LMFDB - Embedded newform 289.4.b.e.288.2

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			288.2
Root			$4.15292 - 1.84776i$ of defining polynomial
Character	$\chi$	$=$	289.288
Dual form			289.4.b.e.288.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.15292 q^{2} +1.99138i q^{3} +1.94089 q^{4} -5.00761i q^{5} -6.27866i q^{6} -2.78516i q^{7} +19.1039 q^{8} +23.0344 q^{9} +O(q^{10})$	\(q-3.15292 q^{2} +1.99138i q^{3} +1.94089 q^{4} -5.00761i q^{5} -6.27866i q^{6} -2.78516i q^{7} +19.1039 q^{8} +23.0344 q^{9} +15.7886i q^{10} +27.2453i q^{11} +3.86505i q^{12} -59.7352 q^{13} +8.78140i q^{14} +9.97206 q^{15} -75.7601 q^{16} -72.6256 q^{18} -33.2605 q^{19} -9.71922i q^{20} +5.54633 q^{21} -85.9023i q^{22} -210.884i q^{23} +38.0431i q^{24} +99.9239 q^{25} +188.340 q^{26} +99.6376i q^{27} -5.40570i q^{28} -20.0521i q^{29} -31.4411 q^{30} +133.659i q^{31} +86.0343 q^{32} -54.2559 q^{33} -13.9470 q^{35} +44.7072 q^{36} -152.772i q^{37} +104.868 q^{38} -118.956i q^{39} -95.6647i q^{40} +261.840i q^{41} -17.4871 q^{42} +316.820 q^{43} +52.8802i q^{44} -115.347i q^{45} +664.899i q^{46} +329.443 q^{47} -150.867i q^{48} +335.243 q^{49} -315.052 q^{50} -115.939 q^{52} +310.540 q^{53} -314.149i q^{54} +136.434 q^{55} -53.2074i q^{56} -66.2344i q^{57} +63.2227i q^{58} +54.7388 q^{59} +19.3547 q^{60} -818.751i q^{61} -421.417i q^{62} -64.1546i q^{63} +334.822 q^{64} +299.130i q^{65} +171.064 q^{66} +731.181 q^{67} +419.950 q^{69} +43.9738 q^{70} -629.179i q^{71} +440.046 q^{72} -496.481i q^{73} +481.678i q^{74} +198.987i q^{75} -64.5550 q^{76} +75.8828 q^{77} +375.057i q^{78} -90.0262i q^{79} +379.377i q^{80} +423.512 q^{81} -825.559i q^{82} -364.025 q^{83} +10.7648 q^{84} -998.907 q^{86} +39.9315 q^{87} +520.492i q^{88} -192.079 q^{89} +363.680i q^{90} +166.372i q^{91} -409.302i q^{92} -266.167 q^{93} -1038.71 q^{94} +166.556i q^{95} +171.327i q^{96} -1350.20i q^{97} -1056.99 q^{98} +627.580i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.15292	−1.11472	−0.557362	−	0.830269i	$-0.688187\pi$
$2$	−3.15292	−1.11472	−0.557362	+	0.830269i	$0.688187\pi$
$3$	1.99138i	0.383242i	0.981469	+	0.191621i	$0.0613744\pi$
$3$	1.99138i	0.383242i	−0.981469	+	0.191621i	$0.938626\pi$
$4$	1.94089	0.242611
$5$	− 5.00761i	− 0.447894i	−0.974601	−	0.223947i	$-0.928106\pi$
$5$	− 5.00761i	− 0.447894i	0.974601	−	0.223947i	$-0.0718943\pi$
$6$	− 6.27866i	− 0.427209i
$7$	− 2.78516i	− 0.150385i	−0.997169	−	0.0751924i	$-0.976043\pi$
$7$	− 2.78516i	− 0.150385i	0.997169	−	0.0751924i	$-0.0239571\pi$
$8$	19.1039	0.844280
$9$	23.0344	0.853126
$10$	15.7886i	0.499279i
$11$	27.2453i	0.746798i	0.927671	+	0.373399i	$0.121808\pi$
$11$	27.2453i	0.746798i	−0.927671	+	0.373399i	$0.878192\pi$
$12$	3.86505i	0.0929787i
$13$	−59.7352	−1.27443	−0.637214	−	0.770687i	$-0.719913\pi$
$13$	−59.7352	−1.27443	−0.637214	+	0.770687i	$0.719913\pi$
$14$	8.78140i	0.167638i
$15$	9.97206	0.171652
$16$	−75.7601	−1.18375
$17$	0	0
$17$	0	0
$18$	−72.6256	−0.951000
$19$	−33.2605	−0.401604	−0.200802	−	0.979632i	$-0.564355\pi$
$19$	−33.2605	−0.401604	−0.200802	+	0.979632i	$0.564355\pi$
$20$	− 9.71922i	− 0.108664i
$21$	5.54633	0.0576337
$22$	− 85.9023i	− 0.832475i
$23$	− 210.884i	− 1.91184i	−0.293630	−	0.955919i	$-0.594863\pi$
$23$	− 210.884i	− 1.91184i	0.293630	−	0.955919i	$-0.405137\pi$
$24$	38.0431i	0.323563i
$25$	99.9239	0.799391
$26$	188.340	1.42064
$27$	99.6376i	0.710195i
$28$	− 5.40570i	− 0.0364850i
$29$	− 20.0521i	− 0.128400i	−0.997937	−	0.0641998i	$-0.979551\pi$
$29$	− 20.0521i	− 0.128400i	0.997937	−	0.0641998i	$-0.0204495\pi$
$30$	−31.4411	−0.191344
$31$	133.659i	0.774385i	0.921999	+	0.387192i	$0.126555\pi$
$31$	133.659i	0.774385i	−0.921999	+	0.387192i	$0.873445\pi$
$32$	86.0343	0.475277
$33$	−54.2559	−0.286204
$34$	0	0
$35$	−13.9470	−0.0673565
$36$	44.7072	0.206978
$37$	− 152.772i	− 0.678800i	−0.940642	−	0.339400i	$-0.889776\pi$
$37$	− 152.772i	− 0.678800i	0.940642	−	0.339400i	$-0.110224\pi$
$38$	104.868	0.447678
$39$	− 118.956i	− 0.488414i
$40$	− 95.6647i	− 0.378148i
$41$	261.840i	0.997377i	0.866781	+	0.498689i	$0.166185\pi$
$41$	261.840i	0.997377i	−0.866781	+	0.498689i	$0.833815\pi$
$42$	−17.4871	−0.0642457
$43$	316.820	1.12359	0.561797	−	0.827275i	$-0.310110\pi$
$43$	316.820	1.12359	0.561797	+	0.827275i	$0.310110\pi$
$44$	52.8802i	0.181182i
$45$	− 115.347i	− 0.382110i
$46$	664.899i	2.13117i
$47$	329.443	1.02243	0.511215	−	0.859453i	$-0.329196\pi$
$47$	329.443	1.02243	0.511215	+	0.859453i	$0.329196\pi$
$48$	− 150.867i	− 0.453663i
$49$	335.243	0.977384
$50$	−315.052	−0.891101
$51$	0	0
$52$	−115.939	−0.309190
$53$	310.540	0.804829	0.402415	−	0.915458i	$-0.368171\pi$
$53$	310.540	0.804829	0.402415	+	0.915458i	$0.368171\pi$
$54$	− 314.149i	− 0.791672i
$55$	136.434	0.334487
$56$	− 53.2074i	− 0.126967i
$57$	− 66.2344i	− 0.153911i
$58$	63.2227i	0.143130i
$59$	54.7388	0.120786	0.0603931	−	0.998175i	$-0.480765\pi$
$59$	54.7388	0.120786	0.0603931	+	0.998175i	$0.480765\pi$
$60$	19.3547	0.0416446
$61$	− 818.751i	− 1.71853i	−0.511531	−	0.859265i	$-0.670921\pi$
$61$	− 818.751i	− 1.71853i	0.511531	−	0.859265i	$-0.329079\pi$
$62$	− 421.417i	− 0.863226i
$63$	− 64.1546i	− 0.128297i
$64$	334.822	0.653948
$65$	299.130i	0.570808i
$66$	171.064	0.319039
$67$	731.181	1.33325	0.666627	−	0.745392i	$-0.267738\pi$
$67$	731.181	1.33325	0.666627	+	0.745392i	$0.267738\pi$
$68$	0	0
$69$	419.950	0.732696
$70$	43.9738	0.0750839
$71$	− 629.179i	− 1.05169i	−0.850581	−	0.525844i	$-0.823750\pi$
$71$	− 629.179i	− 1.05169i	0.850581	−	0.525844i	$-0.176250\pi$
$72$	440.046	0.720277
$73$	− 496.481i	− 0.796010i	−0.917383	−	0.398005i	$-0.869703\pi$
$73$	− 496.481i	− 0.796010i	0.917383	−	0.398005i	$-0.130297\pi$
$74$	481.678i	0.756675i
$75$	198.987i	0.306360i
