
$701$	10.0320	−	24.2193i	0.378902	−	0.914750i	0.992172	−	0.124877i	$-0.0398536\pi$
$702$	−7.25339	+	2.29620i	−0.273762	+	0.0866644i
$703$	−1.57775			−0.0595058
$704$	−7.77256	+	6.05013i	−0.292940	+	0.228023i
$705$	−15.2584			−0.574665
$706$	−9.39772	+	2.97503i	−0.353688	+	0.111967i
$707$	30.6619	−	74.0244i	1.15316	−	2.78397i
$708$	−11.2701	−	16.0165i	−0.423557	−	0.601938i
$709$	2.86478	−	1.18663i	0.107589	−	0.0445648i	−0.328240	−	0.944594i	$-0.606455\pi$
$709$	2.86478	−	1.18663i	0.107589	−	0.0445648i	0.435829	+	0.900030i	$0.356455\pi$
$710$	1.31105	−	15.1874i	0.0492028	−	0.569971i
$711$	−2.00610	+	2.00610i	−0.0752346	+	0.0752346i
$712$	2.86451	+	21.1905i	0.107352	+	0.794147i
$713$	−4.05038	−	4.05038i	−0.151688	−	0.151688i
$714$	2.27676	−	1.91491i	0.0852056	−	0.0716638i
$715$	4.01152	+	9.68467i	0.150022	+	0.362186i
$716$	−44.9891	+	10.0829i	−1.68132	+	0.376817i
$717$	9.14466	+	3.78784i	0.341514	+	0.141460i
$718$	−16.4604	+	31.7095i	−0.614296	+	1.18339i
$719$			28.8542i			1.07608i	0.842920	+	0.538040i	$0.180835\pi$
$719$			28.8542i			1.07608i	−0.842920	+	0.538040i	$0.819165\pi$
$720$	4.25514	−	4.68696i	0.158580	−	0.174673i
$721$		−	1.28207i		−	0.0477469i
$722$	−23.0828	−	11.9823i	−0.859051	−	0.445934i
$723$	4.14076	+	1.71516i	0.153997	+	0.0637874i
$724$	−3.72494	−	2.36097i	−0.138436	−	0.0877447i
$725$	3.15481	+	7.61639i	0.117167	+	0.282866i
$726$	−8.63329	−	10.2647i	−0.320411	−	0.380957i
$727$	−27.0018	−	27.0018i	−1.00144	−	1.00144i	−0.999999	−	0.00144152i	$-0.999541\pi$
$727$	−27.0018	−	27.0018i	−1.00144	−	1.00144i	−0.00144152	−	0.999999i	$-0.500459\pi$
$728$	−19.5101	+	73.8350i	−0.723092	+	2.73651i
$729$	0.707107	−	0.707107i	0.0261891	−	0.0261891i
$730$	−14.8288	−	1.28010i	−0.548839	−	0.0473785i
$731$	1.72697	−	0.715333i	0.0638742	−	0.0264575i
$732$	−0.179613	−	0.0312430i	−0.00663868	−	0.00115477i
$733$	5.85715	−	14.1404i	0.216339	−	0.522288i	−0.778034	−	0.628222i	$-0.783783\pi$
$733$	5.85715	−	14.1404i	0.216339	−	0.522288i	0.994373	+	0.105934i	$0.0337831\pi$
$734$	−2.46446	−	7.78491i	−0.0909649	−	0.287346i
$735$	28.7863			1.06180
$736$	−33.8187	+	31.3503i	−1.24657	+	1.15559i
$737$	−5.92360			−0.218198
$738$	−1.06645	−	3.36879i	−0.0392567	−	0.124007i
$739$	9.07639	−	21.9124i	0.333881	−	0.806059i	−0.664396	−	0.747380i	$-0.731311\pi$
$739$	9.07639	−	21.9124i	0.333881	−	0.806059i	0.998277	−	0.0586786i	$-0.0186887\pi$
$740$	−1.09581	+	6.29969i	−0.0402827	+	0.231581i
$741$	−3.88174	+	1.60787i	−0.142599	+	0.0590665i
$742$	13.4837	+	1.16398i	0.495002	+	0.0427310i
$743$	8.23952	−	8.23952i	0.302279	−	0.302279i	−0.539626	−	0.841905i	$-0.681434\pi$
$743$	8.23952	−	8.23952i	0.302279	−	0.302279i	0.841905	+	0.539626i	$0.181434\pi$
$744$	−0.999675	−	1.71772i	−0.0366499	−	0.0629745i
$745$	21.5119	+	21.5119i	0.788136	+	0.788136i
$746$	−16.4938	−	19.6105i	−0.603880	−	0.717991i
