LMFDB - Embedded newform 325.2.n.e.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(101,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("325.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.n (of order $6$, degree $2$, 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:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 16x^{8} + 84x^{6} + 163x^{4} + 118x^{2} + 27 $ x^10 + 16x^8 + 84x^6 + 163x^4 + 118x^2 + 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.2
Root			$1.36551i$ of defining polynomial
Character	$\chi$	$=$	325.101
Dual form			325.2.n.e.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18257 + 0.682755i) q^{2} +(0.199959 + 0.346339i) q^{3} +(-0.0676905 + 0.117243i) q^{4} +(-0.472929 - 0.273046i) q^{6} +(-3.15550 - 1.82183i) q^{7} -2.91589i q^{8} +(1.42003 - 2.45957i) q^{9} +O(q^{10})$	\(q+(-1.18257 + 0.682755i) q^{2} +(0.199959 + 0.346339i) q^{3} +(-0.0676905 + 0.117243i) q^{4} +(-0.472929 - 0.273046i) q^{6} +(-3.15550 - 1.82183i) q^{7} -2.91589i q^{8} +(1.42003 - 2.45957i) q^{9} +(2.83806 - 1.63856i) q^{11} -0.0541412 q^{12} +(3.53491 - 0.710223i) q^{13} +4.97545 q^{14} +(1.85546 + 3.21374i) q^{16} +(-1.08781 + 1.88413i) q^{17} +3.87814i q^{18} +(-0.742787 - 0.428848i) q^{19} -1.45716i q^{21} +(-2.23747 + 3.87540i) q^{22} +(-0.382526 - 0.662554i) q^{23} +(1.00988 - 0.583057i) q^{24} +(-3.69536 + 3.25336i) q^{26} +2.33555 q^{27} +(0.427194 - 0.246641i) q^{28} +(1.53219 + 2.65382i) q^{29} -8.41833i q^{31} +(0.662062 + 0.382242i) q^{32} +(1.13499 + 0.655288i) q^{33} -2.97082i q^{34} +(0.192245 + 0.332979i) q^{36} +(9.40295 - 5.42880i) q^{37} +1.17119 q^{38} +(0.952814 + 1.08226i) q^{39} +(-6.59344 + 3.80672i) q^{41} +(0.994885 + 1.72319i) q^{42} +(1.91803 - 3.32213i) q^{43} +0.443659i q^{44} +(0.904724 + 0.522343i) q^{46} -4.68303i q^{47} +(-0.742029 + 1.28523i) q^{48} +(3.13810 + 5.43536i) q^{49} -0.870065 q^{51} +(-0.156011 + 0.462520i) q^{52} -3.04646 q^{53} +(-2.76194 + 1.59461i) q^{54} +(-5.31224 + 9.20106i) q^{56} -0.343008i q^{57} +(-3.62382 - 2.09222i) q^{58} +(-11.5378 - 6.66136i) q^{59} +(6.51531 - 11.2848i) q^{61} +(5.74766 + 9.95524i) q^{62} +(-8.96182 + 5.17411i) q^{63} -8.46573 q^{64} -1.78960 q^{66} +(4.02523 - 2.32397i) q^{67} +(-0.147268 - 0.255076i) q^{68} +(0.152979 - 0.264967i) q^{69} +(9.38392 + 5.41781i) q^{71} +(-7.17182 - 4.14065i) q^{72} +7.68313i q^{73} +(-7.41308 + 12.8398i) q^{74} +(0.100559 - 0.0580579i) q^{76} -11.9407 q^{77} +(-1.86569 - 0.629307i) q^{78} -10.2106 q^{79} +(-3.79309 - 6.56982i) q^{81} +(5.19812 - 9.00341i) q^{82} +1.18065i q^{83} +(0.170842 + 0.0986359i) q^{84} +5.23818i q^{86} +(-0.612748 + 1.06131i) q^{87} +(-4.77784 - 8.27547i) q^{88} +(2.82548 - 1.63129i) q^{89} +(-12.4483 - 4.19889i) q^{91} +0.103573 q^{92} +(2.91559 - 1.68332i) q^{93} +(3.19736 + 5.53799i) q^{94} +0.305731i q^{96} +(-4.54898 - 2.62636i) q^{97} +(-7.42204 - 4.28511i) q^{98} -9.30722i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{3} + 6 q^{4} + 9 q^{6} - 6 q^{7} - 8 q^{9}+O(q^{10}) $ 10 * q - 3 * q^3 + 6 * q^4 + 9 * q^6 - 6 * q^7 - 8 * q^9	$ 10 q - 3 q^{3} + 6 q^{4} + 9 q^{6} - 6 q^{7} - 8 q^{9} - 9 q^{11} - 28 q^{12} + 8 q^{13} - 8 q^{14} - 12 q^{16} + 8 q^{17} - 12 q^{22} + 13 q^{23} + 42 q^{24} - 17 q^{26} + 30 q^{27} + 33 q^{28} + 7 q^{29} + 3 q^{32} - 6 q^{33} - 3 q^{36} + 3 q^{37} - 62 q^{38} + 8 q^{39} + 12 q^{41} + 32 q^{42} + 4 q^{43} + 39 q^{46} - 26 q^{48} - q^{49} + 16 q^{51} + 61 q^{52} + 24 q^{53} - 9 q^{54} - 21 q^{56} + 18 q^{58} - 48 q^{59} + 13 q^{61} + 17 q^{62} - 34 q^{64} - 42 q^{66} + 6 q^{67} - 13 q^{68} + 20 q^{69} - 27 q^{71} - 141 q^{72} - 26 q^{74} - 12 q^{76} - 48 q^{77} + 56 q^{78} + 4 q^{79} - 17 q^{81} - q^{82} - 90 q^{84} - 49 q^{87} - 6 q^{88} + 24 q^{89} + 13 q^{91} + 34 q^{92} - 63 q^{93} + 5 q^{94} - 15 q^{97} - 45 q^{98}+O(q^{100}) $ 10 * q - 3 * q^3 + 6 * q^4 + 9 * q^6 - 6 * q^7 - 8 * q^9 - 9 * q^11 - 28 * q^12 + 8 * q^13 - 8 * q^14 - 12 * q^16 + 8 * q^17 - 12 * q^22 + 13 * q^23 + 42 * q^24 - 17 * q^26 + 30 * q^27 + 33 * q^28 + 7 * q^29 + 3 * q^32 - 6 * q^33 - 3 * q^36 + 3 * q^37 - 62 * q^38 + 8 * q^39 + 12 * q^41 + 32 * q^42 + 4 * q^43 + 39 * q^46 - 26 * q^48 - q^49 + 16 * q^51 + 61 * q^52 + 24 * q^53 - 9 * q^54 - 21 * q^56 + 18 * q^58 - 48 * q^59 + 13 * q^61 + 17 * q^62 - 34 * q^64 - 42 * q^66 + 6 * q^67 - 13 * q^68 + 20 * q^69 - 27 * q^71 - 141 * q^72 - 26 * q^74 - 12 * q^76 - 48 * q^77 + 56 * q^78 + 4 * q^79 - 17 * q^81 - q^82 - 90 * q^84 - 49 * q^87 - 6 * q^88 + 24 * q^89 + 13 * q^91 + 34 * q^92 - 63 * q^93 + 5 * q^94 - 15 * q^97 - 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.18257	+	0.682755i	−0.836201	+	0.482781i	−0.855971	−	0.517024i	$-0.827040\pi$
$2$	−1.18257	+	0.682755i	−0.836201	+	0.482781i	0.0197701	+	0.999805i	$0.493707\pi$
$3$	0.199959	+	0.346339i	0.115446	+	0.199959i	0.917958	−	0.396677i	$-0.129837\pi$
$3$	0.199959	+	0.346339i	0.115446	+	0.199959i	−0.802512	+	0.596636i	$0.796504\pi$
$4$	−0.0676905	+	0.117243i	−0.0338452	+	0.0586217i
$5$		0			0
$5$		0			0
$6$	−0.472929	−	0.273046i	−0.193073	−	0.111471i
$7$	−3.15550	−	1.82183i	−1.19267	−	0.688586i	−0.233755	−	0.972295i	$-0.575101\pi$
$7$	−3.15550	−	1.82183i	−1.19267	−	0.688586i	−0.958910	+	0.283710i	$0.908435\pi$
$8$		−	2.91589i		−	1.03092i
$9$	1.42003	−	2.45957i	0.473344	−	0.819856i
$10$		0			0
$11$	2.83806	−	1.63856i	0.855708	−	0.494043i	−0.00686453	−	0.999976i	$-0.502185\pi$
$11$	2.83806	−	1.63856i	0.855708	−	0.494043i	0.862573	+	0.505933i	$0.168852\pi$
$12$	−0.0541412			−0.0156292
$13$	3.53491	−	0.710223i	0.980407	−	0.196980i
$13$	3.53491	−	0.710223i	0.980407	−	0.196980i
$14$	4.97545			1.32974
$15$		0			0
$16$	1.85546	+	3.21374i	0.463864	+	0.803436i
$17$	−1.08781	+	1.88413i	−0.263832	+	0.456970i	−0.967257	−	0.253799i	$-0.918320\pi$
$17$	−1.08781	+	1.88413i	−0.263832	+	0.456970i	0.703425	+	0.710769i	$0.251653\pi$
$18$			3.87814i			0.914086i
$19$	−0.742787	−	0.428848i	−0.170407	−	0.0983846i	0.412371	−	0.911016i	$-0.364701\pi$
$19$	−0.742787	−	0.428848i	−0.170407	−	0.0983846i	−0.582778	+	0.812632i	$0.698034\pi$
$20$		0			0
$21$		−	1.45716i		−	0.317979i
$22$	−2.23747	+	3.87540i	−0.477029	+	0.826239i
$23$	−0.382526	−	0.662554i	−0.0797621	−	0.138152i	0.823385	−	0.567483i	$-0.192083\pi$
$23$	−0.382526	−	0.662554i	−0.0797621	−	0.138152i	−0.903147	+	0.429331i	$0.858749\pi$
$24$	1.00988	−	0.583057i	0.206142	−	0.119016i
$25$		0			0
$26$	−3.69536	+	3.25336i	−0.724719	+	0.638037i
$27$	2.33555			0.449476
$28$	0.427194	−	0.246641i	0.0807321	−	0.0466107i
$29$	1.53219	+	2.65382i	0.284520	+	0.492803i	0.972493	−	0.232934i	$-0.0748325\pi$
$29$	1.53219	+	2.65382i	0.284520	+	0.492803i	−0.687973	+	0.725736i	$0.741499\pi$
$30$		0			0
$31$		−	8.41833i		−	1.51198i	−0.654585	−	0.755988i	$-0.727157\pi$
$31$		−	8.41833i		−	1.51198i	0.654585	−	0.755988i	$-0.272843\pi$
$32$	0.662062	+	0.382242i	0.117037	+	0.0675714i
$33$	1.13499	+	0.655288i	0.197577	+	0.114071i
$34$		−	2.97082i		−	0.509491i
$35$		0			0
$36$	0.192245	+	0.332979i	0.0320409	+	0.0554965i
$37$	9.40295	−	5.42880i	1.54584	−	0.892488i	0.547383	−	0.836882i	$-0.315624\pi$
$37$	9.40295	−	5.42880i	1.54584	−	0.892488i	0.998453	−	0.0556060i	$-0.0177091\pi$
$38$	1.17119			0.189993
$39$	0.952814	+	1.08226i	0.152572	+	0.173300i
$40$		0			0
$41$	−6.59344	+	3.80672i	−1.02972	+	0.594510i	−0.916905	−	0.399106i	$-0.869321\pi$
$41$	−6.59344	+	3.80672i	−1.02972	+	0.594510i	−0.112817	+	0.993616i	$0.535987\pi$
$42$	0.994885	+	1.72319i	0.153514	+	0.265894i
$43$	1.91803	−	3.32213i	0.292497	−	0.506619i	−0.681903	−	0.731443i	$-0.738847\pi$
$43$	1.91803	−	3.32213i	0.292497	−	0.506619i	0.974399	+	0.224824i	$0.0721806\pi$
$44$			0.443659i			0.0668841i
$45$		0			0
$46$	0.904724	+	0.522343i	0.133394	+	0.0770152i
$47$		−	4.68303i		−	0.683090i	−0.939865	−	0.341545i	$-0.889050\pi$
$47$		−	4.68303i		−	0.683090i	0.939865	−	0.341545i	$-0.110950\pi$
$48$	−0.742029	+	1.28523i	−0.107103	+	0.185507i
$49$	3.13810	+	5.43536i	0.448301	+	0.776479i
$50$		0			0
$51$	−0.870065			−0.121834
$52$	−0.156011	+	0.462520i	−0.0216348	+	0.0641400i
$53$	−3.04646			−0.418463			−0.209231	−	0.977866i	$-0.567096\pi$
