LMFDB - Embedded newform 2100.2.bo.i.1949.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1349,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2100.1349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.bo (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:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1949.1
Character	$\chi$	$=$	2100.1949
Dual form			2100.2.bo.i.1349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68420 - 0.404332i) q^{3} +(2.10133 + 1.60761i) q^{7} +(2.67303 + 1.36195i) q^{9} +O(q^{10})$	\(q+(-1.68420 - 0.404332i) q^{3} +(2.10133 + 1.60761i) q^{7} +(2.67303 + 1.36195i) q^{9} +(-2.05856 - 1.18851i) q^{11} -0.748179 q^{13} +(-6.53402 - 3.77242i) q^{17} +(6.11872 - 3.53264i) q^{19} +(-2.88904 - 3.55717i) q^{21} +(1.63394 + 2.83006i) q^{23} +(-3.95123 - 3.37458i) q^{27} +2.48504i q^{29} +(-6.84372 - 3.95123i) q^{31} +(2.98646 + 2.83402i) q^{33} +(3.73959 - 2.15905i) q^{37} +(1.26008 + 0.302513i) q^{39} +10.8663 q^{41} +3.03200i q^{43} +(-5.59088 + 3.22790i) q^{47} +(1.83117 + 6.75624i) q^{49} +(9.47926 + 8.99541i) q^{51} +(-0.0540095 + 0.0935472i) q^{53} +(-11.7335 + 3.47567i) q^{57} +(6.60248 - 11.4358i) q^{59} +(6.90005 - 3.98375i) q^{61} +(3.42743 + 7.15910i) q^{63} +(-5.09859 - 2.94367i) q^{67} +(-1.60758 - 5.42703i) q^{69} -13.9589i q^{71} +(-0.780701 + 1.35221i) q^{73} +(-2.41505 - 5.80681i) q^{77} +(1.27644 + 2.21086i) q^{79} +(5.29018 + 7.28107i) q^{81} +0.901948i q^{83} +(1.00478 - 4.18529i) q^{87} +(2.43223 + 4.21274i) q^{89} +(-1.57217 - 1.20278i) q^{91} +(9.92856 + 9.42178i) q^{93} +12.9183 q^{97} +(-3.88390 - 5.98057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 18 q^{9}+O(q^{10}) $ 32 * q + 18 * q^9	$ 32 q + 18 q^{9} + 36 q^{19} - 22 q^{21} - 36 q^{31} - 24 q^{39} + 36 q^{49} - 2 q^{51} + 72 q^{61} + 14 q^{81} + 40 q^{91} + 60 q^{99}+O(q^{100}) $ 32 * q + 18 * q^9 + 36 * q^19 - 22 * q^21 - 36 * q^31 - 24 * q^39 + 36 * q^49 - 2 * q^51 + 72 * q^61 + 14 * q^81 + 40 * q^91 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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			0
$2$		0			0
$3$	−1.68420	−	0.404332i	−0.972371	−	0.233441i
$3$	−1.68420	−	0.404332i	−0.972371	−	0.233441i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.10133	+	1.60761i	0.794228	+	0.607620i
$7$	2.10133	+	1.60761i	0.794228	+	0.607620i
$8$		0			0
$9$	2.67303	+	1.36195i	0.891010	+	0.453983i
$10$		0			0
$11$	−2.05856	−	1.18851i	−0.620679	−	0.358349i	0.156455	−	0.987685i	$-0.449994\pi$
$11$	−2.05856	−	1.18851i	−0.620679	−	0.358349i	−0.777133	+	0.629336i	$0.783327\pi$
$12$		0			0
$13$	−0.748179			−0.207508			−0.103754	−	0.994603i	$-0.533085\pi$
$13$	−0.748179			−0.207508			−0.103754	+	0.994603i	$0.533085\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.53402	−	3.77242i	−1.58473	−	0.914946i	−0.994155	−	0.107966i	$-0.965566\pi$
$17$	−6.53402	−	3.77242i	−1.58473	−	0.914946i	−0.590578	−	0.806980i	$-0.701100\pi$
$18$		0			0
$19$	6.11872	−	3.53264i	1.40373	−	0.810444i	0.408957	−	0.912553i	$-0.365892\pi$
$19$	6.11872	−	3.53264i	1.40373	−	0.810444i	0.994773	+	0.102109i	$0.0325591\pi$
$20$		0			0
$21$	−2.88904	−	3.55717i	−0.630440	−	0.776238i
$22$		0			0
$23$	1.63394	+	2.83006i	0.340699	+	0.590109i	0.984563	−	0.175032i	$-0.0560028\pi$
$23$	1.63394	+	2.83006i	0.340699	+	0.590109i	−0.643863	+	0.765141i	$0.722669\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.95123	−	3.37458i	−0.760414	−	0.649439i
$28$		0			0
$29$			2.48504i			0.461460i	0.973018	+	0.230730i	$0.0741114\pi$
$29$			2.48504i			0.461460i	−0.973018	+	0.230730i	$0.925889\pi$
$30$		0			0
$31$	−6.84372	−	3.95123i	−1.22917	−	0.709661i	−0.262313	−	0.964983i	$-0.584485\pi$
$31$	−6.84372	−	3.95123i	−1.22917	−	0.709661i	−0.966856	+	0.255322i	$0.917819\pi$
$32$		0			0
$33$	2.98646	+	2.83402i	0.519876	+	0.493340i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.73959	−	2.15905i	0.614784	−	0.354946i	−0.160051	−	0.987109i	$-0.551166\pi$
$37$	3.73959	−	2.15905i	0.614784	−	0.354946i	0.774835	+	0.632163i	$0.217833\pi$
$38$		0			0
$39$	1.26008	+	0.302513i	0.201774	+	0.0484409i
$40$		0			0
$41$	10.8663			1.69703			0.848514	−	0.529173i	$-0.177498\pi$
$41$	10.8663			1.69703			0.848514	+	0.529173i	$0.177498\pi$
$42$		0			0
$43$			3.03200i			0.462375i	0.972909	+	0.231188i	$0.0742611\pi$
$43$			3.03200i			0.462375i	−0.972909	+	0.231188i	$0.925739\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.59088	+	3.22790i	−0.815514	+	0.470837i	−0.848867	−	0.528606i	$-0.822715\pi$
$47$	−5.59088	+	3.22790i	−0.815514	+	0.470837i	0.0333530	+	0.999444i	$0.489381\pi$
$48$		0			0
$49$	1.83117	+	6.75624i	0.261596	+	0.965178i
$50$		0			0
$51$	9.47926	+	8.99541i	1.32736	+	1.25961i
$52$		0			0
$53$	−0.0540095	+	0.0935472i	−0.00741878	+	0.0128497i	−0.869711	−	0.493561i	$-0.835695\pi$
$53$	−0.0540095	+	0.0935472i	−0.00741878	+	0.0128497i	0.862292	+	0.506411i	$0.169028\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−11.7335	+	3.47567i	−1.55414	+	0.460363i
$58$		0			0
$59$	6.60248	−	11.4358i	0.859570	−	1.48882i	−0.0127699	−	0.999918i	$-0.504065\pi$
$59$	6.60248	−	11.4358i	0.859570	−	1.48882i	0.872340	−	0.488900i	$-0.162602\pi$
$60$		0			0
$61$	6.90005	−	3.98375i	0.883461	−	0.510067i	0.0116632	−	0.999932i	$-0.496287\pi$
$61$	6.90005	−	3.98375i	0.883461	−	0.510067i	0.871798	+	0.489865i	$0.162954\pi$
$62$		0			0
$63$	3.42743	+	7.15910i	0.431816	+	0.901962i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−5.09859	−	2.94367i	−0.622892	−	0.359627i	0.155102	−	0.987898i	$-0.450429\pi$
$67$	−5.09859	−	2.94367i	−0.622892	−	0.359627i	−0.777994	+	0.628272i	$0.783763\pi$
$68$		0			0
$69$	−1.60758	−	5.42703i	−0.193530	−	0.653338i
$70$		0			0
$71$		−	13.9589i		−	1.65662i	−0.560273	−	0.828308i	$-0.689304\pi$
$71$		−	13.9589i		−	1.65662i	0.560273	−	0.828308i	$-0.310696\pi$
$72$		0			0
$73$	−0.780701	+	1.35221i	−0.0913742	+	0.158265i	−0.908090	−	0.418776i	$-0.862459\pi$
$73$	−0.780701	+	1.35221i	−0.0913742	+	0.158265i	0.816715	+	0.577041i	$0.195793\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.41505	−	5.80681i	−0.275220	−	0.661747i
$78$		0			0
$79$	1.27644	+	2.21086i	0.143611	+	0.248742i	0.928854	−	0.370446i	$-0.120795\pi$
$79$	1.27644	+	2.21086i	0.143611	+	0.248742i	−0.785243	+	0.619188i	$0.787462\pi$
$80$		0			0
