LMFDB - Embedded newform 414.2.i.c.397.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.i (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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 46)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			397.1
Root			$0.959493 - 0.281733i$ of defining polynomial
Character	$\chi$	$=$	414.397
Dual form			414.2.i.c.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{2} +(-0.654861 - 0.755750i) q^{4} +(0.915415 - 0.588302i) q^{5} +(0.122916 - 0.854902i) q^{7} +(-0.959493 + 0.281733i) q^{8} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{2} +(-0.654861 - 0.755750i) q^{4} +(0.915415 - 0.588302i) q^{5} +(0.122916 - 0.854902i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.154861 - 1.07708i) q^{10} +(-0.273100 - 0.598006i) q^{11} +(-0.882365 - 6.13698i) q^{13} +(-0.726585 - 0.466948i) q^{14} +(-0.142315 + 0.989821i) q^{16} +(3.72871 - 4.30316i) q^{17} +(4.22593 + 4.87698i) q^{19} +(-1.04408 - 0.306569i) q^{20} -0.657415 q^{22} +(-3.73149 - 3.01264i) q^{23} +(-1.58519 + 3.47108i) q^{25} +(-5.94894 - 1.74677i) q^{26} +(-0.726585 + 0.466948i) q^{28} +(0.0667048 - 0.0769815i) q^{29} +(1.48145 - 0.434992i) q^{31} +(0.841254 + 0.540641i) q^{32} +(-2.36533 - 5.17935i) q^{34} +(-0.390421 - 0.854902i) q^{35} +(-6.17287 - 3.96707i) q^{37} +(6.19177 - 1.81807i) q^{38} +(-0.712591 + 0.822373i) q^{40} +(-5.12658 + 3.29466i) q^{41} +(5.15806 + 1.51454i) q^{43} +(-0.273100 + 0.598006i) q^{44} +(-4.29051 + 2.14278i) q^{46} +7.84594 q^{47} +(6.00070 + 1.76196i) q^{49} +(2.49889 + 2.88388i) q^{50} +(-4.06019 + 4.68571i) q^{52} +(-0.676986 + 4.70854i) q^{53} +(-0.601808 - 0.386758i) q^{55} +(0.122916 + 0.854902i) q^{56} +(-0.0423146 - 0.0926561i) q^{58} +(0.808905 + 5.62606i) q^{59} +(-0.215370 + 0.0632384i) q^{61} +(0.219732 - 1.52827i) q^{62} +(0.841254 - 0.540641i) q^{64} +(-4.41813 - 5.09879i) q^{65} +(0.986274 - 2.15964i) q^{67} -5.69389 q^{68} -0.939833 q^{70} +(-2.66709 + 5.84012i) q^{71} +(2.73205 + 3.15296i) q^{73} +(-6.17287 + 3.96707i) q^{74} +(0.918382 - 6.38749i) q^{76} +(-0.544805 + 0.159969i) q^{77} +(2.41930 + 16.8266i) q^{79} +(0.452036 + 0.989821i) q^{80} +(0.867264 + 6.03196i) q^{82} +(14.2960 + 9.18749i) q^{83} +(0.881761 - 6.13278i) q^{85} +(3.52041 - 4.06278i) q^{86} +(0.430515 + 0.496841i) q^{88} +(4.85701 + 1.42615i) q^{89} -5.35498 q^{91} +(0.166803 + 4.79293i) q^{92} +(3.25932 - 7.13692i) q^{94} +(6.73761 + 1.97834i) q^{95} +(-8.27208 + 5.31614i) q^{97} +(4.09552 - 4.72648i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{4} + 4 q^{5} - 7 q^{7} - q^{8}+O(q^{10}) $ 10 * q - q^2 - q^4 + 4 * q^5 - 7 * q^7 - q^8	$ 10 q - q^{2} - q^{4} + 4 q^{5} - 7 q^{7} - q^{8} + 4 q^{10} + 2 q^{11} + 2 q^{13} + 15 q^{14} - q^{16} + 9 q^{17} + 2 q^{19} - 7 q^{20} + 2 q^{22} - 21 q^{23} - 11 q^{25} - 9 q^{26} + 15 q^{28} + 2 q^{29} + 11 q^{31} - q^{32} - 13 q^{34} + 17 q^{35} - 18 q^{37} + 13 q^{38} + 4 q^{40} - 5 q^{41} - 21 q^{43} + 2 q^{44} - 10 q^{46} + 22 q^{47} + 24 q^{49} + 22 q^{50} - 20 q^{52} + 7 q^{53} + 3 q^{55} - 7 q^{56} + 24 q^{58} - 43 q^{59} - 3 q^{61} - 33 q^{62} - q^{64} - 41 q^{65} - q^{67} - 2 q^{68} + 6 q^{70} + 11 q^{71} - 28 q^{73} - 18 q^{74} + 2 q^{76} - 30 q^{77} + 34 q^{79} - 7 q^{80} + 6 q^{82} + 3 q^{83} + 8 q^{85} + 34 q^{86} - 9 q^{88} + 49 q^{89} - 52 q^{91} + q^{92} - 11 q^{94} + 36 q^{95} + 16 q^{97} - 20 q^{98}+O(q^{100}) $ 10 * q - q^2 - q^4 + 4 * q^5 - 7 * q^7 - q^8 + 4 * q^10 + 2 * q^11 + 2 * q^13 + 15 * q^14 - q^16 + 9 * q^17 + 2 * q^19 - 7 * q^20 + 2 * q^22 - 21 * q^23 - 11 * q^25 - 9 * q^26 + 15 * q^28 + 2 * q^29 + 11 * q^31 - q^32 - 13 * q^34 + 17 * q^35 - 18 * q^37 + 13 * q^38 + 4 * q^40 - 5 * q^41 - 21 * q^43 + 2 * q^44 - 10 * q^46 + 22 * q^47 + 24 * q^49 + 22 * q^50 - 20 * q^52 + 7 * q^53 + 3 * q^55 - 7 * q^56 + 24 * q^58 - 43 * q^59 - 3 * q^61 - 33 * q^62 - q^64 - 41 * q^65 - q^67 - 2 * q^68 + 6 * q^70 + 11 * q^71 - 28 * q^73 - 18 * q^74 + 2 * q^76 - 30 * q^77 + 34 * q^79 - 7 * q^80 + 6 * q^82 + 3 * q^83 + 8 * q^85 + 34 * q^86 - 9 * q^88 + 49 * q^89 - 52 * q^91 + q^92 - 11 * q^94 + 36 * q^95 + 16 * q^97 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

Coefficient data

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

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

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

$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$3$		0			0
$3$		0			0
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	0.915415	−	0.588302i	0.409386	−	0.263096i	−0.319700	−	0.947519i	$-0.603582\pi$
$5$	0.915415	−	0.588302i	0.409386	−	0.263096i	0.729086	+	0.684423i	$0.239946\pi$
$6$		0			0
$7$	0.122916	−	0.854902i	0.0464580	−	0.323123i	−0.953318	−	0.301968i	$-0.902357\pi$
$7$	0.122916	−	0.854902i	0.0464580	−	0.323123i	0.999776	−	0.0211550i	$-0.00673436\pi$
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$		0			0
$10$	−0.154861	−	1.07708i	−0.0489713	−	0.340603i
$11$	−0.273100	−	0.598006i	−0.0823428	−	0.180306i	0.863982	−	0.503523i	$-0.167963\pi$
$11$	−0.273100	−	0.598006i	−0.0823428	−	0.180306i	−0.946325	+	0.323217i	$0.895236\pi$
$12$		0			0
$13$	−0.882365	−	6.13698i	−0.244724	−	1.70209i	−0.627799	−	0.778375i	$-0.716044\pi$
$13$	−0.882365	−	6.13698i	−0.244724	−	1.70209i	0.383075	−	0.923717i	$-0.374865\pi$
$14$	−0.726585	−	0.466948i	−0.194188	−	0.124797i
$15$		0			0
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	3.72871	−	4.30316i	0.904344	−	1.04367i	−0.0944960	−	0.995525i	$-0.530124\pi$
$17$	3.72871	−	4.30316i	0.904344	−	1.04367i	0.998840	−	0.0481438i	$-0.0153306\pi$
$18$		0			0
$19$	4.22593	+	4.87698i	0.969494	+	1.11886i	0.992879	+	0.119130i	$0.0380104\pi$
$19$	4.22593	+	4.87698i	0.969494	+	1.11886i	−0.0233844	+	0.999727i	$0.507444\pi$
$20$	−1.04408	−	0.306569i	−0.233463	−	0.0685509i
$21$		0			0
$22$	−0.657415			−0.140161
$23$	−3.73149	−	3.01264i	−0.778069	−	0.628179i
$23$	−3.73149	−	3.01264i	−0.778069	−	0.628179i
$24$		0			0
$25$	−1.58519	+	3.47108i	−0.317038	+	0.694216i
$26$	−5.94894	−	1.74677i	−1.16668	−	0.342569i
$27$		0			0
$28$	−0.726585	+	0.466948i	−0.137312	+	0.0882448i
$29$	0.0667048	−	0.0769815i	0.0123868	−	0.0142951i	−0.749522	−	0.661979i	$-0.769717\pi$
$29$	0.0667048	−	0.0769815i	0.0123868	−	0.0142951i	0.761909	+	0.647684i	$0.224262\pi$
$30$		0			0
$31$	1.48145	−	0.434992i	0.266076	−	0.0781268i	−0.145973	−	0.989289i	$-0.546631\pi$
$31$	1.48145	−	0.434992i	0.266076	−	0.0781268i	0.412049	+	0.911162i	$0.364813\pi$
$32$	0.841254	+	0.540641i	0.148714	+	0.0955727i
$33$		0			0
$34$	−2.36533	−	5.17935i	−0.405651	−	0.888251i
$35$	−0.390421	−	0.854902i	−0.0659931	−	0.144505i
$36$		0			0
$37$	−6.17287	−	3.96707i	−1.01481	−	0.652182i	−0.0761795	−	0.997094i	$-0.524272\pi$
$37$	−6.17287	−	3.96707i	−1.01481	−	0.652182i	−0.938635	+	0.344913i	$0.887909\pi$
$38$	6.19177	−	1.81807i	1.00444	−	0.294930i
$39$		0			0
$40$	−0.712591	+	0.822373i	−0.112670	+	0.130029i
$41$	−5.12658	+	3.29466i	−0.800638	+	0.514539i	−0.875824	−	0.482631i	$-0.839681\pi$
$41$	−5.12658	+	3.29466i	−0.800638	+	0.514539i	0.0751859	+	0.997170i	$0.476045\pi$
$42$		0			0
$43$	5.15806	+	1.51454i	0.786597	+	0.230966i	0.650275	−	0.759699i	$-0.274654\pi$
$43$	5.15806	+	1.51454i	0.786597	+	0.230966i	0.136322	+	0.990665i	$0.456472\pi$
$44$	−0.273100	+	0.598006i	−0.0411714	+	0.0901528i
$45$		0			0
$46$	−4.29051	+	2.14278i	−0.632601	+	0.315936i
$47$	7.84594			1.14445			0.572224	−	0.820097i	$-0.306081\pi$
$47$	7.84594			1.14445			0.572224	+	0.820097i	$0.306081\pi$
$48$		0			0
$49$	6.00070	+	1.76196i	0.857243	+	0.251709i
$50$	2.49889	+	2.88388i	0.353397	+	0.407842i
$51$		0			0
$52$	−4.06019	+	4.68571i	−0.563048	+	0.649792i
$53$	−0.676986	+	4.70854i	−0.0929911	+	0.646768i	0.889009	+	0.457889i	$0.151394\pi$
$53$	−0.676986	+	4.70854i	−0.0929911	+	0.646768i	−0.982000	+	0.188878i	$0.939515\pi$
$54$		0			0
$55$	−0.601808	−	0.386758i	−0.0811477	−	0.0521505i
$56$	0.122916	+	0.854902i	0.0164254	+	0.114241i
$57$		0			0
$58$	−0.0423146	−	0.0926561i	−0.00555618	−	0.0121663i
