LMFDB - Embedded newform 93.2.m.a.10.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(7,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 28]))

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

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

chi := DirichletCharacter("93.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.m (of order $15$, degree $8$, 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:	$0.742608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7 x^{15} + 24 x^{14} - 36 x^{13} + 17 x^{12} + 18 x^{11} - 52 x^{10} + 59 x^{9} + 51 x^{8} + \cdots + 1 $ x^16 - 7x^15 + 24x^14 - 36x^13 + 17x^12 + 18x^11 - 52x^10 + 59x^9 + 51x^8 - 59x^7 - 52x^6 - 18x^5 + 17x^4 + 36x^3 + 24x^2 + 7*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			10.2
Root			$-0.205080 + 0.227764i$ of defining polynomial
Character	$\chi$	$=$	93.10
Dual form			93.2.m.a.28.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05697 + 0.767934i) q^{2} +(0.104528 + 0.994522i) q^{3} +(-0.0905704 - 0.278747i) q^{4} +(0.841054 + 1.45675i) q^{5} +(-0.653243 + 1.13145i) q^{6} +(-2.39861 - 0.509841i) q^{7} +(0.925782 - 2.84927i) q^{8} +(-0.978148 + 0.207912i) q^{9} +O(q^{10})$	\(q+(1.05697 + 0.767934i) q^{2} +(0.104528 + 0.994522i) q^{3} +(-0.0905704 - 0.278747i) q^{4} +(0.841054 + 1.45675i) q^{5} +(-0.653243 + 1.13145i) q^{6} +(-2.39861 - 0.509841i) q^{7} +(0.925782 - 2.84927i) q^{8} +(-0.978148 + 0.207912i) q^{9} +(-0.229717 + 2.18561i) q^{10} +(1.19677 - 1.32915i) q^{11} +(0.267753 - 0.119211i) q^{12} +(-0.345193 - 0.153690i) q^{13} +(-2.14374 - 2.38086i) q^{14} +(-1.36085 + 0.988718i) q^{15} +(2.69234 - 1.95610i) q^{16} +(-0.901634 - 1.00137i) q^{17} +(-1.19354 - 0.531396i) q^{18} +(-5.10172 + 2.27143i) q^{19} +(0.329889 - 0.366379i) q^{20} +(0.256325 - 2.43877i) q^{21} +(2.28565 - 0.485831i) q^{22} +(0.948179 - 2.91819i) q^{23} +(2.93043 + 0.622882i) q^{24} +(1.08526 - 1.87972i) q^{25} +(-0.246835 - 0.427531i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.0751268 + 0.714783i) q^{28} +(7.60048 + 5.52207i) q^{29} -2.19765 q^{30} +(-4.95248 + 2.54419i) q^{31} -1.64391 q^{32} +(1.44697 + 1.05128i) q^{33} +(-0.184017 - 1.75081i) q^{34} +(-1.27465 - 3.92298i) q^{35} +(0.146546 + 0.253825i) q^{36} +(-4.70643 + 8.15178i) q^{37} +(-7.13667 - 1.51695i) q^{38} +(0.116765 - 0.359367i) q^{39} +(4.92929 - 1.04775i) q^{40} +(-0.768985 + 7.31640i) q^{41} +(2.14374 - 2.38086i) q^{42} +(5.41897 - 2.41268i) q^{43} +(-0.478889 - 0.213215i) q^{44} +(-1.12555 - 1.25005i) q^{45} +(3.24318 - 2.35631i) q^{46} +(-1.37964 + 1.00237i) q^{47} +(2.22681 + 2.47312i) q^{48} +(-0.901403 - 0.401330i) q^{49} +(2.59059 - 1.15340i) q^{50} +(0.901634 - 1.00137i) q^{51} +(-0.0115763 + 0.110141i) q^{52} +(3.68888 - 0.784095i) q^{53} +(0.403727 - 1.24254i) q^{54} +(2.94279 + 0.625509i) q^{55} +(-3.67327 + 6.36229i) q^{56} +(-2.79226 - 4.83634i) q^{57} +(3.79290 + 11.6733i) q^{58} +(1.39787 + 13.2999i) q^{59} +(0.398855 + 0.289785i) q^{60} +9.06449 q^{61} +(-7.18840 - 1.11404i) q^{62} +2.45220 q^{63} +(-7.12224 - 5.17461i) q^{64} +(-0.0664385 - 0.632120i) q^{65} +(0.722085 + 2.22235i) q^{66} +(-7.32758 - 12.6917i) q^{67} +(-0.197466 + 0.342022i) q^{68} +(3.00132 + 0.637950i) q^{69} +(1.66532 - 5.12532i) q^{70} +(1.65503 - 0.351787i) q^{71} +(-0.313156 + 2.97948i) q^{72} +(8.60076 - 9.55211i) q^{73} +(-11.2346 + 5.00196i) q^{74} +(1.98286 + 0.882828i) q^{75} +(1.09522 + 1.21636i) q^{76} +(-3.54825 + 2.57796i) q^{77} +(0.399387 - 0.290172i) q^{78} +(-3.92002 - 4.35362i) q^{79} +(5.11394 + 2.27687i) q^{80} +(0.913545 - 0.406737i) q^{81} +(-6.43130 + 7.14269i) q^{82} +(1.63403 - 15.5468i) q^{83} +(-0.703015 + 0.149430i) q^{84} +(0.700415 - 2.15566i) q^{85} +(7.58047 + 1.61128i) q^{86} +(-4.69736 + 8.13606i) q^{87} +(-2.67915 - 4.64043i) q^{88} +(0.0964294 + 0.296779i) q^{89} +(-0.229717 - 2.18561i) q^{90} +(0.749627 + 0.544636i) q^{91} -0.899315 q^{92} +(-3.04793 - 4.65941i) q^{93} -2.22799 q^{94} +(-7.59972 - 5.52152i) q^{95} +(-0.171836 - 1.63491i) q^{96} +(-3.34921 - 10.3078i) q^{97} +(-0.644561 - 1.11641i) q^{98} +(-0.894275 + 1.54893i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} + 6 q^{5} - 5 q^{6} - 9 q^{7} + 10 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 + 6 * q^5 - 5 * q^6 - 9 * q^7 + 10 * q^8 + 2 * q^9	\( 16 q - 2 q^{3} + 6 q^{5} - 5 q^{6} - 9 q^{7} + 10 q^{8} + 2 q^{9} - 16 q^{10} + 10 q^{11} - 10 q^{12} + 3 q^{13} - 12 q^{14} - 8 q^{15} + 6 q^{16} + 3 q^{17} - 32 q^{19} - 10 q^{20} - 6 q^{21} - 9 q^{22} - 22 q^{23} + 20 q^{24} + 12 q^{25} + 18 q^{26} + 4 q^{27} + 30 q^{28} + 38 q^{29} - 2 q^{30} - 8 q^{31} + 10 q^{33} - 52 q^{34} + 3 q^{35} - 5 q^{36} - 8 q^{37} + 7 q^{38} + 6 q^{39} + 37 q^{40} - 40 q^{41} + 12 q^{42} + q^{43} + q^{45} - 7 q^{46} - 23 q^{47} + 18 q^{48} + 25 q^{49} - 21 q^{50} - 3 q^{51} - 45 q^{52} + 30 q^{53} - 5 q^{54} + 46 q^{55} - 6 q^{56} - 8 q^{57} + 48 q^{58} - 40 q^{59} + 15 q^{60} + 26 q^{61} + 40 q^{62} - 12 q^{63} + 38 q^{64} + 12 q^{65} + 12 q^{66} - 32 q^{67} + 15 q^{68} - 11 q^{69} + 33 q^{70} + 17 q^{71} + 5 q^{72} + 27 q^{73} - 70 q^{74} + 3 q^{75} - 15 q^{76} - 9 q^{77} - 9 q^{78} + 21 q^{80} + 2 q^{81} - 32 q^{82} - 17 q^{83} - 15 q^{84} - 64 q^{85} + 26 q^{86} - 6 q^{87} - 22 q^{88} - 43 q^{89} - 16 q^{90} - 140 q^{92} - q^{93} + 88 q^{94} - 2 q^{95} - 35 q^{96} + 12 q^{97} - 32 q^{98}+O(q^{100}) \) 16 * q - 2 * q^3 + 6 * q^5 - 5 * q^6 - 9 * q^7 + 10 * q^8 + 2 * q^9 - 16 * q^10 + 10 * q^11 - 10 * q^12 + 3 * q^13 - 12 * q^14 - 8 * q^15 + 6 * q^16 + 3 * q^17 - 32 * q^19 - 10 * q^20 - 6 * q^21 - 9 * q^22 - 22 * q^23 + 20 * q^24 + 12 * q^25 + 18 * q^26 + 4 * q^27 + 30 * q^28 + 38 * q^29 - 2 * q^30 - 8 * q^31 + 10 * q^33 - 52 * q^34 + 3 * q^35 - 5 * q^36 - 8 * q^37 + 7 * q^38 + 6 * q^39 + 37 * q^40 - 40 * q^41 + 12 * q^42 + q^43 + q^45 - 7 * q^46 - 23 * q^47 + 18 * q^48 + 25 * q^49 - 21 * q^50 - 3 * q^51 - 45 * q^52 + 30 * q^53 - 5 * q^54 + 46 * q^55 - 6 * q^56 - 8 * q^57 + 48 * q^58 - 40 * q^59 + 15 * q^60 + 26 * q^61 + 40 * q^62 - 12 * q^63 + 38 * q^64 + 12 * q^65 + 12 * q^66 - 32 * q^67 + 15 * q^68 - 11 * q^69 + 33 * q^70 + 17 * q^71 + 5 * q^72 + 27 * q^73 - 70 * q^74 + 3 * q^75 - 15 * q^76 - 9 * q^77 - 9 * q^78 + 21 * q^80 + 2 * q^81 - 32 * q^82 - 17 * q^83 - 15 * q^84 - 64 * q^85 + 26 * q^86 - 6 * q^87 - 22 * q^88 - 43 * q^89 - 16 * q^90 - 140 * q^92 - q^93 + 88 * q^94 - 2 * q^95 - 35 * q^96 + 12 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$1$	$e\left(\frac{7}{15}\right)$

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 $

$2$	1.05697	+	0.767934i	0.747391	+	0.543011i	0.895017	−	0.446032i	$-0.147163\pi$
$2$	1.05697	+	0.767934i	0.747391	+	0.543011i	−0.147626	+	0.989043i	$0.547163\pi$
$3$	0.104528	+	0.994522i	0.0603495	+	0.574187i
$3$	0.104528	+	0.994522i	0.0603495	+	0.574187i
$4$	−0.0905704	−	0.278747i	−0.0452852	−	0.139374i
$5$	0.841054	+	1.45675i	0.376131	+	0.651477i	0.990496	−	0.137545i	$-0.0439211\pi$
$5$	0.841054	+	1.45675i	0.376131	+	0.651477i	−0.614365	+	0.789022i	$0.710588\pi$
$6$	−0.653243	+	1.13145i	−0.266686	+	0.461913i
$7$	−2.39861	−	0.509841i	−0.906591	−	0.192702i	−0.269057	−	0.963124i	$-0.586712\pi$
$7$	−2.39861	−	0.509841i	−0.906591	−	0.192702i	−0.637534	+	0.770422i	$0.720045\pi$
$8$	0.925782	−	2.84927i	0.327313	−	1.00737i
$9$	−0.978148	+	0.207912i	−0.326049	+	0.0693039i
$10$	−0.229717	+	2.18561i	−0.0726429	+	0.691151i
$11$	1.19677	−	1.32915i	0.360841	−	0.400754i	−0.535201	−	0.844725i	$-0.679764\pi$
$11$	1.19677	−	1.32915i	0.360841	−	0.400754i	0.896041	+	0.443971i	$0.146431\pi$
$12$	0.267753	−	0.119211i	0.0772936	−	0.0344133i
$13$	−0.345193	−	0.153690i	−0.0957393	−	0.0426259i	0.358308	−	0.933603i	$-0.383354\pi$
$13$	−0.345193	−	0.153690i	−0.0957393	−	0.0426259i	−0.454047	+	0.890977i	$0.650020\pi$
$14$	−2.14374	−	2.38086i	−0.572939	−	0.636313i
$15$	−1.36085	+	0.988718i	−0.351371	+	0.255286i
$16$	2.69234	−	1.95610i	0.673085	−	0.489025i
$17$	−0.901634	−	1.00137i	−0.218678	−	0.242867i	0.623817	−	0.781570i	$-0.285581\pi$
$17$	−0.901634	−	1.00137i	−0.218678	−	0.242867i	−0.842495	+	0.538703i	$0.818914\pi$
$18$	−1.19354	−	0.531396i	−0.281319	−	0.125251i
$19$	−5.10172	+	2.27143i	−1.17041	+	0.521102i	−0.897534	−	0.440946i	$-0.854643\pi$
$19$	−5.10172	+	2.27143i	−1.17041	+	0.521102i	−0.272880	+	0.962048i	$0.587976\pi$
$20$	0.329889	−	0.366379i	0.0737655	−	0.0819249i
$21$	0.256325	−	2.43877i	0.0559347	−	0.532183i
$22$	2.28565	−	0.485831i	0.487303	−	0.103579i
$23$	0.948179	−	2.91819i	0.197709	−	0.608486i	−0.802225	−	0.597021i	$-0.796351\pi$
$23$	0.948179	−	2.91819i	0.197709	−	0.608486i	0.999934	−	0.0114642i	$-0.00364925\pi$
$24$	2.93043	+	0.622882i	0.598171	+	0.127145i
$25$	1.08526	−	1.87972i	0.217052	−	0.375944i
$26$	−0.246835	−	0.427531i	−0.0484083	−	0.0838457i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	0.0751268	+	0.714783i	0.0141976	+	0.135081i
$29$	7.60048	+	5.52207i	1.41137	+	1.02542i	0.993121	+	0.117093i	$0.0373575\pi$
$29$	7.60048	+	5.52207i	1.41137	+	1.02542i	0.418253	+	0.908331i	$0.362643\pi$
$30$	−2.19765			−0.401234
$31$	−4.95248	+	2.54419i	−0.889492	+	0.456951i
$31$	−4.95248	+	2.54419i	−0.889492	+	0.456951i
$32$	−1.64391			−0.290606
$33$	1.44697	+	1.05128i	0.251885	+	0.183005i
$34$	−0.184017	−	1.75081i	−0.0315587	−	0.300261i
$35$	−1.27465	−	3.92298i	−0.215456	−	0.663105i
$36$	0.146546	+	0.253825i	0.0244243	+	0.0423042i
$37$	−4.70643	+	8.15178i	−0.773733	+	1.34014i	0.161771	+	0.986828i	$0.448279\pi$
$37$	−4.70643	+	8.15178i	−0.773733	+	1.34014i	−0.935504	+	0.353316i	$0.885054\pi$
$38$	−7.13667	−	1.51695i	−1.15772	−	0.246081i
$39$	0.116765	−	0.359367i	0.0186974	−	0.0575447i
$40$	4.92929	−	1.04775i	0.779390	−	0.165664i
$41$	−0.768985	+	7.31640i	−0.120095	+	1.14263i	0.754000	+	0.656875i	$0.228122\pi$
$41$	−0.768985	+	7.31640i	−0.120095	+	1.14263i	−0.874095	+	0.485755i	$0.838545\pi$
$42$	2.14374	−	2.38086i	0.330786	−	0.367375i
$43$	5.41897	−	2.41268i	0.826385	−	0.367930i	0.0504372	−	0.998727i	$-0.483939\pi$
