LMFDB - Embedded newform 435.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,4,Mod(1,435)]

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

lf = mfeigenbasis(mf)

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")

//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);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	435.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:	$25.6658308525$
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	$\chi$	$=$	435.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+5.00000 q^{2} -3.00000 q^{3} +17.0000 q^{4} +5.00000 q^{5} -15.0000 q^{6} +16.0000 q^{7} +45.0000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q+5.00000 q^{2} -3.00000 q^{3} +17.0000 q^{4} +5.00000 q^{5} -15.0000 q^{6} +16.0000 q^{7} +45.0000 q^{8} +9.00000 q^{9} +25.0000 q^{10} -44.0000 q^{11} -51.0000 q^{12} +78.0000 q^{13} +80.0000 q^{14} -15.0000 q^{15} +89.0000 q^{16} +18.0000 q^{17} +45.0000 q^{18} -28.0000 q^{19} +85.0000 q^{20} -48.0000 q^{21} -220.000 q^{22} +184.000 q^{23} -135.000 q^{24} +25.0000 q^{25} +390.000 q^{26} -27.0000 q^{27} +272.000 q^{28} +29.0000 q^{29} -75.0000 q^{30} -224.000 q^{31} +85.0000 q^{32} +132.000 q^{33} +90.0000 q^{34} +80.0000 q^{35} +153.000 q^{36} +254.000 q^{37} -140.000 q^{38} -234.000 q^{39} +225.000 q^{40} -78.0000 q^{41} -240.000 q^{42} -260.000 q^{43} -748.000 q^{44} +45.0000 q^{45} +920.000 q^{46} +312.000 q^{47} -267.000 q^{48} -87.0000 q^{49} +125.000 q^{50} -54.0000 q^{51} +1326.00 q^{52} +574.000 q^{53} -135.000 q^{54} -220.000 q^{55} +720.000 q^{56} +84.0000 q^{57} +145.000 q^{58} +180.000 q^{59} -255.000 q^{60} -610.000 q^{61} -1120.00 q^{62} +144.000 q^{63} -287.000 q^{64} +390.000 q^{65} +660.000 q^{66} -340.000 q^{67} +306.000 q^{68} -552.000 q^{69} +400.000 q^{70} +296.000 q^{71} +405.000 q^{72} +394.000 q^{73} +1270.00 q^{74} -75.0000 q^{75} -476.000 q^{76} -704.000 q^{77} -1170.00 q^{78} -960.000 q^{79} +445.000 q^{80} +81.0000 q^{81} -390.000 q^{82} -908.000 q^{83} -816.000 q^{84} +90.0000 q^{85} -1300.00 q^{86} -87.0000 q^{87} -1980.00 q^{88} -990.000 q^{89} +225.000 q^{90} +1248.00 q^{91} +3128.00 q^{92} +672.000 q^{93} +1560.00 q^{94} -140.000 q^{95} -255.000 q^{96} +1234.00 q^{97} -435.000 q^{98} -396.000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	5.00000	1.76777	0.883883	−	0.467707i	$-0.154920\pi$
$2$	5.00000	1.76777	0.883883	+	0.467707i	$0.154920\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	17.0000	2.12500
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−15.0000	−1.02062
$7$	16.0000	0.863919	0.431959	−	0.901893i	$-0.357822\pi$
$7$	16.0000	0.863919	0.431959	+	0.901893i	$0.357822\pi$
$8$	45.0000	1.98874
$9$	9.00000	0.333333
$10$	25.0000	0.790569
$11$	−44.0000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−44.0000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	−51.0000	−1.22687
$13$	78.0000	1.66410	0.832050	−	0.554700i	$-0.187167\pi$
$13$	78.0000	1.66410	0.832050	+	0.554700i	$0.187167\pi$
$14$	80.0000	1.52721
$15$	−15.0000	−0.258199
$16$	89.0000	1.39062
$17$	18.0000	0.256802	0.128401	−	0.991722i	$-0.459015\pi$
$17$	18.0000	0.256802	0.128401	+	0.991722i	$0.459015\pi$
$18$	45.0000	0.589256
$19$	−28.0000	−0.338086	−0.169043	−	0.985609i	$-0.554068\pi$
$19$	−28.0000	−0.338086	−0.169043	+	0.985609i	$0.554068\pi$
$20$	85.0000	0.950329
$21$	−48.0000	−0.498784
$22$	−220.000	−2.13201
$23$	184.000	1.66812	0.834058	−	0.551677i	$-0.186012\pi$
$23$	184.000	1.66812	0.834058	+	0.551677i	$0.186012\pi$
$24$	−135.000	−1.14820
$25$	25.0000	0.200000
$26$	390.000	2.94174
$27$	−27.0000	−0.192450
$28$	272.000	1.83583
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	−75.0000	−0.456435
$31$	−224.000	−1.29779	−0.648897	−	0.760877i	$-0.724769\pi$
$31$	−224.000	−1.29779	−0.648897	+	0.760877i	$0.724769\pi$
$32$	85.0000	0.469563
$33$	132.000	0.696311
$34$	90.0000	0.453967
$35$	80.0000	0.386356
$36$	153.000	0.708333
$37$	254.000	1.12858	0.564288	−	0.825578i	$-0.309151\pi$
$37$	254.000	1.12858	0.564288	+	0.825578i	$0.309151\pi$
$38$	−140.000	−0.597658
$39$	−234.000	−0.960769
$40$	225.000	0.889391
$41$	−78.0000	−0.297111	−0.148556	−	0.988904i	$-0.547462\pi$
$41$	−78.0000	−0.297111	−0.148556	+	0.988904i	$0.547462\pi$
$42$	−240.000	−0.881733
$43$	−260.000	−0.922084	−0.461042	−	0.887378i	$-0.652524\pi$
$43$	−260.000	−0.922084	−0.461042	+	0.887378i	$0.652524\pi$
$44$	−748.000	−2.56285
$45$	45.0000	0.149071
$46$	920.000	2.94884
$47$	312.000	0.968295	0.484148	−	0.874986i	$-0.339130\pi$
$47$	312.000	0.968295	0.484148	+	0.874986i	$0.339130\pi$
$48$	−267.000	−0.802878
$49$	−87.0000	−0.253644
$50$	125.000	0.353553
$51$	−54.0000	−0.148265
$52$	1326.00	3.53621
$53$	574.000	1.48764	0.743820	−	0.668380i	$-0.233012\pi$
$53$	574.000	1.48764	0.743820	+	0.668380i	$0.233012\pi$
$54$	−135.000	−0.340207
$55$	−220.000	−0.539360
$56$	720.000	1.71811
$57$	84.0000	0.195194
$58$	145.000	0.328266
$59$	180.000	0.397187	0.198593	−	0.980082i	$-0.436363\pi$
$59$	180.000	0.397187	0.198593	+	0.980082i	$0.436363\pi$
$60$	−255.000	−0.548673
$61$	−610.000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−610.000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	−1120.00	−2.29420
$63$	144.000	0.287973
$64$	−287.000	−0.560547
$65$	390.000	0.744208
$66$	660.000	1.23091
