LMFDB - Embedded newform 560.4.g.f.449.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,4,Mod(449,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("560.449");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	560.g (of order $2$, degree $1$, 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:	$33.0410696032$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 55x^{8} + 983x^{6} + 6409x^{4} + 13560x^{2} + 3600 $ x^10 + 55x^8 + 983x^6 + 6409x^4 + 13560x^2 + 3600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.5
Root			$4.31366i$ of defining polynomial
Character	$\chi$	$=$	560.449
Dual form			560.4.g.f.449.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.93939i q^{3} +(-2.32771 - 10.9353i) q^{5} +7.00000i q^{7} +23.2388 q^{9} -25.5420 q^{11} -64.1014i q^{13} +(-21.2079 + 4.51433i) q^{15} +27.6952i q^{17} +0.792436 q^{19} +13.5757 q^{21} -108.606i q^{23} +(-114.164 + 50.9086i) q^{25} -97.4324i q^{27} +234.000 q^{29} -129.204 q^{31} +49.5357i q^{33} +(76.5474 - 16.2940i) q^{35} -38.3108i q^{37} -124.317 q^{39} -403.216 q^{41} -172.895i q^{43} +(-54.0931 - 254.124i) q^{45} +206.943i q^{47} -49.0000 q^{49} +53.7117 q^{51} +144.031i q^{53} +(59.4542 + 279.310i) q^{55} -1.53684i q^{57} -679.086 q^{59} -574.717 q^{61} +162.671i q^{63} +(-700.971 + 149.209i) q^{65} +515.640i q^{67} -210.630 q^{69} -556.612 q^{71} -173.243i q^{73} +(98.7314 + 221.407i) q^{75} -178.794i q^{77} +79.3290 q^{79} +438.488 q^{81} -1043.56i q^{83} +(302.856 - 64.4663i) q^{85} -453.817i q^{87} -652.060 q^{89} +448.710 q^{91} +250.576i q^{93} +(-1.84456 - 8.66556i) q^{95} -515.714i q^{97} -593.564 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 6 q^{5} - 46 q^{9} - 84 q^{11} - 8 q^{15} - 72 q^{19} + 140 q^{21} - 362 q^{25} + 88 q^{29} - 120 q^{31} + 28 q^{35} - 212 q^{39} - 852 q^{41} - 510 q^{45} - 490 q^{49} - 1276 q^{51} + 1136 q^{55}+ \cdots + 5304 q^{99}+O(q^{100}) $ 10 * q + 6 * q^5 - 46 * q^9 - 84 * q^11 - 8 * q^15 - 72 * q^19 + 140 * q^21 - 362 * q^25 + 88 * q^29 - 120 * q^31 + 28 * q^35 - 212 * q^39 - 852 * q^41 - 510 * q^45 - 490 * q^49 - 1276 * q^51 + 1136 * q^55 - 864 * q^59 - 884 * q^61 + 520 * q^65 + 4808 * q^69 - 880 * q^71 - 720 * q^75 + 3580 * q^79 - 302 * q^81 + 1572 * q^85 - 1492 * q^89 - 476 * q^91 + 1628 * q^95 + 5304 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		−	1.93939i		−	0.373235i	−0.982433	−	0.186617i	$-0.940247\pi$
$3$		−	1.93939i		−	0.373235i	0.982433	−	0.186617i	$-0.0597525\pi$
$4$		0			0
$5$	−2.32771	−	10.9353i	−0.208197	−	0.978087i
$5$	−2.32771	−	10.9353i	−0.208197	−	0.978087i
$6$		0			0
$7$			7.00000i			0.377964i
$7$			7.00000i			0.377964i
$8$		0			0
$9$	23.2388			0.860696
$10$		0			0
$11$	−25.5420			−0.700108			−0.350054	−	0.936730i	$-0.613837\pi$
$11$	−25.5420			−0.700108			−0.350054	+	0.936730i	$0.613837\pi$
$12$		0			0
$13$		−	64.1014i		−	1.36758i	−0.729679	−	0.683790i	$-0.760330\pi$
$13$		−	64.1014i		−	1.36758i	0.729679	−	0.683790i	$-0.239670\pi$
$14$		0			0
$15$	−21.2079	+	4.51433i	−0.365056	+	0.0777063i
$16$		0			0
$17$			27.6952i			0.395122i	0.980291	+	0.197561i	$0.0633020\pi$
$17$			27.6952i			0.395122i	−0.980291	+	0.197561i	$0.936698\pi$
$18$		0			0
$19$	0.792436			0.00956828			0.00478414	−	0.999989i	$-0.498477\pi$
$19$	0.792436			0.00956828			0.00478414	+	0.999989i	$0.498477\pi$
$20$		0			0
$21$	13.5757			0.141070
$22$		0			0
$23$		−	108.606i		−	0.984609i	−0.870423	−	0.492305i	$-0.836155\pi$
$23$		−	108.606i		−	0.984609i	0.870423	−	0.492305i	$-0.163845\pi$
$24$		0			0
$25$	−114.164	+	50.9086i	−0.913308	+	0.407269i
$26$		0			0
$27$		−	97.4324i		−	0.694477i
$28$		0			0
$29$	234.000			1.49837			0.749186	−	0.662360i	$-0.230445\pi$
$29$	234.000			1.49837			0.749186	+	0.662360i	$0.230445\pi$
$30$		0			0
$31$	−129.204			−0.748570			−0.374285	−	0.927314i	$-0.622112\pi$
$31$	−129.204			−0.748570			−0.374285	+	0.927314i	$0.622112\pi$
$32$		0			0
$33$			49.5357i			0.261305i
$34$		0			0
$35$	76.5474	−	16.2940i	0.369682	−	0.0786909i
$36$		0			0
$37$		−	38.3108i		−	0.170223i	−0.996371	−	0.0851116i	$-0.972875\pi$
$37$		−	38.3108i		−	0.170223i	0.996371	−	0.0851116i	$-0.0271247\pi$
$38$		0			0
$39$	−124.317			−0.510429
$40$		0			0
$41$	−403.216			−1.53590			−0.767949	−	0.640511i	$-0.778722\pi$
$41$	−403.216			−1.53590			−0.767949	+	0.640511i	$0.778722\pi$
$42$		0			0
$43$		−	172.895i		−	0.613167i	−0.951844	−	0.306584i	$-0.900814\pi$
$43$		−	172.895i		−	0.613167i	0.951844	−	0.306584i	$-0.0991859\pi$
$44$		0			0
$45$	−54.0931	−	254.124i	−0.179194	−	0.841835i
