LMFDB - Embedded newform 99.2.m.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(4,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("99.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.m (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			49.1
Root			$0.913545 - 0.406737i$ of defining polynomial
Character	$\chi$	$=$	99.49
Dual form			99.2.m.a.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.255585 + 0.283856i) q^{2} +(0.704489 + 1.58231i) q^{3} +(0.193806 + 1.84395i) q^{4} +(-0.827091 - 0.918578i) q^{5} +(-0.629204 - 0.204441i) q^{6} +(-0.913545 - 0.406737i) q^{7} +(-1.19098 - 0.865300i) q^{8} +(-2.00739 + 2.22943i) q^{9} +O(q^{10})$	\(q+(-0.255585 + 0.283856i) q^{2} +(0.704489 + 1.58231i) q^{3} +(0.193806 + 1.84395i) q^{4} +(-0.827091 - 0.918578i) q^{5} +(-0.629204 - 0.204441i) q^{6} +(-0.913545 - 0.406737i) q^{7} +(-1.19098 - 0.865300i) q^{8} +(-2.00739 + 2.22943i) q^{9} +0.472136 q^{10} +(2.70528 - 1.91872i) q^{11} +(-2.78115 + 1.60570i) q^{12} +(6.33070 + 1.34563i) q^{13} +(0.348943 - 0.155360i) q^{14} +(0.870796 - 1.95584i) q^{15} +(-3.07715 + 0.654069i) q^{16} +(1.50000 - 4.61653i) q^{17} +(-0.119779 - 1.13962i) q^{18} +(-0.809017 - 0.587785i) q^{19} +(1.53351 - 1.70314i) q^{20} -1.73205i q^{21} +(-0.146790 + 1.25830i) q^{22} +(-2.30902 + 3.99933i) q^{23} +(0.530136 - 2.49409i) q^{24} +(0.362937 - 3.45312i) q^{25} +(-2.00000 + 1.45309i) q^{26} +(-4.94183 - 1.60570i) q^{27} +(0.572949 - 1.76336i) q^{28} +(-4.43444 - 1.97434i) q^{29} +(0.332614 + 0.747064i) q^{30} +(-0.604528 - 0.128496i) q^{31} +(2.07295 - 3.59045i) q^{32} +(4.94183 + 2.92887i) q^{33} +(0.927051 + 1.60570i) q^{34} +(0.381966 + 1.17557i) q^{35} +(-4.50000 - 3.26944i) q^{36} +(4.11803 - 2.99193i) q^{37} +(0.373619 - 0.0794152i) q^{38} +(2.33070 + 10.9651i) q^{39} +(0.190206 + 1.80969i) q^{40} +(-2.30932 + 1.02817i) q^{41} +(0.491653 + 0.442686i) q^{42} +(-0.927051 - 1.60570i) q^{43} +(4.06231 + 4.61653i) q^{44} +3.70820 q^{45} +(-0.545085 - 1.67760i) q^{46} +(-1.24852 + 11.8788i) q^{47} +(-3.20276 - 4.40822i) q^{48} +(-4.01478 - 4.45887i) q^{49} +(0.887426 + 0.985587i) q^{50} +(8.36149 - 0.878828i) q^{51} +(-1.25434 + 11.9343i) q^{52} +(1.26393 + 3.88998i) q^{53} +(1.71885 - 0.992377i) q^{54} +(-4.00000 - 0.898056i) q^{55} +(0.736068 + 1.27491i) q^{56} +(0.360114 - 1.69420i) q^{57} +(1.69381 - 0.754131i) q^{58} +(-0.169131 - 1.60917i) q^{59} +(3.77523 + 1.22665i) q^{60} +(-10.6169 + 2.25669i) q^{61} +(0.190983 - 0.138757i) q^{62} +(2.74064 - 1.22021i) q^{63} +(-1.45492 - 4.47777i) q^{64} +(-4.00000 - 6.92820i) q^{65} +(-2.09444 + 0.654194i) q^{66} +(-3.00000 + 5.19615i) q^{67} +(8.80333 + 1.87121i) q^{68} +(-7.95485 - 0.836089i) q^{69} +(-0.431318 - 0.192035i) q^{70} +(-0.899187 + 2.76741i) q^{71} +(4.31990 - 0.918223i) q^{72} +(0.118034 - 0.0857567i) q^{73} +(-0.203232 + 1.93362i) q^{74} +(5.71957 - 1.85840i) q^{75} +(0.927051 - 1.60570i) q^{76} +(-3.25181 + 0.652498i) q^{77} +(-3.70820 - 2.14093i) q^{78} +(7.06756 - 7.84932i) q^{79} +(3.14590 + 2.28563i) q^{80} +(-0.940756 - 8.95070i) q^{81} +(0.298374 - 0.918300i) q^{82} +(9.55057 - 2.03004i) q^{83} +(3.19381 - 0.335683i) q^{84} +(-5.48127 + 2.44042i) q^{85} +(0.692728 + 0.147244i) q^{86} -8.40755i q^{87} +(-4.88220 - 0.0557196i) q^{88} -6.76393 q^{89} +(-0.947762 + 1.05260i) q^{90} +(-5.23607 - 3.80423i) q^{91} +(-7.82206 - 3.48260i) q^{92} +(-0.222562 - 1.04707i) q^{93} +(-3.05278 - 3.39045i) q^{94} +(0.129204 + 1.22930i) q^{95} +(7.14157 + 0.750609i) q^{96} +(4.01478 - 4.45887i) q^{97} +2.29180 q^{98} +(-1.15290 + 9.88285i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 3 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} - 14 q^{8} - 3 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 3 * q^3 - 6 * q^4 + 6 * q^5 - q^7 - 14 * q^8 - 3 * q^9	\( 8 q - 4 q^{2} + 3 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} - 14 q^{8} - 3 q^{9} - 32 q^{10} + q^{11} + 18 q^{12} + 8 q^{13} - q^{14} + 12 q^{15} + 14 q^{16} + 12 q^{17} - 3 q^{18} - 2 q^{19} + 24 q^{20} + 11 q^{22} - 14 q^{23} - 39 q^{24} - 9 q^{25} - 16 q^{26} + 18 q^{28} - 9 q^{29} + 18 q^{30} - 3 q^{31} + 30 q^{32} - 6 q^{34} + 12 q^{35} - 36 q^{36} + 24 q^{37} - 4 q^{38} - 24 q^{39} + 12 q^{40} + 3 q^{41} - 12 q^{42} + 6 q^{43} - 48 q^{44} - 24 q^{45} + 18 q^{46} + 23 q^{47} - 6 q^{49} - 24 q^{50} + 27 q^{51} + 12 q^{52} + 28 q^{53} + 54 q^{54} - 32 q^{55} - 12 q^{56} + 3 q^{57} + 6 q^{58} + 3 q^{59} + 6 q^{62} + 3 q^{63} - 34 q^{64} - 32 q^{65} + 12 q^{66} - 24 q^{67} - 9 q^{68} - 18 q^{69} - 6 q^{70} + 42 q^{71} + 39 q^{72} - 8 q^{73} + 13 q^{74} - 6 q^{76} - 11 q^{77} + 24 q^{78} - 22 q^{79} + 52 q^{80} + 9 q^{81} - 96 q^{82} - 17 q^{83} + 18 q^{84} - 6 q^{85} + 21 q^{86} + 37 q^{88} - 72 q^{89} + 42 q^{90} - 24 q^{91} - 21 q^{92} + 9 q^{93} + 28 q^{94} - 4 q^{95} + 6 q^{97} + 72 q^{98} - 3 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 3 * q^3 - 6 * q^4 + 6 * q^5 - q^7 - 14 * q^8 - 3 * q^9 - 32 * q^10 + q^11 + 18 * q^12 + 8 * q^13 - q^14 + 12 * q^15 + 14 * q^16 + 12 * q^17 - 3 * q^18 - 2 * q^19 + 24 * q^20 + 11 * q^22 - 14 * q^23 - 39 * q^24 - 9 * q^25 - 16 * q^26 + 18 * q^28 - 9 * q^29 + 18 * q^30 - 3 * q^31 + 30 * q^32 - 6 * q^34 + 12 * q^35 - 36 * q^36 + 24 * q^37 - 4 * q^38 - 24 * q^39 + 12 * q^40 + 3 * q^41 - 12 * q^42 + 6 * q^43 - 48 * q^44 - 24 * q^45 + 18 * q^46 + 23 * q^47 - 6 * q^49 - 24 * q^50 + 27 * q^51 + 12 * q^52 + 28 * q^53 + 54 * q^54 - 32 * q^55 - 12 * q^56 + 3 * q^57 + 6 * q^58 + 3 * q^59 + 6 * q^62 + 3 * q^63 - 34 * q^64 - 32 * q^65 + 12 * q^66 - 24 * q^67 - 9 * q^68 - 18 * q^69 - 6 * q^70 + 42 * q^71 + 39 * q^72 - 8 * q^73 + 13 * q^74 - 6 * q^76 - 11 * q^77 + 24 * q^78 - 22 * q^79 + 52 * q^80 + 9 * q^81 - 96 * q^82 - 17 * q^83 + 18 * q^84 - 6 * q^85 + 21 * q^86 + 37 * q^88 - 72 * q^89 + 42 * q^90 - 24 * q^91 - 21 * q^92 + 9 * q^93 + 28 * q^94 - 4 * q^95 + 6 * q^97 + 72 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.255585	+	0.283856i	−0.180726	+	0.200717i	−0.826700	−	0.562643i	$-0.809785\pi$
$2$	−0.255585	+	0.283856i	−0.180726	+	0.200717i	0.645974	+	0.763359i	$0.276451\pi$
$3$	0.704489	+	1.58231i	0.406737	+	0.913545i
$3$	0.704489	+	1.58231i	0.406737	+	0.913545i
$4$	0.193806	+	1.84395i	0.0969032	+	0.921973i
$5$	−0.827091	−	0.918578i	−0.369886	−	0.410800i	0.529252	−	0.848465i	$-0.322473\pi$
$5$	−0.827091	−	0.918578i	−0.369886	−	0.410800i	−0.899139	+	0.437664i	$0.855806\pi$
$6$	−0.629204	−	0.204441i	−0.256872	−	0.0834626i
$7$	−0.913545	−	0.406737i	−0.345288	−	0.153732i	0.226764	−	0.973950i	$-0.427186\pi$
$7$	−0.913545	−	0.406737i	−0.345288	−	0.153732i	−0.572051	+	0.820218i	$0.693852\pi$
$8$	−1.19098	−	0.865300i	−0.421076	−	0.305930i
$9$	−2.00739	+	2.22943i	−0.669131	+	0.743145i
$10$	0.472136			0.149302
$11$	2.70528	−	1.91872i	0.815672	−	0.578514i
$11$	2.70528	−	1.91872i	0.815672	−	0.578514i
$12$	−2.78115	+	1.60570i	−0.802850	+	0.463525i
$13$	6.33070	+	1.34563i	1.75582	+	0.373211i	0.969593	−	0.244724i	$-0.0786974\pi$
$13$	6.33070	+	1.34563i	1.75582	+	0.373211i	0.786229	+	0.617936i	$0.212031\pi$
$14$	0.348943	−	0.155360i	0.0932590	−	0.0415216i
$15$	0.870796	−	1.95584i	0.224838	−	0.504996i
$16$	−3.07715	+	0.654069i	−0.769288	+	0.163517i
$17$	1.50000	−	4.61653i	0.363803	−	1.11967i	−0.586924	−	0.809642i	$-0.699661\pi$
$17$	1.50000	−	4.61653i	0.363803	−	1.11967i	0.950727	−	0.310029i	$-0.100339\pi$
$18$	−0.119779	−	1.13962i	−0.0282322	−	0.268611i
$19$	−0.809017	−	0.587785i	−0.185601	−	0.134847i	0.491105	−	0.871100i	$-0.336593\pi$
$19$	−0.809017	−	0.587785i	−0.185601	−	0.134847i	−0.676706	+	0.736253i	$0.736593\pi$
$20$	1.53351	−	1.70314i	0.342903	−	0.380833i
$21$		−	1.73205i		−	0.377964i
$22$	−0.146790	+	1.25830i	−0.0312957	+	0.268271i
$23$	−2.30902	+	3.99933i	−0.481463	+	0.833919i	−0.999774	−	0.0212736i	$-0.993228\pi$
$23$	−2.30902	+	3.99933i	−0.481463	+	0.833919i	0.518310	+	0.855193i	$0.326561\pi$
$24$	0.530136	−	2.49409i	0.108214	−	0.509105i
$25$	0.362937	−	3.45312i	0.0725874	−	0.690623i
$26$	−2.00000	+	1.45309i	−0.392232	+	0.284973i
$27$	−4.94183	−	1.60570i	−0.951057	−	0.309017i
$28$	0.572949	−	1.76336i	0.108277	−	0.333243i
$29$	−4.43444	−	1.97434i	−0.823455	−	0.366626i	−0.0486422	−	0.998816i	$-0.515489\pi$
$29$	−4.43444	−	1.97434i	−0.823455	−	0.366626i	−0.774813	+	0.632190i	$0.782156\pi$
$30$	0.332614	+	0.747064i	0.0607268	+	0.136395i
$31$	−0.604528	−	0.128496i	−0.108577	−	0.0230787i	0.153303	−	0.988179i	$-0.451009\pi$
$31$	−0.604528	−	0.128496i	−0.108577	−	0.0230787i	−0.261879	+	0.965101i	$0.584342\pi$
$32$	2.07295	−	3.59045i	0.366449	−	0.634708i
$33$	4.94183	+	2.92887i	0.860263	+	0.509851i
$34$	0.927051	+	1.60570i	0.158988	+	0.275375i
$35$	0.381966	+	1.17557i	0.0645640	+	0.198708i
$36$	−4.50000	−	3.26944i	−0.750000	−	0.544907i
$37$	4.11803	−	2.99193i	0.677001	−	0.491870i	−0.195361	−	0.980731i	$-0.562588\pi$
$37$	4.11803	−	2.99193i	0.677001	−	0.491870i	0.872361	+	0.488862i	$0.162588\pi$
$38$	0.373619	−	0.0794152i	0.0606090	−	0.0128828i
$39$	2.33070	+	10.9651i	0.373211	+	1.75582i
$40$	0.190206	+	1.80969i	0.0300743	+	0.286137i
$41$	−2.30932	+	1.02817i	−0.360655	+	0.160574i	−0.579061	−	0.815284i	$-0.696581\pi$
$41$	−2.30932	+	1.02817i	−0.360655	+	0.160574i	0.218406	+	0.975858i	$0.429914\pi$
$42$	0.491653	+	0.442686i	0.0758637	+	0.0683080i
$43$	−0.927051	−	1.60570i	−0.141374	−	0.244867i	0.786640	−	0.617412i	$-0.211819\pi$
$43$	−0.927051	−	1.60570i	−0.141374	−	0.244867i	−0.928014	+	0.372545i	$0.878485\pi$
$44$	4.06231	+	4.61653i	0.612416	+	0.695967i
$45$	3.70820			0.552786
$46$	−0.545085	−	1.67760i	−0.0803684	−	0.247348i
$47$	−1.24852	+	11.8788i	−0.182115	+	1.73271i	0.397313	+	0.917683i	$0.369943\pi$
$47$	−1.24852	+	11.8788i	−0.182115	+	1.73271i	−0.579428	+	0.815024i	$0.696724\pi$
$48$	−3.20276	−	4.40822i	−0.462278	−	0.636271i
$49$	−4.01478	−	4.45887i	−0.573541	−	0.636981i
$50$	0.887426	+	0.985587i	0.125501	+	0.139383i
$51$	8.36149	−	0.878828i	1.17084	−	0.123061i
$52$	−1.25434	+	11.9343i	−0.173946	+	1.65498i
