LMFDB - Embedded newform 880.6.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,6,Mod(1,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("880.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	880.a (trivial)

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:	yes
Analytic conductor:	$141.137761435$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	880.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{3} +25.0000 q^{5} +40.0000 q^{7} -239.000 q^{9} +O(q^{10})$

$q-2.00000 q^{3} +25.0000 q^{5} +40.0000 q^{7} -239.000 q^{9} -121.000 q^{11} +88.0000 q^{13} -50.0000 q^{15} +196.000 q^{17} +116.000 q^{19} -80.0000 q^{21} +2442.00 q^{23} +625.000 q^{25} +964.000 q^{27} -5950.00 q^{29} +5168.00 q^{31} +242.000 q^{33} +1000.00 q^{35} +2618.00 q^{37} -176.000 q^{39} -15082.0 q^{41} +22980.0 q^{43} -5975.00 q^{45} -11802.0 q^{47} -15207.0 q^{49} -392.000 q^{51} +2210.00 q^{53} -3025.00 q^{55} -232.000 q^{57} +10852.0 q^{59} -16510.0 q^{61} -9560.00 q^{63} +2200.00 q^{65} -17714.0 q^{67} -4884.00 q^{69} -52340.0 q^{71} +3556.00 q^{73} -1250.00 q^{75} -4840.00 q^{77} +36648.0 q^{79} +56149.0 q^{81} -61636.0 q^{83} +4900.00 q^{85} +11900.0 q^{87} -18042.0 q^{89} +3520.00 q^{91} -10336.0 q^{93} +2900.00 q^{95} +85078.0 q^{97} +28919.0 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

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
$3$	−2.00000	−0.128300	−0.0641500	−	0.997940i	$-0.520434\pi$
$3$	−2.00000	−0.128300	−0.0641500	+	0.997940i	$0.520434\pi$
$4$	0	0
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	0	0
$7$	40.0000	0.308542	0.154271	−	0.988029i	$-0.450697\pi$
$7$	40.0000	0.308542	0.154271	+	0.988029i	$0.450697\pi$
$8$	0	0
$9$	−239.000	−0.983539
$10$	0	0
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	0	0
$13$	88.0000	0.144419	0.0722095	−	0.997389i	$-0.476995\pi$
$13$	88.0000	0.144419	0.0722095	+	0.997389i	$0.476995\pi$
$14$	0	0
$15$	−50.0000	−0.0573775
$16$	0	0
$17$	196.000	0.164488	0.0822439	−	0.996612i	$-0.473791\pi$
$17$	196.000	0.164488	0.0822439	+	0.996612i	$0.473791\pi$
$18$	0	0
$19$	116.000	0.0737181	0.0368590	−	0.999320i	$-0.488265\pi$
$19$	116.000	0.0737181	0.0368590	+	0.999320i	$0.488265\pi$
$20$	0	0
$21$	−80.0000	−0.0395860
$22$	0	0
$23$	2442.00	0.962556	0.481278	−	0.876568i	$-0.340173\pi$
$23$	2442.00	0.962556	0.481278	+	0.876568i	$0.340173\pi$
$24$	0	0
$25$	625.000	0.200000
$26$	0	0
$27$	964.000	0.254488
$28$	0	0
$29$	−5950.00	−1.31378	−0.656889	−	0.753987i	$-0.728128\pi$
$29$	−5950.00	−1.31378	−0.656889	+	0.753987i	$0.728128\pi$
$30$	0	0
$31$	5168.00	0.965869	0.482935	−	0.875656i	$-0.339571\pi$
$31$	5168.00	0.965869	0.482935	+	0.875656i	$0.339571\pi$
$32$	0	0
$33$	242.000	0.0386839
$34$	0	0
$35$	1000.00	0.137984
$36$	0	0
$37$	2618.00	0.314388	0.157194	−	0.987568i	$-0.449755\pi$
$37$	2618.00	0.314388	0.157194	+	0.987568i	$0.449755\pi$
$38$	0	0
$39$	−176.000	−0.0185290
$40$	0	0
$41$	−15082.0	−1.40120	−0.700599	−	0.713556i	$-0.747084\pi$
$41$	−15082.0	−1.40120	−0.700599	+	0.713556i	$0.747084\pi$
$42$	0	0
$43$	22980.0	1.89530	0.947652	−	0.319305i	$-0.103449\pi$
$43$	22980.0	1.89530	0.947652	+	0.319305i	$0.103449\pi$
$44$	0	0
$45$	−5975.00	−0.439852
$46$	0	0
$47$	−11802.0	−0.779311	−0.389656	−	0.920961i	$-0.627406\pi$
$47$	−11802.0	−0.779311	−0.389656	+	0.920961i	$0.627406\pi$
$48$	0	0
$49$	−15207.0	−0.904802
$50$	0	0
$51$	−392.000	−0.0211038
$52$	0	0
$53$	2210.00	0.108069	0.0540347	−	0.998539i	$-0.482792\pi$
$53$	2210.00	0.108069	0.0540347	+	0.998539i	$0.482792\pi$
$54$	0	0
$55$	−3025.00	−0.134840
$56$	0	0
$57$	−232.000	−0.00945803
$58$	0	0
$59$	10852.0	0.405863	0.202932	−	0.979193i	$-0.434953\pi$
$59$	10852.0	0.405863	0.202932	+	0.979193i	$0.434953\pi$
$60$	0	0
$61$	−16510.0	−0.568097	−0.284048	−	0.958810i	$-0.591678\pi$
$61$	−16510.0	−0.568097	−0.284048	+	0.958810i	$0.591678\pi$
$62$	0	0
$63$	−9560.00	−0.303464
$64$	0	0
$65$	2200.00	0.0645861
$66$	0	0
$67$	−17714.0	−0.482092	−0.241046	−	0.970514i	$-0.577490\pi$
$67$	−17714.0	−0.482092	−0.241046	+	0.970514i	$0.577490\pi$
$68$	0	0
$69$	−4884.00	−0.123496
$70$	0	0
$71$	−52340.0	−1.23222	−0.616109	−	0.787661i	$-0.711292\pi$
$71$	−52340.0	−1.23222	−0.616109	+	0.787661i	$0.711292\pi$
$72$	0	0
$73$	3556.00	0.0781006	0.0390503	−	0.999237i	$-0.487567\pi$
$73$	3556.00	0.0781006	0.0390503	+	0.999237i	$0.487567\pi$
$74$	0	0
$75$	−1250.00	−0.0256600
$76$	0	0
$77$	−4840.00	−0.0930290
$78$	0	0
$79$	36648.0	0.660667	0.330333	−	0.943864i	$-0.392839\pi$
$79$	36648.0	0.660667	0.330333	+	0.943864i	$0.392839\pi$
