LMFDB - Embedded newform 425.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,4,Mod(1,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, 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("425.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	425.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:	$25.0758117524$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	425.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+3.00000 q^{2} +8.00000 q^{3} +1.00000 q^{4} +24.0000 q^{6} +28.0000 q^{7} -21.0000 q^{8} +37.0000 q^{9} +O(q^{10})$

\(q+3.00000 q^{2} +8.00000 q^{3} +1.00000 q^{4} +24.0000 q^{6} +28.0000 q^{7} -21.0000 q^{8} +37.0000 q^{9} -24.0000 q^{11} +8.00000 q^{12} +58.0000 q^{13} +84.0000 q^{14} -71.0000 q^{16} -17.0000 q^{17} +111.000 q^{18} +116.000 q^{19} +224.000 q^{21} -72.0000 q^{22} +60.0000 q^{23} -168.000 q^{24} +174.000 q^{26} +80.0000 q^{27} +28.0000 q^{28} +30.0000 q^{29} -172.000 q^{31} -45.0000 q^{32} -192.000 q^{33} -51.0000 q^{34} +37.0000 q^{36} +58.0000 q^{37} +348.000 q^{38} +464.000 q^{39} -342.000 q^{41} +672.000 q^{42} +148.000 q^{43} -24.0000 q^{44} +180.000 q^{46} -288.000 q^{47} -568.000 q^{48} +441.000 q^{49} -136.000 q^{51} +58.0000 q^{52} -318.000 q^{53} +240.000 q^{54} -588.000 q^{56} +928.000 q^{57} +90.0000 q^{58} +252.000 q^{59} +110.000 q^{61} -516.000 q^{62} +1036.00 q^{63} +433.000 q^{64} -576.000 q^{66} +484.000 q^{67} -17.0000 q^{68} +480.000 q^{69} -708.000 q^{71} -777.000 q^{72} -362.000 q^{73} +174.000 q^{74} +116.000 q^{76} -672.000 q^{77} +1392.00 q^{78} -484.000 q^{79} -359.000 q^{81} -1026.00 q^{82} -756.000 q^{83} +224.000 q^{84} +444.000 q^{86} +240.000 q^{87} +504.000 q^{88} -774.000 q^{89} +1624.00 q^{91} +60.0000 q^{92} -1376.00 q^{93} -864.000 q^{94} -360.000 q^{96} +382.000 q^{97} +1323.00 q^{98} -888.000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	3.00000	1.06066	0.530330	−	0.847791i	$-0.322068\pi$
$2$	3.00000	1.06066	0.530330	+	0.847791i	$0.322068\pi$
$3$	8.00000	1.53960	0.769800	−	0.638285i	$-0.220356\pi$
$3$	8.00000	1.53960	0.769800	+	0.638285i	$0.220356\pi$
$4$	1.00000	0.125000
$5$	0	0
$5$	0	0
$6$	24.0000	1.63299
$7$	28.0000	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$7$	28.0000	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$8$	−21.0000	−0.928078
$9$	37.0000	1.37037
$10$	0	0
$11$	−24.0000	−0.657843	−0.328921	−	0.944357i	$-0.606685\pi$
$11$	−24.0000	−0.657843	−0.328921	+	0.944357i	$0.606685\pi$
$12$	8.00000	0.192450
$13$	58.0000	1.23741	0.618704	−	0.785624i	$-0.287658\pi$
$13$	58.0000	1.23741	0.618704	+	0.785624i	$0.287658\pi$
$14$	84.0000	1.60357
$15$	0	0
$16$	−71.0000	−1.10938
$17$	−17.0000	−0.242536
$17$	−17.0000	−0.242536
$18$	111.000	1.45350
$19$	116.000	1.40064	0.700322	−	0.713827i	$-0.253040\pi$
$19$	116.000	1.40064	0.700322	+	0.713827i	$0.253040\pi$
$20$	0	0
$21$	224.000	2.32766
$22$	−72.0000	−0.697748
$23$	60.0000	0.543951	0.271975	−	0.962304i	$-0.412323\pi$
$23$	60.0000	0.543951	0.271975	+	0.962304i	$0.412323\pi$
$24$	−168.000	−1.42887
$25$	0	0
$26$	174.000	1.31247
$27$	80.0000	0.570222
$28$	28.0000	0.188982
$29$	30.0000	0.192099	0.0960493	−	0.995377i	$-0.469379\pi$
$29$	30.0000	0.192099	0.0960493	+	0.995377i	$0.469379\pi$
$30$	0	0
$31$	−172.000	−0.996520	−0.498260	−	0.867028i	$-0.666027\pi$
$31$	−172.000	−0.996520	−0.498260	+	0.867028i	$0.666027\pi$
$32$	−45.0000	−0.248592
$33$	−192.000	−1.01282
$34$	−51.0000	−0.257248
$35$	0	0
$36$	37.0000	0.171296
$37$	58.0000	0.257707	0.128853	−	0.991664i	$-0.458870\pi$
$37$	58.0000	0.257707	0.128853	+	0.991664i	$0.458870\pi$
$38$	348.000	1.48561
$39$	464.000	1.90511
$40$	0	0
$41$	−342.000	−1.30272	−0.651359	−	0.758770i	$-0.725801\pi$
$41$	−342.000	−1.30272	−0.651359	+	0.758770i	$0.725801\pi$
$42$	672.000	2.46885
$43$	148.000	0.524879	0.262439	−	0.964948i	$-0.415473\pi$
$43$	148.000	0.524879	0.262439	+	0.964948i	$0.415473\pi$
$44$	−24.0000	−0.0822304
$45$	0	0
$46$	180.000	0.576947
$47$	−288.000	−0.893811	−0.446906	−	0.894581i	$-0.647474\pi$
$47$	−288.000	−0.893811	−0.446906	+	0.894581i	$0.647474\pi$
$48$	−568.000	−1.70799
$49$	441.000	1.28571
$50$	0	0
$51$	−136.000	−0.373408
$52$	58.0000	0.154676
$53$	−318.000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−318.000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	240.000	0.604812
$55$	0	0
$56$	−588.000	−1.40312
$57$	928.000	2.15643
$58$	90.0000	0.203751
$59$	252.000	0.556061	0.278031	−	0.960572i	$-0.410318\pi$
$59$	252.000	0.556061	0.278031	+	0.960572i	$0.410318\pi$
$60$	0	0
$61$	110.000	0.230886	0.115443	−	0.993314i	$-0.463171\pi$
$61$	110.000	0.230886	0.115443	+	0.993314i	$0.463171\pi$
$62$	−516.000	−1.05697
$63$	1036.00	2.07181
$64$	433.000	0.845703
$65$	0	0
$66$	−576.000	−1.07425
$67$	484.000	0.882537	0.441269	−	0.897375i	$-0.354529\pi$
$67$	484.000	0.882537	0.441269	+	0.897375i	$0.354529\pi$
$68$	−17.0000	−0.0303170
$69$	480.000	0.837467
$70$	0	0
$71$	−708.000	−1.18344	−0.591719	−	0.806144i	$-0.701551\pi$
$71$	−708.000	−1.18344	−0.591719	+	0.806144i	$0.701551\pi$