$59$	0.808905	+	5.62606i	0.105310	+	0.732450i	0.972234	+	0.234010i	$0.0751847\pi$
$59$	0.808905	+	5.62606i	0.105310	+	0.732450i	−0.866924	+	0.498441i	$0.833906\pi$
$60$		0			0
$61$	−0.215370	+	0.0632384i	−0.0275753	+	0.00809685i	−0.295491	−	0.955345i	$-0.595483\pi$
$61$	−0.215370	+	0.0632384i	−0.0275753	+	0.00809685i	0.267916	+	0.963442i	$0.413665\pi$
$62$	0.219732	−	1.52827i	0.0279060	−	0.194091i
$63$		0			0
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−4.41813	−	5.09879i	−0.548001	−	0.632427i
$66$		0			0
$67$	0.986274	−	2.15964i	0.120493	−	0.263842i	−0.839769	−	0.542944i	$-0.817310\pi$
$67$	0.986274	−	2.15964i	0.120493	−	0.263842i	0.960261	+	0.279102i	$0.0900368\pi$
$68$	−5.69389			−0.690486
$69$		0			0
$70$	−0.939833			−0.112332
$71$	−2.66709	+	5.84012i	−0.316526	+	0.693094i	−0.999295	−	0.0375395i	$-0.988048\pi$
$71$	−2.66709	+	5.84012i	−0.316526	+	0.693094i	0.682770	+	0.730634i	$0.260775\pi$
$72$		0			0
$73$	2.73205	+	3.15296i	0.319763	+	0.369026i	0.892761	−	0.450531i	$-0.148765\pi$
$73$	2.73205	+	3.15296i	0.319763	+	0.369026i	−0.572998	+	0.819557i	$0.694220\pi$
$74$	−6.17287	+	3.96707i	−0.717582	+	0.461162i
$75$		0			0
$76$	0.918382	−	6.38749i	0.105346	−	0.732695i
$77$	−0.544805	+	0.159969i	−0.0620863	+	0.0182302i
$78$		0			0
$79$	2.41930	+	16.8266i	0.272193	+	1.89314i	0.425493	+	0.904962i	$0.360101\pi$
$79$	2.41930	+	16.8266i	0.272193	+	1.89314i	−0.153301	+	0.988180i	$0.548990\pi$
$80$	0.452036	+	0.989821i	0.0505392	+	0.110665i
$81$		0			0
$82$	0.867264	+	6.03196i	0.0957733	+	0.666118i
$83$	14.2960	+	9.18749i	1.56919	+	1.00846i	0.979648	+	0.200721i	$0.0643285\pi$
$83$	14.2960	+	9.18749i	1.56919	+	1.00846i	0.589543	+	0.807737i	$0.299308\pi$
$84$		0			0
$85$	0.881761	−	6.13278i	0.0956404	−	0.665193i
$86$	3.52041	−	4.06278i	0.379616	−	0.438100i
$87$		0			0
$88$	0.430515	+	0.496841i	0.0458931	+	0.0529635i
$89$	4.85701	+	1.42615i	0.514842	+	0.151171i	0.528825	−	0.848731i	$-0.322633\pi$
$89$	4.85701	+	1.42615i	0.514842	+	0.151171i	−0.0139828	+	0.999902i	$0.504451\pi$
$90$		0			0
$91$	−5.35498			−0.561354
$92$	0.166803	+	4.79293i	0.0173904	+	0.499697i
$93$		0			0
$94$	3.25932	−	7.13692i	0.336173	−	0.736117i
$95$	6.73761	+	1.97834i	0.691264	+	0.202974i
$96$		0			0
$97$	−8.27208	+	5.31614i	−0.839903	+	0.539773i	−0.888410	−	0.459050i	$-0.848190\pi$
$97$	−8.27208	+	5.31614i	−0.839903	+	0.539773i	0.0485077	+	0.998823i	$0.484553\pi$
$98$	4.09552	−	4.72648i	0.413710	−	0.477447i
$99$		0			0
$100$	3.66135	−	1.07507i	0.366135	−	0.107507i
$101$	−0.516117	−	0.331688i	−0.0513555	−	0.0330042i	0.514711	−	0.857364i	$-0.327899\pi$
$101$	−0.516117	−	0.331688i	−0.0513555	−	0.0330042i	−0.566067	+	0.824359i	$0.691536\pi$
$102$		0			0
$103$	−3.56423	−	7.80458i	−0.351194	−	0.769008i	−0.999968	−	0.00802641i	$-0.997445\pi$
$103$	−3.56423	−	7.80458i	−0.351194	−	0.769008i	0.648774	−	0.760981i	$-0.275282\pi$
$104$	2.57561	+	5.63980i	0.252559	+	0.553028i
$105$		0			0
$106$	4.00181	+	2.57181i	0.388690	+	0.249796i
$107$	−17.2777	+	5.07320i	−1.67030	+	0.490445i	−0.973856	−	0.227165i	$-0.927054\pi$
$107$	−17.2777	+	5.07320i	−1.67030	+	0.490445i	−0.696446	+	0.717610i	$0.745236\pi$
$108$		0			0
$109$	6.31264	−	7.28517i	0.604641	−	0.697793i	−0.368074	−	0.929796i	$-0.619983\pi$
$109$	6.31264	−	7.28517i	0.604641	−	0.697793i	0.972715	+	0.232004i	$0.0745282\pi$
$110$	−0.601808	+	0.386758i	−0.0573801	+	0.0368760i
$111$		0			0
$112$	0.828708	+	0.243331i	0.0783055	+	0.0229926i
$113$	4.01751	−	8.79711i	0.377935	−	0.827563i	−0.621104	−	0.783729i	$-0.713315\pi$
$113$	4.01751	−	8.79711i	0.377935	−	0.827563i	0.999039	−	0.0438343i	$-0.0139574\pi$
$114$		0			0
$115$	−5.18820	−	0.562577i	−0.483802	−	0.0524606i
$116$	−0.101861			−0.00945756
$117$		0			0
$118$	5.45367	+	1.60134i	0.502051	+	0.147416i
$119$	−3.22046	−	3.71661i	−0.295219	−	0.340701i
$120$		0			0
$121$	6.92044	−	7.98661i	0.629131	−	0.726056i
$122$	−0.0319444	+	0.222178i	−0.00289211	+	0.0201150i
$123$		0			0
$124$	−1.29889	−	0.834743i	−0.116643	−	0.0749621i
$125$	1.36524	+	9.49545i	0.122111	+	0.849299i
$126$		0			0
$127$	5.76874	+	12.6318i	0.511893	+	1.12089i	0.972418	+	0.233243i	$0.0749338\pi$
$127$	5.76874	+	12.6318i	0.511893	+	1.12089i	−0.460525	+	0.887647i	$0.652339\pi$
$128$	−0.142315	−	0.989821i	−0.0125790	−	0.0874887i
$129$		0			0
$130$	−6.47338	+	1.90075i	−0.567753	+	0.166707i
$131$	1.35517	−	9.42539i	0.118401	−	0.823500i	−0.840915	−	0.541167i	$-0.817983\pi$
$131$	1.35517	−	9.42539i	0.118401	−	0.823500i	0.959316	−	0.282333i	$-0.0911083\pi$
$132$		0			0
$133$	4.68878	−	3.01329i	0.406569	−	0.261286i
$134$	−1.55476	−	1.79429i	−0.134311	−	0.155003i
$135$		0			0
$136$	−2.36533	+	5.17935i	−0.202825	+	0.444125i
$137$	−0.366843			−0.0313415			−0.0156707	−	0.999877i	$-0.504988\pi$
$137$	−0.366843			−0.0313415			−0.0156707	+	0.999877i	$0.504988\pi$
$138$		0			0
$139$	1.12658			0.0955552			0.0477776	−	0.998858i	$-0.484786\pi$
$139$	1.12658			0.0955552			0.0477776	+	0.998858i	$0.484786\pi$
$140$	−0.390421	+	0.854902i	−0.0329966	+	0.0722524i
$141$		0			0
$142$	4.20441	+	4.85214i	0.352826	+	0.407183i
$143$	−3.42898	+	2.20367i	−0.286745	+	0.184280i
$144$		0			0
$145$	0.0157743	−	0.109713i	0.00130998	−	0.00911113i
$146$	4.00297	−	1.17538i	0.331288	−	0.0972749i
$147$		0			0
$148$	1.04427	+	7.26302i	0.0858381	+	0.597017i
$149$	−5.69873	−	12.4785i	−0.466858	−	1.02228i	−0.985870	−	0.167510i	$-0.946427\pi$
$149$	−5.69873	−	12.4785i	−0.466858	−	1.02228i	0.519012	−	0.854767i	$-0.326300\pi$
$150$		0			0
$151$	0.900658	+	6.26422i	0.0732945	+	0.509775i	0.993088	+	0.117372i	$0.0374470\pi$
$151$	0.900658	+	6.26422i	0.0732945	+	0.509775i	−0.919793	+	0.392403i	$0.871644\pi$
$152$	−5.42875	−	3.48885i	−0.440330	−	0.282983i
$153$		0			0
$154$	−0.0808071	+	0.562026i	−0.00651162	+	0.0452893i
$155$	1.10023	−	1.26973i	0.0883727	−	0.101988i
$156$		0			0
$157$	−7.74577	−	8.93909i	−0.618180	−	0.713417i	0.357181	−	0.934035i	$-0.383738\pi$
$157$	−7.74577	−	8.93909i	−0.618180	−	0.713417i	−0.975360	+	0.220618i	$0.929193\pi$
$158$	16.3110	+	4.78935i	1.29764	+	0.381020i
$159$		0			0
$160$	1.08816			0.0860263
$161$	−3.03417	+	2.81975i	−0.239126	+	0.222228i
$162$		0			0
$163$	2.27567	−	4.98302i	0.178244	−	0.390301i	−0.799330	−	0.600893i	$-0.794812\pi$
$163$	2.27567	−	4.98302i	0.178244	−	0.390301i	0.977574	+	0.210592i	$0.0675392\pi$
$164$	5.84713	+	1.71687i	0.456584	+	0.134065i
$165$		0			0
$166$	14.2960	−	9.18749i	1.10959	−	0.713088i
$167$	−9.47242	+	10.9318i	−0.732998	+	0.845925i	−0.992806	−	0.119735i	$-0.961795\pi$
$167$	−9.47242	+	10.9318i	−0.732998	+	0.845925i	0.259808	+	0.965660i	$0.416341\pi$
$168$		0			0
$169$	−24.4106	+	7.16759i	−1.87774	+	0.551353i
$170$	−5.21228	−	3.34973i	−0.399763	−	0.256912i
$171$		0			0
$172$	−2.23320	−	4.89002i	−0.170280	−	0.372861i
$173$	3.40568	+	7.45740i	0.258929	+	0.566976i	0.993794	−	0.111238i	$-0.0354816\pi$
$173$	3.40568	+	7.45740i	0.258929	+	0.566976i	−0.734865	+	0.678214i	$0.762754\pi$
$174$		0			0
$175$	2.77259	+	1.78183i	0.209588	+	0.134694i
$176$	0.630785	−	0.185215i	0.0475472	−	0.0139611i
$177$		0			0
$178$	3.31494	−	3.82565i	0.248466	−	0.286745i
$179$	14.2050	−	9.12902i	1.06173	−	0.682335i	0.111466	−	0.993768i	$-0.464445\pi$
$179$	14.2050	−	9.12902i	1.06173	−	0.682335i	0.950268	+	0.311434i	$0.100809\pi$
$180$		0			0
$181$	−15.9951	−	4.69659i	−1.18891	−	0.349095i	−0.373305	−	0.927709i	$-0.621776\pi$
$181$	−15.9951	−	4.69659i	−1.18891	−	0.349095i	−0.815602	+	0.578614i	$0.803594\pi$
$182$	−2.22454	+	4.87106i	−0.164894	+	0.361067i
$183$		0			0
$184$	4.42909	+	1.83933i	0.326517	+	0.135597i
$185$	−7.98457			−0.587037
$186$		0			0
$187$	−3.59162	−	1.05460i	−0.262646	−	0.0771197i
$188$	−5.13800	−	5.92956i	−0.374727	−	0.432458i
$189$		0			0
$190$	4.59847	−	5.30692i	0.333608	−	0.385004i
$191$	2.35195	−	16.3581i	0.170181	−	1.18363i	−0.708319	−	0.705892i	$-0.750546\pi$
$191$	2.35195	−	16.3581i	0.170181	−	1.18363i	0.878500	−	0.477742i	$-0.158545\pi$
$192$		0			0
$193$	−10.4085	−	6.68914i	−0.749220	−	0.481495i	0.109470	−	0.993990i	$-0.465085\pi$
$193$	−10.4085	−	6.68914i	−0.749220	−	0.481495i	−0.858690	+	0.512496i	$0.828721\pi$