$53$	1.26393	+	3.88998i	0.173614	+	0.534330i	0.999567	−	0.0294087i	$-0.00936242\pi$
$53$	1.26393	+	3.88998i	0.173614	+	0.534330i	−0.825953	+	0.563739i	$0.809362\pi$
$54$	1.71885	−	0.992377i	0.233905	−	0.135045i
$55$	−4.00000	−	0.898056i	−0.539360	−	0.121094i
$56$	0.736068	+	1.27491i	0.0983612	+	0.170367i
$57$	0.360114	−	1.69420i	0.0476982	−	0.224402i
$58$	1.69381	−	0.754131i	0.222408	−	0.0990223i
$59$	−0.169131	−	1.60917i	−0.0220189	−	0.209496i	−1.00000		0.000801000i	$-0.999745\pi$
$59$	−0.169131	−	1.60917i	−0.0220189	−	0.209496i	0.977981	−	0.208695i	$-0.0669216\pi$
$60$	3.77523	+	1.22665i	0.487380	+	0.158359i
$61$	−10.6169	+	2.25669i	−1.35936	+	0.288940i	−0.829196	−	0.558957i	$-0.811202\pi$
$61$	−10.6169	+	2.25669i	−1.35936	+	0.288940i	−0.530160	+	0.847898i	$0.677868\pi$
$62$	0.190983	−	0.138757i	0.0242549	−	0.0176222i
$63$	2.74064	−	1.22021i	0.345288	−	0.153732i
$64$	−1.45492	−	4.47777i	−0.181864	−	0.559721i
$65$	−4.00000	−	6.92820i	−0.496139	−	0.859338i
$66$	−2.09444	+	0.654194i	−0.257807	+	0.0805258i
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	−0.989017	−	0.147802i	$-0.952780\pi$
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	0.622509	+	0.782613i	$0.286114\pi$
$68$	8.80333	+	1.87121i	1.06756	+	0.226917i
$69$	−7.95485	−	0.836089i	−0.957652	−	0.100653i
$70$	−0.431318	−	0.192035i	−0.0515523	−	0.0229526i
$71$	−0.899187	+	2.76741i	−0.106714	+	0.328431i	−0.990129	−	0.140160i	$-0.955238\pi$
$71$	−0.899187	+	2.76741i	−0.106714	+	0.328431i	0.883415	+	0.468591i	$0.155238\pi$
$72$	4.31990	−	0.918223i	0.509105	−	0.108214i
$73$	0.118034	−	0.0857567i	0.0138148	−	0.0100371i	−0.580856	−	0.814006i	$-0.697282\pi$
$73$	0.118034	−	0.0857567i	0.0138148	−	0.0100371i	0.594671	+	0.803969i	$0.297282\pi$
$74$	−0.203232	+	1.93362i	−0.0236252	+	0.224779i
$75$	5.71957	−	1.85840i	0.660440	−	0.214590i
$76$	0.927051	−	1.60570i	0.106340	−	0.184186i
$77$	−3.25181	+	0.652498i	−0.370578	+	0.0743590i
$78$	−3.70820	−	2.14093i	−0.419871	−	0.242413i
$79$	7.06756	−	7.84932i	0.795163	−	0.883118i	−0.200156	−	0.979764i	$-0.564145\pi$
$79$	7.06756	−	7.84932i	0.795163	−	0.883118i	0.995319	+	0.0966462i	$0.0308115\pi$
$80$	3.14590	+	2.28563i	0.351722	+	0.255541i
$81$	−0.940756	−	8.95070i	−0.104528	−	0.994522i
$82$	0.298374	−	0.918300i	0.0329499	−	0.101409i
$83$	9.55057	−	2.03004i	1.04831	−	0.222825i	0.348615	−	0.937266i	$-0.386652\pi$
$83$	9.55057	−	2.03004i	1.04831	−	0.222825i	0.699696	+	0.714441i	$0.253319\pi$
$84$	3.19381	−	0.335683i	0.348473	−	0.0366260i
$85$	−5.48127	+	2.44042i	−0.594528	+	0.264701i
$86$	0.692728	+	0.147244i	0.0746988	+	0.0158777i
$87$		−	8.40755i		−	0.901384i
$88$	−4.88220	−	0.0557196i	−0.520445	−	0.00593972i
$89$	−6.76393			−0.716975			−0.358488	−	0.933534i	$-0.616707\pi$
$89$	−6.76393			−0.716975			−0.358488	+	0.933534i	$0.616707\pi$
$90$	−0.947762	+	1.05260i	−0.0999029	+	0.110953i
$91$	−5.23607	−	3.80423i	−0.548889	−	0.398791i
$92$	−7.82206	−	3.48260i	−0.815506	−	0.363087i
$93$	−0.222562	−	1.04707i	−0.0230787	−	0.108577i
$94$	−3.05278	−	3.39045i	−0.314870	−	0.349699i
$95$	0.129204	+	1.22930i	0.0132561	+	0.126123i
$96$	7.14157	+	0.750609i	0.728883	+	0.0766087i
$97$	4.01478	−	4.45887i	0.407640	−	0.452730i	−0.504010	−	0.863698i	$-0.668143\pi$
$97$	4.01478	−	4.45887i	0.407640	−	0.452730i	0.911650	+	0.410968i	$0.134809\pi$
$98$	2.29180			0.231506
$99$	−1.15290	+	9.88285i	−0.115871	+	0.993264i
$100$	6.43769			0.643769
$101$	−5.66897	+	6.29602i	−0.564083	+	0.626478i	−0.955945	−	0.293546i	$-0.905165\pi$
$101$	−5.66897	+	6.29602i	−0.564083	+	0.626478i	0.391862	+	0.920024i	$0.371831\pi$
$102$	−1.88761	+	2.59808i	−0.186902	+	0.257248i
$103$	1.06996	+	10.1800i	0.105426	+	1.00306i	0.911514	+	0.411269i	$0.134914\pi$
$103$	1.06996	+	10.1800i	0.105426	+	1.00306i	−0.806088	+	0.591796i	$0.798419\pi$
$104$	−6.37539	−	7.08058i	−0.625158	−	0.694308i
$105$	−1.59102	+	1.43256i	−0.155268	+	0.139804i
$106$	−1.42724	−	0.635447i	−0.138626	−	0.0617201i
$107$	−11.3541	−	8.24924i	−1.09764	−	0.797484i	−0.116969	−	0.993136i	$-0.537318\pi$
$107$	−11.3541	−	8.24924i	−1.09764	−	0.797484i	−0.980673	+	0.195652i	$0.937318\pi$
$108$	2.00306	−	9.42367i	0.192745	−	0.906793i
$109$	7.14590			0.684453			0.342226	−	0.939618i	$-0.388819\pi$
$109$	7.14590			0.684453			0.342226	+	0.939618i	$0.388819\pi$
$110$	1.27726	−	0.905894i	0.121782	−	0.0863737i
$111$	7.63525	+	4.40822i	0.724706	+	0.418409i
$112$	3.07715	+	0.654069i	0.290764	+	0.0618037i
$113$	15.7459	−	7.01054i	1.48125	−	0.659496i	0.502507	−	0.864573i	$-0.332411\pi$
$113$	15.7459	−	7.01054i	1.48125	−	0.659496i	0.978746	+	0.205077i	$0.0657445\pi$
$114$	0.388870	+	0.535233i	0.0364210	+	0.0501292i
$115$	5.58347	−	1.18680i	0.520661	−	0.110670i
$116$	2.78115	−	8.55951i	0.258224	−	0.794730i
$117$	−15.7082	+	11.4127i	−1.45222	+	1.05510i
$118$	0.500000	+	0.363271i	0.0460287	+	0.0334418i
$119$	−3.24803	+	3.60730i	−0.297746	+	0.330681i
$120$	−2.72949	+	1.57587i	−0.249167	+	0.143857i
$121$	3.63706	−	10.3813i	0.330642	−	0.943756i
$122$	2.07295	−	3.59045i	0.187676	−	0.325064i
$123$	−3.25378	−	2.92971i	−0.293383	−	0.264163i
$124$	0.119779	−	1.13962i	0.0107565	−	0.102341i
$125$	−8.47214	+	6.15537i	−0.757771	+	0.550553i
$126$	−0.354102	+	1.08981i	−0.0315459	+	0.0970883i
$127$	−3.26393	+	10.0453i	−0.289627	+	0.891381i	0.695346	+	0.718675i	$0.255251\pi$
$127$	−3.26393	+	10.0453i	−0.289627	+	0.891381i	−0.984973	+	0.172706i	$0.944749\pi$
$128$	9.21783	+	4.10404i	0.814749	+	0.362749i
$129$	1.88761	−	2.59808i	0.166195	−	0.228748i
$130$	2.98895	+	0.635322i	0.262149	+	0.0557214i
$131$	−10.6180	+	18.3910i	−0.927702	+	1.60683i	−0.140545	+	0.990074i	$0.544885\pi$
$131$	−10.6180	+	18.3910i	−0.927702	+	1.60683i	−0.787157	+	0.616753i	$0.788448\pi$
$132$	−4.44291	+	9.68010i	−0.386706	+	0.842545i
$133$	0.500000	+	0.866025i	0.0433555	+	0.0750939i
$134$	−0.708204	−	2.17963i	−0.0611795	−	0.188291i
$135$	2.61239	+	5.86752i	0.224838	+	0.504996i
$136$	−5.78115	+	4.20025i	−0.495730	+	0.360169i
$137$	8.42971	−	1.79179i	0.720199	−	0.153083i	0.166790	−	0.985993i	$-0.446660\pi$
$137$	8.42971	−	1.79179i	0.720199	−	0.153083i	0.553409	+	0.832910i	$0.313327\pi$
$138$	2.27047	−	2.04434i	0.193275	−	0.174026i
$139$	−1.01478	−	9.65502i	−0.0860728	−	0.818928i	−0.949355	−	0.314206i	$-0.898262\pi$
$139$	−1.01478	−	9.65502i	−0.0860728	−	0.818928i	0.863282	−	0.504722i	$-0.168405\pi$
$140$	−2.09366	+	0.932157i	−0.176947	+	0.0787817i
$141$	−19.6755	+	6.39297i	−1.65698	+	0.538385i
$142$	−0.555728	−	0.962549i	−0.0466357	−	0.0807753i
$143$	19.7082	−	8.50651i	1.64808	−	0.711350i
$144$	4.71885	−	8.17328i	0.393237	−	0.681107i
$145$	1.85410	+	5.70634i	0.153975	+	0.473886i
$146$	−0.00582517	+	0.0554228i	−0.000482095	+	0.00458682i
$147$	4.22693	−	9.49384i	0.348631	−	0.783039i
$148$	6.31505	+	7.01357i	0.519094	+	0.576512i
$149$	−10.1576	−	11.2812i	−0.832145	−	0.924191i	0.165934	−	0.986137i	$-0.446936\pi$
$149$	−10.1576	−	11.2812i	−0.832145	−	0.924191i	−0.998080	+	0.0619457i	$0.980269\pi$
$150$	−0.934319	+	2.09852i	−0.0762869	+	0.171343i
$151$	−0.452215	+	4.30254i	−0.0368007	+	0.350136i	0.960591	+	0.277964i	$0.0896596\pi$
$151$	−0.452215	+	4.30254i	−0.0368007	+	0.350136i	−0.997392	+	0.0721716i	$0.977007\pi$
$152$	0.454915	+	1.40008i	0.0368985	+	0.113562i
$153$	7.28115	+	12.6113i	0.588646	+	1.01957i
$154$	0.645898	−	1.08981i	0.0520479	−	0.0878197i
$155$	0.381966	+	0.661585i	0.0306802	+	0.0531397i
$156$	−19.7673	+	6.42280i	−1.58265	+	0.514235i
$157$	6.52810	−	2.90650i	0.520999	−	0.231964i	−0.129350	−	0.991599i	$-0.541289\pi$
$157$	6.52810	−	2.90650i	0.520999	−	0.231964i	0.650349	+	0.759635i	$0.274622\pi$
$158$	0.421714	+	4.01234i	0.0335498	+	0.319205i
$159$	−5.26472	+	4.74038i	−0.417520	+	0.375936i
$160$	−5.01263	+	1.06547i	−0.396283	+	0.0842325i
$161$	3.73607	−	2.71441i	0.294443	−	0.213926i
$162$	2.78115	+	2.02063i	0.218508	+	0.158755i
$163$	6.39919	+	19.6947i	0.501223	+	1.54261i	0.807029	+	0.590512i	$0.201074\pi$
$163$	6.39919	+	19.6947i	0.501223	+	1.54261i	−0.305806	+	0.952094i	$0.598926\pi$
$164$	−2.34346	−	4.05899i	−0.182993	−	0.316954i
$165$	−1.39695	−	6.96190i	−0.108753	−	0.541983i
$166$	−1.86475	+	3.22983i	−0.144732	+	0.250684i
$167$	5.63798	+	1.19839i	0.436280	+	0.0927341i	0.420815	−	0.907146i	$-0.361744\pi$
$167$	5.63798	+	1.19839i	0.436280	+	0.0927341i	0.0154643	+	0.999880i	$0.495077\pi$
$168$	−1.49874	+	2.06284i	−0.115631	+	0.159152i
$169$	26.3910	+	11.7500i	2.03008	+	0.903848i
$170$	0.708204	−	2.17963i	0.0543168	−	0.167170i
$171$	2.93444	−	0.623735i	0.224402	−	0.0476982i
$172$	2.78115	−	2.02063i	0.212061	−	0.154071i
$173$	2.41358	−	22.9637i	0.183501	−	1.74590i	−0.384732	−	0.923028i	$-0.625706\pi$
$173$	2.41358	−	22.9637i	0.183501	−	1.74590i	0.568233	−	0.822868i	$-0.307627\pi$
$174$	2.38653	+	2.14885i	0.180923	+	0.162904i
$175$	−1.73607	+	3.00696i	−0.131234	+	0.227305i
$176$	−7.06958	+	7.67362i	−0.532890	+	0.578421i
$177$	2.42705	−	1.40126i	0.182428	−	0.105325i
$178$	1.72876	−	1.91998i	0.129576	−	0.143909i
$179$	4.09017	+	2.97168i	0.305714	+	0.222114i	0.730055	−	0.683388i	$-0.239494\pi$
$179$	4.09017	+	2.97168i	0.305714	+	0.222114i	−0.424341	+	0.905502i	$0.639494\pi$
$180$	0.718674	+	6.83772i	0.0535668	+	0.509654i
$181$	−3.06231	+	9.42481i	−0.227619	+	0.700540i	0.770396	+	0.637566i	$0.220059\pi$
$181$	−3.06231	+	9.42481i	−0.227619	+	0.700540i	−0.998015	+	0.0629745i	$0.979941\pi$
$182$	2.41811	−	0.513986i	0.179243	−	0.0380992i
$183$	−11.0503	−	15.2094i	−0.816860	−	1.12431i
$184$	6.21062	−	2.76515i	0.457853	−	0.203849i
$185$	−6.15431	−	1.30814i	−0.452474	−	0.0961762i
$186$	0.354102	+	0.204441i	0.0259640	+	0.0149903i
$187$	−4.79988	−	15.3671i	−0.351002	−	1.12375i
$188$	−22.1459			−1.61516
$189$	3.86149	+	3.47690i	0.280882	+	0.252908i
$190$	−0.381966	−	0.277515i	−0.0277107	−	0.0201330i
$191$	5.43036	+	2.41775i	0.392927	+	0.174942i	0.593683	−	0.804699i	$-0.297673\pi$
$191$	5.43036	+	2.41775i	0.392927	+	0.174942i	−0.200756	+	0.979641i	$0.564340\pi$
$192$	6.06023	−	5.45666i	0.437360	−	0.393800i
