LMFDB - Embedded newform 350.4.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,4,Mod(1,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, 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("350.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	350.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:	$20.6506685020$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q-2.00000 q^{2} +4.00000 q^{3} +4.00000 q^{4} -8.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} -11.0000 q^{9} +5.00000 q^{11} +16.0000 q^{12} -82.0000 q^{13} -14.0000 q^{14} +16.0000 q^{16} +12.0000 q^{17} +22.0000 q^{18} -42.0000 q^{19} +28.0000 q^{21} -10.0000 q^{22} -175.000 q^{23} -32.0000 q^{24} +164.000 q^{26} -152.000 q^{27} +28.0000 q^{28} +1.00000 q^{29} +226.000 q^{31} -32.0000 q^{32} +20.0000 q^{33} -24.0000 q^{34} -44.0000 q^{36} +19.0000 q^{37} +84.0000 q^{38} -328.000 q^{39} +16.0000 q^{41} -56.0000 q^{42} -281.000 q^{43} +20.0000 q^{44} +350.000 q^{46} -334.000 q^{47} +64.0000 q^{48} +49.0000 q^{49} +48.0000 q^{51} -328.000 q^{52} +398.000 q^{53} +304.000 q^{54} -56.0000 q^{56} -168.000 q^{57} -2.00000 q^{58} +106.000 q^{59} +48.0000 q^{61} -452.000 q^{62} -77.0000 q^{63} +64.0000 q^{64} -40.0000 q^{66} -483.000 q^{67} +48.0000 q^{68} -700.000 q^{69} -15.0000 q^{71} +88.0000 q^{72} -1044.00 q^{73} -38.0000 q^{74} -168.000 q^{76} +35.0000 q^{77} +656.000 q^{78} -1253.00 q^{79} -311.000 q^{81} -32.0000 q^{82} -758.000 q^{83} +112.000 q^{84} +562.000 q^{86} +4.00000 q^{87} -40.0000 q^{88} +86.0000 q^{89} -574.000 q^{91} -700.000 q^{92} +904.000 q^{93} +668.000 q^{94} -128.000 q^{96} -710.000 q^{97} -98.0000 q^{98} -55.0000 q^{99} +O(q^{100})\)

Coefficient data

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

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

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

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	4.00000	0.769800	0.384900	−	0.922958i	$-0.374236\pi$
$3$	4.00000	0.769800	0.384900	+	0.922958i	$0.374236\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−8.00000	−0.544331
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	−11.0000	−0.407407
$10$	0	0
$11$	5.00000	0.137051	0.0685253	−	0.997649i	$-0.478171\pi$
$11$	5.00000	0.137051	0.0685253	+	0.997649i	$0.478171\pi$
$12$	16.0000	0.384900
$13$	−82.0000	−1.74944	−0.874720	−	0.484629i	$-0.838954\pi$
$13$	−82.0000	−1.74944	−0.874720	+	0.484629i	$0.838954\pi$
$14$	−14.0000	−0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	12.0000	0.171202	0.0856008	−	0.996330i	$-0.472719\pi$
$17$	12.0000	0.171202	0.0856008	+	0.996330i	$0.472719\pi$
$18$	22.0000	0.288081
$19$	−42.0000	−0.507130	−0.253565	−	0.967318i	$-0.581603\pi$
$19$	−42.0000	−0.507130	−0.253565	+	0.967318i	$0.581603\pi$
$20$	0	0
$21$	28.0000	0.290957
$22$	−10.0000	−0.0969094
$23$	−175.000	−1.58652	−0.793261	−	0.608881i	$-0.791619\pi$
$23$	−175.000	−1.58652	−0.793261	+	0.608881i	$0.791619\pi$
$24$	−32.0000	−0.272166
$25$	0	0
$26$	164.000	1.23704
$27$	−152.000	−1.08342
$28$	28.0000	0.188982
$29$	1.00000	0.00640329	0.00320164	−	0.999995i	$-0.498981\pi$
$29$	1.00000	0.00640329	0.00320164	+	0.999995i	$0.498981\pi$
$30$	0	0
$31$	226.000	1.30938	0.654690	−	0.755897i	$-0.272799\pi$
$31$	226.000	1.30938	0.654690	+	0.755897i	$0.272799\pi$
$32$	−32.0000	−0.176777
$33$	20.0000	0.105502
$34$	−24.0000	−0.121058
$35$	0	0
$36$	−44.0000	−0.203704
$37$	19.0000	0.0844211	0.0422106	−	0.999109i	$-0.486560\pi$
$37$	19.0000	0.0844211	0.0422106	+	0.999109i	$0.486560\pi$
$38$	84.0000	0.358595
$39$	−328.000	−1.34672
$40$	0	0
$41$	16.0000	0.0609459	0.0304729	−	0.999536i	$-0.490299\pi$
$41$	16.0000	0.0609459	0.0304729	+	0.999536i	$0.490299\pi$
$42$	−56.0000	−0.205738
$43$	−281.000	−0.996560	−0.498280	−	0.867016i	$-0.666035\pi$
$43$	−281.000	−0.996560	−0.498280	+	0.867016i	$0.666035\pi$
$44$	20.0000	0.0685253
$45$	0	0
$46$	350.000	1.12184
$47$	−334.000	−1.03657	−0.518286	−	0.855207i	$-0.673430\pi$
$47$	−334.000	−1.03657	−0.518286	+	0.855207i	$0.673430\pi$
$48$	64.0000	0.192450
$49$	49.0000	0.142857
$50$	0	0
$51$	48.0000	0.131791
$52$	−328.000	−0.874720
$53$	398.000	1.03150	0.515750	−	0.856739i	$-0.327513\pi$
$53$	398.000	1.03150	0.515750	+	0.856739i	$0.327513\pi$
$54$	304.000	0.766096
$55$	0	0
$56$	−56.0000	−0.133631
$57$	−168.000	−0.390388
$58$	−2.00000	−0.00452781
$59$	106.000	0.233899	0.116949	−	0.993138i	$-0.462688\pi$
$59$	106.000	0.233899	0.116949	+	0.993138i	$0.462688\pi$
$60$	0	0
$61$	48.0000	0.100750	0.0503752	−	0.998730i	$-0.483958\pi$
$61$	48.0000	0.100750	0.0503752	+	0.998730i	$0.483958\pi$
$62$	−452.000	−0.925872
$63$	−77.0000	−0.153986
$64$	64.0000	0.125000
$65$	0	0
$66$	−40.0000	−0.0746009
$67$	−483.000	−0.880714	−0.440357	−	0.897823i	$-0.645148\pi$
$67$	−483.000	−0.880714	−0.440357	+	0.897823i	$0.645148\pi$
$68$	48.0000	0.0856008
$69$	−700.000	−1.22131
$70$	0	0
$71$	−15.0000	−0.0250729	−0.0125364	−	0.999921i	$-0.503991\pi$
