LMFDB - Embedded newform 315.2.bj.a.206.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(26,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("315.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bj (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 20x^{10} + 144x^{8} + 452x^{6} + 604x^{4} + 312x^{2} + 36 $ x^12 + 20x^10 + 144x^8 + 452x^6 + 604x^4 + 312*x^2 + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			206.1
Root			$2.74137i$ of defining polynomial
Character	$\chi$	$=$	315.206
Dual form			315.2.bj.a.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.37409 + 1.37068i) q^{2} +(2.75754 - 4.77621i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.06138 + 1.65853i) q^{7} +9.63615i q^{8} +O(q^{10})$	\(q+(-2.37409 + 1.37068i) q^{2} +(2.75754 - 4.77621i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.06138 + 1.65853i) q^{7} +9.63615i q^{8} +(2.37409 + 1.37068i) q^{10} +(-0.375529 - 0.216812i) q^{11} +0.0662108i q^{13} +(2.62059 - 6.76300i) q^{14} +(-7.69302 - 13.3247i) q^{16} +(3.72600 - 6.45362i) q^{17} +(4.24962 - 2.45352i) q^{19} -5.51509 q^{20} +1.18872 q^{22} +(2.08861 - 1.20586i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.0907540 - 0.157191i) q^{26} +(2.23713 + 14.4190i) q^{28} -3.72767i q^{29} +(0.711532 + 0.410803i) q^{31} +(19.8376 + 11.4532i) q^{32} +20.4287i q^{34} +(2.46702 + 0.955942i) q^{35} +(-3.79222 - 6.56832i) q^{37} +(-6.72600 + 11.6498i) q^{38} +(8.34515 - 4.81807i) q^{40} +8.74531 q^{41} +9.78575 q^{43} +(-2.07108 + 1.19574i) q^{44} +(-3.30570 + 5.72564i) q^{46} +(-2.24506 - 3.88855i) q^{47} +(1.49856 - 6.83771i) q^{49} -2.74137i q^{50} +(0.316236 + 0.182579i) q^{52} +(-1.45588 - 0.840554i) q^{53} +0.433624i q^{55} +(-15.9818 - 19.8637i) q^{56} +(5.10945 + 8.84983i) q^{58} +(-5.62059 + 9.73514i) q^{59} +(0.472679 - 0.272901i) q^{61} -2.25233 q^{62} -32.0229 q^{64} +(0.0573402 - 0.0331054i) q^{65} +(-0.483197 + 0.836922i) q^{67} +(-20.5492 - 35.5923i) q^{68} +(-7.16722 + 1.11200i) q^{70} -4.44063i q^{71} +(-7.54106 - 4.35383i) q^{73} +(18.0062 + 10.3959i) q^{74} -27.0628i q^{76} +(1.13370 - 0.175895i) q^{77} +(-2.06882 - 3.58331i) q^{79} +(-7.69302 + 13.3247i) q^{80} +(-20.7622 + 11.9871i) q^{82} +8.02296 q^{83} -7.45200 q^{85} +(-23.2323 + 13.4132i) q^{86} +(2.08923 - 3.61866i) q^{88} +(3.40223 + 5.89284i) q^{89} +(-0.109812 - 0.136485i) q^{91} -13.3008i q^{92} +(10.6599 + 6.15452i) q^{94} +(-4.24962 - 2.45352i) q^{95} +11.7306i q^{97} +(5.81461 + 18.2874i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4} - 6 q^{5} - 2 q^{7}+O(q^{10}) $ 12 * q + 8 * q^4 - 6 * q^5 - 2 * q^7	$ 12 q + 8 q^{4} - 6 q^{5} - 2 q^{7} + 12 q^{11} - 12 q^{14} - 16 q^{16} + 6 q^{19} - 16 q^{20} + 32 q^{22} + 12 q^{23} - 6 q^{25} - 20 q^{28} + 6 q^{31} + 60 q^{32} - 2 q^{35} - 10 q^{37} - 36 q^{38} + 24 q^{41} - 4 q^{43} + 12 q^{44} - 4 q^{46} + 6 q^{49} + 12 q^{53} - 60 q^{56} + 20 q^{58} - 24 q^{59} + 24 q^{62} - 56 q^{64} + 18 q^{65} + 6 q^{67} - 60 q^{68} - 12 q^{70} - 42 q^{73} + 84 q^{74} - 36 q^{77} + 18 q^{79} - 16 q^{80} - 72 q^{82} - 24 q^{83} - 84 q^{86} + 4 q^{88} + 12 q^{89} - 18 q^{91} + 12 q^{94} - 6 q^{95} + 12 q^{98}+O(q^{100}) $ 12 * q + 8 * q^4 - 6 * q^5 - 2 * q^7 + 12 * q^11 - 12 * q^14 - 16 * q^16 + 6 * q^19 - 16 * q^20 + 32 * q^22 + 12 * q^23 - 6 * q^25 - 20 * q^28 + 6 * q^31 + 60 * q^32 - 2 * q^35 - 10 * q^37 - 36 * q^38 + 24 * q^41 - 4 * q^43 + 12 * q^44 - 4 * q^46 + 6 * q^49 + 12 * q^53 - 60 * q^56 + 20 * q^58 - 24 * q^59 + 24 * q^62 - 56 * q^64 + 18 * q^65 + 6 * q^67 - 60 * q^68 - 12 * q^70 - 42 * q^73 + 84 * q^74 - 36 * q^77 + 18 * q^79 - 16 * q^80 - 72 * q^82 - 24 * q^83 - 84 * q^86 + 4 * q^88 + 12 * q^89 - 18 * q^91 + 12 * q^94 - 6 * q^95 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.37409	+	1.37068i	−1.67874	+	0.969219i	−0.716269	+	0.697824i	$0.754152\pi$
$2$	−2.37409	+	1.37068i	−1.67874	+	0.969219i	−0.962468	+	0.271395i	$0.912515\pi$
$3$		0			0
$3$		0			0
$4$	2.75754	−	4.77621i	1.37877	−	2.38810i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−2.06138	+	1.65853i	−0.779128	+	0.626865i
$7$	−2.06138	+	1.65853i	−0.779128	+	0.626865i
$8$			9.63615i			3.40689i
$9$		0			0
$10$	2.37409	+	1.37068i	0.750754	+	0.433448i
$11$	−0.375529	−	0.216812i	−0.113226	−	0.0653713i	0.442317	−	0.896859i	$-0.354157\pi$
$11$	−0.375529	−	0.216812i	−0.113226	−	0.0653713i	−0.555544	+	0.831487i	$0.687490\pi$
$12$		0			0
$13$			0.0662108i			0.0183636i	0.999958	+	0.00918178i	$0.00292269\pi$
$13$			0.0662108i			0.0183636i	−0.999958	+	0.00918178i	$0.997077\pi$
$14$	2.62059	−	6.76300i	0.700381	−	1.80749i
$15$		0			0
$16$	−7.69302	−	13.3247i	−1.92325	−	3.33117i
$17$	3.72600	−	6.45362i	0.903687	−	1.56523i	0.0810179	−	0.996713i	$-0.474183\pi$
$17$	3.72600	−	6.45362i	0.903687	−	1.56523i	0.822670	−	0.568520i	$-0.192484\pi$
$18$		0			0
$19$	4.24962	−	2.45352i	0.974930	−	0.562876i	0.0741945	−	0.997244i	$-0.476361\pi$
$19$	4.24962	−	2.45352i	0.974930	−	0.562876i	0.900736	+	0.434368i	$0.143028\pi$
$20$	−5.51509			−1.23321
$21$		0			0
$22$	1.18872			0.253436
$23$	2.08861	−	1.20586i	0.435505	−	0.251439i	−0.266184	−	0.963922i	$-0.585763\pi$
$23$	2.08861	−	1.20586i	0.435505	−	0.251439i	0.701689	+	0.712483i	$0.252430\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.0907540	−	0.157191i	−0.0177983	−	0.0308276i
$27$		0			0
$28$	2.23713	+	14.4190i	0.422779	+	2.72494i
$29$		−	3.72767i		−	0.692210i	−0.938196	−	0.346105i	$-0.887504\pi$
$29$		−	3.72767i		−	0.692210i	0.938196	−	0.346105i	$-0.112496\pi$
$30$		0			0
$31$	0.711532	+	0.410803i	0.127795	+	0.0737825i	0.562535	−	0.826774i	$-0.309826\pi$
$31$	0.711532	+	0.410803i	0.127795	+	0.0737825i	−0.434740	+	0.900556i	$0.643160\pi$
$32$	19.8376	+	11.4532i	3.50682	+	2.02466i
$33$		0			0
$34$			20.4287i			3.50349i
$35$	2.46702	+	0.955942i	0.417002	+	0.161584i
$36$		0			0
$37$	−3.79222	−	6.56832i	−0.623437	−	1.07982i	−0.988841	−	0.148976i	$-0.952402\pi$
$37$	−3.79222	−	6.56832i	−0.623437	−	1.07982i	0.365404	−	0.930849i	$-0.380931\pi$
$38$	−6.72600	+	11.6498i	−1.09110	+	1.88984i
$39$		0			0
$40$	8.34515	−	4.81807i	1.31948	−	0.761804i
$41$	8.74531			1.36579			0.682894	−	0.730517i	$-0.260721\pi$
$41$	8.74531			1.36579			0.682894	+	0.730517i	$0.260721\pi$
$42$		0			0
$43$	9.78575			1.49231			0.746156	−	0.665771i	$-0.231897\pi$
$43$	9.78575			1.49231			0.746156	+	0.665771i	$0.231897\pi$
$44$	−2.07108	+	1.19574i	−0.312227	+	0.180264i
$45$		0			0
$46$	−3.30570	+	5.72564i	−0.487399	+	0.844200i
$47$	−2.24506	−	3.88855i	−0.327475	−	0.567204i	0.654535	−	0.756032i	$-0.272864\pi$
$47$	−2.24506	−	3.88855i	−0.327475	−	0.567204i	−0.982010	+	0.188828i	$0.939531\pi$
$48$		0			0
$49$	1.49856	−	6.83771i	0.214081	−	0.976816i
$50$		−	2.74137i		−	0.387688i
$51$		0			0
$52$	0.316236	+	0.182579i	0.0438541	+	0.0253192i
$53$	−1.45588	−	0.840554i	−0.199981	−	0.115459i	0.396666	−	0.917963i	$-0.370167\pi$
$53$	−1.45588	−	0.840554i	−0.199981	−	0.115459i	−0.596646	+	0.802504i	$0.703501\pi$
$54$		0			0
$55$			0.433624i			0.0584698i
$56$	−15.9818	−	19.8637i	−2.13566	−	2.65441i
$57$		0			0
$58$	5.10945	+	8.84983i	0.670904	+	1.16204i
$59$	−5.62059	+	9.73514i	−0.731738	+	1.26741i	0.224402	+	0.974497i	$0.427957\pi$
$59$	−5.62059	+	9.73514i	−0.731738	+	1.26741i	−0.956140	+	0.292911i	$0.905376\pi$
$60$		0			0
$61$	0.472679	−	0.272901i	0.0605203	−	0.0349414i	−0.469435	−	0.882967i	$-0.655542\pi$
$61$	0.472679	−	0.272901i	0.0605203	−	0.0349414i	0.529955	+	0.848026i	$0.322209\pi$
$62$	−2.25233			−0.286046
$63$		0			0