$81$	5.29018	+	7.28107i	0.587798	+	0.809008i
$82$		0			0
$83$			0.901948i			0.0990016i	0.998774	+	0.0495008i	$0.0157630\pi$
$83$			0.901948i			0.0990016i	−0.998774	+	0.0495008i	$0.984237\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.00478	−	4.18529i	0.107724	−	0.448710i
$88$		0			0
$89$	2.43223	+	4.21274i	0.257816	+	0.446550i	0.965656	−	0.259822i	$-0.0836640\pi$
$89$	2.43223	+	4.21274i	0.257816	+	0.446550i	−0.707841	+	0.706372i	$0.750331\pi$
$90$		0			0
$91$	−1.57217	−	1.20278i	−0.164808	−	0.126086i
$92$		0			0
$93$	9.92856	+	9.42178i	1.02954	+	0.976993i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	12.9183			1.31166			0.655829	−	0.754909i	$-0.272319\pi$
$97$	12.9183			1.31166			0.655829	+	0.754909i	$0.272319\pi$
$98$		0			0
$99$	−3.88390	−	5.98057i	−0.390346	−	0.601070i
$100$		0			0
$101$	1.56718	−	2.71443i	0.155940	−	0.270096i	−0.777461	−	0.628931i	$-0.783493\pi$
$101$	1.56718	−	2.71443i	0.155940	−	0.270096i	0.933401	+	0.358835i	$0.116826\pi$
$102$		0			0
$103$	−7.89048	−	13.6667i	−0.777472	−	1.34662i	−0.933394	−	0.358852i	$-0.883168\pi$
$103$	−7.89048	−	13.6667i	−0.777472	−	1.34662i	0.155922	−	0.987769i	$-0.450165\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.92544	−	11.9952i	−0.669508	−	1.15962i	−0.978042	−	0.208408i	$-0.933172\pi$
$107$	−6.92544	−	11.9952i	−0.669508	−	1.15962i	0.308534	−	0.951213i	$-0.400161\pi$
$108$		0			0
$109$	−0.863166	+	1.49505i	−0.0826763	+	0.143200i	−0.904399	−	0.426688i	$-0.859680\pi$
$109$	−0.863166	+	1.49505i	−0.0826763	+	0.143200i	0.821722	+	0.569888i	$0.193013\pi$
$110$		0			0
$111$	−7.17117	+	2.12423i	−0.680657	+	0.201623i
$112$		0			0
$113$	4.93811			0.464539			0.232269	−	0.972652i	$-0.425385\pi$
$113$	4.93811			0.464539			0.232269	+	0.972652i	$0.425385\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.99991	−	1.01898i	−0.184891	−	0.0942050i
$118$		0			0
$119$	−7.66554	−	18.4313i	−0.702699	−	1.68959i
$120$		0			0
$121$	−2.67489	−	4.63305i	−0.243172	−	0.421186i
$122$		0			0
$123$	−18.3009	−	4.39359i	−1.65014	−	0.396157i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	15.9416i		−	1.41458i	−0.706921	−	0.707292i	$-0.749917\pi$
$127$		−	15.9416i		−	1.41458i	0.706921	−	0.707292i	$-0.250083\pi$
$128$		0			0
$129$	1.22593	−	5.10648i	0.107938	−	0.449600i
$130$		0			0
$131$	−4.17025	−	7.22309i	−0.364357	−	0.631084i	0.624316	−	0.781172i	$-0.285378\pi$
$131$	−4.17025	−	7.22309i	−0.364357	−	0.631084i	−0.988673	+	0.150087i	$0.952044\pi$
$132$		0			0
$133$	18.5366	+	2.41328i	1.60732	+	0.209258i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.01096	+	6.94718i	−0.342679	+	0.593537i	−0.984929	−	0.172958i	$-0.944668\pi$
$137$	−4.01096	+	6.94718i	−0.342679	+	0.593537i	0.642250	+	0.766495i	$0.278001\pi$
$138$		0			0
$139$			4.61654i			0.391570i	0.980647	+	0.195785i	$0.0627254\pi$
$139$			4.61654i			0.391570i	−0.980647	+	0.195785i	$0.937275\pi$
$140$		0			0
$141$	10.7213	−	3.17584i	0.902895	−	0.267454i
$142$		0			0
$143$	1.54017	+	0.889218i	0.128796	+	0.0743601i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.352278	−	12.1192i	−0.0290554	−	0.999578i
$148$		0			0
$149$	15.6215	−	9.01906i	1.27976	−	0.738870i	0.302956	−	0.953004i	$-0.402026\pi$
$149$	15.6215	−	9.01906i	1.27976	−	0.738870i	0.976804	+	0.214134i	$0.0686931\pi$
$150$		0			0
$151$	2.12850	−	3.68667i	0.173215	−	0.300017i	−0.766327	−	0.642451i	$-0.777918\pi$
$151$	2.12850	−	3.68667i	0.173215	−	0.300017i	0.939542	+	0.342434i	$0.111251\pi$
$152$		0			0
$153$	−12.3278	−	18.9828i	−0.996643	−	1.53467i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	8.32830	−	14.4250i	0.664671	−	1.15124i	−0.314703	−	0.949190i	$-0.601905\pi$
$157$	8.32830	−	14.4250i	0.664671	−	1.15124i	0.979374	−	0.202054i	$-0.0647616\pi$
$158$		0			0
$159$	0.128787	−	0.135714i	0.0102135	−	0.0107628i
$160$		0			0
$161$	−1.11620	+	8.57363i	−0.0879690	+	0.675697i
$162$		0			0
$163$	13.9950	−	8.07999i	1.09617	−	0.632874i	0.160957	−	0.986961i	$-0.448542\pi$
$163$	13.9950	−	8.07999i	1.09617	−	0.632874i	0.935212	+	0.354087i	$0.115208\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	17.4029i		−	1.34668i	−0.739335	−	0.673338i	$-0.764860\pi$
$167$		−	17.4029i		−	1.34668i	0.739335	−	0.673338i	$-0.235140\pi$
$168$		0			0
$169$	−12.4402			−0.956941
$170$		0			0
$171$	21.1668	−	1.10948i	1.61867	−	0.0848438i
$172$		0			0
$173$	17.0267	−	9.83038i	1.29452	−	0.747390i	0.315066	−	0.949070i	$-0.397973\pi$
$173$	17.0267	−	9.83038i	1.29452	−	0.747390i	0.979451	+	0.201680i	$0.0646401\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−15.7437	+	16.5906i	−1.18337	+	1.24702i
$178$		0			0
$179$	5.84722	+	3.37589i	0.437042	+	0.252326i	0.702342	−	0.711840i	$-0.252138\pi$
$179$	5.84722	+	3.37589i	0.437042	+	0.252326i	−0.265300	+	0.964166i	$0.585471\pi$
$180$		0			0
$181$		−	7.71256i		−	0.573270i	−0.958040	−	0.286635i	$-0.907463\pi$
$181$		−	7.71256i		−	0.573270i	0.958040	−	0.286635i	$-0.0925367\pi$
$182$		0			0
$183$	−13.2318	+	3.91950i	−0.978123	+	0.289737i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	8.96711	+	15.5315i	0.655740	+	1.13577i
$188$		0			0
$189$	−2.87781	−	13.4431i	−0.209330	−	0.977845i
$190$		0			0
$191$	−12.7009	+	7.33284i	−0.919001	+	0.530586i	−0.883316	−	0.468777i	$-0.844695\pi$
$191$	−12.7009	+	7.33284i	−0.919001	+	0.530586i	−0.0356850	+	0.999363i	$0.511361\pi$
$192$		0			0
$193$	9.21969	+	5.32299i	0.663648	+	0.383157i	0.793666	−	0.608354i	$-0.208170\pi$
$193$	9.21969	+	5.32299i	0.663648	+	0.383157i	−0.130018	+	0.991512i	$0.541503\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−7.53462			−0.536820			−0.268410	−	0.963305i	$-0.586498\pi$
$197$	−7.53462			−0.536820			−0.268410	+	0.963305i	$0.586498\pi$
$198$		0			0
$199$	−0.993782	−	0.573760i	−0.0704473	−	0.0406728i	0.464363	−	0.885645i	$-0.346283\pi$
$199$	−0.993782	−	0.573760i	−0.0704473	−	0.0406728i	−0.534810	+	0.844972i	$0.679617\pi$
$200$		0			0
$201$	7.39680	+	7.01924i	0.521730	+	0.495099i
$202$		0			0
$203$	−3.99497	+	5.22188i	−0.280392	+	0.366504i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.513161	+	9.79018i	0.0356671	+	0.680465i
$208$		0			0
$209$	−16.7943			−1.16169
$210$		0			0
$211$	−11.1248			−0.765862			−0.382931	−	0.923777i	$-0.625085\pi$
$211$	−11.1248			−0.765862			−0.382931	+	0.923777i	$0.625085\pi$
$212$		0			0