$43$	5.41897	−	2.41268i	0.826385	−	0.367930i	0.775948	+	0.630797i	$0.217272\pi$
$44$	−0.478889	−	0.213215i	−0.0721953	−	0.0321434i
$45$	−1.12555	−	1.25005i	−0.167787	−	0.186346i
$46$	3.24318	−	2.35631i	0.478180	−	0.347418i
$47$	−1.37964	+	1.00237i	−0.201241	+	0.146210i	−0.683842	−	0.729630i	$-0.739692\pi$
$47$	−1.37964	+	1.00237i	−0.201241	+	0.146210i	0.482601	+	0.875841i	$0.339692\pi$
$48$	2.22681	+	2.47312i	0.321412	+	0.356964i
$49$	−0.901403	−	0.401330i	−0.128772	−	0.0573329i
$50$	2.59059	−	1.15340i	0.366364	−	0.163116i
$51$	0.901634	−	1.00137i	0.126254	−	0.140219i
$52$	−0.0115763	+	0.110141i	−0.00160535	+	0.0152738i
$53$	3.68888	−	0.784095i	0.506706	−	0.107704i	0.0525368	−	0.998619i	$-0.483269\pi$
$53$	3.68888	−	0.784095i	0.506706	−	0.107704i	0.454170	+	0.890915i	$0.349936\pi$
$54$	0.403727	−	1.24254i	0.0549402	−	0.169089i
$55$	2.94279	+	0.625509i	0.396805	+	0.0843436i
$56$	−3.67327	+	6.36229i	−0.490861	+	0.850196i
$57$	−2.79226	−	4.83634i	−0.369844	−	0.640589i
$58$	3.79290	+	11.6733i	0.498032	+	1.53278i
$59$	1.39787	+	13.2999i	0.181988	+	1.73150i	0.580437	+	0.814305i	$0.302882\pi$
$59$	1.39787	+	13.2999i	0.181988	+	1.73150i	−0.398449	+	0.917190i	$0.630452\pi$
$60$	0.398855	+	0.289785i	0.0514920	+	0.0374111i
$61$	9.06449			1.16059			0.580295	−	0.814407i	$-0.302937\pi$
$61$	9.06449			1.16059			0.580295	+	0.814407i	$0.302937\pi$
$62$	−7.18840	−	1.11404i	−0.912927	−	0.141484i
$63$	2.45220			0.308948
$64$	−7.12224	−	5.17461i	−0.890281	−	0.646827i
$65$	−0.0664385	−	0.632120i	−0.00824068	−	0.0784049i
$66$	0.722085	+	2.22235i	0.0888825	+	0.273552i
$67$	−7.32758	−	12.6917i	−0.895206	−	1.55054i	−0.833549	−	0.552446i	$-0.813695\pi$
$67$	−7.32758	−	12.6917i	−0.895206	−	1.55054i	−0.0616576	−	0.998097i	$-0.519639\pi$
$68$	−0.197466	+	0.342022i	−0.0239463	+	0.0414763i
$69$	3.00132	+	0.637950i	0.361316	+	0.0768002i
$70$	1.66532	−	5.12532i	0.199044	−	0.612593i
$71$	1.65503	−	0.351787i	0.196416	−	0.0417495i	−0.108653	−	0.994080i	$-0.534654\pi$
$71$	1.65503	−	0.351787i	0.196416	−	0.0417495i	0.305069	+	0.952330i	$0.401320\pi$
$72$	−0.313156	+	2.97948i	−0.0369058	+	0.351135i
$73$	8.60076	−	9.55211i	1.00664	−	1.11799i	0.0136389	−	0.999907i	$-0.495658\pi$
$73$	8.60076	−	9.55211i	1.00664	−	1.11799i	0.993004	−	0.118083i	$-0.0376749\pi$
$74$	−11.2346	+	5.00196i	−1.30599	+	0.581466i
$75$	1.98286	+	0.882828i	0.228961	+	0.101940i
$76$	1.09522	+	1.21636i	0.125630	+	0.139527i
$77$	−3.54825	+	2.57796i	−0.404361	+	0.293786i
$78$	0.399387	−	0.290172i	0.0452217	−	0.0328555i
$79$	−3.92002	−	4.35362i	−0.441036	−	0.489820i	0.481111	−	0.876660i	$-0.340233\pi$
$79$	−3.92002	−	4.35362i	−0.441036	−	0.489820i	−0.922147	+	0.386839i	$0.873567\pi$
$80$	5.11394	+	2.27687i	0.571756	+	0.254562i
$81$	0.913545	−	0.406737i	0.101505	−	0.0451930i
$82$	−6.43130	+	7.14269i	−0.710219	+	0.788778i
$83$	1.63403	−	15.5468i	0.179359	−	1.70648i	−0.421254	−	0.906943i	$-0.638410\pi$
$83$	1.63403	−	15.5468i	0.179359	−	1.70648i	0.600613	−	0.799540i	$-0.294923\pi$
$84$	−0.703015	+	0.149430i	−0.0767052	+	0.0163042i
$85$	0.700415	−	2.15566i	0.0759707	−	0.233814i
$86$	7.58047	+	1.61128i	0.817423	+	0.173749i
$87$	−4.69736	+	8.13606i	−0.503609	+	0.872277i
$88$	−2.67915	−	4.64043i	−0.285599	−	0.494671i
$89$	0.0964294	+	0.296779i	0.0102215	+	0.0314585i	0.956037	−	0.293245i	$-0.0947353\pi$
$89$	0.0964294	+	0.296779i	0.0102215	+	0.0314585i	−0.945816	+	0.324704i	$0.894735\pi$
$90$	−0.229717	−	2.18561i	−0.0242143	−	0.230384i
$91$	0.749627	+	0.544636i	0.0785823	+	0.0570934i
$92$	−0.899315			−0.0937601
$93$	−3.04793	−	4.65941i	−0.316056	−	0.483158i
$94$	−2.22799			−0.229800
$95$	−7.59972	−	5.52152i	−0.779715	−	0.566496i
$96$	−0.171836	−	1.63491i	−0.0175379	−	0.166862i
$97$	−3.34921	−	10.3078i	−0.340061	−	1.04660i	−0.964175	−	0.265267i	$-0.914540\pi$
$97$	−3.34921	−	10.3078i	−0.340061	−	1.04660i	0.624114	−	0.781333i	$-0.285460\pi$
$98$	−0.644561	−	1.11641i	−0.0651105	−	0.112775i
$99$	−0.894275	+	1.54893i	−0.0898780	+	0.155673i
$100$	−0.622259	−	0.132265i	−0.0622259	−	0.0132265i
$101$	1.61054	−	4.95674i	0.160255	−	0.493214i	−0.838400	−	0.545055i	$-0.816509\pi$
$101$	1.61054	−	4.95674i	0.160255	−	0.493214i	0.998655	+	0.0518407i	$0.0165088\pi$
$102$	1.72198	−	0.366019i	0.170502	−	0.0362413i
$103$	−0.952788	+	9.06517i	−0.0938810	+	0.893218i	0.841662	+	0.540005i	$0.181578\pi$
$103$	−0.952788	+	9.06517i	−0.0938810	+	0.893218i	−0.935543	+	0.353213i	$0.885089\pi$
$104$	−0.757476	+	0.841263i	−0.0742767	+	0.0824926i
$105$	3.76825	−	1.67773i	0.367744	−	0.163730i
$106$	4.50117	+	2.00405i	0.437192	+	0.194650i
$107$	−7.02280	−	7.79961i	−0.678920	−	0.754017i	0.300953	−	0.953639i	$-0.402695\pi$
$107$	−7.02280	−	7.79961i	−0.678920	−	0.754017i	−0.979873	+	0.199622i	$0.936029\pi$
$108$	−0.237116	+	0.172275i	−0.0228165	+	0.0165772i
$109$	1.41903	−	1.03098i	0.135918	−	0.0987504i	−0.517749	−	0.855533i	$-0.673230\pi$
$109$	1.41903	−	1.03098i	0.135918	−	0.0987504i	0.653667	+	0.756782i	$0.273230\pi$
$110$	2.63009	+	2.92101i	0.250769	+	0.278507i
$111$	−8.59908	−	3.82856i	−0.816189	−	0.363391i
$112$	−7.45518	+	3.31926i	−0.704449	+	0.313641i
$113$	−6.48709	+	7.20465i	−0.610254	+	0.677756i	−0.966509	−	0.256633i	$-0.917387\pi$
$113$	−6.48709	+	7.20465i	−0.610254	+	0.677756i	0.356255	+	0.934389i	$0.384054\pi$
$114$	0.762651	−	7.25614i	0.0714288	−	0.679600i
$115$	5.04854	−	1.07310i	0.470779	−	0.100067i
$116$	0.850883	−	2.61875i	0.0790025	−	0.243145i
$117$	0.369603	+	0.0785616i	0.0341699	+	0.00726303i
$118$	−8.73591	+	15.1310i	−0.804206	+	1.39293i
$119$	1.65214	+	2.86158i	0.151451	+	0.262321i
$120$	1.55727	+	4.79277i	0.142158	+	0.437518i
$121$	0.815436	+	7.75836i	0.0741306	+	0.705305i
$122$	9.58090	+	6.96093i	0.867414	+	0.630213i
$123$	−7.35670			−0.663331
$124$	1.15773	+	1.15006i	0.103968	+	0.103279i
$125$	12.0616			1.07882
$126$	2.59190	+	1.88313i	0.230905	+	0.167762i
$127$	1.31560	+	12.5171i	0.116740	+	1.11071i	0.883388	+	0.468642i	$0.155256\pi$
$127$	1.31560	+	12.5171i	0.116740	+	1.11071i	−0.766648	+	0.642067i	$0.778077\pi$
$128$	−2.53824	−	7.81191i	−0.224351	−	0.690482i
$129$	2.96590	+	5.13709i	0.261133	+	0.452296i
$130$	0.415203	−	0.719153i	0.0364157	−	0.0630738i
$131$	9.10842	+	1.93605i	0.795806	+	0.169154i	0.587835	−	0.808981i	$-0.299981\pi$
$131$	9.10842	+	1.93605i	0.795806	+	0.169154i	0.207971	+	0.978135i	$0.433314\pi$
$132$	0.161990	−	0.498553i	0.0140994	−	0.0433935i
$133$	13.3951	−	2.84722i	1.16150	−	0.246885i
$134$	2.00138	−	19.0419i	0.172893	−	1.64497i
$135$	1.12555	−	1.25005i	0.0968719	−	0.107587i
$136$	−3.68787	+	1.64195i	−0.316233	+	0.140796i
$137$	9.42231	+	4.19508i	0.805002	+	0.358410i	0.767631	−	0.640892i	$-0.221435\pi$
$137$	9.42231	+	4.19508i	0.805002	+	0.358410i	0.0373705	+	0.999301i	$0.488102\pi$
$138$	2.68240	+	2.97911i	0.228341	+	0.253599i
$139$	−1.60825	+	1.16846i	−0.136410	+	0.0991075i	−0.653898	−	0.756583i	$-0.726867\pi$
$139$	−1.60825	+	1.16846i	−0.136410	+	0.0991075i	0.517488	+	0.855691i	$0.326867\pi$
$140$	−0.978073	+	0.710612i	−0.0826623	+	0.0600577i
$141$	−1.14109	−	1.26731i	−0.0960971	−	0.106727i
$142$	2.01947	+	0.899124i	0.169470	+	0.0754528i
$143$	−0.617394	+	0.274882i	−0.0516291	+	0.0229868i
$144$	−2.22681	+	2.47312i	−0.185567	+	0.206093i
$145$	−1.65185	+	15.7163i	−0.137179	+	1.30517i
$146$	16.4261	−	3.49148i	1.35944	−	0.288957i
$147$	0.304910	−	0.938415i	0.0251485	−	0.0773992i
$148$	2.69855	+	0.573594i	0.221819	+	0.0471492i
$149$	6.71662	−	11.6335i	0.550247	−	0.953056i	−0.448009	−	0.894029i	$-0.647867\pi$
$149$	6.71662	−	11.6335i	0.550247	−	0.953056i	0.998256	−	0.0590270i	$-0.0187998\pi$
$150$	1.41787	+	2.45583i	0.115769	+	0.200518i
$151$	0.403111	+	1.24065i	0.0328047	+	0.100963i	0.966118	−	0.258100i	$-0.0830964\pi$
$151$	0.403111	+	1.24065i	0.0328047	+	0.100963i	−0.933313	+	0.359063i	$0.883096\pi$
$152$	1.74883	+	16.6390i	0.141849	+	1.34960i
$153$	1.09013	+	0.792024i	0.0881315	+	0.0640313i
$154$	−5.73010			−0.461745
$155$	−7.87155	−	5.07471i	−0.632258	−	0.407611i
$156$	−0.110748			−0.00886693
$157$	0.883983	+	0.642251i	0.0705495	+	0.0512572i	0.622501	−	0.782619i	$-0.286117\pi$
$157$	0.883983	+	0.642251i	0.0705495	+	0.0512572i	−0.551952	+	0.833876i	$0.686117\pi$
$158$	−0.800049	−	7.61196i	−0.0636485	−	0.605575i
$159$	1.16539	+	3.58671i	0.0924217	+	0.284445i
$160$	−1.38262	−	2.39477i	−0.109306	−	0.189323i
$161$	−3.76213	+	6.51620i	−0.296498	+	0.513549i
$162$	1.27794	+	0.271634i	0.100404	+	0.0213416i
$163$	−4.67862	+	14.3993i	−0.366457	+	1.12784i	0.582606	+	0.812755i	$0.302033\pi$
$163$	−4.67862	+	14.3993i	−0.366457	+	1.12784i	−0.949063	+	0.315085i	$0.897967\pi$
$164$	2.10907	−	0.448297i	0.164691	−	0.0350061i
$165$	−0.314477	+	2.99205i	−0.0244820	+	0.232931i
$166$	13.6660	−	15.1777i	1.06069	−	1.17802i
$167$	3.55802	−	1.58413i	0.275328	−	0.122584i	−0.264428	−	0.964405i	$-0.585183\pi$
$167$	3.55802	−	1.58413i	0.275328	−	0.122584i	0.539756	+	0.841822i	$0.318517\pi$
$168$	−6.71140	−	2.98811i	−0.517795	−	0.230537i
$169$	−8.60316	−	9.55478i	−0.661782	−	0.734983i
$170$	2.39572	−	1.74059i	0.183743	−	0.133497i
$171$	4.51797	−	3.28250i	0.345498	−	0.251019i
$172$	−1.16333	−	1.29200i	−0.0887028	−	0.0985144i
$173$	−4.41918	−	1.96755i	−0.335984	−	0.149590i	0.231808	−	0.972761i	$-0.425536\pi$
$173$	−4.41918	−	1.96755i	−0.335984	−	0.149590i	−0.567793	+	0.823172i	$0.692202\pi$
$174$	−11.2129	+	4.99231i	−0.850049	+	0.378466i
$175$	−3.56148	+	3.95542i	−0.269222	+	0.299002i
$176$	0.622168	−	5.91953i	0.0468977	−	0.446201i
$177$	−13.0809	+	2.78043i	−0.983220	+	0.208990i
$178$	−0.125984	+	0.387738i	−0.00944288	+	0.0290622i
$179$	−8.50714	−	1.80825i	−0.635853	−	0.135155i	−0.121304	−	0.992615i	$-0.538708\pi$
$179$	−8.50714	−	1.80825i	−0.635853	−	0.135155i	−0.514550	+	0.857461i	$0.672041\pi$
$180$	−0.246506	+	0.426961i	−0.0183735	+	0.0318238i
$181$	−9.19060	−	15.9186i	−0.683132	−	1.18322i	−0.974020	−	0.226462i	$-0.927284\pi$
$181$	−9.19060	−	15.9186i	−0.683132	−	1.18322i	0.290888	−	0.956757i	$-0.406049\pi$
$182$	0.374089	+	1.15133i	0.0277293	+	0.0853421i
$183$	0.947497	+	9.01483i	0.0700410	+	0.666396i
