LMFDB - Embedded newform 435.4.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,4,Mod(1,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, 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("435.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$435 = 3 \cdot 5 \cdot 29$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	435.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:	$25.6658308525$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{7} - 2x^{6} - 37x^{5} + 55x^{4} + 336x^{3} - 227x^{2} - 824x - 166$ x^7 - 2x^6 - 37x^5 + 55x^4 + 336x^3 - 227x^2 - 824x - 166
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$2^{3}$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$5.24052$ of defining polynomial
Character	$\chi$	$=$	435.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.24052 q^{2} -3.00000 q^{3} +19.4631 q^{4} +5.00000 q^{5} +15.7216 q^{6} -18.4475 q^{7} -60.0724 q^{8} +9.00000 q^{9} -26.2026 q^{10} +11.5384 q^{11} -58.3892 q^{12} -34.4618 q^{13} +96.6746 q^{14} -15.0000 q^{15} +159.106 q^{16} +70.7681 q^{17} -47.1647 q^{18} +3.52127 q^{19} +97.3153 q^{20} +55.3426 q^{21} -60.4671 q^{22} -18.3117 q^{23} +180.217 q^{24} +25.0000 q^{25} +180.598 q^{26} -27.0000 q^{27} -359.045 q^{28} +29.0000 q^{29} +78.6078 q^{30} -120.558 q^{31} -353.221 q^{32} -34.6151 q^{33} -370.862 q^{34} -92.2376 q^{35} +175.168 q^{36} -182.505 q^{37} -18.4533 q^{38} +103.385 q^{39} -300.362 q^{40} +74.4691 q^{41} -290.024 q^{42} -405.899 q^{43} +224.572 q^{44} +45.0000 q^{45} +95.9626 q^{46} -327.143 q^{47} -477.319 q^{48} -2.68899 q^{49} -131.013 q^{50} -212.304 q^{51} -670.732 q^{52} +409.067 q^{53} +141.494 q^{54} +57.6919 q^{55} +1108.19 q^{56} -10.5638 q^{57} -151.975 q^{58} +120.722 q^{59} -291.946 q^{60} +34.6082 q^{61} +631.788 q^{62} -166.028 q^{63} +578.210 q^{64} -172.309 q^{65} +181.401 q^{66} +671.739 q^{67} +1377.36 q^{68} +54.9350 q^{69} +483.373 q^{70} +873.524 q^{71} -540.652 q^{72} +432.426 q^{73} +956.419 q^{74} -75.0000 q^{75} +68.5347 q^{76} -212.854 q^{77} -541.793 q^{78} -548.355 q^{79} +795.532 q^{80} +81.0000 q^{81} -390.257 q^{82} +511.077 q^{83} +1077.14 q^{84} +353.841 q^{85} +2127.12 q^{86} -87.0000 q^{87} -693.138 q^{88} -788.135 q^{89} -235.823 q^{90} +635.734 q^{91} -356.401 q^{92} +361.675 q^{93} +1714.40 q^{94} +17.6063 q^{95} +1059.66 q^{96} +967.070 q^{97} +14.0917 q^{98} +103.845 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} + 35 q^{5} + 6 q^{6} - 50 q^{7} - 33 q^{8} + 63 q^{9} - 10 q^{10} + 76 q^{11} - 66 q^{12} + 30 q^{13} + 89 q^{14} - 105 q^{15} + 138 q^{16} - 140 q^{17} - 18 q^{18} + 90 q^{19}+ \cdots + 684 q^{99}+O(q^{100})$ 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 + 35 * q^5 + 6 * q^6 - 50 * q^7 - 33 * q^8 + 63 * q^9 - 10 * q^10 + 76 * q^11 - 66 * q^12 + 30 * q^13 + 89 * q^14 - 105 * q^15 + 138 * q^16 - 140 * q^17 - 18 * q^18 + 90 * q^19 + 110 * q^20 + 150 * q^21 + 61 * q^22 + 34 * q^23 + 99 * q^24 + 175 * q^25 - 241 * q^26 - 189 * q^27 - 57 * q^28 + 203 * q^29 + 30 * q^30 + 524 * q^31 - 6 * q^32 - 228 * q^33 + 255 * q^34 - 250 * q^35 + 198 * q^36 - 28 * q^37 + 222 * q^38 - 90 * q^39 - 165 * q^40 + 1532 * q^41 - 267 * q^42 - 464 * q^43 + 1475 * q^44 + 315 * q^45 + 72 * q^46 - 360 * q^47 - 414 * q^48 + 569 * q^49 - 50 * q^50 + 420 * q^51 - 205 * q^52 + 282 * q^53 + 54 * q^54 + 380 * q^55 + 1102 * q^56 - 270 * q^57 - 58 * q^58 + 766 * q^59 - 330 * q^60 + 1200 * q^61 + 2856 * q^62 - 450 * q^63 + 701 * q^64 + 150 * q^65 - 183 * q^66 + 1546 * q^67 + 1801 * q^68 - 102 * q^69 + 445 * q^70 + 1802 * q^71 - 297 * q^72 - 220 * q^73 + 1594 * q^74 - 525 * q^75 + 1960 * q^76 + 3222 * q^77 + 723 * q^78 + 1298 * q^79 + 690 * q^80 + 567 * q^81 + 856 * q^82 + 1652 * q^83 + 171 * q^84 - 700 * q^85 + 7628 * q^86 - 609 * q^87 + 550 * q^88 + 2846 * q^89 - 90 * q^90 - 816 * q^91 + 472 * q^92 - 1572 * q^93 + 745 * q^94 + 450 * q^95 + 18 * q^96 + 1110 * q^97 - 761 * q^98 + 684 * q^99

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

)

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

$2$	−5.24052	−1.85280	−0.926402	−	0.376536i	$-0.877115\pi$
$2$	−5.24052	−1.85280	−0.926402	+	0.376536i	$0.877115\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	19.4631	2.43288
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	15.7216	1.06972
$7$	−18.4475	−0.996072	−0.498036	−	0.867156i	$-0.665945\pi$
$7$	−18.4475	−0.996072	−0.498036	+	0.867156i	$0.665945\pi$
$8$	−60.0724	−2.65485
$9$	9.00000	0.333333
$10$	−26.2026	−0.828599
$11$	11.5384	0.316268	0.158134	−	0.987418i	$-0.449452\pi$
$11$	11.5384	0.316268	0.158134	+	0.987418i	$0.449452\pi$
$12$	−58.3892	−1.40463
$13$	−34.4618	−0.735229	−0.367614	−	0.929978i	$-0.619825\pi$
$13$	−34.4618	−0.735229	−0.367614	+	0.929978i	$0.619825\pi$
$14$	96.6746	1.84553
$15$	−15.0000	−0.258199
$16$	159.106	2.48604
$17$	70.7681	1.00963	0.504817	−	0.863226i	$-0.331560\pi$
$17$	70.7681	1.00963	0.504817	+	0.863226i	$0.331560\pi$
$18$	−47.1647	−0.617601
$19$	3.52127	0.0425176	0.0212588	−	0.999774i	$-0.493233\pi$
$19$	3.52127	0.0425176	0.0212588	+	0.999774i	$0.493233\pi$
$20$	97.3153	1.08802
$21$	55.3426	0.575083
$22$	−60.4671	−0.585983
$23$	−18.3117	−0.166011	−0.0830053	−	0.996549i	$-0.526452\pi$
$23$	−18.3117	−0.166011	−0.0830053	+	0.996549i	$0.526452\pi$
$24$	180.217	1.53278
$25$	25.0000	0.200000
$26$	180.598	1.36224
$27$	−27.0000	−0.192450
$28$	−359.045	−2.42333
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	78.6078	0.478392
$31$	−120.558	−0.698481	−0.349240	−	0.937033i	$-0.613560\pi$
$31$	−120.558	−0.698481	−0.349240	+	0.937033i	$0.613560\pi$