$72$	−777.000	−1.27181
$73$	−362.000	−0.580396	−0.290198	−	0.956967i	$-0.593721\pi$
$73$	−362.000	−0.580396	−0.290198	+	0.956967i	$0.593721\pi$
$74$	174.000	0.273339
$75$	0	0
$76$	116.000	0.175080
$77$	−672.000	−0.994565
$78$	1392.00	2.02068
$79$	−484.000	−0.689294	−0.344647	−	0.938732i	$-0.612001\pi$
$79$	−484.000	−0.689294	−0.344647	+	0.938732i	$0.612001\pi$
$80$	0	0
$81$	−359.000	−0.492455
$82$	−1026.00	−1.38174
$83$	−756.000	−0.999780	−0.499890	−	0.866089i	$-0.666626\pi$
$83$	−756.000	−0.999780	−0.499890	+	0.866089i	$0.666626\pi$
$84$	224.000	0.290957
$85$	0	0
$86$	444.000	0.556718
$87$	240.000	0.295755
$88$	504.000	0.610529
$89$	−774.000	−0.921841	−0.460920	−	0.887441i	$-0.652481\pi$
$89$	−774.000	−0.921841	−0.460920	+	0.887441i	$0.652481\pi$
$90$	0	0
$91$	1624.00	1.87079
$92$	60.0000	0.0679938
$93$	−1376.00	−1.53424
$94$	−864.000	−0.948030
$95$	0	0
$96$	−360.000	−0.382733
$97$	382.000	0.399858	0.199929	−	0.979810i	$-0.435929\pi$
$97$	382.000	0.399858	0.199929	+	0.979810i	$0.435929\pi$
$98$	1323.00	1.36371
$99$	−888.000	−0.901488
$100$	0	0
$101$	−210.000	−0.206889	−0.103444	−	0.994635i	$-0.532986\pi$
$101$	−210.000	−0.206889	−0.103444	+	0.994635i	$0.532986\pi$
$102$	−408.000	−0.396059
$103$	232.000	0.221938	0.110969	−	0.993824i	$-0.464605\pi$
$103$	232.000	0.221938	0.110969	+	0.993824i	$0.464605\pi$
$104$	−1218.00	−1.14841
$105$	0	0
$106$	−954.000	−0.874157
$107$	−432.000	−0.390309	−0.195154	−	0.980773i	$-0.562521\pi$
$107$	−432.000	−0.390309	−0.195154	+	0.980773i	$0.562521\pi$
$108$	80.0000	0.0712778
$109$	−1186.00	−1.04219	−0.521093	−	0.853500i	$-0.674475\pi$
$109$	−1186.00	−1.04219	−0.521093	+	0.853500i	$0.674475\pi$
$110$	0	0
$111$	464.000	0.396765
$112$	−1988.00	−1.67722
$113$	366.000	0.304694	0.152347	−	0.988327i	$-0.451317\pi$
$113$	366.000	0.304694	0.152347	+	0.988327i	$0.451317\pi$
$114$	2784.00	2.28724
$115$	0	0
$116$	30.0000	0.0240123
$117$	2146.00	1.69571
$118$	756.000	0.589792
$119$	−476.000	−0.366679
$120$	0	0
$121$	−755.000	−0.567243
$122$	330.000	0.244892
$123$	−2736.00	−2.00567
$124$	−172.000	−0.124565
$125$	0	0
$126$	3108.00	2.19748
$127$	472.000	0.329789	0.164895	−	0.986311i	$-0.447272\pi$
$127$	472.000	0.329789	0.164895	+	0.986311i	$0.447272\pi$
$128$	1659.00	1.14560
$129$	1184.00	0.808104
$130$	0	0
$131$	2760.00	1.84078	0.920391	−	0.391000i	$-0.127871\pi$
$131$	2760.00	1.84078	0.920391	+	0.391000i	$0.127871\pi$
$132$	−192.000	−0.126602
$133$	3248.00	2.11757
$134$	1452.00	0.936072
$135$	0	0
$136$	357.000	0.225092
$137$	−1098.00	−0.684733	−0.342367	−	0.939566i	$-0.611229\pi$
$137$	−1098.00	−0.684733	−0.342367	+	0.939566i	$0.611229\pi$
$138$	1440.00	0.888268
$139$	2528.00	1.54261	0.771303	−	0.636468i	$-0.219605\pi$
$139$	2528.00	1.54261	0.771303	+	0.636468i	$0.219605\pi$
$140$	0	0
$141$	−2304.00	−1.37611
$142$	−2124.00	−1.25523
$143$	−1392.00	−0.814020
$144$	−2627.00	−1.52025
$145$	0	0
$146$	−1086.00	−0.615603
$147$	3528.00	1.97949
$148$	58.0000	0.0322133
$149$	1614.00	0.887410	0.443705	−	0.896173i	$-0.353664\pi$
$149$	1614.00	0.887410	0.443705	+	0.896173i	$0.353664\pi$
$150$	0	0
$151$	−3328.00	−1.79357	−0.896784	−	0.442468i	$-0.854103\pi$
$151$	−3328.00	−1.79357	−0.896784	+	0.442468i	$0.854103\pi$
$152$	−2436.00	−1.29991
$153$	−629.000	−0.332364
$154$	−2016.00	−1.05490
$155$	0	0
$156$	464.000	0.238139
$157$	2458.00	1.24949	0.624744	−	0.780829i	$-0.285203\pi$
$157$	2458.00	1.24949	0.624744	+	0.780829i	$0.285203\pi$
$158$	−1452.00	−0.731107
$159$	−2544.00	−1.26888
$160$	0	0
$161$	1680.00	0.822376
$162$	−1077.00	−0.522328
$163$	−272.000	−0.130704	−0.0653518	−	0.997862i	$-0.520817\pi$
$163$	−272.000	−0.130704	−0.0653518	+	0.997862i	$0.520817\pi$
$164$	−342.000	−0.162840
$165$	0	0
$166$	−2268.00	−1.06043
$167$	−3516.00	−1.62920	−0.814600	−	0.580024i	$-0.803043\pi$
$167$	−3516.00	−1.62920	−0.814600	+	0.580024i	$0.803043\pi$
$168$	−4704.00	−2.16025
$169$	1167.00	0.531179
$170$	0	0
$171$	4292.00	1.91940
$172$	148.000	0.0656099
$173$	1842.00	0.809507	0.404753	−	0.914426i	$-0.367357\pi$
$173$	1842.00	0.809507	0.404753	+	0.914426i	$0.367357\pi$
$174$	720.000	0.313696
$175$	0	0
$176$	1704.00	0.729795
$177$	2016.00	0.856112
$178$	−2322.00	−0.977760
$179$	−3516.00	−1.46815	−0.734073	−	0.679070i	$-0.762383\pi$
$179$	−3516.00	−1.46815	−0.734073	+	0.679070i	$0.762383\pi$
$180$	0	0
$181$	3398.00	1.39542	0.697711	−	0.716379i	$-0.254202\pi$
$181$	3398.00	1.39542	0.697711	+	0.716379i	$0.254202\pi$
$182$	4872.00	1.98427
$183$	880.000	0.355473
$184$	−1260.00	−0.504828
$185$	0	0
$186$	−4128.00	−1.62731
$187$	408.000	0.159550
$188$	−288.000	−0.111726
$189$	2240.00	0.862095
$190$	0	0
$191$	−2640.00	−1.00012	−0.500062	−	0.865990i	$-0.666689\pi$
$191$	−2640.00	−1.00012	−0.500062	+	0.865990i	$0.666689\pi$
$192$	3464.00	1.30205
$193$	−2882.00	−1.07488	−0.537438	−	0.843304i	$-0.680608\pi$
$193$	−2882.00	−1.07488	−0.537438	+	0.843304i	$0.680608\pi$
$194$	1146.00	0.424113
$195$	0	0
$196$	441.000	0.160714
$197$	42.0000	0.0151897	0.00759486	−	0.999971i	$-0.497582\pi$
