LMFDB - Embedded newform 1840.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1840,4,Mod(1,1840)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1840, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("1840.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1840 = 2^{4} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1840.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:	$108.563514411$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1840.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-7.00000 q^{3} +5.00000 q^{5} -20.0000 q^{7} +22.0000 q^{9} -6.00000 q^{11} +47.0000 q^{13} -35.0000 q^{15} -132.000 q^{17} -146.000 q^{19} +140.000 q^{21} -23.0000 q^{23} +25.0000 q^{25} +35.0000 q^{27} -99.0000 q^{29} +253.000 q^{31} +42.0000 q^{33} -100.000 q^{35} -118.000 q^{37} -329.000 q^{39} +495.000 q^{41} -272.000 q^{43} +110.000 q^{45} -639.000 q^{47} +57.0000 q^{49} +924.000 q^{51} -342.000 q^{53} -30.0000 q^{55} +1022.00 q^{57} -240.000 q^{59} -370.000 q^{61} -440.000 q^{63} +235.000 q^{65} -698.000 q^{67} +161.000 q^{69} +357.000 q^{71} -259.000 q^{73} -175.000 q^{75} +120.000 q^{77} -542.000 q^{79} -839.000 q^{81} +1248.00 q^{83} -660.000 q^{85} +693.000 q^{87} -828.000 q^{89} -940.000 q^{91} -1771.00 q^{93} -730.000 q^{95} +992.000 q^{97} -132.000 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	−7.00000	−1.34715	−0.673575	−	0.739119i	$-0.735242\pi$
$3$	−7.00000	−1.34715	−0.673575	+	0.739119i	$0.735242\pi$
$4$	0	0
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	0	0
$7$	−20.0000	−1.07990	−0.539949	−	0.841698i	$-0.681557\pi$
$7$	−20.0000	−1.07990	−0.539949	+	0.841698i	$0.681557\pi$
$8$	0	0
$9$	22.0000	0.814815
$10$	0	0
$11$	−6.00000	−0.164461	−0.0822304	−	0.996613i	$-0.526204\pi$
$11$	−6.00000	−0.164461	−0.0822304	+	0.996613i	$0.526204\pi$
$12$	0	0
$13$	47.0000	1.00273	0.501364	−	0.865237i	$-0.332832\pi$
$13$	47.0000	1.00273	0.501364	+	0.865237i	$0.332832\pi$
$14$	0	0
$15$	−35.0000	−0.602464
$16$	0	0
$17$	−132.000	−1.88322	−0.941609	−	0.336709i	$-0.890686\pi$
$17$	−132.000	−1.88322	−0.941609	+	0.336709i	$0.890686\pi$
$18$	0	0
$19$	−146.000	−1.76288	−0.881439	−	0.472297i	$-0.843425\pi$
$19$	−146.000	−1.76288	−0.881439	+	0.472297i	$0.843425\pi$
$20$	0	0
$21$	140.000	1.45479
$22$	0	0
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	0	0
$25$	25.0000	0.200000
$26$	0	0
$27$	35.0000	0.249472
$28$	0	0
$29$	−99.0000	−0.633925	−0.316963	−	0.948438i	$-0.602663\pi$
$29$	−99.0000	−0.633925	−0.316963	+	0.948438i	$0.602663\pi$
$30$	0	0
$31$	253.000	1.46581	0.732906	−	0.680330i	$-0.238164\pi$
$31$	253.000	1.46581	0.732906	+	0.680330i	$0.238164\pi$
$32$	0	0
$33$	42.0000	0.221553
$34$	0	0
$35$	−100.000	−0.482945
$36$	0	0
$37$	−118.000	−0.524299	−0.262150	−	0.965027i	$-0.584431\pi$
$37$	−118.000	−0.524299	−0.262150	+	0.965027i	$0.584431\pi$
$38$	0	0
$39$	−329.000	−1.35082
$40$	0	0
$41$	495.000	1.88551	0.942756	−	0.333483i	$-0.108224\pi$
$41$	495.000	1.88551	0.942756	+	0.333483i	$0.108224\pi$
$42$	0	0
$43$	−272.000	−0.964642	−0.482321	−	0.875995i	$-0.660206\pi$
$43$	−272.000	−0.964642	−0.482321	+	0.875995i	$0.660206\pi$
$44$	0	0
$45$	110.000	0.364396
$46$	0	0
$47$	−639.000	−1.98314	−0.991572	−	0.129560i	$-0.958644\pi$
$47$	−639.000	−1.98314	−0.991572	+	0.129560i	$0.958644\pi$
$48$	0	0
$49$	57.0000	0.166181
$50$	0	0
$51$	924.000	2.53698
$52$	0	0
$53$	−342.000	−0.886364	−0.443182	−	0.896432i	$-0.646151\pi$
$53$	−342.000	−0.886364	−0.443182	+	0.896432i	$0.646151\pi$
$54$	0	0
$55$	−30.0000	−0.0735491
$56$	0	0
$57$	1022.00	2.37486
$58$	0	0
$59$	−240.000	−0.529582	−0.264791	−	0.964306i	$-0.585303\pi$
$59$	−240.000	−0.529582	−0.264791	+	0.964306i	$0.585303\pi$
$60$	0	0
$61$	−370.000	−0.776617	−0.388309	−	0.921529i	$-0.626941\pi$
$61$	−370.000	−0.776617	−0.388309	+	0.921529i	$0.626941\pi$
$62$	0	0
$63$	−440.000	−0.879917
$64$	0	0
$65$	235.000	0.448433
$66$	0	0
$67$	−698.000	−1.27275	−0.636375	−	0.771380i	$-0.719567\pi$
$67$	−698.000	−1.27275	−0.636375	+	0.771380i	$0.719567\pi$
$68$	0	0
$69$	161.000	0.280900
$70$	0	0
$71$	357.000	0.596734	0.298367	−	0.954451i	$-0.403558\pi$
$71$	357.000	0.596734	0.298367	+	0.954451i	$0.403558\pi$
$72$	0	0
$73$	−259.000	−0.415256	−0.207628	−	0.978208i	$-0.566574\pi$
$73$	−259.000	−0.415256	−0.207628	+	0.978208i	$0.566574\pi$
$74$	0	0
$75$	−175.000	−0.269430
$76$	0	0
$77$	120.000	0.177601
