LMFDB - Embedded newform 228.3.o.c.125.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,3,Mod(125,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("228.125");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	228.o (of order $6$, 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:	$6.21255002741$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			125.7
Character	$\chi$	$=$	228.125
Dual form			228.3.o.c.197.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.552701 + 2.94865i) q^{3} +(7.75465 + 4.47715i) q^{5} +10.5834 q^{7} +(-8.38904 - 3.25944i) q^{9} +O(q^{10})$	\(q+(-0.552701 + 2.94865i) q^{3} +(7.75465 + 4.47715i) q^{5} +10.5834 q^{7} +(-8.38904 - 3.25944i) q^{9} -10.9240i q^{11} +(1.72924 + 2.99513i) q^{13} +(-17.4875 + 20.3912i) q^{15} +(-14.1724 - 8.18244i) q^{17} +(17.6721 + 6.97825i) q^{19} +(-5.84944 + 31.2066i) q^{21} +(-0.988444 + 0.570678i) q^{23} +(27.5897 + 47.7868i) q^{25} +(14.2476 - 22.9348i) q^{27} +(-31.1423 + 17.9800i) q^{29} -3.92917 q^{31} +(32.2112 + 6.03773i) q^{33} +(82.0703 + 47.3833i) q^{35} -52.4243 q^{37} +(-9.78733 + 3.44350i) q^{39} +(-63.7127 - 36.7846i) q^{41} +(33.6555 - 58.2931i) q^{43} +(-50.4611 - 62.8348i) q^{45} +(-51.9011 + 29.9651i) q^{47} +63.0077 q^{49} +(31.9602 - 37.2670i) q^{51} +(34.2359 - 19.7661i) q^{53} +(48.9086 - 84.7122i) q^{55} +(-30.3438 + 48.2520i) q^{57} +(-14.1519 - 8.17061i) q^{59} +(14.1677 + 24.5392i) q^{61} +(-88.7843 - 34.4959i) q^{63} +30.9682i q^{65} +(-5.39871 - 9.35085i) q^{67} +(-1.13641 - 3.22999i) q^{69} +(81.9916 + 47.3379i) q^{71} +(24.9395 - 43.1965i) q^{73} +(-156.155 + 54.9406i) q^{75} -115.613i q^{77} +(-20.3817 + 35.3022i) q^{79} +(59.7521 + 54.6872i) q^{81} -125.351i q^{83} +(-73.2680 - 126.904i) q^{85} +(-35.8043 - 101.765i) q^{87} +(55.6006 - 32.1010i) q^{89} +(18.3012 + 31.6986i) q^{91} +(2.17166 - 11.5857i) q^{93} +(105.798 + 133.235i) q^{95} +(-50.3465 + 87.2027i) q^{97} +(-35.6063 + 91.6423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{3} + 8 q^{7} + 16 q^{9}+O(q^{10}) $ 24 * q - 8 * q^3 + 8 * q^7 + 16 * q^9	$ 24 q - 8 q^{3} + 8 q^{7} + 16 q^{9} + 10 q^{13} - 11 q^{15} - 6 q^{19} - 24 q^{21} + 138 q^{25} + 196 q^{27} - 80 q^{31} + 53 q^{33} - 16 q^{37} + 54 q^{39} + 142 q^{43} - 154 q^{45} - 288 q^{49} - 23 q^{51} - 120 q^{55} - 213 q^{57} - 30 q^{61} - 20 q^{63} - 140 q^{67} - 142 q^{69} + 224 q^{73} + 162 q^{75} + 122 q^{79} + 40 q^{81} + 18 q^{85} - 394 q^{87} - 292 q^{91} + 130 q^{93} - 132 q^{97} - 197 q^{99}+O(q^{100}) $ 24 * q - 8 * q^3 + 8 * q^7 + 16 * q^9 + 10 * q^13 - 11 * q^15 - 6 * q^19 - 24 * q^21 + 138 * q^25 + 196 * q^27 - 80 * q^31 + 53 * q^33 - 16 * q^37 + 54 * q^39 + 142 * q^43 - 154 * q^45 - 288 * q^49 - 23 * q^51 - 120 * q^55 - 213 * q^57 - 30 * q^61 - 20 * q^63 - 140 * q^67 - 142 * q^69 + 224 * q^73 + 162 * q^75 + 122 * q^79 + 40 * q^81 + 18 * q^85 - 394 * q^87 - 292 * q^91 + 130 * q^93 - 132 * q^97 - 197 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−0.552701	+	2.94865i	−0.184234	+	0.982882i
$3$	−0.552701	+	2.94865i	−0.184234	+	0.982882i
$4$		0			0
$5$	7.75465	+	4.47715i	1.55093	+	0.895430i	0.998066	+	0.0621586i	$0.0197985\pi$
$5$	7.75465	+	4.47715i	1.55093	+	0.895430i	0.552864	+	0.833271i	$0.313535\pi$
$6$		0			0
$7$	10.5834			1.51191			0.755955	−	0.654624i	$-0.227173\pi$
$7$	10.5834			1.51191			0.755955	+	0.654624i	$0.227173\pi$
$8$		0			0
$9$	−8.38904	−	3.25944i	−0.932116	−	0.362160i
$10$		0			0
$11$		−	10.9240i		−	0.993095i	−0.868010	−	0.496547i	$-0.834601\pi$
$11$		−	10.9240i		−	0.993095i	0.868010	−	0.496547i	$-0.165399\pi$
$12$		0			0
$13$	1.72924	+	2.99513i	0.133018	+	0.230395i	0.924839	−	0.380359i	$-0.124200\pi$
$13$	1.72924	+	2.99513i	0.133018	+	0.230395i	−0.791820	+	0.610754i	$0.790866\pi$
$14$		0			0
$15$	−17.4875	+	20.3912i	−1.16584	+	1.35941i
$16$		0			0
$17$	−14.1724	−	8.18244i	−0.833671	−	0.481320i	0.0214371	−	0.999770i	$-0.493176\pi$
$17$	−14.1724	−	8.18244i	−0.833671	−	0.481320i	−0.855108	+	0.518450i	$0.826509\pi$
$18$		0			0
$19$	17.6721	+	6.97825i	0.930112	+	0.367277i
$19$	17.6721	+	6.97825i	0.930112	+	0.367277i
$20$		0			0
$21$	−5.84944	+	31.2066i	−0.278545	+	1.48603i
$22$		0			0
$23$	−0.988444	+	0.570678i	−0.0429758	+	0.0248121i	−0.521334	−	0.853353i	$-0.674565\pi$
$23$	−0.988444	+	0.570678i	−0.0429758	+	0.0248121i	0.478358	+	0.878165i	$0.341232\pi$
$24$		0			0
$25$	27.5897	+	47.7868i	1.10359	+	1.91147i
$26$		0			0
$27$	14.2476	−	22.9348i	0.527688	−	0.849438i
$28$		0			0
$29$	−31.1423	+	17.9800i	−1.07387	+	0.620000i	−0.929237	−	0.369485i	$-0.879534\pi$
$29$	−31.1423	+	17.9800i	−1.07387	+	0.620000i	−0.144635	+	0.989485i	$0.546201\pi$
$30$		0			0
$31$	−3.92917			−0.126747			−0.0633737	−	0.997990i	$-0.520186\pi$
$31$	−3.92917			−0.126747			−0.0633737	+	0.997990i	$0.520186\pi$
$32$		0			0
$33$	32.2112	+	6.03773i	0.976095	+	0.182962i
$34$		0			0
$35$	82.0703	+	47.3833i	2.34487	+	1.35381i
$36$		0			0
$37$	−52.4243			−1.41687			−0.708437	−	0.705774i	$-0.750599\pi$
$37$	−52.4243			−1.41687			−0.708437	+	0.705774i	$0.750599\pi$
$38$		0			0
$39$	−9.78733	+	3.44350i	−0.250957	+	0.0882950i
$40$		0			0
$41$	−63.7127	−	36.7846i	−1.55397	−	0.897184i	−0.997813	−	0.0661064i	$-0.978942\pi$
$41$	−63.7127	−	36.7846i	−1.55397	−	0.897184i	−0.556156	−	0.831078i	$-0.687724\pi$
$42$		0			0
$43$	33.6555	−	58.2931i	0.782686	−	1.35565i	−0.147685	−	0.989034i	$-0.547182\pi$
$43$	33.6555	−	58.2931i	0.782686	−	1.35565i	0.930371	−	0.366618i	$-0.119484\pi$
$44$		0			0
$45$	−50.4611	−	62.8348i	−1.12136	−	1.39633i
$46$		0			0
$47$	−51.9011	+	29.9651i	−1.10428	+	0.637556i	−0.937342	−	0.348412i	$-0.886721\pi$
$47$	−51.9011	+	29.9651i	−1.10428	+	0.637556i	−0.166937	+	0.985968i	$0.553388\pi$
$48$		0			0
$49$	63.0077			1.28587
$50$		0			0
$51$	31.9602	−	37.2670i	0.626671	−	0.730725i
$52$		0			0
$53$	34.2359	−	19.7661i	0.645960	−	0.372945i	−0.140947	−	0.990017i	$-0.545015\pi$
$53$	34.2359	−	19.7661i	0.645960	−	0.372945i	0.786907	+	0.617072i	$0.211681\pi$
$54$		0			0
$55$	48.9086	−	84.7122i	0.889247	−	1.54022i
$56$		0			0
$57$	−30.3438	+	48.2520i	−0.532348	+	0.846526i
$58$		0			0
$59$	−14.1519	−	8.17061i	−0.239863	−	0.138485i	0.375251	−	0.926923i	$-0.377557\pi$
$59$	−14.1519	−	8.17061i	−0.239863	−	0.138485i	−0.615114	+	0.788438i	$0.710890\pi$
$60$		0			0
$61$	14.1677	+	24.5392i	0.232258	+	0.402283i	0.958472	−	0.285186i	$-0.0920553\pi$
$61$	14.1677	+	24.5392i	0.232258	+	0.402283i	−0.726214	+	0.687468i	$0.758722\pi$
$62$		0			0
$63$	−88.7843	−	34.4959i	−1.40927	−	0.547554i
$64$		0			0
$65$			30.9682i			0.476435i
$66$		0			0
$67$	−5.39871	−	9.35085i	−0.0805778	−	0.139565i	0.822920	−	0.568157i	$-0.192343\pi$
