LMFDB - Embedded newform 252.4.i.a.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(25,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 4]))

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

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

chi := DirichletCharacter("252.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	252.25
Dual form			252.4.i.a.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.19442 - 0.133994i) q^{3} +(7.81356 - 13.5335i) q^{5} +(6.71488 - 17.2601i) q^{7} +(26.9641 + 1.39204i) q^{9} +O(q^{10})$	\(q+(-5.19442 - 0.133994i) q^{3} +(7.81356 - 13.5335i) q^{5} +(6.71488 - 17.2601i) q^{7} +(26.9641 + 1.39204i) q^{9} +(0.495432 + 0.858113i) q^{11} +(16.4347 + 28.4657i) q^{13} +(-42.4004 + 69.2517i) q^{15} +(-37.8684 + 65.5900i) q^{17} +(-62.5064 - 108.264i) q^{19} +(-37.1927 + 88.7564i) q^{21} +(104.835 - 181.580i) q^{23} +(-59.6035 - 103.236i) q^{25} +(-139.876 - 10.8439i) q^{27} +(-2.40194 + 4.16028i) q^{29} +4.45003 q^{31} +(-2.45850 - 4.52379i) q^{33} +(-181.122 - 225.738i) q^{35} +(-104.544 - 181.075i) q^{37} +(-81.5545 - 150.065i) q^{39} +(10.3420 + 17.9129i) q^{41} +(103.891 - 179.945i) q^{43} +(229.525 - 354.041i) q^{45} -387.080 q^{47} +(-252.821 - 231.799i) q^{49} +(205.493 - 335.628i) q^{51} +(-251.594 + 435.773i) q^{53} +15.4843 q^{55} +(310.178 + 570.746i) q^{57} -489.937 q^{59} +80.7092 q^{61} +(205.088 - 456.055i) q^{63} +513.654 q^{65} -32.0389 q^{67} +(-568.888 + 929.154i) q^{69} -704.272 q^{71} +(-5.26605 + 9.12107i) q^{73} +(295.773 + 544.239i) q^{75} +(18.1379 - 2.78906i) q^{77} +1317.40 q^{79} +(725.124 + 75.0704i) q^{81} +(-77.8871 + 134.904i) q^{83} +(591.774 + 1024.98i) q^{85} +(13.0341 - 21.2884i) q^{87} +(98.1977 + 170.083i) q^{89} +(601.677 - 92.5200i) q^{91} +(-23.1153 - 0.596277i) q^{93} -1953.59 q^{95} +(859.522 - 1488.74i) q^{97} +(12.1643 + 23.8279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9}+O(q^{10}) $ 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9	$ 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9} + 4 q^{11} - 12 q^{13} - 26 q^{15} + 112 q^{17} + 60 q^{19} - 80 q^{21} + 10 q^{23} - 600 q^{25} + 194 q^{29} + 60 q^{31} - 472 q^{33} + 394 q^{35} - 84 q^{37} + 604 q^{39} + 210 q^{41} + 42 q^{43} + 254 q^{45} - 132 q^{47} - 78 q^{49} - 58 q^{51} - 468 q^{53} + 612 q^{55} + 1476 q^{57} - 916 q^{59} - 804 q^{61} - 444 q^{63} + 1656 q^{65} - 588 q^{67} - 28 q^{69} - 2228 q^{71} - 336 q^{73} - 668 q^{75} - 1216 q^{77} - 768 q^{79} - 104 q^{81} + 1024 q^{83} + 360 q^{85} + 2188 q^{87} + 2922 q^{89} - 120 q^{91} - 1292 q^{93} + 2428 q^{95} - 264 q^{97} - 2246 q^{99}+O(q^{100}) $ 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9 + 4 * q^11 - 12 * q^13 - 26 * q^15 + 112 * q^17 + 60 * q^19 - 80 * q^21 + 10 * q^23 - 600 * q^25 + 194 * q^29 + 60 * q^31 - 472 * q^33 + 394 * q^35 - 84 * q^37 + 604 * q^39 + 210 * q^41 + 42 * q^43 + 254 * q^45 - 132 * q^47 - 78 * q^49 - 58 * q^51 - 468 * q^53 + 612 * q^55 + 1476 * q^57 - 916 * q^59 - 804 * q^61 - 444 * q^63 + 1656 * q^65 - 588 * q^67 - 28 * q^69 - 2228 * q^71 - 336 * q^73 - 668 * q^75 - 1216 * q^77 - 768 * q^79 - 104 * q^81 + 1024 * q^83 + 360 * q^85 + 2188 * q^87 + 2922 * q^89 - 120 * q^91 - 1292 * q^93 + 2428 * q^95 - 264 * q^97 - 2246 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−5.19442	−	0.133994i	−0.999667	−	0.0257872i
$3$	−5.19442	−	0.133994i	−0.999667	−	0.0257872i
$4$		0			0
$5$	7.81356	−	13.5335i	0.698866	−	1.21047i	−0.269994	−	0.962862i	$-0.587022\pi$
$5$	7.81356	−	13.5335i	0.698866	−	1.21047i	0.968860	−	0.247610i	$-0.0796450\pi$
$6$		0			0
$7$	6.71488	−	17.2601i	0.362570	−	0.931957i
$7$	6.71488	−	17.2601i	0.362570	−	0.931957i
$8$		0			0
$9$	26.9641	+	1.39204i	0.998670	+	0.0515572i
$10$		0			0
$11$	0.495432	+	0.858113i	0.0135798	+	0.0235210i	0.872735	−	0.488193i	$-0.162344\pi$
$11$	0.495432	+	0.858113i	0.0135798	+	0.0235210i	−0.859156	+	0.511714i	$0.829011\pi$
$12$		0			0
$13$	16.4347	+	28.4657i	0.350628	+	0.607305i	0.986360	−	0.164605i	$-0.0526349\pi$
$13$	16.4347	+	28.4657i	0.350628	+	0.607305i	−0.635732	+	0.771910i	$0.719302\pi$
$14$		0			0
$15$	−42.4004	+	69.2517i	−0.729848	+	1.19205i
$16$		0			0
$17$	−37.8684	+	65.5900i	−0.540261	+	0.935760i	0.458627	+	0.888629i	$0.348341\pi$
$17$	−37.8684	+	65.5900i	−0.540261	+	0.935760i	−0.998889	+	0.0471313i	$0.984992\pi$
$18$		0			0
$19$	−62.5064	−	108.264i	−0.754735	−	1.30724i	−0.945506	−	0.325604i	$-0.894432\pi$
$19$	−62.5064	−	108.264i	−0.754735	−	1.30724i	0.190771	−	0.981634i	$-0.438901\pi$
$20$		0			0
$21$	−37.1927	+	88.7564i	−0.386482	+	0.922297i
$22$		0			0
$23$	104.835	−	181.580i	0.950418	−	1.64617i	0.205897	−	0.978574i	$-0.433989\pi$
$23$	104.835	−	181.580i	0.950418	−	1.64617i	0.744521	−	0.667599i	$-0.232678\pi$
$24$		0			0
$25$	−59.6035	−	103.236i	−0.476828	−	0.825890i
$26$		0			0
$27$	−139.876	−	10.8439i	−0.997008	−	0.0772929i
$28$		0			0
$29$	−2.40194	+	4.16028i	−0.0153803	+	0.0266394i	−0.873613	−	0.486621i	$-0.838229\pi$
$29$	−2.40194	+	4.16028i	−0.0153803	+	0.0266394i	0.858233	+	0.513261i	$0.171563\pi$
$30$		0			0
$31$	4.45003			0.0257822			0.0128911	−	0.999917i	$-0.495897\pi$
$31$	4.45003			0.0257822			0.0128911	+	0.999917i	$0.495897\pi$
$32$		0			0
$33$	−2.45850	−	4.52379i	−0.0129688	−	0.0238634i
$34$		0			0
$35$	−181.122	−	225.738i	−0.874719	−	1.09019i
$36$		0			0
$37$	−104.544	−	181.075i	−0.464511	−	0.804556i	0.534668	−	0.845062i	$-0.320436\pi$
$37$	−104.544	−	181.075i	−0.464511	−	0.804556i	−0.999179	+	0.0405055i	$0.987103\pi$
$38$		0			0
$39$	−81.5545	−	150.065i	−0.334850	−	0.616145i
$40$		0			0
$41$	10.3420	+	17.9129i	0.0393940	+	0.0682323i	0.885050	−	0.465496i	$-0.154124\pi$
$41$	10.3420	+	17.9129i	0.0393940	+	0.0682323i	−0.845656	+	0.533728i	$0.820791\pi$
$42$		0			0
$43$	103.891	−	179.945i	0.368447	−	0.638169i	−0.620876	−	0.783909i	$-0.713223\pi$
$43$	103.891	−	179.945i	0.368447	−	0.638169i	0.989323	+	0.145740i	$0.0465562\pi$
$44$		0			0
$45$	229.525	−	354.041i	0.760345	−	1.17283i
$46$		0			0
$47$	−387.080			−1.20131			−0.600653	−	0.799510i	$-0.705093\pi$
$47$	−387.080			−1.20131			−0.600653	+	0.799510i	$0.705093\pi$
$48$		0			0
$49$	−252.821	−	231.799i	−0.737086	−	0.675798i
$50$		0			0
$51$	205.493	−	335.628i	0.564212	−	0.921517i
$52$		0			0
$53$	−251.594	+	435.773i	−0.652057	+	1.12940i	0.330565	+	0.943783i	$0.392761\pi$
$53$	−251.594	+	435.773i	−0.652057	+	1.12940i	−0.982623	+	0.185614i	$0.940573\pi$
$54$		0			0
$55$	15.4843			0.0379620
$56$		0			0
$57$	310.178	+	570.746i	0.720774	+	1.32627i
$58$		0			0
$59$	−489.937			−1.08109			−0.540546	−	0.841315i	$-0.681782\pi$
$59$	−489.937			−1.08109			−0.540546	+	0.841315i	$0.681782\pi$
$60$		0			0
$61$	80.7092			0.169406			0.0847029	−	0.996406i	$-0.473006\pi$
$61$	80.7092			0.169406			0.0847029	+	0.996406i	$0.473006\pi$
