LMFDB - Embedded newform 289.4.b.e.288.11

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 34 x^{10} + 124 x^{9} + 671 x^{8} - 1984 x^{7} - 5452 x^{6} + 8264 x^{5} + \cdots + 300356 $ x^12 - 4x^11 - 34x^10 + 124x^9 + 671x^8 - 1984x^7 - 5452x^6 + 8264x^5 + 24252x^4 + 25328x^3 - 31008x^2 - 174688*x + 300356
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			288.11
Root			$-3.86166 + 1.84776i$ of defining polynomial
Character	$\chi$	$=$	289.288
Dual form			289.4.b.e.288.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.86166 q^{2} -5.06554i q^{3} +15.6358 q^{4} +18.5634i q^{5} -24.6269i q^{6} +14.0210i q^{7} +37.1225 q^{8} +1.34032 q^{9} +O(q^{10})$	\(q+4.86166 q^{2} -5.06554i q^{3} +15.6358 q^{4} +18.5634i q^{5} -24.6269i q^{6} +14.0210i q^{7} +37.1225 q^{8} +1.34032 q^{9} +90.2489i q^{10} +19.4791i q^{11} -79.2036i q^{12} +29.9060 q^{13} +68.1655i q^{14} +94.0335 q^{15} +55.3912 q^{16} +6.51621 q^{18} +45.7882 q^{19} +290.253i q^{20} +71.0240 q^{21} +94.7006i q^{22} -89.3259i q^{23} -188.046i q^{24} -219.599 q^{25} +145.393 q^{26} -143.559i q^{27} +219.229i q^{28} -57.9077i q^{29} +457.159 q^{30} -161.949i q^{31} -27.6872 q^{32} +98.6719 q^{33} -260.277 q^{35} +20.9570 q^{36} +135.583i q^{37} +222.607 q^{38} -151.490i q^{39} +689.120i q^{40} -56.8918i q^{41} +345.295 q^{42} -52.1442 q^{43} +304.570i q^{44} +24.8809i q^{45} -434.272i q^{46} -482.699 q^{47} -280.586i q^{48} +146.411 q^{49} -1067.62 q^{50} +467.603 q^{52} +529.972 q^{53} -697.935i q^{54} -361.597 q^{55} +520.496i q^{56} -231.942i q^{57} -281.528i q^{58} +280.058 q^{59} +1470.29 q^{60} -586.656i q^{61} -787.341i q^{62} +18.7927i q^{63} -577.735 q^{64} +555.156i q^{65} +479.710 q^{66} +367.471 q^{67} -452.484 q^{69} -1265.38 q^{70} -60.5496i q^{71} +49.7563 q^{72} +368.086i q^{73} +659.161i q^{74} +1112.39i q^{75} +715.933 q^{76} -273.116 q^{77} -736.493i q^{78} +217.721i q^{79} +1028.25i q^{80} -691.015 q^{81} -276.589i q^{82} +594.154 q^{83} +1110.51 q^{84} -253.508 q^{86} -293.334 q^{87} +723.112i q^{88} -887.553 q^{89} +120.963i q^{90} +419.312i q^{91} -1396.68i q^{92} -820.358 q^{93} -2346.72 q^{94} +849.983i q^{95} +140.251i q^{96} +884.682i q^{97} +711.801 q^{98} +26.1083i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{2} + 16 q^{4} + 96 q^{8} + 36 q^{9}+O(q^{10}) $ 12 * q + 8 * q^2 + 16 * q^4 + 96 * q^8 + 36 * q^9	$ 12 q + 8 q^{2} + 16 q^{4} + 96 q^{8} + 36 q^{9} - 8 q^{13} + 192 q^{15} - 184 q^{16} + 352 q^{19} - 256 q^{21} + 492 q^{25} + 784 q^{26} + 744 q^{30} - 24 q^{32} - 1400 q^{33} - 632 q^{35} + 856 q^{36} - 624 q^{38} + 1664 q^{42} + 1200 q^{43} - 1512 q^{47} + 1052 q^{49} - 2856 q^{50} + 792 q^{52} + 2504 q^{53} - 1424 q^{55} + 3408 q^{59} + 2808 q^{60} + 272 q^{64} - 272 q^{66} - 1080 q^{67} - 344 q^{69} - 2600 q^{70} + 248 q^{72} - 896 q^{76} - 848 q^{77} - 2404 q^{81} + 2960 q^{83} + 4768 q^{84} - 1200 q^{86} + 160 q^{87} - 2144 q^{89} - 3800 q^{93} - 5984 q^{94} + 3464 q^{98}+O(q^{100}) $ 12 * q + 8 * q^2 + 16 * q^4 + 96 * q^8 + 36 * q^9 - 8 * q^13 + 192 * q^15 - 184 * q^16 + 352 * q^19 - 256 * q^21 + 492 * q^25 + 784 * q^26 + 744 * q^30 - 24 * q^32 - 1400 * q^33 - 632 * q^35 + 856 * q^36 - 624 * q^38 + 1664 * q^42 + 1200 * q^43 - 1512 * q^47 + 1052 * q^49 - 2856 * q^50 + 792 * q^52 + 2504 * q^53 - 1424 * q^55 + 3408 * q^59 + 2808 * q^60 + 272 * q^64 - 272 * q^66 - 1080 * q^67 - 344 * q^69 - 2600 * q^70 + 248 * q^72 - 896 * q^76 - 848 * q^77 - 2404 * q^81 + 2960 * q^83 + 4768 * q^84 - 1200 * q^86 + 160 * q^87 - 2144 * q^89 - 3800 * q^93 - 5984 * q^94 + 3464 * 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 $

$2$	4.86166	1.71886	0.859429	−	0.511255i	$-0.170819\pi$
$2$	4.86166	1.71886	0.859429	+	0.511255i	$0.170819\pi$
$3$	− 5.06554i	− 0.974863i	−0.873161	−	0.487432i	$-0.837934\pi$
$3$	− 5.06554i	− 0.974863i	0.873161	−	0.487432i	$-0.162066\pi$
$4$	15.6358	1.95447
$5$	18.5634i	1.66036i	0.557497	+	0.830179i	$0.311762\pi$
$5$	18.5634i	1.66036i	−0.557497	+	0.830179i	$0.688238\pi$
$6$	− 24.6269i	− 1.67565i
$7$	14.0210i	0.757064i	0.925588	+	0.378532i	$0.123571\pi$
$7$	14.0210i	0.757064i	−0.925588	+	0.378532i	$0.876429\pi$
$8$	37.1225	1.64060
$9$	1.34032	0.0496417
$10$	90.2489i	2.85392i
$11$	19.4791i	0.533924i	0.963707	+	0.266962i	$0.0860197\pi$
$11$	19.4791i	0.533924i	−0.963707	+	0.266962i	$0.913980\pi$
$12$	− 79.2036i	− 1.90534i
$13$	29.9060	0.638033	0.319016	−	0.947749i	$-0.396648\pi$
$13$	29.9060	0.638033	0.319016	+	0.947749i	$0.396648\pi$
$14$	68.1655i	1.30128i
$15$	94.0335	1.61862
$16$	55.3912	0.865487
$17$	0	0
$17$	0	0
$18$	6.51621	0.0853269
$19$	45.7882	0.552870	0.276435	−	0.961033i	$-0.410847\pi$
$19$	45.7882	0.552870	0.276435	+	0.961033i	$0.410847\pi$
$20$	290.253i	3.24512i
$21$	71.0240	0.738034
$22$	94.7006i	0.917738i
$23$	− 89.3259i	− 0.809814i	−0.914358	−	0.404907i	$-0.867304\pi$
$23$	− 89.3259i	− 0.809814i	0.914358	−	0.404907i	$-0.132696\pi$
$24$	− 188.046i	− 1.59936i
$25$	−219.599	−1.75679
$26$	145.393	1.09669
$27$	− 143.559i	− 1.02326i
$28$	219.229i	1.47966i
$29$	− 57.9077i	− 0.370800i	−0.982663	−	0.185400i	$-0.940642\pi$
$29$	− 57.9077i	− 0.370800i	0.982663	−	0.185400i	$-0.0593580\pi$
$30$	457.159	2.78218
$31$	− 161.949i	− 0.938286i	−0.883122	−	0.469143i	$-0.844563\pi$
$31$	− 161.949i	− 0.938286i	0.883122	−	0.469143i	$-0.155437\pi$
$32$	−27.6872	−0.152952
$33$	98.6719	0.520502
$34$	0	0
$35$	−260.277	−1.25700
$36$	20.9570	0.0970232
$37$	135.583i	0.602426i	0.953557	+	0.301213i	$0.0973915\pi$
$37$	135.583i	0.602426i	−0.953557	+	0.301213i	$0.902608\pi$
$38$	222.607	0.950304
$39$	− 151.490i	− 0.621994i
$40$	689.120i	2.72398i
$41$	− 56.8918i	− 0.216708i	−0.994112	−	0.108354i	$-0.965442\pi$
$41$	− 56.8918i	− 0.216708i	0.994112	−	0.108354i	$-0.0345579\pi$
$42$	345.295	1.26857
$43$	−52.1442	−0.184928	−0.0924642	−	0.995716i	$-0.529474\pi$
$43$	−52.1442	−0.184928	−0.0924642	+	0.995716i	$0.529474\pi$
$44$	304.570i	1.04354i
$45$	24.8809i	0.0824229i
$46$	− 434.272i	− 1.39196i
$47$	−482.699	−1.49806	−0.749030	−	0.662536i	$-0.769480\pi$
