LMFDB - Embedded newform 1890.2.bf.e.629.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(629,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3, 3]))

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

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

chi := DirichletCharacter("1890.629");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.bf (of order $6$, degree $2$, not 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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			629.9
Character	$\chi$	$=$	1890.629
Dual form			1890.2.bf.e.1259.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.797934 + 2.08885i) q^{5} +(-1.74972 + 1.98456i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.797934 + 2.08885i) q^{5} +(-1.74972 + 1.98456i) q^{7} +1.00000 q^{8} +(-2.20797 - 0.353395i) q^{10} +(4.88737 + 2.82172i) q^{11} +(-0.902958 - 1.56397i) q^{13} +(-0.843817 - 2.50758i) q^{14} +(-0.500000 + 0.866025i) q^{16} -4.43565i q^{17} +4.20599i q^{19} +(1.41003 - 1.73546i) q^{20} +(-4.88737 + 2.82172i) q^{22} +(3.13617 + 5.43200i) q^{23} +(-3.72660 + 3.33353i) q^{25} +1.80592 q^{26} +(2.59354 + 0.523025i) q^{28} +(0.728114 + 0.420377i) q^{29} +(-2.34950 + 1.35649i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.84138 + 2.21782i) q^{34} +(-5.54161 - 2.07136i) q^{35} -3.95176i q^{37} +(-3.64249 - 2.10299i) q^{38} +(0.797934 + 2.08885i) q^{40} +(5.47857 + 9.48915i) q^{41} +(10.1941 + 5.88558i) q^{43} -5.64345i q^{44} -6.27234 q^{46} +(-3.36570 - 1.94319i) q^{47} +(-0.876944 - 6.94485i) q^{49} +(-1.02362 - 4.89410i) q^{50} +(-0.902958 + 1.56397i) q^{52} -0.269360 q^{53} +(-1.99437 + 12.4605i) q^{55} +(-1.74972 + 1.98456i) q^{56} +(-0.728114 + 0.420377i) q^{58} +(-2.74210 - 4.74945i) q^{59} +(-6.75508 - 3.90005i) q^{61} -2.71297i q^{62} +1.00000 q^{64} +(2.54640 - 3.13409i) q^{65} +(-3.51215 + 2.02774i) q^{67} +(-3.84138 + 2.21782i) q^{68} +(4.56466 - 3.76349i) q^{70} -7.50154i q^{71} -11.8343 q^{73} +(3.42233 + 1.97588i) q^{74} +(3.64249 - 2.10299i) q^{76} +(-14.1514 + 4.76204i) q^{77} +(3.09507 - 5.36082i) q^{79} +(-2.20797 - 0.353395i) q^{80} -10.9571 q^{82} +(-6.53949 - 3.77558i) q^{83} +(9.26541 - 3.53935i) q^{85} +(-10.1941 + 5.88558i) q^{86} +(4.88737 + 2.82172i) q^{88} +6.72937 q^{89} +(4.68372 + 0.944539i) q^{91} +(3.13617 - 5.43200i) q^{92} +(3.36570 - 1.94319i) q^{94} +(-8.78568 + 3.35610i) q^{95} +(-7.17388 + 12.4255i) q^{97} +(6.45289 + 2.71297i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 24 q^{11} - 16 q^{16} - 24 q^{22} - 24 q^{23} + 50 q^{25} + 36 q^{29} - 16 q^{32} - 48 q^{35} + 54 q^{43} + 48 q^{46} + 32 q^{49} - 58 q^{50} - 24 q^{53} - 36 q^{58} + 32 q^{64} + 66 q^{65} + 66 q^{67} + 12 q^{70} - 12 q^{74} + 18 q^{77} + 34 q^{79} - 32 q^{85} - 54 q^{86} + 24 q^{88} + 16 q^{91} - 24 q^{92} + 24 q^{95} - 64 q^{98}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 24 * q^11 - 16 * q^16 - 24 * q^22 - 24 * q^23 + 50 * q^25 + 36 * q^29 - 16 * q^32 - 48 * q^35 + 54 * q^43 + 48 * q^46 + 32 * q^49 - 58 * q^50 - 24 * q^53 - 36 * q^58 + 32 * q^64 + 66 * q^65 + 66 * q^67 + 12 * q^70 - 12 * q^74 + 18 * q^77 + 34 * q^79 - 32 * q^85 - 54 * q^86 + 24 * q^88 + 16 * q^91 - 24 * q^92 + 24 * q^95 - 64 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.797934	+	2.08885i	0.356847	+	0.934163i
$5$	0.797934	+	2.08885i	0.356847	+	0.934163i
$6$		0			0
$7$	−1.74972	+	1.98456i	−0.661333	+	0.750093i
$7$	−1.74972	+	1.98456i	−0.661333	+	0.750093i
$8$	1.00000			0.353553
$9$		0			0
$10$	−2.20797	−	0.353395i	−0.698220	−	0.111753i
$11$	4.88737	+	2.82172i	1.47360	+	0.850782i	0.999558	−	0.0297223i	$-0.00946229\pi$
$11$	4.88737	+	2.82172i	1.47360	+	0.850782i	0.474039	+	0.880504i	$0.342796\pi$
$12$		0			0
$13$	−0.902958	−	1.56397i	−0.250436	−	0.433767i	0.713210	−	0.700950i	$-0.247240\pi$
$13$	−0.902958	−	1.56397i	−0.250436	−	0.433767i	−0.963646	+	0.267183i	$0.913907\pi$
$14$	−0.843817	−	2.50758i	−0.225520	−	0.670180i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		−	4.43565i		−	1.07580i	−0.843008	−	0.537901i	$-0.819217\pi$
$17$		−	4.43565i		−	1.07580i	0.843008	−	0.537901i	$-0.180783\pi$
$18$		0			0
$19$			4.20599i			0.964919i	0.875918	+	0.482460i	$0.160257\pi$
$19$			4.20599i			0.964919i	−0.875918	+	0.482460i	$0.839743\pi$
$20$	1.41003	−	1.73546i	0.315293	−	0.388060i
$21$		0			0
$22$	−4.88737	+	2.82172i	−1.04199	+	0.601593i
$23$	3.13617	+	5.43200i	0.653936	+	1.13265i	0.982159	+	0.188051i	$0.0602169\pi$
$23$	3.13617	+	5.43200i	0.653936	+	1.13265i	−0.328223	+	0.944600i	$0.606450\pi$
$24$		0			0
$25$	−3.72660	+	3.33353i	−0.745321	+	0.666706i
$26$	1.80592			0.354169
$27$		0			0
$28$	2.59354	+	0.523025i	0.490133	+	0.0988424i
$29$	0.728114	+	0.420377i	0.135207	+	0.0780620i	0.566078	−	0.824352i	$-0.308460\pi$
$29$	0.728114	+	0.420377i	0.135207	+	0.0780620i	−0.430871	+	0.902414i	$0.641793\pi$
$30$		0			0
$31$	−2.34950	+	1.35649i	−0.421983	+	0.243632i	−0.695925	−	0.718114i	$-0.745006\pi$
$31$	−2.34950	+	1.35649i	−0.421983	+	0.243632i	0.273942	+	0.961746i	$0.411672\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	3.84138	+	2.21782i	0.658792	+	0.380354i
$35$	−5.54161	−	2.07136i	−0.936703	−	0.350125i
$36$		0			0
$37$		−	3.95176i		−	0.649666i	−0.945771	−	0.324833i	$-0.894692\pi$
$37$		−	3.95176i		−	0.649666i	0.945771	−	0.324833i	$-0.105308\pi$
$38$	−3.64249	−	2.10299i	−0.590890	−	0.341151i
$39$		0			0
$40$	0.797934	+	2.08885i	0.126164	+	0.330276i
$41$	5.47857	+	9.48915i	0.855608	+	1.48196i	0.876080	+	0.482166i	$0.160150\pi$
$41$	5.47857	+	9.48915i	0.855608	+	1.48196i	−0.0204715	+	0.999790i	$0.506517\pi$
$42$		0			0
$43$	10.1941	+	5.88558i	1.55459	+	0.897542i	0.997759	+	0.0669162i	$0.0213160\pi$
$43$	10.1941	+	5.88558i	1.55459	+	0.897542i	0.556830	+	0.830626i	$0.312017\pi$
$44$		−	5.64345i		−	0.850782i
$45$		0			0
$46$	−6.27234			−0.924806
$47$	−3.36570	−	1.94319i	−0.490938	−	0.283443i	0.234025	−	0.972230i	$-0.424810\pi$
$47$	−3.36570	−	1.94319i	−0.490938	−	0.283443i	−0.724964	+	0.688787i	$0.758143\pi$
$48$		0			0
$49$	−0.876944	−	6.94485i	−0.125278	−	0.992122i
$50$	−1.02362	−	4.89410i	−0.144762	−	0.692130i
$51$		0			0
$52$	−0.902958	+	1.56397i	−0.125218	+	0.216884i
$53$	−0.269360			−0.0369995			−0.0184997	−	0.999829i	$-0.505889\pi$
$53$	−0.269360			−0.0369995			−0.0184997	+	0.999829i	$0.505889\pi$
$54$		0			0
$55$	−1.99437	+	12.4605i	−0.268920	+	1.68018i
$56$	−1.74972	+	1.98456i	−0.233816	+	0.265198i
$57$		0			0
$58$	−0.728114	+	0.420377i	−0.0956061	+	0.0551982i
$59$	−2.74210	−	4.74945i	−0.356991	−	0.618326i	0.630466	−	0.776217i	$-0.282864\pi$
$59$	−2.74210	−	4.74945i	−0.356991	−	0.618326i	−0.987457	+	0.157891i	$0.949531\pi$
$60$		0			0
$61$	−6.75508	−	3.90005i	−0.864899	−	0.499350i	0.000750547	−	1.00000i	$-0.499761\pi$
$61$	−6.75508	−	3.90005i	−0.864899	−	0.499350i	−0.865650	+	0.500650i	$0.833094\pi$
$62$		−	2.71297i		−	0.344548i
$63$		0			0
$64$	1.00000			0.125000
$65$	2.54640	−	3.13409i	0.315842	−	0.388736i
$66$		0			0
$67$	−3.51215	+	2.02774i	−0.429077	+	0.247728i	−0.698953	−	0.715167i	$-0.746350\pi$
$67$	−3.51215	+	2.02774i	−0.429077	+	0.247728i	0.269876	+	0.962895i	$0.413017\pi$
$68$	−3.84138	+	2.21782i	−0.465836	+	0.268951i
$69$		0			0
$70$	4.56466	−	3.76349i	0.545581	−	0.449823i
$71$		−	7.50154i		−	0.890269i	−0.895464	−	0.445134i	$-0.853156\pi$
$71$		−	7.50154i		−	0.890269i	0.895464	−	0.445134i	$-0.146844\pi$
$72$		0			0
$73$	−11.8343			−1.38510			−0.692551	−	0.721368i	$-0.743513\pi$
