LMFDB - Embedded newform 378.3.s.e.53.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,3,Mod(53,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("378.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.s (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:	$10.2997539928$
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			53.12
Character	$\chi$	$=$	378.53
Dual form			378.3.s.e.107.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(7.50889 - 4.33526i) q^{5} +(-4.86680 + 5.03132i) q^{7} -2.82843i q^{8} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(7.50889 - 4.33526i) q^{5} +(-4.86680 + 5.03132i) q^{7} -2.82843i q^{8} +(6.13099 - 10.6192i) q^{10} +(17.9962 + 10.3901i) q^{11} +14.2723 q^{13} +(-2.40291 + 9.60344i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-20.8984 - 12.0657i) q^{17} +(-5.29128 - 9.16476i) q^{19} -17.3410i q^{20} +29.3876 q^{22} +(-7.83169 + 4.52163i) q^{23} +(25.0890 - 43.4554i) q^{25} +(17.4799 - 10.0920i) q^{26} +(3.84771 + 13.4609i) q^{28} -7.52043i q^{29} +(3.20366 - 5.54890i) q^{31} +(-4.89898 - 2.82843i) q^{32} -34.1269 q^{34} +(-14.7322 + 58.8786i) q^{35} +(-5.11561 - 8.86050i) q^{37} +(-12.9609 - 7.48299i) q^{38} +(-12.2620 - 21.2384i) q^{40} +66.6674i q^{41} -7.07514 q^{43} +(35.9924 - 20.7802i) q^{44} +(-6.39455 + 11.0757i) q^{46} +(24.6311 - 14.2208i) q^{47} +(-1.62846 - 48.9729i) q^{49} -70.9624i q^{50} +(14.2723 - 24.7203i) q^{52} +(-46.7667 - 27.0008i) q^{53} +180.175 q^{55} +(14.2307 + 13.7654i) q^{56} +(-5.31775 - 9.21061i) q^{58} +(-25.3538 - 14.6380i) q^{59} +(-8.95564 - 15.5116i) q^{61} -9.06132i q^{62} -8.00000 q^{64} +(107.169 - 61.8741i) q^{65} +(-47.5167 + 82.3014i) q^{67} +(-41.7968 + 24.1314i) q^{68} +(23.5902 + 82.5284i) q^{70} +107.104i q^{71} +(58.6643 - 101.610i) q^{73} +(-12.5306 - 7.23457i) q^{74} -21.1651 q^{76} +(-139.860 + 39.9781i) q^{77} +(24.7364 + 42.8447i) q^{79} +(-30.0356 - 17.3410i) q^{80} +(47.1410 + 81.6505i) q^{82} +88.9954i q^{83} -209.232 q^{85} +(-8.66524 + 5.00288i) q^{86} +(29.3876 - 50.9009i) q^{88} +(-63.3370 + 36.5677i) q^{89} +(-69.4604 + 71.8085i) q^{91} +18.0865i q^{92} +(20.1112 - 34.8336i) q^{94} +(-79.4633 - 45.8781i) q^{95} -106.700 q^{97} +(-36.6235 - 58.8279i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} + 8 q^{7}+O(q^{10}) $ 24 * q + 24 * q^4 + 8 * q^7	$ 24 q + 24 q^{4} + 8 q^{7} + 8 q^{10} - 16 q^{13} - 48 q^{16} - 36 q^{19} + 64 q^{22} + 128 q^{25} + 32 q^{28} + 176 q^{31} + 16 q^{34} - 72 q^{37} - 16 q^{40} + 216 q^{43} + 64 q^{46} - 24 q^{49} - 16 q^{52} + 448 q^{55} + 104 q^{58} - 268 q^{61} - 192 q^{64} - 248 q^{67} - 80 q^{70} - 116 q^{73} - 144 q^{76} + 152 q^{79} + 240 q^{82} - 536 q^{85} + 64 q^{88} + 428 q^{91} + 144 q^{94} + 16 q^{97}+O(q^{100}) $ 24 * q + 24 * q^4 + 8 * q^7 + 8 * q^10 - 16 * q^13 - 48 * q^16 - 36 * q^19 + 64 * q^22 + 128 * q^25 + 32 * q^28 + 176 * q^31 + 16 * q^34 - 72 * q^37 - 16 * q^40 + 216 * q^43 + 64 * q^46 - 24 * q^49 - 16 * q^52 + 448 * q^55 + 104 * q^58 - 268 * q^61 - 192 * q^64 - 248 * q^67 - 80 * q^70 - 116 * q^73 - 144 * q^76 + 152 * q^79 + 240 * q^82 - 536 * q^85 + 64 * q^88 + 428 * q^91 + 144 * q^94 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	7.50889	−	4.33526i	1.50178	−	0.867052i	0.501781	−	0.864995i	$-0.332678\pi$
$5$	7.50889	−	4.33526i	1.50178	−	0.867052i	0.999998	−	0.00205766i	$-0.000654974\pi$
$6$		0			0
$7$	−4.86680	+	5.03132i	−0.695258	+	0.718761i
$7$	−4.86680	+	5.03132i	−0.695258	+	0.718761i
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	6.13099	−	10.6192i	0.613099	−	1.06192i
$11$	17.9962	+	10.3901i	1.63602	+	0.944555i	0.982185	+	0.187914i	$0.0601728\pi$
$11$	17.9962	+	10.3901i	1.63602	+	0.944555i	0.653831	+	0.756640i	$0.273161\pi$
$12$		0			0
$13$	14.2723			1.09787			0.548934	−	0.835866i	$-0.315034\pi$
$13$	14.2723			1.09787			0.548934	+	0.835866i	$0.315034\pi$
$14$	−2.40291	+	9.60344i	−0.171636	+	0.685960i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−20.8984	−	12.0657i	−1.22932	−	0.709747i	−0.262430	−	0.964951i	$-0.584524\pi$
$17$	−20.8984	−	12.0657i	−1.22932	−	0.709747i	−0.966887	+	0.255204i	$0.917857\pi$
$18$		0			0
$19$	−5.29128	−	9.16476i	−0.278488	−	0.482356i	0.692521	−	0.721398i	$-0.256500\pi$
$19$	−5.29128	−	9.16476i	−0.278488	−	0.482356i	−0.971009	+	0.239042i	$0.923167\pi$
$20$		−	17.3410i		−	0.867052i
$21$		0			0
$22$	29.3876			1.33580
$23$	−7.83169	+	4.52163i	−0.340508	+	0.196593i	−0.660497	−	0.750829i	$-0.729654\pi$
$23$	−7.83169	+	4.52163i	−0.340508	+	0.196593i	0.319988	+	0.947421i	$0.396321\pi$
$24$		0			0
$25$	25.0890	−	43.4554i	1.00356	−	1.73822i
$26$	17.4799	−	10.0920i	0.672304	−	0.388155i
$27$		0			0
$28$	3.84771	+	13.4609i	0.137418	+	0.480746i
$29$		−	7.52043i		−	0.259325i	−0.991558	−	0.129663i	$-0.958611\pi$
$29$		−	7.52043i		−	0.259325i	0.991558	−	0.129663i	$-0.0413894\pi$
$30$		0			0
$31$	3.20366	−	5.54890i	0.103344	−	0.178997i	−0.809716	−	0.586821i	$-0.800379\pi$
$31$	3.20366	−	5.54890i	0.103344	−	0.178997i	0.913060	+	0.407824i	$0.133712\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−34.1269			−1.00373
$35$	−14.7322	+	58.8786i	−0.420920	+	1.68224i
$36$		0			0
$37$	−5.11561	−	8.86050i	−0.138260	−	0.239473i	0.788578	−	0.614934i	$-0.210818\pi$
$37$	−5.11561	−	8.86050i	−0.138260	−	0.239473i	−0.926838	+	0.375462i	$0.877484\pi$
$38$	−12.9609	−	7.48299i	−0.341077	−	0.196921i
$39$		0			0
$40$	−12.2620	−	21.2384i	−0.306549	−	0.530959i
$41$			66.6674i			1.62603i	0.582240	+	0.813017i	$0.302176\pi$
$41$			66.6674i			1.62603i	−0.582240	+	0.813017i	$0.697824\pi$
$42$		0			0
$43$	−7.07514			−0.164538			−0.0822691	−	0.996610i	$-0.526217\pi$
$43$	−7.07514			−0.164538			−0.0822691	+	0.996610i	$0.526217\pi$
$44$	35.9924	−	20.7802i	0.818008	−	0.472277i
$45$		0			0
$46$	−6.39455	+	11.0757i	−0.139012	+	0.240776i
$47$	24.6311	−	14.2208i	0.524066	−	0.302570i	−0.214531	−	0.976717i	$-0.568822\pi$
$47$	24.6311	−	14.2208i	0.524066	−	0.302570i	0.738597	+	0.674148i	$0.235489\pi$
$48$		0			0
$49$	−1.62846	−	48.9729i	−0.0332339	−	0.999448i
$50$		−	70.9624i		−	1.41925i
$51$		0			0
$52$	14.2723	−	24.7203i	0.274467	−	0.475391i
$53$	−46.7667	−	27.0008i	−0.882391	−	0.509449i	−0.0109452	−	0.999940i	$-0.503484\pi$
$53$	−46.7667	−	27.0008i	−0.882391	−	0.509449i	−0.871446	+	0.490491i	$0.836817\pi$
$54$		0			0
$55$	180.175			3.27591
$56$	14.2307	+	13.7654i	0.254120	+	0.245811i
$57$		0			0
$58$	−5.31775	−	9.21061i	−0.0916853	−	0.158804i
$59$	−25.3538	−	14.6380i	−0.429725	−	0.248102i	0.269505	−	0.962999i	$-0.413140\pi$
$59$	−25.3538	−	14.6380i	−0.429725	−	0.248102i	−0.699229	+	0.714897i	$0.746473\pi$
$60$		0			0
$61$	−8.95564	−	15.5116i	−0.146814	−	0.254289i	0.783234	−	0.621727i	$-0.213568\pi$
$61$	−8.95564	−	15.5116i	−0.146814	−	0.254289i	−0.930048	+	0.367438i	$0.880235\pi$
$62$		−	9.06132i		−	0.146150i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	107.169	−	61.8741i	1.64875	−	0.951909i
$66$		0			0
$67$	−47.5167	+	82.3014i	−0.709205	+	1.22838i	0.255947	+	0.966691i	$0.417613\pi$
$67$	−47.5167	+	82.3014i	−0.709205	+	1.22838i	−0.965152	+	0.261688i	$0.915721\pi$
$68$	−41.7968	+	24.1314i	−0.614659	+	0.354873i
$69$		0			0
$70$	23.5902	+	82.5284i	0.337003	+	1.17898i
