LMFDB - Embedded newform 1617.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,4,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, 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("1617.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1617.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:	$95.4060884793$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q-2.00000 q^{2} -3.00000 q^{3} -4.00000 q^{4} -1.00000 q^{5} +6.00000 q^{6} +24.0000 q^{8} +9.00000 q^{9} +2.00000 q^{10} -11.0000 q^{11} +12.0000 q^{12} -7.00000 q^{13} +3.00000 q^{15} -16.0000 q^{16} +14.0000 q^{17} -18.0000 q^{18} +45.0000 q^{19} +4.00000 q^{20} +22.0000 q^{22} -88.0000 q^{23} -72.0000 q^{24} -124.000 q^{25} +14.0000 q^{26} -27.0000 q^{27} -69.0000 q^{29} -6.00000 q^{30} -22.0000 q^{31} -160.000 q^{32} +33.0000 q^{33} -28.0000 q^{34} -36.0000 q^{36} +57.0000 q^{37} -90.0000 q^{38} +21.0000 q^{39} -24.0000 q^{40} +380.000 q^{41} +48.0000 q^{43} +44.0000 q^{44} -9.00000 q^{45} +176.000 q^{46} +385.000 q^{47} +48.0000 q^{48} +248.000 q^{50} -42.0000 q^{51} +28.0000 q^{52} -672.000 q^{53} +54.0000 q^{54} +11.0000 q^{55} -135.000 q^{57} +138.000 q^{58} +469.000 q^{59} -12.0000 q^{60} +342.000 q^{61} +44.0000 q^{62} +448.000 q^{64} +7.00000 q^{65} -66.0000 q^{66} -139.000 q^{67} -56.0000 q^{68} +264.000 q^{69} +132.000 q^{71} +216.000 q^{72} -145.000 q^{73} -114.000 q^{74} +372.000 q^{75} -180.000 q^{76} -42.0000 q^{78} +1244.00 q^{79} +16.0000 q^{80} +81.0000 q^{81} -760.000 q^{82} -522.000 q^{83} -14.0000 q^{85} -96.0000 q^{86} +207.000 q^{87} -264.000 q^{88} -822.000 q^{89} +18.0000 q^{90} +352.000 q^{92} +66.0000 q^{93} -770.000 q^{94} -45.0000 q^{95} +480.000 q^{96} -272.000 q^{97} -99.0000 q^{99} +O(q^{100})\)

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 $

$2$	−2.00000	−0.707107	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−2.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−4.00000	−0.500000
$5$	−1.00000	−0.0894427	−0.0447214	−	0.998999i	$-0.514240\pi$
$5$	−1.00000	−0.0894427	−0.0447214	+	0.998999i	$0.514240\pi$
$6$	6.00000	0.408248
$7$	0	0
$7$	0	0
$8$	24.0000	1.06066
$9$	9.00000	0.333333
$10$	2.00000	0.0632456
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	12.0000	0.288675
$13$	−7.00000	−0.149342	−0.0746712	−	0.997208i	$-0.523791\pi$
$13$	−7.00000	−0.149342	−0.0746712	+	0.997208i	$0.523791\pi$
$14$	0	0
$15$	3.00000	0.0516398
$16$	−16.0000	−0.250000
$17$	14.0000	0.199735	0.0998676	−	0.995001i	$-0.468158\pi$
$17$	14.0000	0.199735	0.0998676	+	0.995001i	$0.468158\pi$
$18$	−18.0000	−0.235702
$19$	45.0000	0.543353	0.271677	−	0.962389i	$-0.412422\pi$
$19$	45.0000	0.543353	0.271677	+	0.962389i	$0.412422\pi$
$20$	4.00000	0.0447214
$21$	0	0
$22$	22.0000	0.213201
$23$	−88.0000	−0.797794	−0.398897	−	0.916996i	$-0.630607\pi$
$23$	−88.0000	−0.797794	−0.398897	+	0.916996i	$0.630607\pi$
$24$	−72.0000	−0.612372
$25$	−124.000	−0.992000
$26$	14.0000	0.105601
$27$	−27.0000	−0.192450
$28$	0	0
$29$	−69.0000	−0.441827	−0.220913	−	0.975293i	$-0.570904\pi$
$29$	−69.0000	−0.441827	−0.220913	+	0.975293i	$0.570904\pi$
$30$	−6.00000	−0.0365148
$31$	−22.0000	−0.127462	−0.0637309	−	0.997967i	$-0.520300\pi$
$31$	−22.0000	−0.127462	−0.0637309	+	0.997967i	$0.520300\pi$
$32$	−160.000	−0.883883
$33$	33.0000	0.174078
$34$	−28.0000	−0.141234
$35$	0	0
$36$	−36.0000	−0.166667
$37$	57.0000	0.253263	0.126632	−	0.991950i	$-0.459583\pi$
$37$	57.0000	0.253263	0.126632	+	0.991950i	$0.459583\pi$
$38$	−90.0000	−0.384209
$39$	21.0000	0.0862229
$40$	−24.0000	−0.0948683
$41$	380.000	1.44746	0.723732	−	0.690081i	$-0.242425\pi$
$41$	380.000	1.44746	0.723732	+	0.690081i	$0.242425\pi$
$42$	0	0
$43$	48.0000	0.170231	0.0851155	−	0.996371i	$-0.472874\pi$
$43$	48.0000	0.170231	0.0851155	+	0.996371i	$0.472874\pi$
$44$	44.0000	0.150756
$45$	−9.00000	−0.0298142
$46$	176.000	0.564126
$47$	385.000	1.19485	0.597426	−	0.801924i	$-0.296190\pi$
$47$	385.000	1.19485	0.597426	+	0.801924i	$0.296190\pi$
$48$	48.0000	0.144338
$49$	0	0
$50$	248.000	0.701450
$51$	−42.0000	−0.115317
$52$	28.0000	0.0746712
$53$	−672.000	−1.74163	−0.870814	−	0.491612i	$-0.836408\pi$
$53$	−672.000	−1.74163	−0.870814	+	0.491612i	$0.836408\pi$
$54$	54.0000	0.136083
$55$	11.0000	0.0269680
$56$	0	0
$57$	−135.000	−0.313705
$58$	138.000	0.312419
$59$	469.000	1.03489	0.517446	−	0.855716i	$-0.326883\pi$
$59$	469.000	1.03489	0.517446	+	0.855716i	$0.326883\pi$
$60$	−12.0000	−0.0258199
$61$	342.000	0.717846	0.358923	−	0.933367i	$-0.383144\pi$
$61$	342.000	0.717846	0.358923	+	0.933367i	$0.383144\pi$
$62$	44.0000	0.0901291
$63$	0	0
$64$	448.000	0.875000
$65$	7.00000	0.0133576
$66$	−66.0000	−0.123091
$67$	−139.000	−0.253456	−0.126728	−	0.991938i	$-0.540448\pi$
$67$	−139.000	−0.253456	−0.126728	+	0.991938i	$0.540448\pi$
$68$	−56.0000	−0.0998676
$69$	264.000	0.460607
$70$	0	0
$71$	132.000	0.220641	0.110321	−	0.993896i	$-0.464812\pi$
$71$	132.000	0.220641	0.110321	+	0.993896i	$0.464812\pi$
$72$	216.000	0.353553
$73$	−145.000	−0.232479	−0.116239	−	0.993221i	$-0.537084\pi$
$73$	−145.000	−0.232479	−0.116239	+	0.993221i	$0.537084\pi$
