LMFDB - Embedded newform 1899.4.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1899,4,Mod(1,1899)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1899, 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("1899.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1899 = 3^{2} \cdot 211 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1899.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:	$112.044627101$
Analytic rank:	$1$
Dimension:	$26$
Twist minimal:	no (minimal twist has level 633)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	1899.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.12278 q^{2} +1.75178 q^{4} -1.07358 q^{5} +20.7048 q^{7} +19.5118 q^{8} +O(q^{10})$	\(q-3.12278 q^{2} +1.75178 q^{4} -1.07358 q^{5} +20.7048 q^{7} +19.5118 q^{8} +3.35257 q^{10} +3.23346 q^{11} +72.4419 q^{13} -64.6566 q^{14} -74.9455 q^{16} +120.076 q^{17} +35.5614 q^{19} -1.88068 q^{20} -10.0974 q^{22} -145.115 q^{23} -123.847 q^{25} -226.220 q^{26} +36.2703 q^{28} -296.234 q^{29} -265.930 q^{31} +77.9439 q^{32} -374.972 q^{34} -22.2283 q^{35} +333.398 q^{37} -111.051 q^{38} -20.9476 q^{40} -203.298 q^{41} +305.333 q^{43} +5.66431 q^{44} +453.163 q^{46} -568.195 q^{47} +85.6885 q^{49} +386.749 q^{50} +126.902 q^{52} -318.210 q^{53} -3.47139 q^{55} +403.989 q^{56} +925.074 q^{58} -799.673 q^{59} +334.008 q^{61} +830.442 q^{62} +356.162 q^{64} -77.7724 q^{65} -612.414 q^{67} +210.347 q^{68} +69.4142 q^{70} +699.292 q^{71} -535.396 q^{73} -1041.13 q^{74} +62.2958 q^{76} +66.9481 q^{77} +221.237 q^{79} +80.4602 q^{80} +634.856 q^{82} +82.2906 q^{83} -128.912 q^{85} -953.490 q^{86} +63.0908 q^{88} -822.625 q^{89} +1499.89 q^{91} -254.210 q^{92} +1774.35 q^{94} -38.1781 q^{95} -1477.98 q^{97} -267.587 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 6 q^{2} + 108 q^{4} - 25 q^{5} + 50 q^{7} - 57 q^{8}+O(q^{10}) $ 26 * q - 6 * q^2 + 108 * q^4 - 25 * q^5 + 50 * q^7 - 57 * q^8	$ 26 q - 6 q^{2} + 108 q^{4} - 25 q^{5} + 50 q^{7} - 57 q^{8} - 32 q^{10} - 73 q^{11} - 61 q^{13} - 243 q^{14} + 440 q^{16} - 96 q^{17} + 71 q^{19} - 277 q^{20} + 206 q^{22} - 678 q^{23} + 597 q^{25} - 335 q^{26} + 354 q^{28} - 224 q^{29} - 188 q^{31} - 502 q^{32} - 261 q^{34} - 624 q^{35} + 223 q^{37} - 737 q^{38} - 562 q^{40} - 106 q^{41} + 607 q^{43} - 767 q^{44} - 529 q^{46} - 1657 q^{47} + 848 q^{49} - 906 q^{50} + 156 q^{52} - 1902 q^{53} + 1215 q^{55} - 3540 q^{56} + 2871 q^{58} - 2790 q^{59} - 1952 q^{61} - 3134 q^{62} + 1659 q^{64} - 3653 q^{65} + 2932 q^{67} - 7363 q^{68} + 4509 q^{70} - 4157 q^{71} + 94 q^{73} - 6271 q^{74} + 2757 q^{76} - 3564 q^{77} + 2365 q^{79} - 6249 q^{80} + 2481 q^{82} - 4852 q^{83} + 640 q^{85} - 5710 q^{86} + 5291 q^{88} - 2504 q^{89} - 812 q^{91} - 9719 q^{92} - 252 q^{94} - 4999 q^{95} - 302 q^{97} - 14279 q^{98}+O(q^{100}) $ 26 * q - 6 * q^2 + 108 * q^4 - 25 * q^5 + 50 * q^7 - 57 * q^8 - 32 * q^10 - 73 * q^11 - 61 * q^13 - 243 * q^14 + 440 * q^16 - 96 * q^17 + 71 * q^19 - 277 * q^20 + 206 * q^22 - 678 * q^23 + 597 * q^25 - 335 * q^26 + 354 * q^28 - 224 * q^29 - 188 * q^31 - 502 * q^32 - 261 * q^34 - 624 * q^35 + 223 * q^37 - 737 * q^38 - 562 * q^40 - 106 * q^41 + 607 * q^43 - 767 * q^44 - 529 * q^46 - 1657 * q^47 + 848 * q^49 - 906 * q^50 + 156 * q^52 - 1902 * q^53 + 1215 * q^55 - 3540 * q^56 + 2871 * q^58 - 2790 * q^59 - 1952 * q^61 - 3134 * q^62 + 1659 * q^64 - 3653 * q^65 + 2932 * q^67 - 7363 * q^68 + 4509 * q^70 - 4157 * q^71 + 94 * q^73 - 6271 * q^74 + 2757 * q^76 - 3564 * q^77 + 2365 * q^79 - 6249 * q^80 + 2481 * q^82 - 4852 * q^83 + 640 * q^85 - 5710 * q^86 + 5291 * q^88 - 2504 * q^89 - 812 * q^91 - 9719 * q^92 - 252 * q^94 - 4999 * q^95 - 302 * q^97 - 14279 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−3.12278	−1.10407	−0.552035	−	0.833821i	$-0.686149\pi$
$2$	−3.12278	−1.10407	−0.552035	+	0.833821i	$0.686149\pi$
$3$	0	0
$3$	0	0
$4$	1.75178	0.218973
$5$	−1.07358	−0.0960242	−0.0480121	−	0.998847i	$-0.515289\pi$
$5$	−1.07358	−0.0960242	−0.0480121	+	0.998847i	$0.515289\pi$
$6$	0	0
$7$	20.7048	1.11795	0.558977	−	0.829183i	$-0.311194\pi$
$7$	20.7048	1.11795	0.558977	+	0.829183i	$0.311194\pi$
$8$	19.5118	0.862310
$9$	0	0
$10$	3.35257	0.106017
$11$	3.23346	0.0886295	0.0443148	−	0.999018i	$-0.485890\pi$
$11$	3.23346	0.0886295	0.0443148	+	0.999018i	$0.485890\pi$
$12$	0	0
$13$	72.4419	1.54552	0.772760	−	0.634698i	$-0.218875\pi$
$13$	72.4419	1.54552	0.772760	+	0.634698i	$0.218875\pi$
$14$	−64.6566	−1.23430
$15$	0	0
$16$	−74.9455	−1.17102
$17$	120.076	1.71310	0.856551	−	0.516062i	$-0.172603\pi$
$17$	120.076	1.71310	0.856551	+	0.516062i	$0.172603\pi$
$18$	0	0
$19$	35.5614	0.429387	0.214693	−	0.976682i	$-0.431125\pi$
$19$	35.5614	0.429387	0.214693	+	0.976682i	$0.431125\pi$
$20$	−1.88068	−0.0210267
$21$	0	0
$22$	−10.0974	−0.0978533
$23$	−145.115	−1.31559	−0.657795	−	0.753197i	$-0.728511\pi$
$23$	−145.115	−1.31559	−0.657795	+	0.753197i	$0.728511\pi$
$24$	0	0
$25$	−123.847	−0.990779
$26$	−226.220	−1.70636
$27$	0	0
$28$	36.2703	0.244801
$29$	−296.234	−1.89687	−0.948435	−	0.316971i	$-0.897334\pi$
$29$	−296.234	−1.89687	−0.948435	+	0.316971i	$0.897334\pi$
$30$	0	0
$31$	−265.930	−1.54072	−0.770362	−	0.637607i	$-0.779925\pi$
$31$	−265.930	−1.54072	−0.770362	+	0.637607i	$0.779925\pi$
$32$	77.9439	0.430583
$33$	0	0
$34$	−374.972	−1.89139
$35$	−22.2283	−0.107351
$36$	0	0
