LMFDB - Embedded newform 420.2.bn.a.269.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(89,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("420.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.bn (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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.4
Character	$\chi$	$=$	420.269
Dual form			420.2.bn.a.89.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.44386 - 0.956690i) q^{3} +(-2.00950 - 0.980773i) q^{5} +(0.477214 + 2.60236i) q^{7} +(1.16949 + 2.76266i) q^{9} +O(q^{10})$	\(q+(-1.44386 - 0.956690i) q^{3} +(-2.00950 - 0.980773i) q^{5} +(0.477214 + 2.60236i) q^{7} +(1.16949 + 2.76266i) q^{9} +(1.34052 + 0.773950i) q^{11} -4.18432 q^{13} +(1.96315 + 3.33857i) q^{15} +(4.42344 + 2.55387i) q^{17} +(4.62984 - 2.67304i) q^{19} +(1.80062 - 4.21400i) q^{21} +(1.82437 + 3.15990i) q^{23} +(3.07617 + 3.94173i) q^{25} +(0.954427 - 5.10775i) q^{27} +9.79665i q^{29} +(6.79882 + 3.92530i) q^{31} +(-1.19510 - 2.39994i) q^{33} +(1.59336 - 5.69747i) q^{35} +(-2.96953 + 1.71446i) q^{37} +(6.04160 + 4.00310i) q^{39} -8.82093 q^{41} -3.79814i q^{43} +(0.359459 - 6.69857i) q^{45} +(-2.16487 + 1.24989i) q^{47} +(-6.54453 + 2.48376i) q^{49} +(-3.94358 - 7.91930i) q^{51} +(0.395246 - 0.684586i) q^{53} +(-1.93471 - 2.87000i) q^{55} +(-9.24212 - 0.569815i) q^{57} +(-2.73316 + 4.73397i) q^{59} +(-6.76285 + 3.90454i) q^{61} +(-6.63134 + 4.36181i) q^{63} +(8.40839 + 4.10387i) q^{65} +(9.67202 + 5.58414i) q^{67} +(0.388903 - 6.30782i) q^{69} -7.97077i q^{71} +(6.19943 - 10.7377i) q^{73} +(-0.670559 - 8.63425i) q^{75} +(-1.37438 + 3.85786i) q^{77} +(-1.12127 - 1.94209i) q^{79} +(-6.26459 + 6.46180i) q^{81} +5.26486i q^{83} +(-6.38412 - 9.47039i) q^{85} +(9.37235 - 14.1450i) q^{87} +(7.65723 + 13.2627i) q^{89} +(-1.99682 - 10.8891i) q^{91} +(-6.06128 - 12.1720i) q^{93} +(-11.9253 + 0.830643i) q^{95} -15.9016 q^{97} +(-0.570438 + 4.60853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 2 q^{15} + 12 q^{19} - 8 q^{21} + 6 q^{25} - 12 q^{31} + 24 q^{39} + 33 q^{45} - 44 q^{49} - 10 q^{51} - 24 q^{61} + 21 q^{75} - 28 q^{79} - 20 q^{81} - 4 q^{85} + 16 q^{91} - 28 q^{99}+O(q^{100}) $ 32 * q + 2 * q^15 + 12 * q^19 - 8 * q^21 + 6 * q^25 - 12 * q^31 + 24 * q^39 + 33 * q^45 - 44 * q^49 - 10 * q^51 - 24 * q^61 + 21 * q^75 - 28 * q^79 - 20 * q^81 - 4 * q^85 + 16 * q^91 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.44386	−	0.956690i	−0.833615	−	0.552345i
$3$	−1.44386	−	0.956690i	−0.833615	−	0.552345i
$4$		0			0
$5$	−2.00950	−	0.980773i	−0.898675	−	0.438615i
$5$	−2.00950	−	0.980773i	−0.898675	−	0.438615i
$6$		0			0
$7$	0.477214	+	2.60236i	0.180370	+	0.983599i
$7$	0.477214	+	2.60236i	0.180370	+	0.983599i
$8$		0			0
$9$	1.16949	+	2.76266i	0.389830	+	0.920887i
$10$		0			0
$11$	1.34052	+	0.773950i	0.404182	+	0.233355i	0.688287	−	0.725438i	$-0.258363\pi$
$11$	1.34052	+	0.773950i	0.404182	+	0.233355i	−0.284105	+	0.958793i	$0.591696\pi$
$12$		0			0
$13$	−4.18432			−1.16052			−0.580261	−	0.814430i	$-0.697050\pi$
$13$	−4.18432			−1.16052			−0.580261	+	0.814430i	$0.697050\pi$
$14$		0			0
$15$	1.96315	+	3.33857i	0.506882	+	0.862015i
$16$		0			0
$17$	4.42344	+	2.55387i	1.07284	+	0.619405i	0.928956	−	0.370189i	$-0.120707\pi$
$17$	4.42344	+	2.55387i	1.07284	+	0.619405i	0.143885	+	0.989594i	$0.454040\pi$
$18$		0			0
$19$	4.62984	−	2.67304i	1.06216	−	0.613237i	0.136129	−	0.990691i	$-0.456534\pi$
$19$	4.62984	−	2.67304i	1.06216	−	0.613237i	0.926028	+	0.377454i	$0.123201\pi$
$20$		0			0
$21$	1.80062	−	4.21400i	0.392927	−	0.919570i
$22$		0			0
$23$	1.82437	+	3.15990i	0.380407	+	0.658885i	0.991120	−	0.132967i	$-0.0424505\pi$
$23$	1.82437	+	3.15990i	0.380407	+	0.658885i	−0.610713	+	0.791852i	$0.709117\pi$
$24$		0			0
$25$	3.07617	+	3.94173i	0.615233	+	0.788345i
$26$		0			0
$27$	0.954427	−	5.10775i	0.183680	−	0.982986i
$28$		0			0
$29$			9.79665i			1.81919i	0.415494	+	0.909596i	$0.363609\pi$
$29$			9.79665i			1.81919i	−0.415494	+	0.909596i	$0.636391\pi$
$30$		0			0
$31$	6.79882	+	3.92530i	1.22110	+	0.705005i	0.965153	−	0.261685i	$-0.0842782\pi$
$31$	6.79882	+	3.92530i	1.22110	+	0.705005i	0.255951	+	0.966690i	$0.417612\pi$
$32$		0			0
$33$	−1.19510	−	2.39994i	−0.208040	−	0.417776i
$34$		0			0
$35$	1.59336	−	5.69747i	0.269328	−	0.963049i
$36$		0			0
$37$	−2.96953	+	1.71446i	−0.488188	+	0.281855i	−0.723822	−	0.689987i	$-0.757616\pi$
$37$	−2.96953	+	1.71446i	−0.488188	+	0.281855i	0.235635	+	0.971842i	$0.424283\pi$
$38$		0			0
$39$	6.04160	+	4.00310i	0.967430	+	0.641009i
$40$		0			0
$41$	−8.82093			−1.37760			−0.688799	−	0.724952i	$-0.741862\pi$
$41$	−8.82093			−1.37760			−0.688799	+	0.724952i	$0.741862\pi$
$42$		0			0
$43$		−	3.79814i		−	0.579211i	−0.957146	−	0.289605i	$-0.906476\pi$
$43$		−	3.79814i		−	0.579211i	0.957146	−	0.289605i	$-0.0935241\pi$
$44$		0			0
$45$	0.359459	−	6.69857i	0.0535851	−	0.998563i
$46$		0			0
$47$	−2.16487	+	1.24989i	−0.315779	+	0.182315i	−0.649510	−	0.760353i	$-0.725026\pi$
$47$	−2.16487	+	1.24989i	−0.315779	+	0.182315i	0.333731	+	0.942669i	$0.391692\pi$
$48$		0			0
$49$	−6.54453	+	2.48376i	−0.934933	+	0.354823i
$50$		0			0
$51$	−3.94358	−	7.91930i	−0.552212	−	1.10892i
$52$		0			0
$53$	0.395246	−	0.684586i	0.0542912	−	0.0940351i	−0.837603	−	0.546280i	$-0.816043\pi$
$53$	0.395246	−	0.684586i	0.0542912	−	0.0940351i	0.891894	+	0.452245i	$0.149377\pi$
$54$		0			0
$55$	−1.93471	−	2.87000i	−0.260876	−	0.386991i
$56$		0			0
$57$	−9.24212	−	0.569815i	−1.22415	−	0.0754738i
$58$		0			0
$59$	−2.73316	+	4.73397i	−0.355827	+	0.616310i	−0.987259	−	0.159121i	$-0.949134\pi$
$59$	−2.73316	+	4.73397i	−0.355827	+	0.616310i	0.631432	+	0.775431i	$0.282467\pi$
$60$		0			0
$61$	−6.76285	+	3.90454i	−0.865895	+	0.499925i	−0.865982	−	0.500075i	$-0.833306\pi$
$61$	−6.76285	+	3.90454i	−0.865895	+	0.499925i	8.71528e−5		1.00000i	$0.499972\pi$
$62$		0			0
$63$	−6.63134	+	4.36181i	−0.835470	+	0.549536i
$64$		0			0
$65$	8.40839	+	4.10387i	1.04293	+	0.509023i
$66$		0			0
$67$	9.67202	+	5.58414i	1.18163	+	0.682212i	0.956390	−	0.292093i	$-0.0943516\pi$
$67$	9.67202	+	5.58414i	1.18163	+	0.682212i	0.225235	+	0.974304i	$0.427685\pi$
$68$		0			0
$69$	0.388903	−	6.30782i	0.0468184	−	0.759373i
$70$		0			0
$71$		−	7.97077i		−	0.945957i	−0.881074	−	0.472978i	$-0.843179\pi$
$71$		−	7.97077i		−	0.945957i	0.881074	−	0.472978i	$-0.156821\pi$
$72$		0			0
$73$	6.19943	−	10.7377i	0.725588	−	1.25676i	−0.233144	−	0.972442i	$-0.574901\pi$
$73$	6.19943	−	10.7377i	0.725588	−	1.25676i	0.958732	−	0.284313i	$-0.0917654\pi$
$74$		0			0
$75$	−0.670559	−	8.63425i	−0.0774294	−	0.996998i
$76$		0			0
$77$	−1.37438	+	3.85786i	−0.156625	+	0.439644i
$78$		0			0
$79$	−1.12127	−	1.94209i	−0.126152	−	0.218502i	0.796030	−	0.605257i	$-0.206929\pi$
$79$	−1.12127	−	1.94209i	−0.126152	−	0.218502i	−0.922183	+	0.386754i	$0.873596\pi$