$78$	0	0
$79$	−542.000	−0.771896	−0.385948	−	0.922521i	$-0.626126\pi$
$79$	−542.000	−0.771896	−0.385948	+	0.922521i	$0.626126\pi$
$80$	0	0
$81$	−839.000	−1.15089
$82$	0	0
$83$	1248.00	1.65043	0.825216	−	0.564818i	$-0.191054\pi$
$83$	1248.00	1.65043	0.825216	+	0.564818i	$0.191054\pi$
$84$	0	0
$85$	−660.000	−0.842201
$86$	0	0
$87$	693.000	0.853993
$88$	0	0
$89$	−828.000	−0.986155	−0.493078	−	0.869985i	$-0.664128\pi$
$89$	−828.000	−0.986155	−0.493078	+	0.869985i	$0.664128\pi$
$90$	0	0
$91$	−940.000	−1.08284
$92$	0	0
$93$	−1771.00	−1.97467
$94$	0	0
$95$	−730.000	−0.788383
$96$	0	0
$97$	992.000	1.03837	0.519187	−	0.854660i	$-0.326235\pi$
$97$	992.000	1.03837	0.519187	+	0.854660i	$0.326235\pi$
$98$	0	0
$99$	−132.000	−0.134005
$100$	0	0
$101$	−1542.00	−1.51916	−0.759578	−	0.650416i	$-0.774594\pi$
$101$	−1542.00	−1.51916	−0.759578	+	0.650416i	$0.774594\pi$
$102$	0	0
$103$	−32.0000	−0.0306122	−0.0153061	−	0.999883i	$-0.504872\pi$
$103$	−32.0000	−0.0306122	−0.0153061	+	0.999883i	$0.504872\pi$
$104$	0	0
$105$	700.000	0.650600
$106$	0	0
$107$	834.000	0.753512	0.376756	−	0.926312i	$-0.377039\pi$
$107$	834.000	0.753512	0.376756	+	0.926312i	$0.377039\pi$
$108$	0	0
$109$	−1192.00	−1.04746	−0.523729	−	0.851885i	$-0.675460\pi$
$109$	−1192.00	−1.04746	−0.523729	+	0.851885i	$0.675460\pi$
$110$	0	0
$111$	826.000	0.706310
$112$	0	0
$113$	−132.000	−0.109890	−0.0549448	−	0.998489i	$-0.517498\pi$
$113$	−132.000	−0.109890	−0.0549448	+	0.998489i	$0.517498\pi$
$114$	0	0
$115$	−115.000	−0.0932505
$116$	0	0
$117$	1034.00	0.817037
$118$	0	0
$119$	2640.00	2.03368
$120$	0	0
$121$	−1295.00	−0.972953
$122$	0	0
$123$	−3465.00	−2.54007
$124$	0	0
$125$	125.000	0.0894427
$126$	0	0
$127$	−89.0000	−0.0621848	−0.0310924	−	0.999517i	$-0.509899\pi$
$127$	−89.0000	−0.0621848	−0.0310924	+	0.999517i	$0.509899\pi$
$128$	0	0
$129$	1904.00	1.29952
$130$	0	0
$131$	1797.00	1.19851	0.599254	−	0.800559i	$-0.295464\pi$
$131$	1797.00	1.19851	0.599254	+	0.800559i	$0.295464\pi$
$132$	0	0
$133$	2920.00	1.90373
$134$	0	0
$135$	175.000	0.111567
$136$	0	0
$137$	−1836.00	−1.14496	−0.572482	−	0.819917i	$-0.694019\pi$
$137$	−1836.00	−1.14496	−0.572482	+	0.819917i	$0.694019\pi$
$138$	0	0
$139$	1027.00	0.626683	0.313342	−	0.949640i	$-0.398551\pi$
$139$	1027.00	0.626683	0.313342	+	0.949640i	$0.398551\pi$
$140$	0	0
$141$	4473.00	2.67159
$142$	0	0
$143$	−282.000	−0.164909
$144$	0	0
$145$	−495.000	−0.283500
$146$	0	0
$147$	−399.000	−0.223871
$148$	0	0
$149$	2310.00	1.27008	0.635042	−	0.772477i	$-0.280983\pi$
$149$	2310.00	1.27008	0.635042	+	0.772477i	$0.280983\pi$
$150$	0	0
$151$	2149.00	1.15817	0.579083	−	0.815268i	$-0.303411\pi$
$151$	2149.00	1.15817	0.579083	+	0.815268i	$0.303411\pi$
$152$	0	0
$153$	−2904.00	−1.53447
$154$	0	0
$155$	1265.00	0.655531
$156$	0	0
$157$	1832.00	0.931271	0.465635	−	0.884977i	$-0.345826\pi$
$157$	1832.00	0.931271	0.465635	+	0.884977i	$0.345826\pi$
$158$	0	0
$159$	2394.00	1.19407
$160$	0	0
$161$	460.000	0.225174
$162$	0	0
$163$	−1217.00	−0.584802	−0.292401	−	0.956296i	$-0.594454\pi$
$163$	−1217.00	−0.584802	−0.292401	+	0.956296i	$0.594454\pi$
$164$	0	0
$165$	210.000	0.0990817
$166$	0	0
$167$	−3048.00	−1.41234	−0.706172	−	0.708041i	$-0.749579\pi$
$167$	−3048.00	−1.41234	−0.706172	+	0.708041i	$0.749579\pi$
$168$	0	0
$169$	12.0000	0.00546199
$170$	0	0
$171$	−3212.00	−1.43642
$172$	0	0
$173$	774.000	0.340151	0.170076	−	0.985431i	$-0.445599\pi$
$173$	774.000	0.340151	0.170076	+	0.985431i	$0.445599\pi$
$174$	0	0
$175$	−500.000	−0.215980
$176$	0	0
$177$	1680.00	0.713427
$178$	0	0
$179$	1875.00	0.782928	0.391464	−	0.920193i	$-0.371969\pi$
$179$	1875.00	0.782928	0.391464	+	0.920193i	$0.371969\pi$
$180$	0	0
$181$	−1606.00	−0.659520	−0.329760	−	0.944065i	$-0.606968\pi$
$181$	−1606.00	−0.659520	−0.329760	+	0.944065i	$0.606968\pi$
$182$	0	0
$183$	2590.00	1.04622
$184$	0	0
$185$	−590.000	−0.234474
$186$	0	0
$187$	792.000	0.309715
$188$	0	0
$189$	−700.000	−0.269405
$190$	0	0
$191$	−2982.00	−1.12969	−0.564843	−	0.825199i	$-0.691063\pi$
$191$	−2982.00	−1.12969	−0.564843	+	0.825199i	$0.691063\pi$
$192$	0	0
$193$	1385.00	0.516552	0.258276	−	0.966071i	$-0.416846\pi$
$193$	1385.00	0.516552	0.258276	+	0.966071i	$0.416846\pi$
$194$	0	0
$195$	−1645.00	−0.604107
$196$	0	0
$197$	957.000	0.346109	0.173054	−	0.984912i	$-0.444636\pi$
$197$	957.000	0.346109	0.173054	+	0.984912i	$0.444636\pi$
$198$	0	0
