LMFDB - Embedded newform 1805.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,4,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1805.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1805.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:	$106.498447560$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-5.00000 q^{2} -4.00000 q^{3} +17.0000 q^{4} +5.00000 q^{5} +20.0000 q^{6} -32.0000 q^{7} -45.0000 q^{8} -11.0000 q^{9} +O(q^{10})$

\(q-5.00000 q^{2} -4.00000 q^{3} +17.0000 q^{4} +5.00000 q^{5} +20.0000 q^{6} -32.0000 q^{7} -45.0000 q^{8} -11.0000 q^{9} -25.0000 q^{10} -12.0000 q^{11} -68.0000 q^{12} +42.0000 q^{13} +160.000 q^{14} -20.0000 q^{15} +89.0000 q^{16} +114.000 q^{17} +55.0000 q^{18} +85.0000 q^{20} +128.000 q^{21} +60.0000 q^{22} +160.000 q^{23} +180.000 q^{24} +25.0000 q^{25} -210.000 q^{26} +152.000 q^{27} -544.000 q^{28} -214.000 q^{29} +100.000 q^{30} +144.000 q^{31} -85.0000 q^{32} +48.0000 q^{33} -570.000 q^{34} -160.000 q^{35} -187.000 q^{36} -94.0000 q^{37} -168.000 q^{39} -225.000 q^{40} +6.00000 q^{41} -640.000 q^{42} -308.000 q^{43} -204.000 q^{44} -55.0000 q^{45} -800.000 q^{46} +184.000 q^{47} -356.000 q^{48} +681.000 q^{49} -125.000 q^{50} -456.000 q^{51} +714.000 q^{52} +274.000 q^{53} -760.000 q^{54} -60.0000 q^{55} +1440.00 q^{56} +1070.00 q^{58} -276.000 q^{59} -340.000 q^{60} -826.000 q^{61} -720.000 q^{62} +352.000 q^{63} -287.000 q^{64} +210.000 q^{65} -240.000 q^{66} -52.0000 q^{67} +1938.00 q^{68} -640.000 q^{69} +800.000 q^{70} +344.000 q^{71} +495.000 q^{72} -166.000 q^{73} +470.000 q^{74} -100.000 q^{75} +384.000 q^{77} +840.000 q^{78} +688.000 q^{79} +445.000 q^{80} -311.000 q^{81} -30.0000 q^{82} +996.000 q^{83} +2176.00 q^{84} +570.000 q^{85} +1540.00 q^{86} +856.000 q^{87} +540.000 q^{88} -1578.00 q^{89} +275.000 q^{90} -1344.00 q^{91} +2720.00 q^{92} -576.000 q^{93} -920.000 q^{94} +340.000 q^{96} -786.000 q^{97} -3405.00 q^{98} +132.000 q^{99} +O(q^{100})\)

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 $

$2$	−5.00000	−1.76777	−0.883883	−	0.467707i	$-0.845080\pi$
$2$	−5.00000	−1.76777	−0.883883	+	0.467707i	$0.845080\pi$
$3$	−4.00000	−0.769800	−0.384900	−	0.922958i	$-0.625764\pi$
$3$	−4.00000	−0.769800	−0.384900	+	0.922958i	$0.625764\pi$
$4$	17.0000	2.12500
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	20.0000	1.36083
$7$	−32.0000	−1.72784	−0.863919	−	0.503631i	$-0.831997\pi$
$7$	−32.0000	−1.72784	−0.863919	+	0.503631i	$0.831997\pi$
$8$	−45.0000	−1.98874
$9$	−11.0000	−0.407407
$10$	−25.0000	−0.790569
$11$	−12.0000	−0.328921	−0.164461	−	0.986384i	$-0.552588\pi$
$11$	−12.0000	−0.328921	−0.164461	+	0.986384i	$0.552588\pi$
$12$	−68.0000	−1.63583
$13$	42.0000	0.896054	0.448027	−	0.894020i	$-0.352127\pi$
$13$	42.0000	0.896054	0.448027	+	0.894020i	$0.352127\pi$
$14$	160.000	3.05441
$15$	−20.0000	−0.344265
$16$	89.0000	1.39062
$17$	114.000	1.62642	0.813208	−	0.581974i	$-0.197719\pi$
$17$	114.000	1.62642	0.813208	+	0.581974i	$0.197719\pi$
$18$	55.0000	0.720201
$19$	0	0
$19$	0	0
$20$	85.0000	0.950329
$21$	128.000	1.33009
$22$	60.0000	0.581456
$23$	160.000	1.45054	0.725268	−	0.688467i	$-0.241716\pi$
$23$	160.000	1.45054	0.725268	+	0.688467i	$0.241716\pi$
$24$	180.000	1.53093
$25$	25.0000	0.200000
$26$	−210.000	−1.58401
$27$	152.000	1.08342
$28$	−544.000	−3.67165
$29$	−214.000	−1.37030	−0.685152	−	0.728400i	$-0.740264\pi$
$29$	−214.000	−1.37030	−0.685152	+	0.728400i	$0.740264\pi$
$30$	100.000	0.608581
$31$	144.000	0.834296	0.417148	−	0.908839i	$-0.363030\pi$
$31$	144.000	0.834296	0.417148	+	0.908839i	$0.363030\pi$
$32$	−85.0000	−0.469563
$33$	48.0000	0.253204
$34$	−570.000	−2.87512
$35$	−160.000	−0.772712
$36$	−187.000	−0.865741
$37$	−94.0000	−0.417662	−0.208831	−	0.977952i	$-0.566966\pi$
$37$	−94.0000	−0.417662	−0.208831	+	0.977952i	$0.566966\pi$
$38$	0	0
$39$	−168.000	−0.689783
$40$	−225.000	−0.889391
$41$	6.00000	0.0228547	0.0114273	−	0.999935i	$-0.496362\pi$
$41$	6.00000	0.0228547	0.0114273	+	0.999935i	$0.496362\pi$
$42$	−640.000	−2.35129
$43$	−308.000	−1.09232	−0.546158	−	0.837682i	$-0.683910\pi$
$43$	−308.000	−1.09232	−0.546158	+	0.837682i	$0.683910\pi$
$44$	−204.000	−0.698958
$45$	−55.0000	−0.182198
$46$	−800.000	−2.56421
$47$	184.000	0.571046	0.285523	−	0.958372i	$-0.407833\pi$
$47$	184.000	0.571046	0.285523	+	0.958372i	$0.407833\pi$
$48$	−356.000	−1.07050
$49$	681.000	1.98542
$50$	−125.000	−0.353553
$51$	−456.000	−1.25202
$52$	714.000	1.90412
$53$	274.000	0.710128	0.355064	−	0.934842i	$-0.384459\pi$
$53$	274.000	0.710128	0.355064	+	0.934842i	$0.384459\pi$
$54$	−760.000	−1.91524
$55$	−60.0000	−0.147098
$56$	1440.00	3.43622
$57$	0	0
$58$	1070.00	2.42238
$59$	−276.000	−0.609019	−0.304510	−	0.952509i	$-0.598493\pi$
$59$	−276.000	−0.609019	−0.304510	+	0.952509i	$0.598493\pi$
$60$	−340.000	−0.731564
$61$	−826.000	−1.73375	−0.866873	−	0.498530i	$-0.833873\pi$
$61$	−826.000	−1.73375	−0.866873	+	0.498530i	$0.833873\pi$
$62$	−720.000	−1.47484
$63$	352.000	0.703934
$64$	−287.000	−0.560547
$65$	210.000	0.400728
$66$	−240.000	−0.447605
$67$	−52.0000	−0.0948181	−0.0474090	−	0.998876i	$-0.515096\pi$
$67$	−52.0000	−0.0948181	−0.0474090	+	0.998876i	$0.515096\pi$
$68$	1938.00	3.45613
$69$	−640.000	−1.11662