$67$	−5.39871	−	9.35085i	−0.0805778	−	0.139565i	−0.903498	+	0.428592i	$0.859010\pi$
$68$		0			0
$69$	−1.13641	−	3.22999i	−0.0164698	−	0.0468114i
$70$		0			0
$71$	81.9916	+	47.3379i	1.15481	+	0.666731i	0.950055	−	0.312082i	$-0.101026\pi$
$71$	81.9916	+	47.3379i	1.15481	+	0.666731i	0.204757	+	0.978813i	$0.434360\pi$
$72$		0			0
$73$	24.9395	−	43.1965i	0.341637	−	0.591733i	−0.643100	−	0.765782i	$-0.722352\pi$
$73$	24.9395	−	43.1965i	0.341637	−	0.591733i	0.984737	+	0.174049i	$0.0556853\pi$
$74$		0			0
$75$	−156.155	+	54.9406i	−2.08207	+	0.732541i
$76$		0			0
$77$		−	115.613i		−	1.50147i
$78$		0			0
$79$	−20.3817	+	35.3022i	−0.257997	+	0.446863i	−0.965705	−	0.259641i	$-0.916396\pi$
$79$	−20.3817	+	35.3022i	−0.257997	+	0.446863i	0.707709	+	0.706504i	$0.249729\pi$
$80$		0			0
$81$	59.7521	+	54.6872i	0.737680	+	0.675151i
$82$		0			0
$83$		−	125.351i		−	1.51025i	−0.655582	−	0.755124i	$-0.727577\pi$
$83$		−	125.351i		−	1.51025i	0.655582	−	0.755124i	$-0.272423\pi$
$84$		0			0
$85$	−73.2680	−	126.904i	−0.861977	−	1.49299i
$86$		0			0
$87$	−35.8043	−	101.765i	−0.411544	−	1.16971i
$88$		0			0
$89$	55.6006	−	32.1010i	0.624725	−	0.360685i	−0.153981	−	0.988074i	$-0.549209\pi$
$89$	55.6006	−	32.1010i	0.624725	−	0.360685i	0.778706	+	0.627388i	$0.215876\pi$
$90$		0			0
$91$	18.3012	+	31.6986i	0.201112	+	0.348336i
$92$		0			0
$93$	2.17166	−	11.5857i	0.0233511	−	0.124578i
$94$		0			0
$95$	105.798	+	133.235i	1.11367	+	1.40247i
$96$		0			0
$97$	−50.3465	+	87.2027i	−0.519036	+	0.898997i	0.480719	+	0.876874i	$0.340376\pi$
$97$	−50.3465	+	87.2027i	−0.519036	+	0.898997i	−0.999755	+	0.0221221i	$0.992958\pi$
$98$		0			0
$99$	−35.6063	+	91.6423i	−0.359659	+	0.925679i
$100$		0			0
$101$	−50.0633	+	28.9040i	−0.495676	+	0.286179i	−0.726926	−	0.686716i	$-0.759052\pi$
$101$	−50.0633	+	28.9040i	−0.495676	+	0.286179i	0.231250	+	0.972894i	$0.425718\pi$
$102$		0			0
$103$	41.7697			0.405532			0.202766	−	0.979227i	$-0.435007\pi$
$103$	41.7697			0.405532			0.202766	+	0.979227i	$0.435007\pi$
$104$		0			0
$105$	−185.077	+	215.808i	−1.76264	+	2.05531i
$106$		0			0
$107$		−	140.173i		−	1.31003i	−0.755616	−	0.655015i	$-0.772662\pi$
$107$		−	140.173i		−	1.31003i	0.755616	−	0.655015i	$-0.227338\pi$
$108$		0			0
$109$	12.3265	−	21.3501i	0.113087	−	0.195873i	−0.803926	−	0.594729i	$-0.797259\pi$
$109$	12.3265	−	21.3501i	0.113087	−	0.195873i	0.917013	+	0.398856i	$0.130593\pi$
$110$		0			0
$111$	28.9750	−	154.581i	0.261036	−	1.39262i
$112$		0			0
$113$			17.6018i			0.155768i	0.996962	+	0.0778839i	$0.0248164\pi$
$113$			17.6018i			0.155768i	−0.996962	+	0.0778839i	$0.975184\pi$
$114$		0			0
$115$	−10.2200			−0.0888700
$116$		0			0
$117$	−4.74421	−	30.7626i	−0.0405488	−	0.262928i
$118$		0			0
$119$	−149.992	−	86.5978i	−1.26043	−	0.727712i
$120$		0			0
$121$	1.66528			0.0137627
$122$		0			0
$123$	143.679	−	167.535i	1.16812	−	1.36208i
$124$		0			0
$125$			270.236i			2.16189i
$126$		0			0
$127$	19.4379	+	33.6674i	0.153054	+	0.265098i	0.932349	−	0.361560i	$-0.117756\pi$
$127$	19.4379	+	33.6674i	0.153054	+	0.265098i	−0.779295	+	0.626658i	$0.784422\pi$
$128$		0			0
$129$	153.284	+	131.457i	1.18825	+	1.01905i
$130$		0			0
$131$	−74.2886	−	42.8906i	−0.567089	−	0.327409i	0.188897	−	0.981997i	$-0.439509\pi$
$131$	−74.2886	−	42.8906i	−0.567089	−	0.327409i	−0.755986	+	0.654588i	$0.772842\pi$
$132$		0			0
$133$	187.031	+	73.8534i	1.40624	+	0.555289i
$134$		0			0
$135$	213.168	−	114.063i	1.57902	−	0.844912i
$136$		0			0
$137$	−3.09764	+	1.78842i	−0.0226105	+	0.0130542i	−0.511263	−	0.859425i	$-0.670822\pi$
$137$	−3.09764	+	1.78842i	−0.0226105	+	0.0130542i	0.488652	+	0.872479i	$0.337489\pi$
$138$		0			0
$139$	−38.3252	−	66.3812i	−0.275721	−	0.477562i	0.694596	−	0.719400i	$-0.255583\pi$
$139$	−38.3252	−	66.3812i	−0.275721	−	0.477562i	−0.970317	+	0.241838i	$0.922250\pi$
$140$		0			0
$141$	−59.6708	−	169.600i	−0.423197	−	1.20284i
$142$		0			0
$143$	32.7189	−	18.8903i	0.228804	−	0.132100i
$144$		0			0
$145$	−321.997			−2.22067
$146$		0			0
$147$	−34.8244	+	185.787i	−0.236901	+	1.26386i
$148$		0			0
$149$	217.996	+	125.860i	1.46306	+	0.844698i	0.999152	−	0.0411851i	$-0.0131133\pi$
$149$	217.996	+	125.860i	1.46306	+	0.844698i	0.463908	+	0.885883i	$0.346447\pi$
$150$		0			0
$151$	160.799			1.06489			0.532447	−	0.846463i	$-0.321273\pi$
$151$	160.799			1.06489			0.532447	+	0.846463i	$0.321273\pi$
$152$		0			0
$153$	92.2227	+	114.837i	0.602763	+	0.750568i
$154$		0			0
$155$	−30.4693	−	17.5915i	−0.196576	−	0.113493i
$156$		0			0
$157$	−60.7094	+	105.152i	−0.386684	+	0.669757i	−0.992001	−	0.126228i	$-0.959713\pi$
$157$	−60.7094	+	105.152i	−0.386684	+	0.669757i	0.605317	+	0.795984i	$0.293046\pi$
$158$		0			0
$159$	39.3610	+	111.874i	0.247554	+	0.703611i
$160$		0			0
$161$	−10.4611	+	6.03970i	−0.0649755	+	0.0375136i
$162$		0			0
$163$	100.071			0.613933			0.306966	−	0.951720i	$-0.400686\pi$
$163$	100.071			0.613933			0.306966	+	0.951720i	$0.400686\pi$
$164$		0			0
$165$	222.754	+	191.035i	1.35003	+	1.15779i
$166$		0			0
$167$	−136.961	+	79.0743i	−0.820124	+	0.473499i	−0.850459	−	0.526041i	$-0.823676\pi$
$167$	−136.961	+	79.0743i	−0.820124	+	0.473499i	0.0303353	+	0.999540i	$0.490343\pi$
$168$		0			0
$169$	78.5195	−	136.000i	0.464612	−	0.804732i
$170$		0			0
$171$	−125.507	−	116.142i	−0.733959	−	0.679194i
$172$		0			0
$173$	−41.9046	−	24.1937i	−0.242223	−	0.139848i	0.373975	−	0.927439i	$-0.377995\pi$
$173$	−41.9046	−	24.1937i	−0.242223	−	0.139848i	−0.616198	+	0.787591i	$0.711328\pi$
$174$		0			0
$175$	291.992	+	505.746i	1.66853	+	2.88998i
$176$		0			0
$177$	31.9140	−	37.2131i	0.180305	−	0.210243i
$178$		0			0
$179$			274.811i			1.53526i	0.640896	+	0.767628i	$0.278563\pi$
$179$			274.811i			1.53526i	−0.640896	+	0.767628i	$0.721437\pi$
$180$		0			0
$181$	17.2137	+	29.8149i	0.0951031	+	0.164723i	0.909652	−	0.415372i	$-0.136349\pi$
$181$	17.2137	+	29.8149i	0.0951031	+	0.164723i	−0.814549	+	0.580095i	$0.803015\pi$
$182$		0			0
$183$	−80.1881	+	28.2128i	−0.438186	+	0.154168i
$184$		0			0
$185$	−406.532	−	234.712i	−2.19747	−	1.26871i
$186$		0			0
$187$	−89.3853	+	154.820i	−0.477996	+	0.827914i
$188$		0			0
$189$	150.787	−	242.728i	0.797817	−	1.28427i
$190$		0			0
$191$		−	10.6557i		−	0.0557888i	−0.999611	−	0.0278944i	$-0.991120\pi$
$191$		−	10.6557i		−	0.0557888i	0.999611	−	0.0278944i	$-0.00888022\pi$
$192$		0			0
$193$	−155.636	+	269.570i	−0.806406	+	1.39674i	0.108933	+	0.994049i	$0.465257\pi$
$193$	−155.636	+	269.570i	−0.806406	+	1.39674i	−0.915338	+	0.402686i	$0.868077\pi$
$194$		0			0
$195$	−91.3144	−	17.1162i	−0.468279	−	0.0877753i
$196$		0			0
$197$		−	32.0956i		−	0.162922i	−0.996677	−	0.0814610i	$-0.974041\pi$
$197$		−	32.0956i		−	0.162922i	0.996677	−	0.0814610i	$-0.0259586\pi$