$71$			107.104i			1.50850i	0.656585	+	0.754252i	$0.272001\pi$
$71$			107.104i			1.50850i	−0.656585	+	0.754252i	$0.727999\pi$
$72$		0			0
$73$	58.6643	−	101.610i	0.803621	−	1.39191i	−0.113597	−	0.993527i	$-0.536237\pi$
$73$	58.6643	−	101.610i	0.803621	−	1.39191i	0.917218	−	0.398386i	$-0.130429\pi$
$74$	−12.5306	−	7.23457i	−0.169333	−	0.0977644i
$75$		0			0
$76$	−21.1651			−0.278488
$77$	−139.860	+	39.9781i	−1.81636	+	0.519196i
$78$		0			0
$79$	24.7364	+	42.8447i	0.313119	+	0.542338i	0.979036	−	0.203688i	$-0.0652928\pi$
$79$	24.7364	+	42.8447i	0.313119	+	0.542338i	−0.665917	+	0.746026i	$0.731960\pi$
$80$	−30.0356	−	17.3410i	−0.375445	−	0.216763i
$81$		0			0
$82$	47.1410	+	81.6505i	0.574890	+	0.995738i
$83$			88.9954i			1.07223i	0.844144	+	0.536117i	$0.180109\pi$
$83$			88.9954i			1.07223i	−0.844144	+	0.536117i	$0.819891\pi$
$84$		0			0
$85$	−209.232			−2.46155
$86$	−8.66524	+	5.00288i	−0.100759	+	0.0581730i
$87$		0			0
$88$	29.3876	−	50.9009i	0.333951	−	0.578419i
$89$	−63.3370	+	36.5677i	−0.711652	+	0.410873i	−0.811672	−	0.584113i	$-0.801443\pi$
$89$	−63.3370	+	36.5677i	−0.711652	+	0.410873i	0.100020	+	0.994985i	$0.468109\pi$
$90$		0			0
$91$	−69.4604	+	71.8085i	−0.763301	+	0.789104i
$92$			18.0865i			0.196593i
$93$		0			0
$94$	20.1112	−	34.8336i	0.213949	−	0.370571i
$95$	−79.4633	−	45.8781i	−0.836455	−	0.482928i
$96$		0			0
$97$	−106.700			−1.10000			−0.550001	−	0.835164i	$-0.685373\pi$
$97$	−106.700			−1.10000			−0.550001	+	0.835164i	$0.685373\pi$
$98$	−36.6235	−	58.8279i	−0.373710	−	0.600284i
$99$		0			0
$100$	−50.1780	−	86.9108i	−0.501780	−	0.869108i
$101$	71.1499	+	41.0784i	0.704455	+	0.406717i	0.809004	−	0.587803i	$-0.200007\pi$
$101$	71.1499	+	41.0784i	0.704455	+	0.406717i	−0.104550	+	0.994520i	$0.533340\pi$
$102$		0			0
$103$	−17.7585	−	30.7586i	−0.172412	−	0.298627i	0.766850	−	0.641826i	$-0.221823\pi$
$103$	−17.7585	−	30.7586i	−0.172412	−	0.298627i	−0.939263	+	0.343199i	$0.888489\pi$
$104$		−	40.3681i		−	0.388155i
$105$		0			0
$106$	−76.3698			−0.720470
$107$	−1.32075	+	0.762537i	−0.0123435	+	0.00712651i	−0.506159	−	0.862440i	$-0.668935\pi$
$107$	−1.32075	+	0.762537i	−0.0123435	+	0.00712651i	0.493816	+	0.869567i	$0.335602\pi$
$108$		0			0
$109$	−100.395	+	173.890i	−0.921059	+	1.59532i	−0.123279	+	0.992372i	$0.539341\pi$
$109$	−100.395	+	173.890i	−0.921059	+	1.59532i	−0.797780	+	0.602948i	$0.793992\pi$
$110$	220.669	−	127.403i	2.00608	−	1.15821i
$111$		0			0
$112$	27.1626	+	6.79645i	0.242523	+	0.0606826i
$113$			111.702i			0.988512i	0.869316	+	0.494256i	$0.164559\pi$
$113$			111.702i			0.988512i	−0.869316	+	0.494256i	$0.835441\pi$
$114$		0			0
$115$	−39.2049	+	67.9049i	−0.340912	+	0.590477i
$116$	−13.0258	−	7.52043i	−0.112291	−	0.0648313i
$117$		0			0
$118$	−41.4025			−0.350869
$119$	162.415	−	46.4253i	1.36483	−	0.390128i
$120$		0			0
$121$	155.408	+	269.175i	1.28437	+	2.22459i
$122$	−21.9367	−	12.6652i	−0.179809	−	0.103813i
$123$		0			0
$124$	−6.40732	−	11.0978i	−0.0516719	−	0.0894984i
$125$		−	218.306i		−	1.74645i
$126$		0			0
$127$	−117.661			−0.926461			−0.463230	−	0.886238i	$-0.653310\pi$
$127$	−117.661			−0.926461			−0.463230	+	0.886238i	$0.653310\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	87.5032	−	151.560i	0.673101	−	1.16585i
$131$	125.964	−	72.7252i	0.961555	−	0.555154i	0.0649037	−	0.997892i	$-0.479326\pi$
$131$	125.964	−	72.7252i	0.961555	−	0.555154i	0.896651	+	0.442737i	$0.145993\pi$
$132$		0			0
$133$	71.8625	+	17.9809i	0.540319	+	0.135195i
$134$			134.398i			1.00297i
$135$		0			0
$136$	−34.1269	+	59.1096i	−0.250933	+	0.434629i
$137$	−49.0580	−	28.3237i	−0.358088	−	0.206742i	0.310154	−	0.950686i	$-0.399619\pi$
$137$	−49.0580	−	28.3237i	−0.358088	−	0.206742i	−0.668242	+	0.743944i	$0.732953\pi$
$138$		0			0
$139$	−24.6609			−0.177416			−0.0887082	−	0.996058i	$-0.528274\pi$
$139$	−24.6609			−0.177416			−0.0887082	+	0.996058i	$0.528274\pi$
$140$	87.2484	+	84.3955i	0.623203	+	0.602825i
$141$		0			0
$142$	75.7339	+	131.175i	0.533337	+	0.923767i
$143$	256.847	+	148.290i	1.79613	+	1.03700i
$144$		0			0
$145$	−32.6030	−	56.4701i	−0.224849	−	0.389449i
$146$		−	165.928i		−	1.13649i
$147$		0			0
$148$	−20.4624			−0.138260
$149$	−93.0248	+	53.7079i	−0.624328	+	0.360456i	−0.778552	−	0.627580i	$-0.784045\pi$
$149$	−93.0248	+	53.7079i	−0.624328	+	0.360456i	0.154224	+	0.988036i	$0.450712\pi$
$150$		0			0
$151$	30.1196	−	52.1687i	0.199468	−	0.345488i	−0.748888	−	0.662696i	$-0.769412\pi$
$151$	30.1196	−	52.1687i	0.199468	−	0.345488i	0.948356	+	0.317208i	$0.102745\pi$
$152$	−25.9219	+	14.9660i	−0.170538	+	0.0984604i
$153$		0			0
$154$	−143.024	+	147.859i	−0.928726	+	0.960122i
$155$		−	55.5548i		−	0.358418i
$156$		0			0
$157$	47.3063	−	81.9369i	0.301314	−	0.521891i	−0.675120	−	0.737708i	$-0.735908\pi$
$157$	47.3063	−	81.9369i	0.301314	−	0.521891i	0.976434	+	0.215817i	$0.0692415\pi$
$158$	60.5915	+	34.9825i	0.383491	+	0.221408i
$159$		0			0
$160$	−49.0479			−0.306549
$161$	15.3655	−	61.4097i	0.0954380	−	0.381427i
$162$		0			0
$163$	−135.827	−	235.260i	−0.833297	−	1.44331i	−0.895410	−	0.445243i	$-0.853117\pi$
$163$	−135.827	−	235.260i	−0.833297	−	1.44331i	0.0621129	−	0.998069i	$-0.480216\pi$
$164$	115.471	+	66.6674i	0.704093	+	0.406508i
$165$		0			0
$166$	62.9292	+	108.997i	0.379092	+	0.656606i
$167$		−	26.0210i		−	0.155815i	−0.996961	−	0.0779073i	$-0.975176\pi$
$167$		−	26.0210i		−	0.155815i	0.996961	−	0.0779073i	$-0.0248238\pi$
$168$		0			0
$169$	34.6981			0.205314
$170$	−256.256	+	147.949i	−1.50739	+	0.870289i
$171$		0			0
$172$	−7.07514	+	12.2545i	−0.0411345	+	0.0712471i
$173$	−80.0949	+	46.2428i	−0.462976	+	0.267299i	−0.713295	−	0.700864i	$-0.752798\pi$
$173$	−80.0949	+	46.2428i	−0.462976	+	0.267299i	0.250319	+	0.968164i	$0.419465\pi$
$174$		0			0
$175$	96.5351	+	337.720i	0.551629	+	1.92983i
$176$		−	83.1208i		−	0.472277i
$177$		0			0
$178$	−51.7145	+	89.5721i	−0.290531	+	0.503214i
$179$	−93.2534	−	53.8399i	−0.520969	−	0.300781i	0.216362	−	0.976313i	$-0.430581\pi$
$179$	−93.2534	−	53.8399i	−0.520969	−	0.300781i	−0.737331	+	0.675532i	$0.763914\pi$
$180$		0			0
$181$	117.141			0.647190			0.323595	−	0.946196i	$-0.395108\pi$
$181$	117.141			0.647190			0.323595	+	0.946196i	$0.395108\pi$
$182$	−34.2950	+	137.063i	−0.188434	+	0.753093i
$183$		0			0
$184$	12.7891	+	22.1514i	0.0695060	+	0.120388i
$185$	−76.8252	−	44.3550i	−0.415271	−	0.239757i
$186$		0			0
$187$	−250.728	−	434.273i	−1.34079	−	2.32232i
$188$		−	56.8831i		−	0.302570i
$189$		0			0
$190$	−129.763			−0.682963
$191$	−126.515	+	73.0436i	−0.662383	+	0.382427i	−0.793184	−	0.608981i	$-0.791578\pi$
$191$	−126.515	+	73.0436i	−0.662383	+	0.382427i	0.130801	+	0.991409i	$0.458245\pi$
$192$		0			0
$193$	48.2616	−	83.5916i	0.250060	−	0.433117i	−0.713482	−	0.700674i	$-0.752883\pi$
$193$	48.2616	−	83.5916i	0.250060	−	0.433117i	0.963542	+	0.267557i	$0.0862162\pi$
$194$	−130.680	+	75.4484i	−0.673611	+	0.388909i
$195$		0			0
$196$	−86.4521	−	46.1524i	−0.441082	−	0.235471i
$197$		−	134.797i		−	0.684247i	−0.939655	−	0.342123i	$-0.888854\pi$
$197$		−	134.797i		−	0.684247i	0.939655	−	0.342123i	$-0.111146\pi$
$198$		0			0
$199$	133.940	−	231.990i	0.673063	−	1.16578i	−0.303967	−	0.952682i	$-0.598311\pi$
$199$	133.940	−	231.990i	0.673063	−	1.16578i	0.977031	−	0.213098i	$-0.0683553\pi$