$199$	358.000	0.127527	0.0637637	−	0.997965i	$-0.479690\pi$
$199$	358.000	0.127527	0.0637637	+	0.997965i	$0.479690\pi$
$200$	0	0
$201$	4886.00	1.71459
$202$	0	0
$203$	1980.00	0.684575
$204$	0	0
$205$	2475.00	0.843227
$206$	0	0
$207$	−506.000	−0.169901
$208$	0	0
$209$	876.000	0.289924
$210$	0	0
$211$	5380.00	1.75533	0.877665	−	0.479275i	$-0.159100\pi$
$211$	5380.00	1.75533	0.877665	+	0.479275i	$0.159100\pi$
$212$	0	0
$213$	−2499.00	−0.803890
$214$	0	0
$215$	−1360.00	−0.431401
$216$	0	0
$217$	−5060.00	−1.58293
$218$	0	0
$219$	1813.00	0.559412
$220$	0	0
$221$	−6204.00	−1.88835
$222$	0	0
$223$	−1040.00	−0.312303	−0.156151	−	0.987733i	$-0.549909\pi$
$223$	−1040.00	−0.312303	−0.156151	+	0.987733i	$0.549909\pi$
$224$	0	0
$225$	550.000	0.162963
$226$	0	0
$227$	3744.00	1.09470	0.547352	−	0.836902i	$-0.315636\pi$
$227$	3744.00	1.09470	0.547352	+	0.836902i	$0.315636\pi$
$228$	0	0
$229$	2804.00	0.809142	0.404571	−	0.914507i	$-0.367421\pi$
$229$	2804.00	0.809142	0.404571	+	0.914507i	$0.367421\pi$
$230$	0	0
$231$	−840.000	−0.239255
$232$	0	0
$233$	−4869.00	−1.36901	−0.684504	−	0.729009i	$-0.739981\pi$
$233$	−4869.00	−1.36901	−0.684504	+	0.729009i	$0.739981\pi$
$234$	0	0
$235$	−3195.00	−0.886889
$236$	0	0
$237$	3794.00	1.03986
$238$	0	0
$239$	2877.00	0.778651	0.389326	−	0.921100i	$-0.372708\pi$
$239$	2877.00	0.778651	0.389326	+	0.921100i	$0.372708\pi$
$240$	0	0
$241$	1622.00	0.433536	0.216768	−	0.976223i	$-0.430448\pi$
$241$	1622.00	0.433536	0.216768	+	0.976223i	$0.430448\pi$
$242$	0	0
$243$	4928.00	1.30095
$244$	0	0
$245$	285.000	0.0743183
$246$	0	0
$247$	−6862.00	−1.76769
$248$	0	0
$249$	−8736.00	−2.22338
$250$	0	0
$251$	4752.00	1.19499	0.597497	−	0.801871i	$-0.296162\pi$
$251$	4752.00	1.19499	0.597497	+	0.801871i	$0.296162\pi$
$252$	0	0
$253$	138.000	0.0342924
$254$	0	0
$255$	4620.00	1.13457
$256$	0	0
$257$	−5073.00	−1.23130	−0.615652	−	0.788018i	$-0.711107\pi$
$257$	−5073.00	−1.23130	−0.615652	+	0.788018i	$0.711107\pi$
$258$	0	0
$259$	2360.00	0.566190
$260$	0	0
$261$	−2178.00	−0.516532
$262$	0	0
$263$	−1314.00	−0.308079	−0.154039	−	0.988065i	$-0.549228\pi$
$263$	−1314.00	−0.308079	−0.154039	+	0.988065i	$0.549228\pi$
$264$	0	0
$265$	−1710.00	−0.396394
$266$	0	0
$267$	5796.00	1.32850
$268$	0	0
$269$	5265.00	1.19336	0.596678	−	0.802481i	$-0.296487\pi$
$269$	5265.00	1.19336	0.596678	+	0.802481i	$0.296487\pi$
$270$	0	0
$271$	2488.00	0.557695	0.278847	−	0.960335i	$-0.410048\pi$
$271$	2488.00	0.557695	0.278847	+	0.960335i	$0.410048\pi$
$272$	0	0
$273$	6580.00	1.45875
$274$	0	0
$275$	−150.000	−0.0328921
$276$	0	0
$277$	5465.00	1.18542	0.592708	−	0.805418i	$-0.298059\pi$
$277$	5465.00	1.18542	0.592708	+	0.805418i	$0.298059\pi$
$278$	0	0
$279$	5566.00	1.19436
$280$	0	0
$281$	8940.00	1.89792	0.948960	−	0.315396i	$-0.102137\pi$
$281$	8940.00	1.89792	0.948960	+	0.315396i	$0.102137\pi$
$282$	0	0
$283$	−842.000	−0.176861	−0.0884306	−	0.996082i	$-0.528185\pi$
$283$	−842.000	−0.176861	−0.0884306	+	0.996082i	$0.528185\pi$
$284$	0	0
$285$	5110.00	1.06207
$286$	0	0
$287$	−9900.00	−2.03616
$288$	0	0
$289$	12511.0	2.54651
$290$	0	0
$291$	−6944.00	−1.39885
$292$	0	0
$293$	−4032.00	−0.803932	−0.401966	−	0.915655i	$-0.631673\pi$
$293$	−4032.00	−0.803932	−0.401966	+	0.915655i	$0.631673\pi$
$294$	0	0
$295$	−1200.00	−0.236836
$296$	0	0
$297$	−210.000	−0.0410284
$298$	0	0
$299$	−1081.00	−0.209083
$300$	0	0
$301$	5440.00	1.04172
$302$	0	0
$303$	10794.0	2.04653
$304$	0	0
$305$	−1850.00	−0.347314
$306$	0	0
$307$	1096.00	0.203753	0.101876	−	0.994797i	$-0.467515\pi$
$307$	1096.00	0.203753	0.101876	+	0.994797i	$0.467515\pi$
$308$	0	0
$309$	224.000	0.0412392
$310$	0	0
$311$	4653.00	0.848384	0.424192	−	0.905572i	$-0.360558\pi$
$311$	4653.00	0.848384	0.424192	+	0.905572i	$0.360558\pi$
$312$	0	0
$313$	3440.00	0.621215	0.310608	−	0.950538i	$-0.399468\pi$
$313$	3440.00	0.621215	0.310608	+	0.950538i	$0.399468\pi$
$314$	0	0
$315$	−2200.00	−0.393511
$316$	0	0
$317$	3066.00	0.543229	0.271615	−	0.962406i	$-0.412442\pi$
$317$	3066.00	0.543229	0.271615	+	0.962406i	$0.412442\pi$
$318$	0	0
$319$	594.000	0.104256
$320$	0	0
$321$	−5838.00	−1.01509
$322$	0	0
$323$	19272.0	3.31988
$324$	0	0
$325$	1175.00	0.200545
$326$	0	0
$327$	8344.00	1.41108
$328$	0	0
$329$	12780.0	2.14159
$330$	0	0
$331$	−1505.00	−0.249916	−0.124958	−	0.992162i	$-0.539880\pi$
$331$	−1505.00	−0.249916	−0.124958	+	0.992162i	$0.539880\pi$