$193$	−7.36044	−	8.17459i	−0.529816	−	0.588420i	0.417518	−	0.908669i	$-0.362900\pi$
$193$	−7.36044	−	8.17459i	−0.529816	−	0.588420i	−0.947333	+	0.320249i	$0.896234\pi$
$194$	0.239558	+	2.27924i	0.0171993	+	0.163640i
$195$	8.14459	−	11.2101i	0.583246	−	0.802770i
$196$	7.44382	−	8.26720i	0.531701	−	0.590514i
$197$	8.23607			0.586796			0.293398	−	0.955990i	$-0.405214\pi$
$197$	8.23607			0.586796			0.293398	+	0.955990i	$0.405214\pi$
$198$	−2.51064	−	2.85317i	−0.178424	−	0.202766i
$199$	−7.14590			−0.506559			−0.253280	−	0.967393i	$-0.581509\pi$
$199$	−7.14590			−0.506559			−0.253280	+	0.967393i	$0.581509\pi$
$200$	−3.42023	+	3.79855i	−0.241847	+	0.268598i
$201$	−10.3354	−	1.08629i	−0.729001	−	0.0766211i
$202$	−0.338261	−	3.21834i	−0.0238000	−	0.226442i
$203$	3.24803	+	3.60730i	0.227967	+	0.253183i
$204$	3.24102	+	15.2478i	0.226917	+	1.06756i
$205$	2.85447	+	1.27089i	0.199365	+	0.0887631i
$206$	−3.16312	−	2.29814i	−0.220385	−	0.160119i
$207$	−4.28115	−	13.1760i	−0.297561	−	0.915798i
$208$	−20.3607			−1.41176
$209$	−3.31641	−	0.0378495i	−0.229401	−	0.00261810i
$210$		−	0.817763i		−	0.0564310i
$211$	−20.0248	−	4.25640i	−1.37856	−	0.293022i	−0.541762	−	0.840532i	$-0.682243\pi$
$211$	−20.0248	−	4.25640i	−1.37856	−	0.293022i	−0.836800	+	0.547509i	$0.815576\pi$
$212$	−6.92796	+	3.08452i	−0.475814	+	0.211846i
$213$	−5.01236	+	0.526821i	−0.343442	+	0.0360972i
$214$	5.24354	−	1.11455i	0.358441	−	0.0761889i
$215$	−0.708204	+	2.17963i	−0.0482991	+	0.148649i
$216$	4.49623	+	6.18853i	0.305930	+	0.421076i
$217$	0.500000	+	0.363271i	0.0339422	+	0.0246605i
$218$	−1.82639	+	2.02841i	−0.123698	+	0.137381i
$219$	0.218847	+	0.126351i	0.0147883	+	0.00853804i
$220$	0.880740	−	7.54983i	0.0593795	−	0.509009i
$221$	15.7082	−	27.2074i	1.05665	−	1.83017i
$222$	−3.20276	+	1.04064i	−0.214955	+	0.0698431i
$223$	1.62088	−	15.4216i	0.108542	−	1.03271i	−0.795701	−	0.605690i	$-0.792897\pi$
$223$	1.62088	−	15.4216i	0.108542	−	1.03271i	0.904243	−	0.427019i	$-0.140436\pi$
$224$	−3.35410	+	2.43690i	−0.224105	+	0.162822i
$225$	6.96994	+	7.74090i	0.464662	+	0.516060i
$226$	−2.03444	+	6.26137i	−0.135329	+	0.416500i
$227$	−15.1813	−	6.75916i	−1.00762	−	0.448621i	−0.164518	−	0.986374i	$-0.552607\pi$
$227$	−15.1813	−	6.75916i	−1.00762	−	0.448621i	−0.843103	+	0.537753i	$0.819273\pi$
$228$	3.19381	+	0.335683i	0.211515	+	0.0222311i
$229$	−9.95788	−	2.11661i	−0.658035	−	0.139870i	−0.133221	−	0.991086i	$-0.542532\pi$
$229$	−9.95788	−	2.11661i	−0.658035	−	0.139870i	−0.524814	+	0.851217i	$0.675865\pi$
$230$	−1.09017	+	1.88823i	−0.0718837	+	0.124506i
$231$	−3.32331	−	4.68568i	−0.218658	−	0.308295i
$232$	3.57295	+	6.18853i	0.234576	+	0.406297i
$233$	−3.43769	−	10.5801i	−0.225211	−	0.693128i	−0.998270	−	0.0587939i	$-0.981275\pi$
$233$	−3.43769	−	10.5801i	−0.225211	−	0.693128i	0.773059	−	0.634334i	$-0.218725\pi$
$234$	0.775226	−	7.37578i	0.0506781	−	0.482170i
$235$	11.9443	−	8.67802i	0.779158	−	0.566092i
$236$	2.93444	−	0.623735i	0.191016	−	0.0406017i
$237$	17.3991	+	5.65330i	1.13019	+	0.367221i
$238$	−0.193806	−	1.84395i	−0.0125626	−	0.119525i
$239$	9.56677	−	4.25940i	0.618823	−	0.275518i	−0.0732857	−	0.997311i	$-0.523349\pi$
$239$	9.56677	−	4.25940i	0.618823	−	0.275518i	0.692109	+	0.721793i	$0.256682\pi$
$240$	−1.40032	+	6.58798i	−0.0903901	+	0.425252i
$241$	13.4164	+	23.2379i	0.864227	+	1.49688i	0.867813	+	0.496891i	$0.165525\pi$
$241$	13.4164	+	23.2379i	0.864227	+	1.49688i	−0.00358606	+	0.999994i	$0.501141\pi$
$242$	2.01722	+	3.68571i	0.129672	+	0.236927i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	−6.21885	−	19.1396i	−0.398121	−	1.22529i
$245$	−0.775226	+	7.37578i	−0.0495274	+	0.471221i
$246$	1.66323	−	0.174813i	0.106044	−	0.0111457i
$247$	−4.33070	−	4.80973i	−0.275556	−	0.306036i
$248$	0.608795	+	0.676135i	0.0386585	+	0.0429346i
$249$	9.94040	+	13.6818i	0.629948	+	0.867048i
$250$	0.418114	−	3.97809i	0.0264438	−	0.251596i
$251$	6.35410	+	19.5559i	0.401067	+	1.23436i	0.924135	+	0.382067i	$0.124788\pi$
$251$	6.35410	+	19.5559i	0.401067	+	1.23436i	−0.523067	+	0.852291i	$0.675212\pi$
$252$	2.78115	+	4.81710i	0.175196	+	0.303449i
$253$	1.42705	+	15.2497i	0.0897179	+	0.958738i
$254$	−2.01722	−	3.49393i	−0.126572	−	0.219229i
$255$	−7.72299	−	6.95381i	−0.483632	−	0.435464i
$256$	5.08142	−	2.26239i	0.317589	−	0.141400i
$257$	1.55850	+	14.8282i	0.0972167	+	0.924955i	0.929056	+	0.369939i	$0.120621\pi$
$257$	1.55850	+	14.8282i	0.0972167	+	0.924955i	−0.831840	+	0.555016i	$0.812712\pi$
$258$	0.255034	+	1.19984i	0.0158777	+	0.0746988i
$259$	−4.97894	+	1.05831i	−0.309376	+	0.0657599i
$260$	12.0000	−	8.71851i	0.744208	−	0.540699i
$261$	13.3033	−	5.92302i	0.823455	−	0.366626i
$262$	−2.50658	−	7.71445i	−0.154857	−	0.476601i
$263$	6.35410	+	11.0056i	0.391811	+	0.678636i	0.992688	−	0.120705i	$-0.0385155\pi$
$263$	6.35410	+	11.0056i	0.391811	+	0.678636i	−0.600878	+	0.799341i	$0.705182\pi$
$264$	−3.35129	−	7.76440i	−0.206258	−	0.477866i
$265$	2.52786	−	4.37839i	0.155285	−	0.268962i
$266$	−0.373619	−	0.0794152i	−0.0229081	−	0.00486926i
$267$	−4.76511	−	10.7026i	−0.291620	−	0.654990i
$268$	−10.1628	−	4.52479i	−0.620794	−	0.276395i
$269$	−6.57295	+	20.2295i	−0.400760	+	1.23341i	0.523625	+	0.851949i	$0.324579\pi$
$269$	−6.57295	+	20.2295i	−0.400760	+	1.23341i	−0.924384	+	0.381463i	$0.875421\pi$
$270$	−2.33322	−	0.758108i	−0.141995	−	0.0461370i
$271$	−8.70820	+	6.32688i	−0.528986	+	0.384331i	−0.819978	−	0.572395i	$-0.806015\pi$
$271$	−8.70820	+	6.32688i	−0.528986	+	0.384331i	0.290993	+	0.956725i	$0.406015\pi$
$272$	−1.59620	+	15.1869i	−0.0967840	+	0.920838i
$273$	2.33070	−	10.9651i	0.141061	−	0.663638i
$274$	−1.64590	+	2.85078i	−0.0994323	+	0.172222i
$275$	−5.64370	−	10.0380i	−0.340328	−	0.605315i
$276$		−	14.8303i		−	0.892682i
$277$	−12.8714	+	14.2952i	−0.773370	+	0.858914i	−0.993176	−	0.116629i	$-0.962791\pi$
$277$	−12.8714	+	14.2952i	−0.773370	+	0.858914i	0.219806	+	0.975544i	$0.429458\pi$
$278$	3.00000	+	2.17963i	0.179928	+	0.130725i
$279$	1.50000	−	1.08981i	0.0898027	−	0.0652454i
$280$	0.562306	−	1.73060i	0.0336042	−	0.103423i
$281$	9.12244	−	1.93903i	0.544199	−	0.115673i	0.0723942	−	0.997376i	$-0.476936\pi$
$281$	9.12244	−	1.93903i	0.544199	−	0.115673i	0.471805	+	0.881703i	$0.343603\pi$
$282$	3.21409	−	7.21897i	0.191396	−	0.429883i
$283$	−15.5303	+	6.91452i	−0.923179	+	0.411026i	−0.812587	−	0.582840i	$-0.801941\pi$
$283$	−15.5303	+	6.91452i	−0.923179	+	0.411026i	−0.110592	+	0.993866i	$0.535275\pi$
$284$	−5.27723	−	1.12171i	−0.313146	−	0.0665612i
$285$	−1.85410	+	1.07047i	−0.109828	+	0.0634089i
$286$	−2.62250	+	7.76843i	−0.155072	+	0.459357i
$287$	2.52786			0.149215
$288$	3.84346	+	11.8290i	0.226478	+	0.697028i
$289$	−5.30902	−	3.85723i	−0.312295	−	0.226896i
$290$	−2.09366	−	0.932157i	−0.122944	−	0.0547382i
$291$	9.88367	+	3.21140i	0.579391	+	0.188256i
$292$	0.181006	+	0.201028i	0.0105926	+	0.0117643i
$293$	3.05018	+	29.0205i	0.178193	+	1.69539i	0.609176	+	0.793035i	$0.291500\pi$
$293$	3.05018	+	29.0205i	0.178193	+	1.69539i	−0.430983	+	0.902360i	$0.641833\pi$
$294$	1.61454	+	3.62633i	0.0941621	+	0.211492i
$295$	−1.33826	+	1.48629i	−0.0779166	+	0.0865351i
$296$	−7.49342			−0.435546
$297$	−16.4499	+	5.13811i	−0.954521	+	0.298143i
$298$	5.79837			0.335891
$299$	−19.9993	+	22.2115i	−1.15659	+	1.28453i
$300$	4.53528	+	10.1864i	0.261845	+	0.588113i
$301$	0.193806	+	1.84395i	0.0111708	+	0.106283i
$302$	−1.10572	−	1.22803i	−0.0636272	−	0.0706651i
$303$	−13.9560	−	4.53457i	−0.801749	−	0.260504i
$304$	2.87392	+	1.27955i	0.164831	+	0.0733873i
$305$	10.8541	+	7.88597i	0.621504	+	0.451549i
$306$	−5.44076	−	1.15647i	−0.311027	−	0.0661109i
$307$	7.85410			0.448257			0.224129	−	0.974560i	$-0.428046\pi$
$307$	7.85410			0.448257			0.224129	+	0.974560i	$0.428046\pi$
$308$	−1.83339	−	5.86969i	−0.104467	−	0.334457i
$309$	−15.3541	+	8.86469i	−0.873464	+	0.504295i
$310$	−0.285420	−	0.0606678i	−0.0162107	−	0.00344570i
$311$	13.8679	−	6.17440i	0.786378	−	0.350118i	0.0260529	−	0.999661i	$-0.491706\pi$
$311$	13.8679	−	6.17440i	0.786378	−	0.350118i	0.760325	+	0.649542i	$0.225040\pi$
$312$	6.71227	−	15.0760i	0.380008	−	0.853511i
$313$	−3.39626	+	0.721898i	−0.191968	+	0.0408041i	−0.302892	−	0.953025i	$-0.597952\pi$
$313$	−3.39626	+	0.721898i	−0.191968	+	0.0408041i	0.110924	+	0.993829i	$0.464619\pi$
$314$	−0.843459	+	2.59590i	−0.0475991	+	0.146495i
$315$	−3.38761	−	1.50826i	−0.190870	−	0.0849810i
$316$	15.8435	+	11.5109i	0.891264	+	0.647541i
$317$	14.0145	−	15.5646i	0.787130	−	0.874197i	−0.207442	−	0.978247i	$-0.566514\pi$
$317$	14.0145	−	15.5646i	0.787130	−	0.874197i	0.994572	+	0.104051i	$0.0331804\pi$
$318$		−	2.70599i		−	0.151745i
$319$	−15.7846	+	3.16729i	−0.883768	+	0.177334i
$320$	−2.90983	+	5.03997i	−0.162664	+	0.281743i
$321$	5.05399	−	23.7772i	0.282086	−	1.32711i
$322$	−0.184381	+	1.75427i	−0.0102752	+	0.0977616i
$323$	−3.92705	+	2.85317i	−0.218507	+	0.158755i
$324$	16.3223	−	3.46941i	0.906793	−	0.192745i
$325$	6.94427	−	21.3723i	0.385199	−	1.18552i
$326$	−7.22599	−	3.21722i	−0.400211	−	0.178185i
$327$	5.03420	+	11.3070i	0.278392	+	0.625279i
$328$	3.64004	+	0.773714i	0.200988	+	0.0427212i
$329$	5.97214	−	10.3440i	0.329255	−	0.570286i
$330$	2.33322	+	1.38282i	0.128439	+	0.0761220i
$331$	−7.20820	−	12.4850i	−0.396199	−	0.686236i	0.597055	−	0.802201i	$-0.296338\pi$
$331$	−7.20820	−	12.4850i	−0.396199	−	0.686236i	−0.993253	+	0.115964i	$0.963004\pi$
$332$	5.59424	+	17.2173i	0.307024	+	0.944921i
$333$	−1.59620	+	15.1869i	−0.0874714	+	0.832235i
$334$	−1.78115	+	1.29408i	−0.0974604	+	0.0708091i
$335$	7.25434	−	1.54196i	0.396347	−	0.0842462i
$336$	1.13288	+	5.32978i	0.0618037	+	0.290764i
$337$	1.19916	+	11.4093i	0.0653227	+	0.621504i	0.977387	+	0.211457i	$0.0678209\pi$
$337$	1.19916	+	11.4093i	0.0653227	+	0.621504i	−0.912065	+	0.410047i	$0.865512\pi$
$338$	−10.0805	+	4.48811i	−0.548305	+	0.244121i
$339$	22.1857	+	19.9761i	1.20496	+	1.08495i
$340$	−5.56231	−	9.63420i	−0.301658	−	0.522488i
$341$	−1.88197	+	0.812299i	−0.101914	+	0.0439885i
$342$	−0.572949	+	0.992377i	−0.0309815	+	0.0536616i