$71$	−15.0000	−0.0250729	−0.0125364	+	0.999921i	$0.503991\pi$
$72$	88.0000	0.144040
$73$	−1044.00	−1.67385	−0.836924	−	0.547319i	$-0.815649\pi$
$73$	−1044.00	−1.67385	−0.836924	+	0.547319i	$0.815649\pi$
$74$	−38.0000	−0.0596947
$75$	0	0
$76$	−168.000	−0.253565
$77$	35.0000	0.0518003
$78$	656.000	0.952274
$79$	−1253.00	−1.78447	−0.892237	−	0.451567i	$-0.850865\pi$
$79$	−1253.00	−1.78447	−0.892237	+	0.451567i	$0.850865\pi$
$80$	0	0
$81$	−311.000	−0.426612
$82$	−32.0000	−0.0430952
$83$	−758.000	−1.00243	−0.501213	−	0.865324i	$-0.667113\pi$
$83$	−758.000	−1.00243	−0.501213	+	0.865324i	$0.667113\pi$
$84$	112.000	0.145479
$85$	0	0
$86$	562.000	0.704675
$87$	4.00000	0.00492925
$88$	−40.0000	−0.0484547
$89$	86.0000	0.102427	0.0512134	−	0.998688i	$-0.483691\pi$
$89$	86.0000	0.102427	0.0512134	+	0.998688i	$0.483691\pi$
$90$	0	0
$91$	−574.000	−0.661226
$92$	−700.000	−0.793261
$93$	904.000	1.00796
$94$	668.000	0.732967
$95$	0	0
$96$	−128.000	−0.136083
$97$	−710.000	−0.743192	−0.371596	−	0.928395i	$-0.621189\pi$
$97$	−710.000	−0.743192	−0.371596	+	0.928395i	$0.621189\pi$
$98$	−98.0000	−0.101015
$99$	−55.0000	−0.0558354
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	−96.0000	−0.0931904
$103$	838.000	0.801656	0.400828	−	0.916153i	$-0.368722\pi$
$103$	838.000	0.801656	0.400828	+	0.916153i	$0.368722\pi$
$104$	656.000	0.618520
$105$	0	0
$106$	−796.000	−0.729381
$107$	2164.00	1.95516	0.977578	−	0.210572i	$-0.0675326\pi$
$107$	2164.00	1.95516	0.977578	+	0.210572i	$0.0675326\pi$
$108$	−608.000	−0.541711
$109$	−1827.00	−1.60546	−0.802729	−	0.596344i	$-0.796619\pi$
$109$	−1827.00	−1.60546	−0.802729	+	0.596344i	$0.796619\pi$
$110$	0	0
$111$	76.0000	0.0649874
$112$	112.000	0.0944911
$113$	93.0000	0.0774222	0.0387111	−	0.999250i	$-0.487675\pi$
$113$	93.0000	0.0774222	0.0387111	+	0.999250i	$0.487675\pi$
$114$	336.000	0.276046
$115$	0	0
$116$	4.00000	0.00320164
$117$	902.000	0.712734
$118$	−212.000	−0.165391
$119$	84.0000	0.0647081
$120$	0	0
$121$	−1306.00	−0.981217
$122$	−96.0000	−0.0712412
$123$	64.0000	0.0469161
$124$	904.000	0.654690
$125$	0	0
$126$	154.000	0.108884
$127$	1433.00	1.00125	0.500623	−	0.865666i	$-0.333104\pi$
$127$	1433.00	1.00125	0.500623	+	0.865666i	$0.333104\pi$
$128$	−128.000	−0.0883883
$129$	−1124.00	−0.767153
$130$	0	0
$131$	868.000	0.578912	0.289456	−	0.957191i	$-0.406526\pi$
$131$	868.000	0.578912	0.289456	+	0.957191i	$0.406526\pi$
$132$	80.0000	0.0527508
$133$	−294.000	−0.191677
$134$	966.000	0.622759
$135$	0	0
$136$	−96.0000	−0.0605289
$137$	2646.00	1.65010	0.825048	−	0.565063i	$-0.191148\pi$
$137$	2646.00	1.65010	0.825048	+	0.565063i	$0.191148\pi$
$138$	1400.00	0.863594
$139$	896.000	0.546746	0.273373	−	0.961908i	$-0.411861\pi$
$139$	896.000	0.546746	0.273373	+	0.961908i	$0.411861\pi$
$140$	0	0
$141$	−1336.00	−0.797954
$142$	30.0000	0.0177292
$143$	−410.000	−0.239762
$144$	−176.000	−0.101852
$145$	0	0
$146$	2088.00	1.18359
$147$	196.000	0.109971
$148$	76.0000	0.0422106
$149$	2523.00	1.38720	0.693598	−	0.720362i	$-0.256024\pi$
$149$	2523.00	1.38720	0.693598	+	0.720362i	$0.256024\pi$
$150$	0	0
$151$	2433.00	1.31122	0.655612	−	0.755098i	$-0.272411\pi$
$151$	2433.00	1.31122	0.655612	+	0.755098i	$0.272411\pi$
$152$	336.000	0.179297
$153$	−132.000	−0.0697488
$154$	−70.0000	−0.0366283
$155$	0	0
$156$	−1312.00	−0.673359
$157$	2572.00	1.30744	0.653720	−	0.756737i	$-0.273208\pi$
$157$	2572.00	1.30744	0.653720	+	0.756737i	$0.273208\pi$
$158$	2506.00	1.26181
$159$	1592.00	0.794049
$160$	0	0
$161$	−1225.00	−0.599649
$162$	622.000	0.301660
$163$	−2488.00	−1.19555	−0.597777	−	0.801663i	$-0.703949\pi$
$163$	−2488.00	−1.19555	−0.597777	+	0.801663i	$0.703949\pi$
$164$	64.0000	0.0304729
$165$	0	0
$166$	1516.00	0.708822
$167$	−3054.00	−1.41512	−0.707562	−	0.706652i	$-0.750205\pi$
$167$	−3054.00	−1.41512	−0.707562	+	0.706652i	$0.750205\pi$
$168$	−224.000	−0.102869
$169$	4527.00	2.06054
$170$	0	0
$171$	462.000	0.206608
$172$	−1124.00	−0.498280
$173$	3894.00	1.71130	0.855651	−	0.517553i	$-0.173157\pi$
$173$	3894.00	1.71130	0.855651	+	0.517553i	$0.173157\pi$
$174$	−8.00000	−0.00348551
$175$	0	0
$176$	80.0000	0.0342627
$177$	424.000	0.180055
$178$	−172.000	−0.0724267
$179$	−1108.00	−0.462658	−0.231329	−	0.972876i	$-0.574307\pi$
$179$	−1108.00	−0.462658	−0.231329	+	0.972876i	$0.574307\pi$
$180$	0	0
$181$	−1920.00	−0.788467	−0.394233	−	0.919010i	$-0.628990\pi$
$181$	−1920.00	−0.788467	−0.394233	+	0.919010i	$0.628990\pi$
$182$	1148.00	0.467557
$183$	192.000	0.0775576
$184$	1400.00	0.560920
$185$	0	0
$186$	−1808.00	−0.712737
$187$	60.0000	0.0234633
$188$	−1336.00	−0.518286
$189$	−1064.00	−0.409495
$190$	0	0
$191$	−936.000	−0.354589	−0.177295	−	0.984158i	$-0.556735\pi$
$191$	−936.000	−0.354589	−0.177295	+	0.984158i	$0.556735\pi$
$192$	256.000	0.0962250
$193$	−3163.00	−1.17968	−0.589839	−	0.807521i	$-0.700809\pi$
$193$	−3163.00	−1.17968	−0.589839	+	0.807521i	$0.700809\pi$
$194$	1420.00	0.525516
$195$	0	0
$196$	196.000	0.0714286