$747$	−3.37619	−	8.15085i	−0.123528	−	0.298224i
$748$	−0.552539	+	0.871750i	−0.0202028	+	0.0318743i
$749$	−43.2936	−	17.9328i	−1.58191	−	0.655250i
$750$	−14.8891	−	7.72894i	−0.543674	−	0.282221i
$751$			28.2969i			1.03257i	0.856417	+	0.516285i	$0.172685\pi$
$751$			28.2969i			1.03257i	−0.856417	+	0.516285i	$0.827315\pi$
$752$	36.3002	+	13.0226i	1.32373	+	0.474885i
$753$			5.13441i			0.187108i
$754$	11.5802	−	22.3083i	0.421727	−	0.812420i
$755$	−3.46318	−	1.43450i	−0.126038	−	0.0522067i
$756$	−2.19520	−	9.79481i	−0.0798388	−	0.356234i
$757$	16.0550	+	38.7601i	0.583527	+	1.40876i	0.889595	+	0.456750i	$0.150987\pi$
$757$	16.0550	+	38.7601i	0.583527	+	1.40876i	−0.306068	+	0.952010i	$0.599013\pi$
$758$	20.3763	−	17.1379i	0.740100	−	0.622476i
$759$	7.09710	+	7.09710i	0.257609	+	0.257609i
$760$	2.11856	−	2.78086i	0.0768482	−	0.100872i
$761$	−0.792041	+	0.792041i	−0.0287115	+	0.0287115i	−0.721317	−	0.692605i	$-0.756463\pi$
$761$	−0.792041	+	0.792041i	−0.0287115	+	0.0287115i	0.692605	+	0.721317i	$0.256463\pi$
$762$	1.77519	−	20.5641i	0.0643085	−	0.744958i
$763$	38.7425	−	16.0477i	1.40257	−	0.580965i
$764$	−17.2173	+	12.1151i	−0.622901	+	0.438308i
$765$	0.253847	−	0.612841i	0.00917785	−	0.0221573i
$766$	10.4670	−	3.31352i	0.378187	−	0.119722i
$767$	52.6796			1.90215
$768$	−14.1233	+	7.51879i	−0.509631	+	0.271311i
$769$	17.0970			0.616534			0.308267	−	0.951300i	$-0.400251\pi$
$769$	17.0970			0.616534			0.308267	+	0.951300i	$0.400251\pi$
$770$	−13.1852	+	4.17404i	−0.475163	+	0.150422i
$771$	−8.34600	+	20.1490i	−0.300574	+	0.725649i
$772$	−23.5542	+	16.5740i	−0.847733	+	0.596512i
$773$	−11.0550	+	4.57913i	−0.397621	+	0.164700i	−0.572528	−	0.819885i	$-0.694037\pi$
$773$	−11.0550	+	4.57913i	−0.397621	+	0.164700i	0.174908	+	0.984585i	$0.444037\pi$
$774$	0.542433	−	6.28362i	0.0194974	−	0.225860i
$775$	−1.23985	+	1.23985i	−0.0445368	+	0.0445368i
$776$	−18.0815	+	23.7341i	−0.649089	+	0.852006i
$777$	7.16943	+	7.16943i	0.257202	+	0.257202i
$778$	25.9202	−	21.8007i	0.929284	−	0.781593i
$779$	−0.746764	−	1.80285i	−0.0267556	−	0.0645937i
$780$	3.72394	+	16.6159i	0.133339	+	0.594944i
$781$	7.74743	+	3.20909i	0.277225	+	0.114830i
$782$	−2.22628	+	4.28873i	−0.0796116	+	0.153365i
$783$			3.30367i			0.118064i
$784$	−68.4836	−	24.5683i	−2.44584	−	0.877439i
$785$		−	24.3331i		−	0.868487i
$786$	−3.45038	−	1.79109i	−0.123071	−	0.0638862i
$787$	−48.0613	−	19.9077i	−1.71320	−	0.709631i	−0.999962	−	0.00871015i	$-0.997227\pi$
$787$	−48.0613	−	19.9077i	−1.71320	−	0.709631i	−0.713239	−	0.700921i	$-0.752773\pi$
$788$	17.6843	−	27.9009i	0.629978	−	0.993927i
$789$	−6.85266	−	16.5438i	−0.243961	−	0.588974i
$790$	4.08712	+	4.85943i	0.145413	+	0.172891i
$791$	−45.7109	−	45.7109i	−1.62529	−	1.62529i
$792$	1.75164	+	3.00980i	0.0622418	+	0.106948i
$793$	0.346761	−	0.346761i	0.0123138	−	0.0123138i