$80$	0	0
$81$	56149.0	0.950888
$82$	0	0
$83$	−61636.0	−0.982063	−0.491031	−	0.871142i	$-0.663380\pi$
$83$	−61636.0	−0.982063	−0.491031	+	0.871142i	$0.663380\pi$
$84$	0	0
$85$	4900.00	0.0735612
$86$	0	0
$87$	11900.0	0.168558
$88$	0	0
$89$	−18042.0	−0.241440	−0.120720	−	0.992687i	$-0.538520\pi$
$89$	−18042.0	−0.241440	−0.120720	+	0.992687i	$0.538520\pi$
$90$	0	0
$91$	3520.00	0.0445594
$92$	0	0
$93$	−10336.0	−0.123921
$94$	0	0
$95$	2900.00	0.0329677
$96$	0	0
$97$	85078.0	0.918096	0.459048	−	0.888412i	$-0.348191\pi$
$97$	85078.0	0.918096	0.459048	+	0.888412i	$0.348191\pi$
$98$	0	0
$99$	28919.0	0.296548
$100$	0	0
$101$	−46818.0	−0.456677	−0.228339	−	0.973582i	$-0.573329\pi$
$101$	−46818.0	−0.456677	−0.228339	+	0.973582i	$0.573329\pi$
$102$	0	0
$103$	44854.0	0.416589	0.208295	−	0.978066i	$-0.433209\pi$
$103$	44854.0	0.416589	0.208295	+	0.978066i	$0.433209\pi$
$104$	0	0
$105$	−2000.00	−0.0177034
$106$	0	0
$107$	−52832.0	−0.446106	−0.223053	−	0.974806i	$-0.571602\pi$
$107$	−52832.0	−0.446106	−0.223053	+	0.974806i	$0.571602\pi$
$108$	0	0
$109$	−228178.	−1.83953	−0.919766	−	0.392466i	$-0.871622\pi$
$109$	−228178.	−1.83953	−0.919766	+	0.392466i	$0.871622\pi$
$110$	0	0
$111$	−5236.00	−0.0403359
$112$	0	0
$113$	127422.	0.938746	0.469373	−	0.883000i	$-0.344480\pi$
$113$	127422.	0.938746	0.469373	+	0.883000i	$0.344480\pi$
$114$	0	0
$115$	61050.0	0.430468
$116$	0	0
$117$	−21032.0	−0.142042
$118$	0	0
$119$	7840.00	0.0507515
$120$	0	0
$121$	14641.0	0.0909091
$122$	0	0
$123$	30164.0	0.179774
$124$	0	0
$125$	15625.0	0.0894427
$126$	0	0
$127$	60324.0	0.331880	0.165940	−	0.986136i	$-0.446934\pi$
$127$	60324.0	0.331880	0.165940	+	0.986136i	$0.446934\pi$
$128$	0	0
$129$	−45960.0	−0.243168
$130$	0	0
$131$	−49812.0	−0.253604	−0.126802	−	0.991928i	$-0.540471\pi$
$131$	−49812.0	−0.253604	−0.126802	+	0.991928i	$0.540471\pi$
$132$	0	0
$133$	4640.00	0.0227452
$134$	0	0
$135$	24100.0	0.113811
$136$	0	0
$137$	119358.	0.543313	0.271657	−	0.962394i	$-0.412429\pi$
$137$	119358.	0.543313	0.271657	+	0.962394i	$0.412429\pi$
$138$	0	0
$139$	244932.	1.07525	0.537624	−	0.843185i	$-0.319322\pi$
$139$	244932.	1.07525	0.537624	+	0.843185i	$0.319322\pi$
$140$	0	0
$141$	23604.0	0.0999857
$142$	0	0
$143$	−10648.0	−0.0435440
$144$	0	0
$145$	−148750.	−0.587539
$146$	0	0
$147$	30414.0	0.116086
$148$	0	0
$149$	−25594.0	−0.0944436	−0.0472218	−	0.998884i	$-0.515037\pi$
$149$	−25594.0	−0.0944436	−0.0472218	+	0.998884i	$0.515037\pi$
$150$	0	0
$151$	−394528.	−1.40811	−0.704053	−	0.710147i	$-0.748628\pi$
$151$	−394528.	−1.40811	−0.704053	+	0.710147i	$0.748628\pi$
$152$	0	0
$153$	−46844.0	−0.161780
$154$	0	0
$155$	129200.	0.431950
$156$	0	0
$157$	−66026.0	−0.213779	−0.106890	−	0.994271i	$-0.534089\pi$
$157$	−66026.0	−0.213779	−0.106890	+	0.994271i	$0.534089\pi$
$158$	0	0
$159$	−4420.00	−0.0138653
$160$	0	0
$161$	97680.0	0.296989
$162$	0	0
$163$	−459954.	−1.35596	−0.677978	−	0.735082i	$-0.737143\pi$
$163$	−459954.	−1.35596	−0.677978	+	0.735082i	$0.737143\pi$
$164$	0	0
$165$	6050.00	0.0173000
$166$	0	0
$167$	−407580.	−1.13089	−0.565447	−	0.824785i	$-0.691296\pi$
$167$	−407580.	−1.13089	−0.565447	+	0.824785i	$0.691296\pi$
$168$	0	0
$169$	−363549.	−0.979143
$170$	0	0
$171$	−27724.0	−0.0725046
$172$	0	0
$173$	515012.	1.30828	0.654142	−	0.756372i	$-0.273030\pi$
$173$	515012.	1.30828	0.654142	+	0.756372i	$0.273030\pi$
$174$	0	0
$175$	25000.0	0.0617085
$176$	0	0
$177$	−21704.0	−0.0520723
$178$	0	0
$179$	−87264.0	−0.203565	−0.101782	−	0.994807i	$-0.532455\pi$
$179$	−87264.0	−0.203565	−0.101782	+	0.994807i	$0.532455\pi$
$180$	0	0
$181$	−575766.	−1.30632	−0.653160	−	0.757220i	$-0.726557\pi$
$181$	−575766.	−1.30632	−0.653160	+	0.757220i	$0.726557\pi$
$182$	0	0
$183$	33020.0	0.0728869
$184$	0	0
$185$	65450.0	0.140598
$186$	0	0
$187$	−23716.0	−0.0495949
$188$	0	0
$189$	38560.0	0.0785204
$190$	0	0
$191$	−837776.	−1.66167	−0.830834	−	0.556520i	$-0.812136\pi$
$191$	−837776.	−1.66167	−0.830834	+	0.556520i	$0.812136\pi$
$192$	0	0
$193$	−210740.	−0.407243	−0.203622	−	0.979050i	$-0.565271\pi$
$193$	−210740.	−0.407243	−0.203622	+	0.979050i	$0.565271\pi$
$194$	0	0
$195$	−4400.00	−0.00828640
$196$	0	0
$197$	−686668.	−1.26061	−0.630306	−	0.776347i	$-0.717070\pi$
$197$	−686668.	−1.26061	−0.630306	+	0.776347i	$0.717070\pi$
$198$	0	0
$199$	7488.00	0.0134040	0.00670198	−	0.999978i	$-0.497867\pi$
$199$	7488.00	0.0134040	0.00670198	+	0.999978i	$0.497867\pi$
$200$	0	0
$201$	35428.0	0.0618524
$202$	0	0
$203$	−238000.	−0.405356
$204$	0	0
