LMFDB - Embedded newform 435.4.a.b.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [435,4,Mod(1,435)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("435.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(435, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	435.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$25.6658308525$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	435.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q-1.00000 q^{2} +3.00000 q^{3} -7.00000 q^{4} +5.00000 q^{5} -3.00000 q^{6} +4.00000 q^{7} +15.0000 q^{8} +9.00000 q^{9} -5.00000 q^{10} -36.0000 q^{11} -21.0000 q^{12} -22.0000 q^{13} -4.00000 q^{14} +15.0000 q^{15} +41.0000 q^{16} -2.00000 q^{17} -9.00000 q^{18} -56.0000 q^{19} -35.0000 q^{20} +12.0000 q^{21} +36.0000 q^{22} -40.0000 q^{23} +45.0000 q^{24} +25.0000 q^{25} +22.0000 q^{26} +27.0000 q^{27} -28.0000 q^{28} +29.0000 q^{29} -15.0000 q^{30} +152.000 q^{31} -161.000 q^{32} -108.000 q^{33} +2.00000 q^{34} +20.0000 q^{35} -63.0000 q^{36} +34.0000 q^{37} +56.0000 q^{38} -66.0000 q^{39} +75.0000 q^{40} -250.000 q^{41} -12.0000 q^{42} -412.000 q^{43} +252.000 q^{44} +45.0000 q^{45} +40.0000 q^{46} -120.000 q^{47} +123.000 q^{48} -327.000 q^{49} -25.0000 q^{50} -6.00000 q^{51} +154.000 q^{52} -762.000 q^{53} -27.0000 q^{54} -180.000 q^{55} +60.0000 q^{56} -168.000 q^{57} -29.0000 q^{58} -188.000 q^{59} -105.000 q^{60} -54.0000 q^{61} -152.000 q^{62} +36.0000 q^{63} -167.000 q^{64} -110.000 q^{65} +108.000 q^{66} -244.000 q^{67} +14.0000 q^{68} -120.000 q^{69} -20.0000 q^{70} +600.000 q^{71} +135.000 q^{72} +6.00000 q^{73} -34.0000 q^{74} +75.0000 q^{75} +392.000 q^{76} -144.000 q^{77} +66.0000 q^{78} -640.000 q^{79} +205.000 q^{80} +81.0000 q^{81} +250.000 q^{82} +664.000 q^{83} -84.0000 q^{84} -10.0000 q^{85} +412.000 q^{86} +87.0000 q^{87} -540.000 q^{88} +150.000 q^{89} -45.0000 q^{90} -88.0000 q^{91} +280.000 q^{92} +456.000 q^{93} +120.000 q^{94} -280.000 q^{95} -483.000 q^{96} -1690.00 q^{97} +327.000 q^{98} -324.000 q^{99} +O(q^{100})\)

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 $

$2$	−1.00000	−0.353553	−0.176777	−	0.984251i	$-0.556567\pi$
$2$	−1.00000	−0.353553	−0.176777	+	0.984251i	$0.556567\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.00000	−0.875000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−3.00000	−0.204124
$7$	4.00000	0.215980	0.107990	−	0.994152i	$-0.465559\pi$
$7$	4.00000	0.215980	0.107990	+	0.994152i	$0.465559\pi$
$8$	15.0000	0.662913
$9$	9.00000	0.333333
$10$	−5.00000	−0.158114
$11$	−36.0000	−0.986764	−0.493382	−	0.869813i	$-0.664240\pi$
$11$	−36.0000	−0.986764	−0.493382	+	0.869813i	$0.664240\pi$
$12$	−21.0000	−0.505181
$13$	−22.0000	−0.469362	−0.234681	−	0.972072i	$-0.575405\pi$
$13$	−22.0000	−0.469362	−0.234681	+	0.972072i	$0.575405\pi$
$14$	−4.00000	−0.0763604
$15$	15.0000	0.258199
$16$	41.0000	0.640625
$17$	−2.00000	−0.0285336	−0.0142668	−	0.999898i	$-0.504541\pi$
$17$	−2.00000	−0.0285336	−0.0142668	+	0.999898i	$0.504541\pi$
$18$	−9.00000	−0.117851
$19$	−56.0000	−0.676173	−0.338086	−	0.941115i	$-0.609780\pi$
$19$	−56.0000	−0.676173	−0.338086	+	0.941115i	$0.609780\pi$
$20$	−35.0000	−0.391312
$21$	12.0000	0.124696
$22$	36.0000	0.348874
$23$	−40.0000	−0.362634	−0.181317	−	0.983425i	$-0.558036\pi$
$23$	−40.0000	−0.362634	−0.181317	+	0.983425i	$0.558036\pi$
$24$	45.0000	0.382733
$25$	25.0000	0.200000
$26$	22.0000	0.165944
$27$	27.0000	0.192450
$28$	−28.0000	−0.188982
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	−15.0000	−0.0912871
$31$	152.000	0.880645	0.440323	−	0.897840i	$-0.354864\pi$
$31$	152.000	0.880645	0.440323	+	0.897840i	$0.354864\pi$
$32$	−161.000	−0.889408
$33$	−108.000	−0.569709
$34$	2.00000	0.0100882
$35$	20.0000	0.0965891
$36$	−63.0000	−0.291667
$37$	34.0000	0.151069	0.0755347	−	0.997143i	$-0.475934\pi$
$37$	34.0000	0.151069	0.0755347	+	0.997143i	$0.475934\pi$
$38$	56.0000	0.239063
$39$	−66.0000	−0.270986
$40$	75.0000	0.296464
$41$	−250.000	−0.952279	−0.476140	−	0.879370i	$-0.657964\pi$
$41$	−250.000	−0.952279	−0.476140	+	0.879370i	$0.657964\pi$
$42$	−12.0000	−0.0440867
$43$	−412.000	−1.46115	−0.730575	−	0.682833i	$-0.760748\pi$
$43$	−412.000	−1.46115	−0.730575	+	0.682833i	$0.760748\pi$
$44$	252.000	0.863419
$45$	45.0000	0.149071
$46$	40.0000	0.128210
$47$	−120.000	−0.372421	−0.186211	−	0.982510i	$-0.559621\pi$
$47$	−120.000	−0.372421	−0.186211	+	0.982510i	$0.559621\pi$
$48$	123.000	0.369865
$49$	−327.000	−0.953353
$50$	−25.0000	−0.0707107
$51$	−6.00000	−0.0164739
$52$	154.000	0.410691
$53$	−762.000	−1.97488	−0.987441	−	0.157988i	$-0.949499\pi$
$53$	−762.000	−1.97488	−0.987441	+	0.157988i	$0.949499\pi$
$54$	−27.0000	−0.0680414
$55$	−180.000	−0.441294
$56$	60.0000	0.143176
$57$	−168.000	−0.390388
$58$	−29.0000	−0.0656532
$59$	−188.000	−0.414839	−0.207420	−	0.978252i	$-0.566507\pi$
$59$	−188.000	−0.414839	−0.207420	+	0.978252i	$0.566507\pi$
$60$	−105.000	−0.225924
$61$	−54.0000	−0.113344	−0.0566721	−	0.998393i	$-0.518049\pi$
$61$	−54.0000	−0.113344	−0.0566721	+	0.998393i	$0.518049\pi$
$62$	−152.000	−0.311355
$63$	36.0000	0.0719932
$64$	−167.000	−0.326172
$65$	−110.000	−0.209905
$66$	108.000	0.201422
$67$	−244.000	−0.444916	−0.222458	−	0.974942i	$-0.571408\pi$
$67$	−244.000	−0.444916	−0.222458	+	0.974942i	$0.571408\pi$
$68$	14.0000	0.0249669
$69$	−120.000	−0.209367
$70$	−20.0000	−0.0341494
