LMFDB - Embedded newform 2100.2.bo.i.1349.11

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			1349.11
Character	$\chi$	$=$	2100.1349
Dual form			2100.2.bo.i.1949.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19226 - 1.25639i) q^{3} +(2.10133 - 1.60761i) q^{7} +(-0.157032 - 2.99589i) q^{9} +O(q^{10})$	\(q+(1.19226 - 1.25639i) q^{3} +(2.10133 - 1.60761i) q^{7} +(-0.157032 - 2.99589i) q^{9} +(2.05856 - 1.18851i) q^{11} -0.748179 q^{13} +(6.53402 - 3.77242i) q^{17} +(6.11872 + 3.53264i) q^{19} +(0.485543 - 4.55678i) q^{21} +(-1.63394 + 2.83006i) q^{23} +(-3.95123 - 3.37458i) q^{27} +2.48504i q^{29} +(-6.84372 + 3.95123i) q^{31} +(0.961106 - 4.00336i) q^{33} +(3.73959 + 2.15905i) q^{37} +(-0.892024 + 0.940005i) q^{39} -10.8663 q^{41} -3.03200i q^{43} +(5.59088 + 3.22790i) q^{47} +(1.83117 - 6.75624i) q^{49} +(3.05062 - 12.7070i) q^{51} +(0.0540095 + 0.0935472i) q^{53} +(11.7335 - 3.47567i) q^{57} +(-6.60248 - 11.4358i) q^{59} +(6.90005 + 3.98375i) q^{61} +(-5.14620 - 6.04290i) q^{63} +(-5.09859 + 2.94367i) q^{67} +(1.60758 + 5.42703i) q^{69} -13.9589i q^{71} +(-0.780701 - 1.35221i) q^{73} +(2.41505 - 5.80681i) q^{77} +(1.27644 - 2.21086i) q^{79} +(-8.95068 + 0.940900i) q^{81} +0.901948i q^{83} +(3.12218 + 2.96281i) q^{87} +(-2.43223 + 4.21274i) q^{89} +(-1.57217 + 1.20278i) q^{91} +(-3.19522 + 13.3093i) q^{93} +12.9183 q^{97} +(-3.88390 - 5.98057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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
$3$	1.19226	−	1.25639i	0.688352	−	0.725377i
$3$	1.19226	−	1.25639i	0.688352	−	0.725377i
$4$		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
$9$	−0.157032	−	2.99589i	−0.0523440	−	0.998629i
$10$		0			0
$11$	2.05856	−	1.18851i	0.620679	−	0.358349i	−0.156455	−	0.987685i	$-0.550006\pi$
$11$	2.05856	−	1.18851i	0.620679	−	0.358349i	0.777133	+	0.629336i	$0.216673\pi$
$12$		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	0.590578	−	0.806980i	$-0.298900\pi$
$17$	6.53402	−	3.77242i	1.58473	−	0.914946i	0.994155	−	0.107966i	$-0.0344336\pi$
$18$		0			0
$19$	6.11872	+	3.53264i	1.40373	+	0.810444i	0.994773	−	0.102109i	$-0.0325591\pi$
$19$	6.11872	+	3.53264i	1.40373	+	0.810444i	0.408957	+	0.912553i	$0.365892\pi$
$20$		0			0
$21$	0.485543	−	4.55678i	0.105954	−	0.994371i
$22$		0			0
$23$	−1.63394	+	2.83006i	−0.340699	+	0.590109i	−0.984563	−	0.175032i	$-0.943997\pi$
$23$	−1.63394	+	2.83006i	−0.340699	+	0.590109i	0.643863	+	0.765141i	$0.277331\pi$
$24$		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	−0.966856	−	0.255322i	$-0.917819\pi$
$31$	−6.84372	+	3.95123i	−1.22917	+	0.709661i	−0.262313	+	0.964983i	$0.584485\pi$
$32$		0			0
$33$	0.961106	−	4.00336i	0.167307	−	0.696896i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.73959	+	2.15905i	0.614784	+	0.354946i	0.774835	−	0.632163i	$-0.217833\pi$
$37$	3.73959	+	2.15905i	0.614784	+	0.354946i	−0.160051	+	0.987109i	$0.551166\pi$
$38$		0			0
$39$	−0.892024	+	0.940005i	−0.142838	+	0.150521i
$40$		0			0
$41$	−10.8663			−1.69703			−0.848514	−	0.529173i	$-0.822502\pi$
$41$	−10.8663			−1.69703			−0.848514	+	0.529173i	$0.822502\pi$
$42$		0			0
$43$		−	3.03200i		−	0.462375i	−0.972909	−	0.231188i	$-0.925739\pi$
$43$		−	3.03200i		−	0.462375i	0.972909	−	0.231188i	$-0.0742611\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.59088	+	3.22790i	0.815514	+	0.470837i	0.848867	−	0.528606i	$-0.177285\pi$
$47$	5.59088	+	3.22790i	0.815514	+	0.470837i	−0.0333530	+	0.999444i	$0.510619\pi$
$48$		0			0
$49$	1.83117	−	6.75624i	0.261596	−	0.965178i
$50$		0			0
$51$	3.05062	−	12.7070i	0.427173	−	1.77933i
$52$		0			0
$53$	0.0540095	+	0.0935472i	0.00741878	+	0.0128497i	0.869711	−	0.493561i	$-0.164305\pi$
$53$	0.0540095	+	0.0935472i	0.00741878	+	0.0128497i	−0.862292	+	0.506411i	$0.830972\pi$
$54$		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	−0.872340	−	0.488900i	$-0.837398\pi$
$59$	−6.60248	−	11.4358i	−0.859570	−	1.48882i	0.0127699	−	0.999918i	$-0.495935\pi$
$60$		0			0
$61$	6.90005	+	3.98375i	0.883461	+	0.510067i	0.871798	−	0.489865i	$-0.162954\pi$
$61$	6.90005	+	3.98375i	0.883461	+	0.510067i	0.0116632	+	0.999932i	$0.496287\pi$
$62$		0			0
$63$	−5.14620	−	6.04290i	−0.648360	−	0.761334i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−5.09859	+	2.94367i	−0.622892	+	0.359627i	−0.777994	−	0.628272i	$-0.783763\pi$
$67$	−5.09859	+	2.94367i	−0.622892	+	0.359627i	0.155102	+	0.987898i	$0.450429\pi$
$68$		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	0.816715	−	0.577041i	$-0.195793\pi$
$73$	−0.780701	−	1.35221i	−0.0913742	−	0.158265i	−0.908090	+	0.418776i	$0.862459\pi$
$74$		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	−0.785243	−	0.619188i	$-0.787462\pi$
$79$	1.27644	−	2.21086i	0.143611	−	0.248742i	0.928854	+	0.370446i	$0.120795\pi$