$70$	800.000	1.36598
$71$	344.000	0.575004	0.287502	−	0.957780i	$-0.407175\pi$
$71$	344.000	0.575004	0.287502	+	0.957780i	$0.407175\pi$
$72$	495.000	0.810227
$73$	−166.000	−0.266148	−0.133074	−	0.991106i	$-0.542485\pi$
$73$	−166.000	−0.266148	−0.133074	+	0.991106i	$0.542485\pi$
$74$	470.000	0.738330
$75$	−100.000	−0.153960
$76$	0	0
$77$	384.000	0.568323
$78$	840.000	1.21938
$79$	688.000	0.979823	0.489912	−	0.871772i	$-0.337029\pi$
$79$	688.000	0.979823	0.489912	+	0.871772i	$0.337029\pi$
$80$	445.000	0.621906
$81$	−311.000	−0.426612
$82$	−30.0000	−0.0404018
$83$	996.000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	996.000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	2176.00	2.82644
$85$	570.000	0.727355
$86$	1540.00	1.93096
$87$	856.000	1.05486
$88$	540.000	0.654139
$89$	−1578.00	−1.87941	−0.939706	−	0.341983i	$-0.888901\pi$
$89$	−1578.00	−1.87941	−0.939706	+	0.341983i	$0.888901\pi$
$90$	275.000	0.322084
$91$	−1344.00	−1.54824
$92$	2720.00	3.08239
$93$	−576.000	−0.642241
$94$	−920.000	−1.00948
$95$	0	0
$96$	340.000	0.361470
$97$	−786.000	−0.822744	−0.411372	−	0.911467i	$-0.634950\pi$
$97$	−786.000	−0.822744	−0.411372	+	0.911467i	$0.634950\pi$
$98$	−3405.00	−3.50976
$99$	132.000	0.134005
$100$	425.000	0.425000
$101$	126.000	0.124133	0.0620667	−	0.998072i	$-0.480231\pi$
$101$	126.000	0.124133	0.0620667	+	0.998072i	$0.480231\pi$
$102$	2280.00	2.21327
$103$	368.000	0.352040	0.176020	−	0.984387i	$-0.443678\pi$
$103$	368.000	0.352040	0.176020	+	0.984387i	$0.443678\pi$
$104$	−1890.00	−1.78202
$105$	640.000	0.594834
$106$	−1370.00	−1.25534
$107$	−204.000	−0.184312	−0.0921562	−	0.995745i	$-0.529376\pi$
$107$	−204.000	−0.184312	−0.0921562	+	0.995745i	$0.529376\pi$
$108$	2584.00	2.30227
$109$	1434.00	1.26011	0.630056	−	0.776549i	$-0.283032\pi$
$109$	1434.00	1.26011	0.630056	+	0.776549i	$0.283032\pi$
$110$	300.000	0.260035
$111$	376.000	0.321517
$112$	−2848.00	−2.40277
$113$	−1218.00	−1.01398	−0.506990	−	0.861952i	$-0.669242\pi$
$113$	−1218.00	−1.01398	−0.506990	+	0.861952i	$0.669242\pi$
$114$	0	0
$115$	800.000	0.648699
$116$	−3638.00	−2.91190
$117$	−462.000	−0.365059
$118$	1380.00	1.07660
$119$	−3648.00	−2.81018
$120$	900.000	0.684653
$121$	−1187.00	−0.891811
$122$	4130.00	3.06486
$123$	−24.0000	−0.0175936
$124$	2448.00	1.77288
$125$	125.000	0.0894427
$126$	−1760.00	−1.24439
$127$	−904.000	−0.631630	−0.315815	−	0.948821i	$-0.602278\pi$
$127$	−904.000	−0.631630	−0.315815	+	0.948821i	$0.602278\pi$
$128$	2115.00	1.46048
$129$	1232.00	0.840865
$130$	−1050.00	−0.708393
$131$	−2180.00	−1.45395	−0.726975	−	0.686664i	$-0.759074\pi$
$131$	−2180.00	−1.45395	−0.726975	+	0.686664i	$0.759074\pi$
$132$	816.000	0.538058
$133$	0	0
$134$	260.000	0.167616
$135$	760.000	0.484521
$136$	−5130.00	−3.23451
$137$	−2566.00	−1.60021	−0.800103	−	0.599863i	$-0.795222\pi$
$137$	−2566.00	−1.60021	−0.800103	+	0.599863i	$0.795222\pi$
$138$	3200.00	1.97393
$139$	1988.00	1.21309	0.606547	−	0.795048i	$-0.292554\pi$
$139$	1988.00	1.21309	0.606547	+	0.795048i	$0.292554\pi$
$140$	−2720.00	−1.64201
$141$	−736.000	−0.439591
$142$	−1720.00	−1.01647
$143$	−504.000	−0.294731
$144$	−979.000	−0.566551
$145$	−1070.00	−0.612818
$146$	830.000	0.470488
$147$	−2724.00	−1.52838
$148$	−1598.00	−0.887532
$149$	1134.00	0.623496	0.311748	−	0.950165i	$-0.399086\pi$
$149$	1134.00	0.623496	0.311748	+	0.950165i	$0.399086\pi$
$150$	500.000	0.272166
$151$	2440.00	1.31500	0.657498	−	0.753456i	$-0.271615\pi$
$151$	2440.00	1.31500	0.657498	+	0.753456i	$0.271615\pi$
$152$	0	0
$153$	−1254.00	−0.662614
$154$	−1920.00	−1.00466
$155$	720.000	0.373108
$156$	−2856.00	−1.46579
$157$	3238.00	1.64599	0.822995	−	0.568048i	$-0.192301\pi$
$157$	3238.00	1.64599	0.822995	+	0.568048i	$0.192301\pi$
$158$	−3440.00	−1.73210
$159$	−1096.00	−0.546657
$160$	−425.000	−0.209995
$161$	−5120.00	−2.50629
$162$	1555.00	0.754150
$163$	−1420.00	−0.682350	−0.341175	−	0.940000i	$-0.610825\pi$
$163$	−1420.00	−0.682350	−0.341175	+	0.940000i	$0.610825\pi$
$164$	102.000	0.0485662
$165$	240.000	0.113236
$166$	−4980.00	−2.32845
$167$	2336.00	1.08243	0.541213	−	0.840886i	$-0.317965\pi$
$167$	2336.00	1.08243	0.541213	+	0.840886i	$0.317965\pi$
$168$	−5760.00	−2.64520
$169$	−433.000	−0.197087
$170$	−2850.00	−1.28579
$171$	0	0
$172$	−5236.00	−2.32117
$173$	−1206.00	−0.530003	−0.265001	−	0.964248i	$-0.585372\pi$
$173$	−1206.00	−0.530003	−0.265001	+	0.964248i	$0.585372\pi$
$174$	−4280.00	−1.86475
$175$	−800.000	−0.345568
$176$	−1068.00	−0.457406
$177$	1104.00	0.468823
$178$	7890.00	3.32236
$179$	1412.00	0.589597	0.294798	−	0.955559i	$-0.404747\pi$
$179$	1412.00	0.589597	0.294798	+	0.955559i	$0.404747\pi$
$180$	−935.000	−0.387171
$181$	−3742.00	−1.53669	−0.768344	−	0.640037i	$-0.778919\pi$
$181$	−3742.00	−1.53669	−0.768344	+	0.640037i	$0.778919\pi$
$182$	6720.00	2.73692
$183$	3304.00	1.33464
$184$	−7200.00	−2.88473
$185$	−470.000	−0.186784
$186$	2880.00	1.13533
$187$	−1368.00	−0.534963
$188$	3128.00	1.21347
$189$	−4864.00	−1.87198
$190$	0	0
$191$	−1472.00	−0.557645	−0.278822	−	0.960343i	$-0.589944\pi$
$191$	−1472.00	−0.557645	−0.278822	+	0.960343i	$0.589944\pi$
$192$	1148.00	0.431509
$193$	−1458.00	−0.543778	−0.271889	−	0.962329i	$-0.587648\pi$
$193$	−1458.00	−0.543778	−0.271889	+	0.962329i	$0.587648\pi$