$197$	42.0000	0.0151897	0.00759486	+	0.999971i	$0.497582\pi$
$198$	−2664.00	−0.956173
$199$	−3220.00	−1.14703	−0.573517	−	0.819194i	$-0.694421\pi$
$199$	−3220.00	−1.14703	−0.573517	+	0.819194i	$0.694421\pi$
$200$	0	0
$201$	3872.00	1.35876
$202$	−630.000	−0.219439
$203$	840.000	0.290426
$204$	−136.000	−0.0466760
$205$	0	0
$206$	696.000	0.235401
$207$	2220.00	0.745414
$208$	−4118.00	−1.37275
$209$	−2784.00	−0.921403
$210$	0	0
$211$	−2080.00	−0.678640	−0.339320	−	0.940671i	$-0.610197\pi$
$211$	−2080.00	−0.678640	−0.339320	+	0.940671i	$0.610197\pi$
$212$	−318.000	−0.103020
$213$	−5664.00	−1.82202
$214$	−1296.00	−0.413985
$215$	0	0
$216$	−1680.00	−0.529211
$217$	−4816.00	−1.50660
$218$	−3558.00	−1.10540
$219$	−2896.00	−0.893578
$220$	0	0
$221$	−986.000	−0.300116
$222$	1392.00	0.420833
$223$	−4664.00	−1.40056	−0.700279	−	0.713869i	$-0.746941\pi$
$223$	−4664.00	−1.40056	−0.700279	+	0.713869i	$0.746941\pi$
$224$	−1260.00	−0.375836
$225$	0	0
$226$	1098.00	0.323176
$227$	1440.00	0.421040	0.210520	−	0.977590i	$-0.432484\pi$
$227$	1440.00	0.421040	0.210520	+	0.977590i	$0.432484\pi$
$228$	928.000	0.269554
$229$	−1186.00	−0.342241	−0.171120	−	0.985250i	$-0.554739\pi$
$229$	−1186.00	−0.342241	−0.171120	+	0.985250i	$0.554739\pi$
$230$	0	0
$231$	−5376.00	−1.53123
$232$	−630.000	−0.178282
$233$	5334.00	1.49975	0.749875	−	0.661579i	$-0.230113\pi$
$233$	5334.00	1.49975	0.749875	+	0.661579i	$0.230113\pi$
$234$	6438.00	1.79857
$235$	0	0
$236$	252.000	0.0695076
$237$	−3872.00	−1.06124
$238$	−1428.00	−0.388922
$239$	5328.00	1.44201	0.721003	−	0.692931i	$-0.243681\pi$
$239$	5328.00	1.44201	0.721003	+	0.692931i	$0.243681\pi$
$240$	0	0
$241$	5618.00	1.50161	0.750803	−	0.660526i	$-0.229667\pi$
$241$	5618.00	1.50161	0.750803	+	0.660526i	$0.229667\pi$
$242$	−2265.00	−0.601652
$243$	−5032.00	−1.32841
$244$	110.000	0.0288608
$245$	0	0
$246$	−8208.00	−2.12733
$247$	6728.00	1.73317
$248$	3612.00	0.924848
$249$	−6048.00	−1.53926
$250$	0	0
$251$	−2028.00	−0.509985	−0.254992	−	0.966943i	$-0.582073\pi$
$251$	−2028.00	−0.509985	−0.254992	+	0.966943i	$0.582073\pi$
$252$	1036.00	0.258976
$253$	−1440.00	−0.357834
$254$	1416.00	0.349794
$255$	0	0
$256$	1513.00	0.369385
$257$	1902.00	0.461648	0.230824	−	0.972996i	$-0.425858\pi$
$257$	1902.00	0.461648	0.230824	+	0.972996i	$0.425858\pi$
$258$	3552.00	0.857123
$259$	1624.00	0.389616
$260$	0	0
$261$	1110.00	0.263246
$262$	8280.00	1.95244
$263$	5472.00	1.28296	0.641479	−	0.767141i	$-0.278321\pi$
$263$	5472.00	1.28296	0.641479	+	0.767141i	$0.278321\pi$
$264$	4032.00	0.939971
$265$	0	0
$266$	9744.00	2.24603
$267$	−6192.00	−1.41927
$268$	484.000	0.110317
$269$	−3570.00	−0.809170	−0.404585	−	0.914500i	$-0.632584\pi$
$269$	−3570.00	−0.809170	−0.404585	+	0.914500i	$0.632584\pi$
$270$	0	0
$271$	272.000	0.0609698	0.0304849	−	0.999535i	$-0.490295\pi$
$271$	272.000	0.0609698	0.0304849	+	0.999535i	$0.490295\pi$
$272$	1207.00	0.269063
$273$	12992.0	2.88026
$274$	−3294.00	−0.726269
$275$	0	0
$276$	480.000	0.104683
$277$	−3830.00	−0.830767	−0.415383	−	0.909646i	$-0.636353\pi$
$277$	−3830.00	−0.830767	−0.415383	+	0.909646i	$0.636353\pi$
$278$	7584.00	1.63618
$279$	−6364.00	−1.36560
$280$	0	0
$281$	8874.00	1.88391	0.941955	−	0.335740i	$-0.108986\pi$
$281$	8874.00	1.88391	0.941955	+	0.335740i	$0.108986\pi$
$282$	−6912.00	−1.45959
$283$	2632.00	0.552849	0.276424	−	0.961036i	$-0.410850\pi$
$283$	2632.00	0.552849	0.276424	+	0.961036i	$0.410850\pi$
$284$	−708.000	−0.147930
$285$	0	0
$286$	−4176.00	−0.863399
$287$	−9576.00	−1.96952
$288$	−1665.00	−0.340663
$289$	289.000	0.0588235
$290$	0	0
$291$	3056.00	0.615622
$292$	−362.000	−0.0725495
$293$	6402.00	1.27648	0.638240	−	0.769837i	$-0.279663\pi$
$293$	6402.00	1.27648	0.638240	+	0.769837i	$0.279663\pi$
$294$	10584.0	2.09956
$295$	0	0
$296$	−1218.00	−0.239172
$297$	−1920.00	−0.375117
$298$	4842.00	0.941240
$299$	3480.00	0.673089
$300$	0	0
$301$	4144.00	0.793542
$302$	−9984.00	−1.90237
$303$	−1680.00	−0.318526
$304$	−8236.00	−1.55384
$305$	0	0
$306$	−1887.00	−0.352525
$307$	8980.00	1.66943	0.834716	−	0.550681i	$-0.185632\pi$
$307$	8980.00	1.66943	0.834716	+	0.550681i	$0.185632\pi$
$308$	−672.000	−0.124321
$309$	1856.00	0.341696
$310$	0	0
$311$	−3972.00	−0.724217	−0.362108	−	0.932136i	$-0.617943\pi$
$311$	−3972.00	−0.724217	−0.362108	+	0.932136i	$0.617943\pi$
$312$	−9744.00	−1.76809
$313$	−4730.00	−0.854171	−0.427085	−	0.904211i	$-0.640460\pi$
$313$	−4730.00	−0.854171	−0.427085	+	0.904211i	$0.640460\pi$
$314$	7374.00	1.32528
$315$	0	0
$316$	−484.000	−0.0861618
$317$	2898.00	0.513463	0.256732	−	0.966483i	$-0.417354\pi$
$317$	2898.00	0.513463	0.256732	+	0.966483i	$0.417354\pi$
$318$	−7632.00	−1.34585
$319$	−720.000	−0.126371
$320$	0	0
$321$	−3456.00	−0.600919
$322$	5040.00	0.872262
$323$	−1972.00	−0.339706
$324$	−359.000	−0.0615569
$325$	0	0
$326$	−816.000	−0.138632
$327$	−9488.00	−1.60455
$328$	7182.00	1.20902
$329$	−8064.00	−1.35132
$330$	0	0
$331$	−4564.00	−0.757886	−0.378943	−	0.925420i	$-0.623712\pi$
$331$	−4564.00	−0.757886	−0.378943	+	0.925420i	$0.623712\pi$