$213$	−5.64404	+	23.5095i	−0.386723	+	1.61085i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−8.02888	−	19.3049i	−0.545036	−	1.31050i
$218$		0			0
$219$	1.86160	−	1.96173i	0.125795	−	0.132561i
$220$		0			0
$221$	4.88862	+	2.82245i	0.328844	+	0.189858i
$222$		0			0
$223$	10.6904			0.715883			0.357942	−	0.933744i	$-0.383479\pi$
$223$	10.6904			0.715883			0.357942	+	0.933744i	$0.383479\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	11.5979	+	6.69603i	0.769777	+	0.444431i	0.832795	−	0.553581i	$-0.186739\pi$
$227$	11.5979	+	6.69603i	0.769777	+	0.444431i	−0.0630180	+	0.998012i	$0.520073\pi$
$228$		0			0
$229$	−8.32905	+	4.80878i	−0.550399	+	0.317773i	−0.749283	−	0.662250i	$-0.769602\pi$
$229$	−8.32905	+	4.80878i	−0.550399	+	0.317773i	0.198884	+	0.980023i	$0.436268\pi$
$230$		0			0
$231$	1.71953	+	10.7563i	0.113137	+	0.707712i
$232$		0			0
$233$	10.7087	+	18.5481i	0.701552	+	1.21512i	0.967921	+	0.251253i	$0.0808427\pi$
$233$	10.7087	+	18.5481i	0.701552	+	1.21512i	−0.266369	+	0.963871i	$0.585824\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.25586	−	4.23964i	−0.0815766	−	0.275394i
$238$		0			0
$239$			25.2806i			1.63527i	0.575738	+	0.817634i	$0.304715\pi$
$239$			25.2806i			1.63527i	−0.575738	+	0.817634i	$0.695285\pi$
$240$		0			0
$241$	−19.7291	−	11.3906i	−1.27086	−	0.733733i	−0.295713	−	0.955277i	$-0.595557\pi$
$241$	−19.7291	−	11.3906i	−1.27086	−	0.733733i	−0.975150	+	0.221543i	$0.928891\pi$
$242$		0			0
$243$	−5.96573	−	14.4017i	−0.382702	−	0.923872i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4.57790	+	2.64305i	−0.291285	+	0.168173i
$248$		0			0
$249$	0.364687	−	1.51906i	0.0231111	−	0.0962663i
$250$		0			0
$251$	16.4201			1.03643			0.518215	−	0.855251i	$-0.326597\pi$
$251$	16.4201			1.03643			0.518215	+	0.855251i	$0.326597\pi$
$252$		0			0
$253$		−	7.76780i		−	0.488357i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.2616	+	5.92452i	−0.640100	+	0.369562i	−0.784653	−	0.619935i	$-0.787159\pi$
$257$	−10.2616	+	5.92452i	−0.640100	+	0.369562i	0.144553	+	0.989497i	$0.453825\pi$
$258$		0			0
$259$	11.3290	+	1.47493i	0.703951	+	0.0916474i
$260$		0			0
$261$	−3.38450	+	6.64258i	−0.209495	+	0.411165i
$262$		0			0
$263$	−2.76844	+	4.79507i	−0.170709	+	0.295677i	−0.938668	−	0.344822i	$-0.887939\pi$
$263$	−2.76844	+	4.79507i	−0.170709	+	0.295677i	0.767959	+	0.640499i	$0.221273\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−2.39300	−	8.07851i	−0.146449	−	0.494397i
$268$		0			0
$269$	−0.504112	+	0.873148i	−0.0307363	+	0.0532368i	−0.880984	−	0.473145i	$-0.843119\pi$
$269$	−0.504112	+	0.873148i	−0.0307363	+	0.0532368i	0.850248	+	0.526382i	$0.176452\pi$
$270$		0			0
$271$	0.991979	−	0.572720i	0.0602585	−	0.0347902i	−0.469568	−	0.882896i	$-0.655590\pi$
$271$	0.991979	−	0.572720i	0.0602585	−	0.0347902i	0.529827	+	0.848106i	$0.322257\pi$
$272$		0			0
$273$	2.16152	+	2.66140i	0.130821	+	0.161075i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	8.08299	+	4.66672i	0.485660	+	0.280396i	0.722772	−	0.691086i	$-0.242868\pi$
$277$	8.08299	+	4.66672i	0.485660	+	0.280396i	−0.237112	+	0.971482i	$0.576201\pi$
$278$		0			0
$279$	−12.9121	−	19.8826i	−0.773028	−	1.19034i
$280$		0			0
$281$		−	0.922818i		−	0.0550507i	−0.999621	−	0.0275253i	$-0.991237\pi$
$281$		−	0.922818i		−	0.0550507i	0.999621	−	0.0275253i	$-0.00876270\pi$
$282$		0			0
$283$	−3.77681	+	6.54162i	−0.224508	+	0.388859i	−0.956172	−	0.292807i	$-0.905411\pi$
$283$	−3.77681	+	6.54162i	−0.224508	+	0.388859i	0.731664	+	0.681666i	$0.238744\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	22.8336	+	17.4688i	1.34783	+	1.03115i
$288$		0			0
$289$	19.9623	+	34.5757i	1.17425	+	2.03386i
$290$		0			0
$291$	−21.7570	−	5.22330i	−1.27542	−	0.306195i
$292$		0			0
$293$		−	21.3909i		−	1.24967i	−0.780758	−	0.624834i	$-0.785167\pi$
$293$		−	21.3909i		−	1.24967i	0.780758	−	0.624834i	$-0.214833\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	4.12310	+	11.6428i	0.239247	+	0.675586i
$298$		0			0
$299$	−1.22248	−	2.11739i	−0.0706977	−	0.122452i
$300$		0			0
$301$	−4.87427	+	6.37122i	−0.280949	+	0.367231i
$302$		0			0
$303$	−3.73696	+	3.93797i	−0.214683	+	0.226230i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	16.7500			0.955972			0.477986	−	0.878368i	$-0.341367\pi$
$307$	16.7500			0.955972			0.477986	+	0.878368i	$0.341367\pi$
$308$		0			0
$309$	7.76322	+	26.2078i	0.441634	+	1.49091i
$310$		0			0
$311$	2.52577	−	4.37477i	0.143224	−	0.248070i	−0.785485	−	0.618880i	$-0.787587\pi$
$311$	2.52577	−	4.37477i	0.143224	−	0.248070i	0.928709	+	0.370810i	$0.120920\pi$
$312$		0			0
$313$	−7.50546	−	12.9998i	−0.424234	−	0.734795i	0.572115	−	0.820174i	$-0.306123\pi$
$313$	−7.50546	−	12.9998i	−0.424234	−	0.734795i	−0.996349	+	0.0853790i	$0.972790\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	12.7324	+	22.0531i	0.715121	+	1.23863i	0.962913	+	0.269812i	$0.0869616\pi$
$317$	12.7324	+	22.0531i	0.715121	+	1.23863i	−0.247792	+	0.968813i	$0.579705\pi$
$318$		0			0
$319$	2.95349	−	5.11559i	0.165364	−	0.286418i
$320$		0			0
$321$	6.81374	+	23.0025i	0.380306	+	1.28387i
$322$		0			0
$323$	−53.3065			−2.96605
$324$		0			0
$325$		0			0
$326$		0			0
$327$	2.05824	−	2.16895i	0.113821	−	0.119943i
$328$		0			0
$329$	−16.9375	−	2.20509i	−0.933794	−	0.121571i
$330$		0			0
$331$	−5.45134	−	9.44199i	−0.299633	−	0.518979i	0.676419	−	0.736517i	$-0.263531\pi$
$331$	−5.45134	−	9.44199i	−0.299633	−	0.518979i	−0.976052	+	0.217538i	$0.930197\pi$
$332$		0			0
$333$	12.9365	−	0.678080i	0.708918	−	0.0371585i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			18.4210i			1.00345i	0.865026	+	0.501727i	$0.167302\pi$
$337$			18.4210i			1.00345i	−0.865026	+	0.501727i	$0.832698\pi$
$338$		0			0
$339$	−8.31675	−	1.99664i	−0.451704	−	0.108443i
$340$		0			0
$341$	9.39213	+	16.2677i	0.508613	+	0.880943i
$342$		0			0
$343$	−7.01353	+	17.1409i	−0.378695	+	0.925522i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.79206	−	8.30010i	0.257252	−	0.445573i	−0.708253	−	0.705959i	$-0.750516\pi$
$347$	4.79206	−	8.30010i	0.257252	−	0.445573i	0.965505	+	0.260386i	$0.0838498\pi$
$348$		0			0
$349$		−	16.5601i		−	0.886441i	−0.896413	−	0.443220i	$-0.853836\pi$
$349$		−	16.5601i		−	0.886441i	0.896413	−	0.443220i	$-0.146164\pi$
$350$		0			0
$351$	2.95623	+	2.52479i	0.157792	+	0.134764i