$64$	−32.0229			−4.00287
$65$	0.0573402	−	0.0331054i	0.00711218	−	0.00410622i
$66$		0			0
$67$	−0.483197	+	0.836922i	−0.0590319	+	0.102246i	−0.894031	−	0.448005i	$-0.852135\pi$
$67$	−0.483197	+	0.836922i	−0.0590319	+	0.102246i	0.834999	+	0.550251i	$0.185468\pi$
$68$	−20.5492	−	35.5923i	−2.49196	−	4.31620i
$69$		0			0
$70$	−7.16722	+	1.11200i	−0.856647	+	0.132910i
$71$		−	4.44063i		−	0.527006i	−0.964659	−	0.263503i	$-0.915122\pi$
$71$		−	4.44063i		−	0.527006i	0.964659	−	0.263503i	$-0.0848778\pi$
$72$		0			0
$73$	−7.54106	−	4.35383i	−0.882614	−	0.509578i	−0.0110948	−	0.999938i	$-0.503532\pi$
$73$	−7.54106	−	4.35383i	−0.882614	−	0.509578i	−0.871519	+	0.490361i	$0.836865\pi$
$74$	18.0062	+	10.3959i	2.09317	+	1.20849i
$75$		0			0
$76$		−	27.0628i		−	3.10431i
$77$	1.13370	−	0.175895i	0.129197	−	0.0200451i
$78$		0			0
$79$	−2.06882	−	3.58331i	−0.232761	−	0.403153i	0.725859	−	0.687844i	$-0.241443\pi$
$79$	−2.06882	−	3.58331i	−0.232761	−	0.403153i	−0.958620	+	0.284690i	$0.908109\pi$
$80$	−7.69302	+	13.3247i	−0.860105	+	1.48975i
$81$		0			0
$82$	−20.7622	+	11.9871i	−2.29280	+	1.32375i
$83$	8.02296			0.880635			0.440317	−	0.897842i	$-0.354866\pi$
$83$	8.02296			0.880635			0.440317	+	0.897842i	$0.354866\pi$
$84$		0			0
$85$	−7.45200			−0.808283
$86$	−23.2323	+	13.4132i	−2.50520	+	1.44638i
$87$		0			0
$88$	2.08923	−	3.61866i	0.222713	−	0.385750i
$89$	3.40223	+	5.89284i	0.360636	+	0.624640i	0.988066	−	0.154033i	$-0.0492263\pi$
$89$	3.40223	+	5.89284i	0.360636	+	0.624640i	−0.627430	+	0.778673i	$0.715893\pi$
$90$		0			0
$91$	−0.109812	−	0.136485i	−0.0115115	−	0.0143076i
$92$		−	13.3008i		−	1.38671i
$93$		0			0
$94$	10.6599	+	6.15452i	1.09949	+	0.634791i
$95$	−4.24962	−	2.45352i	−0.436002	−	0.251726i
$96$		0			0
$97$			11.7306i			1.19107i	0.803331	+	0.595533i	$0.203059\pi$
$97$			11.7306i			1.19107i	−0.803331	+	0.595533i	$0.796941\pi$
$98$	5.81461	+	18.2874i	0.587364	+	1.84731i
$99$		0			0
$100$	2.75754	+	4.77621i	0.275754	+	0.477621i
$101$	2.15430	−	3.73136i	0.214361	−	0.371284i	−0.738714	−	0.674019i	$-0.764566\pi$
$101$	2.15430	−	3.73136i	0.214361	−	0.371284i	0.953075	+	0.302735i	$0.0978997\pi$
$102$		0			0
$103$	12.0742	−	6.97105i	1.18971	−	0.686878i	0.231467	−	0.972843i	$-0.425647\pi$
$103$	12.0742	−	6.97105i	1.18971	−	0.686878i	0.958240	+	0.285965i	$0.0923140\pi$
$104$	−0.638017			−0.0625627
$105$		0			0
$106$	4.60853			0.447620
$107$	−8.11941	+	4.68774i	−0.784933	+	0.453181i	−0.838176	−	0.545401i	$-0.816378\pi$
$107$	−8.11941	+	4.68774i	−0.784933	+	0.453181i	0.0532430	+	0.998582i	$0.483044\pi$
$108$		0			0
$109$	1.12399	−	1.94681i	0.107659	−	0.186471i	−0.807163	−	0.590329i	$-0.798998\pi$
$109$	1.12399	−	1.94681i	0.107659	−	0.186471i	0.914821	+	0.403859i	$0.132331\pi$
$110$	−0.594361	−	1.02946i	−0.0566701	−	0.0981555i
$111$		0			0
$112$	37.9576	+	14.7082i	3.58666	+	1.38979i
$113$		−	0.453677i		−	0.0426783i	−0.999772	−	0.0213392i	$-0.993207\pi$
$113$		−	0.453677i		−	0.0426783i	0.999772	−	0.0213392i	$-0.00679298\pi$
$114$		0			0
$115$	−2.08861	−	1.20586i	−0.194764	−	0.112447i
$116$	−17.8041	−	10.2792i	−1.65307	−	0.954401i
$117$		0			0
$118$		−	30.8162i		−	2.83686i
$119$	3.02282	+	19.4830i	0.277101	+	1.78601i
$120$		0			0
$121$	−5.40599	−	9.36344i	−0.491453	−	0.851222i
$122$	−0.748122	+	1.29579i	−0.0677318	+	0.117315i
$123$		0			0
$124$	3.92416	−	2.26562i	0.352400	−	0.203458i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−13.7976			−1.22434			−0.612169	−	0.790727i	$-0.709703\pi$
$127$	−13.7976			−1.22434			−0.612169	+	0.790727i	$0.709703\pi$
$128$	36.3502	−	20.9868i	3.21294	−	1.85499i
$129$		0			0
$130$	−0.0907540	+	0.157191i	−0.00795965	+	0.0137865i
$131$	5.35585	+	9.27661i	0.467943	+	0.810501i	0.999329	−	0.0366287i	$-0.0116619\pi$
$131$	5.35585	+	9.27661i	0.467943	+	0.810501i	−0.531386	+	0.847130i	$0.678329\pi$
$132$		0			0
$133$	−4.69085	+	12.1058i	−0.406748	+	1.04970i
$134$		−	2.64924i		−	0.228860i
$135$		0			0
$136$	62.1880	+	35.9043i	5.33258	+	3.07877i
$137$	−12.1610	−	7.02118i	−1.03899	−	0.599860i	−0.119441	−	0.992841i	$-0.538110\pi$
$137$	−12.1610	−	7.02118i	−1.03899	−	0.599860i	−0.919546	+	0.392982i	$0.871444\pi$
$138$		0			0
$139$		−	4.71593i		−	0.400000i	−0.979796	−	0.200000i	$-0.935906\pi$
$139$		−	4.71593i		−	0.400000i	0.979796	−	0.200000i	$-0.0640942\pi$
$140$	11.3687	−	9.14694i	0.960829	−	0.773057i
$141$		0			0
$142$	6.08669	+	10.5425i	0.510784	+	0.884704i
$143$	0.0143553	−	0.0248641i	0.00120045	−	0.00207924i
$144$		0			0
$145$	−3.22825	+	1.86383i	−0.268092	+	0.154783i
$146$	23.8709			1.97557
$147$		0			0
$148$	−41.8289			−3.43831
$149$	−10.0183	+	5.78407i	−0.820732	+	0.473850i	−0.850669	−	0.525702i	$-0.823803\pi$
$149$	−10.0183	+	5.78407i	−0.820732	+	0.473850i	0.0299369	+	0.999552i	$0.490469\pi$
$150$		0			0
$151$	−4.63191	+	8.02271i	−0.376940	+	0.652879i	−0.990615	−	0.136679i	$-0.956357\pi$
$151$	−4.63191	+	8.02271i	−0.376940	+	0.652879i	0.613675	+	0.789558i	$0.289690\pi$
$152$	23.6425	+	40.9500i	1.91766	+	3.32148i
$153$		0			0
$154$	−2.45041	+	1.97153i	−0.197459	+	0.158870i
$155$		−	0.821607i		−	0.0659931i
$156$		0			0
$157$	−17.6306	−	10.1791i	−1.40708	−	0.812377i	−0.411972	−	0.911196i	$-0.635160\pi$
$157$	−17.6306	−	10.1791i	−1.40708	−	0.812377i	−0.995105	+	0.0988197i	$0.968493\pi$
$158$	9.82315	+	5.67140i	0.781488	+	0.451192i
$159$		0			0
$160$		−	22.9065i		−	1.81091i
$161$	−2.30546	+	5.94975i	−0.181696	+	0.468906i
$162$		0			0
$163$	3.06713	+	5.31243i	0.240236	+	0.416101i	0.960781	−	0.277307i	$-0.0894418\pi$
$163$	3.06713	+	5.31243i	0.240236	+	0.416101i	−0.720545	+	0.693408i	$0.756108\pi$
$164$	24.1156	−	41.7694i	1.88311	−	3.26164i
$165$		0			0
$166$	−19.0473	+	10.9969i	−1.47835	+	0.853528i
$167$	12.1569			0.940732			0.470366	−	0.882471i	$-0.344122\pi$
$167$	12.1569			0.940732			0.470366	+	0.882471i	$0.344122\pi$
$168$		0			0
$169$	12.9956			0.999663
$170$	17.6917	−	10.2143i	1.35689	−	0.783403i
$171$		0			0
$172$	26.9846	−	46.7388i	2.05756	−	3.56380i
$173$	3.28548	+	5.69062i	0.249791	+	0.432650i	0.963468	−	0.267825i	$-0.0863049\pi$
$173$	3.28548	+	5.69062i	0.249791	+	0.432650i	−0.713677	+	0.700475i	$0.752972\pi$
$174$		0			0
$175$	−0.405639	−	2.61447i	−0.0306634	−	0.197635i
$176$			6.67175i			0.502902i
$177$		0			0
$178$	−16.1544	−	9.32677i	−1.21083	−	0.699071i
$179$	−5.49702	−	3.17370i	−0.410866	−	0.237214i	0.280296	−	0.959914i	$-0.409568\pi$
$179$	−5.49702	−	3.17370i	−0.410866	−	0.237214i	−0.691162	+	0.722700i	$0.742901\pi$
$180$		0			0
$181$			14.6624i			1.08985i	0.838485	+	0.544925i	$0.183442\pi$
$181$			14.6624i			1.08985i	−0.838485	+	0.544925i	$0.816558\pi$
$182$	0.447783	+	0.173511i	0.0331919	+	0.0128615i
$183$		0			0
$184$	11.6198	+	20.1261i	0.856626	+	1.48372i
$185$	−3.79222	+	6.56832i	−0.278810	+	0.482912i
$186$		0			0
$187$	−2.79844	+	1.61568i	−0.204642	+	0.118150i
$188$	−24.7634			−1.80606
$189$		0			0
$190$	13.4520			0.975910
$191$	−8.58662	+	4.95749i	−0.621306	+	0.358711i	−0.777377	−	0.629034i	$-0.783450\pi$
$191$	−8.58662	+	4.95749i	−0.621306	+	0.358711i	0.156071	+	0.987746i	$0.450117\pi$
$192$		0			0
$193$	5.28117	−	9.14725i	0.380147	−	0.658434i	−0.610936	−	0.791680i	$-0.709207\pi$
$193$	5.28117	−	9.14725i	0.380147	−	0.658434i	0.991083	+	0.133246i	$0.0425401\pi$
$194$	−16.0790	−	27.8496i	−1.15440	−	1.99949i
$195$		0			0
$196$	−28.5260	−	26.0127i	−2.03757	−	1.85805i
$197$		−	20.8328i		−	1.48427i	−0.670248	−	0.742137i	$-0.733812\pi$
$197$		−	20.8328i		−	1.48427i	0.670248	−	0.742137i	$-0.266188\pi$
$198$		0			0
