LMFDB - Embedded newform 289.4.b.c.288.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,4,Mod(288,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("289.288");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	289.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$17.0515519917$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 38x^{6} - 20x^{5} + 493x^{4} + 540x^{3} + 1312x^{2} + 840x + 4556 $ x^8 - 38x^6 - 20x^5 + 493x^4 + 540x^3 + 1312x^2 + 840x + 4556
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			288.7
Root			$4.93651 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	289.288
Dual form			289.4.b.c.288.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.93651 q^{2} -0.423991i q^{3} +7.49613 q^{4} -1.95080i q^{5} -1.66905i q^{6} +25.4345i q^{7} -1.98349 q^{8} +26.8202 q^{9} +O(q^{10})$	\(q+3.93651 q^{2} -0.423991i q^{3} +7.49613 q^{4} -1.95080i q^{5} -1.66905i q^{6} +25.4345i q^{7} -1.98349 q^{8} +26.8202 q^{9} -7.67934i q^{10} +32.4303i q^{11} -3.17829i q^{12} +54.6855 q^{13} +100.123i q^{14} -0.827121 q^{15} -67.7771 q^{16} +105.578 q^{18} +46.1336 q^{19} -14.6234i q^{20} +10.7840 q^{21} +127.662i q^{22} +75.2978i q^{23} +0.840984i q^{24} +121.194 q^{25} +215.270 q^{26} -22.8193i q^{27} +190.660i q^{28} -157.040i q^{29} -3.25597 q^{30} +252.606i q^{31} -250.937 q^{32} +13.7502 q^{33} +49.6175 q^{35} +201.048 q^{36} -226.214i q^{37} +181.606 q^{38} -23.1862i q^{39} +3.86940i q^{40} -231.163i q^{41} +42.4513 q^{42} -119.642 q^{43} +243.102i q^{44} -52.3209i q^{45} +296.411i q^{46} +188.319 q^{47} +28.7369i q^{48} -303.913 q^{49} +477.083 q^{50} +409.930 q^{52} -468.212 q^{53} -89.8285i q^{54} +63.2650 q^{55} -50.4491i q^{56} -19.5603i q^{57} -618.188i q^{58} -751.217 q^{59} -6.20021 q^{60} +483.210i q^{61} +994.385i q^{62} +682.159i q^{63} -445.601 q^{64} -106.680i q^{65} +54.1277 q^{66} +533.879 q^{67} +31.9256 q^{69} +195.320 q^{70} +78.1521i q^{71} -53.1977 q^{72} -383.013i q^{73} -890.494i q^{74} -51.3854i q^{75} +345.824 q^{76} -824.848 q^{77} -91.2727i q^{78} -1278.85i q^{79} +132.219i q^{80} +714.471 q^{81} -909.975i q^{82} -591.376 q^{83} +80.8382 q^{84} -470.973 q^{86} -66.5834 q^{87} -64.3253i q^{88} +609.729 q^{89} -205.962i q^{90} +1390.90i q^{91} +564.442i q^{92} +107.103 q^{93} +741.321 q^{94} -89.9974i q^{95} +106.395i q^{96} -1592.06i q^{97} -1196.36 q^{98} +869.788i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 36 q^{4} - 96 q^{8} - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 36 * q^4 - 96 * q^8 - 8 * q^9	$ 8 q - 8 q^{2} + 36 q^{4} - 96 q^{8} - 8 q^{9} + 88 q^{13} - 252 q^{15} + 420 q^{16} + 428 q^{18} + 52 q^{19} + 260 q^{21} + 140 q^{25} + 268 q^{26} + 120 q^{30} - 2336 q^{32} + 816 q^{33} + 1172 q^{35} + 264 q^{36} + 768 q^{38} + 136 q^{42} + 752 q^{43} + 368 q^{47} - 852 q^{49} + 468 q^{50} + 2564 q^{52} + 1156 q^{53} + 1996 q^{55} - 192 q^{59} + 3160 q^{60} + 3044 q^{64} - 1052 q^{66} + 764 q^{67} + 1812 q^{69} - 544 q^{70} - 1404 q^{72} - 896 q^{76} - 3084 q^{77} - 280 q^{81} - 496 q^{83} - 2952 q^{84} - 4244 q^{86} + 2860 q^{87} + 2156 q^{89} + 4012 q^{93} + 3392 q^{94} - 6728 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 36 * q^4 - 96 * q^8 - 8 * q^9 + 88 * q^13 - 252 * q^15 + 420 * q^16 + 428 * q^18 + 52 * q^19 + 260 * q^21 + 140 * q^25 + 268 * q^26 + 120 * q^30 - 2336 * q^32 + 816 * q^33 + 1172 * q^35 + 264 * q^36 + 768 * q^38 + 136 * q^42 + 752 * q^43 + 368 * q^47 - 852 * q^49 + 468 * q^50 + 2564 * q^52 + 1156 * q^53 + 1996 * q^55 - 192 * q^59 + 3160 * q^60 + 3044 * q^64 - 1052 * q^66 + 764 * q^67 + 1812 * q^69 - 544 * q^70 - 1404 * q^72 - 896 * q^76 - 3084 * q^77 - 280 * q^81 - 496 * q^83 - 2952 * q^84 - 4244 * q^86 + 2860 * q^87 + 2156 * q^89 + 4012 * q^93 + 3392 * q^94 - 6728 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	3.93651	1.39177	0.695884	−	0.718155i	$-0.255013\pi$
$2$	3.93651	1.39177	0.695884	+	0.718155i	$0.255013\pi$
$3$	− 0.423991i	− 0.0815972i	−0.999167	−	0.0407986i	$-0.987010\pi$
$3$	− 0.423991i	− 0.0815972i	0.999167	−	0.0407986i	$-0.0129902\pi$
$4$	7.49613	0.937016
$5$	− 1.95080i	− 0.174485i	−0.996187	−	0.0872423i	$-0.972195\pi$
$5$	− 1.95080i	− 0.174485i	0.996187	−	0.0872423i	$-0.0278055\pi$
$6$	− 1.66905i	− 0.113564i
$7$	25.4345i	1.37333i	0.726973	+	0.686667i	$0.240927\pi$
$7$	25.4345i	1.37333i	−0.726973	+	0.686667i	$0.759073\pi$
$8$	−1.98349	−0.0876588
$9$	26.8202	0.993342
$10$	− 7.67934i	− 0.242842i
$11$	32.4303i	0.888918i	0.895799	+	0.444459i	$0.146604\pi$
$11$	32.4303i	0.888918i	−0.895799	+	0.444459i	$0.853396\pi$
$12$	− 3.17829i	− 0.0764579i
$13$	54.6855	1.16669	0.583347	−	0.812223i	$-0.301743\pi$
$13$	54.6855	1.16669	0.583347	+	0.812223i	$0.301743\pi$
$14$	100.123i	1.91136i
$15$	−0.827121	−0.0142375
$16$	−67.7771	−1.05902
$17$	0	0
$17$	0	0
$18$	105.578	1.38250
$19$	46.1336	0.557041	0.278521	−	0.960430i	$-0.410156\pi$
$19$	46.1336	0.557041	0.278521	+	0.960430i	$0.410156\pi$
$20$	− 14.6234i	− 0.163495i
$21$	10.7840	0.112060
$22$	127.662i	1.23717i
$23$	75.2978i	0.682638i	0.939948	+	0.341319i	$0.110874\pi$
$23$	75.2978i	0.682638i	−0.939948	+	0.341319i	$0.889126\pi$
$24$	0.840984i	0.00715271i
$25$	121.194	0.969555
$26$	215.270	1.62377
$27$	− 22.8193i	− 0.162651i
$28$	190.660i	1.28684i
$29$	− 157.040i	− 1.00557i	−0.864412	−	0.502785i	$-0.832309\pi$
$29$	− 157.040i	− 1.00557i	0.864412	−	0.502785i	$-0.167691\pi$
$30$	−3.25597	−0.0198152
$31$	252.606i	1.46353i	0.681559	+	0.731763i	$0.261302\pi$
$31$	252.606i	1.46353i	−0.681559	+	0.731763i	$0.738698\pi$
$32$	−250.937	−1.38625
$33$	13.7502	0.0725332
$34$	0	0
$35$	49.6175	0.239626
$36$	201.048	0.930777
$37$	− 226.214i	− 1.00512i	−0.864543	−	0.502559i	$-0.832392\pi$
$37$	− 226.214i	− 1.00512i	0.864543	−	0.502559i	$-0.167608\pi$
$38$	181.606	0.775272
$39$	− 23.1862i	− 0.0951990i
$40$	3.86940i	0.0152951i
$41$	− 231.163i	− 0.880526i	−0.897869	−	0.440263i	$-0.854885\pi$
$41$	− 231.163i	− 0.880526i	0.897869	−	0.440263i	$-0.145115\pi$
$42$	42.4513	0.155962
$43$	−119.642	−0.424309	−0.212154	−	0.977236i	$-0.568048\pi$
$43$	−119.642	−0.424309	−0.212154	+	0.977236i	$0.568048\pi$
$44$	243.102i	0.832931i