$73$	−11.8343			−1.38510			−0.692551	+	0.721368i	$0.743513\pi$
$74$	3.42233	+	1.97588i	0.397837	+	0.229692i
$75$		0			0
$76$	3.64249	−	2.10299i	0.417822	−	0.241230i
$77$	−14.1514	+	4.76204i	−1.61270	+	0.542684i
$78$		0			0
$79$	3.09507	−	5.36082i	0.348222	−	0.603139i	−0.637711	−	0.770275i	$-0.720119\pi$
$79$	3.09507	−	5.36082i	0.348222	−	0.603139i	0.985934	+	0.167137i	$0.0534521\pi$
$80$	−2.20797	−	0.353395i	−0.246858	−	0.0395108i
$81$		0			0
$82$	−10.9571			−1.21001
$83$	−6.53949	−	3.77558i	−0.717802	−	0.414423i	0.0961409	−	0.995368i	$-0.469350\pi$
$83$	−6.53949	−	3.77558i	−0.717802	−	0.414423i	−0.813943	+	0.580944i	$0.802683\pi$
$84$		0			0
$85$	9.26541	−	3.53935i	1.00497	−	0.383897i
$86$	−10.1941	+	5.88558i	−1.09926	+	0.634658i
$87$		0			0
$88$	4.88737	+	2.82172i	0.520995	+	0.300797i
$89$	6.72937			0.713312			0.356656	−	0.934236i	$-0.383917\pi$
$89$	6.72937			0.713312			0.356656	+	0.934236i	$0.383917\pi$
$90$		0			0
$91$	4.68372	+	0.944539i	0.490987	+	0.0990146i
$92$	3.13617	−	5.43200i	0.326968	−	0.566326i
$93$		0			0
$94$	3.36570	−	1.94319i	0.347146	−	0.200425i
$95$	−8.78568	+	3.35610i	−0.901392	+	0.344328i
$96$		0			0
$97$	−7.17388	+	12.4255i	−0.728397	+	1.26162i	0.229164	+	0.973388i	$0.426401\pi$
$97$	−7.17388	+	12.4255i	−0.728397	+	1.26162i	−0.957560	+	0.288232i	$0.906932\pi$
$98$	6.45289	+	2.71297i	0.651840	+	0.274051i
$99$		0			0
$100$	4.75022	+	1.56057i	0.475022	+	0.156057i
$101$	−3.54952	+	6.14795i	−0.353190	+	0.611744i	−0.986807	−	0.161904i	$-0.948237\pi$
$101$	−3.54952	+	6.14795i	−0.353190	+	0.611744i	0.633616	+	0.773648i	$0.281570\pi$
$102$		0			0
$103$	2.66109	+	4.60915i	0.262205	+	0.454153i	0.966828	−	0.255430i	$-0.0822169\pi$
$103$	2.66109	+	4.60915i	0.262205	+	0.454153i	−0.704622	+	0.709582i	$0.748884\pi$
$104$	−0.902958	−	1.56397i	−0.0885423	−	0.153360i
$105$		0			0
$106$	0.134680	−	0.233273i	0.0130813	−	0.0226575i
$107$	−8.14952			−0.787844			−0.393922	−	0.919144i	$-0.628882\pi$
$107$	−8.14952			−0.787844			−0.393922	+	0.919144i	$0.628882\pi$
$108$		0			0
$109$	−3.46581			−0.331964			−0.165982	−	0.986129i	$-0.553079\pi$
$109$	−3.46581			−0.331964			−0.165982	+	0.986129i	$0.553079\pi$
$110$	−9.79396	−	7.95744i	−0.933817	−	0.758712i
$111$		0			0
$112$	−0.843817	−	2.50758i	−0.0797332	−	0.236944i
$113$	2.76411	+	4.78758i	0.260026	+	0.450378i	0.966248	−	0.257612i	$-0.0829356\pi$
$113$	2.76411	+	4.78758i	0.260026	+	0.450378i	−0.706223	+	0.707990i	$0.749602\pi$
$114$		0			0
$115$	−8.84420	+	10.8854i	−0.824725	+	1.01507i
$116$		−	0.840754i		−	0.0780620i
$117$		0			0
$118$	5.48420			0.504861
$119$	8.80280	+	7.76115i	0.806952	+	0.711464i
$120$		0			0
$121$	10.4242	+	18.0553i	0.947659	+	1.64139i
$122$	6.75508	−	3.90005i	0.611576	−	0.353094i
$123$		0			0
$124$	2.34950	+	1.35649i	0.210991	+	0.121816i
$125$	−9.93683	−	5.12439i	−0.888777	−	0.458339i
$126$		0			0
$127$		−	8.32840i		−	0.739026i	−0.929226	−	0.369513i	$-0.879525\pi$
$127$		−	8.32840i		−	0.739026i	0.929226	−	0.369513i	$-0.120475\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	1.44100	+	3.77229i	0.126384	+	0.330852i
$131$	6.88631	+	11.9274i	0.601659	+	1.04210i	0.992570	+	0.121676i	$0.0388269\pi$
$131$	6.88631	+	11.9274i	0.601659	+	1.04210i	−0.390910	+	0.920429i	$0.627840\pi$
$132$		0			0
$133$	−8.34703	−	7.35931i	−0.723779	−	0.638133i
$134$		−	4.05548i		−	0.350340i
$135$		0			0
$136$		−	4.43565i		−	0.380354i
$137$	−8.53808	+	14.7884i	−0.729457	+	1.26346i	0.227656	+	0.973742i	$0.426894\pi$
$137$	−8.53808	+	14.7884i	−0.729457	+	1.26346i	−0.957113	+	0.289715i	$0.906439\pi$
$138$		0			0
$139$	−6.79834	+	3.92503i	−0.576628	+	0.332916i	−0.759792	−	0.650166i	$-0.774699\pi$
$139$	−6.79834	+	3.92503i	−0.576628	+	0.332916i	0.183164	+	0.983082i	$0.441366\pi$
$140$	0.976951	+	5.83486i	0.0825674	+	0.493135i
$141$		0			0
$142$	6.49652	+	3.75077i	0.545176	+	0.314758i
$143$		−	10.1916i		−	0.852264i
$144$		0			0
$145$	−0.297118	+	1.85636i	−0.0246743	+	0.154162i
$146$	5.91716	−	10.2488i	0.489708	−	0.848199i
$147$		0			0
$148$	−3.42233	+	1.97588i	−0.281314	+	0.162416i
$149$	−15.1280	+	8.73416i	−1.23933	+	0.715530i	−0.968958	−	0.247224i	$-0.920482\pi$
$149$	−15.1280	+	8.73416i	−1.23933	+	0.715530i	−0.270377	+	0.962755i	$0.587148\pi$
$150$		0			0
$151$	2.58414	−	4.47585i	0.210294	−	0.364240i	−0.741513	−	0.670939i	$-0.765891\pi$
$151$	2.58414	−	4.47585i	0.210294	−	0.364240i	0.951807	+	0.306699i	$0.0992246\pi$
$152$			4.20599i			0.341151i
$153$		0			0
$154$	2.95166	−	14.6365i	0.237852	−	1.17944i
$155$	−4.70824	−	3.82537i	−0.378175	−	0.307262i
$156$		0			0
$157$	5.61259	+	9.72130i	0.447934	+	0.775844i	0.998251	−	0.0591113i	$-0.0188267\pi$
$157$	5.61259	+	9.72130i	0.447934	+	0.775844i	−0.550318	+	0.834955i	$0.685493\pi$
$158$	3.09507	+	5.36082i	0.246230	+	0.426484i
$159$		0			0
$160$	1.41003	−	1.73546i	0.111473	−	0.137200i
$161$	−16.2676	−	3.28059i	−1.28206	−	0.258547i
$162$		0			0
$163$			15.8266i			1.23964i	0.784745	+	0.619819i	$0.212794\pi$
$163$			15.8266i			1.23964i	−0.784745	+	0.619819i	$0.787206\pi$
$164$	5.47857	−	9.48915i	0.427804	−	0.740978i
$165$		0			0
$166$	6.53949	−	3.77558i	0.507563	−	0.293042i
$167$	1.89540	−	1.09431i	0.146670	−	0.0846801i	−0.424869	−	0.905255i	$-0.639680\pi$
$167$	1.89540	−	1.09431i	0.146670	−	0.0846801i	0.571539	+	0.820575i	$0.306347\pi$
$168$		0			0
$169$	4.86933	−	8.43393i	0.374564	−	0.648764i
$170$	−1.56754	+	9.79376i	−0.120225	+	0.751147i
$171$		0			0
$172$		−	11.7712i		−	0.897542i
$173$	0.0263269	+	0.0151999i	0.00200160	+	0.00115562i	0.501000	−	0.865447i	$-0.332965\pi$
$173$	0.0263269	+	0.0151999i	0.00200160	+	0.00115562i	−0.498999	+	0.866603i	$0.666299\pi$
$174$		0			0
$175$	−0.0950649	−	13.2284i	−0.00718623	−	0.999974i
$176$	−4.88737	+	2.82172i	−0.368399	+	0.212695i
$177$		0			0
$178$	−3.36469	+	5.82781i	−0.252194	+	0.436813i
$179$		−	21.3664i		−	1.59700i	−0.601997	−	0.798499i	$-0.705628\pi$
$179$		−	21.3664i		−	1.59700i	0.601997	−	0.798499i	$-0.294372\pi$
$180$		0			0
$181$		−	12.3387i		−	0.917131i	−0.888661	−	0.458566i	$-0.848363\pi$
$181$		−	12.3387i		−	0.917131i	0.888661	−	0.458566i	$-0.151637\pi$
$182$	−3.15985	+	3.58395i	−0.234224	+	0.265660i
$183$		0			0
$184$	3.13617	+	5.43200i	0.231201	+	0.400453i
$185$	8.25465	−	3.15324i	0.606894	−	0.231831i
$186$		0			0
$187$	12.5162	−	21.6786i	0.915273	−	1.58530i
$188$			3.88638i			0.283443i
$189$		0			0
$190$	1.48637	−	9.28667i	0.107833	−	0.673726i
$191$	4.89699	+	2.82728i	0.354334	+	0.204575i	0.666592	−	0.745422i	$-0.267752\pi$
$191$	4.89699	+	2.82728i	0.354334	+	0.204575i	−0.312259	+	0.949997i	$0.601086\pi$
$192$		0			0
$193$	−17.4878	+	10.0966i	−1.25880	+	0.726767i	−0.972841	−	0.231475i	$-0.925645\pi$
$193$	−17.4878	+	10.0966i	−1.25880	+	0.726767i	−0.285957	+	0.958242i	$0.592311\pi$
$194$	−7.17388	−	12.4255i	−0.515054	−	0.892100i
$195$		0			0
$196$	−5.57595	+	4.23188i	−0.398282	+	0.302277i
$197$	12.4817			0.889283			0.444641	−	0.895709i	$-0.353331\pi$
$197$	12.4817			0.889283			0.444641	+	0.895709i	$0.353331\pi$
$198$		0			0
$199$		−	2.80089i		−	0.198550i	−0.995060	−	0.0992751i	$-0.968348\pi$
$199$		−	2.80089i		−	0.198550i	0.995060	−	0.0992751i	$-0.0316524\pi$
$200$	−3.72660	+	3.33353i	−0.263511	+	0.235716i
$201$		0			0
$202$	−3.54952	−	6.14795i	−0.249743	−	0.432568i
$203$	−2.10826	+	0.709442i	−0.147971	+	0.0497931i
$204$		0			0
$205$	−15.4499	+	19.0156i	−1.07907	+	1.32811i
$206$	−5.32219			−0.370814
$207$		0			0