$200$	−122.910	−	70.9624i	−0.614552	−	0.354812i
$201$		0			0
$202$	116.187			0.575185
$203$	37.8377	+	36.6005i	0.186393	+	0.180298i
$204$		0			0
$205$	289.021	+	500.598i	1.40986	+	2.44194i
$206$	−43.4992	−	25.1143i	−0.211161	−	0.121914i
$207$		0			0
$208$	−28.5446	−	49.4406i	−0.137233	−	0.237695i
$209$		−	219.908i		−	1.05219i
$210$		0			0
$211$	−251.891			−1.19380			−0.596899	−	0.802316i	$-0.703601\pi$
$211$	−251.891			−1.19380			−0.596899	+	0.802316i	$0.703601\pi$
$212$	−93.5335	+	54.0016i	−0.441196	+	0.254724i
$213$		0			0
$214$	−1.07839	+	1.86783i	−0.00503921	+	0.00872816i
$215$	−53.1265	+	30.6726i	−0.247100	+	0.142663i
$216$		0			0
$217$	12.3267	+	43.1241i	0.0568053	+	0.198728i
$218$			283.961i			1.30257i
$219$		0			0
$220$	180.175	−	312.073i	0.818978	−	1.41851i
$221$	−298.268	−	172.205i	−1.34963	−	0.779208i
$222$		0			0
$223$	427.001			1.91480			0.957401	−	0.288761i	$-0.0932434\pi$
$223$	427.001			1.91480			0.957401	+	0.288761i	$0.0932434\pi$
$224$	38.0731	−	10.8830i	0.169969	−	0.0485846i
$225$		0			0
$226$	78.9851	+	136.806i	0.349492	+	0.605337i
$227$	235.832	+	136.158i	1.03891	+	0.599814i	0.919524	−	0.393034i	$-0.128575\pi$
$227$	235.832	+	136.158i	1.03891	+	0.599814i	0.119384	+	0.992848i	$0.461908\pi$
$228$		0			0
$229$	−38.8763	−	67.3357i	−0.169765	−	0.294042i	0.768572	−	0.639763i	$-0.220968\pi$
$229$	−38.8763	−	67.3357i	−0.169765	−	0.294042i	−0.938337	+	0.345721i	$0.887634\pi$
$230$			110.888i			0.482123i
$231$		0			0
$232$	−21.2710			−0.0916853
$233$	27.7244	−	16.0067i	0.118989	−	0.0686982i	−0.439324	−	0.898329i	$-0.644782\pi$
$233$	27.7244	−	16.0067i	0.118989	−	0.0686982i	0.558313	+	0.829630i	$0.311449\pi$
$234$		0			0
$235$	123.302	−	213.564i	0.524687	−	0.908785i
$236$	−50.7075	+	29.2760i	−0.214862	+	0.124051i
$237$		0			0
$238$	166.089	−	171.704i	0.697853	−	0.721444i
$239$			296.164i			1.23918i	0.784925	+	0.619590i	$0.212701\pi$
$239$			296.164i			1.23918i	−0.784925	+	0.619590i	$0.787299\pi$
$240$		0			0
$241$	99.9257	−	173.076i	0.414629	−	0.718159i	−0.580760	−	0.814075i	$-0.697245\pi$
$241$	99.9257	−	173.076i	0.414629	−	0.718159i	0.995389	+	0.0959157i	$0.0305779\pi$
$242$	380.671	+	219.781i	1.57302	+	0.908185i
$243$		0			0
$244$	−35.8226			−0.146814
$245$	−224.538	−	360.673i	−0.916483	−	1.47213i
$246$		0			0
$247$	−75.5186	−	130.802i	−0.305743	−	0.529563i
$248$	−15.6947	−	9.06132i	−0.0632849	−	0.0365376i
$249$		0			0
$250$	−154.366	−	267.370i	−0.617464	−	1.06948i
$251$			176.183i			0.701926i	0.936389	+	0.350963i	$0.114146\pi$
$251$			176.183i			0.701926i	−0.936389	+	0.350963i	$0.885854\pi$
$252$		0			0
$253$	−187.921			−0.742770
$254$	−144.104	+	83.1985i	−0.567339	+	0.327553i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	251.692	−	145.315i	0.979347	−	0.565426i	0.0772739	−	0.997010i	$-0.475378\pi$
$257$	251.692	−	145.315i	0.979347	−	0.565426i	0.902073	+	0.431584i	$0.142045\pi$
$258$		0			0
$259$	69.4767	+	17.3840i	0.268250	+	0.0671197i
$260$		−	247.496i		−	0.951909i
$261$		0			0
$262$	102.849	−	178.140i	0.392553	−	0.679922i
$263$	22.5084	+	12.9952i	0.0855832	+	0.0494115i	0.542181	−	0.840262i	$-0.317599\pi$
$263$	22.5084	+	12.9952i	0.0855832	+	0.0494115i	−0.456598	+	0.889673i	$0.650932\pi$
$264$		0			0
$265$	−468.222			−1.76688
$266$	100.728	−	28.7924i	0.378675	−	0.108242i
$267$		0			0
$268$	95.0335	+	164.603i	0.354603	+	0.614190i
$269$	61.8759	+	35.7240i	0.230022	+	0.132803i	0.610582	−	0.791953i	$-0.290936\pi$
$269$	61.8759	+	35.7240i	0.230022	+	0.132803i	−0.380560	+	0.924756i	$0.624269\pi$
$270$		0			0
$271$	127.939	+	221.596i	0.472099	+	0.817699i	0.999490	−	0.0319235i	$-0.0101633\pi$
$271$	127.939	+	221.596i	0.472099	+	0.817699i	−0.527392	+	0.849622i	$0.676830\pi$
$272$			96.5256i			0.354873i
$273$		0			0
$274$	−80.1114			−0.292377
$275$	903.012	−	521.354i	3.28368	−	1.89583i
$276$		0			0
$277$	212.019	−	367.227i	0.765410	−	1.32573i	−0.174620	−	0.984636i	$-0.555870\pi$
$277$	212.019	−	367.227i	0.765410	−	1.32573i	0.940030	−	0.341093i	$-0.110797\pi$
$278$	−30.2033	+	17.4379i	−0.108645	+	0.0627262i
$279$		0			0
$280$	166.534	+	41.6689i	0.594763	+	0.148818i
$281$		−	195.647i		−	0.696252i	−0.937448	−	0.348126i	$-0.886818\pi$
$281$		−	195.647i		−	0.696252i	0.937448	−	0.348126i	$-0.113182\pi$
$282$		0			0
$283$	−33.3648	+	57.7896i	−0.117897	+	0.204203i	−0.918934	−	0.394411i	$-0.870949\pi$
$283$	−33.3648	+	57.7896i	−0.117897	+	0.204203i	0.801037	+	0.598615i	$0.204282\pi$
$284$	185.509	+	107.104i	0.653202	+	0.377126i
$285$		0			0
$286$	419.429			1.46653
$287$	−335.425	−	324.457i	−1.16873	−	1.13051i
$288$		0			0
$289$	146.662	+	254.026i	0.507481	+	0.878982i
$290$	−79.8608	−	46.1077i	−0.275382	−	0.158992i
$291$		0			0
$292$	−117.329	−	203.219i	−0.401811	−	0.695956i
$293$			320.934i			1.09534i	0.836695	+	0.547669i	$0.184485\pi$
$293$			320.934i			1.09534i	−0.836695	+	0.547669i	$0.815515\pi$
$294$		0			0
$295$	−253.838			−0.860469
$296$	−25.0613	+	14.4691i	−0.0846665	+	0.0488822i
$297$		0			0
$298$	−75.9544	+	131.557i	−0.254881	+	0.441466i
$299$	−111.776	+	64.5340i	−0.373833	+	0.215833i
$300$		0			0
$301$	34.4333	−	35.5973i	0.114396	−	0.118264i
$302$		−	85.1911i		−	0.282090i
$303$		0			0
$304$	−21.1651	+	36.6590i	−0.0696220	+	0.120589i
$305$	−134.494	−	77.6501i	−0.440964	−	0.254590i
$306$		0			0
$307$	142.642			0.464630			0.232315	−	0.972641i	$-0.425370\pi$
$307$	142.642			0.464630			0.232315	+	0.972641i	$0.425370\pi$
$308$	−70.6158	+	282.222i	−0.229272	+	0.916307i
$309$		0			0
$310$	−39.2832	−	68.0405i	−0.126720	−	0.219485i
$311$	−418.336	−	241.526i	−1.34513	−	0.776611i	−0.357575	−	0.933884i	$-0.616396\pi$
$311$	−418.336	−	241.526i	−1.34513	−	0.776611i	−0.987555	+	0.157273i	$0.949730\pi$
$312$		0			0
$313$	75.6771	+	131.077i	0.241780	+	0.418775i	0.961221	−	0.275778i	$-0.0889355\pi$
$313$	75.6771	+	131.077i	0.241780	+	0.418775i	−0.719442	+	0.694553i	$0.755602\pi$
$314$		−	133.802i		−	0.426122i
$315$		0			0
$316$	98.9456			0.313119
$317$	−132.391	+	76.4361i	−0.417638	+	0.241123i	−0.694066	−	0.719911i	$-0.744182\pi$
$317$	−132.391	+	76.4361i	−0.417638	+	0.241123i	0.276428	+	0.961035i	$0.410849\pi$
$318$		0			0
$319$	78.1381	−	135.339i	0.244947	−	0.424260i
$320$	−60.0712	+	34.6821i	−0.187722	+	0.108382i
$321$		0			0
$322$	−24.6044	−	86.0762i	−0.0764111	−	0.267318i
$323$			255.372i			0.790624i
$324$		0			0
$325$	358.077	−	620.208i	1.10178	−	1.90833i
$326$	−332.708	−	192.089i	−1.02058	−	0.589230i
$327$		0			0
$328$	188.564			0.574890
$329$	−48.3254	+	193.137i	−0.146886	+	0.587042i
$330$		0			0
$331$	−167.428	−	289.994i	−0.505825	−	0.876114i	−0.999977	−	0.00673894i	$-0.997855\pi$
$331$	−167.428	−	289.994i	−0.505825	−	0.876114i	0.494153	−	0.869375i	$-0.335478\pi$
$332$	154.145	+	88.9954i	0.464291	+	0.268058i
$333$		0			0
$334$	−18.3997	−	31.8691i	−0.0550888	−	0.0954166i
$335$			823.990i			2.45967i
$336$		0			0
$337$	−11.6151			−0.0344663			−0.0172331	−	0.999851i	$-0.505486\pi$
$337$	−11.6151			−0.0344663			−0.0172331	+	0.999851i	$0.505486\pi$
$338$	42.4963	−	24.5352i	0.125729	−	0.0725895i
$339$		0			0
$340$	−209.232	+	362.400i	−0.615388	+	1.06588i
$341$	115.307	−	66.5727i	0.338145	−	0.195228i
$342$		0			0
$343$	254.324	+	230.148i	0.741470	+	0.670986i