$80$		0			0
$81$	−8.95068	+	0.940900i	−0.994520	+	0.104544i
$82$		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
$87$	3.12218	+	2.96281i	0.334732	+	0.317647i
$88$		0			0
$89$	−2.43223	+	4.21274i	−0.257816	+	0.446550i	−0.965656	−	0.259822i	$-0.916336\pi$
$89$	−2.43223	+	4.21274i	−0.257816	+	0.446550i	0.707841	+	0.706372i	$0.249669\pi$
$90$		0			0
$91$	−1.57217	+	1.20278i	−0.164808	+	0.126086i
$92$		0			0
$93$	−3.19522	+	13.3093i	−0.331329	+	1.38011i
$94$		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	$-0.216507\pi$
$101$	−1.56718	−	2.71443i	−0.155940	−	0.270096i	−0.933401	+	0.358835i	$0.883174\pi$
$102$		0			0
$103$	−7.89048	+	13.6667i	−0.777472	+	1.34662i	0.155922	+	0.987769i	$0.450165\pi$
$103$	−7.89048	+	13.6667i	−0.777472	+	1.34662i	−0.933394	+	0.358852i	$0.883168\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.92544	−	11.9952i	0.669508	−	1.15962i	−0.308534	−	0.951213i	$-0.599839\pi$
$107$	6.92544	−	11.9952i	0.669508	−	1.15962i	0.978042	−	0.208408i	$-0.0668282\pi$
$108$		0			0
$109$	−0.863166	−	1.49505i	−0.0826763	−	0.143200i	0.821722	−	0.569888i	$-0.193013\pi$
$109$	−0.863166	−	1.49505i	−0.0826763	−	0.143200i	−0.904399	+	0.426688i	$0.859680\pi$
$110$		0			0
$111$	7.17117	−	2.12423i	0.680657	−	0.201623i
$112$		0			0
$113$	−4.93811			−0.464539			−0.232269	−	0.972652i	$-0.574615\pi$
$113$	−4.93811			−0.464539			−0.232269	+	0.972652i	$0.574615\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.117488	+	2.24146i	0.0108618	+	0.207223i
$118$		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
$123$	−12.9554	+	13.6523i	−1.16815	+	1.23099i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			15.9416i			1.41458i	0.706921	+	0.707292i	$0.250083\pi$
$127$			15.9416i			1.41458i	−0.706921	+	0.707292i	$0.749917\pi$
$128$		0			0
$129$	−3.80937	−	3.61493i	−0.335396	−	0.318277i
$130$		0			0
$131$	4.17025	−	7.22309i	0.364357	−	0.631084i	−0.624316	−	0.781172i	$-0.714622\pi$
$131$	4.17025	−	7.22309i	0.364357	−	0.631084i	0.988673	+	0.150087i	$0.0479555\pi$
$132$		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	$-0.0553323\pi$
$137$	4.01096	+	6.94718i	0.342679	+	0.593537i	−0.642250	+	0.766495i	$0.721999\pi$
$138$		0			0
$139$		−	4.61654i		−	0.391570i	−0.980647	−	0.195785i	$-0.937275\pi$
$139$		−	4.61654i		−	0.391570i	0.980647	−	0.195785i	$-0.0627254\pi$
$140$		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
$147$	−6.30525	−	10.3559i	−0.520048	−	0.854137i
$148$		0			0
$149$	−15.6215	−	9.01906i	−1.27976	−	0.738870i	−0.302956	−	0.953004i	$-0.597974\pi$
$149$	−15.6215	−	9.01906i	−1.27976	−	0.738870i	−0.976804	+	0.214134i	$0.931307\pi$
$150$		0			0
$151$	2.12850	+	3.68667i	0.173215	+	0.300017i	0.939542	−	0.342434i	$-0.111251\pi$
$151$	2.12850	+	3.68667i	0.173215	+	0.300017i	−0.766327	+	0.642451i	$0.777918\pi$
$152$		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	0.979374	+	0.202054i	$0.0647616\pi$
$157$	8.32830	+	14.4250i	0.664671	+	1.15124i	−0.314703	+	0.949190i	$0.601905\pi$
$158$		0			0
$159$	0.181925	+	0.0436756i	0.0144276	+	0.00346370i
$160$		0			0
$161$	1.11620	+	8.57363i	0.0879690	+	0.675697i
$162$		0			0
$163$	13.9950	+	8.07999i	1.09617	+	0.632874i	0.935212	−	0.354087i	$-0.115208\pi$
$163$	13.9950	+	8.07999i	1.09617	+	0.632874i	0.160957	+	0.986961i	$0.448542\pi$
$164$		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
$171$	9.62257	−	18.8857i	0.735856	−	1.44423i
$172$		0			0
$173$	−17.0267	−	9.83038i	−1.29452	−	0.747390i	−0.315066	−	0.949070i	$-0.602027\pi$
$173$	−17.0267	−	9.83038i	−1.29452	−	0.747390i	−0.979451	+	0.201680i	$0.935360\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−22.2397	−	5.33920i	−1.67164	−	0.401318i
$178$		0			0
$179$	−5.84722	+	3.37589i	−0.437042	+	0.252326i	−0.702342	−	0.711840i	$-0.747862\pi$
$179$	−5.84722	+	3.37589i	−0.437042	+	0.252326i	0.265300	+	0.964166i	$0.414529\pi$
$180$		0			0
$181$			7.71256i			0.573270i	0.958040	+	0.286635i	$0.0925367\pi$
$181$			7.71256i			0.573270i	−0.958040	+	0.286635i	$0.907463\pi$
$182$		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
$189$	−13.7278	−	0.739073i	−0.998554	−	0.0537597i
$190$		0			0
$191$	12.7009	+	7.33284i	0.919001	+	0.530586i	0.883316	−	0.468777i	$-0.155305\pi$
$191$	12.7009	+	7.33284i	0.919001	+	0.530586i	0.0356850	+	0.999363i	$0.488639\pi$
$192$		0			0
$193$	9.21969	−	5.32299i	0.663648	−	0.383157i	−0.130018	−	0.991512i	$-0.541503\pi$
$193$	9.21969	−	5.32299i	0.663648	−	0.383157i	0.793666	+	0.608354i	$0.208170\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	7.53462			0.536820			0.268410	−	0.963305i	$-0.413502\pi$
$197$	7.53462			0.536820			0.268410	+	0.963305i	$0.413502\pi$
$198$		0			0
$199$	−0.993782	+	0.573760i	−0.0704473	+	0.0406728i	−0.534810	−	0.844972i	$-0.679617\pi$
