LMFDB - Embedded newform 320.3.r.a.111.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,3,Mod(111,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("320.111");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	320.r (of order $4$, degree $2$, not 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:	$8.71936845953$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			111.10
Character	$\chi$	$=$	320.111
Dual form			320.3.r.a.271.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39844 - 1.39844i) q^{3} +(-1.58114 + 1.58114i) q^{5} -9.44746 q^{7} +5.08871i q^{9} +O(q^{10})$	\(q+(1.39844 - 1.39844i) q^{3} +(-1.58114 + 1.58114i) q^{5} -9.44746 q^{7} +5.08871i q^{9} +(7.42460 + 7.42460i) q^{11} +(-16.5749 - 16.5749i) q^{13} +4.42227i q^{15} -16.9526 q^{17} +(-23.4305 + 23.4305i) q^{19} +(-13.2117 + 13.2117i) q^{21} +0.786593 q^{23} -5.00000i q^{25} +(19.7023 + 19.7023i) q^{27} +(17.6103 + 17.6103i) q^{29} -23.5050i q^{31} +20.7658 q^{33} +(14.9377 - 14.9377i) q^{35} +(-25.6902 + 25.6902i) q^{37} -46.3582 q^{39} -19.6072i q^{41} +(5.42827 + 5.42827i) q^{43} +(-8.04596 - 8.04596i) q^{45} -3.62387i q^{47} +40.2544 q^{49} +(-23.7073 + 23.7073i) q^{51} +(-40.5183 + 40.5183i) q^{53} -23.4786 q^{55} +65.5324i q^{57} +(-24.1706 - 24.1706i) q^{59} +(39.1534 + 39.1534i) q^{61} -48.0754i q^{63} +52.4145 q^{65} +(-24.6093 + 24.6093i) q^{67} +(1.10001 - 1.10001i) q^{69} -12.9337 q^{71} -97.1658i q^{73} +(-6.99222 - 6.99222i) q^{75} +(-70.1436 - 70.1436i) q^{77} -54.5533i q^{79} +9.30664 q^{81} +(70.0367 - 70.0367i) q^{83} +(26.8045 - 26.8045i) q^{85} +49.2539 q^{87} -95.6831i q^{89} +(156.591 + 156.591i) q^{91} +(-32.8705 - 32.8705i) q^{93} -74.0937i q^{95} +97.1512 q^{97} +(-37.7816 + 37.7816i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 32 q^{11} + 32 q^{19} + 128 q^{23} + 96 q^{27} + 32 q^{29} - 96 q^{37} - 384 q^{39} - 96 q^{43} + 224 q^{49} + 256 q^{51} - 160 q^{53} + 352 q^{59} - 32 q^{61} - 160 q^{67} + 96 q^{69} - 256 q^{71} + 224 q^{77} - 288 q^{81} + 480 q^{83} + 160 q^{85} + 384 q^{91} + 96 q^{93} - 608 q^{99}+O(q^{100}) $ 32 * q - 32 * q^11 + 32 * q^19 + 128 * q^23 + 96 * q^27 + 32 * q^29 - 96 * q^37 - 384 * q^39 - 96 * q^43 + 224 * q^49 + 256 * q^51 - 160 * q^53 + 352 * q^59 - 32 * q^61 - 160 * q^67 + 96 * q^69 - 256 * q^71 + 224 * q^77 - 288 * q^81 + 480 * q^83 + 160 * q^85 + 384 * q^91 + 96 * q^93 - 608 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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			0
$2$		0			0
$3$	1.39844	−	1.39844i	0.466148	−	0.466148i	−0.434516	−	0.900664i	$-0.643081\pi$
$3$	1.39844	−	1.39844i	0.466148	−	0.466148i	0.900664	+	0.434516i	$0.143081\pi$
$4$		0			0
$5$	−1.58114	+	1.58114i	−0.316228	+	0.316228i
$5$	−1.58114	+	1.58114i	−0.316228	+	0.316228i
$6$		0			0
$7$	−9.44746			−1.34964			−0.674818	−	0.737984i	$-0.735778\pi$
$7$	−9.44746			−1.34964			−0.674818	+	0.737984i	$0.735778\pi$
$8$		0			0
$9$			5.08871i			0.565412i
$10$		0			0
$11$	7.42460	+	7.42460i	0.674964	+	0.674964i	0.958856	−	0.283893i	$-0.0916259\pi$
$11$	7.42460	+	7.42460i	0.674964	+	0.674964i	−0.283893	+	0.958856i	$0.591626\pi$
$12$		0			0
$13$	−16.5749	−	16.5749i	−1.27499	−	1.27499i	−0.943434	−	0.331560i	$-0.892425\pi$
$13$	−16.5749	−	16.5749i	−1.27499	−	1.27499i	−0.331560	−	0.943434i	$-0.607575\pi$
$14$		0			0
$15$			4.42227i			0.294818i
$16$		0			0
$17$	−16.9526			−0.997214			−0.498607	−	0.866828i	$-0.666155\pi$
$17$	−16.9526			−0.997214			−0.498607	+	0.866828i	$0.666155\pi$
$18$		0			0
$19$	−23.4305	+	23.4305i	−1.23318	+	1.23318i	−0.270449	+	0.962734i	$0.587172\pi$
$19$	−23.4305	+	23.4305i	−1.23318	+	1.23318i	−0.962734	+	0.270449i	$0.912828\pi$
$20$		0			0
$21$	−13.2117	+	13.2117i	−0.629130	+	0.629130i
$22$		0			0
$23$	0.786593			0.0341997			0.0170998	−	0.999854i	$-0.494557\pi$
$23$	0.786593			0.0341997			0.0170998	+	0.999854i	$0.494557\pi$
$24$		0			0
$25$		−	5.00000i		−	0.200000i
$26$		0			0
$27$	19.7023	+	19.7023i	0.729714	+	0.729714i
$28$		0			0
$29$	17.6103	+	17.6103i	0.607251	+	0.607251i	0.942227	−	0.334976i	$-0.108728\pi$
$29$	17.6103	+	17.6103i	0.607251	+	0.607251i	−0.334976	+	0.942227i	$0.608728\pi$
$30$		0			0
$31$		−	23.5050i		−	0.758227i	−0.925350	−	0.379113i	$-0.876229\pi$
$31$		−	23.5050i		−	0.758227i	0.925350	−	0.379113i	$-0.123771\pi$
$32$		0			0
$33$	20.7658			0.629266
$34$		0			0
$35$	14.9377	−	14.9377i	0.426793	−	0.426793i
$36$		0			0
$37$	−25.6902	+	25.6902i	−0.694330	+	0.694330i	−0.963182	−	0.268852i	$-0.913356\pi$
$37$	−25.6902	+	25.6902i	−0.694330	+	0.694330i	0.268852	+	0.963182i	$0.413356\pi$
$38$		0			0
$39$	−46.3582			−1.18867
$40$		0			0
$41$		−	19.6072i		−	0.478225i	−0.970992	−	0.239112i	$-0.923144\pi$
$41$		−	19.6072i		−	0.478225i	0.970992	−	0.239112i	$-0.0768564\pi$
$42$		0			0
$43$	5.42827	+	5.42827i	0.126239	+	0.126239i	0.767403	−	0.641165i	$-0.221548\pi$
$43$	5.42827	+	5.42827i	0.126239	+	0.126239i	−0.641165	+	0.767403i	$0.721548\pi$
$44$		0			0
$45$	−8.04596	−	8.04596i	−0.178799	−	0.178799i
$46$		0			0
$47$		−	3.62387i		−	0.0771037i	−0.999257	−	0.0385518i	$-0.987726\pi$
$47$		−	3.62387i		−	0.0771037i	0.999257	−	0.0385518i	$-0.0122745\pi$
$48$		0			0
$49$	40.2544			0.821519
$50$		0			0
$51$	−23.7073	+	23.7073i	−0.464849	+	0.464849i
$52$		0			0
$53$	−40.5183	+	40.5183i	−0.764496	+	0.764496i	−0.977132	−	0.212636i	$-0.931795\pi$
$53$	−40.5183	+	40.5183i	−0.764496	+	0.764496i	0.212636	+	0.977132i	$0.431795\pi$
$54$		0			0
$55$	−23.4786			−0.426884
$56$		0			0
$57$			65.5324i			1.14969i
$58$		0			0
$59$	−24.1706	−	24.1706i	−0.409672	−	0.409672i	0.471952	−	0.881624i	$-0.343549\pi$
$59$	−24.1706	−	24.1706i	−0.409672	−	0.409672i	−0.881624	+	0.471952i	$0.843549\pi$
$60$		0			0
$61$	39.1534	+	39.1534i	0.641859	+	0.641859i	0.951012	−	0.309154i	$-0.100046\pi$
$61$	39.1534	+	39.1534i	0.641859	+	0.641859i	−0.309154	+	0.951012i	$0.600046\pi$
$62$		0			0
$63$		−	48.0754i		−	0.763101i
$64$		0			0
$65$	52.4145			0.806377
$66$		0			0
$67$	−24.6093	+	24.6093i	−0.367302	+	0.367302i	−0.866493	−	0.499190i	$-0.833631\pi$
$67$	−24.6093	+	24.6093i	−0.367302	+	0.367302i	0.499190	+	0.866493i	$0.333631\pi$
$68$		0			0
$69$	1.10001	−	1.10001i	0.0159421	−	0.0159421i
$70$		0			0