$67$	−340.000	−0.619964	−0.309982	−	0.950742i	$-0.600323\pi$
$67$	−340.000	−0.619964	−0.309982	+	0.950742i	$0.600323\pi$
$68$	306.000	0.545705
$69$	−552.000	−0.963087
$70$	400.000	0.682988
$71$	296.000	0.494771	0.247385	−	0.968917i	$-0.420429\pi$
$71$	296.000	0.494771	0.247385	+	0.968917i	$0.420429\pi$
$72$	405.000	0.662913
$73$	394.000	0.631702	0.315851	−	0.948809i	$-0.397710\pi$
$73$	394.000	0.631702	0.315851	+	0.948809i	$0.397710\pi$
$74$	1270.00	1.99506
$75$	−75.0000	−0.115470
$76$	−476.000	−0.718433
$77$	−704.000	−1.04193
$78$	−1170.00	−1.69842
$79$	−960.000	−1.36720	−0.683598	−	0.729859i	$-0.739586\pi$
$79$	−960.000	−1.36720	−0.683598	+	0.729859i	$0.739586\pi$
$80$	445.000	0.621906
$81$	81.0000	0.111111
$82$	−390.000	−0.525223
$83$	−908.000	−1.20079	−0.600397	−	0.799702i	$-0.704991\pi$
$83$	−908.000	−1.20079	−0.600397	+	0.799702i	$0.704991\pi$
$84$	−816.000	−1.05992
$85$	90.0000	0.114846
$86$	−1300.00	−1.63003
$87$	−87.0000	−0.107211
$88$	−1980.00	−2.39851
$89$	−990.000	−1.17910	−0.589549	−	0.807732i	$-0.700695\pi$
$89$	−990.000	−1.17910	−0.589549	+	0.807732i	$0.700695\pi$
$90$	225.000	0.263523
$91$	1248.00	1.43765
$92$	3128.00	3.54475
$93$	672.000	0.749281
$94$	1560.00	1.71172
$95$	−140.000	−0.151197
$96$	−255.000	−0.271102
$97$	1234.00	1.29169	0.645844	−	0.763469i	$-0.276506\pi$
$97$	1234.00	1.29169	0.645844	+	0.763469i	$0.276506\pi$
$98$	−435.000	−0.448384
$99$	−396.000	−0.402015
$100$	425.000	0.425000
$101$	1022.00	1.00686	0.503430	−	0.864036i	$-0.332071\pi$
$101$	1022.00	1.00686	0.503430	+	0.864036i	$0.332071\pi$
$102$	−270.000	−0.262098
$103$	−1248.00	−1.19387	−0.596937	−	0.802288i	$-0.703616\pi$
$103$	−1248.00	−1.19387	−0.596937	+	0.802288i	$0.703616\pi$
$104$	3510.00	3.30946
$105$	−240.000	−0.223063
$106$	2870.00	2.62980
$107$	−116.000	−0.104805	−0.0524025	−	0.998626i	$-0.516688\pi$
$107$	−116.000	−0.104805	−0.0524025	+	0.998626i	$0.516688\pi$
$108$	−459.000	−0.408956
$109$	−826.000	−0.725839	−0.362920	−	0.931820i	$-0.618220\pi$
$109$	−826.000	−0.725839	−0.362920	+	0.931820i	$0.618220\pi$
$110$	−1100.00	−0.953463
$111$	−762.000	−0.651584
$112$	1424.00	1.20139
$113$	−2206.00	−1.83649	−0.918243	−	0.396016i	$-0.870392\pi$
$113$	−2206.00	−1.83649	−0.918243	+	0.396016i	$0.870392\pi$
$114$	420.000	0.345058
$115$	920.000	0.746004
$116$	493.000	0.394603
$117$	702.000	0.554700
$118$	900.000	0.702133
$119$	288.000	0.221856
$120$	−675.000	−0.513490
$121$	605.000	0.454545
$122$	−3050.00	−2.26339
$123$	234.000	0.171537
$124$	−3808.00	−2.75781
$125$	125.000	0.0894427
$126$	720.000	0.509069
$127$	−2056.00	−1.43654	−0.718270	−	0.695765i	$-0.755066\pi$
$127$	−2056.00	−1.43654	−0.718270	+	0.695765i	$0.755066\pi$
$128$	−2115.00	−1.46048
$129$	780.000	0.532366
$130$	1950.00	1.31559
$131$	12.0000	0.00800340	0.00400170	−	0.999992i	$-0.498726\pi$
$131$	12.0000	0.00800340	0.00400170	+	0.999992i	$0.498726\pi$
$132$	2244.00	1.47966
$133$	−448.000	−0.292079
$134$	−1700.00	−1.09595
$135$	−135.000	−0.0860663
$136$	810.000	0.510713
$137$	−2758.00	−1.71994	−0.859970	−	0.510344i	$-0.829518\pi$
$137$	−2758.00	−1.71994	−0.859970	+	0.510344i	$0.829518\pi$
$138$	−2760.00	−1.70251
$139$	−1436.00	−0.876258	−0.438129	−	0.898912i	$-0.644359\pi$
$139$	−1436.00	−0.876258	−0.438129	+	0.898912i	$0.644359\pi$
$140$	1360.00	0.821007
$141$	−936.000	−0.559046
$142$	1480.00	0.874640
$143$	−3432.00	−2.00698
$144$	801.000	0.463542
$145$	145.000	0.0830455
$146$	1970.00	1.11670
$147$	261.000	0.146442
$148$	4318.00	2.39823
$149$	−498.000	−0.273810	−0.136905	−	0.990584i	$-0.543716\pi$
$149$	−498.000	−0.273810	−0.136905	+	0.990584i	$0.543716\pi$
$150$	−375.000	−0.204124
$151$	−2696.00	−1.45296	−0.726481	−	0.687186i	$-0.758846\pi$
$151$	−2696.00	−1.45296	−0.726481	+	0.687186i	$0.758846\pi$
$152$	−1260.00	−0.672365
$153$	162.000	0.0856008
$154$	−3520.00	−1.84188
$155$	−1120.00	−0.580391
$156$	−3978.00	−2.04163
$157$	534.000	0.271451	0.135726	−	0.990746i	$-0.456663\pi$
$157$	534.000	0.271451	0.135726	+	0.990746i	$0.456663\pi$
$158$	−4800.00	−2.41688
$159$	−1722.00	−0.858890
$160$	425.000	0.209995
$161$	2944.00	1.44112
$162$	405.000	0.196419
$163$	1380.00	0.663128	0.331564	−	0.943433i	$-0.392424\pi$
$163$	1380.00	0.663128	0.331564	+	0.943433i	$0.392424\pi$
$164$	−1326.00	−0.631361
$165$	660.000	0.311400
$166$	−4540.00	−2.12272
$167$	2616.00	1.21217	0.606084	−	0.795400i	$-0.292739\pi$
$167$	2616.00	1.21217	0.606084	+	0.795400i	$0.292739\pi$
$168$	−2160.00	−0.991950
$169$	3887.00	1.76923
$170$	450.000	0.203020
$171$	−252.000	−0.112695
$172$	−4420.00	−1.95943
$173$	−330.000	−0.145026	−0.0725128	−	0.997367i	$-0.523102\pi$
$173$	−330.000	−0.145026	−0.0725128	+	0.997367i	$0.523102\pi$
$174$	−435.000	−0.189525
$175$	400.000	0.172784
$176$	−3916.00	−1.67716
$177$	−540.000	−0.229316
$178$	−4950.00	−2.08437
$179$	−372.000	−0.155333	−0.0776664	−	0.996979i	$-0.524747\pi$
$179$	−372.000	−0.155333	−0.0776664	+	0.996979i	$0.524747\pi$
$180$	765.000	0.316776
$181$	−1010.00	−0.414766	−0.207383	−	0.978260i	$-0.566495\pi$
$181$	−1010.00	−0.414766	−0.207383	+	0.978260i	$0.566495\pi$
$182$	6240.00	2.54143
$183$	1830.00	0.739221
$184$	8280.00	3.31744
$185$	1270.00	0.504715
$186$	3360.00	1.32455
$187$	−792.000	−0.309715
$188$	5304.00	2.05763
$189$	−432.000	−0.166261
$190$	−700.000	−0.267281
$191$	2008.00	0.760700	0.380350	−	0.924843i	$-0.375803\pi$
