LMFDB - Embedded newform 350.6.a.n.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [350,6,Mod(1,350)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("350.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(350, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	350.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,4,23] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$56.1343369345$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	350.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q+4.00000 q^{2} +23.0000 q^{3} +16.0000 q^{4} +92.0000 q^{6} -49.0000 q^{7} +64.0000 q^{8} +286.000 q^{9} +555.000 q^{11} +368.000 q^{12} +241.000 q^{13} -196.000 q^{14} +256.000 q^{16} +1491.00 q^{17} +1144.00 q^{18} -2038.00 q^{19} -1127.00 q^{21} +2220.00 q^{22} +1230.00 q^{23} +1472.00 q^{24} +964.000 q^{26} +989.000 q^{27} -784.000 q^{28} -5001.00 q^{29} +5696.00 q^{31} +1024.00 q^{32} +12765.0 q^{33} +5964.00 q^{34} +4576.00 q^{36} +5602.00 q^{37} -8152.00 q^{38} +5543.00 q^{39} -2424.00 q^{41} -4508.00 q^{42} -602.000 q^{43} +8880.00 q^{44} +4920.00 q^{46} +23163.0 q^{47} +5888.00 q^{48} +2401.00 q^{49} +34293.0 q^{51} +3856.00 q^{52} +25296.0 q^{53} +3956.00 q^{54} -3136.00 q^{56} -46874.0 q^{57} -20004.0 q^{58} +5724.00 q^{59} -36112.0 q^{61} +22784.0 q^{62} -14014.0 q^{63} +4096.00 q^{64} +51060.0 q^{66} -66104.0 q^{67} +23856.0 q^{68} +28290.0 q^{69} +16080.0 q^{71} +18304.0 q^{72} +80482.0 q^{73} +22408.0 q^{74} -32608.0 q^{76} -27195.0 q^{77} +22172.0 q^{78} -64147.0 q^{79} -46751.0 q^{81} -9696.00 q^{82} +106284. q^{83} -18032.0 q^{84} -2408.00 q^{86} -115023. q^{87} +35520.0 q^{88} -71676.0 q^{89} -11809.0 q^{91} +19680.0 q^{92} +131008. q^{93} +92652.0 q^{94} +23552.0 q^{96} -151025. q^{97} +9604.00 q^{98} +158730. q^{99} +O(q^{100})\)

Coefficient data

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

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

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

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	23.0000	1.47545	0.737725	−	0.675101i	$-0.235900\pi$
$3$	23.0000	1.47545	0.737725	+	0.675101i	$0.235900\pi$
$4$	16.0000	0.500000
$5$	0	0
$5$	0	0
$6$	92.0000	1.04330
$7$	−49.0000	−0.377964
$7$	−49.0000	−0.377964
$8$	64.0000	0.353553
$9$	286.000	1.17695
$10$	0	0
$11$	555.000	1.38297	0.691483	−	0.722393i	$-0.256958\pi$
$11$	555.000	1.38297	0.691483	+	0.722393i	$0.256958\pi$
$12$	368.000	0.737725
$13$	241.000	0.395511	0.197756	−	0.980251i	$-0.436635\pi$
$13$	241.000	0.395511	0.197756	+	0.980251i	$0.436635\pi$
$14$	−196.000	−0.267261
$15$	0	0
$16$	256.000	0.250000
$17$	1491.00	1.25128	0.625641	−	0.780111i	$-0.284837\pi$
$17$	1491.00	1.25128	0.625641	+	0.780111i	$0.284837\pi$
$18$	1144.00	0.832233
$19$	−2038.00	−1.29515	−0.647575	−	0.762002i	$-0.724217\pi$
$19$	−2038.00	−1.29515	−0.647575	+	0.762002i	$0.724217\pi$
$20$	0	0
$21$	−1127.00	−0.557668
$22$	2220.00	0.977904
$23$	1230.00	0.484826	0.242413	−	0.970173i	$-0.422061\pi$
$23$	1230.00	0.484826	0.242413	+	0.970173i	$0.422061\pi$
$24$	1472.00	0.521651
$25$	0	0
$26$	964.000	0.279669
$27$	989.000	0.261088
$28$	−784.000	−0.188982
$29$	−5001.00	−1.10424	−0.552118	−	0.833766i	$-0.686180\pi$
$29$	−5001.00	−1.10424	−0.552118	+	0.833766i	$0.686180\pi$
$30$	0	0
$31$	5696.00	1.06455	0.532275	−	0.846572i	$-0.321337\pi$
$31$	5696.00	1.06455	0.532275	+	0.846572i	$0.321337\pi$
$32$	1024.00	0.176777
$33$	12765.0	2.04050
$34$	5964.00	0.884790
$35$	0	0
$36$	4576.00	0.588477
$37$	5602.00	0.672727	0.336363	−	0.941732i	$-0.390803\pi$
$37$	5602.00	0.672727	0.336363	+	0.941732i	$0.390803\pi$
$38$	−8152.00	−0.915810
$39$	5543.00	0.583557
$40$	0	0
$41$	−2424.00	−0.225202	−0.112601	−	0.993640i	$-0.535918\pi$
$41$	−2424.00	−0.225202	−0.112601	+	0.993640i	$0.535918\pi$
$42$	−4508.00	−0.394331
$43$	−602.000	−0.0496507	−0.0248253	−	0.999692i	$-0.507903\pi$
$43$	−602.000	−0.0496507	−0.0248253	+	0.999692i	$0.507903\pi$
$44$	8880.00	0.691483
$45$	0	0
$46$	4920.00	0.342823
$47$	23163.0	1.52950	0.764751	−	0.644326i	$-0.222862\pi$
$47$	23163.0	1.52950	0.764751	+	0.644326i	$0.222862\pi$
$48$	5888.00	0.368863
$49$	2401.00	0.142857
$50$	0	0
$51$	34293.0	1.84621
$52$	3856.00	0.197756
$53$	25296.0	1.23698	0.618489	−	0.785793i	$-0.287745\pi$
$53$	25296.0	1.23698	0.618489	+	0.785793i	$0.287745\pi$
$54$	3956.00	0.184617
$55$	0	0
$56$	−3136.00	−0.133631
$57$	−46874.0	−1.91093
$58$	−20004.0	−0.780813
$59$	5724.00	0.214077	0.107038	−	0.994255i	$-0.465863\pi$
$59$	5724.00	0.214077	0.107038	+	0.994255i	$0.465863\pi$
$60$	0	0
$61$	−36112.0	−1.24259	−0.621294	−	0.783578i	$-0.713393\pi$
$61$	−36112.0	−1.24259	−0.621294	+	0.783578i	$0.713393\pi$
$62$	22784.0	0.752750
$63$	−14014.0	−0.444847
$64$	4096.00	0.125000
$65$	0	0
$66$	51060.0	1.44285
$67$	−66104.0	−1.79904	−0.899520	−	0.436880i	$-0.856083\pi$
$67$	−66104.0	−1.79904	−0.899520	+	0.436880i	$0.856083\pi$
$68$	23856.0	0.625641
$69$	28290.0	0.715336
$70$	0	0
$71$	16080.0	0.378565	0.189282	−	0.981923i	$-0.439384\pi$
$71$	16080.0	0.378565	0.189282	+	0.981923i	$0.439384\pi$
$72$	18304.0	0.416116
$73$	80482.0	1.76763	0.883816	−	0.467836i	$-0.154966\pi$