$47$	−482.699	−1.49806	−0.749030	+	0.662536i	$0.769480\pi$
$48$	− 280.586i	− 0.843731i
$49$	146.411	0.426855
$50$	−1067.62	−3.01967
$51$	0	0
$52$	467.603	1.24702
$53$	529.972	1.37353	0.686766	−	0.726879i	$-0.259030\pi$
$53$	529.972	1.37353	0.686766	+	0.726879i	$0.259030\pi$
$54$	− 697.935i	− 1.75883i
$55$	−361.597	−0.886504
$56$	520.496i	1.24204i
$57$	− 231.942i	− 0.538972i
$58$	− 281.528i	− 0.637352i
$59$	280.058	0.617973	0.308986	−	0.951066i	$-0.400010\pi$
$59$	280.058	0.617973	0.308986	+	0.951066i	$0.400010\pi$
$60$	1470.29	3.16355
$61$	− 586.656i	− 1.23137i	−0.787992	−	0.615686i	$-0.788879\pi$
$61$	− 586.656i	− 1.23137i	0.787992	−	0.615686i	$-0.211121\pi$
$62$	− 787.341i	− 1.61278i
$63$	18.7927i	0.0375819i
$64$	−577.735	−1.12839
$65$	555.156i	1.05936i
$66$	479.710	0.894669
$67$	367.471	0.670056	0.335028	−	0.942208i	$-0.391254\pi$
$67$	367.471	0.670056	0.335028	+	0.942208i	$0.391254\pi$
$68$	0	0
$69$	−452.484	−0.789458
$70$	−1265.38	−2.16060
$71$	− 60.5496i	− 0.101210i	−0.998719	−	0.0506051i	$-0.983885\pi$
$71$	− 60.5496i	− 0.101210i	0.998719	−	0.0506051i	$-0.0161150\pi$
$72$	49.7563	0.0814421
$73$	368.086i	0.590154i	0.955473	+	0.295077i	$0.0953453\pi$
$73$	368.086i	0.590154i	−0.955473	+	0.295077i	$0.904655\pi$
$74$	659.161i	1.03548i
$75$	1112.39i	1.71263i
$76$	715.933	1.08057
$77$	−273.116	−0.404214
$78$	− 736.493i	− 1.06912i
$79$	217.721i	0.310070i	0.987909	+	0.155035i	$0.0495490\pi$
$79$	217.721i	0.310070i	−0.987909	+	0.155035i	$0.950451\pi$
$80$	1028.25i	1.43702i
$81$	−691.015	−0.947894
$82$	− 276.589i	− 0.372490i
$83$	594.154	0.785746	0.392873	−	0.919593i	$-0.371481\pi$
$83$	594.154	0.785746	0.392873	+	0.919593i	$0.371481\pi$
$84$	1110.51	1.44247
$85$	0	0
$86$	−253.508	−0.317866
$87$	−293.334	−0.361479
$88$	723.112i	0.875955i
$89$	−887.553	−1.05708	−0.528542	−	0.848907i	$-0.677261\pi$
$89$	−887.553	−1.05708	−0.528542	+	0.848907i	$0.677261\pi$
$90$	120.963i	0.141673i
$91$	419.312i	0.483031i
$92$	− 1396.68i	− 1.58276i
$93$	−820.358	−0.914701
$94$	−2346.72	−2.57495
$95$	849.983i	0.917962i
$96$	140.251i	0.149107i
$97$	884.682i	0.926040i	0.886348	+	0.463020i	$0.153234\pi$
$97$	884.682i	0.926040i	−0.886348	+	0.463020i	$0.846766\pi$
$98$	711.801	0.733702
$99$	26.1083i	0.0265048i
$100$	−3433.60	−3.43360
$101$	−1845.31	−1.81798	−0.908988	−	0.416822i	$-0.863144\pi$
$101$	−1845.31	−1.81798	−0.908988	+	0.416822i	$0.863144\pi$
$102$	0	0
$103$	−1823.07	−1.74400	−0.872002	−	0.489502i	$-0.837178\pi$
$103$	−1823.07	−1.74400	−0.872002	+	0.489502i	$0.837178\pi$
$104$	1110.19	1.04676
$105$	1318.44i	1.22540i
$106$	2576.54	2.36091
$107$	− 1855.35i	− 1.67629i	−0.545445	−	0.838146i	$-0.683639\pi$
$107$	− 1855.35i	− 1.67629i	0.545445	−	0.838146i	$-0.316361\pi$
$108$	− 2244.66i	− 1.99993i
$109$	1387.46i	1.21922i	0.792702	+	0.609610i	$0.208674\pi$
$109$	1387.46i	1.21922i	−0.792702	+	0.609610i	$0.791326\pi$
$110$	−1757.96	−1.52377
$111$	686.803	0.587283
$112$	776.640i	0.655229i
$113$	− 613.115i	− 0.510416i	−0.966886	−	0.255208i	$-0.917856\pi$
$113$	− 613.115i	− 0.510416i	0.966886	−	0.255208i	$-0.0821439\pi$
$114$	− 1127.62i	− 0.926417i
$115$	1658.19	1.34458
$116$	− 905.432i	− 0.724717i
$117$	40.0837	0.0316730
$118$	1361.55	1.06221
$119$	0	0
$120$	3490.76	2.65551
$121$	951.566	0.714926
$122$	− 2852.13i	− 2.11655i
$123$	−288.188	−0.211260
$124$	− 2532.19i	− 1.83385i
$125$	− 1756.07i	− 1.25654i
$126$	91.3639i	0.0645979i
$127$	−111.688	−0.0780368	−0.0390184	−	0.999238i	$-0.512423\pi$
$127$	−111.688	−0.0780368	−0.0390184	+	0.999238i	$0.512423\pi$
$128$	−2587.26	−1.78659
$129$	264.139i	0.180280i
$130$	2698.98i	1.82089i
$131$	− 2132.04i	− 1.42196i	−0.703212	−	0.710981i	$-0.748251\pi$
$131$	− 2132.04i	− 1.42196i	0.703212	−	0.710981i	$-0.251749\pi$
$132$	1542.81	1.01731
$133$	641.996i	0.418558i
$134$	1786.52	1.15173
$135$	2664.94	1.69897
$136$	0	0
$137$	3087.68	1.92554	0.962769	−	0.270327i	$-0.0871317\pi$
$137$	3087.68	1.92554	0.962769	+	0.270327i	$0.0871317\pi$
$138$	−2199.82	−1.35697
$139$	469.825i	0.286691i	0.989673	+	0.143346i	$0.0457860\pi$
$139$	469.825i	0.286691i	−0.989673	+	0.143346i	$0.954214\pi$
$140$	−4069.64	−2.45677
$141$	2445.13i	1.46040i
$142$	− 294.372i	− 0.173966i
$143$	582.540i	0.340661i
$144$	74.2421	0.0429642
$145$	1074.96	0.615660
$146$	1789.51i	1.01439i
$147$	− 741.651i	− 0.416125i
$148$	2119.95i	1.17742i
$149$	−2209.36	−1.21475	−0.607374	−	0.794416i	$-0.707777\pi$
$149$	−2209.36	−1.21475	−0.607374	+	0.794416i	$0.707777\pi$
$150$	5408.05i	2.94377i
$151$	752.366	0.405475	0.202737	−	0.979233i	$-0.435016\pi$
$151$	752.366	0.405475	0.202737	+	0.979233i	$0.435016\pi$
$152$	1699.77	0.907038
$153$	0	0
$154$	−1327.80	−0.694787
$155$	3006.32	1.55789
$156$	− 2368.66i	− 1.21567i
$157$	579.544	0.294603	0.147301	−	0.989092i	$-0.452941\pi$
$157$	579.544	0.294603	0.147301	+	0.989092i	$0.452941\pi$
$158$	1058.49i	0.532966i
$159$	− 2684.59i	− 1.33901i
$160$	− 513.968i	− 0.253955i
$161$	1252.44	0.613081
$162$	−3359.48	−1.62929
$163$	− 1777.74i	− 0.854253i	−0.904192	−	0.427126i	$-0.859526\pi$
$163$	− 1777.74i	− 0.854253i	0.904192	−	0.427126i	$-0.140474\pi$
$164$	− 889.548i	− 0.423549i
$165$	1831.68i	0.864221i
$166$	2888.58	1.35059
$167$	− 3134.84i	− 1.45258i	−0.687388	−	0.726291i	$-0.741243\pi$
$167$	− 3134.84i	− 1.45258i	0.687388	−	0.726291i	$-0.258757\pi$
$168$	2636.59	1.21082
$169$	−1302.63	−0.592914
$170$	0	0
$171$	61.3710	0.0274454
$172$	−815.315	−0.361437
$173$	− 1169.33i	− 0.513886i	−0.966427	−	0.256943i	$-0.917285\pi$
$173$	− 1169.33i	− 0.513886i	0.966427	−	0.256943i	$-0.0827152\pi$
$174$	−1426.09	−0.621331
$175$	− 3079.00i	− 1.33000i
$176$	1078.97i	0.462104i
$177$	− 1418.64i	− 0.602439i
$178$	−4314.99	−1.81698
$179$	1552.54	0.648281	0.324140	−	0.946009i	$-0.394925\pi$
$179$	1552.54	0.648281	0.324140	+	0.946009i	$0.394925\pi$
$180$	389.033i	0.161093i
$181$	− 1495.92i	− 0.614313i	−0.951659	−	0.307156i	$-0.900623\pi$
$181$	− 1495.92i	− 0.614313i	0.951659	−	0.307156i	$-0.0993775\pi$
$182$	2038.55i	0.830262i
$183$	−2971.73	−1.20042
$184$	− 3316.00i	− 1.32858i
$185$	−2516.88	−1.00024
$186$	−3988.30	−1.57224
