LMFDB - Embedded newform 230.4.a.c.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,4,Mod(1,230)] 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("230.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-2,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$13.5704393013$
Analytic rank:	$0$
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	$\chi$	$=$	230.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q-2.00000 q^{2} +7.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -14.0000 q^{6} +20.0000 q^{7} -8.00000 q^{8} +22.0000 q^{9} -10.0000 q^{10} +6.00000 q^{11} +28.0000 q^{12} +47.0000 q^{13} -40.0000 q^{14} +35.0000 q^{15} +16.0000 q^{16} -132.000 q^{17} -44.0000 q^{18} +146.000 q^{19} +20.0000 q^{20} +140.000 q^{21} -12.0000 q^{22} +23.0000 q^{23} -56.0000 q^{24} +25.0000 q^{25} -94.0000 q^{26} -35.0000 q^{27} +80.0000 q^{28} -99.0000 q^{29} -70.0000 q^{30} -253.000 q^{31} -32.0000 q^{32} +42.0000 q^{33} +264.000 q^{34} +100.000 q^{35} +88.0000 q^{36} -118.000 q^{37} -292.000 q^{38} +329.000 q^{39} -40.0000 q^{40} +495.000 q^{41} -280.000 q^{42} +272.000 q^{43} +24.0000 q^{44} +110.000 q^{45} -46.0000 q^{46} +639.000 q^{47} +112.000 q^{48} +57.0000 q^{49} -50.0000 q^{50} -924.000 q^{51} +188.000 q^{52} -342.000 q^{53} +70.0000 q^{54} +30.0000 q^{55} -160.000 q^{56} +1022.00 q^{57} +198.000 q^{58} +240.000 q^{59} +140.000 q^{60} -370.000 q^{61} +506.000 q^{62} +440.000 q^{63} +64.0000 q^{64} +235.000 q^{65} -84.0000 q^{66} +698.000 q^{67} -528.000 q^{68} +161.000 q^{69} -200.000 q^{70} -357.000 q^{71} -176.000 q^{72} -259.000 q^{73} +236.000 q^{74} +175.000 q^{75} +584.000 q^{76} +120.000 q^{77} -658.000 q^{78} +542.000 q^{79} +80.0000 q^{80} -839.000 q^{81} -990.000 q^{82} -1248.00 q^{83} +560.000 q^{84} -660.000 q^{85} -544.000 q^{86} -693.000 q^{87} -48.0000 q^{88} -828.000 q^{89} -220.000 q^{90} +940.000 q^{91} +92.0000 q^{92} -1771.00 q^{93} -1278.00 q^{94} +730.000 q^{95} -224.000 q^{96} +992.000 q^{97} -114.000 q^{98} +132.000 q^{99} +O(q^{100})\)

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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	7.00000	1.34715	0.673575	−	0.739119i	$-0.264758\pi$
$3$	7.00000	1.34715	0.673575	+	0.739119i	$0.264758\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−14.0000	−0.952579
$7$	20.0000	1.07990	0.539949	−	0.841698i	$-0.318443\pi$
$7$	20.0000	1.07990	0.539949	+	0.841698i	$0.318443\pi$
$8$	−8.00000	−0.353553
$9$	22.0000	0.814815
$10$	−10.0000	−0.316228
$11$	6.00000	0.164461	0.0822304	−	0.996613i	$-0.473796\pi$
$11$	6.00000	0.164461	0.0822304	+	0.996613i	$0.473796\pi$
$12$	28.0000	0.673575
$13$	47.0000	1.00273	0.501364	−	0.865237i	$-0.332832\pi$
$13$	47.0000	1.00273	0.501364	+	0.865237i	$0.332832\pi$
$14$	−40.0000	−0.763604
$15$	35.0000	0.602464
$16$	16.0000	0.250000
$17$	−132.000	−1.88322	−0.941609	−	0.336709i	$-0.890686\pi$
$17$	−132.000	−1.88322	−0.941609	+	0.336709i	$0.890686\pi$
$18$	−44.0000	−0.576161
$19$	146.000	1.76288	0.881439	−	0.472297i	$-0.156575\pi$
$19$	146.000	1.76288	0.881439	+	0.472297i	$0.156575\pi$
$20$	20.0000	0.223607
$21$	140.000	1.45479
$22$	−12.0000	−0.116291
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−56.0000	−0.476290
$25$	25.0000	0.200000
$26$	−94.0000	−0.709035
$27$	−35.0000	−0.249472
$28$	80.0000	0.539949
$29$	−99.0000	−0.633925	−0.316963	−	0.948438i	$-0.602663\pi$
$29$	−99.0000	−0.633925	−0.316963	+	0.948438i	$0.602663\pi$
$30$	−70.0000	−0.426006
$31$	−253.000	−1.46581	−0.732906	−	0.680330i	$-0.761836\pi$
$31$	−253.000	−1.46581	−0.732906	+	0.680330i	$0.761836\pi$
$32$	−32.0000	−0.176777
$33$	42.0000	0.221553
$34$	264.000	1.33164
$35$	100.000	0.482945
$36$	88.0000	0.407407
$37$	−118.000	−0.524299	−0.262150	−	0.965027i	$-0.584431\pi$
$37$	−118.000	−0.524299	−0.262150	+	0.965027i	$0.584431\pi$
$38$	−292.000	−1.24654
$39$	329.000	1.35082
$40$	−40.0000	−0.158114
$41$	495.000	1.88551	0.942756	−	0.333483i	$-0.108224\pi$
$41$	495.000	1.88551	0.942756	+	0.333483i	$0.108224\pi$
$42$	−280.000	−1.02869
$43$	272.000	0.964642	0.482321	−	0.875995i	$-0.339794\pi$
$43$	272.000	0.964642	0.482321	+	0.875995i	$0.339794\pi$
$44$	24.0000	0.0822304
$45$	110.000	0.364396
$46$	−46.0000	−0.147442
$47$	639.000	1.98314	0.991572	−	0.129560i	$-0.0413565\pi$
$47$	639.000	1.98314	0.991572	+	0.129560i	$0.0413565\pi$
$48$	112.000	0.336788
$49$	57.0000	0.166181
$50$	−50.0000	−0.141421
$51$	−924.000	−2.53698
$52$	188.000	0.501364
$53$	−342.000	−0.886364	−0.443182	−	0.896432i	$-0.646151\pi$
$53$	−342.000	−0.886364	−0.443182	+	0.896432i	$0.646151\pi$
$54$	70.0000	0.176404
$55$	30.0000	0.0735491
$56$	−160.000	−0.381802
$57$	1022.00	2.37486
$58$	198.000	0.448253
$59$	240.000	0.529582	0.264791	−	0.964306i	$-0.414697\pi$
$59$	240.000	0.529582	0.264791	+	0.964306i	$0.414697\pi$
$60$	140.000	0.301232
$61$	−370.000	−0.776617	−0.388309	−	0.921529i	$-0.626941\pi$
$61$	−370.000	−0.776617	−0.388309	+	0.921529i	$0.626941\pi$
$62$	506.000	1.03648
$63$	440.000	0.879917
$64$	64.0000	0.125000
$65$	235.000	0.448433
$66$	−84.0000	−0.156662
$67$	698.000	1.27275	0.636375	−	0.771380i	$-0.280433\pi$
$67$	698.000	1.27275	0.636375	+	0.771380i	$0.280433\pi$
$68$	−528.000	−0.941609
$69$	161.000	0.280900
$70$	−200.000	−0.341494
$71$	−357.000	−0.596734	−0.298367	−	0.954451i	$-0.596442\pi$
$71$	−357.000	−0.596734	−0.298367	+	0.954451i	$0.596442\pi$