$184$	−7.43690	−	5.40323i	−0.548256	−	0.398331i
$185$	−15.8335			−1.16410
$186$	0.356548	−	7.26547i	0.0261433	−	0.532730i
$187$	−2.41002			−0.176238
$188$	0.404362	+	0.293786i	0.0294911	+	0.0214266i
$189$	0.256325	+	2.43877i	0.0186449	+	0.177394i
$190$	−3.79251	−	11.6722i	−0.275138	−	0.846787i
$191$	10.0513	+	17.4093i	0.727286	+	1.25970i	0.958026	+	0.286681i	$0.0925519\pi$
$191$	10.0513	+	17.4093i	0.727286	+	1.25970i	−0.230740	+	0.973015i	$0.574115\pi$
$192$	4.40179	−	7.62412i	0.317672	−	0.550224i
$193$	−5.00608	−	1.06408i	−0.360345	−	0.0765938i	0.0241814	−	0.999708i	$-0.492302\pi$
$193$	−5.00608	−	1.06408i	−0.360345	−	0.0765938i	−0.384527	+	0.923114i	$0.625635\pi$
$194$	4.37570	−	13.4670i	0.314157	−	0.966876i
$195$	0.621713	−	0.132149i	0.0445218	−	0.00946339i
$196$	−0.0302292	+	0.287612i	−0.00215923	+	0.0205437i
$197$	−12.5701	+	13.9605i	−0.895582	+	0.994644i	0.104418	+	0.994533i	$0.466702\pi$
$197$	−12.5701	+	13.9605i	−0.895582	+	0.994644i	−1.00000		0.000110627i	$0.999965\pi$
$198$	−2.13470	+	0.950428i	−0.151706	+	0.0675440i
$199$	19.6211	+	8.73586i	1.39090	+	0.619269i	0.959195	−	0.282745i	$-0.0912451\pi$
$199$	19.6211	+	8.73586i	1.39090	+	0.619269i	0.431706	+	0.902014i	$0.357912\pi$
$200$	−4.35111	−	4.83240i	−0.307670	−	0.341702i
$201$	11.8563	−	8.61409i	0.836277	−	0.607591i
$202$	5.50874	−	4.00234i	0.387594	−	0.281603i
$203$	−15.4152	−	17.1204i	−1.08194	−	1.20161i
$204$	−0.360789	−	0.160634i	−0.0252603	−	0.0112466i
$205$	−11.3049	+	5.03327i	−0.789569	+	0.351539i
$206$	−7.96852	+	8.84994i	−0.555193	+	0.616604i
$207$	−0.320732	+	3.05156i	−0.0222924	+	0.212098i
$208$	−1.23001	+	0.261446i	−0.0852857	+	0.0181280i
$209$	−3.08652	+	9.49934i	−0.213499	+	0.657083i
$210$	5.27132	+	1.12045i	0.363756	+	0.0773186i
$211$	12.0638	−	20.8951i	0.830505	−	1.43848i	−0.0671338	−	0.997744i	$-0.521385\pi$
$211$	12.0638	−	20.8951i	0.830505	−	1.43848i	0.897639	−	0.440732i	$-0.145281\pi$
$212$	−0.552667	−	0.957248i	−0.0379574	−	0.0657441i
$213$	0.522858	+	1.60919i	0.0358256	+	0.110260i
$214$	−1.43331	−	13.6370i	−0.0979789	−	0.932207i
$215$	8.07231	+	5.86488i	0.550527	+	0.399981i
$216$	−2.99589			−0.203845
$217$	13.1762	−	3.57756i	0.894461	−	0.242860i
$218$	2.29160			0.155207
$219$	10.3988	+	7.55518i	0.702686	+	0.510531i
$220$	−0.0921707	−	0.876946i	−0.00621415	−	0.0591237i
$221$	0.157338	+	0.484236i	0.0105837	+	0.0325733i
$222$	−6.14889	−	10.6502i	−0.412687	−	0.714794i
$223$	−6.30167	+	10.9148i	−0.421991	+	0.730910i	−0.996134	−	0.0878452i	$-0.972002\pi$
$223$	−6.30167	+	10.9148i	−0.421991	+	0.730910i	0.574143	+	0.818755i	$0.305335\pi$
$224$	3.94312	+	0.838135i	0.263461	+	0.0560003i
$225$	−0.670726	+	2.06428i	−0.0447151	+	0.137619i
$226$	−12.3894	+	2.63344i	−0.824128	+	0.175174i
$227$	0.644675	−	6.13367i	0.0427886	−	0.407106i	−0.952074	−	0.305869i	$-0.901053\pi$
$227$	0.644675	−	6.13367i	0.0427886	−	0.407106i	0.994862	−	0.101238i	$-0.0322802\pi$
$228$	−1.09522	+	1.21636i	−0.0725326	+	0.0805557i
$229$	−19.7833	+	8.80808i	−1.30732	+	0.582055i	−0.937802	−	0.347171i	$-0.887142\pi$
$229$	−19.7833	+	8.80808i	−1.30732	+	0.582055i	−0.369514	+	0.929225i	$0.620476\pi$
$230$	6.16023	+	2.74271i	0.406193	+	0.180849i
$231$	−2.93473	−	3.25935i	−0.193091	−	0.214449i
$232$	22.7702	−	16.5435i	1.49494	−	1.08614i
$233$	3.31629	−	2.40942i	0.217257	−	0.157846i	−0.473834	−	0.880614i	$-0.657130\pi$
$233$	3.31629	−	2.40942i	0.217257	−	0.157846i	0.691091	+	0.722768i	$0.257130\pi$
$234$	0.330330	+	0.366868i	0.0215943	+	0.0239829i
$235$	−2.62055	−	1.16674i	−0.170946	−	0.0761100i
$236$	3.58069	−	1.59423i	0.233083	−	0.103775i
$237$	3.92002	−	4.35362i	0.254632	−	0.282798i
$238$	−0.451248	+	4.29334i	−0.0292501	+	0.278296i
$239$	7.94993	−	1.68981i	0.514238	−	0.109305i	0.0565190	−	0.998402i	$-0.482000\pi$
$239$	7.94993	−	1.68981i	0.514238	−	0.109305i	0.457719	+	0.889097i	$0.348667\pi$
$240$	−1.72985	+	5.32393i	−0.111661	+	0.343658i
$241$	13.1540	+	2.79596i	0.847321	+	0.180104i	0.611058	−	0.791586i	$-0.290744\pi$
$241$	13.1540	+	2.79596i	0.847321	+	0.180104i	0.236263	+	0.971689i	$0.424077\pi$
$242$	−5.09601	+	8.82655i	−0.327584	+	0.567392i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−0.820974	−	2.52670i	−0.0525575	−	0.161755i
$245$	−0.173491	−	1.65066i	−0.0110839	−	0.105457i
$246$	−7.77581	−	5.64946i	−0.495768	−	0.360196i
$247$	2.11017			0.134267
$248$	2.66416	+	16.4663i	0.169174	+	1.04561i
$249$	15.6324			0.990665
$250$	12.7487	+	9.26249i	0.806300	+	0.585811i
$251$	−1.09073	−	10.3776i	−0.0688464	−	0.655030i	−0.973469	−	0.228817i	$-0.926514\pi$
$251$	−1.09073	−	10.3776i	−0.0688464	−	0.655030i	0.904623	−	0.426213i	$-0.140152\pi$
$252$	−0.222097	−	0.683544i	−0.0139908	−	0.0430592i
$253$	−2.74397	−	4.75269i	−0.172512	−	0.298799i
$254$	−8.22172	+	14.2404i	−0.515877	+	0.893525i
$255$	2.21706	+	0.471251i	0.138838	+	0.0295109i
$256$	−2.12473	+	6.53924i	−0.132795	+	0.408702i
$257$	−22.7612	+	4.83804i	−1.41980	+	0.301789i	−0.852934	−	0.522019i	$-0.825179\pi$
$257$	−22.7612	+	4.83804i	−1.41980	+	0.301789i	−0.566870	+	0.823807i	$0.691846\pi$
$258$	−0.810077	+	7.70737i	−0.0504332	+	0.479840i
$259$	15.4450	−	17.1535i	0.959708	−	1.06586i
$260$	−0.170184	+	0.0757709i	−0.0105544	+	0.00469911i
$261$	−8.58250	−	3.82117i	−0.531243	−	0.236525i
$262$	8.14056	+	9.04101i	0.502926	+	0.558556i
$263$	1.87967	−	1.36566i	0.115905	−	0.0842100i	−0.528323	−	0.849044i	$-0.677179\pi$
$263$	1.87967	−	1.36566i	0.115905	−	0.0842100i	0.644228	+	0.764834i	$0.277179\pi$
$264$	4.33496	−	3.14953i	0.266798	−	0.193840i
$265$	4.24477	+	4.71430i	0.260754	+	0.289597i
$266$	16.3447	+	7.27714i	1.00216	+	0.446190i
$267$	−0.285074	+	0.126923i	−0.0174462	+	0.00776756i
$268$	−2.87412	+	3.19204i	−0.175565	+	0.194985i
$269$	−3.20765	+	30.5188i	−0.195574	+	1.86076i	0.253586	+	0.967313i	$0.418390\pi$
$269$	−3.20765	+	30.5188i	−0.195574	+	1.86076i	−0.449160	+	0.893451i	$0.648277\pi$
$270$	2.14963	−	0.456917i	0.130822	−	0.0278071i
$271$	−1.86224	+	5.73139i	−0.113123	+	0.348157i	−0.991551	−	0.129718i	$-0.958593\pi$
$271$	−1.86224	+	5.73139i	−0.113123	+	0.348157i	0.878428	+	0.477875i	$0.158593\pi$
$272$	−4.38627	−	0.932331i	−0.265957	−	0.0565309i
$273$	−0.463295	+	0.802451i	−0.0280399	+	0.0485665i
$274$	6.73755	+	11.6698i	0.407030	+	0.704997i
$275$	−1.19963	−	3.69207i	−0.0723402	−	0.222640i
$276$	−0.0940040	−	0.894388i	−0.00565838	−	0.0538359i
$277$	−1.15762	−	0.841060i	−0.0695546	−	0.0505344i	0.552465	−	0.833536i	$-0.313687\pi$
$277$	−1.15762	−	0.841060i	−0.0695546	−	0.0505344i	−0.622019	+	0.783002i	$0.713687\pi$
$278$	−2.59717			−0.155768
$279$	4.31529	−	3.51828i	0.258350	−	0.210634i
$280$	−12.3577			−0.738512
$281$	−22.2899	−	16.1946i	−1.32970	−	0.966086i	−0.999756	−	0.0220866i	$-0.992969\pi$
$281$	−22.2899	−	16.1946i	−1.32970	−	0.966086i	−0.329947	−	0.943999i	$-0.607031\pi$
$282$	−0.232889	−	2.21579i	−0.0138683	−	0.131948i
$283$	3.37385	+	10.3837i	0.200555	+	0.617244i	0.999867	+	0.0163278i	$0.00519754\pi$
$283$	3.37385	+	10.3837i	0.200555	+	0.617244i	−0.799312	+	0.600916i	$0.794802\pi$
$284$	−0.247956	−	0.429473i	−0.0147135	−	0.0254845i
$285$	4.69688	−	8.13524i	0.278219	−	0.481890i
$286$	−0.863658	−	0.183576i	−0.0510692	−	0.0108551i
$287$	5.57470	−	17.1572i	0.329064	−	1.01276i
$288$	1.60799	−	0.341789i	0.0947518	−	0.0201401i
$289$	1.58719	−	15.1011i	0.0933643	−	0.888302i
$290$	−13.8151	+	15.3432i	−0.811249	+	0.900983i
$291$	9.90126	−	4.40833i	0.580422	−	0.258421i
$292$	−3.44160	−	1.53230i	−0.201404	−	0.0896709i
$293$	−17.1429	−	19.0391i	−1.00150	−	1.11228i	−0.993673	−	0.112309i	$-0.964175\pi$
$293$	−17.1429	−	19.0391i	−1.00150	−	1.11228i	−0.00782701	−	0.999969i	$-0.502491\pi$
$294$	1.04292	−	0.757726i	0.0608244	−	0.0441915i
$295$	−18.1989	+	13.2223i	−1.05958	+	0.769829i
$296$	18.8695	+	20.9567i	1.09676	+	1.21808i
$297$	−1.63392	−	0.727469i	−0.0948097	−	0.0422120i
$298$	16.0330	−	7.13837i	0.928770	−	0.413515i
$299$	−0.775801	+	0.861614i	−0.0448657	+	0.0498285i
$300$	0.0664969	−	0.632676i	0.00383920	−	0.0365275i
$301$	−14.2281	+	3.02428i	−0.820095	+	0.174316i
$302$	−0.526660	+	1.62089i	−0.0303059	+	0.0932719i
$303$	5.09794	+	1.08360i	0.292869	+	0.0622512i
$304$	−9.29241	+	16.0949i	−0.532956	+	0.923107i
$305$	7.62372	+	13.2047i	0.436533	+	0.756097i
$306$	0.544010	+	1.67429i	0.0310990	+	0.0957128i
$307$	−0.863844	−	8.21892i	−0.0493022	−	0.469079i	−0.991122	−	0.132959i	$-0.957552\pi$
$307$	−0.863844	−	8.21892i	−0.0493022	−	0.469079i	0.941819	−	0.336120i	$-0.109115\pi$
$308$	1.03996	+	0.755579i	0.0592575	+	0.0430531i
$309$	−9.11510			−0.518540
$310$	−4.42295	−	11.4087i	−0.251207	−	0.647968i
$311$	−6.92587			−0.392730			−0.196365	−	0.980531i	$-0.562914\pi$
$311$	−6.92587			−0.392730			−0.196365	+	0.980531i	$0.562914\pi$
$312$	−0.915832	−	0.665391i	−0.0518488	−	0.0376703i
$313$	−0.550626	−	5.23886i	−0.0311232	−	0.296118i	−0.999001	−	0.0446953i	$-0.985768\pi$
$313$	−0.550626	−	5.23886i	−0.0311232	−	0.296118i	0.967877	−	0.251423i	$-0.0808984\pi$
$314$	0.441137	+	1.35768i	0.0248948	+	0.0766183i
$315$	2.06243	+	3.57224i	0.116205	+	0.201273i
$316$	−0.858521	+	1.48700i	−0.0482956	+	0.0836504i
$317$	28.8910	+	6.14098i	1.62268	+	0.344912i	0.927471	−	0.373895i	$-0.121978\pi$
$317$	28.8910	+	6.14098i	1.62268	+	0.344912i	0.695210	+	0.718807i	$0.255311\pi$
$318$	−1.52257	+	4.68599i	−0.0853815	+	0.262777i
$319$	16.4357	−	3.49352i	0.920224	−	0.195600i
$320$	1.54792	−	14.7274i	0.0865312	−	0.823289i
$321$	7.02280	−	7.79961i	0.391975	−	0.435332i
$322$	−8.98047	+	3.99836i	−0.500462	+	0.222820i
$323$	6.87441	+	3.06069i	0.382503	+	0.170301i
$324$	−0.196117	−	0.217810i	−0.0108954	−	0.0121005i
$325$	−0.663517	+	0.482073i	−0.0368053	+	0.0267406i
$326$	−16.0029	+	11.6268i	−0.886317	+	0.643947i
$327$	1.17366	+	1.30349i	0.0649038	+	0.0720830i
$328$	20.1345	+	8.96444i	1.11174	+	0.494978i
$329$	3.82028	−	1.70090i	0.210619	−	0.0937735i
$330$	−2.63009	+	2.92101i	−0.144782	+	0.160796i
$331$	−1.14477	+	10.8918i	−0.0629223	+	0.598666i	0.916945	+	0.399014i	$0.130648\pi$
