LMFDB - Embedded newform 60.7.b.a.29.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(29,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("60.29");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.b (of order $2$, degree $1$, 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:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 1880 x^{10} + 1266870 x^{8} + 399545800 x^{6} + 62009694600 x^{4} + 4432082624000 x^{2} + 109931031040000 $ x^12 + 1880x^10 + 1266870x^8 + 399545800x^6 + 62009694600x^4 + 4432082624000*x^2 + 109931031040000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{8}\cdot 5^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.12
Root			$18.5699i$ of defining polynomial
Character	$\chi$	$=$	60.29
Dual form			60.7.b.a.29.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(24.4963 + 11.3548i) q^{3} +(124.726 - 8.26448i) q^{5} -577.271i q^{7} +(471.136 + 556.302i) q^{9} +O(q^{10})$	\(q+(24.4963 + 11.3548i) q^{3} +(124.726 - 8.26448i) q^{5} -577.271i q^{7} +(471.136 + 556.302i) q^{9} -1964.28i q^{11} +2091.29i q^{13} +(3149.18 + 1213.80i) q^{15} -1153.08 q^{17} +5613.44 q^{19} +(6554.81 - 14141.0i) q^{21} -3383.70 q^{23} +(15488.4 - 2061.60i) q^{25} +(5224.38 + 18977.0i) q^{27} +5725.09i q^{29} +36900.2 q^{31} +(22304.1 - 48117.7i) q^{33} +(-4770.85 - 72001.0i) q^{35} -32609.3i q^{37} +(-23746.2 + 51228.9i) q^{39} +56515.1i q^{41} +113328. i q^{43} +(63360.7 + 65491.9i) q^{45} -157774. q^{47} -215593. q^{49} +(-28246.1 - 13093.0i) q^{51} -109599. q^{53} +(-16233.8 - 244998. i) q^{55} +(137508. + 63739.6i) q^{57} +227718. i q^{59} -271177. q^{61} +(321137. - 271973. i) q^{63} +(17283.4 + 260840. i) q^{65} +219429. i q^{67} +(-82888.0 - 38421.2i) q^{69} -522399. i q^{71} +1788.95i q^{73} +(402817. + 125366. i) q^{75} -1.13392e6 q^{77} +794759. q^{79} +(-87502.3 + 524188. i) q^{81} -213226. q^{83} +(-143819. + 9529.58i) q^{85} +(-65007.3 + 140243. i) q^{87} -1.24220e6i q^{89} +1.20724e6 q^{91} +(903919. + 418995. i) q^{93} +(700144. - 46392.2i) q^{95} +492715. i q^{97} +(1.09273e6 - 925445. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 712 q^{9}+O(q^{10}) $ 12 * q + 712 * q^9	$ 12 q + 712 q^{9} + 2480 q^{15} - 192 q^{19} + 5348 q^{21} + 18660 q^{25} + 40848 q^{31} - 45312 q^{39} + 45340 q^{45} - 242940 q^{49} - 40720 q^{51} - 24240 q^{55} - 99312 q^{61} + 108460 q^{69} + 126640 q^{75} + 626544 q^{79} - 798268 q^{81} - 732720 q^{85} + 1996032 q^{91} + 1632080 q^{99}+O(q^{100}) $ 12 * q + 712 * q^9 + 2480 * q^15 - 192 * q^19 + 5348 * q^21 + 18660 * q^25 + 40848 * q^31 - 45312 * q^39 + 45340 * q^45 - 242940 * q^49 - 40720 * q^51 - 24240 * q^55 - 99312 * q^61 + 108460 * q^69 + 126640 * q^75 + 626544 * q^79 - 798268 * q^81 - 732720 * q^85 + 1996032 * q^91 + 1632080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	24.4963	+	11.3548i	0.907270	+	0.420549i
$3$	24.4963	+	11.3548i	0.907270	+	0.420549i
$4$		0			0
$5$	124.726	−	8.26448i	0.997812	−	0.0661159i
$5$	124.726	−	8.26448i	0.997812	−	0.0661159i
$6$		0			0
$7$		−	577.271i		−	1.68301i	−0.540252	−	0.841503i	$-0.681671\pi$
$7$		−	577.271i		−	1.68301i	0.540252	−	0.841503i	$-0.318329\pi$
$8$		0			0
$9$	471.136	+	556.302i	0.646277	+	0.763103i
$10$		0			0
$11$		−	1964.28i		−	1.47580i	−0.674912	−	0.737898i	$-0.735819\pi$
$11$		−	1964.28i		−	1.47580i	0.674912	−	0.737898i	$-0.264181\pi$
$12$		0			0
$13$			2091.29i			0.951885i	0.879476	+	0.475943i	$0.157893\pi$
$13$			2091.29i			0.951885i	−0.879476	+	0.475943i	$0.842107\pi$
$14$		0			0
$15$	3149.18	+	1213.80i	0.933090	+	0.359644i
$16$		0			0
$17$	−1153.08			−0.234699			−0.117350	−	0.993091i	$-0.537440\pi$
$17$	−1153.08			−0.234699			−0.117350	+	0.993091i	$0.537440\pi$
$18$		0			0
$19$	5613.44			0.818405			0.409202	−	0.912444i	$-0.365807\pi$
$19$	5613.44			0.818405			0.409202	+	0.912444i	$0.365807\pi$
$20$		0			0
$21$	6554.81	−	14141.0i	0.707786	−	1.52694i
$22$		0			0
$23$	−3383.70			−0.278104			−0.139052	−	0.990285i	$-0.544406\pi$
$23$	−3383.70			−0.278104			−0.139052	+	0.990285i	$0.544406\pi$
$24$		0			0
$25$	15488.4	−	2061.60i	0.991257	−	0.131942i
$26$		0			0
$27$	5224.38	+	18977.0i	0.265426	+	0.964131i
$28$		0			0
$29$			5725.09i			0.234740i	0.993088	+	0.117370i	$0.0374464\pi$
$29$			5725.09i			0.234740i	−0.993088	+	0.117370i	$0.962554\pi$
$30$		0			0
$31$	36900.2			1.23864			0.619318	−	0.785140i	$-0.287409\pi$
$31$	36900.2			1.23864			0.619318	+	0.785140i	$0.287409\pi$
$32$		0			0
$33$	22304.1	−	48117.7i	0.620644	−	1.33894i
$34$		0			0
$35$	−4770.85	−	72001.0i	−0.111273	−	1.67932i
$36$		0			0
$37$		−	32609.3i		−	0.643778i	−0.946777	−	0.321889i	$-0.895682\pi$
$37$		−	32609.3i		−	0.643778i	0.946777	−	0.321889i	$-0.104318\pi$
$38$		0			0
$39$	−23746.2	+	51228.9i	−0.400314	+	0.863617i
$40$		0			0
$41$			56515.1i			0.819998i	0.912086	+	0.409999i	$0.134471\pi$
$41$			56515.1i			0.819998i	−0.912086	+	0.409999i	$0.865529\pi$
$42$		0			0
$43$			113328.i			1.42538i	0.701479	+	0.712690i	$0.252523\pi$
$43$			113328.i			1.42538i	−0.701479	+	0.712690i	$0.747477\pi$
$44$		0			0
$45$	63360.7	+	65491.9i	0.695316	+	0.718704i
$46$		0			0
$47$	−157774.			−1.51964			−0.759822	−	0.650131i	$-0.774714\pi$
$47$	−157774.			−1.51964			−0.759822	+	0.650131i	$0.774714\pi$
$48$		0			0
$49$	−215593.			−1.83251
$50$		0			0
$51$	−28246.1	−	13093.0i	−0.212935	−	0.0987024i
$52$		0			0
$53$	−109599.			−0.736175			−0.368087	−	0.929791i	$-0.619987\pi$
$53$	−109599.			−0.736175			−0.368087	+	0.929791i	$0.619987\pi$
$54$		0			0
$55$	−16233.8	−	244998.i	−0.0975735	−	1.47257i
$56$		0			0
$57$	137508.	+	63739.6i	0.742514	+	0.344179i
$58$		0			0
$59$			227718.i			1.10877i	0.832261	+	0.554384i	$0.187046\pi$
$59$			227718.i			1.10877i	−0.832261	+	0.554384i	$0.812954\pi$
$60$		0			0
$61$	−271177.			−1.19471			−0.597357	−	0.801976i	$-0.703782\pi$
$61$	−271177.			−1.19471			−0.597357	+	0.801976i	$0.703782\pi$
$62$		0			0
$63$	321137.	−	271973.i	1.28431	−	1.08769i
$64$		0			0
$65$	17283.4	+	260840.i	0.0629347	+	0.949803i
$66$		0			0
$67$			219429.i			0.729574i	0.931091	+	0.364787i	$0.118858\pi$
$67$			219429.i			0.729574i	−0.931091	+	0.364787i	$0.881142\pi$
$68$		0			0
$69$	−82888.0	−	38421.2i	−0.252316	−	0.116956i
$70$		0			0