$199$	−0.993782	+	0.573760i	−0.0704473	+	0.0406728i	0.464363	+	0.885645i	$0.346283\pi$
$200$		0			0
$201$	−2.38044	+	9.91544i	−0.167904	+	0.699381i
$202$		0			0
$203$	3.99497	+	5.22188i	0.280392	+	0.366504i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	8.73513	+	4.45068i	0.607133	+	0.309344i
$208$		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
$213$	−17.5378	−	16.6426i	−1.20167	−	1.14033i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−8.02888	+	19.3049i	−0.545036	+	1.31050i
$218$		0			0
$219$	−2.62971	−	0.631326i	−0.177699	−	0.0426610i
$220$		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	$-0.813261\pi$
$227$	−11.5979	+	6.69603i	−0.769777	+	0.444431i	0.0630180	+	0.998012i	$0.479927\pi$
$228$		0			0
$229$	−8.32905	−	4.80878i	−0.550399	−	0.317773i	0.198884	−	0.980023i	$-0.436268\pi$
$229$	−8.32905	−	4.80878i	−0.550399	−	0.317773i	−0.749283	+	0.662250i	$0.769602\pi$
$230$		0			0
$231$	−4.41626	−	9.95747i	−0.290568	−	0.655153i
$232$		0			0
$233$	−10.7087	+	18.5481i	−0.701552	+	1.21512i	0.266369	+	0.963871i	$0.414176\pi$
$233$	−10.7087	+	18.5481i	−0.701552	+	1.21512i	−0.967921	+	0.251253i	$0.919157\pi$
$234$		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	−0.975150	−	0.221543i	$-0.928891\pi$
$241$	−19.7291	+	11.3906i	−1.27086	+	0.733733i	−0.295713	+	0.955277i	$0.595557\pi$
$242$		0			0
$243$	−9.48940	+	12.3673i	−0.608746	+	0.793366i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4.57790	−	2.64305i	−0.291285	−	0.168173i
$248$		0			0
$249$	1.13320	+	1.07536i	0.0718135	+	0.0681479i
$250$		0			0
$251$	−16.4201			−1.03643			−0.518215	−	0.855251i	$-0.673403\pi$
$251$	−16.4201			−1.03643			−0.518215	+	0.855251i	$0.673403\pi$
$252$		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	$-0.212841\pi$
$257$	10.2616	+	5.92452i	0.640100	+	0.369562i	−0.144553	+	0.989497i	$0.546175\pi$
$258$		0			0
$259$	11.3290	−	1.47493i	0.703951	−	0.0916474i
$260$		0			0
$261$	7.44489	−	0.390230i	0.460827	−	0.0241546i
$262$		0			0
$263$	2.76844	+	4.79507i	0.170709	+	0.295677i	0.938668	−	0.344822i	$-0.112061\pi$
$263$	2.76844	+	4.79507i	0.170709	+	0.295677i	−0.767959	+	0.640499i	$0.778727\pi$
$264$		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	$-0.156881\pi$
$269$	0.504112	+	0.873148i	0.0307363	+	0.0532368i	−0.850248	+	0.526382i	$0.823548\pi$
$270$		0			0
$271$	0.991979	+	0.572720i	0.0602585	+	0.0347902i	0.529827	−	0.848106i	$-0.322257\pi$
$271$	0.991979	+	0.572720i	0.0602585	+	0.0347902i	−0.469568	+	0.882896i	$0.655590\pi$
$272$		0			0
$273$	−0.363274	+	3.40929i	−0.0219863	+	0.206340i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	8.08299	−	4.66672i	0.485660	−	0.280396i	−0.237112	−	0.971482i	$-0.576201\pi$
$277$	8.08299	−	4.66672i	0.485660	−	0.280396i	0.722772	+	0.691086i	$0.242868\pi$
$278$		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	0.731664	−	0.681666i	$-0.238744\pi$
$283$	−3.77681	−	6.54162i	−0.224508	−	0.388859i	−0.956172	+	0.292807i	$0.905411\pi$
$284$		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
$291$	15.4020	−	16.2305i	0.902882	−	0.951447i
$292$		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
$297$	−12.1446	−	2.25071i	−0.704698	−	0.130599i
$298$		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
$303$	−5.27886	−	1.26732i	−0.303263	−	0.0728056i
$304$		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	$-0.212413\pi$
$311$	−2.52577	−	4.37477i	−0.143224	−	0.248070i	−0.928709	+	0.370810i	$0.879080\pi$
$312$		0			0
$313$	−7.50546	+	12.9998i	−0.424234	+	0.734795i	−0.996349	−	0.0853790i	$-0.972790\pi$
$313$	−7.50546	+	12.9998i	−0.424234	+	0.734795i	0.572115	+	0.820174i	$0.306123\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−12.7324	+	22.0531i	−0.715121	+	1.23863i	0.247792	+	0.968813i	$0.420295\pi$
$317$	−12.7324	+	22.0531i	−0.715121	+	1.23863i	−0.962913	+	0.269812i	$0.913038\pi$
$318$		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
$327$	−2.90748	−	0.698012i	−0.160784	−	0.0386002i
$328$		0			0
$329$	16.9375	−	2.20509i	0.933794	−	0.121571i
$330$		0			0
$331$	−5.45134	+	9.44199i	−0.299633	+	0.518979i	−0.976052	−	0.217538i	$-0.930197\pi$
$331$	−5.45134	+	9.44199i	−0.299633	+	0.518979i	0.676419	+	0.736517i	$0.263531\pi$
$332$		0			0
$333$	5.88104	−	11.5424i	0.322279	−	0.632521i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	18.4210i		−	1.00345i	−0.865026	−	0.501727i	$-0.832698\pi$
$337$		−	18.4210i		−	1.00345i	0.865026	−	0.501727i	$-0.167302\pi$
$338$		0			0
$339$	−5.88751	+	6.20420i	−0.319766	+	0.336966i
$340$		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	$-0.249484\pi$
$347$	−4.79206	−	8.30010i	−0.257252	−	0.445573i	−0.965505	+	0.260386i	$0.916150\pi$
$348$		0			0
$349$			16.5601i			0.886441i	0.896413	+	0.443220i	$0.146164\pi$
