LMFDB - Embedded newform 2175.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2175,4,Mod(1,2175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2175, 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("2175.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2175 = 3 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2175.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:	$128.329154262$
Analytic rank:	$2$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 435)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

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

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	$-0.845080\pi$
$2$	−5.00000	−1.76777	−0.883883	+	0.467707i	$0.845080\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	17.0000	2.12500
$5$	0	0
$5$	0	0
$6$	−15.0000	−1.02062
$7$	−16.0000	−0.863919	−0.431959	−	0.901893i	$-0.642178\pi$
$7$	−16.0000	−0.863919	−0.431959	+	0.901893i	$0.642178\pi$
$8$	−45.0000	−1.98874
$9$	9.00000	0.333333
$10$	0	0
$11$	−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	$-0.812833\pi$
$13$	−78.0000	−1.66410	−0.832050	+	0.554700i	$0.812833\pi$
$14$	80.0000	1.52721
$15$	0	0
$16$	89.0000	1.39062
$17$	−18.0000	−0.256802	−0.128401	−	0.991722i	$-0.540985\pi$
$17$	−18.0000	−0.256802	−0.128401	+	0.991722i	$0.540985\pi$
$18$	−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	$0.554068\pi$
$20$	0	0
$21$	−48.0000	−0.498784
$22$	220.000	2.13201
$23$	−184.000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−184.000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	−135.000	−1.14820
$25$	0	0
$26$	390.000	2.94174
$27$	27.0000	0.192450
$28$	−272.000	−1.83583
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	0	0
$31$	−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
$35$	0	0
$36$	153.000	0.708333
$37$	−254.000	−1.12858	−0.564288	−	0.825578i	$-0.690849\pi$
$37$	−254.000	−1.12858	−0.564288	+	0.825578i	$0.690849\pi$
$38$	140.000	0.597658
$39$	−234.000	−0.960769
$40$	0	0
$41$	−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	$-0.347476\pi$
$43$	260.000	0.922084	0.461042	+	0.887378i	$0.347476\pi$
$44$	−748.000	−2.56285
$45$	0	0
$46$	920.000	2.94884
$47$	−312.000	−0.968295	−0.484148	−	0.874986i	$-0.660870\pi$
$47$	−312.000	−0.968295	−0.484148	+	0.874986i	$0.660870\pi$
$48$	267.000	0.802878
$49$	−87.0000	−0.253644
$50$	0	0
$51$	−54.0000	−0.148265
$52$	−1326.00	−3.53621
$53$	−574.000	−1.48764	−0.743820	−	0.668380i	$-0.766988\pi$
$53$	−574.000	−1.48764	−0.743820	+	0.668380i	$0.766988\pi$
$54$	−135.000	−0.340207
$55$	0	0
$56$	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	$0.436363\pi$
$60$	0	0
$61$	−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
$65$	0	0
$66$	660.000	1.23091
$67$	340.000	0.619964	0.309982	−	0.950742i	$-0.399677\pi$
$67$	340.000	0.619964	0.309982	+	0.950742i	$0.399677\pi$
$68$	−306.000	−0.545705
$69$	−552.000	−0.963087
$70$	0	0
$71$	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	$-0.602290\pi$
$73$	−394.000	−0.631702	−0.315851	+	0.948809i	$0.602290\pi$
$74$	1270.00	1.99506
$75$	0	0
$76$	−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	$0.739586\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	390.000	0.525223
$83$	908.000	1.20079	0.600397	−	0.799702i	$-0.295009\pi$
$83$	908.000	1.20079	0.600397	+	0.799702i	$0.295009\pi$
$84$	−816.000	−1.05992
$85$	0	0
$86$	−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	$0.700695\pi$
$90$	0	0
$91$	1248.00	1.43765
$92$	−3128.00	−3.54475
$93$	−672.000	−0.749281
$94$	1560.00	1.71172
$95$	0	0
$96$	−255.000	−0.271102
$97$	−1234.00	−1.29169	−0.645844	−	0.763469i	$-0.723494\pi$
