LMFDB - Embedded newform 1775.4.a.h.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1775,4,Mod(1,1775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1775, 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("1775.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1775 = 5^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1775.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:	$104.728390260$
Analytic rank:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	1775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.326193 q^{2} -3.04731 q^{3} -7.89360 q^{4} +0.994014 q^{6} -25.8341 q^{7} +5.18439 q^{8} -17.7139 q^{9} +O(q^{10})$	\(q-0.326193 q^{2} -3.04731 q^{3} -7.89360 q^{4} +0.994014 q^{6} -25.8341 q^{7} +5.18439 q^{8} -17.7139 q^{9} -35.5564 q^{11} +24.0543 q^{12} -89.5646 q^{13} +8.42691 q^{14} +61.4577 q^{16} +82.5682 q^{17} +5.77815 q^{18} +123.112 q^{19} +78.7246 q^{21} +11.5983 q^{22} -15.0796 q^{23} -15.7985 q^{24} +29.2154 q^{26} +136.257 q^{27} +203.924 q^{28} +70.3764 q^{29} -4.21004 q^{31} -61.5222 q^{32} +108.352 q^{33} -26.9332 q^{34} +139.826 q^{36} +41.9137 q^{37} -40.1582 q^{38} +272.931 q^{39} -145.282 q^{41} -25.6795 q^{42} +239.756 q^{43} +280.668 q^{44} +4.91888 q^{46} -87.8415 q^{47} -187.281 q^{48} +324.400 q^{49} -251.611 q^{51} +706.987 q^{52} +715.021 q^{53} -44.4462 q^{54} -133.934 q^{56} -375.160 q^{57} -22.9563 q^{58} +705.927 q^{59} -341.343 q^{61} +1.37329 q^{62} +457.622 q^{63} -471.593 q^{64} -35.3436 q^{66} -945.392 q^{67} -651.760 q^{68} +45.9524 q^{69} +71.0000 q^{71} -91.8356 q^{72} -782.152 q^{73} -13.6720 q^{74} -971.793 q^{76} +918.567 q^{77} -89.0284 q^{78} +314.553 q^{79} +63.0561 q^{81} +47.3902 q^{82} -1451.01 q^{83} -621.420 q^{84} -78.2069 q^{86} -214.459 q^{87} -184.338 q^{88} +272.013 q^{89} +2313.82 q^{91} +119.033 q^{92} +12.8293 q^{93} +28.6533 q^{94} +187.477 q^{96} +495.044 q^{97} -105.817 q^{98} +629.842 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 6 q^{2} - 19 q^{3} + 146 q^{4} + 8 q^{6} - 76 q^{7} - 72 q^{8} + 286 q^{9}+O(q^{10}) $ 35 * q - 6 * q^2 - 19 * q^3 + 146 * q^4 + 8 * q^6 - 76 * q^7 - 72 * q^8 + 286 * q^9	\( 35 q - 6 q^{2} - 19 q^{3} + 146 q^{4} + 8 q^{6} - 76 q^{7} - 72 q^{8} + 286 q^{9} + 29 q^{11} - 228 q^{12} - 206 q^{13} - 48 q^{14} + 542 q^{16} - 347 q^{17} - 280 q^{18} - 59 q^{19} + 284 q^{21} - 605 q^{22} - 168 q^{23} + 100 q^{24} + 655 q^{26} - 727 q^{27} - 749 q^{28} - 522 q^{29} + 84 q^{31} - 1522 q^{32} - 547 q^{33} - 324 q^{34} + 2114 q^{36} - 706 q^{37} - 487 q^{38} - 574 q^{39} + 311 q^{41} - 1602 q^{42} - 928 q^{43} - 1129 q^{44} + 144 q^{46} - 744 q^{47} - 2644 q^{48} + 1649 q^{49} + 277 q^{51} - 2727 q^{52} - 886 q^{53} - 923 q^{54} + 947 q^{56} - 2501 q^{57} - 1181 q^{58} - 434 q^{59} + 466 q^{61} - 1727 q^{62} - 1908 q^{63} + 2102 q^{64} - 884 q^{66} - 2425 q^{67} - 2329 q^{68} - 716 q^{69} + 2485 q^{71} - 4079 q^{72} - 5803 q^{73} - 412 q^{74} - 3109 q^{76} - 732 q^{77} - 2691 q^{78} + 1024 q^{79} + 7 q^{81} - 1325 q^{82} - 4927 q^{83} + 3889 q^{84} - 2716 q^{86} - 2634 q^{87} - 7122 q^{88} + 3279 q^{89} - 3782 q^{91} + 3025 q^{92} - 5256 q^{93} + 1485 q^{94} - 3043 q^{96} - 8548 q^{97} - 5578 q^{98} + 9008 q^{99}+O(q^{100}) \) 35 * q - 6 * q^2 - 19 * q^3 + 146 * q^4 + 8 * q^6 - 76 * q^7 - 72 * q^8 + 286 * q^9 + 29 * q^11 - 228 * q^12 - 206 * q^13 - 48 * q^14 + 542 * q^16 - 347 * q^17 - 280 * q^18 - 59 * q^19 + 284 * q^21 - 605 * q^22 - 168 * q^23 + 100 * q^24 + 655 * q^26 - 727 * q^27 - 749 * q^28 - 522 * q^29 + 84 * q^31 - 1522 * q^32 - 547 * q^33 - 324 * q^34 + 2114 * q^36 - 706 * q^37 - 487 * q^38 - 574 * q^39 + 311 * q^41 - 1602 * q^42 - 928 * q^43 - 1129 * q^44 + 144 * q^46 - 744 * q^47 - 2644 * q^48 + 1649 * q^49 + 277 * q^51 - 2727 * q^52 - 886 * q^53 - 923 * q^54 + 947 * q^56 - 2501 * q^57 - 1181 * q^58 - 434 * q^59 + 466 * q^61 - 1727 * q^62 - 1908 * q^63 + 2102 * q^64 - 884 * q^66 - 2425 * q^67 - 2329 * q^68 - 716 * q^69 + 2485 * q^71 - 4079 * q^72 - 5803 * q^73 - 412 * q^74 - 3109 * q^76 - 732 * q^77 - 2691 * q^78 + 1024 * q^79 + 7 * q^81 - 1325 * q^82 - 4927 * q^83 + 3889 * q^84 - 2716 * q^86 - 2634 * q^87 - 7122 * q^88 + 3279 * q^89 - 3782 * q^91 + 3025 * q^92 - 5256 * q^93 + 1485 * q^94 - 3043 * q^96 - 8548 * q^97 - 5578 * q^98 + 9008 * q^99

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 $

$2$	−0.326193	−0.115327	−0.0576634	−	0.998336i	$-0.518365\pi$
$2$	−0.326193	−0.115327	−0.0576634	+	0.998336i	$0.518365\pi$
$3$	−3.04731	−0.586456	−0.293228	−	0.956043i	$-0.594729\pi$
$3$	−3.04731	−0.586456	−0.293228	+	0.956043i	$0.594729\pi$
$4$	−7.89360	−0.986700
$5$	0	0
$5$	0	0
$6$	0.994014	0.0676341
$7$	−25.8341	−1.39491	−0.697455	−	0.716629i	$-0.745684\pi$
$7$	−25.8341	−1.39491	−0.697455	+	0.716629i	$0.745684\pi$
$8$	5.18439	0.229120
$9$	−17.7139	−0.656069
$10$	0	0
$11$	−35.5564	−0.974605	−0.487303	−	0.873233i	$-0.662019\pi$
$11$	−35.5564	−0.974605	−0.487303	+	0.873233i	$0.662019\pi$
$12$	24.0543	0.578656
$13$	−89.5646	−1.91083	−0.955413	−	0.295272i	$-0.904590\pi$
$13$	−89.5646	−1.91083	−0.955413	+	0.295272i	$0.904590\pi$
$14$	8.42691	0.160871
$15$	0	0
$16$	61.4577	0.960276
$17$	82.5682	1.17798	0.588992	−	0.808139i	$-0.299525\pi$
$17$	82.5682	1.17798	0.588992	+	0.808139i	$0.299525\pi$
$18$	5.77815	0.0756624
$19$	123.112	1.48651	0.743256	−	0.669007i	$-0.233280\pi$
$19$	123.112	1.48651	0.743256	+	0.669007i	$0.233280\pi$
$20$	0	0
$21$	78.7246	0.818053
$22$	11.5983	0.112398
$23$	−15.0796	−0.136710	−0.0683548	−	0.997661i	$-0.521775\pi$
$23$	−15.0796	−0.136710	−0.0683548	+	0.997661i	$0.521775\pi$
$24$	−15.7985	−0.134369
$25$	0	0
$26$	29.2154	0.220370
$27$	136.257	0.971212
$28$	203.924	1.37636
$29$	70.3764	0.450640	0.225320	−	0.974285i	$-0.427657\pi$