$208$	1.80592			0.125218
$209$	−11.8681	+	20.5562i	−0.820936	+	1.42190i
$210$		0			0
$211$	−10.8799	−	18.8446i	−0.749006	−	1.29732i	−0.948300	−	0.317376i	$-0.897198\pi$
$211$	−10.8799	−	18.8446i	−0.749006	−	1.29732i	0.199294	−	0.979940i	$-0.436135\pi$
$212$	0.134680	+	0.233273i	0.00924987	+	0.0160212i
$213$		0			0
$214$	4.07476	−	7.05769i	0.278545	−	0.482454i
$215$	−4.15987	+	25.9903i	−0.283701	+	1.77252i
$216$		0			0
$217$	1.41895	−	7.03620i	0.0963247	−	0.477648i
$218$	1.73290	−	3.00148i	0.117367	−	0.203286i
$219$		0			0
$220$	11.7883	−	4.50310i	0.794769	−	0.303599i
$221$	−6.93722	+	4.00521i	−0.466648	+	0.269419i
$222$		0			0
$223$	−1.82292	+	3.15738i	−0.122071	+	0.211434i	−0.920584	−	0.390544i	$-0.872287\pi$
$223$	−1.82292	+	3.15738i	−0.122071	+	0.211434i	0.798513	+	0.601978i	$0.205620\pi$
$224$	2.59354	+	0.523025i	0.173288	+	0.0349461i
$225$		0			0
$226$	−5.52822			−0.367732
$227$	6.74202	+	3.89251i	0.447484	+	0.258355i	0.706767	−	0.707446i	$-0.250153\pi$
$227$	6.74202	+	3.89251i	0.447484	+	0.258355i	−0.259283	+	0.965801i	$0.583486\pi$
$228$		0			0
$229$	−24.5009	+	14.1456i	−1.61906	+	0.934766i	−0.631899	+	0.775050i	$0.717724\pi$
$229$	−24.5009	+	14.1456i	−1.61906	+	0.934766i	−0.987163	+	0.159716i	$0.948942\pi$
$230$	−5.00491	−	13.1020i	−0.330014	−	0.863919i
$231$		0			0
$232$	0.728114	+	0.420377i	0.0478030	+	0.0275991i
$233$	18.6154			1.21954			0.609768	−	0.792580i	$-0.291263\pi$
$233$	18.6154			1.21954			0.609768	+	0.792580i	$0.291263\pi$
$234$		0			0
$235$	1.37343	−	8.58099i	0.0895925	−	0.559762i
$236$	−2.74210	+	4.74945i	−0.178495	+	0.309163i
$237$		0			0
$238$	−11.1228	+	3.74287i	−0.720981	+	0.242615i
$239$	23.3155	−	13.4612i	1.50816	−	0.870735i	0.508202	−	0.861238i	$-0.330310\pi$
$239$	23.3155	−	13.4612i	1.50816	−	0.870735i	0.999955	−	0.00949675i	$-0.00302296\pi$
$240$		0			0
$241$	1.71843	+	0.992134i	0.110694	+	0.0639090i	0.554325	−	0.832301i	$-0.312977\pi$
$241$	1.71843	+	0.992134i	0.110694	+	0.0639090i	−0.443631	+	0.896210i	$0.646310\pi$
$242$	−20.8485			−1.34019
$243$		0			0
$244$			7.80009i			0.499350i
$245$	13.8070	−	7.37334i	0.882098	−	0.471065i
$246$		0			0
$247$	6.57804	−	3.79783i	0.418550	−	0.241650i
$248$	−2.34950	+	1.35649i	−0.149193	+	0.0861369i
$249$		0			0
$250$	9.40627	−	6.04336i	0.594904	−	0.382216i
$251$	30.9761			1.95519			0.977596	−	0.210491i	$-0.0675064\pi$
$251$	30.9761			1.95519			0.977596	+	0.210491i	$0.0675064\pi$
$252$		0			0
$253$			35.3976i			2.22543i
$254$	7.21260	+	4.16420i	0.452559	+	0.261285i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.17253	+	1.25431i	−0.135519	+	0.0782418i	−0.566227	−	0.824250i	$-0.691597\pi$
$257$	−2.17253	+	1.25431i	−0.135519	+	0.0782418i	0.430708	+	0.902491i	$0.358264\pi$
$258$		0			0
$259$	7.84250	+	6.91449i	0.487309	+	0.429645i
$260$	−3.98740	−	0.638202i	−0.247288	−	0.0395796i
$261$		0			0
$262$	−13.7726			−0.850875
$263$	8.69919	−	15.0674i	0.536415	−	0.929098i	−0.462678	−	0.886526i	$-0.653111\pi$
$263$	8.69919	−	15.0674i	0.536415	−	0.929098i	0.999093	−	0.0425721i	$-0.0135552\pi$
$264$		0			0
$265$	−0.214932	−	0.562654i	−0.0132031	−	0.0345635i
$266$	10.5469	−	3.54908i	0.646670	−	0.217608i
$267$		0			0
$268$	3.51215	+	2.02774i	0.214538	+	0.123864i
$269$	−14.2885			−0.871187			−0.435594	−	0.900143i	$-0.643462\pi$
$269$	−14.2885			−0.871187			−0.435594	+	0.900143i	$0.643462\pi$
$270$		0			0
$271$		−	27.0566i		−	1.64357i	−0.569795	−	0.821787i	$-0.692977\pi$
$271$		−	27.0566i		−	1.64357i	0.569795	−	0.821787i	$-0.307023\pi$
$272$	3.84138	+	2.21782i	0.232918	+	0.134475i
$273$		0			0
$274$	−8.53808	−	14.7884i	−0.515804	−	0.893399i
$275$	−27.6196	+	5.77675i	−1.66552	+	0.348351i
$276$		0			0
$277$	5.40597	+	3.12114i	0.324813	+	0.187531i	0.653536	−	0.756896i	$-0.273285\pi$
$277$	5.40597	+	3.12114i	0.324813	+	0.187531i	−0.328723	+	0.944426i	$0.606618\pi$
$278$		−	7.85005i		−	0.470815i
$279$		0			0
$280$	−5.54161	−	2.07136i	−0.331175	−	0.123788i
$281$	21.4692	+	12.3953i	1.28075	+	0.739440i	0.976985	−	0.213308i	$-0.0684237\pi$
$281$	21.4692	+	12.3953i	1.28075	+	0.739440i	0.303762	+	0.952748i	$0.401757\pi$
$282$		0			0
$283$	0.0617292	+	0.106918i	0.00366942	+	0.00635562i	0.867854	−	0.496819i	$-0.165499\pi$
$283$	0.0617292	+	0.106918i	0.00366942	+	0.00635562i	−0.864185	+	0.503174i	$0.832165\pi$
$284$	−6.49652	+	3.75077i	−0.385498	+	0.222567i
$285$		0			0
$286$	8.82618	+	5.09580i	0.521903	+	0.301321i
$287$	−28.4177	−	5.73085i	−1.67745	−	0.338281i
$288$		0			0
$289$	−2.67498			−0.157351
$290$	−1.45909	−	1.18549i	−0.0856808	−	0.0696143i
$291$		0			0
$292$	5.91716	+	10.2488i	0.346276	+	0.599767i
$293$	17.6820	−	10.2087i	1.03300	−	0.596400i	0.115154	−	0.993348i	$-0.463264\pi$
$293$	17.6820	−	10.2087i	1.03300	−	0.596400i	0.917841	+	0.396947i	$0.129930\pi$
$294$		0			0
$295$	7.73289	−	9.51759i	0.450226	−	0.554135i
$296$		−	3.95176i		−	0.229692i
$297$		0			0
$298$		−	17.4683i		−	1.01191i
$299$	5.66366	−	9.80975i	0.327538	−	0.567312i
$300$		0			0
$301$	−29.5172	+	9.93270i	−1.70134	+	0.572511i
$302$	2.58414	+	4.47585i	0.148700	+	0.257556i
$303$		0			0
$304$	−3.64249	−	2.10299i	−0.208911	−	0.120615i
$305$	2.75651	−	17.2223i	0.157838	−	0.986148i
$306$		0			0
$307$	6.04807			0.345182			0.172591	−	0.984994i	$-0.444786\pi$
$307$	6.04807			0.345182			0.172591	+	0.984994i	$0.444786\pi$
$308$	11.1997	+	9.87447i	0.638165	+	0.562650i
$309$		0			0
$310$	5.66699	−	2.16477i	0.321864	−	0.122951i
$311$	−7.12307	−	12.3375i	−0.403912	−	0.699597i	0.590282	−	0.807197i	$-0.299017\pi$
$311$	−7.12307	−	12.3375i	−0.403912	−	0.699597i	−0.994194	+	0.107601i	$0.965683\pi$
$312$		0			0
$313$	6.34164	−	10.9840i	0.358451	−	0.620855i	−0.629251	−	0.777202i	$-0.716638\pi$
$313$	6.34164	−	10.9840i	0.358451	−	0.620855i	0.987702	+	0.156347i	$0.0499718\pi$
$314$	−11.2252			−0.633474
$315$		0			0
$316$	−6.19014			−0.348222
$317$	13.0119	−	22.5374i	0.730824	−	1.26582i	−0.225708	−	0.974195i	$-0.572469\pi$
$317$	13.0119	−	22.5374i	0.730824	−	1.26582i	0.956532	−	0.291629i	$-0.0941972\pi$
$318$		0			0
$319$	2.37237	+	4.10907i	0.132827	+	0.230064i
$320$	0.797934	+	2.08885i	0.0446059	+	0.116770i
$321$		0			0
$322$	10.9748	−	12.4478i	0.611604	−	0.693690i
$323$	18.6563			1.03806
$324$		0			0
$325$	8.57851	+	2.81826i	0.475850	+	0.156329i
$326$	−13.7063	−	7.91332i	−0.759120	−	0.438278i
$327$		0			0
$328$	5.47857	+	9.48915i	0.302503	+	0.523951i
$329$	9.74542	−	3.27939i	0.537282	−	0.180799i
$330$		0			0
$331$	−14.4807	+	25.0813i	−0.795930	+	1.37859i	0.126318	+	0.991990i	$0.459684\pi$
$331$	−14.4807	+	25.0813i	−0.795930	+	1.37859i	−0.922247	+	0.386601i	$0.873649\pi$
$332$			7.55115i			0.414423i
$333$		0			0
$334$			2.18862i			0.119756i
$335$	−7.03810	−	5.71835i	−0.384533	−	0.312427i
$336$		0			0
$337$	−3.86588	+	2.23197i	−0.210588	+	0.121583i	−0.601585	−	0.798809i	$-0.705464\pi$
$337$	−3.86588	+	2.23197i	−0.210588	+	0.121583i	0.390997	+	0.920392i	$0.372130\pi$
$338$	4.86933	+	8.43393i	0.264857	+	0.458745i
$339$		0			0
$340$	−7.69788	−	6.25441i	−0.417476	−	0.339193i
$341$	−15.3105			−0.829110
$342$		0			0
$343$	15.3169	+	10.4112i	0.827033	+	0.562153i
$344$	10.1941	+	5.88558i	0.549630	+	0.317329i
$345$		0			0
$346$	−0.0263269	+	0.0151999i	−0.00141534	+	0.000817149i
$347$	−4.35704	−	7.54662i	−0.233898	−	0.405124i	0.725054	−	0.688692i	$-0.241815\pi$
$347$	−4.35704	−	7.54662i	−0.233898	−	0.405124i	−0.958952	+	0.283569i	$0.908482\pi$
$348$		0			0