$46$		0			0
$47$			206.943i			0.642250i	0.947037	+	0.321125i	$0.104061\pi$
$47$			206.943i			0.642250i	−0.947037	+	0.321125i	$0.895939\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$		0			0
$51$	53.7117			0.147473
$52$		0			0
$53$			144.031i			0.373287i	0.982428	+	0.186643i	$0.0597609\pi$
$53$			144.031i			0.373287i	−0.982428	+	0.186643i	$0.940239\pi$
$54$		0			0
$55$	59.4542	+	279.310i	0.145760	+	0.684767i
$56$		0			0
$57$		−	1.53684i		−	0.00357122i
$58$		0			0
$59$	−679.086			−1.49846			−0.749232	−	0.662307i	$-0.769577\pi$
$59$	−679.086			−1.49846			−0.749232	+	0.662307i	$0.769577\pi$
$60$		0			0
$61$	−574.717			−1.20631			−0.603155	−	0.797624i	$-0.706090\pi$
$61$	−574.717			−1.20631			−0.603155	+	0.797624i	$0.706090\pi$
$62$		0			0
$63$			162.671i			0.325312i
$64$		0			0
$65$	−700.971	+	149.209i	−1.33761	+	0.284725i
$66$		0			0
$67$			515.640i			0.940230i	0.882605	+	0.470115i	$0.155788\pi$
$67$			515.640i			0.940230i	−0.882605	+	0.470115i	$0.844212\pi$
$68$		0			0
$69$	−210.630			−0.367491
$70$		0			0
$71$	−556.612			−0.930391			−0.465195	−	0.885208i	$-0.654016\pi$
$71$	−556.612			−0.930391			−0.465195	+	0.885208i	$0.654016\pi$
$72$		0			0
$73$		−	173.243i		−	0.277762i	−0.990309	−	0.138881i	$-0.955650\pi$
$73$		−	173.243i		−	0.277762i	0.990309	−	0.138881i	$-0.0443505\pi$
$74$		0			0
$75$	98.7314	+	221.407i	0.152007	+	0.340879i
$76$		0			0
$77$		−	178.794i		−	0.264616i
$78$		0			0
$79$	79.3290			0.112977			0.0564887	−	0.998403i	$-0.482010\pi$
$79$	79.3290			0.112977			0.0564887	+	0.998403i	$0.482010\pi$
$80$		0			0
$81$	438.488			0.601493
$82$		0			0
$83$		−	1043.56i		−	1.38007i	−0.723777	−	0.690034i	$-0.757596\pi$
$83$		−	1043.56i		−	1.38007i	0.723777	−	0.690034i	$-0.242404\pi$
$84$		0			0
$85$	302.856	−	64.4663i	0.386463	−	0.0822630i
$86$		0			0
$87$		−	453.817i		−	0.559245i
$88$		0			0
$89$	−652.060			−0.776609			−0.388304	−	0.921531i	$-0.626939\pi$
$89$	−652.060			−0.776609			−0.388304	+	0.921531i	$0.626939\pi$
$90$		0			0
$91$	448.710			0.516897
$92$		0			0
$93$			250.576i			0.279393i
$94$		0			0
$95$	−1.84456	−	8.66556i	−0.00199208	−	0.00935861i
$96$		0			0
$97$		−	515.714i		−	0.539823i	−0.962885	−	0.269912i	$-0.913005\pi$
$97$		−	515.714i		−	0.539823i	0.962885	−	0.269912i	$-0.0869945\pi$
$98$		0			0
$99$	−593.564			−0.602580
$100$		0			0
$101$	−536.339			−0.528394			−0.264197	−	0.964469i	$-0.585107\pi$
$101$	−536.339			−0.528394			−0.264197	+	0.964469i	$0.585107\pi$
$102$		0			0
$103$		−	381.693i		−	0.365139i	−0.983193	−	0.182570i	$-0.941559\pi$
$103$		−	381.693i		−	0.365139i	0.983193	−	0.182570i	$-0.0584415\pi$
$104$		0			0
$105$	−31.6003	−	148.455i	−0.0293702	−	0.137978i
$106$		0			0
$107$		−	1381.12i		−	1.24783i	−0.781492	−	0.623915i	$-0.785541\pi$
$107$		−	1381.12i		−	1.24783i	0.781492	−	0.623915i	$-0.214459\pi$
$108$		0			0
$109$	390.582			0.343220			0.171610	−	0.985165i	$-0.445103\pi$
$109$	390.582			0.343220			0.171610	+	0.985165i	$0.445103\pi$
$110$		0			0
$111$	−74.2995			−0.0635333
$112$		0			0
$113$			1643.15i			1.36792i	0.729521	+	0.683958i	$0.239743\pi$
$113$			1643.15i			1.36792i	−0.729521	+	0.683958i	$0.760257\pi$
$114$		0			0
$115$	−1187.65	+	252.804i	−0.963033	+	0.204992i
$116$		0			0
$117$		−	1489.64i		−	1.17707i
$118$		0			0
$119$	−193.866			−0.149342
$120$		0			0
$121$	−678.609			−0.509849
$122$		0			0
$123$			781.992i			0.573251i
$124$		0			0
$125$	822.443	+	1129.92i	0.588492	+	0.808503i
$126$		0			0
$127$		−	192.032i		−	0.134174i	−0.997747	−	0.0670869i	$-0.978630\pi$
$127$		−	192.032i		−	0.134174i	0.997747	−	0.0670869i	$-0.0213705\pi$
$128$		0			0
$129$	−335.310			−0.228856
$130$		0			0
$131$	−2082.90			−1.38919			−0.694594	−	0.719402i	$-0.744416\pi$
$131$	−2082.90			−1.38919			−0.694594	+	0.719402i	$0.744416\pi$
$132$		0			0
$133$			5.54705i			0.00361647i
$134$		0			0
$135$	−1065.46	+	226.794i	−0.679259	+	0.144588i
$136$		0			0
$137$			78.1709i			0.0487488i	0.999703	+	0.0243744i	$0.00775939\pi$
$137$			78.1709i			0.0487488i	−0.999703	+	0.0243744i	$0.992241\pi$
$138$		0			0
$139$	1393.67			0.850426			0.425213	−	0.905093i	$-0.360199\pi$
$139$	1393.67			0.850426			0.425213	+	0.905093i	$0.360199\pi$
$140$		0			0
$141$	401.342			0.239710
$142$		0			0
$143$			1637.28i			0.957454i
$144$		0			0
$145$	−544.685	−	2558.88i	−0.311956	−	1.46554i
$146$		0			0
$147$			95.0299i			0.0533193i
$148$		0			0
$149$	−32.5002			−0.0178693			−0.00893463	−	0.999960i	$-0.502844\pi$
$149$	−32.5002			−0.0178693			−0.00893463	+	0.999960i	$0.502844\pi$