$32$	−353.221	−1.95129
$33$	−34.6151	−0.182598
$34$	−370.862	−1.87065
$35$	−92.2376	−0.445457
$36$	175.168	0.810961
$37$	−182.505	−0.810907	−0.405454	−	0.914116i	$-0.632886\pi$
$37$	−182.505	−0.810907	−0.405454	+	0.914116i	$0.632886\pi$
$38$	−18.4533	−0.0787768
$39$	103.385	0.424485
$40$	−300.362	−1.18729
$41$	74.4691	0.283661	0.141831	−	0.989891i	$-0.454701\pi$
$41$	74.4691	0.283661	0.141831	+	0.989891i	$0.454701\pi$
$42$	−290.024	−1.06552
$43$	−405.899	−1.43951	−0.719756	−	0.694227i	$-0.755746\pi$
$43$	−405.899	−1.43951	−0.719756	+	0.694227i	$0.755746\pi$
$44$	224.572	0.769444
$45$	45.0000	0.149071
$46$	95.9626	0.307585
$47$	−327.143	−1.01529	−0.507646	−	0.861566i	$-0.669484\pi$
$47$	−327.143	−1.01529	−0.507646	+	0.861566i	$0.669484\pi$
$48$	−477.319	−1.43531
$49$	−2.68899	−0.00783963
$50$	−131.013	−0.370561
$51$	−212.304	−0.582913
$52$	−670.732	−1.78873
$53$	409.067	1.06018	0.530092	−	0.847940i	$-0.322157\pi$
$53$	409.067	1.06018	0.530092	+	0.847940i	$0.322157\pi$
$54$	141.494	0.356572
$55$	57.6919	0.141440
$56$	1108.19	2.64442
$57$	−10.5638	−0.0245475
$58$	−151.975	−0.344057
$59$	120.722	0.266384	0.133192	−	0.991090i	$-0.457477\pi$
$59$	120.722	0.266384	0.133192	+	0.991090i	$0.457477\pi$
$60$	−291.946	−0.628168
$61$	34.6082	0.0726415	0.0363207	−	0.999340i	$-0.488436\pi$
$61$	34.6082	0.0726415	0.0363207	+	0.999340i	$0.488436\pi$
$62$	631.788	1.29415
$63$	−166.028	−0.332024
$64$	578.210	1.12932
$65$	−172.309	−0.328804
$66$	181.401	0.338318
$67$	671.739	1.22487	0.612433	−	0.790523i	$-0.290191\pi$
$67$	671.739	1.22487	0.612433	+	0.790523i	$0.290191\pi$
$68$	1377.36	2.45632
$69$	54.9350	0.0958463
$70$	483.373	0.825345
$71$	873.524	1.46012	0.730058	−	0.683386i	$-0.239493\pi$
$71$	873.524	1.46012	0.730058	+	0.683386i	$0.239493\pi$
$72$	−540.652	−0.884951
$73$	432.426	0.693311	0.346655	−	0.937993i	$-0.387317\pi$
$73$	432.426	0.693311	0.346655	+	0.937993i	$0.387317\pi$
$74$	956.419	1.50245
$75$	−75.0000	−0.115470
$76$	68.5347	0.103440
$77$	−212.854	−0.315026
$78$	−541.793	−0.786487
$79$	−548.355	−0.780946	−0.390473	−	0.920614i	$-0.627689\pi$
$79$	−548.355	−0.780946	−0.390473	+	0.920614i	$0.627689\pi$
$80$	795.532	1.11179
$81$	81.0000	0.111111
$82$	−390.257	−0.525569
$83$	511.077	0.675879	0.337940	−	0.941168i	$-0.390270\pi$
$83$	511.077	0.675879	0.337940	+	0.941168i	$0.390270\pi$
$84$	1077.14	1.39911
$85$	353.841	0.451522
$86$	2127.12	2.66713
$87$	−87.0000	−0.107211
$88$	−693.138	−0.839646
$89$	−788.135	−0.938676	−0.469338	−	0.883019i	$-0.655507\pi$
$89$	−788.135	−0.938676	−0.469338	+	0.883019i	$0.655507\pi$
$90$	−235.823	−0.276200
$91$	635.734	0.732341
$92$	−356.401	−0.403884
$93$	361.675	0.403268
$94$	1714.40	1.88114
$95$	17.6063	0.0190144
$96$	1059.66	1.12658
$97$	967.070	1.01228	0.506140	−	0.862452i	$-0.331072\pi$
$97$	967.070	1.01228	0.506140	+	0.862452i	$0.331072\pi$
$98$	14.0917	0.0145253
$99$	103.845	0.105423
$100$	486.577	0.486577
$101$	510.016	0.502460	0.251230	−	0.967927i	$-0.419165\pi$
$101$	510.016	0.502460	0.251230	+	0.967927i	$0.419165\pi$
$102$	1112.59	1.08002
$103$	1645.72	1.57435	0.787175	−	0.616730i	$-0.211543\pi$
$103$	1645.72	1.57435	0.787175	+	0.616730i	$0.211543\pi$
$104$	2070.20	1.95192
$105$	276.713	0.257185
$106$	−2143.73	−1.96431
$107$	−1305.35	−1.17937	−0.589687	−	0.807632i	$-0.700749\pi$
$107$	−1305.35	−1.17937	−0.589687	+	0.807632i	$0.700749\pi$
$108$	−525.503	−0.468209
$109$	932.125	0.819095	0.409548	−	0.912289i	$-0.365687\pi$
$109$	932.125	0.819095	0.409548	+	0.912289i	$0.365687\pi$
$110$	−302.336	−0.262060
$111$	547.514	0.468178
$112$	−2935.12	−2.47627
$113$	1719.89	1.43180	0.715901	−	0.698202i	$-0.246016\pi$
$113$	1719.89	1.43180	0.715901	+	0.698202i	$0.246016\pi$
$114$	55.3598	0.0454818
$115$	−91.5583	−0.0742422
$116$	564.429	0.451775
$117$	−310.156	−0.245076
$118$	−632.646	−0.493558
$119$	−1305.50	−1.00567
$120$	901.087	0.685480
$121$	−1197.87	−0.899974
$122$	−181.365	−0.134590
$123$	−223.407	−0.163772
$124$	−2346.43	−1.69932
$125$	125.000	0.0894427
$126$	870.072	0.615176
$127$	−883.792	−0.617511	−0.308756	−	0.951141i	$-0.599912\pi$
$127$	−883.792	−0.617511	−0.308756	+	0.951141i	$0.599912\pi$
$128$	−204.357	−0.141116
$129$	1217.70	0.831102
$130$	902.988	0.609210
$131$	−937.386	−0.625190	−0.312595	−	0.949887i	$-0.601198\pi$
$131$	−937.386	−0.625190	−0.312595	+	0.949887i	$0.601198\pi$
$132$	−673.717	−0.444239
$133$	−64.9587	−0.0423506
$134$	−3520.26	−2.26944
$135$	−135.000	−0.0860663
$136$	−4251.21	−2.68043
$137$	237.650	0.148203	0.0741014	−	0.997251i	$-0.476391\pi$
$137$	237.650	0.148203	0.0741014	+	0.997251i	$0.476391\pi$
$138$	−287.888	−0.177584
$139$	1706.72	1.04146	0.520728	−	0.853723i	$-0.325661\pi$
$139$	1706.72	1.04146	0.520728	+	0.853723i	$0.325661\pi$
$140$	−1795.23	−1.08375
$141$	981.430	0.586179
$142$	−4577.72	−2.70531
$143$	−397.633	−0.232530
$144$	1431.96	0.828679
$145$	145.000	0.0830455
$146$	−2266.14	−1.28457
$147$	8.06698	0.00452621
$148$	−3552.10	−1.97284
$149$	3546.59	1.94999	0.974994	−	0.222230i	$-0.0713334\pi$
$149$	3546.59	1.94999	0.974994	+	0.222230i	$0.0713334\pi$
$150$	393.039	0.213943
$151$	1818.23	0.979901	0.489951	−	0.871750i	$-0.337015\pi$
$151$	1818.23	0.979901	0.489951	+	0.871750i	$0.337015\pi$
$152$	−211.531	−0.112878
$153$	636.913	0.336545
$154$	1115.47	0.583682
$155$	−602.791	−0.312370
$156$	2012.20	1.03272
$157$	−37.7540	−0.0191917	−0.00959585	−	0.999954i	$-0.503055\pi$
$157$	−37.7540	−0.0191917	−0.00959585	+	0.999954i	$0.503055\pi$
$158$	2873.66	1.44694
$159$	−1227.20	−0.612097
$160$	−1766.10	−0.872642
$161$	337.805	0.165359
$162$	−424.482	−0.205867
