LMFDB - Embedded newform 1950.4.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,4,Mod(1,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, 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("1950.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1950.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:	$115.053724511$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1950.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -6.00000 q^{6} +15.0000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -6.00000 q^{6} +15.0000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +39.0000 q^{11} -12.0000 q^{12} +13.0000 q^{13} +30.0000 q^{14} +16.0000 q^{16} +15.0000 q^{17} +18.0000 q^{18} +54.0000 q^{19} -45.0000 q^{21} +78.0000 q^{22} +143.000 q^{23} -24.0000 q^{24} +26.0000 q^{26} -27.0000 q^{27} +60.0000 q^{28} -122.000 q^{29} -246.000 q^{31} +32.0000 q^{32} -117.000 q^{33} +30.0000 q^{34} +36.0000 q^{36} +225.000 q^{37} +108.000 q^{38} -39.0000 q^{39} +469.000 q^{41} -90.0000 q^{42} +484.000 q^{43} +156.000 q^{44} +286.000 q^{46} -234.000 q^{47} -48.0000 q^{48} -118.000 q^{49} -45.0000 q^{51} +52.0000 q^{52} -33.0000 q^{53} -54.0000 q^{54} +120.000 q^{56} -162.000 q^{57} -244.000 q^{58} -831.000 q^{61} -492.000 q^{62} +135.000 q^{63} +64.0000 q^{64} -234.000 q^{66} -772.000 q^{67} +60.0000 q^{68} -429.000 q^{69} -793.000 q^{71} +72.0000 q^{72} +998.000 q^{73} +450.000 q^{74} +216.000 q^{76} +585.000 q^{77} -78.0000 q^{78} -681.000 q^{79} +81.0000 q^{81} +938.000 q^{82} +772.000 q^{83} -180.000 q^{84} +968.000 q^{86} +366.000 q^{87} +312.000 q^{88} -465.000 q^{89} +195.000 q^{91} +572.000 q^{92} +738.000 q^{93} -468.000 q^{94} -96.0000 q^{96} +79.0000 q^{97} -236.000 q^{98} +351.000 q^{99} +O(q^{100})\)

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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−6.00000	−0.408248
$7$	15.0000	0.809924	0.404962	−	0.914334i	$-0.367285\pi$
$7$	15.0000	0.809924	0.404962	+	0.914334i	$0.367285\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	0	0
$11$	39.0000	1.06899	0.534497	−	0.845170i	$-0.320501\pi$
$11$	39.0000	1.06899	0.534497	+	0.845170i	$0.320501\pi$
$12$	−12.0000	−0.288675
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	30.0000	0.572703
$15$	0	0
$16$	16.0000	0.250000
$17$	15.0000	0.214002	0.107001	−	0.994259i	$-0.465875\pi$
$17$	15.0000	0.214002	0.107001	+	0.994259i	$0.465875\pi$
$18$	18.0000	0.235702
$19$	54.0000	0.652024	0.326012	−	0.945366i	$-0.394295\pi$
$19$	54.0000	0.652024	0.326012	+	0.945366i	$0.394295\pi$
$20$	0	0
$21$	−45.0000	−0.467610
$22$	78.0000	0.755893
$23$	143.000	1.29642	0.648208	−	0.761463i	$-0.275519\pi$
$23$	143.000	1.29642	0.648208	+	0.761463i	$0.275519\pi$
$24$	−24.0000	−0.204124
$25$	0	0
$26$	26.0000	0.196116
$27$	−27.0000	−0.192450
$28$	60.0000	0.404962
$29$	−122.000	−0.781201	−0.390601	−	0.920560i	$-0.627733\pi$
$29$	−122.000	−0.781201	−0.390601	+	0.920560i	$0.627733\pi$
$30$	0	0
$31$	−246.000	−1.42525	−0.712627	−	0.701543i	$-0.752495\pi$
$31$	−246.000	−1.42525	−0.712627	+	0.701543i	$0.752495\pi$
$32$	32.0000	0.176777
$33$	−117.000	−0.617184
$34$	30.0000	0.151322
$35$	0	0
$36$	36.0000	0.166667
$37$	225.000	0.999724	0.499862	−	0.866105i	$-0.333384\pi$
$37$	225.000	0.999724	0.499862	+	0.866105i	$0.333384\pi$
$38$	108.000	0.461050
$39$	−39.0000	−0.160128
$40$	0	0
$41$	469.000	1.78648	0.893238	−	0.449585i	$-0.148428\pi$
$41$	469.000	1.78648	0.893238	+	0.449585i	$0.148428\pi$
$42$	−90.0000	−0.330650
$43$	484.000	1.71650	0.858248	−	0.513236i	$-0.171553\pi$
$43$	484.000	1.71650	0.858248	+	0.513236i	$0.171553\pi$
$44$	156.000	0.534497
$45$	0	0
$46$	286.000	0.916704
$47$	−234.000	−0.726221	−0.363111	−	0.931746i	$-0.618285\pi$
$47$	−234.000	−0.726221	−0.363111	+	0.931746i	$0.618285\pi$
$48$	−48.0000	−0.144338
$49$	−118.000	−0.344023
$50$	0	0
$51$	−45.0000	−0.123554
$52$	52.0000	0.138675
$53$	−33.0000	−0.0855264	−0.0427632	−	0.999085i	$-0.513616\pi$
$53$	−33.0000	−0.0855264	−0.0427632	+	0.999085i	$0.513616\pi$
$54$	−54.0000	−0.136083
$55$	0	0
$56$	120.000	0.286351
$57$	−162.000	−0.376446
$58$	−244.000	−0.552393
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	−831.000	−1.74424	−0.872120	−	0.489292i	$-0.837255\pi$
$61$	−831.000	−1.74424	−0.872120	+	0.489292i	$0.837255\pi$
$62$	−492.000	−1.00781
$63$	135.000	0.269975
$64$	64.0000	0.125000
$65$	0	0
$66$	−234.000	−0.436415
$67$	−772.000	−1.40768	−0.703842	−	0.710357i	$-0.748534\pi$
$67$	−772.000	−1.40768	−0.703842	+	0.710357i	$0.748534\pi$
$68$	60.0000	0.107001
$69$	−429.000	−0.748486
$70$	0	0
$71$	−793.000	−1.32552	−0.662759	−	0.748833i	$-0.730615\pi$
$71$	−793.000	−1.32552	−0.662759	+	0.748833i	$0.730615\pi$
$72$	72.0000	0.117851
$73$	998.000	1.60010	0.800048	−	0.599935i	$-0.204807\pi$
$73$	998.000	1.60010	0.800048	+	0.599935i	$0.204807\pi$
$74$	450.000	0.706911
$75$	0	0
$76$	216.000	0.326012
$77$	585.000	0.865804