$80$		0			0
$81$	−6.26459	+	6.46180i	−0.696066	+	0.717978i
$82$		0			0
$83$			5.26486i			0.577894i	0.957345	+	0.288947i	$0.0933051\pi$
$83$			5.26486i			0.577894i	−0.957345	+	0.288947i	$0.906695\pi$
$84$		0			0
$85$	−6.38412	−	9.47039i	−0.692455	−	1.02721i
$86$		0			0
$87$	9.37235	−	14.1450i	1.00482	−	1.51651i
$88$		0			0
$89$	7.65723	+	13.2627i	0.811664	+	1.40584i	0.911698	+	0.410860i	$0.134771\pi$
$89$	7.65723	+	13.2627i	0.811664	+	1.40584i	−0.100034	+	0.994984i	$0.531895\pi$
$90$		0			0
$91$	−1.99682	−	10.8891i	−0.209323	−	1.14149i
$92$		0			0
$93$	−6.06128	−	12.1720i	−0.628525	−	1.26217i
$94$		0			0
$95$	−11.9253	+	0.830643i	−1.22351	+	0.0852222i
$96$		0			0
$97$	−15.9016			−1.61457			−0.807284	−	0.590163i	$-0.799063\pi$
$97$	−15.9016			−1.61457			−0.807284	+	0.590163i	$0.799063\pi$
$98$		0			0
$99$	−0.570438	+	4.60853i	−0.0573312	+	0.463175i
$100$		0			0
$101$	3.83295	−	6.63886i	0.381392	−	0.660591i	−0.609869	−	0.792502i	$-0.708778\pi$
$101$	3.83295	−	6.63886i	0.381392	−	0.660591i	0.991262	+	0.131911i	$0.0421113\pi$
$102$		0			0
$103$	0.554275	+	0.960032i	0.0546143	+	0.0945947i	0.892040	−	0.451956i	$-0.149274\pi$
$103$	0.554275	+	0.960032i	0.0546143	+	0.0945947i	−0.837426	+	0.546551i	$0.815940\pi$
$104$		0			0
$105$	−7.75132	+	6.70202i	−0.756451	+	0.654050i
$106$		0			0
$107$	0.735749	+	1.27436i	0.0711276	+	0.123197i	0.899396	−	0.437135i	$-0.144007\pi$
$107$	0.735749	+	1.27436i	0.0711276	+	0.123197i	−0.828268	+	0.560332i	$0.810674\pi$
$108$		0			0
$109$	−4.66898	+	8.08692i	−0.447208	+	0.774586i	−0.998203	−	0.0599221i	$-0.980915\pi$
$109$	−4.66898	+	8.08692i	−0.447208	+	0.774586i	0.550996	+	0.834508i	$0.314248\pi$
$110$		0			0
$111$	5.92780	+	0.365473i	0.562642	+	0.0346892i
$112$		0			0
$113$	11.9773			1.12673			0.563363	−	0.826210i	$-0.309507\pi$
$113$	11.9773			1.12673			0.563363	+	0.826210i	$0.309507\pi$
$114$		0			0
$115$	−0.566921	−	8.13911i	−0.0528656	−	0.758976i
$116$		0			0
$117$	−4.89352	−	11.5599i	−0.452406	−	1.06871i
$118$		0			0
$119$	−4.53517	+	12.7301i	−0.415738	+	1.16697i
$120$		0			0
$121$	−4.30200	−	7.45129i	−0.391091	−	0.677390i
$122$		0			0
$123$	12.7362	+	8.43890i	1.14839	+	0.760910i
$124$		0			0
$125$	−2.31561	−	10.9379i	−0.207115	−	0.978317i
$126$		0			0
$127$			3.16197i			0.280579i	0.990110	+	0.140290i	$0.0448034\pi$
$127$			3.16197i			0.280579i	−0.990110	+	0.140290i	$0.955197\pi$
$128$		0			0
$129$	−3.63364	+	5.48400i	−0.319924	+	0.482839i
$130$		0			0
$131$	3.13073	+	5.42258i	0.273533	+	0.473773i	0.969764	−	0.244045i	$-0.0784744\pi$
$131$	3.13073	+	5.42258i	0.273533	+	0.473773i	−0.696231	+	0.717818i	$0.745141\pi$
$132$		0			0
$133$	9.16562	+	10.7729i	0.794760	+	0.934127i
$134$		0			0
$135$	−6.92746	+	9.32793i	−0.596221	+	0.802820i
$136$		0			0
$137$	6.98356	−	12.0959i	0.596645	−	1.03342i	−0.396667	−	0.917963i	$-0.629833\pi$
$137$	6.98356	−	12.0959i	0.596645	−	1.03342i	0.993312	−	0.115458i	$-0.0368335\pi$
$138$		0			0
$139$		−	8.07923i		−	0.685271i	−0.939468	−	0.342636i	$-0.888680\pi$
$139$		−	8.07923i		−	0.685271i	0.939468	−	0.342636i	$-0.111320\pi$
$140$		0			0
$141$	4.32154	+	0.266441i	0.363939	+	0.0224384i
$142$		0			0
$143$	−5.60918	−	3.23846i	−0.469063	−	0.270814i
$144$		0			0
$145$	9.60829	−	19.6863i	0.797925	−	1.63486i
$146$		0			0
$147$	11.8256	+	2.67488i	0.975360	+	0.220620i
$148$		0			0
$149$	3.98112	−	2.29850i	0.326146	−	0.188301i	−0.327983	−	0.944684i	$-0.606369\pi$
$149$	3.98112	−	2.29850i	0.326146	−	0.188301i	0.654129	+	0.756383i	$0.273035\pi$
$150$		0			0
$151$	−4.04453	+	7.00534i	−0.329140	+	0.570086i	−0.982341	−	0.187097i	$-0.940092\pi$
$151$	−4.04453	+	7.00534i	−0.329140	+	0.570086i	0.653202	+	0.757184i	$0.273425\pi$
$152$		0			0
$153$	−1.88233	+	15.2072i	−0.152177	+	1.22943i
$154$		0			0
$155$	−9.81238	−	14.5560i	−0.788150	−	1.16916i
$156$		0			0
$157$	−2.09550	+	3.62951i	−0.167239	+	0.289666i	−0.937448	−	0.348125i	$-0.886818\pi$
$157$	−2.09550	+	3.62951i	−0.167239	+	0.289666i	0.770209	+	0.637791i	$0.220152\pi$
$158$		0			0
$159$	−1.22562	+	0.610322i	−0.0971979	+	0.0484017i
$160$		0			0
$161$	−7.35258	+	6.25561i	−0.579464	+	0.493011i
$162$		0			0
$163$	−5.80412	+	3.35101i	−0.454613	+	0.262471i	−0.709777	−	0.704427i	$-0.751204\pi$
$163$	−5.80412	+	3.35101i	−0.454613	+	0.262471i	0.255163	+	0.966898i	$0.417871\pi$
$164$		0			0
$165$	0.0477522	+	5.99480i	0.00371750	+	0.466695i
$166$		0			0
$167$			3.82002i			0.295602i	0.989017	+	0.147801i	$0.0472195\pi$
$167$			3.82002i			0.295602i	−0.989017	+	0.147801i	$0.952780\pi$
$168$		0			0
$169$	4.50857			0.346813
$170$		0			0
$171$	12.7992	+	9.66458i	0.978782	+	0.739069i
$172$		0			0
$173$	2.35226	−	1.35808i	0.178839	−	0.103253i	−0.407908	−	0.913023i	$-0.633742\pi$
$173$	2.35226	−	1.35808i	0.178839	−	0.103253i	0.586747	+	0.809770i	$0.300408\pi$
$174$		0			0
$175$	−8.78979	+	9.88633i	−0.664446	+	0.747337i
$176$		0			0
$177$	8.47524	−	4.22042i	0.637038	−	0.317226i
$178$		0			0
$179$	−0.815115	−	0.470607i	−0.0609246	−	0.0351748i	0.469228	−	0.883077i	$-0.344532\pi$
$179$	−0.815115	−	0.470607i	−0.0609246	−	0.0351748i	−0.530153	+	0.847902i	$0.677865\pi$
$180$		0			0
$181$		−	0.0415289i		−	0.00308682i	−0.999999	−	0.00154341i	$-0.999509\pi$
$181$		−	0.0415289i		−	0.00308682i	0.999999	−	0.00154341i	$-0.000491283\pi$
$182$		0			0
$183$	13.5001	+	0.832335i	0.997954	+	0.0615280i
$184$		0			0
$185$	7.64876	−	0.532766i	0.562348	−	0.0391697i
$186$		0			0
$187$	3.95314	+	6.84704i	0.289082	+	0.500705i
$188$		0			0
$189$	13.7476	+	0.0462754i	0.999994	+	0.00336604i
$190$		0			0
$191$	8.11005	−	4.68234i	0.586822	−	0.338802i	−0.177018	−	0.984208i	$-0.556645\pi$
$191$	8.11005	−	4.68234i	0.586822	−	0.338802i	0.763840	+	0.645406i	$0.223312\pi$
$192$		0			0
$193$	8.90859	+	5.14337i	0.641254	+	0.370228i	0.785097	−	0.619372i	$-0.212613\pi$
$193$	8.90859	+	5.14337i	0.641254	+	0.370228i	−0.143843	+	0.989600i	$0.545946\pi$
$194$		0			0
$195$	−8.21444	−	13.9697i	−0.588248	−	1.00039i
$196$		0			0
$197$	1.19936			0.0854511			0.0427256	−	0.999087i	$-0.486396\pi$
$197$	1.19936			0.0854511			0.0427256	+	0.999087i	$0.486396\pi$
$198$		0			0
$199$	16.7956	+	9.69696i	1.19061	+	0.687400i	0.958445	−	0.285277i	$-0.0920855\pi$
$199$	16.7956	+	9.69696i	1.19061	+	0.687400i	0.232166	+	0.972676i	$0.425419\pi$
$200$		0			0
$201$	−8.62279	−	17.3159i	−0.608205	−	1.22137i
$202$		0			0
$203$	−25.4944	+	4.67509i	−1.78935	+	0.328127i
$204$		0			0
$205$	17.7257	+	8.65134i	1.23801	+	0.604236i
$206$		0			0
$207$	−6.59616	+	8.73558i	−0.458464	+	0.607165i
$208$		0			0
$209$	8.27519			0.572407
$210$		0			0
$211$	9.35510			0.644032			0.322016	−	0.946734i	$-0.395640\pi$
$211$	9.35510			0.644032			0.322016	+	0.946734i	$0.395640\pi$
$212$		0			0
$213$	−7.62556	+	11.5087i	−0.522495	+	0.788564i
$214$		0			0