$187$	0	0
$188$	−7547.37	−2.92792
$189$	2012.84	0.774671
$190$	4132.33i	1.57785i
$191$	3008.79	1.13983	0.569917	−	0.821702i	$-0.306975\pi$
$191$	3008.79	1.13983	0.569917	+	0.821702i	$0.306975\pi$
$192$	2926.54i	1.10002i
$193$	3893.56i	1.45215i	0.687616	+	0.726074i	$0.258657\pi$
$193$	3893.56i	1.45215i	−0.687616	+	0.726074i	$0.741343\pi$
$194$	4301.03i	1.59173i
$195$	2812.16	1.03273
$196$	2289.25	0.834275
$197$	946.676i	0.342375i	0.985238	+	0.171187i	$0.0547604\pi$
$197$	946.676i	0.342375i	−0.985238	+	0.171187i	$0.945240\pi$
$198$	126.930i	0.0455581i
$199$	1765.84i	0.629031i	0.949252	+	0.314515i	$0.101842\pi$
$199$	1765.84i	0.629031i	−0.949252	+	0.314515i	$0.898158\pi$
$200$	−8152.07	−2.88219
$201$	− 1861.44i	− 0.653213i
$202$	−8971.29	−3.12484
$203$	811.925	0.280719
$204$	0	0
$205$	1056.10	0.359812
$206$	−8863.15	−2.99769
$207$	− 119.726i	− 0.0402005i
$208$	1656.53	0.552209
$209$	891.910i	0.295190i
$210$	6409.83i	2.10629i
$211$	− 371.398i	− 0.121176i	−0.998163	−	0.0605879i	$-0.980702\pi$
$211$	− 371.398i	− 0.121176i	0.998163	−	0.0605879i	$-0.0192975\pi$
$212$	8286.52	2.68453
$213$	−306.716	−0.0986660
$214$	− 9020.08i	− 2.88131i
$215$	− 967.973i	− 0.307047i
$216$	− 5329.28i	− 1.67876i
$217$	2270.69	0.710342
$218$	6745.38i	2.09566i
$219$	1864.56	0.575319
$220$	−5653.85	−1.73265
$221$	0	0
$222$	3339.00	1.00946
$223$	−2573.90	−0.772919	−0.386459	−	0.922306i	$-0.626302\pi$
$223$	−2573.90	−0.772919	−0.386459	+	0.922306i	$0.626302\pi$
$224$	− 388.203i	− 0.115794i
$225$	−294.334	−0.0872100
$226$	− 2980.76i	− 0.877332i
$227$	5204.65i	1.52178i	0.648879	+	0.760892i	$0.275238\pi$
$227$	5204.65i	1.52178i	−0.648879	+	0.760892i	$0.724762\pi$
$228$	− 3626.59i	− 1.05341i
$229$	−3198.73	−0.923048	−0.461524	−	0.887128i	$-0.652697\pi$
$229$	−3198.73	−0.923048	−0.461524	+	0.887128i	$0.652697\pi$
$230$	8061.56	2.31115
$231$	1383.48i	0.394053i
$232$	− 2149.68i	− 0.608334i
$233$	853.101i	0.239865i	0.992782	+	0.119932i	$0.0382678\pi$
$233$	853.101i	0.239865i	−0.992782	+	0.119932i	$0.961732\pi$
$234$	194.873	0.0544414
$235$	− 8960.51i	− 2.48732i
$236$	4378.92	1.20781
$237$	1102.87	0.302276
$238$	0	0
$239$	1892.67	0.512246	0.256123	−	0.966644i	$-0.417555\pi$
$239$	1892.67	0.512246	0.256123	+	0.966644i	$0.417555\pi$
$240$	5208.62	1.40090
$241$	1849.42i	0.494322i	0.968974	+	0.247161i	$0.0794976\pi$
$241$	1849.42i	0.494322i	−0.968974	+	0.247161i	$0.920502\pi$
$242$	4626.19	1.22886
$243$	− 375.731i	− 0.0991900i
$244$	− 9172.83i	− 2.40668i
$245$	2717.88i	0.708732i
$246$	−1401.07	−0.363126
$247$	1369.34	0.352749
$248$	− 6011.95i	− 1.53935i
$249$	− 3009.71i	− 0.765995i
$250$	− 8537.43i	− 2.15982i
$251$	1026.39	0.258109	0.129055	−	0.991637i	$-0.458806\pi$
$251$	1026.39	0.258109	0.129055	+	0.991637i	$0.458806\pi$
$252$	293.839i	0.0734527i
$253$	1739.98	0.432379
$254$	−542.987	−0.134134
$255$	0	0
$256$	−7956.49	−1.94250
$257$	−2615.84	−0.634910	−0.317455	−	0.948273i	$-0.602828\pi$
$257$	−2615.84	−0.634910	−0.317455	+	0.948273i	$0.602828\pi$
$258$	1284.15i	0.309875i
$259$	−1901.02	−0.456075
$260$	8680.29i	2.07049i
$261$	− 77.6151i	− 0.0184071i
$262$	− 10365.2i	− 2.44415i
$263$	4992.16	1.17045	0.585227	−	0.810869i	$-0.301005\pi$
$263$	4992.16	1.17045	0.585227	+	0.810869i	$0.301005\pi$
$264$	3662.95	0.853936
$265$	9838.06i	2.28056i
$266$	3121.17i	0.719441i
$267$	4495.94i	1.03051i
$268$	5745.70	1.30961
$269$	3410.52i	0.773023i	0.922284	+	0.386512i	$0.126320\pi$
$269$	3410.52i	0.773023i	−0.922284	+	0.386512i	$0.873680\pi$
$270$	12956.0	2.92029
$271$	75.0911	0.0168319	0.00841597	−	0.999965i	$-0.497321\pi$
$271$	75.0911	0.0168319	0.00841597	+	0.999965i	$0.497321\pi$
$272$	0	0
$273$	2124.04	0.470889
$274$	15011.3	3.30972
$275$	− 4277.58i	− 0.937992i
$276$	−7074.93	−1.54297
$277$	3441.88i	0.746580i	0.927715	+	0.373290i	$0.121770\pi$
$277$	3441.88i	0.746580i	−0.927715	+	0.373290i	$0.878230\pi$
$278$	2284.13i	0.492781i
$279$	− 217.064i	− 0.0465781i
$280$	−9662.16	−2.06223
$281$	−1673.05	−0.355181	−0.177591	−	0.984104i	$-0.556830\pi$
$281$	−1673.05	−0.355181	−0.177591	+	0.984104i	$0.556830\pi$
$282$	11887.4i	2.51023i
$283$	6792.22i	1.42670i	0.700809	+	0.713349i	$0.252822\pi$
$283$	6792.22i	1.42670i	−0.700809	+	0.713349i	$0.747178\pi$
$284$	− 946.740i	− 0.197812i
$285$	4305.62	0.894887
$286$	2832.11i	0.585547i
$287$	797.682	0.164062
$288$	−37.1098	−0.00759277
$289$	0	0
$290$	5226.11	1.05823
$291$	4481.39	0.902762
$292$	5755.31i	1.15344i
$293$	−6436.90	−1.28344	−0.641720	−	0.766939i	$-0.721779\pi$
$293$	−6436.90	−1.28344	−0.641720	+	0.766939i	$0.721779\pi$
$294$	− 3605.66i	− 0.715259i
$295$	5198.81i	1.02606i
$296$	5033.20i	0.988340i
$297$	2796.39	0.546341
$298$	−10741.2	−2.08798
$299$	− 2671.38i	− 0.516688i
$300$	17393.0i	3.34729i
$301$	− 731.115i	− 0.140003i
$302$	3657.75	0.696953
$303$	9347.51i	1.77228i
$304$	2536.26	0.478501
$305$	10890.3	2.04452
$306$	0	0
$307$	5129.87	0.953672	0.476836	−	0.878992i	$-0.341784\pi$
$307$	5129.87	0.953672	0.476836	+	0.878992i	$0.341784\pi$
$308$	−4270.38	−0.790025
$309$	9234.83i	1.70017i
$310$	14615.7	2.67779
$311$	3422.67i	0.624058i	0.950073	+	0.312029i	$0.101009\pi$
$311$	3422.67i	0.624058i	−0.950073	+	0.312029i	$0.898991\pi$
$312$	− 5623.69i	− 1.02044i
$313$	− 4283.53i	− 0.773544i	−0.922175	−	0.386772i	$-0.873590\pi$
$313$	− 4283.53i	− 0.773544i	0.922175	−	0.386772i	$-0.126410\pi$
$314$	2817.55	0.506380
$315$	−348.856	−0.0623994
$316$	3404.23i	0.606022i
$317$	390.350i	0.0691617i	0.999402	+	0.0345808i	$0.0110096\pi$
$317$	390.350i	0.0691617i	−0.999402	+	0.0345808i	$0.988990\pi$
$318$	− 13051.6i	− 2.30156i
$319$	1127.99	0.197979
$320$	− 10724.7i	− 1.87353i
$321$	−9398.34	−1.63416
$322$	6088.94	1.05380
$323$	0	0
$324$	−10804.5	−1.85263
$325$	−6567.31	−1.12089
$326$	− 8642.77i	− 1.46834i
$327$	7028.25	1.18857
$328$	− 2111.97i	− 0.355531i
$329$	− 6767.93i	− 1.13413i
$330$	8905.03i	1.48547i
$331$	−3824.89	−0.635151	−0.317575	−	0.948233i	$-0.602869\pi$
$331$	−3824.89	−0.635151	−0.317575	+	0.948233i	$0.602869\pi$
$332$	9290.06	1.53572
$333$	181.726i	0.0299054i
