LMFDB - Embedded newform 175.6.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,6,Mod(1,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("175.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	175.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:	$28.0671684673$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+10.0000 q^{2} +14.0000 q^{3} +68.0000 q^{4} +140.000 q^{6} +49.0000 q^{7} +360.000 q^{8} -47.0000 q^{9} +O(q^{10})$

\(q+10.0000 q^{2} +14.0000 q^{3} +68.0000 q^{4} +140.000 q^{6} +49.0000 q^{7} +360.000 q^{8} -47.0000 q^{9} +232.000 q^{11} +952.000 q^{12} +140.000 q^{13} +490.000 q^{14} +1424.00 q^{16} +1722.00 q^{17} -470.000 q^{18} -98.0000 q^{19} +686.000 q^{21} +2320.00 q^{22} -1824.00 q^{23} +5040.00 q^{24} +1400.00 q^{26} -4060.00 q^{27} +3332.00 q^{28} +3418.00 q^{29} -7644.00 q^{31} +2720.00 q^{32} +3248.00 q^{33} +17220.0 q^{34} -3196.00 q^{36} +10398.0 q^{37} -980.000 q^{38} +1960.00 q^{39} -17962.0 q^{41} +6860.00 q^{42} -10880.0 q^{43} +15776.0 q^{44} -18240.0 q^{46} -9324.00 q^{47} +19936.0 q^{48} +2401.00 q^{49} +24108.0 q^{51} +9520.00 q^{52} -2262.00 q^{53} -40600.0 q^{54} +17640.0 q^{56} -1372.00 q^{57} +34180.0 q^{58} -2730.00 q^{59} +25648.0 q^{61} -76440.0 q^{62} -2303.00 q^{63} -18368.0 q^{64} +32480.0 q^{66} +48404.0 q^{67} +117096. q^{68} -25536.0 q^{69} -58560.0 q^{71} -16920.0 q^{72} -68082.0 q^{73} +103980. q^{74} -6664.00 q^{76} +11368.0 q^{77} +19600.0 q^{78} +31784.0 q^{79} -45419.0 q^{81} -179620. q^{82} +20538.0 q^{83} +46648.0 q^{84} -108800. q^{86} +47852.0 q^{87} +83520.0 q^{88} -50582.0 q^{89} +6860.00 q^{91} -124032. q^{92} -107016. q^{93} -93240.0 q^{94} +38080.0 q^{96} +58506.0 q^{97} +24010.0 q^{98} -10904.0 q^{99} +O(q^{100})\)

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 $

$2$	10.0000	1.76777	0.883883	−	0.467707i	$-0.154920\pi$
$2$	10.0000	1.76777	0.883883	+	0.467707i	$0.154920\pi$
$3$	14.0000	0.898100	0.449050	−	0.893507i	$-0.351762\pi$
$3$	14.0000	0.898100	0.449050	+	0.893507i	$0.351762\pi$
$4$	68.0000	2.12500
$5$	0	0
$5$	0	0
$6$	140.000	1.58763
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	360.000	1.98874
$9$	−47.0000	−0.193416
$10$	0	0
$11$	232.000	0.578104	0.289052	−	0.957313i	$-0.406660\pi$
$11$	232.000	0.578104	0.289052	+	0.957313i	$0.406660\pi$
$12$	952.000	1.90846
$13$	140.000	0.229757	0.114879	−	0.993380i	$-0.463352\pi$
$13$	140.000	0.229757	0.114879	+	0.993380i	$0.463352\pi$
$14$	490.000	0.668153
$15$	0	0
$16$	1424.00	1.39062
$17$	1722.00	1.44514	0.722572	−	0.691296i	$-0.242960\pi$
$17$	1722.00	1.44514	0.722572	+	0.691296i	$0.242960\pi$
$18$	−470.000	−0.341914
$19$	−98.0000	−0.0622791	−0.0311395	−	0.999515i	$-0.509914\pi$
$19$	−98.0000	−0.0622791	−0.0311395	+	0.999515i	$0.509914\pi$
$20$	0	0
$21$	686.000	0.339450
$22$	2320.00	1.02195
$23$	−1824.00	−0.718961	−0.359480	−	0.933153i	$-0.617046\pi$
$23$	−1824.00	−0.718961	−0.359480	+	0.933153i	$0.617046\pi$
$24$	5040.00	1.78609
$25$	0	0
$26$	1400.00	0.406158
$27$	−4060.00	−1.07181
$28$	3332.00	0.803175
$29$	3418.00	0.754705	0.377352	−	0.926070i	$-0.376835\pi$
$29$	3418.00	0.754705	0.377352	+	0.926070i	$0.376835\pi$
$30$	0	0
$31$	−7644.00	−1.42862	−0.714310	−	0.699830i	$-0.753259\pi$
$31$	−7644.00	−1.42862	−0.714310	+	0.699830i	$0.753259\pi$
$32$	2720.00	0.469563
$33$	3248.00	0.519196
$34$	17220.0	2.55468
$35$	0	0
$36$	−3196.00	−0.411008
$37$	10398.0	1.24866	0.624332	−	0.781159i	$-0.285371\pi$
$37$	10398.0	1.24866	0.624332	+	0.781159i	$0.285371\pi$
$38$	−980.000	−0.110095
$39$	1960.00	0.206345
$40$	0	0
$41$	−17962.0	−1.66876	−0.834382	−	0.551186i	$-0.814175\pi$
$41$	−17962.0	−1.66876	−0.834382	+	0.551186i	$0.814175\pi$
$42$	6860.00	0.600069
$43$	−10880.0	−0.897342	−0.448671	−	0.893697i	$-0.648102\pi$
$43$	−10880.0	−0.897342	−0.448671	+	0.893697i	$0.648102\pi$
$44$	15776.0	1.22847
$45$	0	0
$46$	−18240.0	−1.27096
$47$	−9324.00	−0.615684	−0.307842	−	0.951438i	$-0.599607\pi$
$47$	−9324.00	−0.615684	−0.307842	+	0.951438i	$0.599607\pi$
$48$	19936.0	1.24892
$49$	2401.00	0.142857
$50$	0	0
$51$	24108.0	1.29788
$52$	9520.00	0.488235
$53$	−2262.00	−0.110612	−0.0553061	−	0.998469i	$-0.517613\pi$
$53$	−2262.00	−0.110612	−0.0553061	+	0.998469i	$0.517613\pi$
$54$	−40600.0	−1.89471
$55$	0	0
$56$	17640.0	0.751672
$57$	−1372.00	−0.0559329
$58$	34180.0	1.33414
$59$	−2730.00	−0.102102	−0.0510508	−	0.998696i	$-0.516257\pi$
$59$	−2730.00	−0.102102	−0.0510508	+	0.998696i	$0.516257\pi$
$60$	0	0
$61$	25648.0	0.882529	0.441264	−	0.897377i	$-0.354530\pi$
$61$	25648.0	0.882529	0.441264	+	0.897377i	$0.354530\pi$
$62$	−76440.0	−2.52547
$63$	−2303.00	−0.0731042
$64$	−18368.0	−0.560547
$65$	0	0
$66$	32480.0	0.917817
$67$	48404.0	1.31733	0.658664	−	0.752437i	$-0.271122\pi$
$67$	48404.0	1.31733	0.658664	+	0.752437i	$0.271122\pi$
$68$	117096.	3.07093
$69$	−25536.0	−0.645699
$70$	0	0
$71$	−58560.0	−1.37865	−0.689327	−	0.724450i	$-0.742094\pi$
$71$	−58560.0	−1.37865	−0.689327	+	0.724450i	$0.742094\pi$
$72$	−16920.0	−0.384653
$73$	−68082.0	−1.49529	−0.747645	−	0.664099i	$-0.768815\pi$
$73$	−68082.0	−1.49529	−0.747645	+	0.664099i	$0.768815\pi$
$74$	103980.	2.20735
$75$	0	0
$76$	−6664.00	−0.132343
$77$	11368.0	0.218503
$78$	19600.0	0.364770
