LMFDB - Embedded newform 475.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,4,Mod(1,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("475.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	475.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:	$28.0259072527$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	475.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q-3.00000 q^{2} +5.00000 q^{3} +1.00000 q^{4} -15.0000 q^{6} +1.00000 q^{7} +21.0000 q^{8} -2.00000 q^{9} -24.0000 q^{11} +5.00000 q^{12} +31.0000 q^{13} -3.00000 q^{14} -71.0000 q^{16} -33.0000 q^{17} +6.00000 q^{18} +19.0000 q^{19} +5.00000 q^{21} +72.0000 q^{22} -27.0000 q^{23} +105.000 q^{24} -93.0000 q^{26} -145.000 q^{27} +1.00000 q^{28} +111.000 q^{29} -94.0000 q^{31} +45.0000 q^{32} -120.000 q^{33} +99.0000 q^{34} -2.00000 q^{36} +70.0000 q^{37} -57.0000 q^{38} +155.000 q^{39} -510.000 q^{41} -15.0000 q^{42} +34.0000 q^{43} -24.0000 q^{44} +81.0000 q^{46} +192.000 q^{47} -355.000 q^{48} -342.000 q^{49} -165.000 q^{51} +31.0000 q^{52} +75.0000 q^{53} +435.000 q^{54} +21.0000 q^{56} +95.0000 q^{57} -333.000 q^{58} +45.0000 q^{59} -28.0000 q^{61} +282.000 q^{62} -2.00000 q^{63} +433.000 q^{64} +360.000 q^{66} -371.000 q^{67} -33.0000 q^{68} -135.000 q^{69} +384.000 q^{71} -42.0000 q^{72} +73.0000 q^{73} -210.000 q^{74} +19.0000 q^{76} -24.0000 q^{77} -465.000 q^{78} -1234.00 q^{79} -671.000 q^{81} +1530.00 q^{82} -366.000 q^{83} +5.00000 q^{84} -102.000 q^{86} +555.000 q^{87} -504.000 q^{88} -1578.00 q^{89} +31.0000 q^{91} -27.0000 q^{92} -470.000 q^{93} -576.000 q^{94} +225.000 q^{96} +538.000 q^{97} +1026.00 q^{98} +48.0000 q^{99} +O(q^{100})\)

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 $

$2$	−3.00000	−1.06066	−0.530330	−	0.847791i	$-0.677932\pi$
$2$	−3.00000	−1.06066	−0.530330	+	0.847791i	$0.677932\pi$
$3$	5.00000	0.962250	0.481125	−	0.876652i	$-0.340228\pi$
$3$	5.00000	0.962250	0.481125	+	0.876652i	$0.340228\pi$
$4$	1.00000	0.125000
$5$	0	0
$5$	0	0
$6$	−15.0000	−1.02062
$7$	1.00000	0.0539949	0.0269975	−	0.999636i	$-0.491405\pi$
$7$	1.00000	0.0539949	0.0269975	+	0.999636i	$0.491405\pi$
$8$	21.0000	0.928078
$9$	−2.00000	−0.0740741
$10$	0	0
$11$	−24.0000	−0.657843	−0.328921	−	0.944357i	$-0.606685\pi$
$11$	−24.0000	−0.657843	−0.328921	+	0.944357i	$0.606685\pi$
$12$	5.00000	0.120281
$13$	31.0000	0.661373	0.330687	−	0.943741i	$-0.392720\pi$
$13$	31.0000	0.661373	0.330687	+	0.943741i	$0.392720\pi$
$14$	−3.00000	−0.0572703
$15$	0	0
$16$	−71.0000	−1.10938
$17$	−33.0000	−0.470804	−0.235402	−	0.971898i	$-0.575641\pi$
$17$	−33.0000	−0.470804	−0.235402	+	0.971898i	$0.575641\pi$
$18$	6.00000	0.0785674
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	0	0
$21$	5.00000	0.0519566
$22$	72.0000	0.697748
$23$	−27.0000	−0.244778	−0.122389	−	0.992482i	$-0.539056\pi$
$23$	−27.0000	−0.244778	−0.122389	+	0.992482i	$0.539056\pi$
$24$	105.000	0.893043
$25$	0	0
$26$	−93.0000	−0.701492
$27$	−145.000	−1.03353
$28$	1.00000	0.00674937
$29$	111.000	0.710765	0.355382	−	0.934721i	$-0.384351\pi$
$29$	111.000	0.710765	0.355382	+	0.934721i	$0.384351\pi$
$30$	0	0
$31$	−94.0000	−0.544610	−0.272305	−	0.962211i	$-0.587786\pi$
$31$	−94.0000	−0.544610	−0.272305	+	0.962211i	$0.587786\pi$
$32$	45.0000	0.248592
$33$	−120.000	−0.633010
$34$	99.0000	0.499364
$35$	0	0
$36$	−2.00000	−0.00925926
$37$	70.0000	0.311025	0.155513	−	0.987834i	$-0.450297\pi$
$37$	70.0000	0.311025	0.155513	+	0.987834i	$0.450297\pi$
$38$	−57.0000	−0.243332
$39$	155.000	0.636407
$40$	0	0
$41$	−510.000	−1.94265	−0.971325	−	0.237757i	$-0.923588\pi$
$41$	−510.000	−1.94265	−0.971325	+	0.237757i	$0.923588\pi$
$42$	−15.0000	−0.0551083
$43$	34.0000	0.120580	0.0602901	−	0.998181i	$-0.480797\pi$
$43$	34.0000	0.120580	0.0602901	+	0.998181i	$0.480797\pi$
$44$	−24.0000	−0.0822304
$45$	0	0
$46$	81.0000	0.259626
$47$	192.000	0.595874	0.297937	−	0.954586i	$-0.403701\pi$
$47$	192.000	0.595874	0.297937	+	0.954586i	$0.403701\pi$
$48$	−355.000	−1.06750
$49$	−342.000	−0.997085
$50$	0	0
$51$	−165.000	−0.453032
$52$	31.0000	0.0826717
$53$	75.0000	0.194378	0.0971891	−	0.995266i	$-0.469015\pi$
$53$	75.0000	0.194378	0.0971891	+	0.995266i	$0.469015\pi$
$54$	435.000	1.09622
$55$	0	0
$56$	21.0000	0.0501115
$57$	95.0000	0.220755
$58$	−333.000	−0.753880
$59$	45.0000	0.0992966	0.0496483	−	0.998767i	$-0.484190\pi$
$59$	45.0000	0.0992966	0.0496483	+	0.998767i	$0.484190\pi$
$60$	0	0
$61$	−28.0000	−0.0587710	−0.0293855	−	0.999568i	$-0.509355\pi$
$61$	−28.0000	−0.0587710	−0.0293855	+	0.999568i	$0.509355\pi$
$62$	282.000	0.577646
$63$	−2.00000	−0.00399962
$64$	433.000	0.845703
$65$	0	0
$66$	360.000	0.671408
$67$	−371.000	−0.676491	−0.338245	−	0.941058i	$-0.609833\pi$
$67$	−371.000	−0.676491	−0.338245	+	0.941058i	$0.609833\pi$
$68$	−33.0000	−0.0588506
$69$	−135.000	−0.235538
$70$	0	0
$71$	384.000	0.641865	0.320933	−	0.947102i	$-0.396004\pi$
$71$	384.000	0.641865	0.320933	+	0.947102i	$0.396004\pi$
$72$	−42.0000	−0.0687465