$74$	−114.000	−0.179084
$75$	372.000	0.572731
$76$	−180.000	−0.271677
$77$	0	0
$78$	−42.0000	−0.0609688
$79$	1244.00	1.77166	0.885829	−	0.464012i	$-0.153591\pi$
$79$	1244.00	1.77166	0.885829	+	0.464012i	$0.153591\pi$
$80$	16.0000	0.0223607
$81$	81.0000	0.111111
$82$	−760.000	−1.02351
$83$	−522.000	−0.690325	−0.345162	−	0.938543i	$-0.612176\pi$
$83$	−522.000	−0.690325	−0.345162	+	0.938543i	$0.612176\pi$
$84$	0	0
$85$	−14.0000	−0.0178649
$86$	−96.0000	−0.120371
$87$	207.000	0.255089
$88$	−264.000	−0.319801
$89$	−822.000	−0.979009	−0.489505	−	0.872001i	$-0.662822\pi$
$89$	−822.000	−0.979009	−0.489505	+	0.872001i	$0.662822\pi$
$90$	18.0000	0.0210819
$91$	0	0
$92$	352.000	0.398897
$93$	66.0000	0.0735901
$94$	−770.000	−0.844888
$95$	−45.0000	−0.0485990
$96$	480.000	0.510310
$97$	−272.000	−0.284716	−0.142358	−	0.989815i	$-0.545468\pi$
$97$	−272.000	−0.284716	−0.142358	+	0.989815i	$0.545468\pi$
$98$	0	0
$99$	−99.0000	−0.100504
$100$	496.000	0.496000
$101$	874.000	0.861052	0.430526	−	0.902578i	$-0.358328\pi$
$101$	874.000	0.861052	0.430526	+	0.902578i	$0.358328\pi$
$102$	84.0000	0.0815416
$103$	826.000	0.790177	0.395088	−	0.918643i	$-0.370714\pi$
$103$	826.000	0.790177	0.395088	+	0.918643i	$0.370714\pi$
$104$	−168.000	−0.158401
$105$	0	0
$106$	1344.00	1.23152
$107$	219.000	0.197865	0.0989324	−	0.995094i	$-0.468457\pi$
$107$	219.000	0.197865	0.0989324	+	0.995094i	$0.468457\pi$
$108$	108.000	0.0962250
$109$	1426.00	1.25308	0.626541	−	0.779388i	$-0.284470\pi$
$109$	1426.00	1.25308	0.626541	+	0.779388i	$0.284470\pi$
$110$	−22.0000	−0.0190693
$111$	−171.000	−0.146222
$112$	0	0
$113$	882.000	0.734262	0.367131	−	0.930169i	$-0.380340\pi$
$113$	882.000	0.734262	0.367131	+	0.930169i	$0.380340\pi$
$114$	270.000	0.221823
$115$	88.0000	0.0713569
$116$	276.000	0.220913
$117$	−63.0000	−0.0497808
$118$	−938.000	−0.731779
$119$	0	0
$120$	72.0000	0.0547723
$121$	121.000	0.0909091
$122$	−684.000	−0.507594
$123$	−1140.00	−0.835694
$124$	88.0000	0.0637309
$125$	249.000	0.178170
$126$	0	0
$127$	1826.00	1.27584	0.637918	−	0.770104i	$-0.279796\pi$
$127$	1826.00	1.27584	0.637918	+	0.770104i	$0.279796\pi$
$128$	384.000	0.265165
$129$	−144.000	−0.0982829
$130$	−14.0000	−0.00944524
$131$	−84.0000	−0.0560238	−0.0280119	−	0.999608i	$-0.508918\pi$
$131$	−84.0000	−0.0560238	−0.0280119	+	0.999608i	$0.508918\pi$
$132$	−132.000	−0.0870388
$133$	0	0
$134$	278.000	0.179220
$135$	27.0000	0.0172133
$136$	336.000	0.211851
$137$	−1834.00	−1.14372	−0.571858	−	0.820352i	$-0.693777\pi$
$137$	−1834.00	−1.14372	−0.571858	+	0.820352i	$0.693777\pi$
$138$	−528.000	−0.325698
$139$	−2416.00	−1.47426	−0.737131	−	0.675750i	$-0.763820\pi$
$139$	−2416.00	−1.47426	−0.737131	+	0.675750i	$0.763820\pi$
$140$	0	0
$141$	−1155.00	−0.689848
$142$	−264.000	−0.156017
$143$	77.0000	0.0450284
$144$	−144.000	−0.0833333
$145$	69.0000	0.0395182
$146$	290.000	0.164387
$147$	0	0
$148$	−228.000	−0.126632
$149$	1895.00	1.04191	0.520955	−	0.853584i	$-0.325576\pi$
$149$	1895.00	1.04191	0.520955	+	0.853584i	$0.325576\pi$
$150$	−744.000	−0.404982
$151$	−3478.00	−1.87441	−0.937204	−	0.348782i	$-0.886596\pi$
$151$	−3478.00	−1.87441	−0.937204	+	0.348782i	$0.886596\pi$
$152$	1080.00	0.576313
$153$	126.000	0.0665784
$154$	0	0
$155$	22.0000	0.0114005
$156$	−84.0000	−0.0431114
$157$	952.000	0.483935	0.241968	−	0.970284i	$-0.422207\pi$
$157$	952.000	0.483935	0.241968	+	0.970284i	$0.422207\pi$
$158$	−2488.00	−1.25275
$159$	2016.00	1.00553
$160$	160.000	0.0790569
$161$	0	0
$162$	−162.000	−0.0785674
$163$	−2483.00	−1.19315	−0.596575	−	0.802557i	$-0.703472\pi$
$163$	−2483.00	−1.19315	−0.596575	+	0.802557i	$0.703472\pi$
$164$	−1520.00	−0.723732
$165$	−33.0000	−0.0155700
$166$	1044.00	0.488133
$167$	−468.000	−0.216856	−0.108428	−	0.994104i	$-0.534582\pi$
$167$	−468.000	−0.216856	−0.108428	+	0.994104i	$0.534582\pi$
$168$	0	0
$169$	−2148.00	−0.977697
$170$	28.0000	0.0126324
$171$	405.000	0.181118
$172$	−192.000	−0.0851155
$173$	2148.00	0.943985	0.471993	−	0.881603i	$-0.343535\pi$
$173$	2148.00	0.943985	0.471993	+	0.881603i	$0.343535\pi$
$174$	−414.000	−0.180375
$175$	0	0
$176$	176.000	0.0753778
$177$	−1407.00	−0.597495
$178$	1644.00	0.692264
$179$	−1464.00	−0.611310	−0.305655	−	0.952142i	$-0.598875\pi$
$179$	−1464.00	−0.611310	−0.305655	+	0.952142i	$0.598875\pi$
$180$	36.0000	0.0149071
$181$	−1432.00	−0.588065	−0.294032	−	0.955795i	$-0.594997\pi$
$181$	−1432.00	−0.588065	−0.294032	+	0.955795i	$0.594997\pi$
$182$	0	0
$183$	−1026.00	−0.414449
$184$	−2112.00	−0.846189
$185$	−57.0000	−0.0226526
$186$	−132.000	−0.0520361
$187$	−154.000	−0.0602224
$188$	−1540.00	−0.597426
$189$	0	0
$190$	90.0000	0.0343647
$191$	−1330.00	−0.503850	−0.251925	−	0.967747i	$-0.581064\pi$
$191$	−1330.00	−0.503850	−0.251925	+	0.967747i	$0.581064\pi$
$192$	−1344.00	−0.505181
$193$	−2540.00	−0.947322	−0.473661	−	0.880707i	$-0.657068\pi$
$193$	−2540.00	−0.947322	−0.473661	+	0.880707i	$0.657068\pi$
$194$	544.000	0.201324
$195$	−21.0000	−0.00771201
$196$	0	0
$197$	1606.00	0.580826	0.290413	−	0.956901i	$-0.406207\pi$