$344$			20.0115i			0.0581730i
$345$		0			0
$346$	−65.3972	+	113.271i	−0.189009	+	0.327374i
$347$	513.432	+	296.430i	1.47963	+	0.854265i	0.999734	−	0.0230599i	$-0.00734085\pi$
$347$	513.432	+	296.430i	1.47963	+	0.854265i	0.479897	+	0.877325i	$0.340674\pi$
$348$		0			0
$349$	−304.583			−0.872731			−0.436365	−	0.899770i	$-0.643734\pi$
$349$	−304.583			−0.872731			−0.436365	+	0.899770i	$0.643734\pi$
$350$	357.035	+	345.360i	1.02010	+	0.986743i
$351$		0			0
$352$	−58.7753	−	101.802i	−0.166975	−	0.289210i
$353$	−594.546	−	343.261i	−1.68427	−	0.972412i	−0.958768	−	0.284188i	$-0.908276\pi$
$353$	−594.546	−	343.261i	−1.68427	−	0.972412i	−0.725499	−	0.688224i	$-0.758391\pi$
$354$		0			0
$355$	464.323	+	804.231i	1.30795	+	2.26544i
$356$			146.271i			0.410873i
$357$		0			0
$358$	−152.282			−0.425369
$359$	418.605	−	241.682i	1.16603	−	0.673209i	0.213290	−	0.976989i	$-0.431582\pi$
$359$	418.605	−	241.682i	1.16603	−	0.673209i	0.952742	+	0.303780i	$0.0982488\pi$
$360$		0			0
$361$	124.505	−	215.649i	0.344889	−	0.597365i
$362$	143.468	−	82.8315i	0.396322	−	0.228816i
$363$		0			0
$364$	54.9156	+	192.117i	0.150867	+	0.527795i
$365$		−	1017.30i		−	2.78713i
$366$		0			0
$367$	76.7208	−	132.884i	0.209048	−	0.362082i	−0.742367	−	0.669994i	$-0.766297\pi$
$367$	76.7208	−	132.884i	0.209048	−	0.362082i	0.951415	+	0.307911i	$0.0996300\pi$
$368$	31.3268	+	18.0865i	0.0851271	+	0.0491482i
$369$		0			0
$370$	−125.455			−0.339068
$371$	363.454	−	103.891i	0.979661	−	0.280030i
$372$		0			0
$373$	−138.261	−	239.475i	−0.370672	−	0.642023i	0.618997	−	0.785393i	$-0.287539\pi$
$373$	−138.261	−	239.475i	−0.370672	−	0.642023i	−0.989669	+	0.143370i	$0.954206\pi$
$374$	−614.155	−	354.582i	−1.64212	−	0.948081i
$375$		0			0
$376$	−40.2224	−	69.6673i	−0.106974	−	0.185285i
$377$		−	107.334i		−	0.284705i
$378$		0			0
$379$	−396.161			−1.04528			−0.522640	−	0.852553i	$-0.675053\pi$
$379$	−396.161			−1.04528			−0.522640	+	0.852553i	$0.675053\pi$
$380$	−158.927	+	91.7563i	−0.418228	+	0.241464i
$381$		0			0
$382$	−103.299	+	178.920i	−0.270417	+	0.468376i
$383$	−263.830	+	152.322i	−0.688851	+	0.397708i	−0.803182	−	0.595734i	$-0.796861\pi$
$383$	−263.830	+	152.322i	−0.688851	+	0.397708i	0.114330	+	0.993443i	$0.463528\pi$
$384$		0			0
$385$	−876.877	+	906.520i	−2.27760	+	2.35460i
$386$		−	136.505i		−	0.353639i
$387$		0			0
$388$	−106.700	+	184.810i	−0.275000	+	0.476315i
$389$	408.682	+	235.952i	1.05060	+	0.606561i	0.922816	−	0.385241i	$-0.125882\pi$
$389$	408.682	+	235.952i	1.05060	+	0.606561i	0.127779	+	0.991803i	$0.459215\pi$
$390$		0			0
$391$	218.226			0.558124
$392$	−138.516	+	4.60598i	−0.353358	+	0.0117500i
$393$		0			0
$394$	−95.3156	−	165.091i	−0.241918	−	0.419014i
$395$	371.486	+	214.477i	0.940471	+	0.542981i
$396$		0			0
$397$	−194.550	−	336.970i	−0.490050	−	0.848791i	0.509885	−	0.860243i	$-0.329688\pi$
$397$	−194.550	−	336.970i	−0.490050	−	0.848791i	−0.999934	+	0.0114517i	$0.996355\pi$
$398$		−	378.838i		−	0.951856i
$399$		0			0
$400$	−200.712			−0.501780
$401$	562.454	−	324.733i	1.40263	−	0.809808i	0.407967	−	0.912997i	$-0.366238\pi$
$401$	562.454	−	324.733i	1.40263	−	0.809808i	0.994662	+	0.103189i	$0.0329046\pi$
$402$		0			0
$403$	45.7235	−	79.1955i	0.113458	−	0.196515i
$404$	142.300	−	82.1568i	0.352227	−	0.203359i
$405$		0			0
$406$	72.2220	+	18.0709i	0.177887	+	0.0445096i
$407$		−	212.607i		−	0.522376i
$408$		0			0
$409$	207.497	−	359.396i	0.507328	−	0.878718i	−0.492636	−	0.870235i	$-0.663967\pi$
$409$	207.497	−	359.396i	0.507328	−	0.878718i	0.999964	−	0.00848231i	$-0.00270003\pi$
$410$	707.953	+	408.737i	1.72671	+	0.996919i
$411$		0			0
$412$	−71.0338			−0.172412
$413$	197.040	−	56.3227i	0.477095	−	0.136375i
$414$		0			0
$415$	385.818	+	668.257i	0.929683	+	1.61026i
$416$	−69.9196	−	40.3681i	−0.168076	−	0.0970387i
$417$		0			0
$418$	−155.498	−	269.331i	−0.372005	−	0.644332i
$419$			45.9042i			0.109557i	0.998499	+	0.0547783i	$0.0174452\pi$
$419$			45.9042i			0.109557i	−0.998499	+	0.0547783i	$0.982555\pi$
$420$		0			0
$421$	315.779			0.750068			0.375034	−	0.927011i	$-0.377631\pi$
$421$	315.779			0.750068			0.375034	+	0.927011i	$0.377631\pi$
$422$	−308.503	+	178.114i	−0.731049	+	0.422071i
$423$		0			0
$424$	−76.3698	+	132.276i	−0.180117	+	0.311972i
$425$	−1048.64	+	605.432i	−2.46739	+	1.42455i
$426$		0			0
$427$	121.629	+	30.4333i	0.284846	+	0.0712723i
$428$			3.05015i			0.00712651i
$429$		0			0
$430$	−43.3776	+	75.1322i	−0.100878	+	0.174726i
$431$	27.2604	+	15.7388i	0.0632492	+	0.0365169i	0.531291	−	0.847189i	$-0.321707\pi$
$431$	27.2604	+	15.7388i	0.0632492	+	0.0365169i	−0.468042	+	0.883706i	$0.655040\pi$
$432$		0			0
$433$	−318.863			−0.736404			−0.368202	−	0.929746i	$-0.620026\pi$
$433$	−318.863			−0.736404			−0.368202	+	0.929746i	$0.620026\pi$
$434$	45.5904	+	44.0997i	0.105047	+	0.101612i
$435$		0			0
$436$	200.791	+	347.780i	0.460529	+	0.797660i
$437$	82.8793	+	47.8504i	0.189655	+	0.109497i
$438$		0			0
$439$	−264.483	−	458.098i	−0.602467	−	1.04350i	−0.992446	−	0.122679i	$-0.960851\pi$
$439$	−264.483	−	458.098i	−0.602467	−	1.04350i	0.389980	−	0.920823i	$-0.372482\pi$
$440$		−	509.613i		−	1.15821i
$441$		0			0
$442$	−487.069			−1.10197
$443$	−346.977	+	200.327i	−0.783245	+	0.452206i	−0.837579	−	0.546316i	$-0.816030\pi$
$443$	−346.977	+	200.327i	−0.783245	+	0.452206i	0.0543344	+	0.998523i	$0.482696\pi$
$444$		0			0
$445$	−317.061	+	549.165i	−0.712496	+	1.23408i
$446$	522.967	−	301.935i	1.17257	−	0.676985i
$447$		0			0
$448$	38.9344	−	40.2506i	0.0869072	−	0.0898451i
$449$			410.186i			0.913555i	0.889581	+	0.456777i	$0.150996\pi$
$449$			410.186i			0.913555i	−0.889581	+	0.456777i	$0.849004\pi$
$450$		0			0
$451$	−692.681	+	1199.76i	−1.53588	+	2.66022i
$452$	193.473	+	111.702i	0.428038	+	0.247128i
$453$		0			0
$454$	385.112			0.848265
$455$	−210.262	+	840.331i	−0.462114	+	1.84688i
$456$		0			0
$457$	−90.2981	−	156.401i	−0.197589	−	0.342234i	0.750157	−	0.661259i	$-0.229978\pi$
$457$	−90.2981	−	156.401i	−0.197589	−	0.342234i	−0.947746	+	0.319026i	$0.896644\pi$
$458$	−95.2270	−	54.9794i	−0.207919	−	0.120042i
$459$		0			0
$460$	78.4098	+	135.810i	0.170456	+	0.295239i
$461$			277.708i			0.602403i	0.953560	+	0.301202i	$0.0973877\pi$
$461$			277.708i			0.602403i	−0.953560	+	0.301202i	$0.902612\pi$
$462$		0			0
$463$	−519.910			−1.12292			−0.561458	−	0.827505i	$-0.689759\pi$
$463$	−519.910			−1.12292			−0.561458	+	0.827505i	$0.689759\pi$
$464$	−26.0515	+	15.0409i	−0.0561456	+	0.0324157i
$465$		0			0
$466$	22.6369	−	39.2082i	0.0485770	−	0.0841378i
$467$	−49.5843	+	28.6275i	−0.106176	+	0.0613009i	−0.552148	−	0.833746i	$-0.686192\pi$
$467$	−49.5843	+	28.6275i	−0.106176	+	0.0613009i	0.445972	+	0.895047i	$0.352858\pi$
$468$		0			0
$469$	−182.831	−	639.617i	−0.389831	−	1.36379i
$470$		−	348.749i		−	0.742020i
$471$		0			0
$472$	−41.4025	+	71.7113i	−0.0877172	+	0.151931i
$473$	−127.326	−	73.5115i	−0.269187	−	0.155415i
$474$		0			0
$475$	−531.011			−1.11792
$476$	82.0039	−	327.736i	0.172277	−	0.688521i
$477$		0			0
$478$	209.420	+	362.726i	0.438117	+	0.758840i
$479$	−498.037	−	287.542i	−1.03974	−	0.600296i	−0.119982	−	0.992776i	$-0.538284\pi$
$479$	−498.037	−	287.542i	−1.03974	−	0.600296i	−0.919760	+	0.392480i	$0.871617\pi$
$480$		0			0