$78$	−78.0000	−0.113228
$79$	−681.000	−0.969854	−0.484927	−	0.874555i	$-0.661154\pi$
$79$	−681.000	−0.969854	−0.484927	+	0.874555i	$0.661154\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	938.000	1.26323
$83$	772.000	1.02094	0.510470	−	0.859896i	$-0.329471\pi$
$83$	772.000	1.02094	0.510470	+	0.859896i	$0.329471\pi$
$84$	−180.000	−0.233805
$85$	0	0
$86$	968.000	1.21375
$87$	366.000	0.451027
$88$	312.000	0.377947
$89$	−465.000	−0.553819	−0.276910	−	0.960896i	$-0.589310\pi$
$89$	−465.000	−0.553819	−0.276910	+	0.960896i	$0.589310\pi$
$90$	0	0
$91$	195.000	0.224632
$92$	572.000	0.648208
$93$	738.000	0.822871
$94$	−468.000	−0.513516
$95$	0	0
$96$	−96.0000	−0.102062
$97$	79.0000	0.0826931	0.0413466	−	0.999145i	$-0.486835\pi$
$97$	79.0000	0.0826931	0.0413466	+	0.999145i	$0.486835\pi$
$98$	−236.000	−0.243261
$99$	351.000	0.356332
$100$	0	0
$101$	648.000	0.638400	0.319200	−	0.947687i	$-0.396586\pi$
$101$	648.000	0.638400	0.319200	+	0.947687i	$0.396586\pi$
$102$	−90.0000	−0.0873660
$103$	1140.00	1.09056	0.545279	−	0.838254i	$-0.316424\pi$
$103$	1140.00	1.09056	0.545279	+	0.838254i	$0.316424\pi$
$104$	104.000	0.0980581
$105$	0	0
$106$	−66.0000	−0.0604763
$107$	−913.000	−0.824888	−0.412444	−	0.910983i	$-0.635325\pi$
$107$	−913.000	−0.824888	−0.412444	+	0.910983i	$0.635325\pi$
$108$	−108.000	−0.0962250
$109$	1276.00	1.12127	0.560636	−	0.828062i	$-0.310557\pi$
$109$	1276.00	1.12127	0.560636	+	0.828062i	$0.310557\pi$
$110$	0	0
$111$	−675.000	−0.577191
$112$	240.000	0.202481
$113$	214.000	0.178154	0.0890771	−	0.996025i	$-0.471608\pi$
$113$	214.000	0.178154	0.0890771	+	0.996025i	$0.471608\pi$
$114$	−324.000	−0.266188
$115$	0	0
$116$	−488.000	−0.390601
$117$	117.000	0.0924500
$118$	0	0
$119$	225.000	0.173325
$120$	0	0
$121$	190.000	0.142750
$122$	−1662.00	−1.23336
$123$	−1407.00	−1.03142
$124$	−984.000	−0.712627
$125$	0	0
$126$	270.000	0.190901
$127$	1074.00	0.750410	0.375205	−	0.926942i	$-0.377572\pi$
$127$	1074.00	0.750410	0.375205	+	0.926942i	$0.377572\pi$
$128$	128.000	0.0883883
$129$	−1452.00	−0.991019
$130$	0	0
$131$	1482.00	0.988419	0.494210	−	0.869343i	$-0.335457\pi$
$131$	1482.00	0.988419	0.494210	+	0.869343i	$0.335457\pi$
$132$	−468.000	−0.308592
$133$	810.000	0.528090
$134$	−1544.00	−0.995383
$135$	0	0
$136$	120.000	0.0756611
$137$	−666.000	−0.415330	−0.207665	−	0.978200i	$-0.566586\pi$
$137$	−666.000	−0.415330	−0.207665	+	0.978200i	$0.566586\pi$
$138$	−858.000	−0.529259
$139$	−1583.00	−0.965959	−0.482980	−	0.875632i	$-0.660445\pi$
$139$	−1583.00	−0.965959	−0.482980	+	0.875632i	$0.660445\pi$
$140$	0	0
$141$	702.000	0.419284
$142$	−1586.00	−0.937283
$143$	507.000	0.296486
$144$	144.000	0.0833333
$145$	0	0
$146$	1996.00	1.13144
$147$	354.000	0.198622
$148$	900.000	0.499862
$149$	2135.00	1.17387	0.586933	−	0.809636i	$-0.300335\pi$
$149$	2135.00	1.17387	0.586933	+	0.809636i	$0.300335\pi$
$150$	0	0
$151$	1832.00	0.987325	0.493662	−	0.869654i	$-0.335658\pi$
$151$	1832.00	0.987325	0.493662	+	0.869654i	$0.335658\pi$
$152$	432.000	0.230525
$153$	135.000	0.0713340
$154$	1170.00	0.612216
$155$	0	0
$156$	−156.000	−0.0800641
$157$	1766.00	0.897721	0.448860	−	0.893602i	$-0.351830\pi$
$157$	1766.00	0.897721	0.448860	+	0.893602i	$0.351830\pi$
$158$	−1362.00	−0.685791
$159$	99.0000	0.0493787
$160$	0	0
$161$	2145.00	1.05000
$162$	162.000	0.0785674
$163$	−3989.00	−1.91683	−0.958413	−	0.285385i	$-0.907878\pi$
$163$	−3989.00	−1.91683	−0.958413	+	0.285385i	$0.907878\pi$
$164$	1876.00	0.893238
$165$	0	0
$166$	1544.00	0.721914
$167$	2496.00	1.15656	0.578282	−	0.815837i	$-0.303723\pi$
$167$	2496.00	1.15656	0.578282	+	0.815837i	$0.303723\pi$
$168$	−360.000	−0.165325
$169$	169.000	0.0769231
$170$	0	0
$171$	486.000	0.217341
$172$	1936.00	0.858248
$173$	−566.000	−0.248741	−0.124370	−	0.992236i	$-0.539691\pi$
$173$	−566.000	−0.248741	−0.124370	+	0.992236i	$0.539691\pi$
$174$	732.000	0.318924
$175$	0	0
$176$	624.000	0.267249
$177$	0	0
$178$	−930.000	−0.391609
$179$	−3478.00	−1.45228	−0.726139	−	0.687547i	$-0.758687\pi$
$179$	−3478.00	−1.45228	−0.726139	+	0.687547i	$0.758687\pi$
$180$	0	0
$181$	2573.00	1.05663	0.528314	−	0.849049i	$-0.322824\pi$
$181$	2573.00	1.05663	0.528314	+	0.849049i	$0.322824\pi$
$182$	390.000	0.158839
$183$	2493.00	1.00704
$184$	1144.00	0.458352
$185$	0	0
$186$	1476.00	0.581858
$187$	585.000	0.228767
$188$	−936.000	−0.363111
$189$	−405.000	−0.155870
$190$	0	0
$191$	2592.00	0.981940	0.490970	−	0.871176i	$-0.336642\pi$
$191$	2592.00	0.981940	0.490970	+	0.871176i	$0.336642\pi$
$192$	−192.000	−0.0721688
$193$	2725.00	1.01632	0.508160	−	0.861263i	$-0.330326\pi$
$193$	2725.00	1.01632	0.508160	+	0.861263i	$0.330326\pi$
$194$	158.000	0.0584729
$195$	0	0
$196$	−472.000	−0.172012
$197$	−4564.00	−1.65062	−0.825308	−	0.564682i	$-0.808999\pi$
$197$	−4564.00	−1.65062	−0.825308	+	0.564682i	$0.808999\pi$
$198$	702.000	0.251964
$199$	4244.00	1.51180	0.755902	−	0.654684i	$-0.227198\pi$