$71$	−12.9337			−0.182165			−0.0910826	−	0.995843i	$-0.529033\pi$
$71$	−12.9337			−0.182165			−0.0910826	+	0.995843i	$0.529033\pi$
$72$		0			0
$73$		−	97.1658i		−	1.33104i	−0.746381	−	0.665519i	$-0.768210\pi$
$73$		−	97.1658i		−	1.33104i	0.746381	−	0.665519i	$-0.231790\pi$
$74$		0			0
$75$	−6.99222	−	6.99222i	−0.0932296	−	0.0932296i
$76$		0			0
$77$	−70.1436	−	70.1436i	−0.910955	−	0.910955i
$78$		0			0
$79$		−	54.5533i		−	0.690548i	−0.938502	−	0.345274i	$-0.887786\pi$
$79$		−	54.5533i		−	0.690548i	0.938502	−	0.345274i	$-0.112214\pi$
$80$		0			0
$81$	9.30664			0.114897
$82$		0			0
$83$	70.0367	−	70.0367i	0.843816	−	0.843816i	−0.145537	−	0.989353i	$-0.546491\pi$
$83$	70.0367	−	70.0367i	0.843816	−	0.843816i	0.989353	+	0.145537i	$0.0464910\pi$
$84$		0			0
$85$	26.8045	−	26.8045i	0.315347	−	0.315347i
$86$		0			0
$87$	49.2539			0.566137
$88$		0			0
$89$		−	95.6831i		−	1.07509i	−0.843235	−	0.537545i	$-0.819352\pi$
$89$		−	95.6831i		−	1.07509i	0.843235	−	0.537545i	$-0.180648\pi$
$90$		0			0
$91$	156.591	+	156.591i	1.72078	+	1.72078i
$92$		0			0
$93$	−32.8705	−	32.8705i	−0.353446	−	0.353446i
$94$		0			0
$95$		−	74.0937i		−	0.779934i
$96$		0			0
$97$	97.1512			1.00156			0.500779	−	0.865575i	$-0.333047\pi$
$97$	97.1512			1.00156			0.500779	+	0.865575i	$0.333047\pi$
$98$		0			0
$99$	−37.7816	+	37.7816i	−0.381633	+	0.381633i
$100$		0			0
$101$	−104.137	+	104.137i	−1.03106	+	1.03106i	−0.0315573	+	0.999502i	$0.510047\pi$
$101$	−104.137	+	104.137i	−1.03106	+	1.03106i	−0.999502	+	0.0315573i	$0.989953\pi$
$102$		0			0
$103$	103.860			1.00835			0.504175	−	0.863601i	$-0.331797\pi$
$103$	103.860			1.00835			0.504175	+	0.863601i	$0.331797\pi$
$104$		0			0
$105$		−	41.7792i		−	0.397897i
$106$		0			0
$107$	−41.7712	−	41.7712i	−0.390385	−	0.390385i	0.484439	−	0.874825i	$-0.339024\pi$
$107$	−41.7712	−	41.7712i	−0.390385	−	0.390385i	−0.874825	+	0.484439i	$0.839024\pi$
$108$		0			0
$109$	51.8414	+	51.8414i	0.475609	+	0.475609i	0.903724	−	0.428115i	$-0.140822\pi$
$109$	51.8414	+	51.8414i	0.475609	+	0.475609i	−0.428115	+	0.903724i	$0.640822\pi$
$110$		0			0
$111$			71.8526i			0.647321i
$112$		0			0
$113$	−83.2821			−0.737010			−0.368505	−	0.929626i	$-0.620130\pi$
$113$	−83.2821			−0.737010			−0.368505	+	0.929626i	$0.620130\pi$
$114$		0			0
$115$	−1.24371	+	1.24371i	−0.0108149	+	0.0108149i
$116$		0			0
$117$	84.3450	−	84.3450i	0.720897	−	0.720897i
$118$		0			0
$119$	160.159			1.34588
$120$		0			0
$121$		−	10.7507i		−	0.0888485i
$122$		0			0
$123$	−27.4196	−	27.4196i	−0.222923	−	0.222923i
$124$		0			0
$125$	7.90569	+	7.90569i	0.0632456	+	0.0632456i
$126$		0			0
$127$			174.317i			1.37257i	0.727331	+	0.686287i	$0.240760\pi$
$127$			174.317i			1.37257i	−0.727331	+	0.686287i	$0.759240\pi$
$128$		0			0
$129$	15.1822			0.117692
$130$		0			0
$131$	96.7809	−	96.7809i	0.738785	−	0.738785i	−0.233558	−	0.972343i	$-0.575037\pi$
$131$	96.7809	−	96.7809i	0.738785	−	0.738785i	0.972343	+	0.233558i	$0.0750367\pi$
$132$		0			0
$133$	221.358	−	221.358i	1.66435	−	1.66435i
$134$		0			0
$135$	−62.3040			−0.461511
$136$		0			0
$137$			148.155i			1.08142i	0.841208	+	0.540711i	$0.181845\pi$
$137$			148.155i			1.08142i	−0.841208	+	0.540711i	$0.818155\pi$
$138$		0			0
$139$	6.86586	+	6.86586i	0.0493947	+	0.0493947i	0.731373	−	0.681978i	$-0.238880\pi$
$139$	6.86586	+	6.86586i	0.0493947	+	0.0493947i	−0.681978	+	0.731373i	$0.738880\pi$
$140$		0			0
$141$	−5.06778	−	5.06778i	−0.0359417	−	0.0359417i
$142$		0			0
$143$		−	246.124i		−	1.72115i
$144$		0			0
$145$	−55.6886			−0.384059
$146$		0			0
$147$	56.2935	−	56.2935i	0.382949	−	0.382949i
$148$		0			0
$149$	37.4146	−	37.4146i	0.251104	−	0.251104i	−0.570319	−	0.821423i	$-0.693180\pi$
$149$	37.4146	−	37.4146i	0.251104	−	0.251104i	0.821423	+	0.570319i	$0.193180\pi$
$150$		0			0
$151$	−231.448			−1.53277			−0.766385	−	0.642381i	$-0.777947\pi$
$151$	−231.448			−1.53277			−0.766385	+	0.642381i	$0.777947\pi$
$152$		0			0
$153$		−	86.2671i		−	0.563837i
$154$		0			0
$155$	37.1647	+	37.1647i	0.239772	+	0.239772i
$156$		0			0
$157$	70.9511	+	70.9511i	0.451918	+	0.451918i	0.895991	−	0.444073i	$-0.146467\pi$
$157$	70.9511	+	70.9511i	0.451918	+	0.451918i	−0.444073	+	0.895991i	$0.646467\pi$
$158$		0			0
$159$			113.325i			0.712736i
$160$		0			0
$161$	−7.43130			−0.0461572
$162$		0			0
$163$	7.65938	−	7.65938i	0.0469901	−	0.0469901i	−0.683221	−	0.730211i	$-0.739422\pi$
$163$	7.65938	−	7.65938i	0.0469901	−	0.0469901i	0.730211	+	0.683221i	$0.239422\pi$
$164$		0			0
$165$	−32.8336	+	32.8336i	−0.198991	+	0.198991i
$166$		0			0
$167$	−127.783			−0.765168			−0.382584	−	0.923921i	$-0.624966\pi$
$167$	−127.783			−0.765168			−0.382584	+	0.923921i	$0.624966\pi$
$168$		0			0
$169$			380.456i			2.25122i
$170$		0			0
$171$	−119.231	−	119.231i	−0.697257	−	0.697257i
$172$		0			0
$173$	11.2542	+	11.2542i	0.0650533	+	0.0650533i	0.738885	−	0.673832i	$-0.235353\pi$
$173$	11.2542	+	11.2542i	0.0650533	+	0.0650533i	−0.673832	+	0.738885i	$0.735353\pi$
$174$		0			0
$175$			47.2373i			0.269927i
$176$		0			0
$177$	−67.6025			−0.381935
$178$		0			0
$179$	−52.6138	+	52.6138i	−0.293932	+	0.293932i	−0.838631	−	0.544699i	$-0.816644\pi$
$179$	−52.6138	+	52.6138i	−0.293932	+	0.293932i	0.544699	+	0.838631i	$0.316644\pi$
$180$		0			0
$181$	−195.966	+	195.966i	−1.08268	+	1.08268i	−0.0864259	+	0.996258i	$0.527545\pi$
$181$	−195.966	+	195.966i	−1.08268	+	1.08268i	−0.996258	+	0.0864259i	$0.972455\pi$
$182$		0			0
$183$	109.508			0.598402
$184$		0			0
$185$		−	81.2396i		−	0.439133i
$186$		0			0
$187$	−125.867	−	125.867i	−0.673083	−	0.673083i
$188$		0			0
$189$	−186.136	−	186.136i	−0.984848	−	0.984848i
$190$		0			0
$191$			268.717i			1.40689i	0.710747	+	0.703447i	$0.248357\pi$
$191$			268.717i			1.40689i	−0.710747	+	0.703447i	$0.751643\pi$
$192$		0			0
$193$	−117.323			−0.607889			−0.303944	−	0.952690i	$-0.598304\pi$
$193$	−117.323			−0.607889			−0.303944	+	0.952690i	$0.598304\pi$
$194$		0			0
$195$	73.2988	−	73.2988i	0.375891	−	0.375891i
$196$		0			0
$197$	172.480	−	172.480i	0.875533	−	0.875533i	−0.117536	−	0.993069i	$-0.537499\pi$
$197$	172.480	−	172.480i	0.875533	−	0.875533i	0.993069	+	0.117536i	$0.0374995\pi$
$198$		0			0
$199$	80.4670			0.404357			0.202178	−	0.979349i	$-0.435198\pi$
$199$	80.4670			0.404357			0.202178	+	0.979349i	$0.435198\pi$