$215$	−3.72511	+	7.63236i	−0.254051	+	0.520522i
$216$		0			0
$217$	−6.97055	+	19.5662i	−0.473191	+	1.32824i
$218$		0			0
$219$	−19.2238	+	9.57288i	−1.29902	+	0.646875i
$220$		0			0
$221$	−18.5091	−	10.6862i	−1.24506	−	0.718834i
$222$		0			0
$223$	−6.78138			−0.454115			−0.227057	−	0.973881i	$-0.572910\pi$
$223$	−6.78138			−0.454115			−0.227057	+	0.973881i	$0.572910\pi$
$224$		0			0
$225$	−7.29211	+	13.1082i	−0.486141	+	0.873881i
$226$		0			0
$227$	−12.2912	−	7.09632i	−0.815794	−	0.470999i	0.0331698	−	0.999450i	$-0.489440\pi$
$227$	−12.2912	−	7.09632i	−0.815794	−	0.470999i	−0.848964	+	0.528451i	$0.822773\pi$
$228$		0			0
$229$	9.79882	−	5.65735i	0.647524	−	0.373848i	−0.139983	−	0.990154i	$-0.544705\pi$
$229$	9.79882	−	5.65735i	0.647524	−	0.373848i	0.787507	+	0.616306i	$0.211371\pi$
$230$		0			0
$231$	5.67519	−	4.25536i	0.373400	−	0.279982i
$232$		0			0
$233$	−9.13138	−	15.8160i	−0.598216	−	1.03614i	−0.993084	−	0.117403i	$-0.962543\pi$
$233$	−9.13138	−	15.8160i	−0.598216	−	1.03614i	0.394868	−	0.918738i	$-0.370790\pi$
$234$		0			0
$235$	5.57617	−	0.388402i	0.363749	−	0.0253365i
$236$		0			0
$237$	−0.239022	+	3.87682i	−0.0155261	+	0.251826i
$238$		0			0
$239$		−	18.8834i		−	1.22146i	−0.791838	−	0.610731i	$-0.790876\pi$
$239$		−	18.8834i		−	1.22146i	0.791838	−	0.610731i	$-0.209124\pi$
$240$		0			0
$241$	12.0617	+	6.96381i	0.776961	+	0.448578i	0.835352	−	0.549715i	$-0.185264\pi$
$241$	12.0617	+	6.96381i	0.776961	+	0.448578i	−0.0583914	+	0.998294i	$0.518597\pi$
$242$		0			0
$243$	15.2272	−	3.33669i	0.976823	−	0.214049i
$244$		0			0
$245$	15.5872	+	1.42759i	0.995832	+	0.0912054i
$246$		0			0
$247$	−19.3727	+	11.1849i	−1.23266	+	0.711675i
$248$		0			0
$249$	5.03684	−	7.60175i	0.319197	−	0.481741i
$250$		0			0
$251$	26.8164			1.69264			0.846319	−	0.532676i	$-0.178814\pi$
$251$	26.8164			1.69264			0.846319	+	0.532676i	$0.178814\pi$
$252$		0			0
$253$			5.64789i			0.355079i
$254$		0			0
$255$	0.157572	+	19.7816i	0.00986755	+	1.23877i
$256$		0			0
$257$	−12.1038	+	6.98813i	−0.755014	+	0.435907i	−0.827503	−	0.561462i	$-0.810239\pi$
$257$	−12.1038	+	6.98813i	−0.755014	+	0.435907i	0.0724888	+	0.997369i	$0.476906\pi$
$258$		0			0
$259$	−5.87873	−	6.90961i	−0.365287	−	0.429343i
$260$		0			0
$261$	−27.0648	+	11.4571i	−1.67527	+	0.709175i
$262$		0			0
$263$	15.0823	−	26.1233i	0.930015	−	1.61083i	0.146726	−	0.989177i	$-0.453127\pi$
$263$	15.0823	−	26.1233i	0.930015	−	1.61083i	0.783290	−	0.621657i	$-0.213540\pi$
$264$		0			0
$265$	−1.46567	+	0.988028i	−0.0900354	+	0.0606941i
$266$		0			0
$267$	1.63230	−	26.4751i	0.0998952	−	1.62025i
$268$		0			0
$269$	3.43538	−	5.95025i	0.209459	−	0.362793i	−0.742086	−	0.670305i	$-0.766163\pi$
$269$	3.43538	−	5.95025i	0.209459	−	0.362793i	0.951544	+	0.307512i	$0.0994965\pi$
$270$		0			0
$271$	−19.3996	+	11.2004i	−1.17844	+	0.680375i	−0.955654	−	0.294491i	$-0.904850\pi$
$271$	−19.3996	+	11.2004i	−1.17844	+	0.680375i	−0.222790	+	0.974866i	$0.571516\pi$
$272$		0			0
$273$	−7.53437	+	17.6327i	−0.456001	+	1.06718i
$274$		0			0
$275$	1.07297	+	7.66477i	0.0647024	+	0.462203i
$276$		0			0
$277$	6.04530	+	3.49026i	0.363227	+	0.209709i	0.670495	−	0.741914i	$-0.266082\pi$
$277$	6.04530	+	3.49026i	0.363227	+	0.209709i	−0.307268	+	0.951623i	$0.599415\pi$
$278$		0			0
$279$	−2.89313	+	23.3734i	−0.173207	+	1.39933i
$280$		0			0
$281$			2.38586i			0.142328i	0.997465	+	0.0711642i	$0.0226714\pi$
$281$			2.38586i			0.142328i	−0.997465	+	0.0711642i	$0.977329\pi$
$282$		0			0
$283$	12.1385	−	21.0245i	0.721558	−	1.24977i	−0.238817	−	0.971065i	$-0.576760\pi$
$283$	12.1385	−	21.0245i	0.721558	−	1.24977i	0.960375	−	0.278710i	$-0.0899070\pi$
$284$		0			0
$285$	18.0132	+	10.2095i	1.06701	+	0.604757i
$286$		0			0
$287$	−4.20947	−	22.9552i	−0.248477	−	1.35500i
$288$		0			0
$289$	4.54453	+	7.87136i	0.267326	+	0.463021i
$290$		0			0
$291$	22.9598	+	15.2129i	1.34593	+	0.891799i
$292$		0			0
$293$			24.8305i			1.45062i	0.688425	+	0.725308i	$0.258303\pi$
$293$			24.8305i			1.45062i	−0.688425	+	0.725308i	$0.741697\pi$
$294$		0			0
$295$	10.1352	−	6.83229i	0.590095	−	0.397791i
$296$		0			0
$297$	5.23257	−	6.10836i	0.303625	−	0.354443i
$298$		0			0
$299$	−7.63375	−	13.2220i	−0.441471	−	0.764651i
$300$		0			0
$301$	9.88412	−	1.81252i	0.569711	−	0.104472i
$302$		0			0
$303$	−11.8856	+	5.91867i	−0.682809	+	0.340019i
$304$		0			0
$305$	17.4194	−	1.21333i	0.997432	−	0.0694751i
$306$		0			0
$307$	15.7829			0.900776			0.450388	−	0.892833i	$-0.351286\pi$
$307$	15.7829			0.900776			0.450388	+	0.892833i	$0.351286\pi$
$308$		0			0
$309$	0.118155	−	1.91642i	0.00672163	−	0.109022i
$310$		0			0
$311$	−1.70595	+	2.95479i	−0.0967356	+	0.167551i	−0.910332	−	0.413880i	$-0.864173\pi$
$311$	−1.70595	+	2.95479i	−0.0967356	+	0.167551i	0.813596	+	0.581431i	$0.197507\pi$
$312$		0			0
$313$	−12.9321	−	22.3991i	−0.730967	−	1.26607i	−0.956471	−	0.291829i	$-0.905736\pi$
$313$	−12.9321	−	22.3991i	−0.730967	−	1.26607i	0.225504	−	0.974242i	$-0.427597\pi$
$314$		0			0
$315$	17.6036	−	2.26121i	0.991851	−	0.127404i
$316$		0			0
$317$	8.75318	+	15.1610i	0.491628	+	0.851524i	0.999954	−	0.00964062i	$-0.00306875\pi$
$317$	8.75318	+	15.1610i	0.491628	+	0.851524i	−0.508326	+	0.861165i	$0.669735\pi$
$318$		0			0
$319$	−7.58212	+	13.1326i	−0.424517	+	0.735285i
$320$		0			0
$321$	0.156841	−	2.54388i	0.00875399	−	0.141986i
$322$		0			0
$323$	27.3064			1.51937
$324$		0			0
$325$	−12.8717	−	16.4935i	−0.713992	−	0.914892i
$326$		0			0
$327$	14.4781	−	7.20964i	0.800638	−	0.398694i
$328$		0			0
$329$	−4.28577	−	5.03731i	−0.236282	−	0.277716i
$330$		0			0
$331$	−14.0585	−	24.3500i	−0.772724	−	1.33840i	−0.936065	−	0.351828i	$-0.885560\pi$
$331$	−14.0585	−	24.3500i	−0.772724	−	1.33840i	0.163340	−	0.986570i	$-0.447773\pi$
$332$		0			0
$333$	−8.20930	−	6.19876i	−0.449867	−	0.339690i
$334$		0			0
$335$	−13.9591	−	20.7074i	−0.762669	−	1.13137i
$336$		0			0
$337$			22.6854i			1.23575i	0.786276	+	0.617876i	$0.212007\pi$
$337$			22.6854i			1.23575i	−0.786276	+	0.617876i	$0.787993\pi$
$338$		0			0
$339$	−17.2935	−	11.4585i	−0.939256	−	0.622342i
$340$		0			0
$341$	6.07597	+	10.5239i	0.329032	+	0.569901i
$342$		0			0
$343$	−9.58678	−	15.8459i	−0.517637	−	0.855600i
$344$		0			0
$345$	−6.96805	+	12.2941i	−0.375147	+	0.661894i
$346$		0			0
$347$	−13.5001	+	23.3828i	−0.724722	+	1.25526i	0.234366	+	0.972148i	$0.424698\pi$
$347$	−13.5001	+	23.3828i	−0.724722	+	1.25526i	−0.959088	+	0.283107i	$0.908635\pi$
$348$		0			0
$349$		−	26.4459i		−	1.41562i	−0.706405	−	0.707808i	$-0.749684\pi$
$349$		−	26.4459i		−	1.41562i	0.706405	−	0.707808i	$-0.250316\pi$
$350$		0			0
$351$	−3.99363	+	21.3725i	−0.213164	+	1.14078i
$352$		0			0
$353$	−5.86209	−	3.38448i	−0.312008	−	0.180138i	0.335817	−	0.941927i	$-0.390988\pi$
$353$	−5.86209	−	3.38448i	−0.312008	−	0.180138i	−0.647825	+	0.761790i	$0.724321\pi$