$332$	0	0
$333$	−2596.00	−0.427207
$334$	0	0
$335$	−3490.00	−0.569191
$336$	0	0
$337$	−3268.00	−0.528247	−0.264124	−	0.964489i	$-0.585083\pi$
$337$	−3268.00	−0.528247	−0.264124	+	0.964489i	$0.585083\pi$
$338$	0	0
$339$	924.000	0.148038
$340$	0	0
$341$	−1518.00	−0.241068
$342$	0	0
$343$	5720.00	0.900440
$344$	0	0
$345$	805.000	0.125622
$346$	0	0
$347$	−4164.00	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−4164.00	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	0	0
$349$	−2911.00	−0.446482	−0.223241	−	0.974763i	$-0.571664\pi$
$349$	−2911.00	−0.446482	−0.223241	+	0.974763i	$0.571664\pi$
$350$	0	0
$351$	1645.00	0.250153
$352$	0	0
$353$	9753.00	1.47054	0.735269	−	0.677776i	$-0.237056\pi$
$353$	9753.00	1.47054	0.735269	+	0.677776i	$0.237056\pi$
$354$	0	0
$355$	1785.00	0.266868
$356$	0	0
$357$	−18480.0	−2.73968
$358$	0	0
$359$	−3858.00	−0.567180	−0.283590	−	0.958946i	$-0.591525\pi$
$359$	−3858.00	−0.567180	−0.283590	+	0.958946i	$0.591525\pi$
$360$	0	0
$361$	14457.0	2.10774
$362$	0	0
$363$	9065.00	1.31071
$364$	0	0
$365$	−1295.00	−0.185708
$366$	0	0
$367$	−7856.00	−1.11738	−0.558692	−	0.829375i	$-0.688697\pi$
$367$	−7856.00	−1.11738	−0.558692	+	0.829375i	$0.688697\pi$
$368$	0	0
$369$	10890.0	1.53634
$370$	0	0
$371$	6840.00	0.957184
$372$	0	0
$373$	−34.0000	−0.00471971	−0.00235986	−	0.999997i	$-0.500751\pi$
$373$	−34.0000	−0.00471971	−0.00235986	+	0.999997i	$0.500751\pi$
$374$	0	0
$375$	−875.000	−0.120493
$376$	0	0
$377$	−4653.00	−0.635654
$378$	0	0
$379$	6064.00	0.821865	0.410932	−	0.911666i	$-0.365203\pi$
$379$	6064.00	0.821865	0.410932	+	0.911666i	$0.365203\pi$
$380$	0	0
$381$	623.000	0.0837723
$382$	0	0
$383$	−11868.0	−1.58336	−0.791679	−	0.610937i	$-0.790793\pi$
$383$	−11868.0	−1.58336	−0.791679	+	0.610937i	$0.790793\pi$
$384$	0	0
$385$	600.000	0.0794255
$386$	0	0
$387$	−5984.00	−0.786005
$388$	0	0
$389$	8616.00	1.12300	0.561502	−	0.827475i	$-0.310224\pi$
$389$	8616.00	1.12300	0.561502	+	0.827475i	$0.310224\pi$
$390$	0	0
$391$	3036.00	0.392678
$392$	0	0
$393$	−12579.0	−1.61457
$394$	0	0
$395$	−2710.00	−0.345202
$396$	0	0
$397$	3119.00	0.394303	0.197151	−	0.980373i	$-0.436831\pi$
$397$	3119.00	0.394303	0.197151	+	0.980373i	$0.436831\pi$
$398$	0	0
$399$	−20440.0	−2.56461
$400$	0	0
$401$	7986.00	0.994518	0.497259	−	0.867602i	$-0.334340\pi$
$401$	7986.00	0.994518	0.497259	+	0.867602i	$0.334340\pi$
$402$	0	0
$403$	11891.0	1.46981
$404$	0	0
$405$	−4195.00	−0.514694
$406$	0	0
$407$	708.000	0.0862267
$408$	0	0
$409$	−3475.00	−0.420117	−0.210058	−	0.977689i	$-0.567365\pi$
$409$	−3475.00	−0.420117	−0.210058	+	0.977689i	$0.567365\pi$
$410$	0	0
$411$	12852.0	1.54244
$412$	0	0
$413$	4800.00	0.571895
$414$	0	0
$415$	6240.00	0.738095
$416$	0	0
$417$	−7189.00	−0.844237
$418$	0	0
$419$	−10992.0	−1.28161	−0.640805	−	0.767704i	$-0.721399\pi$
$419$	−10992.0	−1.28161	−0.640805	+	0.767704i	$0.721399\pi$
$420$	0	0
$421$	2012.00	0.232919	0.116459	−	0.993195i	$-0.462845\pi$
$421$	2012.00	0.232919	0.116459	+	0.993195i	$0.462845\pi$
$422$	0	0
$423$	−14058.0	−1.61589
$424$	0	0
$425$	−3300.00	−0.376644
$426$	0	0
$427$	7400.00	0.838668
$428$	0	0
$429$	1974.00	0.222158
$430$	0	0
$431$	9792.00	1.09435	0.547174	−	0.837019i	$-0.315704\pi$
$431$	9792.00	1.09435	0.547174	+	0.837019i	$0.315704\pi$
$432$	0	0
$433$	5786.00	0.642165	0.321082	−	0.947051i	$-0.395953\pi$
$433$	5786.00	0.642165	0.321082	+	0.947051i	$0.395953\pi$
$434$	0	0
$435$	3465.00	0.381917
$436$	0	0
$437$	3358.00	0.367586
$438$	0	0
$439$	−2549.00	−0.277123	−0.138562	−	0.990354i	$-0.544248\pi$
$439$	−2549.00	−0.277123	−0.138562	+	0.990354i	$0.544248\pi$
$440$	0	0
$441$	1254.00	0.135407
$442$	0	0
$443$	−1311.00	−0.140604	−0.0703019	−	0.997526i	$-0.522396\pi$
$443$	−1311.00	−0.140604	−0.0703019	+	0.997526i	$0.522396\pi$
$444$	0	0
$445$	−4140.00	−0.441022
$446$	0	0
$447$	−16170.0	−1.71099
$448$	0	0
$449$	−14610.0	−1.53561	−0.767805	−	0.640684i	$-0.778651\pi$
$449$	−14610.0	−1.53561	−0.767805	+	0.640684i	$0.778651\pi$
$450$	0	0
$451$	−2970.00	−0.310093
$452$	0	0
$453$	−15043.0	−1.56022
$454$	0	0
$455$	−4700.00	−0.484262
$456$	0	0
$457$	80.0000	0.00818871	0.00409436	−	0.999992i	$-0.498697\pi$
$457$	80.0000	0.00818871	0.00409436	+	0.999992i	$0.498697\pi$
$458$	0	0
$459$	−4620.00	−0.469811
$460$	0	0
$461$	−2343.00	−0.236712	−0.118356	−	0.992971i	$-0.537762\pi$
$461$	−2343.00	−0.236712	−0.118356	+	0.992971i	$0.537762\pi$
