LMFDB - Embedded newform 228.3.o.c.125.4

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			125.4
Character	$\chi$	$=$	228.125
Dual form			228.3.o.c.197.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.27725 + 1.95298i) q^{3} +(-7.75465 - 4.47715i) q^{5} +10.5834 q^{7} +(1.37176 - 8.89485i) q^{9} +O(q^{10})$	\(q+(-2.27725 + 1.95298i) q^{3} +(-7.75465 - 4.47715i) q^{5} +10.5834 q^{7} +(1.37176 - 8.89485i) q^{9} +10.9240i q^{11} +(1.72924 + 2.99513i) q^{13} +(26.4031 - 4.94905i) q^{15} +(14.1724 + 8.18244i) q^{17} +(17.6721 + 6.97825i) q^{19} +(-24.1010 + 20.6691i) q^{21} +(0.988444 - 0.570678i) q^{23} +(27.5897 + 47.7868i) q^{25} +(14.2476 + 22.9348i) q^{27} +(31.1423 - 17.9800i) q^{29} -3.92917 q^{31} +(-21.3344 - 24.8768i) q^{33} +(-82.0703 - 47.3833i) q^{35} -52.4243 q^{37} +(-9.78733 - 3.44350i) q^{39} +(63.7127 + 36.7846i) q^{41} +(33.6555 - 58.2931i) q^{43} +(-50.4611 + 62.8348i) q^{45} +(51.9011 - 29.9651i) q^{47} +63.0077 q^{49} +(-48.2543 + 9.04489i) q^{51} +(-34.2359 + 19.7661i) q^{53} +(48.9086 - 84.7122i) q^{55} +(-53.8723 + 18.6220i) q^{57} +(14.1519 + 8.17061i) q^{59} +(14.1677 + 24.5392i) q^{61} +(14.5179 - 94.1374i) q^{63} -30.9682i q^{65} +(-5.39871 - 9.35085i) q^{67} +(-1.13641 + 3.22999i) q^{69} +(-81.9916 - 47.3379i) q^{71} +(24.9395 - 43.1965i) q^{73} +(-156.155 - 54.9406i) q^{75} +115.613i q^{77} +(-20.3817 + 35.3022i) q^{79} +(-77.2365 - 24.4032i) q^{81} +125.351i q^{83} +(-73.2680 - 126.904i) q^{85} +(-35.8043 + 101.765i) q^{87} +(-55.6006 + 32.1010i) q^{89} +(18.3012 + 31.6986i) q^{91} +(8.94771 - 7.67357i) q^{93} +(-105.798 - 133.235i) q^{95} +(-50.3465 + 87.2027i) q^{97} +(97.1677 + 14.9852i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.27725	+	1.95298i	−0.759084	+	0.650992i
$3$	−2.27725	+	1.95298i	−0.759084	+	0.650992i
$4$		0			0
$5$	−7.75465	−	4.47715i	−1.55093	−	0.895430i	−0.998066	−	0.0621586i	$-0.980202\pi$
$5$	−7.75465	−	4.47715i	−1.55093	−	0.895430i	−0.552864	−	0.833271i	$-0.686465\pi$
$6$		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
$9$	1.37176	−	8.89485i	0.152418	−	0.988316i
$10$		0			0
$11$			10.9240i			0.993095i	0.868010	+	0.496547i	$0.165399\pi$
$11$			10.9240i			0.993095i	−0.868010	+	0.496547i	$0.834601\pi$
$12$		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
$15$	26.4031	−	4.94905i	1.76020	−	0.329937i
$16$		0			0
$17$	14.1724	+	8.18244i	0.833671	+	0.481320i	0.855108	−	0.518450i	$-0.173491\pi$
$17$	14.1724	+	8.18244i	0.833671	+	0.481320i	−0.0214371	+	0.999770i	$0.506824\pi$
$18$		0			0
$19$	17.6721	+	6.97825i	0.930112	+	0.367277i
$19$	17.6721	+	6.97825i	0.930112	+	0.367277i
$20$		0			0
$21$	−24.1010	+	20.6691i	−1.14767	+	0.984242i
$22$		0			0
$23$	0.988444	−	0.570678i	0.0429758	−	0.0248121i	−0.478358	−	0.878165i	$-0.658768\pi$
$23$	0.988444	−	0.570678i	0.0429758	−	0.0248121i	0.521334	+	0.853353i	$0.325435\pi$
$24$		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	0.144635	−	0.989485i	$-0.453799\pi$
$29$	31.1423	−	17.9800i	1.07387	−	0.620000i	0.929237	+	0.369485i	$0.120466\pi$
$30$		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
$33$	−21.3344	−	24.8768i	−0.646497	−	0.753843i
$34$		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	$0.0210577\pi$
$41$	63.7127	+	36.7846i	1.55397	+	0.897184i	0.556156	+	0.831078i	$0.312276\pi$
$42$		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	0.166937	−	0.985968i	$-0.446612\pi$
$47$	51.9011	−	29.9651i	1.10428	−	0.637556i	0.937342	+	0.348412i	$0.113279\pi$
$48$		0			0
$49$	63.0077			1.28587
$50$		0			0
$51$	−48.2543	+	9.04489i	−0.946162	+	0.177351i
$52$		0			0
$53$	−34.2359	+	19.7661i	−0.645960	+	0.372945i	−0.786907	−	0.617072i	$-0.788319\pi$
$53$	−34.2359	+	19.7661i	−0.645960	+	0.372945i	0.140947	+	0.990017i	$0.454985\pi$
$54$		0			0
$55$	48.9086	−	84.7122i	0.889247	−	1.54022i
$56$		0			0
$57$	−53.8723	+	18.6220i	−0.945127	+	0.326702i
$58$		0			0