$37$	333.398	1.48136	0.740680	−	0.671858i	$-0.234504\pi$
$37$	333.398	1.48136	0.740680	+	0.671858i	$0.234504\pi$
$38$	−111.051	−0.474073
$39$	0	0
$40$	−20.9476	−0.0828026
$41$	−203.298	−0.774386	−0.387193	−	0.921999i	$-0.626555\pi$
$41$	−203.298	−0.774386	−0.387193	+	0.921999i	$0.626555\pi$
$42$	0	0
$43$	305.333	1.08286	0.541429	−	0.840747i	$-0.317884\pi$
$43$	305.333	1.08286	0.541429	+	0.840747i	$0.317884\pi$
$44$	5.66431	0.0194074
$45$	0	0
$46$	453.163	1.45250
$47$	−568.195	−1.76340	−0.881699	−	0.471812i	$-0.843600\pi$
$47$	−568.195	−1.76340	−0.881699	+	0.471812i	$0.843600\pi$
$48$	0	0
$49$	85.6885	0.249821
$50$	386.749	1.09389
$51$	0	0
$52$	126.902	0.338427
$53$	−318.210	−0.824709	−0.412354	−	0.911024i	$-0.635293\pi$
$53$	−318.210	−0.824709	−0.412354	+	0.911024i	$0.635293\pi$
$54$	0	0
$55$	−3.47139	−0.00851058
$56$	403.989	0.964022
$57$	0	0
$58$	925.074	2.09428
$59$	−799.673	−1.76455	−0.882276	−	0.470732i	$-0.843990\pi$
$59$	−799.673	−1.76455	−0.882276	+	0.470732i	$0.843990\pi$
$60$	0	0
$61$	334.008	0.701070	0.350535	−	0.936550i	$-0.386000\pi$
$61$	334.008	0.701070	0.350535	+	0.936550i	$0.386000\pi$
$62$	830.442	1.70107
$63$	0	0
$64$	356.162	0.695629
$65$	−77.7724	−0.148407
$66$	0	0
$67$	−612.414	−1.11669	−0.558345	−	0.829609i	$-0.688563\pi$
$67$	−612.414	−1.11669	−0.558345	+	0.829609i	$0.688563\pi$
$68$	210.347	0.375122
$69$	0	0
$70$	69.4142	0.118523
$71$	699.292	1.16888	0.584442	−	0.811436i	$-0.301313\pi$
$71$	699.292	1.16888	0.584442	+	0.811436i	$0.301313\pi$
$72$	0	0
$73$	−535.396	−0.858401	−0.429201	−	0.903209i	$-0.641205\pi$
$73$	−535.396	−0.858401	−0.429201	+	0.903209i	$0.641205\pi$
$74$	−1041.13	−1.63553
$75$	0	0
$76$	62.2958	0.0940239
$77$	66.9481	0.0990837
$78$	0	0
$79$	221.237	0.315078	0.157539	−	0.987513i	$-0.449644\pi$
$79$	221.237	0.315078	0.157539	+	0.987513i	$0.449644\pi$
$80$	80.4602	0.112447
$81$	0	0
$82$	634.856	0.854977
$83$	82.2906	0.108826	0.0544130	−	0.998519i	$-0.482671\pi$
$83$	82.2906	0.108826	0.0544130	+	0.998519i	$0.482671\pi$
$84$	0	0
$85$	−128.912	−0.164499
$86$	−953.490	−1.19555
$87$	0	0
$88$	63.0908	0.0764261
$89$	−822.625	−0.979754	−0.489877	−	0.871792i	$-0.662958\pi$
$89$	−822.625	−0.979754	−0.489877	+	0.871792i	$0.662958\pi$
$90$	0	0
$91$	1499.89	1.72782
$92$	−254.210	−0.288078
$93$	0	0
$94$	1774.35	1.94692
$95$	−38.1781	−0.0412315
$96$	0	0
$97$	−1477.98	−1.54707	−0.773536	−	0.633752i	$-0.781514\pi$
$97$	−1477.98	−1.54707	−0.773536	+	0.633752i	$0.781514\pi$
$98$	−267.587	−0.275820
$99$	0	0
$100$	−216.953	−0.216953
$101$	−1215.43	−1.19742	−0.598711	−	0.800965i	$-0.704320\pi$
$101$	−1215.43	−1.19742	−0.598711	+	0.800965i	$0.704320\pi$
$102$	0	0
$103$	−405.523	−0.387936	−0.193968	−	0.981008i	$-0.562136\pi$
$103$	−405.523	−0.387936	−0.193968	+	0.981008i	$0.562136\pi$
$104$	1413.47	1.33272
$105$	0	0
$106$	993.703	0.910537
$107$	−644.391	−0.582202	−0.291101	−	0.956692i	$-0.594022\pi$
$107$	−644.391	−0.582202	−0.291101	+	0.956692i	$0.594022\pi$
$108$	0	0
$109$	1165.80	1.02443	0.512217	−	0.858856i	$-0.328824\pi$
$109$	1165.80	1.02443	0.512217	+	0.858856i	$0.328824\pi$
$110$	10.8404	0.00939628
$111$	0	0
$112$	−1551.73	−1.30915
$113$	−175.116	−0.145783	−0.0728916	−	0.997340i	$-0.523223\pi$
$113$	−175.116	−0.145783	−0.0728916	+	0.997340i	$0.523223\pi$
$114$	0	0
$115$	155.793	0.126328
$116$	−518.937	−0.415363
$117$	0	0
$118$	2497.21	1.94819
$119$	2486.15	1.91517
$120$	0	0
$121$	−1320.54	−0.992145
$122$	−1043.03	−0.774031
$123$	0	0
$124$	−465.851	−0.337376
$125$	267.158	0.191163
$126$	0	0
$127$	−1074.00	−0.750409	−0.375204	−	0.926942i	$-0.622427\pi$
$127$	−1074.00	−0.750409	−0.375204	+	0.926942i	$0.622427\pi$
$128$	−1735.77	−1.19861
$129$	0	0
$130$	242.866	0.163852
$131$	1933.61	1.28962	0.644812	−	0.764341i	$-0.276936\pi$
$131$	1933.61	1.28962	0.644812	+	0.764341i	$0.276936\pi$
$132$	0	0
$133$	736.291	0.480034
$134$	1912.44	1.23291
$135$	0	0
$136$	2342.91	1.47722
$137$	−981.056	−0.611805	−0.305902	−	0.952063i	$-0.598958\pi$
$137$	−981.056	−0.611805	−0.305902	+	0.952063i	$0.598958\pi$
$138$	0	0
$139$	1750.26	1.06802	0.534011	−	0.845477i	$-0.320684\pi$
$139$	1750.26	1.06802	0.534011	+	0.845477i	$0.320684\pi$
$140$	−38.9391	−0.0235068
$141$	0	0
$142$	−2183.74	−1.29053
$143$	234.238	0.136979
$144$	0	0
$145$	318.032	0.182145
$146$	1671.92	0.947736
$147$	0	0
$148$	584.040	0.324377
$149$	2496.05	1.37238	0.686190	−	0.727422i	$-0.259282\pi$
$149$	2496.05	1.37238	0.686190	+	0.727422i	$0.259282\pi$
$150$	0	0
$151$	756.042	0.407456	0.203728	−	0.979028i	$-0.434694\pi$
$151$	756.042	0.407456	0.203728	+	0.979028i	$0.434694\pi$
$152$	693.868	0.370264
$153$	0	0
$154$	−209.065	−0.109395
$155$	285.498	0.147947
$156$	0	0
$157$	−910.641	−0.462911	−0.231456	−	0.972845i	$-0.574349\pi$
$157$	−910.641	−0.462911	−0.231456	+	0.972845i	$0.574349\pi$
$158$	−690.877	−0.347868
$159$	0	0
$160$	−83.6792	−0.0413464
$161$	−3004.58	−1.47077
$162$	0	0
$163$	456.855	0.219531	0.109766	−	0.993957i	$-0.464990\pi$
$163$	456.855	0.219531	0.109766	+	0.993957i	$0.464990\pi$
$164$	−356.133	−0.169569
$165$	0	0
$166$	−256.976	−0.120152
$167$	730.053	0.338283	0.169141	−	0.985592i	$-0.445901\pi$
$167$	730.053	0.338283	0.169141	+	0.985592i	$0.445901\pi$
$168$	0	0
$169$	3050.83	1.38863
$170$	402.563	0.181619
$171$	0	0
$172$	534.877	0.237116
$173$	−1767.17	−0.776623	−0.388312	−	0.921528i	$-0.626942\pi$
