LMFDB - Embedded newform 320.3.r.a.271.1

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			271.1
Character	$\chi$	$=$	320.271
Dual form			320.3.r.a.111.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.81615 - 3.81615i) q^{3} +(1.58114 + 1.58114i) q^{5} +7.06228 q^{7} +20.1260i q^{9} +O(q^{10})$	\(q+(-3.81615 - 3.81615i) q^{3} +(1.58114 + 1.58114i) q^{5} +7.06228 q^{7} +20.1260i q^{9} +(-10.3638 + 10.3638i) q^{11} +(-5.72609 + 5.72609i) q^{13} -12.0677i q^{15} +20.9484 q^{17} +(7.58079 + 7.58079i) q^{19} +(-26.9507 - 26.9507i) q^{21} +13.7305 q^{23} +5.00000i q^{25} +(42.4585 - 42.4585i) q^{27} +(32.5485 - 32.5485i) q^{29} +26.0923i q^{31} +79.0994 q^{33} +(11.1664 + 11.1664i) q^{35} +(19.6248 + 19.6248i) q^{37} +43.7032 q^{39} -28.8892i q^{41} +(-1.30688 + 1.30688i) q^{43} +(-31.8220 + 31.8220i) q^{45} +25.9157i q^{47} +0.875810 q^{49} +(-79.9421 - 79.9421i) q^{51} +(-8.62769 - 8.62769i) q^{53} -32.7731 q^{55} -57.8589i q^{57} +(43.8075 - 43.8075i) q^{59} +(-26.3726 + 26.3726i) q^{61} +142.136i q^{63} -18.1075 q^{65} +(62.9542 + 62.9542i) q^{67} +(-52.3976 - 52.3976i) q^{69} -67.9581 q^{71} +14.0243i q^{73} +(19.0808 - 19.0808i) q^{75} +(-73.1918 + 73.1918i) q^{77} +11.0029i q^{79} -142.922 q^{81} +(70.2950 + 70.2950i) q^{83} +(33.1223 + 33.1223i) q^{85} -248.420 q^{87} +161.754i q^{89} +(-40.4393 + 40.4393i) q^{91} +(99.5721 - 99.5721i) q^{93} +23.9726i q^{95} +125.858 q^{97} +(-208.581 - 208.581i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

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

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
$3$	−3.81615	−	3.81615i	−1.27205	−	1.27205i	−0.945011	−	0.327039i	$-0.893949\pi$
$3$	−3.81615	−	3.81615i	−1.27205	−	1.27205i	−0.327039	−	0.945011i	$-0.606051\pi$
$4$		0			0
$5$	1.58114	+	1.58114i	0.316228	+	0.316228i
$5$	1.58114	+	1.58114i	0.316228	+	0.316228i
$6$		0			0
$7$	7.06228			1.00890			0.504449	−	0.863442i	$-0.331696\pi$
$7$	7.06228			1.00890			0.504449	+	0.863442i	$0.331696\pi$
$8$		0			0
$9$			20.1260i			2.23622i
$10$		0			0
$11$	−10.3638	+	10.3638i	−0.942161	+	0.942161i	−0.998416	−	0.0562558i	$-0.982084\pi$
$11$	−10.3638	+	10.3638i	−0.942161	+	0.942161i	0.0562558	+	0.998416i	$0.482084\pi$
$12$		0			0
$13$	−5.72609	+	5.72609i	−0.440468	+	0.440468i	−0.892169	−	0.451701i	$-0.850817\pi$
$13$	−5.72609	+	5.72609i	−0.440468	+	0.440468i	0.451701	+	0.892169i	$0.350817\pi$
$14$		0			0
$15$		−	12.0677i		−	0.804515i
$16$		0			0
$17$	20.9484			1.23226			0.616128	−	0.787646i	$-0.288700\pi$
$17$	20.9484			1.23226			0.616128	+	0.787646i	$0.288700\pi$
$18$		0			0
$19$	7.58079	+	7.58079i	0.398989	+	0.398989i	0.877876	−	0.478887i	$-0.158960\pi$
$19$	7.58079	+	7.58079i	0.398989	+	0.398989i	−0.478887	+	0.877876i	$0.658960\pi$
$20$		0			0
$21$	−26.9507	−	26.9507i	−1.28337	−	1.28337i
$22$		0			0
$23$	13.7305			0.596978			0.298489	−	0.954413i	$-0.403517\pi$
$23$	13.7305			0.596978			0.298489	+	0.954413i	$0.403517\pi$
$24$		0			0
$25$			5.00000i			0.200000i
$26$		0			0
$27$	42.4585	−	42.4585i	1.57254	−	1.57254i
$28$		0			0
$29$	32.5485	−	32.5485i	1.12236	−	1.12236i	0.130976	−	0.991386i	$-0.458189\pi$
$29$	32.5485	−	32.5485i	1.12236	−	1.12236i	0.991386	−	0.130976i	$-0.0418111\pi$
$30$		0			0
$31$			26.0923i			0.841687i	0.907133	+	0.420843i	$0.138266\pi$
$31$			26.0923i			0.841687i	−0.907133	+	0.420843i	$0.861734\pi$
$32$		0			0
$33$	79.0994			2.39695
$34$		0			0
$35$	11.1664	+	11.1664i	0.319041	+	0.319041i
$36$		0			0
$37$	19.6248	+	19.6248i	0.530401	+	0.530401i	0.920692	−	0.390290i	$-0.127625\pi$
$37$	19.6248	+	19.6248i	0.530401	+	0.530401i	−0.390290	+	0.920692i	$0.627625\pi$
$38$		0			0
$39$	43.7032			1.12060
$40$		0			0
$41$		−	28.8892i		−	0.704614i	−0.935884	−	0.352307i	$-0.885397\pi$
$41$		−	28.8892i		−	0.704614i	0.935884	−	0.352307i	$-0.114603\pi$
$42$		0			0
$43$	−1.30688	+	1.30688i	−0.0303926	+	0.0303926i	−0.722140	−	0.691747i	$-0.756841\pi$
$43$	−1.30688	+	1.30688i	−0.0303926	+	0.0303926i	0.691747	+	0.722140i	$0.256841\pi$
$44$		0			0
$45$	−31.8220	+	31.8220i	−0.707156	+	0.707156i
$46$		0			0
$47$			25.9157i			0.551398i	0.961244	+	0.275699i	$0.0889093\pi$
$47$			25.9157i			0.551398i	−0.961244	+	0.275699i	$0.911091\pi$
$48$		0			0
$49$	0.875810			0.0178737
$50$		0			0
$51$	−79.9421	−	79.9421i	−1.56749	−	1.56749i
$52$		0			0
$53$	−8.62769	−	8.62769i	−0.162787	−	0.162787i	0.621013	−	0.783800i	$-0.286721\pi$
$53$	−8.62769	−	8.62769i	−0.162787	−	0.162787i	−0.783800	+	0.621013i	$0.786721\pi$
$54$		0			0
$55$	−32.7731			−0.595875
$56$		0			0
$57$		−	57.8589i		−	1.01507i
$58$		0			0
$59$	43.8075	−	43.8075i	0.742500	−	0.742500i	−0.230558	−	0.973058i	$-0.574055\pi$
$59$	43.8075	−	43.8075i	0.742500	−	0.742500i	0.973058	+	0.230558i	$0.0740553\pi$
$60$		0			0
$61$	−26.3726	+	26.3726i	−0.432338	+	0.432338i	−0.889423	−	0.457085i	$-0.848894\pi$
$61$	−26.3726	+	26.3726i	−0.432338	+	0.432338i	0.457085	+	0.889423i	$0.348894\pi$
$62$		0			0
$63$			142.136i			2.25612i
$64$		0			0
$65$	−18.1075			−0.278577
$66$		0			0
$67$	62.9542	+	62.9542i	0.939615	+	0.939615i	0.998278	−	0.0586632i	$-0.0186838\pi$
$67$	62.9542	+	62.9542i	0.939615	+	0.939615i	−0.0586632	+	0.998278i	$0.518684\pi$
$68$		0			0
$69$	−52.3976	−	52.3976i	−0.759386	−	0.759386i
$70$		0			0
$71$	−67.9581			−0.957156			−0.478578	−	0.878045i	$-0.658848\pi$
$71$	−67.9581			−0.957156			−0.478578	+	0.878045i	$0.658848\pi$
$72$		0			0
$73$			14.0243i			0.192113i	0.995376	+	0.0960566i	$0.0306230\pi$
$73$			14.0243i			0.192113i	−0.995376	+	0.0960566i	$0.969377\pi$
$74$		0			0
$75$	19.0808	−	19.0808i	0.254410	−	0.254410i
$76$		0			0
$77$	−73.1918	+	73.1918i	−0.950543	+	0.950543i
$78$		0			0
$79$			11.0029i			0.139277i	0.997572	+	0.0696384i	$0.0221845\pi$
$79$			11.0029i			0.139277i	−0.997572	+	0.0696384i	$0.977815\pi$
$80$		0			0
$81$	−142.922			−1.76447
$82$		0			0
$83$	70.2950	+	70.2950i	0.846928	+	0.846928i	0.989749	−	0.142821i	$-0.0456172\pi$
$83$	70.2950	+	70.2950i	0.846928	+	0.846928i	−0.142821	+	0.989749i	$0.545617\pi$