$349$	−15.9295	−	9.19690i	−0.852686	−	0.492299i	0.00887005	−	0.999961i	$-0.497177\pi$
$349$	−15.9295	−	9.19690i	−0.852686	−	0.492299i	−0.861556	+	0.507662i	$0.830510\pi$
$350$	11.5037	+	6.53188i	0.614897	+	0.349144i
$351$		0			0
$352$		−	5.64345i		−	0.300797i
$353$	17.0470	+	9.84206i	0.907318	+	0.523840i	0.879567	−	0.475775i	$-0.157832\pi$
$353$	17.0470	+	9.84206i	0.907318	+	0.523840i	0.0277506	+	0.999615i	$0.491166\pi$
$354$		0			0
$355$	15.6696	−	5.98573i	0.831656	−	0.317690i
$356$	−3.36469	−	5.82781i	−0.178328	−	0.308873i
$357$		0			0
$358$	18.5038	+	10.6832i	0.977957	+	0.564624i
$359$			14.4553i			0.762919i	0.924385	+	0.381460i	$0.124578\pi$
$359$			14.4553i			0.762919i	−0.924385	+	0.381460i	$0.875422\pi$
$360$		0			0
$361$	1.30968			0.0689304
$362$	10.6857	+	6.16937i	0.561626	+	0.324255i
$363$		0			0
$364$	−1.52386	−	4.52849i	−0.0798721	−	0.237357i
$365$	−9.44301	−	24.7201i	−0.494270	−	1.29391i
$366$		0			0
$367$	4.14505	−	7.17944i	0.216370	−	0.374764i	−0.737326	−	0.675538i	$-0.763912\pi$
$367$	4.14505	−	7.17944i	0.216370	−	0.374764i	0.953695	+	0.300774i	$0.0972449\pi$
$368$	−6.27234			−0.326968
$369$		0			0
$370$	−1.39653	+	8.72536i	−0.0726023	+	0.453610i
$371$	0.471306	−	0.534561i	0.0244690	−	0.0277530i
$372$		0			0
$373$	28.7738	−	16.6126i	1.48985	−	0.860165i	0.489917	−	0.871769i	$-0.337027\pi$
$373$	28.7738	−	16.6126i	1.48985	−	0.860165i	0.999933	+	0.0116035i	$0.00369359\pi$
$374$	12.5162	+	21.6786i	0.647196	+	1.12098i
$375$		0			0
$376$	−3.36570	−	1.94319i	−0.173573	−	0.100212i
$377$		−	1.51833i		−	0.0781980i
$378$		0			0
$379$	−7.52860			−0.386718			−0.193359	−	0.981128i	$-0.561938\pi$
$379$	−7.52860			−0.386718			−0.193359	+	0.981128i	$0.561938\pi$
$380$	7.29931	+	5.93057i	0.374447	+	0.304232i
$381$		0			0
$382$	−4.89699	+	2.82728i	−0.250552	+	0.144656i
$383$	18.8877	−	10.9048i	0.965116	−	0.557210i	0.0673718	−	0.997728i	$-0.478539\pi$
$383$	18.8877	−	10.9048i	0.965116	−	0.557210i	0.897744	+	0.440518i	$0.145205\pi$
$384$		0			0
$385$	−21.2391	−	25.7604i	−1.08244	−	1.31287i
$386$		−	20.1931i		−	1.02780i
$387$		0			0
$388$	14.3478			0.728397
$389$	4.33372	+	2.50208i	0.219728	+	0.126860i	0.605825	−	0.795598i	$-0.292843\pi$
$389$	4.33372	+	2.50208i	0.219728	+	0.126860i	−0.386096	+	0.922459i	$0.626177\pi$
$390$		0			0
$391$	24.0945	−	13.9109i	1.21851	−	0.703507i
$392$	−0.876944	−	6.94485i	−0.0442923	−	0.350768i
$393$		0			0
$394$	−6.24084	+	10.8094i	−0.314409	+	0.544572i
$395$	13.6676	+	2.18756i	0.687692	+	0.110068i
$396$		0			0
$397$	18.0729			0.907054			0.453527	−	0.891243i	$-0.350166\pi$
$397$	18.0729			0.907054			0.453527	+	0.891243i	$0.350166\pi$
$398$	2.42565	+	1.40045i	0.121587	+	0.0701981i
$399$		0			0
$400$	−1.02362	−	4.89410i	−0.0511810	−	0.244705i
$401$	−17.9466	+	10.3615i	−0.896213	+	0.517429i	−0.875970	−	0.482366i	$-0.839777\pi$
$401$	−17.9466	+	10.3615i	−0.896213	+	0.517429i	−0.0202431	+	0.999795i	$0.506444\pi$
$402$		0			0
$403$	4.24300	+	2.44970i	0.211359	+	0.122028i
$404$	7.09904			0.353190
$405$		0			0
$406$	0.439735	−	2.18053i	0.0218237	−	0.108218i
$407$	11.1508	−	19.3137i	0.552724	−	0.957346i
$408$		0			0
$409$	1.54820	−	0.893855i	0.0765536	−	0.0441983i	−0.461235	−	0.887278i	$-0.652593\pi$
$409$	1.54820	−	0.893855i	0.0765536	−	0.0441983i	0.537788	+	0.843080i	$0.319260\pi$
$410$	−8.74306	−	22.8878i	−0.431789	−	1.13035i
$411$		0			0
$412$	2.66109	−	4.60915i	0.131103	−	0.227076i
$413$	14.2235	+	2.86837i	0.699892	+	0.141143i
$414$		0			0
$415$	2.66854	−	16.6727i	0.130993	−	0.818430i
$416$	−0.902958	+	1.56397i	−0.0442712	+	0.0766799i
$417$		0			0
$418$	−11.8681	−	20.5562i	−0.580489	−	1.00544i
$419$	10.9180	+	18.9105i	0.533378	+	0.923838i	0.999240	+	0.0389808i	$0.0124111\pi$
$419$	10.9180	+	18.9105i	0.533378	+	0.923838i	−0.465862	+	0.884858i	$0.654256\pi$
$420$		0			0
$421$	10.9611	−	18.9852i	0.534211	−	0.925281i	−0.464990	−	0.885316i	$-0.653942\pi$
$421$	10.9611	−	18.9852i	0.534211	−	0.925281i	0.999201	−	0.0399649i	$-0.0127246\pi$
$422$	21.7599			1.05925
$423$		0			0
$424$	−0.269360			−0.0130813
$425$	14.7864	+	16.5299i	0.717244	+	0.801818i
$426$		0			0
$427$	19.5594	−	6.58185i	0.946545	−	0.318518i
$428$	4.07476	+	7.05769i	0.196961	+	0.341146i
$429$		0			0
$430$	−20.4283	−	16.5977i	−0.985142	−	0.800413i
$431$			28.4966i			1.37263i	0.727303	+	0.686317i	$0.240774\pi$
$431$			28.4966i			1.37263i	−0.727303	+	0.686317i	$0.759226\pi$
$432$		0			0
$433$	11.9364			0.573628			0.286814	−	0.957986i	$-0.407404\pi$
$433$	11.9364			0.573628			0.286814	+	0.957986i	$0.407404\pi$
$434$	5.38405	+	4.74695i	0.258443	+	0.227861i
$435$		0			0
$436$	1.73290	+	3.00148i	0.0829910	+	0.143745i
$437$	−22.8469	+	13.1907i	−1.09292	+	0.630996i
$438$		0			0
$439$	29.8934	+	17.2590i	1.42673	+	0.823725i	0.996862	−	0.0791643i	$-0.0252252\pi$
$439$	29.8934	+	17.2590i	1.42673	+	0.823725i	0.429873	+	0.902890i	$0.358559\pi$
$440$	−1.99437	+	12.4605i	−0.0950777	+	0.594033i
$441$		0			0
$442$		−	8.01041i		−	0.381016i
$443$	−17.7958	+	30.8232i	−0.845504	+	1.46446i	0.0396783	+	0.999213i	$0.487367\pi$
$443$	−17.7958	+	30.8232i	−0.845504	+	1.46446i	−0.885183	+	0.465244i	$0.845967\pi$
$444$		0			0
$445$	5.36959	+	14.0567i	0.254543	+	0.666350i
$446$	−1.82292	−	3.15738i	−0.0863175	−	0.149506i
$447$		0			0
$448$	−1.74972	+	1.98456i	−0.0826666	+	0.0937616i
$449$		−	3.56888i		−	0.168426i	−0.996448	−	0.0842130i	$-0.973162\pi$
$449$		−	3.56888i		−	0.168426i	0.996448	−	0.0842130i	$-0.0268376\pi$
$450$		0			0
$451$			61.8360i			2.91174i
$452$	2.76411	−	4.78758i	0.130013	−	0.225189i
$453$		0			0
$454$	−6.74202	+	3.89251i	−0.316419	+	0.182685i
$455$	1.76429	+	10.5373i	0.0827113	+	0.493995i
$456$		0			0
$457$	−21.2504	−	12.2690i	−0.994054	−	0.573917i	−0.0875704	−	0.996158i	$-0.527910\pi$
$457$	−21.2504	−	12.2690i	−0.994054	−	0.573917i	−0.906484	+	0.422241i	$0.861244\pi$
$458$		−	28.2912i		−	1.32196i
$459$		0			0
$460$	13.8491	+	2.21661i	0.645718	+	0.103350i
$461$	4.76490	−	8.25305i	0.221923	−	0.384383i	−0.733469	−	0.679723i	$-0.762100\pi$
$461$	4.76490	−	8.25305i	0.221923	−	0.384383i	0.955392	+	0.295341i	$0.0954331\pi$
$462$		0			0
$463$	−0.597348	+	0.344879i	−0.0277611	+	0.0160279i	−0.513816	−	0.857900i	$-0.671769\pi$
$463$	−0.597348	+	0.344879i	−0.0277611	+	0.0160279i	0.486055	+	0.873928i	$0.338435\pi$
$464$	−0.728114	+	0.420377i	−0.0338019	+	0.0195155i
$465$		0			0
$466$	−9.30770	+	16.1214i	−0.431171	+	0.746810i
$467$			5.83995i			0.270241i	0.990829	+	0.135120i	$0.0431421\pi$
$467$			5.83995i			0.270241i	−0.990829	+	0.135120i	$0.956858\pi$
$468$		0			0
$469$	2.12111	−	10.5180i	0.0979440	−	0.485678i
$470$	6.74464	+	5.47992i	0.311107	+	0.252770i
$471$		0			0
$472$	−2.74210	−	4.74945i	−0.126215	−	0.218611i
$473$	33.2150	+	57.5300i	1.52723	+	2.64523i
$474$		0			0
$475$	−14.0208	−	15.6740i	−0.643318	−	0.719174i
$476$	2.31995	−	11.5040i	0.106335	−	0.527286i
$477$		0			0
$478$			26.9225i			1.23140i
$479$	14.1442	−	24.4984i	0.646264	−	1.11936i	−0.337744	−	0.941238i	$-0.609664\pi$
$479$	14.1442	−	24.4984i	0.646264	−	1.11936i	0.984008	−	0.178124i	$-0.0570029\pi$
$480$		0			0
$481$	−6.18044	+	3.56828i	−0.281804	+	0.162699i
$482$	−1.71843	+	0.992134i	−0.0782722	+	0.0451905i
$483$		0			0
$484$	10.4242	−	18.0553i	0.473829	−	0.820697i
$485$	−31.6793	−	5.07042i	−1.43848	−	0.230236i
$486$		0			0
$487$			9.80461i			0.444289i	0.975014	+	0.222145i	$0.0713057\pi$
$487$			9.80461i			0.444289i	−0.975014	+	0.222145i	$0.928694\pi$
$488$	−6.75508	−	3.90005i	−0.305788	−	0.176547i