$199$	4244.00	1.51180	0.755902	+	0.654684i	$0.227198\pi$
$200$	0	0
$201$	2316.00	0.812727
$202$	1296.00	0.451417
$203$	−1830.00	−0.632713
$204$	−180.000	−0.0617771
$205$	0	0
$206$	2280.00	0.771141
$207$	1287.00	0.432139
$208$	208.000	0.0693375
$209$	2106.00	0.697010
$210$	0	0
$211$	2244.00	0.732148	0.366074	−	0.930586i	$-0.380702\pi$
$211$	2244.00	0.732148	0.366074	+	0.930586i	$0.380702\pi$
$212$	−132.000	−0.0427632
$213$	2379.00	0.765288
$214$	−1826.00	−0.583284
$215$	0	0
$216$	−216.000	−0.0680414
$217$	−3690.00	−1.15435
$218$	2552.00	0.792859
$219$	−2994.00	−0.923816
$220$	0	0
$221$	195.000	0.0593535
$222$	−1350.00	−0.408135
$223$	272.000	0.0816792	0.0408396	−	0.999166i	$-0.486997\pi$
$223$	272.000	0.0816792	0.0408396	+	0.999166i	$0.486997\pi$
$224$	480.000	0.143176
$225$	0	0
$226$	428.000	0.125974
$227$	1190.00	0.347943	0.173972	−	0.984751i	$-0.444340\pi$
$227$	1190.00	0.347943	0.173972	+	0.984751i	$0.444340\pi$
$228$	−648.000	−0.188223
$229$	50.0000	0.0144284	0.00721418	−	0.999974i	$-0.497704\pi$
$229$	50.0000	0.0144284	0.00721418	+	0.999974i	$0.497704\pi$
$230$	0	0
$231$	−1755.00	−0.499872
$232$	−976.000	−0.276196
$233$	3141.00	0.883149	0.441575	−	0.897225i	$-0.354420\pi$
$233$	3141.00	0.883149	0.441575	+	0.897225i	$0.354420\pi$
$234$	234.000	0.0653720
$235$	0	0
$236$	0	0
$237$	2043.00	0.559946
$238$	450.000	0.122560
$239$	−2857.00	−0.773238	−0.386619	−	0.922239i	$-0.626357\pi$
$239$	−2857.00	−0.773238	−0.386619	+	0.922239i	$0.626357\pi$
$240$	0	0
$241$	−662.000	−0.176943	−0.0884713	−	0.996079i	$-0.528198\pi$
$241$	−662.000	−0.176943	−0.0884713	+	0.996079i	$0.528198\pi$
$242$	380.000	0.100939
$243$	−243.000	−0.0641500
$244$	−3324.00	−0.872120
$245$	0	0
$246$	−2814.00	−0.729326
$247$	702.000	0.180839
$248$	−1968.00	−0.503904
$249$	−2316.00	−0.589440
$250$	0	0
$251$	−512.000	−0.128754	−0.0643768	−	0.997926i	$-0.520506\pi$
$251$	−512.000	−0.128754	−0.0643768	+	0.997926i	$0.520506\pi$
$252$	540.000	0.134987
$253$	5577.00	1.38586
$254$	2148.00	0.530620
$255$	0	0
$256$	256.000	0.0625000
$257$	102.000	0.0247571	0.0123786	−	0.999923i	$-0.496060\pi$
$257$	102.000	0.0247571	0.0123786	+	0.999923i	$0.496060\pi$
$258$	−2904.00	−0.700756
$259$	3375.00	0.809700
$260$	0	0
$261$	−1098.00	−0.260400
$262$	2964.00	0.698918
$263$	−6448.00	−1.51179	−0.755895	−	0.654693i	$-0.772798\pi$
$263$	−6448.00	−1.51179	−0.755895	+	0.654693i	$0.772798\pi$
$264$	−936.000	−0.218208
$265$	0	0
$266$	1620.00	0.373416
$267$	1395.00	0.319748
$268$	−3088.00	−0.703842
$269$	3976.00	0.901193	0.450597	−	0.892728i	$-0.351211\pi$
$269$	3976.00	0.901193	0.450597	+	0.892728i	$0.351211\pi$
$270$	0	0
$271$	7494.00	1.67981	0.839904	−	0.542735i	$-0.182611\pi$
$271$	7494.00	1.67981	0.839904	+	0.542735i	$0.182611\pi$
$272$	240.000	0.0535005
$273$	−585.000	−0.129692
$274$	−1332.00	−0.293683
$275$	0	0
$276$	−1716.00	−0.374243
$277$	5062.00	1.09800	0.549000	−	0.835822i	$-0.315009\pi$
$277$	5062.00	1.09800	0.549000	+	0.835822i	$0.315009\pi$
$278$	−3166.00	−0.683036
$279$	−2214.00	−0.475085
$280$	0	0
$281$	−3990.00	−0.847059	−0.423529	−	0.905882i	$-0.639209\pi$
$281$	−3990.00	−0.847059	−0.423529	+	0.905882i	$0.639209\pi$
$282$	1404.00	0.296479
$283$	6468.00	1.35860	0.679298	−	0.733863i	$-0.262284\pi$
$283$	6468.00	1.35860	0.679298	+	0.733863i	$0.262284\pi$
$284$	−3172.00	−0.662759
$285$	0	0
$286$	1014.00	0.209647
$287$	7035.00	1.44691
$288$	288.000	0.0589256
$289$	−4688.00	−0.954203
$290$	0	0
$291$	−237.000	−0.0477429
$292$	3992.00	0.800048
$293$	4748.00	0.946693	0.473347	−	0.880876i	$-0.343046\pi$
$293$	4748.00	0.946693	0.473347	+	0.880876i	$0.343046\pi$
$294$	708.000	0.140447
$295$	0	0
$296$	1800.00	0.353456
$297$	−1053.00	−0.205728
$298$	4270.00	0.830049
$299$	1859.00	0.359561
$300$	0	0
$301$	7260.00	1.39023
$302$	3664.00	0.698144
$303$	−1944.00	−0.368580
$304$	864.000	0.163006
$305$	0	0
$306$	270.000	0.0504408
$307$	−2981.00	−0.554185	−0.277092	−	0.960843i	$-0.589371\pi$
$307$	−2981.00	−0.554185	−0.277092	+	0.960843i	$0.589371\pi$
$308$	2340.00	0.432902
$309$	−3420.00	−0.629634
$310$	0	0
$311$	2080.00	0.379248	0.189624	−	0.981857i	$-0.439273\pi$
$311$	2080.00	0.379248	0.189624	+	0.981857i	$0.439273\pi$
$312$	−312.000	−0.0566139
$313$	−5618.00	−1.01453	−0.507265	−	0.861790i	$-0.669344\pi$
$313$	−5618.00	−1.01453	−0.507265	+	0.861790i	$0.669344\pi$
$314$	3532.00	0.634784
$315$	0	0
$316$	−2724.00	−0.484927
$317$	8516.00	1.50885	0.754426	−	0.656385i	$-0.227915\pi$
$317$	8516.00	1.50885	0.754426	+	0.656385i	$0.227915\pi$
$318$	198.000	0.0349160
$319$	−4758.00	−0.835100
$320$	0	0
$321$	2739.00	0.476249
$322$	4290.00	0.742461
$323$	810.000	0.139534
$324$	324.000	0.0555556
$325$	0	0
$326$	−7978.00	−1.35540
$327$	−3828.00	−0.647367
$328$	3752.00	0.631614
$329$	−3510.00	−0.588184
$330$	0	0
$331$	11324.0	1.88043	0.940217	−	0.340577i	$-0.110623\pi$
$331$	11324.0	1.88043	0.940217	+	0.340577i	$0.110623\pi$
$332$	3088.00	0.510470