$62$		0			0
$63$	205.088	−	456.055i	0.410137	−	0.912024i
$64$		0			0
$65$	513.654			0.980167
$66$		0			0
$67$	−32.0389			−0.0584205			−0.0292102	−	0.999573i	$-0.509299\pi$
$67$	−32.0389			−0.0584205			−0.0292102	+	0.999573i	$0.509299\pi$
$68$		0			0
$69$	−568.888	+	929.154i	−0.992552	+	1.62112i
$70$		0			0
$71$	−704.272			−1.17721			−0.588603	−	0.808422i	$-0.700322\pi$
$71$	−704.272			−1.17721			−0.588603	+	0.808422i	$0.700322\pi$
$72$		0			0
$73$	−5.26605	+	9.12107i	−0.00844308	+	0.0146238i	−0.870216	−	0.492670i	$-0.836021\pi$
$73$	−5.26605	+	9.12107i	−0.00844308	+	0.0146238i	0.861773	+	0.507294i	$0.169354\pi$
$74$		0			0
$75$	295.773	+	544.239i	0.455372	+	0.837911i
$76$		0			0
$77$	18.1379	−	2.78906i	0.0268442	−	0.00412783i
$78$		0			0
$79$	1317.40			1.87619			0.938093	−	0.346383i	$-0.112590\pi$
$79$	1317.40			1.87619			0.938093	+	0.346383i	$0.112590\pi$
$80$		0			0
$81$	725.124	+	75.0704i	0.994684	+	0.102977i
$82$		0			0
$83$	−77.8871	+	134.904i	−0.103003	+	0.178406i	−0.912920	−	0.408138i	$-0.866178\pi$
$83$	−77.8871	+	134.904i	−0.103003	+	0.178406i	0.809918	+	0.586543i	$0.199512\pi$
$84$		0			0
$85$	591.774	+	1024.98i	0.755141	+	1.30794i
$86$		0			0
$87$	13.0341	−	21.2884i	0.0160621	−	0.0262340i
$88$		0			0
$89$	98.1977	+	170.083i	0.116954	+	0.202571i	0.918559	−	0.395283i	$-0.129354\pi$
$89$	98.1977	+	170.083i	0.116954	+	0.202571i	−0.801605	+	0.597854i	$0.796020\pi$
$90$		0			0
$91$	601.677	−	92.5200i	0.693109	−	0.106579i
$92$		0			0
$93$	−23.1153	−	0.596277i	−0.0257736	−	0.000664850i
$94$		0			0
$95$	−1953.59			−2.10983
$96$		0			0
$97$	859.522	−	1488.74i	0.899704	−	1.55833i	0.0718310	−	0.997417i	$-0.477116\pi$
$97$	859.522	−	1488.74i	0.899704	−	1.55833i	0.827873	−	0.560916i	$-0.189551\pi$
$98$		0			0
$99$	12.1643	+	23.8279i	0.0123491	+	0.0241898i
$100$		0			0
$101$	−264.447	−	458.036i	−0.260529	−	0.451250i	0.705853	−	0.708358i	$-0.250564\pi$
$101$	−264.447	−	458.036i	−0.260529	−	0.451250i	−0.966383	+	0.257108i	$0.917230\pi$
$102$		0			0
$103$	−992.646	+	1719.31i	−0.949596	+	1.64475i	−0.203318	+	0.979113i	$0.565173\pi$
$103$	−992.646	+	1719.31i	−0.949596	+	1.64475i	−0.746277	+	0.665635i	$0.768161\pi$
$104$		0			0
$105$	910.576	+	1196.85i	0.846316	+	1.11239i
$106$		0			0
$107$	129.390	+	224.110i	0.116903	+	0.202481i	0.918539	−	0.395331i	$-0.129370\pi$
$107$	129.390	+	224.110i	0.116903	+	0.202481i	−0.801636	+	0.597812i	$0.796037\pi$
$108$		0			0
$109$	629.592	−	1090.49i	0.553247	−	0.958253i	−0.444790	−	0.895635i	$-0.646722\pi$
$109$	629.592	−	1090.49i	0.553247	−	0.958253i	0.998038	−	0.0626177i	$-0.0199449\pi$
$110$		0			0
$111$	518.782	+	954.590i	0.443609	+	0.816267i
$112$		0			0
$113$	−222.126	−	384.733i	−0.184919	−	0.320289i	0.758630	−	0.651521i	$-0.225869\pi$
$113$	−222.126	−	384.733i	−0.184919	−	0.320289i	−0.943549	+	0.331232i	$0.892536\pi$
$114$		0			0
$115$	−1638.27	−	2837.57i	−1.32843	−	2.30091i
$116$		0			0
$117$	403.521	+	790.430i	0.318850	+	0.624575i
$118$		0			0
$119$	877.807	+	1094.04i	0.676205	+	0.842778i
$120$		0			0
$121$	665.009	−	1151.83i	0.499631	−	0.865387i
$122$		0			0
$123$	−51.3206	−	94.4330i	−0.0376213	−	0.0692255i
$124$		0			0
$125$	90.5289			0.0647772
$126$		0			0
$127$	1658.78			1.15900			0.579499	−	0.814973i	$-0.303248\pi$
$127$	1658.78			1.15900			0.579499	+	0.814973i	$0.303248\pi$
$128$		0			0
$129$	−563.766	+	920.788i	−0.384781	+	0.628456i
$130$		0			0
$131$	832.108	−	1441.25i	0.554974	−	0.961244i	−0.442931	−	0.896556i	$-0.646061\pi$
$131$	832.108	−	1441.25i	0.554974	−	0.961244i	0.997906	−	0.0646881i	$-0.0206053\pi$
$132$		0			0
$133$	−2288.37	+	351.884i	−1.49193	+	0.229415i
$134$		0			0
$135$	−1239.69	+	1808.29i	−0.790336	+	1.15283i
$136$		0			0
$137$	1408.73	+	2440.00i	0.878512	+	1.52163i	0.852973	+	0.521954i	$0.174797\pi$
$137$	1408.73	+	2440.00i	0.878512	+	1.52163i	0.0255389	+	0.999674i	$0.491870\pi$
$138$		0			0
$139$	−1207.54	−	2091.53i	−0.736852	−	1.27627i	−0.953906	−	0.300106i	$-0.902978\pi$
$139$	−1207.54	−	2091.53i	−0.736852	−	1.27627i	0.217054	−	0.976160i	$-0.430355\pi$
$140$		0			0
$141$	2010.66	+	51.8664i	1.20091	+	0.0309783i
$142$		0			0
$143$	−16.2845	+	28.2056i	−0.00952294	+	0.0164942i
$144$		0			0
$145$	37.5354	+	65.0132i	0.0214975	+	0.0372348i
$146$		0			0
$147$	1282.20	+	1237.94i	0.719414	+	0.694581i
$148$		0			0
$149$	−1533.81	+	2656.64i	−0.843321	+	1.46068i	0.0437495	+	0.999043i	$0.486070\pi$
$149$	−1533.81	+	2656.64i	−0.843321	+	1.46068i	−0.887071	+	0.461633i	$0.847264\pi$
$150$		0			0
$151$	971.654	+	1682.95i	0.523656	+	0.906999i	0.999621	+	0.0275344i	$0.00876559\pi$
$151$	971.654	+	1682.95i	0.523656	+	0.906999i	−0.475965	+	0.879464i	$0.657901\pi$
$152$		0			0
$153$	−1112.39	+	1715.86i	−0.587788	+	0.906661i
$154$		0			0
$155$	34.7706	−	60.2244i	0.0180183	−	0.0312086i
$156$		0			0
$157$	970.175			0.493175			0.246587	−	0.969121i	$-0.420691\pi$
$157$	970.175			0.493175			0.246587	+	0.969121i	$0.420691\pi$
$158$		0			0
$159$	1365.28	−	2229.88i	0.680965	−	1.11221i
$160$		0			0
$161$	−2430.12	−	3028.75i	−1.18957	−	1.48260i
$162$		0			0
$163$	1143.31	+	1980.27i	0.549393	+	0.951576i	0.998316	+	0.0580060i	$0.0184743\pi$
$163$	1143.31	+	1980.27i	0.549393	+	0.951576i	−0.448923	+	0.893570i	$0.648192\pi$
$164$		0			0
$165$	−80.4323	−	2.07481i	−0.0379494	−	0.000978932i
$166$		0			0
$167$	19.7833	+	34.2657i	0.00916694	+	0.0158776i	0.870572	−	0.492040i	$-0.163749\pi$
$167$	19.7833	+	34.2657i	0.00916694	+	0.0158776i	−0.861406	+	0.507918i	$0.830415\pi$
$168$		0			0
$169$	558.302	−	967.008i	0.254120	−	0.440149i
$170$		0			0
$171$	−1534.72	−	3006.26i	−0.686333	−	1.34441i
$172$		0			0
$173$	1060.59			0.466101			0.233051	−	0.972465i	$-0.425129\pi$
$173$	1060.59			0.466101			0.233051	+	0.972465i	$0.425129\pi$
$174$		0			0
$175$	−2182.10	+	335.541i	−0.942577	+	0.144940i
$176$		0			0
$177$	2544.94	+	65.6486i	1.08073	+	0.0278783i
$178$		0			0
$179$	−450.866	+	780.922i	−0.188264	+	0.326083i	−0.944672	−	0.328018i	$-0.893619\pi$
$179$	−450.866	+	780.922i	−0.188264	+	0.326083i	0.756407	+	0.654101i	$0.226953\pi$
$180$		0			0
$181$	−1274.85			−0.523531			−0.261766	−	0.965131i	$-0.584305\pi$
$181$	−1274.85			−0.523531			−0.261766	+	0.965131i	$0.584305\pi$
$182$		0			0
$183$	−419.238	−	10.8146i	−0.169350	−	0.00436850i
$184$		0			0
$185$	−3267.44			−1.29852
$186$		0			0
$187$	−75.0449			−0.0293467
$188$		0			0
$189$	−1126.42	+	2341.46i	−0.433519	+	0.901145i
$190$		0			0
$191$	1952.70			0.739752			0.369876	−	0.929081i	$-0.379400\pi$
$191$	1952.70			0.739752			0.369876	+	0.929081i	$0.379400\pi$
$192$		0			0
$193$	3216.22			1.19953			0.599763	−	0.800177i	$-0.295261\pi$
$193$	3216.22			1.19953			0.599763	+	0.800177i	$0.295261\pi$
$194$		0			0
$195$	−2668.13	−	68.8265i	−0.979841	−	0.0252757i
$196$		0			0
$197$	452.996			0.163831			0.0819154	−	0.996639i	$-0.473896\pi$