$349$			16.5601i			0.886441i	−0.896413	+	0.443220i	$0.853836\pi$
$350$		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	$-0.507547\pi$
$353$	15.5984	−	9.00574i	0.830219	−	0.479327i	0.853928	+	0.520392i	$0.174214\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−14.0175	−	31.6058i	−0.741887	−	1.67275i
$358$		0			0
$359$	3.47735	+	2.00765i	0.183527	+	0.105960i	0.588949	−	0.808170i	$-0.299542\pi$
$359$	3.47735	+	2.00765i	0.183527	+	0.105960i	−0.405422	+	0.914130i	$0.632875\pi$
$360$		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	−0.841361	−	0.540473i	$-0.818245\pi$
$367$	−17.0259	−	29.4897i	−0.888744	−	1.53935i	−0.0473832	−	0.998877i	$-0.515088\pi$
$368$		0			0
$369$	1.70635	+	32.5542i	0.0888292	+	1.69470i
$370$		0			0
$371$	0.263879	+	0.109747i	0.0136999	+	0.00569779i
$372$		0			0
$373$	11.6169	+	6.70705i	0.601503	+	0.347278i	0.769632	−	0.638487i	$-0.220439\pi$
$373$	11.6169	+	6.70705i	0.601503	+	0.347278i	−0.168130	+	0.985765i	$0.553773\pi$
$374$		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
$381$	20.0288	+	19.0065i	1.02611	+	0.973731i
$382$		0			0
$383$	21.1422	+	12.2065i	1.08032	+	0.623722i	0.930982	−	0.365065i	$-0.118953\pi$
$383$	21.1422	+	12.2065i	1.08032	+	0.623722i	0.149336	+	0.988787i	$0.452287\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−9.08352	+	0.476120i	−0.461741	+	0.0242026i
$388$		0			0
$389$	−30.1938	+	17.4324i	−1.53089	+	0.883857i	−0.531564	+	0.847018i	$0.678396\pi$
$389$	−30.1938	+	17.4324i	−1.53089	+	0.883857i	−0.999321	+	0.0368391i	$0.988271\pi$
$390$		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	0.431743	+	0.901997i	$0.357899\pi$
$397$	−11.2631	+	19.5083i	−0.565281	+	0.979095i	−0.997024	+	0.0770980i	$0.975435\pi$
$398$		0			0
$399$	19.0684	−	26.1664i	0.954614	−	1.30996i
$400$		0			0
$401$	15.8774	+	9.16683i	0.792881	+	0.457770i	0.840976	−	0.541073i	$-0.181982\pi$
$401$	15.8774	+	9.16683i	0.792881	+	0.457770i	−0.0480950	+	0.998843i	$0.515315\pi$
$402$		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	−0.713465	−	0.700691i	$-0.752875\pi$
$409$	−9.37130	+	5.41052i	−0.463381	+	0.267533i	0.250084	+	0.968224i	$0.419542\pi$
$410$		0			0
$411$	13.5105	+	3.24352i	0.666422	+	0.159991i
$412$		0			0
$413$	−32.2584	−	13.4162i	−1.58733	−	0.660169i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−5.80018	−	5.50412i	−0.284036	−	0.269538i
$418$		0			0
$419$	34.1164			1.66670			0.833348	−	0.552749i	$-0.186421\pi$
$419$	34.1164			1.66670			0.833348	+	0.552749i	$0.186421\pi$
$420$		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
$423$	8.79247	−	17.2565i	0.427505	−	0.839042i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	20.9036	−	2.72144i	1.01160	−	0.131700i
$428$		0			0
$429$	−0.719079	+	2.99523i	−0.0347175	+	0.144611i
$430$		0			0
$431$	32.6954	−	18.8767i	1.57488	−	0.909258i	0.579324	−	0.815097i	$-0.303316\pi$
$431$	32.6954	−	18.8767i	1.57488	−	0.909258i	0.995557	−	0.0941612i	$-0.0300169\pi$
$432$		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	0.768249	−	0.640151i	$-0.221128\pi$
$439$	12.5292	+	7.23374i	0.597987	+	0.345248i	−0.170262	+	0.985399i	$0.554462\pi$
$440$		0			0
$441$	−20.5285	−	4.42503i	−0.977547	−	0.210716i
$442$		0			0
$443$	−5.55285	+	9.61783i	−0.263824	+	0.456957i	−0.967255	−	0.253807i	$-0.918317\pi$
$443$	−5.55285	+	9.61783i	−0.263824	+	0.456957i	0.703431	+	0.710764i	$0.251651\pi$
$444$		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
$453$	7.16962	+	1.72124i	0.336858	+	0.0808711i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	16.4171	+	9.47844i	0.767962	+	0.443383i	0.832147	−	0.554555i	$-0.187112\pi$
$457$	16.4171	+	9.47844i	0.767962	+	0.443383i	−0.0641853	+	0.997938i	$0.520445\pi$
$458$		0			0
$459$	−38.5477	−	7.14392i	−1.79925	−	0.333450i
$460$		0			0
$461$	15.1960			0.707746			0.353873	−	0.935293i	$-0.384864\pi$
$461$	15.1960			0.707746			0.353873	+	0.935293i	$0.384864\pi$
$462$		0			0
$463$			29.3400i			1.36355i	0.731564	+	0.681773i	$0.238791\pi$
$463$			29.3400i			1.36355i	−0.731564	+	0.681773i	$0.761209\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−14.5382	−	8.39365i	−0.672749	−	0.388412i	0.124369	−	0.992236i	$-0.460309\pi$
$467$	−14.5382	−	8.39365i	−0.672749	−	0.388412i	−0.797117	+	0.603824i	$0.793643\pi$
$468$		0			0
$469$	−5.98153	+	14.3822i	−0.276201	+	0.664107i
$470$		0			0
$471$	28.0530	+	6.73481i	1.29261	+	0.310324i
$472$		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	$-0.151014\pi$
$479$	1.07579	+	1.86333i	0.0491542	+	0.0851376i	−0.840401	+	0.541964i	$0.817681\pi$
$480$		0			0
$481$	−2.79788	−	1.61536i	−0.127572	−	0.0736540i
$482$		0			0
$483$	12.1026	+	8.81961i	0.550689	+	0.401306i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−3.02174	+	1.74460i	−0.136928	+	0.0790555i	−0.566899	−	0.823787i	$-0.691857\pi$