$79$	31784.0	0.572982	0.286491	−	0.958083i	$-0.407511\pi$
$79$	31784.0	0.572982	0.286491	+	0.958083i	$0.407511\pi$
$80$	0	0
$81$	−45419.0	−0.769175
$82$	−179620.	−2.94999
$83$	20538.0	0.327237	0.163619	−	0.986524i	$-0.447683\pi$
$83$	20538.0	0.327237	0.163619	+	0.986524i	$0.447683\pi$
$84$	46648.0	0.721331
$85$	0	0
$86$	−108800.	−1.58629
$87$	47852.0	0.677801
$88$	83520.0	1.14970
$89$	−50582.0	−0.676894	−0.338447	−	0.940985i	$-0.609902\pi$
$89$	−50582.0	−0.676894	−0.338447	+	0.940985i	$0.609902\pi$
$90$	0	0
$91$	6860.00	0.0868402
$92$	−124032.	−1.52779
$93$	−107016.	−1.28304
$94$	−93240.0	−1.08839
$95$	0	0
$96$	38080.0	0.421715
$97$	58506.0	0.631351	0.315676	−	0.948867i	$-0.397769\pi$
$97$	58506.0	0.631351	0.315676	+	0.948867i	$0.397769\pi$
$98$	24010.0	0.252538
$99$	−10904.0	−0.111814
$100$	0	0
$101$	38696.0	0.377453	0.188726	−	0.982030i	$-0.439564\pi$
$101$	38696.0	0.377453	0.188726	+	0.982030i	$0.439564\pi$
$102$	241080.	2.29436
$103$	−53060.0	−0.492804	−0.246402	−	0.969168i	$-0.579248\pi$
$103$	−53060.0	−0.492804	−0.246402	+	0.969168i	$0.579248\pi$
$104$	50400.0	0.456927
$105$	0	0
$106$	−22620.0	−0.195537
$107$	146324.	1.23554	0.617769	−	0.786360i	$-0.288037\pi$
$107$	146324.	1.23554	0.617769	+	0.786360i	$0.288037\pi$
$108$	−276080.	−2.27759
$109$	92898.0	0.748928	0.374464	−	0.927241i	$-0.377827\pi$
$109$	92898.0	0.748928	0.374464	+	0.927241i	$0.377827\pi$
$110$	0	0
$111$	145572.	1.12143
$112$	69776.0	0.525607
$113$	83354.0	0.614088	0.307044	−	0.951695i	$-0.400660\pi$
$113$	83354.0	0.614088	0.307044	+	0.951695i	$0.400660\pi$
$114$	−13720.0	−0.0988762
$115$	0	0
$116$	232424.	1.60375
$117$	−6580.00	−0.0444387
$118$	−27300.0	−0.180492
$119$	84378.0	0.546213
$120$	0	0
$121$	−107227.	−0.665795
$122$	256480.	1.56011
$123$	−251468.	−1.49872
$124$	−519792.	−3.03582
$125$	0	0
$126$	−23030.0	−0.129231
$127$	−60384.0	−0.332210	−0.166105	−	0.986108i	$-0.553119\pi$
$127$	−60384.0	−0.332210	−0.166105	+	0.986108i	$0.553119\pi$
$128$	−270720.	−1.46048
$129$	−152320.	−0.805903
$130$	0	0
$131$	−61586.0	−0.313548	−0.156774	−	0.987635i	$-0.550109\pi$
$131$	−61586.0	−0.313548	−0.156774	+	0.987635i	$0.550109\pi$
$132$	220864.	1.10329
$133$	−4802.00	−0.0235393
$134$	484040.	2.32873
$135$	0	0
$136$	619920.	2.87401
$137$	204462.	0.930703	0.465352	−	0.885126i	$-0.345928\pi$
$137$	204462.	0.930703	0.465352	+	0.885126i	$0.345928\pi$
$138$	−255360.	−1.14145
$139$	−35406.0	−0.155432	−0.0777159	−	0.996976i	$-0.524763\pi$
$139$	−35406.0	−0.155432	−0.0777159	+	0.996976i	$0.524763\pi$
$140$	0	0
$141$	−130536.	−0.552946
$142$	−585600.	−2.43714
$143$	32480.0	0.132824
$144$	−66928.0	−0.268969
$145$	0	0
$146$	−680820.	−2.64332
$147$	33614.0	0.128300
$148$	707064.	2.65341
$149$	−20226.0	−0.0746353	−0.0373177	−	0.999303i	$-0.511881\pi$
$149$	−20226.0	−0.0746353	−0.0373177	+	0.999303i	$0.511881\pi$
$150$	0	0
$151$	70904.0	0.253063	0.126531	−	0.991963i	$-0.459616\pi$
$151$	70904.0	0.253063	0.126531	+	0.991963i	$0.459616\pi$
$152$	−35280.0	−0.123857
$153$	−80934.0	−0.279513
$154$	113680.	0.386262
$155$	0	0
$156$	133280.	0.438484
$157$	−293524.	−0.950374	−0.475187	−	0.879885i	$-0.657620\pi$
$157$	−293524.	−0.950374	−0.475187	+	0.879885i	$0.657620\pi$
$158$	317840.	1.01290
$159$	−31668.0	−0.0993408
$160$	0	0
$161$	−89376.0	−0.271742
$162$	−454190.	−1.35972
$163$	−13192.0	−0.0388903	−0.0194452	−	0.999811i	$-0.506190\pi$
$163$	−13192.0	−0.0388903	−0.0194452	+	0.999811i	$0.506190\pi$
$164$	−1.22142e6	−3.54612
$165$	0	0
$166$	205380.	0.578479
$167$	−493612.	−1.36960	−0.684801	−	0.728730i	$-0.740111\pi$
$167$	−493612.	−1.36960	−0.684801	+	0.728730i	$0.740111\pi$
$168$	246960.	0.675077
$169$	−351693.	−0.947212
$170$	0	0
$171$	4606.00	0.0120457
$172$	−739840.	−1.90685
$173$	−240716.	−0.611490	−0.305745	−	0.952113i	$-0.598906\pi$
$173$	−240716.	−0.611490	−0.305745	+	0.952113i	$0.598906\pi$
$174$	478520.	1.19819
$175$	0	0
$176$	330368.	0.803926
$177$	−38220.0	−0.0916975
$178$	−505820.	−1.19659
$179$	294932.	0.688001	0.344001	−	0.938969i	$-0.388218\pi$
$179$	294932.	0.688001	0.344001	+	0.938969i	$0.388218\pi$
$180$	0	0
$181$	−336980.	−0.764553	−0.382277	−	0.924048i	$-0.624860\pi$
$181$	−336980.	−0.764553	−0.382277	+	0.924048i	$0.624860\pi$
$182$	68600.0	0.153513
$183$	359072.	0.792600
$184$	−656640.	−1.42982
$185$	0	0
$186$	−1.07016e6	−2.26812
$187$	399504.	0.835444
$188$	−634032.	−1.30833
$189$	−198940.	−0.405105
$190$	0	0
$191$	358264.	0.710591	0.355296	−	0.934754i	$-0.384380\pi$
$191$	358264.	0.710591	0.355296	+	0.934754i	$0.384380\pi$
$192$	−257152.	−0.503427
$193$	989554.	1.91226	0.956128	−	0.292948i	$-0.0946362\pi$
$193$	989554.	1.91226	0.956128	+	0.292948i	$0.0946362\pi$
$194$	585060.	1.11608
$195$	0	0
$196$	163268.	0.303571
$197$	990050.	1.81757	0.908786	−	0.417263i	$-0.137011\pi$
$197$	990050.	1.81757	0.908786	+	0.417263i	$0.137011\pi$
$198$	−109040.	−0.197662
$199$	−840756.	−1.50500	−0.752501	−	0.658591i	$-0.771153\pi$
$199$	−840756.	−1.50500	−0.752501	+	0.658591i	$0.771153\pi$
$200$	0	0
$201$	677656.	1.18309
$202$	386960.	0.667249
$203$	167482.	0.285252
$204$	1.63934e6	2.75800
$205$	0	0
$206$	−530600.	−0.871163
$207$	85728.0	0.139058
$208$	199360.	0.319506