$331$	−1.14477	+	10.8918i	−0.0629223	+	0.598666i	−0.979867	+	0.199652i	$0.936019\pi$
$332$	−4.48162	+	0.952597i	−0.245961	+	0.0522806i
$333$	2.90874	−	8.95217i	0.159398	−	0.490576i
$334$	4.97723	+	1.05794i	0.272342	+	0.0578880i
$335$	12.3258	−	21.3489i	0.673429	−	1.16641i
$336$	−4.08036	−	7.06739i	−0.222602	−	0.385557i
$337$	−3.23598	−	9.95932i	−0.176275	−	0.542519i	0.823414	−	0.567441i	$-0.192066\pi$
$337$	−3.23598	−	9.95932i	−0.176275	−	0.542519i	−0.999689	+	0.0249218i	$0.992066\pi$
$338$	−1.75585	−	16.7058i	−0.0955055	−	0.908674i
$339$	−7.84326	−	5.69846i	−0.425988	−	0.309498i
$340$	−0.664319			−0.0360278
$341$	−2.54538	+	9.62742i	−0.137840	+	0.521354i
$342$	7.29611			0.394528
$343$	15.8446	+	11.5118i	0.855529	+	0.621578i
$344$	−1.85758	−	17.6737i	−0.100154	−	0.952902i
$345$	1.59494	+	4.90872i	0.0858686	+	0.264276i
$346$	−3.16000	−	5.47328i	−0.169883	−	0.294245i
$347$	13.3226	−	23.0753i	0.715192	−	1.23875i	−0.247693	−	0.968838i	$-0.579673\pi$
$347$	13.3226	−	23.0753i	0.715192	−	1.23875i	0.962885	−	0.269911i	$-0.0869941\pi$
$348$	2.69334	+	0.572488i	0.144378	+	0.0306886i
$349$	−5.48864	+	16.8923i	−0.293800	+	0.904224i	0.689822	+	0.723979i	$0.257689\pi$
$349$	−5.48864	+	16.8923i	−0.293800	+	0.904224i	−0.983622	+	0.180245i	$0.942311\pi$
$350$	−6.80187	+	1.44578i	−0.363575	+	0.0772803i
$351$	−0.0394972	+	0.375791i	−0.00210820	+	0.0200582i
$352$	−1.96739	+	2.18501i	−0.104862	+	0.116461i
$353$	−7.83591	+	3.48877i	−0.417064	+	0.185689i	−0.604530	−	0.796582i	$-0.706639\pi$
$353$	−7.83591	+	3.48877i	−0.417064	+	0.185689i	0.187466	+	0.982271i	$0.439972\pi$
$354$	−15.9613	−	7.10643i	−0.848334	−	0.377702i
$355$	1.90443	+	2.11509i	0.101077	+	0.112257i
$356$	0.0739927	−	0.0537588i	0.00392160	−	0.00284921i
$357$	−2.67321	+	1.94220i	−0.141481	+	0.102792i
$358$	−7.60318	−	8.44418i	−0.401840	−	0.446289i
$359$	6.02860	+	2.68411i	0.318177	+	0.141662i	0.559610	−	0.828756i	$-0.310951\pi$
$359$	6.02860	+	2.68411i	0.318177	+	0.141662i	−0.241433	+	0.970417i	$0.577617\pi$
$360$	−4.60374	+	2.04972i	−0.242638	+	0.108029i
$361$	8.15463	−	9.05664i	0.429191	−	0.476665i
$362$	2.51023	−	23.8832i	0.131935	−	1.25527i
$363$	−7.63062	+	1.62194i	−0.400504	+	0.0851297i
$364$	0.0839217	−	0.258284i	0.00439869	−	0.0135378i
$365$	21.1487	+	4.49530i	1.10697	+	0.235295i
$366$	−5.92132	+	10.2560i	−0.309512	+	0.536091i
$367$	−7.54608	−	13.0702i	−0.393902	−	0.682259i	0.599058	−	0.800706i	$-0.295542\pi$
$367$	−7.54608	−	13.0702i	−0.393902	−	0.682259i	−0.992960	+	0.118447i	$0.962209\pi$
$368$	−3.15546	−	9.71150i	−0.164490	−	0.506247i
$369$	−0.768985	−	7.31640i	−0.0400317	−	0.380877i
$370$	−16.7355	−	12.1590i	−0.870036	−	0.632118i
$371$	−9.24796			−0.480130
$372$	−1.02274	+	1.27161i	−0.0530268	+	0.0659297i
$373$	−2.85472			−0.147812			−0.0739059	−	0.997265i	$-0.523546\pi$
$373$	−2.85472			−0.147812			−0.0739059	+	0.997265i	$0.523546\pi$
$374$	−2.54732	−	1.85073i	−0.131719	−	0.0956992i
$375$	1.26078	+	11.9955i	0.0651063	+	0.619445i
$376$	1.57877	+	4.85894i	0.0814186	+	0.250581i
$377$	−1.77495	−	3.07430i	−0.0914144	−	0.158334i
$378$	−1.60188	+	2.77455i	−0.0823921	+	0.142707i
$379$	−3.76951	−	0.801234i	−0.193627	−	0.0411566i	0.110077	−	0.993923i	$-0.464890\pi$
$379$	−3.76951	−	0.801234i	−0.193627	−	0.0411566i	−0.303704	+	0.952766i	$0.598223\pi$
$380$	−0.850797	+	2.61848i	−0.0436450	+	0.134325i
$381$	−12.3110	+	2.61678i	−0.630710	+	0.134062i
$382$	−2.74531	+	26.1199i	−0.140462	+	1.33641i
$383$	−20.1933	+	22.4269i	−1.03183	+	1.14596i	−0.0426738	+	0.999089i	$0.513588\pi$
$383$	−20.1933	+	22.4269i	−1.03183	+	1.14596i	−0.989155	+	0.146873i	$0.953079\pi$
$384$	7.50380	−	3.34091i	0.382927	−	0.170490i
$385$	−6.73971	−	3.00071i	−0.343487	−	0.152930i
$386$	−4.47414	−	4.96903i	−0.227728	−	0.252917i
$387$	−4.79893	+	3.48663i	−0.243943	+	0.177235i
$388$	−2.56993	+	1.86717i	−0.130469	+	0.0947910i
$389$	−8.13475	−	9.03455i	−0.412448	−	0.458070i	0.500746	−	0.865594i	$-0.333059\pi$
$389$	−8.13475	−	9.03455i	−0.412448	−	0.458070i	−0.913194	+	0.407524i	$0.866392\pi$
$390$	0.758613	+	0.337756i	0.0384139	+	0.0171030i
$391$	−3.77709	+	1.68167i	−0.191016	+	0.0850457i
$392$	−1.97800	+	2.19679i	−0.0999041	+	0.110955i
$393$	−0.973359	+	9.26089i	−0.0490995	+	0.467150i
$394$	−24.0069	+	5.10283i	−1.20945	+	0.257077i
$395$	3.04518	−	9.37210i	0.153220	−	0.471561i
$396$	0.512754	+	0.108989i	0.0257669	+	0.00547692i
$397$	10.2110	−	17.6860i	0.512475	−	0.887633i	−0.487420	−	0.873168i	$-0.662062\pi$
$397$	10.2110	−	17.6860i	0.512475	−	0.887633i	0.999895	−	0.0144657i	$-0.00460472\pi$
$398$	14.0303	+	24.3012i	0.703277	+	1.21811i
$399$	4.23180	+	13.0241i	0.211855	+	0.652022i
$400$	−0.755039	−	7.18372i	−0.0377520	−	0.359186i
$401$	5.48343	+	3.98395i	0.273830	+	0.198949i	0.716222	−	0.697873i	$-0.245870\pi$
$401$	5.48343	+	3.98395i	0.273830	+	0.198949i	−0.442392	+	0.896822i	$0.645870\pi$
$402$	19.1468			0.954954
$403$	2.10058	−	0.117091i	0.104637	−	0.00583273i
$404$	−1.52754			−0.0759982
$405$	1.36085	+	0.988718i	0.0676213	+	0.0491298i
$406$	−3.14615	−	29.9336i	−0.156141	−	1.48558i
$407$	5.20242	+	16.0114i	0.257874	+	0.793655i
$408$	−2.01844	−	3.49604i	−0.0999277	−	0.173080i
$409$	10.1216	−	17.5312i	0.500482	−	0.866860i	−0.499518	−	0.866303i	$-0.666490\pi$
$409$	10.1216	−	17.5312i	0.500482	−	0.866860i	1.00000		0.000556383i	$-0.000177102\pi$
$410$	−15.8142	−	3.36140i	−0.781006	−	0.166008i
$411$	−3.18720	+	9.80920i	−0.157213	+	0.483852i
$412$	2.61318	−	0.555449i	0.128742	−	0.0273650i
$413$	3.42787	−	32.6140i	0.168674	−	1.60483i
$414$	−2.68240	+	2.97911i	−0.131833	+	0.146415i
$415$	24.0221	−	10.6953i	1.17920	−	0.525012i
$416$	0.567467	+	0.252653i	0.0278224	+	0.0123873i
$417$	−1.33017	−	1.47730i	−0.0651386	−	0.0723437i
$418$	−10.5572	+	7.67027i	−0.516371	+	0.375165i
$419$	14.1244	−	10.2619i	0.690020	−	0.501329i	−0.186647	−	0.982427i	$-0.559762\pi$
$419$	14.1244	−	10.2619i	0.690020	−	0.501329i	0.876667	+	0.481098i	$0.159762\pi$
$420$	−0.808955	−	0.898436i	−0.0394730	−	0.0438392i
$421$	−15.6205	−	6.95467i	−0.761294	−	0.338950i	−0.0109001	−	0.999941i	$-0.503470\pi$
$421$	−15.6205	−	6.95467i	−0.761294	−	0.338950i	−0.750394	+	0.660990i	$0.770136\pi$
$422$	28.7971	−	12.8213i	1.40182	−	0.624131i
$423$	1.14109	−	1.26731i	0.0554817	−	0.0616186i
$424$	1.18100	−	11.2365i	0.0573546	−	0.545692i
$425$	−2.86079	+	0.608081i	−0.138769	+	0.0294962i
$426$	−0.683107	+	2.10239i	−0.0330966	+	0.101861i
$427$	−21.7422	−	4.62145i	−1.05218	−	0.223648i
$428$	−1.53806	+	2.66400i	−0.0743450	+	0.128769i
$429$	−0.337911	−	0.585279i	−0.0163145	−	0.0282576i
$430$	4.02835	+	12.3980i	0.194265	+	0.597885i
$431$	2.45226	+	23.3317i	0.118121	+	1.12385i	0.879619	+	0.475680i	$0.157798\pi$
$431$	2.45226	+	23.3317i	0.118121	+	1.12385i	−0.761497	+	0.648168i	$0.775536\pi$
$432$	−2.69234	−	1.95610i	−0.129535	−	0.0941128i
$433$	−4.19606			−0.201650			−0.100825	−	0.994904i	$-0.532148\pi$
$433$	−4.19606			−0.201650			−0.100825	+	0.994904i	$0.532148\pi$
$434$	16.6742	+	6.33710i	0.800388	+	0.304191i
$435$	−15.8029			−0.757692
$436$	−0.415906	−	0.302173i	−0.0199183	−	0.0144715i
$437$	1.79114	+	17.0415i	0.0856817	+	0.815207i
$438$	5.18935	+	15.9712i	0.247957	+	0.763133i
$439$	4.50050	+	7.79509i	0.214797	+	0.372039i	0.953210	−	0.302310i	$-0.0977577\pi$
$439$	4.50050	+	7.79509i	0.214797	+	0.372039i	−0.738413	+	0.674349i	$0.764424\pi$
$440$	4.50662	−	7.80570i	0.214845	−	0.372122i
$441$	0.965146	+	0.205148i	0.0459593	+	0.00976896i
$442$	−0.205560	+	0.632648i	−0.00977749	+	0.0300920i
$443$	32.0535	−	6.81317i	1.52291	−	0.323704i	0.630949	−	0.775824i	$-0.282666\pi$
$443$	32.0535	−	6.81317i	1.52291	−	0.323704i	0.891957	+	0.452120i	$0.149332\pi$
$444$	−0.288377	+	2.74372i	−0.0136858	+	0.130211i
$445$	−0.351230	+	0.390081i	−0.0166499	+	0.0184916i
$446$	−15.0425	+	6.69736i	−0.712284	+	0.317129i
$447$	12.2719	+	5.46379i	0.580440	+	0.258428i
$448$	14.4453	+	16.0431i	0.682476	+	0.757966i
$449$	−19.4430	+	14.1262i	−0.917573	+	0.666656i	−0.942919	−	0.333023i	$-0.891931\pi$
$449$	−19.4430	+	14.1262i	−0.917573	+	0.666656i	0.0253458	+	0.999679i	$0.491931\pi$
$450$	−2.29417	+	1.66681i	−0.108148	+	0.0785743i
$451$	8.80430	+	9.77817i	0.414578	+	0.460436i
$452$	2.59581	+	1.15573i	0.122097	+	0.0543610i
$453$	−1.19172	+	0.530586i	−0.0559917	+	0.0249291i
$454$	5.39166	−	5.98804i	0.253043	−	0.281033i
$455$	−0.162921	+	1.55009i	−0.00763784	+	0.0726692i
$456$	−16.3650	+	3.47850i	−0.766363	+	0.162896i
$457$	−11.1697	+	34.3769i	−0.522498	+	1.60808i	0.246713	+	0.969089i	$0.420650\pi$
$457$	−11.1697	+	34.3769i	−0.522498	+	1.60808i	−0.769211	+	0.638995i	$0.779350\pi$
$458$	−27.6744	−	5.88237i	−1.29314	−	0.274865i
$459$	−0.673735	+	1.16694i	−0.0314473	+	0.0544683i
$460$	−0.756372	−	1.31007i	−0.0352660	−	0.0610825i
$461$	−4.59745	−	14.1495i	−0.214125	−	0.659008i	−0.999215	−	0.0396262i	$-0.987383\pi$
$461$	−4.59745	−	14.1495i	−0.214125	−	0.659008i	0.785090	−	0.619382i	$-0.212617\pi$
$462$	−0.598958	−	5.69871i	−0.0278661	−	0.265128i
$463$	−20.2090	−	14.6827i	−0.939193	−	0.682364i	0.00903297	−	0.999959i	$-0.497125\pi$
$463$	−20.2090	−	14.6827i	−0.939193	−	0.682364i	−0.948226	+	0.317595i	$0.897125\pi$
$464$	31.2648			1.45143
$465$	4.22411	−	8.35888i	0.195889	−	0.387634i
$466$	5.35549			0.248088
$467$	−0.293080	−	0.212935i	−0.0135621	−	0.00985345i	0.580984	−	0.813915i	$-0.302668\pi$
$467$	−0.293080	−	0.212935i	−0.0135621	−	0.00985345i	−0.594546	+	0.804062i	$0.702668\pi$
$468$	−0.0115763	−	0.110141i	−0.000535115	−	0.00509128i
$469$	11.1053	+	34.1785i	0.512794	+	1.57822i
$470$	−1.87386	−	3.24562i	−0.0864348	−	0.149709i
$471$	−0.546331	+	0.946274i	−0.0251736	+	0.0436020i
$472$	39.1890	+	8.32988i	1.80382	+	0.383414i
$473$	3.27846	−	10.0901i	0.150744	−	0.463942i
$474$	7.48663	−	1.59133i	0.343872	−	0.0730923i
$475$	−1.26702	+	12.0549i	−0.0581349	+	0.553116i
$476$	0.648023	−	0.719702i	0.0297021	−	0.0329875i
$477$	−3.44525	+	1.53392i	−0.157747	+	0.0702335i
$478$	9.70050	+	4.31894i	0.443690	+	0.197544i
$479$	14.6720	+	16.2949i	0.670379	+	0.744532i	0.978371	−	0.206857i	$-0.0663236\pi$