$200$		0			0
$201$			68.8293i			0.342435i
$202$		0			0
$203$	−166.372	−	166.372i	−0.819568	−	0.819568i
$204$		0			0
$205$	31.0017	+	31.0017i	0.151228	+	0.151228i
$206$		0			0
$207$			4.00274i			0.0193369i
$208$		0			0
$209$	−347.924			−1.66471
$210$		0			0
$211$	−192.969	+	192.969i	−0.914547	+	0.914547i	−0.996626	−	0.0820786i	$-0.973844\pi$
$211$	−192.969	+	192.969i	−0.914547	+	0.914547i	0.0820786	+	0.996626i	$0.473844\pi$
$212$		0			0
$213$	−18.0871	+	18.0871i	−0.0849159	+	0.0849159i
$214$		0			0
$215$	−17.1657			−0.0798404
$216$		0			0
$217$			222.063i			1.02333i
$218$		0			0
$219$	−135.881	−	135.881i	−0.620461	−	0.620461i
$220$		0			0
$221$	280.989	+	280.989i	1.27144	+	1.27144i
$222$		0			0
$223$			142.903i			0.640819i	0.947279	+	0.320409i	$0.103820\pi$
$223$			142.903i			0.640819i	−0.947279	+	0.320409i	$0.896180\pi$
$224$		0			0
$225$	25.4435			0.113082
$226$		0			0
$227$	−167.235	+	167.235i	−0.736718	+	0.736718i	−0.971941	−	0.235223i	$-0.924418\pi$
$227$	−167.235	+	167.235i	−0.736718	+	0.736718i	0.235223	+	0.971941i	$0.424418\pi$
$228$		0			0
$229$	53.6086	−	53.6086i	0.234099	−	0.234099i	−0.580302	−	0.814401i	$-0.697066\pi$
$229$	53.6086	−	53.6086i	0.234099	−	0.234099i	0.814401	+	0.580302i	$0.197066\pi$
$230$		0			0
$231$	−196.184			−0.849280
$232$		0			0
$233$		−	66.5869i		−	0.285781i	−0.989739	−	0.142890i	$-0.954360\pi$
$233$		−	66.5869i		−	0.285781i	0.989739	−	0.142890i	$-0.0456397\pi$
$234$		0			0
$235$	5.72985	+	5.72985i	0.0243823	+	0.0243823i
$236$		0			0
$237$	−76.2897	−	76.2897i	−0.321898	−	0.321898i
$238$		0			0
$239$			85.6557i			0.358392i	0.983813	+	0.179196i	$0.0573496\pi$
$239$			85.6557i			0.358392i	−0.983813	+	0.179196i	$0.942650\pi$
$240$		0			0
$241$	107.356			0.445459			0.222730	−	0.974880i	$-0.428503\pi$
$241$	107.356			0.445459			0.222730	+	0.974880i	$0.428503\pi$
$242$		0			0
$243$	−164.306	+	164.306i	−0.676155	+	0.676155i
$244$		0			0
$245$	−63.6478	+	63.6478i	−0.259787	+	0.259787i
$246$		0			0
$247$	776.717			3.14460
$248$		0			0
$249$		−	195.885i		−	0.786686i
$250$		0			0
$251$	246.751	+	246.751i	0.983073	+	0.983073i	0.999859	−	0.0167861i	$-0.00534344\pi$
$251$	246.751	+	246.751i	0.983073	+	0.983073i	−0.0167861	+	0.999859i	$0.505343\pi$
$252$		0			0
$253$	5.84014	+	5.84014i	0.0230835	+	0.0230835i
$254$		0			0
$255$		−	74.9691i		−	0.293997i
$256$		0			0
$257$	−490.849			−1.90992			−0.954959	−	0.296737i	$-0.904102\pi$
$257$	−490.849			−1.90992			−0.954959	+	0.296737i	$0.904102\pi$
$258$		0			0
$259$	242.707	−	242.707i	0.937093	−	0.937093i
$260$		0			0
$261$	−89.6136	+	89.6136i	−0.343347	+	0.343347i
$262$		0			0
$263$	−433.389			−1.64787			−0.823933	−	0.566688i	$-0.808225\pi$
$263$	−433.389			−1.64787			−0.823933	+	0.566688i	$0.808225\pi$
$264$		0			0
$265$		−	128.130i		−	0.483510i
$266$		0			0
$267$	−133.807	−	133.807i	−0.501151	−	0.501151i
$268$		0			0
$269$	156.699	+	156.699i	0.582524	+	0.582524i	0.935596	−	0.353072i	$-0.114863\pi$
$269$	156.699	+	156.699i	0.582524	+	0.582524i	−0.353072	+	0.935596i	$0.614863\pi$
$270$		0			0
$271$		−	141.581i		−	0.522439i	−0.965279	−	0.261220i	$-0.915875\pi$
$271$		−	141.581i		−	0.522439i	0.965279	−	0.261220i	$-0.0841247\pi$
$272$		0			0
$273$	437.967			1.60427
$274$		0			0
$275$	37.1230	−	37.1230i	0.134993	−	0.134993i
$276$		0			0
$277$	−76.7118	+	76.7118i	−0.276938	+	0.276938i	−0.831885	−	0.554948i	$-0.812738\pi$
$277$	−76.7118	+	76.7118i	−0.276938	+	0.276938i	0.554948	+	0.831885i	$0.312738\pi$
$278$		0			0
$279$	119.610			0.428711
$280$		0			0
$281$		−	358.740i		−	1.27665i	−0.769765	−	0.638327i	$-0.779627\pi$
$281$		−	358.740i		−	1.27665i	0.769765	−	0.638327i	$-0.220373\pi$
$282$		0			0
$283$	−90.5456	−	90.5456i	−0.319949	−	0.319949i	0.528798	−	0.848747i	$-0.322643\pi$
$283$	−90.5456	−	90.5456i	−0.319949	−	0.319949i	−0.848747	+	0.528798i	$0.822643\pi$
$284$		0			0
$285$	−103.616	−	103.616i	−0.363564	−	0.363564i
$286$		0			0
$287$			185.238i			0.645429i
$288$		0			0
$289$	−1.60798			−0.00556396
$290$		0			0
$291$	135.860	−	135.860i	0.466875	−	0.466875i
$292$		0			0
$293$	116.194	−	116.194i	0.396566	−	0.396566i	−0.480454	−	0.877020i	$-0.659528\pi$
$293$	116.194	−	116.194i	0.396566	−	0.396566i	0.877020	+	0.480454i	$0.159528\pi$
$294$		0			0
$295$	76.4343			0.259099
$296$		0			0
$297$			292.563i			0.985060i
$298$		0			0
$299$	−13.0377	−	13.0377i	−0.0436044	−	0.0436044i
$300$		0			0
$301$	−51.2833	−	51.2833i	−0.170376	−	0.170376i
$302$		0			0
$303$			291.259i			0.961252i
$304$		0			0
$305$	−123.814			−0.405947
$306$		0			0
$307$	−247.496	+	247.496i	−0.806177	+	0.806177i	−0.984053	−	0.177876i	$-0.943077\pi$
$307$	−247.496	+	247.496i	−0.806177	+	0.806177i	0.177876	+	0.984053i	$0.443077\pi$
$308$		0			0
$309$	145.243	−	145.243i	0.470040	−	0.470040i
$310$		0			0
$311$	−303.903			−0.977180			−0.488590	−	0.872513i	$-0.662489\pi$
$311$	−303.903			−0.977180			−0.488590	+	0.872513i	$0.662489\pi$
$312$		0			0
$313$			580.777i			1.85552i	0.373180	+	0.927759i	$0.378268\pi$
$313$			580.777i			1.85552i	−0.373180	+	0.927759i	$0.621732\pi$
$314$		0			0
$315$	76.0138	+	76.0138i	0.241314	+	0.241314i
$316$		0			0
$317$	−191.079	−	191.079i	−0.602774	−	0.602774i	0.338274	−	0.941048i	$-0.390157\pi$
$317$	−191.079	−	191.079i	−0.602774	−	0.602774i	−0.941048	+	0.338274i	$0.890157\pi$
$318$		0			0
$319$			261.498i			0.819744i
$320$		0			0
$321$	−116.829			−0.363955
$322$		0			0
$323$	397.209	−	397.209i	1.22975	−	1.22975i
$324$		0			0
$325$	−82.8746	+	82.8746i	−0.254999	+	0.254999i
$326$		0			0
$327$	144.995			0.443409
$328$		0			0
$329$			34.2364i			0.104062i
$330$		0			0
$331$	264.645	+	264.645i	0.799531	+	0.799531i	0.983022	−	0.183490i	$-0.0587396\pi$
$331$	264.645	+	264.645i	0.799531	+	0.799531i	−0.183490	+	0.983022i	$0.558740\pi$
$332$		0			0
$333$	−130.730	−	130.730i	−0.392583	−	0.392583i
$334$		0			0
$335$		−	77.8213i		−	0.232302i
$336$		0			0
$337$	290.873			0.863124			0.431562	−	0.902083i	$-0.357963\pi$
$337$	290.873			0.863124			0.431562	+	0.902083i	$0.357963\pi$
$338$		0			0
$339$	−116.465	+	116.465i	−0.343556	+	0.343556i
$340$		0			0
$341$	174.515	−	174.515i	0.511776	−	0.511776i
$342$		0			0
$343$	82.6235			0.240885
$344$		0			0
$345$			3.47852i			0.0100827i
