LMFDB - Embedded newform 441.2.bb.e.352.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			352.4
Character	$\chi$	$=$	441.352
Dual form			441.2.bb.e.109.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03880 + 0.963867i) q^{2} +(0.000608887 + 0.00812503i) q^{4} +(0.107830 + 0.274746i) q^{5} +(-1.39076 - 2.25073i) q^{7} +(1.75989 - 2.20683i) q^{8} +O(q^{10})$	\(q+(1.03880 + 0.963867i) q^{2} +(0.000608887 + 0.00812503i) q^{4} +(0.107830 + 0.274746i) q^{5} +(-1.39076 - 2.25073i) q^{7} +(1.75989 - 2.20683i) q^{8} +(-0.152805 + 0.389340i) q^{10} +(5.11416 - 1.57751i) q^{11} +(0.514524 - 2.25428i) q^{13} +(0.724688 - 3.67857i) q^{14} +(3.97137 - 0.598588i) q^{16} +(4.63769 + 3.16192i) q^{17} +(-3.21076 + 5.56120i) q^{19} +(-0.00216666 + 0.00104341i) q^{20} +(6.83311 + 3.29065i) q^{22} +(-5.80770 + 3.95962i) q^{23} +(3.60140 - 3.34161i) q^{25} +(2.70731 - 1.84581i) q^{26} +(0.0174405 - 0.0126704i) q^{28} +(-3.53338 + 1.70159i) q^{29} +(-3.27241 - 5.66798i) q^{31} +(0.0380819 + 0.0259638i) q^{32} +(1.76997 + 7.75473i) q^{34} +(0.468415 - 0.624801i) q^{35} +(0.599368 - 7.99800i) q^{37} +(-8.69560 + 2.68224i) q^{38} +(0.796085 + 0.245560i) q^{40} +(-1.79402 + 2.24963i) q^{41} +(4.17158 + 5.23100i) q^{43} +(0.0159313 + 0.0405922i) q^{44} +(-9.84960 - 1.48459i) q^{46} +(4.12309 + 3.82567i) q^{47} +(-3.13160 + 6.26044i) q^{49} +6.96201 q^{50} +(0.0186294 + 0.00280792i) q^{52} +(-0.232676 - 3.10485i) q^{53} +(0.984874 + 1.23499i) q^{55} +(-7.41455 - 0.891876i) q^{56} +(-5.31059 - 1.63810i) q^{58} +(-1.07811 + 2.74697i) q^{59} +(-0.246792 + 3.29321i) q^{61} +(2.06379 - 9.04207i) q^{62} +(-1.77286 - 7.76739i) q^{64} +(0.674835 - 0.101715i) q^{65} +(-1.22841 - 2.12766i) q^{67} +(-0.0228669 + 0.0396066i) q^{68} +(1.08881 - 0.197554i) q^{70} +(-0.756494 - 0.364308i) q^{71} +(-6.76324 + 6.27537i) q^{73} +(8.33163 - 7.73063i) q^{74} +(-0.0471399 - 0.0227014i) q^{76} +(-10.6631 - 9.31669i) q^{77} +(-6.17678 + 10.6985i) q^{79} +(0.592692 + 1.02657i) q^{80} +(-4.03197 + 0.607721i) q^{82} +(2.83042 + 12.4009i) q^{83} +(-0.368644 + 1.61514i) q^{85} +(-0.708540 + 9.45481i) q^{86} +(5.51905 - 14.0623i) q^{88} +(6.03004 + 1.86002i) q^{89} +(-5.78935 + 1.97709i) q^{91} +(-0.0357083 - 0.0447768i) q^{92} +(0.595637 + 7.94822i) q^{94} +(-1.87413 - 0.282480i) q^{95} +4.63741 q^{97} +(-9.28734 + 3.48491i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) $ 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8	$ 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) $ 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8 - 34 * q^10 + 11 * q^11 - 2 * q^13 - 40 * q^14 - 31 * q^16 + 9 * q^17 - 29 * q^19 + 43 * q^20 + 9 * q^22 + 4 * q^23 + 55 * q^25 - 36 * q^26 - 57 * q^28 - 4 * q^29 - 39 * q^31 + 92 * q^32 - 36 * q^34 + 33 * q^35 - 24 * q^37 - 118 * q^38 - 35 * q^41 + 2 * q^43 - 40 * q^44 - 40 * q^46 + 5 * q^47 + 129 * q^49 + 176 * q^50 - 6 * q^52 - 26 * q^53 + 2 * q^55 - 63 * q^56 + 11 * q^58 + 41 * q^59 + 6 * q^61 - 36 * q^62 + 74 * q^64 + 51 * q^65 - 55 * q^67 + 22 * q^68 - 68 * q^70 + 66 * q^71 + 24 * q^73 - 28 * q^74 + 3 * q^76 + 34 * q^77 - 51 * q^79 + 5 * q^80 - 41 * q^82 - 30 * q^83 + 68 * q^85 - 110 * q^86 + 129 * q^88 - 75 * q^89 + 5 * q^91 + 38 * q^94 - 36 * q^95 - 168 * q^97 - 227 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{21}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.03880	+	0.963867i	0.734544	+	0.681557i	0.955919	−	0.293632i	$-0.0948640\pi$
$2$	1.03880	+	0.963867i	0.734544	+	0.681557i	−0.221375	+	0.975189i	$0.571054\pi$
$3$		0			0
$3$		0			0
$4$	0.000608887		0.00812503i	0.000304443		0.00406252i
$5$	0.107830	+	0.274746i	0.0482230	+	0.122870i	0.952956	−	0.303109i	$-0.0980248\pi$
$5$	0.107830	+	0.274746i	0.0482230	+	0.122870i	−0.904733	+	0.425980i	$0.859930\pi$
$6$		0			0
$7$	−1.39076	−	2.25073i	−0.525656	−	0.850697i
$7$	−1.39076	−	2.25073i	−0.525656	−	0.850697i
$8$	1.75989	−	2.20683i	0.622213	−	0.780231i
$9$		0			0
$10$	−0.152805	+	0.389340i	−0.0483211	+	0.123120i
$11$	5.11416	−	1.57751i	1.54198	−	0.475637i	0.596855	−	0.802349i	$-0.296417\pi$
$11$	5.11416	−	1.57751i	1.54198	−	0.475637i	0.945124	+	0.326712i	$0.105941\pi$
$12$		0			0
$13$	0.514524	−	2.25428i	0.142703	−	0.625224i	−0.852097	−	0.523383i	$-0.824670\pi$
$13$	0.514524	−	2.25428i	0.142703	−	0.625224i	0.994801	−	0.101841i	$-0.0324732\pi$
$14$	0.724688	−	3.67857i	0.193681	−	0.983139i
$15$		0			0
$16$	3.97137	−	0.598588i	0.992843	−	0.149647i
$17$	4.63769	+	3.16192i	1.12481	+	0.766879i	0.975081	−	0.221849i	$-0.0712091\pi$
$17$	4.63769	+	3.16192i	1.12481	+	0.766879i	0.149724	+	0.988728i	$0.452161\pi$
$18$		0			0
$19$	−3.21076	+	5.56120i	−0.736599	+	1.27583i	0.217419	+	0.976078i	$0.430236\pi$
$19$	−3.21076	+	5.56120i	−0.736599	+	1.27583i	−0.954018	+	0.299749i	$0.903097\pi$
$20$	−0.00216666	+	0.00104341i	−0.000484481	+	0.000233314i
$21$		0			0
$22$	6.83311	+	3.29065i	1.45682	+	0.701570i
$23$	−5.80770	+	3.95962i	−1.21099	+	0.825638i	−0.988783	−	0.149361i	$-0.952278\pi$
$23$	−5.80770	+	3.95962i	−1.21099	+	0.825638i	−0.222207	+	0.975000i	$0.571326\pi$
$24$		0			0
$25$	3.60140	−	3.34161i	0.720280	−	0.668322i
$26$	2.70731	−	1.84581i	0.530948	−	0.361994i
$27$		0			0
$28$	0.0174405	−	0.0126704i	0.00329594	−	0.00239448i
$29$	−3.53338	+	1.70159i	−0.656133	+	0.315977i	−0.732164	−	0.681129i	$-0.761489\pi$
$29$	−3.53338	+	1.70159i	−0.656133	+	0.315977i	0.0760312	+	0.997105i	$0.475775\pi$
$30$		0			0
$31$	−3.27241	−	5.66798i	−0.587742	−	1.01800i	−0.994527	−	0.104475i	$-0.966684\pi$
$31$	−3.27241	−	5.66798i	−0.587742	−	1.01800i	0.406786	−	0.913524i	$-0.366650\pi$
$32$	0.0380819	+	0.0259638i	0.00673200	+	0.00458980i
$33$		0			0
$34$	1.76997	+	7.75473i	0.303547	+	1.32992i
$35$	0.468415	−	0.624801i	0.0791766	−	0.105611i
$36$		0			0
$37$	0.599368	−	7.99800i	0.0985354	−	1.31486i	−0.700531	−	0.713622i	$-0.747054\pi$
$37$	0.599368	−	7.99800i	0.0985354	−	1.31486i	0.799067	−	0.601242i	$-0.205327\pi$
$38$	−8.69560	+	2.68224i	−1.41061	+	0.435117i
$39$		0			0
$40$	0.796085	+	0.245560i	0.125872	+	0.0388264i
$41$	−1.79402	+	2.24963i	−0.280178	+	0.351332i	−0.901930	−	0.431882i	$-0.857850\pi$
$41$	−1.79402	+	2.24963i	−0.280178	+	0.351332i	0.621752	+	0.783214i	$0.286421\pi$
$42$		0			0
$43$	4.17158	+	5.23100i	0.636160	+	0.797719i	0.990517	−	0.137391i	$-0.0438716\pi$
$43$	4.17158	+	5.23100i	0.636160	+	0.797719i	−0.354357	+	0.935110i	$0.615300\pi$
$44$	0.0159313	+	0.0405922i	0.00240173	+	0.00611951i
$45$		0			0
$46$	−9.84960	−	1.48459i	−1.45224	−	0.218891i
$47$	4.12309	+	3.82567i	0.601414	+	0.558031i	0.921018	−	0.389520i	$-0.127359\pi$
$47$	4.12309	+	3.82567i	0.601414	+	0.558031i	−0.319603	+	0.947551i	$0.603550\pi$
$48$		0			0
$49$	−3.13160	+	6.26044i	−0.447371	+	0.894348i
$50$	6.96201			0.984577
$51$		0			0
$52$	0.0186294	+	0.00280792i	0.00258343	+	0.000389389i
$53$	−0.232676	−	3.10485i	−0.0319605	−	0.426483i	−0.990118	−	0.140240i	$-0.955213\pi$
$53$	−0.232676	−	3.10485i	−0.0319605	−	0.426483i	0.958157	−	0.286243i	$-0.0924065\pi$
$54$		0			0
$55$	0.984874	+	1.23499i	0.132800	+	0.166526i
$56$	−7.41455	−	0.891876i	−0.990810	−	0.119182i
$57$		0			0
$58$	−5.31059	−	1.63810i	−0.697314	−	0.215093i
$59$	−1.07811	+	2.74697i	−0.140357	+	0.357625i	−0.983717	−	0.179725i	$-0.942479\pi$
$59$	−1.07811	+	2.74697i	−0.140357	+	0.357625i	0.843360	+	0.537350i	$0.180574\pi$
$60$		0			0
$61$	−0.246792	+	3.29321i	−0.0315985	+	0.421652i	0.958864	+	0.283867i	$0.0916174\pi$
$61$	−0.246792	+	3.29321i	−0.0315985	+	0.421652i	−0.990462	+	0.137785i	$0.956002\pi$
$62$	2.06379	−	9.04207i	0.262102	−	1.14834i
$63$		0			0
$64$	−1.77286	−	7.76739i	−0.221607	−	0.970924i
$65$	0.674835	−	0.101715i	0.0837029	−	0.0126162i
$66$		0			0
$67$	−1.22841	−	2.12766i	−0.150074	−	0.259935i	0.781181	−	0.624305i	$-0.214618\pi$
$67$	−1.22841	−	2.12766i	−0.150074	−	0.259935i	−0.931254	+	0.364370i	$0.881284\pi$
$68$	−0.0228669	+	0.0396066i	−0.00277302	+	0.00480301i
$69$		0			0
$70$	1.08881	−	0.197554i	0.130138	−	0.0236122i
$71$	−0.756494	−	0.364308i	−0.0897793	−	0.0432354i	0.388455	−	0.921468i	$-0.373009\pi$