$354$		0			0
$355$	−7.81752	+	16.0173i	−0.414911	+	0.850108i
$356$		0			0
$357$	18.7269	−	14.0418i	0.991135	−	0.743171i
$358$		0			0
$359$	22.0053	−	12.7047i	1.16139	−	0.670531i	0.209756	−	0.977754i	$-0.432733\pi$
$359$	22.0053	−	12.7047i	1.16139	−	0.670531i	0.951637	+	0.307223i	$0.0993999\pi$
$360$		0			0
$361$	4.79025	−	8.29696i	0.252118	−	0.436682i
$362$		0			0
$363$	−0.917063	+	14.8743i	−0.0481333	+	0.780700i
$364$		0			0
$365$	−22.9890	+	15.4972i	−1.20330	+	0.811160i
$366$		0			0
$367$	−9.30540	+	16.1174i	−0.485738	+	0.841323i	−0.999866	−	0.0163906i	$-0.994782\pi$
$367$	−9.30540	+	16.1174i	−0.485738	+	0.841323i	0.514128	+	0.857714i	$0.328116\pi$
$368$		0			0
$369$	−10.3160	−	24.3693i	−0.537029	−	1.26861i
$370$		0			0
$371$	1.97016	+	0.701878i	0.102285	+	0.0364397i
$372$		0			0
$373$	9.69970	−	5.60012i	0.502231	−	0.289963i	−0.227403	−	0.973801i	$-0.573024\pi$
$373$	9.69970	−	5.60012i	0.502231	−	0.289963i	0.729634	+	0.683837i	$0.239690\pi$
$374$		0			0
$375$	−7.12076	+	18.0082i	−0.367715	+	0.929939i
$376$		0			0
$377$		−	40.9923i		−	2.11121i
$378$		0			0
$379$	−21.8808			−1.12394			−0.561971	−	0.827157i	$-0.689957\pi$
$379$	−21.8808			−1.12394			−0.561971	+	0.827157i	$0.689957\pi$
$380$		0			0
$381$	3.02502	−	4.56546i	0.154977	−	0.233895i
$382$		0			0
$383$	−26.2172	+	15.1365i	−1.33964	+	0.773439i	−0.986753	−	0.162229i	$-0.948132\pi$
$383$	−26.2172	+	15.1365i	−1.33964	+	0.773439i	−0.352882	+	0.935668i	$0.614798\pi$
$384$		0			0
$385$	6.54550	−	6.40440i	0.333589	−	0.326398i
$386$		0			0
$387$	10.4930	−	4.44188i	0.533388	−	0.225794i
$388$		0			0
$389$	−17.2125	−	9.93765i	−0.872709	−	0.503859i	−0.00446179	−	0.999990i	$-0.501420\pi$
$389$	−17.2125	−	9.93765i	−0.872709	−	0.503859i	−0.868248	+	0.496131i	$0.834754\pi$
$390$		0			0
$391$			18.6368i			0.942505i
$392$		0			0
$393$	0.667381	−	10.8246i	0.0336649	−	0.546029i
$394$		0			0
$395$	0.348432	+	5.00233i	0.0175315	+	0.251695i
$396$		0			0
$397$	1.06067	+	1.83714i	0.0532337	+	0.0922035i	0.891414	−	0.453189i	$-0.149714\pi$
$397$	1.06067	+	1.83714i	0.0532337	+	0.0922035i	−0.838181	+	0.545393i	$0.816381\pi$
$398$		0			0
$399$	−2.92761	−	24.3232i	−0.146564	−	1.21768i
$400$		0			0
$401$	11.4094	−	6.58723i	0.569759	−	0.328951i	−0.187294	−	0.982304i	$-0.559972\pi$
$401$	11.4094	−	6.58723i	0.569759	−	0.328951i	0.757053	+	0.653353i	$0.226638\pi$
$402$		0			0
$403$	−28.4485	−	16.4247i	−1.41712	−	0.818174i
$404$		0			0
$405$	18.9263	−	6.84083i	0.940453	−	0.339924i
$406$		0			0
$407$	−5.30762			−0.263089
$408$		0			0
$409$	−21.6170	−	12.4806i	−1.06889	−	0.617124i	−0.141013	−	0.990008i	$-0.545036\pi$
$409$	−21.6170	−	12.4806i	−1.06889	−	0.617124i	−0.927878	+	0.372883i	$0.878369\pi$
$410$		0			0
$411$	−21.6553	+	10.7837i	−1.06818	+	0.531921i
$412$		0			0
$413$	−13.6238	−	4.85354i	−0.670382	−	0.238827i
$414$		0			0
$415$	5.16364	−	10.5797i	0.253473	−	0.519339i
$416$		0			0
$417$	−7.72932	+	11.6653i	−0.378506	+	0.571253i
$418$		0			0
$419$	−26.0213			−1.27122			−0.635612	−	0.772009i	$-0.719252\pi$
$419$	−26.0213			−1.27122			−0.635612	+	0.772009i	$0.719252\pi$
$420$		0			0
$421$	−6.60400			−0.321859			−0.160930	−	0.986966i	$-0.551449\pi$
$421$	−6.60400			−0.321859			−0.160930	+	0.986966i	$0.551449\pi$
$422$		0			0
$423$	−5.98482	−	4.51908i	−0.290992	−	0.219725i
$424$		0			0
$425$	3.54057	+	25.2921i	0.171743	+	1.22685i
$426$		0			0
$427$	−13.3883	−	15.7361i	−0.647906	−	0.761522i
$428$		0			0
$429$	5.00069	+	10.0421i	0.241435	+	0.484839i
$430$		0			0
$431$	3.36279	+	1.94151i	0.161980	+	0.0935191i	0.578799	−	0.815470i	$-0.303522\pi$
$431$	3.36279	+	1.94151i	0.161980	+	0.0935191i	−0.416819	+	0.908990i	$0.636855\pi$
$432$		0			0
$433$	26.6809			1.28220			0.641101	−	0.767456i	$-0.278478\pi$
$433$	26.6809			1.28220			0.641101	+	0.767456i	$0.278478\pi$
$434$		0			0
$435$	−32.7068	+	19.2323i	−1.56817	+	0.922116i
$436$		0			0
$437$	16.8931	+	9.75321i	0.808105	+	0.466559i
$438$		0			0
$439$	−2.45130	+	1.41526i	−0.116994	+	0.0675467i	−0.557355	−	0.830274i	$-0.688184\pi$
$439$	−2.45130	+	1.41526i	−0.116994	+	0.0675467i	0.440361	+	0.897821i	$0.354850\pi$
$440$		0			0
$441$	−14.5156	−	15.1756i	−0.691217	−	0.722648i
$442$		0			0
$443$	−16.0602	−	27.8171i	−0.763043	−	1.32163i	−0.941275	−	0.337640i	$-0.890371\pi$
$443$	−16.0602	−	27.8171i	−0.763043	−	1.32163i	0.178232	−	0.983988i	$-0.442962\pi$
$444$		0			0
$445$	−2.37947	−	34.1614i	−0.112798	−	1.61941i
$446$		0			0
$447$	−7.94715	−	0.489974i	−0.375887	−	0.0231750i
$448$		0			0
$449$		−	19.6498i		−	0.927334i	−0.886010	−	0.463667i	$-0.846533\pi$
$449$		−	19.6498i		−	0.927334i	0.886010	−	0.463667i	$-0.153467\pi$
$450$		0			0
$451$	−11.8247	−	6.82697i	−0.556801	−	0.321469i
$452$		0			0
$453$	12.5417	−	6.24539i	0.589260	−	0.293434i
$454$		0			0
$455$	−6.66715	+	23.8401i	−0.312561	+	1.11764i
$456$		0			0
$457$	27.4969	−	15.8753i	1.28625	−	0.742616i	0.308266	−	0.951300i	$-0.400251\pi$
$457$	27.4969	−	15.8753i	1.28625	−	0.742616i	0.977983	+	0.208684i	$0.0669181\pi$
$458$		0			0
$459$	17.2664	−	20.1563i	0.805926	−	0.940816i
$460$		0			0
$461$	−34.2329			−1.59439			−0.797193	−	0.603724i	$-0.793683\pi$
$461$	−34.2329			−1.59439			−0.797193	+	0.603724i	$0.793683\pi$
$462$		0			0
$463$		−	17.0910i		−	0.794288i	−0.917756	−	0.397144i	$-0.870001\pi$
$463$		−	17.0910i		−	0.794288i	0.917756	−	0.397144i	$-0.129999\pi$
$464$		0			0
$465$	0.242188	+	30.4043i	0.0112312	+	1.40996i
$466$		0			0
$467$	6.75254	−	3.89858i	0.312470	−	0.180405i	−0.335561	−	0.942018i	$-0.608926\pi$
$467$	6.75254	−	3.89858i	0.312470	−	0.180405i	0.648031	+	0.761614i	$0.275593\pi$
$468$		0			0
$469$	−9.91632	+	27.8349i	−0.457893	+	1.28530i
$470$		0			0
$471$	6.49793	−	3.23578i	0.299409	−	0.149097i
$472$		0			0
$473$	2.93957	−	5.09149i	0.135162	−	0.234107i
$474$		0			0
$475$	24.7785	+	10.0268i	1.13692	+	0.460063i
$476$		0			0
$477$	2.35352	+	0.291315i	0.107760	+	0.0133384i
$478$		0			0
$479$	17.4180	−	30.1688i	0.795848	−	1.37845i	−0.126452	−	0.991973i	$-0.540359\pi$
$479$	17.4180	−	30.1688i	0.795848	−	1.37845i	0.922300	−	0.386476i	$-0.126308\pi$
$480$		0			0
$481$	12.4255	−	7.17385i	0.566553	−	0.327099i
$482$		0			0
$483$	16.6008	−	1.99811i	0.755363	−	0.0909174i
$484$		0			0
$485$	31.9543	+	15.5959i	1.45097	+	0.708174i
$486$		0			0
$487$	−13.6649	−	7.88941i	−0.619214	−	0.357503i	0.157349	−	0.987543i	$-0.449705\pi$
$487$	−13.6649	−	7.88941i	−0.619214	−	0.357503i	−0.776563	+	0.630040i	$0.783039\pi$
$488$		0			0
$489$	11.5862	+	0.714339i	0.523948	+	0.0323035i
$490$		0			0
$491$			4.36169i			0.196840i	0.995145	+	0.0984201i	$0.0313789\pi$
$491$			4.36169i			0.196840i	−0.995145	+	0.0984201i	$0.968621\pi$
$492$		0			0
$493$	−25.0194	+	43.3349i	−1.12682	+	1.95170i
$494$		0			0
$495$	5.66622	−	8.70137i	0.254678	−	0.391097i
$496$		0			0
