LMFDB - Embedded newform 1890.2.ba.a.1369.46

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(1369,1890)]

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([4, 3, 4]))

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

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

chi := DirichletCharacter("1890.1369");

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.ba (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:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1369.46
Character	$\chi$	$=$	1890.1369
Dual form			1890.2.ba.a.1549.46

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(-0.551777 + 2.16692i) q^{5} +(-0.585831 + 2.58008i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(-0.551777 + 2.16692i) q^{5} +(-0.585831 + 2.58008i) q^{7} +1.00000i q^{8} +(2.16692 + 0.551777i) q^{10} +(2.05292 + 3.55576i) q^{11} +(3.36239 - 1.94128i) q^{13} +(2.58008 + 0.585831i) q^{14} +1.00000 q^{16} +(-2.40480 - 1.38841i) q^{17} +(-1.40977 - 2.44179i) q^{19} +(0.551777 - 2.16692i) q^{20} +(3.55576 - 2.05292i) q^{22} +(5.13166 + 2.96277i) q^{23} +(-4.39109 - 2.39131i) q^{25} +(-1.94128 - 3.36239i) q^{26} +(0.585831 - 2.58008i) q^{28} +(-2.36090 + 4.08921i) q^{29} -3.89489 q^{31} -1.00000i q^{32} +(-1.38841 + 2.40480i) q^{34} +(-5.26758 - 2.69307i) q^{35} +(-0.356887 + 0.206049i) q^{37} +(-2.44179 + 1.40977i) q^{38} +(-2.16692 - 0.551777i) q^{40} +(3.43052 + 5.94183i) q^{41} +(-1.08691 - 0.627530i) q^{43} +(-2.05292 - 3.55576i) q^{44} +(2.96277 - 5.13166i) q^{46} +5.10612i q^{47} +(-6.31361 - 3.02298i) q^{49} +(-2.39131 + 4.39109i) q^{50} +(-3.36239 + 1.94128i) q^{52} +(-4.20182 - 2.42592i) q^{53} +(-8.83781 + 2.48653i) q^{55} +(-2.58008 - 0.585831i) q^{56} +(4.08921 + 2.36090i) q^{58} -12.4810 q^{59} -1.08850 q^{61} +3.89489i q^{62} -1.00000 q^{64} +(2.35131 + 8.35719i) q^{65} +12.5268i q^{67} +(2.40480 + 1.38841i) q^{68} +(-2.69307 + 5.26758i) q^{70} -16.3189 q^{71} +(11.1123 + 6.41567i) q^{73} +(0.206049 + 0.356887i) q^{74} +(1.40977 + 2.44179i) q^{76} +(-10.3768 + 3.21362i) q^{77} +6.02746 q^{79} +(-0.551777 + 2.16692i) q^{80} +(5.94183 - 3.43052i) q^{82} +(13.4228 + 7.74967i) q^{83} +(4.33549 - 4.44491i) q^{85} +(-0.627530 + 1.08691i) q^{86} +(-3.55576 + 2.05292i) q^{88} +(-3.68803 - 6.38786i) q^{89} +(3.03886 + 9.81250i) q^{91} +(-5.13166 - 2.96277i) q^{92} +5.10612 q^{94} +(6.06905 - 1.70754i) q^{95} +(-3.62553 - 2.09320i) q^{97} +(-3.02298 + 6.31361i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 96 q^{4}+O(q^{10}) $ 96 * q - 96 * q^4	$ 96 q - 96 q^{4} - 4 q^{11} + 2 q^{14} + 96 q^{16} - 24 q^{26} - 10 q^{29} + 34 q^{35} - 30 q^{41} + 4 q^{44} - 6 q^{46} - 6 q^{49} + 12 q^{50} + 12 q^{55} - 2 q^{56} - 48 q^{59} + 12 q^{61} - 96 q^{64} + 36 q^{65} + 6 q^{70} + 32 q^{71} - 4 q^{86} + 66 q^{89} + 24 q^{94} + 60 q^{95}+O(q^{100}) $ 96 * q - 96 * q^4 - 4 * q^11 + 2 * q^14 + 96 * q^16 - 24 * q^26 - 10 * q^29 + 34 * q^35 - 30 * q^41 + 4 * q^44 - 6 * q^46 - 6 * q^49 + 12 * q^50 + 12 * q^55 - 2 * q^56 - 48 * q^59 + 12 * q^61 - 96 * q^64 + 36 * q^65 + 6 * q^70 + 32 * q^71 - 4 * q^86 + 66 * q^89 + 24 * q^94 + 60 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−0.551777	+	2.16692i	−0.246762	+	0.969076i
$5$	−0.551777	+	2.16692i	−0.246762	+	0.969076i
$6$		0			0
$7$	−0.585831	+	2.58008i	−0.221423	+	0.975178i
$7$	−0.585831	+	2.58008i	−0.221423	+	0.975178i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	2.16692	+	0.551777i	0.685240	+	0.174487i
$11$	2.05292	+	3.55576i	0.618979	+	1.07210i	0.989672	+	0.143348i	$0.0457867\pi$
$11$	2.05292	+	3.55576i	0.618979	+	1.07210i	−0.370694	+	0.928755i	$0.620880\pi$
$12$		0			0
$13$	3.36239	−	1.94128i	0.932560	−	0.538414i	0.0449397	−	0.998990i	$-0.485690\pi$
$13$	3.36239	−	1.94128i	0.932560	−	0.538414i	0.887620	+	0.460576i	$0.152357\pi$
$14$	2.58008	+	0.585831i	0.689555	+	0.156570i
$15$		0			0
$16$	1.00000			0.250000
$17$	−2.40480	−	1.38841i	−0.583249	−	0.336739i	0.179175	−	0.983817i	$-0.442657\pi$
$17$	−2.40480	−	1.38841i	−0.583249	−	0.336739i	−0.762424	+	0.647078i	$0.775991\pi$
$18$		0			0
$19$	−1.40977	−	2.44179i	−0.323424	−	0.560186i	0.657768	−	0.753220i	$-0.271501\pi$
$19$	−1.40977	−	2.44179i	−0.323424	−	0.560186i	−0.981192	+	0.193034i	$0.938167\pi$
$20$	0.551777	−	2.16692i	0.123381	−	0.484538i
$21$		0			0
$22$	3.55576	−	2.05292i	0.758091	−	0.437684i
$23$	5.13166	+	2.96277i	1.07003	+	0.617780i	0.928188	−	0.372111i	$-0.121366\pi$
$23$	5.13166	+	2.96277i	1.07003	+	0.617780i	0.141837	+	0.989890i	$0.454699\pi$
$24$		0			0
$25$	−4.39109	−	2.39131i	−0.878217	−	0.478262i
$26$	−1.94128	−	3.36239i	−0.380716	−	0.659420i
$27$		0			0
$28$	0.585831	−	2.58008i	0.110712	−	0.487589i
$29$	−2.36090	+	4.08921i	−0.438409	+	0.759346i	−0.997567	−	0.0697147i	$-0.977791\pi$
$29$	−2.36090	+	4.08921i	−0.438409	+	0.759346i	0.559158	+	0.829061i	$0.311124\pi$
$30$		0			0
$31$	−3.89489			−0.699542			−0.349771	−	0.936835i	$-0.613741\pi$
$31$	−3.89489			−0.699542			−0.349771	+	0.936835i	$0.613741\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−1.38841	+	2.40480i	−0.238110	+	0.412419i
$35$	−5.26758	−	2.69307i	−0.890383	−	0.455213i
$36$		0			0
$37$	−0.356887	+	0.206049i	−0.0586718	+	0.0338742i	−0.529049	−	0.848591i	$-0.677451\pi$
$37$	−0.356887	+	0.206049i	−0.0586718	+	0.0338742i	0.470377	+	0.882465i	$0.344118\pi$
$38$	−2.44179	+	1.40977i	−0.396111	+	0.228695i
$39$		0			0
$40$	−2.16692	−	0.551777i	−0.342620	−	0.0872435i
$41$	3.43052	+	5.94183i	0.535757	+	0.927958i	0.999126	+	0.0417929i	$0.0133070\pi$
$41$	3.43052	+	5.94183i	0.535757	+	0.927958i	−0.463369	+	0.886165i	$0.653360\pi$
$42$		0			0
$43$	−1.08691	−	0.627530i	−0.165753	−	0.0956975i	0.414829	−	0.909899i	$-0.363841\pi$
$43$	−1.08691	−	0.627530i	−0.165753	−	0.0956975i	−0.580582	+	0.814202i	$0.697175\pi$
$44$	−2.05292	−	3.55576i	−0.309489	−	0.536051i
$45$		0			0
$46$	2.96277	−	5.13166i	0.436836	−	0.756622i
$47$			5.10612i			0.744804i	0.928072	+	0.372402i	$0.121466\pi$
$47$			5.10612i			0.744804i	−0.928072	+	0.372402i	$0.878534\pi$
$48$		0			0
$49$	−6.31361	−	3.02298i	−0.901944	−	0.431854i
$50$	−2.39131	+	4.39109i	−0.338183	+	0.620993i
$51$		0			0
$52$	−3.36239	+	1.94128i	−0.466280	+	0.269207i
$53$	−4.20182	−	2.42592i	−0.577164	−	0.333226i	0.182842	−	0.983142i	$-0.441470\pi$
$53$	−4.20182	−	2.42592i	−0.577164	−	0.333226i	−0.760006	+	0.649917i	$0.774804\pi$
$54$		0			0
$55$	−8.83781	+	2.48653i	−1.19169	+	0.335283i
$56$	−2.58008	−	0.585831i	−0.344777	−	0.0782849i
$57$		0			0
$58$	4.08921	+	2.36090i	0.536939	+	0.310002i
$59$	−12.4810			−1.62489			−0.812445	−	0.583038i	$-0.801864\pi$
$59$	−12.4810			−1.62489			−0.812445	+	0.583038i	$0.801864\pi$
$60$		0			0
$61$	−1.08850			−0.139369			−0.0696843	−	0.997569i	$-0.522199\pi$
$61$	−1.08850			−0.139369			−0.0696843	+	0.997569i	$0.522199\pi$
$62$			3.89489i			0.494651i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	2.35131	+	8.35719i	0.291644	+	1.03658i
$66$		0			0
$67$			12.5268i			1.53039i	0.643799	+	0.765195i	$0.277357\pi$
$67$			12.5268i			1.53039i	−0.643799	+	0.765195i	$0.722643\pi$
$68$	2.40480	+	1.38841i	0.291625	+	0.168369i
$69$		0			0
$70$	−2.69307	+	5.26758i	−0.321884	+	0.629596i
$71$	−16.3189			−1.93669			−0.968346	−	0.249611i	$-0.919697\pi$
$71$	−16.3189			−1.93669			−0.968346	+	0.249611i	$0.919697\pi$
$72$		0			0
$73$	11.1123	+	6.41567i	1.30059	+	0.750897i	0.980505	−	0.196492i	$-0.0629549\pi$