$163$	1541.87	0.740913	0.370457	−	0.928850i	$-0.379201\pi$
$163$	1541.87	0.740913	0.370457	+	0.928850i	$0.379201\pi$
$164$	1449.40	0.690115
$165$	−173.076	−0.0816601
$166$	−2678.31	−1.25227
$167$	1669.49	0.773586	0.386793	−	0.922167i	$-0.373583\pi$
$167$	1669.49	0.773586	0.386793	+	0.922167i	$0.373583\pi$
$168$	−3324.56	−1.52676
$169$	−1009.39	−0.459438
$170$	−1854.31	−0.836582
$171$	31.6914	0.0141725
$172$	−7900.04	−3.50216
$173$	−728.623	−0.320209	−0.160105	−	0.987100i	$-0.551183\pi$
$173$	−728.623	−0.320209	−0.160105	+	0.987100i	$0.551183\pi$
$174$	455.925	0.198641
$175$	−461.188	−0.199214
$176$	1835.83	0.786255
$177$	−362.166	−0.153797
$178$	4130.24	1.73918
$179$	1926.46	0.804416	0.402208	−	0.915548i	$-0.368243\pi$
$179$	1926.46	0.804416	0.402208	+	0.915548i	$0.368243\pi$
$180$	875.838	0.362673
$181$	3695.62	1.51764	0.758821	−	0.651299i	$-0.225776\pi$
$181$	3695.62	1.51764	0.758821	+	0.651299i	$0.225776\pi$
$182$	−3331.58	−1.35689
$183$	−103.825	−0.0419396
$184$	1100.03	0.440733
$185$	−912.523	−0.362649
$186$	−1895.36	−0.747177
$187$	816.549	0.319315
$188$	−6367.21	−2.47009
$189$	498.083	0.191694
$190$	−92.2664	−0.0352300
$191$	2490.19	0.943370	0.471685	−	0.881767i	$-0.343646\pi$
$191$	2490.19	0.943370	0.471685	+	0.881767i	$0.343646\pi$
$192$	−1734.63	−0.652012
$193$	4493.27	1.67582	0.837909	−	0.545809i	$-0.183778\pi$
$193$	4493.27	1.67582	0.837909	+	0.545809i	$0.183778\pi$
$194$	−5067.95	−1.87555
$195$	516.927	0.189835
$196$	−52.3361	−0.0190729
$197$	1990.23	0.719787	0.359894	−	0.932993i	$-0.382813\pi$
$197$	1990.23	0.719787	0.359894	+	0.932993i	$0.382813\pi$
$198$	−544.204	−0.195328
$199$	−83.8021	−0.0298521	−0.0149261	−	0.999889i	$-0.504751\pi$
$199$	−83.8021	−0.0298521	−0.0149261	+	0.999889i	$0.504751\pi$
$200$	−1501.81	−0.530970
$201$	−2015.22	−0.707176
$202$	−2672.75	−0.930960
$203$	−534.978	−0.184966
$204$	−4132.09	−1.41816
$205$	372.345	0.126857
$206$	−8624.45	−2.91696
$207$	−164.805	−0.0553369
$208$	−5483.09	−1.82781
$209$	40.6297	0.0134470
$210$	−1450.12	−0.476513
$211$	−4369.95	−1.42578	−0.712891	−	0.701275i	$-0.752615\pi$
$211$	−4369.95	−1.42578	−0.712891	+	0.701275i	$0.752615\pi$
$212$	7961.71	2.57930
$213$	−2620.57	−0.842998
$214$	6840.72	2.18515
$215$	−2029.49	−0.643769
$216$	1621.96	0.510926
$217$	2224.00	0.695738
$218$	−4884.82	−1.51762
$219$	−1297.28	−0.400283
$220$	1122.86	0.344106
$221$	−2438.79	−0.742313
$222$	−2869.26	−0.867441
$223$	3633.76	1.09119	0.545594	−	0.838050i	$-0.316304\pi$
$223$	3633.76	1.09119	0.545594	+	0.838050i	$0.316304\pi$
$224$	6516.05	1.94362
$225$	225.000	0.0666667
$226$	−9013.12	−2.65285
$227$	−3692.30	−1.07959	−0.539794	−	0.841797i	$-0.681498\pi$
$227$	−3692.30	−1.07959	−0.539794	+	0.841797i	$0.681498\pi$
$228$	−205.604	−0.0597213
$229$	4833.73	1.39486	0.697428	−	0.716655i	$-0.254328\pi$
$229$	4833.73	1.39486	0.697428	+	0.716655i	$0.254328\pi$
$230$	479.813	0.137556
$231$	638.563	0.181880
$232$	−1742.10	−0.492994
$233$	−4834.45	−1.35929	−0.679647	−	0.733539i	$-0.737867\pi$
$233$	−4834.45	−1.35929	−0.679647	+	0.733539i	$0.737867\pi$
$234$	1625.38	0.454078
$235$	−1635.72	−0.454053
$236$	2349.62	0.648081
$237$	1645.06	0.450879
$238$	6841.48	1.86331
$239$	4019.80	1.08795	0.543974	−	0.839102i	$-0.316919\pi$
$239$	4019.80	1.08795	0.543974	+	0.839102i	$0.316919\pi$
$240$	−2386.60	−0.641892
$241$	1076.81	0.287816	0.143908	−	0.989591i	$-0.454033\pi$
$241$	1076.81	0.287816	0.143908	+	0.989591i	$0.454033\pi$
$242$	6277.44	1.66748
$243$	−243.000	−0.0641500
$244$	673.582	0.176728
$245$	−13.4450	−0.00350599
$246$	1170.77	0.303437
$247$	−121.349	−0.0312602
$248$	7242.23	1.85436
$249$	−1533.23	−0.390219
$250$	−655.065	−0.165720
$251$	−3179.99	−0.799677	−0.399839	−	0.916586i	$-0.630934\pi$
$251$	−3179.99	−0.799677	−0.399839	+	0.916586i	$0.630934\pi$
$252$	−3231.41	−0.807776
$253$	−211.287	−0.0525039
$254$	4631.53	1.14413
$255$	−1061.52	−0.260687
$256$	−3554.74	−0.867858
$257$	3125.29	0.758561	0.379280	−	0.925282i	$-0.376172\pi$
$257$	3125.29	0.758561	0.379280	+	0.925282i	$0.376172\pi$
$258$	−6381.37	−1.53987
$259$	3366.76	0.807722
$260$	−3353.66	−0.799943
$261$	261.000	0.0618984
$262$	4912.39	1.15835
$263$	−4474.30	−1.04904	−0.524519	−	0.851399i	$-0.675755\pi$
$263$	−4474.30	−1.04904	−0.524519	+	0.851399i	$0.675755\pi$
$264$	2079.42	0.484770
$265$	2045.34	0.474129
$266$	340.417	0.0784674
$267$	2364.41	0.541945
$268$	13074.1	2.97995
$269$	4053.04	0.918655	0.459327	−	0.888267i	$-0.348091\pi$
$269$	4053.04	0.918655	0.459327	+	0.888267i	$0.348091\pi$
$270$	707.470	0.159464
$271$	−8045.96	−1.80353	−0.901766	−	0.432225i	$-0.857729\pi$
$271$	−8045.96	−1.80353	−0.901766	+	0.432225i	$0.857729\pi$
$272$	11259.7	2.50999
$273$	−1907.20	−0.422817
$274$	−1245.41	−0.274591
$275$	288.459	0.0632537
$276$	1069.20	0.233183
$277$	4625.74	1.00337	0.501685	−	0.865050i	$-0.332714\pi$
$277$	4625.74	1.00337	0.501685	+	0.865050i	$0.332714\pi$
$278$	−8944.11	−1.92961
$279$	−1085.02	−0.232827
$280$	5540.94	1.18262
$281$	−69.7964	−0.0148174	−0.00740872	−	0.999973i	$-0.502358\pi$
$281$	−69.7964	−0.0148174	−0.00740872	+	0.999973i	$0.502358\pi$
$282$	−5143.20	−1.08608
$283$	1903.58	0.399845	0.199922	−	0.979812i	$-0.435931\pi$
$283$	1903.58	0.399845	0.199922	+	0.979812i	$0.435931\pi$
$284$	17001.4	3.55229
$285$	−52.8190	−0.0109780
$286$	2083.80	0.430832
$287$	−1373.77	−0.282547
$288$	−3178.99	−0.650429
$289$	95.1246	0.0193618
$290$	−759.876	−0.153867
$291$	−2901.21	−0.584440
$292$	8416.34	1.68674
$293$	623.198	0.124258	0.0621290	−	0.998068i	$-0.480211\pi$
$293$	623.198	0.124258	0.0621290	+	0.998068i	$0.480211\pi$
$294$	−42.2752	−0.00838619