$497$	20.7428	−	3.80376i	0.930442	−	0.170622i
$498$		0			0
$499$	3.21195	+	5.56327i	0.143787	+	0.249046i	0.928920	−	0.370281i	$-0.120739\pi$
$499$	3.21195	+	5.56327i	0.143787	+	0.249046i	−0.785133	+	0.619327i	$0.787405\pi$
$500$		0			0
$501$	3.65458	−	5.51559i	0.163274	−	0.246418i
$502$		0			0
$503$			34.7482i			1.54935i	0.632362	+	0.774673i	$0.282086\pi$
$503$			34.7482i			1.54935i	−0.632362	+	0.774673i	$0.717914\pi$
$504$		0			0
$505$	−14.2135	+	9.58152i	−0.632493	+	0.426372i
$506$		0			0
$507$	−6.50976	−	4.31330i	−0.289109	−	0.191561i
$508$		0			0
$509$	4.59595	+	7.96042i	0.203712	+	0.352839i	0.949722	−	0.313096i	$-0.101366\pi$
$509$	4.59595	+	7.96042i	0.203712	+	0.352839i	−0.746010	+	0.665935i	$0.768033\pi$
$510$		0			0
$511$	30.9018	+	11.0089i	1.36702	+	0.487007i
$512$		0			0
$513$	−9.23435	−	26.1992i	−0.407707	−	1.15672i
$514$		0			0
$515$	−0.172240	−	2.47280i	−0.00758981	−	0.108965i
$516$		0			0
$517$	−3.86941			−0.170176
$518$		0			0
$519$	−4.69560	−	0.289503i	−0.206114	−	0.0127078i
$520$		0			0
$521$	−10.3096	+	17.8568i	−0.451673	+	0.782321i	−0.998490	−	0.0549315i	$-0.982506\pi$
$521$	−10.3096	+	17.8568i	−0.451673	+	0.782321i	0.546817	+	0.837252i	$0.315839\pi$
$522$		0			0
$523$	10.1200	+	17.5284i	0.442519	+	0.766465i	0.997876	−	0.0651472i	$-0.0207517\pi$
$523$	10.1200	+	17.5284i	0.442519	+	0.766465i	−0.555357	+	0.831612i	$0.687418\pi$
$524$		0			0
$525$	22.1494	−	5.86542i	0.966680	−	0.255988i
$526$		0			0
$527$	20.0494	+	34.7266i	0.873367	+	1.51272i
$528$		0			0
$529$	4.84335	−	8.38893i	0.210581	−	0.364736i
$530$		0			0
$531$	−16.2747	−	2.01447i	−0.706263	−	0.0874204i
$532$		0			0
$533$	36.9096			1.59873
$534$		0			0
$535$	−0.228633	−	3.28242i	−0.00988468	−	0.141911i
$536$		0			0
$537$	0.726691	+	1.45930i	0.0313590	+	0.0629737i
$538$		0			0
$539$	−10.6954	−	1.73561i	−0.460683	−	0.0747580i
$540$		0			0
$541$	11.0976	+	19.2217i	0.477125	+	0.826404i	0.999656	−	0.0262157i	$-0.00834567\pi$
$541$	11.0976	+	19.2217i	0.477125	+	0.826404i	−0.522532	+	0.852620i	$0.675012\pi$
$542$		0			0
$543$	−0.0397303	+	0.0599621i	−0.00170499	+	0.00257322i
$544$		0			0
$545$	17.3137	−	11.6714i	0.741639	−	0.499949i
$546$		0			0
$547$			23.3955i			1.00032i	0.865933	+	0.500160i	$0.166725\pi$
$547$			23.3955i			1.00032i	−0.865933	+	0.500160i	$0.833275\pi$
$548$		0			0
$549$	−18.6960	−	14.1172i	−0.797925	−	0.602506i
$550$		0			0
$551$	26.1868	+	45.3569i	1.11559	+	1.93227i
$552$		0			0
$553$	4.51893	−	3.84473i	0.192164	−	0.163494i
$554$		0			0
$555$	−11.5535	−	6.54825i	−0.490417	−	0.277958i
$556$		0			0
$557$	−0.615475	+	1.06603i	−0.0260785	+	0.0451693i	−0.878770	−	0.477245i	$-0.841635\pi$
$557$	−0.615475	+	1.06603i	−0.0260785	+	0.0451693i	0.852692	+	0.522415i	$0.174969\pi$
$558$		0			0
$559$			15.8926i			0.672187i
$560$		0			0
$561$	0.842696	−	13.6681i	0.0355787	−	0.577069i
$562$		0			0
$563$	15.5994	+	9.00633i	0.657437	+	0.379571i	0.791300	−	0.611429i	$-0.209405\pi$
$563$	15.5994	+	9.00633i	0.657437	+	0.379571i	−0.133863	+	0.991000i	$0.542738\pi$
$564$		0			0
$565$	−24.0683	−	11.7470i	−1.01256	−	0.494199i
$566$		0			0
$567$	−19.8055	−	13.2191i	−0.831752	−	0.555148i
$568$		0			0
$569$	17.8273	−	10.2926i	0.747361	−	0.431489i	−0.0773783	−	0.997002i	$-0.524655\pi$
$569$	17.8273	−	10.2926i	0.747361	−	0.431489i	0.824740	+	0.565513i	$0.191322\pi$
$570$		0			0
$571$	5.12127	−	8.87029i	0.214318	−	0.371210i	−0.738743	−	0.673987i	$-0.764580\pi$
$571$	5.12127	−	8.87029i	0.214318	−	0.371210i	0.953061	+	0.302777i	$0.0979137\pi$
$572$		0			0
$573$	−16.1894	−	0.998140i	−0.676320	−	0.0416979i
$574$		0			0
$575$	−6.84339	+	16.9115i	−0.285389	+	0.705260i
$576$		0			0
$577$	−11.4478	+	19.8281i	−0.476576	+	0.825455i	−0.999640	−	0.0268392i	$-0.991456\pi$
$577$	−11.4478	+	19.8281i	−0.476576	+	0.825455i	0.523063	+	0.852294i	$0.324789\pi$
$578$		0			0
$579$	−7.94217	−	15.9491i	−0.330066	−	0.662822i
$580$		0			0
$581$	−13.7011	+	2.51247i	−0.568416	+	0.104235i
$582$		0			0
$583$	1.05967	−	0.611802i	0.0438871	−	0.0253382i
$584$		0			0
$585$	−1.50410	+	28.0290i	−0.0621867	+	1.15886i
$586$		0			0
$587$		−	13.1377i		−	0.542251i	−0.962544	−	0.271125i	$-0.912604\pi$
$587$		−	13.1377i		−	0.542251i	0.962544	−	0.271125i	$-0.0873958\pi$
$588$		0			0
$589$	41.9699			1.72934
$590$		0			0
$591$	−1.73172	−	1.14742i	−0.0712334	−	0.0471985i
$592$		0			0
$593$	27.8856	−	16.0998i	1.14512	−	0.661138i	0.197430	−	0.980317i	$-0.436741\pi$
$593$	27.8856	−	16.0998i	1.14512	−	0.661138i	0.947694	+	0.319179i	$0.103407\pi$
$594$		0			0
$595$	21.5988	−	21.1332i	0.885463	−	0.866375i
$596$		0			0
$597$	−14.9736	−	30.0693i	−0.612830	−	1.23066i
$598$		0			0
$599$	−37.7878	−	21.8168i	−1.54397	−	0.891411i	−0.998582	−	0.0532262i	$-0.983050\pi$
$599$	−37.7878	−	21.8168i	−1.54397	−	0.891411i	−0.545387	−	0.838185i	$-0.683617\pi$
$600$		0			0
$601$			23.7804i			0.970024i	0.874508	+	0.485012i	$0.161185\pi$
$601$			23.7804i			0.970024i	−0.874508	+	0.485012i	$0.838815\pi$
$602$		0			0
$603$	−4.11578	+	33.2511i	−0.167607	+	1.35409i
$604$		0			0
$605$	1.33684	+	19.1926i	0.0543504	+	0.780292i
$606$		0			0
$607$	10.6264	+	18.4055i	0.431314	+	0.747058i	0.996987	−	0.0775719i	$-0.0247167\pi$
$607$	10.6264	+	18.4055i	0.431314	+	0.747058i	−0.565673	+	0.824630i	$0.691383\pi$
$608$		0			0
$609$	41.2830	+	17.6400i	1.67287	+	0.714810i
$610$		0			0
$611$	9.05853	−	5.22994i	0.366469	−	0.211581i
$612$		0			0
$613$	7.96699	+	4.59974i	0.321784	+	0.185782i	0.652187	−	0.758058i	$-0.273852\pi$
$613$	7.96699	+	4.59974i	0.321784	+	0.185782i	−0.330404	+	0.943840i	$0.607185\pi$
$614$		0			0
$615$	−17.3168	−	29.4493i	−0.698280	−	1.18751i
$616$		0			0
$617$	−48.7268			−1.96167			−0.980833	−	0.194850i	$-0.937578\pi$
$617$	−48.7268			−1.96167			−0.980833	+	0.194850i	$0.937578\pi$
$618$		0			0
$619$	26.7205	+	15.4271i	1.07399	+	0.620068i	0.929268	−	0.369405i	$-0.120439\pi$
$619$	26.7205	+	15.4271i	1.07399	+	0.620068i	0.144720	+	0.989473i	$0.453772\pi$
$620$		0			0
$621$	17.8812	−	6.30252i	0.717548	−	0.252911i
$622$		0			0
$623$	−30.8602	+	26.2560i	−1.23639	+	1.05192i
$624$		0			0
$625$	−6.07439	+	24.2508i	−0.242976	+	0.970032i
$626$		0			0
$627$	−11.9483	−	7.91679i	−0.477167	−	0.316166i
$628$		0			0
$629$	−17.5140			−0.698330
$630$		0			0
$631$	11.0171			0.438585			0.219293	−	0.975659i	$-0.429625\pi$
$631$	11.0171			0.438585			0.219293	+	0.975659i	$0.429625\pi$
$632$		0			0
$633$	−13.5075	−	8.94994i	−0.536875	−	0.355728i
$634$		0			0
$635$	3.10118	−	6.35397i	0.123066	−	0.252150i
$636$		0			0
$637$	27.3845	−	10.3929i	1.08501	−	0.411780i
$638$		0			0
$639$	22.0205	−	9.32173i	0.871119	−	0.368762i
$640$		0			0
$641$	6.08428	+	3.51276i	0.240314	+	0.138746i	0.615321	−	0.788276i	$-0.289026\pi$
$641$	6.08428	+	3.51276i	0.240314	+	0.138746i	−0.375007	+	0.927022i	$0.622360\pi$
$642$		0			0