$29$	70.3764	0.450640	0.225320	+	0.974285i	$0.427657\pi$
$30$	0	0
$31$	−4.21004	−0.0243918	−0.0121959	−	0.999926i	$-0.503882\pi$
$31$	−4.21004	−0.0243918	−0.0121959	+	0.999926i	$0.503882\pi$
$32$	−61.5222	−0.339865
$33$	108.352	0.571563
$34$	−26.9332	−0.135853
$35$	0	0
$36$	139.826	0.647344
$37$	41.9137	0.186232	0.0931159	−	0.995655i	$-0.470317\pi$
$37$	41.9137	0.186232	0.0931159	+	0.995655i	$0.470317\pi$
$38$	−40.1582	−0.171435
$39$	272.931	1.12062
$40$	0	0
$41$	−145.282	−0.553398	−0.276699	−	0.960957i	$-0.589240\pi$
$41$	−145.282	−0.553398	−0.276699	+	0.960957i	$0.589240\pi$
$42$	−25.6795	−0.0943435
$43$	239.756	0.850290	0.425145	−	0.905125i	$-0.360223\pi$
$43$	239.756	0.850290	0.425145	+	0.905125i	$0.360223\pi$
$44$	280.668	0.961643
$45$	0	0
$46$	4.91888	0.0157663
$47$	−87.8415	−0.272617	−0.136309	−	0.990666i	$-0.543524\pi$
$47$	−87.8415	−0.272617	−0.136309	+	0.990666i	$0.543524\pi$
$48$	−187.281	−0.563160
$49$	324.400	0.945774
$50$	0	0
$51$	−251.611	−0.690836
$52$	706.987	1.88541
$53$	715.021	1.85312	0.926562	−	0.376141i	$-0.122749\pi$
$53$	715.021	1.85312	0.926562	+	0.376141i	$0.122749\pi$
$54$	−44.4462	−0.112007
$55$	0	0
$56$	−133.934	−0.319601
$57$	−375.160	−0.871774
$58$	−22.9563	−0.0519709
$59$	705.927	1.55769	0.778847	−	0.627215i	$-0.215805\pi$
$59$	705.927	1.55769	0.778847	+	0.627215i	$0.215805\pi$
$60$	0	0
$61$	−341.343	−0.716466	−0.358233	−	0.933632i	$-0.616621\pi$
$61$	−341.343	−0.716466	−0.358233	+	0.933632i	$0.616621\pi$
$62$	1.37329	0.00281303
$63$	457.622	0.915158
$64$	−471.593	−0.921080
$65$	0	0
$66$	−35.3436	−0.0659165
$67$	−945.392	−1.72385	−0.861925	−	0.507035i	$-0.830741\pi$
$67$	−945.392	−1.72385	−0.861925	+	0.507035i	$0.830741\pi$
$68$	−651.760	−1.16232
$69$	45.9524	0.0801741
$70$	0	0
$71$	71.0000	0.118678
$71$	71.0000	0.118678
$72$	−91.8356	−0.150318
$73$	−782.152	−1.25403	−0.627013	−	0.779009i	$-0.715723\pi$
$73$	−782.152	−1.25403	−0.627013	+	0.779009i	$0.715723\pi$
$74$	−13.6720	−0.0214775
$75$	0	0
$76$	−971.793	−1.46674
$77$	918.567	1.35949
$78$	−89.0284	−0.129237
$79$	314.553	0.447975	0.223987	−	0.974592i	$-0.428093\pi$
$79$	314.553	0.447975	0.223987	+	0.974592i	$0.428093\pi$
$80$	0	0
$81$	63.0561	0.0864967
$82$	47.3902	0.0638216
$83$	−1451.01	−1.91890	−0.959452	−	0.281874i	$-0.909044\pi$
$83$	−1451.01	−1.91890	−0.959452	+	0.281874i	$0.909044\pi$
$84$	−621.420	−0.807173
$85$	0	0
$86$	−78.2069	−0.0980613
$87$	−214.459	−0.264281
$88$	−184.338	−0.223301
$89$	272.013	0.323970	0.161985	−	0.986793i	$-0.448210\pi$
$89$	272.013	0.323970	0.161985	+	0.986793i	$0.448210\pi$
$90$	0	0
$91$	2313.82	2.66543
$92$	119.033	0.134891
$93$	12.8293	0.0143047
$94$	28.6533	0.0314401
$95$	0	0
$96$	187.477	0.199316
$97$	495.044	0.518186	0.259093	−	0.965852i	$-0.416576\pi$
$97$	495.044	0.518186	0.259093	+	0.965852i	$0.416576\pi$
$98$	−105.817	−0.109073
$99$	629.842	0.639409
$100$	0	0
$101$	−424.847	−0.418553	−0.209277	−	0.977856i	$-0.567111\pi$
$101$	−424.847	−0.418553	−0.209277	+	0.977856i	$0.567111\pi$
$102$	82.0739	0.0796719
$103$	−1368.65	−1.30929	−0.654644	−	0.755937i	$-0.727181\pi$
$103$	−1368.65	−1.30929	−0.654644	+	0.755937i	$0.727181\pi$
$104$	−464.338	−0.437808
$105$	0	0
$106$	−233.235	−0.213715
$107$	649.745	0.587039	0.293520	−	0.955953i	$-0.405173\pi$
$107$	649.745	0.587039	0.293520	+	0.955953i	$0.405173\pi$
$108$	−1075.56	−0.958294
$109$	1791.53	1.57429	0.787145	−	0.616768i	$-0.211558\pi$
$109$	1791.53	1.57429	0.787145	+	0.616768i	$0.211558\pi$
$110$	0	0
$111$	−127.724	−0.109217
$112$	−1587.70	−1.33950
$113$	258.021	0.214802	0.107401	−	0.994216i	$-0.465747\pi$
$113$	258.021	0.214802	0.107401	+	0.994216i	$0.465747\pi$
$114$	122.375	0.100539
$115$	0	0
$116$	−555.523	−0.444646
$117$	1586.54	1.25363
$118$	−230.269	−0.179644
$119$	−2133.07	−1.64318
$120$	0	0
$121$	−66.7429	−0.0501449
$122$	111.344	0.0826278
$123$	442.721	0.324543
$124$	33.2324	0.0240674
$125$	0	0
$126$	−149.273	−0.105542
$127$	2178.48	1.52212	0.761059	−	0.648683i	$-0.224680\pi$
$127$	2178.48	1.52212	0.761059	+	0.648683i	$0.224680\pi$
$128$	646.008	0.446091
$129$	−730.613	−0.498658
$130$	0	0
$131$	−608.618	−0.405917	−0.202959	−	0.979187i	$-0.565056\pi$
$131$	−608.618	−0.405917	−0.202959	+	0.979187i	$0.565056\pi$
$132$	−855.283	−0.563961
$133$	−3180.48	−2.07355
$134$	308.381	0.198806
$135$	0	0
$136$	428.066	0.269899
$137$	2114.72	1.31878	0.659389	−	0.751802i	$-0.270815\pi$
$137$	2114.72	1.31878	0.659389	+	0.751802i	$0.270815\pi$
$138$	−14.9894	−0.00924623
$139$	−404.254	−0.246679	−0.123340	−	0.992365i	$-0.539360\pi$
$139$	−404.254	−0.246679	−0.123340	+	0.992365i	$0.539360\pi$
$140$	0	0
$141$	267.681	0.159878
$142$	−23.1597	−0.0136868
$143$	3184.59	1.86230
$144$	−1088.65	−0.630008
$145$	0	0
$146$	255.133	0.144623
$147$	−988.550	−0.554655
$148$	−330.850	−0.183755
$149$	2249.54	1.23684	0.618422	−	0.785846i	$-0.287772\pi$
$149$	2249.54	1.23684	0.618422	+	0.785846i	$0.287772\pi$
$150$	0	0
$151$	3021.74	1.62852	0.814258	−	0.580503i	$-0.197144\pi$
$151$	3021.74	1.62852	0.814258	+	0.580503i	$0.197144\pi$
$152$	638.258	0.340589
$153$	−1462.60	−0.772839
$154$	−299.631	−0.156785
$155$	0	0
$156$	−2154.41	−1.10571
$157$	−1424.66	−0.724203	−0.362102	−	0.932139i	$-0.617941\pi$
$157$	−1424.66	−0.724203	−0.362102	+	0.932139i	$0.617941\pi$
$158$	−102.605	−0.0516635
$159$	−2178.89	−1.08678
$160$	0	0
$161$	389.569	0.190698
$162$	−20.5685	−0.00997538
$163$	343.511	0.165066	0.0825332	−	0.996588i	$-0.473699\pi$
$163$	343.511	0.165066	0.0825332	+	0.996588i	$0.473699\pi$
$164$	1146.80	0.546037
$165$	0	0
$166$	473.310	0.221301
$167$	−1220.60	−0.565587	−0.282794	−	0.959181i	$-0.591261\pi$
$167$	−1220.60	−0.565587	−0.282794	+	0.959181i	$0.591261\pi$
$168$	408.139	0.187432
$169$	5824.81	2.65126
$170$	0	0
$171$	−2180.78	−0.975255