$84$		0			0
$85$	33.1223	+	33.1223i	0.389674	+	0.389674i
$86$		0			0
$87$	−248.420			−2.85540
$88$		0			0
$89$			161.754i			1.81746i	0.417388	+	0.908728i	$0.362946\pi$
$89$			161.754i			1.81746i	−0.417388	+	0.908728i	$0.637054\pi$
$90$		0			0
$91$	−40.4393	+	40.4393i	−0.444387	+	0.444387i
$92$		0			0
$93$	99.5721	−	99.5721i	1.07067	−	1.07067i
$94$		0			0
$95$			23.9726i			0.252343i
$96$		0			0
$97$	125.858			1.29750			0.648752	−	0.761000i	$-0.275291\pi$
$97$	125.858			1.29750			0.648752	+	0.761000i	$0.275291\pi$
$98$		0			0
$99$	−208.581	−	208.581i	−2.10688	−	2.10688i
$100$		0			0
$101$	35.9589	+	35.9589i	0.356029	+	0.356029i	0.862347	−	0.506318i	$-0.168994\pi$
$101$	35.9589	+	35.9589i	0.356029	+	0.356029i	−0.506318	+	0.862347i	$0.668994\pi$
$102$		0			0
$103$	52.9240			0.513826			0.256913	−	0.966435i	$-0.417295\pi$
$103$	52.9240			0.513826			0.256913	+	0.966435i	$0.417295\pi$
$104$		0			0
$105$		−	85.2257i		−	0.811673i
$106$		0			0
$107$	105.376	−	105.376i	0.984824	−	0.984824i	−0.0150622	−	0.999887i	$-0.504795\pi$
$107$	105.376	−	105.376i	0.984824	−	0.984824i	0.999887	+	0.0150622i	$0.00479463\pi$
$108$		0			0
$109$	−126.083	+	126.083i	−1.15672	+	1.15672i	−0.171548	+	0.985176i	$0.554877\pi$
$109$	−126.083	+	126.083i	−1.15672	+	1.15672i	−0.985176	+	0.171548i	$0.945123\pi$
$110$		0			0
$111$		−	149.783i		−	1.34939i
$112$		0			0
$113$	−63.3329			−0.560468			−0.280234	−	0.959932i	$-0.590412\pi$
$113$	−63.3329			−0.560468			−0.280234	+	0.959932i	$0.590412\pi$
$114$		0			0
$115$	21.7098	+	21.7098i	0.188781	+	0.188781i
$116$		0			0
$117$	−115.243	−	115.243i	−0.984986	−	0.984986i
$118$		0			0
$119$	147.943			1.24322
$120$		0			0
$121$		−	93.8153i		−	0.775333i
$122$		0			0
$123$	−110.245	+	110.245i	−0.896305	+	0.896305i
$124$		0			0
$125$	−7.90569	+	7.90569i	−0.0632456	+	0.0632456i
$126$		0			0
$127$		−	108.702i		−	0.855922i	−0.903797	−	0.427961i	$-0.859232\pi$
$127$		−	108.702i		−	0.855922i	0.903797	−	0.427961i	$-0.140768\pi$
$128$		0			0
$129$	9.97452			0.0773219
$130$		0			0
$131$	0.204051	+	0.204051i	0.00155764	+	0.00155764i	0.707885	−	0.706328i	$-0.249649\pi$
$131$	0.204051	+	0.204051i	0.00155764	+	0.00155764i	−0.706328	+	0.707885i	$0.749649\pi$
$132$		0			0
$133$	53.5377	+	53.5377i	0.402539	+	0.402539i
$134$		0			0
$135$	134.266			0.994560
$136$		0			0
$137$		−	131.227i		−	0.957862i	−0.877853	−	0.478931i	$-0.841024\pi$
$137$		−	131.227i		−	0.957862i	0.877853	−	0.478931i	$-0.158976\pi$
$138$		0			0
$139$	−74.4886	+	74.4886i	−0.535889	+	0.535889i	−0.922319	−	0.386429i	$-0.873708\pi$
$139$	−74.4886	+	74.4886i	−0.535889	+	0.535889i	0.386429	+	0.922319i	$0.373708\pi$
$140$		0			0
$141$	98.8982	−	98.8982i	0.701406	−	0.701406i
$142$		0			0
$143$		−	118.688i		−	0.829984i
$144$		0			0
$145$	102.927			0.709844
$146$		0			0
$147$	−3.34222	−	3.34222i	−0.0227362	−	0.0227362i
$148$		0			0
$149$	−139.785	−	139.785i	−0.938157	−	0.938157i	0.0600393	−	0.998196i	$-0.480877\pi$
$149$	−139.785	−	139.785i	−0.938157	−	0.938157i	−0.998196	+	0.0600393i	$0.980877\pi$
$150$		0			0
$151$	176.707			1.17024			0.585121	−	0.810946i	$-0.301047\pi$
$151$	176.707			1.17024			0.585121	+	0.810946i	$0.301047\pi$
$152$		0			0
$153$			421.607i			2.75560i
$154$		0			0
$155$	−41.2555	+	41.2555i	−0.266165	+	0.266165i
$156$		0			0
$157$	−9.60929	+	9.60929i	−0.0612057	+	0.0612057i	−0.737047	−	0.675841i	$-0.763780\pi$
$157$	−9.60929	+	9.60929i	−0.0612057	+	0.0612057i	0.675841	+	0.737047i	$0.263780\pi$
$158$		0			0
$159$			65.8491i			0.414145i
$160$		0			0
$161$	96.9686			0.602289
$162$		0			0
$163$	−51.3986	−	51.3986i	−0.315329	−	0.315329i	0.531641	−	0.846970i	$-0.321576\pi$
$163$	−51.3986	−	51.3986i	−0.315329	−	0.315329i	−0.846970	+	0.531641i	$0.821576\pi$
$164$		0			0
$165$	125.067	+	125.067i	0.757982	+	0.757982i
$166$		0			0
$167$	−209.405			−1.25392			−0.626961	−	0.779050i	$-0.715702\pi$
$167$	−209.405			−1.25392			−0.626961	+	0.779050i	$0.715702\pi$
$168$		0			0
$169$			103.424i			0.611975i
$170$		0			0
$171$	−152.571	+	152.571i	−0.892229	+	0.892229i
$172$		0			0
$173$	−10.8022	+	10.8022i	−0.0624404	+	0.0624404i	−0.737637	−	0.675197i	$-0.764059\pi$
$173$	−10.8022	+	10.8022i	−0.0624404	+	0.0624404i	0.675197	+	0.737637i	$0.264059\pi$
$174$		0			0
$175$			35.3114i			0.201779i
$176$		0			0
$177$	−334.352			−1.88899
$178$		0			0
$179$	213.052	+	213.052i	1.19024	+	1.19024i	0.977001	+	0.213234i	$0.0683998\pi$
$179$	213.052	+	213.052i	1.19024	+	1.19024i	0.213234	+	0.977001i	$0.431600\pi$
$180$		0			0
$181$	−27.5517	−	27.5517i	−0.152219	−	0.152219i	0.626889	−	0.779108i	$-0.284328\pi$
$181$	−27.5517	−	27.5517i	−0.152219	−	0.152219i	−0.779108	+	0.626889i	$0.784328\pi$
$182$		0			0
$183$	201.284			1.09991
$184$		0			0
$185$			62.0592i			0.335455i
$186$		0			0
$187$	−217.104	+	217.104i	−1.16098	+	1.16098i
$188$		0			0
$189$	299.854	−	299.854i	1.58653	−	1.58653i
$190$		0			0
$191$		−	285.029i		−	1.49230i	−0.665778	−	0.746150i	$-0.731900\pi$
$191$		−	285.029i		−	1.49230i	0.665778	−	0.746150i	$-0.268100\pi$
$192$		0			0
$193$	17.4519			0.0904245			0.0452123	−	0.998977i	$-0.485604\pi$
$193$	17.4519			0.0904245			0.0452123	+	0.998977i	$0.485604\pi$
$194$		0			0
$195$	69.1009	+	69.1009i	0.354364	+	0.354364i
$196$		0			0
$197$	−92.3883	−	92.3883i	−0.468976	−	0.468976i	0.432607	−	0.901583i	$-0.357594\pi$
$197$	−92.3883	−	92.3883i	−0.468976	−	0.468976i	−0.901583	+	0.432607i	$0.857594\pi$
$198$		0			0
$199$	−296.441			−1.48965			−0.744826	−	0.667258i	$-0.767468\pi$
$199$	−296.441			−1.48965			−0.744826	+	0.667258i	$0.767468\pi$
$200$		0			0
$201$		−	480.485i		−	2.39047i
$202$		0			0
$203$	229.867	−	229.867i	1.13235	−	1.13235i
$204$		0			0
$205$	45.6778	−	45.6778i	0.222819	−	0.222819i
$206$		0			0
$207$			276.340i			1.33498i
$208$		0			0
$209$	−157.131			−0.751824
$210$		0			0
$211$	170.896	+	170.896i	0.809932	+	0.809932i	0.984623	−	0.174692i	$-0.0558928\pi$
$211$	170.896	+	170.896i	0.809932	+	0.809932i	−0.174692	+	0.984623i	$0.555893\pi$
$212$		0			0
$213$	259.338	+	259.338i	1.21755	+	1.21755i
