LMFDB - Embedded newform 230.3.c.a.229.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,3,Mod(229,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("230.229");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.c (of order $2$, degree $1$, 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:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.12
Character	$\chi$	$=$	230.229
Dual form			230.3.c.a.229.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +5.56886i q^{3} -2.00000 q^{4} +(0.637273 - 4.95922i) q^{5} +7.87556 q^{6} -10.0249 q^{7} +2.82843i q^{8} -22.0122 q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +5.56886i q^{3} -2.00000 q^{4} +(0.637273 - 4.95922i) q^{5} +7.87556 q^{6} -10.0249 q^{7} +2.82843i q^{8} -22.0122 q^{9} +(-7.01340 - 0.901240i) q^{10} -9.80810i q^{11} -11.1377i q^{12} -14.3185i q^{13} +14.1774i q^{14} +(27.6172 + 3.54888i) q^{15} +4.00000 q^{16} +17.3824 q^{17} +31.1300i q^{18} -8.38799i q^{19} +(-1.27455 + 9.91844i) q^{20} -55.8274i q^{21} -13.8708 q^{22} +(-14.5930 + 17.7777i) q^{23} -15.7511 q^{24} +(-24.1878 - 6.32076i) q^{25} -20.2494 q^{26} -72.4631i q^{27} +20.0498 q^{28} -26.9909 q^{29} +(5.01888 - 39.0566i) q^{30} +4.24200 q^{31} -5.65685i q^{32} +54.6200 q^{33} -24.5825i q^{34} +(-6.38862 + 49.7158i) q^{35} +44.0244 q^{36} -73.2769 q^{37} -11.8624 q^{38} +79.7377 q^{39} +(14.0268 + 1.80248i) q^{40} -19.8591 q^{41} -78.9519 q^{42} +18.1666 q^{43} +19.6162i q^{44} +(-14.0278 + 109.163i) q^{45} +(25.1414 + 20.6376i) q^{46} +10.2217i q^{47} +22.2754i q^{48} +51.4991 q^{49} +(-8.93890 + 34.2067i) q^{50} +96.8003i q^{51} +28.6370i q^{52} -90.6584 q^{53} -102.478 q^{54} +(-48.6406 - 6.25044i) q^{55} -28.3548i q^{56} +46.7115 q^{57} +38.1708i q^{58} +92.9752 q^{59} +(-55.2344 - 7.09777i) q^{60} -36.3479i q^{61} -5.99909i q^{62} +220.671 q^{63} -8.00000 q^{64} +(-71.0086 - 9.12480i) q^{65} -77.2443i q^{66} +41.4414 q^{67} -34.7648 q^{68} +(-99.0013 - 81.2661i) q^{69} +(70.3088 + 9.03487i) q^{70} -22.7302 q^{71} -62.2599i q^{72} +45.3166i q^{73} +103.629i q^{74} +(35.1994 - 134.698i) q^{75} +16.7760i q^{76} +98.3255i q^{77} -112.766i q^{78} +65.6145i q^{79} +(2.54909 - 19.8369i) q^{80} +205.427 q^{81} +28.0850i q^{82} +4.65260 q^{83} +111.655i q^{84} +(11.0774 - 86.2033i) q^{85} -25.6915i q^{86} -150.308i q^{87} +27.7415 q^{88} -121.117i q^{89} +(154.380 + 19.8383i) q^{90} +143.542i q^{91} +(29.1859 - 35.5553i) q^{92} +23.6231i q^{93} +14.4556 q^{94} +(-41.5979 - 5.34544i) q^{95} +31.5022 q^{96} +99.8370 q^{97} -72.8308i q^{98} +215.898i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9}+O(q^{10}) $ 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9	$ 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9} + 96 q^{16} - 16 q^{24} - 48 q^{25} - 32 q^{26} + 100 q^{29} - 124 q^{31} - 28 q^{35} + 192 q^{36} + 192 q^{39} - 116 q^{41} + 148 q^{46} - 76 q^{49} - 144 q^{50} - 16 q^{54} - 224 q^{55} + 84 q^{59} - 192 q^{64} - 340 q^{69} + 328 q^{70} + 196 q^{71} - 496 q^{75} + 1360 q^{81} + 316 q^{85} - 376 q^{94} - 368 q^{95} + 32 q^{96}+O(q^{100}) $ 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9 + 96 * q^16 - 16 * q^24 - 48 * q^25 - 32 * q^26 + 100 * q^29 - 124 * q^31 - 28 * q^35 + 192 * q^36 + 192 * q^39 - 116 * q^41 + 148 * q^46 - 76 * q^49 - 144 * q^50 - 16 * q^54 - 224 * q^55 + 84 * q^59 - 192 * q^64 - 340 * q^69 + 328 * q^70 + 196 * q^71 - 496 * q^75 + 1360 * q^81 + 316 * q^85 - 376 * q^94 - 368 * q^95 + 32 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$			5.56886i			1.85629i	0.372223	+	0.928143i	$0.378596\pi$
$3$			5.56886i			1.85629i	−0.372223	+	0.928143i	$0.621404\pi$
$4$	−2.00000			−0.500000
$5$	0.637273	−	4.95922i	0.127455	−	0.991844i
$5$	0.637273	−	4.95922i	0.127455	−	0.991844i
$6$	7.87556			1.31259
$7$	−10.0249			−1.43213			−0.716066	−	0.698033i	$-0.754059\pi$
$7$	−10.0249			−1.43213			−0.716066	+	0.698033i	$0.754059\pi$
$8$			2.82843i			0.353553i
$9$	−22.0122			−2.44580
$10$	−7.01340	−	0.901240i	−0.701340	−	0.0901240i
$11$		−	9.80810i		−	0.891646i	−0.895121	−	0.445823i	$-0.852911\pi$
$11$		−	9.80810i		−	0.891646i	0.895121	−	0.445823i	$-0.147089\pi$
$12$		−	11.1377i		−	0.928143i
$13$		−	14.3185i		−	1.10142i	−0.834696	−	0.550712i	$-0.814356\pi$
$13$		−	14.3185i		−	1.10142i	0.834696	−	0.550712i	$-0.185644\pi$
$14$			14.1774i			1.01267i
$15$	27.6172	+	3.54888i	1.84115	+	0.236592i
$16$	4.00000			0.250000
$17$	17.3824			1.02250			0.511248	−	0.859433i	$-0.329183\pi$
$17$	17.3824			1.02250			0.511248	+	0.859433i	$0.329183\pi$
$18$			31.1300i			1.72944i
$19$		−	8.38799i		−	0.441473i	−0.975333	−	0.220737i	$-0.929154\pi$
$19$		−	8.38799i		−	0.441473i	0.975333	−	0.220737i	$-0.0708461\pi$
$20$	−1.27455	+	9.91844i	−0.0637273	+	0.495922i
$21$		−	55.8274i		−	2.65845i
$22$	−13.8708			−0.630489
$23$	−14.5930	+	17.7777i	−0.634477	+	0.772942i
$23$	−14.5930	+	17.7777i	−0.634477	+	0.772942i
$24$	−15.7511			−0.656296
$25$	−24.1878	−	6.32076i	−0.967511	−	0.252830i
$26$	−20.2494			−0.778824
$27$		−	72.4631i		−	2.68382i
$28$	20.0498			0.716066
$29$	−26.9909			−0.930719			−0.465360	−	0.885122i	$-0.654075\pi$
$29$	−26.9909			−0.930719			−0.465360	+	0.885122i	$0.654075\pi$
$30$	5.01888	−	39.0566i	0.167296	−	1.30189i
$31$	4.24200			0.136839			0.0684194	−	0.997657i	$-0.478204\pi$
$31$	4.24200			0.136839			0.0684194	+	0.997657i	$0.478204\pi$
$32$		−	5.65685i		−	0.176777i
$33$	54.6200			1.65515
$34$		−	24.5825i		−	0.723013i
$35$	−6.38862	+	49.7158i	−0.182532	+	1.42045i
$36$	44.0244			1.22290
$37$	−73.2769			−1.98046			−0.990229	−	0.139454i	$-0.955465\pi$
$37$	−73.2769			−1.98046			−0.990229	+	0.139454i	$0.955465\pi$
$38$	−11.8624			−0.312169
$39$	79.7377			2.04456
$40$	14.0268	+	1.80248i	0.350670	+	0.0450620i
$41$	−19.8591			−0.484369			−0.242184	−	0.970230i	$-0.577864\pi$
$41$	−19.8591			−0.484369			−0.242184	+	0.970230i	$0.577864\pi$
$42$	−78.9519			−1.87981
$43$	18.1666			0.422480			0.211240	−	0.977434i	$-0.432250\pi$
$43$	18.1666			0.422480			0.211240	+	0.977434i	$0.432250\pi$
$44$			19.6162i			0.445823i
$45$	−14.0278	+	109.163i	−0.311729	+	2.42585i
$46$	25.1414	+	20.6376i	0.546553	+	0.448643i
$47$			10.2217i			0.217482i	0.994070	+	0.108741i	$0.0346820\pi$
$47$			10.2217i			0.217482i	−0.994070	+	0.108741i	$0.965318\pi$
$48$			22.2754i			0.464072i
$49$	51.4991			1.05100
$50$	−8.93890	+	34.2067i	−0.178778	+	0.684133i
$51$			96.8003i			1.89804i
$52$			28.6370i			0.550712i
$53$	−90.6584			−1.71053			−0.855267	−	0.518187i	$-0.826607\pi$
$53$	−90.6584			−1.71053			−0.855267	+	0.518187i	$0.826607\pi$
$54$	−102.478			−1.89775
$55$	−48.6406	−	6.25044i	−0.884374	−	0.113644i
$56$		−	28.3548i		−	0.506335i
$57$	46.7115			0.819501
$58$			38.1708i			0.658118i
$59$	92.9752			1.57585			0.787926	−	0.615770i	$-0.211155\pi$
$59$	92.9752			1.57585			0.787926	+	0.615770i	$0.211155\pi$
$60$	−55.2344	−	7.09777i	−0.920574	−	0.118296i
$61$		−	36.3479i		−	0.595867i	−0.954587	−	0.297934i	$-0.903703\pi$
$61$		−	36.3479i		−	0.595867i	0.954587	−	0.297934i	$-0.0962974\pi$
$62$		−	5.99909i		−	0.0967596i
$63$	220.671			3.50271
$64$	−8.00000			−0.125000
$65$	−71.0086	−	9.12480i	−1.09244	−	0.140381i