$76$	−64.5550	−0.0974337
$77$	75.8828	0.112307
$78$	375.057i	0.544447i
$79$	− 90.0262i	− 0.128212i	−0.997943	−	0.0641059i	$-0.979580\pi$
$79$	− 90.0262i	− 0.128212i	0.997943	−	0.0641059i	$-0.0204196\pi$
$80$	379.377i	0.530195i
$81$	423.512	0.580950
$82$	− 825.559i	− 1.11180i
$83$	−364.025	−0.481409	−0.240704	−	0.970599i	$-0.577378\pi$
$83$	−364.025	−0.481409	−0.240704	+	0.970599i	$0.577378\pi$
$84$	10.7648	0.0139826
$85$	0	0
$86$	−998.907	−1.25250
$87$	39.9315	0.0492081
$88$	520.492i	0.630507i
$89$	−192.079	−0.228767	−0.114384	−	0.993437i	$-0.536489\pi$
$89$	−192.079	−0.228767	−0.114384	+	0.993437i	$0.536489\pi$
$90$	363.680i	0.425948i
$91$	166.372i	0.191654i
$92$	− 409.302i	− 0.463833i
$93$	−266.167	−0.296776
$94$	−1038.71	−1.13973
$95$	166.556i	0.179876i
$96$	171.327i	0.182146i
$97$	− 1350.20i	− 1.41332i	−0.707554	−	0.706659i	$-0.750202\pi$
$97$	− 1350.20i	− 1.41332i	0.707554	−	0.706659i	$-0.249798\pi$
$98$	−1056.99	−1.08951
$99$	627.580i	0.637113i
$100$	193.941	0.193941
$101$	−304.020	−0.299516	−0.149758	−	0.988723i	$-0.547850\pi$
$101$	−304.020	−0.299516	−0.149758	+	0.988723i	$0.547850\pi$
$102$	0	0
$103$	988.515	0.945643	0.472822	−	0.881158i	$-0.343236\pi$
$103$	988.515	0.945643	0.472822	+	0.881158i	$0.343236\pi$
$104$	−1141.17	−1.07597
$105$	− 27.7738i	− 0.0258138i
$106$	−979.107	−0.897163
$107$	1175.01i	1.06162i	0.847492	+	0.530808i	$0.178111\pi$
$107$	1175.01i	1.06162i	−0.847492	+	0.530808i	$0.821889\pi$
$108$	193.386i	0.172301i
$109$	− 838.865i	− 0.737144i	−0.929599	−	0.368572i	$-0.879847\pi$
$109$	− 838.865i	− 0.737144i	0.929599	−	0.368572i	$-0.120153\pi$
$110$	−430.165	−0.372860
$111$	304.228	0.260144
$112$	211.004i	0.178018i
$113$	2026.81i	1.68731i	0.536885	+	0.843655i	$0.319601\pi$
$113$	2026.81i	1.68731i	−0.536885	+	0.843655i	$0.680399\pi$
$114$	208.831i	0.171569i
$115$	−1056.02	−0.856301
$116$	− 38.9190i	− 0.0311512i
$117$	−1375.96	−1.08725
$118$	−172.587	−0.134643
$119$	0	0
$120$	190.505	0.144922
$121$	588.691	0.442292
$122$	2581.45i	1.91569i
$123$	−521.423	−0.382237
$124$	259.418i	0.187874i
$125$	− 1126.33i	− 0.805937i
$126$	202.274i	0.143016i
$127$	1600.30	1.11814	0.559070	−	0.829120i	$-0.311158\pi$
$127$	1600.30	1.11814	0.559070	+	0.829120i	$0.311158\pi$
$128$	−1743.94	−1.20425
$129$	630.909i	0.430608i
$130$	− 943.133i	− 0.636294i
$131$	− 2615.07i	− 1.74412i	−0.489397	−	0.872061i	$-0.662783\pi$
$131$	− 2615.07i	− 1.74412i	0.489397	−	0.872061i	$-0.337217\pi$
$132$	−105.305	−0.0694364
$133$	92.6360i	0.0603952i
$134$	−2305.35	−1.48621
$135$	498.946	0.318092
$136$	0	0
$137$	745.711	0.465039	0.232520	−	0.972592i	$-0.425303\pi$
$137$	745.711	0.465039	0.232520	+	0.972592i	$0.425303\pi$
$138$	−1324.07	−0.816754
$139$	2532.45i	1.54532i	0.634818	+	0.772661i	$0.281075\pi$
$139$	2532.45i	1.54532i	−0.634818	+	0.772661i	$0.718925\pi$
$140$	−27.0696	−0.0163414
$141$	656.047i	0.391837i
$142$	1983.75i	1.17234i
$143$	− 1627.51i	− 0.951740i
$144$	−1745.09	−1.00989
$145$	−100.413	−0.0575094
$146$	1565.36i	0.887332i
$147$	667.597i	0.374574i
$148$	− 296.514i	− 0.164684i
$149$	−1816.70	−0.998858	−0.499429	−	0.866355i	$-0.666457\pi$
$149$	−1816.70	−0.998858	−0.499429	+	0.866355i	$0.666457\pi$
$150$	− 627.388i	− 0.341507i
$151$	2120.50	1.14280	0.571402	−	0.820670i	$-0.306400\pi$
$151$	2120.50	1.14280	0.571402	+	0.820670i	$0.306400\pi$
$152$	−635.404	−0.339066
$153$	0	0
$154$	−239.252	−0.125191
$155$	669.314	0.346842
$156$	− 230.880i	− 0.118495i
$157$	−1607.82	−0.817314	−0.408657	−	0.912688i	$-0.634003\pi$
$157$	−1607.82	−0.817314	−0.408657	+	0.912688i	$0.634003\pi$
$158$	283.845i	0.142921i
$159$	618.404i	0.308444i
$160$	− 430.826i	− 0.212874i
$161$	−587.346	−0.287511
$162$	−1335.30	−0.647599
$163$	− 2278.00i	− 1.09464i	−0.836922	−	0.547322i	$-0.815647\pi$
$163$	− 2278.00i	− 1.09464i	0.836922	−	0.547322i	$-0.184353\pi$
$164$	508.202i	0.241975i
$165$	271.692i	0.128189i
$166$	1147.74	0.536638
$167$	1652.12i	0.765538i	0.923844	+	0.382769i	$0.125029\pi$
$167$	1652.12i	0.765538i	−0.923844	+	0.382769i	$0.874971\pi$
$168$	105.956	0.0486590
$169$	1371.29	0.624165
$170$	0	0
$171$	−766.135	−0.342619
$172$	614.912	0.272597
$173$	− 2210.82i	− 0.971595i	−0.874071	−	0.485797i	$-0.838529\pi$
$173$	− 2210.82i	− 0.971595i	0.874071	−	0.485797i	$-0.161471\pi$
$174$	−125.901	−0.0548534
$175$	− 278.304i	− 0.120216i
$176$	− 2064.11i	− 0.884023i
$177$	109.006i	0.0462903i
$178$	605.608	0.255013
$179$	−20.7548	−0.00866640	−0.00433320	−	0.999991i	$-0.501379\pi$
$179$	−20.7548	−0.00866640	−0.00433320	+	0.999991i	$0.501379\pi$
$180$	− 223.876i	− 0.0927042i
$181$	− 436.498i	− 0.179252i	−0.995975	−	0.0896262i	$-0.971433\pi$
$181$	− 436.498i	− 0.179252i	0.995975	−	0.0896262i	$-0.0285672\pi$
$182$	− 524.558i	− 0.213642i
$183$	1630.45	0.658612
$184$	− 4028.69i	− 1.61413i
$185$	−765.023	−0.304030
$186$	839.202	0.330824
$187$	0	0
$188$	639.412	0.248053
$189$	277.507	0.106803
$190$	− 525.136i	− 0.200512i
$191$	787.808	0.298449	0.149225	−	0.988803i	$-0.452322\pi$
$191$	787.808	0.298449	0.149225	+	0.988803i	$0.452322\pi$
$192$	666.758i	0.250620i
$193$	3726.86i	1.38998i	0.719021	+	0.694988i	$0.244590\pi$
$193$	3726.86i	1.38998i	−0.719021	+	0.694988i	$0.755410\pi$
$194$	4257.06i	1.57546i
$195$	−595.683	−0.218758
$196$	650.669	0.237124
$197$	451.885i	0.163429i	0.996656	+	0.0817144i	$0.0260395\pi$
$197$	451.885i	0.163429i	−0.996656	+	0.0817144i	$0.973960\pi$
$198$	− 1978.71i	− 0.710206i
$199$	3480.16i	1.23971i	0.784716	+	0.619855i	$0.212809\pi$
$199$	3480.16i	1.23971i	−0.784716	+	0.619855i	$0.787191\pi$
$200$	1908.93	0.674910
$201$	1456.06i	0.510958i
$202$	958.551	0.333878
$203$	−55.8485	−0.0193093
$204$	0	0
$205$	1311.19	0.446719
$206$	−3116.71	−1.05413
$207$	− 4857.58i	− 1.63104i
$208$	4525.54	1.50860
