LMFDB - Embedded newform 460.2.w.a.167.57

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(3,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 33, 32]))

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

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

chi := DirichletCharacter("460.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.w (of order $44$, degree $20$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$1360$
Relative dimension:	$68$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			167.57
Character	$\chi$	$=$	460.167
Dual form			460.2.w.a.303.57

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.21312 - 0.726869i) q^{2} +(-0.943178 - 1.72730i) q^{3} +(0.943324 - 1.76356i) q^{4} +(1.91259 + 1.15844i) q^{5} +(-2.39971 - 1.40986i) q^{6} +(0.493361 + 0.659053i) q^{7} +(-0.137510 - 2.82508i) q^{8} +(-0.472063 + 0.734544i) q^{9} +O(q^{10})$	\(q+(1.21312 - 0.726869i) q^{2} +(-0.943178 - 1.72730i) q^{3} +(0.943324 - 1.76356i) q^{4} +(1.91259 + 1.15844i) q^{5} +(-2.39971 - 1.40986i) q^{6} +(0.493361 + 0.659053i) q^{7} +(-0.137510 - 2.82508i) q^{8} +(-0.472063 + 0.734544i) q^{9} +(3.16224 + 0.0151211i) q^{10} +(3.04439 - 1.39033i) q^{11} +(-3.93592 + 0.0339455i) q^{12} +(-2.69421 - 2.01686i) q^{13} +(1.07755 + 0.440902i) q^{14} +(0.197056 - 4.39624i) q^{15} +(-2.22028 - 3.32721i) q^{16} +(-3.61615 + 0.258632i) q^{17} +(-0.0387521 + 1.23422i) q^{18} +(3.53807 + 4.08315i) q^{19} +(3.84717 - 2.28019i) q^{20} +(0.673056 - 1.47379i) q^{21} +(2.68263 - 3.89950i) q^{22} +(0.904421 + 4.70978i) q^{23} +(-4.75007 + 2.90208i) q^{24} +(2.31604 + 4.43125i) q^{25} +(-4.73439 - 0.488357i) q^{26} +(-4.17504 - 0.298605i) q^{27} +(1.62768 - 0.248371i) q^{28} +(-3.45744 - 2.99589i) q^{29} +(-2.95644 - 5.47641i) q^{30} +(-2.59799 - 8.84794i) q^{31} +(-5.11192 - 2.42246i) q^{32} +(-5.27291 - 3.94725i) q^{33} +(-4.19884 + 2.94222i) q^{34} +(0.180127 + 1.83203i) q^{35} +(0.850104 + 1.52542i) q^{36} +(2.48380 + 11.4178i) q^{37} +(7.26002 + 2.38164i) q^{38} +(-0.942605 + 6.55596i) q^{39} +(3.00968 - 5.56254i) q^{40} +(-0.639835 + 0.411197i) q^{41} +(-0.254751 - 2.27710i) q^{42} +(0.839189 + 1.53686i) q^{43} +(0.419923 - 6.68048i) q^{44} +(-1.75379 + 0.858029i) q^{45} +(4.52056 + 5.05614i) q^{46} +(-1.30816 + 1.30816i) q^{47} +(-3.65298 + 6.97325i) q^{48} +(1.78118 - 6.06615i) q^{49} +(6.03057 + 3.69218i) q^{50} +(3.85741 + 6.00225i) q^{51} +(-6.09835 + 2.84884i) q^{52} +(5.80794 + 7.75850i) q^{53} +(-5.28187 + 2.67246i) q^{54} +(7.43329 + 0.867609i) q^{55} +(1.79404 - 1.48441i) q^{56} +(3.71580 - 9.96245i) q^{57} +(-6.37191 - 1.12127i) q^{58} +(0.335959 + 2.33665i) q^{59} +(-7.56714 - 4.49460i) q^{60} +(1.95789 - 0.574887i) q^{61} +(-9.58296 - 8.84522i) q^{62} +(-0.717000 + 0.0512809i) q^{63} +(-7.96218 + 0.776956i) q^{64} +(-2.81652 - 6.97850i) q^{65} +(-9.26581 - 0.955779i) q^{66} +(-0.892055 - 2.39169i) q^{67} +(-2.95509 + 6.62127i) q^{68} +(7.28218 - 6.00437i) q^{69} +(1.55016 + 2.09154i) q^{70} +(15.0695 + 6.88200i) q^{71} +(2.14006 + 1.23261i) q^{72} +(5.33287 + 0.381414i) q^{73} +(11.3124 + 12.0458i) q^{74} +(5.46967 - 8.17995i) q^{75} +(10.5384 - 2.38786i) q^{76} +(2.41828 + 1.32048i) q^{77} +(3.62183 + 8.63832i) q^{78} +(1.49220 + 10.3784i) q^{79} +(-0.392122 - 8.93567i) q^{80} +(4.51019 + 9.87593i) q^{81} +(-0.477311 + 0.963908i) q^{82} +(-1.57878 - 7.25753i) q^{83} +(-1.96420 - 2.57723i) q^{84} +(-7.21584 - 3.69443i) q^{85} +(2.13513 + 1.25442i) q^{86} +(-1.91382 + 8.79770i) q^{87} +(-4.34642 - 8.40946i) q^{88} +(-0.405618 + 1.38141i) q^{89} +(-1.50388 + 2.31567i) q^{90} -2.77066i q^{91} +(9.15914 + 2.84785i) q^{92} +(-12.8327 + 12.8327i) q^{93} +(-0.636097 + 2.53782i) q^{94} +(2.03681 + 11.9081i) q^{95} +(0.637128 + 11.1146i) q^{96} +(-4.17169 - 0.907496i) q^{97} +(-2.24851 - 8.65366i) q^{98} +(-0.415887 + 2.89256i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{11}\right)$

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 $

$2$	1.21312	−	0.726869i	0.857806	−	0.513974i
$2$	1.21312	−	0.726869i	0.857806	−	0.513974i
$3$	−0.943178	−	1.72730i	−0.544544	−	0.997258i	−0.994553	−	0.104234i	$-0.966761\pi$
$3$	−0.943178	−	1.72730i	−0.544544	−	0.997258i	0.450009	−	0.893024i	$-0.351421\pi$
$4$	0.943324	−	1.76356i	0.471662	−	0.881779i
$5$	1.91259	+	1.15844i	0.855338	+	0.518070i
$5$	1.91259	+	1.15844i	0.855338	+	0.518070i
$6$	−2.39971	−	1.40986i	−0.979677	−	0.575572i
$7$	0.493361	+	0.659053i	0.186473	+	0.249098i	0.884030	−	0.467431i	$-0.154820\pi$
$7$	0.493361	+	0.659053i	0.186473	+	0.249098i	−0.697557	+	0.716530i	$0.745729\pi$
$8$	−0.137510	−	2.82508i	−0.0486172	−	0.998817i
$9$	−0.472063	+	0.734544i	−0.157354	+	0.244848i
$10$	3.16224	+	0.0151211i	0.999989	+	0.00478171i
$11$	3.04439	−	1.39033i	0.917917	−	0.419199i	0.100298	−	0.994957i	$-0.468020\pi$
$11$	3.04439	−	1.39033i	0.917917	−	0.419199i	0.817620	+	0.575759i	$0.195293\pi$
$12$	−3.93592	+	0.0339455i	−1.13620	+	0.00979921i
$13$	−2.69421	−	2.01686i	−0.747238	−	0.559376i	0.156389	−	0.987696i	$-0.450015\pi$
$13$	−2.69421	−	2.01686i	−0.747238	−	0.559376i	−0.903627	+	0.428320i	$0.859106\pi$
$14$	1.07755	+	0.440902i	0.287988	+	0.117836i
$15$	0.197056	−	4.39624i	0.0508797	−	1.13510i
$16$	−2.22028	−	3.32721i	−0.555070	−	0.831804i
$17$	−3.61615	+	0.258632i	−0.877045	+	0.0627275i	−0.502598	−	0.864521i	$-0.667622\pi$
$17$	−3.61615	+	0.258632i	−0.877045	+	0.0627275i	−0.374448	+	0.927248i	$0.622168\pi$
$18$	−0.0387521	+	1.23422i	−0.00913395	+	0.290908i
$19$	3.53807	+	4.08315i	0.811689	+	0.936739i	0.998961	−	0.0455689i	$-0.0145101\pi$
$19$	3.53807	+	4.08315i	0.811689	+	0.936739i	−0.187272	+	0.982308i	$0.559965\pi$
$20$	3.84717	−	2.28019i	0.860254	−	0.509866i
$21$	0.673056	−	1.47379i	0.146873	−	0.321607i
$22$	2.68263	−	3.89950i	0.571938	−	0.831377i
$23$	0.904421	+	4.70978i	0.188585	+	0.982057i
$23$	0.904421	+	4.70978i	0.188585	+	0.982057i
$24$	−4.75007	+	2.90208i	−0.969604	+	0.592384i
$25$	2.31604	+	4.43125i	0.463208	+	0.886250i
$26$	−4.73439	−	0.488357i	−0.928490	−	0.0957748i
$27$	−4.17504	−	0.298605i	−0.803486	−	0.0574665i
$28$	1.62768	−	0.248371i	0.307602	−	0.0469376i
$29$	−3.45744	−	2.99589i	−0.642031	−	0.556323i	0.271833	−	0.962344i	$-0.412370\pi$
$29$	−3.45744	−	2.99589i	−0.642031	−	0.556323i	−0.913863	+	0.406022i	$0.866916\pi$
$30$	−2.95644	−	5.47641i	−0.539769	−	0.999850i
$31$	−2.59799	−	8.84794i	−0.466612	−	1.58914i	−0.771162	−	0.636640i	$-0.780324\pi$
$31$	−2.59799	−	8.84794i	−0.466612	−	1.58914i	0.304549	−	0.952497i	$-0.401494\pi$
$32$	−5.11192	−	2.42246i	−0.903668	−	0.428234i
$33$	−5.27291	−	3.94725i	−0.917896	−	0.687128i
$34$	−4.19884	+	2.94222i	−0.720094	+	0.504586i
$35$	0.180127	+	1.83203i	0.0304470	+	0.309669i
$36$	0.850104	+	1.52542i	0.141684	+	0.254237i
$37$	2.48380	+	11.4178i	0.408333	+	1.87708i	0.476122	+	0.879379i	$0.342042\pi$
$37$	2.48380	+	11.4178i	0.408333	+	1.87708i	−0.0677888	+	0.997700i	$0.521594\pi$
$38$	7.26002	+	2.38164i	1.17773	+	0.386353i
$39$	−0.942605	+	6.55596i	−0.150938	+	1.04979i
$40$	3.00968	−	5.56254i	0.475873	−	0.879514i
$41$	−0.639835	+	0.411197i	−0.0999255	+	0.0642182i	−0.589649	−	0.807659i	$-0.700734\pi$
$41$	−0.639835	+	0.411197i	−0.0999255	+	0.0642182i	0.489724	+	0.871878i	$0.337098\pi$
$42$	−0.254751	−	2.27710i	−0.0393090	−	0.351365i
$43$	0.839189	+	1.53686i	0.127975	+	0.234369i	0.933808	−	0.357774i	$-0.116464\pi$
$43$	0.839189	+	1.53686i	0.127975	+	0.234369i	−0.805833	+	0.592143i	$0.798282\pi$
$44$	0.419923	−	6.68048i	0.0633057	−	1.00712i
$45$	−1.75379	+	0.858029i	−0.261440	+	0.127907i
$46$	4.52056	+	5.05614i	0.666521	+	0.745487i
$47$	−1.30816	+	1.30816i	−0.190815	+	0.190815i	−0.796048	−	0.605233i	$-0.793080\pi$
$47$	−1.30816	+	1.30816i	−0.190815	+	0.190815i	0.605233	+	0.796048i	$0.293080\pi$
$48$	−3.65298	+	6.97325i	−0.527263	+	1.00650i
$49$	1.78118	−	6.06615i	0.254455	−	0.866593i
$50$	6.03057	+	3.69218i	0.852851	+	0.522154i
$51$	3.85741	+	6.00225i	0.540145	+	0.840482i
$52$	−6.09835	+	2.84884i	−0.845690	+	0.395063i
$53$	5.80794	+	7.75850i	0.797782	+	1.06571i	0.996328	+	0.0856209i	$0.0272874\pi$
$53$	5.80794	+	7.75850i	0.797782	+	1.06571i	−0.198545	+	0.980092i	$0.563622\pi$
$54$	−5.28187	+	2.67246i	−0.718772	+	0.363676i
$55$	7.43329	+	0.867609i	1.00230	+	0.116988i
$56$	1.79404	−	1.48441i	0.239738	−	0.198363i
$57$	3.71580	−	9.96245i	0.492170	−	1.31956i
$58$	−6.37191	−	1.12127i	−0.836673	−	0.147230i
$59$	0.335959	+	2.33665i	0.0437381	+	0.304205i	0.999934	+	0.0114782i	$0.00365370\pi$
$59$	0.335959	+	2.33665i	0.0437381	+	0.304205i	−0.956196	+	0.292727i	$0.905437\pi$
$60$	−7.56714	−	4.49460i	−0.976914	−	0.580250i
$61$	1.95789	−	0.574887i	0.250682	−	0.0736068i	−0.153978	−	0.988074i	$-0.549208\pi$
$61$	1.95789	−	0.574887i	0.250682	−	0.0736068i	0.404659	+	0.914468i	$0.367390\pi$
$62$	−9.58296	−	8.84522i	−1.21704	−	1.12334i
$63$	−0.717000	+	0.0512809i	−0.0903336	+	0.00646078i
$64$	−7.96218	+	0.776956i	−0.995273	+	0.0971195i
$65$	−2.81652	−	6.97850i	−0.349346	−	0.865577i
$66$	−9.26581	−	0.955779i	−1.14054	−	0.117648i
$67$	−0.892055	−	2.39169i	−0.108982	−	0.292192i	0.870999	−	0.491286i	$-0.163473\pi$
$67$	−0.892055	−	2.39169i	−0.108982	−	0.292192i	−0.979980	+	0.199094i	$0.936200\pi$
$68$	−2.95509	+	6.62127i	−0.358357	+	0.802947i
$69$	7.28218	−	6.00437i	0.876671	−	0.722841i
$70$	1.55016	+	2.09154i	0.185280	+	0.249987i
$71$	15.0695	+	6.88200i	1.78842	+	0.816744i	0.970381	+	0.241579i	$0.0776654\pi$
$71$	15.0695	+	6.88200i	1.78842	+	0.816744i	0.818038	+	0.575164i	$0.195062\pi$