$209$	−22736.0	−0.0360038
$210$	0	0
$211$	1.15073e6	1.77938	0.889689	−	0.456568i	$-0.150921\pi$
$211$	1.15073e6	1.77938	0.889689	+	0.456568i	$0.150921\pi$
$212$	−153816.	−0.235051
$213$	−819840.	−1.23817
$214$	1.46324e6	2.18414
$215$	0	0
$216$	−1.46160e6	−2.13154
$217$	−374556.	−0.539967
$218$	928980.	1.32393
$219$	−953148.	−1.34292
$220$	0	0
$221$	241080.	0.332032
$222$	1.45572e6	1.98242
$223$	824264.	1.10995	0.554976	−	0.831866i	$-0.312727\pi$
$223$	824264.	1.10995	0.554976	+	0.831866i	$0.312727\pi$
$224$	133280.	0.177478
$225$	0	0
$226$	833540.	1.08556
$227$	−74382.0	−0.0958083	−0.0479042	−	0.998852i	$-0.515254\pi$
$227$	−74382.0	−0.0958083	−0.0479042	+	0.998852i	$0.515254\pi$
$228$	−93296.0	−0.118857
$229$	1.13196e6	1.42640	0.713199	−	0.700961i	$-0.247245\pi$
$229$	1.13196e6	1.42640	0.713199	+	0.700961i	$0.247245\pi$
$230$	0	0
$231$	159152.	0.196238
$232$	1.23048e6	1.50091
$233$	198726.	0.239809	0.119904	−	0.992785i	$-0.461741\pi$
$233$	198726.	0.239809	0.119904	+	0.992785i	$0.461741\pi$
$234$	−65800.0	−0.0785572
$235$	0	0
$236$	−185640.	−0.216966
$237$	444976.	0.514595
$238$	843780.	0.965577
$239$	482904.	0.546847	0.273424	−	0.961894i	$-0.411844\pi$
$239$	482904.	0.546847	0.273424	+	0.961894i	$0.411844\pi$
$240$	0	0
$241$	805910.	0.893807	0.446904	−	0.894582i	$-0.352527\pi$
$241$	805910.	0.893807	0.446904	+	0.894582i	$0.352527\pi$
$242$	−1.07227e6	−1.17697
$243$	350714.	0.381011
$244$	1.74406e6	1.87537
$245$	0	0
$246$	−2.51468e6	−2.64938
$247$	−13720.0	−0.0143091
$248$	−2.75184e6	−2.84115
$249$	287532.	0.293892
$250$	0	0
$251$	430738.	0.431548	0.215774	−	0.976443i	$-0.430773\pi$
$251$	430738.	0.431548	0.215774	+	0.976443i	$0.430773\pi$
$252$	−156604.	−0.155347
$253$	−423168.	−0.415634
$254$	−603840.	−0.587270
$255$	0	0
$256$	−2.11942e6	−2.02124
$257$	1.17691e6	1.11150	0.555751	−	0.831349i	$-0.312431\pi$
$257$	1.17691e6	1.11150	0.555751	+	0.831349i	$0.312431\pi$
$258$	−1.52320e6	−1.42465
$259$	509502.	0.471951
$260$	0	0
$261$	−160646.	−0.145972
$262$	−615860.	−0.554279
$263$	−1.29098e6	−1.15088	−0.575438	−	0.817845i	$-0.695169\pi$
$263$	−1.29098e6	−1.15088	−0.575438	+	0.817845i	$0.695169\pi$
$264$	1.16928e6	1.03254
$265$	0	0
$266$	−48020.0	−0.0416119
$267$	−708148.	−0.607919
$268$	3.29147e6	2.79932
$269$	−1.27756e6	−1.07646	−0.538232	−	0.842797i	$-0.680907\pi$
$269$	−1.27756e6	−1.07646	−0.538232	+	0.842797i	$0.680907\pi$
$270$	0	0
$271$	1.65054e6	1.36522	0.682612	−	0.730781i	$-0.260844\pi$
$271$	1.65054e6	1.36522	0.682612	+	0.730781i	$0.260844\pi$
$272$	2.45213e6	2.00965
$273$	96040.0	0.0779912
$274$	2.04462e6	1.64527
$275$	0	0
$276$	−1.73645e6	−1.37211
$277$	1.06409e6	0.833257	0.416628	−	0.909077i	$-0.363212\pi$
$277$	1.06409e6	0.833257	0.416628	+	0.909077i	$0.363212\pi$
$278$	−354060.	−0.274767
$279$	359268.	0.276317
$280$	0	0
$281$	−22342.0	−0.0168794	−0.00843969	−	0.999964i	$-0.502686\pi$
$281$	−22342.0	−0.0168794	−0.00843969	+	0.999964i	$0.502686\pi$
$282$	−1.30536e6	−0.977479
$283$	2.49574e6	1.85239	0.926196	−	0.377042i	$-0.123059\pi$
$283$	2.49574e6	1.85239	0.926196	+	0.377042i	$0.123059\pi$
$284$	−3.98208e6	−2.92964
$285$	0	0
$286$	324800.	0.234802
$287$	−880138.	−0.630734
$288$	−127840.	−0.0908208
$289$	1.54543e6	1.08844
$290$	0	0
$291$	819084.	0.567017
$292$	−4.62958e6	−3.17749
$293$	1.93178e6	1.31458	0.657291	−	0.753637i	$-0.271702\pi$
$293$	1.93178e6	1.31458	0.657291	+	0.753637i	$0.271702\pi$
$294$	336140.	0.226805
$295$	0	0
$296$	3.74328e6	2.48326
$297$	−941920.	−0.619616
$298$	−202260.	−0.131938
$299$	−255360.	−0.165187
$300$	0	0
$301$	−533120.	−0.339163
$302$	709040.	0.447356
$303$	541744.	0.338991
$304$	−139552.	−0.0866068
$305$	0	0
$306$	−809340.	−0.494114
$307$	459074.	0.277995	0.138997	−	0.990293i	$-0.455612\pi$
$307$	459074.	0.277995	0.138997	+	0.990293i	$0.455612\pi$
$308$	773024.	0.464319
$309$	−742840.	−0.442587
$310$	0	0
$311$	667128.	0.391118	0.195559	−	0.980692i	$-0.437348\pi$
$311$	667128.	0.391118	0.195559	+	0.980692i	$0.437348\pi$
$312$	705600.	0.410367
$313$	111034.	0.0640612	0.0320306	−	0.999487i	$-0.489803\pi$
$313$	111034.	0.0640612	0.0320306	+	0.999487i	$0.489803\pi$
$314$	−2.93524e6	−1.68004
$315$	0	0
$316$	2.16131e6	1.21759
$317$	68778.0	0.0384416	0.0192208	−	0.999815i	$-0.493881\pi$
$317$	68778.0	0.0384416	0.0192208	+	0.999815i	$0.493881\pi$
$318$	−316680.	−0.175611
$319$	792976.	0.436298
$320$	0	0
$321$	2.04854e6	1.10964
$322$	−893760.	−0.480376
$323$	−168756.	−0.0900022
$324$	−3.08849e6	−1.63450
$325$	0	0
$326$	−131920.	−0.0687490
$327$	1.30057e6	0.672613
$328$	−6.46632e6	−3.31874
$329$	−456876.	−0.232707
$330$	0	0
$331$	−564448.	−0.283174	−0.141587	−	0.989926i	$-0.545221\pi$
$331$	−564448.	−0.283174	−0.141587	+	0.989926i	$0.545221\pi$
$332$	1.39658e6	0.695379
$333$	−488706.	−0.241511
$334$	−4.93612e6	−2.42114
$335$	0	0
$336$	976864.	0.472048
$337$	−2.07729e6	−0.996376	−0.498188	−	0.867069i	$-0.666001\pi$
$337$	−2.07729e6	−0.996376	−0.498188	+	0.867069i	$0.666001\pi$
$338$	−3.51693e6	−1.67445
$339$	1.16696e6	0.551512
$340$	0	0
$341$	−1.77341e6	−0.825891
$342$	46060.0	0.0212941
$343$	117649.	0.0539949
$344$	−3.91680e6	−1.78458
$345$	0	0
$346$	−2.40716e6	−1.08097
$347$	53248.0	0.0237399	0.0118700	−	0.999930i	$-0.496222\pi$