$72$	−176.000	−0.288081
$73$	−259.000	−0.415256	−0.207628	−	0.978208i	$-0.566574\pi$
$73$	−259.000	−0.415256	−0.207628	+	0.978208i	$0.566574\pi$
$74$	236.000	0.370736
$75$	175.000	0.269430
$76$	584.000	0.881439
$77$	120.000	0.177601
$78$	−658.000	−0.955177
$79$	542.000	0.771896	0.385948	−	0.922521i	$-0.373874\pi$
$79$	542.000	0.771896	0.385948	+	0.922521i	$0.373874\pi$
$80$	80.0000	0.111803
$81$	−839.000	−1.15089
$82$	−990.000	−1.33326
$83$	−1248.00	−1.65043	−0.825216	−	0.564818i	$-0.808946\pi$
$83$	−1248.00	−1.65043	−0.825216	+	0.564818i	$0.808946\pi$
$84$	560.000	0.727393
$85$	−660.000	−0.842201
$86$	−544.000	−0.682105
$87$	−693.000	−0.853993
$88$	−48.0000	−0.0581456
$89$	−828.000	−0.986155	−0.493078	−	0.869985i	$-0.664128\pi$
$89$	−828.000	−0.986155	−0.493078	+	0.869985i	$0.664128\pi$
$90$	−220.000	−0.257667
$91$	940.000	1.08284
$92$	92.0000	0.104257
$93$	−1771.00	−1.97467
$94$	−1278.00	−1.40229
$95$	730.000	0.788383
$96$	−224.000	−0.238145
$97$	992.000	1.03837	0.519187	−	0.854660i	$-0.326235\pi$
$97$	992.000	1.03837	0.519187	+	0.854660i	$0.326235\pi$
$98$	−114.000	−0.117508
$99$	132.000	0.134005
$100$	100.000	0.100000
$101$	−1542.00	−1.51916	−0.759578	−	0.650416i	$-0.774594\pi$
$101$	−1542.00	−1.51916	−0.759578	+	0.650416i	$0.774594\pi$
$102$	1848.00	1.79391
$103$	32.0000	0.0306122	0.0153061	−	0.999883i	$-0.495128\pi$
$103$	32.0000	0.0306122	0.0153061	+	0.999883i	$0.495128\pi$
$104$	−376.000	−0.354518
$105$	700.000	0.650600
$106$	684.000	0.626754
$107$	−834.000	−0.753512	−0.376756	−	0.926312i	$-0.622961\pi$
$107$	−834.000	−0.753512	−0.376756	+	0.926312i	$0.622961\pi$
$108$	−140.000	−0.124736
$109$	−1192.00	−1.04746	−0.523729	−	0.851885i	$-0.675460\pi$
$109$	−1192.00	−1.04746	−0.523729	+	0.851885i	$0.675460\pi$
$110$	−60.0000	−0.0520071
$111$	−826.000	−0.706310
$112$	320.000	0.269975
$113$	−132.000	−0.109890	−0.0549448	−	0.998489i	$-0.517498\pi$
$113$	−132.000	−0.109890	−0.0549448	+	0.998489i	$0.517498\pi$
$114$	−2044.00	−1.67928
$115$	115.000	0.0932505
$116$	−396.000	−0.316963
$117$	1034.00	0.817037
$118$	−480.000	−0.374471
$119$	−2640.00	−2.03368
$120$	−280.000	−0.213003
$121$	−1295.00	−0.972953
$122$	740.000	0.549151
$123$	3465.00	2.54007
$124$	−1012.00	−0.732906
$125$	125.000	0.0894427
$126$	−880.000	−0.622195
$127$	89.0000	0.0621848	0.0310924	−	0.999517i	$-0.490101\pi$
$127$	89.0000	0.0621848	0.0310924	+	0.999517i	$0.490101\pi$
$128$	−128.000	−0.0883883
$129$	1904.00	1.29952
$130$	−470.000	−0.317090
$131$	−1797.00	−1.19851	−0.599254	−	0.800559i	$-0.704536\pi$
$131$	−1797.00	−1.19851	−0.599254	+	0.800559i	$0.704536\pi$
$132$	168.000	0.110777
$133$	2920.00	1.90373
$134$	−1396.00	−0.899970
$135$	−175.000	−0.111567
$136$	1056.00	0.665818
$137$	−1836.00	−1.14496	−0.572482	−	0.819917i	$-0.694019\pi$
$137$	−1836.00	−1.14496	−0.572482	+	0.819917i	$0.694019\pi$
$138$	−322.000	−0.198627
$139$	−1027.00	−0.626683	−0.313342	−	0.949640i	$-0.601449\pi$
$139$	−1027.00	−0.626683	−0.313342	+	0.949640i	$0.601449\pi$
$140$	400.000	0.241473
$141$	4473.00	2.67159
$142$	714.000	0.421955
$143$	282.000	0.164909
$144$	352.000	0.203704
$145$	−495.000	−0.283500
$146$	518.000	0.293630
$147$	399.000	0.223871
$148$	−472.000	−0.262150
$149$	2310.00	1.27008	0.635042	−	0.772477i	$-0.280983\pi$
$149$	2310.00	1.27008	0.635042	+	0.772477i	$0.280983\pi$
$150$	−350.000	−0.190516
$151$	−2149.00	−1.15817	−0.579083	−	0.815268i	$-0.696589\pi$
$151$	−2149.00	−1.15817	−0.579083	+	0.815268i	$0.696589\pi$
$152$	−1168.00	−0.623272
$153$	−2904.00	−1.53447
$154$	−240.000	−0.125583
$155$	−1265.00	−0.655531
$156$	1316.00	0.675412
$157$	1832.00	0.931271	0.465635	−	0.884977i	$-0.345826\pi$
$157$	1832.00	0.931271	0.465635	+	0.884977i	$0.345826\pi$
$158$	−1084.00	−0.545813
$159$	−2394.00	−1.19407
$160$	−160.000	−0.0790569
$161$	460.000	0.225174
$162$	1678.00	0.813803
$163$	1217.00	0.584802	0.292401	−	0.956296i	$-0.405546\pi$
$163$	1217.00	0.584802	0.292401	+	0.956296i	$0.405546\pi$
$164$	1980.00	0.942756
$165$	210.000	0.0990817
$166$	2496.00	1.16703
$167$	3048.00	1.41234	0.706172	−	0.708041i	$-0.250421\pi$
$167$	3048.00	1.41234	0.706172	+	0.708041i	$0.250421\pi$
$168$	−1120.00	−0.514344
$169$	12.0000	0.00546199
$170$	1320.00	0.595526
$171$	3212.00	1.43642
$172$	1088.00	0.482321
$173$	774.000	0.340151	0.170076	−	0.985431i	$-0.445599\pi$
$173$	774.000	0.340151	0.170076	+	0.985431i	$0.445599\pi$
$174$	1386.00	0.603864
$175$	500.000	0.215980
$176$	96.0000	0.0411152
$177$	1680.00	0.713427
$178$	1656.00	0.697317
$179$	−1875.00	−0.782928	−0.391464	−	0.920193i	$-0.628031\pi$
$179$	−1875.00	−0.782928	−0.391464	+	0.920193i	$0.628031\pi$
$180$	440.000	0.182198
$181$	−1606.00	−0.659520	−0.329760	−	0.944065i	$-0.606968\pi$
$181$	−1606.00	−0.659520	−0.329760	+	0.944065i	$0.606968\pi$
$182$	−1880.00	−0.765686
$183$	−2590.00	−1.04622
$184$	−184.000	−0.0737210
$185$	−590.000	−0.234474
$186$	3542.00	1.39630
$187$	−792.000	−0.309715
$188$	2556.00	0.991572
$189$	−700.000	−0.269405
$190$	−1460.00	−0.557471
$191$	2982.00	1.12969	0.564843	−	0.825199i	$-0.308937\pi$
$191$	2982.00	1.12969	0.564843	+	0.825199i	$0.308937\pi$
$192$	448.000	0.168394
$193$	1385.00	0.516552	0.258276	−	0.966071i	$-0.416846\pi$
$193$	1385.00	0.516552	0.258276	+	0.966071i	$0.416846\pi$
$194$	−1984.00	−0.734242
$195$	1645.00	0.604107
$196$	228.000	0.0830904