$150$		0			0
$151$	−466.762			−0.251553			−0.125777	−	0.992059i	$-0.540142\pi$
$151$	−466.762			−0.251553			−0.125777	+	0.992059i	$0.540142\pi$
$152$		0			0
$153$			643.602i			0.340080i
$154$		0			0
$155$	300.749	+	1412.89i	0.155850	+	0.732167i
$156$		0			0
$157$		−	1673.50i		−	0.850701i	−0.905029	−	0.425351i	$-0.860151\pi$
$157$		−	1673.50i		−	0.850701i	0.905029	−	0.425351i	$-0.139849\pi$
$158$		0			0
$159$	279.332			0.139324
$160$		0			0
$161$	760.245			0.372147
$162$		0			0
$163$		−	1869.36i		−	0.898279i	−0.893462	−	0.449139i	$-0.851731\pi$
$163$		−	1869.36i		−	0.898279i	0.893462	−	0.449139i	$-0.148269\pi$
$164$		0			0
$165$	541.690	−	115.305i	0.255579	−	0.0544028i
$166$		0			0
$167$			46.5250i			0.0215581i	0.999942	+	0.0107791i	$0.00343115\pi$
$167$			46.5250i			0.0215581i	−0.999942	+	0.0107791i	$0.996569\pi$
$168$		0			0
$169$	−1911.99			−0.870275
$170$		0			0
$171$	18.4152			0.00823538
$172$		0			0
$173$			2496.28i			1.09704i	0.836137	+	0.548521i	$0.184809\pi$
$173$			2496.28i			1.09704i	−0.836137	+	0.548521i	$0.815191\pi$
$174$		0			0
$175$	−356.360	−	799.145i	−0.153933	−	0.345198i
$176$		0			0
$177$			1317.01i			0.559279i
$178$		0			0
$179$	2975.70			1.24254			0.621269	−	0.783598i	$-0.286618\pi$
$179$	2975.70			1.24254			0.621269	+	0.783598i	$0.286618\pi$
$180$		0			0
$181$	966.273			0.396809			0.198405	−	0.980120i	$-0.436424\pi$
$181$	966.273			0.396809			0.198405	+	0.980120i	$0.436424\pi$
$182$		0			0
$183$			1114.60i			0.450237i
$184$		0			0
$185$	−418.942	+	89.1764i	−0.166493	+	0.0354399i
$186$		0			0
$187$		−	707.389i		−	0.276628i
$188$		0			0
$189$	682.027			0.262488
$190$		0			0
$191$	1545.50			0.585488			0.292744	−	0.956191i	$-0.405432\pi$
$191$	1545.50			0.585488			0.292744	+	0.956191i	$0.405432\pi$
$192$		0			0
$193$		−	2304.05i		−	0.859322i	−0.902990	−	0.429661i	$-0.858633\pi$
$193$		−	2304.05i		−	0.859322i	0.902990	−	0.429661i	$-0.141367\pi$
$194$		0			0
$195$	289.375	+	1359.45i	0.106270	+	0.499244i
$196$		0			0
$197$			222.021i			0.0802960i	0.999194	+	0.0401480i	$0.0127829\pi$
$197$			222.021i			0.0802960i	−0.999194	+	0.0401480i	$0.987217\pi$
$198$		0			0
$199$	3580.56			1.27547			0.637736	−	0.770255i	$-0.279871\pi$
$199$	3580.56			1.27547			0.637736	+	0.770255i	$0.279871\pi$
$200$		0			0
$201$	1000.02			0.350927
$202$		0			0
$203$			1638.00i			0.566331i
$204$		0			0
$205$	938.570	+	4409.31i	0.319769	+	1.50224i
$206$		0			0
$207$		−	2523.88i		−	0.847449i
$208$		0			0
$209$	−20.2404			−0.00669883
$210$		0			0
$211$	4181.04			1.36415			0.682073	−	0.731284i	$-0.261079\pi$
$211$	4181.04			1.36415			0.682073	+	0.731284i	$0.261079\pi$
$212$		0			0
$213$			1079.49i			0.347254i
$214$		0			0
$215$	−1890.66	+	402.449i	−0.599731	+	0.127659i
$216$		0			0
$217$		−	904.426i		−	0.282933i
$218$		0			0
$219$	−335.986			−0.103670
$220$		0			0
$221$	1775.30			0.540361
$222$		0			0
$223$		−	2361.52i		−	0.709145i	−0.935028	−	0.354573i	$-0.884626\pi$
$223$		−	2361.52i		−	0.709145i	0.935028	−	0.354573i	$-0.115374\pi$
$224$		0			0
$225$	−2653.02	+	1183.05i	−0.786081	+	0.350534i
$226$		0			0
$227$			586.877i			0.171596i	0.996313	+	0.0857982i	$0.0273440\pi$
$227$			586.877i			0.171596i	−0.996313	+	0.0857982i	$0.972656\pi$
$228$		0			0
$229$	4619.55			1.33305			0.666526	−	0.745482i	$-0.267781\pi$
$229$	4619.55			1.33305			0.666526	+	0.745482i	$0.267781\pi$
$230$		0			0
$231$	−346.750			−0.0987639
$232$		0			0
$233$		−	5120.44i		−	1.43971i	−0.694127	−	0.719853i	$-0.744209\pi$
$233$		−	5120.44i		−	1.43971i	0.694127	−	0.719853i	$-0.255791\pi$
$234$		0			0
$235$	2262.99	−	481.703i	0.628176	−	0.133714i
$236$		0			0
$237$		−	153.850i		−	0.0421671i
$238$		0			0
$239$	1127.51			0.305158			0.152579	−	0.988291i	$-0.451242\pi$
$239$	1127.51			0.305158			0.152579	+	0.988291i	$0.451242\pi$
$240$		0			0
$241$	−3549.53			−0.948736			−0.474368	−	0.880327i	$-0.657323\pi$
$241$	−3549.53			−0.948736			−0.474368	+	0.880327i	$0.657323\pi$
$242$		0			0
$243$		−	3481.07i		−	0.918975i
$244$		0			0
$245$	114.058	+	535.832i	0.0297424	+	0.139727i
$246$		0			0
$247$		−	50.7963i		−	0.0130854i
$248$		0			0
$249$	−2023.87			−0.515090
$250$		0			0
$251$	−4717.19			−1.18624			−0.593120	−	0.805114i	$-0.702104\pi$
$251$	−4717.19			−1.18624			−0.593120	+	0.805114i	$0.702104\pi$
$252$		0			0
$253$			2774.02i			0.689333i
$254$		0			0
$255$	−125.025	−	587.355i	−0.0307034	−	0.144242i
$256$		0			0
$257$		−	6260.31i		−	1.51948i	−0.650224	−	0.759742i	$-0.725325\pi$
$257$		−	6260.31i		−	1.51948i	0.650224	−	0.759742i	$-0.274675\pi$