$72$	2.14006	+	1.23261i	0.252209	+	0.145264i
$73$	5.33287	+	0.381414i	0.624165	+	0.0446412i	0.379840	−	0.925052i	$-0.375979\pi$
$73$	5.33287	+	0.381414i	0.624165	+	0.0446412i	0.244325	+	0.969693i	$0.421434\pi$
$74$	11.3124	+	12.0458i	1.31504	+	1.40030i
$75$	5.46967	−	8.17995i	0.631583	−	0.944539i
$76$	10.5384	−	2.38786i	1.20884	−	0.273907i
$77$	2.41828	+	1.32048i	0.275588	+	0.150483i
$78$	3.62183	+	8.63832i	0.410091	+	0.978097i
$79$	1.49220	+	10.3784i	0.167885	+	1.16767i	0.883246	+	0.468911i	$0.155353\pi$
$79$	1.49220	+	10.3784i	0.167885	+	1.16767i	−0.715360	+	0.698756i	$0.753738\pi$
$80$	−0.392122	−	8.93567i	−0.0438406	−	0.999039i
$81$	4.51019	+	9.87593i	0.501132	+	1.09733i
$82$	−0.477311	+	0.963908i	−0.0527102	+	0.106446i
$83$	−1.57878	−	7.25753i	−0.173294	−	0.796618i	−0.978928	−	0.204205i	$-0.934539\pi$
$83$	−1.57878	−	7.25753i	−0.173294	−	0.796618i	0.805635	−	0.592413i	$-0.201825\pi$
$84$	−1.96420	−	2.57723i	−0.214312	−	0.281199i
$85$	−7.21584	−	3.69443i	−0.782668	−	0.400717i
$86$	2.13513	+	1.25442i	0.230237	+	0.135267i
$87$	−1.91382	+	8.79770i	−0.205183	+	0.943212i
$88$	−4.34642	−	8.40946i	−0.463330	−	0.896452i
$89$	−0.405618	+	1.38141i	−0.0429955	+	0.146429i	−0.978193	−	0.207697i	$-0.933403\pi$
$89$	−0.405618	+	1.38141i	−0.0429955	+	0.146429i	0.935198	+	0.354126i	$0.115222\pi$
$90$	−1.50388	+	2.31567i	−0.158523	+	0.244093i
$91$		−	2.77066i		−	0.290444i
$92$	9.15914	+	2.84785i	0.954906	+	0.296909i
$93$	−12.8327	+	12.8327i	−1.33069	+	1.33069i
$94$	−0.636097	+	2.53782i	−0.0656084	+	0.261757i
$95$	2.03681	+	11.9081i	0.208973	+	1.22174i
$96$	0.637128	+	11.1146i	0.0650266	+	1.13438i
$97$	−4.17169	−	0.907496i	−0.423571	−	0.0921422i	−0.00427291	−	0.999991i	$-0.501360\pi$
$97$	−4.17169	−	0.907496i	−0.423571	−	0.0921422i	−0.419298	+	0.907849i	$0.637724\pi$
$98$	−2.24851	−	8.65366i	−0.227133	−	0.874151i
$99$	−0.415887	+	2.89256i	−0.0417982	+	0.290713i
$100$	9.99954	+	0.0956332i	0.999954	+	0.00956332i
$101$	8.27442	+	5.31764i	0.823335	+	0.529125i	0.883154	−	0.469084i	$-0.155416\pi$
$101$	8.27442	+	5.31764i	0.823335	+	0.529125i	−0.0598185	+	0.998209i	$0.519052\pi$
$102$	9.04235	+	4.47762i	0.895326	+	0.443350i
$103$	1.38174	−	3.70459i	0.136147	−	0.365024i	−0.850928	−	0.525282i	$-0.823960\pi$
$103$	1.38174	−	3.70459i	0.136147	−	0.365024i	0.987075	+	0.160258i	$0.0512326\pi$
$104$	−5.32731	+	7.88869i	−0.522385	+	0.773550i
$105$	2.99457	−	2.03906i	0.292241	−	0.198992i
$106$	12.6852	+	5.19039i	1.23209	+	0.504135i
$107$	−2.58069	+	4.72619i	−0.249485	+	0.456898i	−0.972169	−	0.234281i	$-0.924726\pi$
$107$	−2.58069	+	4.72619i	−0.249485	+	0.456898i	0.722684	+	0.691179i	$0.242908\pi$
$108$	−4.46502	+	7.08124i	−0.429647	+	0.681393i
$109$	−3.47396	−	3.01021i	−0.332745	−	0.288325i	0.472423	−	0.881372i	$-0.343380\pi$
$109$	−3.47396	−	3.01021i	−0.332745	−	0.288325i	−0.805168	+	0.593047i	$0.797925\pi$
$110$	9.64811	−	4.35051i	0.919911	−	0.414805i
$111$	17.3794	−	15.0593i	1.64958	−	1.42937i
$112$	1.09741	−	3.10480i	0.103696	−	0.293376i
$113$	−3.79276	−	10.1688i	−0.356793	−	0.956598i	−0.984067	−	0.177799i	$-0.943102\pi$
$113$	−3.79276	−	10.1688i	−0.356793	−	0.956598i	0.627274	−	0.778799i	$-0.284171\pi$
$114$	−2.73368	−	14.7866i	−0.256032	−	1.38489i
$115$	−3.72620	+	10.0556i	−0.347470	+	0.937691i
$116$	−8.54491	+	3.27131i	−0.793375	+	0.303733i
$117$	2.75331	−	1.02693i	0.254543	−	0.0949397i
$118$	2.10599	+	2.59044i	0.193872	+	0.238469i
$119$	−1.95452	−	2.25563i	−0.179170	−	0.206774i
$120$	−12.4468	+	0.0478283i	−1.13624	+	0.00436611i
$121$	0.131824	−	0.152133i	0.0119840	−	0.0138303i
$122$	1.95728	−	2.12053i	0.177204	−	0.191984i
$123$	1.31374	+	0.717356i	0.118456	+	0.0646818i
$124$	−18.0546	−	3.76476i	−1.62135	−	0.338086i
$125$	−0.703690	+	11.1582i	−0.0629400	+	0.998017i
$126$	−0.832534	+	0.583375i	−0.0741680	+	0.0519712i
$127$	−8.71323	−	3.24987i	−0.773174	−	0.288379i	−0.0682560	−	0.997668i	$-0.521743\pi$
$127$	−8.71323	−	3.24987i	−0.773174	−	0.288379i	−0.704918	+	0.709289i	$0.749016\pi$
$128$	−9.09434	+	6.73000i	−0.803834	+	0.594854i
$129$	1.86312	−	2.89907i	0.164038	−	0.255248i
$130$	−8.48923	−	6.41853i	−0.744555	−	0.562942i
$131$	−1.51601	−	0.217969i	−0.132454	−	0.0190440i	0.0757689	−	0.997125i	$-0.475859\pi$
$131$	−1.51601	−	0.217969i	−0.132454	−	0.0190440i	−0.208223	+	0.978081i	$0.566768\pi$
$132$	−11.9353	+	5.57555i	−1.03883	+	0.485290i
$133$	−0.945467	+	4.34624i	−0.0819824	+	0.376867i
$134$	−2.82062	−	2.25300i	−0.243664	−	0.194630i
$135$	−7.63924	−	5.40764i	−0.657481	−	0.465415i
$136$	1.22792	+	10.1804i	0.105293	+	0.872959i
$137$	−4.01581	−	4.01581i	−0.343094	−	0.343094i	0.514435	−	0.857529i	$-0.328002\pi$
$137$	−4.01581	−	4.01581i	−0.343094	−	0.343094i	−0.857529	+	0.514435i	$0.828002\pi$
$138$	4.46978	−	12.5772i	0.380493	−	1.07064i
$139$	−10.6976			−0.907362			−0.453681	−	0.891164i	$-0.649889\pi$
$139$	−10.6976			−0.907362			−0.453681	+	0.891164i	$0.649889\pi$
$140$	3.40081	+	1.41053i	0.287421	+	0.119212i
$141$	3.49342	+	1.02576i	0.294199	+	0.0863847i
$142$	23.2834	−	2.60484i	1.95390	−	0.218593i
$143$	−11.0063	−	2.39427i	−0.920393	−	0.200219i
$144$	3.49210	−	0.0602399i	0.291008	−	0.00501999i
$145$	−3.14213	−	9.73516i	−0.260939	−	0.808461i
$146$	6.74665	−	3.41359i	0.558357	−	0.282511i
$147$	−12.1580	+	2.64482i	−1.00278	+	0.218141i
$148$	22.4790	+	6.39038i	1.84776	+	0.525286i
$149$	−14.2519	+	6.50862i	−1.16756	+	0.533207i	−0.902358	−	0.430987i	$-0.858166\pi$
$149$	−14.2519	+	6.50862i	−1.16756	+	0.533207i	−0.265201	+	0.964193i	$0.585438\pi$
$150$	0.689615	−	13.8990i	0.0563069	−	1.13485i
$151$	−2.07246	+	0.297975i	−0.168654	+	0.0242488i	−0.226125	−	0.974098i	$-0.572606\pi$
$151$	−2.07246	+	0.297975i	−0.168654	+	0.0242488i	0.0574703	+	0.998347i	$0.481697\pi$
$152$	11.0487	−	10.5568i	0.896169	−	0.856271i
$153$	1.51707	−	2.77831i	0.122648	−	0.224613i
$154$	3.89348	−	0.155869i	0.313745	−	0.0125603i
$155$	5.28090	−	19.9321i	0.424172	−	1.60099i
$156$	10.6726	+	7.84673i	0.854495	+	0.628241i
$157$	−0.998043	+	13.9545i	−0.0796525	+	1.11369i	0.787722	+	0.616031i	$0.211261\pi$
$157$	−0.998043	+	13.9545i	−0.0796525	+	1.11369i	−0.867374	+	0.497657i	$0.834194\pi$
$158$	9.35398	+	11.5057i	0.744163	+	0.915343i
$159$	7.92335	−	17.3497i	0.628363	−	1.37592i
$160$	−6.97075	−	10.5550i	−0.551086	−	0.834448i
$161$	−2.65779	+	2.91968i	−0.209463	+	0.230103i
$162$	12.6499	+	8.70239i	0.993871	+	0.683724i
$163$	−14.2877	+	5.32904i	−1.11910	+	0.417402i	−0.839851	−	0.542817i	$-0.817358\pi$
$163$	−14.2877	+	5.32904i	−1.11910	+	0.417402i	−0.279248	+	0.960219i	$0.590085\pi$
$164$	0.121599	+	1.51628i	0.00949526	+	0.118402i
$165$	−5.51229	−	13.6578i	−0.429131	−	1.06326i
$166$	−7.19053	−	7.65670i	−0.558093	−	0.594275i
$167$	−1.47206	−	20.5820i	−0.113911	−	1.59269i	−0.657579	−	0.753385i	$-0.728419\pi$
$167$	−1.47206	−	20.5820i	−0.113911	−	1.59269i	0.543668	−	0.839300i	$-0.317035\pi$
$168$	−4.25612	−	1.69878i	−0.328367	−	0.131063i
$169$	−0.471492	−	1.60575i	−0.0362686	−	0.123519i
$170$	−11.4391	+	0.763177i	−0.877335	+	0.0585330i
$171$	−4.66945	+	0.671365i	−0.357082	+	0.0513406i
$172$	3.50197	−	0.0302029i	0.267023	−	0.00230295i
$173$	5.26907	+	1.96526i	0.400600	+	0.149416i	0.541685	−	0.840581i	$-0.317787\pi$
$173$	5.26907	+	1.96526i	0.400600	+	0.149416i	−0.141085	+	0.989997i	$0.545059\pi$
$174$	4.07307	+	12.0638i	0.308779	+	0.914552i
$175$	−1.77778	+	3.71259i	−0.134388	+	0.280646i
$176$	−11.3853	−	7.04242i	−0.858200	−	0.530842i
$177$	3.71922	−	2.78418i	0.279554	−	0.209271i
$178$	0.512039	+	1.97065i	0.0383790	+	0.147706i
$179$	18.3161	−	11.7710i	1.36901	−	0.879809i	0.370218	−	0.928945i	$-0.379283\pi$
$179$	18.3161	−	11.7710i	1.36901	−	0.879809i	0.998792	+	0.0491357i	$0.0156467\pi$
$180$	−0.141206	+	3.90231i	−0.0105249	+	0.290861i
$181$	−18.3860	−	5.39861i	−1.36662	−	0.401276i	−0.485528	−	0.874221i	$-0.661373\pi$
$181$	−18.3860	−	5.39861i	−1.36662	−	0.401276i	−0.881092	+	0.472946i	$0.843191\pi$
$182$	−2.01391	−	3.36115i	−0.149281	−	0.249145i
$183$	−2.83964	−	2.83964i	−0.209912	−	0.209912i
$184$	13.1811	−	3.20271i	0.971727	−	0.236107i
$185$	−8.47636	+	24.7150i	−0.623194	+	1.81708i
$186$	−6.23992	+	24.8953i	−0.457533	+	1.82541i
$187$	−10.6494	+	5.81500i	−0.778760	+	0.425235i
$188$	1.07300	+	3.54105i	0.0782567	+	0.258257i
$189$	−1.86300	−	2.89889i	−0.135514	−	0.210863i
$190$	11.1265	+	12.9654i	0.807201	+	0.940610i
$191$	8.66023	+	1.24515i	0.626632	+	0.0900961i	0.448313	−	0.893877i	$-0.352025\pi$
$191$	8.66023	+	1.24515i	0.626632	+	0.0900961i	0.178319	+	0.983973i	$0.442934\pi$
$192$	8.85179	+	13.0203i	0.638823	+	0.939658i
$193$	10.6587	−	2.31867i	0.767233	−	0.166901i	0.188117	−	0.982147i	$-0.439761\pi$
$193$	10.6587	−	2.31867i	0.767233	−	0.166901i	0.579116	+	0.815245i	$0.303398\pi$
$194$	−5.72039	+	1.93137i	−0.410700	+	0.138664i
$195$	−9.39750	+	11.4469i	−0.672969	+	0.819733i
$196$	−9.01778	−	8.86356i	−0.644127	−	0.633112i
$197$	4.67162	−	6.24055i	0.332839	−	0.444621i	−0.602635	−	0.798017i	$-0.705882\pi$
$197$	4.67162	−	6.24055i	0.332839	−	0.444621i	0.935474	+	0.353396i	$0.114973\pi$
$198$	1.59799	+	3.81132i	0.113564	+	0.270859i
$199$	−9.66289	+	2.83728i	−0.684984	+	0.201129i	−0.605665	−	0.795720i	$-0.707093\pi$
$199$	−9.66289	+	2.83728i	−0.684984	+	0.201129i	−0.0793191	+	0.996849i	$0.525275\pi$
$200$	12.2002	−	7.15234i	0.862682	−	0.505747i
$201$	−3.28980	+	3.79664i	−0.232045	+	0.267794i
$202$	13.9031	+	0.436530i	0.978218	+	0.0307142i
$203$	0.268684	−	3.75669i	0.0188579	−	0.263668i