$197$	452.996			0.163831			0.0819154	+	0.996639i	$0.473896\pi$
$198$		0			0
$199$	1902.63	−	3295.46i	0.677759	−	1.17391i	−0.297895	−	0.954599i	$-0.596284\pi$
$199$	1902.63	−	3295.46i	0.677759	−	1.17391i	0.975654	−	0.219315i	$-0.0703822\pi$
$200$		0			0
$201$	166.423	+	4.29302i	0.0584010	+	0.00150650i
$202$		0			0
$203$	55.6780	+	69.3934i	0.0192504	+	0.0239924i
$204$		0			0
$205$	323.232			0.110124
$206$		0			0
$207$	3079.55	−	4750.20i	1.03403	−	1.59498i
$208$		0			0
$209$	61.9354	−	107.275i	0.0204984	−	0.0355042i
$210$		0			0
$211$	−2541.23	−	4401.55i	−0.829127	−	1.43609i	−0.898724	−	0.438515i	$-0.855505\pi$
$211$	−2541.23	−	4401.55i	−0.829127	−	1.43609i	0.0695967	−	0.997575i	$-0.477829\pi$
$212$		0			0
$213$	3658.29	+	94.3682i	1.17682	+	0.0303568i
$214$		0			0
$215$	−1623.52	−	2812.02i	−0.514991	−	0.891990i
$216$		0			0
$217$	29.8814	−	76.8078i	0.00934785	−	0.0240279i
$218$		0			0
$219$	28.5763	−	46.6731i	0.00881737	−	0.0144012i
$220$		0			0
$221$	−2489.42			−0.757722
$222$		0			0
$223$	−1548.62	+	2682.29i	−0.465038	+	0.805469i	−0.999203	−	0.0399107i	$-0.987293\pi$
$223$	−1548.62	+	2682.29i	−0.465038	+	0.805469i	0.534165	+	0.845380i	$0.320626\pi$
$224$		0			0
$225$	−1463.44	−	2866.64i	−0.433613	−	0.849375i
$226$		0			0
$227$	−1595.30	−	2763.15i	−0.466450	−	0.807914i	0.532816	−	0.846231i	$-0.321134\pi$
$227$	−1595.30	−	2763.15i	−0.466450	−	0.807914i	−0.999266	+	0.0383167i	$0.987800\pi$
$228$		0			0
$229$	495.018	−	857.396i	0.142846	−	0.247416i	−0.785721	−	0.618581i	$-0.787708\pi$
$229$	495.018	−	857.396i	0.142846	−	0.247416i	0.928567	+	0.371164i	$0.121041\pi$
$230$		0			0
$231$	−94.5895	+	12.0572i	−0.0269417	+	0.00343423i
$232$		0			0
$233$	−1070.08	−	1853.43i	−0.300872	−	0.521126i	0.675461	−	0.737395i	$-0.263944\pi$
$233$	−1070.08	−	1853.43i	−0.300872	−	0.521126i	−0.976334	+	0.216269i	$0.930611\pi$
$234$		0			0
$235$	−3024.47	+	5238.54i	−0.839552	+	1.45415i
$236$		0			0
$237$	−6843.12	−	176.523i	−1.87556	−	0.0483815i
$238$		0			0
$239$	−1850.05	−	3204.38i	−0.500710	−	0.867256i	−1.00000		0.000820511i	$-0.999739\pi$
$239$	−1850.05	−	3204.38i	−0.500710	−	0.867256i	0.499289	−	0.866435i	$-0.333595\pi$
$240$		0			0
$241$	2586.24	+	4479.49i	0.691262	+	1.19730i	0.971425	+	0.237348i	$0.0762783\pi$
$241$	2586.24	+	4479.49i	0.691262	+	1.19730i	−0.280162	+	0.959953i	$0.590388\pi$
$242$		0			0
$243$	−3756.55	−	487.110i	−0.991697	−	0.128593i
$244$		0			0
$245$	−5112.48	+	1610.37i	−1.33316	+	0.419930i
$246$		0			0
$247$	2054.55	−	3558.58i	0.529262	−	0.916708i
$248$		0			0
$249$	422.655	−	690.314i	0.107569	−	0.175690i
$250$		0			0
$251$	3529.46			0.887561			0.443781	−	0.896135i	$-0.353637\pi$
$251$	3529.46			0.887561			0.443781	+	0.896135i	$0.353637\pi$
$252$		0			0
$253$	207.755			0.0516261
$254$		0			0
$255$	−2936.59	−	5403.49i	−0.721161	−	1.32698i
$256$		0			0
$257$	−693.932	+	1201.93i	−0.168429	+	0.291728i	−0.937868	−	0.346993i	$-0.887203\pi$
$257$	−693.932	+	1201.93i	−0.168429	+	0.291728i	0.769439	+	0.638721i	$0.220536\pi$
$258$		0			0
$259$	−3827.37	+	588.536i	−0.918229	+	0.141196i
$260$		0			0
$261$	−70.5573	+	108.834i	−0.0167333	+	0.0258111i
$262$		0			0
$263$	3448.72	+	5973.36i	0.808583	+	1.40051i	0.913845	+	0.406062i	$0.133098\pi$
$263$	3448.72	+	5973.36i	0.808583	+	1.40051i	−0.105263	+	0.994444i	$0.533568\pi$
$264$		0			0
$265$	3931.68	+	6809.88i	0.911402	+	1.57859i
$266$		0			0
$267$	−487.290	−	896.643i	−0.111692	−	0.205519i
$268$		0			0
$269$	3729.43	−	6459.56i	0.845306	−	1.46411i	−0.0400499	−	0.999198i	$-0.512752\pi$
$269$	3729.43	−	6459.56i	0.845306	−	1.46411i	0.885356	−	0.464915i	$-0.153915\pi$
$270$		0			0
$271$	113.402	+	196.418i	0.0254195	+	0.0440278i	0.878455	−	0.477825i	$-0.158575\pi$
$271$	113.402	+	196.418i	0.0254195	+	0.0440278i	−0.853036	+	0.521852i	$0.825241\pi$
$272$		0			0
$273$	−3137.76	+	399.967i	−0.695627	+	0.0886707i
$274$		0			0
$275$	59.0589	−	102.293i	0.0129505	−	0.0224309i
$276$		0			0
$277$	−3622.31	−	6274.03i	−0.785718	−	1.36090i	−0.928569	−	0.371159i	$-0.878961\pi$
$277$	−3622.31	−	6274.03i	−0.785718	−	1.36090i	0.142852	−	0.989744i	$-0.454373\pi$
$278$		0			0
$279$	119.991	+	6.19463i	0.0257479	+	0.00132926i
$280$		0			0
$281$	1282.48	−	2221.33i	0.272265	−	0.471578i	−0.697176	−	0.716900i	$-0.745560\pi$
$281$	1282.48	−	2221.33i	0.272265	−	0.471578i	0.969442	+	0.245322i	$0.0788938\pi$
$282$		0			0
$283$	−1921.42			−0.403593			−0.201796	−	0.979427i	$-0.564678\pi$
$283$	−1921.42			−0.403593			−0.201796	+	0.979427i	$0.564678\pi$
$284$		0			0
$285$	10147.8	+	261.770i	2.10913	+	0.0544066i
$286$		0			0
$287$	378.624	−	58.2210i	0.0778726	−	0.0119745i
$288$		0			0
$289$	−411.535	−	712.799i	−0.0837645	−	0.145084i
$290$		0			0
$291$	−4664.21	+	7617.96i	−0.939590	+	1.53461i
$292$		0			0
$293$	3904.33	+	6762.49i	0.778475	+	1.34836i	0.932821	+	0.360341i	$0.117340\pi$
$293$	3904.33	+	6762.49i	0.778475	+	1.34836i	−0.154346	+	0.988017i	$0.549327\pi$
$294$		0			0
$295$	−3828.15	+	6630.56i	−0.755538	+	1.30863i
$296$		0			0
$297$	−59.9939	−	125.402i	−0.0117212	−	0.0245002i
$298$		0			0
$299$	6891.72			1.33297
$300$		0			0
$301$	−2408.24	−	3001.47i	−0.461158	−	0.574758i
$302$		0			0
$303$	1312.28	+	2414.67i	0.248806	+	0.457818i
$304$		0			0
$305$	630.626	−	1092.28i	0.118392	−	0.205061i
$306$		0			0
$307$	−7034.72			−1.30779			−0.653897	−	0.756584i	$-0.726867\pi$
$307$	−7034.72			−1.30779			−0.653897	+	0.756584i	$0.726867\pi$
$308$		0			0
$309$	5386.60	−	8797.84i	0.991693	−	1.61971i
$310$		0			0
$311$	8236.57			1.50178			0.750889	−	0.660429i	$-0.229625\pi$
$311$	8236.57			1.50178			0.750889	+	0.660429i	$0.229625\pi$
$312$		0			0
$313$	2271.45			0.410192			0.205096	−	0.978742i	$-0.434249\pi$
$313$	2271.45			0.410192			0.205096	+	0.978742i	$0.434249\pi$
$314$		0			0
$315$	−4569.55	−	6338.96i	−0.817349	−	1.13384i
$316$		0			0
$317$	5445.54			0.964833			0.482416	−	0.875942i	$-0.339759\pi$
$317$	5445.54			0.964833			0.482416	+	0.875942i	$0.339759\pi$
$318$		0			0
$319$	−4.75998			−0.000835448
$320$		0			0
$321$	−642.076	−	1181.46i	−0.111642	−	0.205429i
$322$		0			0
$323$	9468.08			1.63102
$324$		0			0
$325$	1959.13	−	3393.31i	0.334378	−	0.579160i
$326$		0			0
$327$	−3416.49	+	5580.08i	−0.577774	+	0.943667i
$328$		0			0
$329$	−2599.20	+	6681.03i	−0.435557	+	1.11957i
$330$		0			0
$331$	10338.9			1.71684			0.858422	−	0.512944i	$-0.171445\pi$
$331$	10338.9			1.71684			0.858422	+	0.512944i	$0.171445\pi$
$332$		0			0
$333$	−2566.87	−	5028.06i	−0.422412	−	0.827435i
$334$		0			0
$335$	−250.338	+	433.597i	−0.0408281	+	0.0707163i
$336$		0			0
$337$	1597.04	+	2766.15i	0.258149	+	0.447127i	0.965746	−	0.259489i	$-0.0835542\pi$
$337$	1597.04	+	2766.15i	0.258149	+	0.447127i	−0.707597	+	0.706616i	$0.750221\pi$
$338$		0			0
$339$	1102.26	+	2028.23i	0.176598	+	0.324951i
$340$		0			0