$197$	1606.00	0.580826	0.290413	+	0.956901i	$0.406207\pi$
$198$	198.000	0.0710669
$199$	−288.000	−0.102592	−0.0512959	−	0.998683i	$-0.516335\pi$
$199$	−288.000	−0.102592	−0.0512959	+	0.998683i	$0.516335\pi$
$200$	−2976.00	−1.05217
$201$	417.000	0.146333
$202$	−1748.00	−0.608856
$203$	0	0
$204$	168.000	0.0576586
$205$	−380.000	−0.129465
$206$	−1652.00	−0.558739
$207$	−792.000	−0.265931
$208$	112.000	0.0373356
$209$	−495.000	−0.163827
$210$	0	0
$211$	1482.00	0.483531	0.241766	−	0.970335i	$-0.422273\pi$
$211$	1482.00	0.483531	0.241766	+	0.970335i	$0.422273\pi$
$212$	2688.00	0.870814
$213$	−396.000	−0.127387
$214$	−438.000	−0.139912
$215$	−48.0000	−0.0152259
$216$	−648.000	−0.204124
$217$	0	0
$218$	−2852.00	−0.886063
$219$	435.000	0.134222
$220$	−44.0000	−0.0134840
$221$	−98.0000	−0.0298289
$222$	342.000	0.103394
$223$	−3502.00	−1.05162	−0.525810	−	0.850602i	$-0.676238\pi$
$223$	−3502.00	−1.05162	−0.525810	+	0.850602i	$0.676238\pi$
$224$	0	0
$225$	−1116.00	−0.330667
$226$	−1764.00	−0.519201
$227$	−1830.00	−0.535072	−0.267536	−	0.963548i	$-0.586209\pi$
$227$	−1830.00	−0.535072	−0.267536	+	0.963548i	$0.586209\pi$
$228$	540.000	0.156853
$229$	2268.00	0.654470	0.327235	−	0.944943i	$-0.393883\pi$
$229$	2268.00	0.654470	0.327235	+	0.944943i	$0.393883\pi$
$230$	−176.000	−0.0504569
$231$	0	0
$232$	−1656.00	−0.468628
$233$	2430.00	0.683239	0.341619	−	0.939838i	$-0.389025\pi$
$233$	2430.00	0.683239	0.341619	+	0.939838i	$0.389025\pi$
$234$	126.000	0.0352003
$235$	−385.000	−0.106871
$236$	−1876.00	−0.517446
$237$	−3732.00	−1.02287
$238$	0	0
$239$	−2151.00	−0.582162	−0.291081	−	0.956698i	$-0.594015\pi$
$239$	−2151.00	−0.582162	−0.291081	+	0.956698i	$0.594015\pi$
$240$	−48.0000	−0.0129099
$241$	−2803.00	−0.749200	−0.374600	−	0.927187i	$-0.622220\pi$
$241$	−2803.00	−0.749200	−0.374600	+	0.927187i	$0.622220\pi$
$242$	−242.000	−0.0642824
$243$	−243.000	−0.0641500
$244$	−1368.00	−0.358923
$245$	0	0
$246$	2280.00	0.590925
$247$	−315.000	−0.0811456
$248$	−528.000	−0.135194
$249$	1566.00	0.398559
$250$	−498.000	−0.125985
$251$	5339.00	1.34261	0.671304	−	0.741182i	$-0.265734\pi$
$251$	5339.00	1.34261	0.671304	+	0.741182i	$0.265734\pi$
$252$	0	0
$253$	968.000	0.240544
$254$	−3652.00	−0.902153
$255$	42.0000	0.0103143
$256$	−4352.00	−1.06250
$257$	4439.00	1.07742	0.538711	−	0.842491i	$-0.318912\pi$
$257$	4439.00	1.07742	0.538711	+	0.842491i	$0.318912\pi$
$258$	288.000	0.0694965
$259$	0	0
$260$	−28.0000	−0.00667879
$261$	−621.000	−0.147276
$262$	168.000	0.0396148
$263$	1271.00	0.297997	0.148999	−	0.988837i	$-0.452395\pi$
$263$	1271.00	0.297997	0.148999	+	0.988837i	$0.452395\pi$
$264$	792.000	0.184637
$265$	672.000	0.155776
$266$	0	0
$267$	2466.00	0.565231
$268$	556.000	0.126728
$269$	−3682.00	−0.834556	−0.417278	−	0.908779i	$-0.637016\pi$
$269$	−3682.00	−0.834556	−0.417278	+	0.908779i	$0.637016\pi$
$270$	−54.0000	−0.0121716
$271$	−4127.00	−0.925083	−0.462541	−	0.886598i	$-0.653062\pi$
$271$	−4127.00	−0.925083	−0.462541	+	0.886598i	$0.653062\pi$
$272$	−224.000	−0.0499338
$273$	0	0
$274$	3668.00	0.808730
$275$	1364.00	0.299099
$276$	−1056.00	−0.230303
$277$	−44.0000	−0.00954406	−0.00477203	−	0.999989i	$-0.501519\pi$
$277$	−44.0000	−0.00954406	−0.00477203	+	0.999989i	$0.501519\pi$
$278$	4832.00	1.04246
$279$	−198.000	−0.0424873
$280$	0	0
$281$	−561.000	−0.119098	−0.0595489	−	0.998225i	$-0.518966\pi$
$281$	−561.000	−0.119098	−0.0595489	+	0.998225i	$0.518966\pi$
$282$	2310.00	0.487796
$283$	3845.00	0.807638	0.403819	−	0.914839i	$-0.367683\pi$
$283$	3845.00	0.807638	0.403819	+	0.914839i	$0.367683\pi$
$284$	−528.000	−0.110321
$285$	135.000	0.0280586
$286$	−154.000	−0.0318399
$287$	0	0
$288$	−1440.00	−0.294628
$289$	−4717.00	−0.960106
$290$	−138.000	−0.0279436
$291$	816.000	0.164381
$292$	580.000	0.116239
$293$	−912.000	−0.181842	−0.0909208	−	0.995858i	$-0.528981\pi$
$293$	−912.000	−0.181842	−0.0909208	+	0.995858i	$0.528981\pi$
$294$	0	0
$295$	−469.000	−0.0925635
$296$	1368.00	0.268626
$297$	297.000	0.0580259
$298$	−3790.00	−0.736741
$299$	616.000	0.119144
$300$	−1488.00	−0.286366
$301$	0	0
$302$	6956.00	1.32541
$303$	−2622.00	−0.497129
$304$	−720.000	−0.135838
$305$	−342.000	−0.0642061
$306$	−252.000	−0.0470780
$307$	−6860.00	−1.27531	−0.637656	−	0.770321i	$-0.720096\pi$
$307$	−6860.00	−1.27531	−0.637656	+	0.770321i	$0.720096\pi$
$308$	0	0
$309$	−2478.00	−0.456209
$310$	−44.0000	−0.00806139
$311$	−5472.00	−0.997713	−0.498856	−	0.866685i	$-0.666246\pi$
$311$	−5472.00	−0.997713	−0.498856	+	0.866685i	$0.666246\pi$
$312$	504.000	0.0914531
$313$	−6422.00	−1.15972	−0.579861	−	0.814716i	$-0.696893\pi$
$313$	−6422.00	−1.15972	−0.579861	+	0.814716i	$0.696893\pi$
$314$	−1904.00	−0.342194
$315$	0	0
$316$	−4976.00	−0.885829
$317$	−6476.00	−1.14741	−0.573704	−	0.819063i	$-0.694494\pi$
$317$	−6476.00	−1.14741	−0.573704	+	0.819063i	$0.694494\pi$
$318$	−4032.00	−0.711017
$319$	759.000	0.133216
$320$	−448.000	−0.0782624
$321$	−657.000	−0.114237
$322$	0	0
$323$	630.000	0.108527
$324$	−324.000	−0.0555556
$325$	868.000	0.148148
$326$	4966.00	0.843685
$327$	−4278.00	−0.723468
$328$	9120.00	1.53527