$194$	1.39939	+	9.73296i	0.100470	+	0.698786i
$195$		0			0
$196$	−2.59802	−	5.68887i	−0.185573	−	0.406348i
$197$	−0.148056	−	1.02975i	−0.0105485	−	0.0733667i	0.983867	−	0.178900i	$-0.0572540\pi$
$197$	−0.148056	−	1.02975i	−0.0105485	−	0.0733667i	−0.994416	+	0.105534i	$0.966345\pi$
$198$		0			0
$199$	−10.7444	+	3.15483i	−0.761648	+	0.223640i	−0.639415	−	0.768861i	$-0.720824\pi$
$199$	−10.7444	+	3.15483i	−0.761648	+	0.223640i	−0.122233	+	0.992501i	$0.539005\pi$
$200$	0.543062	−	3.77708i	0.0384003	−	0.267080i
$201$		0			0
$202$	−0.516117	+	0.331688i	−0.0363139	+	0.0233375i
$203$	−0.0576125	−	0.0664884i	−0.00404360	−	0.00466657i
$204$		0			0
$205$	−2.75470	+	6.03196i	−0.192397	+	0.421290i
$206$	−8.57993			−0.597792
$207$		0			0
$208$	6.20009			0.429899
$209$	1.76236	−	3.85903i	0.121905	−	0.266935i
$210$		0			0
$211$	5.60361	+	6.46691i	0.385768	+	0.445200i	0.915108	−	0.403210i	$-0.132106\pi$
$211$	5.60361	+	6.46691i	0.385768	+	0.445200i	−0.529339	+	0.848410i	$0.677560\pi$
$212$	4.00181	−	2.57181i	0.274845	−	0.176632i
$213$		0			0
$214$	−2.56269	+	17.8239i	−0.175182	+	1.21841i
$215$	5.61278	−	1.64806i	0.382788	−	0.112397i
$216$		0			0
$217$	−0.189781	−	1.31996i	−0.0128832	−	0.0896047i
$218$	−4.00446	−	8.76854i	−0.271216	−	0.593881i
$219$		0			0
$220$	0.101808	+	0.708089i	0.00686388	+	0.0477393i
$221$	−29.6985	−	19.0861i	−1.99774	−	1.28387i
$222$		0			0
$223$	0.0709893	−	0.493741i	0.00475379	−	0.0330634i	−0.987306	−	0.158827i	$-0.949229\pi$
$223$	0.0709893	−	0.493741i	0.00475379	−	0.0330634i	0.992060	+	0.125763i	$0.0401380\pi$
$224$	0.565599	−	0.652736i	0.0377907	−	0.0436127i
$225$		0			0
$226$	−6.33320	−	7.30891i	−0.421278	−	0.486181i
$227$	−20.1968	−	5.93031i	−1.34051	−	0.393608i	−0.468657	−	0.883380i	$-0.655262\pi$
$227$	−20.1968	−	5.93031i	−1.34051	−	0.393608i	−0.871851	+	0.489772i	$0.837080\pi$
$228$		0			0
$229$	1.00627			0.0664965			0.0332483	−	0.999447i	$-0.489415\pi$
$229$	1.00627			0.0664965			0.0332483	+	0.999447i	$0.489415\pi$
$230$	−2.66699	+	4.48565i	−0.175856	+	0.295775i
$231$		0			0
$232$	−0.0423146	+	0.0926561i	−0.00277809	+	0.00608317i
$233$	14.7931	+	4.34364i	0.969127	+	0.284561i	0.727729	−	0.685865i	$-0.240576\pi$
$233$	14.7931	+	4.34364i	0.969127	+	0.284561i	0.241398	+	0.970426i	$0.422394\pi$
$234$		0			0
$235$	7.18229	−	4.61578i	0.468521	−	0.301100i
$236$	3.72217	−	4.29561i	0.242293	−	0.279621i
$237$		0			0
$238$	−4.71857	+	1.38550i	−0.305860	+	0.0898085i
$239$	3.53850	+	2.27406i	0.228887	+	0.147097i	0.650058	−	0.759885i	$-0.274745\pi$
$239$	3.53850	+	2.27406i	0.228887	+	0.147097i	−0.421171	+	0.906981i	$0.638381\pi$
$240$		0			0
$241$	−6.52623	−	14.2904i	−0.420391	−	0.920528i	−0.994789	−	0.101952i	$-0.967491\pi$
$241$	−6.52623	−	14.2904i	−0.420391	−	0.920528i	0.574398	−	0.818576i	$-0.305236\pi$
$242$	−4.39002	−	9.61281i	−0.282201	−	0.617935i
$243$		0			0
$244$	0.188830	+	0.121354i	0.0120886	+	0.00776887i
$245$	6.52970	−	1.91729i	0.417167	−	0.122491i
$246$		0			0
$247$	26.2011	−	30.2377i	1.66714	−	1.92398i
$248$	−1.29889	+	0.834743i	−0.0824793	+	0.0530062i
$249$		0			0
$250$	9.20450	+	2.70269i	0.582144	+	0.170933i
$251$	−3.95780	+	8.66638i	−0.249814	+	0.547017i	−0.992446	−	0.122683i	$-0.960850\pi$
$251$	−3.95780	+	8.66638i	−0.249814	+	0.547017i	0.742632	+	0.669700i	$0.233577\pi$
$252$		0			0
$253$	−0.782507	+	3.05420i	−0.0491958	+	0.192016i
$254$	13.8867			0.871329
$255$		0			0
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	4.36038	+	5.03214i	0.271993	+	0.313896i	0.875269	−	0.483636i	$-0.160684\pi$
$257$	4.36038	+	5.03214i	0.271993	+	0.313896i	−0.603277	+	0.797532i	$0.706139\pi$
$258$		0			0
$259$	−4.15020	+	4.78959i	−0.257881	+	0.297610i
$260$	−0.960150	+	6.67799i	−0.0595460	+	0.414151i
$261$		0			0
$262$	−8.01068	−	5.14815i	−0.494902	−	0.318054i
$263$	−1.67846	−	11.6740i	−0.103498	−	0.719847i	−0.973813	−	0.227351i	$-0.926994\pi$
$263$	−1.67846	−	11.6740i	−0.103498	−	0.719847i	0.870315	−	0.492496i	$-0.163916\pi$
$264$		0			0
$265$	2.15032	+	4.70854i	0.132093	+	0.289243i
$266$	−0.793200	−	5.51683i	−0.0486342	−	0.338258i
$267$		0			0
$268$	−2.27802	+	0.668886i	−0.139152	+	0.0408587i
$269$	1.64586	−	11.4472i	0.100350	−	0.697951i	−0.876088	−	0.482152i	$-0.839855\pi$
$269$	1.64586	−	11.4472i	0.100350	−	0.697951i	0.976438	−	0.215799i	$-0.0692355\pi$
$270$		0			0
$271$	−21.4251	+	13.7691i	−1.30148	+	0.836412i	−0.993373	−	0.114939i	$-0.963333\pi$
$271$	−21.4251	+	13.7691i	−1.30148	+	0.836412i	−0.308110	+	0.951351i	$0.599696\pi$
$272$	3.72871	+	4.30316i	0.226086	+	0.260917i
$273$		0			0
$274$	−0.152392	+	0.333692i	−0.00920633	+	0.0201591i
$275$	2.50864			0.151277
$276$		0			0
$277$	25.8732			1.55457			0.777285	−	0.629149i	$-0.216596\pi$
$277$	25.8732			1.55457			0.777285	+	0.629149i	$0.216596\pi$
$278$	0.467998	−	1.02477i	0.0280686	−	0.0614617i
$279$		0			0
$280$	0.615460	+	0.710278i	0.0367808	+	0.0424473i
$281$	−24.0137	+	15.4327i	−1.43254	+	0.920636i	−0.432720	+	0.901529i	$0.642446\pi$
$281$	−24.0137	+	15.4327i	−1.43254	+	0.920636i	−0.999817	+	0.0191071i	$0.993918\pi$
$282$		0			0
$283$	0.0274013	−	0.190580i	0.00162884	−	0.0113288i	−0.988991	−	0.147977i	$-0.952724\pi$
$283$	0.0274013	−	0.190580i	0.00162884	−	0.0113288i	0.990620	+	0.136648i	$0.0436330\pi$
$284$	6.16024	−	1.80881i	0.365543	−	0.107333i
$285$		0			0
$286$	0.580080	+	4.03455i	0.0343008	+	0.238568i
$287$	2.18647	+	4.78770i	0.129063	+	0.282609i
$288$		0			0
$289$	−2.19456	−	15.2635i	−0.129091	−	0.897851i
$290$	−0.0932451	−	0.0599250i	−0.00547554	−	0.00351892i
$291$		0			0
$292$	0.593732	−	4.12950i	0.0347455	−	0.241660i
$293$	17.4920	−	20.1868i	1.02189	−	1.17933i	0.0382374	−	0.999269i	$-0.487826\pi$
$293$	17.4920	−	20.1868i	1.02189	−	1.17933i	0.983656	−	0.180059i	$-0.0576289\pi$
$294$		0			0
$295$	4.05030	+	4.67430i	0.235818	+	0.272148i
$296$	7.04048	+	2.06727i	0.409220	+	0.120158i
$297$		0			0
$298$	−13.7182			−0.794672
$299$	−15.1960	+	25.5583i	−0.878807	+	1.47808i
$300$		0			0
$301$	1.92880	−	4.22348i	0.111174	−	0.243437i
$302$	6.07228	+	1.78298i	0.349420	+	0.102599i
$303$		0			0
$304$	−5.42875	+	3.48885i	−0.311360	+	0.200099i
$305$	−0.159950	+	0.184592i	−0.00915871	+	0.0105697i
$306$		0			0
$307$	−8.73390	+	2.56450i	−0.498470	+	0.146364i	−0.521297	−	0.853375i	$-0.674552\pi$
$307$	−8.73390	+	2.56450i	−0.498470	+	0.146364i	0.0228268	+	0.999739i	$0.492733\pi$
$308$	0.477668	+	0.306979i	0.0272177	+	0.0174917i
$309$		0			0
$310$	−0.697939	−	1.52827i	−0.0396403	−	0.0868001i
$311$	4.36988	+	9.56870i	0.247793	+	0.542591i	0.992130	−	0.125213i	$-0.0399615\pi$
$311$	4.36988	+	9.56870i	0.247793	+	0.542591i	−0.744337	+	0.667804i	$0.767234\pi$
$312$		0			0
$313$	9.30661	+	5.98100i	0.526041	+	0.338066i	0.776558	−	0.630046i	$-0.216964\pi$
$313$	9.30661	+	5.98100i	0.526041	+	0.338066i	−0.250517	+	0.968112i	$0.580601\pi$
$314$	−11.3490	+	3.33237i	−0.640461	+	0.188056i
$315$		0			0
$316$	11.1324	−	12.8475i	0.626246	−	0.722727i
$317$	11.2997	−	7.26190i	0.634657	−	0.407869i	−0.183374	−	0.983043i	$-0.558702\pi$
$317$	11.2997	−	7.26190i	0.634657	−	0.407869i	0.818031	+	0.575174i	$0.195066\pi$
$318$		0			0
$319$	−0.0642525	−	0.0188662i	−0.00359745	−	0.00105631i
$320$	0.452036	−	0.989821i	0.0252696	−	0.0553327i
$321$		0			0
$322$	1.30450	+	3.93135i	0.0726968	+	0.219086i
$323$	36.7437			2.04447
$324$		0			0
$325$	22.7007	+	6.66552i	1.25921	+	0.369736i
$326$	−3.58737	−	4.14005i	−0.198686	−	0.229296i
$327$		0			0
$328$	3.99071	−	4.60553i	0.220350	−	0.254298i
$329$	0.964394	−	6.70751i	0.0531688	−	0.369797i
$330$		0			0
$331$	16.9426	+	10.8883i	0.931249	+	0.598478i	0.915901	−	0.401405i	$-0.131478\pi$
$331$	16.9426	+	10.8883i	0.931249	+	0.598478i	0.0153486	+	0.999882i	$0.495114\pi$
$332$	−2.41846	−	16.8207i	−0.132730	−	0.923158i
$333$		0			0
$334$	6.00889	+	13.1576i	0.328792	+	0.719954i
$335$	−0.367669	−	2.55719i	−0.0200879	−	0.139714i
$336$		0			0
$337$	−3.73953	+	1.09803i	−0.203705	+	0.0598133i	−0.381993	−	0.924165i	$-0.624762\pi$
$337$	−3.73953	+	1.09803i	−0.203705	+	0.0598133i	0.178288	+	0.983978i	$0.442944\pi$