$341$	2.20469	+	3.81863i	0.000350119	+	0.000606423i
$342$		0			0
$343$	−5698.53	+	2807.20i	−0.897060	+	0.441909i
$344$		0			0
$345$	8129.65	+	14959.0i	1.26865	+	2.33440i
$346$		0			0
$347$	6381.63			0.987274			0.493637	−	0.869668i	$-0.335667\pi$
$347$	6381.63			0.987274			0.493637	+	0.869668i	$0.335667\pi$
$348$		0			0
$349$	−2962.36	+	5130.95i	−0.454359	+	0.786973i	−0.998651	−	0.0519230i	$-0.983465\pi$
$349$	−2962.36	+	5130.95i	−0.454359	+	0.786973i	0.544292	+	0.838896i	$0.316798\pi$
$350$		0			0
$351$	−1990.15	−	4159.90i	−0.302638	−	0.632589i
$352$		0			0
$353$	−147.743	−	255.898i	−0.0222764	−	0.0385838i	0.854672	−	0.519168i	$-0.173758\pi$
$353$	−147.743	−	255.898i	−0.0222764	−	0.0385838i	−0.876949	+	0.480584i	$0.840425\pi$
$354$		0			0
$355$	−5502.87	+	9531.25i	−0.822710	+	1.42498i
$356$		0			0
$357$	−4413.11	−	5800.54i	−0.654248	−	0.859935i
$358$		0			0
$359$	−676.640	−	1171.98i	−0.0994755	−	0.172297i	0.811992	−	0.583668i	$-0.198383\pi$
$359$	−676.640	−	1171.98i	−0.0994755	−	0.172297i	−0.911468	+	0.411372i	$0.865050\pi$
$360$		0			0
$361$	−4384.61	+	7594.36i	−0.639249	+	1.10721i
$362$		0			0
$363$	−3608.68	+	5893.98i	−0.521781	+	0.852215i
$364$		0			0
$365$	82.2932	+	142.536i	0.0118012	+	0.0204402i
$366$		0			0
$367$	1901.67	+	3293.79i	0.270481	+	0.468486i	0.968985	−	0.247120i	$-0.0794841\pi$
$367$	1901.67	+	3293.79i	0.270481	+	0.468486i	−0.698504	+	0.715606i	$0.746151\pi$
$368$		0			0
$369$	253.928	+	497.402i	0.0358237	+	0.0701726i
$370$		0			0
$371$	5832.05	+	7268.69i	0.816133	+	1.01717i
$372$		0			0
$373$	575.820	−	997.349i	0.0799325	−	0.138447i	−0.823288	−	0.567624i	$-0.807863\pi$
$373$	575.820	−	997.349i	0.0799325	−	0.138447i	0.903221	+	0.429177i	$0.141196\pi$
$374$		0			0
$375$	−470.245	−	12.1303i	−0.0647556	−	0.00167042i
$376$		0			0
$377$	−157.900			−0.0215710
$378$		0			0
$379$	8342.03			1.13061			0.565305	−	0.824882i	$-0.308758\pi$
$379$	8342.03			1.13061			0.565305	+	0.824882i	$0.308758\pi$
$380$		0			0
$381$	−8616.40	−	222.266i	−1.15861	−	0.0298873i
$382$		0			0
$383$	−6929.36	+	12002.0i	−0.924474	+	1.60124i	−0.132069	+	0.991240i	$0.542162\pi$
$383$	−6929.36	+	12002.0i	−0.924474	+	1.60124i	−0.792405	+	0.609996i	$0.791171\pi$
$384$		0			0
$385$	103.976	−	267.261i	0.0137639	−	0.0353789i
$386$		0			0
$387$	3051.82	−	4707.42i	0.400860	−	0.618325i
$388$		0			0
$389$	−3620.38	−	6270.68i	−0.471878	−	0.817316i	0.527605	−	0.849490i	$-0.323090\pi$
$389$	−3620.38	−	6270.68i	−0.471878	−	0.817316i	−0.999482	+	0.0321738i	$0.989757\pi$
$390$		0			0
$391$	7939.88	+	13752.3i	1.02695	+	1.77873i
$392$		0			0
$393$	−4515.44	+	7374.99i	−0.579578	+	0.946613i
$394$		0			0
$395$	10293.6	−	17829.0i	1.31120	−	2.27107i
$396$		0			0
$397$	−5898.68	−	10216.8i	−0.745708	−	1.29160i	−0.949863	−	0.312666i	$-0.898778\pi$
$397$	−5898.68	−	10216.8i	−0.745708	−	1.29160i	0.204155	−	0.978939i	$-0.434555\pi$
$398$		0			0
$399$	11933.9	−	1521.20i	1.49735	−	0.190866i
$400$		0			0
$401$	−2972.97	+	5149.34i	−0.370232	+	0.641261i	−0.989601	−	0.143839i	$-0.954055\pi$
$401$	−2972.97	+	5149.34i	−0.370232	+	0.641261i	0.619369	+	0.785100i	$0.287389\pi$
$402$		0			0
$403$	73.1348	+	126.673i	0.00903996	+	0.0156577i
$404$		0			0
$405$	6681.77	−	9226.89i	0.819802	−	1.13207i
$406$		0			0
$407$	103.589	−	179.421i	0.0126160	−	0.0218515i
$408$		0			0
$409$	−3855.08			−0.466067			−0.233034	−	0.972469i	$-0.574865\pi$
$409$	−3855.08			−0.466067			−0.233034	+	0.972469i	$0.574865\pi$
$410$		0			0
$411$	−6990.61	−	12863.1i	−0.838982	−	1.54378i
$412$		0			0
$413$	−3289.87	+	8456.35i	−0.391971	+	1.00753i
$414$		0			0
$415$	1217.15	+	2108.17i	0.143970	+	0.249364i
$416$		0			0
$417$	5992.24	+	11026.1i	0.703696	+	1.29484i
$418$		0			0
$419$	−3716.76	−	6437.61i	−0.433354	−	0.750591i	0.563806	−	0.825908i	$-0.309337\pi$
$419$	−3716.76	−	6437.61i	−0.433354	−	0.750591i	−0.997160	+	0.0753161i	$0.976003\pi$
$420$		0			0
$421$	72.4459	−	125.480i	0.00838669	−	0.0145262i	−0.861802	−	0.507246i	$-0.830664\pi$
$421$	72.4459	−	125.480i	0.00838669	−	0.0145262i	0.870188	+	0.492719i	$0.163997\pi$
$422$		0			0
$423$	−10437.3	−	538.832i	−1.19971	−	0.0619359i
$424$		0			0
$425$	9028.36			1.03045
$426$		0			0
$427$	541.953	−	1393.05i	0.0614214	−	0.157879i
$428$		0			0
$429$	88.3682	−	144.330i	0.00994512	−	0.0162432i
$430$		0			0
$431$	4915.76	−	8514.35i	0.549382	−	0.951558i	−0.448935	−	0.893565i	$-0.648196\pi$
$431$	4915.76	−	8514.35i	0.549382	−	0.951558i	0.998317	−	0.0579936i	$-0.0184703\pi$
$432$		0			0
$433$	−583.840			−0.0647980			−0.0323990	−	0.999475i	$-0.510315\pi$
$433$	−583.840			−0.0647980			−0.0323990	+	0.999475i	$0.510315\pi$
$434$		0			0
$435$	−186.263	−	342.735i	−0.0205302	−	0.0377768i
$436$		0			0
$437$	−26211.5			−2.86925
$438$		0			0
$439$	11166.3			1.21398			0.606990	−	0.794710i	$-0.292377\pi$
$439$	11166.3			1.21398			0.606990	+	0.794710i	$0.292377\pi$
$440$		0			0
$441$	−6494.41	−	6602.18i	−0.701264	−	0.712902i
$442$		0			0
$443$	−15477.5			−1.65995			−0.829975	−	0.557801i	$-0.811645\pi$
$443$	−15477.5			−1.65995			−0.829975	+	0.557801i	$0.811645\pi$
$444$		0			0
$445$	3069.09			0.326942
$446$		0			0
$447$	8323.25	−	13594.2i	0.880708	−	1.43844i
$448$		0			0
$449$	11562.2			1.21527			0.607635	−	0.794216i	$-0.292118\pi$
$449$	11562.2			1.21527			0.607635	+	0.794216i	$0.292118\pi$
$450$		0			0
$451$	−10.2475	+	17.7492i	−0.00106993	+	0.00185317i
$452$		0			0
$453$	−4821.68	−	8872.17i	−0.500093	−	0.920201i
$454$		0			0
$455$	3449.12	−	8865.70i	0.355379	−	0.913474i
$456$		0			0
$457$	9511.41			0.973578			0.486789	−	0.873520i	$-0.338168\pi$
$457$	9511.41			0.973578			0.486789	+	0.873520i	$0.338168\pi$
$458$		0			0
$459$	6008.15	−	8763.86i	0.610973	−	0.891202i
$460$		0			0
$461$	7001.12	−	12126.3i	0.707321	−	1.22512i	−0.258527	−	0.966004i	$-0.583237\pi$
$461$	7001.12	−	12126.3i	0.707321	−	1.22512i	0.965847	−	0.259111i	$-0.0834297\pi$
$462$		0			0
$463$	−3709.32	−	6424.74i	−0.372326	−	0.644887i	0.617597	−	0.786495i	$-0.288106\pi$
$463$	−3709.32	−	6424.74i	−0.372326	−	0.644887i	−0.989923	+	0.141607i	$0.954773\pi$
$464$		0			0
$465$	−188.683	+	308.172i	−0.0188171	+	0.0307336i
$466$		0			0
$467$	4071.22	+	7051.56i	0.403412	+	0.698731i	0.994135	−	0.108144i	$-0.0344907\pi$
$467$	4071.22	+	7051.56i	0.403412	+	0.698731i	−0.590723	+	0.806874i	$0.701157\pi$
$468$		0			0
$469$	−215.137	+	552.993i	−0.0211815	+	0.0544453i
$470$		0			0
$471$	−5039.50	−	129.998i	−0.493011	−	0.0127176i
$472$		0			0
$473$	205.884			0.0200138
$474$		0			0
$475$	−7451.20	+	12905.9i	−0.719757	+	1.24666i
$476$		0			0
$477$	−7390.61	+	11400.0i	−0.709419	+	1.09428i
$478$		0			0
$479$	4668.68	+	8086.38i	0.445339	+	0.771349i	0.998076	−	0.0620064i	$-0.0197499\pi$
$479$	4668.68	+	8086.38i	0.445339	+	0.771349i	−0.552737	+	0.833356i	$0.686417\pi$
$480$		0			0
$481$	3436.29	−	5951.83i	0.325741	−	0.564200i