$197$	957.000	0.346109	0.173054	−	0.984912i	$-0.444636\pi$
$197$	957.000	0.346109	0.173054	+	0.984912i	$0.444636\pi$
$198$	−264.000	−0.0947559
$199$	−358.000	−0.127527	−0.0637637	−	0.997965i	$-0.520310\pi$
$199$	−358.000	−0.127527	−0.0637637	+	0.997965i	$0.520310\pi$
$200$	−200.000	−0.0707107
$201$	4886.00	1.71459
$202$	3084.00	1.07421
$203$	−1980.00	−0.684575
$204$	−3696.00	−1.26849
$205$	2475.00	0.843227
$206$	−64.0000	−0.0216461
$207$	506.000	0.169901
$208$	752.000	0.250682
$209$	876.000	0.289924
$210$	−1400.00	−0.460044
$211$	−5380.00	−1.75533	−0.877665	−	0.479275i	$-0.840900\pi$
$211$	−5380.00	−1.75533	−0.877665	+	0.479275i	$0.840900\pi$
$212$	−1368.00	−0.443182
$213$	−2499.00	−0.803890
$214$	1668.00	0.532814
$215$	1360.00	0.431401
$216$	280.000	0.0882018
$217$	−5060.00	−1.58293
$218$	2384.00	0.740664
$219$	−1813.00	−0.559412
$220$	120.000	0.0367745
$221$	−6204.00	−1.88835
$222$	1652.00	0.499437
$223$	1040.00	0.312303	0.156151	−	0.987733i	$-0.450091\pi$
$223$	1040.00	0.312303	0.156151	+	0.987733i	$0.450091\pi$
$224$	−640.000	−0.190901
$225$	550.000	0.162963
$226$	264.000	0.0777036
$227$	−3744.00	−1.09470	−0.547352	−	0.836902i	$-0.684364\pi$
$227$	−3744.00	−1.09470	−0.547352	+	0.836902i	$0.684364\pi$
$228$	4088.00	1.18743
$229$	2804.00	0.809142	0.404571	−	0.914507i	$-0.367421\pi$
$229$	2804.00	0.809142	0.404571	+	0.914507i	$0.367421\pi$
$230$	−230.000	−0.0659380
$231$	840.000	0.239255
$232$	792.000	0.224126
$233$	−4869.00	−1.36901	−0.684504	−	0.729009i	$-0.739981\pi$
$233$	−4869.00	−1.36901	−0.684504	+	0.729009i	$0.739981\pi$
$234$	−2068.00	−0.577732
$235$	3195.00	0.886889
$236$	960.000	0.264791
$237$	3794.00	1.03986
$238$	5280.00	1.43803
$239$	−2877.00	−0.778651	−0.389326	−	0.921100i	$-0.627292\pi$
$239$	−2877.00	−0.778651	−0.389326	+	0.921100i	$0.627292\pi$
$240$	560.000	0.150616
$241$	1622.00	0.433536	0.216768	−	0.976223i	$-0.430448\pi$
$241$	1622.00	0.433536	0.216768	+	0.976223i	$0.430448\pi$
$242$	2590.00	0.687981
$243$	−4928.00	−1.30095
$244$	−1480.00	−0.388309
$245$	285.000	0.0743183
$246$	−6930.00	−1.79610
$247$	6862.00	1.76769
$248$	2024.00	0.518242
$249$	−8736.00	−2.22338
$250$	−250.000	−0.0632456
$251$	−4752.00	−1.19499	−0.597497	−	0.801871i	$-0.703838\pi$
$251$	−4752.00	−1.19499	−0.597497	+	0.801871i	$0.703838\pi$
$252$	1760.00	0.439959
$253$	138.000	0.0342924
$254$	−178.000	−0.0439713
$255$	−4620.00	−1.13457
$256$	256.000	0.0625000
$257$	−5073.00	−1.23130	−0.615652	−	0.788018i	$-0.711107\pi$
$257$	−5073.00	−1.23130	−0.615652	+	0.788018i	$0.711107\pi$
$258$	−3808.00	−0.918898
$259$	−2360.00	−0.566190
$260$	940.000	0.224217
$261$	−2178.00	−0.516532
$262$	3594.00	0.847474
$263$	1314.00	0.308079	0.154039	−	0.988065i	$-0.450772\pi$
$263$	1314.00	0.308079	0.154039	+	0.988065i	$0.450772\pi$
$264$	−336.000	−0.0783309
$265$	−1710.00	−0.396394
$266$	−5840.00	−1.34614
$267$	−5796.00	−1.32850
$268$	2792.00	0.636375
$269$	5265.00	1.19336	0.596678	−	0.802481i	$-0.296487\pi$
$269$	5265.00	1.19336	0.596678	+	0.802481i	$0.296487\pi$
$270$	350.000	0.0788901
$271$	−2488.00	−0.557695	−0.278847	−	0.960335i	$-0.589952\pi$
$271$	−2488.00	−0.557695	−0.278847	+	0.960335i	$0.589952\pi$
$272$	−2112.00	−0.470804
$273$	6580.00	1.45875
$274$	3672.00	0.809612
$275$	150.000	0.0328921
$276$	644.000	0.140450
$277$	5465.00	1.18542	0.592708	−	0.805418i	$-0.298059\pi$
$277$	5465.00	1.18542	0.592708	+	0.805418i	$0.298059\pi$
$278$	2054.00	0.443132
$279$	−5566.00	−1.19436
$280$	−800.000	−0.170747
$281$	8940.00	1.89792	0.948960	−	0.315396i	$-0.102137\pi$
$281$	8940.00	1.89792	0.948960	+	0.315396i	$0.102137\pi$
$282$	−8946.00	−1.88910
$283$	842.000	0.176861	0.0884306	−	0.996082i	$-0.471815\pi$
$283$	842.000	0.176861	0.0884306	+	0.996082i	$0.471815\pi$
$284$	−1428.00	−0.298367
$285$	5110.00	1.06207
$286$	−564.000	−0.116608
$287$	9900.00	2.03616
$288$	−704.000	−0.144040
$289$	12511.0	2.54651
$290$	990.000	0.200465
$291$	6944.00	1.39885
$292$	−1036.00	−0.207628
$293$	−4032.00	−0.803932	−0.401966	−	0.915655i	$-0.631673\pi$
$293$	−4032.00	−0.803932	−0.401966	+	0.915655i	$0.631673\pi$
$294$	−798.000	−0.158300
$295$	1200.00	0.236836
$296$	944.000	0.185368
$297$	−210.000	−0.0410284
$298$	−4620.00	−0.898085
$299$	1081.00	0.209083
$300$	700.000	0.134715
$301$	5440.00	1.04172
$302$	4298.00	0.818947
$303$	−10794.0	−2.04653
$304$	2336.00	0.440720
$305$	−1850.00	−0.347314
$306$	5808.00	1.08504
$307$	−1096.00	−0.203753	−0.101876	−	0.994797i	$-0.532485\pi$
$307$	−1096.00	−0.203753	−0.101876	+	0.994797i	$0.532485\pi$
$308$	480.000	0.0888004
$309$	224.000	0.0412392
$310$	2530.00	0.463530
$311$	−4653.00	−0.848384	−0.424192	−	0.905572i	$-0.639442\pi$
$311$	−4653.00	−0.848384	−0.424192	+	0.905572i	$0.639442\pi$
$312$	−2632.00	−0.477589
$313$	3440.00	0.621215	0.310608	−	0.950538i	$-0.399468\pi$
$313$	3440.00	0.621215	0.310608	+	0.950538i	$0.399468\pi$
$314$	−3664.00	−0.658508
$315$	2200.00	0.393511
$316$	2168.00	0.385948
$317$	3066.00	0.543229	0.271615	−	0.962406i	$-0.412442\pi$
$317$	3066.00	0.543229	0.271615	+	0.962406i	$0.412442\pi$
$318$	4788.00	0.844332
$319$	−594.000	−0.104256
$320$	320.000	0.0559017
$321$	−5838.00	−1.01509
$322$	−920.000	−0.159222
$323$	−19272.0	−3.31988
$324$	−3356.00	−0.575446
$325$	1175.00	0.200545
$326$	−2434.00	−0.413518
$327$	−8344.00	−1.41108
$328$	−3960.00	−0.666629
$329$	12780.0	2.14159