$59$	14.1519	+	8.17061i	0.239863	+	0.138485i	0.615114	−	0.788438i	$-0.289110\pi$
$59$	14.1519	+	8.17061i	0.239863	+	0.138485i	−0.375251	+	0.926923i	$0.622443\pi$
$60$		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
$63$	14.5179	−	94.1374i	0.230442	−	1.49424i
$64$		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	−0.204757	−	0.978813i	$-0.565640\pi$
$71$	−81.9916	−	47.3379i	−1.15481	−	0.666731i	−0.950055	+	0.312082i	$0.898974\pi$
$72$		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
$81$	−77.2365	−	24.4032i	−0.953538	−	0.301274i
$82$		0			0
$83$			125.351i			1.51025i	0.655582	+	0.755124i	$0.272423\pi$
$83$			125.351i			1.51025i	−0.655582	+	0.755124i	$0.727577\pi$
$84$		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	−0.778706	−	0.627388i	$-0.784124\pi$
$89$	−55.6006	+	32.1010i	−0.624725	+	0.360685i	0.153981	+	0.988074i	$0.450791\pi$
$90$		0			0
$91$	18.3012	+	31.6986i	0.201112	+	0.348336i
$92$		0			0
$93$	8.94771	−	7.67357i	0.0962119	−	0.0825116i
$94$		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
$99$	97.1677	+	14.9852i	0.981492	+	0.151366i
$100$		0			0
$101$	50.0633	−	28.9040i	0.495676	−	0.286179i	−0.231250	−	0.972894i	$-0.574282\pi$
$101$	50.0633	−	28.9040i	0.495676	−	0.286179i	0.726926	+	0.686716i	$0.240948\pi$
$102$		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
$105$	279.433	−	52.3776i	2.66127	−	0.498835i
$106$		0			0
$107$			140.173i			1.31003i	0.755616	+	0.655015i	$0.227338\pi$
$107$			140.173i			1.31003i	−0.755616	+	0.655015i	$0.772662\pi$
$108$		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
$111$	119.383	−	102.384i	1.07553	−	0.922374i
$112$		0			0
$113$		−	17.6018i		−	0.155768i	−0.996962	−	0.0778839i	$-0.975184\pi$
$113$		−	17.6018i		−	0.155768i	0.996962	−	0.0778839i	$-0.0248164\pi$
$114$		0			0
$115$	−10.2200			−0.0888700
$116$		0			0
$117$	29.0133	−	11.2727i	0.247977	−	0.0963479i
$118$		0			0
$119$	149.992	+	86.5978i	1.26043	+	0.727712i
$120$		0			0
$121$	1.66528			0.0137627
$122$		0			0
$123$	−216.929	+	40.6617i	−1.76365	+	0.330583i
$124$		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
$129$	37.2029	+	198.477i	0.288394	+	1.53858i
$130$		0			0
$131$	74.2886	+	42.8906i	0.567089	+	0.327409i	0.755986	−	0.654588i	$-0.227158\pi$
$131$	74.2886	+	42.8906i	0.567089	+	0.327409i	−0.188897	+	0.981997i	$0.560491\pi$
$132$		0			0
$133$	187.031	+	73.8534i	1.40624	+	0.555289i
$134$		0			0
$135$	−7.80233	−	241.640i	−0.0577950	−	1.78993i
$136$		0			0
$137$	3.09764	−	1.78842i	0.0226105	−	0.0130542i	−0.488652	−	0.872479i	$-0.662511\pi$
$137$	3.09764	−	1.78842i	0.0226105	−	0.0130542i	0.511263	+	0.859425i	$0.329178\pi$
$138$		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
$147$	−143.484	+	123.053i	−0.976084	+	0.837092i
$148$		0			0
$149$	−217.996	−	125.860i	−1.46306	−	0.844698i	−0.463908	−	0.885883i	$-0.653553\pi$
$149$	−217.996	−	125.860i	−1.46306	−	0.844698i	−0.999152	+	0.0411851i	$0.986887\pi$
$150$		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
$165$	54.0637	+	288.428i	0.327659	+	1.74805i
$166$		0			0
$167$	136.961	−	79.0743i	0.820124	−	0.473499i	−0.0303353	−	0.999540i	$-0.509657\pi$
$167$	136.961	−	79.0743i	0.820124	−	0.473499i	0.850459	+	0.526041i	$0.176324\pi$
$168$		0			0
$169$	78.5195	−	136.000i	0.464612	−	0.804732i
$170$		0			0
$171$	86.3124	−	147.618i	0.504751	−	0.863265i
$172$		0			0
$173$	41.9046	+	24.1937i	0.242223	+	0.139848i	0.616198	−	0.787591i	$-0.288672\pi$
$173$	41.9046	+	24.1937i	0.242223	+	0.139848i	−0.373975	+	0.927439i	$0.622005\pi$
$174$		0			0
$175$	291.992	+	505.746i	1.66853	+	2.88998i
$176$		0			0
$177$	−48.1845	+	9.03181i	−0.272229	+	0.0510272i
$178$		0			0
$179$		−	274.811i		−	1.53526i	−0.640896	−	0.767628i	$-0.721437\pi$
$179$		−	274.811i		−	1.53526i	0.640896	−	0.767628i	$-0.278563\pi$
$180$		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	$0.00888022\pi$