$338$	−3.62065	+	25.1821i	−0.196937	+	1.36973i
$339$		0			0
$340$	−5.21228	+	3.34973i	−0.282675	+	0.181664i
$341$	−0.664711	−	0.767117i	−0.0359961	−	0.0415417i
$342$		0			0
$343$	4.75543	−	10.4129i	0.256769	−	0.562246i
$344$	−5.37582			−0.289845
$345$		0			0
$346$	8.19826			0.440741
$347$	−2.06211	+	4.51538i	−0.110700	+	0.242399i	−0.956871	−	0.290512i	$-0.906174\pi$
$347$	−2.06211	+	4.51538i	−0.110700	+	0.242399i	0.846172	+	0.532910i	$0.178902\pi$
$348$		0			0
$349$	10.3802	+	11.9794i	0.555638	+	0.641241i	0.962187	−	0.272388i	$-0.0878135\pi$
$349$	10.3802	+	11.9794i	0.555638	+	0.641241i	−0.406549	+	0.913629i	$0.633268\pi$
$350$	2.77259	−	1.78183i	0.148201	−	0.0952430i
$351$		0			0
$352$	0.0935599	−	0.650724i	0.00498676	−	0.0346837i
$353$	−22.4141	+	6.58137i	−1.19298	+	0.350291i	−0.817165	−	0.576403i	$-0.804456\pi$
$353$	−22.4141	+	6.58137i	−1.19298	+	0.350291i	−0.375816	+	0.926694i	$0.622638\pi$
$354$		0			0
$355$	0.994253	+	6.91518i	0.0527695	+	0.367020i
$356$	−2.10286	−	4.60461i	−0.111451	−	0.244044i
$357$		0			0
$358$	−2.40306	−	16.7137i	−0.127006	−	0.883345i
$359$	9.30096	+	5.97736i	0.490886	+	0.315473i	0.762562	−	0.646916i	$-0.223941\pi$
$359$	9.30096	+	5.97736i	0.490886	+	0.315473i	−0.271676	+	0.962389i	$0.587578\pi$
$360$		0			0
$361$	−3.22249	+	22.4129i	−0.169605	+	1.17963i
$362$	−10.9168	+	12.5986i	−0.573773	+	0.662169i
$363$		0			0
$364$	3.50676	+	4.04702i	0.183804	+	0.212121i
$365$	4.35585	+	1.27899i	0.227996	+	0.0669456i
$366$		0			0
$367$	−26.5936			−1.38818			−0.694088	−	0.719890i	$-0.744192\pi$
$367$	−26.5936			−1.38818			−0.694088	+	0.719890i	$0.744192\pi$
$368$	3.51302	−	3.26476i	0.183129	−	0.170188i
$369$		0			0
$370$	−3.31691	+	7.26302i	−0.172438	+	0.377587i
$371$	3.94213	+	1.15751i	0.204665	+	0.0600951i
$372$		0			0
$373$	−11.6014	+	7.45575i	−0.600697	+	0.386044i	−0.805358	−	0.592789i	$-0.798027\pi$
$373$	−11.6014	+	7.45575i	−0.600697	+	0.386044i	0.204662	+	0.978833i	$0.434391\pi$
$374$	−2.45131	+	2.82896i	−0.126754	+	0.146282i
$375$		0			0
$376$	−7.52812	+	2.21046i	−0.388233	+	0.113996i
$377$	−0.531292	−	0.341440i	−0.0273629	−	0.0175851i
$378$		0			0
$379$	−1.70460	−	3.73256i	−0.0875595	−	0.191729i	0.860787	−	0.508966i	$-0.169972\pi$
$379$	−1.70460	−	3.73256i	−0.0875595	−	0.191729i	−0.948346	+	0.317237i	$0.897245\pi$
$380$	−2.91707	−	6.38749i	−0.149642	−	0.327671i
$381$		0			0
$382$	−13.9029	−	8.93483i	−0.711332	−	0.457145i
$383$	−3.86384	+	1.13453i	−0.197433	+	0.0579716i	−0.378954	−	0.925415i	$-0.623716\pi$
$383$	−3.86384	+	1.13453i	−0.197433	+	0.0579716i	0.181521	+	0.983387i	$0.441898\pi$
$384$		0			0
$385$	−0.404613	+	0.466948i	−0.0206210	+	0.0237979i
$386$	−10.4085	+	6.68914i	−0.529779	+	0.340468i
$387$		0			0
$388$	9.43473	+	2.77029i	0.478976	+	0.140640i
$389$	−3.79829	+	8.31710i	−0.192581	+	0.421694i	−0.981149	−	0.193254i	$-0.938096\pi$
$389$	−3.79829	+	8.31710i	−0.192581	+	0.421694i	0.788568	+	0.614948i	$0.210823\pi$
$390$		0			0
$391$	−26.8775	+	4.82392i	−1.35925	+	0.243956i
$392$	−6.25403			−0.315876
$393$		0			0
$394$	−0.998199	−	0.293098i	−0.0502885	−	0.0147660i
$395$	12.1138	+	13.9800i	0.609511	+	0.703413i
$396$		0			0
$397$	11.0546	−	12.7577i	0.554815	−	0.640290i	−0.407183	−	0.913346i	$-0.633489\pi$
$397$	11.0546	−	12.7577i	0.554815	−	0.640290i	0.961998	+	0.273056i	$0.0880345\pi$
$398$	−1.59364	+	11.0840i	−0.0798818	+	0.555590i
$399$		0			0
$400$	−3.21015	−	2.06304i	−0.160508	−	0.103152i
$401$	3.95941	+	27.5383i	0.197723	+	1.37520i	0.810870	+	0.585227i	$0.198995\pi$
$401$	3.95941	+	27.5383i	0.197723	+	1.37520i	−0.613146	+	0.789969i	$0.710096\pi$
$402$		0			0
$403$	−3.97671	−	8.70778i	−0.198094	−	0.433766i
$404$	0.0873115	+	0.607265i	0.00434391	+	0.0302125i
$405$		0			0
$406$	−0.0844130	+	0.0247859i	−0.00418935	+	0.00123010i
$407$	−0.686516	+	4.77482i	−0.0340293	+	0.236679i
$408$		0			0
$409$	6.63424	−	4.26357i	0.328042	−	0.210820i	−0.366244	−	0.930519i	$-0.619357\pi$
$409$	6.63424	−	4.26357i	0.328042	−	0.210820i	0.694286	+	0.719699i	$0.255720\pi$
$410$	4.34251	+	5.01153i	0.214462	+	0.247502i
$411$		0			0
$412$	−3.56423	+	7.80458i	−0.175597	+	0.384504i
$413$	4.90916			0.241564
$414$		0			0
$415$	18.4918			0.907727
$416$	2.57561	−	5.63980i	0.126280	−	0.276514i
$417$		0			0
$418$	−2.77819	−	3.20620i	−0.135886	−	0.156820i
$419$	−7.20548	+	4.63068i	−0.352011	+	0.226224i	−0.704681	−	0.709524i	$-0.748910\pi$
$419$	−7.20548	+	4.63068i	−0.352011	+	0.226224i	0.352671	+	0.935748i	$0.385274\pi$
$420$		0			0
$421$	3.49640	−	24.3180i	0.170404	−	1.18519i	−0.707628	−	0.706586i	$-0.750235\pi$
$421$	3.49640	−	24.3180i	0.170404	−	1.18519i	0.878032	−	0.478602i	$-0.158856\pi$
$422$	8.21033	−	2.41077i	0.399673	−	0.117354i
$423$		0			0
$424$	−0.676986	−	4.70854i	−0.0328773	−	0.228667i
$425$	9.02590	+	19.7640i	0.437820	+	0.958693i
$426$		0			0
$427$	0.0275901	+	0.191894i	0.00133518	+	0.00928638i
$428$	15.1486	+	9.73540i	0.732234	+	0.470578i
$429$		0			0
$430$	0.832504	−	5.79019i	0.0401469	−	0.279228i
$431$	1.18776	−	1.37074i	0.0572122	−	0.0660263i	−0.726422	−	0.687249i	$-0.758818\pi$
$431$	1.18776	−	1.37074i	0.0572122	−	0.0660263i	0.783634	+	0.621222i	$0.213364\pi$
$432$		0			0
$433$	21.0824	+	24.3304i	1.01315	+	1.16924i	0.985509	+	0.169625i	$0.0542556\pi$
$433$	21.0824	+	24.3304i	1.01315	+	1.16924i	0.0276458	+	0.999618i	$0.491199\pi$
$434$	−1.27951	−	0.375699i	−0.0614187	−	0.0180342i
$435$		0			0
$436$	−9.63966			−0.461656
$437$	−1.07641	−	30.9296i	−0.0514914	−	1.47956i
$438$		0			0
$439$	5.43997	−	11.9119i	0.259636	−	0.568523i	−0.734257	−	0.678871i	$-0.762469\pi$
$439$	5.43997	−	11.9119i	0.259636	−	0.568523i	0.993893	+	0.110349i	$0.0351967\pi$
$440$	0.686393	+	0.201543i	0.0327225	+	0.00960819i
$441$		0			0
$442$	−29.6985	+	19.0861i	−1.41261	+	0.907831i
$443$	18.0137	−	20.7889i	0.855856	−	0.987710i	−0.144143	−	0.989557i	$-0.546042\pi$
$443$	18.0137	−	20.7889i	0.855856	−	0.987710i	0.999998	+	0.00184672i	$0.000587831\pi$
$444$		0			0
$445$	5.28519	−	1.55187i	0.250542	−	0.0735657i
$446$	−0.419633	−	0.269682i	−0.0198702	−	0.0127698i
$447$		0			0
$448$	−0.358791	−	0.785643i	−0.0169513	−	0.0371181i
$449$	12.5117	+	27.3969i	0.590465	+	1.29294i	0.935160	+	0.354224i	$0.115255\pi$
$449$	12.5117	+	27.3969i	0.590465	+	1.29294i	−0.344695	+	0.938715i	$0.612018\pi$
$450$		0			0
$451$	3.37030	+	2.16596i	0.158701	+	0.101991i
$452$	−9.27932	+	2.72466i	−0.436463	+	0.128157i
$453$		0			0
$454$	−13.7844	+	15.9081i	−0.646936	+	0.746604i
$455$	−4.90202	+	3.15034i	−0.229810	+	0.147690i
$456$		0			0
$457$	−18.0541	−	5.30116i	−0.844535	−	0.247978i	−0.169286	−	0.985567i	$-0.554146\pi$
$457$	−18.0541	−	5.30116i	−0.844535	−	0.247978i	−0.675250	+	0.737589i	$0.735964\pi$
$458$	0.418022	−	0.915340i	0.0195329	−	0.0427710i
$459$		0			0
$460$	2.97238	+	4.28939i	0.138588	+	0.199994i
$461$	−8.21514			−0.382617			−0.191309	−	0.981530i	$-0.561273\pi$
$461$	−8.21514			−0.382617			−0.191309	+	0.981530i	$0.561273\pi$
$462$		0			0
$463$	36.1358	+	10.6104i	1.67937	+	0.493108i	0.976010	−	0.217725i	$-0.0698636\pi$
$463$	36.1358	+	10.6104i	1.67937	+	0.493108i	0.703361	+	0.710833i	$0.251682\pi$
$464$	0.0667048	+	0.0769815i	0.00309669	+	0.00357377i
$465$		0			0
$466$	10.0964	−	11.6518i	0.467706	−	0.539761i
$467$	−0.632529	+	4.39934i	−0.0292700	+	0.203577i	−0.999209	−	0.0397718i	$-0.987337\pi$
$467$	−0.632529	+	4.39934i	−0.0292700	+	0.203577i	0.969939	+	0.243349i	$0.0782460\pi$
$468$		0			0
$469$	−1.72505	−	1.10862i	−0.0796554	−	0.0511914i
$470$	−1.21503	−	8.45070i	−0.0560451	−	0.389802i
$471$		0			0
$472$	−2.36118	−	5.17027i	−0.108682	−	0.237981i
$473$	−0.502962	−	3.49818i	−0.0231262	−	0.160846i
$474$		0			0
$475$	−23.6273	+	6.93760i	−1.08409	+	0.318319i
$476$	−0.699873	+	4.86772i	−0.0320786	+	0.223112i
$477$		0			0
$478$	3.53850	−	2.27406i	0.161847	−	0.104013i
$479$	−18.7925	−	21.6877i	−0.858653	−	0.990938i	−1.00000		0.000977776i	$-0.999689\pi$
$479$	−18.7925	−	21.6877i	−0.858653	−	0.990938i	0.141347	−	0.989960i	$-0.454857\pi$
$480$		0			0
$481$	−18.8991	+	41.3832i	−0.861724	+	1.88691i
$482$	−15.7101			−0.715577