$209$	− 906.194i	− 0.299917i
$210$	87.5686i	0.0287753i
$211$	− 1818.51i	− 0.593323i	−0.954983	−	0.296661i	$-0.904127\pi$
$211$	− 1818.51i	− 0.593323i	0.954983	−	0.296661i	$-0.0958732\pi$
$212$	602.724	0.195261
$213$	1252.94	0.403051
$214$	− 3704.72i	− 1.18341i
$215$	− 1586.51i	− 0.503251i
$216$	1903.46i	0.599603i
$217$	372.263	0.116456
$218$	2644.87i	0.821712i
$219$	988.684	0.305064
$220$	264.803	0.0811502
$221$	0	0
$222$	−959.205	−0.289989
$223$	6507.83	1.95425	0.977123	−	0.212676i	$-0.0682178\pi$
$223$	6507.83	1.95425	0.977123	+	0.212676i	$0.0682178\pi$
$224$	− 239.620i	− 0.0714744i
$225$	2301.69	0.681981
$226$	− 6390.36i	− 1.88089i
$227$	− 2427.16i	− 0.709676i	−0.934928	−	0.354838i	$-0.884536\pi$
$227$	− 2427.16i	− 0.709676i	0.934928	−	0.354838i	$-0.115464\pi$
$228$	− 128.554i	− 0.0373407i
$229$	−655.706	−0.189215	−0.0946076	−	0.995515i	$-0.530160\pi$
$229$	−655.706	−0.189215	−0.0946076	+	0.995515i	$0.530160\pi$
$230$	3329.55	0.954540
$231$	151.112i	0.0430408i
$232$	− 383.073i	− 0.108405i
$233$	1171.70i	0.329445i	0.986340	+	0.164723i	$0.0526729\pi$
$233$	1171.70i	0.329445i	−0.986340	+	0.164723i	$0.947327\pi$
$234$	4338.30	1.21198
$235$	− 1649.72i	− 0.457940i
$236$	106.242	0.0293041
$237$	179.277	0.0491361
$238$	0	0
$239$	−5281.06	−1.42930	−0.714651	−	0.699481i	$-0.753415\pi$
$239$	−5281.06	−1.42930	−0.714651	+	0.699481i	$0.753415\pi$
$240$	−755.484	−0.203193
$241$	− 1327.84i	− 0.354912i	−0.984129	−	0.177456i	$-0.943213\pi$
$241$	− 1327.84i	− 0.354912i	0.984129	−	0.177456i	$-0.0567867\pi$
$242$	−1856.09	−0.493034
$243$	3533.59i	0.932839i
$244$	− 1589.11i	− 0.416935i
$245$	− 1678.77i	− 0.437765i
$246$	1644.00	0.426089
$247$	1986.82	0.511815
$248$	2553.41i	0.653797i
$249$	− 724.912i	− 0.184496i
$250$	3551.23i	0.898397i
$251$	−4280.39	−1.07640	−0.538198	−	0.842818i	$-0.680895\pi$
$251$	−4280.39	−1.07640	−0.538198	+	0.842818i	$0.680895\pi$
$252$	− 124.517i	− 0.0311263i
$253$	5745.60	1.42776
$254$	−5045.62	−1.24642
$255$	0	0
$256$	2819.92	0.688458
$257$	−242.890	−0.0589536	−0.0294768	−	0.999565i	$-0.509384\pi$
$257$	−242.890	−0.0589536	−0.0294768	+	0.999565i	$0.509384\pi$
$258$	− 1989.20i	− 0.480010i
$259$	−425.496	−0.102081
$260$	580.579i	0.138485i
$261$	− 461.889i	− 0.109541i
$262$	8245.11i	1.94422i
$263$	3153.49	0.739364	0.369682	−	0.929158i	$-0.379467\pi$
$263$	3153.49	0.739364	0.369682	+	0.929158i	$0.379467\pi$
$264$	−1036.50	−0.241636
$265$	− 1555.06i	− 0.360478i
$266$	− 292.074i	− 0.0673240i
$267$	− 382.502i	− 0.0876732i
$268$	1419.14	0.323462
$269$	− 210.898i	− 0.0478018i	−0.999714	−	0.0239009i	$-0.992391\pi$
$269$	− 210.898i	− 0.0478018i	0.999714	−	0.0239009i	$-0.00760862\pi$
$270$	−1573.14	−0.354585
$271$	−1627.36	−0.364780	−0.182390	−	0.983226i	$-0.558383\pi$
$271$	−1627.36	−0.364780	−0.182390	+	0.983226i	$0.558383\pi$
$272$	0	0
$273$	−331.311	−0.0734500
$274$	−2351.16	−0.518391
$275$	2722.46i	0.596984i
$276$	815.076	0.177760
$277$	− 4626.89i	− 1.00362i	−0.864978	−	0.501810i	$-0.832668\pi$
$277$	− 4626.89i	− 1.00362i	0.864978	−	0.501810i	$-0.167332\pi$
$278$	− 7984.62i	− 1.72261i
$279$	3078.76i	0.660648i
$280$	−266.442	−0.0568677
$281$	5076.28	1.07767	0.538836	−	0.842411i	$-0.318864\pi$
$281$	5076.28	1.07767	0.538836	+	0.842411i	$0.318864\pi$
$282$	− 2068.46i	− 0.436791i
$283$	2437.04i	0.511898i	0.966690	+	0.255949i	$0.0823879\pi$
$283$	2437.04i	0.511898i	−0.966690	+	0.255949i	$0.917612\pi$
$284$	− 1221.17i	− 0.255151i
$285$	−331.676	−0.0689360
$286$	5131.39i	1.06093i
$287$	729.266	0.149990
$288$	1981.75	0.405471
$289$	0	0
$290$	316.595	0.0641072
$291$	2688.76	0.541642
$292$	− 963.616i	− 0.193121i
$293$	−3300.30	−0.658041	−0.329020	−	0.944323i	$-0.606718\pi$
$293$	−3300.30	−0.658041	−0.329020	+	0.944323i	$0.606718\pi$
$294$	− 2104.88i	− 0.417547i
$295$	− 274.111i	− 0.0540994i
$296$	− 2918.54i	− 0.573097i
$297$	−2714.66	−0.530372
$298$	5727.91	1.11345
$299$	12597.2i	2.43650i
$300$	386.211i	0.0743263i
$301$	− 882.395i	− 0.168971i
$302$	−6685.75	−1.27391
$303$	− 605.420i	− 0.114787i
$304$	2519.82	0.475399
$305$	−4099.98	−0.769719
$306$	0	0
$307$	−1186.40	−0.220558	−0.110279	−	0.993901i	$-0.535174\pi$
$307$	−1186.40	−0.220558	−0.110279	+	0.993901i	$0.535174\pi$
$308$	147.280	0.0272470
$309$	1968.51i	0.362410i
$310$	−2110.29	−0.386634
$311$	657.473i	0.119877i	0.998202	+	0.0599387i	$0.0190905\pi$
$311$	657.473i	0.119877i	−0.998202	+	0.0599387i	$0.980909\pi$
$312$	− 2272.51i	− 0.412358i
$313$	− 6073.66i	− 1.09682i	−0.836211	−	0.548408i	$-0.815234\pi$
$313$	− 6073.66i	− 1.09682i	0.836211	−	0.548408i	$-0.184766\pi$
$314$	5069.34	0.911080
$315$	−321.261	−0.0574635
$316$	− 174.731i	− 0.0311056i
$317$	5753.26i	1.01935i	0.860366	+	0.509677i	$0.170235\pi$
$317$	5753.26i	1.01935i	−0.860366	+	0.509677i	$0.829765\pi$
$318$	− 1949.78i	− 0.343830i
$319$	546.327	0.0958886
$320$	− 1676.66i	− 0.292900i
$321$	−2339.90	−0.406855
$322$	1851.85	0.320496
$323$	0	0
$324$	821.991	0.140945
$325$	−5968.97	−1.01877
$326$	7182.35i	1.22023i
$327$	1670.50	0.282504
$328$	5002.15i	0.842066i
$329$	− 917.553i	− 0.153758i
$330$	− 856.623i	− 0.142896i
$331$	89.8427	0.0149190	0.00745952	−	0.999972i	$-0.497626\pi$
$331$	89.8427	0.0149190	0.00745952	+	0.999972i	$0.497626\pi$
$332$	−706.532	−0.116795
$333$	− 3519.01i	− 0.579101i
$334$	− 5209.00i	− 0.853364i
$335$	− 3661.47i	− 0.597156i
$336$	−420.190	−0.0682240
$337$	847.308i	0.136961i	0.997652	+	0.0684804i	$0.0218151\pi$
$337$	847.308i	0.136961i	−0.997652	+	0.0684804i	$0.978185\pi$
$338$	−4323.56	−0.695772
$339$	−4036.15	−0.646648
$340$	0	0
$341$	−3641.60	−0.578309
$342$	2415.56	0.381926
$343$	− 1889.02i	− 0.297369i
$344$	6052.48	0.948628
$345$	− 2102.94i	− 0.328170i
$346$	6970.55i	1.08306i
$347$	590.322i	0.0913260i	0.998957	+	0.0456630i	$0.0145400\pi$