$794$	26.2170	+	2.26318i	0.930405	+	0.0803172i
$795$	2.78794	−	1.15480i	0.0988782	−	0.0409567i
$796$	2.14479	−	12.3302i	0.0760200	−	0.437032i
$797$	2.54297	−	6.13928i	0.0900767	−	0.217464i	−0.872420	−	0.488756i	$-0.837451\pi$
$797$	2.54297	−	6.13928i	0.0900767	−	0.217464i	0.962497	+	0.271292i	$0.0874508\pi$
$798$	−1.67301	−	5.28481i	−0.0592238	−	0.187080i
$799$	4.04110			0.142964
$800$	9.59659	+	10.3522i	0.339291	+	0.366005i
$801$	7.56011			0.267123
$802$	5.75615	+	18.1829i	0.203257	+	0.642061i
$803$	3.13333	−	7.56452i	0.110573	−	0.266946i
$804$	−9.48001	−	1.64901i	−0.334334	−	0.0581562i
$805$	−59.8214	+	24.7788i	−2.10843	+	0.873339i
$806$	5.32618	+	0.459782i	0.187607	+	0.0161951i
$807$	8.44613	−	8.44613i	0.297318	−	0.297318i
$808$	−11.5355	+	43.6557i	−0.405819	+	1.53580i
$809$	10.3014	+	10.3014i	0.362178	+	0.362178i	0.864614	−	0.502436i	$-0.167563\pi$
$809$	10.3014	+	10.3014i	0.362178	+	0.362178i	−0.502436	+	0.864614i	$0.667563\pi$
$810$	−1.44062	−	1.71285i	−0.0506183	−	0.0601833i
$811$	20.6691	+	49.8997i	0.725791	+	1.75221i	0.656135	+	0.754644i	$0.272190\pi$
$811$	20.6691	+	49.8997i	0.725791	+	1.75221i	0.0696566	+	0.997571i	$0.477810\pi$
$812$	28.0092	+	17.7530i	0.982931	+	0.623009i
$813$	−22.9020	−	9.48634i	−0.803210	−	0.332700i
$814$	−3.12198	−	1.62062i	−0.109425	−	0.0568027i
$815$		−	0.127644i		−	0.00447117i
$816$	−1.12695	+	1.24132i	−0.0394512	+	0.0434548i
$817$		−	3.48299i		−	0.121854i
$818$	2.21141	−	4.26009i	0.0773203	−	0.148951i
$819$	24.9453	+	10.3327i	0.871659	+	0.361053i
$820$	−7.71714	+	1.72956i	−0.269494	+	0.0603988i
$821$	−19.8645	−	47.9571i	−0.693275	−	1.67371i	−0.738076	−	0.674717i	$-0.764266\pi$
$821$	−19.8645	−	47.9571i	−0.693275	−	1.67371i	0.0448018	−	0.998996i	$-0.485734\pi$
$822$	16.1202	−	13.5582i	0.562258	−	0.472898i
$823$	20.2460	+	20.2460i	0.705732	+	0.705732i	0.965635	−	0.259903i	$-0.0836905\pi$
$823$	20.2460	+	20.2460i	0.705732	+	0.705732i	−0.259903	+	0.965635i	$0.583690\pi$
$824$	0.0967892	+	0.716008i	0.00337181	+	0.0249433i
$825$	2.17248	−	2.17248i	0.0756361	−	0.0756361i
$826$	−5.97758	+	69.2450i	−0.207986	+	2.40934i
$827$	−3.66959	+	1.51999i	−0.127604	+	0.0528554i	−0.445572	−	0.895246i	$-0.647000\pi$
$827$	−3.66959	+	1.51999i	−0.127604	+	0.0528554i	0.317968	+	0.948102i	$0.397000\pi$
$828$	9.38238	+	13.3338i	0.326060	+	0.463381i
$829$	−9.44957	+	22.8133i	−0.328197	+	0.792338i	0.670529	+	0.741883i	$0.266067\pi$
$829$	−9.44957	+	22.8133i	−0.328197	+	0.792338i	−0.998726	+	0.0504548i	$0.983933\pi$
$830$	−18.8250	+	5.95940i	−0.653424	+	0.206854i
$831$	1.28103			0.0444383
$832$	5.32180	−	42.7080i	0.184500	−	1.48063i
$833$	−7.62390			−0.264152
$834$	−15.2970	+	4.84256i	−0.529692	+	0.167684i
$835$	−3.17572	+	7.66687i	−0.109900	+	0.265323i
$836$	1.10670	+	1.57279i	0.0382760	+	0.0543959i
$837$	−0.649177	+	0.268898i	−0.0224388	+	0.00929447i