$198$		0			0
$199$	−94.2051	−	163.168i	−0.473392	−	0.819940i	0.526144	−	0.850396i	$-0.323637\pi$
$199$	−94.2051	−	163.168i	−0.473392	−	0.819940i	−0.999536	+	0.0304560i	$0.990304\pi$
$200$		0			0
$201$	30.5562	−	10.7507i	0.152021	−	0.0534860i
$202$		0			0
$203$	−329.590	+	190.289i	−1.62360	+	0.937384i
$204$		0			0
$205$	−329.380	−	570.503i	−1.60673	−	2.78294i
$206$		0			0
$207$	10.1522	−	1.56567i	0.0490444	−	0.00756362i
$208$		0			0
$209$	76.2307	−	193.051i	0.364740	−	0.923689i
$210$		0			0
$211$	71.1052	−	123.158i	0.336992	−	0.583686i	−0.646874	−	0.762597i	$-0.723924\pi$
$211$	71.1052	−	123.158i	0.336992	−	0.583686i	0.983865	+	0.178911i	$0.0572573\pi$
$212$		0			0
$213$	−184.900	+	215.601i	−0.868073	+	1.01221i
$214$		0			0
$215$	521.974	−	301.362i	2.42778	−	1.40168i
$216$		0			0
$217$	−41.5838			−0.191631
$218$		0			0
$219$	113.587	+	97.4126i	0.518663	+	0.444806i
$220$		0			0
$221$		−	56.5976i		−	0.256098i
$222$		0			0
$223$	−128.526	+	222.614i	−0.576352	+	0.998271i	0.419542	+	0.907736i	$0.362191\pi$
$223$	−128.526	+	222.614i	−0.576352	+	0.998271i	−0.995893	+	0.0905344i	$0.971142\pi$
$224$		0			0
$225$	−75.6931	−	490.813i	−0.336414	−	2.18139i
$226$		0			0
$227$			13.3656i			0.0588794i	0.999567	+	0.0294397i	$0.00937231\pi$
$227$			13.3656i			0.0588794i	−0.999567	+	0.0294397i	$0.990628\pi$
$228$		0			0
$229$	85.5614			0.373631			0.186815	−	0.982395i	$-0.440183\pi$
$229$	85.5614			0.373631			0.186815	+	0.982395i	$0.440183\pi$
$230$		0			0
$231$	340.902	+	63.8995i	1.47577	+	0.276621i
$232$		0			0
$233$	160.193	+	92.4877i	0.687525	+	0.396943i	0.802684	−	0.596404i	$-0.203404\pi$
$233$	160.193	+	92.4877i	0.687525	+	0.396943i	−0.115159	+	0.993347i	$0.536738\pi$
$234$		0			0
$235$	−536.633			−2.28355
$236$		0			0
$237$	−92.8287	−	79.6101i	−0.391682	−	0.335908i
$238$		0			0
$239$			37.6449i			0.157510i	0.996894	+	0.0787551i	$0.0250945\pi$
$239$			37.6449i			0.157510i	−0.996894	+	0.0787551i	$0.974905\pi$
$240$		0			0
$241$	−161.354	−	279.474i	−0.669520	−	1.15964i	−0.978038	−	0.208424i	$-0.933166\pi$
$241$	−161.354	−	279.474i	−0.669520	−	1.15964i	0.308518	−	0.951218i	$-0.400167\pi$
$242$		0			0
$243$	−194.278	+	145.962i	−0.799499	+	0.600667i
$244$		0			0
$245$	488.602	+	282.095i	1.99430	+	1.15141i
$246$		0			0
$247$	9.65855	+	64.9974i	0.0391034	+	0.263147i
$248$		0			0
$249$	369.615	+	69.2814i	1.48440	+	0.278239i
$250$		0			0
$251$	−211.914	+	122.349i	−0.844280	+	0.487445i	−0.858717	−	0.512450i	$-0.828738\pi$
$251$	−211.914	+	122.349i	−0.844280	+	0.487445i	0.0144366	+	0.999896i	$0.495405\pi$
$252$		0			0
$253$	6.23411	+	10.7978i	0.0246408	+	0.0426791i
$254$		0			0
$255$	414.690	−	145.902i	1.62624	−	0.572163i
$256$		0			0
$257$	429.600	−	248.030i	1.67160	−	0.965096i	0.704850	−	0.709356i	$-0.251014\pi$
$257$	429.600	−	248.030i	1.67160	−	0.965096i	0.966746	−	0.255740i	$-0.0823190\pi$
$258$		0			0
$259$	−554.826			−2.14219
$260$		0			0
$261$	319.859	−	49.3286i	1.22551	−	0.188998i
$262$		0			0
$263$	49.0983	+	28.3469i	0.186686	+	0.107783i	0.590430	−	0.807089i	$-0.298958\pi$
$263$	49.0983	+	28.3469i	0.186686	+	0.107783i	−0.403744	+	0.914872i	$0.632292\pi$
$264$		0			0
$265$	353.983			1.33578
$266$		0			0
$267$	63.9240	+	181.689i	0.239416	+	0.680482i
$268$		0			0
$269$	−271.312	−	156.642i	−1.00860	−	0.582313i	−0.0978154	−	0.995205i	$-0.531185\pi$
$269$	−271.312	−	156.642i	−1.00860	−	0.582313i	−0.910780	+	0.412892i	$0.864519\pi$
$270$		0			0
$271$	143.096	−	247.849i	0.528028	−	0.914572i	−0.471438	−	0.881899i	$-0.656265\pi$
$271$	143.096	−	247.849i	0.528028	−	0.914572i	0.999466	−	0.0326725i	$-0.0104018\pi$
$272$		0			0
$273$	−103.583	+	36.4439i	−0.379425	+	0.133494i
$274$		0			0
$275$	522.026	−	301.392i	1.89827	−	1.09597i
$276$		0			0
$277$	−383.333			−1.38387			−0.691937	−	0.721958i	$-0.743242\pi$
$277$	−383.333			−1.38387			−0.691937	+	0.721958i	$0.743242\pi$
$278$		0			0
$279$	32.9620	+	12.8069i	0.118143	+	0.0459028i
$280$		0			0
$281$	232.610	−	134.297i	0.827793	−	0.477926i	−0.0253037	−	0.999680i	$-0.508055\pi$
$281$	232.610	−	134.297i	0.827793	−	0.477926i	0.853096	+	0.521754i	$0.174722\pi$
$282$		0			0
$283$	−157.520	+	272.832i	−0.556606	+	0.964070i	0.441171	+	0.897423i	$0.354563\pi$
$283$	−157.520	+	272.832i	−0.556606	+	0.964070i	−0.997777	+	0.0666468i	$0.978770\pi$
$284$		0			0
$285$	−451.337	+	238.323i	−1.58364	+	0.836223i
$286$		0			0
$287$	−674.295	−	389.304i	−2.34946	−	1.35646i
$288$		0			0
$289$	−10.5954	−	18.3517i	−0.0366621	−	0.0635007i
$290$		0			0
$291$	−229.303	−	196.651i	−0.787984	−	0.675777i
$292$		0			0
$293$		−	114.051i		−	0.389251i	−0.980878	−	0.194625i	$-0.937651\pi$
$293$		−	114.051i		−	0.389251i	0.980878	−	0.194625i	$-0.0623491\pi$
$294$		0			0
$295$	−73.1621	−	126.720i	−0.248007	−	0.429561i
$296$		0			0
$297$	−250.541	−	155.641i	−0.843573	−	0.524044i
$298$		0			0
$299$	−3.41851	−	1.97368i	−0.0114331	−	0.00660093i
$300$		0			0
$301$	356.189	−	616.937i	1.18335	−	2.04962i
$302$		0			0
$303$	−57.5578	−	163.594i	−0.189960	−	0.539915i
$304$		0			0
$305$			253.724i			0.831883i
$306$		0			0
$307$	168.284	−	291.476i	0.548155	−	0.949432i	−0.450246	−	0.892905i	$-0.648664\pi$
$307$	168.284	−	291.476i	0.548155	−	0.949432i	0.998401	−	0.0565278i	$-0.0180030\pi$
$308$		0			0
$309$	−23.0862	+	123.164i	−0.0747126	+	0.398590i
$310$		0			0
$311$			493.112i			1.58557i	0.609501	+	0.792785i	$0.291370\pi$
$311$			493.112i			1.58557i	−0.609501	+	0.792785i	$0.708630\pi$
$312$		0			0
$313$	−199.530	−	345.596i	−0.637476	−	1.10414i	−0.985985	−	0.166836i	$-0.946645\pi$
$313$	−199.530	−	345.596i	−0.637476	−	1.10414i	0.348508	−	0.937306i	$-0.386688\pi$
$314$		0			0
$315$	−534.048	−	665.004i	−1.69539	−	2.11112i
$316$		0			0
$317$	−524.958	+	303.084i	−1.65602	+	0.956102i	−0.681492	+	0.731825i	$0.738669\pi$
$317$	−524.958	+	303.084i	−1.65602	+	0.956102i	−0.974525	+	0.224277i	$0.927998\pi$
$318$		0			0
$319$	196.414	+	340.200i	0.615719	+	1.06646i
$320$		0			0
$321$	413.322	+	77.4739i	1.28761	+	0.241352i
$322$		0			0
$323$	−193.357	−	243.500i	−0.598629	−	0.753869i
$324$		0			0
$325$	−95.4185	+	165.270i	−0.293595	+	0.508522i
$326$		0			0
$327$	56.1411	+	48.1467i	0.171685	+	0.147238i
$328$		0			0
$329$	−549.288	+	317.132i	−1.66957	+	0.963927i
$330$		0			0
$331$	94.1225			0.284358			0.142179	−	0.989841i	$-0.454589\pi$
$331$	94.1225			0.284358			0.142179	+	0.989841i	$0.454589\pi$
$332$		0			0
$333$	439.790	+	170.874i	1.32069	+	0.513135i
$334$		0			0
$335$		−	96.6834i		−	0.288607i
$336$		0			0
$337$	−287.367	+	497.734i	−0.852721	+	1.47696i	0.0260215	+	0.999661i	$0.491716\pi$
$337$	−287.367	+	497.734i	−0.852721	+	1.47696i	−0.878743	+	0.477295i	$0.841617\pi$