$352$		0			0
$353$	−15.5984	−	9.00574i	−0.830219	−	0.479327i	0.0237089	−	0.999719i	$-0.492453\pi$
$353$	−15.5984	−	9.00574i	−0.830219	−	0.479327i	−0.853928	+	0.520392i	$0.825786\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	5.45792	+	34.1413i	0.288864	+	1.80695i
$358$		0			0
$359$	−3.47735	+	2.00765i	−0.183527	+	0.105960i	−0.588949	−	0.808170i	$-0.700458\pi$
$359$	−3.47735	+	2.00765i	−0.183527	+	0.105960i	0.405422	+	0.914130i	$0.367125\pi$
$360$		0			0
$361$	15.4592	−	26.7760i	0.813640	−	1.40927i
$362$		0			0
$363$	2.63175	+	8.88451i	0.138131	+	0.466316i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−17.0259	+	29.4897i	−0.888744	+	1.53935i	−0.0473832	+	0.998877i	$0.515088\pi$
$367$	−17.0259	+	29.4897i	−0.888744	+	1.53935i	−0.841361	+	0.540473i	$0.818245\pi$
$368$		0			0
$369$	29.0459	+	14.7993i	1.51207	+	0.770423i
$370$		0			0
$371$	−0.263879	+	0.109747i	−0.0136999	+	0.00569779i
$372$		0			0
$373$	11.6169	−	6.70705i	0.601503	−	0.347278i	−0.168130	−	0.985765i	$-0.553773\pi$
$373$	11.6169	−	6.70705i	0.601503	−	0.347278i	0.769632	+	0.638487i	$0.220439\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	1.85925i		−	0.0957564i
$378$		0			0
$379$	15.3945			0.790764			0.395382	−	0.918517i	$-0.370612\pi$
$379$	15.3945			0.790764			0.395382	+	0.918517i	$0.370612\pi$
$380$		0			0
$381$	−6.44569	+	26.8487i	−0.330223	+	1.37550i
$382$		0			0
$383$	−21.1422	+	12.2065i	−1.08032	+	0.623722i	−0.930982	−	0.365065i	$-0.881047\pi$
$383$	−21.1422	+	12.2065i	−1.08032	+	0.623722i	−0.149336	+	0.988787i	$0.547713\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−4.12943	+	8.10462i	−0.209911	+	0.411981i
$388$		0			0
$389$	30.1938	+	17.4324i	1.53089	+	0.883857i	0.999321	+	0.0368391i	$0.0117289\pi$
$389$	30.1938	+	17.4324i	1.53089	+	0.883857i	0.531564	+	0.847018i	$0.321604\pi$
$390$		0			0
$391$		−	24.6556i		−	1.24689i
$392$		0			0
$393$	4.10299	+	13.8513i	0.206969	+	0.698704i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−11.2631	−	19.5083i	−0.565281	−	0.979095i	−0.997024	−	0.0770980i	$-0.975435\pi$
$397$	−11.2631	−	19.5083i	−0.565281	−	0.979095i	0.431743	−	0.901997i	$-0.357899\pi$
$398$		0			0
$399$	−30.2434	−	11.5594i	−1.51407	−	0.578692i
$400$		0			0
$401$	−15.8774	+	9.16683i	−0.792881	+	0.457770i	−0.840976	−	0.541073i	$-0.818018\pi$
$401$	−15.8774	+	9.16683i	−0.792881	+	0.457770i	0.0480950	+	0.998843i	$0.484685\pi$
$402$		0			0
$403$	5.12033	+	2.95623i	0.255062	+	0.147260i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−10.2642			−0.508778
$408$		0			0
$409$	−9.37130	−	5.41052i	−0.463381	−	0.267533i	0.250084	−	0.968224i	$-0.419542\pi$
$409$	−9.37130	−	5.41052i	−0.463381	−	0.267533i	−0.713465	+	0.700691i	$0.752875\pi$
$410$		0			0
$411$	9.56420	−	10.0786i	0.471767	−	0.497143i
$412$		0			0
$413$	32.2584	−	13.4162i	1.58733	−	0.660169i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.86662	−	7.77516i	0.0914086	−	0.380751i
$418$		0			0
$419$	−34.1164			−1.66670			−0.833348	−	0.552749i	$-0.813579\pi$
$419$	−34.1164			−1.66670			−0.833348	+	0.552749i	$0.813579\pi$
$420$		0			0
$421$	−29.9892			−1.46158			−0.730792	−	0.682600i	$-0.760849\pi$
$421$	−29.9892			−1.46158			−0.730792	+	0.682600i	$0.760849\pi$
$422$		0			0
$423$	−19.3408	+	1.01377i	−0.940384	+	0.0492910i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	20.9036	+	2.72144i	1.01160	+	0.131700i
$428$		0			0
$429$	−2.23441	−	2.12036i	−0.107878	−	0.102372i
$430$		0			0
$431$	−32.6954	−	18.8767i	−1.57488	−	0.909258i	−0.995557	−	0.0941612i	$-0.969983\pi$
$431$	−32.6954	−	18.8767i	−1.57488	−	0.909258i	−0.579324	−	0.815097i	$-0.696684\pi$
$432$		0			0
$433$	−0.221375			−0.0106386			−0.00531930	−	0.999986i	$-0.501693\pi$
$433$	−0.221375			−0.0106386			−0.00531930	+	0.999986i	$0.501693\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	19.9952	+	11.5442i	0.956501	+	0.552236i
$438$		0			0
$439$	12.5292	−	7.23374i	0.597987	−	0.345248i	−0.170262	−	0.985399i	$-0.554462\pi$
$439$	12.5292	−	7.23374i	0.597987	−	0.345248i	0.768249	+	0.640151i	$0.221128\pi$
$440$		0			0
$441$	−4.30690	+	20.5536i	−0.205090	+	0.978743i
$442$		0			0
$443$	5.55285	+	9.61783i	0.263824	+	0.456957i	0.967255	−	0.253807i	$-0.0816828\pi$
$443$	5.55285	+	9.61783i	0.263824	+	0.456957i	−0.703431	+	0.710764i	$0.748349\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−29.9563	+	8.87359i	−1.41688	+	0.419707i
$448$		0			0
$449$			31.1416i			1.46966i	0.678250	+	0.734831i	$0.262739\pi$
$449$			31.1416i			1.46966i	−0.678250	+	0.734831i	$0.737261\pi$
$450$		0			0
$451$	−22.3689	−	12.9147i	−1.05331	−	0.608128i
$452$		0			0
$453$	−5.07545	+	5.34845i	−0.238466	+	0.251292i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	16.4171	−	9.47844i	0.767962	−	0.443383i	−0.0641853	−	0.997938i	$-0.520445\pi$
$457$	16.4171	−	9.47844i	0.767962	−	0.443383i	0.832147	+	0.554555i	$0.187112\pi$
$458$		0			0
$459$	13.0871	+	36.9553i	0.610851	+	1.72492i
$460$		0			0
$461$	−15.1960			−0.707746			−0.353873	−	0.935293i	$-0.615136\pi$
$461$	−15.1960			−0.707746			−0.353873	+	0.935293i	$0.615136\pi$
$462$		0			0
$463$		−	29.3400i		−	1.36355i	−0.731564	−	0.681773i	$-0.761209\pi$
$463$		−	29.3400i		−	1.36355i	0.731564	−	0.681773i	$-0.238791\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	14.5382	−	8.39365i	0.672749	−	0.388412i	−0.124369	−	0.992236i	$-0.539691\pi$
$467$	14.5382	−	8.39365i	0.672749	−	0.388412i	0.797117	+	0.603824i	$0.206357\pi$
$468$		0			0
$469$	−5.98153	−	14.3822i	−0.276201	−	0.664107i
$470$		0			0
$471$	−19.8590	+	20.9272i	−0.915055	+	0.964274i
$472$		0			0
$473$	3.60356	−	6.24154i	0.165692	−	0.286986i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.271776	+	0.176496i	−0.0124438	+	0.00808121i
$478$		0			0
$479$	−1.07579	+	1.86333i	−0.0491542	+	0.0851376i	−0.889556	−	0.456827i	$-0.848986\pi$
$479$	−1.07579	+	1.86333i	−0.0491542	+	0.0851376i	0.840401	+	0.541964i	$0.182319\pi$
$480$		0			0
$481$	−2.79788	+	1.61536i	−0.127572	+	0.0736540i
$482$		0			0
$483$	5.34650	−	13.9884i	0.243274	−	0.636492i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−3.02174	−	1.74460i	−0.136928	−	0.0790555i	0.429971	−	0.902843i	$-0.358524\pi$
$487$	−3.02174	−	1.74460i	−0.136928	−	0.0790555i	−0.566899	+	0.823787i	$0.691857\pi$
$488$		0			0