$71$		−	522399.i		−	1.45958i	−0.683672	−	0.729789i	$-0.739618\pi$
$71$		−	522399.i		−	1.45958i	0.683672	−	0.729789i	$-0.260382\pi$
$72$		0			0
$73$			1788.95i			0.00459864i	0.999997	+	0.00229932i	$0.000731898\pi$
$73$			1788.95i			0.00459864i	−0.999997	+	0.00229932i	$0.999268\pi$
$74$		0			0
$75$	402817.	+	125366.i	0.954826	+	0.297165i
$76$		0			0
$77$	−1.13392e6			−2.48377
$78$		0			0
$79$	794759.			1.61196			0.805979	−	0.591944i	$-0.201639\pi$
$79$	794759.			1.61196			0.805979	+	0.591944i	$0.201639\pi$
$80$		0			0
$81$	−87502.3	+	524188.i	−0.164651	+	0.986352i
$82$		0			0
$83$	−213226.			−0.372912			−0.186456	−	0.982463i	$-0.559700\pi$
$83$	−213226.			−0.372912			−0.186456	+	0.982463i	$0.559700\pi$
$84$		0			0
$85$	−143819.	+	9529.58i	−0.234186	+	0.0155173i
$86$		0			0
$87$	−65007.3	+	140243.i	−0.0987198	+	0.212973i
$88$		0			0
$89$		−	1.24220e6i		−	1.76206i	−0.473061	−	0.881030i	$-0.656851\pi$
$89$		−	1.24220e6i		−	1.76206i	0.473061	−	0.881030i	$-0.343149\pi$
$90$		0			0
$91$	1.20724e6			1.60203
$92$		0			0
$93$	903919.	+	418995.i	1.12378	+	0.520907i
$94$		0			0
$95$	700144.	−	46392.2i	0.816614	−	0.0541095i
$96$		0			0
$97$			492715.i			0.539859i	0.962880	+	0.269929i	$0.0870004\pi$
$97$			492715.i			0.539859i	−0.962880	+	0.269929i	$0.913000\pi$
$98$		0			0
$99$	1.09273e6	−	925445.i	1.12618	−	0.953773i
$100$		0			0
$101$			1.37089e6i			1.33057i	0.746590	+	0.665284i	$0.231690\pi$
$101$			1.37089e6i			1.33057i	−0.746590	+	0.665284i	$0.768310\pi$
$102$		0			0
$103$		−	915262.i		−	0.837595i	−0.908080	−	0.418797i	$-0.862452\pi$
$103$		−	915262.i		−	0.837595i	0.908080	−	0.418797i	$-0.137548\pi$
$104$		0			0
$105$	700690.	−	1.81793e6i	0.605283	−	1.57040i
$106$		0			0
$107$	−2.02000e6			−1.64892			−0.824462	−	0.565917i	$-0.808522\pi$
$107$	−2.02000e6			−1.64892			−0.824462	+	0.565917i	$0.808522\pi$
$108$		0			0
$109$	−72909.5			−0.0562995			−0.0281497	−	0.999604i	$-0.508962\pi$
$109$	−72909.5			−0.0562995			−0.0281497	+	0.999604i	$0.508962\pi$
$110$		0			0
$111$	370272.	−	798806.i	0.270740	−	0.584080i
$112$		0			0
$113$	895459.			0.620598			0.310299	−	0.950639i	$-0.399571\pi$
$113$	895459.			0.620598			0.310299	+	0.950639i	$0.399571\pi$
$114$		0			0
$115$	−422036.	+	27964.5i	−0.277496	+	0.0183871i
$116$		0			0
$117$	−1.16339e6	+	985284.i	−0.726386	+	0.615182i
$118$		0			0
$119$			665638.i			0.395000i
$120$		0			0
$121$	−2.08685e6			−1.17797
$122$		0			0
$123$	−641719.	+	1.38441e6i	−0.344849	+	0.743960i
$124$		0			0
$125$	1.91478e6	−	385140.i	0.980365	−	0.197192i
$126$		0			0
$127$			2.54012e6i			1.24006i	0.784578	+	0.620030i	$0.212879\pi$
$127$			2.54012e6i			1.24006i	−0.784578	+	0.620030i	$0.787121\pi$
$128$		0			0
$129$	−1.28681e6	+	2.77611e6i	−0.599442	+	1.29320i
$130$		0			0
$131$		−	1.17618e6i		−	0.523192i	−0.965178	−	0.261596i	$-0.915751\pi$
$131$		−	1.17618e6i		−	0.523192i	0.965178	−	0.261596i	$-0.0842488\pi$
$132$		0			0
$133$		−	3.24048e6i		−	1.37738i
$134$		0			0
$135$	808454.	+	2.32376e6i	0.328590	+	0.944473i
$136$		0			0
$137$	−3.00301e6			−1.16787			−0.583936	−	0.811800i	$-0.698488\pi$
$137$	−3.00301e6			−1.16787			−0.583936	+	0.811800i	$0.698488\pi$
$138$		0			0
$139$	−3.49837e6			−1.30263			−0.651316	−	0.758807i	$-0.725783\pi$
$139$	−3.49837e6			−1.30263			−0.651316	+	0.758807i	$0.725783\pi$
$140$		0			0
$141$	−3.86488e6	−	1.79150e6i	−1.37873	−	0.639085i
$142$		0			0
$143$	4.10789e6			1.40479
$144$		0			0
$145$	47314.9	+	714070.i	0.0155201	+	0.234227i
$146$		0			0
$147$	−5.28123e6	−	2.44802e6i	−1.66258	−	0.770660i
$148$		0			0
$149$			3.24451e6i			0.980822i	0.871491	+	0.490411i	$0.163153\pi$
$149$			3.24451e6i			0.980822i	−0.871491	+	0.490411i	$0.836847\pi$
$150$		0			0
$151$	2.67601e6			0.777243			0.388622	−	0.921397i	$-0.372951\pi$
$151$	2.67601e6			0.777243			0.388622	+	0.921397i	$0.372951\pi$
$152$		0			0
$153$	−543256.	−	641459.i	−0.151681	−	0.179099i
$154$		0			0
$155$	4.60244e6	−	304961.i	1.23593	−	0.0818935i
$156$		0			0
$157$			1.18905e6i			0.307255i	0.988129	+	0.153628i	$0.0490956\pi$
$157$			1.18905e6i			0.307255i	−0.988129	+	0.153628i	$0.950904\pi$
$158$		0			0
$159$	−2.68478e6	−	1.24448e6i	−0.667909	−	0.309597i
$160$		0			0
$161$			1.95331e6i			0.468051i
$162$		0			0
$163$			1.72124e6i			0.397446i	0.980056	+	0.198723i	$0.0636794\pi$
$163$			1.72124e6i			0.397446i	−0.980056	+	0.198723i	$0.936321\pi$
$164$		0			0
$165$	2.38424e6	−	6.18588e6i	0.530761	−	1.37705i
$166$		0			0
$167$	3.57401e6			0.767372			0.383686	−	0.923464i	$-0.374655\pi$
$167$	3.57401e6			0.767372			0.383686	+	0.923464i	$0.374655\pi$
$168$		0			0
$169$	453305.			0.0939141
$170$		0			0
$171$	2.64469e6	+	3.12277e6i	0.528916	+	0.624527i
$172$		0			0
$173$	2.35434e6			0.454706			0.227353	−	0.973812i	$-0.426993\pi$
$173$	2.35434e6			0.454706			0.227353	+	0.973812i	$0.426993\pi$
$174$		0			0
$175$	−1.19010e6	−	8.94100e6i	−0.222060	−	1.66829i
$176$		0			0
$177$	−2.58569e6	+	5.57824e6i	−0.466291	+	1.00595i
$178$		0			0
$179$			721898.i			0.125868i	0.998018	+	0.0629342i	$0.0200458\pi$
$179$			721898.i			0.125868i	−0.998018	+	0.0629342i	$0.979954\pi$
$180$		0			0
$181$	8.41728e6			1.41950			0.709751	−	0.704452i	$-0.248807\pi$
$181$	8.41728e6			1.41950			0.709751	+	0.704452i	$0.248807\pi$
$182$		0			0
$183$	−6.64283e6	−	3.07917e6i	−1.08393	−	0.502435i
$184$		0			0
$185$	−269499.	−	4.06724e6i	−0.0425639	−	0.642369i
$186$		0			0
$187$			2.26497e6i			0.346368i
$188$		0			0
$189$	1.09549e7	−	3.01589e6i	1.62264	−	0.446714i
$190$		0			0
$191$		−	6.76598e6i		−	0.971025i	−0.874230	−	0.485513i	$-0.838633\pi$
$191$		−	6.76598e6i		−	0.971025i	0.874230	−	0.485513i	$-0.161367\pi$
$192$		0			0
$193$			9.56942e6i			1.33111i	0.746349	+	0.665554i	$0.231805\pi$
$193$			9.56942e6i			1.33111i	−0.746349	+	0.665554i	$0.768195\pi$
$194$		0			0
$195$	−2.53841e6	+	6.58585e6i	−0.342340	+	0.888195i
$196$		0			0
$197$	−155980.			−0.0204019			−0.0102010	−	0.999948i	$-0.503247\pi$
$197$	−155980.			−0.0204019			−0.0102010	+	0.999948i	$0.503247\pi$
$198$		0			0
$199$	29316.1			0.00372003			0.00186002	−	0.999998i	$-0.499408\pi$
$199$	29316.1			0.00372003			0.00186002	+	0.999998i	$0.499408\pi$
$200$		0			0
$201$	−2.49157e6	+	5.37519e6i	−0.306821	+	0.661920i