$71$	−0.756494	−	0.364308i	−0.0897793	−	0.0432354i	−0.478235	+	0.878232i	$0.658723\pi$
$72$		0			0
$73$	−6.76324	+	6.27537i	−0.791578	+	0.734477i	−0.968302	−	0.249784i	$-0.919640\pi$
$73$	−6.76324	+	6.27537i	−0.791578	+	0.734477i	0.176724	+	0.984260i	$0.443450\pi$
$74$	8.33163	−	7.73063i	0.968533	−	0.898667i
$75$		0			0
$76$	−0.0471399	−	0.0227014i	−0.00540732	−	0.00260403i
$77$	−10.6631	−	9.31669i	−1.21517	−	1.06174i
$78$		0			0
$79$	−6.17678	+	10.6985i	−0.694943	+	1.20368i	0.275258	+	0.961371i	$0.411237\pi$
$79$	−6.17678	+	10.6985i	−0.694943	+	1.20368i	−0.970200	+	0.242305i	$0.922096\pi$
$80$	0.592692	+	1.02657i	0.0662650	+	0.114774i
$81$		0			0
$82$	−4.03197	+	0.607721i	−0.445256	+	0.0671116i
$83$	2.83042	+	12.4009i	0.310679	+	1.36117i	0.853399	+	0.521258i	$0.174537\pi$
$83$	2.83042	+	12.4009i	0.310679	+	1.36117i	−0.542721	+	0.839913i	$0.682606\pi$
$84$		0			0
$85$	−0.368644	+	1.61514i	−0.0399851	+	0.175186i
$86$	−0.708540	+	9.45481i	−0.0764039	+	1.01954i
$87$		0			0
$88$	5.51905	−	14.0623i	0.588333	−	1.49905i
$89$	6.03004	+	1.86002i	0.639183	+	0.197162i	0.597373	−	0.801964i	$-0.296211\pi$
$89$	6.03004	+	1.86002i	0.639183	+	0.197162i	0.0418100	+	0.999126i	$0.486688\pi$
$90$		0			0
$91$	−5.78935	+	1.97709i	−0.606889	+	0.207256i
$92$	−0.0357083	−	0.0447768i	−0.00372285	−	0.00466830i
$93$		0			0
$94$	0.595637	+	7.94822i	0.0614352	+	0.819796i
$95$	−1.87413	−	0.282480i	−0.192282	−	0.0289819i
$96$		0			0
$97$	4.63741			0.470858			0.235429	−	0.971892i	$-0.424351\pi$
$97$	4.63741			0.470858			0.235429	+	0.971892i	$0.424351\pi$
$98$	−9.28734	+	3.48491i	−0.938163	+	0.352029i
$99$		0			0
$100$	0.0293436	+	0.0272268i	0.00293436	+	0.00272268i
$101$	−14.5667	−	2.19557i	−1.44944	−	0.218468i	−0.623321	−	0.781966i	$-0.714217\pi$
$101$	−14.5667	−	2.19557i	−1.44944	−	0.218468i	−0.826117	+	0.563498i	$0.809455\pi$
$102$		0			0
$103$	−3.28034	−	8.35816i	−0.323221	−	0.823554i	−0.996455	−	0.0841245i	$-0.973191\pi$
$103$	−3.28034	−	8.35816i	−0.323221	−	0.823554i	0.673234	−	0.739429i	$-0.264905\pi$
$104$	−4.06929	−	5.10273i	−0.399027	−	0.500364i
$105$		0			0
$106$	2.75095	−	3.44959i	0.267196	−	0.335053i
$107$	−0.641470	−	0.197867i	−0.0620132	−	0.0191285i	0.263593	−	0.964634i	$-0.415092\pi$
$107$	−0.641470	−	0.197867i	−0.0620132	−	0.0191285i	−0.325607	+	0.945505i	$0.605568\pi$
$108$		0			0
$109$	8.64048	−	2.66524i	0.827608	−	0.255283i	0.148120	−	0.988969i	$-0.452678\pi$
$109$	8.64048	−	2.66524i	0.827608	−	0.255283i	0.679489	+	0.733686i	$0.262202\pi$
$110$	−0.167280	+	2.23220i	−0.0159495	+	0.212832i
$111$		0			0
$112$	−6.87047	−	8.10601i	−0.649198	−	0.765946i
$113$	2.01162	+	8.81349i	0.189237	+	0.829103i	0.977020	+	0.213149i	$0.0683721\pi$
$113$	2.01162	+	8.81349i	0.189237	+	0.829103i	−0.787782	+	0.615954i	$0.788771\pi$
$114$		0			0
$115$	−1.71413	−	1.16868i	−0.159844	−	0.108980i
$116$	−0.0159769	−	0.0276728i	−0.00148342	−	0.00256935i
$117$		0			0
$118$	−3.76765	+	1.81440i	−0.346840	+	0.167029i
$119$	0.666753	−	14.8357i	0.0611212	−	1.35998i
$120$		0			0
$121$	14.5775	−	9.93878i	1.32523	−	0.903525i
$122$	−3.43058	+	3.18312i	−0.310590	+	0.288186i
$123$		0			0
$124$	0.0440600	−	0.0300396i	0.00395670	−	0.00269763i
$125$	2.63603	+	1.26945i	0.235774	+	0.113543i
$126$		0			0
$127$	3.24779	−	1.56405i	0.288195	−	0.138787i	−0.284201	−	0.958765i	$-0.591728\pi$
$127$	3.24779	−	1.56405i	0.288195	−	0.138787i	0.572396	+	0.819977i	$0.306014\pi$
$128$	5.69118	−	9.85741i	0.503034	−	0.871280i
$129$		0			0
$130$	0.799059	+	0.544789i	0.0700821	+	0.0477812i
$131$	−11.0848	+	1.67077i	−0.968486	+	0.145976i	−0.614190	−	0.789158i	$-0.710517\pi$
$131$	−11.0848	+	1.67077i	−0.968486	+	0.145976i	−0.354295	+	0.935134i	$0.615279\pi$
$132$		0			0
$133$	16.9822	−	0.507705i	1.47254	−	0.0440236i
$134$	0.774713	−	3.39424i	0.0669250	−	0.293218i
$135$		0			0
$136$	15.1396	−	4.66995i	1.29821	−	0.400445i
$137$	1.59837	−	4.07259i	0.136558	−	0.347945i	−0.846193	−	0.532876i	$-0.821111\pi$
$137$	1.59837	−	4.07259i	0.136558	−	0.347945i	0.982751	+	0.184932i	$0.0592064\pi$
$138$		0			0
$139$	−5.95696	+	7.46979i	−0.505262	+	0.633579i	−0.967407	−	0.253225i	$-0.918509\pi$
$139$	−5.95696	+	7.46979i	−0.505262	+	0.633579i	0.462145	+	0.886804i	$0.347080\pi$
$140$	0.00536174	+	0.00342545i	0.000453149	+	0.000289504i
$141$		0			0
$142$	−0.434702	−	1.10760i	−0.0364794	−	0.0929480i
$143$	−0.924786	−	12.3404i	−0.0773345	−	1.03196i
$144$		0			0
$145$	−0.848508	−	0.787301i	−0.0704648	−	0.0653818i
$146$	−13.0743			−1.08204
$147$		0			0
$148$	0.0653490			0.00537165
$149$	3.49201	+	3.24011i	0.286077	+	0.265441i	0.810137	−	0.586241i	$-0.199393\pi$
$149$	3.49201	+	3.24011i	0.286077	+	0.265441i	−0.524060	+	0.851681i	$0.675583\pi$
$150$		0			0
$151$	0.572964	+	7.64567i	0.0466271	+	0.622196i	0.970749	+	0.240098i	$0.0771794\pi$
$151$	0.572964	+	7.64567i	0.0466271	+	0.622196i	−0.924122	+	0.382098i	$0.875202\pi$
$152$	6.62204	+	16.8727i	0.537118	+	1.36855i
$153$		0			0
$154$	−2.09681	−	19.9560i	−0.168965	−	1.60810i
$155$	1.20439	−	1.51026i	0.0967390	−	0.121307i
$156$		0			0
$157$	−5.32378	+	13.5648i	−0.424884	+	1.08259i	0.544874	+	0.838518i	$0.316577\pi$
$157$	−5.32378	+	13.5648i	−0.424884	+	1.08259i	−0.969758	+	0.244068i	$0.921518\pi$
$158$	−16.7284	+	5.16002i	−1.33084	+	0.410509i
$159$		0			0
$160$	−0.00302709	+	0.0132625i	−0.000239312	+	0.00104850i
$161$	16.9891	+	7.56472i	1.33893	+	0.596183i
$162$		0			0
$163$	−14.7771	+	2.22728i	−1.15743	+	0.174454i	−0.699566	−	0.714568i	$-0.746623\pi$
$163$	−14.7771	+	2.22728i	−1.15743	+	0.174454i	−0.457863	+	0.889023i	$0.651385\pi$
$164$	−0.0193706	−	0.0132067i	−0.00151259	−	0.00103127i
$165$		0			0
$166$	−9.01254	+	15.6102i	−0.699509	+	1.21158i
$167$	−8.45408	+	4.07127i	−0.654196	+	0.315044i	−0.731378	−	0.681973i	$-0.761122\pi$
$167$	−8.45408	+	4.07127i	−0.654196	+	0.315044i	0.0771813	+	0.997017i	$0.475408\pi$
$168$		0			0
$169$	6.89556	+	3.32073i	0.530428	+	0.255441i
$170$	−1.93972	+	1.32248i	−0.148770	+	0.101430i
$171$		0			0
$172$	−0.0399620	+	0.0370793i	−0.00304707	+	0.00282727i
$173$	10.6087	−	7.23291i	0.806567	−	0.549908i	−0.0883771	−	0.996087i	$-0.528168\pi$
$173$	10.6087	−	7.23291i	0.806567	−	0.549908i	0.894944	+	0.446179i	$0.147216\pi$
$174$		0			0
$175$	−12.5297	−	3.45843i	−0.947160	−	0.261433i
$176$	19.3660	−	9.32616i	1.45976	−	0.702986i
$177$		0			0
$178$	4.47120	+	7.74434i	0.335131	+	0.580463i
$179$	−9.10511	−	6.20776i	−0.680548	−	0.463990i	0.173056	−	0.984912i	$-0.444636\pi$
$179$	−9.10511	−	6.20776i	−0.680548	−	0.463990i	−0.853604	+	0.520922i	$0.825588\pi$
$180$		0			0
$181$	−1.06259	−	4.65552i	−0.0789818	−	0.346042i	0.919961	−	0.392010i	$-0.128220\pi$
$181$	−1.06259	−	4.65552i	−0.0789818	−	0.346042i	−0.998943	+	0.0459677i	$0.985363\pi$
$182$	−7.91964	−	3.52636i	−0.587043	−	0.261391i
$183$		0			0
$184$	−1.48269	+	19.7851i	−0.109305	+	1.45857i
$185$	2.26205	−	0.697750i	0.166309	−	0.0512996i
$186$		0			0
$187$	28.7059	+	8.85459i	2.09918	+	0.647512i
$188$	−0.0285732	+	0.0358296i	−0.00208391	+	0.00261314i
$189$		0			0
$190$	−1.67458	−	2.09986i	−0.121487	−	0.152340i
$191$	7.10267	+	18.0973i	0.513931	+	1.30948i	0.918664	+	0.395041i	$0.129269\pi$
$191$	7.10267	+	18.0973i	0.513931	+	1.30948i	−0.404732	+	0.914435i	$0.632635\pi$
$192$		0			0
$193$	8.89187	+	1.34023i	0.640051	+	0.0964721i	0.461046	−	0.887376i	$-0.347474\pi$
$193$	8.89187	+	1.34023i	0.640051	+	0.0964721i	0.179005	+	0.983848i	$0.442712\pi$
$194$	4.81735	+	4.46984i	0.345865	+	0.320916i
$195$		0			0
$196$	−0.0527731	−	0.0216324i	−0.00376950	−	0.00154517i
$197$	18.2654			1.30136			0.650680	−	0.759352i	$-0.274484\pi$
$197$	18.2654			1.30136			0.650680	+	0.759352i	$0.274484\pi$
$198$		0			0
$199$	−21.8087	−	3.28713i	−1.54598	−	0.233019i	−0.680042	−	0.733173i	$-0.738039\pi$
$199$	−21.8087	−	3.28713i	−1.54598	−	0.233019i	−0.865936	+	0.500154i	$0.833277\pi$
$200$	−1.03630	−	13.8285i	−0.0732778	−	0.977824i
$201$		0			0
$202$	−13.0156	−	16.3211i	−0.915778	−	1.14835i
$203$	8.74389	+	5.58621i	0.613701	+	0.392075i
$204$		0			0
$205$	−0.811524	−	0.250322i	−0.0566793	−	0.0174832i