$479$	14.6720	+	16.2949i	0.670379	+	0.744532i	−0.307992	+	0.951389i	$0.599657\pi$
$480$	2.23713	−	1.62537i	0.102110	−	0.0741875i
$481$	2.87747	−	2.09061i	0.131201	−	0.0953234i
$482$	11.7562	+	13.0566i	0.535481	+	0.594712i
$483$	−6.87376	−	3.06039i	−0.312767	−	0.139253i
$484$	2.08876	−	0.929978i	0.0949438	−	0.0422717i
$485$	12.1990	−	13.5484i	0.553929	−	0.615200i
$486$	−0.136565	+	1.29933i	−0.00619472	+	0.0589388i
$487$	14.2486	−	3.02863i	0.645666	−	0.137241i	0.126572	−	0.991957i	$-0.459603\pi$
$487$	14.2486	−	3.02863i	0.645666	−	0.137241i	0.519094	+	0.854717i	$0.326269\pi$
$488$	8.39175	−	25.8271i	0.379876	−	1.16914i
$489$	−14.8095	−	3.14785i	−0.669707	−	0.142351i
$490$	1.08422	−	1.87792i	0.0489801	−	0.0848360i
$491$	14.3897	+	24.9236i	0.649397	+	1.12479i	0.983267	+	0.182169i	$0.0583119\pi$
$491$	14.3897	+	24.9236i	0.649397	+	1.12479i	−0.333870	+	0.942619i	$0.608355\pi$
$492$	0.666299	+	2.05066i	0.0300391	+	0.0924508i
$493$	−1.32324	−	12.5898i	−0.0595956	−	0.567014i
$494$	2.23039	+	1.62047i	0.100350	+	0.0729085i
$495$	−3.00853			−0.135223
$496$	−8.35707	+	16.5374i	−0.375243	+	0.742550i
$497$	−4.14913			−0.186114
$498$	16.5230	+	12.0047i	0.740414	+	0.537942i
$499$	1.91786	+	18.2472i	0.0858553	+	0.816859i	0.949713	+	0.313123i	$0.101375\pi$
$499$	1.91786	+	18.2472i	0.0858553	+	0.816859i	−0.863857	+	0.503736i	$0.831958\pi$
$500$	−1.09242	−	3.36213i	−0.0488546	−	0.150359i
$501$	1.94737	+	3.37294i	0.0870020	+	0.150692i
$502$	6.81645	−	11.8064i	0.304233	−	0.526947i
$503$	−37.0163	−	7.86806i	−1.65048	−	0.350820i	−0.713620	−	0.700533i	$-0.752946\pi$
$503$	−37.0163	−	7.86806i	−1.65048	−	0.350820i	−0.936857	+	0.349713i	$0.886279\pi$
$504$	2.27020	−	6.98697i	0.101123	−	0.311224i
$505$	8.57527	−	1.82273i	0.381595	−	0.0811105i
$506$	0.749460	−	7.13064i	0.0333176	−	0.316995i
$507$	8.60316	−	9.55478i	0.382080	−	0.424343i
$508$	3.36994	−	1.50039i	0.149517	−	0.0665692i
$509$	−9.07852	−	4.04202i	−0.402398	−	0.179159i	0.195550	−	0.980694i	$-0.437351\pi$
$509$	−9.07852	−	4.04202i	−0.402398	−	0.179159i	−0.597949	+	0.801534i	$0.704017\pi$
$510$	1.98148	+	2.20065i	0.0877413	+	0.0974466i
$511$	−25.5000	+	18.5268i	−1.12805	+	0.819578i
$512$	−20.5579	+	14.9362i	−0.908539	+	0.660092i
$513$	3.73678	+	4.15011i	0.164983	+	0.183232i
$514$	−27.7732	−	12.3654i	−1.22502	−	0.545415i
$515$	−14.0070	+	6.23632i	−0.617223	+	0.274805i
$516$	1.16333	−	1.29200i	0.0512126	−	0.0568773i
$517$	−0.318819	+	3.03336i	−0.0140216	+	0.133407i
$518$	29.4977	−	6.26992i	1.29605	−	0.275485i
$519$	1.49484	−	4.60064i	0.0656161	−	0.201946i
$520$	−1.86259	−	0.395905i	−0.0816798	−	0.0173616i
$521$	13.2848	−	23.0099i	0.582016	−	1.00808i	−0.413225	−	0.910629i	$-0.635598\pi$
$521$	13.2848	−	23.0099i	0.582016	−	1.00808i	0.995240	−	0.0974514i	$-0.0310690\pi$
$522$	−6.13703	−	10.6297i	−0.268611	−	0.465247i
$523$	−3.90666	−	12.0235i	−0.170826	−	0.525749i	0.828592	−	0.559853i	$-0.189142\pi$
$523$	−3.90666	−	12.0235i	−0.170826	−	0.525749i	−0.999418	+	0.0341038i	$0.989142\pi$
$524$	−0.285284	−	2.71429i	−0.0124627	−	0.118574i
$525$	−4.30603	−	3.12851i	−0.187930	−	0.136539i
$526$	3.03549			0.132353
$527$	7.01300	+	2.66532i	0.305491	+	0.116103i
$528$	5.95214			0.259034
$529$	10.9906	+	7.98512i	0.477851	+	0.347179i
$530$	0.866330	+	8.24258i	0.0376310	+	0.358035i
$531$	−4.13252	−	12.7186i	−0.179336	−	0.551940i
$532$	−2.00686	−	3.47598i	−0.0870082	−	0.150703i
$533$	1.38990	−	2.40738i	0.0602034	−	0.104275i
$534$	−0.398783	−	0.0847640i	−0.0172570	−	0.00366809i
$535$	5.45551	−	16.7903i	0.235862	−	0.725910i
$536$	−42.9459	+	9.12843i	−1.85498	+	0.394288i
$537$	0.909104	−	8.64955i	0.0392307	−	0.373256i
$538$	−26.8268	+	29.7942i	−1.15659	+	1.28452i
$539$	−1.61220	+	0.717799i	−0.0694425	+	0.0309178i
$540$	−0.450389	−	0.200526i	−0.0193817	−	0.00862927i
$541$	−2.01227	−	2.23485i	−0.0865142	−	0.0960837i	0.698333	−	0.715773i	$-0.253925\pi$
$541$	−2.01227	−	2.23485i	−0.0865142	−	0.0960837i	−0.784847	+	0.619689i	$0.787259\pi$
$542$	−6.36966	+	4.62783i	−0.273600	+	0.198782i
$543$	14.8707	−	10.8042i	0.638163	−	0.463652i
$544$	1.48221	+	1.64616i	0.0635492	+	0.0705785i
$545$	2.69536	+	1.20005i	0.115457	+	0.0514046i
$546$	−1.10592	+	0.492387i	−0.0473289	+	0.0210722i
$547$	10.9878	−	12.2032i	0.469806	−	0.521772i	−0.460944	−	0.887429i	$-0.652489\pi$
$547$	10.9878	−	12.2032i	0.469806	−	0.521772i	0.930750	+	0.365657i	$0.119156\pi$
$548$	0.315984	−	3.00639i	0.0134982	−	0.128427i
$549$	−8.86641	+	1.88461i	−0.378409	+	0.0804333i
$550$	1.56730	−	4.82364i	0.0668298	−	0.205681i
$551$	−51.3185	−	10.9081i	−2.18624	−	0.464700i
$552$	4.59626	−	7.96095i	0.195630	−	0.338841i
$553$	7.18295	+	12.4412i	0.305450	+	0.529055i
$554$	−0.577691	−	1.77795i	−0.0245437	−	0.0755379i
$555$	−1.65505	−	15.7467i	−0.0702528	−	0.668411i
$556$	0.471365	+	0.342466i	0.0199903	+	0.0145238i
$557$	29.2708			1.24024			0.620122	−	0.784505i	$-0.287083\pi$
$557$	29.2708			1.24024			0.620122	+	0.784505i	$0.287083\pi$
$558$	7.26294	−	0.404854i	0.307465	−	0.0171388i
$559$	−2.24139			−0.0948009
$560$	−11.1055	−	8.06864i	−0.469294	−	0.340962i
$561$	−0.251916	−	2.39682i	−0.0106359	−	0.101194i
$562$	−11.1234	−	34.2343i	−0.469212	−	1.44409i
$563$	7.03598	+	12.1867i	0.296531	+	0.513607i	0.975340	−	0.220708i	$-0.0708368\pi$
$563$	7.03598	+	12.1867i	0.296531	+	0.513607i	−0.678809	+	0.734315i	$0.737503\pi$
$564$	−0.249909	+	0.432856i	−0.0105231	+	0.0182265i
$565$	−15.9513	−	3.39056i	−0.671078	−	0.142642i
$566$	−4.40790	+	13.5661i	−0.185278	+	0.570226i
$567$	−2.39861	+	0.509841i	−0.100732	+	0.0214113i
$568$	0.529862	−	5.04130i	0.0222325	−	0.211528i
$569$	−10.4041	+	11.5549i	−0.436162	+	0.484407i	−0.920649	−	0.390391i	$-0.872340\pi$
$569$	−10.4041	+	11.5549i	−0.436162	+	0.484407i	0.484487	+	0.874799i	$0.339006\pi$
$570$	11.2118	−	4.99181i	0.469610	−	0.209084i
$571$	−42.2099	−	18.7931i	−1.76643	−	0.786465i	−0.987152	−	0.159785i	$-0.948920\pi$
$571$	−42.2099	−	18.7931i	−1.76643	−	0.786465i	−0.779277	−	0.626680i	$-0.784413\pi$
$572$	0.132540	+	0.147201i	0.00554178	+	0.00615477i
$573$	−16.2633	+	11.8160i	−0.679410	+	0.493621i
$574$	19.0679	−	13.8536i	0.795877	−	0.578239i
$575$	−4.45637	−	4.94930i	−0.185844	−	0.206400i
$576$	8.04247	+	3.58074i	0.335103	+	0.149197i
$577$	−8.01717	+	3.56947i	−0.333759	+	0.148599i	−0.566772	−	0.823874i	$-0.691808\pi$
$577$	−8.01717	+	3.56947i	−0.333759	+	0.148599i	0.233013	+	0.972474i	$0.425141\pi$
$578$	13.2743	−	14.7426i	0.552138	−	0.613211i
$579$	0.534968	−	5.08988i	0.0222325	−	0.211528i
$580$	4.53049	−	0.962986i	0.188118	−	0.0399858i
$581$	−11.8458	+	36.4577i	−0.491447	+	1.51252i
$582$	13.8506	+	2.94404i	0.574127	+	0.122035i
$583$	3.37257	−	5.84146i	0.139678	−	0.241929i
$584$	−19.2541	−	33.3490i	−0.796739	−	1.37999i
$585$	0.196412	+	0.604494i	0.00812063	+	0.0249927i
$586$	−3.49876	−	33.2884i	−0.144532	−	1.37513i
$587$	29.4088	+	21.3667i	1.21383	+	0.881898i	0.995573	−	0.0939930i	$-0.0299631\pi$
$587$	29.4088	+	21.3667i	1.21383	+	0.881898i	0.218256	+	0.975891i	$0.429963\pi$
$588$	−0.289196			−0.0119263
$589$	19.4872	−	24.2290i	0.802956	−	0.998337i
$590$	−29.3895			−1.20995
$591$	−15.1979	−	11.0420i	−0.625160	−	0.454205i
$592$	3.27438	+	31.1536i	0.134576	+	1.28041i
$593$	−6.37621	−	19.6240i	−0.261839	−	0.805859i	−0.992405	−	0.123016i	$-0.960743\pi$
$593$	−6.37621	−	19.6240i	−0.261839	−	0.805859i	0.730565	−	0.682843i	$-0.239257\pi$
$594$	−1.16836	−	2.02366i	−0.0479383	−	0.0830316i
$595$	−2.77907	+	4.81349i	−0.113931	+	0.197334i
$596$	−3.85114	−	0.818585i	−0.157749	−	0.0335305i
$597$	−6.63705	+	20.4267i	−0.271636	+	0.836011i
$598$	−1.48166	+	0.314937i	−0.0605896	+	0.0128787i
$599$	−3.03713	+	28.8964i	−0.124094	+	1.18067i	0.738313	+	0.674458i	$0.235623\pi$
$599$	−3.03713	+	28.8964i	−0.124094	+	1.18067i	−0.862407	+	0.506215i	$0.831044\pi$
$600$	4.35111	−	4.83240i	0.177633	−	0.197282i
$601$	11.9517	−	5.32123i	0.487519	−	0.217057i	−0.148231	−	0.988953i	$-0.547358\pi$
$601$	11.9517	−	5.32123i	0.487519	−	0.217057i	0.635750	+	0.771895i	$0.280691\pi$
$602$	−17.3611	−	7.72967i	−0.707587	−	0.315038i
$603$	9.80622	+	10.8909i	0.399340	+	0.443512i
$604$	0.309317	−	0.224732i	0.0125859	−	0.00914422i
$605$	−10.6161	+	7.71308i	−0.431607	+	0.313581i
$606$	4.55623	+	5.06021i	0.185084	+	0.205557i
$607$	−16.4193	−	7.31036i	−0.666440	−	0.296718i	0.0454937	−	0.998965i	$-0.485514\pi$
$607$	−16.4193	−	7.31036i	−0.666440	−	0.296718i	−0.711934	+	0.702246i	$0.752181\pi$
$608$	8.38678	−	3.73404i	0.340129	−	0.151435i
$609$	15.4152	−	17.1204i	0.624657	−	0.693752i
$610$	−2.08227	+	19.8115i	−0.0843086	+	0.802143i
$611$	0.630296	−	0.133974i	0.0254991	−	0.00541999i
$612$	0.122041	−	0.375604i	0.00493321	−	0.0151829i
$613$	5.24609	+	1.11509i	0.211887	+	0.0450381i	0.312632	−	0.949874i	$-0.398789\pi$
$613$	5.24609	+	1.11509i	0.211887	+	0.0450381i	−0.100745	+	0.994912i	$0.532123\pi$
$614$	5.39853	−	9.35053i	0.217867	−	0.377357i
$615$	−6.18738	−	10.7169i	−0.249499	−	0.432145i
$616$	4.06037	+	12.4965i	0.163597	+	0.503500i
$617$	−1.67378	−	15.9250i	−0.0673839	−	0.641115i	−0.975136	−	0.221608i	$-0.928870\pi$
$617$	−1.67378	−	15.9250i	−0.0673839	−	0.641115i	0.907752	−	0.419507i	$-0.137797\pi$
$618$	−9.63439	−	6.99980i	−0.387552	−	0.281573i
$619$	18.9305			0.760882			0.380441	−	0.924805i	$-0.375772\pi$
$619$	18.9305			0.760882			0.380441	+	0.924805i	$0.375772\pi$
$620$	−0.701632	+	2.65379i	−0.0281782	+	0.106579i
$621$	−3.06837			−0.123129
$622$	−7.32044	−	5.31861i	−0.293523	−	0.213257i
$623$	−0.0799867	−	0.761023i	−0.00320460	−	0.0304897i
$624$	−0.388585	−	1.19594i	−0.0155558	−	0.0478760i
$625$	4.71814	+	8.17206i	0.188726	+	0.326883i
$626$	3.44110	−	5.96016i	0.137534	−	0.238216i
$627$	−9.76993	−	2.07666i	−0.390173	−	0.0829339i
$628$	0.0989629	−	0.304576i	0.00394905	−	0.0121539i
$629$	12.4064	−	2.63706i	0.494676	−	0.105147i
$630$	−0.563313	+	5.35956i	−0.0224429	+	0.213530i
$631$	−0.557166	+	0.618796i	−0.0221804	+	0.0246339i	−0.754133	−	0.656722i	$-0.771943\pi$
$631$	−0.557166	+	0.618796i	−0.0221804	+	0.0246339i	0.731953	+	0.681356i	$0.238609\pi$