$214$		0			0
$215$	−4.13272			−0.0192220
$216$		0			0
$217$			184.271i			0.849175i
$218$		0			0
$219$	53.5187	−	53.5187i	0.244378	−	0.244378i
$220$		0			0
$221$	−119.952	+	119.952i	−0.542770	+	0.542770i
$222$		0			0
$223$			231.463i			1.03795i	0.854789	+	0.518975i	$0.173686\pi$
$223$			231.463i			1.03795i	−0.854789	+	0.518975i	$0.826314\pi$
$224$		0			0
$225$	−100.630			−0.447245
$226$		0			0
$227$	−15.9457	−	15.9457i	−0.0702453	−	0.0702453i	0.671111	−	0.741357i	$-0.265817\pi$
$227$	−15.9457	−	15.9457i	−0.0702453	−	0.0702453i	−0.741357	+	0.671111i	$0.765817\pi$
$228$		0			0
$229$	245.622	+	245.622i	1.07258	+	1.07258i	0.997151	+	0.0754331i	$0.0240339\pi$
$229$	245.622	+	245.622i	1.07258	+	1.07258i	0.0754331	+	0.997151i	$0.475966\pi$
$230$		0			0
$231$	558.622			2.41828
$232$		0			0
$233$		−	343.876i		−	1.47586i	−0.674876	−	0.737931i	$-0.735803\pi$
$233$		−	343.876i		−	1.47586i	0.674876	−	0.737931i	$-0.264197\pi$
$234$		0			0
$235$	−40.9763	+	40.9763i	−0.174367	+	0.174367i
$236$		0			0
$237$	41.9886	−	41.9886i	0.177167	−	0.177167i
$238$		0			0
$239$		−	257.404i		−	1.07700i	−0.842624	−	0.538502i	$-0.818991\pi$
$239$		−	257.404i		−	1.07700i	0.842624	−	0.538502i	$-0.181009\pi$
$240$		0			0
$241$	−181.726			−0.754051			−0.377025	−	0.926203i	$-0.623053\pi$
$241$	−181.726			−0.754051			−0.377025	+	0.926203i	$0.623053\pi$
$242$		0			0
$243$	163.286	+	163.286i	0.671958	+	0.671958i
$244$		0			0
$245$	1.38478	+	1.38478i	0.00565215	+	0.00565215i
$246$		0			0
$247$	−86.8166			−0.351484
$248$		0			0
$249$		−	536.513i		−	2.15467i
$250$		0			0
$251$	−50.3743	+	50.3743i	−0.200695	+	0.200695i	−0.800298	−	0.599603i	$-0.795325\pi$
$251$	−50.3743	+	50.3743i	−0.200695	+	0.200695i	0.599603	+	0.800298i	$0.295325\pi$
$252$		0			0
$253$	−142.300	+	142.300i	−0.562449	+	0.562449i
$254$		0			0
$255$		−	252.799i		−	0.991369i
$256$		0			0
$257$	196.964			0.766398			0.383199	−	0.923666i	$-0.374822\pi$
$257$	196.964			0.766398			0.383199	+	0.923666i	$0.374822\pi$
$258$		0			0
$259$	138.596	+	138.596i	0.535120	+	0.535120i
$260$		0			0
$261$	655.071	+	655.071i	2.50985	+	2.50985i
$262$		0			0
$263$	−44.0635			−0.167542			−0.0837709	−	0.996485i	$-0.526696\pi$
$263$	−44.0635			−0.167542			−0.0837709	+	0.996485i	$0.526696\pi$
$264$		0			0
$265$		−	27.2832i		−	0.102955i
$266$		0			0
$267$	617.276	−	617.276i	2.31190	−	2.31190i
$268$		0			0
$269$	121.781	−	121.781i	0.452717	−	0.452717i	−0.443538	−	0.896255i	$-0.646277\pi$
$269$	121.781	−	121.781i	0.452717	−	0.452717i	0.896255	+	0.443538i	$0.146277\pi$
$270$		0			0
$271$		−	225.635i		−	0.832602i	−0.909227	−	0.416301i	$-0.863326\pi$
$271$		−	225.635i		−	0.832602i	0.909227	−	0.416301i	$-0.136674\pi$
$272$		0			0
$273$	308.645			1.13057
$274$		0			0
$275$	−51.8188	−	51.8188i	−0.188432	−	0.188432i
$276$		0			0
$277$	−25.3569	−	25.3569i	−0.0915410	−	0.0915410i	0.659853	−	0.751394i	$-0.270618\pi$
$277$	−25.3569	−	25.3569i	−0.0915410	−	0.0915410i	−0.751394	+	0.659853i	$0.770618\pi$
$278$		0			0
$279$	−525.134			−1.88220
$280$		0			0
$281$			230.379i			0.819854i	0.912118	+	0.409927i	$0.134446\pi$
$281$			230.379i			0.819854i	−0.912118	+	0.409927i	$0.865554\pi$
$282$		0			0
$283$	72.1310	−	72.1310i	0.254880	−	0.254880i	−0.568088	−	0.822968i	$-0.692317\pi$
$283$	72.1310	−	72.1310i	0.254880	−	0.254880i	0.822968	+	0.568088i	$0.192317\pi$
$284$		0			0
$285$	91.4830	−	91.4830i	0.320993	−	0.320993i
$286$		0			0
$287$		−	204.024i		−	0.710884i
$288$		0			0
$289$	149.833			0.518455
$290$		0			0
$291$	−480.293	−	480.293i	−1.65049	−	1.65049i
$292$		0			0
$293$	−240.920	−	240.920i	−0.822254	−	0.822254i	0.164177	−	0.986431i	$-0.447503\pi$
$293$	−240.920	−	240.920i	−0.822254	−	0.822254i	−0.986431	+	0.164177i	$0.947503\pi$
$294$		0			0
$295$	138.531			0.469598
$296$		0			0
$297$			880.060i			2.96317i
$298$		0			0
$299$	−78.6220	+	78.6220i	−0.262950	+	0.262950i
$300$		0			0
$301$	−9.22957	+	9.22957i	−0.0306630	+	0.0306630i
$302$		0			0
$303$		−	274.449i		−	0.905772i
$304$		0			0
$305$	−83.3976			−0.273435
$306$		0			0
$307$	−270.295	−	270.295i	−0.880439	−	0.880439i	0.113140	−	0.993579i	$-0.463909\pi$
$307$	−270.295	−	270.295i	−0.880439	−	0.880439i	−0.993579	+	0.113140i	$0.963909\pi$
$308$		0			0
$309$	−201.966	−	201.966i	−0.653612	−	0.653612i
$310$		0			0
$311$	−542.105			−1.74310			−0.871552	−	0.490303i	$-0.836886\pi$
$311$	−542.105			−1.74310			−0.871552	+	0.490303i	$0.836886\pi$
$312$		0			0
$313$		−	149.812i		−	0.478633i	−0.970942	−	0.239316i	$-0.923077\pi$
$313$		−	149.812i		−	0.478633i	0.970942	−	0.239316i	$-0.0769233\pi$
$314$		0			0
$315$	−224.736	+	224.736i	−0.713448	+	0.713448i
$316$		0			0
$317$	419.328	−	419.328i	1.32280	−	1.32280i	0.411304	−	0.911498i	$-0.365073\pi$
$317$	419.328	−	419.328i	1.32280	−	1.32280i	0.911498	−	0.411304i	$-0.134927\pi$
$318$		0			0
$319$			674.650i			2.11489i
$320$		0			0
$321$	−804.263			−2.50549
$322$		0			0
$323$	158.805	+	158.805i	0.491657	+	0.491657i
$324$		0			0
$325$	−28.6304	−	28.6304i	−0.0880937	−	0.0880937i
$326$		0			0
$327$	962.302			2.94282
$328$		0			0
$329$			183.024i			0.556304i
$330$		0			0
$331$	−106.842	+	106.842i	−0.322785	+	0.322785i	−0.849835	−	0.527050i	$-0.823298\pi$
$331$	−106.842	+	106.842i	−0.322785	+	0.322785i	0.527050	+	0.849835i	$0.323298\pi$
$332$		0			0
$333$	−394.970	+	394.970i	−1.18610	+	1.18610i
$334$		0			0
$335$			199.079i			0.594264i
$336$		0			0
$337$	291.677			0.865510			0.432755	−	0.901512i	$-0.357542\pi$
$337$	291.677			0.865510			0.432755	+	0.901512i	$0.357542\pi$
$338$		0			0
$339$	241.688	+	241.688i	0.712943	+	0.712943i
$340$		0			0
$341$	−270.414	−	270.414i	−0.793004	−	0.793004i
$342$		0			0
$343$	−339.867			−0.990865
$344$		0			0
$345$		−	165.696i		−	0.480278i
$346$		0			0
$347$	−262.829	+	262.829i	−0.757433	+	0.757433i	−0.975854	−	0.218422i	$-0.929909\pi$
$347$	−262.829	+	262.829i	−0.757433	+	0.757433i	0.218422	+	0.975854i	$0.429909\pi$
$348$		0			0
$349$	−429.583	+	429.583i	−1.23090	+	1.23090i	−0.267277	+	0.963620i	$0.586124\pi$