$838$	−1.09323	+	12.6641i	−0.0377650	+	0.437475i
$839$	−11.4170	+	11.4170i	−0.394157	+	0.394157i	−0.876166	−	0.482009i	$-0.839907\pi$
$839$	−11.4170	+	11.4170i	−0.394157	+	0.394157i	0.482009	+	0.876166i	$0.339907\pi$
$840$	−22.2634	+	3.00954i	−0.768160	+	0.103839i
$841$	12.7886	+	12.7886i	0.440985	+	0.440985i
$842$	31.8430	−	26.7822i	1.09738	−	0.922975i
$843$	−6.10102	−	14.7292i	−0.210130	−	0.507299i
$844$	10.6356	−	2.38365i	0.366094	−	0.0820486i
$845$	−23.3094	−	9.65508i	−0.801869	−	0.332145i
$846$	6.28194	−	12.1016i	0.215978	−	0.416062i
$847$			47.5997i			1.63555i
$848$	−7.61820	+	0.367886i	−0.261610	+	0.0126333i
$849$		−	21.2643i		−	0.729790i
$850$	1.31282	+	0.681482i	0.0450292	+	0.0233747i
$851$	−15.2149	−	6.30222i	−0.521561	−	0.216037i
$852$	11.5055	+	7.29250i	0.394172	+	0.249837i
$853$	−19.3307	−	46.6685i	−0.661871	−	1.59790i	−0.794868	−	0.606782i	$-0.792460\pi$
$853$	−19.3307	−	46.6685i	−0.661871	−	1.59790i	0.132997	−	0.991116i	$-0.457540\pi$
$854$	0.416454	+	0.495148i	0.0142508	+	0.0169436i
$855$	−0.873980	−	0.873980i	−0.0298895	−	0.0298895i
$856$	25.5323	+	6.74663i	0.872676	+	0.230595i
$857$	−24.3711	+	24.3711i	−0.832500	+	0.832500i	−0.987858	−	0.155358i	$-0.950347\pi$
$857$	−24.3711	+	24.3711i	−0.832500	+	0.832500i	0.155358	+	0.987858i	$0.450347\pi$
$858$	−9.33258	−	0.805635i	−0.318609	−	0.0275039i
$859$	17.9730	−	7.44465i	0.613230	−	0.254008i	−0.0543788	−	0.998520i	$-0.517318\pi$
$859$	17.9730	−	7.44465i	0.613230	−	0.254008i	0.667609	+	0.744512i	$0.267318\pi$
$860$	−13.9070	−	2.41908i	−0.474226	−	0.0824899i
$861$	−4.79894	+	11.5857i	−0.163547	+	0.394838i
$862$	−4.82145	−	15.2303i	−0.164219	−	0.518747i
$863$	0.390207			0.0132828			0.00664139	−	0.999978i	$-0.497886\pi$
$863$	0.390207			0.0132828			0.00664139	+	0.999978i	$0.497886\pi$
$864$	1.96542	+	5.30444i	0.0668650	+	0.180461i
$865$	24.8281			0.844180
$866$	−16.5283	−	52.2108i	−0.561656	−	1.77420i
$867$	6.43839	−	15.5436i	0.218659	−	0.527890i
$868$	−1.20873	+	6.94885i	−0.0410268	+	0.235859i
$869$	−3.22713	+	1.33672i	−0.109473	+	0.0453451i
$870$	7.36665	+	0.635926i	0.249753	+	0.0215599i
$871$	18.3021	−	18.3021i	0.620144	−	0.620144i
$872$	−20.4253	+	11.8871i	−0.691687	+	0.402548i
$873$	7.45927	+	7.45927i	0.252458	+	0.252458i
$874$	5.79546	+	6.89058i	0.196034	+	0.233077i
$875$	22.7831	+	55.0032i	0.770208	+	1.85945i
$876$	7.12034	−	11.2339i	0.240574	−	0.379557i
$877$	28.8582	+	11.9535i	0.974472	+	0.403640i	0.812375	−	0.583135i	$-0.198174\pi$
$877$	28.8582	+	11.9535i	0.974472	+	0.403640i	0.162097	+	0.986775i	$0.448174\pi$
$878$	−21.6148	−	11.2203i	−0.729465	−	0.378665i
$879$			14.0674i			0.474482i
$880$	7.04853	−	3.32651i	0.237606	−	0.112137i
$881$		−	48.5009i		−	1.63404i	−0.576611	−	0.817019i	$-0.695625\pi$
$881$		−	48.5009i		−	1.63404i	0.576611	−	0.817019i	$-0.304375\pi$
$882$	−11.8514	+	22.8308i	−0.399059	+	0.768751i