$258$		0			0
$259$	268.176			0.0643383
$260$		0			0
$261$	5437.88			1.28964
$262$		0			0
$263$			5753.04i			1.34885i	0.738344	+	0.674425i	$0.235608\pi$
$263$			5753.04i			1.34885i	−0.738344	+	0.674425i	$0.764392\pi$
$264$		0			0
$265$	1575.03	−	335.262i	0.365107	−	0.0777170i
$266$		0			0
$267$			1264.60i			0.289858i
$268$		0			0
$269$	7059.21			1.60003			0.800014	−	0.599982i	$-0.204826\pi$
$269$	7059.21			1.60003			0.800014	+	0.599982i	$0.204826\pi$
$270$		0			0
$271$	8534.52			1.91305			0.956523	−	0.291658i	$-0.0942069\pi$
$271$	8534.52			1.91305			0.956523	+	0.291658i	$0.0942069\pi$
$272$		0			0
$273$		−	870.222i		−	0.192924i
$274$		0			0
$275$	2915.96	−	1300.30i	0.639415	−	0.285132i
$276$		0			0
$277$			1313.94i			0.285008i	0.989794	+	0.142504i	$0.0455154\pi$
$277$			1313.94i			0.285008i	−0.989794	+	0.142504i	$0.954485\pi$
$278$		0			0
$279$	−3002.54			−0.644291
$280$		0			0
$281$	−247.229			−0.0524856			−0.0262428	−	0.999656i	$-0.508354\pi$
$281$	−247.229			−0.0524856			−0.0262428	+	0.999656i	$0.508354\pi$
$282$		0			0
$283$			9074.90i			1.90617i	0.302697	+	0.953087i	$0.402113\pi$
$283$			9074.90i			1.90617i	−0.302697	+	0.953087i	$0.597887\pi$
$284$		0			0
$285$	−16.8059	+	3.57731i	−0.00349296	+	0.000743515i
$286$		0			0
$287$		−	2822.51i		−	0.580515i
$288$		0			0
$289$	4145.98			0.843879
$290$		0			0
$291$	−1000.17			−0.201481
$292$		0			0
$293$		−	2740.72i		−	0.546466i	−0.961948	−	0.273233i	$-0.911907\pi$
$293$		−	2740.72i		−	0.546466i	0.961948	−	0.273233i	$-0.0880930\pi$
$294$		0			0
$295$	1580.71	+	7426.04i	0.311975	+	1.46563i
$296$		0			0
$297$			2488.61i			0.486209i
$298$		0			0
$299$	−6961.83			−1.34653
$300$		0			0
$301$	1210.26			0.231755
$302$		0			0
$303$			1040.17i			0.197215i
$304$		0			0
$305$	1337.77	+	6284.73i	0.251150	+	1.17988i
$306$		0			0
$307$		−	6985.46i		−	1.29864i	−0.760517	−	0.649318i	$-0.775054\pi$
$307$		−	6985.46i		−	1.29864i	0.760517	−	0.649318i	$-0.224946\pi$
$308$		0			0
$309$	−740.250			−0.136283
$310$		0			0
$311$	356.841			0.0650630			0.0325315	−	0.999471i	$-0.489643\pi$
$311$	356.841			0.0650630			0.0325315	+	0.999471i	$0.489643\pi$
$312$		0			0
$313$			6630.12i			1.19731i	0.801009	+	0.598653i	$0.204297\pi$
$313$			6630.12i			1.19731i	−0.801009	+	0.598653i	$0.795703\pi$
$314$		0			0
$315$	1778.87	−	378.652i	0.318184	−	0.0677289i
$316$		0			0
$317$		−	2494.05i		−	0.441891i	−0.975286	−	0.220946i	$-0.929086\pi$
$317$		−	2494.05i		−	0.441891i	0.975286	−	0.220946i	$-0.0709144\pi$
$318$		0			0
$319$	−5976.83			−1.04902
$320$		0			0
$321$	−2678.52			−0.465734
$322$		0			0
$323$			21.9467i			0.00378063i
$324$		0			0
$325$	3263.31	+	7318.05i	0.556973	+	1.24902i
$326$		0			0
$327$		−	757.489i		−	0.128102i
$328$		0			0
$329$	−1448.60			−0.242748
$330$		0			0
$331$	4682.47			0.777558			0.388779	−	0.921331i	$-0.372897\pi$
$331$	4682.47			0.777558			0.388779	+	0.921331i	$0.372897\pi$
$332$		0			0
$333$		−	890.297i		−	0.146510i
$334$		0			0
$335$	5638.70	−	1200.26i	0.919627	−	0.195753i
$336$		0			0
$337$			3596.60i			0.581363i	0.956820	+	0.290681i	$0.0938820\pi$
$337$			3596.60i			0.581363i	−0.956820	+	0.290681i	$0.906118\pi$
$338$		0			0
$339$	3186.70			0.510554
$340$		0			0
$341$	3300.12			0.524080
$342$		0			0
$343$		−	343.000i		−	0.0539949i
$344$		0			0
$345$	490.285	+	2303.31i	0.0765103	+	0.359438i
$346$		0			0
$347$		−	1899.51i		−	0.293865i	−0.989147	−	0.146932i	$-0.953060\pi$
$347$		−	1899.51i		−	0.293865i	0.989147	−	0.146932i	$-0.0469400\pi$
$348$		0			0
$349$	1037.55			0.159137			0.0795683	−	0.996829i	$-0.474646\pi$
$349$	1037.55			0.159137			0.0795683	+	0.996829i	$0.474646\pi$
$350$		0			0
$351$	−6245.56			−0.949752
$352$		0			0
$353$			4087.08i			0.616242i	0.951347	+	0.308121i	$0.0997001\pi$
$353$			4087.08i			0.616242i	−0.951347	+	0.308121i	$0.900300\pi$
$354$		0			0
$355$	1295.63	+	6086.75i	0.193704	+	0.910003i
$356$		0			0
$357$			375.982i			0.0557397i
$358$		0			0
$359$	3472.67			0.510530			0.255265	−	0.966871i	$-0.417837\pi$
$359$	3472.67			0.510530			0.255265	+	0.966871i	$0.417837\pi$
$360$		0			0
$361$	−6858.37			−0.999908
$362$		0			0
$363$			1316.08i			0.190293i
$364$		0			0
$365$	−1894.48	+	403.260i	−0.271675	+	0.0578290i
$366$		0			0
$367$		−	8769.14i		−	1.24726i	−0.781719	−	0.623631i	$-0.785657\pi$
$367$		−	8769.14i		−	1.24726i	0.781719	−	0.623631i	$-0.214343\pi$
$368$		0			0
$369$	−9370.25			−1.32194
$370$		0			0
$371$	−1008.22			−0.141089
$372$		0			0
$373$		−	11368.9i		−	1.57817i	−0.614284	−	0.789085i	$-0.710555\pi$