$481$	−73.0115	−	126.460i	−0.151791	−	0.262910i
$482$		−	282.632i		−	0.586374i
$483$		0			0
$484$	621.634			1.28437
$485$	−801.200	+	462.573i	−1.65196	+	0.953759i
$486$		0			0
$487$	−98.8020	+	171.130i	−0.202879	+	0.351397i	−0.949455	−	0.313904i	$-0.898363\pi$
$487$	−98.8020	+	171.130i	−0.202879	+	0.351397i	0.746576	+	0.665300i	$0.231696\pi$
$488$	−43.8735	+	25.3304i	−0.0899047	+	0.0519065i
$489$		0			0
$490$	−530.036	−	282.959i	−1.08171	−	0.577468i
$491$			82.1487i			0.167309i	0.996495	+	0.0836545i	$0.0266592\pi$
$491$			82.1487i			0.167309i	−0.996495	+	0.0836545i	$0.973341\pi$
$492$		0			0
$493$	−90.7392	+	157.165i	−0.184055	+	0.318793i
$494$	−184.982	−	106.799i	−0.374457	−	0.216193i
$495$		0			0
$496$	−25.6293			−0.0516719
$497$	−538.874	−	521.253i	−1.08425	−	1.04880i
$498$		0			0
$499$	−93.2348	−	161.487i	−0.186843	−	0.323622i	0.757353	−	0.653006i	$-0.226492\pi$
$499$	−93.2348	−	161.487i	−0.186843	−	0.323622i	−0.944196	+	0.329384i	$0.893159\pi$
$500$	−378.118	−	218.306i	−0.756235	−	0.436613i
$501$		0			0
$502$	124.580	+	215.780i	0.248168	+	0.429840i
$503$			70.5631i			0.140285i	0.997537	+	0.0701423i	$0.0223453\pi$
$503$			70.5631i			0.140285i	−0.997537	+	0.0701423i	$0.977655\pi$
$504$		0			0
$505$	712.343			1.41058
$506$	−230.155	+	132.880i	−0.454852	+	0.262609i
$507$		0			0
$508$	−117.661	+	203.794i	−0.231615	+	0.401169i
$509$	86.1465	−	49.7367i	0.169247	−	0.0977145i	−0.412984	−	0.910738i	$-0.635513\pi$
$509$	86.1465	−	49.7367i	0.169247	−	0.0977145i	0.582231	+	0.813024i	$0.302180\pi$
$510$		0			0
$511$	225.723	+	789.673i	0.441728	+	1.54535i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	205.506	−	355.946i	0.399817	−	0.692503i
$515$	−266.693	−	153.975i	−0.517850	−	0.298981i
$516$		0			0
$517$	591.021			1.14317
$518$	97.3836	−	27.8365i	0.187999	−	0.0537384i
$519$		0			0
$520$	−175.006	−	303.120i	−0.336551	−	0.582923i
$521$	323.761	+	186.924i	0.621423	+	0.358779i	0.777423	−	0.628978i	$-0.216527\pi$
$521$	323.761	+	186.924i	0.621423	+	0.358779i	−0.156000	+	0.987757i	$0.549860\pi$
$522$		0			0
$523$	−78.9282	−	136.708i	−0.150914	−	0.261391i	0.780649	−	0.624969i	$-0.214888\pi$
$523$	−78.9282	−	136.708i	−0.150914	−	0.261391i	−0.931564	+	0.363578i	$0.881555\pi$
$524$		−	290.901i		−	0.555154i
$525$		0			0
$526$	36.7560			0.0698784
$527$	−133.903	+	77.3088i	−0.254085	+	0.146696i
$528$		0			0
$529$	−223.610	+	387.303i	−0.422703	+	0.732143i
$530$	−573.452	+	331.083i	−1.08199	+	0.624685i
$531$		0			0
$532$	103.006	−	106.489i	0.193621	−	0.200166i
$533$			951.496i			1.78517i
$534$		0			0
$535$	−6.61159	+	11.4516i	−0.0123581	+	0.0214049i
$536$	232.784	+	134.398i	0.434298	+	0.250742i
$537$		0			0
$538$	101.043			0.187812
$539$	479.528	−	898.246i	0.889662	−	1.66650i
$540$		0			0
$541$	89.0870	+	154.303i	0.164671	+	0.285218i	0.936538	−	0.350565i	$-0.114010\pi$
$541$	89.0870	+	154.303i	0.164671	+	0.285218i	−0.771867	+	0.635783i	$0.780677\pi$
$542$	313.385	+	180.933i	0.578200	+	0.333824i
$543$		0			0
$544$	68.2539	+	118.219i	0.125467	+	0.217315i
$545$			1740.96i			3.19442i
$546$		0			0
$547$	702.119			1.28358			0.641791	−	0.766880i	$-0.278192\pi$
$547$	702.119			1.28358			0.641791	+	0.766880i	$0.278192\pi$
$548$	−98.1160	+	56.6473i	−0.179044	+	0.103371i
$549$		0			0
$550$	737.306	−	1277.05i	1.34056	−	2.32191i
$551$	−68.9229	+	39.7927i	−0.125087	+	0.0722190i
$552$		0			0
$553$	−335.953	−	84.0598i	−0.607509	−	0.152007i
$554$		−	599.679i		−	1.08245i
$555$		0			0
$556$	−24.6609	+	42.7139i	−0.0443541	+	0.0768236i
$557$	−657.663	−	379.702i	−1.18072	−	0.681691i	−0.224542	−	0.974464i	$-0.572089\pi$
$557$	−657.663	−	379.702i	−1.18072	−	0.681691i	−0.956182	+	0.292773i	$0.905422\pi$
$558$		0			0
$559$	−100.978			−0.180641
$560$	233.426	−	66.7233i	0.416832	−	0.119149i
$561$		0			0
$562$	−138.343	−	239.617i	−0.246162	−	0.426365i
$563$	199.465	+	115.161i	0.354290	+	0.204549i	0.666573	−	0.745440i	$-0.267760\pi$
$563$	199.465	+	115.161i	0.354290	+	0.204549i	−0.312283	+	0.949989i	$0.601094\pi$
$564$		0			0
$565$	484.257	+	838.757i	0.857092	+	1.48453i
$566$			94.3700i			0.166731i
$567$		0			0
$568$	302.935			0.533337
$569$	569.401	−	328.744i	1.00070	−	0.577757i	0.0922477	−	0.995736i	$-0.470595\pi$
$569$	569.401	−	328.744i	1.00070	−	0.577757i	0.908457	+	0.417979i	$0.137262\pi$
$570$		0			0
$571$	−202.408	+	350.581i	−0.354480	+	0.613977i	−0.987029	−	0.160543i	$-0.948675\pi$
$571$	−202.408	+	350.581i	−0.354480	+	0.613977i	0.632549	+	0.774520i	$0.282009\pi$
$572$	513.693	−	296.581i	0.898065	−	0.518498i
$573$		0			0
$574$	−640.236	−	160.196i	−1.11539	−	0.279086i
$575$			453.773i			0.789170i
$576$		0			0
$577$	−133.102	+	230.540i	−0.230680	+	0.399549i	−0.958008	−	0.286740i	$-0.907428\pi$
$577$	−133.102	+	230.540i	−0.230680	+	0.399549i	0.727329	+	0.686289i	$0.240762\pi$
$578$	359.247	+	207.411i	0.621534	+	0.358843i
$579$		0			0
$580$	−130.412			−0.224849
$581$	−447.765	−	433.123i	−0.770679	−	0.745479i
$582$		0			0
$583$	−561.082	−	971.822i	−0.962405	−	1.66693i
$584$	−287.395	−	165.928i	−0.492115	−	0.284123i
$585$		0			0
$586$	226.935	+	393.062i	0.387260	+	0.670755i
$587$		−	1056.47i		−	1.79979i	−0.436112	−	0.899893i	$-0.643645\pi$
$587$		−	1056.47i		−	1.79979i	0.436112	−	0.899893i	$-0.356355\pi$
$588$		0			0
$589$	−67.8058			−0.115120
$590$	−310.887	+	179.491i	−0.526927	+	0.304222i
$591$		0			0
$592$	−20.4624	+	35.4420i	−0.0345649	+	0.0598682i
$593$	356.475	−	205.811i	0.601138	−	0.347067i	−0.168351	−	0.985727i	$-0.553844\pi$
$593$	356.475	−	205.811i	0.601138	−	0.347067i	0.769489	+	0.638660i	$0.220511\pi$
$594$		0			0
$595$	1018.29	−	1052.71i	1.71141	−	1.76927i
$596$			214.832i			0.360456i
$597$		0			0
$598$	−91.2648	+	158.075i	−0.152617	+	0.264340i
$599$	162.408	+	93.7661i	0.271131	+	0.156538i	0.629402	−	0.777080i	$-0.283300\pi$
$599$	162.408	+	93.7661i	0.271131	+	0.156538i	−0.358270	+	0.933618i	$0.616633\pi$
$600$		0			0
$601$	1046.72			1.74163			0.870813	−	0.491614i	$-0.163593\pi$
$601$	1046.72			1.74163			0.870813	+	0.491614i	$0.163593\pi$
$602$	17.0009	−	67.9457i	0.0282407	−	0.112867i
$603$		0			0
$604$	−60.2392	−	104.337i	−0.0997338	−	0.172744i
$605$	2333.89	+	1347.47i	3.85767	+	2.22723i
$606$		0			0
$607$	−419.594	−	726.758i	−0.691259	−	1.19730i	−0.971426	−	0.237344i	$-0.923723\pi$
$607$	−419.594	−	726.758i	−0.691259	−	1.19730i	0.280167	−	0.959951i	$-0.409610\pi$
$608$			59.8639i			0.0984604i
$609$		0			0
$610$	−219.628			−0.360045
$611$	351.542	−	202.963i	0.575355	−	0.332181i
$612$		0			0
$613$	−560.113	+	970.144i	−0.913725	+	1.58262i	−0.104967	+	0.994476i	$0.533474\pi$
$613$	−560.113	+	970.144i	−0.913725	+	1.58262i	−0.808758	+	0.588142i	$0.799860\pi$
$614$	174.699	−	100.863i	0.284527	−	0.164272i
$615$		0			0
$616$	113.075	+	395.583i	0.183563	+	0.642181i
$617$		−	1115.35i		−	1.80769i	−0.427859	−	0.903846i	$-0.640732\pi$
$617$		−	1115.35i		−	1.80769i	0.427859	−	0.903846i	$-0.359268\pi$
$618$		0			0
$619$	98.4595	−	170.537i	0.159062	−	0.275504i	−0.775469	−	0.631386i	$-0.782486\pi$
$619$	98.4595	−	170.537i	0.159062	−	0.275504i	0.934531	+	0.355882i	$0.115820\pi$
$620$	−96.2238	−	55.5548i	−0.155200	−	0.0896045i
$621$		0			0
$622$	−683.139			−1.09829
$623$	124.265	−	496.637i	0.199462	−	0.797170i
$624$		0			0