$73$	80482.0	1.76763	0.883816	+	0.467836i	$0.154966\pi$
$74$	22408.0	0.475690
$75$	0	0
$76$	−32608.0	−0.647575
$77$	−27195.0	−0.522712
$78$	22172.0	0.412637
$79$	−64147.0	−1.15640	−0.578201	−	0.815895i	$-0.696245\pi$
$79$	−64147.0	−1.15640	−0.578201	+	0.815895i	$0.696245\pi$
$80$	0	0
$81$	−46751.0	−0.791732
$82$	−9696.00	−0.159242
$83$	106284.	1.69345	0.846726	−	0.532030i	$-0.178571\pi$
$83$	106284.	1.69345	0.846726	+	0.532030i	$0.178571\pi$
$84$	−18032.0	−0.278834
$85$	0	0
$86$	−2408.00	−0.0351083
$87$	−115023.	−1.62925
$88$	35520.0	0.488952
$89$	−71676.0	−0.959177	−0.479588	−	0.877494i	$-0.659214\pi$
$89$	−71676.0	−0.959177	−0.479588	+	0.877494i	$0.659214\pi$
$90$	0	0
$91$	−11809.0	−0.149489
$92$	19680.0	0.242413
$93$	131008.	1.57069
$94$	92652.0	1.08152
$95$	0	0
$96$	23552.0	0.260825
$97$	−151025.	−1.62974	−0.814872	−	0.579641i	$-0.803193\pi$
$97$	−151025.	−1.62974	−0.814872	+	0.579641i	$0.803193\pi$
$98$	9604.00	0.101015
$99$	158730.	1.62769
$100$	0	0
$101$	−57150.0	−0.557459	−0.278729	−	0.960370i	$-0.589913\pi$
$101$	−57150.0	−0.557459	−0.278729	+	0.960370i	$0.589913\pi$
$102$	137172.	1.30546
$103$	−115889.	−1.07634	−0.538170	−	0.842837i	$-0.680884\pi$
$103$	−115889.	−1.07634	−0.538170	+	0.842837i	$0.680884\pi$
$104$	15424.0	0.139834
$105$	0	0
$106$	101184.	0.874676
$107$	137862.	1.16409	0.582043	−	0.813158i	$-0.302253\pi$
$107$	137862.	1.16409	0.582043	+	0.813158i	$0.302253\pi$
$108$	15824.0	0.130544
$109$	88397.0	0.712642	0.356321	−	0.934364i	$-0.384031\pi$
$109$	88397.0	0.712642	0.356321	+	0.934364i	$0.384031\pi$
$110$	0	0
$111$	128846.	0.992575
$112$	−12544.0	−0.0944911
$113$	−205554.	−1.51436	−0.757181	−	0.653205i	$-0.773424\pi$
$113$	−205554.	−1.51436	−0.757181	+	0.653205i	$0.773424\pi$
$114$	−187496.	−1.35123
$115$	0	0
$116$	−80016.0	−0.552118
$117$	68926.0	0.465499
$118$	22896.0	0.151375
$119$	−73059.0	−0.472940
$120$	0	0
$121$	146974.	0.912593
$122$	−144448.	−0.878642
$123$	−55752.0	−0.332275
$124$	91136.0	0.532275
$125$	0	0
$126$	−56056.0	−0.314554
$127$	−250916.	−1.38044	−0.690222	−	0.723597i	$-0.742487\pi$
$127$	−250916.	−1.38044	−0.690222	+	0.723597i	$0.742487\pi$
$128$	16384.0	0.0883883
$129$	−13846.0	−0.0732572
$130$	0	0
$131$	−52122.0	−0.265365	−0.132682	−	0.991159i	$-0.542359\pi$
$131$	−52122.0	−0.265365	−0.132682	+	0.991159i	$0.542359\pi$
$132$	204240.	1.02025
$133$	99862.0	0.489521
$134$	−264416.	−1.27211
$135$	0	0
$136$	95424.0	0.442395
$137$	135468.	0.616645	0.308323	−	0.951282i	$-0.400232\pi$
$137$	135468.	0.616645	0.308323	+	0.951282i	$0.400232\pi$
$138$	113160.	0.505819
$139$	−349486.	−1.53424	−0.767119	−	0.641505i	$-0.778310\pi$
$139$	−349486.	−1.53424	−0.767119	+	0.641505i	$0.778310\pi$
$140$	0	0
$141$	532749.	2.25671
$142$	64320.0	0.267686
$143$	133755.	0.546978
$144$	73216.0	0.294239
$145$	0	0
$146$	321928.	1.24990
$147$	55223.0	0.210779
$148$	89632.0	0.336363
$149$	176082.	0.649754	0.324877	−	0.945756i	$-0.394677\pi$
$149$	176082.	0.649754	0.324877	+	0.945756i	$0.394677\pi$
$150$	0	0
$151$	383333.	1.36815	0.684075	−	0.729411i	$-0.260206\pi$
$151$	383333.	1.36815	0.684075	+	0.729411i	$0.260206\pi$
$152$	−130432.	−0.457905
$153$	426426.	1.47270
$154$	−108780.	−0.369613
$155$	0	0
$156$	88688.0	0.291779
$157$	−345914.	−1.12000	−0.560001	−	0.828492i	$-0.689199\pi$
$157$	−345914.	−1.12000	−0.560001	+	0.828492i	$0.689199\pi$
$158$	−256588.	−0.817699
$159$	581808.	1.82510
$160$	0	0
$161$	−60270.0	−0.183247
$162$	−187004.	−0.559839
$163$	−91586.0	−0.269998	−0.134999	−	0.990846i	$-0.543103\pi$
$163$	−91586.0	−0.269998	−0.134999	+	0.990846i	$0.543103\pi$
$164$	−38784.0	−0.112601
$165$	0	0
$166$	425136.	1.19745
$167$	−38097.0	−0.105706	−0.0528530	−	0.998602i	$-0.516831\pi$
$167$	−38097.0	−0.105706	−0.0528530	+	0.998602i	$0.516831\pi$
$168$	−72128.0	−0.197165
$169$	−313212.	−0.843571
$170$	0	0
$171$	−582868.	−1.52433
$172$	−9632.00	−0.0248253
$173$	541443.	1.37543	0.687713	−	0.725982i	$-0.258615\pi$
$173$	541443.	1.37543	0.687713	+	0.725982i	$0.258615\pi$
$174$	−460092.	−1.15205
$175$	0	0
$176$	142080.	0.345741
$177$	131652.	0.315860
$178$	−286704.	−0.678241
$179$	166188.	0.387674	0.193837	−	0.981034i	$-0.437907\pi$
$179$	166188.	0.387674	0.193837	+	0.981034i	$0.437907\pi$
$180$	0	0
$181$	−197320.	−0.447687	−0.223844	−	0.974625i	$-0.571860\pi$
$181$	−197320.	−0.447687	−0.223844	+	0.974625i	$0.571860\pi$
$182$	−47236.0	−0.105705
$183$	−830576.	−1.83338
$184$	78720.0	0.171412
$185$	0	0
$186$	524032.	1.11065
$187$	827505.	1.73048
$188$	370608.	0.764751
$189$	−48461.0	−0.0986820
$190$	0	0
$191$	−337221.	−0.668854	−0.334427	−	0.942422i	$-0.608543\pi$
$191$	−337221.	−0.668854	−0.334427	+	0.942422i	$0.608543\pi$
$192$	94208.0	0.184431
$193$	−260516.	−0.503432	−0.251716	−	0.967801i	$-0.580995\pi$
$193$	−260516.	−0.503432	−0.251716	+	0.967801i	$0.580995\pi$
$194$	−604100.	−1.15240
$195$	0	0
$196$	38416.0	0.0714286
$197$	409212.	0.751247	0.375624	−	0.926772i	$-0.377429\pi$
$197$	409212.	0.751247	0.375624	+	0.926772i	$0.377429\pi$
$198$	634920.	1.15095
$199$	300980.	0.538772	0.269386	−	0.963032i	$-0.413179\pi$
$199$	300980.	0.538772	0.269386	+	0.963032i	$0.413179\pi$