$347$	53248.0	0.0237399	0.0118700	+	0.999930i	$0.496222\pi$
$348$	3.25394e6	1.44033
$349$	−2.27200e6	−0.998494	−0.499247	−	0.866460i	$-0.666390\pi$
$349$	−2.27200e6	−0.998494	−0.499247	+	0.866460i	$0.666390\pi$
$350$	0	0
$351$	−568400.	−0.246256
$352$	631040.	0.271456
$353$	−4.00645e6	−1.71129	−0.855644	−	0.517565i	$-0.826838\pi$
$353$	−4.00645e6	−1.71129	−0.855644	+	0.517565i	$0.826838\pi$
$354$	−382200.	−0.162100
$355$	0	0
$356$	−3.43958e6	−1.43840
$357$	1.18129e6	0.490554
$358$	2.94932e6	1.21623
$359$	73784.0	0.0302152	0.0151076	−	0.999886i	$-0.495191\pi$
$359$	73784.0	0.0302152	0.0151076	+	0.999886i	$0.495191\pi$
$360$	0	0
$361$	−2.46650e6	−0.996121
$362$	−3.36980e6	−1.35155
$363$	−1.50118e6	−0.597951
$364$	466480.	0.184535
$365$	0	0
$366$	3.59072e6	1.40113
$367$	−1.40431e6	−0.544250	−0.272125	−	0.962262i	$-0.587726\pi$
$367$	−1.40431e6	−0.544250	−0.272125	+	0.962262i	$0.587726\pi$
$368$	−2.59738e6	−0.999805
$369$	844214.	0.322765
$370$	0	0
$371$	−110838.	−0.0418075
$372$	−7.27709e6	−2.72647
$373$	1.60323e6	0.596657	0.298329	−	0.954463i	$-0.403571\pi$
$373$	1.60323e6	0.596657	0.298329	+	0.954463i	$0.403571\pi$
$374$	3.99504e6	1.47687
$375$	0	0
$376$	−3.35664e6	−1.22443
$377$	478520.	0.173399
$378$	−1.98940e6	−0.716131
$379$	−4.77012e6	−1.70581	−0.852906	−	0.522064i	$-0.825162\pi$
$379$	−4.77012e6	−1.70581	−0.852906	+	0.522064i	$0.825162\pi$
$380$	0	0
$381$	−845376.	−0.298358
$382$	3.58264e6	1.25616
$383$	2.23079e6	0.777072	0.388536	−	0.921434i	$-0.372981\pi$
$383$	2.23079e6	0.777072	0.388536	+	0.921434i	$0.372981\pi$
$384$	−3.79008e6	−1.31166
$385$	0	0
$386$	9.89554e6	3.38042
$387$	511360.	0.173560
$388$	3.97841e6	1.34162
$389$	4.84024e6	1.62178	0.810892	−	0.585196i	$-0.198982\pi$
$389$	4.84024e6	1.62178	0.810892	+	0.585196i	$0.198982\pi$
$390$	0	0
$391$	−3.14093e6	−1.03900
$392$	864360.	0.284105
$393$	−862204.	−0.281597
$394$	9.90050e6	3.21304
$395$	0	0
$396$	−741472.	−0.237606
$397$	−995820.	−0.317106	−0.158553	−	0.987350i	$-0.550683\pi$
$397$	−995820.	−0.317106	−0.158553	+	0.987350i	$0.550683\pi$
$398$	−8.40756e6	−2.66049
$399$	−67228.0	−0.0211406
$400$	0	0
$401$	−3.31605e6	−1.02982	−0.514909	−	0.857245i	$-0.672174\pi$
$401$	−3.31605e6	−1.02982	−0.514909	+	0.857245i	$0.672174\pi$
$402$	6.77656e6	2.09143
$403$	−1.07016e6	−0.328236
$404$	2.63133e6	0.802087
$405$	0	0
$406$	1.67482e6	0.504258
$407$	2.41234e6	0.721858
$408$	8.67888e6	2.58115
$409$	3.07273e6	0.908274	0.454137	−	0.890932i	$-0.349948\pi$
$409$	3.07273e6	0.908274	0.454137	+	0.890932i	$0.349948\pi$
$410$	0	0
$411$	2.86247e6	0.835865
$412$	−3.60808e6	−1.04721
$413$	−133770.	−0.0385908
$414$	857280.	0.245823
$415$	0	0
$416$	380800.	0.107886
$417$	−495684.	−0.139593
$418$	−227360.	−0.0636463
$419$	2.81438e6	0.783154	0.391577	−	0.920145i	$-0.371930\pi$
$419$	2.81438e6	0.783154	0.391577	+	0.920145i	$0.371930\pi$
$420$	0	0
$421$	3.05802e6	0.840883	0.420441	−	0.907320i	$-0.361875\pi$
$421$	3.05802e6	0.840883	0.420441	+	0.907320i	$0.361875\pi$
$422$	1.15073e7	3.14552
$423$	438228.	0.119083
$424$	−814320.	−0.219979
$425$	0	0
$426$	−8.19840e6	−2.18880
$427$	1.25675e6	0.333565
$428$	9.95003e6	2.62552
$429$	454720.	0.119289
$430$	0	0
$431$	1.93750e6	0.502398	0.251199	−	0.967936i	$-0.419175\pi$
$431$	1.93750e6	0.502398	0.251199	+	0.967936i	$0.419175\pi$
$432$	−5.78144e6	−1.49048
$433$	−3.94790e6	−1.01192	−0.505961	−	0.862557i	$-0.668862\pi$
$433$	−3.94790e6	−1.01192	−0.505961	+	0.862557i	$0.668862\pi$
$434$	−3.74556e6	−0.954536
$435$	0	0
$436$	6.31706e6	1.59147
$437$	178752.	0.0447762
$438$	−9.53148e6	−2.37397
$439$	−7.41770e6	−1.83700	−0.918498	−	0.395426i	$-0.870597\pi$
$439$	−7.41770e6	−1.83700	−0.918498	+	0.395426i	$0.870597\pi$
$440$	0	0
$441$	−112847.	−0.0276308
$442$	2.41080e6	0.586956
$443$	−1.40269e6	−0.339589	−0.169794	−	0.985480i	$-0.554310\pi$
$443$	−1.40269e6	−0.339589	−0.169794	+	0.985480i	$0.554310\pi$
$444$	9.89890e6	2.38303
$445$	0	0
$446$	8.24264e6	1.96214
$447$	−283164.	−0.0670300
$448$	−900032.	−0.211867
$449$	−590574.	−0.138248	−0.0691239	−	0.997608i	$-0.522020\pi$
$449$	−590574.	−0.138248	−0.0691239	+	0.997608i	$0.522020\pi$
$450$	0	0
$451$	−4.16718e6	−0.964720
$452$	5.66807e6	1.30494
$453$	992656.	0.227276
$454$	−743820.	−0.169367
$455$	0	0
$456$	−493920.	−0.111236
$457$	2.90484e6	0.650627	0.325313	−	0.945606i	$-0.394530\pi$
$457$	2.90484e6	0.650627	0.325313	+	0.945606i	$0.394530\pi$
$458$	1.13196e7	2.52154
$459$	−6.99132e6	−1.54891
$460$	0	0
$461$	−922684.	−0.202209	−0.101105	−	0.994876i	$-0.532238\pi$
$461$	−922684.	−0.202209	−0.101105	+	0.994876i	$0.532238\pi$
$462$	1.59152e6	0.346902
$463$	−7.18235e6	−1.55709	−0.778546	−	0.627588i	$-0.784042\pi$
$463$	−7.18235e6	−1.55709	−0.778546	+	0.627588i	$0.784042\pi$
$464$	4.86723e6	1.04951
$465$	0	0
$466$	1.98726e6	0.423926
$467$	612570.	0.129976	0.0649881	−	0.997886i	$-0.479299\pi$
$467$	612570.	0.129976	0.0649881	+	0.997886i	$0.479299\pi$
$468$	−447440.	−0.0944322
$469$	2.37180e6	0.497904
$470$	0	0
$471$	−4.10934e6	−0.853531
$472$	−982800.	−0.203053
$473$	−2.52416e6	−0.518757
$474$	4.44976e6	0.909684
$475$	0	0
$476$	5.73770e6	1.16070
$477$	106314.	0.0213941
$478$	4.82904e6	0.966699