$202$		0			0
$203$	3.30493e6			0.395070
$204$		0			0
$205$	467068.	+	7.04893e6i	0.0542149	+	0.818204i
$206$		0			0
$207$	−1.59418e6	−	1.88236e6i	−0.179733	−	0.212222i
$208$		0			0
$209$		−	1.10264e7i		−	1.20780i
$210$		0			0
$211$	3.23485e6			0.344355			0.172178	−	0.985066i	$-0.444920\pi$
$211$	3.23485e6			0.344355			0.172178	+	0.985066i	$0.444920\pi$
$212$		0			0
$213$	5.93175e6	−	1.27968e7i	0.613824	−	1.32423i
$214$		0			0
$215$	936594.	+	1.41350e7i	0.0942402	+	1.42226i
$216$		0			0
$217$		−	2.13014e7i		−	2.08463i
$218$		0			0
$219$	−20313.2	+	43822.7i	−0.00193395	+	0.00417221i
$220$		0			0
$221$		−	2.41142e6i		−	0.223407i
$222$		0			0
$223$		−	977603.i		−	0.0881552i	−0.999028	−	0.0440776i	$-0.985965\pi$
$223$		−	977603.i		−	0.0881552i	0.999028	−	0.0440776i	$-0.0140349\pi$
$224$		0			0
$225$	8.44402e6	+	7.64493e6i	0.741313	+	0.671160i
$226$		0			0
$227$	1.17072e7			1.00086			0.500432	−	0.865776i	$-0.333175\pi$
$227$	1.17072e7			1.00086			0.500432	+	0.865776i	$0.333175\pi$
$228$		0			0
$229$	7.33434e6			0.610738			0.305369	−	0.952234i	$-0.401220\pi$
$229$	7.33434e6			0.610738			0.305369	+	0.952234i	$0.401220\pi$
$230$		0			0
$231$	−2.77769e7	−	1.28755e7i	−2.25345	−	1.04455i
$232$		0			0
$233$	−9.54612e6			−0.754673			−0.377337	−	0.926076i	$-0.623160\pi$
$233$	−9.54612e6			−0.754673			−0.377337	+	0.926076i	$0.623160\pi$
$234$		0			0
$235$	−1.96786e7	+	1.30392e6i	−1.51632	+	0.100473i
$236$		0			0
$237$	1.94686e7	+	9.02434e6i	1.46248	+	0.677907i
$238$		0			0
$239$			1.01433e7i			0.742996i	0.928434	+	0.371498i	$0.121156\pi$
$239$			1.01433e7i			0.742996i	−0.928434	+	0.371498i	$0.878844\pi$
$240$		0			0
$241$	−1.83607e6			−0.131171			−0.0655855	−	0.997847i	$-0.520892\pi$
$241$	−1.83607e6			−0.131171			−0.0655855	+	0.997847i	$0.520892\pi$
$242$		0			0
$243$	−8.09554e6	+	1.18471e7i	−0.564192	+	0.825644i
$244$		0			0
$245$	−2.68902e7	+	1.78176e6i	−1.82850	+	0.121158i
$246$		0			0
$247$			1.17393e7i			0.779027i
$248$		0			0
$249$	−5.22325e6	−	2.42114e6i	−0.338332	−	0.156828i
$250$		0			0
$251$			2.54625e7i			1.61020i	0.593138	+	0.805101i	$0.297889\pi$
$251$			2.54625e7i			1.61020i	−0.593138	+	0.805101i	$0.702111\pi$
$252$		0			0
$253$			6.64654e6i			0.410425i
$254$		0			0
$255$	−3.63124e6	−	1.39960e6i	−0.218995	−	0.0844080i
$256$		0			0
$257$	1.15777e6			0.0682058			0.0341029	−	0.999418i	$-0.489143\pi$
$257$	1.15777e6			0.0682058			0.0341029	+	0.999418i	$0.489143\pi$
$258$		0			0
$259$	−1.88244e7			−1.08348
$260$		0			0
$261$	−3.18488e6	+	2.69730e6i	−0.179131	+	0.151707i
$262$		0			0
$263$	−3.06176e7			−1.68308			−0.841539	−	0.540197i	$-0.818350\pi$
$263$	−3.06176e7			−1.68308			−0.841539	+	0.540197i	$0.818350\pi$
$264$		0			0
$265$	−1.36700e7	+	905783.i	−0.734564	+	0.0486728i
$266$		0			0
$267$	1.41049e7	−	3.04292e7i	0.741032	−	1.59866i
$268$		0			0
$269$		−	1.65595e7i		−	0.850726i	−0.905023	−	0.425363i	$-0.860146\pi$
$269$		−	1.65595e7i		−	0.850726i	0.905023	−	0.425363i	$-0.139854\pi$
$270$		0			0
$271$	1.07489e7			0.540076			0.270038	−	0.962850i	$-0.412964\pi$
$271$	1.07489e7			0.540076			0.270038	+	0.962850i	$0.412964\pi$
$272$		0			0
$273$	2.95730e7	+	1.37080e7i	1.45347	+	0.673731i
$274$		0			0
$275$	−4.04957e6	−	3.04236e7i	−0.194720	−	1.46289i
$276$		0			0
$277$		−	8.05269e6i		−	0.378880i	−0.981892	−	0.189440i	$-0.939333\pi$
$277$		−	8.05269e6i		−	0.378880i	0.981892	−	0.189440i	$-0.0606672\pi$
$278$		0			0
$279$	1.73850e7	+	2.05277e7i	0.800503	+	0.945207i
$280$		0			0
$281$			8.58716e6i			0.387018i	0.981099	+	0.193509i	$0.0619868\pi$
$281$			8.58716e6i			0.387018i	−0.981099	+	0.193509i	$0.938013\pi$
$282$		0			0
$283$		−	2.02701e7i		−	0.894326i	−0.894452	−	0.447163i	$-0.852434\pi$
$283$		−	2.02701e7i		−	0.894326i	0.894452	−	0.447163i	$-0.147566\pi$
$284$		0			0
$285$	1.76777e7	+	6.81358e6i	0.763645	+	0.294334i
$286$		0			0
$287$	3.26245e7			1.38006
$288$		0			0
$289$	−2.28080e7			−0.944916
$290$		0			0
$291$	−5.59468e6	+	1.20697e7i	−0.227037	+	0.489798i
$292$		0			0
$293$	−1.15378e7			−0.458691			−0.229345	−	0.973345i	$-0.573659\pi$
$293$	−1.15378e7			−0.458691			−0.229345	+	0.973345i	$0.573659\pi$
$294$		0			0
$295$	1.88197e6	+	2.84024e7i	0.0733071	+	1.10634i
$296$		0			0
$297$	3.72762e7	−	1.02622e7i	1.42286	−	0.391715i
$298$		0			0
$299$		−	7.07630e6i		−	0.264723i
$300$		0			0
$301$	6.54208e7			2.39892
$302$		0			0
$303$	−1.55662e7	+	3.35816e7i	−0.559569	+	1.20718i
$304$		0			0
$305$	−3.38230e7	+	2.24114e6i	−1.19210	+	0.0789895i
$306$		0			0
$307$		−	1.88025e7i		−	0.649831i	−0.945743	−	0.324915i	$-0.894664\pi$
$307$		−	1.88025e7i		−	0.649831i	0.945743	−	0.324915i	$-0.105336\pi$
$308$		0			0
$309$	1.03926e7	−	2.24205e7i	0.352249	−	0.759924i
$310$		0			0
$311$		−	3.99873e7i		−	1.32935i	−0.747131	−	0.664677i	$-0.768569\pi$
$311$		−	3.99873e7i		−	1.32935i	0.747131	−	0.664677i	$-0.231431\pi$
$312$		0			0
$313$		−	3.56862e7i		−	1.16377i	−0.813271	−	0.581885i	$-0.802315\pi$
$313$		−	3.56862e7i		−	1.16377i	0.813271	−	0.581885i	$-0.197685\pi$
$314$		0			0
$315$	3.78066e7	−	3.65763e7i	1.20958	−	1.17022i
$316$		0			0
$317$	−3.27131e7			−1.02694			−0.513469	−	0.858108i	$-0.671640\pi$
$317$	−3.27131e7			−1.02694			−0.513469	+	0.858108i	$0.671640\pi$
$318$		0			0
$319$	1.12457e7			0.346429
$320$		0			0
$321$	−4.94826e7	−	2.29368e7i	−1.49602	−	0.693453i
$322$		0			0
$323$	−6.47272e6			−0.192079
$324$		0			0
$325$	4.31141e6	+	3.23908e7i	0.125594	+	0.943563i
$326$		0			0
$327$	−1.78601e6	−	827874.i	−0.0510788	−	0.0236767i
$328$		0			0
$329$			9.10784e7i			2.55757i
$330$		0			0
$331$	5.47453e7			1.50960			0.754802	−	0.655953i	$-0.227733\pi$
$331$	5.47453e7			1.50960			0.754802	+	0.655953i	$0.227733\pi$
$332$		0			0
$333$	1.81406e7	−	1.53634e7i	0.491268	−	0.416059i
$334$		0			0
$335$	1.81346e6	+	2.73686e7i	0.0482364	+	0.727977i
$336$		0			0
$337$			4.88792e7i			1.27713i	0.769568	+	0.638564i	$0.220471\pi$
$337$			4.88792e7i			1.27713i	−0.769568	+	0.638564i	$0.779529\pi$
$338$		0			0
$339$	2.19354e7	+	1.01678e7i	0.563050	+	0.260992i
$340$		0			0
$341$		−	7.24825e7i		−	1.82797i
$342$		0			0
$343$			5.65402e7i			1.40112i
$344$		0			0
$345$	−1.06559e7	−	4.10712e6i	−0.259496	−	0.100018i
$346$		0			0