$373$		−	11368.9i		−	1.57817i	0.614284	−	0.789085i	$-0.289445\pi$
$374$		0			0
$375$	2191.35	−	1595.03i	0.301762	−	0.219646i
$376$		0			0
$377$		−	14999.8i		−	2.04914i
$378$		0			0
$379$	−12137.4			−1.64500			−0.822501	−	0.568764i	$-0.807422\pi$
$379$	−12137.4			−1.64500			−0.822501	+	0.568764i	$0.807422\pi$
$380$		0			0
$381$	−372.424			−0.0500784
$382$		0			0
$383$		−	9869.61i		−	1.31675i	−0.752692	−	0.658373i	$-0.771245\pi$
$383$		−	9869.61i		−	1.31675i	0.752692	−	0.658373i	$-0.228755\pi$
$384$		0			0
$385$	−1955.17	+	416.180i	−0.258817	+	0.0550921i
$386$		0			0
$387$		−	4017.86i		−	0.527751i
$388$		0			0
$389$	−57.1166			−0.00744454			−0.00372227	−	0.999993i	$-0.501185\pi$
$389$	−57.1166			−0.00744454			−0.00372227	+	0.999993i	$0.501185\pi$
$390$		0			0
$391$	3007.88			0.389041
$392$		0			0
$393$			4039.54i			0.518494i
$394$		0			0
$395$	−184.655	−	867.490i	−0.0235215	−	0.110502i
$396$		0			0
$397$		−	7436.17i		−	0.940078i	−0.882646	−	0.470039i	$-0.844240\pi$
$397$		−	7436.17i		−	0.940078i	0.882646	−	0.470039i	$-0.155760\pi$
$398$		0			0
$399$	10.7579			0.00134979
$400$		0			0
$401$	−12465.0			−1.55230			−0.776149	−	0.630550i	$-0.782829\pi$
$401$	−12465.0			−1.55230			−0.776149	+	0.630550i	$0.782829\pi$
$402$		0			0
$403$			8282.15i			1.02373i
$404$		0			0
$405$	−1020.67	−	4795.02i	−0.125229	−	0.588312i
$406$		0			0
$407$			978.533i			0.119175i
$408$		0			0
$409$	1708.72			0.206578			0.103289	−	0.994651i	$-0.467063\pi$
$409$	1708.72			0.206578			0.103289	+	0.994651i	$0.467063\pi$
$410$		0			0
$411$	151.604			0.0181948
$412$		0			0
$413$		−	4753.60i		−	0.566366i
$414$		0			0
$415$	−11411.7	+	2429.10i	−1.34983	+	0.287325i
$416$		0			0
$417$		−	2702.86i		−	0.317409i
$418$		0			0
$419$	10618.8			1.23810			0.619050	−	0.785352i	$-0.287518\pi$
$419$	10618.8			1.23810			0.619050	+	0.785352i	$0.287518\pi$
$420$		0			0
$421$	13273.5			1.53661			0.768304	−	0.640085i	$-0.221101\pi$
$421$	13273.5			1.53661			0.768304	+	0.640085i	$0.221101\pi$
$422$		0			0
$423$			4809.10i			0.552781i
$424$		0			0
$425$	−1409.92	−	3161.78i	−0.160921	−	0.360868i
$426$		0			0
$427$		−	4023.02i		−	0.455943i
$428$		0			0
$429$	3175.31			0.357355
$430$		0			0
$431$	−7918.20			−0.884934			−0.442467	−	0.896785i	$-0.645897\pi$
$431$	−7918.20			−0.884934			−0.442467	+	0.896785i	$0.645897\pi$
$432$		0			0
$433$			4433.34i			0.492038i	0.969265	+	0.246019i	$0.0791226\pi$
$433$			4433.34i			0.492038i	−0.969265	+	0.246019i	$0.920877\pi$
$434$		0			0
$435$	−4962.65	+	1056.35i	−0.546990	+	0.116433i
$436$		0			0
$437$		−	86.0637i		−	0.00942102i
$438$		0			0
$439$	12958.4			1.40882			0.704408	−	0.709796i	$-0.251213\pi$
$439$	12958.4			1.40882			0.704408	+	0.709796i	$0.251213\pi$
$440$		0			0
$441$	−1138.70			−0.122957
$442$		0			0
$443$			12040.4i			1.29133i	0.763621	+	0.645664i	$0.223420\pi$
$443$			12040.4i			1.29133i	−0.763621	+	0.645664i	$0.776580\pi$
$444$		0			0
$445$	1517.80	+	7130.50i	0.161687	+	0.759591i
$446$		0			0
$447$			63.0304i			0.00666943i
$448$		0			0
$449$	−11586.3			−1.21780			−0.608899	−	0.793247i	$-0.708389\pi$
$449$	−11586.3			−1.21780			−0.608899	+	0.793247i	$0.708389\pi$
$450$		0			0
$451$	10298.9			1.07529
$452$		0			0
$453$			905.232i			0.0938886i
$454$		0			0
$455$	−1044.47	−	4906.80i	−0.107616	−	0.505570i
$456$		0			0
$457$		−	9734.34i		−	0.996396i	−0.867063	−	0.498198i	$-0.833995\pi$
$457$		−	9734.34i		−	0.996396i	0.867063	−	0.498198i	$-0.166005\pi$
$458$		0			0
$459$	2698.41			0.274403
$460$		0			0
$461$	−1343.41			−0.135724			−0.0678621	−	0.997695i	$-0.521618\pi$
$461$	−1343.41			−0.135724			−0.0678621	+	0.997695i	$0.521618\pi$
$462$		0			0
$463$			6613.72i			0.663857i	0.943305	+	0.331929i	$0.107699\pi$
$463$			6613.72i			0.663857i	−0.943305	+	0.331929i	$0.892301\pi$
$464$		0			0
$465$	2740.13	−	583.268i	0.273270	−	0.0581686i
$466$		0			0
$467$		−	14688.9i		−	1.45551i	−0.685838	−	0.727755i	$-0.740564\pi$
$467$		−	14688.9i		−	1.45551i	0.685838	−	0.727755i	$-0.259436\pi$
$468$		0			0
$469$	−3609.48			−0.355374
$470$		0			0
$471$	−3245.57			−0.317511
$472$		0			0
$473$			4416.07i			0.429283i
$474$		0			0
$475$	−90.4673	+	40.3418i	−0.00873879	+	0.00389686i
$476$		0			0
$477$			3347.11i			0.321286i
$478$		0			0
$479$	−15298.6			−1.45931			−0.729657	−	0.683813i	$-0.760320\pi$
$479$	−15298.6			−1.45931			−0.729657	+	0.683813i	$0.760320\pi$
$480$		0			0
$481$	−2455.78			−0.232794
$482$		0			0
$483$		−	1474.41i		−	0.138898i
$484$		0			0
$485$	−5639.52	+	1200.43i	−0.527994	+	0.112389i