$483$		0			0
$484$	−10.5678			−0.480355
$485$	−4.44489	+	9.73296i	−0.201832	+	0.441951i
$486$		0			0
$487$	21.3216	+	24.6065i	0.966175	+	1.11503i	0.993320	+	0.115394i	$0.0368131\pi$
$487$	21.3216	+	24.6065i	0.966175	+	1.11503i	−0.0271447	+	0.999632i	$0.508641\pi$
$488$	0.188830	−	0.121354i	0.00854793	−	0.00549342i
$489$		0			0
$490$	0.968504	−	6.73610i	0.0437526	−	0.304306i
$491$	−34.6555	+	10.1758i	−1.56398	+	0.459226i	−0.945242	−	0.326371i	$-0.894174\pi$
$491$	−34.6555	+	10.1758i	−1.56398	+	0.459226i	−0.618738	+	0.785597i	$0.712356\pi$
$492$		0			0
$493$	−0.0825406	−	0.574083i	−0.00371744	−	0.0258554i
$494$	−16.6208	−	36.3946i	−0.747807	−	1.63747i
$495$		0			0
$496$	0.219732	+	1.52827i	0.00986628	+	0.0686215i
$497$	4.66490	+	2.99795i	0.209249	+	0.134476i
$498$		0			0
$499$	1.81329	−	12.6117i	0.0811741	−	0.564578i	−0.908127	−	0.418694i	$-0.862488\pi$
$499$	1.81329	−	12.6117i	0.0811741	−	0.564578i	0.989302	−	0.145885i	$-0.0466028\pi$
$500$	6.28214	−	7.24998i	0.280946	−	0.324229i
$501$		0			0
$502$	6.23908	+	7.20029i	0.278464	+	0.321364i
$503$	3.93372	+	1.15504i	0.175396	+	0.0515008i	0.368251	−	0.929726i	$-0.379957\pi$
$503$	3.93372	+	1.15504i	0.175396	+	0.0515008i	−0.192855	+	0.981227i	$0.561775\pi$
$504$		0			0
$505$	−0.667594			−0.0297075
$506$	2.45314	+	1.98056i	0.109055	+	0.0880465i
$507$		0			0
$508$	5.76874	−	12.6318i	0.255947	−	0.560445i
$509$	9.70155	+	2.84863i	0.430014	+	0.126263i	0.489575	−	0.871961i	$-0.337152\pi$
$509$	9.70155	+	2.84863i	0.430014	+	0.126263i	−0.0595612	+	0.998225i	$0.518970\pi$
$510$		0			0
$511$	3.03128	−	1.94809i	0.134096	−	0.0861783i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$		0			0
$514$	6.38876	−	1.87591i	0.281796	−	0.0827428i
$515$	−7.85419	−	5.04758i	−0.346097	−	0.222423i
$516$		0			0
$517$	−2.14273	−	4.69192i	−0.0942370	−	0.206350i
$518$	2.63271	+	5.76482i	0.115674	+	0.253292i
$519$		0			0
$520$	5.67565	+	3.64752i	0.248894	+	0.159954i
$521$	3.05291	−	0.896415i	0.133750	−	0.0392727i	−0.214172	−	0.976796i	$-0.568705\pi$
$521$	3.05291	−	0.896415i	0.133750	−	0.0392727i	0.347923	+	0.937523i	$0.386887\pi$
$522$		0			0
$523$	−8.72675	+	10.0712i	−0.381594	+	0.440383i	−0.913758	−	0.406258i	$-0.866833\pi$
$523$	−8.72675	+	10.0712i	−0.381594	+	0.440383i	0.532164	+	0.846641i	$0.321379\pi$
$524$	−8.01068	+	5.14815i	−0.349948	+	0.224898i
$525$		0			0
$526$	−11.3163	−	3.32276i	−0.493413	−	0.144879i
$527$	3.65204	−	7.99685i	0.159085	−	0.348348i
$528$		0			0
$529$	4.84799	+	22.4833i	0.210782	+	0.977533i
$530$	5.17631			0.224845
$531$		0			0
$532$	−5.34779	−	1.57025i	−0.231856	−	0.0680791i
$533$	24.7428	+	28.5547i	1.07173	+	1.23684i
$534$		0			0
$535$	−12.8317	+	14.8086i	−0.554764	+	0.640232i
$536$	−0.337882	+	2.35002i	−0.0145943	+	0.101506i
$537$		0			0
$538$	−9.72906	−	6.25249i	−0.419449	−	0.269564i
$539$	−0.585127	−	4.06965i	−0.0252032	−	0.175292i
$540$		0			0
$541$	−16.2344	−	35.5484i	−0.697972	−	1.52834i	−0.842414	−	0.538831i	$-0.818866\pi$
$541$	−16.2344	−	35.5484i	−0.697972	−	1.52834i	0.144442	−	0.989513i	$-0.453861\pi$
$542$	3.62448	+	25.2088i	0.155685	+	1.08281i
$543$		0			0
$544$	5.46325	−	1.60416i	0.234235	−	0.0687776i
$545$	1.49280	−	10.3827i	0.0639447	−	0.444745i
$546$		0			0
$547$	28.2157	−	18.1331i	1.20641	−	0.775316i	0.226360	−	0.974044i	$-0.427317\pi$
$547$	28.2157	−	18.1331i	1.20641	−	0.775316i	0.980055	+	0.198728i	$0.0636810\pi$
$548$	0.240231	+	0.277241i	0.0102621	+	0.0118432i
$549$		0			0
$550$	1.04213	−	2.28194i	0.0444365	−	0.0973023i
$551$	0.657327			0.0280031
$552$		0			0
$553$	14.6825			0.624362
$554$	10.7481	−	23.5351i	0.456644	−	0.999910i
$555$		0			0
$556$	−0.737752	−	0.851411i	−0.0312877	−	0.0361079i
$557$	29.5067	−	18.9628i	1.25024	−	0.803479i	0.263321	−	0.964708i	$-0.415182\pi$
$557$	29.5067	−	18.9628i	1.25024	−	0.803479i	0.986917	+	0.161229i	$0.0515459\pi$
$558$		0			0
$559$	4.74344	−	32.9913i	0.200626	−	1.39538i
$560$	0.901763	−	0.264782i	0.0381064	−	0.0111891i
$561$		0			0
$562$	4.06240	+	28.2546i	0.171362	+	1.19185i
$563$	−3.54063	−	7.75289i	−0.149220	−	0.326745i	0.820231	−	0.572033i	$-0.193845\pi$
$563$	−3.54063	−	7.75289i	−0.149220	−	0.326745i	−0.969450	+	0.245287i	$0.921118\pi$
$564$		0			0
$565$	−1.49767	−	10.4165i	−0.0630074	−	0.438226i
$566$	−0.161975	−	0.104095i	−0.00680831	−	0.00437544i
$567$		0			0
$568$	0.913705	−	6.35496i	0.0383382	−	0.266648i
$569$	13.8821	−	16.0208i	0.581969	−	0.671628i	−0.386058	−	0.922474i	$-0.626164\pi$
$569$	13.8821	−	16.0208i	0.581969	−	0.671628i	0.968027	+	0.250847i	$0.0807091\pi$
$570$		0			0
$571$	−22.8730	−	26.3969i	−0.957205	−	1.10467i	−0.994433	−	0.105367i	$-0.966398\pi$
$571$	−22.8730	−	26.3969i	−0.957205	−	1.10467i	0.0372279	−	0.999307i	$-0.488147\pi$
$572$	3.91093	+	1.14835i	0.163524	+	0.0480150i
$573$		0			0
$574$	5.26333			0.219687
$575$	16.3722	−	8.17669i	0.682769	−	0.340991i
$576$		0			0
$577$	−4.98009	+	10.9049i	−0.207324	+	0.453976i	−0.984518	−	0.175285i	$-0.943915\pi$
$577$	−4.98009	+	10.9049i	−0.207324	+	0.453976i	0.777194	+	0.629261i	$0.216643\pi$
$578$	−14.7958	−	4.34444i	−0.615424	−	0.180705i
$579$		0			0
$580$	−0.0932451	+	0.0599250i	−0.00387179	+	0.00248825i
$581$	9.61162	−	11.0924i	0.398757	−	0.460190i
$582$		0			0
$583$	3.00062	−	0.881061i	0.124273	−	0.0364898i
$584$	−3.50968	−	2.25553i	−0.145231	−	0.0933346i
$585$		0			0
$586$	−11.0962	−	24.2972i	−0.458378	−	1.00371i
$587$	−16.2017	−	35.4768i	−0.668716	−	1.46428i	−0.874171	−	0.485618i	$-0.838595\pi$
$587$	−16.2017	−	35.4768i	−0.668716	−	1.46428i	0.205455	−	0.978667i	$-0.434133\pi$
$588$		0			0
$589$	8.38193	+	5.38674i	0.345371	+	0.221957i
$590$	5.93445	−	1.74251i	0.244317	−	0.0717380i
$591$		0			0
$592$	4.80518	−	5.54547i	0.197492	−	0.227917i
$593$	−27.1792	+	17.4670i	−1.11611	+	0.717283i	−0.962617	−	0.270866i	$-0.912690\pi$
$593$	−27.1792	+	17.4670i	−1.11611	+	0.717283i	−0.153497	+	0.988149i	$0.549054\pi$
$594$		0			0
$595$	−5.13454	−	1.50764i	−0.210496	−	0.0618071i
$596$	−5.69873	+	12.4785i	−0.233429	+	0.511138i
$597$		0			0
$598$	16.9360	+	24.4401i	0.692565	+	0.999428i
$599$	−15.1294			−0.618171			−0.309085	−	0.951034i	$-0.600023\pi$
$599$	−15.1294			−0.618171			−0.309085	+	0.951034i	$0.600023\pi$
$600$		0			0
$601$	27.0476	+	7.94190i	1.10330	+	0.323957i	0.782161	−	0.623077i	$-0.214118\pi$
$601$	27.0476	+	7.94190i	1.10330	+	0.323957i	0.321135	+	0.947033i	$0.395936\pi$
$602$	−3.04056	−	3.50899i	−0.123924	−	0.143016i
$603$		0			0
$604$	4.14437	−	4.78286i	0.168632	−	0.194612i
$605$	1.63654	−	11.3824i	0.0665347	−	0.462759i
$606$		0			0
$607$	−12.5932	−	8.09317i	−0.511143	−	0.328492i	0.259517	−	0.965739i	$-0.416437\pi$
$607$	−12.5932	−	8.09317i	−0.511143	−	0.328492i	−0.770660	+	0.637247i	$0.780073\pi$
$608$	0.918382	+	6.38749i	0.0372453	+	0.259047i
$609$		0			0
$610$	0.101465	+	0.222178i	0.00410821	+	0.00899572i
$611$	−6.92298	−	48.1504i	−0.280074	−	1.94796i
$612$		0			0
$613$	−22.3230	+	6.55461i	−0.901616	+	0.264738i	−0.699508	−	0.714625i	$-0.746597\pi$
$613$	−22.3230	+	6.55461i	−0.901616	+	0.264738i	−0.202108	+	0.979363i	$0.564779\pi$
$614$	−1.29544	+	9.00997i	−0.0522796	+	0.363613i
$615$		0			0
$616$	0.477668	−	0.306979i	0.0192458	−	0.0123685i
$617$	2.29440	+	2.64788i	0.0923690	+	0.106600i	0.800052	−	0.599930i	$-0.204805\pi$
$617$	2.29440	+	2.64788i	0.0923690	+	0.106600i	−0.707683	+	0.706530i	$0.750260\pi$
$618$		0			0
$619$	9.37133	−	20.5203i	0.376665	−	0.824782i	−0.622447	−	0.782662i	$-0.713861\pi$
$619$	9.37133	−	20.5203i	0.376665	−	0.824782i	0.999113	−	0.0421203i	$-0.0134113\pi$
$620$	−1.68010			−0.0674744
$621$		0			0
$622$	10.5193			0.421786
$623$	1.81622	−	3.97697i	0.0727654	−	0.159334i
$624$		0			0
$625$	−5.65852	−	6.53028i	−0.226341	−	0.261211i
$626$	9.30661	−	5.98100i	0.371967	−	0.239049i
$627$		0			0
$628$	−1.68332	+	11.7077i	−0.0671716	+	0.467189i
$629$	−40.0878	+	11.7708i	−1.59840	+	0.469334i
$630$		0			0
$631$	1.88999	+	13.1451i	0.0752392	+	0.523300i	0.992232	+	0.124397i	$0.0396997\pi$
$631$	1.88999	+	13.1451i	0.0752392	+	0.523300i	−0.916993	+	0.398903i	$0.869391\pi$