$333$	2025.00	0.333241
$334$	4992.00	0.817815
$335$	0	0
$336$	−720.000	−0.116902
$337$	1716.00	0.277378	0.138689	−	0.990336i	$-0.455711\pi$
$337$	1716.00	0.277378	0.138689	+	0.990336i	$0.455711\pi$
$338$	338.000	0.0543928
$339$	−642.000	−0.102857
$340$	0	0
$341$	−9594.00	−1.52359
$342$	972.000	0.153683
$343$	−6915.00	−1.08856
$344$	3872.00	0.606873
$345$	0	0
$346$	−1132.00	−0.175886
$347$	−8181.00	−1.26565	−0.632823	−	0.774297i	$-0.718104\pi$
$347$	−8181.00	−1.26565	−0.632823	+	0.774297i	$0.718104\pi$
$348$	1464.00	0.225513
$349$	−11108.0	−1.70372	−0.851859	−	0.523771i	$-0.824525\pi$
$349$	−11108.0	−1.70372	−0.851859	+	0.523771i	$0.824525\pi$
$350$	0	0
$351$	−351.000	−0.0533761
$352$	1248.00	0.188973
$353$	4330.00	0.652869	0.326434	−	0.945220i	$-0.394153\pi$
$353$	4330.00	0.652869	0.326434	+	0.945220i	$0.394153\pi$
$354$	0	0
$355$	0	0
$356$	−1860.00	−0.276910
$357$	−675.000	−0.100069
$358$	−6956.00	−1.02692
$359$	−1128.00	−0.165832	−0.0829158	−	0.996557i	$-0.526423\pi$
$359$	−1128.00	−0.165832	−0.0829158	+	0.996557i	$0.526423\pi$
$360$	0	0
$361$	−3943.00	−0.574865
$362$	5146.00	0.747148
$363$	−570.000	−0.0824166
$364$	780.000	0.112316
$365$	0	0
$366$	4986.00	0.712083
$367$	1072.00	0.152474	0.0762370	−	0.997090i	$-0.475709\pi$
$367$	1072.00	0.152474	0.0762370	+	0.997090i	$0.475709\pi$
$368$	2288.00	0.324104
$369$	4221.00	0.595492
$370$	0	0
$371$	−495.000	−0.0692699
$372$	2952.00	0.411436
$373$	−10660.0	−1.47977	−0.739885	−	0.672734i	$-0.765120\pi$
$373$	−10660.0	−1.47977	−0.739885	+	0.672734i	$0.765120\pi$
$374$	1170.00	0.161763
$375$	0	0
$376$	−1872.00	−0.256758
$377$	−1586.00	−0.216666
$378$	−810.000	−0.110217
$379$	6258.00	0.848158	0.424079	−	0.905625i	$-0.360598\pi$
$379$	6258.00	0.848158	0.424079	+	0.905625i	$0.360598\pi$
$380$	0	0
$381$	−3222.00	−0.433250
$382$	5184.00	0.694336
$383$	3250.00	0.433596	0.216798	−	0.976216i	$-0.430439\pi$
$383$	3250.00	0.433596	0.216798	+	0.976216i	$0.430439\pi$
$384$	−384.000	−0.0510310
$385$	0	0
$386$	5450.00	0.718647
$387$	4356.00	0.572165
$388$	316.000	0.0413466
$389$	−6156.00	−0.802369	−0.401185	−	0.915997i	$-0.631401\pi$
$389$	−6156.00	−0.802369	−0.401185	+	0.915997i	$0.631401\pi$
$390$	0	0
$391$	2145.00	0.277436
$392$	−944.000	−0.121631
$393$	−4446.00	−0.570664
$394$	−9128.00	−1.16716
$395$	0	0
$396$	1404.00	0.178166
$397$	−6151.00	−0.777607	−0.388803	−	0.921321i	$-0.627111\pi$
$397$	−6151.00	−0.777607	−0.388803	+	0.921321i	$0.627111\pi$
$398$	8488.00	1.06901
$399$	−2430.00	−0.304893
$400$	0	0
$401$	−8646.00	−1.07671	−0.538355	−	0.842718i	$-0.680954\pi$
$401$	−8646.00	−1.07671	−0.538355	+	0.842718i	$0.680954\pi$
$402$	4632.00	0.574684
$403$	−3198.00	−0.395295
$404$	2592.00	0.319200
$405$	0	0
$406$	−3660.00	−0.447396
$407$	8775.00	1.06870
$408$	−360.000	−0.0436830
$409$	−910.000	−0.110016	−0.0550081	−	0.998486i	$-0.517518\pi$
$409$	−910.000	−0.110016	−0.0550081	+	0.998486i	$0.517518\pi$
$410$	0	0
$411$	1998.00	0.239791
$412$	4560.00	0.545279
$413$	0	0
$414$	2574.00	0.305568
$415$	0	0
$416$	416.000	0.0490290
$417$	4749.00	0.557697
$418$	4212.00	0.492860
$419$	8502.00	0.991288	0.495644	−	0.868526i	$-0.334932\pi$
$419$	8502.00	0.991288	0.495644	+	0.868526i	$0.334932\pi$
$420$	0	0
$421$	−3508.00	−0.406103	−0.203052	−	0.979168i	$-0.565086\pi$
$421$	−3508.00	−0.406103	−0.203052	+	0.979168i	$0.565086\pi$
$422$	4488.00	0.517707
$423$	−2106.00	−0.242074
$424$	−264.000	−0.0302381
$425$	0	0
$426$	4758.00	0.541141
$427$	−12465.0	−1.41270
$428$	−3652.00	−0.412444
$429$	−1521.00	−0.171176
$430$	0	0
$431$	8112.00	0.906592	0.453296	−	0.891360i	$-0.350248\pi$
$431$	8112.00	0.906592	0.453296	+	0.891360i	$0.350248\pi$
$432$	−432.000	−0.0481125
$433$	−728.000	−0.0807978	−0.0403989	−	0.999184i	$-0.512863\pi$
$433$	−728.000	−0.0807978	−0.0403989	+	0.999184i	$0.512863\pi$
$434$	−7380.00	−0.816247
$435$	0	0
$436$	5104.00	0.560636
$437$	7722.00	0.845294
$438$	−5988.00	−0.653237
$439$	−531.000	−0.0577295	−0.0288647	−	0.999583i	$-0.509189\pi$
$439$	−531.000	−0.0577295	−0.0288647	+	0.999583i	$0.509189\pi$
$440$	0	0
$441$	−1062.00	−0.114674
$442$	390.000	0.0419692
$443$	−13441.0	−1.44154	−0.720769	−	0.693176i	$-0.756211\pi$
$443$	−13441.0	−1.44154	−0.720769	+	0.693176i	$0.756211\pi$
$444$	−2700.00	−0.288595
$445$	0	0
$446$	544.000	0.0577559
$447$	−6405.00	−0.677732
$448$	960.000	0.101240
$449$	6029.00	0.633688	0.316844	−	0.948478i	$-0.397377\pi$
$449$	6029.00	0.633688	0.316844	+	0.948478i	$0.397377\pi$
$450$	0	0
$451$	18291.0	1.90973
$452$	856.000	0.0890771
$453$	−5496.00	−0.570032
$454$	2380.00	0.246033
$455$	0	0
$456$	−1296.00	−0.133094
$457$	12051.0	1.23353	0.616764	−	0.787148i	$-0.288443\pi$
$457$	12051.0	1.23353	0.616764	+	0.787148i	$0.288443\pi$
$458$	100.000	0.0102024
$459$	−405.000	−0.0411847
$460$	0	0
$461$	−10099.0	−1.02030	−0.510149	−	0.860086i	$-0.670410\pi$
$461$	−10099.0	−1.02030	−0.510149	+	0.860086i	$0.670410\pi$
$462$	−3510.00	−0.353463