$883$	−37.6860	−	15.6101i	−1.26824	−	0.525320i	−0.355808	−	0.934559i	$-0.615794\pi$
$883$	−37.6860	−	15.6101i	−1.26824	−	0.525320i	−0.912427	+	0.409238i	$0.865794\pi$
$884$	−0.986266	−	4.40063i	−0.0331717	−	0.148009i
$885$	5.93045	+	14.3174i	0.199350	+	0.481274i
$886$	−6.52474	+	5.48776i	−0.219203	+	0.184365i
$887$	25.0095	+	25.0095i	0.839736	+	0.839736i	0.988824	−	0.149088i	$-0.0476337\pi$
$887$	25.0095	+	25.0095i	0.839736	+	0.839736i	−0.149088	+	0.988824i	$0.547634\pi$
$888$	−4.54521	−	3.46271i	−0.152527	−	0.116201i
$889$	−51.7964	+	51.7964i	−1.73719	+	1.73719i
$890$	1.45525	−	16.8578i	0.0487801	−	0.565075i
$891$	1.13749	−	0.471165i	0.0381075	−	0.0157846i
$892$	−10.7184	+	7.54209i	−0.358880	+	0.252528i
$893$	2.88153	−	6.95664i	0.0964268	−	0.232795i
$894$	−25.9179	+	8.20480i	−0.866824	+	0.274410i
$895$	36.4830			1.21949
$896$	55.5339	+	11.8414i	1.85526	+	0.395592i
$897$	−43.8559			−1.46430
$898$	−18.1645	+	5.75032i	−0.606157	+	0.191890i
$899$	0.888350	−	2.14467i	0.0296281	−	0.0715286i
$900$	4.08157	−	2.87202i	0.136052	−	0.0957341i
$901$	−0.738372	+	0.305844i	−0.0245987	+	0.0101891i
$902$	0.374172	−	4.33445i	0.0124586	−	0.144321i
$903$	−15.8270	+	15.8270i	−0.526691	+	0.526691i
$904$	28.9793	+	22.0775i	0.963839	+	0.734288i
$905$	2.46762	+	2.46762i	0.0820264	+	0.0820264i
$906$	2.56352	−	2.15610i	0.0851673	−	0.0716316i
$907$	9.23765	+	22.3017i	0.306731	+	0.740514i	0.999807	+	0.0196496i	$0.00625507\pi$
$907$	9.23765	+	22.3017i	0.306731	+	0.740514i	−0.693076	+	0.720865i	$0.743745\pi$
$908$	8.15703	+	36.3959i	0.270701	+	1.20784i
$909$	14.7491	+	6.10929i	0.489198	+	0.202632i
$910$	27.8419	−	53.6350i	0.922951	−	1.77798i
$911$		−	38.5220i		−	1.27629i	−0.769915	−	0.638146i	$-0.779702\pi$
$911$		−	38.5220i		−	1.27629i	0.769915	−	0.638146i	$-0.220298\pi$
$912$	1.33331	+	2.82514i	0.0441503	+	0.0935498i
$913$		−	10.8623i		−	0.359489i
$914$	−1.43313	−	0.743937i	−0.0474037	−	0.0246072i
$915$	0.133280	+	0.0552065i	0.00440611	+	0.00182507i
$916$	22.6176	−	35.6841i	0.747307	−	1.17904i
$917$	5.27971	+	12.7464i	0.174351	+	0.420922i
$918$	0.381541	+	0.453638i	0.0125927	+	0.0149723i
$919$	−4.31853	−	4.31853i	−0.142455	−	0.142455i	0.632283	−	0.774738i	$-0.282118\pi$
$919$	−4.31853	−	4.31853i	−0.142455	−	0.142455i	−0.774738	+	0.632283i	$0.782118\pi$
$920$	31.5382	−	18.3546i	1.03978	−	0.605132i
$921$	4.16378	−	4.16378i	0.137201	−	0.137201i
$922$	7.35142	+	0.634611i	0.242106	+	0.0208998i
$923$	−33.8524	+	14.0221i	−1.11426	+	0.461544i
$924$	2.11794	−	12.1758i	0.0696751	−	0.400555i
$925$	−1.92916	+	4.65741i	−0.0634304	+	0.153135i
$926$	6.43851	+	20.3384i	0.211583	+	0.668362i
$927$	0.255449			0.00839006
$928$	−16.9827	−	7.80011i	−0.557486	−	0.256051i
$929$	6.77754			0.222364			0.111182	−	0.993800i	$-0.464536\pi$
$929$	6.77754			0.222364			0.111182	+	0.993800i	$0.464536\pi$