$172$	−1892.54	−0.838981
$173$	−2727.07	−1.19847	−0.599236	−	0.800573i	$-0.704529\pi$
$173$	−2727.07	−1.19847	−0.599236	+	0.800573i	$0.704529\pi$
$174$	69.9551	0.0304786
$175$	0	0
$176$	−2185.21	−0.935890
$177$	−2151.18	−0.913518
$178$	−88.7290	−0.0373625
$179$	1020.61	0.426167	0.213084	−	0.977034i	$-0.431649\pi$
$179$	1020.61	0.426167	0.213084	+	0.977034i	$0.431649\pi$
$180$	0	0
$181$	2367.36	0.972178	0.486089	−	0.873909i	$-0.338423\pi$
$181$	2367.36	0.972178	0.486089	+	0.873909i	$0.338423\pi$
$182$	−754.753	−0.307396
$183$	1040.18	0.420176
$184$	−78.1786	−0.0313229
$185$	0	0
$186$	−4.18484	−0.00164972
$187$	−2935.83	−1.14807
$188$	693.386	0.268991
$189$	−3520.08	−1.35475
$190$	0	0
$191$	−4725.14	−1.79005	−0.895024	−	0.446019i	$-0.852841\pi$
$191$	−4725.14	−1.79005	−0.895024	+	0.446019i	$0.852841\pi$
$192$	1437.09	0.540173
$193$	1237.78	0.461644	0.230822	−	0.972996i	$-0.425859\pi$
$193$	1237.78	0.461644	0.230822	+	0.972996i	$0.425859\pi$
$194$	−161.480	−0.0597608
$195$	0	0
$196$	−2560.69	−0.933195
$197$	−4177.96	−1.51100	−0.755502	−	0.655147i	$-0.772607\pi$
$197$	−4177.96	−1.51100	−0.755502	+	0.655147i	$0.772607\pi$
$198$	−205.450	−0.0737410
$199$	2257.29	0.804095	0.402048	−	0.915619i	$-0.368299\pi$
$199$	2257.29	0.804095	0.402048	+	0.915619i	$0.368299\pi$
$200$	0	0
$201$	2880.91	1.01096
$202$	138.582	0.0482704
$203$	−1818.11	−0.628602
$204$	1986.12	0.681647
$205$	0	0
$206$	446.443	0.150996
$207$	267.119	0.0896910
$208$	−5504.43	−1.83492
$209$	−4377.40	−1.44876
$210$	0	0
$211$	1607.36	0.524432	0.262216	−	0.965009i	$-0.415547\pi$
$211$	1607.36	0.524432	0.262216	+	0.965009i	$0.415547\pi$
$212$	−5644.08	−1.82848
$213$	−216.359	−0.0695995
$214$	−211.942	−0.0677013
$215$	0	0
$216$	706.410	0.222524
$217$	108.763	0.0340243
$218$	−584.386	−0.181558
$219$	2383.46	0.735431
$220$	0	0
$221$	−7395.18	−2.25092
$222$	41.6628	0.0125956
$223$	1237.43	0.371591	0.185795	−	0.982588i	$-0.440514\pi$
$223$	1237.43	0.371591	0.185795	+	0.982588i	$0.440514\pi$
$224$	1589.37	0.474082
$225$	0	0
$226$	−84.1649	−0.0247724
$227$	−3157.21	−0.923134	−0.461567	−	0.887105i	$-0.652713\pi$
$227$	−3157.21	−0.923134	−0.461567	+	0.887105i	$0.652713\pi$
$228$	2961.36	0.860179
$229$	2708.35	0.781542	0.390771	−	0.920488i	$-0.372208\pi$
$229$	2708.35	0.781542	0.390771	+	0.920488i	$0.372208\pi$
$230$	0	0
$231$	−2799.16	−0.797279
$232$	364.858	0.103251
$233$	−4221.85	−1.18705	−0.593525	−	0.804816i	$-0.702264\pi$
$233$	−4221.85	−1.18705	−0.593525	+	0.804816i	$0.702264\pi$
$234$	−517.518	−0.144578
$235$	0	0
$236$	−5572.31	−1.53698
$237$	−958.542	−0.262717
$238$	695.795	0.189503
$239$	1976.80	0.535014	0.267507	−	0.963556i	$-0.413800\pi$
$239$	1976.80	0.535014	0.267507	+	0.963556i	$0.413800\pi$
$240$	0	0
$241$	1112.07	0.297239	0.148620	−	0.988894i	$-0.452517\pi$
$241$	1112.07	0.297239	0.148620	+	0.988894i	$0.452517\pi$
$242$	21.7711	0.00578306
$243$	−3871.10	−1.02194
$244$	2694.42	0.706937
$245$	0	0
$246$	−144.413	−0.0374285
$247$	−11026.4	−2.84047
$248$	−21.8265	−0.00558864
$249$	4421.68	1.12535
$250$	0	0
$251$	2300.80	0.578585	0.289293	−	0.957241i	$-0.406580\pi$
$251$	2300.80	0.578585	0.289293	+	0.957241i	$0.406580\pi$
$252$	−3612.28	−0.902986
$253$	536.177	0.133238
$254$	−710.606	−0.175541
$255$	0	0
$256$	3562.02	0.869634
$257$	6919.88	1.67957	0.839787	−	0.542917i	$-0.182680\pi$
$257$	6919.88	1.67957	0.839787	+	0.542917i	$0.182680\pi$
$258$	238.321	0.0575086
$259$	−1082.80	−0.259777
$260$	0	0
$261$	−1246.64	−0.295651
$262$	198.527	0.0468132
$263$	−7233.63	−1.69599	−0.847993	−	0.530007i	$-0.822189\pi$
$263$	−7233.63	−1.69599	−0.847993	+	0.530007i	$0.822189\pi$
$264$	561.736	0.130956
$265$	0	0
$266$	1037.45	0.239136
$267$	−828.910	−0.189994
$268$	7462.54	1.70092
$269$	−5608.35	−1.27118	−0.635590	−	0.772027i	$-0.719243\pi$
$269$	−5608.35	−1.27118	−0.635590	+	0.772027i	$0.719243\pi$
$270$	0	0
$271$	5905.81	1.32381	0.661905	−	0.749588i	$-0.269748\pi$
$271$	5905.81	1.32381	0.661905	+	0.749588i	$0.269748\pi$
$272$	5074.45	1.13119
$273$	−7050.94	−1.56316
$274$	−689.808	−0.152091
$275$	0	0
$276$	−362.729	−0.0791078
$277$	−294.470	−0.0638736	−0.0319368	−	0.999490i	$-0.510168\pi$
$277$	−294.470	−0.0638736	−0.0319368	+	0.999490i	$0.510168\pi$
$278$	131.865	0.0284487
$279$	74.5761	0.0160027
$280$	0	0
$281$	−6296.58	−1.33673	−0.668367	−	0.743832i	$-0.733006\pi$
$281$	−6296.58	−1.33673	−0.668367	+	0.743832i	$0.733006\pi$
$282$	−87.3157	−0.0184382
$283$	−693.844	−0.145741	−0.0728706	−	0.997341i	$-0.523216\pi$
$283$	−693.844	−0.145741	−0.0728706	+	0.997341i	$0.523216\pi$
$284$	−560.445	−0.117100
$285$	0	0
$286$	−1038.79	−0.214773
$287$	3753.24	0.771940
$288$	1089.80	0.222975
$289$	1904.51	0.387646
$290$	0	0
$291$	−1508.55	−0.303893
$292$	6173.99	1.23735
$293$	−5244.95	−1.04578	−0.522890	−	0.852400i	$-0.675146\pi$
$293$	−5244.95	−1.04578	−0.522890	+	0.852400i	$0.675146\pi$
$294$	322.459	0.0639666
$295$	0	0
$296$	217.297	0.0426694
$297$	−4844.82	−0.946548
$298$	−733.786	−0.142641
$299$	1350.60	0.261228
$300$	0	0
$301$	−6193.89	−1.18608
$302$	−985.673	−0.187812
$303$	1294.64	0.245463
$304$	7566.15	1.42746
$305$	0	0
$306$	477.091	0.0891291
$307$	−2576.20	−0.478929	−0.239465	−	0.970905i	$-0.576972\pi$
$307$	−2576.20	−0.478929	−0.239465	+	0.970905i	$0.576972\pi$
$308$	−7250.80	−1.34140
$309$	4170.69	0.767840
$310$	0	0
$311$	10581.8	1.92939	0.964694	−	0.263375i	$-0.0848355\pi$
$311$	10581.8	1.92939	0.964694	+	0.263375i	$0.0848355\pi$
$312$	1414.98	0.256755
$313$	−7664.21	−1.38405	−0.692023	−	0.721875i	$-0.743280\pi$
$313$	−7664.21	−1.38405	−0.692023	+	0.721875i	$0.743280\pi$
$314$	464.713	0.0835200
$315$	0	0
$316$	−2482.96	−0.442016
$317$	4024.75	0.713100	0.356550	−	0.934276i	$-0.383953\pi$
$317$	4024.75	0.713100	0.356550	+	0.934276i	$0.383953\pi$