$191$	2008.00	0.760700	0.380350	+	0.924843i	$0.375803\pi$
$192$	861.000	0.323632
$193$	2578.00	0.961495	0.480747	−	0.876859i	$-0.340365\pi$
$193$	2578.00	0.961495	0.480747	+	0.876859i	$0.340365\pi$
$194$	6170.00	2.28340
$195$	−1170.00	−0.429669
$196$	−1479.00	−0.538994
$197$	526.000	0.190233	0.0951166	−	0.995466i	$-0.469678\pi$
$197$	526.000	0.190233	0.0951166	+	0.995466i	$0.469678\pi$
$198$	−1980.00	−0.710669
$199$	4440.00	1.58162	0.790812	−	0.612059i	$-0.209658\pi$
$199$	4440.00	1.58162	0.790812	+	0.612059i	$0.209658\pi$
$200$	1125.00	0.397748
$201$	1020.00	0.357937
$202$	5110.00	1.77989
$203$	464.000	0.160426
$204$	−918.000	−0.315063
$205$	−390.000	−0.132872
$206$	−6240.00	−2.11049
$207$	1656.00	0.556038
$208$	6942.00	2.31414
$209$	1232.00	0.407747
$210$	−1200.00	−0.394323
$211$	308.000	0.100491	0.0502455	−	0.998737i	$-0.484000\pi$
$211$	308.000	0.100491	0.0502455	+	0.998737i	$0.484000\pi$
$212$	9758.00	3.16124
$213$	−888.000	−0.285656
$214$	−580.000	−0.185271
$215$	−1300.00	−0.412369
$216$	−1215.00	−0.382733
$217$	−3584.00	−1.12119
$218$	−4130.00	−1.28311
$219$	−1182.00	−0.364713
$220$	−3740.00	−1.14614
$221$	1404.00	0.427345
$222$	−3810.00	−1.15185
$223$	4120.00	1.23720	0.618600	−	0.785706i	$-0.287700\pi$
$223$	4120.00	1.23720	0.618600	+	0.785706i	$0.287700\pi$
$224$	1360.00	0.405664
$225$	225.000	0.0666667
$226$	−11030.0	−3.24648
$227$	4932.00	1.44206	0.721032	−	0.692902i	$-0.243668\pi$
$227$	4932.00	1.44206	0.721032	+	0.692902i	$0.243668\pi$
$228$	1428.00	0.414788
$229$	−3050.00	−0.880130	−0.440065	−	0.897966i	$-0.645045\pi$
$229$	−3050.00	−0.880130	−0.440065	+	0.897966i	$0.645045\pi$
$230$	4600.00	1.31876
$231$	2112.00	0.601556
$232$	1305.00	0.369299
$233$	82.0000	0.0230558	0.0115279	−	0.999934i	$-0.496330\pi$
$233$	82.0000	0.0230558	0.0115279	+	0.999934i	$0.496330\pi$
$234$	3510.00	0.980581
$235$	1560.00	0.433035
$236$	3060.00	0.844021
$237$	2880.00	0.789351
$238$	1440.00	0.392190
$239$	−5104.00	−1.38138	−0.690691	−	0.723150i	$-0.742694\pi$
$239$	−5104.00	−1.38138	−0.690691	+	0.723150i	$0.742694\pi$
$240$	−1335.00	−0.359058
$241$	−2158.00	−0.576801	−0.288400	−	0.957510i	$-0.593123\pi$
$241$	−2158.00	−0.576801	−0.288400	+	0.957510i	$0.593123\pi$
$242$	3025.00	0.803530
$243$	−243.000	−0.0641500
$244$	−10370.0	−2.72078
$245$	−435.000	−0.113433
$246$	1170.00	0.303238
$247$	−2184.00	−0.562610
$248$	−10080.0	−2.58097
$249$	2724.00	0.693279
$250$	625.000	0.158114
$251$	6116.00	1.53800	0.769001	−	0.639248i	$-0.220754\pi$
$251$	6116.00	1.53800	0.769001	+	0.639248i	$0.220754\pi$
$252$	2448.00	0.611942
$253$	−8096.00	−2.01182
$254$	−10280.0	−2.53947
$255$	−270.000	−0.0663061
$256$	−8279.00	−2.02124
$257$	3418.00	0.829607	0.414803	−	0.909911i	$-0.363850\pi$
$257$	3418.00	0.829607	0.414803	+	0.909911i	$0.363850\pi$
$258$	3900.00	0.941098
$259$	4064.00	0.974999
$260$	6630.00	1.58144
$261$	261.000	0.0618984
$262$	60.0000	0.0141481
$263$	7440.00	1.74437	0.872186	−	0.489174i	$-0.162702\pi$
$263$	7440.00	1.74437	0.872186	+	0.489174i	$0.162702\pi$
$264$	5940.00	1.38478
$265$	2870.00	0.665293
$266$	−2240.00	−0.516328
$267$	2970.00	0.680753
$268$	−5780.00	−1.31742
$269$	6582.00	1.49186	0.745932	−	0.666022i	$-0.232004\pi$
$269$	6582.00	1.49186	0.745932	+	0.666022i	$0.232004\pi$
$270$	−675.000	−0.152145
$271$	−5504.00	−1.23374	−0.616871	−	0.787064i	$-0.711600\pi$
$271$	−5504.00	−1.23374	−0.616871	+	0.787064i	$0.711600\pi$
$272$	1602.00	0.357116
$273$	−3744.00	−0.830026
$274$	−13790.0	−3.04045
$275$	−1100.00	−0.241209
$276$	−9384.00	−2.04656
$277$	3718.00	0.806473	0.403236	−	0.915096i	$-0.367885\pi$
$277$	3718.00	0.806473	0.403236	+	0.915096i	$0.367885\pi$
$278$	−7180.00	−1.54902
$279$	−2016.00	−0.432598
$280$	3600.00	0.768361
$281$	1754.00	0.372366	0.186183	−	0.982515i	$-0.440388\pi$
$281$	1754.00	0.372366	0.186183	+	0.982515i	$0.440388\pi$
$282$	−4680.00	−0.988262
$283$	3572.00	0.750295	0.375147	−	0.926965i	$-0.377592\pi$
$283$	3572.00	0.750295	0.375147	+	0.926965i	$0.377592\pi$
$284$	5032.00	1.05139
$285$	420.000	0.0872935
$286$	−17160.0	−3.54787
$287$	−1248.00	−0.256680
$288$	765.000	0.156521
$289$	−4589.00	−0.934053
$290$	725.000	0.146805
$291$	−3702.00	−0.745756
$292$	6698.00	1.34237
$293$	126.000	0.0251229	0.0125614	−	0.999921i	$-0.496001\pi$
$293$	126.000	0.0251229	0.0125614	+	0.999921i	$0.496001\pi$
$294$	1305.00	0.258875
$295$	900.000	0.177627
$296$	11430.0	2.24444
$297$	1188.00	0.232104
$298$	−2490.00	−0.484033
$299$	14352.0	2.77591
$300$	−1275.00	−0.245374
$301$	−4160.00	−0.796606
$302$	−13480.0	−2.56850
$303$	−3066.00	−0.581311
$304$	−2492.00	−0.470151
$305$	−3050.00	−0.572598
$306$	810.000	0.151322
$307$	−2412.00	−0.448404	−0.224202	−	0.974543i	$-0.571978\pi$
$307$	−2412.00	−0.448404	−0.224202	+	0.974543i	$0.571978\pi$
$308$	−11968.0	−2.21409
$309$	3744.00	0.689284
$310$	−5600.00	−1.02600
$311$	−2928.00	−0.533864	−0.266932	−	0.963715i	$-0.586010\pi$
$311$	−2928.00	−0.533864	−0.266932	+	0.963715i	$0.586010\pi$
$312$	−10530.0	−1.91072
$313$	2874.00	0.519003	0.259502	−	0.965743i	$-0.416442\pi$
$313$	2874.00	0.519003	0.259502	+	0.965743i	$0.416442\pi$
$314$	2670.00	0.479862
$315$	720.000	0.128785
$316$	−16320.0	−2.90529
$317$	−26.0000	−0.00460664	−0.00230332	−	0.999997i	$-0.500733\pi$
$317$	−26.0000	−0.00460664	−0.00230332	+	0.999997i	$0.500733\pi$