$200$	0	0
$201$	−1.52039e6	−2.65439
$202$	−228600.	−0.394183
$203$	245049.	0.417362
$204$	548688.	0.923103
$205$	0	0
$206$	−463556.	−0.761087
$207$	351780.	0.570618
$208$	61696.0	0.0988778
$209$	−1.13109e6	−1.79115
$210$	0	0
$211$	−1.22618e6	−1.89604	−0.948021	−	0.318209i	$-0.896919\pi$
$211$	−1.22618e6	−1.89604	−0.948021	+	0.318209i	$0.896919\pi$
$212$	404736.	0.618489
$213$	369840.	0.558554
$214$	551448.	0.823133
$215$	0	0
$216$	63296.0	0.0923085
$217$	−279104.	−0.402362
$218$	353588.	0.503914
$219$	1.85109e6	2.60805
$220$	0	0
$221$	359331.	0.494896
$222$	515384.	0.701857
$223$	−621257.	−0.836583	−0.418292	−	0.908313i	$-0.637371\pi$
$223$	−621257.	−0.836583	−0.418292	+	0.908313i	$0.637371\pi$
$224$	−50176.0	−0.0668153
$225$	0	0
$226$	−822216.	−1.07082
$227$	−1.29768e6	−1.67148	−0.835742	−	0.549123i	$-0.814962\pi$
$227$	−1.29768e6	−1.67148	−0.835742	+	0.549123i	$0.814962\pi$
$228$	−749984.	−0.955465
$229$	−124264.	−0.156587	−0.0782937	−	0.996930i	$-0.524947\pi$
$229$	−124264.	−0.156587	−0.0782937	+	0.996930i	$0.524947\pi$
$230$	0	0
$231$	−625485.	−0.771235
$232$	−320064.	−0.390406
$233$	−1.08742e6	−1.31222	−0.656109	−	0.754666i	$-0.727799\pi$
$233$	−1.08742e6	−1.31222	−0.656109	+	0.754666i	$0.727799\pi$
$234$	275704.	0.329157
$235$	0	0
$236$	91584.0	0.107038
$237$	−1.47538e6	−1.70621
$238$	−292236.	−0.334419
$239$	−545631.	−0.617880	−0.308940	−	0.951081i	$-0.599974\pi$
$239$	−545631.	−0.617880	−0.308940	+	0.951081i	$0.599974\pi$
$240$	0	0
$241$	811310.	0.899796	0.449898	−	0.893080i	$-0.351460\pi$
$241$	811310.	0.899796	0.449898	+	0.893080i	$0.351460\pi$
$242$	587896.	0.645301
$243$	−1.31560e6	−1.42925
$244$	−577792.	−0.621294
$245$	0	0
$246$	−223008.	−0.234954
$247$	−491158.	−0.512246
$248$	364544.	0.376375
$249$	2.44453e6	2.49860
$250$	0	0
$251$	−897738.	−0.899426	−0.449713	−	0.893173i	$-0.648474\pi$
$251$	−897738.	−0.899426	−0.449713	+	0.893173i	$0.648474\pi$
$252$	−224224.	−0.222424
$253$	682650.	0.670497
$254$	−1.00366e6	−0.976122
$255$	0	0
$256$	65536.0	0.0625000
$257$	594678.	0.561628	0.280814	−	0.959762i	$-0.409396\pi$
$257$	594678.	0.561628	0.280814	+	0.959762i	$0.409396\pi$
$258$	−55384.0	−0.0518006
$259$	−274498.	−0.254267
$260$	0	0
$261$	−1.43029e6	−1.29964
$262$	−208488.	−0.187641
$263$	−1.02837e6	−0.916769	−0.458385	−	0.888754i	$-0.651572\pi$
$263$	−1.02837e6	−0.916769	−0.458385	+	0.888754i	$0.651572\pi$
$264$	816960.	0.721425
$265$	0	0
$266$	399448.	0.346143
$267$	−1.64855e6	−1.41522
$268$	−1.05766e6	−0.899520
$269$	−1.24390e6	−1.04811	−0.524053	−	0.851685i	$-0.675581\pi$
$269$	−1.24390e6	−1.04811	−0.524053	+	0.851685i	$0.675581\pi$
$270$	0	0
$271$	737624.	0.610115	0.305058	−	0.952334i	$-0.401324\pi$
$271$	737624.	0.610115	0.305058	+	0.952334i	$0.401324\pi$
$272$	381696.	0.312821
$273$	−271607.	−0.220564
$274$	541872.	0.436034
$275$	0	0
$276$	452640.	0.357668
$277$	2.20063e6	1.72325	0.861624	−	0.507548i	$-0.169448\pi$
$277$	2.20063e6	1.72325	0.861624	+	0.507548i	$0.169448\pi$
$278$	−1.39794e6	−1.08487
$279$	1.62906e6	1.25293
$280$	0	0
$281$	173979.	0.131441	0.0657205	−	0.997838i	$-0.479065\pi$
$281$	173979.	0.131441	0.0657205	+	0.997838i	$0.479065\pi$
$282$	2.13100e6	1.59573
$283$	551053.	0.409004	0.204502	−	0.978866i	$-0.434443\pi$
$283$	551053.	0.409004	0.204502	+	0.978866i	$0.434443\pi$
$284$	257280.	0.189282
$285$	0	0
$286$	535020.	0.386772
$287$	118776.	0.0851185
$288$	292864.	0.208058
$289$	803224.	0.565708
$290$	0	0
$291$	−3.47358e6	−2.40461
$292$	1.28771e6	0.883816
$293$	1.67512e6	1.13993	0.569963	−	0.821670i	$-0.306958\pi$
$293$	1.67512e6	1.13993	0.569963	+	0.821670i	$0.306958\pi$
$294$	220892.	0.149043
$295$	0	0
$296$	358528.	0.237845
$297$	548895.	0.361076
$298$	704328.	0.459446
$299$	296430.	0.191754
$300$	0	0
$301$	29498.0	0.0187662
$302$	1.53333e6	0.967428
$303$	−1.31445e6	−0.822503
$304$	−521728.	−0.323788
$305$	0	0
$306$	1.70570e6	1.04136
$307$	−2.33060e6	−1.41131	−0.705655	−	0.708556i	$-0.749347\pi$
$307$	−2.33060e6	−1.41131	−0.705655	+	0.708556i	$0.749347\pi$
$308$	−435120.	−0.261356
$309$	−2.66545e6	−1.58809
$310$	0	0
$311$	706266.	0.414064	0.207032	−	0.978334i	$-0.433620\pi$
$311$	706266.	0.414064	0.207032	+	0.978334i	$0.433620\pi$
$312$	354752.	0.206319
$313$	183565.	0.105908	0.0529540	−	0.998597i	$-0.483136\pi$
$313$	183565.	0.105908	0.0529540	+	0.998597i	$0.483136\pi$
$314$	−1.38366e6	−0.791961
$315$	0	0
$316$	−1.02635e6	−0.578201
$317$	−2.70665e6	−1.51281	−0.756405	−	0.654103i	$-0.773046\pi$
$317$	−2.70665e6	−1.51281	−0.756405	+	0.654103i	$0.773046\pi$
$318$	2.32723e6	1.29054
$319$	−2.77556e6	−1.52712
$320$	0	0
$321$	3.17083e6	1.71755
$322$	−241080.	−0.129575
$323$	−3.03866e6	−1.62060
$324$	−748016.	−0.395866
$325$	0	0
$326$	−366344.	−0.190917
$327$	2.03313e6	1.05147
$328$	−155136.	−0.0796211
$329$	−1.13499e6	−0.578098
$330$	0	0
$331$	−2.14337e6	−1.07529	−0.537647	−	0.843170i	$-0.680687\pi$
$331$	−2.14337e6	−1.07529	−0.537647	+	0.843170i	$0.680687\pi$
$332$	1.70054e6	0.846726
$333$	1.60217e6	0.791769
$334$	−152388.	−0.0747454
$335$	0	0
$336$	−288512.	−0.139417
$337$	−655346.	−0.314337	−0.157169	−	0.987572i	$-0.550237\pi$