$191$			10.6557i			0.0557888i	−0.999611	+	0.0278944i	$0.991120\pi$
$192$		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
$195$	60.4803	+	70.5225i	0.310155	+	0.361654i
$196$		0			0
$197$			32.0956i			0.162922i	0.996677	+	0.0814610i	$0.0259586\pi$
$197$			32.0956i			0.162922i	−0.996677	+	0.0814610i	$0.974041\pi$
$198$		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
$207$	−3.72019	−	9.57489i	−0.0179719	−	0.0462555i
$208$		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
$213$	279.165	−	52.3274i	1.31064	−	0.245669i
$214$		0			0
$215$	−521.974	+	301.362i	−2.42778	+	1.40168i
$216$		0			0
$217$	−41.5838			−0.191631
$218$		0			0
$219$	27.5682	+	147.076i	0.125882	+	0.671578i
$220$		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
$225$	462.903	−	179.854i	2.05735	−	0.799353i
$226$		0			0
$227$		−	13.3656i		−	0.0588794i	−0.999567	−	0.0294397i	$-0.990628\pi$
$227$		−	13.3656i		−	0.0588794i	0.999567	−	0.0294397i	$-0.00937231\pi$
$228$		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
$231$	−225.790	−	263.280i	−0.977445	−	1.13974i
$232$		0			0
$233$	−160.193	−	92.4877i	−0.687525	−	0.396943i	0.115159	−	0.993347i	$-0.463262\pi$
$233$	−160.193	−	92.4877i	−0.687525	−	0.396943i	−0.802684	+	0.596404i	$0.796596\pi$
$234$		0			0
$235$	−536.633			−2.28355
$236$		0			0
$237$	−22.5300	−	120.197i	−0.0950633	−	0.507161i
$238$		0			0
$239$		−	37.6449i		−	0.157510i	−0.996894	−	0.0787551i	$-0.974905\pi$
$239$		−	37.6449i		−	0.157510i	0.996894	−	0.0787551i	$-0.0250945\pi$
$240$		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
$243$	223.546	−	95.2689i	0.919943	−	0.392053i
$244$		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
$249$	−244.807	−	285.455i	−0.983160	−	1.14641i
$250$		0			0
$251$	211.914	−	122.349i	0.844280	−	0.487445i	−0.0144366	−	0.999896i	$-0.504595\pi$
$251$	211.914	−	122.349i	0.844280	−	0.487445i	0.858717	+	0.512450i	$0.171262\pi$
$252$		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	$0.748986\pi$
$257$	−429.600	+	248.030i	−1.67160	+	0.965096i	−0.966746	+	0.255740i	$0.917681\pi$
$258$		0			0
$259$	−554.826			−2.14219
$260$		0			0
$261$	−117.210	−	301.670i	−0.449079	−	1.15582i
$262$		0			0
$263$	−49.0983	−	28.3469i	−0.186686	−	0.107783i	0.403744	−	0.914872i	$-0.367708\pi$
$263$	−49.0983	−	28.3469i	−0.186686	−	0.107783i	−0.590430	+	0.807089i	$0.701042\pi$
$264$		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	0.910780	−	0.412892i	$-0.135481\pi$
$269$	271.312	+	156.642i	1.00860	+	0.582313i	0.0978154	+	0.995205i	$0.468815\pi$
$270$		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
$279$	−5.38988	+	34.9493i	−0.0193186	+	0.125266i
$280$		0			0
$281$	−232.610	+	134.297i	−0.827793	+	0.477926i	−0.853096	−	0.521754i	$-0.825278\pi$
$281$	−232.610	+	134.297i	−0.827793	+	0.477926i	0.0253037	+	0.999680i	$0.491945\pi$
$282$		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
$285$	501.134	+	96.7871i	1.75837	+	0.339604i
$286$		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
$291$	−55.6531	−	296.908i	−0.191248	−	1.02030i
$292$		0			0
$293$			114.051i			0.389251i	0.980878	+	0.194625i	$0.0623491\pi$
$293$			114.051i			0.389251i	−0.980878	+	0.194625i	$0.937651\pi$
$294$		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
$309$	−95.1203	+	81.5754i	−0.307833	+	0.263998i
$310$		0			0
$311$		−	493.112i		−	1.58557i	−0.609501	−	0.792785i	$-0.708630\pi$
$311$		−	493.112i		−	1.58557i	0.609501	−	0.792785i	$-0.291370\pi$
$312$		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	$-0.261331\pi$
$317$	524.958	−	303.084i	1.65602	−	0.956102i	0.974525	−	0.224277i	$-0.0720020\pi$
$318$		0			0
$319$	196.414	+	340.200i	0.615719	+	1.06646i
$320$		0			0
$321$	−273.755	−	319.210i	−0.852820	−	0.994424i
$322$		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
$327$	13.6257	+	72.6930i	0.0416689	+	0.222303i
$328$		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