$318$	−8610.00	−1.51832
$319$	−1276.00	−0.223957
$320$	−1435.00	−0.250684
$321$	348.000	0.0605092
$322$	14720.0	2.54756
$323$	−504.000	−0.0868214
$324$	1377.00	0.236111
$325$	1950.00	0.332820
$326$	6900.00	1.17226
$327$	2478.00	0.419063
$328$	−3510.00	−0.590876
$329$	4992.00	0.836528
$330$	3300.00	0.550482
$331$	9340.00	1.55098	0.775488	−	0.631363i	$-0.217504\pi$
$331$	9340.00	1.55098	0.775488	+	0.631363i	$0.217504\pi$
$332$	−15436.0	−2.55169
$333$	2286.00	0.376192
$334$	13080.0	2.14283
$335$	−1700.00	−0.277256
$336$	−4272.00	−0.693621
$337$	−10302.0	−1.66524	−0.832620	−	0.553845i	$-0.813160\pi$
$337$	−10302.0	−1.66524	−0.832620	+	0.553845i	$0.813160\pi$
$338$	19435.0	3.12759
$339$	6618.00	1.06030
$340$	1530.00	0.244047
$341$	9856.00	1.56520
$342$	−1260.00	−0.199219
$343$	−6880.00	−1.08305
$344$	−11700.0	−1.83378
$345$	−2760.00	−0.430706
$346$	−1650.00	−0.256372
$347$	−8020.00	−1.24074	−0.620369	−	0.784310i	$-0.713017\pi$
$347$	−8020.00	−1.24074	−0.620369	+	0.784310i	$0.713017\pi$
$348$	−1479.00	−0.227824
$349$	−1306.00	−0.200311	−0.100156	−	0.994972i	$-0.531934\pi$
$349$	−1306.00	−0.200311	−0.100156	+	0.994972i	$0.531934\pi$
$350$	2000.00	0.305441
$351$	−2106.00	−0.320256
$352$	−3740.00	−0.566314
$353$	5658.00	0.853102	0.426551	−	0.904464i	$-0.359728\pi$
$353$	5658.00	0.853102	0.426551	+	0.904464i	$0.359728\pi$
$354$	−2700.00	−0.405377
$355$	1480.00	0.221268
$356$	−16830.0	−2.50558
$357$	−864.000	−0.128089
$358$	−1860.00	−0.274592
$359$	−12240.0	−1.79945	−0.899725	−	0.436457i	$-0.856233\pi$
$359$	−12240.0	−1.79945	−0.899725	+	0.436457i	$0.856233\pi$
$360$	2025.00	0.296464
$361$	−6075.00	−0.885698
$362$	−5050.00	−0.733210
$363$	−1815.00	−0.262432
$364$	21216.0	3.05500
$365$	1970.00	0.282506
$366$	9150.00	1.30677
$367$	8984.00	1.27782	0.638911	−	0.769280i	$-0.279385\pi$
$367$	8984.00	1.27782	0.638911	+	0.769280i	$0.279385\pi$
$368$	16376.0	2.31972
$369$	−702.000	−0.0990370
$370$	6350.00	0.892218
$371$	9184.00	1.28520
$372$	11424.0	1.59222
$373$	−938.000	−0.130209	−0.0651043	−	0.997878i	$-0.520738\pi$
$373$	−938.000	−0.130209	−0.0651043	+	0.997878i	$0.520738\pi$
$374$	−3960.00	−0.547505
$375$	−375.000	−0.0516398
$376$	14040.0	1.92569
$377$	2262.00	0.309016
$378$	−2160.00	−0.293911
$379$	−7796.00	−1.05661	−0.528303	−	0.849056i	$-0.677171\pi$
$379$	−7796.00	−1.05661	−0.528303	+	0.849056i	$0.677171\pi$
$380$	−2380.00	−0.321293
$381$	6168.00	0.829386
$382$	10040.0	1.34474
$383$	−6944.00	−0.926428	−0.463214	−	0.886247i	$-0.653304\pi$
$383$	−6944.00	−0.926428	−0.463214	+	0.886247i	$0.653304\pi$
$384$	6345.00	0.843208
$385$	−3520.00	−0.465963
$386$	12890.0	1.69970
$387$	−2340.00	−0.307361
$388$	20978.0	2.74484
$389$	2126.00	0.277101	0.138551	−	0.990355i	$-0.455756\pi$
$389$	2126.00	0.277101	0.138551	+	0.990355i	$0.455756\pi$
$390$	−5850.00	−0.759555
$391$	3312.00	0.428376
$392$	−3915.00	−0.504432
$393$	−36.0000	−0.00462076
$394$	2630.00	0.336288
$395$	−4800.00	−0.611428
$396$	−6732.00	−0.854282
$397$	−3346.00	−0.423000	−0.211500	−	0.977378i	$-0.567835\pi$
$397$	−3346.00	−0.423000	−0.211500	+	0.977378i	$0.567835\pi$
$398$	22200.0	2.79594
$399$	1344.00	0.168632
$400$	2225.00	0.278125
$401$	12850.0	1.60025	0.800123	−	0.599836i	$-0.204768\pi$
$401$	12850.0	1.60025	0.800123	+	0.599836i	$0.204768\pi$
$402$	5100.00	0.632748
$403$	−17472.0	−2.15966
$404$	17374.0	2.13958
$405$	405.000	0.0496904
$406$	2320.00	0.283595
$407$	−11176.0	−1.36111
$408$	−2430.00	−0.294860
$409$	6122.00	0.740131	0.370065	−	0.929006i	$-0.379335\pi$
$409$	6122.00	0.740131	0.370065	+	0.929006i	$0.379335\pi$
$410$	−1950.00	−0.234887
$411$	8274.00	0.993008
$412$	−21216.0	−2.53698
$413$	2880.00	0.343137
$414$	8280.00	0.982946
$415$	−4540.00	−0.537012
$416$	6630.00	0.781400
$417$	4308.00	0.505908
$418$	6160.00	0.720803
$419$	1372.00	0.159968	0.0799840	−	0.996796i	$-0.474513\pi$
$419$	1372.00	0.159968	0.0799840	+	0.996796i	$0.474513\pi$
$420$	−4080.00	−0.474009
$421$	12150.0	1.40654	0.703272	−	0.710921i	$-0.251722\pi$
$421$	12150.0	1.40654	0.703272	+	0.710921i	$0.251722\pi$
$422$	1540.00	0.177645
$423$	2808.00	0.322765
$424$	25830.0	2.95853
$425$	450.000	0.0513605
$426$	−4440.00	−0.504973
$427$	−9760.00	−1.10613
$428$	−1972.00	−0.222711
$429$	10296.0	1.15873
$430$	−6500.00	−0.728972
$431$	6288.00	0.702743	0.351372	−	0.936236i	$-0.385715\pi$
$431$	6288.00	0.702743	0.351372	+	0.936236i	$0.385715\pi$
$432$	−2403.00	−0.267626
$433$	15650.0	1.73693	0.868465	−	0.495750i	$-0.165107\pi$
$433$	15650.0	1.73693	0.868465	+	0.495750i	$0.165107\pi$
$434$	−17920.0	−1.98200
$435$	−435.000	−0.0479463
$436$	−14042.0	−1.54241
$437$	−5152.00	−0.563967
$438$	−5910.00	−0.644728
$439$	−14520.0	−1.57859	−0.789296	−	0.614013i	$-0.789554\pi$
$439$	−14520.0	−1.57859	−0.789296	+	0.614013i	$0.789554\pi$
$440$	−9900.00	−1.07265
$441$	−783.000	−0.0845481
$442$	7020.00	0.755446
$443$	7372.00	0.790642	0.395321	−	0.918543i	$-0.370633\pi$
$443$	7372.00	0.790642	0.395321	+	0.918543i	$0.370633\pi$
$444$	−12954.0	−1.38462
$445$	−4950.00	−0.527309
$446$	20600.0	2.18708
$447$	1494.00	0.158085
$448$	−4592.00	−0.484267
$449$	10666.0	1.12107	0.560534	−	0.828131i	$-0.310596\pi$
$449$	10666.0	1.12107	0.560534	+	0.828131i	$0.310596\pi$
$450$	1125.00	0.117851
$451$	3432.00	0.358329
$452$	−37502.0	−3.90253
$453$	8088.00	0.838868