$205$	−377050.	−0.626634
$206$	0	0
$207$	−583638.	−0.946712
$208$	0	0
$209$	−14036.0	−0.0222268
$210$	0	0
$211$	−484668.	−0.749442	−0.374721	−	0.927138i	$-0.622262\pi$
$211$	−484668.	−0.749442	−0.374721	+	0.927138i	$0.622262\pi$
$212$	0	0
$213$	104680.	0.158094
$214$	0	0
$215$	574500.	0.847606
$216$	0	0
$217$	206720.	0.298012
$218$	0	0
$219$	−7112.00	−0.0100203
$220$	0	0
$221$	17248.0	0.0237552
$222$	0	0
$223$	41186.0	0.0554610	0.0277305	−	0.999615i	$-0.491172\pi$
$223$	41186.0	0.0554610	0.0277305	+	0.999615i	$0.491172\pi$
$224$	0	0
$225$	−149375.	−0.196708
$226$	0	0
$227$	−92524.0	−0.119176	−0.0595881	−	0.998223i	$-0.518979\pi$
$227$	−92524.0	−0.119176	−0.0595881	+	0.998223i	$0.518979\pi$
$228$	0	0
$229$	482894.	0.608504	0.304252	−	0.952592i	$-0.401594\pi$
$229$	482894.	0.608504	0.304252	+	0.952592i	$0.401594\pi$
$230$	0	0
$231$	9680.00	0.0119356
$232$	0	0
$233$	166720.	0.201186	0.100593	−	0.994928i	$-0.467926\pi$
$233$	166720.	0.201186	0.100593	+	0.994928i	$0.467926\pi$
$234$	0	0
$235$	−295050.	−0.348519
$236$	0	0
$237$	−73296.0	−0.0847636
$238$	0	0
$239$	−249552.	−0.282596	−0.141298	−	0.989967i	$-0.545128\pi$
$239$	−249552.	−0.282596	−0.141298	+	0.989967i	$0.545128\pi$
$240$	0	0
$241$	75398.0	0.0836214	0.0418107	−	0.999126i	$-0.486687\pi$
$241$	75398.0	0.0836214	0.0418107	+	0.999126i	$0.486687\pi$
$242$	0	0
$243$	−346550.	−0.376487
$244$	0	0
$245$	−380175.	−0.404640
$246$	0	0
$247$	10208.0	0.0106463
$248$	0	0
$249$	123272.	0.125999
$250$	0	0
$251$	−1.59060e6	−1.59359	−0.796795	−	0.604250i	$-0.793473\pi$
$251$	−1.59060e6	−1.59359	−0.796795	+	0.604250i	$0.793473\pi$
$252$	0	0
$253$	−295482.	−0.290222
$254$	0	0
$255$	−9800.00	−0.00943791
$256$	0	0
$257$	−735438.	−0.694566	−0.347283	−	0.937760i	$-0.612896\pi$
$257$	−735438.	−0.694566	−0.347283	+	0.937760i	$0.612896\pi$
$258$	0	0
$259$	104720.	0.0970019
$260$	0	0
$261$	1.42205e6	1.29215
$262$	0	0
$263$	−116588.	−0.103936	−0.0519678	−	0.998649i	$-0.516549\pi$
$263$	−116588.	−0.103936	−0.0519678	+	0.998649i	$0.516549\pi$
$264$	0	0
$265$	55250.0	0.0483301
$266$	0	0
$267$	36084.0	0.0309768
$268$	0	0
$269$	−1.61606e6	−1.36169	−0.680844	−	0.732429i	$-0.738387\pi$
$269$	−1.61606e6	−1.36169	−0.680844	+	0.732429i	$0.738387\pi$
$270$	0	0
$271$	890488.	0.736554	0.368277	−	0.929716i	$-0.379948\pi$
$271$	890488.	0.736554	0.368277	+	0.929716i	$0.379948\pi$
$272$	0	0
$273$	−7040.00	−0.00571697
$274$	0	0
$275$	−75625.0	−0.0603023
$276$	0	0
$277$	−767248.	−0.600809	−0.300404	−	0.953812i	$-0.597122\pi$
$277$	−767248.	−0.600809	−0.300404	+	0.953812i	$0.597122\pi$
$278$	0	0
$279$	−1.23515e6	−0.949970
$280$	0	0
$281$	−1.04546e6	−0.789843	−0.394922	−	0.918715i	$-0.629228\pi$
$281$	−1.04546e6	−0.789843	−0.394922	+	0.918715i	$0.629228\pi$
$282$	0	0
$283$	1.87167e6	1.38919	0.694597	−	0.719399i	$-0.255583\pi$
$283$	1.87167e6	1.38919	0.694597	+	0.719399i	$0.255583\pi$
$284$	0	0
$285$	−5800.00	−0.00422976
$286$	0	0
$287$	−603280.	−0.432329
$288$	0	0
$289$	−1.38144e6	−0.972944
$290$	0	0
$291$	−170156.	−0.117792
$292$	0	0
$293$	−2.66254e6	−1.81187	−0.905934	−	0.423419i	$-0.860830\pi$
$293$	−2.66254e6	−1.81187	−0.905934	+	0.423419i	$0.860830\pi$
$294$	0	0
$295$	271300.	0.181508
$296$	0	0
$297$	−116644.	−0.0767311
$298$	0	0
$299$	214896.	0.139011
$300$	0	0
$301$	919200.	0.584782
$302$	0	0
$303$	93636.0	0.0585917
$304$	0	0
$305$	−412750.	−0.254061
$306$	0	0
$307$	2.49842e6	1.51293	0.756467	−	0.654031i	$-0.226924\pi$
$307$	2.49842e6	1.51293	0.756467	+	0.654031i	$0.226924\pi$
$308$	0	0
$309$	−89708.0	−0.0534484
$310$	0	0
$311$	961468.	0.563682	0.281841	−	0.959461i	$-0.409055\pi$
$311$	961468.	0.563682	0.281841	+	0.959461i	$0.409055\pi$
$312$	0	0
$313$	−2.90129e6	−1.67390	−0.836950	−	0.547279i	$-0.815664\pi$
$313$	−2.90129e6	−1.67390	−0.836950	+	0.547279i	$0.815664\pi$
$314$	0	0
$315$	−239000.	−0.135713
$316$	0	0
$317$	2.88634e6	1.61324	0.806621	−	0.591069i	$-0.201294\pi$
$317$	2.88634e6	1.61324	0.806621	+	0.591069i	$0.201294\pi$
$318$	0	0
$319$	719950.	0.396119
$320$	0	0
$321$	105664.	0.0572354
$322$	0	0
$323$	22736.0	0.0121257
$324$	0	0
$325$	55000.0	0.0288838
$326$	0	0
$327$	456356.	0.236012
$328$	0	0
$329$	−472080.	−0.240451
$330$	0	0
$331$	−631452.	−0.316789	−0.158395	−	0.987376i	$-0.550632\pi$
$331$	−631452.	−0.316789	−0.158395	+	0.987376i	$0.550632\pi$
$332$	0	0
$333$	−625702.	−0.309212
$334$	0	0
$335$	−442850.	−0.215598
$336$	0	0
$337$	−1.51654e6	−0.727410	−0.363705	−	0.931514i	$-0.618488\pi$
$337$	−1.51654e6	−0.727410	−0.363705	+	0.931514i	$0.618488\pi$
$338$	0	0