$173$	−1767.17	−0.776623	−0.388312	+	0.921528i	$0.626942\pi$
$174$	0	0
$175$	−2564.24	−1.10765
$176$	−242.333	−0.103787
$177$	0	0
$178$	2568.88	1.08172
$179$	3288.17	1.37301	0.686507	−	0.727123i	$-0.259143\pi$
$179$	3288.17	1.37301	0.686507	+	0.727123i	$0.259143\pi$
$180$	0	0
$181$	−3156.92	−1.29642	−0.648210	−	0.761462i	$-0.724482\pi$
$181$	−3156.92	−1.29642	−0.648210	+	0.761462i	$0.724482\pi$
$182$	−4683.85	−1.90764
$183$	0	0
$184$	−2831.46	−1.13445
$185$	−357.930	−0.142246
$186$	0	0
$187$	388.261	0.151831
$188$	−995.352	−0.386136
$189$	0	0
$190$	119.222	0.0455225
$191$	−4491.54	−1.70155	−0.850776	−	0.525529i	$-0.823867\pi$
$191$	−4491.54	−1.70155	−0.850776	+	0.525529i	$0.823867\pi$
$192$	0	0
$193$	−1891.97	−0.705631	−0.352815	−	0.935693i	$-0.614776\pi$
$193$	−1891.97	−0.705631	−0.352815	+	0.935693i	$0.614776\pi$
$194$	4615.41	1.70808
$195$	0	0
$196$	150.107	0.0547039
$197$	−476.998	−0.172511	−0.0862555	−	0.996273i	$-0.527490\pi$
$197$	−476.998	−0.172511	−0.0862555	+	0.996273i	$0.527490\pi$
$198$	0	0
$199$	−2125.65	−0.757204	−0.378602	−	0.925560i	$-0.623595\pi$
$199$	−2125.65	−0.757204	−0.378602	+	0.925560i	$0.623595\pi$
$200$	−2416.49	−0.854359
$201$	0	0
$202$	3795.52	1.32204
$203$	−6133.46	−2.12061
$204$	0	0
$205$	218.257	0.0743597
$206$	1266.36	0.428309
$207$	0	0
$208$	−5429.19	−1.80984
$209$	114.986	0.0380563
$210$	0	0
$211$	−211.000	−0.0688428
$211$	−211.000	−0.0688428
$212$	−557.435	−0.180589
$213$	0	0
$214$	2012.29	0.642793
$215$	−327.800	−0.103980
$216$	0	0
$217$	−5506.03	−1.72246
$218$	−3640.54	−1.13105
$219$	0	0
$220$	−6.08111	−0.00186358
$221$	8698.54	2.64763
$222$	0	0
$223$	741.249	0.222591	0.111295	−	0.993787i	$-0.464500\pi$
$223$	741.249	0.222591	0.111295	+	0.993787i	$0.464500\pi$
$224$	1613.81	0.481372
$225$	0	0
$226$	546.849	0.160955
$227$	1516.19	0.443316	0.221658	−	0.975124i	$-0.428853\pi$
$227$	1516.19	0.443316	0.221658	+	0.975124i	$0.428853\pi$
$228$	0	0
$229$	−6109.39	−1.76297	−0.881485	−	0.472212i	$-0.843456\pi$
$229$	−6109.39	−1.76297	−0.881485	+	0.472212i	$0.843456\pi$
$230$	−486.508	−0.139476
$231$	0	0
$232$	−5780.07	−1.63569
$233$	4286.15	1.20513	0.602564	−	0.798071i	$-0.294146\pi$
$233$	4286.15	1.20513	0.602564	+	0.798071i	$0.294146\pi$
$234$	0	0
$235$	610.004	0.169329
$236$	−1400.85	−0.386388
$237$	0	0
$238$	−7763.71	−2.11448
$239$	5585.58	1.51172	0.755860	−	0.654734i	$-0.227219\pi$
$239$	5585.58	1.51172	0.755860	+	0.654734i	$0.227219\pi$
$240$	0	0
$241$	3827.03	1.02291	0.511454	−	0.859311i	$-0.329107\pi$
$241$	3827.03	1.02291	0.511454	+	0.859311i	$0.329107\pi$
$242$	4123.78	1.09540
$243$	0	0
$244$	585.108	0.153515
$245$	−91.9937	−0.0239888
$246$	0	0
$247$	2576.14	0.663626
$248$	−5188.79	−1.32858
$249$	0	0
$250$	−834.278	−0.211057
$251$	−4839.36	−1.21696	−0.608481	−	0.793568i	$-0.708221\pi$
$251$	−4839.36	−1.21696	−0.608481	+	0.793568i	$0.708221\pi$
$252$	0	0
$253$	−469.224	−0.116600
$254$	3353.86	0.828504
$255$	0	0
$256$	2571.13	0.627718
$257$	−2366.64	−0.574424	−0.287212	−	0.957867i	$-0.592728\pi$
$257$	−2366.64	−0.574424	−0.287212	+	0.957867i	$0.592728\pi$
$258$	0	0
$259$	6902.94	1.65609
$260$	−136.240	−0.0324971
$261$	0	0
$262$	−6038.26	−1.42384
$263$	−2303.45	−0.540063	−0.270031	−	0.962852i	$-0.587034\pi$
$263$	−2303.45	−0.540063	−0.270031	+	0.962852i	$0.587034\pi$
$264$	0	0
$265$	341.625	0.0791920
$266$	−2299.28	−0.529992
$267$	0	0
$268$	−1072.81	−0.244525
$269$	−7098.65	−1.60897	−0.804483	−	0.593975i	$-0.797558\pi$
$269$	−7098.65	−1.60897	−0.804483	+	0.593975i	$0.797558\pi$
$270$	0	0
$271$	953.281	0.213681	0.106841	−	0.994276i	$-0.465927\pi$
$271$	953.281	0.213681	0.106841	+	0.994276i	$0.465927\pi$
$272$	−8999.17	−2.00608
$273$	0	0
$274$	3063.63	0.675476
$275$	−400.456	−0.0878123
$276$	0	0
$277$	4937.55	1.07101	0.535503	−	0.844533i	$-0.320122\pi$
$277$	4937.55	1.07101	0.535503	+	0.844533i	$0.320122\pi$
$278$	−5465.69	−1.17917
$279$	0	0
$280$	−433.715	−0.0925694
$281$	883.788	0.187624	0.0938121	−	0.995590i	$-0.470095\pi$
$281$	883.788	0.187624	0.0938121	+	0.995590i	$0.470095\pi$
$282$	0	0
$283$	1546.01	0.324738	0.162369	−	0.986730i	$-0.448086\pi$
$283$	1546.01	0.324738	0.162369	+	0.986730i	$0.448086\pi$
$284$	1225.01	0.255953
$285$	0	0
$286$	−731.475	−0.151234
$287$	−4209.24	−0.865727
$288$	0	0
$289$	9505.27	1.93472
$290$	−993.144	−0.201101
$291$	0	0
$292$	−937.895	−0.187966
$293$	9399.54	1.87415	0.937077	−	0.349124i	$-0.113521\pi$
$293$	9399.54	1.87415	0.937077	+	0.349124i	$0.113521\pi$
$294$	0	0
$295$	858.515	0.169440
$296$	6505.21	1.27739
$297$	0	0
$298$	−7794.64	−1.51521
$299$	−10512.4	−2.03327
$300$	0	0
$301$	6321.86	1.21058
$302$	−2360.96	−0.449860
$303$	0	0
$304$	−2665.17	−0.502822
$305$	−358.585	−0.0673197
$306$	0	0
$307$	4309.12	0.801089	0.400544	−	0.916277i	$-0.368821\pi$
$307$	4309.12	0.801089	0.400544	+	0.916277i	$0.368821\pi$
$308$	117.278	0.0216966
$309$	0	0
$310$	−891.549	−0.163344
$311$	3587.63	0.654135	0.327067	−	0.945001i	$-0.393940\pi$
$311$	3587.63	0.654135	0.327067	+	0.945001i	$0.393940\pi$
$312$	0	0
$313$	−9891.73	−1.78631	−0.893153	−	0.449754i	$-0.851512\pi$
$313$	−9891.73	−1.78631	−0.893153	+	0.449754i	$0.851512\pi$
$314$	2843.74	0.511087
$315$	0	0
$316$	387.559	0.0689934
$317$	3792.99	0.672037	0.336019	−	0.941855i	$-0.390920\pi$
$317$	3792.99	0.672037	0.336019	+	0.941855i	$0.390920\pi$
$318$	0	0
$319$	−957.860	−0.168119
$320$	−382.369	−0.0667972