$45$	− 52.3209i	− 0.173323i
$46$	296.411i	0.950073i
$47$	188.319	0.584451	0.292225	−	0.956349i	$-0.405604\pi$
$47$	188.319	0.584451	0.292225	+	0.956349i	$0.405604\pi$
$48$	28.7369i	0.0864128i
$49$	−303.913	−0.886044
$50$	477.083	1.34940
$51$	0	0
$52$	409.930	1.09321
$53$	−468.212	−1.21347	−0.606734	−	0.794905i	$-0.707521\pi$
$53$	−468.212	−1.21347	−0.606734	+	0.794905i	$0.707521\pi$
$54$	− 89.8285i	− 0.226372i
$55$	63.2650	0.155103
$56$	− 50.4491i	− 0.120385i
$57$	− 19.5603i	− 0.0454530i
$58$	− 618.188i	− 1.39952i
$59$	−751.217	−1.65763	−0.828815	−	0.559523i	$-0.810984\pi$
$59$	−751.217	−1.65763	−0.828815	+	0.559523i	$0.810984\pi$
$60$	−6.20021	−0.0133407
$61$	483.210i	1.01424i	0.861875	+	0.507121i	$0.169290\pi$
$61$	483.210i	1.01424i	−0.861875	+	0.507121i	$0.830710\pi$
$62$	994.385i	2.03689i
$63$	682.159i	1.36419i
$64$	−445.601	−0.870315
$65$	− 106.680i	− 0.203570i
$66$	54.1277	0.100949
$67$	533.879	0.973487	0.486744	−	0.873545i	$-0.338185\pi$
$67$	533.879	0.973487	0.486744	+	0.873545i	$0.338185\pi$
$68$	0	0
$69$	31.9256	0.0557013
$70$	195.320	0.333503
$71$	78.1521i	0.130633i	0.997865	+	0.0653165i	$0.0208057\pi$
$71$	78.1521i	0.130633i	−0.997865	+	0.0653165i	$0.979194\pi$
$72$	−53.1977	−0.0870752
$73$	− 383.013i	− 0.614085i	−0.951696	−	0.307043i	$-0.900661\pi$
$73$	− 383.013i	− 0.614085i	0.951696	−	0.307043i	$-0.0993395\pi$
$74$	− 890.494i	− 1.39889i
$75$	− 51.3854i	− 0.0791129i
$76$	345.824	0.521957
$77$	−824.848	−1.22078
$78$	− 91.2727i	− 0.132495i
$79$	− 1278.85i	− 1.82129i	−0.413187	−	0.910646i	$-0.635584\pi$
$79$	− 1278.85i	− 1.82129i	0.413187	−	0.910646i	$-0.364416\pi$
$80$	132.219i	0.184782i
$81$	714.471	0.980070
$82$	− 909.975i	− 1.22549i
$83$	−591.376	−0.782071	−0.391036	−	0.920376i	$-0.627883\pi$
$83$	−591.376	−0.782071	−0.391036	+	0.920376i	$0.627883\pi$
$84$	80.8382	0.105002
$85$	0	0
$86$	−470.973	−0.590539
$87$	−66.5834	−0.0820516
$88$	− 64.3253i	− 0.0779215i
$89$	609.729	0.726192	0.363096	−	0.931752i	$-0.381720\pi$
$89$	609.729	0.726192	0.363096	+	0.931752i	$0.381720\pi$
$90$	− 205.962i	− 0.241225i
$91$	1390.90i	1.60226i
$92$	564.442i	0.639643i
$93$	107.103	0.119420
$94$	741.321	0.813420
$95$	− 89.9974i	− 0.0971952i
$96$	106.395i	0.113114i
$97$	− 1592.06i	− 1.66648i	−0.552908	−	0.833242i	$-0.686482\pi$
$97$	− 1592.06i	− 1.66648i	0.552908	−	0.833242i	$-0.313518\pi$
$98$	−1196.36	−1.23317
$99$	869.788i	0.883000i
$100$	908.489	0.908489
$101$	−666.897	−0.657017	−0.328508	−	0.944501i	$-0.606546\pi$
$101$	−666.897	−0.657017	−0.328508	+	0.944501i	$0.606546\pi$
$102$	0	0
$103$	−872.373	−0.834538	−0.417269	−	0.908783i	$-0.637013\pi$
$103$	−872.373	−0.834538	−0.417269	+	0.908783i	$0.637013\pi$
$104$	−108.468	−0.102271
$105$	− 21.0374i	− 0.0195528i
$106$	−1843.12	−1.68887
$107$	346.327i	0.312904i	0.987686	+	0.156452i	$0.0500056\pi$
$107$	346.327i	0.312904i	−0.987686	+	0.156452i	$0.949994\pi$
$108$	− 171.056i	− 0.152407i
$109$	− 135.821i	− 0.119351i	−0.998218	−	0.0596757i	$-0.980993\pi$
$109$	− 135.821i	− 0.119351i	0.998218	−	0.0596757i	$-0.0190067\pi$
$110$	249.043	0.215867
$111$	−95.9128	−0.0820147
$112$	− 1723.88i	− 1.45438i
$113$	− 885.947i	− 0.737548i	−0.929519	−	0.368774i	$-0.879778\pi$
$113$	− 885.947i	− 0.737548i	0.929519	−	0.368774i	$-0.120222\pi$
$114$	− 76.9992i	− 0.0632600i
$115$	146.891	0.119110
$116$	− 1177.19i	− 0.942235i
$117$	1466.68	1.15893
$118$	−2957.18	−2.30703
$119$	0	0
$120$	1.64059	0.00124804
$121$	279.276	0.209824
$122$	1902.16i	1.41159i
$123$	−98.0110	−0.0718484
$124$	1893.56i	1.37135i
$125$	− 480.276i	− 0.343657i
$126$	2685.33i	1.89863i
$127$	1971.07	1.37720	0.688598	−	0.725144i	$-0.258227\pi$
$127$	1971.07	1.37720	0.688598	+	0.725144i	$0.258227\pi$
$128$	253.384	0.174970
$129$	50.7273i	0.0346224i
$130$	− 419.949i	− 0.283323i
$131$	− 250.787i	− 0.167262i	−0.996497	−	0.0836312i	$-0.973348\pi$
$131$	− 250.787i	− 0.167262i	0.996497	−	0.0836312i	$-0.0266518\pi$
$132$	103.073	0.0679648
$133$	1173.39i	0.765003i
$134$	2101.62	1.35487
$135$	−44.5159	−0.0283801
$136$	0	0
$137$	436.372	0.272130	0.136065	−	0.990700i	$-0.456554\pi$
$137$	436.372	0.272130	0.136065	+	0.990700i	$0.456554\pi$
$138$	125.676	0.0775233
$139$	− 83.7228i	− 0.0510883i	−0.999674	−	0.0255441i	$-0.991868\pi$
$139$	− 83.7228i	− 0.0510883i	0.999674	−	0.0255441i	$-0.00813184\pi$
$140$	371.940	0.224533
$141$	− 79.8457i	− 0.0476895i
$142$	307.647i	0.181811i
$143$	1773.47i	1.03710i
$144$	−1817.80	−1.05197
$145$	−306.353	−0.175457
$146$	− 1507.73i	− 0.854664i
$147$	128.856i	0.0722986i
$148$	− 1695.73i	− 0.941811i
$149$	2357.45	1.29617	0.648085	−	0.761568i	$-0.275570\pi$
$149$	2357.45	1.29617	0.648085	+	0.761568i	$0.275570\pi$
$150$	− 202.279i	− 0.110107i
$151$	−149.746	−0.0807031	−0.0403515	−	0.999186i	$-0.512848\pi$
$151$	−149.746	−0.0807031	−0.0403515	+	0.999186i	$0.512848\pi$
$152$	−91.5058	−0.0488296
$153$	0	0
$154$	−3247.02	−1.69904
$155$	492.783	0.255363
$156$	− 173.807i	− 0.0892030i
$157$	119.280	0.0606343	0.0303172	−	0.999540i	$-0.490348\pi$
$157$	119.280	0.0606343	0.0303172	+	0.999540i	$0.490348\pi$
$158$	− 5034.22i	− 2.53481i
$159$	198.518i	0.0990156i
$160$	489.528i	0.241879i
$161$	−1915.16	−0.937489
$162$	2812.52	1.36403
$163$	152.626i	0.0733411i	0.999327	+	0.0366705i	$0.0116752\pi$
$163$	152.626i	0.0733411i	−0.999327	+	0.0366705i	$0.988325\pi$
$164$	− 1732.83i	− 0.825067i
$165$	− 26.8238i	− 0.0126559i
$166$	−2327.96	−1.08846
$167$	− 2525.07i	− 1.17003i	−0.811021	−	0.585017i	$-0.801088\pi$
$167$	− 2525.07i	− 1.17003i	0.811021	−	0.585017i	$-0.198912\pi$
$168$	−21.3900	−0.00982306
$169$	793.506	0.361177
$170$	0	0
$171$	1237.31	0.553332
$172$	−896.854	−0.397584
$173$	328.274i	0.144267i	0.997395	+	0.0721335i	$0.0229808\pi$
$173$	328.274i	0.144267i	−0.997395	+	0.0721335i	$0.977019\pi$
$174$	−262.106	−0.114197
$175$	3082.52i	1.33152i
$176$	− 2198.03i	− 0.941379i
$177$	318.509i	0.135258i
$178$	2400.20	1.01069
$179$	−4155.11	−1.73501	−0.867506	−	0.497427i	$-0.834278\pi$
$179$	−4155.11	−1.73501	−0.867506	+	0.497427i	$0.834278\pi$
$180$	− 392.204i	− 0.162406i
$181$	− 955.425i	− 0.392355i	−0.980568	−	0.196177i	$-0.937147\pi$
$181$	− 955.425i	− 0.392355i	0.980568	−	0.196177i	$-0.0628528\pi$