$66$		−	77.2443i		−	1.17037i
$67$	41.4414			0.618528			0.309264	−	0.950976i	$-0.399917\pi$
$67$	41.4414			0.618528			0.309264	+	0.950976i	$0.399917\pi$
$68$	−34.7648			−0.511248
$69$	−99.0013	−	81.2661i	−1.43480	−	1.17777i
$70$	70.3088	+	9.03487i	1.00441	+	0.129070i
$71$	−22.7302			−0.320143			−0.160072	−	0.987105i	$-0.551173\pi$
$71$	−22.7302			−0.320143			−0.160072	+	0.987105i	$0.551173\pi$
$72$		−	62.2599i		−	0.864721i
$73$			45.3166i			0.620775i	0.950610	+	0.310388i	$0.100459\pi$
$73$			45.3166i			0.620775i	−0.950610	+	0.310388i	$0.899541\pi$
$74$			103.629i			1.40039i
$75$	35.1994	−	134.698i	0.469326	−	1.79598i
$76$			16.7760i			0.220737i
$77$			98.3255i			1.27695i
$78$		−	112.766i		−	1.44572i
$79$			65.6145i			0.830563i	0.909693	+	0.415281i	$0.136317\pi$
$79$			65.6145i			0.830563i	−0.909693	+	0.415281i	$0.863683\pi$
$80$	2.54909	−	19.8369i	0.0318637	−	0.247961i
$81$	205.427			2.53614
$82$			28.0850i			0.342500i
$83$	4.65260			0.0560554			0.0280277	−	0.999607i	$-0.491077\pi$
$83$	4.65260			0.0560554			0.0280277	+	0.999607i	$0.491077\pi$
$84$			111.655i			1.32922i
$85$	11.0774	−	86.2033i	0.130322	−	1.01416i
$86$		−	25.6915i		−	0.298739i
$87$		−	150.308i		−	1.72768i
$88$	27.7415			0.315244
$89$		−	121.117i		−	1.36086i	−0.732812	−	0.680431i	$-0.761793\pi$
$89$		−	121.117i		−	1.36086i	0.732812	−	0.680431i	$-0.238207\pi$
$90$	154.380	+	19.8383i	1.71534	+	0.220425i
$91$			143.542i			1.57738i
$92$	29.1859	−	35.5553i	0.317238	−	0.386471i
$93$			23.6231i			0.254012i
$94$	14.4556			0.153783
$95$	−41.5979	−	5.34544i	−0.437873	−	0.0562678i
$96$	31.5022			0.328148
$97$	99.8370			1.02925			0.514624	−	0.857416i	$-0.327932\pi$
$97$	99.8370			1.02925			0.514624	+	0.857416i	$0.327932\pi$
$98$		−	72.8308i		−	0.743171i
$99$			215.898i			2.18079i
$100$	48.3755	+	12.6415i	0.483755	+	0.126415i
$101$	144.610			1.43178			0.715890	−	0.698213i	$-0.246021\pi$
$101$	144.610			1.43178			0.715890	+	0.698213i	$0.246021\pi$
$102$	136.896			1.34212
$103$	−113.571			−1.10263			−0.551315	−	0.834297i	$-0.685874\pi$
$103$	−113.571			−1.10263			−0.551315	+	0.834297i	$0.685874\pi$
$104$	40.4988			0.389412
$105$	−276.860	−	35.5773i	−2.63677	−	0.338831i
$106$			128.210i			1.20953i
$107$	−20.2694			−0.189433			−0.0947166	−	0.995504i	$-0.530195\pi$
$107$	−20.2694			−0.189433			−0.0947166	+	0.995504i	$0.530195\pi$
$108$			144.926i			1.34191i
$109$		−	54.8745i		−	0.503436i	−0.967801	−	0.251718i	$-0.919004\pi$
$109$		−	54.8745i		−	0.503436i	0.967801	−	0.251718i	$-0.0809955\pi$
$110$	−8.83946	+	68.7881i	−0.0803587	+	0.625347i
$111$		−	408.069i		−	3.67630i
$112$	−40.0997			−0.358033
$113$	−154.079			−1.36353			−0.681765	−	0.731571i	$-0.738787\pi$
$113$	−154.079			−1.36353			−0.681765	+	0.731571i	$0.738787\pi$
$114$		−	66.0601i		−	0.579475i
$115$	78.8637	+	83.6990i	0.685771	+	0.727817i
$116$	53.9817			0.465360
$117$			315.182i			2.69386i
$118$		−	131.487i		−	1.11430i
$119$	−174.257			−1.46435
$120$	−10.0378	+	78.1133i	−0.0836480	+	0.650944i
$121$	24.8011			0.204968
$122$	−51.4037			−0.421342
$123$		−	110.593i		−	0.899127i
$124$	−8.48400			−0.0684194
$125$	−46.7603	+	115.924i	−0.374082	+	0.927396i
$126$		−	312.075i		−	2.47679i
$127$			50.5842i			0.398301i	0.979969	+	0.199150i	$0.0638182\pi$
$127$			50.5842i			0.398301i	−0.979969	+	0.199150i	$0.936182\pi$
$128$			11.3137i			0.0883883i
$129$			101.167i			0.784244i
$130$	−12.9044	+	100.421i	−0.0992647	+	0.772472i
$131$	−190.024			−1.45056			−0.725281	−	0.688453i	$-0.758290\pi$
$131$	−190.024			−1.45056			−0.725281	+	0.688453i	$0.758290\pi$
$132$	−109.240			−0.827575
$133$			84.0890i			0.632248i
$134$		−	58.6070i		−	0.437366i
$135$	−359.361	−	46.1788i	−2.66193	−	0.342065i
$136$			49.1649i			0.361507i
$137$	181.592			1.32549			0.662744	−	0.748846i	$-0.269392\pi$
$137$	181.592			1.32549			0.662744	+	0.748846i	$0.269392\pi$
$138$	−114.928	+	140.009i	−0.832809	+	1.01456i
$139$	85.0630			0.611964			0.305982	−	0.952037i	$-0.401015\pi$
$139$	85.0630			0.611964			0.305982	+	0.952037i	$0.401015\pi$
$140$	12.7772	−	99.4317i	0.0912659	−	0.710226i
$141$	−56.9231			−0.403710
$142$			32.1453i			0.226375i
$143$	−140.437			−0.982079
$144$	−88.0488			−0.611450
$145$	−17.2006	+	133.854i	−0.118624	+	0.923129i
$146$	64.0873			0.438954
$147$			286.791i			1.95096i
$148$	146.554			0.990229
$149$		−	100.742i		−	0.676119i	−0.941125	−	0.338060i	$-0.890229\pi$
$149$		−	100.742i		−	0.676119i	0.941125	−	0.338060i	$-0.109771\pi$
$150$	−190.492	−	49.7795i	−1.26995	−	0.331863i
$151$	191.818			1.27032			0.635160	−	0.772381i	$-0.280934\pi$
$151$	191.818			1.27032			0.635160	+	0.772381i	$0.280934\pi$
$152$	23.7248			0.156084
$153$	−382.625			−2.50082
$154$	139.053			0.902943
$155$	2.70331	−	21.0370i	0.0174407	−	0.135723i
$156$	−159.475			−1.02228
$157$	45.4351			0.289395			0.144698	−	0.989476i	$-0.453779\pi$
$157$	45.4351			0.289395			0.144698	+	0.989476i	$0.453779\pi$
$158$	92.7929			0.587297
$159$		−	504.864i		−	3.17524i
$160$	−28.0536	−	3.60496i	−0.175335	−	0.0225310i
$161$	146.293	−	178.220i	0.908654	−	1.10696i
$162$		−	290.518i		−	1.79332i
$163$		−	182.925i		−	1.12224i	−0.827734	−	0.561121i	$-0.810370\pi$
$163$		−	182.925i		−	1.12224i	0.827734	−	0.561121i	$-0.189630\pi$
$164$	39.7182			0.242184
$165$	34.8078	−	270.872i	0.210957	−	1.64165i
$166$		−	6.57976i		−	0.0396371i
$167$			255.235i			1.52835i	0.645007	+	0.764177i	$0.276855\pi$
$167$			255.235i			1.52835i	−0.645007	+	0.764177i	$0.723145\pi$
$168$	157.904			0.939903
$169$	−36.0195			−0.213133
$170$	−121.910	−	15.6657i	−0.717117	−	0.0921514i
$171$			184.638i			1.07976i
$172$	−36.3333			−0.211240
$173$		−	168.860i		−	0.976072i	−0.872823	−	0.488036i	$-0.837713\pi$
$173$		−	168.860i		−	0.976072i	0.872823	−	0.488036i	$-0.162287\pi$
$174$	−212.568			−1.22166
$175$	242.481	+	63.3651i	1.38560	+	0.362086i
$176$		−	39.2324i		−	0.222911i
$177$			517.766i			2.92523i
$178$	−171.285			−0.962274
$179$	−7.59730			−0.0424430			−0.0212215	−	0.999775i	$-0.506756\pi$
$179$	−7.59730			−0.0424430			−0.0212215	+	0.999775i	$0.506756\pi$
$180$	28.0556	−	218.327i	0.155864	−	1.21293i
$181$		−	40.4613i		−	0.223543i	−0.993734	−	0.111772i	$-0.964348\pi$
$181$		−	40.4613i		−	0.223543i	0.993734	−	0.111772i	$-0.0356525\pi$
$182$	202.999			1.11538
$183$	202.416			1.10610
$184$	−50.2828	−	41.2751i	−0.273276	−	0.224321i
$185$	−46.6974	+	363.397i	−0.252418	+	1.96431i
$186$	33.4081			0.179613
$187$		−	170.489i		−	0.911704i
$188$		−	20.4433i		−	0.108741i
$189$			726.437i			3.84358i
$190$	−7.55960	+	58.8283i	−0.0397874	+	0.309623i
$191$		−	48.7133i		−	0.255043i	−0.991836	−	0.127522i	$-0.959298\pi$
$191$		−	48.7133i		−	0.255043i	0.991836	−	0.127522i	$-0.0407022\pi$
$192$		−	44.5509i		−	0.232036i
$193$		−	189.753i		−	0.983178i	−0.870827	−	0.491589i	$-0.836416\pi$
$193$		−	189.753i		−	0.983178i	0.870827	−	0.491589i	$-0.163584\pi$
$194$		−	141.191i		−	0.727788i
$195$	50.8147	−	395.437i	0.260588	−	2.02788i
$196$	−102.998			−0.525501
$197$		−	338.960i		−	1.72061i	−0.509779	−	0.860305i	$-0.670273\pi$
$197$		−	338.960i		−	1.72061i	0.509779	−	0.860305i	$-0.329727\pi$
$198$	305.326			1.54205