$330$	−420.000	−0.0700613
$331$	1505.00	0.249916	0.124958	−	0.992162i	$-0.460120\pi$
$331$	1505.00	0.249916	0.124958	+	0.992162i	$0.460120\pi$
$332$	−4992.00	−0.825216
$333$	−2596.00	−0.427207
$334$	−6096.00	−0.998677
$335$	3490.00	0.569191
$336$	2240.00	0.363696
$337$	−3268.00	−0.528247	−0.264124	−	0.964489i	$-0.585083\pi$
$337$	−3268.00	−0.528247	−0.264124	+	0.964489i	$0.585083\pi$
$338$	−24.0000	−0.00386221
$339$	−924.000	−0.148038
$340$	−2640.00	−0.421100
$341$	−1518.00	−0.241068
$342$	−6424.00	−1.01570
$343$	−5720.00	−0.900440
$344$	−2176.00	−0.341052
$345$	805.000	0.125622
$346$	−1548.00	−0.240523
$347$	4164.00	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	4164.00	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	−2772.00	−0.426997
$349$	−2911.00	−0.446482	−0.223241	−	0.974763i	$-0.571664\pi$
$349$	−2911.00	−0.446482	−0.223241	+	0.974763i	$0.571664\pi$
$350$	−1000.00	−0.152721
$351$	−1645.00	−0.250153
$352$	−192.000	−0.0290728
$353$	9753.00	1.47054	0.735269	−	0.677776i	$-0.237056\pi$
$353$	9753.00	1.47054	0.735269	+	0.677776i	$0.237056\pi$
$354$	−3360.00	−0.504469
$355$	−1785.00	−0.266868
$356$	−3312.00	−0.493078
$357$	−18480.0	−2.73968
$358$	3750.00	0.553614
$359$	3858.00	0.567180	0.283590	−	0.958946i	$-0.408475\pi$
$359$	3858.00	0.567180	0.283590	+	0.958946i	$0.408475\pi$
$360$	−880.000	−0.128834
$361$	14457.0	2.10774
$362$	3212.00	0.466351
$363$	−9065.00	−1.31071
$364$	3760.00	0.541422
$365$	−1295.00	−0.185708
$366$	5180.00	0.739789
$367$	7856.00	1.11738	0.558692	−	0.829375i	$-0.311303\pi$
$367$	7856.00	1.11738	0.558692	+	0.829375i	$0.311303\pi$
$368$	368.000	0.0521286
$369$	10890.0	1.53634
$370$	1180.00	0.165798
$371$	−6840.00	−0.957184
$372$	−7084.00	−0.987334
$373$	−34.0000	−0.00471971	−0.00235986	−	0.999997i	$-0.500751\pi$
$373$	−34.0000	−0.00471971	−0.00235986	+	0.999997i	$0.500751\pi$
$374$	1584.00	0.219002
$375$	875.000	0.120493
$376$	−5112.00	−0.701147
$377$	−4653.00	−0.635654
$378$	1400.00	0.190498
$379$	−6064.00	−0.821865	−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−6064.00	−0.821865	−0.410932	+	0.911666i	$0.634797\pi$
$380$	2920.00	0.394192
$381$	623.000	0.0837723
$382$	−5964.00	−0.798808
$383$	11868.0	1.58336	0.791679	−	0.610937i	$-0.209207\pi$
$383$	11868.0	1.58336	0.791679	+	0.610937i	$0.209207\pi$
$384$	−896.000	−0.119072
$385$	600.000	0.0794255
$386$	−2770.00	−0.365257
$387$	5984.00	0.786005
$388$	3968.00	0.519187
$389$	8616.00	1.12300	0.561502	−	0.827475i	$-0.310224\pi$
$389$	8616.00	1.12300	0.561502	+	0.827475i	$0.310224\pi$
$390$	−3290.00	−0.427168
$391$	−3036.00	−0.392678
$392$	−456.000	−0.0587538
$393$	−12579.0	−1.61457
$394$	−1914.00	−0.244736
$395$	2710.00	0.345202
$396$	528.000	0.0670025
$397$	3119.00	0.394303	0.197151	−	0.980373i	$-0.436831\pi$
$397$	3119.00	0.394303	0.197151	+	0.980373i	$0.436831\pi$
$398$	716.000	0.0901755
$399$	20440.0	2.56461
$400$	400.000	0.0500000
$401$	7986.00	0.994518	0.497259	−	0.867602i	$-0.334340\pi$
$401$	7986.00	0.994518	0.497259	+	0.867602i	$0.334340\pi$
$402$	−9772.00	−1.21240
$403$	−11891.0	−1.46981
$404$	−6168.00	−0.759578
$405$	−4195.00	−0.514694
$406$	3960.00	0.484068
$407$	−708.000	−0.0862267
$408$	7392.00	0.896957
$409$	−3475.00	−0.420117	−0.210058	−	0.977689i	$-0.567365\pi$
$409$	−3475.00	−0.420117	−0.210058	+	0.977689i	$0.567365\pi$
$410$	−4950.00	−0.596251
$411$	−12852.0	−1.54244
$412$	128.000	0.0153061
$413$	4800.00	0.571895
$414$	−1012.00	−0.120138
$415$	−6240.00	−0.738095
$416$	−1504.00	−0.177259
$417$	−7189.00	−0.844237
$418$	−1752.00	−0.205007
$419$	10992.0	1.28161	0.640805	−	0.767704i	$-0.278601\pi$
$419$	10992.0	1.28161	0.640805	+	0.767704i	$0.278601\pi$
$420$	2800.00	0.325300
$421$	2012.00	0.232919	0.116459	−	0.993195i	$-0.462845\pi$
$421$	2012.00	0.232919	0.116459	+	0.993195i	$0.462845\pi$
$422$	10760.0	1.24121
$423$	14058.0	1.61589
$424$	2736.00	0.313377
$425$	−3300.00	−0.376644
$426$	4998.00	0.568436
$427$	−7400.00	−0.838668
$428$	−3336.00	−0.376756
$429$	1974.00	0.222158
$430$	−2720.00	−0.305047
$431$	−9792.00	−1.09435	−0.547174	−	0.837019i	$-0.684296\pi$
$431$	−9792.00	−1.09435	−0.547174	+	0.837019i	$0.684296\pi$
$432$	−560.000	−0.0623681
$433$	5786.00	0.642165	0.321082	−	0.947051i	$-0.395953\pi$
$433$	5786.00	0.642165	0.321082	+	0.947051i	$0.395953\pi$
$434$	10120.0	1.11930
$435$	−3465.00	−0.381917
$436$	−4768.00	−0.523729
$437$	3358.00	0.367586
$438$	3626.00	0.395564
$439$	2549.00	0.277123	0.138562	−	0.990354i	$-0.455752\pi$
$439$	2549.00	0.277123	0.138562	+	0.990354i	$0.455752\pi$
$440$	−240.000	−0.0260035
$441$	1254.00	0.135407
$442$	12408.0	1.33527
$443$	1311.00	0.140604	0.0703019	−	0.997526i	$-0.477604\pi$
$443$	1311.00	0.140604	0.0703019	+	0.997526i	$0.477604\pi$
$444$	−3304.00	−0.353155
$445$	−4140.00	−0.441022
$446$	−2080.00	−0.220832
$447$	16170.0	1.71099
$448$	1280.00	0.134987
$449$	−14610.0	−1.53561	−0.767805	−	0.640684i	$-0.778651\pi$
$449$	−14610.0	−1.53561	−0.767805	+	0.640684i	$0.778651\pi$
$450$	−1100.00	−0.115232
$451$	2970.00	0.310093
$452$	−528.000	−0.0549448
$453$	−15043.0	−1.56022
$454$	7488.00	0.774073
$455$	4700.00	0.484262
$456$	−8176.00	−0.839641
$457$	80.0000	0.00818871	0.00409436	−	0.999992i	$-0.498697\pi$
$457$	80.0000	0.00818871	0.00409436	+	0.999992i	$0.498697\pi$
$458$	−5608.00	−0.572150
$459$	4620.00	0.469811
$460$	460.000	0.0466252