$462$	0	0
$463$	3400.00	0.341277	0.170639	−	0.985334i	$-0.445417\pi$
$463$	3400.00	0.341277	0.170639	+	0.985334i	$0.445417\pi$
$464$	0	0
$465$	−8855.00	−0.883098
$466$	0	0
$467$	1374.00	0.136148	0.0680740	−	0.997680i	$-0.478315\pi$
$467$	1374.00	0.136148	0.0680740	+	0.997680i	$0.478315\pi$
$468$	0	0
$469$	13960.0	1.37444
$470$	0	0
$471$	−12824.0	−1.25456
$472$	0	0
$473$	1632.00	0.158646
$474$	0	0
$475$	−3650.00	−0.352576
$476$	0	0
$477$	−7524.00	−0.722223
$478$	0	0
$479$	−4536.00	−0.432683	−0.216341	−	0.976318i	$-0.569412\pi$
$479$	−4536.00	−0.432683	−0.216341	+	0.976318i	$0.569412\pi$
$480$	0	0
$481$	−5546.00	−0.525729
$482$	0	0
$483$	−3220.00	−0.303344
$484$	0	0
$485$	4960.00	0.464375
$486$	0	0
$487$	11455.0	1.06586	0.532932	−	0.846158i	$-0.321090\pi$
$487$	11455.0	1.06586	0.532932	+	0.846158i	$0.321090\pi$
$488$	0	0
$489$	8519.00	0.787817
$490$	0	0
$491$	10395.0	0.955437	0.477719	−	0.878513i	$-0.341464\pi$
$491$	10395.0	0.955437	0.477719	+	0.878513i	$0.341464\pi$
$492$	0	0
$493$	13068.0	1.19382
$494$	0	0
$495$	−660.000	−0.0599289
$496$	0	0
$497$	−7140.00	−0.644412
$498$	0	0
$499$	5497.00	0.493145	0.246573	−	0.969124i	$-0.420696\pi$
$499$	5497.00	0.493145	0.246573	+	0.969124i	$0.420696\pi$
$500$	0	0
$501$	21336.0	1.90264
$502$	0	0
$503$	−7158.00	−0.634512	−0.317256	−	0.948340i	$-0.602761\pi$
$503$	−7158.00	−0.634512	−0.317256	+	0.948340i	$0.602761\pi$
$504$	0	0
$505$	−7710.00	−0.679387
$506$	0	0
$507$	−84.0000	−0.00735813
$508$	0	0
$509$	12801.0	1.11472	0.557362	−	0.830270i	$-0.311814\pi$
$509$	12801.0	1.11472	0.557362	+	0.830270i	$0.311814\pi$
$510$	0	0
$511$	5180.00	0.448434
$512$	0	0
$513$	−5110.00	−0.439789
$514$	0	0
$515$	−160.000	−0.0136902
$516$	0	0
$517$	3834.00	0.326149
$518$	0	0
$519$	−5418.00	−0.458235
$520$	0	0
$521$	16788.0	1.41170	0.705850	−	0.708361i	$-0.250565\pi$
$521$	16788.0	1.41170	0.705850	+	0.708361i	$0.250565\pi$
$522$	0	0
$523$	−19040.0	−1.59189	−0.795947	−	0.605366i	$-0.793027\pi$
$523$	−19040.0	−1.59189	−0.795947	+	0.605366i	$0.793027\pi$
$524$	0	0
$525$	3500.00	0.290957
$526$	0	0
$527$	−33396.0	−2.76044
$528$	0	0
$529$	529.000	0.0434783
$530$	0	0
$531$	−5280.00	−0.431511
$532$	0	0
$533$	23265.0	1.89065
$534$	0	0
$535$	4170.00	0.336981
$536$	0	0
$537$	−13125.0	−1.05472
$538$	0	0
$539$	−342.000	−0.0273302
$540$	0	0
$541$	−13339.0	−1.06005	−0.530026	−	0.847981i	$-0.677818\pi$
$541$	−13339.0	−1.06005	−0.530026	+	0.847981i	$0.677818\pi$
$542$	0	0
$543$	11242.0	0.888472
$544$	0	0
$545$	−5960.00	−0.468437
$546$	0	0
$547$	22975.0	1.79587	0.897934	−	0.440130i	$-0.145068\pi$
$547$	22975.0	1.79587	0.897934	+	0.440130i	$0.145068\pi$
$548$	0	0
$549$	−8140.00	−0.632799
$550$	0	0
$551$	14454.0	1.11753
$552$	0	0
$553$	10840.0	0.833569
$554$	0	0
$555$	4130.00	0.315872
$556$	0	0
$557$	−17964.0	−1.36653	−0.683267	−	0.730169i	$-0.739441\pi$
$557$	−17964.0	−1.36653	−0.683267	+	0.730169i	$0.739441\pi$
$558$	0	0
$559$	−12784.0	−0.967273
$560$	0	0
$561$	−5544.00	−0.417233
$562$	0	0
$563$	−12636.0	−0.945904	−0.472952	−	0.881088i	$-0.656812\pi$
$563$	−12636.0	−0.945904	−0.472952	+	0.881088i	$0.656812\pi$
$564$	0	0
$565$	−660.000	−0.0491441
$566$	0	0
$567$	16780.0	1.24285
$568$	0	0
$569$	−10302.0	−0.759020	−0.379510	−	0.925188i	$-0.623907\pi$
$569$	−10302.0	−0.759020	−0.379510	+	0.925188i	$0.623907\pi$
$570$	0	0
$571$	−12380.0	−0.907333	−0.453666	−	0.891172i	$-0.649884\pi$
$571$	−12380.0	−0.907333	−0.453666	+	0.891172i	$0.649884\pi$
$572$	0	0
$573$	20874.0	1.52186
$574$	0	0
$575$	−575.000	−0.0417029
$576$	0	0
$577$	1913.00	0.138023	0.0690115	−	0.997616i	$-0.478015\pi$
$577$	1913.00	0.138023	0.0690115	+	0.997616i	$0.478015\pi$
$578$	0	0
$579$	−9695.00	−0.695873
$580$	0	0
$581$	−24960.0	−1.78230
$582$	0	0
$583$	2052.00	0.145772
$584$	0	0
$585$	5170.00	0.365390
$586$	0	0
$587$	−16767.0	−1.17896	−0.589479	−	0.807784i	$-0.700667\pi$
$587$	−16767.0	−1.17896	−0.589479	+	0.807784i	$0.700667\pi$
$588$	0	0
$589$	−36938.0	−2.58405
$590$	0	0
$591$	−6699.00	−0.466261
$592$	0	0
$593$	−16722.0	−1.15799	−0.578997	−	0.815330i	$-0.696556\pi$
$593$	−16722.0	−1.15799	−0.578997	+	0.815330i	$0.696556\pi$
$594$	0	0
$595$	13200.0	0.909491
$596$	0	0
$597$	−2506.00	−0.171799
$598$	0	0
$599$	4200.00	0.286490	0.143245	−	0.989687i	$-0.454246\pi$
$599$	4200.00	0.286490	0.143245	+	0.989687i	$0.454246\pi$
$600$	0	0
$601$	−19915.0	−1.35166	−0.675832	−	0.737056i	$-0.736215\pi$