$321$	0	0
$322$	9382.64	1.62383
$323$	4270.07	0.735583
$324$	0	0
$325$	−8971.74	−1.53127
$326$	−1426.66	−0.242378
$327$	0	0
$328$	−3966.72	−0.667760
$329$	−11764.4	−1.97140
$330$	0	0
$331$	6398.94	1.06259	0.531296	−	0.847187i	$-0.321705\pi$
$331$	6398.94	1.06259	0.531296	+	0.847187i	$0.321705\pi$
$332$	144.155	0.0238299
$333$	0	0
$334$	−2279.80	−0.373488
$335$	657.477	0.107229
$336$	0	0
$337$	−2014.02	−0.325551	−0.162776	−	0.986663i	$-0.552045\pi$
$337$	−2014.02	−0.325551	−0.162776	+	0.986663i	$0.552045\pi$
$338$	−9527.08	−1.53315
$339$	0	0
$340$	−225.825	−0.0360208
$341$	−859.874	−0.136554
$342$	0	0
$343$	−5327.58	−0.838666
$344$	5957.61	0.933759
$345$	0	0
$346$	5518.50	0.857447
$347$	−9660.92	−1.49460	−0.747299	−	0.664488i	$-0.768650\pi$
$347$	−9660.92	−1.49460	−0.747299	+	0.664488i	$0.768650\pi$
$348$	0	0
$349$	−3135.75	−0.480954	−0.240477	−	0.970655i	$-0.577304\pi$
$349$	−3135.75	−0.480954	−0.240477	+	0.970655i	$0.577304\pi$
$350$	8007.55	1.22292
$351$	0	0
$352$	252.029	0.0381624
$353$	3735.24	0.563192	0.281596	−	0.959533i	$-0.409136\pi$
$353$	3735.24	0.563192	0.281596	+	0.959533i	$0.409136\pi$
$354$	0	0
$355$	−750.748	−0.112241
$356$	−1441.06	−0.214539
$357$	0	0
$358$	−10268.3	−1.51590
$359$	−5378.11	−0.790657	−0.395328	−	0.918540i	$-0.629369\pi$
$359$	−5378.11	−0.790657	−0.395328	+	0.918540i	$0.629369\pi$
$360$	0	0
$361$	−5594.39	−0.815627
$362$	9858.38	1.43134
$363$	0	0
$364$	2627.49	0.378345
$365$	574.791	0.0824273
$366$	0	0
$367$	608.057	0.0864859	0.0432429	−	0.999065i	$-0.486231\pi$
$367$	608.057	0.0864859	0.0432429	+	0.999065i	$0.486231\pi$
$368$	10875.7	1.54059
$369$	0	0
$370$	1117.74	0.157050
$371$	−6588.48	−0.921986
$372$	0	0
$373$	−3294.55	−0.457333	−0.228666	−	0.973505i	$-0.573436\pi$
$373$	−3294.55	−0.457333	−0.228666	+	0.973505i	$0.573436\pi$
$374$	−1212.46	−0.167633
$375$	0	0
$376$	−11086.5	−1.52060
$377$	−21459.7	−2.93165
$378$	0	0
$379$	−6408.74	−0.868588	−0.434294	−	0.900771i	$-0.643002\pi$
$379$	−6408.74	−0.868588	−0.434294	+	0.900771i	$0.643002\pi$
$380$	−66.8797	−0.00902856
$381$	0	0
$382$	14026.1	1.87863
$383$	3430.63	0.457694	0.228847	−	0.973462i	$-0.426504\pi$
$383$	3430.63	0.457694	0.228847	+	0.973462i	$0.426504\pi$
$384$	0	0
$385$	−71.8744	−0.00951443
$386$	5908.20	0.779066
$387$	0	0
$388$	−2589.09	−0.338766
$389$	678.505	0.0884359	0.0442179	−	0.999022i	$-0.485920\pi$
$389$	678.505	0.0884359	0.0442179	+	0.999022i	$0.485920\pi$
$390$	0	0
$391$	−17424.8	−2.25374
$392$	1671.94	0.215423
$393$	0	0
$394$	1489.56	0.190464
$395$	−237.517	−0.0302551
$396$	0	0
$397$	4727.37	0.597633	0.298816	−	0.954311i	$-0.403408\pi$
$397$	4727.37	0.597633	0.298816	+	0.954311i	$0.403408\pi$
$398$	6637.95	0.836007
$399$	0	0
$400$	9281.81	1.16023
$401$	−10632.9	−1.32414	−0.662071	−	0.749441i	$-0.730322\pi$
$401$	−10632.9	−1.32414	−0.662071	+	0.749441i	$0.730322\pi$
$402$	0	0
$403$	−19264.5	−2.38122
$404$	−2129.16	−0.262203
$405$	0	0
$406$	19153.5	2.34131
$407$	1078.03	0.131292
$408$	0	0
$409$	−8161.41	−0.986689	−0.493345	−	0.869834i	$-0.664226\pi$
$409$	−8161.41	−0.986689	−0.493345	+	0.869834i	$0.664226\pi$
$410$	−681.570	−0.0820984
$411$	0	0
$412$	−710.388	−0.0849473
$413$	−16557.1	−1.97269
$414$	0	0
$415$	−88.3457	−0.0104499
$416$	5646.41	0.665475
$417$	0	0
$418$	−359.078	−0.0420169
$419$	−4035.18	−0.470481	−0.235240	−	0.971937i	$-0.575588\pi$
$419$	−4035.18	−0.470481	−0.235240	+	0.971937i	$0.575588\pi$
$420$	0	0
$421$	−3124.70	−0.361731	−0.180866	−	0.983508i	$-0.557890\pi$
$421$	−3124.70	−0.361731	−0.180866	+	0.983508i	$0.557890\pi$
$422$	658.907	0.0760074
$423$	0	0
$424$	−6208.87	−0.711154
$425$	−14871.1	−1.69731
$426$	0	0
$427$	6915.56	0.783764
$428$	−1128.83	−0.127486
$429$	0	0
$430$	1023.65	0.114802
$431$	14174.2	1.58410	0.792049	−	0.610457i	$-0.209014\pi$
$431$	14174.2	1.58410	0.792049	+	0.610457i	$0.209014\pi$
$432$	0	0
$433$	3754.98	0.416750	0.208375	−	0.978049i	$-0.433183\pi$
$433$	3754.98	0.416750	0.208375	+	0.978049i	$0.433183\pi$
$434$	17194.1	1.90172
$435$	0	0
$436$	2042.22	0.224323
$437$	−5160.49	−0.564897
$438$	0	0
$439$	−1264.57	−0.137482	−0.0687410	−	0.997635i	$-0.521898\pi$
$439$	−1264.57	−0.137482	−0.0687410	+	0.997635i	$0.521898\pi$
$440$	−67.7332	−0.00733875
$441$	0	0
$442$	−27163.7	−2.92318
$443$	7542.78	0.808958	0.404479	−	0.914547i	$-0.367453\pi$
$443$	7542.78	0.808958	0.404479	+	0.914547i	$0.367453\pi$
$444$	0	0
$445$	883.156	0.0940800
$446$	−2314.76	−0.245756
$447$	0	0
$448$	7374.26	0.777681
$449$	8931.19	0.938728	0.469364	−	0.883005i	$-0.344483\pi$
$449$	8931.19	0.938728	0.469364	+	0.883005i	$0.344483\pi$
$450$	0	0
$451$	−657.356	−0.0686334
$452$	−306.764	−0.0319225
$453$	0	0
$454$	−4734.72	−0.489452
$455$	−1610.26	−0.165913
$456$	0	0
$457$	9885.00	1.01182	0.505909	−	0.862587i	$-0.331157\pi$
$457$	9885.00	1.01182	0.505909	+	0.862587i	$0.331157\pi$
$458$	19078.3	1.94644
$459$	0	0
$460$	272.915	0.0276625
$461$	−13787.1	−1.39291	−0.696453	−	0.717603i	$-0.745239\pi$
$461$	−13787.1	−1.39291	−0.696453	+	0.717603i	$0.745239\pi$
$462$	0	0
$463$	−16644.2	−1.67068	−0.835338	−	0.549736i	$-0.814728\pi$
$463$	−16644.2	−1.67068	−0.835338	+	0.549736i	$0.814728\pi$
$464$	22201.4	2.22128
$465$	0	0
$466$	−13384.7	−1.33055
$467$	13223.0	1.31025	0.655125	−	0.755520i	$-0.272616\pi$
$467$	13223.0	1.31025	0.655125	+	0.755520i	$0.272616\pi$
$468$	0	0
$469$	−12679.9	−1.24841