$206$	4.64853	−	11.8443i	0.323879	−	0.825230i
$207$		0			0
$208$	0.693983	−	9.26056i	0.0481191	−	0.642104i
$209$	−7.64751	+	33.5059i	−0.528989	+	2.31765i
$210$		0			0
$211$	−3.91907	−	17.1706i	−0.269800	−	1.18207i	−0.910246	−	0.414067i	$-0.864108\pi$
$211$	−3.91907	−	17.1706i	−0.269800	−	1.18207i	0.640447	−	0.768003i	$-0.278749\pi$
$212$	0.0250853	−	0.00378100i	0.00172287	−	0.000259680i
$213$		0			0
$214$	−0.475642	−	0.823836i	−0.0325142	−	0.0563163i
$215$	−0.987374	+	1.71018i	−0.0673384	+	0.116633i
$216$		0			0
$217$	−8.20599	+	15.2481i	−0.557059	+	1.03511i
$218$	11.5447	+	5.55962i	0.781904	+	0.376545i
$219$		0			0
$220$	−0.00943468	+	0.00875411i	−0.000636086	+	0.000590202i
$221$	9.51406	−	8.82776i	0.639985	−	0.593819i
$222$		0			0
$223$	4.21292	+	2.02884i	0.282118	+	0.135861i	0.569592	−	0.821928i	$-0.307101\pi$
$223$	4.21292	+	2.02884i	0.282118	+	0.135861i	−0.287474	+	0.957788i	$0.592815\pi$
$224$	0.00547498	−	0.121822i	0.000365812	−	0.00813955i
$225$		0			0
$226$	−6.40535	+	11.0944i	−0.426078	+	0.737988i
$227$	−1.07960	−	1.86992i	−0.0716555	−	0.124111i	0.827971	−	0.560770i	$-0.189495\pi$
$227$	−1.07960	−	1.86992i	−0.0716555	−	0.124111i	−0.899627	+	0.436659i	$0.856162\pi$
$228$		0			0
$229$	9.32059	−	1.40485i	0.615922	−	0.0928353i	0.166331	−	0.986070i	$-0.446808\pi$
$229$	9.32059	−	1.40485i	0.615922	−	0.0928353i	0.449591	+	0.893235i	$0.351570\pi$
$230$	−0.654196	−	2.86622i	−0.0431364	−	0.188993i
$231$		0			0
$232$	−2.46324	+	10.7922i	−0.161720	+	0.708540i
$233$	−0.747043	+	9.96860i	−0.0489404	+	0.653065i	0.917757	+	0.397143i	$0.129998\pi$
$233$	−0.747043	+	9.96860i	−0.0489404	+	0.653065i	−0.966697	+	0.255922i	$0.917621\pi$
$234$		0			0
$235$	−0.606495	+	1.54532i	−0.0395633	+	0.100806i
$236$	−0.0229756	−	0.00708705i	−0.00149559	−	0.000461328i
$237$		0			0
$238$	14.9922	−	14.7687i	0.971802	−	0.957309i
$239$	−12.4260	−	15.5817i	−0.803772	−	1.00790i	−0.999628	−	0.0272656i	$-0.991320\pi$
$239$	−12.4260	−	15.5817i	−0.803772	−	1.00790i	0.195856	−	0.980633i	$-0.437251\pi$
$240$		0			0
$241$	−1.88583	−	25.1647i	−0.121477	−	1.62100i	−0.641690	−	0.766964i	$-0.721767\pi$
$241$	−1.88583	−	25.1647i	−0.121477	−	1.62100i	0.520213	−	0.854037i	$-0.325853\pi$
$242$	24.7228	+	3.72636i	1.58924	+	0.239540i
$243$		0			0
$244$	−0.0269077			−0.00172259
$245$	−2.05771	−	0.185332i	−0.131462	−	0.0118404i
$246$		0			0
$247$	10.8845	+	10.0993i	0.692563	+	0.642604i
$248$	−18.2673	−	2.75335i	−1.15997	−	0.174838i
$249$		0			0
$250$	1.51474	+	3.85948i	0.0958003	+	0.244095i
$251$	−7.53070	−	9.44320i	−0.475334	−	0.596050i	0.485134	−	0.874440i	$-0.338771\pi$
$251$	−7.53070	−	9.44320i	−0.475334	−	0.596050i	−0.960468	+	0.278390i	$0.910199\pi$
$252$		0			0
$253$	−23.4552	+	29.4119i	−1.47461	+	1.84911i
$254$	4.88135	+	1.50570i	0.306283	+	0.0944758i
$255$		0			0
$256$	0.186857	−	0.0576377i	0.0116786	−	0.00360236i
$257$	0.937302	−	12.5074i	0.0584673	−	0.780192i	−0.888503	−	0.458871i	$-0.848254\pi$
$257$	0.937302	−	12.5074i	0.0584673	−	0.780192i	0.946970	−	0.321321i	$-0.104127\pi$
$258$		0			0
$259$	−18.8349	+	9.77425i	−1.17035	+	0.607342i
$260$	0.00123734	+	0.00542112i	7.67363e−5	+	0.000336204i
$261$		0			0
$262$	−13.1253	−	8.94870i	−0.810886	−	0.552852i
$263$	4.85395	+	8.40729i	0.299307	+	0.518416i	0.975978	−	0.217870i	$-0.0699110\pi$
$263$	4.85395	+	8.40729i	0.299307	+	0.518416i	−0.676670	+	0.736286i	$0.736578\pi$
$264$		0			0
$265$	0.827954	−	0.398722i	0.0508608	−	0.0244933i
$266$	18.1305	+	15.8411i	1.11165	+	0.971283i
$267$		0			0
$268$	0.0165394	−	0.0112764i	0.00101030	−	0.000688813i
$269$	1.31561	−	1.22070i	0.0802139	−	0.0744277i	−0.639047	−	0.769168i	$-0.720671\pi$
$269$	1.31561	−	1.22070i	0.0802139	−	0.0744277i	0.719261	+	0.694740i	$0.244481\pi$
$270$		0			0
$271$	26.7728	−	18.2534i	1.62633	−	1.10881i	0.713348	−	0.700810i	$-0.247178\pi$
$271$	26.7728	−	18.2534i	1.62633	−	1.10881i	0.912981	−	0.408002i	$-0.133774\pi$
$272$	20.3107	+	9.78111i	1.23152	+	0.593067i
$273$		0			0
$274$	5.58582	−	2.68999i	0.337452	−	0.162508i
$275$	13.1467	−	22.7708i	0.792778	−	1.37313i
$276$		0			0
$277$	12.3319	+	8.40774i	0.740951	+	0.505172i	0.873993	−	0.485938i	$-0.161522\pi$
$277$	12.3319	+	8.40774i	0.740951	+	0.505172i	−0.133042	+	0.991110i	$0.542474\pi$
$278$	−13.3880	+	2.01791i	−0.802957	+	0.121026i
$279$		0			0
$280$	−0.554470	−	2.13329i	−0.0331359	−	0.127488i
$281$	2.94605	−	12.9075i	0.175746	−	0.769995i	−0.807817	−	0.589433i	$-0.799351\pi$
$281$	2.94605	−	12.9075i	0.175746	−	0.769995i	0.983564	−	0.180562i	$-0.0577916\pi$
$282$		0			0
$283$	25.3155	−	7.80880i	1.50485	−	0.464185i	0.570729	−	0.821139i	$-0.306661\pi$
$283$	25.3155	−	7.80880i	1.50485	−	0.464185i	0.934122	+	0.356954i	$0.116185\pi$
$284$	0.00249940	−	0.00636836i	0.000148312	−	0.000377893i
$285$		0			0
$286$	10.9338	−	13.7106i	0.646532	−	0.810725i
$287$	7.55834	+	0.909173i	0.446155	+	0.0536668i
$288$		0			0
$289$	5.29961	+	13.5032i	0.311742	+	0.794306i
$290$	−0.122579	−	1.63570i	−0.00719806	−	0.0960515i
$291$		0			0
$292$	−0.0551056	−	0.0511306i	−0.00322481	−	0.00299219i
$293$	15.5543			0.908691			0.454345	−	0.890826i	$-0.349873\pi$
$293$	15.5543			0.908691			0.454345	+	0.890826i	$0.349873\pi$
$294$		0			0
$295$	−0.870970			−0.0507098
$296$	−16.5954	−	15.3983i	−0.964587	−	0.895006i
$297$		0			0
$298$	0.504469	+	6.73167i	0.0292231	+	0.389955i
$299$	5.93789	+	15.1295i	0.343397	+	0.874961i
$300$		0			0
$301$	5.97193	−	16.6641i	0.344216	−	0.960506i
$302$	−6.77422	+	8.49460i	−0.389812	+	0.488809i
$303$		0			0
$304$	−9.42226	+	24.0075i	−0.540404	+	1.37693i
$305$	−0.931407	+	0.287301i	−0.0533322	+	0.0164508i
$306$		0			0
$307$	−0.295880	+	1.29633i	−0.0168868	+	0.0739857i	−0.982669	−	0.185368i	$-0.940652\pi$
$307$	−0.295880	+	1.29633i	−0.0168868	+	0.0739857i	0.965782	+	0.259354i	$0.0835095\pi$
$308$	0.0692058	−	0.0923109i	0.00394336	−	0.00525990i
$309$		0			0
$310$	2.70681	−	0.407986i	0.153737	−	0.0231720i
$311$	5.77642	+	3.93830i	0.327551	+	0.223320i	0.715918	−	0.698184i	$-0.246008\pi$
$311$	5.77642	+	3.93830i	0.327551	+	0.223320i	−0.388367	+	0.921505i	$0.626961\pi$
$312$		0			0
$313$	10.9959	−	19.0454i	0.621524	−	1.07651i	−0.367678	−	0.929953i	$-0.619847\pi$
$313$	10.9959	−	19.0454i	0.621524	−	1.07651i	0.989202	−	0.146558i	$-0.0468195\pi$
$314$	−18.6050	+	8.95968i	−1.04994	+	0.505624i
$315$		0			0
$316$	−0.0906867	−	0.0436724i	−0.00510152	−	0.00245676i
$317$	−13.7261	+	9.35828i	−0.770933	+	0.525613i	−0.883726	−	0.468005i	$-0.844973\pi$
$317$	−13.7261	+	9.35828i	−0.770933	+	0.525613i	0.112792	+	0.993619i	$0.464020\pi$
$318$		0			0
$319$	−15.3860	+	14.2761i	−0.861452	+	0.799311i
$320$	1.94289	−	1.32464i	0.108611	−	0.0740497i
$321$		0			0
$322$	10.3570	+	24.2335i	0.577171	+	1.35048i
$323$	−32.4746	+	15.6390i	−1.80694	+	0.870175i
$324$		0			0
$325$	−5.67991	−	9.83790i	−0.315065	−	0.545708i
$326$	−17.4972	−	11.9294i	−0.969082	−	0.660709i
$327$		0			0
$328$	1.80727	+	7.91816i	0.0997897	+	0.437207i
$329$	2.87635	−	14.6005i	0.158578	−	0.804954i
$330$		0			0
$331$	1.58846	−	21.1965i	0.0873095	−	1.16506i	−0.765710	−	0.643186i	$-0.777612\pi$
$331$	1.58846	−	21.1965i	0.0873095	−	1.16506i	0.853020	−	0.521879i	$-0.174769\pi$
$332$	−0.0990340	+	0.0305479i	−0.00543520	+	0.00167654i
$333$		0			0
$334$	−12.7063	−	3.91937i	−0.695256	−	0.214458i
$335$	0.452108	−	0.566925i	0.0247013	−	0.0309744i
$336$		0			0
$337$	−17.5050	−	21.9505i	−0.953556	−	1.19572i	−0.980587	−	0.196086i	$-0.937177\pi$
$337$	−17.5050	−	21.9505i	−0.953556	−	1.19572i	0.0270311	−	0.999635i	$-0.491395\pi$
$338$	3.96238	+	10.0960i	0.215525	+	0.549149i
$339$		0			0
$340$	−0.0133475	−	0.00201181i	−0.000723870	−	0.000109106i
$341$	−25.6769	−	23.8247i	−1.39048	−	1.29018i
$342$		0			0
$343$	18.4459	−	1.65835i	0.995983	−	0.0895423i
$344$	18.8854			1.01823
$345$		0			0
$346$	17.9919	+	2.71185i	0.967252	+	0.145790i
$347$	−0.225676	−	3.01144i	−0.0121149	−	0.161663i	−0.999980	−	0.00634709i	$-0.997980\pi$
$347$	−0.225676	−	3.01144i	−0.0121149	−	0.161663i	0.987865	−	0.155315i	$-0.0496394\pi$
$348$		0			0