$337$	−655346.	−0.314337	−0.157169	+	0.987572i	$0.550237\pi$
$338$	−1.25285e6	−0.596495
$339$	−4.72774e6	−2.23437
$340$	0	0
$341$	3.16128e6	1.47223
$342$	−2.33147e6	−1.07787
$343$	−117649.	−0.0539949
$344$	−38528.0	−0.0175542
$345$	0	0
$346$	2.16577e6	0.972574
$347$	4.22275e6	1.88266	0.941329	−	0.337491i	$-0.109578\pi$
$347$	4.22275e6	1.88266	0.941329	+	0.337491i	$0.109578\pi$
$348$	−1.84037e6	−0.814623
$349$	3.01710e6	1.32595	0.662974	−	0.748643i	$-0.269294\pi$
$349$	3.01710e6	1.32595	0.662974	+	0.748643i	$0.269294\pi$
$350$	0	0
$351$	238349.	0.103263
$352$	568320.	0.244476
$353$	−2.25258e6	−0.962150	−0.481075	−	0.876679i	$-0.659754\pi$
$353$	−2.25258e6	−0.962150	−0.481075	+	0.876679i	$0.659754\pi$
$354$	526608.	0.223347
$355$	0	0
$356$	−1.14682e6	−0.479588
$357$	−1.68036e6	−0.697800
$358$	664752.	0.274127
$359$	−1.83950e6	−0.753294	−0.376647	−	0.926357i	$-0.622923\pi$
$359$	−1.83950e6	−0.753294	−0.376647	+	0.926357i	$0.622923\pi$
$360$	0	0
$361$	1.67735e6	0.677414
$362$	−789280.	−0.316563
$363$	3.38040e6	1.34649
$364$	−188944.	−0.0747446
$365$	0	0
$366$	−3.32230e6	−1.29639
$367$	1.68832e6	0.654320	0.327160	−	0.944969i	$-0.393908\pi$
$367$	1.68832e6	0.654320	0.327160	+	0.944969i	$0.393908\pi$
$368$	314880.	0.121206
$369$	−693264.	−0.265053
$370$	0	0
$371$	−1.23950e6	−0.467534
$372$	2.09613e6	0.785345
$373$	−1.81212e6	−0.674394	−0.337197	−	0.941434i	$-0.609479\pi$
$373$	−1.81212e6	−0.674394	−0.337197	+	0.941434i	$0.609479\pi$
$374$	3.31002e6	1.22363
$375$	0	0
$376$	1.48243e6	0.540761
$377$	−1.20524e6	−0.436738
$378$	−193844.	−0.0697787
$379$	−4.76708e6	−1.70472	−0.852362	−	0.522952i	$-0.824831\pi$
$379$	−4.76708e6	−1.70472	−0.852362	+	0.522952i	$0.824831\pi$
$380$	0	0
$381$	−5.77107e6	−2.03678
$382$	−1.34888e6	−0.472951
$383$	69996.0	0.0243824	0.0121912	−	0.999926i	$-0.496119\pi$
$383$	69996.0	0.0243824	0.0121912	+	0.999926i	$0.496119\pi$
$384$	376832.	0.130413
$385$	0	0
$386$	−1.04206e6	−0.355980
$387$	−172172.	−0.0584366
$388$	−2.41640e6	−0.814872
$389$	3.98895e6	1.33655	0.668275	−	0.743915i	$-0.267033\pi$
$389$	3.98895e6	1.33655	0.668275	+	0.743915i	$0.267033\pi$
$390$	0	0
$391$	1.83393e6	0.606654
$392$	153664.	0.0505076
$393$	−1.19881e6	−0.391532
$394$	1.63685e6	0.531212
$395$	0	0
$396$	2.53968e6	0.813844
$397$	3.05904e6	0.974110	0.487055	−	0.873371i	$-0.338071\pi$
$397$	3.05904e6	0.974110	0.487055	+	0.873371i	$0.338071\pi$
$398$	1.20392e6	0.380969
$399$	2.29683e6	0.722264
$400$	0	0
$401$	4.30794e6	1.33785	0.668927	−	0.743329i	$-0.266754\pi$
$401$	4.30794e6	1.33785	0.668927	+	0.743329i	$0.266754\pi$
$402$	−6.08157e6	−1.87694
$403$	1.37274e6	0.421041
$404$	−914400.	−0.278729
$405$	0	0
$406$	980196.	0.295119
$407$	3.10911e6	0.930358
$408$	2.19475e6	0.652732
$409$	−239206.	−0.0707072	−0.0353536	−	0.999375i	$-0.511256\pi$
$409$	−239206.	−0.0707072	−0.0353536	+	0.999375i	$0.511256\pi$
$410$	0	0
$411$	3.11576e6	0.909829
$412$	−1.85422e6	−0.538170
$413$	−280476.	−0.0809134
$414$	1.40712e6	0.403488
$415$	0	0
$416$	246784.	0.0699171
$417$	−8.03818e6	−2.26369
$418$	−4.52436e6	−1.26653
$419$	4.63462e6	1.28967	0.644835	−	0.764322i	$-0.276926\pi$
$419$	4.63462e6	1.28967	0.644835	+	0.764322i	$0.276926\pi$
$420$	0	0
$421$	−2.10108e6	−0.577745	−0.288873	−	0.957368i	$-0.593280\pi$
$421$	−2.10108e6	−0.577745	−0.288873	+	0.957368i	$0.593280\pi$
$422$	−4.90472e6	−1.34070
$423$	6.62462e6	1.80016
$424$	1.61894e6	0.437338
$425$	0	0
$426$	1.47936e6	0.394957
$427$	1.76949e6	0.469654
$428$	2.20579e6	0.582043
$429$	3.07636e6	0.807039
$430$	0	0
$431$	1.65484e6	0.429104	0.214552	−	0.976713i	$-0.431171\pi$
$431$	1.65484e6	0.429104	0.214552	+	0.976713i	$0.431171\pi$
$432$	253184.	0.0652720
$433$	1.84031e6	0.471705	0.235852	−	0.971789i	$-0.424212\pi$
$433$	1.84031e6	0.471705	0.235852	+	0.971789i	$0.424212\pi$
$434$	−1.11642e6	−0.284513
$435$	0	0
$436$	1.41435e6	0.356321
$437$	−2.50674e6	−0.627922
$438$	7.40434e6	1.84417
$439$	5.83684e6	1.44549	0.722747	−	0.691113i	$-0.242879\pi$
$439$	5.83684e6	1.44549	0.722747	+	0.691113i	$0.242879\pi$
$440$	0	0
$441$	686686.	0.168136
$442$	1.43732e6	0.349944
$443$	−1.19704e6	−0.289801	−0.144901	−	0.989446i	$-0.546286\pi$
$443$	−1.19704e6	−0.289801	−0.144901	+	0.989446i	$0.546286\pi$
$444$	2.06154e6	0.496288
$445$	0	0
$446$	−2.48503e6	−0.591554
$447$	4.04989e6	0.958681
$448$	−200704.	−0.0472456
$449$	−3.42570e6	−0.801924	−0.400962	−	0.916095i	$-0.631324\pi$
$449$	−3.42570e6	−0.801924	−0.400962	+	0.916095i	$0.631324\pi$
$450$	0	0
$451$	−1.34532e6	−0.311447
$452$	−3.28886e6	−0.757181
$453$	8.81666e6	2.01864
$454$	−5.19071e6	−1.18192
$455$	0	0
$456$	−2.99994e6	−0.675616
$457$	−5.29742e6	−1.18652	−0.593258	−	0.805012i	$-0.702159\pi$
$457$	−5.29742e6	−1.18652	−0.593258	+	0.805012i	$0.702159\pi$
$458$	−497056.	−0.110724
$459$	1.47460e6	0.326695
$460$	0	0
$461$	8.87731e6	1.94549	0.972745	−	0.231876i	$-0.0744863\pi$
$461$	8.87731e6	1.94549	0.972745	+	0.231876i	$0.0744863\pi$
$462$	−2.50194e6	−0.545346
$463$	2.17475e6	0.471473	0.235737	−	0.971817i	$-0.424250\pi$
$463$	2.17475e6	0.471473	0.235737	+	0.971817i	$0.424250\pi$
$464$	−1.28026e6	−0.276059
$465$	0	0
$466$	−4.34966e6	−0.927878