$333$	−71.9137	+	466.306i	−0.215957	+	1.40032i
$334$		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
$339$	34.3758	+	40.0837i	0.101404	+	0.118241i
$340$		0			0
$341$		−	42.9224i		−	0.125872i
$342$		0			0
$343$	148.248			0.432211
$344$		0			0
$345$	23.2736	−	19.9595i	0.0674598	−	0.0578537i
$346$		0			0
$347$	−131.087	−	75.6830i	−0.377772	−	0.218107i	0.299077	−	0.954229i	$-0.403321\pi$
$347$	−131.087	−	75.6830i	−0.377772	−	0.218107i	−0.676848	+	0.736123i	$0.736655\pi$
$348$		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
$351$	−44.0553	+	82.3331i	−0.125514	+	0.234567i
$352$		0			0
$353$		−	354.875i		−	1.00531i	−0.864487	−	0.502656i	$-0.832356\pi$
$353$		−	354.875i		−	1.00531i	0.864487	−	0.502656i	$-0.167644\pi$
$354$		0			0
$355$	423.878	+	734.178i	1.19402	+	2.06811i
$356$		0			0
$357$	−510.693	+	95.7254i	−1.43051	+	0.268138i
$358$		0			0
$359$	35.7018	+	20.6125i	0.0994480	+	0.0574163i	0.548899	−	0.835889i	$-0.315047\pi$
$359$	35.7018	+	20.6125i	0.0994480	+	0.0574163i	−0.449451	+	0.893305i	$0.648380\pi$
$360$		0			0
$361$	263.608	+	246.641i	0.730216	+	0.683216i
$362$		0			0
$363$	−3.79227	+	3.25226i	−0.0104470	+	0.00895938i
$364$		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
$375$	527.765	+	615.396i	1.40737	+	1.64106i
$376$		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	0.0897438	−	0.995965i	$-0.471395\pi$
$383$	−278.792	−	160.960i	−0.727915	−	0.420262i	−0.817659	+	0.575703i	$0.804729\pi$
$384$		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	0.128073	−	0.991765i	$-0.459121\pi$
$389$	408.840	−	236.044i	1.05100	−	0.606797i	0.922930	+	0.384968i	$0.125788\pi$
$390$		0			0
$391$	18.6782			0.0477702
$392$		0			0
$393$	−252.938	+	47.4113i	−0.643609	+	0.120640i
$394$		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
$399$	−570.150	+	197.084i	−1.42895	+	0.493944i
$400$		0			0
$401$	−250.935	−	144.877i	−0.625773	−	0.361290i	0.153340	−	0.988173i	$-0.450997\pi$
$401$	−250.935	−	144.877i	−0.625773	−	0.361290i	−0.779113	+	0.626883i	$0.784330\pi$
$402$		0			0
$403$	−6.79447	−	11.7684i	−0.0168597	−	0.0292019i
$404$		0			0
$405$	489.686	+	535.038i	1.20910	+	1.32108i
$406$		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	$0.151530\pi$
$419$			384.029i			0.916536i	−0.888814	+	0.458268i	$0.848470\pi$
$420$		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
$423$	−195.339	−	502.757i	−0.461795	−	1.18855i
$424$		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	−0.602711	−	0.797960i	$-0.705913\pi$
$431$	−91.8083	+	53.0055i	−0.213012	+	0.122983i	0.389698	+	0.920943i	$0.372579\pi$
$432$		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
$435$	733.268	−	628.852i	1.68567	−	1.44564i
$436$		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
$441$	86.4315	−	560.443i	0.195990	−	1.27085i
$442$		0			0
$443$	−131.335	+	75.8264i	−0.296468	+	0.171166i	−0.640855	−	0.767662i	$-0.721420\pi$
$443$	−131.335	+	75.8264i	−0.296468	+	0.171166i	0.344387	+	0.938828i	$0.388087\pi$
$444$		0			0
$445$	574.884			1.29187
$446$		0			0
$447$	742.234	−	139.126i	1.66048	−	0.311244i
$448$		0			0
$449$			434.271i			0.967195i	0.875290	+	0.483598i	$0.160670\pi$
$449$			434.271i			0.967195i	−0.875290	+	0.483598i	$0.839330\pi$
$450$		0			0
$451$	−401.836	+	696.000i	−0.890989	+	1.54324i
$452$		0			0
$453$	−366.180	+	314.037i	−0.808345	+	0.693238i
$454$		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
$459$	14.2595	+	441.622i	0.0310665	+	0.962139i
$460$		0			0
$461$	−305.614	−	176.446i	−0.662936	−	0.382746i	0.130459	−	0.991454i	$-0.458355\pi$
$461$	−305.614	−	176.446i	−0.662936	−	0.382746i	−0.793395	+	0.608707i	$0.791688\pi$
$462$		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
$465$	−103.742	+	19.4457i	−0.223101	+	0.0418186i
$466$		0			0
$467$			161.913i			0.346709i	0.984860	+	0.173354i	$0.0554606\pi$
$467$			161.913i			0.346709i	−0.984860	+	0.173354i	$0.944539\pi$
$468$		0			0