$199$	7.82977	+	4.52052i	0.555037	+	0.320451i	0.751151	−	0.660130i	$-0.229499\pi$
$199$	7.82977	+	4.52052i	0.555037	+	0.320451i	−0.196114	+	0.980581i	$0.562832\pi$
$200$	−8.34515	−	4.81807i	−0.590091	−	0.340689i
$201$		0			0
$202$			11.8115i			0.831052i
$203$	6.18244	+	7.68413i	0.433922	+	0.539320i
$204$		0			0
$205$	−4.37266	−	7.57366i	−0.305400	−	0.528968i
$206$	−19.1102	+	33.0998i	−1.33147	+	2.30618i
$207$		0			0
$208$	0.882238	−	0.509360i	0.0611722	−	0.0353178i
$209$	−2.12781			−0.147184
$210$		0			0
$211$	19.7448			1.35929			0.679643	−	0.733543i	$-0.262135\pi$
$211$	19.7448			1.35929			0.679643	+	0.733543i	$0.262135\pi$
$212$	−8.02932	+	4.63573i	−0.551456	+	0.318383i
$213$		0			0
$214$	12.8508	−	22.2583i	0.878464	−	1.52154i
$215$	−4.89287	−	8.47471i	−0.333691	−	0.577970i
$216$		0			0
$217$	−2.14807	+	0.333276i	−0.145820	+	0.0226242i
$218$			6.16255i			0.417380i
$219$		0			0
$220$	2.07108	+	1.19574i	0.139632	+	0.0806166i
$221$	0.427299	+	0.246701i	0.0287432	+	0.0165949i
$222$		0			0
$223$			19.9931i			1.33884i	0.742885	+	0.669420i	$0.233457\pi$
$223$			19.9931i			1.33884i	−0.742885	+	0.669420i	$0.766543\pi$
$224$	−59.8883	+	9.29175i	−4.00145	+	0.620831i
$225$		0			0
$226$	0.621847	+	1.07707i	0.0413647	+	0.0716457i
$227$	−1.21899	+	2.11135i	−0.0809069	+	0.140135i	−0.903640	−	0.428293i	$-0.859115\pi$
$227$	−1.21899	+	2.11135i	−0.0809069	+	0.140135i	0.822733	+	0.568428i	$0.192448\pi$
$228$		0			0
$229$	−12.7699	+	7.37270i	−0.843858	+	0.487201i	−0.858574	−	0.512690i	$-0.828649\pi$
$229$	−12.7699	+	7.37270i	−0.843858	+	0.487201i	0.0147160	+	0.999892i	$0.495316\pi$
$230$	6.61140			0.435943
$231$		0			0
$232$	35.9204			2.35829
$233$	9.73742	−	5.62190i	0.637919	−	0.368303i	−0.145893	−	0.989300i	$-0.546606\pi$
$233$	9.73742	−	5.62190i	0.637919	−	0.368303i	0.783813	+	0.620997i	$0.213272\pi$
$234$		0			0
$235$	−2.24506	+	3.88855i	−0.146451	+	0.253661i
$236$	30.9980	+	53.6902i	2.01780	+	3.49493i
$237$		0			0
$238$	−33.8815	−	42.1112i	−2.19621	−	2.72966i
$239$			6.92953i			0.448234i	0.974562	+	0.224117i	$0.0719498\pi$
$239$			6.92953i			0.448234i	−0.974562	+	0.224117i	$0.928050\pi$
$240$		0			0
$241$	4.05555	+	2.34147i	0.261241	+	0.150828i	0.624901	−	0.780704i	$-0.285139\pi$
$241$	4.05555	+	2.34147i	0.261241	+	0.150828i	−0.363659	+	0.931532i	$0.618473\pi$
$242$	25.6686	+	14.8198i	1.65004	+	0.952652i
$243$		0			0
$244$		−	3.01015i		−	0.192705i
$245$	−6.67091	+	2.12106i	−0.426189	+	0.135510i
$246$		0			0
$247$	0.162449	+	0.281371i	0.0103364	+	0.0179032i
$248$	−3.95856	+	6.85643i	−0.251369	+	0.435384i
$249$		0			0
$250$	−2.37409	+	1.37068i	−0.150151	+	0.0866896i
$251$	−11.7105			−0.739159			−0.369580	−	0.929199i	$-0.620498\pi$
$251$	−11.7105			−0.739159			−0.369580	+	0.929199i	$0.620498\pi$
$252$		0			0
$253$	−1.04578			−0.0657476
$254$	32.7568	−	18.9121i	2.05534	−	1.18665i
$255$		0			0
$256$	−25.5097	+	44.1840i	−1.59435	+	2.76150i
$257$	−6.33266	−	10.9685i	−0.395020	−	0.684195i	0.598084	−	0.801434i	$-0.295929\pi$
$257$	−6.33266	−	10.9685i	−0.395020	−	0.684195i	−0.993104	+	0.117239i	$0.962596\pi$
$258$		0			0
$259$	18.7109	+	7.25028i	1.16264	+	0.450511i
$260$		−	0.365158i		−	0.0226462i
$261$		0			0
$262$	−25.4306	−	14.6824i	−1.57111	−	0.907079i
$263$	−8.73849	−	5.04517i	−0.538839	−	0.311099i	0.205770	−	0.978600i	$-0.434030\pi$
$263$	−8.73849	−	5.04517i	−0.538839	−	0.311099i	−0.744608	+	0.667502i	$0.767364\pi$
$264$		0			0
$265$			1.68111i			0.103270i
$266$	−5.45665	−	35.1699i	−0.334569	−	2.15640i
$267$		0			0
$268$	2.66488	+	4.61570i	0.162783	+	0.281949i
$269$	−3.95174	+	6.84462i	−0.240942	+	0.417324i	−0.960983	−	0.276608i	$-0.910790\pi$
$269$	−3.95174	+	6.84462i	−0.240942	+	0.417324i	0.720041	+	0.693932i	$0.244123\pi$
$270$		0			0
$271$	25.7378	−	14.8597i	1.56346	−	0.902663i	0.566554	−	0.824024i	$-0.308276\pi$
$271$	25.7378	−	14.8597i	1.56346	−	0.902663i	0.996903	−	0.0786381i	$-0.0250572\pi$
$272$	−114.657			−6.95208
$273$		0			0
$274$	38.4952			2.32558
$275$	0.375529	−	0.216812i	0.0226453	−	0.0130743i
$276$		0			0
$277$	−10.8253	+	18.7499i	−0.650428	+	1.12657i	0.332592	+	0.943071i	$0.392077\pi$
$277$	−10.8253	+	18.7499i	−0.650428	+	1.12657i	−0.983019	+	0.183503i	$0.941256\pi$
$278$	6.46404	+	11.1961i	0.387688	+	0.671495i
$279$		0			0
$280$	−9.21160	+	23.7725i	−0.550498	+	1.42068i
$281$		−	15.9467i		−	0.951302i	−0.879634	−	0.475651i	$-0.842213\pi$
$281$		−	15.9467i		−	0.951302i	0.879634	−	0.475651i	$-0.157787\pi$
$282$		0			0
$283$	4.72115	+	2.72576i	0.280643	+	0.162029i	0.633715	−	0.773567i	$-0.281529\pi$
$283$	4.72115	+	2.72576i	0.280643	+	0.162029i	−0.353071	+	0.935596i	$0.614863\pi$
$284$	−21.2094	−	12.2452i	−1.25854	−	0.726621i
$285$		0			0
$286$			0.0787062i			0.00465400i
$287$	−18.0274	+	14.5044i	−1.06412	+	0.856165i
$288$		0			0
$289$	−19.2661	−	33.3699i	−1.13330	−	1.96294i
$290$	5.10945	−	8.84983i	0.300037	−	0.519680i
$291$		0			0
$292$	−41.5896	+	24.0118i	−2.43385	+	1.40518i
$293$	6.09337			0.355978			0.177989	−	0.984032i	$-0.443041\pi$
$293$	6.09337			0.355978			0.177989	+	0.984032i	$0.443041\pi$
$294$		0			0
$295$	11.2412			0.654486
$296$	63.2933	−	36.5424i	3.67885	−	2.12398i
$297$		0			0
$298$	15.8563	−	27.4639i	0.918529	−	1.59094i
$299$	0.0798409	+	0.138288i	0.00461732	+	0.00799743i
$300$		0			0
$301$	−20.1721	+	16.2299i	−1.16270	+	0.935479i
$302$		−	25.3955i		−	1.46135i
$303$		0			0
$304$	−65.3848	−	37.7499i	−3.75008	−	2.16511i
$305$	−0.472679	−	0.272901i	−0.0270655	−	0.0156263i
$306$		0			0
$307$			8.28665i			0.472944i	0.971638	+	0.236472i	$0.0759912\pi$
$307$			8.28665i			0.472944i	−0.971638	+	0.236472i	$0.924009\pi$
$308$	2.28611	−	5.89981i	0.130263	−	0.336173i
$309$		0			0
$310$	1.12616	+	1.95057i	0.0639617	+	0.110785i
$311$	10.2466	−	17.7476i	0.581029	−	1.00637i	−0.414328	−	0.910127i	$-0.635984\pi$
$311$	10.2466	−	17.7476i	0.581029	−	1.00637i	0.995358	−	0.0962448i	$-0.0306832\pi$
$312$		0			0
$313$	18.5309	−	10.6988i	1.04743	−	0.604734i	0.125501	−	0.992093i	$-0.459946\pi$
$313$	18.5309	−	10.6988i	1.04743	−	0.604734i	0.921929	+	0.387359i	$0.126613\pi$
$314$	55.8090			3.14948
$315$		0			0
$316$	−22.8195			−1.28370
$317$	14.6270	−	8.44489i	0.821533	−	0.474312i	−0.0294117	−	0.999567i	$-0.509363\pi$
$317$	14.6270	−	8.44489i	0.821533	−	0.474312i	0.850945	+	0.525255i	$0.176030\pi$
$318$		0			0
$319$	−0.808203	+	1.39985i	−0.0452507	+	0.0783765i
$320$	16.0115	+	27.7327i	0.895068	+	1.55030i
$321$		0			0
$322$	−2.68184	−	17.2853i	−0.149453	−	0.963273i
$323$		−	36.5673i		−	2.03466i
$324$		0			0
$325$	−0.0573402	−	0.0331054i	−0.00318066	−	0.00183636i
$326$	−14.5633	−	8.40813i	−0.806587	−	0.465683i
$327$		0			0
$328$			84.2711i			4.65309i
$329$	11.0772	+	4.29229i	0.610705	+	0.236641i
$330$		0			0
$331$	6.31935	+	10.9454i	0.347343	+	0.601616i	0.985777	−	0.168061i	$-0.0537506\pi$
$331$	6.31935	+	10.9454i	0.347343	+	0.601616i	−0.638433	+	0.769677i	$0.720417\pi$
$332$	22.1237	−	38.3193i	1.21419	−	2.10305i
$333$		0			0
$334$	−28.8617	+	16.6633i	−1.57924	+	0.911776i
$335$	0.966394			0.0527998
$336$		0			0
$337$	17.2336			0.938774			0.469387	−	0.882992i	$-0.344475\pi$
$337$	17.2336			0.938774			0.469387	+	0.882992i	$0.344475\pi$
$338$	−30.8528	+	17.8129i	−1.67817	+	0.968893i
$339$		0			0
$340$	−20.5492	+	35.5923i	−1.11444	+	1.93026i
$341$	−0.178134	−	0.308538i	−0.00964651	−	0.0167082i
$342$		0			0
$343$	8.25144	+	16.5805i	0.445536	+	0.895264i
$344$			94.2969i			5.08415i
$345$		0			0
$346$	−15.6001	−	9.00671i	−0.838666	−	0.484204i
