LMFDB - Embedded newform 230.2.g.d.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(31,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("230.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.g (of order $11$, degree $10$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			31.2
Character	$\chi$	$=$	230.31
Dual form			230.2.g.d.141.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(-0.0488649 - 0.106999i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.112864 - 0.0331400i) q^{6} +(1.43095 + 0.919619i) q^{7} +(0.415415 - 0.909632i) q^{8} +(1.95552 - 2.25679i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.0488649 - 0.106999i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.112864 - 0.0331400i) q^{6} +(1.43095 + 0.919619i) q^{7} +(0.415415 - 0.909632i) q^{8} +(1.95552 - 2.25679i) q^{9} +(-0.841254 + 0.540641i) q^{10} +(0.922449 + 6.41578i) q^{11} +(0.0167404 + 0.116432i) q^{12} +(-0.840347 + 0.540058i) q^{13} +(-1.11390 + 1.28551i) q^{14} +(0.0488649 - 0.106999i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-4.80092 + 1.40968i) q^{17} +(1.95552 + 2.25679i) q^{18} +(3.14704 + 0.924055i) q^{19} +(-0.415415 - 0.909632i) q^{20} +(0.0284750 - 0.198048i) q^{21} -6.48175 q^{22} +(3.59066 - 3.17917i) q^{23} -0.117629 q^{24} +(-0.142315 + 0.989821i) q^{25} +(-0.414967 - 0.908651i) q^{26} +(-0.675625 - 0.198381i) q^{27} +(-1.11390 - 1.28551i) q^{28} +(-0.346560 + 0.101759i) q^{29} +(0.0989560 + 0.0635951i) q^{30} +(3.99557 - 8.74908i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(0.641408 - 0.412208i) q^{33} +(-0.712087 - 4.95267i) q^{34} +(0.242075 + 1.68367i) q^{35} +(-2.51212 + 1.61444i) q^{36} +(-5.41383 + 6.24790i) q^{37} +(-1.36252 + 2.98350i) q^{38} +(0.0988493 + 0.0635266i) q^{39} +(0.959493 - 0.281733i) q^{40} +(-2.84864 - 3.28750i) q^{41} +(0.191980 + 0.0563704i) q^{42} +(-3.89973 - 8.53921i) q^{43} +(0.922449 - 6.41578i) q^{44} +2.98616 q^{45} +(2.63581 + 4.00656i) q^{46} +0.735530 q^{47} +(0.0167404 - 0.116432i) q^{48} +(-1.70597 - 3.73556i) q^{49} +(-0.959493 - 0.281733i) q^{50} +(0.385431 + 0.444812i) q^{51} +(0.958459 - 0.281429i) q^{52} +(0.0471159 + 0.0302796i) q^{53} +(0.292513 - 0.640515i) q^{54} +(-4.24464 + 4.89858i) q^{55} +(1.43095 - 0.919619i) q^{56} +(-0.0549068 - 0.381885i) q^{57} +(-0.0514028 - 0.357514i) q^{58} +(12.0681 - 7.75573i) q^{59} +(-0.0770307 + 0.0888982i) q^{60} +(4.22418 - 9.24967i) q^{61} +(8.09139 + 5.20002i) q^{62} +(4.87365 - 1.43103i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-0.958459 - 0.281429i) q^{65} +(0.316730 + 0.693543i) q^{66} +(0.568761 - 3.95582i) q^{67} +5.00360 q^{68} +(-0.515627 - 0.228849i) q^{69} -1.70098 q^{70} +(-1.52497 + 10.6064i) q^{71} +(-1.24050 - 2.71631i) q^{72} +(-8.05279 - 2.36451i) q^{73} +(-5.41383 - 6.24790i) q^{74} +(0.112864 - 0.0331400i) q^{75} +(-2.75923 - 1.77325i) q^{76} +(-4.58008 + 10.0290i) q^{77} +(-0.0769477 + 0.0888024i) q^{78} +(-6.62928 + 4.26038i) q^{79} +(0.142315 + 0.989821i) q^{80} +(-1.26314 - 8.78532i) q^{81} +(3.65944 - 2.35178i) q^{82} +(-6.26936 + 7.23523i) q^{83} +(-0.0831182 + 0.182004i) q^{84} +(-4.20930 - 2.70515i) q^{85} +(9.00728 - 2.64478i) q^{86} +(0.0278228 + 0.0321092i) q^{87} +(6.21919 + 1.82612i) q^{88} +(3.35980 + 7.35694i) q^{89} +(-0.424975 + 2.95577i) q^{90} -1.69915 q^{91} +(-4.34089 + 2.03878i) q^{92} -1.13139 q^{93} +(-0.104677 + 0.728043i) q^{94} +(1.36252 + 2.98350i) q^{95} +(0.112864 + 0.0331400i) q^{96} +(-9.33518 - 10.7734i) q^{97} +(3.94032 - 1.15698i) q^{98} +(16.2829 + 10.4644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9}+O(q^{10}) $ 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9	\( 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9} + 3 q^{10} - 3 q^{11} - q^{12} + 12 q^{13} - 3 q^{14} + q^{15} - 3 q^{16} - 26 q^{17} + 12 q^{18} - 25 q^{19} + 3 q^{20} - 11 q^{21} - 14 q^{22} + 14 q^{23} + 10 q^{24} - 3 q^{25} - 10 q^{26} - 52 q^{27} - 3 q^{28} + 4 q^{29} + q^{30} + 5 q^{31} - 3 q^{32} + 9 q^{33} + 7 q^{34} + 3 q^{35} + 12 q^{36} - 20 q^{37} + 19 q^{38} + 41 q^{39} + 3 q^{40} + 32 q^{41} + 22 q^{42} - 46 q^{43} - 3 q^{44} - 56 q^{45} + 3 q^{46} + 80 q^{47} - q^{48} - 41 q^{49} - 3 q^{50} - 34 q^{51} - 21 q^{52} + 29 q^{53} + 47 q^{54} + 3 q^{55} + 8 q^{56} - 33 q^{57} - 7 q^{58} - 3 q^{59} + q^{60} - q^{61} - 28 q^{62} - 8 q^{63} - 3 q^{64} + 21 q^{65} - 46 q^{66} - 63 q^{67} - 4 q^{68} + 78 q^{69} - 8 q^{70} + 55 q^{71} - 32 q^{72} - 36 q^{73} - 20 q^{74} - q^{75} - 3 q^{76} - 9 q^{77} - 80 q^{78} - 29 q^{79} + 3 q^{80} + 15 q^{81} - 23 q^{82} - 63 q^{83} + 4 q^{85} + 31 q^{86} + 63 q^{87} - 3 q^{88} - 95 q^{89} + 10 q^{90} - 12 q^{91} + 14 q^{92} + 126 q^{93} + 3 q^{94} - 19 q^{95} - q^{96} + 11 q^{97} + 58 q^{98} + 97 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9 + 3 * q^10 - 3 * q^11 - q^12 + 12 * q^13 - 3 * q^14 + q^15 - 3 * q^16 - 26 * q^17 + 12 * q^18 - 25 * q^19 + 3 * q^20 - 11 * q^21 - 14 * q^22 + 14 * q^23 + 10 * q^24 - 3 * q^25 - 10 * q^26 - 52 * q^27 - 3 * q^28 + 4 * q^29 + q^30 + 5 * q^31 - 3 * q^32 + 9 * q^33 + 7 * q^34 + 3 * q^35 + 12 * q^36 - 20 * q^37 + 19 * q^38 + 41 * q^39 + 3 * q^40 + 32 * q^41 + 22 * q^42 - 46 * q^43 - 3 * q^44 - 56 * q^45 + 3 * q^46 + 80 * q^47 - q^48 - 41 * q^49 - 3 * q^50 - 34 * q^51 - 21 * q^52 + 29 * q^53 + 47 * q^54 + 3 * q^55 + 8 * q^56 - 33 * q^57 - 7 * q^58 - 3 * q^59 + q^60 - q^61 - 28 * q^62 - 8 * q^63 - 3 * q^64 + 21 * q^65 - 46 * q^66 - 63 * q^67 - 4 * q^68 + 78 * q^69 - 8 * q^70 + 55 * q^71 - 32 * q^72 - 36 * q^73 - 20 * q^74 - q^75 - 3 * q^76 - 9 * q^77 - 80 * q^78 - 29 * q^79 + 3 * q^80 + 15 * q^81 - 23 * q^82 - 63 * q^83 + 4 * q^85 + 31 * q^86 + 63 * q^87 - 3 * q^88 - 95 * q^89 + 10 * q^90 - 12 * q^91 + 14 * q^92 + 126 * q^93 + 3 * q^94 - 19 * q^95 - q^96 + 11 * q^97 + 58 * q^98 + 97 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$3$	−0.0488649	−	0.106999i	−0.0282122	−	0.0617761i	0.895001	−	0.446063i	$-0.147174\pi$
$3$	−0.0488649	−	0.106999i	−0.0282122	−	0.0617761i	−0.923214	+	0.384287i	$0.874447\pi$
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	0.654861	+	0.755750i	0.292863	+	0.337981i
$5$	0.654861	+	0.755750i	0.292863	+	0.337981i
$6$	0.112864	−	0.0331400i	0.0460767	−	0.0135293i
$7$	1.43095	+	0.919619i	0.540850	+	0.347583i	0.782371	−	0.622812i	$-0.214010\pi$
$7$	1.43095	+	0.919619i	0.540850	+	0.347583i	−0.241521	+	0.970396i	$0.577646\pi$
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	1.95552	−	2.25679i	0.651840	−	0.752264i
$10$	−0.841254	+	0.540641i	−0.266028	+	0.170966i
$11$	0.922449	+	6.41578i	0.278129	+	1.93443i	0.349403	+	0.936972i	$0.386384\pi$
$11$	0.922449	+	6.41578i	0.278129	+	1.93443i	−0.0712744	+	0.997457i	$0.522707\pi$
$12$	0.0167404	+	0.116432i	0.00483253	+	0.0336110i
$13$	−0.840347	+	0.540058i	−0.233070	+	0.149785i	−0.651964	−	0.758250i	$-0.726054\pi$
$13$	−0.840347	+	0.540058i	−0.233070	+	0.149785i	0.418893	+	0.908035i	$0.362418\pi$
$14$	−1.11390	+	1.28551i	−0.297703	+	0.343568i
$15$	0.0488649	−	0.106999i	0.0126169	−	0.0276271i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	−4.80092	+	1.40968i	−1.16439	+	0.341897i	−0.806139	−	0.591726i	$-0.798447\pi$
$17$	−4.80092	+	1.40968i	−1.16439	+	0.341897i	−0.358256	+	0.933623i	$0.616628\pi$
$18$	1.95552	+	2.25679i	0.460921	+	0.531931i
$19$	3.14704	+	0.924055i	0.721981	+	0.211993i	0.622023	−	0.782999i	$-0.286311\pi$
$19$	3.14704	+	0.924055i	0.721981	+	0.211993i	0.0999579	+	0.994992i	$0.468129\pi$
$20$	−0.415415	−	0.909632i	−0.0928896	−	0.203400i
$21$	0.0284750	−	0.198048i	0.00621376	−	0.0432177i
$22$	−6.48175			−1.38191
$23$	3.59066	−	3.17917i	0.748705	−	0.662903i
$23$	3.59066	−	3.17917i	0.748705	−	0.662903i
$24$	−0.117629			−0.0240110
$25$	−0.142315	+	0.989821i	−0.0284630	+	0.197964i
$26$	−0.414967	−	0.908651i	−0.0813818	−	0.178201i
$27$	−0.675625	−	0.198381i	−0.130024	−	0.0381785i
$28$	−1.11390	−	1.28551i	−0.210508	−	0.242939i
$29$	−0.346560	+	0.101759i	−0.0643546	+	0.0188962i	−0.313751	−	0.949505i	$-0.601586\pi$
$29$	−0.346560	+	0.101759i	−0.0643546	+	0.0188962i	0.249397	+	0.968401i	$0.419768\pi$
$30$	0.0989560	+	0.0635951i	0.0180668	+	0.0116108i
$31$	3.99557	−	8.74908i	0.717625	−	1.57138i	−0.0995771	−	0.995030i	$-0.531749\pi$
$31$	3.99557	−	8.74908i	0.717625	−	1.57138i	0.817202	−	0.576351i	$-0.195524\pi$
$32$	−0.654861	+	0.755750i	−0.115764	+	0.133599i
$33$	0.641408	−	0.412208i	0.111655	−	0.0717562i
$34$	−0.712087	−	4.95267i	−0.122122	−	0.849377i
$35$	0.242075	+	1.68367i	0.0409181	+	0.284591i
$36$	−2.51212	+	1.61444i	−0.418687	+	0.269074i
$37$	−5.41383	+	6.24790i	−0.890029	+	1.02715i	0.109421	+	0.993995i	$0.465100\pi$
$37$	−5.41383	+	6.24790i	−0.890029	+	1.02715i	−0.999450	+	0.0331527i	$0.989445\pi$
$38$	−1.36252	+	2.98350i	−0.221030	+	0.483988i
$39$	0.0988493	+	0.0635266i	0.0158286	+	0.0101724i
$40$	0.959493	−	0.281733i	0.151709	−	0.0445458i
$41$	−2.84864	−	3.28750i	−0.444882	−	0.513422i	0.488373	−	0.872635i	$-0.337591\pi$
$41$	−2.84864	−	3.28750i	−0.444882	−	0.513422i	−0.933256	+	0.359213i	$0.883045\pi$
$42$	0.191980	+	0.0563704i	0.0296231	+	0.00869814i
$43$	−3.89973	−	8.53921i	−0.594703	−	1.30222i	−0.932558	−	0.361019i	$-0.882429\pi$
$43$	−3.89973	−	8.53921i	−0.594703	−	1.30222i	0.337856	−	0.941198i	$-0.390298\pi$
$44$	0.922449	−	6.41578i	0.139064	−	0.967215i
$45$	2.98616			0.445151
$46$	2.63581	+	4.00656i	0.388628	+	0.590735i
$47$	0.735530			0.107288			0.0536440	−	0.998560i	$-0.482916\pi$
$47$	0.735530			0.107288			0.0536440	+	0.998560i	$0.482916\pi$
$48$	0.0167404	−	0.116432i	0.00241627	−	0.0168055i
$49$	−1.70597	−	3.73556i	−0.243710	−	0.533651i
$50$	−0.959493	−	0.281733i	−0.135693	−	0.0398430i
$51$	0.385431	+	0.444812i	0.0539712	+	0.0622861i
$52$	0.958459	−	0.281429i	0.132914	−	0.0390272i
$53$	0.0471159	+	0.0302796i	0.00647187	+	0.00415922i	0.543873	−	0.839168i	$-0.316957\pi$