$469$	−57.1366	−	98.9634i	−0.121826	−	0.211009i
$470$		0			0
$471$	−67.1084	−	358.021i	−0.142481	−	0.760130i
$472$		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
$477$	128.853	+	331.637i	0.270132	+	0.695256i
$478$		0			0
$479$	−184.208	+	106.352i	−0.384567	+	0.222030i	−0.679803	−	0.733394i	$-0.737935\pi$
$479$	−184.208	+	106.352i	−0.384567	+	0.222030i	0.295237	+	0.955424i	$0.404602\pi$
$480$		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
$489$	−227.887	+	195.437i	−0.466027	+	0.399666i
$490$		0			0
$491$	−432.733	−	249.839i	−0.881330	−	0.508836i	−0.0102334	−	0.999948i	$-0.503257\pi$
$491$	−432.733	−	249.839i	−0.881330	−	0.508836i	−0.871097	+	0.491111i	$0.836591\pi$
$492$		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	−0.539145	−	0.842213i	$-0.681253\pi$
$503$	−39.9078	+	23.0408i	−0.0793396	+	0.0458068i	0.459805	+	0.888020i	$0.347919\pi$
$504$		0			0
$505$	−517.631			−1.02501
$506$		0			0
$507$	86.7956	+	463.052i	0.171194	+	0.913318i
$508$		0			0
$509$	−454.053	+	262.148i	−0.892050	+	0.515025i	−0.874613	−	0.484823i	$-0.838884\pi$
$509$	−454.053	+	262.148i	−0.892050	+	0.515025i	−0.0174376	+	0.999848i	$0.505551\pi$
$510$		0			0
$511$	263.944	−	457.164i	0.516525	−	0.894647i
$512$		0			0
$513$	91.7399	+	504.730i	0.178830	+	0.983880i
$514$		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
$519$	−142.677	+	26.7437i	−0.274908	+	0.0515293i
$520$		0			0
$521$			222.969i			0.427963i	0.976838	+	0.213982i	$0.0686433\pi$
$521$			222.969i			0.427963i	−0.976838	+	0.213982i	$0.931357\pi$
$522$		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
$537$	536.699	+	625.814i	0.999440	+	1.16539i
$538$		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
$549$	237.707	−	92.3578i	0.432983	−	0.168229i
$550$		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
$555$	−1384.16	+	259.451i	−2.49399	+	0.467479i
$556$		0			0
$557$	147.833	−	85.3514i	0.265409	−	0.153234i	−0.361390	−	0.932415i	$-0.617698\pi$
$557$	147.833	−	85.3514i	0.265409	−	0.153234i	0.626800	+	0.779181i	$0.284364\pi$
$558$		0			0
$559$	232.794			0.416447
$560$		0			0
$561$	−98.8068	−	527.132i	−0.176126	−	0.939629i
$562$		0			0
$563$		−	608.088i		−	1.08009i	−0.841637	−	0.540043i	$-0.818408\pi$
$563$		−	608.088i		−	1.08009i	0.841637	−	0.540043i	$-0.181592\pi$
$564$		0			0
$565$	−78.8058	+	136.496i	−0.139479	+	0.241585i
$566$		0			0
$567$	−817.423	−	258.268i	−1.44166	−	0.455500i
$568$		0			0
$569$		−	907.829i		−	1.59548i	−0.603001	−	0.797741i	$-0.706028\pi$
$569$		−	907.829i		−	1.59548i	0.603001	−	0.797741i	$-0.293972\pi$
$570$		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
$573$	−20.8103	−	24.2656i	−0.0363181	−	0.0423484i
$574$		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
$579$	−172.041	−	917.833i	−0.297134	−	1.58520i
$580$		0			0
$581$			1326.63i			2.28336i
$582$		0			0
$583$	−215.926	−	373.994i	−0.370370	−	0.641499i
$584$		0			0
$585$	−275.458	−	42.4811i	−0.470868	−	0.0726172i
$586$		0			0
$587$	602.214	+	347.688i	1.02592	+	0.592314i	0.915813	−	0.401606i	$-0.131548\pi$
$587$	602.214	+	347.688i	1.02592	+	0.592314i	0.110106	+	0.993920i	$0.464881\pi$
$588$		0			0
$589$	−69.4367	−	27.4187i	−0.117889	−	0.0465513i
$590$		0			0
$591$	−62.6821	−	73.0899i	−0.106061	−	0.123672i
$592$		0			0
$593$	438.550	−	253.197i	0.739544	−	0.426976i	−0.0823594	−	0.996603i	$-0.526246\pi$
$593$	438.550	−	253.197i	0.739544	−	0.426976i	0.821904	+	0.569627i	$0.192912\pi$
$594$		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	$-0.224329\pi$
$599$	1020.52	−	589.198i	1.70371	−	0.983637i	0.941936	−	0.335792i	$-0.109004\pi$
$600$		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
$603$	−90.5801	+	35.1936i	−0.150216	+	0.0583642i
$604$		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	−0.604401	−	0.796680i	$-0.706588\pi$
$617$	−133.677	+	77.1786i	−0.216657	+	0.125087i	0.387744	+	0.921767i	$0.373254\pi$