$182$	5475.29i	2.22997i
$183$	204.877	0.0827592
$184$	− 149.353i	− 0.0598393i
$185$	−441.298	−0.175378
$186$	421.611	0.166204
$187$	0	0
$188$	1411.67	0.547640
$189$	580.397	0.223374
$190$	− 354.276i	− 0.135273i
$191$	889.758	0.337072	0.168536	−	0.985696i	$-0.446096\pi$
$191$	889.758	0.337072	0.168536	+	0.985696i	$0.446096\pi$
$192$	188.931i	0.0710152i
$193$	1732.07i	0.645997i	0.946399	+	0.322999i	$0.104691\pi$
$193$	1732.07i	0.645997i	−0.946399	+	0.322999i	$0.895309\pi$
$194$	− 6267.16i	− 2.31936i
$195$	−45.2316	−0.0166108
$196$	−2278.17	−0.830237
$197$	4443.91i	1.60718i	0.595181	+	0.803592i	$0.297081\pi$
$197$	4443.91i	1.60718i	−0.595181	+	0.803592i	$0.702919\pi$
$198$	3423.93i	1.22893i
$199$	− 3118.38i	− 1.11083i	−0.831572	−	0.555417i	$-0.812559\pi$
$199$	− 3118.38i	− 1.11083i	0.831572	−	0.555417i	$-0.187441\pi$
$200$	−240.388	−0.0849901
$201$	− 226.360i	− 0.0794338i
$202$	−2625.25	−0.914415
$203$	3994.22	1.38098
$204$	0	0
$205$	−450.952	−0.153638
$206$	−3434.11	−1.16148
$207$	2019.50i	0.678093i
$208$	−3706.42	−1.23555
$209$	1496.13i	0.495164i
$210$	− 82.8140i	− 0.0272129i
$211$	− 4532.53i	− 1.47883i	−0.673252	−	0.739413i	$-0.735103\pi$
$211$	− 4532.53i	− 1.47883i	0.673252	−	0.739413i	$-0.264897\pi$
$212$	−3509.78	−1.13704
$213$	33.1358	0.0106593
$214$	1363.32i	0.435489i
$215$	233.398i	0.0740354i
$216$	45.2619i	0.0142578i
$217$	−6424.89	−2.00991
$218$	− 534.661i	− 0.166109i
$219$	−162.394	−0.0501076
$220$	474.242	0.145334
$221$	0	0
$222$	−377.562	−0.114145
$223$	−123.574	−0.0371082	−0.0185541	−	0.999828i	$-0.505906\pi$
$223$	−123.574	−0.0371082	−0.0185541	+	0.999828i	$0.505906\pi$
$224$	− 6382.46i	− 1.90378i
$225$	3250.46	0.963100
$226$	− 3487.54i	− 1.02649i
$227$	− 780.134i	− 0.228103i	−0.993475	−	0.114051i	$-0.963617\pi$
$227$	− 780.134i	− 0.228103i	0.993475	−	0.114051i	$-0.0363829\pi$
$228$	− 146.626i	− 0.0425902i
$229$	2776.64	0.801247	0.400624	−	0.916243i	$-0.368794\pi$
$229$	2776.64	0.801247	0.400624	+	0.916243i	$0.368794\pi$
$230$	578.237	0.165773
$231$	349.728i	0.0996122i
$232$	311.487i	0.0881471i
$233$	5047.60i	1.41922i	0.704593	+	0.709612i	$0.251130\pi$
$233$	5047.60i	1.41922i	−0.704593	+	0.709612i	$0.748870\pi$
$234$	5773.60	1.61296
$235$	− 367.373i	− 0.101978i
$236$	−5631.22	−1.55323
$237$	−542.222	−0.148612
$238$	0	0
$239$	2254.20	0.610092	0.305046	−	0.952338i	$-0.401328\pi$
$239$	2254.20	0.610092	0.305046	+	0.952338i	$0.401328\pi$
$240$	56.0599	0.0150777
$241$	− 1729.12i	− 0.462168i	−0.972934	−	0.231084i	$-0.925773\pi$
$241$	− 1729.12i	− 0.462168i	0.972934	−	0.231084i	$-0.0742272\pi$
$242$	1099.37	0.292027
$243$	− 919.051i	− 0.242622i
$244$	3622.21i	0.950360i
$245$	592.873i	0.154601i
$246$	−385.821	−0.0999962
$247$	2522.84	0.649897
$248$	− 501.042i	− 0.128291i
$249$	250.738i	0.0638148i
$250$	− 1890.61i	− 0.478291i
$251$	1314.25	0.330496	0.165248	−	0.986252i	$-0.447158\pi$
$251$	1314.25	0.330496	0.165248	+	0.986252i	$0.447158\pi$
$252$	5113.55i	1.27827i
$253$	−2441.93	−0.606809
$254$	7759.13	1.91674
$255$	0	0
$256$	4562.26	1.11383
$257$	6039.96	1.46600	0.733001	−	0.680228i	$-0.238119\pi$
$257$	6039.96	1.46600	0.733001	+	0.680228i	$0.238119\pi$
$258$	199.689i	0.0481863i
$259$	5753.64	1.38036
$260$	− 799.690i	− 0.190749i
$261$	− 4211.84i	− 0.998874i
$262$	− 987.226i	− 0.232790i
$263$	−990.368	−0.232201	−0.116100	−	0.993237i	$-0.537039\pi$
$263$	−990.368	−0.232201	−0.116100	+	0.993237i	$0.537039\pi$
$264$	−27.2733	−0.00635818
$265$	913.386i	0.211732i
$266$	4619.05i	1.06471i
$267$	− 258.520i	− 0.0592552i
$268$	4002.02	0.912173
$269$	3390.55i	0.768497i	0.923230	+	0.384248i	$0.125539\pi$
$269$	3390.55i	0.768497i	−0.923230	+	0.384248i	$0.874461\pi$
$270$	−175.237	−0.0394985
$271$	−3706.24	−0.830767	−0.415383	−	0.909646i	$-0.636353\pi$
$271$	−3706.24	−0.830767	−0.415383	+	0.909646i	$0.636353\pi$
$272$	0	0
$273$	589.729	0.130740
$274$	1717.79	0.378742
$275$	3930.37i	0.861855i
$276$	239.318	0.0521930
$277$	7651.83i	1.65976i	0.557942	+	0.829880i	$0.311591\pi$
$277$	7651.83i	1.65976i	−0.557942	+	0.829880i	$0.688409\pi$
$278$	− 329.576i	− 0.0711030i
$279$	6774.94i	1.45378i
$280$	−98.4161	−0.0210053
$281$	3194.87	0.678256	0.339128	−	0.940740i	$-0.389868\pi$
$281$	3194.87	0.678256	0.339128	+	0.940740i	$0.389868\pi$
$282$	− 314.314i	− 0.0663727i
$283$	5989.81i	1.25815i	0.777344	+	0.629076i	$0.216567\pi$
$283$	5989.81i	1.25815i	−0.777344	+	0.629076i	$0.783433\pi$
$284$	585.838i	0.122405i
$285$	−38.1581	−0.00793085
$286$	6981.27i	1.44340i
$287$	5879.50	1.20925
$288$	−6730.20	−1.37702
$289$	0	0
$290$	−1205.96	−0.244195
$291$	−675.019	−0.135980
$292$	− 2871.11i	− 0.575408i
$293$	−5372.44	−1.07120	−0.535600	−	0.844472i	$-0.679914\pi$
$293$	−5372.44	−1.07120	−0.535600	+	0.844472i	$0.679914\pi$
$294$	507.245i	0.100623i
$295$	1465.47i	0.289231i
$296$	448.694i	0.0881074i
$297$	740.037	0.144583
$298$	9280.11	1.80397
$299$	4117.70i	0.796430i
$300$	− 385.191i	− 0.0741301i
$301$	− 3043.04i	− 0.582717i
$302$	−589.477	−0.112320
$303$	282.758i	0.0536107i
$304$	−3126.80	−0.589916
$305$	942.645	0.176970
$306$	0	0
$307$	7020.91	1.30523	0.652613	−	0.757692i	$-0.273673\pi$
$307$	7020.91	1.30523	0.652613	+	0.757692i	$0.273673\pi$
$308$	−6183.16	−1.14389
$309$	369.878i	0.0680960i
$310$	1939.84	0.355406
$311$	1026.01i	0.187072i	0.995616	+	0.0935362i	$0.0298171\pi$
$311$	1026.01i	0.187072i	−0.995616	+	0.0935362i	$0.970183\pi$
$312$	45.9896i	0.00834503i
$313$	− 2490.87i	− 0.449815i	−0.974380	−	0.224907i	$-0.927792\pi$
$313$	− 2490.87i	− 0.449815i	0.974380	−	0.224907i	$-0.0722080\pi$
$314$	469.548	0.0843889
$315$	1330.75	0.238030
$316$	− 9586.44i	− 1.70658i
$317$	2775.18i	0.491702i	0.969308	+	0.245851i	$0.0790674\pi$
$317$	2775.18i	0.491702i	−0.969308	+	0.245851i	$0.920933\pi$
$318$	781.467i	0.137807i
$319$	5092.84	0.893869
$320$	869.278i	0.151857i
$321$	146.840	0.0255321
$322$	−7539.05	−1.30477
$323$	0	0
$324$	5355.77	0.918341
$325$	6627.58	1.13117
$326$	600.815i	0.102074i
$327$	−57.5870	−0.00973873
$328$	458.510i	0.0771859i
$329$	4789.80i	0.802646i
$330$	− 105.592i	− 0.0176141i
$331$	6017.90	0.999317	0.499659	−	0.866222i	$-0.333459\pi$