$318$	710.740	0.125334
$319$	−2502.33	−0.439196
$320$	0	0
$321$	−1979.98	−0.344273
$322$	−127.075	−0.0219925
$323$	10165.1	1.75109
$324$	−497.739	−0.0853462
$325$	0	0
$326$	−112.051	−0.0190366
$327$	−5459.36	−0.923251
$328$	−753.200	−0.126794
$329$	2269.31	0.380276
$330$	0	0
$331$	189.285	0.0314321	0.0157161	−	0.999876i	$-0.494997\pi$
$331$	189.285	0.0314321	0.0157161	+	0.999876i	$0.494997\pi$
$332$	11453.7	1.89338
$333$	−742.455	−0.122181
$334$	398.153	0.0652274
$335$	0	0
$336$	4838.23	0.785557
$337$	1899.42	0.307027	0.153514	−	0.988147i	$-0.450941\pi$
$337$	1899.42	0.307027	0.153514	+	0.988147i	$0.450941\pi$
$338$	−1900.02	−0.305761
$339$	−786.272	−0.125972
$340$	0	0
$341$	149.694	0.0237724
$342$	711.357	0.112473
$343$	480.502	0.0756405
$344$	1242.99	0.194818
$345$	0	0
$346$	889.554	0.138216
$347$	−9610.54	−1.48680	−0.743402	−	0.668845i	$-0.766789\pi$
$347$	−9610.54	−1.48680	−0.743402	+	0.668845i	$0.766789\pi$
$348$	1692.85	0.260766
$349$	−8676.73	−1.33082	−0.665408	−	0.746480i	$-0.731742\pi$
$349$	−8676.73	−1.33082	−0.665408	+	0.746480i	$0.731742\pi$
$350$	0	0
$351$	−12203.8	−1.85582
$352$	2187.51	0.331234
$353$	1729.23	0.260730	0.130365	−	0.991466i	$-0.458385\pi$
$353$	1729.23	0.260730	0.130365	+	0.991466i	$0.458385\pi$
$354$	701.702	0.105353
$355$	0	0
$356$	−2147.16	−0.319661
$357$	6500.15	0.963654
$358$	−332.916	−0.0491485
$359$	3373.00	0.495878	0.247939	−	0.968776i	$-0.420247\pi$
$359$	3373.00	0.495878	0.247939	+	0.968776i	$0.420247\pi$
$360$	0	0
$361$	8297.45	1.20972
$362$	−772.216	−0.112118
$363$	203.387	0.0294078
$364$	−18264.4	−2.62998
$365$	0	0
$366$	−339.299	−0.0484575
$367$	−5555.89	−0.790231	−0.395116	−	0.918631i	$-0.629295\pi$
$367$	−5555.89	−0.790231	−0.395116	+	0.918631i	$0.629295\pi$
$368$	−926.759	−0.131279
$369$	2573.51	0.363067
$370$	0	0
$371$	−18471.9	−2.58494
$372$	−101.269	−0.0141145
$373$	−2680.19	−0.372051	−0.186026	−	0.982545i	$-0.559561\pi$
$373$	−2680.19	−0.372051	−0.186026	+	0.982545i	$0.559561\pi$
$374$	957.648	0.132403
$375$	0	0
$376$	−455.405	−0.0624620
$377$	−6303.23	−0.861095
$378$	1148.23	0.156239
$379$	−13616.4	−1.84545	−0.922726	−	0.385456i	$-0.874044\pi$
$379$	−13616.4	−1.84545	−0.922726	+	0.385456i	$0.874044\pi$
$380$	0	0
$381$	−6638.52	−0.892655
$382$	1541.31	0.206440
$383$	5287.47	0.705423	0.352711	−	0.935732i	$-0.385260\pi$
$383$	5287.47	0.705423	0.352711	+	0.935732i	$0.385260\pi$
$384$	−1968.59	−0.261612
$385$	0	0
$386$	−403.755	−0.0532399
$387$	−4247.01	−0.557850
$388$	−3907.67	−0.511294
$389$	−5495.38	−0.716265	−0.358132	−	0.933671i	$-0.616586\pi$
$389$	−5495.38	−0.716265	−0.358132	+	0.933671i	$0.616586\pi$
$390$	0	0
$391$	−1245.10	−0.161042
$392$	1681.82	0.216695
$393$	1854.65	0.238053
$394$	1362.82	0.174259
$395$	0	0
$396$	−4971.72	−0.630904
$397$	12297.0	1.55458	0.777288	−	0.629145i	$-0.216595\pi$
$397$	12297.0	1.55458	0.777288	+	0.629145i	$0.216595\pi$
$398$	−736.313	−0.0927337
$399$	9691.91	1.21605
$400$	0	0
$401$	−10343.3	−1.28808	−0.644042	−	0.764991i	$-0.722744\pi$
$401$	−10343.3	−1.28808	−0.644042	+	0.764991i	$0.722744\pi$
$402$	−939.733	−0.116591
$403$	377.070	0.0466085
$404$	3353.57	0.412986
$405$	0	0
$406$	593.056	0.0724947
$407$	−1490.30	−0.181502
$408$	−1304.45	−0.158284
$409$	5592.91	0.676165	0.338083	−	0.941116i	$-0.390222\pi$
$409$	5592.91	0.676165	0.338083	+	0.941116i	$0.390222\pi$
$410$	0	0
$411$	−6444.22	−0.773406
$412$	10803.5	1.29187
$413$	−18237.0	−2.17284
$414$	−87.1324	−0.0103438
$415$	0	0
$416$	5510.21	0.649424
$417$	1231.89	0.144666
$418$	1427.88	0.167081
$419$	12374.7	1.44282	0.721410	−	0.692508i	$-0.243494\pi$
$419$	12374.7	1.44282	0.721410	+	0.692508i	$0.243494\pi$
$420$	0	0
$421$	6154.59	0.712486	0.356243	−	0.934393i	$-0.384058\pi$
$421$	6154.59	0.712486	0.356243	+	0.934393i	$0.384058\pi$
$422$	−524.310	−0.0604810
$423$	1556.01	0.178856
$424$	3706.94	0.424588
$425$	0	0
$426$	70.5750	0.00802669
$427$	8818.28	0.999406
$428$	−5128.82	−0.579231
$429$	−9704.46	−1.09216
$430$	0	0
$431$	−3559.23	−0.397777	−0.198888	−	0.980022i	$-0.563733\pi$
$431$	−3559.23	−0.397777	−0.198888	+	0.980022i	$0.563733\pi$
$432$	8374.05	0.932631
$433$	669.878	0.0743471	0.0371735	−	0.999309i	$-0.488165\pi$
$433$	669.878	0.0743471	0.0371735	+	0.999309i	$0.488165\pi$
$434$	−35.4776	−0.00392392
$435$	0	0
$436$	−14141.6	−1.55335
$437$	−1856.48	−0.203220
$438$	−777.470	−0.0848149
$439$	−5161.00	−0.561095	−0.280548	−	0.959840i	$-0.590516\pi$
$439$	−5161.00	−0.561095	−0.280548	+	0.959840i	$0.590516\pi$
$440$	0	0
$441$	−5746.39	−0.620493
$442$	2412.26	0.259592
$443$	11389.1	1.22148	0.610739	−	0.791832i	$-0.290872\pi$
$443$	11389.1	1.22148	0.610739	+	0.791832i	$0.290872\pi$
$444$	1008.20	0.107764
$445$	0	0
$446$	−403.643	−0.0428544
$447$	−6855.07	−0.725355
$448$	12183.2	1.28482
$449$	4692.38	0.493201	0.246600	−	0.969117i	$-0.420686\pi$
$449$	4692.38	0.493201	0.246600	+	0.969117i	$0.420686\pi$
$450$	0	0
$451$	5165.72	0.539344
$452$	−2036.72	−0.211945
$453$	−9208.20	−0.955053
$454$	1029.86	0.106462
$455$	0	0
$456$	−1944.97	−0.199741
$457$	13137.0	1.34469	0.672347	−	0.740236i	$-0.265286\pi$
$457$	13137.0	1.34469	0.672347	+	0.740236i	$0.265286\pi$
$458$	−883.448	−0.0901327
$459$	11250.5	1.14407
$460$	0	0
$461$	−800.350	−0.0808591	−0.0404295	−	0.999182i	$-0.512873\pi$
$461$	−800.350	−0.0808591	−0.0404295	+	0.999182i	$0.512873\pi$
$462$	913.069	0.0919476
$463$	6794.47	0.682000	0.341000	−	0.940063i	$-0.389234\pi$
$463$	6794.47	0.682000	0.341000	+	0.940063i	$0.389234\pi$
$464$	4325.17	0.432739
$465$	0	0
$466$	1377.14	0.136899
$467$	−3659.45	−0.362611	−0.181305	−	0.983427i	$-0.558032\pi$
$467$	−3659.45	−0.362611	−0.181305	+	0.983427i	$0.558032\pi$
$468$	−12523.5	−1.23696
$469$	24423.3	2.40462
$470$	0	0
$471$	4341.37	0.424713
$472$	3659.80	0.356898