$295$	603.610	0.119131
$296$	10963.5	2.15284
$297$	−311.536	−0.0608659
$298$	−18586.0	−3.61295
$299$	631.052	0.122056
$300$	−1459.73	−0.280925
$301$	7487.83	1.43386
$302$	−9528.45	−1.81557
$303$	−1530.05	−0.290095
$304$	560.256	0.105700
$305$	173.041	0.0324863
$306$	−3337.76	−0.623552
$307$	−6899.90	−1.28273	−0.641365	−	0.767236i	$-0.721632\pi$
$307$	−6899.90	−1.28273	−0.641365	+	0.767236i	$0.721632\pi$
$308$	−4142.80	−0.766422
$309$	−4937.17	−0.908951
$310$	3158.94	0.578761
$311$	−181.369	−0.0330692	−0.0165346	−	0.999863i	$-0.505263\pi$
$311$	−181.369	−0.0330692	−0.0165346	+	0.999863i	$0.505263\pi$
$312$	−6210.61	−1.12694
$313$	−3839.22	−0.693308	−0.346654	−	0.937993i	$-0.612682\pi$
$313$	−3839.22	−0.693308	−0.346654	+	0.937993i	$0.612682\pi$
$314$	197.851	0.0355585
$315$	−830.138	−0.148486
$316$	−10672.7	−1.89995
$317$	7000.08	1.24026	0.620132	−	0.784497i	$-0.287079\pi$
$317$	7000.08	1.24026	0.620132	+	0.784497i	$0.287079\pi$
$318$	6431.18	1.13410
$319$	334.613	0.0587296
$320$	2891.05	0.505046
$321$	3916.05	0.680912
$322$	−1770.27	−0.306377
$323$	249.193	0.0429272
$324$	1576.51	0.270320
$325$	−861.544	−0.147046
$326$	−8080.22	−1.37277
$327$	−2796.38	−0.472905
$328$	−4473.54	−0.753079
$329$	6034.98	1.01130
$330$	907.007	0.151300
$331$	−1176.84	−0.195423	−0.0977115	−	0.995215i	$-0.531152\pi$
$331$	−1176.84	−0.195423	−0.0977115	+	0.995215i	$0.531152\pi$
$332$	9947.12	1.64433
$333$	−1642.54	−0.270302
$334$	−8748.99	−1.43330
$335$	3358.69	0.547776
$336$	8805.35	1.42968
$337$	−174.049	−0.0281336	−0.0140668	−	0.999901i	$-0.504478\pi$
$337$	−174.049	−0.0281336	−0.0140668	+	0.999901i	$0.504478\pi$
$338$	5289.71	0.851249
$339$	−5159.67	−0.826652
$340$	6886.82	1.09850
$341$	−1391.05	−0.220907
$342$	−166.080	−0.0262589
$343$	6377.10	1.00388
$344$	24383.3	3.82169
$345$	274.675	0.0428637
$346$	3818.37	0.593285
$347$	−10895.5	−1.68560	−0.842799	−	0.538228i	$-0.819094\pi$
$347$	−10895.5	−1.68560	−0.842799	+	0.538228i	$0.819094\pi$
$348$	−1693.29	−0.260832
$349$	−11820.3	−1.81298	−0.906488	−	0.422232i	$-0.861247\pi$
$349$	−11820.3	−1.81298	−0.906488	+	0.422232i	$0.861247\pi$
$350$	2416.87	0.369105
$351$	930.468	0.141495
$352$	−4075.60	−0.617131
$353$	9795.13	1.47689	0.738445	−	0.674314i	$-0.235561\pi$
$353$	9795.13	1.47689	0.738445	+	0.674314i	$0.235561\pi$
$354$	1897.94	0.284956
$355$	4367.62	0.652983
$356$	−15339.5	−2.28369
$357$	3916.49	0.580623
$358$	−10095.7	−1.49042
$359$	8894.06	1.30755	0.653775	−	0.756689i	$-0.273184\pi$
$359$	8894.06	1.30755	0.653775	+	0.756689i	$0.273184\pi$
$360$	−2703.26	−0.395762
$361$	−6846.60	−0.998192
$362$	−19367.0	−2.81189
$363$	3593.60	0.519600
$364$	12373.3	1.78170
$365$	2162.13	0.310058
$366$	544.096	0.0777058
$367$	11113.1	1.58066	0.790329	−	0.612683i	$-0.209910\pi$
$367$	11113.1	1.58066	0.790329	+	0.612683i	$0.209910\pi$
$368$	−2913.50	−0.412708
$369$	670.222	0.0945538
$370$	4782.10	0.671917
$371$	−7546.28	−1.05602
$372$	7039.30	0.981104
$373$	13469.8	1.86981	0.934907	−	0.354892i	$-0.115482\pi$
$373$	13469.8	1.86981	0.934907	+	0.354892i	$0.115482\pi$
$374$	−4279.14	−0.591629
$375$	−375.000	−0.0516398
$376$	19652.3	2.69545
$377$	−999.391	−0.136529
$378$	−2610.21	−0.355172
$379$	−3750.71	−0.508341	−0.254170	−	0.967159i	$-0.581802\pi$
$379$	−3750.71	−0.508341	−0.254170	+	0.967159i	$0.581802\pi$
$380$	342.673	0.0462599
$381$	2651.38	0.356520
$382$	−13049.9	−1.74788
$383$	12404.3	1.65490	0.827451	−	0.561537i	$-0.189790\pi$
$383$	12404.3	1.65490	0.827451	+	0.561537i	$0.189790\pi$
$384$	613.072	0.0814732
$385$	−1064.27	−0.140884
$386$	−23547.1	−3.10496
$387$	−3653.09	−0.479837
$388$	18822.1	2.46276
$389$	−7718.67	−1.00605	−0.503023	−	0.864273i	$-0.667779\pi$
$389$	−7718.67	−1.00605	−0.503023	+	0.864273i	$0.667779\pi$
$390$	−2708.97	−0.351728
$391$	−1295.88	−0.167610
$392$	161.534	0.0208131
$393$	2812.16	0.360953
$394$	−10429.8	−1.33362
$395$	−2741.77	−0.349250
$396$	2021.15	0.256481
$397$	−6747.40	−0.853004	−0.426502	−	0.904487i	$-0.640254\pi$
$397$	−6747.40	−0.853004	−0.426502	+	0.904487i	$0.640254\pi$
$398$	439.167	0.0553101
$399$	194.876	0.0244511
$400$	3977.66	0.497207
$401$	−5047.40	−0.628567	−0.314283	−	0.949329i	$-0.601764\pi$
$401$	−5047.40	−0.628567	−0.314283	+	0.949329i	$0.601764\pi$
$402$	10560.8	1.31026
$403$	4154.65	0.513543
$404$	9926.47	1.22243
$405$	405.000	0.0496904
$406$	2803.56	0.342706
$407$	−2105.81	−0.256464
$408$	12753.6	1.54755
$409$	5317.14	0.642826	0.321413	−	0.946939i	$-0.395842\pi$
$409$	5317.14	0.642826	0.321413	+	0.946939i	$0.395842\pi$
$410$	−1951.28	−0.235042
$411$	−712.949	−0.0855649
$412$	32030.8	3.83021
$413$	−2227.02	−0.265338
$414$	863.663	0.102528
$415$	2555.38	0.302262
$416$	12172.6	1.43464
$417$	−5120.17	−0.601284
$418$	−212.921	−0.0249146
$419$	2953.43	0.344355	0.172177	−	0.985066i	$-0.444920\pi$
$419$	2953.43	0.344355	0.172177	+	0.985066i	$0.444920\pi$
$420$	5385.68	0.625701
$421$	7427.88	0.859888	0.429944	−	0.902855i	$-0.358533\pi$
$421$	7427.88	0.859888	0.429944	+	0.902855i	$0.358533\pi$
$422$	22900.8	2.64170
$423$	−2944.29	−0.338431
$424$	−24573.7	−2.81463
$425$	1769.20	0.201927
$426$	13733.2	1.56191
$427$	−638.436	−0.0723562
$428$	−25406.1	−2.86928
$429$	1192.90	0.134251
$430$	10635.6	1.19278
$431$	3302.08	0.369038	0.184519	−	0.982829i	$-0.440927\pi$
$431$	3302.08	0.369038	0.184519	+	0.982829i	$0.440927\pi$
$432$	−4295.87	−0.478438
$433$	9352.89	1.03804	0.519020	−	0.854762i	$-0.326297\pi$
$433$	9352.89	1.03804	0.519020	+	0.854762i	$0.326297\pi$
$434$	−11654.9	−1.28907
$435$	−435.000	−0.0479463
$436$	18142.0	1.99276
$437$	−64.4802	−0.00705837
$438$	6798.42	0.741646
