LMFDB - Embedded newform 320.3.r.a.271.12

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			271.12
Character	$\chi$	$=$	320.271
Dual form			320.3.r.a.111.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.45771 + 1.45771i) q^{3} +(-1.58114 - 1.58114i) q^{5} +11.3889 q^{7} -4.75014i q^{9} +O(q^{10})$	\(q+(1.45771 + 1.45771i) q^{3} +(-1.58114 - 1.58114i) q^{5} +11.3889 q^{7} -4.75014i q^{9} +(1.50884 - 1.50884i) q^{11} +(-0.454934 + 0.454934i) q^{13} -4.60970i q^{15} -1.99478 q^{17} +(-5.07749 - 5.07749i) q^{19} +(16.6018 + 16.6018i) q^{21} +41.9677 q^{23} +5.00000i q^{25} +(20.0438 - 20.0438i) q^{27} +(7.01958 - 7.01958i) q^{29} +33.3169i q^{31} +4.39891 q^{33} +(-18.0075 - 18.0075i) q^{35} +(44.5560 + 44.5560i) q^{37} -1.32633 q^{39} -51.6250i q^{41} +(-37.7501 + 37.7501i) q^{43} +(-7.51063 + 7.51063i) q^{45} +16.2073i q^{47} +80.7075 q^{49} +(-2.90782 - 2.90782i) q^{51} +(-67.7628 - 67.7628i) q^{53} -4.77137 q^{55} -14.8031i q^{57} +(-34.2172 + 34.2172i) q^{59} +(-67.1838 + 67.1838i) q^{61} -54.0990i q^{63} +1.43863 q^{65} +(9.87270 + 9.87270i) q^{67} +(61.1769 + 61.1769i) q^{69} +74.7263 q^{71} -101.825i q^{73} +(-7.28857 + 7.28857i) q^{75} +(17.1840 - 17.1840i) q^{77} -63.6444i q^{79} +15.6849 q^{81} +(-57.1418 - 57.1418i) q^{83} +(3.15403 + 3.15403i) q^{85} +20.4651 q^{87} +33.6218i q^{89} +(-5.18121 + 5.18121i) q^{91} +(-48.5665 + 48.5665i) q^{93} +16.0564i q^{95} -98.2875 q^{97} +(-7.16720 - 7.16720i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.45771	+	1.45771i	0.485905	+	0.485905i	0.907011	−	0.421107i	$-0.138358\pi$
$3$	1.45771	+	1.45771i	0.485905	+	0.485905i	−0.421107	+	0.907011i	$0.638358\pi$
$4$		0			0
$5$	−1.58114	−	1.58114i	−0.316228	−	0.316228i
$5$	−1.58114	−	1.58114i	−0.316228	−	0.316228i
$6$		0			0
$7$	11.3889			1.62699			0.813494	−	0.581573i	$-0.197562\pi$
$7$	11.3889			1.62699			0.813494	+	0.581573i	$0.197562\pi$
$8$		0			0
$9$		−	4.75014i		−	0.527794i
$10$		0			0
$11$	1.50884	−	1.50884i	0.137167	−	0.137167i	−0.635189	−	0.772356i	$-0.719078\pi$
$11$	1.50884	−	1.50884i	0.137167	−	0.137167i	0.772356	+	0.635189i	$0.219078\pi$
$12$		0			0
$13$	−0.454934	+	0.454934i	−0.0349949	+	0.0349949i	−0.724388	−	0.689393i	$-0.757877\pi$
$13$	−0.454934	+	0.454934i	−0.0349949	+	0.0349949i	0.689393	+	0.724388i	$0.257877\pi$
$14$		0			0
$15$		−	4.60970i		−	0.307313i
$16$		0			0
$17$	−1.99478			−0.117340			−0.0586701	−	0.998277i	$-0.518686\pi$
$17$	−1.99478			−0.117340			−0.0586701	+	0.998277i	$0.518686\pi$
$18$		0			0
$19$	−5.07749	−	5.07749i	−0.267236	−	0.267236i	0.560749	−	0.827986i	$-0.310513\pi$
$19$	−5.07749	−	5.07749i	−0.267236	−	0.267236i	−0.827986	+	0.560749i	$0.810513\pi$
$20$		0			0
$21$	16.6018	+	16.6018i	0.790561	+	0.790561i
$22$		0			0
$23$	41.9677			1.82468			0.912341	−	0.409431i	$-0.134273\pi$
$23$	41.9677			1.82468			0.912341	+	0.409431i	$0.134273\pi$
$24$		0			0
$25$			5.00000i			0.200000i
$26$		0			0
$27$	20.0438	−	20.0438i	0.742362	−	0.742362i
$28$		0			0
$29$	7.01958	−	7.01958i	0.242054	−	0.242054i	−0.575645	−	0.817700i	$-0.695249\pi$
$29$	7.01958	−	7.01958i	0.242054	−	0.242054i	0.817700	+	0.575645i	$0.195249\pi$
$30$		0			0
$31$			33.3169i			1.07474i	0.843347	+	0.537370i	$0.180582\pi$
$31$			33.3169i			1.07474i	−0.843347	+	0.537370i	$0.819418\pi$
$32$		0			0
$33$	4.39891			0.133300
$34$		0			0
$35$	−18.0075	−	18.0075i	−0.514499	−	0.514499i
$36$		0			0
$37$	44.5560	+	44.5560i	1.20422	+	1.20422i	0.972872	+	0.231343i	$0.0743119\pi$
$37$	44.5560	+	44.5560i	1.20422	+	1.20422i	0.231343	+	0.972872i	$0.425688\pi$
$38$		0			0
$39$	−1.32633			−0.0340084
$40$		0			0
$41$		−	51.6250i		−	1.25915i	−0.776941	−	0.629573i	$-0.783230\pi$
$41$		−	51.6250i		−	1.25915i	0.776941	−	0.629573i	$-0.216770\pi$
$42$		0			0
$43$	−37.7501	+	37.7501i	−0.877909	+	0.877909i	−0.993318	−	0.115409i	$-0.963182\pi$
$43$	−37.7501	+	37.7501i	−0.877909	+	0.877909i	0.115409	+	0.993318i	$0.463182\pi$
$44$		0			0
$45$	−7.51063	+	7.51063i	−0.166903	+	0.166903i
$46$		0			0
$47$			16.2073i			0.344836i	0.985024	+	0.172418i	$0.0551580\pi$
$47$			16.2073i			0.344836i	−0.985024	+	0.172418i	$0.944842\pi$
$48$		0			0
$49$	80.7075			1.64709
$50$		0			0
$51$	−2.90782	−	2.90782i	−0.0570161	−	0.0570161i
$52$		0			0
$53$	−67.7628	−	67.7628i	−1.27854	−	1.27854i	−0.941483	−	0.337060i	$-0.890567\pi$
$53$	−67.7628	−	67.7628i	−1.27854	−	1.27854i	−0.337060	−	0.941483i	$-0.609433\pi$
$54$		0			0
$55$	−4.77137			−0.0867521
$56$		0			0
$57$		−	14.8031i		−	0.259703i
$58$		0			0
$59$	−34.2172	+	34.2172i	−0.579952	+	0.579952i	−0.934890	−	0.354938i	$-0.884502\pi$
$59$	−34.2172	+	34.2172i	−0.579952	+	0.579952i	0.354938	+	0.934890i	$0.384502\pi$
$60$		0			0
$61$	−67.1838	+	67.1838i	−1.10137	+	1.10137i	−0.107128	+	0.994245i	$0.534165\pi$
$61$	−67.1838	+	67.1838i	−1.10137	+	1.10137i	−0.994245	+	0.107128i	$0.965835\pi$
$62$		0			0
$63$		−	54.0990i		−	0.858714i
$64$		0			0
$65$	1.43863			0.0221327
$66$		0			0
$67$	9.87270	+	9.87270i	0.147354	+	0.147354i	0.776935	−	0.629581i	$-0.216773\pi$
$67$	9.87270	+	9.87270i	0.147354	+	0.147354i	−0.629581	+	0.776935i	$0.716773\pi$
$68$		0			0
$69$	61.1769	+	61.1769i	0.886622	+	0.886622i
$70$		0			0
$71$	74.7263			1.05248			0.526242	−	0.850335i	$-0.323601\pi$
$71$	74.7263			1.05248			0.526242	+	0.850335i	$0.323601\pi$
$72$		0			0
$73$		−	101.825i		−	1.39486i	−0.716653	−	0.697430i	$-0.754327\pi$
$73$		−	101.825i		−	1.39486i	0.716653	−	0.697430i	$-0.245673\pi$
$74$		0			0
$75$	−7.28857	+	7.28857i	−0.0971809	+	0.0971809i
$76$		0			0
$77$	17.1840	−	17.1840i	0.223169	−	0.223169i
$78$		0			0
$79$		−	63.6444i		−	0.805626i	−0.915282	−	0.402813i	$-0.868033\pi$
$79$		−	63.6444i		−	0.805626i	0.915282	−	0.402813i	$-0.131967\pi$
$80$		0			0
$81$	15.6849			0.193641
$82$		0			0
$83$	−57.1418	−	57.1418i	−0.688456	−	0.688456i	0.273435	−	0.961890i	$-0.411840\pi$
$83$	−57.1418	−	57.1418i	−0.688456	−	0.688456i	−0.961890	+	0.273435i	$0.911840\pi$
$84$		0			0
$85$	3.15403	+	3.15403i	0.0371062	+	0.0371062i
$86$		0			0
$87$	20.4651			0.235231
$88$		0			0