$473$	−8524.87	−0.828697
$474$	312.670	0.0302984
$475$	0	0
$476$	16837.6	1.62133
$477$	−12665.8	−1.21578
$478$	−644.818	−0.0617014
$479$	7681.96	0.732772	0.366386	−	0.930463i	$-0.380595\pi$
$479$	7681.96	0.732772	0.366386	+	0.930463i	$0.380595\pi$
$480$	0	0
$481$	−3753.99	−0.355857
$482$	−362.750	−0.0342797
$483$	−1187.14	−0.111836
$484$	526.842	0.0494780
$485$	0	0
$486$	1262.73	0.117857
$487$	2142.07	0.199315	0.0996577	−	0.995022i	$-0.468225\pi$
$487$	2142.07	0.199315	0.0996577	+	0.995022i	$0.468225\pi$
$488$	−1769.65	−0.164157
$489$	−1046.78	−0.0968042
$490$	0	0
$491$	17772.7	1.63355	0.816773	−	0.576960i	$-0.195761\pi$
$491$	17772.7	1.63355	0.816773	+	0.576960i	$0.195761\pi$
$492$	−3494.66	−0.320227
$493$	5810.85	0.530847
$494$	3596.75	0.327582
$495$	0	0
$496$	−258.739	−0.0234229
$497$	−1834.22	−0.165545
$498$	−1442.32	−0.129783
$499$	915.316	0.0821146	0.0410573	−	0.999157i	$-0.486927\pi$
$499$	915.316	0.0821146	0.0410573	+	0.999157i	$0.486927\pi$
$500$	0	0
$501$	3719.56	0.331692
$502$	−750.505	−0.0667264
$503$	10319.4	0.914751	0.457375	−	0.889274i	$-0.348790\pi$
$503$	10319.4	0.914751	0.457375	+	0.889274i	$0.348790\pi$
$504$	2372.49	0.209681
$505$	0	0
$506$	−174.897	−0.0153659
$507$	−17750.0	−1.55485
$508$	−17196.1	−1.50187
$509$	5414.23	0.471477	0.235738	−	0.971817i	$-0.424249\pi$
$509$	5414.23	0.471477	0.235738	+	0.971817i	$0.424249\pi$
$510$	0	0
$511$	20206.2	1.74925
$512$	−6329.97	−0.546383
$513$	16774.8	1.44372
$514$	−2257.22	−0.193700
$515$	0	0
$516$	5767.16	0.492026
$517$	3123.33	0.265694
$518$	353.203	0.0299592
$519$	8310.25	0.702851
$520$	0	0
$521$	−4885.54	−0.410824	−0.205412	−	0.978676i	$-0.565854\pi$
$521$	−4885.54	−0.410824	−0.205412	+	0.978676i	$0.565854\pi$
$522$	406.645	0.0340965
$523$	4111.95	0.343792	0.171896	−	0.985115i	$-0.445011\pi$
$523$	4111.95	0.343792	0.171896	+	0.985115i	$0.445011\pi$
$524$	4804.18	0.400519
$525$	0	0
$526$	2359.56	0.195593
$527$	−347.615	−0.0287331
$528$	6659.03	0.548858
$529$	−11939.6	−0.981311
$530$	0	0
$531$	−12504.7	−1.02195
$532$	25105.4	2.04597
$533$	13012.2	1.05745
$534$	270.385	0.0219114
$535$	0	0
$536$	−4901.28	−0.394968
$537$	−3110.12	−0.249928
$538$	1829.41	0.146601
$539$	−11534.5	−0.921756
$540$	0	0
$541$	17593.1	1.39813	0.699064	−	0.715059i	$-0.253600\pi$
$541$	17593.1	1.39813	0.699064	+	0.715059i	$0.253600\pi$
$542$	−1926.44	−0.152671
$543$	−7214.08	−0.570140
$544$	−5079.78	−0.400356
$545$	0	0
$546$	2299.97	0.180274
$547$	6906.89	0.539885	0.269943	−	0.962876i	$-0.412995\pi$
$547$	6906.89	0.539885	0.269943	+	0.962876i	$0.412995\pi$
$548$	−16692.7	−1.30124
$549$	6046.50	0.470052
$550$	0	0
$551$	8664.14	0.669882
$552$	238.235	0.0183695
$553$	−8126.20	−0.624884
$554$	96.0541	0.00736633
$555$	0	0
$556$	3191.02	0.243398
$557$	−8661.91	−0.658917	−0.329459	−	0.944170i	$-0.606866\pi$
$557$	−8661.91	−0.658917	−0.329459	+	0.944170i	$0.606866\pi$
$558$	−24.3262	−0.00184554
$559$	−21473.7	−1.62476
$560$	0	0
$561$	8946.39	0.673292
$562$	2053.90	0.154161
$563$	4459.52	0.333830	0.166915	−	0.985971i	$-0.446619\pi$
$563$	4459.52	0.333830	0.166915	+	0.985971i	$0.446619\pi$
$564$	−2112.96	−0.157751
$565$	0	0
$566$	226.328	0.0168079
$567$	−1629.00	−0.120655
$568$	368.092	0.0271915
$569$	−23536.4	−1.73409	−0.867046	−	0.498229i	$-0.833984\pi$
$569$	−23536.4	−1.73409	−0.867046	+	0.498229i	$0.833984\pi$
$570$	0	0
$571$	2454.48	0.179889	0.0899446	−	0.995947i	$-0.471331\pi$
$571$	2454.48	0.179889	0.0899446	+	0.995947i	$0.471331\pi$
$572$	−25137.9	−1.83753
$573$	14399.0	1.04978
$574$	−1224.28	−0.0890254
$575$	0	0
$576$	8353.74	0.604293
$577$	−21003.1	−1.51537	−0.757687	−	0.652618i	$-0.773671\pi$
$577$	−21003.1	−1.51537	−0.757687	+	0.652618i	$0.773671\pi$
$578$	−621.237	−0.0447060
$579$	−3771.90	−0.270734
$580$	0	0
$581$	37485.5	2.67670
$582$	492.080	0.0350470
$583$	−25423.6	−1.80607
$584$	−4054.98	−0.287322
$585$	0	0
$586$	1710.87	0.120606
$587$	3291.28	0.231424	0.115712	−	0.993283i	$-0.463085\pi$
$587$	3291.28	0.231424	0.115712	+	0.993283i	$0.463085\pi$
$588$	7803.22	0.547278
$589$	−518.304	−0.0362587
$590$	0	0
$591$	12731.6	0.886137
$592$	2575.92	0.178834
$593$	−8736.81	−0.605022	−0.302511	−	0.953146i	$-0.597825\pi$
$593$	−8736.81	−0.605022	−0.302511	+	0.953146i	$0.597825\pi$
$594$	1580.35	0.109162
$595$	0	0
$596$	−17757.0	−1.22039
$597$	−6878.67	−0.471566
$598$	−440.557	−0.0301266
$599$	−1375.61	−0.0938326	−0.0469163	−	0.998899i	$-0.514939\pi$
$599$	−1375.61	−0.0938326	−0.0469163	+	0.998899i	$0.514939\pi$
$600$	0	0
$601$	−28536.8	−1.93684	−0.968421	−	0.249322i	$-0.919792\pi$
$601$	−28536.8	−1.93684	−0.968421	+	0.249322i	$0.919792\pi$
$602$	2020.41	0.136787
$603$	16746.6	1.13097
$604$	−23852.4	−1.60686
$605$	0	0
$606$	−422.304	−0.0283085
$607$	1927.94	0.128917	0.0644584	−	0.997920i	$-0.479468\pi$
$607$	1927.94	0.128917	0.0644584	+	0.997920i	$0.479468\pi$
$608$	−7574.09	−0.505214
$609$	5540.35	0.368648
$610$	0	0
$611$	7867.49	0.520924
$612$	11545.2	0.762560
$613$	17659.3	1.16354	0.581770	−	0.813353i	$-0.302360\pi$
$613$	17659.3	1.16354	0.581770	+	0.813353i	$0.302360\pi$
$614$	840.339	0.0552334
$615$	0	0
$616$	4762.21	0.311485
$617$	21380.3	1.39504	0.697519	−	0.716567i	$-0.254287\pi$
$617$	21380.3	1.39504	0.697519	+	0.716567i	$0.254287\pi$
$618$	−1360.45	−0.0885525
$619$	8618.57	0.559628	0.279814	−	0.960054i	$-0.409727\pi$
$619$	8618.57	0.559628	0.279814	+	0.960054i	$0.409727\pi$
$620$	0	0
$621$	−2054.71	−0.132774
$622$	−3451.72	−0.222510
$623$	−7027.22	−0.451909
$624$	16773.7	1.07610
$625$	0	0
$626$	2500.01	0.159618
$627$	13339.3	0.849635
$628$	11245.7	0.714571
$629$	3460.74	0.219378
$630$	0	0
$631$	25842.8	1.63040	0.815202	−	0.579177i	$-0.196626\pi$
$631$	25842.8	1.63040	0.815202	+	0.579177i	$0.196626\pi$
$632$	1630.77	0.102640
$633$	−4898.12	−0.307556