$643$	35.3578			1.39438			0.697188	−	0.716889i	$-0.254434\pi$
$643$	35.3578			1.39438			0.697188	+	0.716889i	$0.254434\pi$
$644$		0			0
$645$	12.6804	−	7.45631i	0.499289	−	0.293592i
$646$		0			0
$647$	−0.107907	−	0.0623003i	−0.00424227	−	0.00244928i	0.497877	−	0.867247i	$-0.334113\pi$
$647$	−0.107907	−	0.0623003i	−0.00424227	−	0.00244928i	−0.502120	+	0.864798i	$0.667446\pi$
$648$		0			0
$649$	−7.32771	+	4.23065i	−0.287638	+	0.166068i
$650$		0			0
$651$	28.7833	−	21.5822i	1.12811	−	0.845875i
$652$		0			0
$653$	10.9304	+	18.9320i	0.427741	+	0.740868i	0.996672	−	0.0815166i	$-0.0259764\pi$
$653$	10.9304	+	18.9320i	0.427741	+	0.740868i	−0.568931	+	0.822385i	$0.692643\pi$
$654$		0			0
$655$	−0.972870	−	13.9672i	−0.0380132	−	0.545744i
$656$		0			0
$657$	36.9148	+	4.56927i	1.44019	+	0.178264i
$658$		0			0
$659$			16.4975i			0.642651i	0.946969	+	0.321326i	$0.104128\pi$
$659$			16.4975i			0.642651i	−0.946969	+	0.321326i	$0.895872\pi$
$660$		0			0
$661$	−30.8643	−	17.8195i	−1.20048	−	0.693098i	−0.239818	−	0.970818i	$-0.577088\pi$
$661$	−30.8643	−	17.8195i	−1.20048	−	0.693098i	−0.960662	+	0.277720i	$0.910421\pi$
$662$		0			0
$663$	16.5012	+	33.1369i	0.640854	+	1.28693i
$664$		0			0
$665$	−7.85254	−	30.6375i	−0.304509	−	1.18807i
$666$		0			0
$667$	−30.9564	+	17.8727i	−1.19864	+	0.692034i
$668$		0			0
$669$	9.79139	+	6.48768i	0.378557	+	0.250828i
$670$		0			0
$671$	−12.0877			−0.466639
$672$		0			0
$673$			15.6461i			0.603113i	0.953448	+	0.301557i	$0.0975062\pi$
$673$			15.6461i			0.603113i	−0.953448	+	0.301557i	$0.902494\pi$
$674$		0			0
$675$	23.0693	−	11.9502i	0.887938	−	0.459963i
$676$		0			0
$677$	−21.9298	+	12.6612i	−0.842831	+	0.486609i	−0.858225	−	0.513273i	$-0.828433\pi$
$677$	−21.9298	+	12.6612i	−0.842831	+	0.486609i	0.0153946	+	0.999881i	$0.495100\pi$
$678$		0			0
$679$	−7.58848	−	41.3818i	−0.291219	−	1.58809i
$680$		0			0
$681$	10.9578	+	22.0050i	0.419905	+	0.843232i
$682$		0			0
$683$	10.5605	−	18.2913i	0.404086	−	0.699898i	−0.590128	−	0.807309i	$-0.700923\pi$
$683$	10.5605	−	18.2913i	0.404086	−	0.699898i	0.994215	+	0.107411i	$0.0342562\pi$
$684$		0			0
$685$	−25.8968	+	17.4574i	−0.989464	+	0.667011i
$686$		0			0
$687$	−19.5605	−	1.20598i	−0.746279	−	0.0460112i
$688$		0			0
$689$	−1.65384	+	2.86453i	−0.0630062	+	0.109130i
$690$		0			0
$691$	12.3309	−	7.11924i	0.469089	−	0.270829i	−0.246769	−	0.969074i	$-0.579369\pi$
$691$	12.3309	−	7.11924i	0.469089	−	0.270829i	0.715858	+	0.698245i	$0.246036\pi$
$692$		0			0
$693$	−12.2653	+	0.714770i	−0.465919	+	0.0271519i
$694$		0			0
$695$	−7.92389	+	16.2352i	−0.300570	+	0.615836i
$696$		0			0
$697$	−39.0189	−	22.5275i	−1.47794	−	0.853292i
$698$		0			0
$699$	−1.94655	+	31.5721i	−0.0736252	+	1.19417i
$700$		0			0
$701$		−	12.1825i		−	0.460127i	−0.973176	−	0.230063i	$-0.926107\pi$
$701$		−	12.1825i		−	0.460127i	0.973176	−	0.230063i	$-0.0738934\pi$
$702$		0			0
$703$	−9.16562	+	15.8753i	−0.345688	+	0.598749i
$704$		0			0
$705$	−8.42281	−	4.77386i	−0.317221	−	0.179794i
$706$		0			0
$707$	19.1058	+	6.80655i	0.718548	+	0.255987i
$708$		0			0
$709$	−12.5140	−	21.6748i	−0.469971	−	0.814014i	0.529439	−	0.848348i	$-0.322402\pi$
$709$	−12.5140	−	21.6748i	−0.469971	−	0.814014i	−0.999410	+	0.0343336i	$0.989069\pi$
$710$		0			0
$711$	4.05403	−	5.36893i	0.152038	−	0.201351i
$712$		0			0
$713$			28.6448i			1.07276i
$714$		0			0
$715$	8.09543	+	12.0090i	0.302752	+	0.449111i
$716$		0			0
$717$	−18.0655	+	27.2650i	−0.674669	+	1.01823i
$718$		0			0
$719$	5.93961	+	10.2877i	0.221510	+	0.383666i	0.955267	−	0.295746i	$-0.0955682\pi$
$719$	5.93961	+	10.2877i	0.221510	+	0.383666i	−0.733757	+	0.679412i	$0.762235\pi$
$720$		0			0
$721$	−2.23384	+	1.90056i	−0.0831925	+	0.0707806i
$722$		0			0
$723$	−10.7532	−	21.5941i	−0.399916	−	0.803092i
$724$		0			0
$725$	−38.6157	+	30.1361i	−1.43415	+	1.11923i
$726$		0			0
$727$	11.1429			0.413265			0.206633	−	0.978419i	$-0.433749\pi$
$727$	11.1429			0.413265			0.206633	+	0.978419i	$0.433749\pi$
$728$		0			0
$729$	−25.1781	−	9.74995i	−0.932524	−	0.361109i
$730$		0			0
$731$	9.69997	−	16.8008i	0.358766	−	0.621401i
$732$		0			0
$733$	16.8594	+	29.2014i	0.622717	+	1.07858i	0.988978	+	0.148065i	$0.0473043\pi$
$733$	16.8594	+	29.2014i	0.622717	+	1.07858i	−0.366261	+	0.930512i	$0.619362\pi$
$734$		0			0
$735$	−21.1401	−	16.9734i	−0.779764	−	0.626073i
$736$		0			0
$737$	8.64370	+	14.9713i	0.318395	+	0.551476i
$738$		0			0
$739$	−0.619063	+	1.07225i	−0.0227726	+	0.0394433i	−0.877187	−	0.480149i	$-0.840583\pi$
$739$	−0.619063	+	1.07225i	−0.0227726	+	0.0394433i	0.854415	+	0.519592i	$0.173916\pi$
$740$		0			0
$741$	38.6720	+	2.38429i	1.42065	+	0.0875891i
$742$		0			0
$743$	42.5482			1.56094			0.780472	−	0.625191i	$-0.214979\pi$
$743$	42.5482			1.56094			0.780472	+	0.625191i	$0.214979\pi$
$744$		0			0
$745$	−10.2544	+	0.714256i	−0.375691	+	0.0261683i
$746$		0			0
$747$	−14.5450	+	6.15720i	−0.532175	+	0.225280i
$748$		0			0
$749$	−2.96522	+	2.52282i	−0.108347	+	0.0921819i
$750$		0			0
$751$	11.5563	+	20.0161i	0.421695	+	0.730397i	0.996105	−	0.0881704i	$-0.0281020\pi$
$751$	11.5563	+	20.0161i	0.421695	+	0.730397i	−0.574411	+	0.818567i	$0.694769\pi$
$752$		0			0
$753$	−38.7193	−	25.6550i	−1.41101	−	0.934921i
$754$		0			0
$755$	14.9981	−	10.1104i	0.545838	−	0.367957i
$756$		0			0
$757$		−	37.9224i		−	1.37831i	−0.724613	−	0.689156i	$-0.757981\pi$
$757$		−	37.9224i		−	1.37831i	0.724613	−	0.689156i	$-0.242019\pi$
$758$		0			0
$759$	5.40328	−	8.15478i	0.196126	−	0.296000i
$760$		0			0
$761$	−18.1928	−	31.5108i	−0.659488	−	1.14227i	−0.980748	−	0.195275i	$-0.937440\pi$
$761$	−18.1928	−	31.5108i	−0.659488	−	1.14227i	0.321261	−	0.946991i	$-0.395893\pi$
$762$		0			0
$763$	−23.2732	−	8.29118i	−0.842545	−	0.300161i
$764$		0			0
$765$	18.6973	−	28.7127i	0.676004	−	1.03811i
$766$		0			0
$767$	11.4364	−	19.8084i	0.412945	−	0.715242i
$768$		0			0
$769$		−	3.93239i		−	0.141805i	−0.997483	−	0.0709027i	$-0.977412\pi$
$769$		−	3.93239i		−	0.141805i	0.997483	−	0.0709027i	$-0.0225880\pi$
$770$		0			0
$771$	24.1617	+	1.48967i	0.870163	+	0.0536491i
$772$		0			0
$773$	−39.6236	−	22.8767i	−1.42516	−	0.822817i	−0.428427	−	0.903577i	$-0.640932\pi$
$773$	−39.6236	−	22.8767i	−1.42516	−	0.822817i	−0.996734	+	0.0807599i	$0.974265\pi$
$774$		0			0
$775$	5.44185	+	38.8740i	0.195477	+	1.39639i
$776$		0			0
$777$	1.87774	+	15.6007i	0.0673634	+	0.559671i
$778$		0			0
$779$	−40.8395	+	23.5787i	−1.46323	+	0.844794i
$780$		0			0
$781$	6.16898	−	10.6850i	0.220744	−	0.382339i
$782$		0			0
$783$	50.0388	+	9.35019i	1.78824	+	0.334148i
$784$		0			0
$785$	7.77062	−	5.23828i	0.277345	−	0.186962i
$786$		0			0
$787$	5.77342	−	9.99986i	0.205800	−	0.356457i	−0.744587	−	0.667525i	$-0.767354\pi$
$787$	5.77342	−	9.99986i	0.205800	−	0.356457i	0.950387	+	0.311069i	$0.100687\pi$
$788$		0			0