$97$	−1234.00	−1.29169	−0.645844	+	0.763469i	$0.723494\pi$
$98$	435.000	0.448384
$99$	−396.000	−0.402015
$100$	0	0
$101$	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	$-0.296384\pi$
$103$	1248.00	1.19387	0.596937	+	0.802288i	$0.296384\pi$
$104$	3510.00	3.30946
$105$	0	0
$106$	2870.00	2.62980
$107$	116.000	0.104805	0.0524025	−	0.998626i	$-0.483312\pi$
$107$	116.000	0.104805	0.0524025	+	0.998626i	$0.483312\pi$
$108$	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	$0.618220\pi$
$110$	0	0
$111$	−762.000	−0.651584
$112$	−1424.00	−1.20139
$113$	2206.00	1.83649	0.918243	−	0.396016i	$-0.129608\pi$
$113$	2206.00	1.83649	0.918243	+	0.396016i	$0.129608\pi$
$114$	420.000	0.345058
$115$	0	0
$116$	493.000	0.394603
$117$	−702.000	−0.554700
$118$	−900.000	−0.702133
$119$	288.000	0.221856
$120$	0	0
$121$	605.000	0.454545
$122$	3050.00	2.26339
$123$	−234.000	−0.171537
$124$	−3808.00	−2.75781
$125$	0	0
$126$	720.000	0.509069
$127$	2056.00	1.43654	0.718270	−	0.695765i	$-0.244934\pi$
$127$	2056.00	1.43654	0.718270	+	0.695765i	$0.244934\pi$
$128$	2115.00	1.46048
$129$	780.000	0.532366
$130$	0	0
$131$	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
$135$	0	0
$136$	810.000	0.510713
$137$	2758.00	1.71994	0.859970	−	0.510344i	$-0.170482\pi$
$137$	2758.00	1.71994	0.859970	+	0.510344i	$0.170482\pi$
$138$	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	$0.644359\pi$
$140$	0	0
$141$	−936.000	−0.559046
$142$	−1480.00	−0.874640
$143$	3432.00	2.00698
$144$	801.000	0.463542
$145$	0	0
$146$	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	$0.543716\pi$
$150$	0	0
$151$	−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
$155$	0	0
$156$	−3978.00	−2.04163
$157$	−534.000	−0.271451	−0.135726	−	0.990746i	$-0.543337\pi$
$157$	−534.000	−0.271451	−0.135726	+	0.990746i	$0.543337\pi$
$158$	4800.00	2.41688
$159$	−1722.00	−0.858890
$160$	0	0
$161$	2944.00	1.44112
$162$	−405.000	−0.196419
$163$	−1380.00	−0.663128	−0.331564	−	0.943433i	$-0.607576\pi$
$163$	−1380.00	−0.663128	−0.331564	+	0.943433i	$0.607576\pi$
$164$	−1326.00	−0.631361
$165$	0	0
$166$	−4540.00	−2.12272
$167$	−2616.00	−1.21217	−0.606084	−	0.795400i	$-0.707261\pi$
$167$	−2616.00	−1.21217	−0.606084	+	0.795400i	$0.707261\pi$
$168$	2160.00	0.991950
$169$	3887.00	1.76923
$170$	0	0
$171$	−252.000	−0.112695
$172$	4420.00	1.95943
$173$	330.000	0.145026	0.0725128	−	0.997367i	$-0.476898\pi$
$173$	330.000	0.145026	0.0725128	+	0.997367i	$0.476898\pi$
$174$	−435.000	−0.189525
$175$	0	0
$176$	−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	$0.524747\pi$
$180$	0	0
$181$	−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
$185$	0	0
$186$	3360.00	1.32455
$187$	792.000	0.309715
$188$	−5304.00	−2.05763
$189$	−432.000	−0.166261
$190$	0	0
$191$	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	$-0.659635\pi$
$193$	−2578.00	−0.961495	−0.480747	+	0.876859i	$0.659635\pi$
$194$	6170.00	2.28340
$195$	0	0
$196$	−1479.00	−0.538994
$197$	−526.000	−0.190233	−0.0951166	−	0.995466i	$-0.530322\pi$
$197$	−526.000	−0.190233	−0.0951166	+	0.995466i	$0.530322\pi$
$198$	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	$0.209658\pi$
$200$	0	0
$201$	1020.00	0.357937
$202$	−5110.00	−1.77989
$203$	−464.000	−0.160426
$204$	−918.000	−0.315063
$205$	0	0
$206$	−6240.00	−2.11049
$207$	−1656.00	−0.556038
$208$	−6942.00	−2.31414
$209$	1232.00	0.407747
$210$	0	0
$211$	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
$215$	0	0
$216$	−1215.00	−0.382733
$217$	3584.00	1.12119
$218$	4130.00	1.28311
$219$	−1182.00	−0.364713
$220$	0	0
$221$	1404.00	0.427345
$222$	3810.00	1.15185