$73$	73.0000	0.117041	0.0585206	−	0.998286i	$-0.481362\pi$
$73$	73.0000	0.117041	0.0585206	+	0.998286i	$0.481362\pi$
$74$	−210.000	−0.329892
$75$	0	0
$76$	19.0000	0.0286770
$77$	−24.0000	−0.0355202
$78$	−465.000	−0.675011
$79$	−1234.00	−1.75742	−0.878708	−	0.477360i	$-0.841594\pi$
$79$	−1234.00	−1.75742	−0.878708	+	0.477360i	$0.841594\pi$
$80$	0	0
$81$	−671.000	−0.920439
$82$	1530.00	2.06049
$83$	−366.000	−0.484021	−0.242010	−	0.970274i	$-0.577807\pi$
$83$	−366.000	−0.484021	−0.242010	+	0.970274i	$0.577807\pi$
$84$	5.00000	0.00649458
$85$	0	0
$86$	−102.000	−0.127895
$87$	555.000	0.683934
$88$	−504.000	−0.610529
$89$	−1578.00	−1.87941	−0.939706	−	0.341983i	$-0.888901\pi$
$89$	−1578.00	−1.87941	−0.939706	+	0.341983i	$0.888901\pi$
$90$	0	0
$91$	31.0000	0.0357108
$92$	−27.0000	−0.0305972
$93$	−470.000	−0.524051
$94$	−576.000	−0.632020
$95$	0	0
$96$	225.000	0.239208
$97$	538.000	0.563151	0.281575	−	0.959539i	$-0.409143\pi$
$97$	538.000	0.563151	0.281575	+	0.959539i	$0.409143\pi$
$98$	1026.00	1.05757
$99$	48.0000	0.0487291
$100$	0	0
$101$	−1356.00	−1.33591	−0.667956	−	0.744201i	$-0.732830\pi$
$101$	−1356.00	−1.33591	−0.667956	+	0.744201i	$0.732830\pi$
$102$	495.000	0.480513
$103$	−368.000	−0.352040	−0.176020	−	0.984387i	$-0.556322\pi$
$103$	−368.000	−0.352040	−0.176020	+	0.984387i	$0.556322\pi$
$104$	651.000	0.613806
$105$	0	0
$106$	−225.000	−0.206169
$107$	−1557.00	−1.40674	−0.703369	−	0.710825i	$-0.748322\pi$
$107$	−1557.00	−1.40674	−0.703369	+	0.710825i	$0.748322\pi$
$108$	−145.000	−0.129191
$109$	−151.000	−0.132690	−0.0663448	−	0.997797i	$-0.521134\pi$
$109$	−151.000	−0.132690	−0.0663448	+	0.997797i	$0.521134\pi$
$110$	0	0
$111$	350.000	0.299284
$112$	−71.0000	−0.0599006
$113$	−1128.00	−0.939056	−0.469528	−	0.882918i	$-0.655576\pi$
$113$	−1128.00	−0.939056	−0.469528	+	0.882918i	$0.655576\pi$
$114$	−285.000	−0.234146
$115$	0	0
$116$	111.000	0.0888456
$117$	−62.0000	−0.0489906
$118$	−135.000	−0.105320
$119$	−33.0000	−0.0254211
$120$	0	0
$121$	−755.000	−0.567243
$122$	84.0000	0.0623361
$123$	−2550.00	−1.86932
$124$	−94.0000	−0.0680762
$125$	0	0
$126$	6.00000	0.00424224
$127$	−1370.00	−0.957227	−0.478614	−	0.878026i	$-0.658860\pi$
$127$	−1370.00	−0.957227	−0.478614	+	0.878026i	$0.658860\pi$
$128$	−1659.00	−1.14560
$129$	170.000	0.116028
$130$	0	0
$131$	228.000	0.152065	0.0760323	−	0.997105i	$-0.475775\pi$
$131$	228.000	0.152065	0.0760323	+	0.997105i	$0.475775\pi$
$132$	−120.000	−0.0791262
$133$	19.0000	0.0123873
$134$	1113.00	0.717527
$135$	0	0
$136$	−693.000	−0.436943
$137$	−2349.00	−1.46488	−0.732440	−	0.680831i	$-0.761619\pi$
$137$	−2349.00	−1.46488	−0.732440	+	0.680831i	$0.761619\pi$
$138$	405.000	0.249825
$139$	−196.000	−0.119601	−0.0598004	−	0.998210i	$-0.519046\pi$
$139$	−196.000	−0.119601	−0.0598004	+	0.998210i	$0.519046\pi$
$140$	0	0
$141$	960.000	0.573380
$142$	−1152.00	−0.680801
$143$	−744.000	−0.435080
$144$	142.000	0.0821759
$145$	0	0
$146$	−219.000	−0.124141
$147$	−1710.00	−0.959445
$148$	70.0000	0.0388781
$149$	1980.00	1.08864	0.544322	−	0.838876i	$-0.316787\pi$
$149$	1980.00	1.08864	0.544322	+	0.838876i	$0.316787\pi$
$150$	0	0
$151$	74.0000	0.0398810	0.0199405	−	0.999801i	$-0.493652\pi$
$151$	74.0000	0.0398810	0.0199405	+	0.999801i	$0.493652\pi$
$152$	399.000	0.212916
$153$	66.0000	0.0348744
$154$	72.0000	0.0376748
$155$	0	0
$156$	155.000	0.0795508
$157$	3166.00	1.60939	0.804695	−	0.593688i	$-0.202329\pi$
$157$	3166.00	1.60939	0.804695	+	0.593688i	$0.202329\pi$
$158$	3702.00	1.86402
$159$	375.000	0.187040
$160$	0	0
$161$	−27.0000	−0.0132168
$162$	2013.00	0.976273
$163$	2530.00	1.21574	0.607868	−	0.794038i	$-0.292025\pi$
$163$	2530.00	1.21574	0.607868	+	0.794038i	$0.292025\pi$
$164$	−510.000	−0.242831
$165$	0	0
$166$	1098.00	0.513381
$167$	−3294.00	−1.52633	−0.763166	−	0.646203i	$-0.776356\pi$
$167$	−3294.00	−1.52633	−0.763166	+	0.646203i	$0.776356\pi$
$168$	105.000	0.0482198
$169$	−1236.00	−0.562585
$170$	0	0
$171$	−38.0000	−0.0169938
$172$	34.0000	0.0150725
$173$	2178.00	0.957169	0.478585	−	0.878041i	$-0.341150\pi$
$173$	2178.00	0.957169	0.478585	+	0.878041i	$0.341150\pi$
$174$	−1665.00	−0.725421
$175$	0	0
$176$	1704.00	0.729795
$177$	225.000	0.0955482
$178$	4734.00	1.99342
$179$	4440.00	1.85397	0.926987	−	0.375095i	$-0.122390\pi$
$179$	4440.00	1.85397	0.926987	+	0.375095i	$0.122390\pi$
$180$	0	0
$181$	3422.00	1.40528	0.702639	−	0.711547i	$-0.252005\pi$
$181$	3422.00	1.40528	0.702639	+	0.711547i	$0.252005\pi$
$182$	−93.0000	−0.0378770
$183$	−140.000	−0.0565524
$184$	−567.000	−0.227173
$185$	0	0
$186$	1410.00	0.555840
$187$	792.000	0.309715
$188$	192.000	0.0744843
$189$	−145.000	−0.0558053
$190$	0	0
$191$	−519.000	−0.196615	−0.0983076	−	0.995156i	$-0.531343\pi$
$191$	−519.000	−0.196615	−0.0983076	+	0.995156i	$0.531343\pi$
$192$	2165.00	0.813778
$193$	3298.00	1.23003	0.615014	−	0.788517i	$-0.289151\pi$
$193$	3298.00	1.23003	0.615014	+	0.788517i	$0.289151\pi$
$194$	−1614.00	−0.597312
$195$	0	0
$196$	−342.000	−0.124636
$197$	−1566.00	−0.566360	−0.283180	−	0.959067i	$-0.591389\pi$