$343$	4.01722	+	12.3637i	0.216910	+	0.667579i
$344$	−0.285309	+	2.71454i	−0.0153829	+	0.146358i
$345$	5.81137	+	7.99867i	0.312874	+	0.430634i
$346$	5.90150	+	6.55428i	0.317267	+	0.352361i
$347$	−5.94760	−	6.60548i	−0.319284	−	0.354600i	0.562043	−	0.827108i	$-0.310016\pi$
$347$	−5.94760	−	6.60548i	−0.319284	−	0.354600i	−0.881327	+	0.472508i	$0.843349\pi$
$348$	15.5031	−	1.62944i	0.831051	−	0.0873470i
$349$	0.433364	−	4.12319i	0.0231975	−	0.220709i	−0.976782	−	0.214238i	$-0.931273\pi$
$349$	0.433364	−	4.12319i	0.0231975	−	0.220709i	0.999979	−	0.00647159i	$-0.00205999\pi$
$350$	−0.409830	−	1.26133i	−0.0219063	−	0.0674208i
$351$	−29.1246	−	16.8151i	−1.55456	−	0.897524i
$352$	−1.28115	−	13.6906i	−0.0682857	−	0.729710i
$353$	8.20820	+	14.2170i	0.436879	+	0.756696i	0.997447	−	0.0714123i	$-0.0227506\pi$
$353$	8.20820	+	14.2170i	0.436879	+	0.756696i	−0.560568	+	0.828108i	$0.689417\pi$
$354$	−0.222562	+	1.04707i	−0.0118291	+	0.0556514i
$355$	3.28579	−	1.46293i	0.174392	−	0.0776442i
$356$	−1.31089	−	12.4723i	−0.0694772	−	0.661032i
$357$	−7.99606	−	2.59808i	−0.423196	−	0.137505i
$358$	−1.88892	+	0.401502i	−0.0998324	+	0.0212200i
$359$	18.4894	−	13.4333i	0.975831	−	0.708983i	0.0190579	−	0.999818i	$-0.493933\pi$
$359$	18.4894	−	13.4333i	0.975831	−	0.708983i	0.956773	+	0.290836i	$0.0939333\pi$
$360$	−4.41641	−	3.20871i	−0.232765	−	0.169114i
$361$	−5.56231	−	17.1190i	−0.292753	−	0.901001i
$362$	−1.89261	−	3.27810i	−0.0994733	−	0.172293i
$363$	18.9887	−	1.55857i	0.996648	−	0.0818037i
$364$	6.00000	−	10.3923i	0.314485	−	0.544705i
$365$	−0.176399	−	0.0374948i	−0.00923315	−	0.00196257i
$366$	7.14157	+	0.750609i	0.373296	+	0.0392350i
$367$	−11.6095	−	5.16889i	−0.606012	−	0.269814i	0.0807058	−	0.996738i	$-0.474283\pi$
$367$	−11.6095	−	5.16889i	−0.606012	−	0.269814i	−0.686718	+	0.726924i	$0.740949\pi$
$368$	4.48936	−	13.8168i	0.234024	−	0.720252i
$369$	2.34346	−	7.21242i	0.121996	−	0.375464i
$370$	1.94427	−	1.41260i	0.101078	−	0.0734374i
$371$	0.427539	−	4.06776i	0.0221967	−	0.211188i
$372$	1.88761	−	0.613323i	0.0978682	−	0.0317993i
$373$	2.82624	−	4.89519i	0.146337	−	0.253463i	−0.783534	−	0.621349i	$-0.786585\pi$
$373$	2.82624	−	4.89519i	0.146337	−	0.253463i	0.929871	+	0.367886i	$0.119918\pi$
$374$	5.58881	+	2.56512i	0.288991	+	0.132639i
$375$	−15.7082	−	9.06914i	−0.811168	−	0.468328i
$376$	11.7657	−	13.0672i	0.606771	−	0.673887i
$377$	−25.4164	−	18.4661i	−1.30901	−	0.951053i
$378$	−1.97388	+	0.207463i	−0.101525	+	0.0106708i
$379$	4.88197	−	15.0251i	0.250770	−	0.771790i	−0.743864	−	0.668331i	$-0.767009\pi$
$379$	4.88197	−	15.0251i	0.250770	−	0.771790i	0.994634	−	0.103459i	$-0.0329910\pi$
$380$	−2.24171	+	0.476491i	−0.114998	+	0.0244435i
$381$	−18.1942	+	1.91229i	−0.932119	+	0.0979696i
$382$	−2.07421	+	0.923500i	−0.106126	+	0.0472503i
$383$	−19.4202	−	4.12790i	−0.992328	−	0.210926i	−0.316986	−	0.948430i	$-0.602671\pi$
$383$	−19.4202	−	4.12790i	−0.992328	−	0.210926i	−0.675342	+	0.737504i	$0.736004\pi$
$384$			17.4767i			0.891853i
$385$	3.28891	+	2.44736i	0.167618	+	0.124729i
$386$	4.20163			0.213857
$387$	5.44076	+	1.15647i	0.276569	+	0.0587866i
$388$	9.00000	+	6.53888i	0.456906	+	0.331961i
$389$	−20.6941	−	9.21359i	−1.04923	−	0.467148i	−0.191632	−	0.981467i	$-0.561378\pi$
$389$	−20.6941	−	9.21359i	−1.04923	−	0.467148i	−0.857599	+	0.514319i	$0.828045\pi$
$390$	1.10041	+	5.17702i	0.0557214	+	0.262149i
$391$	14.9995	+	16.6586i	0.758558	+	0.842464i
$392$	0.923281	+	8.78443i	0.0466327	+	0.443681i
$393$	−36.5805	−	3.84476i	−1.84524	−	0.193943i
$394$	−2.10502	+	2.33786i	−0.106049	+	0.117780i
$395$	−13.0557			−0.656905
$396$	−18.4469	−	0.210530i	−0.926991	−	0.0105795i
$397$	−2.12461			−0.106631			−0.0533156	−	0.998578i	$-0.516979\pi$
$397$	−2.12461			−0.106631			−0.0533156	+	0.998578i	$0.516979\pi$
$398$	1.82639	−	2.02841i	0.0915484	−	0.101675i
$399$	−1.01807	+	1.40126i	−0.0509674	+	0.0701507i
$400$	1.14176	+	10.8631i	0.0570881	+	0.543157i
$401$	9.74408	+	10.8219i	0.486596	+	0.540420i	0.935578	−	0.353121i	$-0.114880\pi$
$401$	9.74408	+	10.8219i	0.486596	+	0.540420i	−0.448981	+	0.893541i	$0.648213\pi$
$402$	2.94992	−	2.65612i	0.147129	−	0.132475i
$403$	−3.65418	−	1.62695i	−0.182028	−	0.0810440i
$404$	−12.7082	−	9.23305i	−0.632257	−	0.459361i
$405$	−7.44382	+	8.26720i	−0.369886	+	0.410800i
$406$	−1.85410			−0.0920175
$407$	5.39977	−	15.9953i	0.267657	−	0.792859i
$408$	−10.7188	−	6.18853i	−0.530662	−	0.306378i
$409$	33.0053	+	7.01549i	1.63201	+	0.346894i	0.930648	−	0.365915i	$-0.119244\pi$
$409$	33.0053	+	7.01549i	1.63201	+	0.346894i	0.701358	+	0.712809i	$0.252577\pi$
$410$	−1.09031	+	0.485438i	−0.0538467	+	0.0239741i
$411$	8.77380	+	12.0761i	0.432779	+	0.595670i
$412$	−18.5640	+	3.94590i	−0.914582	+	0.194400i
$413$	−0.500000	+	1.53884i	−0.0246034	+	0.0757215i
$414$	4.83430	+	2.15237i	0.237593	+	0.105783i
$415$	−9.76393	−	7.09391i	−0.479293	−	0.348226i
$416$	17.9547	−	19.9407i	0.880300	−	0.977672i
$417$	14.5623	−	8.40755i	0.713119	−	0.411720i
$418$	0.858369	−	0.931709i	0.0419842	−	0.0455714i
$419$	−4.04508	+	7.00629i	−0.197615	+	0.342280i	−0.947755	−	0.319000i	$-0.896653\pi$
$419$	−4.04508	+	7.00629i	−0.197615	+	0.342280i	0.750139	+	0.661280i	$0.229986\pi$
$420$	−2.94992	−	2.65612i	−0.143941	−	0.129605i
$421$	−1.06996	+	10.1800i	−0.0521467	+	0.496143i	0.937013	+	0.349296i	$0.113579\pi$
$421$	−1.06996	+	10.1800i	−0.0521467	+	0.496143i	−0.989159	+	0.146847i	$0.953088\pi$
$422$	6.32624	−	4.59628i	0.307956	−	0.223743i
$423$	−23.9768	−	26.6290i	−1.16579	−	1.29474i
$424$	1.86068	−	5.72658i	0.0903626	−	0.278107i
$425$	−15.3970	−	6.85518i	−0.746864	−	0.332525i
$426$	1.13154	−	1.55744i	0.0548235	−	0.0754581i
$427$	10.6169	+	2.25669i	0.513788	+	0.109209i
$428$	13.0106	−	22.5351i	0.628893	−	1.08927i
$429$	27.3441	+	25.1917i	1.32019	+	1.21627i
$430$	−0.437694	−	0.758108i	−0.0211075	−	0.0365592i
$431$	−10.5279	−	32.4014i	−0.507109	−	1.56072i	−0.797195	−	0.603722i	$-0.793684\pi$
$431$	−10.5279	−	32.4014i	−0.507109	−	1.56072i	0.290086	−	0.957001i	$-0.406316\pi$
$432$	16.2570	+	1.70868i	0.782166	+	0.0822090i
$433$	−11.9271	+	8.66551i	−0.573177	+	0.416438i	−0.836258	−	0.548336i	$-0.815261\pi$
$433$	−11.9271	+	8.66551i	−0.573177	+	0.416438i	0.263081	+	0.964774i	$0.415261\pi$
$434$	−0.230909	+	0.0490813i	−0.0110840	+	0.00235598i
$435$	−7.72299	+	6.95381i	−0.370289	+	0.333410i
$436$	1.38492	+	13.1766i	0.0663257	+	0.631047i
$437$	4.21878	−	1.87832i	0.201812	−	0.0898524i
$438$	−0.0917997	+	0.0298275i	−0.00438636	+	0.00142521i
$439$	0.354102	+	0.613323i	0.0169004	+	0.0292723i	0.874352	−	0.485292i	$-0.161287\pi$
$439$	0.354102	+	0.613323i	0.0169004	+	0.0292723i	−0.857452	+	0.514565i	$0.827954\pi$
$440$	3.98684	+	4.53077i	0.190065	+	0.215996i
$441$	18.0000			0.857143
$442$	3.70820	+	11.4127i	0.176381	+	0.542846i
$443$	0.129204	−	1.22930i	0.00613868	−	0.0584056i	−0.991024	−	0.133686i	$-0.957319\pi$
$443$	0.129204	−	1.22930i	0.00613868	−	0.0584056i	0.997162	+	0.0752806i	$0.0239852\pi$
$444$	−6.64875	+	14.9333i	−0.315536	+	0.708705i
$445$	5.59439	+	6.21320i	0.265199	+	0.294534i
$446$	3.96325	+	4.40164i	0.187665	+	0.208424i
$447$	10.6944	−	24.0200i	0.505827	−	1.13611i
$448$	−0.492141	+	4.68241i	−0.0232515	+	0.221223i
$449$	2.30902	+	7.10642i	0.108969	+	0.335373i	0.990642	−	0.136489i	$-0.0435820\pi$
$449$	2.30902	+	7.10642i	0.108969	+	0.335373i	−0.881672	+	0.471862i	$0.843582\pi$
$450$	−3.97871			−0.187558
$451$	−4.27458	+	7.21242i	−0.201282	+	0.339620i
$452$	15.9787	+	27.6759i	0.751575	+	1.30177i
$453$	−7.12652	+	2.31555i	−0.334833	+	0.108794i
$454$	5.79875	−	2.58177i	0.272149	−	0.121169i
$455$	0.836228	+	7.95618i	0.0392030	+	0.372991i
$456$	−1.89488	+	1.70616i	−0.0887359	+	0.0798982i
$457$	0.978148	−	0.207912i	0.0457558	−	0.00972570i	−0.184977	−	0.982743i	$-0.559221\pi$
$457$	0.978148	−	0.207912i	0.0457558	−	0.00972570i	0.230733	+	0.973017i	$0.425888\pi$
$458$	3.14590	−	2.28563i	0.146998	−	0.106800i
$459$	−14.8255	+	20.4056i	−0.691995	+	0.952450i
$460$	3.27051	+	10.0656i	0.152488	+	0.469311i
$461$	8.07295	+	13.9828i	0.375995	+	0.651242i	0.990475	−	0.137690i	$-0.0439677\pi$
$461$	8.07295	+	13.9828i	0.375995	+	0.651242i	−0.614481	+	0.788932i	$0.710634\pi$
$462$	2.17945	+	0.254248i	0.101397	+	0.0118287i
$463$	−8.50000	+	14.7224i	−0.395029	+	0.684209i	−0.993105	−	0.117230i	$-0.962599\pi$
$463$	−8.50000	+	14.7224i	−0.395029	+	0.684209i	0.598076	+	0.801439i	$0.295932\pi$
$464$	14.9368	+	3.17492i	0.693424	+	0.147392i
$465$	−0.777739	+	1.07047i	−0.0360668	+	0.0496417i
$466$	3.88186	+	1.72831i	0.179824	+	0.0800626i
$467$	−0.236068	+	0.726543i	−0.0109239	+	0.0336204i	−0.956370	−	0.292159i	$-0.905627\pi$
$467$	−0.236068	+	0.726543i	−0.0109239	+	0.0336204i	0.945446	+	0.325779i	$0.105627\pi$
$468$	−24.0887	−	26.7532i	−1.11350	−	1.23667i
$469$	4.85410	−	3.52671i	0.224142	−	0.162848i
$470$	−0.589469	+	5.60843i	−0.0271902	+	0.258697i
$471$	9.19795	+	8.28187i	0.423819	+	0.381608i
$472$	−1.19098	+	2.06284i	−0.0548194	+	0.0949500i
$473$	−5.58881	−	2.56512i	−0.256974	−	0.117944i
$474$	−6.05166	+	3.49393i	−0.277962	+	0.160481i
$475$	−2.32331	+	2.58030i	−0.106601	+	0.118392i
$476$	−7.28115	−	5.29007i	−0.333731	−	0.242470i
$477$	−11.2097	−	4.99087i	−0.513255	−	0.228516i
$478$	−1.23607	+	3.80423i	−0.0565364	+	0.174001i
$479$	11.5069	−	2.44586i	0.525762	−	0.111754i	0.0626186	−	0.998038i	$-0.480055\pi$
$479$	11.5069	−	2.44586i	0.525762	−	0.111754i	0.463143	+	0.886283i	$0.346722\pi$
$480$	−5.21723	−	7.18091i	−0.238133	−	0.327762i
$481$	30.0961	−	13.3996i	1.37226	−	0.610971i
$482$	−10.0253	−	2.13093i	−0.456638	−	0.0970614i
$483$	6.92705	+	3.99933i	0.315192	+	0.181976i
$484$	19.8475	+	4.69458i	0.902158	+	0.213390i
$485$	−7.41641			−0.336762
$486$	−1.23796	+	5.82415i	−0.0561550	+	0.264189i
$487$	10.5000	+	7.62870i	0.475800	+	0.345689i	0.799698	−	0.600403i	$-0.204993\pi$
$487$	10.5000	+	7.62870i	0.475800	+	0.345689i	−0.323897	+	0.946092i	$0.604993\pi$
$488$	14.5973	+	6.49913i	0.660788	+	0.294202i
$489$	−26.6549	+	24.0001i	−1.20537	+	1.08532i