$71$	600.000	1.00291	0.501457	−	0.865183i	$-0.332798\pi$
$71$	600.000	1.00291	0.501457	+	0.865183i	$0.332798\pi$
$72$	135.000	0.220971
$73$	6.00000	0.00961982	0.00480991	−	0.999988i	$-0.498469\pi$
$73$	6.00000	0.00961982	0.00480991	+	0.999988i	$0.498469\pi$
$74$	−34.0000	−0.0534111
$75$	75.0000	0.115470
$76$	392.000	0.591651
$77$	−144.000	−0.213121
$78$	66.0000	0.0958081
$79$	−640.000	−0.911464	−0.455732	−	0.890117i	$-0.650622\pi$
$79$	−640.000	−0.911464	−0.455732	+	0.890117i	$0.650622\pi$
$80$	205.000	0.286496
$81$	81.0000	0.111111
$82$	250.000	0.336681
$83$	664.000	0.878114	0.439057	−	0.898459i	$-0.355313\pi$
$83$	664.000	0.878114	0.439057	+	0.898459i	$0.355313\pi$
$84$	−84.0000	−0.109109
$85$	−10.0000	−0.0127606
$86$	412.000	0.516594
$87$	87.0000	0.107211
$88$	−540.000	−0.654139
$89$	150.000	0.178651	0.0893257	−	0.996002i	$-0.471529\pi$
$89$	150.000	0.178651	0.0893257	+	0.996002i	$0.471529\pi$
$90$	−45.0000	−0.0527046
$91$	−88.0000	−0.101373
$92$	280.000	0.317305
$93$	456.000	0.508441
$94$	120.000	0.131671
$95$	−280.000	−0.302394
$96$	−483.000	−0.513500
$97$	−1690.00	−1.76901	−0.884503	−	0.466535i	$-0.845502\pi$
$97$	−1690.00	−1.76901	−0.884503	+	0.466535i	$0.845502\pi$
$98$	327.000	0.337061
$99$	−324.000	−0.328921
$100$	−175.000	−0.175000
$101$	502.000	0.494563	0.247282	−	0.968944i	$-0.420463\pi$
$101$	502.000	0.494563	0.247282	+	0.968944i	$0.420463\pi$
$102$	6.00000	0.00582440
$103$	−828.000	−0.792090	−0.396045	−	0.918231i	$-0.629618\pi$
$103$	−828.000	−0.792090	−0.396045	+	0.918231i	$0.629618\pi$
$104$	−330.000	−0.311146
$105$	60.0000	0.0557657
$106$	762.000	0.698226
$107$	−1176.00	−1.06251	−0.531253	−	0.847213i	$-0.678279\pi$
$107$	−1176.00	−1.06251	−0.531253	+	0.847213i	$0.678279\pi$
$108$	−189.000	−0.168394
$109$	−1922.00	−1.68894	−0.844469	−	0.535605i	$-0.820084\pi$
$109$	−1922.00	−1.68894	−0.844469	+	0.535605i	$0.820084\pi$
$110$	180.000	0.156021
$111$	102.000	0.0872199
$112$	164.000	0.138362
$113$	−322.000	−0.268064	−0.134032	−	0.990977i	$-0.542792\pi$
$113$	−322.000	−0.268064	−0.134032	+	0.990977i	$0.542792\pi$
$114$	168.000	0.138023
$115$	−200.000	−0.162175
$116$	−203.000	−0.162483
$117$	−198.000	−0.156454
$118$	188.000	0.146668
$119$	−8.00000	−0.00616268
$120$	225.000	0.171163
$121$	−35.0000	−0.0262960
$122$	54.0000	0.0400732
$123$	−750.000	−0.549799
$124$	−1064.00	−0.770565
$125$	125.000	0.0894427
$126$	−36.0000	−0.0254535
$127$	1568.00	1.09557	0.547785	−	0.836619i	$-0.315471\pi$
$127$	1568.00	1.09557	0.547785	+	0.836619i	$0.315471\pi$
$128$	1455.00	1.00473
$129$	−1236.00	−0.843595
$130$	110.000	0.0742126
$131$	1124.00	0.749651	0.374826	−	0.927095i	$-0.377703\pi$
$131$	1124.00	0.749651	0.374826	+	0.927095i	$0.377703\pi$
$132$	756.000	0.498495
$133$	−224.000	−0.146040
$134$	244.000	0.157301
$135$	135.000	0.0860663
$136$	−30.0000	−0.0189153
$137$	2646.00	1.65010	0.825048	−	0.565063i	$-0.191148\pi$
$137$	2646.00	1.65010	0.825048	+	0.565063i	$0.191148\pi$
$138$	120.000	0.0740223
$139$	−1956.00	−1.19357	−0.596783	−	0.802402i	$-0.703555\pi$
$139$	−1956.00	−1.19357	−0.596783	+	0.802402i	$0.703555\pi$
$140$	−140.000	−0.0845154
$141$	−360.000	−0.215018
$142$	−600.000	−0.354584
$143$	792.000	0.463149
$144$	369.000	0.213542
$145$	145.000	0.0830455
$146$	−6.00000	−0.00340112
$147$	−981.000	−0.550418
$148$	−238.000	−0.132186
$149$	2126.00	1.16892	0.584459	−	0.811423i	$-0.301307\pi$
$149$	2126.00	1.16892	0.584459	+	0.811423i	$0.301307\pi$
$150$	−75.0000	−0.0408248
$151$	1208.00	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	1208.00	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	−840.000	−0.448243
$153$	−18.0000	−0.00951120
$154$	144.000	0.0753497
$155$	760.000	0.393837
$156$	462.000	0.237113
$157$	490.000	0.249084	0.124542	−	0.992214i	$-0.460254\pi$
$157$	490.000	0.249084	0.124542	+	0.992214i	$0.460254\pi$
$158$	640.000	0.322251
$159$	−2286.00	−1.14020
$160$	−805.000	−0.397755
$161$	−160.000	−0.0783215
$162$	−81.0000	−0.0392837
$163$	1780.00	0.855340	0.427670	−	0.903935i	$-0.359335\pi$
$163$	1780.00	0.855340	0.427670	+	0.903935i	$0.359335\pi$
$164$	1750.00	0.833244
$165$	−540.000	−0.254781
$166$	−664.000	−0.310460
$167$	2520.00	1.16769	0.583843	−	0.811867i	$-0.301548\pi$
$167$	2520.00	1.16769	0.583843	+	0.811867i	$0.301548\pi$
$168$	180.000	0.0826625
$169$	−1713.00	−0.779700
$170$	10.0000	0.00451156
$171$	−504.000	−0.225391
$172$	2884.00	1.27851
$173$	382.000	0.167878	0.0839391	−	0.996471i	$-0.473250\pi$
$173$	382.000	0.167878	0.0839391	+	0.996471i	$0.473250\pi$
$174$	−87.0000	−0.0379049
$175$	100.000	0.0431959
$176$	−1476.00	−0.632146
$177$	−564.000	−0.239508
$178$	−150.000	−0.0631628
$179$	−1908.00	−0.796707	−0.398354	−	0.917232i	$-0.630418\pi$
$179$	−1908.00	−0.796707	−0.398354	+	0.917232i	$0.630418\pi$
$180$	−315.000	−0.130437
$181$	−450.000	−0.184797	−0.0923984	−	0.995722i	$-0.529453\pi$
$181$	−450.000	−0.184797	−0.0923984	+	0.995722i	$0.529453\pi$
$182$	88.0000	0.0358406
$183$	−162.000	−0.0654393
$184$	−600.000	−0.240394
$185$	170.000	0.0675603
$186$	−456.000	−0.179761
$187$	72.0000	0.0281559
$188$	840.000	0.325869
$189$	108.000	0.0415653
$190$	280.000	0.106912
$191$	1412.00	0.534915	0.267457	−	0.963570i	$-0.413817\pi$
$191$	1412.00	0.534915	0.267457	+	0.963570i	$0.413817\pi$
$192$	−501.000	−0.188315
$193$	−418.000	−0.155898	−0.0779490	−	0.996957i	$-0.524837\pi$