$489$	−26.8373	+	7.94967i	−1.21362	+	0.359497i
$490$		0			0
$491$			26.1361i			1.17950i	0.807584	+	0.589752i	$0.200775\pi$
$491$			26.1361i			1.17950i	−0.807584	+	0.589752i	$0.799225\pi$
$492$		0			0
$493$	9.37460	−	16.2373i	0.422211	−	0.731290i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	22.4405	−	29.3322i	1.00659	−	1.31573i
$498$		0			0
$499$	7.15545	+	12.3936i	0.320322	+	0.554814i	0.980554	−	0.196247i	$-0.0628756\pi$
$499$	7.15545	+	12.3936i	0.320322	+	0.554814i	−0.660232	+	0.751061i	$0.729542\pi$
$500$		0			0
$501$	−7.03656	+	29.3099i	−0.314370	+	1.30947i
$502$		0			0
$503$		−	39.3226i		−	1.75331i	−0.481123	−	0.876653i	$-0.659771\pi$
$503$		−	39.3226i		−	1.75331i	0.481123	−	0.876653i	$-0.340229\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	20.9518	+	5.02999i	0.930501	+	0.223390i
$508$		0			0
$509$	17.4284	+	30.1868i	0.772498	+	1.33801i	0.936190	+	0.351495i	$0.114326\pi$
$509$	17.4284	+	30.1868i	0.772498	+	1.33801i	−0.163692	+	0.986512i	$0.552340\pi$
$510$		0			0
$511$	−3.81435	+	1.58638i	−0.168737	+	0.0701774i
$512$		0			0
$513$	−36.0977	−	6.68985i	−1.59375	−	0.295364i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	15.3455			0.674896
$518$		0			0
$519$	−32.6511	+	9.67183i	−1.43322	+	0.424546i
$520$		0			0
$521$	−12.3030	+	21.3094i	−0.539005	+	0.933584i	0.459953	+	0.887943i	$0.347866\pi$
$521$	−12.3030	+	21.3094i	−0.539005	+	0.933584i	−0.998958	+	0.0456406i	$0.985467\pi$
$522$		0			0
$523$	13.8335	+	23.9603i	0.604897	+	1.04771i	0.992068	+	0.125704i	$0.0401190\pi$
$523$	13.8335	+	23.9603i	0.604897	+	1.04771i	−0.387171	+	0.922008i	$0.626548\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	29.8114	+	51.6348i	1.29860	+	2.24925i
$528$		0			0
$529$	6.16050	−	10.6703i	0.267848	−	0.463926i
$530$		0			0
$531$	33.2237	−	21.5761i	1.44178	−	0.936322i
$532$		0			0
$533$	−8.12993			−0.352146
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−8.48288	−	8.04989i	−0.366063	−	0.347378i
$538$		0			0
$539$	4.26029	−	16.0845i	0.183504	−	0.692808i
$540$		0			0
$541$	7.90334	+	13.6890i	0.339791	+	0.588536i	0.984393	−	0.175983i	$-0.0563103\pi$
$541$	7.90334	+	13.6890i	0.339791	+	0.588536i	−0.644602	+	0.764518i	$0.722977\pi$
$542$		0			0
$543$	−3.11844	+	12.9895i	−0.133825	+	0.557431i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	13.9288i		−	0.595553i	−0.954636	−	0.297776i	$-0.903755\pi$
$547$		−	13.9288i		−	0.595553i	0.954636	−	0.297776i	$-0.0962450\pi$
$548$		0			0
$549$	23.8697	−	1.25115i	1.01873	−	0.0533978i
$550$		0			0
$551$	8.77875	+	15.2052i	0.373987	+	0.647765i
$552$		0			0
$553$	−0.871984	+	6.69778i	−0.0370805	+	0.284818i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−17.2950	+	29.9559i	−0.732814	+	1.26927i	0.222862	+	0.974850i	$0.428460\pi$
$557$	−17.2950	+	29.9559i	−0.732814	+	1.26927i	−0.955676	+	0.294421i	$0.904873\pi$
$558$		0			0
$559$		−	2.26848i		−	0.0959464i
$560$		0			0
$561$	−8.82248	−	29.7838i	−0.372485	−	1.25747i
$562$		0			0
$563$	25.0789	+	14.4793i	1.05695	+	0.610229i	0.924586	−	0.380972i	$-0.124411\pi$
$563$	25.0789	+	14.4793i	1.05695	+	0.610229i	0.132361	+	0.991202i	$0.457744\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.588712	+	23.8045i	−0.0247236	+	0.999694i
$568$		0			0
$569$	10.1544	−	5.86266i	0.425696	−	0.245775i	−0.271816	−	0.962349i	$-0.587624\pi$
$569$	10.1544	−	5.86266i	0.425696	−	0.245775i	0.697511	+	0.716574i	$0.254291\pi$
$570$		0			0
$571$	17.5541	−	30.4045i	0.734614	−	1.27239i	−0.220278	−	0.975437i	$-0.570696\pi$
$571$	17.5541	−	30.4045i	0.734614	−	1.27239i	0.954892	−	0.296952i	$-0.0959703\pi$
$572$		0			0
$573$	24.3556	−	7.21457i	1.01747	−	0.301393i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−10.0423	+	17.3937i	−0.418065	+	0.724110i	−0.995745	−	0.0921536i	$-0.970625\pi$
$577$	−10.0423	+	17.3937i	−0.418065	+	0.724110i	0.577680	+	0.816263i	$0.303958\pi$
$578$		0			0
$579$	−13.3755	−	12.6928i	−0.555867	−	0.527494i
$580$		0			0
$581$	−1.44998	+	1.89529i	−0.0601554	+	0.0786298i
$582$		0			0
$583$	0.222363	−	0.128382i	0.00920935	−	0.00531702i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	32.7111i		−	1.35013i	−0.737757	−	0.675066i	$-0.764115\pi$
$587$		−	32.7111i		−	1.35013i	0.737757	−	0.675066i	$-0.235885\pi$
$588$		0			0
$589$	−55.8331			−2.30056
$590$		0			0
$591$	12.6898	+	3.04649i	0.521988	+	0.125316i
$592$		0			0
$593$	−3.86664	+	2.23240i	−0.158784	+	0.0916738i	−0.577286	−	0.816542i	$-0.695888\pi$
$593$	−3.86664	+	2.23240i	−0.158784	+	0.0916738i	0.418503	+	0.908216i	$0.362555\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.44173	+	1.36814i	0.0590062	+	0.0559944i
$598$		0			0
$599$	−31.6126	−	18.2515i	−1.29165	−	0.745737i	−0.312707	−	0.949850i	$-0.601236\pi$
$599$	−31.6126	−	18.2515i	−1.29165	−	0.745737i	−0.978947	+	0.204112i	$0.934569\pi$
$600$		0			0
$601$			32.4566i			1.32393i	0.749534	+	0.661966i	$0.230278\pi$
$601$			32.4566i			1.32393i	−0.749534	+	0.661966i	$0.769722\pi$
$602$		0			0
$603$	−9.61955	−	14.8125i	−0.391738	−	0.603213i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	10.4608	+	18.1187i	0.424593	+	0.735416i	0.996382	−	0.0849841i	$-0.0270840\pi$
$607$	10.4608	+	18.1187i	0.424593	+	0.735416i	−0.571790	+	0.820400i	$0.693751\pi$
$608$		0			0
$609$	8.83970	−	7.17937i	0.358203	−	0.290923i
$610$		0			0
$611$	4.18298	−	2.41505i	0.169225	−	0.0977023i
$612$		0			0
$613$	−33.6783	−	19.4442i	−1.36025	−	0.785343i	−0.370596	−	0.928794i	$-0.620847\pi$
$613$	−33.6783	−	19.4442i	−1.36025	−	0.785343i	−0.989657	+	0.143451i	$0.954180\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−12.8874			−0.518828			−0.259414	−	0.965766i	$-0.583529\pi$
$617$	−12.8874			−0.518828			−0.259414	+	0.965766i	$0.583529\pi$
$618$		0			0
$619$	−8.89767	−	5.13707i	−0.357628	−	0.206476i	0.310412	−	0.950602i	$-0.399533\pi$
$619$	−8.89767	−	5.13707i	−0.357628	−	0.206476i	−0.668040	+	0.744126i	$0.732866\pi$
$620$		0			0
$621$	3.09423	−	16.6961i	0.124167	−	0.669990i
$622$		0			0
$623$	−1.66154	+	12.7624i	−0.0665683	+	0.511316i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	28.2849	+	6.79049i	1.12959	+	0.271186i
$628$		0			0
$629$	−32.5794			−1.29902
$630$		0			0
$631$	44.9308			1.78866			0.894332	−	0.447403i	$-0.147651\pi$
$631$	44.9308			1.78866			0.894332	+	0.447403i	$0.147651\pi$
$632$		0			0