$463$	12447.0	1.24938	0.624688	−	0.780874i	$-0.285226\pi$
$463$	12447.0	1.24938	0.624688	+	0.780874i	$0.285226\pi$
$464$	−1952.00	−0.195300
$465$	0	0
$466$	6282.00	0.624481
$467$	2135.00	0.211555	0.105777	−	0.994390i	$-0.466267\pi$
$467$	2135.00	0.211555	0.105777	+	0.994390i	$0.466267\pi$
$468$	468.000	0.0462250
$469$	−11580.0	−1.14012
$470$	0	0
$471$	−5298.00	−0.518299
$472$	0	0
$473$	18876.0	1.83492
$474$	4086.00	0.395941
$475$	0	0
$476$	900.000	0.0866627
$477$	−297.000	−0.0285088
$478$	−5714.00	−0.546762
$479$	6405.00	0.610964	0.305482	−	0.952198i	$-0.401182\pi$
$479$	6405.00	0.610964	0.305482	+	0.952198i	$0.401182\pi$
$480$	0	0
$481$	2925.00	0.277273
$482$	−1324.00	−0.125117
$483$	−6435.00	−0.606217
$484$	760.000	0.0713749
$485$	0	0
$486$	−486.000	−0.0453609
$487$	−7619.00	−0.708932	−0.354466	−	0.935069i	$-0.615337\pi$
$487$	−7619.00	−0.708932	−0.354466	+	0.935069i	$0.615337\pi$
$488$	−6648.00	−0.616682
$489$	11967.0	1.10668
$490$	0	0
$491$	−9692.00	−0.890822	−0.445411	−	0.895326i	$-0.646943\pi$
$491$	−9692.00	−0.890822	−0.445411	+	0.895326i	$0.646943\pi$
$492$	−5628.00	−0.515711
$493$	−1830.00	−0.167179
$494$	1404.00	0.127872
$495$	0	0
$496$	−3936.00	−0.356314
$497$	−11895.0	−1.07357
$498$	−4632.00	−0.416797
$499$	−12994.0	−1.16571	−0.582857	−	0.812575i	$-0.698065\pi$
$499$	−12994.0	−1.16571	−0.582857	+	0.812575i	$0.698065\pi$
$500$	0	0
$501$	−7488.00	−0.667743
$502$	−1024.00	−0.0910425
$503$	−12228.0	−1.08394	−0.541968	−	0.840399i	$-0.682321\pi$
$503$	−12228.0	−1.08394	−0.541968	+	0.840399i	$0.682321\pi$
$504$	1080.00	0.0954504
$505$	0	0
$506$	11154.0	0.979952
$507$	−507.000	−0.0444116
$508$	4296.00	0.375205
$509$	7931.00	0.690639	0.345320	−	0.938485i	$-0.387771\pi$
$509$	7931.00	0.690639	0.345320	+	0.938485i	$0.387771\pi$
$510$	0	0
$511$	14970.0	1.29596
$512$	512.000	0.0441942
$513$	−1458.00	−0.125482
$514$	204.000	0.0175059
$515$	0	0
$516$	−5808.00	−0.495510
$517$	−9126.00	−0.776327
$518$	6750.00	0.572544
$519$	1698.00	0.143611
$520$	0	0
$521$	−7210.00	−0.606288	−0.303144	−	0.952945i	$-0.598036\pi$
$521$	−7210.00	−0.606288	−0.303144	+	0.952945i	$0.598036\pi$
$522$	−2196.00	−0.184131
$523$	19700.0	1.64708	0.823538	−	0.567261i	$-0.191997\pi$
$523$	19700.0	1.64708	0.823538	+	0.567261i	$0.191997\pi$
$524$	5928.00	0.494210
$525$	0	0
$526$	−12896.0	−1.06900
$527$	−3690.00	−0.305007
$528$	−1872.00	−0.154296
$529$	8282.00	0.680694
$530$	0	0
$531$	0	0
$532$	3240.00	0.264045
$533$	6097.00	0.495479
$534$	2790.00	0.226096
$535$	0	0
$536$	−6176.00	−0.497691
$537$	10434.0	0.838474
$538$	7952.00	0.637240
$539$	−4602.00	−0.367759
$540$	0	0
$541$	7694.00	0.611443	0.305722	−	0.952121i	$-0.401102\pi$
$541$	7694.00	0.611443	0.305722	+	0.952121i	$0.401102\pi$
$542$	14988.0	1.18780
$543$	−7719.00	−0.610044
$544$	480.000	0.0378306
$545$	0	0
$546$	−1170.00	−0.0917058
$547$	−76.0000	−0.00594063	−0.00297032	−	0.999996i	$-0.500945\pi$
$547$	−76.0000	−0.00594063	−0.00297032	+	0.999996i	$0.500945\pi$
$548$	−2664.00	−0.207665
$549$	−7479.00	−0.581413
$550$	0	0
$551$	−6588.00	−0.509362
$552$	−3432.00	−0.264630
$553$	−10215.0	−0.785508
$554$	10124.0	0.776404
$555$	0	0
$556$	−6332.00	−0.482980
$557$	−1914.00	−0.145599	−0.0727996	−	0.997347i	$-0.523193\pi$
$557$	−1914.00	−0.145599	−0.0727996	+	0.997347i	$0.523193\pi$
$558$	−4428.00	−0.335936
$559$	6292.00	0.476070
$560$	0	0
$561$	−1755.00	−0.132079
$562$	−7980.00	−0.598961
$563$	21563.0	1.61416	0.807080	−	0.590442i	$-0.201047\pi$
$563$	21563.0	1.61416	0.807080	+	0.590442i	$0.201047\pi$
$564$	2808.00	0.209642
$565$	0	0
$566$	12936.0	0.960673
$567$	1215.00	0.0899915
$568$	−6344.00	−0.468641
$569$	−22752.0	−1.67630	−0.838149	−	0.545441i	$-0.816362\pi$
$569$	−22752.0	−1.67630	−0.838149	+	0.545441i	$0.816362\pi$
$570$	0	0
$571$	−25201.0	−1.84699	−0.923493	−	0.383615i	$-0.874679\pi$
$571$	−25201.0	−1.84699	−0.923493	+	0.383615i	$0.874679\pi$
$572$	2028.00	0.148243
$573$	−7776.00	−0.566923
$574$	14070.0	1.02312
$575$	0	0
$576$	576.000	0.0416667
$577$	−8629.00	−0.622582	−0.311291	−	0.950315i	$-0.600761\pi$
$577$	−8629.00	−0.622582	−0.311291	+	0.950315i	$0.600761\pi$
$578$	−9376.00	−0.674724
$579$	−8175.00	−0.586773
$580$	0	0
$581$	11580.0	0.826884
$582$	−474.000	−0.0337593
$583$	−1287.00	−0.0914273
$584$	7984.00	0.565720
$585$	0	0
$586$	9496.00	0.669413
$587$	−7074.00	−0.497402	−0.248701	−	0.968580i	$-0.580004\pi$
$587$	−7074.00	−0.497402	−0.248701	+	0.968580i	$0.580004\pi$
$588$	1416.00	0.0993110
$589$	−13284.0	−0.929300
$590$	0	0
$591$	13692.0	0.952984
$592$	3600.00	0.249931
$593$	−3672.00	−0.254285	−0.127142	−	0.991884i	$-0.540581\pi$
$593$	−3672.00	−0.254285	−0.127142	+	0.991884i	$0.540581\pi$
$594$	−2106.00	−0.145472
$595$	0	0
$596$	8540.00	0.586933
$597$	−12732.0	−0.872841
$598$	3718.00	0.254248
$599$	−24516.0	−1.67228	−0.836141	−	0.548515i	$-0.815193\pi$
$599$	−24516.0	−1.67228	−0.836141	+	0.548515i	$0.815193\pi$
$600$	0	0