$487$	−3.02174	+	1.74460i	−0.136928	+	0.0790555i	0.429971	+	0.902843i	$0.358524\pi$
$488$		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	−0.660232	−	0.751061i	$-0.729542\pi$
$499$	7.15545	−	12.3936i	0.320322	−	0.554814i	0.980554	+	0.196247i	$0.0628756\pi$
$500$		0			0
$501$	−21.8648	−	20.7488i	−0.976848	−	0.926987i
$502$		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
$507$	−14.8320	+	15.6298i	−0.658712	+	0.694143i
$508$		0			0
$509$	−17.4284	+	30.1868i	−0.772498	+	1.33801i	0.163692	+	0.986512i	$0.447660\pi$
$509$	−17.4284	+	30.1868i	−0.772498	+	1.33801i	−0.936190	+	0.351495i	$0.885674\pi$
$510$		0			0
$511$	−3.81435	−	1.58638i	−0.168737	−	0.0701774i
$512$		0			0
$513$	−12.2552	−	34.6064i	−0.541082	−	1.52791i
$514$		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	0.998958	+	0.0456406i	$0.0145329\pi$
$521$	12.3030	+	21.3094i	0.539005	+	0.933584i	−0.459953	+	0.887943i	$0.652134\pi$
$522$		0			0
$523$	13.8335	−	23.9603i	0.604897	−	1.04771i	−0.387171	−	0.922008i	$-0.626548\pi$
$523$	13.8335	−	23.9603i	0.604897	−	1.04771i	0.992068	−	0.125704i	$-0.0401190\pi$
$524$		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
$537$	−2.72997	+	11.3713i	−0.117807	+	0.490709i
$538$		0			0
$539$	−4.26029	−	16.0845i	−0.183504	−	0.692808i
$540$		0			0
$541$	7.90334	−	13.6890i	0.339791	−	0.588536i	−0.644602	−	0.764518i	$-0.722977\pi$
$541$	7.90334	−	13.6890i	0.339791	−	0.588536i	0.984393	+	0.175983i	$0.0563103\pi$
$542$		0			0
$543$	9.68998	+	9.19537i	0.415837	+	0.394611i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			13.9288i			0.595553i	0.954636	+	0.297776i	$0.0962450\pi$
$547$			13.9288i			0.595553i	−0.954636	+	0.297776i	$0.903755\pi$
$548$		0			0
$549$	10.8513	−	21.2974i	0.463123	−	0.908949i
$550$		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	0.955676	+	0.294421i	$0.0951269\pi$
$557$	17.2950	+	29.9559i	0.732814	+	1.26927i	−0.222862	+	0.974850i	$0.571540\pi$
$558$		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	$-0.875589\pi$
$563$	−25.0789	+	14.4793i	−1.05695	+	0.610229i	−0.132361	+	0.991202i	$0.542256\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−17.2957	+	16.3664i	−0.726352	+	0.687323i
$568$		0			0
$569$	−10.1544	−	5.86266i	−0.425696	−	0.245775i	0.271816	−	0.962349i	$-0.412376\pi$
$569$	−10.1544	−	5.86266i	−0.425696	−	0.245775i	−0.697511	+	0.716574i	$0.745709\pi$
$570$		0			0
$571$	17.5541	+	30.4045i	0.734614	+	1.27239i	0.954892	+	0.296952i	$0.0959703\pi$
$571$	17.5541	+	30.4045i	0.734614	+	1.27239i	−0.220278	+	0.975437i	$0.570696\pi$
$572$		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	0.577680	−	0.816263i	$-0.303958\pi$
$577$	−10.0423	−	17.3937i	−0.418065	−	0.724110i	−0.995745	+	0.0921536i	$0.970625\pi$
$578$		0			0
$579$	4.30452	−	17.9299i	0.178890	−	0.745142i
$580$		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
$591$	8.98323	−	9.46643i	0.369521	−	0.389397i
$592$		0			0
$593$	3.86664	+	2.23240i	0.158784	+	0.0916738i	0.577286	−	0.816542i	$-0.304112\pi$
$593$	3.86664	+	2.23240i	0.158784	+	0.0916738i	−0.418503	+	0.908216i	$0.637445\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.463980	+	1.93265i	−0.0189894	+	0.0790981i
$598$		0			0
$599$	31.6126	−	18.2515i	1.29165	−	0.745737i	0.312707	−	0.949850i	$-0.398764\pi$
$599$	31.6126	−	18.2515i	1.29165	−	0.745737i	0.978947	+	0.204112i	$0.0654308\pi$
$600$		0			0
$601$		−	32.4566i		−	1.32393i	−0.749534	−	0.661966i	$-0.769722\pi$
$601$		−	32.4566i		−	1.32393i	0.749534	−	0.661966i	$-0.230278\pi$
$602$		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	−0.571790	−	0.820400i	$-0.693751\pi$
$607$	10.4608	−	18.1187i	0.424593	−	0.735416i	0.996382	+	0.0849841i	$0.0270840\pi$
$608$		0			0
$609$	11.3238	+	1.20659i	0.458862	+	0.0488936i
$610$		0			0
$611$	−4.18298	−	2.41505i	−0.169225	−	0.0977023i
$612$		0			0
$613$	−33.6783	+	19.4442i	−1.36025	+	0.785343i	−0.989657	−	0.143451i	$-0.954180\pi$
$613$	−33.6783	+	19.4442i	−1.36025	+	0.785343i	−0.370596	+	0.928794i	$0.620847\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	12.8874			0.518828			0.259414	−	0.965766i	$-0.416471\pi$
$617$	12.8874			0.518828			0.259414	+	0.965766i	$0.416471\pi$
$618$		0			0
$619$	−8.89767	+	5.13707i	−0.357628	+	0.206476i	−0.668040	−	0.744126i	$-0.732866\pi$
$619$	−8.89767	+	5.13707i	−0.357628	+	0.206476i	0.310412	+	0.950602i	$0.399533\pi$
$620$		0			0
$621$	16.0063	−	5.66836i	0.642312	−	0.227463i
$622$		0			0
$623$	1.66154	+	12.7624i	0.0665683	+	0.511316i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	20.0232	−	21.1002i	0.799649	−	0.842661i
$628$		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
$633$	−13.2636	+	13.9771i	−0.527182	+	0.555538i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.37004	+	5.05488i	−0.0542831	+	0.200282i