$331$	6017.90	0.999317	0.499659	+	0.866222i	$0.333459\pi$
$332$	−4433.03	−0.732813
$333$	− 6067.11i	− 0.998425i
$334$	− 9939.96i	− 1.62841i
$335$	− 1041.49i	− 0.169859i
$336$	−730.908	−0.118674
$337$	474.374i	0.0766789i	0.999265	+	0.0383395i	$0.0122068\pi$
$337$	474.374i	0.0766789i	−0.999265	+	0.0383395i	$0.987793\pi$
$338$	3123.64	0.502674
$339$	−375.634	−0.0601818
$340$	0	0
$341$	−8192.07	−1.30095
$342$	4870.71	0.770110
$343$	994.158i	0.156500i
$344$	237.310	0.0371944
$345$	− 62.2804i	− 0.00971903i
$346$	1292.25i	0.200786i
$347$	1475.45i	0.228261i	0.993466	+	0.114130i	$0.0364082\pi$
$347$	1475.45i	0.228261i	−0.993466	+	0.114130i	$0.963592\pi$
$348$	−499.118	−0.0768837
$349$	−6855.25	−1.05144	−0.525721	−	0.850657i	$-0.676204\pi$
$349$	−6855.25	−1.05144	−0.525721	+	0.850657i	$0.676204\pi$
$350$	12134.4i	1.85317i
$351$	− 1247.89i	− 0.189764i
$352$	− 8137.97i	− 1.23226i
$353$	−7485.74	−1.12868	−0.564342	−	0.825541i	$-0.690870\pi$
$353$	−7485.74	−1.12868	−0.564342	+	0.825541i	$0.690870\pi$
$354$	1253.82i	0.188247i
$355$	152.459	0.0227935
$356$	4570.60	0.680454
$357$	0	0
$358$	−16356.6	−2.41473
$359$	−7169.54	−1.05402	−0.527011	−	0.849859i	$-0.676687\pi$
$359$	−7169.54	−1.05402	−0.527011	+	0.849859i	$0.676687\pi$
$360$	103.778i	0.0151933i
$361$	−4730.69	−0.689705
$362$	− 3761.04i	− 0.546067i
$363$	− 118.411i	− 0.0171211i
$364$	10426.4i	1.50134i
$365$	−747.180	−0.107149
$366$	806.500	0.115182
$367$	− 6608.80i	− 0.939991i	−0.882669	−	0.469995i	$-0.844256\pi$
$367$	− 6608.80i	− 0.939991i	0.882669	−	0.469995i	$-0.155744\pi$
$368$	− 5103.46i	− 0.722925i
$369$	− 6199.84i	− 0.874663i
$370$	−1737.17	−0.244085
$371$	− 11908.7i	− 1.66650i
$372$	802.855	0.111898
$373$	−1602.91	−0.222508	−0.111254	−	0.993792i	$-0.535487\pi$
$373$	−1602.91	−0.222508	−0.111254	+	0.993792i	$0.535487\pi$
$374$	0	0
$375$	−203.633	−0.0280415
$376$	−373.530	−0.0512323
$377$	− 8587.79i	− 1.17319i
$378$	2284.74	0.310885
$379$	− 1743.08i	− 0.236243i	−0.992999	−	0.118121i	$-0.962313\pi$
$379$	− 1743.08i	− 0.236243i	0.992999	−	0.118121i	$-0.0376872\pi$
$380$	− 674.632i	− 0.0910734i
$381$	− 835.715i	− 0.112375i
$382$	3502.55	0.469125
$383$	1155.24	0.154125	0.0770627	−	0.997026i	$-0.475446\pi$
$383$	1155.24	0.154125	0.0770627	+	0.997026i	$0.475446\pi$
$384$	− 107.432i	− 0.0142771i
$385$	1609.11i	0.213008i
$386$	6818.33i	0.899078i
$387$	−3208.83	−0.421484
$388$	− 11934.3i	− 1.56152i
$389$	−3698.95	−0.482119	−0.241060	−	0.970510i	$-0.577495\pi$
$389$	−3698.95	−0.482119	−0.241060	+	0.970510i	$0.577495\pi$
$390$	−178.055	−0.0231183
$391$	0	0
$392$	602.809	0.0776696
$393$	−106.332	−0.0136481
$394$	17493.5i	2.23683i
$395$	−2494.78	−0.317788
$396$	6520.04i	0.827385i
$397$	− 13587.9i	− 1.71778i	−0.512159	−	0.858891i	$-0.671154\pi$
$397$	− 13587.9i	− 1.71778i	0.512159	−	0.858891i	$-0.328846\pi$
$398$	− 12275.5i	− 1.54602i
$399$	497.505	0.0624221
$400$	−8214.20	−1.02678
$401$	− 2664.34i	− 0.331798i	−0.986143	−	0.165899i	$-0.946947\pi$
$401$	− 2664.34i	− 0.331798i	0.986143	−	0.165899i	$-0.0530526\pi$
$402$	− 891.068i	− 0.110553i
$403$	13813.9i	1.70749i
$404$	−4999.14	−0.615635
$405$	− 1393.79i	− 0.171007i
$406$	15723.3	1.92201
$407$	7336.19	0.893467
$408$	0	0
$409$	4145.86	0.501222	0.250611	−	0.968088i	$-0.419368\pi$
$409$	4145.86	0.501222	0.250611	+	0.968088i	$0.419368\pi$
$410$	−1775.18	−0.213829
$411$	− 185.018i	− 0.0222050i
$412$	−6539.42	−0.781976
$413$	− 19106.8i	− 2.27648i
$414$	7949.80i	0.943748i
$415$	1153.65i	0.136459i
$416$	−13722.6	−1.61733
$417$	−35.4977	−0.00416866
$418$	5889.52i	0.689153i
$419$	− 14247.5i	− 1.66118i	−0.556882	−	0.830592i	$-0.688003\pi$
$419$	− 14247.5i	− 1.66118i	0.556882	−	0.830592i	$-0.311997\pi$
$420$	− 157.699i	− 0.0183213i
$421$	3191.61	0.369477	0.184738	−	0.982788i	$-0.440856\pi$
$421$	3191.61	0.369477	0.184738	+	0.982788i	$0.440856\pi$
$422$	− 17842.4i	− 2.05818i
$423$	5050.77	0.580560
$424$	928.695	0.106371
$425$	0	0
$426$	130.439	0.0148352
$427$	−12290.2	−1.39289
$428$	2596.11i	0.293196i
$429$	751.935	0.0846241
$430$	918.774i	0.103040i
$431$	1639.42i	0.183220i	0.995795	+	0.0916101i	$0.0292013\pi$
$431$	1639.42i	0.183220i	−0.995795	+	0.0916101i	$0.970799\pi$
$432$	1546.63i	0.172250i
$433$	−16579.9	−1.84013	−0.920066	−	0.391764i	$-0.871865\pi$
$433$	−16579.9	−1.84013	−0.920066	+	0.391764i	$0.871865\pi$
$434$	−25291.7	−2.79732
$435$	129.891i	0.0143168i
$436$	− 1018.13i	− 0.111834i
$437$	3473.76i	0.380258i
$438$	−639.266	−0.0697382
$439$	7347.09i	0.798764i	0.916785	+	0.399382i	$0.130775\pi$
$439$	7347.09i	0.798764i	−0.916785	+	0.399382i	$0.869225\pi$
$440$	−125.486	−0.0135961
$441$	−8151.02	−0.880144
$442$	0	0
$443$	−13325.5	−1.42915	−0.714575	−	0.699559i	$-0.753380\pi$
$443$	−13325.5	−1.42915	−0.714575	+	0.699559i	$0.753380\pi$
$444$	−718.974	−0.0768491
$445$	− 1189.46i	− 0.126709i
$446$	−486.451	−0.0516460
$447$	− 999.536i	− 0.105764i
$448$	− 11333.6i	− 1.19523i
$449$	− 9686.35i	− 1.01810i	−0.860737	−	0.509050i	$-0.829997\pi$
$449$	− 9686.35i	− 1.01810i	0.860737	−	0.509050i	$-0.170003\pi$
$450$	12795.5	1.34041
$451$	7496.67	0.782715
$452$	− 6641.17i	− 0.691094i
$453$	63.4910i	0.00658514i
$454$	− 3071.01i	− 0.317466i
$455$	2713.36	0.279570
$456$	38.7976i	0.00398436i
$457$	−698.065	−0.0714532	−0.0357266	−	0.999362i	$-0.511375\pi$
$457$	−698.065	−0.0714532	−0.0357266	+	0.999362i	$0.511375\pi$
$458$	10930.3	1.11515
$459$	0	0
$460$	1101.11	0.111608
$461$	−6505.58	−0.657256	−0.328628	−	0.944459i	$-0.606586\pi$
$461$	−6505.58	−0.657256	−0.328628	+	0.944459i	$0.606586\pi$
$462$	1376.71i	0.138637i
$463$	−1181.74	−0.118618	−0.0593089	−	0.998240i	$-0.518890\pi$
$463$	−1181.74	−0.118618	−0.0593089	+	0.998240i	$0.518890\pi$
$464$	10643.7i	1.06492i
$465$	− 208.935i	− 0.0208369i
$466$	19869.9i	1.97523i
$467$	−2950.96	−0.292407	−0.146204	−	0.989255i	$-0.546705\pi$
$467$	−2950.96	−0.292407	−0.146204	+	0.989255i	$0.546705\pi$
$468$	10994.4	1.08593
$469$	13578.9i	1.33692i
$470$	− 1446.17i	− 0.141929i
$471$	− 50.5737i	− 0.00494759i
$472$	1490.03	0.145306
$473$	− 3880.03i	− 0.377176i
$474$	−2134.46	−0.206834
$475$	5591.14	0.540082
$476$	0	0
$477$	−12557.5	−1.20539
$478$	8873.69	0.849107