$634$	−1312.85	−0.0822395
$635$	0	0
$636$	17199.3	1.07232
$637$	−29054.8	−1.80721
$638$	816.244	0.0506511
$639$	−1257.69	−0.0778611
$640$	0	0
$641$	−18831.3	−1.16036	−0.580182	−	0.814487i	$-0.697019\pi$
$641$	−18831.3	−1.16036	−0.580182	+	0.814487i	$0.697019\pi$
$642$	645.855	0.0397039
$643$	11148.4	0.683749	0.341875	−	0.939746i	$-0.388938\pi$
$643$	11148.4	0.683749	0.341875	+	0.939746i	$0.388938\pi$
$644$	−3075.10	−0.188161
$645$	0	0
$646$	−3315.79	−0.201947
$647$	4164.15	0.253029	0.126515	−	0.991965i	$-0.459621\pi$
$647$	4164.15	0.253029	0.126515	+	0.991965i	$0.459621\pi$
$648$	326.907	0.0198181
$649$	−25100.2	−1.51814
$650$	0	0
$651$	−331.434	−0.0199538
$652$	−2711.53	−0.162871
$653$	17925.5	1.07424	0.537119	−	0.843506i	$-0.319512\pi$
$653$	17925.5	1.07424	0.537119	+	0.843506i	$0.319512\pi$
$654$	1780.81	0.106476
$655$	0	0
$656$	−8928.72	−0.531414
$657$	13854.9	0.822729
$658$	−740.233	−0.0438560
$659$	5470.06	0.323344	0.161672	−	0.986845i	$-0.448311\pi$
$659$	5470.06	0.323344	0.161672	+	0.986845i	$0.448311\pi$
$660$	0	0
$661$	−1514.42	−0.0891137	−0.0445568	−	0.999007i	$-0.514188\pi$
$661$	−1514.42	−0.0891137	−0.0445568	+	0.999007i	$0.514188\pi$
$662$	−61.7435	−0.00362497
$663$	22535.5	1.32007
$664$	−7522.60	−0.439659
$665$	0	0
$666$	242.184	0.0140907
$667$	−1061.25	−0.0616068
$668$	9634.95	0.558065
$669$	−3770.85	−0.217922
$670$	0	0
$671$	12136.9	0.698272
$672$	−4843.31	−0.278028
$673$	14539.5	0.832773	0.416386	−	0.909188i	$-0.363296\pi$
$673$	14539.5	0.832773	0.416386	+	0.909188i	$0.363296\pi$
$674$	−619.579	−0.0354085
$675$	0	0
$676$	−45978.7	−2.61600
$677$	−3505.40	−0.199001	−0.0995004	−	0.995038i	$-0.531724\pi$
$677$	−3505.40	−0.199001	−0.0995004	+	0.995038i	$0.531724\pi$
$678$	256.477	0.0145279
$679$	−12789.0	−0.722823
$680$	0	0
$681$	9621.01	0.541377
$682$	−48.8292	−0.00274159
$683$	−25548.2	−1.43129	−0.715647	−	0.698463i	$-0.753868\pi$
$683$	−25548.2	−1.43129	−0.715647	+	0.698463i	$0.753868\pi$
$684$	17214.2	0.962284
$685$	0	0
$686$	−156.737	−0.00872338
$687$	−8253.21	−0.458340
$688$	14734.9	0.816514
$689$	−64040.5	−3.54100
$690$	0	0
$691$	−32139.8	−1.76940	−0.884699	−	0.466162i	$-0.845636\pi$
$691$	−32139.8	−1.76940	−0.884699	+	0.466162i	$0.845636\pi$
$692$	21526.4	1.18253
$693$	−16271.4	−0.891918
$694$	3134.90	0.171468
$695$	0	0
$696$	−1111.84	−0.0605519
$697$	−11995.7	−0.651894
$698$	2830.29	0.153479
$699$	12865.3	0.696152
$700$	0	0
$701$	−10877.9	−0.586098	−0.293049	−	0.956097i	$-0.594670\pi$
$701$	−10877.9	−0.586098	−0.293049	+	0.956097i	$0.594670\pi$
$702$	3980.81	0.214025
$703$	5160.06	0.276836
$704$	16768.2	0.897690
$705$	0	0
$706$	−564.064	−0.0300692
$707$	10975.5	0.583844
$708$	16980.6	0.901368
$709$	−31432.4	−1.66498	−0.832489	−	0.554041i	$-0.813085\pi$
$709$	−31432.4	−1.66498	−0.832489	+	0.554041i	$0.813085\pi$
$710$	0	0
$711$	−5571.96	−0.293902
$712$	1410.22	0.0742280
$713$	63.4858	0.00333459
$714$	−2120.31	−0.111135
$715$	0	0
$716$	−8056.28	−0.420499
$717$	−6023.92	−0.313762
$718$	−1100.25	−0.0571880
$719$	17397.1	0.902370	0.451185	−	0.892430i	$-0.351001\pi$
$719$	17397.1	0.902370	0.451185	+	0.892430i	$0.351001\pi$
$720$	0	0
$721$	35357.7	1.82634
$722$	−2706.58	−0.139513
$723$	−3388.83	−0.174318
$724$	−18687.0	−0.959248
$725$	0	0
$726$	−66.3434	−0.00339151
$727$	−2184.75	−0.111455	−0.0557275	−	0.998446i	$-0.517748\pi$
$727$	−2184.75	−0.111455	−0.0557275	+	0.998446i	$0.517748\pi$
$728$	11995.7	0.610703
$729$	10093.9	0.512825
$730$	0	0
$731$	19796.2	1.00163
$732$	−8210.75	−0.414587
$733$	−25682.1	−1.29412	−0.647061	−	0.762438i	$-0.724002\pi$
$733$	−25682.1	−1.29412	−0.647061	+	0.762438i	$0.724002\pi$
$734$	1812.29	0.0911348
$735$	0	0
$736$	927.732	0.0464628
$737$	33614.7	1.68007
$738$	−839.464	−0.0418714
$739$	10339.7	0.514684	0.257342	−	0.966320i	$-0.417153\pi$
$739$	10339.7	0.514684	0.257342	+	0.966320i	$0.417153\pi$
$740$	0	0
$741$	33601.0	1.66581
$742$	6025.42	0.298113
$743$	12868.5	0.635399	0.317699	−	0.948192i	$-0.397090\pi$
$743$	12868.5	0.635399	0.317699	+	0.948192i	$0.397090\pi$
$744$	66.5121	0.00327749
$745$	0	0
$746$	874.261	0.0429075
$747$	25703.0	1.25893
$748$	23174.2	1.13280
$749$	−16785.6	−0.818867
$750$	0	0
$751$	27898.9	1.35558	0.677792	−	0.735253i	$-0.262937\pi$
$751$	27898.9	1.35558	0.677792	+	0.735253i	$0.262937\pi$
$752$	−5398.53	−0.261788
$753$	−7011.25	−0.339315
$754$	2056.07	0.0993074
$755$	0	0
$756$	27786.1	1.33673
$757$	−8340.62	−0.400456	−0.200228	−	0.979749i	$-0.564168\pi$
$757$	−8340.62	−0.400456	−0.200228	+	0.979749i	$0.564168\pi$
$758$	4441.57	0.212830
$759$	−1633.90	−0.0781381
$760$	0	0
$761$	−29341.9	−1.39769	−0.698845	−	0.715273i	$-0.746302\pi$
$761$	−29341.9	−1.39769	−0.698845	+	0.715273i	$0.746302\pi$
$762$	2165.44	0.102947
$763$	−46282.6	−2.19599
$764$	37298.3	1.76624
$765$	0	0
$766$	−1724.74	−0.0813542
$767$	−63226.1	−2.97648
$768$	−10854.6	−0.510002
$769$	−686.301	−0.0321829	−0.0160915	−	0.999871i	$-0.505122\pi$
$769$	−686.301	−0.0321829	−0.0160915	+	0.999871i	$0.505122\pi$
$770$	0	0
$771$	−21087.1	−0.984996
$772$	−9770.53	−0.455504
$773$	−10123.8	−0.471056	−0.235528	−	0.971868i	$-0.575682\pi$
$773$	−10123.8	−0.471056	−0.235528	+	0.971868i	$0.575682\pi$
$774$	1385.35	0.0643350
$775$	0	0
$776$	2566.50	0.118727
$777$	3299.64	0.152347
$778$	1792.56	0.0826046
$779$	−17885.9	−0.822632
$780$	0	0
$781$	−2524.50	−0.115664
$782$	406.143	0.0185724
$783$	9589.29	0.437667
$784$	19936.9	0.908204
$785$	0	0
$786$	−604.975	−0.0274539
$787$	−11991.0	−0.543118	−0.271559	−	0.962422i	$-0.587539\pi$
$787$	−11991.0	−0.543118	−0.271559	+	0.962422i	$0.587539\pi$
$788$	32979.2	1.49091
$789$	22043.1	0.994622
$790$	0	0
$791$	−6665.75	−0.299629
$792$	3265.34	0.146501
$793$	30572.2	1.36904
$794$	−4011.19	−0.179284
$795$	0	0
$796$	−17818.1	−0.793400