$53$	−3.04646			−0.418463			−0.209231	+	0.977866i	$0.567096\pi$
$54$	−2.76194	+	1.59461i	−0.375852	+	0.216998i
$55$		0			0
$56$	−5.31224	+	9.20106i	−0.709878	+	1.22954i
$57$		−	0.343008i		−	0.0454325i
$58$	−3.62382	−	2.09222i	−0.475832	−	0.274721i
$59$	−11.5378	−	6.66136i	−1.50210	−	0.867235i	−0.999997	−	0.00242501i	$-0.999228\pi$
$59$	−11.5378	−	6.66136i	−1.50210	−	0.867235i	−0.502099	−	0.864810i	$-0.667439\pi$
$60$		0			0
$61$	6.51531	−	11.2848i	0.834200	−	1.44488i	−0.0604805	−	0.998169i	$-0.519263\pi$
$61$	6.51531	−	11.2848i	0.834200	−	1.44488i	0.894680	−	0.446707i	$-0.147403\pi$
$62$	5.74766	+	9.95524i	0.729953	+	1.26432i
$63$	−8.96182	+	5.17411i	−1.12908	+	0.651876i
$64$	−8.46573			−1.05822
$65$		0			0
$66$	−1.78960			−0.220285
$67$	4.02523	−	2.32397i	0.491760	−	0.283918i	−0.233544	−	0.972346i	$-0.575032\pi$
$67$	4.02523	−	2.32397i	0.491760	−	0.283918i	0.725304	+	0.688428i	$0.241699\pi$
$68$	−0.147268	−	0.255076i	−0.0178589	−	0.0309325i
$69$	0.152979	−	0.264967i	0.0184165	−	0.0318983i
$70$		0			0
$71$	9.38392	+	5.41781i	1.11367	+	0.642976i	0.939777	−	0.341789i	$-0.111033\pi$
$71$	9.38392	+	5.41781i	1.11367	+	0.642976i	0.173890	+	0.984765i	$0.444366\pi$
$72$	−7.17182	−	4.14065i	−0.845207	−	0.487981i
$73$			7.68313i			0.899242i	0.893219	+	0.449621i	$0.148441\pi$
$73$			7.68313i			0.899242i	−0.893219	+	0.449621i	$0.851559\pi$
$74$	−7.41308	+	12.8398i	−0.861753	+	1.49260i
$75$		0			0
$76$	0.100559	−	0.0580579i	0.0115349	−	0.00665970i
$77$	−11.9407			−1.36076
$78$	−1.86569	−	0.629307i	−0.211247	−	0.0712550i
$79$	−10.2106			−1.14879			−0.574394	−	0.818579i	$-0.694762\pi$
$79$	−10.2106			−1.14879			−0.574394	+	0.818579i	$0.694762\pi$
$80$		0			0
$81$	−3.79309	−	6.56982i	−0.421454	−	0.729980i
$82$	5.19812	−	9.00341i	0.574036	−	0.994260i
$83$			1.18065i			0.129593i	0.997899	+	0.0647964i	$0.0206398\pi$
$83$			1.18065i			0.129593i	−0.997899	+	0.0647964i	$0.979360\pi$
$84$	0.170842	+	0.0986359i	0.0186404	+	0.0107621i
$85$		0			0
$86$			5.23818i			0.564848i
$87$	−0.612748	+	1.06131i	−0.0656935	+	0.113785i
$88$	−4.77784	−	8.27547i	−0.509320	−	0.882168i
$89$	2.82548	−	1.63129i	0.299500	−	0.172916i	−0.342718	−	0.939438i	$-0.611348\pi$
$89$	2.82548	−	1.63129i	0.299500	−	0.172916i	0.642218	+	0.766522i	$0.278014\pi$
$90$		0			0
$91$	−12.4483	−	4.19889i	−1.30494	−	0.440163i
$92$	0.103573			0.0107983
$93$	2.91559	−	1.68332i	0.302333	−	0.174552i
$94$	3.19736	+	5.53799i	0.329783	+	0.571200i
$95$		0			0
$96$			0.305731i			0.0312035i
$97$	−4.54898	−	2.62636i	−0.461879	−	0.266666i	0.250955	−	0.967999i	$-0.419255\pi$
$97$	−4.54898	−	2.62636i	−0.461879	−	0.266666i	−0.712834	+	0.701333i	$0.752589\pi$
$98$	−7.42204	−	4.28511i	−0.749739	−	0.432862i
$99$		−	9.30722i		−	0.935410i
$100$		0			0
$101$	8.53815	+	14.7885i	0.849577	+	1.47151i	0.881586	+	0.472024i	$0.156476\pi$
$101$	8.53815	+	14.7885i	0.849577	+	1.47151i	−0.0320085	+	0.999488i	$0.510190\pi$
$102$	1.02891	−	0.594042i	0.101877	−	0.0588189i
$103$	0.810478			0.0798588			0.0399294	−	0.999203i	$-0.487287\pi$
$103$	0.810478			0.0798588			0.0399294	+	0.999203i	$0.487287\pi$
$104$	−2.07093	−	10.3074i	−0.203071	−	1.01072i
$105$		0			0
$106$	3.60264	−	2.07998i	0.349919	−	0.202026i
$107$	6.69352	+	11.5935i	0.647087	+	1.12079i	0.983815	+	0.179185i	$0.0573462\pi$
$107$	6.69352	+	11.5935i	0.647087	+	1.12079i	−0.336728	+	0.941602i	$0.609320\pi$
$108$	−0.158094	+	0.273827i	−0.0152126	+	0.0263490i
$109$			5.61232i			0.537562i	0.963201	+	0.268781i	$0.0866208\pi$
$109$			5.61232i			0.537562i	−0.963201	+	0.268781i	$0.913379\pi$
$110$		0			0
$111$	3.76041	+	2.17107i	0.356922	+	0.206069i
$112$		−	13.5213i		−	1.27764i
$113$	−9.11615	+	15.7896i	−0.857575	+	1.48536i	0.0166601	+	0.999861i	$0.494697\pi$
$113$	−9.11615	+	15.7896i	−0.857575	+	1.48536i	−0.874235	+	0.485503i	$0.838637\pi$
$114$	0.234191	+	0.405630i	0.0219340	+	0.0379907i
$115$		0			0
$116$	−0.414858			−0.0385186
$117$	3.27285	−	9.70289i	0.302575	−	0.897033i
$118$	18.1923			1.67474
$119$	6.86513	−	3.96359i	0.629326	−	0.363341i
$120$		0			0
$121$	−0.130266	+	0.225627i	−0.0118423	+	0.0205115i
$122$			17.7934i			1.61094i
$123$	−2.63683	−	1.52238i	−0.237755	−	0.137268i
$124$	0.986993	+	0.569841i	0.0886346	+	0.0511732i
$125$		0			0
$126$	7.06530	−	12.2375i	0.629427	−	1.09020i
$127$	8.48513	+	14.6967i	0.752933	+	1.30412i	0.946395	+	0.323011i	$0.104695\pi$
$127$	8.48513	+	14.6967i	0.752933	+	1.30412i	−0.193462	+	0.981108i	$0.561972\pi$
$128$	8.68717	−	5.01554i	0.767844	−	0.443315i
$129$	1.53411			0.135071
$130$		0			0
$131$	−17.7226			−1.54843			−0.774215	−	0.632923i	$-0.781855\pi$
$131$	−17.7226			−1.54843			−0.774215	+	0.632923i	$0.781855\pi$
$132$	−0.153656	+	0.0887135i	−0.0133741	+	0.00772152i
$133$	1.56258	+	2.70646i	0.135492	+	0.234680i
$134$	−3.17340	+	5.49649i	−0.274140	+	0.474825i
$135$		0			0
$136$	5.49392	+	3.17192i	0.471100	+	0.271990i
$137$	−13.9505	−	8.05434i	−1.19187	−	0.688129i	−0.233143	−	0.972443i	$-0.574901\pi$
$137$	−13.9505	−	8.05434i	−1.19187	−	0.688129i	−0.958731	+	0.284314i	$0.908234\pi$
$138$			0.417788i			0.0355645i
$139$	1.71547	−	2.97129i	0.145505	−	0.252021i	−0.784057	−	0.620689i	$-0.786853\pi$
$139$	1.71547	−	2.97129i	0.145505	−	0.252021i	0.929561	+	0.368668i	$0.120186\pi$
$140$		0			0
$141$	1.62191	−	0.936412i	0.136590	−	0.0788602i
$142$	−14.7962			−1.24167
$143$	8.86856	−	7.80781i	0.741626	−	0.652922i
$144$	10.5392			0.878269
$145$		0			0
$146$	−5.24569	−	9.08581i	−0.434137	−	0.751947i
$147$	−1.25498	+	2.17369i	−0.103509	+	0.179283i
$148$			1.46991i			0.120826i
$149$	16.1603	+	9.33018i	1.32391	+	0.764358i	0.984350	−	0.176227i	$-0.0563893\pi$
$149$	16.1603	+	9.33018i	1.32391	+	0.764358i	0.339558	+	0.940585i	$0.389723\pi$
$150$		0			0
$151$		−	6.63134i		−	0.539651i	−0.962909	−	0.269826i	$-0.913034\pi$
$151$		−	6.63134i		−	0.539651i	0.962909	−	0.269826i	$-0.0869660\pi$
$152$	−1.25047	+	2.16588i	−0.101427	+	0.175676i
$153$	3.08944	+	5.35107i	0.249766	+	0.432608i
$154$	14.1206	−	8.15255i	1.13787	−	0.656951i
$155$		0			0
$156$	−0.191384	+	0.0384523i	−0.0153230	+	0.00307865i
$157$	4.61502			0.368319			0.184159	−	0.982896i	$-0.441044\pi$
$157$	4.61502			0.368319			0.184159	+	0.982896i	$0.441044\pi$
$158$	12.0748	−	6.97137i	0.960617	−	0.554613i
$159$	−0.609166	−	1.05511i	−0.0483100	−	0.0836754i
$160$		0			0
$161$			2.78758i			0.219692i
$162$	8.97115	+	5.17950i	0.704840	+	0.406940i
$163$	−8.44402	−	4.87516i	−0.661387	−	0.381852i	0.131418	−	0.991327i	$-0.458047\pi$
$163$	−8.44402	−	4.87516i	−0.661387	−	0.381852i	−0.792805	+	0.609475i	$0.791380\pi$
$164$		−	1.03072i		−	0.0804853i
$165$		0			0
$166$	−0.806093	−	1.39619i	−0.0625649	−	0.108366i
$167$	8.99356	−	5.19243i	0.695943	−	0.401803i	−0.109892	−	0.993944i	$-0.535050\pi$
$167$	8.99356	−	5.19243i	0.695943	−	0.401803i	0.805834	+	0.592141i	$0.201717\pi$
$168$	−4.24892			−0.327811
$169$	11.9912	−	5.02115i	0.922397	−	0.386242i
$170$		0			0
$171$	−2.10956	+	1.21796i	−0.161322	+	0.0931396i
$172$	0.259665	+	0.449753i	0.0197993	+	0.0342933i
$173$	7.64543	−	13.2423i	0.581271	−	1.00679i	−0.414058	−	0.910251i	$-0.635889\pi$
$173$	7.64543	−	13.2423i	0.581271	−	1.00679i	0.995329	−	0.0965406i	$-0.0307778\pi$
$174$		−	1.67343i		−	0.126862i
$175$		0			0
$176$	10.5318	+	6.08054i	0.793864	+	0.458338i
$177$		−	5.32799i		−	0.400476i
$178$	−2.22754	+	3.85822i	−0.166961	+	0.289186i
$179$	5.80307	+	10.0512i	0.433742	+	0.751263i	0.997192	−	0.0748869i	$-0.0238596\pi$
$179$	5.80307	+	10.0512i	0.433742	+	0.751263i	−0.563450	+	0.826150i	$0.690526\pi$
$180$		0			0
$181$	4.01543			0.298464			0.149232	−	0.988802i	$-0.452320\pi$
$181$	4.01543			0.298464			0.149232	+	0.988802i	$0.452320\pi$
$182$	17.5878	−	3.53368i	1.30369	−	0.261933i
$183$	5.21117			0.385221
$184$	−1.93193	+	1.11540i	−0.142424	+	0.0822284i
$185$		0			0
$186$	−2.29859	+	3.98128i	−0.168541	+	0.291921i
$187$			7.12972i			0.521377i
$188$	0.549054	+	0.316996i	0.0400439	+	0.0231193i
$189$	−7.36981	−	4.25496i	−0.536074	−	0.309503i
$190$		0			0
$191$	0.964496	−	1.67056i	0.0697884	−	0.120877i	−0.829020	−	0.559219i	$-0.811101\pi$
$191$	0.964496	−	1.67056i	0.0697884	−	0.120877i	0.898808	+	0.438342i	$0.144434\pi$
$192$	−1.69280	−	2.93201i	−0.122167	−	0.211600i