$338$		0			0
$339$	−51.9014	−	9.72852i	−0.153101	−	0.0286977i
$340$		0			0
$341$			42.9224i			0.125872i
$342$		0			0
$343$	148.248			0.432211
$344$		0			0
$345$	5.64863	−	30.1353i	0.0163729	−	0.0873488i
$346$		0			0
$347$	131.087	+	75.6830i	0.377772	+	0.218107i	0.676848	−	0.736123i	$-0.263345\pi$
$347$	131.087	+	75.6830i	0.377772	+	0.218107i	−0.299077	+	0.954229i	$0.596679\pi$
$348$		0			0
$349$	35.1952			0.100846			0.0504229	−	0.998728i	$-0.483943\pi$
$349$	35.1952			0.100846			0.0504229	+	0.998728i	$0.483943\pi$
$350$		0			0
$351$	93.3303	+	3.01354i	0.265898	+	0.00858559i
$352$		0			0
$353$			354.875i			1.00531i	0.864487	+	0.502656i	$0.167644\pi$
$353$			354.875i			1.00531i	−0.864487	+	0.502656i	$0.832356\pi$
$354$		0			0
$355$	423.878	+	734.178i	1.19402	+	2.06811i
$356$		0			0
$357$	338.247	−	394.410i	0.947470	−	1.10479i
$358$		0			0
$359$	−35.7018	−	20.6125i	−0.0994480	−	0.0574163i	0.449451	−	0.893305i	$-0.351620\pi$
$359$	−35.7018	−	20.6125i	−0.0994480	−	0.0574163i	−0.548899	+	0.835889i	$0.684953\pi$
$360$		0			0
$361$	263.608	+	246.641i	0.730216	+	0.683216i
$362$		0			0
$363$	−0.920403	+	4.91033i	−0.00253555	+	0.0135271i
$364$		0			0
$365$	386.794	−	223.316i	1.05971	−	0.611824i
$366$		0			0
$367$	296.738	+	513.965i	0.808550	+	1.40045i	0.913868	+	0.406011i	$0.133081\pi$
$367$	296.738	+	513.965i	0.808550	+	1.40045i	−0.105318	+	0.994439i	$0.533586\pi$
$368$		0			0
$369$	414.592	+	516.255i	1.12355	+	1.39907i
$370$		0			0
$371$	362.331	−	209.192i	0.976633	−	0.563859i
$372$		0			0
$373$	68.9767			0.184924			0.0924621	−	0.995716i	$-0.470526\pi$
$373$	68.9767			0.184924			0.0924621	+	0.995716i	$0.470526\pi$
$374$		0			0
$375$	−796.832	−	149.360i	−2.12488	−	0.398293i
$376$		0			0
$377$	−107.705	−	62.1834i	−0.285689	−	0.164943i
$378$		0			0
$379$	−371.205			−0.979434			−0.489717	−	0.871881i	$-0.662900\pi$
$379$	−371.205			−0.979434			−0.489717	+	0.871881i	$0.662900\pi$
$380$		0			0
$381$	−110.017	+	38.7074i	−0.288757	+	0.101594i
$382$		0			0
$383$	278.792	+	160.960i	0.727915	+	0.420262i	0.817659	−	0.575703i	$-0.195271\pi$
$383$	278.792	+	160.960i	0.727915	+	0.420262i	−0.0897438	+	0.995965i	$0.528605\pi$
$384$		0			0
$385$	517.617	−	896.540i	1.34446	−	2.32867i
$386$		0			0
$387$	−472.340	+	379.325i	−1.22052	+	0.980167i
$388$		0			0
$389$	−408.840	+	236.044i	−1.05100	+	0.606797i	−0.922930	−	0.384968i	$-0.874212\pi$
$389$	−408.840	+	236.044i	−1.05100	+	0.606797i	−0.128073	+	0.991765i	$0.540879\pi$
$390$		0			0
$391$	18.6782			0.0477702
$392$		0			0
$393$	167.529	−	195.345i	0.426281	−	0.497062i
$394$		0			0
$395$	−316.106	+	182.504i	−0.800269	+	0.462036i
$396$		0			0
$397$	−130.531	+	226.087i	−0.328794	+	0.569488i	−0.982273	−	0.187457i	$-0.939976\pi$
$397$	−130.531	+	226.087i	−0.328794	+	0.569488i	0.653479	+	0.756945i	$0.273309\pi$
$398$		0			0
$399$	−321.140	+	510.668i	−0.804861	+	1.27987i
$400$		0			0
$401$	250.935	+	144.877i	0.625773	+	0.361290i	0.779113	−	0.626883i	$-0.215670\pi$
$401$	250.935	+	144.877i	0.625773	+	0.361290i	−0.153340	+	0.988173i	$0.549003\pi$
$402$		0			0
$403$	−6.79447	−	11.7684i	−0.0168597	−	0.0292019i
$404$		0			0
$405$	218.514	+	691.599i	0.539540	+	1.70765i
$406$		0			0
$407$			572.686i			1.40709i
$408$		0			0
$409$	241.502	+	418.293i	0.590469	+	1.02272i	0.994169	+	0.107831i	$0.0343904\pi$
$409$	241.502	+	418.293i	0.590469	+	1.02272i	−0.403701	+	0.914891i	$0.632276\pi$
$410$		0			0
$411$	−3.56136	−	10.1223i	−0.00866511	−	0.0246285i
$412$		0			0
$413$	−149.775	−	86.4726i	−0.362651	−	0.209377i
$414$		0			0
$415$	561.214	−	972.050i	1.35232	−	2.34229i
$416$		0			0
$417$	216.917	−	76.3185i	0.520185	−	0.183018i
$418$		0			0
$419$		−	384.029i		−	0.916536i	−0.888814	−	0.458268i	$-0.848470\pi$
$419$		−	384.029i		−	0.916536i	0.888814	−	0.458268i	$-0.151530\pi$
$420$		0			0
$421$	101.636	−	176.039i	0.241416	−	0.418146i	−0.719702	−	0.694284i	$-0.755721\pi$
$421$	101.636	−	176.039i	0.241416	−	0.418146i	0.961118	+	0.276138i	$0.0890547\pi$
$422$		0			0
$423$	533.070	−	82.2100i	1.26021	−	0.194350i
$424$		0			0
$425$		−	903.006i		−	2.12472i
$426$		0			0
$427$	149.942	+	259.708i	0.351153	+	0.608215i
$428$		0			0
$429$	37.6170	+	106.917i	0.0876853	+	0.249224i
$430$		0			0
$431$	91.8083	−	53.0055i	0.213012	−	0.122983i	−0.389698	−	0.920943i	$-0.627421\pi$
$431$	91.8083	−	53.0055i	0.213012	−	0.122983i	0.602711	+	0.797960i	$0.294087\pi$
$432$		0			0
$433$	−192.469	−	333.366i	−0.444501	−	0.769898i	0.553516	−	0.832838i	$-0.313286\pi$
$433$	−192.469	−	333.366i	−0.444501	−	0.769898i	−0.998017	+	0.0629400i	$0.979952\pi$
$434$		0			0
$435$	177.968	−	949.455i	0.409122	−	2.18265i
$436$		0			0
$437$	−21.4502	+	3.18749i	−0.0490852	+	0.00729402i
$438$		0			0
$439$	−5.24286	+	9.08090i	−0.0119427	+	0.0206854i	−0.871935	−	0.489622i	$-0.837135\pi$
$439$	−5.24286	+	9.08090i	−0.0119427	+	0.0206854i	0.859992	+	0.510307i	$0.170468\pi$
$440$		0			0
$441$	−528.574	−	205.370i	−1.19858	−	0.465691i
$442$		0			0
$443$	131.335	−	75.8264i	0.296468	−	0.171166i	−0.344387	−	0.938828i	$-0.611913\pi$
$443$	131.335	−	75.8264i	0.296468	−	0.171166i	0.640855	+	0.767662i	$0.278580\pi$
$444$		0			0
$445$	574.884			1.29187
$446$		0			0
$447$	−491.603	+	573.230i	−1.09978	+	1.28239i
$448$		0			0
$449$		−	434.271i		−	0.967195i	−0.875290	−	0.483598i	$-0.839330\pi$
$449$		−	434.271i		−	0.967195i	0.875290	−	0.483598i	$-0.160670\pi$
$450$		0			0
$451$	−401.836	+	696.000i	−0.890989	+	1.54324i
$452$		0			0
$453$	−88.8738	+	474.140i	−0.196189	+	1.04667i
$454$		0			0
$455$			327.748i			0.720326i
$456$		0			0
$457$	63.2573			0.138419			0.0692093	−	0.997602i	$-0.477952\pi$
$457$	63.2573			0.138419			0.0692093	+	0.997602i	$0.477952\pi$
$458$		0			0
$459$	−389.585	+	208.462i	−0.848770	+	0.454165i
$460$		0			0
$461$	305.614	+	176.446i	0.662936	+	0.382746i	0.793395	−	0.608707i	$-0.208312\pi$
$461$	305.614	+	176.446i	0.662936	+	0.382746i	−0.130459	+	0.991454i	$0.541645\pi$
$462$		0			0
$463$	−289.091			−0.624387			−0.312193	−	0.950019i	$-0.601064\pi$
$463$	−289.091			−0.624387			−0.312193	+	0.950019i	$0.601064\pi$
$464$		0			0
$465$	68.7115	−	80.1205i	0.147767	−	0.172302i
$466$		0			0
$467$		−	161.913i		−	0.346709i	−0.984860	−	0.173354i	$-0.944539\pi$
$467$		−	161.913i		−	0.346709i	0.984860	−	0.173354i	$-0.0554606\pi$
$468$		0			0
$469$	−57.1366	−	98.9634i	−0.121826	−	0.211009i
$470$		0			0
$471$	−276.501	−	237.128i	−0.587052	−	0.503457i
$472$		0			0
$473$	−636.796	−	367.654i	−1.34629	−	0.777282i
$474$		0			0
$475$	154.101	+	1037.02i	0.324423	+	2.18321i
$476$		0			0
$477$	−351.633	+	54.2287i	−0.737175	+	0.113687i
$478$		0			0
$479$	184.208	−	106.352i	0.384567	−	0.222030i	−0.295237	−	0.955424i	$-0.595398\pi$