$347$	18.0978	+	10.4488i	0.971541	+	0.560919i	0.899706	−	0.436497i	$-0.143781\pi$
$347$	18.0978	+	10.4488i	0.971541	+	0.560919i	0.0718354	+	0.997417i	$0.477114\pi$
$348$		0			0
$349$			14.7971i			0.792072i	0.918235	+	0.396036i	$0.129614\pi$
$349$			14.7971i			0.792072i	−0.918235	+	0.396036i	$0.870386\pi$
$350$	4.54664	+	5.65099i	0.243028	+	0.302058i
$351$		0			0
$352$	−4.96639	−	8.60205i	−0.264710	−	0.458491i
$353$	3.63273	−	6.29207i	0.193351	−	0.334893i	−0.753008	−	0.658011i	$-0.771398\pi$
$353$	3.63273	−	6.29207i	0.193351	−	0.334893i	0.946359	+	0.323118i	$0.104731\pi$
$354$		0			0
$355$	−3.84570	+	2.22031i	−0.204108	+	0.117842i
$356$	37.5272			1.98894
$357$		0			0
$358$	17.4006			0.919649
$359$	1.23490	−	0.712967i	0.0651753	−	0.0376290i	−0.467058	−	0.884227i	$-0.654686\pi$
$359$	1.23490	−	0.712967i	0.0651753	−	0.0376290i	0.532234	+	0.846598i	$0.321353\pi$
$360$		0			0
$361$	2.53953	−	4.39859i	0.133659	−	0.231505i
$362$	−20.0975	−	34.8100i	−1.05630	−	1.82957i
$363$		0			0
$364$	−0.954696	+	0.148122i	−0.0500396	+	0.00776372i
$365$			8.70767i			0.455780i
$366$		0			0
$367$	23.1809	+	13.3835i	1.21003	+	0.698613i	0.962766	−	0.270335i	$-0.0871344\pi$
$367$	23.1809	+	13.3835i	1.21003	+	0.698613i	0.247266	+	0.968948i	$0.420468\pi$
$368$	−32.1354	−	18.5534i	−1.67517	−	0.967162i
$369$		0			0
$370$		−	20.7917i		−	1.08091i
$371$	4.39521	−	0.681922i	0.228188	−	0.0354036i
$372$		0			0
$373$	9.72437	+	16.8431i	0.503509	+	0.872103i	0.999992	+	0.00405638i	$0.00129119\pi$
$373$	9.72437	+	16.8431i	0.503509	+	0.872103i	−0.496483	+	0.868046i	$0.665375\pi$
$374$	4.42918	−	7.67156i	0.229027	−	0.396687i
$375$		0			0
$376$	37.4707	−	21.6337i	1.93240	−	1.11567i
$377$	0.246812			0.0127114
$378$		0			0
$379$	−0.910889			−0.0467892			−0.0233946	−	0.999726i	$-0.507447\pi$
$379$	−0.910889			−0.0467892			−0.0233946	+	0.999726i	$0.507447\pi$
$380$	−23.4370	+	13.5314i	−1.20230	+	0.694145i
$381$		0			0
$382$	13.5903	−	23.5391i	0.695340	−	1.20436i
$383$	11.9596	+	20.7147i	0.611109	+	1.05847i	0.991054	+	0.133463i	$0.0426096\pi$
$383$	11.9596	+	20.7147i	0.611109	+	1.05847i	−0.379945	+	0.925009i	$0.624057\pi$
$384$		0			0
$385$	−0.719178	−	0.893863i	−0.0366527	−	0.0455555i
$386$			28.9552i			1.47378i
$387$		0			0
$388$	56.0280	+	32.3478i	2.84439	+	1.64221i
$389$	−19.1528	−	11.0579i	−0.971085	−	0.560656i	−0.0715182	−	0.997439i	$-0.522784\pi$
$389$	−19.1528	−	11.0579i	−0.971085	−	0.560656i	−0.899567	+	0.436783i	$0.856118\pi$
$390$		0			0
$391$		−	17.9721i		−	0.908889i
$392$	65.8892	+	14.4404i	3.32791	+	0.729349i
$393$		0			0
$394$	28.5551	+	49.4590i	1.43859	+	2.49171i
$395$	−2.06882	+	3.58331i	−0.104094	+	0.180296i
$396$		0			0
$397$	25.2248	−	14.5635i	1.26600	−	0.730923i	0.291768	−	0.956489i	$-0.405757\pi$
$397$	25.2248	−	14.5635i	1.26600	−	0.730923i	0.974228	+	0.225566i	$0.0724232\pi$
$398$	−24.7848			−1.24235
$399$		0			0
$400$	15.3860			0.769302
$401$	7.22899	−	4.17366i	0.360998	−	0.208423i	−0.308520	−	0.951218i	$-0.599834\pi$
$401$	7.22899	−	4.17366i	0.360998	−	0.208423i	0.669519	+	0.742795i	$0.266500\pi$
$402$		0			0
$403$	−0.0271996	+	0.0471111i	−0.00135491	+	0.00234677i
$404$	−11.8812	−	20.5788i	−0.591111	−	1.02383i
$405$		0			0
$406$	−25.2102	−	9.76867i	−1.25116	−	0.484811i
$407$			3.28879i			0.163019i
$408$		0			0
$409$	−2.10871	−	1.21746i	−0.104269	−	0.0601996i	0.446959	−	0.894555i	$-0.352507\pi$
$409$	−2.10871	−	1.21746i	−0.104269	−	0.0601996i	−0.551228	+	0.834355i	$0.685840\pi$
$410$	20.7622	+	11.9871i	1.02537	+	0.591998i
$411$		0			0
$412$		−	76.8919i		−	3.78819i
$413$	−4.55986	−	29.3897i	−0.224376	−	1.44617i
$414$		0			0
$415$	−4.01148	−	6.94809i	−0.196916	−	0.341068i
$416$	−0.758327	+	1.31346i	−0.0371800	+	0.0643977i
$417$		0			0
$418$	5.05162	−	2.91655i	0.247083	−	0.142653i
$419$	−17.9311			−0.875989			−0.437995	−	0.898978i	$-0.644311\pi$
$419$	−17.9311			−0.875989			−0.437995	+	0.898978i	$0.644311\pi$
$420$		0			0
$421$	−28.1024			−1.36963			−0.684814	−	0.728718i	$-0.740117\pi$
$421$	−28.1024			−1.36963			−0.684814	+	0.728718i	$0.740117\pi$
$422$	−46.8759	+	27.0638i	−2.28188	+	1.31745i
$423$		0			0
$424$	8.09970	−	14.0291i	0.393356	−	0.681313i
$425$	3.72600	+	6.45362i	0.180737	+	0.313047i
$426$		0			0
$427$	−0.521755	+	1.34650i	−0.0252495	+	0.0651619i
$428$			51.7066i			2.49933i
$429$		0			0
$430$	23.2323	+	13.4132i	1.12036	+	0.646840i
$431$	−11.9181	−	6.88094i	−0.574076	−	0.331443i	0.184699	−	0.982795i	$-0.440869\pi$
$431$	−11.9181	−	6.88094i	−0.574076	−	0.331443i	−0.758776	+	0.651352i	$0.774202\pi$
$432$		0			0
$433$		−	5.67857i		−	0.272895i	−0.990647	−	0.136447i	$-0.956432\pi$
$433$		−	5.67857i		−	0.272895i	0.990647	−	0.136447i	$-0.0435684\pi$
$434$	4.64290	−	3.73555i	0.222866	−	0.179312i
$435$		0			0
$436$	−6.19892	−	10.7368i	−0.296874	−	0.514201i
$437$	5.91720	−	10.2489i	0.283058	−	0.490271i
$438$		0			0
$439$	−25.3659	+	14.6450i	−1.21065	+	0.698969i	−0.962901	−	0.269855i	$-0.913024\pi$
$439$	−25.3659	+	14.6450i	−1.21065	+	0.698969i	−0.247749	+	0.968824i	$0.579691\pi$
$440$	−4.17846			−0.199200
$441$		0			0
$442$	−1.35260			−0.0643365
$443$	−30.7504	+	17.7538i	−1.46100	+	0.843506i	−0.999058	−	0.0434055i	$-0.986179\pi$
$443$	−30.7504	+	17.7538i	−1.46100	+	0.843506i	−0.461939	+	0.886912i	$0.652846\pi$
$444$		0			0
$445$	3.40223	−	5.89284i	0.161281	−	0.279347i
$446$	−27.4043	−	47.4656i	−1.29763	−	2.24756i
$447$		0			0
$448$	66.0114	−	53.1109i	3.11874	−	2.50926i
$449$			0.464903i			0.0219401i	0.999940	+	0.0109701i	$0.00349195\pi$
$449$			0.464903i			0.0219401i	−0.999940	+	0.0109701i	$0.996508\pi$
$450$		0			0
$451$	−3.28412	−	1.89609i	−0.154643	−	0.0892833i
$452$	−2.16686	−	1.25103i	−0.101920	−	0.0588437i
$453$		0			0
$454$		−	6.68337i		−	0.313666i
$455$	−0.0632936	+	0.163343i	−0.00296725	+	0.00765764i
$456$		0			0
$457$	1.03237	+	1.78811i	0.0482920	+	0.0836442i	0.889161	−	0.457595i	$-0.151289\pi$
$457$	1.03237	+	1.78811i	0.0482920	+	0.0836442i	−0.840869	+	0.541239i	$0.817956\pi$
$458$	20.2113	−	35.0069i	0.944410	−	1.63577i
$459$		0			0
$460$	−11.5189	+	6.65042i	−0.537070	+	0.310077i
$461$	11.7679			0.548086			0.274043	−	0.961717i	$-0.411639\pi$
$461$	11.7679			0.548086			0.274043	+	0.961717i	$0.411639\pi$
$462$		0			0
$463$	−24.3625			−1.13222			−0.566111	−	0.824329i	$-0.691553\pi$
$463$	−24.3625			−1.13222			−0.566111	+	0.824329i	$0.691553\pi$
$464$	−49.6700	+	28.6770i	−2.30587	+	1.33130i
$465$		0			0
$466$	−15.4117	+	26.6938i	−0.713933	+	1.23657i
$467$	15.5789	+	26.9835i	0.720907	+	1.24865i	0.960637	+	0.277808i	$0.0896080\pi$
$467$	15.5789	+	26.9835i	0.720907	+	1.24865i	−0.239729	+	0.970840i	$0.577059\pi$
$468$		0			0
$469$	−0.392007	−	2.52661i	−0.0181012	−	0.116668i
$470$		−	12.3090i		−	0.567774i
$471$		0			0
$472$	−93.8093	−	54.1608i	−4.31792	−	2.49295i
$473$	−3.67484	−	2.12167i	−0.168969	−	0.0975544i
$474$		0			0
$475$			4.90704i			0.225150i
$476$	101.391	+	39.2877i	4.64723	+	1.80075i
$477$		0			0
$478$	−9.49819	−	16.4513i	−0.434437	−	0.752467i
$479$	−14.7300	+	25.5131i	−0.673032	+	1.16572i	0.304008	+	0.952669i	$0.401675\pi$
$479$	−14.7300	+	25.5131i	−0.673032	+	1.16572i	−0.977040	+	0.213056i	$0.931658\pi$
$480$		0			0
$481$	0.434893	−	0.251086i	0.0198294	−	0.0114485i
$482$	−12.8377			−0.584740
$483$		0			0
$484$	−59.6290			−2.71041
$485$	10.1590	−	5.86532i	0.461298	−	0.266330i
$486$		0			0
$487$	6.30542	−	10.9213i	0.285726	−	0.494892i	−0.687059	−	0.726602i	$-0.741099\pi$
$487$	6.30542	−	10.9213i	0.285726	−	0.494892i	0.972785	+	0.231710i	$0.0744319\pi$
$488$	2.62972	+	4.55480i	0.119042	+	0.206186i