$461$	−2343.00	−0.236712	−0.118356	−	0.992971i	$-0.537762\pi$
$461$	−2343.00	−0.236712	−0.118356	+	0.992971i	$0.537762\pi$
$462$	−1680.00	−0.169179
$463$	−3400.00	−0.341277	−0.170639	−	0.985334i	$-0.554583\pi$
$463$	−3400.00	−0.341277	−0.170639	+	0.985334i	$0.554583\pi$
$464$	−1584.00	−0.158481
$465$	−8855.00	−0.883098
$466$	9738.00	0.968035
$467$	−1374.00	−0.136148	−0.0680740	−	0.997680i	$-0.521685\pi$
$467$	−1374.00	−0.136148	−0.0680740	+	0.997680i	$0.521685\pi$
$468$	4136.00	0.408519
$469$	13960.0	1.37444
$470$	−6390.00	−0.627125
$471$	12824.0	1.25456
$472$	−1920.00	−0.187236
$473$	1632.00	0.158646
$474$	−7588.00	−0.735292
$475$	3650.00	0.352576
$476$	−10560.0	−1.01684
$477$	−7524.00	−0.722223
$478$	5754.00	0.550590
$479$	4536.00	0.432683	0.216341	−	0.976318i	$-0.430588\pi$
$479$	4536.00	0.432683	0.216341	+	0.976318i	$0.430588\pi$
$480$	−1120.00	−0.106502
$481$	−5546.00	−0.525729
$482$	−3244.00	−0.306556
$483$	3220.00	0.303344
$484$	−5180.00	−0.486476
$485$	4960.00	0.464375
$486$	9856.00	0.919912
$487$	−11455.0	−1.06586	−0.532932	−	0.846158i	$-0.678910\pi$
$487$	−11455.0	−1.06586	−0.532932	+	0.846158i	$0.678910\pi$
$488$	2960.00	0.274576
$489$	8519.00	0.787817
$490$	−570.000	−0.0525510
$491$	−10395.0	−0.955437	−0.477719	−	0.878513i	$-0.658536\pi$
$491$	−10395.0	−0.955437	−0.477719	+	0.878513i	$0.658536\pi$
$492$	13860.0	1.27003
$493$	13068.0	1.19382
$494$	−13724.0	−1.24994
$495$	660.000	0.0599289
$496$	−4048.00	−0.366453
$497$	−7140.00	−0.644412
$498$	17472.0	1.57217
$499$	−5497.00	−0.493145	−0.246573	−	0.969124i	$-0.579304\pi$
$499$	−5497.00	−0.493145	−0.246573	+	0.969124i	$0.579304\pi$
$500$	500.000	0.0447214
$501$	21336.0	1.90264
$502$	9504.00	0.844989
$503$	7158.00	0.634512	0.317256	−	0.948340i	$-0.397239\pi$
$503$	7158.00	0.634512	0.317256	+	0.948340i	$0.397239\pi$
$504$	−3520.00	−0.311098
$505$	−7710.00	−0.679387
$506$	−276.000	−0.0242484
$507$	84.0000	0.00735813
$508$	356.000	0.0310924
$509$	12801.0	1.11472	0.557362	−	0.830270i	$-0.311814\pi$
$509$	12801.0	1.11472	0.557362	+	0.830270i	$0.311814\pi$
$510$	9240.00	0.802263
$511$	−5180.00	−0.448434
$512$	−512.000	−0.0441942
$513$	−5110.00	−0.439789
$514$	10146.0	0.870663
$515$	160.000	0.0136902
$516$	7616.00	0.649759
$517$	3834.00	0.326149
$518$	4720.00	0.400357
$519$	5418.00	0.458235
$520$	−1880.00	−0.158545
$521$	16788.0	1.41170	0.705850	−	0.708361i	$-0.250565\pi$
$521$	16788.0	1.41170	0.705850	+	0.708361i	$0.250565\pi$
$522$	4356.00	0.365243
$523$	19040.0	1.59189	0.795947	−	0.605366i	$-0.206973\pi$
$523$	19040.0	1.59189	0.795947	+	0.605366i	$0.206973\pi$
$524$	−7188.00	−0.599254
$525$	3500.00	0.290957
$526$	−2628.00	−0.217845
$527$	33396.0	2.76044
$528$	672.000	0.0553883
$529$	529.000	0.0434783
$530$	3420.00	0.280293
$531$	5280.00	0.431511
$532$	11680.0	0.951865
$533$	23265.0	1.89065
$534$	11592.0	0.939391
$535$	−4170.00	−0.336981
$536$	−5584.00	−0.449985
$537$	−13125.0	−1.05472
$538$	−10530.0	−0.843830
$539$	342.000	0.0273302
$540$	−700.000	−0.0557837
$541$	−13339.0	−1.06005	−0.530026	−	0.847981i	$-0.677818\pi$
$541$	−13339.0	−1.06005	−0.530026	+	0.847981i	$0.677818\pi$
$542$	4976.00	0.394350
$543$	−11242.0	−0.888472
$544$	4224.00	0.332909
$545$	−5960.00	−0.468437
$546$	−13160.0	−1.03149
$547$	−22975.0	−1.79587	−0.897934	−	0.440130i	$-0.854932\pi$
$547$	−22975.0	−1.79587	−0.897934	+	0.440130i	$0.854932\pi$
$548$	−7344.00	−0.572482
$549$	−8140.00	−0.632799
$550$	−300.000	−0.0232583
$551$	−14454.0	−1.11753
$552$	−1288.00	−0.0993133
$553$	10840.0	0.833569
$554$	−10930.0	−0.838215
$555$	−4130.00	−0.315872
$556$	−4108.00	−0.313342
$557$	−17964.0	−1.36653	−0.683267	−	0.730169i	$-0.739441\pi$
$557$	−17964.0	−1.36653	−0.683267	+	0.730169i	$0.739441\pi$
$558$	11132.0	0.844543
$559$	12784.0	0.967273
$560$	1600.00	0.120736
$561$	−5544.00	−0.417233
$562$	−17880.0	−1.34203
$563$	12636.0	0.945904	0.472952	−	0.881088i	$-0.343188\pi$
$563$	12636.0	0.945904	0.472952	+	0.881088i	$0.343188\pi$
$564$	17892.0	1.33580
$565$	−660.000	−0.0491441
$566$	−1684.00	−0.125060
$567$	−16780.0	−1.24285
$568$	2856.00	0.210977
$569$	−10302.0	−0.759020	−0.379510	−	0.925188i	$-0.623907\pi$
$569$	−10302.0	−0.759020	−0.379510	+	0.925188i	$0.623907\pi$
$570$	−10220.0	−0.750998
$571$	12380.0	0.907333	0.453666	−	0.891172i	$-0.350116\pi$
$571$	12380.0	0.907333	0.453666	+	0.891172i	$0.350116\pi$
$572$	1128.00	0.0824546
$573$	20874.0	1.52186
$574$	−19800.0	−1.43978
$575$	575.000	0.0417029
$576$	1408.00	0.101852
$577$	1913.00	0.138023	0.0690115	−	0.997616i	$-0.478015\pi$
$577$	1913.00	0.138023	0.0690115	+	0.997616i	$0.478015\pi$
$578$	−25022.0	−1.80065
$579$	9695.00	0.695873
$580$	−1980.00	−0.141750
$581$	−24960.0	−1.78230
$582$	−13888.0	−0.989134
$583$	−2052.00	−0.145772
$584$	2072.00	0.146815
$585$	5170.00	0.365390
$586$	8064.00	0.568465
$587$	16767.0	1.17896	0.589479	−	0.807784i	$-0.299333\pi$
$587$	16767.0	1.17896	0.589479	+	0.807784i	$0.299333\pi$
$588$	1596.00	0.111935
$589$	−36938.0	−2.58405
$590$	−2400.00	−0.167469
$591$	6699.00	0.466261
$592$	−1888.00	−0.131075
$593$	−16722.0	−1.15799	−0.578997	−	0.815330i	$-0.696556\pi$
$593$	−16722.0	−1.15799	−0.578997	+	0.815330i	$0.696556\pi$
$594$	420.000	0.0290115
$595$	−13200.0	−0.909491
$596$	9240.00	0.635042
$597$	−2506.00	−0.171799
$598$	−2162.00	−0.147844
$599$	−4200.00	−0.286490	−0.143245	−	0.989687i	$-0.545754\pi$