$601$	−19915.0	−1.35166	−0.675832	+	0.737056i	$0.736215\pi$
$602$	0	0
$603$	−15356.0	−1.03706
$604$	0	0
$605$	−6475.00	−0.435118
$606$	0	0
$607$	−24044.0	−1.60777	−0.803885	−	0.594785i	$-0.797237\pi$
$607$	−24044.0	−1.60777	−0.803885	+	0.594785i	$0.797237\pi$
$608$	0	0
$609$	−13860.0	−0.922226
$610$	0	0
$611$	−30033.0	−1.98855
$612$	0	0
$613$	3452.00	0.227447	0.113723	−	0.993512i	$-0.463722\pi$
$613$	3452.00	0.227447	0.113723	+	0.993512i	$0.463722\pi$
$614$	0	0
$615$	−17325.0	−1.13595
$616$	0	0
$617$	−16374.0	−1.06838	−0.534192	−	0.845363i	$-0.679384\pi$
$617$	−16374.0	−1.06838	−0.534192	+	0.845363i	$0.679384\pi$
$618$	0	0
$619$	12760.0	0.828542	0.414271	−	0.910154i	$-0.364037\pi$
$619$	12760.0	0.828542	0.414271	+	0.910154i	$0.364037\pi$
$620$	0	0
$621$	−805.000	−0.0520186
$622$	0	0
$623$	16560.0	1.06495
$624$	0	0
$625$	625.000	0.0400000
$626$	0	0
$627$	−6132.00	−0.390572
$628$	0	0
$629$	15576.0	0.987370
$630$	0	0
$631$	−29420.0	−1.85609	−0.928044	−	0.372470i	$-0.878511\pi$
$631$	−29420.0	−1.85609	−0.928044	+	0.372470i	$0.878511\pi$
$632$	0	0
$633$	−37660.0	−2.36469
$634$	0	0
$635$	−445.000	−0.0278099
$636$	0	0
$637$	2679.00	0.166634
$638$	0	0
$639$	7854.00	0.486228
$640$	0	0
$641$	−13692.0	−0.843684	−0.421842	−	0.906669i	$-0.638616\pi$
$641$	−13692.0	−0.843684	−0.421842	+	0.906669i	$0.638616\pi$
$642$	0	0
$643$	−27398.0	−1.68036	−0.840180	−	0.542307i	$-0.817551\pi$
$643$	−27398.0	−1.68036	−0.840180	+	0.542307i	$0.817551\pi$
$644$	0	0
$645$	9520.00	0.581162
$646$	0	0
$647$	6417.00	0.389920	0.194960	−	0.980811i	$-0.437542\pi$
$647$	6417.00	0.389920	0.194960	+	0.980811i	$0.437542\pi$
$648$	0	0
$649$	1440.00	0.0870954
$650$	0	0
$651$	35420.0	2.13244
$652$	0	0
$653$	14583.0	0.873931	0.436965	−	0.899478i	$-0.356053\pi$
$653$	14583.0	0.873931	0.436965	+	0.899478i	$0.356053\pi$
$654$	0	0
$655$	8985.00	0.535989
$656$	0	0
$657$	−5698.00	−0.338356
$658$	0	0
$659$	9624.00	0.568889	0.284444	−	0.958693i	$-0.408191\pi$
$659$	9624.00	0.568889	0.284444	+	0.958693i	$0.408191\pi$
$660$	0	0
$661$	−24586.0	−1.44672	−0.723362	−	0.690469i	$-0.757404\pi$
$661$	−24586.0	−1.44672	−0.723362	+	0.690469i	$0.757404\pi$
$662$	0	0
$663$	43428.0	2.54390
$664$	0	0
$665$	14600.0	0.851374
$666$	0	0
$667$	2277.00	0.132183
$668$	0	0
$669$	7280.00	0.420719
$670$	0	0
$671$	2220.00	0.127723
$672$	0	0
$673$	14339.0	0.821289	0.410645	−	0.911795i	$-0.365304\pi$
$673$	14339.0	0.821289	0.410645	+	0.911795i	$0.365304\pi$
$674$	0	0
$675$	875.000	0.0498945
$676$	0	0
$677$	14658.0	0.832131	0.416066	−	0.909335i	$-0.363409\pi$
$677$	14658.0	0.832131	0.416066	+	0.909335i	$0.363409\pi$
$678$	0	0
$679$	−19840.0	−1.12134
$680$	0	0
$681$	−26208.0	−1.47473
$682$	0	0
$683$	−16797.0	−0.941024	−0.470512	−	0.882394i	$-0.655931\pi$
$683$	−16797.0	−0.941024	−0.470512	+	0.882394i	$0.655931\pi$
$684$	0	0
$685$	−9180.00	−0.512043
$686$	0	0
$687$	−19628.0	−1.09004
$688$	0	0
$689$	−16074.0	−0.888782
$690$	0	0
$691$	−8132.00	−0.447693	−0.223846	−	0.974624i	$-0.571861\pi$
$691$	−8132.00	−0.447693	−0.223846	+	0.974624i	$0.571861\pi$
$692$	0	0
$693$	2640.00	0.144712
$694$	0	0
$695$	5135.00	0.280261
$696$	0	0
$697$	−65340.0	−3.55083
$698$	0	0
$699$	34083.0	1.84426
$700$	0	0
$701$	19668.0	1.05970	0.529850	−	0.848091i	$-0.322248\pi$
$701$	19668.0	1.05970	0.529850	+	0.848091i	$0.322248\pi$
$702$	0	0
$703$	17228.0	0.924276
$704$	0	0
$705$	22365.0	1.19477
$706$	0	0
$707$	30840.0	1.64053
$708$	0	0
$709$	18200.0	0.964055	0.482028	−	0.876156i	$-0.339900\pi$
$709$	18200.0	0.964055	0.482028	+	0.876156i	$0.339900\pi$
$710$	0	0
$711$	−11924.0	−0.628952
$712$	0	0
$713$	−5819.00	−0.305643
$714$	0	0
$715$	−1410.00	−0.0737497
$716$	0	0
$717$	−20139.0	−1.04896
$718$	0	0
$719$	11880.0	0.616202	0.308101	−	0.951354i	$-0.400307\pi$
$719$	11880.0	0.616202	0.308101	+	0.951354i	$0.400307\pi$
$720$	0	0
$721$	640.000	0.0330580
$722$	0	0
$723$	−11354.0	−0.584038
$724$	0	0
$725$	−2475.00	−0.126785
$726$	0	0
$727$	2554.00	0.130292	0.0651462	−	0.997876i	$-0.479249\pi$
$727$	2554.00	0.130292	0.0651462	+	0.997876i	$0.479249\pi$
$728$	0	0
$729$	−11843.0	−0.601687
$730$	0	0
$731$	35904.0	1.81663
$732$	0	0
$733$	6308.00	0.317860	0.158930	−	0.987290i	$-0.449196\pi$
$733$	6308.00	0.317860	0.158930	+	0.987290i	$0.449196\pi$
$734$	0	0
$735$	−1995.00	−0.100118
$736$	0	0
$737$	4188.00	0.209317
$738$	0	0