$489$		0			0
$490$	−0.518015	+	15.6439i	−0.0234015	+	0.706719i
$491$	3.52362	−	2.03436i	0.159019	−	0.0918094i	−0.418379	−	0.908273i	$-0.637402\pi$
$491$	3.52362	−	2.03436i	0.159019	−	0.0918094i	0.577398	+	0.816463i	$0.304068\pi$
$492$		0			0
$493$	1.86464	−	3.22966i	0.0839793	−	0.145456i
$494$			7.59566i			0.341745i
$495$		0			0
$496$		−	2.71297i		−	0.121816i
$497$	14.8872	+	13.1256i	0.667784	+	0.588764i
$498$		0			0
$499$	11.7622	+	20.3728i	0.526550	+	0.912011i	0.999521	+	0.0309334i	$0.00984797\pi$
$499$	11.7622	+	20.3728i	0.526550	+	0.912011i	−0.472972	+	0.881078i	$0.656819\pi$
$500$	0.530569	+	11.1677i	0.0237278	+	0.499437i
$501$		0			0
$502$	−15.4880	+	26.8261i	−0.691265	+	1.19731i
$503$			41.4509i			1.84821i	0.382144	+	0.924103i	$0.375186\pi$
$503$			41.4509i			1.84821i	−0.382144	+	0.924103i	$0.624814\pi$
$504$		0			0
$505$	−15.6744	−	2.50877i	−0.697503	−	0.111639i
$506$	−30.6552	−	17.6988i	−1.36279	−	0.786808i
$507$		0			0
$508$	−7.21260	+	4.16420i	−0.320008	+	0.184756i
$509$	−2.75349	−	4.76918i	−0.122046	−	0.211390i	0.798528	−	0.601957i	$-0.205612\pi$
$509$	−2.75349	−	4.76918i	−0.122046	−	0.211390i	−0.920574	+	0.390567i	$0.872279\pi$
$510$		0			0
$511$	20.7068	−	23.4859i	0.916014	−	1.03896i
$512$	1.00000			0.0441942
$513$		0			0
$514$		−	2.50862i		−	0.110651i
$515$	−7.50445	+	9.23642i	−0.330686	+	0.407005i
$516$		0			0
$517$	−10.9663	−	18.9942i	−0.482297	−	0.835362i
$518$	−9.90937	+	3.33456i	−0.435393	+	0.146512i
$519$		0			0
$520$	2.54640	−	3.13409i	0.111667	−	0.137439i
$521$	18.7123			0.819803			0.409901	−	0.912130i	$-0.365563\pi$
$521$	18.7123			0.819803			0.409901	+	0.912130i	$0.365563\pi$
$522$		0			0
$523$	−7.49417			−0.327697			−0.163849	−	0.986486i	$-0.552391\pi$
$523$	−7.49417			−0.327697			−0.163849	+	0.986486i	$0.552391\pi$
$524$	6.88631	−	11.9274i	0.300830	−	0.521052i
$525$		0			0
$526$	8.69919	+	15.0674i	0.379303	+	0.656972i
$527$	6.01689	+	10.4216i	0.262100	+	0.453970i
$528$		0			0
$529$	−8.17111	+	14.1528i	−0.355266	+	0.615338i
$530$	0.594738	+	0.0951906i	0.0258338	+	0.00413481i
$531$		0			0
$532$	−2.19984	+	10.9084i	−0.0953750	+	0.472939i
$533$	9.89383	−	17.1366i	0.428549	−	0.742269i
$534$		0			0
$535$	−6.50278	−	17.0231i	−0.281140	−	0.735975i
$536$	−3.51215	+	2.02774i	−0.151702	+	0.0875850i
$537$		0			0
$538$	7.14427	−	12.3742i	0.308011	−	0.533491i
$539$	15.3105	−	36.4165i	0.659470	−	1.56857i
$540$		0			0
$541$	29.1523			1.25335			0.626677	−	0.779279i	$-0.284415\pi$
$541$	29.1523			1.25335			0.626677	+	0.779279i	$0.284415\pi$
$542$	23.4317	+	13.5283i	1.00648	+	0.581091i
$543$		0			0
$544$	−3.84138	+	2.21782i	−0.164698	+	0.0950884i
$545$	−2.76548	−	7.23955i	−0.118460	−	0.310108i
$546$		0			0
$547$	−25.7181	−	14.8484i	−1.09963	−	0.634871i	−0.163505	−	0.986543i	$-0.552280\pi$
$547$	−25.7181	−	14.8484i	−1.09963	−	0.634871i	−0.936123	+	0.351672i	$0.885613\pi$
$548$	17.0762			0.729457
$549$		0			0
$550$	8.80698	−	26.8076i	0.375531	−	1.14308i
$551$	−1.76810	+	3.06244i	−0.0753236	+	0.130464i
$552$		0			0
$553$	5.22334	+	15.5223i	0.222119	+	0.660075i
$554$	−5.40597	+	3.12114i	−0.229677	+	0.132604i
$555$		0			0
$556$	6.79834	+	3.92503i	0.288314	+	0.166458i
$557$	−2.38993			−0.101265			−0.0506323	−	0.998717i	$-0.516124\pi$
$557$	−2.38993			−0.101265			−0.0506323	+	0.998717i	$0.516124\pi$
$558$		0			0
$559$		−	21.2577i		−	0.899106i
$560$	4.56466	−	3.76349i	0.192892	−	0.159037i
$561$		0			0
$562$	−21.4692	+	12.3953i	−0.905625	+	0.522863i
$563$	22.1073	−	12.7637i	0.931712	−	0.537924i	0.0443592	−	0.999016i	$-0.485875\pi$
$563$	22.1073	−	12.7637i	0.931712	−	0.537924i	0.887353	+	0.461092i	$0.152542\pi$
$564$		0			0
$565$	−7.79497	+	9.59399i	−0.327937	+	0.403622i
$566$	−0.123458			−0.00518934
$567$		0			0
$568$		−	7.50154i		−	0.314758i
$569$	−23.6351	−	13.6457i	−0.990834	−	0.572059i	−0.0853109	−	0.996354i	$-0.527188\pi$
$569$	−23.6351	−	13.6457i	−0.990834	−	0.572059i	−0.905524	+	0.424296i	$0.860522\pi$
$570$		0			0
$571$	2.38381	+	4.12888i	0.0997593	+	0.172788i	0.911585	−	0.411112i	$-0.134859\pi$
$571$	2.38381	+	4.12888i	0.0997593	+	0.172788i	−0.811826	+	0.583900i	$0.801526\pi$
$572$	−8.82618	+	5.09580i	−0.369041	+	0.213066i
$573$		0			0
$574$	19.1719	−	21.7451i	0.800221	−	0.907622i
$575$	−29.7950	−	9.78841i	−1.24254	−	0.408205i
$576$		0			0
$577$	26.5870			1.10683			0.553415	−	0.832906i	$-0.313324\pi$
$577$	26.5870			1.10683			0.553415	+	0.832906i	$0.313324\pi$
$578$	1.33749	−	2.31660i	0.0556321	−	0.0963577i
$579$		0			0
$580$	1.75621	−	0.670866i	0.0729227	−	0.0278562i
$581$	18.9351	−	6.37179i	0.785562	−	0.264346i
$582$		0			0
$583$	−1.31646	−	0.760060i	−0.0545223	−	0.0314785i
$584$	−11.8343			−0.489708
$585$		0			0
$586$			20.4175i			0.843437i
$587$	13.1619	+	7.59901i	0.543248	+	0.313645i	0.746394	−	0.665504i	$-0.231783\pi$
$587$	13.1619	+	7.59901i	0.543248	+	0.313645i	−0.203146	+	0.979148i	$0.565117\pi$
$588$		0			0
$589$	−5.70536	−	9.88197i	−0.235085	−	0.407180i
$590$	4.37603	+	11.4557i	0.180158	+	0.471623i
$591$		0			0
$592$	3.42233	+	1.97588i	0.140657	+	0.0812082i
$593$			3.34294i			0.137278i	0.997642	+	0.0686391i	$0.0218657\pi$
$593$			3.34294i			0.137278i	−0.997642	+	0.0686391i	$0.978134\pi$
$594$		0			0
$595$	−9.18784	+	24.5806i	−0.376665	+	1.00771i
$596$	15.1280	+	8.73416i	0.619667	+	0.357765i
$597$		0			0
$598$	5.66366	+	9.80975i	0.231604	+	0.401150i
$599$	−22.2908	+	12.8696i	−0.910776	+	0.525837i	−0.880681	−	0.473710i	$-0.842914\pi$
$599$	−22.2908	+	12.8696i	−0.910776	+	0.525837i	−0.0300955	+	0.999547i	$0.509581\pi$
$600$		0			0
$601$	−16.1414	−	9.31926i	−0.658423	−	0.380141i	0.133253	−	0.991082i	$-0.457458\pi$
$601$	−16.1414	−	9.31926i	−0.658423	−	0.380141i	−0.791676	+	0.610941i	$0.790791\pi$
$602$	6.15661	−	30.5290i	0.250925	−	1.24427i
$603$		0			0
$604$	−5.16827			−0.210294
$605$	−29.3970	+	36.1817i	−1.19516	+	1.47099i
$606$		0			0
$607$	−3.57886	−	6.19876i	−0.145261	−	0.251600i	0.784209	−	0.620497i	$-0.213069\pi$
$607$	−3.57886	−	6.19876i	−0.145261	−	0.251600i	−0.929470	+	0.368897i	$0.879736\pi$
$608$	3.64249	−	2.10299i	0.147723	−	0.0852876i
$609$		0			0
$610$	13.5367	+	10.9984i	0.548086	+	0.445311i
$611$			7.01848i			0.283937i
$612$		0			0
$613$			39.7227i			1.60438i	0.597066	+	0.802192i	$0.296333\pi$
$613$			39.7227i			1.60438i	−0.597066	+	0.802192i	$0.703667\pi$
$614$	−3.02404	+	5.23778i	−0.122040	+	0.211380i
$615$		0			0
$616$	−14.1514	+	4.76204i	−0.570177	+	0.191868i
$617$	7.52264	+	13.0296i	0.302850	+	0.524551i	0.976780	−	0.214243i	$-0.0687286\pi$
$617$	7.52264	+	13.0296i	0.302850	+	0.524551i	−0.673930	+	0.738795i	$0.735395\pi$
$618$		0			0
$619$	12.2351	+	7.06394i	0.491770	+	0.283924i	0.725309	−	0.688424i	$-0.241697\pi$
$619$	12.2351	+	7.06394i	0.491770	+	0.283924i	−0.233538	+	0.972348i	$0.575030\pi$
$620$	−0.958750	+	5.99015i	−0.0385043	+	0.240570i
$621$		0			0
$622$	14.2461			0.571218
$623$	−11.7745	+	13.3548i	−0.471737	+	0.535050i
$624$		0			0
$625$	2.77515	−	24.8455i	0.111006	−	0.993820i
$626$	6.34164	+	10.9840i	0.253463	+	0.439011i
$627$		0			0
$628$	5.61259	−	9.72130i	0.223967	−	0.387922i
$629$	−17.5286			−0.698912
$630$		0			0
$631$	29.9801			1.19349			0.596745	−	0.802431i	$-0.296460\pi$
$631$	29.9801			1.19349			0.596745	+	0.802431i	$0.296460\pi$
$632$	3.09507	−	5.36082i	0.123115	−	0.213242i
$633$		0			0
$634$	13.0119	+	22.5374i	0.516770	+	0.895073i
$635$	17.3968	−	6.64551i	0.690371	−	0.263719i
$636$		0			0
$637$	−10.0697	+	7.64243i	−0.398976	+	0.302804i