$638$		0			0
$639$	−41.8193	+	2.19199i	−1.65435	+	0.0867139i
$640$		0			0
$641$	−33.7953	+	19.5118i	−1.33484	+	0.770668i	−0.986036	−	0.166529i	$-0.946744\pi$
$641$	−33.7953	+	19.5118i	−1.33484	+	0.770668i	−0.348799	+	0.937197i	$0.613411\pi$
$642$		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	$-0.774247\pi$
$647$	−14.6082	+	8.43406i	−0.574308	+	0.331577i	0.184560	+	0.982821i	$0.440914\pi$
$648$		0			0
$649$	−27.1832	−	15.6942i	−1.06703	−	0.616052i
$650$		0			0
$651$	14.6819	+	33.1038i	0.575431	+	1.29744i
$652$		0			0
$653$	−10.8531	+	18.7980i	−0.424713	+	0.735624i	−0.996394	−	0.0848520i	$-0.972958\pi$
$653$	−10.8531	+	18.7980i	−0.424713	+	0.735624i	0.571681	+	0.820476i	$0.306292\pi$
$654$		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	−0.225537	−	0.974235i	$-0.572414\pi$
$661$	12.9940	−	7.50207i	0.505407	−	0.291797i	0.730944	+	0.682438i	$0.239080\pi$
$662$		0			0
$663$	−2.28241	+	9.50710i	−0.0886416	+	0.369225i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−7.03281	−	4.06039i	−0.272311	−	0.157219i
$668$		0			0
$669$	12.7458	−	13.4313i	0.492779	−	0.519285i
$670$		0			0
$671$	18.9389			0.731127
$672$		0			0
$673$			0.119232i			0.00459606i	0.999997	+	0.00229803i	$0.000731486\pi$
$673$			0.119232i			0.00459606i	−0.999997	+	0.00229803i	$0.999269\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−20.6622	−	11.9293i	−0.794114	−	0.458482i	0.0472948	−	0.998881i	$-0.484940\pi$
$677$	−20.6622	−	11.9293i	−0.794114	−	0.458482i	−0.841409	+	0.540399i	$0.818273\pi$
$678$		0			0
$679$	27.1457	−	20.7677i	1.04176	−	0.796990i
$680$		0			0
$681$	−5.41484	+	22.5548i	−0.207497	+	0.864304i
$682$		0			0
$683$	14.6082	+	25.3022i	0.558968	+	0.968161i	0.997583	+	0.0694856i	$0.0221358\pi$
$683$	14.6082	+	25.3022i	0.558968	+	0.968161i	−0.438615	+	0.898675i	$0.644531\pi$
$684$		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	−0.379822	−	0.925059i	$-0.624015\pi$
$691$	−36.0356	−	20.8052i	−1.37086	−	0.791465i	−0.991036	+	0.133594i	$0.957348\pi$
$692$		0			0
$693$	−17.7758	−	6.32335i	−0.675246	−	0.240204i
$694$		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	0.268398	+	0.963308i	$0.413506\pi$
$709$	−18.6403	+	32.2859i	−0.700050	+	1.21252i	−0.968448	+	0.249214i	$0.919828\pi$
$710$		0			0
$711$	−6.82394	−	3.47690i	−0.255918	−	0.130394i
$712$		0			0
$713$		−	25.8242i		−	0.967125i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	31.7624	+	30.1411i	1.18619	+	1.12564i
$718$		0			0
$719$	15.8612	−	27.4724i	0.591522	−	1.02455i	−0.402505	−	0.915418i	$-0.631861\pi$
$719$	15.8612	−	27.4724i	0.591522	−	1.02455i	0.994028	−	0.109129i	$-0.0348061\pi$
$720$		0			0
$721$	5.39027	+	41.4031i	0.200744	+	1.54193i
$722$		0			0
$723$	−9.21118	+	38.3680i	−0.342568	+	1.42692i
$724$		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	−0.887219	−	0.461348i	$-0.847366\pi$
$733$	−1.19316	+	2.06661i	−0.0440703	+	0.0763321i	0.843149	+	0.537680i	$0.180699\pi$
$734$		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	0.820676	−	0.571394i	$-0.193597\pi$
$739$	−2.29721	−	3.97889i	−0.0845043	−	0.146366i	−0.905180	+	0.425029i	$0.860264\pi$
$740$		0			0
$741$	−8.77875	+	2.60042i	−0.322496	+	0.0955289i
$742$		0			0
$743$	12.5047			0.458753			0.229376	−	0.973338i	$-0.426331\pi$
$743$	12.5047			0.458753			0.229376	+	0.973338i	$0.426331\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.70213	−	0.141635i	0.0988659	−	0.00518214i
$748$		0			0
$749$	−4.73102	−	36.3393i	−0.172868	−	1.32781i
$750$		0			0
$751$	−17.3708	+	30.0872i	−0.633871	+	1.09790i	0.352883	+	0.935668i	$0.385202\pi$
$751$	−17.3708	+	30.0872i	−0.633871	+	1.09790i	−0.986753	+	0.162229i	$0.948132\pi$
$752$		0			0
$753$	−19.5771	+	20.6301i	−0.713428	+	0.751802i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			14.5066i			0.527250i	0.964625	+	0.263625i	$0.0849182\pi$
$757$			14.5066i			0.527250i	−0.964625	+	0.263625i	$0.915082\pi$
$758$		0			0
$759$	9.75938	+	9.26123i	0.354243	+	0.336161i
$760$		0			0
$761$	20.2457	−	35.0666i	0.733906	−	1.27116i	−0.221296	−	0.975207i	$-0.571029\pi$
$761$	20.2457	−	35.0666i	0.733906	−	1.27116i	0.955202	−	0.295955i	$-0.0956379\pi$
$762$		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	$-0.746135\pi$
$769$		−	39.6907i		−	1.43128i	0.698468	−	0.715641i	$-0.253865\pi$
$770$		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	$-0.699124\pi$
$773$	−4.90181	+	2.83006i	−0.176306	+	0.101790i	0.409250	+	0.912422i	$0.365790\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	11.6541	−	15.9922i	0.418087	−	0.573715i
$778$		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	0.836200	−	0.548425i	$-0.184772\pi$
$787$	−1.59485	−	2.76237i	−0.0568504	−	0.0984677i	−0.893050	+	0.449958i	$0.851439\pi$