$332$	−756.000	−0.124973
$333$	2146.00	0.353153
$334$	−10548.0	−1.72803
$335$	0	0
$336$	−15904.0	−2.58225
$337$	−722.000	−0.116706	−0.0583529	−	0.998296i	$-0.518585\pi$
$337$	−722.000	−0.116706	−0.0583529	+	0.998296i	$0.518585\pi$
$338$	3501.00	0.563400
$339$	2928.00	0.469107
$340$	0	0
$341$	4128.00	0.655553
$342$	12876.0	2.03583
$343$	2744.00	0.431959
$344$	−3108.00	−0.487128
$345$	0	0
$346$	5526.00	0.858612
$347$	−5544.00	−0.857687	−0.428844	−	0.903379i	$-0.641079\pi$
$347$	−5544.00	−0.857687	−0.428844	+	0.903379i	$0.641079\pi$
$348$	240.000	0.0369694
$349$	11126.0	1.70648	0.853239	−	0.521519i	$-0.174635\pi$
$349$	11126.0	1.70648	0.853239	+	0.521519i	$0.174635\pi$
$350$	0	0
$351$	4640.00	0.705598
$352$	1080.00	0.163535
$353$	−7842.00	−1.18240	−0.591200	−	0.806525i	$-0.701346\pi$
$353$	−7842.00	−1.18240	−0.591200	+	0.806525i	$0.701346\pi$
$354$	6048.00	0.908044
$355$	0	0
$356$	−774.000	−0.115230
$357$	−3808.00	−0.564540
$358$	−10548.0	−1.55720
$359$	5040.00	0.740950	0.370475	−	0.928842i	$-0.379195\pi$
$359$	5040.00	0.740950	0.370475	+	0.928842i	$0.379195\pi$
$360$	0	0
$361$	6597.00	0.961802
$362$	10194.0	1.48007
$363$	−6040.00	−0.873327
$364$	1624.00	0.233848
$365$	0	0
$366$	2640.00	0.377036
$367$	8404.00	1.19533	0.597664	−	0.801747i	$-0.296096\pi$
$367$	8404.00	1.19533	0.597664	+	0.801747i	$0.296096\pi$
$368$	−4260.00	−0.603445
$369$	−12654.0	−1.78521
$370$	0	0
$371$	−8904.00	−1.24602
$372$	−1376.00	−0.191780
$373$	8098.00	1.12412	0.562062	−	0.827095i	$-0.310008\pi$
$373$	8098.00	1.12412	0.562062	+	0.827095i	$0.310008\pi$
$374$	1224.00	0.169229
$375$	0	0
$376$	6048.00	0.829526
$377$	1740.00	0.237704
$378$	6720.00	0.914390
$379$	320.000	0.0433702	0.0216851	−	0.999765i	$-0.493097\pi$
$379$	320.000	0.0433702	0.0216851	+	0.999765i	$0.493097\pi$
$380$	0	0
$381$	3776.00	0.507744
$382$	−7920.00	−1.06079
$383$	10872.0	1.45048	0.725239	−	0.688497i	$-0.241729\pi$
$383$	10872.0	1.45048	0.725239	+	0.688497i	$0.241729\pi$
$384$	13272.0	1.76376
$385$	0	0
$386$	−8646.00	−1.14008
$387$	5476.00	0.719278
$388$	382.000	0.0499822
$389$	1374.00	0.179086	0.0895431	−	0.995983i	$-0.471459\pi$
$389$	1374.00	0.179086	0.0895431	+	0.995983i	$0.471459\pi$
$390$	0	0
$391$	−1020.00	−0.131927
$392$	−9261.00	−1.19324
$393$	22080.0	2.83407
$394$	126.000	0.0161111
$395$	0	0
$396$	−888.000	−0.112686
$397$	7522.00	0.950928	0.475464	−	0.879735i	$-0.342280\pi$
$397$	7522.00	0.950928	0.475464	+	0.879735i	$0.342280\pi$
$398$	−9660.00	−1.21661
$399$	25984.0	3.26022
$400$	0	0
$401$	2706.00	0.336986	0.168493	−	0.985703i	$-0.446110\pi$
$401$	2706.00	0.336986	0.168493	+	0.985703i	$0.446110\pi$
$402$	11616.0	1.44118
$403$	−9976.00	−1.23310
$404$	−210.000	−0.0258611
$405$	0	0
$406$	2520.00	0.308043
$407$	−1392.00	−0.169530
$408$	2856.00	0.346552
$409$	266.000	0.0321586	0.0160793	−	0.999871i	$-0.494882\pi$
$409$	266.000	0.0321586	0.0160793	+	0.999871i	$0.494882\pi$
$410$	0	0
$411$	−8784.00	−1.05422
$412$	232.000	0.0277423
$413$	7056.00	0.840685
$414$	6660.00	0.790631
$415$	0	0
$416$	−2610.00	−0.307610
$417$	20224.0	2.37500
$418$	−8352.00	−0.977296
$419$	2688.00	0.313407	0.156703	−	0.987646i	$-0.449913\pi$
$419$	2688.00	0.313407	0.156703	+	0.987646i	$0.449913\pi$
$420$	0	0
$421$	−13810.0	−1.59871	−0.799357	−	0.600857i	$-0.794826\pi$
$421$	−13810.0	−1.59871	−0.799357	+	0.600857i	$0.794826\pi$
$422$	−6240.00	−0.719807
$423$	−10656.0	−1.22485
$424$	6678.00	0.764888
$425$	0	0
$426$	−16992.0	−1.93255
$427$	3080.00	0.349067
$428$	−432.000	−0.0487886
$429$	−11136.0	−1.25327
$430$	0	0
$431$	3036.00	0.339302	0.169651	−	0.985504i	$-0.445736\pi$
$431$	3036.00	0.339302	0.169651	+	0.985504i	$0.445736\pi$
$432$	−5680.00	−0.632591
$433$	11422.0	1.26768	0.633841	−	0.773463i	$-0.281477\pi$
$433$	11422.0	1.26768	0.633841	+	0.773463i	$0.281477\pi$
$434$	−14448.0	−1.59799
$435$	0	0
$436$	−1186.00	−0.130273
$437$	6960.00	0.761881
$438$	−8688.00	−0.947782
$439$	−52.0000	−0.00565336	−0.00282668	−	0.999996i	$-0.500900\pi$
$439$	−52.0000	−0.00565336	−0.00282668	+	0.999996i	$0.500900\pi$
$440$	0	0
$441$	16317.0	1.76190
$442$	−2958.00	−0.318321
$443$	−3108.00	−0.333331	−0.166665	−	0.986014i	$-0.553300\pi$
$443$	−3108.00	−0.333331	−0.166665	+	0.986014i	$0.553300\pi$
$444$	464.000	0.0495956
$445$	0	0
$446$	−13992.0	−1.48552
$447$	12912.0	1.36626
$448$	12124.0	1.27858
$449$	6114.00	0.642622	0.321311	−	0.946974i	$-0.395876\pi$
$449$	6114.00	0.642622	0.321311	+	0.946974i	$0.395876\pi$
$450$	0	0
$451$	8208.00	0.856984
$452$	366.000	0.0380867
$453$	−26624.0	−2.76138
$454$	4320.00	0.446581
$455$	0	0
$456$	−19488.0	−2.00134
$457$	−4106.00	−0.420286	−0.210143	−	0.977671i	$-0.567393\pi$
$457$	−4106.00	−0.420286	−0.210143	+	0.977671i	$0.567393\pi$
$458$	−3558.00	−0.363001
$459$	−1360.00	−0.138299
$460$	0	0
$461$	3366.00	0.340066	0.170033	−	0.985438i	$-0.445613\pi$
$461$	3366.00	0.340066	0.170033	+	0.985438i	$0.445613\pi$
$462$	−16128.0	−1.62412
$463$	−896.000	−0.0899366	−0.0449683	−	0.998988i	$-0.514319\pi$
$463$	−896.000	−0.0899366	−0.0449683	+	0.998988i	$0.514319\pi$