$197$	349.000	0.126219	0.0631097	−	0.998007i	$-0.479898\pi$
$197$	349.000	0.126219	0.0631097	+	0.998007i	$0.479898\pi$
$198$	110.000	0.0394816
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	0	0
$201$	−1932.00	−0.677974
$202$	0	0
$203$	7.00000	0.00242022
$204$	192.000	0.0658955
$205$	0	0
$206$	−1676.00	−0.566857
$207$	1925.00	0.646361
$208$	−1312.00	−0.437360
$209$	−210.000	−0.0695024
$210$	0	0
$211$	1676.00	0.546827	0.273414	−	0.961897i	$-0.411847\pi$
$211$	1676.00	0.546827	0.273414	+	0.961897i	$0.411847\pi$
$212$	1592.00	0.515750
$213$	−60.0000	−0.0193011
$214$	−4328.00	−1.38250
$215$	0	0
$216$	1216.00	0.383048
$217$	1582.00	0.494899
$218$	3654.00	1.13523
$219$	−4176.00	−1.28853
$220$	0	0
$221$	−984.000	−0.299507
$222$	−152.000	−0.0459530
$223$	−1176.00	−0.353143	−0.176571	−	0.984288i	$-0.556501\pi$
$223$	−1176.00	−0.353143	−0.176571	+	0.984288i	$0.556501\pi$
$224$	−224.000	−0.0668153
$225$	0	0
$226$	−186.000	−0.0547457
$227$	−2234.00	−0.653197	−0.326599	−	0.945163i	$-0.605903\pi$
$227$	−2234.00	−0.653197	−0.326599	+	0.945163i	$0.605903\pi$
$228$	−672.000	−0.195194
$229$	4274.00	1.23334	0.616668	−	0.787223i	$-0.288482\pi$
$229$	4274.00	1.23334	0.616668	+	0.787223i	$0.288482\pi$
$230$	0	0
$231$	140.000	0.0398759
$232$	−8.00000	−0.00226390
$233$	5427.00	1.52590	0.762950	−	0.646458i	$-0.223750\pi$
$233$	5427.00	1.52590	0.762950	+	0.646458i	$0.223750\pi$
$234$	−1804.00	−0.503979
$235$	0	0
$236$	424.000	0.116949
$237$	−5012.00	−1.37369
$238$	−168.000	−0.0457556
$239$	3516.00	0.951595	0.475797	−	0.879555i	$-0.342160\pi$
$239$	3516.00	0.951595	0.475797	+	0.879555i	$0.342160\pi$
$240$	0	0
$241$	−3890.00	−1.03974	−0.519869	−	0.854246i	$-0.674019\pi$
$241$	−3890.00	−1.03974	−0.519869	+	0.854246i	$0.674019\pi$
$242$	2612.00	0.693825
$243$	2860.00	0.755017
$244$	192.000	0.0503752
$245$	0	0
$246$	−128.000	−0.0331747
$247$	3444.00	0.887192
$248$	−1808.00	−0.462936
$249$	−3032.00	−0.771667
$250$	0	0
$251$	2512.00	0.631697	0.315849	−	0.948810i	$-0.397711\pi$
$251$	2512.00	0.631697	0.315849	+	0.948810i	$0.397711\pi$
$252$	−308.000	−0.0769928
$253$	−875.000	−0.217434
$254$	−2866.00	−0.707988
$255$	0	0
$256$	256.000	0.0625000
$257$	−6934.00	−1.68300	−0.841500	−	0.540257i	$-0.818327\pi$
$257$	−6934.00	−1.68300	−0.841500	+	0.540257i	$0.818327\pi$
$258$	2248.00	0.542459
$259$	133.000	0.0319082
$260$	0	0
$261$	−11.0000	−0.00260875
$262$	−1736.00	−0.409353
$263$	−5505.00	−1.29070	−0.645348	−	0.763889i	$-0.723287\pi$
$263$	−5505.00	−1.29070	−0.645348	+	0.763889i	$0.723287\pi$
$264$	−160.000	−0.0373005
$265$	0	0
$266$	588.000	0.135536
$267$	344.000	0.0788482
$268$	−1932.00	−0.440357
$269$	−8698.00	−1.97147	−0.985737	−	0.168294i	$-0.946174\pi$
$269$	−8698.00	−1.97147	−0.985737	+	0.168294i	$0.946174\pi$
$270$	0	0
$271$	2054.00	0.460412	0.230206	−	0.973142i	$-0.426060\pi$
$271$	2054.00	0.460412	0.230206	+	0.973142i	$0.426060\pi$
$272$	192.000	0.0428004
$273$	−2296.00	−0.509012
$274$	−5292.00	−1.16679
$275$	0	0
$276$	−2800.00	−0.610653
$277$	−8450.00	−1.83289	−0.916446	−	0.400158i	$-0.868955\pi$
$277$	−8450.00	−1.83289	−0.916446	+	0.400158i	$0.868955\pi$
$278$	−1792.00	−0.386608
$279$	−2486.00	−0.533451
$280$	0	0
$281$	4469.00	0.948748	0.474374	−	0.880323i	$-0.342674\pi$
$281$	4469.00	0.948748	0.474374	+	0.880323i	$0.342674\pi$
$282$	2672.00	0.564239
$283$	794.000	0.166779	0.0833894	−	0.996517i	$-0.473425\pi$
$283$	794.000	0.166779	0.0833894	+	0.996517i	$0.473425\pi$
$284$	−60.0000	−0.0125364
$285$	0	0
$286$	820.000	0.169537
$287$	112.000	0.0230354
$288$	352.000	0.0720201
$289$	−4769.00	−0.970690
$290$	0	0
$291$	−2840.00	−0.572109
$292$	−4176.00	−0.836924
$293$	6462.00	1.28844	0.644222	−	0.764839i	$-0.277181\pi$
$293$	6462.00	1.28844	0.644222	+	0.764839i	$0.277181\pi$
$294$	−392.000	−0.0777616
$295$	0	0
$296$	−152.000	−0.0298474
$297$	−760.000	−0.148484
$298$	−5046.00	−0.980896
$299$	14350.0	2.77552
$300$	0	0
$301$	−1967.00	−0.376664
$302$	−4866.00	−0.927175
$303$	0	0
$304$	−672.000	−0.126782
$305$	0	0
$306$	264.000	0.0493199
$307$	−56.0000	−0.0104107	−0.00520536	−	0.999986i	$-0.501657\pi$
$307$	−56.0000	−0.0104107	−0.00520536	+	0.999986i	$0.501657\pi$
$308$	140.000	0.0259001
$309$	3352.00	0.617115
$310$	0	0
$311$	10656.0	1.94291	0.971457	−	0.237215i	$-0.0762347\pi$
$311$	10656.0	1.94291	0.971457	+	0.237215i	$0.0762347\pi$
$312$	2624.00	0.476137
$313$	2010.00	0.362977	0.181489	−	0.983393i	$-0.441908\pi$
$313$	2010.00	0.362977	0.181489	+	0.983393i	$0.441908\pi$
$314$	−5144.00	−0.924499
$315$	0	0
$316$	−5012.00	−0.892237
$317$	−3903.00	−0.691528	−0.345764	−	0.938322i	$-0.612380\pi$
$317$	−3903.00	−0.691528	−0.345764	+	0.938322i	$0.612380\pi$
$318$	−3184.00	−0.561478
$319$	5.00000	0.000877574 0
$320$	0	0
$321$	8656.00	1.50508
$322$	2450.00	0.424016
$323$	−504.000	−0.0868214
$324$	−1244.00	−0.213306
$325$	0	0
$326$	4976.00	0.845384
$327$	−7308.00	−1.23588
$328$	−128.000	−0.0215476
$329$	−2338.00	−0.391788
$330$	0	0
$331$	−3277.00	−0.544170	−0.272085	−	0.962273i	$-0.587713\pi$