$486$		0			0
$487$		−	9653.80i		−	0.898266i	−0.893465	−	0.449133i	$-0.851733\pi$
$487$		−	9653.80i		−	0.898266i	0.893465	−	0.449133i	$-0.148267\pi$
$488$		0			0
$489$	−3625.41			−0.335269
$490$		0			0
$491$	−20142.6			−1.85137			−0.925684	−	0.378297i	$-0.876510\pi$
$491$	−20142.6			−1.85137			−0.925684	+	0.378297i	$0.876510\pi$
$492$		0			0
$493$			6480.69i			0.592039i
$494$		0			0
$495$	1381.64	+	6490.83i	0.125455	+	0.589376i
$496$		0			0
$497$		−	3896.29i		−	0.351655i
$498$		0			0
$499$	−1309.29			−0.117459			−0.0587293	−	0.998274i	$-0.518705\pi$
$499$	−1309.29			−0.117459			−0.0587293	+	0.998274i	$0.518705\pi$
$500$		0			0
$501$	90.2299			0.00804625
$502$		0			0
$503$		−	2186.17i		−	0.193791i	−0.995295	−	0.0968953i	$-0.969109\pi$
$503$		−	2186.17i		−	0.193791i	0.995295	−	0.0968953i	$-0.0308912\pi$
$504$		0			0
$505$	1248.44	+	5865.06i	0.110010	+	0.516815i
$506$		0			0
$507$			3708.09i			0.324817i
$508$		0			0
$509$	−3591.11			−0.312718			−0.156359	−	0.987700i	$-0.549976\pi$
$509$	−3591.11			−0.312718			−0.156359	+	0.987700i	$0.549976\pi$
$510$		0			0
$511$	1212.70			0.104984
$512$		0			0
$513$		−	77.2089i		−	0.00664495i
$514$		0			0
$515$	−4173.94	+	888.470i	−0.357138	+	0.0760207i
$516$		0			0
$517$		−	5285.73i		−	0.449644i
$518$		0			0
$519$	4841.24			0.409455
$520$		0			0
$521$	−8605.34			−0.723621			−0.361811	−	0.932252i	$-0.617841\pi$
$521$	−8605.34			−0.723621			−0.361811	+	0.932252i	$0.617841\pi$
$522$		0			0
$523$		−	22536.4i		−	1.88423i	−0.335297	−	0.942113i	$-0.608837\pi$
$523$		−	22536.4i		−	1.88423i	0.335297	−	0.942113i	$-0.391163\pi$
$524$		0			0
$525$	−1549.85	+	691.120i	−0.128840	+	0.0574532i
$526$		0			0
$527$		−	3578.32i		−	0.295776i
$528$		0			0
$529$	371.637			0.0305447
$530$		0			0
$531$	−15781.1			−1.28972
$532$		0			0
$533$			25846.7i			2.10046i
$534$		0			0
$535$	−15103.0	+	3214.84i	−1.22049	+	0.259794i
$536$		0			0
$537$		−	5771.03i		−	0.463758i
$538$		0			0
$539$	1251.56			0.100015
$540$		0			0
$541$	8782.44			0.697942			0.348971	−	0.937134i	$-0.386531\pi$
$541$	8782.44			0.697942			0.348971	+	0.937134i	$0.386531\pi$
$542$		0			0
$543$		−	1873.98i		−	0.148103i
$544$		0			0
$545$	−909.161	−	4271.15i	−0.0714572	−	0.335699i
$546$		0			0
$547$			22593.0i			1.76601i	0.469366	+	0.883004i	$0.344482\pi$
$547$			22593.0i			1.76601i	−0.469366	+	0.883004i	$0.655518\pi$
$548$		0			0
$549$	−13355.7			−1.03827
$550$		0			0
$551$	185.430			0.0143368
$552$		0			0
$553$			555.303i			0.0427014i
$554$		0			0
$555$	172.947	+	812.490i	0.0132274	+	0.0621411i
$556$		0			0
$557$			7264.13i			0.552587i	0.961073	+	0.276294i	$0.0891062\pi$
$557$			7264.13i			0.552587i	−0.961073	+	0.276294i	$0.910894\pi$
$558$		0			0
$559$	−11082.8			−0.838555
$560$		0			0
$561$	−1371.90			−0.103247
$562$		0			0
$563$		−	3851.42i		−	0.288309i	−0.989555	−	0.144154i	$-0.953954\pi$
$563$		−	3851.42i		−	0.288309i	0.989555	−	0.144154i	$-0.0460462\pi$
$564$		0			0
$565$	17968.4	−	3824.78i	1.33794	−	0.284796i
$566$		0			0
$567$			3069.42i			0.227343i
$568$		0			0
$569$	−16580.3			−1.22158			−0.610792	−	0.791791i	$-0.709149\pi$
$569$	−16580.3			−1.22158			−0.610792	+	0.791791i	$0.709149\pi$
$570$		0			0
$571$	−6385.86			−0.468021			−0.234010	−	0.972234i	$-0.575185\pi$
$571$	−6385.86			−0.468021			−0.234010	+	0.972234i	$0.575185\pi$
$572$		0			0
$573$		−	2997.32i		−	0.218525i
$574$		0			0
$575$	5529.00	+	12398.9i	0.401001	+	0.899252i
$576$		0			0
$577$			11059.1i			0.797912i	0.916970	+	0.398956i	$0.130627\pi$
$577$			11059.1i			0.797912i	−0.916970	+	0.398956i	$0.869373\pi$
$578$		0			0
$579$	−4468.44			−0.320729
$580$		0			0
$581$	7304.92			0.521617
$582$		0			0
$583$		−	3678.84i		−	0.261341i
$584$		0			0
$585$	−16289.7	+	3467.45i	−1.15128	+	0.245062i
$586$		0			0
$587$		−	7871.25i		−	0.553461i	−0.960948	−	0.276730i	$-0.910749\pi$
$587$		−	7871.25i		−	0.553461i	0.960948	−	0.276730i	$-0.0892509\pi$
$588$		0			0
$589$	−102.386			−0.00716253
$590$		0			0
$591$	430.584			0.0299693
$592$		0			0
$593$		−	2018.06i		−	0.139750i	−0.997556	−	0.0698750i	$-0.977740\pi$
$593$		−	2018.06i		−	0.139750i	0.997556	−	0.0698750i	$-0.0222600\pi$
$594$		0			0
$595$	451.264	+	2120.00i	0.0310925	+	0.146069i
$596$		0			0
$597$		−	6944.08i		−	0.476051i
$598$		0			0
$599$	−1356.67			−0.0925409			−0.0462705	−	0.998929i	$-0.514734\pi$
$599$	−1356.67			−0.0925409			−0.0462705	+	0.998929i	$0.514734\pi$
$600$		0			0
$601$	11178.7			0.758715			0.379358	−	0.925250i	$-0.376145\pi$
$601$	11178.7			0.758715			0.379358	+	0.925250i	$0.376145\pi$