$199$			42.5881i			0.214011i	0.994258	+	0.107005i	$0.0341262\pi$
$199$			42.5881i			0.214011i	−0.994258	+	0.107005i	$0.965874\pi$
$200$	17.8778	−	68.4133i	0.0893890	−	0.342067i
$201$			230.781i			1.14817i
$202$		−	204.509i		−	1.01242i
$203$	270.581			1.33291
$204$		−	193.601i		−	0.949022i
$205$	−12.6557	+	98.4857i	−0.0617350	+	0.480418i
$206$			160.613i			0.779677i
$207$	321.223	−	391.326i	1.55180	−	1.89046i
$208$		−	57.2740i		−	0.275356i
$209$	−82.2703			−0.393638
$210$	−50.3139	+	391.540i	−0.239590	+	1.86448i
$211$	33.7084			0.159755			0.0798777	−	0.996805i	$-0.474547\pi$
$211$	33.7084			0.159755			0.0798777	+	0.996805i	$0.474547\pi$
$212$	181.317			0.855267
$213$		−	126.581i		−	0.594278i
$214$			28.6652i			0.133950i
$215$	11.5771	−	90.0924i	0.0538470	−	0.419034i
$216$	204.957			0.948873
$217$	−42.5257			−0.195971
$218$	−77.6043			−0.355983
$219$	−252.362			−1.15234
$220$	97.2811	+	12.5009i	0.442187	+	0.0568222i
$221$		−	248.890i		−	1.12620i
$222$	−577.097			−2.59953
$223$		−	355.037i		−	1.59209i	−0.605236	−	0.796046i	$-0.706921\pi$
$223$		−	355.037i		−	1.59209i	0.605236	−	0.796046i	$-0.293079\pi$
$224$			56.7095i			0.253168i
$225$	532.426	+	139.134i	2.36634	+	0.618372i
$226$			217.900i			0.964161i
$227$	−280.641			−1.23630			−0.618151	−	0.786059i	$-0.712118\pi$
$227$	−280.641			−1.23630			−0.618151	+	0.786059i	$0.712118\pi$
$228$	−93.4231			−0.409750
$229$			294.263i			1.28499i	0.766290	+	0.642495i	$0.222101\pi$
$229$			294.263i			1.28499i	−0.766290	+	0.642495i	$0.777899\pi$
$230$	118.368	−	111.530i	0.514644	−	0.484914i
$231$	−547.561			−2.37039
$232$		−	76.3417i		−	0.329059i
$233$			73.8157i			0.316805i	0.987375	+	0.158403i	$0.0506344\pi$
$233$			73.8157i			0.316805i	−0.987375	+	0.158403i	$0.949366\pi$
$234$	445.734			1.90485
$235$	50.6915	+	6.51400i	0.215709	+	0.0277191i
$236$	−185.950			−0.787926
$237$	−365.398			−1.54176
$238$			246.437i			1.03545i
$239$	−371.921			−1.55616			−0.778078	−	0.628168i	$-0.783805\pi$
$239$	−371.921			−1.55616			−0.778078	+	0.628168i	$0.783805\pi$
$240$	110.469	+	14.1955i	0.460287	+	0.0591481i
$241$		−	193.519i		−	0.802983i	−0.915863	−	0.401492i	$-0.868492\pi$
$241$		−	193.519i		−	0.802983i	0.915863	−	0.401492i	$-0.131508\pi$
$242$		−	35.0741i		−	0.144934i
$243$			491.827i			2.02398i
$244$			72.6958i			0.297934i
$245$	32.8190	−	255.396i	0.133955	−	1.04243i
$246$	−156.402			−0.635779
$247$	−120.103			−0.486249
$248$			11.9982i			0.0483798i
$249$			25.9097i			0.104055i
$250$	163.942	+	66.1290i	0.655768	+	0.264516i
$251$		−	7.30977i		−	0.0291226i	−0.999894	−	0.0145613i	$-0.995365\pi$
$251$		−	7.30977i		−	0.0291226i	0.999894	−	0.0145613i	$-0.00463517\pi$
$252$	−441.341			−1.75135
$253$	174.365	+	143.129i	0.689191	+	0.565728i
$254$	71.5368			0.281641
$255$	480.054	+	61.6882i	1.88256	+	0.241915i
$256$	16.0000			0.0625000
$257$		−	34.2768i		−	0.133373i	−0.997774	−	0.0666864i	$-0.978757\pi$
$257$		−	34.2768i		−	0.133373i	0.997774	−	0.0666864i	$-0.0212427\pi$
$258$	143.072			0.554544
$259$	734.596			2.83628
$260$	142.017	+	18.2496i	0.546220	+	0.0701907i
$261$	594.128			2.27635
$262$			268.734i			1.02570i
$263$	−209.565			−0.796826			−0.398413	−	0.917206i	$-0.630439\pi$
$263$	−209.565			−0.796826			−0.398413	+	0.917206i	$0.630439\pi$
$264$			154.489i			0.585184i
$265$	−57.7741	+	449.595i	−0.218016	+	1.69658i
$266$	118.920			0.447067
$267$	674.482			2.52615
$268$	−82.8828			−0.309264
$269$	−369.879			−1.37501			−0.687507	−	0.726178i	$-0.741295\pi$
$269$	−369.879			−1.37501			−0.687507	+	0.726178i	$0.741295\pi$
$270$	−65.3067	+	508.213i	−0.241877	+	1.88227i
$271$	−313.530			−1.15694			−0.578470	−	0.815704i	$-0.696350\pi$
$271$	−313.530			−1.15694			−0.578470	+	0.815704i	$0.696350\pi$
$272$	69.5297			0.255624
$273$	−799.365			−2.92808
$274$		−	256.810i		−	0.937262i
$275$	−61.9946	+	237.236i	−0.225435	+	0.862677i
$276$	198.003	+	162.532i	0.717401	+	0.588885i
$277$		−	296.723i		−	1.07120i	−0.844472	−	0.535600i	$-0.820085\pi$
$277$		−	296.723i		−	1.07120i	0.844472	−	0.535600i	$-0.179915\pi$
$278$		−	120.297i		−	0.432724i
$279$	−93.3757			−0.334680
$280$	−140.618	−	18.0697i	−0.502206	−	0.0645348i
$281$			352.294i			1.25372i	0.779134	+	0.626858i	$0.215659\pi$
$281$			352.294i			1.25372i	−0.779134	+	0.626858i	$0.784341\pi$
$282$			80.5014i			0.285466i
$283$	−71.8786			−0.253988			−0.126994	−	0.991903i	$-0.540533\pi$
$283$	−71.8786			−0.253988			−0.126994	+	0.991903i	$0.540533\pi$
$284$	45.4603			0.160072
$285$	29.7680	−	231.653i	0.104449	−	0.812817i
$286$			198.608i			0.694435i
$287$	199.086			0.693680
$288$			124.520i			0.432360i
$289$	13.1486			0.0454967
$290$	189.298	+	24.3253i	0.652751	+	0.0838802i
$291$			555.978i			1.91058i
$292$		−	90.6332i		−	0.310388i
$293$	302.565			1.03264			0.516322	−	0.856395i	$-0.327301\pi$
$293$	302.565			1.03264			0.516322	+	0.856395i	$0.327301\pi$
$294$	405.584			1.37954
$295$	59.2506	−	461.085i	0.200850	−	1.56300i
$296$		−	207.258i		−	0.700197i
$297$	−710.726			−2.39302
$298$	−142.470			−0.478088
$299$	254.550	+	208.949i	0.851336	+	0.698827i
$300$	−70.3988	+	269.397i	−0.234663	+	0.897989i
$301$	−182.119			−0.605047
$302$		−	271.272i		−	0.898251i
$303$			805.311i			2.65779i
$304$		−	33.5520i		−	0.110368i
$305$	−180.257	−	23.1635i	−0.591008	−	0.0759460i
$306$			541.114i			1.76835i
$307$		−	17.8780i		−	0.0582345i	−0.999576	−	0.0291173i	$-0.990730\pi$
$307$		−	17.8780i		−	0.0582345i	0.999576	−	0.0291173i	$-0.00926962\pi$
$308$		−	196.651i		−	0.638477i
$309$		−	632.460i		−	2.04680i
$310$	−29.7508	−	3.82306i	−0.0959704	−	0.0123325i
$311$	−135.270			−0.434951			−0.217475	−	0.976066i	$-0.569782\pi$
$311$	−135.270			−0.434951			−0.217475	+	0.976066i	$0.569782\pi$
$312$			225.532i			0.722860i
$313$	127.874			0.408544			0.204272	−	0.978914i	$-0.434517\pi$
$313$	127.874			0.408544			0.204272	+	0.978914i	$0.434517\pi$
$314$		−	64.2549i		−	0.204633i
$315$	140.627	−	1094.35i	0.446436	−	3.47414i
$316$		−	131.229i		−	0.415281i
$317$		−	116.383i		−	0.367138i	−0.983007	−	0.183569i	$-0.941235\pi$
$317$		−	116.383i		−	0.367138i	0.983007	−	0.183569i	$-0.0587652\pi$
$318$	−713.985			−2.24524
$319$			264.729i			0.829872i
$320$	−5.09819	+	39.6738i	−0.0159318	+	0.123981i
$321$		−	112.877i		−	0.351642i
$322$	−252.041	−	206.890i	−0.782736	−	0.642516i
$323$		−	145.804i		−	0.451404i
$324$	−410.854			−1.26807
$325$	−90.5038	+	346.333i	−0.278473	+	1.06564i
$326$	−258.696			−0.793545
$327$	305.589			0.934522
$328$		−	56.1701i		−	0.171250i
$329$		−	102.472i		−	0.311464i
$330$	−383.072	−	49.2257i	−1.16082	−	0.149169i
$331$	204.670			0.618337			0.309169	−	0.951007i	$-0.399949\pi$
$331$	204.670			0.618337			0.309169	+	0.951007i	$0.399949\pi$
$332$	−9.30519			−0.0280277
$333$	1612.99			4.84380
$334$	360.957			1.08071
$335$	26.4095	−	205.517i	0.0788343	−	0.613484i
$336$		−	223.310i		−	0.664612i
$337$	470.134			1.39506			0.697528	−	0.716557i	$-0.254283\pi$
$337$	470.134			1.39506			0.697528	+	0.716557i	$0.254283\pi$
$338$			50.9393i			0.150708i
$339$		−	858.044i		−	2.53110i
$340$	−22.1547	+	172.407i	−0.0651609	+	0.507078i
$341$		−	41.6060i		−	0.122012i
$342$	261.118			0.763502
$343$	−25.0535			−0.0730422