$479$	2.60330e6	0.518424	0.259212	−	0.965820i	$-0.416537\pi$
$479$	2.60330e6	0.518424	0.259212	+	0.965820i	$0.416537\pi$
$480$	0	0
$481$	1.45572e6	0.286890
$482$	8.05910e6	1.58004
$483$	−1.25126e6	−0.244051
$484$	−7.29144e6	−1.41482
$485$	0	0
$486$	3.50714e6	0.673539
$487$	−5.46309e6	−1.04380	−0.521898	−	0.853008i	$-0.674776\pi$
$487$	−5.46309e6	−1.04380	−0.521898	+	0.853008i	$0.674776\pi$
$488$	9.23328e6	1.75512
$489$	−184688.	−0.0349274
$490$	0	0
$491$	1.64090e6	0.307170	0.153585	−	0.988135i	$-0.450918\pi$
$491$	1.64090e6	0.307170	0.153585	+	0.988135i	$0.450918\pi$
$492$	−1.70998e7	−3.18478
$493$	5.88580e6	1.09066
$494$	−137200.	−0.0252951
$495$	0	0
$496$	−1.08851e7	−1.98667
$497$	−2.86944e6	−0.521082
$498$	2.87532e6	0.519533
$499$	2.99796e6	0.538983	0.269491	−	0.963003i	$-0.413144\pi$
$499$	2.99796e6	0.538983	0.269491	+	0.963003i	$0.413144\pi$
$500$	0	0
$501$	−6.91057e6	−1.23004
$502$	4.30738e6	0.762876
$503$	6.89405e6	1.21494	0.607469	−	0.794343i	$-0.292185\pi$
$503$	6.89405e6	1.21494	0.607469	+	0.794343i	$0.292185\pi$
$504$	−829080.	−0.145385
$505$	0	0
$506$	−4.23168e6	−0.734745
$507$	−4.92370e6	−0.850691
$508$	−4.10611e6	−0.705946
$509$	2.30476e6	0.394305	0.197152	−	0.980373i	$-0.436831\pi$
$509$	2.30476e6	0.394305	0.197152	+	0.980373i	$0.436831\pi$
$510$	0	0
$511$	−3.33602e6	−0.565166
$512$	−1.25312e7	−2.11260
$513$	397880.	0.0667511
$514$	1.17691e7	1.96488
$515$	0	0
$516$	−1.03578e7	−1.71254
$517$	−2.16317e6	−0.355929
$518$	5.09502e6	0.834299
$519$	−3.37002e6	−0.549180
$520$	0	0
$521$	−1.20960e7	−1.95231	−0.976155	−	0.217073i	$-0.930349\pi$
$521$	−1.20960e7	−1.95231	−0.976155	+	0.217073i	$0.930349\pi$
$522$	−1.60646e6	−0.258044
$523$	−5.48443e6	−0.876753	−0.438377	−	0.898791i	$-0.644446\pi$
$523$	−5.48443e6	−0.876753	−0.438377	+	0.898791i	$0.644446\pi$
$524$	−4.18785e6	−0.666289
$525$	0	0
$526$	−1.29098e7	−2.03448
$527$	−1.31630e7	−2.06456
$528$	4.62515e6	0.722007
$529$	−3.10937e6	−0.483095
$530$	0	0
$531$	128310.	0.0197480
$532$	−326536.	−0.0500210
$533$	−2.51468e6	−0.383411
$534$	−7.08148e6	−1.07466
$535$	0	0
$536$	1.74254e7	2.61982
$537$	4.12905e6	0.617894
$538$	−1.27756e7	−1.90294
$539$	557032.	0.0825863
$540$	0	0
$541$	−6.71799e6	−0.986839	−0.493420	−	0.869791i	$-0.664253\pi$
$541$	−6.71799e6	−0.986839	−0.493420	+	0.869791i	$0.664253\pi$
$542$	1.65054e7	2.41340
$543$	−4.71772e6	−0.686646
$544$	4.68384e6	0.678586
$545$	0	0
$546$	960400.	0.137870
$547$	5.00235e6	0.714835	0.357418	−	0.933945i	$-0.383657\pi$
$547$	5.00235e6	0.714835	0.357418	+	0.933945i	$0.383657\pi$
$548$	1.39034e7	1.97774
$549$	−1.20546e6	−0.170695
$550$	0	0
$551$	−334964.	−0.0470023
$552$	−9.19296e6	−1.28413
$553$	1.55742e6	0.216567
$554$	1.06409e7	1.47300
$555$	0	0
$556$	−2.40761e6	−0.330293
$557$	−9.01961e6	−1.23183	−0.615913	−	0.787814i	$-0.711213\pi$
$557$	−9.01961e6	−1.23183	−0.615913	+	0.787814i	$0.711213\pi$
$558$	3.59268e6	0.488465
$559$	−1.52320e6	−0.206171
$560$	0	0
$561$	5.59306e6	0.750312
$562$	−223420.	−0.0298388
$563$	−1.24051e7	−1.64941	−0.824707	−	0.565561i	$-0.808660\pi$
$563$	−1.24051e7	−1.64941	−0.824707	+	0.565561i	$0.808660\pi$
$564$	−8.87645e6	−1.17501
$565$	0	0
$566$	2.49574e7	3.27460
$567$	−2.22553e6	−0.290721
$568$	−2.10816e7	−2.74178
$569$	6.48804e6	0.840103	0.420052	−	0.907500i	$-0.362012\pi$
$569$	6.48804e6	0.840103	0.420052	+	0.907500i	$0.362012\pi$
$570$	0	0
$571$	−1.02285e7	−1.31287	−0.656435	−	0.754382i	$-0.727936\pi$
$571$	−1.02285e7	−1.31287	−0.656435	+	0.754382i	$0.727936\pi$
$572$	2.20864e6	0.282251
$573$	5.01570e6	0.638182
$574$	−8.80138e6	−1.11499
$575$	0	0
$576$	863296.	0.108419
$577$	−2.65338e6	−0.331787	−0.165894	−	0.986144i	$-0.553051\pi$
$577$	−2.65338e6	−0.331787	−0.165894	+	0.986144i	$0.553051\pi$
$578$	1.54543e7	1.92411
$579$	1.38538e7	1.71740
$580$	0	0
$581$	1.00636e6	0.123684
$582$	8.19084e6	1.00235
$583$	−524784.	−0.0639454
$584$	−2.45095e7	−2.97374
$585$	0	0
$586$	1.93178e7	2.32387
$587$	1.43044e7	1.71346	0.856729	−	0.515766i	$-0.172493\pi$
$587$	1.43044e7	1.71346	0.856729	+	0.515766i	$0.172493\pi$
$588$	2.28575e6	0.272638
$589$	749112.	0.0889731
$590$	0	0
$591$	1.38607e7	1.63236
$592$	1.48068e7	1.73642
$593$	1.00265e7	1.17088	0.585442	−	0.810714i	$-0.300921\pi$
$593$	1.00265e7	1.17088	0.585442	+	0.810714i	$0.300921\pi$
$594$	−9.41920e6	−1.09534
$595$	0	0
$596$	−1.37537e6	−0.158600
$597$	−1.17706e7	−1.35164
$598$	−2.55360e6	−0.292011
$599$	−7.52292e6	−0.856681	−0.428341	−	0.903617i	$-0.640902\pi$
$599$	−7.52292e6	−0.856681	−0.428341	+	0.903617i	$0.640902\pi$
$600$	0	0
$601$	3.38625e6	0.382413	0.191207	−	0.981550i	$-0.438760\pi$
$601$	3.38625e6	0.382413	0.191207	+	0.981550i	$0.438760\pi$
$602$	−5.33120e6	−0.599562
$603$	−2.27499e6	−0.254792
$604$	4.82147e6	0.537759
$605$	0	0
$606$	5.41744e6	0.599256
$607$	6.90861e6	0.761060	0.380530	−	0.924769i	$-0.375742\pi$
$607$	6.90861e6	0.761060	0.380530	+	0.924769i	$0.375742\pi$
$608$	−266560.	−0.0292439
$609$	2.34475e6	0.256185
$610$	0	0
$611$	−1.30536e6	−0.141458
$612$	−5.50351e6	−0.593966
$613$	9.68896e6	1.04142	0.520710	−	0.853734i	$-0.325667\pi$
$613$	9.68896e6	1.04142	0.520710	+	0.853734i	$0.325667\pi$
$614$	4.59074e6	0.491430
$615$	0	0
$616$	4.09248e6	0.434545