$193$	4.60933	−	2.66120i	0.331787	−	0.191557i	−0.324847	−	0.945766i	$-0.605313\pi$
$193$	4.60933	−	2.66120i	0.331787	−	0.191557i	0.656634	+	0.754209i	$0.271980\pi$
$194$	7.17263			0.514965
$195$		0			0
$196$	−0.849679			−0.0606914
$197$	−13.2873	+	7.67142i	−0.946681	+	0.546566i	−0.892048	−	0.451940i	$-0.850732\pi$
$197$	−13.2873	+	7.67142i	−0.946681	+	0.546566i	−0.0546323	+	0.998507i	$0.517399\pi$
$198$	6.35455	+	11.0064i	0.451598	+	0.782191i
$199$	10.6435	−	18.4351i	0.754500	−	1.30683i	−0.191123	−	0.981566i	$-0.561213\pi$
$199$	10.6435	−	18.4351i	0.754500	−	1.30683i	0.945623	−	0.325266i	$-0.105454\pi$
$200$		0			0
$201$	1.60976	+	0.929396i	0.113544	+	0.0655545i
$202$	−20.1939	−	11.6589i	−1.42083	−	0.820319i
$203$		−	11.1655i		−	0.783665i
$204$	0.0588951	−	0.102009i	0.00412349	−	0.00714209i
$205$		0			0
$206$	−0.958444	+	0.553358i	−0.0667780	+	0.0385543i
$207$	−2.17280			−0.151020
$208$	8.84134	+	10.0425i	0.613037	+	0.696322i
$209$	−2.81077			−0.194425
$210$		0			0
$211$	6.82083	+	11.8140i	0.469566	+	0.813311i	0.999395	−	0.0347931i	$-0.0110772\pi$
$211$	6.82083	+	11.8140i	0.469566	+	0.813311i	−0.529829	+	0.848105i	$0.677744\pi$
$212$	0.206216	−	0.357177i	0.0141630	−	0.0245310i
$213$			4.33336i			0.296917i
$214$	−15.8311	−	9.14007i	−1.08219	−	0.624802i
$215$		0			0
$216$		−	6.81018i		−	0.463374i
$217$	−15.3367	+	26.5640i	−1.04113	+	1.80328i
$218$	−3.83184	−	6.63694i	−0.259525	−	0.449510i
$219$	−2.66096	+	1.53631i	−0.179811	+	0.103814i
$220$		0			0
$221$	−2.50714	+	7.43283i	−0.168648	+	0.499986i
$222$	−5.92924			−0.397945
$223$	−21.4013	+	12.3560i	−1.43314	+	0.827422i	−0.997359	−	0.0726324i	$-0.976860\pi$
$223$	−21.4013	+	12.3560i	−1.43314	+	0.827422i	−0.435778	+	0.900054i	$0.643527\pi$
$224$	−1.39276	−	2.41233i	−0.0930575	−	0.161180i
$225$		0			0
$226$		−	24.8964i		−	1.65608i
$227$	−10.2349	−	5.90911i	−0.679313	−	0.392201i	0.120283	−	0.992740i	$-0.461620\pi$
$227$	−10.2349	−	5.90911i	−0.679313	−	0.392201i	−0.799596	+	0.600538i	$0.794953\pi$
$228$	0.0402154	+	0.0232184i	0.00266333	+	0.00153768i
$229$			2.98379i			0.197174i	0.995128	+	0.0985872i	$0.0314323\pi$
$229$			2.98379i			0.197174i	−0.995128	+	0.0985872i	$0.968568\pi$
$230$		0			0
$231$	−2.38764	−	4.13552i	−0.157095	−	0.272097i
$232$	7.73825	−	4.46768i	0.508041	−	0.293317i
$233$	6.88071			0.450770			0.225385	−	0.974270i	$-0.427636\pi$
$233$	6.88071			0.450770			0.225385	+	0.974270i	$0.427636\pi$
$234$	2.75434	+	13.7089i	0.180057	+	0.896177i
$235$		0			0
$236$	1.56200	−	0.901821i	0.101678	−	0.0587036i
$237$	−2.04171	−	3.53634i	−0.132623	−	0.229710i
$238$	−5.41232	+	9.37441i	−0.350829	+	0.607653i
$239$			18.3427i			1.18649i	0.805021	+	0.593246i	$0.202154\pi$
$239$			18.3427i			1.18649i	−0.805021	+	0.593246i	$0.797846\pi$
$240$		0			0
$241$	14.4077	+	8.31828i	0.928080	+	0.535827i	0.886204	−	0.463296i	$-0.153333\pi$
$241$	14.4077	+	8.31828i	0.928080	+	0.535827i	0.0418762	+	0.999123i	$0.486667\pi$
$242$		−	0.355758i		−	0.0228690i
$243$	5.02024	−	8.69531i	0.322049	−	0.557804i
$244$	0.882049	+	1.52775i	0.0564674	+	0.0978044i
$245$		0			0
$246$	4.15764			0.265081
$247$	−2.93026	−	0.988396i	−0.186448	−	0.0628901i
$248$	−24.5469			−1.55873
$249$	−0.408904	+	0.236081i	−0.0259132	+	0.0149610i
$250$		0			0
$251$	−1.40485	+	2.43327i	−0.0886733	+	0.153587i	−0.906951	−	0.421237i	$-0.861596\pi$
$251$	−1.40485	+	2.43327i	−0.0886733	+	0.153587i	0.818277	+	0.574824i	$0.194929\pi$
$252$		−	1.40095i		−	0.0882516i
$253$	−2.17126	−	1.25358i	−0.136506	−	0.0788119i
$254$	−20.0685	−	11.5865i	−1.25921	−	0.727003i
$255$		0			0
$256$	1.61696	−	2.80066i	0.101060	−	0.175041i
$257$	−1.65946	−	2.87428i	−0.103515	−	0.179292i	0.809616	−	0.586960i	$-0.199675\pi$
$257$	−1.65946	−	2.87428i	−0.103515	−	0.179292i	−0.913130	+	0.407668i	$0.866342\pi$
$258$	−1.81419	+	1.04742i	−0.112946	+	0.0652096i
$259$	−39.5613			−2.45822
$260$		0			0
$261$	8.70302			0.538703
$262$	20.9581	−	12.1002i	1.29480	−	0.747552i
$263$	−12.4809	−	21.6176i	−0.769606	−	1.33300i	−0.937777	−	0.347239i	$-0.887119\pi$
$263$	−12.4809	−	21.6176i	−0.769606	−	1.33300i	0.168171	−	0.985758i	$-0.446214\pi$
$264$	1.91074	−	3.30951i	0.117598	−	0.203686i
$265$		0			0
$266$	−3.69570	−	2.13371i	−0.226598	−	0.130826i
$267$	1.12996	+	0.652382i	0.0691523	+	0.0399251i
$268$			0.629242i			0.0384371i
$269$	−5.76837	+	9.99111i	−0.351704	+	0.609169i	−0.986548	−	0.163471i	$-0.947731\pi$
$269$	−5.76837	+	9.99111i	−0.351704	+	0.609169i	0.634844	+	0.772640i	$0.281064\pi$
$270$		0			0
$271$	−17.3047	+	9.99086i	−1.05118	+	0.606902i	−0.922981	−	0.384846i	$-0.874254\pi$
$271$	−17.3047	+	9.99086i	−1.05118	+	0.606902i	−0.128204	+	0.991748i	$0.540921\pi$
$272$	−8.07350			−0.489528
$273$	−1.03491	−	5.15093i	−0.0626356	−	0.311749i
$274$	21.9966			1.32886
$275$		0			0
$276$	0.0207104	+	0.0358715i	0.00124662	+	0.00215921i
$277$	3.06053	−	5.30099i	0.183889	−	0.318506i	−0.759312	−	0.650726i	$-0.774465\pi$
$277$	3.06053	−	5.30099i	0.183889	−	0.318506i	0.943202	+	0.332221i	$0.107798\pi$
$278$			4.68499i			0.280987i
$279$	−20.7055	−	11.9543i	−1.23960	−	0.715686i
$280$		0			0
$281$			25.6283i			1.52885i	0.644711	+	0.764427i	$0.276978\pi$
$281$			25.6283i			1.52885i	−0.644711	+	0.764427i	$0.723022\pi$
$282$	−1.27868	+	2.21474i	−0.0761444	+	0.131886i
$283$	8.84118	+	15.3134i	0.525553	+	0.910285i	0.999557	+	0.0297622i	$0.00947501\pi$
$283$	8.84118	+	15.3134i	0.525553	+	0.910285i	−0.474004	+	0.880523i	$0.657192\pi$
$284$	−1.27040	+	0.733468i	−0.0753846	+	0.0435233i
$285$		0			0
$286$	−5.15684	+	15.2883i	−0.304930	+	0.904016i
$287$	27.7407			1.63748
$288$	1.88030	−	1.08559i	0.110798	−	0.0639691i
$289$	6.13336	+	10.6233i	0.360786	+	0.624899i
$290$		0			0
$291$		−	2.10065i		−	0.123142i
$292$	−0.900795	−	0.520074i	−0.0527151	−	0.0304351i
$293$	19.0564	+	11.0022i	1.11329	+	0.642757i	0.939679	−	0.342058i	$-0.111124\pi$
$293$	19.0564	+	11.0022i	1.11329	+	0.642757i	0.173609	+	0.984815i	$0.444457\pi$
$294$		−	3.42739i		−	0.199889i
$295$		0			0
$296$	−15.8297	−	27.4179i	−0.920085	−	1.59363i
$297$	6.62843	−	3.82692i	0.384620	−	0.222061i
$298$	−25.4809			−1.47607
$299$	−1.82275	−	2.07039i	−0.105413	−	0.119734i
$300$		0			0
$301$	−12.1047	+	6.98864i	−0.697702	+	0.402818i
$302$	4.52759	+	7.84201i	0.260533	+	0.451257i
$303$	−3.41456	+	5.91418i	−0.196161	+	0.339761i
$304$		−	3.18284i		−	0.182548i
$305$		0			0
$306$	−7.30694	−	4.21866i	−0.417710	−	0.241165i
$307$		−	1.63084i		−	0.0930769i	−0.998917	−	0.0465384i	$-0.985181\pi$
$307$		−	1.63084i		−	0.0930769i	0.998917	−	0.0465384i	$-0.0148190\pi$
$308$	0.808269	−	1.39996i	0.0460554	−	0.0797703i
$309$	0.162062	+	0.280700i	0.00921940	+	0.0159685i
$310$		0			0
$311$	19.0053			1.07769			0.538845	−	0.842405i	$-0.318861\pi$
$311$	19.0053			1.07769			0.538845	+	0.842405i	$0.318861\pi$
$312$	3.15575	−	2.77830i	0.178659	−	0.157290i
$313$	−11.1004			−0.627434			−0.313717	−	0.949517i	$-0.601574\pi$
$313$	−11.1004			−0.627434			−0.313717	+	0.949517i	$0.601574\pi$
$314$	−5.45757	+	3.15093i	−0.307989	+	0.177817i
$315$		0			0
$316$	0.691164	−	1.19713i	0.0388810	−	0.0673438i
$317$		−	5.22062i		−	0.293219i	−0.989194	−	0.146610i	$-0.953164\pi$
$317$		−	5.22062i		−	0.293219i	0.989194	−	0.146610i	$-0.0468361\pi$
$318$	1.44076	+	0.831822i	0.0807937	+	0.0466463i
$319$	8.69688	+	5.02115i	0.486932	+	0.281130i
$320$		0			0
$321$	−2.67686	+	4.63645i	−0.149408	+	0.258781i
$322$	−1.90324	−	3.29650i	−0.106063	−	0.183707i
$323$	1.61602	−	0.933008i	0.0899176	−	0.0519139i
$324$	1.02702			0.0570568
$325$		0			0
$326$	13.3142			0.737403
$327$	−1.94376	+	1.12223i	−0.107490	+	0.0620596i
$328$	11.1000	+	19.2257i	0.612893	+	1.06156i
$329$	−8.53166	+	14.7773i	−0.470366	+	0.814697i
$330$		0			0
$331$	−22.2027	−	12.8187i	−1.22037	−	0.704582i	−0.255374	−	0.966842i	$-0.582199\pi$
$331$	−22.2027	−	12.8187i	−1.22037	−	0.704582i	−0.964997	+	0.262261i	$0.915532\pi$
$332$	−0.138423	−	0.0799185i	−0.00759695	−	0.00438610i
$333$		−	30.8363i		−	1.68982i
$334$	−7.09032	+	12.2808i	−0.387965	+	0.671975i
$335$		0			0
$336$	4.68294	−	2.70370i	0.255475	−	0.147499i
$337$	36.1447			1.96892			0.984462	−	0.175596i	$-0.0561852\pi$
$337$	36.1447			1.96892			0.984462	+	0.175596i	$0.0561852\pi$