$204$	14.2241	−	1.14071i	0.995886	−	0.0798655i
$205$	−1.70009	+	0.0452434i	−0.118740	+	0.00315993i
$206$	−1.01653	−	5.49846i	−0.0708252	−	0.383096i
$207$	−3.88648	−	1.55898i	−0.270129	−	0.108356i
$208$	−0.728623	+	13.4422i	−0.0505209	+	0.932048i
$209$	16.4482	+	7.51163i	1.13774	+	0.519590i
$210$	2.15065	−	4.65029i	0.148409	−	0.320901i
$211$	−12.3570	+	10.7074i	−0.850692	+	0.737129i	−0.966643	−	0.256126i	$-0.917554\pi$
$211$	−12.3570	+	10.7074i	−0.850692	+	0.737129i	0.115952	+	0.993255i	$0.463008\pi$
$212$	19.1614	−	2.92387i	1.31601	−	0.200812i
$213$	−2.32591	−	32.5205i	−0.159369	−	2.22827i
$214$	0.304625	+	7.60926i	0.0208237	+	0.520158i
$215$	−0.175330	+	3.91154i	−0.0119574	+	0.266765i
$216$	−0.269472	+	11.8359i	−0.0183353	+	0.805330i
$217$	4.54951	−	6.07743i	0.308841	−	0.412563i
$218$	−6.40236	−	1.12663i	−0.433622	−	0.0763049i
$219$	−4.37103	−	9.57121i	−0.295367	−	0.646762i
$220$	8.54208	−	12.2906i	0.575907	−	0.828632i
$221$	10.2643	+	6.59645i	0.690450	+	0.443725i
$222$	10.1371	−	30.9013i	0.680359	−	2.07396i
$223$	−4.05736	+	3.03730i	−0.271701	+	0.203393i	−0.726436	−	0.687234i	$-0.758825\pi$
$223$	−4.05736	+	3.03730i	−0.271701	+	0.203393i	0.454735	+	0.890627i	$0.349734\pi$
$224$	−0.925490	−	4.56417i	−0.0618369	−	0.304956i
$225$	−4.34826	−	0.390596i	−0.289884	−	0.0260397i
$226$	−11.9924	−	9.57912i	−0.797725	−	0.637193i
$227$	−23.9911	+	13.1001i	−1.59235	+	0.869486i	−0.594485	+	0.804107i	$0.702644\pi$
$227$	−23.9911	+	13.1001i	−1.59235	+	0.869486i	−0.997860	+	0.0653792i	$0.979174\pi$
$228$	−14.0642	−	15.9509i	−0.931422	−	1.05637i
$229$			21.9201i			1.44852i	0.689525	+	0.724262i	$0.257819\pi$
$229$			21.9201i			1.44852i	−0.689525	+	0.724262i	$0.742181\pi$
$230$	2.78878	+	14.9071i	0.183887	+	0.982947i
$231$		−	5.42254i		−	0.356777i
$232$	−7.98820	+	10.1795i	−0.524451	+	0.668318i
$233$	12.4394	−	6.79241i	0.814931	−	0.444986i	−0.0170068	−	0.999855i	$-0.505414\pi$
$233$	12.4394	−	6.79241i	0.814931	−	0.444986i	0.831937	+	0.554870i	$0.187232\pi$
$234$	2.59365	−	3.24708i	0.169552	−	0.212268i
$235$	−4.01742	+	0.986559i	−0.262067	+	0.0643560i
$236$	4.43773	+	1.61173i	0.288872	+	0.104915i
$237$	16.5193	−	12.3662i	1.07304	−	0.803270i
$238$	−4.01062	−	1.31568i	−0.259970	−	0.0852828i
$239$	25.2064	+	16.1991i	1.63046	+	1.04784i	0.948658	+	0.316303i	$0.102442\pi$
$239$	25.2064	+	16.1991i	1.63046	+	1.04784i	0.681806	+	0.731533i	$0.261195\pi$
$240$	−15.0648	+	9.10524i	−0.972426	+	0.587741i
$241$	−6.56114	−	14.3669i	−0.422640	−	0.925453i	−0.994464	−	0.105076i	$-0.966491\pi$
$241$	−6.56114	−	14.3669i	−0.422640	−	0.925453i	0.571824	−	0.820376i	$-0.306236\pi$
$242$	0.0493377	−	0.280375i	0.00317155	−	0.0180232i
$243$	5.27961	−	7.05273i	0.338687	−	0.452433i
$244$	0.833073	−	3.99515i	0.0533320	−	0.255763i
$245$	10.4339	−	9.53870i	0.666600	−	0.609405i
$246$	2.11515	−	0.0846767i	0.134857	−	0.00539879i
$247$	−1.29716	−	18.1366i	−0.0825362	−	1.15401i
$248$	−24.6389	+	8.55621i	−1.56457	+	0.543320i
$249$	−11.0469	+	9.57218i	−0.700068	+	0.606612i
$250$	7.25687	+	14.0477i	0.458964	+	0.888455i
$251$	−13.5639	−	6.19441i	−0.856144	−	0.390988i	−0.0615316	−	0.998105i	$-0.519599\pi$
$251$	−13.5639	−	6.19441i	−0.856144	−	0.390988i	−0.794612	+	0.607117i	$0.792326\pi$
$252$	−0.585927	+	1.31285i	−0.0369099	+	0.0827016i
$253$	9.30153	+	13.0810i	0.584782	+	0.822393i
$254$	−12.9324	+	2.39089i	−0.811452	+	0.150018i
$255$	0.424425	+	15.9484i	0.0265785	+	0.998730i
$256$	−6.14071	+	14.7747i	−0.383794	+	0.923419i
$257$	1.23814	−	17.3114i	0.0772329	−	1.07986i	−0.800066	−	0.599912i	$-0.795202\pi$
$257$	1.23814	−	17.3114i	0.0772329	−	1.07986i	0.877299	−	0.479945i	$-0.159343\pi$
$258$	0.152945	−	4.87116i	0.00952194	−	0.303265i
$259$	−6.29954	+	7.27006i	−0.391434	+	0.451739i
$260$	−14.9639	−	1.61589i	−0.928021	−	0.100213i
$261$	3.83274	−	1.12539i	0.237241	−	0.0696602i
$262$	−1.99753	+	0.837515i	−0.123408	+	0.0517418i
$263$	18.7986	−	25.1120i	1.15917	−	1.54847i	0.376056	−	0.926597i	$-0.377280\pi$
$263$	18.7986	−	25.1120i	1.15917	−	1.54847i	0.783116	−	0.621875i	$-0.213629\pi$
$264$	−10.4262	+	15.4392i	−0.641690	+	0.950217i
$265$	2.12049	+	21.5670i	0.130261	+	1.32485i
$266$	2.01218	+	5.95974i	0.123375	+	0.365415i
$267$	2.76868	−	0.602289i	0.169440	−	0.0368595i
$268$	−5.05938	−	0.682948i	−0.309051	−	0.0417177i
$269$	9.37412	+	1.34780i	0.571550	+	0.0821765i	0.422030	−	0.906582i	$-0.361318\pi$
$269$	9.37412	+	1.34780i	0.571550	+	0.0821765i	0.149521	+	0.988759i	$0.452227\pi$
$270$	−13.1980	−	1.00739i	−0.803202	−	0.0613079i
$271$	−15.4322	−	24.0130i	−0.937439	−	1.45868i	−0.887966	−	0.459908i	$-0.847882\pi$
$271$	−15.4322	−	24.0130i	−0.937439	−	1.45868i	−0.0494726	−	0.998775i	$-0.515754\pi$
$272$	8.88939	+	11.4575i	0.538999	+	0.694711i
$273$	−4.78577	+	2.61323i	−0.289648	+	0.158160i
$274$	−7.79063	−	1.95270i	−0.470649	−	0.117967i
$275$	13.2118	+	10.2704i	0.796701	+	0.619328i
$276$	−3.71960	−	18.5066i	−0.223894	−	1.11397i
$277$	−8.81023	−	8.81023i	−0.529355	−	0.529355i	0.391025	−	0.920380i	$-0.372121\pi$
$277$	−8.81023	−	8.81023i	−0.529355	−	0.529355i	−0.920380	+	0.391025i	$0.872121\pi$
$278$	−12.9775	+	7.77578i	−0.778340	+	0.466360i
$279$	7.72561	+	2.26844i	0.462520	+	0.135808i
$280$	5.15086	−	0.760795i	0.307823	−	0.0454662i
$281$	−4.57318	+	2.93900i	−0.272813	+	0.175326i	−0.669893	−	0.742458i	$-0.733660\pi$
$281$	−4.57318	+	2.93900i	−0.272813	+	0.175326i	0.397080	+	0.917784i	$0.370024\pi$
$282$	4.98354	−	1.29489i	0.296765	−	0.0771094i
$283$	−14.1730	+	10.6098i	−0.842498	+	0.630686i	−0.930849	−	0.365403i	$-0.880931\pi$
$283$	−14.1730	+	10.6098i	−0.842498	+	0.630686i	0.0883511	+	0.996089i	$0.471840\pi$
$284$	26.3522	−	20.0840i	1.56372	−	1.19176i
$285$	18.6477	−	14.7496i	1.10460	−	0.873691i
$286$	−15.0923	+	5.09559i	−0.892426	+	0.301308i
$287$	−0.586670	−	0.218817i	−0.0346300	−	0.0129163i
$288$	4.19255	−	2.61137i	0.247048	−	0.153877i
$289$	−3.81731	+	0.548847i	−0.224548	+	0.0322851i
$290$	−10.8880	−	9.52600i	−0.639363	−	0.559386i
$291$	2.36713	+	8.06169i	0.138763	+	0.472585i
$292$	5.70327	−	9.04503i	0.333758	−	0.529320i
$293$	0.845277	+	11.8185i	0.0493816	+	0.690445i	0.960496	+	0.278293i	$0.0897685\pi$
$293$	0.845277	+	11.8185i	0.0493816	+	0.690445i	−0.911115	+	0.412153i	$0.864777\pi$
$294$	−12.8267	+	12.0458i	−0.748070	+	0.702524i
$295$	−2.06431	+	4.85825i	−0.120189	+	0.282858i
$296$	31.9147	−	8.58700i	1.85501	−	0.499109i
$297$	−13.1256	+	4.89559i	−0.761624	+	0.284071i
$298$	−12.5583	+	18.2550i	−0.727485	+	1.05748i
$299$	7.06226	−	14.5132i	0.408421	−	0.839320i
$300$	−9.26616	−	17.3624i	−0.534982	−	1.00242i
$301$	−0.598849	+	1.31130i	−0.0345171	+	0.0755819i
$302$	−2.29755	+	1.86788i	−0.132209	+	0.107485i
$303$	1.38093	−	19.3079i	0.0793322	−	1.10921i
$304$	5.73001	−	20.8377i	0.328639	−	1.19512i
$305$	4.41061	+	1.16857i	0.252551	+	0.0669119i
$306$	−0.179075	−	4.47314i	−0.0102371	−	0.255713i
$307$	5.84270	−	10.7001i	0.333460	−	0.610687i	−0.656122	−	0.754655i	$-0.727804\pi$
$307$	5.84270	−	10.7001i	0.333460	−	0.610687i	0.989582	+	0.143968i	$0.0459862\pi$
$308$	4.60996	−	3.01914i	0.262677	−	0.172031i
$309$	−7.70217	+	1.10741i	−0.438161	+	0.0629981i
$310$	−8.08168	−	28.0186i	−0.459008	−	1.59135i
$311$	24.5609	−	11.2166i	1.39272	−	0.636034i	0.429087	−	0.903263i	$-0.358835\pi$
$311$	24.5609	−	11.2166i	1.39272	−	0.636034i	0.963633	+	0.267229i	$0.0861082\pi$
$312$	18.6507	+	1.76142i	1.05589	+	0.0997210i
$313$	18.7180	−	4.07184i	1.05800	−	0.230154i	0.350280	−	0.936645i	$-0.386087\pi$
$313$	18.7180	−	4.07184i	1.05800	−	0.230154i	0.707722	+	0.706491i	$0.249723\pi$
$314$	8.93232	+	17.6539i	0.504080	+	0.996267i
$315$	−1.43074	−	0.732522i	−0.0806129	−	0.0412729i
$316$	19.7106	+	7.15866i	1.10881	+	0.402706i
$317$	−15.0606	−	3.27624i	−0.845890	−	0.184012i	−0.231323	−	0.972877i	$-0.574306\pi$
$317$	−15.0606	−	3.27624i	−0.845890	−	0.184012i	−0.614567	+	0.788865i	$0.710669\pi$
$318$	−2.99899	−	26.8065i	−0.168175	−	1.50324i
$319$	−14.6910	−	4.31368i	−0.822541	−	0.241520i
$320$	−16.1285	−	7.73770i	−0.901610	−	0.432551i
$321$	10.5976			0.591501
$322$	−1.10199	+	5.47379i	−0.0614116	+	0.305042i
$323$	−13.8502	−	13.8502i	−0.770647	−	0.770647i
$324$	21.6714	+	1.36222i	1.20396	+	0.0756789i
$325$	2.69731	−	16.6098i	0.149620	−	0.921347i
$326$	−13.4592	+	16.8500i	−0.745436	+	0.933238i
$327$	−1.92297	+	8.83974i	−0.106340	+	0.488839i
$328$	1.24965	+	1.75104i	0.0690004	+	0.0966852i
$329$	−1.50755	−	0.216752i	−0.0831137	−	0.0119499i
$330$	−16.6145	−	12.5619i	−0.914600	−	0.691509i
$331$	−3.16156	+	4.91948i	−0.173775	+	0.270399i	−0.917206	−	0.398414i	$-0.869561\pi$
$331$	−3.16156	+	4.91948i	−0.173775	+	0.270399i	0.743431	+	0.668813i	$0.233197\pi$
$332$	−14.2884	−	4.06193i	−0.784177	−	0.222928i
$333$	−9.55940	−	3.56547i	−0.523852	−	0.195387i
$334$	−16.7462	−	23.8985i	−0.916312	−	1.30767i
$335$	1.06449	−	5.60773i	0.0581593	−	0.306383i
$336$	−6.39797	+	1.03282i	−0.349038	+	0.0563449i
$337$	−12.9537	−	7.07326i	−0.705634	−	0.385305i	0.0860050	−	0.996295i	$-0.472590\pi$
$337$	−12.9537	−	7.07326i	−0.705634	−	0.385305i	−0.791639	+	0.610990i	$0.790772\pi$
$338$	−1.73915	−	1.60526i	−0.0945972	−	0.0873146i
$339$	−13.9873	+	16.1422i	−0.759686	+	0.876724i
$340$	−13.3222	+	9.24051i	−0.722499	+	0.501137i
$341$	−20.2108	−	23.3245i	−1.09448	−	1.26309i
$342$	−5.17661	+	4.20852i	−0.279919	+	0.227571i
$343$	10.2761	−	3.83280i	0.554859	−	0.206952i
$344$	4.22636	−	2.58211i	0.227870	−	0.139218i
$345$	20.8836	−	3.04796i	1.12433	−	0.164097i