$73$	11.1123	+	6.41567i	1.30059	+	0.750897i	0.320086	+	0.947389i	$0.396288\pi$
$74$	0.206049	+	0.356887i	0.0239527	+	0.0414872i
$75$		0			0
$76$	1.40977	+	2.44179i	0.161712	+	0.280093i
$77$	−10.3768	+	3.21362i	−1.18255	+	0.366226i
$78$		0			0
$79$	6.02746			0.678142			0.339071	−	0.940761i	$-0.389887\pi$
$79$	6.02746			0.678142			0.339071	+	0.940761i	$0.389887\pi$
$80$	−0.551777	+	2.16692i	−0.0616905	+	0.242269i
$81$		0			0
$82$	5.94183	−	3.43052i	0.656165	−	0.378837i
$83$	13.4228	+	7.74967i	1.47335	+	0.850637i	0.999550	−	0.0299982i	$-0.00955017\pi$
$83$	13.4228	+	7.74967i	1.47335	+	0.850637i	0.473796	+	0.880635i	$0.342884\pi$
$84$		0			0
$85$	4.33549	−	4.44491i	0.470249	−	0.482118i
$86$	−0.627530	+	1.08691i	−0.0676683	+	0.117205i
$87$		0			0
$88$	−3.55576	+	2.05292i	−0.379046	+	0.218842i
$89$	−3.68803	−	6.38786i	−0.390931	−	0.677112i	0.601642	−	0.798766i	$-0.294513\pi$
$89$	−3.68803	−	6.38786i	−0.390931	−	0.677112i	−0.992573	+	0.121654i	$0.961180\pi$
$90$		0			0
$91$	3.03886	+	9.81250i	0.318559	+	1.02863i
$92$	−5.13166	−	2.96277i	−0.535013	−	0.308890i
$93$		0			0
$94$	5.10612			0.526656
$95$	6.06905	−	1.70754i	0.622672	−	0.175189i
$96$		0			0
$97$	−3.62553	−	2.09320i	−0.368117	−	0.212532i	0.304519	−	0.952506i	$-0.401504\pi$
$97$	−3.62553	−	2.09320i	−0.368117	−	0.212532i	−0.672635	+	0.739974i	$0.734838\pi$
$98$	−3.02298	+	6.31361i	−0.305367	+	0.637770i
$99$		0			0
$100$	4.39109	+	2.39131i	0.439109	+	0.239131i
$101$	−6.33196	−	10.9673i	−0.630053	−	1.09128i	−0.987540	−	0.157366i	$-0.949700\pi$
$101$	−6.33196	−	10.9673i	−0.630053	−	1.09128i	0.357487	−	0.933918i	$-0.383634\pi$
$102$		0			0
$103$	3.79293	+	2.18985i	0.373729	+	0.215772i	0.675086	−	0.737739i	$-0.264106\pi$
$103$	3.79293	+	2.18985i	0.373729	+	0.215772i	−0.301357	+	0.953511i	$0.597440\pi$
$104$	1.94128	+	3.36239i	0.190358	+	0.329710i
$105$		0			0
$106$	−2.42592	+	4.20182i	−0.235626	+	0.408117i
$107$	−2.83265	+	1.63543i	−0.273843	+	0.158103i	−0.630633	−	0.776081i	$-0.717205\pi$
$107$	−2.83265	+	1.63543i	−0.273843	+	0.158103i	0.356790	+	0.934185i	$0.383871\pi$
$108$		0			0
$109$	−1.65955	+	2.87443i	−0.158956	+	0.275321i	−0.934493	−	0.355983i	$-0.884146\pi$
$109$	−1.65955	+	2.87443i	−0.158956	+	0.275321i	0.775536	+	0.631303i	$0.217480\pi$
$110$	2.48653	+	8.83781i	0.237081	+	0.842652i
$111$		0			0
$112$	−0.585831	+	2.58008i	−0.0553558	+	0.243794i
$113$	−6.85140	+	3.95566i	−0.644526	+	0.372117i	−0.786356	−	0.617774i	$-0.788035\pi$
$113$	−6.85140	+	3.95566i	−0.644526	+	0.372117i	0.141830	+	0.989891i	$0.454701\pi$
$114$		0			0
$115$	−9.25161	+	9.48512i	−0.862717	+	0.884492i
$116$	2.36090	−	4.08921i	0.219204	−	0.379673i
$117$		0			0
$118$			12.4810i			1.14897i
$119$	4.99101	−	5.39119i	0.457525	−	0.494210i
$120$		0			0
$121$	−2.92897	+	5.07312i	−0.266270	+	0.461193i
$122$			1.08850i			0.0985485i
$123$		0			0
$124$	3.89489			0.349771
$125$	7.60468	−	8.19566i	0.680183	−	0.733042i
$126$		0			0
$127$		−	7.37701i		−	0.654604i	−0.944920	−	0.327302i	$-0.893861\pi$
$127$		−	7.37701i		−	0.654604i	0.944920	−	0.327302i	$-0.106139\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	8.35719	−	2.35131i	0.732974	−	0.206223i
$131$	5.96168	−	10.3259i	0.520874	−	0.902181i	−0.478831	−	0.877907i	$-0.658939\pi$
$131$	5.96168	−	10.3259i	0.520874	−	0.902181i	0.999705	−	0.0242736i	$-0.00772729\pi$
$132$		0			0
$133$	7.12591	−	2.20684i	0.617894	−	0.191357i
$134$	12.5268			1.08215
$135$		0			0
$136$	1.38841	−	2.40480i	0.119055	−	0.206210i
$137$	−17.1599	+	9.90727i	−1.46607	+	0.846435i	−0.999280	−	0.0379338i	$-0.987922\pi$
$137$	−17.1599	+	9.90727i	−1.46607	+	0.846435i	−0.466788	+	0.884369i	$0.654589\pi$
$138$		0			0
$139$	2.84915	+	4.93488i	0.241662	+	0.418571i	0.961188	−	0.275895i	$-0.0889741\pi$
$139$	2.84915	+	4.93488i	0.241662	+	0.418571i	−0.719526	+	0.694466i	$0.755641\pi$
$140$	5.26758	+	2.69307i	0.445191	+	0.227606i
$141$		0			0
$142$			16.3189i			1.36945i
$143$	13.8055	+	7.97058i	1.15447	+	0.666534i
$144$		0			0
$145$	−7.55829	−	7.37222i	−0.627682	−	0.612229i
$146$	6.41567	−	11.1123i	0.530964	−	0.919657i
$147$		0			0
$148$	0.356887	−	0.206049i	0.0293359	−	0.0169371i
$149$	−10.4021	+	18.0169i	−0.852169	+	1.47600i	0.0270774	+	0.999633i	$0.491380\pi$
$149$	−10.4021	+	18.0169i	−0.852169	+	1.47600i	−0.879247	+	0.476367i	$0.841953\pi$
$150$		0			0
$151$	−8.13217	−	14.0853i	−0.661786	−	1.14625i	−0.980146	−	0.198278i	$-0.936465\pi$
$151$	−8.13217	−	14.0853i	−0.661786	−	1.14625i	0.318359	−	0.947970i	$-0.396868\pi$
$152$	2.44179	−	1.40977i	0.198056	−	0.114347i
$153$		0			0
$154$	3.21362	+	10.3768i	0.258961	+	0.836187i
$155$	2.14911	−	8.43991i	0.172620	−	0.677910i
$156$		0			0
$157$		−	20.2586i		−	1.61681i	−0.588625	−	0.808406i	$-0.700331\pi$
$157$		−	20.2586i		−	1.61681i	0.588625	−	0.808406i	$-0.299669\pi$
$158$		−	6.02746i		−	0.479519i
$159$		0			0
$160$	2.16692	+	0.551777i	0.171310	+	0.0436218i
$161$	−10.6505	+	11.5044i	−0.839373	+	0.906674i
$162$		0			0
$163$	−6.81431	+	3.93424i	−0.533738	+	0.308154i	−0.742537	−	0.669805i	$-0.766378\pi$
$163$	−6.81431	+	3.93424i	−0.533738	+	0.308154i	0.208799	+	0.977958i	$0.433044\pi$
$164$	−3.43052	−	5.94183i	−0.267878	−	0.463979i
$165$		0			0
$166$	7.74967	−	13.4228i	0.601491	−	1.04181i
$167$	18.3747	−	10.6086i	1.42187	−	0.820919i	0.425415	−	0.904999i	$-0.360128\pi$
$167$	18.3747	−	10.6086i	1.42187	−	0.820919i	0.996459	+	0.0840795i	$0.0267950\pi$
$168$		0			0
$169$	1.03712	−	1.79635i	0.0797788	−	0.138181i
$170$	−4.44491	−	4.33549i	−0.340909	−	0.332517i
$171$		0			0
$172$	1.08691	+	0.627530i	0.0828764	+	0.0478487i
$173$		−	4.93214i		−	0.374984i	−0.982266	−	0.187492i	$-0.939964\pi$
$173$		−	4.93214i		−	0.374984i	0.982266	−	0.187492i	$-0.0600358\pi$
$174$		0			0
$175$	8.74220	−	9.92844i	0.660848	−	0.750519i
$176$	2.05292	+	3.55576i	0.154745	+	0.268026i
$177$		0			0
$178$	−6.38786	+	3.68803i	−0.478790	+	0.276430i
$179$	2.63272	−	4.56000i	0.196779	−	0.340831i	−0.750703	−	0.660639i	$-0.770285\pi$
$179$	2.63272	−	4.56000i	0.196779	−	0.340831i	0.947482	+	0.319809i	$0.103619\pi$
$180$		0			0
$181$	20.1029			1.49423			0.747117	−	0.664692i	$-0.231437\pi$
$181$	20.1029			1.49423			0.747117	+	0.664692i	$0.231437\pi$
$182$	9.81250	−	3.03886i	0.727351	−	0.225255i
$183$		0			0
$184$	−2.96277	+	5.13166i	−0.218418	+	0.378311i
$185$	−0.249569	−	0.887037i	−0.0183487	−	0.0652163i
$186$		0			0
$187$		−	11.4012i		−	0.833737i
$188$		−	5.10612i		−	0.372402i
$189$		0			0
$190$	−1.70754	−	6.06905i	−0.123878	−	0.440295i
$191$	2.99287			0.216557			0.108278	−	0.994121i	$-0.465466\pi$
$191$	2.99287			0.216557			0.108278	+	0.994121i	$0.465466\pi$
$192$		0			0
$193$			21.4412i			1.54337i	0.636003	+	0.771687i	$0.280587\pi$
$193$			21.4412i			1.54337i	−0.636003	+	0.771687i	$0.719413\pi$
$194$	−2.09320	+	3.62553i	−0.150283	+	0.260298i
$195$		0			0
$196$	6.31361	+	3.02298i	0.450972	+	0.215927i
$197$		−	3.13660i		−	0.223474i	−0.993738	−	0.111737i	$-0.964359\pi$
$197$		−	3.13660i		−	0.223474i	0.993738	−	0.111737i	$-0.0356414\pi$
$198$		0			0
$199$	−7.45046	+	12.9046i	−0.528149	+	0.914781i	0.471313	+	0.881966i	$0.343780\pi$
$199$	−7.45046	+	12.9046i	−0.528149	+	0.914781i	−0.999461	+	0.0328145i	$0.989553\pi$
$200$	2.39131	−	4.39109i	0.169091	−	0.310497i
$201$		0			0
$202$	−10.9673	+	6.33196i	−0.771655	+	0.445515i
$203$	−9.16738	−	8.48690i	−0.643424	−	0.595663i
$204$		0			0
$205$	−14.7684	+	4.15509i	−1.03147	+	0.290204i
$206$	2.18985	−	3.79293i	0.152574	−	0.264266i