$482$		0			0
$483$	12217.3	+	16058.2i	1.15094	+	1.51278i
$484$		0			0
$485$	−13431.9	−	23264.7i	−1.25755	−	2.17813i
$486$		0			0
$487$	−6556.19	+	11355.7i	−0.610040	+	1.05662i	0.381194	+	0.924495i	$0.375513\pi$
$487$	−6556.19	+	11355.7i	−0.610040	+	1.05662i	−0.991233	+	0.132124i	$0.957820\pi$
$488$		0			0
$489$	−5673.50	−	10439.6i	−0.524672	−	0.965427i
$490$		0			0
$491$	6486.77	+	11235.4i	0.596220	+	1.03268i	0.993374	+	0.114931i	$0.0366646\pi$
$491$	6486.77	+	11235.4i	0.596220	+	1.03268i	−0.397154	+	0.917752i	$0.630002\pi$
$492$		0			0
$493$	−181.915	−	315.086i	−0.0166188	−	0.0287845i
$494$		0			0
$495$	417.521	+	21.5549i	0.0379115	+	0.00195721i
$496$		0			0
$497$	−4729.10	+	12155.8i	−0.426819	+	1.09711i
$498$		0			0
$499$	−1322.53	+	2290.69i	−0.118647	+	0.205502i	−0.919232	−	0.393717i	$-0.871189\pi$
$499$	−1322.53	+	2290.69i	−0.118647	+	0.205502i	0.800585	+	0.599219i	$0.204522\pi$
$500$		0			0
$501$	−98.1716	−	180.641i	−0.00875445	−	0.0161087i
$502$		0			0
$503$	−15490.8			−1.37316			−0.686579	−	0.727055i	$-0.740889\pi$
$503$	−15490.8			−1.37316			−0.686579	+	0.727055i	$0.740889\pi$
$504$		0			0
$505$	−8265.09			−0.728301
$506$		0			0
$507$	−3029.63	+	4948.24i	−0.265386	+	0.433450i
$508$		0			0
$509$	−154.607	+	267.788i	−0.0134634	+	0.0233192i	−0.872679	−	0.488295i	$-0.837619\pi$
$509$	−154.607	+	267.788i	−0.0134634	+	0.0233192i	0.859215	+	0.511614i	$0.170952\pi$
$510$		0			0
$511$	122.069	+	152.139i	0.0105676	+	0.0131707i
$512$		0			0
$513$	7569.17	+	15821.4i	0.651437	+	1.36166i
$514$		0			0
$515$	15512.2	+	26867.9i	1.32728	+	2.29892i
$516$		0			0
$517$	−191.772	−	332.158i	−0.0163136	−	0.0282559i
$518$		0			0
$519$	−5509.18	−	142.113i	−0.465946	−	0.0120194i
$520$		0			0
$521$	−2986.91	+	5173.47i	−0.251168	+	0.435036i	−0.963848	−	0.266454i	$-0.914148\pi$
$521$	−2986.91	+	5173.47i	−0.251168	+	0.435036i	0.712679	+	0.701490i	$0.247481\pi$
$522$		0			0
$523$	1889.85	+	3273.32i	0.158007	+	0.273675i	0.934150	−	0.356881i	$-0.116160\pi$
$523$	1889.85	+	3273.32i	0.158007	+	0.273675i	−0.776143	+	0.630557i	$0.782827\pi$
$524$		0			0
$525$	11379.7	−	1450.56i	0.946001	−	0.120586i
$526$		0			0
$527$	−168.516	+	291.878i	−0.0139291	+	0.0241260i
$528$		0			0
$529$	−15897.3	−	27534.9i	−1.30659	−	2.26308i
$530$		0			0
$531$	−13210.7	−	682.014i	−1.07965	−	0.0557380i
$532$		0			0
$533$	−339.936	+	588.786i	−0.0276252	+	0.0478483i
$534$		0			0
$535$	4043.98			0.326797
$536$		0			0
$537$	2446.63	−	3996.03i	0.196610	−	0.321120i
$538$		0			0
$539$	73.6543	−	331.789i	0.00588592	−	0.0265142i
$540$		0			0
$541$	−11722.6	−	20304.2i	−0.931598	−	1.61357i	−0.780591	−	0.625042i	$-0.785082\pi$
$541$	−11722.6	−	20304.2i	−0.931598	−	1.61357i	−0.151006	−	0.988533i	$-0.548251\pi$
$542$		0			0
$543$	6622.13	+	170.823i	0.523357	+	0.0135004i
$544$		0			0
$545$	−9838.71	−	17041.1i	−0.773292	−	1.33938i
$546$		0			0
$547$	313.145	−	542.383i	0.0244774	−	0.0423960i	−0.853527	−	0.521048i	$-0.825541\pi$
$547$	313.145	−	542.383i	0.0244774	−	0.0423960i	0.878005	+	0.478652i	$0.158875\pi$
$548$		0			0
$549$	2176.25	+	112.351i	0.169181	+	0.00873409i
$550$		0			0
$551$	600.546			0.0464322
$552$		0			0
$553$	8846.17	−	22738.4i	0.680248	−	1.74852i
$554$		0			0
$555$	16972.5	+	437.817i	1.29809	+	0.0334852i
$556$		0			0
$557$	315.651	−	546.723i	0.0240118	−	0.0415896i	−0.853770	−	0.520651i	$-0.825689\pi$
$557$	315.651	−	546.723i	0.0240118	−	0.0415896i	0.877782	+	0.479061i	$0.159023\pi$
$558$		0			0
$559$	6829.66			0.516751
$560$		0			0
$561$	389.815	+	10.0556i	0.0293369	+	0.000756767i
$562$		0			0
$563$	9612.73			0.719588			0.359794	−	0.933032i	$-0.382847\pi$
$563$	9612.73			0.719588			0.359794	+	0.933032i	$0.382847\pi$
$564$		0			0
$565$	−6942.37			−0.516934
$566$		0			0
$567$	6164.85	−	12011.6i	0.456612	−	0.889666i
$568$		0			0
$569$	991.255			0.0730327			0.0365163	−	0.999333i	$-0.488374\pi$
$569$	991.255			0.0730327			0.0365163	+	0.999333i	$0.488374\pi$
$570$		0			0
$571$	−23845.9			−1.74767			−0.873836	−	0.486221i	$-0.838375\pi$
$571$	−23845.9			−1.74767			−0.873836	+	0.486221i	$0.838375\pi$
$572$		0			0
$573$	−10143.2	−	261.650i	−0.739506	−	0.0190761i
$574$		0			0
$575$	−24994.1			−1.81274
$576$		0			0
$577$	4184.68	−	7248.07i	0.301924	−	0.522948i	−0.674647	−	0.738140i	$-0.735704\pi$
$577$	4184.68	−	7248.07i	0.301924	−	0.522948i	0.976572	+	0.215192i	$0.0690376\pi$
$578$		0			0
$579$	−16706.4	−	430.954i	−1.19913	−	0.0309324i
$580$		0			0
$581$	1805.46	+	2250.20i	0.128921	+	0.160679i
$582$		0			0
$583$	−498.590			−0.0354194
$584$		0			0
$585$	13850.2	+	715.028i	0.978864	+	0.0505347i
$586$		0			0
$587$	9079.32	−	15725.9i	0.638405	−	1.10575i	−0.347378	−	0.937725i	$-0.612928\pi$
$587$	9079.32	−	15725.9i	0.638405	−	1.10575i	0.985783	−	0.168025i	$-0.0537389\pi$
$588$		0			0
$589$	−278.155	−	481.779i	−0.0194587	−	0.0337035i
$590$		0			0
$591$	−2353.06	−	60.6988i	−0.163776	−	0.00422473i
$592$		0			0
$593$	−442.576	−	766.564i	−0.0306482	−	0.0530843i	0.850294	−	0.526307i	$-0.176424\pi$
$593$	−442.576	−	766.564i	−0.0306482	−	0.0530843i	−0.880943	+	0.473223i	$0.843091\pi$
$594$		0			0
$595$	21665.0	−	3331.43i	1.49274	−	0.229538i
$596$		0			0
$597$	−10324.7	+	16863.1i	−0.707806	+	1.15605i
$598$		0			0
$599$	−10166.1			−0.693445			−0.346723	−	0.937968i	$-0.612705\pi$
$599$	−10166.1			−0.693445			−0.346723	+	0.937968i	$0.612705\pi$
$600$		0			0
$601$	1222.15	−	2116.83i	0.0829493	−	0.143672i	−0.821566	−	0.570113i	$-0.806899\pi$
$601$	1222.15	−	2116.83i	0.0829493	−	0.143672i	0.904516	+	0.426441i	$0.140233\pi$
$602$		0			0
$603$	−863.899	−	44.5995i	−0.0583428	−	0.00301199i
$604$		0			0
$605$	−10392.2	−	17999.8i	−0.698351	−	1.20958i
$606$		0			0
$607$	−6064.03	+	10503.2i	−0.405488	+	0.702326i	−0.994378	−	0.105887i	$-0.966232\pi$
$607$	−6064.03	+	10503.2i	−0.405488	+	0.702326i	0.588890	+	0.808213i	$0.299565\pi$
$608$		0			0
$609$	−279.917	−	367.919i	−0.0186253	−	0.0244809i
$610$		0			0
$611$	−6361.53	−	11018.5i	−0.421211	−	0.729559i
$612$		0			0
$613$	6407.98	−	11099.0i	0.422212	−	0.731293i	−0.573944	−	0.818895i	$-0.694587\pi$
$613$	6407.98	−	11099.0i	0.422212	−	0.731293i	0.996156	+	0.0876022i	$0.0279204\pi$
$614$		0			0
$615$	−1679.00	−	43.3112i	−0.110088	−	0.00283980i
$616$		0			0
$617$	−1090.02	−	1887.96i	−0.0711222	−	0.123187i	0.828271	−	0.560327i	$-0.189325\pi$
$617$	−1090.02	−	1887.96i	−0.0711222	−	0.123187i	−0.899393	+	0.437140i	$0.855991\pi$
$618$		0			0
$619$	−5261.33	−	9112.90i	−0.341633	−	0.591726i	0.643103	−	0.765780i	$-0.277647\pi$
$619$	−5261.33	−	9112.90i	−0.341633	−	0.591726i	−0.984736	+	0.174054i	$0.944313\pi$
$620$		0			0
$621$	−16633.0	+	24261.9i	−1.07481	+	1.56779i
$622$		0			0
$623$	3595.04	−	552.810i	0.231191	−	0.0355503i
$624$		0			0
$625$	8157.79	−	14129.7i	0.522098	−	0.904301i
$626$		0			0