$344$			51.3830i			0.149369i
$345$	−466.108	+	439.181i	−1.35104	+	1.27299i
$346$	−238.805			−0.690187
$347$			157.548i			0.454030i	0.973891	+	0.227015i	$0.0728966\pi$
$347$			157.548i			0.454030i	−0.973891	+	0.227015i	$0.927103\pi$
$348$			300.617i			0.863841i
$349$	240.406			0.688844			0.344422	−	0.938815i	$-0.388075\pi$
$349$	240.406			0.688844			0.344422	+	0.938815i	$0.388075\pi$
$350$	89.6118	−	342.919i	0.256034	−	0.979769i
$351$	−1037.56			−2.95602
$352$	−55.4830			−0.157622
$353$		−	155.151i		−	0.439520i	−0.975554	−	0.219760i	$-0.929473\pi$
$353$		−	155.151i		−	0.439520i	0.975554	−	0.219760i	$-0.0705274\pi$
$354$	732.232			2.06845
$355$	−14.4853	+	112.724i	−0.0408037	+	0.317532i
$356$			242.233i			0.680431i
$357$		−	970.415i		−	2.71825i
$358$			10.7442i			0.0300117i
$359$			435.157i			1.21214i	0.795413	+	0.606068i	$0.207254\pi$
$359$			435.157i			1.21214i	−0.795413	+	0.606068i	$0.792746\pi$
$360$	−308.761	−	39.6766i	−0.857669	−	0.110213i
$361$	290.642			0.805101
$362$	−57.2209			−0.158069
$363$			138.114i			0.380479i
$364$		−	287.084i		−	0.788692i
$365$	224.735	+	28.8790i	0.615712	+	0.0791207i
$366$		−	286.260i		−	0.782131i
$367$	−176.265			−0.480287			−0.240144	−	0.970737i	$-0.577195\pi$
$367$	−176.265			−0.480287			−0.240144	+	0.970737i	$0.577195\pi$
$368$	−58.3718	+	71.1107i	−0.158619	+	0.193236i
$369$	437.143			1.18467
$370$	513.920	+	66.0401i	1.38897	+	0.178487i
$371$	908.843			2.44971
$372$		−	47.2462i		−	0.127006i
$373$	157.008			0.420932			0.210466	−	0.977601i	$-0.432502\pi$
$373$	157.008			0.420932			0.210466	+	0.977601i	$0.432502\pi$
$374$	−241.107			−0.644672
$375$	−645.567	−	260.401i	−1.72151	−	0.694404i
$376$	−28.9113			−0.0768916
$377$			386.469i			1.02512i
$378$	1027.34			2.71782
$379$			142.008i			0.374692i	0.982294	+	0.187346i	$0.0599885\pi$
$379$			142.008i			0.374692i	−0.982294	+	0.187346i	$0.940011\pi$
$380$	83.1958	+	10.6909i	0.218936	+	0.0281339i
$381$	−281.696			−0.739360
$382$	−68.8909			−0.180343
$383$	−37.1634			−0.0970324			−0.0485162	−	0.998822i	$-0.515449\pi$
$383$	−37.1634			−0.0970324			−0.0485162	+	0.998822i	$0.515449\pi$
$384$	−63.0045			−0.164074
$385$	487.618	+	62.6602i	1.26654	+	0.162754i
$386$	−268.352			−0.695212
$387$	−399.888			−1.03330
$388$	−199.674			−0.514624
$389$			484.710i			1.24604i	0.782206	+	0.623020i	$0.214094\pi$
$389$			484.710i			1.24604i	−0.782206	+	0.623020i	$0.785906\pi$
$390$	−559.233	−	71.8629i	−1.43393	−	0.184264i
$391$	−253.661	+	309.019i	−0.648749	+	0.790330i
$392$			145.662i			0.371585i
$393$		−	1058.21i		−	2.69266i
$394$	−479.362			−1.21666
$395$	325.397	+	41.8143i	0.823789	+	0.105859i
$396$		−	431.796i		−	1.09039i
$397$			468.421i			1.17990i	0.807439	+	0.589951i	$0.200853\pi$
$397$			468.421i			1.17990i	−0.807439	+	0.589951i	$0.799147\pi$
$398$	60.2287			0.151328
$399$	−468.280			−1.17363
$400$	−96.7511	−	25.2830i	−0.241878	−	0.0632076i
$401$		−	557.589i		−	1.39050i	−0.718770	−	0.695248i	$-0.755295\pi$
$401$		−	557.589i		−	1.39050i	0.718770	−	0.695248i	$-0.244705\pi$
$402$	326.374			0.811876
$403$		−	60.7391i		−	0.150717i
$404$	−289.219			−0.715890
$405$	130.913	−	1018.76i	0.323242	−	2.51545i
$406$		−	382.660i		−	0.942512i
$407$			718.708i			1.76587i
$408$	−273.792			−0.671060
$409$	−295.128			−0.721585			−0.360793	−	0.932646i	$-0.617494\pi$
$409$	−295.128			−0.721585			−0.360793	+	0.932646i	$0.617494\pi$
$410$	139.280	+	17.8978i	0.339707	+	0.0436533i
$411$			1011.26i			2.46049i
$412$	227.142			0.551315
$413$	−932.070			−2.25683
$414$	−553.418	−	454.278i	−1.33676	−	1.09729i
$415$	2.96497	−	23.0733i	0.00714452	−	0.0555982i
$416$	−80.9977			−0.194706
$417$			473.704i			1.13598i
$418$			116.348i			0.278344i
$419$		−	148.452i		−	0.354300i	−0.984184	−	0.177150i	$-0.943312\pi$
$419$		−	148.452i		−	0.354300i	0.984184	−	0.177150i	$-0.0566878\pi$
$420$	553.721	+	71.1546i	1.31838	+	0.169416i
$421$		−	384.346i		−	0.912937i	−0.889740	−	0.456468i	$-0.849114\pi$
$421$		−	384.346i		−	0.912937i	0.889740	−	0.456468i	$-0.150886\pi$
$422$		−	47.6708i		−	0.112964i
$423$		−	225.002i		−	0.531918i
$424$		−	256.421i		−	0.604765i
$425$	−420.442	−	109.870i	−0.989275	−	0.258518i
$426$	−179.013			−0.420218
$427$			364.385i			0.853361i
$428$	40.5387			0.0947166
$429$		−	782.076i		−	1.82302i
$430$	−127.410	−	16.3725i	−0.296302	−	0.0380756i
$431$			138.478i			0.321295i	0.987012	+	0.160647i	$0.0513582\pi$
$431$			138.478i			0.321295i	−0.987012	+	0.160647i	$0.948642\pi$
$432$		−	289.852i		−	0.670955i
$433$	−720.106			−1.66306			−0.831532	−	0.555477i	$-0.812536\pi$
$433$	−720.106			−1.66306			−0.831532	+	0.555477i	$0.812536\pi$
$434$			60.1405i			0.138572i
$435$	−745.412	−	95.7875i	−1.71359	−	0.220201i
$436$			109.749i			0.251718i
$437$	149.119	+	122.406i	0.341233	+	0.280104i
$438$			356.893i			0.814825i
$439$	386.990			0.881525			0.440763	−	0.897624i	$-0.354708\pi$
$439$	386.990			0.881525			0.440763	+	0.897624i	$0.354708\pi$
$440$	17.6789	−	137.576i	0.0401794	−	0.312673i
$441$	−1133.61			−2.57054
$442$	−351.984			−0.796344
$443$		−	320.366i		−	0.723174i	−0.932338	−	0.361587i	$-0.882235\pi$
$443$		−	320.366i		−	0.723174i	0.932338	−	0.361587i	$-0.117765\pi$
$444$			816.138i			1.83815i
$445$	−600.644	−	77.1844i	−1.34976	−	0.173448i
$446$	−502.098			−1.12578
$447$	561.017			1.25507
$448$	80.1994			0.179017
$449$	−408.120			−0.908954			−0.454477	−	0.890759i	$-0.650174\pi$
$449$	−408.120			−0.908954			−0.454477	+	0.890759i	$0.650174\pi$
$450$	196.765	−	752.964i	0.437255	−	1.67325i
$451$			194.780i			0.431885i
$452$	308.158			0.681765
$453$			1068.21i			2.35808i
$454$			396.886i			0.874198i
$455$	711.856	+	91.4754i	1.56452	+	0.201045i
$456$			132.120i			0.289737i
$457$	−628.660			−1.37562			−0.687812	−	0.725889i	$-0.741429\pi$
$457$	−628.660			−1.37562			−0.687812	+	0.725889i	$0.741429\pi$
$458$	416.150			0.908625
$459$		−	1259.58i		−	2.74419i
$460$	−157.727	−	167.398i	−0.342886	−	0.363909i
$461$	468.319			1.01588			0.507938	−	0.861394i	$-0.330408\pi$
$461$	468.319			1.01588			0.507938	+	0.861394i	$0.330408\pi$
$462$			774.368i			1.67612i
$463$		−	489.151i		−	1.05648i	−0.849095	−	0.528240i	$-0.822852\pi$
$463$		−	489.151i		−	1.05648i	0.849095	−	0.528240i	$-0.177148\pi$
$464$	−107.963			−0.232680
$465$	117.152	+	15.0544i	0.251940	+	0.0323750i
$466$	104.391			0.224015
$467$	−638.769			−1.36781			−0.683907	−	0.729569i	$-0.739721\pi$
$467$	−638.769			−1.36781			−0.683907	+	0.729569i	$0.739721\pi$
$468$		−	630.363i		−	1.34693i
$469$	−415.447			−0.885814
$470$	9.21218	−	71.6887i	0.0196004	−	0.152529i
$471$			253.022i			0.537201i
$472$			262.974i			0.557148i
$473$		−	178.180i		−	0.376703i
$474$			516.750i			1.09019i
$475$	−53.0185	+	202.887i	−0.111618	+	0.427130i
$476$	348.515			0.732174
$477$	1995.59			4.18363
$478$			525.976i			1.10037i
$479$			780.804i			1.63007i	0.579411	+	0.815035i	$0.303283\pi$
$479$			780.804i			1.63007i	−0.579411	+	0.815035i	$0.696717\pi$
$480$	20.0755	−	156.227i	0.0418240	−	0.325472i
$481$			1049.22i			2.18132i
$482$	−273.677			−0.567795
$483$	992.481	+	814.687i	2.05483	+	1.68672i
$484$	−49.6022			−0.102484
$485$	63.6234	−	495.114i	0.131182	−	1.02085i