$638$	−4.74475			−0.187846
$639$		0			0
$640$	−2.20797	−	0.353395i	−0.0872775	−	0.0139692i
$641$	29.5845	+	17.0806i	1.16852	+	0.674644i	0.953330	−	0.301929i	$-0.0976306\pi$
$641$	29.5845	+	17.0806i	1.16852	+	0.674644i	0.215187	+	0.976573i	$0.430964\pi$
$642$		0			0
$643$	10.6355	+	18.4212i	0.419423	+	0.726463i	0.995882	−	0.0906641i	$-0.0288990\pi$
$643$	10.6355	+	18.4212i	0.419423	+	0.726463i	−0.576458	+	0.817127i	$0.695566\pi$
$644$	5.29270	+	15.7284i	0.208562	+	0.619786i
$645$		0			0
$646$	−9.32814	+	16.1568i	−0.367011	+	0.635681i
$647$		−	36.4298i		−	1.43220i	−0.697997	−	0.716101i	$-0.745925\pi$
$647$		−	36.4298i		−	1.43220i	0.697997	−	0.716101i	$-0.254075\pi$
$648$		0			0
$649$		−	30.9498i		−	1.21488i
$650$	−6.72994	+	6.02008i	−0.263970	+	0.236127i
$651$		0			0
$652$	13.7063	−	7.91332i	0.536779	−	0.309909i
$653$	−19.6024	−	33.9524i	−0.767102	−	1.32866i	−0.939128	−	0.343567i	$-0.888365\pi$
$653$	−19.6024	−	33.9524i	−0.767102	−	1.32866i	0.172027	−	0.985092i	$-0.444968\pi$
$654$		0			0
$655$	−19.4198	+	23.9018i	−0.758795	+	0.933920i
$656$	−10.9571			−0.427804
$657$		0			0
$658$	−2.03267	+	10.0795i	−0.0792418	+	0.392939i
$659$	−18.3584	−	10.5993i	−0.715143	−	0.412888i	0.0978191	−	0.995204i	$-0.468813\pi$
$659$	−18.3584	−	10.5993i	−0.715143	−	0.412888i	−0.812963	+	0.582316i	$0.802147\pi$
$660$		0			0
$661$	40.3282	−	23.2835i	1.56859	−	0.905624i	0.572252	−	0.820078i	$-0.306070\pi$
$661$	40.3282	−	23.2835i	1.56859	−	0.905624i	0.996334	−	0.0855461i	$-0.0272635\pi$
$662$	−14.4807	−	25.0813i	−0.562807	−	0.974811i
$663$		0			0
$664$	−6.53949	−	3.77558i	−0.253781	−	0.146521i
$665$	8.71213	−	23.3079i	0.337842	−	0.903843i
$666$		0			0
$667$			5.27349i			0.204190i
$668$	−1.89540	−	1.09431i	−0.0733351	−	0.0423400i
$669$		0			0
$670$	8.47129	−	3.23600i	0.327274	−	0.125018i
$671$	−22.0097	−	38.1219i	−0.849675	−	1.47168i
$672$		0			0
$673$	−8.59103	−	4.96004i	−0.331160	−	0.191195i	0.325196	−	0.945647i	$-0.394570\pi$
$673$	−8.59103	−	4.96004i	−0.331160	−	0.191195i	−0.656356	+	0.754451i	$0.727903\pi$
$674$		−	4.46394i		−	0.171944i
$675$		0			0
$676$	−9.73867			−0.374564
$677$	−20.7940	−	12.0054i	−0.799180	−	0.461407i	0.0440045	−	0.999031i	$-0.485988\pi$
$677$	−20.7940	−	12.0054i	−0.799180	−	0.461407i	−0.843184	+	0.537625i	$0.819322\pi$
$678$		0			0
$679$	−12.1069	−	35.9782i	−0.464619	−	1.38072i
$680$	9.26541	−	3.53935i	0.355312	−	0.135728i
$681$		0			0
$682$	7.65525	−	13.2593i	0.293135	−	0.507724i
$683$	13.0462			0.499200			0.249600	−	0.968349i	$-0.419701\pi$
$683$	13.0462			0.499200			0.249600	+	0.968349i	$0.419701\pi$
$684$		0			0
$685$	−37.7036	−	6.03463i	−1.44058	−	0.230571i
$686$	−16.6748	+	8.05919i	−0.636647	+	0.307701i
$687$		0			0
$688$	−10.1941	+	5.88558i	−0.388647	+	0.224386i
$689$	0.243221	+	0.421271i	0.00926599	+	0.0160492i
$690$		0			0
$691$	9.45113	+	5.45661i	0.359538	+	0.207579i	0.668878	−	0.743372i	$-0.266775\pi$
$691$	9.45113	+	5.45661i	0.359538	+	0.207579i	−0.309340	+	0.950951i	$0.600108\pi$
$692$		−	0.0303997i		−	0.00115562i
$693$		0			0
$694$	8.71409			0.330782
$695$	−13.6234	−	11.0688i	−0.516766	−	0.419864i
$696$		0			0
$697$	42.0905	−	24.3010i	1.59429	−	0.920466i
$698$	15.9295	−	9.19690i	0.602940	−	0.348108i
$699$		0			0
$700$	−11.4086	+	6.69654i	−0.431205	+	0.253105i
$701$		−	13.5970i		−	0.513550i	−0.966471	−	0.256775i	$-0.917340\pi$
$701$		−	13.5970i		−	0.513550i	0.966471	−	0.256775i	$-0.0826600\pi$
$702$		0			0
$703$	16.6211			0.626875
$704$	4.88737	+	2.82172i	0.184200	+	0.106348i
$705$		0			0
$706$	−17.0470	+	9.84206i	−0.641571	+	0.370411i
$707$	−5.99029	−	17.8014i	−0.225288	−	0.669492i
$708$		0			0
$709$	−13.1389	+	22.7573i	−0.493443	+	0.854669i	−0.999971	−	0.00755436i	$-0.997595\pi$
$709$	−13.1389	+	22.7573i	−0.493443	+	0.854669i	0.506528	+	0.862224i	$0.330929\pi$
$710$	−2.65101	+	16.5631i	−0.0994905	+	0.621604i
$711$		0			0
$712$	6.72937			0.252194
$713$	−14.7369	−	8.50833i	−0.551900	−	0.318640i
$714$		0			0
$715$	21.2887	−	8.13222i	0.796153	−	0.304128i
$716$	−18.5038	+	10.6832i	−0.691520	+	0.399249i
$717$		0			0
$718$	−12.5186	−	7.22763i	−0.467191	−	0.269733i
$719$	−4.83977			−0.180493			−0.0902466	−	0.995919i	$-0.528766\pi$
$719$	−4.83977			−0.180493			−0.0902466	+	0.995919i	$0.528766\pi$
$720$		0			0
$721$	−13.8033	−	2.78363i	−0.514062	−	0.103668i
$722$	−0.654839	+	1.13421i	−0.0243706	+	0.0422111i
$723$		0			0
$724$	−10.6857	+	6.16937i	−0.397130	+	0.229283i
$725$	−4.11473	+	0.860613i	−0.152817	+	0.0319624i
$726$		0			0
$727$	6.24558	−	10.8177i	0.231636	−	0.401205i	−0.726654	−	0.687004i	$-0.758926\pi$
$727$	6.24558	−	10.8177i	0.231636	−	0.401205i	0.958290	+	0.285799i	$0.0922589\pi$
$728$	4.68372	+	0.944539i	0.173590	+	0.0350070i
$729$		0			0
$730$	26.1298	+	4.18219i	0.967107	+	0.154790i
$731$	26.1064	−	45.2175i	0.965579	−	1.67243i
$732$		0			0
$733$	−14.5921	−	25.2742i	−0.538971	−	0.933526i	−0.998960	−	0.0456007i	$-0.985480\pi$
$733$	−14.5921	−	25.2742i	−0.538971	−	0.933526i	0.459988	−	0.887925i	$-0.347854\pi$
$734$	4.14505	+	7.17944i	0.152997	+	0.264998i
$735$		0			0
$736$	3.13617	−	5.43200i	0.115601	−	0.200226i
$737$	−22.8869			−0.843049
$738$		0			0
$739$	3.48340			0.128139			0.0640695	−	0.997945i	$-0.479592\pi$
$739$	3.48340			0.128139			0.0640695	+	0.997945i	$0.479592\pi$
$740$	−6.85811	−	5.57211i	−0.252109	−	0.204835i
$741$		0			0
$742$	0.227291	+	0.675443i	0.00834411	+	0.0247963i
$743$	1.90488	+	3.29936i	0.0698834	+	0.121042i	0.898850	−	0.438257i	$-0.144404\pi$
$743$	1.90488	+	3.29936i	0.0698834	+	0.121042i	−0.828966	+	0.559298i	$0.811071\pi$
$744$		0			0
$745$	−30.3155	−	24.6309i	−1.11067	−	0.902406i
$746$			33.2251i			1.21646i
$747$		0			0
$748$	−25.0323			−0.915273
$749$	14.2594	−	16.1732i	0.521027	−	0.590956i
$750$		0			0
$751$	5.37484	+	9.30949i	0.196131	+	0.339708i	0.947271	−	0.320435i	$-0.103829\pi$
$751$	5.37484	+	9.30949i	0.196131	+	0.339708i	−0.751140	+	0.660143i	$0.770496\pi$
$752$	3.36570	−	1.94319i	0.122735	−	0.0708608i
$753$		0			0
$754$	1.31491	+	0.759166i	0.0478863	+	0.0276472i
$755$	11.4114	+	1.82644i	0.415302	+	0.0664710i
$756$		0			0
$757$			36.1893i			1.31532i	0.753314	+	0.657661i	$0.228454\pi$
$757$			36.1893i			1.31532i	−0.753314	+	0.657661i	$0.771546\pi$
$758$	3.76430	−	6.51996i	0.136726	−	0.236816i
$759$		0			0
$760$	−8.78568	+	3.35610i	−0.318690	+	0.121738i
$761$	−16.8769	−	29.2317i	−0.611788	−	1.05965i	−0.990939	−	0.134313i	$-0.957117\pi$
$761$	−16.8769	−	29.2317i	−0.611788	−	1.05965i	0.379151	−	0.925335i	$-0.376216\pi$
$762$		0			0
$763$	6.06420	−	6.87809i	0.219539	−	0.249004i
$764$		−	5.65456i		−	0.204575i
$765$		0			0
$766$			21.8096i			0.788014i
$767$	−4.95200	+	8.57712i	−0.178806	+	0.309702i
$768$		0			0
$769$	−5.14392	+	2.96984i	−0.185494	+	0.107095i	−0.589872	−	0.807497i	$-0.700822\pi$
$769$	−5.14392	+	2.96984i	−0.185494	+	0.107095i	0.404377	+	0.914592i	$0.367488\pi$
$770$	32.9287	−	5.51337i	1.18667	−	0.198688i
$771$		0			0
$772$	17.4878	+	10.0966i	0.629399	+	0.363384i
$773$			40.6646i			1.46260i	0.682054	+	0.731302i	$0.261087\pi$
$773$			40.6646i			1.46260i	−0.682054	+	0.731302i	$0.738913\pi$
$774$		0			0
$775$	4.23377	−	12.8872i	0.152082	−	0.462923i
$776$	−7.17388	+	12.4255i	−0.257527	+	0.446050i
$777$		0			0
$778$	−4.33372	+	2.50208i	−0.155371	+	0.0897038i
$779$	−39.9113	+	23.0428i	−1.42997	+	0.825593i
$780$		0			0
$781$	21.1673	−	36.6628i	0.757424	−	1.31190i
$782$			27.8219i			0.994908i
$783$		0			0