$346$		0			0
$347$	−33.3752	−	33.3752i	−0.0961820	−	0.0961820i	0.657379	−	0.753561i	$-0.271665\pi$
$347$	−33.3752	−	33.3752i	−0.0961820	−	0.0961820i	−0.753561	+	0.657379i	$0.771665\pi$
$348$		0			0
$349$	−266.420	−	266.420i	−0.763382	−	0.763382i	0.213550	−	0.976932i	$-0.431497\pi$
$349$	−266.420	−	266.420i	−0.763382	−	0.763382i	−0.976932	+	0.213550i	$0.931497\pi$
$350$		0			0
$351$		−	653.127i		−	1.86076i
$352$		0			0
$353$	206.876			0.586051			0.293026	−	0.956105i	$-0.405338\pi$
$353$	206.876			0.586051			0.293026	+	0.956105i	$0.405338\pi$
$354$		0			0
$355$	20.4500	−	20.4500i	0.0576057	−	0.0576057i
$356$		0			0
$357$	223.974	−	223.974i	0.627378	−	0.627378i
$358$		0			0
$359$	−2.31695			−0.00645391			−0.00322695	−	0.999995i	$-0.501027\pi$
$359$	−2.31695			−0.00645391			−0.00322695	+	0.999995i	$0.501027\pi$
$360$		0			0
$361$		−	736.975i		−	2.04148i
$362$		0			0
$363$	−15.0342	−	15.0342i	−0.0414165	−	0.0414165i
$364$		0			0
$365$	153.633	+	153.633i	0.420911	+	0.420911i
$366$		0			0
$367$		−	480.218i		−	1.30850i	−0.756280	−	0.654248i	$-0.772985\pi$
$367$		−	480.218i		−	1.30850i	0.756280	−	0.654248i	$-0.227015\pi$
$368$		0			0
$369$	99.7754			0.270394
$370$		0			0
$371$	382.795	−	382.795i	1.03179	−	1.03179i
$372$		0			0
$373$	−131.035	+	131.035i	−0.351300	+	0.351300i	−0.860593	−	0.509293i	$-0.829907\pi$
$373$	−131.035	+	131.035i	−0.351300	+	0.351300i	0.509293	+	0.860593i	$0.329907\pi$
$374$		0			0
$375$	22.1113			0.0589636
$376$		0			0
$377$		−	583.778i		−	1.54848i
$378$		0			0
$379$	298.411	+	298.411i	0.787364	+	0.787364i	0.981061	−	0.193698i	$-0.0620481\pi$
$379$	298.411	+	298.411i	0.787364	+	0.787364i	−0.193698	+	0.981061i	$0.562048\pi$
$380$		0			0
$381$	243.772	+	243.772i	0.639822	+	0.639822i
$382$		0			0
$383$			71.3554i			0.186306i	0.995652	+	0.0931532i	$0.0296946\pi$
$383$			71.3554i			0.186306i	−0.995652	+	0.0931532i	$0.970305\pi$
$384$		0			0
$385$	221.813			0.576139
$386$		0			0
$387$	−27.6229	+	27.6229i	−0.0713769	+	0.0713769i
$388$		0			0
$389$	−256.984	+	256.984i	−0.660627	+	0.660627i	−0.955528	−	0.294901i	$-0.904713\pi$
$389$	−256.984	+	256.984i	−0.660627	+	0.660627i	0.294901	+	0.955528i	$0.404713\pi$
$390$		0			0
$391$	−13.3348			−0.0341044
$392$		0			0
$393$		−	270.685i		−	0.688767i
$394$		0			0
$395$	86.2564	+	86.2564i	0.218371	+	0.218371i
$396$		0			0
$397$	387.935	+	387.935i	0.977166	+	0.977166i	0.999745	−	0.0225786i	$-0.00718760\pi$
$397$	387.935	+	387.935i	0.977166	+	0.977166i	−0.0225786	+	0.999745i	$0.507188\pi$
$398$		0			0
$399$		−	619.115i		−	1.55167i
$400$		0			0
$401$	207.256			0.516847			0.258424	−	0.966032i	$-0.416797\pi$
$401$	207.256			0.516847			0.258424	+	0.966032i	$0.416797\pi$
$402$		0			0
$403$	−389.594	+	389.594i	−0.966735	+	0.966735i
$404$		0			0
$405$	−14.7151	+	14.7151i	−0.0363336	+	0.0363336i
$406$		0			0
$407$	−381.479			−0.937295
$408$		0			0
$409$			665.750i			1.62775i	0.581039	+	0.813875i	$0.302646\pi$
$409$			665.750i			1.62775i	−0.581039	+	0.813875i	$0.697354\pi$
$410$		0			0
$411$	207.186	+	207.186i	0.504103	+	0.504103i
$412$		0			0
$413$	228.351	+	228.351i	0.552908	+	0.552908i
$414$		0			0
$415$			221.476i			0.533676i
$416$		0			0
$417$	19.2031			0.0460505
$418$		0			0
$419$	6.76675	−	6.76675i	0.0161498	−	0.0161498i	−0.698986	−	0.715136i	$-0.746365\pi$
$419$	6.76675	−	6.76675i	0.0161498	−	0.0161498i	0.715136	+	0.698986i	$0.246365\pi$
$420$		0			0
$421$	−78.0758	+	78.0758i	−0.185453	+	0.185453i	−0.793727	−	0.608274i	$-0.791862\pi$
$421$	−78.0758	+	78.0758i	−0.185453	+	0.185453i	0.608274	+	0.793727i	$0.291862\pi$
$422$		0			0
$423$	18.4408			0.0435954
$424$		0			0
$425$			84.7632i			0.199443i
$426$		0			0
$427$	−369.900	−	369.900i	−0.866276	−	0.866276i
$428$		0			0
$429$	−344.191	−	344.191i	−0.802310	−	0.802310i
$430$		0			0
$431$		−	611.541i		−	1.41889i	−0.704762	−	0.709444i	$-0.748946\pi$
$431$		−	611.541i		−	1.41889i	0.704762	−	0.709444i	$-0.251054\pi$
$432$		0			0
$433$	−134.105			−0.309711			−0.154855	−	0.987937i	$-0.549491\pi$
$433$	−134.105			−0.309711			−0.154855	+	0.987937i	$0.549491\pi$
$434$		0			0
$435$	−77.8773	+	77.8773i	−0.179028	+	0.179028i
$436$		0			0
$437$	−18.4303	+	18.4303i	−0.0421745	+	0.0421745i
$438$		0			0
$439$	−213.213			−0.485679			−0.242840	−	0.970066i	$-0.578079\pi$
$439$	−213.213			−0.485679			−0.242840	+	0.970066i	$0.578079\pi$
$440$		0			0
$441$			204.843i			0.464497i
$442$		0			0
$443$	408.029	+	408.029i	0.921060	+	0.921060i	0.997104	−	0.0760447i	$-0.0242292\pi$
$443$	408.029	+	408.029i	0.921060	+	0.921060i	−0.0760447	+	0.997104i	$0.524229\pi$
$444$		0			0
$445$	151.288	+	151.288i	0.339973	+	0.339973i
$446$		0			0
$447$		−	104.644i		−	0.234104i
$448$		0			0
$449$	835.151			1.86002			0.930012	−	0.367529i	$-0.119796\pi$
$449$	835.151			1.86002			0.930012	+	0.367529i	$0.119796\pi$
$450$		0			0
$451$	145.576	−	145.576i	0.322784	−	0.322784i
$452$		0			0
$453$	−323.667	+	323.667i	−0.714498	+	0.714498i
$454$		0			0
$455$	−495.184			−1.08832
$456$		0			0
$457$			134.397i			0.294086i	0.989130	+	0.147043i	$0.0469756\pi$
$457$			134.397i			0.294086i	−0.989130	+	0.147043i	$0.953024\pi$
$458$		0			0
$459$	−334.005	−	334.005i	−0.727681	−	0.727681i
$460$		0			0
$461$	−289.089	−	289.089i	−0.627091	−	0.627091i	0.320244	−	0.947335i	$-0.396235\pi$
$461$	−289.089	−	289.089i	−0.627091	−	0.627091i	−0.947335	+	0.320244i	$0.896235\pi$
$462$		0			0
$463$		−	394.123i		−	0.851238i	−0.904903	−	0.425619i	$-0.860056\pi$
$463$		−	394.123i		−	0.851238i	0.904903	−	0.425619i	$-0.139944\pi$
$464$		0			0
$465$	103.946			0.223539
$466$		0			0
$467$	35.3871	−	35.3871i	0.0757754	−	0.0757754i	−0.668203	−	0.743979i	$-0.732936\pi$
$467$	35.3871	−	35.3871i	0.0757754	−	0.0757754i	0.743979	+	0.668203i	$0.232936\pi$
$468$		0			0
$469$	232.495	−	232.495i	0.495725	−	0.495725i
$470$		0			0
$471$	198.442			0.421321
$472$		0			0
$473$			80.6054i			0.170413i
$474$		0			0
$475$	117.152	+	117.152i	0.246637	+	0.246637i
$476$		0			0
$477$	−206.186	−	206.186i	−0.432255	−	0.432255i
$478$		0			0
$479$			235.611i			0.491880i	0.969285	+	0.245940i	$0.0790967\pi$
$479$			235.611i			0.491880i	−0.969285	+	0.245940i	$0.920903\pi$
$480$		0			0
$481$	851.627			1.77053
$482$		0			0
$483$	−10.3923	+	10.3923i	−0.0215161	+	0.0215161i