$194$	3930.00	1.45442
$195$	−840.000	−0.308480
$196$	11577.0	4.21902
$197$	2046.00	0.739957	0.369978	−	0.929040i	$-0.379365\pi$
$197$	2046.00	0.739957	0.369978	+	0.929040i	$0.379365\pi$
$198$	−660.000	−0.236890
$199$	−1496.00	−0.532908	−0.266454	−	0.963848i	$-0.585852\pi$
$199$	−1496.00	−0.532908	−0.266454	+	0.963848i	$0.585852\pi$
$200$	−1125.00	−0.397748
$201$	208.000	0.0729910
$202$	−630.000	−0.219439
$203$	6848.00	2.36766
$204$	−7752.00	−2.66053
$205$	30.0000	0.0102209
$206$	−1840.00	−0.622325
$207$	−1760.00	−0.590959
$208$	3738.00	1.24608
$209$	0	0
$210$	−3200.00	−1.05153
$211$	−844.000	−0.275371	−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−844.000	−0.275371	−0.137686	+	0.990476i	$0.543966\pi$
$212$	4658.00	1.50902
$213$	−1376.00	−0.442638
$214$	1020.00	0.325821
$215$	−1540.00	−0.488498
$216$	−6840.00	−2.15464
$217$	−4608.00	−1.44153
$218$	−7170.00	−2.22759
$219$	664.000	0.204881
$220$	−1020.00	−0.312584
$221$	4788.00	1.45736
$222$	−1880.00	−0.568366
$223$	3400.00	1.02099	0.510495	−	0.859881i	$-0.329462\pi$
$223$	3400.00	1.02099	0.510495	+	0.859881i	$0.329462\pi$
$224$	2720.00	0.811329
$225$	−275.000	−0.0814815
$226$	6090.00	1.79248
$227$	−1844.00	−0.539166	−0.269583	−	0.962977i	$-0.586886\pi$
$227$	−1844.00	−0.539166	−0.269583	+	0.962977i	$0.586886\pi$
$228$	0	0
$229$	−1090.00	−0.314538	−0.157269	−	0.987556i	$-0.550269\pi$
$229$	−1090.00	−0.314538	−0.157269	+	0.987556i	$0.550269\pi$
$230$	−4000.00	−1.14675
$231$	−1536.00	−0.437495
$232$	9630.00	2.72517
$233$	2842.00	0.799080	0.399540	−	0.916716i	$-0.369170\pi$
$233$	2842.00	0.799080	0.399540	+	0.916716i	$0.369170\pi$
$234$	2310.00	0.645339
$235$	920.000	0.255380
$236$	−4692.00	−1.29417
$237$	−2752.00	−0.754268
$238$	18240.0	4.96775
$239$	−2400.00	−0.649553	−0.324776	−	0.945791i	$-0.605289\pi$
$239$	−2400.00	−0.649553	−0.324776	+	0.945791i	$0.605289\pi$
$240$	−1780.00	−0.478744
$241$	−2130.00	−0.569317	−0.284658	−	0.958629i	$-0.591880\pi$
$241$	−2130.00	−0.569317	−0.284658	+	0.958629i	$0.591880\pi$
$242$	5935.00	1.57651
$243$	−2860.00	−0.755017
$244$	−14042.0	−3.68421
$245$	3405.00	0.887908
$246$	120.000	0.0311013
$247$	0	0
$248$	−6480.00	−1.65920
$249$	−3984.00	−1.01396
$250$	−625.000	−0.158114
$251$	−2364.00	−0.594480	−0.297240	−	0.954803i	$-0.596066\pi$
$251$	−2364.00	−0.594480	−0.297240	+	0.954803i	$0.596066\pi$
$252$	5984.00	1.49586
$253$	−1920.00	−0.477112
$254$	4520.00	1.11657
$255$	−2280.00	−0.559918
$256$	−8279.00	−2.02124
$257$	−6290.00	−1.52669	−0.763345	−	0.645991i	$-0.776444\pi$
$257$	−6290.00	−1.52669	−0.763345	+	0.645991i	$0.776444\pi$
$258$	−6160.00	−1.48645
$259$	3008.00	0.721653
$260$	3570.00	0.851546
$261$	2354.00	0.558272
$262$	10900.0	2.57025
$263$	8112.00	1.90193	0.950965	−	0.309300i	$-0.100095\pi$
$263$	8112.00	1.90193	0.950965	+	0.309300i	$0.100095\pi$
$264$	−2160.00	−0.503556
$265$	1370.00	0.317579
$266$	0	0
$267$	6312.00	1.44677
$268$	−884.000	−0.201488
$269$	4794.00	1.08660	0.543300	−	0.839539i	$-0.317175\pi$
$269$	4794.00	1.08660	0.543300	+	0.839539i	$0.317175\pi$
$270$	−3800.00	−0.856521
$271$	304.000	0.0681427	0.0340714	−	0.999419i	$-0.489153\pi$
$271$	304.000	0.0681427	0.0340714	+	0.999419i	$0.489153\pi$
$272$	10146.0	2.26173
$273$	5376.00	1.19183
$274$	12830.0	2.82879
$275$	−300.000	−0.0657843
$276$	−10880.0	−2.37282
$277$	2062.00	0.447269	0.223635	−	0.974673i	$-0.428208\pi$
$277$	2062.00	0.447269	0.223635	+	0.974673i	$0.428208\pi$
$278$	−9940.00	−2.14447
$279$	−1584.00	−0.339898
$280$	7200.00	1.53672
$281$	4054.00	0.860645	0.430323	−	0.902675i	$-0.358400\pi$
$281$	4054.00	0.860645	0.430323	+	0.902675i	$0.358400\pi$
$282$	3680.00	0.777095
$283$	7996.00	1.67955	0.839775	−	0.542934i	$-0.182687\pi$
$283$	7996.00	1.67955	0.839775	+	0.542934i	$0.182687\pi$
$284$	5848.00	1.22188
$285$	0	0
$286$	2520.00	0.521017
$287$	−192.000	−0.0394892
$288$	935.000	0.191303
$289$	8083.00	1.64523
$290$	5350.00	1.08332
$291$	3144.00	0.633349
$292$	−2822.00	−0.565565
$293$	3906.00	0.778809	0.389404	−	0.921067i	$-0.372681\pi$
$293$	3906.00	0.778809	0.389404	+	0.921067i	$0.372681\pi$
$294$	13620.0	2.70182
$295$	−1380.00	−0.272362
$296$	4230.00	0.830621
$297$	−1824.00	−0.356361
$298$	−5670.00	−1.10220
$299$	6720.00	1.29976
$300$	−1700.00	−0.327165
$301$	9856.00	1.88734
$302$	−12200.0	−2.32461
$303$	−504.000	−0.0955579
$304$	0	0
$305$	−4130.00	−0.775354
$306$	6270.00	1.17135
$307$	1820.00	0.338348	0.169174	−	0.985586i	$-0.445890\pi$
$307$	1820.00	0.338348	0.169174	+	0.985586i	$0.445890\pi$
$308$	6528.00	1.20769
$309$	−1472.00	−0.271000
$310$	−3600.00	−0.659569
$311$	712.000	0.129819	0.0649097	−	0.997891i	$-0.479324\pi$
$311$	712.000	0.129819	0.0649097	+	0.997891i	$0.479324\pi$
$312$	7560.00	1.37180
$313$	9130.00	1.64875	0.824374	−	0.566046i	$-0.191527\pi$
$313$	9130.00	1.64875	0.824374	+	0.566046i	$0.191527\pi$
$314$	−16190.0	−2.90973
$315$	1760.00	0.314809
$316$	11696.0	2.08212
$317$	−6342.00	−1.12367	−0.561833	−	0.827251i	$-0.689904\pi$
$317$	−6342.00	−1.12367	−0.561833	+	0.827251i	$0.689904\pi$
$318$	5480.00	0.966362
$319$	2568.00	0.450722
$320$	−1435.00	−0.250684
$321$	816.000	0.141884
$322$	25600.0	4.43053
$323$	0	0
$324$	−5287.00	−0.906550
$325$	1050.00	0.179211