$53$	0.0471159	+	0.0302796i	0.00647187	+	0.00415922i	−0.537401	+	0.843327i	$0.680594\pi$
$54$	0.292513	−	0.640515i	0.0398060	−	0.0871631i
$55$	−4.24464	+	4.89858i	−0.572348	+	0.660524i
$56$	1.43095	−	0.919619i	0.191219	−	0.122889i
$57$	−0.0549068	−	0.381885i	−0.00727258	−	0.0505819i
$58$	−0.0514028	−	0.357514i	−0.00674952	−	0.0469439i
$59$	12.0681	−	7.75573i	1.57114	−	1.00971i	0.592142	−	0.805833i	$-0.298282\pi$
$59$	12.0681	−	7.75573i	1.57114	−	1.00971i	0.978997	−	0.203876i	$-0.0653541\pi$
$60$	−0.0770307	+	0.0888982i	−0.00994463	+	0.0114767i
$61$	4.22418	−	9.24967i	0.540851	−	1.18430i	−0.420073	−	0.907490i	$-0.637996\pi$
$61$	4.22418	−	9.24967i	0.540851	−	1.18430i	0.960925	−	0.276809i	$-0.0892770\pi$
$62$	8.09139	+	5.20002i	1.02761	+	0.660404i
$63$	4.87365	−	1.43103i	0.614022	−	0.180293i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	−0.958459	−	0.281429i	−0.118882	−	0.0349069i
$66$	0.316730	+	0.693543i	0.0389868	+	0.0853692i
$67$	0.568761	−	3.95582i	0.0694853	−	0.483281i	−0.925131	−	0.379649i	$-0.876045\pi$
$67$	0.568761	−	3.95582i	0.0694853	−	0.483281i	0.994616	−	0.103631i	$-0.0330462\pi$
$68$	5.00360			0.606776
$69$	−0.515627	−	0.228849i	−0.0620741	−	0.0275501i
$70$	−1.70098			−0.203306
$71$	−1.52497	+	10.6064i	−0.180980	+	1.25875i	0.673471	+	0.739214i	$0.264803\pi$
$71$	−1.52497	+	10.6064i	−0.180980	+	1.25875i	−0.854451	+	0.519532i	$0.826106\pi$
$72$	−1.24050	−	2.71631i	−0.146194	−	0.320120i
$73$	−8.05279	−	2.36451i	−0.942508	−	0.276745i	−0.225843	−	0.974164i	$-0.572514\pi$
$73$	−8.05279	−	2.36451i	−0.942508	−	0.276745i	−0.716664	+	0.697418i	$0.754332\pi$
$74$	−5.41383	−	6.24790i	−0.629346	−	0.726303i
$75$	0.112864	−	0.0331400i	0.0130325	−	0.00382667i
$76$	−2.75923	−	1.77325i	−0.316505	−	0.203406i
$77$	−4.58008	+	10.0290i	−0.521949	+	1.14291i
$78$	−0.0769477	+	0.0888024i	−0.00871261	+	0.0100549i
$79$	−6.62928	+	4.26038i	−0.745852	+	0.479330i	−0.857543	−	0.514413i	$-0.828010\pi$
$79$	−6.62928	+	4.26038i	−0.745852	+	0.479330i	0.111690	+	0.993743i	$0.464374\pi$
$80$	0.142315	+	0.989821i	0.0159113	+	0.110665i
$81$	−1.26314	−	8.78532i	−0.140349	−	0.976147i
$82$	3.65944	−	2.35178i	0.404118	−	0.259711i
$83$	−6.26936	+	7.23523i	−0.688152	+	0.794170i	−0.987101	−	0.160099i	$-0.948819\pi$
$83$	−6.26936	+	7.23523i	−0.688152	+	0.794170i	0.298949	+	0.954269i	$0.403364\pi$
$84$	−0.0831182	+	0.182004i	−0.00906894	+	0.0198582i
$85$	−4.20930	−	2.70515i	−0.456563	−	0.293415i
$86$	9.00728	−	2.64478i	0.971280	−	0.285194i
$87$	0.0278228	+	0.0321092i	0.00298292	+	0.00344247i
$88$	6.21919	+	1.82612i	0.662968	+	0.194665i
$89$	3.35980	+	7.35694i	0.356138	+	0.779834i	0.999893	+	0.0146024i	$0.00464825\pi$
$89$	3.35980	+	7.35694i	0.356138	+	0.779834i	−0.643755	+	0.765232i	$0.722624\pi$
$90$	−0.424975	+	2.95577i	−0.0447963	+	0.311565i
$91$	−1.69915			−0.178119
$92$	−4.34089	+	2.03878i	−0.452569	+	0.212558i
$93$	−1.13139			−0.117319
$94$	−0.104677	+	0.728043i	−0.0107966	+	0.0750919i
$95$	1.36252	+	2.98350i	0.139792	+	0.306101i
$96$	0.112864	+	0.0331400i	0.0115192	+	0.00338233i
$97$	−9.33518	−	10.7734i	−0.947844	−	1.09387i	−0.995477	−	0.0950049i	$-0.969713\pi$
$97$	−9.33518	−	10.7734i	−0.947844	−	1.09387i	0.0476332	−	0.998865i	$-0.484832\pi$
$98$	3.94032	−	1.15698i	0.398033	−	0.116873i
$99$	16.2829	+	10.4644i	1.63650	+	1.05171i
$100$	0.415415	−	0.909632i	0.0415415	−	0.0909632i
$101$	−6.95953	+	8.03173i	−0.692499	+	0.799187i	−0.987719	−	0.156243i	$-0.950062\pi$
$101$	−6.95953	+	8.03173i	−0.692499	+	0.799187i	0.295220	+	0.955429i	$0.404607\pi$
$102$	−0.495137	+	0.318205i	−0.0490258	+	0.0315070i
$103$	0.124056	+	0.862830i	0.0122236	+	0.0850172i	0.995020	−	0.0996749i	$-0.0317803\pi$
$103$	0.124056	+	0.862830i	0.0122236	+	0.0850172i	−0.982796	+	0.184692i	$0.940871\pi$
$104$	0.142161	+	0.988754i	0.0139401	+	0.0969553i
$105$	0.168322	−	0.108174i	0.0164265	−	0.0105567i
$106$	−0.0366767	+	0.0423271i	−0.00356235	+	0.00411118i
$107$	−3.92644	+	8.59769i	−0.379583	+	0.831170i	0.619356	+	0.785110i	$0.287394\pi$
$107$	−3.92644	+	8.59769i	−0.379583	+	0.831170i	−0.998939	+	0.0460600i	$0.985333\pi$
$108$	0.592367	+	0.380691i	0.0570005	+	0.0366320i
$109$	9.62091	−	2.82495i	0.921516	−	0.270582i	0.213635	−	0.976913i	$-0.431470\pi$
$109$	9.62091	−	2.82495i	0.921516	−	0.270582i	0.707881	+	0.706332i	$0.249651\pi$
$110$	−4.24464	−	4.89858i	−0.404711	−	0.467061i
$111$	0.933067	+	0.273973i	0.0885628	+	0.0260044i
$112$	0.706612	+	1.54726i	0.0667686	+	0.146203i
$113$	1.28293	−	8.92300i	0.120688	−	0.839405i	−0.836091	−	0.548590i	$-0.815165\pi$
$113$	1.28293	−	8.92300i	0.120688	−	0.839405i	0.956779	−	0.290815i	$-0.0939263\pi$
$114$	0.385812			0.0361346
$115$	4.75404	+	0.631729i	0.443317	+	0.0589091i
$116$	0.361191			0.0335357
$117$	−0.424517	+	2.95258i	−0.0392466	+	0.272966i
$118$	5.95931	+	13.0491i	0.548599	+	1.20126i
$119$	−8.16627	−	2.39783i	−0.748601	−	0.219809i
$120$	−0.0770307	−	0.0888982i	−0.00703191	−	0.00811526i
$121$	−29.7568	+	8.73740i	−2.70517	+	0.794309i
$122$	8.55436	+	5.49755i	0.774476	+	0.497725i
$123$	−0.212562	+	0.465446i	−0.0191661	+	0.0419678i
$124$	−6.29862	+	7.26900i	−0.565633	+	0.652775i
$125$	−0.841254	+	0.540641i	−0.0752440	+	0.0483564i
$126$	0.722874	+	5.02770i	0.0643987	+	0.447903i
$127$	1.22049	+	8.48871i	0.108301	+	0.753251i	0.969519	+	0.245016i	$0.0787931\pi$
$127$	1.22049	+	8.48871i	0.108301	+	0.753251i	−0.861218	+	0.508236i	$0.830298\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$	−0.723129	+	0.834536i	−0.0636680	+	0.0734768i
$130$	0.414967	−	0.908651i	0.0363950	−	0.0796940i
$131$	−1.73843	−	1.11722i	−0.151887	−	0.0976119i	0.462490	−	0.886625i	$-0.346956\pi$
$131$	−1.73843	−	1.11722i	−0.151887	−	0.0976119i	−0.614377	+	0.789013i	$0.710593\pi$
$132$	−0.731559	+	0.214805i	−0.0636740	+	0.0186964i
$133$	3.65350	+	4.21636i	0.316798	+	0.365605i
$134$	3.83461	+	1.12594i	0.331260	+	0.0972668i
$135$	−0.292513	−	0.640515i	−0.0251756	−	0.0551268i
$136$	−0.712087	+	4.95267i	−0.0610610	+	0.424688i
$137$	18.2723			1.56111			0.780555	−	0.625087i	$-0.214936\pi$
$137$	18.2723			1.56111			0.780555	+	0.625087i	$0.214936\pi$
$138$	0.299901	−	0.477810i	0.0255292	−	0.0406739i
$139$	−2.91535			−0.247277			−0.123638	−	0.992327i	$-0.539456\pi$
$139$	−2.91535			−0.247277			−0.123638	+	0.992327i	$0.539456\pi$
$140$	0.242075	−	1.68367i	0.0204590	−	0.142296i
$141$	−0.0359416	−	0.0787012i	−0.00302683	−	0.00662784i
$142$	−10.2814	−	3.01889i	−0.862796	−	0.253340i
$143$	−4.24007	−	4.89330i	−0.354572	−	0.409198i
$144$	2.86520	−	0.841299i	0.238767	−	0.0701083i
$145$	−0.303853	−	0.195274i	−0.0252336	−	0.0162167i
$146$	3.48648	−	7.63432i	0.288543	−	0.631821i
$147$	−0.316340	+	0.365076i	−0.0260913	+	0.0301109i
$148$	6.95477	−	4.46956i	0.571679	−	0.367396i
$149$	0.478367	+	3.32712i	0.0391894	+	0.272568i	0.999989	−	0.00467542i	$-0.00148824\pi$
$149$	0.478367	+	3.32712i	0.0391894	+	0.272568i	−0.960800	+	0.277243i	$0.910579\pi$
$150$	0.0167404	+	0.116432i	0.00136685	+	0.00950662i
$151$	4.98945	−	3.20653i	0.406036	−	0.260944i	−0.321643	−	0.946861i	$-0.604235\pi$
$151$	4.98945	−	3.20653i	0.406036	−	0.260944i	0.727679	+	0.685917i	$0.240599\pi$
$152$	2.14788	−	2.47878i	0.174216	−	0.201056i
$153$	−6.20696	+	13.5913i	−0.501803	+	1.09879i
$154$	−9.27509	−	5.96074i	−0.747408	−	0.480330i
$155$	9.22865	−	2.70978i	0.741263	−	0.217655i
$156$	−0.0769477	−	0.0888024i	−0.00616075	−	0.00710988i
$157$	20.4497	+	6.00456i	1.63206	+	0.479216i	0.964224	−	0.265091i	$-0.0854019\pi$
$157$	20.4497	+	6.00456i	1.63206	+	0.479216i	0.667838	+	0.744307i	$0.267220\pi$
$158$	−3.27357	−	7.16812i	−0.260431	−	0.570265i
$159$	0.000937576	−	0.00652098i	7.43546e−5	−	0.000517148i
$160$	−1.00000			−0.0790569
$161$	8.06170	−	1.24721i	0.635351	−	0.0982936i
$162$	8.87566			0.697338
$163$	0.454484	−	3.16101i	0.0355979	−	0.247589i	−0.964251	−	0.264992i	$-0.914631\pi$
$163$	0.454484	−	3.16101i	0.0355979	−	0.247589i	0.999849	+	0.0174029i	$0.00553978\pi$
$164$	1.80705	+	3.95689i	0.141107	+	0.308981i
$165$	0.731559	+	0.214805i	0.0569518	+	0.0167226i
$166$	−6.26936	−	7.23523i	−0.486597	−	0.561563i
$167$	6.57105	−	1.92944i	0.508484	−	0.149304i	−0.0174203	−	0.999848i	$-0.505545\pi$
$167$	6.57105	−	1.92944i	0.508484	−	0.149304i	0.525904	+	0.850544i	$0.323727\pi$
$168$	−0.168322	−	0.108174i	−0.0129863	−	0.00834581i
$169$	−4.98588	+	10.9175i	−0.383529	+	0.839811i
$170$	3.27666	−	3.78147i	0.251309	−	0.290026i
$171$	8.23951	−	5.29521i	0.630091	−	0.404935i
$172$	1.33599	+	9.29199i	0.101868	+	0.708508i
$173$	−2.20075	−	15.3066i	−0.167320	−	1.16374i	−0.884394	−	0.466741i	$-0.845428\pi$
$173$	−2.20075	−	15.3066i	−0.167320	−	1.16374i	0.717074	−	0.696997i	$-0.245481\pi$
$174$	−0.0357420	+	0.0229700i	−0.00270959	+	0.00174135i
$175$	−1.11390	+	1.28551i	−0.0842032	+	0.0971757i
$176$	−2.69262	+	5.89601i	−0.202964	+	0.444428i
$177$	−1.41957	−	0.912300i	−0.106701	−	0.0685727i
$178$	−7.76020	+	2.27860i	−0.581652	+	0.170788i
$179$	−5.03785	−	5.81398i	−0.376546	−	0.434558i	0.535569	−	0.844492i	$-0.320097\pi$
$179$	−5.03785	−	5.81398i	−0.376546	−	0.434558i	−0.912115	+	0.409934i	$0.865552\pi$
$180$	−2.86520	−	0.841299i	−0.213560	−	0.0627068i
$181$	−6.19725	−	13.5701i	−0.460638	−	1.00866i	−0.987342	−	0.158608i	$-0.949299\pi$
$181$	−6.19725	−	13.5701i	−0.460638	−	1.00866i	0.526703	−	0.850049i	$-0.323428\pi$
$182$	0.241814	−	1.68185i	0.0179244	−	0.124667i
$183$	−1.19612			−0.0884200
$184$	−1.40026	−	4.58686i	−0.103228	−	0.338148i
$185$	−8.26715			−0.607813
$186$	0.161013	−	1.11987i	0.0118061	−	0.0821130i
$187$	−13.4728	−	29.5013i	−0.985228	−	2.15735i
$188$	−0.705736	−	0.207223i	−0.0514711	−	0.0151133i
$189$	−0.784353	−	0.905192i	−0.0570533	−	0.0658430i
$190$	−3.14704	+	0.924055i	−0.228310	+	0.0670380i
$191$	7.78717	+	5.00451i	0.563460	+	0.362114i	0.791152	−	0.611620i	$-0.209482\pi$
$191$	7.78717	+	5.00451i	0.563460	+	0.362114i	−0.227692	+	0.973733i	$0.573118\pi$
$192$	−0.0488649	+	0.106999i	−0.00352652	+	0.00772201i