$930$	0.474638	+	1.49932i	0.0155640	+	0.0491646i
$931$	−5.43627	+	13.1243i	−0.178167	+	0.430132i
$932$	−34.3389	−	5.97312i	−1.12481	−	0.195656i
$933$	15.7161	−	6.50981i	0.514521	−	0.213122i
$934$	−26.1445	−	2.25692i	−0.855473	−	0.0738487i
$935$	0.577498	−	0.577498i	0.0188862	−	0.0188862i
$936$	−14.7114	−	3.88733i	−0.480857	−	0.127061i
$937$	−39.7932	−	39.7932i	−1.29999	−	1.29999i	−0.928396	−	0.371593i	$-0.878812\pi$
$937$	−39.7932	−	39.7932i	−1.29999	−	1.29999i	−0.371593	−	0.928396i	$-0.621188\pi$
$938$	21.9806	+	26.1341i	0.717692	+	0.853308i
$939$	9.78979	+	23.6346i	0.319478	+	0.771287i
$940$	−25.7754	−	16.3372i	−0.840701	−	0.532860i
$941$	−16.5648	−	6.86138i	−0.539998	−	0.223675i	0.0959776	−	0.995383i	$-0.469402\pi$
$941$	−16.5648	−	6.86138i	−0.539998	−	0.223675i	−0.635976	+	0.771709i	$0.719402\pi$
$942$	19.2989	+	10.0181i	0.628792	+	0.326406i
$943$		−	20.3686i		−	0.663292i
$944$	−1.88927	−	39.1230i	−0.0614904	−	1.27334i
$945$			7.94289i			0.258382i
$946$	3.57764	−	6.89200i	0.116319	−	0.224078i
$947$	1.69908	+	0.703781i	0.0552126	+	0.0228698i	0.410119	−	0.912032i	$-0.365487\pi$
$947$	1.69908	+	0.703781i	0.0552126	+	0.0228698i	−0.354906	+	0.934902i	$0.615487\pi$
$948$	−5.53675	+	1.24089i	−0.179825	+	0.0403023i
$949$	13.6911	+	33.0532i	0.444431	+	1.07295i
$950$	2.10926	−	1.77404i	0.0684335	−	0.0575573i
$951$	−11.6415	−	11.6415i	−0.377502	−	0.377502i
$952$	5.89634	−	0.797061i	0.191101	−	0.0258329i
$953$	14.7617	−	14.7617i	0.478177	−	0.478177i	−0.426371	−	0.904548i	$-0.640208\pi$
$953$	14.7617	−	14.7617i	0.478177	−	0.478177i	0.904548	+	0.426371i	$0.140208\pi$
$954$	−0.231920	+	2.68659i	−0.00750868	+	0.0869815i
$955$	15.3908	−	6.37508i	0.498035	−	0.206293i
$956$	11.3921	+	16.1898i	0.368446	+	0.523617i
$957$	−1.55657	+	3.75790i	−0.0503169	+	0.121476i
$958$	18.1994	−	5.76138i	0.587997	−	0.186142i
$959$	−74.7535			−2.41392
$960$	12.2064	−	3.36152i	0.393959	−	0.108493i
$961$	−30.5063			−0.984073
$962$	14.6532	−	4.63875i	0.472438	−	0.149559i
$963$	3.57306	−	8.62613i	0.115140	−	0.277973i
$964$	5.15840	+	7.33086i	0.166141	+	0.236111i
$965$	21.0554	−	8.72143i	0.677797	−	0.280753i
$966$	4.97634	−	57.6465i	0.160111	−	1.85475i
$967$	−31.0181	+	31.0181i	−0.997474	+	0.997474i	−0.999997	−	0.00252299i	$-0.999197\pi$
$967$	−31.0181	+	31.0181i	−0.997474	+	0.997474i	0.00252299	+	0.999997i	$0.499197\pi$
$968$	−3.59351	−	26.5833i	−0.115500	−	0.854421i
$969$	0.231469	+	0.231469i	0.00743585	+	0.00743585i
$970$	18.0688	−	15.1971i	0.580154	−	0.487950i
$971$	−15.9371	−	38.4755i	−0.511444	−	1.23474i	−0.943043	−	0.332670i	$-0.892050\pi$
$971$	−15.9371	−	38.4755i	−0.511444	−	1.23474i	0.431599	−	0.902066i	$-0.357950\pi$
$972$	1.95159	−	0.437388i	0.0625972	−	0.0140292i
$973$	52.6083	+	21.7911i	1.68654	+	0.698589i
$974$	−17.4403	+	33.5971i	−0.558823	+	1.07652i
$975$			13.4246i			0.429932i