$484$		0			0
$485$	−153.610	+	153.610i	−0.316721	+	0.316721i
$486$		0			0
$487$	299.364			0.614710			0.307355	−	0.951595i	$-0.400556\pi$
$487$	299.364			0.614710			0.307355	+	0.951595i	$0.400556\pi$
$488$		0			0
$489$		−	21.4224i		−	0.0438086i
$490$		0			0
$491$	−319.571	−	319.571i	−0.650857	−	0.650857i	0.302342	−	0.953200i	$-0.402232\pi$
$491$	−319.571	−	319.571i	−0.650857	−	0.650857i	−0.953200	+	0.302342i	$0.902232\pi$
$492$		0			0
$493$	−298.541	−	298.541i	−0.605559	−	0.605559i
$494$		0			0
$495$		−	119.476i		−	0.241366i
$496$		0			0
$497$	122.191			0.245857
$498$		0			0
$499$	−194.846	+	194.846i	−0.390473	+	0.390473i	−0.874856	−	0.484383i	$-0.839044\pi$
$499$	−194.846	+	194.846i	−0.390473	+	0.390473i	0.484383	+	0.874856i	$0.339044\pi$
$500$		0			0
$501$	−178.697	+	178.697i	−0.356682	+	0.356682i
$502$		0			0
$503$	543.099			1.07972			0.539860	−	0.841755i	$-0.318477\pi$
$503$	543.099			1.07972			0.539860	+	0.841755i	$0.318477\pi$
$504$		0			0
$505$		−	329.310i		−	0.652099i
$506$		0			0
$507$	532.047	+	532.047i	1.04940	+	1.04940i
$508$		0			0
$509$	179.627	+	179.627i	0.352902	+	0.352902i	0.861188	−	0.508287i	$-0.169721\pi$
$509$	179.627	+	179.627i	0.352902	+	0.352902i	−0.508287	+	0.861188i	$0.669721\pi$
$510$		0			0
$511$			917.970i			1.79642i
$512$		0			0
$513$	−923.267			−1.79974
$514$		0			0
$515$	−164.217	+	164.217i	−0.318868	+	0.318868i
$516$		0			0
$517$	26.9058	−	26.9058i	0.0520422	−	0.0520422i
$518$		0			0
$519$	31.4768			0.0606489
$520$		0			0
$521$		−	947.587i		−	1.81878i	−0.415940	−	0.909392i	$-0.636547\pi$
$521$		−	947.587i		−	1.81878i	0.415940	−	0.909392i	$-0.363453\pi$
$522$		0			0
$523$	698.258	+	698.258i	1.33510	+	1.33510i	0.900737	+	0.434366i	$0.143027\pi$
$523$	698.258	+	698.258i	1.33510	+	1.33510i	0.434366	+	0.900737i	$0.356973\pi$
$524$		0			0
$525$	66.0587	+	66.0587i	0.125826	+	0.125826i
$526$		0			0
$527$			398.472i			0.756115i
$528$		0			0
$529$	−528.381			−0.998830
$530$		0			0
$531$	122.997	−	122.997i	0.231633	−	0.231633i
$532$		0			0
$533$	−324.988	+	324.988i	−0.609734	+	0.609734i
$534$		0			0
$535$	132.092			0.246901
$536$		0			0
$537$			147.155i			0.274032i
$538$		0			0
$539$	298.873	+	298.873i	0.554495	+	0.554495i
$540$		0			0
$541$	−537.443	−	537.443i	−0.993425	−	0.993425i	0.00655365	−	0.999979i	$-0.497914\pi$
$541$	−537.443	−	537.443i	−0.993425	−	0.993425i	−0.999979	+	0.00655365i	$0.997914\pi$
$542$		0			0
$543$			548.094i			1.00938i
$544$		0			0
$545$	−163.937			−0.300802
$546$		0			0
$547$	304.402	−	304.402i	0.556493	−	0.556493i	−0.371814	−	0.928307i	$-0.621264\pi$
$547$	304.402	−	304.402i	0.556493	−	0.556493i	0.928307	+	0.371814i	$0.121264\pi$
$548$		0			0
$549$	−199.240	+	199.240i	−0.362915	+	0.362915i
$550$		0			0
$551$	−825.234			−1.49770
$552$		0			0
$553$			515.390i			0.931989i
$554$		0			0
$555$	−113.609	−	113.609i	−0.204701	−	0.204701i
$556$		0			0
$557$	−138.676	−	138.676i	−0.248969	−	0.248969i	0.571578	−	0.820548i	$-0.306331\pi$
$557$	−138.676	−	138.676i	−0.248969	−	0.248969i	−0.820548	+	0.571578i	$0.806331\pi$
$558$		0			0
$559$		−	179.946i		−	0.321907i
$560$		0			0
$561$	−352.035			−0.627513
$562$		0			0
$563$	−526.491	+	526.491i	−0.935152	+	0.935152i	−0.998022	−	0.0628694i	$-0.979975\pi$
$563$	−526.491	+	526.491i	−0.935152	+	0.935152i	0.0628694	+	0.998022i	$0.479975\pi$
$564$		0			0
$565$	131.681	−	131.681i	0.233063	−	0.233063i
$566$		0			0
$567$	−87.9241			−0.155069
$568$		0			0
$569$		−	980.294i		−	1.72284i	−0.507896	−	0.861418i	$-0.669577\pi$
$569$		−	980.294i		−	1.72284i	0.507896	−	0.861418i	$-0.330423\pi$
$570$		0			0
$571$	−363.399	−	363.399i	−0.636425	−	0.636425i	0.313246	−	0.949672i	$-0.398583\pi$
$571$	−363.399	−	363.399i	−0.636425	−	0.636425i	−0.949672	+	0.313246i	$0.898583\pi$
$572$		0			0
$573$	375.785	+	375.785i	0.655821	+	0.655821i
$574$		0			0
$575$		−	3.93296i		−	0.00683994i
$576$		0			0
$577$	−91.7574			−0.159025			−0.0795125	−	0.996834i	$-0.525336\pi$
$577$	−91.7574			−0.159025			−0.0795125	+	0.996834i	$0.525336\pi$
$578$		0			0
$579$	−164.069	+	164.069i	−0.283366	+	0.283366i
$580$		0			0
$581$	−661.669	+	661.669i	−1.13884	+	1.13884i
$582$		0			0
$583$	−601.664			−1.03201
$584$		0			0
$585$			266.722i			0.455936i
$586$		0			0
$587$	−463.359	−	463.359i	−0.789368	−	0.789368i	0.192023	−	0.981390i	$-0.438495\pi$
$587$	−463.359	−	463.359i	−0.789368	−	0.789368i	−0.981390	+	0.192023i	$0.938495\pi$
$588$		0			0
$589$	550.734	+	550.734i	0.935033	+	0.935033i
$590$		0			0
$591$		−	482.407i		−	0.816256i
$592$		0			0
$593$	−485.015			−0.817900			−0.408950	−	0.912557i	$-0.634105\pi$
$593$	−485.015			−0.817900			−0.408950	+	0.912557i	$0.634105\pi$
$594$		0			0
$595$	−253.234	+	253.234i	−0.425604	+	0.425604i
$596$		0			0
$597$	112.529	−	112.529i	0.188490	−	0.188490i
$598$		0			0
$599$	73.5740			0.122828			0.0614140	−	0.998112i	$-0.480439\pi$
$599$	73.5740			0.122828			0.0614140	+	0.998112i	$0.480439\pi$
$600$		0			0
$601$			528.447i			0.879279i	0.898174	+	0.439639i	$0.144894\pi$
$601$			528.447i			0.879279i	−0.898174	+	0.439639i	$0.855106\pi$
$602$		0			0
$603$	−125.229	−	125.229i	−0.207677	−	0.207677i
$604$		0			0
$605$	16.9983	+	16.9983i	0.0280964	+	0.0280964i
$606$		0			0
$607$		−	476.934i		−	0.785723i	−0.919598	−	0.392862i	$-0.871485\pi$
$607$		−	476.934i		−	0.785723i	0.919598	−	0.392862i	$-0.128515\pi$
$608$		0			0
$609$	−465.324			−0.764080
$610$		0			0
$611$	−60.0654	+	60.0654i	−0.0983068	+	0.0983068i
$612$		0			0
$613$	−374.073	+	374.073i	−0.610233	+	0.610233i	−0.943007	−	0.332774i	$-0.892015\pi$
$613$	−374.073	+	374.073i	−0.610233	+	0.610233i	0.332774	+	0.943007i	$0.392015\pi$
$614$		0			0
$615$	86.7083			0.140989
$616$		0			0
$617$		−	66.9578i		−	0.108522i	−0.998527	−	0.0542608i	$-0.982720\pi$
$617$		−	66.9578i		−	0.108522i	0.998527	−	0.0542608i	$-0.0172802\pi$
$618$		0			0
$619$	−744.224	−	744.224i	−1.20230	−	1.20230i	−0.973465	−	0.228836i	$-0.926508\pi$
$619$	−744.224	−	744.224i	−1.20230	−	1.20230i	−0.228836	−	0.973465i	$-0.573492\pi$
$620$		0			0
$621$	15.4977	+	15.4977i	0.0249560	+	0.0249560i
$622$		0			0
$623$			903.961i			1.45098i
$624$		0			0
$625$	−25.0000			−0.0400000
$626$		0			0
$627$	−486.552	+	486.552i	−0.776000	+	0.776000i
$628$		0			0