$618$		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
$621$	27.1713	+	14.5390i	0.0437542	+	0.0234122i
$622$		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
$627$	−203.428	−	588.503i	−0.324446	−	0.938601i
$628$		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
$633$	78.5999	+	419.328i	0.124170	+	0.662446i
$634$		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	0.833865	−	0.551968i	$-0.186123\pi$
$641$	495.352	+	285.992i	0.772780	+	0.446165i	−0.0610854	+	0.998133i	$0.519456\pi$
$642$		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	$0.0358340\pi$
$647$			145.366i			0.224676i	−0.993670	+	0.112338i	$0.964166\pi$
$648$		0			0
$649$	−89.2561	+	154.596i	−0.137529	+	0.238207i
$650$		0			0
$651$	94.6969	−	81.2123i	0.145464	−	0.124750i
$652$		0			0
$653$		−	870.468i		−	1.33303i	−0.745492	−	0.666515i	$-0.767785\pi$
$653$		−	870.468i		−	1.33303i	0.745492	−	0.666515i	$-0.232215\pi$
$654$		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	−0.910903	−	0.412620i	$-0.864614\pi$
$659$	−664.941	+	383.904i	−1.00902	+	0.582555i	−0.0981122	+	0.995175i	$0.531280\pi$
$660$		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
$663$	−110.534	−	128.887i	−0.166718	−	0.194400i
$664$		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
$669$	−142.073	−	757.958i	−0.212367	−	1.13297i
$670$		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
$675$	−702.896	+	1313.61i	−1.04133	+	1.94609i
$676$		0			0
$677$			499.075i			0.737186i	0.929591	+	0.368593i	$0.120160\pi$
$677$			499.075i			0.737186i	−0.929591	+	0.368593i	$0.879840\pi$
$678$		0			0
$679$	−532.835	+	922.898i	−0.784735	+	1.35920i
$680$		0			0
$681$	26.1028	+	30.4369i	0.0383301	+	0.0446945i
$682$		0			0
$683$			613.170i			0.897760i	0.893592	+	0.448880i	$0.148177\pi$
$683$			613.170i			0.897760i	−0.893592	+	0.448880i	$0.851823\pi$
$684$		0			0
$685$	−32.0282			−0.0467564
$686$		0			0
$687$	−194.845	+	167.099i	−0.283617	+	0.243231i
$688$		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
$693$	1028.36	+	158.594i	1.48393	+	0.228851i
$694$		0			0
$695$			686.351i			0.987555i
$696$		0			0
$697$	601.975	+	1042.65i	0.863665	+	1.49591i
$698$		0			0
$699$	545.427	−	102.236i	0.780297	−	0.146261i
$700$		0			0
$701$	−711.997	−	411.072i	−1.01569	−	0.586408i	−0.102836	−	0.994698i	$-0.532792\pi$
$701$	−711.997	−	411.072i	−1.01569	−	0.586408i	−0.912852	+	0.408291i	$0.866125\pi$
$702$		0			0
$703$	−926.449	−	365.830i	−1.31785	−	0.520384i
$704$		0			0
$705$	1222.05	−	1048.03i	1.73340	−	1.48657i
$706$		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
$717$	73.5197	+	85.7270i	0.102538	+	0.119563i
$718$		0			0
$719$	−24.2365	−	13.9929i	−0.0337086	−	0.0194617i	0.483051	−	0.875592i	$-0.339529\pi$
$719$	−24.2365	−	13.9929i	−0.0337086	−	0.0194617i	−0.516760	+	0.856131i	$0.672862\pi$
$720$		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
$735$	1663.60	−	311.828i	2.26340	−	0.424256i
$736$		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
$741$	−148.933	−	129.153i	−0.200990	−	0.174295i
$742$		0			0
$743$	−187.081	−	108.011i	−0.251792	−	0.145372i	0.368793	−	0.929512i	$-0.379771\pi$
$743$	−187.081	−	108.011i	−0.251792	−	0.145372i	−0.620584	+	0.784140i	$0.713105\pi$
$744$		0			0
$745$	1126.99	+	1952.00i	1.51274	+	2.62014i
$746$		0			0
$747$	1114.97	+	171.951i	1.49260	+	0.230189i
$748$		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	$-0.898410\pi$
$761$		−	477.550i		−	0.627529i	0.949501	−	0.313765i	$-0.101590\pi$
$762$		0			0
$763$	130.456	−	225.956i	0.170978	−	0.296142i
$764$		0			0
$765$	−1229.30	+	477.626i	−1.60692	+	0.624347i
$766$		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	−0.759409	−	0.650613i	$-0.774512\pi$
$773$	−444.990	+	256.915i	−0.575667	+	0.332361i	0.183743	+	0.982974i	$0.441179\pi$
$774$		0			0
$775$	−108.405	−	187.763i	−0.139877	−	0.242274i
$776$		0			0
$777$	1263.48	−	1083.56i	1.62610	−	1.39455i