$470$	−1904.91	−0.186951
$471$	0	0
$472$	−15603.1	−1.52159
$473$	987.283	0.0959732
$474$	0	0
$475$	−4404.19	−0.425427
$476$	4355.19	0.419369
$477$	0	0
$478$	−17442.5	−1.66905
$479$	−12027.6	−1.14730	−0.573649	−	0.819102i	$-0.694472\pi$
$479$	−12027.6	−1.14730	−0.573649	+	0.819102i	$0.694472\pi$
$480$	0	0
$481$	24152.0	2.28947
$482$	−11951.0	−1.12936
$483$	0	0
$484$	−2313.30	−0.217252
$485$	1586.73	0.148556
$486$	0	0
$487$	3367.24	0.313315	0.156657	−	0.987653i	$-0.449928\pi$
$487$	3367.24	0.313315	0.156657	+	0.987653i	$0.449928\pi$
$488$	6517.10	0.604540
$489$	0	0
$490$	287.277	0.0264854
$491$	−2664.80	−0.244930	−0.122465	−	0.992473i	$-0.539080\pi$
$491$	−2664.80	−0.244930	−0.122465	+	0.992473i	$0.539080\pi$
$492$	0	0
$493$	−35570.6	−3.24953
$494$	−8044.71	−0.732690
$495$	0	0
$496$	19930.3	1.80422
$497$	14478.7	1.30676
$498$	0	0
$499$	20172.2	1.80968	0.904842	−	0.425747i	$-0.139989\pi$
$499$	20172.2	1.80968	0.904842	+	0.425747i	$0.139989\pi$
$500$	468.003	0.0418594
$501$	0	0
$502$	15112.3	1.34361
$503$	−16391.2	−1.45298	−0.726488	−	0.687180i	$-0.758849\pi$
$503$	−16391.2	−1.45298	−0.726488	+	0.687180i	$0.758849\pi$
$504$	0	0
$505$	1304.86	0.114982
$506$	1465.28	0.128735
$507$	0	0
$508$	−1881.41	−0.164319
$509$	11919.7	1.03798	0.518988	−	0.854781i	$-0.326309\pi$
$509$	11919.7	1.03798	0.518988	+	0.854781i	$0.326309\pi$
$510$	0	0
$511$	−11085.3	−0.959653
$512$	5857.05	0.505562
$513$	0	0
$514$	7390.50	0.634204
$515$	435.363	0.0372512
$516$	0	0
$517$	−1837.23	−0.156289
$518$	−21556.4	−1.82844
$519$	0	0
$520$	−1517.48	−0.127973
$521$	−384.241	−0.0323108	−0.0161554	−	0.999869i	$-0.505143\pi$
$521$	−384.241	−0.0323108	−0.0161554	+	0.999869i	$0.505143\pi$
$522$	0	0
$523$	9494.83	0.793843	0.396922	−	0.917853i	$-0.370078\pi$
$523$	9494.83	0.793843	0.396922	+	0.917853i	$0.370078\pi$
$524$	3387.27	0.282392
$525$	0	0
$526$	7193.16	0.596268
$527$	−31931.9	−2.63942
$528$	0	0
$529$	8891.37	0.730777
$530$	−1066.82	−0.0874336
$531$	0	0
$532$	1289.82	0.105114
$533$	−14727.3	−1.19683
$534$	0	0
$535$	691.807	0.0559055
$536$	−11949.3	−0.962933
$537$	0	0
$538$	22167.5	1.77641
$539$	277.070	0.0221415
$540$	0	0
$541$	−16443.8	−1.30679	−0.653396	−	0.757016i	$-0.726656\pi$
$541$	−16443.8	−1.30679	−0.653396	+	0.757016i	$0.726656\pi$
$542$	−2976.89	−0.235919
$543$	0	0
$544$	9359.20	0.737633
$545$	−1251.58	−0.0983704
$546$	0	0
$547$	3859.10	0.301651	0.150826	−	0.988560i	$-0.451807\pi$
$547$	3859.10	0.301651	0.150826	+	0.988560i	$0.451807\pi$
$548$	−1718.59	−0.133968
$549$	0	0
$550$	1250.54	0.0969510
$551$	−10534.5	−0.814491
$552$	0	0
$553$	4580.67	0.352243
$554$	−15418.9	−1.18247
$555$	0	0
$556$	3066.07	0.233868
$557$	−11816.1	−0.898858	−0.449429	−	0.893316i	$-0.648373\pi$
$557$	−11816.1	−0.898858	−0.449429	+	0.893316i	$0.648373\pi$
$558$	0	0
$559$	22118.9	1.67358
$560$	1665.91	0.125710
$561$	0	0
$562$	−2759.88	−0.207150
$563$	10537.6	0.788823	0.394412	−	0.918934i	$-0.370948\pi$
$563$	10537.6	0.788823	0.394412	+	0.918934i	$0.370948\pi$
$564$	0	0
$565$	188.001	0.0139987
$566$	−4827.86	−0.358534
$567$	0	0
$568$	13644.5	1.00794
$569$	5208.89	0.383775	0.191888	−	0.981417i	$-0.438539\pi$
$569$	5208.89	0.383775	0.191888	+	0.981417i	$0.438539\pi$
$570$	0	0
$571$	16481.6	1.20794	0.603968	−	0.797008i	$-0.293585\pi$
$571$	16481.6	1.20794	0.603968	+	0.797008i	$0.293585\pi$
$572$	410.334	0.0299946
$573$	0	0
$574$	13144.6	0.955824
$575$	17972.1	1.30346
$576$	0	0
$577$	−26581.0	−1.91782	−0.958911	−	0.283707i	$-0.908436\pi$
$577$	−26581.0	−1.91782	−0.958911	+	0.283707i	$0.908436\pi$
$578$	−29682.9	−2.13607
$579$	0	0
$580$	557.121	0.0398848
$581$	1703.81	0.121663
$582$	0	0
$583$	−1028.92	−0.0730936
$584$	−10446.6	−0.740208
$585$	0	0
$586$	−29352.7	−2.06920
$587$	9943.98	0.699203	0.349602	−	0.936898i	$-0.386317\pi$
$587$	9943.98	0.699203	0.349602	+	0.936898i	$0.386317\pi$
$588$	0	0
$589$	−9456.85	−0.661566
$590$	−2680.96	−0.187073
$591$	0	0
$592$	−24986.7	−1.73471
$593$	−6134.10	−0.424785	−0.212392	−	0.977184i	$-0.568125\pi$
$593$	−6134.10	−0.424785	−0.212392	+	0.977184i	$0.568125\pi$
$594$	0	0
$595$	−2669.09	−0.183903
$596$	4372.54	0.300514
$597$	0	0
$598$	32828.0	2.24488
$599$	−12721.3	−0.867744	−0.433872	−	0.900974i	$-0.642853\pi$
$599$	−12721.3	−0.867744	−0.433872	+	0.900974i	$0.642853\pi$
$600$	0	0
$601$	15148.0	1.02812	0.514060	−	0.857754i	$-0.328141\pi$
$601$	15148.0	1.02812	0.514060	+	0.857754i	$0.328141\pi$
$602$	−19741.8	−1.33657
$603$	0	0
$604$	1324.42	0.0892216
$605$	1417.71	0.0952699
$606$	0	0
$607$	19162.9	1.28138	0.640691	−	0.767799i	$-0.278648\pi$
$607$	19162.9	1.28138	0.640691	+	0.767799i	$0.278648\pi$
$608$	2771.79	0.184887
$609$	0	0
$610$	1119.78	0.0743257
$611$	−41161.1	−2.72537
$612$	0	0
$613$	−13311.6	−0.877078	−0.438539	−	0.898712i	$-0.644504\pi$
$613$	−13311.6	−0.877078	−0.438539	+	0.898712i	$0.644504\pi$
$614$	−13456.4	−0.884459
$615$	0	0
$616$	1306.28	0.0854409
$617$	−4089.44	−0.266831	−0.133416	−	0.991060i	$-0.542594\pi$
$617$	−4089.44	−0.266831	−0.133416	+	0.991060i	$0.542594\pi$
$618$	0	0
$619$	−19072.2	−1.23841	−0.619206	−	0.785229i	$-0.712545\pi$
$619$	−19072.2	−1.23841	−0.619206	+	0.785229i	$0.712545\pi$
$620$	500.130	0.0323963
$621$	0	0
$622$	−11203.4	−0.722211
$623$	−17032.3	−1.09532
$624$	0	0
$625$	15194.1	0.972423
$626$	30889.7	1.97221
$627$	0	0
$628$	−1595.24	−0.101365
$629$	40033.1	2.53772