$193$	−418.000	−0.155898	−0.0779490	+	0.996957i	$0.524837\pi$
$194$	1690.00	0.625438
$195$	−330.000	−0.121189
$196$	2289.00	0.834184
$197$	3182.00	1.15080	0.575401	−	0.817871i	$-0.304846\pi$
$197$	3182.00	1.15080	0.575401	+	0.817871i	$0.304846\pi$
$198$	324.000	0.116291
$199$	4976.00	1.77256	0.886280	−	0.463151i	$-0.153281\pi$
$199$	4976.00	1.77256	0.886280	+	0.463151i	$0.153281\pi$
$200$	375.000	0.132583
$201$	−732.000	−0.256872
$202$	−502.000	−0.174854
$203$	116.000	0.0401064
$204$	42.0000	0.0144146
$205$	−1250.00	−0.425872
$206$	828.000	0.280046
$207$	−360.000	−0.120878
$208$	−902.000	−0.300685
$209$	2016.00	0.667223
$210$	−60.0000	−0.0197162
$211$	−640.000	−0.208812	−0.104406	−	0.994535i	$-0.533294\pi$
$211$	−640.000	−0.208812	−0.104406	+	0.994535i	$0.533294\pi$
$212$	5334.00	1.72802
$213$	1800.00	0.579033
$214$	1176.00	0.375653
$215$	−2060.00	−0.653446
$216$	405.000	0.127578
$217$	608.000	0.190202
$218$	1922.00	0.597130
$219$	18.0000	0.00555401
$220$	1260.00	0.386133
$221$	44.0000	0.0133926
$222$	−102.000	−0.0308369
$223$	−1724.00	−0.517702	−0.258851	−	0.965917i	$-0.583344\pi$
$223$	−1724.00	−0.517702	−0.258851	+	0.965917i	$0.583344\pi$
$224$	−644.000	−0.192094
$225$	225.000	0.0666667
$226$	322.000	0.0947749
$227$	1216.00	0.355545	0.177773	−	0.984072i	$-0.443111\pi$
$227$	1216.00	0.355545	0.177773	+	0.984072i	$0.443111\pi$
$228$	1176.00	0.341590
$229$	−1806.00	−0.521152	−0.260576	−	0.965453i	$-0.583912\pi$
$229$	−1806.00	−0.521152	−0.260576	+	0.965453i	$0.583912\pi$
$230$	200.000	0.0573374
$231$	−432.000	−0.123046
$232$	435.000	0.123100
$233$	3654.00	1.02739	0.513694	−	0.857973i	$-0.328277\pi$
$233$	3654.00	1.02739	0.513694	+	0.857973i	$0.328277\pi$
$234$	198.000	0.0553148
$235$	−600.000	−0.166552
$236$	1316.00	0.362984
$237$	−1920.00	−0.526234
$238$	8.00000	0.00217884
$239$	−5304.00	−1.43551	−0.717756	−	0.696295i	$-0.754831\pi$
$239$	−5304.00	−1.43551	−0.717756	+	0.696295i	$0.754831\pi$
$240$	615.000	0.165409
$241$	4402.00	1.17659	0.588294	−	0.808647i	$-0.299800\pi$
$241$	4402.00	1.17659	0.588294	+	0.808647i	$0.299800\pi$
$242$	35.0000	0.00929705
$243$	243.000	0.0641500
$244$	378.000	0.0991761
$245$	−1635.00	−0.426352
$246$	750.000	0.194383
$247$	1232.00	0.317370
$248$	2280.00	0.583791
$249$	1992.00	0.506979
$250$	−125.000	−0.0316228
$251$	2268.00	0.570338	0.285169	−	0.958477i	$-0.407950\pi$
$251$	2268.00	0.570338	0.285169	+	0.958477i	$0.407950\pi$
$252$	−252.000	−0.0629941
$253$	1440.00	0.357834
$254$	−1568.00	−0.387343
$255$	−30.0000	−0.00736734
$256$	−119.000	−0.0290527
$257$	534.000	0.129611	0.0648055	−	0.997898i	$-0.479357\pi$
$257$	534.000	0.129611	0.0648055	+	0.997898i	$0.479357\pi$
$258$	1236.00	0.298256
$259$	136.000	0.0326279
$260$	770.000	0.183667
$261$	261.000	0.0618984
$262$	−1124.00	−0.265042
$263$	5592.00	1.31109	0.655547	−	0.755155i	$-0.272438\pi$
$263$	5592.00	1.31109	0.655547	+	0.755155i	$0.272438\pi$
$264$	−1620.00	−0.377667
$265$	−3810.00	−0.883194
$266$	224.000	0.0516328
$267$	450.000	0.103144
$268$	1708.00	0.389301
$269$	−6562.00	−1.48733	−0.743666	−	0.668552i	$-0.766915\pi$
$269$	−6562.00	−1.48733	−0.743666	+	0.668552i	$0.766915\pi$
$270$	−135.000	−0.0304290
$271$	1192.00	0.267191	0.133596	−	0.991036i	$-0.457348\pi$
$271$	1192.00	0.267191	0.133596	+	0.991036i	$0.457348\pi$
$272$	−82.0000	−0.0182793
$273$	−264.000	−0.0585275
$274$	−2646.00	−0.583397
$275$	−900.000	−0.197353
$276$	840.000	0.183196
$277$	6474.00	1.40428	0.702139	−	0.712040i	$-0.252229\pi$
$277$	6474.00	1.40428	0.702139	+	0.712040i	$0.252229\pi$
$278$	1956.00	0.421990
$279$	1368.00	0.293548
$280$	300.000	0.0640301
$281$	−3758.00	−0.797806	−0.398903	−	0.916993i	$-0.630609\pi$
$281$	−3758.00	−0.797806	−0.398903	+	0.916993i	$0.630609\pi$
$282$	360.000	0.0760202
$283$	292.000	0.0613343	0.0306671	−	0.999530i	$-0.490237\pi$
$283$	292.000	0.0613343	0.0306671	+	0.999530i	$0.490237\pi$
$284$	−4200.00	−0.877550
$285$	−840.000	−0.174587
$286$	−792.000	−0.163748
$287$	−1000.00	−0.205673
$288$	−1449.00	−0.296469
$289$	−4909.00	−0.999186
$290$	−145.000	−0.0293610
$291$	−5070.00	−1.02134
$292$	−42.0000	−0.00841734
$293$	−1382.00	−0.275554	−0.137777	−	0.990463i	$-0.543996\pi$
$293$	−1382.00	−0.275554	−0.137777	+	0.990463i	$0.543996\pi$
$294$	981.000	0.194602
$295$	−940.000	−0.185522
$296$	510.000	0.100146
$297$	−972.000	−0.189903
$298$	−2126.00	−0.413275
$299$	880.000	0.170206
$300$	−525.000	−0.101036
$301$	−1648.00	−0.315579
$302$	−1208.00	−0.230174
$303$	1506.00	0.285536
$304$	−2296.00	−0.433173
$305$	−270.000	−0.0506890
$306$	18.0000	0.00336272
$307$	−3948.00	−0.733955	−0.366978	−	0.930230i	$-0.619607\pi$
$307$	−3948.00	−0.733955	−0.366978	+	0.930230i	$0.619607\pi$
$308$	1008.00	0.186481
$309$	−2484.00	−0.457313
$310$	−760.000	−0.139242
$311$	−7396.00	−1.34852	−0.674258	−	0.738496i	$-0.735537\pi$
$311$	−7396.00	−1.34852	−0.674258	+	0.738496i	$0.735537\pi$
$312$	−990.000	−0.179640
$313$	3290.00	0.594127	0.297064	−	0.954858i	$-0.403993\pi$
$313$	3290.00	0.594127	0.297064	+	0.954858i	$0.403993\pi$
$314$	−490.000	−0.0880646
$315$	180.000	0.0321964
$316$	4480.00	0.797531
$317$	−1670.00	−0.295888	−0.147944	−	0.988996i	$-0.547266\pi$
$317$	−1670.00	−0.295888	−0.147944	+	0.988996i	$0.547266\pi$
$318$	2286.00	0.403121
$319$	−1044.00	−0.183238
$320$	−835.000	−0.145868
$321$	−3528.00	−0.613438
$322$	160.000	0.0276908
$323$	112.000	0.0192936
$324$	−567.000	−0.0972222