$464$	−2130.00	−0.213109
$465$	0	0
$466$	16002.0	1.59073
$467$	10236.0	1.01427	0.507137	−	0.861866i	$-0.330704\pi$
$467$	10236.0	1.01427	0.507137	+	0.861866i	$0.330704\pi$
$468$	2146.00	0.211963
$469$	13552.0	1.33427
$470$	0	0
$471$	19664.0	1.92371
$472$	−5292.00	−0.516068
$473$	−3552.00	−0.345288
$474$	−11616.0	−1.12561
$475$	0	0
$476$	−476.000	−0.0458349
$477$	−11766.0	−1.12941
$478$	15984.0	1.52948
$479$	5172.00	0.493350	0.246675	−	0.969098i	$-0.420662\pi$
$479$	5172.00	0.493350	0.246675	+	0.969098i	$0.420662\pi$
$480$	0	0
$481$	3364.00	0.318888
$482$	16854.0	1.59269
$483$	13440.0	1.26613
$484$	−755.000	−0.0709053
$485$	0	0
$486$	−15096.0	−1.40899
$487$	15052.0	1.40056	0.700278	−	0.713870i	$-0.253059\pi$
$487$	15052.0	1.40056	0.700278	+	0.713870i	$0.253059\pi$
$488$	−2310.00	−0.214280
$489$	−2176.00	−0.201231
$490$	0	0
$491$	8700.00	0.799645	0.399822	−	0.916593i	$-0.369072\pi$
$491$	8700.00	0.799645	0.399822	+	0.916593i	$0.369072\pi$
$492$	−2736.00	−0.250708
$493$	−510.000	−0.0465908
$494$	20184.0	1.83830
$495$	0	0
$496$	12212.0	1.10551
$497$	−19824.0	−1.78919
$498$	−18144.0	−1.63263
$499$	−1168.00	−0.104783	−0.0523916	−	0.998627i	$-0.516684\pi$
$499$	−1168.00	−0.104783	−0.0523916	+	0.998627i	$0.516684\pi$
$500$	0	0
$501$	−28128.0	−2.50832
$502$	−6084.00	−0.540921
$503$	1740.00	0.154240	0.0771200	−	0.997022i	$-0.475428\pi$
$503$	1740.00	0.154240	0.0771200	+	0.997022i	$0.475428\pi$
$504$	−21756.0	−1.92280
$505$	0	0
$506$	−4320.00	−0.379540
$507$	9336.00	0.817803
$508$	472.000	0.0412236
$509$	−12570.0	−1.09461	−0.547304	−	0.836934i	$-0.684346\pi$
$509$	−12570.0	−1.09461	−0.547304	+	0.836934i	$0.684346\pi$
$510$	0	0
$511$	−10136.0	−0.877476
$512$	−8733.00	−0.753804
$513$	9280.00	0.798678
$514$	5706.00	0.489651
$515$	0	0
$516$	1184.00	0.101013
$517$	6912.00	0.587987
$518$	4872.00	0.413250
$519$	14736.0	1.24632
$520$	0	0
$521$	11658.0	0.980319	0.490160	−	0.871633i	$-0.336939\pi$
$521$	11658.0	0.980319	0.490160	+	0.871633i	$0.336939\pi$
$522$	3330.00	0.279215
$523$	−13700.0	−1.14543	−0.572714	−	0.819755i	$-0.694110\pi$
$523$	−13700.0	−1.14543	−0.572714	+	0.819755i	$0.694110\pi$
$524$	2760.00	0.230098
$525$	0	0
$526$	16416.0	1.36078
$527$	2924.00	0.241692
$528$	13632.0	1.12359
$529$	−8567.00	−0.704118
$530$	0	0
$531$	9324.00	0.762010
$532$	3248.00	0.264697
$533$	−19836.0	−1.61199
$534$	−18576.0	−1.50536
$535$	0	0
$536$	−10164.0	−0.819063
$537$	−28128.0	−2.26036
$538$	−10710.0	−0.858254
$539$	−10584.0	−0.845798
$540$	0	0
$541$	17822.0	1.41632	0.708159	−	0.706053i	$-0.249526\pi$
$541$	17822.0	1.41632	0.708159	+	0.706053i	$0.249526\pi$
$542$	816.000	0.0646683
$543$	27184.0	2.14839
$544$	765.000	0.0602925
$545$	0	0
$546$	38976.0	3.05498
$547$	−3800.00	−0.297032	−0.148516	−	0.988910i	$-0.547450\pi$
$547$	−3800.00	−0.297032	−0.148516	+	0.988910i	$0.547450\pi$
$548$	−1098.00	−0.0855917
$549$	4070.00	0.316400
$550$	0	0
$551$	3480.00	0.269062
$552$	−10080.0	−0.777234
$553$	−13552.0	−1.04212
$554$	−11490.0	−0.881161
$555$	0	0
$556$	2528.00	0.192826
$557$	10074.0	0.766336	0.383168	−	0.923679i	$-0.374833\pi$
$557$	10074.0	0.766336	0.383168	+	0.923679i	$0.374833\pi$
$558$	−19092.0	−1.44844
$559$	8584.00	0.649489
$560$	0	0
$561$	3264.00	0.245644
$562$	26622.0	1.99819
$563$	15948.0	1.19383	0.596917	−	0.802303i	$-0.296392\pi$
$563$	15948.0	1.19383	0.596917	+	0.802303i	$0.296392\pi$
$564$	−2304.00	−0.172014
$565$	0	0
$566$	7896.00	0.586385
$567$	−10052.0	−0.744523
$568$	14868.0	1.09832
$569$	21834.0	1.60866	0.804331	−	0.594181i	$-0.202524\pi$
$569$	21834.0	1.60866	0.804331	+	0.594181i	$0.202524\pi$
$570$	0	0
$571$	−21208.0	−1.55434	−0.777169	−	0.629292i	$-0.783345\pi$
$571$	−21208.0	−1.55434	−0.777169	+	0.629292i	$0.783345\pi$
$572$	−1392.00	−0.101753
$573$	−21120.0	−1.53979
$574$	−28728.0	−2.08900
$575$	0	0
$576$	16021.0	1.15893
$577$	−12530.0	−0.904039	−0.452020	−	0.892008i	$-0.649296\pi$
$577$	−12530.0	−0.904039	−0.452020	+	0.892008i	$0.649296\pi$
$578$	867.000	0.0623918
$579$	−23056.0	−1.65488
$580$	0	0
$581$	−21168.0	−1.51153
$582$	9168.00	0.652965
$583$	7632.00	0.542170
$584$	7602.00	0.538652
$585$	0	0
$586$	19206.0	1.35391
$587$	−2220.00	−0.156097	−0.0780487	−	0.996950i	$-0.524869\pi$
$587$	−2220.00	−0.156097	−0.0780487	+	0.996950i	$0.524869\pi$
$588$	3528.00	0.247436
$589$	−19952.0	−1.39577
$590$	0	0
$591$	336.000	0.0233861
$592$	−4118.00	−0.285893
$593$	25038.0	1.73387	0.866937	−	0.498418i	$-0.166085\pi$
$593$	25038.0	1.73387	0.866937	+	0.498418i	$0.166085\pi$
$594$	−5760.00	−0.397871
$595$	0	0
$596$	1614.00	0.110926
$597$	−25760.0	−1.76597
$598$	10440.0	0.713919
$599$	5784.00	0.394537	0.197269	−	0.980349i	$-0.436793\pi$
$599$	5784.00	0.394537	0.197269	+	0.980349i	$0.436793\pi$
$600$	0	0
$601$	−4198.00	−0.284925	−0.142463	−	0.989800i	$-0.545502\pi$
$601$	−4198.00	−0.284925	−0.142463	+	0.989800i	$0.545502\pi$
$602$	12432.0	0.841679
$603$	17908.0	1.20940
$604$	−3328.00	−0.224196
$605$	0	0
$606$	−5040.00	−0.337848
$607$	12124.0	0.810705	0.405353	−	0.914160i	$-0.367149\pi$