$617$	7.84742e6	0.829877	0.414939	−	0.909849i	$-0.363803\pi$
$617$	7.84742e6	0.829877	0.414939	+	0.909849i	$0.363803\pi$
$618$	−7.42840e6	−0.782391
$619$	−1.01972e7	−1.06968	−0.534840	−	0.844953i	$-0.679628\pi$
$619$	−1.01972e7	−1.06968	−0.534840	+	0.844953i	$0.679628\pi$
$620$	0	0
$621$	7.40544e6	0.770587
$622$	6.67128e6	0.691406
$623$	−2.47852e6	−0.255842
$624$	2.79104e6	0.286949
$625$	0	0
$626$	1.11034e6	0.113245
$627$	−318304.	−0.0323350
$628$	−1.99596e7	−2.01954
$629$	1.79054e7	1.80450
$630$	0	0
$631$	−8.36258e6	−0.836116	−0.418058	−	0.908420i	$-0.637289\pi$
$631$	−8.36258e6	−0.836116	−0.418058	+	0.908420i	$0.637289\pi$
$632$	1.14422e7	1.13951
$633$	1.61102e7	1.59806
$634$	687780.	0.0679558
$635$	0	0
$636$	−2.15342e6	−0.211099
$637$	336140.	0.0328225
$638$	7.92976e6	0.771273
$639$	2.75232e6	0.266653
$640$	0	0
$641$	1.10283e6	0.106014	0.0530070	−	0.998594i	$-0.483119\pi$
$641$	1.10283e6	0.106014	0.0530070	+	0.998594i	$0.483119\pi$
$642$	2.04854e7	1.96158
$643$	−1.71354e7	−1.63443	−0.817217	−	0.576330i	$-0.804484\pi$
$643$	−1.71354e7	−1.63443	−0.817217	+	0.576330i	$0.804484\pi$
$644$	−6.07757e6	−0.577451
$645$	0	0
$646$	−1.68756e6	−0.159103
$647$	54964.0	0.00516200	0.00258100	−	0.999997i	$-0.499178\pi$
$647$	54964.0	0.00516200	0.00258100	+	0.999997i	$0.499178\pi$
$648$	−1.63508e7	−1.52969
$649$	−633360.	−0.0590254
$650$	0	0
$651$	−5.24378e6	−0.484945
$652$	−897056.	−0.0826420
$653$	485166.	0.0445254	0.0222627	−	0.999752i	$-0.492913\pi$
$653$	485166.	0.0445254	0.0222627	+	0.999752i	$0.492913\pi$
$654$	1.30057e7	1.18902
$655$	0	0
$656$	−2.55779e7	−2.32063
$657$	3.19985e6	0.289212
$658$	−4.56876e6	−0.411371
$659$	−2.72136e6	−0.244103	−0.122051	−	0.992524i	$-0.538947\pi$
$659$	−2.72136e6	−0.244103	−0.122051	+	0.992524i	$0.538947\pi$
$660$	0	0
$661$	−2.14525e6	−0.190974	−0.0954869	−	0.995431i	$-0.530441\pi$
$661$	−2.14525e6	−0.190974	−0.0954869	+	0.995431i	$0.530441\pi$
$662$	−5.64448e6	−0.500586
$663$	3.37512e6	0.298198
$664$	7.39368e6	0.650789
$665$	0	0
$666$	−4.88706e6	−0.426935
$667$	−6.23443e6	−0.542603
$668$	−3.35656e7	−2.91041
$669$	1.15397e7	0.996848
$670$	0	0
$671$	5.95034e6	0.510194
$672$	1.86592e6	0.159393
$673$	−2.92796e6	−0.249188	−0.124594	−	0.992208i	$-0.539763\pi$
$673$	−2.92796e6	−0.249188	−0.124594	+	0.992208i	$0.539763\pi$
$674$	−2.07729e7	−1.76136
$675$	0	0
$676$	−2.39151e7	−2.01282
$677$	1.34992e7	1.13198	0.565988	−	0.824414i	$-0.308495\pi$
$677$	1.34992e7	1.13198	0.565988	+	0.824414i	$0.308495\pi$
$678$	1.16696e7	0.974945
$679$	2.86679e6	0.238628
$680$	0	0
$681$	−1.04135e6	−0.0860455
$682$	−1.77341e7	−1.45998
$683$	5.42972e6	0.445375	0.222688	−	0.974890i	$-0.428517\pi$
$683$	5.42972e6	0.445375	0.222688	+	0.974890i	$0.428517\pi$
$684$	313208.	0.0255972
$685$	0	0
$686$	1.17649e6	0.0954504
$687$	1.58474e7	1.28105
$688$	−1.54931e7	−1.24787
$689$	−316680.	−0.0254140
$690$	0	0
$691$	2.08280e7	1.65940	0.829702	−	0.558207i	$-0.188510\pi$
$691$	2.08280e7	1.65940	0.829702	+	0.558207i	$0.188510\pi$
$692$	−1.63687e7	−1.29942
$693$	−534296.	−0.0422619
$694$	532480.	0.0419667
$695$	0	0
$696$	1.72267e7	1.34797
$697$	−3.09306e7	−2.41160
$698$	−2.27200e7	−1.76510
$699$	2.78216e6	0.215372
$700$	0	0
$701$	2.35141e7	1.80731	0.903655	−	0.428261i	$-0.140874\pi$
$701$	2.35141e7	1.80731	0.903655	+	0.428261i	$0.140874\pi$
$702$	−5.68400e6	−0.435323
$703$	−1.01900e6	−0.0777656
$704$	−4.26138e6	−0.324055
$705$	0	0
$706$	−4.00645e7	−3.02516
$707$	1.89610e6	0.142664
$708$	−2.59896e6	−0.194857
$709$	−1.95747e7	−1.46244	−0.731221	−	0.682140i	$-0.761049\pi$
$709$	−1.95747e7	−1.46244	−0.731221	+	0.682140i	$0.761049\pi$
$710$	0	0
$711$	−1.49385e6	−0.110824
$712$	−1.82095e7	−1.34617
$713$	1.39427e7	1.02712
$714$	1.18129e7	0.867185
$715$	0	0
$716$	2.00554e7	1.46200
$717$	6.76066e6	0.491124
$718$	737840.	0.0534135
$719$	−2.61152e7	−1.88396	−0.941978	−	0.335674i	$-0.891036\pi$
$719$	−2.61152e7	−1.88396	−0.941978	+	0.335674i	$0.891036\pi$
$720$	0	0
$721$	−2.59994e6	−0.186262
$722$	−2.46650e7	−1.76091
$723$	1.12827e7	0.802729
$724$	−2.29146e7	−1.62468
$725$	0	0
$726$	−1.50118e7	−1.05704
$727$	−1.54126e7	−1.08154	−0.540768	−	0.841172i	$-0.681866\pi$
$727$	−1.54126e7	−1.08154	−0.540768	+	0.841172i	$0.681866\pi$
$728$	2.46960e6	0.172702
$729$	1.59468e7	1.11136
$730$	0	0
$731$	−1.87354e7	−1.29679
$732$	2.44169e7	1.68427
$733$	1.69868e7	1.16776	0.583878	−	0.811841i	$-0.301535\pi$
$733$	1.69868e7	1.16776	0.583878	+	0.811841i	$0.301535\pi$
$734$	−1.40431e7	−0.962107
$735$	0	0
$736$	−4.96128e6	−0.337597
$737$	1.12297e7	0.761554
$738$	8.44214e6	0.570574
$739$	2.01511e6	0.135734	0.0678669	−	0.997694i	$-0.478381\pi$
$739$	2.01511e6	0.135734	0.0678669	+	0.997694i	$0.478381\pi$
$740$	0	0
$741$	−192080.	−0.0128510
$742$	−1.10838e6	−0.0739059
$743$	1.51381e7	1.00600	0.503001	−	0.864286i	$-0.332229\pi$
$743$	1.51381e7	1.00600	0.503001	+	0.864286i	$0.332229\pi$
$744$	−3.85258e7	−2.55164
$745$	0	0
$746$	1.60323e7	1.05475
$747$	−965286.	−0.0632928
$748$	2.71663e7	1.77532
$749$	7.16988e6	0.466989
$750$	0	0
$751$	7.21401e6	0.466742	0.233371	−	0.972388i	$-0.425024\pi$
$751$	7.21401e6	0.466742	0.233371	+	0.972388i	$0.425024\pi$
$752$	−1.32774e7	−0.856185
$753$	6.03033e6	0.387573
$754$	4.78520e6	0.306529