$601$	−18045.0	−1.22474	−0.612372	−	0.790570i	$-0.709784\pi$
$601$	−18045.0	−1.22474	−0.612372	+	0.790570i	$0.709784\pi$
$602$	14520.0	0.983042
$603$	−6948.00	−0.469228
$604$	7328.00	0.493662
$605$	0	0
$606$	−3888.00	−0.260626
$607$	−25236.0	−1.68748	−0.843738	−	0.536756i	$-0.819650\pi$
$607$	−25236.0	−1.68748	−0.843738	+	0.536756i	$0.819650\pi$
$608$	1728.00	0.115263
$609$	5490.00	0.365297
$610$	0	0
$611$	−3042.00	−0.201418
$612$	540.000	0.0356670
$613$	26191.0	1.72568	0.862842	−	0.505473i	$-0.168682\pi$
$613$	26191.0	1.72568	0.862842	+	0.505473i	$0.168682\pi$
$614$	−5962.00	−0.391868
$615$	0	0
$616$	4680.00	0.306108
$617$	−18666.0	−1.21793	−0.608967	−	0.793196i	$-0.708416\pi$
$617$	−18666.0	−1.21793	−0.608967	+	0.793196i	$0.708416\pi$
$618$	−6840.00	−0.445219
$619$	3082.00	0.200123	0.100061	−	0.994981i	$-0.468096\pi$
$619$	3082.00	0.200123	0.100061	+	0.994981i	$0.468096\pi$
$620$	0	0
$621$	−3861.00	−0.249495
$622$	4160.00	0.268168
$623$	−6975.00	−0.448551
$624$	−624.000	−0.0400320
$625$	0	0
$626$	−11236.0	−0.717382
$627$	−6318.00	−0.402419
$628$	7064.00	0.448860
$629$	3375.00	0.213943
$630$	0	0
$631$	7452.00	0.470142	0.235071	−	0.971978i	$-0.424468\pi$
$631$	7452.00	0.470142	0.235071	+	0.971978i	$0.424468\pi$
$632$	−5448.00	−0.342895
$633$	−6732.00	−0.422706
$634$	17032.0	1.06692
$635$	0	0
$636$	396.000	0.0246893
$637$	−1534.00	−0.0954149
$638$	−9516.00	−0.590505
$639$	−7137.00	−0.441839
$640$	0	0
$641$	4768.00	0.293798	0.146899	−	0.989151i	$-0.453071\pi$
$641$	4768.00	0.293798	0.146899	+	0.989151i	$0.453071\pi$
$642$	5478.00	0.336759
$643$	−10753.0	−0.659498	−0.329749	−	0.944069i	$-0.606964\pi$
$643$	−10753.0	−0.659498	−0.329749	+	0.944069i	$0.606964\pi$
$644$	8580.00	0.524999
$645$	0	0
$646$	1620.00	0.0986657
$647$	−5427.00	−0.329764	−0.164882	−	0.986313i	$-0.552724\pi$
$647$	−5427.00	−0.329764	−0.164882	+	0.986313i	$0.552724\pi$
$648$	648.000	0.0392837
$649$	0	0
$650$	0	0
$651$	11070.0	0.666463
$652$	−15956.0	−0.958413
$653$	5718.00	0.342669	0.171334	−	0.985213i	$-0.445192\pi$
$653$	5718.00	0.342669	0.171334	+	0.985213i	$0.445192\pi$
$654$	−7656.00	−0.457757
$655$	0	0
$656$	7504.00	0.446619
$657$	8982.00	0.533366
$658$	−7020.00	−0.415909
$659$	−17248.0	−1.01955	−0.509777	−	0.860306i	$-0.670272\pi$
$659$	−17248.0	−1.01955	−0.509777	+	0.860306i	$0.670272\pi$
$660$	0	0
$661$	14532.0	0.855112	0.427556	−	0.903989i	$-0.359375\pi$
$661$	14532.0	0.855112	0.427556	+	0.903989i	$0.359375\pi$
$662$	22648.0	1.32967
$663$	−585.000	−0.0342677
$664$	6176.00	0.360957
$665$	0	0
$666$	4050.00	0.235637
$667$	−17446.0	−1.01276
$668$	9984.00	0.578282
$669$	−816.000	−0.0471575
$670$	0	0
$671$	−32409.0	−1.86458
$672$	−1440.00	−0.0826625
$673$	−3198.00	−0.183171	−0.0915853	−	0.995797i	$-0.529193\pi$
$673$	−3198.00	−0.183171	−0.0915853	+	0.995797i	$0.529193\pi$
$674$	3432.00	0.196136
$675$	0	0
$676$	676.000	0.0384615
$677$	3711.00	0.210673	0.105336	−	0.994437i	$-0.466408\pi$
$677$	3711.00	0.210673	0.105336	+	0.994437i	$0.466408\pi$
$678$	−1284.00	−0.0727312
$679$	1185.00	0.0669751
$680$	0	0
$681$	−3570.00	−0.200885
$682$	−19188.0	−1.07734
$683$	4764.00	0.266895	0.133448	−	0.991056i	$-0.457395\pi$
$683$	4764.00	0.266895	0.133448	+	0.991056i	$0.457395\pi$
$684$	1944.00	0.108671
$685$	0	0
$686$	−13830.0	−0.769726
$687$	−150.000	−0.00833021
$688$	7744.00	0.429124
$689$	−429.000	−0.0237208
$690$	0	0
$691$	23462.0	1.29166	0.645830	−	0.763482i	$-0.276512\pi$
$691$	23462.0	1.29166	0.645830	+	0.763482i	$0.276512\pi$
$692$	−2264.00	−0.124370
$693$	5265.00	0.288601
$694$	−16362.0	−0.894947
$695$	0	0
$696$	2928.00	0.159462
$697$	7035.00	0.382309
$698$	−22216.0	−1.20471
$699$	−9423.00	−0.509886
$700$	0	0
$701$	−4908.00	−0.264440	−0.132220	−	0.991220i	$-0.542211\pi$
$701$	−4908.00	−0.264440	−0.132220	+	0.991220i	$0.542211\pi$
$702$	−702.000	−0.0377426
$703$	12150.0	0.651843
$704$	2496.00	0.133624
$705$	0	0
$706$	8660.00	0.461648
$707$	9720.00	0.517055
$708$	0	0
$709$	−1996.00	−0.105728	−0.0528641	−	0.998602i	$-0.516835\pi$
$709$	−1996.00	−0.105728	−0.0528641	+	0.998602i	$0.516835\pi$
$710$	0	0
$711$	−6129.00	−0.323285
$712$	−3720.00	−0.195805
$713$	−35178.0	−1.84772
$714$	−1350.00	−0.0707598
$715$	0	0
$716$	−13912.0	−0.726139
$717$	8571.00	0.446429
$718$	−2256.00	−0.117261
$719$	10296.0	0.534042	0.267021	−	0.963691i	$-0.413961\pi$
$719$	10296.0	0.534042	0.267021	+	0.963691i	$0.413961\pi$
$720$	0	0
$721$	17100.0	0.883269
$722$	−7886.00	−0.406491
$723$	1986.00	0.102158
$724$	10292.0	0.528314
$725$	0	0
$726$	−1140.00	−0.0582774
$727$	−3954.00	−0.201714	−0.100857	−	0.994901i	$-0.532158\pi$
$727$	−3954.00	−0.201714	−0.100857	+	0.994901i	$0.532158\pi$
$728$	1560.00	0.0794196
$729$	729.000	0.0370370
$730$	0	0
$731$	7260.00	0.367334
$732$	9972.00	0.503519
$733$	25837.0	1.30193	0.650963	−	0.759110i	$-0.274365\pi$
$733$	25837.0	1.30193	0.650963	+	0.759110i	$0.274365\pi$
$734$	2144.00	0.107815
$735$	0	0