$489$		0			0
$490$	12.9301	−	14.1793i	0.584121	−	0.640556i
$491$		−	16.0235i		−	0.723132i	−0.932347	−	0.361566i	$-0.882242\pi$
$491$		−	16.0235i		−	0.723132i	0.932347	−	0.361566i	$-0.117758\pi$
$492$		0			0
$493$	−24.0569	−	13.8893i	−1.08347	−	0.625542i
$494$	−0.771340	−	0.445334i	−0.0347042	−	0.0200365i
$495$		0			0
$496$		−	12.6413i		−	0.567610i
$497$	7.36491	+	9.15382i	0.330361	+	0.410605i
$498$		0			0
$499$	−20.4502	−	35.4208i	−0.915476	−	1.58565i	−0.806203	−	0.591640i	$-0.798481\pi$
$499$	−20.4502	−	35.4208i	−0.915476	−	1.58565i	−0.109274	−	0.994012i	$-0.534852\pi$
$500$	2.75754	−	4.77621i	0.123321	−	0.213598i
$501$		0			0
$502$	27.8018	−	16.0514i	1.24085	−	0.716407i
$503$	31.1734			1.38995			0.694977	−	0.719032i	$-0.255415\pi$
$503$	31.1734			1.38995			0.694977	+	0.719032i	$0.255415\pi$
$504$		0			0
$505$	−4.30861			−0.191730
$506$	2.48278	−	1.43343i	0.110373	−	0.0637238i
$507$		0			0
$508$	−38.0475	+	65.9002i	−1.68808	+	2.92385i
$509$	−11.5864	−	20.0682i	−0.513558	−	0.889509i	−0.999876	−	0.0157272i	$-0.994994\pi$
$509$	−11.5864	−	20.0682i	−0.513558	−	0.889509i	0.486318	−	0.873782i	$-0.338340\pi$
$510$		0			0
$511$	22.7659	−	3.53217i	1.00711	−	0.156254i
$512$		−	55.9153i		−	2.47113i
$513$		0			0
$514$	30.0686	+	17.3601i	1.32627	+	0.765722i
$515$	−12.0742	−	6.97105i	−0.532053	−	0.307181i
$516$		0			0
$517$			1.94702i			0.0856299i
$518$	−54.3594	+	8.43393i	−2.38841	+	0.370566i
$519$		0			0
$520$	0.319008	+	0.552539i	0.0139894	+	0.0242304i
$521$	−19.2970	+	33.4233i	−0.845415	+	1.46430i	0.0398455	+	0.999206i	$0.487313\pi$
$521$	−19.2970	+	33.4233i	−0.845415	+	1.46430i	−0.885260	+	0.465096i	$0.846020\pi$
$522$		0			0
$523$	−2.12410	+	1.22635i	−0.0928803	+	0.0536245i	−0.545721	−	0.837967i	$-0.683744\pi$
$523$	−2.12410	+	1.22635i	−0.0928803	+	0.0536245i	0.452840	+	0.891592i	$0.350411\pi$
$524$	59.0760			2.58075
$525$		0			0
$526$	27.6613			1.20609
$527$	5.30234	−	3.06131i	0.230973	−	0.133353i
$528$		0			0
$529$	−8.59181	+	14.8814i	−0.373557	+	0.647019i
$530$	−2.30427	−	3.99110i	−0.100091	−	0.173362i
$531$		0			0
$532$	44.8844	+	55.7866i	1.94599	+	2.41866i
$533$			0.579034i			0.0250807i
$534$		0			0
$535$	8.11941	+	4.68774i	0.351033	+	0.202669i
$536$	−8.06470	−	4.65616i	−0.348342	−	0.201115i
$537$		0			0
$538$		−	21.6663i		−	0.934102i
$539$	−2.04525	+	2.24286i	−0.0880953	+	0.0966066i
$540$		0			0
$541$	−5.98037	−	10.3583i	−0.257116	−	0.445338i	0.708352	−	0.705859i	$-0.249439\pi$
$541$	−5.98037	−	10.3583i	−0.257116	−	0.445338i	−0.965468	+	0.260521i	$0.916106\pi$
$542$	−40.7359	+	70.5566i	−1.74976	+	3.03067i
$543$		0			0
$544$	147.830	−	85.3494i	6.33814	−	3.65933i
$545$	−2.24798			−0.0962931
$546$		0			0
$547$	−25.9365			−1.10896			−0.554482	−	0.832195i	$-0.687084\pi$
$547$	−25.9365			−1.10896			−0.554482	+	0.832195i	$0.687084\pi$
$548$	−67.0692	+	38.7224i	−2.86505	+	1.65414i
$549$		0			0
$550$	−0.594361	+	1.02946i	−0.0253436	+	0.0438965i
$551$	−9.14591	−	15.8412i	−0.389629	−	0.674857i
$552$		0			0
$553$	10.2076	+	3.95535i	0.434073	+	0.168198i
$554$		−	59.3521i		−	2.52163i
$555$		0			0
$556$	−22.5243	−	13.0044i	−0.955241	−	0.551509i
$557$	−9.05199	−	5.22617i	−0.383545	−	0.221440i	0.295814	−	0.955245i	$-0.404409\pi$
$557$	−9.05199	−	5.22617i	−0.383545	−	0.221440i	−0.679360	+	0.733806i	$0.737742\pi$
$558$		0			0
$559$			0.647922i			0.0274042i
$560$	−6.24117	−	40.2263i	−0.263738	−	1.69987i
$561$		0			0
$562$	21.8579	+	37.8590i	0.922020	+	1.59699i
$563$	0.618373	−	1.07105i	0.0260613	−	0.0451395i	−0.852701	−	0.522400i	$-0.825037\pi$
$563$	0.618373	−	1.07105i	0.0260613	−	0.0451395i	0.878762	+	0.477260i	$0.158370\pi$
$564$		0			0
$565$	−0.392896	+	0.226838i	−0.0165293	+	0.00954317i
$566$	−14.9446			−0.628168
$567$		0			0
$568$	42.7905			1.79545
$569$	39.0346	−	22.5366i	1.63642	−	0.944785i	0.654362	−	0.756181i	$-0.272937\pi$
$569$	39.0346	−	22.5366i	1.63642	−	0.944785i	0.982053	−	0.188603i	$-0.0603961\pi$
$570$		0			0
$571$	−12.5981	+	21.8205i	−0.527214	+	0.913161i	0.472283	+	0.881447i	$0.343430\pi$
$571$	−12.5981	+	21.8205i	−0.527214	+	0.913161i	−0.999497	+	0.0317141i	$0.989903\pi$
$572$	−0.0791707	−	0.137128i	−0.00331029	−	0.00573360i
$573$		0			0
$574$	22.9178	−	59.1445i	0.956573	−	2.46865i
$575$			2.41172i			0.100576i
$576$		0			0
$577$	8.93980	+	5.16140i	0.372169	+	0.214872i	0.674406	−	0.738361i	$-0.264400\pi$
$577$	8.93980	+	5.16140i	0.372169	+	0.214872i	−0.302237	+	0.953233i	$0.597733\pi$
$578$	91.4792	+	52.8155i	3.80503	+	2.19684i
$579$		0			0
$580$			20.5584i			0.853642i
$581$	−16.5384	+	13.3063i	−0.686127	+	0.552039i
$582$		0			0
$583$	0.364484	+	0.631305i	0.0150954	+	0.0261460i
$584$	41.9542	−	72.6668i	1.73608	−	3.00697i
$585$		0			0
$586$	−14.4662	+	8.35208i	−0.597594	+	0.345021i
$587$	7.37487			0.304393			0.152197	−	0.988350i	$-0.451365\pi$
$587$	7.37487			0.304393			0.152197	+	0.988350i	$0.451365\pi$
$588$		0			0
$589$	4.03166			0.166122
$590$	−26.6876	+	15.4081i	−1.09871	+	0.634341i
$591$		0			0
$592$	−58.3472	+	101.060i	−2.39806	+	4.15355i
$593$	13.5990	+	23.5542i	0.558444	+	0.967254i	0.997627	+	0.0688559i	$0.0219349\pi$
$593$	13.5990	+	23.5542i	0.558444	+	0.967254i	−0.439182	+	0.898398i	$0.644732\pi$
$594$		0			0
$595$	15.3614	−	12.3594i	0.629756	−	0.506684i
$596$			63.7994i			2.61332i
$597$		0			0
$598$	−0.379099	−	0.218873i	−0.0155025	−	0.00895038i
$599$	30.8088	+	17.7874i	1.25881	+	0.726775i	0.972844	−	0.231464i	$-0.0743515\pi$
$599$	30.8088	+	17.7874i	1.25881	+	0.726775i	0.285968	+	0.958239i	$0.407685\pi$
$600$		0			0
$601$		−	28.4029i		−	1.15858i	−0.815122	−	0.579289i	$-0.803330\pi$
$601$		−	28.4029i		−	1.15858i	0.815122	−	0.579289i	$-0.196670\pi$
$602$	25.6444	−	66.1810i	1.04519	−	2.69734i
$603$		0			0
$604$	25.5454	+	44.2460i	1.03943	+	1.80034i
$605$	−5.40599	+	9.36344i	−0.219785	+	0.380678i
$606$		0			0
$607$	2.68797	−	1.55190i	0.109101	−	0.0629897i	−0.444456	−	0.895801i	$-0.646603\pi$
$607$	2.68797	−	1.55190i	0.109101	−	0.0629897i	0.553558	+	0.832811i	$0.313270\pi$
$608$	112.403			4.55854
$609$		0			0
$610$	1.49624			0.0605812
$611$	0.257464	−	0.148647i	0.0104159	−	0.00601361i
$612$		0			0
$613$	−14.0062	+	24.2595i	−0.565706	+	0.979832i	0.431277	+	0.902219i	$0.358063\pi$
$613$	−14.0062	+	24.2595i	−0.565706	+	0.979832i	−0.996984	+	0.0776127i	$0.975270\pi$
$614$	−11.3584	−	19.6733i	−0.458387	−	0.793949i
$615$		0			0
$616$	1.69495	+	10.9245i	0.0682914	+	0.440160i
$617$			46.7561i			1.88233i	0.337949	+	0.941164i	$0.390267\pi$
$617$			46.7561i			1.88233i	−0.337949	+	0.941164i	$0.609733\pi$
$618$		0			0
$619$	−7.08932	−	4.09302i	−0.284944	−	0.164512i	0.350716	−	0.936482i	$-0.385938\pi$
$619$	−7.08932	−	4.09302i	−0.284944	−	0.164512i	−0.635659	+	0.771970i	$0.719272\pi$
$620$	−3.92416	−	2.26562i	−0.157598	−	0.0909894i
$621$		0			0
$622$			56.1792i			2.25258i
$623$	−16.7867	−	6.50467i	−0.672546	−	0.260604i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−29.3294	+	50.8001i	−1.17224	+	2.03038i
$627$		0			0
$628$	−97.2345	+	56.1384i	−3.88008	+	2.24016i
$629$	−56.5192			−2.25357
$630$		0			0
$631$	−24.3593			−0.969730			−0.484865	−	0.874589i	$-0.661131\pi$
$631$	−24.3593			−0.969730			−0.484865	+	0.874589i	$0.661131\pi$
$632$	34.5293	−	19.9355i	1.37350	−	0.792991i
$633$		0			0
$634$	−23.1505	+	40.0979i	−0.919425	+	1.59249i
$635$	6.89880	+	11.9491i	0.273770	+	0.474184i
$636$		0			0
$637$	0.452730	+	0.0992210i	0.0179378	+	0.00393128i
$638$		−	4.43116i		−	0.175431i
$639$		0			0
$640$	−36.3502	−	20.9868i	−1.43687	−	0.829577i