$632$	−7.06190	−	15.4634i	−0.280907	−	0.615102i
$633$		0			0
$634$	−1.91158	−	13.2953i	−0.0759184	−	0.528024i
$635$	12.7121	+	8.16957i	0.504464	+	0.324199i
$636$		0			0
$637$	5.51834	−	38.3809i	0.218645	−	1.52071i
$638$	−0.0438528	+	0.0506088i	−0.00173615	+	0.00200362i
$639$		0			0
$640$	−0.712591	−	0.822373i	−0.0281676	−	0.0325072i
$641$	−21.0906	−	6.19275i	−0.833028	−	0.244599i	−0.162711	−	0.986674i	$-0.552024\pi$
$641$	−21.0906	−	6.19275i	−0.833028	−	0.244599i	−0.670317	+	0.742075i	$0.733842\pi$
$642$		0			0
$643$	28.4536			1.12210			0.561049	−	0.827782i	$-0.310398\pi$
$643$	28.4536			1.12210			0.561049	+	0.827782i	$0.310398\pi$
$644$	4.11799	+	0.446530i	0.162271	+	0.0175957i
$645$		0			0
$646$	15.2639	−	33.4232i	0.600549	−	1.31502i
$647$	−4.65843	−	1.36784i	−0.183142	−	0.0537753i	0.188876	−	0.982001i	$-0.439516\pi$
$647$	−4.65843	−	1.36784i	−0.183142	−	0.0537753i	−0.372018	+	0.928226i	$0.621334\pi$
$648$		0			0
$649$	3.14350	−	2.02021i	0.123393	−	0.0793001i
$650$	15.4934	−	17.8803i	0.607700	−	0.701323i
$651$		0			0
$652$	−5.25617	+	1.54335i	−0.205847	+	0.0604422i
$653$	−22.6323	−	14.5449i	−0.885671	−	0.569186i	0.0168378	−	0.999858i	$-0.494640\pi$
$653$	−22.6323	−	14.5449i	−0.885671	−	0.569186i	−0.902508	+	0.430672i	$0.858276\pi$
$654$		0			0
$655$	−4.30443	−	9.42539i	−0.168188	−	0.368281i
$656$	−2.53153	−	5.54328i	−0.0988397	−	0.216429i
$657$		0			0
$658$	−5.70074	−	3.66364i	−0.222238	−	0.142824i
$659$	−13.5039	+	3.96509i	−0.526036	+	0.154458i	−0.533959	−	0.845511i	$-0.679296\pi$
$659$	−13.5039	+	3.96509i	−0.526036	+	0.154458i	0.00792281	+	0.999969i	$0.497478\pi$
$660$		0			0
$661$	−5.51044	+	6.35939i	−0.214331	+	0.247352i	−0.852727	−	0.522357i	$-0.825053\pi$
$661$	−5.51044	+	6.35939i	−0.214331	+	0.247352i	0.638396	+	0.769708i	$0.279598\pi$
$662$	16.9426	−	10.8883i	0.658493	−	0.423188i
$663$		0			0
$664$	−16.3053	−	4.78768i	−0.632770	−	0.185798i
$665$	2.51945	−	5.51683i	0.0977001	−	0.213933i
$666$		0			0
$667$	−0.480826	+	0.0862977i	−0.0186176	+	0.00334146i
$668$	14.4648			0.559660
$669$		0			0
$670$	−2.47884	−	0.727853i	−0.0957659	−	0.0281194i
$671$	0.0966346	+	0.111522i	0.00373054	+	0.00430527i
$672$		0			0
$673$	−10.1454	+	11.7084i	−0.391075	+	0.451325i	−0.916810	−	0.399323i	$-0.869245\pi$
$673$	−10.1454	+	11.7084i	−0.391075	+	0.451325i	0.525735	+	0.850649i	$0.323791\pi$
$674$	−0.554658	+	3.85773i	−0.0213646	+	0.148594i
$675$		0			0
$676$	21.4024	+	13.7545i	0.823170	+	0.529019i
$677$	1.84571	+	12.8372i	0.0709364	+	0.493374i	0.994057	+	0.108863i	$0.0347209\pi$
$677$	1.84571	+	12.8372i	0.0709364	+	0.493374i	−0.923120	+	0.384511i	$0.874370\pi$
$678$		0			0
$679$	3.52801	+	7.72526i	0.135393	+	0.296468i
$680$	0.881761	+	6.13278i	0.0338140	+	0.235181i
$681$		0			0
$682$	−0.973925	+	0.285970i	−0.0372935	+	0.0109504i
$683$	0.117099	−	0.814439i	0.00448066	−	0.0311637i	−0.987458	−	0.157879i	$-0.949534\pi$
$683$	0.117099	−	0.814439i	0.00448066	−	0.0311637i	0.991939	+	0.126715i	$0.0404435\pi$
$684$		0			0
$685$	−0.335813	+	0.215814i	−0.0128308	+	0.00824583i
$686$	−7.49647	−	8.65138i	−0.286216	−	0.330311i
$687$		0			0
$688$	−2.23320	+	4.89002i	−0.0851398	+	0.186430i
$689$	29.4936			1.12362
$690$		0			0
$691$	−10.6220			−0.404079			−0.202039	−	0.979377i	$-0.564757\pi$
$691$	−10.6220			−0.404079			−0.202039	+	0.979377i	$0.564757\pi$
$692$	3.40568	−	7.45740i	0.129465	−	0.283488i
$693$		0			0
$694$	3.25071	+	3.75152i	0.123395	+	0.142406i
$695$	1.03129	−	0.662768i	0.0391189	−	0.0251402i
$696$		0			0
$697$	−4.93811	+	34.3453i	−0.187044	+	1.30092i
$698$	15.2089	−	4.46574i	0.575665	−	0.169031i
$699$		0			0
$700$	−0.469039	−	3.26224i	−0.0177280	−	0.123301i
$701$	5.89812	+	12.9151i	0.222769	+	0.487796i	0.987709	−	0.156306i	$-0.0499586\pi$
$701$	5.89812	+	12.9151i	0.222769	+	0.487796i	−0.764940	+	0.644102i	$0.777231\pi$
$702$		0			0
$703$	−6.73882	−	46.8695i	−0.254159	−	1.76772i
$704$	−0.553053	−	0.355426i	−0.0208440	−	0.0133956i
$705$		0			0
$706$	−3.32452	+	23.1226i	−0.125120	+	0.870229i
$707$	−0.347000	+	0.400459i	−0.0130503	+	0.0150608i
$708$		0			0
$709$	0.577037	+	0.665936i	0.0216711	+	0.0250098i	0.766482	−	0.642266i	$-0.222006\pi$
$709$	0.577037	+	0.665936i	0.0216711	+	0.0250098i	−0.744811	+	0.667276i	$0.767460\pi$
$710$	6.70330	+	1.96827i	0.251570	+	0.0738677i
$711$		0			0
$712$	−5.06206			−0.189709
$713$	−6.83847	−	2.83990i	−0.256103	−	0.106355i
$714$		0			0
$715$	−1.84251	+	4.03455i	−0.0689062	+	0.150883i
$716$	−16.2016	−	4.75721i	−0.605481	−	0.177785i
$717$		0			0
$718$	9.30096	−	5.97736i	0.347109	−	0.223073i
$719$	−19.8875	+	22.9514i	−0.741678	+	0.855942i	−0.993734	−	0.111770i	$-0.964348\pi$
$719$	−19.8875	+	22.9514i	−0.741678	+	0.855942i	0.252056	+	0.967713i	$0.418893\pi$
$720$		0			0
$721$	−7.11025	+	2.08776i	−0.264800	+	0.0777522i
$722$	19.0488	+	12.2419i	0.708925	+	0.455598i
$723$		0			0
$724$	6.92512	+	15.1639i	0.257370	+	0.563562i
$725$	0.161469	+	0.353568i	0.00599681	+	0.0131312i
$726$		0			0
$727$	−18.2448	−	11.7252i	−0.676661	−	0.434864i	0.156660	−	0.987653i	$-0.449927\pi$
$727$	−18.2448	−	11.7252i	−0.676661	−	0.434864i	−0.833321	+	0.552789i	$0.813564\pi$
$728$	5.13806	−	1.50867i	0.190429	−	0.0559151i
$729$		0			0
$730$	2.97290	−	3.43091i	0.110032	−	0.126984i
$731$	25.7502	−	16.5487i	0.952407	−	0.612075i
$732$		0			0
$733$	14.3151	+	4.20328i	0.528739	+	0.155252i	0.535197	−	0.844727i	$-0.320237\pi$
$733$	14.3151	+	4.20328i	0.528739	+	0.155252i	−0.00645790	+	0.999979i	$0.502056\pi$
$734$	−11.0474	+	24.1904i	−0.407766	+	0.892884i
$735$		0			0
$736$	−1.51037	−	4.55179i	−0.0556730	−	0.167781i
$737$	−1.56083			−0.0574938
$738$		0			0
$739$	−26.5313	−	7.79029i	−0.975969	−	0.286570i	−0.245410	−	0.969419i	$-0.578922\pi$
$739$	−26.5313	−	7.79029i	−0.975969	−	0.286570i	−0.730559	+	0.682849i	$0.760741\pi$
$740$	5.22878	+	6.03434i	0.192214	+	0.221827i
$741$		0			0
$742$	2.69053	−	3.10504i	0.0987725	−	0.113989i
$743$	−1.62071	+	11.2723i	−0.0594581	+	0.413540i	0.938255	+	0.345945i	$0.112442\pi$
$743$	−1.62071	+	11.2723i	−0.0594581	+	0.413540i	−0.997713	+	0.0675949i	$0.978467\pi$
$744$		0			0
$745$	−12.5578	−	8.07041i	−0.460083	−	0.295677i
$746$	1.96260	+	13.6502i	0.0718561	+	0.499770i
$747$		0			0
$748$	1.55500	+	3.40498i	0.0568566	+	0.124498i
$749$	2.21337	+	15.3944i	0.0808749	+	0.562497i
$750$		0			0
$751$	−43.0680	+	12.6459i	−1.57157	+	0.461456i	−0.947459	−	0.319876i	$-0.896359\pi$
$751$	−43.0680	+	12.6459i	−1.57157	+	0.461456i	−0.624115	+	0.781332i	$0.714541\pi$
$752$	−1.11659	+	7.76608i	−0.0407180	+	0.283200i
$753$		0			0
$754$	−0.531292	+	0.341440i	−0.0193485	+	0.0124345i
$755$	4.50972	+	5.20450i	0.164126	+	0.189411i
$756$		0			0
$757$	7.13329	−	15.6197i	0.259264	−	0.567709i	−0.734577	−	0.678525i	$-0.762619\pi$
$757$	7.13329	−	15.6197i	0.259264	−	0.567709i	0.993841	+	0.110817i	$0.0353466\pi$
$758$	−4.10337			−0.149041
$759$		0			0
$760$	−7.02206			−0.254717
$761$	−3.02266	+	6.61871i	−0.109571	+	0.239928i	−0.956472	−	0.291823i	$-0.905738\pi$
$761$	−3.02266	+	6.61871i	−0.109571	+	0.239928i	0.846901	+	0.531751i	$0.178466\pi$
$762$		0			0
$763$	−5.45218	−	6.29215i	−0.197382	−	0.227791i
$764$	−13.9029	+	8.93483i	−0.502988	+	0.323251i
$765$		0			0
$766$	−0.573097	+	3.98597i	−0.0207068	+	0.144019i
$767$	33.8133	−	9.92847i	1.22093	−	0.358496i
$768$		0			0
$769$	5.06208	+	35.2076i	0.182543	+	1.26962i	0.850722	+	0.525616i	$0.176165\pi$
$769$	5.06208	+	35.2076i	0.182543	+	1.26962i	−0.668178	+	0.744001i	$0.732926\pi$
$770$	0.256669	+	0.562026i	0.00924969	+	0.0202540i
$771$		0			0
$772$	1.76081	+	12.2467i	0.0633728	+	0.440767i
$773$	23.0322	+	14.8019i	0.828412	+	0.532388i	0.884773	−	0.466022i	$-0.154313\pi$
$773$	23.0322	+	14.8019i	0.828412	+	0.532388i	−0.0563607	+	0.998410i	$0.517950\pi$
$774$		0			0
$775$	−0.838481	+	5.83176i	−0.0301191	+	0.209483i
$776$	6.43927	−	7.43132i	0.231156	−	0.266769i
$777$		0			0
$778$	5.98764	+	6.91010i	0.214667	+	0.247739i
$779$	−37.7325	−	11.0793i	−1.35191	−	0.396956i
$780$		0			0
$781$	4.22081			0.151032
$782$	−6.77732	+	26.4526i	−0.242356	+	0.945941i
$783$		0			0