$89$			33.6218i			0.377773i	0.981999	+	0.188887i	$0.0604879\pi$
$89$			33.6218i			0.377773i	−0.981999	+	0.188887i	$0.939512\pi$
$90$		0			0
$91$	−5.18121	+	5.18121i	−0.0569363	+	0.0569363i
$92$		0			0
$93$	−48.5665	+	48.5665i	−0.522221	+	0.522221i
$94$		0			0
$95$			16.0564i			0.169015i
$96$		0			0
$97$	−98.2875			−1.01327			−0.506637	−	0.862160i	$-0.669111\pi$
$97$	−98.2875			−1.01327			−0.506637	+	0.862160i	$0.669111\pi$
$98$		0			0
$99$	−7.16720	−	7.16720i	−0.0723959	−	0.0723959i
$100$		0			0
$101$	−20.2805	−	20.2805i	−0.200797	−	0.200797i	0.599544	−	0.800341i	$-0.295348\pi$
$101$	−20.2805	−	20.2805i	−0.200797	−	0.200797i	−0.800341	+	0.599544i	$0.795348\pi$
$102$		0			0
$103$	−118.028			−1.14590			−0.572949	−	0.819591i	$-0.694201\pi$
$103$	−118.028			−1.14590			−0.572949	+	0.819591i	$0.694201\pi$
$104$		0			0
$105$		−	52.4995i		−	0.499995i
$106$		0			0
$107$	−34.7734	+	34.7734i	−0.324985	+	0.324985i	−0.850676	−	0.525691i	$-0.823807\pi$
$107$	−34.7734	+	34.7734i	−0.324985	+	0.324985i	0.525691	+	0.850676i	$0.323807\pi$
$108$		0			0
$109$	−67.9335	+	67.9335i	−0.623243	+	0.623243i	−0.946359	−	0.323116i	$-0.895269\pi$
$109$	−67.9335	+	67.9335i	−0.623243	+	0.623243i	0.323116	+	0.946359i	$0.395269\pi$
$110$		0			0
$111$			129.900i			1.17027i
$112$		0			0
$113$	−196.955			−1.74297			−0.871483	−	0.490426i	$-0.836841\pi$
$113$	−196.955			−1.74297			−0.871483	+	0.490426i	$0.836841\pi$
$114$		0			0
$115$	−66.3568	−	66.3568i	−0.577015	−	0.577015i
$116$		0			0
$117$	2.16100	+	2.16100i	0.0184701	+	0.0184701i
$118$		0			0
$119$	−22.7184			−0.190911
$120$		0			0
$121$			116.447i			0.962370i
$122$		0			0
$123$	75.2545	−	75.2545i	0.611825	−	0.611825i
$124$		0			0
$125$	7.90569	−	7.90569i	0.0632456	−	0.0632456i
$126$		0			0
$127$			56.0107i			0.441029i	0.975384	+	0.220514i	$0.0707736\pi$
$127$			56.0107i			0.441029i	−0.975384	+	0.220514i	$0.929226\pi$
$128$		0			0
$129$	−110.058			−0.853160
$130$		0			0
$131$	−10.7281	−	10.7281i	−0.0818939	−	0.0818939i	0.664973	−	0.746867i	$-0.268443\pi$
$131$	−10.7281	−	10.7281i	−0.0818939	−	0.0818939i	−0.746867	+	0.664973i	$0.768443\pi$
$132$		0			0
$133$	−57.8271	−	57.8271i	−0.434791	−	0.434791i
$134$		0			0
$135$	−63.3840			−0.469511
$136$		0			0
$137$			82.2389i			0.600284i	0.953895	+	0.300142i	$0.0970341\pi$
$137$			82.2389i			0.600284i	−0.953895	+	0.300142i	$0.902966\pi$
$138$		0			0
$139$	−38.7552	+	38.7552i	−0.278815	+	0.278815i	−0.832636	−	0.553821i	$-0.813169\pi$
$139$	−38.7552	+	38.7552i	−0.278815	+	0.278815i	0.553821	+	0.832636i	$0.313169\pi$
$140$		0			0
$141$	−23.6256	+	23.6256i	−0.167557	+	0.167557i
$142$		0			0
$143$			1.37284i			0.00960031i
$144$		0			0
$145$	−22.1978			−0.153089
$146$		0			0
$147$	117.648	+	117.648i	0.800330	+	0.800330i
$148$		0			0
$149$	−123.879	−	123.879i	−0.831404	−	0.831404i	0.156305	−	0.987709i	$-0.450042\pi$
$149$	−123.879	−	123.879i	−0.831404	−	0.831404i	−0.987709	+	0.156305i	$0.950042\pi$
$150$		0			0
$151$	234.509			1.55304			0.776518	−	0.630095i	$-0.216984\pi$
$151$	234.509			1.55304			0.776518	+	0.630095i	$0.216984\pi$
$152$		0			0
$153$			9.47550i			0.0619313i
$154$		0			0
$155$	52.6787	−	52.6787i	0.339862	−	0.339862i
$156$		0			0
$157$	193.424	−	193.424i	1.23200	−	1.23200i	0.268806	−	0.963194i	$-0.413371\pi$
$157$	193.424	−	193.424i	1.23200	−	1.23200i	0.963194	−	0.268806i	$-0.0866291\pi$
$158$		0			0
$159$		−	197.557i		−	1.24250i
$160$		0			0
$161$	477.967			2.96874
$162$		0			0
$163$	34.8389	+	34.8389i	0.213736	+	0.213736i	0.805852	−	0.592117i	$-0.201708\pi$
$163$	34.8389	+	34.8389i	0.213736	+	0.213736i	−0.592117	+	0.805852i	$0.701708\pi$
$164$		0			0
$165$	−6.95529	−	6.95529i	−0.0421533	−	0.0421533i
$166$		0			0
$167$	−209.450			−1.25419			−0.627095	−	0.778943i	$-0.715756\pi$
$167$	−209.450			−1.25419			−0.627095	+	0.778943i	$0.715756\pi$
$168$		0			0
$169$			168.586i			0.997551i
$170$		0			0
$171$	−24.1188	+	24.1188i	−0.141046	+	0.141046i
$172$		0			0
$173$	86.1955	−	86.1955i	0.498240	−	0.498240i	−0.412650	−	0.910890i	$-0.635397\pi$
$173$	86.1955	−	86.1955i	0.498240	−	0.498240i	0.910890	+	0.412650i	$0.135397\pi$
$174$		0			0
$175$			56.9446i			0.325398i
$176$		0			0
$177$	−99.7577			−0.563603
$178$		0			0
$179$	62.1898	+	62.1898i	0.347429	+	0.347429i	0.859151	−	0.511722i	$-0.170992\pi$
$179$	62.1898	+	62.1898i	0.347429	+	0.347429i	−0.511722	+	0.859151i	$0.670992\pi$
$180$		0			0
$181$	103.422	+	103.422i	0.571394	+	0.571394i	0.932518	−	0.361124i	$-0.117607\pi$
$181$	103.422	+	103.422i	0.571394	+	0.571394i	−0.361124	+	0.932518i	$0.617607\pi$
$182$		0			0
$183$	−195.869			−1.07032
$184$		0			0
$185$		−	140.898i		−	0.761613i
$186$		0			0
$187$	−3.00980	+	3.00980i	−0.0160952	+	0.0160952i
$188$		0			0
$189$	228.277	−	228.277i	1.20781	−	1.20781i
$190$		0			0
$191$			113.284i			0.593111i	0.955016	+	0.296556i	$0.0958380\pi$
$191$			113.284i			0.593111i	−0.955016	+	0.296556i	$0.904162\pi$
$192$		0			0
$193$	51.3584			0.266106			0.133053	−	0.991109i	$-0.457522\pi$
$193$	51.3584			0.266106			0.133053	+	0.991109i	$0.457522\pi$
$194$		0			0
$195$	2.09711	+	2.09711i	0.0107544	+	0.0107544i
$196$		0			0
$197$	11.8197	+	11.8197i	0.0599986	+	0.0599986i	0.736469	−	0.676471i	$-0.236492\pi$
$197$	11.8197	+	11.8197i	0.0599986	+	0.0599986i	−0.676471	+	0.736469i	$0.736492\pi$
$198$		0			0
$199$	−109.879			−0.552157			−0.276078	−	0.961135i	$-0.589035\pi$
$199$	−109.879			−0.552157			−0.276078	+	0.961135i	$0.589035\pi$
$200$		0			0
$201$			28.7831i			0.143200i
$202$		0			0
$203$	79.9454	−	79.9454i	0.393820	−	0.393820i
$204$		0			0
$205$	−81.6263	+	81.6263i	−0.398177	+	0.398177i
$206$		0			0
$207$		−	199.352i		−	0.963056i
$208$		0			0
$209$	−15.3222			−0.0733121
$210$		0			0
$211$	−7.62800	−	7.62800i	−0.0361516	−	0.0361516i	0.688800	−	0.724952i	$-0.258138\pi$
$211$	−7.62800	−	7.62800i	−0.0361516	−	0.0361516i	−0.724952	+	0.688800i	$0.758138\pi$
$212$		0			0
$213$	108.930	+	108.930i	0.511407	+	0.511407i
$214$		0			0
$215$	119.376			0.555239
$216$		0			0
$217$			379.444i			1.74859i
$218$		0			0