$347$	590.322i	0.0913260i	−0.998957	+	0.0456630i	$0.985460\pi$
$348$	77.5026	0.0119384
$349$	−9387.68	−1.43986	−0.719930	−	0.694047i	$-0.755826\pi$
$349$	−9387.68	−1.43986	−0.719930	+	0.694047i	$0.755826\pi$
$350$	877.471i	0.134008i
$351$	− 5951.87i	− 0.905092i
$352$	2344.03i	0.354936i
$353$	−6176.09	−0.931218	−0.465609	−	0.884990i	$-0.654165\pi$
$353$	−6176.09	−0.931218	−0.465609	+	0.884990i	$0.654165\pi$
$354$	− 343.687i	− 0.0516009i
$355$	−3150.68	−0.471045
$356$	−372.804	−0.0555015
$357$	0	0
$358$	65.4382	0.00966066
$359$	−7151.14	−1.05132	−0.525658	−	0.850696i	$-0.676181\pi$
$359$	−7151.14	−1.05132	−0.525658	+	0.850696i	$0.676181\pi$
$360$	− 2203.58i	− 0.322608i
$361$	−5752.74	−0.838714
$362$	1376.24i	0.199817i
$363$	1172.31i	0.169505i
$364$	322.910i	0.0464975i
$365$	−2486.18	−0.356528
$366$	−5140.66	−0.734171
$367$	− 3358.05i	− 0.477626i	−0.971066	−	0.238813i	$-0.923242\pi$
$367$	− 3358.05i	− 0.477626i	0.971066	−	0.238813i	$-0.0767583\pi$
$368$	15976.6i	2.26314i
$369$	6031.32i	0.850888i
$370$	2412.05	0.338910
$371$	− 864.905i	− 0.121034i
$372$	−516.600	−0.0720013
$373$	8379.14	1.16315	0.581576	−	0.813492i	$-0.302436\pi$
$373$	8379.14	1.16315	0.581576	+	0.813492i	$0.302436\pi$
$374$	0	0
$375$	2242.95	0.308868
$376$	6293.64	0.863217
$377$	1197.82i	0.163636i
$378$	−874.957	−0.119055
$379$	6395.71i	0.866821i	0.901196	+	0.433411i	$0.142690\pi$
$379$	6395.71i	0.866821i	−0.901196	+	0.433411i	$0.857310\pi$
$380$	323.266i	0.0436400i
$381$	3186.81i	0.428518i
$382$	−2483.89	−0.332689
$383$	204.687	0.0273081	0.0136541	−	0.999907i	$-0.495654\pi$
$383$	204.687	0.0273081	0.0136541	+	0.999907i	$0.495654\pi$
$384$	− 3472.85i	− 0.461518i
$385$	− 379.991i	− 0.0503017i
$386$	− 11750.5i	− 1.54944i
$387$	7297.75	0.958567
$388$	− 2620.59i	− 0.342887i
$389$	−5770.56	−0.752131	−0.376066	−	0.926593i	$-0.622723\pi$
$389$	−5770.56	−0.752131	−0.376066	+	0.926593i	$0.622723\pi$
$390$	1878.14	0.243854
$391$	0	0
$392$	6404.44	0.825186
$393$	5207.61	0.668420
$394$	− 1424.76i	− 0.182178i
$395$	−450.816	−0.0574253
$396$	1218.06i	0.154571i
$397$	7144.37i	0.903188i	0.892223	+	0.451594i	$0.149145\pi$
$397$	7144.37i	0.903188i	−0.892223	+	0.451594i	$0.850855\pi$
$398$	− 10972.7i	− 1.38194i
$399$	−184.474	−0.0231459
$400$	−7570.24	−0.946280
$401$	− 6364.52i	− 0.792591i	−0.918123	−	0.396296i	$-0.870296\pi$
$401$	− 6364.52i	− 0.792591i	0.918123	−	0.396296i	$-0.129704\pi$
$402$	− 4590.84i	− 0.569578i
$403$	− 7984.16i	− 0.986897i
$404$	−590.070	−0.0726660
$405$	− 2120.78i	− 0.260204i
$406$	176.086	0.0215246
$407$	4162.33	0.506926
$408$	0	0
$409$	2997.87	0.362433	0.181217	−	0.983443i	$-0.441997\pi$
$409$	2997.87	0.362433	0.181217	+	0.983443i	$0.441997\pi$
$410$	−4134.07	−0.497969
$411$	1485.00i	0.178222i
$412$	1918.60	0.229424
$413$	− 152.457i	− 0.0181644i
$414$	15315.5i	1.81816i
$415$	1822.89i	0.215620i
$416$	−5139.27	−0.605705
$417$	−5043.08	−0.592232
$418$	2857.15i	0.334325i
$419$	− 11747.3i	− 1.36967i	−0.728698	−	0.684835i	$-0.759874\pi$
$419$	− 11747.3i	− 1.36967i	0.728698	−	0.684835i	$-0.240126\pi$
$420$	− 53.9060i	− 0.00626272i
$421$	8842.15	1.02361	0.511805	−	0.859102i	$-0.328977\pi$
$421$	8842.15	1.02361	0.511805	+	0.859102i	$0.328977\pi$
$422$	5733.60i	0.661391i
$423$	7588.52	0.872261
$424$	5932.52	0.679501
$425$	0	0
$426$	−3950.41	−0.449291
$427$	−2280.36	−0.258441
$428$	2280.57i	0.257560i
$429$	3240.98	0.364746
$430$	5002.13i	0.560987i
$431$	3099.38i	0.346385i	0.984888	+	0.173192i	$0.0554082\pi$
$431$	3099.38i	0.346385i	−0.984888	+	0.173192i	$0.944592\pi$
$432$	− 7548.55i	− 0.840694i
$433$	−10072.8	−1.11794	−0.558970	−	0.829188i	$-0.688803\pi$
$433$	−10072.8	−1.11794	−0.558970	+	0.829188i	$0.688803\pi$
$434$	−1173.72	−0.129816
$435$	− 199.961i	− 0.0220400i
$436$	− 1628.14i	− 0.178839i
$437$	7014.09i	0.767802i
$438$	−3117.24	−0.340063
$439$	− 17357.9i	− 1.88712i	−0.331199	−	0.943561i	$-0.607453\pi$
$439$	− 17357.9i	− 1.88712i	0.331199	−	0.943561i	$-0.392547\pi$
$440$	2606.42	0.282400
$441$	7722.12	0.833832
$442$	0	0
$443$	6979.90	0.748589	0.374295	−	0.927310i	$-0.377885\pi$
$443$	6979.90	0.748589	0.374295	+	0.927310i	$0.377885\pi$
$444$	590.472	0.0631139
$445$	961.855i	0.102464i
$446$	−20518.7	−2.17845
$447$	− 3617.74i	− 0.382804i
$448$	− 932.533i	− 0.0983439i
$449$	9230.50i	0.970188i	0.874462	+	0.485094i	$0.161215\pi$
$449$	9230.50i	0.970188i	−0.874462	+	0.485094i	$0.838785\pi$
$450$	−7257.03	−0.760221
$451$	−7133.91	−0.744840
$452$	3933.81i	0.409361i
$453$	4222.72i	0.437970i
$454$	7652.64i	0.791093i
$455$	833.127	0.0858409
$456$	− 1265.33i	− 0.129944i
$457$	−12250.6	−1.25396	−0.626979	−	0.779036i	$-0.715709\pi$
$457$	−12250.6	−1.25396	−0.626979	+	0.779036i	$0.715709\pi$
$458$	2067.39	0.210923
$459$	0	0
$460$	−2049.62	−0.207748
$461$	−6259.50	−0.632395	−0.316198	−	0.948693i	$-0.602406\pi$
$461$	−6259.50	−0.632395	−0.316198	+	0.948693i	$0.602406\pi$
$462$	− 476.442i	− 0.0479786i
$463$	10195.0	1.02333	0.511665	−	0.859185i	$-0.329029\pi$
$463$	10195.0	1.02333	0.511665	+	0.859185i	$0.329029\pi$
$464$	1519.15i	0.151993i
$465$	1332.86i	0.132924i
$466$	− 3694.28i	− 0.367241i
$467$	14783.0	1.46483	0.732417	−	0.680856i	$-0.238392\pi$
$467$	14783.0	1.46483	0.732417	+	0.680856i	$0.238392\pi$
$468$	−2670.59	−0.263778
$469$	− 2036.46i	− 0.200501i
$470$	5201.43i	0.510477i
$471$	− 3201.79i	− 0.313229i
$472$	1045.72	0.101977
$473$	8631.86i	0.839098i
$474$	−565.244	−0.0547732
$475$	−3323.52	−0.321039
$476$	0	0
$477$	7153.10	0.686620
$478$	16650.7	1.59328
$479$	16370.0i	1.56152i	0.624834	+	0.780758i	$0.285167\pi$
$479$	16370.0i	1.56152i	−0.624834	+	0.780758i	$0.714833\pi$
$480$	857.939	0.0815820
$481$	9125.87i	0.865081i
$482$	4186.57i	0.395629i
$483$	− 1169.63i	− 0.110186i
$484$	1142.58	0.107305