$630$	0	0
$631$	3461.04	0.218355	0.109177	−	0.994022i	$-0.465178\pi$
$631$	3461.04	0.218355	0.109177	+	0.994022i	$0.465178\pi$
$632$	4316.75	0.271695
$633$	0	0
$634$	−11844.7	−0.741977
$635$	1153.03	0.0720574
$636$	0	0
$637$	6207.44	0.386103
$638$	2991.19	0.185615
$639$	0	0
$640$	1863.49	0.115095
$641$	1951.89	0.120273	0.0601366	−	0.998190i	$-0.480846\pi$
$641$	1951.89	0.120273	0.0601366	+	0.998190i	$0.480846\pi$
$642$	0	0
$643$	−5415.61	−0.332147	−0.166074	−	0.986113i	$-0.553109\pi$
$643$	−5415.61	−0.332147	−0.166074	+	0.986113i	$0.553109\pi$
$644$	−5263.36	−0.322058
$645$	0	0
$646$	−13334.5	−0.812136
$647$	−26914.3	−1.63541	−0.817705	−	0.575638i	$-0.804754\pi$
$647$	−26914.3	−1.63541	−0.817705	+	0.575638i	$0.804754\pi$
$648$	0	0
$649$	−2585.71	−0.156391
$650$	28016.8	1.69063
$651$	0	0
$652$	800.309	0.0480714
$653$	19937.0	1.19479	0.597393	−	0.801949i	$-0.296203\pi$
$653$	19937.0	1.19479	0.597393	+	0.801949i	$0.296203\pi$
$654$	0	0
$655$	−2075.90	−0.123835
$656$	15236.3	0.906824
$657$	0	0
$658$	36737.5	2.17656
$659$	−1271.14	−0.0751391	−0.0375696	−	0.999294i	$-0.511962\pi$
$659$	−1271.14	−0.0751391	−0.0375696	+	0.999294i	$0.511962\pi$
$660$	0	0
$661$	15949.2	0.938506	0.469253	−	0.883064i	$-0.344523\pi$
$661$	15949.2	0.938506	0.469253	+	0.883064i	$0.344523\pi$
$662$	−19982.5	−1.17318
$663$	0	0
$664$	1605.64	0.0938418
$665$	−790.470	−0.0460949
$666$	0	0
$667$	42988.0	2.49550
$668$	1278.89	0.0740746
$669$	0	0
$670$	−2053.16	−0.118389
$671$	1080.00	0.0621355
$672$	0	0
$673$	5130.42	0.293853	0.146926	−	0.989147i	$-0.453062\pi$
$673$	5130.42	0.293853	0.146926	+	0.989147i	$0.453062\pi$
$674$	6289.36	0.359432
$675$	0	0
$676$	5344.38	0.304073
$677$	24635.2	1.39854	0.699268	−	0.714860i	$-0.253510\pi$
$677$	24635.2	1.39854	0.699268	+	0.714860i	$0.253510\pi$
$678$	0	0
$679$	−30601.3	−1.72956
$680$	−2515.30	−0.141849
$681$	0	0
$682$	2685.20	0.150765
$683$	7124.60	0.399144	0.199572	−	0.979883i	$-0.436045\pi$
$683$	7124.60	0.399144	0.199572	+	0.979883i	$0.436045\pi$
$684$	0	0
$685$	1053.24	0.0587480
$686$	16636.9	0.925946
$687$	0	0
$688$	−22883.4	−1.26805
$689$	−23051.8	−1.27460
$690$	0	0
$691$	28973.9	1.59511	0.797553	−	0.603249i	$-0.206128\pi$
$691$	28973.9	1.59511	0.797553	+	0.603249i	$0.206128\pi$
$692$	−3095.70	−0.170059
$693$	0	0
$694$	30169.0	1.65014
$695$	−1879.05	−0.102556
$696$	0	0
$697$	−24411.2	−1.32660
$698$	9792.28	0.531007
$699$	0	0
$700$	−4491.98	−0.242544
$701$	9287.65	0.500413	0.250207	−	0.968192i	$-0.419501\pi$
$701$	9287.65	0.500413	0.250207	+	0.968192i	$0.419501\pi$
$702$	0	0
$703$	11856.1	0.636076
$704$	1151.64	0.0616533
$705$	0	0
$706$	−11664.3	−0.621804
$707$	−25165.2	−1.33866
$708$	0	0
$709$	29816.2	1.57937	0.789684	−	0.613513i	$-0.210244\pi$
$709$	29816.2	1.57937	0.789684	+	0.613513i	$0.210244\pi$
$710$	2344.43	0.123922
$711$	0	0
$712$	−16050.9	−0.844851
$713$	38590.5	2.02696
$714$	0	0
$715$	−251.474	−0.0131533
$716$	5760.16	0.300652
$717$	0	0
$718$	16794.7	0.872941
$719$	4977.57	0.258181	0.129090	−	0.991633i	$-0.458794\pi$
$719$	4977.57	0.258181	0.129090	+	0.991633i	$0.458794\pi$
$720$	0	0
$721$	−8396.28	−0.433695
$722$	17470.1	0.900510
$723$	0	0
$724$	−5530.23	−0.283880
$725$	36687.8	1.87938
$726$	0	0
$727$	−11647.8	−0.594215	−0.297107	−	0.954844i	$-0.596022\pi$
$727$	−11647.8	−0.594215	−0.297107	+	0.954844i	$0.596022\pi$
$728$	29265.7	1.48992
$729$	0	0
$730$	−1794.95	−0.0910056
$731$	36663.2	1.85505
$732$	0	0
$733$	−49.3710	−0.00248780	−0.00124390	−	0.999999i	$-0.500396\pi$
$733$	−49.3710	−0.00248780	−0.00124390	+	0.999999i	$0.500396\pi$
$734$	−1898.83	−0.0954865
$735$	0	0
$736$	−11310.8	−0.566471
$737$	−1980.22	−0.0989717
$738$	0	0
$739$	−1360.22	−0.0677085	−0.0338542	−	0.999427i	$-0.510778\pi$
$739$	−1360.22	−0.0677085	−0.0338542	+	0.999427i	$0.510778\pi$
$740$	−627.016	−0.0311480
$741$	0	0
$742$	20574.4	1.01794
$743$	−14170.2	−0.699667	−0.349834	−	0.936812i	$-0.613762\pi$
$743$	−14170.2	−0.699667	−0.349834	+	0.936812i	$0.613762\pi$
$744$	0	0
$745$	−2679.72	−0.131782
$746$	10288.2	0.504928
$747$	0	0
$748$	680.149	0.0332469
$749$	−13342.0	−0.650875
$750$	0	0
$751$	29825.3	1.44919	0.724595	−	0.689175i	$-0.242027\pi$
$751$	29825.3	1.44919	0.724595	+	0.689175i	$0.242027\pi$
$752$	42583.6	2.06498
$753$	0	0
$754$	67014.1	3.23675
$755$	−811.674	−0.0391256
$756$	0	0
$757$	11895.8	0.571150	0.285575	−	0.958356i	$-0.407815\pi$
$757$	11895.8	0.571150	0.285575	+	0.958356i	$0.407815\pi$
$758$	20013.1	0.958983
$759$	0	0
$760$	−744.925	−0.0355543
$761$	2787.21	0.132768	0.0663838	−	0.997794i	$-0.478854\pi$
$761$	2787.21	0.132768	0.0663838	+	0.997794i	$0.478854\pi$
$762$	0	0
$763$	24137.6	1.14527
$764$	−7868.19	−0.372593
$765$	0	0
$766$	−10713.1	−0.505327
$767$	−57929.8	−2.72715
$768$	0	0
$769$	−16883.9	−0.791743	−0.395872	−	0.918306i	$-0.629557\pi$
$769$	−16883.9	−0.791743	−0.395872	+	0.918306i	$0.629557\pi$
$770$	224.448	0.0105046
$771$	0	0
$772$	−3314.31	−0.154514
$773$	31566.8	1.46880	0.734398	−	0.678719i	$-0.237464\pi$
$773$	31566.8	1.46880	0.734398	+	0.678719i	$0.237464\pi$
$774$	0	0
$775$	32934.8	1.52652
$776$	−28838.1	−1.33406
$777$	0	0
$778$	−2118.82	−0.0976395
$779$	−7229.56	−0.332511
$780$	0	0
$781$	2261.13	0.103598
$782$	54414.0	2.48829
$783$	0	0
$784$	−6421.97	−0.292546
$785$	977.648	0.0444507
$786$	0	0
$787$	16548.1	0.749525	0.374763	−	0.927121i	$-0.377724\pi$