$439$	−6109.74	−0.664241	−0.332120	−	0.943237i	$-0.607764\pi$
$439$	−6109.74	−0.664241	−0.332120	+	0.943237i	$0.607764\pi$
$440$	−3465.69	−0.375501
$441$	−24.2009	−0.00261321
$442$	12780.6	1.37536
$443$	14282.0	1.53173	0.765865	−	0.643002i	$-0.222311\pi$
$443$	14282.0	1.53173	0.765865	+	0.643002i	$0.222311\pi$
$444$	10656.3	1.13902
$445$	−3940.68	−0.419789
$446$	−19042.8	−2.02176
$447$	−10639.8	−1.12583
$448$	−10666.5	−1.12488
$449$	−16406.0	−1.72439	−0.862193	−	0.506581i	$-0.830909\pi$
$449$	−16406.0	−1.72439	−0.862193	+	0.506581i	$0.830909\pi$
$450$	−1179.12	−0.123520
$451$	859.252	0.0897131
$452$	33474.3	3.48341
$453$	−5454.68	−0.565746
$454$	19349.6	2.00026
$455$	3178.67	0.327513
$456$	634.593	0.0651701
$457$	−15726.2	−1.60971	−0.804856	−	0.593470i	$-0.797757\pi$
$457$	−15726.2	−1.60971	−0.804856	+	0.593470i	$0.797757\pi$
$458$	−25331.3	−2.58440
$459$	−1910.74	−0.194304
$460$	−1782.00	−0.180623
$461$	−14091.2	−1.42363	−0.711816	−	0.702366i	$-0.752127\pi$
$461$	−14091.2	−1.42363	−0.711816	+	0.702366i	$0.752127\pi$
$462$	−3346.41	−0.336989
$463$	−8794.40	−0.882743	−0.441372	−	0.897324i	$-0.645508\pi$
$463$	−8794.40	−0.882743	−0.441372	+	0.897324i	$0.645508\pi$
$464$	4614.08	0.461645
$465$	1808.37	0.180347
$466$	25335.0	2.51850
$467$	−8746.05	−0.866636	−0.433318	−	0.901241i	$-0.642657\pi$
$467$	−8746.05	−0.866636	−0.433318	+	0.901241i	$0.642657\pi$
$468$	−6036.59	−0.596242
$469$	−12391.9	−1.22005
$470$	8572.00	0.841270
$471$	113.262	0.0110803
$472$	−7252.06	−0.707210
$473$	−4683.41	−0.455272
$474$	−8620.99	−0.835391
$475$	88.0317	0.00850352
$476$	−25409.0	−2.44668
$477$	3681.61	0.353395
$478$	−21065.9	−2.01575
$479$	−11452.6	−1.09245	−0.546225	−	0.837638i	$-0.683936\pi$
$479$	−11452.6	−1.09245	−0.546225	+	0.837638i	$0.683936\pi$
$480$	5298.31	0.503820
$481$	6289.43	0.596203
$482$	−5643.06	−0.533266
$483$	−1013.41	−0.0954698
$484$	−23314.1	−2.18953
$485$	4835.35	0.452705
$486$	1273.45	0.118857
$487$	1635.31	0.152163	0.0760813	−	0.997102i	$-0.475759\pi$
$487$	1635.31	0.152163	0.0760813	+	0.997102i	$0.475759\pi$
$488$	−2079.00	−0.192852
$489$	−4625.62	−0.427766
$490$	70.4586	0.00649591
$491$	2106.92	0.193654	0.0968270	−	0.995301i	$-0.469131\pi$
$491$	2106.92	0.193654	0.0968270	+	0.995301i	$0.469131\pi$
$492$	−4348.19	−0.398438
$493$	2052.28	0.187484
$494$	635.933	0.0579190
$495$	519.227	0.0471465
$496$	−19181.6	−1.73645
$497$	−16114.3	−1.45438
$498$	8034.93	0.722999
$499$	−8865.74	−0.795361	−0.397681	−	0.917524i	$-0.630185\pi$
$499$	−8865.74	−0.795361	−0.397681	+	0.917524i	$0.630185\pi$
$500$	2432.88	0.217604
$501$	−5008.46	−0.446630
$502$	16664.8	1.48165
$503$	−14591.9	−1.29348	−0.646738	−	0.762712i	$-0.723867\pi$
$503$	−14591.9	−1.29348	−0.646738	+	0.762712i	$0.723867\pi$
$504$	9973.69	0.881475
$505$	2550.08	0.224707
$506$	1107.25	0.0972794
$507$	3028.16	0.265257
$508$	−17201.3	−1.50233
$509$	13600.3	1.18432	0.592162	−	0.805819i	$-0.298274\pi$
$509$	13600.3	1.18432	0.592162	+	0.805819i	$0.298274\pi$
$510$	5562.93	0.483001
$511$	−7977.19	−0.690588
$512$	20263.6	1.74909
$513$	−95.0742	−0.00818251
$514$	−16378.1	−1.40546
$515$	8228.62	0.704070
$516$	23700.1	2.02197
$517$	−3774.70	−0.321105
$518$	−17643.6	−1.49655
$519$	2185.87	0.184873
$520$	10351.0	0.872927
$521$	8355.92	0.702647	0.351324	−	0.936254i	$-0.385732\pi$
$521$	8355.92	0.702647	0.351324	+	0.936254i	$0.385732\pi$
$522$	−1367.78	−0.114686
$523$	926.372	0.0774520	0.0387260	−	0.999250i	$-0.487670\pi$
$523$	926.372	0.0774520	0.0387260	+	0.999250i	$0.487670\pi$
$524$	−18244.4	−1.52101
$525$	1383.56	0.115017
$526$	23447.7	1.94366
$527$	−8531.68	−0.705210
$528$	−5507.49	−0.453944
$529$	−11831.7	−0.972440
$530$	−10718.6	−0.878467
$531$	1086.50	0.0887947
$532$	−1264.29	−0.103034
$533$	−2566.34	−0.208556
$534$	−12390.7	−1.00412
$535$	−6526.75	−0.527432
$536$	−40353.0	−3.25184
$537$	−5779.38	−0.464430
$538$	−21240.0	−1.70209
$539$	−31.0266	−0.00247943
$540$	−2627.51	−0.209389
$541$	13503.6	1.07313	0.536565	−	0.843859i	$-0.319722\pi$
$541$	13503.6	1.07313	0.536565	+	0.843859i	$0.319722\pi$
$542$	42165.0	3.34159
$543$	−11086.9	−0.876211
$544$	−24996.8	−1.97009
$545$	4660.63	0.366311
$546$	9994.74	0.783398
$547$	−20425.4	−1.59658	−0.798288	−	0.602275i	$-0.794261\pi$
$547$	−20425.4	−1.59658	−0.798288	+	0.602275i	$0.794261\pi$
$548$	4625.39	0.360560
$549$	311.474	0.0242138
$550$	−1511.68	−0.117197
$551$	102.117	0.00789532
$552$	−3300.08	−0.254458
$553$	10115.8	0.777879
$554$	−24241.3	−1.85905
$555$	2737.57	0.209375
$556$	33218.0	2.53374
$557$	−3929.12	−0.298891	−0.149446	−	0.988770i	$-0.547749\pi$
$557$	−3929.12	−0.298891	−0.149446	+	0.988770i	$0.547749\pi$
$558$	5686.09	0.431383
$559$	13988.0	1.05837
$560$	−14675.6	−1.10742
$561$	−2449.65	−0.184357
$562$	365.769	0.0274538
$563$	4452.67	0.333318	0.166659	−	0.986015i	$-0.446702\pi$
$563$	4452.67	0.333318	0.166659	+	0.986015i	$0.446702\pi$
$564$	19101.6	1.42611
$565$	8599.45	0.640322
$566$	−9975.75	−0.740834
$567$	−1494.25	−0.110675
$568$	−52474.7	−3.87639
$569$	−5462.20	−0.402438	−0.201219	−	0.979546i	$-0.564490\pi$
$569$	−5462.20	−0.402438	−0.201219	+	0.979546i	$0.564490\pi$
$570$	276.799	0.0203401
$571$	−7228.87	−0.529805	−0.264902	−	0.964275i	$-0.585340\pi$
$571$	−7228.87	−0.529805	−0.264902	+	0.964275i	$0.585340\pi$
$572$	−7739.16	−0.565717
$573$	−7470.57	−0.544655
$574$	7199.27	0.523505
$575$	−457.791	−0.0332021
$576$	5203.89	0.376439
$577$	12771.6	0.921468	0.460734	−	0.887538i	$-0.347586\pi$
$577$	12771.6	0.921468	0.460734	+	0.887538i	$0.347586\pi$
$578$	−498.502	−0.0358736
$579$	−13479.8	−0.967534
$580$	2822.14	0.202040