$632$	−16.0337	+	7.13866i	−0.637786	+	0.283961i
$633$	22.0416	+	9.81356i	0.876076	+	0.390054i
$634$	25.8211	+	28.6772i	1.02549	+	1.13892i
$635$	−17.1277	+	12.4440i	−0.679692	+	0.493825i
$636$	0.894235	−	0.649700i	0.0354587	−	0.0257623i
$637$	0.249477	+	0.277073i	0.00988466	+	0.0109780i
$638$	20.0549	+	8.92900i	0.793979	+	0.353502i
$639$	−1.54572	+	0.688200i	−0.0611478	+	0.0272248i
$640$	9.24519	−	10.2678i	0.365448	−	0.405871i
$641$	−1.50671	+	14.3353i	−0.0595113	+	0.566212i	0.923620	+	0.383310i	$0.125216\pi$
$641$	−1.50671	+	14.3353i	−0.0595113	+	0.566212i	−0.983131	+	0.182902i	$0.941451\pi$
$642$	13.4125	−	2.85091i	0.529348	−	0.112516i
$643$	8.40269	−	25.8608i	0.331370	−	1.01985i	−0.637113	−	0.770770i	$-0.719872\pi$
$643$	8.40269	−	25.8608i	0.331370	−	1.01985i	0.968483	−	0.249080i	$-0.0801284\pi$
$644$	2.15711	+	0.458508i	0.0850020	+	0.0180677i
$645$	−4.98896	+	8.64114i	−0.196440	+	0.340244i
$646$	4.91565	+	8.51415i	0.193404	+	0.334985i
$647$	−4.59079	−	14.1290i	−0.180482	−	0.555468i	0.819359	−	0.573281i	$-0.194330\pi$
$647$	−4.59079	−	14.1290i	−0.180482	−	0.555468i	−0.999841	+	0.0178130i	$0.994330\pi$
$648$	−0.313156	−	2.97948i	−0.0123019	−	0.117045i
$649$	19.3505	+	14.0589i	0.759573	+	0.551862i
$650$	−1.07152			−0.0420284
$651$	4.93525	+	12.7301i	0.193428	+	0.498932i
$652$	4.43751			0.173786
$653$	10.3487	+	7.51879i	0.404977	+	0.294233i	0.771565	−	0.636150i	$-0.219474\pi$
$653$	10.3487	+	7.51879i	0.404977	+	0.294233i	−0.366588	+	0.930383i	$0.619474\pi$
$654$	0.239537	+	2.27904i	0.00936664	+	0.0891177i
$655$	4.84033	+	14.8970i	0.189127	+	0.582074i
$656$	12.2412	+	21.2024i	0.477940	+	0.827816i
$657$	−6.42682	+	11.1316i	−0.250734	+	0.434284i
$658$	5.34410	+	1.13592i	0.208335	+	0.0442829i
$659$	−5.02581	+	15.4679i	−0.195778	+	0.602542i	0.804189	+	0.594374i	$0.202600\pi$
$659$	−5.02581	+	15.4679i	−0.195778	+	0.602542i	−0.999967	+	0.00816819i	$0.997400\pi$
$660$	0.862508	−	0.183332i	0.0335731	−	0.00713617i
$661$	−1.25189	+	11.9110i	−0.0486930	+	0.463283i	0.942823	+	0.333295i	$0.108161\pi$
$661$	−1.25189	+	11.9110i	−0.0486930	+	0.463283i	−0.991516	+	0.129988i	$0.958506\pi$
$662$	−9.57415	+	10.6332i	−0.372110	+	0.413270i
$663$	−0.465137	+	0.207092i	−0.0180644	+	0.00804281i
$664$	−42.7842	−	19.0487i	−1.66035	−	0.739235i
$665$	15.4137	+	17.1186i	0.597718	+	0.663833i
$666$	9.94912	−	7.22846i	0.385521	−	0.280097i
$667$	23.3211	−	16.9438i	0.902996	−	0.656065i
$668$	−0.763823	−	0.848312i	−0.0295532	−	0.0328222i
$669$	−11.5137	−	5.12624i	−0.445146	−	0.198192i
$670$	29.4225	−	13.0997i	1.13669	−	0.506087i
$671$	10.8481	−	12.0481i	0.418788	−	0.465111i
$672$	−0.421376	+	4.00913i	−0.0162549	+	0.154655i
$673$	−15.8119	+	3.36093i	−0.609505	+	0.129554i	−0.502316	−	0.864684i	$-0.667519\pi$
$673$	−15.8119	+	3.36093i	−0.609505	+	0.129554i	−0.107190	+	0.994239i	$0.534185\pi$
$674$	4.22777	−	13.0117i	0.162847	−	0.501193i
$675$	−2.12308	−	0.451276i	−0.0817176	−	0.0173696i
$676$	−1.88417	+	3.26349i	−0.0724682	+	0.125519i
$677$	4.86968	+	8.43453i	0.187157	+	0.324165i	0.944301	−	0.329082i	$-0.106739\pi$
$677$	4.86968	+	8.43453i	0.187157	+	0.324165i	−0.757144	+	0.653248i	$0.773406\pi$
$678$	−3.91405	−	12.0462i	−0.150318	−	0.462632i
$679$	2.77812	+	26.4321i	0.106614	+	1.01437i
$680$	−5.49360	−	3.99134i	−0.210670	−	0.153061i
$681$	6.16746			0.236338
$682$	−10.0836	+	8.22121i	−0.386121	+	0.314806i
$683$	14.2908			0.546823			0.273412	−	0.961897i	$-0.411848\pi$
$683$	14.2908			0.546823			0.273412	+	0.961897i	$0.411848\pi$
$684$	−1.32418	−	0.962075i	−0.0506314	−	0.0367858i
$685$	1.81349	+	17.2542i	0.0692899	+	0.659249i
$686$	7.90699	+	24.3352i	0.301890	+	0.929123i
$687$	−10.8277	−	18.7542i	−0.413104	−	0.715518i
$688$	9.87026	−	17.0958i	0.376300	−	0.651771i
$689$	−1.39388	−	0.296279i	−0.0531027	−	0.0112873i
$690$	−2.08377	+	6.41317i	−0.0793276	+	0.244145i
$691$	−46.3485	+	9.85167i	−1.76318	+	0.374775i	−0.971662	−	0.236373i	$-0.924041\pi$
$691$	−46.3485	+	9.85167i	−1.76318	+	0.374775i	−0.791516	+	0.611148i	$0.790708\pi$
$692$	−0.148201	+	1.41004i	−0.00563375	+	0.0536015i
$693$	2.93473	−	3.25935i	0.111481	−	0.123812i
$694$	31.8019	−	14.1591i	1.20718	−	0.537472i
$695$	−3.05478	−	1.36007i	−0.115874	−	0.0515905i
$696$	18.8331	+	20.9162i	0.713865	+	0.792828i
$697$	8.01974	−	5.82668i	0.303769	−	0.220701i
$698$	−18.7735	+	13.6397i	−0.710587	+	0.516272i
$699$	2.74287	+	3.04626i	0.103745	+	0.115220i
$700$	1.42513	+	0.634507i	0.0538647	+	0.0239821i
$701$	27.1306	−	12.0793i	1.02471	−	0.456229i	0.175606	−	0.984460i	$-0.443811\pi$
$701$	27.1306	−	12.0793i	1.02471	−	0.456229i	0.849100	+	0.528232i	$0.177145\pi$
$702$	−0.330330	+	0.366868i	−0.0124675	+	0.0138466i
$703$	5.49468	−	52.2784i	0.207236	−	1.97172i
$704$	−15.4016	+	3.27370i	−0.580468	+	0.123382i
$705$	0.886431	−	2.72815i	0.0333849	−	0.102748i
$706$	−10.9615	−	2.32993i	−0.412540	−	0.0876882i
$707$	−6.39022	+	11.0682i	−0.240329	+	0.416262i
$708$	1.95978	+	3.39444i	0.0736530	+	0.127571i
$709$	−9.54932	−	29.3898i	−0.358632	−	1.10376i	−0.953873	−	0.300209i	$-0.902943\pi$
$709$	−9.54932	−	29.3898i	−0.358632	−	1.10376i	0.595241	−	0.803547i	$-0.297057\pi$
$710$	0.388682	+	3.69806i	0.0145870	+	0.138786i
$711$	4.73952	+	3.44346i	0.177746	+	0.129140i
$712$	0.934875			0.0350359
$713$	2.72861	+	16.8647i	0.102187	+	0.631586i
$714$	−4.31699			−0.161559
$715$	−0.919695	−	0.668198i	−0.0343946	−	0.0249892i
$716$	0.266451	+	2.53511i	0.00995775	+	0.0947416i
$717$	2.51155	+	7.72974i	0.0937954	+	0.288673i
$718$	4.31083	+	7.46658i	0.160879	+	0.278650i
$719$	−6.25895	+	10.8408i	−0.233420	+	0.404295i	−0.958812	−	0.284041i	$-0.908325\pi$
$719$	−6.25895	+	10.8408i	−0.233420	+	0.404295i	0.725393	+	0.688335i	$0.241658\pi$
$720$	−5.47558	−	1.16387i	−0.204063	−	0.0433749i
$721$	6.90717	−	21.2581i	0.257236	−	0.791692i
$722$	15.5741	−	3.31038i	0.579608	−	0.123199i
$723$	−1.40568	+	13.3742i	−0.0522778	+	0.497390i
$724$	−3.60486	+	4.00360i	−0.133974	+	0.148793i
$725$	18.6284	−	8.29392i	0.691843	−	0.308028i
$726$	−9.31088	−	4.14547i	−0.345559	−	0.153853i
$727$	14.9579	+	16.6124i	0.554757	+	0.616120i	0.953665	−	0.300871i	$-0.0972773\pi$
$727$	14.9579	+	16.6124i	0.554757	+	0.616120i	−0.398908	+	0.916991i	$0.630611\pi$
$728$	2.24580	−	1.63167i	0.0832351	−	0.0604738i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	18.9015	+	20.9922i	0.699575	+	0.776956i
$731$	−7.30191	−	3.25102i	−0.270071	−	0.120243i
$732$	2.42704	−	1.08059i	0.0897061	−	0.0399397i
$733$	−8.38765	+	9.31542i	−0.309805	+	0.344073i	−0.877860	−	0.478917i	$-0.841029\pi$
$733$	−8.38765	+	9.31542i	−0.309805	+	0.344073i	0.568055	+	0.822990i	$0.307696\pi$
$734$	2.06106	−	19.6097i	0.0760752	−	0.723807i
$735$	1.62348	−	0.345081i	0.0598829	−	0.0127285i
$736$	−1.55872	+	4.79726i	−0.0574554	+	0.176829i
$737$	−25.6387	−	5.44967i	−0.944413	−	0.200741i
$738$	4.80572	−	8.32375i	0.176901	−	0.306401i
$739$	−5.13557	−	8.89507i	−0.188915	−	0.327210i	0.755974	−	0.654602i	$-0.227164\pi$
$739$	−5.13557	−	8.89507i	−0.188915	−	0.327210i	−0.944889	+	0.327391i	$0.893830\pi$
$740$	1.43404	+	4.41353i	0.0527164	+	0.162244i
$741$	0.220573	+	2.09861i	0.00810295	+	0.0770944i
$742$	−9.77482	−	7.10182i	−0.358845	−	0.260716i
$743$	19.1333			0.701931			0.350966	−	0.936388i	$-0.385853\pi$
$743$	19.1333			0.701931			0.350966	+	0.936388i	$0.385853\pi$
$744$	−16.0976	+	4.37076i	−0.590167	+	0.160240i
$745$	22.5962			0.827859
$746$	−3.01735	−	2.19224i	−0.110473	−	0.0802635i
$747$	1.63403	+	15.5468i	0.0597862	+	0.568827i
$748$	0.218276	+	0.671785i	0.00798097	+	0.0245629i
$749$	12.8684	+	22.2888i	0.470203	+	0.814415i
$750$	−7.87915	+	13.6471i	−0.287706	+	0.498321i
$751$	−30.8275	−	6.55259i	−1.12491	−	0.239107i	−0.392355	−	0.919814i	$-0.628340\pi$
$751$	−30.8275	−	6.55259i	−1.12491	−	0.239107i	−0.732556	+	0.680706i	$0.761673\pi$
$752$	−1.75373	+	5.39743i	−0.0639520	+	0.196824i
$753$	10.2068	−	2.16951i	0.371955	−	0.0790615i
$754$	0.484791	−	4.61248i	0.0176551	−	0.167977i
$755$	−1.46827	+	1.63068i	−0.0534360	+	0.0593467i
$756$	0.656584	−	0.292330i	0.0238797	−	0.0106319i
$757$	0.216041	+	0.0961875i	0.00785213	+	0.00349599i	0.410659	−	0.911789i	$-0.365299\pi$
$757$	0.216041	+	0.0961875i	0.00785213	+	0.00349599i	−0.402807	+	0.915285i	$0.631965\pi$
$758$	−3.36897	−	3.74161i	−0.122366	−	0.135902i
$759$	4.43983	−	3.22573i	0.161156	−	0.117086i
$760$	−22.7680	+	16.5419i	−0.825880	+	0.600037i
$761$	−19.0132	−	21.1163i	−0.689227	−	0.765464i	0.292395	−	0.956298i	$-0.405548\pi$
$761$	−19.0132	−	21.1163i	−0.689227	−	0.765464i	−0.981622	+	0.190833i	$0.938881\pi$
$762$	−15.0218	−	6.68815i	−0.544184	−	0.242286i
$763$	−3.92934	+	1.74945i	−0.142252	+	0.0633345i
$764$	3.94245	−	4.37854i	0.142633	−	0.158410i
$765$	−0.236923	+	2.25417i	−0.00856598	+	0.0814998i
$766$	−38.5661	+	8.19748i	−1.39345	+	0.296187i
$767$	1.56152	−	4.80586i	0.0563832	−	0.173530i
$768$	−6.72551	−	1.42955i	−0.242686	−	0.0515845i
$769$	−22.6276	+	39.1921i	−0.815972	+	1.41330i	0.0926563	+	0.995698i	$0.470464\pi$
$769$	−22.6276	+	39.1921i	−0.815972	+	1.41330i	−0.908628	+	0.417606i	$0.862869\pi$
$770$	−4.81932	−	8.34731i	−0.173676	−	0.300816i
$771$	−7.19073	−	22.1308i	−0.258968	−	0.797021i
$772$	0.156795	+	1.49180i	0.00564317	+	0.0536912i
$773$	−17.5433	−	12.7460i	−0.630990	−	0.458441i	0.225753	−	0.974185i	$-0.427516\pi$
$773$	−17.5433	−	12.7460i	−0.630990	−	0.458441i	−0.856743	+	0.515743i	$0.827516\pi$
$774$	−7.74982			−0.278562
$775$	−0.592346	+	12.0704i	−0.0212777	+	0.433581i
$776$	−32.4703			−1.16562
$777$	18.6739	+	13.5674i	0.669924	+	0.486728i
$778$	−1.66025	−	15.7962i	−0.0595228	−	0.566321i
$779$	−12.6956	−	39.0729i	−0.454865	−	1.39993i
$780$	−0.0931449	−	0.161332i	−0.00333512	−	0.00577660i
$781$	1.51312	−	2.62079i	0.0541435	−	0.0937794i
$782$	−5.28368	−	1.12308i	−0.188944	−	0.0401613i
$783$	2.90313	−	8.93490i	0.103749	−	0.319307i
$784$	−3.21192	+	0.682715i	−0.114712	+	0.0243827i
$785$	−0.192121	+	1.82791i	−0.00685708	+	0.0652408i
$786$	−8.14056	+	9.04101i	−0.290364	+	0.322482i
$787$	21.0440	−	9.36940i	0.750138	−	0.333983i	0.00419356	−	0.999991i	$-0.498665\pi$