$347$	7.06967e7			1.69204			0.846020	−	0.533150i	$-0.178992\pi$
$347$	7.06967e7			1.69204			0.846020	+	0.533150i	$0.178992\pi$
$348$		0			0
$349$	−1.99983e7			−0.470454			−0.235227	−	0.971940i	$-0.575583\pi$
$349$	−1.99983e7			−0.470454			−0.235227	+	0.971940i	$0.575583\pi$
$350$		0			0
$351$	−3.96864e7	+	1.09257e7i	−0.917742	+	0.252655i
$352$		0			0
$353$	−772050.			−0.0175518			−0.00877590	−	0.999961i	$-0.502793\pi$
$353$	−772050.			−0.0175518			−0.00877590	+	0.999961i	$0.502793\pi$
$354$		0			0
$355$	−4.31736e6	−	6.51570e7i	−0.0965013	−	1.45638i
$356$		0			0
$357$	−7.55820e6	+	1.63057e7i	−0.166117	+	0.358372i
$358$		0			0
$359$		−	6.53083e7i		−	1.41151i	−0.708455	−	0.705756i	$-0.750607\pi$
$359$		−	6.53083e7i		−	1.41151i	0.708455	−	0.705756i	$-0.249393\pi$
$360$		0			0
$361$	−1.55352e7			−0.330214
$362$		0			0
$363$	−5.11201e7	−	2.36958e7i	−1.06874	−	0.495395i
$364$		0			0
$365$	14784.8	+	223130.i	0.000304043	+	0.00458858i
$366$		0			0
$367$		−	7.64905e7i		−	1.54742i	−0.633538	−	0.773712i	$-0.718398\pi$
$367$		−	7.64905e7i		−	1.54742i	0.633538	−	0.773712i	$-0.281602\pi$
$368$		0			0
$369$	−3.14395e7	+	2.66263e7i	−0.625743	+	0.529946i
$370$		0			0
$371$			6.32686e7i			1.23899i
$372$		0			0
$373$		−	3.27687e6i		−	0.0631441i	−0.999501	−	0.0315721i	$-0.989949\pi$
$373$		−	3.27687e6i		−	0.0631441i	0.999501	−	0.0315721i	$-0.0100514\pi$
$374$		0			0
$375$	5.12781e7	+	1.23074e7i	0.972384	+	0.233385i
$376$		0			0
$377$	−1.19728e7			−0.223446
$378$		0			0
$379$	−2.34796e7			−0.431293			−0.215647	−	0.976471i	$-0.569186\pi$
$379$	−2.34796e7			−0.431293			−0.215647	+	0.976471i	$0.569186\pi$
$380$		0			0
$381$	−2.88426e7	+	6.22234e7i	−0.521506	+	1.12507i
$382$		0			0
$383$	4.17247e7			0.742672			0.371336	−	0.928499i	$-0.378900\pi$
$383$	4.17247e7			0.742672			0.371336	+	0.928499i	$0.378900\pi$
$384$		0			0
$385$	−1.41430e8	+	9.37130e6i	−2.47834	+	0.164217i
$386$		0			0
$387$	−6.30444e7	+	5.33928e7i	−1.08771	+	0.921190i
$388$		0			0
$389$		−	1.14875e7i		−	0.195154i	−0.995228	−	0.0975772i	$-0.968891\pi$
$389$		−	1.14875e7i		−	0.195154i	0.995228	−	0.0975772i	$-0.0311093\pi$
$390$		0			0
$391$	3.90166e6			0.0652708
$392$		0			0
$393$	1.33553e7	−	2.88121e7i	0.220028	−	0.474676i
$394$		0			0
$395$	9.91274e7	−	6.56827e6i	1.60843	−	0.106576i
$396$		0			0
$397$		−	4.37851e7i		−	0.699768i	−0.936793	−	0.349884i	$-0.886221\pi$
$397$		−	4.37851e7i		−	0.699768i	0.936793	−	0.349884i	$-0.113779\pi$
$398$		0			0
$399$	3.67950e7	−	7.93796e7i	0.579256	−	1.24966i
$400$		0			0
$401$			9.48066e7i			1.47030i	0.677905	+	0.735149i	$0.262888\pi$
$401$			9.48066e7i			1.47030i	−0.677905	+	0.735149i	$0.737112\pi$
$402$		0			0
$403$			7.71692e7i			1.17904i
$404$		0			0
$405$	−6.58172e6	+	6.61033e7i	−0.0990773	+	0.995080i
$406$		0			0
$407$	−6.40539e7			−0.950084
$408$		0			0
$409$	−7.61855e7			−1.11353			−0.556766	−	0.830669i	$-0.687958\pi$
$409$	−7.61855e7			−1.11353			−0.556766	+	0.830669i	$0.687958\pi$
$410$		0			0
$411$	−7.35626e7	−	3.40986e7i	−1.05957	−	0.491147i
$412$		0			0
$413$	1.31455e8			1.86606
$414$		0			0
$415$	−2.65950e7	+	1.76220e6i	−0.372096	+	0.0246554i
$416$		0			0
$417$	−8.56971e7	−	3.97234e7i	−1.18184	−	0.547820i
$418$		0			0
$419$		−	2.04931e7i		−	0.278590i	−0.990251	−	0.139295i	$-0.955516\pi$
$419$		−	2.04931e7i		−	0.278590i	0.990251	−	0.139295i	$-0.0444837\pi$
$420$		0			0
$421$	8.38839e7			1.12417			0.562086	−	0.827079i	$-0.309999\pi$
$421$	8.38839e7			1.12417			0.562086	+	0.827079i	$0.309999\pi$
$422$		0			0
$423$	−7.43331e7	−	8.77700e7i	−0.982112	−	1.15964i
$424$		0			0
$425$	−1.78593e7	+	2.37718e6i	−0.232647	+	0.0309668i
$426$		0			0
$427$			1.56543e8i			2.01071i
$428$		0			0
$429$	1.00628e8	+	4.66444e7i	1.27452	+	0.590782i
$430$		0			0
$431$			8.73808e7i			1.09140i	0.837980	+	0.545700i	$0.183736\pi$
$431$			8.73808e7i			1.09140i	−0.837980	+	0.545700i	$0.816264\pi$
$432$		0			0
$433$		−	6.07750e7i		−	0.748619i	−0.927304	−	0.374310i	$-0.877880\pi$
$433$		−	6.07750e7i		−	0.748619i	0.927304	−	0.374310i	$-0.122120\pi$
$434$		0			0
$435$	−6.94909e6	+	1.80293e7i	−0.0844229	+	0.219034i
$436$		0			0
$437$	−1.89942e7			−0.227602
$438$		0			0
$439$	7.05339e7			0.833690			0.416845	−	0.908978i	$-0.363136\pi$
$439$	7.05339e7			0.833690			0.416845	+	0.908978i	$0.363136\pi$
$440$		0			0
$441$	−1.01574e8	−	1.19935e8i	−1.18431	−	1.39839i
$442$		0			0
$443$	−9.46818e7			−1.08907			−0.544534	−	0.838739i	$-0.683294\pi$
$443$	−9.46818e7			−1.08907			−0.544534	+	0.838739i	$0.683294\pi$
$444$		0			0
$445$	−1.02661e7	−	1.54935e8i	−0.116500	−	1.75820i
$446$		0			0
$447$	−3.68408e7	+	7.94784e7i	−0.412484	+	0.889870i
$448$		0			0
$449$		−	6.22686e7i		−	0.687907i	−0.938987	−	0.343954i	$-0.888234\pi$
$449$		−	6.22686e7i		−	0.687907i	0.938987	−	0.343954i	$-0.111766\pi$
$450$		0			0
$451$	1.11012e8			1.21015
$452$		0			0
$453$	6.55523e7	+	3.03856e7i	0.705169	+	0.326869i
$454$		0			0
$455$	1.50575e8	−	9.97724e6i	1.59852	−	0.105920i
$456$		0			0
$457$			1.06549e8i			1.11635i	0.829724	+	0.558174i	$0.188498\pi$
$457$			1.06549e8i			1.11635i	−0.829724	+	0.558174i	$0.811502\pi$
$458$		0			0
$459$	−6.02411e6	−	2.18819e7i	−0.0622953	−	0.226281i
$460$		0			0
$461$		−	1.54272e8i		−	1.57465i	−0.616538	−	0.787325i	$-0.711465\pi$
$461$		−	1.54272e8i		−	1.57465i	0.616538	−	0.787325i	$-0.288535\pi$
$462$		0			0
$463$		−	2.79213e7i		−	0.281315i	−0.990058	−	0.140658i	$-0.955078\pi$
$463$		−	2.79213e7i		−	0.281315i	0.990058	−	0.140658i	$-0.0449217\pi$
$464$		0			0
$465$	1.16205e8	+	4.47894e7i	1.15576	+	0.445468i
$466$		0			0
$467$	3.44176e6			0.0337933			0.0168966	−	0.999857i	$-0.494621\pi$
$467$	3.44176e6			0.0337933			0.0168966	+	0.999857i	$0.494621\pi$
$468$		0			0
$469$	1.26670e8			1.22788
$470$		0			0
$471$	−1.35014e7	+	2.91272e7i	−0.129216	+	0.278764i
$472$		0			0
$473$	2.22608e8			2.10357
$474$		0			0
$475$	8.69431e7	−	1.15727e7i	0.811250	−	0.107982i
$476$		0			0
$477$	−5.16363e7	−	6.09704e7i	−0.475773	−	0.561777i
$478$		0			0
$479$			5.09773e7i			0.463843i	0.972735	+	0.231921i	$0.0745012\pi$
$479$			5.09773e7i			0.463843i	−0.972735	+	0.231921i	$0.925499\pi$
$480$		0			0
$481$	6.81955e7			0.612803
$482$		0			0
$483$	−2.21795e7	+	4.78488e7i	−0.196838	+	0.424649i
$484$		0			0