$326$	7100.00	1.20624
$327$	−5736.00	−0.970035
$328$	−270.000	−0.0454520
$329$	−5888.00	−0.986675
$330$	−1200.00	−0.200175
$331$	4748.00	0.788440	0.394220	−	0.919016i	$-0.371015\pi$
$331$	4748.00	0.788440	0.394220	+	0.919016i	$0.371015\pi$
$332$	16932.0	2.79899
$333$	1034.00	0.170159
$334$	−11680.0	−1.91348
$335$	−260.000	−0.0424039
$336$	11392.0	1.84966
$337$	−5154.00	−0.833105	−0.416552	−	0.909112i	$-0.636762\pi$
$337$	−5154.00	−0.833105	−0.416552	+	0.909112i	$0.636762\pi$
$338$	2165.00	0.348404
$339$	4872.00	0.780563
$340$	9690.00	1.54563
$341$	−1728.00	−0.274418
$342$	0	0
$343$	−10816.0	−1.70265
$344$	13860.0	2.17233
$345$	−3200.00	−0.499369
$346$	6030.00	0.936921
$347$	−12148.0	−1.87936	−0.939681	−	0.342051i	$-0.888878\pi$
$347$	−12148.0	−1.87936	−0.939681	+	0.342051i	$0.888878\pi$
$348$	14552.0	2.24158
$349$	−602.000	−0.0923333	−0.0461666	−	0.998934i	$-0.514701\pi$
$349$	−602.000	−0.0923333	−0.0461666	+	0.998934i	$0.514701\pi$
$350$	4000.00	0.610883
$351$	6384.00	0.970805
$352$	1020.00	0.154449
$353$	2.00000	0.000301556 0	0.000150778	−	1.00000i	$-0.499952\pi$
$353$	2.00000	0.000301556 0	0.000150778		1.00000i	$0.499952\pi$
$354$	−5520.00	−0.828770
$355$	1720.00	0.257150
$356$	−26826.0	−3.99375
$357$	14592.0	2.16328
$358$	−7060.00	−1.04227
$359$	1960.00	0.288147	0.144074	−	0.989567i	$-0.453980\pi$
$359$	1960.00	0.288147	0.144074	+	0.989567i	$0.453980\pi$
$360$	2475.00	0.362344
$361$	0	0
$362$	18710.0	2.71651
$363$	4748.00	0.686516
$364$	−22848.0	−3.29000
$365$	−830.000	−0.119025
$366$	−16520.0	−2.35933
$367$	−5864.00	−0.834055	−0.417028	−	0.908894i	$-0.636928\pi$
$367$	−5864.00	−0.834055	−0.417028	+	0.908894i	$0.636928\pi$
$368$	14240.0	2.01715
$369$	−66.0000	−0.00931117
$370$	2350.00	0.330191
$371$	−8768.00	−1.22699
$372$	−9792.00	−1.36476
$373$	−558.000	−0.0774588	−0.0387294	−	0.999250i	$-0.512331\pi$
$373$	−558.000	−0.0774588	−0.0387294	+	0.999250i	$0.512331\pi$
$374$	6840.00	0.945690
$375$	−500.000	−0.0688530
$376$	−8280.00	−1.13566
$377$	−8988.00	−1.22787
$378$	24320.0	3.30922
$379$	4876.00	0.660853	0.330427	−	0.943832i	$-0.392807\pi$
$379$	4876.00	0.660853	0.330427	+	0.943832i	$0.392807\pi$
$380$	0	0
$381$	3616.00	0.486229
$382$	7360.00	0.985786
$383$	424.000	0.0565676	0.0282838	−	0.999600i	$-0.490996\pi$
$383$	424.000	0.0565676	0.0282838	+	0.999600i	$0.490996\pi$
$384$	−8460.00	−1.12428
$385$	1920.00	0.254162
$386$	7290.00	0.961273
$387$	3388.00	0.445017
$388$	−13362.0	−1.74833
$389$	−9890.00	−1.28906	−0.644528	−	0.764581i	$-0.722946\pi$
$389$	−9890.00	−1.28906	−0.644528	+	0.764581i	$0.722946\pi$
$390$	4200.00	0.545321
$391$	18240.0	2.35917
$392$	−30645.0	−3.94849
$393$	8720.00	1.11925
$394$	−10230.0	−1.30807
$395$	3440.00	0.438190
$396$	2244.00	0.284761
$397$	−234.000	−0.0295822	−0.0147911	−	0.999891i	$-0.504708\pi$
$397$	−234.000	−0.0295822	−0.0147911	+	0.999891i	$0.504708\pi$
$398$	7480.00	0.942057
$399$	0	0
$400$	2225.00	0.278125
$401$	−11602.0	−1.44483	−0.722414	−	0.691461i	$-0.756968\pi$
$401$	−11602.0	−1.44483	−0.722414	+	0.691461i	$0.756968\pi$
$402$	−1040.00	−0.129031
$403$	6048.00	0.747574
$404$	2142.00	0.263783
$405$	−1555.00	−0.190787
$406$	−34240.0	−4.18547
$407$	1128.00	0.137378
$408$	20520.0	2.48993
$409$	14806.0	1.79000	0.894999	−	0.446067i	$-0.147176\pi$
$409$	14806.0	1.79000	0.894999	+	0.446067i	$0.147176\pi$
$410$	−150.000	−0.0180682
$411$	10264.0	1.23184
$412$	6256.00	0.748085
$413$	8832.00	1.05229
$414$	8800.00	1.04468
$415$	4980.00	0.589057
$416$	−3570.00	−0.420754
$417$	−7952.00	−0.933840
$418$	0	0
$419$	6252.00	0.728950	0.364475	−	0.931213i	$-0.381248\pi$
$419$	6252.00	0.728950	0.364475	+	0.931213i	$0.381248\pi$
$420$	10880.0	1.26402
$421$	10482.0	1.21345	0.606724	−	0.794913i	$-0.292483\pi$
$421$	10482.0	1.21345	0.606724	+	0.794913i	$0.292483\pi$
$422$	4220.00	0.486792
$423$	−2024.00	−0.232648
$424$	−12330.0	−1.41226
$425$	2850.00	0.325283
$426$	6880.00	0.782481
$427$	26432.0	2.99563
$428$	−3468.00	−0.391664
$429$	2016.00	0.226884
$430$	7700.00	0.863551
$431$	−3936.00	−0.439885	−0.219943	−	0.975513i	$-0.570587\pi$
$431$	−3936.00	−0.439885	−0.219943	+	0.975513i	$0.570587\pi$
$432$	13528.0	1.50663
$433$	−10946.0	−1.21485	−0.607426	−	0.794376i	$-0.707798\pi$
$433$	−10946.0	−1.21485	−0.607426	+	0.794376i	$0.707798\pi$
$434$	23040.0	2.54828
$435$	4280.00	0.471748
$436$	24378.0	2.67774
$437$	0	0
$438$	−3320.00	−0.362182
$439$	7800.00	0.848004	0.424002	−	0.905661i	$-0.360625\pi$
$439$	7800.00	0.848004	0.424002	+	0.905661i	$0.360625\pi$
$440$	2700.00	0.292540
$441$	−7491.00	−0.808876
$442$	−23940.0	−2.57627
$443$	−11364.0	−1.21878	−0.609390	−	0.792870i	$-0.708586\pi$
$443$	−11364.0	−1.21878	−0.609390	+	0.792870i	$0.708586\pi$
$444$	6392.00	0.683223
$445$	−7890.00	−0.840499
$446$	−17000.0	−1.80487
$447$	−4536.00	−0.479967
$448$	9184.00	0.968534
$449$	−7330.00	−0.770432	−0.385216	−	0.922826i	$-0.625873\pi$
$449$	−7330.00	−0.770432	−0.385216	+	0.922826i	$0.625873\pi$
$450$	1375.00	0.144040
$451$	−72.0000	−0.00751740
$452$	−20706.0	−2.15471
$453$	−9760.00	−1.01228
$454$	9220.00	0.953119
$455$	−6720.00	−0.692392
$456$	0	0
$457$	−12774.0	−1.30753	−0.653766	−	0.756696i	$-0.726812\pi$
$457$	−12774.0	−1.30753	−0.653766	+	0.756696i	$0.726812\pi$
$458$	5450.00	0.556030