$193$	0.974618	−	1.12477i	0.0701545	−	0.0809627i	−0.719587	−	0.694402i	$-0.755669\pi$
$193$	0.974618	−	1.12477i	0.0701545	−	0.0809627i	0.789742	+	0.613439i	$0.210214\pi$
$194$	11.9922	−	7.70695i	0.860993	−	0.553327i
$195$	0.0167223	+	0.116306i	0.00119751	+	0.00832887i
$196$	0.584440	+	4.06487i	0.0417457	+	0.290348i
$197$	2.47676	−	1.59171i	0.176462	−	0.113405i	−0.449428	−	0.893316i	$-0.648372\pi$
$197$	2.47676	−	1.59171i	0.176462	−	0.113405i	0.625890	+	0.779911i	$0.284736\pi$
$198$	−12.6752	+	14.6280i	−0.900787	+	1.03956i
$199$	−2.75030	+	6.02232i	−0.194964	+	0.426911i	−0.981714	−	0.190360i	$-0.939034\pi$
$199$	−2.75030	+	6.02232i	−0.194964	+	0.426911i	0.786751	+	0.617271i	$0.211762\pi$
$200$	0.841254	+	0.540641i	0.0594856	+	0.0382291i
$201$	−0.451063	+	0.132444i	−0.0318155	+	0.00934187i
$202$	−6.95953	−	8.03173i	−0.489671	−	0.565110i
$203$	−0.589491	−	0.173090i	−0.0413742	−	0.0121486i
$204$	−0.244501	−	0.535382i	−0.0171185	−	0.0374842i
$205$	0.619068	−	4.30571i	0.0432376	−	0.300724i
$206$	−0.871703			−0.0607344
$207$	−0.153105	−	14.3203i	−0.0106416	−	0.995331i
$208$	−0.998922			−0.0692628
$209$	−3.02554	+	21.0431i	−0.209281	+	1.45558i
$210$	0.0831182	+	0.182004i	0.00573570	+	0.0125594i
$211$	5.33104	+	1.56533i	0.367004	+	0.107762i	0.460034	−	0.887901i	$-0.347837\pi$
$211$	5.33104	+	1.56533i	0.367004	+	0.107762i	−0.0930304	+	0.995663i	$0.529655\pi$
$212$	−0.0366767	−	0.0423271i	−0.00251896	−	0.00290704i
$213$	1.20939	−	0.355110i	0.0828662	−	0.0243317i
$214$	−7.95139	−	5.11005i	−0.543546	−	0.349316i
$215$	3.89973	−	8.53921i	0.265959	−	0.582369i
$216$	−0.461119	+	0.532159i	−0.0313751	+	0.0362088i
$217$	13.7633	−	8.84513i	0.934313	−	0.600447i
$218$	1.42700	+	9.92502i	0.0966488	+	0.672207i
$219$	0.140498	+	0.977184i	0.00949397	+	0.0660320i
$220$	5.45280	−	3.50430i	0.367627	−	0.236260i
$221$	3.27313	−	3.77739i	0.220175	−	0.254095i
$222$	−0.403974	+	0.884580i	−0.0271130	+	0.0593691i
$223$	16.7498	+	10.7644i	1.12165	+	0.720839i	0.963801	−	0.266624i	$-0.0859083\pi$
$223$	16.7498	+	10.7644i	1.12165	+	0.720839i	0.157847	+	0.987464i	$0.449545\pi$
$224$	−1.63208	+	0.479221i	−0.109048	+	0.0320193i
$225$	1.95552	+	2.25679i	0.130368	+	0.150453i
$226$	8.64959	+	2.53975i	0.575362	+	0.168942i
$227$	−2.44929	−	5.36319i	−0.162565	−	0.355968i	0.810767	−	0.585369i	$-0.199050\pi$
$227$	−2.44929	−	5.36319i	−0.162565	−	0.355968i	−0.973332	+	0.229401i	$0.926323\pi$
$228$	−0.0549068	+	0.381885i	−0.00363629	+	0.0252910i
$229$	−3.97930			−0.262959			−0.131480	−	0.991319i	$-0.541973\pi$
$229$	−3.97930			−0.262959			−0.131480	+	0.991319i	$0.541973\pi$
$230$	−1.30187	+	4.61575i	−0.0858428	+	0.304353i
$231$	1.29690			0.0853297
$232$	−0.0514028	+	0.357514i	−0.00337476	+	0.0234720i
$233$	−11.0519	−	24.2004i	−0.724037	−	1.58542i	−0.808159	−	0.588964i	$-0.799536\pi$
$233$	−11.0519	−	24.2004i	−0.724037	−	1.58542i	0.0841219	−	0.996455i	$-0.473191\pi$
$234$	−2.86211	−	0.840392i	−0.187102	−	0.0549382i
$235$	0.481670	+	0.555877i	0.0314207	+	0.0362614i
$236$	−13.7643	+	4.04158i	−0.895982	+	0.263084i
$237$	0.779797	+	0.501145i	0.0506533	+	0.0325529i
$238$	3.53561	−	7.74190i	0.229179	−	0.501833i
$239$	1.22683	−	1.41583i	0.0793567	−	0.0915825i	−0.714683	−	0.699449i	$-0.753429\pi$
$239$	1.22683	−	1.41583i	0.0793567	−	0.0915825i	0.794039	+	0.607866i	$0.207974\pi$
$240$	0.0989560	−	0.0635951i	0.00638758	−	0.00410505i
$241$	−1.01988	−	7.09341i	−0.0656961	−	0.456927i	−0.995943	−	0.0899912i	$-0.971316\pi$
$241$	−1.01988	−	7.09341i	−0.0656961	−	0.456927i	0.930246	−	0.366935i	$-0.119593\pi$
$242$	−4.41362	−	30.6974i	−0.283718	−	1.97331i
$243$	−2.65540	+	1.70652i	−0.170344	+	0.109473i
$244$	−6.65901	+	7.68491i	−0.426299	+	0.491976i
$245$	1.70597	−	3.73556i	0.108991	−	0.238656i
$246$	−0.430458	−	0.276638i	−0.0274450	−	0.0176378i
$247$	−3.14365	+	0.923059i	−0.200026	+	0.0587328i
$248$	−6.29862	−	7.26900i	−0.399963	−	0.461582i
$249$	1.08052	+	0.317268i	0.0684750	+	0.0201061i
$250$	−0.415415	−	0.909632i	−0.0262732	−	0.0575302i
$251$	−2.59223	+	18.0294i	−0.163620	+	1.13800i	0.728118	+	0.685451i	$0.240395\pi$
$251$	−2.59223	+	18.0294i	−0.163620	+	1.13800i	−0.891738	+	0.452551i	$0.850514\pi$
$252$	−5.07940			−0.319972
$253$	23.7091	+	20.1043i	1.49058	+	1.26394i
$254$	−8.57600			−0.538106
$255$	−0.0837622	+	0.582579i	−0.00524539	+	0.0364825i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−10.8504	−	3.18596i	−0.676828	−	0.198735i	−0.0747865	−	0.997200i	$-0.523828\pi$
$257$	−10.8504	−	3.18596i	−0.676828	−	0.198735i	−0.602041	+	0.798465i	$0.705646\pi$
$258$	−0.723129	−	0.834536i	−0.0450201	−	0.0519559i
$259$	−13.4926	+	3.96180i	−0.838392	+	0.246174i
$260$	0.840347	+	0.540058i	0.0521161	+	0.0334930i
$261$	−0.448056	+	0.981106i	−0.0277340	+	0.0607289i
$262$	1.35325	−	1.56174i	0.0836042	−	0.0964844i
$263$	−22.6352	+	14.5468i	−1.39575	+	0.896994i	−0.999774	−	0.0212676i	$-0.993230\pi$
$263$	−22.6352	+	14.5468i	−1.39575	+	0.896994i	−0.395975	+	0.918261i	$0.629593\pi$
$264$	−0.108507	−	0.754683i	−0.00667814	−	0.0464475i
$265$	0.00797060	+	0.0554368i	0.000489630	+	0.00340545i
$266$	−4.69339	+	3.01626i	−0.287770	+	0.184939i
$267$	0.623011	−	0.718993i	0.0381276	−	0.0440016i
$268$	−1.66021	+	3.63534i	−0.101413	+	0.222064i
$269$	10.6799	+	6.86354i	0.651163	+	0.418477i	0.824091	−	0.566457i	$-0.191686\pi$
$269$	10.6799	+	6.86354i	0.651163	+	0.418477i	−0.172928	+	0.984935i	$0.555323\pi$
$270$	0.675625	−	0.198381i	0.0411172	−	0.0120731i
$271$	10.4540	+	12.0645i	0.635035	+	0.732869i	0.978489	−	0.206300i	$-0.0661424\pi$
$271$	10.4540	+	12.0645i	0.635035	+	0.732869i	−0.343454	+	0.939169i	$0.611597\pi$
$272$	−4.80092	−	1.40968i	−0.291099	−	0.0854743i
$273$	0.0830286	+	0.181807i	0.00502512	+	0.0110035i
$274$	−2.60042	+	18.0863i	−0.157097	+	1.09264i
$275$	−6.48175			−0.390864
$276$	0.430266	+	0.364847i	0.0258990	+	0.0219612i
$277$	9.33186			0.560697			0.280349	−	0.959898i	$-0.409550\pi$
$277$	9.33186			0.560697			0.280349	+	0.959898i	$0.409550\pi$
$278$	0.414897	−	2.88567i	0.0248839	−	0.173071i
$279$	−11.9314	−	26.1262i	−0.714316	−	1.56413i
$280$	1.63208	+	0.479221i	0.0975353	+	0.0286389i
$281$	−10.2106	−	11.7836i	−0.609112	−	0.702953i	0.364489	−	0.931208i	$-0.381244\pi$
$281$	−10.2106	−	11.7836i	−0.609112	−	0.702953i	−0.973601	+	0.228255i	$0.926698\pi$
$282$	0.0830151	−	0.0243754i	0.00494348	−	0.00145154i
$283$	9.52213	+	6.11950i	0.566032	+	0.363766i	0.792143	−	0.610335i	$-0.208965\pi$
$283$	9.52213	+	6.11950i	0.566032	+	0.363766i	−0.226112	+	0.974101i	$0.572601\pi$
$284$	4.45136	−	9.74711i	0.264140	−	0.578385i
$285$	0.252653	−	0.291577i	0.0149659	−	0.0172716i
$286$	5.44692	−	3.50052i	0.322083	−	0.206990i
$287$	−1.05302	−	7.32393i	−0.0621579	−	0.432318i
$288$	0.424975	+	2.95577i	0.0250419	+	0.174170i
$289$	6.76036	−	4.34462i	0.397668	−	0.255566i
$290$	0.236530	−	0.272970i	0.0138895	−	0.0160293i
$291$	−0.696580	+	1.52530i	−0.0408342	+	0.0894145i
$292$	7.06043	+	4.53747i	0.413181	+	0.265535i
$293$	−13.2194	+	3.88157i	−0.772285	+	0.226763i	−0.644053	−	0.764981i	$-0.722748\pi$
$293$	−13.2194	+	3.88157i	−0.772285	+	0.226763i	−0.128232	+	0.991744i	$0.540930\pi$
$294$	−0.316340	−	0.365076i	−0.0184493	−	0.0212916i
$295$	13.7643	+	4.04158i	0.801391	+	0.235310i
$296$	3.43430	+	7.52007i	0.199615	+	0.437095i
$297$	0.649540	−	4.51765i	0.0376902	−	0.262141i
$298$	−3.36133			−0.194717
$299$	−1.30047	+	4.61077i	−0.0752079	+	0.266648i
$300$	−0.117629			−0.00679132
$301$	2.27249	−	15.8055i	0.130984	−	0.911013i
$302$	2.46382	+	5.39501i	0.141777	+	0.310448i
$303$	1.19947	+	0.352195i	0.0689075	+	0.0202331i
$304$	2.14788	+	2.47878i	0.123189	+	0.142168i
$305$	9.75669	−	2.86482i	0.558666	−	0.164039i
$306$	−12.5697	−	8.07803i	−0.718559	−	0.461790i
$307$	9.35097	−	20.4758i	0.533688	−	1.16861i	−0.430304	−	0.902684i	$-0.641594\pi$
$307$	9.35097	−	20.4758i	0.533688	−	1.16861i	0.963992	−	0.265930i	$-0.0856791\pi$
$308$	7.22005	−	8.33238i	0.411401	−	0.474782i
$309$	0.0862602	−	0.0554361i	0.00490717	−	0.00315365i
$310$	1.36882	+	9.52036i	0.0777438	+	0.540720i
$311$	0.797301	+	5.54535i	0.0452108	+	0.314448i	0.999860	+	0.0167160i	$0.00532111\pi$
$311$	0.797301	+	5.54535i	0.0452108	+	0.314448i	−0.954649	+	0.297732i	$0.903770\pi$
$312$	0.0988493	−	0.0635266i	0.00559624	−	0.00359648i
$313$	1.35056	−	1.55863i	0.0763383	−	0.0880992i	−0.716296	−	0.697797i	$-0.754164\pi$
$313$	1.35056	−	1.55863i	0.0763383	−	0.0880992i	0.792634	+	0.609698i	$0.208709\pi$
$314$	−8.85374	+	19.3870i	−0.499645	+	1.09407i
$315$	4.27306	+	2.74613i	0.240760	+	0.154727i
$316$	7.56104	−	2.22012i	0.425341	−	0.124892i
$317$	10.4540	+	12.0645i	0.587154	+	0.677612i	0.969127	−	0.246562i	$-0.0793007\pi$
$317$	10.4540	+	12.0645i	0.587154	+	0.677612i	−0.381973	+	0.924173i	$0.624755\pi$
$318$	0.00632118	+	0.00185607i	0.000354474	+	0.000104083i
$319$	−0.972548	−	2.12958i	−0.0544523	−	0.119234i
$320$	0.142315	−	0.989821i	0.00795564	−	0.0553327i
$321$	1.11181			0.0620553
$322$	0.0872119	+	8.15714i	0.00486013	+	0.454580i
$323$	−16.4113			−0.913151
$324$	−1.26314	+	8.78532i	−0.0701744	+	0.488073i
$325$	−0.414967	−	0.908651i	−0.0230182	−	0.0504029i
$326$	3.06415	+	0.899716i	0.169708	+	0.0498307i
$327$	−0.772393	−	0.891389i	−0.0427134	−	0.0492939i
$328$	−4.17379	+	1.22553i	−0.230459	+	0.0676688i
$329$	1.05251	+	0.676407i	0.0580268	+	0.0372915i
$330$	−0.316730	+	0.693543i	−0.0174354	+	0.0381783i
$331$	−14.0153	+	16.1745i	−0.770352	+	0.889033i	−0.996373	−	0.0850889i	$-0.972883\pi$
$331$	−14.0153	+	16.1745i	−0.770352	+	0.889033i	0.226022	+	0.974122i	$0.427428\pi$
$332$	8.05381	−	5.17587i	0.442010	−	0.284063i
$333$	3.51334	+	24.4358i	0.192530	+	1.33907i
$334$	0.974638	+	6.77876i	0.0533298	+	0.370917i
$335$	3.36207	−	2.16067i	0.183690	−	0.118050i
$336$	0.131028	−	0.151214i	0.00714815	−	0.00824940i
$337$	−5.16204	+	11.3033i	−0.281194	+	0.615730i	−0.996547	−	0.0830343i	$-0.973539\pi$