$479$	8890.21i	0.848025i	0.905656	+	0.424013i	$0.139379\pi$
$479$	8890.21i	0.848025i	−0.905656	+	0.424013i	$0.860621\pi$
$480$	207.556	0.0197366
$481$	− 12370.6i	− 1.17267i
$482$	− 6806.70i	− 0.643230i
$483$	812.011i	0.0764965i
$484$	2093.49	0.196609
$485$	−3105.78	−0.290776
$486$	− 3617.85i	− 0.337673i
$487$	7104.47i	0.661056i	0.943796	+	0.330528i	$0.107227\pi$
$487$	7104.47i	0.661056i	−0.943796	+	0.330528i	$0.892773\pi$
$488$	− 958.444i	− 0.0889072i
$489$	64.7121	0.00598442
$490$	2333.85i	0.215169i
$491$	−7638.33	−0.702063	−0.351031	−	0.936364i	$-0.614169\pi$
$491$	−7638.33	−0.702063	−0.351031	+	0.936364i	$0.614169\pi$
$492$	−734.703	−0.0673231
$493$	0	0
$494$	9931.20	0.904505
$495$	1696.78	0.154070
$496$	− 17120.9i	− 1.54990i
$497$	−1987.76	−0.179403
$498$	987.033i	0.0888153i
$499$	20202.5i	1.81241i	0.422843	+	0.906203i	$0.361032\pi$
$499$	20202.5i	1.81241i	−0.422843	+	0.906203i	$0.638968\pi$
$500$	− 3600.21i	− 0.322012i
$501$	−1070.61	−0.0954714
$502$	5173.54	0.459973
$503$	− 20469.5i	− 1.81449i	−0.420604	−	0.907244i	$-0.638182\pi$
$503$	− 20469.5i	− 1.81449i	0.420604	−	0.907244i	$-0.361818\pi$
$504$	− 1353.06i	− 0.119583i
$505$	1300.98i	0.114639i
$506$	−9612.68	−0.844537
$507$	− 336.439i	− 0.0294710i
$508$	14775.4	1.29045
$509$	−19503.1	−1.69835	−0.849173	−	0.528116i	$-0.822899\pi$
$509$	−19503.1	−1.69835	−0.849173	+	0.528116i	$0.822899\pi$
$510$	0	0
$511$	9741.73	0.843344
$512$	15932.3	1.37523
$513$	− 1052.74i	− 0.0906033i
$514$	23776.4	2.04033
$515$	1701.82i	0.145614i
$516$	380.258i	0.0324417i
$517$	6107.25i	0.519529i
$518$	22649.3	1.92114
$519$	139.185	0.0117718
$520$	211.600i	0.0178447i
$521$	− 6963.51i	− 0.585561i	−0.956180	−	0.292780i	$-0.905420\pi$
$521$	− 6963.51i	− 0.585561i	0.956180	−	0.292780i	$-0.0945805\pi$
$522$	− 16580.0i	− 1.39020i
$523$	2507.22	0.209623	0.104812	−	0.994492i	$-0.466576\pi$
$523$	2507.22	0.209623	0.104812	+	0.994492i	$0.466576\pi$
$524$	− 1879.93i	− 0.156728i
$525$	1306.96	0.108648
$526$	−3898.60	−0.323169
$527$	0	0
$528$	−931.946	−0.0768139
$529$	6497.24	0.534005
$530$	3595.56i	0.294681i
$531$	−20147.8	−1.64659
$532$	8795.85i	0.716820i
$533$	− 12641.3i	− 1.02730i
$534$	− 1017.67i	− 0.0824695i
$535$	675.614	0.0545969
$536$	−1058.94	−0.0853348
$537$	1761.73i	0.141572i
$538$	13346.9i	1.06957i
$539$	− 9855.99i	− 0.787620i
$540$	−333.697	−0.0265926
$541$	19376.1i	1.53982i	0.638149	+	0.769912i	$0.279700\pi$
$541$	19376.1i	1.53982i	−0.638149	+	0.769912i	$0.720300\pi$
$542$	−14589.6	−1.15623
$543$	−405.092	−0.0320150
$544$	0	0
$545$	−264.960	−0.0208250
$546$	2321.47	0.181960
$547$	− 2956.31i	− 0.231083i	−0.993303	−	0.115542i	$-0.963140\pi$
$547$	− 2956.31i	− 0.231083i	0.993303	−	0.115542i	$-0.0368604\pi$
$548$	3271.10	0.254990
$549$	12959.8i	1.00749i
$550$	15471.9i	1.19950i
$551$	− 7244.81i	− 0.560144i
$552$	−63.3242	−0.00488271
$553$	32526.9	2.50124
$554$	30121.5i	2.31000i
$555$	187.106i	0.0143103i
$556$	− 627.597i	− 0.0478706i
$557$	3920.00	0.298197	0.149099	−	0.988822i	$-0.452363\pi$
$557$	3920.00	0.298197	0.149099	+	0.988822i	$0.452363\pi$
$558$	26669.6i	2.02333i
$559$	−6542.70	−0.495039
$560$	−3362.93	−0.253768
$561$	0	0
$562$	12576.6	0.943975
$563$	−20821.5	−1.55865	−0.779326	−	0.626618i	$-0.784439\pi$
$563$	−20821.5	−1.55865	−0.779326	+	0.626618i	$0.784439\pi$
$564$	− 598.534i	− 0.0446859i
$565$	−1728.30	−0.128691
$566$	23579.0i	1.75106i
$567$	18172.2i	1.34596i
$568$	− 155.014i	− 0.0114511i
$569$	7849.66	0.578339	0.289170	−	0.957278i	$-0.406621\pi$
$569$	7849.66	0.578339	0.289170	+	0.957278i	$0.406621\pi$
$570$	−150.210	−0.0110379
$571$	− 24535.7i	− 1.79822i	−0.437719	−	0.899112i	$-0.644214\pi$
$571$	− 24535.7i	− 1.79822i	0.437719	−	0.899112i	$-0.355786\pi$
$572$	13294.1i	0.971776i
$573$	− 377.250i	− 0.0275041i
$574$	23144.7	1.68300
$575$	9125.67i	0.661855i
$576$	−11951.1	−0.864521
$577$	−7549.37	−0.544687	−0.272343	−	0.962200i	$-0.587799\pi$
$577$	−7549.37	−0.544687	−0.272343	+	0.962200i	$0.587799\pi$
$578$	0	0
$579$	734.384	0.0527115
$580$	−2296.46	−0.164406
$581$	− 15041.3i	− 1.07404i
$582$	−2657.22	−0.189253
$583$	− 15184.2i	− 1.07867i
$584$	759.703i	0.0538300i
$585$	− 2861.19i	− 0.202215i
$586$	−21148.7	−1.49086
$587$	−6451.77	−0.453651	−0.226826	−	0.973935i	$-0.572835\pi$
$587$	−6451.77	−0.453651	−0.226826	+	0.973935i	$0.572835\pi$
$588$	965.925i	0.0677450i
$589$	11653.6i	0.815244i
$590$	5768.85i	0.402542i
$591$	1884.18	0.131142
$592$	15332.1i	1.06444i
$593$	−176.420	−0.0122170	−0.00610850	−	0.999981i	$-0.501944\pi$
$593$	−176.420	−0.0122170	−0.00610850	+	0.999981i	$0.501944\pi$
$594$	2913.16	0.201227
$595$	0	0
$596$	17671.7	1.21453
$597$	−1322.16	−0.0906408
$598$	16209.4i	1.10845i
$599$	11248.7	0.767292	0.383646	−	0.923480i	$-0.374668\pi$
$599$	11248.7	0.767292	0.383646	+	0.923480i	$0.374668\pi$
$600$	101.923i	0.00693495i
$601$	− 25418.5i	− 1.72519i	−0.505893	−	0.862596i	$-0.668837\pi$
$601$	− 25418.5i	− 1.72519i	0.505893	−	0.862596i	$-0.331163\pi$
$602$	− 11979.0i	− 0.811007i
$603$	14318.7	0.967006
$604$	−1122.52	−0.0756201
$605$	− 544.812i	− 0.0366112i
$606$	1113.08i	0.0746136i
$607$	19680.4i	1.31599i	0.753024	+	0.657993i	$0.228594\pi$
$607$	19680.4i	1.31599i	−0.753024	+	0.657993i	$0.771406\pi$
$608$	−11576.7	−0.772196
$609$	− 1693.51i	− 0.112684i
$610$	3710.74	0.246300
$611$	10298.3	0.681876
$612$	0	0
$613$	3619.34	0.238473	0.119236	−	0.992866i	$-0.461955\pi$
$613$	3619.34	0.238473	0.119236	+	0.992866i	$0.461955\pi$
$614$	27637.9	1.81657
$615$	191.200i	0.0125364i
$616$	1636.08	0.107012
$617$	− 19744.9i	− 1.28833i	−0.764887	−	0.644164i	$-0.777205\pi$
$617$	− 19744.9i	− 1.28833i	0.764887	−	0.644164i	$-0.222795\pi$
$618$	1456.03i	0.0947737i
$619$	18695.9i	1.21397i	0.794712	+	0.606987i	$0.207622\pi$
$619$	18695.9i	1.21397i	−0.794712	+	0.606987i	$0.792378\pi$
$620$	3693.96	0.239279
$621$	1718.24	0.111032
$622$	4038.89i	0.260361i
$623$	15508.1i	0.997304i
$624$	1571.49i	0.100817i
$625$	14212.4	0.909592
$626$	− 9805.33i	− 0.626038i
$627$	634.345	0.0404040
$628$	894.139	0.0568153
$629$	0	0
$630$	5238.53	0.331283
$631$	10087.2	0.636394	0.318197	−	0.948025i	$-0.396923\pi$
$631$	10087.2	0.636394	0.318197	+	0.948025i	$0.396923\pi$
$632$	2536.59i	0.159652i