$755$	0	0
$756$	−1.35279e7	−0.860848
$757$	1.09697e7	0.695755	0.347877	−	0.937540i	$-0.386903\pi$
$757$	1.09697e7	0.695755	0.347877	+	0.937540i	$0.386903\pi$
$758$	−4.77012e7	−3.01548
$759$	−5.92435e6	−0.373281
$760$	0	0
$761$	1.92442e7	1.20459	0.602293	−	0.798275i	$-0.294254\pi$
$761$	1.92442e7	1.20459	0.602293	+	0.798275i	$0.294254\pi$
$762$	−8.45376e6	−0.527427
$763$	4.55200e6	0.283068
$764$	2.43620e7	1.51001
$765$	0	0
$766$	2.23079e7	1.37368
$767$	−382200.	−0.0234586
$768$	−2.96719e7	−1.81528
$769$	8.21185e6	0.500755	0.250378	−	0.968148i	$-0.419445\pi$
$769$	8.21185e6	0.500755	0.250378	+	0.968148i	$0.419445\pi$
$770$	0	0
$771$	1.64767e7	0.998241
$772$	6.72897e7	4.06355
$773$	−1.86187e7	−1.12073	−0.560363	−	0.828247i	$-0.689338\pi$
$773$	−1.86187e7	−1.12073	−0.560363	+	0.828247i	$0.689338\pi$
$774$	5.11360e6	0.306813
$775$	0	0
$776$	2.10622e7	1.25559
$777$	7.13303e6	0.423859
$778$	4.84024e7	2.86694
$779$	1.76028e6	0.103929
$780$	0	0
$781$	−1.35859e7	−0.797006
$782$	−3.14093e7	−1.83671
$783$	−1.38771e7	−0.808898
$784$	3.41902e6	0.198661
$785$	0	0
$786$	−8.62204e6	−0.497799
$787$	−2.62501e7	−1.51075	−0.755377	−	0.655291i	$-0.772546\pi$
$787$	−2.62501e7	−1.51075	−0.755377	+	0.655291i	$0.772546\pi$
$788$	6.73234e7	3.86234
$789$	−1.80737e7	−1.03360
$790$	0	0
$791$	4.08435e6	0.232103
$792$	−3.92544e6	−0.222370
$793$	3.59072e6	0.202768
$794$	−9.95820e6	−0.560570
$795$	0	0
$796$	−5.71714e7	−3.19813
$797$	1.00373e7	0.559720	0.279860	−	0.960041i	$-0.409712\pi$
$797$	1.00373e7	0.559720	0.279860	+	0.960041i	$0.409712\pi$
$798$	−672280.	−0.0373717
$799$	−1.60559e7	−0.889751
$800$	0	0
$801$	2.37735e6	0.130922
$802$	−3.31605e7	−1.82048
$803$	−1.57950e7	−0.864433
$804$	4.60806e7	2.51407
$805$	0	0
$806$	−1.07016e7	−0.580245
$807$	−1.78858e7	−0.966772
$808$	1.39306e7	0.750655
$809$	1.40884e7	0.756816	0.378408	−	0.925639i	$-0.376472\pi$
$809$	1.40884e7	0.756816	0.378408	+	0.925639i	$0.376472\pi$
$810$	0	0
$811$	1.81433e7	0.968646	0.484323	−	0.874889i	$-0.339066\pi$
$811$	1.81433e7	0.968646	0.484323	+	0.874889i	$0.339066\pi$
$812$	1.13888e7	0.606160
$813$	2.31076e7	1.22611
$814$	2.41234e7	1.27608
$815$	0	0
$816$	3.43298e7	1.80487
$817$	1.06624e6	0.0558856
$818$	3.07273e7	1.60562
$819$	−322420.	−0.0167962
$820$	0	0
$821$	−2.13669e7	−1.10633	−0.553164	−	0.833072i	$-0.686580\pi$
$821$	−2.13669e7	−1.10633	−0.553164	+	0.833072i	$0.686580\pi$
$822$	2.86247e7	1.47761
$823$	−1.78017e7	−0.916142	−0.458071	−	0.888916i	$-0.651459\pi$
$823$	−1.78017e7	−0.916142	−0.458071	+	0.888916i	$0.651459\pi$
$824$	−1.91016e7	−0.980058
$825$	0	0
$826$	−1.33770e6	−0.0682195
$827$	−1.62921e7	−0.828350	−0.414175	−	0.910197i	$-0.635930\pi$
$827$	−1.62921e7	−0.828350	−0.414175	+	0.910197i	$0.635930\pi$
$828$	5.82950e6	0.295499
$829$	−2.08499e6	−0.105370	−0.0526851	−	0.998611i	$-0.516778\pi$
$829$	−2.08499e6	−0.105370	−0.0526851	+	0.998611i	$0.516778\pi$
$830$	0	0
$831$	1.48973e7	0.748348
$832$	−2.57152e6	−0.128790
$833$	4.13452e6	0.206449
$834$	−4.95684e6	−0.246769
$835$	0	0
$836$	−1.54605e6	−0.0765081
$837$	3.10346e7	1.53120
$838$	2.81438e7	1.38443
$839$	−2.27850e7	−1.11749	−0.558745	−	0.829340i	$-0.688717\pi$
$839$	−2.27850e7	−1.11749	−0.558745	+	0.829340i	$0.688717\pi$
$840$	0	0
$841$	−8.82842e6	−0.430421
$842$	3.05802e7	1.48648
$843$	−312788.	−0.0151594
$844$	7.82498e7	3.78118
$845$	0	0
$846$	4.38228e6	0.210511
$847$	−5.25412e6	−0.251647
$848$	−3.22109e6	−0.153820
$849$	3.49403e7	1.66363
$850$	0	0
$851$	−1.89660e7	−0.897740
$852$	−5.57491e7	−2.63111
$853$	2.26975e7	1.06808	0.534042	−	0.845458i	$-0.320672\pi$
$853$	2.26975e7	1.06808	0.534042	+	0.845458i	$0.320672\pi$
$854$	1.25675e7	0.589664
$855$	0	0
$856$	5.26766e7	2.45716
$857$	−2.52900e7	−1.17624	−0.588120	−	0.808774i	$-0.700132\pi$
$857$	−2.52900e7	−1.17624	−0.588120	+	0.808774i	$0.700132\pi$
$858$	4.54720e6	0.210875
$859$	−1.03947e7	−0.480652	−0.240326	−	0.970692i	$-0.577254\pi$
$859$	−1.03947e7	−0.480652	−0.240326	+	0.970692i	$0.577254\pi$
$860$	0	0
$861$	−1.23219e7	−0.566462
$862$	1.93750e7	0.888122
$863$	−4.33399e7	−1.98089	−0.990447	−	0.137892i	$-0.955967\pi$
$863$	−4.33399e7	−1.98089	−0.990447	+	0.137892i	$0.955967\pi$
$864$	−1.10432e7	−0.503281
$865$	0	0
$866$	−3.94790e7	−1.78884
$867$	2.16360e7	0.977527
$868$	−2.54698e7	−1.14743
$869$	7.37389e6	0.331243
$870$	0	0
$871$	6.77656e6	0.302666
$872$	3.34433e7	1.48942
$873$	−2.74978e6	−0.122113
$874$	1.78752e6	0.0791539
$875$	0	0
$876$	−6.48141e7	−2.85370
$877$	−3.71659e7	−1.63172	−0.815861	−	0.578248i	$-0.803736\pi$
$877$	−3.71659e7	−1.63172	−0.815861	+	0.578248i	$0.803736\pi$
$878$	−7.41770e7	−3.24738
$879$	2.70449e7	1.18063
$880$	0	0
$881$	9.04785e6	0.392740	0.196370	−	0.980530i	$-0.437085\pi$
$881$	9.04785e6	0.392740	0.196370	+	0.980530i	$0.437085\pi$
$882$	−1.12847e6	−0.0488448
$883$	−3.29679e7	−1.42295	−0.711474	−	0.702712i	$-0.751972\pi$
$883$	−3.29679e7	−1.42295	−0.711474	+	0.702712i	$0.751972\pi$
$884$	1.63934e7	0.705569
$885$	0	0
$886$	−1.40269e7	−0.600313
$887$	1.61099e7	0.687517	0.343758	−	0.939058i	$-0.388300\pi$
$887$	1.61099e7	0.687517	0.343758	+	0.939058i	$0.388300\pi$
$888$	5.24059e7	2.23022
$889$	−2.95882e6	−0.125564
$890$	0	0
$891$	−1.05372e7	−0.444663