$784$	−2.59802	+	5.68887i	−0.0927864	+	0.203174i
$785$	−12.3495	−	3.62613i	−0.440772	−	0.129422i
$786$		0			0
$787$	−6.55158	+	4.21045i	−0.233539	+	0.150086i	−0.652177	−	0.758067i	$-0.726144\pi$
$787$	−6.55158	+	4.21045i	−0.233539	+	0.150086i	0.418638	+	0.908153i	$0.362508\pi$
$788$	−0.681278	+	0.786236i	−0.0242695	+	0.0280085i
$789$		0			0
$790$	17.7489	−	5.21156i	0.631479	−	0.185419i
$791$	−7.02685	−	4.51589i	−0.249846	−	0.160566i
$792$		0			0
$793$	0.578128	+	1.26592i	0.0205299	+	0.0449543i
$794$	−7.01256	−	15.3554i	−0.248866	−	0.544941i
$795$		0			0
$796$	9.42033	+	6.05408i	0.333895	+	0.214581i
$797$	−12.1511	+	3.56789i	−0.430415	+	0.126381i	−0.489762	−	0.871856i	$-0.662916\pi$
$797$	−12.1511	+	3.56789i	−0.430415	+	0.126381i	0.0593469	+	0.998237i	$0.481098\pi$
$798$		0			0
$799$	29.2552	−	33.7623i	1.03497	−	1.19442i
$800$	−3.21015	+	2.06304i	−0.113496	+	0.0729395i
$801$		0			0
$802$	26.6945	+	7.83821i	0.942616	+	0.276777i
$803$	1.13936	−	2.49486i	0.0402073	−	0.0880416i
$804$		0			0
$805$	−1.11866	+	4.36625i	−0.0394277	+	0.153890i
$806$	−9.57287			−0.337190
$807$		0			0
$808$	0.588658	+	0.172846i	0.0207089	+	0.00608068i
$809$	−14.0347	−	16.1969i	−0.493435	−	0.569454i	0.453345	−	0.891335i	$-0.350230\pi$
$809$	−14.0347	−	16.1969i	−0.493435	−	0.569454i	−0.946780	+	0.321881i	$0.895685\pi$
$810$		0			0
$811$	−10.3951	+	11.9966i	−0.365022	+	0.421258i	−0.908316	−	0.418285i	$-0.862631\pi$
$811$	−10.3951	+	11.9966i	−0.365022	+	0.421258i	0.543294	+	0.839543i	$0.317177\pi$
$812$	−0.0125204	+	0.0870812i	−0.000439380	+	0.00305595i
$813$		0			0
$814$	4.05814	+	2.60801i	0.142238	+	0.0914107i
$815$	−0.848337	−	5.90032i	−0.0297160	−	0.206679i
$816$		0			0
$817$	14.4112	+	31.5561i	0.504184	+	1.10401i
$818$	−1.12231	−	7.80587i	−0.0392408	−	0.272926i
$819$		0			0
$820$	6.36259	−	1.86823i	0.222191	−	0.0652413i
$821$	2.36779	−	16.4684i	0.0826366	−	0.574750i	−0.905868	−	0.423560i	$-0.860780\pi$
$821$	2.36779	−	16.4684i	0.0826366	−	0.574750i	0.988505	−	0.151190i	$-0.0483106\pi$
$822$		0			0
$823$	−31.3902	+	20.1733i	−1.09419	+	0.703196i	−0.957793	−	0.287457i	$-0.907190\pi$
$823$	−31.3902	+	20.1733i	−1.09419	+	0.703196i	−0.136402	+	0.990654i	$0.543554\pi$
$824$	5.61866	+	6.48428i	0.195735	+	0.225890i
$825$		0			0
$826$	2.03934	−	4.46552i	0.0709576	−	0.155375i
$827$	−0.531764			−0.0184913			−0.00924563	−	0.999957i	$-0.502943\pi$
$827$	−0.531764			−0.0184913			−0.00924563	+	0.999957i	$0.502943\pi$
$828$		0			0
$829$	23.5271			0.817131			0.408565	−	0.912729i	$-0.366029\pi$
$829$	23.5271			0.817131			0.408565	+	0.912729i	$0.366029\pi$
$830$	7.68177	−	16.8207i	0.266638	−	0.583856i
$831$		0			0
$832$	−4.06019	−	4.68571i	−0.140762	−	0.162448i
$833$	29.9569	−	19.2521i	1.03794	−	0.667046i
$834$		0			0
$835$	−2.24003	+	15.5797i	−0.0775194	+	0.539159i
$836$	−4.07057	+	1.19523i	−0.140783	+	0.0413377i
$837$		0			0
$838$	1.21895	+	8.47799i	0.0421080	+	0.292867i
$839$	16.6522	+	36.4632i	0.574897	+	1.25885i	0.944149	+	0.329520i	$0.106887\pi$
$839$	16.6522	+	36.4632i	0.574897	+	1.25885i	−0.369251	+	0.929330i	$0.620386\pi$
$840$		0			0
$841$	4.12565	+	28.6946i	0.142264	+	0.989467i
$842$	−20.6680	−	13.2825i	−0.712266	−	0.457746i
$843$		0			0
$844$	1.21778	−	8.46985i	0.0419177	−	0.291544i
$845$	−18.1291	+	20.9221i	−0.623660	+	0.719742i
$846$		0			0
$847$	−5.97714	−	6.89799i	−0.205377	−	0.237018i
$848$	−4.56427	−	1.34019i	−0.156738	−	0.0460223i
$849$		0			0
$850$	21.7274			0.745244
$851$	11.0827	+	33.3997i	0.379909	+	1.14493i
$852$		0			0
$853$	−4.31523	+	9.44903i	−0.147751	+	0.323529i	−0.969008	−	0.247029i	$-0.920546\pi$
$853$	−4.31523	+	9.44903i	−0.147751	+	0.323529i	0.821258	+	0.570558i	$0.193273\pi$
$854$	0.186014	+	0.0546186i	0.00636526	+	0.00186901i
$855$		0			0
$856$	15.1486	−	9.73540i	0.517768	−	0.332749i
$857$	−35.3327	+	40.7761i	−1.20694	+	1.39288i	−0.309998	+	0.950737i	$0.600328\pi$
$857$	−35.3327	+	40.7761i	−1.20694	+	1.39288i	−0.896943	+	0.442146i	$0.854217\pi$
$858$		0			0
$859$	−48.4959	+	14.2397i	−1.65466	+	0.485851i	−0.970019	−	0.243031i	$-0.921858\pi$
$859$	−48.4959	+	14.2397i	−1.65466	+	0.485851i	−0.684639	+	0.728882i	$0.740040\pi$
$860$	−4.92111	−	3.16260i	−0.167808	−	0.107844i
$861$		0			0
$862$	−0.753460	−	1.64985i	−0.0256629	−	0.0561940i
$863$	2.57261	+	5.63324i	0.0875728	+	0.191758i	0.948351	−	0.317222i	$-0.102750\pi$
$863$	2.57261	+	5.63324i	0.0875728	+	0.191758i	−0.860778	+	0.508980i	$0.830023\pi$
$864$		0			0
$865$	7.50481	+	4.82305i	0.255171	+	0.163989i
$866$	30.8896	−	9.07001i	1.04967	−	0.308211i
$867$		0			0
$868$	−0.873278	+	1.00782i	−0.0296410	+	0.0342075i
$869$	9.40170	−	6.04211i	0.318931	−	0.204964i
$870$		0			0
$871$	−14.1239	−	4.14715i	−0.478570	−	0.140521i
$872$	−4.00446	+	8.76854i	−0.135608	+	0.296940i
$873$		0			0
$874$	−28.5817	−	11.8695i	−0.966790	−	0.401491i
$875$	8.28549			0.280101
$876$		0			0
$877$	−28.8617	−	8.47457i	−0.974592	−	0.286166i	−0.244602	−	0.969624i	$-0.578657\pi$
$877$	−28.8617	−	8.47457i	−0.974592	−	0.286166i	−0.729990	+	0.683458i	$0.760475\pi$
$878$	−8.57558	−	9.89674i	−0.289412	−	0.333999i
$879$		0			0
$880$	0.468468	−	0.540641i	0.0157921	−	0.0182250i
$881$	2.42250	−	16.8489i	0.0816162	−	0.567653i	−0.907448	−	0.420165i	$-0.861972\pi$
$881$	2.42250	−	16.8489i	0.0816162	−	0.567653i	0.989064	−	0.147488i	$-0.0471188\pi$
$882$		0			0
$883$	5.17450	+	3.32545i	0.174136	+	0.111910i	0.624805	−	0.780781i	$-0.285178\pi$
$883$	5.17450	+	3.32545i	0.174136	+	0.111910i	−0.450669	+	0.892691i	$0.648815\pi$
$884$	5.02409	+	34.9433i	0.168978	+	1.17527i
$885$		0			0
$886$	−11.4271	−	25.0218i	−0.383901	−	0.840625i
$887$	0.687735	+	4.78330i	0.0230919	+	0.160608i	0.998104	−	0.0615419i	$-0.0196018\pi$
$887$	0.687735	+	4.78330i	0.0230919	+	0.160608i	−0.975013	+	0.222149i	$0.928693\pi$
$888$		0			0
$889$	11.5080	−	3.37906i	0.385966	−	0.113330i
$890$	0.783914	−	5.45224i	0.0262769	−	0.182760i
$891$		0			0
$892$	−0.419633	+	0.269682i	−0.0140504	+	0.00902961i
$893$	33.1564	+	38.2645i	1.10954	+	1.28047i
$894$		0			0
$895$	7.63288	−	16.7137i	0.255139	−	0.558677i
$896$	−0.863693			−0.0288540
$897$		0			0
$898$	30.1186			1.00507
$899$	0.0653333	−	0.143060i	0.00217899	−	0.00477132i
$900$		0			0
$901$	17.7373	+	20.4699i	0.590915	+	0.681953i
$902$	3.37030	−	2.16596i	0.112219	−	0.0721185i
$903$		0			0
$904$	−1.37634	+	9.57263i	−0.0457763	+	0.318381i
$905$	−17.4052	+	5.11062i	−0.578567	+	0.169883i
$906$		0			0
$907$	−3.79740	−	26.4115i	−0.126091	−	0.876980i	−0.950442	−	0.310902i	$-0.899369\pi$
$907$	−3.79740	−	26.4115i	−0.126091	−	0.876980i	0.824351	−	0.566078i	$-0.191540\pi$
$908$	8.74425	+	19.1472i	0.290188	+	0.635423i
$909$		0			0
$910$	0.829275	+	5.76774i	0.0274902	+	0.191199i
$911$	−50.0899	−	32.1908i	−1.65955	−	1.06653i	−0.918779	−	0.394771i	$-0.870824\pi$
$911$	−50.0899	−	32.1908i	−1.65955	−	1.06653i	−0.740771	−	0.671757i	$-0.765540\pi$
$912$		0			0
$913$	1.58993	−	11.0582i	0.0526190	−	0.365973i
$914$	−12.3221	+	14.2204i	−0.407577	+	0.470369i
$915$		0			0
$916$	−0.658970	−	0.760492i	−0.0217730	−	0.0251274i
$917$	−7.89122	−	2.31707i	−0.260591	−	0.0765164i
$918$		0			0
$919$	−25.3496			−0.836206			−0.418103	−	0.908400i	$-0.637305\pi$
$919$	−25.3496			−0.836206			−0.418103	+	0.908400i	$0.637305\pi$
$920$	5.13654	−	0.921896i	0.169347	−	0.0303940i
$921$		0			0
$922$	−3.41269	+	7.47276i	−0.112391	+	0.246102i
$923$	38.1940	+	11.2148i	1.25717	+	0.369139i
$924$		0			0
$925$	23.5552	−	15.1380i	0.774489	−	0.497734i
$926$	24.6629	−	28.4625i	0.810473	−	0.935336i
$927$		0			0
$928$	0.0977350	−	0.0286976i	0.00320831	−	0.000942044i
$929$	34.2348	+	22.0014i	1.12321	+	0.721841i	0.964131	−	0.265425i	$-0.0855124\pi$
$929$	34.2348	+	22.0014i	1.12321	+	0.721841i	0.159075	+	0.987266i	$0.449149\pi$
$930$		0			0
$931$	16.7655	+	36.7112i	0.549466	+	1.20316i
$932$	−6.40470	−	14.0243i	−0.209793	−	0.459383i
$933$		0			0
$934$	3.73902	+	2.40292i	0.122344	+	0.0786259i
$935$	−3.90825	+	1.14757i	−0.127813	+	0.0375294i
$936$		0			0
$937$	−10.1247	+	11.6846i	−0.330761	+	0.381718i	−0.896633	−	0.442775i	$-0.853994\pi$