$334$	− 15240.5i	− 2.49678i
$335$	6821.51i	1.11253i
$336$	3934.10	0.638758
$337$	− 2376.90i	− 0.384208i	−0.981375	−	0.192104i	$-0.938469\pi$
$337$	− 2376.90i	− 0.384208i	0.981375	−	0.192104i	$-0.0615311\pi$
$338$	−6332.96	−1.01914
$339$	−3105.76	−0.497586
$340$	0	0
$341$	3154.61	0.500973
$342$	298.365	0.0471747
$343$	6862.04i	1.08022i
$344$	−1935.73	−0.303394
$345$	− 8399.62i	− 1.31078i
$346$	− 5684.87i	− 0.883296i
$347$	− 11923.2i	− 1.84459i	−0.386491	−	0.922293i	$-0.626313\pi$
$347$	− 11923.2i	− 1.84459i	0.386491	−	0.922293i	$-0.373687\pi$
$348$	−4586.50	−0.706500
$349$	7389.94	1.13345	0.566726	−	0.823906i	$-0.308210\pi$
$349$	7389.94	1.13345	0.566726	+	0.823906i	$0.308210\pi$
$350$	− 14969.1i	− 2.28608i
$351$	− 4293.27i	− 0.652871i
$352$	− 539.321i	− 0.0816645i
$353$	2966.18	0.447235	0.223617	−	0.974677i	$-0.428213\pi$
$353$	2966.18	0.447235	0.223617	+	0.974677i	$0.428213\pi$
$354$	− 6896.96i	− 1.03551i
$355$	1124.01	0.168045
$356$	−13877.6	−2.06604
$357$	0	0
$358$	7547.93	1.11430
$359$	6526.33	0.959460	0.479730	−	0.877416i	$-0.340735\pi$
$359$	6526.33	0.959460	0.479730	+	0.877416i	$0.340735\pi$
$360$	923.644i	0.135223i
$361$	−4762.44	−0.694335
$362$	− 7272.64i	− 1.05592i
$363$	− 4820.19i	− 0.696955i
$364$	6556.27i	0.944071i
$365$	−6832.92	−0.979867
$366$	−14447.6	−2.06335
$367$	− 5896.51i	− 0.838679i	−0.907829	−	0.419340i	$-0.862262\pi$
$367$	− 5896.51i	− 0.838679i	0.907829	−	0.419340i	$-0.137738\pi$
$368$	− 4947.86i	− 0.700884i
$369$	− 76.2536i	− 0.0107577i
$370$	−12236.2	−1.71928
$371$	7430.74i	1.03985i
$372$	−12826.9	−1.78776
$373$	−9234.98	−1.28195	−0.640977	−	0.767560i	$-0.721471\pi$
$373$	−9234.98	−1.28195	−0.640977	+	0.767560i	$0.721471\pi$
$374$	0	0
$375$	−8895.45	−1.22496
$376$	−17919.0	−2.45772
$377$	− 1731.79i	− 0.236582i
$378$	9785.77	1.33155
$379$	1449.66i	0.196475i	0.995163	+	0.0982373i	$0.0313204\pi$
$379$	1449.66i	0.196475i	−0.995163	+	0.0982373i	$0.968680\pi$
$380$	13290.1i	1.79413i
$381$	565.758i	0.0760752i
$382$	14627.7	1.95921
$383$	−8159.07	−1.08854	−0.544268	−	0.838911i	$-0.683192\pi$
$383$	−8159.07	−1.08854	−0.544268	+	0.838911i	$0.683192\pi$
$384$	13105.8i	1.74168i
$385$	− 5069.96i	− 0.671140i
$386$	18929.2i	2.49604i
$387$	−69.8902	−0.00918015
$388$	13832.7i	1.80992i
$389$	1467.86	0.191320	0.0956598	−	0.995414i	$-0.469504\pi$
$389$	1467.86	0.191320	0.0956598	+	0.995414i	$0.469504\pi$
$390$	13671.8	1.77512
$391$	0	0
$392$	5435.15	0.700298
$393$	−10799.9	−1.38622
$394$	4602.42i	0.588494i
$395$	−4041.63	−0.514827
$396$	408.223i	0.0518030i
$397$	6018.22i	0.760821i	0.924818	+	0.380411i	$0.124217\pi$
$397$	6018.22i	0.760821i	−0.924818	+	0.380411i	$0.875783\pi$
$398$	8584.92i	1.08121i
$399$	3252.06	0.408036
$400$	−12163.8	−1.52048
$401$	− 5899.13i	− 0.734634i	−0.930096	−	0.367317i	$-0.880276\pi$
$401$	− 5899.13i	− 0.734634i	0.930096	−	0.367317i	$-0.119724\pi$
$402$	− 9049.70i	− 1.12278i
$403$	− 4843.24i	− 0.598657i
$404$	−28852.9	−3.55318
$405$	− 12827.6i	− 1.57384i
$406$	3947.31	0.482516
$407$	−2641.04	−0.321649
$408$	0	0
$409$	−9261.09	−1.11964	−0.559818	−	0.828616i	$-0.689129\pi$
$409$	−9261.09	−1.11964	−0.559818	+	0.828616i	$0.689129\pi$
$410$	5134.42	0.618466
$411$	− 15640.8i	− 1.87714i
$412$	−28505.1	−3.40861
$413$	3926.69i	0.467845i
$414$	− 582.066i	− 0.0690990i
$415$	11029.5i	1.30462i
$416$	−828.013	−0.0975881
$417$	2379.92	0.279485
$418$	4336.17i	0.507390i
$419$	8538.07i	0.995494i	0.867322	+	0.497747i	$0.165839\pi$
$419$	8538.07i	0.995494i	−0.867322	+	0.497747i	$0.834161\pi$
$420$	20614.9i	2.39501i
$421$	−1617.31	−0.187228	−0.0936140	−	0.995609i	$-0.529842\pi$
$421$	−1617.31	−0.187228	−0.0936140	+	0.995609i	$0.529842\pi$
$422$	− 1805.61i	− 0.208284i
$423$	−646.973	−0.0743662
$424$	19673.9	2.25342
$425$	0	0
$426$	−1491.15	−0.169593
$427$	8225.52	0.932227
$428$	− 29009.8i	− 3.27627i
$429$	2950.88	0.332097
$430$	− 4705.96i	− 0.527771i
$431$	− 2537.10i	− 0.283544i	−0.989899	−	0.141772i	$-0.954720\pi$
$431$	− 2537.10i	− 0.283544i	0.989899	−	0.141772i	$-0.0452801\pi$
$432$	− 7951.90i	− 0.885616i
$433$	−1833.33	−0.203474	−0.101737	−	0.994811i	$-0.532440\pi$
$433$	−1833.33	−0.203474	−0.101737	+	0.994811i	$0.532440\pi$
$434$	11039.3	1.22098
$435$	− 5445.26i	− 0.600185i
$436$	21694.1i	2.38293i
$437$	− 4090.07i	− 0.447722i
$438$	9064.84	0.988892
$439$	10398.5i	1.13051i	0.824915	+	0.565257i	$0.191223\pi$
$439$	10398.5i	1.13051i	−0.824915	+	0.565257i	$0.808777\pi$
$440$	−13423.4	−1.45440
$441$	196.238	0.0211898
$442$	0	0
$443$	−3984.14	−0.427296	−0.213648	−	0.976911i	$-0.568535\pi$
$443$	−3984.14	−0.427296	−0.213648	+	0.976911i	$0.568535\pi$
$444$	10738.7	1.14783
$445$	− 16476.0i	− 1.75514i
$446$	−12513.4	−1.32854
$447$	11191.6i	1.18421i
$448$	− 8100.43i	− 0.854262i
$449$	13184.1i	1.38574i	0.721064	+	0.692868i	$0.243653\pi$
$449$	13184.1i	1.38574i	−0.721064	+	0.692868i	$0.756347\pi$
$450$	−1430.95	−0.149902
$451$	1108.20	0.115705
$452$	− 9586.52i	− 0.997593i
$453$	− 3811.14i	− 0.395282i
$454$	25303.3i	2.61573i
$455$	−7783.85	−0.802005
$456$	− 8610.26i	− 0.884238i
$457$	16241.9	1.66250	0.831252	−	0.555896i	$-0.187625\pi$
$457$	16241.9	1.66250	0.831252	+	0.555896i	$0.187625\pi$
$458$	−15551.2	−1.58659
$459$	0	0
$460$	25927.1	2.62795
$461$	−11054.7	−1.11685	−0.558425	−	0.829555i	$-0.688594\pi$
$461$	−11054.7	−1.11685	−0.558425	+	0.829555i	$0.688594\pi$
$462$	6726.02i	0.677322i
$463$	14185.7	1.42390	0.711952	−	0.702228i	$-0.247811\pi$
$463$	14185.7	1.42390	0.711952	+	0.702228i	$0.247811\pi$
$464$	− 3207.58i	− 0.320922i
$465$	− 15228.6i	− 1.51873i
$466$	4147.49i	0.412293i
$467$	−9689.39	−0.960110	−0.480055	−	0.877238i	$-0.659383\pi$
$467$	−9689.39	−0.960110	−0.480055	+	0.877238i	$0.659383\pi$
$468$	626.740	0.0619040
$469$	5152.32i	0.507275i
$470$	− 43563.0i	− 4.27534i
$471$	− 2935.70i	− 0.287197i
$472$	10396.5	1.01385
$473$	− 1015.72i	− 0.0987376i
$474$	5361.80	0.519569
$475$	−10055.0	−0.971276
$476$	0	0
$477$	710.334	0.0681844
$478$	9201.54	0.880478
$479$	13237.0i	1.26266i	0.775514	+	0.631330i	$0.217491\pi$
$479$	13237.0i	1.26266i	−0.775514	+	0.631330i	$0.782509\pi$