$207$		0			0
$208$	3.36239	−	1.94128i	0.233140	−	0.134603i
$209$	5.78829	−	10.0256i	0.400385	−	0.693487i
$210$		0			0
$211$	7.20990	+	12.4879i	0.496350	+	0.859704i	0.999991	−	0.00420922i	$-0.00133984\pi$
$211$	7.20990	+	12.4879i	0.496350	+	0.859704i	−0.503641	+	0.863913i	$0.668007\pi$
$212$	4.20182	+	2.42592i	0.288582	+	0.166613i
$213$		0			0
$214$	1.63543	+	2.83265i	0.111796	+	0.193636i
$215$	1.95954	−	2.00900i	0.133640	−	0.137013i
$216$		0			0
$217$	2.28174	−	10.0491i	0.154895	−	0.682178i
$218$	2.87443	+	1.65955i	0.194681	+	0.112399i
$219$		0			0
$220$	8.83781	−	2.48653i	0.595845	−	0.167642i
$221$	−10.7812			−0.725220
$222$		0			0
$223$	15.8455	+	9.14843i	1.06110	+	0.612624i	0.925735	−	0.378172i	$-0.123447\pi$
$223$	15.8455	+	9.14843i	1.06110	+	0.612624i	0.135361	+	0.990796i	$0.456781\pi$
$224$	2.58008	+	0.585831i	0.172389	+	0.0391425i
$225$		0			0
$226$	3.95566	+	6.85140i	0.263126	+	0.455748i
$227$	−7.81588	+	4.51250i	−0.518758	+	0.299505i	−0.736426	−	0.676518i	$-0.763488\pi$
$227$	−7.81588	+	4.51250i	−0.518758	+	0.299505i	0.217668	+	0.976023i	$0.430155\pi$
$228$		0			0
$229$	−8.59266	+	14.8829i	−0.567819	+	0.983492i	0.428962	+	0.903322i	$0.358879\pi$
$229$	−8.59266	+	14.8829i	−0.567819	+	0.983492i	−0.996781	+	0.0801691i	$0.974454\pi$
$230$	9.48512	+	9.25161i	0.625430	+	0.610033i
$231$		0			0
$232$	−4.08921	−	2.36090i	−0.268469	−	0.155001i
$233$	4.18657	−	2.41712i	0.274272	−	0.158351i	−0.356556	−	0.934274i	$-0.616049\pi$
$233$	4.18657	−	2.41712i	0.274272	−	0.158351i	0.630827	+	0.775923i	$0.282716\pi$
$234$		0			0
$235$	−11.0645	−	2.81744i	−0.721772	−	0.183789i
$236$	12.4810			0.812445
$237$		0			0
$238$	−5.39119	−	4.99101i	−0.349459	−	0.323519i
$239$	8.08215	+	13.9987i	0.522791	+	0.905500i	0.999648	+	0.0265194i	$0.00844237\pi$
$239$	8.08215	+	13.9987i	0.522791	+	0.905500i	−0.476858	+	0.878981i	$0.658224\pi$
$240$		0			0
$241$	4.83873	+	8.38092i	0.311690	+	0.539862i	0.978728	−	0.205161i	$-0.0657717\pi$
$241$	4.83873	+	8.38092i	0.311690	+	0.539862i	−0.667039	+	0.745023i	$0.732438\pi$
$242$	5.07312	+	2.92897i	0.326113	+	0.188281i
$243$		0			0
$244$	1.08850			0.0696843
$245$	10.0342	−	12.0131i	0.641065	−	0.767487i
$246$		0			0
$247$	−9.48041	−	5.47352i	−0.603224	−	0.348271i
$248$		−	3.89489i		−	0.247325i
$249$		0			0
$250$	−8.19566	−	7.60468i	−0.518339	−	0.480962i
$251$	−17.3945			−1.09793			−0.548967	−	0.835844i	$-0.684979\pi$
$251$	−17.3945			−1.09793			−0.548967	+	0.835844i	$0.684979\pi$
$252$		0			0
$253$			24.3293i			1.52957i
$254$	−7.37701			−0.462875
$255$		0			0
$256$	1.00000			0.0625000
$257$	4.02404	+	2.32328i	0.251013	+	0.144922i	0.620228	−	0.784422i	$-0.287040\pi$
$257$	4.02404	+	2.32328i	0.251013	+	0.144922i	−0.369215	+	0.929344i	$0.620373\pi$
$258$		0			0
$259$	−0.322546	−	1.04150i	−0.0200421	−	0.0647160i
$260$	−2.35131	−	8.35719i	−0.145822	−	0.518291i
$261$		0			0
$262$	−10.3259	−	5.96168i	−0.637938	−	0.368314i
$263$	24.3416	−	14.0537i	1.50097	−	0.866586i	0.500971	−	0.865464i	$-0.332976\pi$
$263$	24.3416	−	14.0537i	1.50097	−	0.866586i	0.999999	−	0.00112136i	$-0.000356940\pi$
$264$		0			0
$265$	7.57524	−	7.76644i	0.465343	−	0.477088i
$266$	−2.20684	−	7.12591i	−0.135310	−	0.436917i
$267$		0			0
$268$		−	12.5268i		−	0.765195i
$269$	−14.0809	+	24.3889i	−0.858529	+	1.48702i	0.0148033	+	0.999890i	$0.495288\pi$
$269$	−14.0809	+	24.3889i	−0.858529	+	1.48702i	−0.873332	+	0.487125i	$0.838046\pi$
$270$		0			0
$271$	−10.1408	−	17.5644i	−0.616009	−	1.06696i	−0.990207	−	0.139610i	$-0.955415\pi$
$271$	−10.1408	−	17.5644i	−0.616009	−	1.06696i	0.374197	−	0.927349i	$-0.377918\pi$
$272$	−2.40480	−	1.38841i	−0.145812	−	0.0841847i
$273$		0			0
$274$	9.90727	+	17.1599i	0.598520	+	1.03667i
$275$	−0.511612	−	20.5228i	−0.0308514	−	1.23757i
$276$		0			0
$277$	8.86564	−	5.11858i	0.532685	−	0.307546i	−0.209424	−	0.977825i	$-0.567159\pi$
$277$	8.86564	−	5.11858i	0.532685	−	0.307546i	0.742109	+	0.670279i	$0.233826\pi$
$278$	4.93488	−	2.84915i	0.295974	−	0.170881i
$279$		0			0
$280$	2.69307	−	5.26758i	0.160942	−	0.314798i
$281$	−10.5038	+	18.1931i	−0.626604	+	1.08531i	0.361625	+	0.932324i	$0.382222\pi$
$281$	−10.5038	+	18.1931i	−0.626604	+	1.08531i	−0.988228	+	0.152986i	$0.951111\pi$
$282$		0			0
$283$			4.88129i			0.290162i	0.989420	+	0.145081i	$0.0463443\pi$
$283$			4.88129i			0.290162i	−0.989420	+	0.145081i	$0.953656\pi$
$284$	16.3189			0.968346
$285$		0			0
$286$	7.97058	−	13.8055i	0.471310	−	0.816334i
$287$	−17.3401	+	5.37010i	−1.02355	+	0.316987i
$288$		0			0
$289$	−4.64463	−	8.04474i	−0.273214	−	0.473220i
$290$	−7.37222	+	7.55829i	−0.432912	+	0.443838i
$291$		0			0
$292$	−11.1123	−	6.41567i	−0.650296	−	0.375448i
$293$	3.55724	−	2.05377i	0.207816	−	0.119983i	−0.392480	−	0.919761i	$-0.628383\pi$
$293$	3.55724	−	2.05377i	0.207816	−	0.119983i	0.600296	+	0.799778i	$0.295049\pi$
$294$		0			0
$295$	6.88673	−	27.0454i	0.400961	−	1.57464i
$296$	−0.206049	−	0.356887i	−0.0119763	−	0.0207436i
$297$		0			0
$298$	18.0169	+	10.4021i	1.04369	+	0.602575i
$299$	23.0062			1.33048
$300$		0			0
$301$	2.25582	−	2.43670i	0.130024	−	0.140449i
$302$	−14.0853	+	8.13217i	−0.810520	+	0.467954i
$303$		0			0
$304$	−1.40977	−	2.44179i	−0.0808559	−	0.140047i
$305$	0.600611	−	2.35870i	0.0343909	−	0.135059i
$306$		0			0
$307$		−	7.22215i		−	0.412190i	−0.978532	−	0.206095i	$-0.933924\pi$
$307$		−	7.22215i		−	0.412190i	0.978532	−	0.206095i	$-0.0660755\pi$
$308$	10.3768	−	3.21362i	0.591274	−	0.183113i
$309$		0			0
$310$	−8.43991	−	2.14911i	−0.479354	−	0.122061i
$311$	23.2889			1.32059			0.660296	−	0.751005i	$-0.270431\pi$
$311$	23.2889			1.32059			0.660296	+	0.751005i	$0.270431\pi$
$312$		0			0
$313$		−	18.1702i		−	1.02704i	−0.858078	−	0.513520i	$-0.828341\pi$
$313$		−	18.1702i		−	1.02704i	0.858078	−	0.513520i	$-0.171659\pi$
$314$	−20.2586			−1.14326
$315$		0			0
$316$	−6.02746			−0.339071
$317$			0.679752i			0.0381787i	0.999818	+	0.0190893i	$0.00607670\pi$
$317$			0.679752i			0.0381787i	−0.999818	+	0.0190893i	$0.993923\pi$
$318$		0			0
$319$	−19.3870			−1.08546
$320$	0.551777	−	2.16692i	0.0308453	−	0.121135i
$321$		0			0
$322$	11.5044	+	10.6505i	0.641116	+	0.593527i
$323$			7.82936i			0.435637i
$324$		0			0
$325$	−19.4068	+	0.483790i	−1.07649	+	0.0268358i
$326$	3.93424	+	6.81431i	0.217898	+	0.377410i
$327$		0			0
$328$	−5.94183	+	3.43052i	−0.328083	+	0.189419i
$329$	−13.1742	−	2.99132i	−0.726316	−	0.164917i
$330$		0			0
$331$	12.7220			0.699262			0.349631	−	0.936888i	$-0.386307\pi$
$331$	12.7220			0.699262			0.349631	+	0.936888i	$0.386307\pi$
$332$	−13.4228	−	7.74967i	−0.736673	−	0.425318i
$333$		0			0
$334$	−10.6086	−	18.3747i	−0.580477	−	1.00542i
$335$	−27.1445	−	6.91198i	−1.48306	−	0.377642i
$336$		0			0
$337$	14.7645	−	8.52431i	0.804276	−	0.464349i	−0.0406882	−	0.999172i	$-0.512955\pi$
$337$	14.7645	−	8.52431i	0.804276	−	0.464349i	0.844964	+	0.534823i	$0.179622\pi$
$338$	−1.79635	−	1.03712i	−0.0977087	−	0.0564122i
$339$		0			0
$340$	−4.33549	+	4.44491i	−0.235125	+	0.241059i
$341$	−7.99589	−	13.8493i	−0.433002	−	0.749981i
$342$		0			0
$343$	11.4982	−	14.5186i	0.620846	−	0.783933i
$344$	0.627530	−	1.08691i	0.0338342	−	0.0586025i
$345$		0			0
$346$	−4.93214			−0.265154
$347$			25.1265i			1.34886i	0.738337	+	0.674431i	$0.235611\pi$
$347$			25.1265i			1.34886i	−0.738337	+	0.674431i	$0.764389\pi$
$348$		0			0
$349$	4.80323	−	8.31944i	0.257111	−	0.445329i	−0.708356	−	0.705856i	$-0.750563\pi$