$479$	184.208	−	106.352i	0.384567	−	0.222030i	0.679803	+	0.733394i	$0.262065\pi$
$480$		0			0
$481$	−90.6542	−	157.018i	−0.188470	−	0.326440i
$482$		0			0
$483$	−12.0271	−	34.1841i	−0.0249008	−	0.0707746i
$484$		0			0
$485$	−780.839	+	450.818i	−1.60998	+	0.929521i
$486$		0			0
$487$	764.802			1.57043			0.785217	−	0.619220i	$-0.212551\pi$
$487$	764.802			1.57043			0.785217	+	0.619220i	$0.212551\pi$
$488$		0			0
$489$	−55.3094	+	295.074i	−0.113107	+	0.603424i
$490$		0			0
$491$	432.733	+	249.839i	0.881330	+	0.508836i	0.871097	−	0.491111i	$-0.163409\pi$
$491$	432.733	+	249.839i	0.881330	+	0.508836i	0.0102334	+	0.999948i	$0.496743\pi$
$492$		0			0
$493$	588.481			1.19367
$494$		0			0
$495$	−686.411	+	551.239i	−1.38669	+	1.11361i
$496$		0			0
$497$	867.748	+	500.994i	1.74597	+	1.00804i
$498$		0			0
$499$	23.2594	−	40.2865i	0.0466121	−	0.0807345i	−0.841778	−	0.539824i	$-0.818491\pi$
$499$	23.2594	−	40.2865i	0.0466121	−	0.0807345i	0.888390	+	0.459089i	$0.151824\pi$
$500$		0			0
$501$	−157.464	−	447.553i	−0.314299	−	0.893320i
$502$		0			0
$503$	39.9078	−	23.0408i	0.0793396	−	0.0458068i	−0.459805	−	0.888020i	$-0.652081\pi$
$503$	39.9078	−	23.0408i	0.0793396	−	0.0458068i	0.539145	+	0.842213i	$0.318747\pi$
$504$		0			0
$505$	−517.631			−1.02501
$506$		0			0
$507$	357.617	+	306.693i	0.705360	+	0.604918i
$508$		0			0
$509$	454.053	−	262.148i	0.892050	−	0.515025i	0.0174376	−	0.999848i	$-0.494449\pi$
$509$	454.053	−	262.148i	0.892050	−	0.515025i	0.874613	+	0.484823i	$0.161116\pi$
$510$		0			0
$511$	263.944	−	457.164i	0.516525	−	0.894647i
$512$		0			0
$513$	411.830	−	305.884i	0.802788	−	0.596265i
$514$		0			0
$515$	323.910	+	187.009i	0.628951	+	0.363125i
$516$		0			0
$517$	327.340	+	566.970i	0.633153	+	1.09665i
$518$		0			0
$519$	94.4993	−	110.190i	0.182080	−	0.212312i
$520$		0			0
$521$		−	222.969i		−	0.427963i	−0.976838	−	0.213982i	$-0.931357\pi$
$521$		−	222.969i		−	0.427963i	0.976838	−	0.213982i	$-0.0686433\pi$
$522$		0			0
$523$	−424.134	−	734.621i	−0.810963	−	1.40463i	−0.912191	−	0.409765i	$-0.865611\pi$
$523$	−424.134	−	734.621i	−0.810963	−	1.40463i	0.101228	−	0.994863i	$-0.467723\pi$
$524$		0			0
$525$	−1652.65	+	581.456i	−3.14791	+	1.10754i
$526$		0			0
$527$	55.6857	+	32.1502i	0.105666	+	0.0610060i
$528$		0			0
$529$	−263.849	+	456.999i	−0.498769	+	0.863893i
$530$		0			0
$531$	92.0894	+	114.671i	0.173426	+	0.215953i
$532$		0			0
$533$		−	254.437i		−	0.477368i
$534$		0			0
$535$	627.577	−	1086.99i	1.17304	−	2.03177i
$536$		0			0
$537$	−810.320	−	151.888i	−1.50898	−	0.282846i
$538$		0			0
$539$		−	688.298i		−	1.27699i
$540$		0			0
$541$	−311.347	−	539.268i	−0.575502	−	0.996799i	−0.995987	−	0.0894995i	$-0.971473\pi$
$541$	−311.347	−	539.268i	−0.575502	−	0.996799i	0.420485	−	0.907300i	$-0.361860\pi$
$542$		0			0
$543$	−97.4277	+	34.2782i	−0.179425	+	0.0631275i
$544$		0			0
$545$	191.175	−	110.375i	0.350781	−	0.202523i
$546$		0			0
$547$	−154.019	−	266.768i	−0.281570	−	0.487694i	0.690202	−	0.723617i	$-0.257522\pi$
$547$	−154.019	−	266.768i	−0.281570	−	0.487694i	−0.971772	+	0.235924i	$0.924189\pi$
$548$		0			0
$549$	−38.8695	−	252.040i	−0.0708006	−	0.459089i
$550$		0			0
$551$	−675.819	+	100.426i	−1.22653	+	0.182262i
$552$		0			0
$553$	−215.707	+	373.616i	−0.390067	+	0.675617i
$554$		0			0
$555$	916.773	−	1069.00i	1.65184	−	1.92612i
$556$		0			0
$557$	−147.833	+	85.3514i	−0.265409	+	0.153234i	−0.626800	−	0.779181i	$-0.715636\pi$
$557$	−147.833	+	85.3514i	−0.265409	+	0.153234i	0.361390	+	0.932415i	$0.382302\pi$
$558$		0			0
$559$	232.794			0.416447
$560$		0			0
$561$	−407.106	−	349.135i	−0.725679	−	0.622344i
$562$		0			0
$563$			608.088i			1.08009i	0.841637	+	0.540043i	$0.181592\pi$
$563$			608.088i			1.08009i	−0.841637	+	0.540043i	$0.818408\pi$
$564$		0			0
$565$	−78.8058	+	136.496i	−0.139479	+	0.241585i
$566$		0			0
$567$	632.378	+	578.775i	1.11531	+	1.02077i
$568$		0			0
$569$			907.829i			1.59548i	0.603001	+	0.797741i	$0.293972\pi$
$569$			907.829i			1.59548i	−0.603001	+	0.797741i	$0.706028\pi$
$570$		0			0
$571$	1120.80			1.96286			0.981432	−	0.191810i	$-0.0614359\pi$
$571$	1120.80			1.96286			0.981432	+	0.191810i	$0.0614359\pi$
$572$		0			0
$573$	31.4198	+	5.88940i	0.0548339	+	0.0102782i
$574$		0			0
$575$	−54.5418	−	31.4897i	−0.0948554	−	0.0547648i
$576$		0			0
$577$	−704.819			−1.22152			−0.610762	−	0.791814i	$-0.709137\pi$
$577$	−704.819			−1.22152			−0.610762	+	0.791814i	$0.709137\pi$
$578$		0			0
$579$	−708.846	−	607.908i	−1.22426	−	1.04993i
$580$		0			0
$581$		−	1326.63i		−	2.28336i
$582$		0			0
$583$	−215.926	−	373.994i	−0.370370	−	0.641499i
$584$		0			0
$585$	100.939	−	259.794i	0.172546	−	0.444092i
$586$		0			0
$587$	−602.214	−	347.688i	−1.02592	−	0.592314i	−0.110106	−	0.993920i	$-0.535119\pi$
$587$	−602.214	−	347.688i	−1.02592	−	0.592314i	−0.915813	+	0.401606i	$0.868452\pi$
$588$		0			0
$589$	−69.4367	−	27.4187i	−0.117889	−	0.0465513i
$590$		0			0
$591$	94.6388	+	17.7393i	0.160133	+	0.0300157i
$592$		0			0
$593$	−438.550	+	253.197i	−0.739544	+	0.426976i	−0.821904	−	0.569627i	$-0.807088\pi$
$593$	−438.550	+	253.197i	−0.739544	+	0.426976i	0.0823594	+	0.996603i	$0.473754\pi$
$594$		0			0
$595$	−775.422	−	1343.07i	−1.30323	−	2.25726i
$596$		0			0
$597$	533.192	−	187.594i	0.893119	−	0.314229i
$598$		0			0
$599$	−1020.52	+	589.198i	−1.70371	+	0.983637i	−0.761773	+	0.647845i	$0.775671\pi$
$599$	−1020.52	+	589.198i	−1.70371	+	0.983637i	−0.941936	+	0.335792i	$0.890996\pi$
$600$		0			0
$601$	163.286			0.271691			0.135845	−	0.990730i	$-0.456625\pi$
$601$	163.286			0.271691			0.135845	+	0.990730i	$0.456625\pi$
$602$		0			0
$603$	14.8115	+	96.0414i	0.0245630	+	0.159273i
$604$		0			0
$605$	12.9137	+	7.45572i	0.0213449	+	0.0123235i
$606$		0			0
$607$	−429.672			−0.707861			−0.353931	−	0.935272i	$-0.615155\pi$
$607$	−429.672			−0.707861			−0.353931	+	0.935272i	$0.615155\pi$
$608$		0			0
$609$	−378.930	−	1077.02i	−0.622217	−	1.76850i
$610$		0			0
$611$	−179.499	−	103.634i	−0.293779	−	0.169613i
$612$		0			0
$613$	223.578	−	387.248i	0.364727	−	0.631726i	−0.624005	−	0.781420i	$-0.714496\pi$
$613$	223.578	−	387.248i	0.364727	−	0.631726i	0.988732	+	0.149694i	$0.0478289\pi$
$614$		0			0
$615$	1864.26	−	655.908i	3.03132	−	1.06652i
$616$		0			0
$617$	133.677	−	77.1786i	0.216657	−	0.125087i	−0.387744	−	0.921767i	$-0.626746\pi$
$617$	133.677	−	77.1786i	0.216657	−	0.125087i	0.604401	+	0.796680i	$0.293412\pi$
$618$		0			0
$619$	13.5069			0.0218205			0.0109103	−	0.999940i	$-0.496527\pi$
$619$	13.5069			0.0218205			0.0109103	+	0.999940i	$0.496527\pi$
$620$		0			0
$621$	−0.994521	+	30.8006i	−0.00160148	+	0.0495983i
$622$		0			0
$623$	588.441	−	339.737i	0.944528	−	0.545324i