$325$	−550.000	−0.0938723
$326$	−1780.00	−0.302408
$327$	−5766.00	−0.975109
$328$	−3750.00	−0.631278
$329$	−480.000	−0.0804354
$330$	540.000	0.0900789
$331$	912.000	0.151444	0.0757221	−	0.997129i	$-0.475874\pi$
$331$	912.000	0.151444	0.0757221	+	0.997129i	$0.475874\pi$
$332$	−4648.00	−0.768350
$333$	306.000	0.0503564
$334$	−2520.00	−0.412839
$335$	−1220.00	−0.198972
$336$	492.000	0.0798833
$337$	−3082.00	−0.498182	−0.249091	−	0.968480i	$-0.580132\pi$
$337$	−3082.00	−0.498182	−0.249091	+	0.968480i	$0.580132\pi$
$338$	1713.00	0.275665
$339$	−966.000	−0.154767
$340$	70.0000	0.0111655
$341$	−5472.00	−0.868989
$342$	504.000	0.0796877
$343$	−2680.00	−0.421885
$344$	−6180.00	−0.968614
$345$	−600.000	−0.0936316
$346$	−382.000	−0.0593539
$347$	−4536.00	−0.701744	−0.350872	−	0.936423i	$-0.614115\pi$
$347$	−4536.00	−0.701744	−0.350872	+	0.936423i	$0.614115\pi$
$348$	−609.000	−0.0938098
$349$	−7130.00	−1.09358	−0.546791	−	0.837269i	$-0.684151\pi$
$349$	−7130.00	−1.09358	−0.546791	+	0.837269i	$0.684151\pi$
$350$	−100.000	−0.0152721
$351$	−594.000	−0.0903287
$352$	5796.00	0.877636
$353$	6814.00	1.02740	0.513701	−	0.857970i	$-0.328274\pi$
$353$	6814.00	1.02740	0.513701	+	0.857970i	$0.328274\pi$
$354$	564.000	0.0846787
$355$	3000.00	0.448517
$356$	−1050.00	−0.156320
$357$	−24.0000	−0.00355802
$358$	1908.00	0.281679
$359$	8188.00	1.20375	0.601875	−	0.798590i	$-0.294421\pi$
$359$	8188.00	1.20375	0.601875	+	0.798590i	$0.294421\pi$
$360$	675.000	0.0988212
$361$	−3723.00	−0.542790
$362$	450.000	0.0653356
$363$	−105.000	−0.0151820
$364$	616.000	0.0887010
$365$	30.0000	0.00430211
$366$	162.000	0.0231363
$367$	624.000	0.0887535	0.0443768	−	0.999015i	$-0.485870\pi$
$367$	624.000	0.0887535	0.0443768	+	0.999015i	$0.485870\pi$
$368$	−1640.00	−0.232312
$369$	−2250.00	−0.317426
$370$	−170.000	−0.0238862
$371$	−3048.00	−0.426534
$372$	−3192.00	−0.444886
$373$	−1206.00	−0.167411	−0.0837055	−	0.996491i	$-0.526676\pi$
$373$	−1206.00	−0.167411	−0.0837055	+	0.996491i	$0.526676\pi$
$374$	−72.0000	−0.00995463
$375$	375.000	0.0516398
$376$	−1800.00	−0.246883
$377$	−638.000	−0.0871583
$378$	−108.000	−0.0146956
$379$	−1728.00	−0.234199	−0.117099	−	0.993120i	$-0.537360\pi$
$379$	−1728.00	−0.234199	−0.117099	+	0.993120i	$0.537360\pi$
$380$	1960.00	0.264594
$381$	4704.00	0.632528
$382$	−1412.00	−0.189121
$383$	3752.00	0.500570	0.250285	−	0.968172i	$-0.419476\pi$
$383$	3752.00	0.500570	0.250285	+	0.968172i	$0.419476\pi$
$384$	4365.00	0.580079
$385$	−720.000	−0.0953106
$386$	418.000	0.0551182
$387$	−3708.00	−0.487050
$388$	11830.0	1.54788
$389$	−1250.00	−0.162924	−0.0814621	−	0.996676i	$-0.525959\pi$
$389$	−1250.00	−0.162924	−0.0814621	+	0.996676i	$0.525959\pi$
$390$	330.000	0.0428467
$391$	80.0000	0.0103472
$392$	−4905.00	−0.631990
$393$	3372.00	0.432811
$394$	−3182.00	−0.406870
$395$	−3200.00	−0.407619
$396$	2268.00	0.287806
$397$	3210.00	0.405807	0.202903	−	0.979199i	$-0.434962\pi$
$397$	3210.00	0.405807	0.202903	+	0.979199i	$0.434962\pi$
$398$	−4976.00	−0.626694
$399$	−672.000	−0.0843160
$400$	1025.00	0.128125
$401$	11314.0	1.40896	0.704482	−	0.709722i	$-0.251180\pi$
$401$	11314.0	1.40896	0.704482	+	0.709722i	$0.251180\pi$
$402$	732.000	0.0908180
$403$	−3344.00	−0.413341
$404$	−3514.00	−0.432743
$405$	405.000	0.0496904
$406$	−116.000	−0.0141798
$407$	−1224.00	−0.149070
$408$	−90.0000	−0.0109207
$409$	−2518.00	−0.304418	−0.152209	−	0.988348i	$-0.548639\pi$
$409$	−2518.00	−0.304418	−0.152209	+	0.988348i	$0.548639\pi$
$410$	1250.00	0.150569
$411$	7938.00	0.952683
$412$	5796.00	0.693079
$413$	−752.000	−0.0895969
$414$	360.000	0.0427368
$415$	3320.00	0.392705
$416$	3542.00	0.417454
$417$	−5868.00	−0.689106
$418$	−2016.00	−0.235899
$419$	−4172.00	−0.486433	−0.243217	−	0.969972i	$-0.578203\pi$
$419$	−4172.00	−0.486433	−0.243217	+	0.969972i	$0.578203\pi$
$420$	−420.000	−0.0487950
$421$	−15838.0	−1.83348	−0.916742	−	0.399479i	$-0.869191\pi$
$421$	−15838.0	−1.83348	−0.916742	+	0.399479i	$0.869191\pi$
$422$	640.000	0.0738263
$423$	−1080.00	−0.124140
$424$	−11430.0	−1.30917
$425$	−50.0000	−0.00570672
$426$	−1800.00	−0.204719
$427$	−216.000	−0.0244800
$428$	8232.00	0.929693
$429$	2376.00	0.267399
$430$	2060.00	0.231028
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	1107.00	0.123288
$433$	7718.00	0.856590	0.428295	−	0.903639i	$-0.359114\pi$
$433$	7718.00	0.856590	0.428295	+	0.903639i	$0.359114\pi$
$434$	−608.000	−0.0672464
$435$	435.000	0.0479463
$436$	13454.0	1.47782
$437$	2240.00	0.245203
$438$	−18.0000	−0.00196364
$439$	6720.00	0.730588	0.365294	−	0.930892i	$-0.380968\pi$
$439$	6720.00	0.730588	0.365294	+	0.930892i	$0.380968\pi$
$440$	−2700.00	−0.292540
$441$	−2943.00	−0.317784
$442$	−44.0000	−0.00473499
$443$	−8652.00	−0.927921	−0.463960	−	0.885856i	$-0.653572\pi$
$443$	−8652.00	−0.927921	−0.463960	+	0.885856i	$0.653572\pi$
$444$	−714.000	−0.0763174
$445$	750.000	0.0798953
$446$	1724.00	0.183035
$447$	6378.00	0.674875
$448$	−668.000	−0.0704465
$449$	4606.00	0.484122	0.242061	−	0.970261i	$-0.422177\pi$
$449$	4606.00	0.484122	0.242061	+	0.970261i	$0.422177\pi$
$450$	−225.000	−0.0235702
$451$	9000.00	0.939675
$452$	2254.00	0.234556
$453$	3624.00	0.375873
$454$	−1216.00	−0.125704
$455$	−440.000	−0.0453352
$456$	−2520.00	−0.258793
$457$	1642.00	0.168073	0.0840367	−	0.996463i	$-0.473219\pi$
$457$	1642.00	0.168073	0.0840367	+	0.996463i	$0.473219\pi$