$787$	16548.1	0.749525	0.374763	+	0.927121i	$0.377724\pi$
$788$	−835.595	−0.0377752
$789$	0	0
$790$	741.713	0.0334038
$791$	−3625.74	−0.162979
$792$	0	0
$793$	24196.1	1.08352
$794$	−14762.6	−0.659829
$795$	0	0
$796$	−3723.68	−0.165807
$797$	5276.20	0.234495	0.117248	−	0.993103i	$-0.462593\pi$
$797$	5276.20	0.234495	0.117248	+	0.993103i	$0.462593\pi$
$798$	0	0
$799$	−68226.6	−3.02088
$800$	−9653.15	−0.426613
$801$	0	0
$802$	33204.2	1.46195
$803$	−1731.18	−0.0760797
$804$	0	0
$805$	3225.66	0.141229
$806$	60158.8	2.62904
$807$	0	0
$808$	−23715.3	−1.03255
$809$	19348.3	0.840854	0.420427	−	0.907326i	$-0.361880\pi$
$809$	19348.3	0.840854	0.420427	+	0.907326i	$0.361880\pi$
$810$	0	0
$811$	−37524.7	−1.62475	−0.812375	−	0.583136i	$-0.801826\pi$
$811$	−37524.7	−1.62475	−0.812375	+	0.583136i	$0.801826\pi$
$812$	−10744.5	−0.464356
$813$	0	0
$814$	−3366.45	−0.144956
$815$	−490.471	−0.0210803
$816$	0	0
$817$	10858.1	0.464964
$818$	25486.3	1.08937
$819$	0	0
$820$	382.339	0.0162827
$821$	−4240.46	−0.180260	−0.0901298	−	0.995930i	$-0.528728\pi$
$821$	−4240.46	−0.180260	−0.0901298	+	0.995930i	$0.528728\pi$
$822$	0	0
$823$	489.899	0.0207495	0.0103747	−	0.999946i	$-0.496698\pi$
$823$	489.899	0.0207495	0.0103747	+	0.999946i	$0.496698\pi$
$824$	−7912.51	−0.334521
$825$	0	0
$826$	51704.2	2.17799
$827$	−26030.0	−1.09450	−0.547249	−	0.836970i	$-0.684325\pi$
$827$	−26030.0	−1.09450	−0.547249	+	0.836970i	$0.684325\pi$
$828$	0	0
$829$	16566.5	0.694062	0.347031	−	0.937854i	$-0.387190\pi$
$829$	16566.5	0.694062	0.347031	+	0.937854i	$0.387190\pi$
$830$	275.885	0.0115375
$831$	0	0
$832$	25801.1	1.07511
$833$	10289.1	0.427968
$834$	0	0
$835$	−783.772	−0.0324833
$836$	201.431	0.00833329
$837$	0	0
$838$	12601.0	0.519444
$839$	30926.1	1.27257	0.636286	−	0.771453i	$-0.280470\pi$
$839$	30926.1	1.27257	0.636286	+	0.771453i	$0.280470\pi$
$840$	0	0
$841$	63365.5	2.59812
$842$	9757.78	0.399377
$843$	0	0
$844$	−369.626	−0.0150747
$845$	−3275.32	−0.133342
$846$	0	0
$847$	−27341.6	−1.10917
$848$	23848.4	0.965753
$849$	0	0
$850$	46439.3	1.87395
$851$	−48381.1	−1.94886
$852$	0	0
$853$	−19096.5	−0.766533	−0.383267	−	0.923638i	$-0.625201\pi$
$853$	−19096.5	−0.766533	−0.383267	+	0.923638i	$0.625201\pi$
$854$	−21595.8	−0.865331
$855$	0	0
$856$	−12573.3	−0.502039
$857$	−19072.6	−0.760220	−0.380110	−	0.924941i	$-0.624114\pi$
$857$	−19072.6	−0.760220	−0.380110	+	0.924941i	$0.624114\pi$
$858$	0	0
$859$	−43796.1	−1.73959	−0.869793	−	0.493417i	$-0.835748\pi$
$859$	−43796.1	−1.73959	−0.869793	+	0.493417i	$0.835748\pi$
$860$	−574.234	−0.0227689
$861$	0	0
$862$	−44262.9	−1.74896
$863$	584.888	0.0230705	0.0115352	−	0.999933i	$-0.496328\pi$
$863$	584.888	0.0230705	0.0115352	+	0.999933i	$0.496328\pi$
$864$	0	0
$865$	1897.21	0.0745746
$866$	−11726.0	−0.460121
$867$	0	0
$868$	−9645.35	−0.377171
$869$	715.362	0.0279252
$870$	0	0
$871$	−44364.4	−1.72587
$872$	22746.9	0.883379
$873$	0	0
$874$	16115.1	0.623686
$875$	5531.46	0.213711
$876$	0	0
$877$	−31081.6	−1.19675	−0.598375	−	0.801216i	$-0.704187\pi$
$877$	−31081.6	−1.19675	−0.598375	+	0.801216i	$0.704187\pi$
$878$	3948.98	0.151790
$879$	0	0
$880$	260.165	0.00996609
$881$	46352.7	1.77260	0.886301	−	0.463109i	$-0.153266\pi$
$881$	46352.7	1.77260	0.886301	+	0.463109i	$0.153266\pi$
$882$	0	0
$883$	49606.9	1.89061	0.945304	−	0.326191i	$-0.105765\pi$
$883$	49606.9	1.89061	0.945304	+	0.326191i	$0.105765\pi$
$884$	15237.9	0.579759
$885$	0	0
$886$	−23554.5	−0.893147
$887$	50220.1	1.90105	0.950523	−	0.310655i	$-0.100548\pi$
$887$	50220.1	1.90105	0.950523	+	0.310655i	$0.100548\pi$
$888$	0	0
$889$	−22236.9	−0.838922
$890$	−2757.91	−0.103871
$891$	0	0
$892$	1298.51	0.0487412
$893$	−20205.8	−0.757179
$894$	0	0
$895$	−3530.12	−0.131843
$896$	−35938.7	−1.33999
$897$	0	0
$898$	−27890.2	−1.03642
$899$	78777.5	2.92255
$900$	0	0
$901$	−38209.5	−1.41281
$902$	2052.78	0.0757762
$903$	0	0
$904$	−3416.83	−0.125710
$905$	3389.21	0.124488
$906$	0	0
$907$	−35690.8	−1.30661	−0.653304	−	0.757095i	$-0.726618\pi$
$907$	−35690.8	−1.30661	−0.653304	+	0.757095i	$0.726618\pi$
$908$	2656.02	0.0970740
$909$	0	0
$910$	5028.50	0.183179
$911$	−19646.9	−0.714522	−0.357261	−	0.934005i	$-0.616289\pi$
$911$	−19646.9	−0.714522	−0.357261	+	0.934005i	$0.616289\pi$
$912$	0	0
$913$	266.083	0.00964520
$914$	−30868.7	−1.11712
$915$	0	0
$916$	−10702.3	−0.386042
$917$	40035.1	1.44174
$918$	0	0
$919$	22996.5	0.825447	0.412723	−	0.910856i	$-0.364578\pi$
$919$	22996.5	0.825447	0.412723	+	0.910856i	$0.364578\pi$
$920$	3039.81	0.108934
$921$	0	0
$922$	43054.2	1.53787
$923$	50658.1	1.80653
$924$	0	0
$925$	−41290.5	−1.46770
$926$	51976.4	1.84455
$927$	0	0
$928$	−23089.6	−0.816761
$929$	18009.6	0.636033	0.318016	−	0.948085i	$-0.396983\pi$
$929$	18009.6	0.636033	0.318016	+	0.948085i	$0.396983\pi$
$930$	0	0
$931$	3047.20	0.107270
$932$	7508.39	0.263890
$933$	0	0
$934$	−41292.5	−1.44661
$935$	−416.831	−0.0145795
$936$	0	0
$937$	−55181.5	−1.92391	−0.961954	−	0.273212i	$-0.911914\pi$
$937$	−55181.5	−1.92391	−0.961954	+	0.273212i	$0.911914\pi$
$938$	39596.6	1.37833
$939$	0	0
$940$	1068.59	0.0370784
$941$	−23849.2	−0.826209	−0.413104	−	0.910684i	$-0.635556\pi$
$941$	−23849.2	−0.826209	−0.413104	+	0.910684i	$0.635556\pi$
$942$	0	0
$943$	29501.6	1.01877
$944$	59931.9	2.06633
$945$	0	0
$946$	−3083.07	−0.105961
$947$	2948.37	0.101171	0.0505855	−	0.998720i	$-0.483891\pi$