$339$	−254844.	−0.120441
$340$	0	0
$341$	−625328.	−0.291220
$342$	0	0
$343$	−1.28056e6	−0.587712
$344$	0	0
$345$	−122100.	−0.0552291
$346$	0	0
$347$	−1.60057e6	−0.713593	−0.356796	−	0.934182i	$-0.616131\pi$
$347$	−1.60057e6	−0.713593	−0.356796	+	0.934182i	$0.616131\pi$
$348$	0	0
$349$	416866.	0.183203	0.0916016	−	0.995796i	$-0.470801\pi$
$349$	416866.	0.183203	0.0916016	+	0.995796i	$0.470801\pi$
$350$	0	0
$351$	84832.0	0.0367529
$352$	0	0
$353$	−1.48422e6	−0.633960	−0.316980	−	0.948432i	$-0.602669\pi$
$353$	−1.48422e6	−0.633960	−0.316980	+	0.948432i	$0.602669\pi$
$354$	0	0
$355$	−1.30850e6	−0.551065
$356$	0	0
$357$	−15680.0	−0.00651142
$358$	0	0
$359$	1.99205e6	0.815762	0.407881	−	0.913035i	$-0.366268\pi$
$359$	1.99205e6	0.815762	0.407881	+	0.913035i	$0.366268\pi$
$360$	0	0
$361$	−2.46264e6	−0.994566
$362$	0	0
$363$	−29282.0	−0.0116636
$364$	0	0
$365$	88900.0	0.0349277
$366$	0	0
$367$	−4.66195e6	−1.80677	−0.903383	−	0.428834i	$-0.858925\pi$
$367$	−4.66195e6	−1.80677	−0.903383	+	0.428834i	$0.858925\pi$
$368$	0	0
$369$	3.60460e6	1.37813
$370$	0	0
$371$	88400.0	0.0333440
$372$	0	0
$373$	−3.80940e6	−1.41770	−0.708851	−	0.705358i	$-0.750786\pi$
$373$	−3.80940e6	−1.41770	−0.708851	+	0.705358i	$0.750786\pi$
$374$	0	0
$375$	−31250.0	−0.0114755
$376$	0	0
$377$	−523600.	−0.189734
$378$	0	0
$379$	32564.0	0.0116450	0.00582250	−	0.999983i	$-0.498147\pi$
$379$	32564.0	0.0116450	0.00582250	+	0.999983i	$0.498147\pi$
$380$	0	0
$381$	−120648.	−0.0425802
$382$	0	0
$383$	714342.	0.248834	0.124417	−	0.992230i	$-0.460294\pi$
$383$	714342.	0.248834	0.124417	+	0.992230i	$0.460294\pi$
$384$	0	0
$385$	−121000.	−0.0416039
$386$	0	0
$387$	−5.49222e6	−1.86411
$388$	0	0
$389$	3.03075e6	1.01549	0.507746	−	0.861507i	$-0.330479\pi$
$389$	3.03075e6	1.01549	0.507746	+	0.861507i	$0.330479\pi$
$390$	0	0
$391$	478632.	0.158329
$392$	0	0
$393$	99624.0	0.0325374
$394$	0	0
$395$	916200.	0.295459
$396$	0	0
$397$	3.04282e6	0.968948	0.484474	−	0.874806i	$-0.339011\pi$
$397$	3.04282e6	0.968948	0.484474	+	0.874806i	$0.339011\pi$
$398$	0	0
$399$	−9280.00	−0.00291820
$400$	0	0
$401$	1.05523e6	0.327707	0.163854	−	0.986485i	$-0.447608\pi$
$401$	1.05523e6	0.327707	0.163854	+	0.986485i	$0.447608\pi$
$402$	0	0
$403$	454784.	0.139490
$404$	0	0
$405$	1.40373e6	0.425250
$406$	0	0
$407$	−316778.	−0.0947914
$408$	0	0
$409$	5.08460e6	1.50296	0.751482	−	0.659753i	$-0.229339\pi$
$409$	5.08460e6	1.50296	0.751482	+	0.659753i	$0.229339\pi$
$410$	0	0
$411$	−238716.	−0.0697071
$412$	0	0
$413$	434080.	0.125226
$414$	0	0
$415$	−1.54090e6	−0.439192
$416$	0	0
$417$	−489864.	−0.137954
$418$	0	0
$419$	−4.82820e6	−1.34354	−0.671769	−	0.740760i	$-0.734465\pi$
$419$	−4.82820e6	−1.34354	−0.671769	+	0.740760i	$0.734465\pi$
$420$	0	0
$421$	3.20474e6	0.881227	0.440614	−	0.897697i	$-0.354761\pi$
$421$	3.20474e6	0.881227	0.440614	+	0.897697i	$0.354761\pi$
$422$	0	0
$423$	2.82068e6	0.766483
$424$	0	0
$425$	122500.	0.0328976
$426$	0	0
$427$	−660400.	−0.175282
$428$	0	0
$429$	21296.0	0.00558669
$430$	0	0
$431$	−5.05027e6	−1.30955	−0.654774	−	0.755824i	$-0.727236\pi$
$431$	−5.05027e6	−1.30955	−0.654774	+	0.755824i	$0.727236\pi$
$432$	0	0
$433$	808246.	0.207169	0.103584	−	0.994621i	$-0.466969\pi$
$433$	808246.	0.207169	0.103584	+	0.994621i	$0.466969\pi$
$434$	0	0
$435$	297500.	0.0753813
$436$	0	0
$437$	283272.	0.0709578
$438$	0	0
$439$	−4.75554e6	−1.17771	−0.588855	−	0.808239i	$-0.700421\pi$
$439$	−4.75554e6	−1.17771	−0.588855	+	0.808239i	$0.700421\pi$
$440$	0	0
$441$	3.63447e6	0.889908
$442$	0	0
$443$	4.51569e6	1.09324	0.546620	−	0.837381i	$-0.315914\pi$
$443$	4.51569e6	1.09324	0.546620	+	0.837381i	$0.315914\pi$
$444$	0	0
$445$	−451050.	−0.107975
$446$	0	0
$447$	51188.0	0.0121171
$448$	0	0
$449$	2.30538e6	0.539668	0.269834	−	0.962907i	$-0.413031\pi$
$449$	2.30538e6	0.539668	0.269834	+	0.962907i	$0.413031\pi$
$450$	0	0
$451$	1.82492e6	0.422477
$452$	0	0
$453$	789056.	0.180660
$454$	0	0
$455$	88000.0	0.0199276
$456$	0	0
$457$	−4.59171e6	−1.02845	−0.514226	−	0.857655i	$-0.671921\pi$
$457$	−4.59171e6	−1.02845	−0.514226	+	0.857655i	$0.671921\pi$
$458$	0	0
$459$	188944.	0.0418602
$460$	0	0
$461$	−2.06394e6	−0.452318	−0.226159	−	0.974090i	$-0.572617\pi$
$461$	−2.06394e6	−0.452318	−0.226159	+	0.974090i	$0.572617\pi$
$462$	0	0
$463$	−185126.	−0.0401342	−0.0200671	−	0.999799i	$-0.506388\pi$
$463$	−185126.	−0.0401342	−0.0200671	+	0.999799i	$0.506388\pi$
$464$	0	0
$465$	−258400.	−0.0554192
$466$	0	0
$467$	4.87121e6	1.03358	0.516790	−	0.856112i	$-0.327127\pi$