$789$	−46.7688	+	23.2895i	−1.66501	+	0.829127i
$790$		0			0
$791$	5.71571	+	31.1691i	0.203227	+	1.10825i
$792$		0			0
$793$	28.2980	−	16.3378i	1.00489	−	0.580174i
$794$		0			0
$795$	3.06147	−	0.0243864i	0.108579	−	0.000864897i
$796$		0			0
$797$			5.24845i			0.185910i	0.995670	+	0.0929548i	$0.0296312\pi$
$797$			5.24845i			0.185910i	−0.995670	+	0.0929548i	$0.970369\pi$
$798$		0			0
$799$	−12.7682			−0.451708
$800$		0			0
$801$	−27.6853	+	36.6649i	−0.978213	+	1.29549i
$802$		0			0
$803$	16.6209	−	9.59609i	0.586540	−	0.338639i
$804$		0			0
$805$	20.9103	−	5.35942i	0.736992	−	0.188895i
$806$		0			0
$807$	−10.6528	+	5.30476i	−0.374995	+	0.186736i
$808$		0			0
$809$	40.9993	+	23.6710i	1.44146	+	0.832227i	0.997947	−	0.0640417i	$-0.0203991\pi$
$809$	40.9993	+	23.6710i	1.44146	+	0.832227i	0.443512	+	0.896268i	$0.353732\pi$
$810$		0			0
$811$		−	31.5218i		−	1.10688i	−0.832889	−	0.553440i	$-0.813315\pi$
$811$		−	31.5218i		−	1.10688i	0.832889	−	0.553440i	$-0.186685\pi$
$812$		0			0
$813$	38.7257	+	2.38760i	1.35817	+	0.0837368i
$814$		0			0
$815$	14.9499	−	1.04132i	0.523674	−	0.0364759i
$816$		0			0
$817$	−10.1526	−	17.5848i	−0.355193	−	0.615213i
$818$		0			0
$819$	27.7477	−	18.2512i	0.969582	−	0.637749i
$820$		0			0
$821$	−17.1600	+	9.90735i	−0.598890	+	0.345769i	−0.768605	−	0.639724i	$-0.779049\pi$
$821$	−17.1600	+	9.90735i	−0.598890	+	0.345769i	0.169715	+	0.985493i	$0.445715\pi$
$822$		0			0
$823$	5.98542	+	3.45569i	0.208639	+	0.120458i	0.600679	−	0.799491i	$-0.294897\pi$
$823$	5.98542	+	3.45569i	0.208639	+	0.120458i	−0.392040	+	0.919948i	$0.628230\pi$
$824$		0			0
$825$	5.78359	−	12.0934i	0.201359	−	0.421037i
$826$		0			0
$827$	27.6374			0.961045			0.480523	−	0.876982i	$-0.340447\pi$
$827$	27.6374			0.961045			0.480523	+	0.876982i	$0.340447\pi$
$828$		0			0
$829$	22.5579	+	13.0238i	0.783468	+	0.452336i	0.837658	−	0.546195i	$-0.183924\pi$
$829$	22.5579	+	13.0238i	0.783468	+	0.452336i	−0.0541897	+	0.998531i	$0.517258\pi$
$830$		0			0
$831$	−5.38950	−	10.8229i	−0.186960	−	0.375444i
$832$		0			0
$833$	−35.2926	−	5.72714i	−1.22281	−	0.198434i
$834$		0			0
$835$	3.74658	−	7.67633i	0.129656	−	0.265650i
$836$		0			0
$837$	26.5384	−	30.9802i	0.917302	−	1.07083i
$838$		0			0
$839$	57.2133			1.97522			0.987611	−	0.156924i	$-0.0501577\pi$
$839$	57.2133			1.97522			0.987611	+	0.156924i	$0.0501577\pi$
$840$		0			0
$841$	−66.9743			−2.30946
$842$		0			0
$843$	2.28253	−	3.44486i	0.0786144	−	0.118647i
$844$		0			0
$845$	−9.05996	−	4.42188i	−0.311672	−	0.152117i
$846$		0			0
$847$	17.3379	−	14.7512i	0.595739	−	0.506857i
$848$		0			0
$849$	−37.6402	+	18.7437i	−1.29181	+	0.643283i
$850$		0			0
$851$	−10.8350	−	6.25561i	−0.371420	−	0.214440i
$852$		0			0
$853$	−36.1034			−1.23616			−0.618078	−	0.786117i	$-0.712088\pi$
$853$	−36.1034			−1.23616			−0.618078	+	0.786117i	$0.712088\pi$
$854$		0			0
$855$	−16.2413	−	31.9741i	−0.555440	−	1.09349i
$856$		0			0
$857$	41.1470	+	23.7562i	1.40555	+	0.811497i	0.994955	−	0.100320i	$-0.0319866\pi$
$857$	41.1470	+	23.7562i	1.40555	+	0.811497i	0.410598	+	0.911816i	$0.365320\pi$
$858$		0			0
$859$	5.37937	−	3.10578i	0.183542	−	0.105968i	−0.405414	−	0.914133i	$-0.632873\pi$
$859$	5.37937	−	3.10578i	0.183542	−	0.105968i	0.588956	+	0.808165i	$0.299539\pi$
$860$		0			0
$861$	−15.8831	+	37.1714i	−0.541296	+	1.26680i
$862$		0			0
$863$	−21.9393	−	38.0000i	−0.746824	−	1.29354i	−0.949338	−	0.314257i	$-0.898245\pi$
$863$	−21.9393	−	38.0000i	−0.746824	−	1.29354i	0.202514	−	0.979279i	$-0.435089\pi$
$864$		0			0
$865$	−6.05882	+	0.422021i	−0.206006	+	0.0143491i
$866$		0			0
$867$	0.968764	−	15.7129i	0.0329010	−	0.533638i
$868$		0			0
$869$		−	3.47122i		−	0.117753i
$870$		0			0
$871$	−40.4709	−	23.3659i	−1.37130	−	0.791722i
$872$		0			0
$873$	−18.5968	−	43.9309i	−0.629406	−	1.48683i
$874$		0			0
$875$	27.3593	−	11.2458i	0.924914	−	0.380177i
$876$		0			0
$877$	19.4790	−	11.2462i	0.657758	−	0.379757i	−0.133664	−	0.991027i	$-0.542674\pi$
$877$	19.4790	−	11.2462i	0.657758	−	0.379757i	0.791422	+	0.611270i	$0.209341\pi$
$878$		0			0
$879$	23.7551	−	35.8519i	0.801241	−	1.20926i
$880$		0			0
$881$	5.24052			0.176558			0.0882788	−	0.996096i	$-0.471863\pi$
$881$	5.24052			0.176558			0.0882788	+	0.996096i	$0.471863\pi$
$882$		0			0
$883$		−	35.5284i		−	1.19562i	−0.801636	−	0.597812i	$-0.796037\pi$
$883$		−	35.5284i		−	1.19562i	0.801636	−	0.597812i	$-0.203963\pi$
$884$		0			0
$885$	−21.1703	+	0.168634i	−0.711631	+	0.00566856i
$886$		0			0
$887$	−6.45224	+	3.72520i	−0.216645	+	0.125080i	−0.604396	−	0.796684i	$-0.706585\pi$
$887$	−6.45224	+	3.72520i	−0.216645	+	0.125080i	0.387751	+	0.921764i	$0.373252\pi$
$888$		0			0
$889$	−8.22858	+	1.50894i	−0.275978	+	0.0506081i
$890$		0			0
$891$	−13.3989	+	3.81370i	−0.448881	+	0.127764i
$892$		0			0
$893$	−6.68200	+	11.5736i	−0.223605	+	0.387295i
$894$		0			0
$895$	1.17641	+	1.74513i	0.0393232	+	0.0583332i
$896$		0			0
$897$	−1.62730	+	26.3940i	−0.0543339	+	0.881269i
$898$		0			0
$899$	−38.4548	+	66.6056i	−1.28254	+	2.22142i
$900$		0			0
$901$	3.49669	−	2.01882i	0.116492	−	0.0672565i
$902$		0			0
$903$	−16.0054	−	6.83900i	−0.532625	−	0.227588i
$904$		0			0
$905$	−0.0407304	+	0.0834523i	−0.00135393	+	0.00277405i
$906$		0			0
$907$	17.8957	+	10.3321i	0.594218	+	0.343072i	0.766764	−	0.641929i	$-0.221866\pi$
$907$	17.8957	+	10.3321i	0.594218	+	0.343072i	−0.172545	+	0.985002i	$0.555199\pi$
$908$		0			0
$909$	22.8235	+	2.82506i	0.757008	+	0.0937015i
$910$		0			0
$911$		−	9.23666i		−	0.306024i	−0.988224	−	0.153012i	$-0.951103\pi$
$911$		−	9.23666i		−	0.306024i	0.988224	−	0.153012i	$-0.0488974\pi$
$912$		0			0
$913$	−4.07474	+	7.05766i	−0.134854	+	0.233575i
$914$		0			0
$915$	−26.3120	−	14.9131i	−0.869849	−	0.493012i
$916$		0			0
$917$	−12.6175	+	10.7350i	−0.416665	+	0.354501i
$918$		0			0
$919$	−20.0585	−	34.7423i	−0.661669	−	1.14604i	−0.980177	−	0.198123i	$-0.936515\pi$
$919$	−20.0585	−	34.7423i	−0.661669	−	1.14604i	0.318509	−	0.947920i	$-0.396818\pi$
$920$		0			0
$921$	−22.7883	−	15.0993i	−0.750901	−	0.497539i
$922$		0			0
$923$			33.3523i			1.09780i
$924$		0			0
$925$	−15.8927	−	6.43111i	−0.522548	−	0.211453i
$926$		0			0
$927$	−2.00402	+	2.65402i	−0.0658208	+	0.0871694i
$928$		0			0
$929$	6.25279	+	10.8301i	0.205147	+	0.355326i	0.950180	−	0.311703i	$-0.100899\pi$
$929$	6.25279	+	10.8301i	0.205147	+	0.355326i	−0.745032	+	0.667028i	$0.767566\pi$
$930$		0			0
$931$	−23.6609	+	28.9932i	−0.775456	+	0.950213i
$932$		0			0
$933$	5.28998	−	2.63426i	0.173186	−	0.0862417i
$934$		0			0
$935$	−1.22843	−	17.6363i	−0.0401741	−	0.576767i
$936$		0			0
$937$	15.6057			0.509817			0.254908	−	0.966965i	$-0.417955\pi$
$937$	15.6057			0.509817			0.254908	+	0.966965i	$0.417955\pi$
$938$		0			0
$939$	−2.75676	+	44.7133i	−0.0899634	+	1.45916i
$940$		0			0