$581$	−9428.10	−0.673224
$582$	15203.9	1.08285
$583$	4719.97	0.335303
$584$	−25976.9	−1.84064
$585$	−1550.78	−0.109601
$586$	−3265.88	−0.230226
$587$	6986.93	0.491280	0.245640	−	0.969361i	$-0.421002\pi$
$587$	6986.93	0.491280	0.245640	+	0.969361i	$0.421002\pi$
$588$	157.008	0.0110117
$589$	−424.518	−0.0296977
$590$	−3163.23	−0.220726
$591$	−5970.69	−0.415569
$592$	−29037.6	−2.01595
$593$	4323.42	0.299396	0.149698	−	0.988732i	$-0.452170\pi$
$593$	4323.42	0.299396	0.149698	+	0.988732i	$0.452170\pi$
$594$	1632.61	0.112773
$595$	−6527.48	−0.449749
$596$	69027.6	4.74409
$597$	251.406	0.0172351
$598$	−3307.04	−0.226145
$599$	13443.7	0.917019	0.458510	−	0.888689i	$-0.348383\pi$
$599$	13443.7	0.917019	0.458510	+	0.888689i	$0.348383\pi$
$600$	4505.43	0.306556
$601$	−7179.72	−0.487299	−0.243650	−	0.969863i	$-0.578345\pi$
$601$	−7179.72	−0.487299	−0.243650	+	0.969863i	$0.578345\pi$
$602$	−39240.1	−2.65666
$603$	6045.65	0.408288
$604$	35388.2	2.38399
$605$	−5989.33	−0.402481
$606$	8018.24	0.537490
$607$	−8560.81	−0.572442	−0.286221	−	0.958164i	$-0.592399\pi$
$607$	−8560.81	−0.572442	−0.286221	+	0.958164i	$0.592399\pi$
$608$	−1243.79	−0.0829641
$609$	1604.93	0.106790
$610$	−906.826	−0.0601907
$611$	11273.9	0.746472
$612$	12396.3	0.818774
$613$	19634.3	1.29367	0.646837	−	0.762628i	$-0.276091\pi$
$613$	19634.3	1.29367	0.646837	+	0.762628i	$0.276091\pi$
$614$	36159.1	2.37665
$615$	−1117.04	−0.0732410
$616$	12786.7	0.836348
$617$	14268.5	0.931003	0.465502	−	0.885047i	$-0.345874\pi$
$617$	14268.5	0.931003	0.465502	+	0.885047i	$0.345874\pi$
$618$	25873.3	1.68411
$619$	1663.48	0.108014	0.0540071	−	0.998541i	$-0.482801\pi$
$619$	1663.48	0.108014	0.0540071	+	0.998541i	$0.482801\pi$
$620$	−11732.2	−0.759960
$621$	494.415	0.0319488
$622$	950.470	0.0612707
$623$	14539.1	0.934990
$624$	16449.3	1.05528
$625$	625.000	0.0400000
$626$	20119.5	1.28456
$627$	−121.889	−0.00776361
$628$	−734.808	−0.0466912
$629$	−12915.5	−0.818720
$630$	4350.36	0.275115
$631$	13448.3	0.848444	0.424222	−	0.905558i	$-0.360548\pi$
$631$	13448.3	0.848444	0.424222	+	0.905558i	$0.360548\pi$
$632$	32941.0	2.07330
$633$	13109.9	0.823176
$634$	−36684.1	−2.29797
$635$	−4418.96	−0.276159
$636$	−23885.1	−1.48916
$637$	92.6675	0.00576392
$638$	−1753.55	−0.108814
$639$	7861.71	0.486705
$640$	−1021.79	−0.0631088
$641$	7644.92	0.471070	0.235535	−	0.971866i	$-0.424316\pi$
$641$	7644.92	0.471070	0.235535	+	0.971866i	$0.424316\pi$
$642$	−20522.1	−1.26160
$643$	1814.60	0.111292	0.0556462	−	0.998451i	$-0.482278\pi$
$643$	1814.60	0.111292	0.0556462	+	0.998451i	$0.482278\pi$
$644$	6574.71	0.402298
$645$	6088.48	0.371680
$646$	−1305.90	−0.0795357
$647$	18746.6	1.13911	0.569556	−	0.821952i	$-0.307115\pi$
$647$	18746.6	1.13911	0.569556	+	0.821952i	$0.307115\pi$
$648$	−4865.87	−0.294984
$649$	1392.94	0.0842489
$650$	4514.94	0.272447
$651$	−6672.00	−0.401684
$652$	30009.6	1.80256
$653$	8299.18	0.497354	0.248677	−	0.968586i	$-0.420004\pi$
$653$	8299.18	0.497354	0.248677	+	0.968586i	$0.420004\pi$
$654$	14654.5	0.876200
$655$	−4686.93	−0.279593
$656$	11848.5	0.705192
$657$	3891.84	0.231104
$658$	−31626.4	−1.87375
$659$	12624.7	0.746262	0.373131	−	0.927779i	$-0.378284\pi$
$659$	12624.7	0.746262	0.373131	+	0.927779i	$0.378284\pi$
$660$	−3368.58	−0.198670
$661$	−10912.8	−0.642144	−0.321072	−	0.947055i	$-0.604043\pi$
$661$	−10912.8	−0.642144	−0.321072	+	0.947055i	$0.604043\pi$
$662$	6167.26	0.362081
$663$	7316.38	0.428574
$664$	−30701.6	−1.79436
$665$	−324.793	−0.0189398
$666$	8607.77	0.500817
$667$	−531.038	−0.0308274
$668$	32493.4	1.88204
$669$	−10901.3	−0.629998
$670$	−17601.3	−1.01492
$671$	399.323	0.0229742
$672$	−19548.1	−1.12215
$673$	6292.15	0.360393	0.180197	−	0.983631i	$-0.442327\pi$
$673$	6292.15	0.360393	0.180197	+	0.983631i	$0.442327\pi$
$674$	912.105	0.0521261
$675$	−675.000	−0.0384900
$676$	−19645.7	−1.11776
$677$	16630.8	0.944125	0.472062	−	0.881565i	$-0.343510\pi$
$677$	16630.8	0.944125	0.472062	+	0.881565i	$0.343510\pi$
$678$	27039.4	1.53162
$679$	−17840.0	−1.00830
$680$	−21256.1	−1.19872
$681$	11076.9	0.623300
$682$	7289.81	0.409298
$683$	11843.7	0.663521	0.331761	−	0.943364i	$-0.392357\pi$
$683$	11843.7	0.663521	0.331761	+	0.943364i	$0.392357\pi$
$684$	616.812	0.0344801
$685$	1188.25	0.0662783
$686$	−33419.4	−1.86000
$687$	−14501.2	−0.805321
$688$	−64581.1	−3.57868
$689$	−14097.2	−0.779478
$690$	−1439.44	−0.0794181
$691$	20458.3	1.12630	0.563149	−	0.826356i	$-0.309590\pi$
$691$	20458.3	1.12630	0.563149	+	0.826356i	$0.309590\pi$
$692$	−14181.2	−0.779032
$693$	−1915.69	−0.105009
$694$	57098.2	3.12308
$695$	8533.61	0.465753
$696$	5226.30	0.284630
$697$	5270.03	0.286394
$698$	61944.8	3.35909
$699$	14503.4	0.784789
$700$	−8976.13	−0.484666
$701$	23987.6	1.29244	0.646220	−	0.763151i	$-0.276349\pi$
$701$	23987.6	1.29244	0.646220	+	0.763151i	$0.276349\pi$
$702$	−4876.14	−0.262162
$703$	−642.648	−0.0344778
$704$	6671.61	0.357167
$705$	4907.15	0.262147
$706$	−51331.6	−2.73639
$707$	−9408.52	−0.500487
$708$	−7048.86	−0.374170
$709$	6275.84	0.332432	0.166216	−	0.986089i	$-0.446845\pi$
$709$	6275.84	0.332432	0.166216	+	0.986089i	$0.446845\pi$
$710$	−22888.6	−1.20985
$711$	−4935.19	−0.260315
$712$	47345.2	2.49205
$713$	2207.62	0.115955
$714$	−20524.4	−1.07578
$715$	−1988.16	−0.103990
$716$	37494.8	1.95705
$717$	−12059.4	−0.628127
$718$	−46609.5	−2.42263
$719$	−15544.4	−0.806273	−0.403136	−	0.915140i	$-0.632080\pi$
$719$	−15544.4	−0.806273	−0.403136	+	0.915140i	$0.632080\pi$
$720$	7159.79	0.370597
$721$	−30359.5	−1.56817
$722$	35879.8	1.84945
$723$	−3230.44	−0.166170
$724$	71928.1	3.69225
$725$	725.000	0.0371391