$454$	24660.0	2.54923
$455$	6240.00	0.642936
$456$	3780.00	0.388190
$457$	−8006.00	−0.819486	−0.409743	−	0.912201i	$-0.634382\pi$
$457$	−8006.00	−0.819486	−0.409743	+	0.912201i	$0.634382\pi$
$458$	−15250.0	−1.55586
$459$	−486.000	−0.0494217
$460$	15640.0	1.58526
$461$	1254.00	0.126691	0.0633456	−	0.997992i	$-0.479823\pi$
$461$	1254.00	0.126691	0.0633456	+	0.997992i	$0.479823\pi$
$462$	10560.0	1.06341
$463$	−4584.00	−0.460122	−0.230061	−	0.973176i	$-0.573893\pi$
$463$	−4584.00	−0.460122	−0.230061	+	0.973176i	$0.573893\pi$
$464$	2581.00	0.258233
$465$	3360.00	0.335089
$466$	410.000	0.0407573
$467$	11588.0	1.14824	0.574121	−	0.818771i	$-0.305344\pi$
$467$	11588.0	1.14824	0.574121	+	0.818771i	$0.305344\pi$
$468$	11934.0	1.17874
$469$	−5440.00	−0.535599
$470$	7800.00	0.765505
$471$	−1602.00	−0.156722
$472$	8100.00	0.789900
$473$	11440.0	1.11208
$474$	14400.0	1.39539
$475$	−700.000	−0.0676173
$476$	4896.00	0.471445
$477$	5166.00	0.495880
$478$	−25520.0	−2.44196
$479$	−18200.0	−1.73607	−0.868037	−	0.496500i	$-0.834618\pi$
$479$	−18200.0	−1.73607	−0.868037	+	0.496500i	$0.834618\pi$
$480$	−1275.00	−0.121241
$481$	19812.0	1.87807
$482$	−10790.0	−1.01965
$483$	−8832.00	−0.832029
$484$	10285.0	0.965909
$485$	6170.00	0.577660
$486$	−1215.00	−0.113402
$487$	3824.00	0.355815	0.177908	−	0.984047i	$-0.443067\pi$
$487$	3824.00	0.355815	0.177908	+	0.984047i	$0.443067\pi$
$488$	−27450.0	−2.54632
$489$	−4140.00	−0.382857
$490$	−2175.00	−0.200523
$491$	−3100.00	−0.284931	−0.142465	−	0.989800i	$-0.545503\pi$
$491$	−3100.00	−0.284931	−0.142465	+	0.989800i	$0.545503\pi$
$492$	3978.00	0.364516
$493$	522.000	0.0476870
$494$	−10920.0	−0.994563
$495$	−1980.00	−0.179787
$496$	−19936.0	−1.80474
$497$	4736.00	0.427442
$498$	13620.0	1.22556
$499$	19740.0	1.77091	0.885455	−	0.464726i	$-0.153847\pi$
$499$	19740.0	1.77091	0.885455	+	0.464726i	$0.153847\pi$
$500$	2125.00	0.190066
$501$	−7848.00	−0.699846
$502$	30580.0	2.71883
$503$	−6720.00	−0.595686	−0.297843	−	0.954615i	$-0.596267\pi$
$503$	−6720.00	−0.595686	−0.297843	+	0.954615i	$0.596267\pi$
$504$	6480.00	0.572703
$505$	5110.00	0.450281
$506$	−40480.0	−3.55643
$507$	−11661.0	−1.02147
$508$	−34952.0	−3.05265
$509$	10886.0	0.947964	0.473982	−	0.880535i	$-0.342816\pi$
$509$	10886.0	0.947964	0.473982	+	0.880535i	$0.342816\pi$
$510$	−1350.00	−0.117214
$511$	6304.00	0.545739
$512$	−24475.0	−2.11260
$513$	756.000	0.0650647
$514$	17090.0	1.46655
$515$	−6240.00	−0.533917
$516$	13260.0	1.13128
$517$	−13728.0	−1.16781
$518$	20320.0	1.72357
$519$	990.000	0.0837306
$520$	17550.0	1.48004
$521$	22522.0	1.89387	0.946935	−	0.321424i	$-0.104161\pi$
$521$	22522.0	1.89387	0.946935	+	0.321424i	$0.104161\pi$
$522$	1305.00	0.109422
$523$	−13212.0	−1.10463	−0.552314	−	0.833636i	$-0.686255\pi$
$523$	−13212.0	−1.10463	−0.552314	+	0.833636i	$0.686255\pi$
$524$	204.000	0.0170072
$525$	−1200.00	−0.0997567
$526$	37200.0	3.08364
$527$	−4032.00	−0.333276
$528$	11748.0	0.968307
$529$	21689.0	1.78261
$530$	14350.0	1.17608
$531$	1620.00	0.132396
$532$	−7616.00	−0.620668
$533$	−6084.00	−0.494423
$534$	14850.0	1.20341
$535$	−580.000	−0.0468703
$536$	−15300.0	−1.23295
$537$	1116.00	0.0896815
$538$	32910.0	2.63727
$539$	3828.00	0.305907
$540$	−2295.00	−0.182891
$541$	−4642.00	−0.368900	−0.184450	−	0.982842i	$-0.559050\pi$
$541$	−4642.00	−0.368900	−0.184450	+	0.982842i	$0.559050\pi$
$542$	−27520.0	−2.18097
$543$	3030.00	0.239465
$544$	1530.00	0.120585
$545$	−4130.00	−0.324605
$546$	−18720.0	−1.46729
$547$	4060.00	0.317355	0.158677	−	0.987330i	$-0.449277\pi$
$547$	4060.00	0.317355	0.158677	+	0.987330i	$0.449277\pi$
$548$	−46886.0	−3.65487
$549$	−5490.00	−0.426790
$550$	−5500.00	−0.426401
$551$	−812.000	−0.0627811
$552$	−24840.0	−1.91533
$553$	−15360.0	−1.18115
$554$	18590.0	1.42566
$555$	−3810.00	−0.291397
$556$	−24412.0	−1.86205
$557$	−1386.00	−0.105434	−0.0527170	−	0.998609i	$-0.516788\pi$
$557$	−1386.00	−0.105434	−0.0527170	+	0.998609i	$0.516788\pi$
$558$	−10080.0	−0.764732
$559$	−20280.0	−1.53444
$560$	7120.00	0.537277
$561$	2376.00	0.178814
$562$	8770.00	0.658256
$563$	2452.00	0.183551	0.0917757	−	0.995780i	$-0.470746\pi$
$563$	2452.00	0.183551	0.0917757	+	0.995780i	$0.470746\pi$
$564$	−15912.0	−1.18797
$565$	−11030.0	−0.821302
$566$	17860.0	1.32635
$567$	1296.00	0.0959910
$568$	13320.0	0.983970
$569$	−20862.0	−1.53705	−0.768524	−	0.639821i	$-0.779009\pi$
$569$	−20862.0	−1.53705	−0.768524	+	0.639821i	$0.779009\pi$
$570$	2100.00	0.154315
$571$	−9420.00	−0.690394	−0.345197	−	0.938530i	$-0.612188\pi$
$571$	−9420.00	−0.690394	−0.345197	+	0.938530i	$0.612188\pi$
$572$	−58344.0	−4.26483
$573$	−6024.00	−0.439191
$574$	−6240.00	−0.453750
$575$	4600.00	0.333623
$576$	−2583.00	−0.186849
$577$	13202.0	0.952524	0.476262	−	0.879303i	$-0.341991\pi$
$577$	13202.0	0.952524	0.476262	+	0.879303i	$0.341991\pi$
$578$	−22945.0	−1.65119
$579$	−7734.00	−0.555119
$580$	2465.00	0.176472
$581$	−14528.0	−1.03739
$582$	−18510.0	−1.31832
$583$	−25256.0	−1.79416
$584$	17730.0	1.25629
$585$	3510.00	0.248069
$586$	630.000	0.0444114
$587$	−8708.00	−0.612296	−0.306148	−	0.951984i	$-0.599040\pi$
$587$	−8708.00	−0.612296	−0.306148	+	0.951984i	$0.599040\pi$
$588$	4437.00	0.311188
$589$	6272.00	0.438766
$590$	4500.00	0.314004
$591$	−1578.00	−0.109831
$592$	22606.0	1.56943
$593$	−4390.00	−0.304006	−0.152003	−	0.988380i	$-0.548572\pi$