$480$	−2603.52	−0.247571
$481$	4054.75i	0.384367i
$482$	8991.25i	0.849669i
$483$	− 6344.28i	− 0.597670i
$484$	14878.5	1.39730
$485$	−16422.7	−1.53756
$486$	− 1826.68i	− 0.170493i
$487$	19300.3i	1.79585i	0.440150	+	0.897924i	$0.354925\pi$
$487$	19300.3i	1.79585i	−0.440150	+	0.897924i	$0.645075\pi$
$488$	− 21778.2i	− 2.02019i
$489$	−9005.20	−0.832780
$490$	13213.4i	1.21821i
$491$	72.2707	0.00664263	0.00332131	−	0.999994i	$-0.498943\pi$
$491$	72.2707	0.00664263	0.00332131	+	0.999994i	$0.498943\pi$
$492$	−4506.04	−0.412902
$493$	0	0
$494$	6657.27	0.606325
$495$	−484.658	−0.0440075
$496$	− 8970.53i	− 0.812074i
$497$	848.967	0.0766225
$498$	− 14632.2i	− 1.31664i
$499$	14805.5i	1.32823i	0.747630	+	0.664116i	$0.231192\pi$
$499$	14805.5i	1.32823i	−0.747630	+	0.664116i	$0.768808\pi$
$500$	− 27457.6i	− 2.45588i
$501$	−15879.6	−1.41607
$502$	4989.98	0.443653
$503$	− 6693.90i	− 0.593372i	−0.954975	−	0.296686i	$-0.904118\pi$
$503$	− 6693.90i	− 0.593372i	0.954975	−	0.296686i	$-0.0958816\pi$
$504$	697.633i	0.0616569i
$505$	− 34255.2i	− 3.01849i
$506$	8459.22	0.743198
$507$	6598.54i	0.578011i
$508$	−1746.32	−0.152521
$509$	4414.17	0.384390	0.192195	−	0.981357i	$-0.438439\pi$
$509$	4414.17	0.384390	0.192195	+	0.981357i	$0.438439\pi$
$510$	0	0
$511$	−5160.94	−0.446784
$512$	−17983.7	−1.55230
$513$	− 6573.30i	− 0.565728i
$514$	−12717.4	−1.09132
$515$	− 33842.3i	− 2.89567i
$516$	4130.01i	0.352352i
$517$	− 9402.52i	− 0.799850i
$518$	−9242.10	−0.783928
$519$	−5923.27	−0.500968
$520$	20608.8i	1.73799i
$521$	− 1152.08i	− 0.0968781i	−0.998826	−	0.0484391i	$-0.984575\pi$
$521$	− 1152.08i	− 0.0968781i	0.998826	−	0.0484391i	$-0.0154247\pi$
$522$	− 377.339i	− 0.0316392i
$523$	8548.79	0.714747	0.357373	−	0.933962i	$-0.383672\pi$
$523$	8548.79	0.714747	0.357373	+	0.933962i	$0.383672\pi$
$524$	− 33336.0i	− 2.77918i
$525$	−15596.8	−1.29657
$526$	24270.2	2.01185
$527$	0	0
$528$	5465.55	0.450488
$529$	4187.89	0.344201
$530$	47829.3i	3.91995i
$531$	375.368	0.0306772
$532$	10038.1i	0.818059i
$533$	− 1701.41i	− 0.138267i
$534$	21857.7i	1.77130i
$535$	34441.5	2.78325
$536$	13641.5	1.09929
$537$	− 7864.45i	− 0.631985i
$538$	16580.8i	1.32872i
$539$	2851.95i	0.227908i
$540$	41668.4	3.32060
$541$	1820.54i	0.144679i	0.997380	+	0.0723393i	$0.0230464\pi$
$541$	1820.54i	0.144679i	−0.997380	+	0.0723393i	$0.976954\pi$
$542$	365.067	0.0289317
$543$	−7577.62	−0.598871
$544$	0	0
$545$	−25756.0	−2.02434
$546$	10326.4	0.809392
$547$	− 82.7848i	− 0.00647097i	−0.999995	−	0.00323549i	$-0.998970\pi$
$547$	− 82.7848i	− 0.00647097i	0.999995	−	0.00323549i	$-0.00102989\pi$
$548$	48278.3	3.76341
$549$	− 786.310i	− 0.0611273i
$550$	− 20796.1i	− 1.61227i
$551$	− 2651.49i	− 0.205004i
$552$	−16797.3	−1.29519
$553$	−3052.67	−0.234743
$554$	16733.3i	1.28326i
$555$	12749.4i	0.975100i
$556$	7346.08i	0.560329i
$557$	−12671.9	−0.963963	−0.481981	−	0.876181i	$-0.660083\pi$
$557$	−12671.9	−0.963963	−0.481981	+	0.876181i	$0.660083\pi$
$558$	− 1055.29i	− 0.0800611i
$559$	−1559.42	−0.117990
$560$	−14417.1	−1.08791
$561$	0	0
$562$	−8133.82	−0.610506
$563$	−4708.47	−0.352466	−0.176233	−	0.984348i	$-0.556391\pi$
$563$	−4708.47	−0.352466	−0.176233	+	0.984348i	$0.556391\pi$
$564$	38231.5i	2.85432i
$565$	11381.5	0.847473
$566$	33021.5i	2.45229i
$567$	− 9688.73i	− 0.717616i
$568$	− 2247.76i	− 0.166045i
$569$	−8492.74	−0.625719	−0.312860	−	0.949799i	$-0.601287\pi$
$569$	−8492.74	−0.625719	−0.312860	+	0.949799i	$0.601287\pi$
$570$	20932.5	1.53818
$571$	− 1128.62i	− 0.0827166i	−0.999144	−	0.0413583i	$-0.986831\pi$
$571$	− 1128.62i	− 0.0827166i	0.999144	−	0.0413583i	$-0.0131685\pi$
$572$	9108.47i	0.665811i
$573$	− 15241.1i	− 1.11118i
$574$	3878.06	0.281998
$575$	19615.9i	1.42267i
$576$	−774.353	−0.0560151
$577$	18288.9	1.31955	0.659773	−	0.751465i	$-0.270652\pi$
$577$	18288.9	1.31955	0.659773	+	0.751465i	$0.270652\pi$
$578$	0	0
$579$	19723.0	1.41565
$580$	16807.9	1.20329
$581$	8330.65i	0.594860i
$582$	21787.0	1.55172
$583$	10323.4i	0.733361i
$584$	13664.3i	0.968207i
$585$	744.089i	0.0525885i
$586$	−31294.1	−2.20605
$587$	−11310.2	−0.795265	−0.397633	−	0.917545i	$-0.630168\pi$
$587$	−11310.2	−0.795265	−0.397633	+	0.917545i	$0.630168\pi$
$588$	− 11596.3i	− 0.813304i
$589$	− 7415.34i	− 0.518750i
$590$	25274.9i	1.76364i
$591$	4795.42	0.333769
$592$	7510.12i	0.521392i
$593$	−5283.47	−0.365879	−0.182939	−	0.983124i	$-0.558561\pi$
$593$	−5283.47	−0.365879	−0.182939	+	0.983124i	$0.558561\pi$
$594$	13595.1	0.939082
$595$	0	0
$596$	−34545.0	−2.37419
$597$	8944.93	0.613219
$598$	− 12987.3i	− 0.888113i
$599$	−22287.6	−1.52028	−0.760138	−	0.649762i	$-0.774869\pi$
$599$	−22287.6	−1.52028	−0.760138	+	0.649762i	$0.774869\pi$
$600$	41294.6i	2.80974i
$601$	− 15046.8i	− 1.02125i	−0.859804	−	0.510625i	$-0.829414\pi$
$601$	− 15046.8i	− 1.02125i	0.859804	−	0.510625i	$-0.170586\pi$
$602$	− 3554.44i	− 0.240644i
$603$	492.531	0.0332627
$604$	11763.8	0.792489
$605$	17664.3i	1.18703i
$606$	45444.4i	3.04629i
$607$	− 11288.7i	− 0.754848i	−0.926041	−	0.377424i	$-0.876810\pi$
$607$	− 11288.7i	− 0.754848i	0.926041	−	0.377424i	$-0.123190\pi$
$608$	−1267.75	−0.0845623
$609$	− 4112.84i	− 0.273663i
$610$	52945.1	3.51424
$611$	−14435.6	−0.955811
$612$	0	0
$613$	14753.0	0.972054	0.486027	−	0.873944i	$-0.338446\pi$
$613$	14753.0	0.972054	0.486027	+	0.873944i	$0.338446\pi$
$614$	24939.7	1.63923
$615$	− 5349.74i	− 0.350768i
$616$	−10138.8	−0.663154
$617$	− 6693.56i	− 0.436747i	−0.975865	−	0.218373i	$-0.929925\pi$
$617$	− 6693.56i	− 0.436747i	0.975865	−	0.218373i	$-0.0700750\pi$
$618$	44896.6i	2.92234i
$619$	1285.36i	0.0834617i	0.999129	+	0.0417308i	$0.0132872\pi$
$619$	1285.36i	0.0834617i	−0.999129	+	0.0417308i	$0.986713\pi$
$620$	47006.1	3.04485
$621$	−12823.5	−0.828648
$622$	16639.9i	1.07267i
$623$	− 12444.4i	− 0.800280i
$624$	− 8391.20i	− 0.538328i
$625$	5148.78	0.329522
$626$	− 20825.1i	− 1.32961i
$627$	4518.01	0.287770
$628$	9061.61	0.575792
$629$	0	0
$630$	−1696.02	−0.107256
$631$	−27186.8	−1.71520	−0.857598	−	0.514320i	$-0.828044\pi$
$631$	−27186.8	−1.71520	−0.857598	+	0.514320i	$0.828044\pi$