$337$	−5.16204	+	11.3033i	−0.281194	+	0.615730i	0.715352	+	0.698764i	$0.246266\pi$
$338$	−10.0969	−	6.48885i	−0.549197	−	0.352947i
$339$	−1.01744	+	0.298749i	−0.0552600	+	0.0162258i
$340$	3.27666	+	3.78147i	0.177702	+	0.205079i
$341$	59.8178	+	17.5641i	3.23932	+	0.951149i
$342$	4.06871	+	8.90923i	0.220011	+	0.481756i
$343$	2.68864	−	18.6999i	0.145173	−	1.00970i
$344$	−9.38754			−0.506142
$345$	−0.164711	−	0.539549i	−0.00886776	−	0.0290483i
$346$	15.4640			0.831349
$347$	−4.09683	+	28.4941i	−0.219930	+	1.52964i	0.518361	+	0.855162i	$0.326542\pi$
$347$	−4.09683	+	28.4941i	−0.219930	+	1.52964i	−0.738291	+	0.674482i	$0.764367\pi$
$348$	−0.0176496	−	0.0386472i	−0.000946116	−	0.00207171i
$349$	3.27384	+	0.961286i	0.175245	+	0.0514565i	0.368178	−	0.929755i	$-0.379982\pi$
$349$	3.27384	+	0.961286i	0.175245	+	0.0514565i	−0.192933	+	0.981212i	$0.561800\pi$
$350$	−1.11390	−	1.28551i	−0.0595407	−	0.0687136i
$351$	0.674896	−	0.198167i	0.0360233	−	0.0105774i
$352$	−5.45280	−	3.50430i	−0.290635	−	0.186780i
$353$	−5.91134	+	12.9440i	−0.314629	+	0.688941i	−0.999199	−	0.0400056i	$-0.987262\pi$
$353$	−5.91134	+	12.9440i	−0.314629	+	0.688941i	0.684571	+	0.728946i	$0.259990\pi$
$354$	1.10504	−	1.27528i	0.0587322	−	0.0677806i
$355$	−9.01441	+	5.79321i	−0.478435	+	0.307472i
$356$	−1.15102	−	8.00550i	−0.0610038	−	0.424290i
$357$	0.142478	+	0.990955i	0.00754072	+	0.0524469i
$358$	6.47177	−	4.15915i	0.342043	−	0.219818i
$359$	−3.59191	+	4.14528i	−0.189574	+	0.218780i	−0.842578	−	0.538575i	$-0.818963\pi$
$359$	−3.59191	+	4.14528i	−0.189574	+	0.218780i	0.653004	+	0.757354i	$0.273508\pi$
$360$	1.24050	−	2.71631i	0.0653799	−	0.143162i
$361$	−6.93382	−	4.45610i	−0.364938	−	0.234531i
$362$	14.3139	−	4.20295i	0.752323	−	0.220902i
$363$	2.38896	+	2.75701i	0.125388	+	0.144705i
$364$	1.63032	+	0.478704i	0.0854519	+	0.0250909i
$365$	−3.48648	−	7.63432i	−0.182490	−	0.399598i
$366$	0.170226	−	1.18395i	0.00889786	−	0.0618860i
$367$	18.7393			0.978183			0.489091	−	0.872233i	$-0.337328\pi$
$367$	18.7393			0.978183			0.489091	+	0.872233i	$0.337328\pi$
$368$	4.73945	−	0.733229i	0.247061	−	0.0382222i
$369$	−12.9898			−0.676221
$370$	1.17654	−	8.18301i	0.0611653	−	0.425414i
$371$	0.0395751	+	0.0866574i	0.00205464	+	0.00449903i
$372$	1.08556	+	0.318749i	0.0562836	+	0.0165264i
$373$	11.8231	+	13.6446i	0.612179	+	0.706493i	0.974202	−	0.225677i	$-0.0724592\pi$
$373$	11.8231	+	13.6446i	0.612179	+	0.706493i	−0.362023	+	0.932169i	$0.617914\pi$
$374$	31.1184	−	9.13718i	1.60909	−	0.472472i
$375$	0.0989560	+	0.0635951i	0.00511006	+	0.00328404i
$376$	0.305550	−	0.669062i	0.0157575	−	0.0345042i
$377$	0.236275	−	0.272675i	0.0121688	−	0.0140435i
$378$	1.00760	−	0.647547i	0.0518255	−	0.0333062i
$379$	2.16382	+	15.0497i	0.111148	+	0.773052i	0.966806	+	0.255510i	$0.0822435\pi$
$379$	2.16382	+	15.0497i	0.111148	+	0.773052i	−0.855658	+	0.517541i	$0.826847\pi$
$380$	−0.466779	−	3.24652i	−0.0239452	−	0.166543i
$381$	0.848647	−	0.545392i	0.0434775	−	0.0279413i
$382$	−6.06180	+	6.99569i	−0.310149	+	0.357931i
$383$	10.4784	−	22.9446i	0.535424	−	1.17241i	−0.427840	−	0.903855i	$-0.640725\pi$
$383$	10.4784	−	22.9446i	0.535424	−	1.17241i	0.963263	−	0.268559i	$-0.0865476\pi$
$384$	−0.0989560	−	0.0635951i	−0.00504983	−	0.00324533i
$385$	−10.5787	+	3.10619i	−0.539141	+	0.158306i
$386$	0.974618	+	1.12477i	0.0496068	+	0.0572493i
$387$	−26.8972	−	7.89774i	−1.36726	−	0.401464i
$388$	5.92183	+	12.9670i	0.300635	+	0.658299i
$389$	−2.53958	+	17.6632i	−0.128762	+	0.895559i	0.818365	+	0.574699i	$0.194881\pi$
$389$	−2.53958	+	17.6632i	−0.128762	+	0.895559i	−0.947127	+	0.320860i	$0.896028\pi$
$390$	−0.117502			−0.00594996
$391$	−12.7569	+	20.3246i	−0.645144	+	1.02786i
$392$	−4.10667			−0.207418
$393$	−0.0345935	+	0.240603i	−0.00174501	+	0.0121368i
$394$	1.22303	+	2.67807i	0.0616156	+	0.134919i
$395$	−7.56104	−	2.22012i	−0.380437	−	0.111706i
$396$	−12.6752	−	14.6280i	−0.636953	−	0.735083i
$397$	−9.19582	+	2.70014i	−0.461525	+	0.135516i	−0.504226	−	0.863572i	$-0.668222\pi$
$397$	−9.19582	+	2.70014i	−0.461525	+	0.135516i	0.0427006	+	0.999088i	$0.486404\pi$
$398$	−5.56961	−	3.57937i	−0.279179	−	0.179418i
$399$	0.272620	−	0.596954i	0.0136480	−	0.0298851i
$400$	−0.654861	+	0.755750i	−0.0327430	+	0.0377875i
$401$	0.856388	−	0.550367i	0.0427660	−	0.0274840i	−0.519083	−	0.854724i	$-0.673727\pi$
$401$	0.856388	−	0.550367i	0.0427660	−	0.0274840i	0.561849	+	0.827240i	$0.310090\pi$
$402$	−0.0669029	−	0.465320i	−0.00333682	−	0.0232081i
$403$	1.36735	+	9.51010i	0.0681123	+	0.473732i
$404$	8.94042	−	5.74566i	0.444802	−	0.285857i
$405$	5.81232	−	6.70778i	0.288817	−	0.333312i
$406$	0.255222	−	0.558858i	0.0126664	−	0.0277356i
$407$	−45.0791	−	28.9706i	−2.23449	−	1.43602i
$408$	0.564729	−	0.165819i	0.0279582	−	0.00820928i
$409$	−5.57614	−	6.43521i	−0.275723	−	0.318201i	0.600952	−	0.799285i	$-0.294788\pi$
$409$	−5.57614	−	6.43521i	−0.275723	−	0.318201i	−0.876674	+	0.481085i	$0.840243\pi$
$410$	4.17379	+	1.22553i	0.206129	+	0.0605248i
$411$	−0.892876	−	1.95513i	−0.0440423	−	0.0964393i
$412$	0.124056	−	0.862830i	0.00611181	−	0.0425086i
$413$	24.4013			1.20071
$414$	14.1963	+	1.88645i	0.697712	+	0.0927138i
$415$	−9.57358			−0.469949
$416$	0.142161	−	0.988754i	0.00697004	−	0.0484777i
$417$	0.142458	+	0.311940i	0.00697621	+	0.0152758i
$418$	−20.3983	−	5.98949i	−0.997716	−	0.292956i
$419$	−14.7907	−	17.0693i	−0.722571	−	0.833892i	0.269043	−	0.963128i	$-0.413293\pi$
$419$	−14.7907	−	17.0693i	−0.722571	−	0.833892i	−0.991614	+	0.129237i	$0.958747\pi$
$420$	−0.191980	+	0.0563704i	−0.00936766	+	0.00275059i
$421$	11.4849	+	7.38090i	0.559740	+	0.359723i	0.789715	−	0.613474i	$-0.210228\pi$
$421$	11.4849	+	7.38090i	0.559740	+	0.359723i	−0.229976	+	0.973196i	$0.573865\pi$
$422$	−2.30809	+	5.05400i	−0.112356	+	0.246025i
$423$	1.43834	−	1.65994i	0.0699347	−	0.0807090i
$424$	0.0471159	−	0.0302796i	0.00228815	−	0.00147051i
$425$	−0.712087	−	4.95267i	−0.0345413	−	0.240240i
$426$	0.179381	+	1.24762i	0.00869102	+	0.0604474i
$427$	14.5508	−	9.35122i	0.704162	−	0.452537i
$428$	6.18964	−	7.14322i	0.299187	−	0.345281i
$429$	−0.316389	+	0.692795i	−0.0152754	+	0.0334485i
$430$	7.89730	+	5.07529i	0.380842	+	0.244752i
$431$	−23.1569	+	6.79947i	−1.11543	+	0.327519i	−0.786965	−	0.616998i	$-0.788349\pi$
$431$	−23.1569	+	6.79947i	−1.11543	+	0.327519i	−0.328463	+	0.944517i	$0.606531\pi$
$432$	−0.461119	−	0.532159i	−0.0221856	−	0.0256035i
$433$	−35.3276	−	10.3731i	−1.69773	−	0.498500i	−0.717536	−	0.696521i	$-0.754730\pi$
$433$	−35.3276	−	10.3731i	−1.69773	−	0.498500i	−0.980198	+	0.198021i	$0.936548\pi$
$434$	6.79638	+	14.8820i	0.326237	+	0.714359i
$435$	−0.00604647	+	0.0420541i	−0.000289906	+	0.00201634i
$436$	−10.0271			−0.480210
$437$	14.2377	−	6.68701i	0.681082	−	0.319883i
$438$	−0.987233			−0.0471718
$439$	1.96598	−	13.6737i	0.0938309	−	0.652608i	−0.887575	−	0.460664i	$-0.847611\pi$
$439$	1.96598	−	13.6737i	0.0938309	−	0.652608i	0.981406	−	0.191945i	$-0.0614794\pi$
$440$	2.69262	+	5.89601i	0.128365	+	0.281081i
$441$	−11.7664	−	3.45494i	−0.560307	−	0.164521i
$442$	3.27313	+	3.77739i	0.155687	+	0.179672i
$443$	−18.5210	+	5.43825i	−0.879959	+	0.258379i	−0.690346	−	0.723480i	$-0.742542\pi$
$443$	−18.5210	+	5.43825i	−0.879959	+	0.258379i	−0.189613	+	0.981859i	$0.560723\pi$
$444$	−0.818084	−	0.525751i	−0.0388246	−	0.0249510i
$445$	−3.35980	+	7.35694i	−0.159270	+	0.348752i
$446$	−13.0386	+	15.0473i	−0.617396	+	0.712512i
$447$	0.332624	−	0.213764i	0.0157326	−	0.0101107i
$448$	−0.242075	−	1.68367i	−0.0114369	−	0.0795457i
$449$	−2.72900	−	18.9806i	−0.128789	−	0.895750i	−0.947092	−	0.320962i	$-0.895994\pi$
$449$	−2.72900	−	18.9806i	−0.128789	−	0.895750i	0.818302	−	0.574788i	$-0.194915\pi$
$450$	−2.51212	+	1.61444i	−0.118422	+	0.0761055i
$451$	18.4642	−	21.3088i	0.869443	−	1.00339i
$452$	−3.74486	+	8.20011i	−0.176144	+	0.385701i
$453$	−0.586906	−	0.377181i	−0.0275752	−	0.0177215i
$454$	5.65717	−	1.66110i	0.265504	−	0.0779591i
$455$	−1.11270	−	1.28413i	−0.0521643	−	0.0602009i
$456$	−0.370184	−	0.108696i	−0.0173355	−	0.00509015i
$457$	14.9189	+	32.6678i	0.697875	+	1.52813i	0.842529	+	0.538651i	$0.181066\pi$
$457$	14.9189	+	32.6678i	0.697875	+	1.52813i	−0.144654	+	0.989482i	$0.546207\pi$
$458$	0.566313	−	3.93879i	0.0264621	−	0.184048i
$459$	3.52328			0.164452
$460$	−4.38349	−	1.94551i	−0.204381	−	0.0907098i
$461$	−35.4620			−1.65163			−0.825816	−	0.563940i	$-0.809285\pi$
$461$	−35.4620			−1.65163			−0.825816	+	0.563940i	$0.809285\pi$
$462$	−0.184568	+	1.28370i	−0.00858688	+	0.0597231i
$463$	8.07768	+	17.6876i	0.375401	+	0.822015i	0.999183	+	0.0404158i	$0.0128682\pi$
$463$	8.07768	+	17.6876i	0.375401	+	0.822015i	−0.623781	+	0.781599i	$0.714404\pi$
$464$	−0.346560	−	0.101759i	−0.0160886	−	0.00472405i
$465$	−0.740902	−	0.855046i	−0.0343585	−	0.0396518i
$466$	25.5269	−	7.49538i	1.18251	−	0.347217i
$467$	4.32232	+	2.77779i	0.200013	+	0.128541i	0.636814	−	0.771018i	$-0.280252\pi$
$467$	4.32232	+	2.77779i	0.200013	+	0.128541i	−0.436800	+	0.899558i	$0.643888\pi$
$468$	1.23916	−	2.71338i	0.0572802	−	0.125426i
$469$	4.45172	−	5.13756i	0.205561	−	0.237230i
$470$	−0.618767	+	0.397658i	−0.0285416	+	0.0183426i
$471$	−0.356788	−	2.48151i	−0.0164399	−	0.114342i
$472$	−2.04157	−	14.1994i	−0.0939708	−	0.653581i
$473$	51.1884	−	32.8968i	2.35364	−	1.51259i
$474$	−0.607021	+	0.700539i	−0.0278814	+	0.0321768i
$475$	−1.36252	+	2.98350i	−0.0625167	+	0.136893i
$476$	7.15993	+	4.60141i	0.328175	+	0.210905i
$477$	0.160471	−	0.0471185i	0.00734746	−	0.00215741i
$478$	1.22683	+	1.41583i	0.0561137	+	0.0647586i
$479$	−26.9193	−	7.90423i	−1.22998	−	0.361153i	−0.398735	−	0.917066i	$-0.630551\pi$
$479$	−26.9193	−	7.90423i	−1.22998	−	0.361153i	−0.831240	+	0.555913i	$0.812369\pi$
$480$	0.0488649	+	0.106999i	0.00223037	+	0.00488383i
$481$	1.17527	−	8.17418i	0.0535877	−	0.372711i
$482$	7.16635			0.326418
$483$	−0.527385	−	0.801652i	−0.0239968	−	0.0364764i