$607$	12124.0	0.810705	0.405353	+	0.914160i	$0.367149\pi$
$608$	−5220.00	−0.348189
$609$	6720.00	0.447140
$610$	0	0
$611$	−16704.0	−1.10601
$612$	−629.000	−0.0415455
$613$	−7454.00	−0.491133	−0.245566	−	0.969380i	$-0.578974\pi$
$613$	−7454.00	−0.491133	−0.245566	+	0.969380i	$0.578974\pi$
$614$	26940.0	1.77070
$615$	0	0
$616$	14112.0	0.923034
$617$	−28842.0	−1.88190	−0.940952	−	0.338539i	$-0.890067\pi$
$617$	−28842.0	−1.88190	−0.940952	+	0.338539i	$0.890067\pi$
$618$	5568.00	0.362424
$619$	−17224.0	−1.11840	−0.559201	−	0.829032i	$-0.688892\pi$
$619$	−17224.0	−1.11840	−0.559201	+	0.829032i	$0.688892\pi$
$620$	0	0
$621$	4800.00	0.310173
$622$	−11916.0	−0.768148
$623$	−21672.0	−1.39369
$624$	−32944.0	−2.11349
$625$	0	0
$626$	−14190.0	−0.905985
$627$	−22272.0	−1.41859
$628$	2458.00	0.156186
$629$	−986.000	−0.0625030
$630$	0	0
$631$	−12448.0	−0.785336	−0.392668	−	0.919680i	$-0.628448\pi$
$631$	−12448.0	−0.785336	−0.392668	+	0.919680i	$0.628448\pi$
$632$	10164.0	0.639719
$633$	−16640.0	−1.04484
$634$	8694.00	0.544610
$635$	0	0
$636$	−2544.00	−0.158610
$637$	25578.0	1.59095
$638$	−2160.00	−0.134036
$639$	−26196.0	−1.62175
$640$	0	0
$641$	−25182.0	−1.55168	−0.775842	−	0.630927i	$-0.782675\pi$
$641$	−25182.0	−1.55168	−0.775842	+	0.630927i	$0.782675\pi$
$642$	−10368.0	−0.637371
$643$	−17048.0	−1.04558	−0.522790	−	0.852462i	$-0.675109\pi$
$643$	−17048.0	−1.04558	−0.522790	+	0.852462i	$0.675109\pi$
$644$	1680.00	0.102797
$645$	0	0
$646$	−5916.00	−0.360313
$647$	−7128.00	−0.433123	−0.216562	−	0.976269i	$-0.569484\pi$
$647$	−7128.00	−0.433123	−0.216562	+	0.976269i	$0.569484\pi$
$648$	7539.00	0.457037
$649$	−6048.00	−0.365801
$650$	0	0
$651$	−38528.0	−2.31956
$652$	−272.000	−0.0163379
$653$	−18462.0	−1.10639	−0.553196	−	0.833051i	$-0.686592\pi$
$653$	−18462.0	−1.10639	−0.553196	+	0.833051i	$0.686592\pi$
$654$	−28464.0	−1.70188
$655$	0	0
$656$	24282.0	1.44520
$657$	−13394.0	−0.795357
$658$	−24192.0	−1.43329
$659$	28092.0	1.66056	0.830280	−	0.557347i	$-0.188181\pi$
$659$	28092.0	1.66056	0.830280	+	0.557347i	$0.188181\pi$
$660$	0	0
$661$	10910.0	0.641982	0.320991	−	0.947082i	$-0.395984\pi$
$661$	10910.0	0.641982	0.320991	+	0.947082i	$0.395984\pi$
$662$	−13692.0	−0.803859
$663$	−7888.00	−0.462058
$664$	15876.0	0.927874
$665$	0	0
$666$	6438.00	0.374576
$667$	1800.00	0.104492
$668$	−3516.00	−0.203650
$669$	−37312.0	−2.15630
$670$	0	0
$671$	−2640.00	−0.151887
$672$	−10080.0	−0.578638
$673$	28414.0	1.62746	0.813729	−	0.581244i	$-0.197434\pi$
$673$	28414.0	1.62746	0.813729	+	0.581244i	$0.197434\pi$
$674$	−2166.00	−0.123785
$675$	0	0
$676$	1167.00	0.0663974
$677$	6042.00	0.343003	0.171501	−	0.985184i	$-0.445138\pi$
$677$	6042.00	0.343003	0.171501	+	0.985184i	$0.445138\pi$
$678$	8784.00	0.497563
$679$	10696.0	0.604528
$680$	0	0
$681$	11520.0	0.648234
$682$	12384.0	0.695319
$683$	−34752.0	−1.94692	−0.973461	−	0.228851i	$-0.926503\pi$
$683$	−34752.0	−1.94692	−0.973461	+	0.228851i	$0.926503\pi$
$684$	4292.00	0.239925
$685$	0	0
$686$	8232.00	0.458162
$687$	−9488.00	−0.526914
$688$	−10508.0	−0.582287
$689$	−18444.0	−1.01983
$690$	0	0
$691$	18320.0	1.00858	0.504288	−	0.863536i	$-0.331755\pi$
$691$	18320.0	1.00858	0.504288	+	0.863536i	$0.331755\pi$
$692$	1842.00	0.101188
$693$	−24864.0	−1.36292
$694$	−16632.0	−0.909715
$695$	0	0
$696$	−5040.00	−0.274484
$697$	5814.00	0.315955
$698$	33378.0	1.80999
$699$	42672.0	2.30902
$700$	0	0
$701$	−22890.0	−1.23330	−0.616650	−	0.787237i	$-0.711511\pi$
$701$	−22890.0	−1.23330	−0.616650	+	0.787237i	$0.711511\pi$
$702$	13920.0	0.748400
$703$	6728.00	0.360955
$704$	−10392.0	−0.556340
$705$	0	0
$706$	−23526.0	−1.25413
$707$	−5880.00	−0.312787
$708$	2016.00	0.107014
$709$	22886.0	1.21227	0.606137	−	0.795361i	$-0.292718\pi$
$709$	22886.0	1.21227	0.606137	+	0.795361i	$0.292718\pi$
$710$	0	0
$711$	−17908.0	−0.944589
$712$	16254.0	0.855540
$713$	−10320.0	−0.542058
$714$	−11424.0	−0.598785
$715$	0	0
$716$	−3516.00	−0.183518
$717$	42624.0	2.22011
$718$	15120.0	0.785896
$719$	−13452.0	−0.697740	−0.348870	−	0.937171i	$-0.613435\pi$
$719$	−13452.0	−0.697740	−0.348870	+	0.937171i	$0.613435\pi$
$720$	0	0
$721$	6496.00	0.335539
$722$	19791.0	1.02015
$723$	44944.0	2.31187
$724$	3398.00	0.174428
$725$	0	0
$726$	−18120.0	−0.926303
$727$	27304.0	1.39292	0.696458	−	0.717598i	$-0.254758\pi$
$727$	27304.0	1.39292	0.696458	+	0.717598i	$0.254758\pi$
$728$	−34104.0	−1.73623
$729$	−30563.0	−1.55276
$730$	0	0
$731$	−2516.00	−0.127302
$732$	880.000	0.0444341
$733$	−24470.0	−1.23304	−0.616521	−	0.787338i	$-0.711459\pi$
$733$	−24470.0	−1.23304	−0.616521	+	0.787338i	$0.711459\pi$
$734$	25212.0	1.26784
$735$	0	0
$736$	−2700.00	−0.135222
$737$	−11616.0	−0.580571
$738$	−37962.0	−1.89350
$739$	35252.0	1.75476	0.877379	−	0.479798i	$-0.159290\pi$
$739$	35252.0	1.75476	0.877379	+	0.479798i	$0.159290\pi$
$740$	0	0
$741$	53824.0	2.66839
$742$	−26712.0	−1.32160
$743$	−1548.00	−0.0764342	−0.0382171	−	0.999269i	$-0.512168\pi$
$743$	−1548.00	−0.0764342	−0.0382171	+	0.999269i	$0.512168\pi$