$349$	4.80323	−	8.31944i	0.257111	−	0.445329i	0.965467	+	0.260526i	$0.0838961\pi$
$350$	−9.92844	−	8.74220i	−0.530697	−	0.467290i
$351$		0			0
$352$	3.55576	−	2.05292i	0.189523	−	0.109421i
$353$	23.4317	−	13.5283i	1.24715	−	0.720040i	0.276606	−	0.960983i	$-0.410790\pi$
$353$	23.4317	−	13.5283i	1.24715	−	0.720040i	0.970539	+	0.240944i	$0.0774569\pi$
$354$		0			0
$355$	9.00437	−	35.3617i	0.477902	−	1.87680i
$356$	3.68803	+	6.38786i	0.195465	+	0.338556i
$357$		0			0
$358$	−4.56000	−	2.63272i	−0.241004	−	0.139144i
$359$	4.43043	+	7.67373i	0.233829	+	0.405004i	0.958932	−	0.283637i	$-0.0915410\pi$
$359$	4.43043	+	7.67373i	0.233829	+	0.405004i	−0.725103	+	0.688641i	$0.758208\pi$
$360$		0			0
$361$	5.52509	−	9.56974i	0.290794	−	0.503671i
$362$		−	20.1029i		−	1.05658i
$363$		0			0
$364$	−3.03886	−	9.81250i	−0.159279	−	0.514315i
$365$	−20.0337	+	20.5394i	−1.04861	+	1.07508i
$366$		0			0
$367$	9.32611	−	5.38443i	0.486819	−	0.281065i	−0.236435	−	0.971647i	$-0.575979\pi$
$367$	9.32611	−	5.38443i	0.486819	−	0.281065i	0.723254	+	0.690582i	$0.242646\pi$
$368$	5.13166	+	2.96277i	0.267506	+	0.154445i
$369$		0			0
$370$	−0.887037	+	0.249569i	−0.0461149	+	0.0129745i
$371$	8.72062	−	9.41984i	0.452752	−	0.489054i
$372$		0			0
$373$	−4.25812	−	2.45843i	−0.220477	−	0.127293i	0.385694	−	0.922627i	$-0.373962\pi$
$373$	−4.25812	−	2.45843i	−0.220477	−	0.127293i	−0.606171	+	0.795334i	$0.707295\pi$
$374$	−11.4012			−0.589541
$375$		0			0
$376$	−5.10612			−0.263328
$377$			18.3327i			0.944181i
$378$		0			0
$379$	36.3873			1.86909			0.934544	−	0.355848i	$-0.115808\pi$
$379$	36.3873			1.86909			0.934544	+	0.355848i	$0.115808\pi$
$380$	−6.06905	+	1.70754i	−0.311336	+	0.0875947i
$381$		0			0
$382$		−	2.99287i		−	0.153129i
$383$	−8.10908	−	4.68178i	−0.414355	−	0.239228i	0.278304	−	0.960493i	$-0.410228\pi$
$383$	−8.10908	−	4.68178i	−0.414355	−	0.239228i	−0.692659	+	0.721265i	$0.743561\pi$
$384$		0			0
$385$	−1.23798	−	24.2589i	−0.0630932	−	1.23635i
$386$	21.4412			1.09133
$387$		0			0
$388$	3.62553	+	2.09320i	0.184058	+	0.106266i
$389$	−1.02428	−	1.77411i	−0.0519332	−	0.0899509i	0.838890	−	0.544301i	$-0.183205\pi$
$389$	−1.02428	−	1.77411i	−0.0519332	−	0.0899509i	−0.890823	+	0.454350i	$0.849872\pi$
$390$		0			0
$391$	−8.22707	−	14.2497i	−0.416061	−	0.720639i
$392$	3.02298	−	6.31361i	0.152683	−	0.318885i
$393$		0			0
$394$	−3.13660			−0.158020
$395$	−3.32581	+	13.0610i	−0.167340	+	0.657171i
$396$		0			0
$397$	−25.1640	+	14.5284i	−1.26294	+	0.729161i	−0.973643	−	0.228077i	$-0.926756\pi$
$397$	−25.1640	+	14.5284i	−1.26294	+	0.729161i	−0.289302	+	0.957238i	$0.593423\pi$
$398$	12.9046	+	7.45046i	0.646848	+	0.373458i
$399$		0			0
$400$	−4.39109	−	2.39131i	−0.219554	−	0.119566i
$401$	−10.0005	+	17.3213i	−0.499399	+	0.864985i	−1.00000		0.000693636i	$-0.999779\pi$
$401$	−10.0005	+	17.3213i	−0.499399	+	0.864985i	0.500601	+	0.865678i	$0.333113\pi$
$402$		0			0
$403$	−13.0961	+	7.56106i	−0.652365	+	0.376643i
$404$	6.33196	+	10.9673i	0.315027	+	0.545642i
$405$		0			0
$406$	−8.48690	+	9.16738i	−0.421198	+	0.454969i
$407$	−1.46532	−	0.846003i	−0.0726332	−	0.0419348i
$408$		0			0
$409$	−21.0715			−1.04192			−0.520959	−	0.853582i	$-0.674426\pi$
$409$	−21.0715			−1.04192			−0.520959	+	0.853582i	$0.674426\pi$
$410$	4.15509	+	14.7684i	0.205205	+	0.729357i
$411$		0			0
$412$	−3.79293	−	2.18985i	−0.186864	−	0.107886i
$413$	7.31176	−	32.2020i	0.359788	−	1.58456i
$414$		0			0
$415$	−24.1993	+	24.8101i	−1.18790	+	1.21788i
$416$	−1.94128	−	3.36239i	−0.0951790	−	0.164855i
$417$		0			0
$418$	−10.0256	−	5.78829i	−0.490369	−	0.283115i
$419$	10.8551	+	18.8016i	0.530306	+	0.918517i	0.999375	+	0.0353551i	$0.0112562\pi$
$419$	10.8551	+	18.8016i	0.530306	+	0.918517i	−0.469069	+	0.883162i	$0.655410\pi$
$420$		0			0
$421$	−10.3520	+	17.9301i	−0.504524	+	0.873861i	0.495463	+	0.868629i	$0.334999\pi$
$421$	−10.3520	+	17.9301i	−0.504524	+	0.873861i	−0.999986	+	0.00523148i	$0.998335\pi$
$422$	12.4879	−	7.20990i	0.607902	−	0.350973i
$423$		0			0
$424$	2.42592	−	4.20182i	0.117813	−	0.204058i
$425$	7.23955	+	11.8472i	0.351170	+	0.574676i
$426$		0			0
$427$	0.637678	−	2.80842i	0.0308594	−	0.135909i
$428$	2.83265	−	1.63543i	0.136921	−	0.0790516i
$429$		0			0
$430$	−2.00900	−	1.95954i	−0.0968826	−	0.0944975i
$431$	1.15807	−	2.00583i	0.0557821	−	0.0966174i	−0.836786	−	0.547530i	$-0.815568\pi$
$431$	1.15807	−	2.00583i	0.0557821	−	0.0966174i	0.892568	+	0.450913i	$0.148901\pi$
$432$		0			0
$433$			22.2752i			1.07048i	0.844701	+	0.535238i	$0.179778\pi$
$433$			22.2752i			1.07048i	−0.844701	+	0.535238i	$0.820222\pi$
$434$	−10.0491	−	2.28174i	−0.482373	−	0.109527i
$435$		0			0
$436$	1.65955	−	2.87443i	0.0794782	−	0.137660i
$437$		−	16.7073i		−	0.799218i
$438$		0			0
$439$	20.7548			0.990575			0.495287	−	0.868729i	$-0.335063\pi$
$439$	20.7548			0.990575			0.495287	+	0.868729i	$0.335063\pi$
$440$	−2.48653	−	8.83781i	−0.118541	−	0.421326i
$441$		0			0
$442$			10.7812i			0.512808i
$443$		−	18.7632i		−	0.891467i	−0.895166	−	0.445733i	$-0.852943\pi$
$443$		−	18.7632i		−	0.891467i	0.895166	−	0.445733i	$-0.147057\pi$
$444$		0			0
$445$	15.8770	−	4.46700i	0.752640	−	0.211756i
$446$	9.14843	−	15.8455i	0.433191	−	0.750308i
$447$		0			0
$448$	0.585831	−	2.58008i	0.0276779	−	0.121897i
$449$	−4.33662			−0.204658			−0.102329	−	0.994751i	$-0.532629\pi$
$449$	−4.33662			−0.204658			−0.102329	+	0.994751i	$0.532629\pi$
$450$		0			0
$451$	−14.0852	+	24.3962i	−0.663244	+	1.14877i
$452$	6.85140	−	3.95566i	0.322263	−	0.186059i
$453$		0			0
$454$	4.51250	+	7.81588i	0.211782	+	0.366817i
$455$	−22.9397	+	1.17065i	−1.07543	+	0.0548811i
$456$		0			0
$457$		−	22.7169i		−	1.06265i	−0.847168	−	0.531325i	$-0.821694\pi$
$457$		−	22.7169i		−	1.06265i	0.847168	−	0.531325i	$-0.178306\pi$
$458$	14.8829	+	8.59266i	0.695434	+	0.401509i
$459$		0			0
$460$	9.25161	−	9.48512i	0.431358	−	0.442246i
$461$	−8.41648	+	14.5778i	−0.391995	+	0.678955i	−0.992713	−	0.120506i	$-0.961548\pi$
$461$	−8.41648	+	14.5778i	−0.391995	+	0.678955i	0.600718	+	0.799461i	$0.294882\pi$
$462$		0			0
$463$	−24.0438	+	13.8817i	−1.11741	+	0.645138i	−0.940739	−	0.339132i	$-0.889867\pi$
$463$	−24.0438	+	13.8817i	−1.11741	+	0.645138i	−0.176673	+	0.984270i	$0.556533\pi$
$464$	−2.36090	+	4.08921i	−0.109602	+	0.189837i
$465$		0			0
$466$	−2.41712	−	4.18657i	−0.111971	−	0.193939i
$467$	29.8191	−	17.2161i	1.37986	−	0.796665i	0.387721	−	0.921777i	$-0.373262\pi$
$467$	29.8191	−	17.2161i	1.37986	−	0.796665i	0.992143	+	0.125112i	$0.0399291\pi$
$468$		0			0
$469$	−32.3201	−	7.33857i	−1.49240	−	0.338864i
$470$	−2.81744	+	11.0645i	−0.129959	+	0.510370i
$471$		0			0
$472$		−	12.4810i		−	0.574486i
$473$		−	5.15308i		−	0.236939i
$474$		0			0
$475$	0.351332	+	14.0933i	0.0161202	+	0.646646i
$476$	−4.99101	+	5.39119i	−0.228763	+	0.247105i
$477$		0			0
$478$	13.9987	−	8.08215i	0.640285	−	0.369669i
$479$	−5.64351	−	9.77485i	−0.257859	−	0.446624i	0.707809	−	0.706403i	$-0.249684\pi$
$479$	−5.64351	−	9.77485i	−0.257859	−	0.446624i	−0.965668	+	0.259779i	$0.916350\pi$
$480$		0			0
$481$	−0.799995	+	1.38563i	−0.0364766	+	0.0631794i
$482$	8.38092	−	4.83873i	0.381740	−	0.220398i
$483$		0			0
$484$	2.92897	−	5.07312i	0.133135	−	0.230596i
$485$	6.53628	−	6.70125i	0.296797	−	0.304288i
$486$		0			0
$487$	−21.2703	−	12.2804i	−0.963848	−	0.556478i	−0.0664931	−	0.997787i	$-0.521181\pi$
$487$	−21.2703	−	12.2804i	−0.963848	−	0.556478i	−0.897355	+	0.441309i	$0.854514\pi$
$488$		−	1.08850i		−	0.0492742i