$778$		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
$783$	856.070	+	458.071i	1.09332	+	0.585021i
$784$		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
$789$	167.170	−	31.3347i	0.211876	−	0.0397145i
$790$		0			0
$791$		−	186.286i		−	0.235507i
$792$		0			0
$793$	−48.9988	+	84.8684i	−0.0617891	+	0.107022i
$794$		0			0
$795$	−806.109	+	691.320i	−1.01397	+	0.869586i
$796$		0			0
$797$		−	127.132i		−	0.159513i	−0.996814	−	0.0797563i	$-0.974586\pi$
$797$		−	127.132i		−	0.159513i	0.996814	−	0.0797563i	$-0.0254142\pi$
$798$		0			0
$799$	980.751			1.22747
$800$		0			0
$801$	209.263	+	538.593i	0.261252	+	0.672401i
$802$		0			0
$803$	471.880	+	272.440i	0.587647	+	0.339278i
$804$		0			0
$805$	−108.163			−0.134363
$806$		0			0
$807$	−923.765	+	173.153i	−1.14469	+	0.214563i
$808$		0			0
$809$		−	14.0273i		−	0.0173390i	−0.999962	−	0.00866951i	$-0.997240\pi$
$809$		−	14.0273i		−	0.0173390i	0.999962	−	0.00866951i	$-0.00275962\pi$
$810$		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
$813$	158.178	+	843.877i	0.194561	+	1.03798i
$814$		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
$819$	307.059	−	119.303i	0.374919	−	0.145669i
$820$		0			0
$821$	−565.065	+	326.241i	−0.688265	+	0.397370i	−0.802962	−	0.596031i	$-0.796744\pi$
$821$	−565.065	+	326.241i	−0.688265	+	0.397370i	0.114697	+	0.993401i	$0.463410\pi$
$822$		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	−0.354590	−	0.935022i	$-0.615380\pi$
$827$	229.796	−	132.673i	0.277867	−	0.160427i	0.632457	+	0.774595i	$0.282046\pi$
$828$		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
$831$	872.946	−	748.640i	1.05048	−	0.900891i
$832$		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	−0.304076	−	0.952648i	$-0.598348\pi$
$839$	−1074.87	−	620.576i	−1.28113	−	0.739661i	−0.977055	+	0.212987i	$0.931681\pi$
$840$		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
$849$	−174.122	−	928.939i	−0.205091	−	1.09416i
$850$		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
$855$	−1330.23	+	758.295i	−1.55583	+	0.886895i
$856$		0			0
$857$	−353.544	−	204.119i	−0.412537	−	0.238178i	0.279342	−	0.960192i	$-0.409884\pi$
$857$	−353.544	−	204.119i	−0.412537	−	0.238178i	−0.691879	+	0.722013i	$0.743217\pi$
$858$		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
$861$	−2295.84	+	430.338i	−2.66648	+	0.499812i
$862$		0			0
$863$			928.867i			1.07632i	0.842842	+	0.538162i	$0.180881\pi$
$863$			928.867i			1.07632i	−0.842842	+	0.538162i	$0.819119\pi$
$864$		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
$879$	−222.738	−	259.722i	−0.253399	−	0.295474i
$880$		0			0
$881$		−	1569.09i		−	1.78103i	−0.454955	−	0.890514i	$-0.650345\pi$
$881$		−	1569.09i		−	1.78103i	0.454955	−	0.890514i	$-0.349655\pi$
$882$		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	−0.964819	−	0.262915i	$-0.915316\pi$
$887$	−1081.73	+	624.537i	−1.21954	+	0.704100i	−0.254719	+	0.967015i	$0.581983\pi$
$888$		0			0
$889$	205.718	+	356.314i	0.231404	+	0.400804i
$890$		0			0
$891$	266.582	−	843.735i	0.299194	−	0.946953i
$892$		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
$897$	−11.6394	+	2.18171i	−0.0129759	+	0.00243223i
$898$		0			0
$899$	−122.363	+	70.6465i	−0.136110	+	0.0785834i
$900$		0			0
$901$	−646.939			−0.718024
$902$		0			0
$903$	393.732	+	2100.55i	0.436026	+	2.32619i
$904$		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
$909$	−188.422	−	484.955i	−0.207285	−	0.533503i
$910$		0			0
$911$			1216.03i			1.33483i	0.744685	+	0.667416i	$0.232600\pi$
$911$			1216.03i			1.33483i	−0.744685	+	0.667416i	$0.767400\pi$
$912$		0			0
$913$	−1369.34			−1.49982
$914$		0			0
$915$	495.518	+	577.794i	0.541549	+	0.631469i
$916$		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
$921$	186.021	+	992.418i	0.201977	+	1.07754i
$922$		0			0
$923$		−	327.434i		−	0.354750i
$924$		0			0
$925$	−1446.37	−	2505.19i	−1.56365	−	2.70832i