$467$	4.87121e6	1.03358	0.516790	+	0.856112i	$0.327127\pi$
$468$	0	0
$469$	−708560.	−0.148746
$470$	0	0
$471$	132052.	0.0274279
$472$	0	0
$473$	−2.78058e6	−0.571456
$474$	0	0
$475$	72500.0	0.0147436
$476$	0	0
$477$	−528190.	−0.106290
$478$	0	0
$479$	−824416.	−0.164175	−0.0820876	−	0.996625i	$-0.526159\pi$
$479$	−824416.	−0.164175	−0.0820876	+	0.996625i	$0.526159\pi$
$480$	0	0
$481$	230384.	0.0454035
$482$	0	0
$483$	−195360.	−0.0381038
$484$	0	0
$485$	2.12695e6	0.410585
$486$	0	0
$487$	5.31976e6	1.01641	0.508206	−	0.861236i	$-0.330309\pi$
$487$	5.31976e6	1.01641	0.508206	+	0.861236i	$0.330309\pi$
$488$	0	0
$489$	919908.	0.173969
$490$	0	0
$491$	6.35676e6	1.18996	0.594980	−	0.803741i	$-0.297160\pi$
$491$	6.35676e6	1.18996	0.594980	+	0.803741i	$0.297160\pi$
$492$	0	0
$493$	−1.16620e6	−0.216100
$494$	0	0
$495$	722975.	0.132620
$496$	0	0
$497$	−2.09360e6	−0.380192
$498$	0	0
$499$	−2.65430e6	−0.477198	−0.238599	−	0.971118i	$-0.576688\pi$
$499$	−2.65430e6	−0.477198	−0.238599	+	0.971118i	$0.576688\pi$
$500$	0	0
$501$	815160.	0.145094
$502$	0	0
$503$	3.70236e6	0.652467	0.326234	−	0.945289i	$-0.394220\pi$
$503$	3.70236e6	0.652467	0.326234	+	0.945289i	$0.394220\pi$
$504$	0	0
$505$	−1.17045e6	−0.204232
$506$	0	0
$507$	727098.	0.125624
$508$	0	0
$509$	−6.66095e6	−1.13957	−0.569786	−	0.821793i	$-0.692974\pi$
$509$	−6.66095e6	−1.13957	−0.569786	+	0.821793i	$0.692974\pi$
$510$	0	0
$511$	142240.	0.0240974
$512$	0	0
$513$	111824.	0.0187604
$514$	0	0
$515$	1.12135e6	0.186304
$516$	0	0
$517$	1.42804e6	0.234971
$518$	0	0
$519$	−1.03002e6	−0.167853
$520$	0	0
$521$	−1.64022e6	−0.264733	−0.132366	−	0.991201i	$-0.542258\pi$
$521$	−1.64022e6	−0.264733	−0.132366	+	0.991201i	$0.542258\pi$
$522$	0	0
$523$	−1.37522e6	−0.219845	−0.109923	−	0.993940i	$-0.535060\pi$
$523$	−1.37522e6	−0.219845	−0.109923	+	0.993940i	$0.535060\pi$
$524$	0	0
$525$	−50000.0	−0.00791720
$526$	0	0
$527$	1.01293e6	0.158874
$528$	0	0
$529$	−472979.	−0.0734857
$530$	0	0
$531$	−2.59363e6	−0.399182
$532$	0	0
$533$	−1.32722e6	−0.202359
$534$	0	0
$535$	−1.32080e6	−0.199504
$536$	0	0
$537$	174528.	0.0261174
$538$	0	0
$539$	1.84005e6	0.272808
$540$	0	0
$541$	3.45508e6	0.507533	0.253767	−	0.967265i	$-0.418330\pi$
$541$	3.45508e6	0.507533	0.253767	+	0.967265i	$0.418330\pi$
$542$	0	0
$543$	1.15153e6	0.167601
$544$	0	0
$545$	−5.70445e6	−0.822664
$546$	0	0
$547$	−3.21040e6	−0.458766	−0.229383	−	0.973336i	$-0.573671\pi$
$547$	−3.21040e6	−0.458766	−0.229383	+	0.973336i	$0.573671\pi$
$548$	0	0
$549$	3.94589e6	0.558746
$550$	0	0
$551$	−690200.	−0.0968492
$552$	0	0
$553$	1.46592e6	0.203844
$554$	0	0
$555$	−130900.	−0.0180388
$556$	0	0
$557$	9.12953e6	1.24684	0.623420	−	0.781887i	$-0.285743\pi$
$557$	9.12953e6	1.24684	0.623420	+	0.781887i	$0.285743\pi$
$558$	0	0
$559$	2.02224e6	0.273718
$560$	0	0
$561$	47432.0	0.00636303
$562$	0	0
$563$	−736224.	−0.0978901	−0.0489451	−	0.998801i	$-0.515586\pi$
$563$	−736224.	−0.0978901	−0.0489451	+	0.998801i	$0.515586\pi$
$564$	0	0
$565$	3.18555e6	0.419820
$566$	0	0
$567$	2.24596e6	0.293389
$568$	0	0
$569$	4.22599e6	0.547202	0.273601	−	0.961843i	$-0.411785\pi$
$569$	4.22599e6	0.547202	0.273601	+	0.961843i	$0.411785\pi$
$570$	0	0
$571$	7.06863e6	0.907287	0.453644	−	0.891183i	$-0.350124\pi$
$571$	7.06863e6	0.907287	0.453644	+	0.891183i	$0.350124\pi$
$572$	0	0
$573$	1.67555e6	0.213192
$574$	0	0
$575$	1.52625e6	0.192511
$576$	0	0
$577$	−1.42234e7	−1.77855	−0.889273	−	0.457377i	$-0.848789\pi$
$577$	−1.42234e7	−1.77855	−0.889273	+	0.457377i	$0.848789\pi$
$578$	0	0
$579$	421480.	0.0522493
$580$	0	0
$581$	−2.46544e6	−0.303008
$582$	0	0
$583$	−267410.	−0.0325841
$584$	0	0
$585$	−525800.	−0.0635230
$586$	0	0
$587$	−1.44274e6	−0.172819	−0.0864096	−	0.996260i	$-0.527539\pi$
$587$	−1.44274e6	−0.172819	−0.0864096	+	0.996260i	$0.527539\pi$
$588$	0	0
$589$	599488.	0.0712020
$590$	0	0
$591$	1.37334e6	0.161737
$592$	0	0
$593$	−4.06607e6	−0.474830	−0.237415	−	0.971408i	$-0.576300\pi$
$593$	−4.06607e6	−0.474830	−0.237415	+	0.971408i	$0.576300\pi$
$594$	0	0
$595$	196000.	0.0226967
$596$	0	0
$597$	−14976.0	−0.00171973
$598$	0	0
$599$	9.01115e6	1.02616	0.513078	−	0.858342i	$-0.328505\pi$
$599$	9.01115e6	1.02616	0.513078	+	0.858342i	$0.328505\pi$
$600$	0	0
$601$	1.89761e6	0.214299	0.107149	−	0.994243i	$-0.465828\pi$
$601$	1.89761e6	0.214299	0.107149	+	0.994243i	$0.465828\pi$
$602$	0	0
$603$	4.23365e6	0.474156
$604$	0	0
$605$	366025.	0.0406558
$606$	0	0
$607$	2.96051e6	0.326133	0.163066	−	0.986615i	$-0.447862\pi$
$607$	2.96051e6	0.326133	0.163066	+	0.986615i	$0.447862\pi$