$338$	−10.7521	+	14.1249i	−0.584839	+	0.768292i
$339$	−7.29142			−0.396015
$340$		0			0
$341$	−13.7939	−	23.8918i	−0.746982	−	1.29381i
$342$	1.66313	−	2.88063i	0.0899320	−	0.155767i
$343$			2.63725i			0.142398i
$344$	−9.68694	−	5.59276i	−0.522285	−	0.301541i
$345$		0			0
$346$			20.8798i			1.12251i
$347$	−7.20541	+	12.4801i	−0.386806	+	0.669968i	−0.992018	−	0.126096i	$-0.959755\pi$
$347$	−7.20541	+	12.4801i	−0.386806	+	0.669968i	0.605212	+	0.796065i	$0.293089\pi$
$348$	−0.0829545	−	0.143681i	−0.00444683	−	0.00770213i
$349$	−2.89197	+	1.66968i	−0.154803	+	0.0893758i	−0.575401	−	0.817872i	$-0.695154\pi$
$349$	−2.89197	+	1.66968i	−0.154803	+	0.0893758i	0.420597	+	0.907247i	$0.361821\pi$
$350$		0			0
$351$	8.25594	−	1.65876i	0.440670	−	0.0885379i
$352$	2.50530			0.133533
$353$	10.1157	−	5.84028i	0.538403	−	0.310847i	−0.206029	−	0.978546i	$-0.566054\pi$
$353$	10.1157	−	5.84028i	0.538403	−	0.310847i	0.744431	+	0.667699i	$0.232721\pi$
$354$	3.63771	+	6.30071i	0.193342	+	0.334879i
$355$		0			0
$356$			0.441691i			0.0234096i
$357$	2.74549	+	1.58511i	0.145307	+	0.0838928i
$358$	−13.7250	−	7.92416i	−0.725391	−	0.418805i
$359$		−	6.54679i		−	0.345526i	−0.984963	−	0.172763i	$-0.944730\pi$
$359$		−	6.54679i		−	0.345526i	0.984963	−	0.172763i	$-0.0552695\pi$
$360$		0			0
$361$	−9.13218	−	15.8174i	−0.480641	−	0.832495i
$362$	−4.74851	+	2.74155i	−0.249576	+	0.144093i
$363$	−0.104191			−0.00546861
$364$	1.33492	−	1.17526i	0.0699690	−	0.0616001i
$365$		0			0
$366$	−6.16256	+	3.55796i	−0.322122	+	0.185977i
$367$	11.3109	+	19.5911i	0.590425	+	1.02265i	0.994175	+	0.107777i	$0.0343731\pi$
$367$	11.3109	+	19.5911i	0.590425	+	1.02265i	−0.403750	+	0.914869i	$0.632294\pi$
$368$	1.41952	−	2.45868i	0.0739975	−	0.128167i
$369$			21.6227i			1.12563i
$370$		0			0
$371$	9.61308	+	5.55011i	0.499086	+	0.288148i
$372$			0.455779i			0.0236310i
$373$	2.12583	−	3.68204i	0.110071	−	0.190649i	−0.805728	−	0.592286i	$-0.798225\pi$
$373$	2.12583	−	3.68204i	0.110071	−	0.190649i	0.915799	+	0.401637i	$0.131559\pi$
$374$	−4.86786	−	8.43138i	−0.251711	−	0.435976i
$375$		0			0
$376$	−13.6552			−0.704211
$377$	7.30095	+	8.29283i	0.376018	+	0.427103i
$378$	11.6204			0.597688
$379$	9.64880	−	5.57074i	0.495626	−	0.286150i	−0.231280	−	0.972887i	$-0.574291\pi$
$379$	9.64880	−	5.57074i	0.495626	−	0.286150i	0.726905	+	0.686738i	$0.240958\pi$
$380$		0			0
$381$	−3.39335	+	5.87746i	−0.173847	+	0.301111i
$382$			2.63406i			0.134770i
$383$	−4.75384	−	2.74463i	−0.242910	−	0.140244i	0.373604	−	0.927588i	$-0.378122\pi$
$383$	−4.75384	−	2.74463i	−0.242910	−	0.140244i	−0.616513	+	0.787344i	$0.711455\pi$
$384$	3.47415	+	2.00580i	0.177290	+	0.102358i
$385$		0			0
$386$	−3.63389	+	6.29409i	−0.184960	+	0.320361i
$387$	−5.44733	−	9.43506i	−0.276903	−	0.479611i
$388$	0.615846	−	0.355559i	0.0312648	−	0.0180508i
$389$	25.9475			1.31559			0.657794	−	0.753198i	$-0.271490\pi$
$389$	25.9475			1.31559			0.657794	+	0.753198i	$0.271490\pi$
$390$		0			0
$391$	1.66445			0.0841751
$392$	15.8489	−	9.15035i	0.800489	−	0.462163i
$393$	−3.54379	−	6.13802i	−0.178760	−	0.309622i
$394$	10.4754	−	18.1439i	0.527743	−	0.914079i
$395$		0			0
$396$	1.09121	+	0.630010i	0.0548353	+	0.0316592i
$397$	−12.0123	−	6.93530i	−0.602880	−	0.348073i	0.167294	−	0.985907i	$-0.446497\pi$
$397$	−12.0123	−	6.93530i	−0.602880	−	0.348073i	−0.770174	+	0.637834i	$0.779830\pi$
$398$			29.0677i			1.45703i
$399$	−0.624901	+	1.08236i	−0.0312842	+	0.0541858i
$400$		0			0
$401$	−1.09405	+	0.631649i	−0.0546341	+	0.0315430i	−0.527068	−	0.849823i	$-0.676709\pi$
$401$	−1.09405	+	0.631649i	−0.0546341	+	0.0315430i	0.472434	+	0.881366i	$0.343375\pi$
$402$	−2.53820			−0.126594
$403$	−5.97889	−	29.7580i	−0.297830	−	1.48235i
$404$	−2.31181			−0.115017
$405$		0			0
$406$	7.62331	+	13.2040i	0.378339	+	0.655302i
$407$	17.7908	−	30.8145i	0.881856	−	1.52742i
$408$			2.53701i			0.125601i
$409$	19.0947	+	11.0243i	0.944171	+	0.545117i	0.891265	−	0.453482i	$-0.149818\pi$
$409$	19.0947	+	11.0243i	0.944171	+	0.545117i	0.0529055	+	0.998600i	$0.483152\pi$
$410$		0			0
$411$		−	6.44215i		−	0.317768i
$412$	−0.0548616	+	0.0950231i	−0.00270284	+	0.00468145i
$413$	24.2717	+	42.0398i	1.19433	+	2.06864i
$414$	2.56948	−	1.48349i	0.126283	−	0.0729095i
$415$		0			0
$416$	2.61181	+	0.880978i	0.128054	+	0.0431935i
$417$	1.37210			0.0671918
$418$	3.32392	−	1.91907i	0.162578	−	0.0938647i
$419$	−5.84019	−	10.1155i	−0.285312	−	0.494175i	0.687373	−	0.726305i	$-0.258764\pi$
$419$	−5.84019	−	10.1155i	−0.285312	−	0.494175i	−0.972685	+	0.232130i	$0.925431\pi$
$420$		0			0
$421$			21.9773i			1.07111i	0.844501	+	0.535555i	$0.179897\pi$
$421$			21.9773i			1.07111i	−0.844501	+	0.535555i	$0.820103\pi$
$422$	−16.1322	−	9.31392i	−0.785302	−	0.453395i
$423$	−11.5182	−	6.65005i	−0.560035	−	0.323337i
$424$			8.88312i			0.431402i
$425$		0			0
$426$	−2.95862	−	5.12448i	−0.143346	−	0.248282i
$427$	−41.1181	+	23.7395i	−1.98984	+	1.14884i
$428$	−1.81235			−0.0876032
$429$	4.47749	+	1.51029i	0.216175	+	0.0729173i
$430$		0			0
$431$	20.8856	−	12.0583i	1.00602	−	0.580828i	0.0959983	−	0.995382i	$-0.469396\pi$
$431$	20.8856	−	12.0583i	1.00602	−	0.580828i	0.910025	+	0.414554i	$0.136062\pi$
$432$	4.33350	+	7.50584i	0.208496	+	0.361125i
$433$	3.34590	−	5.79527i	0.160794	−	0.278503i	−0.774360	−	0.632746i	$-0.781928\pi$
$433$	3.34590	−	5.79527i	0.160794	−	0.278503i	0.935154	+	0.354243i	$0.115261\pi$
$434$		−	41.8850i		−	2.01054i
$435$		0			0
$436$	−0.658007	−	0.379900i	−0.0315128	−	0.0181939i
$437$			0.656182i			0.0313894i
$438$	2.09785	−	3.63358i	0.100239	−	0.173619i
$439$	−13.9887	−	24.2292i	−0.667646	−	1.15640i	−0.978561	−	0.205959i	$-0.933969\pi$
$439$	−13.9887	−	24.2292i	−0.667646	−	1.15640i	0.310915	−	0.950438i	$-0.399365\pi$
$440$		0			0
$441$	17.8248			0.848802
$442$	−2.10994	−	10.5016i	−0.100360	−	0.499509i
$443$	19.4755			0.925309			0.462655	−	0.886539i	$-0.346897\pi$
$443$	19.4755			0.925309			0.462655	+	0.886539i	$0.346897\pi$
$444$	−0.509087	+	0.293922i	−0.0241602	+	0.0139489i
$445$		0			0
$446$	16.8723	−	29.2237i	0.798927	−	1.38378i
$447$			7.46261i			0.352969i
$448$	26.7136	+	15.4231i	1.26210	+	0.728673i
$449$	11.4203	+	6.59349i	0.538955	+	0.311166i	0.744655	−	0.667449i	$-0.232614\pi$
$449$	11.4203	+	6.59349i	0.538955	+	0.311166i	−0.205700	+	0.978615i	$0.565947\pi$
$450$		0			0
$451$	−12.4751	+	21.6074i	−0.587428	+	1.01745i
$452$	−1.23415	−	2.13762i	−0.0580497	−	0.100545i
$453$	2.29669	−	1.32600i	0.107908	−	0.0623007i
$454$	16.1379			0.757389
$455$		0			0
$456$	−1.00017			−0.0468374
$457$	−12.0014	+	6.92898i	−0.561400	+	0.324124i	−0.753707	−	0.657211i	$-0.771736\pi$
$457$	−12.0014	+	6.92898i	−0.561400	+	0.324124i	0.192307	+	0.981335i	$0.438403\pi$
$458$	−2.03720	−	3.52853i	−0.0951920	−	0.164877i
$459$	−2.54062	+	4.40048i	−0.118586	+	0.205397i
$460$		0			0
$461$	−12.1823	−	7.03343i	−0.567384	−	0.327580i	0.188720	−	0.982031i	$-0.439566\pi$
$461$	−12.1823	−	7.03343i	−0.567384	−	0.327580i	−0.756104	+	0.654451i	$0.772900\pi$
$462$	5.64709	+	3.26035i	0.262726	+	0.151685i
$463$		−	4.86555i		−	0.226121i	−0.993588	−	0.113061i	$-0.963935\pi$
$463$		−	4.86555i		−	0.226121i	0.993588	−	0.113061i	$-0.0360655\pi$
$464$	−5.68580	+	9.84810i	−0.263957	+	0.457187i
$465$		0			0
$466$	−8.13690	+	4.69784i	−0.376934	+	0.217623i
$467$	−26.6409			−1.23279			−0.616397	−	0.787436i	$-0.711408\pi$
$467$	−26.6409			−1.23279			−0.616397	+	0.787436i	$0.711408\pi$
$468$	0.916059	+	1.04051i	0.0423449	+	0.0480977i
$469$	−16.9355			−0.782007
$470$		0			0
$471$	0.922815	+	1.59836i	0.0425210	+	0.0736486i
$472$	−19.4238	+	33.6429i	−0.894051	+	1.54854i
$473$		−	12.5712i		−	0.578024i
$474$	4.82891	+	2.78798i	0.221799	+	0.128056i
$475$		0			0
$476$			1.07319i			0.0491895i
$477$	−4.32607	+	7.49297i	−0.198077	+	0.343079i
$478$	−12.5236	−	21.6915i	−0.572816	−	0.992146i
$479$	−2.61805	+	1.51153i	−0.119622	+	0.0690637i	−0.558617	−	0.829426i	$-0.688668\pi$
$479$	−2.61805	+	1.51153i	−0.119622	+	0.0690637i	0.438995	+	0.898489i	$0.355335\pi$
$480$		0			0
$481$	29.3829	−	25.8685i	1.33975	−	1.17950i
$482$	−22.7174			−1.03475
$483$	−0.965448	+	0.557402i	−0.0439294	+	0.0253627i