$726$	−18832.3	−0.962718
$727$	−25002.9	−1.27552	−0.637762	−	0.770233i	$-0.720140\pi$
$727$	−25002.9	−1.27552	−0.637762	+	0.770233i	$0.720140\pi$
$728$	−38190.1	−1.94426
$729$	729.000	0.0370370
$730$	−11330.7	−0.574477
$731$	−28724.7	−1.45338
$732$	−2020.75	−0.102034
$733$	−16981.1	−0.855678	−0.427839	−	0.903855i	$-0.640725\pi$
$733$	−16981.1	−0.855678	−0.427839	+	0.903855i	$0.640725\pi$
$734$	−58238.7	−2.92865
$735$	40.3349	0.00202418
$736$	6468.06	0.323934
$737$	7750.78	0.387386
$738$	−3512.31	−0.175190
$739$	920.528	0.0458216	0.0229108	−	0.999738i	$-0.492707\pi$
$739$	920.528	0.0458216	0.0229108	+	0.999738i	$0.492707\pi$
$740$	−17760.5	−0.882282
$741$	364.047	0.0180481
$742$	39546.4	1.95660
$743$	6708.21	0.331225	0.165613	−	0.986191i	$-0.447040\pi$
$743$	6708.21	0.331225	0.165613	+	0.986191i	$0.447040\pi$
$744$	−21726.7	−1.07062
$745$	17733.0	0.872061
$746$	−70588.9	−3.46440
$747$	4599.69	0.225293
$748$	15892.5	0.776857
$749$	24080.5	1.17474
$750$	1965.20	0.0956784
$751$	34311.4	1.66717	0.833583	−	0.552394i	$-0.186286\pi$
$751$	34311.4	1.66717	0.833583	+	0.552394i	$0.186286\pi$
$752$	−52050.6	−2.52405
$753$	9539.96	0.461694
$754$	5237.33	0.252961
$755$	9091.13	0.438225
$756$	9694.22	0.466370
$757$	−12405.6	−0.595628	−0.297814	−	0.954624i	$-0.596257\pi$
$757$	−12405.6	−0.595628	−0.297814	+	0.954624i	$0.596257\pi$
$758$	19655.7	0.941856
$759$	633.860	0.0303131
$760$	−1057.66	−0.0504805
$761$	−18869.8	−0.898857	−0.449428	−	0.893316i	$-0.648372\pi$
$761$	−18869.8	−0.898857	−0.449428	+	0.893316i	$0.648372\pi$
$762$	−13894.6	−0.660562
$763$	−17195.4	−0.815878
$764$	48466.7	2.29511
$765$	3184.56	0.150507
$766$	−65004.8	−3.06621
$767$	−4160.29	−0.195853
$768$	10664.2	0.501058
$769$	38269.7	1.79459	0.897295	−	0.441432i	$-0.145529\pi$
$769$	38269.7	1.79459	0.897295	+	0.441432i	$0.145529\pi$
$770$	5577.34	0.261030
$771$	−9375.86	−0.437955
$772$	87452.9	4.07707
$773$	37398.4	1.74014	0.870069	−	0.492930i	$-0.164074\pi$
$773$	37398.4	1.74014	0.870069	+	0.492930i	$0.164074\pi$
$774$	19144.1	0.889044
$775$	−3013.96	−0.139696
$776$	−58094.2	−2.68745
$777$	−10100.3	−0.466339
$778$	40449.9	1.86401
$779$	262.226	0.0120606
$780$	10061.0	0.461847
$781$	10079.0	0.461788
$782$	6791.09	0.310549
$783$	−783.000	−0.0357371
$784$	−427.836	−0.0194896
$785$	−188.770	−0.00858279
$786$	−14737.2	−0.668776
$787$	−22352.2	−1.01241	−0.506206	−	0.862413i	$-0.668952\pi$
$787$	−22352.2	−1.01241	−0.506206	+	0.862413i	$0.668952\pi$
$788$	38736.0	1.75116
$789$	13422.9	0.605663
$790$	14368.3	0.647091
$791$	−31727.7	−1.42618
$792$	−6238.25	−0.279882
$793$	−1192.66	−0.0534081
$794$	35359.9	1.58045
$795$	−6136.01	−0.273738
$796$	−1631.05	−0.0726267
$797$	−29993.8	−1.33304	−0.666521	−	0.745487i	$-0.732217\pi$
$797$	−29993.8	−1.33304	−0.666521	+	0.745487i	$0.732217\pi$
$798$	−1021.25	−0.0453032
$799$	−23151.3	−1.02507
$800$	−8830.52	−0.390258
$801$	−7093.22	−0.312892
$802$	26451.0	1.16461
$803$	4989.50	0.219272
$804$	−39222.3	−1.72048
$805$	1689.02	0.0739506
$806$	−21772.5	−0.951495
$807$	−12159.1	−0.530385
$808$	−30637.9	−1.33396
$809$	28328.9	1.23114	0.615569	−	0.788083i	$-0.288926\pi$
$809$	28328.9	1.23114	0.615569	+	0.788083i	$0.288926\pi$
$810$	−2122.41	−0.0920666
$811$	4087.14	0.176965	0.0884826	−	0.996078i	$-0.471798\pi$
$811$	4087.14	0.176965	0.0884826	+	0.996078i	$0.471798\pi$
$812$	−10412.3	−0.450001
$813$	24137.9	1.04127
$814$	11035.5	0.475178
$815$	7709.37	0.331347
$816$	−33779.0	−1.44914
$817$	−1429.28	−0.0612046
$818$	−27864.6	−1.19103
$819$	5721.61	0.244114
$820$	7246.98	0.308629
$821$	−9552.90	−0.406088	−0.203044	−	0.979170i	$-0.565084\pi$
$821$	−9552.90	−0.406088	−0.203044	+	0.979170i	$0.565084\pi$
$822$	3736.23	0.158535
$823$	26863.5	1.13779	0.568895	−	0.822410i	$-0.307371\pi$
$823$	26863.5	1.13779	0.568895	+	0.822410i	$0.307371\pi$
$824$	−98862.6	−4.17966
$825$	−865.378	−0.0365195
$826$	11670.8	0.491619
$827$	−43901.7	−1.84596	−0.922981	−	0.384846i	$-0.874254\pi$
$827$	−43901.7	−1.84596	−0.922981	+	0.384846i	$0.874254\pi$
$828$	−3207.61	−0.134628
$829$	−9622.68	−0.403148	−0.201574	−	0.979473i	$-0.564606\pi$
$829$	−9622.68	−0.403148	−0.201574	+	0.979473i	$0.564606\pi$
$830$	−13391.5	−0.560033
$831$	−13877.2	−0.579296
$832$	−19926.2	−0.830307
$833$	−190.295	−0.00791516
$834$	26832.3	1.11406
$835$	8347.44	0.345958
$836$	790.779	0.0327149
$837$	3255.07	0.134423
$838$	−15477.5	−0.638022
$839$	26742.6	1.10043	0.550214	−	0.835024i	$-0.314546\pi$
$839$	26742.6	1.10043	0.550214	+	0.835024i	$0.314546\pi$
$840$	−16622.8	−0.682788
$841$	841.000	0.0344828
$842$	−38926.0	−1.59320
$843$	209.389	0.00855486
$844$	−85052.7	−3.46876
$845$	−5046.93	−0.205467
$846$	15429.6	0.627046
$847$	22097.7	0.896440
$848$	65085.2	2.63566
$849$	−5710.74	−0.230851
$850$	−9271.54	−0.374131
$851$	3341.96	0.134619
$852$	−51004.3	−2.05092
$853$	−16600.5	−0.666341	−0.333171	−	0.942867i	$-0.608119\pi$
$853$	−16600.5	−0.666341	−0.333171	+	0.942867i	$0.608119\pi$
$854$	3345.74	0.134062
$855$	158.457	0.00633815
$856$	78415.6	3.13106
$857$	15752.2	0.627869	0.313935	−	0.949445i	$-0.398353\pi$
$857$	15752.2	0.627869	0.313935	+	0.949445i	$0.398353\pi$
$858$	−6251.41	−0.248741
$859$	−35249.8	−1.40012	−0.700062	−	0.714082i	$-0.746844\pi$
$859$	−35249.8	−1.40012	−0.700062	+	0.714082i	$0.746844\pi$
$860$	−39500.2	−1.56622
$861$	4121.31	0.163129
$862$	−17304.6	−0.683755
$863$	−36020.7	−1.42081	−0.710404	−	0.703794i	$-0.751488\pi$
$863$	−36020.7	−1.42081	−0.710404	+	0.703794i	$0.751488\pi$
$864$	9536.96	0.375526
$865$	−3643.12	−0.143202
$866$	−49014.0	−1.92328
$867$	−285.374	−0.0111785
$868$	43285.9	1.69265