$625$	−319.190	−	552.854i	−0.510705	−	0.884566i
$626$	185.370	+	107.024i	0.296118	+	0.170964i
$627$		0			0
$628$	−94.6125	−	163.874i	−0.150657	−	0.260945i
$629$			246.894i			0.392518i
$630$		0			0
$631$	−820.657			−1.30057			−0.650283	−	0.759692i	$-0.725350\pi$
$631$	−820.657			−1.30057			−0.650283	+	0.759692i	$0.725350\pi$
$632$	121.183	−	69.9651i	0.191745	−	0.110704i
$633$		0			0
$634$	−108.097	+	187.229i	−0.170500	+	0.295314i
$635$	−883.500	+	510.089i	−1.39134	+	0.803290i
$636$		0			0
$637$	−23.2419	−	698.956i	−0.0364864	−	1.09726i
$638$		−	221.008i		−	0.346407i
$639$		0			0
$640$	−49.0479	+	84.9534i	−0.0766373	+	0.132740i
$641$	−329.497	−	190.235i	−0.514035	−	0.296778i	0.220456	−	0.975397i	$-0.429246\pi$
$641$	−329.497	−	190.235i	−0.514035	−	0.296778i	−0.734491	+	0.678619i	$0.762579\pi$
$642$		0			0
$643$	134.072			0.208510			0.104255	−	0.994551i	$-0.466754\pi$
$643$	134.072			0.208510			0.104255	+	0.994551i	$0.466754\pi$
$644$	−90.9992	−	88.0235i	−0.141303	−	0.136683i
$645$		0			0
$646$	180.575	+	312.765i	0.279528	+	0.484157i
$647$	443.702	+	256.172i	0.685784	+	0.395938i	0.802031	−	0.597283i	$-0.203753\pi$
$647$	443.702	+	256.172i	0.685784	+	0.395938i	−0.116247	+	0.993220i	$0.537086\pi$
$648$		0			0
$649$	−304.181	−	526.856i	−0.468691	−	0.811797i
$650$		−	1012.80i		−	1.55815i
$651$		0			0
$652$	−543.309			−0.833297
$653$	609.551	−	351.924i	0.933463	−	0.538935i	0.0455575	−	0.998962i	$-0.485494\pi$
$653$	609.551	−	351.924i	0.933463	−	0.538935i	0.887905	+	0.460027i	$0.152160\pi$
$654$		0			0
$655$	630.565	−	1092.17i	0.962695	−	1.66744i
$656$	230.943	−	133.335i	0.352047	−	0.203254i
$657$		0			0
$658$	77.3820	+	270.714i	0.117602	+	0.411420i
$659$			664.121i			1.00777i	0.863771	+	0.503885i	$0.168097\pi$
$659$			664.121i			1.00777i	−0.863771	+	0.503885i	$0.831903\pi$
$660$		0			0
$661$	507.932	−	879.765i	0.768430	−	1.33096i	−0.169984	−	0.985447i	$-0.554372\pi$
$661$	507.932	−	879.765i	0.768430	−	1.33096i	0.938414	−	0.345513i	$-0.112295\pi$
$662$	−410.113	−	236.779i	−0.619506	−	0.357672i
$663$		0			0
$664$	251.717			0.379092
$665$	617.560	−	176.526i	0.928661	−	0.265452i
$666$		0			0
$667$	34.0046	+	58.8977i	0.0509814	+	0.0883024i
$668$	−45.0698	−	26.0210i	−0.0674697	−	0.0389536i
$669$		0			0
$670$	582.649	+	1009.18i	0.869625	+	1.50624i
$671$		−	372.200i		−	0.554695i
$672$		0			0
$673$	832.049			1.23633			0.618164	−	0.786049i	$-0.287877\pi$
$673$	832.049			1.23633			0.618164	+	0.786049i	$0.287877\pi$
$674$	−14.2256	+	8.21314i	−0.0211062	+	0.0121857i
$675$		0			0
$676$	34.6981	−	60.0988i	0.0513285	−	0.0889036i
$677$	265.283	−	153.161i	0.391850	−	0.226235i	−0.291111	−	0.956689i	$-0.594025\pi$
$677$	265.283	−	153.161i	0.391850	−	0.226235i	0.682962	+	0.730454i	$0.260692\pi$
$678$		0			0
$679$	519.289	−	536.843i	0.764785	−	0.790638i
$680$			591.797i			0.870289i
$681$		0			0
$682$	94.1480	−	163.069i	0.138047	−	0.239104i
$683$	−32.8662	−	18.9753i	−0.0481203	−	0.0277823i	0.475747	−	0.879582i	$-0.342178\pi$
$683$	−32.8662	−	18.9753i	−0.0481203	−	0.0277823i	−0.523867	+	0.851800i	$0.675511\pi$
$684$		0			0
$685$	−491.162			−0.717025
$686$	474.222	+	102.039i	0.691285	+	0.148744i
$687$		0			0
$688$	14.1503	+	24.5090i	0.0205673	+	0.0356236i
$689$	−667.468	−	385.363i	−0.968749	−	0.559308i
$690$		0			0
$691$	149.036	+	258.138i	0.215682	+	0.373572i	0.953483	−	0.301446i	$-0.0974692\pi$
$691$	149.036	+	258.138i	0.215682	+	0.373572i	−0.737801	+	0.675018i	$0.764136\pi$
$692$			184.971i			0.267299i
$693$		0			0
$694$	838.431			1.20811
$695$	−185.176	+	106.911i	−0.266440	+	0.153829i
$696$		0			0
$697$	804.388	−	1393.24i	1.15407	−	1.99891i
$698$	−373.036	+	215.373i	−0.534436	+	0.308557i
$699$		0			0
$700$	681.483	+	170.516i	0.973547	+	0.243594i
$701$			102.414i			0.146097i	0.997328	+	0.0730487i	$0.0232728\pi$
$701$			102.414i			0.146097i	−0.997328	+	0.0730487i	$0.976727\pi$
$702$		0			0
$703$	−54.1362	+	93.7667i	−0.0770074	+	0.133381i
$704$	−143.969	−	83.1208i	−0.204502	−	0.118069i
$705$		0			0
$706$	−970.890			−1.37520
$707$	−552.951	+	158.058i	−0.782110	+	0.223561i
$708$		0			0
$709$	219.076	+	379.450i	0.308993	+	0.535191i	0.978142	−	0.207937i	$-0.0666748\pi$
$709$	219.076	+	379.450i	0.308993	+	0.535191i	−0.669150	+	0.743128i	$0.733341\pi$
$710$	1137.35	+	656.652i	1.60191	+	0.924862i
$711$		0			0
$712$	103.429	+	179.144i	0.145265	+	0.251607i
$713$			57.9431i			0.0812666i
$714$		0			0
$715$	2571.51			3.59652
$716$	−186.507	+	107.680i	−0.260484	+	0.150391i
$717$		0			0
$718$	341.790	−	591.998i	0.476031	−	0.824509i
$719$	−1183.93	+	683.542i	−1.64663	+	0.950685i	−0.668238	+	0.743948i	$0.732951\pi$
$719$	−1183.93	+	683.542i	−1.64663	+	0.950685i	−0.978397	+	0.206737i	$0.933716\pi$
$720$		0			0
$721$	241.183	+	60.3472i	0.334512	+	0.0836993i
$722$		−	352.153i		−	0.487746i
$723$		0			0
$724$	117.141	−	202.895i	0.161798	−	0.280242i
$725$	−326.803	−	188.680i	−0.450763	−	0.260248i
$726$		0			0
$727$	−695.754			−0.957021			−0.478510	−	0.878082i	$-0.658823\pi$
$727$	−695.754			−0.957021			−0.478510	+	0.878082i	$0.658823\pi$
$728$	203.105	+	196.464i	0.278991	+	0.269868i
$729$		0			0
$730$	−719.341	−	1245.93i	−0.985398	−	1.70676i
$731$	147.859	+	85.3665i	0.202270	+	0.116780i
$732$		0			0
$733$	570.340	+	987.857i	0.778090	+	1.34769i	0.933042	+	0.359769i	$0.117144\pi$
$733$	570.340	+	987.857i	0.778090	+	1.34769i	−0.154952	+	0.987922i	$0.549522\pi$
$734$		−	216.999i		−	0.295639i
$735$		0			0
$736$	51.1564			0.0695060
$737$	−1710.24	+	987.408i	−2.32054	+	1.33977i
$738$		0			0
$739$	143.021	−	247.719i	0.193533	−	0.335209i	−0.752886	−	0.658151i	$-0.771339\pi$
$739$	143.021	−	247.719i	0.193533	−	0.335209i	0.946419	+	0.322942i	$0.104672\pi$
$740$	−153.650	+	88.7101i	−0.207636	+	0.119878i
$741$		0			0
$742$	371.677	−	384.241i	0.500912	−	0.517845i
$743$			928.085i			1.24910i	0.780983	+	0.624552i	$0.214718\pi$
$743$			928.085i			1.24910i	−0.780983	+	0.624552i	$0.785282\pi$
$744$		0			0
$745$	−465.676	+	806.574i	−0.625068	+	1.08265i
$746$	−338.668	−	195.530i	−0.453979	−	0.262105i
$747$		0			0
$748$	−1002.91			−1.34079
$749$	2.59127	−	10.3563i	0.00345964	−	0.0138268i
$750$		0			0
$751$	522.842	+	905.589i	0.696194	+	1.20584i	0.969776	+	0.243995i	$0.0784581\pi$
$751$	522.842	+	905.589i	0.696194	+	1.20584i	−0.273582	+	0.961849i	$0.588209\pi$
$752$	−98.5244	−	56.8831i	−0.131016	−	0.0756424i
$753$		0			0
$754$	−75.8964	−	131.456i	−0.100658	−	0.174345i
$755$		−	522.306i		−	0.691796i
$756$		0			0
$757$	−823.084			−1.08730			−0.543648	−	0.839313i	$-0.682957\pi$
$757$	−823.084			−1.08730			−0.543648	+	0.839313i	$0.682957\pi$
$758$	−485.197	+	280.128i	−0.640101	+	0.369562i
$759$		0			0
$760$	−129.763	+	224.756i	−0.170741	+	0.295732i
$761$	661.169	−	381.726i	0.868816	−	0.501611i	0.00186153	−	0.999998i	$-0.499407\pi$
$761$	661.169	−	381.726i	0.868816	−	0.501611i	0.866955	+	0.498387i	$0.166074\pi$
$762$		0			0
$763$	−386.292	−	1351.41i	−0.506281	−	1.77118i
$764$			292.174i			0.382427i
$765$		0			0
$766$	−215.416	+	373.112i	−0.281222	+	0.487091i
$767$	−361.856	−	208.918i	−0.471781	−	0.272383i
$768$		0			0
$769$	−310.039			−0.403172			−0.201586	−	0.979471i	$-0.564610\pi$
$769$	−310.039			−0.403172			−0.201586	+	0.979471i	$0.564610\pi$