$486$	695.548			1.43117
$487$		−	308.473i		−	0.633414i	−0.948523	−	0.316707i	$-0.897423\pi$
$487$		−	308.473i		−	0.633414i	0.948523	−	0.316707i	$-0.102577\pi$
$488$	102.807			0.210671
$489$	1018.69			2.08320
$490$	−361.184	−	46.4131i	−0.737110	−	0.0947206i
$491$	503.424			1.02530			0.512651	−	0.858597i	$-0.328663\pi$
$491$	503.424			1.02530			0.512651	+	0.858597i	$0.328663\pi$
$492$			221.185i			0.449563i
$493$	−469.166			−0.951656
$494$			169.852i			0.343830i
$495$	1070.69	+	137.586i	2.16300	+	0.277951i
$496$	16.9680			0.0342097
$497$	227.868			0.458487
$498$	36.6418			0.0735779
$499$	−262.884			−0.526821			−0.263411	−	0.964684i	$-0.584847\pi$
$499$	−262.884			−0.526821			−0.263411	+	0.964684i	$0.584847\pi$
$500$	93.5205	−	231.849i	0.187041	−	0.463698i
$501$	−1421.37			−2.83706
$502$	−10.3376			−0.0205928
$503$	162.810			0.323677			0.161839	−	0.986817i	$-0.448258\pi$
$503$	162.810			0.323677			0.161839	+	0.986817i	$0.448258\pi$
$504$			624.151i			1.23839i
$505$	92.1559	−	717.152i	0.182487	−	1.42010i
$506$	202.415	−	246.590i	0.400030	−	0.487331i
$507$		−	200.588i		−	0.395636i
$508$		−	101.168i		−	0.199150i
$509$	577.023			1.13364			0.566820	−	0.823841i	$-0.308173\pi$
$509$	577.023			1.13364			0.566820	+	0.823841i	$0.308173\pi$
$510$	87.2403	−	678.899i	0.171059	−	1.33117i
$511$		−	454.295i		−	0.889032i
$512$		−	22.6274i		−	0.0441942i
$513$	−607.820			−1.18483
$514$	−48.4747			−0.0943088
$515$	−72.3757	+	563.223i	−0.140535	+	1.09364i
$516$		−	202.335i		−	0.392122i
$517$	100.255			0.193917
$518$		−	1038.88i		−	2.00555i
$519$	940.360			1.81187
$520$	25.8088	−	200.843i	0.0496324	−	0.386236i
$521$		−	971.255i		−	1.86421i	−0.362185	−	0.932106i	$-0.617969\pi$
$521$		−	971.255i		−	1.86421i	0.362185	−	0.932106i	$-0.382031\pi$
$522$		−	840.224i		−	1.60962i
$523$	−170.780			−0.326539			−0.163269	−	0.986582i	$-0.552204\pi$
$523$	−170.780			−0.326539			−0.163269	+	0.986582i	$0.552204\pi$
$524$	380.047			0.725281
$525$	−352.872	+	1350.34i	−0.672136	+	2.57208i
$526$			296.370i			0.563441i
$527$	73.7362			0.139917
$528$	218.480			0.413788
$529$	−103.091	−	518.858i	−0.194879	−	0.980827i
$530$	635.823	+	81.7050i	1.19967	+	0.154160i
$531$	−2046.59			−3.85422
$532$		−	168.178i		−	0.316124i
$533$			284.353i			0.533495i
$534$		−	953.861i		−	1.78626i
$535$	−12.9171	+	100.520i	−0.0241441	+	0.187888i
$536$			117.214i			0.218683i
$537$		−	42.3083i		−	0.0787864i
$538$			523.088i			0.972282i
$539$		−	505.109i		−	0.937122i
$540$	718.721	+	92.3576i	1.33097	+	0.171033i
$541$	314.463			0.581263			0.290631	−	0.956835i	$-0.406135\pi$
$541$	314.463			0.581263			0.290631	+	0.956835i	$0.406135\pi$
$542$			443.399i			0.818079i
$543$	225.323			0.414960
$544$		−	98.3298i		−	0.180753i
$545$	−272.135	−	34.9701i	−0.499330	−	0.0641653i
$546$			1130.47i			2.07046i
$547$		−	526.082i		−	0.961759i	−0.876787	−	0.480879i	$-0.840318\pi$
$547$		−	526.082i		−	0.961759i	0.876787	−	0.480879i	$-0.159682\pi$
$548$	−363.184			−0.662744
$549$			800.097i			1.45737i
$550$	335.503	+	87.6737i	0.610005	+	0.159407i
$551$			226.399i			0.410888i
$552$	229.855	−	280.018i	0.416405	−	0.507279i
$553$		−	657.780i		−	1.18948i
$554$	−419.629			−0.757453
$555$	−2023.70	−	260.051i	−3.64631	−	0.468561i
$556$	−170.126			−0.305982
$557$	−709.862			−1.27444			−0.637219	−	0.770683i	$-0.719915\pi$
$557$	−709.862			−1.27444			−0.637219	+	0.770683i	$0.719915\pi$
$558$			132.053i			0.236655i
$559$		−	260.119i		−	0.465329i
$560$	−25.5545	+	198.863i	−0.0456330	+	0.355113i
$561$	949.427			1.69238
$562$	498.219			0.886511
$563$	−404.353			−0.718212			−0.359106	−	0.933297i	$-0.616918\pi$
$563$	−404.353			−0.718212			−0.359106	+	0.933297i	$0.616918\pi$
$564$	113.846			0.201855
$565$	−98.1903	+	764.111i	−0.173788	+	1.35241i
$566$			101.652i			0.179597i
$567$	−2059.39			−3.63208
$568$		−	64.2906i		−	0.113188i
$569$			47.5931i			0.0836433i	0.999125	+	0.0418217i	$0.0133161\pi$
$569$			47.5931i			0.0836433i	−0.999125	+	0.0418217i	$0.986684\pi$
$570$	−327.607	−	42.0983i	−0.574749	−	0.0738567i
$571$		−	178.905i		−	0.313319i	−0.987653	−	0.156660i	$-0.949927\pi$
$571$		−	178.905i		−	0.313319i	0.987653	−	0.156660i	$-0.0500725\pi$
$572$	280.875			0.491040
$573$	271.277			0.473433
$574$		−	281.550i		−	0.490506i
$575$	465.339	−	337.764i	0.809286	−	0.587415i
$576$	176.098			0.305725
$577$			463.415i			0.803146i	0.915827	+	0.401573i	$0.131536\pi$
$577$			463.415i			0.803146i	−0.915827	+	0.401573i	$0.868464\pi$
$578$		−	18.5949i		−	0.0321710i
$579$	1056.71			1.82506
$580$	34.4011	−	267.707i	0.0593122	−	0.461564i
$581$	−46.6419			−0.0802787
$582$	786.272			1.35098
$583$			889.186i			1.52519i
$584$	−128.175			−0.219477
$585$	1563.06	+	200.857i	2.67189	+	0.343345i
$586$		−	427.891i		−	0.730189i
$587$			627.786i			1.06948i	0.845016	+	0.534741i	$0.179591\pi$
$587$			627.786i			1.06948i	−0.845016	+	0.534741i	$0.820409\pi$
$588$		−	573.583i		−	0.975481i
$589$		−	35.5819i		−	0.0604106i
$590$	−652.072	−	83.7930i	−1.10521	−	0.142022i
$591$	1887.62			3.19395
$592$	−293.108			−0.495114
$593$			60.2309i			0.101570i	0.998710	+	0.0507849i	$0.0161723\pi$
$593$			60.2309i			0.101570i	−0.998710	+	0.0507849i	$0.983828\pi$
$594$			1005.12i			1.69212i
$595$	−111.050	+	864.181i	−0.186638	+	1.45241i
$596$			201.484i			0.338060i
$597$	−237.167			−0.397265
$598$	295.499	−	359.987i	0.494145	−	0.601986i
$599$	−434.361			−0.725143			−0.362572	−	0.931956i	$-0.618101\pi$
$599$	−434.361			−0.725143			−0.362572	+	0.931956i	$0.618101\pi$
$600$	380.984	+	99.5590i	0.634974	+	0.165932i
$601$	−121.753			−0.202583			−0.101292	−	0.994857i	$-0.532298\pi$
$601$	−121.753			−0.202583			−0.101292	+	0.994857i	$0.532298\pi$
$602$			257.555i			0.427833i
$603$	−912.216			−1.51280
$604$	−383.636			−0.635160
$605$	15.8051	−	122.994i	0.0261241	−	0.203296i
$606$	1138.88			1.87934
$607$		−	962.161i		−	1.58511i	−0.609801	−	0.792554i	$-0.708751\pi$
$607$		−	962.161i		−	1.58511i	0.609801	−	0.792554i	$-0.291249\pi$
$608$	−47.4496			−0.0780422
$609$			1506.83i			2.47427i
$610$	−32.7582	+	254.922i	−0.0537020	+	0.417905i
$611$	146.359			0.239540
$612$	765.251			1.25041
$613$	−261.958			−0.427338			−0.213669	−	0.976906i	$-0.568541\pi$
$613$	−261.958			−0.427338			−0.213669	+	0.976906i	$0.568541\pi$
$614$	−25.2833			−0.0411780
$615$	−548.453	−	70.4777i	−0.891794	−	0.114598i
$616$	−278.107			−0.451472
$617$	315.081			0.510666			0.255333	−	0.966853i	$-0.417815\pi$
$617$	315.081			0.510666			0.255333	+	0.966853i	$0.417815\pi$
$618$	−894.434			−1.44730
$619$		−	465.857i		−	0.752596i	−0.926499	−	0.376298i	$-0.877197\pi$
$619$		−	465.857i		−	0.752596i	0.926499	−	0.376298i	$-0.122803\pi$
$620$	−5.40663	+	42.0740i	−0.00872036	+	0.0678614i
$621$	1288.23	+	1057.45i	2.07444	+	1.70282i
$622$			191.300i			0.307557i
$623$			1214.19i			1.94893i
$624$	318.951			0.511139
$625$	545.096	+	305.770i	0.872154	+	0.489232i
$626$		−	180.842i		−	0.288884i
$627$		−	458.152i		−	0.730704i
$628$	−90.8701			−0.144698
$629$	−1273.73			−2.02501
$630$	−1547.65	−	198.877i	−2.45659	−	0.315678i
$631$		−	15.6603i		−	0.0248182i	−0.999923	−	0.0124091i	$-0.996050\pi$
$631$		−	15.6603i		−	0.0248182i	0.999923	−	0.0124091i	$-0.00395003\pi$