$602$		0			0
$603$			11982.8i			0.809252i
$604$		0			0
$605$	1579.60	+	7420.82i	0.106149	+	0.498676i
$606$		0			0
$607$			9404.67i			0.628870i	0.949279	+	0.314435i	$0.101815\pi$
$607$			9404.67i			0.628870i	−0.949279	+	0.314435i	$0.898185\pi$
$608$		0			0
$609$	3176.72			0.211375
$610$		0			0
$611$	13265.3			0.878328
$612$		0			0
$613$		−	18938.0i		−	1.24779i	−0.781507	−	0.623897i	$-0.785548\pi$
$613$		−	18938.0i		−	1.24779i	0.781507	−	0.623897i	$-0.214452\pi$
$614$		0			0
$615$	8551.35	−	1820.25i	0.560689	−	0.119349i
$616$		0			0
$617$		−	17716.9i		−	1.15600i	−0.816036	−	0.578001i	$-0.803833\pi$
$617$		−	17716.9i		−	1.15600i	0.816036	−	0.578001i	$-0.196167\pi$
$618$		0			0
$619$	−6240.33			−0.405202			−0.202601	−	0.979261i	$-0.564939\pi$
$619$	−6240.33			−0.405202			−0.202601	+	0.979261i	$0.564939\pi$
$620$		0			0
$621$	−10581.8			−0.683788
$622$		0			0
$623$		−	4564.42i		−	0.293531i
$624$		0			0
$625$	10441.6	−	11623.8i	0.668264	−	0.743924i
$626$		0			0
$627$			39.2539i			0.00250024i
$628$		0			0
$629$	1061.03			0.0672589
$630$		0			0
$631$	25887.7			1.63323			0.816617	−	0.577179i	$-0.195847\pi$
$631$	25887.7			1.63323			0.816617	+	0.577179i	$0.195847\pi$
$632$		0			0
$633$		−	8108.65i		−	0.509147i
$634$		0			0
$635$	−2099.94	+	446.994i	−0.131234	+	0.0279345i
$636$		0			0
$637$			3140.97i			0.195369i
$638$		0			0
$639$	−12935.0			−0.800783
$640$		0			0
$641$	18798.4			1.15834			0.579168	−	0.815208i	$-0.303378\pi$
$641$	18798.4			1.15834			0.579168	+	0.815208i	$0.303378\pi$
$642$		0			0
$643$			2287.70i			0.140308i	0.997536	+	0.0701541i	$0.0223491\pi$
$643$			2287.70i			0.140308i	−0.997536	+	0.0701541i	$0.977651\pi$
$644$		0			0
$645$	780.503	+	3666.73i	0.0476469	+	0.223841i
$646$		0			0
$647$			1769.31i			0.107510i	0.998554	+	0.0537548i	$0.0171189\pi$
$647$			1769.31i			0.107510i	−0.998554	+	0.0537548i	$0.982881\pi$
$648$		0			0
$649$	17345.2			1.04909
$650$		0			0
$651$	−1754.03			−0.105600
$652$		0			0
$653$			3891.48i			0.233209i	0.993178	+	0.116604i	$0.0372010\pi$
$653$			3891.48i			0.233209i	−0.993178	+	0.116604i	$0.962799\pi$
$654$		0			0
$655$	4848.38	+	22777.2i	0.289224	+	1.35875i
$656$		0			0
$657$		−	4025.96i		−	0.239068i
$658$		0			0
$659$	20097.6			1.18800			0.594001	−	0.804465i	$-0.297548\pi$
$659$	20097.6			1.18800			0.594001	+	0.804465i	$0.297548\pi$
$660$		0			0
$661$	−27167.9			−1.59865			−0.799326	−	0.600898i	$-0.794810\pi$
$661$	−27167.9			−1.59865			−0.799326	+	0.600898i	$0.794810\pi$
$662$		0			0
$663$		−	3442.99i		−	0.201681i
$664$		0			0
$665$	60.6589	−	12.9119i	0.00353722	−	0.000752937i
$666$		0			0
$667$		−	25414.0i		−	1.47531i
$668$		0			0
$669$	−4579.91			−0.264678
$670$		0			0
$671$	14679.4			0.844548
$672$		0			0
$673$			25909.7i			1.48402i	0.670389	+	0.742010i	$0.266127\pi$
$673$			25909.7i			1.48402i	−0.670389	+	0.742010i	$0.733873\pi$
$674$		0			0
$675$	4960.15	+	11123.2i	0.282839	+	0.634271i
$676$		0			0
$677$		−	4359.22i		−	0.247472i	−0.992315	−	0.123736i	$-0.960512\pi$
$677$		−	4359.22i		−	0.247472i	0.992315	−	0.123736i	$-0.0394875\pi$
$678$		0			0
$679$	3610.00			0.204034
$680$		0			0
$681$	1138.18			0.0640458
$682$		0			0
$683$		−	29721.9i		−	1.66512i	−0.553937	−	0.832559i	$-0.686875\pi$
$683$		−	29721.9i		−	1.66512i	0.553937	−	0.832559i	$-0.313125\pi$
$684$		0			0
$685$	854.826	−	181.959i	0.0476806	−	0.0101493i
$686$		0			0
$687$		−	8959.10i		−	0.497541i
$688$		0			0
$689$	9232.60			0.510499
$690$		0			0
$691$	4929.13			0.271365			0.135682	−	0.990752i	$-0.456677\pi$
$691$	4929.13			0.271365			0.135682	+	0.990752i	$0.456677\pi$
$692$		0			0
$693$		−	4154.95i		−	0.227754i
$694$		0			0
$695$	−3244.05	−	15240.2i	−0.177056	−	0.831791i
$696$		0			0
$697$		−	11167.1i		−	0.606866i
$698$		0			0
$699$	−9930.51			−0.537348
$700$		0			0
$701$	−19358.8			−1.04304			−0.521520	−	0.853239i	$-0.674635\pi$
$701$	−19358.8			−1.04304			−0.521520	+	0.853239i	$0.674635\pi$
$702$		0			0
$703$		−	30.3589i		−	0.00162874i
$704$		0			0
$705$	−934.208	−	4388.82i	−0.0499068	−	0.234457i
$706$		0			0
$707$		−	3754.38i		−	0.199714i
$708$		0			0
$709$	17186.3			0.910359			0.455180	−	0.890400i	$-0.349575\pi$
$709$	17186.3			0.910359			0.455180	+	0.890400i	$0.349575\pi$
$710$		0			0
$711$	1843.51			0.0972392
$712$		0			0
$713$			14032.4i			0.737049i
$714$		0			0
$715$	17904.2	−	3811.10i	0.936473	−	0.199339i
$716$		0			0
$717$		−	2186.68i		−	0.113896i
$718$		0			0
$719$	−15107.3			−0.783598			−0.391799	−	0.920051i	$-0.628147\pi$
$719$	−15107.3			−0.783598			−0.391799	+	0.920051i	$0.628147\pi$