$349$	−429.583	+	429.583i	−1.23090	+	1.23090i	−0.963620	+	0.267277i	$0.913876\pi$
$350$		0			0
$351$			486.243i			1.38531i
$352$		0			0
$353$	−240.396			−0.681008			−0.340504	−	0.940243i	$-0.610598\pi$
$353$	−240.396			−0.681008			−0.340504	+	0.940243i	$0.610598\pi$
$354$		0			0
$355$	−107.451	−	107.451i	−0.302679	−	0.302679i
$356$		0			0
$357$	−564.573	−	564.573i	−1.58144	−	1.58144i
$358$		0			0
$359$	−57.3483			−0.159744			−0.0798722	−	0.996805i	$-0.525451\pi$
$359$	−57.3483			−0.159744			−0.0798722	+	0.996805i	$0.525451\pi$
$360$		0			0
$361$		−	246.063i		−	0.681615i
$362$		0			0
$363$	−358.013	+	358.013i	−0.986263	+	0.986263i
$364$		0			0
$365$	−22.1743	+	22.1743i	−0.0607515	+	0.0607515i
$366$		0			0
$367$			67.9139i			0.185052i	0.995710	+	0.0925258i	$0.0294941\pi$
$367$			67.9139i			0.185052i	−0.995710	+	0.0925258i	$0.970506\pi$
$368$		0			0
$369$	581.424			1.57568
$370$		0			0
$371$	−60.9312	−	60.9312i	−0.164235	−	0.164235i
$372$		0			0
$373$	23.4566	+	23.4566i	0.0628862	+	0.0628862i	0.737850	−	0.674964i	$-0.235841\pi$
$373$	23.4566	+	23.4566i	0.0628862	+	0.0628862i	−0.674964	+	0.737850i	$0.735841\pi$
$374$		0			0
$375$	60.3386			0.160903
$376$		0			0
$377$			372.751i			0.988730i
$378$		0			0
$379$	200.977	−	200.977i	0.530283	−	0.530283i	−0.390374	−	0.920657i	$-0.627654\pi$
$379$	200.977	−	200.977i	0.530283	−	0.530283i	0.920657	+	0.390374i	$0.127654\pi$
$380$		0			0
$381$	−414.823	+	414.823i	−1.08878	+	1.08878i
$382$		0			0
$383$		−	128.871i		−	0.336479i	−0.985746	−	0.168239i	$-0.946192\pi$
$383$		−	128.871i		−	0.336479i	0.985746	−	0.168239i	$-0.0538082\pi$
$384$		0			0
$385$	−231.453			−0.601176
$386$		0			0
$387$	−26.3023	−	26.3023i	−0.0679647	−	0.0679647i
$388$		0			0
$389$	−104.010	−	104.010i	−0.267379	−	0.267379i	0.560664	−	0.828043i	$-0.310546\pi$
$389$	−104.010	−	104.010i	−0.267379	−	0.267379i	−0.828043	+	0.560664i	$0.810546\pi$
$390$		0			0
$391$	287.631			0.735629
$392$		0			0
$393$		−	1.55738i		−	0.00396279i
$394$		0			0
$395$	−17.3971	+	17.3971i	−0.0440432	+	0.0440432i
$396$		0			0
$397$	87.2509	−	87.2509i	0.219776	−	0.219776i	−0.588628	−	0.808404i	$-0.700332\pi$
$397$	87.2509	−	87.2509i	0.219776	−	0.219776i	0.808404	+	0.588628i	$0.200332\pi$
$398$		0			0
$399$		−	408.616i		−	1.02410i
$400$		0			0
$401$	416.906			1.03967			0.519833	−	0.854268i	$-0.325994\pi$
$401$	416.906			1.03967			0.519833	+	0.854268i	$0.325994\pi$
$402$		0			0
$403$	−149.407	−	149.407i	−0.370736	−	0.370736i
$404$		0			0
$405$	−225.980	−	225.980i	−0.557975	−	0.557975i
$406$		0			0
$407$	−406.775			−0.999446
$408$		0			0
$409$		−	364.415i		−	0.890990i	−0.895284	−	0.445495i	$-0.853028\pi$
$409$		−	364.415i		−	0.890990i	0.895284	−	0.445495i	$-0.146972\pi$
$410$		0			0
$411$	−500.782	+	500.782i	−1.21845	+	1.21845i
$412$		0			0
$413$	309.381	−	309.381i	0.749106	−	0.749106i
$414$		0			0
$415$			222.292i			0.535644i
$416$		0			0
$417$	568.520			1.36336
$418$		0			0
$419$	−206.623	−	206.623i	−0.493134	−	0.493134i	0.416159	−	0.909292i	$-0.363376\pi$
$419$	−206.623	−	206.623i	−0.493134	−	0.493134i	−0.909292	+	0.416159i	$0.863376\pi$
$420$		0			0
$421$	−262.161	−	262.161i	−0.622710	−	0.622710i	0.323513	−	0.946224i	$-0.395136\pi$
$421$	−262.161	−	262.161i	−0.622710	−	0.622710i	−0.946224	+	0.323513i	$0.895136\pi$
$422$		0			0
$423$	−521.580			−1.23305
$424$		0			0
$425$			104.742i			0.246451i
$426$		0			0
$427$	−186.251	+	186.251i	−0.436185	+	0.436185i
$428$		0			0
$429$	−452.930	+	452.930i	−1.05578	+	1.05578i
$430$		0			0
$431$		−	272.447i		−	0.632128i	−0.948738	−	0.316064i	$-0.897639\pi$
$431$		−	272.447i		−	0.632128i	0.948738	−	0.316064i	$-0.102361\pi$
$432$		0			0
$433$	−477.786			−1.10343			−0.551716	−	0.834032i	$-0.686027\pi$
$433$	−477.786			−1.10343			−0.551716	+	0.834032i	$0.686027\pi$
$434$		0			0
$435$	−392.786	−	392.786i	−0.902957	−	0.902957i
$436$		0			0
$437$	104.088	+	104.088i	0.238188	+	0.238188i
$438$		0			0
$439$	304.402			0.693398			0.346699	−	0.937977i	$-0.387303\pi$
$439$	304.402			0.693398			0.346699	+	0.937977i	$0.387303\pi$
$440$		0			0
$441$			17.6266i			0.0399695i
$442$		0			0
$443$	541.093	−	541.093i	1.22143	−	1.22143i	0.254304	−	0.967124i	$-0.418154\pi$
$443$	541.093	−	541.093i	1.22143	−	1.22143i	0.967124	−	0.254304i	$-0.0818463\pi$
$444$		0			0
$445$	−255.755	+	255.755i	−0.574730	+	0.574730i
$446$		0			0
$447$			1066.88i			2.38676i
$448$		0			0
$449$	467.626			1.04148			0.520742	−	0.853714i	$-0.325656\pi$
$449$	467.626			1.04148			0.520742	+	0.853714i	$0.325656\pi$
$450$		0			0
$451$	299.401	+	299.401i	0.663860	+	0.663860i
$452$		0			0
$453$	−674.339	−	674.339i	−1.48861	−	1.48861i
$454$		0			0
$455$	−127.880			−0.281055
$456$		0			0
$457$			388.024i			0.849069i	0.905412	+	0.424534i	$0.139562\pi$
$457$			388.024i			0.849069i	−0.905412	+	0.424534i	$0.860438\pi$
$458$		0			0
$459$	889.436	−	889.436i	1.93777	−	1.93777i
$460$		0			0
$461$	513.706	−	513.706i	1.11433	−	1.11433i	0.121772	−	0.992558i	$-0.461142\pi$
$461$	513.706	−	513.706i	1.11433	−	1.11433i	0.992558	−	0.121772i	$-0.0388576\pi$
$462$		0			0
$463$		−	338.087i		−	0.730209i	−0.930967	−	0.365105i	$-0.881033\pi$
$463$		−	338.087i		−	0.730209i	0.930967	−	0.365105i	$-0.118967\pi$
$464$		0			0
$465$	314.875			0.677150
$466$		0			0
$467$	368.745	+	368.745i	0.789604	+	0.789604i	0.981429	−	0.191825i	$-0.0614407\pi$
$467$	368.745	+	368.745i	0.789604	+	0.789604i	−0.191825	+	0.981429i	$0.561441\pi$
$468$		0			0
$469$	444.600	+	444.600i	0.947975	+	0.947975i
$470$		0			0
$471$	73.3410			0.155713
$472$		0			0
$473$		−	27.0884i		−	0.0572694i
$474$		0			0
$475$	−37.9040	+	37.9040i	−0.0797978	+	0.0797978i
$476$		0			0
$477$	173.641	−	173.641i	0.364027	−	0.364027i
$478$		0			0
$479$			448.127i			0.935547i	0.883848	+	0.467773i	$0.154944\pi$
$479$			448.127i			0.935547i	−0.883848	+	0.467773i	$0.845056\pi$
$480$		0			0
$481$	−224.747			−0.467250
$482$		0			0
$483$	−370.047	−	370.047i	−0.766142	−	0.766142i
$484$		0			0
$485$	198.999	+	198.999i	0.410307	+	0.410307i
$486$		0			0