$349$	−0.611775	−	0.767142i	−0.0327476	−	0.0410642i	0.765188	−	0.643807i	$-0.222646\pi$
$349$	−0.611775	−	0.767142i	−0.0327476	−	0.0410642i	−0.797936	+	0.602743i	$0.794075\pi$
$350$	−9.68245	−	15.6696i	−0.517549	−	0.837577i
$351$		0			0
$352$	0.235715	+	0.0727086i	0.0125637	+	0.00387538i
$353$	4.19772	−	10.6956i	0.223422	−	0.569271i	−0.774578	−	0.632478i	$-0.782038\pi$
$353$	4.19772	−	10.6956i	0.223422	−	0.569271i	0.998000	+	0.0632075i	$0.0201330\pi$
$354$		0			0
$355$	0.0185196	−	0.247127i	0.000982919	−	0.0131161i
$356$	−0.0114411	+	0.0501268i	−0.000606378	+	0.00265671i
$357$		0			0
$358$	−3.47495	−	15.2247i	−0.183657	−	0.804653i
$359$	−9.35161	+	1.40953i	−0.493559	+	0.0743921i	−0.391106	−	0.920346i	$-0.627907\pi$
$359$	−9.35161	+	1.40953i	−0.493559	+	0.0743921i	−0.102453	+	0.994738i	$0.532669\pi$
$360$		0			0
$361$	−11.1180	−	19.2569i	−0.585157	−	1.01352i
$362$	3.38348	−	5.86036i	0.177832	−	0.308014i
$363$		0			0
$364$	−0.0195890	−	0.0458349i	−0.00102674	−	0.00240240i
$365$	−2.45341	−	1.18150i	−0.128417	−	0.0618426i
$366$		0			0
$367$	18.8774	−	17.5157i	0.985394	−	0.914312i	−0.0109333	−	0.999940i	$-0.503480\pi$
$367$	18.8774	−	17.5157i	0.985394	−	0.914312i	0.996327	+	0.0856283i	$0.0272898\pi$
$368$	−20.6944	+	19.2016i	−1.07877	+	1.00095i
$369$		0			0
$370$	3.02236	+	1.45549i	0.157125	+	0.0756674i
$371$	−6.66458	+	4.84177i	−0.346008	+	0.251372i
$372$		0			0
$373$	3.35239	−	5.80651i	0.173580	−	0.300650i	−0.766089	−	0.642735i	$-0.777800\pi$
$373$	3.35239	−	5.80651i	0.173580	−	0.300650i	0.939669	+	0.342085i	$0.111133\pi$
$374$	21.2851	+	36.8668i	1.10062	+	1.90634i
$375$		0			0
$376$	15.6987	−	2.36621i	0.809601	−	0.122028i
$377$	2.01784	+	8.84073i	0.103924	+	0.455321i
$378$		0			0
$379$	3.75095	−	16.4340i	0.192673	−	0.844157i	−0.782489	−	0.622665i	$-0.786050\pi$
$379$	3.75095	−	16.4340i	0.192673	−	0.844157i	0.975162	−	0.221493i	$-0.0710928\pi$
$380$	0.00115403	−	0.0153994i	5.92002e−5	−	0.000789972i
$381$		0			0
$382$	−10.0651	+	25.6455i	−0.514977	+	1.31214i
$383$	−2.27723	−	0.702434i	−0.116361	−	0.0358927i	0.236028	−	0.971746i	$-0.424154\pi$
$383$	−2.27723	−	0.702434i	−0.116361	−	0.0358927i	−0.352389	+	0.935854i	$0.614631\pi$
$384$		0			0
$385$	1.40992	−	3.93426i	0.0718562	−	0.200509i
$386$	7.94508	+	9.96281i	0.404394	+	0.507094i
$387$		0			0
$388$	0.00282366	+	0.0376791i	0.000143350	+	0.00191287i
$389$	−9.47962	−	1.42882i	−0.480636	−	0.0724442i	−0.0957441	−	0.995406i	$-0.530523\pi$
$389$	−9.47962	−	1.42882i	−0.480636	−	0.0724442i	−0.384892	+	0.922962i	$0.625761\pi$
$390$		0			0
$391$	−39.4543			−1.99529
$392$	8.30444	+	17.9285i	0.419438	+	0.905528i
$393$		0			0
$394$	18.9742	+	17.6055i	0.955905	+	0.886950i
$395$	−3.60541	−	0.543428i	−0.181408	−	0.0273429i
$396$		0			0
$397$	7.39215	+	18.8349i	0.371001	+	0.945296i	0.987454	+	0.157904i	$0.0504738\pi$
$397$	7.39215	+	18.8349i	0.371001	+	0.945296i	−0.616453	+	0.787392i	$0.711431\pi$
$398$	−19.4866	−	24.4354i	−0.976773	−	1.22483i
$399$		0			0
$400$	12.3023	−	15.4265i	0.615113	−	0.771327i
$401$	13.2509	+	4.08737i	0.661720	+	0.204114i	0.607383	−	0.794409i	$-0.292219\pi$
$401$	13.2509	+	4.08737i	0.661720	+	0.204114i	0.0543371	+	0.998523i	$0.482695\pi$
$402$		0			0
$403$	−14.4609	+	4.46061i	−0.720350	+	0.222199i
$404$	0.00896965	−	0.119692i	0.000446257	−	0.00595488i
$405$		0			0
$406$	3.69880	+	14.2309i	0.183569	+	0.706268i
$407$	−9.55167	−	41.8486i	−0.473459	−	2.07436i
$408$		0			0
$409$	−8.02904	−	5.47411i	−0.397011	−	0.270677i	0.348315	−	0.937377i	$-0.386754\pi$
$409$	−8.02904	−	5.47411i	−0.397011	−	0.270677i	−0.745326	+	0.666700i	$0.767706\pi$
$410$	−0.601735	−	1.04224i	−0.0297176	−	0.0514724i
$411$		0			0
$412$	0.0659130	−	0.0317420i	0.00324730	−	0.00156382i
$413$	7.68207	−	1.39383i	0.378010	−	0.0685860i
$414$		0			0
$415$	−3.10188	+	2.11483i	−0.152265	+	0.103813i
$416$	0.0781237	−	0.0724882i	0.00383033	−	0.00355403i
$417$		0			0
$418$	−40.2395	+	27.4348i	−1.96818	+	1.34188i
$419$	−17.2662	−	8.31495i	−0.843508	−	0.406212i	−0.0383440	−	0.999265i	$-0.512208\pi$
$419$	−17.2662	−	8.31495i	−0.843508	−	0.406212i	−0.805164	+	0.593053i	$0.797923\pi$
$420$		0			0
$421$	−22.9543	+	11.0542i	−1.11872	+	0.538748i	−0.899497	−	0.436926i	$-0.856067\pi$
$421$	−22.9543	+	11.0542i	−1.11872	+	0.538748i	−0.219225	+	0.975674i	$0.570353\pi$
$422$	12.4790	−	21.6143i	0.607468	−	1.05217i
$423$		0			0
$424$	−7.26134	−	4.95070i	−0.352642	−	0.240427i
$425$	27.2681	−	4.11001i	1.32270	−	0.199365i
$426$		0			0
$427$	7.75536	−	4.02459i	0.375308	−	0.194763i
$428$	0.00121710	−	0.00533244i	5.88305e−5	−	0.000257753i
$429$		0			0
$430$	−2.67407	+	0.824842i	−0.128955	+	0.0397774i
$431$	−8.64196	+	22.0193i	−0.416268	+	1.06063i	0.556908	+	0.830574i	$0.311988\pi$
$431$	−8.64196	+	22.0193i	−0.416268	+	1.06063i	−0.973176	+	0.230060i	$0.926108\pi$
$432$		0			0
$433$	−13.6957	+	17.1738i	−0.658172	+	0.825322i	−0.993143	−	0.116907i	$-0.962702\pi$
$433$	−13.6957	+	17.1738i	−0.658172	+	0.825322i	0.334971	+	0.942229i	$0.391274\pi$
$434$	−23.2215	+	7.93026i	−1.11467	+	0.380665i
$435$		0			0
$436$	0.0269162	+	0.0685814i	0.00128905	+	0.00328445i
$437$	−3.37312	−	45.0112i	−0.161358	−	2.15318i
$438$		0			0
$439$	−26.1375	−	24.2520i	−1.24747	−	1.15749i	−0.981076	−	0.193623i	$-0.937976\pi$
$439$	−26.1375	−	24.2520i	−1.24747	−	1.15749i	−0.266397	−	0.963863i	$-0.585833\pi$
$440$	4.45868			0.212559
$441$		0			0
$442$	18.3920			0.874818
$443$	25.1744	+	23.3584i	1.19607	+	1.10979i	0.991387	+	0.130962i	$0.0418067\pi$
$443$	25.1744	+	23.3584i	1.19607	+	1.10979i	0.204683	+	0.978828i	$0.434384\pi$
$444$		0			0
$445$	0.139185	+	1.85729i	0.00659800	+	0.0880442i
$446$	2.42086	+	6.16825i	0.114631	+	0.292075i
$447$		0			0
$448$	−15.0167	+	14.7928i	−0.709473	+	0.698893i
$449$	−18.4950	+	23.1920i	−0.872832	+	1.09450i	0.121956	+	0.992535i	$0.461083\pi$
$449$	−18.4950	+	23.1920i	−0.872832	+	1.09450i	−0.994788	+	0.101961i	$0.967488\pi$
$450$		0			0
$451$	−5.62609	+	14.3350i	−0.264922	+	0.675010i
$452$	−0.0703850	+	0.0217109i	−0.00331063	+	0.00102119i
$453$		0			0
$454$	0.680865	−	2.98307i	0.0319546	−	0.140002i
$455$	−1.16746	−	1.37741i	−0.0547315	−	0.0645741i
$456$		0			0
$457$	−23.9192	+	3.60524i	−1.11889	+	0.168646i	−0.682342	−	0.731034i	$-0.739038\pi$
$457$	−23.9192	+	3.60524i	−1.11889	+	0.168646i	−0.436551	+	0.899679i	$0.643800\pi$
$458$	11.0363	+	7.52444i	0.515694	+	0.351594i
$459$		0			0
$460$	0.00845182	−	0.0146390i	0.000394068	−	0.000682546i
$461$	14.0557	−	6.76889i	0.654641	−	0.315259i	−0.0769170	−	0.997038i	$-0.524508\pi$
$461$	14.0557	−	6.76889i	0.654641	−	0.315259i	0.731558	+	0.681779i	$0.238793\pi$
$462$		0			0
$463$	9.50079	+	4.57534i	0.441539	+	0.212634i	0.641426	−	0.767185i	$-0.278343\pi$
$463$	9.50079	+	4.57534i	0.441539	+	0.212634i	−0.199887	+	0.979819i	$0.564057\pi$
$464$	−13.0138	+	8.87267i	−0.604152	+	0.411904i
$465$		0			0
$466$	−10.3844	+	9.63535i	−0.481050	+	0.446349i
$467$	−4.97635	+	3.39282i	−0.230278	+	0.157001i	−0.672963	−	0.739676i	$-0.734979\pi$
$467$	−4.97635	+	3.39282i	−0.230278	+	0.157001i	0.442684	+	0.896677i	$0.354026\pi$
$468$		0			0
$469$	−3.08039	+	5.72388i	−0.142239	+	0.264304i
$470$	−2.11951	+	1.02070i	−0.0977659	+	0.0470816i
$471$		0			0
$472$	4.16474	+	7.21354i	0.191698	+	0.332030i
$473$	29.5861	+	20.1715i	1.36037	+	0.927485i
$474$		0			0
$475$	7.02014	+	30.7572i	0.322106	+	1.41124i
$476$	0.120946	−	0.00361585i	0.00554356	−	0.000165732i
$477$		0			0
$478$	2.11055	−	28.1633i	0.0965344	−	1.28816i
$479$	−37.3458	+	11.5196i	−1.70637	+	0.526346i	−0.985929	−	0.167167i	$-0.946538\pi$
$479$	−37.3458	+	11.5196i	−1.70637	+	0.526346i	−0.720444	+	0.693513i	$0.756062\pi$
$480$		0			0
$481$	−17.7213	−	5.46631i	−0.808023	−	0.249242i
$482$	22.2964	−	27.9588i	1.01557	−	1.27349i
$483$		0			0
$484$	0.0896289	+	0.112391i	0.00407404	+	0.00510869i
$485$	0.500051	+	1.27411i	0.0227061	+	0.0578543i
$486$		0			0
$487$	−0.465905	−	0.0702239i	−0.0211122	−	0.00318215i	0.138478	−	0.990366i	$-0.455779\pi$
$487$	−0.465905	−	0.0702239i	−0.0211122	−	0.00318215i	−0.159590	+	0.987183i	$0.551017\pi$