$459$	17328.0	1.76210
$460$	13600.0	1.37849
$461$	−3786.00	−0.382498	−0.191249	−	0.981542i	$-0.561254\pi$
$461$	−3786.00	−0.382498	−0.191249	+	0.981542i	$0.561254\pi$
$462$	7680.00	0.773389
$463$	−19448.0	−1.95211	−0.976053	−	0.217532i	$-0.930199\pi$
$463$	−19448.0	−1.95211	−0.976053	+	0.217532i	$0.930199\pi$
$464$	−19046.0	−1.90558
$465$	−2880.00	−0.287219
$466$	−14210.0	−1.41259
$467$	4596.00	0.455412	0.227706	−	0.973730i	$-0.426877\pi$
$467$	4596.00	0.455412	0.227706	+	0.973730i	$0.426877\pi$
$468$	−7854.00	−0.775751
$469$	1664.00	0.163830
$470$	−4600.00	−0.451451
$471$	−12952.0	−1.26708
$472$	12420.0	1.21118
$473$	3696.00	0.359286
$474$	13760.0	1.33337
$475$	0	0
$476$	−62016.0	−5.97164
$477$	−3014.00	−0.289311
$478$	12000.0	1.14826
$479$	12432.0	1.18587	0.592936	−	0.805250i	$-0.297969\pi$
$479$	12432.0	1.18587	0.592936	+	0.805250i	$0.297969\pi$
$480$	1700.00	0.161654
$481$	−3948.00	−0.374248
$482$	10650.0	1.00642
$483$	20480.0	1.92934
$484$	−20179.0	−1.89510
$485$	−3930.00	−0.367942
$486$	14300.0	1.33469
$487$	18016.0	1.67635	0.838175	−	0.545401i	$-0.183622\pi$
$487$	18016.0	1.67635	0.838175	+	0.545401i	$0.183622\pi$
$488$	37170.0	3.44796
$489$	5680.00	0.525273
$490$	−17025.0	−1.56961
$491$	1972.00	0.181253	0.0906264	−	0.995885i	$-0.471113\pi$
$491$	1972.00	0.181253	0.0906264	+	0.995885i	$0.471113\pi$
$492$	−408.000	−0.0373863
$493$	−24396.0	−2.22868
$494$	0	0
$495$	660.000	0.0599289
$496$	12816.0	1.16019
$497$	−11008.0	−0.993514
$498$	19920.0	1.79244
$499$	18780.0	1.68479	0.842393	−	0.538864i	$-0.181146\pi$
$499$	18780.0	1.68479	0.842393	+	0.538864i	$0.181146\pi$
$500$	2125.00	0.190066
$501$	−9344.00	−0.833252
$502$	11820.0	1.05090
$503$	8256.00	0.731843	0.365921	−	0.930646i	$-0.380754\pi$
$503$	8256.00	0.731843	0.365921	+	0.930646i	$0.380754\pi$
$504$	−15840.0	−1.39994
$505$	630.000	0.0555141
$506$	9600.00	0.843423
$507$	1732.00	0.151718
$508$	−15368.0	−1.34221
$509$	13290.0	1.15731	0.578653	−	0.815574i	$-0.303579\pi$
$509$	13290.0	1.15731	0.578653	+	0.815574i	$0.303579\pi$
$510$	11400.0	0.989805
$511$	5312.00	0.459861
$512$	24475.0	2.11260
$513$	0	0
$514$	31450.0	2.69883
$515$	1840.00	0.157437
$516$	20944.0	1.78684
$517$	−2208.00	−0.187829
$518$	−15040.0	−1.27571
$519$	4824.00	0.407996
$520$	−9450.00	−0.796942
$521$	−7610.00	−0.639924	−0.319962	−	0.947430i	$-0.603670\pi$
$521$	−7610.00	−0.639924	−0.319962	+	0.947430i	$0.603670\pi$
$522$	−11770.0	−0.986894
$523$	13636.0	1.14008	0.570039	−	0.821618i	$-0.306928\pi$
$523$	13636.0	1.14008	0.570039	+	0.821618i	$0.306928\pi$
$524$	−37060.0	−3.08964
$525$	3200.00	0.266018
$526$	−40560.0	−3.36217
$527$	16416.0	1.35691
$528$	4272.00	0.352112
$529$	13433.0	1.10405
$530$	−6850.00	−0.561406
$531$	3036.00	0.248119
$532$	0	0
$533$	252.000	0.0204790
$534$	−31560.0	−2.55756
$535$	−1020.00	−0.0824270
$536$	2340.00	0.188568
$537$	−5648.00	−0.453872
$538$	−23970.0	−1.92086
$539$	−8172.00	−0.653048
$540$	12920.0	1.02961
$541$	1350.00	0.107285	0.0536424	−	0.998560i	$-0.482917\pi$
$541$	1350.00	0.107285	0.0536424	+	0.998560i	$0.482917\pi$
$542$	−1520.00	−0.120460
$543$	14968.0	1.18294
$544$	−9690.00	−0.763705
$545$	7170.00	0.563540
$546$	−26880.0	−2.10688
$547$	20396.0	1.59428	0.797139	−	0.603796i	$-0.206346\pi$
$547$	20396.0	1.59428	0.797139	+	0.603796i	$0.206346\pi$
$548$	−43622.0	−3.40044
$549$	9086.00	0.706341
$550$	1500.00	0.116291
$551$	0	0
$552$	28800.0	2.22067
$553$	−22016.0	−1.69298
$554$	−10310.0	−0.790668
$555$	1880.00	0.143787
$556$	33796.0	2.57782
$557$	−4458.00	−0.339123	−0.169562	−	0.985520i	$-0.554235\pi$
$557$	−4458.00	−0.339123	−0.169562	+	0.985520i	$0.554235\pi$
$558$	7920.00	0.600861
$559$	−12936.0	−0.978774
$560$	−14240.0	−1.07455
$561$	5472.00	0.411815
$562$	−20270.0	−1.52142
$563$	−18228.0	−1.36451	−0.682255	−	0.731115i	$-0.739000\pi$
$563$	−18228.0	−1.36451	−0.682255	+	0.731115i	$0.739000\pi$
$564$	−12512.0	−0.934132
$565$	−6090.00	−0.453466
$566$	−39980.0	−2.96905
$567$	9952.00	0.737116
$568$	−15480.0	−1.14353
$569$	8246.00	0.607540	0.303770	−	0.952745i	$-0.401755\pi$
$569$	8246.00	0.607540	0.303770	+	0.952745i	$0.401755\pi$
$570$	0	0
$571$	−924.000	−0.0677201	−0.0338601	−	0.999427i	$-0.510780\pi$
$571$	−924.000	−0.0677201	−0.0338601	+	0.999427i	$0.510780\pi$
$572$	−8568.00	−0.626304
$573$	5888.00	0.429275
$574$	960.000	0.0698077
$575$	4000.00	0.290107
$576$	3157.00	0.228371
$577$	16322.0	1.17763	0.588816	−	0.808267i	$-0.299594\pi$
$577$	16322.0	1.17763	0.588816	+	0.808267i	$0.299594\pi$
$578$	−40415.0	−2.90838
$579$	5832.00	0.418600
$580$	−18190.0	−1.30224
$581$	−31872.0	−2.27586
$582$	−15720.0	−1.11961
$583$	−3288.00	−0.233576
$584$	7470.00	0.529299
$585$	−2310.00	−0.163259
$586$	−19530.0	−1.37675
$587$	17500.0	1.23050	0.615249	−	0.788333i	$-0.289055\pi$
$587$	17500.0	1.23050	0.615249	+	0.788333i	$0.289055\pi$
$588$	−46308.0	−3.24781
$589$	0	0
$590$	6900.00	0.481472
$591$	−8184.00	−0.569619
$592$	−8366.00	−0.580812
$593$	−1486.00	−0.102905	−0.0514525	−	0.998675i	$-0.516385\pi$
$593$	−1486.00	−0.102905	−0.0514525	+	0.998675i	$0.516385\pi$
$594$	9120.00	0.629963
$595$	−18240.0	−1.25675
$596$	19278.0	1.32493
$597$	5984.00	0.410233
$598$	−33600.0	−2.29767
$599$	−24616.0	−1.67910	−0.839551	−	0.543280i	$-0.817182\pi$