$487$	333.697			0.685210			0.342605	−	0.939480i	$-0.388691\pi$
$487$	333.697			0.685210			0.342605	+	0.939480i	$0.388691\pi$
$488$		0			0
$489$			392.290i			0.802229i
$490$		0			0
$491$	118.839	−	118.839i	0.242034	−	0.242034i	−0.575657	−	0.817691i	$-0.695254\pi$
$491$	118.839	−	118.839i	0.242034	−	0.242034i	0.817691	+	0.575657i	$0.195254\pi$
$492$		0			0
$493$	681.837	−	681.837i	1.38304	−	1.38304i
$494$		0			0
$495$		−	659.592i		−	1.33251i
$496$		0			0
$497$	−479.939			−0.965672
$498$		0			0
$499$	−148.915	−	148.915i	−0.298427	−	0.298427i	0.541970	−	0.840398i	$-0.317679\pi$
$499$	−148.915	−	148.915i	−0.298427	−	0.298427i	−0.840398	+	0.541970i	$0.817679\pi$
$500$		0			0
$501$	799.121	+	799.121i	1.59505	+	1.59505i
$502$		0			0
$503$	−347.840			−0.691530			−0.345765	−	0.938321i	$-0.612381\pi$
$503$	−347.840			−0.691530			−0.345765	+	0.938321i	$0.612381\pi$
$504$		0			0
$505$			113.712i			0.225172i
$506$		0			0
$507$	394.681	−	394.681i	0.778463	−	0.778463i
$508$		0			0
$509$	129.882	−	129.882i	0.255171	−	0.255171i	−0.567916	−	0.823087i	$-0.692250\pi$
$509$	129.882	−	129.882i	0.255171	−	0.255171i	0.823087	+	0.567916i	$0.192250\pi$
$510$		0			0
$511$			99.0433i			0.193823i
$512$		0			0
$513$	643.739			1.25485
$514$		0			0
$515$	83.6802	+	83.6802i	0.162486	+	0.162486i
$516$		0			0
$517$	−268.584	−	268.584i	−0.519505	−	0.519505i
$518$		0			0
$519$	82.4456			0.158855
$520$		0			0
$521$		−	240.395i		−	0.461411i	−0.973024	−	0.230706i	$-0.925897\pi$
$521$		−	240.395i		−	0.461411i	0.973024	−	0.230706i	$-0.0741034\pi$
$522$		0			0
$523$	501.537	−	501.537i	0.958962	−	0.958962i	−0.0402281	−	0.999191i	$-0.512808\pi$
$523$	501.537	−	501.537i	0.958962	−	0.958962i	0.999191	+	0.0402281i	$0.0128085\pi$
$524$		0			0
$525$	134.754	−	134.754i	0.256674	−	0.256674i
$526$		0			0
$527$			546.590i			1.03717i
$528$		0			0
$529$	−340.474			−0.643618
$530$		0			0
$531$	881.670	+	881.670i	1.66040	+	1.66040i
$532$		0			0
$533$	165.422	+	165.422i	0.310360	+	0.310360i
$534$		0			0
$535$	333.229			0.622858
$536$		0			0
$537$		−	1626.08i		−	3.02808i
$538$		0			0
$539$	−9.07669	+	9.07669i	−0.0168399	+	0.0168399i
$540$		0			0
$541$	−675.194	+	675.194i	−1.24805	+	1.24805i	−0.291467	+	0.956581i	$0.594143\pi$
$541$	−675.194	+	675.194i	−1.24805	+	1.24805i	−0.956581	+	0.291467i	$0.905857\pi$
$542$		0			0
$543$			210.283i			0.387261i
$544$		0			0
$545$	−398.709			−0.731576
$546$		0			0
$547$	−324.268	−	324.268i	−0.592811	−	0.592811i	0.345579	−	0.938390i	$-0.387683\pi$
$547$	−324.268	−	324.268i	−0.592811	−	0.592811i	−0.938390	+	0.345579i	$0.887683\pi$
$548$		0			0
$549$	−530.776	−	530.776i	−0.966805	−	0.966805i
$550$		0			0
$551$	493.487			0.895620
$552$		0			0
$553$			77.7053i			0.140516i
$554$		0			0
$555$	236.827	−	236.827i	0.426716	−	0.426716i
$556$		0			0
$557$	−454.039	+	454.039i	−0.815151	+	0.815151i	−0.985401	−	0.170250i	$-0.945543\pi$
$557$	−454.039	+	454.039i	−0.815151	+	0.815151i	0.170250	+	0.985401i	$0.445543\pi$
$558$		0			0
$559$		−	14.9667i		−	0.0267740i
$560$		0			0
$561$	1657.00			2.95366
$562$		0			0
$563$	−530.844	−	530.844i	−0.942885	−	0.942885i	0.0555697	−	0.998455i	$-0.482302\pi$
$563$	−530.844	−	530.844i	−0.942885	−	0.942885i	−0.998455	+	0.0555697i	$0.982302\pi$
$564$		0			0
$565$	−100.138	−	100.138i	−0.177235	−	0.177235i
$566$		0			0
$567$	−1009.36			−1.78017
$568$		0			0
$569$			444.904i			0.781906i	0.920411	+	0.390953i	$0.127854\pi$
$569$			444.904i			0.781906i	−0.920411	+	0.390953i	$0.872146\pi$
$570$		0			0
$571$	144.285	−	144.285i	0.252688	−	0.252688i	−0.569384	−	0.822072i	$-0.692818\pi$
$571$	144.285	−	144.285i	0.252688	−	0.252688i	0.822072	+	0.569384i	$0.192818\pi$
$572$		0			0
$573$	−1087.71	+	1087.71i	−1.89828	+	1.89828i
$574$		0			0
$575$			68.6524i			0.119396i
$576$		0			0
$577$	572.779			0.992685			0.496343	−	0.868127i	$-0.334676\pi$
$577$	572.779			0.992685			0.496343	+	0.868127i	$0.334676\pi$
$578$		0			0
$579$	−66.5992	−	66.5992i	−0.115025	−	0.115025i
$580$		0			0
$581$	496.443	+	496.443i	0.854463	+	0.854463i
$582$		0			0
$583$	178.831			0.306742
$584$		0			0
$585$		−	364.431i		−	0.622960i
$586$		0			0
$587$	44.1122	−	44.1122i	0.0751486	−	0.0751486i	−0.668533	−	0.743682i	$-0.733078\pi$
$587$	44.1122	−	44.1122i	0.0751486	−	0.0751486i	0.743682	+	0.668533i	$0.233078\pi$
$588$		0			0
$589$	−197.800	+	197.800i	−0.335824	+	0.335824i
$590$		0			0
$591$			705.135i			1.19312i
$592$		0			0
$593$	−463.508			−0.781632			−0.390816	−	0.920469i	$-0.627807\pi$
$593$	−463.508			−0.781632			−0.390816	+	0.920469i	$0.627807\pi$
$594$		0			0
$595$	233.919	+	233.919i	0.393141	+	0.393141i
$596$		0			0
$597$	1131.26	+	1131.26i	1.89491	+	1.89491i
$598$		0			0
$599$	−441.512			−0.737082			−0.368541	−	0.929612i	$-0.620143\pi$
$599$	−441.512			−0.737082			−0.368541	+	0.929612i	$0.620143\pi$
$600$		0			0
$601$			403.814i			0.671904i	0.941879	+	0.335952i	$0.109058\pi$
$601$			403.814i			0.671904i	−0.941879	+	0.335952i	$0.890942\pi$
$602$		0			0
$603$	−1267.02	+	1267.02i	−2.10119	+	2.10119i
$604$		0			0
$605$	148.335	−	148.335i	0.245182	−	0.245182i
$606$		0			0
$607$		−	789.688i		−	1.30097i	−0.759520	−	0.650484i	$-0.774566\pi$
$607$		−	789.688i		−	1.30097i	0.759520	−	0.650484i	$-0.225434\pi$
$608$		0			0
$609$	−1754.41			−2.88081
$610$		0			0
$611$	−148.396	−	148.396i	−0.242873	−	0.242873i
$612$		0			0
$613$	664.045	+	664.045i	1.08327	+	1.08327i	0.996202	+	0.0870678i	$0.0277497\pi$
$613$	664.045	+	664.045i	1.08327	+	1.08327i	0.0870678	+	0.996202i	$0.472250\pi$
$614$		0			0
$615$	−348.627			−0.566873
$616$		0			0
$617$			934.518i			1.51462i	0.653058	+	0.757308i	$0.273486\pi$
$617$			934.518i			1.51462i	−0.653058	+	0.757308i	$0.726514\pi$
$618$		0			0
$619$	−496.720	+	496.720i	−0.802455	+	0.802455i	−0.983479	−	0.181024i	$-0.942059\pi$
$619$	−496.720	+	496.720i	−0.802455	+	0.802455i	0.181024	+	0.983479i	$0.442059\pi$
$620$		0			0
$621$	582.976	−	582.976i	0.938770	−	0.938770i
$622$		0			0
$623$			1142.35i			1.83363i
$624$		0			0
$625$	−25.0000			−0.0400000