$490$	−1.89552	−	2.10519i	−0.0856310	−	0.0951029i
$491$	−0.765800	−	7.28610i	−0.0345601	−	0.328817i	−0.998118	−	0.0613184i	$-0.980469\pi$
$491$	−0.765800	−	7.28610i	−0.0345601	−	0.328817i	0.963558	−	0.267499i	$-0.0861972\pi$
$492$	4.77163	−	6.56758i	0.215122	−	0.296090i
$493$	−15.7663	+	17.5102i	−0.710077	+	0.788620i
$494$	2.47214			0.111227
$495$	10.0317	−	7.11499i	0.450892	−	0.319795i
$496$	1.94427			0.0873004
$497$	1.94706	−	2.16243i	0.0873374	−	0.0969980i
$498$	−6.42428	−	0.675219i	−0.287879	−	0.0302573i
$499$	−4.01561	−	38.2060i	−0.179763	−	1.71033i	−0.597586	−	0.801805i	$-0.703873\pi$
$499$	−4.01561	−	38.2060i	−0.179763	−	1.71033i	0.417823	−	0.908529i	$-0.362793\pi$
$500$	−12.9921	−	14.4292i	−0.581025	−	0.645294i
$501$	2.07567	+	9.76526i	0.0927341	+	0.436280i
$502$	−7.17508	−	3.19455i	−0.320239	−	0.142580i
$503$	7.70820	+	5.60034i	0.343692	+	0.249707i	0.746218	−	0.665702i	$-0.231868\pi$
$503$	7.70820	+	5.60034i	0.343692	+	0.249707i	−0.402526	+	0.915409i	$0.631868\pi$
$504$	−4.31990	−	0.918223i	−0.192424	−	0.0409009i
$505$	10.4721			0.466004
$506$	−4.69344	−	3.49251i	−0.208649	−	0.155261i
$507$			50.0364i			2.22220i
$508$	−19.1556	−	4.07166i	−0.849894	−	0.180651i
$509$	−24.8305	+	11.0552i	−1.10059	+	0.490015i	−0.874959	−	0.484198i	$-0.839112\pi$
$509$	−24.8305	+	11.0552i	−1.10059	+	0.490015i	−0.225633	+	0.974212i	$0.572445\pi$
$510$	3.94776	−	0.414926i	0.174810	−	0.0183733i
$511$	−0.142710	+	0.0303339i	−0.00631311	+	0.00134189i
$512$	−6.89261	+	21.2133i	−0.304613	+	0.937503i
$513$	3.05422	+	4.20378i	0.134847	+	0.185601i
$514$	−4.60739	−	3.34747i	−0.203223	−	0.147650i
$515$	8.46616	−	9.40262i	0.373064	−	0.414329i
$516$	5.15654	+	2.97713i	0.227004	+	0.131061i
$517$	19.4145	+	34.5311i	0.853850	+	1.51868i
$518$	0.972136	−	1.68379i	0.0427132	−	0.0739814i
$519$	38.0359	−	12.3586i	1.66959	−	0.542483i
$520$	−1.23104	+	11.7126i	−0.0539847	+	0.513630i
$521$	32.6525	−	23.7234i	1.43053	−	1.03934i	0.440613	−	0.897697i	$-0.354761\pi$
$521$	32.6525	−	23.7234i	1.43053	−	1.03934i	0.989918	−	0.141645i	$-0.0452390\pi$
$522$	−1.71885	+	5.29007i	−0.0752319	+	0.231540i
$523$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$523$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$524$	−35.9698	−	16.0148i	−1.57135	−	0.699609i
$525$	−5.98097	−	0.628625i	−0.261031	−	0.0274355i
$526$	−4.74803	−	1.00922i	−0.207024	−	0.0440043i
$527$	−1.50000	+	2.59808i	−0.0653410	+	0.113174i
$528$	−17.1225	−	5.78027i	−0.745159	−	0.251554i
$529$	0.836881	+	1.44952i	0.0363861	+	0.0630226i
$530$	0.596748	+	1.83660i	0.0259211	+	0.0797768i
$531$	3.92705	+	2.85317i	0.170419	+	0.123817i
$532$	−1.50000	+	1.08981i	−0.0650332	+	0.0472494i
$533$	−16.0032	+	3.40158i	−0.693174	+	0.147339i
$534$	4.25590	+	1.38282i	0.184171	+	0.0598407i
$535$	1.81331	+	17.2525i	0.0783962	+	0.745890i
$536$	8.06918	−	3.59263i	0.348535	−	0.155178i
$537$	−1.82064	+	8.56542i	−0.0785663	+	0.369625i
$538$	−4.06231	−	7.03612i	−0.175138	−	0.303349i
$539$	−19.4164	−	4.35926i	−0.836324	−	0.187766i
$540$	−10.3131	+	5.95426i	−0.443804	+	0.256231i
$541$	−3.68034	−	11.3269i	−0.158230	−	0.486982i	0.840244	−	0.542209i	$-0.182412\pi$
$541$	−3.68034	−	11.3269i	−0.158230	−	0.486982i	−0.998474	+	0.0552266i	$0.982412\pi$
$542$	0.429764	−	4.08893i	0.0184600	−	0.175635i
$543$	−17.0703	+	1.79416i	−0.732557	+	0.0769948i
$544$	−13.4660	−	14.9555i	−0.577350	−	0.641212i
$545$	−5.91031	−	6.56406i	−0.253170	−	0.281173i
$546$	2.51682	+	3.46410i	0.107710	+	0.148250i
$547$	3.37901	−	32.1492i	0.144476	−	1.37460i	−0.646576	−	0.762850i	$-0.723800\pi$
$547$	3.37901	−	32.1492i	0.144476	−	1.37460i	0.791052	−	0.611749i	$-0.209534\pi$
$548$	4.93769	+	15.1967i	0.210928	+	0.649169i
$549$	16.2812	−	28.1998i	0.694863	−	1.20354i
$550$	4.29180	+	0.963568i	0.183003	+	0.0410867i
$551$	2.42705	+	4.20378i	0.103396	+	0.179087i
$552$	8.75063	+	7.87910i	0.372451	+	0.335357i
$553$	−9.64915	+	4.29608i	−0.410323	+	0.182688i
$554$	−0.768025	−	7.30727i	−0.0326303	−	0.310456i
$555$	−2.26576	−	10.6596i	−0.0961762	−	0.452474i
$556$	17.6067	−	3.74241i	0.746689	−	0.158714i
$557$	0.527864	−	0.383516i	0.0223663	−	0.0162501i	−0.576546	−	0.817065i	$-0.695600\pi$
$557$	0.527864	−	0.383516i	0.0223663	−	0.0162501i	0.598912	+	0.800815i	$0.295600\pi$
$558$	−0.0740275	+	0.704324i	−0.00313383	+	0.0298164i
$559$	−3.70820	−	11.4127i	−0.156840	−	0.482705i
$560$	−1.94427	−	3.36758i	−0.0821605	−	0.142306i
$561$	20.9339	−	18.4208i	0.883832	−	0.777727i
$562$	−1.78115	+	3.08505i	−0.0751334	+	0.130135i
$563$	19.8612	+	4.22164i	0.837051	+	0.177921i	0.606444	−	0.795126i	$-0.292595\pi$
$563$	19.8612	+	4.22164i	0.837051	+	0.177921i	0.230607	+	0.973047i	$0.425929\pi$
$564$	−15.6015	−	35.0416i	−0.656943	−	1.47552i
$565$	−19.4630	−	8.66550i	−0.818816	−	0.364561i
$566$	2.00658	−	6.17561i	0.0843428	−	0.259580i
$567$	−2.78115	+	8.55951i	−0.116797	+	0.359466i
$568$	3.46556	−	2.51788i	0.145412	−	0.105648i
$569$	−4.05553	+	38.5858i	−0.170017	+	1.61760i	0.493710	+	0.869627i	$0.335641\pi$
$569$	−4.05553	+	38.5858i	−0.170017	+	1.61760i	−0.663726	+	0.747975i	$0.731026\pi$
$570$	0.170023	−	0.799893i	0.00712146	−	0.0335038i
$571$	9.26393	−	16.0456i	0.387683	−	0.671488i	−0.604454	−	0.796640i	$-0.706609\pi$
$571$	9.26393	−	16.0456i	0.387683	−	0.671488i	0.992138	+	0.125153i	$0.0399420\pi$
$572$	19.5051	+	34.6922i	0.815550	+	1.45055i
$573$			10.2958i			0.430112i
$574$	−0.646085	+	0.717550i	−0.0269670	+	0.0299499i
$575$	12.9721	+	9.42481i	0.540975	+	0.393042i
$576$	12.9035	+	5.74500i	0.537645	+	0.239375i
$577$	10.9443	−	33.6830i	0.455616	−	1.40224i	−0.414794	−	0.909915i	$-0.636147\pi$
$577$	10.9443	−	33.6830i	0.455616	−	1.40224i	0.870410	−	0.492327i	$-0.163853\pi$
$578$	2.45180	−	0.521147i	0.101982	−	0.0216769i
$579$	7.74937	−	17.4054i	0.322053	−	0.723343i
$580$	−10.1628	+	4.52479i	−0.421989	+	0.187882i
$581$	−9.55057	−	2.03004i	−0.396224	−	0.0842201i
$582$	−3.43769	+	1.98475i	−0.142497	+	0.0822707i
$583$	10.8831	+	8.09836i	0.450730	+	0.335400i
$584$	−0.214782			−0.00888773
$585$	23.4755	+	4.98988i	0.970594	+	0.206306i
$586$	−9.01722	−	6.55139i	−0.372498	−	0.270636i
$587$	12.2565	+	5.45694i	0.505880	+	0.225232i	0.643775	−	0.765215i	$-0.277367\pi$
$587$	12.2565	+	5.45694i	0.505880	+	0.225232i	−0.137895	+	0.990447i	$0.544034\pi$
$588$	18.3253	+	5.95426i	0.755724	+	0.245550i
$589$	0.413545	+	0.459289i	0.0170398	+	0.0189247i
$590$	−0.0798526	−	0.759747i	−0.00328748	−	0.0312783i
$591$	5.80222	+	13.0320i	0.238671	+	0.536064i
$592$	−10.7149	+	11.9001i	−0.440379	+	0.489091i
$593$	−10.9443			−0.449427			−0.224714	−	0.974425i	$-0.572145\pi$
$593$	−10.9443			−0.449427			−0.224714	+	0.974425i	$0.572145\pi$
$594$	2.74587	−	5.98263i	0.112664	−	0.245470i
$595$	6.00000			0.245976
$596$	18.8333	−	20.9165i	0.771441	−	0.856772i
$597$	−5.03420	−	11.3070i	−0.206036	−	0.462765i
$598$	−1.19334	−	11.3539i	−0.0487993	−	0.464294i
$599$	−8.94004	−	9.92892i	−0.365280	−	0.405685i	0.532286	−	0.846565i	$-0.321333\pi$
$599$	−8.94004	−	9.92892i	−0.365280	−	0.405685i	−0.897566	+	0.440880i	$0.854666\pi$
$600$	−8.41999	−	2.73582i	−0.343745	−	0.111689i
$601$	−15.9616	−	7.10656i	−0.651087	−	0.289883i	0.0544917	−	0.998514i	$-0.482646\pi$
$601$	−15.9616	−	7.10656i	−0.651087	−	0.289883i	−0.705579	+	0.708632i	$0.749313\pi$
$602$	−0.572949	−	0.416272i	−0.0233517	−	0.0169660i
$603$	−5.56231	−	17.1190i	−0.226515	−	0.697140i
$604$	−8.02129			−0.326382
$605$	−12.5442	+	5.24537i	−0.509995	+	0.213255i
$606$	4.85410	−	2.80252i	0.197184	−	0.113844i
$607$	3.50528	+	0.745071i	0.142275	+	0.0302415i	0.278499	−	0.960437i	$-0.410163\pi$
$607$	3.50528	+	0.745071i	0.142275	+	0.0302415i	−0.136224	+	0.990678i	$0.543497\pi$
$608$	−3.78747	+	1.68629i	−0.153602	+	0.0683880i
$609$	−3.41966	+	7.68068i	−0.138572	+	0.311237i
$610$	−5.01263	+	1.06547i	−0.202955	+	0.0431395i
$611$	−23.8885	+	73.5214i	−0.966427	+	2.97436i
$612$	−21.8435	+	15.8702i	−0.882969	+	0.641515i
$613$	−16.0623	−	11.6699i	−0.648750	−	0.471345i	0.214095	−	0.976813i	$-0.431320\pi$
$613$	−16.0623	−	11.6699i	−0.648750	−	0.471345i	−0.862845	+	0.505468i	$0.831320\pi$
$614$	−2.00739	+	2.22943i	−0.0810117	+	0.0899727i
$615$			5.41199i			0.218232i
$616$	4.43745	+	2.03667i	0.178790	+	0.0820599i
$617$	13.5795	−	23.5204i	0.546691	−	0.946897i	−0.451807	−	0.892116i	$-0.649221\pi$
$617$	13.5795	−	23.5204i	0.546691	−	0.946897i	0.998498	−	0.0547813i	$-0.0174462\pi$
$618$	1.40798	−	6.62404i	0.0566374	−	0.266458i
$619$	−2.88105	+	27.4113i	−0.115799	+	1.10175i	0.770115	+	0.637905i	$0.220199\pi$
$619$	−2.88105	+	27.4113i	−0.115799	+	1.10175i	−0.885914	+	0.463849i	$0.846468\pi$
$620$	−1.14590	+	0.832544i	−0.0460204	+	0.0334358i
$621$	17.8325	−	16.0565i	0.715594	−	0.644324i
$622$	−1.79180	+	5.51458i	−0.0718445	+	0.221115i
$623$	6.17916	+	2.75114i	0.247563	+	0.110222i
$624$	−14.3439	−	32.2168i	−0.574214	−	1.28971i
$625$	−4.31990	−	0.918223i	−0.172796	−	0.0367289i
$626$	0.663119	−	1.14856i	0.0265036	−	0.0459055i
$627$	−2.27648	−	5.27424i	−0.0909140	−	0.210633i
$628$	6.62461	+	11.4742i	0.264351	+	0.457869i
$629$	−7.63525	−	23.4989i	−0.304438	−	0.936962i
$630$	1.29395	−	0.576105i	0.0515523	−	0.0229526i
$631$	8.80902	−	6.40013i	0.350681	−	0.254785i	−0.398473	−	0.917180i	$-0.630460\pi$
$631$	8.80902	−	6.40013i	0.350681	−	0.254785i	0.749155	+	0.662395i	$0.230460\pi$
$632$	−15.2094	+	3.23285i	−0.604996	+	0.128596i
$633$	−7.37229	−	34.6839i	−0.293022	−	1.37856i
$634$	0.836228	+	7.95618i	0.0332108	+	0.315980i
$635$	11.9270	−	5.31024i	0.473309	−	0.210731i
$636$	−9.76133	−	8.78914i	−0.387062	−	0.348512i
$637$	−19.4164	−	33.6302i	−0.769306	−	1.33248i
$638$	3.13525	−	5.29007i	0.124126	−	0.209436i
$639$	−4.36475	−	7.55996i	−0.172667	−	0.299067i
$640$	−3.85410	−	11.8617i	−0.152347	−	0.468875i
$641$	2.13770	−	20.3388i	0.0844339	−	0.803335i	−0.867584	−	0.497291i	$-0.834328\pi$
$641$	2.13770	−	20.3388i	0.0844339	−	0.803335i	0.952017	−	0.306044i	$-0.0990053\pi$
$642$	5.45757	+	7.51170i	0.215393	+	0.296463i
$643$	−4.58629	−	5.09359i	−0.180866	−	0.200872i	0.645894	−	0.763427i	$-0.276485\pi$