$489$		0			0
$490$	−12.0131	−	10.0342i	−0.542695	−	0.453301i
$491$	9.08350	+	15.7331i	0.409933	+	0.710024i	0.994882	−	0.101046i	$-0.0322188\pi$
$491$	9.08350	+	15.7331i	0.409933	+	0.710024i	−0.584949	+	0.811070i	$0.698885\pi$
$492$		0			0
$493$	11.3550	−	6.55581i	0.511403	−	0.295259i
$494$	−5.47352	+	9.48041i	−0.246265	+	0.426544i
$495$		0			0
$496$	−3.89489			−0.174886
$497$	9.56009	−	42.1039i	0.428829	−	1.88862i
$498$		0			0
$499$	5.69190	−	9.85866i	0.254805	−	0.441334i	−0.710038	−	0.704164i	$-0.751322\pi$
$499$	5.69190	−	9.85866i	0.254805	−	0.441334i	0.964842	+	0.262829i	$0.0846555\pi$
$500$	−7.60468	+	8.19566i	−0.340092	+	0.366521i
$501$		0			0
$502$			17.3945i			0.776357i
$503$			7.11598i			0.317286i	0.987336	+	0.158643i	$0.0507118\pi$
$503$			7.11598i			0.317286i	−0.987336	+	0.158643i	$0.949288\pi$
$504$		0			0
$505$	27.2590	−	7.66936i	1.21301	−	0.341282i
$506$	24.3293			1.08157
$507$		0			0
$508$			7.37701i			0.327302i
$509$	12.2001	−	21.1313i	0.540762	−	0.936627i	−0.458099	−	0.888901i	$-0.651469\pi$
$509$	12.2001	−	21.1313i	0.540762	−	0.936627i	0.998860	−	0.0477257i	$-0.0151973\pi$
$510$		0			0
$511$	−23.0628	+	24.9120i	−1.02024	+	1.10204i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	2.32328	−	4.02404i	0.102476	−	0.177493i
$515$	−6.83809	+	7.01068i	−0.301322	+	0.308927i
$516$		0			0
$517$	−18.1561	+	10.4825i	−0.798506	+	0.461018i
$518$	−1.04150	+	0.322546i	−0.0457611	+	0.0141719i
$519$		0			0
$520$	−8.35719	+	2.35131i	−0.366487	+	0.103112i
$521$	10.6836	−	18.5046i	0.468058	−	0.810701i	−0.531275	−	0.847199i	$-0.678287\pi$
$521$	10.6836	−	18.5046i	0.468058	−	0.810701i	0.999334	+	0.0364984i	$0.0116204\pi$
$522$		0			0
$523$	22.4124	−	12.9398i	0.980028	−	0.565819i	0.0777491	−	0.996973i	$-0.475227\pi$
$523$	22.4124	−	12.9398i	0.980028	−	0.565819i	0.902278	+	0.431154i	$0.141893\pi$
$524$	−5.96168	+	10.3259i	−0.260437	+	0.451090i
$525$		0			0
$526$	−14.0537	−	24.3416i	−0.612769	−	1.06135i
$527$	9.36641	+	5.40770i	0.408007	+	0.235563i
$528$		0			0
$529$	6.05597	+	10.4892i	0.263303	+	0.456054i
$530$	−7.76644	−	7.57524i	−0.337352	−	0.329047i
$531$		0			0
$532$	−7.12591	+	2.20684i	−0.308947	+	0.0956787i
$533$	23.0695	+	13.3192i	0.999251	+	0.576918i
$534$		0			0
$535$	−1.98086	−	7.04052i	−0.0856400	−	0.304388i
$536$	−12.5268			−0.541075
$537$		0			0
$538$	24.3889	+	14.0809i	1.05148	+	0.607072i
$539$	−2.21234	−	28.6556i	−0.0952922	−	1.23428i
$540$		0			0
$541$	−18.0736	−	31.3045i	−0.777047	−	1.34588i	−0.933637	−	0.358221i	$-0.883384\pi$
$541$	−18.0736	−	31.3045i	−0.777047	−	1.34588i	0.156590	−	0.987664i	$-0.449950\pi$
$542$	−17.5644	+	10.1408i	−0.754454	+	0.435584i
$543$		0			0
$544$	−1.38841	+	2.40480i	−0.0595276	+	0.103105i
$545$	−5.31296	−	5.18216i	−0.227582	−	0.221979i
$546$		0			0
$547$	8.13044	+	4.69411i	0.347633	+	0.200706i	0.663642	−	0.748050i	$-0.269010\pi$
$547$	8.13044	+	4.69411i	0.347633	+	0.200706i	−0.316010	+	0.948756i	$0.602343\pi$
$548$	17.1599	−	9.90727i	0.733034	−	0.423218i
$549$		0			0
$550$	−20.5228	+	0.511612i	−0.875096	+	0.0218152i
$551$	13.3133			0.567167
$552$		0			0
$553$	−3.53107	+	15.5513i	−0.150156	+	0.661309i
$554$	−5.11858	−	8.86564i	−0.217468	−	0.376665i
$555$		0			0
$556$	−2.84915	−	4.93488i	−0.120831	−	0.209285i
$557$	−18.3702	−	10.6060i	−0.778370	−	0.449392i	0.0574826	−	0.998347i	$-0.481693\pi$
$557$	−18.3702	−	10.6060i	−0.778370	−	0.449392i	−0.835852	+	0.548955i	$0.815026\pi$
$558$		0			0
$559$	−4.87284			−0.206099
$560$	−5.26758	−	2.69307i	−0.222596	−	0.113803i
$561$		0			0
$562$	18.1931	+	10.5038i	0.767429	+	0.443076i
$563$		−	22.5552i		−	0.950588i	−0.879827	−	0.475294i	$-0.842342\pi$
$563$		−	22.5552i		−	0.950588i	0.879827	−	0.475294i	$-0.157658\pi$
$564$		0			0
$565$	−4.79115	−	17.0291i	−0.201565	−	0.716419i
$566$	4.88129			0.205176
$567$		0			0
$568$		−	16.3189i		−	0.684724i
$569$	−9.13134			−0.382806			−0.191403	−	0.981512i	$-0.561304\pi$
$569$	−9.13134			−0.382806			−0.191403	+	0.981512i	$0.561304\pi$
$570$		0			0
$571$	43.9976			1.84124			0.920621	−	0.390457i	$-0.127683\pi$
$571$	43.9976			1.84124			0.920621	+	0.390457i	$0.127683\pi$
$572$	−13.8055	−	7.97058i	−0.577235	−	0.333267i
$573$		0			0
$574$	5.37010	+	17.3401i	0.224144	+	0.723761i
$575$	−15.4487	−	25.2812i	−0.644254	−	1.05430i
$576$		0			0
$577$	16.2964	+	9.40875i	0.678429	+	0.391691i	0.799263	−	0.600981i	$-0.205223\pi$
$577$	16.2964	+	9.40875i	0.678429	+	0.391691i	−0.120834	+	0.992673i	$0.538557\pi$
$578$	−8.04474	+	4.64463i	−0.334617	+	0.193191i
$579$		0			0
$580$	7.55829	+	7.37222i	0.313841	+	0.306115i
$581$	−27.8582	+	30.0919i	−1.15575	+	1.24842i
$582$		0			0
$583$		−	19.9209i		−	0.825039i
$584$	−6.41567	+	11.1123i	−0.265482	+	0.459828i
$585$		0			0
$586$	−2.05377	−	3.55724i	−0.0848405	−	0.146948i
$587$	−13.2631	−	7.65744i	−0.547426	−	0.316056i	0.200657	−	0.979661i	$-0.435692\pi$
$587$	−13.2631	−	7.65744i	−0.547426	−	0.316056i	−0.748083	+	0.663605i	$0.769026\pi$
$588$		0			0
$589$	5.49090	+	9.51051i	0.226248	+	0.391874i
$590$	−27.0454	−	6.88673i	−1.11344	−	0.283522i
$591$		0			0
$592$	−0.356887	+	0.206049i	−0.0146679	+	0.00846854i
$593$	−18.6589	+	10.7727i	−0.766231	+	0.442384i	−0.831528	−	0.555482i	$-0.812534\pi$
$593$	−18.6589	+	10.7727i	−0.766231	+	0.442384i	0.0652975	+	0.997866i	$0.479200\pi$
$594$		0			0
$595$	8.92836	+	13.7899i	0.366027	+	0.565329i
$596$	10.4021	−	18.0169i	0.426085	−	0.738000i
$597$		0			0
$598$		−	23.0062i		−	0.940794i
$599$	37.8675			1.54722			0.773612	−	0.633659i	$-0.218448\pi$
$599$	37.8675			1.54722			0.773612	+	0.633659i	$0.218448\pi$
$600$		0			0
$601$	−16.2700	+	28.1804i	−0.663666	+	1.14950i	0.315979	+	0.948766i	$0.397667\pi$
$601$	−16.2700	+	28.1804i	−0.663666	+	1.14950i	−0.979645	+	0.200737i	$0.935666\pi$
$602$	−2.43670	−	2.25582i	−0.0993124	−	0.0919405i
$603$		0			0
$604$	8.13217	+	14.0853i	0.330893	+	0.573124i
$605$	−9.37691	−	9.14607i	−0.381226	−	0.371840i
$606$		0			0
$607$	28.9715	+	16.7267i	1.17592	+	0.678916i	0.955067	−	0.296391i	$-0.0957833\pi$
$607$	28.9715	+	16.7267i	1.17592	+	0.678916i	0.220851	+	0.975308i	$0.429117\pi$
$608$	−2.44179	+	1.40977i	−0.0990278	+	0.0571737i
$609$		0			0
$610$	−2.35870	−	0.600611i	−0.0955010	−	0.0243180i
$611$	9.91240	+	17.1688i	0.401013	+	0.694574i
$612$		0			0
$613$	−14.1077	−	8.14510i	−0.569806	−	0.328978i	0.187266	−	0.982309i	$-0.440037\pi$
$613$	−14.1077	−	8.14510i	−0.569806	−	0.328978i	−0.757072	+	0.653332i	$0.773371\pi$
$614$	−7.22215			−0.291462
$615$		0			0
$616$	−3.21362	−	10.3768i	−0.129480	−	0.418094i
$617$	−3.39147	+	1.95807i	−0.136536	+	0.0788289i	−0.566712	−	0.823916i	$-0.691785\pi$
$617$	−3.39147	+	1.95807i	−0.136536	+	0.0788289i	0.430176	+	0.902745i	$0.358451\pi$
$618$		0			0
$619$	11.5743	+	20.0474i	0.465212	+	0.805771i	0.999211	−	0.0397140i	$-0.0126447\pi$
$619$	11.5743	+	20.0474i	0.465212	+	0.805771i	−0.533999	+	0.845485i	$0.679311\pi$
$620$	−2.14911	+	8.43991i	−0.0863102	+	0.338955i
$621$		0			0
$622$		−	23.2889i		−	0.933800i
$623$	18.6417	−	5.77321i	0.746866	−	0.231299i
$624$		0			0
$625$	13.5633	+	21.0009i	0.542530	+	0.840036i
$626$	−18.1702			−0.726227
$627$		0			0
$628$			20.2586i			0.808406i
$629$	1.14432			0.0456270
$630$		0			0
$631$	29.9516			1.19235			0.596177	−	0.802853i	$-0.296686\pi$
$631$	29.9516			1.19235			0.596177	+	0.802853i	$0.296686\pi$
$632$			6.02746i			0.239759i
$633$		0			0
$634$	0.679752			0.0269964
$635$	15.9854	+	4.07046i	0.634361	+	0.161531i