$331$	−3277.00	−0.544170	−0.272085	+	0.962273i	$0.587713\pi$
$332$	−3032.00	−0.501213
$333$	−209.000	−0.0343938
$334$	6108.00	1.00064
$335$	0	0
$336$	448.000	0.0727393
$337$	−6462.00	−1.04453	−0.522266	−	0.852782i	$-0.674913\pi$
$337$	−6462.00	−1.04453	−0.522266	+	0.852782i	$0.674913\pi$
$338$	−9054.00	−1.45702
$339$	372.000	0.0595996
$340$	0	0
$341$	1130.00	0.179451
$342$	−924.000	−0.146094
$343$	343.000	0.0539949
$344$	2248.00	0.352337
$345$	0	0
$346$	−7788.00	−1.21007
$347$	3787.00	0.585870	0.292935	−	0.956132i	$-0.405368\pi$
$347$	3787.00	0.585870	0.292935	+	0.956132i	$0.405368\pi$
$348$	16.0000	0.00246463
$349$	7398.00	1.13469	0.567344	−	0.823481i	$-0.307971\pi$
$349$	7398.00	1.13469	0.567344	+	0.823481i	$0.307971\pi$
$350$	0	0
$351$	12464.0	1.89538
$352$	−160.000	−0.0242274
$353$	9654.00	1.45561	0.727805	−	0.685784i	$-0.240540\pi$
$353$	9654.00	1.45561	0.727805	+	0.685784i	$0.240540\pi$
$354$	−848.000	−0.127318
$355$	0	0
$356$	344.000	0.0512134
$357$	336.000	0.0498123
$358$	2216.00	0.327149
$359$	−7691.00	−1.13068	−0.565342	−	0.824857i	$-0.691256\pi$
$359$	−7691.00	−1.13068	−0.565342	+	0.824857i	$0.691256\pi$
$360$	0	0
$361$	−5095.00	−0.742820
$362$	3840.00	0.557530
$363$	−5224.00	−0.755341
$364$	−2296.00	−0.330613
$365$	0	0
$366$	−384.000	−0.0548415
$367$	6836.00	0.972306	0.486153	−	0.873874i	$-0.338400\pi$
$367$	6836.00	0.972306	0.486153	+	0.873874i	$0.338400\pi$
$368$	−2800.00	−0.396631
$369$	−176.000	−0.0248298
$370$	0	0
$371$	2786.00	0.389870
$372$	3616.00	0.503981
$373$	−12123.0	−1.68286	−0.841428	−	0.540370i	$-0.818284\pi$
$373$	−12123.0	−1.68286	−0.841428	+	0.540370i	$0.818284\pi$
$374$	−120.000	−0.0165910
$375$	0	0
$376$	2672.00	0.366484
$377$	−82.0000	−0.0112022
$378$	2128.00	0.289557
$379$	10811.0	1.46523	0.732617	−	0.680641i	$-0.238299\pi$
$379$	10811.0	1.46523	0.732617	+	0.680641i	$0.238299\pi$
$380$	0	0
$381$	5732.00	0.770759
$382$	1872.00	0.250733
$383$	12778.0	1.70477	0.852383	−	0.522918i	$-0.175157\pi$
$383$	12778.0	1.70477	0.852383	+	0.522918i	$0.175157\pi$
$384$	−512.000	−0.0680414
$385$	0	0
$386$	6326.00	0.834158
$387$	3091.00	0.406006
$388$	−2840.00	−0.371596
$389$	−383.000	−0.0499200	−0.0249600	−	0.999688i	$-0.507946\pi$
$389$	−383.000	−0.0499200	−0.0249600	+	0.999688i	$0.507946\pi$
$390$	0	0
$391$	−2100.00	−0.271615
$392$	−392.000	−0.0505076
$393$	3472.00	0.445647
$394$	−698.000	−0.0892506
$395$	0	0
$396$	−220.000	−0.0279177
$397$	−12050.0	−1.52336	−0.761678	−	0.647956i	$-0.775624\pi$
$397$	−12050.0	−1.52336	−0.761678	+	0.647956i	$0.775624\pi$
$398$	0	0
$399$	−1176.00	−0.147553
$400$	0	0
$401$	−7523.00	−0.936860	−0.468430	−	0.883501i	$-0.655180\pi$
$401$	−7523.00	−0.936860	−0.468430	+	0.883501i	$0.655180\pi$
$402$	3864.00	0.479400
$403$	−18532.0	−2.29068
$404$	0	0
$405$	0	0
$406$	−14.0000	−0.00171135
$407$	95.0000	0.0115700
$408$	−384.000	−0.0465952
$409$	−4534.00	−0.548146	−0.274073	−	0.961709i	$-0.588371\pi$
$409$	−4534.00	−0.548146	−0.274073	+	0.961709i	$0.588371\pi$
$410$	0	0
$411$	10584.0	1.27024
$412$	3352.00	0.400828
$413$	742.000	0.0884054
$414$	−3850.00	−0.457046
$415$	0	0
$416$	2624.00	0.309260
$417$	3584.00	0.420885
$418$	420.000	0.0491456
$419$	8494.00	0.990356	0.495178	−	0.868792i	$-0.335103\pi$
$419$	8494.00	0.990356	0.495178	+	0.868792i	$0.335103\pi$
$420$	0	0
$421$	−8765.00	−1.01468	−0.507340	−	0.861746i	$-0.669371\pi$
$421$	−8765.00	−1.01468	−0.507340	+	0.861746i	$0.669371\pi$
$422$	−3352.00	−0.386665
$423$	3674.00	0.422307
$424$	−3184.00	−0.364690
$425$	0	0
$426$	120.000	0.0136479
$427$	336.000	0.0380800
$428$	8656.00	0.977578
$429$	−1640.00	−0.184569
$430$	0	0
$431$	−6696.00	−0.748341	−0.374170	−	0.927360i	$-0.622073\pi$
$431$	−6696.00	−0.748341	−0.374170	+	0.927360i	$0.622073\pi$
$432$	−2432.00	−0.270856
$433$	4148.00	0.460370	0.230185	−	0.973147i	$-0.426067\pi$
$433$	4148.00	0.460370	0.230185	+	0.973147i	$0.426067\pi$
$434$	−3164.00	−0.349947
$435$	0	0
$436$	−7308.00	−0.802729
$437$	7350.00	0.804572
$438$	8352.00	0.911128
$439$	6182.00	0.672097	0.336049	−	0.941845i	$-0.390909\pi$
$439$	6182.00	0.672097	0.336049	+	0.941845i	$0.390909\pi$
$440$	0	0
$441$	−539.000	−0.0582011
$442$	1968.00	0.211783
$443$	−616.000	−0.0660656	−0.0330328	−	0.999454i	$-0.510517\pi$
$443$	−616.000	−0.0660656	−0.0330328	+	0.999454i	$0.510517\pi$
$444$	304.000	0.0324937
$445$	0	0
$446$	2352.00	0.249709
$447$	10092.0	1.06786
$448$	448.000	0.0472456
$449$	−8653.00	−0.909488	−0.454744	−	0.890622i	$-0.650269\pi$
$449$	−8653.00	−0.909488	−0.454744	+	0.890622i	$0.650269\pi$
$450$	0	0
$451$	80.0000	0.00835267
$452$	372.000	0.0387111
$453$	9732.00	1.00938
$454$	4468.00	0.461880
$455$	0	0
$456$	1344.00	0.138023
$457$	7785.00	0.796864	0.398432	−	0.917198i	$-0.369554\pi$
$457$	7785.00	0.796864	0.398432	+	0.917198i	$0.369554\pi$
$458$	−8548.00	−0.872100
$459$	−1824.00	−0.185484
$460$	0	0
$461$	−14718.0	−1.48695	−0.743477	−	0.668762i	$-0.766825\pi$