$485$	4.07203e6	+	6.14546e7i	0.0356932	+	0.538678i
$486$		0			0
$487$		−	1.88123e8i		−	1.62875i	−0.580339	−	0.814375i	$-0.697080\pi$
$487$		−	1.88123e8i		−	1.62875i	0.580339	−	0.814375i	$-0.302920\pi$
$488$		0			0
$489$	−1.95443e7	+	4.21639e7i	−0.167145	+	0.360591i
$490$		0			0
$491$		−	1.88211e8i		−	1.59001i	−0.606601	−	0.795006i	$-0.707468\pi$
$491$		−	1.88211e8i		−	1.59001i	0.606601	−	0.795006i	$-0.292532\pi$
$492$		0			0
$493$		−	6.60146e6i		−	0.0550934i
$494$		0			0
$495$	1.28645e8	−	1.24458e8i	1.06066	−	1.02615i
$496$		0			0
$497$	−3.01566e8			−2.45648
$498$		0			0
$499$	−1.48935e8			−1.19866			−0.599329	−	0.800503i	$-0.704566\pi$
$499$	−1.48935e8			−1.19866			−0.599329	+	0.800503i	$0.704566\pi$
$500$		0			0
$501$	8.75499e7	+	4.05822e7i	0.696214	+	0.322717i
$502$		0			0
$503$	−1.03064e8			−0.809848			−0.404924	−	0.914350i	$-0.632702\pi$
$503$	−1.03064e8			−0.809848			−0.404924	+	0.914350i	$0.632702\pi$
$504$		0			0
$505$	1.13297e7	+	1.70986e8i	0.0879717	+	1.32766i
$506$		0			0
$507$	1.11043e7	+	5.14720e6i	0.0852054	+	0.0394955i
$508$		0			0
$509$		−	3.52846e7i		−	0.267566i	−0.991011	−	0.133783i	$-0.957287\pi$
$509$		−	3.52846e7i		−	0.267566i	0.991011	−	0.133783i	$-0.0427126\pi$
$510$		0			0
$511$	1.03271e6			0.00773955
$512$		0			0
$513$	2.93267e7	+	1.06526e8i	0.217226	+	0.789049i
$514$		0			0
$515$	−7.56417e6	−	1.14157e8i	−0.0553783	−	0.835762i
$516$		0			0
$517$			3.09913e8i			2.24269i
$518$		0			0
$519$	5.76726e7	+	2.67331e7i	0.412541	+	0.191226i
$520$		0			0
$521$			1.46705e8i			1.03736i	0.854968	+	0.518681i	$0.173577\pi$
$521$			1.46705e8i			1.03736i	−0.854968	+	0.518681i	$0.826423\pi$
$522$		0			0
$523$		−	2.08549e6i		−	0.0145782i	−0.999973	−	0.00728910i	$-0.997680\pi$
$523$		−	2.08549e6i		−	0.0145782i	0.999973	−	0.00728910i	$-0.00232021\pi$
$524$		0			0
$525$	7.23704e7	−	2.32535e8i	0.500130	−	1.60698i
$526$		0			0
$527$	−4.25488e7			−0.290707
$528$		0			0
$529$	−1.36586e8			−0.922658
$530$		0			0
$531$	−1.26680e8	+	1.07286e8i	−0.846104	+	0.716572i
$532$		0			0
$533$	−1.18190e8			−0.780544
$534$		0			0
$535$	−2.51948e8	+	1.66943e7i	−1.64532	+	0.109020i
$536$		0			0
$537$	−8.19702e6	+	1.76838e7i	−0.0529338	+	0.114197i
$538$		0			0
$539$			4.23486e8i			2.70441i
$540$		0			0
$541$	6.27649e7			0.396392			0.198196	−	0.980162i	$-0.436492\pi$
$541$	6.27649e7			0.396392			0.198196	+	0.980162i	$0.436492\pi$
$542$		0			0
$543$	2.06192e8	+	9.55767e7i	1.28787	+	0.596970i
$544$		0			0
$545$	−9.09374e6	+	602559.i	−0.0561763	+	0.00372229i
$546$		0			0
$547$		−	1.73173e8i		−	1.05808i	−0.848598	−	0.529039i	$-0.822553\pi$
$547$		−	1.73173e8i		−	1.05808i	0.848598	−	0.529039i	$-0.177447\pi$
$548$		0			0
$549$	−1.27761e8	−	1.50856e8i	−0.772116	−	0.911689i
$550$		0			0
$551$			3.21374e7i			0.192113i
$552$		0			0
$553$		−	4.58791e8i		−	2.71294i
$554$		0			0
$555$	3.95811e7	−	1.02692e8i	0.231531	−	0.600702i
$556$		0			0
$557$	5.17506e7			0.299468			0.149734	−	0.988726i	$-0.452158\pi$
$557$	5.17506e7			0.299468			0.149734	+	0.988726i	$0.452158\pi$
$558$		0			0
$559$	−2.37001e8			−1.35680
$560$		0			0
$561$	−2.57183e7	+	5.54834e7i	−0.145665	+	0.314249i
$562$		0			0
$563$	−9.07620e7			−0.508603			−0.254301	−	0.967125i	$-0.581846\pi$
$563$	−9.07620e7			−0.508603			−0.254301	+	0.967125i	$0.581846\pi$
$564$		0			0
$565$	1.11687e8	−	7.40051e6i	0.619240	−	0.0410314i
$566$		0			0
$567$	3.02598e8	+	5.05126e7i	1.66004	+	0.277109i
$568$		0			0
$569$		−	1.75126e8i		−	0.950633i	−0.879815	−	0.475317i	$-0.842333\pi$
$569$		−	1.75126e8i		−	0.950633i	0.879815	−	0.475317i	$-0.157667\pi$
$570$		0			0
$571$	−1.10251e8			−0.592209			−0.296104	−	0.955156i	$-0.595688\pi$
$571$	−1.10251e8			−0.592209			−0.296104	+	0.955156i	$0.595688\pi$
$572$		0			0
$573$	7.68265e7	−	1.65741e8i	0.408364	−	0.880982i
$574$		0			0
$575$	−5.24080e7	+	6.97583e6i	−0.275673	+	0.0366937i
$576$		0			0
$577$		−	9.96873e6i		−	0.0518934i	−0.999663	−	0.0259467i	$-0.991740\pi$
$577$		−	9.96873e6i		−	0.0518934i	0.999663	−	0.0259467i	$-0.00826003\pi$
$578$		0			0
$579$	−1.08659e8	+	2.34415e8i	−0.559796	+	1.20767i
$580$		0			0
$581$			1.23089e8i			0.627613i
$582$		0			0
$583$			2.15285e8i			1.08644i
$584$		0			0
$585$	−1.36963e8	+	1.32506e8i	−0.684124	+	0.661862i
$586$		0			0
$587$	−2.37250e8			−1.17298			−0.586492	−	0.809955i	$-0.699491\pi$
$587$	−2.37250e8			−1.17298			−0.586492	+	0.809955i	$0.699491\pi$
$588$		0			0
$589$	2.07137e8			1.01371
$590$		0			0
$591$	−3.82094e6	−	1.77113e6i	−0.0185101	−	0.00858001i
$592$		0			0
$593$	1.60386e8			0.769135			0.384567	−	0.923097i	$-0.374351\pi$
$593$	1.60386e8			0.769135			0.384567	+	0.923097i	$0.374351\pi$
$594$		0			0
$595$	5.50115e6	+	8.30227e7i	0.0261158	+	0.394136i
$596$		0			0
$597$	718135.	+	332879.i	0.00337507	+	0.00156445i
$598$		0			0
$599$		−	2.76259e8i		−	1.28539i	−0.766121	−	0.642697i	$-0.777815\pi$
$599$		−	2.76259e8i		−	1.28539i	0.766121	−	0.642697i	$-0.222185\pi$
$600$		0			0
$601$	−1.13920e8			−0.524777			−0.262389	−	0.964962i	$-0.584510\pi$
$601$	−1.13920e8			−0.524777			−0.262389	+	0.964962i	$0.584510\pi$
$602$		0			0
$603$	−1.22069e8	+	1.03381e8i	−0.556739	+	0.471507i
$604$		0			0
$605$	−2.60286e8	+	1.72467e7i	−1.17540	+	0.0778827i
$606$		0			0
$607$			1.44632e8i			0.646691i	0.946281	+	0.323346i	$0.104808\pi$
$607$			1.44632e8i			0.646691i	−0.946281	+	0.323346i	$0.895192\pi$
$608$		0			0
$609$	8.09584e7	+	3.75268e7i	0.358435	+	0.166146i
$610$		0			0
$611$		−	3.29952e8i		−	1.44653i
$612$		0			0
$613$			3.45683e8i			1.50071i	0.661035	+	0.750355i	$0.270118\pi$
$613$			3.45683e8i			1.50071i	−0.661035	+	0.750355i	$0.729882\pi$
$614$		0			0
$615$	−6.85979e7	+	1.77976e8i	−0.294907	+	0.765132i
$616$		0			0
$617$	3.46558e8			1.47544			0.737718	−	0.675109i	$-0.235904\pi$
$617$	3.46558e8			1.47544			0.737718	+	0.675109i	$0.235904\pi$
$618$		0			0
$619$	6.62514e7			0.279333			0.139667	−	0.990199i	$-0.455397\pi$
$619$	6.62514e7			0.279333			0.139667	+	0.990199i	$0.455397\pi$
$620$		0			0
$621$	−1.76777e7	−	6.42124e7i	−0.0738162	−	0.268129i
$622$		0			0
$623$	−7.17085e8			−2.96556
$624$		0			0
$625$	2.35640e8	−	6.38618e7i	0.965182	−	0.261578i
$626$		0			0
$627$	1.25203e8	−	2.70105e8i	0.507938	−	1.09580i
$628$		0			0
$629$			3.76010e7i			0.151094i