$626$		0			0
$627$	599.636	+	599.636i	0.956358	+	0.956358i
$628$		0			0
$629$	411.108	+	411.108i	0.653590	+	0.653590i
$630$		0			0
$631$	767.372			1.21612			0.608060	−	0.793891i	$-0.291948\pi$
$631$	767.372			1.21612			0.608060	+	0.793891i	$0.291948\pi$
$632$		0			0
$633$		−	1304.33i		−	2.06055i
$634$		0			0
$635$	171.873	−	171.873i	0.270666	−	0.270666i
$636$		0			0
$637$	−5.01497	+	5.01497i	−0.00787279	+	0.00787279i
$638$		0			0
$639$		−	1367.73i		−	2.14041i
$640$		0			0
$641$	670.734			1.04639			0.523193	−	0.852214i	$-0.324741\pi$
$641$	670.734			1.04639			0.523193	+	0.852214i	$0.324741\pi$
$642$		0			0
$643$	−329.050	−	329.050i	−0.511743	−	0.511743i	0.403317	−	0.915060i	$-0.367857\pi$
$643$	−329.050	−	329.050i	−0.511743	−	0.511743i	−0.915060	+	0.403317i	$0.867857\pi$
$644$		0			0
$645$	15.7711	+	15.7711i	0.0244513	+	0.0244513i
$646$		0			0
$647$	−576.907			−0.891664			−0.445832	−	0.895117i	$-0.647092\pi$
$647$	−576.907			−0.891664			−0.445832	+	0.895117i	$0.647092\pi$
$648$		0			0
$649$			908.021i			1.39911i
$650$		0			0
$651$	703.206	−	703.206i	1.08019	−	1.08019i
$652$		0			0
$653$	905.010	−	905.010i	1.38593	−	1.38593i	0.552243	−	0.833683i	$-0.313772\pi$
$653$	905.010	−	905.010i	1.38593	−	1.38593i	0.833683	−	0.552243i	$-0.186228\pi$
$654$		0			0
$655$			0.645265i			0.000985138i
$656$		0			0
$657$	−282.253			−0.429608
$658$		0			0
$659$	420.842	+	420.842i	0.638606	+	0.638606i	0.950212	−	0.311605i	$-0.100867\pi$
$659$	420.842	+	420.842i	0.638606	+	0.638606i	−0.311605	+	0.950212i	$0.600867\pi$
$660$		0			0
$661$	−661.814	−	661.814i	−1.00123	−	1.00123i	−0.999999	−	0.00123192i	$-0.999608\pi$
$661$	−661.814	−	661.814i	−1.00123	−	1.00123i	−0.00123192	−	0.999999i	$-0.500392\pi$
$662$		0			0
$663$	915.511			1.38086
$664$		0			0
$665$			169.301i			0.254588i
$666$		0			0
$667$	446.907	−	446.907i	0.670025	−	0.670025i
$668$		0			0
$669$	883.297	−	883.297i	1.32032	−	1.32032i
$670$		0			0
$671$		−	546.640i		−	0.814664i
$672$		0			0
$673$	−469.242			−0.697240			−0.348620	−	0.937264i	$-0.613350\pi$
$673$	−469.242			−0.697240			−0.348620	+	0.937264i	$0.613350\pi$
$674$		0			0
$675$	212.293	+	212.293i	0.314508	+	0.314508i
$676$		0			0
$677$	−656.674	−	656.674i	−0.969977	−	0.969977i	0.0295853	−	0.999562i	$-0.490581\pi$
$677$	−656.674	−	656.674i	−0.969977	−	0.969977i	−0.999562	+	0.0295853i	$0.990581\pi$
$678$		0			0
$679$	888.844			1.30905
$680$		0			0
$681$			121.702i			0.178711i
$682$		0			0
$683$	21.1806	−	21.1806i	0.0310111	−	0.0310111i	−0.691431	−	0.722442i	$-0.743019\pi$
$683$	21.1806	−	21.1806i	0.0310111	−	0.0310111i	0.722442	+	0.691431i	$0.243019\pi$
$684$		0			0
$685$	207.488	−	207.488i	0.302902	−	0.302902i
$686$		0			0
$687$		−	1874.66i		−	2.72876i
$688$		0			0
$689$	98.8059			0.143405
$690$		0			0
$691$	117.463	+	117.463i	0.169990	+	0.169990i	0.786975	−	0.616985i	$-0.211646\pi$
$691$	117.463	+	117.463i	0.169990	+	0.169990i	−0.616985	+	0.786975i	$0.711646\pi$
$692$		0			0
$693$	−1473.06	−	1473.06i	−2.12563	−	2.12563i
$694$		0			0
$695$	−235.554			−0.338926
$696$		0			0
$697$		−	605.181i		−	0.868265i
$698$		0			0
$699$	−1312.28	+	1312.28i	−1.87737	+	1.87737i
$700$		0			0
$701$	475.012	−	475.012i	0.677620	−	0.677620i	−0.281841	−	0.959461i	$-0.590945\pi$
$701$	475.012	−	475.012i	0.677620	−	0.677620i	0.959461	+	0.281841i	$0.0909450\pi$
$702$		0			0
$703$			297.544i			0.423249i
$704$		0			0
$705$	312.744			0.443608
$706$		0			0
$707$	253.952	+	253.952i	0.359196	+	0.359196i
$708$		0			0
$709$	−459.941	−	459.941i	−0.648718	−	0.648718i	0.303965	−	0.952683i	$-0.401689\pi$
$709$	−459.941	−	459.941i	−0.648718	−	0.648718i	−0.952683	+	0.303965i	$0.901689\pi$
$710$		0			0
$711$	−221.444			−0.311454
$712$		0			0
$713$			358.260i			0.502468i
$714$		0			0
$715$	187.662	−	187.662i	0.262464	−	0.262464i
$716$		0			0
$717$	−982.292	+	982.292i	−1.37000	+	1.37000i
$718$		0			0
$719$		−	79.4499i		−	0.110501i	−0.998473	−	0.0552503i	$-0.982404\pi$
$719$		−	79.4499i		−	0.110501i	0.998473	−	0.0552503i	$-0.0175957\pi$
$720$		0			0
$721$	373.764			0.518397
$722$		0			0
$723$	693.495	+	693.495i	0.959191	+	0.959191i
$724$		0			0
$725$	162.742	+	162.742i	0.224472	+	0.224472i
$726$		0			0
$727$	645.074			0.887310			0.443655	−	0.896198i	$-0.353682\pi$
$727$	645.074			0.887310			0.443655	+	0.896198i	$0.353682\pi$
$728$		0			0
$729$			40.0535i			0.0549431i
$730$		0			0
$731$	−27.3770	+	27.3770i	−0.0374515	+	0.0374515i
$732$		0			0
$733$	673.917	−	673.917i	0.919396	−	0.919396i	−0.0775895	−	0.996985i	$-0.524722\pi$
$733$	673.917	−	673.917i	0.919396	−	0.919396i	0.996985	+	0.0775895i	$0.0247224\pi$
$734$		0			0
$735$		−	10.5690i		−	0.0143796i
$736$		0			0
$737$	−1304.88			−1.77054
$738$		0			0
$739$	−489.699	−	489.699i	−0.662651	−	0.662651i	0.293353	−	0.956004i	$-0.405229\pi$
$739$	−489.699	−	489.699i	−0.662651	−	0.662651i	−0.956004	+	0.293353i	$0.905229\pi$
$740$		0			0
$741$	331.305	+	331.305i	0.447106	+	0.447106i
$742$		0			0
$743$	444.077			0.597681			0.298840	−	0.954303i	$-0.403400\pi$
$743$	444.077			0.597681			0.298840	+	0.954303i	$0.403400\pi$
$744$		0			0
$745$		−	442.040i		−	0.593342i
$746$		0			0
$747$	−1414.76	+	1414.76i	−1.89392	+	1.89392i
$748$		0			0
$749$	744.196	−	744.196i	0.993587	−	0.993587i
$750$		0			0
$751$			739.796i			0.985081i	0.870289	+	0.492541i	$0.163932\pi$
$751$			739.796i			0.985081i	−0.870289	+	0.492541i	$0.836068\pi$
$752$		0			0
$753$	384.472			0.510587
$754$		0			0
$755$	279.398	+	279.398i	0.370063	+	0.370063i
$756$		0			0
$757$	705.538	+	705.538i	0.932019	+	0.932019i	0.997832	−	0.0658133i	$-0.0209642\pi$
$757$	705.538	+	705.538i	0.932019	+	0.932019i	−0.0658133	+	0.997832i	$0.520964\pi$
$758$		0			0
$759$	1086.07			1.43093
$760$		0			0
$761$			1439.41i			1.89148i	0.324929	+	0.945738i	$0.394660\pi$
$761$			1439.41i			1.89148i	−0.324929	+	0.945738i	$0.605340\pi$
$762$		0			0
$763$	−890.433	+	890.433i	−1.16702	+	1.16702i
$764$		0			0
$765$	−666.619	+	666.619i	−0.871397	+	0.871397i
$766$		0			0
$767$			501.691i			0.654096i
$768$		0			0