$461$	−14718.0	−1.48695	−0.743477	+	0.668762i	$0.766825\pi$
$462$	−280.000	−0.0281965
$463$	−2864.00	−0.287476	−0.143738	−	0.989616i	$-0.545912\pi$
$463$	−2864.00	−0.287476	−0.143738	+	0.989616i	$0.545912\pi$
$464$	16.0000	0.00160082
$465$	0	0
$466$	−10854.0	−1.07897
$467$	1878.00	0.186089	0.0930444	−	0.995662i	$-0.470340\pi$
$467$	1878.00	0.186089	0.0930444	+	0.995662i	$0.470340\pi$
$468$	3608.00	0.356367
$469$	−3381.00	−0.332879
$470$	0	0
$471$	10288.0	1.00647
$472$	−848.000	−0.0826957
$473$	−1405.00	−0.136579
$474$	10024.0	0.971345
$475$	0	0
$476$	336.000	0.0323541
$477$	−4378.00	−0.420241
$478$	−7032.00	−0.672879
$479$	−9914.00	−0.945683	−0.472842	−	0.881147i	$-0.656772\pi$
$479$	−9914.00	−0.945683	−0.472842	+	0.881147i	$0.656772\pi$
$480$	0	0
$481$	−1558.00	−0.147690
$482$	7780.00	0.735206
$483$	−4900.00	−0.461610
$484$	−5224.00	−0.490609
$485$	0	0
$486$	−5720.00	−0.533878
$487$	12883.0	1.19874	0.599368	−	0.800474i	$-0.295419\pi$
$487$	12883.0	1.19874	0.599368	+	0.800474i	$0.295419\pi$
$488$	−384.000	−0.0356206
$489$	−9952.00	−0.920337
$490$	0	0
$491$	−16567.0	−1.52273	−0.761363	−	0.648326i	$-0.775469\pi$
$491$	−16567.0	−1.52273	−0.761363	+	0.648326i	$0.775469\pi$
$492$	256.000	0.0234581
$493$	12.0000	0.00109625
$494$	−6888.00	−0.627340
$495$	0	0
$496$	3616.00	0.327345
$497$	−105.000	−0.00947665
$498$	6064.00	0.545651
$499$	2044.00	0.183371	0.0916854	−	0.995788i	$-0.470775\pi$
$499$	2044.00	0.183371	0.0916854	+	0.995788i	$0.470775\pi$
$500$	0	0
$501$	−12216.0	−1.08936
$502$	−5024.00	−0.446677
$503$	14610.0	1.29508	0.647542	−	0.762029i	$-0.275797\pi$
$503$	14610.0	1.29508	0.647542	+	0.762029i	$0.275797\pi$
$504$	616.000	0.0544421
$505$	0	0
$506$	1750.00	0.153749
$507$	18108.0	1.58620
$508$	5732.00	0.500623
$509$	18074.0	1.57390	0.786951	−	0.617016i	$-0.211659\pi$
$509$	18074.0	1.57390	0.786951	+	0.617016i	$0.211659\pi$
$510$	0	0
$511$	−7308.00	−0.632655
$512$	−512.000	−0.0441942
$513$	6384.00	0.549436
$514$	13868.0	1.19006
$515$	0	0
$516$	−4496.00	−0.383576
$517$	−1670.00	−0.142063
$518$	−266.000	−0.0225625
$519$	15576.0	1.31736
$520$	0	0
$521$	−13554.0	−1.13975	−0.569877	−	0.821730i	$-0.693009\pi$
$521$	−13554.0	−1.13975	−0.569877	+	0.821730i	$0.693009\pi$
$522$	22.0000	0.00184466
$523$	−11984.0	−1.00196	−0.500979	−	0.865460i	$-0.667027\pi$
$523$	−11984.0	−1.00196	−0.500979	+	0.865460i	$0.667027\pi$
$524$	3472.00	0.289456
$525$	0	0
$526$	11010.0	0.912659
$527$	2712.00	0.224168
$528$	320.000	0.0263754
$529$	18458.0	1.51705
$530$	0	0
$531$	−1166.00	−0.0952921
$532$	−1176.00	−0.0958385
$533$	−1312.00	−0.106621
$534$	−688.000	−0.0557541
$535$	0	0
$536$	3864.00	0.311379
$537$	−4432.00	−0.356154
$538$	17396.0	1.39404
$539$	245.000	0.0195787
$540$	0	0
$541$	3863.00	0.306993	0.153497	−	0.988149i	$-0.450947\pi$
$541$	3863.00	0.306993	0.153497	+	0.988149i	$0.450947\pi$
$542$	−4108.00	−0.325560
$543$	−7680.00	−0.606962
$544$	−384.000	−0.0302645
$545$	0	0
$546$	4592.00	0.359926
$547$	−19579.0	−1.53042	−0.765208	−	0.643783i	$-0.777364\pi$
$547$	−19579.0	−1.53042	−0.765208	+	0.643783i	$0.777364\pi$
$548$	10584.0	0.825048
$549$	−528.000	−0.0410464
$550$	0	0
$551$	−42.0000	−0.00324730
$552$	5600.00	0.431797
$553$	−8771.00	−0.674468
$554$	16900.0	1.29605
$555$	0	0
$556$	3584.00	0.273373
$557$	7437.00	0.565738	0.282869	−	0.959159i	$-0.408714\pi$
$557$	7437.00	0.565738	0.282869	+	0.959159i	$0.408714\pi$
$558$	4972.00	0.377207
$559$	23042.0	1.74342
$560$	0	0
$561$	240.000	0.0180620
$562$	−8938.00	−0.670866
$563$	5690.00	0.425941	0.212971	−	0.977059i	$-0.431686\pi$
$563$	5690.00	0.425941	0.212971	+	0.977059i	$0.431686\pi$
$564$	−5344.00	−0.398977
$565$	0	0
$566$	−1588.00	−0.117930
$567$	−2177.00	−0.161244
$568$	120.000	0.00886459
$569$	−24771.0	−1.82505	−0.912526	−	0.409019i	$-0.865871\pi$
$569$	−24771.0	−1.82505	−0.912526	+	0.409019i	$0.865871\pi$
$570$	0	0
$571$	−8633.00	−0.632714	−0.316357	−	0.948640i	$-0.602460\pi$
$571$	−8633.00	−0.632714	−0.316357	+	0.948640i	$0.602460\pi$
$572$	−1640.00	−0.119881
$573$	−3744.00	−0.272963
$574$	−224.000	−0.0162885
$575$	0	0
$576$	−704.000	−0.0509259
$577$	−1666.00	−0.120202	−0.0601009	−	0.998192i	$-0.519142\pi$
$577$	−1666.00	−0.120202	−0.0601009	+	0.998192i	$0.519142\pi$
$578$	9538.00	0.686381
$579$	−12652.0	−0.908116
$580$	0	0
$581$	−5306.00	−0.378881
$582$	5680.00	0.404542
$583$	1990.00	0.141368
$584$	8352.00	0.591795
$585$	0	0
$586$	−12924.0	−0.911067
$587$	7536.00	0.529888	0.264944	−	0.964264i	$-0.414647\pi$
$587$	7536.00	0.529888	0.264944	+	0.964264i	$0.414647\pi$
$588$	784.000	0.0549857
$589$	−9492.00	−0.664026
$590$	0	0
$591$	1396.00	0.0971637
$592$	304.000	0.0211053
$593$	−3568.00	−0.247083	−0.123541	−	0.992339i	$-0.539425\pi$
$593$	−3568.00	−0.247083	−0.123541	+	0.992339i	$0.539425\pi$
$594$	1520.00	0.104994
$595$	0	0
$596$	10092.0	0.693598
$597$	0	0
$598$	−28700.0	−1.96259
$599$	−24901.0	−1.69854	−0.849272	−	0.527956i	$-0.822958\pi$
$599$	−24901.0	−1.69854	−0.849272	+	0.527956i	$0.822958\pi$
$600$	0	0