$197$	−1566.00	−0.566360	−0.283180	+	0.959067i	$0.591389\pi$
$198$	−144.000	−0.0516850
$199$	809.000	0.288183	0.144092	−	0.989564i	$-0.453974\pi$
$199$	809.000	0.288183	0.144092	+	0.989564i	$0.453974\pi$
$200$	0	0
$201$	−1855.00	−0.650953
$202$	4068.00	1.41695
$203$	111.000	0.0383777
$204$	−165.000	−0.0566290
$205$	0	0
$206$	1104.00	0.373395
$207$	54.0000	0.0181317
$208$	−2201.00	−0.733711
$209$	−456.000	−0.150920
$210$	0	0
$211$	−2575.00	−0.840144	−0.420072	−	0.907491i	$-0.637995\pi$
$211$	−2575.00	−0.840144	−0.420072	+	0.907491i	$0.637995\pi$
$212$	75.0000	0.0242973
$213$	1920.00	0.617635
$214$	4671.00	1.49207
$215$	0	0
$216$	−3045.00	−0.959194
$217$	−94.0000	−0.0294062
$218$	453.000	0.140739
$219$	365.000	0.112623
$220$	0	0
$221$	−1023.00	−0.311377
$222$	−1050.00	−0.317439
$223$	6142.00	1.84439	0.922194	−	0.386726i	$-0.126394\pi$
$223$	6142.00	1.84439	0.922194	+	0.386726i	$0.126394\pi$
$224$	45.0000	0.0134227
$225$	0	0
$226$	3384.00	0.996019
$227$	−1395.00	−0.407883	−0.203941	−	0.978983i	$-0.565375\pi$
$227$	−1395.00	−0.407883	−0.203941	+	0.978983i	$0.565375\pi$
$228$	95.0000	0.0275944
$229$	−730.000	−0.210654	−0.105327	−	0.994438i	$-0.533589\pi$
$229$	−730.000	−0.210654	−0.105327	+	0.994438i	$0.533589\pi$
$230$	0	0
$231$	−120.000	−0.0341793
$232$	2331.00	0.659645
$233$	−1818.00	−0.511164	−0.255582	−	0.966787i	$-0.582267\pi$
$233$	−1818.00	−0.511164	−0.255582	+	0.966787i	$0.582267\pi$
$234$	186.000	0.0519624
$235$	0	0
$236$	45.0000	0.0124121
$237$	−6170.00	−1.69107
$238$	99.0000	0.0269631
$239$	1701.00	0.460370	0.230185	−	0.973147i	$-0.426067\pi$
$239$	1701.00	0.460370	0.230185	+	0.973147i	$0.426067\pi$
$240$	0	0
$241$	2588.00	0.691733	0.345867	−	0.938284i	$-0.387585\pi$
$241$	2588.00	0.691733	0.345867	+	0.938284i	$0.387585\pi$
$242$	2265.00	0.601652
$243$	560.000	0.147835
$244$	−28.0000	−0.00734638
$245$	0	0
$246$	7650.00	1.98271
$247$	589.000	0.151729
$248$	−1974.00	−0.505440
$249$	−1830.00	−0.465749
$250$	0	0
$251$	−1836.00	−0.461702	−0.230851	−	0.972989i	$-0.574151\pi$
$251$	−1836.00	−0.461702	−0.230851	+	0.972989i	$0.574151\pi$
$252$	−2.00000	−0.000499953 0
$253$	648.000	0.161025
$254$	4110.00	1.01529
$255$	0	0
$256$	1513.00	0.369385
$257$	582.000	0.141261	0.0706307	−	0.997503i	$-0.477499\pi$
$257$	582.000	0.141261	0.0706307	+	0.997503i	$0.477499\pi$
$258$	−510.000	−0.123067
$259$	70.0000	0.0167938
$260$	0	0
$261$	−222.000	−0.0526493
$262$	−684.000	−0.161289
$263$	3288.00	0.770900	0.385450	−	0.922729i	$-0.374046\pi$
$263$	3288.00	0.770900	0.385450	+	0.922729i	$0.374046\pi$
$264$	−2520.00	−0.587482
$265$	0	0
$266$	−57.0000	−0.0131387
$267$	−7890.00	−1.80847
$268$	−371.000	−0.0845613
$269$	−5682.00	−1.28787	−0.643936	−	0.765079i	$-0.722700\pi$
$269$	−5682.00	−1.28787	−0.643936	+	0.765079i	$0.722700\pi$
$270$	0	0
$271$	2549.00	0.571368	0.285684	−	0.958324i	$-0.407779\pi$
$271$	2549.00	0.571368	0.285684	+	0.958324i	$0.407779\pi$
$272$	2343.00	0.522299
$273$	155.000	0.0343627
$274$	7047.00	1.55374
$275$	0	0
$276$	−135.000	−0.0294422
$277$	6244.00	1.35439	0.677194	−	0.735804i	$-0.263196\pi$
$277$	6244.00	1.35439	0.677194	+	0.735804i	$0.263196\pi$
$278$	588.000	0.126856
$279$	188.000	0.0403415
$280$	0	0
$281$	4734.00	1.00501	0.502503	−	0.864575i	$-0.332413\pi$
$281$	4734.00	1.00501	0.502503	+	0.864575i	$0.332413\pi$
$282$	−2880.00	−0.608161
$283$	4858.00	1.02042	0.510209	−	0.860051i	$-0.329568\pi$
$283$	4858.00	1.02042	0.510209	+	0.860051i	$0.329568\pi$
$284$	384.000	0.0802331
$285$	0	0
$286$	2232.00	0.461472
$287$	−510.000	−0.104893
$288$	−90.0000	−0.0184142
$289$	−3824.00	−0.778343
$290$	0	0
$291$	2690.00	0.541892
$292$	73.0000	0.0146301
$293$	1437.00	0.286520	0.143260	−	0.989685i	$-0.454241\pi$
$293$	1437.00	0.286520	0.143260	+	0.989685i	$0.454241\pi$
$294$	5130.00	1.01765
$295$	0	0
$296$	1470.00	0.288655
$297$	3480.00	0.679899
$298$	−5940.00	−1.15468
$299$	−837.000	−0.161889
$300$	0	0
$301$	34.0000	0.00651072
$302$	−222.000	−0.0423002
$303$	−6780.00	−1.28548
$304$	−1349.00	−0.254508
$305$	0	0
$306$	−198.000	−0.0369899
$307$	−7220.00	−1.34224	−0.671119	−	0.741349i	$-0.734186\pi$
$307$	−7220.00	−1.34224	−0.671119	+	0.741349i	$0.734186\pi$
$308$	−24.0000	−0.00444002
$309$	−1840.00	−0.338751
$310$	0	0
$311$	−9111.00	−1.66121	−0.830607	−	0.556859i	$-0.812006\pi$
$311$	−9111.00	−1.66121	−0.830607	+	0.556859i	$0.812006\pi$
$312$	3255.00	0.590635
$313$	1357.00	0.245055	0.122527	−	0.992465i	$-0.460900\pi$
$313$	1357.00	0.245055	0.122527	+	0.992465i	$0.460900\pi$
$314$	−9498.00	−1.70702
$315$	0	0
$316$	−1234.00	−0.219677
$317$	−8559.00	−1.51647	−0.758236	−	0.651981i	$-0.773938\pi$
$317$	−8559.00	−1.51647	−0.758236	+	0.651981i	$0.773938\pi$
$318$	−1125.00	−0.198386
$319$	−2664.00	−0.467572
$320$	0	0
$321$	−7785.00	−1.35363
$322$	81.0000	0.0140185
$323$	−627.000	−0.108010
$324$	−671.000	−0.115055
$325$	0	0
$326$	−7590.00	−1.28948
$327$	−755.000	−0.127681
$328$	−10710.0	−1.80293
$329$	192.000	0.0321742
$330$	0	0