$484$	31.0131			1.40969
$485$	2.02873	−	14.1101i	0.0921198	−	0.640707i
$486$	−1.31125	−	2.87123i	−0.0594795	−	0.130242i
$487$	−3.08638	−	0.906242i	−0.139857	−	0.0410658i	0.211055	−	0.977474i	$-0.432310\pi$
$487$	−3.08638	−	0.906242i	−0.139857	−	0.0410658i	−0.350912	+	0.936408i	$0.614128\pi$
$488$	−6.65901	−	7.68491i	−0.301439	−	0.347879i
$489$	−0.360434	+	0.105833i	−0.0162994	+	0.00478593i
$490$	3.45475	+	2.22023i	0.156070	+	0.100300i
$491$	−14.5815	+	31.9290i	−0.658053	+	1.44094i	0.226272	+	0.974064i	$0.427346\pi$
$491$	−14.5815	+	31.9290i	−0.658053	+	1.44094i	−0.884325	+	0.466871i	$0.845381\pi$
$492$	0.335083	−	0.386706i	0.0151067	−	0.0174341i
$493$	1.52036	−	0.977076i	0.0684736	−	0.0440053i
$494$	−0.466275	−	3.24302i	−0.0209787	−	0.145910i
$495$	2.75458	+	19.1586i	0.123809	+	0.861113i
$496$	8.09139	−	5.20002i	0.363314	−	0.233488i
$497$	−11.9360	+	13.7749i	−0.535402	+	0.617887i
$498$	−0.467813	+	1.02437i	−0.0209632	+	0.0459030i
$499$	−21.0798	−	13.5472i	−0.943662	−	0.606454i	−0.0242308	−	0.999706i	$-0.507714\pi$
$499$	−21.0798	−	13.5472i	−0.943662	−	0.606454i	−0.919431	+	0.393252i	$0.871350\pi$
$500$	0.959493	−	0.281733i	0.0429098	−	0.0125995i
$501$	−0.527542	−	0.608816i	−0.0235689	−	0.0271999i
$502$	−17.4769	−	5.13169i	−0.780033	−	0.229038i
$503$	−6.93270	−	15.1805i	−0.309114	−	0.676865i	0.689773	−	0.724025i	$-0.257710\pi$
$503$	−6.93270	−	15.1805i	−0.309114	−	0.676865i	−0.998887	+	0.0471602i	$0.984983\pi$
$504$	0.722874	−	5.02770i	0.0321994	−	0.223952i
$505$	−10.6275			−0.472917
$506$	−23.2738	+	20.6066i	−1.03465	+	0.916075i
$507$	1.41180			0.0627004
$508$	1.22049	−	8.48871i	0.0541506	−	0.376626i
$509$	1.92400	+	4.21296i	0.0852796	+	0.186736i	0.947467	−	0.319853i	$-0.103633\pi$
$509$	1.92400	+	4.21296i	0.0852796	+	0.186736i	−0.862188	+	0.506589i	$0.830906\pi$
$510$	−0.564729	−	0.165819i	−0.0250066	−	0.00734260i
$511$	−9.34872	−	10.7890i	−0.413563	−	0.477277i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	−1.94290	−	1.24863i	−0.0857813	−	0.0551283i
$514$	4.69770	−	10.2865i	0.207207	−	0.453719i
$515$	−0.570844	+	0.658789i	−0.0251544	+	0.0290297i
$516$	0.928954	−	0.597002i	0.0408949	−	0.0262816i
$517$	0.678489	+	4.71900i	0.0298399	+	0.207541i
$518$	−2.00127	−	13.9191i	−0.0879306	−	0.611571i
$519$	−1.53025	+	0.983434i	−0.0671707	+	0.0431680i
$520$	−0.654155	+	0.754935i	−0.0286866	+	0.0331061i
$521$	16.0495	−	35.1435i	0.703140	−	1.53966i	−0.132981	−	0.991119i	$-0.542455\pi$
$521$	16.0495	−	35.1435i	0.703140	−	1.53966i	0.836122	−	0.548544i	$-0.184818\pi$
$522$	−0.907355	−	0.583122i	−0.0397138	−	0.0255225i
$523$	20.3431	−	5.97328i	0.889542	−	0.261193i	0.195136	−	0.980776i	$-0.437485\pi$
$523$	20.3431	−	5.97328i	0.889542	−	0.261193i	0.694406	+	0.719583i	$0.255667\pi$
$524$	1.35325	+	1.56174i	0.0591171	+	0.0682247i
$525$	0.191980	+	0.0563704i	0.00837869	+	0.00246021i
$526$	−11.1774	−	24.4751i	−0.487358	−	1.06716i
$527$	−6.84904	+	47.6361i	−0.298349	+	2.07506i
$528$	0.762443			0.0331811
$529$	2.78575	−	22.8307i	0.121119	−	0.992638i
$530$	−0.0560068			−0.00243278
$531$	6.09646	−	42.4018i	0.264564	−	1.84008i
$532$	−2.31762	−	5.07488i	−0.100481	−	0.220024i
$533$	4.16929	+	1.22421i	0.180592	+	0.0530265i
$534$	0.623011	+	0.718993i	0.0269603	+	0.0311139i
$535$	−9.06897	+	2.66289i	−0.392086	+	0.115127i
$536$	−3.36207	−	2.16067i	−0.145219	−	0.0933268i
$537$	−0.375918	+	0.823146i	−0.0162221	+	0.0355214i
$538$	−8.31358	+	9.59438i	−0.358424	+	0.413643i
$539$	22.3928	−	14.3910i	0.964528	−	0.619864i
$540$	0.100211	+	0.696980i	0.00431238	+	0.0299933i
$541$	1.97495	+	13.7361i	0.0849099	+	0.590561i	0.987207	+	0.159446i	$0.0509707\pi$
$541$	1.97495	+	13.7361i	0.0849099	+	0.590561i	−0.902297	+	0.431115i	$0.858120\pi$
$542$	−13.4295	+	8.63062i	−0.576847	+	0.370717i
$543$	−1.14916	+	1.32620i	−0.0493152	+	0.0569128i
$544$	2.07857	−	4.55144i	0.0891181	−	0.195141i
$545$	8.43532	+	5.42105i	0.361329	+	0.232212i
$546$	−0.191773	+	0.0563096i	−0.00820712	+	0.00240983i
$547$	4.53542	+	5.23415i	0.193921	+	0.223796i	0.844380	−	0.535745i	$-0.179969\pi$
$547$	4.53542	+	5.23415i	0.193921	+	0.223796i	−0.650459	+	0.759541i	$0.725424\pi$
$548$	−17.5322	−	5.14791i	−0.748937	−	0.219908i
$549$	−12.6141	−	27.6210i	−0.538357	−	1.17884i
$550$	0.922449	−	6.41578i	0.0393334	−	0.273570i
$551$	−1.18467			−0.0504686
$552$	−0.422367	+	0.373963i	−0.0179771	+	0.0159169i
$553$	−13.4041			−0.570001
$554$	−1.32806	+	9.23688i	−0.0564240	+	0.392437i
$555$	0.403974	+	0.884580i	0.0171477	+	0.0375483i
$556$	2.79726	+	0.821349i	0.118630	+	0.0348329i
$557$	23.4886	+	27.1072i	0.995242	+	1.14857i	0.988899	+	0.148591i	$0.0474738\pi$
$557$	23.4886	+	27.1072i	0.995242	+	1.14857i	0.00634348	+	0.999980i	$0.497981\pi$
$558$	27.5583	−	8.09184i	1.16663	−	0.342555i
$559$	7.88879	+	5.06982i	0.333660	+	0.214430i
$560$	−0.706612	+	1.54726i	−0.0298598	+	0.0653839i
$561$	−2.49827	+	2.88316i	−0.105477	+	0.121727i
$562$	13.1168	−	8.42966i	0.553299	−	0.355584i
$563$	−0.898099	−	6.24642i	−0.0378504	−	0.263255i	0.962105	−	0.272678i	$-0.0879095\pi$
$563$	−0.898099	−	6.24642i	−0.0378504	−	0.263255i	−0.999956	+	0.00942332i	$0.997000\pi$
$564$	0.0123131	+	0.0856392i	0.000518473	+	0.00360606i
$565$	7.58369	−	4.87374i	0.319048	−	0.205040i
$566$	−7.41235	+	8.55431i	−0.311564	+	0.359564i
$567$	6.27165	−	13.7330i	0.263385	−	0.576732i
$568$	9.01441	+	5.79321i	0.378236	+	0.243078i
$569$	−11.6109	+	3.40926i	−0.486753	+	0.142924i	−0.515895	−	0.856652i	$-0.672541\pi$
$569$	−11.6109	+	3.40926i	−0.486753	+	0.142924i	0.0291422	+	0.999575i	$0.490722\pi$
$570$	0.252653	+	0.291577i	0.0105825	+	0.0122128i
$571$	29.1867	+	8.56999i	1.22143	+	0.358643i	0.828008	−	0.560716i	$-0.189474\pi$
$571$	29.1867	+	8.56999i	1.22143	+	0.358643i	0.393418	+	0.919360i	$0.371292\pi$
$572$	2.68971	+	5.88965i	0.112463	+	0.246259i
$573$	0.154959	−	1.07777i	0.00647352	−	0.0450243i
$574$	7.39924			0.308838
$575$	2.63581	+	4.00656i	0.109921	+	0.167085i
$576$	−2.98616			−0.124423
$577$	−4.34540	+	30.2229i	−0.180901	+	1.25820i	0.673736	+	0.738972i	$0.264688\pi$
$577$	−4.34540	+	30.2229i	−0.180901	+	1.25820i	−0.854637	+	0.519225i	$0.826221\pi$
$578$	3.33830	+	7.30985i	0.138855	+	0.304050i
$579$	−0.167974	−	0.0493217i	−0.00698077	−	0.00204974i
$580$	0.236530	+	0.272970i	0.00982136	+	0.0113345i
$581$	−15.6248	+	4.58786i	−0.648227	+	0.190337i
$582$	−1.41064	−	0.906562i	−0.0584728	−	0.0375782i
$583$	−0.150805	+	0.330217i	−0.00624570	+	0.0136762i
$584$	−5.49609	+	6.34282i	−0.227430	+	0.262468i
$585$	−2.50941	+	1.61270i	−0.103751	+	0.0666770i
$586$	−1.96074	−	13.6372i	−0.0809974	−	0.563350i
$587$	−1.15177	−	8.01076i	−0.0475387	−	0.330639i	−0.999687	−	0.0250038i	$-0.992040\pi$
$587$	−1.15177	−	8.01076i	−0.0475387	−	0.330639i	0.952149	−	0.305635i	$-0.0988689\pi$
$588$	0.406380	−	0.261164i	0.0167588	−	0.0107702i
$589$	20.6589	−	23.8416i	0.851233	−	0.982376i
$590$	−5.95931	+	13.0491i	−0.245341	+	0.537222i
$591$	−0.291339	−	0.187232i	−0.0119841	−	0.00770170i
$592$	−7.93228	+	2.32913i	−0.326015	+	0.0957265i
$593$	14.3294	+	16.5370i	0.588436	+	0.679092i	0.969397	−	0.245500i	$-0.0789520\pi$
$593$	14.3294	+	16.5370i	0.588436	+	0.679092i	−0.380960	+	0.924591i	$0.624407\pi$
$594$	4.37923	+	1.28586i	0.179682	+	0.0527594i
$595$	−3.53561	−	7.74190i	−0.144946	−	0.317387i
$596$	0.478367	−	3.32712i	0.0195947	−	0.136284i
$597$	0.778777			0.0318732
$598$	−4.37877	−	1.94341i	−0.179061	−	0.0794720i
$599$	27.0523			1.10533			0.552663	−	0.833405i	$-0.313612\pi$
$599$	27.0523			1.10533			0.552663	+	0.833405i	$0.313612\pi$
$600$	0.0167404	−	0.116432i	0.000683423	−	0.00475331i
$601$	−3.07707	−	6.73785i	−0.125516	−	0.274843i	0.836434	−	0.548068i	$-0.184637\pi$
$601$	−3.07707	−	6.73785i	−0.125516	−	0.274843i	−0.961950	+	0.273226i	$0.911909\pi$
$602$	15.3212	+	4.49871i	0.624445	+	0.183354i
$603$	−7.81524	−	9.01927i	−0.318261	−	0.367293i
$604$	−5.69073	+	1.67095i	−0.231553	+	0.0679900i
$605$	−26.0899	−	16.7669i	−1.06070	−	0.681673i
$606$	−0.519312	+	1.13713i	−0.0210956	+	0.0461929i
$607$	10.8301	−	12.4986i	0.439579	−	0.507301i	−0.492123	−	0.870526i	$-0.663779\pi$
$607$	10.8301	−	12.4986i	0.439579	−	0.507301i	0.931701	+	0.363225i	$0.118324\pi$
$608$	−2.75923	+	1.77325i	−0.111901	+	0.0719147i
$609$	0.0102849	+	0.0715332i	0.000416766	+	0.00289867i
$610$	1.44714	+	10.0651i	0.0585930	+	0.407524i
$611$	−0.618100	+	0.397229i	−0.0250057	+	0.0160702i
$612$	9.78465	−	11.2921i	0.395521	−	0.456456i
$613$	−14.2790	+	31.2666i	−0.576723	+	1.26285i	0.366417	+	0.930451i	$0.380584\pi$
$613$	−14.2790	+	31.2666i	−0.576723	+	1.26285i	−0.943140	+	0.332396i	$0.892143\pi$
$614$	18.9366	+	12.1698i	0.764218	+	0.491133i
$615$	−0.490959	+	0.144159i	−0.0197974	+	0.00581303i
$616$	7.22005	+	8.33238i	0.290904	+	0.335721i
$617$	−38.5788	−	11.3278i	−1.55312	−	0.456038i	−0.611091	−	0.791560i	$-0.709269\pi$
$617$	−38.5788	−	11.3278i	−1.55312	−	0.456038i	−0.942032	+	0.335522i	$0.891087\pi$
$618$	0.0425957	+	0.0932716i	0.00171345	+	0.00375193i
$619$	4.07668	−	28.3539i	0.163856	−	1.13964i	−0.727424	−	0.686188i	$-0.759283\pi$
$619$	4.07668	−	28.3539i	0.163856	−	1.13964i	0.891280	−	0.453453i	$-0.149808\pi$
$620$	−9.61826			−0.386279
$621$	−3.05663	+	1.43561i	−0.122658	+	0.0576089i
$622$	−5.60238			−0.224635
$623$	−1.95785	+	13.6172i	−0.0784398	+	0.545561i
$624$	0.0488123	+	0.106884i	0.00195405	+	0.00427878i
$625$	−0.959493	−	0.281733i	−0.0383797	−	0.0112693i
$626$	1.35056	+	1.55863i	0.0539794	+	0.0622955i
$627$	2.39944	−	0.704539i	0.0958244	−	0.0281366i
$628$	−17.9296	−	11.5227i	−0.715470	−	0.459805i
$629$	17.1839	−	37.6274i	0.685166	−	1.50030i
$630$	−3.32630	+	3.83876i	−0.132523	+	0.152940i
$631$	−16.7047	+	10.7354i	−0.665002	+	0.427371i	−0.829121	−	0.559070i	$-0.811158\pi$
$631$	−16.7047	+	10.7354i	−0.665002	+	0.427371i	0.164118	+	0.986441i	$0.447522\pi$
$632$	1.12148	+	7.80003i	0.0446099	+	0.310269i
$633$	−0.0930112	−	0.646907i	−0.00369686	−	0.0257122i