$593$	−4390.00	−0.304006	−0.152003	+	0.988380i	$0.548572\pi$
$594$	5940.00	0.410305
$595$	1440.00	0.0992172
$596$	−8466.00	−0.581847
$597$	−13320.0	−0.913151
$598$	71760.0	4.90716
$599$	−20256.0	−1.38170	−0.690850	−	0.722999i	$-0.742763\pi$
$599$	−20256.0	−1.38170	−0.690850	+	0.722999i	$0.742763\pi$
$600$	−3375.00	−0.229640
$601$	9610.00	0.652246	0.326123	−	0.945327i	$-0.394258\pi$
$601$	9610.00	0.652246	0.326123	+	0.945327i	$0.394258\pi$
$602$	−20800.0	−1.40821
$603$	−3060.00	−0.206655
$604$	−45832.0	−3.08755
$605$	3025.00	0.203279
$606$	−15330.0	−1.02762
$607$	10376.0	0.693820	0.346910	−	0.937898i	$-0.387231\pi$
$607$	10376.0	0.693820	0.346910	+	0.937898i	$0.387231\pi$
$608$	−2380.00	−0.158753
$609$	−1392.00	−0.0926218
$610$	−15250.0	−1.01222
$611$	24336.0	1.61134
$612$	2754.00	0.181902
$613$	6822.00	0.449491	0.224746	−	0.974417i	$-0.427845\pi$
$613$	6822.00	0.449491	0.224746	+	0.974417i	$0.427845\pi$
$614$	−12060.0	−0.792674
$615$	1170.00	0.0767137
$616$	−31680.0	−2.07212
$617$	−20070.0	−1.30954	−0.654771	−	0.755827i	$-0.727235\pi$
$617$	−20070.0	−1.30954	−0.654771	+	0.755827i	$0.727235\pi$
$618$	18720.0	1.21849
$619$	19228.0	1.24853	0.624264	−	0.781214i	$-0.285399\pi$
$619$	19228.0	1.24853	0.624264	+	0.781214i	$0.285399\pi$
$620$	−19040.0	−1.23333
$621$	−4968.00	−0.321029
$622$	−14640.0	−0.943747
$623$	−15840.0	−1.01865
$624$	−20826.0	−1.33607
$625$	625.000	0.0400000
$626$	14370.0	0.917477
$627$	−3696.00	−0.235413
$628$	9078.00	0.576834
$629$	4572.00	0.289821
$630$	3600.00	0.227663
$631$	6552.00	0.413361	0.206681	−	0.978408i	$-0.433734\pi$
$631$	6552.00	0.413361	0.206681	+	0.978408i	$0.433734\pi$
$632$	−43200.0	−2.71899
$633$	−924.000	−0.0580185
$634$	−130.000	−0.00814347
$635$	−10280.0	−0.642440
$636$	−29274.0	−1.82514
$637$	−6786.00	−0.422090
$638$	−6380.00	−0.395904
$639$	2664.00	0.164924
$640$	−10575.0	−0.653146
$641$	−14422.0	−0.888666	−0.444333	−	0.895862i	$-0.646559\pi$
$641$	−14422.0	−0.888666	−0.444333	+	0.895862i	$0.646559\pi$
$642$	1740.00	0.106966
$643$	−6212.00	−0.380991	−0.190496	−	0.981688i	$-0.561009\pi$
$643$	−6212.00	−0.380991	−0.190496	+	0.981688i	$0.561009\pi$
$644$	50048.0	3.06237
$645$	3900.00	0.238081
$646$	−2520.00	−0.153480
$647$	22024.0	1.33826	0.669129	−	0.743146i	$-0.266667\pi$
$647$	22024.0	1.33826	0.669129	+	0.743146i	$0.266667\pi$
$648$	3645.00	0.220971
$649$	−7920.00	−0.479025
$650$	9750.00	0.588348
$651$	10752.0	0.647318
$652$	23460.0	1.40915
$653$	16630.0	0.996604	0.498302	−	0.867004i	$-0.333957\pi$
$653$	16630.0	0.996604	0.498302	+	0.867004i	$0.333957\pi$
$654$	12390.0	0.740806
$655$	60.0000	0.00357923
$656$	−6942.00	−0.413170
$657$	3546.00	0.210567
$658$	24960.0	1.47879
$659$	−24468.0	−1.44634	−0.723170	−	0.690670i	$-0.757316\pi$
$659$	−24468.0	−1.44634	−0.723170	+	0.690670i	$0.757316\pi$
$660$	11220.0	0.661724
$661$	−10226.0	−0.601733	−0.300866	−	0.953666i	$-0.597276\pi$
$661$	−10226.0	−0.601733	−0.300866	+	0.953666i	$0.597276\pi$
$662$	46700.0	2.74176
$663$	−4212.00	−0.246728
$664$	−40860.0	−2.38807
$665$	−2240.00	−0.130622
$666$	11430.0	0.665020
$667$	5336.00	0.309761
$668$	44472.0	2.57586
$669$	−12360.0	−0.714298
$670$	−8500.00	−0.490125
$671$	26840.0	1.54418
$672$	−4080.00	−0.234210
$673$	13458.0	0.770829	0.385414	−	0.922744i	$-0.374059\pi$
$673$	13458.0	0.770829	0.385414	+	0.922744i	$0.374059\pi$
$674$	−51510.0	−2.94376
$675$	−675.000	−0.0384900
$676$	66079.0	3.75962
$677$	22174.0	1.25881	0.629406	−	0.777076i	$-0.283298\pi$
$677$	22174.0	1.25881	0.629406	+	0.777076i	$0.283298\pi$
$678$	33090.0	1.87436
$679$	19744.0	1.11591
$680$	4050.00	0.228398
$681$	−14796.0	−0.832576
$682$	49280.0	2.76690
$683$	−2404.00	−0.134680	−0.0673400	−	0.997730i	$-0.521451\pi$
$683$	−2404.00	−0.134680	−0.0673400	+	0.997730i	$0.521451\pi$
$684$	−4284.00	−0.239478
$685$	−13790.0	−0.769181
$686$	−34400.0	−1.91457
$687$	9150.00	0.508143
$688$	−23140.0	−1.28227
$689$	44772.0	2.47558
$690$	−13800.0	−0.761387
$691$	−5956.00	−0.327897	−0.163949	−	0.986469i	$-0.552423\pi$
$691$	−5956.00	−0.327897	−0.163949	+	0.986469i	$0.552423\pi$
$692$	−5610.00	−0.308179
$693$	−6336.00	−0.347308
$694$	−40100.0	−2.19334
$695$	−7180.00	−0.391875
$696$	−3915.00	−0.213215
$697$	−1404.00	−0.0762988
$698$	−6530.00	−0.354103
$699$	−246.000	−0.0133113
$700$	6800.00	0.367165
$701$	−14586.0	−0.785885	−0.392943	−	0.919563i	$-0.628543\pi$
$701$	−14586.0	−0.785885	−0.392943	+	0.919563i	$0.628543\pi$
$702$	−10530.0	−0.566139
$703$	−7112.00	−0.381556
$704$	12628.0	0.676045
$705$	−4680.00	−0.250013
$706$	28290.0	1.50809
$707$	16352.0	0.869845
$708$	−9180.00	−0.487296
$709$	−4370.00	−0.231479	−0.115740	−	0.993280i	$-0.536924\pi$
$709$	−4370.00	−0.231479	−0.115740	+	0.993280i	$0.536924\pi$
$710$	7400.00	0.391151
$711$	−8640.00	−0.455732
$712$	−44550.0	−2.34492
$713$	−41216.0	−2.16487
$714$	−4320.00	−0.226431
$715$	−17160.0	−0.897549
$716$	−6324.00	−0.330082
$717$	15312.0	0.797541
$718$	−61200.0	−3.18101
$719$	144.000	0.00746912	0.00373456	−	0.999993i	$-0.498811\pi$
$719$	144.000	0.00746912	0.00373456	+	0.999993i	$0.498811\pi$
$720$	4005.00	0.207302
$721$	−19968.0	−1.03141
$722$	−30375.0	−1.56571
$723$	6474.00	0.333016
$724$	−17170.0	−0.881378
$725$	725.000	0.0371391
$726$	−9075.00	−0.463919
$727$	−9632.00	−0.491377	−0.245689	−	0.969349i	$-0.579014\pi$