$797$	−5625.26	−0.250008	−0.125004	−	0.992156i	$-0.539894\pi$
$797$	−5625.26	−0.250008	−0.125004	+	0.992156i	$0.539894\pi$
$798$	−3161.44	−0.140243
$799$	−7252.91	−0.321139
$800$	0	0
$801$	−4818.41	−0.212547
$802$	3373.93	0.148551
$803$	27810.5	1.22218
$804$	−22740.7	−0.997516
$805$	0	0
$806$	−122.998	−0.00537521
$807$	17090.4	0.745491
$808$	−2202.57	−0.0958988
$809$	−26825.0	−1.16578	−0.582891	−	0.812550i	$-0.698079\pi$
$809$	−26825.0	−1.16578	−0.582891	+	0.812550i	$0.698079\pi$
$810$	0	0
$811$	−30680.6	−1.32841	−0.664205	−	0.747551i	$-0.731230\pi$
$811$	−30680.6	−1.32841	−0.664205	+	0.747551i	$0.731230\pi$
$812$	14351.4	0.620242
$813$	−17996.9	−0.776356
$814$	486.127	0.0209321
$815$	0	0
$816$	−15463.4	−0.663393
$817$	29516.8	1.26397
$818$	−1824.37	−0.0779800
$819$	−40986.7	−1.74871
$820$	0	0
$821$	13700.5	0.582400	0.291200	−	0.956662i	$-0.405946\pi$
$821$	13700.5	0.582400	0.291200	+	0.956662i	$0.405946\pi$
$822$	2102.06	0.0891944
$823$	−20931.6	−0.886549	−0.443274	−	0.896386i	$-0.646183\pi$
$823$	−20931.6	−0.886549	−0.443274	+	0.896386i	$0.646183\pi$
$824$	−7095.59	−0.299984
$825$	0	0
$826$	5948.79	0.250587
$827$	8248.27	0.346820	0.173410	−	0.984850i	$-0.444521\pi$
$827$	8248.27	0.346820	0.173410	+	0.984850i	$0.444521\pi$
$828$	−2108.53	−0.0884980
$829$	42609.3	1.78514	0.892571	−	0.450907i	$-0.148899\pi$
$829$	42609.3	1.78514	0.892571	+	0.450907i	$0.148899\pi$
$830$	0	0
$831$	897.342	0.0374590
$832$	42238.0	1.76002
$833$	26785.2	1.11411
$834$	−401.835	−0.0166839
$835$	0	0
$836$	34553.5	1.42949
$837$	−573.648	−0.0236896
$838$	−4036.53	−0.166396
$839$	−15698.9	−0.645990	−0.322995	−	0.946401i	$-0.604690\pi$
$839$	−15698.9	−0.645990	−0.322995	+	0.946401i	$0.604690\pi$
$840$	0	0
$841$	−19436.2	−0.796923
$842$	−2007.59	−0.0821687
$843$	19187.7	0.783936
$844$	−12687.8	−0.517457
$845$	0	0
$846$	−507.562	−0.0206269
$847$	1724.24	0.0699477
$848$	43943.5	1.77951
$849$	2114.36	0.0854708
$850$	0	0
$851$	−632.043	−0.0254597
$852$	1707.85	0.0686738
$853$	32917.5	1.32131	0.660653	−	0.750692i	$-0.270280\pi$
$853$	32917.5	1.32131	0.660653	+	0.750692i	$0.270280\pi$
$854$	−2876.46	−0.115258
$855$	0	0
$856$	3368.53	0.134502
$857$	15855.3	0.631980	0.315990	−	0.948763i	$-0.397663\pi$
$857$	15855.3	0.631980	0.315990	+	0.948763i	$0.397663\pi$
$858$	3165.53	0.125955
$859$	−32285.2	−1.28237	−0.641186	−	0.767385i	$-0.721557\pi$
$859$	−32285.2	−1.28237	−0.641186	+	0.767385i	$0.721557\pi$
$860$	0	0
$861$	−11437.3	−0.452709
$862$	1161.00	0.0458744
$863$	−18316.5	−0.722480	−0.361240	−	0.932473i	$-0.617646\pi$
$863$	−18316.5	−0.722480	−0.361240	+	0.932473i	$0.617646\pi$
$864$	−8382.84	−0.330081
$865$	0	0
$866$	−218.510	−0.00857421
$867$	−5803.63	−0.227337
$868$	−858.528	−0.0335718
$869$	−11184.4	−0.436598
$870$	0	0
$871$	84673.6	3.29398
$872$	9287.99	0.360701
$873$	−8769.14	−0.339966
$874$	605.570	0.0234368
$875$	0	0
$876$	−18814.1	−0.725650
$877$	−42713.0	−1.64460	−0.822300	−	0.569054i	$-0.807310\pi$
$877$	−42713.0	−1.64460	−0.822300	+	0.569054i	$0.807310\pi$
$878$	1683.48	0.0647093
$879$	15983.0	0.613303
$880$	0	0
$881$	1722.48	0.0658703	0.0329352	−	0.999457i	$-0.489515\pi$
$881$	1722.48	0.0658703	0.0329352	+	0.999457i	$0.489515\pi$
$882$	1874.43	0.0715595
$883$	14721.1	0.561046	0.280523	−	0.959847i	$-0.409492\pi$
$883$	14721.1	0.561046	0.280523	+	0.959847i	$0.409492\pi$
$884$	58374.6	2.22099
$885$	0	0
$886$	−3715.07	−0.140869
$887$	35980.9	1.36203	0.681015	−	0.732269i	$-0.261539\pi$
$887$	35980.9	1.36203	0.681015	+	0.732269i	$0.261539\pi$
$888$	−662.172	−0.0250237
$889$	−56279.1	−2.12322
$890$	0	0
$891$	−2242.05	−0.0843001
$892$	−9767.81	−0.366648
$893$	−10814.3	−0.405248
$894$	2236.08	0.0836528
$895$	0	0
$896$	−16689.0	−0.622256
$897$	−4115.70	−0.153199
$898$	−1530.62	−0.0568793
$899$	−296.287	−0.0109919
$900$	0	0
$901$	59038.0	2.18295
$902$	−1685.02	−0.0622008
$903$	18874.7	0.695583
$904$	1337.68	0.0492154
$905$	0	0
$906$	3003.65	0.110143
$907$	22727.9	0.832047	0.416023	−	0.909354i	$-0.363423\pi$
$907$	22727.9	0.832047	0.416023	+	0.909354i	$0.363423\pi$
$908$	24921.7	0.910856
$909$	7525.69	0.274600
$910$	0	0
$911$	39309.5	1.42962	0.714809	−	0.699320i	$-0.246514\pi$
$911$	39309.5	1.42962	0.714809	+	0.699320i	$0.246514\pi$
$912$	−23056.4	−0.837143
$913$	51592.7	1.87017
$914$	−4285.22	−0.155079
$915$	0	0
$916$	−21378.7	−0.771147
$917$	15723.1	0.566218
$918$	−3669.84	−0.131942
$919$	9565.57	0.343350	0.171675	−	0.985154i	$-0.445082\pi$
$919$	9565.57	0.343350	0.171675	+	0.985154i	$0.445082\pi$
$920$	0	0
$921$	7850.48	0.280871
$922$	261.069	0.00932522
$923$	−6359.08	−0.226773
$924$	22095.5	0.786675
$925$	0	0
$926$	−2216.31	−0.0786528
$927$	24244.0	0.858984
$928$	−4329.71	−0.153157
$929$	−13866.2	−0.489704	−0.244852	−	0.969560i	$-0.578739\pi$
$929$	−13866.2	−0.489704	−0.244852	+	0.969560i	$0.578739\pi$
$930$	0	0
$931$	39937.4	1.40590
$932$	33325.6	1.17126
$933$	−32246.1	−1.13150
$934$	1193.69	0.0418188
$935$	0	0
$936$	8225.22	0.287233
$937$	−31599.9	−1.10173	−0.550866	−	0.834594i	$-0.685703\pi$
$937$	−31599.9	−1.10173	−0.550866	+	0.834594i	$0.685703\pi$
$938$	−7966.73	−0.277317
$939$	23355.2	0.811682
$940$	0	0
$941$	−49882.4	−1.72808	−0.864038	−	0.503427i	$-0.832072\pi$
$941$	−49882.4	−1.72808	−0.864038	+	0.503427i	$0.832072\pi$
$942$	−1416.13	−0.0489808
$943$	2190.80	0.0756547
$944$	43384.6	1.49582
$945$	0	0
$946$	2780.76	0.0955710
$947$	−56735.7	−1.94684	−0.973422	−	0.229018i	$-0.926449\pi$
$947$	−56735.7	−1.94684	−0.973422	+	0.229018i	$0.926449\pi$
$948$	7566.35	0.259223
$949$	70053.1	2.39623
$950$	0	0
$951$	−12264.7	−0.418202
$952$	−11058.7	−0.376485
$953$	−13138.3	−0.446580	−0.223290	−	0.974752i	$-0.571680\pi$
$953$	−13138.3	−0.446580	−0.223290	+	0.974752i	$0.571680\pi$
$954$	4131.50	0.140212
$955$	0	0