$941$	15.0129	−	26.0032i	0.489408	−	0.847679i	−0.510518	−	0.859867i	$-0.670546\pi$
$941$	15.0129	−	26.0032i	0.489408	−	0.847679i	0.999926	+	0.0121879i	$0.00387962\pi$
$942$		0			0
$943$	−16.0926	−	27.8733i	−0.524049	−	0.907679i
$944$		0			0
$945$	−27.5805	−	13.5763i	−0.897193	−	0.441638i
$946$		0			0
$947$	−10.7820	−	18.6750i	−0.350368	−	0.606854i	0.635946	−	0.771733i	$-0.280610\pi$
$947$	−10.7820	−	18.6750i	−0.350368	−	0.606854i	−0.986314	+	0.164879i	$0.947277\pi$
$948$		0			0
$949$	−25.9404	+	44.9301i	−0.842061	+	1.45849i
$950$		0			0
$951$	1.86593	−	30.2644i	0.0605068	−	0.981392i
$952$		0			0
$953$	32.6140			1.05647			0.528236	−	0.849098i	$-0.322854\pi$
$953$	32.6140			1.05647			0.528236	+	0.849098i	$0.322854\pi$
$954$		0			0
$955$	−20.8894	+	1.45503i	−0.675966	+	0.0470837i
$956$		0			0
$957$	23.5114	−	11.7080i	0.760015	−	0.378465i
$958$		0			0
$959$	34.8104	+	12.4014i	1.12409	+	0.400462i
$960$		0			0
$961$	15.3160	+	26.5280i	0.494063	+	0.855742i
$962$		0			0
$963$	−2.66016	+	3.52297i	−0.0857225	+	0.113526i
$964$		0			0
$965$	−12.8573	−	19.0729i	−0.413891	−	0.613979i
$966$		0			0
$967$		−	8.08819i		−	0.260099i	−0.991508	−	0.130049i	$-0.958486\pi$
$967$		−	8.08819i		−	0.260099i	0.991508	−	0.130049i	$-0.0415136\pi$
$968$		0			0
$969$	−39.4267	−	26.1237i	−1.26657	−	0.839216i
$970$		0			0
$971$	−28.7921	−	49.8694i	−0.923983	−	1.60039i	−0.793189	−	0.608976i	$-0.791581\pi$
$971$	−28.7921	−	49.8694i	−0.923983	−	1.60039i	−0.130794	−	0.991410i	$-0.541753\pi$
$972$		0			0
$973$	21.0250	−	3.85552i	0.674032	−	0.123602i
$974$		0			0
$975$	2.80583	+	36.1285i	0.0898586	+	1.15704i
$976$		0			0
$977$	10.4121	−	18.0342i	0.333112	−	0.576966i	−0.650009	−	0.759927i	$-0.725235\pi$
$977$	10.4121	−	18.0342i	0.333112	−	0.576966i	0.983120	+	0.182961i	$0.0585681\pi$
$978$		0			0
$979$			23.7053i			0.757623i
$980$		0			0
$981$	−27.8017	−	3.44126i	−0.887641	−	0.109871i
$982$		0			0
$983$	8.49526	+	4.90474i	0.270957	+	0.156437i	0.629322	−	0.777144i	$-0.283333\pi$
$983$	8.49526	+	4.90474i	0.270957	+	0.156437i	−0.358366	+	0.933581i	$0.616666\pi$
$984$		0			0
$985$	−2.41012	−	1.17630i	−0.0767928	−	0.0374802i
$986$		0			0
$987$	1.36892	+	11.3733i	0.0435733	+	0.362017i
$988$		0			0
$989$	12.0017	−	6.92921i	0.381633	−	0.220336i
$990$		0			0
$991$	19.9849	−	34.6149i	0.634843	−	1.09958i	−0.351706	−	0.936111i	$-0.614398\pi$
$991$	19.9849	−	34.6149i	0.634843	−	1.09958i	0.986548	−	0.163469i	$-0.0522684\pi$
$992$		0			0
$993$	−2.99687	+	48.6077i	−0.0951027	+	1.54252i
$994$		0			0
$995$	−24.2403	−	35.9587i	−0.768468	−	1.13997i
$996$		0			0
$997$	11.6761	−	20.2236i	0.369786	−	0.640489i	−0.619746	−	0.784803i	$-0.712764\pi$
$997$	11.6761	−	20.2236i	0.369786	−	0.640489i	0.989532	+	0.144314i	$0.0460975\pi$
$998$		0			0
$999$	5.92282	+	16.8039i	0.187390	+	0.531653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.bn.a.269.4	yes	32
3.2	odd	2	inner	420.2.bn.a.269.15	yes	32
5.2	odd	4		2100.2.bi.n.101.5		32
5.3	odd	4		2100.2.bi.n.101.12		32
5.4	even	2	inner	420.2.bn.a.269.13	yes	32
7.3	odd	6		2940.2.f.a.1469.17		32
7.4	even	3		2940.2.f.a.1469.16		32
7.5	odd	6	inner	420.2.bn.a.89.2	✓	32
15.2	even	4		2100.2.bi.n.101.10		32
15.8	even	4		2100.2.bi.n.101.7		32
15.14	odd	2	inner	420.2.bn.a.269.2	yes	32
21.5	even	6	inner	420.2.bn.a.89.13	yes	32
21.11	odd	6		2940.2.f.a.1469.13		32
21.17	even	6		2940.2.f.a.1469.20		32
35.4	even	6		2940.2.f.a.1469.18		32
35.12	even	12		2100.2.bi.n.1601.10		32
35.19	odd	6	inner	420.2.bn.a.89.15	yes	32
35.24	odd	6		2940.2.f.a.1469.15		32
35.33	even	12		2100.2.bi.n.1601.7		32
105.47	odd	12		2100.2.bi.n.1601.5		32
105.59	even	6		2940.2.f.a.1469.14		32
105.68	odd	12		2100.2.bi.n.1601.12		32
105.74	odd	6		2940.2.f.a.1469.19		32
105.89	even	6	inner	420.2.bn.a.89.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bn.a.89.2	✓	32	7.5	odd	6	inner
420.2.bn.a.89.4	yes	32	105.89	even	6	inner
420.2.bn.a.89.13	yes	32	21.5	even	6	inner
420.2.bn.a.89.15	yes	32	35.19	odd	6	inner
420.2.bn.a.269.2	yes	32	15.14	odd	2	inner
420.2.bn.a.269.4	yes	32	1.1	even	1	trivial
420.2.bn.a.269.13	yes	32	5.4	even	2	inner
420.2.bn.a.269.15	yes	32	3.2	odd	2	inner
2100.2.bi.n.101.5		32	5.2	odd	4
2100.2.bi.n.101.7		32	15.8	even	4
2100.2.bi.n.101.10		32	15.2	even	4
2100.2.bi.n.101.12		32	5.3	odd	4
2100.2.bi.n.1601.5		32	105.47	odd	12
2100.2.bi.n.1601.7		32	35.33	even	12
2100.2.bi.n.1601.10		32	35.12	even	12
2100.2.bi.n.1601.12		32	105.68	odd	12
2940.2.f.a.1469.13		32	21.11	odd	6
2940.2.f.a.1469.14		32	105.59	even	6
2940.2.f.a.1469.15		32	35.24	odd	6
2940.2.f.a.1469.16		32	7.4	even	3
2940.2.f.a.1469.17		32	7.3	odd	6
2940.2.f.a.1469.18		32	35.4	even	6
2940.2.f.a.1469.19		32	105.74	odd	6
2940.2.f.a.1469.20		32	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.44386 - 0.956690i) q^{3} +(-2.00950 - 0.980773i) q^{5} +(0.477214 + 2.60236i) q^{7} +(1.16949 + 2.76266i) q^{9} +O(q^{10})\)	\(q+(-1.44386 - 0.956690i) q^{3} +(-2.00950 - 0.980773i) q^{5} +(0.477214 + 2.60236i) q^{7} +(1.16949 + 2.76266i) q^{9} +(1.34052 + 0.773950i) q^{11} -4.18432 q^{13} +(1.96315 + 3.33857i) q^{15} +(4.42344 + 2.55387i) q^{17} +(4.62984 - 2.67304i) q^{19} +(1.80062 - 4.21400i) q^{21} +(1.82437 + 3.15990i) q^{23} +(3.07617 + 3.94173i) q^{25} +(0.954427 - 5.10775i) q^{27} +9.79665i q^{29} +(6.79882 + 3.92530i) q^{31} +(-1.19510 - 2.39994i) q^{33} +(1.59336 - 5.69747i) q^{35} +(-2.96953 + 1.71446i) q^{37} +(6.04160 + 4.00310i) q^{39} -8.82093 q^{41} -3.79814i q^{43} +(0.359459 - 6.69857i) q^{45} +(-2.16487 + 1.24989i) q^{47} +(-6.54453 + 2.48376i) q^{49} +(-3.94358 - 7.91930i) q^{51} +(0.395246 - 0.684586i) q^{53} +(-1.93471 - 2.87000i) q^{55} +(-9.24212 - 0.569815i) q^{57} +(-2.73316 + 4.73397i) q^{59} +(-6.76285 + 3.90454i) q^{61} +(-6.63134 + 4.36181i) q^{63} +(8.40839 + 4.10387i) q^{65} +(9.67202 + 5.58414i) q^{67} +(0.388903 - 6.30782i) q^{69} -7.97077i q^{71} +(6.19943 - 10.7377i) q^{73} +(-0.670559 - 8.63425i) q^{75} +(-1.37438 + 3.85786i) q^{77} +(-1.12127 - 1.94209i) q^{79} +(-6.26459 + 6.46180i) q^{81} +5.26486i q^{83} +(-6.38412 - 9.47039i) q^{85} +(9.37235 - 14.1450i) q^{87} +(7.65723 + 13.2627i) q^{89} +(-1.99682 - 10.8891i) q^{91} +(-6.06128 - 12.1720i) q^{93} +(-11.9253 + 0.830643i) q^{95} -15.9016 q^{97} +(-0.570438 + 4.60853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 2 q^{15} + 12 q^{19} - 8 q^{21} + 6 q^{25} - 12 q^{31} + 24 q^{39} + 33 q^{45} - 44 q^{49} - 10 q^{51} - 24 q^{61} + 21 q^{75} - 28 q^{79} - 20 q^{81} - 4 q^{85} + 16 q^{91} - 28 q^{99}+O(q^{100}) \) 32 * q + 2 * q^15 + 12 * q^19 - 8 * q^21 + 6 * q^25 - 12 * q^31 + 24 * q^39 + 33 * q^45 - 44 * q^49 - 10 * q^51 - 24 * q^61 + 21 * q^75 - 28 * q^79 - 20 * q^81 - 4 * q^85 + 16 * q^91 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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