$485$	−6761.26	−0.633017
$486$	− 11141.1i	− 1.03986i
$487$	− 4106.31i	− 0.382084i	−0.981582	−	0.191042i	$-0.938813\pi$
$487$	− 4106.31i	− 0.382084i	0.981582	−	0.191042i	$-0.0611866\pi$
$488$	− 15641.3i	− 1.45092i
$489$	4536.37	0.419513
$490$	5293.01i	0.487987i
$491$	878.001	0.0806999	0.0403499	−	0.999186i	$-0.487153\pi$
$491$	878.001	0.0806999	0.0403499	+	0.999186i	$0.487153\pi$
$492$	−1012.02	−0.0927349
$493$	0	0
$494$	−6264.28	−0.570533
$495$	3142.68	0.285359
$496$	− 10126.0i	− 0.916679i
$497$	−1752.37	−0.158158
$498$	2285.59i	0.205662i
$499$	− 13819.6i	− 1.23978i	−0.784687	−	0.619892i	$-0.787176\pi$
$499$	− 13819.6i	− 1.23978i	0.784687	−	0.619892i	$-0.212824\pi$
$500$	− 2186.08i	− 0.195529i
$501$	−3290.00	−0.293386
$502$	13495.7	1.19989
$503$	4721.43i	0.418525i	0.977859	+	0.209263i	$0.0671063\pi$
$503$	4721.43i	0.418525i	−0.977859	+	0.209263i	$0.932894\pi$
$504$	− 1225.60i	− 0.108319i
$505$	1522.41i	0.134152i
$506$	−18115.4	−1.59156
$507$	2730.76i	0.239206i
$508$	3106.01	0.271273
$509$	−16554.3	−1.44156	−0.720782	−	0.693161i	$-0.756217\pi$
$509$	−16554.3	−1.44156	−0.720782	+	0.693161i	$0.756217\pi$
$510$	0	0
$511$	−1382.78	−0.119708
$512$	5060.53	0.436808
$513$	− 3314.00i	− 0.285217i
$514$	765.813	0.0657171
$515$	− 4950.09i	− 0.423548i
$516$	1224.53i	0.104470i
$517$	8975.79i	0.763548i
$518$	1341.55	0.113792
$519$	4402.60	0.372356
$520$	5714.55i	0.481922i
$521$	14755.5i	1.24079i	0.784290	+	0.620394i	$0.213027\pi$
$521$	14755.5i	1.24079i	−0.784290	+	0.620394i	$0.786973\pi$
$522$	1456.30i	0.122108i
$523$	7800.86	0.652214	0.326107	−	0.945333i	$-0.394263\pi$
$523$	7800.86	0.652214	0.326107	+	0.945333i	$0.394263\pi$
$524$	− 5075.57i	− 0.423144i
$525$	554.210	0.0460719
$526$	−9942.71	−0.824188
$527$	0	0
$528$	4110.43	0.338795
$529$	−32304.9	−2.65512
$530$	4902.98i	0.401834i
$531$	1260.88	0.103046
$532$	179.796i	0.0146525i
$533$	− 15641.0i	− 1.27108i
$534$	1206.00i	0.0977315i
$535$	5884.01	0.475491
$536$	13968.4	1.12564
$537$	− 41.3307i	− 0.00332133i
$538$	664.944i	0.0532859i
$539$	9133.81i	0.729909i
$540$	968.399	0.0771727
$541$	23028.5i	1.83007i	0.403369	+	0.915037i	$0.367839\pi$
$541$	23028.5i	1.83007i	−0.403369	+	0.915037i	$0.632161\pi$
$542$	5130.95	0.406629
$543$	869.235	0.0686970
$544$	0	0
$545$	−4200.71	−0.330162
$546$	1044.60	0.0818765
$547$	2641.77i	0.206497i	0.994656	+	0.103249i	$0.0329238\pi$
$547$	2641.77i	0.206497i	−0.994656	+	0.103249i	$0.967076\pi$
$548$	1447.34	0.112824
$549$	− 18859.4i	− 1.46612i
$550$	− 8583.69i	− 0.665473i
$551$	666.944i	0.0515658i
$552$	8022.67	0.618601
$553$	−250.738	−0.0192811
$554$	14588.2i	1.11876i
$555$	− 1523.45i	− 0.116517i
$556$	4915.21i	0.374913i
$557$	−19800.8	−1.50626	−0.753129	−	0.657873i	$-0.771456\pi$
$557$	−19800.8	−1.50626	−0.753129	+	0.657873i	$0.771456\pi$
$558$	− 9707.08i	− 0.736440i
$559$	−18925.3	−1.43194
$560$	1056.63	0.0797333
$561$	0	0
$562$	−16005.1	−1.20131
$563$	9733.93	0.728661	0.364331	−	0.931270i	$-0.381298\pi$
$563$	9733.93	0.728661	0.364331	+	0.931270i	$0.381298\pi$
$564$	1273.31i	0.0950642i
$565$	10149.5	0.755736
$566$	− 7683.80i	− 0.570626i
$567$	− 1179.55i	− 0.0873660i
$568$	− 12019.8i	− 0.887919i
$569$	−6340.67	−0.467161	−0.233581	−	0.972337i	$-0.575044\pi$
$569$	−6340.67	−0.467161	−0.233581	+	0.972337i	$0.575044\pi$
$570$	1045.75	0.0768447
$571$	12377.7i	0.907166i	0.891214	+	0.453583i	$0.149854\pi$
$571$	12377.7i	0.907166i	−0.891214	+	0.453583i	$0.850146\pi$
$572$	− 3158.81i	− 0.230903i
$573$	1568.83i	0.114378i
$574$	−2299.32	−0.167198
$575$	− 21072.3i	− 1.52831i
$576$	7712.41	0.557900
$577$	−36.6040	−0.00264098	−0.00132049	−	0.999999i	$-0.500420\pi$
$577$	−36.6040	−0.00264098	−0.00132049	+	0.999999i	$0.500420\pi$
$578$	0	0
$579$	−7421.61	−0.532697
$580$	−194.891	−0.0139524
$581$	1013.87i	0.0723965i
$582$	−8477.44	−0.603782
$583$	8460.77i	0.601045i
$584$	− 9484.72i	− 0.672055i
$585$	6890.29i	0.486971i
$586$	10405.6	0.733534
$587$	20350.4	1.43092	0.715462	−	0.698651i	$-0.246216\pi$
$587$	20350.4	1.43092	0.715462	+	0.698651i	$0.246216\pi$
$588$	1295.73i	0.0908760i
$589$	− 4445.58i	− 0.310996i
$590$	864.248i	0.0603060i
$591$	−899.876	−0.0626328
$592$	11574.0i	0.803530i
$593$	20387.4	1.41182	0.705910	−	0.708301i	$-0.250538\pi$
$593$	20387.4	1.41182	0.705910	+	0.708301i	$0.250538\pi$
$594$	8559.10	0.591219
$595$	0	0
$596$	−3526.02	−0.242334
$597$	−6930.33	−0.475108
$598$	− 39717.8i	− 2.71603i
$599$	316.417	0.0215834	0.0107917	−	0.999942i	$-0.496565\pi$
$599$	316.417	0.0215834	0.0107917	+	0.999942i	$0.496565\pi$
$600$	3801.41i	0.258653i
$601$	1331.85i	0.0903950i	0.998978	+	0.0451975i	$0.0143917\pi$
$601$	1331.85i	0.0903950i	−0.998978	+	0.0451975i	$0.985608\pi$
$602$	2782.12i	0.188357i
$603$	16842.3	1.13743
$604$	4115.65	0.277257
$605$	− 2947.93i	− 0.198100i
$606$	1908.84i	0.127956i
$607$	− 13873.2i	− 0.927668i	−0.885922	−	0.463834i	$-0.846473\pi$
$607$	− 13873.2i	− 0.927668i	0.885922	−	0.463834i	$-0.153527\pi$
$608$	−2861.54	−0.190873
$609$	− 111.216i	− 0.00740014i
$610$	12926.9	0.858025
$611$	−19679.3	−1.30301
$612$	0	0
$613$	15297.0	1.00790	0.503948	−	0.863734i	$-0.331880\pi$
$613$	15297.0	1.00790	0.503948	+	0.863734i	$0.331880\pi$
$614$	3740.61	0.245861
$615$	2611.08i	0.171201i
$616$	1449.66	0.0948186
$617$	− 15116.8i	− 0.986354i	−0.869929	−	0.493177i	$-0.835835\pi$
$617$	− 15116.8i	− 0.986354i	0.869929	−	0.493177i	$-0.164165\pi$
$618$	− 6206.55i	− 0.403987i
$619$	22412.1i	1.45528i	0.685960	+	0.727639i	$0.259382\pi$
$619$	22412.1i	1.45528i	−0.685960	+	0.727639i	$0.740618\pi$
$620$	1299.06	0.0841479
$621$	21011.9	1.35778
$622$	− 2072.96i	− 0.133630i
$623$	534.971i	0.0344031i
$624$	9012.08i	0.578160i
$625$	6850.26	0.438417
$626$	19149.7i	1.22265i
$627$	1804.58	0.114941
$628$	−3120.61	−0.198290