$331$	7451.00	1.23729	0.618647	−	0.785669i	$-0.287681\pi$
$331$	7451.00	1.23729	0.618647	+	0.785669i	$0.287681\pi$
$332$	−366.000	−0.0605026
$333$	−140.000	−0.0230389
$334$	9882.00	1.61892
$335$	0	0
$336$	−355.000	−0.0576394
$337$	9166.00	1.48161	0.740807	−	0.671718i	$-0.234443\pi$
$337$	9166.00	1.48161	0.740807	+	0.671718i	$0.234443\pi$
$338$	3708.00	0.596712
$339$	−5640.00	−0.903607
$340$	0	0
$341$	2256.00	0.358268
$342$	114.000	0.0180246
$343$	−685.000	−0.107832
$344$	714.000	0.111908
$345$	0	0
$346$	−6534.00	−1.01523
$347$	762.000	0.117886	0.0589428	−	0.998261i	$-0.481227\pi$
$347$	762.000	0.117886	0.0589428	+	0.998261i	$0.481227\pi$
$348$	555.000	0.0854917
$349$	4538.00	0.696027	0.348014	−	0.937489i	$-0.386856\pi$
$349$	4538.00	0.696027	0.348014	+	0.937489i	$0.386856\pi$
$350$	0	0
$351$	−4495.00	−0.683548
$352$	−1080.00	−0.163535
$353$	6813.00	1.02725	0.513625	−	0.858015i	$-0.328302\pi$
$353$	6813.00	1.02725	0.513625	+	0.858015i	$0.328302\pi$
$354$	−675.000	−0.101344
$355$	0	0
$356$	−1578.00	−0.234926
$357$	−165.000	−0.0244614
$358$	−13320.0	−1.96644
$359$	−11997.0	−1.76373	−0.881863	−	0.471506i	$-0.843710\pi$
$359$	−11997.0	−1.76373	−0.881863	+	0.471506i	$0.843710\pi$
$360$	0	0
$361$	361.000	0.0526316
$362$	−10266.0	−1.49052
$363$	−3775.00	−0.545830
$364$	31.0000	0.00446385
$365$	0	0
$366$	420.000	0.0599829
$367$	4264.00	0.606482	0.303241	−	0.952914i	$-0.401931\pi$
$367$	4264.00	0.606482	0.303241	+	0.952914i	$0.401931\pi$
$368$	1917.00	0.271550
$369$	1020.00	0.143900
$370$	0	0
$371$	75.0000	0.0104954
$372$	−470.000	−0.0655064
$373$	−5447.00	−0.756126	−0.378063	−	0.925780i	$-0.623410\pi$
$373$	−5447.00	−0.756126	−0.378063	+	0.925780i	$0.623410\pi$
$374$	−2376.00	−0.328503
$375$	0	0
$376$	4032.00	0.553017
$377$	3441.00	0.470081
$378$	435.000	0.0591904
$379$	7277.00	0.986265	0.493132	−	0.869954i	$-0.335852\pi$
$379$	7277.00	0.986265	0.493132	+	0.869954i	$0.335852\pi$
$380$	0	0
$381$	−6850.00	−0.921092
$382$	1557.00	0.208542
$383$	−12096.0	−1.61378	−0.806889	−	0.590704i	$-0.798850\pi$
$383$	−12096.0	−1.61378	−0.806889	+	0.590704i	$0.798850\pi$
$384$	−8295.00	−1.10235
$385$	0	0
$386$	−9894.00	−1.30464
$387$	−68.0000	−0.00893187
$388$	538.000	0.0703938
$389$	−2160.00	−0.281533	−0.140767	−	0.990043i	$-0.544957\pi$
$389$	−2160.00	−0.281533	−0.140767	+	0.990043i	$0.544957\pi$
$390$	0	0
$391$	891.000	0.115242
$392$	−7182.00	−0.925372
$393$	1140.00	0.146324
$394$	4698.00	0.600715
$395$	0	0
$396$	48.0000	0.00609114
$397$	14116.0	1.78454	0.892269	−	0.451504i	$-0.149112\pi$
$397$	14116.0	1.78454	0.892269	+	0.451504i	$0.149112\pi$
$398$	−2427.00	−0.305665
$399$	95.0000	0.0119197
$400$	0	0
$401$	−2502.00	−0.311581	−0.155790	−	0.987790i	$-0.549792\pi$
$401$	−2502.00	−0.311581	−0.155790	+	0.987790i	$0.549792\pi$
$402$	5565.00	0.690440
$403$	−2914.00	−0.360190
$404$	−1356.00	−0.166989
$405$	0	0
$406$	−333.000	−0.0407057
$407$	−1680.00	−0.204606
$408$	−3465.00	−0.420449
$409$	−13966.0	−1.68845	−0.844223	−	0.535992i	$-0.819938\pi$
$409$	−13966.0	−1.68845	−0.844223	+	0.535992i	$0.819938\pi$
$410$	0	0
$411$	−11745.0	−1.40958
$412$	−368.000	−0.0440050
$413$	45.0000	0.00536151
$414$	−162.000	−0.0192316
$415$	0	0
$416$	1395.00	0.164412
$417$	−980.000	−0.115086
$418$	1368.00	0.160074
$419$	174.000	0.0202875	0.0101437	−	0.999949i	$-0.496771\pi$
$419$	174.000	0.0202875	0.0101437	+	0.999949i	$0.496771\pi$
$420$	0	0
$421$	15275.0	1.76831	0.884154	−	0.467195i	$-0.154735\pi$
$421$	15275.0	1.76831	0.884154	+	0.467195i	$0.154735\pi$
$422$	7725.00	0.891107
$423$	−384.000	−0.0441388
$424$	1575.00	0.180398
$425$	0	0
$426$	−5760.00	−0.655101
$427$	−28.0000	−0.00317334
$428$	−1557.00	−0.175842
$429$	−3720.00	−0.418656
$430$	0	0
$431$	−5580.00	−0.623617	−0.311809	−	0.950145i	$-0.600935\pi$
$431$	−5580.00	−0.623617	−0.311809	+	0.950145i	$0.600935\pi$
$432$	10295.0	1.14657
$433$	−6428.00	−0.713418	−0.356709	−	0.934216i	$-0.616101\pi$
$433$	−6428.00	−0.713418	−0.356709	+	0.934216i	$0.616101\pi$
$434$	282.000	0.0311899
$435$	0	0
$436$	−151.000	−0.0165862
$437$	−513.000	−0.0561559
$438$	−1095.00	−0.119455
$439$	7970.00	0.866486	0.433243	−	0.901277i	$-0.357369\pi$
$439$	7970.00	0.866486	0.433243	+	0.901277i	$0.357369\pi$
$440$	0	0
$441$	684.000	0.0738581
$442$	3069.00	0.330266
$443$	10656.0	1.14285	0.571424	−	0.820655i	$-0.306391\pi$
$443$	10656.0	1.14285	0.571424	+	0.820655i	$0.306391\pi$
$444$	350.000	0.0374105
$445$	0	0
$446$	−18426.0	−1.95627
$447$	9900.00	1.04755
$448$	433.000	0.0456637
$449$	5070.00	0.532891	0.266446	−	0.963850i	$-0.414151\pi$
$449$	5070.00	0.532891	0.266446	+	0.963850i	$0.414151\pi$
$450$	0	0
$451$	12240.0	1.27796
$452$	−1128.00	−0.117382
$453$	370.000	0.0383755
$454$	4185.00	0.432625
$455$	0	0
$456$	1995.00	0.204878
$457$	121.000	0.0123854	0.00619271	−	0.999981i	$-0.498029\pi$
$457$	121.000	0.0123854	0.00619271	+	0.999981i	$0.498029\pi$
$458$	2190.00	0.223432
$459$	4785.00	0.486590
$460$	0	0
$461$	11094.0	1.12082	0.560411	−	0.828215i	$-0.310643\pi$