$484$	−0.0176355	−	0.0305455i	−0.000801612	−	0.00138843i
$485$		0			0
$486$			13.7104i			0.621916i
$487$	−10.2365	−	5.91003i	−0.463859	−	0.267809i	0.249807	−	0.968296i	$-0.419633\pi$
$487$	−10.2365	−	5.91003i	−0.463859	−	0.267809i	−0.713665	+	0.700487i	$0.752966\pi$
$488$	−32.9053	−	18.9979i	−1.48955	−	0.859994i
$489$		−	3.89932i		−	0.176333i
$490$		0			0
$491$	4.82314	+	8.35393i	0.217665	+	0.377008i	0.954094	−	0.299508i	$-0.0968225\pi$
$491$	4.82314	+	8.35393i	0.217665	+	0.377008i	−0.736428	+	0.676516i	$0.763489\pi$
$492$	0.356977	−	0.206101i	0.0160938	−	0.00929173i
$493$	−6.66688			−0.300261
$494$	4.14007	−	0.831809i	0.186270	−	0.0374249i
$495$		0			0
$496$	27.0543	−	15.6198i	1.21478	−	0.701351i
$497$	−19.7406	−	34.1918i	−0.885488	−	1.53371i
$498$	0.322371	−	0.558362i	0.0144458	−	0.0250208i
$499$			10.0807i			0.451274i	0.974211	+	0.225637i	$0.0724463\pi$
$499$			10.0807i			0.451274i	−0.974211	+	0.225637i	$0.927554\pi$
$500$		0			0
$501$	3.59668	+	2.07655i	0.160688	+	0.0927732i
$502$		−	3.83667i		−	0.171239i
$503$	−8.37337	+	14.5031i	−0.373350	+	0.646661i	−0.990079	−	0.140515i	$-0.955124\pi$
$503$	−8.37337	+	14.5031i	−0.373350	+	0.646661i	0.616728	+	0.787176i	$0.288458\pi$
$504$	15.0871	+	26.1316i	0.672033	+	1.16400i
$505$		0			0
$506$	3.42355			0.152195
$507$	4.13676	+	3.14898i	0.183720	+	0.139851i
$508$	−2.29745			−0.101933
$509$	27.2473	−	15.7313i	1.20772	−	0.697276i	0.245457	−	0.969407i	$-0.421062\pi$
$509$	27.2473	−	15.7313i	1.20772	−	0.697276i	0.962260	+	0.272132i	$0.0877286\pi$
$510$		0			0
$511$	13.9973	−	24.2441i	0.619205	−	1.07249i
$512$			24.4781i			1.08179i
$513$	−1.73481	−	1.00160i	−0.0765939	−	0.0442215i
$514$	3.92485	+	2.26602i	0.173118	+	0.0999497i
$515$		0			0
$516$	−0.103845	+	0.179864i	−0.00457150	+	0.00791807i
$517$	−7.67340	−	13.2907i	−0.337476	−	0.584525i
$518$	46.7839	−	27.0107i	2.05557	−	1.18678i
$519$	6.11508			0.268422
$520$		0			0
$521$	6.44923			0.282546			0.141273	−	0.989971i	$-0.454880\pi$
$521$	6.44923			0.282546			0.141273	+	0.989971i	$0.454880\pi$
$522$	−10.2919	+	5.94203i	−0.450464	+	0.260076i
$523$	5.84076	+	10.1165i	0.255399	+	0.442364i	0.965004	−	0.262236i	$-0.0844599\pi$
$523$	5.84076	+	10.1165i	0.255399	+	0.442364i	−0.709605	+	0.704600i	$0.751127\pi$
$524$	1.19965	−	2.07785i	0.0524070	−	0.0907715i
$525$		0			0
$526$	29.5190	+	17.0428i	1.28709	+	0.743102i
$527$	15.8613	+	9.15751i	0.690928	+	0.398907i
$528$			4.86343i			0.211654i
$529$	11.2073	−	19.4117i	0.487276	−	0.843987i
$530$		0			0
$531$	−32.7682	+	18.9187i	−1.42202	+	0.821002i
$532$	−0.423086			−0.0183431
$533$	−20.6036	+	18.1392i	−0.892440	+	0.785697i
$534$	−1.78167			−0.0771003
$535$		0			0
$536$	−6.77642	−	11.7371i	−0.292697	−	0.506966i
$537$	−2.32075	+	4.01966i	−0.100148	+	0.173461i
$538$		−	15.7535i		−	0.679183i
$539$	17.8123	+	10.2839i	0.767229	+	0.442960i
$540$		0			0
$541$			10.5675i			0.454330i	0.973856	+	0.227165i	$0.0729457\pi$
$541$			10.5675i			0.454330i	−0.973856	+	0.227165i	$0.927054\pi$
$542$	13.6426	−	23.6297i	0.586001	−	1.01498i
$543$	0.802920	+	1.39070i	0.0344566	+	0.0596806i
$544$	−1.44039	+	0.831610i	−0.0617562	+	0.0356550i
$545$		0			0
$546$	4.74068	+	5.38473i	0.202882	+	0.230445i
$547$	11.1484			0.476669			0.238335	−	0.971183i	$-0.423399\pi$
$547$	11.1484			0.476669			0.238335	+	0.971183i	$0.423399\pi$
$548$	1.88864	−	1.09040i	0.0806785	−	0.0465798i
$549$	−18.5039	−	32.0497i	−0.789727	−	1.36785i
$550$		0			0
$551$		−	2.62830i		−	0.111969i
$552$	−0.772613	−	0.446069i	−0.0328846	−	0.0189859i
$553$	32.2197	+	18.6020i	1.37012	+	0.791039i
$554$			8.35837i			0.355113i
$555$		0			0
$556$	0.232242	+	0.402256i	0.00984927	+	0.0170594i
$557$	10.7694	−	6.21770i	0.456313	−	0.263453i	−0.254180	−	0.967157i	$-0.581805\pi$
$557$	10.7694	−	6.21770i	0.456313	−	0.263453i	0.710493	+	0.703705i	$0.248472\pi$
$558$	32.6475			1.38208
$559$	4.42061	−	13.1056i	0.186972	−	0.554310i
$560$		0			0
$561$	−2.46930	+	1.42565i	−0.104254	+	0.0601910i
$562$	−17.4978	−	30.3071i	−0.738101	−	1.27843i
$563$	−8.77737	+	15.2029i	−0.369922	+	0.640724i	−0.989553	−	0.144169i	$-0.953949\pi$
$563$	−8.77737	+	15.2029i	−0.369922	+	0.640724i	0.619631	+	0.784893i	$0.287282\pi$
$564$			0.253545i			0.0106762i
$565$		0			0
$566$	−20.9106	−	12.0727i	−0.878936	−	0.507454i
$567$			27.6414i			1.16083i
$568$	15.7977	−	27.3624i	0.662857	−	1.14810i
$569$	−15.3084	−	26.5150i	−0.641763	−	1.11157i	−0.985039	−	0.172331i	$-0.944870\pi$
$569$	−15.3084	−	26.5150i	−0.641763	−	1.11157i	0.343276	−	0.939235i	$-0.388463\pi$
$570$		0			0
$571$	−5.33906			−0.223433			−0.111716	−	0.993740i	$-0.535635\pi$
$571$	−5.33906			−0.223433			−0.111716	+	0.993740i	$0.535635\pi$
$572$	0.315097	+	1.56829i	0.0131748	+	0.0655736i
$573$	0.771438			0.0322273
$574$	−32.8053	+	18.9401i	−1.36927	+	0.790546i
$575$		0			0
$576$	−12.0216	+	20.8220i	−0.500901	+	0.867585i
$577$			2.82977i			0.117805i	0.998264	+	0.0589024i	$0.0187601\pi$
$577$			2.82977i			0.117805i	−0.998264	+	0.0589024i	$0.981240\pi$
$578$	−14.5062	−	8.37516i	−0.603379	−	0.348361i
$579$	1.84335	+	1.06426i	0.0766071	+	0.0442291i
$580$		0			0
$581$	2.15093	−	3.72553i	0.0892357	−	0.154561i
$582$	1.43423	+	2.48416i	0.0594508	+	0.102972i
$583$	−8.64603	+	4.99179i	−0.358082	+	0.206739i
$584$	22.4031			0.927047
$585$		0			0
$586$	−30.0473			−1.24124
$587$	7.44364	−	4.29759i	0.307232	−	0.177380i	−0.338455	−	0.940982i	$-0.609904\pi$
$587$	7.44364	−	4.29759i	0.307232	−	0.177380i	0.645687	+	0.763602i	$0.276571\pi$
$588$	−0.169901	−	0.294277i	−0.00700659	−	0.0121358i
$589$	−3.61019	+	6.25303i	−0.148755	+	0.257652i
$590$		0			0
$591$	−5.31382	−	3.06794i	−0.218582	−	0.126198i
$592$	34.8935	+	20.1458i	1.43411	+	0.827986i
$593$			15.6269i			0.641720i	0.947127	+	0.320860i	$0.103972\pi$
$593$			15.6269i			0.641720i	−0.947127	+	0.320860i	$0.896028\pi$
$594$	−5.22570	+	9.05119i	−0.214413	+	0.371375i
$595$		0			0
$596$	−2.18780	+	1.26313i	−0.0896159	+	0.0517398i
$597$	8.51307			0.348417
$598$	3.56910	+	1.20388i	0.145951	+	0.0492303i
$599$	5.84438			0.238795			0.119398	−	0.992847i	$-0.461904\pi$
$599$	5.84438			0.238795			0.119398	+	0.992847i	$0.461904\pi$
$600$		0			0
$601$	−11.8757	−	20.5694i	−0.484421	−	0.839042i	0.515419	−	0.856939i	$-0.327636\pi$
$601$	−11.8757	−	20.5694i	−0.484421	−	0.839042i	−0.999840	+	0.0178963i	$0.994303\pi$
$602$	9.54306	−	16.5291i	0.388946	−	0.673674i
$603$		−	13.2004i		−	0.537564i
$604$	0.777481	+	0.448879i	0.0316353	+	0.0182646i
$605$		0			0
$606$		−	9.32522i		−	0.378811i
$607$	18.6540	−	32.3096i	0.757141	−	1.31141i	−0.187162	−	0.982329i	$-0.559929\pi$
$607$	18.6540	−	32.3096i	0.757141	−	1.31141i	0.944303	−	0.329078i	$-0.106738\pi$
$608$	−0.327848	−	0.567849i	−0.0132960	−	0.0230293i
$609$	3.86705	−	2.23264i	0.156701	−	0.0904712i
$610$		0			0
$611$	−3.32599	−	16.5541i	−0.134555	−	0.669706i
$612$	−0.836503			−0.0338136
$613$	−35.9007	+	20.7273i	−1.45002	+	0.837168i	−0.998482	−	0.0550852i	$-0.982457\pi$
$613$	−35.9007	+	20.7273i	−1.45002	+	0.837168i	−0.451536	+	0.892253i	$0.649124\pi$
$614$	1.11346	+	1.92858i	0.0449357	+	0.0778310i
$615$		0			0
$616$			34.8176i			1.40284i
$617$	7.89098	+	4.55586i	0.317679	+	0.183412i	0.650358	−	0.759628i	$-0.274619\pi$
$617$	7.89098	+	4.55586i	0.317679	+	0.183412i	−0.332679	+	0.943040i	$0.607952\pi$
$618$	−0.383299	−	0.221298i	−0.0154185	−	0.00890190i
$619$			33.6828i			1.35382i	0.736064	+	0.676912i	$0.236682\pi$
$619$			33.6828i			1.35382i	−0.736064	+	0.676912i	$0.763318\pi$
$620$		0			0
$621$	−0.893406	−	1.54742i	−0.0358512	−	0.0620960i
$622$	−22.4750	+	12.9760i	−0.901166	+	0.520289i
$623$	−11.8877			−0.476271
$624$	−1.71020	+	5.07019i	−0.0684630	+	0.202970i
$625$		0			0
$626$	13.1270	−	7.57888i	0.524661	−	0.302913i
$627$	−0.562038	−	0.973479i	−0.0224456	−	0.0388770i
$628$	−0.312393	+	0.541081i	−0.0124658	+	0.0215915i
$629$			23.6219i			0.941867i
$630$		0			0
$631$	22.3619	+	12.9106i	0.890213	+	0.513965i	0.874012	−	0.485904i	$-0.161510\pi$
$631$	22.3619	+	12.9106i	0.890213	+	0.513965i	0.0162010	+	0.999869i	$0.494843\pi$
$632$			29.7731i			1.18431i
$633$	−2.72777	+	4.72464i	−0.108419	+	0.187788i
$634$	3.56440	+	6.17373i	0.141561	+	0.245190i
$635$		0			0
$636$	0.164939			0.00654025