$599$	−4200.00	−0.286490	−0.143245	+	0.989687i	$0.545754\pi$
$600$	−1400.00	−0.0952579
$601$	−19915.0	−1.35166	−0.675832	−	0.737056i	$-0.736215\pi$
$601$	−19915.0	−1.35166	−0.675832	+	0.737056i	$0.736215\pi$
$602$	−10880.0	−0.736604
$603$	15356.0	1.03706
$604$	−8596.00	−0.579083
$605$	−6475.00	−0.435118
$606$	21588.0	1.44712
$607$	24044.0	1.60777	0.803885	−	0.594785i	$-0.202763\pi$
$607$	24044.0	1.60777	0.803885	+	0.594785i	$0.202763\pi$
$608$	−4672.00	−0.311636
$609$	−13860.0	−0.922226
$610$	3700.00	0.245588
$611$	30033.0	1.98855
$612$	−11616.0	−0.767237
$613$	3452.00	0.227447	0.113723	−	0.993512i	$-0.463722\pi$
$613$	3452.00	0.227447	0.113723	+	0.993512i	$0.463722\pi$
$614$	2192.00	0.144075
$615$	17325.0	1.13595
$616$	−960.000	−0.0627914
$617$	−16374.0	−1.06838	−0.534192	−	0.845363i	$-0.679384\pi$
$617$	−16374.0	−1.06838	−0.534192	+	0.845363i	$0.679384\pi$
$618$	−448.000	−0.0291605
$619$	−12760.0	−0.828542	−0.414271	−	0.910154i	$-0.635963\pi$
$619$	−12760.0	−0.828542	−0.414271	+	0.910154i	$0.635963\pi$
$620$	−5060.00	−0.327765
$621$	−805.000	−0.0520186
$622$	9306.00	0.599898
$623$	−16560.0	−1.06495
$624$	5264.00	0.337706
$625$	625.000	0.0400000
$626$	−6880.00	−0.439265
$627$	6132.00	0.390572
$628$	7328.00	0.465635
$629$	15576.0	0.987370
$630$	−4400.00	−0.278254
$631$	29420.0	1.85609	0.928044	−	0.372470i	$-0.121489\pi$
$631$	29420.0	1.85609	0.928044	+	0.372470i	$0.121489\pi$
$632$	−4336.00	−0.272906
$633$	−37660.0	−2.36469
$634$	−6132.00	−0.384121
$635$	445.000	0.0278099
$636$	−9576.00	−0.597033
$637$	2679.00	0.166634
$638$	1188.00	0.0737200
$639$	−7854.00	−0.486228
$640$	−640.000	−0.0395285
$641$	−13692.0	−0.843684	−0.421842	−	0.906669i	$-0.638616\pi$
$641$	−13692.0	−0.843684	−0.421842	+	0.906669i	$0.638616\pi$
$642$	11676.0	0.717780
$643$	27398.0	1.68036	0.840180	−	0.542307i	$-0.182449\pi$
$643$	27398.0	1.68036	0.840180	+	0.542307i	$0.182449\pi$
$644$	1840.00	0.112587
$645$	9520.00	0.581162
$646$	38544.0	2.34751
$647$	−6417.00	−0.389920	−0.194960	−	0.980811i	$-0.562458\pi$
$647$	−6417.00	−0.389920	−0.194960	+	0.980811i	$0.562458\pi$
$648$	6712.00	0.406902
$649$	1440.00	0.0870954
$650$	−2350.00	−0.141807
$651$	−35420.0	−2.13244
$652$	4868.00	0.292401
$653$	14583.0	0.873931	0.436965	−	0.899478i	$-0.356053\pi$
$653$	14583.0	0.873931	0.436965	+	0.899478i	$0.356053\pi$
$654$	16688.0	0.997787
$655$	−8985.00	−0.535989
$656$	7920.00	0.471378
$657$	−5698.00	−0.338356
$658$	−25560.0	−1.51434
$659$	−9624.00	−0.568889	−0.284444	−	0.958693i	$-0.591809\pi$
$659$	−9624.00	−0.568889	−0.284444	+	0.958693i	$0.591809\pi$
$660$	840.000	0.0495408
$661$	−24586.0	−1.44672	−0.723362	−	0.690469i	$-0.757404\pi$
$661$	−24586.0	−1.44672	−0.723362	+	0.690469i	$0.757404\pi$
$662$	−3010.00	−0.176717
$663$	−43428.0	−2.54390
$664$	9984.00	0.583516
$665$	14600.0	0.851374
$666$	5192.00	0.302081
$667$	−2277.00	−0.132183
$668$	12192.0	0.706172
$669$	7280.00	0.420719
$670$	−6980.00	−0.402479
$671$	−2220.00	−0.127723
$672$	−4480.00	−0.257172
$673$	14339.0	0.821289	0.410645	−	0.911795i	$-0.365304\pi$
$673$	14339.0	0.821289	0.410645	+	0.911795i	$0.365304\pi$
$674$	6536.00	0.373527
$675$	−875.000	−0.0498945
$676$	48.0000	0.00273100
$677$	14658.0	0.832131	0.416066	−	0.909335i	$-0.363409\pi$
$677$	14658.0	0.832131	0.416066	+	0.909335i	$0.363409\pi$
$678$	1848.00	0.104678
$679$	19840.0	1.12134
$680$	5280.00	0.297763
$681$	−26208.0	−1.47473
$682$	3036.00	0.170461
$683$	16797.0	0.941024	0.470512	−	0.882394i	$-0.344069\pi$
$683$	16797.0	0.941024	0.470512	+	0.882394i	$0.344069\pi$
$684$	12848.0	0.718210
$685$	−9180.00	−0.512043
$686$	11440.0	0.636707
$687$	19628.0	1.09004
$688$	4352.00	0.241161
$689$	−16074.0	−0.888782
$690$	−1610.00	−0.0888285
$691$	8132.00	0.447693	0.223846	−	0.974624i	$-0.428139\pi$
$691$	8132.00	0.447693	0.223846	+	0.974624i	$0.428139\pi$
$692$	3096.00	0.170076
$693$	2640.00	0.144712
$694$	−8328.00	−0.455514
$695$	−5135.00	−0.280261
$696$	5544.00	0.301932
$697$	−65340.0	−3.55083
$698$	5822.00	0.315711
$699$	−34083.0	−1.84426
$700$	2000.00	0.107990
$701$	19668.0	1.05970	0.529850	−	0.848091i	$-0.322248\pi$
$701$	19668.0	1.05970	0.529850	+	0.848091i	$0.322248\pi$
$702$	3290.00	0.176885
$703$	−17228.0	−0.924276
$704$	384.000	0.0205576
$705$	22365.0	1.19477
$706$	−19506.0	−1.03983
$707$	−30840.0	−1.64053
$708$	6720.00	0.356713
$709$	18200.0	0.964055	0.482028	−	0.876156i	$-0.339900\pi$
$709$	18200.0	0.964055	0.482028	+	0.876156i	$0.339900\pi$
$710$	3570.00	0.188704
$711$	11924.0	0.628952
$712$	6624.00	0.348659
$713$	−5819.00	−0.305643
$714$	36960.0	1.93725
$715$	1410.00	0.0737497
$716$	−7500.00	−0.391464
$717$	−20139.0	−1.04896
$718$	−7716.00	−0.401056
$719$	−11880.0	−0.616202	−0.308101	−	0.951354i	$-0.599693\pi$
$719$	−11880.0	−0.616202	−0.308101	+	0.951354i	$0.599693\pi$
$720$	1760.00	0.0910991
$721$	640.000	0.0330580
$722$	−28914.0	−1.49040
$723$	11354.0	0.584038
$724$	−6424.00	−0.329760
$725$	−2475.00	−0.126785
$726$	18130.0	0.926815
$727$	−2554.00	−0.130292	−0.0651462	−	0.997876i	$-0.520751\pi$
$727$	−2554.00	−0.130292	−0.0651462	+	0.997876i	$0.520751\pi$
$728$	−7520.00	−0.382843
$729$	−11843.0	−0.601687
$730$	2590.00	0.131315
$731$	−35904.0	−1.81663
$732$	−10360.0	−0.523110
$733$	6308.00	0.317860	0.158930	−	0.987290i	$-0.449196\pi$
$733$	6308.00	0.317860	0.158930	+	0.987290i	$0.449196\pi$