$624$		0			0
$625$	−520.145	+	900.917i	−0.832232	+	1.44147i
$626$		0			0
$627$	527.107	+	331.477i	0.840680	+	0.528672i
$628$		0			0
$629$	742.979	+	428.959i	1.18121	+	0.681970i
$630$		0			0
$631$	242.045	+	419.234i	0.383589	+	0.664396i	0.991572	−	0.129554i	$-0.0413546\pi$
$631$	242.045	+	419.234i	0.383589	+	0.664396i	−0.607983	+	0.793950i	$0.708021\pi$
$632$		0			0
$633$	323.849	+	277.734i	0.511610	+	0.438758i
$634$		0			0
$635$			348.105i			0.548197i
$636$		0			0
$637$	108.955	+	188.716i	0.171044	+	0.296258i
$638$		0			0
$639$	−533.536	−	664.367i	−0.834955	−	1.03970i
$640$		0			0
$641$	−495.352	−	285.992i	−0.772780	−	0.446165i	0.0610854	−	0.998133i	$-0.480544\pi$
$641$	−495.352	−	285.992i	−0.772780	−	0.446165i	−0.833865	+	0.551968i	$0.813877\pi$
$642$		0			0
$643$	422.656	−	732.062i	0.657319	−	1.13851i	−0.323988	−	0.946061i	$-0.605024\pi$
$643$	422.656	−	732.062i	0.657319	−	1.13851i	0.981307	−	0.192449i	$-0.0616430\pi$
$644$		0			0
$645$	600.114	+	1705.68i	0.930409	+	2.64446i
$646$		0			0
$647$		−	145.366i		−	0.224676i	−0.993670	−	0.112338i	$-0.964166\pi$
$647$		−	145.366i		−	0.224676i	0.993670	−	0.112338i	$-0.0358340\pi$
$648$		0			0
$649$	−89.2561	+	154.596i	−0.137529	+	0.238207i
$650$		0			0
$651$	22.9834	−	122.616i	0.0353048	−	0.188350i
$652$		0			0
$653$			870.468i			1.33303i	0.745492	+	0.666515i	$0.232215\pi$
$653$			870.468i			1.33303i	−0.745492	+	0.666515i	$0.767785\pi$
$654$		0			0
$655$	−384.055	−	665.203i	−0.586343	−	1.01558i
$656$		0			0
$657$	−350.015	+	281.088i	−0.532748	+	0.427836i
$658$		0			0
$659$	664.941	−	383.904i	1.00902	−	0.582555i	0.0981122	−	0.995175i	$-0.468720\pi$
$659$	664.941	−	383.904i	1.00902	−	0.582555i	0.910903	+	0.412620i	$0.135386\pi$
$660$		0			0
$661$	17.4517	+	30.2272i	0.0264020	+	0.0457295i	0.878924	−	0.476961i	$-0.158262\pi$
$661$	17.4517	+	30.2272i	0.0264020	+	0.0457295i	−0.852523	+	0.522690i	$0.824928\pi$
$662$		0			0
$663$	166.886	+	31.2815i	0.251714	+	0.0471818i
$664$		0			0
$665$	1119.70	+	1410.07i	1.68377	+	2.12041i
$666$		0			0
$667$	20.5216	−	35.5444i	0.0307670	−	0.0532900i
$668$		0			0
$669$	−585.374	−	502.018i	−0.874999	−	0.750401i
$670$		0			0
$671$	268.068	−	154.769i	0.399505	−	0.230654i
$672$		0			0
$673$	−1075.74			−1.59843			−0.799215	−	0.601045i	$-0.794751\pi$
$673$	−1075.74			−1.59843			−0.799215	+	0.601045i	$0.794751\pi$
$674$		0			0
$675$	1489.07	+	48.0806i	2.20603	+	0.0712306i
$676$		0			0
$677$		−	499.075i		−	0.737186i	−0.929591	−	0.368593i	$-0.879840\pi$
$677$		−	499.075i		−	0.737186i	0.929591	−	0.368593i	$-0.120160\pi$
$678$		0			0
$679$	−532.835	+	922.898i	−0.784735	+	1.35920i
$680$		0			0
$681$	−39.4105	−	7.38720i	−0.0578716	−	0.0108476i
$682$		0			0
$683$		−	613.170i		−	0.897760i	−0.893592	−	0.448880i	$-0.851823\pi$
$683$		−	613.170i		−	0.897760i	0.893592	−	0.448880i	$-0.148177\pi$
$684$		0			0
$685$	−32.0282			−0.0467564
$686$		0			0
$687$	−47.2899	+	252.290i	−0.0688354	+	0.367235i
$688$		0			0
$689$	118.404	+	68.3606i	0.171849	+	0.0992171i
$690$		0			0
$691$	−360.800			−0.522142			−0.261071	−	0.965320i	$-0.584076\pi$
$691$	−360.800			−0.522142			−0.261071	+	0.965320i	$0.584076\pi$
$692$		0			0
$693$	−376.834	+	969.884i	−0.543773	+	1.39954i
$694$		0			0
$695$		−	686.351i		−	0.987555i
$696$		0			0
$697$	601.975	+	1042.65i	0.863665	+	1.49591i
$698$		0			0
$699$	−361.253	+	421.236i	−0.516814	+	0.602626i
$700$		0			0
$701$	711.997	+	411.072i	1.01569	+	0.586408i	0.912852	−	0.408291i	$-0.133875\pi$
$701$	711.997	+	411.072i	1.01569	+	0.586408i	0.102836	+	0.994698i	$0.467208\pi$
$702$		0			0
$703$	−926.449	−	365.830i	−1.31785	−	0.520384i
$704$		0			0
$705$	296.598	−	1582.34i	0.420706	−	2.24446i
$706$		0			0
$707$	−529.838	+	305.902i	−0.749417	+	0.432676i
$708$		0			0
$709$	−81.2178	−	140.673i	−0.114553	−	0.198411i	0.803048	−	0.595914i	$-0.203210\pi$
$709$	−81.2178	−	140.673i	−0.114553	−	0.198411i	−0.917601	+	0.397503i	$0.869877\pi$
$710$		0			0
$711$	286.049	−	229.718i	0.402319	−	0.323092i
$712$		0			0
$713$	3.88376	−	2.24229i	0.00544707	−	0.00314487i
$714$		0			0
$715$	338.298			0.473145
$716$		0			0
$717$	−111.002	−	20.8064i	−0.154814	−	0.0290187i
$718$		0			0
$719$	24.2365	+	13.9929i	0.0337086	+	0.0194617i	0.516760	−	0.856131i	$-0.327138\pi$
$719$	24.2365	+	13.9929i	0.0337086	+	0.0194617i	−0.483051	+	0.875592i	$0.660471\pi$
$720$		0			0
$721$	442.065			0.613127
$722$		0			0
$723$	913.251	−	321.311i	1.26314	−	0.444414i
$724$		0			0
$725$	−1718.42	−	992.128i	−2.37023	−	1.36845i
$726$		0			0
$727$	−609.249	+	1055.25i	−0.838031	+	1.45151i	0.0535074	+	0.998567i	$0.482960\pi$
$727$	−609.249	+	1055.25i	−0.838031	+	1.45151i	−0.891538	+	0.452945i	$0.850373\pi$
$728$		0			0
$729$	−323.013	−	653.532i	−0.443091	−	0.896477i
$730$		0			0
$731$	−953.959	+	550.768i	−1.30501	+	0.753445i
$732$		0			0
$733$	372.715			0.508479			0.254239	−	0.967141i	$-0.418175\pi$
$733$	372.715			0.508479			0.254239	+	0.967141i	$0.418175\pi$
$734$		0			0
$735$	−1101.85	+	1284.80i	−1.49911	+	1.74803i
$736$		0			0
$737$	−102.149	+	58.9758i	−0.138601	+	0.0800214i
$738$		0			0
$739$	−481.595	+	834.147i	−0.651684	+	1.12875i	0.331030	+	0.943620i	$0.392604\pi$
$739$	−481.595	+	834.147i	−0.651684	+	1.12875i	−0.982714	+	0.185130i	$0.940729\pi$
$740$		0			0
$741$	−196.993	−	7.44447i	−0.265847	−	0.0100465i
$742$		0			0
$743$	187.081	+	108.011i	0.251792	+	0.145372i	0.620584	−	0.784140i	$-0.286895\pi$
$743$	187.081	+	108.011i	0.251792	+	0.145372i	−0.368793	+	0.929512i	$0.620229\pi$
$744$		0			0
$745$	1126.99	+	1952.00i	1.51274	+	2.62014i
$746$		0			0
$747$	−408.573	+	1051.57i	−0.546952	+	1.40773i
$748$		0			0
$749$		−	1483.51i		−	1.98065i
$750$		0			0
$751$	−580.370	−	1005.23i	−0.772796	−	1.33852i	−0.936025	−	0.351934i	$-0.885524\pi$
$751$	−580.370	−	1005.23i	−0.772796	−	1.33852i	0.163229	−	0.986588i	$-0.447809\pi$
$752$		0			0
$753$	−243.638	−	692.483i	−0.323557	−	0.919632i
$754$		0			0
$755$	1246.94	+	719.921i	1.65158	+	0.953538i
$756$		0			0
$757$	88.5848	−	153.433i	0.117021	−	0.202686i	−0.801565	−	0.597908i	$-0.795999\pi$
$757$	88.5848	−	153.433i	0.117021	−	0.202686i	0.918586	+	0.395222i	$0.129332\pi$
$758$		0			0
$759$	−35.2845	+	12.4142i	−0.0464882	+	0.0163561i
$760$		0			0
$761$			477.550i			0.627529i	0.949501	+	0.313765i	$0.101590\pi$
$761$			477.550i			0.627529i	−0.949501	+	0.313765i	$0.898410\pi$
$762$		0			0
$763$	130.456	−	225.956i	0.170978	−	0.296142i
$764$		0			0
$765$	201.013	+	1303.42i	0.262762	+	1.70381i
$766$		0			0
$767$		−	56.5158i		−	0.0736842i
$768$		0			0
$769$	726.158	+	1257.74i	0.944289	+	1.63556i	0.757169	+	0.653219i	$0.226582\pi$
$769$	726.158	+	1257.74i	0.944289	+	1.63556i	0.187120	+	0.982337i	$0.440085\pi$