$637$	14.9532	+	16.9847i	0.592468	+	0.672960i
$638$	−13.7129			−0.542897
$639$	26.6510	−	15.3869i	1.05430	−	0.608698i
$640$		0			0
$641$	6.61778	−	11.4623i	0.261387	−	0.452735i	−0.705224	−	0.708985i	$-0.749154\pi$
$641$	6.61778	−	11.4623i	0.261387	−	0.452735i	0.966611	+	0.256250i	$0.0824869\pi$
$642$		−	7.31055i		−	0.288524i
$643$	19.8080	+	11.4361i	0.781151	+	0.450998i	0.836838	−	0.547451i	$-0.184402\pi$
$643$	19.8080	+	11.4361i	0.781151	+	0.450998i	−0.0556871	+	0.998448i	$0.517735\pi$
$644$	−0.326825	−	0.188693i	−0.0128787	−	0.00743554i
$645$		0			0
$646$	−1.27403	+	2.20669i	−0.0501261	+	0.0868210i
$647$	−2.13016	−	3.68955i	−0.0837454	−	0.145051i	0.821111	−	0.570769i	$-0.193355\pi$
$647$	−2.13016	−	3.68955i	−0.0837454	−	0.145051i	−0.904856	+	0.425718i	$0.860022\pi$
$648$	−19.1568	+	11.0602i	−0.752551	+	0.434486i
$649$	−43.6601			−1.71381
$650$		0			0
$651$	−12.2669			−0.480776
$652$	1.14316	−	0.660003i	0.0447696	−	0.0258477i
$653$	−6.33210	−	10.9675i	−0.247794	−	0.429192i	0.715119	−	0.699002i	$-0.246372\pi$
$653$	−6.33210	−	10.9675i	−0.247794	−	0.429192i	−0.962914	+	0.269810i	$0.913039\pi$
$654$	1.53242	−	2.65423i	0.0599224	−	0.103789i
$655$		0			0
$656$	−24.4676	−	14.1264i	−0.955301	−	0.551543i
$657$	18.8972	+	10.9103i	0.737249	+	0.425651i
$658$		−	23.3001i		−	0.908334i
$659$	13.6330	−	23.6130i	0.531066	−	0.919833i	−0.468277	−	0.883582i	$-0.655125\pi$
$659$	13.6330	−	23.6130i	0.531066	−	0.919833i	0.999343	−	0.0362512i	$-0.0115417\pi$
$660$		0			0
$661$	−3.94278	+	2.27636i	−0.153356	+	0.0885403i	−0.574714	−	0.818354i	$-0.694887\pi$
$661$	−3.94278	+	2.27636i	−0.153356	+	0.0885403i	0.421358	+	0.906894i	$0.361554\pi$
$662$	35.0082			1.36063
$663$	−3.07560	+	0.617940i	−0.119447	+	0.0239988i
$664$	3.44263			0.133600
$665$		0			0
$666$	21.0536	+	36.4660i	0.815812	+	1.41303i
$667$	1.17220	−	2.03031i	0.0453878	−	0.0786140i
$668$			1.40591i			0.0543964i
$669$	−8.55876	−	4.94140i	−0.330901	−	0.191046i
$670$		0			0
$671$		−	42.7028i		−	1.64852i
$672$	0.556988	−	0.964731i	0.0214863	−	0.0372153i
$673$	−10.3306	−	17.8932i	−0.398217	−	0.689732i	0.595289	−	0.803512i	$-0.297037\pi$
$673$	−10.3306	−	17.8932i	−0.398217	−	0.689732i	−0.993506	+	0.113780i	$0.963704\pi$
$674$	−42.7435	+	24.6780i	−1.64642	+	0.950559i
$675$		0			0
$676$	−0.222992	+	1.74577i	−0.00857661	+	0.0671449i
$677$	−36.1528			−1.38947			−0.694733	−	0.719268i	$-0.744477\pi$
$677$	−36.1528			−1.38947			−0.694733	+	0.719268i	$0.744477\pi$
$678$	8.62259	−	4.97825i	0.331149	−	0.191189i
$679$	9.56953	+	16.5749i	0.367245	+	0.636087i
$680$		0			0
$681$		−	4.72632i		−	0.181113i
$682$	32.6244	+	18.8357i	1.24925	+	0.721257i
$683$	31.7208	+	18.3140i	1.21376	+	0.700765i	0.963577	−	0.267433i	$-0.0861753\pi$
$683$	31.7208	+	18.3140i	1.21376	+	0.700765i	0.250185	+	0.968198i	$0.419509\pi$
$684$		−	0.329777i		−	0.0126093i
$685$		0			0
$686$	−1.80059	−	3.11872i	−0.0687470	−	0.119073i
$687$	−1.03340	+	0.596635i	−0.0394268	+	0.0227631i
$688$	14.2353			0.542715
$689$	−10.7689	+	2.16366i	−0.410264	+	0.0824290i
$690$		0			0
$691$	−25.4551	+	14.6965i	−0.968359	+	0.559082i	−0.898735	−	0.438491i	$-0.855513\pi$
$691$	−25.4551	+	14.6965i	−0.968359	+	0.559082i	−0.0696233	+	0.997573i	$0.522180\pi$
$692$	1.03505	+	1.79275i	0.0393465	+	0.0681502i
$693$	−16.9561	+	29.3689i	−0.644110	+	1.11563i
$694$		−	19.6781i		−	0.746971i
$695$		0			0
$696$	3.09466	+	1.78670i	0.117303	+	0.0677248i
$697$		−	16.5639i		−	0.627402i
$698$	2.27996	−	3.94901i	0.0862979	−	0.149472i
$699$	1.37586	+	2.38306i	0.0520397	+	0.0901355i
$700$		0			0
$701$	−19.8074			−0.748116			−0.374058	−	0.927405i	$-0.622034\pi$
$701$	−19.8074			−0.748116			−0.374058	+	0.927405i	$0.622034\pi$
$702$	−8.63068	+	7.59838i	−0.325744	+	0.286782i
$703$	−9.31252			−0.351228
$704$	−24.0263	+	13.8716i	−0.905524	+	0.522805i
$705$		0			0
$706$	−7.97497	+	13.8131i	−0.300142	+	0.519861i
$707$		−	62.2201i		−	2.34003i
$708$	0.624672	+	0.360654i	0.0234766	+	0.0135542i
$709$	11.6423	+	6.72169i	0.437236	+	0.252438i	0.702424	−	0.711758i	$-0.252101\pi$
$709$	11.6423	+	6.72169i	0.437236	+	0.252438i	−0.265189	+	0.964197i	$0.585434\pi$
$710$		0			0
$711$	−14.4995	+	25.1138i	−0.543772	+	0.941841i
$712$	−4.75666	−	8.23877i	−0.178263	−	0.308761i
$713$	−5.57760	+	3.22023i	−0.208883	+	0.120598i
$714$	−4.32896			−0.162007
$715$		0			0
$716$	−1.57125			−0.0587204
$717$	−6.35280	+	3.66779i	−0.237250	+	0.136976i
$718$	4.46985	+	7.74201i	0.166813	+	0.288929i
$719$	−7.11118	+	12.3169i	−0.265202	+	0.459344i	−0.967617	−	0.252425i	$-0.918772\pi$
$719$	−7.11118	+	12.3169i	−0.265202	+	0.459344i	0.702414	+	0.711768i	$0.252105\pi$
$720$		0			0
$721$	−2.55746	−	1.47655i	−0.0952448	−	0.0549896i
$722$	21.5988	+	12.4701i	0.803825	+	0.464089i
$723$			6.65325i			0.247437i
$724$	−0.271806	+	0.470782i	−0.0101016	+	0.0174965i
$725$		0			0
$726$	0.123213	−	0.0711369i	0.00457286	−	0.00264014i
$727$	47.6220			1.76620			0.883101	−	0.469183i	$-0.155452\pi$
$727$	47.6220			1.76620			0.883101	+	0.469183i	$0.155452\pi$
$728$	−12.2435	+	36.2978i	−0.453773	+	1.34529i
$729$	−18.7431			−0.694191
$730$		0			0
$731$	4.17289	+	7.22765i	0.154340	+	0.267324i
$732$	−0.352747	+	0.610976i	−0.0130379	+	0.0225823i
$733$		−	16.0484i		−	0.592762i	−0.955070	−	0.296381i	$-0.904220\pi$
$733$		−	16.0484i		−	0.592762i	0.955070	−	0.296381i	$-0.0957799\pi$
$734$	−26.7518	−	15.4452i	−0.987428	−	0.570092i
$735$		0			0
$736$		−	0.584869i		−	0.0215586i
$737$	7.61591	−	13.1911i	0.280535	−	0.485902i
$738$	−14.7630	−	25.5703i	−0.543434	−	0.941254i
$739$	−7.81546	+	4.51226i	−0.287496	+	0.165986i	−0.636812	−	0.771019i	$-0.719747\pi$
$739$	−7.81546	+	4.51226i	−0.287496	+	0.165986i	0.349316	+	0.937005i	$0.386414\pi$
$740$		0			0
$741$	−0.243612	−	1.21250i	−0.00894932	−	0.0445424i
$742$	−15.1575			−0.556449
$743$	−31.9885	+	18.4686i	−1.17355	+	0.677547i	−0.954512	−	0.298171i	$-0.903623\pi$
$743$	−31.9885	+	18.4686i	−1.17355	+	0.677547i	−0.219033	+	0.975718i	$0.570290\pi$
$744$	−4.90837	−	8.50154i	−0.179949	−	0.311682i
$745$		0			0
$746$			5.80568i			0.212561i
$747$	2.90388	+	1.67656i	0.106247	+	0.0613420i
$748$	−0.835913	−	0.482614i	−0.0305640	−	0.0176461i
$749$		−	48.7777i		−	1.78230i
$750$		0			0
$751$	2.29939	+	3.98265i	0.0839058	+	0.145329i	0.904924	−	0.425572i	$-0.139927\pi$
$751$	2.29939	+	3.98265i	0.0839058	+	0.145329i	−0.821019	+	0.570901i	$0.806594\pi$
$752$	15.0500	−	8.68914i	0.548818	−	0.316861i
$753$	−1.12365			−0.0409480
$754$	−14.2958	−	4.82207i	−0.520623	−	0.175609i
$755$		0			0
$756$	0.997731	−	0.576040i	0.0362871	−	0.0209504i
$757$	7.84265	+	13.5839i	0.285046	+	0.493714i	0.972620	−	0.232400i	$-0.0746578\pi$
$757$	7.84265	+	13.5839i	0.285046	+	0.493714i	−0.687574	+	0.726114i	$0.741324\pi$
$758$	−7.60690	+	13.1755i	−0.276295	+	0.478557i
$759$		−	1.00266i		−	0.0363942i
$760$		0			0
$761$	−20.2736	−	11.7049i	−0.734916	−	0.424304i	0.0853021	−	0.996355i	$-0.472814\pi$
$761$	−20.2736	−	11.7049i	−0.734916	−	0.424304i	−0.820218	+	0.572051i	$0.806148\pi$
$762$		−	9.26731i		−	0.335719i
$763$	10.2247	−	17.7096i	0.370158	−	0.641132i
$764$	0.130574	+	0.226161i	0.00472401	+	0.00818223i
$765$		0			0
$766$	7.49564			0.270829
$767$	−45.5162	−	15.3529i	−1.64349	−	0.554361i
$768$	1.29330			0.0466680
$769$	−24.8331	+	14.3374i	−0.895504	+	0.517020i	−0.875739	−	0.482785i	$-0.839625\pi$
$769$	−24.8331	+	14.3374i	−0.895504	+	0.517020i	−0.0197654	+	0.999805i	$0.506292\pi$
$770$		0			0
$771$	0.663649	−	1.14947i	0.0239007	−	0.0413973i
$772$			0.720551i			0.0259332i
$773$	−24.7267	−	14.2759i	−0.889356	−	0.513470i	−0.0156243	−	0.999878i	$-0.504974\pi$
$773$	−24.7267	−	14.2759i	−0.889356	−	0.513470i	−0.873732	+	0.486408i	$0.838307\pi$
$774$	12.8837	+	7.43839i	0.463094	+	0.267367i
$775$		0			0
$776$	−7.65815	+	13.2643i	−0.274912	+	0.476161i
$777$	−7.91063	−	13.7016i	−0.283792	−	0.491543i
$778$	−30.6846	+	17.7158i	−1.10010	+	0.635141i
$779$	6.53003			0.233963
$780$		0			0
$781$	35.5096			1.27063
$782$	−1.96833	+	1.13642i	−0.0703873	+	0.0406381i
$783$	3.57849	+	6.19813i	0.127885	+	0.221503i
$784$	−11.6452	+	20.1701i	−0.415901	+	0.720361i
$785$		0			0
$786$	8.38153	+	4.83908i	0.298959	+	0.172604i