$739$	−9557.00	−0.475724	−0.237862	−	0.971299i	$-0.576447\pi$
$739$	−9557.00	−0.475724	−0.237862	+	0.971299i	$0.576447\pi$
$740$	0	0
$741$	48034.0	2.38134
$742$	0	0
$743$	−19128.0	−0.944466	−0.472233	−	0.881474i	$-0.656552\pi$
$743$	−19128.0	−0.944466	−0.472233	+	0.881474i	$0.656552\pi$
$744$	0	0
$745$	11550.0	0.567999
$746$	0	0
$747$	27456.0	1.34480
$748$	0	0
$749$	−16680.0	−0.813717
$750$	0	0
$751$	18448.0	0.896374	0.448187	−	0.893940i	$-0.352070\pi$
$751$	18448.0	0.896374	0.448187	+	0.893940i	$0.352070\pi$
$752$	0	0
$753$	−33264.0	−1.60984
$754$	0	0
$755$	10745.0	0.517948
$756$	0	0
$757$	−5602.00	−0.268967	−0.134484	−	0.990916i	$-0.542938\pi$
$757$	−5602.00	−0.268967	−0.134484	+	0.990916i	$0.542938\pi$
$758$	0	0
$759$	−966.000	−0.0461971
$760$	0	0
$761$	4005.00	0.190777	0.0953884	−	0.995440i	$-0.469591\pi$
$761$	4005.00	0.190777	0.0953884	+	0.995440i	$0.469591\pi$
$762$	0	0
$763$	23840.0	1.13115
$764$	0	0
$765$	−14520.0	−0.686238
$766$	0	0
$767$	−11280.0	−0.531026
$768$	0	0
$769$	41726.0	1.95667	0.978334	−	0.207032i	$-0.0663803\pi$
$769$	41726.0	1.95667	0.978334	+	0.207032i	$0.0663803\pi$
$770$	0	0
$771$	35511.0	1.65875
$772$	0	0
$773$	34116.0	1.58741	0.793705	−	0.608303i	$-0.208150\pi$
$773$	34116.0	1.58741	0.793705	+	0.608303i	$0.208150\pi$
$774$	0	0
$775$	6325.00	0.293162
$776$	0	0
$777$	−16520.0	−0.762743
$778$	0	0
$779$	−72270.0	−3.32393
$780$	0	0
$781$	−2142.00	−0.0981393
$782$	0	0
$783$	−3465.00	−0.158147
$784$	0	0
$785$	9160.00	0.416477
$786$	0	0
$787$	−1652.00	−0.0748252	−0.0374126	−	0.999300i	$-0.511912\pi$
$787$	−1652.00	−0.0748252	−0.0374126	+	0.999300i	$0.511912\pi$
$788$	0	0
$789$	9198.00	0.415028
$790$	0	0
$791$	2640.00	0.118670
$792$	0	0
$793$	−17390.0	−0.778735
$794$	0	0
$795$	11970.0	0.534003
$796$	0	0
$797$	12486.0	0.554927	0.277463	−	0.960736i	$-0.410506\pi$
$797$	12486.0	0.554927	0.277463	+	0.960736i	$0.410506\pi$
$798$	0	0
$799$	84348.0	3.73469
$800$	0	0
$801$	−18216.0	−0.803534
$802$	0	0
$803$	1554.00	0.0682932
$804$	0	0
$805$	2300.00	0.100701
$806$	0	0
$807$	−36855.0	−1.60763
$808$	0	0
$809$	5490.00	0.238589	0.119294	−	0.992859i	$-0.461937\pi$
$809$	5490.00	0.238589	0.119294	+	0.992859i	$0.461937\pi$
$810$	0	0
$811$	14785.0	0.640162	0.320081	−	0.947390i	$-0.396290\pi$
$811$	14785.0	0.640162	0.320081	+	0.947390i	$0.396290\pi$
$812$	0	0
$813$	−17416.0	−0.751299
$814$	0	0
$815$	−6085.00	−0.261532
$816$	0	0
$817$	39712.0	1.70055
$818$	0	0
$819$	−20680.0	−0.882317
$820$	0	0
$821$	−12486.0	−0.530773	−0.265386	−	0.964142i	$-0.585500\pi$
$821$	−12486.0	−0.530773	−0.265386	+	0.964142i	$0.585500\pi$
$822$	0	0
$823$	39805.0	1.68592	0.842962	−	0.537973i	$-0.180810\pi$
$823$	39805.0	1.68592	0.842962	+	0.537973i	$0.180810\pi$
$824$	0	0
$825$	1050.00	0.0443107
$826$	0	0
$827$	−15024.0	−0.631724	−0.315862	−	0.948805i	$-0.602294\pi$
$827$	−15024.0	−0.631724	−0.315862	+	0.948805i	$0.602294\pi$
$828$	0	0
$829$	14618.0	0.612430	0.306215	−	0.951962i	$-0.400937\pi$
$829$	14618.0	0.612430	0.306215	+	0.951962i	$0.400937\pi$
$830$	0	0
$831$	−38255.0	−1.59693
$832$	0	0
$833$	−7524.00	−0.312955
$834$	0	0
$835$	−15240.0	−0.631619
$836$	0	0
$837$	8855.00	0.365679
$838$	0	0
$839$	10152.0	0.417743	0.208871	−	0.977943i	$-0.433021\pi$
$839$	10152.0	0.417743	0.208871	+	0.977943i	$0.433021\pi$
$840$	0	0
$841$	−14588.0	−0.598139
$842$	0	0
$843$	−62580.0	−2.55678
$844$	0	0
$845$	60.0000	0.00244268
$846$	0	0
$847$	25900.0	1.05069
$848$	0	0
$849$	5894.00	0.238259
$850$	0	0
$851$	2714.00	0.109324
$852$	0	0
$853$	−22306.0	−0.895361	−0.447680	−	0.894194i	$-0.647750\pi$
$853$	−22306.0	−0.895361	−0.447680	+	0.894194i	$0.647750\pi$
$854$	0	0
$855$	−16060.0	−0.642386
$856$	0	0
$857$	1731.00	0.0689963	0.0344982	−	0.999405i	$-0.489017\pi$
$857$	1731.00	0.0689963	0.0344982	+	0.999405i	$0.489017\pi$
$858$	0	0
$859$	12649.0	0.502419	0.251210	−	0.967933i	$-0.419172\pi$
$859$	12649.0	0.502419	0.251210	+	0.967933i	$0.419172\pi$
$860$	0	0
$861$	69300.0	2.74302
$862$	0	0
$863$	16143.0	0.636749	0.318374	−	0.947965i	$-0.396863\pi$
$863$	16143.0	0.636749	0.318374	+	0.947965i	$0.396863\pi$
$864$	0	0
$865$	3870.00	0.152120
$866$	0	0
$867$	−87577.0	−3.43053
$868$	0	0
$869$	3252.00	0.126947
$870$	0	0
$871$	−32806.0	−1.27622
$872$	0	0
$873$	21824.0	0.846083
$874$	0	0
$875$	−2500.00	−0.0965891
$876$	0	0
$877$	4094.00	0.157633	0.0788167	−	0.996889i	$-0.474886\pi$
$877$	4094.00	0.157633	0.0788167	+	0.996889i	$0.474886\pi$