$219$	148.431	−	148.431i	0.677769	−	0.677769i
$220$		0			0
$221$	0.907494	−	0.907494i	0.00410631	−	0.00410631i
$222$		0			0
$223$		−	275.773i		−	1.23665i	−0.785922	−	0.618325i	$-0.787812\pi$
$223$		−	275.773i		−	1.23665i	0.785922	−	0.618325i	$-0.212188\pi$
$224$		0			0
$225$	23.7507			0.105559
$226$		0			0
$227$	198.273	+	198.273i	0.873451	+	0.873451i	0.992847	−	0.119396i	$-0.0380957\pi$
$227$	198.273	+	198.273i	0.873451	+	0.873451i	−0.119396	+	0.992847i	$0.538096\pi$
$228$		0			0
$229$	62.9484	+	62.9484i	0.274884	+	0.274884i	0.831063	−	0.556179i	$-0.187733\pi$
$229$	62.9484	+	62.9484i	0.274884	+	0.274884i	−0.556179	+	0.831063i	$0.687733\pi$
$230$		0			0
$231$	50.0988			0.216878
$232$		0			0
$233$		−	47.2495i		−	0.202788i	−0.994846	−	0.101394i	$-0.967670\pi$
$233$		−	47.2495i		−	0.202788i	0.994846	−	0.101394i	$-0.0323302\pi$
$234$		0			0
$235$	25.6260	−	25.6260i	0.109047	−	0.109047i
$236$		0			0
$237$	92.7754	−	92.7754i	0.391457	−	0.391457i
$238$		0			0
$239$			379.374i			1.58734i	0.608350	+	0.793669i	$0.291832\pi$
$239$			379.374i			1.58734i	−0.608350	+	0.793669i	$0.708168\pi$
$240$		0			0
$241$	55.4642			0.230142			0.115071	−	0.993357i	$-0.463290\pi$
$241$	55.4642			0.230142			0.115071	+	0.993357i	$0.463290\pi$
$242$		0			0
$243$	−157.530	−	157.530i	−0.648271	−	0.648271i
$244$		0			0
$245$	−127.610	−	127.610i	−0.520856	−	0.520856i
$246$		0			0
$247$	4.61985			0.0187038
$248$		0			0
$249$		−	166.593i		−	0.669047i
$250$		0			0
$251$	263.223	−	263.223i	1.04870	−	1.04870i	0.0499470	−	0.998752i	$-0.484095\pi$
$251$	263.223	−	263.223i	1.04870	−	1.04870i	0.998752	−	0.0499470i	$-0.0159052\pi$
$252$		0			0
$253$	63.3225	−	63.3225i	0.250287	−	0.250287i
$254$		0			0
$255$			9.19534i			0.0360601i
$256$		0			0
$257$	54.6002			0.212452			0.106226	−	0.994342i	$-0.466123\pi$
$257$	54.6002			0.212452			0.106226	+	0.994342i	$0.466123\pi$
$258$		0			0
$259$	507.444	+	507.444i	1.95924	+	1.95924i
$260$		0			0
$261$	−33.3440	−	33.3440i	−0.127755	−	0.127755i
$262$		0			0
$263$	−143.832			−0.546889			−0.273444	−	0.961888i	$-0.588163\pi$
$263$	−143.832			−0.546889			−0.273444	+	0.961888i	$0.588163\pi$
$264$		0			0
$265$			214.285i			0.808622i
$266$		0			0
$267$	−49.0110	+	49.0110i	−0.183562	+	0.183562i
$268$		0			0
$269$	6.26368	−	6.26368i	0.0232851	−	0.0232851i	−0.695368	−	0.718653i	$-0.744759\pi$
$269$	6.26368	−	6.26368i	0.0232851	−	0.0232851i	0.718653	+	0.695368i	$0.244759\pi$
$270$		0			0
$271$			309.505i			1.14209i	0.820920	+	0.571043i	$0.193461\pi$
$271$			309.505i			1.14209i	−0.820920	+	0.571043i	$0.806539\pi$
$272$		0			0
$273$	−15.1054			−0.0553313
$274$		0			0
$275$	7.54419	+	7.54419i	0.0274334	+	0.0274334i
$276$		0			0
$277$	81.0256	+	81.0256i	0.292511	+	0.292511i	0.838072	−	0.545560i	$-0.183683\pi$
$277$	81.0256	+	81.0256i	0.292511	+	0.292511i	−0.545560	+	0.838072i	$0.683683\pi$
$278$		0			0
$279$	158.260			0.567240
$280$		0			0
$281$		−	296.145i		−	1.05390i	−0.849898	−	0.526948i	$-0.823336\pi$
$281$		−	296.145i		−	1.05390i	0.849898	−	0.526948i	$-0.176664\pi$
$282$		0			0
$283$	−249.833	+	249.833i	−0.882801	+	0.882801i	−0.993818	−	0.111017i	$-0.964589\pi$
$283$	−249.833	+	249.833i	−0.882801	+	0.882801i	0.111017	+	0.993818i	$0.464589\pi$
$284$		0			0
$285$	−23.4057	+	23.4057i	−0.0821252	+	0.0821252i
$286$		0			0
$287$		−	587.953i		−	2.04862i
$288$		0			0
$289$	−285.021			−0.986231
$290$		0			0
$291$	−143.275	−	143.275i	−0.492354	−	0.492354i
$292$		0			0
$293$	−276.126	−	276.126i	−0.942410	−	0.942410i	0.0560201	−	0.998430i	$-0.482159\pi$
$293$	−276.126	−	276.126i	−0.942410	−	0.942410i	−0.998430	+	0.0560201i	$0.982159\pi$
$294$		0			0
$295$	108.204			0.366794
$296$		0			0
$297$		−	60.4856i		−	0.203655i
$298$		0			0
$299$	−19.0925	+	19.0925i	−0.0638546	+	0.0638546i
$300$		0			0
$301$	−429.933	+	429.933i	−1.42835	+	1.42835i
$302$		0			0
$303$		−	59.1263i		−	0.195136i
$304$		0			0
$305$	212.454			0.696570
$306$		0			0
$307$	122.996	+	122.996i	0.400639	+	0.400639i	0.878458	−	0.477819i	$-0.158572\pi$
$307$	122.996	+	122.996i	0.400639	+	0.400639i	−0.477819	+	0.878458i	$0.658572\pi$
$308$		0			0
$309$	−172.050	−	172.050i	−0.556797	−	0.556797i
$310$		0			0
$311$	−211.420			−0.679808			−0.339904	−	0.940460i	$-0.610395\pi$
$311$	−211.420			−0.679808			−0.339904	+	0.940460i	$0.610395\pi$
$312$		0			0
$313$			388.990i			1.24278i	0.783502	+	0.621390i	$0.213432\pi$
$313$			388.990i			1.24278i	−0.783502	+	0.621390i	$0.786568\pi$
$314$		0			0
$315$	−85.5380	+	85.5380i	−0.271549	+	0.271549i
$316$		0			0
$317$	−153.866	+	153.866i	−0.485381	+	0.485381i	−0.906845	−	0.421464i	$-0.861516\pi$
$317$	−153.866	+	153.866i	−0.485381	+	0.485381i	0.421464	+	0.906845i	$0.361516\pi$
$318$		0			0
$319$		−	21.1828i		−	0.0664038i
$320$		0			0
$321$	−101.379			−0.315824
$322$		0			0
$323$	10.1285	+	10.1285i	0.0313575	+	0.0313575i
$324$		0			0
$325$	−2.27467	−	2.27467i	−0.00699898	−	0.00699898i
$326$		0			0
$327$	−198.055			−0.605673
$328$		0			0
$329$			184.584i			0.561044i
$330$		0			0
$331$	−76.4441	+	76.4441i	−0.230949	+	0.230949i	−0.813089	−	0.582140i	$-0.802216\pi$
$331$	−76.4441	+	76.4441i	−0.230949	+	0.230949i	0.582140	+	0.813089i	$0.302216\pi$
$332$		0			0
$333$	211.647	−	211.647i	0.635577	−	0.635577i
$334$		0			0
$335$		−	31.2202i		−	0.0931947i
$336$		0			0
$337$	−321.325			−0.953487			−0.476744	−	0.879042i	$-0.658183\pi$
$337$	−321.325			−0.953487			−0.476744	+	0.879042i	$0.658183\pi$
$338$		0			0
$339$	−287.104	−	287.104i	−0.846915	−	0.846915i
$340$		0			0
$341$	50.2698	+	50.2698i	0.147419	+	0.147419i
$342$		0			0
$343$	361.114			1.05281
$344$		0			0
$345$		−	193.458i		−	0.560749i
$346$		0			0
$347$	307.964	−	307.964i	0.887504	−	0.887504i	−0.106779	−	0.994283i	$-0.534054\pi$
$347$	307.964	−	307.964i	0.887504	−	0.887504i	0.994283	+	0.106779i	$0.0340536\pi$
$348$		0			0
$349$	101.138	−	101.138i	0.289794	−	0.289794i	−0.547205	−	0.836999i	$-0.684308\pi$
$349$	101.138	−	101.138i	0.289794	−	0.289794i	0.836999	+	0.547205i	$0.184308\pi$
$350$		0			0
$351$			18.2372i			0.0519578i