$770$	−432.945	+	1730.30i	−0.562266	+	2.24715i
$771$		0			0
$772$	−96.5233	−	167.183i	−0.125030	−	0.216559i
$773$	−348.526	−	201.222i	−0.450875	−	0.260313i	0.257325	−	0.966325i	$-0.417159\pi$
$773$	−348.526	−	201.222i	−0.450875	−	0.260313i	−0.708200	+	0.706012i	$0.750492\pi$
$774$		0			0
$775$	−160.753	−	278.433i	−0.207423	−	0.359268i
$776$			301.794i			0.388909i
$777$		0			0
$778$	667.374			0.857807
$779$	610.991	−	352.756i	0.784327	−	0.452831i
$780$		0			0
$781$	−1112.82	+	1927.46i	−1.42487	+	2.46794i
$782$	267.272	−	154.309i	0.341780	−	0.197327i
$783$		0			0
$784$	−166.390	+	103.587i	−0.212233	+	0.132126i
$785$		−	820.340i		−	1.04502i
$786$		0			0
$787$	−311.572	+	539.658i	−0.395898	+	0.685715i	−0.993215	−	0.116290i	$-0.962900\pi$
$787$	−311.572	+	539.658i	−0.395898	+	0.685715i	0.597317	+	0.802005i	$0.296233\pi$
$788$	−233.475	−	134.797i	−0.296288	−	0.171062i
$789$		0			0
$790$	606.634			0.767891
$791$	−562.008	−	543.631i	−0.710504	−	0.687270i
$792$		0			0
$793$	−127.817	−	221.386i	−0.161182	−	0.279176i
$794$	−476.548	−	275.135i	−0.600186	−	0.346518i
$795$		0			0
$796$	−267.879	−	463.980i	−0.336532	−	0.582890i
$797$		−	221.306i		−	0.277673i	−0.990315	−	0.138837i	$-0.955664\pi$
$797$		−	221.306i		−	0.277673i	0.990315	−	0.138837i	$-0.0443363\pi$
$798$		0			0
$799$	−686.334			−0.858991
$800$	−245.821	+	141.925i	−0.307276	+	0.177406i
$801$		0			0
$802$	459.242	−	795.430i	0.572621	−	0.991808i
$803$	2111.47	−	1219.06i	2.62948	−	1.51813i
$804$		0			0
$805$	−150.849	−	527.732i	−0.187390	−	0.655568i
$806$		−	129.326i		−	0.160454i
$807$		0			0
$808$	116.187	−	201.242i	0.143796	−	0.249062i
$809$	1114.71	+	643.579i	1.37789	+	0.795524i	0.991905	−	0.126982i	$-0.0405290\pi$
$809$	1114.71	+	643.579i	1.37789	+	0.795524i	0.385983	+	0.922506i	$0.373862\pi$
$810$		0			0
$811$	999.374			1.23227			0.616137	−	0.787639i	$-0.288697\pi$
$811$	999.374			1.23227			0.616137	+	0.787639i	$0.288697\pi$
$812$	101.232	−	28.9364i	0.124669	−	0.0356360i
$813$		0			0
$814$	−150.336	−	260.389i	−0.184688	−	0.319888i
$815$	−2039.83	−	1177.69i	−2.50285	−	1.44502i
$816$		0			0
$817$	37.4365	+	64.8420i	0.0458219	+	0.0793659i
$818$		−	586.890i		−	0.717470i
$819$		0			0
$820$	1156.08			1.40986
$821$	947.645	−	547.123i	1.15426	−	0.666411i	0.204336	−	0.978901i	$-0.434496\pi$
$821$	947.645	−	547.123i	1.15426	−	0.666411i	0.949921	+	0.312490i	$0.101163\pi$
$822$		0			0
$823$	−167.539	+	290.187i	−0.203571	+	0.352596i	−0.949677	−	0.313232i	$-0.898588\pi$
$823$	−167.539	+	290.187i	−0.203571	+	0.352596i	0.746105	+	0.665828i	$0.231922\pi$
$824$	−86.9983	+	50.2285i	−0.105580	+	0.0609569i
$825$		0			0
$826$	201.498	−	208.310i	0.243944	−	0.252191i
$827$		−	275.340i		−	0.332938i	−0.986047	−	0.166469i	$-0.946763\pi$
$827$		−	275.340i		−	0.332938i	0.986047	−	0.166469i	$-0.0532366\pi$
$828$		0			0
$829$	−210.758	+	365.043i	−0.254231	+	0.440342i	−0.964686	−	0.263401i	$-0.915156\pi$
$829$	−210.758	+	365.043i	−0.254231	+	0.440342i	0.710455	+	0.703742i	$0.248489\pi$
$830$	945.058	+	545.630i	1.13862	+	0.657385i
$831$		0			0
$832$	−114.178			−0.137233
$833$	−556.860	+	1043.10i	−0.668500	+	1.25223i
$834$		0			0
$835$	−112.808	−	195.389i	−0.135099	−	0.233999i
$836$	−380.891	−	219.908i	−0.455611	−	0.263047i
$837$		0			0
$838$	32.4592	+	56.2210i	0.0387341	+	0.0670895i
$839$		−	682.819i		−	0.813848i	−0.913462	−	0.406924i	$-0.866601\pi$
$839$		−	682.819i		−	0.813848i	0.913462	−	0.406924i	$-0.133399\pi$
$840$		0			0
$841$	784.443			0.932750
$842$	386.748	−	223.289i	0.459321	−	0.265189i
$843$		0			0
$844$	−251.891	+	436.289i	−0.298449	+	0.516930i
$845$	260.544	−	150.425i	0.308336	−	0.178018i
$846$		0			0
$847$	−2110.65	−	528.113i	−2.49191	−	0.623510i
$848$			216.006i			0.254724i
$849$		0			0
$850$	−856.210	+	1483.00i	−1.00731	+	1.74471i
$851$	80.1278	+	46.2618i	0.0941572	+	0.0543617i
$852$		0			0
$853$	249.493			0.292489			0.146244	−	0.989249i	$-0.453281\pi$
$853$	249.493			0.292489			0.146244	+	0.989249i	$0.453281\pi$
$854$	170.484	−	48.7319i	0.199631	−	0.0570632i
$855$		0			0
$856$	2.15678	+	3.73565i	0.00251960	+	0.00436408i
$857$	244.741	+	141.301i	0.285578	+	0.164879i	0.635946	−	0.771733i	$-0.280610\pi$
$857$	244.741	+	141.301i	0.285578	+	0.164879i	−0.350368	+	0.936612i	$0.613943\pi$
$858$		0			0
$859$	2.67788	+	4.63823i	0.00311744	+	0.00539957i	0.867580	−	0.497298i	$-0.165674\pi$
$859$	2.67788	+	4.63823i	0.00311744	+	0.00539957i	−0.864462	+	0.502697i	$0.832341\pi$
$860$			122.690i			0.142663i
$861$		0			0
$862$	44.5161			0.0516428
$863$	−73.1639	+	42.2412i	−0.0847786	+	0.0489470i	−0.541790	−	0.840514i	$-0.682253\pi$
$863$	−73.1639	+	42.2412i	−0.0847786	+	0.0489470i	0.457011	+	0.889461i	$0.348920\pi$
$864$		0			0
$865$	−400.949	+	694.465i	−0.463525	+	0.802849i
$866$	−390.526	+	225.470i	−0.450953	+	0.260358i
$867$		0			0
$868$	87.0198	+	21.7735i	0.100253	+	0.0250847i
$869$			1028.05i			1.18303i
$870$		0			0
$871$	−678.172	+	1174.63i	−0.778613	+	1.34860i
$872$	491.835	+	283.961i	0.564031	+	0.325643i
$873$		0			0
$874$	135.341			0.154853
$875$	1098.37	+	1062.45i	1.25528	+	1.21423i
$876$		0			0
$877$	−721.477	−	1249.63i	−0.822664	−	1.42490i	−0.903691	−	0.428185i	$-0.859153\pi$
$877$	−721.477	−	1249.63i	−0.822664	−	1.42490i	0.0810269	−	0.996712i	$-0.474180\pi$
$878$	−647.848	−	374.035i	−0.737868	−	0.426008i
$879$		0			0
$880$	−360.351	−	624.145i	−0.409489	−	0.709256i
$881$		−	437.949i		−	0.497104i	−0.968619	−	0.248552i	$-0.920045\pi$
$881$		−	437.949i		−	0.497104i	0.968619	−	0.248552i	$-0.0799548\pi$
$882$		0			0
$883$	956.951			1.08375			0.541875	−	0.840459i	$-0.317715\pi$
$883$	956.951			1.08375			0.541875	+	0.840459i	$0.317715\pi$
$884$	−596.536	+	344.410i	−0.674814	+	0.389604i
$885$		0			0
$886$	−283.306	+	490.700i	−0.319758	+	0.553837i
$887$	181.342	−	104.698i	0.204444	−	0.118036i	−0.394283	−	0.918989i	$-0.629007\pi$
$887$	181.342	−	104.698i	0.204444	−	0.118036i	0.598727	+	0.800953i	$0.295674\pi$
$888$		0			0
$889$	572.630	−	591.988i	0.644129	−	0.665904i
$890$			896.783i			1.00762i
$891$		0			0
$892$	427.001	−	739.587i	0.478701	−	0.829134i
$893$	−260.660	−	150.492i	−0.291892	−	0.168524i
$894$		0			0
$895$	−933.640			−1.04317
$896$	19.2233	−	76.8275i	0.0214545	−	0.0857450i
$897$		0			0
$898$	290.045	+	502.373i	0.322990	+	0.559436i
$899$	−41.7301	−	24.0929i	−0.0464184	−	0.0267997i
$900$		0			0
$901$	651.567	+	1128.55i	0.723159	+	1.25255i
$902$			1959.20i			2.17206i
$903$		0			0
$904$	315.941			0.349492
$905$	879.603	−	507.839i	0.971937	−	0.561148i
$906$		0			0
$907$	70.9229	−	122.842i	0.0781951	−	0.135438i	−0.824276	−	0.566188i	$-0.808418\pi$
$907$	70.9229	−	122.842i	0.0781951	−	0.135438i	0.902471	+	0.430750i	$0.141751\pi$
$908$	471.664	−	272.315i	0.519454	−	0.299907i
$909$		0			0
$910$	336.687	+	1177.87i	0.369985	+	1.29436i
$911$			200.004i			0.219543i	0.993957	+	0.109772i	$0.0350120\pi$
$911$			200.004i			0.219543i	−0.993957	+	0.109772i	$0.964988\pi$
$912$		0			0
$913$	−924.671	+	1601.58i	−1.01278	+	1.75419i
$914$	−221.184	−	127.701i	−0.241996	−	0.139716i
$915$		0			0
$916$	−155.505			−0.169765
$917$	−247.136	+	987.703i	−0.269505	+	1.07710i
$918$		0			0
$919$	244.112	+	422.815i	0.265628	+	0.460081i	0.967728	−	0.251997i	$-0.0810874\pi$