$632$	−185.586			−0.293648
$633$			187.717i			0.296552i
$634$	−164.590			−0.259606
$635$	250.858	+	32.2359i	0.395052	+	0.0507653i
$636$			1009.73i			1.58762i
$637$		−	737.390i		−	1.15760i
$638$	374.384			0.586808
$639$	500.341			0.783006
$640$	56.1072	+	7.20992i	0.0876675	+	0.0112655i
$641$			553.144i			0.862939i	0.902128	+	0.431469i	$0.142005\pi$
$641$			553.144i			0.862939i	−0.902128	+	0.431469i	$0.857995\pi$
$642$	−159.632			−0.248649
$643$	583.117			0.906870			0.453435	−	0.891289i	$-0.350198\pi$
$643$	583.117			0.906870			0.453435	+	0.891289i	$0.350198\pi$
$644$	−292.587	+	356.440i	−0.454327	+	0.553478i
$645$	501.712	+	64.4713i	0.777848	+	0.0999555i
$646$	−206.197			−0.319191
$647$			868.461i			1.34229i	0.741326	+	0.671145i	$0.234197\pi$
$647$			868.461i			1.34229i	−0.741326	+	0.671145i	$0.765803\pi$
$648$			581.036i			0.896660i
$649$		−	911.911i		−	1.40510i
$650$	489.788	+	127.992i	0.753520	+	0.196910i
$651$		−	236.820i		−	0.363779i
$652$			365.851i			0.561121i
$653$		−	381.114i		−	0.583635i	−0.956474	−	0.291817i	$-0.905740\pi$
$653$		−	381.114i		−	0.583635i	0.956474	−	0.291817i	$-0.0942600\pi$
$654$		−	432.167i		−	0.660806i
$655$	−121.097	+	942.369i	−0.184881	+	1.43873i
$656$	−79.4365			−0.121092
$657$		−	997.518i		−	1.51829i
$658$	−144.917			−0.220238
$659$			1117.10i			1.69514i	0.530683	+	0.847571i	$0.321936\pi$
$659$			1117.10i			1.69514i	−0.530683	+	0.847571i	$0.678064\pi$
$660$	−69.6157	+	541.745i	−0.105478	+	0.820826i
$661$		−	1079.84i		−	1.63365i	−0.576889	−	0.816823i	$-0.695733\pi$
$661$		−	1079.84i		−	1.63365i	0.576889	−	0.816823i	$-0.304267\pi$
$662$		−	289.447i		−	0.437230i
$663$	1386.03			2.09055
$664$			13.1595i			0.0198186i
$665$	417.016	+	53.5877i	0.627092	+	0.0805829i
$666$		−	2281.11i		−	3.42509i
$667$	393.877	−	479.835i	0.590520	−	0.719392i
$668$		−	510.470i		−	0.764177i
$669$	1977.15			2.95538
$670$	−290.645	−	37.3487i	−0.433799	−	0.0557443i
$671$	−356.504			−0.531302
$672$	−315.807			−0.469952
$673$		−	750.860i		−	1.11569i	−0.829945	−	0.557845i	$-0.811628\pi$
$673$		−	750.860i		−	1.11569i	0.829945	−	0.557845i	$-0.188372\pi$
$674$		−	664.870i		−	0.986454i
$675$	−458.022	+	1752.72i	−0.678551	+	2.59662i
$676$	72.0390			0.106567
$677$	505.958			0.747353			0.373676	−	0.927559i	$-0.378097\pi$
$677$	505.958			0.747353			0.373676	+	0.927559i	$0.378097\pi$
$678$	−1213.46			−1.78976
$679$	−1000.86			−1.47402
$680$	243.820	+	31.3315i	0.358558	+	0.0460757i
$681$		−	1562.85i		−	2.29493i
$682$	−58.8397			−0.0862753
$683$			336.348i			0.492457i	0.969212	+	0.246229i	$0.0791914\pi$
$683$			336.348i			0.492457i	−0.969212	+	0.246229i	$0.920809\pi$
$684$		−	369.276i		−	0.539878i
$685$	115.724	−	900.555i	0.168940	−	1.31468i
$686$			35.4310i			0.0516486i
$687$	−1638.71			−2.38531
$688$	72.6666			0.105620
$689$			1298.09i			1.88402i
$690$	621.096	+	659.176i	0.900139	+	0.955327i
$691$	−331.910			−0.480333			−0.240167	−	0.970732i	$-0.577202\pi$
$691$	−331.910			−0.480333			−0.240167	+	0.970732i	$0.577202\pi$
$692$			337.721i			0.488036i
$693$		−	2164.36i		−	3.12318i
$694$	222.807			0.321047
$695$	54.2084	−	421.846i	0.0779976	−	0.606973i
$696$	425.136			0.610828
$697$	−345.199			−0.495265
$698$		−	339.986i		−	0.487086i
$699$	−411.069			−0.588082
$700$	−484.961	−	126.730i	−0.692802	−	0.181043i
$701$			1083.72i			1.54596i	0.634429	+	0.772981i	$0.281235\pi$
$701$			1083.72i			1.54596i	−0.634429	+	0.772981i	$0.718765\pi$
$702$			1467.34i			2.09022i
$703$			614.646i			0.874319i
$704$			78.4648i			0.111456i
$705$	−36.2755	+	282.294i	−0.0514547	+	0.400417i
$706$	−219.416			−0.310788
$707$	−1449.70			−2.05050
$708$		−	1035.53i		−	1.46262i
$709$		−	526.644i		−	0.742799i	−0.928473	−	0.371400i	$-0.878878\pi$
$709$		−	526.644i		−	0.742799i	0.928473	−	0.371400i	$-0.121122\pi$
$710$	159.416	+	20.4853i	0.224529	+	0.0288526i
$711$		−	1444.32i		−	2.03139i
$712$	342.570			0.481137
$713$	−61.9033	+	75.4129i	−0.0868209	+	0.105768i
$714$	−1372.37			−1.92209
$715$	−89.4970	+	696.460i	−0.125171	+	0.974070i
$716$	15.1946			0.0212215
$717$		−	2071.18i		−	2.88867i
$718$	615.405			0.857110
$719$	−975.723			−1.35706			−0.678528	−	0.734575i	$-0.737382\pi$
$719$	−975.723			−1.35706			−0.678528	+	0.734575i	$0.737382\pi$
$720$	−56.1111	+	436.654i	−0.0779321	+	0.606463i
$721$	1138.54			1.57911
$722$		−	411.029i		−	0.569293i
$723$	1077.68			1.49057
$724$			80.9226i			0.111772i
$725$	652.849	+	170.603i	0.900481	+	0.235314i
$726$	195.323			0.269039
$727$	578.127			0.795223			0.397612	−	0.917554i	$-0.369839\pi$
$727$	578.127			0.795223			0.397612	+	0.917554i	$0.369839\pi$
$728$	−405.998			−0.557689
$729$	−890.070			−1.22095
$730$	40.8411	−	317.823i	0.0559468	−	0.435374i
$731$	315.780			0.431984
$732$	−404.833			−0.553050
$733$	1179.77			1.60952			0.804758	−	0.593604i	$-0.202295\pi$
$733$	1179.77			1.60952			0.804758	+	0.593604i	$0.202295\pi$
$734$			249.277i			0.339614i
$735$	1422.26	+	182.764i	1.93505	+	0.248659i
$736$	100.566	+	82.5502i	0.136638	+	0.112161i
$737$		−	406.462i		−	0.551508i
$738$		−	618.213i		−	0.837687i
$739$	−532.708			−0.720850			−0.360425	−	0.932788i	$-0.617368\pi$
$739$	−532.708			−0.720850			−0.360425	+	0.932788i	$0.617368\pi$
$740$	93.3948	−	726.793i	0.126209	−	0.982153i
$741$		−	668.839i		−	0.902617i
$742$		−	1285.30i		−	1.73221i
$743$	−930.836			−1.25281			−0.626404	−	0.779499i	$-0.715474\pi$
$743$	−930.836			−1.25281			−0.626404	+	0.779499i	$0.715474\pi$
$744$	−66.8162			−0.0898067
$745$	−499.601	−	64.2000i	−0.670605	−	0.0861745i
$746$		−	222.042i		−	0.297644i
$747$	−102.414			−0.137100
$748$			340.977i			0.455852i
$749$	203.199			0.271293
$750$	−368.263	+	912.970i	−0.491017	+	1.21729i
$751$		−	1425.78i		−	1.89851i	−0.314512	−	0.949254i	$-0.601841\pi$
$751$		−	1425.78i		−	1.89851i	0.314512	−	0.949254i	$-0.398159\pi$
$752$			40.8867i			0.0543706i
$753$	40.7071			0.0540599
$754$	546.549			0.724866
$755$	122.241	−	951.269i	0.161908	−	1.25996i
$756$		−	1452.87i		−	1.92179i
$757$	715.631			0.945351			0.472676	−	0.881236i	$-0.343288\pi$
$757$	715.631			0.945351			0.472676	+	0.881236i	$0.343288\pi$
$758$	200.830			0.264947
$759$	−797.067	+	971.015i	−1.05015	+	1.27934i
$760$	15.1192	−	117.657i	0.0198937	−	0.154811i
$761$	−1406.78			−1.84859			−0.924297	−	0.381674i	$-0.875348\pi$
$761$	−1406.78			−1.84859			−0.924297	+	0.381674i	$0.875348\pi$
$762$			398.379i			0.522806i
$763$			550.113i			0.720987i
$764$			97.4265i			0.127522i
$765$	−243.837	+	1897.52i	−0.318741	+	2.48042i
$766$			52.5570i			0.0686123i
$767$		−	1331.27i		−	1.73568i
$768$			89.1018i			0.116018i
$769$		−	409.262i		−	0.532200i	−0.963945	−	0.266100i	$-0.914265\pi$
$769$		−	409.262i		−	0.532200i	0.963945	−	0.266100i	$-0.0857352\pi$
$770$	88.6149	−	689.596i	0.115084	−	0.895579i
$771$	190.883			0.247578
$772$			379.507i			0.491589i
$773$	346.261			0.447944			0.223972	−	0.974596i	$-0.428098\pi$
$773$	346.261			0.447944			0.223972	+	0.974596i	$0.428098\pi$
$774$			565.527i			0.730655i
$775$	−102.604	−	26.8127i	−0.132393	−	0.0345970i
$776$			282.382i			0.363894i
$777$			4090.86i			5.26494i
$778$	685.483			0.881083
$779$			166.578i			0.213836i