$346$	7.82050	−	1.44582i	0.420433	−	0.0777279i
$347$	−9.51688	−	25.5157i	−0.510893	−	1.36976i	−0.894834	−	0.446399i	$-0.852706\pi$
$347$	−9.51688	−	25.5157i	−0.510893	−	1.36976i	0.383941	−	0.923358i	$-0.374567\pi$
$348$	13.7099	+	11.6742i	0.734928	+	0.625804i
$349$	2.84202	−	2.46262i	0.152130	−	0.131821i	−0.575471	−	0.817822i	$-0.695181\pi$
$349$	2.84202	−	2.46262i	0.152130	−	0.131821i	0.727600	+	0.686001i	$0.240636\pi$
$350$	0.541902	+	5.79604i	0.0289659	+	0.309811i
$351$	10.6462	+	9.22496i	0.568250	+	0.492392i
$352$	−18.9307	−	0.267681i	−1.00901	−	0.0142674i
$353$	−6.53175	+	11.9620i	−0.347650	+	0.636673i	−0.991738	−	0.128278i	$-0.959055\pi$
$353$	−6.53175	+	11.9620i	−0.347650	+	0.636673i	0.644088	+	0.764951i	$0.277237\pi$
$354$	2.48814	−	6.08093i	0.132243	−	0.323198i
$355$	20.8494	+	30.6196i	1.10657	+	1.62512i
$356$	2.05357	+	2.01845i	0.108839	+	0.106978i
$357$	−2.05270	+	5.50351i	−0.108640	+	0.291276i
$358$	13.6636	−	27.5931i	0.722146	−	1.45834i
$359$	11.5598	+	7.42905i	0.610105	+	0.392090i	0.808896	−	0.587951i	$-0.200065\pi$
$359$	11.5598	+	7.42905i	0.610105	+	0.392090i	−0.198792	+	0.980042i	$0.563702\pi$
$360$	2.66517	+	4.83661i	0.140467	+	0.254912i
$361$	−1.45020	+	10.0863i	−0.0763262	+	0.530860i
$362$	−26.2285	+	6.81503i	−1.37854	+	0.358190i
$363$	−0.387113	−	0.0842113i	−0.0203182	−	0.00441995i
$364$	−4.88622	−	2.61363i	−0.256108	−	0.136991i
$365$	9.75777	+	6.90729i	0.510745	+	0.361544i
$366$	−5.50887	−	1.38078i	−0.287953	−	0.0721745i
$367$	−7.98721	+	7.98721i	−0.416929	+	0.416929i	−0.884144	−	0.467215i	$-0.845257\pi$
$367$	−7.98721	+	7.98721i	−0.416929	+	0.416929i	0.467215	+	0.884144i	$0.345257\pi$
$368$	13.6624	−	13.4662i	0.712201	−	0.701976i
$369$		−	0.664098i		−	0.0345716i
$370$	7.68171	+	36.1435i	0.399353	+	1.87901i
$371$	−2.24785	+	7.65548i	−0.116703	+	0.397453i
$372$	10.5258	+	34.7366i	0.545738	+	1.80101i
$373$	2.83458	−	13.0304i	0.146769	−	0.674687i	−0.843684	−	0.536840i	$-0.819618\pi$
$373$	2.83458	−	13.0304i	0.146769	−	0.674687i	0.990453	−	0.137847i	$-0.0440183\pi$
$374$	−8.69224	+	14.7950i	−0.449465	+	0.765031i
$375$	19.9372	−	9.30866i	1.02955	−	0.480697i
$376$	3.87556	+	3.51578i	0.199867	+	0.181313i
$377$	3.27278	+	15.0447i	0.168556	+	0.774842i
$378$	−4.36716	−	2.16254i	−0.224622	−	0.111229i
$379$	−1.33708	−	2.92780i	−0.0686812	−	0.150391i	0.872178	−	0.489189i	$-0.162707\pi$
$379$	−1.33708	−	2.92780i	−0.0686812	−	0.150391i	−0.940859	+	0.338798i	$0.889980\pi$
$380$	22.9219	+	7.64111i	1.17587	+	0.391981i
$381$	2.60463	+	18.1156i	0.133439	+	0.928089i
$382$	11.4110	−	4.78433i	0.583836	−	0.244788i
$383$	6.89897	+	3.76712i	0.352521	+	0.192491i	0.645746	−	0.763553i	$-0.276547\pi$
$383$	6.89897	+	3.76712i	0.352521	+	0.192491i	−0.293225	+	0.956043i	$0.594728\pi$
$384$	20.2023	+	9.36108i	1.03095	+	0.477706i
$385$	3.09549	+	5.32697i	0.157761	+	0.271488i
$386$	11.2450	−	10.5603i	0.572354	−	0.537507i
$387$	−1.52504	−	0.109073i	−0.0775222	−	0.00554450i
$388$	−5.53568	+	6.50096i	−0.281031	+	0.330036i
$389$	10.1331	+	4.62763i	0.513768	+	0.234630i	0.655390	−	0.755291i	$-0.272504\pi$
$389$	10.1331	+	4.62763i	0.513768	+	0.234630i	−0.141622	+	0.989921i	$0.545232\pi$
$390$	−3.07988	+	20.7173i	−0.155956	+	1.04906i
$391$	−4.48862	−	16.7974i	−0.226999	−	0.849479i
$392$	−17.3823	−	4.19783i	−0.877939	−	0.212022i
$393$	1.05337	+	2.82418i	0.0531353	+	0.142461i
$394$	1.13118	−	10.9662i	0.0569878	−	0.552469i
$395$	−9.16883	+	21.5784i	−0.461334	+	1.08573i
$396$	4.70888	+	3.46206i	0.236630	+	0.173975i
$397$	15.9077	−	1.13774i	0.798384	−	0.0571015i	0.333815	−	0.942639i	$-0.391664\pi$
$397$	15.9077	−	1.13774i	0.798384	−	0.0571015i	0.464569	+	0.885537i	$0.346209\pi$
$398$	−9.65992	+	10.4656i	−0.484208	+	0.524594i
$399$	8.39901	−	2.46617i	0.420476	−	0.123463i
$400$	9.60146	−	17.5446i	0.480073	−	0.877229i
$401$	−0.470294	−	3.27097i	−0.0234854	−	0.163344i	0.974704	−	0.223502i	$-0.0717488\pi$
$401$	−0.470294	−	3.27097i	−0.0234854	−	0.163344i	−0.998189	+	0.0601574i	$0.980840\pi$
$402$	−1.23127	+	6.99704i	−0.0614103	+	0.348980i
$403$	−10.8455	+	29.0779i	−0.540253	+	1.44847i
$404$	17.1834	−	9.57616i	0.854908	−	0.476432i
$405$	−2.81451	+	24.1134i	−0.139854	+	1.19821i
$406$	−2.40467	−	4.75261i	−0.119342	−	0.235868i
$407$	23.4361	+	31.3070i	1.16169	+	1.55183i
$408$	16.4264	−	11.7229i	0.813228	−	0.580368i
$409$	−6.65042	−	10.3483i	−0.328842	−	0.511689i	0.636985	−	0.770877i	$-0.280181\pi$
$409$	−6.65042	−	10.3483i	−0.328842	−	0.511689i	−0.965827	+	0.259188i	$0.916545\pi$
$410$	−2.02953	+	1.29063i	−0.100231	+	0.0637397i
$411$	−3.14889	+	10.7241i	−0.155323	+	0.528983i
$412$	−5.22983	−	5.93141i	−0.257655	−	0.292220i
$413$	−1.37422	+	1.37422i	−0.0676211	+	0.0676211i
$414$	−5.84795	+	0.933739i	−0.287411	+	0.0458908i
$415$	5.38785	−	15.7096i	0.264479	−	0.771156i
$416$	8.88680	+	16.8366i	0.435711	+	0.825483i
$417$	10.0898	+	18.4780i	0.494098	+	0.904874i
$418$	25.4136	−	2.84315i	1.24302	−	0.139063i
$419$	−9.70890	+	6.23953i	−0.474311	+	0.304821i	−0.755869	−	0.654723i	$-0.772785\pi$
$419$	−9.70890	+	6.23953i	−0.474311	+	0.304821i	0.281558	+	0.959544i	$0.409149\pi$
$420$	−0.771153	−	7.20460i	−0.0376284	−	0.351549i
$421$	5.41059	−	37.6315i	0.263696	−	1.83405i	−0.240730	−	0.970592i	$-0.577387\pi$
$421$	5.41059	−	37.6315i	0.263696	−	1.83405i	0.504426	−	0.863455i	$-0.331704\pi$
$422$	−7.20766	+	21.9713i	−0.350864	+	1.06955i
$423$	−0.343369	−	1.57844i	−0.0166951	−	0.0767464i
$424$	21.1198	−	17.4748i	1.02567	−	0.848651i
$425$	−9.52120	−	15.4251i	−0.461846	−	0.748225i
$426$	−26.4597	−	37.7607i	−1.28198	−	1.82951i
$427$	1.34482	+	1.00672i	0.0650806	+	0.0487187i
$428$	5.90048	+	9.00953i	0.285211	+	0.435492i
$429$	6.24526	+	21.2694i	0.301524	+	1.02690i
$430$	2.63048	+	4.87261i	0.126853	+	0.234978i
$431$	−8.09339	−	7.01296i	−0.389845	−	0.337802i	0.437782	−	0.899081i	$-0.355764\pi$
$431$	−8.09339	−	7.01296i	−0.389845	−	0.337802i	−0.827627	+	0.561279i	$0.810310\pi$
$432$	8.27623	+	14.5542i	0.398191	+	0.700241i
$433$	−26.1601	−	1.87101i	−1.25717	−	0.0899148i	−0.573196	−	0.819418i	$-0.694297\pi$
$433$	−26.1601	−	1.87101i	−1.25717	−	0.0899148i	−0.683977	+	0.729503i	$0.739751\pi$
$434$	1.10161	−	10.6796i	0.0528789	−	0.512635i
$435$	−13.8520	+	14.6094i	−0.664151	+	0.700466i
$436$	−8.58574	+	3.28694i	−0.411183	+	0.157416i
$437$	−16.0308	+	20.3564i	−0.766859	+	0.973780i
$438$	−12.2596	−	8.43387i	−0.585786	−	0.402986i
$439$	−0.0222409	+	0.0487008i	−0.00106150	+	0.00232436i	−0.910162	−	0.414252i	$-0.864043\pi$
$439$	−0.0222409	+	0.0487008i	−0.00106150	+	0.00232436i	0.909101	+	0.416577i	$0.136770\pi$
$440$	1.42891	−	21.1190i	0.0681208	−	1.00681i
$441$	3.61502	+	4.17196i	0.172144	+	0.198665i
$442$	17.2466	+	0.541509i	0.820335	+	0.0257569i
$443$	26.3874	−	1.88727i	1.25370	−	0.0896667i	0.571361	−	0.820699i	$-0.306416\pi$
$443$	26.3874	−	1.88727i	1.25370	−	0.0896667i	0.682343	+	0.731032i	$0.260961\pi$
$444$	−10.1636	−	44.8553i	−0.482343	−	2.12874i
$445$	−2.37606	+	2.17219i	−0.112636	+	0.102972i
$446$	−2.71435	+	6.63378i	−0.128528	+	0.314118i
$447$	24.6844	+	18.4785i	1.16753	+	0.874003i
$448$	−4.44028	−	4.86418i	−0.209784	−	0.229811i
$449$	−29.3178	+	13.3890i	−1.38359	+	0.631866i	−0.961530	−	0.274701i	$-0.911421\pi$
$449$	−29.3178	+	13.3890i	−1.38359	+	0.631866i	−0.422063	+	0.906566i	$0.638694\pi$
$450$	−5.55888	+	2.68678i	−0.262048	+	0.126656i
$451$	−1.37621	+	2.14142i	−0.0648031	+	0.100836i
$452$	−21.5110	−	2.90370i	−1.01179	−	0.136578i
$453$	2.46939	+	3.29872i	0.116022	+	0.154987i
$454$	−19.5820	+	33.3304i	−0.919030	+	1.56427i
$455$	3.20964	−	5.29915i	0.150470	−	0.248428i
$456$	−28.6557	−	9.12751i	−1.34193	−	0.427435i
$457$	−7.10379	−	13.0096i	−0.332301	−	0.608565i	0.657095	−	0.753808i	$-0.271785\pi$
$457$	−7.10379	−	13.0096i	−0.332301	−	0.608565i	−0.989396	+	0.145244i	$0.953603\pi$
$458$	15.9331	+	26.5918i	0.744503	+	1.24255i
$459$	15.1748			0.708299
$460$	14.2187	+	16.0571i	0.662948	+	0.748665i
$461$	−34.7801			−1.61987			−0.809935	−	0.586519i	$-0.800498\pi$
$461$	−34.7801			−1.61987			−0.809935	+	0.586519i	$0.800498\pi$
$462$	−3.94148	−	6.57820i	−0.183374	−	0.306046i
$463$	−9.70525	−	17.7738i	−0.451041	−	0.826020i	0.548910	−	0.835881i	$-0.315043\pi$
$463$	−9.70525	−	17.7738i	−0.451041	−	0.826020i	−0.999951	+	0.00986098i	$0.996861\pi$
$464$	−2.29148	+	18.1554i	−0.106379	+	0.842841i
$465$	−39.4096	+	9.67784i	−1.82758	+	0.448799i
$466$	10.1533	−	17.2818i	0.470341	−	0.800564i
$467$	21.4303	+	28.6276i	0.991677	+	1.32473i	0.945440	+	0.325795i	$0.105632\pi$
$467$	21.4303	+	28.6276i	0.991677	+	1.32473i	0.0462370	+	0.998930i	$0.485277\pi$
$468$	0.786207	−	5.82434i	0.0363424	−	0.269230i
$469$	1.13615	−	1.76788i	0.0524623	−	0.0816330i
$470$	−4.15651	+	4.11695i	−0.191726	+	0.189901i
$471$	25.0449	−	11.4376i	1.15401	−	0.527018i
$472$	6.55502	−	1.27042i	0.301719	−	0.0584760i
$473$	4.69155	+	3.51205i	0.215718	+	0.161484i
$474$	11.0513	−	27.0090i	0.507603	−	1.24057i
$475$	−9.89915	+	25.1348i	−0.454204	+	1.15326i
$476$	−5.82169	+	1.31911i	−0.266837	+	0.0604615i
$477$	−8.44068	+	0.603689i	−0.386472	+	0.0276410i
$478$	42.3530	+	1.32980i	1.93718	+	0.0608238i
$479$	6.52533	+	7.53063i	0.298150	+	0.344083i	0.884982	−	0.465625i	$-0.154171\pi$
$479$	6.52533	+	7.53063i	0.298150	+	0.344083i	−0.586832	+	0.809709i	$0.699625\pi$
$480$	−11.6571	+	21.9959i	−0.532069	+	1.00397i
$481$	16.3363	−	35.7714i	0.744870	−	1.63104i
$482$	−18.4023	−	12.6597i	−0.838201	−	0.576633i
$483$	7.54993	+	1.83702i	0.343534	+	0.0835874i
$484$	−0.143943	−	0.375990i	−0.00654286	−	0.0170905i