$892$	5.60500e7	2.35865
$893$	913752.	0.0383442
$894$	−2.83164e6	−0.118493
$895$	0	0
$896$	−1.32653e7	−0.552009
$897$	−3.57504e6	−0.148354
$898$	−5.90574e6	−0.244390
$899$	−2.61272e7	−1.07819
$900$	0	0
$901$	−3.89516e6	−0.159850
$902$	−4.16718e7	−1.70540
$903$	−7.46368e6	−0.304603
$904$	3.00074e7	1.22126
$905$	0	0
$906$	9.92656e6	0.401771
$907$	4.47286e7	1.80537	0.902686	−	0.430300i	$-0.141592\pi$
$907$	4.47286e7	1.80537	0.902686	+	0.430300i	$0.141592\pi$
$908$	−5.05798e6	−0.203593
$909$	−1.81871e6	−0.0730053
$910$	0	0
$911$	−6.60518e6	−0.263687	−0.131844	−	0.991271i	$-0.542090\pi$
$911$	−6.60518e6	−0.263687	−0.131844	+	0.991271i	$0.542090\pi$
$912$	−1.95373e6	−0.0777816
$913$	4.76482e6	0.189177
$914$	2.90484e7	1.15016
$915$	0	0
$916$	7.69730e7	3.03110
$917$	−3.01771e6	−0.118510
$918$	−6.99132e7	−2.73812
$919$	−3.08930e7	−1.20662	−0.603311	−	0.797506i	$-0.706152\pi$
$919$	−3.08930e7	−1.20662	−0.603311	+	0.797506i	$0.706152\pi$
$920$	0	0
$921$	6.42704e6	0.249667
$922$	−9.22684e6	−0.357459
$923$	−8.19840e6	−0.316756
$924$	1.08223e7	0.417005
$925$	0	0
$926$	−7.18235e7	−2.75258
$927$	2.49382e6	0.0953160
$928$	9.29696e6	0.354381
$929$	−4.87215e6	−0.185217	−0.0926087	−	0.995703i	$-0.529521\pi$
$929$	−4.87215e6	−0.185217	−0.0926087	+	0.995703i	$0.529521\pi$
$930$	0	0
$931$	−235298.	−0.00889701
$932$	1.35134e7	0.509593
$933$	9.33979e6	0.351264
$934$	6.12570e6	0.229767
$935$	0	0
$936$	−2.36880e6	−0.0883769
$937$	3.25004e7	1.20932	0.604658	−	0.796485i	$-0.293310\pi$
$937$	3.25004e7	1.20932	0.604658	+	0.796485i	$0.293310\pi$
$938$	2.37180e7	0.880177
$939$	1.55448e6	0.0575334
$940$	0	0
$941$	−2.64040e6	−0.0972066	−0.0486033	−	0.998818i	$-0.515477\pi$
$941$	−2.64040e6	−0.0972066	−0.0486033	+	0.998818i	$0.515477\pi$
$942$	−4.10934e7	−1.50884
$943$	3.27627e7	1.19978
$944$	−3.88752e6	−0.141985
$945$	0	0
$946$	−2.52416e7	−0.917042
$947$	4.08179e7	1.47903	0.739513	−	0.673142i	$-0.235056\pi$
$947$	4.08179e7	1.47903	0.739513	+	0.673142i	$0.235056\pi$
$948$	3.02584e7	1.09351
$949$	−9.53148e6	−0.343554
$950$	0	0
$951$	962892.	0.0345244
$952$	3.03761e7	1.08627
$953$	6.71983e6	0.239677	0.119838	−	0.992793i	$-0.461762\pi$
$953$	6.71983e6	0.239677	0.119838	+	0.992793i	$0.461762\pi$
$954$	1.06314e6	0.0378198
$955$	0	0
$956$	3.28375e7	1.16205
$957$	1.11017e7	0.391840
$958$	2.60330e7	0.916454
$959$	1.00186e7	0.351773
$960$	0	0
$961$	2.98016e7	1.04095
$962$	1.45572e7	0.507154
$963$	−6.87723e6	−0.238972
$964$	5.48019e7	1.89934
$965$	0	0
$966$	−1.25126e7	−0.431426
$967$	2.78979e6	0.0959413	0.0479707	−	0.998849i	$-0.484725\pi$
$967$	2.78979e6	0.0959413	0.0479707	+	0.998849i	$0.484725\pi$
$968$	−3.86017e7	−1.32409
$969$	−2.36258e6	−0.0808310
$970$	0	0
$971$	3.33594e7	1.13545	0.567727	−	0.823217i	$-0.307823\pi$
$971$	3.33594e7	1.13545	0.567727	+	0.823217i	$0.307823\pi$
$972$	2.38486e7	0.809648
$973$	−1.73489e6	−0.0587477
$974$	−5.46309e7	−1.84519
$975$	0	0
$976$	3.65228e7	1.22727
$977$	7.60033e6	0.254739	0.127370	−	0.991855i	$-0.459347\pi$
$977$	7.60033e6	0.254739	0.127370	+	0.991855i	$0.459347\pi$
$978$	−1.84688e6	−0.0617435
$979$	−1.17350e7	−0.391316
$980$	0	0
$981$	−4.36621e6	−0.144854
$982$	1.64090e7	0.543004
$983$	5.79760e6	0.191366	0.0956829	−	0.995412i	$-0.469497\pi$
$983$	5.79760e6	0.191366	0.0956829	+	0.995412i	$0.469497\pi$
$984$	−9.05285e7	−2.98056
$985$	0	0
$986$	5.88580e7	1.92803
$987$	−6.39626e6	−0.208994
$988$	−932960.	−0.0304068
$989$	1.98451e7	0.645153
$990$	0	0
$991$	1.26825e7	0.410224	0.205112	−	0.978739i	$-0.434244\pi$
$991$	1.26825e7	0.410224	0.205112	+	0.978739i	$0.434244\pi$
$992$	−2.07917e7	−0.670827
$993$	−7.90227e6	−0.254319
$994$	−2.86944e7	−0.921152
$995$	0	0
$996$	1.95522e7	0.624521
$997$	−1.44400e7	−0.460077	−0.230039	−	0.973182i	$-0.573885\pi$
$997$	−1.44400e7	−0.460077	−0.230039	+	0.973182i	$0.573885\pi$
$998$	2.99796e7	0.952796
$999$	−4.22159e7	−1.33833

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.6.a.b.1.1		1
5.2	odd	4		175.6.b.a.99.2		2
5.3	odd	4		175.6.b.a.99.1		2
5.4	even	2		7.6.a.a.1.1	✓	1
15.14	odd	2		63.6.a.e.1.1		1
20.19	odd	2		112.6.a.g.1.1		1
35.4	even	6		49.6.c.c.30.1		2
35.9	even	6		49.6.c.c.18.1		2
35.19	odd	6		49.6.c.b.18.1		2
35.24	odd	6		49.6.c.b.30.1		2
35.34	odd	2		49.6.a.a.1.1		1
40.19	odd	2		448.6.a.c.1.1		1
40.29	even	2		448.6.a.m.1.1		1
55.54	odd	2		847.6.a.b.1.1		1
60.59	even	2		1008.6.a.y.1.1		1
105.104	even	2		441.6.a.k.1.1		1
140.139	even	2		784.6.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.6.a.a.1.1	✓	1	5.4	even	2
49.6.a.a.1.1		1	35.34	odd	2
49.6.c.b.18.1		2	35.19	odd	6
49.6.c.b.30.1		2	35.24	odd	6
49.6.c.c.18.1		2	35.9	even	6
49.6.c.c.30.1		2	35.4	even	6
63.6.a.e.1.1		1	15.14	odd	2
112.6.a.g.1.1		1	20.19	odd	2
175.6.a.b.1.1		1	1.1	even	1	trivial
175.6.b.a.99.1		2	5.3	odd	4
175.6.b.a.99.2		2	5.2	odd	4
441.6.a.k.1.1		1	105.104	even	2
448.6.a.c.1.1		1	40.19	odd	2
448.6.a.m.1.1		1	40.29	even	2
784.6.a.c.1.1		1	140.139	even	2
847.6.a.b.1.1		1	55.54	odd	2
1008.6.a.y.1.1		1	60.59	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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	175.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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