$352$		0			0
$353$	339.179			0.960847			0.480423	−	0.877037i	$-0.340483\pi$
$353$	339.179			0.960847			0.480423	+	0.877037i	$0.340483\pi$
$354$		0			0
$355$	−118.153	−	118.153i	−0.332824	−	0.332824i
$356$		0			0
$357$	−33.1169	−	33.1169i	−0.0927645	−	0.0927645i
$358$		0			0
$359$	−102.544			−0.285638			−0.142819	−	0.989749i	$-0.545617\pi$
$359$	−102.544			−0.285638			−0.142819	+	0.989749i	$0.545617\pi$
$360$		0			0
$361$		−	309.438i		−	0.857169i
$362$		0			0
$363$	−169.746	+	169.746i	−0.467620	+	0.467620i
$364$		0			0
$365$	−160.999	+	160.999i	−0.441094	+	0.441094i
$366$		0			0
$367$			224.409i			0.611468i	0.952117	+	0.305734i	$0.0989018\pi$
$367$			224.409i			0.611468i	−0.952117	+	0.305734i	$0.901098\pi$
$368$		0			0
$369$	−245.226			−0.664569
$370$		0			0
$371$	−771.745	−	771.745i	−2.08018	−	2.08018i
$372$		0			0
$373$	376.228	+	376.228i	1.00865	+	1.00865i	0.999962	+	0.00869067i	$0.00276636\pi$
$373$	376.228	+	376.228i	1.00865	+	1.00865i	0.00869067	+	0.999962i	$0.497234\pi$
$374$		0			0
$375$	23.0485			0.0614626
$376$		0			0
$377$			6.38689i			0.0169413i
$378$		0			0
$379$	−44.5603	+	44.5603i	−0.117573	+	0.117573i	−0.763446	−	0.645872i	$-0.776494\pi$
$379$	−44.5603	+	44.5603i	−0.117573	+	0.117573i	0.645872	+	0.763446i	$0.276494\pi$
$380$		0			0
$381$	−81.6475	+	81.6475i	−0.214298	+	0.214298i
$382$		0			0
$383$			432.227i			1.12853i	0.825594	+	0.564265i	$0.190840\pi$
$383$			432.227i			1.12853i	−0.825594	+	0.564265i	$0.809160\pi$
$384$		0			0
$385$	−54.3407			−0.141145
$386$		0			0
$387$	179.318	+	179.318i	0.463355	+	0.463355i
$388$		0			0
$389$	309.922	+	309.922i	0.796715	+	0.796715i	0.982576	−	0.185861i	$-0.0595075\pi$
$389$	309.922	+	309.922i	0.796715	+	0.796715i	−0.185861	+	0.982576i	$0.559507\pi$
$390$		0			0
$391$	−83.7164			−0.214108
$392$		0			0
$393$		−	31.2770i		−	0.0795853i
$394$		0			0
$395$	−100.631	+	100.631i	−0.254761	+	0.254761i
$396$		0			0
$397$	414.353	−	414.353i	1.04371	−	1.04371i	0.0447092	−	0.999000i	$-0.485764\pi$
$397$	414.353	−	414.353i	1.04371	−	1.04371i	0.999000	−	0.0447092i	$-0.0142361\pi$
$398$		0			0
$399$		−	168.591i		−	0.422533i
$400$		0			0
$401$	66.3078			0.165356			0.0826781	−	0.996576i	$-0.473653\pi$
$401$	66.3078			0.165356			0.0826781	+	0.996576i	$0.473653\pi$
$402$		0			0
$403$	−15.1570	−	15.1570i	−0.0376104	−	0.0376104i
$404$		0			0
$405$	−24.8000	−	24.8000i	−0.0612345	−	0.0612345i
$406$		0			0
$407$	134.456			0.330358
$408$		0			0
$409$		−	510.262i		−	1.24758i	−0.781590	−	0.623792i	$-0.785591\pi$
$409$		−	510.262i		−	1.24758i	0.781590	−	0.623792i	$-0.214409\pi$
$410$		0			0
$411$	−119.881	+	119.881i	−0.291681	+	0.291681i
$412$		0			0
$413$	−389.697	+	389.697i	−0.943575	+	0.943575i
$414$		0			0
$415$			180.698i			0.435418i
$416$		0			0
$417$	−112.988			−0.270954
$418$		0			0
$419$	−417.302	−	417.302i	−0.995946	−	0.995946i	0.00404536	−	0.999992i	$-0.498712\pi$
$419$	−417.302	−	417.302i	−0.995946	−	0.995946i	−0.999992	+	0.00404536i	$0.998712\pi$
$420$		0			0
$421$	−226.536	−	226.536i	−0.538091	−	0.538091i	0.384877	−	0.922968i	$-0.374244\pi$
$421$	−226.536	−	226.536i	−0.538091	−	0.538091i	−0.922968	+	0.384877i	$0.874244\pi$
$422$		0			0
$423$	76.9870			0.182002
$424$		0			0
$425$		−	9.97391i		−	0.0234680i
$426$		0			0
$427$	−765.151	+	765.151i	−1.79192	+	1.79192i
$428$		0			0
$429$	−2.00121	+	2.00121i	−0.00466483	+	0.00466483i
$430$		0			0
$431$			623.188i			1.44591i	0.690894	+	0.722956i	$0.257217\pi$
$431$			623.188i			1.44591i	−0.690894	+	0.722956i	$0.742783\pi$
$432$		0			0
$433$	−128.798			−0.297455			−0.148727	−	0.988878i	$-0.547518\pi$
$433$	−128.798			−0.297455			−0.148727	+	0.988878i	$0.547518\pi$
$434$		0			0
$435$	−32.3581	−	32.3581i	−0.0743864	−	0.0743864i
$436$		0			0
$437$	−213.091	−	213.091i	−0.487621	−	0.487621i
$438$		0			0
$439$	−157.190			−0.358063			−0.179032	−	0.983843i	$-0.557296\pi$
$439$	−157.190			−0.358063			−0.179032	+	0.983843i	$0.557296\pi$
$440$		0			0
$441$		−	383.372i		−	0.869324i
$442$		0			0
$443$	359.787	−	359.787i	0.812160	−	0.812160i	−0.172798	−	0.984957i	$-0.555281\pi$
$443$	359.787	−	359.787i	0.812160	−	0.812160i	0.984957	+	0.172798i	$0.0552806\pi$
$444$		0			0
$445$	53.1607	−	53.1607i	0.119462	−	0.119462i
$446$		0			0
$447$		−	361.161i		−	0.807966i
$448$		0			0
$449$	−454.715			−1.01273			−0.506364	−	0.862320i	$-0.669011\pi$
$449$	−454.715			−1.01273			−0.506364	+	0.862320i	$0.669011\pi$
$450$		0			0
$451$	−77.8938	−	77.8938i	−0.172714	−	0.172714i
$452$		0			0
$453$	341.846	+	341.846i	0.754628	+	0.754628i
$454$		0			0
$455$	16.3844			0.0360097
$456$		0			0
$457$		−	390.576i		−	0.854652i	−0.904098	−	0.427326i	$-0.859456\pi$
$457$		−	390.576i		−	0.854652i	0.904098	−	0.427326i	$-0.140544\pi$
$458$		0			0
$459$	−39.9829	+	39.9829i	−0.0871088	+	0.0871088i
$460$		0			0
$461$	−228.455	+	228.455i	−0.495564	+	0.495564i	−0.910054	−	0.414490i	$-0.863960\pi$
$461$	−228.455	+	228.455i	−0.495564	+	0.495564i	0.414490	+	0.910054i	$0.363960\pi$
$462$		0			0
$463$			231.759i			0.500559i	0.968174	+	0.250280i	$0.0805225\pi$
$463$			231.759i			0.500559i	−0.968174	+	0.250280i	$0.919477\pi$
$464$		0			0
$465$	153.581			0.330281
$466$		0			0
$467$	−278.305	−	278.305i	−0.595943	−	0.595943i	0.343287	−	0.939230i	$-0.388460\pi$
$467$	−278.305	−	278.305i	−0.595943	−	0.595943i	−0.939230	+	0.343287i	$0.888460\pi$
$468$		0			0
$469$	112.439	+	112.439i	0.239743	+	0.239743i
$470$		0			0
$471$	563.914			1.19727
$472$		0			0
$473$			113.918i			0.240841i
$474$		0			0
$475$	25.3875	−	25.3875i	0.0534473	−	0.0534473i
$476$		0			0
$477$	−321.883	+	321.883i	−0.674807	+	0.674807i
$478$		0			0
$479$		−	332.325i		−	0.693789i	−0.937904	−	0.346894i	$-0.887236\pi$
$479$		−	332.325i		−	0.693789i	0.937904	−	0.346894i	$-0.112764\pi$
$480$		0			0
$481$	−40.5400			−0.0842828
$482$		0			0
$483$	696.739	+	696.739i	1.44252	+	1.44252i
$484$		0			0
$485$	155.406	+	155.406i	0.320425	+	0.320425i
$486$		0			0
$487$	−134.197			−0.275559			−0.137779	−	0.990463i	$-0.543996\pi$