$727$	−9632.00	−0.491377	−0.245689	+	0.969349i	$0.579014\pi$
$728$	56160.0	2.85910
$729$	729.000	0.0370370
$730$	9850.00	0.499404
$731$	−4680.00	−0.236794
$732$	31110.0	1.57085
$733$	−19306.0	−0.972829	−0.486414	−	0.873728i	$-0.661695\pi$
$733$	−19306.0	−0.972829	−0.486414	+	0.873728i	$0.661695\pi$
$734$	44920.0	2.25889
$735$	1305.00	0.0654907
$736$	15640.0	0.783285
$737$	14960.0	0.747705
$738$	−3510.00	−0.175074
$739$	−36540.0	−1.81887	−0.909435	−	0.415845i	$-0.863486\pi$
$739$	−36540.0	−1.81887	−0.909435	+	0.415845i	$0.863486\pi$
$740$	21590.0	1.07252
$741$	6552.00	0.324823
$742$	45920.0	2.27194
$743$	5408.00	0.267026	0.133513	−	0.991047i	$-0.457374\pi$
$743$	5408.00	0.267026	0.133513	+	0.991047i	$0.457374\pi$
$744$	30240.0	1.49012
$745$	−2490.00	−0.122452
$746$	−4690.00	−0.230178
$747$	−8172.00	−0.400265
$748$	−13464.0	−0.658145
$749$	−1856.00	−0.0905431
$750$	−1875.00	−0.0912871
$751$	−13952.0	−0.677917	−0.338959	−	0.940801i	$-0.610075\pi$
$751$	−13952.0	−0.677917	−0.338959	+	0.940801i	$0.610075\pi$
$752$	27768.0	1.34654
$753$	−18348.0	−0.887966
$754$	11310.0	0.546268
$755$	−13480.0	−0.649785
$756$	−7344.00	−0.353305
$757$	−4274.00	−0.205206	−0.102603	−	0.994722i	$-0.532717\pi$
$757$	−4274.00	−0.205206	−0.102603	+	0.994722i	$0.532717\pi$
$758$	−38980.0	−1.86783
$759$	24288.0	1.16153
$760$	−6300.00	−0.300691
$761$	−230.000	−0.0109560	−0.00547799	−	0.999985i	$-0.501744\pi$
$761$	−230.000	−0.0109560	−0.00547799	+	0.999985i	$0.501744\pi$
$762$	30840.0	1.46616
$763$	−13216.0	−0.627066
$764$	34136.0	1.61649
$765$	810.000	0.0382818
$766$	−34720.0	−1.63771
$767$	14040.0	0.660958
$768$	24837.0	1.16696
$769$	−7854.00	−0.368300	−0.184150	−	0.982898i	$-0.558953\pi$
$769$	−7854.00	−0.368300	−0.184150	+	0.982898i	$0.558953\pi$
$770$	−17600.0	−0.823714
$771$	−10254.0	−0.478974
$772$	43826.0	2.04318
$773$	19550.0	0.909657	0.454828	−	0.890579i	$-0.349701\pi$
$773$	19550.0	0.909657	0.454828	+	0.890579i	$0.349701\pi$
$774$	−11700.0	−0.543343
$775$	−5600.00	−0.259559
$776$	55530.0	2.56883
$777$	−12192.0	−0.562916
$778$	10630.0	0.489851
$779$	2184.00	0.100449
$780$	−19890.0	−0.913046
$781$	−13024.0	−0.596716
$782$	16560.0	0.757269
$783$	−783.000	−0.0357371
$784$	−7743.00	−0.352724
$785$	2670.00	0.121397
$786$	−180.000	−0.00816843
$787$	27228.0	1.23326	0.616629	−	0.787254i	$-0.288498\pi$
$787$	27228.0	1.23326	0.616629	+	0.787254i	$0.288498\pi$
$788$	8942.00	0.404246
$789$	−22320.0	−1.00711
$790$	−24000.0	−1.08086
$791$	−35296.0	−1.58658
$792$	−17820.0	−0.799503
$793$	−47580.0	−2.13066
$794$	−16730.0	−0.747765
$795$	−8610.00	−0.384107
$796$	75480.0	3.36095
$797$	−3386.00	−0.150487	−0.0752436	−	0.997165i	$-0.523973\pi$
$797$	−3386.00	−0.150487	−0.0752436	+	0.997165i	$0.523973\pi$
$798$	6720.00	0.298102
$799$	5616.00	0.248661
$800$	2125.00	0.0939126
$801$	−8910.00	−0.393033
$802$	64250.0	2.82886
$803$	−17336.0	−0.761861
$804$	17340.0	0.760615
$805$	14720.0	0.644487
$806$	−87360.0	−3.81777
$807$	−19746.0	−0.861329
$808$	45990.0	2.00238
$809$	26994.0	1.17313	0.586563	−	0.809904i	$-0.300481\pi$
$809$	26994.0	1.17313	0.586563	+	0.809904i	$0.300481\pi$
$810$	2025.00	0.0878410
$811$	8356.00	0.361799	0.180899	−	0.983502i	$-0.442099\pi$
$811$	8356.00	0.361799	0.180899	+	0.983502i	$0.442099\pi$
$812$	7888.00	0.340905
$813$	16512.0	0.712302
$814$	−55880.0	−2.40613
$815$	6900.00	0.296560
$816$	−4806.00	−0.206181
$817$	7280.00	0.311744
$818$	30610.0	1.30838
$819$	11232.0	0.479216
$820$	−6630.00	−0.282353
$821$	9838.00	0.418208	0.209104	−	0.977893i	$-0.432945\pi$
$821$	9838.00	0.418208	0.209104	+	0.977893i	$0.432945\pi$
$822$	41370.0	1.75541
$823$	−29552.0	−1.25166	−0.625831	−	0.779959i	$-0.715240\pi$
$823$	−29552.0	−1.25166	−0.625831	+	0.779959i	$0.715240\pi$
$824$	−56160.0	−2.37430
$825$	3300.00	0.139262
$826$	14400.0	0.606586
$827$	18556.0	0.780236	0.390118	−	0.920765i	$-0.372434\pi$
$827$	18556.0	0.780236	0.390118	+	0.920765i	$0.372434\pi$
$828$	28152.0	1.18158
$829$	7966.00	0.333740	0.166870	−	0.985979i	$-0.446634\pi$
$829$	7966.00	0.333740	0.166870	+	0.985979i	$0.446634\pi$
$830$	−22700.0	−0.949311
$831$	−11154.0	−0.465617
$832$	−22386.0	−0.932806
$833$	−1566.00	−0.0651365
$834$	21540.0	0.894328
$835$	13080.0	0.542098
$836$	20944.0	0.866463
$837$	6048.00	0.249760
$838$	6860.00	0.282786
$839$	−42048.0	−1.73022	−0.865112	−	0.501578i	$-0.832753\pi$
$839$	−42048.0	−1.73022	−0.865112	+	0.501578i	$0.832753\pi$
$840$	−10800.0	−0.443614
$841$	841.000	0.0344828
$842$	60750.0	2.48644
$843$	−5262.00	−0.214986
$844$	5236.00	0.213543
$845$	19435.0	0.791224
$846$	14040.0	0.570573
$847$	9680.00	0.392690
$848$	51086.0	2.06875
$849$	−10716.0	−0.433183
$850$	2250.00	0.0907934
$851$	46736.0	1.88260
$852$	−15096.0	−0.607019
$853$	29950.0	1.20219	0.601095	−	0.799177i	$-0.294731\pi$
$853$	29950.0	1.20219	0.601095	+	0.799177i	$0.294731\pi$
$854$	−48800.0	−1.95539
$855$	−1260.00	−0.0503989
$856$	−5220.00	−0.208430
$857$	−31454.0	−1.25373	−0.626866	−	0.779127i	$-0.715663\pi$
$857$	−31454.0	−1.25373	−0.626866	+	0.779127i	$0.715663\pi$
$858$	51480.0	2.04837
$859$	−22036.0	−0.875272	−0.437636	−	0.899152i	$-0.644184\pi$
$859$	−22036.0	−0.875272	−0.437636	+	0.899152i	$0.644184\pi$
$860$	−22100.0	−0.876283
$861$	3744.00	0.148194
$862$	31440.0	1.24229
$863$	14048.0	0.554113	0.277056	−	0.960854i	$-0.410641\pi$