$485$	−6.92747	−	6.56832i	−0.314560	−	0.298252i
$486$	1.27839	−	12.3934i	0.0579891	−	0.562176i
$487$	−6.13179	−	0.438554i	−0.277858	−	0.0198728i	−0.0682852	−	0.997666i	$-0.521753\pi$
$487$	−6.13179	−	0.438554i	−0.277858	−	0.0198728i	−0.209573	+	0.977793i	$0.567207\pi$
$488$	−1.89333	−	5.45214i	−0.0857072	−	0.246807i
$489$	22.6807	+	19.6529i	1.02566	+	0.888736i
$490$	5.72426	−	19.1557i	0.258595	−	0.865366i
$491$	0.999382	+	3.40358i	0.0451015	+	0.153602i	0.978965	−	0.204028i	$-0.0654033\pi$
$491$	0.999382	+	3.40358i	0.0451015	+	0.153602i	−0.933864	+	0.357629i	$0.883585\pi$
$492$	2.50438	−	1.64016i	0.112906	−	0.0739441i
$493$	13.2775	+	9.93938i	0.597987	+	0.447647i
$494$	−14.7566	−	21.0591i	−0.663929	−	0.947492i
$495$	−4.14628	+	5.05051i	−0.186361	+	0.227004i
$496$	−23.6707	+	28.2890i	−1.06285	+	1.27021i
$497$	2.89909	+	13.3269i	0.130042	+	0.597793i
$498$	−6.44348	+	19.6418i	−0.288739	+	0.880172i
$499$	−2.34020	+	16.2764i	−0.104762	+	0.728633i	0.867956	+	0.496641i	$0.165434\pi$
$499$	−2.34020	+	16.2764i	−0.104762	+	0.728633i	−0.972718	+	0.231992i	$0.925476\pi$
$500$	19.0143	+	11.7668i	0.850345	+	0.526226i
$501$	−34.1630	+	21.9552i	−1.52629	+	0.980886i
$502$	−20.9571	+	2.34458i	−0.935363	+	0.104644i
$503$	5.49445	+	10.0623i	0.244986	+	0.448658i	0.971019	−	0.239002i	$-0.0768201\pi$
$503$	5.49445	+	10.0623i	0.244986	+	0.448658i	−0.726034	+	0.687659i	$0.758638\pi$
$504$	0.243468	+	2.01853i	0.0108449	+	0.0899126i
$505$	9.66544	+	19.7559i	0.430106	+	0.879126i
$506$	20.7920	+	9.10779i	0.924318	+	0.404890i
$507$	−2.32892	+	2.32892i	−0.103431	+	0.103431i
$508$	−13.9507	+	12.3006i	−0.618963	+	0.545752i
$509$	8.65809	−	29.4867i	0.383763	−	1.30698i	−0.510671	−	0.859776i	$-0.670603\pi$
$509$	8.65809	−	29.4867i	0.383763	−	1.30698i	0.894434	−	0.447200i	$-0.147579\pi$
$510$	12.1073	+	19.0389i	0.536120	+	0.843056i
$511$	2.37965	+	3.70281i	0.105270	+	0.163803i
$512$	3.28985	+	22.3870i	0.145392	+	0.989374i
$513$	−13.5523	−	18.1038i	−0.598350	−	0.799302i
$514$	−11.0811	−	21.9008i	−0.488767	−	0.966003i
$515$	6.93425	−	5.48472i	0.305560	−	0.241686i
$516$	−3.35515	−	6.02047i	−0.147702	−	0.265037i
$517$	−2.16378	+	5.80133i	−0.0951631	+	0.255142i
$518$	−2.35773	+	13.3984i	−0.103593	+	0.588692i
$519$	−1.57507	−	10.9549i	−0.0691379	−	0.480865i
$520$	−19.3275	+	8.91651i	−0.847569	+	0.391015i
$521$	19.5200	−	5.73160i	0.855188	−	0.251106i	0.175384	−	0.984500i	$-0.443883\pi$
$521$	19.5200	−	5.73160i	0.855188	−	0.251106i	0.679804	+	0.733394i	$0.262065\pi$
$522$	3.83156	−	4.15114i	0.167703	−	0.181690i
$523$	18.8696	−	1.34958i	0.825109	−	0.0590130i	0.347603	−	0.937642i	$-0.386996\pi$
$523$	18.8696	−	1.34958i	0.825109	−	0.0590130i	0.477506	+	0.878629i	$0.341541\pi$
$524$	−1.81449	+	2.46795i	−0.0792662	+	0.107813i
$525$	8.08954	−	0.430868i	0.353056	−	0.0188046i
$526$	4.55185	−	44.1280i	0.198470	−	1.92407i
$527$	11.6831	+	31.3235i	0.508923	+	1.36447i
$528$	−1.42601	+	26.3081i	−0.0620591	+	1.14491i
$529$	−21.3640	+	8.51924i	−0.928872	+	0.370402i
$530$	18.2488	+	24.6221i	0.792677	+	1.06952i
$531$	−1.87496	−	0.856267i	−0.0813665	−	0.0371588i
$532$	6.77297	+	5.76730i	0.293646	+	0.250044i
$533$	2.55317	+	0.182607i	0.110590	+	0.00790957i
$534$	2.92096	−	2.74312i	0.126402	−	0.118706i
$535$	−10.4108	+	6.04971i	−0.450099	+	0.261552i
$536$	−6.63406	+	2.84901i	−0.286548	+	0.123058i
$537$	−37.6075	−	20.5352i	−1.62288	−	0.886161i
$538$	12.3516	−	5.17872i	0.532516	−	0.223270i
$539$	−3.01131	−	20.9441i	−0.129706	−	0.902128i
$540$	−16.7430	+	8.37110i	−0.720502	+	0.360235i
$541$	16.5983	+	36.3453i	0.713618	+	1.56260i	0.822638	+	0.568565i	$0.192501\pi$
$541$	16.5983	+	36.3453i	0.713618	+	1.56260i	−0.109021	+	0.994039i	$0.534772\pi$
$542$	−36.1754	−	17.9134i	−1.55387	−	0.769448i
$543$	8.01622	+	36.8500i	0.344009	+	1.58138i
$544$	19.1120	+	7.43787i	0.819420	+	0.318896i
$545$	−3.15714	−	9.78168i	−0.135237	−	0.419001i
$546$	−3.90624	+	6.64878i	−0.167172	+	0.284542i
$547$	2.79243	−	12.8366i	0.119396	−	0.548854i	−0.878122	−	0.478437i	$-0.841203\pi$
$547$	2.79243	−	12.8366i	0.119396	−	0.548854i	0.997518	−	0.0704168i	$-0.0224329\pi$
$548$	−10.8703	+	3.29391i	−0.464357	+	0.140709i
$549$	−0.501965	+	1.70954i	−0.0214234	+	0.0729612i
$550$	23.4927	+	2.85599i	1.00173	+	0.121780i
$551$		−	24.7169i		−	1.05298i
$552$	−17.9642	−	19.7471i	−0.764607	−	0.840492i
$553$	−6.10375	+	6.10375i	−0.259558	+	0.259558i
$554$	−17.0918	−	4.28399i	−0.726159	−	0.182009i
$555$	50.6850	−	8.66941i	2.15146	−	0.367996i
$556$	−10.0913	+	18.8659i	−0.427968	+	0.800093i
$557$	−2.17256	−	0.472611i	−0.0920542	−	0.0200252i	0.166302	−	0.986075i	$-0.446817\pi$
$557$	−2.17256	−	0.472611i	−0.0920542	−	0.0200252i	−0.258356	+	0.966050i	$0.583181\pi$
$558$	11.0210	−	2.86361i	0.466555	−	0.121226i
$559$	0.838679	−	5.83314i	0.0354724	−	0.246716i
$560$	5.69562	−	4.66694i	0.240684	−	0.197214i
$561$	20.0885	+	12.9101i	0.848138	+	0.545065i
$562$	−3.41155	+	6.88946i	−0.143907	+	0.290615i
$563$	12.2865	−	32.9413i	0.517812	−	1.38831i	−0.370399	−	0.928873i	$-0.620779\pi$
$563$	12.2865	−	32.9413i	0.517812	−	1.38831i	0.888211	−	0.459436i	$-0.151948\pi$
$564$	5.10442	−	5.19323i	0.214935	−	0.218675i
$565$	4.52590	−	23.8424i	0.190406	−	1.00306i
$566$	−9.48166	+	23.1729i	−0.398544	+	0.974029i
$567$	−4.28361	+	7.84485i	−0.179895	+	0.329453i
$568$	17.3700	−	43.5189i	0.728830	−	1.82601i
$569$	14.1711	+	12.2793i	0.594084	+	0.514776i	0.899200	−	0.437539i	$-0.144150\pi$
$569$	14.1711	+	12.2793i	0.594084	+	0.514776i	−0.305116	+	0.952315i	$0.598695\pi$
$570$	11.9009	−	31.4475i	0.498474	−	1.31719i
$571$	−16.3353	+	14.1546i	−0.683611	+	0.592352i	−0.925862	−	0.377861i	$-0.876660\pi$
$571$	−16.3353	+	14.1546i	−0.683611	+	0.592352i	0.242251	+	0.970214i	$0.422114\pi$
$572$	−14.6049	+	17.1517i	−0.610663	+	0.717148i
$573$	−6.01738	−	16.1332i	−0.251380	−	0.673975i
$574$	−0.870753	+	0.160981i	−0.0363445	+	0.00671922i
$575$	−18.7755	+	14.9157i	−0.782994	+	0.622029i
$576$	3.18794	−	6.21535i	0.132831	−	0.258973i
$577$	33.9165	−	12.6502i	1.41196	−	0.526634i	0.476221	−	0.879326i	$-0.342006\pi$
$577$	33.9165	−	12.6502i	1.41196	−	0.526634i	0.935740	+	0.352691i	$0.114733\pi$
$578$	−4.23192	+	3.44050i	−0.176025	+	0.143106i
$579$	−14.0581	−	16.2240i	−0.584236	−	0.674244i
$580$	−20.1326	−	3.64208i	−0.835959	−	0.151229i
$581$	4.00419	−	4.62108i	0.166122	−	0.191715i
$582$	8.73140	+	8.05922i	0.361928	+	0.334065i
$583$	28.4685	+	15.5450i	1.17904	+	0.643807i
$584$	0.344203	−	15.1182i	0.0142432	−	0.625597i
$585$	6.45559	+	1.22544i	0.266906	+	0.0506655i
$586$	9.61594	+	13.7229i	0.397231	+	0.566887i
$587$	−1.03557	−	0.386247i	−0.0427424	−	0.0159421i	0.328002	−	0.944677i	$-0.393625\pi$
$587$	−1.03557	−	0.386247i	−0.0427424	−	0.0159421i	−0.370744	+	0.928735i	$0.620897\pi$
$588$	−6.80467	+	23.9363i	−0.280620	+	0.987118i
$589$	26.9356	−	41.9126i	1.10986	−	1.72698i
$590$	1.02705	+	7.39412i	0.0422830	+	0.304411i
$591$	−15.1855	−	2.18334i	−0.624647	−	0.0898107i
$592$	32.4748	−	33.6149i	1.33471	−	1.38156i
$593$	−5.05869	+	23.2544i	−0.207736	+	0.954945i	0.748679	+	0.662933i	$0.230689\pi$
$593$	−5.05869	+	23.2544i	−0.207736	+	0.954945i	−0.956414	+	0.292013i	$0.905675\pi$
$594$	−12.3645	+	15.4795i	−0.507321	+	0.635133i
$595$	−1.12519	−	6.57830i	−0.0461282	−	0.269684i
$596$	−1.96581	+	31.2738i	−0.0805227	+	1.28102i
$597$	14.0147	+	14.0147i	0.573582	+	0.573582i
$598$	−1.98182	−	22.7396i	−0.0810427	−	0.929891i
$599$	5.48953			0.224296			0.112148	−	0.993692i	$-0.464227\pi$
$599$	5.48953			0.224296			0.112148	+	0.993692i	$0.464227\pi$
$600$	−23.8612	−	14.3274i	−0.974128	−	0.584915i
$601$	−30.4760	−	8.94856i	−1.24314	−	0.365019i	−0.406947	−	0.913452i	$-0.633407\pi$
$601$	−30.4760	−	8.94856i	−1.24314	−	0.365019i	−0.836195	+	0.548432i	$0.815225\pi$
$602$	0.226664	+	2.02605i	0.00923814	+	0.0825754i
$603$	2.17791	+	0.473775i	0.0886913	+	0.0192936i
$604$	−1.42950	+	3.93599i	−0.0581657	+	0.160153i
$605$	0.428363	−	0.138259i	0.0174154	−	0.00562102i
$606$	−12.3591	−	24.4266i	−0.502053	−	0.992261i
$607$	31.9811	−	6.95706i	1.29807	−	0.282378i	0.490135	−	0.871646i	$-0.336947\pi$
$607$	31.9811	−	6.95706i	1.29807	−	0.282378i	0.807938	+	0.589268i	$0.200584\pi$
$608$	−8.19505	−	29.4436i	−0.332353	−	1.19409i
$609$	−6.74235	+	3.07913i	−0.273214	+	0.124773i
$610$	6.20000	−	1.78833i	0.251031	−	0.0724072i
$611$	6.16284	−	0.886083i	0.249322	−	0.0358471i
$612$	−3.46863	−	5.29630i	−0.140211	−	0.214090i
$613$	−12.3825	+	22.6769i	−0.500125	+	0.915911i	0.498668	+	0.866793i	$0.333823\pi$
$613$	−12.3825	+	22.6769i	−0.500125	+	0.915911i	−0.998793	+	0.0491178i	$0.984359\pi$
$614$	−0.689671	−	17.2274i	−0.0278329	−	0.695241i
$615$	1.68164	+	2.89390i	0.0678102	+	0.116693i
$616$	3.39793	−	7.01342i	0.136906	−	0.282579i
$617$	−1.62851	+	22.7696i	−0.0655615	+	0.916670i	0.853131	+	0.521697i	$0.174701\pi$
$617$	−1.62851	+	22.7696i	−0.0655615	+	0.916670i	−0.918693	+	0.394973i	$0.870754\pi$
$618$	−8.53873	+	6.94188i	−0.343478	+	0.279243i
$619$	1.41304	−	3.09413i	0.0567949	−	0.124364i	−0.879107	−	0.476625i	$-0.841860\pi$
$619$	1.41304	−	3.09413i	0.0567949	−	0.124364i	0.935902	+	0.352261i	$0.114587\pi$
$620$	−30.1699	−	28.1156i	−1.21165	−	1.12915i
$621$	−2.36963	−	19.9336i	−0.0950899	−	0.799907i
$622$	21.6423	−	31.4596i	0.867779	−	1.26142i
$623$	−1.11054	+	0.414209i	−0.0444927	+	0.0165949i
$624$	23.9059	−	11.4198i	0.957003	−	0.457159i
$625$	−14.2719	+	20.5259i	−0.570878	+	0.821035i
$626$	19.7474	−	18.5451i	0.789267	−	0.741213i