$633$	18.7363	+	4.49811i	0.744701	+	0.178784i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.37004	−	5.05488i	−0.0542831	−	0.200282i
$638$		0			0
$639$	19.0113	−	37.3126i	0.752076	−	1.47606i
$640$		0			0
$641$	33.7953	+	19.5118i	1.33484	+	0.770668i	0.986036	−	0.166529i	$-0.0532561\pi$
$641$	33.7953	+	19.5118i	1.33484	+	0.770668i	0.348799	+	0.937197i	$0.386589\pi$
$642$		0			0
$643$	−12.2206			−0.481932			−0.240966	−	0.970534i	$-0.577464\pi$
$643$	−12.2206			−0.481932			−0.240966	+	0.970534i	$0.577464\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	14.6082	+	8.43406i	0.574308	+	0.331577i	0.758868	−	0.651244i	$-0.225753\pi$
$647$	14.6082	+	8.43406i	0.574308	+	0.331577i	−0.184560	+	0.982821i	$0.559086\pi$
$648$		0			0
$649$	−27.1832	+	15.6942i	−1.06703	+	0.616052i
$650$		0			0
$651$	5.71662	+	35.7595i	0.224052	+	1.40153i
$652$		0			0
$653$	10.8531	+	18.7980i	0.424713	+	0.735624i	0.996394	−	0.0848520i	$-0.0270418\pi$
$653$	10.8531	+	18.7980i	0.424713	+	0.735624i	−0.571681	+	0.820476i	$0.693708\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−3.92849	+	2.55123i	−0.153265	+	0.0995331i
$658$		0			0
$659$			36.3752i			1.41698i	0.705722	+	0.708489i	$0.250623\pi$
$659$			36.3752i			1.41698i	−0.705722	+	0.708489i	$0.749377\pi$
$660$		0			0
$661$	12.9940	+	7.50207i	0.505407	+	0.291797i	0.730944	−	0.682438i	$-0.239080\pi$
$661$	12.9940	+	7.50207i	0.505407	+	0.291797i	−0.225537	+	0.974235i	$0.572414\pi$
$662$		0			0
$663$	−7.09219	−	6.73018i	−0.275438	−	0.261379i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−7.03281	+	4.06039i	−0.272311	+	0.157219i
$668$		0			0
$669$	−18.0048	−	4.32248i	−0.696104	−	0.167117i
$670$		0			0
$671$	−18.9389			−0.731127
$672$		0			0
$673$		−	0.119232i		−	0.00459606i	−0.999997	−	0.00229803i	$-0.999269\pi$
$673$		−	0.119232i		−	0.00459606i	0.999997	−	0.00229803i	$-0.000731486\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	20.6622	−	11.9293i	0.794114	−	0.458482i	−0.0472948	−	0.998881i	$-0.515060\pi$
$677$	20.6622	−	11.9293i	0.794114	−	0.458482i	0.841409	+	0.540399i	$0.181727\pi$
$678$		0			0
$679$	27.1457	+	20.7677i	1.04176	+	0.796990i
$680$		0			0
$681$	−16.8256	−	15.9668i	−0.644760	−	0.611850i
$682$		0			0
$683$	−14.6082	+	25.3022i	−0.558968	+	0.968161i	0.438615	+	0.898675i	$0.355469\pi$
$683$	−14.6082	+	25.3022i	−0.558968	+	0.968161i	−0.997583	+	0.0694856i	$0.977864\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	15.9721	−	4.73122i	0.609374	−	0.180507i
$688$		0			0
$689$	0.0404088	−	0.0699901i	0.00153945	−	0.00266641i
$690$		0			0
$691$	−36.0356	+	20.8052i	−1.37086	+	0.791465i	−0.991036	−	0.133594i	$-0.957348\pi$
$691$	−36.0356	+	20.8052i	−1.37086	+	0.791465i	−0.379822	+	0.925059i	$0.624015\pi$
$692$		0			0
$693$	1.45309	−	18.8110i	0.0551984	−	0.714569i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−71.0005	−	40.9922i	−2.68934	−	1.55269i
$698$		0			0
$699$	−10.5360	−	35.5685i	−0.398509	−	1.34532i
$700$		0			0
$701$		−	14.6976i		−	0.555122i	−0.960708	−	0.277561i	$-0.910474\pi$
$701$		−	14.6976i		−	0.555122i	0.960708	−	0.277561i	$-0.0895261\pi$
$702$		0			0
$703$	15.2543	−	26.4213i	0.575328	−	0.996497i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	7.65690	−	3.18450i	0.287967	−	0.119765i
$708$		0			0
$709$	−18.6403	−	32.2859i	−0.700050	−	1.21252i	−0.968448	−	0.249214i	$-0.919828\pi$
$709$	−18.6403	−	32.2859i	−0.700050	−	1.21252i	0.268398	−	0.963308i	$-0.413506\pi$
$710$		0			0
$711$	0.400885	+	7.64816i	0.0150343	+	0.286828i
$712$		0			0
$713$		−	25.8242i		−	0.967125i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	10.2218	−	42.5776i	0.381740	−	1.59009i
$718$		0			0
$719$	−15.8612	−	27.4724i	−0.591522	−	1.02455i	−0.994028	−	0.109129i	$-0.965194\pi$
$719$	−15.8612	−	27.4724i	−0.591522	−	1.02455i	0.402505	−	0.915418i	$-0.368139\pi$
$720$		0			0
$721$	5.39027	−	41.4031i	0.200744	−	1.54193i
$722$		0			0
$723$	28.6221	+	27.1611i	1.06447	+	1.01013i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	30.3126			1.12423			0.562117	−	0.827058i	$-0.309987\pi$
$727$	30.3126			1.12423			0.562117	+	0.827058i	$0.309987\pi$
$728$		0			0
$729$	4.22437	+	26.6675i	0.156458	+	0.987685i
$730$		0			0
$731$	11.4380	−	19.8111i	0.423048	−	0.732741i
$732$		0			0
$733$	−1.19316	−	2.06661i	−0.0440703	−	0.0763321i	0.843149	−	0.537680i	$-0.180699\pi$
$733$	−1.19316	−	2.06661i	−0.0440703	−	0.0763321i	−0.887219	+	0.461348i	$0.847366\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.99716	+	12.1194i	0.257744	+	0.446425i
$738$		0			0
$739$	−2.29721	+	3.97889i	−0.0845043	+	0.146366i	−0.905180	−	0.425029i	$-0.860264\pi$
$739$	−2.29721	+	3.97889i	−0.0845043	+	0.146366i	0.820676	+	0.571394i	$0.193597\pi$
$740$		0			0
$741$	8.77875	−	2.60042i	0.322496	−	0.0955289i
$742$		0			0
$743$	−12.5047			−0.458753			−0.229376	−	0.973338i	$-0.573669\pi$
$743$	−12.5047			−0.458753			−0.229376	+	0.973338i	$0.573669\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−1.22841	+	2.41093i	−0.0449451	+	0.0882114i
$748$		0			0
$749$	4.73102	−	36.3393i	0.172868	−	1.32781i
$750$		0			0
$751$	−17.3708	−	30.0872i	−0.633871	−	1.09790i	−0.986753	−	0.162229i	$-0.948132\pi$
$751$	−17.3708	−	30.0872i	−0.633871	−	1.09790i	0.352883	−	0.935668i	$-0.385202\pi$
$752$		0			0
$753$	−27.6547	−	6.63919i	−1.00779	−	0.241946i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	14.5066i		−	0.527250i	−0.964625	−	0.263625i	$-0.915082\pi$
$757$		−	14.5066i		−	0.527250i	0.964625	−	0.263625i	$-0.0849182\pi$
$758$		0			0
$759$	−3.14077	+	13.0825i	−0.114003	+	0.474864i
$760$		0			0
$761$	−20.2457	−	35.0666i	−0.733906	−	1.27116i	−0.955202	−	0.295955i	$-0.904362\pi$
$761$	−20.2457	−	35.0666i	−0.733906	−	1.27116i	0.221296	−	0.975207i	$-0.428971\pi$
$762$		0			0
$763$	−4.21725	+	1.75395i	−0.152675	+	0.0634973i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.93984	+	8.55606i	−0.178367	+	0.308941i
$768$		0			0
$769$			39.6907i			1.43128i	0.698468	+	0.715641i	$0.253865\pi$
$769$			39.6907i			1.43128i	−0.698468	+	0.715641i	$0.746135\pi$
$770$		0			0
$771$	19.6780	−	5.82897i	0.708685	−	0.209925i
$772$		0			0
$773$	4.90181	+	2.83006i	0.176306	+	0.101790i	0.585556	−	0.810632i	$-0.300876\pi$
$773$	4.90181	+	2.83006i	0.176306	+	0.101790i	−0.409250	+	0.912422i	$0.634210\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−18.4839	−	7.06475i	−0.663107	−	0.253447i