$770$		0			0
$771$	493.912	+	1403.83i	0.640612	+	1.82079i
$772$		0			0
$773$	444.990	−	256.915i	0.575667	−	0.332361i	−0.183743	−	0.982974i	$-0.558821\pi$
$773$	444.990	−	256.915i	0.575667	−	0.332361i	0.759409	+	0.650613i	$0.225488\pi$
$774$		0			0
$775$	−108.405	−	187.763i	−0.139877	−	0.242274i
$776$		0			0
$777$	306.653	−	1635.99i	0.394663	−	2.10552i
$778$		0			0
$779$	−869.247	−	1094.66i	−1.11585	−	1.40522i
$780$		0			0
$781$	517.121	−	895.680i	0.662127	−	1.14684i
$782$		0			0
$783$	−31.3337	+	970.414i	−0.0400176	+	1.23935i
$784$		0			0
$785$	−941.561	+	543.611i	−1.19944	+	0.692497i
$786$		0			0
$787$	−385.590			−0.489950			−0.244975	−	0.969529i	$-0.578780\pi$
$787$	−385.590			−0.489950			−0.244975	+	0.969529i	$0.578780\pi$
$788$		0			0
$789$	−110.722	+	129.106i	−0.140332	+	0.163633i
$790$		0			0
$791$			186.286i			0.235507i
$792$		0			0
$793$	−48.9988	+	84.8684i	−0.0617891	+	0.107022i
$794$		0			0
$795$	−195.647	+	1043.77i	−0.246097	+	1.31292i
$796$		0			0
$797$			127.132i			0.159513i	0.996814	+	0.0797563i	$0.0254142\pi$
$797$			127.132i			0.159513i	−0.996814	+	0.0797563i	$0.974586\pi$
$798$		0			0
$799$	980.751			1.22747
$800$		0			0
$801$	−571.067	+	88.0699i	−0.712942	+	0.109950i
$802$		0			0
$803$	−471.880	−	272.440i	−0.587647	−	0.339278i
$804$		0			0
$805$	−108.163			−0.134363
$806$		0			0
$807$	611.837	−	713.428i	0.758162	−	0.884049i
$808$		0			0
$809$			14.0273i			0.0173390i	0.999962	+	0.00866951i	$0.00275962\pi$
$809$			14.0273i			0.0173390i	−0.999962	+	0.00866951i	$0.997240\pi$
$810$		0			0
$811$	233.980	+	405.265i	0.288508	+	0.499710i	0.973454	−	0.228884i	$-0.0735076\pi$
$811$	233.980	+	405.265i	0.288508	+	0.499710i	−0.684946	+	0.728594i	$0.740174\pi$
$812$		0			0
$813$	651.730	+	558.925i	0.801636	+	0.687485i
$814$		0			0
$815$	776.016	+	448.033i	0.952167	+	0.549734i
$816$		0			0
$817$	1001.55	−	795.306i	1.22589	−	0.973446i
$818$		0			0
$819$	−50.2097	−	325.572i	−0.0613061	−	0.397524i
$820$		0			0
$821$	565.065	−	326.241i	0.688265	−	0.397370i	−0.114697	−	0.993401i	$-0.536590\pi$
$821$	565.065	−	326.241i	0.688265	−	0.397370i	0.802962	+	0.596031i	$0.203256\pi$
$822$		0			0
$823$	−190.854	−	330.569i	−0.231900	−	0.401663i	0.726467	−	0.687201i	$-0.241161\pi$
$823$	−190.854	−	330.569i	−0.231900	−	0.401663i	−0.958367	+	0.285538i	$0.907828\pi$
$824$		0			0
$825$	600.173	+	1705.85i	0.727483	+	2.06770i
$826$		0			0
$827$	−229.796	+	132.673i	−0.277867	+	0.160427i	−0.632457	−	0.774595i	$-0.717954\pi$
$827$	−229.796	+	132.673i	−0.277867	+	0.160427i	0.354590	+	0.935022i	$0.384620\pi$
$828$		0			0
$829$	−227.204			−0.274070			−0.137035	−	0.990566i	$-0.543757\pi$
$829$	−227.204			−0.274070			−0.137035	+	0.990566i	$0.543757\pi$
$830$		0			0
$831$	211.869	−	1130.31i	0.254956	−	1.36019i
$832$		0			0
$833$	−892.970	−	515.556i	−1.07199	−	0.618915i
$834$		0			0
$835$	−1416.11			−1.69594
$836$		0			0
$837$	−55.9811	+	90.1148i	−0.0668831	+	0.107664i
$838$		0			0
$839$	1074.87	+	620.576i	1.28113	+	0.739661i	0.977055	−	0.212987i	$-0.0683191\pi$
$839$	1074.87	+	620.576i	1.28113	+	0.739661i	0.304076	+	0.952648i	$0.401652\pi$
$840$		0			0
$841$	226.061	−	391.549i	0.268800	−	0.465576i
$842$		0			0
$843$	267.432	+	760.110i	0.317238	+	0.901673i
$844$		0			0
$845$	1217.78	−	703.087i	1.44116	−	0.832056i
$846$		0			0
$847$	17.6243			0.0208079
$848$		0			0
$849$	−717.424	−	615.264i	−0.845022	−	0.724693i
$850$		0			0
$851$	51.8185	−	29.9174i	0.0608913	−	0.0351556i
$852$		0			0
$853$	−686.303	+	1188.71i	−0.804576	+	1.39357i	0.112001	+	0.993708i	$0.464274\pi$
$853$	−686.303	+	1188.71i	−0.804576	+	1.39357i	−0.916577	+	0.399858i	$0.869059\pi$
$854$		0			0
$855$	−453.277	−	1462.56i	−0.530149	−	1.71059i
$856$		0			0
$857$	353.544	+	204.119i	0.412537	+	0.238178i	0.691879	−	0.722013i	$-0.256783\pi$
$857$	353.544	+	204.119i	0.412537	+	0.238178i	−0.279342	+	0.960192i	$0.590116\pi$
$858$		0			0
$859$	−268.989	−	465.902i	−0.313142	−	0.542378i	0.665899	−	0.746042i	$-0.268048\pi$
$859$	−268.989	−	465.902i	−0.313142	−	0.542378i	−0.979041	+	0.203664i	$0.934715\pi$
$860$		0			0
$861$	1520.61	−	1773.09i	1.76609	−	2.05934i
$862$		0			0
$863$		−	928.867i		−	1.07632i	−0.842842	−	0.538162i	$-0.819119\pi$
$863$		−	928.867i		−	1.07632i	0.842842	−	0.538162i	$-0.180881\pi$
$864$		0			0
$865$	−216.637	−	375.227i	−0.250448	−	0.433788i
$866$		0			0
$867$	59.9687	−	21.0990i	0.0691681	−	0.0243356i
$868$		0			0
$869$	385.643	+	222.651i	0.443777	+	0.256215i
$870$		0			0
$871$	18.6713	−	32.3397i	0.0214367	−	0.0371294i
$872$		0			0
$873$	706.591	−	567.445i	0.809382	−	0.649995i
$874$		0			0
$875$			2860.01i			3.26858i
$876$		0			0
$877$	−451.631	+	782.248i	−0.514973	+	0.891959i	0.484876	+	0.874583i	$0.338865\pi$
$877$	−451.631	+	782.248i	−0.514973	+	0.891959i	−0.999849	+	0.0173762i	$0.994469\pi$
$878$		0			0
$879$	336.295	+	63.0359i	0.382588	+	0.0717132i
$880$		0			0
$881$			1569.09i			1.78103i	0.454955	+	0.890514i	$0.349655\pi$
$881$			1569.09i			1.78103i	−0.454955	+	0.890514i	$0.650345\pi$
$882$		0			0
$883$	−522.375	−	904.780i	−0.591591	−	1.02467i	−0.994018	−	0.109213i	$-0.965167\pi$
$883$	−522.375	−	904.780i	−0.591591	−	1.02467i	0.402427	−	0.915452i	$-0.368167\pi$
$884$		0			0
$885$	414.091	−	145.691i	0.467899	−	0.164622i
$886$		0			0
$887$	1081.73	−	624.537i	1.21954	−	0.704100i	0.254719	−	0.967015i	$-0.418017\pi$
$887$	1081.73	−	624.537i	1.21954	−	0.704100i	0.964819	+	0.262915i	$0.0846838\pi$
$888$		0			0
$889$	205.718	+	356.314i	0.231404	+	0.400804i
$890$		0			0
$891$	597.405	−	652.734i	0.670489	−	0.732586i
$892$		0			0
$893$	−1126.31	+	167.368i	−1.26126	+	0.187422i
$894$		0			0
$895$	−1230.37	+	2131.06i	−1.37471	+	2.38108i
$896$		0			0
$897$	7.70909	−	8.98913i	0.00859431	−	0.0100213i
$898$		0			0
$899$	122.363	−	70.6465i	0.136110	−	0.0785834i
$900$		0			0
$901$	−646.939			−0.718024
$902$		0			0
$903$	1622.26	+	1391.26i	1.79653	+	1.54071i
$904$		0			0
$905$			308.272i			0.340633i
$906$		0			0
$907$	830.449	−	1438.38i	0.915599	−	1.58586i	0.109578	−	0.993978i	$-0.465050\pi$
$907$	830.449	−	1438.38i	0.915599	−	1.58586i	0.806021	−	0.591887i	$-0.201617\pi$
$908$		0			0
$909$	514.194	−	79.2989i	0.565670	−	0.0872376i
$910$		0			0
$911$		−	1216.03i		−	1.33483i	−0.744685	−	0.667416i	$-0.767400\pi$
$911$		−	1216.03i		−	1.33483i	0.744685	−	0.667416i	$-0.232600\pi$
$912$		0			0
$913$	−1369.34			−1.49982
$914$		0			0
$915$	−748.144	−	140.234i	−0.817643	−	0.153261i
$916$		0			0
$917$	−786.224	−	453.927i	−0.857387	−	0.495013i
$918$		0			0
$919$	874.438			0.951511			0.475755	−	0.879578i	$-0.342175\pi$
$919$	874.438			0.951511			0.475755	+	0.879578i	$0.342175\pi$
$920$		0			0
$921$	766.449	+	657.308i	0.832192	+	0.713689i