$636$		0			0
$637$	−27.0973	+	2.09203i	−1.07363	+	0.0828892i
$638$			19.3870i			0.767538i
$639$		0			0
$640$	−2.16692	−	0.551777i	−0.0856550	−	0.0218109i
$641$	−7.38355	−	12.7887i	−0.291633	−	0.505123i	0.682563	−	0.730827i	$-0.260865\pi$
$641$	−7.38355	−	12.7887i	−0.291633	−	0.505123i	−0.974196	+	0.225704i	$0.927532\pi$
$642$		0			0
$643$	6.76719	−	3.90704i	0.266872	−	0.154078i	−0.360593	−	0.932723i	$-0.617426\pi$
$643$	6.76719	−	3.90704i	0.266872	−	0.154078i	0.627465	+	0.778645i	$0.284092\pi$
$644$	10.6505	−	11.5044i	0.419687	−	0.453337i
$645$		0			0
$646$	7.82936			0.308042
$647$	21.1027	+	12.1837i	0.829634	+	0.478989i	0.853727	−	0.520720i	$-0.174337\pi$
$647$	21.1027	+	12.1837i	0.829634	+	0.478989i	−0.0240933	+	0.999710i	$0.507670\pi$
$648$		0			0
$649$	−25.6225	−	44.3795i	−1.00577	−	1.74205i
$650$	0.483790	+	19.4068i	0.0189758	+	0.761196i
$651$		0			0
$652$	6.81431	−	3.93424i	0.266869	−	0.154077i
$653$	17.7518	+	10.2490i	0.694680	+	0.401074i	0.805363	−	0.592782i	$-0.201970\pi$
$653$	17.7518	+	10.2490i	0.694680	+	0.401074i	−0.110683	+	0.993856i	$0.535304\pi$
$654$		0			0
$655$	19.0859	+	18.6161i	0.745750	+	0.727391i
$656$	3.43052	+	5.94183i	0.133939	+	0.231990i
$657$		0			0
$658$	−2.99132	+	13.1742i	−0.116614	+	0.513583i
$659$	5.19823	−	9.00360i	0.202494	−	0.350731i	−0.746837	−	0.665007i	$-0.768429\pi$
$659$	5.19823	−	9.00360i	0.202494	−	0.350731i	0.949332	+	0.314276i	$0.101762\pi$
$660$		0			0
$661$	−25.7189			−1.00035			−0.500174	−	0.865925i	$-0.666731\pi$
$661$	−25.7189			−1.00035			−0.500174	+	0.865925i	$0.666731\pi$
$662$		−	12.7220i		−	0.494453i
$663$		0			0
$664$	−7.74967	+	13.4228i	−0.300745	+	0.520906i
$665$	0.850138	+	16.6590i	0.0329669	+	0.646006i
$666$		0			0
$667$	−24.2307	+	13.9896i	−0.938217	+	0.541680i
$668$	−18.3747	+	10.6086i	−0.710937	+	0.410460i
$669$		0			0
$670$	−6.91198	+	27.1445i	−0.267033	+	1.04868i
$671$	−2.23461	−	3.87046i	−0.0862662	−	0.149417i
$672$		0			0
$673$	12.4068	+	7.16309i	0.478248	+	0.276117i	0.719686	−	0.694300i	$-0.244286\pi$
$673$	12.4068	+	7.16309i	0.478248	+	0.276117i	−0.241438	+	0.970416i	$0.577619\pi$
$674$	−8.52431	−	14.7645i	−0.328344	−	0.568709i
$675$		0			0
$676$	−1.03712	+	1.79635i	−0.0398894	+	0.0690905i
$677$			0.895442i			0.0344146i	0.999852	+	0.0172073i	$0.00547753\pi$
$677$			0.895442i			0.0344146i	−0.999852	+	0.0172073i	$0.994522\pi$
$678$		0			0
$679$	7.52456	−	8.12789i	0.288766	−	0.311920i
$680$	4.44491	+	4.33549i	0.170455	+	0.166258i
$681$		0			0
$682$	−13.8493	+	7.99589i	−0.530317	+	0.306179i
$683$	17.0207	+	9.82692i	0.651280	+	0.376016i	0.788946	−	0.614462i	$-0.210627\pi$
$683$	17.0207	+	9.82692i	0.651280	+	0.376016i	−0.137667	+	0.990479i	$0.543960\pi$
$684$		0			0
$685$	−11.9998	−	42.6507i	−0.458490	−	1.62960i
$686$	−14.5186	−	11.4982i	−0.554324	−	0.439004i
$687$		0			0
$688$	−1.08691	−	0.627530i	−0.0414382	−	0.0239244i
$689$	−18.8375			−0.717653
$690$		0			0
$691$	19.3254			0.735171			0.367586	−	0.929990i	$-0.380184\pi$
$691$	19.3254			0.735171			0.367586	+	0.929990i	$0.380184\pi$
$692$			4.93214i			0.187492i
$693$		0			0
$694$	25.1265			0.953790
$695$	−12.2656	+	3.45094i	−0.465260	+	0.130901i
$696$		0			0
$697$		−	19.0519i		−	0.721641i
$698$	−8.31944	−	4.80323i	−0.314895	−	0.181805i
$699$		0			0
$700$	−8.74220	+	9.92844i	−0.330424	+	0.375260i
$701$	37.8106			1.42809			0.714044	−	0.700101i	$-0.246862\pi$
$701$	37.8106			1.42809			0.714044	+	0.700101i	$0.246862\pi$
$702$		0			0
$703$	1.00626	+	0.580962i	0.0379517	+	0.0219114i
$704$	−2.05292	−	3.55576i	−0.0773724	−	0.134013i
$705$		0			0
$706$	−13.5283	−	23.4317i	−0.509145	−	0.881865i
$707$	32.0059	−	9.91198i	1.20370	−	0.372778i
$708$		0			0
$709$	43.4760			1.63277			0.816387	−	0.577505i	$-0.195974\pi$
$709$	43.4760			1.63277			0.816387	+	0.577505i	$0.195974\pi$
$710$	−35.3617	−	9.00437i	−1.32710	−	0.337928i
$711$		0			0
$712$	6.38786	−	3.68803i	0.239395	−	0.138215i
$713$	−19.9872	−	11.5396i	−0.748528	−	0.432163i
$714$		0			0
$715$	−24.8891	+	25.5173i	−0.930801	+	0.954294i
$716$	−2.63272	+	4.56000i	−0.0983894	+	0.170415i
$717$		0			0
$718$	7.67373	−	4.43043i	0.286381	−	0.165342i
$719$	−14.5195	−	25.1485i	−0.541486	−	0.937881i	−0.998819	−	0.0485854i	$-0.984529\pi$
$719$	−14.5195	−	25.1485i	−0.541486	−	0.937881i	0.457333	−	0.889295i	$-0.348805\pi$
$720$		0			0
$721$	−7.87200	+	8.50318i	−0.293169	+	0.316675i
$722$	−9.56974	−	5.52509i	−0.356149	−	0.205623i
$723$		0			0
$724$	−20.1029			−0.747117
$725$	20.1455	−	12.3104i	0.748185	−	0.457196i
$726$		0			0
$727$	1.94247	+	1.12149i	0.0720423	+	0.0415936i	0.535588	−	0.844479i	$-0.320090\pi$
$727$	1.94247	+	1.12149i	0.0720423	+	0.0415936i	−0.463546	+	0.886073i	$0.653423\pi$
$728$	−9.81250	+	3.03886i	−0.363675	+	0.112628i
$729$		0			0
$730$	20.5394	+	20.0337i	0.760196	+	0.741481i
$731$	1.74254	+	3.01817i	0.0644501	+	0.111631i
$732$		0			0
$733$	−0.753946	−	0.435291i	−0.0278476	−	0.0160778i	0.486012	−	0.873952i	$-0.338451\pi$
$733$	−0.753946	−	0.435291i	−0.0278476	−	0.0160778i	−0.513859	+	0.857875i	$0.671785\pi$
$734$	−5.38443	−	9.32611i	−0.198743	−	0.344233i
$735$		0			0
$736$	2.96277	−	5.13166i	0.109209	−	0.189156i
$737$	−44.5423	+	25.7165i	−1.64074	+	0.947279i
$738$		0			0
$739$	9.25114	−	16.0234i	0.340309	−	0.589432i	−0.644181	−	0.764873i	$-0.722802\pi$
$739$	9.25114	−	16.0234i	0.340309	−	0.589432i	0.984490	+	0.175441i	$0.0561351\pi$
$740$	0.249569	+	0.887037i	0.00917434	+	0.0326081i
$741$		0			0
$742$	−9.41984	−	8.72062i	−0.345813	−	0.320144i
$743$	−7.22866	+	4.17347i	−0.265194	+	0.153110i	−0.626701	−	0.779259i	$-0.715595\pi$
$743$	−7.22866	+	4.17347i	−0.265194	+	0.153110i	0.361508	+	0.932369i	$0.382262\pi$
$744$		0			0
$745$	−33.3015	−	32.4817i	−1.22007	−	1.19004i
$746$	−2.45843	+	4.25812i	−0.0900095	+	0.155901i
$747$		0			0
$748$			11.4012i			0.416869i
$749$	−2.56009	−	8.26655i	−0.0935436	−	0.302053i
$750$		0			0
$751$	−19.5031	+	33.7804i	−0.711678	+	1.23266i	0.252548	+	0.967584i	$0.418731\pi$
$751$	−19.5031	+	33.7804i	−0.711678	+	1.23266i	−0.964227	+	0.265079i	$0.914602\pi$
$752$			5.10612i			0.186201i
$753$		0			0
$754$	18.3327			0.667637
$755$	35.0089	−	9.84980i	1.27410	−	0.358471i
$756$		0			0
$757$			37.6562i			1.36864i	0.729182	+	0.684320i	$0.239901\pi$
$757$			37.6562i			1.36864i	−0.729182	+	0.684320i	$0.760099\pi$
$758$		−	36.3873i		−	1.32164i
$759$		0			0
$760$	1.70754	+	6.06905i	0.0619388	+	0.220148i
$761$	18.1162	−	31.3783i	0.656714	−	1.13746i	−0.324748	−	0.945801i	$-0.605279\pi$
$761$	18.1162	−	31.3783i	0.656714	−	1.13746i	0.981461	−	0.191661i	$-0.0613873\pi$
$762$		0			0
$763$	−6.44404	−	5.96571i	−0.233290	−	0.215973i
$764$	−2.99287			−0.108278
$765$		0			0
$766$	−4.68178	+	8.10908i	−0.169160	+	0.292993i
$767$	−41.9661	+	24.2291i	−1.51531	+	0.874863i
$768$		0			0
$769$	6.17687	+	10.6986i	0.222744	+	0.385803i	0.955640	−	0.294537i	$-0.0951654\pi$
$769$	6.17687	+	10.6986i	0.222744	+	0.385803i	−0.732897	+	0.680340i	$0.761832\pi$
$770$	−24.2589	+	1.23798i	−0.874231	+	0.0446137i
$771$		0			0
$772$		−	21.4412i		−	0.771687i
$773$	37.1712	+	21.4608i	1.33695	+	0.771891i	0.986355	−	0.164634i	$-0.0526443\pi$
$773$	37.1712	+	21.4608i	1.33695	+	0.771891i	0.350600	+	0.936525i	$0.385978\pi$
$774$		0			0
$775$	17.1028	+	9.31389i	0.614350	+	0.334565i
$776$	2.09320	−	3.62553i	0.0751415	−	0.130149i
$777$		0			0
$778$	−1.77411	+	1.02428i	−0.0636049	+	0.0367223i
$779$	9.67249	−	16.7532i	0.346553	−	0.600247i