$632$	8082.35i	0.508700i
$633$	−1881.33	−0.118130
$634$	1897.75i	0.118879i
$635$	− 2073.30i	− 0.129569i
$636$	− 41975.7i	− 2.61705i
$637$	4378.57	0.272347
$638$	5483.90	0.340297
$639$	− 81.1562i	− 0.00502424i
$640$	− 48028.2i	− 2.96638i
$641$	− 12321.5i	− 0.759236i	−0.925143	−	0.379618i	$-0.876055\pi$
$641$	− 12321.5i	− 0.759236i	0.925143	−	0.379618i	$-0.123945\pi$
$642$	−45691.6	−2.80888
$643$	25577.1i	1.56868i	0.620330	+	0.784341i	$0.286999\pi$
$643$	25577.1i	1.56868i	−0.620330	+	0.784341i	$0.713001\pi$
$644$	19582.9	1.19825
$645$	−4903.30	−0.299329
$646$	0	0
$647$	−28275.5	−1.71812	−0.859062	−	0.511872i	$-0.828952\pi$
$647$	−28275.5	−1.71812	−0.859062	+	0.511872i	$0.828952\pi$
$648$	−25652.2	−1.55512
$649$	5455.26i	0.329950i
$650$	−31928.1	−1.92665
$651$	− 11502.3i	− 0.692487i
$652$	− 27796.3i	− 1.66961i
$653$	2354.19i	0.141082i	0.997509	+	0.0705411i	$0.0224726\pi$
$653$	2354.19i	0.141082i	−0.997509	+	0.0705411i	$0.977527\pi$
$654$	34169.0	2.04299
$655$	39577.8	2.36097
$656$	− 3151.31i	− 0.187558i
$657$	493.355i	0.0292962i
$658$	− 32903.4i	− 1.94940i
$659$	21272.6	1.25745	0.628727	−	0.777626i	$-0.283576\pi$
$659$	21272.6	1.25745	0.628727	+	0.777626i	$0.283576\pi$
$660$	28639.8i	1.68909i
$661$	16621.3	0.978051	0.489026	−	0.872269i	$-0.337352\pi$
$661$	16621.3	0.978051	0.489026	+	0.872269i	$0.337352\pi$
$662$	−18595.3	−1.09173
$663$	0	0
$664$	22056.5	1.28910
$665$	−11917.6	−0.694956
$666$	883.489i	0.0514032i
$667$	−5172.66	−0.300279
$668$	− 49015.6i	− 2.83903i
$669$	13038.2i	0.753490i
$670$	33163.9i	1.91229i
$671$	11427.5	0.657458
$672$	−1966.46	−0.112883
$673$	228.679i	0.0130979i	0.999979	+	0.00654897i	$0.00208462\pi$
$673$	228.679i	0.0130979i	−0.999979	+	0.00654897i	$0.997915\pi$
$674$	− 11555.7i	− 0.660399i
$675$	31525.4i	1.79765i
$676$	−20367.7	−1.15883
$677$	− 9975.67i	− 0.566316i	−0.959073	−	0.283158i	$-0.908618\pi$
$677$	− 9975.67i	− 0.566316i	0.959073	−	0.283158i	$-0.0913821\pi$
$678$	−15099.1	−0.855279
$679$	−12404.1	−0.701071
$680$	0	0
$681$	26364.4	1.48353
$682$	15336.7	0.861101
$683$	− 31110.8i	− 1.74293i	−0.490459	−	0.871464i	$-0.663171\pi$
$683$	− 31110.8i	− 1.74293i	0.490459	−	0.871464i	$-0.336829\pi$
$684$	959.583	0.0536412
$685$	57317.8i	3.19708i
$686$	33360.9i	1.85674i
$687$	16203.3i	0.899846i
$688$	−2888.33	−0.160053
$689$	15849.3	0.876358
$690$	− 40836.1i	− 2.25305i
$691$	− 5108.91i	− 0.281262i	−0.990062	−	0.140631i	$-0.955087\pi$
$691$	− 5108.91i	− 0.281262i	0.990062	−	0.140631i	$-0.0449132\pi$
$692$	− 18283.3i	− 1.00437i
$693$	−366.064	−0.0200659
$694$	− 57966.6i	− 3.17058i
$695$	−8721.54	−0.476010
$696$	−10889.3	−0.593043
$697$	0	0
$698$	35927.4	1.94824
$699$	4321.41	0.233835
$700$	− 48142.5i	− 2.59945i
$701$	11204.5	0.603691	0.301846	−	0.953357i	$-0.402397\pi$
$701$	11204.5	0.603691	0.301846	+	0.953357i	$0.402397\pi$
$702$	− 20872.4i	− 1.12219i
$703$	6208.11i	0.333063i
$704$	− 11253.7i	− 0.602473i
$705$	−45389.8	−2.42479
$706$	14420.6	0.768733
$707$	− 25873.2i	− 1.37632i
$708$	− 22181.6i	− 1.17745i
$709$	33950.0i	1.79833i	0.437605	+	0.899167i	$0.355827\pi$
$709$	33950.0i	1.79833i	−0.437605	+	0.899167i	$0.644173\pi$
$710$	5464.54	0.288846
$711$	291.817i	0.0153924i
$712$	−32948.2	−1.73425
$713$	−14466.2	−0.759838
$714$	0	0
$715$	−10813.9	−0.565619
$716$	24275.2	1.26705
$717$	− 9587.41i	− 0.499370i
$718$	31728.8	1.64918
$719$	− 6231.07i	− 0.323198i	−0.986856	−	0.161599i	$-0.948335\pi$
$719$	− 6231.07i	− 0.323198i	0.986856	−	0.161599i	$-0.0516652\pi$
$720$	1378.18i	0.0713360i
$721$	− 25561.3i	− 1.32032i
$722$	−23153.4	−1.19346
$723$	9368.30	0.481896
$724$	− 23389.8i	− 1.20066i
$725$	12716.5i	0.651417i
$726$	− 23434.2i	− 1.19797i
$727$	−5206.88	−0.265629	−0.132815	−	0.991141i	$-0.542402\pi$
$727$	−5206.88	−0.265629	−0.132815	+	0.991141i	$0.542402\pi$
$728$	15565.9i	0.792461i
$729$	−20560.7	−1.04459
$730$	−33219.4	−1.68425
$731$	0	0
$732$	−46465.3	−2.34618
$733$	−3817.57	−0.192367	−0.0961835	−	0.995364i	$-0.530664\pi$
$733$	−3817.57	−0.192367	−0.0961835	+	0.995364i	$0.530664\pi$
$734$	− 28666.8i	− 1.44157i
$735$	13767.5	0.690916
$736$	2473.18i	0.123862i
$737$	7158.00i	0.357759i
$738$	− 370.719i	− 0.0184910i
$739$	9211.40	0.458521	0.229260	−	0.973365i	$-0.426369\pi$
$739$	9211.40	0.458521	0.229260	+	0.973365i	$0.426369\pi$
$740$	−39353.4	−1.95495
$741$	− 6936.44i	− 0.343882i
$742$	36125.8i	1.78736i
$743$	23138.9i	1.14251i	0.820773	+	0.571255i	$0.193543\pi$
$743$	23138.9i	1.14251i	−0.820773	+	0.571255i	$0.806457\pi$
$744$	−30453.8	−1.50066
$745$	− 41013.1i	− 2.01692i
$746$	−44897.4	−2.20350
$747$	796.360	0.0390057
$748$	0	0
$749$	26013.9	1.26906
$750$	−43246.7	−2.10553
$751$	31141.4i	1.51314i	0.653914	+	0.756569i	$0.273126\pi$
$751$	31141.4i	1.51314i	−0.653914	+	0.756569i	$0.726874\pi$
$752$	−26737.2	−1.29655
$753$	− 5199.24i	− 0.251621i
$754$	− 8419.36i	− 0.406651i
$755$	13966.4i	0.673233i
$756$	31472.4	1.51407
$757$	−30991.3	−1.48798	−0.743988	−	0.668193i	$-0.767068\pi$
$757$	−30991.3	−1.48798	−0.743988	+	0.668193i	$0.767068\pi$
$758$	7047.74i	0.337712i
$759$	− 8813.96i	− 0.421510i
$760$	31553.5i	1.50601i
$761$	−14150.5	−0.674053	−0.337026	−	0.941495i	$-0.609421\pi$
$761$	−14150.5	−0.674053	−0.337026	+	0.941495i	$0.609421\pi$
$762$	2750.52i	0.130762i
$763$	−19453.7	−0.923027
$764$	47044.7	2.22777
$765$	0	0
$766$	−39666.7	−1.87104
$767$	8375.39	0.394287
$768$	40303.9i	1.89367i
$769$	−619.823	−0.0290655	−0.0145328	−	0.999894i	$-0.504626\pi$
$769$	−619.823	−0.0290655	−0.0145328	+	0.999894i	$0.504626\pi$
$770$	− 24648.4i	− 1.15359i
$771$	13250.7i	0.618950i
$772$	60878.8i	2.83818i
$773$	−10196.4	−0.474436	−0.237218	−	0.971456i	$-0.576236\pi$
$773$	−10196.4	−0.474436	−0.237218	+	0.971456i	$0.576236\pi$
$774$	−339.783	−0.0157794
$775$	35563.8i	1.64837i
$776$	32841.7i	1.51926i
$777$	9629.67i	0.444611i
$778$	7136.23	0.328851
$779$	− 2604.97i	− 0.119811i
$780$	43970.3	2.01845
$781$	1179.45	0.0540385
$782$	0	0
$783$	−8313.17	−0.379423
$784$	8109.88	0.369437
$785$	10758.3i	0.489146i
$786$	−52505.5	−2.38271