$630$		0			0
$631$	4.64322e7			0.184812			0.0924062	−	0.995721i	$-0.470544\pi$
$631$	4.64322e7			0.184812			0.0924062	+	0.995721i	$0.470544\pi$
$632$		0			0
$633$	7.92418e7	+	3.67311e7i	0.312423	+	0.144818i
$634$		0			0
$635$	2.09928e7	+	3.16820e8i	0.0819876	+	1.23735i
$636$		0			0
$637$		−	4.50868e8i		−	1.74434i
$638$		0			0
$639$	2.90612e8	−	2.46121e8i	1.11381	−	0.943293i
$640$		0			0
$641$			3.05739e7i			0.116085i	0.998314	+	0.0580427i	$0.0184859\pi$
$641$			3.05739e7i			0.116085i	−0.998314	+	0.0580427i	$0.981514\pi$
$642$		0			0
$643$			1.79228e7i			0.0674176i	0.999432	+	0.0337088i	$0.0107319\pi$
$643$			1.79228e7i			0.0674176i	−0.999432	+	0.0337088i	$0.989268\pi$
$644$		0			0
$645$	−1.37557e8	+	3.56889e8i	−0.512629	+	1.33001i
$646$		0			0
$647$	2.35543e8			0.869674			0.434837	−	0.900509i	$-0.356806\pi$
$647$	2.35543e8			0.869674			0.434837	+	0.900509i	$0.356806\pi$
$648$		0			0
$649$	4.47302e8			1.63631
$650$		0			0
$651$	2.41874e8	−	5.21806e8i	0.876690	−	1.89133i
$652$		0			0
$653$	4.09475e8			1.47058			0.735289	−	0.677754i	$-0.237046\pi$
$653$	4.09475e8			1.47058			0.735289	+	0.677754i	$0.237046\pi$
$654$		0			0
$655$	−9.72054e6	−	1.46701e8i	−0.0345913	−	0.522047i
$656$		0			0
$657$	−995197.	+	842840.i	−0.00350924	+	0.00297200i
$658$		0			0
$659$		−	4.99908e7i		−	0.174676i	−0.996179	−	0.0873381i	$-0.972164\pi$
$659$		−	4.99908e7i		−	0.174676i	0.996179	−	0.0873381i	$-0.0278361\pi$
$660$		0			0
$661$	−2.04661e8			−0.708647			−0.354323	−	0.935123i	$-0.615289\pi$
$661$	−2.04661e8			−0.708647			−0.354323	+	0.935123i	$0.615289\pi$
$662$		0			0
$663$	2.73812e7	−	5.90708e7i	0.0939534	−	0.202690i
$664$		0			0
$665$	−2.67808e7	−	4.04173e8i	−0.0910667	−	1.37437i
$666$		0			0
$667$		−	1.93719e7i		−	0.0652823i
$668$		0			0
$669$	1.11005e7	−	2.39476e7i	0.0370736	−	0.0799806i
$670$		0			0
$671$			5.32669e8i			1.76315i
$672$		0			0
$673$			2.22290e8i			0.729246i	0.931155	+	0.364623i	$0.118802\pi$
$673$			2.22290e8i			0.729246i	−0.931155	+	0.364623i	$0.881198\pi$
$674$		0			0
$675$	1.20040e8	+	2.83153e8i	0.390315	+	0.920681i
$676$		0			0
$677$	1.74942e8			0.563805			0.281902	−	0.959443i	$-0.409035\pi$
$677$	1.74942e8			0.563805			0.281902	+	0.959443i	$0.409035\pi$
$678$		0			0
$679$	2.84430e8			0.908586
$680$		0			0
$681$	2.86782e8	+	1.32933e8i	0.908053	+	0.420912i
$682$		0			0
$683$	1.36393e8			0.428084			0.214042	−	0.976825i	$-0.431337\pi$
$683$	1.36393e8			0.428084			0.214042	+	0.976825i	$0.431337\pi$
$684$		0			0
$685$	−3.74555e8	+	2.48183e7i	−1.16532	+	0.0772148i
$686$		0			0
$687$	1.79664e8	+	8.32801e7i	0.554104	+	0.256845i
$688$		0			0
$689$		−	2.29205e8i		−	0.700754i
$690$		0			0
$691$	1.64003e8			0.497069			0.248535	−	0.968623i	$-0.420051\pi$
$691$	1.64003e8			0.497069			0.248535	+	0.968623i	$0.420051\pi$
$692$		0			0
$693$	−5.34233e8	−	6.30804e8i	−1.60521	−	1.89537i
$694$		0			0
$695$	−4.36340e8	+	2.89122e7i	−1.29978	+	0.0861246i
$696$		0			0
$697$		−	6.51662e7i		−	0.192453i
$698$		0			0
$699$	−2.33844e8	−	1.08394e8i	−0.684692	−	0.317377i
$700$		0			0
$701$			2.66072e6i			0.00772406i	0.999993	+	0.00386203i	$0.00122933\pi$
$701$			2.66072e6i			0.00772406i	−0.999993	+	0.00386203i	$0.998771\pi$
$702$		0			0
$703$		−	1.83050e8i		−	0.526871i
$704$		0			0
$705$	−4.96859e8	−	1.91506e8i	−1.41797	−	0.546531i
$706$		0			0
$707$	7.91373e8			2.23935
$708$		0			0
$709$	−1.59069e8			−0.446322			−0.223161	−	0.974782i	$-0.571638\pi$
$709$	−1.59069e8			−0.446322			−0.223161	+	0.974782i	$0.571638\pi$
$710$		0			0
$711$	3.74440e8	+	4.42126e8i	1.04177	+	1.23009i
$712$		0			0
$713$	−1.24859e8			−0.344470
$714$		0			0
$715$	5.12363e8	−	3.39496e7i	1.40171	−	0.0928788i
$716$		0			0
$717$	−1.15176e8	+	2.48474e8i	−0.312466	+	0.674098i
$718$		0			0
$719$		−	5.30930e8i		−	1.42840i	−0.699940	−	0.714201i	$-0.746790\pi$
$719$		−	5.30930e8i		−	1.42840i	0.699940	−	0.714201i	$-0.253210\pi$
$720$		0			0
$721$	−5.28354e8			−1.40968
$722$		0			0
$723$	−4.49769e7	−	2.08482e7i	−0.119008	−	0.0551638i
$724$		0			0
$725$	1.18028e7	+	8.86724e7i	0.0309722	+	0.232688i
$726$		0			0
$727$			1.05344e8i			0.274162i	0.990560	+	0.137081i	$0.0437720\pi$
$727$			1.05344e8i			0.274162i	−0.990560	+	0.137081i	$0.956228\pi$
$728$		0			0
$729$	−3.32832e8	+	1.98286e8i	−0.859098	+	0.511811i
$730$		0			0
$731$		−	1.30675e8i		−	0.334535i
$732$		0			0
$733$			5.05103e8i			1.28253i	0.767319	+	0.641266i	$0.221590\pi$
$733$			5.05103e8i			1.28253i	−0.767319	+	0.641266i	$0.778410\pi$
$734$		0			0
$735$	−6.78941e8	−	2.61686e8i	−1.70990	−	0.659051i
$736$		0			0
$737$	4.31020e8			1.07670
$738$		0			0
$739$	−3.95184e8			−0.979189			−0.489594	−	0.871950i	$-0.662855\pi$
$739$	−3.95184e8			−0.979189			−0.489594	+	0.871950i	$0.662855\pi$
$740$		0			0
$741$	−1.33298e8	+	2.87570e8i	−0.327619	+	0.706788i
$742$		0			0
$743$	3.65070e7			0.0890041			0.0445020	−	0.999009i	$-0.485830\pi$
$743$	3.65070e7			0.0890041			0.0445020	+	0.999009i	$0.485830\pi$
$744$		0			0
$745$	2.68142e7	+	4.04676e8i	0.0648479	+	0.978676i
$746$		0			0
$747$	−1.00459e8	−	1.18618e8i	−0.241005	−	0.284570i
$748$		0			0
$749$			1.16609e9i			2.77515i
$750$		0			0
$751$	−3.56142e7			−0.0840821			−0.0420411	−	0.999116i	$-0.513386\pi$
$751$	−3.56142e7			−0.0840821			−0.0420411	+	0.999116i	$0.513386\pi$
$752$		0			0
$753$	−2.89122e8	+	6.23738e8i	−0.677169	+	1.46089i
$754$		0			0
$755$	3.33769e8	−	2.21158e7i	0.775543	−	0.0513881i
$756$		0			0
$757$		−	6.62243e8i		−	1.52661i	−0.646035	−	0.763307i	$-0.723574\pi$
$757$		−	6.62243e8i		−	1.52661i	0.646035	−	0.763307i	$-0.276426\pi$
$758$		0			0
$759$	−7.54702e7	+	1.62816e8i	−0.172604	+	0.372366i
$760$		0			0
$761$		−	2.67728e8i		−	0.607491i	−0.952753	−	0.303746i	$-0.901763\pi$
$761$		−	2.67728e8i		−	0.607491i	0.952753	−	0.303746i	$-0.0982373\pi$
$762$		0			0
$763$			4.20885e7i			0.0947524i
$764$		0			0
$765$	−7.30598e7	−	7.55171e7i	−0.163190	−	0.168679i
$766$		0			0
$767$	−4.76224e8			−1.05542
$768$		0			0
$769$	−1.59472e8			−0.350675			−0.175337	−	0.984508i	$-0.556102\pi$
$769$	−1.59472e8			−0.350675			−0.175337	+	0.984508i	$0.556102\pi$
$770$		0			0
$771$	2.83609e7	+	1.31462e7i	0.0618810	+	0.0286839i
$772$		0			0
$773$	2.52540e8			0.546754			0.273377	−	0.961907i	$-0.411859\pi$