$641$	43.7491	+	25.2586i	1.72799	+	0.997653i	0.898229	+	0.439529i	$0.144854\pi$
$641$	43.7491	+	25.2586i	1.72799	+	0.997653i	0.829757	+	0.558124i	$0.188479\pi$
$642$		0			0
$643$		−	46.4983i		−	1.83371i	−0.399215	−	0.916857i	$-0.630717\pi$
$643$		−	46.4983i		−	1.83371i	0.399215	−	0.916857i	$-0.369283\pi$
$644$	22.0598	+	27.4181i	0.869279	+	1.08042i
$645$		0			0
$646$	50.1221	+	86.8141i	1.97203	+	3.41565i
$647$	−3.20881	+	5.55783i	−0.126151	+	0.218501i	−0.922182	−	0.386755i	$-0.873596\pi$
$647$	−3.20881	+	5.55783i	−0.126151	+	0.218501i	0.796031	+	0.605256i	$0.206929\pi$
$648$		0			0
$649$	4.22139	−	2.43722i	0.165704	−	0.0956693i
$650$	0.181508			0.00711933
$651$		0			0
$652$	33.8310			1.32492
$653$	−5.20786	+	3.00676i	−0.203799	+	0.117664i	−0.598426	−	0.801178i	$-0.704207\pi$
$653$	−5.20786	+	3.00676i	−0.203799	+	0.117664i	0.394627	+	0.918841i	$0.370874\pi$
$654$		0			0
$655$	5.35585	−	9.27661i	0.209271	−	0.362467i
$656$	−67.2778	−	116.529i	−2.62676	−	4.54968i
$657$		0			0
$658$	−32.1816	+	4.99303i	−1.25457	+	0.194649i
$659$		−	12.0203i		−	0.468245i	−0.972207	−	0.234123i	$-0.924778\pi$
$659$		−	12.0203i		−	0.468245i	0.972207	−	0.234123i	$-0.0752217\pi$
$660$		0			0
$661$	−5.91170	−	3.41312i	−0.229938	−	0.132755i	0.380605	−	0.924738i	$-0.375716\pi$
$661$	−5.91170	−	3.41312i	−0.229938	−	0.132755i	−0.610544	+	0.791983i	$0.709049\pi$
$662$	−30.0055	−	17.3237i	−1.16620	−	0.673303i
$663$		0			0
$664$			77.3105i			3.00023i
$665$	12.8293	−	1.99049i	0.497500	−	0.0771878i
$666$		0			0
$667$	−4.49504	−	7.78564i	−0.174049	−	0.301461i
$668$	33.5233	−	58.0641i	1.29706	−	2.24657i
$669$		0			0
$670$	−2.29431	+	1.32462i	−0.0886369	+	0.0511746i
$671$	−0.236673			−0.00913666
$672$		0			0
$673$	4.71419			0.181719			0.0908593	−	0.995864i	$-0.471039\pi$
$673$	4.71419			0.181719			0.0908593	+	0.995864i	$0.471039\pi$
$674$	−40.9142	+	23.6218i	−1.57596	+	0.909878i
$675$		0			0
$676$	35.8360	−	62.0698i	1.37831	−	2.38730i
$677$	−3.28642	−	5.69225i	−0.126307	−	0.218771i	0.795936	−	0.605381i	$-0.206979\pi$
$677$	−3.28642	−	5.69225i	−0.126307	−	0.218771i	−0.922243	+	0.386610i	$0.873646\pi$
$678$		0			0
$679$	−19.4556	−	24.1813i	−0.746637	−	0.927992i
$680$		−	71.8085i		−	2.75373i
$681$		0			0
$682$	0.845814	+	0.488331i	0.0323879	+	0.0186992i
$683$	3.80578	+	2.19727i	0.145624	+	0.0840761i	0.571042	−	0.820921i	$-0.306539\pi$
$683$	3.80578	+	2.19727i	0.145624	+	0.0840761i	−0.425418	+	0.904997i	$0.639873\pi$
$684$		0			0
$685$			14.0424i			0.536531i
$686$	−42.3163	−	28.0536i	−1.61564	−	1.07109i
$687$		0			0
$688$	−75.2819	−	130.392i	−2.87010	−	4.97115i
$689$	0.0556537	−	0.0963950i	0.00212024	−	0.00367236i
$690$		0			0
$691$	21.8506	−	12.6155i	0.831237	−	0.479915i	−0.0230392	−	0.999735i	$-0.507334\pi$
$691$	21.8506	−	12.6155i	0.831237	−	0.479915i	0.854276	+	0.519820i	$0.174001\pi$
$692$	36.2395			1.37762
$693$		0			0
$694$	−57.2878			−2.17462
$695$	−4.08411	+	2.35796i	−0.154919	+	0.0894427i
$696$		0			0
$697$	32.5850	−	56.4389i	1.23425	−	2.13778i
$698$	−20.2822	−	35.1298i	−0.767692	−	1.32968i
$699$		0			0
$700$	−13.6058	−	5.27210i	−0.514252	−	0.199267i
$701$			32.1522i			1.21437i	0.794560	+	0.607186i	$0.207702\pi$
$701$			32.1522i			1.21437i	−0.794560	+	0.607186i	$0.792298\pi$
$702$		0			0
$703$	−32.2310	−	18.6086i	−1.21562	−	0.701836i
$704$	12.0255	+	6.94295i	0.453230	+	0.261672i
$705$		0			0
$706$			19.9173i			0.749597i
$707$	1.74774	+	11.2647i	0.0657305	+	0.423654i
$708$		0			0
$709$	−19.1583	−	33.1832i	−0.719505	−	1.24622i	−0.961196	−	0.275867i	$-0.911035\pi$
$709$	−19.1583	−	33.1832i	−0.719505	−	1.24622i	0.241690	−	0.970353i	$-0.422298\pi$
$710$	6.08669	−	10.5425i	0.228430	−	0.395652i
$711$		0			0
$712$	−56.7843	+	32.7844i	−2.12808	+	1.22865i
$713$	1.98148			0.0742072
$714$		0			0
$715$	−0.0287106			−0.00107371
$716$	−30.3165	+	17.5033i	−1.13298	+	0.654128i
$717$		0			0
$718$	−1.95450	+	3.38530i	−0.0729414	+	0.126338i
$719$	−16.9595	−	29.3748i	−0.632483	−	1.09549i	−0.987042	−	0.160460i	$-0.948702\pi$
$719$	−16.9595	−	29.3748i	−0.632483	−	1.09549i	0.354559	−	0.935034i	$-0.384631\pi$
$720$		0			0
$721$	−13.3278	+	34.3954i	−0.496355	+	1.28095i
$722$			13.9235i			0.518181i
$723$		0			0
$724$	70.0308	+	40.4323i	2.60267	+	1.50266i
$725$	3.22825	+	1.86383i	0.119894	+	0.0692210i
$726$		0			0
$727$		−	39.7369i		−	1.47376i	−0.676024	−	0.736880i	$-0.736298\pi$
$727$		−	39.7369i		−	1.47376i	0.676024	−	0.736880i	$-0.263702\pi$
$728$	1.31519	−	1.05817i	0.0487443	−	0.0392184i
$729$		0			0
$730$	−11.9355	−	20.6728i	−0.441751	−	0.765135i
$731$	36.4617	−	63.1535i	1.34858	−	2.33582i
$732$		0			0
$733$	−10.3750	+	5.99001i	−0.383209	+	0.221246i	−0.679214	−	0.733941i	$-0.737679\pi$
$733$	−10.3750	+	5.99001i	−0.383209	+	0.221246i	0.296004	+	0.955187i	$0.404346\pi$
$734$	−73.3781			−2.70844
$735$		0			0
$736$	55.2439			2.03632
$737$	0.362909	−	0.209526i	0.0133679	−	0.00771799i
$738$		0			0
$739$	−17.3997	+	30.1371i	−0.640058	+	1.10861i	0.345362	+	0.938470i	$0.387756\pi$
$739$	−17.3997	+	30.1371i	−0.640058	+	1.10861i	−0.985419	+	0.170143i	$0.945577\pi$
$740$	20.9144	+	36.2249i	0.768830	+	1.33165i
$741$		0			0
$742$	−9.49993	+	7.64338i	−0.348753	+	0.280597i
$743$			7.48447i			0.274579i	0.990531	+	0.137289i	$0.0438390\pi$
$743$			7.48447i			0.274579i	−0.990531	+	0.137289i	$0.956161\pi$
$744$		0			0
$745$	10.0183	+	5.78407i	0.367042	+	0.211912i
$746$	−46.1731	−	26.6581i	−1.69052	−	0.976021i
$747$		0			0
$748$			17.8213i			0.651610i
$749$	8.96241	−	23.1295i	0.327480	−	0.845133i
$750$		0			0
$751$	26.6412	+	46.1439i	0.972151	+	1.68381i	0.689034	+	0.724729i	$0.258035\pi$
$751$	26.6412	+	46.1439i	0.972151	+	1.68381i	0.283116	+	0.959086i	$0.408632\pi$
$752$	−34.5425	+	59.8294i	−1.25964	+	2.18175i
$753$		0			0
$754$	−0.585954	+	0.338301i	−0.0213392	+	0.0123202i
$755$	9.26383			0.337145
$756$		0			0
$757$	26.7285			0.971463			0.485731	−	0.874108i	$-0.338553\pi$
$757$	26.7285			0.971463			0.485731	+	0.874108i	$0.338553\pi$
$758$	2.16254	−	1.24854i	0.0785468	−	0.0453490i
$759$		0			0
$760$	23.6425	−	40.9500i	0.857603	−	1.48541i
$761$	23.2490	+	40.2684i	0.842775	+	1.45973i	0.887540	+	0.460732i	$0.152413\pi$
$761$	23.2490	+	40.2684i	0.842775	+	1.45973i	−0.0447645	+	0.998998i	$0.514254\pi$
$762$		0			0
$763$	0.911870	+	5.87729i	0.0330119	+	0.212772i
$764$			54.6820i			1.97833i
$765$		0			0
$766$	−56.7866	−	32.7857i	−2.05178	−	1.18460i
$767$	−0.644571	−	0.372143i	−0.0232741	−	0.0134373i
$768$		0			0
$769$			37.6036i			1.35602i	0.735052	+	0.678011i	$0.237158\pi$
$769$			37.6036i			1.35602i	−0.735052	+	0.678011i	$0.762842\pi$
$770$	2.93260	+	1.13635i	0.105684	+	0.0409512i
$771$		0			0
$772$	−29.1261	−	50.4479i	−1.04827	−	1.81566i
$773$	20.4437	−	35.4095i	0.735309	−	1.27359i	−0.219279	−	0.975662i	$-0.570370\pi$
$773$	20.4437	−	35.4095i	0.735309	−	1.27359i	0.954588	−	0.297930i	$-0.0962963\pi$
$774$		0			0
$775$	−0.711532	+	0.410803i	−0.0255590	+	0.0147565i
$776$	−113.038			−4.05783
$777$		0			0
$778$	60.6273			2.17360
$779$	37.1643	−	21.4568i	1.33155	−	0.768770i
$780$		0			0
$781$	−0.962781	+	1.66759i	−0.0344510	+	0.0596709i
$782$	24.6341	+	42.6675i	0.880913	+	1.52579i
$783$		0			0
$784$	−102.639	+	32.6347i	−3.66568	+	1.16553i
$785$			20.3581i			0.726612i
$786$		0			0
$787$	3.35123	+	1.93484i	0.119459	+	0.0689695i	0.558539	−	0.829478i	$-0.311362\pi$
$787$	3.35123	+	1.93484i	0.119459	+	0.0689695i	−0.439080	+	0.898448i	$0.644696\pi$
$788$	−99.5017	−	57.4473i	−3.54460	−	2.04648i
$789$		0			0
$790$		−	11.3428i		−	0.403559i