$488$	6.83322	+	6.34030i	0.309325	+	0.287012i
$489$		0			0
$490$	−1.95892	−	2.17588i	−0.0884948	−	0.0982963i
$491$	−37.0047			−1.67000			−0.834999	−	0.550252i	$-0.814532\pi$
$491$	−37.0047			−1.67000			−0.834999	+	0.550252i	$0.814532\pi$
$492$		0			0
$493$	−21.7670	−	3.28085i	−0.980337	−	0.147762i
$494$	1.57241	+	20.9824i	0.0707462	+	0.944042i
$495$		0			0
$496$	−16.3887	−	20.5508i	−0.735876	−	0.922759i
$497$	0.232137	+	2.20933i	0.0104128	+	0.0991020i
$498$		0			0
$499$	−10.3963	−	3.20683i	−0.465402	−	0.143558i	0.0531807	−	0.998585i	$-0.483064\pi$
$499$	−10.3963	−	3.20683i	−0.465402	−	0.143558i	−0.518583	+	0.855027i	$0.673540\pi$
$500$	−0.00870924	+	0.0221908i	−0.000389489	+	0.000992402i
$501$		0			0
$502$	1.27908	−	17.0682i	0.0570884	−	0.761791i
$503$	8.26162	−	36.1965i	0.368367	−	1.61392i	−0.362897	−	0.931829i	$-0.618212\pi$
$503$	8.26162	−	36.1965i	0.368367	−	1.61392i	0.731265	−	0.682094i	$-0.238930\pi$
$504$		0			0
$505$	−0.967498	−	4.23888i	−0.0430531	−	0.188628i
$506$	−52.7144	+	7.94542i	−2.34344	+	0.353217i
$507$		0			0
$508$	0.0146855	+	0.0254361i	0.000651565	+	0.00112854i
$509$	−3.47500	+	6.01888i	−0.154027	+	0.266782i	−0.932704	−	0.360642i	$-0.882557\pi$
$509$	−3.47500	+	6.01888i	−0.154027	+	0.266782i	0.778678	+	0.627424i	$0.215891\pi$
$510$		0			0
$511$	23.5302	+	6.49475i	1.04091	+	0.287311i
$512$	−20.2606	−	9.75700i	−0.895402	−	0.431203i
$513$		0			0
$514$	13.0292	−	12.0893i	0.574692	−	0.533236i
$515$	1.94265	−	1.80252i	0.0856035	−	0.0794284i
$516$		0			0
$517$	27.1212	+	13.0609i	1.19279	+	0.574417i
$518$	−28.9868	−	8.00087i	−1.27361	−	0.351538i
$519$		0			0
$520$	0.963164	−	1.66825i	0.0422375	−	0.0731576i
$521$	2.50142	+	4.33258i	0.109589	+	0.189814i	0.915604	−	0.402082i	$-0.131713\pi$
$521$	2.50142	+	4.33258i	0.109589	+	0.189814i	−0.806015	+	0.591895i	$0.798380\pi$
$522$		0			0
$523$	−25.5103	+	3.84506i	−1.11549	+	0.168133i	−0.680814	−	0.732456i	$-0.738374\pi$
$523$	−25.5103	+	3.84506i	−1.11549	+	0.168133i	−0.434673	+	0.900589i	$0.643136\pi$
$524$	−0.0203245	−	0.0890472i	−0.000887878	−	0.00389005i
$525$		0			0
$526$	−3.06122	+	13.4121i	−0.133475	+	0.584794i
$527$	2.74530	−	36.6334i	0.119587	−	1.59578i
$528$		0			0
$529$	9.64792	−	24.5825i	0.419475	−	1.06880i
$530$	1.24439	+	0.383845i	0.0540531	+	0.0166732i
$531$		0			0
$532$	0.0144653	+	0.137672i	0.000627152	+	0.00596882i
$533$	4.14821	+	5.20170i	0.179679	+	0.225310i
$534$		0			0
$535$	−0.0148064	−	0.197577i	−0.000640135	−	0.00854201i
$536$	−6.85724	−	1.03356i	−0.296188	−	0.0446431i
$537$		0			0
$538$	2.54325			0.109647
$539$	−6.13960	+	36.9570i	−0.264451	+	1.59185i
$540$		0			0
$541$	13.5725	+	12.5934i	0.583526	+	0.541433i	0.915740	−	0.401771i	$-0.131605\pi$
$541$	13.5725	+	12.5934i	0.583526	+	0.541433i	−0.332214	+	0.943204i	$0.607796\pi$
$542$	45.4054	+	6.84376i	1.95033	+	0.293965i
$543$		0			0
$544$	0.0945166	+	0.240824i	0.00405237	+	0.0103253i
$545$	1.66396	+	2.08655i	0.0712764	+	0.0893778i
$546$		0			0
$547$	−22.3923	+	28.0790i	−0.957424	+	1.20057i	0.0222047	+	0.999753i	$0.492931\pi$
$547$	−22.3923	+	28.0790i	−0.957424	+	1.20057i	−0.979629	+	0.200818i	$0.935640\pi$
$548$	0.0340631	+	0.0105071i	0.00145510	+	0.000448840i
$549$		0			0
$550$	35.6049	−	10.9826i	1.51820	−	0.468302i
$551$	1.88198	−	25.1132i	0.0801749	−	1.06986i
$552$		0			0
$553$	32.6699	−	0.976710i	1.38926	−	0.0415339i
$554$	4.70644	+	20.6203i	0.199958	+	0.876071i
$555$		0			0
$556$	−0.0643194	−	0.0438522i	−0.00272775	−	0.00185975i
$557$	9.47566	+	16.4123i	0.401496	+	0.695412i	0.993907	−	0.110224i	$-0.0351569\pi$
$557$	9.47566	+	16.4123i	0.401496	+	0.695412i	−0.592410	+	0.805636i	$0.701824\pi$
$558$		0			0
$559$	13.9385	−	6.71243i	0.589536	−	0.283905i
$560$	1.48625	−	2.76170i	0.0628056	−	0.116703i
$561$		0			0
$562$	15.5014	−	10.5687i	0.653889	−	0.445814i
$563$	2.19141	−	2.03333i	0.0923570	−	0.0856948i	−0.632643	−	0.774443i	$-0.718030\pi$
$563$	2.19141	−	2.03333i	0.0923570	−	0.0856948i	0.725000	+	0.688749i	$0.241840\pi$
$564$		0			0
$565$	−2.20456	+	1.50304i	−0.0927464	+	0.0632334i
$566$	33.8244	+	16.2890i	1.42175	+	0.684677i
$567$		0			0
$568$	−2.13531	+	1.02831i	−0.0895955	+	0.0431469i
$569$	11.6579	−	20.1920i	0.488723	−	0.846492i	−0.511193	−	0.859466i	$-0.670796\pi$
$569$	11.6579	−	20.1920i	0.488723	−	0.846492i	0.999916	+	0.0129734i	$0.00412967\pi$
$570$		0			0
$571$	19.9538	+	13.6043i	0.835042	+	0.569322i	0.903626	−	0.428323i	$-0.140896\pi$
$571$	19.9538	+	13.6043i	0.835042	+	0.569322i	−0.0685835	+	0.997645i	$0.521848\pi$
$572$	0.0997032	−	0.0150278i	0.00416880	−	0.000628345i
$573$		0			0
$574$	6.97530	+	8.22969i	0.291143	+	0.343501i
$575$	−7.68434	+	33.6673i	−0.320459	+	1.40402i
$576$		0			0
$577$	31.5073	−	9.71870i	1.31166	−	0.404595i	0.441458	−	0.897282i	$-0.354461\pi$
$577$	31.5073	−	9.71870i	1.31166	−	0.404595i	0.870207	+	0.492687i	$0.163985\pi$
$578$	−7.51004	+	19.1353i	−0.312376	+	0.795922i
$579$		0			0
$580$	0.00588020	−	0.00737353i	0.000244162	−	0.000306169i
$581$	23.9746	−	23.6171i	0.994635	−	0.979801i
$582$		0			0
$583$	−6.08787	−	15.5116i	−0.252134	−	0.642427i
$584$	1.94612	+	25.9692i	0.0805312	+	1.07461i
$585$		0			0
$586$	16.1578	+	14.9923i	0.667473	+	0.619324i
$587$	−46.8141			−1.93223			−0.966113	−	0.258120i	$-0.916897\pi$
$587$	−46.8141			−1.93223			−0.966113	+	0.258120i	$0.916897\pi$
$588$		0			0
$589$	42.0277			1.73172
$590$	−0.904765	−	0.839499i	−0.0372486	−	0.0345616i
$591$		0			0
$592$	−2.40720	−	32.1218i	−0.0989352	−	1.32020i
$593$	−14.4406	−	36.7939i	−0.593002	−	1.51095i	−0.840364	−	0.542022i	$-0.817659\pi$
$593$	−14.4406	−	36.7939i	−0.593002	−	1.51095i	0.247362	−	0.968923i	$-0.420436\pi$
$594$		0			0
$595$	4.14794	−	1.41654i	0.170049	−	0.0580725i
$596$	−0.0241998	+	0.0303456i	−0.000991262	+	0.00124300i
$597$		0			0
$598$	−8.41453	+	21.4399i	−0.344096	+	0.876741i
$599$	2.71357	−	0.837027i	0.110874	−	0.0342000i	−0.238822	−	0.971063i	$-0.576761\pi$
$599$	2.71357	−	0.837027i	0.110874	−	0.0342000i	0.349696	+	0.936863i	$0.386285\pi$
$600$		0			0
$601$	1.44133	−	6.31487i	0.0587930	−	0.257589i	−0.936987	−	0.349365i	$-0.886397\pi$
$601$	1.44133	−	6.31487i	0.0587930	−	0.257589i	0.995780	+	0.0917761i	$0.0292544\pi$
$602$	22.2657	−	11.5546i	0.907481	−	0.470930i
$603$		0			0
$604$	−0.0617725	+	0.00931070i	−0.00251349	+	0.000378847i
$605$	4.30253	+	2.93341i	0.174923	+	0.119260i
$606$		0			0
$607$	5.24760	−	9.08911i	0.212994	−	0.368916i	−0.739656	−	0.672985i	$-0.765012\pi$
$607$	5.24760	−	9.08911i	0.212994	−	0.368916i	0.952650	+	0.304069i	$0.0983453\pi$
$608$	−0.266662	+	0.128418i	−0.0108146	+	0.00520803i
$609$		0			0
$610$	−1.24447	−	0.599304i	−0.0503870	−	0.0242651i
$611$	10.7455	−	7.32619i	0.434718	−	0.296386i
$612$		0			0
$613$	−8.39112	+	7.78582i	−0.338914	+	0.314466i	−0.831207	−	0.555963i	$-0.812349\pi$
$613$	−8.39112	+	7.78582i	−0.338914	+	0.314466i	0.492293	+	0.870430i	$0.336159\pi$
$614$	−1.55685	+	1.06144i	−0.0628295	+	0.0428364i
$615$		0			0
$616$	−39.3262	+	7.13532i	−1.58450	+	0.287490i
$617$	−2.49873	+	1.20333i	−0.100595	+	0.0484441i	−0.483505	−	0.875342i	$-0.660636\pi$
$617$	−2.49873	+	1.20333i	−0.100595	+	0.0484441i	0.382909	+	0.923786i	$0.374922\pi$
$618$		0			0
$619$	−11.0641	−	19.1636i	−0.444705	−	0.770251i	0.553327	−	0.832964i	$-0.313358\pi$
$619$	−11.0641	−	19.1636i	−0.444705	−	0.770251i	−0.998032	+	0.0627129i	$0.980025\pi$
$620$	0.0130042	+	0.00886614i	0.000522263	+	0.000356073i
$621$		0			0
$622$	2.20456	+	9.65881i	0.0883949	+	0.387283i
$623$	−4.19990	−	16.1588i	−0.168265	−	0.647390i
$624$		0			0
$625$	1.77117	−	23.6346i	0.0708468	−	0.945385i
$626$	29.7798	−	9.18585i	1.19024	−	0.367140i
$627$		0			0
$628$	−0.113456	−	0.0349965i	−0.00452738	−	0.00139651i
$629$	28.0688	−	35.1971i	1.11917	−	1.40340i
$630$		0			0
$631$	11.0002	+	13.7938i	0.437911	+	0.549123i	0.950991	−	0.309218i	$-0.100067\pi$
$631$	11.0002	+	13.7938i	0.437911	+	0.549123i	−0.513080	+	0.858341i	$0.671496\pi$
$632$	12.7393	+	32.4592i	0.506742	+	1.29116i
$633$		0			0
$634$	−23.2788	−	3.50872i	−0.924519	−	0.139349i
$635$	0.779926	+	0.723666i	0.0309504	+	0.0287178i