$467$	378969.	0.0804103	0.0402051	−	0.999191i	$-0.487199\pi$
$467$	378969.	0.0804103	0.0402051	+	0.999191i	$0.487199\pi$
$468$	1.10282e6	0.232749
$469$	3.23910e6	0.679973
$470$	0	0
$471$	−7.95602e6	−1.65251
$472$	366336.	0.0756876
$473$	−334110.	−0.0686652
$474$	−5.90152e6	−1.20647
$475$	0	0
$476$	−1.16894e6	−0.236470
$477$	7.23466e6	1.45587
$478$	−2.18252e6	−0.436907
$479$	1.88489e6	0.375360	0.187680	−	0.982230i	$-0.439903\pi$
$479$	1.88489e6	0.375360	0.187680	+	0.982230i	$0.439903\pi$
$480$	0	0
$481$	1.35008e6	0.266071
$482$	3.24524e6	0.636252
$483$	−1.38621e6	−0.270372
$484$	2.35158e6	0.456296
$485$	0	0
$486$	−5.26240e6	−1.01063
$487$	−3.67689e6	−0.702518	−0.351259	−	0.936278i	$-0.614246\pi$
$487$	−3.67689e6	−0.702518	−0.351259	+	0.936278i	$0.614246\pi$
$488$	−2.31117e6	−0.439321
$489$	−2.10648e6	−0.398368
$490$	0	0
$491$	9.54015e6	1.78588	0.892939	−	0.450178i	$-0.148640\pi$
$491$	9.54015e6	1.78588	0.892939	+	0.450178i	$0.148640\pi$
$492$	−892032.	−0.166138
$493$	−7.45649e6	−1.38171
$494$	−1.96463e6	−0.362213
$495$	0	0
$496$	1.45818e6	0.266137
$497$	−787920.	−0.143084
$498$	9.77813e6	1.76678
$499$	4.78243e6	0.859800	0.429900	−	0.902877i	$-0.358549\pi$
$499$	4.78243e6	0.859800	0.429900	+	0.902877i	$0.358549\pi$
$500$	0	0
$501$	−876231.	−0.155964
$502$	−3.59095e6	−0.635990
$503$	1.08395e7	1.91024	0.955120	−	0.296220i	$-0.0957260\pi$
$503$	1.08395e7	1.91024	0.955120	+	0.296220i	$0.0957260\pi$
$504$	−896896.	−0.157277
$505$	0	0
$506$	2.73060e6	0.474113
$507$	−7.20388e6	−1.24465
$508$	−4.01466e6	−0.690222
$509$	−7.64177e6	−1.30737	−0.653687	−	0.756765i	$-0.726779\pi$
$509$	−7.64177e6	−1.30737	−0.653687	+	0.756765i	$0.726779\pi$
$510$	0	0
$511$	−3.94362e6	−0.668102
$512$	262144.	0.0441942
$513$	−2.01558e6	−0.338148
$514$	2.37871e6	0.397131
$515$	0	0
$516$	−221536.	−0.0366286
$517$	1.28555e7	2.11525
$518$	−1.09799e6	−0.179794
$519$	1.24532e7	2.02937
$520$	0	0
$521$	6.44011e6	1.03944	0.519719	−	0.854337i	$-0.326037\pi$
$521$	6.44011e6	1.03944	0.519719	+	0.854337i	$0.326037\pi$
$522$	−5.72114e6	−0.918981
$523$	4.77929e6	0.764028	0.382014	−	0.924157i	$-0.375231\pi$
$523$	4.77929e6	0.764028	0.382014	+	0.924157i	$0.375231\pi$
$524$	−833952.	−0.132682
$525$	0	0
$526$	−4.11348e6	−0.648254
$527$	8.49274e6	1.33205
$528$	3.26784e6	0.510124
$529$	−4.92344e6	−0.764944
$530$	0	0
$531$	1.63706e6	0.251959
$532$	1.59779e6	0.244760
$533$	−584184.	−0.0890700
$534$	−6.59419e6	−1.00071
$535$	0	0
$536$	−4.23066e6	−0.636057
$537$	3.82232e6	0.571994
$538$	−4.97561e6	−0.741123
$539$	1.33256e6	0.197566
$540$	0	0
$541$	−2.05678e6	−0.302130	−0.151065	−	0.988524i	$-0.548270\pi$
$541$	−2.05678e6	−0.302130	−0.151065	+	0.988524i	$0.548270\pi$
$542$	2.95050e6	0.431417
$543$	−4.53836e6	−0.660540
$544$	1.52678e6	0.221198
$545$	0	0
$546$	−1.08643e6	−0.155962
$547$	1.20189e7	1.71750	0.858751	−	0.512393i	$-0.171241\pi$
$547$	1.20189e7	1.71750	0.858751	+	0.512393i	$0.171241\pi$
$548$	2.16749e6	0.308323
$549$	−1.03280e7	−1.46247
$550$	0	0
$551$	1.01920e7	1.43015
$552$	1.81056e6	0.252910
$553$	3.14320e6	0.437079
$554$	8.80252e6	1.21852
$555$	0	0
$556$	−5.59178e6	−0.767119
$557$	−8.69942e6	−1.18810	−0.594049	−	0.804429i	$-0.702472\pi$
$557$	−8.69942e6	−1.18810	−0.594049	+	0.804429i	$0.702472\pi$
$558$	6.51622e6	0.885953
$559$	−145082.	−0.0196374
$560$	0	0
$561$	1.90326e7	2.55324
$562$	695916.	0.0929429
$563$	7.35942e6	0.978527	0.489263	−	0.872136i	$-0.337266\pi$
$563$	7.35942e6	0.978527	0.489263	+	0.872136i	$0.337266\pi$
$564$	8.52398e6	1.12835
$565$	0	0
$566$	2.20421e6	0.289209
$567$	2.29080e6	0.299247
$568$	1.02912e6	0.133843
$569$	−7.50029e6	−0.971175	−0.485588	−	0.874188i	$-0.661394\pi$
$569$	−7.50029e6	−0.971175	−0.485588	+	0.874188i	$0.661394\pi$
$570$	0	0
$571$	−2.22879e6	−0.286074	−0.143037	−	0.989717i	$-0.545687\pi$
$571$	−2.22879e6	−0.286074	−0.143037	+	0.989717i	$0.545687\pi$
$572$	2.14008e6	0.273489
$573$	−7.75608e6	−0.986861
$574$	475104.	0.0601879
$575$	0	0
$576$	1.17146e6	0.147119
$577$	5.10946e6	0.638903	0.319452	−	0.947603i	$-0.396501\pi$
$577$	5.10946e6	0.638903	0.319452	+	0.947603i	$0.396501\pi$
$578$	3.21290e6	0.400016
$579$	−5.99187e6	−0.742790
$580$	0	0
$581$	−5.20792e6	−0.640064
$582$	−1.38943e7	−1.70031
$583$	1.40393e7	1.71070
$584$	5.15085e6	0.624952
$585$	0	0
$586$	6.70048e6	0.806049
$587$	−1.10646e7	−1.32537	−0.662687	−	0.748896i	$-0.730584\pi$
$587$	−1.10646e7	−1.32537	−0.662687	+	0.748896i	$0.730584\pi$
$588$	883568.	0.105389
$589$	−1.16084e7	−1.37875
$590$	0	0
$591$	9.41188e6	1.10843
$592$	1.43411e6	0.168182
$593$	−9.10043e6	−1.06274	−0.531368	−	0.847141i	$-0.678322\pi$
$593$	−9.10043e6	−1.06274	−0.531368	+	0.847141i	$0.678322\pi$
$594$	2.19558e6	0.255319
$595$	0	0
$596$	2.81731e6	0.324877
$597$	6.92254e6	0.794931
$598$	1.18572e6	0.135590
$599$	−1.28615e7	−1.46462	−0.732309	−	0.680973i	$-0.761557\pi$
$599$	−1.28615e7	−1.46462	−0.732309	+	0.680973i	$0.761557\pi$
$600$	0	0
$601$	1.58163e6	0.178615	0.0893074	−	0.996004i	$-0.471535\pi$
$601$	1.58163e6	0.178615	0.0893074	+	0.996004i	$0.471535\pi$
$602$	117992.	0.0132697
$603$	−1.89057e7	−2.11739
$604$	6.13333e6	0.684075
$605$	0	0