$780$		0			0
$781$	−33.5013	−	58.0260i	−1.19877	−	2.07633i
$782$	−14.2497	+	8.22707i	−0.509568	+	0.294199i
$783$		0			0
$784$	−6.31361	−	3.02298i	−0.225486	−	0.107963i
$785$	43.8988	+	11.1782i	1.56681	+	0.398968i
$786$		0			0
$787$			32.1303i			1.14532i	0.819792	+	0.572662i	$0.194089\pi$
$787$			32.1303i			1.14532i	−0.819792	+	0.572662i	$0.805911\pi$
$788$			3.13660i			0.111737i
$789$		0			0
$790$	13.0610	+	3.32581i	0.464690	+	0.118327i
$791$	−6.19215	−	19.9945i	−0.220167	−	0.710922i
$792$		0			0
$793$	−3.65998	+	2.11309i	−0.129970	+	0.0750380i
$794$	14.5284	+	25.1640i	0.515595	+	0.893037i
$795$		0			0
$796$	7.45046	−	12.9046i	0.264074	−	0.457390i
$797$	31.8223	−	18.3726i	1.12720	−	0.650791i	0.183973	−	0.982931i	$-0.441104\pi$
$797$	31.8223	−	18.3726i	1.12720	−	0.650791i	0.943230	+	0.332140i	$0.107771\pi$
$798$		0			0
$799$	7.08939	−	12.2792i	0.250805	−	0.434406i
$800$	−2.39131	+	4.39109i	−0.0845456	+	0.155248i
$801$		0			0
$802$	17.3213	+	10.0005i	0.611637	+	0.353129i
$803$			52.6834i			1.85916i
$804$		0			0
$805$	−19.0525	−	29.4265i	−0.671511	−	1.03715i
$806$	7.56106	+	13.0961i	0.266327	+	0.461292i
$807$		0			0
$808$	10.9673	−	6.33196i	0.385827	−	0.222757i
$809$	−1.13309	+	1.96256i	−0.0398372	+	0.0690001i	−0.885257	−	0.465103i	$-0.846017\pi$
$809$	−1.13309	+	1.96256i	−0.0398372	+	0.0690001i	0.845419	+	0.534103i	$0.179351\pi$
$810$		0			0
$811$	27.0434			0.949622			0.474811	−	0.880088i	$-0.342516\pi$
$811$	27.0434			0.949622			0.474811	+	0.880088i	$0.342516\pi$
$812$	9.16738	+	8.48690i	0.321712	+	0.297832i
$813$		0			0
$814$	−0.846003	+	1.46532i	−0.0296524	+	0.0513594i
$815$	−4.76521	−	16.9369i	−0.166918	−	0.593273i
$816$		0			0
$817$			3.53869i			0.123803i
$818$			21.0715i			0.736747i
$819$		0			0
$820$	14.7684	−	4.15509i	0.515733	−	0.145102i
$821$	−10.1500			−0.354238			−0.177119	−	0.984189i	$-0.556678\pi$
$821$	−10.1500			−0.354238			−0.177119	+	0.984189i	$0.556678\pi$
$822$		0			0
$823$		−	8.13372i		−	0.283524i	−0.989901	−	0.141762i	$-0.954723\pi$
$823$		−	8.13372i		−	0.283524i	0.989901	−	0.141762i	$-0.0452767\pi$
$824$	−2.18985	+	3.79293i	−0.0762871	+	0.132133i
$825$		0			0
$826$	−32.2020	−	7.31176i	−1.12045	−	0.254409i
$827$		−	2.64164i		−	0.0918589i	−0.998945	−	0.0459294i	$-0.985375\pi$
$827$		−	2.64164i		−	0.0918589i	0.998945	−	0.0459294i	$-0.0146249\pi$
$828$		0			0
$829$	14.6215	−	25.3252i	0.507827	−	0.879582i	−0.492132	−	0.870521i	$-0.663782\pi$
$829$	14.6215	−	25.3252i	0.507827	−	0.879582i	0.999959	−	0.00906143i	$-0.00288438\pi$
$830$	24.8101	+	24.1993i	0.861171	+	0.839970i
$831$		0			0
$832$	−3.36239	+	1.94128i	−0.116570	+	0.0673017i
$833$	10.9858	+	16.0355i	0.380636	+	0.555598i
$834$		0			0
$835$	12.8493	+	45.6700i	0.444669	+	1.58048i
$836$	−5.78829	+	10.0256i	−0.200192	+	0.346743i
$837$		0			0
$838$	18.8016	−	10.8551i	0.649489	−	0.374983i
$839$	3.93007	−	6.80707i	0.135681	−	0.235006i	−0.790176	−	0.612879i	$-0.790011\pi$
$839$	3.93007	−	6.80707i	0.135681	−	0.235006i	0.925857	+	0.377873i	$0.123344\pi$
$840$		0			0
$841$	3.35227	+	5.80630i	0.115595	+	0.200217i
$842$	17.9301	+	10.3520i	0.617913	+	0.356752i
$843$		0			0
$844$	−7.20990	−	12.4879i	−0.248175	−	0.429852i
$845$	3.32029	+	3.23855i	0.114222	+	0.111410i
$846$		0			0
$847$	−11.3732	−	10.5290i	−0.390787	−	0.361779i
$848$	−4.20182	−	2.42592i	−0.144291	−	0.0833064i
$849$		0			0
$850$	11.8472	−	7.23955i	0.406357	−	0.248314i
$851$	−2.44189			−0.0837071
$852$		0			0
$853$	−6.09946	−	3.52152i	−0.208841	−	0.120575i	0.391931	−	0.919994i	$-0.371807\pi$
$853$	−6.09946	−	3.52152i	−0.208841	−	0.120575i	−0.600773	+	0.799420i	$0.705140\pi$
$854$	−2.80842	−	0.637678i	−0.0961023	−	0.0218209i
$855$		0			0
$856$	−1.63543	−	2.83265i	−0.0558979	−	0.0968180i
$857$	−2.71486	+	1.56742i	−0.0927377	+	0.0535422i	−0.545652	−	0.838012i	$-0.683718\pi$
$857$	−2.71486	+	1.56742i	−0.0927377	+	0.0535422i	0.452914	+	0.891554i	$0.350384\pi$
$858$		0			0
$859$	−15.3632	+	26.6099i	−0.524187	+	0.907918i	0.475417	+	0.879761i	$0.342297\pi$
$859$	−15.3632	+	26.6099i	−0.524187	+	0.907918i	−0.999604	+	0.0281573i	$0.991036\pi$
$860$	−1.95954	+	2.00900i	−0.0668198	+	0.0685063i
$861$		0			0
$862$	−2.00583	−	1.15807i	−0.0683188	−	0.0394439i
$863$	−26.0574	+	15.0443i	−0.887004	+	0.512112i	−0.872962	−	0.487789i	$-0.837804\pi$
$863$	−26.0574	+	15.0443i	−0.887004	+	0.512112i	−0.0140430	+	0.999901i	$0.504470\pi$
$864$		0			0
$865$	10.6876	+	2.72144i	0.363388	+	0.0925317i
$866$	22.2752			0.756941
$867$		0			0
$868$	−2.28174	+	10.0491i	−0.0774474	+	0.341089i
$869$	12.3739	+	21.4322i	0.419756	+	0.727038i
$870$		0			0
$871$	24.3180	+	42.1200i	0.823983	+	1.42718i
$872$	−2.87443	−	1.65955i	−0.0973405	−	0.0561996i
$873$		0			0
$874$	−16.7073			−0.565132
$875$	16.6904	+	24.4219i	0.564238	+	0.825612i
$876$		0			0
$877$	14.2261	+	8.21347i	0.480383	+	0.277349i	0.720576	−	0.693376i	$-0.243877\pi$
$877$	14.2261	+	8.21347i	0.480383	+	0.277349i	−0.240193	+	0.970725i	$0.577211\pi$
$878$		−	20.7548i		−	0.700442i
$879$		0			0
$880$	−8.83781	+	2.48653i	−0.297922	+	0.0838209i
$881$	33.4780			1.12790			0.563951	−	0.825808i	$-0.309281\pi$
$881$	33.4780			1.12790			0.563951	+	0.825808i	$0.309281\pi$
$882$		0			0
$883$			44.7104i			1.50462i	0.658807	+	0.752312i	$0.271061\pi$
$883$			44.7104i			1.50462i	−0.658807	+	0.752312i	$0.728939\pi$
$884$	10.7812			0.362610
$885$		0			0
$886$	−18.7632			−0.630362
$887$	−20.4666	−	11.8164i	−0.687201	−	0.396755i	0.115362	−	0.993324i	$-0.463197\pi$
$887$	−20.4666	−	11.8164i	−0.687201	−	0.396755i	−0.802562	+	0.596568i	$0.796531\pi$
$888$		0			0
$889$	19.0333	+	4.32168i	0.638355	+	0.144944i
$890$	−4.46700	−	15.8770i	−0.149734	−	0.532197i
$891$		0			0
$892$	−15.8455	−	9.14843i	−0.530548	−	0.306312i
$893$	12.4681	−	7.19846i	0.417229	−	0.240887i
$894$		0			0
$895$	8.42849	+	8.22100i	0.281733	+	0.274798i
$896$	−2.58008	−	0.585831i	−0.0861944	−	0.0195712i
$897$		0			0
$898$			4.33662i			0.144715i
$899$	9.19545	−	15.9270i	0.306685	−	0.531195i
$900$		0			0
$901$	6.73635	+	11.6677i	0.224420	+	0.388707i
$902$	24.3962	+	14.0852i	0.812305	+	0.468985i
$903$		0			0
$904$	−3.95566	−	6.85140i	−0.131563	−	0.227874i
$905$	−11.0923	+	43.5613i	−0.368720	+	1.44803i
$906$		0			0
$907$	44.1604	−	25.4960i	1.46632	−	0.846582i	0.467033	−	0.884240i	$-0.345323\pi$
$907$	44.1604	−	25.4960i	1.46632	−	0.846582i	0.999291	+	0.0376579i	$0.0119897\pi$
$908$	7.81588	−	4.51250i	0.259379	−	0.149753i
$909$		0			0
$910$	1.17065	+	22.9397i	0.0388068	+	0.760443i
$911$	−23.6679	+	40.9939i	−0.784151	+	1.35819i	0.145354	+	0.989380i	$0.453568\pi$
$911$	−23.6679	+	40.9939i	−0.784151	+	1.35819i	−0.929505	+	0.368810i	$0.879765\pi$
$912$		0			0
$913$			63.6378i			2.10610i
$914$	−22.7169			−0.751407
$915$		0			0
$916$	8.59266	−	14.8829i	0.283910	−	0.491746i
$917$	23.1492	+	21.4308i	0.764453	+	0.707709i
$918$		0			0
$919$	−25.2990	−	43.8191i	−0.834536	−	1.44546i	−0.894408	−	0.447253i	$-0.852402\pi$
$919$	−25.2990	−	43.8191i	−0.834536	−	1.44546i	0.0598717	−	0.998206i	$-0.480931\pi$
$920$	−9.48512	−	9.25161i	−0.312715	−	0.305017i
$921$		0			0
$922$	14.5778	+	8.41648i	0.480093	+	0.277182i
$923$	−54.8704	+	31.6795i	−1.80608	+	1.04274i
$924$		0			0
$925$	2.05985	−	0.0513497i	0.0677273	−	0.00168837i
$926$	13.8817	+	24.0438i	0.456181	+	0.790129i
$927$		0			0
$928$	4.08921	+	2.36090i	0.134235	+	0.0775005i
$929$	1.06340			0.0348891			0.0174446	−	0.999848i	$-0.494447\pi$