$736$	4576.00	0.229176
$737$	−30108.0	−1.50481
$738$	8442.00	0.421076
$739$	−1378.00	−0.0685934	−0.0342967	−	0.999412i	$-0.510919\pi$
$739$	−1378.00	−0.0685934	−0.0342967	+	0.999412i	$0.510919\pi$
$740$	0	0
$741$	−2106.00	−0.104407
$742$	−990.000	−0.0489812
$743$	−7674.00	−0.378912	−0.189456	−	0.981889i	$-0.560672\pi$
$743$	−7674.00	−0.378912	−0.189456	+	0.981889i	$0.560672\pi$
$744$	5904.00	0.290929
$745$	0	0
$746$	−21320.0	−1.04635
$747$	6948.00	0.340313
$748$	2340.00	0.114384
$749$	−13695.0	−0.668097
$750$	0	0
$751$	11937.0	0.580010	0.290005	−	0.957025i	$-0.406343\pi$
$751$	11937.0	0.580010	0.290005	+	0.957025i	$0.406343\pi$
$752$	−3744.00	−0.181555
$753$	1536.00	0.0743359
$754$	−3172.00	−0.153206
$755$	0	0
$756$	−1620.00	−0.0779350
$757$	−3620.00	−0.173806	−0.0869030	−	0.996217i	$-0.527697\pi$
$757$	−3620.00	−0.173806	−0.0869030	+	0.996217i	$0.527697\pi$
$758$	12516.0	0.599738
$759$	−16731.0	−0.800128
$760$	0	0
$761$	−36170.0	−1.72295	−0.861473	−	0.507804i	$-0.830457\pi$
$761$	−36170.0	−1.72295	−0.861473	+	0.507804i	$0.830457\pi$
$762$	−6444.00	−0.306354
$763$	19140.0	0.908145
$764$	10368.0	0.490970
$765$	0	0
$766$	6500.00	0.306599
$767$	0	0
$768$	−768.000	−0.0360844
$769$	−17936.0	−0.841078	−0.420539	−	0.907275i	$-0.638159\pi$
$769$	−17936.0	−0.841078	−0.420539	+	0.907275i	$0.638159\pi$
$770$	0	0
$771$	−306.000	−0.0142935
$772$	10900.0	0.508160
$773$	−21364.0	−0.994062	−0.497031	−	0.867733i	$-0.665576\pi$
$773$	−21364.0	−0.994062	−0.497031	+	0.867733i	$0.665576\pi$
$774$	8712.00	0.404582
$775$	0	0
$776$	632.000	0.0292364
$777$	−10125.0	−0.467481
$778$	−12312.0	−0.567361
$779$	25326.0	1.16482
$780$	0	0
$781$	−30927.0	−1.41697
$782$	4290.00	0.196177
$783$	3294.00	0.150342
$784$	−1888.00	−0.0860058
$785$	0	0
$786$	−8892.00	−0.403521
$787$	−32004.0	−1.44958	−0.724790	−	0.688970i	$-0.758063\pi$
$787$	−32004.0	−1.44958	−0.724790	+	0.688970i	$0.758063\pi$
$788$	−18256.0	−0.825308
$789$	19344.0	0.872832
$790$	0	0
$791$	3210.00	0.144291
$792$	2808.00	0.125982
$793$	−10803.0	−0.483765
$794$	−12302.0	−0.549851
$795$	0	0
$796$	16976.0	0.755902
$797$	9909.00	0.440395	0.220197	−	0.975455i	$-0.429330\pi$
$797$	9909.00	0.440395	0.220197	+	0.975455i	$0.429330\pi$
$798$	−4860.00	−0.215592
$799$	−3510.00	−0.155413
$800$	0	0
$801$	−4185.00	−0.184606
$802$	−17292.0	−0.761349
$803$	38922.0	1.71050
$804$	9264.00	0.406363
$805$	0	0
$806$	−6396.00	−0.279515
$807$	−11928.0	−0.520304
$808$	5184.00	0.225709
$809$	−20546.0	−0.892903	−0.446452	−	0.894808i	$-0.647313\pi$
$809$	−20546.0	−0.892903	−0.446452	+	0.894808i	$0.647313\pi$
$810$	0	0
$811$	−19468.0	−0.842927	−0.421464	−	0.906845i	$-0.638483\pi$
$811$	−19468.0	−0.842927	−0.421464	+	0.906845i	$0.638483\pi$
$812$	−7320.00	−0.316357
$813$	−22482.0	−0.969838
$814$	17550.0	0.755684
$815$	0	0
$816$	−720.000	−0.0308885
$817$	26136.0	1.11920
$818$	−1820.00	−0.0777932
$819$	1755.00	0.0748775
$820$	0	0
$821$	−38951.0	−1.65578	−0.827892	−	0.560887i	$-0.810460\pi$
$821$	−38951.0	−1.65578	−0.827892	+	0.560887i	$0.810460\pi$
$822$	3996.00	0.169558
$823$	39908.0	1.69029	0.845143	−	0.534540i	$-0.179515\pi$
$823$	39908.0	1.69029	0.845143	+	0.534540i	$0.179515\pi$
$824$	9120.00	0.385571
$825$	0	0
$826$	0	0
$827$	3570.00	0.150110	0.0750551	−	0.997179i	$-0.476087\pi$
$827$	3570.00	0.150110	0.0750551	+	0.997179i	$0.476087\pi$
$828$	5148.00	0.216069
$829$	−22266.0	−0.932847	−0.466423	−	0.884562i	$-0.654458\pi$
$829$	−22266.0	−0.932847	−0.466423	+	0.884562i	$0.654458\pi$
$830$	0	0
$831$	−15186.0	−0.633931
$832$	832.000	0.0346688
$833$	−1770.00	−0.0736217
$834$	9498.00	0.394351
$835$	0	0
$836$	8424.00	0.348505
$837$	6642.00	0.274290
$838$	17004.0	0.700947
$839$	36711.0	1.51061	0.755307	−	0.655372i	$-0.227488\pi$
$839$	36711.0	1.51061	0.755307	+	0.655372i	$0.227488\pi$
$840$	0	0
$841$	−9505.00	−0.389725
$842$	−7016.00	−0.287158
$843$	11970.0	0.489049
$844$	8976.00	0.366074
$845$	0	0
$846$	−4212.00	−0.171172
$847$	2850.00	0.115616
$848$	−528.000	−0.0213816
$849$	−19404.0	−0.784386
$850$	0	0
$851$	32175.0	1.29606
$852$	9516.00	0.382644
$853$	33167.0	1.33132	0.665660	−	0.746255i	$-0.268150\pi$
$853$	33167.0	1.33132	0.665660	+	0.746255i	$0.268150\pi$
$854$	−24930.0	−0.998931
$855$	0	0
$856$	−7304.00	−0.291642
$857$	−10379.0	−0.413699	−0.206849	−	0.978373i	$-0.566321\pi$
$857$	−10379.0	−0.413699	−0.206849	+	0.978373i	$0.566321\pi$
$858$	−3042.00	−0.121040
$859$	5053.00	0.200706	0.100353	−	0.994952i	$-0.468003\pi$
$859$	5053.00	0.200706	0.100353	+	0.994952i	$0.468003\pi$
$860$	0	0
$861$	−21105.0	−0.835373
$862$	16224.0	0.641058
$863$	18054.0	0.712127	0.356063	−	0.934462i	$-0.384119\pi$
$863$	18054.0	0.712127	0.356063	+	0.934462i	$0.384119\pi$
$864$	−864.000	−0.0340207
$865$	0	0
$866$	−1456.00	−0.0571327
$867$	14064.0	0.550909
$868$	−14760.0	−0.577174
$869$	−26559.0	−1.03677
$870$	0	0
$871$	−10036.0	−0.390421
$872$	10208.0	0.396429
$873$	711.000	0.0275644
$874$	15444.0	0.597713