$458$	1806.00	0.184255
$459$	−54.0000	−0.00549129
$460$	1400.00	0.141903
$461$	−3930.00	−0.397046	−0.198523	−	0.980096i	$-0.563615\pi$
$461$	−3930.00	−0.397046	−0.198523	+	0.980096i	$0.563615\pi$
$462$	432.000	0.0435032
$463$	−10076.0	−1.01139	−0.505693	−	0.862714i	$-0.668763\pi$
$463$	−10076.0	−1.01139	−0.505693	+	0.862714i	$0.668763\pi$
$464$	1189.00	0.118961
$465$	2280.00	0.227382
$466$	−3654.00	−0.363237
$467$	−3348.00	−0.331749	−0.165875	−	0.986147i	$-0.553045\pi$
$467$	−3348.00	−0.331749	−0.165875	+	0.986147i	$0.553045\pi$
$468$	1386.00	0.136897
$469$	−976.000	−0.0960927
$470$	600.000	0.0588850
$471$	1470.00	0.143809
$472$	−2820.00	−0.275002
$473$	14832.0	1.44181
$474$	1920.00	0.186052
$475$	−1400.00	−0.135235
$476$	56.0000	0.00539234
$477$	−6858.00	−0.658294
$478$	5304.00	0.507530
$479$	3412.00	0.325466	0.162733	−	0.986670i	$-0.447969\pi$
$479$	3412.00	0.325466	0.162733	+	0.986670i	$0.447969\pi$
$480$	−2415.00	−0.229644
$481$	−748.000	−0.0709062
$482$	−4402.00	−0.415987
$483$	−480.000	−0.0452190
$484$	245.000	0.0230090
$485$	−8450.00	−0.791123
$486$	−243.000	−0.0226805
$487$	−13084.0	−1.21744	−0.608719	−	0.793386i	$-0.708316\pi$
$487$	−13084.0	−1.21744	−0.608719	+	0.793386i	$0.708316\pi$
$488$	−810.000	−0.0751372
$489$	5340.00	0.493831
$490$	1635.00	0.150738
$491$	11788.0	1.08347	0.541736	−	0.840549i	$-0.317767\pi$
$491$	11788.0	1.08347	0.541736	+	0.840549i	$0.317767\pi$
$492$	5250.00	0.481074
$493$	−58.0000	−0.00529856
$494$	−1232.00	−0.112207
$495$	−1620.00	−0.147098
$496$	6232.00	0.564163
$497$	2400.00	0.216609
$498$	−1992.00	−0.179244
$499$	−17484.0	−1.56852	−0.784260	−	0.620432i	$-0.786957\pi$
$499$	−17484.0	−1.56852	−0.784260	+	0.620432i	$0.786957\pi$
$500$	−875.000	−0.0782624
$501$	7560.00	0.674163
$502$	−2268.00	−0.201645
$503$	8992.00	0.797084	0.398542	−	0.917150i	$-0.369516\pi$
$503$	8992.00	0.797084	0.398542	+	0.917150i	$0.369516\pi$
$504$	540.000	0.0477252
$505$	2510.00	0.221175
$506$	−1440.00	−0.126513
$507$	−5139.00	−0.450160
$508$	−10976.0	−0.958625
$509$	1510.00	0.131492	0.0657461	−	0.997836i	$-0.479057\pi$
$509$	1510.00	0.131492	0.0657461	+	0.997836i	$0.479057\pi$
$510$	30.0000	0.00260475
$511$	24.0000	0.00207769
$512$	−11521.0	−0.994455
$513$	−1512.00	−0.130129
$514$	−534.000	−0.0458244
$515$	−4140.00	−0.354233
$516$	8652.00	0.738145
$517$	4320.00	0.367492
$518$	−136.000	−0.0115357
$519$	1146.00	0.0969245
$520$	−1650.00	−0.139149
$521$	1482.00	0.124621	0.0623106	−	0.998057i	$-0.480153\pi$
$521$	1482.00	0.124621	0.0623106	+	0.998057i	$0.480153\pi$
$522$	−261.000	−0.0218844
$523$	−7524.00	−0.629066	−0.314533	−	0.949247i	$-0.601848\pi$
$523$	−7524.00	−0.629066	−0.314533	+	0.949247i	$0.601848\pi$
$524$	−7868.00	−0.655945
$525$	300.000	0.0249392
$526$	−5592.00	−0.463541
$527$	−304.000	−0.0251280
$528$	−4428.00	−0.364970
$529$	−10567.0	−0.868497
$530$	3810.00	0.312256
$531$	−1692.00	−0.138280
$532$	1568.00	0.127785
$533$	5500.00	0.446963
$534$	−450.000	−0.0364670
$535$	−5880.00	−0.475167
$536$	−3660.00	−0.294940
$537$	−5724.00	−0.459979
$538$	6562.00	0.525851
$539$	11772.0	0.940735
$540$	−945.000	−0.0753080
$541$	7426.00	0.590145	0.295073	−	0.955475i	$-0.404656\pi$
$541$	7426.00	0.590145	0.295073	+	0.955475i	$0.404656\pi$
$542$	−1192.00	−0.0944664
$543$	−1350.00	−0.106693
$544$	322.000	0.0253780
$545$	−9610.00	−0.755316
$546$	264.000	0.0206926
$547$	25156.0	1.96635	0.983174	−	0.182669i	$-0.0584736\pi$
$547$	25156.0	1.96635	0.983174	+	0.182669i	$0.0584736\pi$
$548$	−18522.0	−1.44383
$549$	−486.000	−0.0377814
$550$	900.000	0.0697748
$551$	−1624.00	−0.125562
$552$	−1800.00	−0.138792
$553$	−2560.00	−0.196858
$554$	−6474.00	−0.496487
$555$	510.000	0.0390059
$556$	13692.0	1.04437
$557$	−8890.00	−0.676268	−0.338134	−	0.941098i	$-0.609796\pi$
$557$	−8890.00	−0.676268	−0.338134	+	0.941098i	$0.609796\pi$
$558$	−1368.00	−0.103785
$559$	9064.00	0.685807
$560$	820.000	0.0618774
$561$	216.000	0.0162558
$562$	3758.00	0.282067
$563$	−18028.0	−1.34954	−0.674769	−	0.738029i	$-0.735757\pi$
$563$	−18028.0	−1.34954	−0.674769	+	0.738029i	$0.735757\pi$
$564$	2520.00	0.188140
$565$	−1610.00	−0.119882
$566$	−292.000	−0.0216849
$567$	324.000	0.0239977
$568$	9000.00	0.664844
$569$	−6706.00	−0.494078	−0.247039	−	0.969006i	$-0.579458\pi$
$569$	−6706.00	−0.494078	−0.247039	+	0.969006i	$0.579458\pi$
$570$	840.000	0.0617258
$571$	10060.0	0.737299	0.368650	−	0.929568i	$-0.379820\pi$
$571$	10060.0	0.737299	0.368650	+	0.929568i	$0.379820\pi$
$572$	−5544.00	−0.405256
$573$	4236.00	0.308833
$574$	1000.00	0.0727164
$575$	−1000.00	−0.0725268
$576$	−1503.00	−0.108724
$577$	2974.00	0.214574	0.107287	−	0.994228i	$-0.465784\pi$
$577$	2974.00	0.214574	0.107287	+	0.994228i	$0.465784\pi$
$578$	4909.00	0.353266
$579$	−1254.00	−0.0900077
$580$	−1015.00	−0.0726648
$581$	2656.00	0.189655
$582$	5070.00	0.361097
$583$	27432.0	1.94874
$584$	90.0000	0.00637710
$585$	−990.000	−0.0699683
$586$	1382.00	0.0974230
$587$	2424.00	0.170442	0.0852208	−	0.996362i	$-0.472840\pi$
$587$	2424.00	0.170442	0.0852208	+	0.996362i	$0.472840\pi$
$588$	6867.00	0.481616
$589$	−8512.00	−0.595468
$590$	940.000	0.0655918
$591$	9546.00	0.664416
$592$	1394.00	0.0967788
$593$	−15002.0	−1.03888	−0.519442	−	0.854506i	$-0.673860\pi$
$593$	−15002.0	−1.03888	−0.519442	+	0.854506i	$0.673860\pi$
$594$	972.000	0.0671408
$595$	−40.0000	−0.00275603
$596$	−14882.0	−1.02280
$597$	14928.0	1.02339