$634$	−13.4295	+	8.63061i	−0.533353	+	0.342765i
$635$	−5.61609	+	6.48131i	−0.222868	+	0.257203i
$636$	−0.00273677	+	0.00599269i	−0.000108520	+	0.000237626i
$637$	3.45103	+	2.21784i	0.136735	+	0.0878740i
$638$	2.24632	−	0.659578i	0.0889325	−	0.0261129i
$639$	20.9543	+	24.1825i	0.828939	+	0.956646i
$640$	0.959493	+	0.281733i	0.0379273	+	0.0111365i
$641$	−4.75940	−	10.4216i	−0.187985	−	0.411630i	0.792050	−	0.610457i	$-0.209014\pi$
$641$	−4.75940	−	10.4216i	−0.187985	−	0.411630i	−0.980035	+	0.198827i	$0.936287\pi$
$642$	−0.158227	+	1.10050i	−0.00624474	+	0.0434331i
$643$	37.2279			1.46813			0.734063	−	0.679082i	$-0.237622\pi$
$643$	37.2279			1.46813			0.734063	+	0.679082i	$0.237622\pi$
$644$	−8.08653	−	1.07456i	−0.318654	−	0.0423435i
$645$	−1.10425			−0.0434798
$646$	2.33558	−	16.2443i	0.0918920	−	0.639123i
$647$	−4.33824	−	9.49942i	−0.170554	−	0.373461i	0.804983	−	0.593298i	$-0.202175\pi$
$647$	−4.33824	−	9.49942i	−0.170554	−	0.373461i	−0.975536	+	0.219838i	$0.929447\pi$
$648$	−8.51614	−	2.50056i	−0.334545	−	0.0982314i
$649$	60.8913	+	70.2723i	2.39019	+	2.75843i
$650$	0.958459	−	0.281429i	0.0375938	−	0.0110385i
$651$	−1.61896	−	1.04045i	−0.0634522	−	0.0407783i
$652$	−1.32663	+	2.90492i	−0.0519549	+	0.113765i
$653$	−21.7553	+	25.1069i	−0.851350	+	0.982510i	−0.999980	−	0.00638307i	$-0.997968\pi$
$653$	−21.7553	+	25.1069i	−0.851350	+	0.982510i	0.148630	+	0.988893i	$0.452514\pi$
$654$	0.992239	−	0.637674i	0.0387996	−	0.0249350i
$655$	−0.294090	−	2.04544i	−0.0114910	−	0.0799219i
$656$	−0.619068	−	4.30571i	−0.0241706	−	0.168110i
$657$	−21.0836	+	13.5496i	−0.822550	+	0.528621i
$658$	−0.819310	+	0.945534i	−0.0319400	+	0.0368608i
$659$	−15.9203	+	34.8606i	−0.620166	+	1.35797i	0.295232	+	0.955426i	$0.404603\pi$
$659$	−15.9203	+	34.8606i	−0.620166	+	1.35797i	−0.915398	+	0.402549i	$0.868124\pi$
$660$	−0.641408	−	0.412208i	−0.0249668	−	0.0160452i
$661$	5.88717	−	1.72863i	0.228984	−	0.0672358i	−0.165228	−	0.986255i	$-0.552836\pi$
$661$	5.88717	−	1.72863i	0.228984	−	0.0672358i	0.394212	+	0.919020i	$0.371018\pi$
$662$	−14.0153	−	16.1745i	−0.544721	−	0.628642i
$663$	−0.564120	−	0.165641i	−0.0219086	−	0.00643295i
$664$	3.97701	+	8.70844i	0.154338	+	0.337953i
$665$	−0.793981	+	5.52226i	−0.0307892	+	0.214144i
$666$	−24.6871			−0.956605
$667$	−0.920871	+	1.46716i	−0.0356563	+	0.0568085i
$668$	−6.84847			−0.264975
$669$	0.333309	−	2.31822i	0.0128865	−	0.0896274i
$670$	1.66021	+	3.63534i	0.0641394	+	0.140446i
$671$	63.2404	+	18.5691i	2.44137	+	0.716851i
$672$	0.131028	+	0.151214i	0.00505450	+	0.00583321i
$673$	31.0051	−	9.10391i	1.19516	−	0.350930i	0.377158	−	0.926149i	$-0.376901\pi$
$673$	31.0051	−	9.10391i	1.19516	−	0.350930i	0.818000	+	0.575219i	$0.195083\pi$
$674$	−10.4536	−	6.71812i	−0.402658	−	0.258772i
$675$	0.292513	−	0.640515i	0.0112588	−	0.0246534i
$676$	7.85974	−	9.07062i	0.302298	−	0.348870i
$677$	−15.5932	+	10.0211i	−0.599296	+	0.385144i	−0.804830	−	0.593506i	$-0.797743\pi$
$677$	−15.5932	+	10.0211i	−0.599296	+	0.385144i	0.205534	+	0.978650i	$0.434107\pi$
$678$	−0.150910	−	1.04961i	−0.00579568	−	0.0403098i
$679$	−3.45082	−	24.0010i	−0.132430	−	0.921074i
$680$	−4.20930	+	2.70515i	−0.161419	+	0.103738i
$681$	−0.454174	+	0.524144i	−0.0174040	+	0.0200852i
$682$	−25.8983	+	56.7093i	−0.991697	+	2.17151i
$683$	16.9621	+	10.9009i	0.649035	+	0.417110i	0.823314	−	0.567587i	$-0.192123\pi$
$683$	16.9621	+	10.9009i	0.649035	+	0.417110i	−0.174278	+	0.984696i	$0.555759\pi$
$684$	−9.39758	+	2.75938i	−0.359326	+	0.105507i
$685$	11.9658	+	13.8093i	0.457191	+	0.527626i
$686$	18.1269	+	5.32255i	0.692090	+	0.203216i
$687$	0.194448	+	0.425782i	0.00741866	+	0.0162446i
$688$	1.33599	−	9.29199i	0.0509340	−	0.354254i
$689$	−0.0559465			−0.00213139
$690$	0.557498	−	0.0862491i	0.0212236	−	0.00328345i
$691$	3.99821			0.152099			0.0760495	−	0.997104i	$-0.475769\pi$
$691$	3.99821			0.152099			0.0760495	+	0.997104i	$0.475769\pi$
$692$	−2.20075	+	15.3066i	−0.0836601	+	0.581869i
$693$	13.6769	+	29.9482i	0.519542	+	1.13764i
$694$	−27.6210	−	8.11027i	−1.04848	−	0.307862i
$695$	−1.90915	−	2.20327i	−0.0724181	−	0.0835749i
$696$	0.0407656	−	0.0119699i	0.00154522	−	0.000453716i
$697$	18.3104	+	11.7674i	0.693556	+	0.445722i
$698$	−1.41742	+	3.10371i	−0.0536500	+	0.117477i
$699$	−2.04937	+	2.36510i	−0.0775143	+	0.0894563i
$700$	1.43095	−	0.919619i	0.0540850	−	0.0347583i
$701$	−3.52245	−	24.4992i	−0.133041	−	0.925321i	−0.941559	−	0.336849i	$-0.890639\pi$
$701$	−3.52245	−	24.4992i	−0.133041	−	0.925321i	0.808518	−	0.588472i	$-0.200270\pi$
$702$	0.100103	+	0.696229i	0.00377813	+	0.0262775i
$703$	−22.8110	+	14.6597i	−0.860332	+	0.552902i
$704$	4.24464	−	4.89858i	0.159976	−	0.184622i
$705$	0.0359416	−	0.0787012i	0.00135364	−	0.00296406i
$706$	−11.9710	−	7.69330i	−0.450535	−	0.289541i
$707$	−17.3449	+	5.09292i	−0.652322	+	0.191539i
$708$	1.10504	+	1.27528i	0.0415299	+	0.0479281i
$709$	−10.9118	−	3.20400i	−0.409801	−	0.120329i	0.0703328	−	0.997524i	$-0.477594\pi$
$709$	−10.9118	−	3.20400i	−0.409801	−	0.120329i	−0.480134	+	0.877195i	$0.659412\pi$
$710$	−4.45136	−	9.74711i	−0.167056	−	0.365803i
$711$	−3.34891	+	23.2922i	−0.125594	+	0.873525i
$712$	8.08782			0.303104
$713$	−13.4681	−	44.1176i	−0.504383	−	1.65222i
$714$	−1.00115			−0.0374669
$715$	0.921455	−	6.40886i	0.0344605	−	0.239678i
$716$	3.19579	+	6.99780i	0.119432	+	0.261520i
$717$	−0.211442	−	0.0620849i	−0.00789643	−	0.00231860i
$718$	−3.59191	−	4.14528i	−0.134049	−	0.154701i
$719$	6.16255	−	1.80949i	0.229824	−	0.0674825i	−0.164793	−	0.986328i	$-0.552695\pi$
$719$	6.16255	−	1.80949i	0.229824	−	0.0674825i	0.394617	+	0.918846i	$0.370877\pi$
$720$	2.51212	+	1.61444i	0.0936212	+	0.0601667i
$721$	−0.615956	+	1.34876i	−0.0229394	+	0.0502303i
$722$	5.39752	−	6.22907i	0.200875	−	0.231822i
$723$	−0.709153	+	0.455745i	−0.0263737	+	0.0169493i
$724$	2.12308	+	14.7664i	0.0789038	+	0.548788i
$725$	−0.0514028	−	0.357514i	−0.00190905	−	0.0132778i
$726$	−3.06893	+	1.97228i	−0.113899	+	0.0731982i
$727$	−11.7408	+	13.5496i	−0.435441	+	0.502526i	−0.930479	−	0.366346i	$-0.880609\pi$
$727$	−11.7408	+	13.5496i	−0.435441	+	0.502526i	0.495038	+	0.868871i	$0.335154\pi$
$728$	−0.705850	+	1.54560i	−0.0261606	+	0.0572836i
$729$	−22.0877	−	14.1949i	−0.818063	−	0.525737i
$730$	8.05279	−	2.36451i	0.298047	−	0.0875145i
$731$	30.7598	+	35.4987i	1.13769	+	1.31297i
$732$	1.14767	+	0.336987i	0.0424192	+	0.0124554i
$733$	7.09093	+	15.5270i	0.261909	+	0.573501i	0.994207	−	0.107483i	$-0.0342792\pi$
$733$	7.09093	+	15.5270i	0.261909	+	0.573501i	−0.732298	+	0.680985i	$0.761552\pi$
$734$	−2.66688	+	18.5485i	−0.0984363	+	0.684639i
$735$	−0.483064			−0.0178181
$736$	0.0512716	+	4.79556i	0.00188990	+	0.176767i
$737$	25.9043			0.954198
$738$	1.84864	−	12.8576i	0.0680493	−	0.473293i
$739$	−17.7630	−	38.8956i	−0.653423	−	1.43080i	−0.888526	−	0.458827i	$-0.848270\pi$
$739$	−17.7630	−	38.8956i	−0.653423	−	1.43080i	0.235103	−	0.971971i	$-0.424457\pi$
$740$	7.93228	+	2.32913i	0.291596	+	0.0856204i
$741$	0.252381	+	0.291263i	0.00927144	+	0.0106998i
$742$	−0.0914075	+	0.0268397i	−0.00335567	+	0.000985315i
$743$	−18.5716	−	11.9352i	−0.681326	−	0.437861i	0.153667	−	0.988123i	$-0.450892\pi$
$743$	−18.5716	−	11.9352i	−0.681326	−	0.437861i	−0.834993	+	0.550261i	$0.814528\pi$
$744$	−0.469996	+	1.02915i	−0.0172309	+	0.0377304i
$745$	−2.20120	+	2.54032i	−0.0806458	+	0.0930703i
$746$	−15.1884	+	9.76097i	−0.556086	+	0.357375i
$747$	4.06854	+	28.2973i	0.148860	+	1.03534i
$748$	4.61557	+	32.1020i	0.168762	+	1.17377i
$749$	−13.5251	+	8.69209i	−0.494198	+	0.317602i
$750$	−0.0770307	+	0.0888982i	−0.00281276	+	0.00324610i
$751$	6.68811	−	14.6449i	0.244053	−	0.534401i	−0.747476	−	0.664289i	$-0.768735\pi$
$751$	6.68811	−	14.6449i	0.244053	−	0.534401i	0.991529	+	0.129888i	$0.0414618\pi$
$752$	0.618767	+	0.397658i	0.0225641	+	0.0145011i
$753$	2.05580	−	0.603636i	0.0749174	−	0.0219977i
$754$	0.236275	+	0.272675i	0.00860462	+	0.00993026i
$755$	5.69073	+	1.67095i	0.207107	+	0.0608121i
$756$	0.497559	+	1.08950i	0.0180961	+	0.0396248i
$757$	1.76694	−	12.2894i	0.0642206	−	0.446664i	−0.932187	−	0.361977i	$-0.882102\pi$
$757$	1.76694	−	12.2894i	0.0642206	−	0.446664i	0.996408	−	0.0846870i	$-0.0269890\pi$
$758$	−15.2045			−0.552251
$759$	0.992602	−	3.51925i	0.0360292	−	0.127741i
$760$	3.27990			0.118975
$761$	1.16038	−	8.07061i	0.0420637	−	0.292560i	−0.957921	−	0.287032i	$-0.907331\pi$
$761$	1.16038	−	8.07061i	0.0420637	−	0.292560i	0.999985	−	0.00552758i	$-0.00175949\pi$
$762$	0.419066	+	0.917626i	0.0151812	+	0.0332421i
$763$	16.3650	+	4.80519i	0.592452	+	0.173959i
$764$	−6.06180	−	6.99569i	−0.219308	−	0.253095i
$765$	−14.3363	+	4.20953i	−0.518332	+	0.152196i
$766$	21.2198	+	13.6371i	0.766703	+	0.492730i
$767$	−5.95288	+	13.0350i	−0.214946	+	0.470667i
$768$	0.0770307	−	0.0888982i	0.00277961	−	0.00320784i
$769$	−23.6595	+	15.2051i	−0.853185	+	0.548309i	−0.892567	−	0.450916i	$-0.851098\pi$
$769$	−23.6595	+	15.2051i	−0.853185	+	0.548309i	0.0393818	+	0.999224i	$0.487461\pi$
$770$	−1.56907	−	10.9131i	−0.0565452	−	0.393281i
$771$	0.189308	+	1.31666i	0.00681775	+	0.0474185i
$772$	−1.25202	+	0.804627i	−0.0450613	+	0.0289591i
$773$	34.3420	−	39.6328i	1.23520	−	1.42549i	0.366301	−	0.930496i	$-0.380624\pi$
$773$	34.3420	−	39.6328i	1.23520	−	1.42549i	0.868895	−	0.494996i	$-0.164830\pi$
$774$	11.6452	−	25.4995i	0.418579	−	0.916560i
$775$	8.09139	+	5.20002i	0.290651	+	0.186790i
$776$	−13.6778	+	4.01616i	−0.491003	+	0.144172i
$777$	1.08323	+	1.25011i	0.0388605	+	0.0448474i
$778$	−17.1220	−	5.02747i	−0.613853	−	0.180243i
$779$	−5.92695	−	12.9782i	−0.212355	−	0.464993i
$780$	0.0167223	−	0.116306i	0.000598756	−	0.00416444i
$781$	−69.4549			−2.48529
$782$	−18.3023	−	15.5195i	−0.654488	−	0.554978i
$783$	0.254332			0.00908907
$784$	0.584440	−	4.06487i	0.0208729	−	0.145174i
$785$	8.85374	+	19.3870i	0.316003	+	0.691951i