$329$	0	0
$330$	66.0000	0.0110096
$331$	−11840.0	−1.96612	−0.983059	−	0.183288i	$-0.941326\pi$
$331$	−11840.0	−1.96612	−0.983059	+	0.183288i	$0.941326\pi$
$332$	2088.00	0.345162
$333$	513.000	0.0844211
$334$	936.000	0.153340
$335$	139.000	0.0226698
$336$	0	0
$337$	1640.00	0.265093	0.132547	−	0.991177i	$-0.457685\pi$
$337$	1640.00	0.265093	0.132547	+	0.991177i	$0.457685\pi$
$338$	4296.00	0.691336
$339$	−2646.00	−0.423926
$340$	56.0000	0.00893243
$341$	242.000	0.0384312
$342$	−810.000	−0.128070
$343$	0	0
$344$	1152.00	0.180557
$345$	−264.000	−0.0411979
$346$	−4296.00	−0.667498
$347$	2032.00	0.314362	0.157181	−	0.987570i	$-0.449759\pi$
$347$	2032.00	0.314362	0.157181	+	0.987570i	$0.449759\pi$
$348$	−828.000	−0.127544
$349$	−1755.00	−0.269178	−0.134589	−	0.990902i	$-0.542971\pi$
$349$	−1755.00	−0.269178	−0.134589	+	0.990902i	$0.542971\pi$
$350$	0	0
$351$	189.000	0.0287410
$352$	1760.00	0.266501
$353$	1101.00	0.166007	0.0830033	−	0.996549i	$-0.473549\pi$
$353$	1101.00	0.166007	0.0830033	+	0.996549i	$0.473549\pi$
$354$	2814.00	0.422493
$355$	−132.000	−0.0197347
$356$	3288.00	0.489505
$357$	0	0
$358$	2928.00	0.432261
$359$	5020.00	0.738010	0.369005	−	0.929427i	$-0.379699\pi$
$359$	5020.00	0.738010	0.369005	+	0.929427i	$0.379699\pi$
$360$	−216.000	−0.0316228
$361$	−4834.00	−0.704767
$362$	2864.00	0.415825
$363$	−363.000	−0.0524864
$364$	0	0
$365$	145.000	0.0207936
$366$	2052.00	0.293059
$367$	−11638.0	−1.65531	−0.827655	−	0.561237i	$-0.810325\pi$
$367$	−11638.0	−1.65531	−0.827655	+	0.561237i	$0.810325\pi$
$368$	1408.00	0.199449
$369$	3420.00	0.482488
$370$	114.000	0.0160178
$371$	0	0
$372$	−264.000	−0.0367951
$373$	−8834.00	−1.22629	−0.613146	−	0.789969i	$-0.710096\pi$
$373$	−8834.00	−1.22629	−0.613146	+	0.789969i	$0.710096\pi$
$374$	308.000	0.0425837
$375$	−747.000	−0.102866
$376$	9240.00	1.26733
$377$	483.000	0.0659835
$378$	0	0
$379$	7507.00	1.01744	0.508719	−	0.860933i	$-0.330119\pi$
$379$	7507.00	1.01744	0.508719	+	0.860933i	$0.330119\pi$
$380$	180.000	0.0242995
$381$	−5478.00	−0.736605
$382$	2660.00	0.356276
$383$	−3608.00	−0.481358	−0.240679	−	0.970605i	$-0.577370\pi$
$383$	−3608.00	−0.481358	−0.240679	+	0.970605i	$0.577370\pi$
$384$	−1152.00	−0.153093
$385$	0	0
$386$	5080.00	0.669858
$387$	432.000	0.0567437
$388$	1088.00	0.142358
$389$	−7896.00	−1.02916	−0.514580	−	0.857442i	$-0.672052\pi$
$389$	−7896.00	−1.02916	−0.514580	+	0.857442i	$0.672052\pi$
$390$	42.0000	0.00545321
$391$	−1232.00	−0.159348
$392$	0	0
$393$	252.000	0.0323453
$394$	−3212.00	−0.410706
$395$	−1244.00	−0.158462
$396$	396.000	0.0502519
$397$	−6934.00	−0.876593	−0.438297	−	0.898830i	$-0.644418\pi$
$397$	−6934.00	−0.876593	−0.438297	+	0.898830i	$0.644418\pi$
$398$	576.000	0.0725434
$399$	0	0
$400$	1984.00	0.248000
$401$	−700.000	−0.0871729	−0.0435864	−	0.999050i	$-0.513878\pi$
$401$	−700.000	−0.0871729	−0.0435864	+	0.999050i	$0.513878\pi$
$402$	−834.000	−0.103473
$403$	154.000	0.0190355
$404$	−3496.00	−0.430526
$405$	−81.0000	−0.00993808
$406$	0	0
$407$	−627.000	−0.0763618
$408$	−1008.00	−0.122312
$409$	11550.0	1.39636	0.698179	−	0.715923i	$-0.253994\pi$
$409$	11550.0	1.39636	0.698179	+	0.715923i	$0.253994\pi$
$410$	760.000	0.0915457
$411$	5502.00	0.660325
$412$	−3304.00	−0.395088
$413$	0	0
$414$	1584.00	0.188042
$415$	522.000	0.0617445
$416$	1120.00	0.132001
$417$	7248.00	0.851166
$418$	990.000	0.115843
$419$	4555.00	0.531089	0.265545	−	0.964099i	$-0.414448\pi$
$419$	4555.00	0.531089	0.265545	+	0.964099i	$0.414448\pi$
$420$	0	0
$421$	−161.000	−0.0186381	−0.00931907	−	0.999957i	$-0.502966\pi$
$421$	−161.000	−0.0186381	−0.00931907	+	0.999957i	$0.502966\pi$
$422$	−2964.00	−0.341908
$423$	3465.00	0.398284
$424$	−16128.0	−1.84728
$425$	−1736.00	−0.198137
$426$	792.000	0.0900764
$427$	0	0
$428$	−876.000	−0.0989324
$429$	−231.000	−0.0259972
$430$	96.0000	0.0107664
$431$	−3249.00	−0.363106	−0.181553	−	0.983381i	$-0.558112\pi$
$431$	−3249.00	−0.363106	−0.181553	+	0.983381i	$0.558112\pi$
$432$	432.000	0.0481125
$433$	−1792.00	−0.198887	−0.0994434	−	0.995043i	$-0.531706\pi$
$433$	−1792.00	−0.198887	−0.0994434	+	0.995043i	$0.531706\pi$
$434$	0	0
$435$	−207.000	−0.0228158
$436$	−5704.00	−0.626541
$437$	−3960.00	−0.433484
$438$	−870.000	−0.0949092
$439$	−9319.00	−1.01315	−0.506574	−	0.862197i	$-0.669088\pi$
$439$	−9319.00	−1.01315	−0.506574	+	0.862197i	$0.669088\pi$
$440$	264.000	0.0286039
$441$	0	0
$442$	196.000	0.0210922
$443$	5608.00	0.601454	0.300727	−	0.953710i	$-0.402771\pi$
$443$	5608.00	0.601454	0.300727	+	0.953710i	$0.402771\pi$
$444$	684.000	0.0731108
$445$	822.000	0.0875653
$446$	7004.00	0.743608
$447$	−5685.00	−0.601546
$448$	0	0
$449$	−4384.00	−0.460788	−0.230394	−	0.973097i	$-0.574001\pi$
$449$	−4384.00	−0.460788	−0.230394	+	0.973097i	$0.574001\pi$
$450$	2232.00	0.233817
$451$	−4180.00	−0.436427
$452$	−3528.00	−0.367131
$453$	10434.0	1.08219
$454$	3660.00	0.378353
$455$	0	0
$456$	−3240.00	−0.332734
$457$	324.000	0.0331643	0.0165821	−	0.999863i	$-0.494721\pi$
$457$	324.000	0.0331643	0.0165821	+	0.999863i	$0.494721\pi$
$458$	−4536.00	−0.462780
$459$	−378.000	−0.0384391