$606$	−5.25780e6	−0.581597
$607$	688297.	0.0758236	0.0379118	−	0.999281i	$-0.487929\pi$
$607$	688297.	0.0758236	0.0379118	+	0.999281i	$0.487929\pi$
$608$	−2.08691e6	−0.228952
$609$	5.63613e6	0.615797
$610$	0	0
$611$	5.58228e6	0.604935
$612$	6.82282e6	0.736351
$613$	6.02150e6	0.647223	0.323611	−	0.946190i	$-0.395103\pi$
$613$	6.02150e6	0.647223	0.323611	+	0.946190i	$0.395103\pi$
$614$	−9.32241e6	−0.997947
$615$	0	0
$616$	−1.74048e6	−0.184807
$617$	−3.36137e6	−0.355471	−0.177735	−	0.984078i	$-0.556877\pi$
$617$	−3.36137e6	−0.355471	−0.177735	+	0.984078i	$0.556877\pi$
$618$	−1.06618e7	−1.12295
$619$	1.31769e7	1.38225	0.691126	−	0.722734i	$-0.257115\pi$
$619$	1.31769e7	1.38225	0.691126	+	0.722734i	$0.257115\pi$
$620$	0	0
$621$	1.21647e6	0.126582
$622$	2.82506e6	0.292787
$623$	3.51212e6	0.362535
$624$	1.41901e6	0.145889
$625$	0	0
$626$	734260.	0.0748883
$627$	−2.60151e7	−2.64275
$628$	−5.53462e6	−0.560001
$629$	8.35258e6	0.841771
$630$	0	0
$631$	1.26264e6	0.126243	0.0631213	−	0.998006i	$-0.479895\pi$
$631$	1.26264e6	0.126243	0.0631213	+	0.998006i	$0.479895\pi$
$632$	−4.10541e6	−0.408850
$633$	−2.82021e7	−2.79752
$634$	−1.08266e7	−1.06972
$635$	0	0
$636$	9.30893e6	0.912550
$637$	578641.	0.0565016
$638$	−1.11022e7	−1.07984
$639$	4.59888e6	0.445554
$640$	0	0
$641$	−1.58859e7	−1.52710	−0.763550	−	0.645749i	$-0.776545\pi$
$641$	−1.58859e7	−1.52710	−0.763550	+	0.645749i	$0.776545\pi$
$642$	1.26833e7	1.21449
$643$	−1.80880e6	−0.172529	−0.0862647	−	0.996272i	$-0.527493\pi$
$643$	−1.80880e6	−0.172529	−0.0862647	+	0.996272i	$0.527493\pi$
$644$	−964320.	−0.0916234
$645$	0	0
$646$	−1.21546e7	−1.14594
$647$	−95712.0	−0.00898888	−0.00449444	−	0.999990i	$-0.501431\pi$
$647$	−95712.0	−0.00898888	−0.00449444	+	0.999990i	$0.501431\pi$
$648$	−2.99206e6	−0.279920
$649$	3.17682e6	0.296061
$650$	0	0
$651$	−6.41939e6	−0.593665
$652$	−1.46538e6	−0.134999
$653$	−3.06736e6	−0.281502	−0.140751	−	0.990045i	$-0.544952\pi$
$653$	−3.06736e6	−0.281502	−0.140751	+	0.990045i	$0.544952\pi$
$654$	8.13252e6	0.743500
$655$	0	0
$656$	−620544.	−0.0563006
$657$	2.30179e7	2.08042
$658$	−4.53995e6	−0.408777
$659$	−1.32961e6	−0.119264	−0.0596321	−	0.998220i	$-0.518993\pi$
$659$	−1.32961e6	−0.119264	−0.0596321	+	0.998220i	$0.518993\pi$
$660$	0	0
$661$	−7.37188e6	−0.656258	−0.328129	−	0.944633i	$-0.606418\pi$
$661$	−7.37188e6	−0.656258	−0.328129	+	0.944633i	$0.606418\pi$
$662$	−8.57349e6	−0.760348
$663$	8.26461e6	0.730195
$664$	6.80218e6	0.598725
$665$	0	0
$666$	6.40869e6	0.559865
$667$	−6.15123e6	−0.535362
$668$	−609552.	−0.0528530
$669$	−1.42889e7	−1.23434
$670$	0	0
$671$	−2.00422e7	−1.71846
$672$	−1.15405e6	−0.0985827
$673$	−8.48476e6	−0.722108	−0.361054	−	0.932545i	$-0.617583\pi$
$673$	−8.48476e6	−0.722108	−0.361054	+	0.932545i	$0.617583\pi$
$674$	−2.62138e6	−0.222270
$675$	0	0
$676$	−5.01139e6	−0.421785
$677$	4.35891e6	0.365516	0.182758	−	0.983158i	$-0.441497\pi$
$677$	4.35891e6	0.365516	0.182758	+	0.983158i	$0.441497\pi$
$678$	−1.89110e7	−1.57994
$679$	7.40022e6	0.615985
$680$	0	0
$681$	−2.98466e7	−2.46619
$682$	1.26451e7	1.04103
$683$	1.58732e7	1.30200	0.651001	−	0.759077i	$-0.274349\pi$
$683$	1.58732e7	1.30200	0.651001	+	0.759077i	$0.274349\pi$
$684$	−9.32589e6	−0.762167
$685$	0	0
$686$	−470596.	−0.0381802
$687$	−2.85807e6	−0.231037
$688$	−154112.	−0.0124127
$689$	6.09634e6	0.489239
$690$	0	0
$691$	−554956.	−0.0442144	−0.0221072	−	0.999756i	$-0.507038\pi$
$691$	−554956.	−0.0442144	−0.0221072	+	0.999756i	$0.507038\pi$
$692$	8.66309e6	0.687713
$693$	−7.77777e6	−0.615208
$694$	1.68910e7	1.33124
$695$	0	0
$696$	−7.36147e6	−0.576025
$697$	−3.61418e6	−0.281792
$698$	1.20684e7	0.937587
$699$	−2.50106e7	−1.93611
$700$	0	0
$701$	−7.74720e6	−0.595456	−0.297728	−	0.954651i	$-0.596229\pi$
$701$	−7.74720e6	−0.595456	−0.297728	+	0.954651i	$0.596229\pi$
$702$	953396.	0.0730181
$703$	−1.14169e7	−0.871282
$704$	2.27328e6	0.172871
$705$	0	0
$706$	−9.01031e6	−0.680343
$707$	2.80035e6	0.210700
$708$	2.10643e6	0.157930
$709$	−1.89055e7	−1.41245	−0.706225	−	0.707987i	$-0.749603\pi$
$709$	−1.89055e7	−1.41245	−0.706225	+	0.707987i	$0.749603\pi$
$710$	0	0
$711$	−1.83460e7	−1.36103
$712$	−4.58726e6	−0.339120
$713$	7.00608e6	0.516121
$714$	−6.72143e6	−0.493419
$715$	0	0
$716$	2.65901e6	0.193837
$717$	−1.25495e7	−0.911652
$718$	−7.35802e6	−0.532659
$719$	−1.83928e7	−1.32686	−0.663430	−	0.748238i	$-0.730900\pi$
$719$	−1.83928e7	−1.32686	−0.663430	+	0.748238i	$0.730900\pi$
$720$	0	0
$721$	5.67856e6	0.406818
$722$	6.70938e6	0.479004
$723$	1.86601e7	1.32761
$724$	−3.15712e6	−0.223844
$725$	0	0
$726$	1.35216e7	0.952109
$727$	1.34259e7	0.942123	0.471061	−	0.882100i	$-0.343871\pi$
$727$	1.34259e7	0.942123	0.471061	+	0.882100i	$0.343871\pi$
$728$	−755776.	−0.0528524
$729$	−1.88983e7	−1.31706
$730$	0	0
$731$	−897582.	−0.0621270
$732$	−1.32892e7	−0.916688
$733$	−1.08473e7	−0.745697	−0.372848	−	0.927892i	$-0.621619\pi$
$733$	−1.08473e7	−0.745697	−0.372848	+	0.927892i	$0.621619\pi$
$734$	6.75329e6	0.462674
$735$	0	0
$736$	1.25952e6	0.0857059
$737$	−3.66877e7	−2.48801
$738$	−2.77306e6	−0.187421
$739$	2.64323e7	1.78043	0.890214	−	0.455542i	$-0.150555\pi$