$786$	−0.233231	−	0.0684828i	−0.00831908	−	0.00244270i
$787$	2.93639	+	3.38878i	0.104671	+	0.120797i	0.805668	−	0.592368i	$-0.201807\pi$
$787$	2.93639	+	3.38878i	0.104671	+	0.120797i	−0.700997	+	0.713165i	$0.747261\pi$
$788$	−2.82487	+	0.829456i	−0.100632	+	0.0295481i
$789$	2.66257	+	1.71113i	0.0947899	+	0.0609177i
$790$	3.27357	−	7.16812i	0.116468	−	0.255030i
$791$	10.0416	−	11.5886i	0.357037	−	0.412043i
$792$	16.2829	−	10.4644i	0.578589	−	0.371837i
$793$	1.44558	+	10.0542i	0.0513341	+	0.357036i
$794$	−1.36395	−	9.48649i	−0.0484048	−	0.336663i
$795$	0.00554221	−	0.00356176i	0.000196562	−	0.000126323i
$796$	4.33558	−	5.00352i	0.153670	−	0.177345i
$797$	21.0251	−	46.0384i	0.744746	−	1.63077i	−0.0308410	−	0.999524i	$-0.509819\pi$
$797$	21.0251	−	46.0384i	0.744746	−	1.63077i	0.775587	−	0.631241i	$-0.217454\pi$
$798$	0.552080	+	0.354800i	0.0195434	+	0.0125598i
$799$	−3.53122	+	1.03686i	−0.124926	+	0.0366815i
$800$	−0.654861	−	0.755750i	−0.0231528	−	0.0267198i
$801$	23.1732	+	6.80428i	0.818786	+	0.240417i
$802$	0.422888	+	0.925996i	0.0149327	+	0.0326981i
$803$	7.74189	−	53.8460i	0.273205	−	1.90019i
$804$	0.470105			0.0165793
$805$	6.22187	+	5.27588i	0.219292	+	0.185950i
$806$	−9.60789			−0.338423
$807$	0.212522	−	1.47812i	0.00748114	−	0.0520325i
$808$	4.41482	+	9.66711i	0.155313	+	0.340088i
$809$	29.7543	+	8.73666i	1.04611	+	0.307165i	0.759243	−	0.650807i	$-0.225569\pi$
$809$	29.7543	+	8.73666i	1.04611	+	0.307165i	0.286864	+	0.957971i	$0.407387\pi$
$810$	5.81232	+	6.70778i	0.204224	+	0.235687i
$811$	−26.1035	+	7.66468i	−0.916618	+	0.269143i	−0.705824	−	0.708387i	$-0.749423\pi$
$811$	−26.1035	+	7.66468i	−0.916618	+	0.269143i	−0.210794	+	0.977530i	$0.567605\pi$
$812$	0.516848	+	0.332158i	0.0181378	+	0.0116565i
$813$	0.780064	−	1.70810i	0.0273580	−	0.0599058i
$814$	35.0911	−	40.4973i	1.22994	−	1.41943i
$815$	2.68655	−	1.72654i	0.0941058	−	0.0604782i
$816$	0.0837622	+	0.582579i	0.00293226	+	0.0203944i
$817$	−4.38190	−	30.4768i	−0.153303	−	1.06625i
$818$	7.16328	−	4.60356i	0.250458	−	0.160960i
$819$	−3.32271	+	3.83462i	−0.116105	+	0.133992i
$820$	−1.80705	+	3.95689i	−0.0631050	+	0.138181i
$821$	22.0052	+	14.1419i	0.767985	+	0.493554i	0.865026	−	0.501726i	$-0.167301\pi$
$821$	22.0052	+	14.1419i	0.767985	+	0.493554i	−0.0970412	+	0.995280i	$0.530938\pi$
$822$	2.06230	−	0.605544i	0.0719308	−	0.0211208i
$823$	−20.6355	−	23.8147i	−0.719310	−	0.830127i	0.271914	−	0.962321i	$-0.412343\pi$
$823$	−20.6355	−	23.8147i	−0.719310	−	0.830127i	−0.991224	+	0.132194i	$0.957798\pi$
$824$	0.836393	+	0.245587i	0.0291371	+	0.00855543i
$825$	0.316730	+	0.693543i	0.0110271	+	0.0241461i
$826$	−3.47266	+	24.1529i	−0.120829	+	0.840387i
$827$	−7.78953			−0.270869			−0.135434	−	0.990786i	$-0.543243\pi$
$827$	−7.78953			−0.270869			−0.135434	+	0.990786i	$0.543243\pi$
$828$	−3.88760	+	13.7834i	−0.135103	+	0.479006i
$829$	−1.14872			−0.0398969			−0.0199484	−	0.999801i	$-0.506350\pi$
$829$	−1.14872			−0.0398969			−0.0199484	+	0.999801i	$0.506350\pi$
$830$	1.36246	−	9.47614i	0.0472918	−	0.328922i
$831$	−0.456001	−	0.998502i	−0.0158185	−	0.0346377i
$832$	0.958459	+	0.281429i	0.0332286	+	0.00975679i
$833$	13.4562	+	15.5293i	0.466229	+	0.538057i
$834$	−0.329039	+	0.0966146i	−0.0113937	+	0.00334549i
$835$	5.76130	+	3.70256i	0.199378	+	0.128132i
$836$	8.83152	−	19.3383i	0.305444	−	0.668830i
$837$	−4.43516	+	5.11845i	−0.153301	+	0.176919i
$838$	19.0005	−	12.2109i	0.656362	−	0.421818i
$839$	0.745991	+	5.18848i	0.0257545	+	0.179126i	0.998638	−	0.0521680i	$-0.0166131\pi$
$839$	0.745991	+	5.18848i	0.0257545	+	0.179126i	−0.972884	+	0.231294i	$0.925704\pi$
$840$	−0.0284750	−	0.198048i	−0.000982482	−	0.00683331i
$841$	−24.2866	+	15.6081i	−0.837469	+	0.538209i
$842$	−8.94024	+	10.3176i	−0.308101	+	0.355568i
$843$	−0.761901	+	1.66833i	−0.0262413	+	0.0574604i
$844$	−4.67409	−	3.00385i	−0.160889	−	0.103397i
$845$	−11.5160	+	3.38140i	−0.396162	+	0.116324i
$846$	1.43834	+	1.65994i	0.0494513	+	0.0570698i
$847$	−50.6158	−	14.8621i	−1.73918	−	0.510669i
$848$	0.0232661	+	0.0509456i	0.000798960	+	0.00174948i
$849$	0.189484	−	1.31789i	0.00650307	−	0.0452298i
$850$	5.00360			0.171622
$851$	0.423870	+	39.6456i	0.0145301	+	1.35903i
$852$	−1.26045			−0.0431823
$853$	3.09396	−	21.5189i	0.105935	−	0.736794i	−0.865744	−	0.500488i	$-0.833154\pi$
$853$	3.09396	−	21.5189i	0.105935	−	0.736794i	0.971679	−	0.236306i	$-0.0759369\pi$
$854$	7.18525	+	15.7335i	0.245874	+	0.538389i
$855$	9.39758	+	2.75938i	0.321391	+	0.0943688i
$856$	6.18964	+	7.14322i	0.211557	+	0.244150i
$857$	48.9177	−	14.3635i	1.67100	−	0.490649i	0.696973	−	0.717097i	$-0.254530\pi$
$857$	48.9177	−	14.3635i	1.67100	−	0.490649i	0.974023	+	0.226449i	$0.0727116\pi$
$858$	−0.640716	−	0.411763i	−0.0218737	−	0.0140574i
$859$	−9.85850	+	21.5871i	−0.336368	+	0.736543i	−0.999933	−	0.0115758i	$-0.996315\pi$
$859$	−9.85850	+	21.5871i	−0.336368	+	0.736543i	0.663565	+	0.748118i	$0.269043\pi$
$860$	−6.14753	+	7.09463i	−0.209629	+	0.241925i
$861$	−0.732199	+	0.470556i	−0.0249533	+	0.0160365i
$862$	−3.43470	−	23.8888i	−0.116986	−	0.813657i
$863$	5.73631	+	39.8969i	0.195266	+	1.35811i	0.817795	+	0.575509i	$0.195196\pi$
$863$	5.73631	+	39.8969i	0.195266	+	1.35811i	−0.622529	+	0.782596i	$0.713895\pi$
$864$	0.592367	−	0.380691i	0.0201527	−	0.0129514i
$865$	10.1268	−	11.6869i	0.344320	−	0.397366i
$866$	15.2952	−	33.4917i	0.519751	−	1.13810i
$867$	−0.795216	−	0.511054i	−0.0270069	−	0.0173563i
$868$	−15.6977	+	4.60927i	−0.532816	+	0.156449i
$869$	−33.4488	−	38.6020i	−1.13467	−	1.30948i
$870$	−0.0407656	−	0.0119699i	−0.00138208	−	0.000405816i
$871$	1.65842	+	3.63143i	0.0561933	+	0.123046i
$872$	1.42700	−	9.92502i	0.0483244	−	0.336104i
$873$	−42.5684			−1.44072
$874$	4.59271	+	15.0444i	0.155351	+	0.508886i
$875$	−1.70098			−0.0575036
$876$	0.140498	−	0.977184i	0.00474698	−	0.0330160i
$877$	−18.3490	−	40.1787i	−0.619602	−	1.35674i	−0.915809	−	0.401615i	$-0.868449\pi$
$877$	−18.3490	−	40.1787i	−0.619602	−	1.35674i	0.296207	−	0.955124i	$-0.404278\pi$
$878$	13.2547	+	3.89193i	0.447324	+	0.131346i
$879$	1.06129	+	1.22479i	0.0357964	+	0.0413113i
$880$	−6.21919	+	1.82612i	−0.209649	+	0.0615585i
$881$	−4.18543	−	2.68981i	−0.141011	−	0.0906222i	0.468233	−	0.883605i	$-0.344891\pi$
$881$	−4.18543	−	2.68981i	−0.141011	−	0.0906222i	−0.609244	+	0.792983i	$0.708527\pi$
$882$	5.09431	−	11.1550i	0.171534	−	0.375608i
$883$	22.8229	−	26.3390i	0.768050	−	0.886377i	−0.228136	−	0.973629i	$-0.573263\pi$
$883$	22.8229	−	26.3390i	0.768050	−	0.886377i	0.996186	+	0.0872521i	$0.0278086\pi$
$884$	−4.20476	+	2.70224i	−0.141421	+	0.0908860i
$885$	−0.240148	−	1.67027i	−0.00807249	−	0.0561454i
$886$	−2.74709	−	19.1064i	−0.0922903	−	0.641893i
$887$	8.40627	−	5.40238i	0.282255	−	0.181394i	−0.391851	−	0.920029i	$-0.628165\pi$
$887$	8.40627	−	5.40238i	0.282255	−	0.181394i	0.674106	+	0.738634i	$0.264529\pi$
$888$	0.636825	−	0.734935i	0.0213704	−	0.0246628i
$889$	−6.05991	+	13.2693i	−0.203243	+	0.445040i
$890$	−6.80391	−	4.37260i	−0.228067	−	0.146570i
$891$	55.1995	−	16.2080i	1.84925	−	0.542989i
$892$	−13.0386	−	15.0473i	−0.436565	−	0.503822i
$893$	2.31474	+	0.679670i	0.0774600	+	0.0227443i
$894$	0.164251	+	0.359660i	0.00549338	+	0.0120288i
$895$	1.09483	−	7.61470i	0.0365961	−	0.254531i
$896$	1.70098			0.0568257
$897$	0.556896	−	0.0861561i	0.0185942	−	0.00287667i
$898$	19.1758			0.639904
$899$	−0.494406	+	3.43867i	−0.0164893	+	0.114686i
$900$	−1.24050	−	2.71631i	−0.0413499	−	0.0905437i
$901$	−0.268885	−	0.0789516i	−0.00895784	−	0.00263026i
$902$	18.4642	+	21.3088i	0.614789	+	0.709505i
$903$	−1.80222	+	0.529180i	−0.0599741	+	0.0176100i
$904$	−7.58369	−	4.87374i	−0.252230	−	0.162098i
$905$	6.19725	−	13.5701i	0.206004	−	0.451085i
$906$	0.456867	−	0.527253i	0.0151784	−	0.0175168i
$907$	3.05468	−	1.96312i	0.101429	−	0.0651844i	−0.488943	−	0.872316i	$-0.662617\pi$
$907$	3.05468	−	1.96312i	0.101429	−	0.0651844i	0.590372	+	0.807131i	$0.298981\pi$
$908$	0.839089	+	5.83599i	0.0278461	+	0.193674i
$909$	4.51642	+	31.4124i	0.149800	+	1.04188i
$910$	1.42941	−	0.918627i	0.0473845	−	0.0304522i
$911$	35.1069	−	40.5155i	1.16314	−	1.34234i	0.234168	−	0.972196i	$-0.424763\pi$
$911$	35.1069	−	40.5155i	1.16314	−	1.34234i	0.928975	−	0.370142i	$-0.120691\pi$
$912$	0.160272	−	0.350947i	0.00530714	−	0.0116210i
$913$	−52.2028	−	33.5487i	−1.72766	−	1.11030i
$914$	−34.4584	+	10.1179i	−1.13978	+	0.334671i
$915$	−0.783294	−	0.903969i	−0.0258949	−	0.0298843i
$916$	3.81811	+	1.12110i	0.126154	+	0.0370421i
$917$	−1.46019	−	3.19738i	−0.0482199	−	0.105587i
$918$	−0.501414	+	3.48741i	−0.0165491	+	0.115102i
$919$	40.8147			1.34635			0.673176	−	0.739482i	$-0.264930\pi$
$919$	40.8147			1.34635			0.673176	+	0.739482i	$0.264930\pi$
$920$	2.54954	−	4.06200i	0.0840559	−	0.133920i
$921$	−2.64783			−0.0872489
$922$	5.04677	−	35.1011i	0.166207	−	1.15599i
$923$	−4.44656	−	9.73661i	−0.146360	−	0.320484i
$924$	−1.24437	−	0.365379i	−0.0409366	−	0.0120201i
$925$	−5.41383	−	6.24790i	−0.178006	−	0.205430i
$926$	−18.6572	+	5.47824i	−0.613113	+	0.180026i
$927$	2.18982	+	1.40731i	0.0719232	+	0.0462222i
$928$	0.150044	−	0.328551i	0.00492544	−	0.0107852i
$929$	−7.46942	+	8.62017i	−0.245064	+	0.282819i	−0.864934	−	0.501886i	$-0.832640\pi$
$929$	−7.46942	+	8.62017i	−0.245064	+	0.282819i	0.619870	+	0.784704i	$0.287185\pi$
$930$	0.951784	−	0.611675i	0.0312102	−	0.0200576i
$931$	−1.91691	−	13.3324i	−0.0628241	−	0.436951i
$932$	3.78623	+	26.3338i	0.124022	+	0.862592i
$933$	0.554389	−	0.356284i	0.0181499	−	0.0116642i
$934$	−3.36464	+	3.88301i	−0.110095	+	0.127056i
$935$	13.4728	−	29.5013i	0.440607	−	0.964795i
$936$	2.50941	+	1.61270i	0.0820227	+	0.0527128i
$937$	−39.7834	+	11.6815i	−1.29967	+	0.381616i	−0.857114	−	0.515127i	$-0.827745\pi$
$937$	−39.7834	+	11.6815i	−1.29967	+	0.381616i	−0.442552	+	0.896743i	$0.645927\pi$
$938$	4.45172	+	5.13756i	0.145354	+	0.167747i
$939$	−0.232768	−	0.0683468i	−0.00759609	−	0.00223041i