$788$		0			0
$789$	9.32518	+	2.23874i	0.331985	+	0.0797012i
$790$		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
$801$	13.0028	+	6.62514i	0.459433	+	0.234088i
$802$		0			0
$803$	−3.21424	−	1.85574i	−0.113428	−	0.0654877i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.69805	+	0.407658i	0.0597741	+	0.0143502i
$808$		0			0
$809$	−24.5995	+	14.2025i	−0.864873	+	0.499335i	−0.865641	−	0.500665i	$-0.833089\pi$
$809$	−24.5995	+	14.2025i	−0.864873	+	0.499335i	0.000767968		1.00000i	$0.499756\pi$
$810$		0			0
$811$		−	46.9628i		−	1.64909i	−0.565799	−	0.824543i	$-0.691432\pi$
$811$		−	46.9628i		−	1.64909i	0.565799	−	0.824543i	$-0.308568\pi$
$812$		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
$819$	3.85028	+	4.52117i	0.134540	+	0.157983i
$820$		0			0
$821$	−16.9019	−	9.75831i	−0.589880	−	0.340567i	0.175170	−	0.984538i	$-0.443952\pi$
$821$	−16.9019	−	9.75831i	−0.589880	−	0.340567i	−0.765050	+	0.643971i	$0.777286\pi$
$822$		0			0
$823$	21.7033	−	12.5304i	0.756529	−	0.436782i	−0.0715193	−	0.997439i	$-0.522785\pi$
$823$	21.7033	−	12.5304i	0.756529	−	0.436782i	0.828048	+	0.560657i	$0.189451\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	40.2141			1.39838			0.699191	−	0.714935i	$-0.253544\pi$
$827$	40.2141			1.39838			0.699191	+	0.714935i	$0.253544\pi$
$828$		0			0
$829$	−5.52711	+	3.19108i	−0.191964	+	0.110831i	−0.592902	−	0.805275i	$-0.702018\pi$
$829$	−5.52711	+	3.19108i	−0.191964	+	0.110831i	0.400937	+	0.916105i	$0.368684\pi$
$830$		0			0
$831$	3.77381	−	15.7193i	0.130912	−	0.545297i
$832$		0			0
$833$	−13.5225	−	51.0534i	−0.468526	−	1.76889i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	40.3748	+	7.48253i	1.39556	+	0.258634i
$838$		0			0
$839$	15.2513			0.526534			0.263267	−	0.964723i	$-0.415200\pi$
$839$	15.2513			0.526534			0.263267	+	0.964723i	$0.415200\pi$
$840$		0			0
$841$	22.8246			0.787055
$842$		0			0
$843$	−1.15942	−	1.10024i	−0.0399325	−	0.0378942i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	1.82732	+	14.0358i	0.0627873	+	0.482274i
$848$		0			0
$849$	−12.7218	−	3.05417i	−0.436610	−	0.104819i
$850$		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	$-0.559331\pi$
$857$	16.7758	−	9.68551i	0.573050	−	0.330851i	0.758367	+	0.651828i	$0.225998\pi$
$858$		0			0
$859$	−42.4714	−	24.5208i	−1.44910	−	0.836641i	−0.450676	−	0.892688i	$-0.648817\pi$
$859$	−42.4714	−	24.5208i	−1.44910	−	0.836641i	−0.998428	+	0.0560471i	$0.982150\pi$
$860$		0			0
$861$	−5.27605	+	49.5153i	−0.179807	+	1.68748i
$862$		0			0
$863$	11.2358	−	19.4609i	0.382470	−	0.662458i	−0.608944	−	0.793213i	$-0.708407\pi$
$863$	11.2358	−	19.4609i	0.382470	−	0.662458i	0.991415	+	0.130755i	$0.0417401\pi$
$864$		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
$873$	−2.02859	−	38.7019i	−0.0686574	−	1.30986i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−26.8618	−	15.5087i	−0.907059	−	0.523691i	−0.0275755	−	0.999620i	$-0.508779\pi$
$877$	−26.8618	−	15.5087i	−0.907059	−	0.523691i	−0.879484	+	0.475929i	$0.842112\pi$
$878$		0			0
$879$	−26.8753	−	25.5035i	−0.906480	−	0.860211i
$880$		0			0
$881$	−21.8713			−0.736864			−0.368432	−	0.929655i	$-0.620105\pi$
$881$	−21.8713			−0.736864			−0.368432	+	0.929655i	$0.620105\pi$
$882$		0			0
$883$		−	34.3430i		−	1.15573i	−0.816131	−	0.577867i	$-0.803885\pi$
$883$		−	34.3430i		−	1.15573i	0.816131	−	0.577867i	$-0.196115\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	48.4807	+	27.9903i	1.62782	+	0.939824i	0.984741	+	0.174027i	$0.0556779\pi$
$887$	48.4807	+	27.9903i	1.62782	+	0.939824i	0.643082	+	0.765797i	$0.277655\pi$
$888$		0			0
$889$	25.6278	+	33.4985i	0.859530	+	1.12350i
$890$		0			0
$891$	−17.3072	+	12.5749i	−0.579814	+	0.421274i
$892$		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
$903$	−13.8161	−	1.47217i	−0.459773	−	0.0489906i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.856413	+	0.494450i	−0.0284367	+	0.0164180i	−0.514151	−	0.857700i	$-0.671893\pi$
$907$	−0.856413	+	0.494450i	−0.0284367	+	0.0164180i	0.485714	+	0.874118i	$0.338560\pi$
$908$		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	−0.888245	−	0.459369i	$-0.848075\pi$
$919$	−1.40350	+	2.43093i	−0.0462971	+	0.0801889i	0.841948	+	0.539558i	$0.181409\pi$
$920$		0			0
$921$	19.9703	−	21.0445i	0.658045	−	0.693440i
$922$		0			0
$923$			10.4438i			0.343761i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	42.1830	+	21.4929i	1.38547	+	0.705919i
$928$		0			0
$929$	−6.57702	+	11.3917i	−0.215785	+	0.373751i	−0.953515	−	0.301345i	$-0.902564\pi$
$929$	−6.57702	+	11.3917i	−0.215785	+	0.373751i	0.737730	+	0.675096i	$0.235898\pi$
$930$		0			0
$931$	35.0718	−	34.8707i	1.14943	−	1.14284i
$932$		0			0
$933$	−8.50780	−	2.04251i	−0.278533	−	0.0668686i