$773$	2.52540e8			0.546754			0.273377	+	0.961907i	$0.411859\pi$
$774$		0			0
$775$	5.71525e8	−	7.60735e7i	1.22781	−	0.163429i
$776$		0			0
$777$	−4.61128e8	−	2.13748e8i	−0.983011	−	0.455657i
$778$		0			0
$779$			3.17244e8i			0.671090i
$780$		0			0
$781$	−1.02614e9			−2.15404
$782$		0			0
$783$	−1.08645e8	+	2.99100e7i	−0.226321	+	0.0623063i
$784$		0			0
$785$	9.82684e6	+	1.48305e8i	0.0203145	+	0.306583i
$786$		0			0
$787$		−	3.29615e8i		−	0.676212i	−0.941108	−	0.338106i	$-0.890214\pi$
$787$		−	3.29615e8i		−	0.676212i	0.941108	−	0.338106i	$-0.109786\pi$
$788$		0			0
$789$	−7.50018e8	−	3.47657e8i	−1.52701	−	0.707816i
$790$		0			0
$791$		−	5.16923e8i		−	1.04447i
$792$		0			0
$793$		−	5.67111e8i		−	1.13723i
$794$		0			0
$795$	−3.45148e8	−	1.33032e8i	−0.686917	−	0.264761i
$796$		0			0
$797$	6.26420e8			1.23734			0.618672	−	0.785649i	$-0.287671\pi$
$797$	6.26420e8			1.23734			0.618672	+	0.785649i	$0.287671\pi$
$798$		0			0
$799$	1.81926e8			0.356659
$800$		0			0
$801$	6.91037e8	−	5.85244e8i	1.34463	−	1.13878i
$802$		0			0
$803$	3.51401e6			0.00678666
$804$		0			0
$805$	1.61431e7	+	2.43629e8i	0.0309456	+	0.467027i
$806$		0			0
$807$	1.88030e8	−	4.05646e8i	0.357772	−	0.771838i
$808$		0			0
$809$			7.89370e8i			1.49085i	0.666588	+	0.745427i	$0.267754\pi$
$809$			7.89370e8i			1.49085i	−0.666588	+	0.745427i	$0.732246\pi$
$810$		0			0
$811$	−3.61805e8			−0.678284			−0.339142	−	0.940735i	$-0.610137\pi$
$811$	−3.61805e8			−0.678284			−0.339142	+	0.940735i	$0.610137\pi$
$812$		0			0
$813$	2.63307e8	+	1.22051e8i	0.489995	+	0.227128i
$814$		0			0
$815$	1.42251e7	+	2.14684e8i	0.0262775	+	0.396576i
$816$		0			0
$817$			6.36158e8i			1.16654i
$818$		0			0
$819$	5.68776e8	+	6.71591e8i	1.03536	+	1.22251i
$820$		0			0
$821$		−	5.19435e7i		−	0.0938647i	−0.998898	−	0.0469323i	$-0.985055\pi$
$821$		−	5.19435e7i		−	0.0938647i	0.998898	−	0.0469323i	$-0.0149445\pi$
$822$		0			0
$823$		−	1.92402e7i		−	0.0345153i	−0.999851	−	0.0172576i	$-0.994506\pi$
$823$		−	1.92402e7i		−	0.0345153i	0.999851	−	0.0172576i	$-0.00549355\pi$
$824$		0			0
$825$	2.46255e8	−	7.91248e8i	0.438554	−	1.40913i
$826$		0			0
$827$	7.80571e7			0.138005			0.0690027	−	0.997616i	$-0.478018\pi$
$827$	7.80571e7			0.138005			0.0690027	+	0.997616i	$0.478018\pi$
$828$		0			0
$829$	−2.14440e8			−0.376394			−0.188197	−	0.982131i	$-0.560264\pi$
$829$	−2.14440e8			−0.376394			−0.188197	+	0.982131i	$0.560264\pi$
$830$		0			0
$831$	9.14368e7	−	1.97261e8i	0.159337	−	0.343746i
$832$		0			0
$833$	2.48595e8			0.430088
$834$		0			0
$835$	4.45773e8	−	2.95373e7i	0.765693	−	0.0507355i
$836$		0			0
$837$	1.92781e8	+	7.00255e8i	0.328767	+	1.19421i
$838$		0			0
$839$		−	5.80826e8i		−	0.983468i	−0.870746	−	0.491734i	$-0.836363\pi$
$839$		−	5.80826e8i		−	0.983468i	0.870746	−	0.491734i	$-0.163637\pi$
$840$		0			0
$841$	5.62047e8			0.944897
$842$		0			0
$843$	−9.75057e7	+	2.10354e8i	−0.162760	+	0.351129i
$844$		0			0
$845$	5.65392e7	−	3.74633e6i	0.0937086	−	0.00620921i
$846$		0			0
$847$			1.20468e9i			1.98254i
$848$		0			0
$849$	2.30163e8	−	4.96542e8i	0.376108	−	0.811395i
$850$		0			0
$851$			1.10340e8i			0.179037i
$852$		0			0
$853$		−	1.11351e9i		−	1.79411i	−0.441921	−	0.897054i	$-0.645703\pi$
$853$		−	1.11351e9i		−	1.79411i	0.441921	−	0.897054i	$-0.354297\pi$
$854$		0			0
$855$	3.55671e8	+	3.67635e8i	0.569050	+	0.588190i
$856$		0			0
$857$	−1.01919e9			−1.61925			−0.809624	−	0.586949i	$-0.800329\pi$
$857$	−1.01919e9			−1.61925			−0.809624	+	0.586949i	$0.800329\pi$
$858$		0			0
$859$	2.16974e8			0.342316			0.171158	−	0.985244i	$-0.445249\pi$
$859$	2.16974e8			0.342316			0.171158	+	0.985244i	$0.445249\pi$
$860$		0			0
$861$	7.99180e8	+	3.70446e8i	1.25209	+	0.580384i
$862$		0			0
$863$	6.60488e7			0.102762			0.0513810	−	0.998679i	$-0.483638\pi$
$863$	6.60488e7			0.102762			0.0513810	+	0.998679i	$0.483638\pi$
$864$		0			0
$865$	2.93649e8	−	1.94574e7i	0.453711	−	0.0300633i
$866$		0			0
$867$	−5.58711e8	−	2.58980e8i	−0.857294	−	0.397383i
$868$		0			0
$869$		−	1.56113e9i		−	2.37892i
$870$		0			0
$871$	−4.58890e8			−0.694470
$872$		0			0
$873$	−2.74098e8	+	2.32136e8i	−0.411968	+	0.348899i
$874$		0			0
$875$	−2.22330e8	−	1.10534e9i	−0.331875	−	1.64996i
$876$		0			0
$877$		−	9.63996e7i		−	0.142915i	−0.997444	−	0.0714573i	$-0.977235\pi$
$877$		−	9.63996e7i		−	0.142915i	0.997444	−	0.0714573i	$-0.0227650\pi$
$878$		0			0
$879$	−2.82633e8	−	1.31010e8i	−0.416156	−	0.192902i
$880$		0			0
$881$			5.50201e8i			0.804626i	0.915502	+	0.402313i	$0.131794\pi$
$881$			5.50201e8i			0.804626i	−0.915502	+	0.402313i	$0.868206\pi$
$882$		0			0
$883$		−	1.98530e8i		−	0.288366i	−0.989551	−	0.144183i	$-0.953945\pi$
$883$		−	1.98530e8i		−	0.288366i	0.989551	−	0.144183i	$-0.0460553\pi$
$884$		0			0
$885$	−2.76403e8	+	7.17123e8i	−0.398761	+	1.03458i
$886$		0			0
$887$	−1.16431e9			−1.66839			−0.834197	−	0.551467i	$-0.814068\pi$
$887$	−1.16431e9			−1.66839			−0.834197	+	0.551467i	$0.814068\pi$
$888$		0			0
$889$	1.46634e9			2.08703
$890$		0			0
$891$	1.02965e9	+	1.71879e8i	1.45565	+	0.242991i
$892$		0			0
$893$	−8.85655e8			−1.24368
$894$		0			0
$895$	5.96611e6	+	9.00398e7i	0.00832189	+	0.125593i
$896$		0			0
$897$	8.03501e7	−	1.73343e8i	0.111329	−	0.240176i
$898$		0			0
$899$			2.11257e8i			0.290758i
$900$		0			0
$901$	1.26377e8			0.172780
$902$		0			0
$903$	1.60257e9	+	7.42841e8i	2.17647	+	1.00886i
$904$		0			0
$905$	1.04986e9	−	6.95645e7i	1.41640	−	0.0938516i
$906$		0			0
$907$			3.90178e8i			0.522927i	0.965213	+	0.261464i	$0.0842052\pi$
$907$			3.90178e8i			0.522927i	−0.965213	+	0.261464i	$0.915795\pi$
$908$		0			0
$909$	−7.62626e8	+	6.45874e8i	−1.01536	+	0.859916i
$910$		0			0
$911$			8.26135e8i			1.09269i	0.837561	+	0.546343i	$0.183981\pi$
$911$			8.26135e8i			1.09269i	−0.837561	+	0.546343i	$0.816019\pi$
$912$		0			0
$913$			4.18837e8i			0.550342i
$914$		0			0
$915$	−8.53985e8	−	3.29154e8i	−1.11477	−	0.429671i
$916$		0			0
$917$	−6.78976e8			−0.880535
$918$		0			0
$919$	1.12183e9			1.44538			0.722689	−	0.691173i	$-0.242906\pi$
$919$	1.12183e9			1.44538			0.722689	+	0.691173i	$0.242906\pi$
$920$		0			0
$921$	2.13499e8	−	4.60591e8i	0.273286	−	0.589572i
$922$		0			0
$923$	1.09249e9			1.38935
$924$		0			0