$787$	−6.70528	−	3.87129i	−0.239017	−	0.137997i	0.375708	−	0.926738i	$-0.377400\pi$
$787$	−6.70528	−	3.87129i	−0.239017	−	0.137997i	−0.614725	+	0.788742i	$0.710733\pi$
$788$		−	2.07713i		−	0.0739947i
$789$	4.99134	−	8.64525i	0.177696	−	0.307779i
$790$		0			0
$791$	57.5319	−	33.2161i	2.04560	−	1.18103i
$792$	−27.1388			−0.964334
$793$	15.0163	−	44.5182i	0.533243	−	1.58089i
$794$	18.9404			0.672171
$795$		0			0
$796$	1.44093	+	2.49577i	0.0510724	+	0.0884601i
$797$	−16.4245	+	28.4481i	−0.581787	+	1.00768i	0.413480	+	0.910513i	$0.364313\pi$
$797$	−16.4245	+	28.4481i	−0.581787	+	1.00768i	−0.995268	+	0.0971719i	$0.969020\pi$
$798$		−	1.70662i		−	0.0604137i
$799$	8.82345	+	5.09422i	0.312151	+	0.180221i
$800$		0			0
$801$		−	9.26594i		−	0.327396i
$802$	0.862523	−	1.49393i	0.0304567	−	0.0527526i
$803$	12.5892	+	21.8052i	0.444264	+	0.769489i
$804$	−0.217931	+	0.125823i	−0.00768583	+	0.00443742i
$805$		0			0
$806$	27.3879	+	31.1087i	0.964697	+	1.09576i
$807$	−4.61375			−0.162412
$808$	43.1216	−	24.8963i	1.51701	−	0.875847i
$809$	12.7521	+	22.0873i	0.448341	+	0.776549i	0.998278	−	0.0586568i	$-0.0186818\pi$
$809$	12.7521	+	22.0873i	0.448341	+	0.776549i	−0.549937	+	0.835206i	$0.685348\pi$
$810$		0			0
$811$		−	2.12653i		−	0.0746726i	−0.999303	−	0.0373363i	$-0.988113\pi$
$811$		−	2.12653i		−	0.0746726i	0.999303	−	0.0373363i	$-0.0118873\pi$
$812$	1.30908	+	0.755799i	0.0459398	+	0.0265233i
$813$	−6.92045	−	3.99552i	−0.242711	−	0.140129i
$814$			48.5870i			1.70297i
$815$		0			0
$816$	−1.61437	−	2.79617i	−0.0565142	−	0.0978854i
$817$	−2.84938	+	1.64509i	−0.0996871	+	0.0575544i
$818$	−30.1076			−1.05269
$819$	−28.0044	+	24.6549i	−0.978554	+	0.861511i
$820$		0			0
$821$	−13.5719	+	7.83574i	−0.473662	+	0.273469i	−0.717772	−	0.696279i	$-0.754838\pi$
$821$	−13.5719	+	7.83574i	−0.473662	+	0.273469i	0.244109	+	0.969748i	$0.421504\pi$
$822$	4.39841	+	7.61827i	0.153412	+	0.265718i
$823$	17.2139	−	29.8154i	0.600040	−	1.03930i	−0.392775	−	0.919635i	$-0.628485\pi$
$823$	17.2139	−	29.8154i	0.600040	−	1.03930i	0.992814	−	0.119664i	$-0.0381818\pi$
$824$		−	2.36326i		−	0.0823281i
$825$		0			0
$826$	−57.4058	−	33.1432i	−1.99740	−	1.15320i
$827$			37.6478i			1.30914i	0.756000	+	0.654572i	$0.227151\pi$
$827$			37.6478i			1.30914i	−0.756000	+	0.654572i	$0.772849\pi$
$828$	0.147078	−	0.254746i	0.00511130	−	0.00885303i
$829$	−16.6669	−	28.8679i	−0.578865	−	1.00262i	−0.995610	−	0.0936002i	$-0.970162\pi$
$829$	−16.6669	−	28.8679i	−0.578865	−	1.00262i	0.416745	−	0.909024i	$-0.363171\pi$
$830$		0			0
$831$	2.44792			0.0849174
$832$	−29.9256	+	6.01256i	−1.03748	+	0.208448i
$833$	−13.6546			−0.473104
$834$	−1.62260	+	0.936806i	−0.0561859	+	0.0324389i
$835$		0			0
$836$	0.190262	−	0.329544i	0.00658036	−	0.0113975i
$837$		−	19.6614i		−	0.679597i
$838$	13.8128	+	7.97484i	0.477156	+	0.275486i
$839$	−3.77053	−	2.17692i	−0.130173	−	0.0751556i	0.433499	−	0.901154i	$-0.357279\pi$
$839$	−3.77053	−	2.17692i	−0.130173	−	0.0751556i	−0.563673	+	0.825998i	$0.690612\pi$
$840$		0			0
$841$	9.80481	−	16.9824i	0.338097	−	0.585601i
$842$	−15.0051	−	25.9897i	−0.517111	−	0.895663i
$843$	−8.87606	+	5.12460i	−0.305708	+	0.176500i
$844$	−1.84682			−0.0635702
$845$		0			0
$846$	18.1614			0.624403
$847$	0.822105	−	0.474642i	0.0282479	−	0.0163089i
$848$	−5.65256	−	9.79052i	−0.194110	−	0.336208i
$849$	−3.53574	+	6.12409i	−0.121346	+	0.210178i
$850$		0			0
$851$	−7.19374	−	4.15331i	−0.246598	−	0.142374i
$852$	−0.508057	−	0.293327i	−0.0174058	−	0.0100492i
$853$		−	11.2955i		−	0.386751i	−0.981125	−	0.193375i	$-0.938056\pi$
$853$		−	11.2955i		−	0.386751i	0.981125	−	0.193375i	$-0.0619435\pi$
$854$	32.4166	−	56.1471i	1.10927	−	1.92132i
$855$		0			0
$856$	33.8054	−	19.5175i	1.15544	−	0.667095i
$857$	−9.88043			−0.337509			−0.168754	−	0.985658i	$-0.553974\pi$
$857$	−9.88043			−0.337509			−0.168754	+	0.985658i	$0.553974\pi$
$858$	−6.32609	+	1.27102i	−0.215969	+	0.0433918i
$859$	0.0855154			0.00291775			0.00145887	−	0.999999i	$-0.499536\pi$
$859$	0.0855154			0.00291775			0.00145887	+	0.999999i	$0.499536\pi$
$860$		0			0
$861$	5.54701	+	9.60770i	0.189042	+	0.327430i
$862$	−16.4657	+	28.5195i	−0.560825	+	0.971377i
$863$			43.5513i			1.48250i	0.671227	+	0.741252i	$0.265767\pi$
$863$			43.5513i			1.48250i	−0.671227	+	0.741252i	$0.734233\pi$
$864$	1.54628	+	0.892743i	0.0526054	+	0.0303717i
$865$		0			0
$866$			9.13773i			0.310513i
$867$	−2.45284	+	4.24844i	−0.0833027	+	0.144285i
$868$	−2.07630	−	3.59626i	−0.0704743	−	0.122065i
$869$	−28.9785	+	16.7307i	−0.983027	+	0.567551i
$870$		0			0
$871$	12.5783	−	11.0738i	0.426199	−	0.375222i
$872$	16.3649			0.554184
$873$	−12.9194	+	7.45903i	−0.437256	+	0.252450i
$874$	−0.448012	−	0.775979i	−0.0151542	−	0.0262479i
$875$		0			0
$876$		−	0.415974i		−	0.0140545i
$877$	−10.6901	−	6.17191i	−0.360978	−	0.208411i	0.308532	−	0.951214i	$-0.400162\pi$
$877$	−10.6901	−	6.17191i	−0.360978	−	0.208411i	−0.669510	+	0.742803i	$0.733496\pi$
$878$	33.0852	+	19.1018i	1.11657	+	0.644653i
$879$			8.79997i			0.296816i
$880$		0			0
$881$	25.2655	+	43.7612i	0.851217	+	1.47435i	0.880111	+	0.474769i	$0.157468\pi$
$881$	25.2655	+	43.7612i	0.851217	+	1.47435i	−0.0288935	+	0.999582i	$0.509198\pi$
$882$	−21.0791	+	12.1700i	−0.709769	+	0.409785i
$883$	23.8742			0.803432			0.401716	−	0.915764i	$-0.368414\pi$
$883$	23.8742			0.803432			0.401716	+	0.915764i	$0.368414\pi$
$884$	−0.701740	−	0.797077i	−0.0236021	−	0.0268086i
$885$		0			0
$886$	−23.0311	+	13.2970i	−0.773745	+	0.446722i
$887$	−18.1599	−	31.4538i	−0.609748	−	1.05611i	−0.991282	−	0.131760i	$-0.957937\pi$
$887$	−18.1599	−	31.4538i	−0.609748	−	1.05611i	0.381533	−	0.924355i	$-0.375396\pi$
$888$	6.33059	−	10.9649i	0.212441	−	0.367958i
$889$		−	61.8337i		−	2.07384i
$890$		0			0
$891$	−21.5300	−	12.4304i	−0.721283	−	0.416433i
$892$		−	3.34555i		−	0.112017i
$893$	−2.00831	+	3.47849i	−0.0672055	+	0.116403i
$894$	−5.09514	−	8.82503i	−0.170407	−	0.295153i
$895$		0			0
$896$	−36.5498			−1.22104
$897$	0.352580	−	1.04528i	0.0117723	−	0.0349010i
$898$	−18.0070			−0.600900
$899$	22.3408	−	12.8984i	0.745106	−	0.430187i
$900$		0			0
$901$	3.31395	−	5.73993i	0.110404	−	0.191225i
$902$		−	34.0696i		−	1.13440i
$903$	−4.84087	−	2.79488i	−0.161094	−	0.0930078i
$904$	46.0408	+	26.5816i	1.53129	+	0.884092i
$905$		0			0
$906$	−1.81066	+	3.13616i	−0.0601552	+	0.104192i
$907$	15.2261	+	26.3724i	0.505575	+	0.875681i	0.999979	+	0.00644938i	$0.00205292\pi$
$907$	15.2261	+	26.3724i	0.505575	+	0.875681i	−0.494404	+	0.869232i	$0.664614\pi$
$908$	1.38561	−	0.799981i	0.0459830	−	0.0265483i
$909$	48.4978			1.60857
$910$		0			0
$911$	29.8054			0.987498			0.493749	−	0.869604i	$-0.335626\pi$
$911$	29.8054			0.987498			0.493749	+	0.869604i	$0.335626\pi$
$912$	1.10234	−	0.636436i	0.0365021	−	0.0210745i
$913$	1.93456	+	3.35075i	0.0640245	+	0.110894i
$914$	9.46160	−	16.3880i	0.312962	−	0.542066i
$915$		0			0
$916$	−0.349830	−	0.201974i	−0.0115587	−	0.00667341i
$917$	55.9235	+	32.2875i	1.84676	+	1.06623i
$918$		−	6.93849i		−	0.229004i
$919$	4.86112	−	8.41970i	0.160353	−	0.277740i	−0.774642	−	0.632400i	$-0.782070\pi$
$919$	4.86112	−	8.41970i	0.160353	−	0.277740i	0.934995	+	0.354660i	$0.115403\pi$
$920$		0			0
$921$	0.564823	−	0.326101i	0.0186115	−	0.0107454i
$922$	19.2084			0.632597
$923$	37.0192	+	12.4868i	1.21850	+	0.411008i
$924$	0.646482			0.0212677
$925$		0			0
$926$	3.32198	+	5.75384i	0.109167	+	0.189083i
$927$	1.15091	−	1.99343i	0.0378007	−	0.0654727i
$928$			2.34266i			0.0769017i
$929$	3.71589	+	2.14537i	0.121914	+	0.0703874i	0.559717	−	0.828684i	$-0.310910\pi$
$929$	3.71589	+	2.14537i	0.121914	+	0.0703874i	−0.437803	+	0.899071i	$0.644243\pi$
$930$		0			0
$931$		−	5.38308i		−	0.176423i
$932$	−0.465758	+	0.806717i	−0.0152564	+	0.0264249i
$933$	3.80027	+	6.58227i	0.124415	+	0.215494i
$934$	31.5046	−	18.1892i	1.03086	−	0.595169i
$935$		0			0
$936$	−28.2925	−	9.54324i	−0.924770	−	0.311931i
$937$	8.43750			0.275641			0.137821	−	0.990457i	$-0.455990\pi$
$937$	8.43750			0.275641			0.137821	+	0.990457i	$0.455990\pi$
$938$	20.0273	−	11.5628i	0.653915	−	0.377538i
$939$	−2.21963	−	3.84451i	−0.0724349	−	0.125461i
$940$		0			0
$941$		−	22.1898i		−	0.723368i	−0.932301	−	0.361684i	$-0.882202\pi$