$601$	−23744.0	−1.61154	−0.805772	−	0.592226i	$-0.798249\pi$
$601$	−23744.0	−1.61154	−0.805772	+	0.592226i	$0.798249\pi$
$602$	3934.00	0.266342
$603$	5313.00	0.358809
$604$	9732.00	0.655612
$605$	0	0
$606$	0	0
$607$	22894.0	1.53087	0.765436	−	0.643513i	$-0.222524\pi$
$607$	22894.0	1.53087	0.765436	+	0.643513i	$0.222524\pi$
$608$	1344.00	0.0896487
$609$	28.0000	0.00186308
$610$	0	0
$611$	27388.0	1.81342
$612$	−528.000	−0.0348744
$613$	7811.00	0.514655	0.257327	−	0.966324i	$-0.417158\pi$
$613$	7811.00	0.514655	0.257327	+	0.966324i	$0.417158\pi$
$614$	112.000	0.00736149
$615$	0	0
$616$	−280.000	−0.0183142
$617$	−11833.0	−0.772089	−0.386044	−	0.922480i	$-0.626159\pi$
$617$	−11833.0	−0.772089	−0.386044	+	0.922480i	$0.626159\pi$
$618$	−6704.00	−0.436366
$619$	−4186.00	−0.271809	−0.135904	−	0.990722i	$-0.543394\pi$
$619$	−4186.00	−0.271809	−0.135904	+	0.990722i	$0.543394\pi$
$620$	0	0
$621$	26600.0	1.71887
$622$	−21312.0	−1.37385
$623$	602.000	0.0387137
$624$	−5248.00	−0.336680
$625$	0	0
$626$	−4020.00	−0.256664
$627$	−840.000	−0.0535030
$628$	10288.0	0.653720
$629$	228.000	0.0144530
$630$	0	0
$631$	12079.0	0.762056	0.381028	−	0.924563i	$-0.375570\pi$
$631$	12079.0	0.762056	0.381028	+	0.924563i	$0.375570\pi$
$632$	10024.0	0.630907
$633$	6704.00	0.420948
$634$	7806.00	0.488984
$635$	0	0
$636$	6368.00	0.397025
$637$	−4018.00	−0.249920
$638$	−10.0000	−0.000620539 0
$639$	165.000	0.0102149
$640$	0	0
$641$	4017.00	0.247523	0.123761	−	0.992312i	$-0.460504\pi$
$641$	4017.00	0.247523	0.123761	+	0.992312i	$0.460504\pi$
$642$	−17312.0	−1.06425
$643$	−13508.0	−0.828466	−0.414233	−	0.910171i	$-0.635950\pi$
$643$	−13508.0	−0.828466	−0.414233	+	0.910171i	$0.635950\pi$
$644$	−4900.00	−0.299825
$645$	0	0
$646$	1008.00	0.0613920
$647$	1346.00	0.0817878	0.0408939	−	0.999163i	$-0.486979\pi$
$647$	1346.00	0.0817878	0.0408939	+	0.999163i	$0.486979\pi$
$648$	2488.00	0.150830
$649$	530.000	0.0320560
$650$	0	0
$651$	6328.00	0.380974
$652$	−9952.00	−0.597777
$653$	10274.0	0.615701	0.307850	−	0.951435i	$-0.400390\pi$
$653$	10274.0	0.615701	0.307850	+	0.951435i	$0.400390\pi$
$654$	14616.0	0.873900
$655$	0	0
$656$	256.000	0.0152365
$657$	11484.0	0.681938
$658$	4676.00	0.277036
$659$	−13116.0	−0.775306	−0.387653	−	0.921805i	$-0.626714\pi$
$659$	−13116.0	−0.775306	−0.387653	+	0.921805i	$0.626714\pi$
$660$	0	0
$661$	23070.0	1.35752	0.678759	−	0.734361i	$-0.262518\pi$
$661$	23070.0	1.35752	0.678759	+	0.734361i	$0.262518\pi$
$662$	6554.00	0.384786
$663$	−3936.00	−0.230560
$664$	6064.00	0.354411
$665$	0	0
$666$	418.000	0.0243201
$667$	−175.000	−0.0101590
$668$	−12216.0	−0.707562
$669$	−4704.00	−0.271849
$670$	0	0
$671$	240.000	0.0138079
$672$	−896.000	−0.0514344
$673$	−24922.0	−1.42745	−0.713724	−	0.700427i	$-0.752993\pi$
$673$	−24922.0	−1.42745	−0.713724	+	0.700427i	$0.752993\pi$
$674$	12924.0	0.738596
$675$	0	0
$676$	18108.0	1.03027
$677$	−14294.0	−0.811467	−0.405733	−	0.913991i	$-0.632984\pi$
$677$	−14294.0	−0.811467	−0.405733	+	0.913991i	$0.632984\pi$
$678$	−744.000	−0.0421433
$679$	−4970.00	−0.280900
$680$	0	0
$681$	−8936.00	−0.502832
$682$	−2260.00	−0.126891
$683$	4979.00	0.278940	0.139470	−	0.990226i	$-0.455460\pi$
$683$	4979.00	0.278940	0.139470	+	0.990226i	$0.455460\pi$
$684$	1848.00	0.103304
$685$	0	0
$686$	−686.000	−0.0381802
$687$	17096.0	0.949422
$688$	−4496.00	−0.249140
$689$	−32636.0	−1.80455
$690$	0	0
$691$	6744.00	0.371279	0.185640	−	0.982618i	$-0.440564\pi$
$691$	6744.00	0.371279	0.185640	+	0.982618i	$0.440564\pi$
$692$	15576.0	0.855651
$693$	−385.000	−0.0211038
$694$	−7574.00	−0.414272
$695$	0	0
$696$	−32.0000	−0.00174275
$697$	192.000	0.0104340
$698$	−14796.0	−0.802345
$699$	21708.0	1.17464
$700$	0	0
$701$	−17682.0	−0.952696	−0.476348	−	0.879257i	$-0.658040\pi$
$701$	−17682.0	−0.952696	−0.476348	+	0.879257i	$0.658040\pi$
$702$	−24928.0	−1.34024
$703$	−798.000	−0.0428124
$704$	320.000	0.0171313
$705$	0	0
$706$	−19308.0	−1.02927
$707$	0	0
$708$	1696.00	0.0900277
$709$	−3514.00	−0.186137	−0.0930684	−	0.995660i	$-0.529668\pi$
$709$	−3514.00	−0.186137	−0.0930684	+	0.995660i	$0.529668\pi$
$710$	0	0
$711$	13783.0	0.727008
$712$	−688.000	−0.0362133
$713$	−39550.0	−2.07736
$714$	−672.000	−0.0352226
$715$	0	0
$716$	−4432.00	−0.231329
$717$	14064.0	0.732538
$718$	15382.0	0.799514
$719$	−34132.0	−1.77039	−0.885194	−	0.465222i	$-0.845974\pi$
$719$	−34132.0	−1.77039	−0.885194	+	0.465222i	$0.845974\pi$
$720$	0	0
$721$	5866.00	0.302998
$722$	10190.0	0.525253
$723$	−15560.0	−0.800391
$724$	−7680.00	−0.394233
$725$	0	0
$726$	10448.0	0.534107
$727$	−22112.0	−1.12804	−0.564022	−	0.825759i	$-0.690747\pi$
$727$	−22112.0	−1.12804	−0.564022	+	0.825759i	$0.690747\pi$
$728$	4592.00	0.233779
$729$	19837.0	1.00782
$730$	0	0
$731$	−3372.00	−0.170613
$732$	768.000	0.0387788
$733$	22180.0	1.11765	0.558825	−	0.829286i	$-0.311252\pi$
$733$	22180.0	1.11765	0.558825	+	0.829286i	$0.311252\pi$
$734$	−13672.0	−0.687524
$735$	0	0
$736$	5600.00	0.280460