$633$	−1921.75	−0.120668
$634$	10924.5i	0.684335i
$635$	− 3845.15i	− 0.240300i
$636$	1488.11i	0.0927792i
$637$	−16619.6	−1.03374
$638$	20048.0	1.24406
$639$	2096.06i	0.129763i
$640$	− 494.300i	− 0.0305296i
$641$	− 10265.1i	− 0.632523i	−0.948672	−	0.316261i	$-0.897572\pi$
$641$	− 10265.1i	− 0.632523i	0.948672	−	0.316261i	$-0.102428\pi$
$642$	578.036	0.0355347
$643$	− 7778.26i	− 0.477052i	−0.971136	−	0.238526i	$-0.923336\pi$
$643$	− 7778.26i	− 0.477052i	0.971136	−	0.238526i	$-0.0766642\pi$
$644$	−14356.3	−0.878443
$645$	98.9587	0.00604108
$646$	0	0
$647$	5015.28	0.304746	0.152373	−	0.988323i	$-0.451308\pi$
$647$	5015.28	0.304746	0.152373	+	0.988323i	$0.451308\pi$
$648$	−1417.15	−0.0859118
$649$	− 24362.2i	− 1.47350i
$650$	26089.5	1.57433
$651$	2724.10i	0.164003i
$652$	1144.10i	0.0687218i
$653$	− 14563.9i	− 0.872784i	−0.899757	−	0.436392i	$-0.856256\pi$
$653$	− 14563.9i	− 0.872784i	0.899757	−	0.436392i	$-0.143744\pi$
$654$	−226.692	−0.0135541
$655$	−489.235	−0.0291847
$656$	15667.5i	0.932491i
$657$	− 10272.5i	− 0.609997i
$658$	18855.1i	1.11710i
$659$	−6199.21	−0.366445	−0.183222	−	0.983072i	$-0.558653\pi$
$659$	−6199.21	−0.366445	−0.183222	+	0.983072i	$0.558653\pi$
$660$	− 201.075i	− 0.0118588i
$661$	−15131.8	−0.890406	−0.445203	−	0.895430i	$-0.646868\pi$
$661$	−15131.8	−0.890406	−0.445203	+	0.895430i	$0.646868\pi$
$662$	23689.6	1.39082
$663$	0	0
$664$	1172.99	0.0685554
$665$	2289.04	0.133481
$666$	− 23883.3i	− 1.38958i
$667$	11824.7	0.686440
$668$	− 18928.2i	− 1.09634i
$669$	52.3943i	0.00302792i
$670$	− 4099.84i	− 0.236404i
$671$	−15670.6	−0.901577
$672$	−2706.11	−0.155343
$673$	27043.8i	1.54898i	0.632589	+	0.774488i	$0.281992\pi$
$673$	27043.8i	1.54898i	−0.632589	+	0.774488i	$0.718008\pi$
$674$	1867.38i	0.106719i
$675$	− 2765.57i	− 0.157699i
$676$	5948.22	0.338429
$677$	2671.45i	0.151658i	0.997121	+	0.0758288i	$0.0241602\pi$
$677$	2671.45i	0.151658i	−0.997121	+	0.0758288i	$0.975840\pi$
$678$	−1478.69	−0.0837591
$679$	40493.2	2.28864
$680$	0	0
$681$	−330.770	−0.0186125
$682$	−32248.2	−1.81063
$683$	14786.6i	0.828393i	0.910187	+	0.414197i	$0.135937\pi$
$683$	14786.6i	0.828393i	−0.910187	+	0.414197i	$0.864063\pi$
$684$	9275.07	0.518481
$685$	− 851.274i	− 0.0474825i
$686$	3913.52i	0.217812i
$687$	− 1177.27i	− 0.0653795i
$688$	8109.01	0.449350
$689$	−25604.4	−1.41575
$690$	− 245.168i	− 0.0135266i
$691$	18670.1i	1.02785i	0.857836	+	0.513924i	$0.171809\pi$
$691$	18670.1i	1.02785i	−0.857836	+	0.513924i	$0.828191\pi$
$692$	2460.78i	0.135181i
$693$	−22122.6	−1.21265
$694$	5808.14i	0.317686i
$695$	−163.326	−0.00891413
$696$	132.068	0.00719255
$697$	0	0
$698$	−26985.8	−1.46336
$699$	2140.14	0.115805
$700$	23106.9i	1.24766i
$701$	−27668.5	−1.49076	−0.745381	−	0.666638i	$-0.767733\pi$
$701$	−27668.5	−1.49076	−0.745381	+	0.666638i	$0.767733\pi$
$702$	− 4912.32i	− 0.264107i
$703$	− 10436.1i	− 0.559892i
$704$	− 14451.0i	− 0.773639i
$705$	−155.763	−0.00832109
$706$	−29467.7	−1.57087
$707$	− 16962.2i	− 0.902303i
$708$	2387.59i	0.126739i
$709$	10439.9i	0.553002i	0.961014	+	0.276501i	$0.0891749\pi$
$709$	10439.9i	0.553002i	−0.961014	+	0.276501i	$0.910825\pi$
$710$	600.157	0.0317232
$711$	− 34299.1i	− 1.80917i
$712$	−1209.39	−0.0636572
$713$	−19020.6	−0.999059
$714$	0	0
$715$	3459.68	0.180957
$716$	−31147.2	−1.62573
$717$	− 955.761i	− 0.0497818i
$718$	−28223.0	−1.46695
$719$	17815.1i	0.924050i	0.886867	+	0.462025i	$0.152877\pi$
$719$	17815.1i	0.924050i	−0.886867	+	0.462025i	$0.847123\pi$
$720$	3546.16i	0.183552i
$721$	− 22188.4i	− 1.14610i
$722$	−18622.4	−0.959909
$723$	−733.132	−0.0377116
$724$	− 7161.99i	− 0.367643i
$725$	− 19032.3i	− 0.974955i
$726$	− 466.125i	− 0.0238286i
$727$	4296.42	0.219182	0.109591	−	0.993977i	$-0.465046\pi$
$727$	4296.42	0.219182	0.109591	+	0.993977i	$0.465046\pi$
$728$	− 2758.84i	− 0.140452i
$729$	18901.0	0.960273
$730$	−2941.28	−0.149126
$731$	0	0
$732$	1535.78	0.0775467
$733$	28559.1	1.43909	0.719546	−	0.694445i	$-0.244350\pi$
$733$	28559.1	1.43909	0.719546	+	0.694445i	$0.244350\pi$
$734$	− 26015.6i	− 1.30825i
$735$	251.373	0.0126150
$736$	− 18895.0i	− 0.946304i
$737$	17313.8i	0.865351i
$738$	− 24405.7i	− 1.21733i
$739$	10646.9	0.529974	0.264987	−	0.964252i	$-0.414632\pi$
$739$	10646.9	0.529974	0.264987	+	0.964252i	$0.414632\pi$
$740$	−3308.03	−0.164332
$741$	− 1069.66i	− 0.0530298i
$742$	− 46878.8i	− 2.31937i
$743$	13964.7i	0.689521i	0.938691	+	0.344760i	$0.112040\pi$
$743$	13964.7i	0.689521i	−0.938691	+	0.344760i	$0.887960\pi$
$744$	−212.437	−0.0104682
$745$	− 4598.90i	− 0.226162i
$746$	−6309.87	−0.309679
$747$	−15860.8	−0.776864
$748$	0	0
$749$	−8808.65	−0.429721
$750$	−801.602	−0.0390272
$751$	26761.0i	1.30030i	0.759807	+	0.650149i	$0.225293\pi$
$751$	26761.0i	1.30030i	−0.759807	+	0.650149i	$0.774707\pi$
$752$	−12763.7	−0.618943
$753$	− 557.229i	− 0.0269675i
$754$	− 33805.9i	− 1.63281i
$755$	292.124i	0.0140815i
$756$	4350.73	0.209305
$757$	1399.40	0.0671889	0.0335945	−	0.999436i	$-0.489305\pi$
$757$	1399.40	0.0671889	0.0335945	+	0.999436i	$0.489305\pi$
$758$	− 6861.66i	− 0.328795i
$759$	1035.36i	0.0495139i
$760$	178.509i	0.00852002i
$761$	−29282.9	−1.39488	−0.697440	−	0.716644i	$-0.745677\pi$
$761$	−29282.9	−1.39488	−0.697440	+	0.716644i	$0.745677\pi$
$762$	− 3289.80i	− 0.156400i
$763$	3454.54	0.163909
$764$	6669.74	0.315841
$765$	0	0
$766$	4547.62	0.214507
$767$	−41080.7	−1.93395
$768$	− 1934.36i	− 0.0908856i
$769$	11804.9	0.553571	0.276786	−	0.960932i	$-0.410731\pi$
$769$	11804.9	0.553571	0.276786	+	0.960932i	$0.410731\pi$
$770$	6334.29i	0.296457i
$771$	− 2560.89i	− 0.119622i
$772$	12983.9i	0.605310i
$773$	18421.7	0.857155	0.428578	−	0.903505i	$-0.359015\pi$
$773$	18421.7	0.857155	0.428578	+	0.903505i	$0.359015\pi$
$774$	−12631.6	−0.586607
$775$	30614.4i	1.41897i
$776$	3157.84i	0.146082i
$777$	− 2439.49i	− 0.112634i
$778$	−14561.0	−0.670998
$779$	− 10664.4i	− 0.490489i
$780$	−339.062	−0.0155646
$781$	−2534.49	−0.116122
$782$	0	0
$783$	−3583.53	−0.163557
$784$	20598.3	0.938335
$785$	− 232.691i	− 0.0105798i
$786$	−418.575	−0.0189950
$787$	22391.5i	1.01419i	0.861889	+	0.507096i	$0.169281\pi$
$787$	22391.5i	1.01419i	−0.861889	+	0.507096i	$0.830719\pi$