$869$	−6327.12	−0.246988
$870$	2279.63	0.0888352
$871$	−23149.3	−0.900556
$872$	−55995.0	−2.17458
$873$	8703.63	0.337426
$874$	337.910	0.0130778
$875$	−2305.94	−0.0890914
$876$	−25249.0	−0.973842
$877$	1353.74	0.0521239	0.0260620	−	0.999660i	$-0.491703\pi$
$877$	1353.74	0.0521239	0.0260620	+	0.999660i	$0.491703\pi$
$878$	32018.2	1.23071
$879$	−1869.59	−0.0717404
$880$	9179.15	0.351624
$881$	−1774.07	−0.0678435	−0.0339217	−	0.999424i	$-0.510800\pi$
$881$	−1774.07	−0.0678435	−0.0339217	+	0.999424i	$0.510800\pi$
$882$	126.826	0.00484177
$883$	1483.09	0.0565233	0.0282616	−	0.999601i	$-0.491003\pi$
$883$	1483.09	0.0565233	0.0282616	+	0.999601i	$0.491003\pi$
$884$	−47466.4	−1.80596
$885$	−1810.83	−0.0687801
$886$	−74844.9	−2.83799
$887$	18524.8	0.701244	0.350622	−	0.936517i	$-0.385970\pi$
$887$	18524.8	0.701244	0.350622	+	0.936517i	$0.385970\pi$
$888$	−32890.5	−1.24294
$889$	16303.8	0.615086
$890$	20651.2	0.777786
$891$	934.609	0.0351409
$892$	70724.2	2.65473
$893$	−1151.96	−0.0431678
$894$	55758.0	2.08594
$895$	9632.30	0.359746
$896$	3769.89	0.140561
$897$	−1893.16	−0.0704689
$898$	85976.2	3.19495
$899$	−3496.19	−0.129705
$900$	4379.19	0.162192
$901$	28948.9	1.07040
$902$	−4502.93	−0.166221
$903$	−22463.5	−0.827838
$904$	−103318.	−3.80122
$905$	18478.1	0.678710
$906$	28585.4	1.04822
$907$	−26687.1	−0.976991	−0.488495	−	0.872567i	$-0.662454\pi$
$907$	−26687.1	−0.976991	−0.488495	+	0.872567i	$0.662454\pi$
$908$	−71863.4	−2.62651
$909$	4590.14	0.167487
$910$	−16657.9	−0.606817
$911$	−4443.10	−0.161588	−0.0807939	−	0.996731i	$-0.525746\pi$
$911$	−4443.10	−0.161588	−0.0807939	+	0.996731i	$0.525746\pi$
$912$	−1680.77	−0.0610261
$913$	5897.00	0.213759
$914$	82413.2	2.98248
$915$	−519.124	−0.0187559
$916$	94079.3	3.39352
$917$	17292.5	0.622734
$918$	10013.3	0.360008
$919$	17674.0	0.634398	0.317199	−	0.948359i	$-0.397258\pi$
$919$	17674.0	0.634398	0.317199	+	0.948359i	$0.397258\pi$
$920$	5500.13	0.197102
$921$	20699.7	0.740585
$922$	73845.4	2.63771
$923$	−30103.2	−1.07352
$924$	12428.4	0.442494
$925$	−4562.61	−0.162181
$926$	46087.2	1.63555
$927$	14811.5	0.524783
$928$	−10243.4	−0.362345
$929$	10760.5	0.380021	0.190010	−	0.981782i	$-0.439148\pi$
$929$	10760.5	0.380021	0.190010	+	0.981782i	$0.439148\pi$
$930$	−9476.82	−0.334148
$931$	−9.46867	−0.000333322 0
$932$	−94093.2	−3.30700
$933$	544.108	0.0190925
$934$	45833.9	1.60571
$935$	4082.75	0.142802
$936$	18631.8	0.650641
$937$	22210.3	0.774365	0.387182	−	0.922003i	$-0.373448\pi$
$937$	22210.3	0.774365	0.387182	+	0.922003i	$0.373448\pi$
$938$	64940.1	2.26052
$939$	11517.6	0.400281
$940$	−31836.0	−1.10466
$941$	34977.1	1.21171	0.605855	−	0.795575i	$-0.292831\pi$
$941$	34977.1	1.21171	0.605855	+	0.795575i	$0.292831\pi$
$942$	−593.552	−0.0205297
$943$	−1363.65	−0.0470908
$944$	19207.6	0.662241
$945$	2490.42	0.0857283
$946$	24543.5	0.843530
$947$	42798.4	1.46860	0.734298	−	0.678827i	$-0.237511\pi$
$947$	42798.4	1.46860	0.734298	+	0.678827i	$0.237511\pi$
$948$	32018.0	1.09694
$949$	−14902.2	−0.509742
$950$	−461.332	−0.0157554
$951$	−21000.2	−0.716067
$952$	78424.3	2.66990
$953$	−15363.5	−0.522217	−0.261108	−	0.965309i	$-0.584088\pi$
$953$	−15363.5	−0.522217	−0.261108	+	0.965309i	$0.584088\pi$
$954$	−19293.5	−0.654771
$955$	12450.9	0.421888
$956$	78237.7	2.64685
$957$	−1003.84	−0.0339075
$958$	60017.7	2.02410
$959$	−4384.05	−0.147621
$960$	−8673.16	−0.291588
$961$	−15256.7	−0.512125
$962$	−32959.9	−1.10465
$963$	−11748.2	−0.393125
$964$	20958.1	0.700222
$965$	22466.4	0.749449
$966$	5310.82	0.176887
$967$	−44310.2	−1.47355	−0.736774	−	0.676139i	$-0.763652\pi$
$967$	−44310.2	−1.47355	−0.736774	+	0.676139i	$0.763652\pi$
$968$	71958.7	2.38930
$969$	−747.580	−0.0247840
$970$	−25339.8	−0.838774
$971$	50163.2	1.65789	0.828946	−	0.559328i	$-0.188941\pi$
$971$	50163.2	1.65789	0.828946	+	0.559328i	$0.188941\pi$
$972$	−4729.52	−0.156070
$973$	−31484.8	−1.03736
$974$	−8569.90	−0.281927
$975$	2584.63	0.0848969
$976$	5506.39	0.180589
$977$	−2549.65	−0.0834908	−0.0417454	−	0.999128i	$-0.513292\pi$
$977$	−2549.65	−0.0834908	−0.0417454	+	0.999128i	$0.513292\pi$
$978$	24240.7	0.792568
$979$	−9093.80	−0.296874
$980$	−261.680	−0.00852966
$981$	8389.13	0.273032
$982$	−11041.4	−0.358803
$983$	25382.0	0.823561	0.411781	−	0.911283i	$-0.364907\pi$
$983$	25382.0	0.823561	0.411781	+	0.911283i	$0.364907\pi$
$984$	13420.6	0.434790
$985$	9951.15	0.321899
$986$	−10755.0	−0.347372
$987$	−18104.9	−0.583877
$988$	−2361.83	−0.0760523
$989$	7432.68	0.238974
$990$	−2721.02	−0.0873532
$991$	−44583.2	−1.42909	−0.714547	−	0.699588i	$-0.753367\pi$
$991$	−44583.2	−1.42909	−0.714547	+	0.699588i	$0.753367\pi$
$992$	42583.7	1.36294
$993$	3530.52	0.112828
$994$	84447.6	2.69468
$995$	−419.010	−0.0133503
$996$	−29841.4	−0.949357
$997$	−39668.0	−1.26008	−0.630039	−	0.776563i	$-0.716961\pi$
$997$	−39668.0	−1.26008	−0.630039	+	0.776563i	$0.716961\pi$
$998$	46461.1	1.47365
$999$	4927.62	0.156059

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.4.a.i.1.1	✓	7
3.2	odd	2		1305.4.a.n.1.7		7
5.4	even	2		2175.4.a.n.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.i.1.1	✓	7	1.1	even	1	trivial
1305.4.a.n.1.7		7	3.2	odd	2
2175.4.a.n.1.7		7	5.4	even	2

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Classical	Maass
Hilbert	Bianchi

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

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Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	435.4.a.i.1.1

Level	$435$
Weight	$4$
Character	435.1
Self dual	yes
Analytic conductor	$25.666$
Analytic rank	$0$
Dimension	$7$
CM	no
Inner twists	$1$