$919$	244.112	+	422.815i	0.265628	+	0.460081i	−0.702100	+	0.712078i	$0.747754\pi$
$920$	192.064	+	110.888i	0.208765	+	0.120531i
$921$		0			0
$922$	196.369	+	340.121i	0.212982	+	0.368895i
$923$			1528.62i			1.65614i
$924$		0			0
$925$	−513.382			−0.555008
$926$	−636.757	+	367.632i	−0.687643	+	0.397011i
$927$		0			0
$928$	−21.2710	+	36.8424i	−0.0229213	+	0.0397009i
$929$	1147.06	−	662.255i	1.23472	−	0.712868i	0.266713	−	0.963776i	$-0.414062\pi$
$929$	1147.06	−	662.255i	1.23472	−	0.712868i	0.968011	+	0.250908i	$0.0807290\pi$
$930$		0			0
$931$	−440.208	+	274.054i	−0.472834	+	0.294365i
$932$		−	64.0267i		−	0.0686982i
$933$		0			0
$934$	−40.4854	+	70.1228i	−0.0433462	+	0.0750779i
$935$	−3765.37	−	2173.94i	−4.02714	−	2.32507i
$936$		0			0
$937$	1196.41			1.27685			0.638427	−	0.769683i	$-0.279586\pi$
$937$	1196.41			1.27685			0.638427	+	0.769683i	$0.279586\pi$
$938$	−676.198	−	654.087i	−0.720894	−	0.697321i
$939$		0			0
$940$	−246.603	−	427.129i	−0.262344	−	0.454393i
$941$	−939.143	−	542.214i	−0.998027	−	0.576211i	−0.0903628	−	0.995909i	$-0.528803\pi$
$941$	−939.143	−	542.214i	−0.998027	−	0.576211i	−0.907664	+	0.419698i	$0.862136\pi$
$942$		0			0
$943$	−301.445	−	522.119i	−0.319666	−	0.553678i
$944$			117.104i			0.124051i
$945$		0			0
$946$	−207.922			−0.219790
$947$	1009.73	−	582.965i	1.06624	−	0.615592i	0.139085	−	0.990280i	$-0.455584\pi$
$947$	1009.73	−	582.965i	1.06624	−	0.615592i	0.927151	+	0.374689i	$0.122250\pi$
$948$		0			0
$949$	837.274	−	1450.20i	0.882270	−	1.52814i
$950$	−650.353	+	375.482i	−0.684582	+	0.395244i
$951$		0			0
$952$	−131.310	−	459.378i	−0.137931	−	0.482540i
$953$		−	1337.53i		−	1.40350i	−0.712425	−	0.701748i	$-0.752403\pi$
$953$		−	1337.53i		−	1.40350i	0.712425	−	0.701748i	$-0.247597\pi$
$954$		0			0
$955$	−633.326	+	1096.95i	−0.663169	+	1.14864i
$956$	512.971	+	296.164i	0.536581	+	0.309795i
$957$		0			0
$958$	−813.291			−0.848946
$959$	381.261	−	108.981i	0.397561	−	0.113640i
$960$		0			0
$961$	459.973	+	796.697i	0.478640	+	0.829029i
$962$	−178.841	−	103.254i	−0.185905	−	0.107332i
$963$		0			0
$964$	−199.851	−	346.153i	−0.207315	−	0.359079i
$965$		−	836.907i		−	0.867261i
$966$		0			0
$967$	−1002.76			−1.03698			−0.518490	−	0.855084i	$-0.673506\pi$
$967$	−1002.76			−1.03698			−0.518490	+	0.855084i	$0.673506\pi$
$968$	761.343	−	439.561i	0.786511	−	0.454092i
$969$		0			0
$970$	−654.177	+	1133.07i	−0.674410	+	1.16811i
$971$	−190.222	+	109.825i	−0.195904	+	0.113105i	−0.594743	−	0.803916i	$-0.702746\pi$
$971$	−190.222	+	109.825i	−0.195904	+	0.113105i	0.398840	+	0.917021i	$0.369413\pi$
$972$		0			0
$973$	120.020	−	124.077i	0.123350	−	0.127520i
$974$			279.454i			0.286914i
$975$		0			0
$976$	−35.8226	+	62.0465i	−0.0367034	+	0.0635722i
$977$	1602.04	+	924.941i	1.63976	+	0.946715i	0.980915	+	0.194436i	$0.0622876\pi$
$977$	1602.04	+	924.941i	1.63976	+	0.946715i	0.658844	+	0.752280i	$0.271046\pi$
$978$		0			0
$979$	−1519.77			−1.55237
$980$	−849.242	+	28.2392i	−0.866573	+	0.0288155i
$981$		0			0
$982$	58.0879	+	100.611i	0.0591527	+	0.102455i
$983$	−274.830	−	158.673i	−0.279583	−	0.161417i	0.353652	−	0.935377i	$-0.384940\pi$
$983$	−274.830	−	158.673i	−0.279583	−	0.161417i	−0.633234	+	0.773960i	$0.718273\pi$
$984$		0			0
$985$	−584.379	−	1012.17i	−0.593278	−	1.02759i
$986$			256.649i			0.260293i
$987$		0			0
$988$	−302.074			−0.305743
$989$	55.4103	−	31.9912i	0.0560266	−	0.0323470i
$990$		0			0
$991$	−807.465	+	1398.57i	−0.814798	+	1.41127i	0.0946750	+	0.995508i	$0.469819\pi$
$991$	−807.465	+	1398.57i	−0.814798	+	1.41127i	−0.909473	+	0.415763i	$0.863515\pi$
$992$	−31.3893	+	18.1226i	−0.0316425	+	0.0182688i
$993$		0			0
$994$	−1028.57	−	257.361i	−1.03477	−	0.258914i
$995$		−	2322.65i		−	2.33433i
$996$		0			0
$997$	−8.16943	+	14.1499i	−0.00819401	+	0.0141924i	−0.870093	−	0.492887i	$-0.835942\pi$
$997$	−8.16943	+	14.1499i	−0.00819401	+	0.0141924i	0.861899	+	0.507079i	$0.169275\pi$
$998$	−228.378	−	131.854i	−0.228835	−	0.132118i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.s.e.53.12	yes	24
3.2	odd	2	inner	378.3.s.e.53.1	✓	24
7.2	even	3	inner	378.3.s.e.107.1	yes	24
21.2	odd	6	inner	378.3.s.e.107.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.3.s.e.53.1	✓	24	3.2	odd	2	inner
378.3.s.e.53.12	yes	24	1.1	even	1	trivial
378.3.s.e.107.1	yes	24	7.2	even	3	inner
378.3.s.e.107.12	yes	24	21.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	378.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(7.50889 - 4.33526i) q^{5} +(-4.86680 + 5.03132i) q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(7.50889 - 4.33526i) q^{5} +(-4.86680 + 5.03132i) q^{7} -2.82843i q^{8} +(6.13099 - 10.6192i) q^{10} +(17.9962 + 10.3901i) q^{11} +14.2723 q^{13} +(-2.40291 + 9.60344i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-20.8984 - 12.0657i) q^{17} +(-5.29128 - 9.16476i) q^{19} -17.3410i q^{20} +29.3876 q^{22} +(-7.83169 + 4.52163i) q^{23} +(25.0890 - 43.4554i) q^{25} +(17.4799 - 10.0920i) q^{26} +(3.84771 + 13.4609i) q^{28} -7.52043i q^{29} +(3.20366 - 5.54890i) q^{31} +(-4.89898 - 2.82843i) q^{32} -34.1269 q^{34} +(-14.7322 + 58.8786i) q^{35} +(-5.11561 - 8.86050i) q^{37} +(-12.9609 - 7.48299i) q^{38} +(-12.2620 - 21.2384i) q^{40} +66.6674i q^{41} -7.07514 q^{43} +(35.9924 - 20.7802i) q^{44} +(-6.39455 + 11.0757i) q^{46} +(24.6311 - 14.2208i) q^{47} +(-1.62846 - 48.9729i) q^{49} -70.9624i q^{50} +(14.2723 - 24.7203i) q^{52} +(-46.7667 - 27.0008i) q^{53} +180.175 q^{55} +(14.2307 + 13.7654i) q^{56} +(-5.31775 - 9.21061i) q^{58} +(-25.3538 - 14.6380i) q^{59} +(-8.95564 - 15.5116i) q^{61} -9.06132i q^{62} -8.00000 q^{64} +(107.169 - 61.8741i) q^{65} +(-47.5167 + 82.3014i) q^{67} +(-41.7968 + 24.1314i) q^{68} +(23.5902 + 82.5284i) q^{70} +107.104i q^{71} +(58.6643 - 101.610i) q^{73} +(-12.5306 - 7.23457i) q^{74} -21.1651 q^{76} +(-139.860 + 39.9781i) q^{77} +(24.7364 + 42.8447i) q^{79} +(-30.0356 - 17.3410i) q^{80} +(47.1410 + 81.6505i) q^{82} +88.9954i q^{83} -209.232 q^{85} +(-8.66524 + 5.00288i) q^{86} +(29.3876 - 50.9009i) q^{88} +(-63.3370 + 36.5677i) q^{89} +(-69.4604 + 71.8085i) q^{91} +18.0865i q^{92} +(20.1112 - 34.8336i) q^{94} +(-79.4633 - 45.8781i) q^{95} -106.700 q^{97} +(-36.6235 - 58.8279i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} + 8 q^{7}+O(q^{10}) \) 24 * q + 24 * q^4 + 8 * q^7	\( 24 q + 24 q^{4} + 8 q^{7} + 8 q^{10} - 16 q^{13} - 48 q^{16} - 36 q^{19} + 64 q^{22} + 128 q^{25} + 32 q^{28} + 176 q^{31} + 16 q^{34} - 72 q^{37} - 16 q^{40} + 216 q^{43} + 64 q^{46} - 24 q^{49} - 16 q^{52} + 448 q^{55} + 104 q^{58} - 268 q^{61} - 192 q^{64} - 248 q^{67} - 80 q^{70} - 116 q^{73} - 144 q^{76} + 152 q^{79} + 240 q^{82} - 536 q^{85} + 64 q^{88} + 428 q^{91} + 144 q^{94} + 16 q^{97}+O(q^{100}) \) 24 * q + 24 * q^4 + 8 * q^7 + 8 * q^10 - 16 * q^13 - 48 * q^16 - 36 * q^19 + 64 * q^22 + 128 * q^25 + 32 * q^28 + 176 * q^31 + 16 * q^34 - 72 * q^37 - 16 * q^40 + 216 * q^43 + 64 * q^46 - 24 * q^49 - 16 * q^52 + 448 * q^55 + 104 * q^58 - 268 * q^61 - 192 * q^64 - 248 * q^67 - 80 * q^70 - 116 * q^73 - 144 * q^76 + 152 * q^79 + 240 * q^82 - 536 * q^85 + 64 * q^88 + 428 * q^91 + 144 * q^94 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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