$734$	−15712.0	−0.790110
$735$	1995.00	0.100118
$736$	−736.000	−0.0368605
$737$	4188.00	0.209317
$738$	−21780.0	−1.08636
$739$	9557.00	0.475724	0.237862	−	0.971299i	$-0.423553\pi$
$739$	9557.00	0.475724	0.237862	+	0.971299i	$0.423553\pi$
$740$	−2360.00	−0.117237
$741$	48034.0	2.38134
$742$	13680.0	0.676831
$743$	19128.0	0.944466	0.472233	−	0.881474i	$-0.343448\pi$
$743$	19128.0	0.944466	0.472233	+	0.881474i	$0.343448\pi$
$744$	14168.0	0.698151
$745$	11550.0	0.567999
$746$	68.0000	0.00333734
$747$	−27456.0	−1.34480
$748$	−3168.00	−0.154858
$749$	−16680.0	−0.813717
$750$	−1750.00	−0.0852013
$751$	−18448.0	−0.896374	−0.448187	−	0.893940i	$-0.647930\pi$
$751$	−18448.0	−0.896374	−0.448187	+	0.893940i	$0.647930\pi$
$752$	10224.0	0.495786
$753$	−33264.0	−1.60984
$754$	9306.00	0.449476
$755$	−10745.0	−0.517948
$756$	−2800.00	−0.134702
$757$	−5602.00	−0.268967	−0.134484	−	0.990916i	$-0.542938\pi$
$757$	−5602.00	−0.268967	−0.134484	+	0.990916i	$0.542938\pi$
$758$	12128.0	0.581146
$759$	966.000	0.0461971
$760$	−5840.00	−0.278736
$761$	4005.00	0.190777	0.0953884	−	0.995440i	$-0.469591\pi$
$761$	4005.00	0.190777	0.0953884	+	0.995440i	$0.469591\pi$
$762$	−1246.00	−0.0592360
$763$	−23840.0	−1.13115
$764$	11928.0	0.564843
$765$	−14520.0	−0.686238
$766$	−23736.0	−1.11960
$767$	11280.0	0.531026
$768$	1792.00	0.0841969
$769$	41726.0	1.95667	0.978334	−	0.207032i	$-0.0663803\pi$
$769$	41726.0	1.95667	0.978334	+	0.207032i	$0.0663803\pi$
$770$	−1200.00	−0.0561623
$771$	−35511.0	−1.65875
$772$	5540.00	0.258276
$773$	34116.0	1.58741	0.793705	−	0.608303i	$-0.208150\pi$
$773$	34116.0	1.58741	0.793705	+	0.608303i	$0.208150\pi$
$774$	−11968.0	−0.555789
$775$	−6325.00	−0.293162
$776$	−7936.00	−0.367121
$777$	−16520.0	−0.762743
$778$	−17232.0	−0.794084
$779$	72270.0	3.32393
$780$	6580.00	0.302054
$781$	−2142.00	−0.0981393
$782$	6072.00	0.277665
$783$	3465.00	0.158147
$784$	912.000	0.0415452
$785$	9160.00	0.416477
$786$	25158.0	1.14167
$787$	1652.00	0.0748252	0.0374126	−	0.999300i	$-0.488088\pi$
$787$	1652.00	0.0748252	0.0374126	+	0.999300i	$0.488088\pi$
$788$	3828.00	0.173054
$789$	9198.00	0.415028
$790$	−5420.00	−0.244095
$791$	−2640.00	−0.118670
$792$	−1056.00	−0.0473779
$793$	−17390.0	−0.778735
$794$	−6238.00	−0.278814
$795$	−11970.0	−0.534003
$796$	−1432.00	−0.0637637
$797$	12486.0	0.554927	0.277463	−	0.960736i	$-0.410506\pi$
$797$	12486.0	0.554927	0.277463	+	0.960736i	$0.410506\pi$
$798$	−40880.0	−1.81345
$799$	−84348.0	−3.73469
$800$	−800.000	−0.0353553
$801$	−18216.0	−0.803534
$802$	−15972.0	−0.703231
$803$	−1554.00	−0.0682932
$804$	19544.0	0.857293
$805$	2300.00	0.100701
$806$	23782.0	1.03931
$807$	36855.0	1.60763
$808$	12336.0	0.537103
$809$	5490.00	0.238589	0.119294	−	0.992859i	$-0.461937\pi$
$809$	5490.00	0.238589	0.119294	+	0.992859i	$0.461937\pi$
$810$	8390.00	0.363944
$811$	−14785.0	−0.640162	−0.320081	−	0.947390i	$-0.603710\pi$
$811$	−14785.0	−0.640162	−0.320081	+	0.947390i	$0.603710\pi$
$812$	−7920.00	−0.342288
$813$	−17416.0	−0.751299
$814$	1416.00	0.0609715
$815$	6085.00	0.261532
$816$	−14784.0	−0.634245
$817$	39712.0	1.70055
$818$	6950.00	0.297067
$819$	20680.0	0.882317
$820$	9900.00	0.421613
$821$	−12486.0	−0.530773	−0.265386	−	0.964142i	$-0.585500\pi$
$821$	−12486.0	−0.530773	−0.265386	+	0.964142i	$0.585500\pi$
$822$	25704.0	1.09067
$823$	−39805.0	−1.68592	−0.842962	−	0.537973i	$-0.819190\pi$
$823$	−39805.0	−1.68592	−0.842962	+	0.537973i	$0.819190\pi$
$824$	−256.000	−0.0108230
$825$	1050.00	0.0443107
$826$	−9600.00	−0.404391
$827$	15024.0	0.631724	0.315862	−	0.948805i	$-0.397706\pi$
$827$	15024.0	0.631724	0.315862	+	0.948805i	$0.397706\pi$
$828$	2024.00	0.0849503
$829$	14618.0	0.612430	0.306215	−	0.951962i	$-0.400937\pi$
$829$	14618.0	0.612430	0.306215	+	0.951962i	$0.400937\pi$
$830$	12480.0	0.521912
$831$	38255.0	1.59693
$832$	3008.00	0.125341
$833$	−7524.00	−0.312955
$834$	14378.0	0.596966
$835$	15240.0	0.631619
$836$	3504.00	0.144962
$837$	8855.00	0.365679
$838$	−21984.0	−0.906235
$839$	−10152.0	−0.417743	−0.208871	−	0.977943i	$-0.566979\pi$
$839$	−10152.0	−0.417743	−0.208871	+	0.977943i	$0.566979\pi$
$840$	−5600.00	−0.230022
$841$	−14588.0	−0.598139
$842$	−4024.00	−0.164699
$843$	62580.0	2.55678
$844$	−21520.0	−0.877665
$845$	60.0000	0.00244268
$846$	−28116.0	−1.14261
$847$	−25900.0	−1.05069
$848$	−5472.00	−0.221591
$849$	5894.00	0.238259
$850$	6600.00	0.266327
$851$	−2714.00	−0.109324
$852$	−9996.00	−0.401945
$853$	−22306.0	−0.895361	−0.447680	−	0.894194i	$-0.647750\pi$
$853$	−22306.0	−0.895361	−0.447680	+	0.894194i	$0.647750\pi$
$854$	14800.0	0.593028
$855$	16060.0	0.642386
$856$	6672.00	0.266407
$857$	1731.00	0.0689963	0.0344982	−	0.999405i	$-0.489017\pi$
$857$	1731.00	0.0689963	0.0344982	+	0.999405i	$0.489017\pi$
$858$	−3948.00	−0.157089
$859$	−12649.0	−0.502419	−0.251210	−	0.967933i	$-0.580828\pi$
$859$	−12649.0	−0.502419	−0.251210	+	0.967933i	$0.580828\pi$
$860$	5440.00	0.215701
$861$	69300.0	2.74302
$862$	19584.0	0.773821
$863$	−16143.0	−0.636749	−0.318374	−	0.947965i	$-0.603137\pi$
$863$	−16143.0	−0.636749	−0.318374	+	0.947965i	$0.603137\pi$
$864$	1120.00	0.0441009
$865$	3870.00	0.152120
$866$	−11572.0	−0.454079
$867$	87577.0	3.43053
$868$	−20240.0	−0.791464
$869$	3252.00	0.126947
$870$	6930.00	0.270056
$871$	32806.0	1.27622
$872$	9536.00	0.370332
$873$	21824.0	0.846083