$956$	−15604.0	−0.527898
$957$	7625.39	0.257569
$958$	−2505.81	−0.0845083
$959$	−54631.9	−1.83958
$960$	0	0
$961$	−29773.3	−0.999405
$962$	1224.53	0.0410398
$963$	−11509.5	−0.385138
$964$	−8778.23	−0.293286
$965$	0	0
$966$	387.237	0.0128977
$967$	40698.7	1.35345	0.676723	−	0.736238i	$-0.263399\pi$
$967$	40698.7	1.35345	0.676723	+	0.736238i	$0.263399\pi$
$968$	−346.021	−0.0114892
$969$	−30976.2	−1.02694
$970$	0	0
$971$	−1198.12	−0.0395979	−0.0197989	−	0.999804i	$-0.506303\pi$
$971$	−1198.12	−0.0395979	−0.0197989	+	0.999804i	$0.506303\pi$
$972$	30556.9	1.00835
$973$	10443.5	0.344095
$974$	−698.731	−0.0229864
$975$	0	0
$976$	−20978.1	−0.688005
$977$	−39376.1	−1.28941	−0.644704	−	0.764432i	$-0.723019\pi$
$977$	−39376.1	−1.28941	−0.644704	+	0.764432i	$0.723019\pi$
$978$	341.454	0.0111641
$979$	−9671.81	−0.315743
$980$	0	0
$981$	−31735.0	−1.03284
$982$	−5797.34	−0.188392
$983$	41658.8	1.35169	0.675844	−	0.737045i	$-0.263779\pi$
$983$	41658.8	1.35169	0.675844	+	0.737045i	$0.263779\pi$
$984$	2295.24	0.0743593
$985$	0	0
$986$	−1895.46	−0.0612209
$987$	−6915.29	−0.223015
$988$	87038.2	2.80269
$989$	−3615.43	−0.116243
$990$	0	0
$991$	406.291	0.0130235	0.00651173	−	0.999979i	$-0.497927\pi$
$991$	406.291	0.0130235	0.00651173	+	0.999979i	$0.497927\pi$
$992$	259.011	0.00828992
$993$	−576.810	−0.0184336
$994$	598.311	0.0190918
$995$	0	0
$996$	−34903.0	−1.11038
$997$	−35209.5	−1.11845	−0.559225	−	0.829016i	$-0.688901\pi$
$997$	−35209.5	−1.11845	−0.559225	+	0.829016i	$0.688901\pi$
$998$	−298.570	−0.00947001
$999$	5711.05	0.180870

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1775.4.a.h.1.18	✓	35
5.4	even	2		1775.4.a.k.1.18	yes	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1775.4.a.h.1.18	✓	35	1.1	even	1	trivial
1775.4.a.k.1.18	yes	35	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1775 = 5^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1775.a (trivial)

\(f(q)\)	\(=\)	\(q-0.326193 q^{2} -3.04731 q^{3} -7.89360 q^{4} +0.994014 q^{6} -25.8341 q^{7} +5.18439 q^{8} -17.7139 q^{9} +O(q^{10})\)	\(q-0.326193 q^{2} -3.04731 q^{3} -7.89360 q^{4} +0.994014 q^{6} -25.8341 q^{7} +5.18439 q^{8} -17.7139 q^{9} -35.5564 q^{11} +24.0543 q^{12} -89.5646 q^{13} +8.42691 q^{14} +61.4577 q^{16} +82.5682 q^{17} +5.77815 q^{18} +123.112 q^{19} +78.7246 q^{21} +11.5983 q^{22} -15.0796 q^{23} -15.7985 q^{24} +29.2154 q^{26} +136.257 q^{27} +203.924 q^{28} +70.3764 q^{29} -4.21004 q^{31} -61.5222 q^{32} +108.352 q^{33} -26.9332 q^{34} +139.826 q^{36} +41.9137 q^{37} -40.1582 q^{38} +272.931 q^{39} -145.282 q^{41} -25.6795 q^{42} +239.756 q^{43} +280.668 q^{44} +4.91888 q^{46} -87.8415 q^{47} -187.281 q^{48} +324.400 q^{49} -251.611 q^{51} +706.987 q^{52} +715.021 q^{53} -44.4462 q^{54} -133.934 q^{56} -375.160 q^{57} -22.9563 q^{58} +705.927 q^{59} -341.343 q^{61} +1.37329 q^{62} +457.622 q^{63} -471.593 q^{64} -35.3436 q^{66} -945.392 q^{67} -651.760 q^{68} +45.9524 q^{69} +71.0000 q^{71} -91.8356 q^{72} -782.152 q^{73} -13.6720 q^{74} -971.793 q^{76} +918.567 q^{77} -89.0284 q^{78} +314.553 q^{79} +63.0561 q^{81} +47.3902 q^{82} -1451.01 q^{83} -621.420 q^{84} -78.2069 q^{86} -214.459 q^{87} -184.338 q^{88} +272.013 q^{89} +2313.82 q^{91} +119.033 q^{92} +12.8293 q^{93} +28.6533 q^{94} +187.477 q^{96} +495.044 q^{97} -105.817 q^{98} +629.842 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 6 q^{2} - 19 q^{3} + 146 q^{4} + 8 q^{6} - 76 q^{7} - 72 q^{8} + 286 q^{9}+O(q^{10}) \) 35 * q - 6 * q^2 - 19 * q^3 + 146 * q^4 + 8 * q^6 - 76 * q^7 - 72 * q^8 + 286 * q^9	\( 35 q - 6 q^{2} - 19 q^{3} + 146 q^{4} + 8 q^{6} - 76 q^{7} - 72 q^{8} + 286 q^{9} + 29 q^{11} - 228 q^{12} - 206 q^{13} - 48 q^{14} + 542 q^{16} - 347 q^{17} - 280 q^{18} - 59 q^{19} + 284 q^{21} - 605 q^{22} - 168 q^{23} + 100 q^{24} + 655 q^{26} - 727 q^{27} - 749 q^{28} - 522 q^{29} + 84 q^{31} - 1522 q^{32} - 547 q^{33} - 324 q^{34} + 2114 q^{36} - 706 q^{37} - 487 q^{38} - 574 q^{39} + 311 q^{41} - 1602 q^{42} - 928 q^{43} - 1129 q^{44} + 144 q^{46} - 744 q^{47} - 2644 q^{48} + 1649 q^{49} + 277 q^{51} - 2727 q^{52} - 886 q^{53} - 923 q^{54} + 947 q^{56} - 2501 q^{57} - 1181 q^{58} - 434 q^{59} + 466 q^{61} - 1727 q^{62} - 1908 q^{63} + 2102 q^{64} - 884 q^{66} - 2425 q^{67} - 2329 q^{68} - 716 q^{69} + 2485 q^{71} - 4079 q^{72} - 5803 q^{73} - 412 q^{74} - 3109 q^{76} - 732 q^{77} - 2691 q^{78} + 1024 q^{79} + 7 q^{81} - 1325 q^{82} - 4927 q^{83} + 3889 q^{84} - 2716 q^{86} - 2634 q^{87} - 7122 q^{88} + 3279 q^{89} - 3782 q^{91} + 3025 q^{92} - 5256 q^{93} + 1485 q^{94} - 3043 q^{96} - 8548 q^{97} - 5578 q^{98} + 9008 q^{99}+O(q^{100}) \) 35 * q - 6 * q^2 - 19 * q^3 + 146 * q^4 + 8 * q^6 - 76 * q^7 - 72 * q^8 + 286 * q^9 + 29 * q^11 - 228 * q^12 - 206 * q^13 - 48 * q^14 + 542 * q^16 - 347 * q^17 - 280 * q^18 - 59 * q^19 + 284 * q^21 - 605 * q^22 - 168 * q^23 + 100 * q^24 + 655 * q^26 - 727 * q^27 - 749 * q^28 - 522 * q^29 + 84 * q^31 - 1522 * q^32 - 547 * q^33 - 324 * q^34 + 2114 * q^36 - 706 * q^37 - 487 * q^38 - 574 * q^39 + 311 * q^41 - 1602 * q^42 - 928 * q^43 - 1129 * q^44 + 144 * q^46 - 744 * q^47 - 2644 * q^48 + 1649 * q^49 + 277 * q^51 - 2727 * q^52 - 886 * q^53 - 923 * q^54 + 947 * q^56 - 2501 * q^57 - 1181 * q^58 - 434 * q^59 + 466 * q^61 - 1727 * q^62 - 1908 * q^63 + 2102 * q^64 - 884 * q^66 - 2425 * q^67 - 2329 * q^68 - 716 * q^69 + 2485 * q^71 - 4079 * q^72 - 5803 * q^73 - 412 * q^74 - 3109 * q^76 - 732 * q^77 - 2691 * q^78 + 1024 * q^79 + 7 * q^81 - 1325 * q^82 - 4927 * q^83 + 3889 * q^84 - 2716 * q^86 - 2634 * q^87 - 7122 * q^88 + 3279 * q^89 - 3782 * q^91 + 3025 * q^92 - 5256 * q^93 + 1485 * q^94 - 3043 * q^96 - 8548 * q^97 - 5578 * q^98 + 9008 * q^99

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