$976$	−0.269961	−	0.245089i	−0.00864124	−	0.00784510i
$977$			55.3040i			1.76933i	0.466225	+	0.884666i	$0.345614\pi$
$977$			55.3040i			1.76933i	−0.466225	+	0.884666i	$0.654386\pi$
$978$	0.101236	+	0.0525515i	0.00323717	+	0.00168041i
$979$	8.59957	+	3.56206i	0.274843	+	0.113844i
$980$	48.6276	+	30.8215i	1.55335	+	0.984557i
$981$	3.19745	+	7.71934i	0.102087	+	0.246459i
$982$	27.4261	+	32.6085i	0.875201	+	1.04058i
$983$	−25.0055	−	25.0055i	−0.797553	−	0.797553i	0.185156	−	0.982709i	$-0.440721\pi$
$983$	−25.0055	−	25.0055i	−0.797553	−	0.797553i	−0.982709	+	0.185156i	$0.940721\pi$
$984$	1.80544	−	6.83261i	0.0575554	−	0.217816i
$985$	−18.4832	+	18.4832i	−0.588923	+	0.588923i
$986$	−1.95102	−	0.168422i	−0.0621330	−	0.00536363i
$987$	−44.7056	+	18.5177i	−1.42299	+	0.589423i
$988$	−8.27881	−	1.44007i	−0.263384	−	0.0458147i
$989$	13.9126	−	33.5881i	0.442396	−	1.06804i
$990$	−0.831665	−	2.62712i	−0.0264321	−	0.0834954i
$991$	59.9489			1.90434			0.952169	−	0.305572i	$-0.0988476\pi$
$991$	59.9489			1.90434			0.952169	+	0.305572i	$0.0988476\pi$
$992$	0.150447	−	3.97202i	0.00477669	−	0.126112i
$993$	9.35032			0.296723
$994$	−14.5902	−	46.0885i	−0.462773	−	1.46184i
$995$	−3.78985	+	9.14952i	−0.120146	+	0.290059i
$996$	3.02385	−	17.3838i	0.0958143	−	0.550827i
$997$	−32.0316	+	13.2679i	−1.01445	+	0.420199i	−0.827076	−	0.562090i	$-0.809998\pi$
$997$	−32.0316	+	13.2679i	−1.01445	+	0.420199i	−0.187374	+	0.982289i	$0.559998\pi$
$998$	−7.28141	−	0.628567i	−0.230489	−	0.0198970i
$999$	−1.42849	+	1.42849i	−0.0451954	+	0.0451954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.2.n.a.13.7	✓	32
3.2	odd	2		288.2.v.d.109.2		32
4.3	odd	2		384.2.n.a.145.1		32
8.3	odd	2		768.2.n.b.289.8		32
8.5	even	2		768.2.n.a.289.4		32
12.11	even	2		1152.2.v.c.145.6		32
32.5	even	8	inner	96.2.n.a.37.7	yes	32
32.11	odd	8		768.2.n.b.481.8		32
32.21	even	8		768.2.n.a.481.4		32
32.27	odd	8		384.2.n.a.241.1		32
96.5	odd	8		288.2.v.d.37.2		32
96.59	even	8		1152.2.v.c.1009.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.13.7	✓	32	1.1	even	1	trivial
96.2.n.a.37.7	yes	32	32.5	even	8	inner
288.2.v.d.37.2		32	96.5	odd	8
288.2.v.d.109.2		32	3.2	odd	2
384.2.n.a.145.1		32	4.3	odd	2
384.2.n.a.241.1		32	32.27	odd	8
768.2.n.a.289.4		32	8.5	even	2
768.2.n.a.481.4		32	32.21	even	8
768.2.n.b.289.8		32	8.3	odd	2
768.2.n.b.481.8		32	32.11	odd	8
1152.2.v.c.145.6		32	12.11	even	2
1152.2.v.c.1009.6		32	96.59	even	8

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)