$934$		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	0.950825	+	0.309729i	$0.100238\pi$
$941$	22.8119	+	39.5113i	0.743646	+	1.28803i	−0.207179	+	0.978303i	$0.566428\pi$
$942$		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	0.210880	−	0.977512i	$-0.432367\pi$
$947$	29.2959	−	50.7421i	0.951990	−	1.64890i	0.741110	−	0.671383i	$-0.234300\pi$
$948$		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	$-0.643623\pi$
$953$	−26.9224			−0.872101			−0.436051	+	0.899922i	$0.643623\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	9.94851	+	2.38838i	0.321590	+	0.0772054i
$958$		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
$963$	−37.0238	−	18.8642i	−1.19308	−	0.607891i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	17.4008i		−	0.559572i	−0.960062	−	0.279786i	$-0.909737\pi$
$967$		−	17.4008i		−	0.559572i	0.960062	−	0.279786i	$-0.0902635\pi$
$968$		0			0
$969$	63.5552	−	66.9737i	2.04169	−	2.15151i
$970$		0			0
$971$	12.6200	−	21.8585i	0.404996	−	0.701474i	−0.589325	−	0.807896i	$-0.700606\pi$
$971$	12.6200	−	21.8585i	0.404996	−	0.701474i	0.994321	+	0.106422i	$0.0339395\pi$
$972$		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	$-0.204943\pi$
$977$	−3.74960	−	6.49450i	−0.119960	−	0.207778i	−0.919752	+	0.392501i	$0.871610\pi$
$978$		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	$-0.801684\pi$
$983$	−22.3498	+	12.9037i	−0.712848	+	0.411563i	0.0992666	+	0.995061i	$0.468350\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	17.4234	−	23.9091i	0.554594	−	0.761036i
$988$		0			0
$989$	8.58074	+	4.95409i	0.272852	+	0.157531i
$990$		0			0
$991$	−11.4009	−	19.7469i	−0.362161	−	0.627280i	0.626156	−	0.779698i	$-0.284627\pi$
$991$	−11.4009	−	19.7469i	−0.362161	−	0.627280i	−0.988316	+	0.152418i	$0.951294\pi$
$992$		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	0.756995	−	0.653421i	$-0.226667\pi$
$997$	−5.91662	−	10.2479i	−0.187381	−	0.324554i	−0.944376	+	0.328867i	$0.893333\pi$
$998$		0			0
$999$	−7.49005	−	21.1504i	−0.236975	−	0.669170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bo.i.1349.11		32
3.2	odd	2	inner	2100.2.bo.i.1349.1		32
5.2	odd	4		2100.2.bi.l.1601.2	yes	16
5.3	odd	4		2100.2.bi.m.1601.7	yes	16
5.4	even	2	inner	2100.2.bo.i.1349.6		32
7.3	odd	6	inner	2100.2.bo.i.1949.16		32
15.2	even	4		2100.2.bi.l.1601.5	yes	16
15.8	even	4		2100.2.bi.m.1601.4	yes	16
15.14	odd	2	inner	2100.2.bo.i.1349.16		32
21.17	even	6	inner	2100.2.bo.i.1949.6		32
35.3	even	12		2100.2.bi.m.101.4	yes	16
35.17	even	12		2100.2.bi.l.101.5	yes	16
35.24	odd	6	inner	2100.2.bo.i.1949.1		32
105.17	odd	12		2100.2.bi.l.101.2	✓	16
105.38	odd	12		2100.2.bi.m.101.7	yes	16
105.59	even	6	inner	2100.2.bo.i.1949.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.bi.l.101.2	✓	16	105.17	odd	12
2100.2.bi.l.101.5	yes	16	35.17	even	12
2100.2.bi.l.1601.2	yes	16	5.2	odd	4
2100.2.bi.l.1601.5	yes	16	15.2	even	4
2100.2.bi.m.101.4	yes	16	35.3	even	12
2100.2.bi.m.101.7	yes	16	105.38	odd	12
2100.2.bi.m.1601.4	yes	16	15.8	even	4
2100.2.bi.m.1601.7	yes	16	5.3	odd	4
2100.2.bo.i.1349.1		32	3.2	odd	2	inner
2100.2.bo.i.1349.6		32	5.4	even	2	inner
2100.2.bo.i.1349.11		32	1.1	even	1	trivial
2100.2.bo.i.1349.16		32	15.14	odd	2	inner
2100.2.bo.i.1949.1		32	35.24	odd	6	inner
2100.2.bo.i.1949.6		32	21.17	even	6	inner
2100.2.bo.i.1949.11		32	105.59	even	6	inner
2100.2.bo.i.1949.16		32	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.19226 - 1.25639i) q^{3} +(2.10133 - 1.60761i) q^{7} +(-0.157032 - 2.99589i) q^{9} +O(q^{10})\)	\(q+(1.19226 - 1.25639i) q^{3} +(2.10133 - 1.60761i) q^{7} +(-0.157032 - 2.99589i) q^{9} +(2.05856 - 1.18851i) q^{11} -0.748179 q^{13} +(6.53402 - 3.77242i) q^{17} +(6.11872 + 3.53264i) q^{19} +(0.485543 - 4.55678i) q^{21} +(-1.63394 + 2.83006i) q^{23} +(-3.95123 - 3.37458i) q^{27} +2.48504i q^{29} +(-6.84372 + 3.95123i) q^{31} +(0.961106 - 4.00336i) q^{33} +(3.73959 + 2.15905i) q^{37} +(-0.892024 + 0.940005i) q^{39} -10.8663 q^{41} -3.03200i q^{43} +(5.59088 + 3.22790i) q^{47} +(1.83117 - 6.75624i) q^{49} +(3.05062 - 12.7070i) q^{51} +(0.0540095 + 0.0935472i) q^{53} +(11.7335 - 3.47567i) q^{57} +(-6.60248 - 11.4358i) q^{59} +(6.90005 + 3.98375i) q^{61} +(-5.14620 - 6.04290i) q^{63} +(-5.09859 + 2.94367i) q^{67} +(1.60758 + 5.42703i) q^{69} -13.9589i q^{71} +(-0.780701 - 1.35221i) q^{73} +(2.41505 - 5.80681i) q^{77} +(1.27644 - 2.21086i) q^{79} +(-8.95068 + 0.940900i) q^{81} +0.901948i q^{83} +(3.12218 + 2.96281i) q^{87} +(-2.43223 + 4.21274i) q^{89} +(-1.57217 + 1.20278i) q^{91} +(-3.19522 + 13.3093i) q^{93} +12.9183 q^{97} +(-3.88390 - 5.98057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 18 q^{9}+O(q^{10}) \) 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

Groups

Database

Properties

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