$598$	−880.000	−0.0601771
$599$	3636.00	0.248018	0.124009	−	0.992281i	$-0.460425\pi$
$599$	3636.00	0.248018	0.124009	+	0.992281i	$0.460425\pi$
$600$	1125.00	0.0765466
$601$	−13534.0	−0.918575	−0.459287	−	0.888288i	$-0.651895\pi$
$601$	−13534.0	−0.918575	−0.459287	+	0.888288i	$0.651895\pi$
$602$	1648.00	0.111574
$603$	−2196.00	−0.148305
$604$	−8456.00	−0.569652
$605$	−175.000	−0.0117599
$606$	−1506.00	−0.100952
$607$	6760.00	0.452026	0.226013	−	0.974124i	$-0.427431\pi$
$607$	6760.00	0.452026	0.226013	+	0.974124i	$0.427431\pi$
$608$	9016.00	0.601393
$609$	348.000	0.0231555
$610$	270.000	0.0179213
$611$	2640.00	0.174800
$612$	126.000	0.00832230
$613$	15762.0	1.03853	0.519267	−	0.854612i	$-0.326205\pi$
$613$	15762.0	1.03853	0.519267	+	0.854612i	$0.326205\pi$
$614$	3948.00	0.259492
$615$	−3750.00	−0.245877
$616$	−2160.00	−0.141281
$617$	−27786.0	−1.81300	−0.906501	−	0.422204i	$-0.861257\pi$
$617$	−27786.0	−1.81300	−0.906501	+	0.422204i	$0.861257\pi$
$618$	2484.00	0.161685
$619$	17648.0	1.14593	0.572967	−	0.819579i	$-0.305792\pi$
$619$	17648.0	1.14593	0.572967	+	0.819579i	$0.305792\pi$
$620$	−5320.00	−0.344607
$621$	−1080.00	−0.0697889
$622$	7396.00	0.476773
$623$	600.000	0.0385851
$624$	−2706.00	−0.173600
$625$	625.000	0.0400000
$626$	−3290.00	−0.210056
$627$	6048.00	0.385221
$628$	−3430.00	−0.217949
$629$	−68.0000	−0.00431055
$630$	−180.000	−0.0113831
$631$	−13136.0	−0.828742	−0.414371	−	0.910108i	$-0.635998\pi$
$631$	−13136.0	−0.828742	−0.414371	+	0.910108i	$0.635998\pi$
$632$	−9600.00	−0.604221
$633$	−1920.00	−0.120558
$634$	1670.00	0.104612
$635$	7840.00	0.489954
$636$	16002.0	0.997674
$637$	7194.00	0.447467
$638$	1044.00	0.0647843
$639$	5400.00	0.334305
$640$	7275.00	0.449328
$641$	21974.0	1.35401	0.677005	−	0.735978i	$-0.263277\pi$
$641$	21974.0	1.35401	0.677005	+	0.735978i	$0.263277\pi$
$642$	3528.00	0.216883
$643$	21748.0	1.33384	0.666919	−	0.745131i	$-0.267613\pi$
$643$	21748.0	1.33384	0.666919	+	0.745131i	$0.267613\pi$
$644$	1120.00	0.0685313
$645$	−6180.00	−0.377267
$646$	−112.000	−0.00682133
$647$	31128.0	1.89145	0.945725	−	0.324968i	$-0.105354\pi$
$647$	31128.0	1.89145	0.945725	+	0.324968i	$0.105354\pi$
$648$	1215.00	0.0736570
$649$	6768.00	0.409349
$650$	550.000	0.0331889
$651$	1824.00	0.109813
$652$	−12460.0	−0.748422
$653$	−22.0000	−0.00131842	−0.000659209	−	1.00000i	$-0.500210\pi$
$653$	−22.0000	−0.00131842	−0.000659209		1.00000i	$0.500210\pi$
$654$	5766.00	0.344753
$655$	5620.00	0.335254
$656$	−10250.0	−0.610054
$657$	54.0000	0.00320661
$658$	480.000	0.0284382
$659$	25396.0	1.50120	0.750598	−	0.660760i	$-0.229766\pi$
$659$	25396.0	1.50120	0.750598	+	0.660760i	$0.229766\pi$
$660$	3780.00	0.222934
$661$	23534.0	1.38482	0.692410	−	0.721504i	$-0.256549\pi$
$661$	23534.0	1.38482	0.692410	+	0.721504i	$0.256549\pi$
$662$	−912.000	−0.0535436
$663$	132.000	0.00773221
$664$	9960.00	0.582113
$665$	−1120.00	−0.0653109
$666$	−306.000	−0.0178037
$667$	−1160.00	−0.0673394
$668$	−17640.0	−1.02172
$669$	−5172.00	−0.298895
$670$	1220.00	0.0703473
$671$	1944.00	0.111844
$672$	−1932.00	−0.110906
$673$	−28670.0	−1.64212	−0.821060	−	0.570841i	$-0.806617\pi$
$673$	−28670.0	−1.64212	−0.821060	+	0.570841i	$0.806617\pi$
$674$	3082.00	0.176134
$675$	675.000	0.0384900
$676$	11991.0	0.682237
$677$	−1686.00	−0.0957138	−0.0478569	−	0.998854i	$-0.515239\pi$
$677$	−1686.00	−0.0957138	−0.0478569	+	0.998854i	$0.515239\pi$
$678$	966.000	0.0547183
$679$	−6760.00	−0.382069
$680$	−150.000	−0.00845917
$681$	3648.00	0.205274
$682$	5472.00	0.307234
$683$	−13128.0	−0.735474	−0.367737	−	0.929930i	$-0.619867\pi$
$683$	−13128.0	−0.735474	−0.367737	+	0.929930i	$0.619867\pi$
$684$	3528.00	0.197217
$685$	13230.0	0.737945
$686$	2680.00	0.149159
$687$	−5418.00	−0.300887
$688$	−16892.0	−0.936049
$689$	16764.0	0.926934
$690$	600.000	0.0331038
$691$	3052.00	0.168023	0.0840113	−	0.996465i	$-0.473227\pi$
$691$	3052.00	0.168023	0.0840113	+	0.996465i	$0.473227\pi$
$692$	−2674.00	−0.146893
$693$	−1296.00	−0.0710404
$694$	4536.00	0.248104
$695$	−9780.00	−0.533779
$696$	1305.00	0.0710717
$697$	500.000	0.0271720
$698$	7130.00	0.386640
$699$	10962.0	0.593163
$700$	−700.000	−0.0377964
$701$	−11130.0	−0.599678	−0.299839	−	0.953990i	$-0.596933\pi$
$701$	−11130.0	−0.599678	−0.299839	+	0.953990i	$0.596933\pi$
$702$	594.000	0.0319360
$703$	−1904.00	−0.102149
$704$	6012.00	0.321855
$705$	−1800.00	−0.0961588
$706$	−6814.00	−0.363241
$707$	2008.00	0.106816
$708$	3948.00	0.209569
$709$	−17082.0	−0.904835	−0.452417	−	0.891806i	$-0.649438\pi$
$709$	−17082.0	−0.904835	−0.452417	+	0.891806i	$0.649438\pi$
$710$	−3000.00	−0.158575
$711$	−5760.00	−0.303821
$712$	2250.00	0.118430
$713$	−6080.00	−0.319352
$714$	24.0000	0.00125795
$715$	3960.00	0.207127
$716$	13356.0	0.697119
$717$	−15912.0	−0.828793
$718$	−8188.00	−0.425590
$719$	5064.00	0.262664	0.131332	−	0.991338i	$-0.458075\pi$
$719$	5064.00	0.262664	0.131332	+	0.991338i	$0.458075\pi$
$720$	1845.00	0.0954987
$721$	−3312.00	−0.171075
$722$	3723.00	0.191905
$723$	13206.0	0.679303
$724$	3150.00	0.161697
$725$	725.000	0.0371391
$726$	105.000	0.00536765
$727$	16240.0	0.828485	0.414242	−	0.910167i	$-0.364047\pi$
$727$	16240.0	0.828485	0.414242	+	0.910167i	$0.364047\pi$
$728$	−1320.00	−0.0672012
$729$	729.000	0.0370370
$730$	−30.0000	−0.00152103
$731$	824.000	0.0416918
$732$	1134.00	0.0572594
$733$	−25878.0	−1.30399	−0.651996	−	0.758223i	$-0.726068\pi$