$487$	−134.197			−0.275559			−0.137779	+	0.990463i	$0.543996\pi$
$488$		0			0
$489$			101.570i			0.207710i
$490$		0			0
$491$	−289.568	+	289.568i	−0.589751	+	0.589751i	−0.937564	−	0.347813i	$-0.886924\pi$
$491$	−289.568	+	289.568i	−0.589751	+	0.589751i	0.347813	+	0.937564i	$0.386924\pi$
$492$		0			0
$493$	−14.0025	+	14.0025i	−0.0284027	+	0.0284027i
$494$		0			0
$495$			22.6647i			0.0457872i
$496$		0			0
$497$	851.052			1.71238
$498$		0			0
$499$	39.4128	+	39.4128i	0.0789835	+	0.0789835i	0.745495	−	0.666511i	$-0.232213\pi$
$499$	39.4128	+	39.4128i	0.0789835	+	0.0789835i	−0.666511	+	0.745495i	$0.732213\pi$
$500$		0			0
$501$	−305.318	−	305.318i	−0.609417	−	0.609417i
$502$		0			0
$503$	770.015			1.53084			0.765422	−	0.643529i	$-0.222530\pi$
$503$	770.015			1.53084			0.765422	+	0.643529i	$0.222530\pi$
$504$		0			0
$505$			64.1326i			0.126995i
$506$		0			0
$507$	−245.750	+	245.750i	−0.484714	+	0.484714i
$508$		0			0
$509$	−307.000	+	307.000i	−0.603144	+	0.603144i	−0.941146	−	0.338001i	$-0.890249\pi$
$509$	−307.000	+	307.000i	−0.603144	+	0.603144i	0.338001	+	0.941146i	$0.390249\pi$
$510$		0			0
$511$		−	1159.67i		−	2.26942i
$512$		0			0
$513$	−203.544			−0.396772
$514$		0			0
$515$	186.618	+	186.618i	0.362365	+	0.362365i
$516$		0			0
$517$	24.4542	+	24.4542i	0.0473002	+	0.0473002i
$518$		0			0
$519$	251.297			0.484194
$520$		0			0
$521$			119.147i			0.228690i	0.993441	+	0.114345i	$0.0364769\pi$
$521$			119.147i			0.228690i	−0.993441	+	0.114345i	$0.963523\pi$
$522$		0			0
$523$	298.312	−	298.312i	0.570385	−	0.570385i	−0.361851	−	0.932236i	$-0.617855\pi$
$523$	298.312	−	298.312i	0.570385	−	0.570385i	0.932236	+	0.361851i	$0.117855\pi$
$524$		0			0
$525$	−83.0089	+	83.0089i	−0.158112	+	0.158112i
$526$		0			0
$527$		−	66.4600i		−	0.126110i
$528$		0			0
$529$	1232.29			2.32947
$530$		0			0
$531$	162.536	+	162.536i	0.306095	+	0.306095i
$532$		0			0
$533$	23.4860	+	23.4860i	0.0440637	+	0.0440637i
$534$		0			0
$535$	109.963			0.205539
$536$		0			0
$537$			181.310i			0.337635i
$538$		0			0
$539$	121.775	−	121.775i	0.225927	−	0.225927i
$540$		0			0
$541$	−181.552	+	181.552i	−0.335587	+	0.335587i	−0.854703	−	0.519117i	$-0.826261\pi$
$541$	−181.552	+	181.552i	−0.335587	+	0.335587i	0.519117	+	0.854703i	$0.326261\pi$
$542$		0			0
$543$			301.520i			0.555286i
$544$		0			0
$545$	214.825			0.394173
$546$		0			0
$547$	−36.9088	−	36.9088i	−0.0674749	−	0.0674749i	0.672564	−	0.740039i	$-0.265193\pi$
$547$	−36.9088	−	36.9088i	−0.0674749	−	0.0674749i	−0.740039	+	0.672564i	$0.765193\pi$
$548$		0			0
$549$	319.132	+	319.132i	0.581298	+	0.581298i
$550$		0			0
$551$	−71.2837			−0.129371
$552$		0			0
$553$		−	724.842i		−	1.31074i
$554$		0			0
$555$	205.389	−	205.389i	0.370071	−	0.370071i
$556$		0			0
$557$	340.215	−	340.215i	0.610799	−	0.610799i	−0.332355	−	0.943154i	$-0.607843\pi$
$557$	340.215	−	340.215i	0.610799	−	0.610799i	0.943154	+	0.332355i	$0.107843\pi$
$558$		0			0
$559$		−	34.3476i		−	0.0614447i
$560$		0			0
$561$	−8.77487			−0.0156415
$562$		0			0
$563$	34.7067	+	34.7067i	0.0616459	+	0.0616459i	0.737258	−	0.675612i	$-0.236120\pi$
$563$	34.7067	+	34.7067i	0.0616459	+	0.0616459i	−0.675612	+	0.737258i	$0.736120\pi$
$564$		0			0
$565$	311.413	+	311.413i	0.551174	+	0.551174i
$566$		0			0
$567$	178.634			0.315051
$568$		0			0
$569$			885.111i			1.55556i	0.628540	+	0.777778i	$0.283653\pi$
$569$			885.111i			1.55556i	−0.628540	+	0.777778i	$0.716347\pi$
$570$		0			0
$571$	628.714	−	628.714i	1.10108	−	1.10108i	0.106795	−	0.994281i	$-0.465941\pi$
$571$	628.714	−	628.714i	1.10108	−	1.10108i	0.994281	−	0.106795i	$-0.0340587\pi$
$572$		0			0
$573$	−165.136	+	165.136i	−0.288196	+	0.288196i
$574$		0			0
$575$			209.838i			0.364936i
$576$		0			0
$577$	−1004.14			−1.74028			−0.870139	−	0.492806i	$-0.835971\pi$
$577$	−1004.14			−1.74028			−0.870139	+	0.492806i	$0.835971\pi$
$578$		0			0
$579$	74.8659	+	74.8659i	0.129302	+	0.129302i
$580$		0			0
$581$	−650.784	−	650.784i	−1.12011	−	1.12011i
$582$		0			0
$583$	−204.486			−0.350748
$584$		0			0
$585$		−	6.83368i		−	0.0116815i
$586$		0			0
$587$	739.432	−	739.432i	1.25968	−	1.25968i	0.308435	−	0.951245i	$-0.400195\pi$
$587$	739.432	−	739.432i	1.25968	−	1.25968i	0.951245	−	0.308435i	$-0.0998052\pi$
$588$		0			0
$589$	169.166	−	169.166i	0.287209	−	0.287209i
$590$		0			0
$591$			34.4596i			0.0583072i
$592$		0			0
$593$	25.9184			0.0437073			0.0218536	−	0.999761i	$-0.493043\pi$
$593$	25.9184			0.0437073			0.0218536	+	0.999761i	$0.493043\pi$
$594$		0			0
$595$	35.9210	+	35.9210i	0.0603714	+	0.0603714i
$596$		0			0
$597$	−160.172	−	160.172i	−0.268295	−	0.268295i
$598$		0			0
$599$	43.8841			0.0732622			0.0366311	−	0.999329i	$-0.488337\pi$
$599$	43.8841			0.0732622			0.0366311	+	0.999329i	$0.488337\pi$
$600$		0			0
$601$		−	368.651i		−	0.613396i	−0.951807	−	0.306698i	$-0.900776\pi$
$601$		−	368.651i		−	0.613396i	0.951807	−	0.306698i	$-0.0992242\pi$
$602$		0			0
$603$	46.8967	−	46.8967i	0.0777724	−	0.0777724i
$604$		0			0
$605$	184.119	−	184.119i	0.304328	−	0.304328i
$606$		0			0
$607$			283.845i			0.467619i	0.972282	+	0.233810i	$0.0751193\pi$
$607$			283.845i			0.467619i	−0.972282	+	0.233810i	$0.924881\pi$
$608$		0			0
$609$	233.075			0.382718
$610$		0			0
$611$	−7.37325	−	7.37325i	−0.0120675	−	0.0120675i
$612$		0			0
$613$	232.620	+	232.620i	0.379478	+	0.379478i	0.870914	−	0.491436i	$-0.163528\pi$
$613$	232.620	+	232.620i	0.379478	+	0.379478i	−0.491436	+	0.870914i	$0.663528\pi$
$614$		0			0
$615$	−237.976			−0.386952
$616$		0			0
$617$		−	361.239i		−	0.585476i	−0.956193	−	0.292738i	$-0.905434\pi$
$617$		−	361.239i		−	0.585476i	0.956193	−	0.292738i	$-0.0945664\pi$
$618$		0			0
$619$	−323.747	+	323.747i	−0.523016	+	0.523016i	−0.918481	−	0.395465i	$-0.870584\pi$
$619$	−323.747	+	323.747i	−0.523016	+	0.523016i	0.395465	+	0.918481i	$0.370584\pi$
$620$		0			0
$621$	841.191	−	841.191i	1.35457	−	1.35457i
$622$		0			0
$623$			382.916i			0.614633i
$624$		0			0
$625$	−25.0000			−0.0400000
$626$		0			0
$627$	−22.3354	−	22.3354i	−0.0356227	−	0.0356227i
$628$		0			0