$627$	−2.53871	−	35.4957i	−0.101386	−	1.41756i
$628$	23.6681	+	14.9237i	0.944458	+	0.595520i
$629$	−11.9348	−	40.6462i	−0.475871	−	1.62067i
$630$	−2.26810	+	0.151321i	−0.0903634	+	0.00602876i
$631$	−45.9291	+	6.60361i	−1.82841	+	0.262886i	−0.968760	−	0.247999i	$-0.920227\pi$
$631$	−45.9291	+	6.60361i	−1.82841	+	0.262886i	−0.859649	+	0.510885i	$0.829318\pi$
$632$	29.1148	−	5.64272i	1.15812	−	0.224455i
$633$	30.1498	+	11.2453i	1.19835	+	0.446960i
$634$	−20.6518	+	6.97264i	−0.820187	+	0.276919i
$635$	−12.9001	−	16.3094i	−0.511925	−	0.647220i
$636$	−23.1230	−	30.3397i	−0.916885	−	1.20305i
$637$	−17.0334	+	12.7511i	−0.674889	+	0.505216i
$638$	−20.9575	+	5.44545i	−0.829715	+	0.215587i
$639$	−12.1689	+	7.82047i	−0.481394	+	0.309373i
$640$	−25.1901	+	2.33652i	−0.995726	+	0.0923592i
$641$	46.0143	+	13.5110i	1.81746	+	0.533654i	0.999154	−	0.0411332i	$-0.0130968\pi$
$641$	46.0143	+	13.5110i	1.81746	+	0.533654i	0.818303	+	0.574787i	$0.194915\pi$
$642$	12.8562	−	7.70307i	0.507393	−	0.304016i
$643$	−16.2934	−	16.2934i	−0.642548	−	0.642548i	0.308633	−	0.951181i	$-0.400129\pi$
$643$	−16.2934	−	16.2934i	−0.642548	−	0.642548i	−0.951181	+	0.308633i	$0.900129\pi$
$644$	2.64187	+	7.44137i	0.104104	+	0.293231i
$645$	6.92178	−	3.38643i	0.272545	−	0.133341i
$646$	−26.8693	−	6.73470i	−1.05716	−	0.264973i
$647$	−8.25250	+	4.50621i	−0.324439	+	0.177157i	−0.633212	−	0.773979i	$-0.718264\pi$
$647$	−8.25250	+	4.50621i	−0.324439	+	0.177157i	0.308772	+	0.951136i	$0.400082\pi$
$648$	27.2801	−	14.0997i	1.07166	−	0.553888i
$649$	4.27149	+	6.64656i	0.167671	+	0.260900i
$650$	−8.80099	−	22.1103i	−0.345203	−	0.867237i
$651$	−14.7886	−	2.12627i	−0.579609	−	0.0833352i
$652$	−4.07986	+	30.2242i	−0.159779	+	1.18367i
$653$	6.70024	−	1.45755i	0.262201	−	0.0570383i	−0.0795431	−	0.996831i	$-0.525346\pi$
$653$	6.70024	−	1.45755i	0.262201	−	0.0570383i	0.341744	+	0.939793i	$0.388982\pi$
$654$	4.09254	+	12.1214i	0.160031	+	0.473985i
$655$	−2.64700	−	2.17309i	−0.103427	−	0.0849095i
$656$	2.78875	+	1.21590i	0.108883	+	0.0474728i
$657$	−2.79761	+	3.73718i	−0.109145	+	0.145801i
$658$	−1.98638	+	0.832841i	−0.0774373	+	0.0324675i
$659$	4.24514	−	1.24649i	0.165367	−	0.0485562i	−0.198001	−	0.980202i	$-0.563445\pi$
$659$	4.24514	−	1.24649i	0.165367	−	0.0485562i	0.363368	+	0.931646i	$0.381627\pi$
$660$	−29.2863	−	3.16251i	−1.13997	−	0.123101i
$661$	−6.27076	+	7.23685i	−0.243904	+	0.281481i	−0.864481	−	0.502665i	$-0.832353\pi$
$661$	−6.27076	+	7.23685i	−0.243904	+	0.281481i	0.620577	+	0.784146i	$0.286898\pi$
$662$	−0.259535	+	8.26596i	−0.0100871	+	0.321266i
$663$	1.71302	−	23.9511i	0.0665281	−	0.930185i
$664$	−20.2860	+	5.45817i	−0.787251	+	0.211818i
$665$	−6.84315	+	7.21733i	−0.265366	+	0.279876i
$666$	−14.1883	+	2.62308i	−0.549787	+	0.101642i
$667$	10.9830	−	18.9933i	0.425263	−	0.735424i
$668$	−37.6863	−	16.8195i	−1.45813	−	0.650765i
$669$	9.07314	+	4.14357i	0.350788	+	0.160199i
$670$	−2.78473	−	7.57659i	−0.107583	−	0.292709i
$671$	5.16128	−	4.47228i	0.199249	−	0.172650i
$672$	−7.01079	+	5.90342i	−0.270447	+	0.227729i
$673$	−1.99582	−	27.9052i	−0.0769332	−	1.07567i	−0.878494	−	0.477753i	$-0.841451\pi$
$673$	−1.99582	−	27.9052i	−0.0769332	−	1.07567i	0.801561	−	0.597913i	$-0.204003\pi$
$674$	−20.8557	+	0.834927i	−0.803333	+	0.0321602i
$675$	−8.34635	−	19.1922i	−0.321251	−	0.738709i
$676$	−3.27661	−	0.683242i	−0.126023	−	0.0262785i
$677$	15.6529	−	20.9098i	0.601589	−	0.803628i	−0.391601	−	0.920135i	$-0.628079\pi$
$677$	15.6529	−	20.9098i	0.601589	−	0.803628i	0.993190	+	0.116507i	$0.0371697\pi$
$678$	−5.23502	+	29.7494i	−0.201050	+	1.14252i
$679$	−1.46006	−	3.19709i	−0.0560320	−	0.122693i
$680$	−9.44482	+	20.8934i	−0.362192	+	0.801224i
$681$	45.2557	+	29.0841i	1.73420	+	1.11451i
$682$	−41.4720	−	13.6048i	−1.58804	−	0.520956i
$683$	5.40918	−	4.04926i	0.206976	−	0.154941i	−0.490761	−	0.871294i	$-0.663281\pi$
$683$	5.40918	−	4.04926i	0.206976	−	0.154941i	0.697737	+	0.716354i	$0.254190\pi$
$684$	−3.22081	+	8.86816i	−0.123151	+	0.339083i
$685$	−3.02855	−	12.3327i	−0.115715	−	0.471208i
$686$	9.68026	−	12.1191i	0.369594	−	0.462708i
$687$	37.8627	−	20.6746i	1.44455	−	0.788785i
$688$	3.25023	−	6.20442i	0.123914	−	0.236541i
$689$		−	32.6168i		−	1.24260i
$690$	23.1188	−	18.8771i	0.880118	−	0.718641i
$691$			22.7318i			0.864758i	0.901692	+	0.432379i	$0.142326\pi$
$691$			22.7318i			0.864758i	−0.901692	+	0.432379i	$0.857674\pi$
$692$	8.43629	−	7.43843i	0.320700	−	0.282767i
$693$	−2.11153	+	1.15298i	−0.0802104	+	0.0437982i
$694$	−30.0917	−	24.0362i	−1.14227	−	0.912400i
$695$	−20.4602	−	12.3926i	−0.776101	−	0.470077i
$696$	25.1174	+	4.19693i	0.952072	+	0.159084i
$697$	2.20739	−	1.65243i	0.0836109	−	0.0625904i
$698$	1.65771	−	5.05323i	0.0627451	−	0.191268i
$699$	−23.4651	−	15.0801i	−0.887531	−	0.570382i
$700$	4.87035	+	6.63741i	0.184082	+	0.250870i
$701$	−19.5763	−	42.8661i	−0.739387	−	1.61903i	−0.784561	−	0.620052i	$-0.787112\pi$
$701$	−19.5763	−	42.8661i	−0.739387	−	1.61903i	0.0451741	−	0.998979i	$-0.485616\pi$
$702$	19.6204	+	3.45262i	0.740525	+	0.130311i
$703$	−37.8329	+	50.5388i	−1.42689	+	1.90611i
$704$	−23.1597	+	13.4354i	−0.872866	+	0.506365i
$705$	5.49322	+	6.00879i	0.206887	+	0.226304i
$706$	0.771007	+	19.2591i	0.0290172	+	0.724825i
$707$	0.577664	+	8.07679i	0.0217253	+	0.303759i
$708$	−1.40163	−	9.18545i	−0.0526763	−	0.345210i
$709$	8.93217	−	7.73977i	0.335455	−	0.290673i	−0.470802	−	0.882239i	$-0.656035\pi$
$709$	8.93217	−	7.73977i	0.335455	−	0.290673i	0.806257	+	0.591566i	$0.201490\pi$
$710$	47.5493	+	21.9904i	1.78449	+	0.825286i
$711$	−8.32784	−	3.80320i	−0.312318	−	0.142631i
$712$	3.95837	+	0.955947i	0.148346	+	0.0358256i
$713$	39.3222	−	20.2382i	1.47263	−	0.757927i
$714$	1.51015	+	8.16846i	0.0565160	+	0.305697i
$715$	−18.2770	−	17.3294i	−0.683520	−	0.648083i
$716$	−3.48092	−	43.4054i	−0.130088	−	1.62214i
$717$	4.20672	−	58.8177i	0.157103	−	2.19659i
$718$	19.4234	+	0.609858i	0.724875	+	0.0227597i
$719$	−15.8253	+	18.2634i	−0.590186	+	0.681111i	−0.969763	−	0.244049i	$-0.921524\pi$
$719$	−15.8253	+	18.2634i	−0.590186	+	0.681111i	0.379577	+	0.925160i	$0.376070\pi$
$720$	6.74875	+	3.93017i	0.251511	+	0.146469i
$721$	3.12322	−	0.917059i	0.116315	−	0.0341531i
$722$	5.57219	+	13.2901i	0.207375	+	0.494605i
$723$	−18.6276	+	24.8836i	−0.692769	+	0.925431i
$724$	−26.8647	+	27.3321i	−0.998419	+	1.01579i
$725$	5.26797	−	22.2594i	0.195647	−	0.826692i
$726$	−0.530826	+	0.179222i	−0.0197008	+	0.00665155i
$727$	−43.8395	+	9.53669i	−1.62592	+	0.353696i	−0.930893	−	0.365291i	$-0.880969\pi$
$727$	−43.8395	+	9.53669i	−1.62592	+	0.353696i	−0.695023	+	0.718988i	$0.744606\pi$
$728$	−7.82735	+	0.380994i	−0.290101	+	0.0141206i
$729$	15.0779	+	2.16787i	0.558439	+	0.0802915i
$730$	16.8580	+	1.28676i	0.623944	+	0.0476252i
$731$	−3.43212	−	5.34048i	−0.126941	−	0.197525i
$732$	−7.68657	+	2.32917i	−0.284104	+	0.0860886i
$733$	−29.7007	+	16.2178i	−1.09702	+	0.599019i	−0.922641	−	0.385659i	$-0.873974\pi$
$733$	−29.7007	+	16.2178i	−1.09702	+	0.599019i	−0.174380	+	0.984678i	$0.555792\pi$
$734$	−3.88379	+	15.4951i	−0.143353	+	0.571934i
$735$	−26.3173	−	9.02588i	−0.970727	−	0.332925i
$736$	6.78593	−	26.2669i	0.250133	−	0.968212i
$737$	−6.04099	−	6.04099i	−0.222523	−	0.222523i
$738$	−0.482712	−	0.805631i	−0.0177689	−	0.0296557i
$739$	−15.0535	−	4.42010i	−0.553752	−	0.162596i	−0.00712804	−	0.999975i	$-0.502269\pi$
$739$	−15.0535	−	4.42010i	−0.553752	−	0.162596i	−0.546624	+	0.837378i	$0.684087\pi$
$740$	35.5904	+	38.2628i	1.30833	+	1.40657i
$741$	−30.1040	+	19.3467i	−1.10590	+	0.710717i
$742$	2.83761	+	10.9209i	0.104172	+	0.400919i
$743$	−13.1653	+	9.85542i	−0.482988	+	0.361560i	−0.812854	−	0.582467i	$-0.802087\pi$
$743$	−13.1653	+	9.85542i	−0.482988	+	0.361560i	0.329866	+	0.944028i	$0.392996\pi$
$744$	38.0180	+	34.4888i	1.39381	+	1.26442i
$745$	−34.7979	−	4.06159i	−1.27490	−	0.148805i
$746$	−6.03267	−	17.8678i	−0.220872	−	0.654186i
$747$	6.07626	+	2.26633i	0.222319	+	0.0829206i
$748$	0.209285	+	24.2662i	0.00765222	+	0.887262i
$749$	−4.38802	+	0.630902i	−0.160335	+	0.0230527i
$750$	17.4201	−	25.7843i	0.636092	−	0.941509i
$751$	−10.9649	−	37.3432i	−0.400117	−	1.36267i	−0.875638	−	0.482968i	$-0.839559\pi$
$751$	−10.9649	−	37.3432i	−0.400117	−	1.36267i	0.475522	−	0.879704i	$-0.342259\pi$
$752$	7.25703	+	1.44805i	0.264637	+	0.0528050i
$753$	2.09353	+	29.2713i	0.0762923	+	1.06671i
$754$	14.9058	+	15.8722i	0.542837	+	0.578030i
$755$	−4.30896	−	1.83091i	−0.156819	−	0.0666337i
$756$	−6.86978	+	0.550925i	−0.249851	+	0.0200369i
$757$	27.4085	−	10.2229i	0.996180	−	0.371556i	0.202097	−	0.979365i	$-0.435224\pi$
$757$	27.4085	−	10.2229i	0.996180	−	0.371556i	0.794083	+	0.607809i	$0.207952\pi$
$758$	−3.75017	−	2.57989i	−0.136212	−	0.0937059i
$759$	13.8218	−	28.4042i	0.501698	−	1.03101i
$760$	33.3611	−	7.39165i	1.21014	−	0.268123i
$761$	11.8973	−	26.0515i	0.431278	−	0.944367i	−0.561840	−	0.827246i	$-0.689906\pi$
$761$	11.8973	−	26.0515i	0.431278	−	0.944367i	0.993118	−	0.117121i	$-0.0373665\pi$
$762$	16.3274	+	20.0832i	0.591478	+	0.727536i
$763$	0.269968	−	3.77464i	0.00977348	−	0.136651i
$764$	10.3653	−	14.0982i	0.375003	−	0.510057i
$765$	6.12005	−	3.55635i	0.221271	−	0.128580i
$766$	11.1075	−	0.444671i	0.401330	−	0.0160666i
$767$	3.80754	−	6.97299i	0.137482	−	0.251780i
$768$	31.3121	−	3.32832i	1.12988	−	0.120100i
$769$	7.56271	−	1.08735i	0.272718	−	0.0392110i	−0.00459874	−	0.999989i	$-0.501464\pi$
$769$	7.56271	−	1.08735i	0.272718	−	0.0392110i	0.277317	+	0.960778i	$0.410555\pi$