$778$		0			0
$779$	66.4877	−	38.3867i	2.38217	−	1.37535i
$780$		0			0
$781$	−16.5903	+	28.7352i	−0.593647	+	1.02823i
$782$		0			0
$783$	8.38596	−	9.81894i	0.299690	−	0.350900i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−1.59485	+	2.76237i	−0.0568504	+	0.0984677i	−0.893050	−	0.449958i	$-0.851439\pi$
$787$	−1.59485	+	2.76237i	−0.0568504	+	0.0984677i	0.836200	+	0.548425i	$0.184772\pi$
$788$		0			0
$789$	6.60139	−	6.95647i	0.235016	−	0.247657i
$790$		0			0
$791$	10.3766	+	7.93857i	0.368949	+	0.282263i
$792$		0			0
$793$	−5.16248	+	2.98056i	−0.183325	+	0.105843i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	18.7853i		−	0.665410i	−0.943031	−	0.332705i	$-0.892039\pi$
$797$		−	18.7853i		−	0.665410i	0.943031	−	0.332705i	$-0.107961\pi$
$798$		0			0
$799$	48.7079			1.72316
$800$		0			0
$801$	0.763875	+	14.5734i	0.0269902	+	0.514924i
$802$		0			0
$803$	3.21424	−	1.85574i	0.113428	−	0.0654877i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.20207	−	1.26672i	0.0423147	−	0.0445908i
$808$		0			0
$809$	24.5995	+	14.2025i	0.864873	+	0.499335i	0.865641	−	0.500665i	$-0.166911\pi$
$809$	24.5995	+	14.2025i	0.864873	+	0.499335i	−0.000767968		1.00000i	$0.500244\pi$
$810$		0			0
$811$			46.9628i			1.64909i	0.565799	+	0.824543i	$0.308568\pi$
$811$			46.9628i			1.64909i	−0.565799	+	0.824543i	$0.691432\pi$
$812$		0			0
$813$	−1.90226	+	0.563482i	−0.0667151	+	0.0197622i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	10.7110	+	18.5519i	0.374729	+	0.649050i
$818$		0			0
$819$	−2.56433	−	5.35629i	−0.0896050	−	0.187164i
$820$		0			0
$821$	16.9019	−	9.75831i	0.589880	−	0.340567i	−0.175170	−	0.984538i	$-0.556048\pi$
$821$	16.9019	−	9.75831i	0.589880	−	0.340567i	0.765050	+	0.643971i	$0.222714\pi$
$822$		0			0
$823$	21.7033	+	12.5304i	0.756529	+	0.436782i	0.828048	−	0.560657i	$-0.189451\pi$
$823$	21.7033	+	12.5304i	0.756529	+	0.436782i	−0.0715193	+	0.997439i	$0.522785\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−40.2141			−1.39838			−0.699191	−	0.714935i	$-0.746456\pi$
$827$	−40.2141			−1.39838			−0.699191	+	0.714935i	$0.746456\pi$
$828$		0			0
$829$	−5.52711	−	3.19108i	−0.191964	−	0.110831i	0.400937	−	0.916105i	$-0.368684\pi$
$829$	−5.52711	−	3.19108i	−0.191964	−	0.110831i	−0.592902	+	0.805275i	$0.702018\pi$
$830$		0			0
$831$	−11.7264	−	11.1279i	−0.406785	−	0.386022i
$832$		0			0
$833$	13.5225	−	51.0534i	0.468526	−	1.76889i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	13.7074	+	38.7069i	0.473796	+	1.33791i
$838$		0			0
$839$	−15.2513			−0.526534			−0.263267	−	0.964723i	$-0.584800\pi$
$839$	−15.2513			−0.526534			−0.263267	+	0.964723i	$0.584800\pi$
$840$		0			0
$841$	22.8246			0.787055
$842$		0			0
$843$	−0.373125	+	1.55421i	−0.0128511	+	0.0535297i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	1.82732	−	14.0358i	0.0627873	−	0.482274i
$848$		0			0
$849$	9.00587	−	9.49028i	0.309081	−	0.325706i
$850$		0			0
$851$	12.2205	+	7.05551i	0.418913	+	0.241860i
$852$		0			0
$853$	16.7815			0.574586			0.287293	−	0.957843i	$-0.407245\pi$
$853$	16.7815			0.574586			0.287293	+	0.957843i	$0.407245\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−16.7758	−	9.68551i	−0.573050	−	0.330851i	0.185317	−	0.982679i	$-0.440669\pi$
$857$	−16.7758	−	9.68551i	−0.573050	−	0.330851i	−0.758367	+	0.651828i	$0.774002\pi$
$858$		0			0
$859$	−42.4714	+	24.5208i	−1.44910	+	0.836641i	−0.998428	−	0.0560471i	$-0.982150\pi$
$859$	−42.4714	+	24.5208i	−1.44910	+	0.836641i	−0.450676	+	0.892688i	$0.648817\pi$
$860$		0			0
$861$	−31.3931	−	38.6532i	−1.06987	−	1.31730i
$862$		0			0
$863$	−11.2358	−	19.4609i	−0.382470	−	0.662458i	0.608944	−	0.793213i	$-0.291593\pi$
$863$	−11.2358	−	19.4609i	−0.382470	−	0.662458i	−0.991415	+	0.130755i	$0.958260\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−19.6403	−	66.3036i	−0.667020	−	2.25179i
$868$		0			0
$869$		−	6.06826i		−	0.205851i
$870$		0			0
$871$	3.81466	+	2.20239i	0.129255	+	0.0746253i
$872$		0			0
$873$	34.5311	+	17.5941i	1.16870	+	0.595471i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−26.8618	+	15.5087i	−0.907059	+	0.523691i	−0.879484	−	0.475929i	$-0.842112\pi$
$877$	−26.8618	+	15.5087i	−0.907059	+	0.523691i	−0.0275755	+	0.999620i	$0.508779\pi$
$878$		0			0
$879$	−8.64902	+	36.0264i	−0.291724	+	1.21514i
$880$		0			0
$881$	21.8713			0.736864			0.368432	−	0.929655i	$-0.379895\pi$
$881$	21.8713			0.736864			0.368432	+	0.929655i	$0.379895\pi$
$882$		0			0
$883$			34.3430i			1.15573i	0.816131	+	0.577867i	$0.196115\pi$
$883$			34.3430i			1.15573i	−0.816131	+	0.577867i	$0.803885\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−48.4807	+	27.9903i	−1.62782	+	0.939824i	−0.643082	+	0.765797i	$0.722345\pi$
$887$	−48.4807	+	27.9903i	−1.62782	+	0.939824i	−0.984741	+	0.174027i	$0.944322\pi$
$888$		0			0
$889$	25.6278	−	33.4985i	0.859530	−	1.12350i
$890$		0			0
$891$	−2.23654	−	21.2759i	−0.0749268	−	0.712771i
$892$		0			0
$893$	−22.8060	+	39.5012i	−0.763175	+	1.32186i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1.20276	+	4.06039i	0.0401590	+	0.135573i
$898$		0			0
$899$	9.81894	−	17.0069i	0.327480	−	0.567212i
$900$		0			0
$901$	0.705799	−	0.407493i	0.0235136	−	0.0135756i
$902$		0			0
$903$	10.7853	−	8.75956i	0.358913	−	0.291500i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.856413	−	0.494450i	−0.0284367	−	0.0164180i	0.485714	−	0.874118i	$-0.338560\pi$
$907$	−0.856413	−	0.494450i	−0.0284367	−	0.0164180i	−0.514151	+	0.857700i	$0.671893\pi$
$908$		0			0
$909$	7.88602	−	5.12133i	0.261563	−	0.169864i
$910$		0			0
$911$		−	28.5096i		−	0.944567i	−0.881447	−	0.472283i	$-0.843430\pi$
$911$		−	28.5096i		−	0.944567i	0.881447	−	0.472283i	$-0.156570\pi$
$912$		0			0
$913$	1.07197	−	1.85671i	0.0354771	−	0.0614482i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.84885	−	21.8822i	0.0940774	−	0.722615i
$918$		0			0
$919$	−1.40350	−	2.43093i	−0.0462971	−	0.0801889i	0.841948	−	0.539558i	$-0.181409\pi$
$919$	−1.40350	−	2.43093i	−0.0462971	−	0.0801889i	−0.888245	+	0.459369i	$0.848075\pi$
$920$		0			0
$921$	−28.2102	−	6.77256i	−0.929559	−	0.223163i
$922$		0			0
$923$			10.4438i			0.343761i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−2.47812	−	47.2780i	−0.0813920	−	1.55281i
$928$		0			0