$941$		−	22.1898i		−	0.723368i	0.932301	−	0.361684i	$-0.117798\pi$
$942$	−2.18258	−	1.26011i	−0.0711123	−	0.0410567i
$943$	5.04432	+	2.91234i	0.164266	+	0.0948388i
$944$		−	49.4394i		−	1.60912i
$945$		0			0
$946$	8.58305	+	14.8663i	0.279059	+	0.483345i
$947$	10.5323	−	6.08080i	0.342252	−	0.197599i	−0.319015	−	0.947750i	$-0.603352\pi$
$947$	10.5323	−	6.08080i	0.342252	−	0.197599i	0.661268	+	0.750150i	$0.270019\pi$
$948$	0.552817			0.0179547
$949$	5.45673	+	27.1591i	0.177133	+	0.881623i
$950$		0			0
$951$	1.80810	−	1.04391i	0.0586317	−	0.0338511i
$952$	−11.5574	−	20.0179i	−0.374576	−	0.648785i
$953$	27.8920	−	48.3104i	0.903512	−	1.56493i	0.0806088	−	0.996746i	$-0.474314\pi$
$953$	27.8920	−	48.3104i	0.903512	−	1.56493i	0.822903	−	0.568182i	$-0.192353\pi$
$954$		−	11.8146i		−	0.382511i
$955$		0			0
$956$	−2.15056	−	1.24163i	−0.0695542	−	0.0401571i
$957$			4.01609i			0.129822i
$958$	2.06401	−	3.57498i	0.0666853	−	0.115502i
$959$	29.3472	+	50.8309i	0.947671	+	1.64141i
$960$		0			0
$961$	−39.8683			−1.28607
$962$	−17.0854	+	50.6526i	−0.550856	+	1.63310i
$963$	38.0201			1.22518
$964$	−1.95052	+	1.12614i	−0.0628222	+	0.0362704i
$965$		0			0
$966$	0.761138	−	1.31833i	0.0244892	−	0.0424165i
$967$		−	12.5378i		−	0.403190i	−0.979469	−	0.201595i	$-0.935388\pi$
$967$		−	12.5378i		−	0.403190i	0.979469	−	0.201595i	$-0.0646124\pi$
$968$	0.657901	+	0.379839i	0.0211457	+	0.0122085i
$969$	0.646274	+	0.373126i	0.0207613	+	0.0119865i
$970$		0			0
$971$	−10.3267	+	17.8864i	−0.331400	+	0.574001i	−0.982787	−	0.184745i	$-0.940854\pi$
$971$	−10.3267	+	17.8864i	−0.331400	+	0.574001i	0.651387	+	0.758746i	$0.274187\pi$
$972$	0.679645	+	1.17718i	0.0217996	+	0.0377581i
$973$	−10.8263	+	6.25059i	−0.347076	+	0.200385i
$974$	16.1404			0.517172
$975$		0			0
$976$	48.3554			1.54782
$977$	−16.6632	+	9.62051i	−0.533103	+	0.307787i	−0.742279	−	0.670091i	$-0.766255\pi$
$977$	−16.6632	+	9.62051i	−0.533103	+	0.307787i	0.209176	+	0.977878i	$0.432922\pi$
$978$	2.66228	+	4.61121i	0.0851304	+	0.147450i
$979$	5.34592	−	9.25941i	0.170856	−	0.295932i
$980$		0			0
$981$	13.8039	+	7.96967i	0.440724	+	0.254452i
$982$	−11.4074	−	6.58605i	−0.364024	−	0.210169i
$983$			28.9070i			0.921990i	0.887403	+	0.460995i	$0.152507\pi$
$983$			28.9070i			0.921990i	−0.887403	+	0.460995i	$0.847493\pi$
$984$	−4.43907	+	7.68870i	−0.141512	+	0.245107i
$985$		0			0
$986$	7.88403	−	4.55185i	0.251079	−	0.144960i
$987$	−6.82392			−0.217208
$988$	0.314234	−	0.276649i	0.00999711	−	0.00880138i
$989$	−2.93478			−0.0933207
$990$		0			0
$991$	19.2004	+	33.2561i	0.609922	+	1.05642i	0.991253	+	0.131977i	$0.0421324\pi$
$991$	19.2004	+	33.2561i	0.609922	+	1.05642i	−0.381331	+	0.924438i	$0.624534\pi$
$992$	3.21784	−	5.57346i	0.102166	−	0.176957i
$993$		−	10.2529i		−	0.325365i
$994$	46.6892	+	26.9560i	1.48089	+	0.854993i
$995$		0			0
$996$		−	0.0639217i		−	0.00202544i
$997$	26.4900	−	45.8820i	0.838947	−	1.45310i	−0.0518287	−	0.998656i	$-0.516505\pi$
$997$	26.4900	−	45.8820i	0.838947	−	1.45310i	0.890776	−	0.454443i	$-0.150162\pi$
$998$	−6.88265	−	11.9211i	−0.217867	−	0.377356i
$999$	21.9610	−	12.6792i	0.694816	−	0.401152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.n.e.101.2	✓	10
5.2	odd	4		325.2.m.d.49.3		20
5.3	odd	4		325.2.m.d.49.8		20
5.4	even	2		325.2.n.f.101.4	yes	10
13.2	odd	12		4225.2.a.bv.1.3		10
13.4	even	6	inner	325.2.n.e.251.2	yes	10
13.11	odd	12		4225.2.a.bv.1.8		10
65.4	even	6		325.2.n.f.251.4	yes	10
65.17	odd	12		325.2.m.d.199.8		20
65.24	odd	12		4225.2.a.bu.1.3		10
65.43	odd	12		325.2.m.d.199.3		20
65.54	odd	12		4225.2.a.bu.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.m.d.49.3		20	5.2	odd	4
325.2.m.d.49.8		20	5.3	odd	4
325.2.m.d.199.3		20	65.43	odd	12
325.2.m.d.199.8		20	65.17	odd	12
325.2.n.e.101.2	✓	10	1.1	even	1	trivial
325.2.n.e.251.2	yes	10	13.4	even	6	inner
325.2.n.f.101.4	yes	10	5.4	even	2
325.2.n.f.251.4	yes	10	65.4	even	6
4225.2.a.bu.1.3		10	65.24	odd	12
4225.2.a.bu.1.8		10	65.54	odd	12
4225.2.a.bv.1.3		10	13.2	odd	12
4225.2.a.bv.1.8		10	13.11	odd	12

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18257 + 0.682755i) q^{2} +(0.199959 + 0.346339i) q^{3} +(-0.0676905 + 0.117243i) q^{4} +(-0.472929 - 0.273046i) q^{6} +(-3.15550 - 1.82183i) q^{7} -2.91589i q^{8} +(1.42003 - 2.45957i) q^{9} +O(q^{10})\)	\(q+(-1.18257 + 0.682755i) q^{2} +(0.199959 + 0.346339i) q^{3} +(-0.0676905 + 0.117243i) q^{4} +(-0.472929 - 0.273046i) q^{6} +(-3.15550 - 1.82183i) q^{7} -2.91589i q^{8} +(1.42003 - 2.45957i) q^{9} +(2.83806 - 1.63856i) q^{11} -0.0541412 q^{12} +(3.53491 - 0.710223i) q^{13} +4.97545 q^{14} +(1.85546 + 3.21374i) q^{16} +(-1.08781 + 1.88413i) q^{17} +3.87814i q^{18} +(-0.742787 - 0.428848i) q^{19} -1.45716i q^{21} +(-2.23747 + 3.87540i) q^{22} +(-0.382526 - 0.662554i) q^{23} +(1.00988 - 0.583057i) q^{24} +(-3.69536 + 3.25336i) q^{26} +2.33555 q^{27} +(0.427194 - 0.246641i) q^{28} +(1.53219 + 2.65382i) q^{29} -8.41833i q^{31} +(0.662062 + 0.382242i) q^{32} +(1.13499 + 0.655288i) q^{33} -2.97082i q^{34} +(0.192245 + 0.332979i) q^{36} +(9.40295 - 5.42880i) q^{37} +1.17119 q^{38} +(0.952814 + 1.08226i) q^{39} +(-6.59344 + 3.80672i) q^{41} +(0.994885 + 1.72319i) q^{42} +(1.91803 - 3.32213i) q^{43} +0.443659i q^{44} +(0.904724 + 0.522343i) q^{46} -4.68303i q^{47} +(-0.742029 + 1.28523i) q^{48} +(3.13810 + 5.43536i) q^{49} -0.870065 q^{51} +(-0.156011 + 0.462520i) q^{52} -3.04646 q^{53} +(-2.76194 + 1.59461i) q^{54} +(-5.31224 + 9.20106i) q^{56} -0.343008i q^{57} +(-3.62382 - 2.09222i) q^{58} +(-11.5378 - 6.66136i) q^{59} +(6.51531 - 11.2848i) q^{61} +(5.74766 + 9.95524i) q^{62} +(-8.96182 + 5.17411i) q^{63} -8.46573 q^{64} -1.78960 q^{66} +(4.02523 - 2.32397i) q^{67} +(-0.147268 - 0.255076i) q^{68} +(0.152979 - 0.264967i) q^{69} +(9.38392 + 5.41781i) q^{71} +(-7.17182 - 4.14065i) q^{72} +7.68313i q^{73} +(-7.41308 + 12.8398i) q^{74} +(0.100559 - 0.0580579i) q^{76} -11.9407 q^{77} +(-1.86569 - 0.629307i) q^{78} -10.2106 q^{79} +(-3.79309 - 6.56982i) q^{81} +(5.19812 - 9.00341i) q^{82} +1.18065i q^{83} +(0.170842 + 0.0986359i) q^{84} +5.23818i q^{86} +(-0.612748 + 1.06131i) q^{87} +(-4.77784 - 8.27547i) q^{88} +(2.82548 - 1.63129i) q^{89} +(-12.4483 - 4.19889i) q^{91} +0.103573 q^{92} +(2.91559 - 1.68332i) q^{93} +(3.19736 + 5.53799i) q^{94} +0.305731i q^{96} +(-4.54898 - 2.62636i) q^{97} +(-7.42204 - 4.28511i) q^{98} -9.30722i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{3} + 6 q^{4} + 9 q^{6} - 6 q^{7} - 8 q^{9}+O(q^{10}) \) 10 * q - 3 * q^3 + 6 * q^4 + 9 * q^6 - 6 * q^7 - 8 * q^9	\( 10 q - 3 q^{3} + 6 q^{4} + 9 q^{6} - 6 q^{7} - 8 q^{9} - 9 q^{11} - 28 q^{12} + 8 q^{13} - 8 q^{14} - 12 q^{16} + 8 q^{17} - 12 q^{22} + 13 q^{23} + 42 q^{24} - 17 q^{26} + 30 q^{27} + 33 q^{28} + 7 q^{29} + 3 q^{32} - 6 q^{33} - 3 q^{36} + 3 q^{37} - 62 q^{38} + 8 q^{39} + 12 q^{41} + 32 q^{42} + 4 q^{43} + 39 q^{46} - 26 q^{48} - q^{49} + 16 q^{51} + 61 q^{52} + 24 q^{53} - 9 q^{54} - 21 q^{56} + 18 q^{58} - 48 q^{59} + 13 q^{61} + 17 q^{62} - 34 q^{64} - 42 q^{66} + 6 q^{67} - 13 q^{68} + 20 q^{69} - 27 q^{71} - 141 q^{72} - 26 q^{74} - 12 q^{76} - 48 q^{77} + 56 q^{78} + 4 q^{79} - 17 q^{81} - q^{82} - 90 q^{84} - 49 q^{87} - 6 q^{88} + 24 q^{89} + 13 q^{91} + 34 q^{92} - 63 q^{93} + 5 q^{94} - 15 q^{97} - 45 q^{98}+O(q^{100}) \) 10 * q - 3 * q^3 + 6 * q^4 + 9 * q^6 - 6 * q^7 - 8 * q^9 - 9 * q^11 - 28 * q^12 + 8 * q^13 - 8 * q^14 - 12 * q^16 + 8 * q^17 - 12 * q^22 + 13 * q^23 + 42 * q^24 - 17 * q^26 + 30 * q^27 + 33 * q^28 + 7 * q^29 + 3 * q^32 - 6 * q^33 - 3 * q^36 + 3 * q^37 - 62 * q^38 + 8 * q^39 + 12 * q^41 + 32 * q^42 + 4 * q^43 + 39 * q^46 - 26 * q^48 - q^49 + 16 * q^51 + 61 * q^52 + 24 * q^53 - 9 * q^54 - 21 * q^56 + 18 * q^58 - 48 * q^59 + 13 * q^61 + 17 * q^62 - 34 * q^64 - 42 * q^66 + 6 * q^67 - 13 * q^68 + 20 * q^69 - 27 * q^71 - 141 * q^72 - 26 * q^74 - 12 * q^76 - 48 * q^77 + 56 * q^78 + 4 * q^79 - 17 * q^81 - q^82 - 90 * q^84 - 49 * q^87 - 6 * q^88 + 24 * q^89 + 13 * q^91 + 34 * q^92 - 63 * q^93 + 5 * q^94 - 15 * q^97 - 45 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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