$744$	28896.0	1.42390
$745$	0	0
$746$	24294.0	1.19231
$747$	−27972.0	−1.37007
$748$	408.000	0.0199438
$749$	−12096.0	−0.590091
$750$	0	0
$751$	2948.00	0.143241	0.0716205	−	0.997432i	$-0.477183\pi$
$751$	2948.00	0.143241	0.0716205	+	0.997432i	$0.477183\pi$
$752$	20448.0	0.991572
$753$	−16224.0	−0.785173
$754$	5220.00	0.252124
$755$	0	0
$756$	2240.00	0.107762
$757$	754.000	0.0362016	0.0181008	−	0.999836i	$-0.494238\pi$
$757$	754.000	0.0362016	0.0181008	+	0.999836i	$0.494238\pi$
$758$	960.000	0.0460010
$759$	−11520.0	−0.550922
$760$	0	0
$761$	−41574.0	−1.98036	−0.990182	−	0.139787i	$-0.955358\pi$
$761$	−41574.0	−1.98036	−0.990182	+	0.139787i	$0.955358\pi$
$762$	11328.0	0.538543
$763$	−33208.0	−1.57564
$764$	−2640.00	−0.125016
$765$	0	0
$766$	32616.0	1.53846
$767$	14616.0	0.688075
$768$	12104.0	0.568705
$769$	−15118.0	−0.708932	−0.354466	−	0.935069i	$-0.615337\pi$
$769$	−15118.0	−0.708932	−0.354466	+	0.935069i	$0.615337\pi$
$770$	0	0
$771$	15216.0	0.710753
$772$	−2882.00	−0.134359
$773$	−23550.0	−1.09578	−0.547888	−	0.836552i	$-0.684568\pi$
$773$	−23550.0	−1.09578	−0.547888	+	0.836552i	$0.684568\pi$
$774$	16428.0	0.762910
$775$	0	0
$776$	−8022.00	−0.371099
$777$	12992.0	0.599853
$778$	4122.00	0.189950
$779$	−39672.0	−1.82464
$780$	0	0
$781$	16992.0	0.778517
$782$	−3060.00	−0.139930
$783$	2400.00	0.109539
$784$	−31311.0	−1.42634
$785$	0	0
$786$	66240.0	3.00598
$787$	−5240.00	−0.237339	−0.118670	−	0.992934i	$-0.537863\pi$
$787$	−5240.00	−0.237339	−0.118670	+	0.992934i	$0.537863\pi$
$788$	42.0000	0.00189872
$789$	43776.0	1.97524
$790$	0	0
$791$	10248.0	0.460654
$792$	18648.0	0.836651
$793$	6380.00	0.285700
$794$	22566.0	1.00861
$795$	0	0
$796$	−3220.00	−0.143379
$797$	−5526.00	−0.245597	−0.122799	−	0.992432i	$-0.539187\pi$
$797$	−5526.00	−0.245597	−0.122799	+	0.992432i	$0.539187\pi$
$798$	77952.0	3.45798
$799$	4896.00	0.216781
$800$	0	0
$801$	−28638.0	−1.26326
$802$	8118.00	0.357427
$803$	8688.00	0.381809
$804$	3872.00	0.169844
$805$	0	0
$806$	−29928.0	−1.30790
$807$	−28560.0	−1.24580
$808$	4410.00	0.192009
$809$	−438.000	−0.0190349	−0.00951747	−	0.999955i	$-0.503030\pi$
$809$	−438.000	−0.0190349	−0.00951747	+	0.999955i	$0.503030\pi$
$810$	0	0
$811$	−30448.0	−1.31834	−0.659170	−	0.751994i	$-0.729092\pi$
$811$	−30448.0	−1.31834	−0.659170	+	0.751994i	$0.729092\pi$
$812$	840.000	0.0363032
$813$	2176.00	0.0938692
$814$	−4176.00	−0.179814
$815$	0	0
$816$	9656.00	0.414250
$817$	17168.0	0.735168
$818$	798.000	0.0341093
$819$	60088.0	2.56367
$820$	0	0
$821$	−21930.0	−0.932232	−0.466116	−	0.884724i	$-0.654347\pi$
$821$	−21930.0	−0.932232	−0.466116	+	0.884724i	$0.654347\pi$
$822$	−26352.0	−1.11816
$823$	27436.0	1.16204	0.581020	−	0.813889i	$-0.302654\pi$
$823$	27436.0	1.16204	0.581020	+	0.813889i	$0.302654\pi$
$824$	−4872.00	−0.205976
$825$	0	0
$826$	21168.0	0.891681
$827$	17832.0	0.749794	0.374897	−	0.927067i	$-0.377678\pi$
$827$	17832.0	0.749794	0.374897	+	0.927067i	$0.377678\pi$
$828$	2220.00	0.0931767
$829$	−4090.00	−0.171353	−0.0856765	−	0.996323i	$-0.527305\pi$
$829$	−4090.00	−0.171353	−0.0856765	+	0.996323i	$0.527305\pi$
$830$	0	0
$831$	−30640.0	−1.27905
$832$	25114.0	1.04648
$833$	−7497.00	−0.311832
$834$	60672.0	2.51906
$835$	0	0
$836$	−2784.00	−0.115175
$837$	−13760.0	−0.568238
$838$	8064.00	0.332418
$839$	−2508.00	−0.103201	−0.0516006	−	0.998668i	$-0.516432\pi$
$839$	−2508.00	−0.103201	−0.0516006	+	0.998668i	$0.516432\pi$
$840$	0	0
$841$	−23489.0	−0.963098
$842$	−41430.0	−1.69569
$843$	70992.0	2.90047
$844$	−2080.00	−0.0848300
$845$	0	0
$846$	−31968.0	−1.29915
$847$	−21140.0	−0.857590
$848$	22578.0	0.914306
$849$	21056.0	0.851166
$850$	0	0
$851$	3480.00	0.140180
$852$	−5664.00	−0.227753
$853$	42442.0	1.70362	0.851809	−	0.523852i	$-0.175506\pi$
$853$	42442.0	1.70362	0.851809	+	0.523852i	$0.175506\pi$
$854$	9240.00	0.370242
$855$	0	0
$856$	9072.00	0.362237
$857$	−32730.0	−1.30459	−0.652296	−	0.757964i	$-0.726194\pi$
$857$	−32730.0	−1.30459	−0.652296	+	0.757964i	$0.726194\pi$
$858$	−33408.0	−1.32929
$859$	−6148.00	−0.244199	−0.122100	−	0.992518i	$-0.538963\pi$
$859$	−6148.00	−0.244199	−0.122100	+	0.992518i	$0.538963\pi$
$860$	0	0
$861$	−76608.0	−3.03228
$862$	9108.00	0.359884
$863$	22512.0	0.887969	0.443985	−	0.896034i	$-0.353564\pi$
$863$	22512.0	0.887969	0.443985	+	0.896034i	$0.353564\pi$
$864$	−3600.00	−0.141753
$865$	0	0
$866$	34266.0	1.34458
$867$	2312.00	0.0905647
$868$	−4816.00	−0.188325
$869$	11616.0	0.453447
$870$	0	0
$871$	28072.0	1.09206
$872$	24906.0	0.967229
$873$	14134.0	0.547954
$874$	20880.0	0.808097
$875$	0	0
$876$	−2896.00	−0.111697
$877$	−9182.00	−0.353539	−0.176770	−	0.984252i	$-0.556565\pi$
$877$	−9182.00	−0.353539	−0.176770	+	0.984252i	$0.556565\pi$
$878$	−156.000	−0.00599629
$879$	51216.0	1.96527
$880$	0	0
$881$	28530.0	1.09103	0.545517	−	0.838100i	$-0.316334\pi$
$881$	28530.0	1.09103	0.545517	+	0.838100i	$0.316334\pi$
$882$	48951.0	1.86878
$883$	12436.0	0.473958	0.236979	−	0.971515i	$-0.423843\pi$
$883$	12436.0	0.473958	0.236979	+	0.971515i	$0.423843\pi$