$787$	− 33206.7i	− 1.50405i	−0.659132	−	0.752027i	$-0.729076\pi$
$787$	− 33206.7i	− 1.50405i	0.659132	−	0.752027i	$-0.270924\pi$
$788$	14802.0i	0.669162i
$789$	− 25288.0i	− 1.14103i
$790$	−19649.1	−0.884914
$791$	8596.49	0.386417
$792$	969.205i	0.0434839i
$793$	− 17544.5i	− 0.785655i
$794$	29258.6i	1.30774i
$795$	49835.1	2.22323
$796$	27610.3i	1.22942i
$797$	4351.64	0.193404	0.0967020	−	0.995313i	$-0.469171\pi$
$797$	4351.64	0.193404	0.0967020	+	0.995313i	$0.469171\pi$
$798$	15810.4	0.701356
$799$	0	0
$800$	6080.08	0.268704
$801$	−1189.61	−0.0524754
$802$	− 28679.6i	− 1.26273i
$803$	−7169.98	−0.315097
$804$	− 29105.1i	− 1.27669i
$805$	23249.5i	1.01793i
$806$	− 23546.2i	− 1.02901i
$807$	17276.1	0.753592
$808$	−68502.7	−2.98257
$809$	13515.2i	0.587355i	0.955905	+	0.293678i	$0.0948792\pi$
$809$	13515.2i	0.587355i	−0.955905	+	0.293678i	$0.905121\pi$
$810$	− 62363.3i	− 2.70521i
$811$	− 5758.39i	− 0.249327i	−0.992199	−	0.124664i	$-0.960215\pi$
$811$	− 5758.39i	− 0.249327i	0.992199	−	0.124664i	$-0.0397852\pi$
$812$	12695.1	0.548657
$813$	− 380.377i	− 0.0164088i
$814$	−12839.8	−0.552870
$815$	33000.8	1.41837
$816$	0	0
$817$	−2387.59	−0.102241
$818$	−45024.3	−1.92450
$819$	562.014i	0.0239785i
$820$	16513.0	0.703243
$821$	27956.3i	1.18841i	0.804315	+	0.594203i	$0.202532\pi$
$821$	27956.3i	1.18841i	−0.804315	+	0.594203i	$0.797468\pi$
$822$	− 76040.2i	− 3.22653i
$823$	− 38040.6i	− 1.61119i	−0.592465	−	0.805596i	$-0.701845\pi$
$823$	− 38040.6i	− 1.61119i	0.592465	−	0.805596i	$-0.298155\pi$
$824$	−67677.0	−2.86121
$825$	−21668.2	−0.914414
$826$	19090.3i	0.804159i
$827$	14467.5i	0.608324i	0.952620	+	0.304162i	$0.0983763\pi$
$827$	14467.5i	0.608324i	−0.952620	+	0.304162i	$0.901624\pi$
$828$	− 1872.00i	− 0.0785708i
$829$	−24519.4	−1.02726	−0.513628	−	0.858013i	$-0.671699\pi$
$829$	−24519.4	−1.02726	−0.513628	+	0.858013i	$0.671699\pi$
$830$	53621.8i	2.24246i
$831$	17435.0	0.727813
$832$	−17277.7	−0.719949
$833$	0	0
$834$	11570.4	0.480394
$835$	58193.2	2.41181
$836$	13945.7i	0.576941i
$837$	−23249.2	−0.960108
$838$	41509.2i	1.71111i
$839$	− 38066.2i	− 1.56638i	−0.621785	−	0.783188i	$-0.713592\pi$
$839$	− 38066.2i	− 1.56638i	0.621785	−	0.783188i	$-0.286408\pi$
$840$	48944.0i	2.01039i
$841$	21035.7	0.862508
$842$	−7862.83	−0.321818
$843$	8474.91i	0.346253i
$844$	− 5807.09i	− 0.236835i
$845$	− 24181.3i	− 0.984451i
$846$	−3145.36	−0.127825
$847$	13341.9i	0.541244i
$848$	29355.7	1.18877
$849$	34406.2	1.39083
$850$	0	0
$851$	12111.1	0.487853
$852$	−4795.75	−0.192840
$853$	37413.0i	1.50175i	0.660442	+	0.750877i	$0.270369\pi$
$853$	37413.0i	1.50175i	−0.660442	+	0.750877i	$0.729631\pi$
$854$	39989.7	1.60237
$855$	1139.25i	0.0455691i
$856$	− 68875.3i	− 2.75013i
$857$	29090.0i	1.15951i	0.814793	+	0.579753i	$0.196851\pi$
$857$	29090.0i	1.15951i	−0.814793	+	0.579753i	$0.803149\pi$
$858$	14346.2	0.570828
$859$	43523.6	1.72876	0.864381	−	0.502837i	$-0.167710\pi$
$859$	43523.6	1.72876	0.864381	+	0.502837i	$0.167710\pi$
$860$	− 15135.0i	− 0.600115i
$861$	− 4040.69i	− 0.159938i
$862$	− 12334.5i	− 0.487373i
$863$	15659.4	0.617672	0.308836	−	0.951115i	$-0.400061\pi$
$863$	15659.4	0.617672	0.308836	+	0.951115i	$0.400061\pi$
$864$	3974.75i	0.156509i
$865$	21706.6	0.853234
$866$	−8913.05	−0.349743
$867$	0	0
$868$	35503.9	1.38834
$869$	−4241.00	−0.165553
$870$	− 26473.0i	− 1.03163i
$871$	10989.6	0.427518
$872$	51506.2i	2.00025i
$873$	1185.76i	0.0459702i
$874$	− 19884.5i	− 0.769570i
$875$	24621.9	0.951283
$876$	29153.8	1.12445
$877$	− 28891.8i	− 1.11244i	−0.831036	−	0.556219i	$-0.812252\pi$
$877$	− 28891.8i	− 1.11244i	0.831036	−	0.556219i	$-0.187748\pi$
$878$	50554.2i	1.94319i
$879$	32606.4i	1.25118i
$880$	−20029.3	−0.767258
$881$	− 22094.9i	− 0.844943i	−0.906376	−	0.422471i	$-0.861163\pi$
$881$	− 22094.9i	− 0.844943i	0.906376	−	0.422471i	$-0.138837\pi$
$882$	954.045	0.0364222
$883$	40158.3	1.53050	0.765252	−	0.643731i	$-0.222615\pi$
$883$	40158.3	1.53050	0.765252	+	0.643731i	$0.222615\pi$
$884$	0	0
$885$	26334.8	1.00026
$886$	−19369.6	−0.734462
$887$	− 27801.7i	− 1.05241i	−0.850357	−	0.526207i	$-0.823614\pi$
$887$	− 27801.7i	− 1.05241i	0.850357	−	0.526207i	$-0.176386\pi$
$888$	25495.9	0.963497
$889$	− 1565.97i	− 0.0590788i
$890$	− 80100.7i	− 3.01683i
$891$	− 13460.3i	− 0.506103i
$892$	−40244.9	−1.51065
$893$	−22101.9	−0.828232
$894$	54409.7i	2.03550i
$895$	28820.4i	1.07638i
$896$	− 36276.0i	− 1.35256i
$897$	−13532.0	−0.503700
$898$	64096.6i	2.38188i
$899$	−9378.09	−0.347916
$900$	−4602.13	−0.170449
$901$	0	0
$902$	5387.70	0.198881
$903$	−3703.49	−0.136483
$904$	− 22760.4i	− 0.837388i
$905$	27769.3	1.01998
$906$	− 18528.5i	− 0.679434i
$907$	18413.3i	0.674095i	0.941488	+	0.337048i	$0.109428\pi$
$907$	18413.3i	0.674095i	−0.941488	+	0.337048i	$0.890572\pi$
$908$	81378.8i	2.97428i
$909$	−2473.32	−0.0902473
$910$	−37842.4	−1.37853
$911$	32271.8i	1.17367i	0.809708	+	0.586834i	$0.199626\pi$
$911$	32271.8i	1.17367i	−0.809708	+	0.586834i	$0.800374\pi$
$912$	− 12847.5i	− 0.466473i
$913$	11573.6i	0.419528i
$914$	78962.7	2.85761
$915$	− 55165.3i	− 1.99313i
$916$	−50014.6	−1.80407
$917$	29893.3	1.07652
$918$	0	0
$919$	19185.3	0.688643	0.344322	−	0.938852i	$-0.388109\pi$
$919$	19185.3	0.688643	0.344322	+	0.938852i	$0.388109\pi$
$920$	61556.2	2.20592
$921$	− 25985.6i	− 0.929700i
$922$	−53744.2	−1.91971
$923$	− 1810.80i	− 0.0645754i
$924$	21631.8i	0.770166i
$925$	− 29773.9i	− 1.05834i
$926$	68966.3	2.44749
$927$	−2443.51	−0.0865752
$928$	1603.30i	0.0567144i
$929$	− 20823.7i	− 0.735419i	−0.929941	−	0.367709i	$-0.880142\pi$
$929$	− 20823.7i	− 0.735419i	0.929941	−	0.367709i	$-0.119858\pi$
$930$	− 74036.4i	− 2.61048i
$931$	6703.89	0.235995
$932$	13338.9i	0.468809i
$933$	17337.7	0.608371
$934$	−47106.5	−1.65029
$935$	0	0
$936$	1488.01	0.0519627
$937$	−21072.0	−0.734677	−0.367338	−	0.930087i	$-0.619731\pi$
$937$	−21072.0	−0.734677	−0.367338	+	0.930087i	$0.619731\pi$
$938$	25048.9i	0.871934i
$939$	−21698.4	−0.754100
$940$	− 140105.i	− 4.86139i
$941$	11156.4i	0.386491i	0.981150	+	0.193245i	$0.0619014\pi$
$941$	11156.4i	0.386491i	−0.981150	+	0.193245i	$0.938099\pi$