$608$	0	0
$609$	476000.	0.0520072
$610$	0	0
$611$	−1.03858e6	−0.112547
$612$	0	0
$613$	1.32511e7	1.42430	0.712150	−	0.702027i	$-0.247722\pi$
$613$	1.32511e7	1.42430	0.712150	+	0.702027i	$0.247722\pi$
$614$	0	0
$615$	754100.	0.0803972
$616$	0	0
$617$	−806394.	−0.0852775	−0.0426387	−	0.999091i	$-0.513576\pi$
$617$	−806394.	−0.0852775	−0.0426387	+	0.999091i	$0.513576\pi$
$618$	0	0
$619$	8.71482e6	0.914181	0.457090	−	0.889420i	$-0.348892\pi$
$619$	8.71482e6	0.914181	0.457090	+	0.889420i	$0.348892\pi$
$620$	0	0
$621$	2.35409e6	0.244959
$622$	0	0
$623$	−721680.	−0.0744946
$624$	0	0
$625$	390625.	0.0400000
$626$	0	0
$627$	28072.0	0.00285170
$628$	0	0
$629$	513128.	0.0517129
$630$	0	0
$631$	−7.42042e6	−0.741917	−0.370958	−	0.928650i	$-0.620971\pi$
$631$	−7.42042e6	−0.741917	−0.370958	+	0.928650i	$0.620971\pi$
$632$	0	0
$633$	969336.	0.0961535
$634$	0	0
$635$	1.50810e6	0.148421
$636$	0	0
$637$	−1.33822e6	−0.130671
$638$	0	0
$639$	1.25093e7	1.21194
$640$	0	0
$641$	−2.47576e6	−0.237992	−0.118996	−	0.992895i	$-0.537968\pi$
$641$	−2.47576e6	−0.237992	−0.118996	+	0.992895i	$0.537968\pi$
$642$	0	0
$643$	−1.44717e7	−1.38036	−0.690182	−	0.723636i	$-0.742469\pi$
$643$	−1.44717e7	−1.38036	−0.690182	+	0.723636i	$0.742469\pi$
$644$	0	0
$645$	−1.14900e6	−0.108748
$646$	0	0
$647$	−106150.	−0.00996918	−0.00498459	−	0.999988i	$-0.501587\pi$
$647$	−106150.	−0.00996918	−0.00498459	+	0.999988i	$0.501587\pi$
$648$	0	0
$649$	−1.31309e6	−0.122372
$650$	0	0
$651$	−413440.	−0.0382349
$652$	0	0
$653$	1.28392e7	1.17830	0.589149	−	0.808025i	$-0.299463\pi$
$653$	1.28392e7	1.17830	0.589149	+	0.808025i	$0.299463\pi$
$654$	0	0
$655$	−1.24530e6	−0.113415
$656$	0	0
$657$	−849884.	−0.0768150
$658$	0	0
$659$	1.87933e6	0.168574	0.0842869	−	0.996442i	$-0.473139\pi$
$659$	1.87933e6	0.168574	0.0842869	+	0.996442i	$0.473139\pi$
$660$	0	0
$661$	−5.04602e6	−0.449206	−0.224603	−	0.974450i	$-0.572109\pi$
$661$	−5.04602e6	−0.449206	−0.224603	+	0.974450i	$0.572109\pi$
$662$	0	0
$663$	−34496.0	−0.00304779
$664$	0	0
$665$	116000.	0.0101719
$666$	0	0
$667$	−1.45299e7	−1.26459
$668$	0	0
$669$	−82372.0	−0.00711565
$670$	0	0
$671$	1.99771e6	0.171288
$672$	0	0
$673$	1.86144e7	1.58420	0.792102	−	0.610389i	$-0.208987\pi$
$673$	1.86144e7	1.58420	0.792102	+	0.610389i	$0.208987\pi$
$674$	0	0
$675$	602500.	0.0508976
$676$	0	0
$677$	−1.97330e6	−0.165470	−0.0827352	−	0.996572i	$-0.526366\pi$
$677$	−1.97330e6	−0.165470	−0.0827352	+	0.996572i	$0.526366\pi$
$678$	0	0
$679$	3.40312e6	0.283271
$680$	0	0
$681$	185048.	0.0152903
$682$	0	0
$683$	2.12738e7	1.74499	0.872495	−	0.488623i	$-0.162501\pi$
$683$	2.12738e7	1.74499	0.872495	+	0.488623i	$0.162501\pi$
$684$	0	0
$685$	2.98395e6	0.242977
$686$	0	0
$687$	−965788.	−0.0780710
$688$	0	0
$689$	194480.	0.0156073
$690$	0	0
$691$	1.06952e7	0.852110	0.426055	−	0.904697i	$-0.359903\pi$
$691$	1.06952e7	0.852110	0.426055	+	0.904697i	$0.359903\pi$
$692$	0	0
$693$	1.15676e6	0.0914977
$694$	0	0
$695$	6.12330e6	0.480865
$696$	0	0
$697$	−2.95607e6	−0.230480
$698$	0	0
$699$	−333440.	−0.0258122
$700$	0	0
$701$	1.00808e7	0.774817	0.387409	−	0.921908i	$-0.373370\pi$
$701$	1.00808e7	0.774817	0.387409	+	0.921908i	$0.373370\pi$
$702$	0	0
$703$	303688.	0.0231760
$704$	0	0
$705$	590100.	0.0447150
$706$	0	0
$707$	−1.87272e6	−0.140904
$708$	0	0
$709$	2.58327e7	1.92999	0.964994	−	0.262273i	$-0.0844722\pi$
$709$	2.58327e7	1.92999	0.964994	+	0.262273i	$0.0844722\pi$
$710$	0	0
$711$	−8.75887e6	−0.649792
$712$	0	0
$713$	1.26203e7	0.929703
$714$	0	0
$715$	−266200.	−0.0194735
$716$	0	0
$717$	499104.	0.0362571
$718$	0	0
$719$	1.52264e7	1.09844	0.549220	−	0.835678i	$-0.314925\pi$
$719$	1.52264e7	1.09844	0.549220	+	0.835678i	$0.314925\pi$
$720$	0	0
$721$	1.79416e6	0.128535
$722$	0	0
$723$	−150796.	−0.0107286
$724$	0	0
$725$	−3.71875e6	−0.262756
$726$	0	0
$727$	−1.92309e7	−1.34947	−0.674736	−	0.738059i	$-0.735742\pi$
$727$	−1.92309e7	−1.34947	−0.674736	+	0.738059i	$0.735742\pi$
$728$	0	0
$729$	−1.29511e7	−0.902585
$730$	0	0
$731$	4.50408e6	0.311754
$732$	0	0
$733$	2.14740e7	1.47623	0.738114	−	0.674676i	$-0.235717\pi$
$733$	2.14740e7	1.47623	0.738114	+	0.674676i	$0.235717\pi$
$734$	0	0
$735$	760350.	0.0519153
$736$	0	0
$737$	2.14339e6	0.145356
$738$	0	0
$739$	2.87132e7	1.93406	0.967032	−	0.254656i	$-0.0819623\pi$
$739$	2.87132e7	1.93406	0.967032	+	0.254656i	$0.0819623\pi$
$740$	0	0
$741$	−20416.0	−0.00136592
$742$	0	0
$743$	−1.17259e7	−0.779242	−0.389621	−	0.920975i	$-0.627394\pi$
$743$	−1.17259e7	−0.779242	−0.389621	+	0.920975i	$0.627394\pi$