$884$	−986.000	−0.0375144
$885$	0	0
$886$	−9324.00	−0.353551
$887$	−7404.00	−0.280273	−0.140136	−	0.990132i	$-0.544754\pi$
$887$	−7404.00	−0.280273	−0.140136	+	0.990132i	$0.544754\pi$
$888$	−9744.00	−0.368229
$889$	13216.0	0.498594
$890$	0	0
$891$	8616.00	0.323958
$892$	−4664.00	−0.175070
$893$	−33408.0	−1.25191
$894$	38736.0	1.44913
$895$	0	0
$896$	46452.0	1.73198
$897$	27840.0	1.03629
$898$	18342.0	0.681604
$899$	−5160.00	−0.191430
$900$	0	0
$901$	5406.00	0.199889
$902$	24624.0	0.908968
$903$	33152.0	1.22174
$904$	−7686.00	−0.282779
$905$	0	0
$906$	−79872.0	−2.92888
$907$	−15368.0	−0.562609	−0.281304	−	0.959619i	$-0.590767\pi$
$907$	−15368.0	−0.562609	−0.281304	+	0.959619i	$0.590767\pi$
$908$	1440.00	0.0526300
$909$	−7770.00	−0.283514
$910$	0	0
$911$	27276.0	0.991980	0.495990	−	0.868328i	$-0.334805\pi$
$911$	27276.0	0.991980	0.495990	+	0.868328i	$0.334805\pi$
$912$	−65888.0	−2.39229
$913$	18144.0	0.657699
$914$	−12318.0	−0.445780
$915$	0	0
$916$	−1186.00	−0.0427801
$917$	77280.0	2.78300
$918$	−4080.00	−0.146689
$919$	−46456.0	−1.66751	−0.833755	−	0.552134i	$-0.813814\pi$
$919$	−46456.0	−1.66751	−0.833755	+	0.552134i	$0.813814\pi$
$920$	0	0
$921$	71840.0	2.57026
$922$	10098.0	0.360694
$923$	−41064.0	−1.46440
$924$	−5376.00	−0.191404
$925$	0	0
$926$	−2688.00	−0.0953922
$927$	8584.00	0.304138
$928$	−1350.00	−0.0477542
$929$	13026.0	0.460031	0.230016	−	0.973187i	$-0.426122\pi$
$929$	13026.0	0.460031	0.230016	+	0.973187i	$0.426122\pi$
$930$	0	0
$931$	51156.0	1.80083
$932$	5334.00	0.187469
$933$	−31776.0	−1.11500
$934$	30708.0	1.07580
$935$	0	0
$936$	−45066.0	−1.57375
$937$	−26330.0	−0.917997	−0.458999	−	0.888437i	$-0.651792\pi$
$937$	−26330.0	−0.917997	−0.458999	+	0.888437i	$0.651792\pi$
$938$	40656.0	1.41521
$939$	−37840.0	−1.31508
$940$	0	0
$941$	28254.0	0.978803	0.489402	−	0.872058i	$-0.337215\pi$
$941$	28254.0	0.978803	0.489402	+	0.872058i	$0.337215\pi$
$942$	58992.0	2.04041
$943$	−20520.0	−0.708614
$944$	−17892.0	−0.616880
$945$	0	0
$946$	−10656.0	−0.366233
$947$	−49272.0	−1.69073	−0.845367	−	0.534186i	$-0.820618\pi$
$947$	−49272.0	−1.69073	−0.845367	+	0.534186i	$0.820618\pi$
$948$	−3872.00	−0.132655
$949$	−20996.0	−0.718187
$950$	0	0
$951$	23184.0	0.790529
$952$	9996.00	0.340307
$953$	−32922.0	−1.11904	−0.559522	−	0.828816i	$-0.689015\pi$
$953$	−32922.0	−1.11904	−0.559522	+	0.828816i	$0.689015\pi$
$954$	−35298.0	−1.19792
$955$	0	0
$956$	5328.00	0.180251
$957$	−5760.00	−0.194560
$958$	15516.0	0.523277
$959$	−30744.0	−1.03522
$960$	0	0
$961$	−207.000	−0.00694841
$962$	10092.0	0.338232
$963$	−15984.0	−0.534867
$964$	5618.00	0.187701
$965$	0	0
$966$	40320.0	1.34293
$967$	1168.00	0.0388421	0.0194211	−	0.999811i	$-0.493818\pi$
$967$	1168.00	0.0388421	0.0194211	+	0.999811i	$0.493818\pi$
$968$	15855.0	0.526445
$969$	−15776.0	−0.523011
$970$	0	0
$971$	−19812.0	−0.654786	−0.327393	−	0.944888i	$-0.606170\pi$
$971$	−19812.0	−0.654786	−0.327393	+	0.944888i	$0.606170\pi$
$972$	−5032.00	−0.166051
$973$	70784.0	2.33220
$974$	45156.0	1.48551
$975$	0	0
$976$	−7810.00	−0.256139
$977$	28494.0	0.933064	0.466532	−	0.884504i	$-0.345503\pi$
$977$	28494.0	0.933064	0.466532	+	0.884504i	$0.345503\pi$
$978$	−6528.00	−0.213438
$979$	18576.0	0.606426
$980$	0	0
$981$	−43882.0	−1.42818
$982$	26100.0	0.848151
$983$	42708.0	1.38573	0.692866	−	0.721067i	$-0.256348\pi$
$983$	42708.0	1.38573	0.692866	+	0.721067i	$0.256348\pi$
$984$	57456.0	1.86141
$985$	0	0
$986$	−1530.00	−0.0494170
$987$	−64512.0	−2.08049
$988$	6728.00	0.216646
$989$	8880.00	0.285508
$990$	0	0
$991$	−29500.0	−0.945609	−0.472804	−	0.881167i	$-0.656758\pi$
$991$	−29500.0	−0.945609	−0.472804	+	0.881167i	$0.656758\pi$
$992$	7740.00	0.247727
$993$	−36512.0	−1.16684
$994$	−59472.0	−1.89772
$995$	0	0
$996$	−6048.00	−0.192408
$997$	9322.00	0.296119	0.148060	−	0.988978i	$-0.452697\pi$
$997$	9322.00	0.296119	0.148060	+	0.988978i	$0.452697\pi$
$998$	−3504.00	−0.111139
$999$	4640.00	0.146950

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.4.a.d.1.1		1
5.2	odd	4		425.4.b.c.324.2		2
5.3	odd	4		425.4.b.c.324.1		2
5.4	even	2		17.4.a.a.1.1	✓	1
15.14	odd	2		153.4.a.d.1.1		1
20.19	odd	2		272.4.a.d.1.1		1
35.34	odd	2		833.4.a.a.1.1		1
40.19	odd	2		1088.4.a.a.1.1		1
40.29	even	2		1088.4.a.l.1.1		1
55.54	odd	2		2057.4.a.d.1.1		1
60.59	even	2		2448.4.a.f.1.1		1
85.4	even	4		289.4.b.a.288.2		2
85.64	even	4		289.4.b.a.288.1		2
85.84	even	2		289.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.a.a.1.1	✓	1	5.4	even	2
153.4.a.d.1.1		1	15.14	odd	2
272.4.a.d.1.1		1	20.19	odd	2
289.4.a.a.1.1		1	85.84	even	2
289.4.b.a.288.1		2	85.64	even	4
289.4.b.a.288.2		2	85.4	even	4
425.4.a.d.1.1		1	1.1	even	1	trivial
425.4.b.c.324.1		2	5.3	odd	4
425.4.b.c.324.2		2	5.2	odd	4
833.4.a.a.1.1		1	35.34	odd	2
1088.4.a.a.1.1		1	40.19	odd	2
1088.4.a.l.1.1		1	40.29	even	2
2057.4.a.d.1.1		1	55.54	odd	2
2448.4.a.f.1.1		1	60.59	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	425.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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