$629$	−88.8794	−	88.8794i	−0.141303	−	0.141303i
$630$		0			0
$631$	366.481			0.580794			0.290397	−	0.956906i	$-0.406213\pi$
$631$	366.481			0.580794			0.290397	+	0.956906i	$0.406213\pi$
$632$		0			0
$633$		−	22.2389i		−	0.0351325i
$634$		0			0
$635$	88.5606	−	88.5606i	0.139466	−	0.139466i
$636$		0			0
$637$	−36.7166	+	36.7166i	−0.0576399	+	0.0576399i
$638$		0			0
$639$		−	354.961i		−	0.555494i
$640$		0			0
$641$	410.184			0.639913			0.319957	−	0.947432i	$-0.396332\pi$
$641$	410.184			0.639913			0.319957	+	0.947432i	$0.396332\pi$
$642$		0			0
$643$	387.593	+	387.593i	0.602789	+	0.602789i	0.941052	−	0.338263i	$-0.109839\pi$
$643$	387.593	+	387.593i	0.602789	+	0.602789i	−0.338263	+	0.941052i	$0.609839\pi$
$644$		0			0
$645$	174.016	+	174.016i	0.269793	+	0.269793i
$646$		0			0
$647$	30.7975			0.0476005			0.0238002	−	0.999717i	$-0.492423\pi$
$647$	30.7975			0.0476005			0.0238002	+	0.999717i	$0.492423\pi$
$648$		0			0
$649$			103.256i			0.159101i
$650$		0			0
$651$	−553.120	+	553.120i	−0.849647	+	0.849647i
$652$		0			0
$653$	272.833	−	272.833i	0.417814	−	0.417814i	−0.466635	−	0.884450i	$-0.654534\pi$
$653$	272.833	−	272.833i	0.417814	−	0.417814i	0.884450	+	0.466635i	$0.154534\pi$
$654$		0			0
$655$			33.9252i			0.0517943i
$656$		0			0
$657$	−483.682			−0.736198
$658$		0			0
$659$	5.97726	+	5.97726i	0.00907020	+	0.00907020i	0.711627	−	0.702557i	$-0.247958\pi$
$659$	5.97726	+	5.97726i	0.00907020	+	0.00907020i	−0.702557	+	0.711627i	$0.747958\pi$
$660$		0			0
$661$	635.655	+	635.655i	0.961657	+	0.961657i	0.999292	−	0.0376349i	$-0.0119824\pi$
$661$	635.655	+	635.655i	0.961657	+	0.961657i	−0.0376349	+	0.999292i	$0.511982\pi$
$662$		0			0
$663$	2.64573			0.00399055
$664$		0			0
$665$			182.865i			0.274986i
$666$		0			0
$667$	294.595	−	294.595i	0.441672	−	0.441672i
$668$		0			0
$669$	401.998	−	401.998i	0.600894	−	0.600894i
$670$		0			0
$671$			202.739i			0.302144i
$672$		0			0
$673$	279.631			0.415499			0.207749	−	0.978182i	$-0.433386\pi$
$673$	279.631			0.415499			0.207749	+	0.978182i	$0.433386\pi$
$674$		0			0
$675$	100.219	+	100.219i	0.148472	+	0.148472i
$676$		0			0
$677$	30.3635	+	30.3635i	0.0448501	+	0.0448501i	0.729176	−	0.684326i	$-0.239903\pi$
$677$	30.3635	+	30.3635i	0.0448501	+	0.0448501i	−0.684326	+	0.729176i	$0.739903\pi$
$678$		0			0
$679$	−1119.39			−1.64858
$680$		0			0
$681$			578.052i			0.848828i
$682$		0			0
$683$	−311.913	+	311.913i	−0.456681	+	0.456681i	−0.897564	−	0.440883i	$-0.854665\pi$
$683$	−311.913	+	311.913i	−0.456681	+	0.456681i	0.440883	+	0.897564i	$0.354665\pi$
$684$		0			0
$685$	130.031	−	130.031i	0.189826	−	0.189826i
$686$		0			0
$687$			183.521i			0.267134i
$688$		0			0
$689$	61.6552			0.0894850
$690$		0			0
$691$	178.583	+	178.583i	0.258441	+	0.258441i	0.824420	−	0.565979i	$-0.191502\pi$
$691$	178.583	+	178.583i	0.258441	+	0.258441i	−0.565979	+	0.824420i	$0.691502\pi$
$692$		0			0
$693$	−81.6267	−	81.6267i	−0.117787	−	0.117787i
$694$		0			0
$695$	122.555			0.176338
$696$		0			0
$697$			102.981i			0.147748i
$698$		0			0
$699$	68.8763	−	68.8763i	0.0985355	−	0.0985355i
$700$		0			0
$701$	67.9066	−	67.9066i	0.0968710	−	0.0968710i	−0.657010	−	0.753881i	$-0.728179\pi$
$701$	67.9066	−	67.9066i	0.0968710	−	0.0968710i	0.753881	+	0.657010i	$0.228179\pi$
$702$		0			0
$703$		−	452.465i		−	0.643620i
$704$		0			0
$705$	74.7107			0.105973
$706$		0			0
$707$	−230.973	−	230.973i	−0.326695	−	0.326695i
$708$		0			0
$709$	−923.262	−	923.262i	−1.30220	−	1.30220i	−0.926903	−	0.375300i	$-0.877540\pi$
$709$	−923.262	−	923.262i	−1.30220	−	1.30220i	−0.375300	−	0.926903i	$-0.622460\pi$
$710$		0			0
$711$	−302.320			−0.425204
$712$		0			0
$713$			1398.23i			1.96106i
$714$		0			0
$715$	2.17066	−	2.17066i	0.00303588	−	0.00303588i
$716$		0			0
$717$	−553.018	+	553.018i	−0.771295	+	0.771295i
$718$		0			0
$719$			731.025i			1.01672i	0.861143	+	0.508362i	$0.169749\pi$
$719$			731.025i			1.01672i	−0.861143	+	0.508362i	$0.830251\pi$
$720$		0			0
$721$	−1344.21			−1.86436
$722$		0			0
$723$	80.8509	+	80.8509i	0.111827	+	0.111827i
$724$		0			0
$725$	35.0979	+	35.0979i	0.0484109	+	0.0484109i
$726$		0			0
$727$	−777.047			−1.06884			−0.534420	−	0.845219i	$-0.679470\pi$
$727$	−777.047			−1.06884			−0.534420	+	0.845219i	$0.679470\pi$
$728$		0			0
$729$		−	600.431i		−	0.823636i
$730$		0			0
$731$	75.3032	−	75.3032i	0.103014	−	0.103014i
$732$		0			0
$733$	510.271	−	510.271i	0.696141	−	0.696141i	−0.267435	−	0.963576i	$-0.586176\pi$
$733$	510.271	−	510.271i	0.696141	−	0.696141i	0.963576	+	0.267435i	$0.0861760\pi$
$734$		0			0
$735$		−	372.037i		−	0.506173i
$736$		0			0
$737$	29.7926			0.0404242
$738$		0			0
$739$	40.7107	+	40.7107i	0.0550890	+	0.0550890i	0.734115	−	0.679026i	$-0.237597\pi$
$739$	40.7107	+	40.7107i	0.0550890	+	0.0550890i	−0.679026	+	0.734115i	$0.737597\pi$
$740$		0			0
$741$	6.73441	+	6.73441i	0.00908828	+	0.00908828i
$742$		0			0
$743$	−602.696			−0.811166			−0.405583	−	0.914058i	$-0.632931\pi$
$743$	−602.696			−0.811166			−0.405583	+	0.914058i	$0.632931\pi$
$744$		0			0
$745$			391.740i			0.525826i
$746$		0			0
$747$	−271.432	+	271.432i	−0.363362	+	0.363362i
$748$		0			0
$749$	−396.032	+	396.032i	−0.528747	+	0.528747i
$750$		0			0
$751$		−	853.452i		−	1.13642i	−0.822883	−	0.568210i	$-0.807636\pi$
$751$		−	853.452i		−	1.13642i	0.822883	−	0.568210i	$-0.192364\pi$
$752$		0			0
$753$	767.409			1.01914
$754$		0			0
$755$	−370.791	−	370.791i	−0.491113	−	0.491113i
$756$		0			0
$757$	−52.9121	−	52.9121i	−0.0698971	−	0.0698971i	0.671294	−	0.741191i	$-0.265739\pi$
$757$	−52.9121	−	52.9121i	−0.0698971	−	0.0698971i	−0.741191	+	0.671294i	$0.765739\pi$
$758$		0			0
$759$	184.612			0.243231
$760$		0			0
$761$			164.185i			0.215749i	0.994165	+	0.107874i	$0.0344045\pi$
$761$			164.185i			0.215749i	−0.994165	+	0.107874i	$0.965596\pi$
$762$		0			0
$763$	−773.689	+	773.689i	−1.01401	+	1.01401i
$764$		0			0
$765$	14.9821	−	14.9821i	0.0195844	−	0.0195844i
$766$		0			0
$767$		−	31.1331i		−	0.0405907i
$768$		0			0
$769$	−466.767			−0.606979			−0.303489	−	0.952835i	$-0.598152\pi$