$739$	2.64323e7	1.78043	0.890214	+	0.455542i	$0.150555\pi$
$740$	0	0
$741$	−1.12966e7	−0.755794
$742$	−4.95802e6	−0.330596
$743$	−2.03120e7	−1.34984	−0.674918	−	0.737893i	$-0.735821\pi$
$743$	−2.03120e7	−1.34984	−0.674918	+	0.737893i	$0.735821\pi$
$744$	8.38451e6	0.555323
$745$	0	0
$746$	−7.24846e6	−0.476869
$747$	3.03972e7	1.99312
$748$	1.32401e7	0.865240
$749$	−6.75524e6	−0.439983
$750$	0	0
$751$	−3.95388e6	−0.255813	−0.127907	−	0.991786i	$-0.540826\pi$
$751$	−3.95388e6	−0.255813	−0.127907	+	0.991786i	$0.540826\pi$
$752$	5.92973e6	0.382376
$753$	−2.06480e7	−1.32706
$754$	−4.82096e6	−0.308820
$755$	0	0
$756$	−775376.	−0.0493410
$757$	2.62165e7	1.66278	0.831391	−	0.555688i	$-0.187545\pi$
$757$	2.62165e7	1.66278	0.831391	+	0.555688i	$0.187545\pi$
$758$	−1.90683e7	−1.20542
$759$	1.57010e7	0.989285
$760$	0	0
$761$	1.14329e7	0.715638	0.357819	−	0.933791i	$-0.383521\pi$
$761$	1.14329e7	0.715638	0.357819	+	0.933791i	$0.383521\pi$
$762$	−2.30843e7	−1.44022
$763$	−4.33145e6	−0.269353
$764$	−5.39554e6	−0.334427
$765$	0	0
$766$	279984.	0.0172410
$767$	1.37948e6	0.0846697
$768$	1.50733e6	0.0922157
$769$	2.37076e7	1.44568	0.722840	−	0.691015i	$-0.242836\pi$
$769$	2.37076e7	1.44568	0.722840	+	0.691015i	$0.242836\pi$
$770$	0	0
$771$	1.36776e7	0.828655
$772$	−4.16826e6	−0.251716
$773$	1.24180e7	0.747484	0.373742	−	0.927533i	$-0.378075\pi$
$773$	1.24180e7	0.747484	0.373742	+	0.927533i	$0.378075\pi$
$774$	−688688.	−0.0413209
$775$	0	0
$776$	−9.66560e6	−0.576202
$777$	−6.31345e6	−0.375158
$778$	1.59558e7	0.945083
$779$	4.94011e6	0.291671
$780$	0	0
$781$	8.92440e6	0.523542
$782$	7.33572e6	0.428969
$783$	−4.94599e6	−0.288303
$784$	614656.	0.0357143
$785$	0	0
$786$	−4.79522e6	−0.276855
$787$	−3.06553e7	−1.76428	−0.882142	−	0.470984i	$-0.843899\pi$
$787$	−3.06553e7	−1.76428	−0.882142	+	0.470984i	$0.843899\pi$
$788$	6.54739e6	0.375624
$789$	−2.36525e7	−1.35265
$790$	0	0
$791$	1.00721e7	0.572375
$792$	1.01587e7	0.575474
$793$	−8.70299e6	−0.491457
$794$	1.22361e7	0.688800
$795$	0	0
$796$	4.81568e6	0.269386
$797$	1.51870e7	0.846886	0.423443	−	0.905923i	$-0.360821\pi$
$797$	1.51870e7	0.846886	0.423443	+	0.905923i	$0.360821\pi$
$798$	9.18730e6	0.510718
$799$	3.45360e7	1.91384
$800$	0	0
$801$	−2.04993e7	−1.12891
$802$	1.72317e7	0.946005
$803$	4.46675e7	2.44457
$804$	−2.43263e7	−1.32720
$805$	0	0
$806$	5.49094e6	0.297721
$807$	−2.86097e7	−1.54643
$808$	−3.65760e6	−0.197091
$809$	539721.	0.0289933	0.0144967	−	0.999895i	$-0.495385\pi$
$809$	539721.	0.0289933	0.0144967	+	0.999895i	$0.495385\pi$
$810$	0	0
$811$	1.39772e7	0.746221	0.373111	−	0.927787i	$-0.378291\pi$
$811$	1.39772e7	0.746221	0.373111	+	0.927787i	$0.378291\pi$
$812$	3.92078e6	0.208681
$813$	1.69654e7	0.900195
$814$	1.24364e7	0.657862
$815$	0	0
$816$	8.77901e6	0.461551
$817$	1.22688e6	0.0643051
$818$	−956824.	−0.0499976
$819$	−3.37737e6	−0.175942
$820$	0	0
$821$	−1.78137e7	−0.922350	−0.461175	−	0.887309i	$-0.652572\pi$
$821$	−1.78137e7	−0.922350	−0.461175	+	0.887309i	$0.652572\pi$
$822$	1.24631e7	0.643347
$823$	−1.91010e7	−0.983005	−0.491502	−	0.870876i	$-0.663552\pi$
$823$	−1.91010e7	−0.983005	−0.491502	+	0.870876i	$0.663552\pi$
$824$	−7.41690e6	−0.380543
$825$	0	0
$826$	−1.12190e6	−0.0572144
$827$	−3.19225e6	−0.162305	−0.0811526	−	0.996702i	$-0.525860\pi$
$827$	−3.19225e6	−0.162305	−0.0811526	+	0.996702i	$0.525860\pi$
$828$	5.62848e6	0.285309
$829$	8.56842e6	0.433026	0.216513	−	0.976280i	$-0.430532\pi$
$829$	8.56842e6	0.433026	0.216513	+	0.976280i	$0.430532\pi$
$830$	0	0
$831$	5.06145e7	2.54257
$832$	987136.	0.0494389
$833$	3.57989e6	0.178755
$834$	−3.21527e7	−1.60067
$835$	0	0
$836$	−1.80974e7	−0.895574
$837$	5.63334e6	0.277941
$838$	1.85385e7	0.911935
$839$	3.56751e7	1.74969	0.874843	−	0.484407i	$-0.160964\pi$
$839$	3.56751e7	1.74969	0.874843	+	0.484407i	$0.160964\pi$
$840$	0	0
$841$	4.49885e6	0.219337
$842$	−8.40430e6	−0.408528
$843$	4.00152e6	0.193935
$844$	−1.96189e7	−0.948021
$845$	0	0
$846$	2.64985e7	1.27290
$847$	−7.20173e6	−0.344928
$848$	6.47578e6	0.309245
$849$	1.26742e7	0.603465
$850$	0	0
$851$	6.89046e6	0.326155
$852$	5.91744e6	0.279277
$853$	−3.06355e7	−1.44163	−0.720814	−	0.693129i	$-0.756232\pi$
$853$	−3.06355e7	−1.44163	−0.720814	+	0.693129i	$0.756232\pi$
$854$	7.07795e6	0.332095
$855$	0	0
$856$	8.82317e6	0.411567
$857$	4.46188e6	0.207523	0.103761	−	0.994602i	$-0.466912\pi$
$857$	4.46188e6	0.207523	0.103761	+	0.994602i	$0.466912\pi$
$858$	1.23055e7	0.570663
$859$	2.63974e7	1.22061	0.610307	−	0.792165i	$-0.291046\pi$
$859$	2.63974e7	1.22061	0.610307	+	0.792165i	$0.291046\pi$
$860$	0	0
$861$	2.73185e6	0.125588
$862$	6.61936e6	0.303422
$863$	2.17530e7	0.994244	0.497122	−	0.867681i	$-0.334390\pi$
$863$	2.17530e7	0.994244	0.497122	+	0.867681i	$0.334390\pi$
$864$	1.01274e6	0.0461543
$865$	0	0
$866$	7.36122e6	0.333546
$867$	1.84742e7	0.834674
$868$	−4.46566e6	−0.201181
$869$	−3.56016e7	−1.59926
$870$	0	0
$871$	−1.59311e7	−0.711540
$872$	5.65741e6	0.251957
$873$	−4.31932e7	−1.91814
$874$	−1.00270e7	−0.444008
$875$	0	0
$876$	2.96174e7	1.30403
$877$	1.58383e7	0.695361	0.347680	−	0.937613i	$-0.386969\pi$
$877$	1.58383e7	0.695361	0.347680	+	0.937613i	$0.386969\pi$