$643$	−4.58629	−	5.09359i	−0.180866	−	0.200872i	−0.826759	+	0.562556i	$0.809818\pi$
$644$	5.72930	+	6.36303i	0.225766	+	0.250739i
$645$	−3.94776	+	0.414926i	−0.155443	+	0.0163377i
$646$	0.193806	−	1.84395i	0.00762521	−	0.0725490i
$647$	−1.29180	−	3.97574i	−0.0507857	−	0.156302i	0.922447	−	0.386123i	$-0.126186\pi$
$647$	−1.29180	−	3.97574i	−0.0507857	−	0.156302i	−0.973233	+	0.229821i	$0.926186\pi$
$648$	−6.62461	+	11.4742i	−0.260239	+	0.450748i
$649$	−3.54508	−	4.02874i	−0.139157	−	0.158142i
$650$	4.29180	+	7.43361i	0.168338	+	0.291570i
$651$	−0.222562	+	1.04707i	−0.00872291	+	0.0410381i
$652$	−35.0757	+	15.6167i	−1.37367	+	0.611597i
$653$	0.142230	+	1.35323i	0.00556588	+	0.0529558i	0.996952	−	0.0780135i	$-0.0248577\pi$
$653$	0.142230	+	1.35323i	0.00556588	+	0.0529558i	−0.991386	+	0.130969i	$0.958191\pi$
$654$	−4.49623	−	1.46091i	−0.175816	−	0.0571262i
$655$	25.6756	−	5.45752i	1.00323	−	0.213243i
$656$	6.43363	−	4.67430i	0.251191	−	0.182501i
$657$	−0.0457515	+	0.435296i	−0.00178494	+	0.0169825i
$658$	1.40983	+	4.33901i	0.0549609	+	0.169152i
$659$	−4.98936	−	8.64182i	−0.194358	−	0.336637i	0.752332	−	0.658784i	$-0.228929\pi$
$659$	−4.98936	−	8.64182i	−0.194358	−	0.336637i	−0.946690	+	0.322147i	$0.895596\pi$
$660$	12.5666	−	3.92517i	0.489155	−	0.152787i
$661$	2.14590	−	3.71680i	0.0834658	−	0.144567i	−0.821271	−	0.570539i	$-0.806734\pi$
$661$	2.14590	−	3.71680i	0.0834658	−	0.144567i	0.904736	+	0.425972i	$0.140068\pi$
$662$	5.38625	+	1.14488i	0.209342	+	0.0444971i
$663$	54.1167	+	5.68790i	2.10172	+	0.220900i
$664$	−13.1312	−	5.84637i	−0.509588	−	0.226883i
$665$	0.381966	−	1.17557i	0.0148120	−	0.0455867i
$666$	−3.90292	−	4.33463i	−0.151235	−	0.167963i
$667$	18.1353	−	13.1760i	0.702200	−	0.510178i
$668$	−1.11709	+	10.6284i	−0.0432214	+	0.411224i
$669$	25.5436	−	8.29963i	0.987574	−	0.320882i
$670$	−1.41641	+	2.45329i	−0.0547206	+	0.0947789i
$671$	−24.3918	+	26.4758i	−0.941633	+	1.02209i
$672$	−6.21885	−	3.59045i	−0.239897	−	0.138505i
$673$	−19.7810	+	21.9691i	−0.762503	+	0.846846i	−0.991970	−	0.126471i	$-0.959635\pi$
$673$	−19.7810	+	21.9691i	−0.762503	+	0.846846i	0.229467	+	0.973316i	$0.426302\pi$
$674$	−3.54508	−	2.57565i	−0.136552	−	0.0992105i
$675$	−7.33824	+	16.4820i	−0.282449	+	0.634391i
$676$	−16.5517	+	50.9408i	−0.636602	+	1.95926i
$677$	−5.92340	+	1.25906i	−0.227655	+	0.0483895i	−0.320326	−	0.947307i	$-0.603793\pi$
$677$	−5.92340	+	1.25906i	−0.227655	+	0.0483895i	0.0926718	+	0.995697i	$0.470459\pi$
$678$	−11.3406	+	1.19195i	−0.435535	+	0.0457766i
$679$	−5.48127	+	2.44042i	−0.210352	+	0.0936547i
$680$	8.63980	+	1.83645i	0.331321	+	0.0704245i
$681$		−	28.7833i		−	1.10298i
$682$	0.250426	−	0.741819i	0.00958933	−	0.0284057i
$683$	−5.52786			−0.211518			−0.105759	−	0.994392i	$-0.533727\pi$
$683$	−5.52786			−0.211518			−0.105759	+	0.994392i	$0.533727\pi$
$684$	1.71885	+	5.29007i	0.0657218	+	0.202271i
$685$	−8.61803	−	6.26137i	−0.329278	−	0.239235i
$686$	−4.53626	−	2.01967i	−0.173195	−	0.0771115i
$687$	−3.66608	−	17.2475i	−0.139870	−	0.658035i
$688$	3.90292	+	4.33463i	0.148797	+	0.165256i
$689$	2.76709	+	26.3271i	0.105418	+	1.00298i
$690$	−3.75577	−	0.394748i	−0.142980	−	0.0150278i
$691$	9.76713	−	10.8475i	0.371559	−	0.412658i	−0.528148	−	0.849152i	$-0.677113\pi$
$691$	9.76713	−	10.8475i	0.371559	−	0.412658i	0.899707	+	0.436494i	$0.143780\pi$
$692$	42.8115			1.62745
$693$	5.07295	−	8.55951i	0.192705	−	0.325149i
$694$	3.39512			0.128877
$695$	−8.02957	+	8.91774i	−0.304579	+	0.338269i
$696$	−7.27505	+	10.0133i	−0.275760	+	0.379551i
$697$	1.28262	+	12.2033i	0.0485826	+	0.462233i
$698$	1.05963	+	1.17684i	0.0401076	+	0.0445440i
$699$	14.3192	−	12.8931i	0.541602	−	0.487661i
$700$	−5.88113	−	2.61845i	−0.222286	−	0.0989680i
$701$	38.6074	+	28.0499i	1.45818	+	1.05943i	0.983832	+	0.179094i	$0.0573165\pi$
$701$	38.6074	+	28.0499i	1.45818	+	1.05943i	0.474349	+	0.880337i	$0.342683\pi$
$702$	12.2169	−	3.96951i	0.461097	−	0.149819i
$703$	−5.09017			−0.191979
$704$	−12.5275	−	9.32204i	−0.472148	−	0.351338i
$705$	22.1459	+	12.7859i	0.834063	+	0.481546i
$706$	−6.13348	−	1.30371i	−0.230837	−	0.0490659i
$707$	7.73968	−	3.44593i	0.291081	−	0.129597i
$708$	3.05422	+	4.20378i	0.114785	+	0.157988i
$709$	25.2009	−	5.35662i	0.946441	−	0.201172i	0.291260	−	0.956644i	$-0.405926\pi$
$709$	25.2009	−	5.35662i	0.946441	−	0.201172i	0.655181	+	0.755472i	$0.272592\pi$
$710$	−0.424538	+	1.30660i	−0.0159326	+	0.0490356i
$711$	3.31218	+	31.5133i	0.124217	+	1.18184i
$712$	8.05573	+	5.85283i	0.301901	+	0.219344i
$713$	1.90977	−	2.12101i	0.0715213	−	0.0794325i
$714$	2.78115	−	1.60570i	0.104082	−	0.0600918i
$715$	−24.1144	−	11.0679i	−0.901826	−	0.413914i
$716$	−4.68692	+	8.11798i	−0.175158	+	0.303383i
$717$	13.4794	+	12.1369i	0.503396	+	0.453260i
$718$	−0.912480	+	8.68167i	−0.0340535	+	0.323997i
$719$	15.8541	−	11.5187i	0.591258	−	0.429574i	−0.251507	−	0.967855i	$-0.580926\pi$
$719$	15.8541	−	11.5187i	0.591258	−	0.429574i	0.842765	+	0.538281i	$0.180926\pi$
$720$	−11.4107	+	2.42542i	−0.425252	+	0.0903901i
$721$	3.16312	−	9.73508i	0.117801	−	0.362553i
$722$	6.28098	+	2.79647i	0.233754	+	0.104074i
$723$	−27.3178	+	37.5997i	−1.01596	+	1.39835i
$724$	−17.9723	−	3.82014i	−0.667936	−	0.141974i
$725$	−8.42705	+	14.5961i	−0.312973	+	0.542085i
$726$	−4.41082	+	5.78841i	−0.163701	+	0.214828i
$727$	−9.41641	−	16.3097i	−0.349235	−	0.604893i	0.636879	−	0.770964i	$-0.280225\pi$
$727$	−9.41641	−	16.3097i	−0.349235	−	0.604893i	−0.986114	+	0.166071i	$0.946892\pi$
$728$	2.94427	+	9.06154i	0.109122	+	0.335843i
$729$	21.8435	+	15.8702i	0.809017	+	0.587785i
$730$	0.0557281	−	0.0404888i	0.00206259	−	0.00149856i
$731$	−8.80333	+	1.87121i	−0.325603	+	0.0692090i
$732$	25.9037	−	23.3238i	0.957428	−	0.862072i
$733$	−5.06672	−	48.2066i	−0.187143	−	1.78055i	−0.536836	−	0.843687i	$-0.680381\pi$
$733$	−5.06672	−	48.2066i	−0.187143	−	1.78055i	0.349692	−	0.936865i	$-0.386286\pi$
$734$	4.43444	−	1.97434i	0.163678	−	0.0728743i
$735$	−12.2169	+	3.96951i	−0.450627	+	0.146417i
$736$	9.57295	+	16.5808i	0.352864	+	0.611178i
$737$	1.85410	+	19.8132i	0.0682967	+	0.729828i
$738$	1.44834	+	2.50859i	0.0533140	+	0.0923426i
$739$	13.1459	+	40.4589i	0.483580	+	1.48831i	0.834027	+	0.551723i	$0.186029\pi$
$739$	13.1459	+	40.4589i	0.483580	+	1.48831i	−0.350448	+	0.936582i	$0.613971\pi$
$740$	1.21939	−	11.6017i	0.0448257	−	0.426488i
$741$	4.55955	−	10.2409i	0.167499	−	0.376209i
$742$	1.04539	+	1.16102i	0.0383774	+	0.0426224i
$743$	−28.3448	−	31.4801i	−1.03987	−	1.15489i	−0.987717	−	0.156255i	$-0.950058\pi$
$743$	−28.3448	−	31.4801i	−1.03987	−	1.15489i	−0.0521540	−	0.998639i	$-0.516609\pi$
$744$	−0.640965	+	1.43963i	−0.0234989	+	0.0527794i
$745$	−1.96136	+	18.6611i	−0.0718589	+	0.683691i
$746$	0.667184	+	2.05338i	0.0244274	+	0.0751797i
$747$	−14.6459	+	25.3674i	−0.535865	+	0.928146i
$748$	27.4058	−	11.8290i	1.00205	−	0.432509i
$749$	7.01722	+	12.1542i	0.256404	+	0.444104i
$750$	6.58911	−	2.14093i	0.240600	−	0.0781758i
$751$	−28.5476	+	12.7102i	−1.04172	+	0.463802i	−0.855009	−	0.518614i	$-0.826448\pi$
$751$	−28.5476	+	12.7102i	−1.04172	+	0.463802i	−0.186707	+	0.982416i	$0.559782\pi$
$752$	−3.92771	−	37.3696i	−0.143229	−	1.36273i
$753$	−26.4671	+	23.8311i	−0.964514	+	0.868452i
$754$	11.7378	−	2.49494i	0.427464	−	0.0908604i
$755$	4.32624	−	3.14320i	0.157448	−	0.114393i
$756$	−5.66284	+	7.79423i	−0.205955	+	0.283473i
$757$	3.39919	+	10.4616i	0.123546	+	0.380234i	0.993633	−	0.112663i	$-0.0359380\pi$
$757$	3.39919	+	10.4616i	0.123546	+	0.380234i	−0.870088	+	0.492897i	$0.835938\pi$
$758$	3.01722	+	5.22598i	0.109590	+	0.189816i
$759$	−23.1243	+	13.0012i	−0.839359	+	0.471915i
$760$	0.909830	−	1.57587i	0.0330030	−	0.0571629i
$761$	−6.82621	−	1.45096i	−0.247450	−	0.0525971i	0.0825167	−	0.996590i	$-0.473704\pi$
$761$	−6.82621	−	1.45096i	−0.247450	−	0.0525971i	−0.329967	+	0.943993i	$0.607038\pi$
$762$	4.10736	−	5.65330i	0.148794	−	0.204797i
$763$	−6.52810	−	2.90650i	−0.236333	−	0.105222i
$764$	−3.40576	+	10.4819i	−0.123216	+	0.379221i
$765$	5.56231	−	17.1190i	0.201106	−	0.618939i
$766$	6.13525	−	4.45752i	0.221676	−	0.161057i
$767$	1.09464	−	10.4148i	0.0395250	−	0.376055i
$768$	7.15960	+	6.44654i	0.258350	+	0.232619i
$769$	7.89919	−	13.6818i	0.284852	−	0.493378i	−0.687721	−	0.725975i	$-0.741389\pi$
$769$	7.89919	−	13.6818i	0.284852	−	0.493378i	0.972573	+	0.232597i	$0.0747222\pi$
$770$	−1.53529	+	0.308068i	−0.0553282	+	0.0111020i
$771$	−22.3647	+	12.9123i	−0.805447	+	0.465025i
$772$	13.6470	−	15.1565i	0.491166	−	0.545495i
$773$	−19.1353	−	13.9026i	−0.688247	−	0.500041i	0.187836	−	0.982200i	$-0.439853\pi$
$773$	−19.1353	−	13.9026i	−0.688247	−	0.500041i	−0.876083	+	0.482159i	$0.839853\pi$
$774$	−1.71885	+	1.24882i	−0.0617827	+	0.0448877i
$775$	−0.663119	+	2.04087i	−0.0238199	+	0.0733102i
$776$	−8.63980	+	1.83645i	−0.310151	+	0.0659246i
$777$	−5.18217	−	7.13264i	−0.185909	−	0.255882i
$778$	7.90443	−	3.51928i	0.283388	−	0.126172i
$779$	2.47262	+	0.525572i	0.0885910	+	0.0188306i
$780$	22.2492	+	12.8456i	0.796650	+	0.459946i
$781$	2.87733	+	9.21191i	0.102959	+	0.329628i
$782$	−8.56231			−0.306187
$783$	18.7441	+	16.8772i	0.669859	+	0.603144i
$784$	15.2705	+	11.0947i	0.545375	+	0.396238i
$785$	−8.06918	−	3.59263i	−0.288001	−	0.128226i
$786$	10.4408	−	9.40092i	0.372410	−	0.335320i
$787$	24.0887	+	26.7532i	0.858669	+	0.953649i	0.999337	−	0.0364078i	$-0.0115915\pi$
$787$	24.0887	+	26.7532i	0.858669	+	0.953649i	−0.140668	+	0.990057i	$0.544925\pi$
$788$	1.59620	+	15.1869i	0.0568624	+	0.541009i
$789$	−12.9379	+	17.8075i	−0.460601	+	0.633963i
$790$	3.33685	−	3.70595i	0.118720	−	0.131852i
$791$	−17.2361			−0.612844
$792$	9.92472	−	10.7727i	0.352660	−	0.382791i
$793$	−70.2492			−2.49462
$794$	0.543019	−	0.603084i	0.0192710	−	0.0214026i
$795$	8.70881	+	0.915333i	0.308870	+	0.0324635i
$796$	−1.38492	−	13.1766i	−0.0490872	−	0.467034i
$797$	16.2401	+	18.0365i	0.575255	+	0.638886i	0.958612	−	0.284714i	$-0.0918988\pi$
$797$	16.2401	+	18.0365i	0.575255	+	0.638886i	−0.383357	+	0.923600i	$0.625232\pi$