$223$	−4120.00	−1.23720	−0.618600	−	0.785706i	$-0.712300\pi$
$223$	−4120.00	−1.23720	−0.618600	+	0.785706i	$0.712300\pi$
$224$	1360.00	0.405664
$225$	0	0
$226$	−11030.0	−3.24648
$227$	−4932.00	−1.44206	−0.721032	−	0.692902i	$-0.756332\pi$
$227$	−4932.00	−1.44206	−0.721032	+	0.692902i	$0.756332\pi$
$228$	−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	$0.645045\pi$
$230$	0	0
$231$	2112.00	0.601556
$232$	−1305.00	−0.369299
$233$	−82.0000	−0.0230558	−0.0115279	−	0.999934i	$-0.503670\pi$
$233$	−82.0000	−0.0230558	−0.0115279	+	0.999934i	$0.503670\pi$
$234$	3510.00	0.980581
$235$	0	0
$236$	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	$0.742694\pi$
$240$	0	0
$241$	−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
$245$	0	0
$246$	1170.00	0.303238
$247$	2184.00	0.562610
$248$	10080.0	2.58097
$249$	2724.00	0.693279
$250$	0	0
$251$	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
$255$	0	0
$256$	−8279.00	−2.02124
$257$	−3418.00	−0.829607	−0.414803	−	0.909911i	$-0.636150\pi$
$257$	−3418.00	−0.829607	−0.414803	+	0.909911i	$0.636150\pi$
$258$	−3900.00	−0.941098
$259$	4064.00	0.974999
$260$	0	0
$261$	261.000	0.0618984
$262$	−60.0000	−0.0141481
$263$	−7440.00	−1.74437	−0.872186	−	0.489174i	$-0.837298\pi$
$263$	−7440.00	−1.74437	−0.872186	+	0.489174i	$0.837298\pi$
$264$	5940.00	1.38478
$265$	0	0
$266$	−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	$0.232004\pi$
$270$	0	0
$271$	−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
$275$	0	0
$276$	−9384.00	−2.04656
$277$	−3718.00	−0.806473	−0.403236	−	0.915096i	$-0.632115\pi$
$277$	−3718.00	−0.806473	−0.403236	+	0.915096i	$0.632115\pi$
$278$	7180.00	1.54902
$279$	−2016.00	−0.432598
$280$	0	0
$281$	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	$-0.622408\pi$
$283$	−3572.00	−0.750295	−0.375147	+	0.926965i	$0.622408\pi$
$284$	5032.00	1.05139
$285$	0	0
$286$	−17160.0	−3.54787
$287$	1248.00	0.256680
$288$	−765.000	−0.156521
$289$	−4589.00	−0.934053
$290$	0	0
$291$	−3702.00	−0.745756
$292$	−6698.00	−1.34237
$293$	−126.000	−0.0251229	−0.0125614	−	0.999921i	$-0.503999\pi$
$293$	−126.000	−0.0251229	−0.0125614	+	0.999921i	$0.503999\pi$
$294$	1305.00	0.258875
$295$	0	0
$296$	11430.0	2.24444
$297$	−1188.00	−0.232104
$298$	2490.00	0.484033
$299$	14352.0	2.77591
$300$	0	0
$301$	−4160.00	−0.796606
$302$	13480.0	2.56850
$303$	3066.00	0.581311
$304$	−2492.00	−0.470151
$305$	0	0
$306$	810.000	0.151322
$307$	2412.00	0.448404	0.224202	−	0.974543i	$-0.428022\pi$
$307$	2412.00	0.448404	0.224202	+	0.974543i	$0.428022\pi$
$308$	11968.0	2.21409
$309$	3744.00	0.689284
$310$	0	0
$311$	−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	$-0.583558\pi$
$313$	−2874.00	−0.519003	−0.259502	+	0.965743i	$0.583558\pi$
$314$	2670.00	0.479862
$315$	0	0
$316$	−16320.0	−2.90529
$317$	26.0000	0.00460664	0.00230332	−	0.999997i	$-0.499267\pi$
$317$	26.0000	0.00460664	0.00230332	+	0.999997i	$0.499267\pi$
$318$	8610.00	1.51832
$319$	−1276.00	−0.223957
$320$	0	0
$321$	348.000	0.0605092
$322$	−14720.0	−2.54756
$323$	504.000	0.0868214
$324$	1377.00	0.236111
$325$	0	0
$326$	6900.00	1.17226
$327$	−2478.00	−0.419063
$328$	3510.00	0.590876
$329$	4992.00	0.836528
$330$	0	0
$331$	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
$335$	0	0
$336$	−4272.00	−0.693621
$337$	10302.0	1.66524	0.832620	−	0.553845i	$-0.186840\pi$
$337$	10302.0	1.66524	0.832620	+	0.553845i	$0.186840\pi$
$338$	−19435.0	−3.12759
$339$	6618.00	1.06030
$340$	0	0
$341$	9856.00	1.56520
$342$	1260.00	0.199219
$343$	6880.00	1.08305
$344$	−11700.0	−1.83378
$345$	0	0
$346$	−1650.00	−0.256372
$347$	8020.00	1.24074	0.620369	−	0.784310i	$-0.286983\pi$