$937$	−10.1247	+	11.6846i	−0.330761	+	0.381718i	0.565872	+	0.824493i	$0.308540\pi$
$938$	−1.72505	+	1.10862i	−0.0563249	+	0.0361978i
$939$		0			0
$940$	−8.19177	−	2.40532i	−0.267186	−	0.0784529i
$941$	−4.61138	+	10.0975i	−0.150327	+	0.329170i	−0.969782	−	0.243974i	$-0.921549\pi$
$941$	−4.61138	+	10.0975i	−0.150327	+	0.329170i	0.819455	+	0.573143i	$0.194276\pi$
$942$		0			0
$943$	29.0554	+	3.15059i	0.946174	+	0.102597i
$944$	−5.68391			−0.184996
$945$		0			0
$946$	−3.39099	−	0.995684i	−0.110251	−	0.0323725i
$947$	21.5963	+	24.9235i	0.701786	+	0.809904i	0.988993	−	0.147964i	$-0.0472721\pi$
$947$	21.5963	+	24.9235i	0.701786	+	0.809904i	−0.287207	+	0.957869i	$0.592727\pi$
$948$		0			0
$949$	16.9390	−	19.5486i	0.549862	−	0.634575i
$950$	−3.50447	+	24.3741i	−0.113700	+	0.790801i
$951$		0			0
$952$	4.13710	+	2.65875i	0.134084	+	0.0861706i
$953$	−1.21805	−	8.47175i	−0.0394566	−	0.274427i	0.960536	−	0.278154i	$-0.0897226\pi$
$953$	−1.21805	−	8.47175i	−0.0394566	−	0.274427i	−0.999993	+	0.00372731i	$0.998814\pi$
$954$		0			0
$955$	−7.47052	−	16.3581i	−0.241740	−	0.529337i
$956$	−0.598609	−	4.16341i	−0.0193604	−	0.134654i
$957$		0			0
$958$	−27.5346	+	8.08488i	−0.889601	+	0.261210i
$959$	−0.0450910	+	0.313614i	−0.00145606	+	0.0101271i
$960$		0			0
$961$	−24.0734	+	15.4710i	−0.776561	+	0.499066i
$962$	29.7925	+	34.3824i	0.960550	+	1.10853i
$963$		0			0
$964$	−6.52623	+	14.2904i	−0.210196	+	0.460264i
$965$	−13.4633			−0.433400
$966$		0			0
$967$	−11.0128			−0.354148			−0.177074	−	0.984197i	$-0.556663\pi$
$967$	−11.0128			−0.354148			−0.177074	+	0.984197i	$0.556663\pi$
$968$	−4.39002	+	9.61281i	−0.141101	+	0.308968i
$969$		0			0
$970$	7.00693	+	8.08643i	0.224979	+	0.259640i
$971$	−33.4884	+	21.5217i	−1.07469	+	0.690664i	−0.953326	−	0.301943i	$-0.902365\pi$
$971$	−33.4884	+	21.5217i	−1.07469	+	0.690664i	−0.121369	+	0.992608i	$0.538728\pi$
$972$		0			0
$973$	0.138475	−	0.963114i	0.00443930	−	0.0308760i
$974$	31.2402	−	9.17294i	1.00100	−	0.293920i
$975$		0			0
$976$	−0.0319444	−	0.222178i	−0.00102251	−	0.00711174i
$977$	−23.1477	−	50.6865i	−0.740561	−	1.62160i	−0.782629	−	0.622489i	$-0.786122\pi$
$977$	−23.1477	−	50.6865i	−0.740561	−	1.62160i	0.0420673	−	0.999115i	$-0.486606\pi$
$978$		0			0
$979$	−0.473606	−	3.29400i	−0.0151365	−	0.105277i
$980$	−5.72504	−	3.67926i	−0.182880	−	0.117530i
$981$		0			0
$982$	−5.14020	+	35.7509i	−0.164030	+	1.14086i
$983$	−4.77814	+	5.51427i	−0.152399	+	0.175878i	−0.826815	−	0.562473i	$-0.809850\pi$
$983$	−4.77814	+	5.51427i	−0.152399	+	0.175878i	0.674416	+	0.738351i	$0.264395\pi$
$984$		0			0
$985$	−0.741336	−	0.855548i	−0.0236209	−	0.0272600i
$986$	−0.556493	−	0.163401i	−0.0177223	−	0.00520375i
$987$		0			0
$988$	−40.0102			−1.27289
$989$	−14.6845	−	21.1909i	−0.466939	−	0.673831i
$990$		0			0
$991$	16.1987	−	35.4701i	0.514567	−	1.12675i	−0.456888	−	0.889524i	$-0.651036\pi$
$991$	16.1987	−	35.4701i	0.514567	−	1.12675i	0.971456	−	0.237221i	$-0.0762366\pi$
$992$	1.48145	+	0.434992i	0.0470360	+	0.0138110i
$993$		0			0
$994$	4.66490	−	2.99795i	0.147962	−	0.0950891i
$995$	−7.97956	+	9.20891i	−0.252969	+	0.291942i
$996$		0			0
$997$	−3.25601	+	0.956050i	−0.103119	+	0.0302784i	−0.332885	−	0.942967i	$-0.608022\pi$
$997$	−3.25601	+	0.956050i	−0.103119	+	0.0302784i	0.229766	+	0.973246i	$0.426204\pi$
$998$	−10.7188	−	6.88853i	−0.339296	−	0.218053i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.c.397.1		10
3.2	odd	2		46.2.c.b.29.1	yes	10
12.11	even	2		368.2.m.a.305.1		10
23.2	even	11		9522.2.a.bz.1.4		5
23.4	even	11	inner	414.2.i.c.73.1		10
23.21	odd	22		9522.2.a.bw.1.2		5
69.2	odd	22		1058.2.a.j.1.2		5
69.44	even	22		1058.2.a.k.1.2		5
69.50	odd	22		46.2.c.b.27.1	✓	10
276.71	even	22		8464.2.a.bu.1.4		5
276.119	even	22		368.2.m.a.257.1		10
276.251	odd	22		8464.2.a.bv.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.2.c.b.27.1	✓	10	69.50	odd	22
46.2.c.b.29.1	yes	10	3.2	odd	2
368.2.m.a.257.1		10	276.119	even	22
368.2.m.a.305.1		10	12.11	even	2
414.2.i.c.73.1		10	23.4	even	11	inner
414.2.i.c.397.1		10	1.1	even	1	trivial
1058.2.a.j.1.2		5	69.2	odd	22
1058.2.a.k.1.2		5	69.44	even	22
8464.2.a.bu.1.4		5	276.71	even	22
8464.2.a.bv.1.4		5	276.251	odd	22
9522.2.a.bw.1.2		5	23.21	odd	22
9522.2.a.bz.1.4		5	23.2	even	11

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{2} +(-0.654861 - 0.755750i) q^{4} +(0.915415 - 0.588302i) q^{5} +(0.122916 - 0.854902i) q^{7} +(-0.959493 + 0.281733i) q^{8} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{2} +(-0.654861 - 0.755750i) q^{4} +(0.915415 - 0.588302i) q^{5} +(0.122916 - 0.854902i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.154861 - 1.07708i) q^{10} +(-0.273100 - 0.598006i) q^{11} +(-0.882365 - 6.13698i) q^{13} +(-0.726585 - 0.466948i) q^{14} +(-0.142315 + 0.989821i) q^{16} +(3.72871 - 4.30316i) q^{17} +(4.22593 + 4.87698i) q^{19} +(-1.04408 - 0.306569i) q^{20} -0.657415 q^{22} +(-3.73149 - 3.01264i) q^{23} +(-1.58519 + 3.47108i) q^{25} +(-5.94894 - 1.74677i) q^{26} +(-0.726585 + 0.466948i) q^{28} +(0.0667048 - 0.0769815i) q^{29} +(1.48145 - 0.434992i) q^{31} +(0.841254 + 0.540641i) q^{32} +(-2.36533 - 5.17935i) q^{34} +(-0.390421 - 0.854902i) q^{35} +(-6.17287 - 3.96707i) q^{37} +(6.19177 - 1.81807i) q^{38} +(-0.712591 + 0.822373i) q^{40} +(-5.12658 + 3.29466i) q^{41} +(5.15806 + 1.51454i) q^{43} +(-0.273100 + 0.598006i) q^{44} +(-4.29051 + 2.14278i) q^{46} +7.84594 q^{47} +(6.00070 + 1.76196i) q^{49} +(2.49889 + 2.88388i) q^{50} +(-4.06019 + 4.68571i) q^{52} +(-0.676986 + 4.70854i) q^{53} +(-0.601808 - 0.386758i) q^{55} +(0.122916 + 0.854902i) q^{56} +(-0.0423146 - 0.0926561i) q^{58} +(0.808905 + 5.62606i) q^{59} +(-0.215370 + 0.0632384i) q^{61} +(0.219732 - 1.52827i) q^{62} +(0.841254 - 0.540641i) q^{64} +(-4.41813 - 5.09879i) q^{65} +(0.986274 - 2.15964i) q^{67} -5.69389 q^{68} -0.939833 q^{70} +(-2.66709 + 5.84012i) q^{71} +(2.73205 + 3.15296i) q^{73} +(-6.17287 + 3.96707i) q^{74} +(0.918382 - 6.38749i) q^{76} +(-0.544805 + 0.159969i) q^{77} +(2.41930 + 16.8266i) q^{79} +(0.452036 + 0.989821i) q^{80} +(0.867264 + 6.03196i) q^{82} +(14.2960 + 9.18749i) q^{83} +(0.881761 - 6.13278i) q^{85} +(3.52041 - 4.06278i) q^{86} +(0.430515 + 0.496841i) q^{88} +(4.85701 + 1.42615i) q^{89} -5.35498 q^{91} +(0.166803 + 4.79293i) q^{92} +(3.25932 - 7.13692i) q^{94} +(6.73761 + 1.97834i) q^{95} +(-8.27208 + 5.31614i) q^{97} +(4.09552 - 4.72648i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{4} + 4 q^{5} - 7 q^{7} - q^{8}+O(q^{10}) \) 10 * q - q^2 - q^4 + 4 * q^5 - 7 * q^7 - q^8	\( 10 q - q^{2} - q^{4} + 4 q^{5} - 7 q^{7} - q^{8} + 4 q^{10} + 2 q^{11} + 2 q^{13} + 15 q^{14} - q^{16} + 9 q^{17} + 2 q^{19} - 7 q^{20} + 2 q^{22} - 21 q^{23} - 11 q^{25} - 9 q^{26} + 15 q^{28} + 2 q^{29} + 11 q^{31} - q^{32} - 13 q^{34} + 17 q^{35} - 18 q^{37} + 13 q^{38} + 4 q^{40} - 5 q^{41} - 21 q^{43} + 2 q^{44} - 10 q^{46} + 22 q^{47} + 24 q^{49} + 22 q^{50} - 20 q^{52} + 7 q^{53} + 3 q^{55} - 7 q^{56} + 24 q^{58} - 43 q^{59} - 3 q^{61} - 33 q^{62} - q^{64} - 41 q^{65} - q^{67} - 2 q^{68} + 6 q^{70} + 11 q^{71} - 28 q^{73} - 18 q^{74} + 2 q^{76} - 30 q^{77} + 34 q^{79} - 7 q^{80} + 6 q^{82} + 3 q^{83} + 8 q^{85} + 34 q^{86} - 9 q^{88} + 49 q^{89} - 52 q^{91} + q^{92} - 11 q^{94} + 36 q^{95} + 16 q^{97} - 20 q^{98}+O(q^{100}) \) 10 * q - q^2 - q^4 + 4 * q^5 - 7 * q^7 - q^8 + 4 * q^10 + 2 * q^11 + 2 * q^13 + 15 * q^14 - q^16 + 9 * q^17 + 2 * q^19 - 7 * q^20 + 2 * q^22 - 21 * q^23 - 11 * q^25 - 9 * q^26 + 15 * q^28 + 2 * q^29 + 11 * q^31 - q^32 - 13 * q^34 + 17 * q^35 - 18 * q^37 + 13 * q^38 + 4 * q^40 - 5 * q^41 - 21 * q^43 + 2 * q^44 - 10 * q^46 + 22 * q^47 + 24 * q^49 + 22 * q^50 - 20 * q^52 + 7 * q^53 + 3 * q^55 - 7 * q^56 + 24 * q^58 - 43 * q^59 - 3 * q^61 - 33 * q^62 - q^64 - 41 * q^65 - q^67 - 2 * q^68 + 6 * q^70 + 11 * q^71 - 28 * q^73 - 18 * q^74 + 2 * q^76 - 30 * q^77 + 34 * q^79 - 7 * q^80 + 6 * q^82 + 3 * q^83 + 8 * q^85 + 34 * q^86 - 9 * q^88 + 49 * q^89 - 52 * q^91 + q^92 - 11 * q^94 + 36 * q^95 + 16 * q^97 - 20 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more