$733$	−25878.0	−1.30399	−0.651996	+	0.758223i	$0.726068\pi$
$734$	−624.000	−0.0313791
$735$	−4905.00	−0.246155
$736$	6440.00	0.322529
$737$	8784.00	0.439027
$738$	2250.00	0.112227
$739$	20896.0	1.04015	0.520076	−	0.854120i	$-0.325904\pi$
$739$	20896.0	1.04015	0.520076	+	0.854120i	$0.325904\pi$
$740$	−1190.00	−0.0591152
$741$	3696.00	0.183233
$742$	3048.00	0.150803
$743$	−14376.0	−0.709831	−0.354915	−	0.934898i	$-0.615490\pi$
$743$	−14376.0	−0.709831	−0.354915	+	0.934898i	$0.615490\pi$
$744$	6840.00	0.337052
$745$	10630.0	0.522756
$746$	1206.00	0.0591887
$747$	5976.00	0.292705
$748$	−504.000	−0.0246365
$749$	−4704.00	−0.229480
$750$	−375.000	−0.0182574
$751$	−18320.0	−0.890155	−0.445077	−	0.895492i	$-0.646824\pi$
$751$	−18320.0	−0.890155	−0.445077	+	0.895492i	$0.646824\pi$
$752$	−4920.00	−0.238582
$753$	6804.00	0.329285
$754$	638.000	0.0308151
$755$	6040.00	0.291150
$756$	−756.000	−0.0363696
$757$	−2606.00	−0.125121	−0.0625606	−	0.998041i	$-0.519927\pi$
$757$	−2606.00	−0.125121	−0.0625606	+	0.998041i	$0.519927\pi$
$758$	1728.00	0.0828018
$759$	4320.00	0.206596
$760$	−4200.00	−0.200461
$761$	−33070.0	−1.57528	−0.787639	−	0.616137i	$-0.788697\pi$
$761$	−33070.0	−1.57528	−0.787639	+	0.616137i	$0.788697\pi$
$762$	−4704.00	−0.223632
$763$	−7688.00	−0.364776
$764$	−9884.00	−0.468050
$765$	−90.0000	−0.00425354
$766$	−3752.00	−0.176978
$767$	4136.00	0.194710
$768$	−357.000	−0.0167736
$769$	−3214.00	−0.150715	−0.0753575	−	0.997157i	$-0.524010\pi$
$769$	−3214.00	−0.150715	−0.0753575	+	0.997157i	$0.524010\pi$
$770$	720.000	0.0336974
$771$	1602.00	0.0748309
$772$	2926.00	0.136411
$773$	19954.0	0.928455	0.464227	−	0.885716i	$-0.346332\pi$
$773$	19954.0	0.928455	0.464227	+	0.885716i	$0.346332\pi$
$774$	3708.00	0.172198
$775$	3800.00	0.176129
$776$	−25350.0	−1.17270
$777$	408.000	0.0188377
$778$	1250.00	0.0576024
$779$	14000.0	0.643905
$780$	2310.00	0.106040
$781$	−21600.0	−0.989640
$782$	−80.0000	−0.00365830
$783$	783.000	0.0357371
$784$	−13407.0	−0.610742
$785$	2450.00	0.111394
$786$	−3372.00	−0.153022
$787$	21108.0	0.956060	0.478030	−	0.878344i	$-0.341351\pi$
$787$	21108.0	0.956060	0.478030	+	0.878344i	$0.341351\pi$
$788$	−22274.0	−1.00695
$789$	16776.0	0.756960
$790$	3200.00	0.144115
$791$	−1288.00	−0.0578963
$792$	−4860.00	−0.218046
$793$	1188.00	0.0531994
$794$	−3210.00	−0.143474
$795$	−11430.0	−0.509912
$796$	−34832.0	−1.55099
$797$	25946.0	1.15314	0.576571	−	0.817047i	$-0.304390\pi$
$797$	25946.0	1.15314	0.576571	+	0.817047i	$0.304390\pi$
$798$	672.000	0.0298102
$799$	240.000	0.0106265
$800$	−4025.00	−0.177882
$801$	1350.00	0.0595504
$802$	−11314.0	−0.498144
$803$	−216.000	−0.00949250
$804$	5124.00	0.224763
$805$	−800.000	−0.0350265
$806$	3344.00	0.146138
$807$	−19686.0	−0.858711
$808$	7530.00	0.327852
$809$	−1082.00	−0.0470224	−0.0235112	−	0.999724i	$-0.507485\pi$
$809$	−1082.00	−0.0470224	−0.0235112	+	0.999724i	$0.507485\pi$
$810$	−405.000	−0.0175682
$811$	−25076.0	−1.08574	−0.542871	−	0.839816i	$-0.682663\pi$
$811$	−25076.0	−1.08574	−0.542871	+	0.839816i	$0.682663\pi$
$812$	−812.000	−0.0350931
$813$	3576.00	0.154263
$814$	1224.00	0.0527041
$815$	8900.00	0.382520
$816$	−246.000	−0.0105536
$817$	23072.0	0.987989
$818$	2518.00	0.107628
$819$	−792.000	−0.0337909
$820$	8750.00	0.372638
$821$	−18194.0	−0.773417	−0.386708	−	0.922202i	$-0.626388\pi$
$821$	−18194.0	−0.773417	−0.386708	+	0.922202i	$0.626388\pi$
$822$	−7938.00	−0.336824
$823$	−21008.0	−0.889785	−0.444892	−	0.895584i	$-0.646758\pi$
$823$	−21008.0	−0.889785	−0.444892	+	0.895584i	$0.646758\pi$
$824$	−12420.0	−0.525086
$825$	−2700.00	−0.113942
$826$	752.000	0.0316773
$827$	−21708.0	−0.912770	−0.456385	−	0.889782i	$-0.650856\pi$
$827$	−21708.0	−0.912770	−0.456385	+	0.889782i	$0.650856\pi$
$828$	2520.00	0.105768
$829$	−6110.00	−0.255982	−0.127991	−	0.991775i	$-0.540853\pi$
$829$	−6110.00	−0.255982	−0.127991	+	0.991775i	$0.540853\pi$
$830$	−3320.00	−0.138842
$831$	19422.0	0.810760
$832$	3674.00	0.153093
$833$	654.000	0.0272026
$834$	5868.00	0.243636
$835$	12600.0	0.522205
$836$	−14112.0	−0.583820
$837$	4104.00	0.169480
$838$	4172.00	0.171980
$839$	28588.0	1.17636	0.588181	−	0.808729i	$-0.299844\pi$
$839$	28588.0	1.17636	0.588181	+	0.808729i	$0.299844\pi$
$840$	900.000	0.0369678
$841$	841.000	0.0344828
$842$	15838.0	0.648235
$843$	−11274.0	−0.460614
$844$	4480.00	0.182711
$845$	−8565.00	−0.348692
$846$	1080.00	0.0438903
$847$	−140.000	−0.00567941
$848$	−31242.0	−1.26516
$849$	876.000	0.0354114
$850$	50.0000	0.00201763
$851$	−1360.00	−0.0547828
$852$	−12600.0	−0.506654
$853$	242.000	0.00971386	0.00485693	−	0.999988i	$-0.498454\pi$
$853$	242.000	0.00971386	0.00485693	+	0.999988i	$0.498454\pi$
$854$	216.000	0.00865500
$855$	−2520.00	−0.100798
$856$	−17640.0	−0.704349
$857$	−12002.0	−0.478390	−0.239195	−	0.970972i	$-0.576884\pi$
$857$	−12002.0	−0.478390	−0.239195	+	0.970972i	$0.576884\pi$
$858$	−2376.00	−0.0945400
$859$	−34896.0	−1.38607	−0.693036	−	0.720903i	$-0.743727\pi$
$859$	−34896.0	−1.38607	−0.693036	+	0.720903i	$0.743727\pi$
$860$	14420.0	0.571765
$861$	−3000.00	−0.118745
$862$	0	0
$863$	4488.00	0.177026	0.0885129	−	0.996075i	$-0.471789\pi$
$863$	4488.00	0.177026	0.0885129	+	0.996075i	$0.471789\pi$
$864$	−4347.00	−0.171167
$865$	1910.00	0.0750774
$866$	−7718.00	−0.302850
$867$	−14727.0	−0.576880
$868$	−4256.00	−0.166426
$869$	23040.0	0.899400