$461$	11094.0	1.12082	0.560411	+	0.828215i	$0.310643\pi$
$462$	360.000	0.0362526
$463$	−2096.00	−0.210387	−0.105194	−	0.994452i	$-0.533546\pi$
$463$	−2096.00	−0.210387	−0.105194	+	0.994452i	$0.533546\pi$
$464$	−7881.00	−0.788505
$465$	0	0
$466$	5454.00	0.542171
$467$	−12504.0	−1.23901	−0.619503	−	0.784994i	$-0.712666\pi$
$467$	−12504.0	−1.23901	−0.619503	+	0.784994i	$0.712666\pi$
$468$	−62.0000	−0.00612383
$469$	−371.000	−0.0365271
$470$	0	0
$471$	15830.0	1.54864
$472$	945.000	0.0921550
$473$	−816.000	−0.0793229
$474$	18510.0	1.79365
$475$	0	0
$476$	−33.0000	−0.00317763
$477$	−150.000	−0.0143984
$478$	−5103.00	−0.488297
$479$	8664.00	0.826447	0.413224	−	0.910630i	$-0.364403\pi$
$479$	8664.00	0.826447	0.413224	+	0.910630i	$0.364403\pi$
$480$	0	0
$481$	2170.00	0.205704
$482$	−7764.00	−0.733694
$483$	−135.000	−0.0127178
$484$	−755.000	−0.0709053
$485$	0	0
$486$	−1680.00	−0.156803
$487$	−13430.0	−1.24963	−0.624817	−	0.780772i	$-0.714826\pi$
$487$	−13430.0	−1.24963	−0.624817	+	0.780772i	$0.714826\pi$
$488$	−588.000	−0.0545441
$489$	12650.0	1.16984
$490$	0	0
$491$	10110.0	0.929242	0.464621	−	0.885510i	$-0.346191\pi$
$491$	10110.0	0.929242	0.464621	+	0.885510i	$0.346191\pi$
$492$	−2550.00	−0.233664
$493$	−3663.00	−0.334631
$494$	−1767.00	−0.160933
$495$	0	0
$496$	6674.00	0.604176
$497$	384.000	0.0346575
$498$	5490.00	0.494002
$499$	−18814.0	−1.68784	−0.843918	−	0.536472i	$-0.819757\pi$
$499$	−18814.0	−1.68784	−0.843918	+	0.536472i	$0.819757\pi$
$500$	0	0
$501$	−16470.0	−1.46871
$502$	5508.00	0.489709
$503$	17985.0	1.59426	0.797129	−	0.603809i	$-0.206351\pi$
$503$	17985.0	1.59426	0.797129	+	0.603809i	$0.206351\pi$
$504$	−42.0000	−0.00371196
$505$	0	0
$506$	−1944.00	−0.170793
$507$	−6180.00	−0.541348
$508$	−1370.00	−0.119653
$509$	7566.00	0.658855	0.329427	−	0.944181i	$-0.393144\pi$
$509$	7566.00	0.658855	0.329427	+	0.944181i	$0.393144\pi$
$510$	0	0
$511$	73.0000	0.00631963
$512$	8733.00	0.753804
$513$	−2755.00	−0.237108
$514$	−1746.00	−0.149830
$515$	0	0
$516$	170.000	0.0145036
$517$	−4608.00	−0.391992
$518$	−210.000	−0.0178125
$519$	10890.0	0.921037
$520$	0	0
$521$	1752.00	0.147325	0.0736627	−	0.997283i	$-0.476531\pi$
$521$	1752.00	0.147325	0.0736627	+	0.997283i	$0.476531\pi$
$522$	666.000	0.0558430
$523$	−11033.0	−0.922446	−0.461223	−	0.887284i	$-0.652589\pi$
$523$	−11033.0	−0.922446	−0.461223	+	0.887284i	$0.652589\pi$
$524$	228.000	0.0190081
$525$	0	0
$526$	−9864.00	−0.817663
$527$	3102.00	0.256405
$528$	8520.00	0.702245
$529$	−11438.0	−0.940084
$530$	0	0
$531$	−90.0000	−0.00735531
$532$	19.0000	0.00154841
$533$	−15810.0	−1.28482
$534$	23670.0	1.91817
$535$	0	0
$536$	−7791.00	−0.627836
$537$	22200.0	1.78399
$538$	17046.0	1.36599
$539$	8208.00	0.655925
$540$	0	0
$541$	−17212.0	−1.36784	−0.683920	−	0.729557i	$-0.739726\pi$
$541$	−17212.0	−1.36784	−0.683920	+	0.729557i	$0.739726\pi$
$542$	−7647.00	−0.606027
$543$	17110.0	1.35223
$544$	−1485.00	−0.117038
$545$	0	0
$546$	−465.000	−0.0364472
$547$	13684.0	1.06963	0.534813	−	0.844970i	$-0.320382\pi$
$547$	13684.0	1.06963	0.534813	+	0.844970i	$0.320382\pi$
$548$	−2349.00	−0.183110
$549$	56.0000	0.00435341
$550$	0	0
$551$	2109.00	0.163061
$552$	−2835.00	−0.218597
$553$	−1234.00	−0.0948915
$554$	−18732.0	−1.43655
$555$	0	0
$556$	−196.000	−0.0149501
$557$	3792.00	0.288460	0.144230	−	0.989544i	$-0.453929\pi$
$557$	3792.00	0.288460	0.144230	+	0.989544i	$0.453929\pi$
$558$	−564.000	−0.0427886
$559$	1054.00	0.0797486
$560$	0	0
$561$	3960.00	0.298024
$562$	−14202.0	−1.06597
$563$	11724.0	0.877634	0.438817	−	0.898577i	$-0.355398\pi$
$563$	11724.0	0.877634	0.438817	+	0.898577i	$0.355398\pi$
$564$	960.000	0.0716725
$565$	0	0
$566$	−14574.0	−1.08232
$567$	−671.000	−0.0496990
$568$	8064.00	0.595701
$569$	−18192.0	−1.34033	−0.670165	−	0.742212i	$-0.733777\pi$
$569$	−18192.0	−1.34033	−0.670165	+	0.742212i	$0.733777\pi$
$570$	0	0
$571$	−12766.0	−0.935623	−0.467811	−	0.883828i	$-0.654957\pi$
$571$	−12766.0	−0.935623	−0.467811	+	0.883828i	$0.654957\pi$
$572$	−744.000	−0.0543850
$573$	−2595.00	−0.189193
$574$	1530.00	0.111256
$575$	0	0
$576$	−866.000	−0.0626447
$577$	−6653.00	−0.480014	−0.240007	−	0.970771i	$-0.577150\pi$
$577$	−6653.00	−0.480014	−0.240007	+	0.970771i	$0.577150\pi$
$578$	11472.0	0.825558
$579$	16490.0	1.18359
$580$	0	0
$581$	−366.000	−0.0261347
$582$	−8070.00	−0.574763
$583$	−1800.00	−0.127870
$584$	1533.00	0.108623
$585$	0	0
$586$	−4311.00	−0.303901
$587$	8514.00	0.598655	0.299327	−	0.954150i	$-0.403238\pi$
$587$	8514.00	0.598655	0.299327	+	0.954150i	$0.403238\pi$
$588$	−1710.00	−0.119931
$589$	−1786.00	−0.124942
$590$	0	0
$591$	−7830.00	−0.544980
$592$	−4970.00	−0.345043
$593$	−9246.00	−0.640283	−0.320141	−	0.947370i	$-0.603730\pi$
$593$	−9246.00	−0.640283	−0.320141	+	0.947370i	$0.603730\pi$
$594$	−10440.0	−0.721142
$595$	0	0
$596$	1980.00	0.136080
$597$	4045.00	0.277305
$598$	2511.00	0.171710
$599$	−25482.0	−1.73817	−0.869087	−	0.494659i	$-0.835293\pi$
$599$	−25482.0	−1.73817	−0.869087	+	0.494659i	$0.835293\pi$
$600$	0	0