$875$	0	0
$876$	−11976.0	−0.461908
$877$	−32434.0	−1.24882	−0.624412	−	0.781095i	$-0.714661\pi$
$877$	−32434.0	−1.24882	−0.624412	+	0.781095i	$0.714661\pi$
$878$	−1062.00	−0.0408209
$879$	−14244.0	−0.546574
$880$	0	0
$881$	−35614.0	−1.36194	−0.680968	−	0.732313i	$-0.738441\pi$
$881$	−35614.0	−1.36194	−0.680968	+	0.732313i	$0.738441\pi$
$882$	−2124.00	−0.0810871
$883$	−11548.0	−0.440115	−0.220057	−	0.975487i	$-0.570624\pi$
$883$	−11548.0	−0.440115	−0.220057	+	0.975487i	$0.570624\pi$
$884$	780.000	0.0296767
$885$	0	0
$886$	−26882.0	−1.01932
$887$	−27807.0	−1.05261	−0.526306	−	0.850295i	$-0.676424\pi$
$887$	−27807.0	−1.05261	−0.526306	+	0.850295i	$0.676424\pi$
$888$	−5400.00	−0.204068
$889$	16110.0	0.607775
$890$	0	0
$891$	3159.00	0.118777
$892$	1088.00	0.0408396
$893$	−12636.0	−0.473514
$894$	−12810.0	−0.479229
$895$	0	0
$896$	1920.00	0.0715878
$897$	−5577.00	−0.207593
$898$	12058.0	0.448085
$899$	30012.0	1.11341
$900$	0	0
$901$	−495.000	−0.0183028
$902$	36582.0	1.35039
$903$	−21780.0	−0.802650
$904$	1712.00	0.0629870
$905$	0	0
$906$	−10992.0	−0.403074
$907$	19190.0	0.702529	0.351264	−	0.936276i	$-0.385752\pi$
$907$	19190.0	0.702529	0.351264	+	0.936276i	$0.385752\pi$
$908$	4760.00	0.173972
$909$	5832.00	0.212800
$910$	0	0
$911$	20024.0	0.728238	0.364119	−	0.931352i	$-0.381370\pi$
$911$	20024.0	0.728238	0.364119	+	0.931352i	$0.381370\pi$
$912$	−2592.00	−0.0941115
$913$	30108.0	1.09138
$914$	24102.0	0.872236
$915$	0	0
$916$	200.000	0.00721418
$917$	22230.0	0.800544
$918$	−810.000	−0.0291220
$919$	42119.0	1.51184	0.755918	−	0.654666i	$-0.227191\pi$
$919$	42119.0	1.51184	0.755918	+	0.654666i	$0.227191\pi$
$920$	0	0
$921$	8943.00	0.319959
$922$	−20198.0	−0.721460
$923$	−10309.0	−0.367633
$924$	−7020.00	−0.249936
$925$	0	0
$926$	24894.0	0.883442
$927$	10260.0	0.363520
$928$	−3904.00	−0.138098
$929$	34999.0	1.23604	0.618019	−	0.786163i	$-0.287935\pi$
$929$	34999.0	1.23604	0.618019	+	0.786163i	$0.287935\pi$
$930$	0	0
$931$	−6372.00	−0.224311
$932$	12564.0	0.441575
$933$	−6240.00	−0.218959
$934$	4270.00	0.149592
$935$	0	0
$936$	936.000	0.0326860
$937$	−16718.0	−0.582874	−0.291437	−	0.956590i	$-0.594133\pi$
$937$	−16718.0	−0.582874	−0.291437	+	0.956590i	$0.594133\pi$
$938$	−23160.0	−0.806184
$939$	16854.0	0.585740
$940$	0	0
$941$	−30889.0	−1.07009	−0.535044	−	0.844824i	$-0.679705\pi$
$941$	−30889.0	−1.07009	−0.535044	+	0.844824i	$0.679705\pi$
$942$	−10596.0	−0.366493
$943$	67067.0	2.31601
$944$	0	0
$945$	0	0
$946$	37752.0	1.29749
$947$	4908.00	0.168415	0.0842073	−	0.996448i	$-0.473164\pi$
$947$	4908.00	0.168415	0.0842073	+	0.996448i	$0.473164\pi$
$948$	8172.00	0.279973
$949$	12974.0	0.443787
$950$	0	0
$951$	−25548.0	−0.871136
$952$	1800.00	0.0612798
$953$	−11633.0	−0.395414	−0.197707	−	0.980261i	$-0.563350\pi$
$953$	−11633.0	−0.395414	−0.197707	+	0.980261i	$0.563350\pi$
$954$	−594.000	−0.0201588
$955$	0	0
$956$	−11428.0	−0.386619
$957$	14274.0	0.482145
$958$	12810.0	0.432017
$959$	−9990.00	−0.336386
$960$	0	0
$961$	30725.0	1.03135
$962$	5850.00	0.196062
$963$	−8217.00	−0.274963
$964$	−2648.00	−0.0884713
$965$	0	0
$966$	−12870.0	−0.428660
$967$	−7936.00	−0.263914	−0.131957	−	0.991255i	$-0.542126\pi$
$967$	−7936.00	−0.263914	−0.131957	+	0.991255i	$0.542126\pi$
$968$	1520.00	0.0504697
$969$	−2430.00	−0.0805602
$970$	0	0
$971$	−6960.00	−0.230028	−0.115014	−	0.993364i	$-0.536691\pi$
$971$	−6960.00	−0.230028	−0.115014	+	0.993364i	$0.536691\pi$
$972$	−972.000	−0.0320750
$973$	−23745.0	−0.782353
$974$	−15238.0	−0.501291
$975$	0	0
$976$	−13296.0	−0.436060
$977$	−35120.0	−1.15004	−0.575020	−	0.818140i	$-0.695006\pi$
$977$	−35120.0	−1.15004	−0.575020	+	0.818140i	$0.695006\pi$
$978$	23934.0	0.782541
$979$	−18135.0	−0.592030
$980$	0	0
$981$	11484.0	0.373757
$982$	−19384.0	−0.629907
$983$	−7244.00	−0.235043	−0.117522	−	0.993070i	$-0.537495\pi$
$983$	−7244.00	−0.235043	−0.117522	+	0.993070i	$0.537495\pi$
$984$	−11256.0	−0.364663
$985$	0	0
$986$	−3660.00	−0.118213
$987$	10530.0	0.339588
$988$	2808.00	0.0904194
$989$	69212.0	2.22529
$990$	0	0
$991$	16813.0	0.538933	0.269466	−	0.963010i	$-0.413153\pi$
$991$	16813.0	0.538933	0.269466	+	0.963010i	$0.413153\pi$
$992$	−7872.00	−0.251952
$993$	−33972.0	−1.08567
$994$	−23790.0	−0.759128
$995$	0	0
$996$	−9264.00	−0.294720
$997$	−34112.0	−1.08359	−0.541794	−	0.840511i	$-0.682255\pi$
$997$	−34112.0	−1.08359	−0.541794	+	0.840511i	$0.682255\pi$
$998$	−25988.0	−0.824284
$999$	−6075.00	−0.192397

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.4.a.n.1.1		1
5.4	even	2		390.4.a.c.1.1	✓	1
15.14	odd	2		1170.4.a.m.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.4.a.c.1.1	✓	1	5.4	even	2
1170.4.a.m.1.1		1	15.14	odd	2
1950.4.a.n.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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1950.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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