$780$	−101.629	+	790.874i	−0.130294	+	1.01394i
$781$			222.940i			0.285454i
$782$	437.019	+	358.731i	0.558848	+	0.458735i
$783$			1955.84i			2.49788i
$784$	205.996			0.262751
$785$	28.9545	−	225.323i	0.0368848	−	0.287035i
$786$	−1496.54			−1.90400
$787$	−620.806			−0.788826			−0.394413	−	0.918933i	$-0.629052\pi$
$787$	−620.806			−0.788826			−0.394413	+	0.918933i	$0.629052\pi$
$788$			677.921i			0.860305i
$789$		−	1167.04i		−	1.47914i
$790$	59.1344	−	460.180i	0.0748537	−	0.582507i
$791$	1544.63			1.95275
$792$	−610.652			−0.771025
$793$	−520.448			−0.656302
$794$	662.448			0.834317
$795$	−2503.73	−	321.736i	−3.14935	−	0.404699i
$796$		−	85.1762i		−	0.107005i
$797$	379.000			0.475533			0.237767	−	0.971322i	$-0.423585\pi$
$797$	379.000			0.475533			0.237767	+	0.971322i	$0.423585\pi$
$798$			662.248i			0.829884i
$799$			177.677i			0.222375i
$800$	−35.7556	+	136.827i	−0.0446945	+	0.171033i
$801$			2666.04i			3.32840i
$802$	−788.549			−0.983229
$803$	444.470			0.553512
$804$		−	461.563i		−	0.574083i
$805$	−790.603	−	839.076i	−0.982115	−	1.04233i
$806$	−85.8980			−0.106573
$807$		−	2059.80i		−	2.55242i
$808$			409.018i			0.506210i
$809$	−110.128			−0.136128			−0.0680642	−	0.997681i	$-0.521682\pi$
$809$	−110.128			−0.136128			−0.0680642	+	0.997681i	$0.521682\pi$
$810$	−1440.74	−	185.139i	−1.77869	−	0.228567i
$811$	−1115.03			−1.37488			−0.687439	−	0.726242i	$-0.741265\pi$
$811$	−1115.03			−1.37488			−0.687439	+	0.726242i	$0.741265\pi$
$812$	−541.163			−0.666457
$813$		−	1746.01i		−	2.14761i
$814$	1016.41			1.24866
$815$	−907.168	−	116.573i	−1.11309	−	0.143035i
$816$			387.201i			0.474511i
$817$		−	152.382i		−	0.186514i
$818$			417.375i			0.510238i
$819$		−	3159.67i		−	3.85796i
$820$	25.3114	−	196.971i	0.0308675	−	0.240209i
$821$	−297.005			−0.361760			−0.180880	−	0.983505i	$-0.557895\pi$
$821$	−297.005			−0.361760			−0.180880	+	0.983505i	$0.557895\pi$
$822$	1430.14			1.73983
$823$		−	1245.37i		−	1.51321i	−0.653872	−	0.756605i	$-0.726857\pi$
$823$		−	1245.37i		−	1.51321i	0.653872	−	0.756605i	$-0.273143\pi$
$824$		−	321.227i		−	0.389839i
$825$	−1321.13	−	345.240i	−1.60138	−	0.418472i
$826$			1318.15i			1.59582i
$827$	162.409			0.196384			0.0981918	−	0.995168i	$-0.468694\pi$
$827$	162.409			0.196384			0.0981918	+	0.995168i	$0.468694\pi$
$828$	−642.446	+	782.651i	−0.775901	+	0.945231i
$829$	58.6874			0.0707930			0.0353965	−	0.999373i	$-0.488731\pi$
$829$	58.6874			0.0707930			0.0353965	+	0.999373i	$0.488731\pi$
$830$	−32.6305	−	4.19311i	−0.0393139	−	0.00505194i
$831$	1652.41			1.98845
$832$			114.548i			0.137678i
$833$	895.179			1.07465
$834$	669.918			0.803259
$835$	1265.77	+	162.654i	1.51589	+	0.194796i
$836$	164.541			0.196819
$837$		−	307.388i		−	0.367250i
$838$	−209.942			−0.250528
$839$			666.002i			0.793805i	0.917861	+	0.396902i	$0.129915\pi$
$839$			666.002i			0.793805i	−0.917861	+	0.396902i	$0.870085\pi$
$840$	100.628	−	783.080i	0.119795	−	0.932238i
$841$	−112.493			−0.133762
$842$	−543.548			−0.645544
$843$	−1961.88			−2.32726
$844$	−67.4168			−0.0798777
$845$	−22.9543	+	178.629i	−0.0271648	+	0.211395i
$846$	−318.200			−0.376123
$847$	−248.629			−0.293541
$848$	−362.633			−0.427634
$849$		−	400.282i		−	0.471475i
$850$	−155.380	+	594.595i	−0.182800	+	0.699523i
$851$	1069.33	−	1302.69i	1.25655	−	1.53078i
$852$			253.162i			0.297139i
$853$			920.684i			1.07935i	0.841874	+	0.539674i	$0.181453\pi$
$853$			920.684i			1.07935i	−0.841874	+	0.539674i	$0.818547\pi$
$854$	515.318			0.603417
$855$	915.662	+	117.665i	1.07095	+	0.137620i
$856$		−	57.3304i		−	0.0669748i
$857$		−	628.758i		−	0.733673i	−0.930285	−	0.366836i	$-0.880441\pi$
$857$		−	628.758i		−	0.733673i	0.930285	−	0.366836i	$-0.119559\pi$
$858$	−1106.02			−1.28907
$859$	908.763			1.05793			0.528965	−	0.848643i	$-0.322580\pi$
$859$	908.763			1.05793			0.528965	+	0.848643i	$0.322580\pi$
$860$	−23.1542	+	180.185i	−0.0269235	+	0.209517i
$861$			1108.68i			1.28767i
$862$	195.837			0.227190
$863$			12.6014i			0.0146019i	0.999973	+	0.00730093i	$0.00232398\pi$
$863$			12.6014i			0.0146019i	−0.999973	+	0.00730093i	$0.997676\pi$
$864$	−409.913			−0.474437
$865$	−837.417	−	107.610i	−0.968112	−	0.124405i
$866$			1018.38i			1.17596i
$867$			73.2225i			0.0844550i
$868$	85.0515			0.0979855
$869$	643.553			0.740568
$870$	−135.464	+	1054.17i	−0.155706	+	1.21169i
$871$		−	593.379i		−	0.681262i
$872$	155.209			0.177992
$873$	−2197.63			−2.51733
$874$	173.108	−	210.886i	0.198064	−	0.241288i
$875$	468.768	−	1162.13i	0.535735	−	1.32815i
$876$	504.723			0.576168
$877$			1224.19i			1.39588i	0.716156	+	0.697940i	$0.245900\pi$
$877$			1224.19i			1.39588i	−0.716156	+	0.697940i	$0.754100\pi$
$878$		−	547.286i		−	0.623333i
$879$			1684.94i			1.91688i
$880$	−194.562	−	25.0018i	−0.221093	−	0.0284111i
$881$		−	710.448i		−	0.806411i	−0.915110	−	0.403205i	$-0.867896\pi$
$881$		−	710.448i		−	0.806411i	0.915110	−	0.403205i	$-0.132104\pi$
$882$			1603.16i			1.81765i
$883$			231.686i			0.262385i	0.991357	+	0.131193i	$0.0418806\pi$
$883$			231.686i			0.262385i	−0.991357	+	0.131193i	$0.958119\pi$
$884$			497.780i			0.563100i
$885$	2567.72	+	329.958i	2.90137	+	0.372834i
$886$	−453.066			−0.511361
$887$		−	530.453i		−	0.598030i	−0.954248	−	0.299015i	$-0.903342\pi$
$887$		−	530.453i		−	0.598030i	0.954248	−	0.299015i	$-0.0966581\pi$
$888$	1154.19			1.29977
$889$		−	507.103i		−	0.570419i
$890$	−109.155	+	849.440i	−0.122646	+	0.954427i
$891$		−	2014.85i		−	2.26134i
$892$			710.073i			0.796046i
$893$	85.7393			0.0960127
$894$		−	793.397i		−	0.887469i
$895$	−4.84155	+	37.6767i	−0.00540956	+	0.0420968i
$896$		−	113.419i		−	0.126584i
$897$	−1163.61	+	1417.55i	−1.29722	+	1.58032i
$898$			577.169i			0.642727i
$899$	−114.495			−0.127358
$900$	−1064.85	−	278.268i	−1.18317	−	0.309186i
$901$	−1575.86			−1.74901
$902$	275.461			0.305389
$903$		−	1014.20i		−	1.12314i
$904$		−	435.801i		−	0.482081i
$905$	−200.657	−	25.7849i	−0.221720	−	0.0284916i
$906$	1510.68			1.66741
$907$	262.781			0.289725			0.144863	−	0.989452i	$-0.453726\pi$
$907$	262.781			0.289725			0.144863	+	0.989452i	$0.453726\pi$
$908$	561.281			0.618151
$909$	−3183.18			−3.50185
$910$	129.366	−	1006.72i	0.142160	−	1.10628i
$911$			1223.98i			1.34355i	0.740755	+	0.671776i	$0.234468\pi$
$911$			1223.98i			1.34355i	−0.740755	+	0.671776i	$0.765532\pi$
$912$	186.846			0.204875
$913$		−	45.6331i		−	0.0499815i
$914$			889.059i			0.972713i
$915$	128.995	−	1003.83i	0.140978	−	1.09708i
$916$		−	588.525i		−	0.642495i
$917$	1904.97			2.07740
$918$	−1781.32			−1.94044
$919$			502.048i			0.546298i	0.961972	+	0.273149i	$0.0880651\pi$
$919$			502.048i			0.546298i	−0.961972	+	0.273149i	$0.911935\pi$
$920$	−236.736	+	223.060i	−0.257322	+	0.242457i
$921$	99.5600			0.108100
$922$		−	662.302i		−	0.718332i
$923$			325.462i			0.352613i
$924$	1095.12			1.18520
$925$	1772.40	+	463.166i	1.91611	+	0.500720i
$926$	−691.763			−0.747045
$927$	2499.94			2.69681
$928$			152.683i			0.164529i
$929$	12.5466			0.0135055			0.00675273	−	0.999977i	$-0.497851\pi$
$929$	12.5466			0.0135055			0.00675273	+	0.999977i	$0.497851\pi$
$930$	21.2901	−	165.678i	0.0228926	−	0.178149i