$769$	994.407			1.29312			0.646558	−	0.762865i	$-0.276208\pi$
$769$	994.407			1.29312			0.646558	+	0.762865i	$0.276208\pi$
$770$		0			0
$771$	−751.645	−	751.645i	−0.974897	−	0.974897i
$772$		0			0
$773$	−506.461	−	506.461i	−0.655188	−	0.655188i	0.299049	−	0.954238i	$-0.403331\pi$
$773$	−506.461	−	506.461i	−0.655188	−	0.655188i	−0.954238	+	0.299049i	$0.903331\pi$
$774$		0			0
$775$	−130.461			−0.168337
$776$		0			0
$777$		−	1057.81i		−	1.36140i
$778$		0			0
$779$	219.003	−	219.003i	0.281134	−	0.281134i
$780$		0			0
$781$	704.302	−	704.302i	0.901795	−	0.901795i
$782$		0			0
$783$		−	2763.92i		−	3.52991i
$784$		0			0
$785$	−30.3873			−0.0387099
$786$		0			0
$787$	168.801	+	168.801i	0.214487	+	0.214487i	0.806170	−	0.591684i	$-0.201537\pi$
$787$	168.801	+	168.801i	0.214487	+	0.214487i	−0.591684	+	0.806170i	$0.701537\pi$
$788$		0			0
$789$	168.153	+	168.153i	0.213122	+	0.213122i
$790$		0			0
$791$	−447.274			−0.565454
$792$		0			0
$793$		−	302.024i		−	0.380863i
$794$		0			0
$795$	−104.117	+	104.117i	−0.130964	+	0.130964i
$796$		0			0
$797$	−994.677	+	994.677i	−1.24803	+	1.24803i	−0.291435	+	0.956591i	$0.594133\pi$
$797$	−994.677	+	994.677i	−1.24803	+	1.24803i	−0.956591	+	0.291435i	$0.905867\pi$
$798$		0			0
$799$			542.891i			0.679463i
$800$		0			0
$801$	−3255.46			−4.06424
$802$		0			0
$803$	−145.344	−	145.344i	−0.181002	−	0.181002i
$804$		0			0
$805$	153.321	+	153.321i	0.190461	+	0.190461i
$806$		0			0
$807$	−929.468			−1.15176
$808$		0			0
$809$		−	219.139i		−	0.270876i	−0.990786	−	0.135438i	$-0.956756\pi$
$809$		−	219.139i		−	0.270876i	0.990786	−	0.135438i	$-0.0432441\pi$
$810$		0			0
$811$	−942.641	+	942.641i	−1.16232	+	1.16232i	−0.178352	+	0.983967i	$0.557077\pi$
$811$	−942.641	+	942.641i	−1.16232	+	1.16232i	−0.983967	+	0.178352i	$0.942923\pi$
$812$		0			0
$813$	−861.057	+	861.057i	−1.05911	+	1.05911i
$814$		0			0
$815$		−	162.537i		−	0.199432i
$816$		0			0
$817$	−19.8144			−0.0242526
$818$		0			0
$819$	−813.881	−	813.881i	−0.993749	−	0.993749i
$820$		0			0
$821$	−476.861	−	476.861i	−0.580830	−	0.580830i	0.354301	−	0.935131i	$-0.384719\pi$
$821$	−476.861	−	476.861i	−0.580830	−	0.580830i	−0.935131	+	0.354301i	$0.884719\pi$
$822$		0			0
$823$	−1372.74			−1.66797			−0.833985	−	0.551788i	$-0.813946\pi$
$823$	−1372.74			−1.66797			−0.833985	+	0.551788i	$0.813946\pi$
$824$		0			0
$825$			395.497i			0.479390i
$826$		0			0
$827$	−171.863	+	171.863i	−0.207815	+	0.207815i	−0.803338	−	0.595523i	$-0.796945\pi$
$827$	−171.863	+	171.863i	−0.207815	+	0.207815i	0.595523	+	0.803338i	$0.296945\pi$
$828$		0			0
$829$	100.485	−	100.485i	0.121212	−	0.121212i	−0.643899	−	0.765111i	$-0.722684\pi$
$829$	100.485	−	100.485i	0.121212	−	0.121212i	0.765111	+	0.643899i	$0.222684\pi$
$830$		0			0
$831$			193.531i			0.232889i
$832$		0			0
$833$	18.3468			0.0220249
$834$		0			0
$835$	−331.099	−	331.099i	−0.396525	−	0.396525i
$836$		0			0
$837$	1107.84	+	1107.84i	1.32358	+	1.32358i
$838$		0			0
$839$	519.265			0.618909			0.309455	−	0.950914i	$-0.399853\pi$
$839$	519.265			0.618909			0.309455	+	0.950914i	$0.399853\pi$
$840$		0			0
$841$		−	1277.81i		−	1.51939i
$842$		0			0
$843$	879.161	−	879.161i	1.04290	−	1.04290i
$844$		0			0
$845$	−163.527	+	163.527i	−0.193524	+	0.193524i
$846$		0			0
$847$		−	662.550i		−	0.782232i
$848$		0			0
$849$	−550.525			−0.648440
$850$		0			0
$851$	269.459	+	269.459i	0.316638	+	0.316638i
$852$		0			0
$853$	989.103	+	989.103i	1.15956	+	1.15956i	0.984571	+	0.174987i	$0.0559885\pi$
$853$	989.103	+	989.103i	1.15956	+	1.15956i	0.174987	+	0.984571i	$0.444012\pi$
$854$		0			0
$855$	−482.472			−0.564295
$856$		0			0
$857$		−	271.282i		−	0.316549i	−0.987395	−	0.158274i	$-0.949407\pi$
$857$		−	271.282i		−	0.316549i	0.987395	−	0.158274i	$-0.0505931\pi$
$858$		0			0
$859$	−397.195	+	397.195i	−0.462393	+	0.462393i	−0.899439	−	0.437046i	$-0.856025\pi$
$859$	−397.195	+	397.195i	−0.462393	+	0.462393i	0.437046	+	0.899439i	$0.356025\pi$
$860$		0			0
$861$	−778.585	+	778.585i	−0.904280	+	0.904280i
$862$		0			0
$863$		−	84.9753i		−	0.0984649i	−0.998787	−	0.0492325i	$-0.984322\pi$
$863$		−	84.9753i		−	0.0984649i	0.998787	−	0.0492325i	$-0.0156775\pi$
$864$		0			0
$865$	−34.1595			−0.0394908
$866$		0			0
$867$	−571.787	−	571.787i	−0.659500	−	0.659500i
$868$		0			0
$869$	−114.031	−	114.031i	−0.131221	−	0.131221i
$870$		0			0
$871$	−720.963			−0.827741
$872$		0			0
$873$			2533.02i			2.90151i
$874$		0			0
$875$	−55.8322	+	55.8322i	−0.0638083	+	0.0638083i
$876$		0			0
$877$	264.532	−	264.532i	0.301633	−	0.301633i	−0.540020	−	0.841652i	$-0.681583\pi$
$877$	264.532	−	264.532i	0.301633	−	0.301633i	0.841652	+	0.540020i	$0.181583\pi$
$878$		0			0
$879$			1838.78i			2.09190i
$880$		0			0
$881$	−199.022			−0.225905			−0.112952	−	0.993600i	$-0.536031\pi$
$881$	−199.022			−0.225905			−0.112952	+	0.993600i	$0.536031\pi$
$882$		0			0
$883$	−403.210	−	403.210i	−0.456636	−	0.456636i	0.440913	−	0.897550i	$-0.354655\pi$
$883$	−403.210	−	403.210i	−0.456636	−	0.456636i	−0.897550	+	0.440913i	$0.854655\pi$
$884$		0			0
$885$	−528.657	−	528.657i	−0.597353	−	0.597353i
$886$		0			0
$887$	794.907			0.896174			0.448087	−	0.893990i	$-0.352105\pi$
$887$	794.907			0.896174			0.448087	+	0.893990i	$0.352105\pi$
$888$		0			0
$889$		−	767.684i		−	0.863537i
$890$		0			0
$891$	1481.21	−	1481.21i	1.66242	−	1.66242i
$892$		0			0
$893$	−196.462	+	196.462i	−0.220002	+	0.220002i
$894$		0			0
$895$			673.730i			0.752771i
$896$		0			0
$897$	600.067			0.668971
$898$		0			0
$899$	849.264	+	849.264i	0.944677	+	0.944677i
$900$		0			0
$901$	−180.736	−	180.736i	−0.200595	−	0.200595i
$902$		0			0
$903$	70.4429			0.0780098
$904$		0			0
$905$		−	87.1261i		−	0.0962720i
$906$		0			0
$907$	779.778	−	779.778i	0.859733	−	0.859733i	−0.131573	−	0.991306i	$-0.542003\pi$
$907$	779.778	−	779.778i	0.859733	−	0.859733i	0.991306	+	0.131573i	$0.0420029\pi$
$908$		0			0
$909$	−723.709	+	723.709i	−0.796159	+	0.796159i
$910$		0			0
$911$		−	491.368i		−	0.539372i	−0.962948	−	0.269686i	$-0.913080\pi$