$744$	0	0
$745$	−639850.	−0.0422365
$746$	0	0
$747$	1.47310e7	0.965897
$748$	0	0
$749$	−2.11328e6	−0.137642
$750$	0	0
$751$	8.74978e6	0.566105	0.283053	−	0.959104i	$-0.408653\pi$
$751$	8.74978e6	0.566105	0.283053	+	0.959104i	$0.408653\pi$
$752$	0	0
$753$	3.18120e6	0.204458
$754$	0	0
$755$	−9.86320e6	−0.629724
$756$	0	0
$757$	−6.25156e6	−0.396505	−0.198253	−	0.980151i	$-0.563527\pi$
$757$	−6.25156e6	−0.396505	−0.198253	+	0.980151i	$0.563527\pi$
$758$	0	0
$759$	590964.	0.0372354
$760$	0	0
$761$	−2.59670e7	−1.62540	−0.812700	−	0.582683i	$-0.802003\pi$
$761$	−2.59670e7	−1.62540	−0.812700	+	0.582683i	$0.802003\pi$
$762$	0	0
$763$	−9.12712e6	−0.567574
$764$	0	0
$765$	−1.17110e6	−0.0723503
$766$	0	0
$767$	954976.	0.0586144
$768$	0	0
$769$	−5.40701e6	−0.329717	−0.164858	−	0.986317i	$-0.552717\pi$
$769$	−5.40701e6	−0.329717	−0.164858	+	0.986317i	$0.552717\pi$
$770$	0	0
$771$	1.47088e6	0.0891128
$772$	0	0
$773$	−6.31406e6	−0.380067	−0.190033	−	0.981778i	$-0.560860\pi$
$773$	−6.31406e6	−0.380067	−0.190033	+	0.981778i	$0.560860\pi$
$774$	0	0
$775$	3.23000e6	0.193174
$776$	0	0
$777$	−209440.	−0.0124453
$778$	0	0
$779$	−1.74951e6	−0.103294
$780$	0	0
$781$	6.33314e6	0.371528
$782$	0	0
$783$	−5.73580e6	−0.334341
$784$	0	0
$785$	−1.65065e6	−0.0956051
$786$	0	0
$787$	1.12241e7	0.645972	0.322986	−	0.946404i	$-0.395313\pi$
$787$	1.12241e7	0.645972	0.322986	+	0.946404i	$0.395313\pi$
$788$	0	0
$789$	233176.	0.0133349
$790$	0	0
$791$	5.09688e6	0.289643
$792$	0	0
$793$	−1.45288e6	−0.0820440
$794$	0	0
$795$	−110500.	−0.00620075
$796$	0	0
$797$	2.72116e7	1.51743	0.758715	−	0.651423i	$-0.225828\pi$
$797$	2.72116e7	1.51743	0.758715	+	0.651423i	$0.225828\pi$
$798$	0	0
$799$	−2.31319e6	−0.128187
$800$	0	0
$801$	4.31204e6	0.237466
$802$	0	0
$803$	−430276.	−0.0235482
$804$	0	0
$805$	2.44200e6	0.132818
$806$	0	0
$807$	3.23212e6	0.174705
$808$	0	0
$809$	−2.13472e7	−1.14675	−0.573377	−	0.819292i	$-0.694367\pi$
$809$	−2.13472e7	−1.14675	−0.573377	+	0.819292i	$0.694367\pi$
$810$	0	0
$811$	−2.46759e7	−1.31741	−0.658706	−	0.752400i	$-0.728896\pi$
$811$	−2.46759e7	−1.31741	−0.658706	+	0.752400i	$0.728896\pi$
$812$	0	0
$813$	−1.78098e6	−0.0945000
$814$	0	0
$815$	−1.14988e7	−0.606402
$816$	0	0
$817$	2.66568e6	0.139718
$818$	0	0
$819$	−841280.	−0.0438259
$820$	0	0
$821$	1.52060e7	0.787331	0.393666	−	0.919254i	$-0.371207\pi$
$821$	1.52060e7	0.787331	0.393666	+	0.919254i	$0.371207\pi$
$822$	0	0
$823$	1.91052e7	0.983223	0.491612	−	0.870815i	$-0.336408\pi$
$823$	1.91052e7	0.983223	0.491612	+	0.870815i	$0.336408\pi$
$824$	0	0
$825$	151250.	0.00773678
$826$	0	0
$827$	−1.36618e6	−0.0694613	−0.0347306	−	0.999397i	$-0.511057\pi$
$827$	−1.36618e6	−0.0694613	−0.0347306	+	0.999397i	$0.511057\pi$
$828$	0	0
$829$	3.16305e6	0.159853	0.0799264	−	0.996801i	$-0.474531\pi$
$829$	3.16305e6	0.159853	0.0799264	+	0.996801i	$0.474531\pi$
$830$	0	0
$831$	1.53450e6	0.0770838
$832$	0	0
$833$	−2.98057e6	−0.148829
$834$	0	0
$835$	−1.01895e7	−0.505751
$836$	0	0
$837$	4.98195e6	0.245802
$838$	0	0
$839$	3.16660e7	1.55306	0.776531	−	0.630079i	$-0.216978\pi$
$839$	3.16660e7	1.55306	0.776531	+	0.630079i	$0.216978\pi$
$840$	0	0
$841$	1.48914e7	0.726013
$842$	0	0
$843$	2.09092e6	0.101337
$844$	0	0
$845$	−9.08872e6	−0.437886
$846$	0	0
$847$	585640.	0.0280493
$848$	0	0
$849$	−3.74334e6	−0.178234
$850$	0	0
$851$	6.39316e6	0.302616
$852$	0	0
$853$	2.80651e7	1.32067	0.660335	−	0.750971i	$-0.270414\pi$
$853$	2.80651e7	1.32067	0.660335	+	0.750971i	$0.270414\pi$
$854$	0	0
$855$	−693100.	−0.0324250
$856$	0	0
$857$	−3.62523e7	−1.68610	−0.843051	−	0.537834i	$-0.819243\pi$
$857$	−3.62523e7	−1.68610	−0.843051	+	0.537834i	$0.819243\pi$
$858$	0	0
$859$	2.20268e7	1.01852	0.509259	−	0.860613i	$-0.329920\pi$
$859$	2.20268e7	1.01852	0.509259	+	0.860613i	$0.329920\pi$
$860$	0	0
$861$	1.20656e6	0.0554678
$862$	0	0
$863$	−7.71875e6	−0.352793	−0.176397	−	0.984319i	$-0.556444\pi$
$863$	−7.71875e6	−0.352793	−0.176397	+	0.984319i	$0.556444\pi$
$864$	0	0
$865$	1.28753e7	0.585082
$866$	0	0
$867$	2.76288e6	0.124829
$868$	0	0
$869$	−4.43441e6	−0.199199
$870$	0	0
$871$	−1.55883e6	−0.0696232
$872$	0	0
$873$	−2.03336e7	−0.902983
$874$	0	0
$875$	625000.	0.0275969
$876$	0	0
$877$	−2.06155e7	−0.905097	−0.452548	−	0.891740i	$-0.649485\pi$
$877$	−2.06155e7	−0.905097	−0.452548	+	0.891740i	$0.649485\pi$
$878$	0	0
$879$	5.32507e6	0.232463
$880$	0	0
$881$	−3.37756e7	−1.46610	−0.733050	−	0.680175i	$-0.761904\pi$
$881$	−3.37756e7	−1.46610	−0.733050	+	0.680175i	$0.761904\pi$