$931$		−	431.974i		−	0.463989i
$932$		−	147.631i		−	0.158403i
$933$		−	753.298i		−	0.807393i
$934$			903.356i			0.967191i
$935$	−845.491	−	108.648i	−0.904268	−	0.116201i
$936$	−891.469			−0.952424
$937$	−789.304			−0.842374			−0.421187	−	0.906974i	$-0.638386\pi$
$937$	−789.304			−0.842374			−0.421187	+	0.906974i	$0.638386\pi$
$938$			587.531i			0.626365i
$939$			712.114i			0.758375i
$940$	−101.383	−	13.0280i	−0.107854	−	0.0138596i
$941$		−	851.539i		−	0.904929i	−0.891782	−	0.452465i	$-0.850545\pi$
$941$		−	851.539i		−	0.904929i	0.891782	−	0.452465i	$-0.149455\pi$
$942$	357.826			0.379858
$943$	289.803	−	353.049i	0.307321	−	0.374389i
$944$	371.901			0.393963
$945$	3602.56	+	462.939i	3.81224	+	0.489882i
$946$	−251.985			−0.266369
$947$		−	990.158i		−	1.04557i	−0.852464	−	0.522787i	$-0.824892\pi$
$947$		−	990.158i		−	1.04557i	0.852464	−	0.522787i	$-0.175108\pi$
$948$	730.796			0.770881
$949$	648.866			0.683736
$950$	286.925	+	74.9794i	0.302027	+	0.0789257i
$951$	648.120			0.681514
$952$		−	492.875i		−	0.517725i
$953$	88.4608			0.0928235			0.0464118	−	0.998922i	$-0.485221\pi$
$953$	88.4608			0.0928235			0.0464118	+	0.998922i	$0.485221\pi$
$954$		−	2822.19i		−	2.95827i
$955$	−241.580	−	31.0436i	−0.252963	−	0.0325064i
$956$	743.842			0.778078
$957$	−1474.24			−1.54048
$958$	1104.22			1.15263
$959$	−1820.45			−1.89827
$960$	−220.938	−	28.3911i	−0.230143	−	0.0295740i
$961$	−943.005			−0.981275
$962$	1483.82			1.54243
$963$	446.173			0.463316
$964$			387.038i			0.401492i
$965$	−941.029	−	120.925i	−0.975160	−	0.125311i
$966$	1152.14	−	1403.58i	1.19269	−	1.45298i
$967$			1463.10i			1.51303i	0.653976	+	0.756515i	$0.273100\pi$
$967$			1463.10i			1.51303i	−0.653976	+	0.756515i	$0.726900\pi$
$968$			70.1481i			0.0724671i
$969$	811.960			0.837936
$970$	−700.197	−	89.9771i	−0.721852	−	0.0927599i
$971$		−	301.283i		−	0.310281i	−0.987892	−	0.155140i	$-0.950417\pi$
$971$		−	301.283i		−	0.310281i	0.987892	−	0.155140i	$-0.0495830\pi$
$972$		−	983.654i		−	1.01199i
$973$	−852.750			−0.876413
$974$	−436.246			−0.447891
$975$	−1928.68	−	504.003i	−1.97813	−	0.516926i
$976$		−	145.392i		−	0.148967i
$977$	1083.35			1.10886			0.554429	−	0.832231i	$-0.312937\pi$
$977$	1083.35			1.10886			0.554429	+	0.832231i	$0.312937\pi$
$978$		−	1440.64i		−	1.47305i
$979$	−1187.92			−1.21341
$980$	−65.6380	+	510.791i	−0.0669776	+	0.521215i
$981$			1207.91i			1.23130i
$982$		−	711.949i		−	0.724999i
$983$	1143.57			1.16335			0.581673	−	0.813423i	$-0.302398\pi$
$983$	1143.57			1.16335			0.581673	+	0.813423i	$0.302398\pi$
$984$	312.803			0.317889
$985$	−1680.98	−	216.010i	−1.70658	−	0.219300i
$986$			663.502i			0.672923i
$987$	570.649			0.578166
$988$	240.207			0.243124
$989$	−265.105	+	322.961i	−0.268054	+	0.326553i
$990$	194.576	−	1514.18i	0.196541	−	1.52947i
$991$	1358.12			1.37046			0.685229	−	0.728328i	$-0.259702\pi$
$991$	1358.12			1.37046			0.685229	+	0.728328i	$0.259702\pi$
$992$		−	23.9964i		−	0.0241899i
$993$			1139.78i			1.14781i
$994$		−	322.254i		−	0.324200i
$995$	211.204	+	27.1403i	0.212265	+	0.0272766i
$996$		−	51.8193i		−	0.0520274i
$997$		−	635.885i		−	0.637798i	−0.947789	−	0.318899i	$-0.896687\pi$
$997$		−	635.885i		−	0.637798i	0.947789	−	0.318899i	$-0.103313\pi$
$998$			371.774i			0.372519i
$999$			5309.87i			5.31519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.c.a.229.12	yes	24
5.2	odd	4		1150.3.d.e.551.24		24
5.3	odd	4		1150.3.d.e.551.1		24
5.4	even	2	inner	230.3.c.a.229.13	yes	24
23.22	odd	2	inner	230.3.c.a.229.11	✓	24
115.22	even	4		1150.3.d.e.551.13		24
115.68	even	4		1150.3.d.e.551.12		24
115.114	odd	2	inner	230.3.c.a.229.14	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.c.a.229.11	✓	24	23.22	odd	2	inner
230.3.c.a.229.12	yes	24	1.1	even	1	trivial
230.3.c.a.229.13	yes	24	5.4	even	2	inner
230.3.c.a.229.14	yes	24	115.114	odd	2	inner
1150.3.d.e.551.1		24	5.3	odd	4
1150.3.d.e.551.12		24	115.68	even	4
1150.3.d.e.551.13		24	115.22	even	4
1150.3.d.e.551.24		24	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +5.56886i q^{3} -2.00000 q^{4} +(0.637273 - 4.95922i) q^{5} +7.87556 q^{6} -10.0249 q^{7} +2.82843i q^{8} -22.0122 q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +5.56886i q^{3} -2.00000 q^{4} +(0.637273 - 4.95922i) q^{5} +7.87556 q^{6} -10.0249 q^{7} +2.82843i q^{8} -22.0122 q^{9} +(-7.01340 - 0.901240i) q^{10} -9.80810i q^{11} -11.1377i q^{12} -14.3185i q^{13} +14.1774i q^{14} +(27.6172 + 3.54888i) q^{15} +4.00000 q^{16} +17.3824 q^{17} +31.1300i q^{18} -8.38799i q^{19} +(-1.27455 + 9.91844i) q^{20} -55.8274i q^{21} -13.8708 q^{22} +(-14.5930 + 17.7777i) q^{23} -15.7511 q^{24} +(-24.1878 - 6.32076i) q^{25} -20.2494 q^{26} -72.4631i q^{27} +20.0498 q^{28} -26.9909 q^{29} +(5.01888 - 39.0566i) q^{30} +4.24200 q^{31} -5.65685i q^{32} +54.6200 q^{33} -24.5825i q^{34} +(-6.38862 + 49.7158i) q^{35} +44.0244 q^{36} -73.2769 q^{37} -11.8624 q^{38} +79.7377 q^{39} +(14.0268 + 1.80248i) q^{40} -19.8591 q^{41} -78.9519 q^{42} +18.1666 q^{43} +19.6162i q^{44} +(-14.0278 + 109.163i) q^{45} +(25.1414 + 20.6376i) q^{46} +10.2217i q^{47} +22.2754i q^{48} +51.4991 q^{49} +(-8.93890 + 34.2067i) q^{50} +96.8003i q^{51} +28.6370i q^{52} -90.6584 q^{53} -102.478 q^{54} +(-48.6406 - 6.25044i) q^{55} -28.3548i q^{56} +46.7115 q^{57} +38.1708i q^{58} +92.9752 q^{59} +(-55.2344 - 7.09777i) q^{60} -36.3479i q^{61} -5.99909i q^{62} +220.671 q^{63} -8.00000 q^{64} +(-71.0086 - 9.12480i) q^{65} -77.2443i q^{66} +41.4414 q^{67} -34.7648 q^{68} +(-99.0013 - 81.2661i) q^{69} +(70.3088 + 9.03487i) q^{70} -22.7302 q^{71} -62.2599i q^{72} +45.3166i q^{73} +103.629i q^{74} +(35.1994 - 134.698i) q^{75} +16.7760i q^{76} +98.3255i q^{77} -112.766i q^{78} +65.6145i q^{79} +(2.54909 - 19.8369i) q^{80} +205.427 q^{81} +28.0850i q^{82} +4.65260 q^{83} +111.655i q^{84} +(11.0774 - 86.2033i) q^{85} -25.6915i q^{86} -150.308i q^{87} +27.7415 q^{88} -121.117i q^{89} +(154.380 + 19.8383i) q^{90} +143.542i q^{91} +(29.1859 - 35.5553i) q^{92} +23.6231i q^{93} +14.4556 q^{94} +(-41.5979 - 5.34544i) q^{95} +31.5022 q^{96} +99.8370 q^{97} -72.8308i q^{98} +215.898i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9}+O(q^{10}) \) 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9	\( 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9} + 96 q^{16} - 16 q^{24} - 48 q^{25} - 32 q^{26} + 100 q^{29} - 124 q^{31} - 28 q^{35} + 192 q^{36} + 192 q^{39} - 116 q^{41} + 148 q^{46} - 76 q^{49} - 144 q^{50} - 16 q^{54} - 224 q^{55} + 84 q^{59} - 192 q^{64} - 340 q^{69} + 328 q^{70} + 196 q^{71} - 496 q^{75} + 1360 q^{81} + 316 q^{85} - 376 q^{94} - 368 q^{95} + 32 q^{96}+O(q^{100}) \) 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9 + 96 * q^16 - 16 * q^24 - 48 * q^25 - 32 * q^26 + 100 * q^29 - 124 * q^31 - 28 * q^35 + 192 * q^36 + 192 * q^39 - 116 * q^41 + 148 * q^46 - 76 * q^49 - 144 * q^50 - 16 * q^54 - 224 * q^55 + 84 * q^59 - 192 * q^64 - 340 * q^69 + 328 * q^70 + 196 * q^71 - 496 * q^75 + 1360 * q^81 + 316 * q^85 - 376 * q^94 - 368 * q^95 + 32 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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