$601$	−14866.0	−1.00898	−0.504490	−	0.863418i	$-0.668319\pi$
$601$	−14866.0	−1.00898	−0.504490	+	0.863418i	$0.668319\pi$
$602$	−102.000	−0.00690566
$603$	742.000	0.0501104
$604$	74.0000	0.00498513
$605$	0	0
$606$	20340.0	1.36346
$607$	22498.0	1.50439	0.752196	−	0.658940i	$-0.228995\pi$
$607$	22498.0	1.50439	0.752196	+	0.658940i	$0.228995\pi$
$608$	855.000	0.0570310
$609$	555.000	0.0369290
$610$	0	0
$611$	5952.00	0.394095
$612$	66.0000	0.00435930
$613$	−2288.00	−0.150753	−0.0753764	−	0.997155i	$-0.524016\pi$
$613$	−2288.00	−0.150753	−0.0753764	+	0.997155i	$0.524016\pi$
$614$	21660.0	1.42366
$615$	0	0
$616$	−504.000	−0.0329655
$617$	−25134.0	−1.63996	−0.819981	−	0.572391i	$-0.806016\pi$
$617$	−25134.0	−1.63996	−0.819981	+	0.572391i	$0.806016\pi$
$618$	5520.00	0.359299
$619$	−16480.0	−1.07009	−0.535046	−	0.844823i	$-0.679706\pi$
$619$	−16480.0	−1.07009	−0.535046	+	0.844823i	$0.679706\pi$
$620$	0	0
$621$	3915.00	0.252985
$622$	27333.0	1.76198
$623$	−1578.00	−0.101479
$624$	−11005.0	−0.706014
$625$	0	0
$626$	−4071.00	−0.259920
$627$	−2280.00	−0.145222
$628$	3166.00	0.201174
$629$	−2310.00	−0.146432
$630$	0	0
$631$	19232.0	1.21333	0.606667	−	0.794956i	$-0.292506\pi$
$631$	19232.0	1.21333	0.606667	+	0.794956i	$0.292506\pi$
$632$	−25914.0	−1.63102
$633$	−12875.0	−0.808429
$634$	25677.0	1.60846
$635$	0	0
$636$	375.000	0.0233801
$637$	−10602.0	−0.659445
$638$	7992.00	0.495935
$639$	−768.000	−0.0475456
$640$	0	0
$641$	18276.0	1.12614	0.563072	−	0.826408i	$-0.309619\pi$
$641$	18276.0	1.12614	0.563072	+	0.826408i	$0.309619\pi$
$642$	23355.0	1.43575
$643$	19186.0	1.17671	0.588353	−	0.808604i	$-0.299777\pi$
$643$	19186.0	1.17671	0.588353	+	0.808604i	$0.299777\pi$
$644$	−27.0000	−0.00165209
$645$	0	0
$646$	1881.00	0.114562
$647$	−27735.0	−1.68528	−0.842639	−	0.538478i	$-0.818999\pi$
$647$	−27735.0	−1.68528	−0.842639	+	0.538478i	$0.818999\pi$
$648$	−14091.0	−0.854239
$649$	−1080.00	−0.0653216
$650$	0	0
$651$	−470.000	−0.0282961
$652$	2530.00	0.151967
$653$	−21588.0	−1.29373	−0.646863	−	0.762606i	$-0.723920\pi$
$653$	−21588.0	−1.29373	−0.646863	+	0.762606i	$0.723920\pi$
$654$	2265.00	0.135426
$655$	0	0
$656$	36210.0	2.15513
$657$	−146.000	−0.00866971
$658$	−576.000	−0.0341259
$659$	8451.00	0.499551	0.249776	−	0.968304i	$-0.419643\pi$
$659$	8451.00	0.499551	0.249776	+	0.968304i	$0.419643\pi$
$660$	0	0
$661$	24725.0	1.45490	0.727452	−	0.686159i	$-0.240705\pi$
$661$	24725.0	1.45490	0.727452	+	0.686159i	$0.240705\pi$
$662$	−22353.0	−1.31235
$663$	−5115.00	−0.299623
$664$	−7686.00	−0.449209
$665$	0	0
$666$	420.000	0.0244364
$667$	−2997.00	−0.173979
$668$	−3294.00	−0.190791
$669$	30710.0	1.77476
$670$	0	0
$671$	672.000	0.0386621
$672$	225.000	0.0129160
$673$	−5612.00	−0.321436	−0.160718	−	0.987000i	$-0.551381\pi$
$673$	−5612.00	−0.321436	−0.160718	+	0.987000i	$0.551381\pi$
$674$	−27498.0	−1.57149
$675$	0	0
$676$	−1236.00	−0.0703232
$677$	−32631.0	−1.85245	−0.926227	−	0.376967i	$-0.876967\pi$
$677$	−32631.0	−1.85245	−0.926227	+	0.376967i	$0.876967\pi$
$678$	16920.0	0.958420
$679$	538.000	0.0304073
$680$	0	0
$681$	−6975.00	−0.392485
$682$	−6768.00	−0.380000
$683$	23964.0	1.34254	0.671272	−	0.741211i	$-0.265748\pi$
$683$	23964.0	1.34254	0.671272	+	0.741211i	$0.265748\pi$
$684$	−38.0000	−0.00212422
$685$	0	0
$686$	2055.00	0.114374
$687$	−3650.00	−0.202702
$688$	−2414.00	−0.133769
$689$	2325.00	0.128557
$690$	0	0
$691$	−10222.0	−0.562754	−0.281377	−	0.959597i	$-0.590791\pi$
$691$	−10222.0	−0.562754	−0.281377	+	0.959597i	$0.590791\pi$
$692$	2178.00	0.119646
$693$	48.0000	0.00263112
$694$	−2286.00	−0.125037
$695$	0	0
$696$	11655.0	0.634744
$697$	16830.0	0.914608
$698$	−13614.0	−0.738249
$699$	−9090.00	−0.491867
$700$	0	0
$701$	32520.0	1.75216	0.876079	−	0.482167i	$-0.160150\pi$
$701$	32520.0	1.75216	0.876079	+	0.482167i	$0.160150\pi$
$702$	13485.0	0.725012
$703$	1330.00	0.0713541
$704$	−10392.0	−0.556340
$705$	0	0
$706$	−20439.0	−1.08956
$707$	−1356.00	−0.0721324
$708$	225.000	0.0119435
$709$	−682.000	−0.0361256	−0.0180628	−	0.999837i	$-0.505750\pi$
$709$	−682.000	−0.0361256	−0.0180628	+	0.999837i	$0.505750\pi$
$710$	0	0
$711$	2468.00	0.130179
$712$	−33138.0	−1.74424
$713$	2538.00	0.133308
$714$	495.000	0.0259453
$715$	0	0
$716$	4440.00	0.231747
$717$	8505.00	0.442992
$718$	35991.0	1.87071
$719$	−19395.0	−1.00600	−0.502998	−	0.864287i	$-0.667770\pi$
$719$	−19395.0	−1.00600	−0.502998	+	0.864287i	$0.667770\pi$
$720$	0	0
$721$	−368.000	−0.0190084
$722$	−1083.00	−0.0558242
$723$	12940.0	0.665621
$724$	3422.00	0.175660
$725$	0	0
$726$	11325.0	0.578940
$727$	9541.00	0.486735	0.243367	−	0.969934i	$-0.421748\pi$
$727$	9541.00	0.486735	0.243367	+	0.969934i	$0.421748\pi$
$728$	651.000	0.0331424
$729$	20917.0	1.06269
$730$	0	0
$731$	−1122.00	−0.0567697
$732$	−140.000	−0.00706906
$733$	10096.0	0.508737	0.254369	−	0.967107i	$-0.418132\pi$
$733$	10096.0	0.508737	0.254369	+	0.967107i	$0.418132\pi$
$734$	−12792.0	−0.643272
$735$	0	0
$736$	−1215.00	−0.0608499
$737$	8904.00	0.445024
$738$	−3060.00	−0.152629