$737$	−2415.00	−0.120702
$738$	352.000	0.0175573
$739$	−16279.0	−0.810328	−0.405164	−	0.914244i	$-0.632786\pi$
$739$	−16279.0	−0.810328	−0.405164	+	0.914244i	$0.632786\pi$
$740$	0	0
$741$	13776.0	0.682961
$742$	−5572.00	−0.275680
$743$	−29068.0	−1.43526	−0.717632	−	0.696422i	$-0.754774\pi$
$743$	−29068.0	−1.43526	−0.717632	+	0.696422i	$0.754774\pi$
$744$	−7232.00	−0.356368
$745$	0	0
$746$	24246.0	1.18996
$747$	8338.00	0.408396
$748$	240.000	0.0117316
$749$	15148.0	0.738980
$750$	0	0
$751$	20.0000	0.000971785 0	0.000485892	−	1.00000i	$-0.499845\pi$
$751$	20.0000	0.000971785 0	0.000485892		1.00000i	$0.499845\pi$
$752$	−5344.00	−0.259143
$753$	10048.0	0.486281
$754$	164.000	0.00792112
$755$	0	0
$756$	−4256.00	−0.204748
$757$	−22961.0	−1.10242	−0.551210	−	0.834367i	$-0.685834\pi$
$757$	−22961.0	−1.10242	−0.551210	+	0.834367i	$0.685834\pi$
$758$	−21622.0	−1.03608
$759$	−3500.00	−0.167381
$760$	0	0
$761$	2832.00	0.134901	0.0674507	−	0.997723i	$-0.478513\pi$
$761$	2832.00	0.134901	0.0674507	+	0.997723i	$0.478513\pi$
$762$	−11464.0	−0.545009
$763$	−12789.0	−0.606806
$764$	−3744.00	−0.177295
$765$	0	0
$766$	−25556.0	−1.20545
$767$	−8692.00	−0.409192
$768$	1024.00	0.0481125
$769$	−20204.0	−0.947432	−0.473716	−	0.880678i	$-0.657088\pi$
$769$	−20204.0	−0.947432	−0.473716	+	0.880678i	$0.657088\pi$
$770$	0	0
$771$	−27736.0	−1.29557
$772$	−12652.0	−0.589839
$773$	27882.0	1.29734	0.648671	−	0.761069i	$-0.275325\pi$
$773$	27882.0	1.29734	0.648671	+	0.761069i	$0.275325\pi$
$774$	−6182.00	−0.287090
$775$	0	0
$776$	5680.00	0.262758
$777$	532.000	0.0245629
$778$	766.000	0.0352988
$779$	−672.000	−0.0309074
$780$	0	0
$781$	−75.0000	−0.00343625
$782$	4200.00	0.192061
$783$	−152.000	−0.00693747
$784$	784.000	0.0357143
$785$	0	0
$786$	−6944.00	−0.315120
$787$	−36304.0	−1.64434	−0.822171	−	0.569240i	$-0.807238\pi$
$787$	−36304.0	−1.64434	−0.822171	+	0.569240i	$0.807238\pi$
$788$	1396.00	0.0631097
$789$	−22020.0	−0.993578
$790$	0	0
$791$	651.000	0.0292628
$792$	440.000	0.0197408
$793$	−3936.00	−0.176257
$794$	24100.0	1.07718
$795$	0	0
$796$	0	0
$797$	21096.0	0.937589	0.468795	−	0.883307i	$-0.344688\pi$
$797$	21096.0	0.937589	0.468795	+	0.883307i	$0.344688\pi$
$798$	2352.00	0.104336
$799$	−4008.00	−0.177463
$800$	0	0
$801$	−946.000	−0.0417294
$802$	15046.0	0.662460
$803$	−5220.00	−0.229402
$804$	−7728.00	−0.338987
$805$	0	0
$806$	37064.0	1.61976
$807$	−34792.0	−1.51764
$808$	0	0
$809$	15879.0	0.690081	0.345041	−	0.938588i	$-0.387865\pi$
$809$	15879.0	0.690081	0.345041	+	0.938588i	$0.387865\pi$
$810$	0	0
$811$	33402.0	1.44624	0.723121	−	0.690721i	$-0.242707\pi$
$811$	33402.0	1.44624	0.723121	+	0.690721i	$0.242707\pi$
$812$	28.0000	0.00121011
$813$	8216.00	0.354425
$814$	−190.000	−0.00818120
$815$	0	0
$816$	768.000	0.0329478
$817$	11802.0	0.505385
$818$	9068.00	0.387598
$819$	6314.00	0.269388
$820$	0	0
$821$	10506.0	0.446604	0.223302	−	0.974749i	$-0.428316\pi$
$821$	10506.0	0.446604	0.223302	+	0.974749i	$0.428316\pi$
$822$	−21168.0	−0.898198
$823$	−1035.00	−0.0438370	−0.0219185	−	0.999760i	$-0.506977\pi$
$823$	−1035.00	−0.0438370	−0.0219185	+	0.999760i	$0.506977\pi$
$824$	−6704.00	−0.283428
$825$	0	0
$826$	−1484.00	−0.0625121
$827$	−30137.0	−1.26719	−0.633595	−	0.773665i	$-0.718421\pi$
$827$	−30137.0	−1.26719	−0.633595	+	0.773665i	$0.718421\pi$
$828$	7700.00	0.323181
$829$	35464.0	1.48578	0.742892	−	0.669411i	$-0.233453\pi$
$829$	35464.0	1.48578	0.742892	+	0.669411i	$0.233453\pi$
$830$	0	0
$831$	−33800.0	−1.41096
$832$	−5248.00	−0.218680
$833$	588.000	0.0244574
$834$	−7168.00	−0.297611
$835$	0	0
$836$	−840.000	−0.0347512
$837$	−34352.0	−1.41861
$838$	−16988.0	−0.700287
$839$	−1492.00	−0.0613940	−0.0306970	−	0.999529i	$-0.509773\pi$
$839$	−1492.00	−0.0613940	−0.0306970	+	0.999529i	$0.509773\pi$
$840$	0	0
$841$	−24388.0	−0.999959
$842$	17530.0	0.717487
$843$	17876.0	0.730347
$844$	6704.00	0.273414
$845$	0	0
$846$	−7348.00	−0.298616
$847$	−9142.00	−0.370865
$848$	6368.00	0.257875
$849$	3176.00	0.128386
$850$	0	0
$851$	−3325.00	−0.133936
$852$	−240.000	−0.00965055
$853$	−19288.0	−0.774219	−0.387109	−	0.922034i	$-0.626526\pi$
$853$	−19288.0	−0.774219	−0.387109	+	0.922034i	$0.626526\pi$
$854$	−672.000	−0.0269267
$855$	0	0
$856$	−17312.0	−0.691252
$857$	−2656.00	−0.105866	−0.0529330	−	0.998598i	$-0.516857\pi$
$857$	−2656.00	−0.105866	−0.0529330	+	0.998598i	$0.516857\pi$
$858$	3280.00	0.130510
$859$	3786.00	0.150380	0.0751901	−	0.997169i	$-0.476044\pi$
$859$	3786.00	0.150380	0.0751901	+	0.997169i	$0.476044\pi$
$860$	0	0
$861$	448.000	0.0177326
$862$	13392.0	0.529157
$863$	45503.0	1.79483	0.897416	−	0.441185i	$-0.145442\pi$
$863$	45503.0	1.79483	0.897416	+	0.441185i	$0.145442\pi$
$864$	4864.00	0.191524
$865$	0	0
$866$	−8296.00	−0.325531
$867$	−19076.0	−0.747238
$868$	6328.00	0.247450
$869$	−6265.00	−0.244563
$870$	0	0
$871$	39606.0	1.54076
$872$	14616.0	0.567615
$873$	7810.00	0.302782
$874$	−14700.0	−0.568919
$875$	0	0
$876$	−16704.0	−0.644265