$940$	−0.305550	−	0.669062i	−0.00996595	−	0.0218224i
$941$	−4.21856	+	29.3408i	−0.137521	+	0.956481i	0.797861	+	0.602842i	$0.205965\pi$
$941$	−4.21856	+	29.3408i	−0.137521	+	0.956481i	−0.935382	+	0.353639i	$0.884944\pi$
$942$	2.50703			0.0816835
$943$	−20.6800	−	2.74802i	−0.673435	−	0.0894877i
$944$	14.3454			0.466904
$945$	0.170456	−	1.18555i	0.00554494	−	0.0385659i
$946$	25.2771	+	55.3490i	0.821828	+	1.79955i
$947$	−27.2022	−	7.98728i	−0.883952	−	0.259552i	−0.191913	−	0.981412i	$-0.561469\pi$
$947$	−27.2022	−	7.98728i	−0.883952	−	0.259552i	−0.692039	+	0.721860i	$0.743287\pi$
$948$	−0.607021	−	0.700539i	−0.0197151	−	0.0227525i
$949$	8.04411	−	2.36196i	0.261123	−	0.0766726i
$950$	−2.75923	−	1.77325i	−0.0895212	−	0.0575318i
$951$	0.780064	−	1.70810i	0.0252953	−	0.0553890i
$952$	−5.57354	+	6.43220i	−0.180639	+	0.208469i
$953$	−9.20503	+	5.91572i	−0.298180	+	0.191629i	−0.681173	−	0.732123i	$-0.738530\pi$
$953$	−9.20503	+	5.91572i	−0.298180	+	0.191629i	0.382993	+	0.923751i	$0.374893\pi$
$954$	0.0238015	+	0.165543i	0.000770603	+	0.00535966i
$955$	1.31735	+	9.16240i	0.0426286	+	0.296488i
$956$	−1.57602	+	1.01284i	−0.0509720	+	0.0327577i
$957$	−0.180340	+	0.208124i	−0.00582958	+	0.00672769i
$958$	11.6548	−	25.5204i	0.376549	−	0.824528i
$959$	26.1469	+	16.8036i	0.844326	+	0.542616i
$960$	−0.112864	+	0.0331400i	−0.00364268	+	0.00106959i
$961$	−40.2811	−	46.4868i	−1.29939	−	1.49958i
$962$	7.92372	+	2.32662i	0.255471	+	0.0750131i
$963$	11.7250	+	25.6741i	0.377832	+	0.827337i
$964$	−1.01988	+	7.09341i	−0.0328481	+	0.228463i
$965$	1.48828			0.0479095
$966$	0.868547	−	0.407930i	0.0279450	−	0.0131249i
$967$	59.2938			1.90676			0.953379	−	0.301775i	$-0.0975791\pi$
$967$	59.2938			1.90676			0.953379	+	0.301775i	$0.0975791\pi$
$968$	−4.41362	+	30.6974i	−0.141859	+	0.986653i
$969$	0.801939	+	1.75600i	0.0257620	+	0.0564109i
$970$	13.6778	+	4.01616i	0.439167	+	0.128951i
$971$	8.35187	+	9.63857i	0.268024	+	0.309316i	0.873768	−	0.486344i	$-0.161670\pi$
$971$	8.35187	+	9.63857i	0.268024	+	0.309316i	−0.605743	+	0.795660i	$0.707124\pi$
$972$	3.02862	−	0.889283i	0.0971430	−	0.0285238i
$973$	−4.17173	−	2.68101i	−0.133740	−	0.0859492i
$974$	1.33626	−	2.92599i	0.0428164	−	0.0937548i
$975$	−0.0769477	+	0.0888024i	−0.00246430	+	0.00284395i
$976$	8.55436	−	5.49755i	0.273818	−	0.175972i
$977$	−8.36259	−	58.1631i	−0.267543	−	1.86080i	−0.471560	−	0.881834i	$-0.656309\pi$
$977$	−8.36259	−	58.1631i	−0.267543	−	1.86080i	0.204017	−	0.978967i	$-0.434600\pi$
$978$	−0.0534606	−	0.371827i	−0.00170948	−	0.0118897i
$979$	−44.1012	+	28.3421i	−1.40948	+	0.905819i
$980$	−2.68930	+	3.10361i	−0.0859065	+	0.0991413i
$981$	12.4386	−	27.2367i	0.397133	−	0.869599i
$982$	−29.5288	−	18.9770i	−0.942303	−	0.605582i
$983$	−14.5884	+	4.28354i	−0.465297	+	0.136624i	−0.505974	−	0.862549i	$-0.668867\pi$
$983$	−14.5884	+	4.28354i	−0.465297	+	0.136624i	0.0406766	+	0.999172i	$0.487049\pi$
$984$	0.335083	+	0.386706i	0.0106821	+	0.0123277i
$985$	2.82487	+	0.829456i	0.0900078	+	0.0264287i
$986$	0.750761	+	1.64394i	0.0239091	+	0.0523536i
$987$	0.0209442	−	0.145670i	0.000666663	−	0.00463674i
$988$	3.27637			0.104235
$989$	−41.1502	−	18.2635i	−1.30850	−	0.580747i
$990$	−19.3556			−0.615160
$991$	2.38414	−	16.5820i	0.0757346	−	0.526746i	−0.916272	−	0.400557i	$-0.868816\pi$
$991$	2.38414	−	16.5820i	0.0757346	−	0.526746i	0.992006	−	0.126188i	$-0.0402744\pi$
$992$	3.99557	+	8.74908i	0.126859	+	0.277783i
$993$	2.41552	+	0.709261i	0.0766543	+	0.0225077i
$994$	−11.9360	−	13.7749i	−0.378586	−	0.436912i
$995$	−6.35243	+	1.86524i	−0.201385	+	0.0591321i
$996$	−0.947363	−	0.608833i	−0.0300184	−	0.0192916i
$997$	−19.6650	+	43.0603i	−0.622796	+	1.36373i	0.290672	+	0.956823i	$0.406121\pi$
$997$	−19.6650	+	43.0603i	−0.622796	+	1.36373i	−0.913468	+	0.406910i	$0.866606\pi$
$998$	16.4092	−	18.9373i	0.519426	−	0.599449i
$999$	4.89719	−	3.14723i	0.154940	−	0.0995740i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.g.d.31.2	✓	30
23.3	even	11	inner	230.2.g.d.141.2	yes	30
23.7	odd	22		5290.2.a.bl.1.7		15
23.16	even	11		5290.2.a.bk.1.7		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.d.31.2	✓	30	1.1	even	1	trivial
230.2.g.d.141.2	yes	30	23.3	even	11	inner
5290.2.a.bk.1.7		15	23.16	even	11
5290.2.a.bl.1.7		15	23.7	odd	22

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.0488649 - 0.106999i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.112864 - 0.0331400i) q^{6} +(1.43095 + 0.919619i) q^{7} +(0.415415 - 0.909632i) q^{8} +(1.95552 - 2.25679i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.0488649 - 0.106999i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.112864 - 0.0331400i) q^{6} +(1.43095 + 0.919619i) q^{7} +(0.415415 - 0.909632i) q^{8} +(1.95552 - 2.25679i) q^{9} +(-0.841254 + 0.540641i) q^{10} +(0.922449 + 6.41578i) q^{11} +(0.0167404 + 0.116432i) q^{12} +(-0.840347 + 0.540058i) q^{13} +(-1.11390 + 1.28551i) q^{14} +(0.0488649 - 0.106999i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-4.80092 + 1.40968i) q^{17} +(1.95552 + 2.25679i) q^{18} +(3.14704 + 0.924055i) q^{19} +(-0.415415 - 0.909632i) q^{20} +(0.0284750 - 0.198048i) q^{21} -6.48175 q^{22} +(3.59066 - 3.17917i) q^{23} -0.117629 q^{24} +(-0.142315 + 0.989821i) q^{25} +(-0.414967 - 0.908651i) q^{26} +(-0.675625 - 0.198381i) q^{27} +(-1.11390 - 1.28551i) q^{28} +(-0.346560 + 0.101759i) q^{29} +(0.0989560 + 0.0635951i) q^{30} +(3.99557 - 8.74908i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(0.641408 - 0.412208i) q^{33} +(-0.712087 - 4.95267i) q^{34} +(0.242075 + 1.68367i) q^{35} +(-2.51212 + 1.61444i) q^{36} +(-5.41383 + 6.24790i) q^{37} +(-1.36252 + 2.98350i) q^{38} +(0.0988493 + 0.0635266i) q^{39} +(0.959493 - 0.281733i) q^{40} +(-2.84864 - 3.28750i) q^{41} +(0.191980 + 0.0563704i) q^{42} +(-3.89973 - 8.53921i) q^{43} +(0.922449 - 6.41578i) q^{44} +2.98616 q^{45} +(2.63581 + 4.00656i) q^{46} +0.735530 q^{47} +(0.0167404 - 0.116432i) q^{48} +(-1.70597 - 3.73556i) q^{49} +(-0.959493 - 0.281733i) q^{50} +(0.385431 + 0.444812i) q^{51} +(0.958459 - 0.281429i) q^{52} +(0.0471159 + 0.0302796i) q^{53} +(0.292513 - 0.640515i) q^{54} +(-4.24464 + 4.89858i) q^{55} +(1.43095 - 0.919619i) q^{56} +(-0.0549068 - 0.381885i) q^{57} +(-0.0514028 - 0.357514i) q^{58} +(12.0681 - 7.75573i) q^{59} +(-0.0770307 + 0.0888982i) q^{60} +(4.22418 - 9.24967i) q^{61} +(8.09139 + 5.20002i) q^{62} +(4.87365 - 1.43103i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-0.958459 - 0.281429i) q^{65} +(0.316730 + 0.693543i) q^{66} +(0.568761 - 3.95582i) q^{67} +5.00360 q^{68} +(-0.515627 - 0.228849i) q^{69} -1.70098 q^{70} +(-1.52497 + 10.6064i) q^{71} +(-1.24050 - 2.71631i) q^{72} +(-8.05279 - 2.36451i) q^{73} +(-5.41383 - 6.24790i) q^{74} +(0.112864 - 0.0331400i) q^{75} +(-2.75923 - 1.77325i) q^{76} +(-4.58008 + 10.0290i) q^{77} +(-0.0769477 + 0.0888024i) q^{78} +(-6.62928 + 4.26038i) q^{79} +(0.142315 + 0.989821i) q^{80} +(-1.26314 - 8.78532i) q^{81} +(3.65944 - 2.35178i) q^{82} +(-6.26936 + 7.23523i) q^{83} +(-0.0831182 + 0.182004i) q^{84} +(-4.20930 - 2.70515i) q^{85} +(9.00728 - 2.64478i) q^{86} +(0.0278228 + 0.0321092i) q^{87} +(6.21919 + 1.82612i) q^{88} +(3.35980 + 7.35694i) q^{89} +(-0.424975 + 2.95577i) q^{90} -1.69915 q^{91} +(-4.34089 + 2.03878i) q^{92} -1.13139 q^{93} +(-0.104677 + 0.728043i) q^{94} +(1.36252 + 2.98350i) q^{95} +(0.112864 + 0.0331400i) q^{96} +(-9.33518 - 10.7734i) q^{97} +(3.94032 - 1.15698i) q^{98} +(16.2829 + 10.4644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9}+O(q^{10}) \) 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9	\( 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9} + 3 q^{10} - 3 q^{11} - q^{12} + 12 q^{13} - 3 q^{14} + q^{15} - 3 q^{16} - 26 q^{17} + 12 q^{18} - 25 q^{19} + 3 q^{20} - 11 q^{21} - 14 q^{22} + 14 q^{23} + 10 q^{24} - 3 q^{25} - 10 q^{26} - 52 q^{27} - 3 q^{28} + 4 q^{29} + q^{30} + 5 q^{31} - 3 q^{32} + 9 q^{33} + 7 q^{34} + 3 q^{35} + 12 q^{36} - 20 q^{37} + 19 q^{38} + 41 q^{39} + 3 q^{40} + 32 q^{41} + 22 q^{42} - 46 q^{43} - 3 q^{44} - 56 q^{45} + 3 q^{46} + 80 q^{47} - q^{48} - 41 q^{49} - 3 q^{50} - 34 q^{51} - 21 q^{52} + 29 q^{53} + 47 q^{54} + 3 q^{55} + 8 q^{56} - 33 q^{57} - 7 q^{58} - 3 q^{59} + q^{60} - q^{61} - 28 q^{62} - 8 q^{63} - 3 q^{64} + 21 q^{65} - 46 q^{66} - 63 q^{67} - 4 q^{68} + 78 q^{69} - 8 q^{70} + 55 q^{71} - 32 q^{72} - 36 q^{73} - 20 q^{74} - q^{75} - 3 q^{76} - 9 q^{77} - 80 q^{78} - 29 q^{79} + 3 q^{80} + 15 q^{81} - 23 q^{82} - 63 q^{83} + 4 q^{85} + 31 q^{86} + 63 q^{87} - 3 q^{88} - 95 q^{89} + 10 q^{90} - 12 q^{91} + 14 q^{92} + 126 q^{93} + 3 q^{94} - 19 q^{95} - q^{96} + 11 q^{97} + 58 q^{98} + 97 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9 + 3 * q^10 - 3 * q^11 - q^12 + 12 * q^13 - 3 * q^14 + q^15 - 3 * q^16 - 26 * q^17 + 12 * q^18 - 25 * q^19 + 3 * q^20 - 11 * q^21 - 14 * q^22 + 14 * q^23 + 10 * q^24 - 3 * q^25 - 10 * q^26 - 52 * q^27 - 3 * q^28 + 4 * q^29 + q^30 + 5 * q^31 - 3 * q^32 + 9 * q^33 + 7 * q^34 + 3 * q^35 + 12 * q^36 - 20 * q^37 + 19 * q^38 + 41 * q^39 + 3 * q^40 + 32 * q^41 + 22 * q^42 - 46 * q^43 - 3 * q^44 - 56 * q^45 + 3 * q^46 + 80 * q^47 - q^48 - 41 * q^49 - 3 * q^50 - 34 * q^51 - 21 * q^52 + 29 * q^53 + 47 * q^54 + 3 * q^55 + 8 * q^56 - 33 * q^57 - 7 * q^58 - 3 * q^59 + q^60 - q^61 - 28 * q^62 - 8 * q^63 - 3 * q^64 + 21 * q^65 - 46 * q^66 - 63 * q^67 - 4 * q^68 + 78 * q^69 - 8 * q^70 + 55 * q^71 - 32 * q^72 - 36 * q^73 - 20 * q^74 - q^75 - 3 * q^76 - 9 * q^77 - 80 * q^78 - 29 * q^79 + 3 * q^80 + 15 * q^81 - 23 * q^82 - 63 * q^83 + 4 * q^85 + 31 * q^86 + 63 * q^87 - 3 * q^88 - 95 * q^89 + 10 * q^90 - 12 * q^91 + 14 * q^92 + 126 * q^93 + 3 * q^94 - 19 * q^95 - q^96 + 11 * q^97 + 58 * q^98 + 97 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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