$929$	1.06340			0.0348891			0.0174446	+	0.999848i	$0.494447\pi$
$930$		0			0
$931$	1.51925	+	19.6782i	0.0497913	+	0.644928i
$932$	−4.18657	+	2.41712i	−0.137136	+	0.0791754i
$933$		0			0
$934$	−17.2161	−	29.8191i	−0.563327	−	0.975711i
$935$	24.7055	+	6.29091i	0.807955	+	0.205735i
$936$		0			0
$937$		−	39.6086i		−	1.29396i	−0.762508	−	0.646978i	$-0.776032\pi$
$937$		−	39.6086i		−	1.29396i	0.762508	−	0.646978i	$-0.223968\pi$
$938$	−7.33857	+	32.3201i	−0.239613	+	1.05529i
$939$		0			0
$940$	11.0645	+	2.81744i	0.360886	+	0.0918947i
$941$	2.41836			0.0788363			0.0394182	−	0.999223i	$-0.487450\pi$
$941$	2.41836			0.0788363			0.0394182	+	0.999223i	$0.487450\pi$
$942$		0			0
$943$			40.6553i			1.32392i
$944$	−12.4810			−0.406223
$945$		0			0
$946$	−5.15308			−0.167541
$947$			35.4602i			1.15230i	0.817343	+	0.576151i	$0.195446\pi$
$947$			35.4602i			1.15230i	−0.817343	+	0.576151i	$0.804554\pi$
$948$		0			0
$949$	49.8184			1.61717
$950$	14.0933	−	0.351332i	0.457248	−	0.0113987i
$951$		0			0
$952$	5.39119	+	4.99101i	0.174730	+	0.161760i
$953$		−	50.6918i		−	1.64207i	−0.570878	−	0.821035i	$-0.693397\pi$
$953$		−	50.6918i		−	1.64207i	0.570878	−	0.821035i	$-0.306603\pi$
$954$		0			0
$955$	−1.65140	+	6.48531i	−0.0534379	+	0.209860i
$956$	−8.08215	−	13.9987i	−0.261395	−	0.452750i
$957$		0			0
$958$	−9.77485	+	5.64351i	−0.315811	+	0.182334i
$959$	−15.5087	−	50.0778i	−0.500803	−	1.61710i
$960$		0			0
$961$	−15.8299			−0.510641
$962$	1.38563	+	0.799995i	0.0446746	+	0.0257929i
$963$		0			0
$964$	−4.83873	−	8.38092i	−0.155845	−	0.269931i
$965$	−46.4614	−	11.8308i	−1.49565	−	0.380846i
$966$		0			0
$967$	−18.4021	+	10.6245i	−0.591772	+	0.341659i	−0.765798	−	0.643082i	$-0.777656\pi$
$967$	−18.4021	+	10.6245i	−0.591772	+	0.341659i	0.174026	+	0.984741i	$0.444322\pi$
$968$	−5.07312	−	2.92897i	−0.163056	−	0.0941406i
$969$		0			0
$970$	−6.70125	−	6.53628i	−0.215164	−	0.209867i
$971$	3.26795	+	5.66026i	0.104874	+	0.181646i	0.913687	−	0.406420i	$-0.133223\pi$
$971$	3.26795	+	5.66026i	0.104874	+	0.181646i	−0.808813	+	0.588066i	$0.799890\pi$
$972$		0			0
$973$	−14.4015	+	4.46003i	−0.461691	+	0.142982i
$974$	−12.2804	+	21.2703i	−0.393489	+	0.681544i
$975$		0			0
$976$	−1.08850			−0.0348421
$977$			33.2788i			1.06468i	0.846529	+	0.532342i	$0.178688\pi$
$977$			33.2788i			1.06468i	−0.846529	+	0.532342i	$0.821312\pi$
$978$		0			0
$979$	15.1425	−	26.2275i	0.483956	−	0.838236i
$980$	−10.0342	+	12.0131i	−0.320532	+	0.383743i
$981$		0			0
$982$	15.7331	−	9.08350i	0.502063	−	0.289866i
$983$	−20.3932	+	11.7740i	−0.650441	+	0.375532i	−0.788625	−	0.614874i	$-0.789207\pi$
$983$	−20.3932	+	11.7740i	−0.650441	+	0.375532i	0.138184	+	0.990407i	$0.455873\pi$
$984$		0			0
$985$	6.79677	+	1.73070i	0.216563	+	0.0551448i
$986$	−6.55581	−	11.3550i	−0.208779	−	0.361617i
$987$		0			0
$988$	9.48041	+	5.47352i	0.301612	+	0.174136i
$989$	−3.71845	−	6.44055i	−0.118240	−	0.204797i
$990$		0			0
$991$	−17.3486	+	30.0487i	−0.551097	+	0.954527i	0.447099	+	0.894484i	$0.352457\pi$
$991$	−17.3486	+	30.0487i	−0.551097	+	0.954527i	−0.998196	+	0.0600429i	$0.980876\pi$
$992$			3.89489i			0.123663i
$993$		0			0
$994$	−42.1039	−	9.56009i	−1.33546	−	0.303228i
$995$	−23.8522	−	23.2650i	−0.756165	−	0.737550i
$996$		0			0
$997$	−42.7308	+	24.6707i	−1.35330	+	0.781328i	−0.988710	−	0.149841i	$-0.952124\pi$
$997$	−42.7308	+	24.6707i	−1.35330	+	0.781328i	−0.364589	+	0.931168i	$0.618791\pi$
$998$	−9.85866	−	5.69190i	−0.312071	−	0.180174i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.ba.a.1369.46		96
3.2	odd	2		630.2.ba.a.529.39	yes	96
5.4	even	2	inner	1890.2.ba.a.1369.7		96
7.2	even	3		1890.2.bq.a.289.18		96
9.4	even	3		1890.2.bq.a.739.47		96
9.5	odd	6		630.2.bq.a.319.6	yes	96
15.14	odd	2		630.2.ba.a.529.10	yes	96
21.2	odd	6		630.2.bq.a.79.43	yes	96
35.9	even	6		1890.2.bq.a.289.47		96
45.4	even	6		1890.2.bq.a.739.18		96
45.14	odd	6		630.2.bq.a.319.43	yes	96
63.23	odd	6		630.2.ba.a.499.34	yes	96
63.58	even	3	inner	1890.2.ba.a.1549.7		96
105.44	odd	6		630.2.bq.a.79.6	yes	96
315.149	odd	6		630.2.ba.a.499.15	✓	96
315.184	even	6	inner	1890.2.ba.a.1549.46		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ba.a.499.15	✓	96	315.149	odd	6
630.2.ba.a.499.34	yes	96	63.23	odd	6
630.2.ba.a.529.10	yes	96	15.14	odd	2
630.2.ba.a.529.39	yes	96	3.2	odd	2
630.2.bq.a.79.6	yes	96	105.44	odd	6
630.2.bq.a.79.43	yes	96	21.2	odd	6
630.2.bq.a.319.6	yes	96	9.5	odd	6
630.2.bq.a.319.43	yes	96	45.14	odd	6
1890.2.ba.a.1369.7		96	5.4	even	2	inner
1890.2.ba.a.1369.46		96	1.1	even	1	trivial
1890.2.ba.a.1549.7		96	63.58	even	3	inner
1890.2.ba.a.1549.46		96	315.184	even	6	inner
1890.2.bq.a.289.18		96	7.2	even	3
1890.2.bq.a.289.47		96	35.9	even	6
1890.2.bq.a.739.18		96	45.4	even	6
1890.2.bq.a.739.47		96	9.4	even	3

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.ba (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-0.551777 + 2.16692i) q^{5} +(-0.585831 + 2.58008i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-0.551777 + 2.16692i) q^{5} +(-0.585831 + 2.58008i) q^{7} +1.00000i q^{8} +(2.16692 + 0.551777i) q^{10} +(2.05292 + 3.55576i) q^{11} +(3.36239 - 1.94128i) q^{13} +(2.58008 + 0.585831i) q^{14} +1.00000 q^{16} +(-2.40480 - 1.38841i) q^{17} +(-1.40977 - 2.44179i) q^{19} +(0.551777 - 2.16692i) q^{20} +(3.55576 - 2.05292i) q^{22} +(5.13166 + 2.96277i) q^{23} +(-4.39109 - 2.39131i) q^{25} +(-1.94128 - 3.36239i) q^{26} +(0.585831 - 2.58008i) q^{28} +(-2.36090 + 4.08921i) q^{29} -3.89489 q^{31} -1.00000i q^{32} +(-1.38841 + 2.40480i) q^{34} +(-5.26758 - 2.69307i) q^{35} +(-0.356887 + 0.206049i) q^{37} +(-2.44179 + 1.40977i) q^{38} +(-2.16692 - 0.551777i) q^{40} +(3.43052 + 5.94183i) q^{41} +(-1.08691 - 0.627530i) q^{43} +(-2.05292 - 3.55576i) q^{44} +(2.96277 - 5.13166i) q^{46} +5.10612i q^{47} +(-6.31361 - 3.02298i) q^{49} +(-2.39131 + 4.39109i) q^{50} +(-3.36239 + 1.94128i) q^{52} +(-4.20182 - 2.42592i) q^{53} +(-8.83781 + 2.48653i) q^{55} +(-2.58008 - 0.585831i) q^{56} +(4.08921 + 2.36090i) q^{58} -12.4810 q^{59} -1.08850 q^{61} +3.89489i q^{62} -1.00000 q^{64} +(2.35131 + 8.35719i) q^{65} +12.5268i q^{67} +(2.40480 + 1.38841i) q^{68} +(-2.69307 + 5.26758i) q^{70} -16.3189 q^{71} +(11.1123 + 6.41567i) q^{73} +(0.206049 + 0.356887i) q^{74} +(1.40977 + 2.44179i) q^{76} +(-10.3768 + 3.21362i) q^{77} +6.02746 q^{79} +(-0.551777 + 2.16692i) q^{80} +(5.94183 - 3.43052i) q^{82} +(13.4228 + 7.74967i) q^{83} +(4.33549 - 4.44491i) q^{85} +(-0.627530 + 1.08691i) q^{86} +(-3.55576 + 2.05292i) q^{88} +(-3.68803 - 6.38786i) q^{89} +(3.03886 + 9.81250i) q^{91} +(-5.13166 - 2.96277i) q^{92} +5.10612 q^{94} +(6.06905 - 1.70754i) q^{95} +(-3.62553 - 2.09320i) q^{97} +(-3.02298 + 6.31361i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 96 q^{4}+O(q^{10}) \) 96 * q - 96 * q^4	\( 96 q - 96 q^{4} - 4 q^{11} + 2 q^{14} + 96 q^{16} - 24 q^{26} - 10 q^{29} + 34 q^{35} - 30 q^{41} + 4 q^{44} - 6 q^{46} - 6 q^{49} + 12 q^{50} + 12 q^{55} - 2 q^{56} - 48 q^{59} + 12 q^{61} - 96 q^{64} + 36 q^{65} + 6 q^{70} + 32 q^{71} - 4 q^{86} + 66 q^{89} + 24 q^{94} + 60 q^{95}+O(q^{100}) \) 96 * q - 96 * q^4 - 4 * q^11 + 2 * q^14 + 96 * q^16 - 24 * q^26 - 10 * q^29 + 34 * q^35 - 30 * q^41 + 4 * q^44 - 6 * q^46 - 6 * q^49 + 12 * q^50 + 12 * q^55 - 2 * q^56 - 48 * q^59 + 12 * q^61 - 96 * q^64 + 36 * q^65 + 6 * q^70 + 32 * q^71 - 4 * q^86 + 66 * q^89 + 24 * q^94 + 60 * q^95

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