$627$	−336.093	+	548.934i	−0.0214071	+	0.0349638i
$628$		0			0
$629$	15835.6			1.00383
$630$		0			0
$631$	15500.4			0.977909			0.488954	−	0.872309i	$-0.337378\pi$
$631$	15500.4			0.977909			0.488954	+	0.872309i	$0.337378\pi$
$632$		0			0
$633$	12610.5	+	23204.0i	0.791819	+	1.45699i
$634$		0			0
$635$	12961.0	−	22449.0i	0.809984	−	1.40293i
$636$		0			0
$637$	2443.29	−	11006.3i	0.151973	−	0.684590i
$638$		0			0
$639$	−18990.0	−	980.377i	−1.17564	−	0.0606934i
$640$		0			0
$641$	3736.79	+	6472.31i	0.230257	+	0.398816i	0.957884	−	0.287157i	$-0.0927101\pi$
$641$	3736.79	+	6472.31i	0.230257	+	0.398816i	−0.727627	+	0.685973i	$0.759377\pi$
$642$		0			0
$643$	10610.4	+	18377.7i	0.650750	+	1.12713i	0.982941	+	0.183921i	$0.0588789\pi$
$643$	10610.4	+	18377.7i	0.650750	+	1.12713i	−0.332191	+	0.943212i	$0.607788\pi$
$644$		0			0
$645$	8056.45	+	14824.3i	0.491818	+	0.904974i
$646$		0			0
$647$	−4092.70	+	7088.77i	−0.248687	+	0.430739i	−0.963162	−	0.268922i	$-0.913333\pi$
$647$	−4092.70	+	7088.77i	−0.248687	+	0.430739i	0.714474	+	0.699661i	$0.246666\pi$
$648$		0			0
$649$	−242.730	−	420.421i	−0.0146811	−	0.0254283i
$650$		0			0
$651$	−165.509	+	394.969i	−0.00996435	+	0.0237789i
$652$		0			0
$653$	−817.342	+	1415.68i	−0.0489817	+	0.0848388i	−0.889477	−	0.456980i	$-0.848931\pi$
$653$	−817.342	+	1415.68i	−0.0489817	+	0.0848388i	0.840495	+	0.541819i	$0.182264\pi$
$654$		0			0
$655$	−13003.5	−	22522.6i	−0.775706	−	1.34356i
$656$		0			0
$657$	−154.691	+	238.611i	−0.00918581	+	0.0141691i
$658$		0			0
$659$	751.673	−	1301.94i	0.0444325	−	0.0769593i	−0.842954	−	0.537986i	$-0.819185\pi$
$659$	751.673	−	1301.94i	0.0444325	−	0.0769593i	0.887386	+	0.461027i	$0.152519\pi$
$660$		0			0
$661$	6362.85			0.374412			0.187206	−	0.982321i	$-0.440057\pi$
$661$	6362.85			0.374412			0.187206	+	0.982321i	$0.440057\pi$
$662$		0			0
$663$	12931.1	+	333.568i	0.757470	+	0.0195395i
$664$		0			0
$665$	−13118.1	+	33719.1i	−0.764962	+	1.96627i
$666$		0			0
$667$	503.614	+	872.286i	0.0292354	+	0.0506372i
$668$		0			0
$669$	8403.62	−	13725.5i	0.485654	−	0.793209i
$670$		0			0
$671$	39.9859	+	69.2576i	0.00230051	+	0.00398459i
$672$		0			0
$673$	−12398.8	+	21475.4i	−0.710163	+	1.23004i	0.254632	+	0.967038i	$0.418046\pi$
$673$	−12398.8	+	21475.4i	−0.710163	+	1.23004i	−0.964796	+	0.263001i	$0.915288\pi$
$674$		0			0
$675$	7217.64	+	15086.6i	0.411566	+	0.860275i
$676$		0			0
$677$	−17779.1			−1.00932			−0.504658	−	0.863319i	$-0.668381\pi$
$677$	−17779.1			−1.00932			−0.504658	+	0.863319i	$0.668381\pi$
$678$		0			0
$679$	−19924.1	−	24832.1i	−1.12609	−	1.40349i
$680$		0			0
$681$	7916.44	+	14566.7i	0.445461	+	0.819674i
$682$		0			0
$683$	−13508.7	+	23397.8i	−0.756805	+	1.31082i	0.187667	+	0.982233i	$0.439907\pi$
$683$	−13508.7	+	23397.8i	−0.756805	+	1.31082i	−0.944472	+	0.328591i	$0.893426\pi$
$684$		0			0
$685$	44028.9			2.45585
$686$		0			0
$687$	−2686.22	+	4387.35i	−0.149178	+	0.243650i
$688$		0			0
$689$	−16539.4			−0.914518
$690$		0			0
$691$	5123.17			0.282047			0.141024	−	0.990006i	$-0.454961\pi$
$691$	5123.17			0.282047			0.141024	+	0.990006i	$0.454961\pi$
$692$		0			0
$693$	492.954	−	49.9558i	0.0270213	−	0.00273833i
$694$		0			0
$695$	−37740.8			−2.05984
$696$		0			0
$697$	−1566.54			−0.0851321
$698$		0			0
$699$	5310.10	+	9770.90i	0.287334	+	0.528711i
$700$		0			0
$701$	−11580.9			−0.623971			−0.311985	−	0.950087i	$-0.600994\pi$
$701$	−11580.9			−0.623971			−0.311985	+	0.950087i	$0.600994\pi$
$702$		0			0
$703$	−13069.3	+	22636.7i	−0.701165	+	1.21445i
$704$		0			0
$705$	16412.3	−	26805.9i	0.876771	−	1.43201i
$706$		0			0
$707$	−9681.47	+	1488.72i	−0.515006	+	0.0791925i
$708$		0			0
$709$	17482.1			0.926030			0.463015	−	0.886351i	$-0.346768\pi$
$709$	17482.1			0.926030			0.463015	+	0.886351i	$0.346768\pi$
$710$		0			0
$711$	35522.4	+	1833.87i	1.87369	+	0.0967309i
$712$		0			0
$713$	466.519	−	808.035i	0.0245039	−	0.0424420i
$714$		0			0
$715$	254.480	+	440.773i	0.0133105	+	0.0230545i
$716$		0			0
$717$	9180.58	+	16892.8i	0.478180	+	0.879879i
$718$		0			0
$719$	16416.4	+	28434.1i	0.851502	+	1.47484i	0.879853	+	0.475246i	$0.157641\pi$
$719$	16416.4	+	28434.1i	0.851502	+	1.47484i	−0.0283515	+	0.999598i	$0.509026\pi$
$720$		0			0
$721$	23010.0	+	28678.1i	1.18854	+	1.48132i
$722$		0			0
$723$	−12833.8	−	23614.9i	−0.660157	−	1.21473i
$724$		0			0
$725$	572.655			0.0293350
$726$		0			0
$727$	6753.93	−	11698.2i	0.344552	−	0.596782i	−0.640720	−	0.767775i	$-0.721364\pi$
$727$	6753.93	−	11698.2i	0.344552	−	0.596782i	0.985272	+	0.170992i	$0.0546974\pi$
$728$		0			0
$729$	19447.8	+	3033.61i	0.988052	+	0.154123i
$730$		0			0
$731$	7868.38	+	13628.4i	0.398116	+	0.689557i
$732$		0			0
$733$	−10793.4	+	18694.7i	−0.543878	+	0.942024i	0.454799	+	0.890594i	$0.349711\pi$
$733$	−10793.4	+	18694.7i	−0.543878	+	0.942024i	−0.998677	+	0.0514295i	$0.983622\pi$
$734$		0			0
$735$	26772.2	−	7679.90i	1.34355	−	0.385412i
$736$		0			0
$737$	−15.8731	−	27.4930i	−0.000793341	−	0.00137411i
$738$		0			0
$739$	−3845.24	+	6660.15i	−0.191406	+	0.331526i	−0.945717	−	0.324993i	$-0.894638\pi$
$739$	−3845.24	+	6660.15i	−0.191406	+	0.331526i	0.754310	+	0.656518i	$0.227972\pi$
$740$		0			0
$741$	−11149.0	+	18209.5i	−0.552725	+	0.902755i
$742$		0			0
$743$	−8064.14	−	13967.5i	−0.398176	−	0.689661i	0.595325	−	0.803485i	$-0.297023\pi$
$743$	−8064.14	−	13967.5i	−0.398176	−	0.689661i	−0.993501	+	0.113824i	$0.963690\pi$
$744$		0			0
$745$	23969.1	+	41515.7i	1.17874	+	2.04163i
$746$		0			0
$747$	−2287.95	+	3529.15i	−0.112064	+	0.172858i
$748$		0			0
$749$	4736.99	−	728.407i	0.231089	−	0.0355346i
$750$		0			0
$751$	16818.3	−	29130.1i	0.817188	−	1.41541i	−0.0905589	−	0.995891i	$-0.528865\pi$
$751$	16818.3	−	29130.1i	0.817188	−	1.41541i	0.907746	−	0.419519i	$-0.137801\pi$
$752$		0			0
$753$	−18333.5	−	472.927i	−0.887266	−	0.0228877i
$754$		0			0
$755$	30368.3			1.46386
$756$		0			0
$757$	15532.6			0.745762			0.372881	−	0.927879i	$-0.378370\pi$
$757$	15532.6			0.745762			0.372881	+	0.927879i	$0.378370\pi$
$758$		0			0
$759$	−1079.17	−	27.8379i	−0.0516090	−	0.00133129i
$760$		0			0
$761$	−3089.94	+	5351.93i	−0.147188	+	0.254937i	−0.930187	−	0.367086i	$-0.880356\pi$
$761$	−3089.94	+	5351.93i	−0.147188	+	0.254937i	0.782999	+	0.622023i	$0.213689\pi$
$762$		0			0
$763$	−14594.2	−	18189.3i	−0.692459	−	0.863036i
$764$		0			0
$765$	14529.8	+	28461.5i	0.686703	+	1.34514i
$766$		0			0
$767$	−8051.96	−	13946.4i	−0.379060	−	0.656552i
$768$		0			0
$769$	2756.45	+	4774.30i	0.129259	+	0.223883i	0.923390	−	0.383864i	$-0.125407\pi$
$769$	2756.45	+	4774.30i	0.129259	+	0.223883i	−0.794131	+	0.607747i	$0.792074\pi$
$770$		0			0
$771$	3765.63	−	6150.33i	0.175896	−	0.287288i
$772$		0			0
$773$	−11526.8	+	19965.1i	−0.536341	+	0.928969i	0.462756	+	0.886485i	$0.346860\pi$
$773$	−11526.8	+	19965.1i	−0.536341	+	0.928969i	−0.999097	+	0.0424839i	$0.986473\pi$