$863$	14048.0	0.554113	0.277056	+	0.960854i	$0.410641\pi$
$864$	−2295.00	−0.0903675
$865$	−1650.00	−0.0648574
$866$	78250.0	3.07049
$867$	13767.0	0.539275
$868$	−60928.0	−2.38252
$869$	42240.0	1.64890
$870$	−2175.00	−0.0847579
$871$	−26520.0	−1.03168
$872$	−37170.0	−1.44350
$873$	11106.0	0.430563
$874$	−25760.0	−0.996962
$875$	2000.00	0.0772712
$876$	−20094.0	−0.775015
$877$	−39922.0	−1.53714	−0.768569	−	0.639767i	$-0.779031\pi$
$877$	−39922.0	−1.53714	−0.768569	+	0.639767i	$0.779031\pi$
$878$	−72600.0	−2.79058
$879$	−378.000	−0.0145047
$880$	−19580.0	−0.750047
$881$	38730.0	1.48110	0.740549	−	0.672003i	$-0.234566\pi$
$881$	38730.0	1.48110	0.740549	+	0.672003i	$0.234566\pi$
$882$	−3915.00	−0.149461
$883$	−32948.0	−1.25571	−0.627853	−	0.778332i	$-0.716066\pi$
$883$	−32948.0	−1.25571	−0.627853	+	0.778332i	$0.716066\pi$
$884$	23868.0	0.908108
$885$	−2700.00	−0.102553
$886$	36860.0	1.39767
$887$	−21680.0	−0.820680	−0.410340	−	0.911933i	$-0.634590\pi$
$887$	−21680.0	−0.820680	−0.410340	+	0.911933i	$0.634590\pi$
$888$	−34290.0	−1.29583
$889$	−32896.0	−1.24105
$890$	−24750.0	−0.932159
$891$	−3564.00	−0.134005
$892$	70040.0	2.62905
$893$	−8736.00	−0.327367
$894$	7470.00	0.279457
$895$	−1860.00	−0.0694670
$896$	−33840.0	−1.26174
$897$	−43056.0	−1.60267
$898$	53330.0	1.98179
$899$	−6496.00	−0.240994
$900$	3825.00	0.141667
$901$	10332.0	0.382030
$902$	17160.0	0.633443
$903$	12480.0	0.459921
$904$	−99270.0	−3.65229
$905$	−5050.00	−0.185489
$906$	40440.0	1.48292
$907$	2236.00	0.0818580	0.0409290	−	0.999162i	$-0.486968\pi$
$907$	2236.00	0.0818580	0.0409290	+	0.999162i	$0.486968\pi$
$908$	83844.0	3.06438
$909$	9198.00	0.335620
$910$	31200.0	1.13656
$911$	35816.0	1.30257	0.651283	−	0.758835i	$-0.274231\pi$
$911$	35816.0	1.30257	0.651283	+	0.758835i	$0.274231\pi$
$912$	7476.00	0.271442
$913$	39952.0	1.44821
$914$	−40030.0	−1.44866
$915$	9150.00	0.330590
$916$	−51850.0	−1.87028
$917$	192.000	0.00691428
$918$	−2430.00	−0.0873660
$919$	39704.0	1.42515	0.712576	−	0.701595i	$-0.247529\pi$
$919$	39704.0	1.42515	0.712576	+	0.701595i	$0.247529\pi$
$920$	41400.0	1.48361
$921$	7236.00	0.258886
$922$	6270.00	0.223960
$923$	23088.0	0.823349
$924$	35904.0	1.27831
$925$	6350.00	0.225715
$926$	−22920.0	−0.813389
$927$	−11232.0	−0.397958
$928$	2465.00	0.0871957
$929$	−19534.0	−0.689871	−0.344935	−	0.938626i	$-0.612099\pi$
$929$	−19534.0	−0.689871	−0.344935	+	0.938626i	$0.612099\pi$
$930$	16800.0	0.592359
$931$	2436.00	0.0857537
$932$	1394.00	0.0489935
$933$	8784.00	0.308226
$934$	57940.0	2.02982
$935$	−3960.00	−0.138509
$936$	31590.0	1.10315
$937$	−8678.00	−0.302559	−0.151280	−	0.988491i	$-0.548339\pi$
$937$	−8678.00	−0.302559	−0.151280	+	0.988491i	$0.548339\pi$
$938$	−27200.0	−0.946814
$939$	−8622.00	−0.299647
$940$	26520.0	0.920199
$941$	−7050.00	−0.244233	−0.122117	−	0.992516i	$-0.538968\pi$
$941$	−7050.00	−0.244233	−0.122117	+	0.992516i	$0.538968\pi$
$942$	−8010.00	−0.277049
$943$	−14352.0	−0.495616
$944$	16020.0	0.552337
$945$	−2160.00	−0.0743543
$946$	57200.0	1.96589
$947$	23396.0	0.802817	0.401409	−	0.915899i	$-0.368521\pi$
$947$	23396.0	0.802817	0.401409	+	0.915899i	$0.368521\pi$
$948$	48960.0	1.67737
$949$	30732.0	1.05121
$950$	−3500.00	−0.119532
$951$	78.0000	0.00265965
$952$	12960.0	0.441214
$953$	−36126.0	−1.22795	−0.613975	−	0.789326i	$-0.710430\pi$
$953$	−36126.0	−1.22795	−0.613975	+	0.789326i	$0.710430\pi$
$954$	25830.0	0.876601
$955$	10040.0	0.340196
$956$	−86768.0	−2.93544
$957$	3828.00	0.129302
$958$	−91000.0	−3.06897
$959$	−44128.0	−1.48589
$960$	4305.00	0.144733
$961$	20385.0	0.684267
$962$	99060.0	3.31998
$963$	−1044.00	−0.0349350
$964$	−36686.0	−1.22570
$965$	12890.0	0.429994
$966$	−44160.0	−1.47083
$967$	38624.0	1.28445	0.642225	−	0.766516i	$-0.278011\pi$
$967$	38624.0	1.28445	0.642225	+	0.766516i	$0.278011\pi$
$968$	27225.0	0.903972
$969$	1512.00	0.0501264
$970$	30850.0	1.02117
$971$	−7292.00	−0.241000	−0.120500	−	0.992713i	$-0.538450\pi$
$971$	−7292.00	−0.241000	−0.120500	+	0.992713i	$0.538450\pi$
$972$	−4131.00	−0.136319
$973$	−22976.0	−0.757016
$974$	19120.0	0.628998
$975$	−5850.00	−0.192154
$976$	−54290.0	−1.78051
$977$	−26838.0	−0.878837	−0.439418	−	0.898282i	$-0.644815\pi$
$977$	−26838.0	−0.878837	−0.439418	+	0.898282i	$0.644815\pi$
$978$	−20700.0	−0.676803
$979$	43560.0	1.42205
$980$	−7395.00	−0.241046
$981$	−7434.00	−0.241946
$982$	−15500.0	−0.503691
$983$	20192.0	0.655163	0.327581	−	0.944823i	$-0.393766\pi$
$983$	20192.0	0.655163	0.327581	+	0.944823i	$0.393766\pi$
$984$	10530.0	0.341142
$985$	2630.00	0.0850749
$986$	2610.00	0.0842995
$987$	−14976.0	−0.482970
$988$	−37128.0	−1.19555
$989$	−47840.0	−1.53814
$990$	−9900.00	−0.317821
$991$	34400.0	1.10268	0.551338	−	0.834282i	$-0.314117\pi$
$991$	34400.0	1.10268	0.551338	+	0.834282i	$0.314117\pi$
$992$	−19040.0	−0.609396
$993$	−28020.0	−0.895456
$994$	23680.0	0.755618
$995$	22200.0	0.707324
$996$	46308.0	1.47322
$997$	58430.0	1.85606	0.928032	−	0.372499i	$-0.121499\pi$
$997$	58430.0	1.85606	0.928032	+	0.372499i	$0.121499\pi$
$998$	98700.0	3.13056
$999$	−6858.00	−0.217195

Twists

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

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

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

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