$770$	7.62721	+	4.21224i	0.274866	+	0.151799i
$771$	−31.0698	+	14.1891i	−1.11895	+	0.511009i
$772$	5.96554	−	20.9846i	0.214705	−	0.755252i
$773$	22.9564	−	4.99386i	0.825685	−	0.179617i	0.220181	−	0.975459i	$-0.429335\pi$
$773$	22.9564	−	4.99386i	0.825685	−	0.179617i	0.605504	+	0.795842i	$0.292972\pi$
$774$	−1.92934	+	0.976186i	−0.0693488	+	0.0350883i
$775$	33.1904	−	32.0045i	1.19223	−	1.14964i
$776$	−1.99010	+	11.9102i	−0.0714404	+	0.427550i
$777$	18.4992	+	4.02425i	0.663654	+	0.144369i
$778$	15.6563	−	1.75156i	0.561307	−	0.0627963i
$779$	−3.94276	−	1.15770i	−0.141264	−	0.0414789i
$780$	11.3225	+	27.3712i	0.405410	+	0.980047i
$781$	55.4456			1.98400
$782$	−17.6547	−	17.1146i	−0.631331	−	0.612016i
$783$	13.5404	+	13.5404i	0.483893	+	0.483893i
$784$	−24.1381	+	7.54218i	−0.862075	+	0.269364i
$785$	−18.0743	+	25.5331i	−0.645098	+	0.911314i
$786$	3.33067	+	2.66042i	0.118801	+	0.0948939i
$787$	0.382567	−	1.75863i	0.0136370	−	0.0626884i	−0.969826	−	0.243800i	$-0.921606\pi$
$787$	0.382567	−	1.75863i	0.0136370	−	0.0626884i	0.983463	+	0.181112i	$0.0579695\pi$
$788$	−6.59873	−	14.1255i	−0.235070	−	0.503201i
$789$	−61.1064	−	8.78578i	−2.17545	−	0.312782i
$790$	4.56175	+	32.8417i	0.162300	+	1.16846i
$791$	4.83056	−	7.51650i	0.171755	−	0.267256i
$792$	8.22890	+	0.777159i	0.292401	+	0.0276151i
$793$	−6.43441	−	2.39991i	−0.228493	−	0.0852234i
$794$	18.4709	−	12.9430i	0.655509	−	0.459330i
$795$	35.2528	−	24.0043i	1.25029	−	0.851343i
$796$	−4.11152	+	19.7175i	−0.145729	+	0.698870i
$797$	28.6331	+	15.6348i	1.01424	+	0.553815i	0.898272	−	0.439439i	$-0.144823\pi$
$797$	28.6331	+	15.6348i	1.01424	+	0.553815i	0.115963	+	0.993254i	$0.463005\pi$
$798$	8.39643	−	9.09674i	0.297230	−	0.322021i
$799$	4.39218	−	5.06885i	0.155384	−	0.179323i
$800$	−1.10487	−	28.2627i	−0.0390630	−	0.999237i
$801$	−0.823229	−	0.950057i	−0.0290874	−	0.0335686i
$802$	−2.94809	−	3.62624i	−0.104101	−	0.128047i
$803$	16.7656	−	6.25325i	0.591645	−	0.220672i
$804$	3.59224	+	9.38322i	0.126689	+	0.330921i
$805$	−8.46554	+	2.50528i	−0.298371	+	0.0882996i
$806$	7.97893	+	43.1583i	0.281046	+	1.52019i
$807$	−6.51342	−	17.4631i	−0.229283	−	0.614732i
$808$	13.8850	−	24.1071i	0.488471	−	0.848086i
$809$	2.01116	−	1.74268i	0.0707087	−	0.0612694i	−0.618789	−	0.785557i	$-0.712377\pi$
$809$	2.01116	−	1.74268i	0.0707087	−	0.0612694i	0.689498	+	0.724287i	$0.257831\pi$
$810$	14.1130	+	31.2983i	0.495879	+	1.09971i
$811$	26.7521	+	23.1808i	0.939394	+	0.813989i	0.982725	−	0.185071i	$-0.0592516\pi$
$811$	26.7521	+	23.1808i	0.939394	+	0.813989i	−0.0433313	+	0.999061i	$0.513797\pi$
$812$	−6.37169	−	4.01761i	−0.223602	−	0.140991i
$813$	−26.9223	+	49.3045i	−0.944207	+	1.72919i
$814$	51.1869	+	20.9442i	1.79410	+	0.734093i
$815$	−33.4999	−	6.35914i	−1.17345	−	0.222751i
$816$	11.4062	−	26.1611i	0.399298	−	0.915821i
$817$	−3.30612	+	8.86406i	−0.115667	+	0.310114i
$818$	−15.5896	−	7.71971i	−0.545077	−	0.269913i
$819$	2.03517	+	1.30793i	0.0711147	+	0.0457026i
$820$	−1.52395	+	3.04089i	−0.0532186	+	0.106193i
$821$	−5.36802	+	37.3354i	−0.187345	+	1.30301i	0.651502	+	0.758647i	$0.274139\pi$
$821$	−5.36802	+	37.3354i	−0.187345	+	1.30301i	−0.838847	+	0.544367i	$0.816770\pi$
$822$	3.97505	+	15.2985i	0.138646	+	0.533596i
$823$	26.7347	+	5.81578i	0.931914	+	0.202725i	0.652798	−	0.757532i	$-0.273595\pi$
$823$	26.7347	+	5.81578i	0.931914	+	0.202725i	0.279116	+	0.960257i	$0.409959\pi$
$824$	−10.6558	−	3.39411i	−0.371212	−	0.118240i
$825$	5.27899	−	32.5076i	0.183791	−	1.13177i
$826$	−0.668219	+	2.66598i	−0.0232503	+	0.0927613i
$827$	−17.6761	+	17.6761i	−0.614658	+	0.614658i	−0.944156	−	0.329498i	$-0.893120\pi$
$827$	−17.6761	+	17.6761i	−0.614658	+	0.614658i	0.329498	+	0.944156i	$0.393120\pi$
$828$	−6.41556	+	5.38343i	−0.222956	+	0.187087i
$829$		−	23.9521i		−	0.831890i	−0.909390	−	0.415945i	$-0.863451\pi$
$829$		−	23.9521i		−	0.831890i	0.909390	−	0.415945i	$-0.136549\pi$
$830$	−4.88274	−	22.9740i	−0.169482	−	0.797437i
$831$	−6.90831	+	23.5275i	−0.239647	+	0.816161i
$832$	23.0188	+	13.9653i	0.798032	+	0.484160i
$833$	−4.87212	+	22.3968i	−0.168809	+	0.776002i
$834$	25.6712	+	15.0822i	0.888922	+	0.522252i
$835$	21.0276	−	41.0704i	0.727690	−	1.42130i
$836$	28.7631	−	21.9214i	0.994794	−	0.758168i
$837$	8.20467	+	37.7162i	0.283595	+	1.30366i
$838$	−7.24275	+	14.6264i	−0.250197	+	0.505261i
$839$	6.23157	+	13.6452i	0.215138	+	0.471086i	0.986176	−	0.165703i	$-0.0529894\pi$
$839$	6.23157	+	13.6452i	0.215138	+	0.471086i	−0.771038	+	0.636789i	$0.780262\pi$
$840$	−6.17230	−	8.17953i	−0.212965	−	0.282221i
$841$	−1.14859	−	7.98861i	−0.0396065	−	0.275469i
$842$	−20.7895	−	49.5843i	−0.716452	−	1.70879i
$843$	9.38986	+	5.12725i	0.323404	+	0.176592i
$844$	7.22649	+	31.8929i	0.248746	+	1.09780i
$845$	0.958394	−	3.61735i	0.0329698	−	0.124441i
$846$	−1.56387	−	1.66525i	−0.0537668	−	0.0572526i
$847$	0.165301	+	0.0118225i	0.00567979	+	0.000406227i
$848$	12.9189	−	36.5503i	0.443638	−	1.25514i
$849$	31.6940	+	14.4742i	1.08773	+	0.496752i
$850$	−22.7624	−	11.7918i	−0.780743	−	0.404455i
$851$	−51.5290	+	22.0246i	−1.76639	+	0.754995i
$852$	−59.5459	−	26.5755i	−2.04001	−	0.910461i
$853$	0.908554	+	2.43593i	0.0311083	+	0.0834046i	0.951575	−	0.307416i	$-0.0994642\pi$
$853$	0.908554	+	2.43593i	0.0311083	+	0.0834046i	−0.920467	+	0.390820i	$0.872191\pi$
$854$	2.36319	+	0.243766i	0.0808667	+	0.00834149i
$855$	−9.70850	−	4.12522i	−0.332024	−	0.141080i
$856$	13.7067	+	6.64077i	0.468487	+	0.226977i
$857$	−41.6774	+	2.98082i	−1.42367	+	0.101823i	−0.761809	−	0.647802i	$-0.775688\pi$
$857$	−41.6774	+	2.98082i	−1.42367	+	0.101823i	−0.661863	+	0.749625i	$0.730234\pi$
$858$	23.0363	+	21.2629i	0.786447	+	0.725903i
$859$	−22.5008	+	6.60683i	−0.767717	+	0.225422i	−0.642063	−	0.766652i	$-0.721921\pi$
$859$	−22.5008	+	6.60683i	−0.767717	+	0.225422i	−0.125654	+	0.992074i	$0.540103\pi$
$860$	6.73284	+	3.99905i	0.229588	+	0.136367i
$861$	0.175372	+	1.21974i	0.00597666	+	0.0415686i
$862$	−14.9158	−	2.62474i	−0.508033	−	0.0893989i
$863$	5.19841	−	13.9375i	0.176956	−	0.474437i	−0.817945	−	0.575297i	$-0.804887\pi$
$863$	5.19841	−	13.9375i	0.176956	−	0.474437i	0.994901	+	0.100860i	$0.0321593\pi$
$864$	20.6191	+	11.6403i	0.701476	+	0.396011i
$865$	7.80095	+	9.86264i	0.265240	+	0.335340i
$866$	−33.0953	+	16.7452i	−1.12462	+	0.569025i
$867$	4.54843	+	6.07599i	0.154473	+	0.206351i
$868$	−6.42625	−	13.7563i	−0.218121	−	0.466920i
$869$	18.9722	+	29.5214i	0.643589	+	1.00144i
$870$	−6.18500	+	27.7915i	−0.209691	+	0.942220i
$871$	−2.42032	+	8.24285i	−0.0820094	+	0.279298i
$872$	−8.02637	+	10.2282i	−0.271807	+	0.346369i
$873$	2.63590	−	2.63590i	0.0892115	−	0.0892115i
$874$	−4.65090	+	36.3471i	−0.157319	+	1.22946i
$875$	−7.70100	+	5.04123i	−0.260341	+	0.170425i
$876$	−21.0027	−	1.32019i	−0.709615	−	0.0446051i
$877$	19.8869	+	36.4202i	0.671534	+	1.22982i	0.962029	+	0.272946i	$0.0879982\pi$
$877$	19.8869	+	36.4202i	0.671534	+	1.22982i	−0.290495	+	0.956876i	$0.593820\pi$
$878$	0.00841817	+	0.0752461i	0.000284100	+	0.00253943i
$879$	19.6169	−	12.6070i	0.661662	−	0.425224i
$880$	−13.6173	−	26.6585i	−0.459038	−	0.898657i
$881$	4.30999	−	29.9766i	0.145207	−	1.00994i	−0.778721	−	0.627371i	$-0.784131\pi$
$881$	4.30999	−	29.9766i	0.145207	−	1.00994i	0.923928	−	0.382567i	$-0.124960\pi$
$882$	7.41793	+	2.43344i	0.249775	+	0.0819383i
$883$	5.10322	+	23.4591i	0.171737	+	0.789463i	0.979738	+	0.200282i	$0.0641858\pi$
$883$	5.10322	+	23.4591i	0.171737	+	0.789463i	−0.808001	+	0.589181i	$0.799451\pi$
$884$	21.3158	−	11.8791i	0.716927	−	0.399536i
$885$	10.3387	−	1.01651i	0.347530	−	0.0341695i
$886$	30.6393	−	21.4697i	1.02935	−	0.721288i
$887$	−38.5348	−	28.8468i	−1.29387	−	0.968581i	−0.999919	−	0.0127618i	$-0.995938\pi$
$887$	−38.5348	−	28.8468i	−1.29387	−	0.968581i	−0.293954	−	0.955819i	$-0.594971\pi$
$888$	−44.9336	−	47.0273i	−1.50787	−	1.57813i
$889$	−2.15693	−	7.34583i	−0.0723411	−	0.246371i
$890$	−1.30355	+	4.36222i	−0.0436951	+	0.146222i
$891$	27.4615	+	23.7955i	0.919996	+	0.797181i
$892$	1.52906	+	10.0205i	0.0511966	+	0.335513i
$893$	−9.96981	−	0.713055i	−0.333627	−	0.0238615i
$894$	43.3766	+	4.47435i	1.45073	+	0.149644i
$895$	48.6673	−	1.29515i	1.62677	−	0.0432921i
$896$	−8.92222	−	2.67333i	−0.298070	−	0.0893098i
$897$	−31.7296	+	1.48988i	−1.05942	+	0.0497458i
$898$	−25.8340	+	37.5527i	−0.862092	+	1.25315i
$899$	−17.5250	+	38.3745i	−0.584493	+	1.27986i
$900$	−4.79066	+	7.29996i	−0.159689	+	0.243332i
$901$	−23.0090	−	26.5538i	−0.766541	−	0.884635i
$902$	−0.112974	+	3.59813i	−0.00376163	+	0.119805i
$903$	2.82982	−	0.202393i	0.0941707	−	0.00673522i
$904$	−28.2061	+	12.1132i	−0.938121	+	0.402878i
$905$	−28.9110	−	31.6244i	−0.961033	−	1.05123i
$906$	5.39340	+	2.20682i	0.179184	+	0.0733167i
$907$	−3.97966	−	2.97914i	−0.132143	−	0.0989207i	0.531162	−	0.847270i	$-0.321756\pi$
$907$	−3.97966	−	2.97914i	−0.132143	−	0.0989207i	−0.663304	+	0.748350i	$0.730847\pi$
$908$	0.471481	+	54.6674i	0.0156466	+	1.81420i
$909$	−7.81209	+	3.56766i	−0.259111	+	0.118332i
$910$	0.0418955	−	8.76150i	0.00138882	−	0.290441i
$911$	−12.9686	+	20.1795i	−0.429669	+	0.668578i	−0.986818	−	0.161834i	$-0.948259\pi$
$911$	−12.9686	+	20.1795i	−0.429669	+	0.668578i	0.557149	+	0.830413i	$0.311895\pi$
$912$	−41.3973	+	9.75617i	−1.37080	+	0.323059i
$913$	−14.8968	−	19.8997i	−0.493011	−	0.658585i
$914$	−18.0740	−	10.6187i	−0.597836	−	0.351236i
$915$	−2.14153	−	8.72063i	−0.0707968	−	0.288295i
$916$	38.6575	+	20.6778i	1.27728	+	0.683214i