$347$	8020.00	1.24074	0.620369	+	0.784310i	$0.286983\pi$
$348$	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	$0.531934\pi$
$350$	0	0
$351$	−2106.00	−0.320256
$352$	3740.00	0.566314
$353$	−5658.00	−0.853102	−0.426551	−	0.904464i	$-0.640272\pi$
$353$	−5658.00	−0.853102	−0.426551	+	0.904464i	$0.640272\pi$
$354$	−2700.00	−0.405377
$355$	0	0
$356$	−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	$0.856233\pi$
$360$	0	0
$361$	−6075.00	−0.885698
$362$	5050.00	0.733210
$363$	1815.00	0.262432
$364$	21216.0	3.05500
$365$	0	0
$366$	9150.00	1.30677
$367$	−8984.00	−1.27782	−0.638911	−	0.769280i	$-0.720615\pi$
$367$	−8984.00	−1.27782	−0.638911	+	0.769280i	$0.720615\pi$
$368$	−16376.0	−2.31972
$369$	−702.000	−0.0990370
$370$	0	0
$371$	9184.00	1.28520
$372$	−11424.0	−1.59222
$373$	938.000	0.130209	0.0651043	−	0.997878i	$-0.479262\pi$
$373$	938.000	0.130209	0.0651043	+	0.997878i	$0.479262\pi$
$374$	−3960.00	−0.547505
$375$	0	0
$376$	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	$0.677171\pi$
$380$	0	0
$381$	6168.00	0.829386
$382$	−10040.0	−1.34474
$383$	6944.00	0.926428	0.463214	−	0.886247i	$-0.346696\pi$
$383$	6944.00	0.926428	0.463214	+	0.886247i	$0.346696\pi$
$384$	6345.00	0.843208
$385$	0	0
$386$	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	$0.455756\pi$
$390$	0	0
$391$	3312.00	0.428376
$392$	3915.00	0.504432
$393$	36.0000	0.00462076
$394$	2630.00	0.336288
$395$	0	0
$396$	−6732.00	−0.854282
$397$	3346.00	0.423000	0.211500	−	0.977378i	$-0.432165\pi$
$397$	3346.00	0.423000	0.211500	+	0.977378i	$0.432165\pi$
$398$	−22200.0	−2.79594
$399$	1344.00	0.168632
$400$	0	0
$401$	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
$405$	0	0
$406$	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	$0.379335\pi$
$410$	0	0
$411$	8274.00	0.993008
$412$	21216.0	2.53698
$413$	−2880.00	−0.343137
$414$	8280.00	0.982946
$415$	0	0
$416$	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	$0.474513\pi$
$420$	0	0
$421$	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
$425$	0	0
$426$	−4440.00	−0.504973
$427$	9760.00	1.10613
$428$	1972.00	0.222711
$429$	10296.0	1.15873
$430$	0	0
$431$	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	$-0.834893\pi$
$433$	−15650.0	−1.73693	−0.868465	+	0.495750i	$0.834893\pi$
$434$	−17920.0	−1.98200
$435$	0	0
$436$	−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	$0.789554\pi$
$440$	0	0
$441$	−783.000	−0.0845481
$442$	−7020.00	−0.755446
$443$	−7372.00	−0.790642	−0.395321	−	0.918543i	$-0.629367\pi$
$443$	−7372.00	−0.790642	−0.395321	+	0.918543i	$0.629367\pi$
$444$	−12954.0	−1.38462
$445$	0	0
$446$	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	$0.310596\pi$
$450$	0	0
$451$	3432.00	0.358329
$452$	37502.0	3.90253
$453$	−8088.00	−0.838868
$454$	24660.0	2.54923
$455$	0	0
$456$	3780.00	0.388190
$457$	8006.00	0.819486	0.409743	−	0.912201i	$-0.365618\pi$
$457$	8006.00	0.819486	0.409743	+	0.912201i	$0.365618\pi$
$458$	15250.0	1.55586
$459$	−486.000	−0.0494217
$460$	0	0
$461$	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	$-0.426107\pi$
$463$	4584.00	0.460122	0.230061	+	0.973176i	$0.426107\pi$
$464$	2581.00	0.258233
$465$	0	0
$466$	410.000	0.0407573
$467$	−11588.0	−1.14824	−0.574121	−	0.818771i	$-0.694656\pi$
$467$	−11588.0	−1.14824	−0.574121	+	0.818771i	$0.694656\pi$
$468$	−11934.0	−1.17874
$469$	−5440.00	−0.535599
$470$	0	0
$471$	−1602.00	−0.156722
$472$	−8100.00	−0.789900
$473$	−11440.0	−1.11208
$474$	14400.0	1.39539
$475$	0	0
$476$	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	$0.834618\pi$
$480$	0	0
$481$	19812.0	1.87807
$482$	10790.0	1.01965
$483$	8832.00	0.832029