$947$	2948.37	0.101171	0.0505855	+	0.998720i	$0.483891\pi$
$948$	0	0
$949$	−38785.1	−1.32668
$950$	13753.3	0.469702
$951$	0	0
$952$	48509.4	1.65147
$953$	−21740.9	−0.738989	−0.369495	−	0.929233i	$-0.620469\pi$
$953$	−21740.9	−0.738989	−0.369495	+	0.929233i	$0.620469\pi$
$954$	0	0
$955$	4822.04	0.163390
$956$	9784.70	0.331025
$957$	0	0
$958$	37559.6	1.26670
$959$	−20312.6	−0.683969
$960$	0	0
$961$	40927.8	1.37383
$962$	−75421.5	−2.52774
$963$	0	0
$964$	6704.12	0.223989
$965$	2031.18	0.0677576
$966$	0	0
$967$	−30670.3	−1.01995	−0.509975	−	0.860189i	$-0.670345\pi$
$967$	−30670.3	−1.01995	−0.509975	+	0.860189i	$0.670345\pi$
$968$	−25766.3	−0.855536
$969$	0	0
$970$	−4955.02	−0.164017
$971$	35183.0	1.16280	0.581399	−	0.813619i	$-0.302506\pi$
$971$	35183.0	1.16280	0.581399	+	0.813619i	$0.302506\pi$
$972$	0	0
$973$	36238.8	1.19400
$974$	−10515.2	−0.345922
$975$	0	0
$976$	−25032.4	−0.820970
$977$	−24673.0	−0.807941	−0.403970	−	0.914772i	$-0.632370\pi$
$977$	−24673.0	−0.807941	−0.403970	+	0.914772i	$0.632370\pi$
$978$	0	0
$979$	−2659.93	−0.0868351
$980$	−161.153	−0.00525290
$981$	0	0
$982$	8321.58	0.270420
$983$	−27224.7	−0.883349	−0.441675	−	0.897175i	$-0.645615\pi$
$983$	−27224.7	−0.883349	−0.441675	+	0.897175i	$0.645615\pi$
$984$	0	0
$985$	512.096	0.0165652
$986$	111079.	3.58771
$987$	0	0
$988$	4512.82	0.145316
$989$	−44308.4	−1.42460
$990$	0	0
$991$	12272.4	0.393385	0.196692	−	0.980465i	$-0.436980\pi$
$991$	12272.4	0.393385	0.196692	+	0.980465i	$0.436980\pi$
$992$	−20727.6	−0.663410
$993$	0	0
$994$	−45213.9	−1.44275
$995$	2282.06	0.0727098
$996$	0	0
$997$	−4457.13	−0.141584	−0.0707918	−	0.997491i	$-0.522553\pi$
$997$	−4457.13	−0.141584	−0.0707918	+	0.997491i	$0.522553\pi$
$998$	−62993.5	−1.99802
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1899.4.a.d.1.7		26
3.2	odd	2		633.4.a.d.1.20	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
633.4.a.d.1.20	✓	26	3.2	odd	2
1899.4.a.d.1.7		26	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:	\( N \)	\(=\)	\( 1899 = 3^{2} \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1899.a (trivial)

\(f(q)\)	\(=\)	\(q-3.12278 q^{2} +1.75178 q^{4} -1.07358 q^{5} +20.7048 q^{7} +19.5118 q^{8} +O(q^{10})\)	\(q-3.12278 q^{2} +1.75178 q^{4} -1.07358 q^{5} +20.7048 q^{7} +19.5118 q^{8} +3.35257 q^{10} +3.23346 q^{11} +72.4419 q^{13} -64.6566 q^{14} -74.9455 q^{16} +120.076 q^{17} +35.5614 q^{19} -1.88068 q^{20} -10.0974 q^{22} -145.115 q^{23} -123.847 q^{25} -226.220 q^{26} +36.2703 q^{28} -296.234 q^{29} -265.930 q^{31} +77.9439 q^{32} -374.972 q^{34} -22.2283 q^{35} +333.398 q^{37} -111.051 q^{38} -20.9476 q^{40} -203.298 q^{41} +305.333 q^{43} +5.66431 q^{44} +453.163 q^{46} -568.195 q^{47} +85.6885 q^{49} +386.749 q^{50} +126.902 q^{52} -318.210 q^{53} -3.47139 q^{55} +403.989 q^{56} +925.074 q^{58} -799.673 q^{59} +334.008 q^{61} +830.442 q^{62} +356.162 q^{64} -77.7724 q^{65} -612.414 q^{67} +210.347 q^{68} +69.4142 q^{70} +699.292 q^{71} -535.396 q^{73} -1041.13 q^{74} +62.2958 q^{76} +66.9481 q^{77} +221.237 q^{79} +80.4602 q^{80} +634.856 q^{82} +82.2906 q^{83} -128.912 q^{85} -953.490 q^{86} +63.0908 q^{88} -822.625 q^{89} +1499.89 q^{91} -254.210 q^{92} +1774.35 q^{94} -38.1781 q^{95} -1477.98 q^{97} -267.587 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 6 q^{2} + 108 q^{4} - 25 q^{5} + 50 q^{7} - 57 q^{8}+O(q^{10}) \) 26 * q - 6 * q^2 + 108 * q^4 - 25 * q^5 + 50 * q^7 - 57 * q^8	\( 26 q - 6 q^{2} + 108 q^{4} - 25 q^{5} + 50 q^{7} - 57 q^{8} - 32 q^{10} - 73 q^{11} - 61 q^{13} - 243 q^{14} + 440 q^{16} - 96 q^{17} + 71 q^{19} - 277 q^{20} + 206 q^{22} - 678 q^{23} + 597 q^{25} - 335 q^{26} + 354 q^{28} - 224 q^{29} - 188 q^{31} - 502 q^{32} - 261 q^{34} - 624 q^{35} + 223 q^{37} - 737 q^{38} - 562 q^{40} - 106 q^{41} + 607 q^{43} - 767 q^{44} - 529 q^{46} - 1657 q^{47} + 848 q^{49} - 906 q^{50} + 156 q^{52} - 1902 q^{53} + 1215 q^{55} - 3540 q^{56} + 2871 q^{58} - 2790 q^{59} - 1952 q^{61} - 3134 q^{62} + 1659 q^{64} - 3653 q^{65} + 2932 q^{67} - 7363 q^{68} + 4509 q^{70} - 4157 q^{71} + 94 q^{73} - 6271 q^{74} + 2757 q^{76} - 3564 q^{77} + 2365 q^{79} - 6249 q^{80} + 2481 q^{82} - 4852 q^{83} + 640 q^{85} - 5710 q^{86} + 5291 q^{88} - 2504 q^{89} - 812 q^{91} - 9719 q^{92} - 252 q^{94} - 4999 q^{95} - 302 q^{97} - 14279 q^{98}+O(q^{100}) \) 26 * q - 6 * q^2 + 108 * q^4 - 25 * q^5 + 50 * q^7 - 57 * q^8 - 32 * q^10 - 73 * q^11 - 61 * q^13 - 243 * q^14 + 440 * q^16 - 96 * q^17 + 71 * q^19 - 277 * q^20 + 206 * q^22 - 678 * q^23 + 597 * q^25 - 335 * q^26 + 354 * q^28 - 224 * q^29 - 188 * q^31 - 502 * q^32 - 261 * q^34 - 624 * q^35 + 223 * q^37 - 737 * q^38 - 562 * q^40 - 106 * q^41 + 607 * q^43 - 767 * q^44 - 529 * q^46 - 1657 * q^47 + 848 * q^49 - 906 * q^50 + 156 * q^52 - 1902 * q^53 + 1215 * q^55 - 3540 * q^56 + 2871 * q^58 - 2790 * q^59 - 1952 * q^61 - 3134 * q^62 + 1659 * q^64 - 3653 * q^65 + 2932 * q^67 - 7363 * q^68 + 4509 * q^70 - 4157 * q^71 + 94 * q^73 - 6271 * q^74 + 2757 * q^76 - 3564 * q^77 + 2365 * q^79 - 6249 * q^80 + 2481 * q^82 - 4852 * q^83 + 640 * q^85 - 5710 * q^86 + 5291 * q^88 - 2504 * q^89 - 812 * q^91 - 9719 * q^92 - 252 * q^94 - 4999 * q^95 - 302 * q^97 - 14279 * q^98

Introduction

L-functions

Modular forms

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Database

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