$636$		0			0
$637$	12.5015	+	10.2806i	0.495327	+	0.407334i
$638$	−29.7433			−1.17755
$639$		0			0
$640$	3.32196	+	0.500705i	0.131312	+	0.0197921i
$641$	−1.16854	−	15.5931i	−0.0461545	−	0.615888i	−0.971542	−	0.236867i	$-0.923880\pi$
$641$	−1.16854	−	15.5931i	−0.0461545	−	0.615888i	0.925388	−	0.379022i	$-0.123739\pi$
$642$		0			0
$643$	−6.97587	−	8.74747i	−0.275102	−	0.344966i	0.625017	−	0.780611i	$-0.285092\pi$
$643$	−6.97587	−	8.74747i	−0.275102	−	0.344966i	−0.900119	+	0.435645i	$0.856520\pi$
$644$	−0.0511191	+	0.142643i	−0.00201437	+	0.00562094i
$645$		0			0
$646$	−48.8086	−	15.0554i	−1.92035	−	0.592349i
$647$	1.06904	−	2.72387i	0.0420283	−	0.107086i	−0.908318	−	0.418279i	$-0.862633\pi$
$647$	1.06904	−	2.72387i	0.0420283	−	0.107086i	0.950347	+	0.311193i	$0.100729\pi$
$648$		0			0
$649$	−1.18024	+	15.7492i	−0.0463284	+	0.618209i
$650$	3.58212	−	15.6943i	0.140502	−	0.615581i
$651$		0			0
$652$	−0.0270943	−	0.118708i	−0.00106110	−	0.00464896i
$653$	−30.6786	+	4.62405i	−1.20055	+	0.180953i	−0.718711	−	0.695309i	$-0.755267\pi$
$653$	−30.6786	+	4.62405i	−1.20055	+	0.180953i	−0.481835	+	0.876262i	$0.660029\pi$
$654$		0			0
$655$	−1.65431	−	2.86535i	−0.0646393	−	0.111959i
$656$	−5.77811	+	10.0080i	−0.225597	+	0.390746i
$657$		0			0
$658$	17.0609	−	12.3946i	0.665104	−	0.483194i
$659$	38.9163	+	18.7411i	1.51597	+	0.730050i	0.992528	−	0.122014i	$-0.0389353\pi$
$659$	38.9163	+	18.7411i	1.51597	+	0.730050i	0.523437	+	0.852064i	$0.324650\pi$
$660$		0			0
$661$	−12.6084	+	11.6989i	−0.490409	+	0.455033i	−0.886197	−	0.463309i	$-0.846662\pi$
$661$	−12.6084	+	11.6989i	−0.490409	+	0.455033i	0.395788	+	0.918342i	$0.370472\pi$
$662$	22.0807	−	20.4879i	0.858190	−	0.796284i
$663$		0			0
$664$	32.3478	+	15.5779i	1.25534	+	0.604538i
$665$	1.97067	+	4.61104i	0.0764195	+	0.178808i
$666$		0			0
$667$	13.7832	−	23.8732i	0.533687	−	0.924373i
$668$	−0.0382268	−	0.0662107i	−0.00147904	−	0.00256177i
$669$		0			0
$670$	1.01609	−	0.153151i	0.0392550	−	0.00591674i
$671$	3.93294	+	17.2313i	0.151829	+	0.665208i
$672$		0			0
$673$	0.471605	−	2.06623i	0.0181790	−	0.0796475i	−0.965025	−	0.262159i	$-0.915566\pi$
$673$	0.471605	−	2.06623i	0.0181790	−	0.0796475i	0.983204	+	0.182511i	$0.0584227\pi$
$674$	2.97321	−	39.6747i	0.114524	−	1.52821i
$675$		0			0
$676$	−0.0227824	+	0.0580486i	−0.000876246	+	0.00223264i
$677$	35.2324	+	10.8677i	1.35409	+	0.417681i	0.885050	−	0.465496i	$-0.154124\pi$
$677$	35.2324	+	10.8677i	1.35409	+	0.417681i	0.469040	+	0.883177i	$0.344600\pi$
$678$		0			0
$679$	−6.44950	−	10.4376i	−0.247509	−	0.400557i
$680$	2.91555	+	3.65599i	0.111806	+	0.140201i
$681$		0			0
$682$	−3.70938	−	49.4983i	−0.142040	−	1.89539i
$683$	24.1571	+	3.64110i	0.924347	+	0.139323i	0.593934	−	0.804514i	$-0.297574\pi$
$683$	24.1571	+	3.64110i	0.924347	+	0.139323i	0.330413	+	0.943837i	$0.392812\pi$
$684$		0			0
$685$	1.29128			0.0493372
$686$	20.7600	+	16.0567i	0.792621	+	0.613046i
$687$		0			0
$688$	19.6981	+	18.2772i	0.750983	+	0.696811i
$689$	−7.11890	−	1.07300i	−0.271209	−	0.0408781i
$690$		0			0
$691$	9.41992	+	24.0016i	0.358350	+	0.913062i	0.990412	+	0.138144i	$0.0441137\pi$
$691$	9.41992	+	24.0016i	0.358350	+	0.913062i	−0.632062	+	0.774918i	$0.717791\pi$
$692$	0.0652271	+	0.0817922i	0.00247956	+	0.00310927i
$693$		0			0
$694$	2.66819	−	3.34581i	0.101283	−	0.127005i
$695$	−2.69463	−	0.831184i	−0.102213	−	0.0315286i
$696$		0			0
$697$	−15.4332	+	4.76052i	−0.584576	+	0.180318i
$698$	0.103910	−	1.38658i	0.00393304	−	0.0524828i
$699$		0			0
$700$	0.0204706	−	0.103910i	0.000773717	−	0.00392744i
$701$	−5.54248	−	24.2832i	−0.209336	−	0.917163i	−0.965010	−	0.262214i	$-0.915547\pi$
$701$	−5.54248	−	24.2832i	−0.209336	−	0.917163i	0.755673	−	0.654949i	$-0.227310\pi$
$702$		0			0
$703$	42.5541	+	29.0129i	1.60496	+	1.09424i
$704$	−21.3198	−	36.9270i	−0.803521	−	1.39174i
$705$		0			0
$706$	14.6698	−	7.06458i	0.552104	−	0.265879i
$707$	15.3170	+	35.8392i	0.576057	+	1.34787i
$708$		0			0
$709$	−14.5679	+	9.93224i	−0.547110	+	0.373013i	−0.805104	−	0.593133i	$-0.797891\pi$
$709$	−14.5679	+	9.93224i	−0.547110	+	0.373013i	0.257995	+	0.966146i	$0.416938\pi$
$710$	0.257436	−	0.238865i	0.00966139	−	0.00896446i
$711$		0			0
$712$	14.7169	−	10.0338i	0.551540	−	0.376033i
$713$	41.4482	+	19.9604i	1.55225	+	0.747523i
$714$		0			0
$715$	3.29076	−	1.58475i	0.123067	−	0.0592661i
$716$	0.0448943	−	0.0777592i	0.00167778	−	0.00290600i
$717$		0			0
$718$	−11.0731	−	7.54949i	−0.413243	−	0.281744i
$719$	−44.1084	+	6.64827i	−1.64497	+	0.247939i	−0.905219	−	0.424946i	$-0.860293\pi$
$719$	−44.1084	+	6.64827i	−1.64497	+	0.247939i	−0.739747	+	0.672885i	$0.765055\pi$
$720$		0			0
$721$	−14.2498	+	19.0073i	−0.530692	+	0.707869i
$722$	7.01172	−	30.7204i	0.260949	−	1.14329i
$723$		0			0
$724$	0.0371792	−	0.0114683i	0.00138176	−	0.000426215i
$725$	−7.03908	+	17.9353i	−0.261425	+	0.666100i
$726$		0			0
$727$	10.4756	−	13.1360i	0.388519	−	0.487187i	−0.548656	−	0.836049i	$-0.684860\pi$
$727$	10.4756	−	13.1360i	0.388519	−	0.487187i	0.937174	+	0.348861i	$0.113432\pi$
$728$	−5.82550	+	16.2556i	−0.215907	+	0.602471i
$729$		0			0
$730$	−1.40980	−	3.59211i	−0.0521790	−	0.132950i
$731$	2.80649	+	37.4500i	0.103802	+	1.38514i
$732$		0			0
$733$	1.24123	+	1.15169i	0.0458458	+	0.0425387i	0.702763	−	0.711424i	$-0.251949\pi$
$733$	1.24123	+	1.15169i	0.0458458	+	0.0425387i	−0.656917	+	0.753963i	$0.728140\pi$
$734$	36.4927			1.34697
$735$		0			0
$736$	−0.323975			−0.0119419
$737$	−9.63869	−	8.94339i	−0.355046	−	0.329434i
$738$		0			0
$739$	1.98367	+	26.4702i	0.0729704	+	0.973722i	0.906762	+	0.421643i	$0.138546\pi$
$739$	1.98367	+	26.4702i	0.0729704	+	0.973722i	−0.833792	+	0.552079i	$0.813835\pi$
$740$	0.00704657	+	0.0179544i	0.000259037	+	0.000660016i
$741$		0			0
$742$	−11.5900	−	1.39413i	−0.425482	−	0.0511802i
$743$	11.2973	−	14.1664i	0.414458	−	0.519714i	−0.530155	−	0.847901i	$-0.677866\pi$
$743$	11.2973	−	14.1664i	0.414458	−	0.519714i	0.944613	+	0.328187i	$0.106438\pi$
$744$		0			0
$745$	−0.513665	+	1.30880i	−0.0188192	+	0.0479506i
$746$	9.07917	−	2.80055i	0.332412	−	0.102536i
$747$		0			0
$748$	−0.0544652	+	0.238628i	−0.00199145	+	0.00872509i
$749$	0.446781	+	1.71896i	0.0163250	+	0.0628095i
$750$		0			0
$751$	24.6711	−	3.71857i	0.900260	−	0.135692i	0.317425	−	0.948283i	$-0.397182\pi$
$751$	24.6711	−	3.71857i	0.900260	−	0.135692i	0.582835	+	0.812591i	$0.301944\pi$
$752$	18.6643	+	12.7251i	0.680618	+	0.464037i
$753$		0			0
$754$	−6.42515	+	11.1287i	−0.233990	+	0.405283i
$755$	−2.03883	+	0.981851i	−0.0742008	+	0.0357332i
$756$		0			0
$757$	−13.1042	−	6.31063i	−0.476279	−	0.229364i	0.180314	−	0.983609i	$-0.442289\pi$
$757$	−13.1042	−	6.31063i	−0.476279	−	0.229364i	−0.656593	+	0.754245i	$0.728003\pi$
$758$	19.7367	−	13.4562i	0.716868	−	0.488752i
$759$		0			0
$760$	−3.92164	+	3.63875i	−0.142253	+	0.131992i
$761$	10.4488	−	7.12388i	0.378769	−	0.258240i	−0.358938	−	0.933361i	$-0.616861\pi$
$761$	10.4488	−	7.12388i	0.378769	−	0.258240i	0.737707	+	0.675121i	$0.235909\pi$
$762$		0			0
$763$	−18.0155	−	15.7407i	−0.652206	−	0.569853i
$764$	−0.142717	+	0.0687287i	−0.00516330	+	0.00248652i
$765$		0			0
$766$	−1.68854	−	2.92464i	−0.0610095	−	0.105672i
$767$	5.63772	+	3.84373i	0.203566	+	0.138789i
$768$		0			0
$769$	−12.0564	−	52.8226i	−0.434766	−	1.90483i	−0.425680	−	0.904874i	$-0.639965\pi$
$769$	−12.0564	−	52.8226i	−0.434766	−	1.90483i	−0.00908592	−	0.999959i	$-0.502892\pi$
$770$	5.25673	−	2.72794i	0.189440	−	0.0983082i
$771$		0			0
$772$	−0.00547530	+	0.0730628i	−0.000197060	+	0.00262959i
$773$	33.7278	−	10.4037i	1.21311	−	0.374194i	0.378792	−	0.925482i	$-0.376340\pi$
$773$	33.7278	−	10.4037i	1.21311	−	0.374194i	0.834315	+	0.551288i	$0.185864\pi$
$774$		0			0
$775$	−30.7254	−	9.47754i	−1.10369	−	0.340443i
$776$	8.16131	−	10.2340i	0.292974	−	0.367378i
$777$		0			0
$778$	−8.47024	−	10.6213i	−0.303673	−	0.380794i
$779$	−6.75046	−	17.1999i	−0.241860	−	0.616250i
$780$		0			0
$781$	−4.44354	−	0.669755i	−0.159002	−	0.0239657i
$782$	−40.9852	−	38.0287i	−1.46563	−	1.35990i
$783$		0			0