$484$	10285.0	0.965909
$485$	0	0
$486$	−1215.00	−0.113402
$487$	−3824.00	−0.355815	−0.177908	−	0.984047i	$-0.556933\pi$
$487$	−3824.00	−0.355815	−0.177908	+	0.984047i	$0.556933\pi$
$488$	27450.0	2.54632
$489$	−4140.00	−0.382857
$490$	0	0
$491$	−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
$495$	0	0
$496$	−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	$0.153847\pi$
$500$	0	0
$501$	−7848.00	−0.699846
$502$	−30580.0	−2.71883
$503$	6720.00	0.595686	0.297843	−	0.954615i	$-0.403733\pi$
$503$	6720.00	0.595686	0.297843	+	0.954615i	$0.403733\pi$
$504$	6480.00	0.572703
$505$	0	0
$506$	−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	$0.342816\pi$
$510$	0	0
$511$	6304.00	0.545739
$512$	24475.0	2.11260
$513$	−756.000	−0.0650647
$514$	17090.0	1.46655
$515$	0	0
$516$	13260.0	1.13128
$517$	13728.0	1.16781
$518$	−20320.0	−1.72357
$519$	990.000	0.0837306
$520$	0	0
$521$	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	$-0.313745\pi$
$523$	13212.0	1.10463	0.552314	+	0.833636i	$0.313745\pi$
$524$	204.000	0.0170072
$525$	0	0
$526$	37200.0	3.08364
$527$	4032.00	0.333276
$528$	−11748.0	−0.968307
$529$	21689.0	1.78261
$530$	0	0
$531$	1620.00	0.132396
$532$	7616.00	0.620668
$533$	6084.00	0.494423
$534$	14850.0	1.20341
$535$	0	0
$536$	−15300.0	−1.23295
$537$	−1116.00	−0.0896815
$538$	−32910.0	−2.63727
$539$	3828.00	0.305907
$540$	0	0
$541$	−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
$545$	0	0
$546$	−18720.0	−1.46729
$547$	−4060.00	−0.317355	−0.158677	−	0.987330i	$-0.550723\pi$
$547$	−4060.00	−0.317355	−0.158677	+	0.987330i	$0.550723\pi$
$548$	46886.0	3.65487
$549$	−5490.00	−0.426790
$550$	0	0
$551$	−812.000	−0.0627811
$552$	24840.0	1.91533
$553$	15360.0	1.18115
$554$	18590.0	1.42566
$555$	0	0
$556$	−24412.0	−1.86205
$557$	1386.00	0.105434	0.0527170	−	0.998609i	$-0.483212\pi$
$557$	1386.00	0.105434	0.0527170	+	0.998609i	$0.483212\pi$
$558$	10080.0	0.764732
$559$	−20280.0	−1.53444
$560$	0	0
$561$	2376.00	0.178814
$562$	−8770.00	−0.658256
$563$	−2452.00	−0.183551	−0.0917757	−	0.995780i	$-0.529254\pi$
$563$	−2452.00	−0.183551	−0.0917757	+	0.995780i	$0.529254\pi$
$564$	−15912.0	−1.18797
$565$	0	0
$566$	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	$0.779009\pi$
$570$	0	0
$571$	−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
$575$	0	0
$576$	−2583.00	−0.186849
$577$	−13202.0	−0.952524	−0.476262	−	0.879303i	$-0.658009\pi$
$577$	−13202.0	−0.952524	−0.476262	+	0.879303i	$0.658009\pi$
$578$	22945.0	1.65119
$579$	−7734.00	−0.555119
$580$	0	0
$581$	−14528.0	−1.03739
$582$	18510.0	1.31832
$583$	25256.0	1.79416
$584$	17730.0	1.25629
$585$	0	0
$586$	630.000	0.0444114
$587$	8708.00	0.612296	0.306148	−	0.951984i	$-0.400960\pi$
$587$	8708.00	0.612296	0.306148	+	0.951984i	$0.400960\pi$
$588$	−4437.00	−0.311188
$589$	6272.00	0.438766
$590$	0	0
$591$	−1578.00	−0.109831
$592$	−22606.0	−1.56943
$593$	4390.00	0.304006	0.152003	−	0.988380i	$-0.451428\pi$
$593$	4390.00	0.304006	0.152003	+	0.988380i	$0.451428\pi$
$594$	5940.00	0.410305
$595$	0	0
$596$	−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	$0.742763\pi$
$600$	0	0
$601$	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
$605$	0	0
$606$	−15330.0	−1.02762
$607$	−10376.0	−0.693820	−0.346910	−	0.937898i	$-0.612769\pi$
$607$	−10376.0	−0.693820	−0.346910	+	0.937898i	$0.612769\pi$
$608$	2380.00	0.158753
$609$	−1392.00	−0.0926218
$610$	0	0
$611$	24336.0	1.61134
$612$	−2754.00	−0.181902
$613$	−6822.00	−0.449491	−0.224746	−	0.974417i	$-0.572155\pi$
$613$	−6822.00	−0.449491	−0.224746	+	0.974417i	$0.572155\pi$
$614$	−12060.0	−0.792674
$615$	0	0
$616$	−31680.0	−2.07212