$942$	− 14272.4i	− 0.493651i
$943$	−5081.91	−0.175493
$944$	15512.7	0.534847
$945$	37365.2i	1.28623i
$946$	− 4938.09i	− 0.169716i
$947$	− 3045.57i	− 0.104506i	−0.998634	−	0.0522532i	$-0.983360\pi$
$947$	− 3045.57i	− 0.104506i	0.998634	−	0.0522532i	$-0.0166403\pi$
$948$	17244.3	0.590789
$949$	11008.0i	0.376537i
$950$	−48884.1	−1.66949
$951$	1977.33	0.0674232
$952$	0	0
$953$	6037.53	0.205220	0.102610	−	0.994722i	$-0.467281\pi$
$953$	6037.53	0.205220	0.102610	+	0.994722i	$0.467281\pi$
$954$	3453.41	0.117199
$955$	55853.2i	1.89253i
$956$	29593.4	1.00117
$957$	− 5713.87i	− 0.193002i
$958$	64353.9i	2.17033i
$959$	43292.5i	1.45775i
$960$	−54326.4	−1.82644
$961$	3563.58	0.119619
$962$	19712.8i	0.660673i
$963$	− 2486.77i	− 0.0832140i
$964$	28917.1i	0.966138i
$965$	−72277.6	−2.41109
$966$	− 30843.8i	− 1.02731i
$967$	11151.0	0.370829	0.185414	−	0.982660i	$-0.440637\pi$
$967$	11151.0	0.370829	0.185414	+	0.982660i	$0.440637\pi$
$968$	35324.6	1.17291
$969$	0	0
$970$	−79841.6	−2.64284
$971$	−29051.5	−0.960152	−0.480076	−	0.877227i	$-0.659391\pi$
$971$	−29051.5	−0.960152	−0.480076	+	0.877227i	$0.659391\pi$
$972$	− 5874.85i	− 0.193864i
$973$	−6587.43	−0.217043
$974$	93831.4i	3.08681i
$975$	33267.0i	1.09271i
$976$	− 32495.6i	− 1.06574i
$977$	−2430.15	−0.0795778	−0.0397889	−	0.999208i	$-0.512669\pi$
$977$	−2430.15	−0.0795778	−0.0397889	+	0.999208i	$0.512669\pi$
$978$	−43780.3	−1.43143
$979$	− 17288.7i	− 0.564402i
$980$	42496.2i	1.38520i
$981$	1859.65i	0.0605241i
$982$	351.356	0.0114177
$983$	2167.32i	0.0703222i	0.999382	+	0.0351611i	$0.0111944\pi$
$983$	2167.32i	0.0703222i	−0.999382	+	0.0351611i	$0.988806\pi$
$984$	−10698.3	−0.346594
$985$	−17573.5	−0.568465
$986$	0	0
$987$	−34283.2	−1.10562
$988$	21410.7	0.689437
$989$	4657.83i	0.149758i
$990$	−2356.24	−0.0756427
$991$	− 19533.1i	− 0.626124i	−0.949733	−	0.313062i	$-0.898645\pi$
$991$	− 19533.1i	− 0.626124i	0.949733	−	0.313062i	$-0.101355\pi$
$992$	4483.91i	0.143512i
$993$	19375.1i	0.619185i
$994$	4127.39	0.131703
$995$	−32780.0	−1.04442
$996$	− 47059.2i	− 1.49712i
$997$	− 8892.06i	− 0.282462i	−0.989977	−	0.141231i	$-0.954894\pi$
$997$	− 8892.06i	− 0.282462i	0.989977	−	0.141231i	$-0.0451060\pi$
$998$	71979.6i	2.28304i
$999$	19464.2	0.616437

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.b.e.288.11		12
17.4	even	4		289.4.a.g.1.1		12
17.7	odd	16		17.4.d.a.2.1	✓	12
17.12	odd	16		17.4.d.a.9.1	yes	12
17.13	even	4		289.4.a.g.1.2		12
17.16	even	2	inner	289.4.b.e.288.12		12
51.29	even	16		153.4.l.a.145.3		12
51.41	even	16		153.4.l.a.19.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.d.a.2.1	✓	12	17.7	odd	16
17.4.d.a.9.1	yes	12	17.12	odd	16
153.4.l.a.19.3		12	51.41	even	16
153.4.l.a.145.3		12	51.29	even	16
289.4.a.g.1.1		12	17.4	even	4
289.4.a.g.1.2		12	17.13	even	4
289.4.b.e.288.11		12	1.1	even	1	trivial
289.4.b.e.288.12		12	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)

\(f(q)\)	\(=\)	\(q+4.86166 q^{2} -5.06554i q^{3} +15.6358 q^{4} +18.5634i q^{5} -24.6269i q^{6} +14.0210i q^{7} +37.1225 q^{8} +1.34032 q^{9} +O(q^{10})\)	\(q+4.86166 q^{2} -5.06554i q^{3} +15.6358 q^{4} +18.5634i q^{5} -24.6269i q^{6} +14.0210i q^{7} +37.1225 q^{8} +1.34032 q^{9} +90.2489i q^{10} +19.4791i q^{11} -79.2036i q^{12} +29.9060 q^{13} +68.1655i q^{14} +94.0335 q^{15} +55.3912 q^{16} +6.51621 q^{18} +45.7882 q^{19} +290.253i q^{20} +71.0240 q^{21} +94.7006i q^{22} -89.3259i q^{23} -188.046i q^{24} -219.599 q^{25} +145.393 q^{26} -143.559i q^{27} +219.229i q^{28} -57.9077i q^{29} +457.159 q^{30} -161.949i q^{31} -27.6872 q^{32} +98.6719 q^{33} -260.277 q^{35} +20.9570 q^{36} +135.583i q^{37} +222.607 q^{38} -151.490i q^{39} +689.120i q^{40} -56.8918i q^{41} +345.295 q^{42} -52.1442 q^{43} +304.570i q^{44} +24.8809i q^{45} -434.272i q^{46} -482.699 q^{47} -280.586i q^{48} +146.411 q^{49} -1067.62 q^{50} +467.603 q^{52} +529.972 q^{53} -697.935i q^{54} -361.597 q^{55} +520.496i q^{56} -231.942i q^{57} -281.528i q^{58} +280.058 q^{59} +1470.29 q^{60} -586.656i q^{61} -787.341i q^{62} +18.7927i q^{63} -577.735 q^{64} +555.156i q^{65} +479.710 q^{66} +367.471 q^{67} -452.484 q^{69} -1265.38 q^{70} -60.5496i q^{71} +49.7563 q^{72} +368.086i q^{73} +659.161i q^{74} +1112.39i q^{75} +715.933 q^{76} -273.116 q^{77} -736.493i q^{78} +217.721i q^{79} +1028.25i q^{80} -691.015 q^{81} -276.589i q^{82} +594.154 q^{83} +1110.51 q^{84} -253.508 q^{86} -293.334 q^{87} +723.112i q^{88} -887.553 q^{89} +120.963i q^{90} +419.312i q^{91} -1396.68i q^{92} -820.358 q^{93} -2346.72 q^{94} +849.983i q^{95} +140.251i q^{96} +884.682i q^{97} +711.801 q^{98} +26.1083i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{2} + 16 q^{4} + 96 q^{8} + 36 q^{9}+O(q^{10}) \) 12 * q + 8 * q^2 + 16 * q^4 + 96 * q^8 + 36 * q^9	\( 12 q + 8 q^{2} + 16 q^{4} + 96 q^{8} + 36 q^{9} - 8 q^{13} + 192 q^{15} - 184 q^{16} + 352 q^{19} - 256 q^{21} + 492 q^{25} + 784 q^{26} + 744 q^{30} - 24 q^{32} - 1400 q^{33} - 632 q^{35} + 856 q^{36} - 624 q^{38} + 1664 q^{42} + 1200 q^{43} - 1512 q^{47} + 1052 q^{49} - 2856 q^{50} + 792 q^{52} + 2504 q^{53} - 1424 q^{55} + 3408 q^{59} + 2808 q^{60} + 272 q^{64} - 272 q^{66} - 1080 q^{67} - 344 q^{69} - 2600 q^{70} + 248 q^{72} - 896 q^{76} - 848 q^{77} - 2404 q^{81} + 2960 q^{83} + 4768 q^{84} - 1200 q^{86} + 160 q^{87} - 2144 q^{89} - 3800 q^{93} - 5984 q^{94} + 3464 q^{98}+O(q^{100}) \) 12 * q + 8 * q^2 + 16 * q^4 + 96 * q^8 + 36 * q^9 - 8 * q^13 + 192 * q^15 - 184 * q^16 + 352 * q^19 - 256 * q^21 + 492 * q^25 + 784 * q^26 + 744 * q^30 - 24 * q^32 - 1400 * q^33 - 632 * q^35 + 856 * q^36 - 624 * q^38 + 1664 * q^42 + 1200 * q^43 - 1512 * q^47 + 1052 * q^49 - 2856 * q^50 + 792 * q^52 + 2504 * q^53 - 1424 * q^55 + 3408 * q^59 + 2808 * q^60 + 272 * q^64 - 272 * q^66 - 1080 * q^67 - 344 * q^69 - 2600 * q^70 + 248 * q^72 - 896 * q^76 - 848 * q^77 - 2404 * q^81 + 2960 * q^83 + 4768 * q^84 - 1200 * q^86 + 160 * q^87 - 2144 * q^89 - 3800 * q^93 - 5984 * q^94 + 3464 * q^98

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