\(f(q)\)	\(=\)	\(q+(1.34827 - 0.426820i) q^{2} +(0.382683 - 0.923880i) q^{3} +(1.63565 - 1.15093i) q^{4} +(-1.46213 + 0.605634i) q^{5} +(0.121630 - 1.40897i) q^{6} +(-3.54889 + 3.54889i) q^{7} +(1.71405 - 2.24989i) q^{8} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})\)	\(q+(1.34827 - 0.426820i) q^{2} +(0.382683 - 0.923880i) q^{3} +(1.63565 - 1.15093i) q^{4} +(-1.46213 + 0.605634i) q^{5} +(0.121630 - 1.40897i) q^{6} +(-3.54889 + 3.54889i) q^{7} +(1.71405 - 2.24989i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(-1.71285 + 1.44062i) q^{10} +(-0.471165 - 1.13749i) q^{11} +(-0.437388 - 1.95159i) q^{12} +(4.97028 + 2.05876i) q^{13} +(-3.27012 + 6.29959i) q^{14} +1.58260i q^{15} +(1.35070 - 3.76505i) q^{16} -0.419142i q^{17} +(-1.25518 - 0.651562i) q^{18} +(-0.721541 - 0.298872i) q^{19} +(-1.69449 + 2.67342i) q^{20} +(1.92065 + 4.63685i) q^{21} +(-1.12076 - 1.33254i) q^{22} +(-5.76431 - 5.76431i) q^{23} +(-1.42269 - 2.44458i) q^{24} +(-1.76450 + 1.76450i) q^{25} +(7.57998 + 0.654342i) q^{26} +(-0.923880 + 0.382683i) q^{27} +(-1.72020 + 9.88929i) q^{28} +(1.26426 - 3.05219i) q^{29} +(0.675484 + 2.13377i) q^{30} +0.702664 q^{31} +(0.214109 - 5.65280i) q^{32} -1.23121 q^{33} +(-0.178898 - 0.565116i) q^{34} +(3.03961 - 7.33827i) q^{35} +(-1.97041 - 0.342746i) q^{36} +(1.86641 - 0.773092i) q^{37} +(-1.10039 - 0.0949916i) q^{38} +(3.80408 - 3.80408i) q^{39} +(-1.14355 + 4.32773i) q^{40} +(1.76678 + 1.76678i) q^{41} +(4.56865 + 5.43195i) q^{42} +(1.70666 + 4.12024i) q^{43} +(-2.07984 - 1.31826i) q^{44} +(1.46213 + 0.605634i) q^{45} +(-10.2322 - 5.31151i) q^{46} +9.64136i q^{47} +(-2.96156 - 2.68871i) q^{48} -18.1893i q^{49} +(-1.62590 + 3.13215i) q^{50} +(-0.387237 - 0.160399i) q^{51} +(10.4991 - 2.35306i) q^{52} +(-0.729689 - 1.76163i) q^{53} +(-1.08230 + 0.910290i) q^{54} +(1.37781 + 1.37781i) q^{55} +(1.90165 + 14.0676i) q^{56} +(-0.552244 + 0.552244i) q^{57} +(0.401824 - 4.65478i) q^{58} +(9.04676 - 3.74729i) q^{59} +(1.82147 + 2.58858i) q^{60} +(0.0348835 - 0.0842161i) q^{61} +(0.947379 - 0.299911i) q^{62} +5.01889 q^{63} +(-2.12405 - 7.71287i) q^{64} -8.51404 q^{65} +(-1.66001 + 0.525506i) q^{66} +(1.84116 - 4.44495i) q^{67} +(-0.482405 - 0.685570i) q^{68} +(-7.53144 + 3.11962i) q^{69} +(0.966091 - 11.1913i) q^{70} +(-4.81608 + 4.81608i) q^{71} +(-2.80293 + 0.378898i) q^{72} +(4.70238 + 4.70238i) q^{73} +(2.18645 - 1.83896i) q^{74} +(0.954942 + 2.30543i) q^{75} +(-1.52417 + 0.341596i) q^{76} +(5.70896 + 2.36473i) q^{77} +(3.50526 - 6.75258i) q^{78} -2.83705i q^{79} +(0.305342 + 6.32302i) q^{80} +1.00000i q^{81} +(3.13619 + 1.62800i) q^{82} +(8.15085 + 3.37619i) q^{83} +(8.47822 + 5.37373i) q^{84} +(0.253847 + 0.612841i) q^{85} +(4.05963 + 4.82675i) q^{86} +(-2.33605 - 2.33605i) q^{87} +(-3.36684 - 0.889651i) q^{88} +(-5.34580 + 5.34580i) q^{89} +(2.22984 + 0.192491i) q^{90} +(-24.9453 + 10.3327i) q^{91} +(-16.0627 - 2.79405i) q^{92} +(0.268898 - 0.649177i) q^{93} +(4.11512 + 12.9991i) q^{94} +1.23599 q^{95} +(-5.14057 - 2.36104i) q^{96} -10.5490 q^{97} +(-7.76354 - 24.5240i) q^{98} +(-0.471165 + 1.13749i) 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

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