$629$	0	0
$630$	1012.91	0.0640560
$631$	4830.94	0.304781	0.152390	−	0.988320i	$-0.451303\pi$
$631$	4830.94	0.304781	0.152390	+	0.988320i	$0.451303\pi$
$632$	− 1719.85i	− 0.108247i
$633$	3621.34	0.227386
$634$	− 18139.6i	− 1.13630i
$635$	− 8013.68i	− 0.500808i
$636$	1200.25i	0.0748320i
$637$	−20025.8	−1.24561
$638$	−1722.53	−0.106889
$639$	− 14492.8i	− 0.897222i
$640$	8732.96i	0.539376i
$641$	23007.3i	1.41768i	0.705370	+	0.708839i	$0.250781\pi$
$641$	23007.3i	1.41768i	−0.705370	+	0.708839i	$0.749219\pi$
$642$	7377.52	0.453532
$643$	− 5689.90i	− 0.348970i	−0.984660	−	0.174485i	$-0.944174\pi$
$643$	− 5689.90i	− 0.348970i	0.984660	−	0.174485i	$-0.0558260\pi$
$644$	−1139.97	−0.0697535
$645$	3159.35	0.192867
$646$	0	0
$647$	−15949.0	−0.969122	−0.484561	−	0.874758i	$-0.661021\pi$
$647$	−15949.0	−0.969122	−0.484561	+	0.874758i	$0.661021\pi$
$648$	8090.72	0.490484
$649$	1491.38i	0.0902029i
$650$	18819.7	1.13564
$651$	741.318i	0.0446307i
$652$	− 4421.35i	− 0.265573i
$653$	− 10764.6i	− 0.645101i	−0.946552	−	0.322550i	$-0.895460\pi$
$653$	− 10764.6i	− 0.645101i	0.946552	−	0.322550i	$-0.104540\pi$
$654$	−5266.95	−0.314914
$655$	−13095.3	−0.781182
$656$	− 19837.0i	− 1.18065i
$657$	− 11436.1i	− 0.679097i
$658$	2892.97i	0.171398i
$659$	25208.2	1.49010	0.745048	−	0.667011i	$-0.232427\pi$
$659$	25208.2	1.49010	0.745048	+	0.667011i	$0.232427\pi$
$660$	527.325i	0.0311001i
$661$	−14419.5	−0.848492	−0.424246	−	0.905547i	$-0.639461\pi$
$661$	−14419.5	−0.848492	−0.424246	+	0.905547i	$0.639461\pi$
$662$	−283.267	−0.0166306
$663$	0	0
$664$	−6954.28	−0.406444
$665$	463.885	0.0270506
$666$	11095.2i	0.645539i
$667$	−4228.67	−0.245479
$668$	3206.58i	0.185728i
$669$	12959.6i	0.748948i
$670$	11544.3i	0.665665i
$671$	22307.2	1.28339
$672$	477.174	0.0273920
$673$	− 2110.64i	− 0.120890i	−0.998172	−	0.0604451i	$-0.980748\pi$
$673$	− 2110.64i	− 0.120890i	0.998172	−	0.0604451i	$-0.0192520\pi$
$674$	− 2671.49i	− 0.152674i
$675$	9956.17i	0.567723i
$676$	2661.52	0.151429
$677$	− 11944.5i	− 0.678087i	−0.940771	−	0.339043i	$-0.889897\pi$
$677$	− 11944.5i	− 0.678087i	0.940771	−	0.339043i	$-0.110103\pi$
$678$	12725.6	0.720834
$679$	−3760.52	−0.212541
$680$	0	0
$681$	4833.41	0.271977
$682$	11481.6	0.644656
$683$	− 19085.8i	− 1.06925i	−0.845089	−	0.534626i	$-0.820453\pi$
$683$	− 19085.8i	− 1.06925i	0.845089	−	0.534626i	$-0.179547\pi$
$684$	−1486.98	−0.0831232
$685$	− 3734.23i	− 0.208288i
$686$	5955.92i	0.331484i
$687$	− 1305.76i	− 0.0725152i
$688$	−24002.3	−1.33006
$689$	−18550.2	−1.02570
$690$	6630.41i	0.365819i
$691$	− 28316.8i	− 1.55893i	−0.626445	−	0.779465i	$-0.715491\pi$
$691$	− 28316.8i	− 1.55893i	0.626445	−	0.779465i	$-0.284509\pi$
$692$	− 4290.97i	− 0.235720i
$693$	1747.91	0.0958121
$694$	− 1861.24i	− 0.101803i
$695$	12681.5	0.692141
$696$	762.846	0.0415454
$697$	0	0
$698$	29598.6	1.60505
$699$	−2333.31	−0.126257
$700$	− 540.158i	− 0.0291658i
$701$	−5916.75	−0.318791	−0.159396	−	0.987215i	$-0.550955\pi$
$701$	−5916.75	−0.318791	−0.159396	+	0.987215i	$0.550955\pi$
$702$	18765.8i	1.00893i
$703$	5081.28i	0.272609i
$704$	9122.33i	0.488368i
$705$	3285.22	0.175502
$706$	19472.7	1.03805
$707$	846.747i	0.0450427i
$708$	211.568i	0.0112305i
$709$	18499.8i	0.979936i	0.871740	+	0.489968i	$0.162992\pi$
$709$	18499.8i	0.979936i	−0.871740	+	0.489968i	$0.837008\pi$
$710$	9933.85	0.525085
$711$	− 2073.70i	− 0.109381i
$712$	−3669.45	−0.193144
$713$	28186.6	1.48050
$714$	0	0
$715$	−8149.91	−0.426279
$716$	−40.2828	−0.00210257
$717$	− 10516.6i	− 0.547768i
$718$	22546.9	1.17193
$719$	22206.5i	1.15182i	0.817511	+	0.575912i	$0.195353\pi$
$719$	22206.5i	1.15182i	−0.817511	+	0.575912i	$0.804647\pi$
$720$	8738.72i	0.452323i
$721$	− 2753.18i	− 0.142210i
$722$	18137.9	0.934935
$723$	2644.24	0.136017
$724$	− 847.195i	− 0.0434886i
$725$	− 2003.69i	− 0.102641i
$726$	− 3696.19i	− 0.188951i
$727$	3777.02	0.192685	0.0963424	−	0.995348i	$-0.469286\pi$
$727$	3777.02	0.192685	0.0963424	+	0.995348i	$0.469286\pi$
$728$	3178.36i	0.161810i
$729$	4398.10	0.223447
$730$	7838.73	0.397431
$731$	0	0
$732$	3164.52	0.159787
$733$	19956.4	1.00560	0.502801	−	0.864402i	$-0.332303\pi$
$733$	19956.4	1.00560	0.502801	+	0.864402i	$0.332303\pi$
$734$	10587.7i	0.532422i
$735$	3343.06	0.167770
$736$	− 18143.2i	− 0.908652i
$737$	19921.3i	0.995671i
$738$	− 19016.2i	− 0.948506i
$739$	−23268.4	−1.15824	−0.579121	−	0.815241i	$-0.696604\pi$
$739$	−23268.4	−1.15824	−0.579121	+	0.815241i	$0.696604\pi$
$740$	−1484.83	−0.0737612
$741$	3956.52i	0.196149i
$742$	2726.97i	0.134920i
$743$	− 12587.1i	− 0.621502i	−0.950491	−	0.310751i	$-0.899420\pi$
$743$	− 12587.1i	− 0.621502i	0.950491	−	0.310751i	$-0.100580\pi$
$744$	−5084.82	−0.250562
$745$	9097.32i	0.447383i
$746$	−26418.7	−1.29659
$747$	−8385.09	−0.410702
$748$	0	0
$749$	3272.61	0.159651
$750$	−7071.85	−0.344303
$751$	− 2662.79i	− 0.129383i	−0.997905	−	0.0646914i	$-0.979394\pi$
$751$	− 2662.79i	− 0.129383i	0.997905	−	0.0646914i	$-0.0206063\pi$
$752$	−24958.6	−1.21030
$753$	− 8523.89i	− 0.412520i
$754$	− 3776.62i	− 0.182409i
$755$	− 10618.6i	− 0.511855i
$756$	538.611	0.0259115
$757$	−26430.2	−1.26899	−0.634493	−	0.772929i	$-0.718791\pi$
$757$	−26430.2	−1.26899	−0.634493	+	0.772929i	$0.718791\pi$
$758$	− 20165.1i	− 0.966267i
$759$	11441.7i	0.547176i
$760$	3181.86i	0.151866i
$761$	−8469.75	−0.403454	−0.201727	−	0.979442i	$-0.564655\pi$
$761$	−8469.75	−0.403454	−0.201727	+	0.979442i	$0.564655\pi$
$762$	− 10047.8i	− 0.477680i
$763$	−2336.38	−0.110855
$764$	1529.05	0.0724071
$765$	0	0
$766$	−645.361	−0.0304410
$767$	−3269.83	−0.153933
$768$	5615.54i	0.263846i
$769$	−8452.54	−0.396367	−0.198184	−	0.980165i	$-0.563504\pi$
$769$	−8452.54	−0.396367	−0.198184	+	0.980165i	$0.563504\pi$
$770$	1198.08i	0.0560725i