$798$	−0.137551	−	0.647127i	−0.00486926	−	0.0229081i
$799$	52.9662	+	23.5821i	1.87381	+	0.834274i
$800$	−11.6459	−	8.46124i	−0.411745	−	0.299150i
$801$	13.5779	−	15.0797i	0.479750	−	0.532817i
$802$	−5.56231			−0.196412
$803$	0.154772	−	0.458469i	0.00546179	−	0.0161790i
$804$		−	19.2684i		−	0.679544i
$805$	−5.58347	−	1.18680i	−0.196791	−	0.0418293i
$806$	1.39577	−	0.621438i	0.0491640	−	0.0218892i
$807$	−36.6398	+	3.85100i	−1.28978	+	0.135561i
$808$	12.1996	−	2.59310i	0.429180	−	0.0912250i
$809$	−5.59017	+	17.2048i	−0.196540	+	0.604888i	0.803415	+	0.595419i	$0.203014\pi$
$809$	−5.59017	+	17.2048i	−0.196540	+	0.604888i	−0.999955	+	0.00946853i	$0.996986\pi$
$810$	−0.444165	−	4.22595i	−0.0156064	−	0.148485i
$811$	−7.02786	−	5.10604i	−0.246782	−	0.179297i	0.457518	−	0.889201i	$-0.348739\pi$
$811$	−7.02786	−	5.10604i	−0.246782	−	0.179297i	−0.704299	+	0.709903i	$0.748739\pi$
$812$	−6.02218	+	6.68830i	−0.211337	+	0.234713i
$813$	−16.1459	−	9.32184i	−0.566261	−	0.326931i
$814$	3.16027	+	5.62093i	0.110767	+	0.197013i
$815$	12.7984	−	22.1674i	0.448307	−	0.776491i
$816$	−25.1548	+	8.17328i	−0.880593	+	0.286122i
$817$	−0.193806	+	1.84395i	−0.00678043	+	0.0645115i
$818$	−10.4271	+	7.57570i	−0.364573	+	0.264878i
$819$	18.9921	−	4.03690i	0.663638	−	0.141061i
$820$	−1.79024	+	5.50980i	−0.0625180	+	0.192411i
$821$	34.9109	+	15.5434i	1.21840	+	0.542467i	0.912296	−	0.409531i	$-0.134308\pi$
$821$	34.9109	+	15.5434i	1.21840	+	0.542467i	0.306104	+	0.951998i	$0.400974\pi$
$822$	−5.67032	−	0.595975i	−0.197775	−	0.0207870i
$823$	41.3676	+	8.79296i	1.44198	+	0.306503i	0.861496	−	0.507765i	$-0.169528\pi$
$823$	41.3676	+	8.79296i	1.44198	+	0.306503i	0.580489	+	0.814268i	$0.302861\pi$
$824$	7.53444	−	13.0500i	0.262475	−	0.454620i
$825$	11.9073	−	16.0017i	0.414559	−	0.557109i
$826$	−0.309017	−	0.535233i	−0.0107521	−	0.0186231i
$827$	−17.6246	−	54.2430i	−0.612868	−	1.88621i	−0.429147	−	0.903235i	$-0.641186\pi$
$827$	−17.6246	−	54.2430i	−0.612868	−	1.88621i	−0.183721	−	0.982978i	$-0.558814\pi$
$828$	23.4662	−	10.4478i	0.815506	−	0.363087i
$829$	−35.2254	+	25.5928i	−1.22343	+	0.888874i	−0.996380	−	0.0850096i	$-0.972908\pi$
$829$	−35.2254	+	25.5928i	−1.22343	+	0.888874i	−0.227049	+	0.973883i	$0.572908\pi$
$830$	4.50917	−	0.958453i	0.156515	−	0.0332684i
$831$	−31.6872	−	10.2958i	−1.09922	−	0.357157i
$832$	−3.18521	−	30.3052i	−0.110427	−	1.05064i
$833$	−26.6067	+	11.8460i	−0.921866	+	0.410441i
$834$	−1.33537	+	6.28244i	−0.0462402	+	0.217543i
$835$	−3.56231	−	6.17009i	−0.123279	−	0.213525i
$836$	−0.572949	−	6.12261i	−0.0198159	−	0.211755i
$837$	2.78115	+	1.60570i	0.0961307	+	0.0555011i
$838$	−0.954915	−	2.93893i	−0.0329870	−	0.101524i
$839$	1.80748	−	17.1971i	0.0624013	−	0.593709i	−0.917984	−	0.396618i	$-0.870184\pi$
$839$	1.80748	−	17.1971i	0.0624013	−	0.593709i	0.980385	−	0.197091i	$-0.0631495\pi$
$840$	3.13448	−	0.329447i	0.108150	−	0.0113670i
$841$	−3.63853	−	4.04099i	−0.125466	−	0.139345i
$842$	−2.61619	−	2.90557i	−0.0901598	−	0.100133i
$843$	9.49480	+	13.0685i	0.327018	+	0.450102i
$844$	3.96763	−	37.7495i	0.136572	−	1.29939i
$845$	−11.0344	−	33.9605i	−0.379596	−	1.16828i
$846$	13.6869			0.470566
$847$	−7.54508	+	8.00448i	−0.259252	+	0.275037i
$848$	−6.43363	−	11.1434i	−0.220932	−	0.382665i
$849$	−21.8818	−	19.7025i	−0.750981	−	0.676187i
$850$	5.88113	−	2.61845i	0.201721	−	0.0898120i
$851$	2.45711	+	23.3778i	0.0842285	+	0.801381i
$852$	−1.94286	−	9.14042i	−0.0665612	−	0.313146i
$853$	34.6633	−	7.36791i	1.18685	−	0.252272i	0.428146	−	0.903710i	$-0.359167\pi$
$853$	34.6633	−	7.36791i	1.18685	−	0.252272i	0.758703	+	0.651437i	$0.225834\pi$
$854$	−3.35410	+	2.43690i	−0.114775	+	0.0833889i
$855$	−3.00000	−	2.17963i	−0.102598	−	0.0745417i
$856$	6.38448	+	19.6494i	0.218217	+	0.671603i
$857$	−12.6803	−	21.9630i	−0.433152	−	0.750242i	0.563991	−	0.825781i	$-0.309265\pi$
$857$	−12.6803	−	21.9630i	−0.433152	−	0.750242i	−0.997143	+	0.0755396i	$0.975932\pi$
$858$	−14.1396	+	1.32317i	−0.482717	+	0.0451722i
$859$	16.2812	−	28.1998i	0.555506	−	0.962164i	−0.442358	−	0.896838i	$-0.645858\pi$
$859$	16.2812	−	28.1998i	0.555506	−	0.962164i	0.997864	−	0.0653258i	$-0.0208087\pi$
$860$	−4.15637	−	0.883463i	−0.141731	−	0.0301258i
$861$	1.78085	+	3.99986i	0.0606912	+	0.136315i
$862$	11.8881	+	5.29293i	0.404911	+	0.180278i
$863$	4.46556	−	13.7436i	0.152009	−	0.467837i	−0.845836	−	0.533443i	$-0.820898\pi$
$863$	4.46556	−	13.7436i	0.152009	−	0.467837i	0.997846	+	0.0656059i	$0.0208980\pi$
$864$	−16.0094	+	14.4149i	−0.544649	+	0.490405i
$865$	−23.0902	+	16.7760i	−0.785089	+	0.570401i
$866$	0.588620	−	5.60034i	0.0200021	−	0.190307i
$867$	2.36318	−	11.1179i	0.0802577	−	0.377583i
$868$	−0.572949	+	0.992377i	−0.0194472	+	0.0336835i
$869$	4.05911	−	34.7952i	0.137696	−	1.18035i
$870$		−	3.96951i		−	0.134579i
$871$	−25.9842	+	28.8584i	−0.880442	+	0.977830i
$872$	−8.51064	−	6.18334i	−0.288207	−	0.209394i
$873$	1.88151	+	17.9014i	0.0636795	+	0.605870i
$874$	−0.545085	+	1.67760i	−0.0184378	+	0.0567456i
$875$	10.2433	−	2.17728i	0.346287	−	0.0736055i
$876$	−0.190571	+	0.428030i	−0.00643880	+	0.0144618i
$877$	10.5942	−	4.71682i	0.357739	−	0.159276i	−0.219994	−	0.975501i	$-0.570604\pi$
$877$	10.5942	−	4.71682i	0.357739	−	0.159276i	0.577734	+	0.816225i	$0.303937\pi$
$878$	−0.264599	−	0.0562422i	−0.00892977	−	0.00189808i
$879$	−43.7705	+	25.2709i	−1.47634	+	0.852367i
$880$	12.8960	+	0.147179i	0.434724	+	0.00496141i
$881$	1.81966			0.0613059			0.0306530	−	0.999530i	$-0.490241\pi$
$881$	1.81966			0.0613059			0.0306530	+	0.999530i	$0.490241\pi$
$882$	−4.60053	+	5.10941i	−0.154908	+	0.172043i
$883$	28.8435	+	20.9560i	0.970660	+	0.705226i	0.955602	−	0.294661i	$-0.0952068\pi$
$883$	28.8435	+	20.9560i	0.970660	+	0.705226i	0.0150579	+	0.999887i	$0.495207\pi$
$884$	53.2133	+	23.6921i	1.78976	+	0.796851i
$885$	−3.29456	−	1.07047i	−0.110745	−	0.0359833i
$886$	0.315921	+	0.350865i	0.0106136	+	0.0117876i
$887$	0.421714	+	4.01234i	0.0141598	+	0.134721i	0.999318	−	0.0369278i	$-0.0117572\pi$
$887$	0.421714	+	4.01234i	0.0141598	+	0.134721i	−0.985158	+	0.171649i	$0.945090\pi$
$888$	−5.27903	−	11.8569i	−0.177153	−	0.397891i
$889$	7.06756	−	7.84932i	0.237038	−	0.263258i
$890$	−3.19350			−0.107046
$891$	−19.7188	−	22.4091i	−0.660606	−	0.750733i
$892$	28.7508			0.962647
$893$	7.99228	−	8.87632i	0.267451	−	0.297035i
$894$	4.08489	+	9.17481i	0.136619	+	0.306851i
$895$	−0.653222	−	6.21499i	−0.0218348	−	0.207744i
$896$	−6.75164	−	7.49846i	−0.225557	−	0.250506i
$897$	−49.2347	−	15.9973i	−1.64390	−	0.534136i
$898$	−2.60735	−	1.16087i	−0.0870085	−	0.0387387i
$899$	2.42705	+	1.76336i	0.0809467	+	0.0588112i
$900$	−12.9230	+	14.3524i	−0.430766	+	0.478414i
$901$	19.8541			0.661436
$902$	−0.954773	−	3.05675i	−0.0317904	−	0.101779i
$903$	−2.78115	+	1.60570i	−0.0925510	+	0.0534343i
$904$	−24.8194	−	5.27552i	−0.825480	−	0.175461i
$905$	11.1902	−	4.98221i	0.371976	−	0.165614i
$906$	1.16415	−	2.61472i	0.0386763	−	0.0868684i
$907$	14.2649	−	3.03210i	0.473658	−	0.100679i	0.0351037	−	0.999384i	$-0.488824\pi$
$907$	14.2649	−	3.03210i	0.473658	−	0.100679i	0.438555	+	0.898704i	$0.355491\pi$
$908$	9.52129	−	29.3035i	0.315975	−	0.972471i
$909$	−2.65674	−	25.2772i	−0.0881184	−	0.838391i
$910$	−2.47214	−	1.79611i	−0.0819505	−	0.0595405i
$911$	−12.8342	+	14.2538i	−0.425214	+	0.472248i	−0.917242	−	0.398331i	$-0.869589\pi$
$911$	−12.8342	+	14.2538i	−0.425214	+	0.472248i	0.492027	+	0.870580i	$0.336256\pi$
$912$			5.44886i			0.180430i
$913$	21.9419	−	23.8166i	0.726170	−	0.788215i
$914$	−0.190983	+	0.330792i	−0.00631716	+	0.0109416i
$915$	−4.83143	+	22.7301i	−0.159722	+	0.751434i
$916$	1.97302	−	18.7720i	0.0651903	−	0.620244i
$917$	17.1803	−	12.4822i	0.567345	−	0.412200i
$918$	−2.00306	−	9.42367i	−0.0661109	−	0.311027i
$919$	−8.30244	+	25.5523i	−0.273872	+	0.842892i	0.715643	+	0.698466i	$0.246134\pi$
$919$	−8.30244	+	25.5523i	−0.273872	+	0.842892i	−0.989516	+	0.144426i	$0.953866\pi$
$920$	−7.67675	−	3.41791i	−0.253095	−	0.112685i
$921$	5.53312	+	12.4276i	0.182323	+	0.409503i
$922$	−6.03242	−	1.28223i	−0.198667	−	0.0422280i
$923$	−9.41641	+	16.3097i	−0.309945	+	0.536840i
$924$	7.99606	−	7.03612i	0.263051	−	0.231471i
$925$	−8.83688	−	15.3059i	−0.290555	−	0.503256i
$926$	−2.00658	−	6.17561i	−0.0659402	−	0.202943i
$927$	−24.8435	−	18.0498i	−0.815966	−	0.592834i
$928$	−16.2812	+	11.8290i	−0.534455	+	0.388304i
$929$	47.2157	−	10.0360i	1.54910	−	0.329271i	0.647574	−	0.762003i	$-0.275784\pi$
$929$	47.2157	−	10.0360i	1.54910	−	0.329271i	0.901523	+	0.432732i	$0.142450\pi$
$930$	−0.105080	−	0.494361i	−0.00344570	−	0.0162107i
$931$	0.627171	+	5.96713i	0.0205547	+	0.195565i
$932$	18.8429	−	8.38942i	0.617221	−	0.274804i
$933$	19.5396	+	17.5935i	0.639698	+	0.575986i
$934$	−0.145898	−	0.252703i	−0.00477393	−	0.00826869i
$935$	−10.1459	+	17.1190i	−0.331806	+	0.559852i
$936$	28.5836			0.934284
$937$	−7.11803	−	21.9071i	−0.232536	−	0.715672i	−0.997439	−	0.0715265i	$-0.977213\pi$
$937$	−7.11803	−	21.9071i	−0.232536	−	0.715672i	0.764903	−	0.644146i	$-0.222787\pi$
$938$	−0.239558	+	2.27924i	−0.00782184	+	0.0744199i
$939$	−3.53489	−	4.86536i	−0.115357	−	0.158775i
$940$	18.3167	+	20.3427i	0.597424	+	0.663507i
$941$	18.1730	+	20.1831i	0.592421	+	0.657951i	0.962574	−	0.271021i	$-0.0873611\pi$
$941$	18.1730	+	20.1831i	0.592421	+	0.657951i	−0.370152	+	0.928971i	$0.620694\pi$
$942$	−4.70172	+	0.494170i	−0.153190	+	0.0161009i
$943$	1.22024	−	11.6098i	0.0397365	−	0.378067i
$944$	1.57295	+	4.84104i	0.0511951	+	0.157562i
$945$		−	6.42280i		−	0.208934i
$946$	2.15654	−	0.930812i	0.0701152	−	0.0302633i
$947$	−18.3541	−	31.7902i	−0.596428	−	1.03304i	−0.993344	−	0.115189i	$-0.963253\pi$
$947$	−18.3541	−	31.7902i	−0.596428	−	1.03304i	0.396915	−	0.917855i	$-0.370081\pi$
$948$	−7.05232	+	33.1785i	−0.229049	+	1.07759i
$949$	0.862635	−	0.384070i	0.0280023	−	0.0124674i
$950$	−0.138630	−	1.31897i	−0.00449774	−	0.0427931i
$951$	34.5010	+	11.2101i	1.11877	+	0.363511i
$952$	6.98974	−	1.48572i	0.226539	−	0.0481523i