$617$	20070.0	1.30954	0.654771	−	0.755827i	$-0.272765\pi$
$617$	20070.0	1.30954	0.654771	+	0.755827i	$0.272765\pi$
$618$	−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	$0.285399\pi$
$620$	0	0
$621$	−4968.00	−0.321029
$622$	14640.0	0.943747
$623$	15840.0	1.01865
$624$	−20826.0	−1.33607
$625$	0	0
$626$	14370.0	0.917477
$627$	3696.00	0.235413
$628$	−9078.00	−0.576834
$629$	4572.00	0.289821
$630$	0	0
$631$	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
$635$	0	0
$636$	−29274.0	−1.82514
$637$	6786.00	0.422090
$638$	6380.00	0.395904
$639$	2664.00	0.164924
$640$	0	0
$641$	−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	$-0.438991\pi$
$643$	6212.00	0.380991	0.190496	+	0.981688i	$0.438991\pi$
$644$	50048.0	3.06237
$645$	0	0
$646$	−2520.00	−0.153480
$647$	−22024.0	−1.33826	−0.669129	−	0.743146i	$-0.733333\pi$
$647$	−22024.0	−1.33826	−0.669129	+	0.743146i	$0.733333\pi$
$648$	−3645.00	−0.220971
$649$	−7920.00	−0.479025
$650$	0	0
$651$	10752.0	0.647318
$652$	−23460.0	−1.40915
$653$	−16630.0	−0.996604	−0.498302	−	0.867004i	$-0.666043\pi$
$653$	−16630.0	−0.996604	−0.498302	+	0.867004i	$0.666043\pi$
$654$	12390.0	0.740806
$655$	0	0
$656$	−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	$0.757316\pi$
$660$	0	0
$661$	−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
$665$	0	0
$666$	11430.0	0.665020
$667$	−5336.00	−0.309761
$668$	−44472.0	−2.57586
$669$	−12360.0	−0.714298
$670$	0	0
$671$	26840.0	1.54418
$672$	4080.00	0.234210
$673$	−13458.0	−0.770829	−0.385414	−	0.922744i	$-0.625941\pi$
$673$	−13458.0	−0.770829	−0.385414	+	0.922744i	$0.625941\pi$
$674$	−51510.0	−2.94376
$675$	0	0
$676$	66079.0	3.75962
$677$	−22174.0	−1.25881	−0.629406	−	0.777076i	$-0.716702\pi$
$677$	−22174.0	−1.25881	−0.629406	+	0.777076i	$0.716702\pi$
$678$	−33090.0	−1.87436
$679$	19744.0	1.11591
$680$	0	0
$681$	−14796.0	−0.832576
$682$	−49280.0	−2.76690
$683$	2404.00	0.134680	0.0673400	−	0.997730i	$-0.478549\pi$
$683$	2404.00	0.134680	0.0673400	+	0.997730i	$0.478549\pi$
$684$	−4284.00	−0.239478
$685$	0	0
$686$	−34400.0	−1.91457
$687$	−9150.00	−0.508143
$688$	23140.0	1.28227
$689$	44772.0	2.47558
$690$	0	0
$691$	−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
$695$	0	0
$696$	−3915.00	−0.213215
$697$	1404.00	0.0762988
$698$	6530.00	0.354103
$699$	−246.000	−0.0133113
$700$	0	0
$701$	−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
$705$	0	0
$706$	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	$0.536924\pi$
$710$	0	0
$711$	−8640.00	−0.455732
$712$	44550.0	2.34492
$713$	41216.0	2.16487
$714$	−4320.00	−0.226431
$715$	0	0
$716$	−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	$0.498811\pi$
$720$	0	0
$721$	−19968.0	−1.03141
$722$	30375.0	1.56571
$723$	−6474.00	−0.333016
$724$	−17170.0	−0.881378
$725$	0	0
$726$	−9075.00	−0.463919
$727$	9632.00	0.491377	0.245689	−	0.969349i	$-0.420986\pi$
$727$	9632.00	0.491377	0.245689	+	0.969349i	$0.420986\pi$
$728$	−56160.0	−2.85910
$729$	729.000	0.0370370
$730$	0	0
$731$	−4680.00	−0.236794
$732$	−31110.0	−1.57085
$733$	19306.0	0.972829	0.486414	−	0.873728i	$-0.338305\pi$
$733$	19306.0	0.972829	0.486414	+	0.873728i	$0.338305\pi$
$734$	44920.0	2.25889
$735$	0	0
$736$	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	$0.863486\pi$
$740$	0	0
$741$	6552.00	0.324823
$742$	−45920.0	−2.27194
$743$	−5408.00	−0.267026	−0.133513	−	0.991047i	$-0.542626\pi$
$743$	−5408.00	−0.267026	−0.133513	+	0.991047i	$0.542626\pi$
$744$	30240.0	1.49012
$745$	0	0
$746$	−4690.00	−0.230178
$747$	8172.00	0.400265
$748$	13464.0	0.658145
$749$	−1856.00	−0.0905431
$750$	0	0
$751$	−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