$784$	−8.68932	+	26.7371i	−0.310333	+	0.954895i
$785$	−4.30093			−0.153507
$786$		0			0
$787$	−0.229411	−	0.0345782i	−0.00817762	−	0.00123258i	0.144952	−	0.989439i	$-0.453697\pi$
$787$	−0.229411	−	0.0345782i	−0.00817762	−	0.00123258i	−0.153130	+	0.988206i	$0.548935\pi$
$788$	0.0111216	+	0.148407i	0.000396190	+	0.00528679i
$789$		0			0
$790$	−3.22151	−	4.03965i	−0.114616	−	0.143724i
$791$	17.0391	−	16.7850i	0.605842	−	0.596807i
$792$		0			0
$793$	7.29683	+	2.25077i	0.259118	+	0.0799273i
$794$	−10.4754	+	26.6908i	−0.371756	+	0.947220i
$795$		0			0
$796$	0.0134290	−	0.179198i	0.000475979	−	0.00635150i
$797$	−11.0103	+	48.2392i	−0.390004	+	1.70872i	0.274630	+	0.961550i	$0.411445\pi$
$797$	−11.0103	+	48.2392i	−0.390004	+	1.70872i	−0.664634	+	0.747169i	$0.731413\pi$
$798$		0			0
$799$	7.02514	+	30.7792i	0.248532	+	1.08889i
$800$	0.223909	−	0.0337489i	0.00791639	−	0.00119320i
$801$		0			0
$802$	9.82541	+	17.0181i	0.346947	+	0.600930i
$803$	−24.6889	+	42.7624i	−0.871251	+	1.50905i
$804$		0			0
$805$	−0.246438	+	5.48340i	−0.00868581	+	0.193264i
$806$	−19.3215	−	9.30473i	−0.680570	−	0.327745i
$807$		0			0
$808$	−30.4809	+	28.2822i	−1.07232	+	0.994963i
$809$	−24.2324	+	22.4843i	−0.851964	+	0.790507i	−0.979525	−	0.201324i	$-0.935476\pi$
$809$	−24.2324	+	22.4843i	−0.851964	+	0.790507i	0.127561	+	0.991831i	$0.459285\pi$
$810$		0			0
$811$	40.6811	+	19.5910i	1.42851	+	0.687933i	0.978720	−	0.205202i	$-0.0657851\pi$
$811$	40.6811	+	19.5910i	1.42851	+	0.687933i	0.449788	+	0.893135i	$0.351499\pi$
$812$	−0.0400641	+	0.0744458i	−0.00140597	+	0.00261253i
$813$		0			0
$814$	30.4142	−	52.6789i	1.06602	−	1.84640i
$815$	−2.20535	−	3.81977i	−0.0772499	−	0.133801i
$816$		0			0
$817$	−42.4846	+	6.40352i	−1.48635	+	0.224031i
$818$	−3.06427	−	13.4254i	−0.107140	−	0.469410i
$819$		0			0
$820$	0.00153975	−	0.00674608i	5.37703e−5	−	0.000235583i
$821$	−0.778090	+	10.3829i	−0.0271555	+	0.362365i	0.967028	+	0.254669i	$0.0819665\pi$
$821$	−0.778090	+	10.3829i	−0.0271555	+	0.362365i	−0.994184	+	0.107696i	$0.965653\pi$
$822$		0			0
$823$	1.95131	−	4.97186i	0.0680184	−	0.173308i	−0.892822	−	0.450409i	$-0.851278\pi$
$823$	1.95131	−	4.97186i	0.0680184	−	0.173308i	0.960841	+	0.277101i	$0.0893735\pi$
$824$	−24.2180	−	7.47027i	−0.843674	−	0.260239i
$825$		0			0
$826$	9.32362	+	5.95658i	0.324410	+	0.207256i
$827$	−2.88791	−	3.62132i	−0.100422	−	0.125926i	0.729081	−	0.684428i	$-0.239948\pi$
$827$	−2.88791	−	3.62132i	−0.100422	−	0.125926i	−0.829503	+	0.558502i	$0.811376\pi$
$828$		0			0
$829$	1.58100	+	21.0970i	0.0549104	+	0.732729i	0.954921	+	0.296860i	$0.0959396\pi$
$829$	1.58100	+	21.0970i	0.0549104	+	0.732729i	−0.900010	+	0.435868i	$0.856441\pi$
$830$	−5.26065	−	0.792916i	−0.182600	−	0.0275225i
$831$		0			0
$832$	−18.4220			−0.638669
$833$	−34.3184	+	19.1321i	−1.18906	+	0.662888i
$834$		0			0
$835$	−2.03017	−	1.88372i	−0.0702568	−	0.0651888i
$836$	−0.276893	−	0.0417349i	−0.00957655	−	0.00144343i
$837$		0			0
$838$	−9.92162	−	25.2799i	−0.342737	−	0.873279i
$839$	−19.7857	−	24.8104i	−0.683077	−	0.856551i	0.312557	−	0.949899i	$-0.398814\pi$
$839$	−19.7857	−	24.8104i	−0.683077	−	0.856551i	−0.995634	+	0.0933481i	$0.970243\pi$
$840$		0			0
$841$	−8.49181	+	10.6484i	−0.292821	+	0.367186i
$842$	−34.4997	−	10.6417i	−1.18894	−	0.366739i
$843$		0			0
$844$	0.137125	−	0.0422975i	0.00472004	−	0.00145594i
$845$	−0.168809	+	2.25260i	−0.00580721	+	0.0774918i
$846$		0			0
$847$	−42.6433	−	18.9877i	−1.46524	−	0.652424i
$848$	−2.78257	−	12.1912i	−0.0955537	−	0.418648i
$849$		0			0
$850$	32.2877	+	22.0133i	1.10746	+	0.755052i
$851$	28.1881	+	48.8233i	0.966277	+	1.67364i
$852$		0			0
$853$	−12.5985	+	6.06711i	−0.431364	+	0.207734i	−0.636950	−	0.770905i	$-0.719804\pi$
$853$	−12.5985	+	6.06711i	−0.431364	+	0.207734i	0.205586	+	0.978639i	$0.434090\pi$
$854$	11.9354	+	3.29439i	0.408423	+	0.112732i
$855$		0			0
$856$	−1.56557	+	1.06739i	−0.0535101	+	0.0364826i
$857$	1.29576	−	1.20229i	0.0442622	−	0.0410693i	−0.657732	−	0.753252i	$-0.728484\pi$
$857$	1.29576	−	1.20229i	0.0442622	−	0.0410693i	0.701994	+	0.712183i	$0.252293\pi$
$858$		0			0
$859$	−5.36135	+	3.65531i	−0.182927	+	0.124717i	−0.651321	−	0.758802i	$-0.725785\pi$
$859$	−5.36135	+	3.65531i	−0.182927	+	0.124717i	0.468394	+	0.883519i	$0.344833\pi$
$860$	−0.0144965	−	0.00698114i	−0.000494326	−	0.000238055i
$861$		0			0
$862$	−30.2010	+	14.5440i	−1.02865	+	0.495372i
$863$	16.8325	−	29.1548i	0.572985	−	0.992439i	−0.423272	−	0.906003i	$-0.639119\pi$
$863$	16.8325	−	29.1548i	0.572985	−	0.992439i	0.996257	−	0.0864368i	$-0.0275481\pi$
$864$		0			0
$865$	3.13115	+	2.13478i	0.106462	+	0.0725847i
$866$	−30.7804	+	4.63940i	−1.04596	+	0.157653i
$867$		0			0
$868$	−0.128888	−	0.0573895i	−0.00437473	−	0.00194793i
$869$	−14.7121	+	64.4579i	−0.499073	+	2.18658i
$870$		0			0
$871$	−5.42839	+	1.67444i	−0.183934	+	0.0567361i
$872$	9.32454	−	23.7586i	0.315769	−	0.804566i
$873$		0			0
$874$	39.8808	−	50.0089i	1.34899	−	1.69158i
$875$	−0.808891	−	7.69849i	−0.0273455	−	0.260256i
$876$		0			0
$877$	8.39419	+	21.3881i	0.283452	+	0.722223i	0.999703	+	0.0243806i	$0.00776136\pi$
$877$	8.39419	+	21.3881i	0.283452	+	0.722223i	−0.716251	+	0.697843i	$0.754143\pi$
$878$	−3.77592	−	50.3861i	−0.127431	−	1.70045i
$879$		0			0
$880$	4.65055	+	4.31508i	0.156770	+	0.145461i
$881$	−4.10439			−0.138280			−0.0691402	−	0.997607i	$-0.522026\pi$
$881$	−4.10439			−0.138280			−0.0691402	+	0.997607i	$0.522026\pi$
$882$		0			0
$883$	−12.7735			−0.429861			−0.214931	−	0.976629i	$-0.568953\pi$
$883$	−12.7735			−0.429861			−0.214931	+	0.976629i	$0.568953\pi$
$884$	0.0775188	+	0.0719269i	0.00260724	+	0.00241916i
$885$		0			0
$886$	3.63678	+	48.5295i	0.122180	+	1.63038i
$887$	−12.1219	−	30.8862i	−0.407015	−	1.03706i	−0.976588	−	0.215116i	$-0.930987\pi$
$887$	−12.1219	−	30.8862i	−0.407015	−	1.03706i	0.569574	−	0.821940i	$-0.307108\pi$
$888$		0			0
$889$	−8.03715	−	5.13469i	−0.269557	−	0.172212i
$890$	−1.64560	+	2.06351i	−0.0551606	+	0.0691692i
$891$		0			0
$892$	−0.0139192	+	0.0354654i	−0.000466048	+	0.00118747i
$893$	−34.5136	+	10.6460i	−1.15495	+	0.356256i
$894$		0			0
$895$	0.723754	−	3.17098i	0.0241924	−	0.105994i
$896$	−30.1014	+	0.899923i	−1.00562	+	0.0300643i
$897$		0			0
$898$	−41.5666	+	6.26515i	−1.38709	+	0.209071i
$899$	21.2072	+	14.4588i	0.707301	+	0.482229i
$900$		0			0
$901$	8.73821	−	15.1350i	0.291112	−	0.504221i
$902$	−19.6614	+	9.46845i	−0.654655	+	0.315265i
$903$		0			0
$904$	22.9901	+	11.0714i	0.764638	+	0.368230i
$905$	1.16451	−	0.793947i	0.0387095	−	0.0263917i
$906$		0			0
$907$	36.3948	−	33.7695i	1.20847	−	1.12130i	0.219126	−	0.975696i	$-0.429679\pi$
$907$	36.3948	−	33.7695i	1.20847	−	1.12130i	0.989344	−	0.145600i	$-0.0465112\pi$
$908$	0.0145358	−	0.00991034i	0.000482388	−	0.000328886i
$909$		0			0
$910$	0.114879	−	2.55614i	0.00380822	−	0.0847351i
$911$	0.925275	−	0.445589i	0.0306557	−	0.0147630i	−0.418493	−	0.908220i	$-0.637442\pi$
$911$	0.925275	−	0.445589i	0.0306557	−	0.0147630i	0.449149	+	0.893457i	$0.351727\pi$
$912$		0			0
$913$	34.0377	+	58.9550i	1.12648	+	1.95113i
$914$	−28.3223	−	19.3098i	−0.936817	−	0.638711i
$915$		0			0
$916$	0.0170897	+	0.0748747i	0.000564658	+	0.00247393i
$917$	19.1767	+	22.6253i	0.633271	+	0.747155i
$918$		0			0
$919$	−2.67570	+	35.7047i	−0.0882631	+	1.17779i	0.760616	+	0.649202i	$0.224897\pi$
$919$	−2.67570	+	35.7047i	−0.0882631	+	1.17779i	−0.848879	+	0.528587i	$0.822722\pi$
$920$	−5.59574	+	1.72606i	−0.184486	+	0.0569065i
$921$		0			0
$922$	21.1254	+	6.51634i	0.695729	+	0.214604i
$923$	−1.21049	+	1.51790i	−0.0398437	+	0.0499624i
$924$		0			0
$925$	−24.5677	−	30.8069i	−0.807780	−	1.01292i
$926$	5.45942	+	13.9104i	0.179408	+	0.457123i
$927$		0			0
$928$	−0.178738	−	0.0269404i	−0.00586735	−	0.000884361i
$929$	−29.0716	−	26.9745i	−0.953808	−	0.885005i	0.0396485	−	0.999214i	$-0.487376\pi$
$929$	−29.0716	−	26.9745i	−0.953808	−	0.885005i	−0.993457	+	0.114209i	$0.963567\pi$
$930$		0			0
$931$	−24.7608	−	37.5162i	−0.811501	−	1.22954i
$932$	−0.0814501			−0.00266799
$933$		0			0