$953$	7.68034	−	5.58009i	0.248791	−	0.180757i	−0.456400	−	0.889775i	$-0.650861\pi$
$953$	7.68034	−	5.58009i	0.248791	−	0.180757i	0.705191	+	0.709018i	$0.250861\pi$
$954$	4.28171	−	1.90634i	0.138626	−	0.0617201i
$955$	−2.27051	−	6.98791i	−0.0734720	−	0.226123i
$956$	9.70820	+	16.8151i	0.313986	+	0.543839i
$957$	−16.1317	−	22.7448i	−0.521464	−	0.735234i
$958$	−2.24671	+	3.89142i	−0.0725879	+	0.125726i
$959$	−8.42971	−	1.79179i	−0.272210	−	0.0578599i
$960$	−10.0247	−	1.05364i	−0.323547	−	0.0340061i
$961$	−27.9710	−	12.4535i	−0.902289	−	0.401725i
$962$	−3.88854	+	11.9677i	−0.125372	+	0.385854i
$963$	41.1833	−	8.75377i	1.32711	−	0.282086i
$964$	−40.2492	+	29.2428i	−1.29634	+	0.941846i
$965$	−1.42125	+	13.5223i	−0.0457516	+	0.435297i
$966$	−2.90569	+	0.944115i	−0.0934889	+	0.0303764i
$967$	−26.2426	+	45.4536i	−0.843907	+	1.46169i	0.0426608	+	0.999090i	$0.486417\pi$
$967$	−26.2426	+	45.4536i	−0.843907	+	1.46169i	−0.886567	+	0.462599i	$0.846917\pi$
$968$	−13.3146	+	9.21682i	−0.427949	+	0.296240i
$969$	−7.28115	−	4.20378i	−0.233904	−	0.135045i
$970$	1.89552	−	2.10519i	0.0608616	−	0.0675937i
$971$	−7.50000	−	5.44907i	−0.240686	−	0.174869i	0.460903	−	0.887451i	$-0.347526\pi$
$971$	−7.50000	−	5.44907i	−0.240686	−	0.174869i	−0.701589	+	0.712582i	$0.747526\pi$
$972$	16.9885	+	23.3827i	0.544907	+	0.750000i
$973$	−3.00000	+	9.23305i	−0.0961756	+	0.295998i
$974$	−4.84910	+	1.03071i	−0.155375	+	0.0330260i
$975$	38.7097	−	4.06855i	1.23970	−	0.130298i
$976$	31.1938	−	13.8884i	0.998490	−	0.444556i
$977$	−15.4195	−	3.27751i	−0.493312	−	0.104857i	−0.0454632	−	0.998966i	$-0.514476\pi$
$977$	−15.4195	−	3.27751i	−0.493312	−	0.104857i	−0.447849	+	0.894109i	$0.647810\pi$
$978$		−	13.7002i		−	0.438085i
$979$	−18.2983	+	12.9781i	−0.584817	+	0.414781i
$980$	−13.7508			−0.439252
$981$	−14.3446	+	15.9313i	−0.457988	+	0.508648i
$982$	2.26393	+	1.64484i	0.0722450	+	0.0524890i
$983$	8.45701	+	3.76531i	0.269737	+	0.120095i	0.537148	−	0.843488i	$-0.319502\pi$
$983$	8.45701	+	3.76531i	0.269737	+	0.120095i	−0.267411	+	0.963582i	$0.586168\pi$
$984$	1.34011	+	6.30473i	0.0427212	+	0.200988i
$985$	−6.81198	−	7.56547i	−0.217048	−	0.241056i
$986$	−0.940756	−	8.95070i	−0.0299598	−	0.285048i
$987$	20.5748	+	2.16249i	0.654902	+	0.0688329i
$988$	8.02957	−	8.91774i	0.255455	−	0.283711i
$989$	8.56231			0.272265
$990$	−0.544327	+	4.66605i	−0.0172999	+	0.148297i
$991$	20.5967			0.654277			0.327139	−	0.944976i	$-0.393916\pi$
$991$	20.5967			0.654277			0.327139	+	0.944976i	$0.393916\pi$
$992$	−1.71452	+	1.90416i	−0.0544360	+	0.0604573i
$993$	14.6770	−	20.2011i	0.465760	−	0.641063i
$994$	0.116179	+	1.10537i	0.00368497	+	0.0350601i
$995$	5.91031	+	6.56406i	0.187369	+	0.208095i
$996$	−23.3020	+	20.9812i	−0.738351	+	0.664814i
$997$	6.74376	+	3.00252i	0.213577	+	0.0950906i	0.510737	−	0.859737i	$-0.329373\pi$
$997$	6.74376	+	3.00252i	0.213577	+	0.0950906i	−0.297160	+	0.954828i	$0.596039\pi$
$998$	11.8713	+	8.62502i	0.375780	+	0.273020i
$999$	−25.1548	+	8.17328i	−0.795862	+	0.258591i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.m.a.49.1	yes	8
3.2	odd	2		297.2.n.a.280.1		8
9.2	odd	6		297.2.n.a.181.1		8
9.4	even	3		891.2.f.b.82.1		4
9.5	odd	6		891.2.f.a.82.1		4
9.7	even	3	inner	99.2.m.a.16.1	✓	8
11.3	even	5		1089.2.e.g.364.1		4
11.8	odd	10		1089.2.e.d.364.2		4
11.9	even	5	inner	99.2.m.a.31.1	yes	8
33.20	odd	10		297.2.n.a.64.1		8
99.14	odd	30		9801.2.a.bb.1.1		2
99.20	odd	30		297.2.n.a.262.1		8
99.25	even	15		1089.2.e.g.727.1		4
99.31	even	15		891.2.f.b.163.1		4
99.41	even	30		9801.2.a.m.1.2		2
99.52	odd	30		1089.2.e.d.727.2		4
99.58	even	15		9801.2.a.n.1.2		2
99.85	odd	30		9801.2.a.bc.1.1		2
99.86	odd	30		891.2.f.a.163.1		4
99.97	even	15	inner	99.2.m.a.97.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.a.16.1	✓	8	9.7	even	3	inner
99.2.m.a.31.1	yes	8	11.9	even	5	inner
99.2.m.a.49.1	yes	8	1.1	even	1	trivial
99.2.m.a.97.1	yes	8	99.97	even	15	inner
297.2.n.a.64.1		8	33.20	odd	10
297.2.n.a.181.1		8	9.2	odd	6
297.2.n.a.262.1		8	99.20	odd	30
297.2.n.a.280.1		8	3.2	odd	2
891.2.f.a.82.1		4	9.5	odd	6
891.2.f.a.163.1		4	99.86	odd	30
891.2.f.b.82.1		4	9.4	even	3
891.2.f.b.163.1		4	99.31	even	15
1089.2.e.d.364.2		4	11.8	odd	10
1089.2.e.d.727.2		4	99.52	odd	30
1089.2.e.g.364.1		4	11.3	even	5
1089.2.e.g.727.1		4	99.25	even	15
9801.2.a.m.1.2		2	99.41	even	30
9801.2.a.n.1.2		2	99.58	even	15
9801.2.a.bb.1.1		2	99.14	odd	30
9801.2.a.bc.1.1		2	99.85	odd	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.255585 + 0.283856i) q^{2} +(0.704489 + 1.58231i) q^{3} +(0.193806 + 1.84395i) q^{4} +(-0.827091 - 0.918578i) q^{5} +(-0.629204 - 0.204441i) q^{6} +(-0.913545 - 0.406737i) q^{7} +(-1.19098 - 0.865300i) q^{8} +(-2.00739 + 2.22943i) q^{9} +O(q^{10})\)	\(q+(-0.255585 + 0.283856i) q^{2} +(0.704489 + 1.58231i) q^{3} +(0.193806 + 1.84395i) q^{4} +(-0.827091 - 0.918578i) q^{5} +(-0.629204 - 0.204441i) q^{6} +(-0.913545 - 0.406737i) q^{7} +(-1.19098 - 0.865300i) q^{8} +(-2.00739 + 2.22943i) q^{9} +0.472136 q^{10} +(2.70528 - 1.91872i) q^{11} +(-2.78115 + 1.60570i) q^{12} +(6.33070 + 1.34563i) q^{13} +(0.348943 - 0.155360i) q^{14} +(0.870796 - 1.95584i) q^{15} +(-3.07715 + 0.654069i) q^{16} +(1.50000 - 4.61653i) q^{17} +(-0.119779 - 1.13962i) q^{18} +(-0.809017 - 0.587785i) q^{19} +(1.53351 - 1.70314i) q^{20} -1.73205i q^{21} +(-0.146790 + 1.25830i) q^{22} +(-2.30902 + 3.99933i) q^{23} +(0.530136 - 2.49409i) q^{24} +(0.362937 - 3.45312i) q^{25} +(-2.00000 + 1.45309i) q^{26} +(-4.94183 - 1.60570i) q^{27} +(0.572949 - 1.76336i) q^{28} +(-4.43444 - 1.97434i) q^{29} +(0.332614 + 0.747064i) q^{30} +(-0.604528 - 0.128496i) q^{31} +(2.07295 - 3.59045i) q^{32} +(4.94183 + 2.92887i) q^{33} +(0.927051 + 1.60570i) q^{34} +(0.381966 + 1.17557i) q^{35} +(-4.50000 - 3.26944i) q^{36} +(4.11803 - 2.99193i) q^{37} +(0.373619 - 0.0794152i) q^{38} +(2.33070 + 10.9651i) q^{39} +(0.190206 + 1.80969i) q^{40} +(-2.30932 + 1.02817i) q^{41} +(0.491653 + 0.442686i) q^{42} +(-0.927051 - 1.60570i) q^{43} +(4.06231 + 4.61653i) q^{44} +3.70820 q^{45} +(-0.545085 - 1.67760i) q^{46} +(-1.24852 + 11.8788i) q^{47} +(-3.20276 - 4.40822i) q^{48} +(-4.01478 - 4.45887i) q^{49} +(0.887426 + 0.985587i) q^{50} +(8.36149 - 0.878828i) q^{51} +(-1.25434 + 11.9343i) q^{52} +(1.26393 + 3.88998i) q^{53} +(1.71885 - 0.992377i) q^{54} +(-4.00000 - 0.898056i) q^{55} +(0.736068 + 1.27491i) q^{56} +(0.360114 - 1.69420i) q^{57} +(1.69381 - 0.754131i) q^{58} +(-0.169131 - 1.60917i) q^{59} +(3.77523 + 1.22665i) q^{60} +(-10.6169 + 2.25669i) q^{61} +(0.190983 - 0.138757i) q^{62} +(2.74064 - 1.22021i) q^{63} +(-1.45492 - 4.47777i) q^{64} +(-4.00000 - 6.92820i) q^{65} +(-2.09444 + 0.654194i) q^{66} +(-3.00000 + 5.19615i) q^{67} +(8.80333 + 1.87121i) q^{68} +(-7.95485 - 0.836089i) q^{69} +(-0.431318 - 0.192035i) q^{70} +(-0.899187 + 2.76741i) q^{71} +(4.31990 - 0.918223i) q^{72} +(0.118034 - 0.0857567i) q^{73} +(-0.203232 + 1.93362i) q^{74} +(5.71957 - 1.85840i) q^{75} +(0.927051 - 1.60570i) q^{76} +(-3.25181 + 0.652498i) q^{77} +(-3.70820 - 2.14093i) q^{78} +(7.06756 - 7.84932i) q^{79} +(3.14590 + 2.28563i) q^{80} +(-0.940756 - 8.95070i) q^{81} +(0.298374 - 0.918300i) q^{82} +(9.55057 - 2.03004i) q^{83} +(3.19381 - 0.335683i) q^{84} +(-5.48127 + 2.44042i) q^{85} +(0.692728 + 0.147244i) q^{86} -8.40755i q^{87} +(-4.88220 - 0.0557196i) q^{88} -6.76393 q^{89} +(-0.947762 + 1.05260i) q^{90} +(-5.23607 - 3.80423i) q^{91} +(-7.82206 - 3.48260i) q^{92} +(-0.222562 - 1.04707i) q^{93} +(-3.05278 - 3.39045i) q^{94} +(0.129204 + 1.22930i) q^{95} +(7.14157 + 0.750609i) q^{96} +(4.01478 - 4.45887i) q^{97} +2.29180 q^{98} +(-1.15290 + 9.88285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 3 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} - 14 q^{8} - 3 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 3 * q^3 - 6 * q^4 + 6 * q^5 - q^7 - 14 * q^8 - 3 * q^9	\( 8 q - 4 q^{2} + 3 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} - 14 q^{8} - 3 q^{9} - 32 q^{10} + q^{11} + 18 q^{12} + 8 q^{13} - q^{14} + 12 q^{15} + 14 q^{16} + 12 q^{17} - 3 q^{18} - 2 q^{19} + 24 q^{20} + 11 q^{22} - 14 q^{23} - 39 q^{24} - 9 q^{25} - 16 q^{26} + 18 q^{28} - 9 q^{29} + 18 q^{30} - 3 q^{31} + 30 q^{32} - 6 q^{34} + 12 q^{35} - 36 q^{36} + 24 q^{37} - 4 q^{38} - 24 q^{39} + 12 q^{40} + 3 q^{41} - 12 q^{42} + 6 q^{43} - 48 q^{44} - 24 q^{45} + 18 q^{46} + 23 q^{47} - 6 q^{49} - 24 q^{50} + 27 q^{51} + 12 q^{52} + 28 q^{53} + 54 q^{54} - 32 q^{55} - 12 q^{56} + 3 q^{57} + 6 q^{58} + 3 q^{59} + 6 q^{62} + 3 q^{63} - 34 q^{64} - 32 q^{65} + 12 q^{66} - 24 q^{67} - 9 q^{68} - 18 q^{69} - 6 q^{70} + 42 q^{71} + 39 q^{72} - 8 q^{73} + 13 q^{74} - 6 q^{76} - 11 q^{77} + 24 q^{78} - 22 q^{79} + 52 q^{80} + 9 q^{81} - 96 q^{82} - 17 q^{83} + 18 q^{84} - 6 q^{85} + 21 q^{86} + 37 q^{88} - 72 q^{89} + 42 q^{90} - 24 q^{91} - 21 q^{92} + 9 q^{93} + 28 q^{94} - 4 q^{95} + 6 q^{97} + 72 q^{98} - 3 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 3 * q^3 - 6 * q^4 + 6 * q^5 - q^7 - 14 * q^8 - 3 * q^9 - 32 * q^10 + q^11 + 18 * q^12 + 8 * q^13 - q^14 + 12 * q^15 + 14 * q^16 + 12 * q^17 - 3 * q^18 - 2 * q^19 + 24 * q^20 + 11 * q^22 - 14 * q^23 - 39 * q^24 - 9 * q^25 - 16 * q^26 + 18 * q^28 - 9 * q^29 + 18 * q^30 - 3 * q^31 + 30 * q^32 - 6 * q^34 + 12 * q^35 - 36 * q^36 + 24 * q^37 - 4 * q^38 - 24 * q^39 + 12 * q^40 + 3 * q^41 - 12 * q^42 + 6 * q^43 - 48 * q^44 - 24 * q^45 + 18 * q^46 + 23 * q^47 - 6 * q^49 - 24 * q^50 + 27 * q^51 + 12 * q^52 + 28 * q^53 + 54 * q^54 - 32 * q^55 - 12 * q^56 + 3 * q^57 + 6 * q^58 + 3 * q^59 + 6 * q^62 + 3 * q^63 - 34 * q^64 - 32 * q^65 + 12 * q^66 - 24 * q^67 - 9 * q^68 - 18 * q^69 - 6 * q^70 + 42 * q^71 + 39 * q^72 - 8 * q^73 + 13 * q^74 - 6 * q^76 - 11 * q^77 + 24 * q^78 - 22 * q^79 + 52 * q^80 + 9 * q^81 - 96 * q^82 - 17 * q^83 + 18 * q^84 - 6 * q^85 + 21 * q^86 + 37 * q^88 - 72 * q^89 + 42 * q^90 - 24 * q^91 - 21 * q^92 + 9 * q^93 + 28 * q^94 - 4 * q^95 + 6 * q^97 + 72 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more