$784$	6.45289	+	2.71297i	0.230460	+	0.0968918i
$785$	−15.8279	+	19.4808i	−0.564921	+	0.695301i
$786$		0			0
$787$	−5.14964	−	8.91943i	−0.183565	−	0.317943i	0.759527	−	0.650475i	$-0.225430\pi$
$787$	−5.14964	−	8.91943i	−0.183565	−	0.317943i	−0.943092	+	0.332532i	$0.892097\pi$
$788$	−6.24084	−	10.8094i	−0.222321	−	0.385071i
$789$		0			0
$790$	−8.72829	+	10.7427i	−0.310539	+	0.382209i
$791$	−14.3377	−	2.89140i	−0.509788	−	0.102806i
$792$		0			0
$793$			14.0863i			0.500220i
$794$	−9.03646	+	15.6516i	−0.320692	+	0.555455i
$795$		0			0
$796$	−2.42565	+	1.40045i	−0.0859747	+	0.0496375i
$797$	7.18170	−	4.14636i	0.254389	−	0.146871i	−0.367383	−	0.930070i	$-0.619746\pi$
$797$	7.18170	−	4.14636i	0.254389	−	0.146871i	0.621772	+	0.783198i	$0.286413\pi$
$798$		0			0
$799$	−8.61930	+	14.9291i	−0.304929	+	0.528153i
$800$	4.75022	+	1.56057i	0.167946	+	0.0551744i
$801$		0			0
$802$		−	20.7230i		−	0.731755i
$803$	−57.8387	−	33.3932i	−2.04108	−	1.17842i
$804$		0			0
$805$	−6.12777	−	36.5982i	−0.215975	−	1.28992i
$806$	−4.24300	+	2.44970i	−0.149453	+	0.0862870i
$807$		0			0
$808$	−3.54952	+	6.14795i	−0.124872	+	0.216284i
$809$			36.6387i			1.28815i	0.764962	+	0.644075i	$0.222757\pi$
$809$			36.6387i			1.28815i	−0.764962	+	0.644075i	$0.777243\pi$
$810$		0			0
$811$			18.7297i			0.657688i	0.944384	+	0.328844i	$0.106659\pi$
$811$			18.7297i			0.657688i	−0.944384	+	0.328844i	$0.893341\pi$
$812$	1.66852	+	1.47109i	0.0585537	+	0.0516250i
$813$		0			0
$814$	11.1508	+	19.3137i	0.390835	+	0.676946i
$815$	−33.0595	+	12.6286i	−1.15802	+	0.442361i
$816$		0			0
$817$	−24.7547	+	42.8763i	−0.866056	+	1.50005i
$818$			1.78771i			0.0625058i
$819$		0			0
$820$	24.1930	+	3.87220i	0.844855	+	0.135223i
$821$	−26.0040	−	15.0134i	−0.907545	−	0.523971i	−0.0279044	−	0.999611i	$-0.508883\pi$
$821$	−26.0040	−	15.0134i	−0.907545	−	0.523971i	−0.879640	+	0.475639i	$0.842217\pi$
$822$		0			0
$823$	−12.0727	+	6.97019i	−0.420829	+	0.242966i	−0.695432	−	0.718592i	$-0.744787\pi$
$823$	−12.0727	+	6.97019i	−0.420829	+	0.242966i	0.274603	+	0.961558i	$0.411454\pi$
$824$	2.66109	+	4.60915i	0.0927036	+	0.160567i
$825$		0			0
$826$	−9.59582	+	10.8837i	−0.333881	+	0.378693i
$827$	48.3520			1.68136			0.840682	−	0.541530i	$-0.182155\pi$
$827$	48.3520			1.68136			0.840682	+	0.541530i	$0.182155\pi$
$828$		0			0
$829$		−	33.3374i		−	1.15786i	−0.815379	−	0.578928i	$-0.803471\pi$
$829$		−	33.3374i		−	1.15786i	0.815379	−	0.578928i	$-0.196529\pi$
$830$	13.1047	+	10.6474i	0.454871	+	0.369576i
$831$		0			0
$832$	−0.902958	−	1.56397i	−0.0313044	−	0.0542209i
$833$	−30.8049	+	3.88981i	−1.06733	+	0.134774i
$834$		0			0
$835$	3.79825	+	3.08602i	0.131444	+	0.106796i
$836$	23.7363			0.820936
$837$		0			0
$838$	−21.8360			−0.754311
$839$	−4.06188	+	7.03539i	−0.140232	+	0.242888i	−0.927584	−	0.373615i	$-0.878118\pi$
$839$	−4.06188	+	7.03539i	−0.140232	+	0.242888i	0.787352	+	0.616504i	$0.211451\pi$
$840$		0			0
$841$	−14.1466	−	24.5026i	−0.487813	−	0.844916i
$842$	10.9611	+	18.9852i	0.377744	+	0.654272i
$843$		0			0
$844$	−10.8799	+	18.8446i	−0.374503	+	0.648658i
$845$	21.5026	+	3.44160i	0.739713	+	0.118394i
$846$		0			0
$847$	−54.0714	−	10.9043i	−1.85791	−	0.374675i
$848$	0.134680	−	0.233273i	0.00462494	−	0.00801062i
$849$		0			0
$850$	−21.7085	+	4.54042i	−0.744595	+	0.155735i
$851$	21.4660	−	12.3934i	0.735845	−	0.424840i
$852$		0			0
$853$	2.81660	−	4.87849i	0.0964385	−	0.167036i	−0.813770	−	0.581188i	$-0.802588\pi$
$853$	2.81660	−	4.87849i	0.0964385	−	0.167036i	0.910208	+	0.414151i	$0.135922\pi$
$854$	−4.07964	+	20.2298i	−0.139603	+	0.692251i
$855$		0			0
$856$	−8.14952			−0.278545
$857$	14.4855	+	8.36321i	0.494815	+	0.285682i	0.726570	−	0.687092i	$-0.241113\pi$
$857$	14.4855	+	8.36321i	0.494815	+	0.285682i	−0.231755	+	0.972774i	$0.574447\pi$
$858$		0			0
$859$	−6.75863	+	3.90210i	−0.230601	+	0.133138i	−0.610849	−	0.791747i	$-0.709172\pi$
$859$	−6.75863	+	3.90210i	−0.230601	+	0.133138i	0.380248	+	0.924885i	$0.375839\pi$
$860$	24.5882	−	9.39260i	0.838451	−	0.320285i
$861$		0			0
$862$	−24.6788	−	14.2483i	−0.840563	−	0.485299i
$863$	23.4139			0.797019			0.398510	−	0.917164i	$-0.369528\pi$
$863$	23.4139			0.797019			0.398510	+	0.917164i	$0.369528\pi$
$864$		0			0
$865$	−0.0107431	+	0.0671215i	−0.000365277	+	0.00228220i
$866$	−5.96821	+	10.3372i	−0.202808	+	0.351274i
$867$		0			0
$868$	−6.80300	+	2.28925i	−0.230909	+	0.0777022i
$869$	30.2535	−	17.4669i	1.02628	−	0.592522i
$870$		0			0
$871$	6.34264	+	3.66193i	0.214912	+	0.124080i
$872$	−3.46581			−0.117367
$873$		0			0
$874$		−	26.3814i		−	0.892363i
$875$	27.5563	−	10.7540i	0.931574	−	0.363551i
$876$		0			0
$877$	35.6421	−	20.5780i	1.20355	−	0.694870i	0.242207	−	0.970225i	$-0.422129\pi$
$877$	35.6421	−	20.5780i	1.20355	−	0.694870i	0.961343	+	0.275355i	$0.0887954\pi$
$878$	−29.8934	+	17.2590i	−1.00885	+	0.582462i
$879$		0			0
$880$	−9.79396	−	7.95744i	−0.330154	−	0.268245i
$881$	−36.8717			−1.24224			−0.621120	−	0.783715i	$-0.713322\pi$
$881$	−36.8717			−1.24224			−0.621120	+	0.783715i	$0.713322\pi$
$882$		0			0
$883$		−	30.0605i		−	1.01162i	−0.862646	−	0.505808i	$-0.831194\pi$
$883$		−	30.0605i		−	1.01162i	0.862646	−	0.505808i	$-0.168806\pi$
$884$	6.93722	+	4.00521i	0.233324	+	0.134710i
$885$		0			0
$886$	−17.7958	−	30.8232i	−0.597862	−	1.03553i
$887$	−11.0365	+	6.37193i	−0.370570	+	0.213948i	−0.673707	−	0.738998i	$-0.735299\pi$
$887$	−11.0365	+	6.37193i	−0.370570	+	0.213948i	0.303138	+	0.952947i	$0.401966\pi$
$888$		0			0
$889$	16.5282	+	14.5724i	0.554338	+	0.488742i
$890$	−14.8582	−	2.37813i	−0.498049	−	0.0797150i
$891$		0			0
$892$	3.64583			0.122071
$893$	8.17303	−	14.1561i	0.273500	−	0.473716i
$894$		0			0
$895$	44.6312	−	17.0489i	1.49186	−	0.569883i
$896$	−0.843817	−	2.50758i	−0.0281899	−	0.0837725i
$897$		0			0
$898$	3.09074	+	1.78444i	0.103139	+	0.0595476i
$899$	−2.28094			−0.0760736
$900$		0			0
$901$			1.19479i			0.0398041i
$902$	−53.5515	−	30.9180i	−1.78307	−	1.02946i
$903$		0			0
$904$	2.76411	+	4.78758i	0.0919330	+	0.159233i
$905$	25.7738	−	9.84550i	0.856750	−	0.327275i
$906$		0			0
$907$	15.9432	+	9.20480i	0.529385	+	0.305640i	0.740766	−	0.671763i	$-0.234463\pi$
$907$	15.9432	+	9.20480i	0.529385	+	0.305640i	−0.211381	+	0.977404i	$0.567796\pi$
$908$		−	7.78502i		−	0.258355i
$909$		0			0
$910$	−10.0077	−	3.74071i	−0.331752	−	0.124003i
$911$	20.5233	+	11.8491i	0.679966	+	0.392578i	0.799842	−	0.600210i	$-0.204916\pi$
$911$	20.5233	+	11.8491i	0.679966	+	0.392578i	−0.119876	+	0.992789i	$0.538250\pi$
$912$		0			0
$913$	−21.3073	−	36.9053i	−0.705168	−	1.22139i
$914$	21.2504	−	12.2690i	0.702902	−	0.405821i
$915$		0			0
$916$	24.5009	+	14.1456i	0.809531	+	0.467383i
$917$	−35.7198	−	7.20342i	−1.17957	−	0.237878i
$918$		0			0
$919$	−36.3030			−1.19752			−0.598762	−	0.800927i	$-0.704341\pi$
$919$	−36.3030			−1.19752			−0.598762	+	0.800927i	$0.704341\pi$
$920$	−8.84420	+	10.8854i	−0.291584	+	0.358880i
$921$		0			0
$922$	4.76490	+	8.25305i	0.156924	+	0.271800i
$923$	−11.7322	+	6.77358i	−0.386169	+	0.222955i
$924$		0			0
$925$	13.1733	+	14.7267i	0.433136	+	0.484209i
$926$		−	0.689758i		−	0.0226669i
$927$		0			0
$928$		−	0.840754i		−	0.0275991i
$929$	−3.52383	+	6.10345i	−0.115613	+	0.200248i	−0.918025	−	0.396523i	$-0.870217\pi$
$929$	−3.52383	+	6.10345i	−0.115613	+	0.200248i	0.802412	+	0.596771i	$0.203550\pi$
$930$		0			0
$931$	29.2100	−	3.68841i	0.957318	−	0.120883i
$932$	−9.30770	−	16.1214i	−0.304884	−	0.528074i