$911$		−	491.368i		−	0.539372i	0.962948	−	0.269686i	$-0.0869199\pi$
$912$		0			0
$913$	−1457.04			−1.59588
$914$		0			0
$915$	318.258	+	318.258i	0.347823	+	0.347823i
$916$		0			0
$917$	1.44106	+	1.44106i	0.00157150	+	0.00157150i
$918$		0			0
$919$	−1434.03			−1.56042			−0.780212	−	0.625515i	$-0.784889\pi$
$919$	−1434.03			−1.56042			−0.780212	+	0.625515i	$0.784889\pi$
$920$		0			0
$921$			2062.97i			2.23993i
$922$		0			0
$923$	389.134	−	389.134i	0.421597	−	0.421597i
$924$		0			0
$925$	−98.1242	+	98.1242i	−0.106080	+	0.106080i
$926$		0			0
$927$			1065.15i			1.14903i
$928$		0			0
$929$	429.452			0.462273			0.231137	−	0.972921i	$-0.425756\pi$
$929$	429.452			0.462273			0.231137	+	0.972921i	$0.425756\pi$
$930$		0			0
$931$	6.63934	+	6.63934i	0.00713140	+	0.00713140i
$932$		0			0
$933$	2068.76	+	2068.76i	2.21732	+	2.21732i
$934$		0			0
$935$	−686.543			−0.734270
$936$		0			0
$937$		−	1739.01i		−	1.85594i	−0.372660	−	0.927968i	$-0.621554\pi$
$937$		−	1739.01i		−	1.85594i	0.372660	−	0.927968i	$-0.378446\pi$
$938$		0			0
$939$	−571.705	+	571.705i	−0.608845	+	0.608845i
$940$		0			0
$941$	−732.880	+	732.880i	−0.778831	+	0.778831i	−0.979632	−	0.200801i	$-0.935645\pi$
$941$	−732.880	+	732.880i	−0.778831	+	0.778831i	0.200801	+	0.979632i	$0.435645\pi$
$942$		0			0
$943$		−	396.663i		−	0.420639i
$944$		0			0
$945$	948.222			1.00341
$946$		0			0
$947$	1044.83	+	1044.83i	1.10330	+	1.10330i	0.994009	+	0.109296i	$0.0348595\pi$
$947$	1044.83	+	1044.83i	1.10330	+	1.10330i	0.109296	+	0.994009i	$0.465140\pi$
$948$		0			0
$949$	−80.3042	−	80.3042i	−0.0846198	−	0.0846198i
$950$		0			0
$951$	−3200.44			−3.36534
$952$		0			0
$953$			759.754i			0.797224i	0.917120	+	0.398612i	$0.130508\pi$
$953$			759.754i			0.797224i	−0.917120	+	0.398612i	$0.869492\pi$
$954$		0			0
$955$	450.671	−	450.671i	0.471907	−	0.471907i
$956$		0			0
$957$	2574.57	−	2574.57i	2.69025	−	2.69025i
$958$		0			0
$959$		−	926.762i		−	0.966384i
$960$		0			0
$961$	280.193			0.291564
$962$		0			0
$963$	2120.80	+	2120.80i	2.20229	+	2.20229i
$964$		0			0
$965$	27.5939	+	27.5939i	0.0285947	+	0.0285947i
$966$		0			0
$967$	44.4105			0.0459260			0.0229630	−	0.999736i	$-0.492690\pi$
$967$	44.4105			0.0459260			0.0229630	+	0.999736i	$0.492690\pi$
$968$		0			0
$969$		−	1212.05i		−	1.25082i
$970$		0			0
$971$	−519.035	+	519.035i	−0.534537	+	0.534537i	−0.921919	−	0.387382i	$-0.873379\pi$
$971$	−519.035	+	519.035i	−0.534537	+	0.534537i	0.387382	+	0.921919i	$0.373379\pi$
$972$		0			0
$973$	−526.060	+	526.060i	−0.540657	+	0.540657i
$974$		0			0
$975$			218.516i			0.224119i
$976$		0			0
$977$	−797.585			−0.816361			−0.408181	−	0.912901i	$-0.633837\pi$
$977$	−797.585			−0.816361			−0.408181	+	0.912901i	$0.633837\pi$
$978$		0			0
$979$	−1676.38	−	1676.38i	−1.71234	−	1.71234i
$980$		0			0
$981$	−2537.55	−	2537.55i	−2.58669	−	2.58669i
$982$		0			0
$983$	1432.42			1.45720			0.728599	−	0.684941i	$-0.240172\pi$
$983$	1432.42			1.45720			0.728599	+	0.684941i	$0.240172\pi$
$984$		0			0
$985$		−	292.157i		−	0.296606i
$986$		0			0
$987$	698.447	−	698.447i	0.707646	−	0.707646i
$988$		0			0
$989$	−17.9441	+	17.9441i	−0.0181437	+	0.0181437i
$990$		0			0
$991$		−	1885.38i		−	1.90250i	−0.308424	−	0.951249i	$-0.599802\pi$
$991$		−	1885.38i		−	1.90250i	0.308424	−	0.951249i	$-0.400198\pi$
$992$		0			0
$993$	815.449			0.821197
$994$		0			0
$995$	−468.714	−	468.714i	−0.471070	−	0.471070i
$996$		0			0
$997$	396.902	+	396.902i	0.398096	+	0.398096i	0.877561	−	0.479465i	$-0.159169\pi$
$997$	396.902	+	396.902i	0.398096	+	0.398096i	−0.479465	+	0.877561i	$0.659169\pi$
$998$		0			0
$999$	1666.48			1.66815

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.3.r.a.271.1		32
4.3	odd	2		80.3.r.a.11.2	✓	32
8.3	odd	2		640.3.r.a.31.1		32
8.5	even	2		640.3.r.b.31.16		32
16.3	odd	4	inner	320.3.r.a.111.1		32
16.5	even	4		640.3.r.a.351.1		32
16.11	odd	4		640.3.r.b.351.16		32
16.13	even	4		80.3.r.a.51.2	yes	32
20.3	even	4		400.3.k.g.299.8		32
20.7	even	4		400.3.k.h.299.9		32
20.19	odd	2		400.3.r.f.251.15		32
80.13	odd	4		400.3.k.h.99.9		32
80.29	even	4		400.3.r.f.51.15		32
80.77	odd	4		400.3.k.g.99.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.r.a.11.2	✓	32	4.3	odd	2
80.3.r.a.51.2	yes	32	16.13	even	4
320.3.r.a.111.1		32	16.3	odd	4	inner
320.3.r.a.271.1		32	1.1	even	1	trivial
400.3.k.g.99.8		32	80.77	odd	4
400.3.k.g.299.8		32	20.3	even	4
400.3.k.h.99.9		32	80.13	odd	4
400.3.k.h.299.9		32	20.7	even	4
400.3.r.f.51.15		32	80.29	even	4
400.3.r.f.251.15		32	20.19	odd	2
640.3.r.a.31.1		32	8.3	odd	2
640.3.r.a.351.1		32	16.5	even	4
640.3.r.b.31.16		32	8.5	even	2
640.3.r.b.351.16		32	16.11	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-3.81615 - 3.81615i) q^{3} +(1.58114 + 1.58114i) q^{5} +7.06228 q^{7} +20.1260i q^{9} +O(q^{10})\)	\(q+(-3.81615 - 3.81615i) q^{3} +(1.58114 + 1.58114i) q^{5} +7.06228 q^{7} +20.1260i q^{9} +(-10.3638 + 10.3638i) q^{11} +(-5.72609 + 5.72609i) q^{13} -12.0677i q^{15} +20.9484 q^{17} +(7.58079 + 7.58079i) q^{19} +(-26.9507 - 26.9507i) q^{21} +13.7305 q^{23} +5.00000i q^{25} +(42.4585 - 42.4585i) q^{27} +(32.5485 - 32.5485i) q^{29} +26.0923i q^{31} +79.0994 q^{33} +(11.1664 + 11.1664i) q^{35} +(19.6248 + 19.6248i) q^{37} +43.7032 q^{39} -28.8892i q^{41} +(-1.30688 + 1.30688i) q^{43} +(-31.8220 + 31.8220i) q^{45} +25.9157i q^{47} +0.875810 q^{49} +(-79.9421 - 79.9421i) q^{51} +(-8.62769 - 8.62769i) q^{53} -32.7731 q^{55} -57.8589i q^{57} +(43.8075 - 43.8075i) q^{59} +(-26.3726 + 26.3726i) q^{61} +142.136i q^{63} -18.1075 q^{65} +(62.9542 + 62.9542i) q^{67} +(-52.3976 - 52.3976i) q^{69} -67.9581 q^{71} +14.0243i q^{73} +(19.0808 - 19.0808i) q^{75} +(-73.1918 + 73.1918i) q^{77} +11.0029i q^{79} -142.922 q^{81} +(70.2950 + 70.2950i) q^{83} +(33.1223 + 33.1223i) q^{85} -248.420 q^{87} +161.754i q^{89} +(-40.4393 + 40.4393i) q^{91} +(99.5721 - 99.5721i) q^{93} +23.9726i q^{95} +125.858 q^{97} +(-208.581 - 208.581i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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