$929$	6.57702	+	11.3917i	0.215785	+	0.373751i	0.953515	−	0.301345i	$-0.0974356\pi$
$929$	6.57702	+	11.3917i	0.215785	+	0.373751i	−0.737730	+	0.675096i	$0.764102\pi$
$930$		0			0
$931$	35.0718	+	34.8707i	1.14943	+	1.14284i
$932$		0			0
$933$	−6.02276	+	6.34672i	−0.197176	+	0.207782i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	20.2219			0.660622			0.330311	−	0.943872i	$-0.392846\pi$
$937$	20.2219			0.660622			0.330311	+	0.943872i	$0.392846\pi$
$938$		0			0
$939$	7.38441	+	24.9290i	0.240981	+	0.813527i
$940$		0			0
$941$	−22.8119	+	39.5113i	−0.743646	+	1.28803i	0.207179	+	0.978303i	$0.433572\pi$
$941$	−22.8119	+	39.5113i	−0.743646	+	1.28803i	−0.950825	+	0.309729i	$0.899762\pi$
$942$		0			0
$943$	17.7548	+	30.7523i	0.578177	+	1.00143i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−29.2959	−	50.7421i	−0.951990	−	1.64890i	−0.741110	−	0.671383i	$-0.765700\pi$
$947$	−29.2959	−	50.7421i	−0.951990	−	1.64890i	−0.210880	−	0.977512i	$-0.567633\pi$
$948$		0			0
$949$	0.584105	−	1.01170i	0.0189608	−	0.0328411i
$950$		0			0
$951$	−12.5270	−	42.2898i	−0.406216	−	1.37134i
$952$		0			0
$953$	26.9224			0.872101			0.436051	−	0.899922i	$-0.356377\pi$
$953$	26.9224			0.872101			0.436051	+	0.899922i	$0.356377\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−7.04265	+	7.42147i	−0.227657	+	0.239902i
$958$		0			0
$959$	−19.5967	+	8.15025i	−0.632811	+	0.263185i
$960$		0			0
$961$	15.7244	+	27.2354i	0.507238	+	0.878562i
$962$		0			0
$963$	−2.17503	−	41.4957i	−0.0700894	−	1.33718i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			17.4008i			0.559572i	0.960062	+	0.279786i	$0.0902635\pi$
$967$			17.4008i			0.559572i	−0.960062	+	0.279786i	$0.909737\pi$
$968$		0			0
$969$	89.7785	+	21.5535i	2.88410	+	0.692399i
$970$		0			0
$971$	−12.6200	−	21.8585i	−0.404996	−	0.701474i	0.589325	−	0.807896i	$-0.299394\pi$
$971$	−12.6200	−	21.8585i	−0.404996	−	0.701474i	−0.994321	+	0.106422i	$0.966060\pi$
$972$		0			0
$973$	−7.42160	+	9.70087i	−0.237926	+	0.310996i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	3.74960	−	6.49450i	0.119960	−	0.207778i	−0.799791	−	0.600278i	$-0.795057\pi$
$977$	3.74960	−	6.49450i	0.119960	−	0.207778i	0.919752	+	0.392501i	$0.128390\pi$
$978$		0			0
$979$		−	11.5629i		−	0.369552i
$980$		0			0
$981$	−4.34345	+	2.82072i	−0.138676	+	0.0900586i
$982$		0			0
$983$	22.3498	+	12.9037i	0.712848	+	0.411563i	0.812115	−	0.583498i	$-0.198316\pi$
$983$	22.3498	+	12.9037i	0.712848	+	0.411563i	−0.0992666	+	0.995061i	$0.531650\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	27.6345	+	10.5622i	0.879615	+	0.336198i
$988$		0			0
$989$	−8.58074	+	4.95409i	−0.272852	+	0.157531i
$990$		0			0
$991$	−11.4009	+	19.7469i	−0.362161	+	0.627280i	−0.988316	−	0.152418i	$-0.951294\pi$
$991$	−11.4009	+	19.7469i	−0.362161	+	0.627280i	0.626156	+	0.779698i	$0.284627\pi$
$992$		0			0
$993$	5.36341	+	18.1063i	0.170203	+	0.574586i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−5.91662	+	10.2479i	−0.187381	+	0.324554i	−0.944376	−	0.328867i	$-0.893333\pi$
$997$	−5.91662	+	10.2479i	−0.187381	+	0.324554i	0.756995	+	0.653421i	$0.226667\pi$
$998$		0			0
$999$	−22.0618	−	4.08865i	−0.698006	−	0.129359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bo.i.1949.1		32
3.2	odd	2	inner	2100.2.bo.i.1949.11		32
5.2	odd	4		2100.2.bi.m.101.4	yes	16
5.3	odd	4		2100.2.bi.l.101.5	yes	16
5.4	even	2	inner	2100.2.bo.i.1949.16		32
7.5	odd	6	inner	2100.2.bo.i.1349.6		32
15.2	even	4		2100.2.bi.m.101.7	yes	16
15.8	even	4		2100.2.bi.l.101.2	✓	16
15.14	odd	2	inner	2100.2.bo.i.1949.6		32
21.5	even	6	inner	2100.2.bo.i.1349.16		32
35.12	even	12		2100.2.bi.m.1601.7	yes	16
35.19	odd	6	inner	2100.2.bo.i.1349.11		32
35.33	even	12		2100.2.bi.l.1601.2	yes	16
105.47	odd	12		2100.2.bi.m.1601.4	yes	16
105.68	odd	12		2100.2.bi.l.1601.5	yes	16
105.89	even	6	inner	2100.2.bo.i.1349.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.bi.l.101.2	✓	16	15.8	even	4
2100.2.bi.l.101.5	yes	16	5.3	odd	4
2100.2.bi.l.1601.2	yes	16	35.33	even	12
2100.2.bi.l.1601.5	yes	16	105.68	odd	12
2100.2.bi.m.101.4	yes	16	5.2	odd	4
2100.2.bi.m.101.7	yes	16	15.2	even	4
2100.2.bi.m.1601.4	yes	16	105.47	odd	12
2100.2.bi.m.1601.7	yes	16	35.12	even	12
2100.2.bo.i.1349.1		32	105.89	even	6	inner
2100.2.bo.i.1349.6		32	7.5	odd	6	inner
2100.2.bo.i.1349.11		32	35.19	odd	6	inner
2100.2.bo.i.1349.16		32	21.5	even	6	inner
2100.2.bo.i.1949.1		32	1.1	even	1	trivial
2100.2.bo.i.1949.6		32	15.14	odd	2	inner
2100.2.bo.i.1949.11		32	3.2	odd	2	inner
2100.2.bo.i.1949.16		32	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.bo (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.68420 - 0.404332i) q^{3} +(2.10133 + 1.60761i) q^{7} +(2.67303 + 1.36195i) q^{9} +O(q^{10})\)	\(q+(-1.68420 - 0.404332i) q^{3} +(2.10133 + 1.60761i) q^{7} +(2.67303 + 1.36195i) q^{9} +(-2.05856 - 1.18851i) q^{11} -0.748179 q^{13} +(-6.53402 - 3.77242i) q^{17} +(6.11872 - 3.53264i) q^{19} +(-2.88904 - 3.55717i) q^{21} +(1.63394 + 2.83006i) q^{23} +(-3.95123 - 3.37458i) q^{27} +2.48504i q^{29} +(-6.84372 - 3.95123i) q^{31} +(2.98646 + 2.83402i) q^{33} +(3.73959 - 2.15905i) q^{37} +(1.26008 + 0.302513i) q^{39} +10.8663 q^{41} +3.03200i q^{43} +(-5.59088 + 3.22790i) q^{47} +(1.83117 + 6.75624i) q^{49} +(9.47926 + 8.99541i) q^{51} +(-0.0540095 + 0.0935472i) q^{53} +(-11.7335 + 3.47567i) q^{57} +(6.60248 - 11.4358i) q^{59} +(6.90005 - 3.98375i) q^{61} +(3.42743 + 7.15910i) q^{63} +(-5.09859 - 2.94367i) q^{67} +(-1.60758 - 5.42703i) q^{69} -13.9589i q^{71} +(-0.780701 + 1.35221i) q^{73} +(-2.41505 - 5.80681i) q^{77} +(1.27644 + 2.21086i) q^{79} +(5.29018 + 7.28107i) q^{81} +0.901948i q^{83} +(1.00478 - 4.18529i) q^{87} +(2.43223 + 4.21274i) q^{89} +(-1.57217 - 1.20278i) q^{91} +(9.92856 + 9.42178i) q^{93} +12.9183 q^{97} +(-3.88390 - 5.98057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 18 q^{9}+O(q^{10}) \) 32 * q + 18 * q^9	\( 32 q + 18 q^{9} + 36 q^{19} - 22 q^{21} - 36 q^{31} - 24 q^{39} + 36 q^{49} - 2 q^{51} + 72 q^{61} + 14 q^{81} + 40 q^{91} + 60 q^{99}+O(q^{100}) \) 32 * q + 18 * q^9 + 36 * q^19 - 22 * q^21 - 36 * q^31 - 24 * q^39 + 36 * q^49 - 2 * q^51 + 72 * q^61 + 14 * q^81 + 40 * q^91 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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