$877$	32626.0	1.25622	0.628108	−	0.778126i	$-0.283830\pi$
$877$	32626.0	1.25622	0.628108	+	0.778126i	$0.283830\pi$
$878$	−12364.0	−0.475245
$879$	25848.0	0.991845
$880$	0	0
$881$	−25754.0	−0.984874	−0.492437	−	0.870348i	$-0.663894\pi$
$881$	−25754.0	−0.984874	−0.492437	+	0.870348i	$0.663894\pi$
$882$	1078.00	0.0411544
$883$	9165.00	0.349294	0.174647	−	0.984631i	$-0.444122\pi$
$883$	9165.00	0.349294	0.174647	+	0.984631i	$0.444122\pi$
$884$	−3936.00	−0.149753
$885$	0	0
$886$	1232.00	0.0467154
$887$	−1472.00	−0.0557214	−0.0278607	−	0.999612i	$-0.508869\pi$
$887$	−1472.00	−0.0557214	−0.0278607	+	0.999612i	$0.508869\pi$
$888$	−608.000	−0.0229765
$889$	10031.0	0.378435
$890$	0	0
$891$	−1555.00	−0.0584674
$892$	−4704.00	−0.176571
$893$	14028.0	0.525677
$894$	−20184.0	−0.755094
$895$	0	0
$896$	−896.000	−0.0334077
$897$	57400.0	2.13660
$898$	17306.0	0.643105
$899$	226.000	0.00838434
$900$	0	0
$901$	4776.00	0.176594
$902$	−160.000	−0.00590623
$903$	−7868.00	−0.289956
$904$	−744.000	−0.0273729
$905$	0	0
$906$	−19464.0	−0.713740
$907$	−22412.0	−0.820483	−0.410242	−	0.911977i	$-0.634556\pi$
$907$	−22412.0	−0.820483	−0.410242	+	0.911977i	$0.634556\pi$
$908$	−8936.00	−0.326599
$909$	0	0
$910$	0	0
$911$	15163.0	0.551452	0.275726	−	0.961236i	$-0.411082\pi$
$911$	15163.0	0.551452	0.275726	+	0.961236i	$0.411082\pi$
$912$	−2688.00	−0.0975971
$913$	−3790.00	−0.137383
$914$	−15570.0	−0.563468
$915$	0	0
$916$	17096.0	0.616668
$917$	6076.00	0.218808
$918$	3648.00	0.131157
$919$	−6501.00	−0.233350	−0.116675	−	0.993170i	$-0.537224\pi$
$919$	−6501.00	−0.233350	−0.116675	+	0.993170i	$0.537224\pi$
$920$	0	0
$921$	−224.000	−0.00801417
$922$	29436.0	1.05143
$923$	1230.00	0.0438634
$924$	560.000	0.0199379
$925$	0	0
$926$	5728.00	0.203276
$927$	−9218.00	−0.326601
$928$	−32.0000	−0.00113195
$929$	1464.00	0.0517032	0.0258516	−	0.999666i	$-0.491770\pi$
$929$	1464.00	0.0517032	0.0258516	+	0.999666i	$0.491770\pi$
$930$	0	0
$931$	−2058.00	−0.0724471
$932$	21708.0	0.762950
$933$	42624.0	1.49566
$934$	−3756.00	−0.131585
$935$	0	0
$936$	−7216.00	−0.251990
$937$	14064.0	0.490342	0.245171	−	0.969480i	$-0.421156\pi$
$937$	14064.0	0.490342	0.245171	+	0.969480i	$0.421156\pi$
$938$	6762.00	0.235381
$939$	8040.00	0.279420
$940$	0	0
$941$	−39114.0	−1.35503	−0.677513	−	0.735511i	$-0.736942\pi$
$941$	−39114.0	−1.35503	−0.677513	+	0.735511i	$0.736942\pi$
$942$	−20576.0	−0.711680
$943$	−2800.00	−0.0966920
$944$	1696.00	0.0584747
$945$	0	0
$946$	2810.00	0.0965761
$947$	15068.0	0.517048	0.258524	−	0.966005i	$-0.416764\pi$
$947$	15068.0	0.517048	0.258524	+	0.966005i	$0.416764\pi$
$948$	−20048.0	−0.686845
$949$	85608.0	2.92830
$950$	0	0
$951$	−15612.0	−0.532338
$952$	−672.000	−0.0228778
$953$	−27847.0	−0.946540	−0.473270	−	0.880917i	$-0.656927\pi$
$953$	−27847.0	−0.946540	−0.473270	+	0.880917i	$0.656927\pi$
$954$	8756.00	0.297155
$955$	0	0
$956$	14064.0	0.475797
$957$	20.0000	0.000675557 0
$958$	19828.0	0.668699
$959$	18522.0	0.623677
$960$	0	0
$961$	21285.0	0.714478
$962$	3116.00	0.104432
$963$	−23804.0	−0.796545
$964$	−15560.0	−0.519869
$965$	0	0
$966$	9800.00	0.326408
$967$	33704.0	1.12084	0.560418	−	0.828210i	$-0.310641\pi$
$967$	33704.0	1.12084	0.560418	+	0.828210i	$0.310641\pi$
$968$	10448.0	0.346913
$969$	−2016.00	−0.0668351
$970$	0	0
$971$	−30006.0	−0.991698	−0.495849	−	0.868409i	$-0.665143\pi$
$971$	−30006.0	−0.991698	−0.495849	+	0.868409i	$0.665143\pi$
$972$	11440.0	0.377508
$973$	6272.00	0.206651
$974$	−25766.0	−0.847634
$975$	0	0
$976$	768.000	0.0251876
$977$	−14457.0	−0.473409	−0.236704	−	0.971582i	$-0.576067\pi$
$977$	−14457.0	−0.473409	−0.236704	+	0.971582i	$0.576067\pi$
$978$	19904.0	0.650777
$979$	430.000	0.0140377
$980$	0	0
$981$	20097.0	0.654075
$982$	33134.0	1.07673
$983$	43742.0	1.41928	0.709640	−	0.704564i	$-0.248857\pi$
$983$	43742.0	1.41928	0.709640	+	0.704564i	$0.248857\pi$
$984$	−512.000	−0.0165874
$985$	0	0
$986$	−24.0000	−0.000775168 0
$987$	−9352.00	−0.301598
$988$	13776.0	0.443596
$989$	49175.0	1.58107
$990$	0	0
$991$	−8201.00	−0.262879	−0.131440	−	0.991324i	$-0.541960\pi$
$991$	−8201.00	−0.262879	−0.131440	+	0.991324i	$0.541960\pi$
$992$	−7232.00	−0.231468
$993$	−13108.0	−0.418902
$994$	210.000	0.00670100
$995$	0	0
$996$	−12128.0	−0.385834
$997$	−4274.00	−0.135766	−0.0678831	−	0.997693i	$-0.521624\pi$
$997$	−4274.00	−0.135766	−0.0678831	+	0.997693i	$0.521624\pi$
$998$	−4088.00	−0.129663
$999$	−2888.00	−0.0914637

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.4.a.h.1.1	✓	1
5.2	odd	4		350.4.c.c.99.1		2
5.3	odd	4		350.4.c.c.99.2		2
5.4	even	2		350.4.a.n.1.1	yes	1
7.6	odd	2		2450.4.a.e.1.1		1
35.34	odd	2		2450.4.a.bk.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.4.a.h.1.1	✓	1	1.1	even	1	trivial
350.4.a.n.1.1	yes	1	5.4	even	2
350.4.c.c.99.1		2	5.2	odd	4
350.4.c.c.99.2		2	5.3	odd	4
2450.4.a.e.1.1		1	7.6	odd	2
2450.4.a.bk.1.1		1	35.34	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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