$769$	−466.767			−0.606979			−0.303489	+	0.952835i	$0.598152\pi$
$770$		0			0
$771$	79.5914	+	79.5914i	0.103231	+	0.103231i
$772$		0			0
$773$	−514.162	−	514.162i	−0.665152	−	0.665152i	0.291438	−	0.956590i	$-0.405866\pi$
$773$	−514.162	−	514.162i	−0.665152	−	0.665152i	−0.956590	+	0.291438i	$0.905866\pi$
$774$		0			0
$775$	−166.585			−0.214948
$776$		0			0
$777$			1479.42i			1.90401i
$778$		0			0
$779$	−262.126	+	262.126i	−0.336490	+	0.336490i
$780$		0			0
$781$	112.750	−	112.750i	0.144366	−	0.144366i
$782$		0			0
$783$		−	281.397i		−	0.359384i
$784$		0			0
$785$	−611.661			−0.779186
$786$		0			0
$787$	−562.867	−	562.867i	−0.715206	−	0.715206i	0.252413	−	0.967620i	$-0.418776\pi$
$787$	−562.867	−	562.867i	−0.715206	−	0.715206i	−0.967620	+	0.252413i	$0.918776\pi$
$788$		0			0
$789$	−209.665	−	209.665i	−0.265736	−	0.265736i
$790$		0			0
$791$	−2243.11			−2.83579
$792$		0			0
$793$		−	61.1284i		−	0.0770849i
$794$		0			0
$795$	−312.366	+	312.366i	−0.392913	+	0.392913i
$796$		0			0
$797$	177.052	−	177.052i	0.222148	−	0.222148i	−0.587255	−	0.809402i	$-0.699791\pi$
$797$	177.052	−	177.052i	0.222148	−	0.222148i	0.809402	+	0.587255i	$0.199791\pi$
$798$		0			0
$799$		−	32.3300i		−	0.0404631i
$800$		0			0
$801$	159.708			0.199386
$802$		0			0
$803$	−153.637	−	153.637i	−0.191329	−	0.191329i
$804$		0			0
$805$	−755.732	−	755.732i	−0.938797	−	0.938797i
$806$		0			0
$807$	18.2613			0.0226286
$808$		0			0
$809$		−	810.967i		−	1.00243i	−0.865322	−	0.501216i	$-0.832886\pi$
$809$		−	810.967i		−	1.00243i	0.865322	−	0.501216i	$-0.167114\pi$
$810$		0			0
$811$	744.288	−	744.288i	0.917741	−	0.917741i	−0.0791234	−	0.996865i	$-0.525212\pi$
$811$	744.288	−	744.288i	0.917741	−	0.917741i	0.996865	+	0.0791234i	$0.0252121\pi$
$812$		0			0
$813$	−451.170	+	451.170i	−0.554945	+	0.554945i
$814$		0			0
$815$		−	110.170i		−	0.135178i
$816$		0			0
$817$	383.352			0.469219
$818$		0			0
$819$	24.6115	+	24.6115i	0.0300506	+	0.0300506i
$820$		0			0
$821$	194.321	+	194.321i	0.236688	+	0.236688i	0.815477	−	0.578789i	$-0.196475\pi$
$821$	194.321	+	194.321i	0.236688	+	0.236688i	−0.578789	+	0.815477i	$0.696475\pi$
$822$		0			0
$823$	1224.32			1.48764			0.743818	−	0.668383i	$-0.233013\pi$
$823$	1224.32			1.48764			0.743818	+	0.668383i	$0.233013\pi$
$824$		0			0
$825$			21.9946i			0.0266601i
$826$		0			0
$827$	864.192	−	864.192i	1.04497	−	1.04497i	0.0460328	−	0.998940i	$-0.485342\pi$
$827$	864.192	−	864.192i	1.04497	−	1.04497i	0.998940	−	0.0460328i	$-0.0146579\pi$
$828$		0			0
$829$	−61.9818	+	61.9818i	−0.0747669	+	0.0747669i	−0.743501	−	0.668734i	$-0.766836\pi$
$829$	−61.9818	+	61.9818i	−0.0747669	+	0.0747669i	0.668734	+	0.743501i	$0.266836\pi$
$830$		0			0
$831$			236.224i			0.284265i
$832$		0			0
$833$	−160.994			−0.193270
$834$		0			0
$835$	331.169	+	331.169i	0.396610	+	0.396610i
$836$		0			0
$837$	667.796	+	667.796i	0.797845	+	0.797845i
$838$		0			0
$839$	−163.655			−0.195060			−0.0975299	−	0.995233i	$-0.531094\pi$
$839$	−163.655			−0.195060			−0.0975299	+	0.995233i	$0.531094\pi$
$840$		0			0
$841$			742.451i			0.882819i
$842$		0			0
$843$	431.694	−	431.694i	0.512093	−	0.512093i
$844$		0			0
$845$	266.558	−	266.558i	0.315453	−	0.315453i
$846$		0			0
$847$			1326.20i			1.56577i
$848$		0			0
$849$	−728.369			−0.857914
$850$		0			0
$851$	1869.91	+	1869.91i	2.19731	+	2.19731i
$852$		0			0
$853$	−659.967	−	659.967i	−0.773701	−	0.773701i	0.205050	−	0.978751i	$-0.434264\pi$
$853$	−659.967	−	659.967i	−0.773701	−	0.773701i	−0.978751	+	0.205050i	$0.934264\pi$
$854$		0			0
$855$	76.2703			0.0892051
$856$		0			0
$857$		−	1409.73i		−	1.64495i	−0.568798	−	0.822477i	$-0.692591\pi$
$857$		−	1409.73i		−	1.64495i	0.568798	−	0.822477i	$-0.307409\pi$
$858$		0			0
$859$	699.811	−	699.811i	0.814682	−	0.814682i	−0.170650	−	0.985332i	$-0.554587\pi$
$859$	699.811	−	699.811i	0.814682	−	0.814682i	0.985332	+	0.170650i	$0.0545868\pi$
$860$		0			0
$861$	857.067	−	857.067i	0.995432	−	0.995432i
$862$		0			0
$863$			339.525i			0.393424i	0.980461	+	0.196712i	$0.0630263\pi$
$863$			339.525i			0.393424i	−0.980461	+	0.196712i	$0.936974\pi$
$864$		0			0
$865$	−272.574			−0.315114
$866$		0			0
$867$	−415.479	−	415.479i	−0.479214	−	0.479214i
$868$		0			0
$869$	−96.0292	−	96.0292i	−0.110505	−	0.110505i
$870$		0			0
$871$	−8.98286			−0.0103133
$872$		0			0
$873$			466.880i			0.534799i
$874$		0			0
$875$	90.0373	−	90.0373i	0.102900	−	0.102900i
$876$		0			0
$877$	−422.906	+	422.906i	−0.482219	+	0.482219i	−0.905840	−	0.423621i	$-0.860759\pi$
$877$	−422.906	+	422.906i	−0.482219	+	0.482219i	0.423621	+	0.905840i	$0.360759\pi$
$878$		0			0
$879$		−	805.025i		−	0.915842i
$880$		0			0
$881$	−1229.78			−1.39590			−0.697948	−	0.716148i	$-0.745903\pi$
$881$	−1229.78			−1.39590			−0.697948	+	0.716148i	$0.745903\pi$
$882$		0			0
$883$	−973.124	−	973.124i	−1.10207	−	1.10207i	−0.994161	−	0.107904i	$-0.965586\pi$
$883$	−973.124	−	973.124i	−1.10207	−	1.10207i	−0.107904	−	0.994161i	$-0.534414\pi$
$884$		0			0
$885$	157.731	+	157.731i	0.178227	+	0.178227i
$886$		0			0
$887$	429.295			0.483986			0.241993	−	0.970278i	$-0.422199\pi$
$887$	429.295			0.483986			0.241993	+	0.970278i	$0.422199\pi$
$888$		0			0
$889$			637.901i			0.717549i
$890$		0			0
$891$	23.6660	−	23.6660i	0.0265611	−	0.0265611i
$892$		0			0
$893$	82.2924	−	82.2924i	0.0921527	−	0.0921527i
$894$		0			0
$895$		−	196.661i		−	0.219733i
$896$		0			0
$897$	−55.6629			−0.0620545
$898$		0			0
$899$	233.871	+	233.871i	0.260145	+	0.260145i
$900$		0			0
$901$	135.172	+	135.172i	0.150024	+	0.150024i
$902$		0			0
$903$	−1253.44			−1.38808
$904$		0			0
$905$		−	327.050i		−	0.361381i
$906$		0			0
$907$	0.726060	−	0.726060i	0.000800507	−	0.000800507i	−0.706706	−	0.707507i	$-0.749820\pi$
$907$	0.726060	−	0.726060i	0.000800507	−	0.000800507i	0.707507	+	0.706706i	$0.249820\pi$
$908$		0			0
$909$	−96.3353	+	96.3353i	−0.105979	+	0.105979i
$910$		0			0
$911$			222.151i			0.243854i	0.992539	+	0.121927i	$0.0389074\pi$
$911$			222.151i			0.243854i	−0.992539	+	0.121927i	$0.961093\pi$