$739$	5666.00	0.282039	0.141020	−	0.990007i	$-0.454962\pi$
$739$	5666.00	0.282039	0.141020	+	0.990007i	$0.454962\pi$
$740$	0	0
$741$	2945.00	0.146002
$742$	−225.000	−0.0111321
$743$	22422.0	1.10711	0.553555	−	0.832812i	$-0.313271\pi$
$743$	22422.0	1.10711	0.553555	+	0.832812i	$0.313271\pi$
$744$	−9870.00	−0.486360
$745$	0	0
$746$	16341.0	0.801993
$747$	732.000	0.0358534
$748$	792.000	0.0387144
$749$	−1557.00	−0.0759567
$750$	0	0
$751$	7310.00	0.355187	0.177594	−	0.984104i	$-0.443169\pi$
$751$	7310.00	0.355187	0.177594	+	0.984104i	$0.443169\pi$
$752$	−13632.0	−0.661048
$753$	−9180.00	−0.444273
$754$	−10323.0	−0.498596
$755$	0	0
$756$	−145.000	−0.00697566
$757$	−20222.0	−0.970913	−0.485456	−	0.874261i	$-0.661347\pi$
$757$	−20222.0	−0.970913	−0.485456	+	0.874261i	$0.661347\pi$
$758$	−21831.0	−1.04609
$759$	3240.00	0.154947
$760$	0	0
$761$	−25749.0	−1.22654	−0.613272	−	0.789872i	$-0.710147\pi$
$761$	−25749.0	−1.22654	−0.613272	+	0.789872i	$0.710147\pi$
$762$	20550.0	0.976966
$763$	−151.000	−0.00716457
$764$	−519.000	−0.0245769
$765$	0	0
$766$	36288.0	1.71167
$767$	1395.00	0.0656721
$768$	7565.00	0.355441
$769$	−2191.00	−0.102743	−0.0513716	−	0.998680i	$-0.516359\pi$
$769$	−2191.00	−0.102743	−0.0513716	+	0.998680i	$0.516359\pi$
$770$	0	0
$771$	2910.00	0.135929
$772$	3298.00	0.153753
$773$	−36003.0	−1.67521	−0.837605	−	0.546276i	$-0.816045\pi$
$773$	−36003.0	−1.67521	−0.837605	+	0.546276i	$0.816045\pi$
$774$	204.000	0.00947368
$775$	0	0
$776$	11298.0	0.522648
$777$	350.000	0.0161598
$778$	6480.00	0.298611
$779$	−9690.00	−0.445674
$780$	0	0
$781$	−9216.00	−0.422246
$782$	−2673.00	−0.122233
$783$	−16095.0	−0.734596
$784$	24282.0	1.10614
$785$	0	0
$786$	−3420.00	−0.155200
$787$	25993.0	1.17732	0.588660	−	0.808381i	$-0.299656\pi$
$787$	25993.0	1.17732	0.588660	+	0.808381i	$0.299656\pi$
$788$	−1566.00	−0.0707950
$789$	16440.0	0.741799
$790$	0	0
$791$	−1128.00	−0.0507043
$792$	1008.00	0.0452244
$793$	−868.000	−0.0388696
$794$	−42348.0	−1.89279
$795$	0	0
$796$	809.000	0.0360229
$797$	40167.0	1.78518	0.892590	−	0.450870i	$-0.148886\pi$
$797$	40167.0	1.78518	0.892590	+	0.450870i	$0.148886\pi$
$798$	−285.000	−0.0126427
$799$	−6336.00	−0.280540
$800$	0	0
$801$	3156.00	0.139216
$802$	7506.00	0.330481
$803$	−1752.00	−0.0769947
$804$	−1855.00	−0.0813692
$805$	0	0
$806$	8742.00	0.382039
$807$	−28410.0	−1.23926
$808$	−28476.0	−1.23983
$809$	−29295.0	−1.27312	−0.636562	−	0.771226i	$-0.719644\pi$
$809$	−29295.0	−1.27312	−0.636562	+	0.771226i	$0.719644\pi$
$810$	0	0
$811$	−31849.0	−1.37900	−0.689500	−	0.724285i	$-0.742170\pi$
$811$	−31849.0	−1.37900	−0.689500	+	0.724285i	$0.742170\pi$
$812$	111.000	0.00479721
$813$	12745.0	0.549799
$814$	5040.00	0.217017
$815$	0	0
$816$	11715.0	0.502582
$817$	646.000	0.0276630
$818$	41898.0	1.79087
$819$	−62.0000	−0.00264524
$820$	0	0
$821$	−28872.0	−1.22733	−0.613666	−	0.789566i	$-0.710306\pi$
$821$	−28872.0	−1.22733	−0.613666	+	0.789566i	$0.710306\pi$
$822$	35235.0	1.49509
$823$	−21809.0	−0.923711	−0.461855	−	0.886955i	$-0.652816\pi$
$823$	−21809.0	−0.923711	−0.461855	+	0.886955i	$0.652816\pi$
$824$	−7728.00	−0.326720
$825$	0	0
$826$	−135.000	−0.00568674
$827$	27477.0	1.15534	0.577672	−	0.816269i	$-0.303961\pi$
$827$	27477.0	1.15534	0.577672	+	0.816269i	$0.303961\pi$
$828$	54.0000	0.00226646
$829$	6521.00	0.273201	0.136601	−	0.990626i	$-0.456382\pi$
$829$	6521.00	0.273201	0.136601	+	0.990626i	$0.456382\pi$
$830$	0	0
$831$	31220.0	1.30326
$832$	13423.0	0.559325
$833$	11286.0	0.469432
$834$	2940.00	0.122067
$835$	0	0
$836$	−456.000	−0.0188649
$837$	13630.0	0.562869
$838$	−522.000	−0.0215181
$839$	16152.0	0.664635	0.332318	−	0.943168i	$-0.392169\pi$
$839$	16152.0	0.664635	0.332318	+	0.943168i	$0.392169\pi$
$840$	0	0
$841$	−12068.0	−0.494813
$842$	−45825.0	−1.87557
$843$	23670.0	0.967068
$844$	−2575.00	−0.105018
$845$	0	0
$846$	1152.00	0.0468163
$847$	−755.000	−0.0306282
$848$	−5325.00	−0.215638
$849$	24290.0	0.981897
$850$	0	0
$851$	−1890.00	−0.0761320
$852$	1920.00	0.0772044
$853$	−9938.00	−0.398910	−0.199455	−	0.979907i	$-0.563917\pi$
$853$	−9938.00	−0.398910	−0.199455	+	0.979907i	$0.563917\pi$
$854$	84.0000	0.00336583
$855$	0	0
$856$	−32697.0	−1.30556
$857$	22392.0	0.892528	0.446264	−	0.894901i	$-0.352754\pi$
$857$	22392.0	0.892528	0.446264	+	0.894901i	$0.352754\pi$
$858$	11160.0	0.444051
$859$	40520.0	1.60946	0.804729	−	0.593642i	$-0.202311\pi$
$859$	40520.0	1.60946	0.804729	+	0.593642i	$0.202311\pi$
$860$	0	0
$861$	−2550.00	−0.100934
$862$	16740.0	0.661446
$863$	34704.0	1.36887	0.684437	−	0.729072i	$-0.260048\pi$
$863$	34704.0	1.36887	0.684437	+	0.729072i	$0.260048\pi$
$864$	−6525.00	−0.256927
$865$	0	0
$866$	19284.0	0.756694
$867$	−19120.0	−0.748961
$868$	−94.0000	−0.00367577
$869$	29616.0	1.15610
$870$	0	0
$871$	−11501.0	−0.447413
$872$	−3171.00	−0.123146
$873$	−1076.00	−0.0417149
$874$	1539.00	0.0595623
$875$	0	0
$876$	365.000	0.0140779
$877$	−20039.0	−0.771572	−0.385786	−	0.922588i	$-0.626070\pi$