$755$	0	0
$756$	−7344.00	−0.353305
$757$	4274.00	0.205206	0.102603	−	0.994722i	$-0.467283\pi$
$757$	4274.00	0.205206	0.102603	+	0.994722i	$0.467283\pi$
$758$	38980.0	1.86783
$759$	24288.0	1.16153
$760$	0	0
$761$	−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
$765$	0	0
$766$	−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	$0.558953\pi$
$770$	0	0
$771$	−10254.0	−0.478974
$772$	−43826.0	−2.04318
$773$	−19550.0	−0.909657	−0.454828	−	0.890579i	$-0.650299\pi$
$773$	−19550.0	−0.909657	−0.454828	+	0.890579i	$0.650299\pi$
$774$	−11700.0	−0.543343
$775$	0	0
$776$	55530.0	2.56883
$777$	12192.0	0.562916
$778$	−10630.0	−0.489851
$779$	2184.00	0.100449
$780$	0	0
$781$	−13024.0	−0.596716
$782$	−16560.0	−0.757269
$783$	783.000	0.0357371
$784$	−7743.00	−0.352724
$785$	0	0
$786$	−180.000	−0.00816843
$787$	−27228.0	−1.23326	−0.616629	−	0.787254i	$-0.711502\pi$
$787$	−27228.0	−1.23326	−0.616629	+	0.787254i	$0.711502\pi$
$788$	−8942.00	−0.404246
$789$	−22320.0	−1.00711
$790$	0	0
$791$	−35296.0	−1.58658
$792$	17820.0	0.799503
$793$	47580.0	2.13066
$794$	−16730.0	−0.747765
$795$	0	0
$796$	75480.0	3.36095
$797$	3386.00	0.150487	0.0752436	−	0.997165i	$-0.476027\pi$
$797$	3386.00	0.150487	0.0752436	+	0.997165i	$0.476027\pi$
$798$	−6720.00	−0.298102
$799$	5616.00	0.248661
$800$	0	0
$801$	−8910.00	−0.393033
$802$	−64250.0	−2.82886
$803$	17336.0	0.761861
$804$	17340.0	0.760615
$805$	0	0
$806$	−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	$0.300481\pi$
$810$	0	0
$811$	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
$815$	0	0
$816$	−4806.00	−0.206181
$817$	−7280.00	−0.311744
$818$	−30610.0	−1.30838
$819$	11232.0	0.479216
$820$	0	0
$821$	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	$-0.284760\pi$
$823$	29552.0	1.25166	0.625831	+	0.779959i	$0.284760\pi$
$824$	−56160.0	−2.37430
$825$	0	0
$826$	14400.0	0.606586
$827$	−18556.0	−0.780236	−0.390118	−	0.920765i	$-0.627566\pi$
$827$	−18556.0	−0.780236	−0.390118	+	0.920765i	$0.627566\pi$
$828$	−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	$0.446634\pi$
$830$	0	0
$831$	−11154.0	−0.465617
$832$	22386.0	0.932806
$833$	1566.00	0.0651365
$834$	21540.0	0.894328
$835$	0	0
$836$	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	$0.832753\pi$
$840$	0	0
$841$	841.000	0.0344828
$842$	−60750.0	−2.48644
$843$	5262.00	0.214986
$844$	5236.00	0.213543
$845$	0	0
$846$	14040.0	0.570573
$847$	−9680.00	−0.392690
$848$	−51086.0	−2.06875
$849$	−10716.0	−0.433183
$850$	0	0
$851$	46736.0	1.88260
$852$	15096.0	0.607019
$853$	−29950.0	−1.20219	−0.601095	−	0.799177i	$-0.705269\pi$
$853$	−29950.0	−1.20219	−0.601095	+	0.799177i	$0.705269\pi$
$854$	−48800.0	−1.95539
$855$	0	0
$856$	−5220.00	−0.208430
$857$	31454.0	1.25373	0.626866	−	0.779127i	$-0.284337\pi$
$857$	31454.0	1.25373	0.626866	+	0.779127i	$0.284337\pi$
$858$	−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	$0.644184\pi$
$860$	0	0
$861$	3744.00	0.148194
$862$	−31440.0	−1.24229
$863$	−14048.0	−0.554113	−0.277056	−	0.960854i	$-0.589359\pi$
$863$	−14048.0	−0.554113	−0.277056	+	0.960854i	$0.589359\pi$
$864$	−2295.00	−0.0903675
$865$	0	0
$866$	78250.0	3.07049
$867$	−13767.0	−0.539275
$868$	60928.0	2.38252
$869$	42240.0	1.64890
$870$	0	0
$871$	−26520.0	−1.03168
$872$	37170.0	1.44350
$873$	−11106.0	−0.430563
$874$	−25760.0	−0.996962
$875$	0	0
$876$	−20094.0	−0.775015
$877$	39922.0	1.53714	0.768569	−	0.639767i	$-0.220969\pi$
$877$	39922.0	1.53714	0.768569	+	0.639767i	$0.220969\pi$
$878$	72600.0	2.79058
$879$	−378.000	−0.0145047
$880$	0	0
$881$	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	$-0.283934\pi$