$774$		0			0
$775$	−265.237	−	459.404i	−0.0122937	−	0.0212933i
$776$		0			0
$777$	19959.9	−	2544.26i	0.921565	−	0.117471i
$778$		0			0
$779$	1292.89	−	2239.34i	0.0594640	−	0.102995i
$780$		0			0
$781$	−348.919	−	604.345i	−0.0159863	−	0.0276891i
$782$		0			0
$783$	381.088	−	555.878i	0.0173933	−	0.0253710i
$784$		0			0
$785$	7580.52	−	13129.9i	0.344663	−	0.596974i
$786$		0			0
$787$	38828.1			1.75867			0.879334	−	0.476205i	$-0.157988\pi$
$787$	38828.1			1.75867			0.879334	+	0.476205i	$0.157988\pi$
$788$		0			0
$789$	−17113.7	−	31490.3i	−0.772199	−	1.42089i
$790$		0			0
$791$	−8132.07	+	1250.47i	−0.365541	+	0.0562093i
$792$		0			0
$793$	1326.43	+	2297.44i	0.0593984	+	0.102881i
$794$		0			0
$795$	−19510.4	−	35900.2i	−0.870391	−	1.60157i
$796$		0			0
$797$	19759.4	+	34224.2i	0.878184	+	1.52106i	0.853332	+	0.521368i	$0.174578\pi$
$797$	19759.4	+	34224.2i	0.878184	+	1.52106i	0.0248524	+	0.999691i	$0.492088\pi$
$798$		0			0
$799$	14658.1	−	25388.6i	0.649019	−	1.12413i
$800$		0			0
$801$	2411.05	+	4722.84i	0.106355	+	0.208331i
$802$		0			0
$803$	−10.4359			−0.000458623
$804$		0			0
$805$	−59977.4	+	9222.74i	−2.62600	+	0.403800i
$806$		0			0
$807$	−20237.8	+	33054.0i	−0.882780	+	1.44183i
$808$		0			0
$809$	1189.01	−	2059.43i	0.0516729	−	0.0895002i	−0.839032	−	0.544082i	$-0.816878\pi$
$809$	1189.01	−	2059.43i	0.0516729	−	0.0895002i	0.890705	+	0.454582i	$0.150211\pi$
$810$		0			0
$811$	−41327.5			−1.78940			−0.894701	−	0.446666i	$-0.852611\pi$
$811$	−41327.5			−1.78940			−0.894701	+	0.446666i	$0.852611\pi$
$812$		0			0
$813$	−562.739	−	1035.47i	−0.0242757	−	0.0446687i
$814$		0			0
$815$	35733.3			1.53581
$816$		0			0
$817$	−25975.4			−1.11232
$818$		0			0
$819$	16352.5	−	1657.16i	0.697682	−	0.0707030i
$820$		0			0
$821$	−41466.1			−1.76270			−0.881351	−	0.472462i	$-0.843365\pi$
$821$	−41466.1			−1.76270			−0.881351	+	0.472462i	$0.843365\pi$
$822$		0			0
$823$	6803.84			0.288174			0.144087	−	0.989565i	$-0.453976\pi$
$823$	6803.84			0.288174			0.144087	+	0.989565i	$0.453976\pi$
$824$		0			0
$825$	−320.484	+	523.440i	−0.0135246	+	0.0220895i
$826$		0			0
$827$	5919.95			0.248920			0.124460	−	0.992225i	$-0.460280\pi$
$827$	5919.95			0.248920			0.124460	+	0.992225i	$0.460280\pi$
$828$		0			0
$829$	3639.50	−	6303.79i	0.152479	−	0.264101i	−0.779659	−	0.626204i	$-0.784608\pi$
$829$	3639.50	−	6303.79i	0.152479	−	0.264101i	0.932138	+	0.362103i	$0.117941\pi$
$830$		0			0
$831$	17975.2	+	33075.4i	0.750363	+	1.38071i
$832$		0			0
$833$	24777.6	−	7804.66i	1.03060	−	0.324628i
$834$		0			0
$835$	618.313			0.0256259
$836$		0			0
$837$	−622.454	−	48.2556i	−0.0257051	−	0.00199278i
$838$		0			0
$839$	21548.2	−	37322.5i	0.886681	−	1.53578i	0.0429071	−	0.999079i	$-0.486338\pi$
$839$	21548.2	−	37322.5i	0.886681	−	1.53578i	0.843774	−	0.536698i	$-0.180329\pi$
$840$		0			0
$841$	12183.0	+	21101.5i	0.499527	+	0.865206i
$842$		0			0
$843$	−6959.41	+	11366.7i	−0.284336	+	0.464400i
$844$		0			0
$845$	−8724.66	−	15111.6i	−0.355192	−	0.615211i
$846$		0			0
$847$	−15415.2	−	19212.5i	−0.625352	−	0.779398i
$848$		0			0
$849$	9980.69	+	257.459i	0.403459	+	0.0104075i
$850$		0			0
$851$	−43839.4			−1.76592
$852$		0			0
$853$	7861.69	−	13616.8i	0.315567	−	0.546579i	−0.663991	−	0.747741i	$-0.731138\pi$
$853$	7861.69	−	13616.8i	0.315567	−	0.546579i	0.979558	+	0.201162i	$0.0644718\pi$
$854$		0			0
$855$	−52676.8	−	2719.48i	−2.10703	−	0.108777i
$856$		0			0
$857$	6919.75	+	11985.4i	0.275816	+	0.477727i	0.970341	−	0.241742i	$-0.0777187\pi$
$857$	6919.75	+	11985.4i	0.275816	+	0.477727i	−0.694525	+	0.719469i	$0.744385\pi$
$858$		0			0
$859$	−9584.30	+	16600.5i	−0.380689	+	0.659373i	−0.991161	−	0.132665i	$-0.957647\pi$
$859$	−9584.30	+	16600.5i	−0.380689	+	0.659373i	0.610472	+	0.792038i	$0.290980\pi$
$860$		0			0
$861$	−1974.53	+	251.691i	−0.0781555	+	0.00996239i
$862$		0			0
$863$	−7511.29	−	13009.9i	−0.296277	−	0.513167i	0.679004	−	0.734135i	$-0.262412\pi$
$863$	−7511.29	−	13009.9i	−0.296277	−	0.513167i	−0.975281	+	0.220967i	$0.929079\pi$
$864$		0			0
$865$	8287.02	−	14353.5i	0.325742	−	0.564202i
$866$		0			0
$867$	2042.18	+	3757.73i	0.0799953	+	0.147196i
$868$		0			0
$869$	652.680	+	1130.48i	0.0254783	+	0.0441298i
$870$		0			0
$871$	−526.549	−	912.009i	−0.0204838	−	0.0354790i
$872$		0			0
$873$	25248.6	−	38945.9i	0.978850	−	1.50987i
$874$		0			0
$875$	607.891	−	1562.54i	0.0234862	−	0.0603695i
$876$		0			0
$877$	7648.75	−	13248.0i	0.294504	−	0.510095i	−0.680366	−	0.732873i	$-0.738179\pi$
$877$	7648.75	−	13248.0i	0.294504	−	0.510095i	0.974869	+	0.222777i	$0.0715123\pi$
$878$		0			0
$879$	−19374.6	−	35650.4i	−0.743446	−	1.36798i
$880$		0			0
$881$	−9633.83			−0.368413			−0.184207	−	0.982888i	$-0.558972\pi$
$881$	−9633.83			−0.368413			−0.184207	+	0.982888i	$0.558972\pi$
$882$		0			0
$883$	−29700.6			−1.13194			−0.565970	−	0.824426i	$-0.691498\pi$
$883$	−29700.6			−1.13194			−0.565970	+	0.824426i	$0.691498\pi$
$884$		0			0
$885$	20773.5	−	33929.0i	0.789032	−	1.28871i
$886$		0			0
$887$	14432.1	−	24997.1i	0.546316	−	0.946247i	−0.452207	−	0.891913i	$-0.649363\pi$
$887$	14432.1	−	24997.1i	0.546316	−	0.946247i	0.998523	−	0.0543341i	$-0.0173036\pi$
$888$		0			0
$889$	11138.5	−	28630.6i	0.420218	−	1.08014i
$890$		0			0
$891$	294.831	+	659.431i	0.0110855	+	0.0247944i
$892$		0			0
$893$	24195.0	+	41906.9i	0.906667	+	1.57039i
$894$		0			0
$895$	7045.73	+	12203.6i	0.263143	+	0.455777i
$896$		0			0
$897$	−35798.5	−	923.450i	−1.33253	−	0.0343736i
$898$		0			0
$899$	−10.6887	+	18.5134i	−0.000396538	+	0.000686824i
$900$		0			0
$901$	−19054.9	−	33004.1i	−0.704563	−	1.22034i
$902$		0			0
$903$	12107.2	+	15913.6i	0.446184	+	0.586459i
$904$		0			0
$905$	−9961.15	+	17253.2i	−0.365878	+	0.633720i
$906$		0			0
$907$	11819.1	+	20471.3i	0.432688	+	0.749438i	0.997104	−	0.0760530i	$-0.0242318\pi$
$907$	11819.1	+	20471.3i	0.432688	+	0.749438i	−0.564416	+	0.825491i	$0.690898\pi$
$908$		0			0
$909$	−6492.97	−	12718.6i	−0.236918	−	0.464082i
$910$		0			0
$911$	−11625.4	+	20135.8i	−0.422796	+	0.732304i	−0.996212	−	0.0869607i	$-0.972285\pi$
$911$	−11625.4	+	20135.8i	−0.422796	+	0.732304i	0.573416	+	0.819264i	$0.305618\pi$
$912$		0			0
$913$	−154.351			−0.00559504
$914$		0			0
$915$	−3422.10	+	5589.25i	−0.123641	+	0.201940i
$916$		0			0
$917$	−19288.6	−	24040.1i	−0.694621	−	0.865730i
$918$		0			0
$919$	−5122.55	−	8872.51i	−0.183871	−	0.318473i	0.759325	−	0.650712i	$-0.225529\pi$
$919$	−5122.55	−	8872.51i	−0.183871	−	0.318473i	−0.943195	+	0.332239i	$0.892196\pi$
$920$		0			0
$921$	36541.3	+	942.610i	1.30736	+	0.0337243i
$922$		0			0
$923$	−11574.5	−	20047.6i	−0.412761	−	0.714924i
$924$		0			0
$925$	−12462.4	+	21585.4i	−0.442983	+	0.767270i
$926$		0			0
$927$	−29159.2	+	44977.9i	−1.03313	+	1.59360i
$928$		0			0
$929$	13245.6			0.467786			0.233893	−	0.972262i	$-0.424853\pi$