$877$	−20039.0	−0.771572	−0.385786	+	0.922588i	$0.626070\pi$
$878$	−23910.0	−0.919047
$879$	7185.00	0.275704
$880$	0	0
$881$	−29022.0	−1.10985	−0.554924	−	0.831901i	$-0.687253\pi$
$881$	−29022.0	−1.10985	−0.554924	+	0.831901i	$0.687253\pi$
$882$	−2052.00	−0.0783384
$883$	13678.0	0.521293	0.260646	−	0.965434i	$-0.416064\pi$
$883$	13678.0	0.521293	0.260646	+	0.965434i	$0.416064\pi$
$884$	−1023.00	−0.0389222
$885$	0	0
$886$	−31968.0	−1.21217
$887$	17844.0	0.675471	0.337736	−	0.941241i	$-0.390339\pi$
$887$	17844.0	0.675471	0.337736	+	0.941241i	$0.390339\pi$
$888$	7350.00	0.277759
$889$	−1370.00	−0.0516854
$890$	0	0
$891$	16104.0	0.605504
$892$	6142.00	0.230549
$893$	3648.00	0.136703
$894$	−29700.0	−1.11109
$895$	0	0
$896$	−1659.00	−0.0618564
$897$	−4185.00	−0.155778
$898$	−15210.0	−0.565216
$899$	−10434.0	−0.387089
$900$	0	0
$901$	−2475.00	−0.0915141
$902$	−36720.0	−1.35548
$903$	170.000	0.00626495
$904$	−23688.0	−0.871517
$905$	0	0
$906$	−1110.00	−0.0407034
$907$	19231.0	0.704030	0.352015	−	0.935994i	$-0.385497\pi$
$907$	19231.0	0.704030	0.352015	+	0.935994i	$0.385497\pi$
$908$	−1395.00	−0.0509854
$909$	2712.00	0.0989564
$910$	0	0
$911$	6648.00	0.241776	0.120888	−	0.992666i	$-0.461426\pi$
$911$	6648.00	0.241776	0.120888	+	0.992666i	$0.461426\pi$
$912$	−6745.00	−0.244901
$913$	8784.00	0.318410
$914$	−363.000	−0.0131367
$915$	0	0
$916$	−730.000	−0.0263317
$917$	228.000	0.00821071
$918$	−14355.0	−0.516106
$919$	26099.0	0.936808	0.468404	−	0.883514i	$-0.344829\pi$
$919$	26099.0	0.936808	0.468404	+	0.883514i	$0.344829\pi$
$920$	0	0
$921$	−36100.0	−1.29157
$922$	−33282.0	−1.18881
$923$	11904.0	0.424512
$924$	−120.000	−0.00427241
$925$	0	0
$926$	6288.00	0.223150
$927$	736.000	0.0260770
$928$	4995.00	0.176691
$929$	39669.0	1.40097	0.700483	−	0.713669i	$-0.252968\pi$
$929$	39669.0	1.40097	0.700483	+	0.713669i	$0.252968\pi$
$930$	0	0
$931$	−6498.00	−0.228747
$932$	−1818.00	−0.0638955
$933$	−45555.0	−1.59850
$934$	37512.0	1.31417
$935$	0	0
$936$	−1302.00	−0.0454671
$937$	27805.0	0.969423	0.484712	−	0.874674i	$-0.338925\pi$
$937$	27805.0	0.969423	0.484712	+	0.874674i	$0.338925\pi$
$938$	1113.00	0.0387428
$939$	6785.00	0.235804
$940$	0	0
$941$	−34881.0	−1.20838	−0.604191	−	0.796839i	$-0.706504\pi$
$941$	−34881.0	−1.20838	−0.604191	+	0.796839i	$0.706504\pi$
$942$	−47490.0	−1.64258
$943$	13770.0	0.475517
$944$	−3195.00	−0.110157
$945$	0	0
$946$	2448.00	0.0841346
$947$	5940.00	0.203827	0.101913	−	0.994793i	$-0.467504\pi$
$947$	5940.00	0.203827	0.101913	+	0.994793i	$0.467504\pi$
$948$	−6170.00	−0.211384
$949$	2263.00	0.0774079
$950$	0	0
$951$	−42795.0	−1.45922
$952$	−693.000	−0.0235927
$953$	8340.00	0.283483	0.141741	−	0.989904i	$-0.454730\pi$
$953$	8340.00	0.283483	0.141741	+	0.989904i	$0.454730\pi$
$954$	450.000	0.0152718
$955$	0	0
$956$	1701.00	0.0575463
$957$	−13320.0	−0.449921
$958$	−25992.0	−0.876580
$959$	−2349.00	−0.0790961
$960$	0	0
$961$	−20955.0	−0.703400
$962$	−6510.00	−0.218182
$963$	3114.00	0.104203
$964$	2588.00	0.0864667
$965$	0	0
$966$	405.000	0.0134893
$967$	−6236.00	−0.207380	−0.103690	−	0.994610i	$-0.533065\pi$
$967$	−6236.00	−0.207380	−0.103690	+	0.994610i	$0.533065\pi$
$968$	−15855.0	−0.526445
$969$	−3135.00	−0.103933
$970$	0	0
$971$	−35916.0	−1.18702	−0.593511	−	0.804826i	$-0.702259\pi$
$971$	−35916.0	−1.18702	−0.593511	+	0.804826i	$0.702259\pi$
$972$	560.000	0.0184794
$973$	−196.000	−0.00645783
$974$	40290.0	1.32544
$975$	0	0
$976$	1988.00	0.0651991
$977$	39498.0	1.29340	0.646701	−	0.762744i	$-0.276148\pi$
$977$	39498.0	1.29340	0.646701	+	0.762744i	$0.276148\pi$
$978$	−37950.0	−1.24080
$979$	37872.0	1.23636
$980$	0	0
$981$	302.000	0.00982887
$982$	−30330.0	−0.985610
$983$	−38334.0	−1.24381	−0.621905	−	0.783093i	$-0.713641\pi$
$983$	−38334.0	−1.24381	−0.621905	+	0.783093i	$0.713641\pi$
$984$	−53550.0	−1.73487
$985$	0	0
$986$	10989.0	0.354930
$987$	960.000	0.0309596
$988$	589.000	0.0189662
$989$	−918.000	−0.0295154
$990$	0	0
$991$	31202.0	1.00017	0.500083	−	0.865978i	$-0.333303\pi$
$991$	31202.0	1.00017	0.500083	+	0.865978i	$0.333303\pi$
$992$	−4230.00	−0.135386
$993$	37255.0	1.19059
$994$	−1152.00	−0.0367598
$995$	0	0
$996$	−1830.00	−0.0582186
$997$	1906.00	0.0605453	0.0302726	−	0.999542i	$-0.490362\pi$
$997$	1906.00	0.0605453	0.0302726	+	0.999542i	$0.490362\pi$
$998$	56442.0	1.79022
$999$	−10150.0	−0.321453

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.4.a.c.1.1		1
5.2	odd	4		475.4.b.b.324.1		2
5.3	odd	4		475.4.b.b.324.2		2
5.4	even	2		95.4.a.b.1.1	✓	1
15.14	odd	2		855.4.a.d.1.1		1
20.19	odd	2		1520.4.a.h.1.1		1
95.94	odd	2		1805.4.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.4.a.b.1.1	✓	1	5.4	even	2
475.4.a.c.1.1		1	1.1	even	1	trivial
475.4.b.b.324.1		2	5.2	odd	4
475.4.b.b.324.2		2	5.3	odd	4
855.4.a.d.1.1		1	15.14	odd	2
1520.4.a.h.1.1		1	20.19	odd	2
1805.4.a.d.1.1		1	95.94	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	475.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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