$883$	32948.0	1.25571	0.627853	+	0.778332i	$0.283934\pi$
$884$	23868.0	0.908108
$885$	0	0
$886$	36860.0	1.39767
$887$	21680.0	0.820680	0.410340	−	0.911933i	$-0.365410\pi$
$887$	21680.0	0.820680	0.410340	+	0.911933i	$0.365410\pi$
$888$	34290.0	1.29583
$889$	−32896.0	−1.24105
$890$	0	0
$891$	−3564.00	−0.134005
$892$	−70040.0	−2.62905
$893$	8736.00	0.327367
$894$	7470.00	0.279457
$895$	0	0
$896$	−33840.0	−1.26174
$897$	43056.0	1.60267
$898$	−53330.0	−1.98179
$899$	−6496.00	−0.240994
$900$	0	0
$901$	10332.0	0.382030
$902$	−17160.0	−0.633443
$903$	−12480.0	−0.459921
$904$	−99270.0	−3.65229
$905$	0	0
$906$	40440.0	1.48292
$907$	−2236.00	−0.0818580	−0.0409290	−	0.999162i	$-0.513032\pi$
$907$	−2236.00	−0.0818580	−0.0409290	+	0.999162i	$0.513032\pi$
$908$	−83844.0	−3.06438
$909$	9198.00	0.335620
$910$	0	0
$911$	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
$915$	0	0
$916$	−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	$0.247529\pi$
$920$	0	0
$921$	7236.00	0.258886
$922$	−6270.00	−0.223960
$923$	−23088.0	−0.823349
$924$	35904.0	1.27831
$925$	0	0
$926$	−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	$0.612099\pi$
$930$	0	0
$931$	2436.00	0.0857537
$932$	−1394.00	−0.0489935
$933$	−8784.00	−0.308226
$934$	57940.0	2.02982
$935$	0	0
$936$	31590.0	1.10315
$937$	8678.00	0.302559	0.151280	−	0.988491i	$-0.451661\pi$
$937$	8678.00	0.302559	0.151280	+	0.988491i	$0.451661\pi$
$938$	27200.0	0.946814
$939$	−8622.00	−0.299647
$940$	0	0
$941$	−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
$945$	0	0
$946$	57200.0	1.96589
$947$	−23396.0	−0.802817	−0.401409	−	0.915899i	$-0.631479\pi$
$947$	−23396.0	−0.802817	−0.401409	+	0.915899i	$0.631479\pi$
$948$	−48960.0	−1.67737
$949$	30732.0	1.05121
$950$	0	0
$951$	78.0000	0.00265965
$952$	−12960.0	−0.441214
$953$	36126.0	1.22795	0.613975	−	0.789326i	$-0.289570\pi$
$953$	36126.0	1.22795	0.613975	+	0.789326i	$0.289570\pi$
$954$	25830.0	0.876601
$955$	0	0
$956$	−86768.0	−2.93544
$957$	−3828.00	−0.129302
$958$	91000.0	3.06897
$959$	−44128.0	−1.48589
$960$	0	0
$961$	20385.0	0.684267
$962$	−99060.0	−3.31998
$963$	1044.00	0.0349350
$964$	−36686.0	−1.22570
$965$	0	0
$966$	−44160.0	−1.47083
$967$	−38624.0	−1.28445	−0.642225	−	0.766516i	$-0.721989\pi$
$967$	−38624.0	−1.28445	−0.642225	+	0.766516i	$0.721989\pi$
$968$	−27225.0	−0.903972
$969$	1512.00	0.0501264
$970$	0	0
$971$	−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
$975$	0	0
$976$	−54290.0	−1.78051
$977$	26838.0	0.878837	0.439418	−	0.898282i	$-0.355185\pi$
$977$	26838.0	0.878837	0.439418	+	0.898282i	$0.355185\pi$
$978$	20700.0	0.676803
$979$	43560.0	1.42205
$980$	0	0
$981$	−7434.00	−0.241946
$982$	15500.0	0.503691
$983$	−20192.0	−0.655163	−0.327581	−	0.944823i	$-0.606234\pi$
$983$	−20192.0	−0.655163	−0.327581	+	0.944823i	$0.606234\pi$
$984$	10530.0	0.341142
$985$	0	0
$986$	2610.00	0.0842995
$987$	14976.0	0.482970
$988$	37128.0	1.19555
$989$	−47840.0	−1.53814
$990$	0	0
$991$	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
$995$	0	0
$996$	46308.0	1.47322
$997$	−58430.0	−1.85606	−0.928032	−	0.372499i	$-0.878501\pi$
$997$	−58430.0	−1.85606	−0.928032	+	0.372499i	$0.878501\pi$
$998$	−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	2175.4.a.a.1.1		1
5.4	even	2		435.4.a.c.1.1	✓	1
15.14	odd	2		1305.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.c.1.1	✓	1	5.4	even	2
1305.4.a.a.1.1		1	15.14	odd	2
2175.4.a.a.1.1		1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2175 = 3 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2175.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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