$874$	−6716.00	−0.259922
$875$	2500.00	0.0965891
$876$	−7252.00	−0.279706
$877$	4094.00	0.157633	0.0788167	−	0.996889i	$-0.474886\pi$
$877$	4094.00	0.157633	0.0788167	+	0.996889i	$0.474886\pi$
$878$	−5098.00	−0.195956
$879$	−28224.0	−1.08302
$880$	480.000	0.0183873
$881$	30396.0	1.16239	0.581196	−	0.813764i	$-0.302585\pi$
$881$	30396.0	1.16239	0.581196	+	0.813764i	$0.302585\pi$
$882$	−2508.00	−0.0957469
$883$	−21148.0	−0.805987	−0.402994	−	0.915203i	$-0.632030\pi$
$883$	−21148.0	−0.805987	−0.402994	+	0.915203i	$0.632030\pi$
$884$	−24816.0	−0.944177
$885$	8400.00	0.319054
$886$	−2622.00	−0.0994219
$887$	5031.00	0.190445	0.0952223	−	0.995456i	$-0.469644\pi$
$887$	5031.00	0.190445	0.0952223	+	0.995456i	$0.469644\pi$
$888$	6608.00	0.249718
$889$	1780.00	0.0671533
$890$	8280.00	0.311850
$891$	−5034.00	−0.189276
$892$	4160.00	0.156151
$893$	93294.0	3.49604
$894$	−32340.0	−1.20986
$895$	−9375.00	−0.350136
$896$	−2560.00	−0.0954504
$897$	7567.00	0.281666
$898$	29220.0	1.08584
$899$	25047.0	0.929215
$900$	2200.00	0.0814815
$901$	45144.0	1.66922
$902$	−5940.00	−0.219269
$903$	38080.0	1.40335
$904$	1056.00	0.0388518
$905$	−8030.00	−0.294946
$906$	30086.0	1.10325
$907$	−538.000	−0.0196957	−0.00984785	−	0.999952i	$-0.503135\pi$
$907$	−538.000	−0.0196957	−0.00984785	+	0.999952i	$0.503135\pi$
$908$	−14976.0	−0.547352
$909$	−33924.0	−1.23783
$910$	−9400.00	−0.342425
$911$	3078.00	0.111941	0.0559707	−	0.998432i	$-0.482175\pi$
$911$	3078.00	0.111941	0.0559707	+	0.998432i	$0.482175\pi$
$912$	16352.0	0.593716
$913$	−7488.00	−0.271431
$914$	−160.000	−0.00579029
$915$	−12950.0	−0.467884
$916$	11216.0	0.404571
$917$	−35940.0	−1.29427
$918$	−9240.00	−0.332206
$919$	20288.0	0.728226	0.364113	−	0.931355i	$-0.381372\pi$
$919$	20288.0	0.728226	0.364113	+	0.931355i	$0.381372\pi$
$920$	−920.000	−0.0329690
$921$	−7672.00	−0.274485
$922$	4686.00	0.167381
$923$	−16779.0	−0.598361
$924$	3360.00	0.119628
$925$	−2950.00	−0.104860
$926$	6800.00	0.241320
$927$	704.000	0.0249433
$928$	3168.00	0.112063
$929$	28911.0	1.02103	0.510516	−	0.859868i	$-0.329454\pi$
$929$	28911.0	1.02103	0.510516	+	0.859868i	$0.329454\pi$
$930$	17710.0	0.624445
$931$	8322.00	0.292957
$932$	−19476.0	−0.684504
$933$	−32571.0	−1.14290
$934$	2748.00	0.0962712
$935$	−3960.00	−0.138509
$936$	−8272.00	−0.288866
$937$	14810.0	0.516352	0.258176	−	0.966098i	$-0.416879\pi$
$937$	14810.0	0.516352	0.258176	+	0.966098i	$0.416879\pi$
$938$	−27920.0	−0.971877
$939$	24080.0	0.836870
$940$	12780.0	0.443444
$941$	−2544.00	−0.0881318	−0.0440659	−	0.999029i	$-0.514031\pi$
$941$	−2544.00	−0.0881318	−0.0440659	+	0.999029i	$0.514031\pi$
$942$	−25648.0	−0.887109
$943$	11385.0	0.393157
$944$	3840.00	0.132396
$945$	−3500.00	−0.120481
$946$	−3264.00	−0.112179
$947$	−11145.0	−0.382433	−0.191216	−	0.981548i	$-0.561243\pi$
$947$	−11145.0	−0.382433	−0.191216	+	0.981548i	$0.561243\pi$
$948$	15176.0	0.519930
$949$	−12173.0	−0.416388
$950$	−7300.00	−0.249309
$951$	21462.0	0.731812
$952$	21120.0	0.719016
$953$	−4386.00	−0.149083	−0.0745417	−	0.997218i	$-0.523749\pi$
$953$	−4386.00	−0.149083	−0.0745417	+	0.997218i	$0.523749\pi$
$954$	15048.0	0.510689
$955$	14910.0	0.505211
$956$	−11508.0	−0.389326
$957$	−4158.00	−0.140448
$958$	−9072.00	−0.305953
$959$	−36720.0	−1.23644
$960$	2240.00	0.0753080
$961$	34218.0	1.14860
$962$	11092.0	0.371747
$963$	−18348.0	−0.613973
$964$	6488.00	0.216768
$965$	6925.00	0.231009
$966$	−6440.00	−0.214496
$967$	56381.0	1.87496	0.937482	−	0.348033i	$-0.113150\pi$
$967$	56381.0	1.87496	0.937482	+	0.348033i	$0.113150\pi$
$968$	10360.0	0.343991
$969$	−134904.	−4.47238
$970$	−9920.00	−0.328363
$971$	43782.0	1.44699	0.723497	−	0.690327i	$-0.242534\pi$
$971$	43782.0	1.44699	0.723497	+	0.690327i	$0.242534\pi$
$972$	−19712.0	−0.650476
$973$	−20540.0	−0.676755
$974$	22910.0	0.753679
$975$	8225.00	0.270165
$976$	−5920.00	−0.194154
$977$	3714.00	0.121619	0.0608093	−	0.998149i	$-0.480632\pi$
$977$	3714.00	0.121619	0.0608093	+	0.998149i	$0.480632\pi$
$978$	−17038.0	−0.557071
$979$	−4968.00	−0.162184
$980$	1140.00	0.0371591
$981$	−26224.0	−0.853484
$982$	20790.0	0.675596
$983$	−4662.00	−0.151266	−0.0756331	−	0.997136i	$-0.524098\pi$
$983$	−4662.00	−0.151266	−0.0756331	+	0.997136i	$0.524098\pi$
$984$	−27720.0	−0.898050
$985$	4785.00	0.154785
$986$	−26136.0	−0.844158
$987$	89460.0	2.88505
$988$	27448.0	0.883843
$989$	6256.00	0.201142
$990$	−1320.00	−0.0423761
$991$	51440.0	1.64889	0.824443	−	0.565945i	$-0.191489\pi$
$991$	51440.0	1.64889	0.824443	+	0.565945i	$0.191489\pi$
$992$	8096.00	0.259121
$993$	10535.0	0.336675
$994$	14280.0	0.455668
$995$	−1790.00	−0.0570320
$996$	−34944.0	−1.11169
$997$	686.000	0.0217912	0.0108956	−	0.999941i	$-0.496532\pi$
$997$	686.000	0.0217912	0.0108956	+	0.999941i	$0.496532\pi$
$998$	10994.0	0.348706
$999$	4130.00	0.130798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.a.c.1.1	✓	1
3.2	odd	2		2070.4.a.j.1.1		1
4.3	odd	2		1840.4.a.a.1.1		1
5.2	odd	4		1150.4.b.b.599.1		2
5.3	odd	4		1150.4.b.b.599.2		2
5.4	even	2		1150.4.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.c.1.1	✓	1	1.1	even	1	trivial
1150.4.a.e.1.1		1	5.4	even	2
1150.4.b.b.599.1		2	5.2	odd	4
1150.4.b.b.599.2		2	5.3	odd	4
1840.4.a.a.1.1		1	4.3	odd	2
2070.4.a.j.1.1		1	3.2	odd	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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