$925$	−6.72273e7	−	5.05065e8i	−0.0849416	−	0.638149i
$926$		0			0
$927$	5.09162e8	−	4.31213e8i	0.639171	−	0.541318i
$928$		0			0
$929$		−	1.13531e9i		−	1.41601i	−0.706205	−	0.708007i	$-0.749594\pi$
$929$		−	1.13531e9i		−	1.41601i	0.706205	−	0.708007i	$-0.250406\pi$
$930$		0			0
$931$	−1.21022e9			−1.49973
$932$		0			0
$933$	4.54048e8	−	9.79540e8i	0.559058	−	1.20608i
$934$		0			0
$935$	1.87188e7	+	2.82502e8i	0.0229004	+	0.345610i
$936$		0			0
$937$			2.58349e8i			0.314042i	0.987595	+	0.157021i	$0.0501890\pi$
$937$			2.58349e8i			0.314042i	−0.987595	+	0.157021i	$0.949811\pi$
$938$		0			0
$939$	4.05210e8	−	8.74180e8i	0.489422	−	1.05585i
$940$		0			0
$941$		−	4.16085e7i		−	0.0499359i	−0.999688	−	0.0249679i	$-0.992052\pi$
$941$		−	4.16085e7i		−	0.0499359i	0.999688	−	0.0249679i	$-0.00794837\pi$
$942$		0			0
$943$		−	1.91230e8i		−	0.228045i
$944$		0			0
$945$	1.34144e9	−	4.66697e8i	1.58955	−	0.553019i
$946$		0			0
$947$	−8.06748e8			−0.949922			−0.474961	−	0.880007i	$-0.657538\pi$
$947$	−8.06748e8			−0.949922			−0.474961	+	0.880007i	$0.657538\pi$
$948$		0			0
$949$	−3.74122e6			−0.00437738
$950$		0			0
$951$	−8.01350e8	−	3.71452e8i	−0.931710	−	0.431878i
$952$		0			0
$953$	−6.21593e8			−0.718170			−0.359085	−	0.933305i	$-0.616911\pi$
$953$	−6.21593e8			−0.718170			−0.359085	+	0.933305i	$0.616911\pi$
$954$		0			0
$955$	−5.59173e7	−	8.43897e8i	−0.0642002	−	0.968901i
$956$		0			0
$957$	2.75478e8	+	1.27693e8i	0.314305	+	0.145690i
$958$		0			0
$959$			1.73355e9i			1.96554i
$960$		0			0
$961$	4.74123e8			0.534221
$962$		0			0
$963$	−9.51697e8	−	1.12373e9i	−1.06566	−	1.25830i
$964$		0			0
$965$	7.90863e7	+	1.19356e9i	0.0880074	+	1.32820i
$966$		0			0
$967$		−	1.47002e9i		−	1.62571i	−0.582465	−	0.812856i	$-0.697912\pi$
$967$		−	1.47002e9i		−	1.62571i	0.582465	−	0.812856i	$-0.302088\pi$
$968$		0			0
$969$	−1.58558e8	−	7.34966e7i	−0.174267	−	0.0807785i
$970$		0			0
$971$			1.08128e9i			1.18108i	0.807008	+	0.590541i	$0.201085\pi$
$971$			1.08128e9i			1.18108i	−0.807008	+	0.590541i	$0.798915\pi$
$972$		0			0
$973$			2.01951e9i			2.19234i
$974$		0			0
$975$	−2.62178e8	+	8.42409e8i	−0.282867	+	0.908885i
$976$		0			0
$977$	−1.28592e9			−1.37889			−0.689447	−	0.724336i	$-0.742147\pi$
$977$	−1.28592e9			−1.37889			−0.689447	+	0.724336i	$0.742147\pi$
$978$		0			0
$979$	−2.44003e9			−2.60044
$980$		0			0
$981$	−3.43503e7	−	4.05597e7i	−0.0363851	−	0.0429623i
$982$		0			0
$983$	−1.47592e8			−0.155383			−0.0776915	−	0.996977i	$-0.524755\pi$
$983$	−1.47592e8			−0.155383			−0.0776915	+	0.996977i	$0.524755\pi$
$984$		0			0
$985$	−1.94549e7	+	1.28910e6i	−0.0203573	+	0.00134889i
$986$		0			0
$987$	−1.03418e9	+	2.23108e9i	−1.07558	+	2.32041i
$988$		0			0
$989$		−	3.83466e8i		−	0.396404i
$990$		0			0
$991$	−1.60988e9			−1.65414			−0.827070	−	0.562099i	$-0.809994\pi$
$991$	−1.60988e9			−1.65414			−0.827070	+	0.562099i	$0.809994\pi$
$992$		0			0
$993$	1.34106e9	+	6.21623e8i	1.36962	+	0.634862i
$994$		0			0
$995$	3.65649e6	−	242282.i	0.00371189	−	0.000245953i
$996$		0			0
$997$			5.54253e8i			0.559271i	0.960106	+	0.279635i	$0.0902136\pi$
$997$			5.54253e8i			0.559271i	−0.960106	+	0.279635i	$0.909786\pi$
$998$		0			0
$999$	6.18826e8	−	1.70363e8i	0.620686	−	0.170875i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.b.a.29.12	yes	12
3.2	odd	2	inner	60.7.b.a.29.2	yes	12
4.3	odd	2		240.7.c.e.209.1		12
5.2	odd	4		300.7.g.i.101.7		12
5.3	odd	4		300.7.g.i.101.6		12
5.4	even	2	inner	60.7.b.a.29.1	✓	12
12.11	even	2		240.7.c.e.209.11		12
15.2	even	4		300.7.g.i.101.8		12
15.8	even	4		300.7.g.i.101.5		12
15.14	odd	2	inner	60.7.b.a.29.11	yes	12
20.19	odd	2		240.7.c.e.209.12		12
60.59	even	2		240.7.c.e.209.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.b.a.29.1	✓	12	5.4	even	2	inner
60.7.b.a.29.2	yes	12	3.2	odd	2	inner
60.7.b.a.29.11	yes	12	15.14	odd	2	inner
60.7.b.a.29.12	yes	12	1.1	even	1	trivial
240.7.c.e.209.1		12	4.3	odd	2
240.7.c.e.209.2		12	60.59	even	2
240.7.c.e.209.11		12	12.11	even	2
240.7.c.e.209.12		12	20.19	odd	2
300.7.g.i.101.5		12	15.8	even	4
300.7.g.i.101.6		12	5.3	odd	4
300.7.g.i.101.7		12	5.2	odd	4
300.7.g.i.101.8		12	15.2	even	4

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(24.4963 + 11.3548i) q^{3} +(124.726 - 8.26448i) q^{5} -577.271i q^{7} +(471.136 + 556.302i) q^{9} +O(q^{10})\)	\(q+(24.4963 + 11.3548i) q^{3} +(124.726 - 8.26448i) q^{5} -577.271i q^{7} +(471.136 + 556.302i) q^{9} -1964.28i q^{11} +2091.29i q^{13} +(3149.18 + 1213.80i) q^{15} -1153.08 q^{17} +5613.44 q^{19} +(6554.81 - 14141.0i) q^{21} -3383.70 q^{23} +(15488.4 - 2061.60i) q^{25} +(5224.38 + 18977.0i) q^{27} +5725.09i q^{29} +36900.2 q^{31} +(22304.1 - 48117.7i) q^{33} +(-4770.85 - 72001.0i) q^{35} -32609.3i q^{37} +(-23746.2 + 51228.9i) q^{39} +56515.1i q^{41} +113328. i q^{43} +(63360.7 + 65491.9i) q^{45} -157774. q^{47} -215593. q^{49} +(-28246.1 - 13093.0i) q^{51} -109599. q^{53} +(-16233.8 - 244998. i) q^{55} +(137508. + 63739.6i) q^{57} +227718. i q^{59} -271177. q^{61} +(321137. - 271973. i) q^{63} +(17283.4 + 260840. i) q^{65} +219429. i q^{67} +(-82888.0 - 38421.2i) q^{69} -522399. i q^{71} +1788.95i q^{73} +(402817. + 125366. i) q^{75} -1.13392e6 q^{77} +794759. q^{79} +(-87502.3 + 524188. i) q^{81} -213226. q^{83} +(-143819. + 9529.58i) q^{85} +(-65007.3 + 140243. i) q^{87} -1.24220e6i q^{89} +1.20724e6 q^{91} +(903919. + 418995. i) q^{93} +(700144. - 46392.2i) q^{95} +492715. i q^{97} +(1.09273e6 - 925445. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 712 q^{9}+O(q^{10}) \) 12 * q + 712 * q^9	\( 12 q + 712 q^{9} + 2480 q^{15} - 192 q^{19} + 5348 q^{21} + 18660 q^{25} + 40848 q^{31} - 45312 q^{39} + 45340 q^{45} - 242940 q^{49} - 40720 q^{51} - 24240 q^{55} - 99312 q^{61} + 108460 q^{69} + 126640 q^{75} + 626544 q^{79} - 798268 q^{81} - 732720 q^{85} + 1996032 q^{91} + 1632080 q^{99}+O(q^{100}) \) 12 * q + 712 * q^9 + 2480 * q^15 - 192 * q^19 + 5348 * q^21 + 18660 * q^25 + 40848 * q^31 - 45312 * q^39 + 45340 * q^45 - 242940 * q^49 - 40720 * q^51 - 24240 * q^55 - 99312 * q^61 + 108460 * q^69 + 126640 * q^75 + 626544 * q^79 - 798268 * q^81 - 732720 * q^85 + 1996032 * q^91 + 1632080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more