$878$	0	0
$879$	28224.0	1.08302
$880$	0	0
$881$	30396.0	1.16239	0.581196	−	0.813764i	$-0.302585\pi$
$881$	30396.0	1.16239	0.581196	+	0.813764i	$0.302585\pi$
$882$	0	0
$883$	21148.0	0.805987	0.402994	−	0.915203i	$-0.367970\pi$
$883$	21148.0	0.805987	0.402994	+	0.915203i	$0.367970\pi$
$884$	0	0
$885$	8400.00	0.319054
$886$	0	0
$887$	−5031.00	−0.190445	−0.0952223	−	0.995456i	$-0.530356\pi$
$887$	−5031.00	−0.190445	−0.0952223	+	0.995456i	$0.530356\pi$
$888$	0	0
$889$	1780.00	0.0671533
$890$	0	0
$891$	5034.00	0.189276
$892$	0	0
$893$	93294.0	3.49604
$894$	0	0
$895$	9375.00	0.350136
$896$	0	0
$897$	7567.00	0.281666
$898$	0	0
$899$	−25047.0	−0.929215
$900$	0	0
$901$	45144.0	1.66922
$902$	0	0
$903$	−38080.0	−1.40335
$904$	0	0
$905$	−8030.00	−0.294946
$906$	0	0
$907$	538.000	0.0196957	0.00984785	−	0.999952i	$-0.496865\pi$
$907$	538.000	0.0196957	0.00984785	+	0.999952i	$0.496865\pi$
$908$	0	0
$909$	−33924.0	−1.23783
$910$	0	0
$911$	−3078.00	−0.111941	−0.0559707	−	0.998432i	$-0.517825\pi$
$911$	−3078.00	−0.111941	−0.0559707	+	0.998432i	$0.517825\pi$
$912$	0	0
$913$	−7488.00	−0.271431
$914$	0	0
$915$	12950.0	0.467884
$916$	0	0
$917$	−35940.0	−1.29427
$918$	0	0
$919$	−20288.0	−0.728226	−0.364113	−	0.931355i	$-0.618628\pi$
$919$	−20288.0	−0.728226	−0.364113	+	0.931355i	$0.618628\pi$
$920$	0	0
$921$	−7672.00	−0.274485
$922$	0	0
$923$	16779.0	0.598361
$924$	0	0
$925$	−2950.00	−0.104860
$926$	0	0
$927$	−704.000	−0.0249433
$928$	0	0
$929$	28911.0	1.02103	0.510516	−	0.859868i	$-0.329454\pi$
$929$	28911.0	1.02103	0.510516	+	0.859868i	$0.329454\pi$
$930$	0	0
$931$	−8322.00	−0.292957
$932$	0	0
$933$	−32571.0	−1.14290
$934$	0	0
$935$	3960.00	0.138509
$936$	0	0
$937$	14810.0	0.516352	0.258176	−	0.966098i	$-0.416879\pi$
$937$	14810.0	0.516352	0.258176	+	0.966098i	$0.416879\pi$
$938$	0	0
$939$	−24080.0	−0.836870
$940$	0	0
$941$	−2544.00	−0.0881318	−0.0440659	−	0.999029i	$-0.514031\pi$
$941$	−2544.00	−0.0881318	−0.0440659	+	0.999029i	$0.514031\pi$
$942$	0	0
$943$	−11385.0	−0.393157
$944$	0	0
$945$	−3500.00	−0.120481
$946$	0	0
$947$	11145.0	0.382433	0.191216	−	0.981548i	$-0.438757\pi$
$947$	11145.0	0.382433	0.191216	+	0.981548i	$0.438757\pi$
$948$	0	0
$949$	−12173.0	−0.416388
$950$	0	0
$951$	−21462.0	−0.731812
$952$	0	0
$953$	−4386.00	−0.149083	−0.0745417	−	0.997218i	$-0.523749\pi$
$953$	−4386.00	−0.149083	−0.0745417	+	0.997218i	$0.523749\pi$
$954$	0	0
$955$	−14910.0	−0.505211
$956$	0	0
$957$	−4158.00	−0.140448
$958$	0	0
$959$	36720.0	1.23644
$960$	0	0
$961$	34218.0	1.14860
$962$	0	0
$963$	18348.0	0.613973
$964$	0	0
$965$	6925.00	0.231009
$966$	0	0
$967$	−56381.0	−1.87496	−0.937482	−	0.348033i	$-0.886850\pi$
$967$	−56381.0	−1.87496	−0.937482	+	0.348033i	$0.886850\pi$
$968$	0	0
$969$	−134904.	−4.47238
$970$	0	0
$971$	−43782.0	−1.44699	−0.723497	−	0.690327i	$-0.757466\pi$
$971$	−43782.0	−1.44699	−0.723497	+	0.690327i	$0.757466\pi$
$972$	0	0
$973$	−20540.0	−0.676755
$974$	0	0
$975$	−8225.00	−0.270165
$976$	0	0
$977$	3714.00	0.121619	0.0608093	−	0.998149i	$-0.480632\pi$
$977$	3714.00	0.121619	0.0608093	+	0.998149i	$0.480632\pi$
$978$	0	0
$979$	4968.00	0.162184
$980$	0	0
$981$	−26224.0	−0.853484
$982$	0	0
$983$	4662.00	0.151266	0.0756331	−	0.997136i	$-0.475902\pi$
$983$	4662.00	0.151266	0.0756331	+	0.997136i	$0.475902\pi$
$984$	0	0
$985$	4785.00	0.154785
$986$	0	0
$987$	−89460.0	−2.88505
$988$	0	0
$989$	6256.00	0.201142
$990$	0	0
$991$	−51440.0	−1.64889	−0.824443	−	0.565945i	$-0.808511\pi$
$991$	−51440.0	−1.64889	−0.824443	+	0.565945i	$0.808511\pi$
$992$	0	0
$993$	10535.0	0.336675
$994$	0	0
$995$	1790.00	0.0570320
$996$	0	0
$997$	686.000	0.0217912	0.0108956	−	0.999941i	$-0.496532\pi$
$997$	686.000	0.0217912	0.0108956	+	0.999941i	$0.496532\pi$
$998$	0	0
$999$	−4130.00	−0.130798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1840.4.a.a.1.1		1
4.3	odd	2		230.4.a.c.1.1	✓	1
12.11	even	2		2070.4.a.j.1.1		1
20.3	even	4		1150.4.b.b.599.2		2
20.7	even	4		1150.4.b.b.599.1		2
20.19	odd	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	4.3	odd	2
1150.4.a.e.1.1		1	20.19	odd	2
1150.4.b.b.599.1		2	20.7	even	4
1150.4.b.b.599.2		2	20.3	even	4
1840.4.a.a.1.1		1	1.1	even	1	trivial
2070.4.a.j.1.1		1	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1840.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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