$629$	435.517	−	435.517i	0.692396	−	0.692396i
$630$		0			0
$631$	799.274			1.26668			0.633339	−	0.773874i	$-0.281684\pi$
$631$	799.274			1.26668			0.633339	+	0.773874i	$0.281684\pi$
$632$		0			0
$633$			539.714i			0.852629i
$634$		0			0
$635$	−275.619	−	275.619i	−0.434046	−	0.434046i
$636$		0			0
$637$	−667.214	−	667.214i	−1.04743	−	1.04743i
$638$		0			0
$639$		−	65.8160i		−	0.102998i
$640$		0			0
$641$	−674.264			−1.05189			−0.525947	−	0.850517i	$-0.676289\pi$
$641$	−674.264			−1.05189			−0.525947	+	0.850517i	$0.676289\pi$
$642$		0			0
$643$	−118.699	+	118.699i	−0.184601	+	0.184601i	−0.793357	−	0.608756i	$-0.791669\pi$
$643$	−118.699	+	118.699i	−0.184601	+	0.184601i	0.608756	+	0.793357i	$0.291669\pi$
$644$		0			0
$645$	−24.0052	+	24.0052i	−0.0372174	+	0.0372174i
$646$		0			0
$647$	−194.792			−0.301070			−0.150535	−	0.988605i	$-0.548100\pi$
$647$	−194.792			−0.301070			−0.150535	+	0.988605i	$0.548100\pi$
$648$		0			0
$649$		−	358.915i		−	0.553027i
$650$		0			0
$651$	310.542	+	310.542i	0.477024	+	0.477024i
$652$		0			0
$653$	659.224	+	659.224i	1.00953	+	1.00953i	0.999954	+	0.00957734i	$0.00304861\pi$
$653$	659.224	+	659.224i	1.00953	+	1.00953i	0.00957734	+	0.999954i	$0.496951\pi$
$654$		0			0
$655$			306.048i			0.467249i
$656$		0			0
$657$	494.449			0.752585
$658$		0			0
$659$	422.163	−	422.163i	0.640612	−	0.640612i	−0.310094	−	0.950706i	$-0.600361\pi$
$659$	422.163	−	422.163i	0.640612	−	0.640612i	0.950706	+	0.310094i	$0.100361\pi$
$660$		0			0
$661$	695.502	−	695.502i	1.05220	−	1.05220i	0.0536363	−	0.998561i	$-0.482919\pi$
$661$	695.502	−	695.502i	1.05220	−	1.05220i	0.998561	−	0.0536363i	$-0.0170812\pi$
$662$		0			0
$663$	785.894			1.18536
$664$		0			0
$665$			699.997i			1.05263i
$666$		0			0
$667$	13.8521	+	13.8521i	0.0207678	+	0.0207678i
$668$		0			0
$669$	199.841	+	199.841i	0.298716	+	0.298716i
$670$		0			0
$671$			581.396i			0.866462i
$672$		0			0
$673$	577.294			0.857791			0.428896	−	0.903354i	$-0.358903\pi$
$673$	577.294			0.857791			0.428896	+	0.903354i	$0.358903\pi$
$674$		0			0
$675$	98.5113	−	98.5113i	0.145943	−	0.145943i
$676$		0			0
$677$	79.4876	−	79.4876i	0.117412	−	0.117412i	−0.645960	−	0.763371i	$-0.723543\pi$
$677$	79.4876	−	79.4876i	0.117412	−	0.117412i	0.763371	+	0.645960i	$0.223543\pi$
$678$		0			0
$679$	−917.832			−1.35174
$680$		0			0
$681$			467.737i			0.686839i
$682$		0			0
$683$	−311.838	−	311.838i	−0.456571	−	0.456571i	0.440957	−	0.897528i	$-0.354639\pi$
$683$	−311.838	−	311.838i	−0.456571	−	0.456571i	−0.897528	+	0.440957i	$0.854639\pi$
$684$		0			0
$685$	−234.253	−	234.253i	−0.341976	−	0.341976i
$686$		0			0
$687$		−	149.937i		−	0.218249i
$688$		0			0
$689$	1343.17			1.94946
$690$		0			0
$691$	132.258	−	132.258i	0.191401	−	0.191401i	−0.604900	−	0.796301i	$-0.706787\pi$
$691$	132.258	−	132.258i	0.191401	−	0.191401i	0.796301	+	0.604900i	$0.206787\pi$
$692$		0			0
$693$	356.940	−	356.940i	0.515065	−	0.515065i
$694$		0			0
$695$	−21.7118			−0.0312400
$696$		0			0
$697$			332.394i			0.476892i
$698$		0			0
$699$	−93.1181	−	93.1181i	−0.133216	−	0.133216i
$700$		0			0
$701$	194.341	+	194.341i	0.277234	+	0.277234i	0.832004	−	0.554770i	$-0.187194\pi$
$701$	194.341	+	194.341i	0.277234	+	0.277234i	−0.554770	+	0.832004i	$0.687194\pi$
$702$		0			0
$703$		−	1203.87i		−	1.71247i
$704$		0			0
$705$	16.0257			0.0227315
$706$		0			0
$707$	983.830	−	983.830i	1.39156	−	1.39156i
$708$		0			0
$709$	360.168	−	360.168i	0.507994	−	0.507994i	−0.405916	−	0.913910i	$-0.633048\pi$
$709$	360.168	−	360.168i	0.507994	−	0.507994i	0.913910	+	0.405916i	$0.133048\pi$
$710$		0			0
$711$	277.606			0.390444
$712$		0			0
$713$		−	18.4889i		−	0.0259311i
$714$		0			0
$715$	389.157	+	389.157i	0.544275	+	0.544275i
$716$		0			0
$717$	119.785	+	119.785i	0.167064	+	0.167064i
$718$		0			0
$719$			578.314i			0.804331i	0.915567	+	0.402165i	$0.131742\pi$
$719$			578.314i			0.804331i	−0.915567	+	0.402165i	$0.868258\pi$
$720$		0			0
$721$	−981.214			−1.36091
$722$		0			0
$723$	150.131	−	150.131i	0.207650	−	0.207650i
$724$		0			0
$725$	88.0514	−	88.0514i	0.121450	−	0.121450i
$726$		0			0
$727$	12.0551			0.0165819			0.00829096	−	0.999966i	$-0.497361\pi$
$727$	12.0551			0.0165819			0.00829096	+	0.999966i	$0.497361\pi$
$728$		0			0
$729$			543.304i			0.745273i
$730$		0			0
$731$	−92.0234	−	92.0234i	−0.125887	−	0.125887i
$732$		0			0
$733$	−579.816	−	579.816i	−0.791018	−	0.791018i	0.190641	−	0.981660i	$-0.438943\pi$
$733$	−579.816	−	579.816i	−0.791018	−	0.791018i	−0.981660	+	0.190641i	$0.938943\pi$
$734$		0			0
$735$			178.016i			0.242198i
$736$		0			0
$737$	−365.428			−0.495832
$738$		0			0
$739$	−48.3765	+	48.3765i	−0.0654621	+	0.0654621i	−0.739080	−	0.673618i	$-0.764739\pi$
$739$	−48.3765	+	48.3765i	−0.0654621	+	0.0654621i	0.673618	+	0.739080i	$0.264739\pi$
$740$		0			0
$741$	1086.20	−	1086.20i	1.46585	−	1.46585i
$742$		0			0
$743$	−360.599			−0.485329			−0.242664	−	0.970110i	$-0.578021\pi$
$743$	−360.599			−0.485329			−0.242664	+	0.970110i	$0.578021\pi$
$744$		0			0
$745$			118.315i			0.158812i
$746$		0			0
$747$	356.396	+	356.396i	0.477104	+	0.477104i
$748$		0			0
$749$	394.632	+	394.632i	0.526878	+	0.526878i
$750$		0			0
$751$		−	834.167i		−	1.11074i	−0.831603	−	0.555371i	$-0.812576\pi$
$751$		−	834.167i		−	1.11074i	0.831603	−	0.555371i	$-0.187424\pi$
$752$		0			0
$753$	690.136			0.916515
$754$		0			0
$755$	365.952	−	365.952i	0.484704	−	0.484704i
$756$		0			0
$757$	−284.381	+	284.381i	−0.375668	+	0.375668i	−0.869537	−	0.493868i	$-0.835582\pi$
$757$	−284.381	+	284.381i	−0.375668	+	0.375668i	0.493868	+	0.869537i	$0.335582\pi$
$758$		0			0
$759$	16.3342			0.0215207
$760$		0			0
$761$			575.145i			0.755775i	0.925851	+	0.377888i	$0.123349\pi$
$761$			575.145i			0.755775i	−0.925851	+	0.377888i	$0.876651\pi$
$762$		0			0
$763$	−489.769	−	489.769i	−0.641900	−	0.641900i
$764$		0			0
$765$	136.400	+	136.400i	0.178301	+	0.178301i
$766$		0			0
$767$			801.253i			1.04466i
$768$		0			0
$769$	−993.063			−1.29137			−0.645685	−	0.763604i	$-0.723428\pi$
$769$	−993.063			−1.29137			−0.645685	+	0.763604i	$0.723428\pi$
$770$		0			0
$771$	−686.425	+	686.425i	−0.890305	+	0.890305i
$772$		0			0
$773$	635.157	−	635.157i	0.821678	−	0.821678i	−0.164671	−	0.986349i	$-0.552656\pi$