$787$	21.0440	−	9.36940i	0.750138	−	0.333983i	0.745944	+	0.666008i	$0.231998\pi$
$788$	5.02992	+	2.23947i	0.179184	+	0.0797777i
$789$	1.55465	+	1.72662i	0.0553472	+	0.0614693i
$790$	10.4158	−	7.56753i	0.370578	−	0.269241i
$791$	19.2333	−	13.9738i	0.683856	−	0.496851i
$792$	3.58541	+	3.98200i	0.127402	+	0.141494i
$793$	−3.12900	−	1.39312i	−0.111114	−	0.0494711i
$794$	24.3744	−	10.8522i	0.865014	−	0.385129i
$795$	−4.24477	+	4.71430i	−0.150547	+	0.167199i
$796$	0.658008	−	6.26053i	0.0233225	−	0.221898i
$797$	37.4601	−	7.96240i	1.32691	−	0.282043i	0.510678	−	0.859772i	$-0.329395\pi$
$797$	37.4601	−	7.96240i	1.32691	−	0.282043i	0.816228	+	0.577730i	$0.196061\pi$
$798$	−5.52879	+	17.0159i	−0.195717	+	0.602355i
$799$	2.24767	+	0.477757i	0.0795169	+	0.0169018i
$800$	−1.78407	+	3.09010i	−0.0630764	+	0.109252i
$801$	−0.156026	−	0.270245i	−0.00551291	−	0.00954864i
$802$	2.73642	+	8.42183i	0.0966262	+	0.297385i
$803$	−2.40304	−	22.8634i	−0.0848015	−	0.806832i
$804$	−3.47498	−	2.52472i	−0.122553	−	0.0890400i
$805$	−12.6566			−0.446087
$806$	2.31017	+	1.48934i	0.0813721	+	0.0524599i
$807$	−30.6869			−1.08023
$808$	−12.6321	−	9.17773i	−0.444394	−	0.322871i
$809$	−1.93394	−	18.4002i	−0.0679939	−	0.646918i	−0.974448	−	0.224614i	$-0.927888\pi$
$809$	−1.93394	−	18.4002i	−0.0679939	−	0.646918i	0.906454	−	0.422305i	$-0.138779\pi$
$810$	0.679112	+	2.09009i	0.0238615	+	0.0734383i
$811$	2.71042	+	4.69458i	0.0951756	+	0.164849i	0.909682	−	0.415306i	$-0.136325\pi$
$811$	2.71042	+	4.69458i	0.0951756	+	0.164849i	−0.814506	+	0.580155i	$0.802992\pi$
$812$	−3.37609	+	5.84755i	−0.118477	+	0.205209i
$813$	−5.89465	−	1.25295i	−0.206734	−	0.0439427i
$814$	−6.79689	+	20.9187i	−0.238231	+	0.733199i
$815$	−24.9111	+	5.29502i	−0.872598	+	0.185476i
$816$	0.468733	−	4.45970i	0.0164090	−	0.156121i
$817$	−22.1658	+	24.6176i	−0.775484	+	0.861262i
$818$	24.1610	−	10.7572i	0.844770	−	0.376116i
$819$	−0.846482	−	0.376878i	−0.0295785	−	0.0131692i
$820$	2.42690	+	2.69534i	0.0847510	+	0.0941255i
$821$	44.3600	−	32.2294i	1.54817	−	1.12481i	0.603237	−	0.797562i	$-0.293877\pi$
$821$	44.3600	−	32.2294i	1.54817	−	1.12481i	0.944937	−	0.327252i	$-0.106123\pi$
$822$	−10.9016	+	7.92047i	−0.380237	+	0.276258i
$823$	−15.8076	−	17.5562i	−0.551020	−	0.611969i	0.401718	−	0.915763i	$-0.368413\pi$
$823$	−15.8076	−	17.5562i	−0.551020	−	0.611969i	−0.952738	+	0.303794i	$0.901747\pi$
$824$	24.9470	+	11.1071i	0.869070	+	0.386935i
$825$	3.54645	−	1.57898i	0.123472	−	0.0549731i
$826$	28.6685	−	31.8396i	0.997505	−	1.10784i
$827$	−0.122897	+	1.16929i	−0.00427354	+	0.0406601i	−0.996451	−	0.0841766i	$-0.973174\pi$
$827$	−0.122897	+	1.16929i	−0.00427354	+	0.0406601i	0.992177	+	0.124837i	$0.0398407\pi$
$828$	0.879663	−	0.186978i	0.0305704	−	0.00649794i
$829$	6.95578	−	21.4077i	0.241584	−	0.743520i	−0.754595	−	0.656190i	$-0.772167\pi$
$829$	6.95578	−	21.4077i	0.241584	−	0.743520i	0.996180	−	0.0873293i	$-0.0278332\pi$
$830$	33.6039	+	7.14273i	1.16641	+	0.247928i
$831$	0.715448	−	1.23919i	0.0248186	−	0.0429871i
$832$	1.66326	+	2.88086i	0.0576633	+	0.0998757i
$833$	0.410857	+	1.26449i	0.0142353	+	0.0438119i
$834$	−0.271478	−	2.58294i	−0.00940052	−	0.0894400i
$835$	5.30017	+	3.85080i	0.183420	+	0.133262i
$836$	2.92746			0.101248
$837$	3.95007	+	3.92389i	0.136534	+	0.135630i
$838$	22.8095			0.787942
$839$	−26.6133	−	19.3357i	−0.918793	−	0.667542i	0.0244306	−	0.999702i	$-0.492223\pi$
$839$	−26.6133	−	19.3357i	−0.918793	−	0.667542i	−0.943223	+	0.332160i	$0.892223\pi$
$840$	−1.29173	−	12.2900i	−0.0445688	−	0.424044i
$841$	18.3125	+	56.3602i	0.631467	+	1.94345i
$842$	−11.1696	−	19.3464i	−0.384931	−	0.666720i
$843$	13.7759	−	23.8606i	0.474468	−	0.821802i
$844$	−6.91706	−	1.47027i	−0.238095	−	0.0506087i
$845$	6.68318	−	20.5687i	0.229908	−	0.707585i
$846$	2.17931	−	0.463226i	0.0749261	−	0.0159260i
$847$	1.99961	−	19.0251i	0.0687075	−	0.653709i
$848$	8.39794	−	9.32686i	0.288387	−	0.320286i
$849$	−9.97411	+	4.44076i	−0.342311	+	0.152406i
$850$	−3.49074	−	1.55418i	−0.119731	−	0.0533079i
$851$	19.3259	+	21.4636i	0.662485	+	0.735764i
$852$	0.401202	−	0.291490i	0.0137449	−	0.00998629i
$853$	3.55696	−	2.58429i	0.121788	−	0.0884843i	−0.525224	−	0.850964i	$-0.676018\pi$
$853$	3.55696	−	2.58429i	0.121788	−	0.0884843i	0.647012	+	0.762480i	$0.276018\pi$
$854$	−19.4319	−	21.5813i	−0.664946	−	0.738498i
$855$	8.58163	+	3.82079i	0.293486	+	0.130668i
$856$	−28.7248	+	12.7891i	−0.981792	+	0.437122i
$857$	11.7362	−	13.0344i	0.400901	−	0.445245i	−0.508566	−	0.861023i	$-0.669824\pi$
$857$	11.7362	−	13.0344i	0.400901	−	0.445245i	0.909466	+	0.415778i	$0.136491\pi$
$858$	0.0922937	−	0.878116i	0.00315086	−	0.0299784i
$859$	28.3647	−	6.02910i	0.967791	−	0.205710i	0.303208	−	0.952924i	$-0.401942\pi$
$859$	28.3647	−	6.02910i	0.967791	−	0.205710i	0.664583	+	0.747214i	$0.268609\pi$
$860$	0.903705	−	2.78132i	0.0308161	−	0.0948421i
$861$	17.6459	+	3.75075i	0.601370	+	0.127825i
$862$	−15.3252	+	26.5441i	−0.521979	+	0.904094i
$863$	22.4463	+	38.8781i	0.764081	+	1.32343i	0.940731	+	0.339153i	$0.110141\pi$
$863$	22.4463	+	38.8781i	0.764081	+	1.32343i	−0.176650	+	0.984274i	$0.556526\pi$
$864$	0.507997	+	1.56346i	0.0172824	+	0.0531898i
$865$	−0.850551	−	8.09245i	−0.0289196	−	0.275152i
$866$	−4.43511	−	3.22229i	−0.150711	−	0.109498i
$867$	15.1843			0.515687
$868$	−2.19061	−	3.34881i	−0.0743542	−	0.113666i
$869$	−10.4780			−0.355441
$870$	−16.7032	−	12.1356i	−0.566292	−	0.411435i
$871$	0.578838	+	5.50727i	0.0196132	+	0.186607i
$872$	−1.62384	−	4.99765i	−0.0549900	−	0.169242i
$873$	5.41914	+	9.38623i	0.183410	+	0.317676i
$874$	−11.1936	+	19.3879i	−0.378629	+	0.655804i
$875$	−28.9311	−	6.14949i	−0.978049	−	0.207891i
$876$	1.16416	−	3.58291i	0.0393333	−	0.121055i
$877$	−34.7310	+	7.38231i	−1.17278	+	0.249283i	−0.752800	−	0.658249i	$-0.771297\pi$
$877$	−34.7310	+	7.38231i	−1.17278	+	0.249283i	−0.419983	+	0.907532i	$0.637964\pi$
$878$	−1.22922	+	11.6953i	−0.0414842	+	0.394696i
$879$	17.1429	−	19.0391i	0.578216	−	0.642174i
$880$	9.14654	−	4.07230i	0.308330	−	0.137277i
$881$	−0.414657	−	0.184617i	−0.0139702	−	0.00621991i	0.399740	−	0.916629i	$-0.369101\pi$
$881$	−0.414657	−	0.184617i	−0.0139702	−	0.00621991i	−0.413710	+	0.910409i	$0.635767\pi$
$882$	0.862590	+	0.958004i	0.0290449	+	0.0322577i
$883$	−43.8554	+	31.8628i	−1.47585	+	1.07227i	−0.496988	+	0.867757i	$0.665561\pi$
$883$	−43.8554	+	31.8628i	−1.47585	+	1.07227i	−0.978864	+	0.204512i	$0.934439\pi$
$884$	0.120729	−	0.0877150i	0.00406057	−	0.00295017i
$885$	−15.0521	−	16.7171i	−0.505971	−	0.561938i
$886$	39.1116	+	17.4136i	1.31398	+	0.585022i
$887$	17.9525	−	7.99295i	0.602785	−	0.268377i	−0.0825715	−	0.996585i	$-0.526313\pi$
$887$	17.9525	−	7.99295i	0.602785	−	0.268377i	0.685356	+	0.728208i	$0.259647\pi$
$888$	−18.8695	+	20.9567i	−0.633217	+	0.703259i
$889$	3.22610	−	30.6943i	0.108200	−	1.02945i
$890$	−0.670796	+	0.142582i	−0.0224851	+	0.00477936i
$891$	0.552692	−	1.70101i	0.0185159	−	0.0569860i
$892$	3.61321	+	0.768013i	0.120979	+	0.0257150i
$893$	4.76173	−	8.24756i	0.159345	−	0.275994i
$894$	8.77518	+	15.1991i	0.293486	+	0.508332i
$895$	−4.52080	−	13.9136i	−0.151114	−	0.465080i
$896$	2.10543	+	20.0319i	0.0703376	+	0.669218i
$897$	−0.937988	−	0.681488i	−0.0313185	−	0.0227542i
$898$	−31.3987			−1.04779
$899$	−51.6905	−	8.01088i	−1.72397	−	0.267178i
$900$	0.636161			0.0212054
$901$	−4.11119	−	2.98695i	−0.136963	−	0.0995098i
$902$	1.79690	+	17.0964i	0.0598302	+	0.569246i
$903$	−4.49495	−	13.8340i	−0.149583	−	0.460368i
$904$	14.5223	+	25.1534i	0.483005	+	0.836589i
$905$	15.4596	−	26.7768i	0.513893	−	0.890090i
$906$	−1.66706	−	0.354345i	−0.0553845	−	0.0117723i
$907$	−9.41933	+	28.9897i	−0.312764	+	0.962588i	0.663901	+	0.747820i	$0.268899\pi$
$907$	−9.41933	+	28.9897i	−0.312764	+	0.962588i	−0.976665	+	0.214768i	$0.931101\pi$
$908$	−1.76813	+	0.375828i	−0.0586775	+	0.0124723i
$909$	−0.544784	+	5.18328i	−0.0180694	+	0.171918i
$910$	−1.36257	+	1.51328i	−0.0451686	+	0.0501648i
$911$	12.5079	−	5.56887i	0.414405	−	0.184505i	−0.188934	−	0.981990i	$-0.560503\pi$
$911$	12.5079	−	5.56887i	0.414405	−	0.184505i	0.603339	+	0.797485i	$0.293837\pi$
$912$	−16.9781	−	7.55912i	−0.562200	−	0.250308i
$913$	−18.7085	−	20.7779i	−0.619160	−	0.687647i
$914$	−38.2053	+	27.7577i	−1.26372	+	0.918145i
$915$	−12.3354	+	8.96222i	−0.407797	+	0.296282i
$916$	4.24701	+	4.71678i	0.140325	+	0.155847i
$917$	−20.8605	−	9.28770i	−0.688875	−	0.306707i
$918$	−1.60825	+	0.716041i	−0.0530803	+	0.0236329i
$919$	−7.05387	+	7.83412i	−0.232686	+	0.258424i	−0.848168	−	0.529727i	$-0.822294\pi$
$919$	−7.05387	+	7.83412i	−0.232686	+	0.258424i	0.615483	+	0.788150i	$0.288961\pi$
$920$	1.61630	−	15.3781i	0.0532879	−	0.507001i
$921$	8.08360	−	1.71822i	0.266364	−	0.0566174i
$922$	6.00651	−	18.4861i	0.197814	−	0.608809i
$923$	−0.625370	−	0.132927i	−0.0205843	−	0.00437533i
$924$	−0.642734	+	1.11325i	−0.0211444	+	0.0366231i
$925$	10.2154	+	17.6936i	0.335880	+	0.581761i
$926$	−10.0850	−	31.0384i	−0.331413	−	1.01998i
$927$	−0.952788	−	9.06517i	−0.0312937	−	0.297739i
$928$	−12.4945	−	9.07781i	−0.410153	−	0.297994i
$929$	18.1098			0.594163			0.297081	−	0.954852i	$-0.403987\pi$
$929$	18.1098			0.594163			0.297081	+	0.954852i	$0.403987\pi$
$930$	10.8838	−	5.59125i	0.356895	−	0.183344i
$931$	5.51030			0.180593
$932$	−0.971976	−	0.706182i	−0.0318381	−	0.0231318i
$933$	−0.723951	−	6.88793i	−0.0237011	−	0.225501i
$934$	−0.146257	−	0.450132i	−0.00478566	−	0.0147288i
$935$	−2.02695	−	3.51079i	−0.0662885	−	0.114815i
$936$	0.566015	−	0.980367i	0.0185008	−	0.0320443i
$937$	14.6311	+	3.10994i	0.477977	+	0.101597i	0.440599	−	0.897704i	$-0.354766\pi$
$937$	14.6311	+	3.10994i	0.477977	+	0.101597i	0.0373781	+	0.999301i	$0.488099\pi$
$938$	−14.5089	+	44.6538i	−0.473732	+	1.45800i
$939$	5.15260	−	1.09522i	0.168149	−	0.0357412i
$940$	−0.0878822	+	0.836143i	−0.00286640	+	0.0272720i
$941$	34.4883	−	38.3031i	1.12429	−	1.24865i	0.159048	−	0.987271i	$-0.449157\pi$
$941$	34.4883	−	38.3031i	1.12429	−	1.24865i	0.965237	−	0.261375i	$-0.0841759\pi$