$878$	2.33474e7	1.02212
$879$	3.85277e7	1.68190
$880$	0	0
$881$	1.97427e7	0.856974	0.428487	−	0.903548i	$-0.359047\pi$
$881$	1.97427e7	0.856974	0.428487	+	0.903548i	$0.359047\pi$
$882$	2.74674e6	0.118890
$883$	1.72899e7	0.746263	0.373131	−	0.927779i	$-0.378284\pi$
$883$	1.72899e7	0.746263	0.373131	+	0.927779i	$0.378284\pi$
$884$	5.74930e6	0.247448
$885$	0	0
$886$	−4.78817e6	−0.204920
$887$	4.44693e7	1.89780	0.948901	−	0.315574i	$-0.102197\pi$
$887$	4.44693e7	1.89780	0.948901	+	0.315574i	$0.102197\pi$
$888$	8.24614e6	0.350928
$889$	1.22949e7	0.521759
$890$	0	0
$891$	−2.59468e7	−1.09494
$892$	−9.94011e6	−0.418292
$893$	−4.72062e7	−1.98094
$894$	1.61995e7	0.677890
$895$	0	0
$896$	−802816.	−0.0334077
$897$	6.81789e6	0.282923
$898$	−1.37028e7	−0.567046
$899$	−2.84857e7	−1.17551
$900$	0	0
$901$	3.77163e7	1.54781
$902$	−5.38128e6	−0.220226
$903$	678454.	0.0276886
$904$	−1.31555e7	−0.535408
$905$	0	0
$906$	3.52666e7	1.42739
$907$	−2.56887e6	−0.103687	−0.0518434	−	0.998655i	$-0.516510\pi$
$907$	−2.56887e6	−0.103687	−0.0518434	+	0.998655i	$0.516510\pi$
$908$	−2.07628e7	−0.835742
$909$	−1.63449e7	−0.656104
$910$	0	0
$911$	1.12692e7	0.449882	0.224941	−	0.974372i	$-0.427781\pi$
$911$	1.12692e7	0.449882	0.224941	+	0.974372i	$0.427781\pi$
$912$	−1.19997e7	−0.477733
$913$	5.89876e7	2.34198
$914$	−2.11897e7	−0.838994
$915$	0	0
$916$	−1.98822e6	−0.0782937
$917$	2.55398e6	0.100298
$918$	5.89840e6	0.231008
$919$	3.18378e7	1.24353	0.621763	−	0.783205i	$-0.286417\pi$
$919$	3.18378e7	1.24353	0.621763	+	0.783205i	$0.286417\pi$
$920$	0	0
$921$	−5.36039e7	−2.08232
$922$	3.55092e7	1.37567
$923$	3.87528e6	0.149727
$924$	−1.00078e7	−0.385618
$925$	0	0
$926$	8.69901e6	0.333382
$927$	−3.31443e7	−1.26680
$928$	−5.12102e6	−0.195203
$929$	1.88558e7	0.716813	0.358407	−	0.933566i	$-0.383320\pi$
$929$	1.88558e7	0.716813	0.358407	+	0.933566i	$0.383320\pi$
$930$	0	0
$931$	−4.89324e6	−0.185021
$932$	−1.73987e7	−0.656109
$933$	1.62441e7	0.610931
$934$	1.51588e6	0.0568586
$935$	0	0
$936$	4.41126e6	0.164579
$937$	−1.12946e7	−0.420265	−0.210132	−	0.977673i	$-0.567390\pi$
$937$	−1.12946e7	−0.420265	−0.210132	+	0.977673i	$0.567390\pi$
$938$	1.29564e7	0.480814
$939$	4.22200e6	0.156262
$940$	0	0
$941$	−2.91941e7	−1.07478	−0.537392	−	0.843333i	$-0.680590\pi$
$941$	−2.91941e7	−1.07478	−0.537392	+	0.843333i	$0.680590\pi$
$942$	−3.18241e7	−1.16850
$943$	−2.98152e6	−0.109184
$944$	1.46534e6	0.0535192
$945$	0	0
$946$	−1.33644e6	−0.0485536
$947$	−1.05892e7	−0.383697	−0.191848	−	0.981425i	$-0.561448\pi$
$947$	−1.05892e7	−0.383697	−0.191848	+	0.981425i	$0.561448\pi$
$948$	−2.36061e7	−0.853107
$949$	1.93962e7	0.699118
$950$	0	0
$951$	−6.22530e7	−2.23208
$952$	−4.67578e6	−0.167210
$953$	3.90317e7	1.39215	0.696074	−	0.717970i	$-0.254929\pi$
$953$	3.90317e7	1.39215	0.696074	+	0.717970i	$0.254929\pi$
$954$	2.89386e7	1.02945
$955$	0	0
$956$	−8.73010e6	−0.308940
$957$	−6.38378e7	−2.25319
$958$	7.53958e6	0.265420
$959$	−6.63793e6	−0.233070
$960$	0	0
$961$	3.81526e6	0.133265
$962$	5.40033e6	0.188141
$963$	3.94285e7	1.37008
$964$	1.29810e7	0.449898
$965$	0	0
$966$	−5.54484e6	−0.191182
$967$	3.43395e7	1.18094	0.590470	−	0.807059i	$-0.298942\pi$
$967$	3.43395e7	1.18094	0.590470	+	0.807059i	$0.298942\pi$
$968$	9.40634e6	0.322650
$969$	−6.98891e7	−2.39111
$970$	0	0
$971$	−1.81464e7	−0.617651	−0.308826	−	0.951119i	$-0.599936\pi$
$971$	−1.81464e7	−0.617651	−0.308826	+	0.951119i	$0.599936\pi$
$972$	−2.10496e7	−0.714625
$973$	1.71248e7	0.579888
$974$	−1.47075e7	−0.496756
$975$	0	0
$976$	−9.24467e6	−0.310647
$977$	1.05223e7	0.352675	0.176338	−	0.984330i	$-0.443575\pi$
$977$	1.05223e7	0.352675	0.176338	+	0.984330i	$0.443575\pi$
$978$	−8.42591e6	−0.281689
$979$	−3.97802e7	−1.32651
$980$	0	0
$981$	2.52815e7	0.838747
$982$	3.81606e7	1.26281
$983$	7.91353e6	0.261208	0.130604	−	0.991435i	$-0.458308\pi$
$983$	7.91353e6	0.261208	0.130604	+	0.991435i	$0.458308\pi$
$984$	−3.56813e6	−0.117477
$985$	0	0
$986$	−2.98260e7	−0.977017
$987$	−2.61047e7	−0.852954
$988$	−7.85853e6	−0.256123
$989$	−740460.	−0.0240719
$990$	0	0
$991$	4.01556e7	1.29886	0.649429	−	0.760422i	$-0.275008\pi$
$991$	4.01556e7	1.29886	0.649429	+	0.760422i	$0.275008\pi$
$992$	5.83270e6	0.188187
$993$	−4.92976e7	−1.58654
$994$	−3.15168e6	−0.101176
$995$	0	0
$996$	3.91125e7	1.24930
$997$	4.93478e7	1.57228	0.786140	−	0.618048i	$-0.212076\pi$
$997$	4.93478e7	1.57228	0.786140	+	0.618048i	$0.212076\pi$
$998$	1.91297e7	0.607970
$999$	5.54038e6	0.175641

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.6.a.n.1.1		1
5.2	odd	4		350.6.c.h.99.2		2
5.3	odd	4		350.6.c.h.99.1		2
5.4	even	2		70.6.a.a.1.1	✓	1
15.14	odd	2		630.6.a.j.1.1		1
20.19	odd	2		560.6.a.i.1.1		1
35.34	odd	2		490.6.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.6.a.a.1.1	✓	1	5.4	even	2
350.6.a.n.1.1		1	1.1	even	1	trivial
350.6.c.h.99.1		2	5.3	odd	4
350.6.c.h.99.2		2	5.2	odd	4
490.6.a.i.1.1		1	35.34	odd	2
560.6.a.i.1.1		1	20.19	odd	2
630.6.a.j.1.1		1	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	350.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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