$773$	635.157	−	635.157i	0.821678	−	0.821678i	0.986349	+	0.164671i	$0.0526562\pi$
$774$		0			0
$775$	−117.525			−0.151645
$776$		0			0
$777$		−	678.824i		−	0.873648i
$778$		0			0
$779$	459.406	+	459.406i	0.589738	+	0.589738i
$780$		0			0
$781$	−96.0277	−	96.0277i	−0.122955	−	0.122955i
$782$		0			0
$783$			693.925i			0.886238i
$784$		0			0
$785$	−224.367			−0.285818
$786$		0			0
$787$	899.878	−	899.878i	1.14343	−	1.14343i	0.155609	−	0.987819i	$-0.450266\pi$
$787$	899.878	−	899.878i	1.14343	−	1.14343i	0.987819	−	0.155609i	$-0.0497341\pi$
$788$		0			0
$789$	−606.070	+	606.070i	−0.768149	+	0.768149i
$790$		0			0
$791$	786.804			0.994696
$792$		0			0
$793$		−	1297.93i		−	1.63673i
$794$		0			0
$795$	−179.183	−	179.183i	−0.225387	−	0.225387i
$796$		0			0
$797$	569.080	+	569.080i	0.714028	+	0.714028i	0.967375	−	0.253347i	$-0.0815315\pi$
$797$	569.080	+	569.080i	0.714028	+	0.714028i	−0.253347	+	0.967375i	$0.581532\pi$
$798$		0			0
$799$			61.4342i			0.0768889i
$800$		0			0
$801$	486.903			0.607869
$802$		0			0
$803$	721.417	−	721.417i	0.898402	−	0.898402i
$804$		0			0
$805$	11.7499	−	11.7499i	0.0145962	−	0.0145962i
$806$		0			0
$807$	438.270			0.543085
$808$		0			0
$809$			992.986i			1.22742i	0.789530	+	0.613712i	$0.210324\pi$
$809$			992.986i			1.22742i	−0.789530	+	0.613712i	$0.789676\pi$
$810$		0			0
$811$	−1076.53	−	1076.53i	−1.32741	−	1.32741i	−0.907626	−	0.419779i	$-0.862107\pi$
$811$	−1076.53	−	1076.53i	−1.32741	−	1.32741i	−0.419779	−	0.907626i	$-0.637893\pi$
$812$		0			0
$813$	−197.993	−	197.993i	−0.243534	−	0.243534i
$814$		0			0
$815$			24.2211i			0.0297191i
$816$		0			0
$817$	−254.374			−0.311351
$818$		0			0
$819$	−796.846	+	796.846i	−0.972949	+	0.972949i
$820$		0			0
$821$	325.078	−	325.078i	0.395954	−	0.395954i	−0.480849	−	0.876803i	$-0.659672\pi$
$821$	325.078	−	325.078i	0.395954	−	0.395954i	0.876803	+	0.480849i	$0.159672\pi$
$822$		0			0
$823$	−145.698			−0.177033			−0.0885166	−	0.996075i	$-0.528213\pi$
$823$	−145.698			−0.177033			−0.0885166	+	0.996075i	$0.528213\pi$
$824$		0			0
$825$		−	103.829i		−	0.125853i
$826$		0			0
$827$	648.282	+	648.282i	0.783895	+	0.783895i	0.980486	−	0.196590i	$-0.0629869\pi$
$827$	648.282	+	648.282i	0.783895	+	0.783895i	−0.196590	+	0.980486i	$0.562987\pi$
$828$		0			0
$829$	−406.014	−	406.014i	−0.489763	−	0.489763i	0.418468	−	0.908231i	$-0.362567\pi$
$829$	−406.014	−	406.014i	−0.489763	−	0.489763i	−0.908231	+	0.418468i	$0.862567\pi$
$830$		0			0
$831$			214.554i			0.258188i
$832$		0			0
$833$	−682.419			−0.819230
$834$		0			0
$835$	202.043	−	202.043i	0.241967	−	0.241967i
$836$		0			0
$837$	463.103	−	463.103i	0.553289	−	0.553289i
$838$		0			0
$839$	1580.30			1.88355			0.941774	−	0.336247i	$-0.109158\pi$
$839$	1580.30			1.88355			0.941774	+	0.336247i	$0.109158\pi$
$840$		0			0
$841$		−	220.757i		−	0.262493i
$842$		0			0
$843$	−501.678	−	501.678i	−0.595110	−	0.595110i
$844$		0			0
$845$	−601.554	−	601.554i	−0.711899	−	0.711899i
$846$		0			0
$847$			101.566i			0.119913i
$848$		0			0
$849$	−253.246			−0.298287
$850$		0			0
$851$	−20.2077	+	20.2077i	−0.0237459	+	0.0237459i
$852$		0			0
$853$	130.076	−	130.076i	0.152492	−	0.152492i	−0.626738	−	0.779230i	$-0.715610\pi$
$853$	130.076	−	130.076i	0.152492	−	0.152492i	0.779230	+	0.626738i	$0.215610\pi$
$854$		0			0
$855$	377.041			0.440984
$856$		0			0
$857$		−	530.038i		−	0.618481i	−0.950984	−	0.309240i	$-0.899925\pi$
$857$		−	530.038i		−	0.618481i	0.950984	−	0.309240i	$-0.100075\pi$
$858$		0			0
$859$	−207.354	−	207.354i	−0.241390	−	0.241390i	0.576035	−	0.817425i	$-0.304599\pi$
$859$	−207.354	−	207.354i	−0.241390	−	0.241390i	−0.817425	+	0.576035i	$0.804599\pi$
$860$		0			0
$861$	259.045	+	259.045i	0.300866	+	0.300866i
$862$		0			0
$863$			226.029i			0.261911i	0.991388	+	0.130955i	$0.0418045\pi$
$863$			226.029i			0.261911i	−0.991388	+	0.130955i	$0.958196\pi$
$864$		0			0
$865$	−35.5890			−0.0411433
$866$		0			0
$867$	−2.24868	+	2.24868i	−0.00259363	+	0.00259363i
$868$		0			0
$869$	405.036	−	405.036i	0.466095	−	0.466095i
$870$		0			0
$871$	815.793			0.936617
$872$		0			0
$873$			494.374i			0.566294i
$874$		0			0
$875$	−74.6887	−	74.6887i	−0.0853585	−	0.0853585i
$876$		0			0
$877$	548.446	+	548.446i	0.625366	+	0.625366i	0.946899	−	0.321532i	$-0.104198\pi$
$877$	548.446	+	548.446i	0.625366	+	0.625366i	−0.321532	+	0.946899i	$0.604198\pi$
$878$		0			0
$879$		−	324.981i		−	0.369717i
$880$		0			0
$881$	−80.5354			−0.0914137			−0.0457068	−	0.998955i	$-0.514554\pi$
$881$	−80.5354			−0.0914137			−0.0457068	+	0.998955i	$0.514554\pi$
$882$		0			0
$883$	130.018	−	130.018i	0.147246	−	0.147246i	−0.629640	−	0.776887i	$-0.716798\pi$
$883$	130.018	−	130.018i	0.147246	−	0.147246i	0.776887	+	0.629640i	$0.216798\pi$
$884$		0			0
$885$	106.889	−	106.889i	0.120779	−	0.120779i
$886$		0			0
$887$	−1654.80			−1.86562			−0.932809	−	0.360371i	$-0.882650\pi$
$887$	−1654.80			−1.86562			−0.932809	+	0.360371i	$0.882650\pi$
$888$		0			0
$889$		−	1646.85i		−	1.85248i
$890$		0			0
$891$	69.0981	+	69.0981i	0.0775512	+	0.0775512i
$892$		0			0
$893$	84.9091	+	84.9091i	0.0950830	+	0.0950830i
$894$		0			0
$895$		−	166.380i		−	0.185899i
$896$		0			0
$897$	−36.4650			−0.0406522
$898$		0			0
$899$	413.930	−	413.930i	0.460434	−	0.460434i
$900$		0			0
$901$	686.892	−	686.892i	0.762366	−	0.762366i
$902$		0			0
$903$	−143.434			−0.158841
$904$		0			0
$905$		−	619.698i		−	0.684750i
$906$		0			0
$907$	−135.454	−	135.454i	−0.149343	−	0.149343i	0.628482	−	0.777824i	$-0.283677\pi$
$907$	−135.454	−	135.454i	−0.149343	−	0.149343i	−0.777824	+	0.628482i	$0.783677\pi$
$908$		0			0
$909$	−529.923	−	529.923i	−0.582973	−	0.582973i
$910$		0			0
$911$			114.919i			0.126146i	0.998009	+	0.0630732i	$0.0200902\pi$
$911$			114.919i			0.126146i	−0.998009	+	0.0630732i	$0.979910\pi$
$912$		0			0
$913$	1039.99			1.13909
$914$		0			0
$915$	−173.147	+	173.147i	−0.189231	+	0.189231i
$916$		0			0
$917$	−914.333	+	914.333i	−0.997092	+	0.997092i
$918$		0			0
$919$	1485.24			1.61615			0.808074	−	0.589081i	$-0.200510\pi$
$919$	1485.24			1.61615			0.808074	+	0.589081i	$0.200510\pi$
$920$		0			0
$921$			692.219i			0.751595i
$922$		0			0
$923$	214.376	+	214.376i	0.232260	+	0.232260i
$924$		0			0
$925$	128.451	+	128.451i	0.138866	+	0.138866i
$926$		0			0