$942$	−1.30413	+	0.580637i	−0.0424909	+	0.0189182i
$943$	20.6215	+	9.18130i	0.671530	+	0.298984i
$944$	29.7794	+	33.0734i	0.969237	+	1.07645i
$945$	−3.33709	+	2.42454i	−0.108555	+	0.0788701i
$946$	11.2137	−	8.14726i	0.364590	−	0.264890i
$947$	15.8926	+	17.6505i	0.516439	+	0.573564i	0.943800	−	0.330517i	$-0.107223\pi$
$947$	15.8926	+	17.6505i	0.516439	+	0.573564i	−0.427360	+	0.904081i	$0.640556\pi$
$948$	−1.56860	−	0.698384i	−0.0509456	−	0.0226824i
$949$	−4.43698	+	1.97547i	−0.144031	+	0.0641265i
$950$	−10.5966	+	11.7687i	−0.343798	+	0.381826i
$951$	−3.08740	+	29.3747i	−0.100116	+	0.952538i
$952$	9.68292	−	2.05817i	0.313825	−	0.0667056i
$953$	−13.4754	+	41.4730i	−0.436511	+	1.34344i	0.455020	+	0.890481i	$0.349632\pi$
$953$	−13.4754	+	41.4730i	−0.436511	+	1.34344i	−0.891531	+	0.452960i	$0.850368\pi$
$954$	−4.81947	−	1.02441i	−0.156036	−	0.0331665i
$955$	−16.9073	+	29.2844i	−0.547109	+	0.947620i
$956$	−1.19106	−	2.06297i	−0.0385216	−	0.0667213i
$957$	5.19238	+	15.9805i	0.167846	+	0.516577i
$958$	2.99445	+	28.4903i	0.0967463	+	0.920479i
$959$	−20.4617	−	14.8663i	−0.660741	−	0.480057i
$960$	14.8086			0.477944
$961$	18.0542	−	25.2001i	0.582392	−	0.812908i
$962$	4.64685			0.149820
$963$	8.49097	+	6.16905i	0.273618	+	0.198795i
$964$	−0.411994	−	3.91986i	−0.0132694	−	0.126250i
$965$	−2.66029	−	8.18754i	−0.0856378	−	0.263566i
$966$	−4.91518	−	8.51333i	−0.158143	−	0.273912i
$967$	20.4025	−	35.3381i	0.656100	−	1.13640i	−0.325517	−	0.945536i	$-0.605538\pi$
$967$	20.4025	−	35.3381i	0.656100	−	1.13640i	0.981617	−	0.190862i	$-0.0611283\pi$
$968$	22.8605	+	4.85916i	0.734765	+	0.156179i
$969$	−2.32535	+	7.15668i	−0.0747009	+	0.229906i
$970$	23.2983	−	4.95220i	0.748062	−	0.159006i
$971$	−3.31993	+	31.5870i	−0.106542	+	1.01368i	0.802410	+	0.596773i	$0.203551\pi$
$971$	−3.31993	+	31.5870i	−0.106542	+	1.01368i	−0.908951	+	0.416902i	$0.863116\pi$
$972$	0.196117	−	0.217810i	0.00629045	−	0.00698625i
$973$	4.45330	−	1.98274i	0.142766	−	0.0635636i
$974$	17.3861	+	7.74081i	0.557088	+	0.248031i
$975$	−0.548789	−	0.609492i	−0.0175753	−	0.0195194i
$976$	24.4047	−	17.7310i	0.781175	−	0.567557i
$977$	1.64740	−	1.19691i	0.0527051	−	0.0382925i	−0.561121	−	0.827734i	$-0.689630\pi$
$977$	1.64740	−	1.19691i	0.0527051	−	0.0382925i	0.613826	+	0.789441i	$0.289630\pi$
$978$	−13.2358	−	14.6999i	−0.423235	−	0.470050i
$979$	0.509869	+	0.227008i	0.0162955	+	0.00725521i
$980$	−0.444402	+	0.197861i	−0.0141959	+	0.00632043i
$981$	−1.17366	+	1.30349i	−0.0374722	+	0.0416171i
$982$	−3.93025	+	37.3939i	−0.125419	+	1.19329i
$983$	−18.7233	+	3.97975i	−0.597180	+	0.126934i	−0.496578	−	0.867992i	$-0.665410\pi$
$983$	−18.7233	+	3.97975i	−0.597180	+	0.126934i	−0.100602	+	0.994927i	$0.532077\pi$
$984$	−6.81070	+	20.9612i	−0.217117	+	0.668218i
$985$	−30.9090	−	6.56992i	−0.984844	−	0.209335i
$986$	8.26948	−	14.3232i	0.263354	−	0.456142i
$987$	2.09091	+	3.62156i	0.0665543	+	0.115275i
$988$	−0.191119	−	0.588204i	−0.00608031	−	0.0187133i
$989$	−1.90252	−	18.1013i	−0.0604966	−	0.575587i
$990$	−3.17993	−	2.31035i	−0.101065	−	0.0734278i
$991$	9.57396			0.304127			0.152063	−	0.988371i	$-0.451408\pi$
$991$	9.57396			0.304127			0.152063	+	0.988371i	$0.451408\pi$
$992$	8.14146	−	4.18243i	0.258492	−	0.132792i
$993$	−10.9518			−0.347544
$994$	−4.38551	−	3.18626i	−0.139100	−	0.101062i
$995$	3.77642	+	35.9303i	0.119721	+	1.13907i
$996$	−1.41584	−	4.35749i	−0.0448625	−	0.138072i
$997$	−0.492743	−	0.853456i	−0.0156053	−	0.0270292i	0.858117	−	0.513454i	$-0.171634\pi$
$997$	−0.492743	−	0.853456i	−0.0156053	−	0.0270292i	−0.873723	+	0.486425i	$0.838301\pi$
$998$	−11.9856	+	20.7596i	−0.379396	+	0.657133i
$999$	9.20717	+	1.95705i	0.291302	+	0.0619182i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.m.a.10.2	✓	16
3.2	odd	2		279.2.y.b.10.1		16
31.11	odd	30		2883.2.a.n.1.4		8
31.20	even	15		2883.2.a.m.1.4		8
31.28	even	15	inner	93.2.m.a.28.2	yes	16
93.11	even	30		8649.2.a.bi.1.5		8
93.20	odd	30		8649.2.a.bj.1.5		8
93.59	odd	30		279.2.y.b.28.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.m.a.10.2	✓	16	1.1	even	1	trivial
93.2.m.a.28.2	yes	16	31.28	even	15	inner
279.2.y.b.10.1		16	3.2	odd	2
279.2.y.b.28.1		16	93.59	odd	30
2883.2.a.m.1.4		8	31.20	even	15
2883.2.a.n.1.4		8	31.11	odd	30
8649.2.a.bi.1.5		8	93.11	even	30
8649.2.a.bj.1.5		8	93.20	odd	30

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:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.05697 + 0.767934i) q^{2} +(0.104528 + 0.994522i) q^{3} +(-0.0905704 - 0.278747i) q^{4} +(0.841054 + 1.45675i) q^{5} +(-0.653243 + 1.13145i) q^{6} +(-2.39861 - 0.509841i) q^{7} +(0.925782 - 2.84927i) q^{8} +(-0.978148 + 0.207912i) q^{9} +O(q^{10})\)	\(q+(1.05697 + 0.767934i) q^{2} +(0.104528 + 0.994522i) q^{3} +(-0.0905704 - 0.278747i) q^{4} +(0.841054 + 1.45675i) q^{5} +(-0.653243 + 1.13145i) q^{6} +(-2.39861 - 0.509841i) q^{7} +(0.925782 - 2.84927i) q^{8} +(-0.978148 + 0.207912i) q^{9} +(-0.229717 + 2.18561i) q^{10} +(1.19677 - 1.32915i) q^{11} +(0.267753 - 0.119211i) q^{12} +(-0.345193 - 0.153690i) q^{13} +(-2.14374 - 2.38086i) q^{14} +(-1.36085 + 0.988718i) q^{15} +(2.69234 - 1.95610i) q^{16} +(-0.901634 - 1.00137i) q^{17} +(-1.19354 - 0.531396i) q^{18} +(-5.10172 + 2.27143i) q^{19} +(0.329889 - 0.366379i) q^{20} +(0.256325 - 2.43877i) q^{21} +(2.28565 - 0.485831i) q^{22} +(0.948179 - 2.91819i) q^{23} +(2.93043 + 0.622882i) q^{24} +(1.08526 - 1.87972i) q^{25} +(-0.246835 - 0.427531i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.0751268 + 0.714783i) q^{28} +(7.60048 + 5.52207i) q^{29} -2.19765 q^{30} +(-4.95248 + 2.54419i) q^{31} -1.64391 q^{32} +(1.44697 + 1.05128i) q^{33} +(-0.184017 - 1.75081i) q^{34} +(-1.27465 - 3.92298i) q^{35} +(0.146546 + 0.253825i) q^{36} +(-4.70643 + 8.15178i) q^{37} +(-7.13667 - 1.51695i) q^{38} +(0.116765 - 0.359367i) q^{39} +(4.92929 - 1.04775i) q^{40} +(-0.768985 + 7.31640i) q^{41} +(2.14374 - 2.38086i) q^{42} +(5.41897 - 2.41268i) q^{43} +(-0.478889 - 0.213215i) q^{44} +(-1.12555 - 1.25005i) q^{45} +(3.24318 - 2.35631i) q^{46} +(-1.37964 + 1.00237i) q^{47} +(2.22681 + 2.47312i) q^{48} +(-0.901403 - 0.401330i) q^{49} +(2.59059 - 1.15340i) q^{50} +(0.901634 - 1.00137i) q^{51} +(-0.0115763 + 0.110141i) q^{52} +(3.68888 - 0.784095i) q^{53} +(0.403727 - 1.24254i) q^{54} +(2.94279 + 0.625509i) q^{55} +(-3.67327 + 6.36229i) q^{56} +(-2.79226 - 4.83634i) q^{57} +(3.79290 + 11.6733i) q^{58} +(1.39787 + 13.2999i) q^{59} +(0.398855 + 0.289785i) q^{60} +9.06449 q^{61} +(-7.18840 - 1.11404i) q^{62} +2.45220 q^{63} +(-7.12224 - 5.17461i) q^{64} +(-0.0664385 - 0.632120i) q^{65} +(0.722085 + 2.22235i) q^{66} +(-7.32758 - 12.6917i) q^{67} +(-0.197466 + 0.342022i) q^{68} +(3.00132 + 0.637950i) q^{69} +(1.66532 - 5.12532i) q^{70} +(1.65503 - 0.351787i) q^{71} +(-0.313156 + 2.97948i) q^{72} +(8.60076 - 9.55211i) q^{73} +(-11.2346 + 5.00196i) q^{74} +(1.98286 + 0.882828i) q^{75} +(1.09522 + 1.21636i) q^{76} +(-3.54825 + 2.57796i) q^{77} +(0.399387 - 0.290172i) q^{78} +(-3.92002 - 4.35362i) q^{79} +(5.11394 + 2.27687i) q^{80} +(0.913545 - 0.406737i) q^{81} +(-6.43130 + 7.14269i) q^{82} +(1.63403 - 15.5468i) q^{83} +(-0.703015 + 0.149430i) q^{84} +(0.700415 - 2.15566i) q^{85} +(7.58047 + 1.61128i) q^{86} +(-4.69736 + 8.13606i) q^{87} +(-2.67915 - 4.64043i) q^{88} +(0.0964294 + 0.296779i) q^{89} +(-0.229717 - 2.18561i) q^{90} +(0.749627 + 0.544636i) q^{91} -0.899315 q^{92} +(-3.04793 - 4.65941i) q^{93} -2.22799 q^{94} +(-7.59972 - 5.52152i) q^{95} +(-0.171836 - 1.63491i) q^{96} +(-3.34921 - 10.3078i) q^{97} +(-0.644561 - 1.11641i) q^{98} +(-0.894275 + 1.54893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} + 6 q^{5} - 5 q^{6} - 9 q^{7} + 10 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 + 6 * q^5 - 5 * q^6 - 9 * q^7 + 10 * q^8 + 2 * q^9	\( 16 q - 2 q^{3} + 6 q^{5} - 5 q^{6} - 9 q^{7} + 10 q^{8} + 2 q^{9} - 16 q^{10} + 10 q^{11} - 10 q^{12} + 3 q^{13} - 12 q^{14} - 8 q^{15} + 6 q^{16} + 3 q^{17} - 32 q^{19} - 10 q^{20} - 6 q^{21} - 9 q^{22} - 22 q^{23} + 20 q^{24} + 12 q^{25} + 18 q^{26} + 4 q^{27} + 30 q^{28} + 38 q^{29} - 2 q^{30} - 8 q^{31} + 10 q^{33} - 52 q^{34} + 3 q^{35} - 5 q^{36} - 8 q^{37} + 7 q^{38} + 6 q^{39} + 37 q^{40} - 40 q^{41} + 12 q^{42} + q^{43} + q^{45} - 7 q^{46} - 23 q^{47} + 18 q^{48} + 25 q^{49} - 21 q^{50} - 3 q^{51} - 45 q^{52} + 30 q^{53} - 5 q^{54} + 46 q^{55} - 6 q^{56} - 8 q^{57} + 48 q^{58} - 40 q^{59} + 15 q^{60} + 26 q^{61} + 40 q^{62} - 12 q^{63} + 38 q^{64} + 12 q^{65} + 12 q^{66} - 32 q^{67} + 15 q^{68} - 11 q^{69} + 33 q^{70} + 17 q^{71} + 5 q^{72} + 27 q^{73} - 70 q^{74} + 3 q^{75} - 15 q^{76} - 9 q^{77} - 9 q^{78} + 21 q^{80} + 2 q^{81} - 32 q^{82} - 17 q^{83} - 15 q^{84} - 64 q^{85} + 26 q^{86} - 6 q^{87} - 22 q^{88} - 43 q^{89} - 16 q^{90} - 140 q^{92} - q^{93} + 88 q^{94} - 2 q^{95} - 35 q^{96} + 12 q^{97} - 32 q^{98}+O(q^{100}) \) 16 * q - 2 * q^3 + 6 * q^5 - 5 * q^6 - 9 * q^7 + 10 * q^8 + 2 * q^9 - 16 * q^10 + 10 * q^11 - 10 * q^12 + 3 * q^13 - 12 * q^14 - 8 * q^15 + 6 * q^16 + 3 * q^17 - 32 * q^19 - 10 * q^20 - 6 * q^21 - 9 * q^22 - 22 * q^23 + 20 * q^24 + 12 * q^25 + 18 * q^26 + 4 * q^27 + 30 * q^28 + 38 * q^29 - 2 * q^30 - 8 * q^31 + 10 * q^33 - 52 * q^34 + 3 * q^35 - 5 * q^36 - 8 * q^37 + 7 * q^38 + 6 * q^39 + 37 * q^40 - 40 * q^41 + 12 * q^42 + q^43 + q^45 - 7 * q^46 - 23 * q^47 + 18 * q^48 + 25 * q^49 - 21 * q^50 - 3 * q^51 - 45 * q^52 + 30 * q^53 - 5 * q^54 + 46 * q^55 - 6 * q^56 - 8 * q^57 + 48 * q^58 - 40 * q^59 + 15 * q^60 + 26 * q^61 + 40 * q^62 - 12 * q^63 + 38 * q^64 + 12 * q^65 + 12 * q^66 - 32 * q^67 + 15 * q^68 - 11 * q^69 + 33 * q^70 + 17 * q^71 + 5 * q^72 + 27 * q^73 - 70 * q^74 + 3 * q^75 - 15 * q^76 - 9 * q^77 - 9 * q^78 + 21 * q^80 + 2 * q^81 - 32 * q^82 - 17 * q^83 - 15 * q^84 - 64 * q^85 + 26 * q^86 - 6 * q^87 - 22 * q^88 - 43 * q^89 - 16 * q^90 - 140 * q^92 - q^93 + 88 * q^94 - 2 * q^95 - 35 * q^96 + 12 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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