$912$		0			0
$913$	−172.436			−0.188867
$914$		0			0
$915$	309.697	+	309.697i	0.338466	+	0.338466i
$916$		0			0
$917$	−122.182	−	122.182i	−0.133240	−	0.133240i
$918$		0			0
$919$	1236.70			1.34570			0.672852	−	0.739777i	$-0.265069\pi$
$919$	1236.70			1.34570			0.672852	+	0.739777i	$0.265069\pi$
$920$		0			0
$921$			358.587i			0.389345i
$922$		0			0
$923$	−33.9955	+	33.9955i	−0.0368316	+	0.0368316i
$924$		0			0
$925$	−222.780	+	222.780i	−0.240843	+	0.240843i
$926$		0			0
$927$			560.647i			0.604798i
$928$		0			0
$929$	1227.29			1.32109			0.660544	−	0.750787i	$-0.270326\pi$
$929$	1227.29			1.32109			0.660544	+	0.750787i	$0.270326\pi$
$930$		0			0
$931$	−409.792	−	409.792i	−0.440163	−	0.440163i
$932$		0			0
$933$	−308.190	−	308.190i	−0.330322	−	0.330322i
$934$		0			0
$935$	9.51784			0.0101795
$936$		0			0
$937$		−	1674.94i		−	1.78756i	−0.448505	−	0.893780i	$-0.648044\pi$
$937$		−	1674.94i		−	1.78756i	0.448505	−	0.893780i	$-0.351956\pi$
$938$		0			0
$939$	−567.036	+	567.036i	−0.603872	+	0.603872i
$940$		0			0
$941$	−657.722	+	657.722i	−0.698961	+	0.698961i	−0.964186	−	0.265226i	$-0.914554\pi$
$941$	−657.722	+	657.722i	−0.698961	+	0.698961i	0.265226	+	0.964186i	$0.414554\pi$
$942$		0			0
$943$		−	2166.58i		−	2.29754i
$944$		0			0
$945$	−721.875			−0.763889
$946$		0			0
$947$	697.347	+	697.347i	0.736375	+	0.736375i	0.971875	−	0.235499i	$-0.0756725\pi$
$947$	697.347	+	697.347i	0.736375	+	0.736375i	−0.235499	+	0.971875i	$0.575672\pi$
$948$		0			0
$949$	46.3236	+	46.3236i	0.0488130	+	0.0488130i
$950$		0			0
$951$	−448.585			−0.471698
$952$		0			0
$953$		−	12.1701i		−	0.0127703i	−0.999980	−	0.00638514i	$-0.997968\pi$
$953$		−	12.1701i		−	0.0127703i	0.999980	−	0.00638514i	$-0.00203247\pi$
$954$		0			0
$955$	179.118	−	179.118i	0.187558	−	0.187558i
$956$		0			0
$957$	30.8785	−	30.8785i	0.0322659	−	0.0322659i
$958$		0			0
$959$			936.612i			0.976655i
$960$		0			0
$961$	−149.016			−0.155064
$962$		0			0
$963$	165.179	+	165.179i	0.171525	+	0.171525i
$964$		0			0
$965$	−81.2048	−	81.2048i	−0.0841501	−	0.0841501i
$966$		0			0
$967$	463.554			0.479373			0.239687	−	0.970850i	$-0.422955\pi$
$967$	463.554			0.479373			0.239687	+	0.970850i	$0.422955\pi$
$968$		0			0
$969$			29.5289i			0.0304735i
$970$		0			0
$971$	−886.831	+	886.831i	−0.913317	+	0.913317i	−0.996532	−	0.0832148i	$-0.973481\pi$
$971$	−886.831	+	886.831i	−0.913317	+	0.913317i	0.0832148	+	0.996532i	$0.473481\pi$
$972$		0			0
$973$	−441.380	+	441.380i	−0.453628	+	0.453628i
$974$		0			0
$975$		−	6.63163i		−	0.00680168i
$976$		0			0
$977$	1489.58			1.52465			0.762323	−	0.647197i	$-0.224059\pi$
$977$	1489.58			1.52465			0.762323	+	0.647197i	$0.224059\pi$
$978$		0			0
$979$	50.7299	+	50.7299i	0.0518181	+	0.0518181i
$980$		0			0
$981$	322.694	+	322.694i	0.328944	+	0.328944i
$982$		0			0
$983$	−1077.91			−1.09655			−0.548274	−	0.836299i	$-0.684715\pi$
$983$	−1077.91			−1.09655			−0.548274	+	0.836299i	$0.684715\pi$
$984$		0			0
$985$		−	37.3773i		−	0.0379465i
$986$		0			0
$987$	−269.070	+	269.070i	−0.272614	+	0.272614i
$988$		0			0
$989$	−1584.28	+	1584.28i	−1.60191	+	1.60191i
$990$		0			0
$991$		−	1483.84i		−	1.49731i	−0.662958	−	0.748656i	$-0.730699\pi$
$991$		−	1483.84i		−	1.49731i	0.662958	−	0.748656i	$-0.269301\pi$
$992$		0			0
$993$	−222.867			−0.224438
$994$		0			0
$995$	173.734	+	173.734i	0.174607	+	0.174607i
$996$		0			0
$997$	68.1920	+	68.1920i	0.0683972	+	0.0683972i	0.740478	−	0.672081i	$-0.234599\pi$
$997$	68.1920	+	68.1920i	0.0683972	+	0.0683972i	−0.672081	+	0.740478i	$0.734599\pi$
$998$		0			0
$999$	1786.14			1.78793

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.3.r.a.271.12		32
4.3	odd	2		80.3.r.a.11.8	✓	32
8.3	odd	2		640.3.r.a.31.12		32
8.5	even	2		640.3.r.b.31.5		32
16.3	odd	4	inner	320.3.r.a.111.12		32
16.5	even	4		640.3.r.a.351.12		32
16.11	odd	4		640.3.r.b.351.5		32
16.13	even	4		80.3.r.a.51.8	yes	32
20.3	even	4		400.3.k.g.299.15		32
20.7	even	4		400.3.k.h.299.2		32
20.19	odd	2		400.3.r.f.251.9		32
80.13	odd	4		400.3.k.h.99.2		32
80.29	even	4		400.3.r.f.51.9		32
80.77	odd	4		400.3.k.g.99.15		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.r.a.11.8	✓	32	4.3	odd	2
80.3.r.a.51.8	yes	32	16.13	even	4
320.3.r.a.111.12		32	16.3	odd	4	inner
320.3.r.a.271.12		32	1.1	even	1	trivial
400.3.k.g.99.15		32	80.77	odd	4
400.3.k.g.299.15		32	20.3	even	4
400.3.k.h.99.2		32	80.13	odd	4
400.3.k.h.299.2		32	20.7	even	4
400.3.r.f.51.9		32	80.29	even	4
400.3.r.f.251.9		32	20.19	odd	2
640.3.r.a.31.12		32	8.3	odd	2
640.3.r.a.351.12		32	16.5	even	4
640.3.r.b.31.5		32	8.5	even	2
640.3.r.b.351.5		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)

\(f(q)\)	\(=\)	\(q+(1.45771 + 1.45771i) q^{3} +(-1.58114 - 1.58114i) q^{5} +11.3889 q^{7} -4.75014i q^{9} +O(q^{10})\)	\(q+(1.45771 + 1.45771i) q^{3} +(-1.58114 - 1.58114i) q^{5} +11.3889 q^{7} -4.75014i q^{9} +(1.50884 - 1.50884i) q^{11} +(-0.454934 + 0.454934i) q^{13} -4.60970i q^{15} -1.99478 q^{17} +(-5.07749 - 5.07749i) q^{19} +(16.6018 + 16.6018i) q^{21} +41.9677 q^{23} +5.00000i q^{25} +(20.0438 - 20.0438i) q^{27} +(7.01958 - 7.01958i) q^{29} +33.3169i q^{31} +4.39891 q^{33} +(-18.0075 - 18.0075i) q^{35} +(44.5560 + 44.5560i) q^{37} -1.32633 q^{39} -51.6250i q^{41} +(-37.7501 + 37.7501i) q^{43} +(-7.51063 + 7.51063i) q^{45} +16.2073i q^{47} +80.7075 q^{49} +(-2.90782 - 2.90782i) q^{51} +(-67.7628 - 67.7628i) q^{53} -4.77137 q^{55} -14.8031i q^{57} +(-34.2172 + 34.2172i) q^{59} +(-67.1838 + 67.1838i) q^{61} -54.0990i q^{63} +1.43863 q^{65} +(9.87270 + 9.87270i) q^{67} +(61.1769 + 61.1769i) q^{69} +74.7263 q^{71} -101.825i q^{73} +(-7.28857 + 7.28857i) q^{75} +(17.1840 - 17.1840i) q^{77} -63.6444i q^{79} +15.6849 q^{81} +(-57.1418 - 57.1418i) q^{83} +(3.15403 + 3.15403i) q^{85} +20.4651 q^{87} +33.6218i q^{89} +(-5.18121 + 5.18121i) q^{91} +(-48.5665 + 48.5665i) q^{93} +16.0564i q^{95} -98.2875 q^{97} +(-7.16720 - 7.16720i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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