$771$	− 483.687i	− 0.0225935i
$772$	7233.43i	0.337224i
$773$	−33936.2	−1.57904	−0.789521	−	0.613724i	$-0.789671\pi$
$773$	−33936.2	−1.57904	−0.789521	+	0.613724i	$0.789671\pi$
$774$	−23009.2	−1.06854
$775$	13355.8i	0.619036i
$776$	− 25794.0i	− 1.19324i
$777$	− 847.324i	− 0.0391217i
$778$	18194.1	0.838419
$779$	− 8708.91i	− 0.400551i
$780$	−1156.15	−0.0530730
$781$	17142.2	0.785399
$782$	0	0
$783$	1997.95	0.0911887
$784$	−25398.0	−1.15698
$785$	8051.35i	0.366070i
$786$	−16419.2	−0.745105
$787$	34379.1i	1.55716i	0.627547	+	0.778578i	$0.284059\pi$
$787$	34379.1i	1.55716i	−0.627547	+	0.778578i	$0.715941\pi$
$788$	877.059i	0.0396497i
$789$	6279.81i	0.283355i
$790$	1421.39	0.0640134
$791$	5645.00	0.253746
$792$	11989.2i	0.537902i
$793$	48908.2i	2.19014i
$794$	− 22525.6i	− 1.00681i
$795$	3096.72	0.138150
$796$	6754.61i	0.300768i
$797$	3329.26	0.147965	0.0739826	−	0.997260i	$-0.476429\pi$
$797$	3329.26	0.147965	0.0739826	+	0.997260i	$0.476429\pi$
$798$	581.630	0.0258014
$799$	0	0
$800$	8596.87	0.379932
$801$	−4424.42	−0.195167
$802$	20066.8i	0.883521i
$803$	13526.8	0.594459
$804$	2826.05i	0.123964i
$805$	2941.20i	0.128775i
$806$	25173.4i	1.10012i
$807$	419.979	0.0183196
$808$	−5807.97	−0.252876
$809$	− 7217.64i	− 0.313670i	−0.987625	−	0.156835i	$-0.949871\pi$
$809$	− 7217.64i	− 0.313670i	0.987625	−	0.156835i	$-0.0501290\pi$
$810$	6686.66i	0.290056i
$811$	− 36564.1i	− 1.58316i	−0.611067	−	0.791579i	$-0.709259\pi$
$811$	− 36564.1i	− 1.58316i	0.611067	−	0.791579i	$-0.290741\pi$
$812$	−108.396	−0.00468466
$813$	− 3240.70i	− 0.139799i
$814$	−13123.5	−0.565083
$815$	−11407.3	−0.490284
$816$	0	0
$817$	−10537.6	−0.451240
$818$	−9452.04	−0.404013
$819$	3832.29i	0.163505i
$820$	2544.88	0.108379
$821$	− 23140.5i	− 0.983691i	−0.870683	−	0.491845i	$-0.836323\pi$
$821$	− 23140.5i	− 0.983691i	0.870683	−	0.491845i	$-0.163677\pi$
$822$	− 4682.07i	− 0.198669i
$823$	− 41287.9i	− 1.74873i	−0.485269	−	0.874365i	$-0.661278\pi$
$823$	− 41287.9i	− 1.74873i	0.485269	−	0.874365i	$-0.338722\pi$
$824$	18884.5	0.798388
$825$	−5421.46	−0.228789
$826$	480.683i	0.0202483i
$827$	− 10008.0i	− 0.420811i	−0.977614	−	0.210405i	$-0.932522\pi$
$827$	− 10008.0i	− 0.420811i	0.977614	−	0.210405i	$-0.0674784\pi$
$828$	− 9428.02i	− 0.395708i
$829$	−44643.6	−1.87037	−0.935185	−	0.354159i	$-0.884767\pi$
$829$	−44643.6	−1.87037	−0.935185	+	0.354159i	$0.884767\pi$
$830$	− 5747.43i	− 0.240357i
$831$	9213.90	0.384629
$832$	−20000.6	−0.833410
$833$	0	0
$834$	15900.4	0.660176
$835$	8273.17	0.342880
$836$	− 1758.82i	− 0.0727633i
$837$	−13317.5	−0.549964
$838$	37038.2i	1.52681i
$839$	14235.3i	0.585765i	0.956148	+	0.292882i	$0.0946145\pi$
$839$	14235.3i	0.585765i	−0.956148	+	0.292882i	$0.905386\pi$
$840$	− 530.588i	− 0.0217941i
$841$	23986.9	0.983514
$842$	−27878.6	−1.14104
$843$	10108.8i	0.413008i
$844$	− 3529.52i	− 0.143947i
$845$	− 6866.88i	− 0.279560i
$846$	−23926.0	−0.972331
$847$	− 1639.60i	− 0.0665140i
$848$	−23526.5	−0.952717
$849$	−4853.08	−0.196181
$850$	0	0
$851$	−32217.1	−1.29775
$852$	2431.81	0.0977846
$853$	27729.0i	1.11304i	0.830834	+	0.556520i	$0.187864\pi$
$853$	27729.0i	1.11304i	−0.830834	+	0.556520i	$0.812136\pi$
$854$	7189.78	0.288090
$855$	3836.51i	0.153457i
$856$	22447.3i	0.896301i
$857$	− 31280.7i	− 1.24682i	−0.781894	−	0.623411i	$-0.785746\pi$
$857$	− 31280.7i	− 1.24682i	0.781894	−	0.623411i	$-0.214254\pi$
$858$	−10218.6	−0.406592
$859$	55.2890	0.00219608	0.00109804	−	0.999999i	$-0.499650\pi$
$859$	55.2890	0.00219608	0.00109804	+	0.999999i	$0.499650\pi$
$860$	− 3079.24i	− 0.122094i
$861$	1452.25i	0.0574826i
$862$	− 9772.09i	− 0.386124i
$863$	−22900.4	−0.903291	−0.451646	−	0.892197i	$-0.649163\pi$
$863$	−22900.4	−0.903291	−0.451646	+	0.892197i	$0.649163\pi$
$864$	8572.25i	0.337539i
$865$	−11070.9	−0.435172
$866$	31758.7	1.24620
$867$	0	0
$868$	722.522	0.0282535
$869$	2452.79	0.0957484
$870$	630.461i	0.0245685i
$871$	−43677.2	−1.69913
$872$	− 16025.6i	− 0.622356i
$873$	− 31101.0i	− 1.20574i
$874$	− 22114.9i	− 0.855888i
$875$	−3137.02	−0.121201
$876$	1918.93	0.0740120
$877$	− 1782.50i	− 0.0686326i	−0.999411	−	0.0343163i	$-0.989075\pi$
$877$	− 1782.50i	− 0.0686326i	0.999411	−	0.0343163i	$-0.0109254\pi$
$878$	54728.0i	2.10362i
$879$	− 6572.17i	− 0.252189i
$880$	−10336.3	−0.395949
$881$	17232.6i	0.659001i	0.944155	+	0.329500i	$0.106880\pi$
$881$	17232.6i	0.659001i	−0.944155	+	0.329500i	$0.893120\pi$
$882$	−24347.2	−0.929493
$883$	10188.2	0.388291	0.194145	−	0.980973i	$-0.437807\pi$
$883$	10188.2	0.388291	0.194145	+	0.980973i	$0.437807\pi$
$884$	0	0
$885$	545.859	0.0207332
$886$	−22007.1	−0.834471
$887$	15671.6i	0.593238i	0.954996	+	0.296619i	$0.0958592\pi$
$887$	15671.6i	0.593238i	−0.954996	+	0.296619i	$0.904141\pi$
$888$	5811.93	0.219635
$889$	− 4457.10i	− 0.168151i
$890$	− 3032.65i	− 0.114219i
$891$	11538.7i	0.433852i
$892$	12631.0	0.474122
$893$	−10957.4	−0.410612
$894$	11406.4i	0.426721i
$895$	103.932i	0.00388163i
$896$	4857.16i	0.181101i
$897$	−25085.8	−0.933768
$898$	− 29103.0i	− 1.08149i
$899$	2680.15	0.0994307
$900$	4467.32	0.165456
$901$	0	0
$902$	22492.6	0.830291
$903$	1757.19	0.0647569
$904$	38719.9i	1.42456i
$905$	−2185.81	−0.0802861
$906$	− 13313.9i	− 0.488216i
$907$	16908.3i	0.618999i	0.950900	+	0.309500i	$0.100162\pi$
$907$	16908.3i	0.618999i	−0.950900	+	0.309500i	$0.899838\pi$
$908$	− 4710.86i	− 0.172175i
$909$	−7002.92	−0.255525
$910$	−2626.78	−0.0956890
$911$	36100.6i	1.31292i	0.754362	+	0.656458i	$0.227946\pi$
$911$	36100.6i	1.31292i	−0.754362	+	0.656458i	$0.772054\pi$
$912$	5017.92i	0.182193i
$913$	− 9917.98i	− 0.359515i
$914$	38625.1	1.39782
$915$	− 8164.63i	− 0.294988i
$916$	−1272.65	−0.0459057
$917$	−7283.41	−0.262290
$918$	0	0
$919$	20016.2	0.718470	0.359235	−	0.933247i	$-0.383038\pi$