$791$	0.752436	+	0.935200i	0.0267536	+	0.0332519i
$792$		0			0
$793$	0.0180690	+	0.0312964i	0.000641649	+	0.00111137i
$794$	−39.9240	+	69.1504i	−1.41685	+	2.45406i
$795$		0			0
$796$	43.1819	−	24.9311i	1.53054	−	0.883658i
$797$	−32.6176			−1.15538			−0.577688	−	0.816258i	$-0.696045\pi$
$797$	−32.6176			−1.15538			−0.577688	+	0.816258i	$0.696045\pi$
$798$		0			0
$799$	−33.4603			−1.18374
$800$	−19.8376	+	11.4532i	−0.701364	+	0.404933i
$801$		0			0
$802$	−11.4415	+	19.8173i	−0.404014	+	0.699773i
$803$	1.88793	+	3.26998i	0.0666235	+	0.115395i
$804$		0			0
$805$	6.30537	−	0.978287i	0.222235	−	0.0344801i
$806$		−	0.149128i		−	0.00525282i
$807$		0			0
$808$	35.9560	+	20.7592i	1.26493	+	0.730306i
$809$	17.3080	+	9.99277i	0.608516	+	0.351327i	0.772384	−	0.635155i	$-0.219064\pi$
$809$	17.3080	+	9.99277i	0.608516	+	0.351327i	−0.163868	+	0.986482i	$0.552397\pi$
$810$		0			0
$811$		−	27.2039i		−	0.955257i	−0.878562	−	0.477629i	$-0.841496\pi$
$811$		−	27.2039i		−	0.955257i	0.878562	−	0.477629i	$-0.158504\pi$
$812$	53.7494	−	8.33929i	1.88623	−	0.292652i
$813$		0			0
$814$	−4.50790	−	7.80790i	−0.158002	−	0.273667i
$815$	3.06713	−	5.31243i	0.107437	−	0.186086i
$816$		0			0
$817$	41.5857	−	24.0095i	1.45490	−	0.839987i
$818$	6.67502			0.233386
$819$		0			0
$820$	−48.2312			−1.68431
$821$	−9.46053	+	5.46204i	−0.330175	+	0.190627i	−0.655919	−	0.754832i	$-0.727719\pi$
$821$	−9.46053	+	5.46204i	−0.330175	+	0.190627i	0.325744	+	0.945458i	$0.394385\pi$
$822$		0			0
$823$	11.4047	−	19.7535i	0.397542	−	0.688563i	−0.595880	−	0.803074i	$-0.703197\pi$
$823$	11.4047	−	19.7535i	0.397542	−	0.688563i	0.993422	+	0.114510i	$0.0365299\pi$
$824$	67.1741	+	116.349i	2.34012	+	4.05321i
$825$		0			0
$826$	51.1095	+	63.5238i	1.77833	+	2.21028i
$827$			27.3703i			0.951757i	0.879511	+	0.475879i	$0.157870\pi$
$827$			27.3703i			0.951757i	−0.879511	+	0.475879i	$0.842130\pi$
$828$		0			0
$829$	24.0847	+	13.9053i	0.836497	+	0.482952i	0.856072	−	0.516857i	$-0.172898\pi$
$829$	24.0847	+	13.9053i	0.836497	+	0.482952i	−0.0195749	+	0.999808i	$0.506231\pi$
$830$	19.0473	+	10.9969i	0.661140	+	0.381709i
$831$		0			0
$832$		−	2.12026i		−	0.0735069i
$833$	−38.5443	−	35.1485i	−1.33548	−	1.21782i
$834$		0			0
$835$	−6.07847	−	10.5282i	−0.210354	−	0.364344i
$836$	−5.86753	+	10.1629i	−0.202933	+	0.351490i
$837$		0			0
$838$	42.5700	−	24.5778i	1.47056	−	0.849026i
$839$	−5.02286			−0.173408			−0.0867041	−	0.996234i	$-0.527633\pi$
$839$	−5.02286			−0.173408			−0.0867041	+	0.996234i	$0.527633\pi$
$840$		0			0
$841$	15.1045			0.520845
$842$	66.7178	−	38.5195i	2.29925	−	1.32747i
$843$		0			0
$844$	54.4471	−	94.3051i	1.87414	−	3.24611i
$845$	−6.49781	−	11.2545i	−0.223531	−	0.387168i
$846$		0			0
$847$	26.6733	+	10.3356i	0.916506	+	0.355136i
$848$			25.8656i			0.888227i
$849$		0			0
$850$	−17.6917	−	10.2143i	−0.606821	−	0.350349i
$851$	−15.8409	−	9.14576i	−0.543020	−	0.313513i
$852$		0			0
$853$			24.9266i			0.853471i	0.904376	+	0.426736i	$0.140336\pi$
$853$			24.9266i			0.853471i	−0.904376	+	0.426736i	$0.859664\pi$
$854$	−0.606935	−	3.91189i	−0.0207689	−	0.133862i
$855$		0			0
$856$	−45.1718	−	78.2398i	−1.54394	−	2.67418i
$857$	14.1775	−	24.5562i	0.484296	−	0.838825i	−0.515541	−	0.856865i	$-0.672409\pi$
$857$	14.1775	−	24.5562i	0.484296	−	0.838825i	0.999837	+	0.0180397i	$0.00574251\pi$
$858$		0			0
$859$	−36.9865	+	21.3542i	−1.26196	+	0.728595i	−0.973454	−	0.228882i	$-0.926493\pi$
$859$	−36.9865	+	21.3542i	−1.26196	+	0.728595i	−0.288509	+	0.957477i	$0.593160\pi$
$860$	−53.9693			−1.84034
$861$		0			0
$862$	37.7263			1.28496
$863$	29.3309	−	16.9342i	0.998434	−	0.576446i	0.0906495	−	0.995883i	$-0.471106\pi$
$863$	29.3309	−	16.9342i	0.998434	−	0.576446i	0.907785	+	0.419437i	$0.137772\pi$
$864$		0			0
$865$	3.28548	−	5.69062i	0.111710	−	0.193487i
$866$	7.78352	+	13.4815i	0.264495	+	0.458118i
$867$		0			0
$868$	−4.33160	+	11.1786i	−0.147024	+	0.379428i
$869$			1.79418i			0.0608635i
$870$		0			0
$871$	−0.0554133	−	0.0319929i	−0.00187761	−	0.00108404i
$872$	18.7598	+	10.8310i	0.635286	+	0.366782i
$873$		0			0
$874$			32.4424i			1.09738i
$875$	−2.06138	+	1.65853i	−0.0696873	+	0.0560685i
$876$		0			0
$877$	19.3146	+	33.4538i	0.652206	+	1.12965i	0.982586	+	0.185807i	$0.0594898\pi$
$877$	19.3146	+	33.4538i	0.652206	+	1.12965i	−0.330380	+	0.943848i	$0.607177\pi$
$878$	40.1474	−	69.5373i	1.35491	−	2.34677i
$879$		0			0
$880$	5.77791	−	3.33588i	0.194773	−	0.112452i
$881$	−47.5426			−1.60175			−0.800875	−	0.598831i	$-0.795632\pi$
$881$	−47.5426			−1.60175			−0.800875	+	0.598831i	$0.795632\pi$
$882$		0			0
$883$	−45.8701			−1.54365			−0.771826	−	0.635833i	$-0.780657\pi$
$883$	−45.8701			−1.54365			−0.771826	+	0.635833i	$0.780657\pi$
$884$	2.35659	−	1.36058i	0.0792608	−	0.0457612i
$885$		0			0
$886$	48.6696	−	84.2981i	1.63509	−	2.83205i
$887$	4.44812	+	7.70438i	0.149353	+	0.258688i	0.930989	−	0.365048i	$-0.118947\pi$
$887$	4.44812	+	7.70438i	0.149353	+	0.258688i	−0.781635	+	0.623736i	$0.785614\pi$
$888$		0			0
$889$	28.4421	−	22.8837i	0.953916	−	0.767495i
$890$			18.6535i			0.625268i
$891$		0			0
$892$	95.4914	+	55.1320i	3.19729	+	1.84595i
$893$	−19.0813	−	11.0166i	−0.638531	−	0.368656i
$894$		0			0
$895$			6.34741i			0.212170i
$896$	−40.1244	+	103.550i	−1.34046	+	3.45935i
$897$		0			0
$898$	−0.637235	−	1.10372i	−0.0212648	−	0.0368317i
$899$	1.53134	−	2.65236i	0.0510730	−	0.0884610i
$900$		0			0
$901$	−10.8492	+	6.26380i	−0.361440	+	0.208678i
$902$	10.3957			0.346141
$903$		0			0
$904$	4.37170			0.145401
$905$	12.6980	−	7.33122i	0.422097	−	0.243698i
$906$		0			0
$907$	−26.2555	+	45.4758i	−0.871799	+	1.51000i	−0.0116649	+	0.999932i	$0.503713\pi$
$907$	−26.2555	+	45.4758i	−0.871799	+	1.51000i	−0.860134	+	0.510068i	$0.829620\pi$
$908$	6.72282	+	11.6443i	0.223105	+	0.386428i
$909$		0			0
$910$	−0.0736267	−	0.474547i	−0.00244070	−	0.0157311i
$911$		−	26.0848i		−	0.864229i	−0.901819	−	0.432114i	$-0.857768\pi$
$911$		−	26.0848i		−	0.864229i	0.901819	−	0.432114i	$-0.142232\pi$
$912$		0			0
$913$	−3.01286	−	1.73947i	−0.0997111	−	0.0575682i
$914$	−4.90186	−	2.83009i	−0.162139	−	0.0936111i
$915$		0			0
$916$			81.3222i			2.68696i
$917$	−26.4260	−	10.2398i	−0.872662	−	0.338147i
$918$		0			0
$919$	8.99375	+	15.5776i	0.296676	+	0.513859i	0.975373	−	0.220560i	$-0.0707884\pi$
$919$	8.99375	+	15.5776i	0.296676	+	0.513859i	−0.678697	+	0.734418i	$0.737455\pi$
$920$	11.6198	−	20.1261i	0.383095	−	0.663539i
$921$		0			0
$922$	−27.9381	+	16.1301i	−0.920092	+	0.531216i
$923$	0.294017			0.00967770
$924$		0			0
$925$	7.58444			0.249375
$926$	57.8389	−	33.3933i	1.90070	−	1.09737i
$927$		0			0
$928$	42.6938	−	73.9479i	1.40149	−	2.42746i
$929$	0.528327	+	0.915089i	0.0173338	+	0.0300231i	0.874562	−	0.484913i	$-0.161149\pi$
$929$	0.528327	+	0.915089i	0.0173338	+	0.0300231i	−0.857228	+	0.514936i	$0.827816\pi$
$930$		0			0
$931$	−10.4081	−	32.7345i	−0.341113	−	1.07283i
$932$		−	62.0106i		−	2.03122i
$933$		0			0
$934$	−73.9717	−	42.7076i	−2.42043	−	1.39743i
$935$	2.79844	+	1.61568i	0.0915189	+	0.0528385i
$936$		0			0
$937$		−	10.1689i		−	0.332203i	−0.986109	−	0.166102i	$-0.946882\pi$
$937$		−	10.1689i		−	0.332203i	0.986109	−	0.166102i	$-0.0531180\pi$
$938$	4.39384	+	5.46109i	0.143464	+	0.178311i
$939$		0			0
$940$	12.3817	+	21.4457i	0.403846	+	0.699482i
$941$	11.2243	−	19.4410i	0.365900	−	0.633758i	−0.623020	−	0.782206i	$-0.714094\pi$
$941$	11.2243	−	19.4410i	0.365900	−	0.633758i	0.988920	+	0.148448i	$0.0474278\pi$
$942$		0			0
$943$	18.2655	−	10.5456i	0.594808	−	0.343412i