$882$	0	0
$883$	−2.96606e7	−1.28020	−0.640100	−	0.768292i	$-0.721107\pi$
$883$	−2.96606e7	−1.28020	−0.640100	+	0.768292i	$0.721107\pi$
$884$	0	0
$885$	−542600.	−0.0232874
$886$	0	0
$887$	−3.87996e7	−1.65584	−0.827919	−	0.560848i	$-0.810475\pi$
$887$	−3.87996e7	−1.65584	−0.827919	+	0.560848i	$0.810475\pi$
$888$	0	0
$889$	2.41296e6	0.102399
$890$	0	0
$891$	−6.79403e6	−0.286704
$892$	0	0
$893$	−1.36903e6	−0.0574493
$894$	0	0
$895$	−2.18160e6	−0.0910369
$896$	0	0
$897$	−429792.	−0.0178352
$898$	0	0
$899$	−3.07496e7	−1.26894
$900$	0	0
$901$	433160.	0.0177761
$902$	0	0
$903$	−1.83840e6	−0.0750275
$904$	0	0
$905$	−1.43942e7	−0.584204
$906$	0	0
$907$	−5.83885e6	−0.235673	−0.117836	−	0.993033i	$-0.537596\pi$
$907$	−5.83885e6	−0.235673	−0.117836	+	0.993033i	$0.537596\pi$
$908$	0	0
$909$	1.11895e7	0.449160
$910$	0	0
$911$	3.05353e7	1.21901	0.609504	−	0.792783i	$-0.291369\pi$
$911$	3.05353e7	1.21901	0.609504	+	0.792783i	$0.291369\pi$
$912$	0	0
$913$	7.45796e6	0.296103
$914$	0	0
$915$	825500.	0.0325960
$916$	0	0
$917$	−1.99248e6	−0.0782475
$918$	0	0
$919$	−3.19273e7	−1.24702	−0.623510	−	0.781816i	$-0.714294\pi$
$919$	−3.19273e7	−1.24702	−0.623510	+	0.781816i	$0.714294\pi$
$920$	0	0
$921$	−4.99685e6	−0.194110
$922$	0	0
$923$	−4.60592e6	−0.177956
$924$	0	0
$925$	1.63625e6	0.0628775
$926$	0	0
$927$	−1.07201e7	−0.409732
$928$	0	0
$929$	4.87013e7	1.85140	0.925702	−	0.378253i	$-0.123475\pi$
$929$	4.87013e7	1.85140	0.925702	+	0.378253i	$0.123475\pi$
$930$	0	0
$931$	−1.76401e6	−0.0667002
$932$	0	0
$933$	−1.92294e6	−0.0723204
$934$	0	0
$935$	−592900.	−0.0221795
$936$	0	0
$937$	1.20434e7	0.448126	0.224063	−	0.974575i	$-0.428068\pi$
$937$	1.20434e7	0.448126	0.224063	+	0.974575i	$0.428068\pi$
$938$	0	0
$939$	5.80257e6	0.214762
$940$	0	0
$941$	−6.62272e6	−0.243816	−0.121908	−	0.992541i	$-0.538901\pi$
$941$	−6.62272e6	−0.243816	−0.121908	+	0.992541i	$0.538901\pi$
$942$	0	0
$943$	−3.68302e7	−1.34873
$944$	0	0
$945$	964000.	0.0351154
$946$	0	0
$947$	−1.70527e7	−0.617901	−0.308951	−	0.951078i	$-0.599978\pi$
$947$	−1.70527e7	−0.617901	−0.308951	+	0.951078i	$0.599978\pi$
$948$	0	0
$949$	312928.	0.0112792
$950$	0	0
$951$	−5.77268e6	−0.206979
$952$	0	0
$953$	2.96401e7	1.05718	0.528589	−	0.848878i	$-0.322721\pi$
$953$	2.96401e7	1.05718	0.528589	+	0.848878i	$0.322721\pi$
$954$	0	0
$955$	−2.09444e7	−0.743121
$956$	0	0
$957$	−1.43990e6	−0.0508221
$958$	0	0
$959$	4.77432e6	0.167635
$960$	0	0
$961$	−1.92093e6	−0.0670969
$962$	0	0
$963$	1.26268e7	0.438762
$964$	0	0
$965$	−5.26850e6	−0.182125
$966$	0	0
$967$	−1.23356e6	−0.0424224	−0.0212112	−	0.999775i	$-0.506752\pi$
$967$	−1.23356e6	−0.0424224	−0.0212112	+	0.999775i	$0.506752\pi$
$968$	0	0
$969$	−45472.0	−0.00155573
$970$	0	0
$971$	3.22762e7	1.09859	0.549294	−	0.835629i	$-0.314897\pi$
$971$	3.22762e7	1.09859	0.549294	+	0.835629i	$0.314897\pi$
$972$	0	0
$973$	9.79728e6	0.331760
$974$	0	0
$975$	−110000.	−0.00370579
$976$	0	0
$977$	−5.65074e7	−1.89395	−0.946975	−	0.321306i	$-0.895878\pi$
$977$	−5.65074e7	−1.89395	−0.946975	+	0.321306i	$0.895878\pi$
$978$	0	0
$979$	2.18308e6	0.0727970
$980$	0	0
$981$	5.45345e7	1.80925
$982$	0	0
$983$	3.15430e7	1.04116	0.520582	−	0.853811i	$-0.325715\pi$
$983$	3.15430e7	1.04116	0.520582	+	0.853811i	$0.325715\pi$
$984$	0	0
$985$	−1.71667e7	−0.563763
$986$	0	0
$987$	944160.	0.0308498
$988$	0	0
$989$	5.61172e7	1.82434
$990$	0	0
$991$	3.15636e7	1.02094	0.510472	−	0.859894i	$-0.329471\pi$
$991$	3.15636e7	1.02094	0.510472	+	0.859894i	$0.329471\pi$
$992$	0	0
$993$	1.26290e6	0.0406441
$994$	0	0
$995$	187200.	0.00599443
$996$	0	0
$997$	1.50290e7	0.478842	0.239421	−	0.970916i	$-0.423042\pi$
$997$	1.50290e7	0.478842	0.239421	+	0.970916i	$0.423042\pi$
$998$	0	0
$999$	2.52375e6	0.0800079

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.6.a.c.1.1		1
4.3	odd	2		110.6.a.a.1.1	✓	1
12.11	even	2		990.6.a.d.1.1		1
20.3	even	4		550.6.b.e.199.2		2
20.7	even	4		550.6.b.e.199.1		2
20.19	odd	2		550.6.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.6.a.a.1.1	✓	1	4.3	odd	2
550.6.a.e.1.1		1	20.19	odd	2
550.6.b.e.199.1		2	20.7	even	4
550.6.b.e.199.2		2	20.3	even	4
880.6.a.c.1.1		1	1.1	even	1	trivial
990.6.a.d.1.1		1	12.11	even	2

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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	880.a (trivial)

Introduction

L-functions

Modular forms

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Fields

Representations

Groups

Database

Properties

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