$934$	−8.43967	−	1.27208i	−0.276155	−	0.0416236i
$935$	0.662587	+	8.84161i	0.0216689	+	0.289152i
$936$		0			0
$937$	6.70641	+	8.40957i	0.219089	+	0.274729i	0.879214	−	0.476427i	$-0.158068\pi$
$937$	6.70641	+	8.40957i	0.219089	+	0.274729i	−0.660125	+	0.751155i	$0.729497\pi$
$938$	−8.71697	+	2.97689i	−0.284619	+	0.0971988i
$939$		0			0
$940$	−0.0129251	−	0.00398686i	−0.000421570	−	0.000130037i
$941$	−9.09685	+	23.1784i	−0.296549	+	0.755595i	0.702487	+	0.711697i	$0.252073\pi$
$941$	−9.09685	+	23.1784i	−0.296549	+	0.755595i	−0.999036	+	0.0438980i	$0.986022\pi$
$942$		0			0
$943$	1.51144	−	20.1688i	0.0492193	−	0.656786i
$944$	−2.63726	+	11.5546i	−0.0858353	+	0.376069i
$945$		0			0
$946$	11.2915	+	49.4712i	0.367118	+	1.60845i
$947$	44.6304	−	6.72695i	1.45029	−	0.218596i	0.623817	−	0.781570i	$-0.285581\pi$
$947$	44.6304	−	6.72695i	1.45029	−	0.218596i	0.826475	+	0.562974i	$0.190343\pi$
$948$		0			0
$949$	10.6666	+	18.4751i	0.346252	+	0.599726i
$950$	−22.3534	+	38.7172i	−0.725239	+	1.25615i
$951$		0			0
$952$	−31.5663	−	27.5805i	−1.02307	−	0.893888i
$953$	36.5566	+	17.6047i	1.18418	+	0.570273i	0.919128	−	0.393959i	$-0.128895\pi$
$953$	36.5566	+	17.6047i	1.18418	+	0.570273i	0.265057	+	0.964233i	$0.414609\pi$
$954$		0			0
$955$	−4.20628	+	3.90286i	−0.136112	+	0.126294i
$956$	0.119036	−	0.110449i	0.00384990	−	0.00357218i
$957$		0			0
$958$	−49.8983	−	24.0297i	−1.61214	−	0.776366i
$959$	−11.3893	+	2.06646i	−0.367778	+	0.0667296i
$960$		0			0
$961$	−5.91732	+	10.2491i	−0.190881	+	0.330616i
$962$	−13.1402	−	22.7594i	−0.423656	−	0.733793i
$963$		0			0
$964$	0.203316	−	0.0306449i	0.00654836	−	0.000987006i
$965$	0.590585	+	2.58752i	0.0190116	+	0.0832953i
$966$		0			0
$967$	6.57562	−	28.8097i	0.211458	−	0.926457i	−0.752119	−	0.659027i	$-0.770968\pi$
$967$	6.57562	−	28.8097i	0.211458	−	0.926457i	0.963577	−	0.267430i	$-0.0861745\pi$
$968$	3.72159	−	49.6611i	0.119616	−	1.59617i
$969$		0			0
$970$	−0.708618	+	1.80553i	−0.0227524	+	0.0579720i
$971$	41.6573	+	12.8496i	1.33685	+	0.412362i	0.879065	−	0.476702i	$-0.158168\pi$
$971$	41.6573	+	12.8496i	1.33685	+	0.412362i	0.457781	+	0.889065i	$0.348644\pi$
$972$		0			0
$973$	25.0972	+	3.01887i	0.804578	+	0.0967806i
$974$	−0.416297	−	0.522020i	−0.0133390	−	0.0167266i
$975$		0			0
$976$	0.991173	+	13.2263i	0.0317267	+	0.423363i
$977$	−48.8711	−	7.36613i	−1.56352	−	0.235663i	−0.690497	−	0.723335i	$-0.742608\pi$
$977$	−48.8711	−	7.36613i	−1.56352	−	0.235663i	−0.873027	+	0.487671i	$0.837846\pi$
$978$		0			0
$979$	33.7728			1.07938
$980$	0.000252916	−	0.0168318i	8.07909e−6	−	0.000537672i
$981$		0			0
$982$	−38.4405	−	35.6676i	−1.22669	−	1.13820i
$983$	−46.1383	−	6.95424i	−1.47158	−	0.221806i	−0.636223	−	0.771506i	$-0.719504\pi$
$983$	−46.1383	−	6.95424i	−1.47158	−	0.221806i	−0.835362	+	0.549700i	$0.814742\pi$
$984$		0			0
$985$	1.96956	+	5.01836i	0.0627554	+	0.159898i
$986$	−19.4493	−	24.3887i	−0.619392	−	0.776693i
$987$		0			0
$988$	−0.0754299	+	0.0945861i	−0.00239974	+	0.00300918i
$989$	−44.9401	−	13.8622i	−1.42901	−	0.440791i
$990$		0			0
$991$	−27.9470	+	8.62050i	−0.887765	+	0.273839i	−0.704907	−	0.709300i	$-0.749011\pi$
$991$	−27.9470	+	8.62050i	−0.887765	+	0.273839i	−0.182858	+	0.983139i	$0.558535\pi$
$992$	0.0225427	−	0.300812i	0.000715732	−	0.00955078i
$993$		0			0
$994$	−1.88836	+	2.51880i	−0.0598950	+	0.0798916i
$995$	−1.44850	−	6.34631i	−0.0459206	−	0.201191i
$996$		0			0
$997$	−8.63799	−	5.88928i	−0.273568	−	0.186515i	0.418763	−	0.908095i	$-0.362464\pi$
$997$	−8.63799	−	5.88928i	−0.273568	−	0.186515i	−0.692331	+	0.721580i	$0.743416\pi$
$998$	−7.70873	−	13.3519i	−0.244016	−	0.422647i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.e.352.4		60
3.2	odd	2		147.2.m.b.58.2	✓	60
49.11	even	21	inner	441.2.bb.e.109.4		60
147.11	odd	42		147.2.m.b.109.2	yes	60
147.65	odd	42		7203.2.a.n.1.22		30
147.131	even	42		7203.2.a.m.1.22		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.b.58.2	✓	60	3.2	odd	2
147.2.m.b.109.2	yes	60	147.11	odd	42
441.2.bb.e.109.4		60	49.11	even	21	inner
441.2.bb.e.352.4		60	1.1	even	1	trivial
7203.2.a.m.1.22		30	147.131	even	42
7203.2.a.n.1.22		30	147.65	odd	42

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.03880 + 0.963867i) q^{2} +(0.000608887 + 0.00812503i) q^{4} +(0.107830 + 0.274746i) q^{5} +(-1.39076 - 2.25073i) q^{7} +(1.75989 - 2.20683i) q^{8} +O(q^{10})\)	\(q+(1.03880 + 0.963867i) q^{2} +(0.000608887 + 0.00812503i) q^{4} +(0.107830 + 0.274746i) q^{5} +(-1.39076 - 2.25073i) q^{7} +(1.75989 - 2.20683i) q^{8} +(-0.152805 + 0.389340i) q^{10} +(5.11416 - 1.57751i) q^{11} +(0.514524 - 2.25428i) q^{13} +(0.724688 - 3.67857i) q^{14} +(3.97137 - 0.598588i) q^{16} +(4.63769 + 3.16192i) q^{17} +(-3.21076 + 5.56120i) q^{19} +(-0.00216666 + 0.00104341i) q^{20} +(6.83311 + 3.29065i) q^{22} +(-5.80770 + 3.95962i) q^{23} +(3.60140 - 3.34161i) q^{25} +(2.70731 - 1.84581i) q^{26} +(0.0174405 - 0.0126704i) q^{28} +(-3.53338 + 1.70159i) q^{29} +(-3.27241 - 5.66798i) q^{31} +(0.0380819 + 0.0259638i) q^{32} +(1.76997 + 7.75473i) q^{34} +(0.468415 - 0.624801i) q^{35} +(0.599368 - 7.99800i) q^{37} +(-8.69560 + 2.68224i) q^{38} +(0.796085 + 0.245560i) q^{40} +(-1.79402 + 2.24963i) q^{41} +(4.17158 + 5.23100i) q^{43} +(0.0159313 + 0.0405922i) q^{44} +(-9.84960 - 1.48459i) q^{46} +(4.12309 + 3.82567i) q^{47} +(-3.13160 + 6.26044i) q^{49} +6.96201 q^{50} +(0.0186294 + 0.00280792i) q^{52} +(-0.232676 - 3.10485i) q^{53} +(0.984874 + 1.23499i) q^{55} +(-7.41455 - 0.891876i) q^{56} +(-5.31059 - 1.63810i) q^{58} +(-1.07811 + 2.74697i) q^{59} +(-0.246792 + 3.29321i) q^{61} +(2.06379 - 9.04207i) q^{62} +(-1.77286 - 7.76739i) q^{64} +(0.674835 - 0.101715i) q^{65} +(-1.22841 - 2.12766i) q^{67} +(-0.0228669 + 0.0396066i) q^{68} +(1.08881 - 0.197554i) q^{70} +(-0.756494 - 0.364308i) q^{71} +(-6.76324 + 6.27537i) q^{73} +(8.33163 - 7.73063i) q^{74} +(-0.0471399 - 0.0227014i) q^{76} +(-10.6631 - 9.31669i) q^{77} +(-6.17678 + 10.6985i) q^{79} +(0.592692 + 1.02657i) q^{80} +(-4.03197 + 0.607721i) q^{82} +(2.83042 + 12.4009i) q^{83} +(-0.368644 + 1.61514i) q^{85} +(-0.708540 + 9.45481i) q^{86} +(5.51905 - 14.0623i) q^{88} +(6.03004 + 1.86002i) q^{89} +(-5.78935 + 1.97709i) q^{91} +(-0.0357083 - 0.0447768i) q^{92} +(0.595637 + 7.94822i) q^{94} +(-1.87413 - 0.282480i) q^{95} +4.63741 q^{97} +(-9.28734 + 3.48491i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8}+O(q^{10}) \) 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8	\( 60 q - q^{2} + 5 q^{4} + 2 q^{5} + 5 q^{7} - 6 q^{8} - 34 q^{10} + 11 q^{11} - 2 q^{13} - 40 q^{14} - 31 q^{16} + 9 q^{17} - 29 q^{19} + 43 q^{20} + 9 q^{22} + 4 q^{23} + 55 q^{25} - 36 q^{26} - 57 q^{28} - 4 q^{29} - 39 q^{31} + 92 q^{32} - 36 q^{34} + 33 q^{35} - 24 q^{37} - 118 q^{38} - 35 q^{41} + 2 q^{43} - 40 q^{44} - 40 q^{46} + 5 q^{47} + 129 q^{49} + 176 q^{50} - 6 q^{52} - 26 q^{53} + 2 q^{55} - 63 q^{56} + 11 q^{58} + 41 q^{59} + 6 q^{61} - 36 q^{62} + 74 q^{64} + 51 q^{65} - 55 q^{67} + 22 q^{68} - 68 q^{70} + 66 q^{71} + 24 q^{73} - 28 q^{74} + 3 q^{76} + 34 q^{77} - 51 q^{79} + 5 q^{80} - 41 q^{82} - 30 q^{83} + 68 q^{85} - 110 q^{86} + 129 q^{88} - 75 q^{89} + 5 q^{91} + 38 q^{94} - 36 q^{95} - 168 q^{97} - 227 q^{98}+O(q^{100}) \) 60 * q - q^2 + 5 * q^4 + 2 * q^5 + 5 * q^7 - 6 * q^8 - 34 * q^10 + 11 * q^11 - 2 * q^13 - 40 * q^14 - 31 * q^16 + 9 * q^17 - 29 * q^19 + 43 * q^20 + 9 * q^22 + 4 * q^23 + 55 * q^25 - 36 * q^26 - 57 * q^28 - 4 * q^29 - 39 * q^31 + 92 * q^32 - 36 * q^34 + 33 * q^35 - 24 * q^37 - 118 * q^38 - 35 * q^41 + 2 * q^43 - 40 * q^44 - 40 * q^46 + 5 * q^47 + 129 * q^49 + 176 * q^50 - 6 * q^52 - 26 * q^53 + 2 * q^55 - 63 * q^56 + 11 * q^58 + 41 * q^59 + 6 * q^61 - 36 * q^62 + 74 * q^64 + 51 * q^65 - 55 * q^67 + 22 * q^68 - 68 * q^70 + 66 * q^71 + 24 * q^73 - 28 * q^74 + 3 * q^76 + 34 * q^77 - 51 * q^79 + 5 * q^80 - 41 * q^82 - 30 * q^83 + 68 * q^85 - 110 * q^86 + 129 * q^88 - 75 * q^89 + 5 * q^91 + 38 * q^94 - 36 * q^95 - 168 * q^97 - 227 * q^98

Introduction

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