$460$	−352.000	−0.0356784
$461$	18360.0	1.85490	0.927452	−	0.373943i	$-0.121994\pi$
$461$	18360.0	1.85490	0.927452	+	0.373943i	$0.121994\pi$
$462$	0	0
$463$	−1667.00	−0.167326	−0.0836631	−	0.996494i	$-0.526662\pi$
$463$	−1667.00	−0.167326	−0.0836631	+	0.996494i	$0.526662\pi$
$464$	1104.00	0.110457
$465$	−66.0000	−0.00658210
$466$	−4860.00	−0.483123
$467$	−10839.0	−1.07402	−0.537012	−	0.843575i	$-0.680447\pi$
$467$	−10839.0	−1.07402	−0.537012	+	0.843575i	$0.680447\pi$
$468$	252.000	0.0248904
$469$	0	0
$470$	770.000	0.0755690
$471$	−2856.00	−0.279400
$472$	11256.0	1.09767
$473$	−528.000	−0.0513266
$474$	7464.00	0.723276
$475$	−5580.00	−0.539006
$476$	0	0
$477$	−6048.00	−0.580543
$478$	4302.00	0.411650
$479$	910.000	0.0868037	0.0434018	−	0.999058i	$-0.486180\pi$
$479$	910.000	0.0868037	0.0434018	+	0.999058i	$0.486180\pi$
$480$	−480.000	−0.0456435
$481$	−399.000	−0.0378229
$482$	5606.00	0.529764
$483$	0	0
$484$	−484.000	−0.0454545
$485$	272.000	0.0254657
$486$	486.000	0.0453609
$487$	12032.0	1.11955	0.559776	−	0.828644i	$-0.310887\pi$
$487$	12032.0	1.11955	0.559776	+	0.828644i	$0.310887\pi$
$488$	8208.00	0.761391
$489$	7449.00	0.688866
$490$	0	0
$491$	4243.00	0.389988	0.194994	−	0.980804i	$-0.437531\pi$
$491$	4243.00	0.389988	0.194994	+	0.980804i	$0.437531\pi$
$492$	4560.00	0.417847
$493$	−966.000	−0.0882484
$494$	630.000	0.0573786
$495$	99.0000	0.00898933
$496$	352.000	0.0318655
$497$	0	0
$498$	−3132.00	−0.281824
$499$	−5869.00	−0.526518	−0.263259	−	0.964725i	$-0.584797\pi$
$499$	−5869.00	−0.526518	−0.263259	+	0.964725i	$0.584797\pi$
$500$	−996.000	−0.0890849
$501$	1404.00	0.125202
$502$	−10678.0	−0.949367
$503$	−148.000	−0.0131193	−0.00655964	−	0.999978i	$-0.502088\pi$
$503$	−148.000	−0.0131193	−0.00655964	+	0.999978i	$0.502088\pi$
$504$	0	0
$505$	−874.000	−0.0770148
$506$	−1936.00	−0.170090
$507$	6444.00	0.564474
$508$	−7304.00	−0.637918
$509$	−12114.0	−1.05490	−0.527450	−	0.849586i	$-0.676852\pi$
$509$	−12114.0	−1.05490	−0.527450	+	0.849586i	$0.676852\pi$
$510$	−84.0000	−0.00729330
$511$	0	0
$512$	5632.00	0.486136
$513$	−1215.00	−0.104568
$514$	−8878.00	−0.761852
$515$	−826.000	−0.0706756
$516$	576.000	0.0491414
$517$	−4235.00	−0.360261
$518$	0	0
$519$	−6444.00	−0.545010
$520$	168.000	0.0141679
$521$	14943.0	1.25655	0.628277	−	0.777990i	$-0.283760\pi$
$521$	14943.0	1.25655	0.628277	+	0.777990i	$0.283760\pi$
$522$	1242.00	0.104140
$523$	−16589.0	−1.38697	−0.693486	−	0.720470i	$-0.743926\pi$
$523$	−16589.0	−1.38697	−0.693486	+	0.720470i	$0.743926\pi$
$524$	336.000	0.0280119
$525$	0	0
$526$	−2542.00	−0.210716
$527$	−308.000	−0.0254586
$528$	−528.000	−0.0435194
$529$	−4423.00	−0.363524
$530$	−1344.00	−0.110150
$531$	4221.00	0.344964
$532$	0	0
$533$	−2660.00	−0.216168
$534$	−4932.00	−0.399679
$535$	−219.000	−0.0176976
$536$	−3336.00	−0.268831
$537$	4392.00	0.352940
$538$	7364.00	0.590120
$539$	0	0
$540$	−108.000	−0.00860663
$541$	3232.00	0.256848	0.128424	−	0.991719i	$-0.459008\pi$
$541$	3232.00	0.256848	0.128424	+	0.991719i	$0.459008\pi$
$542$	8254.00	0.654132
$543$	4296.00	0.339519
$544$	−2240.00	−0.176543
$545$	−1426.00	−0.112079
$546$	0	0
$547$	−16468.0	−1.28724	−0.643621	−	0.765345i	$-0.722568\pi$
$547$	−16468.0	−1.28724	−0.643621	+	0.765345i	$0.722568\pi$
$548$	7336.00	0.571858
$549$	3078.00	0.239282
$550$	−2728.00	−0.211495
$551$	−3105.00	−0.240068
$552$	6336.00	0.488547
$553$	0	0
$554$	88.0000	0.00674867
$555$	171.000	0.0130785
$556$	9664.00	0.737131
$557$	14143.0	1.07587	0.537934	−	0.842987i	$-0.319205\pi$
$557$	14143.0	1.07587	0.537934	+	0.842987i	$0.319205\pi$
$558$	396.000	0.0300430
$559$	−336.000	−0.0254227
$560$	0	0
$561$	462.000	0.0347694
$562$	1122.00	0.0842148
$563$	22916.0	1.71544	0.857721	−	0.514115i	$-0.171879\pi$
$563$	22916.0	1.71544	0.857721	+	0.514115i	$0.171879\pi$
$564$	4620.00	0.344924
$565$	−882.000	−0.0656744
$566$	−7690.00	−0.571086
$567$	0	0
$568$	3168.00	0.234025
$569$	−294.000	−0.0216610	−0.0108305	−	0.999941i	$-0.503448\pi$
$569$	−294.000	−0.0216610	−0.0108305	+	0.999941i	$0.503448\pi$
$570$	−270.000	−0.0198404
$571$	13292.0	0.974173	0.487087	−	0.873354i	$-0.338060\pi$
$571$	13292.0	0.974173	0.487087	+	0.873354i	$0.338060\pi$
$572$	−308.000	−0.0225142
$573$	3990.00	0.290898
$574$	0	0
$575$	10912.0	0.791412
$576$	4032.00	0.291667
$577$	−9630.00	−0.694804	−0.347402	−	0.937716i	$-0.612936\pi$
$577$	−9630.00	−0.694804	−0.347402	+	0.937716i	$0.612936\pi$
$578$	9434.00	0.678897
$579$	7620.00	0.546937
$580$	−276.000	−0.0197591
$581$	0	0
$582$	−1632.00	−0.116235
$583$	7392.00	0.525121
$584$	−3480.00	−0.246581
$585$	63.0000	0.00445253
$586$	1824.00	0.128581
$587$	17015.0	1.19640	0.598198	−	0.801348i	$-0.295884\pi$
$587$	17015.0	1.19640	0.598198	+	0.801348i	$0.295884\pi$
$588$	0	0
$589$	−990.000	−0.0692568
$590$	938.000	0.0654523
$591$	−4818.00	−0.335340
$592$	−912.000	−0.0633158
$593$	12028.0	0.832936	0.416468	−	0.909150i	$-0.363268\pi$
$593$	12028.0	0.832936	0.416468	+	0.909150i	$0.363268\pi$
$594$	−594.000	−0.0410305
$595$	0	0
$596$	−7580.00	−0.520955
$597$	864.000	0.0592314
$598$	−1232.00	−0.0842479