$926$		0			0
$927$	57.2981	−	371.535i	0.0618103	−	0.400793i
$928$		0			0
$929$	1005.25	+	580.384i	1.08208	+	0.624740i	0.931457	−	0.363851i	$-0.118538\pi$
$929$	1005.25	+	580.384i	1.08208	+	0.624740i	0.150625	+	0.988591i	$0.451871\pi$
$930$		0			0
$931$	1113.48	+	439.683i	1.19600	+	0.472270i
$932$		0			0
$933$	963.037	+	1122.94i	1.03219	+	1.20358i
$934$		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	−0.923042	−	0.384699i	$-0.874305\pi$
$941$	−989.372	+	571.214i	−1.05140	+	0.607029i	−0.128362	+	0.991727i	$0.540972\pi$
$942$		0			0
$943$	83.9686			0.0890441
$944$		0			0
$945$	−82.5749	−	2557.37i	−0.0873808	−	2.70621i
$946$		0			0
$947$	1274.54	+	735.857i	1.34587	+	0.777040i	0.987662	−	0.156600i	$-0.0500534\pi$
$947$	1274.54	+	735.857i	1.34587	+	0.777040i	0.358211	+	0.933640i	$0.383387\pi$
$948$		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	0.147592	−	0.989048i	$-0.452848\pi$
$953$	−605.300	−	349.470i	−0.635153	−	0.366706i	−0.782745	+	0.622343i	$0.786181\pi$
$954$		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
$963$	1246.82	+	192.284i	1.29472	+	0.199672i
$964$		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
$969$	−915.873	−	176.888i	−0.945173	−	0.182547i
$970$		0			0
$971$	−180.874	−	104.428i	−0.186276	−	0.107547i	0.403962	−	0.914776i	$-0.367633\pi$
$971$	−180.874	−	104.428i	−0.186276	−	0.107547i	−0.590238	+	0.807229i	$0.700966\pi$
$972$		0			0
$973$	−405.610	−	702.536i	−0.416865	−	0.722031i
$974$		0			0
$975$	−105.476	−	562.711i	−0.108180	−	0.577140i
$976$		0			0
$977$		−	1922.54i		−	1.96780i	−0.178721	−	0.983900i	$-0.557196\pi$
$977$		−	1922.54i		−	1.96780i	0.178721	−	0.983900i	$-0.442804\pi$
$978$		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	0.895144	−	0.445776i	$-0.147072\pi$
$983$	940.400	+	542.940i	0.956663	+	0.552330i	0.0615186	+	0.998106i	$0.480406\pi$
$984$		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
$993$	−214.341	+	183.819i	−0.215852	+	0.185115i
$994$		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.125.4	✓	24
3.2	odd	2	inner	228.3.o.c.125.7	yes	24
19.7	even	3	inner	228.3.o.c.197.7	yes	24
57.26	odd	6	inner	228.3.o.c.197.4	yes	24

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

\(f(q)\)	\(=\)	\(q+(-2.27725 + 1.95298i) q^{3} +(-7.75465 - 4.47715i) q^{5} +10.5834 q^{7} +(1.37176 - 8.89485i) q^{9} +O(q^{10})\)	\(q+(-2.27725 + 1.95298i) q^{3} +(-7.75465 - 4.47715i) q^{5} +10.5834 q^{7} +(1.37176 - 8.89485i) q^{9} +10.9240i q^{11} +(1.72924 + 2.99513i) q^{13} +(26.4031 - 4.94905i) q^{15} +(14.1724 + 8.18244i) q^{17} +(17.6721 + 6.97825i) q^{19} +(-24.1010 + 20.6691i) q^{21} +(0.988444 - 0.570678i) q^{23} +(27.5897 + 47.7868i) q^{25} +(14.2476 + 22.9348i) q^{27} +(31.1423 - 17.9800i) q^{29} -3.92917 q^{31} +(-21.3344 - 24.8768i) q^{33} +(-82.0703 - 47.3833i) q^{35} -52.4243 q^{37} +(-9.78733 - 3.44350i) q^{39} +(63.7127 + 36.7846i) q^{41} +(33.6555 - 58.2931i) q^{43} +(-50.4611 + 62.8348i) q^{45} +(51.9011 - 29.9651i) q^{47} +63.0077 q^{49} +(-48.2543 + 9.04489i) q^{51} +(-34.2359 + 19.7661i) q^{53} +(48.9086 - 84.7122i) q^{55} +(-53.8723 + 18.6220i) q^{57} +(14.1519 + 8.17061i) q^{59} +(14.1677 + 24.5392i) q^{61} +(14.5179 - 94.1374i) q^{63} -30.9682i q^{65} +(-5.39871 - 9.35085i) q^{67} +(-1.13641 + 3.22999i) q^{69} +(-81.9916 - 47.3379i) q^{71} +(24.9395 - 43.1965i) q^{73} +(-156.155 - 54.9406i) q^{75} +115.613i q^{77} +(-20.3817 + 35.3022i) q^{79} +(-77.2365 - 24.4032i) q^{81} +125.351i q^{83} +(-73.2680 - 126.904i) q^{85} +(-35.8043 + 101.765i) q^{87} +(-55.6006 + 32.1010i) q^{89} +(18.3012 + 31.6986i) q^{91} +(8.94771 - 7.67357i) q^{93} +(-105.798 - 133.235i) q^{95} +(-50.3465 + 87.2027i) q^{97} +(97.1677 + 14.9852i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{3} + 8 q^{7} + 16 q^{9}+O(q^{10}) \) 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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