$929$	13245.6			0.467786			0.233893	+	0.972262i	$0.424853\pi$
$930$		0			0
$931$	−9292.63	+	41860.4i	−0.327125	+	1.47360i
$932$		0			0
$933$	−42784.2	−	1103.65i	−1.50128	−	0.0387266i
$934$		0			0
$935$	−586.368	+	1015.62i	−0.0205094	+	0.0355233i
$936$		0			0
$937$	738.124			0.0257348			0.0128674	−	0.999917i	$-0.495904\pi$
$937$	738.124			0.0257348			0.0128674	+	0.999917i	$0.495904\pi$
$938$		0			0
$939$	−11798.9	−	304.361i	−0.410056	−	0.0105777i
$940$		0			0
$941$	23602.4			0.817658			0.408829	−	0.912611i	$-0.365937\pi$
$941$	23602.4			0.817658			0.408829	+	0.912611i	$0.365937\pi$
$942$		0			0
$943$	4336.82			0.149763
$944$		0			0
$945$	22886.8	+	33539.6i	0.787838	+	1.15454i
$946$		0			0
$947$	−35105.7			−1.20463			−0.602313	−	0.798260i	$-0.705754\pi$
$947$	−35105.7			−1.20463			−0.602313	+	0.798260i	$0.705754\pi$
$948$		0			0
$949$	−346.183			−0.0118415
$950$		0			0
$951$	−28286.4	−	729.670i	−0.964512	−	0.0248803i
$952$		0			0
$953$	26937.0			0.915610			0.457805	−	0.889053i	$-0.348636\pi$
$953$	26937.0			0.915610			0.457805	+	0.889053i	$0.348636\pi$
$954$		0			0
$955$	15257.6	−	26426.9i	0.516987	−	0.895448i
$956$		0			0
$957$	24.7254	+	0.637809i	0.000835170	+	2.15438e-5i
$958$		0			0
$959$	51574.0	−	7930.55i	1.73661	−	0.267039i
$960$		0			0
$961$	−29771.2			−0.999335
$962$		0			0
$963$	3176.91	+	6223.03i	0.106308	+	0.208239i
$964$		0			0
$965$	25130.1	−	43526.7i	0.838309	−	1.45199i
$966$		0			0
$967$	−17417.2	−	30167.6i	−0.579215	−	1.00323i	−0.995570	−	0.0940274i	$-0.970026\pi$
$967$	−17417.2	−	30167.6i	−0.579215	−	1.00323i	0.416355	−	0.909202i	$-0.363307\pi$
$968$		0			0
$969$	−49181.2	−	1268.67i	−1.63047	−	0.0420593i
$970$		0			0
$971$	16400.6	+	28406.6i	0.542039	+	0.938839i	0.998787	+	0.0492429i	$0.0156808\pi$
$971$	16400.6	+	28406.6i	0.542039	+	0.938839i	−0.456748	+	0.889596i	$0.650986\pi$
$972$		0			0
$973$	−44208.4	+	6797.93i	−1.45658	+	0.223979i
$974$		0			0
$975$	−10631.2	+	17363.8i	−0.349202	+	0.570345i
$976$		0			0
$977$	36476.4			1.19446			0.597228	−	0.802071i	$-0.296269\pi$
$977$	36476.4			1.19446			0.597228	+	0.802071i	$0.296269\pi$
$978$		0			0
$979$	−97.3005	+	168.529i	−0.00317644	+	0.00550176i
$980$		0			0
$981$	18494.4	−	28527.5i	0.601916	−	0.928454i
$982$		0			0
$983$	−12839.9	−	22239.3i	−0.416611	−	0.721591i	0.578985	−	0.815338i	$-0.303449\pi$
$983$	−12839.9	−	22239.3i	−0.416611	−	0.721591i	−0.995596	+	0.0937471i	$0.970115\pi$
$984$		0			0
$985$	3539.51	−	6130.62i	0.114496	−	0.198312i
$986$		0			0
$987$	14396.5	−	34355.8i	0.464283	−	1.10796i
$988$		0			0
$989$	−21782.8	−	37729.0i	−0.700358	−	1.21306i
$990$		0			0
$991$	2633.00	−	4560.49i	0.0843996	−	0.146184i	−0.820736	−	0.571308i	$-0.806436\pi$
$991$	2633.00	−	4560.49i	0.0843996	−	0.146184i	0.905135	+	0.425124i	$0.139769\pi$
$992$		0			0
$993$	−53704.5	−	1385.35i	−1.71627	−	0.0442725i
$994$		0			0
$995$	−29732.7	−	51498.5i	−0.947326	−	1.64082i
$996$		0			0
$997$	26710.6	+	46264.0i	0.848477	+	1.46961i	0.882567	+	0.470187i	$0.155814\pi$
$997$	26710.6	+	46264.0i	0.848477	+	1.46961i	−0.0340895	+	0.999419i	$0.510853\pi$
$998$		0			0
$999$	12659.7	+	26461.8i	0.400935	+	0.838053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.i.a.25.2	✓	48
3.2	odd	2		756.4.i.a.613.4		48
7.2	even	3		252.4.l.a.205.17	yes	48
9.4	even	3		252.4.l.a.193.17	yes	48
9.5	odd	6		756.4.l.a.361.21		48
21.2	odd	6		756.4.l.a.289.21		48
63.23	odd	6		756.4.i.a.37.4		48
63.58	even	3	inner	252.4.i.a.121.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.i.a.25.2	✓	48	1.1	even	1	trivial
252.4.i.a.121.2	yes	48	63.58	even	3	inner
252.4.l.a.193.17	yes	48	9.4	even	3
252.4.l.a.205.17	yes	48	7.2	even	3
756.4.i.a.37.4		48	63.23	odd	6
756.4.i.a.613.4		48	3.2	odd	2
756.4.l.a.289.21		48	21.2	odd	6
756.4.l.a.361.21		48	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.19442 - 0.133994i) q^{3} +(7.81356 - 13.5335i) q^{5} +(6.71488 - 17.2601i) q^{7} +(26.9641 + 1.39204i) q^{9} +O(q^{10})\)	\(q+(-5.19442 - 0.133994i) q^{3} +(7.81356 - 13.5335i) q^{5} +(6.71488 - 17.2601i) q^{7} +(26.9641 + 1.39204i) q^{9} +(0.495432 + 0.858113i) q^{11} +(16.4347 + 28.4657i) q^{13} +(-42.4004 + 69.2517i) q^{15} +(-37.8684 + 65.5900i) q^{17} +(-62.5064 - 108.264i) q^{19} +(-37.1927 + 88.7564i) q^{21} +(104.835 - 181.580i) q^{23} +(-59.6035 - 103.236i) q^{25} +(-139.876 - 10.8439i) q^{27} +(-2.40194 + 4.16028i) q^{29} +4.45003 q^{31} +(-2.45850 - 4.52379i) q^{33} +(-181.122 - 225.738i) q^{35} +(-104.544 - 181.075i) q^{37} +(-81.5545 - 150.065i) q^{39} +(10.3420 + 17.9129i) q^{41} +(103.891 - 179.945i) q^{43} +(229.525 - 354.041i) q^{45} -387.080 q^{47} +(-252.821 - 231.799i) q^{49} +(205.493 - 335.628i) q^{51} +(-251.594 + 435.773i) q^{53} +15.4843 q^{55} +(310.178 + 570.746i) q^{57} -489.937 q^{59} +80.7092 q^{61} +(205.088 - 456.055i) q^{63} +513.654 q^{65} -32.0389 q^{67} +(-568.888 + 929.154i) q^{69} -704.272 q^{71} +(-5.26605 + 9.12107i) q^{73} +(295.773 + 544.239i) q^{75} +(18.1379 - 2.78906i) q^{77} +1317.40 q^{79} +(725.124 + 75.0704i) q^{81} +(-77.8871 + 134.904i) q^{83} +(591.774 + 1024.98i) q^{85} +(13.0341 - 21.2884i) q^{87} +(98.1977 + 170.083i) q^{89} +(601.677 - 92.5200i) q^{91} +(-23.1153 - 0.596277i) q^{93} -1953.59 q^{95} +(859.522 - 1488.74i) q^{97} +(12.1643 + 23.8279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9}+O(q^{10}) \) 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9	\( 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9} + 4 q^{11} - 12 q^{13} - 26 q^{15} + 112 q^{17} + 60 q^{19} - 80 q^{21} + 10 q^{23} - 600 q^{25} + 194 q^{29} + 60 q^{31} - 472 q^{33} + 394 q^{35} - 84 q^{37} + 604 q^{39} + 210 q^{41} + 42 q^{43} + 254 q^{45} - 132 q^{47} - 78 q^{49} - 58 q^{51} - 468 q^{53} + 612 q^{55} + 1476 q^{57} - 916 q^{59} - 804 q^{61} - 444 q^{63} + 1656 q^{65} - 588 q^{67} - 28 q^{69} - 2228 q^{71} - 336 q^{73} - 668 q^{75} - 1216 q^{77} - 768 q^{79} - 104 q^{81} + 1024 q^{83} + 360 q^{85} + 2188 q^{87} + 2922 q^{89} - 120 q^{91} - 1292 q^{93} + 2428 q^{95} - 264 q^{97} - 2246 q^{99}+O(q^{100}) \) 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9 + 4 * q^11 - 12 * q^13 - 26 * q^15 + 112 * q^17 + 60 * q^19 - 80 * q^21 + 10 * q^23 - 600 * q^25 + 194 * q^29 + 60 * q^31 - 472 * q^33 + 394 * q^35 - 84 * q^37 + 604 * q^39 + 210 * q^41 + 42 * q^43 + 254 * q^45 - 132 * q^47 - 78 * q^49 - 58 * q^51 - 468 * q^53 + 612 * q^55 + 1476 * q^57 - 916 * q^59 - 804 * q^61 - 444 * q^63 + 1656 * q^65 - 588 * q^67 - 28 * q^69 - 2228 * q^71 - 336 * q^73 - 668 * q^75 - 1216 * q^77 - 768 * q^79 - 104 * q^81 + 1024 * q^83 + 360 * q^85 + 2188 * q^87 + 2922 * q^89 - 120 * q^91 - 1292 * q^93 + 2428 * q^95 - 264 * q^97 - 2246 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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