$599$	1252.00	0.0854012	0.0427006	−	0.999088i	$-0.486404\pi$
$599$	1252.00	0.0854012	0.0427006	+	0.999088i	$0.486404\pi$
$600$	8928.00	0.607473
$601$	19699.0	1.33700	0.668502	−	0.743711i	$-0.266936\pi$
$601$	19699.0	1.33700	0.668502	+	0.743711i	$0.266936\pi$
$602$	0	0
$603$	−1251.00	−0.0844853
$604$	13912.0	0.937204
$605$	−121.000	−0.00813116
$606$	5244.00	0.351523
$607$	−29855.0	−1.99634	−0.998169	−	0.0604881i	$-0.980734\pi$
$607$	−29855.0	−1.99634	−0.998169	+	0.0604881i	$0.980734\pi$
$608$	−7200.00	−0.480261
$609$	0	0
$610$	684.000	0.0454006
$611$	−2695.00	−0.178442
$612$	−504.000	−0.0332892
$613$	−3178.00	−0.209393	−0.104697	−	0.994504i	$-0.533387\pi$
$613$	−3178.00	−0.209393	−0.104697	+	0.994504i	$0.533387\pi$
$614$	13720.0	0.901782
$615$	1140.00	0.0747467
$616$	0	0
$617$	−14394.0	−0.939191	−0.469595	−	0.882882i	$-0.655600\pi$
$617$	−14394.0	−0.939191	−0.469595	+	0.882882i	$0.655600\pi$
$618$	4956.00	0.322588
$619$	−3878.00	−0.251809	−0.125905	−	0.992042i	$-0.540183\pi$
$619$	−3878.00	−0.251809	−0.125905	+	0.992042i	$0.540183\pi$
$620$	−88.0000	−0.00570027
$621$	2376.00	0.153536
$622$	10944.0	0.705489
$623$	0	0
$624$	−336.000	−0.0215557
$625$	15251.0	0.976064
$626$	12844.0	0.820047
$627$	1485.00	0.0945856
$628$	−3808.00	−0.241968
$629$	798.000	0.0505856
$630$	0	0
$631$	18100.0	1.14192	0.570958	−	0.820979i	$-0.306572\pi$
$631$	18100.0	1.14192	0.570958	+	0.820979i	$0.306572\pi$
$632$	29856.0	1.87913
$633$	−4446.00	−0.279167
$634$	12952.0	0.811340
$635$	−1826.00	−0.114114
$636$	−8064.00	−0.502765
$637$	0	0
$638$	−1518.00	−0.0941978
$639$	1188.00	0.0735470
$640$	−384.000	−0.0237171
$641$	−7470.00	−0.460292	−0.230146	−	0.973156i	$-0.573920\pi$
$641$	−7470.00	−0.460292	−0.230146	+	0.973156i	$0.573920\pi$
$642$	1314.00	0.0807779
$643$	−25400.0	−1.55782	−0.778910	−	0.627136i	$-0.784227\pi$
$643$	−25400.0	−1.55782	−0.778910	+	0.627136i	$0.784227\pi$
$644$	0	0
$645$	144.000	0.00879069
$646$	−1260.00	−0.0767400
$647$	−25061.0	−1.52280	−0.761398	−	0.648284i	$-0.775487\pi$
$647$	−25061.0	−1.52280	−0.761398	+	0.648284i	$0.775487\pi$
$648$	1944.00	0.117851
$649$	−5159.00	−0.312032
$650$	−1736.00	−0.104756
$651$	0	0
$652$	9932.00	0.596575
$653$	−1832.00	−0.109788	−0.0548941	−	0.998492i	$-0.517482\pi$
$653$	−1832.00	−0.109788	−0.0548941	+	0.998492i	$0.517482\pi$
$654$	8556.00	0.511569
$655$	84.0000	0.00501092
$656$	−6080.00	−0.361866
$657$	−1305.00	−0.0774930
$658$	0	0
$659$	−27809.0	−1.64383	−0.821916	−	0.569609i	$-0.807095\pi$
$659$	−27809.0	−1.64383	−0.821916	+	0.569609i	$0.807095\pi$
$660$	132.000	0.00778499
$661$	29612.0	1.74247	0.871235	−	0.490865i	$-0.163319\pi$
$661$	29612.0	1.74247	0.871235	+	0.490865i	$0.163319\pi$
$662$	23680.0	1.39026
$663$	294.000	0.0172217
$664$	−12528.0	−0.732200
$665$	0	0
$666$	−1026.00	−0.0596947
$667$	6072.00	0.352487
$668$	1872.00	0.108428
$669$	10506.0	0.607153
$670$	−278.000	−0.0160300
$671$	−3762.00	−0.216439
$672$	0	0
$673$	−3892.00	−0.222921	−0.111460	−	0.993769i	$-0.535553\pi$
$673$	−3892.00	−0.222921	−0.111460	+	0.993769i	$0.535553\pi$
$674$	−3280.00	−0.187449
$675$	3348.00	0.190910
$676$	8592.00	0.488848
$677$	−10518.0	−0.597104	−0.298552	−	0.954393i	$-0.596504\pi$
$677$	−10518.0	−0.597104	−0.298552	+	0.954393i	$0.596504\pi$
$678$	5292.00	0.299761
$679$	0	0
$680$	−336.000	−0.0189485
$681$	5490.00	0.308924
$682$	−484.000	−0.0271750
$683$	12902.0	0.722813	0.361407	−	0.932408i	$-0.382297\pi$
$683$	12902.0	0.722813	0.361407	+	0.932408i	$0.382297\pi$
$684$	−1620.00	−0.0905588
$685$	1834.00	0.102297
$686$	0	0
$687$	−6804.00	−0.377859
$688$	−768.000	−0.0425577
$689$	4704.00	0.260099
$690$	528.000	0.0291313
$691$	−30386.0	−1.67285	−0.836424	−	0.548083i	$-0.815358\pi$
$691$	−30386.0	−1.67285	−0.836424	+	0.548083i	$0.815358\pi$
$692$	−8592.00	−0.471993
$693$	0	0
$694$	−4064.00	−0.222287
$695$	2416.00	0.131862
$696$	4968.00	0.270563
$697$	5320.00	0.289110
$698$	3510.00	0.190337
$699$	−7290.00	−0.394468
$700$	0	0
$701$	−26842.0	−1.44623	−0.723116	−	0.690727i	$-0.757291\pi$
$701$	−26842.0	−1.44623	−0.723116	+	0.690727i	$0.757291\pi$
$702$	−378.000	−0.0203229
$703$	2565.00	0.137611
$704$	−4928.00	−0.263822
$705$	1155.00	0.0617019
$706$	−2202.00	−0.117384
$707$	0	0
$708$	5628.00	0.298747
$709$	−5701.00	−0.301982	−0.150991	−	0.988535i	$-0.548247\pi$
$709$	−5701.00	−0.301982	−0.150991	+	0.988535i	$0.548247\pi$
$710$	264.000	0.0139546
$711$	11196.0	0.590552
$712$	−19728.0	−1.03840
$713$	1936.00	0.101688
$714$	0	0
$715$	−77.0000	−0.00402746
$716$	5856.00	0.305655
$717$	6453.00	0.336111
$718$	−10040.0	−0.521852
$719$	23919.0	1.24065	0.620326	−	0.784344i	$-0.287000\pi$
$719$	23919.0	1.24065	0.620326	+	0.784344i	$0.287000\pi$
$720$	144.000	0.00745356
$721$	0	0
$722$	9668.00	0.498346
$723$	8409.00	0.432551
$724$	5728.00	0.294032
$725$	8556.00	0.438292
$726$	726.000	0.0371135
$727$	−19188.0	−0.978877	−0.489438	−	0.872038i	$-0.662798\pi$
$727$	−19188.0	−0.978877	−0.489438	+	0.872038i	$0.662798\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−290.000	−0.0147033
$731$	672.000	0.0340011
$732$	4104.00	0.207224