$599$	−24616.0	−1.67910	−0.839551	+	0.543280i	$0.817182\pi$
$600$	4500.00	0.306186
$601$	13334.0	0.905000	0.452500	−	0.891764i	$-0.350532\pi$
$601$	13334.0	0.905000	0.452500	+	0.891764i	$0.350532\pi$
$602$	−49280.0	−3.33638
$603$	572.000	0.0386296
$604$	41480.0	2.79437
$605$	−5935.00	−0.398830
$606$	2520.00	0.168924
$607$	12056.0	0.806158	0.403079	−	0.915165i	$-0.367940\pi$
$607$	12056.0	0.806158	0.403079	+	0.915165i	$0.367940\pi$
$608$	0	0
$609$	−27392.0	−1.82263
$610$	20650.0	1.37065
$611$	7728.00	0.511688
$612$	−21318.0	−1.40805
$613$	−98.0000	−0.00645707	−0.00322853	−	0.999995i	$-0.501028\pi$
$613$	−98.0000	−0.00645707	−0.00322853	+	0.999995i	$0.501028\pi$
$614$	−9100.00	−0.598121
$615$	−120.000	−0.00786808
$616$	−17280.0	−1.13025
$617$	2938.00	0.191701	0.0958504	−	0.995396i	$-0.469443\pi$
$617$	2938.00	0.191701	0.0958504	+	0.995396i	$0.469443\pi$
$618$	7360.00	0.479066
$619$	25316.0	1.64384	0.821919	−	0.569604i	$-0.192903\pi$
$619$	25316.0	1.64384	0.821919	+	0.569604i	$0.192903\pi$
$620$	12240.0	0.792855
$621$	24320.0	1.57154
$622$	−3560.00	−0.229490
$623$	50496.0	3.24732
$624$	−14952.0	−0.959229
$625$	625.000	0.0400000
$626$	−45650.0	−2.91460
$627$	0	0
$628$	55046.0	3.49773
$629$	−10716.0	−0.679292
$630$	−8800.00	−0.556509
$631$	1256.00	0.0792402	0.0396201	−	0.999215i	$-0.487385\pi$
$631$	1256.00	0.0792402	0.0396201	+	0.999215i	$0.487385\pi$
$632$	−30960.0	−1.94861
$633$	3376.00	0.211981
$634$	31710.0	1.98638
$635$	−4520.00	−0.282474
$636$	−18632.0	−1.16165
$637$	28602.0	1.77905
$638$	−12840.0	−0.796772
$639$	−3784.00	−0.234261
$640$	10575.0	0.653146
$641$	−20290.0	−1.25024	−0.625122	−	0.780527i	$-0.714951\pi$
$641$	−20290.0	−1.25024	−0.625122	+	0.780527i	$0.714951\pi$
$642$	−4080.00	−0.250817
$643$	10676.0	0.654775	0.327388	−	0.944890i	$-0.393832\pi$
$643$	10676.0	0.654775	0.327388	+	0.944890i	$0.393832\pi$
$644$	−87040.0	−5.32586
$645$	6160.00	0.376046
$646$	0	0
$647$	11264.0	0.684441	0.342221	−	0.939620i	$-0.388821\pi$
$647$	11264.0	0.684441	0.342221	+	0.939620i	$0.388821\pi$
$648$	13995.0	0.848419
$649$	3312.00	0.200320
$650$	−5250.00	−0.316803
$651$	18432.0	1.10969
$652$	−24140.0	−1.44999
$653$	25878.0	1.55082	0.775409	−	0.631459i	$-0.217544\pi$
$653$	25878.0	1.55082	0.775409	+	0.631459i	$0.217544\pi$
$654$	28680.0	1.71480
$655$	−10900.0	−0.650226
$656$	534.000	0.0317823
$657$	1826.00	0.108431
$658$	29440.0	1.74421
$659$	−1500.00	−0.0886672	−0.0443336	−	0.999017i	$-0.514116\pi$
$659$	−1500.00	−0.0886672	−0.0443336	+	0.999017i	$0.514116\pi$
$660$	4080.00	0.240627
$661$	7618.00	0.448269	0.224135	−	0.974558i	$-0.428044\pi$
$661$	7618.00	0.448269	0.224135	+	0.974558i	$0.428044\pi$
$662$	−23740.0	−1.39378
$663$	−19152.0	−1.12187
$664$	−44820.0	−2.61951
$665$	0	0
$666$	−5170.00	−0.300801
$667$	−34240.0	−1.98767
$668$	39712.0	2.30015
$669$	−13600.0	−0.785959
$670$	1300.00	0.0749603
$671$	9912.00	0.570266
$672$	−10880.0	−0.624561
$673$	4110.00	0.235407	0.117703	−	0.993049i	$-0.462447\pi$
$673$	4110.00	0.235407	0.117703	+	0.993049i	$0.462447\pi$
$674$	25770.0	1.47273
$675$	3800.00	0.216685
$676$	−7361.00	−0.418810
$677$	21474.0	1.21907	0.609537	−	0.792758i	$-0.291355\pi$
$677$	21474.0	1.21907	0.609537	+	0.792758i	$0.291355\pi$
$678$	−24360.0	−1.37985
$679$	25152.0	1.42157
$680$	−25650.0	−1.44652
$681$	7376.00	0.415050
$682$	8640.00	0.485107
$683$	−4668.00	−0.261517	−0.130758	−	0.991414i	$-0.541741\pi$
$683$	−4668.00	−0.261517	−0.130758	+	0.991414i	$0.541741\pi$
$684$	0	0
$685$	−12830.0	−0.715634
$686$	54080.0	3.00989
$687$	4360.00	0.242132
$688$	−27412.0	−1.51900
$689$	11508.0	0.636313
$690$	16000.0	0.882768
$691$	13292.0	0.731768	0.365884	−	0.930661i	$-0.380767\pi$
$691$	13292.0	0.731768	0.365884	+	0.930661i	$0.380767\pi$
$692$	−20502.0	−1.12626
$693$	−4224.00	−0.231539
$694$	60740.0	3.32228
$695$	9940.00	0.542512
$696$	−38520.0	−2.09784
$697$	684.000	0.0371712
$698$	3010.00	0.163224
$699$	−11368.0	−0.615132
$700$	−13600.0	−0.734331
$701$	7206.00	0.388255	0.194128	−	0.980976i	$-0.437812\pi$
$701$	7206.00	0.388255	0.194128	+	0.980976i	$0.437812\pi$
$702$	−31920.0	−1.71616
$703$	0	0
$704$	3444.00	0.184376
$705$	−3680.00	−0.196591
$706$	−10.0000	−0.000533081 0
$707$	−4032.00	−0.214482
$708$	18768.0	0.996249
$709$	−5666.00	−0.300128	−0.150064	−	0.988676i	$-0.547948\pi$
$709$	−5666.00	−0.300128	−0.150064	+	0.988676i	$0.547948\pi$
$710$	−8600.00	−0.454581
$711$	−7568.00	−0.399187
$712$	71010.0	3.73766
$713$	23040.0	1.21018
$714$	−72960.0	−3.82417
$715$	−2520.00	−0.131808
$716$	24004.0	1.25289
$717$	9600.00	0.500026
$718$	−9800.00	−0.509377
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	−4895.00	−0.253369
$721$	−11776.0	−0.608268
$722$	0	0
$723$	8520.00	0.438260
$724$	−63614.0	−3.26546
$725$	−5350.00	−0.274061
$726$	−23740.0	−1.21360
$727$	−4048.00	−0.206509	−0.103254	−	0.994655i	$-0.532926\pi$
$727$	−4048.00	−0.206509	−0.103254	+	0.994655i	$0.532926\pi$
$728$	60480.0	3.07904
$729$	19837.0	1.00782
$730$	4150.00	0.210409
$731$	−35112.0	−1.77656
$732$	56168.0	2.83611
$733$	12134.0	0.611432	0.305716	−	0.952123i	$-0.401104\pi$
$733$	12134.0	0.611432	0.305716	+	0.952123i	$0.401104\pi$
$734$	29320.0	1.47442
$735$	−13620.0	−0.683512
$736$	−13600.0	−0.681118
$737$	624.000	0.0311877