$919$	20016.2	0.718470	0.359235	+	0.933247i	$0.383038\pi$
$920$	−20174.1	−0.722958
$921$	− 2362.57i	− 0.0845269i
$922$	19735.7	0.704947
$923$	37584.1i	1.34030i
$924$	293.291i	0.0104422i
$925$	− 15265.6i	− 0.542626i
$926$	−32144.0	−1.14073
$927$	22769.8	0.806753
$928$	− 1725.17i	− 0.0610253i
$929$	− 30630.3i	− 1.08175i	−0.841103	−	0.540875i	$-0.818093\pi$
$929$	− 30630.3i	− 1.08175i	0.841103	−	0.540875i	$-0.181907\pi$
$930$	− 4202.40i	− 0.148174i
$931$	−11150.3	−0.392522
$932$	2274.15i	0.0799272i
$933$	−1309.28	−0.0459420
$934$	−46609.7	−1.63289
$935$	0	0
$936$	−26286.2	−0.917941
$937$	−3883.68	−0.135405	−0.0677025	−	0.997706i	$-0.521567\pi$
$937$	−3883.68	−0.135405	−0.0677025	+	0.997706i	$0.521567\pi$
$938$	6420.79i	0.223503i
$939$	12095.0	0.420346
$940$	− 3201.93i	− 0.111101i
$941$	21696.0i	0.751613i	0.926698	+	0.375807i	$0.122634\pi$
$941$	21696.0i	0.751613i	−0.926698	+	0.375807i	$0.877366\pi$
$942$	10095.0i	0.349164i
$943$	55217.7	1.90682
$944$	−4147.02	−0.142981
$945$	− 1389.65i	− 0.0478362i
$946$	− 27215.6i	− 0.935364i
$947$	15904.8i	0.545763i	0.962048	+	0.272882i	$0.0879767\pi$
$947$	15904.8i	0.545763i	−0.962048	+	0.272882i	$0.912023\pi$
$948$	347.956	0.0119210
$949$	29657.4i	1.01446i
$950$	10478.8	0.357870
$951$	−11456.9	−0.390659
$952$	0	0
$953$	−81.8493	−0.00278212	−0.00139106	−	0.999999i	$-0.500443\pi$
$953$	−81.8493	−0.00278212	−0.00139106	+	0.999999i	$0.500443\pi$
$954$	−22553.1	−0.765393
$955$	− 3945.03i	− 0.133674i
$956$	−10250.0	−0.346765
$957$	1087.95i	0.0367485i
$958$	− 51613.4i	− 1.74066i
$959$	− 2076.93i	− 0.0699348i
$960$	3338.86	0.112251
$961$	11926.2	0.400328
$962$	− 28773.1i	− 0.964327i
$963$	27065.7i	0.905692i
$964$	− 2577.19i	− 0.0861056i
$965$	18662.7	0.622562
$966$	3687.75i	0.122827i
$967$	19279.7	0.641151	0.320576	−	0.947223i	$-0.396124\pi$
$967$	19279.7	0.641151	0.320576	+	0.947223i	$0.396124\pi$
$968$	11246.3	0.373419
$969$	0	0
$970$	21317.7	0.705639
$971$	53776.3	1.77731	0.888653	−	0.458581i	$-0.151642\pi$
$971$	53776.3	1.77731	0.888653	+	0.458581i	$0.151642\pi$
$972$	6858.31i	0.226317i
$973$	7053.30	0.232393
$974$	12946.9i	0.425918i
$975$	− 11886.5i	− 0.390433i
$976$	62028.6i	2.03431i
$977$	−54738.2	−1.79246	−0.896228	−	0.443594i	$-0.853703\pi$
$977$	−54738.2	−1.79246	−0.896228	+	0.443594i	$0.853703\pi$
$978$	−14302.8	−0.467641
$979$	− 5233.25i	− 0.170843i
$980$	− 3258.30i	− 0.106207i
$981$	− 19322.7i	− 0.628876i
$982$	−2768.27	−0.0899581
$983$	− 3405.32i	− 0.110491i	−0.998473	−	0.0552456i	$-0.982406\pi$
$983$	− 3405.32i	− 0.110491i	0.998473	−	0.0552456i	$-0.0175942\pi$
$984$	−9961.19	−0.322715
$985$	2262.86	0.0731988
$986$	0	0
$987$	1827.20	0.0589264
$988$	3856.20	0.124172
$989$	− 66812.1i	− 2.14813i
$990$	−9908.60	−0.318097
$991$	− 29925.7i	− 0.959256i	−0.877472	−	0.479628i	$-0.840772\pi$
$991$	− 29925.7i	− 0.959256i	0.877472	−	0.479628i	$-0.159228\pi$
$992$	11499.3i	0.368047i
$993$	178.911i	0.00571759i
$994$	5525.07	0.176302
$995$	17427.3	0.555259
$996$	− 1406.98i	− 0.0447608i
$997$	32714.5i	1.03920i	0.854411	+	0.519598i	$0.173918\pi$
$997$	32714.5i	1.03920i	−0.854411	+	0.519598i	$0.826082\pi$
$998$	43572.2i	1.38202i
$999$	15221.8	0.482080

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.4.b.e.288.2		12
17.4	even	4		289.4.a.g.1.12		12
17.5	odd	16		17.4.d.a.9.3	yes	12
17.10	odd	16		17.4.d.a.2.3	✓	12
17.13	even	4		289.4.a.g.1.11		12
17.16	even	2	inner	289.4.b.e.288.1		12
51.5	even	16		153.4.l.a.145.1		12
51.44	even	16		153.4.l.a.19.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.d.a.2.3	✓	12	17.10	odd	16
17.4.d.a.9.3	yes	12	17.5	odd	16
153.4.l.a.19.1		12	51.44	even	16
153.4.l.a.145.1		12	51.5	even	16
289.4.a.g.1.11		12	17.13	even	4
289.4.a.g.1.12		12	17.4	even	4
289.4.b.e.288.1		12	17.16	even	2	inner
289.4.b.e.288.2		12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-3.15292 q^{2} +1.99138i q^{3} +1.94089 q^{4} -5.00761i q^{5} -6.27866i q^{6} -2.78516i q^{7} +19.1039 q^{8} +23.0344 q^{9} +O(q^{10})\)	\(q-3.15292 q^{2} +1.99138i q^{3} +1.94089 q^{4} -5.00761i q^{5} -6.27866i q^{6} -2.78516i q^{7} +19.1039 q^{8} +23.0344 q^{9} +15.7886i q^{10} +27.2453i q^{11} +3.86505i q^{12} -59.7352 q^{13} +8.78140i q^{14} +9.97206 q^{15} -75.7601 q^{16} -72.6256 q^{18} -33.2605 q^{19} -9.71922i q^{20} +5.54633 q^{21} -85.9023i q^{22} -210.884i q^{23} +38.0431i q^{24} +99.9239 q^{25} +188.340 q^{26} +99.6376i q^{27} -5.40570i q^{28} -20.0521i q^{29} -31.4411 q^{30} +133.659i q^{31} +86.0343 q^{32} -54.2559 q^{33} -13.9470 q^{35} +44.7072 q^{36} -152.772i q^{37} +104.868 q^{38} -118.956i q^{39} -95.6647i q^{40} +261.840i q^{41} -17.4871 q^{42} +316.820 q^{43} +52.8802i q^{44} -115.347i q^{45} +664.899i q^{46} +329.443 q^{47} -150.867i q^{48} +335.243 q^{49} -315.052 q^{50} -115.939 q^{52} +310.540 q^{53} -314.149i q^{54} +136.434 q^{55} -53.2074i q^{56} -66.2344i q^{57} +63.2227i q^{58} +54.7388 q^{59} +19.3547 q^{60} -818.751i q^{61} -421.417i q^{62} -64.1546i q^{63} +334.822 q^{64} +299.130i q^{65} +171.064 q^{66} +731.181 q^{67} +419.950 q^{69} +43.9738 q^{70} -629.179i q^{71} +440.046 q^{72} -496.481i q^{73} +481.678i q^{74} +198.987i q^{75} -64.5550 q^{76} +75.8828 q^{77} +375.057i q^{78} -90.0262i q^{79} +379.377i q^{80} +423.512 q^{81} -825.559i q^{82} -364.025 q^{83} +10.7648 q^{84} -998.907 q^{86} +39.9315 q^{87} +520.492i q^{88} -192.079 q^{89} +363.680i q^{90} +166.372i q^{91} -409.302i q^{92} -266.167 q^{93} -1038.71 q^{94} +166.556i q^{95} +171.327i q^{96} -1350.20i q^{97} -1056.99 q^{98} +627.580i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{2} + 16 q^{4} + 96 q^{8} + 36 q^{9}+O(q^{10}) \) 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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