$733$	5670.00	0.285711	0.142856	−	0.989744i	$-0.454372\pi$
$733$	5670.00	0.285711	0.142856	+	0.989744i	$0.454372\pi$
$734$	23276.0	1.17048
$735$	0	0
$736$	14080.0	0.705157
$737$	1529.00	0.0764199
$738$	−6840.00	−0.341171
$739$	17276.0	0.859957	0.429978	−	0.902839i	$-0.358521\pi$
$739$	17276.0	0.859957	0.429978	+	0.902839i	$0.358521\pi$
$740$	228.000	0.0113263
$741$	945.000	0.0468494
$742$	0	0
$743$	15367.0	0.758763	0.379381	−	0.925240i	$-0.376137\pi$
$743$	15367.0	0.758763	0.379381	+	0.925240i	$0.376137\pi$
$744$	1584.00	0.0780541
$745$	−1895.00	−0.0931912
$746$	17668.0	0.867120
$747$	−4698.00	−0.230108
$748$	616.000	0.0301112
$749$	0	0
$750$	1494.00	0.0727376
$751$	−38123.0	−1.85237	−0.926184	−	0.377072i	$-0.876931\pi$
$751$	−38123.0	−1.85237	−0.926184	+	0.377072i	$0.876931\pi$
$752$	−6160.00	−0.298713
$753$	−16017.0	−0.775155
$754$	−966.000	−0.0466574
$755$	3478.00	0.167652
$756$	0	0
$757$	23417.0	1.12431	0.562157	−	0.827031i	$-0.309972\pi$
$757$	23417.0	1.12431	0.562157	+	0.827031i	$0.309972\pi$
$758$	−15014.0	−0.719437
$759$	−2904.00	−0.138878
$760$	−1080.00	−0.0515470
$761$	16332.0	0.777969	0.388985	−	0.921244i	$-0.372826\pi$
$761$	16332.0	0.777969	0.388985	+	0.921244i	$0.372826\pi$
$762$	10956.0	0.520858
$763$	0	0
$764$	5320.00	0.251925
$765$	−126.000	−0.00595495
$766$	7216.00	0.340372
$767$	−3283.00	−0.154553
$768$	13056.0	0.613435
$769$	−19523.0	−0.915497	−0.457749	−	0.889082i	$-0.651344\pi$
$769$	−19523.0	−0.915497	−0.457749	+	0.889082i	$0.651344\pi$
$770$	0	0
$771$	−13317.0	−0.622049
$772$	10160.0	0.473661
$773$	−21525.0	−1.00155	−0.500776	−	0.865577i	$-0.666952\pi$
$773$	−21525.0	−1.00155	−0.500776	+	0.865577i	$0.666952\pi$
$774$	−864.000	−0.0401238
$775$	2728.00	0.126442
$776$	−6528.00	−0.301987
$777$	0	0
$778$	15792.0	0.727726
$779$	17100.0	0.786484
$780$	84.0000	0.00385600
$781$	−1452.00	−0.0665258
$782$	2464.00	0.112676
$783$	1863.00	0.0850296
$784$	0	0
$785$	−952.000	−0.0432845
$786$	−504.000	−0.0228716
$787$	3707.00	0.167904	0.0839519	−	0.996470i	$-0.473246\pi$
$787$	3707.00	0.167904	0.0839519	+	0.996470i	$0.473246\pi$
$788$	−6424.00	−0.290413
$789$	−3813.00	−0.172049
$790$	2488.00	0.112049
$791$	0	0
$792$	−2376.00	−0.106600
$793$	−2394.00	−0.107205
$794$	13868.0	0.619845
$795$	−2016.00	−0.0899373
$796$	1152.00	0.0512959
$797$	7621.00	0.338707	0.169354	−	0.985555i	$-0.445832\pi$
$797$	7621.00	0.338707	0.169354	+	0.985555i	$0.445832\pi$
$798$	0	0
$799$	5390.00	0.238654
$800$	19840.0	0.876812
$801$	−7398.00	−0.326336
$802$	1400.00	0.0616405
$803$	1595.00	0.0700951
$804$	−1668.00	−0.0731664
$805$	0	0
$806$	−308.000	−0.0134601
$807$	11046.0	0.481831
$808$	20976.0	0.913284
$809$	23451.0	1.01915	0.509576	−	0.860426i	$-0.329802\pi$
$809$	23451.0	1.01915	0.509576	+	0.860426i	$0.329802\pi$
$810$	162.000	0.00702728
$811$	4499.00	0.194798	0.0973990	−	0.995245i	$-0.468948\pi$
$811$	4499.00	0.194798	0.0973990	+	0.995245i	$0.468948\pi$
$812$	0	0
$813$	12381.0	0.534097
$814$	1254.00	0.0539959
$815$	2483.00	0.106719
$816$	672.000	0.0288293
$817$	2160.00	0.0924955
$818$	−23100.0	−0.987375
$819$	0	0
$820$	1520.00	0.0647326
$821$	−30215.0	−1.28442	−0.642211	−	0.766528i	$-0.721983\pi$
$821$	−30215.0	−1.28442	−0.642211	+	0.766528i	$0.721983\pi$
$822$	−11004.0	−0.466920
$823$	−19947.0	−0.844847	−0.422423	−	0.906399i	$-0.638820\pi$
$823$	−19947.0	−0.844847	−0.422423	+	0.906399i	$0.638820\pi$
$824$	19824.0	0.838109
$825$	−4092.00	−0.172685
$826$	0	0
$827$	−20341.0	−0.855291	−0.427646	−	0.903946i	$-0.640657\pi$
$827$	−20341.0	−0.855291	−0.427646	+	0.903946i	$0.640657\pi$
$828$	3168.00	0.132966
$829$	14024.0	0.587544	0.293772	−	0.955876i	$-0.405089\pi$
$829$	14024.0	0.587544	0.293772	+	0.955876i	$0.405089\pi$
$830$	−1044.00	−0.0436600
$831$	132.000	0.00551026
$832$	−3136.00	−0.130675
$833$	0	0
$834$	−14496.0	−0.601865
$835$	468.000	0.0193962
$836$	1980.00	0.0819136
$837$	594.000	0.0245300
$838$	−9110.00	−0.375537
$839$	37193.0	1.53045	0.765223	−	0.643765i	$-0.222628\pi$
$839$	37193.0	1.53045	0.765223	+	0.643765i	$0.222628\pi$
$840$	0	0
$841$	−19628.0	−0.804789
$842$	322.000	0.0131792
$843$	1683.00	0.0687611
$844$	−5928.00	−0.241766
$845$	2148.00	0.0874479
$846$	−6930.00	−0.281629
$847$	0	0
$848$	10752.0	0.435407
$849$	−11535.0	−0.466290
$850$	3472.00	0.140104
$851$	−5016.00	−0.202052
$852$	1584.00	0.0636936
$853$	37042.0	1.48686	0.743431	−	0.668812i	$-0.233197\pi$
$853$	37042.0	1.48686	0.743431	+	0.668812i	$0.233197\pi$
$854$	0	0
$855$	−405.000	−0.0161997
$856$	5256.00	0.209867
$857$	41962.0	1.67257	0.836286	−	0.548293i	$-0.184722\pi$
$857$	41962.0	1.67257	0.836286	+	0.548293i	$0.184722\pi$
$858$	462.000	0.0183828
$859$	9372.00	0.372257	0.186128	−	0.982525i	$-0.440406\pi$
$859$	9372.00	0.372257	0.186128	+	0.982525i	$0.440406\pi$
$860$	192.000	0.00761296
$861$	0	0
$862$	6498.00	0.256755
$863$	18096.0	0.713783	0.356892	−	0.934146i	$-0.383837\pi$
$863$	18096.0	0.713783	0.356892	+	0.934146i	$0.383837\pi$
$864$	4320.00	0.170103
$865$	−2148.00	−0.0844326
$866$	3584.00	0.140634
$867$	14151.0	0.554317
$868$	0	0
$869$	−13684.0	−0.534175