$738$	330.000	0.0164600
$739$	−13556.0	−0.674784	−0.337392	−	0.941364i	$-0.609545\pi$
$739$	−13556.0	−0.674784	−0.337392	+	0.941364i	$0.609545\pi$
$740$	−7990.00	−0.396917
$741$	0	0
$742$	43840.0	2.16903
$743$	−4368.00	−0.215675	−0.107837	−	0.994169i	$-0.534393\pi$
$743$	−4368.00	−0.215675	−0.107837	+	0.994169i	$0.534393\pi$
$744$	25920.0	1.27725
$745$	5670.00	0.278836
$746$	2790.00	0.136929
$747$	−10956.0	−0.536625
$748$	−23256.0	−1.13680
$749$	6528.00	0.318462
$750$	2500.00	0.121716
$751$	−3872.00	−0.188138	−0.0940688	−	0.995566i	$-0.529987\pi$
$751$	−3872.00	−0.188138	−0.0940688	+	0.995566i	$0.529987\pi$
$752$	16376.0	0.794111
$753$	9456.00	0.457631
$754$	44940.0	2.17058
$755$	12200.0	0.588084
$756$	−82688.0	−3.97795
$757$	6190.00	0.297199	0.148599	−	0.988897i	$-0.452524\pi$
$757$	6190.00	0.297199	0.148599	+	0.988897i	$0.452524\pi$
$758$	−24380.0	−1.16823
$759$	7680.00	0.367281
$760$	0	0
$761$	−7062.00	−0.336396	−0.168198	−	0.985753i	$-0.553795\pi$
$761$	−7062.00	−0.336396	−0.168198	+	0.985753i	$0.553795\pi$
$762$	−18080.0	−0.859540
$763$	−45888.0	−2.17727
$764$	−25024.0	−1.18500
$765$	−6270.00	−0.296330
$766$	−2120.00	−0.0999983
$767$	−11592.0	−0.545714
$768$	33116.0	1.55595
$769$	−5438.00	−0.255006	−0.127503	−	0.991838i	$-0.540696\pi$
$769$	−5438.00	−0.255006	−0.127503	+	0.991838i	$0.540696\pi$
$770$	−9600.00	−0.449299
$771$	25160.0	1.17525
$772$	−24786.0	−1.15553
$773$	−1182.00	−0.0549982	−0.0274991	−	0.999622i	$-0.508754\pi$
$773$	−1182.00	−0.0549982	−0.0274991	+	0.999622i	$0.508754\pi$
$774$	−16940.0	−0.786687
$775$	3600.00	0.166859
$776$	35370.0	1.63622
$777$	−12032.0	−0.555528
$778$	49450.0	2.27875
$779$	0	0
$780$	−14280.0	−0.655521
$781$	−4128.00	−0.189131
$782$	−91200.0	−4.17047
$783$	−32528.0	−1.48462
$784$	60609.0	2.76098
$785$	16190.0	0.736109
$786$	−43600.0	−1.97858
$787$	−12452.0	−0.563997	−0.281999	−	0.959415i	$-0.590997\pi$
$787$	−12452.0	−0.563997	−0.281999	+	0.959415i	$0.590997\pi$
$788$	34782.0	1.57241
$789$	−32448.0	−1.46411
$790$	−17200.0	−0.774618
$791$	38976.0	1.75199
$792$	−5940.00	−0.266501
$793$	−34692.0	−1.55353
$794$	1170.00	0.0522944
$795$	−5480.00	−0.244472
$796$	−25432.0	−1.13243
$797$	−15526.0	−0.690037	−0.345018	−	0.938596i	$-0.612127\pi$
$797$	−15526.0	−0.690037	−0.345018	+	0.938596i	$0.612127\pi$
$798$	0	0
$799$	20976.0	0.928758
$800$	−2125.00	−0.0939126
$801$	17358.0	0.765686
$802$	58010.0	2.55412
$803$	1992.00	0.0875419
$804$	3536.00	0.155106
$805$	−25600.0	−1.12085
$806$	−30240.0	−1.32154
$807$	−19176.0	−0.836465
$808$	−5670.00	−0.246869
$809$	31034.0	1.34870	0.674349	−	0.738412i	$-0.264424\pi$
$809$	31034.0	1.34870	0.674349	+	0.738412i	$0.264424\pi$
$810$	7775.00	0.337266
$811$	34636.0	1.49967	0.749836	−	0.661623i	$-0.230132\pi$
$811$	34636.0	1.49967	0.749836	+	0.661623i	$0.230132\pi$
$812$	116416.	5.03128
$813$	−1216.00	−0.0524563
$814$	−5640.00	−0.242852
$815$	−7100.00	−0.305156
$816$	−40584.0	−1.74108
$817$	0	0
$818$	−74030.0	−3.16430
$819$	14784.0	0.630763
$820$	510.000	0.0217195
$821$	−20082.0	−0.853674	−0.426837	−	0.904328i	$-0.640372\pi$
$821$	−20082.0	−0.853674	−0.426837	+	0.904328i	$0.640372\pi$
$822$	−51320.0	−2.17760
$823$	33568.0	1.42176	0.710879	−	0.703314i	$-0.248297\pi$
$823$	33568.0	1.42176	0.710879	+	0.703314i	$0.248297\pi$
$824$	−16560.0	−0.700115
$825$	1200.00	0.0506408
$826$	−44160.0	−1.86020
$827$	−19644.0	−0.825984	−0.412992	−	0.910735i	$-0.635516\pi$
$827$	−19644.0	−0.825984	−0.412992	+	0.910735i	$0.635516\pi$
$828$	−29920.0	−1.25579
$829$	−726.000	−0.0304162	−0.0152081	−	0.999884i	$-0.504841\pi$
$829$	−726.000	−0.0304162	−0.0152081	+	0.999884i	$0.504841\pi$
$830$	−24900.0	−1.04132
$831$	−8248.00	−0.344308
$832$	−12054.0	−0.502280
$833$	77634.0	3.22912
$834$	39760.0	1.65081
$835$	11680.0	0.484076
$836$	0	0
$837$	21888.0	0.903895
$838$	−31260.0	−1.28861
$839$	−3512.00	−0.144515	−0.0722573	−	0.997386i	$-0.523020\pi$
$839$	−3512.00	−0.144515	−0.0722573	+	0.997386i	$0.523020\pi$
$840$	−28800.0	−1.18297
$841$	21407.0	0.877732
$842$	−52410.0	−2.14509
$843$	−16216.0	−0.662525
$844$	−14348.0	−0.585164
$845$	−2165.00	−0.0881400
$846$	10120.0	0.411268
$847$	37984.0	1.54090
$848$	24386.0	0.987522
$849$	−31984.0	−1.29292
$850$	−14250.0	−0.575025
$851$	−15040.0	−0.605834
$852$	−23392.0	−0.940606
$853$	−39442.0	−1.58320	−0.791599	−	0.611041i	$-0.790751\pi$
$853$	−39442.0	−1.58320	−0.791599	+	0.611041i	$0.790751\pi$
$854$	−132160.	−5.29558
$855$	0	0
$856$	9180.00	0.366549
$857$	40454.0	1.61246	0.806232	−	0.591599i	$-0.201503\pi$
$857$	40454.0	1.61246	0.806232	+	0.591599i	$0.201503\pi$
$858$	−10080.0	−0.401079
$859$	−3436.00	−0.136478	−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−3436.00	−0.136478	−0.0682391	+	0.997669i	$0.521738\pi$
$860$	−26180.0	−1.03806
$861$	768.000	0.0303988
$862$	19680.0	0.777614
$863$	10056.0	0.396651	0.198326	−	0.980136i	$-0.436450\pi$
$863$	10056.0	0.396651	0.198326	+	0.980136i	$0.436450\pi$
$864$	−12920.0	−0.508735
$865$	−6030.00	−0.237024
$866$	54730.0	2.14758
$867$	−32332.0	−1.26650
$868$	−78336.0	−3.06325
$869$	−8256.00	−0.322285
$870$	−21400.0	−0.833940
$871$	−2184.00	−0.0849621
$872$	−64530.0	−2.50603
$873$	8646.00	0.335192
$874$	0	0
$875$	−4000.00	−0.154542
$876$	11288.0	0.435372