$788$	33312.1i	1.50596i
$789$	419.908i	0.0189469i
$790$	−9820.74	−0.442286
$791$	22533.6	1.01290
$792$	− 1725.22i	− 0.0774027i
$793$	26424.6i	1.18331i
$794$	− 53489.1i	− 2.39075i
$795$	387.268	0.0172767
$796$	− 23375.7i	− 1.04087i
$797$	13676.1	0.607818	0.303909	−	0.952701i	$-0.401708\pi$
$797$	13676.1	0.607818	0.303909	+	0.952701i	$0.401708\pi$
$798$	1958.43	0.0868770
$799$	0	0
$800$	−30412.2	−1.34404
$801$	16353.1	0.721357
$802$	− 10488.2i	− 0.461786i
$803$	12421.2	0.545872
$804$	− 1696.82i	− 0.0744308i
$805$	3736.09i	0.163578i
$806$	54378.5i	2.37643i
$807$	1437.56	0.0627071
$808$	1322.79	0.0575933
$809$	− 100.880i	− 0.00438410i	−0.999998	−	0.00219205i	$-0.999302\pi$
$809$	− 100.880i	− 0.00438410i	0.999998	−	0.00219205i	$-0.000697752\pi$
$810$	− 5486.67i	− 0.238002i
$811$	− 16719.6i	− 0.723926i	−0.932192	−	0.361963i	$-0.882107\pi$
$811$	− 16719.6i	− 0.723926i	0.932192	−	0.361963i	$-0.117893\pi$
$812$	29941.2	1.29400
$813$	1571.41i	0.0677882i
$814$	28879.0	1.24350
$815$	297.743	0.0127969
$816$	0	0
$817$	−5519.54	−0.236358
$818$	16320.2	0.697584
$819$	37304.2i	1.59159i
$820$	−3380.39	−0.143962
$821$	4932.52i	0.209679i	0.994489	+	0.104839i	$0.0334328\pi$
$821$	4932.52i	0.209679i	−0.994489	+	0.104839i	$0.966567\pi$
$822$	− 728.326i	− 0.0309042i
$823$	26576.3i	1.12563i	0.826583	+	0.562814i	$0.190281\pi$
$823$	26576.3i	1.12563i	−0.826583	+	0.562814i	$0.809719\pi$
$824$	1730.35	0.0731547
$825$	1666.44	0.0703249
$826$	− 75214.2i	− 3.16833i
$827$	− 31136.7i	− 1.30923i	−0.755965	−	0.654613i	$-0.772832\pi$
$827$	− 31136.7i	− 1.30923i	0.755965	−	0.654613i	$-0.227168\pi$
$828$	15138.5i	0.635384i
$829$	−17274.9	−0.723742	−0.361871	−	0.932228i	$-0.617862\pi$
$829$	−17274.9	−0.723742	−0.361871	+	0.932228i	$0.617862\pi$
$830$	4541.37i	0.189920i
$831$	3244.31	0.135432
$832$	−24367.9	−1.01539
$833$	0	0
$834$	−139.737	−0.00580180
$835$	−4925.90	−0.204153
$836$	11215.2i	0.463977i
$837$	5764.28	0.238044
$838$	− 56085.4i	− 2.31198i
$839$	− 5614.44i	− 0.231027i	−0.993306	−	0.115514i	$-0.963149\pi$
$839$	− 5614.44i	− 0.231027i	0.993306	−	0.115514i	$-0.0368514\pi$
$840$	41.7276i	0.00171397i
$841$	−272.434	−0.0111704
$842$	12563.8	0.514226
$843$	− 1354.60i	− 0.0553438i
$844$	− 33976.4i	− 1.38568i
$845$	− 1547.97i	− 0.0630198i
$846$	19882.4	0.808004
$847$	7103.25i	0.288159i
$848$	31734.0	1.28508
$849$	2539.63	0.102662
$850$	0	0
$851$	17033.4	0.686132
$852$	248.390	0.00998792
$853$	3799.83i	0.152525i	0.997088	+	0.0762625i	$0.0242987\pi$
$853$	3799.83i	0.152525i	−0.997088	+	0.0762625i	$0.975701\pi$
$854$	−48380.5	−1.93858
$855$	− 2413.75i	− 0.0965480i
$856$	− 686.938i	− 0.0274288i
$857$	42210.3i	1.68247i	0.540669	+	0.841235i	$0.318171\pi$
$857$	42210.3i	1.68247i	−0.540669	+	0.841235i	$0.681829\pi$
$858$	2960.00	0.117777
$859$	−3132.98	−0.124442	−0.0622212	−	0.998062i	$-0.519818\pi$
$859$	−3132.98	−0.124442	−0.0622212	+	0.998062i	$0.519818\pi$
$860$	1749.58i	0.0693724i
$861$	− 2492.86i	− 0.0986718i
$862$	6453.58i	0.255000i
$863$	31934.9	1.25965	0.629824	−	0.776738i	$-0.283127\pi$
$863$	31934.9	1.25965	0.629824	+	0.776738i	$0.283127\pi$
$864$	5726.22i	0.225474i
$865$	640.396	0.0251724
$866$	−65266.8	−2.56104
$867$	0	0
$868$	−48161.8	−1.88332
$869$	41473.5	1.61898
$870$	511.317i	0.0199256i
$871$	29195.4	1.13576
$872$	269.400i	0.0104622i
$873$	− 42699.4i	− 1.65539i
$874$	13674.5i	0.529230i
$875$	12215.6	0.471956
$876$	−1217.33	−0.0469517
$877$	− 15340.7i	− 0.590670i	−0.955394	−	0.295335i	$-0.904569\pi$
$877$	− 15340.7i	− 0.590670i	0.955394	−	0.295335i	$-0.0954312\pi$
$878$	28921.9i	1.11169i
$879$	2277.87i	0.0874068i
$880$	−4287.91	−0.164256
$881$	46287.9i	1.77012i	0.465472	+	0.885062i	$0.345884\pi$
$881$	46287.9i	1.77012i	−0.465472	+	0.885062i	$0.654116\pi$
$882$	−32086.6	−1.22496
$883$	−26455.9	−1.00828	−0.504140	−	0.863622i	$-0.668190\pi$
$883$	−26455.9	−1.00828	−0.504140	+	0.863622i	$0.668190\pi$
$884$	0	0
$885$	621.348	0.0236004
$886$	−52456.0	−1.98904
$887$	− 18030.9i	− 0.682546i	−0.939964	−	0.341273i	$-0.889142\pi$
$887$	− 18030.9i	− 0.682546i	0.939964	−	0.341273i	$-0.110858\pi$
$888$	190.242	0.00718932
$889$	50133.0i	1.89135i
$890$	− 4682.31i	− 0.176350i
$891$	23170.5i	0.871202i
$892$	−926.327	−0.0347710
$893$	8687.85	0.325563
$894$	− 3934.69i	− 0.147199i
$895$	8105.77i	0.302733i
$896$	6444.68i	0.240292i
$897$	1745.87	0.0649864
$898$	− 38130.4i	− 1.41696i
$899$	39669.1	1.47168
$900$	24365.9	0.902440
$901$	0	0
$902$	29510.7	1.08936
$903$	−1290.22	−0.0475481
$904$	1757.27i	0.0646526i
$905$	−1863.84	−0.0684599
$906$	249.933i	0.00916498i
$907$	45743.1i	1.67461i	0.546733	+	0.837307i	$0.315871\pi$
$907$	45743.1i	1.67461i	−0.546733	+	0.837307i	$0.684129\pi$
$908$	− 5847.99i	− 0.213736i
$909$	−17886.3	−0.652642
$910$	10681.2	0.389096
$911$	− 1701.39i	− 0.0618766i	−0.999521	−	0.0309383i	$-0.990150\pi$
$911$	− 1701.39i	− 0.0618766i	0.999521	−	0.0309383i	$-0.00984954\pi$
$912$	1325.74i	0.0481355i
$913$	− 19178.5i	− 0.695197i
$914$	−2747.94	−0.0994462
$915$	− 399.673i	− 0.0144402i
$916$	20814.1	0.750782
$917$	6378.64	0.229707
$918$	0	0
$919$	30814.5	1.10607	0.553035	−	0.833158i	$-0.313470\pi$
$919$	30814.5	1.10607	0.553035	+	0.833158i	$0.313470\pi$
$920$	−291.357	−0.0104410
$921$	− 2976.80i	− 0.106503i
$922$	−25609.3	−0.914747
$923$	4273.79i	0.152409i
$924$	2621.61i	0.0933383i
$925$	− 27415.9i	− 0.974517i
$926$	−4651.93	−0.165088
$927$	−23397.2	−0.828982
$928$	39407.1i	1.39397i
$929$	− 4093.21i	− 0.144558i	−0.997384	−	0.0722788i	$-0.976973\pi$
$929$	− 4093.21i	− 0.144558i	0.997384	−	0.0722788i	$-0.0230271\pi$
$930$	− 822.477i	− 0.0290001i
$931$	−14020.6	−0.493563
$932$	37837.4i	1.32984i
$933$	435.018	0.0152646
$934$	−11616.5	−0.406963
$935$	0	0
$936$	−2909.15	−0.101590
$937$	16517.3	0.575877	0.287939	−	0.957649i	$-0.407030\pi$
$937$	16517.3	0.575877	0.287939	+	0.957649i	$0.407030\pi$
$938$	53453.6i	1.86068i
$939$	−1056.11	−0.0367036
$940$	− 2753.88i	− 0.0955548i
$941$	6860.74i	0.237677i	0.992914	+	0.118838i	$0.0379170\pi$
$941$	6860.74i	0.237677i	−0.992914	+	0.118838i	$0.962083\pi$
$942$	− 199.084i	− 0.00688589i
$943$	17406.0	0.601080
$944$	50915.3	1.75546