$870$	414.000	0.0161332
$871$	973.000	0.0378517
$872$	34224.0	1.32910
$873$	−2448.00	−0.0949052
$874$	7920.00	0.306519
$875$	0	0
$876$	−1740.00	−0.0671109
$877$	−28848.0	−1.11075	−0.555375	−	0.831600i	$-0.687425\pi$
$877$	−28848.0	−1.11075	−0.555375	+	0.831600i	$0.687425\pi$
$878$	18638.0	0.716403
$879$	2736.00	0.104986
$880$	−176.000	−0.00674200
$881$	−26273.0	−1.00472	−0.502361	−	0.864658i	$-0.667535\pi$
$881$	−26273.0	−1.00472	−0.502361	+	0.864658i	$0.667535\pi$
$882$	0	0
$883$	−33821.0	−1.28898	−0.644489	−	0.764614i	$-0.722930\pi$
$883$	−33821.0	−1.28898	−0.644489	+	0.764614i	$0.722930\pi$
$884$	392.000	0.0149145
$885$	1407.00	0.0534416
$886$	−11216.0	−0.425292
$887$	14134.0	0.535032	0.267516	−	0.963553i	$-0.413797\pi$
$887$	14134.0	0.535032	0.267516	+	0.963553i	$0.413797\pi$
$888$	−4104.00	−0.155091
$889$	0	0
$890$	−1644.00	−0.0619180
$891$	−891.000	−0.0335013
$892$	14008.0	0.525810
$893$	17325.0	0.649226
$894$	11370.0	0.425358
$895$	1464.00	0.0546772
$896$	0	0
$897$	−1848.00	−0.0687881
$898$	8768.00	0.325826
$899$	1518.00	0.0563161
$900$	4464.00	0.165333
$901$	−9408.00	−0.347865
$902$	8360.00	0.308600
$903$	0	0
$904$	21168.0	0.778802
$905$	1432.00	0.0525981
$906$	−20868.0	−0.765224
$907$	−35748.0	−1.30870	−0.654351	−	0.756191i	$-0.727058\pi$
$907$	−35748.0	−1.30870	−0.654351	+	0.756191i	$0.727058\pi$
$908$	7320.00	0.267536
$909$	7866.00	0.287017
$910$	0	0
$911$	−9522.00	−0.346299	−0.173149	−	0.984896i	$-0.555394\pi$
$911$	−9522.00	−0.346299	−0.173149	+	0.984896i	$0.555394\pi$
$912$	2160.00	0.0784263
$913$	5742.00	0.208141
$914$	−648.000	−0.0234507
$915$	1026.00	0.0370694
$916$	−9072.00	−0.327235
$917$	0	0
$918$	756.000	0.0271805
$919$	−33260.0	−1.19385	−0.596924	−	0.802298i	$-0.703611\pi$
$919$	−33260.0	−1.19385	−0.596924	+	0.802298i	$0.703611\pi$
$920$	2112.00	0.0756854
$921$	20580.0	0.736302
$922$	−36720.0	−1.31161
$923$	−924.000	−0.0329511
$924$	0	0
$925$	−7068.00	−0.251237
$926$	3334.00	0.118318
$927$	7434.00	0.263392
$928$	11040.0	0.390523
$929$	55101.0	1.94597	0.972984	−	0.230871i	$-0.0741574\pi$
$929$	55101.0	1.94597	0.972984	+	0.230871i	$0.0741574\pi$
$930$	132.000	0.00465425
$931$	0	0
$932$	−9720.00	−0.341619
$933$	16416.0	0.576030
$934$	21678.0	0.759449
$935$	154.000	0.00538646
$936$	−1512.00	−0.0528005
$937$	19474.0	0.678962	0.339481	−	0.940613i	$-0.389748\pi$
$937$	19474.0	0.678962	0.339481	+	0.940613i	$0.389748\pi$
$938$	0	0
$939$	19266.0	0.669566
$940$	1540.00	0.0534354
$941$	−52104.0	−1.80504	−0.902520	−	0.430649i	$-0.858285\pi$
$941$	−52104.0	−1.80504	−0.902520	+	0.430649i	$0.858285\pi$
$942$	5712.00	0.197566
$943$	−33440.0	−1.15478
$944$	−7504.00	−0.258723
$945$	0	0
$946$	1056.00	0.0362934
$947$	16830.0	0.577510	0.288755	−	0.957403i	$-0.406759\pi$
$947$	16830.0	0.577510	0.288755	+	0.957403i	$0.406759\pi$
$948$	14928.0	0.511433
$949$	1015.00	0.0347190
$950$	11160.0	0.381135
$951$	19428.0	0.662456
$952$	0	0
$953$	−13997.0	−0.475768	−0.237884	−	0.971294i	$-0.576454\pi$
$953$	−13997.0	−0.475768	−0.237884	+	0.971294i	$0.576454\pi$
$954$	12096.0	0.410506
$955$	1330.00	0.0450657
$956$	8604.00	0.291081
$957$	−2277.00	−0.0769122
$958$	−1820.00	−0.0613795
$959$	0	0
$960$	1344.00	0.0451848
$961$	−29307.0	−0.983753
$962$	798.000	0.0267449
$963$	1971.00	0.0659549
$964$	11212.0	0.374600
$965$	2540.00	0.0847311
$966$	0	0
$967$	9574.00	0.318386	0.159193	−	0.987247i	$-0.449111\pi$
$967$	9574.00	0.318386	0.159193	+	0.987247i	$0.449111\pi$
$968$	2904.00	0.0964237
$969$	−1890.00	−0.0626579
$970$	−544.000	−0.0180070
$971$	−32585.0	−1.07693	−0.538467	−	0.842647i	$-0.680996\pi$
$971$	−32585.0	−1.07693	−0.538467	+	0.842647i	$0.680996\pi$
$972$	972.000	0.0320750
$973$	0	0
$974$	−24064.0	−0.791643
$975$	−2604.00	−0.0855331
$976$	−5472.00	−0.179462
$977$	42036.0	1.37651	0.688255	−	0.725469i	$-0.258377\pi$
$977$	42036.0	1.37651	0.688255	+	0.725469i	$0.258377\pi$
$978$	−14898.0	−0.487102
$979$	9042.00	0.295182
$980$	0	0
$981$	12834.0	0.417694
$982$	−8486.00	−0.275763
$983$	−42336.0	−1.37366	−0.686830	−	0.726818i	$-0.740999\pi$
$983$	−42336.0	−1.37366	−0.686830	+	0.726818i	$0.740999\pi$
$984$	−27360.0	−0.886387
$985$	−1606.00	−0.0519507
$986$	1932.00	0.0624010
$987$	0	0
$988$	1260.00	0.0405728
$989$	−4224.00	−0.135809
$990$	−198.000	−0.00635642
$991$	−4691.00	−0.150368	−0.0751839	−	0.997170i	$-0.523954\pi$
$991$	−4691.00	−0.150368	−0.0751839	+	0.997170i	$0.523954\pi$
$992$	3520.00	0.112661
$993$	35520.0	1.13514
$994$	0	0
$995$	288.000	0.00917609
$996$	−6264.00	−0.199280
$997$	−18518.0	−0.588236	−0.294118	−	0.955769i	$-0.595026\pi$
$997$	−18518.0	−0.588236	−0.294118	+	0.955769i	$0.595026\pi$
$998$	11738.0	0.372305
$999$	−1539.00	−0.0487405

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.4.a.c.1.1		1
7.6	odd	2		231.4.a.b.1.1	✓	1
21.20	even	2		693.4.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.4.a.b.1.1	✓	1	7.6	odd	2
693.4.a.e.1.1		1	21.20	even	2
1617.4.a.c.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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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