$944$	172.957			5.62927
$945$		0			0
$946$	11.6325			0.378206
$947$	−10.1578	+	5.86460i	−0.330084	+	0.190574i	−0.655878	−	0.754867i	$-0.727702\pi$
$947$	−10.1578	+	5.86460i	−0.330084	+	0.190574i	0.325795	+	0.945441i	$0.394368\pi$
$948$		0			0
$949$	0.288271	−	0.499299i	0.00935766	−	0.0162079i
$950$	−6.72600	−	11.6498i	−0.218220	−	0.377968i
$951$		0			0
$952$	−187.741	+	29.1283i	−6.08473	+	0.944055i
$953$			1.51744i			0.0491546i	0.999698	+	0.0245773i	$0.00782399\pi$
$953$			1.51744i			0.0491546i	−0.999698	+	0.0245773i	$0.992176\pi$
$954$		0			0
$955$	8.58662	+	4.95749i	0.277857	+	0.160421i
$956$	33.0969	+	19.1085i	1.07043	+	0.618013i
$957$		0			0
$958$		−	80.7607i		−	2.60926i
$959$	36.7133	−	5.69612i	1.18553	−	0.183937i
$960$		0			0
$961$	−15.1625	−	26.2622i	−0.489112	−	0.847167i
$962$	−0.688318	+	1.19220i	−0.0221923	+	0.0384381i
$963$		0			0
$964$	22.3667	−	12.9134i	0.720384	−	0.415914i
$965$	−10.5623			−0.340014
$966$		0			0
$967$	−15.2090			−0.489088			−0.244544	−	0.969638i	$-0.578638\pi$
$967$	−15.2090			−0.489088			−0.244544	+	0.969638i	$0.578638\pi$
$968$	90.2275	−	52.0929i	2.90002	−	1.67433i
$969$		0			0
$970$	−16.0790	+	27.8496i	−0.516265	+	0.894197i
$971$	−28.0370	−	48.5615i	−0.899750	−	1.55841i	−0.827814	−	0.561003i	$-0.810416\pi$
$971$	−28.0370	−	48.5615i	−0.899750	−	1.55841i	−0.0719357	−	0.997409i	$-0.522918\pi$
$972$		0			0
$973$	7.82150	+	9.72131i	0.250746	+	0.311651i
$974$			34.5710i			1.10772i
$975$		0			0
$976$	−7.27265	−	4.19887i	−0.232792	−	0.134402i
$977$	14.3187	+	8.26689i	0.458095	+	0.264481i	0.711243	−	0.702946i	$-0.248133\pi$
$977$	14.3187	+	8.26689i	0.458095	+	0.264481i	−0.253148	+	0.967428i	$0.581466\pi$
$978$		0			0
$979$		−	2.95058i		−	0.0943009i
$980$	−8.26471	+	37.7106i	−0.264007	+	1.20462i
$981$		0			0
$982$	21.9632	+	38.0413i	0.700873	+	1.21395i
$983$	−26.1570	+	45.3053i	−0.834280	+	1.44502i	0.0603356	+	0.998178i	$0.480783\pi$
$983$	−26.1570	+	45.3053i	−0.834280	+	1.44502i	−0.894615	+	0.446837i	$0.852550\pi$
$984$		0			0
$985$	−18.0417	+	10.4164i	−0.574857	+	0.331894i
$986$	76.1512			2.42515
$987$		0			0
$988$	1.79185			0.0570062
$989$	20.4386	−	11.8002i	0.649910	−	0.375226i
$990$		0			0
$991$	−7.47878	+	12.9536i	−0.237571	+	0.411486i	−0.960017	−	0.279942i	$-0.909685\pi$
$991$	−7.47878	+	12.9536i	−0.237571	+	0.411486i	0.722446	+	0.691428i	$0.243018\pi$
$992$	9.41005	+	16.2987i	0.298769	+	0.517484i
$993$		0			0
$994$	−30.0320	−	11.6371i	−0.952556	−	0.369105i
$995$		−	9.04104i		−	0.286620i
$996$		0			0
$997$	15.7542	+	9.09570i	0.498941	+	0.288064i	0.728276	−	0.685284i	$-0.240322\pi$
$997$	15.7542	+	9.09570i	0.498941	+	0.288064i	−0.229335	+	0.973347i	$0.573655\pi$
$998$	97.1013	+	56.0615i	3.07369	+	1.77459i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bj.a.206.1	yes	12
3.2	odd	2		315.2.bj.b.206.6	yes	12
5.2	odd	4		1575.2.bc.d.899.1		24
5.3	odd	4		1575.2.bc.d.899.12		24
5.4	even	2		1575.2.bk.f.1151.6		12
7.3	odd	6		2205.2.b.a.881.1		12
7.4	even	3		2205.2.b.b.881.1		12
7.5	odd	6		315.2.bj.b.26.6	yes	12
15.2	even	4		1575.2.bc.c.899.12		24
15.8	even	4		1575.2.bc.c.899.1		24
15.14	odd	2		1575.2.bk.e.1151.1		12
21.5	even	6	inner	315.2.bj.a.26.1	✓	12
21.11	odd	6		2205.2.b.a.881.12		12
21.17	even	6		2205.2.b.b.881.12		12
35.12	even	12		1575.2.bc.c.1349.1		24
35.19	odd	6		1575.2.bk.e.26.1		12
35.33	even	12		1575.2.bc.c.1349.12		24
105.47	odd	12		1575.2.bc.d.1349.12		24
105.68	odd	12		1575.2.bc.d.1349.1		24
105.89	even	6		1575.2.bk.f.26.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bj.a.26.1	✓	12	21.5	even	6	inner
315.2.bj.a.206.1	yes	12	1.1	even	1	trivial
315.2.bj.b.26.6	yes	12	7.5	odd	6
315.2.bj.b.206.6	yes	12	3.2	odd	2
1575.2.bc.c.899.1		24	15.8	even	4
1575.2.bc.c.899.12		24	15.2	even	4
1575.2.bc.c.1349.1		24	35.12	even	12
1575.2.bc.c.1349.12		24	35.33	even	12
1575.2.bc.d.899.1		24	5.2	odd	4
1575.2.bc.d.899.12		24	5.3	odd	4
1575.2.bc.d.1349.1		24	105.68	odd	12
1575.2.bc.d.1349.12		24	105.47	odd	12
1575.2.bk.e.26.1		12	35.19	odd	6
1575.2.bk.e.1151.1		12	15.14	odd	2
1575.2.bk.f.26.6		12	105.89	even	6
1575.2.bk.f.1151.6		12	5.4	even	2
2205.2.b.a.881.1		12	7.3	odd	6
2205.2.b.a.881.12		12	21.11	odd	6
2205.2.b.b.881.1		12	7.4	even	3
2205.2.b.b.881.12		12	21.17	even	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.37409 + 1.37068i) q^{2} +(2.75754 - 4.77621i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.06138 + 1.65853i) q^{7} +9.63615i q^{8} +O(q^{10})\)	\(q+(-2.37409 + 1.37068i) q^{2} +(2.75754 - 4.77621i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.06138 + 1.65853i) q^{7} +9.63615i q^{8} +(2.37409 + 1.37068i) q^{10} +(-0.375529 - 0.216812i) q^{11} +0.0662108i q^{13} +(2.62059 - 6.76300i) q^{14} +(-7.69302 - 13.3247i) q^{16} +(3.72600 - 6.45362i) q^{17} +(4.24962 - 2.45352i) q^{19} -5.51509 q^{20} +1.18872 q^{22} +(2.08861 - 1.20586i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.0907540 - 0.157191i) q^{26} +(2.23713 + 14.4190i) q^{28} -3.72767i q^{29} +(0.711532 + 0.410803i) q^{31} +(19.8376 + 11.4532i) q^{32} +20.4287i q^{34} +(2.46702 + 0.955942i) q^{35} +(-3.79222 - 6.56832i) q^{37} +(-6.72600 + 11.6498i) q^{38} +(8.34515 - 4.81807i) q^{40} +8.74531 q^{41} +9.78575 q^{43} +(-2.07108 + 1.19574i) q^{44} +(-3.30570 + 5.72564i) q^{46} +(-2.24506 - 3.88855i) q^{47} +(1.49856 - 6.83771i) q^{49} -2.74137i q^{50} +(0.316236 + 0.182579i) q^{52} +(-1.45588 - 0.840554i) q^{53} +0.433624i q^{55} +(-15.9818 - 19.8637i) q^{56} +(5.10945 + 8.84983i) q^{58} +(-5.62059 + 9.73514i) q^{59} +(0.472679 - 0.272901i) q^{61} -2.25233 q^{62} -32.0229 q^{64} +(0.0573402 - 0.0331054i) q^{65} +(-0.483197 + 0.836922i) q^{67} +(-20.5492 - 35.5923i) q^{68} +(-7.16722 + 1.11200i) q^{70} -4.44063i q^{71} +(-7.54106 - 4.35383i) q^{73} +(18.0062 + 10.3959i) q^{74} -27.0628i q^{76} +(1.13370 - 0.175895i) q^{77} +(-2.06882 - 3.58331i) q^{79} +(-7.69302 + 13.3247i) q^{80} +(-20.7622 + 11.9871i) q^{82} +8.02296 q^{83} -7.45200 q^{85} +(-23.2323 + 13.4132i) q^{86} +(2.08923 - 3.61866i) q^{88} +(3.40223 + 5.89284i) q^{89} +(-0.109812 - 0.136485i) q^{91} -13.3008i q^{92} +(10.6599 + 6.15452i) q^{94} +(-4.24962 - 2.45352i) q^{95} +11.7306i q^{97} +(5.81461 + 18.2874i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4} - 6 q^{5} - 2 q^{7}+O(q^{10}) \) 12 * q + 8 * q^4 - 6 * q^5 - 2 * q^7	\( 12 q + 8 q^{4} - 6 q^{5} - 2 q^{7} + 12 q^{11} - 12 q^{14} - 16 q^{16} + 6 q^{19} - 16 q^{20} + 32 q^{22} + 12 q^{23} - 6 q^{25} - 20 q^{28} + 6 q^{31} + 60 q^{32} - 2 q^{35} - 10 q^{37} - 36 q^{38} + 24 q^{41} - 4 q^{43} + 12 q^{44} - 4 q^{46} + 6 q^{49} + 12 q^{53} - 60 q^{56} + 20 q^{58} - 24 q^{59} + 24 q^{62} - 56 q^{64} + 18 q^{65} + 6 q^{67} - 60 q^{68} - 12 q^{70} - 42 q^{73} + 84 q^{74} - 36 q^{77} + 18 q^{79} - 16 q^{80} - 72 q^{82} - 24 q^{83} - 84 q^{86} + 4 q^{88} + 12 q^{89} - 18 q^{91} + 12 q^{94} - 6 q^{95} + 12 q^{98}+O(q^{100}) \) 12 * q + 8 * q^4 - 6 * q^5 - 2 * q^7 + 12 * q^11 - 12 * q^14 - 16 * q^16 + 6 * q^19 - 16 * q^20 + 32 * q^22 + 12 * q^23 - 6 * q^25 - 20 * q^28 + 6 * q^31 + 60 * q^32 - 2 * q^35 - 10 * q^37 - 36 * q^38 + 24 * q^41 - 4 * q^43 + 12 * q^44 - 4 * q^46 + 6 * q^49 + 12 * q^53 - 60 * q^56 + 20 * q^58 - 24 * q^59 + 24 * q^62 - 56 * q^64 + 18 * q^65 + 6 * q^67 - 60 * q^68 - 12 * q^70 - 42 * q^73 + 84 * q^74 - 36 * q^77 + 18 * q^79 - 16 * q^80 - 72 * q^82 - 24 * q^83 - 84 * q^86 + 4 * q^88 + 12 * q^89 - 18 * q^91 + 12 * q^94 - 6 * q^95 + 12 * q^98

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