$917$	−0.604285	−	1.10666i	−0.0199552	−	0.0365453i
$918$	18.4089	−	11.0301i	0.607583	−	0.364047i
$919$	19.0196			0.627398			0.313699	−	0.949522i	$-0.398432\pi$
$919$	19.0196			0.627398			0.313699	+	0.949522i	$0.398432\pi$
$920$	28.9203	+	9.14408i	0.953475	+	0.301471i
$921$	−23.9930			−0.790596
$922$	−42.1924	+	25.2806i	−1.38953	+	0.832571i
$923$	−26.7203	−	48.9345i	−0.879509	−	1.61070i
$924$	−9.56297	−	5.11521i	−0.314599	−	0.168278i
$925$	−44.8427	+	37.4504i	−1.47442	+	1.23136i
$926$	−24.6929	−	14.5074i	−0.811459	−	0.476742i
$927$	2.06892	+	2.76375i	0.0679521	+	0.0907734i
$928$	10.4167	+	23.6902i	0.341946	+	0.777670i
$929$	−4.96973	+	7.73305i	−0.163052	+	0.253713i	−0.913160	−	0.407602i	$-0.866365\pi$
$929$	−4.96973	+	7.73305i	−0.163052	+	0.253713i	0.750108	+	0.661315i	$0.230001\pi$
$930$	−40.7741	+	40.3860i	−1.33704	+	1.32431i
$931$	31.0710	−	14.1896i	1.01831	−	0.465046i
$932$	−0.244463	−	28.3450i	−0.00800764	−	0.928472i
$933$	−42.5397	−	31.8448i	−1.39269	−	1.04255i
$934$	46.8061	+	19.1517i	1.53154	+	0.626661i
$935$	−27.1043	−	1.21492i	−0.886405	−	0.0397320i
$936$	−3.27977	−	7.63710i	−0.107203	−	0.249626i
$937$	−25.3191	+	1.81086i	−0.827139	+	0.0591581i	−0.478487	−	0.878094i	$-0.658815\pi$
$937$	−25.3191	+	1.81086i	−0.827139	+	0.0591581i	−0.348651	+	0.937253i	$0.613360\pi$
$938$	0.0932672	−	2.97048i	0.00304528	−	0.0969895i
$939$	−24.6877	−	28.4911i	−0.805651	−	0.929771i
$940$	−2.04987	+	8.01559i	−0.0668593	+	0.261440i
$941$	−9.86305	+	21.5971i	−0.321526	+	0.704044i	−0.999519	−	0.0310247i	$-0.990123\pi$
$941$	−9.86305	+	21.5971i	−0.321526	+	0.704044i	0.677992	+	0.735069i	$0.262850\pi$
$942$	22.0688	−	32.0796i	0.719042	−	1.04521i
$943$	−2.51533	−	2.64159i	−0.0819104	−	0.0860219i
$944$	7.02860	−	6.30582i	0.228761	−	0.205237i
$945$	−0.204983	−	7.70258i	−0.00666811	−	0.250565i
$946$	8.24422	+	0.850401i	0.268043	+	0.0276489i
$947$	44.6864	+	3.19603i	1.45211	+	0.103857i	0.774971	−	0.631997i	$-0.217764\pi$
$947$	44.6864	+	3.19603i	1.45211	+	0.103857i	0.677141	+	0.735854i	$0.263219\pi$
$948$	−6.22546	−	40.7981i	−0.202194	−	1.32506i
$949$	−13.5986	−	11.7832i	−0.441429	−	0.382500i
$950$	6.26083	+	37.6869i	0.203128	+	1.22273i
$951$	8.54581	+	29.1044i	0.277117	+	0.943774i
$952$	−6.10359	+	5.83185i	−0.197818	+	0.189011i
$953$	−41.7865	−	31.2810i	−1.35360	−	1.01329i	−0.996868	−	0.0790827i	$-0.974801\pi$
$953$	−41.7865	−	31.2810i	−1.35360	−	1.01329i	−0.356729	−	0.934208i	$-0.616108\pi$
$954$	−9.80076	+	6.86761i	−0.317311	+	0.222347i
$955$	15.1211	+	12.4138i	0.489307	+	0.401702i
$956$	52.3459	−	29.1719i	1.69299	−	0.943486i
$957$	6.40524	+	29.4444i	0.207052	+	0.951803i
$958$	13.3898	+	4.39251i	0.432605	+	0.141915i
$959$	0.665387	−	4.62787i	0.0214865	−	0.149442i
$960$	1.84669	+	35.1568i	0.0596016	+	1.13468i
$961$	−45.4576	+	29.2138i	−1.46637	+	0.942381i
$962$	−6.18327	−	55.2694i	−0.199357	−	1.78196i
$963$	−2.25334	−	4.12669i	−0.0726130	−	0.132981i
$964$	−31.5261	−	1.98167i	−1.01539	−	0.0638254i
$965$	23.0719	+	7.91284i	0.742711	+	0.254723i
$966$	10.4943	−	3.25928i	0.337647	−	0.104866i
$967$	21.9571	−	21.9571i	0.706094	−	0.706094i	−0.259618	−	0.965711i	$-0.583597\pi$
$967$	21.9571	−	21.9571i	0.706094	−	0.706094i	0.965711	+	0.259618i	$0.0835966\pi$
$968$	−0.447916	−	0.351494i	−0.0143966	−	0.0112974i
$969$	−10.8603	+	36.9868i	−0.348883	+	1.18819i
$970$	−13.1782	−	2.93280i	−0.423125	−	0.0941666i
$971$	10.7475	+	16.7235i	0.344904	+	0.536682i	0.969761	−	0.244058i	$-0.0784788\pi$
$971$	10.7475	+	16.7235i	0.344904	+	0.536682i	−0.624856	+	0.780740i	$0.714842\pi$
$972$	−7.45753	−	15.9639i	−0.239200	−	0.512043i
$973$	−5.27779	−	7.05031i	−0.169198	−	0.226022i
$974$	−7.75737	+	3.92499i	−0.248562	+	0.125765i
$975$	−31.2342	+	11.0069i	−1.00029	+	0.352504i
$976$	−6.25983	−	5.23790i	−0.200372	−	0.167661i
$977$	21.0519	−	56.4424i	0.673511	−	1.80575i	0.0863793	−	0.996262i	$-0.472470\pi$
$977$	21.0519	−	56.4424i	0.673511	−	1.80575i	0.587132	−	0.809491i	$-0.300257\pi$
$978$	41.7995	+	7.35549i	1.33660	+	0.235203i
$979$	0.685749	+	4.76949i	0.0219166	+	0.152433i
$980$	−6.97946	−	27.3990i	−0.222951	−	0.875228i
$981$	3.85106	−	1.13077i	0.122955	−	0.0361028i
$982$	3.68633	+	3.40254i	0.117636	+	0.108579i
$983$	−47.9517	+	3.42958i	−1.52942	+	0.109387i	−0.810515	−	0.585718i	$-0.800812\pi$
$983$	−47.9517	+	3.42958i	−1.52942	+	0.109387i	−0.718908	+	0.695105i	$0.755358\pi$
$984$	1.84594	−	3.81007i	0.0588463	−	0.121461i
$985$	16.1642	−	6.52386i	0.515035	−	0.207867i
$986$	23.3318	+	2.40670i	0.743035	+	0.0766449i
$987$	1.04749	+	2.80842i	0.0333419	+	0.0893930i
$988$	−33.2087	−	14.8211i	−1.05651	−	0.471522i
$989$	−6.47929	+	5.34236i	−0.206030	+	0.169877i
$990$	−1.35887	+	9.14068i	−0.0431879	+	0.290510i
$991$	29.6323	+	13.5326i	0.941301	+	0.429878i	0.826137	−	0.563469i	$-0.190533\pi$
$991$	29.6323	+	13.5326i	0.941301	+	0.429878i	0.115164	+	0.993347i	$0.463261\pi$
$992$	−8.15307	+	51.5234i	−0.258860	+	1.63587i
$993$	11.4793	+	0.821018i	0.364286	+	0.0260542i
$994$	13.2038	+	14.0599i	0.418801	+	0.445952i
$995$	−21.7680	−	5.76730i	−0.690092	−	0.182836i
$996$	6.46031	+	28.5115i	0.204703	+	0.903421i
$997$	50.5884	+	27.6233i	1.60215	+	0.874840i	0.996889	+	0.0788127i	$0.0251129\pi$
$997$	50.5884	+	27.6233i	1.60215	+	0.874840i	0.605261	+	0.796027i	$0.293069\pi$
$998$	8.99189	+	21.4463i	0.284633	+	0.678871i
$999$	−6.96053	−	48.4115i	−0.220221	−	1.53167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.w.a.167.57	yes	1360
4.3	odd	2	inner	460.2.w.a.167.65	yes	1360
5.3	odd	4	inner	460.2.w.a.443.22	yes	1360
20.3	even	4	inner	460.2.w.a.443.31	yes	1360
23.4	even	11	inner	460.2.w.a.27.31	yes	1360
92.27	odd	22	inner	460.2.w.a.27.22	✓	1360
115.73	odd	44	inner	460.2.w.a.303.65	yes	1360
460.303	even	44	inner	460.2.w.a.303.57	yes	1360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.w.a.27.22	✓	1360	92.27	odd	22	inner
460.2.w.a.27.31	yes	1360	23.4	even	11	inner
460.2.w.a.167.57	yes	1360	1.1	even	1	trivial
460.2.w.a.167.65	yes	1360	4.3	odd	2	inner
460.2.w.a.303.57	yes	1360	460.303	even	44	inner
460.2.w.a.303.65	yes	1360	115.73	odd	44	inner
460.2.w.a.443.22	yes	1360	5.3	odd	4	inner
460.2.w.a.443.31	yes	1360	20.3	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.21312 - 0.726869i) q^{2} +(-0.943178 - 1.72730i) q^{3} +(0.943324 - 1.76356i) q^{4} +(1.91259 + 1.15844i) q^{5} +(-2.39971 - 1.40986i) q^{6} +(0.493361 + 0.659053i) q^{7} +(-0.137510 - 2.82508i) q^{8} +(-0.472063 + 0.734544i) q^{9} +O(q^{10})\)	\(q+(1.21312 - 0.726869i) q^{2} +(-0.943178 - 1.72730i) q^{3} +(0.943324 - 1.76356i) q^{4} +(1.91259 + 1.15844i) q^{5} +(-2.39971 - 1.40986i) q^{6} +(0.493361 + 0.659053i) q^{7} +(-0.137510 - 2.82508i) q^{8} +(-0.472063 + 0.734544i) q^{9} +(3.16224 + 0.0151211i) q^{10} +(3.04439 - 1.39033i) q^{11} +(-3.93592 + 0.0339455i) q^{12} +(-2.69421 - 2.01686i) q^{13} +(1.07755 + 0.440902i) q^{14} +(0.197056 - 4.39624i) q^{15} +(-2.22028 - 3.32721i) q^{16} +(-3.61615 + 0.258632i) q^{17} +(-0.0387521 + 1.23422i) q^{18} +(3.53807 + 4.08315i) q^{19} +(3.84717 - 2.28019i) q^{20} +(0.673056 - 1.47379i) q^{21} +(2.68263 - 3.89950i) q^{22} +(0.904421 + 4.70978i) q^{23} +(-4.75007 + 2.90208i) q^{24} +(2.31604 + 4.43125i) q^{25} +(-4.73439 - 0.488357i) q^{26} +(-4.17504 - 0.298605i) q^{27} +(1.62768 - 0.248371i) q^{28} +(-3.45744 - 2.99589i) q^{29} +(-2.95644 - 5.47641i) q^{30} +(-2.59799 - 8.84794i) q^{31} +(-5.11192 - 2.42246i) q^{32} +(-5.27291 - 3.94725i) q^{33} +(-4.19884 + 2.94222i) q^{34} +(0.180127 + 1.83203i) q^{35} +(0.850104 + 1.52542i) q^{36} +(2.48380 + 11.4178i) q^{37} +(7.26002 + 2.38164i) q^{38} +(-0.942605 + 6.55596i) q^{39} +(3.00968 - 5.56254i) q^{40} +(-0.639835 + 0.411197i) q^{41} +(-0.254751 - 2.27710i) q^{42} +(0.839189 + 1.53686i) q^{43} +(0.419923 - 6.68048i) q^{44} +(-1.75379 + 0.858029i) q^{45} +(4.52056 + 5.05614i) q^{46} +(-1.30816 + 1.30816i) q^{47} +(-3.65298 + 6.97325i) q^{48} +(1.78118 - 6.06615i) q^{49} +(6.03057 + 3.69218i) q^{50} +(3.85741 + 6.00225i) q^{51} +(-6.09835 + 2.84884i) q^{52} +(5.80794 + 7.75850i) q^{53} +(-5.28187 + 2.67246i) q^{54} +(7.43329 + 0.867609i) q^{55} +(1.79404 - 1.48441i) q^{56} +(3.71580 - 9.96245i) q^{57} +(-6.37191 - 1.12127i) q^{58} +(0.335959 + 2.33665i) q^{59} +(-7.56714 - 4.49460i) q^{60} +(1.95789 - 0.574887i) q^{61} +(-9.58296 - 8.84522i) q^{62} +(-0.717000 + 0.0512809i) q^{63} +(-7.96218 + 0.776956i) q^{64} +(-2.81652 - 6.97850i) q^{65} +(-9.26581 - 0.955779i) q^{66} +(-0.892055 - 2.39169i) q^{67} +(-2.95509 + 6.62127i) q^{68} +(7.28218 - 6.00437i) q^{69} +(1.55016 + 2.09154i) q^{70} +(15.0695 + 6.88200i) q^{71} +(2.14006 + 1.23261i) q^{72} +(5.33287 + 0.381414i) q^{73} +(11.3124 + 12.0458i) q^{74} +(5.46967 - 8.17995i) q^{75} +(10.5384 - 2.38786i) q^{76} +(2.41828 + 1.32048i) q^{77} +(3.62183 + 8.63832i) q^{78} +(1.49220 + 10.3784i) q^{79} +(-0.392122 - 8.93567i) q^{80} +(4.51019 + 9.87593i) q^{81} +(-0.477311 + 0.963908i) q^{82} +(-1.57878 - 7.25753i) q^{83} +(-1.96420 - 2.57723i) q^{84} +(-7.21584 - 3.69443i) q^{85} +(2.13513 + 1.25442i) q^{86} +(-1.91382 + 8.79770i) q^{87} +(-4.34642 - 8.40946i) q^{88} +(-0.405618 + 1.38141i) q^{89} +(-1.50388 + 2.31567i) q^{90} -2.77066i q^{91} +(9.15914 + 2.84785i) q^{92} +(-12.8327 + 12.8327i) q^{93} +(-0.636097 + 2.53782i) q^{94} +(2.03681 + 11.9081i) q^{95} +(0.637128 + 11.1146i) q^{96} +(-4.17169 - 0.907496i) q^{97} +(-2.24851 - 8.65366i) q^{98} +(-0.415887 + 2.89256i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more