$720$		0			0
$721$	2671.85			0.138010
$722$		0			0
$723$			6883.91i			0.354102i
$724$		0			0
$725$	−26714.3	+	11912.6i	−1.36848	+	0.610240i
$726$		0			0
$727$		−	15840.9i		−	0.808124i	−0.914732	−	0.404062i	$-0.867598\pi$
$727$		−	15840.9i		−	0.808124i	0.914732	−	0.404062i	$-0.132402\pi$
$728$		0			0
$729$	5088.04			0.258499
$730$		0			0
$731$	4788.35			0.242276
$732$		0			0
$733$		−	27639.7i		−	1.39276i	−0.717671	−	0.696382i	$-0.754792\pi$
$733$		−	27639.7i		−	1.39276i	0.717671	−	0.696382i	$-0.245208\pi$
$734$		0			0
$735$	1039.18	−	221.202i	0.0521509	−	0.0111009i
$736$		0			0
$737$		−	13170.4i		−	0.658263i
$738$		0			0
$739$	34874.4			1.73596			0.867982	−	0.496597i	$-0.165417\pi$
$739$	34874.4			1.73596			0.867982	+	0.496597i	$0.165417\pi$
$740$		0			0
$741$	−98.5136			−0.00488392
$742$		0			0
$743$			27686.7i			1.36706i	0.729922	+	0.683530i	$0.239556\pi$
$743$			27686.7i			1.36706i	−0.729922	+	0.683530i	$0.760444\pi$
$744$		0			0
$745$	75.6510	+	355.401i	0.00372032	+	0.0174777i
$746$		0			0
$747$		−	24251.1i		−	1.18782i
$748$		0			0
$749$	9667.83			0.471635
$750$		0			0
$751$	−4806.85			−0.233561			−0.116781	−	0.993158i	$-0.537257\pi$
$751$	−4806.85			−0.233561			−0.116781	+	0.993158i	$0.537257\pi$
$752$		0			0
$753$			9148.45i			0.442747i
$754$		0			0
$755$	1086.49	+	5104.21i	0.0523726	+	0.246041i
$756$		0			0
$757$			40166.6i			1.92851i	0.264983	+	0.964253i	$0.414634\pi$
$757$			40166.6i			1.92851i	−0.264983	+	0.964253i	$0.585366\pi$
$758$		0			0
$759$	5379.90			0.257283
$760$		0			0
$761$	25912.3			1.23432			0.617162	−	0.786836i	$-0.288282\pi$
$761$	25912.3			1.23432			0.617162	+	0.786836i	$0.288282\pi$
$762$		0			0
$763$			2734.07i			0.129725i
$764$		0			0
$765$	7038.01	−	1498.12i	0.332627	−	0.0708034i
$766$		0			0
$767$			43530.4i			2.04927i
$768$		0			0
$769$	23231.3			1.08939			0.544697	−	0.838633i	$-0.316645\pi$
$769$	23231.3			1.08939			0.544697	+	0.838633i	$0.316645\pi$
$770$		0			0
$771$	−12141.2			−0.567125
$772$		0			0
$773$			836.306i			0.0389131i	0.999811	+	0.0194566i	$0.00619360\pi$
$773$			836.306i			0.0389131i	−0.999811	+	0.0194566i	$0.993806\pi$
$774$		0			0
$775$	14750.4	−	6577.58i	0.683675	−	0.304869i
$776$		0			0
$777$		−	520.096i		−	0.0240133i
$778$		0			0
$779$	−319.523			−0.0146959
$780$		0			0
$781$	14217.0			0.651374
$782$		0			0
$783$		−	22799.2i		−	1.04058i
$784$		0			0
$785$	−18300.3	+	3895.43i	−0.832060	+	0.177113i
$786$		0			0
$787$			31945.6i			1.44693i	0.690359	+	0.723467i	$0.257453\pi$
$787$			31945.6i			1.44693i	−0.690359	+	0.723467i	$0.742547\pi$
$788$		0			0
$789$	11157.4			0.503438
$790$		0			0
$791$	−11502.1			−0.517024
$792$		0			0
$793$			36840.2i			1.64973i
$794$		0			0

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	560.g (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.93939i q^{3} +(-2.32771 - 10.9353i) q^{5} +7.00000i q^{7} +23.2388 q^{9} -25.5420 q^{11} -64.1014i q^{13} +(-21.2079 + 4.51433i) q^{15} +27.6952i q^{17} +0.792436 q^{19} +13.5757 q^{21} -108.606i q^{23} +(-114.164 + 50.9086i) q^{25} -97.4324i q^{27} +234.000 q^{29} -129.204 q^{31} +49.5357i q^{33} +(76.5474 - 16.2940i) q^{35} -38.3108i q^{37} -124.317 q^{39} -403.216 q^{41} -172.895i q^{43} +(-54.0931 - 254.124i) q^{45} +206.943i q^{47} -49.0000 q^{49} +53.7117 q^{51} +144.031i q^{53} +(59.4542 + 279.310i) q^{55} -1.53684i q^{57} -679.086 q^{59} -574.717 q^{61} +162.671i q^{63} +(-700.971 + 149.209i) q^{65} +515.640i q^{67} -210.630 q^{69} -556.612 q^{71} -173.243i q^{73} +(98.7314 + 221.407i) q^{75} -178.794i q^{77} +79.3290 q^{79} +438.488 q^{81} -1043.56i q^{83} +(302.856 - 64.4663i) q^{85} -453.817i q^{87} -652.060 q^{89} +448.710 q^{91} +250.576i q^{93} +(-1.84456 - 8.66556i) q^{95} -515.714i q^{97} -593.564 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 6 q^{5} - 46 q^{9} - 84 q^{11} - 8 q^{15} - 72 q^{19} + 140 q^{21} - 362 q^{25} + 88 q^{29} - 120 q^{31} + 28 q^{35} - 212 q^{39} - 852 q^{41} - 510 q^{45} - 490 q^{49} - 1276 q^{51} + 1136 q^{55}+ \cdots + 5304 q^{99}+O(q^{100}) \) 10 * q + 6 * q^5 - 46 * q^9 - 84 * q^11 - 8 * q^15 - 72 * q^19 + 140 * q^21 - 362 * q^25 + 88 * q^29 - 120 * q^31 + 28 * q^35 - 212 * q^39 - 852 * q^41 - 510 * q^45 - 490 * q^49 - 1276 * q^51 + 1136 * q^55 - 864 * q^59 - 884 * q^61 + 520 * q^65 + 4808 * q^69 - 880 * q^71 - 720 * q^75 + 3580 * q^79 - 302 * q^81 + 1572 * q^85 - 1492 * q^89 - 476 * q^91 + 1628 * q^95 + 5304 * q^99

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