$945$	− 1132.24i	− 0.0389754i
$946$	− 15273.8i	− 0.524941i
$947$	− 33298.8i	− 1.14262i	−0.820733	−	0.571312i	$-0.806435\pi$
$947$	− 33298.8i	− 1.14262i	0.820733	−	0.571312i	$-0.193565\pi$
$948$	−4064.57	−0.139252
$949$	− 20945.2i	− 0.716450i
$950$	22009.6	0.751669
$951$	1176.65	0.0401215
$952$	0	0
$953$	−24857.5	−0.844925	−0.422462	−	0.906380i	$-0.638834\pi$
$953$	−24857.5	−0.844925	−0.422462	+	0.906380i	$0.638834\pi$
$954$	−49432.9	−1.67762
$955$	− 1735.74i	− 0.0588138i
$956$	16897.8	0.571666
$957$	− 2159.32i	− 0.0729372i
$958$	34996.4i	1.18025i
$959$	11098.9i	0.373725i
$960$	368.566	0.0123911
$961$	−34018.6	−1.14191
$962$	− 48697.1i	− 1.63208i
$963$	9288.57i	0.310820i
$964$	− 12961.7i	− 0.433059i
$965$	3378.93	0.112717
$966$	3196.49i	0.106465i
$967$	−15832.2	−0.526504	−0.263252	−	0.964727i	$-0.584795\pi$
$967$	−15832.2	−0.526504	−0.263252	+	0.964727i	$0.584795\pi$
$968$	−553.943	−0.0183930
$969$	0	0
$970$	−12226.0	−0.404693
$971$	39521.9	1.30620	0.653098	−	0.757273i	$-0.273469\pi$
$971$	39521.9	1.30620	0.653098	+	0.757273i	$0.273469\pi$
$972$	− 6889.32i	− 0.227341i
$973$	2129.45	0.0701612
$974$	27966.8i	0.920036i
$975$	− 2810.03i	− 0.0923007i
$976$	− 32750.6i	− 1.07410i
$977$	11587.3	0.379438	0.189719	−	0.981838i	$-0.439242\pi$
$977$	11587.3	0.379438	0.189719	+	0.981838i	$0.439242\pi$
$978$	254.740	0.00832893
$979$	19773.7i	0.645525i
$980$	4444.25i	0.144864i
$981$	− 3642.75i	− 0.118557i
$982$	−30068.4	−0.977108
$983$	− 32119.5i	− 1.04217i	−0.853505	−	0.521085i	$-0.825528\pi$
$983$	− 32119.5i	− 1.04217i	0.853505	−	0.521085i	$-0.174472\pi$
$984$	194.404	0.00629815
$985$	8669.17	0.280429
$986$	0	0
$987$	2030.83	0.0654936
$988$	18911.5	0.608964
$989$	− 9008.80i	− 0.289649i
$990$	6679.40	0.214429
$991$	18717.3i	0.599976i	0.953943	+	0.299988i	$0.0969826\pi$
$991$	18717.3i	0.599976i	−0.953943	+	0.299988i	$0.903017\pi$
$992$	− 63388.2i	− 2.02881i
$993$	− 2551.54i	− 0.0815414i
$994$	−7824.83	−0.249687
$995$	−6083.32	−0.193823
$996$	1879.56i	0.0597955i
$997$	11611.3i	0.368840i	0.982848	+	0.184420i	$0.0590406\pi$
$997$	11611.3i	0.368840i	−0.982848	+	0.184420i	$0.940959\pi$
$998$	79527.6i	2.52245i
$999$	−5162.05	−0.163483

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.b.c.288.7		8
17.2	even	8		17.4.c.a.13.4	yes	8
17.4	even	4		289.4.a.f.1.1		8
17.8	even	8		17.4.c.a.4.1	✓	8
17.13	even	4		289.4.a.f.1.2		8
17.16	even	2	inner	289.4.b.c.288.8		8
51.2	odd	8		153.4.f.a.64.1		8
51.8	odd	8		153.4.f.a.55.4		8
68.19	odd	8		272.4.o.e.81.3		8
68.59	odd	8		272.4.o.e.225.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.c.a.4.1	✓	8	17.8	even	8
17.4.c.a.13.4	yes	8	17.2	even	8
153.4.f.a.55.4		8	51.8	odd	8
153.4.f.a.64.1		8	51.2	odd	8
272.4.o.e.81.3		8	68.19	odd	8
272.4.o.e.225.3		8	68.59	odd	8
289.4.a.f.1.1		8	17.4	even	4
289.4.a.f.1.2		8	17.13	even	4
289.4.b.c.288.7		8	1.1	even	1	trivial
289.4.b.c.288.8		8	17.16	even	2	inner

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	289.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+3.93651 q^{2} -0.423991i q^{3} +7.49613 q^{4} -1.95080i q^{5} -1.66905i q^{6} +25.4345i q^{7} -1.98349 q^{8} +26.8202 q^{9} +O(q^{10})\)	\(q+3.93651 q^{2} -0.423991i q^{3} +7.49613 q^{4} -1.95080i q^{5} -1.66905i q^{6} +25.4345i q^{7} -1.98349 q^{8} +26.8202 q^{9} -7.67934i q^{10} +32.4303i q^{11} -3.17829i q^{12} +54.6855 q^{13} +100.123i q^{14} -0.827121 q^{15} -67.7771 q^{16} +105.578 q^{18} +46.1336 q^{19} -14.6234i q^{20} +10.7840 q^{21} +127.662i q^{22} +75.2978i q^{23} +0.840984i q^{24} +121.194 q^{25} +215.270 q^{26} -22.8193i q^{27} +190.660i q^{28} -157.040i q^{29} -3.25597 q^{30} +252.606i q^{31} -250.937 q^{32} +13.7502 q^{33} +49.6175 q^{35} +201.048 q^{36} -226.214i q^{37} +181.606 q^{38} -23.1862i q^{39} +3.86940i q^{40} -231.163i q^{41} +42.4513 q^{42} -119.642 q^{43} +243.102i q^{44} -52.3209i q^{45} +296.411i q^{46} +188.319 q^{47} +28.7369i q^{48} -303.913 q^{49} +477.083 q^{50} +409.930 q^{52} -468.212 q^{53} -89.8285i q^{54} +63.2650 q^{55} -50.4491i q^{56} -19.5603i q^{57} -618.188i q^{58} -751.217 q^{59} -6.20021 q^{60} +483.210i q^{61} +994.385i q^{62} +682.159i q^{63} -445.601 q^{64} -106.680i q^{65} +54.1277 q^{66} +533.879 q^{67} +31.9256 q^{69} +195.320 q^{70} +78.1521i q^{71} -53.1977 q^{72} -383.013i q^{73} -890.494i q^{74} -51.3854i q^{75} +345.824 q^{76} -824.848 q^{77} -91.2727i q^{78} -1278.85i q^{79} +132.219i q^{80} +714.471 q^{81} -909.975i q^{82} -591.376 q^{83} +80.8382 q^{84} -470.973 q^{86} -66.5834 q^{87} -64.3253i q^{88} +609.729 q^{89} -205.962i q^{90} +1390.90i q^{91} +564.442i q^{92} +107.103 q^{93} +741.321 q^{94} -89.9974i q^{95} +106.395i q^{96} -1592.06i q^{97} -1196.36 q^{98} +869.788i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 36 q^{4} - 96 q^{8} - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 36 * q^4 - 96 * q^8 - 8 * q^9	\( 8 q - 8 q^{2} + 36 q^{4} - 96 q^{8} - 8 q^{9} + 88 q^{13} - 252 q^{15} + 420 q^{16} + 428 q^{18} + 52 q^{19} + 260 q^{21} + 140 q^{25} + 268 q^{26} + 120 q^{30} - 2336 q^{32} + 816 q^{33} + 1172 q^{35} + 264 q^{36} + 768 q^{38} + 136 q^{42} + 752 q^{43} + 368 q^{47} - 852 q^{49} + 468 q^{50} + 2564 q^{52} + 1156 q^{53} + 1996 q^{55} - 192 q^{59} + 3160 q^{60} + 3044 q^{64} - 1052 q^{66} + 764 q^{67} + 1812 q^{69} - 544 q^{70} - 1404 q^{72} - 896 q^{76} - 3084 q^{77} - 280 q^{81} - 496 q^{83} - 2952 q^{84} - 4244 q^{86} + 2860 q^{87} + 2156 q^{89} + 4012 q^{93} + 3392 q^{94} - 6728 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 36 * q^4 - 96 * q^8 - 8 * q^9 + 88 * q^13 - 252 * q^15 + 420 * q^16 + 428 * q^18 + 52 * q^19 + 260 * q^21 + 140 * q^25 + 268 * q^26 + 120 * q^30 - 2336 * q^32 + 816 * q^33 + 1172 * q^35 + 264 * q^36 + 768 * q^38 + 136 * q^42 + 752 * q^43 + 368 * q^47 - 852 * q^49 + 468 * q^50 + 2564 * q^52 + 1156 * q^53 + 1996 * q^55 - 192 * q^59 + 3160 * q^60 + 3044 * q^64 - 1052 * q^66 + 764 * q^67 + 1812 * q^69 - 544 * q^70 - 1404 * q^72 - 896 * q^76 - 3084 * q^77 - 280 * q^81 - 496 * q^83 - 2952 * q^84 - 4244 * q^86 + 2860 * q^87 + 2156 * q^89 + 4012 * q^93 + 3392 * q^94 - 6728 * q^98

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