$870$	−435.000	−0.0169516
$871$	5368.00	0.208826
$872$	−28830.0	−1.11962
$873$	−15210.0	−0.589668
$874$	−2240.00	−0.0866924
$875$	500.000	0.0193178
$876$	−126.000	−0.00485976
$877$	5794.00	0.223089	0.111545	−	0.993759i	$-0.464420\pi$
$877$	5794.00	0.223089	0.111545	+	0.993759i	$0.464420\pi$
$878$	−6720.00	−0.258302
$879$	−4146.00	−0.159091
$880$	−7380.00	−0.282704
$881$	−14034.0	−0.536683	−0.268341	−	0.963324i	$-0.586476\pi$
$881$	−14034.0	−0.536683	−0.268341	+	0.963324i	$0.586476\pi$
$882$	2943.00	0.112354
$883$	29884.0	1.13893	0.569466	−	0.822015i	$-0.307150\pi$
$883$	29884.0	1.13893	0.569466	+	0.822015i	$0.307150\pi$
$884$	−308.000	−0.0117185
$885$	−2820.00	−0.107111
$886$	8652.00	0.328070
$887$	11440.0	0.433053	0.216526	−	0.976277i	$-0.430527\pi$
$887$	11440.0	0.433053	0.216526	+	0.976277i	$0.430527\pi$
$888$	1530.00	0.0578192
$889$	6272.00	0.236621
$890$	−750.000	−0.0282473
$891$	−2916.00	−0.109640
$892$	12068.0	0.452989
$893$	6720.00	0.251821
$894$	−6378.00	−0.238604
$895$	−9540.00	−0.356298
$896$	5820.00	0.217001
$897$	2640.00	0.0982687
$898$	−4606.00	−0.171163
$899$	4408.00	0.163532
$900$	−1575.00	−0.0583333
$901$	1524.00	0.0563505
$902$	−9000.00	−0.332225
$903$	−4944.00	−0.182199
$904$	−4830.00	−0.177703
$905$	−2250.00	−0.0826437
$906$	−3624.00	−0.132891
$907$	−2532.00	−0.0926942	−0.0463471	−	0.998925i	$-0.514758\pi$
$907$	−2532.00	−0.0926942	−0.0463471	+	0.998925i	$0.514758\pi$
$908$	−8512.00	−0.311102
$909$	4518.00	0.164854
$910$	440.000	0.0160284
$911$	18188.0	0.661466	0.330733	−	0.943724i	$-0.392704\pi$
$911$	18188.0	0.661466	0.330733	+	0.943724i	$0.392704\pi$
$912$	−6888.00	−0.250093
$913$	−23904.0	−0.866492
$914$	−1642.00	−0.0594229
$915$	−810.000	−0.0292653
$916$	12642.0	0.456008
$917$	4496.00	0.161909
$918$	54.0000	0.00194147
$919$	−12680.0	−0.455141	−0.227571	−	0.973762i	$-0.573078\pi$
$919$	−12680.0	−0.455141	−0.227571	+	0.973762i	$0.573078\pi$
$920$	−3000.00	−0.107508
$921$	−11844.0	−0.423749
$922$	3930.00	0.140377
$923$	−13200.0	−0.470729
$924$	3024.00	0.107665
$925$	850.000	0.0302139
$926$	10076.0	0.357579
$927$	−7452.00	−0.264030
$928$	−4669.00	−0.165159
$929$	32090.0	1.13330	0.566652	−	0.823957i	$-0.308239\pi$
$929$	32090.0	1.13330	0.566652	+	0.823957i	$0.308239\pi$
$930$	−2280.00	−0.0803916
$931$	18312.0	0.644631
$932$	−25578.0	−0.898965
$933$	−22188.0	−0.778566
$934$	3348.00	0.117291
$935$	360.000	0.0125917
$936$	−2970.00	−0.103715
$937$	49914.0	1.74026	0.870128	−	0.492826i	$-0.164036\pi$
$937$	49914.0	1.74026	0.870128	+	0.492826i	$0.164036\pi$
$938$	976.000	0.0339739
$939$	9870.00	0.343019
$940$	4200.00	0.145733
$941$	−36842.0	−1.27632	−0.638159	−	0.769905i	$-0.720304\pi$
$941$	−36842.0	−1.27632	−0.638159	+	0.769905i	$0.720304\pi$
$942$	−1470.00	−0.0508441
$943$	10000.0	0.345329
$944$	−7708.00	−0.265756
$945$	540.000	0.0185886
$946$	−14832.0	−0.509757
$947$	31788.0	1.09078	0.545391	−	0.838182i	$-0.316381\pi$
$947$	31788.0	1.09078	0.545391	+	0.838182i	$0.316381\pi$
$948$	13440.0	0.460455
$949$	−132.000	−0.00451518
$950$	1400.00	0.0478126
$951$	−5010.00	−0.170831
$952$	−120.000	−0.00408532
$953$	−34122.0	−1.15983	−0.579916	−	0.814676i	$-0.696915\pi$
$953$	−34122.0	−1.15983	−0.579916	+	0.814676i	$0.696915\pi$
$954$	6858.00	0.232742
$955$	7060.00	0.239221
$956$	37128.0	1.25607
$957$	−3132.00	−0.105792
$958$	−3412.00	−0.115070
$959$	10584.0	0.356387
$960$	−2505.00	−0.0842172
$961$	−6687.00	−0.224464
$962$	748.000	0.0250691
$963$	−10584.0	−0.354169
$964$	−30814.0	−1.02951
$965$	−2090.00	−0.0697197
$966$	480.000	0.0159873
$967$	−6200.00	−0.206183	−0.103091	−	0.994672i	$-0.532873\pi$
$967$	−6200.00	−0.206183	−0.103091	+	0.994672i	$0.532873\pi$
$968$	−525.000	−0.0174320
$969$	336.000	0.0111392
$970$	8450.00	0.279704
$971$	19788.0	0.653993	0.326996	−	0.945026i	$-0.393963\pi$
$971$	19788.0	0.653993	0.326996	+	0.945026i	$0.393963\pi$
$972$	−1701.00	−0.0561313
$973$	−7824.00	−0.257786
$974$	13084.0	0.430430
$975$	−1650.00	−0.0541972
$976$	−2214.00	−0.0726111
$977$	−23226.0	−0.760558	−0.380279	−	0.924872i	$-0.624172\pi$
$977$	−23226.0	−0.760558	−0.380279	+	0.924872i	$0.624172\pi$
$978$	−5340.00	−0.174595
$979$	−5400.00	−0.176287
$980$	11445.0	0.373058
$981$	−17298.0	−0.562979
$982$	−11788.0	−0.383065
$983$	43056.0	1.39702	0.698511	−	0.715599i	$-0.253846\pi$
$983$	43056.0	1.39702	0.698511	+	0.715599i	$0.253846\pi$
$984$	−11250.0	−0.364468
$985$	15910.0	0.514655
$986$	58.0000	0.00187332
$987$	−1440.00	−0.0464394
$988$	−8624.00	−0.277698
$989$	16480.0	0.529862
$990$	1620.00	0.0520071
$991$	−24200.0	−0.775720	−0.387860	−	0.921718i	$-0.626786\pi$
$991$	−24200.0	−0.775720	−0.387860	+	0.921718i	$0.626786\pi$
$992$	−24472.0	−0.783253
$993$	2736.00	0.0874364
$994$	−2400.00	−0.0765829
$995$	24880.0	0.792713
$996$	−13944.0	−0.443607
$997$	−31582.0	−1.00322	−0.501611	−	0.865093i	$-0.667259\pi$
$997$	−31582.0	−1.00322	−0.501611	+	0.865093i	$0.667259\pi$
$998$	17484.0	0.554555
$999$	918.000	0.0290733

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.4.a.b.1.1	✓	1
3.2	odd	2		1305.4.a.c.1.1		1
5.4	even	2		2175.4.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.b.1.1	✓	1	1.1	even	1	trivial
1305.4.a.c.1.1		1	3.2	odd	2
2175.4.a.b.1.1		1	5.4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	435.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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