$877$	44394.0	1.70933	0.854663	−	0.519183i	$-0.173764\pi$
$877$	44394.0	1.70933	0.854663	+	0.519183i	$0.173764\pi$
$878$	−39000.0	−1.49907
$879$	−15624.0	−0.599527
$880$	−5340.00	−0.204558
$881$	−18222.0	−0.696839	−0.348419	−	0.937339i	$-0.613281\pi$
$881$	−18222.0	−0.696839	−0.348419	+	0.937339i	$0.613281\pi$
$882$	37455.0	1.42990
$883$	−29404.0	−1.12064	−0.560319	−	0.828277i	$-0.689321\pi$
$883$	−29404.0	−1.12064	−0.560319	+	0.828277i	$0.689321\pi$
$884$	81396.0	3.09688
$885$	5520.00	0.209664
$886$	56820.0	2.15452
$887$	−18576.0	−0.703180	−0.351590	−	0.936154i	$-0.614359\pi$
$887$	−18576.0	−0.703180	−0.351590	+	0.936154i	$0.614359\pi$
$888$	−16920.0	−0.639412
$889$	28928.0	1.09135
$890$	39450.0	1.48581
$891$	3732.00	0.140322
$892$	57800.0	2.16960
$893$	0	0
$894$	22680.0	0.848471
$895$	7060.00	0.263676
$896$	−67680.0	−2.52347
$897$	−26880.0	−1.00055
$898$	36650.0	1.36194
$899$	−30816.0	−1.14324
$900$	−4675.00	−0.173148
$901$	31236.0	1.15496
$902$	360.000	0.0132890
$903$	−39424.0	−1.45288
$904$	54810.0	2.01654
$905$	−18710.0	−0.687228
$906$	48800.0	1.78948
$907$	2644.00	0.0967945	0.0483972	−	0.998828i	$-0.484589\pi$
$907$	2644.00	0.0967945	0.0483972	+	0.998828i	$0.484589\pi$
$908$	−31348.0	−1.14573
$909$	−1386.00	−0.0505728
$910$	33600.0	1.22399
$911$	−39744.0	−1.44542	−0.722710	−	0.691151i	$-0.757104\pi$
$911$	−39744.0	−1.44542	−0.722710	+	0.691151i	$0.757104\pi$
$912$	0	0
$913$	−11952.0	−0.433246
$914$	63870.0	2.31141
$915$	16520.0	0.596868
$916$	−18530.0	−0.668393
$917$	69760.0	2.51219
$918$	−86640.0	−3.11497
$919$	−19720.0	−0.707838	−0.353919	−	0.935276i	$-0.615151\pi$
$919$	−19720.0	−0.707838	−0.353919	+	0.935276i	$0.615151\pi$
$920$	−36000.0	−1.29009
$921$	−7280.00	−0.260461
$922$	18930.0	0.676167
$923$	14448.0	0.515235
$924$	−26112.0	−0.929677
$925$	−2350.00	−0.0835325
$926$	97240.0	3.45087
$927$	−4048.00	−0.143424
$928$	18190.0	0.643444
$929$	36258.0	1.28050	0.640251	−	0.768166i	$-0.278830\pi$
$929$	36258.0	1.28050	0.640251	+	0.768166i	$0.278830\pi$
$930$	14400.0	0.507736
$931$	0	0
$932$	48314.0	1.69804
$933$	−2848.00	−0.0999350
$934$	−22980.0	−0.805063
$935$	−6840.00	−0.239243
$936$	20790.0	0.726007
$937$	14586.0	0.508542	0.254271	−	0.967133i	$-0.418164\pi$
$937$	14586.0	0.508542	0.254271	+	0.967133i	$0.418164\pi$
$938$	−8320.00	−0.289614
$939$	−36520.0	−1.26921
$940$	15640.0	0.542681
$941$	−30182.0	−1.04560	−0.522798	−	0.852457i	$-0.675112\pi$
$941$	−30182.0	−1.04560	−0.522798	+	0.852457i	$0.675112\pi$
$942$	64760.0	2.23991
$943$	960.000	0.0331515
$944$	−24564.0	−0.846917
$945$	−24320.0	−0.837174
$946$	−18480.0	−0.635134
$947$	15828.0	0.543127	0.271563	−	0.962421i	$-0.412459\pi$
$947$	15828.0	0.543127	0.271563	+	0.962421i	$0.412459\pi$
$948$	−46784.0	−1.60282
$949$	−6972.00	−0.238483
$950$	0	0
$951$	25368.0	0.864999
$952$	164160.	5.58871
$953$	−22746.0	−0.773153	−0.386577	−	0.922257i	$-0.626343\pi$
$953$	−22746.0	−0.773153	−0.386577	+	0.922257i	$0.626343\pi$
$954$	15070.0	0.511435
$955$	−7360.00	−0.249386
$956$	−40800.0	−1.38030
$957$	−10272.0	−0.346966
$958$	−62160.0	−2.09634
$959$	82112.0	2.76490
$960$	5740.00	0.192977
$961$	−9055.00	−0.303951
$962$	19740.0	0.661583
$963$	2244.00	0.0750902
$964$	−36210.0	−1.20980
$965$	−7290.00	−0.243185
$966$	−102400.	−3.41063
$967$	16480.0	0.548047	0.274023	−	0.961723i	$-0.411645\pi$
$967$	16480.0	0.548047	0.274023	+	0.961723i	$0.411645\pi$
$968$	53415.0	1.77358
$969$	0	0
$970$	19650.0	0.650437
$971$	16940.0	0.559867	0.279933	−	0.960019i	$-0.409688\pi$
$971$	16940.0	0.559867	0.279933	+	0.960019i	$0.409688\pi$
$972$	−48620.0	−1.60441
$973$	−63616.0	−2.09603
$974$	−90080.0	−2.96340
$975$	−4200.00	−0.137957
$976$	−73514.0	−2.41099
$977$	40062.0	1.31187	0.655935	−	0.754817i	$-0.272275\pi$
$977$	40062.0	1.31187	0.655935	+	0.754817i	$0.272275\pi$
$978$	−28400.0	−0.928560
$979$	18936.0	0.618179
$980$	57885.0	1.88680
$981$	−15774.0	−0.513379
$982$	−9860.00	−0.320413
$983$	−4832.00	−0.156782	−0.0783911	−	0.996923i	$-0.524978\pi$
$983$	−4832.00	−0.156782	−0.0783911	+	0.996923i	$0.524978\pi$
$984$	1080.00	0.0349890
$985$	10230.0	0.330919
$986$	121980.	3.93979
$987$	23552.0	0.759542
$988$	0	0
$989$	−49280.0	−1.58444
$990$	−3300.00	−0.105940
$991$	4144.00	0.132834	0.0664170	−	0.997792i	$-0.478843\pi$
$991$	4144.00	0.132834	0.0664170	+	0.997792i	$0.478843\pi$
$992$	−12240.0	−0.391754
$993$	−18992.0	−0.606941
$994$	55040.0	1.75630
$995$	−7480.00	−0.238324
$996$	−67728.0	−2.15466
$997$	35294.0	1.12114	0.560568	−	0.828109i	$-0.310583\pi$
$997$	35294.0	1.12114	0.560568	+	0.828109i	$0.310583\pi$
$998$	−93900.0	−2.97831
$999$	−14288.0	−0.452505

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.4.a.a.1.1		1
19.18	odd	2		95.4.a.d.1.1	✓	1
57.56	even	2		855.4.a.a.1.1		1
76.75	even	2		1520.4.a.c.1.1		1
95.18	even	4		475.4.b.a.324.1		2
95.37	even	4		475.4.b.a.324.2		2
95.94	odd	2		475.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.4.a.d.1.1	✓	1	19.18	odd	2
475.4.a.a.1.1		1	95.94	odd	2
475.4.b.a.324.1		2	95.18	even	4
475.4.b.a.324.2		2	95.37	even	4
855.4.a.a.1.1		1	57.56	even	2
1520.4.a.c.1.1		1	76.75	even	2
1805.4.a.a.1.1		1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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