$922$		0			0
$923$			327.434i			0.354750i
$924$		0			0
$925$	−1446.37	−	2505.19i	−1.56365	−	2.70832i
$926$		0			0
$927$	−350.408	−	136.146i	−0.378002	−	0.146867i
$928$		0			0
$929$	−1005.25	−	580.384i	−1.08208	−	0.624740i	−0.150625	−	0.988591i	$-0.548129\pi$
$929$	−1005.25	−	580.384i	−1.08208	−	0.624740i	−0.931457	+	0.363851i	$0.881462\pi$
$930$		0			0
$931$	1113.48	+	439.683i	1.19600	+	0.472270i
$932$		0			0
$933$	−1454.01	−	272.544i	−1.55843	−	0.292116i
$934$		0			0
$935$	−1386.30	+	800.383i	−1.48268	+	0.856025i
$936$		0			0
$937$	606.946	+	1051.26i	0.647755	+	1.12194i	0.983658	+	0.180048i	$0.0576253\pi$
$937$	606.946	+	1051.26i	0.647755	+	1.12194i	−0.335903	+	0.941897i	$0.609041\pi$
$938$		0			0
$939$	1129.32	−	397.332i	1.20269	−	0.423144i
$940$		0			0
$941$	989.372	−	571.214i	1.05140	−	0.607029i	0.128362	−	0.991727i	$-0.459028\pi$
$941$	989.372	−	571.214i	1.05140	−	0.607029i	0.923042	+	0.384699i	$0.125695\pi$
$942$		0			0
$943$	83.9686			0.0890441
$944$		0			0
$945$	2256.03	−	1207.17i	2.38734	−	1.27743i
$946$		0			0
$947$	−1274.54	−	735.857i	−1.34587	−	0.777040i	−0.358211	−	0.933640i	$-0.616613\pi$
$947$	−1274.54	−	735.857i	−1.34587	−	0.777040i	−0.987662	+	0.156600i	$0.949947\pi$
$948$		0			0
$949$	172.506			0.181776
$950$		0			0
$951$	−603.544	−	1715.43i	−0.634642	−	1.80382i
$952$		0			0
$953$	605.300	+	349.470i	0.635153	+	0.366706i	0.782745	−	0.622343i	$-0.213819\pi$
$953$	605.300	+	349.470i	0.635153	+	0.366706i	−0.147592	+	0.989048i	$0.547152\pi$
$954$		0			0
$955$	47.7070	−	82.6310i	0.0499550	−	0.0865246i
$956$		0			0
$957$	−1111.69	+	391.128i	−1.16164	+	0.408702i
$958$		0			0
$959$	−32.7835	+	18.9275i	−0.0341851	+	0.0197368i
$960$		0			0
$961$	−945.562			−0.983935
$962$		0			0
$963$	−456.887	+	1175.92i	−0.474441	+	1.22110i
$964$		0			0
$965$	−2413.81	+	1393.61i	−2.50136	+	1.44416i
$966$		0			0
$967$	89.3996	−	154.845i	0.0924505	−	0.160129i	−0.816091	−	0.577923i	$-0.803863\pi$
$967$	89.3996	−	154.845i	0.0924505	−	0.160129i	0.908542	+	0.417794i	$0.137197\pi$
$968$		0			0
$969$	824.864	−	435.560i	0.851252	−	0.449494i
$970$		0			0
$971$	180.874	+	104.428i	0.186276	+	0.107547i	0.590238	−	0.807229i	$-0.299034\pi$
$971$	180.874	+	104.428i	0.186276	+	0.107547i	−0.403962	+	0.914776i	$0.632367\pi$
$972$		0			0
$973$	−405.610	−	702.536i	−0.416865	−	0.722031i
$974$		0			0
$975$	−434.584	−	372.700i	−0.445727	−	0.382257i
$976$		0			0
$977$			1922.54i			1.96780i	0.178721	+	0.983900i	$0.442804\pi$
$977$			1922.54i			1.96780i	−0.178721	+	0.983900i	$0.557196\pi$
$978$		0			0
$979$	−350.673	−	607.383i	−0.358195	−	0.620412i
$980$		0			0
$981$	−172.997	+	138.930i	−0.176348	+	0.141620i
$982$		0			0
$983$	−940.400	−	542.940i	−0.956663	−	0.552330i	−0.0615186	−	0.998106i	$-0.519594\pi$
$983$	−940.400	−	542.940i	−0.956663	−	0.552330i	−0.895144	+	0.445776i	$0.852928\pi$
$984$		0			0
$985$	143.697	−	248.891i	0.145885	−	0.252681i
$986$		0			0
$987$	−631.518	−	1794.94i	−0.639835	−	1.81858i
$988$		0			0
$989$			76.8259i			0.0776804i
$990$		0			0
$991$	−659.704	+	1142.64i	−0.665695	+	1.15302i	0.313401	+	0.949621i	$0.398532\pi$
$991$	−659.704	+	1142.64i	−0.665695	+	1.15302i	−0.979096	+	0.203397i	$0.934802\pi$
$992$		0			0
$993$	−52.0216	+	277.534i	−0.0523884	+	0.279491i
$994$		0			0
$995$		−	1687.08i		−	1.69556i
$996$		0			0
$997$	−235.148	−	407.289i	−0.235856	−	0.408515i	0.723665	−	0.690151i	$-0.242456\pi$
$997$	−235.148	−	407.289i	−0.235856	−	0.408515i	−0.959521	+	0.281637i	$0.909123\pi$
$998$		0			0
$999$	−746.920	+	1202.34i	−0.747667	+	1.20355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.3.o.c.125.7	yes	24
3.2	odd	2	inner	228.3.o.c.125.4	✓	24
19.7	even	3	inner	228.3.o.c.197.4	yes	24
57.26	odd	6	inner	228.3.o.c.197.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.3.o.c.125.4	✓	24	3.2	odd	2	inner
228.3.o.c.125.7	yes	24	1.1	even	1	trivial
228.3.o.c.197.4	yes	24	19.7	even	3	inner
228.3.o.c.197.7	yes	24	57.26	odd	6	inner

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:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	228.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.552701 + 2.94865i) q^{3} +(7.75465 + 4.47715i) q^{5} +10.5834 q^{7} +(-8.38904 - 3.25944i) q^{9} +O(q^{10})\)	\(q+(-0.552701 + 2.94865i) q^{3} +(7.75465 + 4.47715i) q^{5} +10.5834 q^{7} +(-8.38904 - 3.25944i) q^{9} -10.9240i q^{11} +(1.72924 + 2.99513i) q^{13} +(-17.4875 + 20.3912i) q^{15} +(-14.1724 - 8.18244i) q^{17} +(17.6721 + 6.97825i) q^{19} +(-5.84944 + 31.2066i) q^{21} +(-0.988444 + 0.570678i) q^{23} +(27.5897 + 47.7868i) q^{25} +(14.2476 - 22.9348i) q^{27} +(-31.1423 + 17.9800i) q^{29} -3.92917 q^{31} +(32.2112 + 6.03773i) q^{33} +(82.0703 + 47.3833i) q^{35} -52.4243 q^{37} +(-9.78733 + 3.44350i) q^{39} +(-63.7127 - 36.7846i) q^{41} +(33.6555 - 58.2931i) q^{43} +(-50.4611 - 62.8348i) q^{45} +(-51.9011 + 29.9651i) q^{47} +63.0077 q^{49} +(31.9602 - 37.2670i) q^{51} +(34.2359 - 19.7661i) q^{53} +(48.9086 - 84.7122i) q^{55} +(-30.3438 + 48.2520i) q^{57} +(-14.1519 - 8.17061i) q^{59} +(14.1677 + 24.5392i) q^{61} +(-88.7843 - 34.4959i) q^{63} +30.9682i q^{65} +(-5.39871 - 9.35085i) q^{67} +(-1.13641 - 3.22999i) q^{69} +(81.9916 + 47.3379i) q^{71} +(24.9395 - 43.1965i) q^{73} +(-156.155 + 54.9406i) q^{75} -115.613i q^{77} +(-20.3817 + 35.3022i) q^{79} +(59.7521 + 54.6872i) q^{81} -125.351i q^{83} +(-73.2680 - 126.904i) q^{85} +(-35.8043 - 101.765i) q^{87} +(55.6006 - 32.1010i) q^{89} +(18.3012 + 31.6986i) q^{91} +(2.17166 - 11.5857i) q^{93} +(105.798 + 133.235i) q^{95} +(-50.3465 + 87.2027i) q^{97} +(-35.6063 + 91.6423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{3} + 8 q^{7} + 16 q^{9}+O(q^{10}) \) 24 * q - 8 * q^3 + 8 * q^7 + 16 * q^9	\( 24 q - 8 q^{3} + 8 q^{7} + 16 q^{9} + 10 q^{13} - 11 q^{15} - 6 q^{19} - 24 q^{21} + 138 q^{25} + 196 q^{27} - 80 q^{31} + 53 q^{33} - 16 q^{37} + 54 q^{39} + 142 q^{43} - 154 q^{45} - 288 q^{49} - 23 q^{51} - 120 q^{55} - 213 q^{57} - 30 q^{61} - 20 q^{63} - 140 q^{67} - 142 q^{69} + 224 q^{73} + 162 q^{75} + 122 q^{79} + 40 q^{81} + 18 q^{85} - 394 q^{87} - 292 q^{91} + 130 q^{93} - 132 q^{97} - 197 q^{99}+O(q^{100}) \) 24 * q - 8 * q^3 + 8 * q^7 + 16 * q^9 + 10 * q^13 - 11 * q^15 - 6 * q^19 - 24 * q^21 + 138 * q^25 + 196 * q^27 - 80 * q^31 + 53 * q^33 - 16 * q^37 + 54 * q^39 + 142 * q^43 - 154 * q^45 - 288 * q^49 - 23 * q^51 - 120 * q^55 - 213 * q^57 - 30 * q^61 - 20 * q^63 - 140 * q^67 - 142 * q^69 + 224 * q^73 + 162 * q^75 + 122 * q^79 + 40 * q^81 + 18 * q^85 - 394 * q^87 - 292 * q^91 + 130 * q^93 - 132 * q^97 - 197 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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