$933$		0			0
$934$	−5.05754	−	2.91997i	−0.165488	−	0.0955444i
$935$	55.2706	+	8.84631i	1.80754	+	0.289305i
$936$		0			0
$937$	−23.6279			−0.771891			−0.385945	−	0.922522i	$-0.626125\pi$
$937$	−23.6279			−0.771891			−0.385945	+	0.922522i	$0.626125\pi$
$938$	8.04833	+	7.09596i	0.262787	+	0.231691i
$939$		0			0
$940$	−8.11807	+	3.10107i	−0.264782	+	0.101146i
$941$	0.386180	+	0.668884i	0.0125891	+	0.0218050i	0.872251	−	0.489058i	$-0.162659\pi$
$941$	0.386180	+	0.668884i	0.0125891	+	0.0218050i	−0.859662	+	0.510863i	$0.829326\pi$
$942$		0			0
$943$	−34.3634	+	59.5192i	−1.11903	+	1.93821i
$944$	5.48420			0.178495
$945$		0			0
$946$	−66.4299			−2.15982
$947$	−19.6859	+	34.0970i	−0.639706	+	1.10800i	0.345791	+	0.938312i	$0.387611\pi$
$947$	−19.6859	+	34.0970i	−0.639706	+	1.10800i	−0.985497	+	0.169692i	$0.945723\pi$
$948$		0			0
$949$	10.6859	+	18.5085i	0.346879	+	0.600812i
$950$	20.5845	−	4.30533i	0.667850	−	0.139683i
$951$		0			0
$952$	8.80280	+	7.76115i	0.285300	+	0.251540i
$953$	−32.0737			−1.03897			−0.519484	−	0.854480i	$-0.673876\pi$
$953$	−32.0737			−1.03897			−0.519484	+	0.854480i	$0.673876\pi$
$954$		0			0
$955$	−1.99829	+	12.4851i	−0.0646632	+	0.404007i
$956$	−23.3155	−	13.4612i	−0.754078	−	0.435367i
$957$		0			0
$958$	14.1442	+	24.4984i	0.456978	+	0.791509i
$959$	−14.4091	−	42.8199i	−0.465296	−	1.38273i
$960$		0			0
$961$	−11.8199	+	20.4727i	−0.381287	+	0.660408i
$962$		−	7.13655i		−	0.230092i
$963$		0			0
$964$		−	1.98427i		−	0.0639090i
$965$	−35.0443	−	28.4730i	−1.12812	−	0.916578i
$966$		0			0
$967$	−42.4402	+	24.5028i	−1.36478	+	0.787958i	−0.990256	−	0.139257i	$-0.955528\pi$
$967$	−42.4402	+	24.5028i	−1.36478	+	0.787958i	−0.374528	+	0.927216i	$0.622195\pi$
$968$	10.4242	+	18.0553i	0.335048	+	0.580320i
$969$		0			0
$970$	20.2308	−	24.8999i	0.649571	−	0.799488i
$971$	−11.8846			−0.381396			−0.190698	−	0.981649i	$-0.561075\pi$
$971$	−11.8846			−0.381396			−0.190698	+	0.981649i	$0.561075\pi$
$972$		0			0
$973$	4.10577	−	20.3594i	0.131625	−	0.652693i
$974$	−8.49104	−	4.90231i	−0.272071	−	0.157080i
$975$		0			0
$976$	6.75508	−	3.90005i	0.216225	−	0.124837i
$977$	−6.89918	−	11.9497i	−0.220724	−	0.382306i	0.734304	−	0.678821i	$-0.237509\pi$
$977$	−6.89918	−	11.9497i	−0.220724	−	0.382306i	−0.955028	+	0.296515i	$0.904175\pi$
$978$		0			0
$979$	32.8889	+	18.9884i	1.05113	+	0.606873i
$980$	−13.2890	−	8.27056i	−0.424502	−	0.264193i
$981$		0			0
$982$			4.06872i			0.129838i
$983$	−27.1098	−	15.6518i	−0.864668	−	0.499216i	0.000904535	−	1.00000i	$-0.499712\pi$
$983$	−27.1098	−	15.6518i	−0.864668	−	0.499216i	−0.865573	+	0.500783i	$0.833045\pi$
$984$		0			0
$985$	9.95955	+	26.0724i	0.317338	+	0.830735i
$986$	1.86464	+	3.22966i	0.0593824	+	0.102853i
$987$		0			0
$988$	−6.57804	−	3.79783i	−0.209275	−	0.120825i
$989$			73.8327i			2.34774i
$990$		0			0
$991$	15.6457			0.497003			0.248502	−	0.968631i	$-0.420062\pi$
$991$	15.6457			0.497003			0.248502	+	0.968631i	$0.420062\pi$
$992$	2.34950	+	1.35649i	0.0745967	+	0.0430685i
$993$		0			0
$994$	−18.8107	+	6.32992i	−0.596640	+	0.200773i
$995$	5.85065	−	2.23493i	0.185478	−	0.0708520i
$996$		0			0
$997$	−10.9510	+	18.9676i	−0.346821	+	0.600711i	−0.985683	−	0.168610i	$-0.946072\pi$
$997$	−10.9510	+	18.9676i	−0.346821	+	0.600711i	0.638862	+	0.769321i	$0.279405\pi$
$998$	−23.5245			−0.744654
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bf.e.629.9		32
3.2	odd	2		630.2.bf.f.209.9	yes	32
5.4	even	2		1890.2.bf.f.629.14		32
7.6	odd	2	inner	1890.2.bf.e.629.8		32
9.4	even	3		630.2.bf.e.419.9	yes	32
9.5	odd	6		1890.2.bf.f.1259.3		32
15.14	odd	2		630.2.bf.e.209.8	✓	32
21.20	even	2		630.2.bf.f.209.8	yes	32
35.34	odd	2		1890.2.bf.f.629.3		32
45.4	even	6		630.2.bf.f.419.8	yes	32
45.14	odd	6	inner	1890.2.bf.e.1259.8		32
63.13	odd	6		630.2.bf.e.419.8	yes	32
63.41	even	6		1890.2.bf.f.1259.14		32
105.104	even	2		630.2.bf.e.209.9	yes	32
315.104	even	6	inner	1890.2.bf.e.1259.9		32
315.139	odd	6		630.2.bf.f.419.9	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bf.e.209.8	✓	32	15.14	odd	2
630.2.bf.e.209.9	yes	32	105.104	even	2
630.2.bf.e.419.8	yes	32	63.13	odd	6
630.2.bf.e.419.9	yes	32	9.4	even	3
630.2.bf.f.209.8	yes	32	21.20	even	2
630.2.bf.f.209.9	yes	32	3.2	odd	2
630.2.bf.f.419.8	yes	32	45.4	even	6
630.2.bf.f.419.9	yes	32	315.139	odd	6
1890.2.bf.e.629.8		32	7.6	odd	2	inner
1890.2.bf.e.629.9		32	1.1	even	1	trivial
1890.2.bf.e.1259.8		32	45.14	odd	6	inner
1890.2.bf.e.1259.9		32	315.104	even	6	inner
1890.2.bf.f.629.3		32	35.34	odd	2
1890.2.bf.f.629.14		32	5.4	even	2
1890.2.bf.f.1259.3		32	9.5	odd	6
1890.2.bf.f.1259.14		32	63.41	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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.bf (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.797934 + 2.08885i) q^{5} +(-1.74972 + 1.98456i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.797934 + 2.08885i) q^{5} +(-1.74972 + 1.98456i) q^{7} +1.00000 q^{8} +(-2.20797 - 0.353395i) q^{10} +(4.88737 + 2.82172i) q^{11} +(-0.902958 - 1.56397i) q^{13} +(-0.843817 - 2.50758i) q^{14} +(-0.500000 + 0.866025i) q^{16} -4.43565i q^{17} +4.20599i q^{19} +(1.41003 - 1.73546i) q^{20} +(-4.88737 + 2.82172i) q^{22} +(3.13617 + 5.43200i) q^{23} +(-3.72660 + 3.33353i) q^{25} +1.80592 q^{26} +(2.59354 + 0.523025i) q^{28} +(0.728114 + 0.420377i) q^{29} +(-2.34950 + 1.35649i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.84138 + 2.21782i) q^{34} +(-5.54161 - 2.07136i) q^{35} -3.95176i q^{37} +(-3.64249 - 2.10299i) q^{38} +(0.797934 + 2.08885i) q^{40} +(5.47857 + 9.48915i) q^{41} +(10.1941 + 5.88558i) q^{43} -5.64345i q^{44} -6.27234 q^{46} +(-3.36570 - 1.94319i) q^{47} +(-0.876944 - 6.94485i) q^{49} +(-1.02362 - 4.89410i) q^{50} +(-0.902958 + 1.56397i) q^{52} -0.269360 q^{53} +(-1.99437 + 12.4605i) q^{55} +(-1.74972 + 1.98456i) q^{56} +(-0.728114 + 0.420377i) q^{58} +(-2.74210 - 4.74945i) q^{59} +(-6.75508 - 3.90005i) q^{61} -2.71297i q^{62} +1.00000 q^{64} +(2.54640 - 3.13409i) q^{65} +(-3.51215 + 2.02774i) q^{67} +(-3.84138 + 2.21782i) q^{68} +(4.56466 - 3.76349i) q^{70} -7.50154i q^{71} -11.8343 q^{73} +(3.42233 + 1.97588i) q^{74} +(3.64249 - 2.10299i) q^{76} +(-14.1514 + 4.76204i) q^{77} +(3.09507 - 5.36082i) q^{79} +(-2.20797 - 0.353395i) q^{80} -10.9571 q^{82} +(-6.53949 - 3.77558i) q^{83} +(9.26541 - 3.53935i) q^{85} +(-10.1941 + 5.88558i) q^{86} +(4.88737 + 2.82172i) q^{88} +6.72937 q^{89} +(4.68372 + 0.944539i) q^{91} +(3.13617 - 5.43200i) q^{92} +(3.36570 - 1.94319i) q^{94} +(-8.78568 + 3.35610i) q^{95} +(-7.17388 + 12.4255i) q^{97} +(6.45289 + 2.71297i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 24 q^{11} - 16 q^{16} - 24 q^{22} - 24 q^{23} + 50 q^{25} + 36 q^{29} - 16 q^{32} - 48 q^{35} + 54 q^{43} + 48 q^{46} + 32 q^{49} - 58 q^{50} - 24 q^{53} - 36 q^{58} + 32 q^{64} + 66 q^{65} + 66 q^{67} + 12 q^{70} - 12 q^{74} + 18 q^{77} + 34 q^{79} - 32 q^{85} - 54 q^{86} + 24 q^{88} + 16 q^{91} - 24 q^{92} + 24 q^{95} - 64 q^{98}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 24 * q^11 - 16 * q^16 - 24 * q^22 - 24 * q^23 + 50 * q^25 + 36 * q^29 - 16 * q^32 - 48 * q^35 + 54 * q^43 + 48 * q^46 + 32 * q^49 - 58 * q^50 - 24 * q^53 - 36 * q^58 + 32 * q^64 + 66 * q^65 + 66 * q^67 + 12 * q^70 - 12 * q^74 + 18 * q^77 + 34 * q^79 - 32 * q^85 - 54 * q^86 + 24 * q^88 + 16 * q^91 - 24 * q^92 + 24 * q^95 - 64 * q^98

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