$927$			528.514i			0.570134i
$928$		0			0
$929$	−757.800			−0.815715			−0.407858	−	0.913046i	$-0.633724\pi$
$929$	−757.800			−0.815715			−0.407858	+	0.913046i	$0.633724\pi$
$930$		0			0
$931$	−943.180	+	943.180i	−1.01308	+	1.01308i
$932$		0			0
$933$	−424.991	+	424.991i	−0.455511	+	0.455511i
$934$		0			0
$935$	398.025			0.425695
$936$		0			0
$937$			276.108i			0.294672i	0.989086	+	0.147336i	$0.0470699\pi$
$937$			276.108i			0.294672i	−0.989086	+	0.147336i	$0.952930\pi$
$938$		0			0
$939$	812.184	+	812.184i	0.864946	+	0.864946i
$940$		0			0
$941$	621.544	+	621.544i	0.660514	+	0.660514i	0.955501	−	0.294987i	$-0.0953153\pi$
$941$	621.544	+	621.544i	0.660514	+	0.660514i	−0.294987	+	0.955501i	$0.595315\pi$
$942$		0			0
$943$		−	15.4229i		−	0.0163551i
$944$		0			0
$945$	588.615			0.622873
$946$		0			0
$947$	−964.382	+	964.382i	−1.01835	+	1.01835i	−0.0185266	+	0.999828i	$0.505898\pi$
$947$	−964.382	+	964.382i	−1.01835	+	1.01835i	−0.999828	+	0.0185266i	$0.994102\pi$
$948$		0			0
$949$	−1610.52	+	1610.52i	−1.69707	+	1.69707i
$950$		0			0
$951$	−534.428			−0.561964
$952$		0			0
$953$		−	997.130i		−	1.04631i	−0.852239	−	0.523153i	$-0.824756\pi$
$953$		−	997.130i		−	1.04631i	0.852239	−	0.523153i	$-0.175244\pi$
$954$		0			0
$955$	−424.879	−	424.879i	−0.444899	−	0.444899i
$956$		0			0
$957$	365.691	+	365.691i	0.382122	+	0.382122i
$958$		0			0
$959$		−	1399.69i		−	1.45953i
$960$		0			0
$961$	408.513			0.425092
$962$		0			0
$963$	212.562	−	212.562i	0.220729	−	0.220729i
$964$		0			0
$965$	185.503	−	185.503i	0.192231	−	0.192231i
$966$		0			0
$967$	−1490.34			−1.54120			−0.770599	−	0.637321i	$-0.780043\pi$
$967$	−1490.34			−1.54120			−0.770599	+	0.637321i	$0.780043\pi$
$968$		0			0
$969$		−	1110.95i		−	1.14649i
$970$		0			0
$971$	−764.898	−	764.898i	−0.787742	−	0.787742i	0.193381	−	0.981124i	$-0.438055\pi$
$971$	−764.898	−	764.898i	−0.787742	−	0.787742i	−0.981124	+	0.193381i	$0.938055\pi$
$972$		0			0
$973$	−64.8650	−	64.8650i	−0.0666649	−	0.0666649i
$974$		0			0
$975$			231.791i			0.237734i
$976$		0			0
$977$	−556.769			−0.569877			−0.284938	−	0.958546i	$-0.591973\pi$
$977$	−556.769			−0.569877			−0.284938	+	0.958546i	$0.591973\pi$
$978$		0			0
$979$	710.408	−	710.408i	0.725647	−	0.725647i
$980$		0			0
$981$	−263.806	+	263.806i	−0.268915	+	0.268915i
$982$		0			0
$983$	−65.7460			−0.0668830			−0.0334415	−	0.999441i	$-0.510647\pi$
$983$	−65.7460			−0.0668830			−0.0334415	+	0.999441i	$0.510647\pi$
$984$		0			0
$985$			545.430i			0.553736i
$986$		0			0
$987$	47.8777	+	47.8777i	0.0485083	+	0.0485083i
$988$		0			0
$989$	4.26984	+	4.26984i	0.00431733	+	0.00431733i
$990$		0			0
$991$			1721.37i			1.73700i	0.495685	+	0.868502i	$0.334917\pi$
$991$			1721.37i			1.73700i	−0.495685	+	0.868502i	$0.665083\pi$
$992$		0			0
$993$	740.182			0.745400
$994$		0			0
$995$	−127.229	+	127.229i	−0.127869	+	0.127869i
$996$		0			0
$997$	−763.807	+	763.807i	−0.766106	+	0.766106i	−0.977418	−	0.211313i	$-0.932226\pi$
$997$	−763.807	+	763.807i	−0.766106	+	0.766106i	0.211313	+	0.977418i	$0.432226\pi$
$998$		0			0
$999$	−1012.31			−1.01332

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.3.r.a.111.10		32
4.3	odd	2		80.3.r.a.51.16	yes	32
8.3	odd	2		640.3.r.a.351.10		32
8.5	even	2		640.3.r.b.351.7		32
16.3	odd	4		640.3.r.b.31.7		32
16.5	even	4		80.3.r.a.11.16	✓	32
16.11	odd	4	inner	320.3.r.a.271.10		32
16.13	even	4		640.3.r.a.31.10		32
20.3	even	4		400.3.k.h.99.8		32
20.7	even	4		400.3.k.g.99.9		32
20.19	odd	2		400.3.r.f.51.1		32
80.37	odd	4		400.3.k.h.299.8		32
80.53	odd	4		400.3.k.g.299.9		32
80.69	even	4		400.3.r.f.251.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.r.a.11.16	✓	32	16.5	even	4
80.3.r.a.51.16	yes	32	4.3	odd	2
320.3.r.a.111.10		32	1.1	even	1	trivial
320.3.r.a.271.10		32	16.11	odd	4	inner
400.3.k.g.99.9		32	20.7	even	4
400.3.k.g.299.9		32	80.53	odd	4
400.3.k.h.99.8		32	20.3	even	4
400.3.k.h.299.8		32	80.37	odd	4
400.3.r.f.51.1		32	20.19	odd	2
400.3.r.f.251.1		32	80.69	even	4
640.3.r.a.31.10		32	16.13	even	4
640.3.r.a.351.10		32	8.3	odd	2
640.3.r.b.31.7		32	16.3	odd	4
640.3.r.b.351.7		32	8.5	even	2

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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	320.r (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.39844 - 1.39844i) q^{3} +(-1.58114 + 1.58114i) q^{5} -9.44746 q^{7} +5.08871i q^{9} +O(q^{10})\)	\(q+(1.39844 - 1.39844i) q^{3} +(-1.58114 + 1.58114i) q^{5} -9.44746 q^{7} +5.08871i q^{9} +(7.42460 + 7.42460i) q^{11} +(-16.5749 - 16.5749i) q^{13} +4.42227i q^{15} -16.9526 q^{17} +(-23.4305 + 23.4305i) q^{19} +(-13.2117 + 13.2117i) q^{21} +0.786593 q^{23} -5.00000i q^{25} +(19.7023 + 19.7023i) q^{27} +(17.6103 + 17.6103i) q^{29} -23.5050i q^{31} +20.7658 q^{33} +(14.9377 - 14.9377i) q^{35} +(-25.6902 + 25.6902i) q^{37} -46.3582 q^{39} -19.6072i q^{41} +(5.42827 + 5.42827i) q^{43} +(-8.04596 - 8.04596i) q^{45} -3.62387i q^{47} +40.2544 q^{49} +(-23.7073 + 23.7073i) q^{51} +(-40.5183 + 40.5183i) q^{53} -23.4786 q^{55} +65.5324i q^{57} +(-24.1706 - 24.1706i) q^{59} +(39.1534 + 39.1534i) q^{61} -48.0754i q^{63} +52.4145 q^{65} +(-24.6093 + 24.6093i) q^{67} +(1.10001 - 1.10001i) q^{69} -12.9337 q^{71} -97.1658i q^{73} +(-6.99222 - 6.99222i) q^{75} +(-70.1436 - 70.1436i) q^{77} -54.5533i q^{79} +9.30664 q^{81} +(70.0367 - 70.0367i) q^{83} +(26.8045 - 26.8045i) q^{85} +49.2539 q^{87} -95.6831i q^{89} +(156.591 + 156.591i) q^{91} +(-32.8705 - 32.8705i) q^{93} -74.0937i q^{95} +97.1512 q^{97} +(-37.7816 + 37.7816i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 32 q^{11} + 32 q^{19} + 128 q^{23} + 96 q^{27} + 32 q^{29} - 96 q^{37} - 384 q^{39} - 96 q^{43} + 224 q^{49} + 256 q^{51} - 160 q^{53} + 352 q^{59} - 32 q^{61} - 160 q^{67} + 96 q^{69} - 256 q^{71} + 224 q^{77} - 288 q^{81} + 480 q^{83} + 160 q^{85} + 384 q^{91} + 96 q^{93} - 608 q^{99}+O(q^{100}) \) 32 * q - 32 * q^11 + 32 * q^19 + 128 * q^23 + 96 * q^27 + 32 * q^29 - 96 * q^37 - 384 * q^39 - 96 * q^43 + 224 * q^49 + 256 * q^51 - 160 * q^53 + 352 * q^59 - 32 * q^61 - 160 * q^67 + 96 * q^69 - 256 * q^71 + 224 * q^77 - 288 * q^81 + 480 * q^83 + 160 * q^85 + 384 * q^91 + 96 * q^93 - 608 * q^99

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