LMFDB - Embedded newform 722.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(1,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("722.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.87939$ of defining polynomial
Character	$\chi$	$=$	722.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.87939 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.87939 q^{6} +5.06418 q^{7} +1.00000 q^{8} +0.532089 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.87939 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.87939 q^{6} +5.06418 q^{7} +1.00000 q^{8} +0.532089 q^{9} +2.00000 q^{10} -1.41147 q^{11} -1.87939 q^{12} -1.30541 q^{13} +5.06418 q^{14} -3.75877 q^{15} +1.00000 q^{16} +2.38919 q^{17} +0.532089 q^{18} +2.00000 q^{20} -9.51754 q^{21} -1.41147 q^{22} -3.06418 q^{23} -1.87939 q^{24} -1.00000 q^{25} -1.30541 q^{26} +4.63816 q^{27} +5.06418 q^{28} +8.45336 q^{29} -3.75877 q^{30} +0.369585 q^{31} +1.00000 q^{32} +2.65270 q^{33} +2.38919 q^{34} +10.1284 q^{35} +0.532089 q^{36} +4.82295 q^{37} +2.45336 q^{39} +2.00000 q^{40} -1.53209 q^{41} -9.51754 q^{42} -0.758770 q^{43} -1.41147 q^{44} +1.06418 q^{45} -3.06418 q^{46} -10.2121 q^{47} -1.87939 q^{48} +18.6459 q^{49} -1.00000 q^{50} -4.49020 q^{51} -1.30541 q^{52} +1.67499 q^{53} +4.63816 q^{54} -2.82295 q^{55} +5.06418 q^{56} +8.45336 q^{58} +0.716881 q^{59} -3.75877 q^{60} +9.75877 q^{61} +0.369585 q^{62} +2.69459 q^{63} +1.00000 q^{64} -2.61081 q^{65} +2.65270 q^{66} -1.40373 q^{67} +2.38919 q^{68} +5.75877 q^{69} +10.1284 q^{70} -6.36959 q^{71} +0.532089 q^{72} -4.55943 q^{73} +4.82295 q^{74} +1.87939 q^{75} -7.14796 q^{77} +2.45336 q^{78} -2.24123 q^{79} +2.00000 q^{80} -10.3131 q^{81} -1.53209 q^{82} -3.98545 q^{83} -9.51754 q^{84} +4.77837 q^{85} -0.758770 q^{86} -15.8871 q^{87} -1.41147 q^{88} -10.6459 q^{89} +1.06418 q^{90} -6.61081 q^{91} -3.06418 q^{92} -0.694593 q^{93} -10.2121 q^{94} -1.87939 q^{96} -1.53209 q^{97} +18.6459 q^{98} -0.751030 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{4} + 6 q^{5} + 6 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 + 6 * q^7 + 3 * q^8 - 3 * q^9	$ 3 q + 3 q^{2} + 3 q^{4} + 6 q^{5} + 6 q^{7} + 3 q^{8} - 3 q^{9} + 6 q^{10} + 6 q^{11} - 6 q^{13} + 6 q^{14} + 3 q^{16} + 3 q^{17} - 3 q^{18} + 6 q^{20} - 6 q^{21} + 6 q^{22} - 3 q^{25} - 6 q^{26} - 3 q^{27} + 6 q^{28} + 12 q^{29} - 6 q^{31} + 3 q^{32} + 9 q^{33} + 3 q^{34} + 12 q^{35} - 3 q^{36} - 6 q^{37} - 6 q^{39} + 6 q^{40} - 6 q^{42} + 9 q^{43} + 6 q^{44} - 6 q^{45} - 6 q^{47} + 15 q^{49} - 3 q^{50} - 12 q^{51} - 6 q^{52} - 3 q^{54} + 12 q^{55} + 6 q^{56} + 12 q^{58} - 6 q^{59} + 18 q^{61} - 6 q^{62} + 6 q^{63} + 3 q^{64} - 12 q^{65} + 9 q^{66} - 18 q^{67} + 3 q^{68} + 6 q^{69} + 12 q^{70} - 12 q^{71} - 3 q^{72} + 12 q^{73} - 6 q^{74} - 6 q^{77} - 6 q^{78} - 18 q^{79} + 6 q^{80} - 9 q^{81} + 6 q^{83} - 6 q^{84} + 6 q^{85} + 9 q^{86} - 18 q^{87} + 6 q^{88} + 9 q^{89} - 6 q^{90} - 24 q^{91} - 6 q^{94} + 15 q^{98} - 15 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 + 6 * q^7 + 3 * q^8 - 3 * q^9 + 6 * q^10 + 6 * q^11 - 6 * q^13 + 6 * q^14 + 3 * q^16 + 3 * q^17 - 3 * q^18 + 6 * q^20 - 6 * q^21 + 6 * q^22 - 3 * q^25 - 6 * q^26 - 3 * q^27 + 6 * q^28 + 12 * q^29 - 6 * q^31 + 3 * q^32 + 9 * q^33 + 3 * q^34 + 12 * q^35 - 3 * q^36 - 6 * q^37 - 6 * q^39 + 6 * q^40 - 6 * q^42 + 9 * q^43 + 6 * q^44 - 6 * q^45 - 6 * q^47 + 15 * q^49 - 3 * q^50 - 12 * q^51 - 6 * q^52 - 3 * q^54 + 12 * q^55 + 6 * q^56 + 12 * q^58 - 6 * q^59 + 18 * q^61 - 6 * q^62 + 6 * q^63 + 3 * q^64 - 12 * q^65 + 9 * q^66 - 18 * q^67 + 3 * q^68 + 6 * q^69 + 12 * q^70 - 12 * q^71 - 3 * q^72 + 12 * q^73 - 6 * q^74 - 6 * q^77 - 6 * q^78 - 18 * q^79 + 6 * q^80 - 9 * q^81 + 6 * q^83 - 6 * q^84 + 6 * q^85 + 9 * q^86 - 18 * q^87 + 6 * q^88 + 9 * q^89 - 6 * q^90 - 24 * q^91 - 6 * q^94 + 15 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.87939	−1.08506	−0.542532	−	0.840035i	$-0.682534\pi$
$3$	−1.87939	−1.08506	−0.542532	+	0.840035i	$0.682534\pi$
$4$	1.00000	0.500000
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	−1.87939	−0.767256
$7$	5.06418	1.91408	0.957040	−	0.289957i	$-0.0936410\pi$
$7$	5.06418	1.91408	0.957040	+	0.289957i	$0.0936410\pi$
$8$	1.00000	0.353553
$9$	0.532089	0.177363
$10$	2.00000	0.632456
$11$	−1.41147	−0.425575	−0.212788	−	0.977098i	$-0.568254\pi$
$11$	−1.41147	−0.425575	−0.212788	+	0.977098i	$0.568254\pi$
$12$	−1.87939	−0.542532
$13$	−1.30541	−0.362055	−0.181027	−	0.983478i	$-0.557942\pi$
$13$	−1.30541	−0.362055	−0.181027	+	0.983478i	$0.557942\pi$
$14$	5.06418	1.35346
$15$	−3.75877	−0.970510
$16$	1.00000	0.250000
$17$	2.38919	0.579463	0.289731	−	0.957108i	$-0.406434\pi$
$17$	2.38919	0.579463	0.289731	+	0.957108i	$0.406434\pi$
$18$	0.532089	0.125415
$19$	0	0
$19$	0	0
$20$	2.00000	0.447214
$21$	−9.51754	−2.07690
$22$	−1.41147	−0.300927
$23$	−3.06418	−0.638925	−0.319463	−	0.947599i	$-0.603502\pi$
$23$	−3.06418	−0.638925	−0.319463	+	0.947599i	$0.603502\pi$
$24$	−1.87939	−0.383628
$25$	−1.00000	−0.200000
$26$	−1.30541	−0.256011
$27$	4.63816	0.892613
$28$	5.06418	0.957040
$29$	8.45336	1.56975	0.784875	−	0.619654i	$-0.212727\pi$
$29$	8.45336	1.56975	0.784875	+	0.619654i	$0.212727\pi$
$30$	−3.75877	−0.686254
$31$	0.369585	0.0663794	0.0331897	−	0.999449i	$-0.489433\pi$
$31$	0.369585	0.0663794	0.0331897	+	0.999449i	$0.489433\pi$
$32$	1.00000	0.176777
$33$	2.65270	0.461776
$34$	2.38919	0.409742
$35$	10.1284	1.71200
$36$	0.532089	0.0886815
$37$	4.82295	0.792888	0.396444	−	0.918059i	$-0.370244\pi$
$37$	4.82295	0.792888	0.396444	+	0.918059i	$0.370244\pi$
$38$	0	0
$39$	2.45336	0.392853
$40$	2.00000	0.316228
$41$	−1.53209	−0.239272	−0.119636	−	0.992818i	$-0.538173\pi$
$41$	−1.53209	−0.239272	−0.119636	+	0.992818i	$0.538173\pi$
$42$	−9.51754	−1.46859
$43$	−0.758770	−0.115711	−0.0578557	−	0.998325i	$-0.518426\pi$
$43$	−0.758770	−0.115711	−0.0578557	+	0.998325i	$0.518426\pi$
$44$	−1.41147	−0.212788
$45$	1.06418	0.158638
$46$	−3.06418	−0.451788
$47$	−10.2121	−1.48959	−0.744796	−	0.667292i	$-0.767453\pi$
$47$	−10.2121	−1.48959	−0.744796	+	0.667292i	$0.767453\pi$
$48$	−1.87939	−0.271266
$49$	18.6459	2.66370
$50$	−1.00000	−0.141421
$51$	−4.49020	−0.628754
$52$	−1.30541	−0.181027
$53$	1.67499	0.230078	0.115039	−	0.993361i	$-0.463301\pi$
$53$	1.67499	0.230078	0.115039	+	0.993361i	$0.463301\pi$
$54$	4.63816	0.631173
$55$	−2.82295	−0.380646
$56$	5.06418	0.676729
$57$	0	0
$58$	8.45336	1.10998
$59$	0.716881	0.0933300	0.0466650	−	0.998911i	$-0.485141\pi$
$59$	0.716881	0.0933300	0.0466650	+	0.998911i	$0.485141\pi$
$60$	−3.75877	−0.485255
$61$	9.75877	1.24948	0.624741	−	0.780832i	$-0.285204\pi$
$61$	9.75877	1.24948	0.624741	+	0.780832i	$0.285204\pi$
$62$	0.369585	0.0469373
$63$	2.69459	0.339487
$64$	1.00000	0.125000
$65$	−2.61081	−0.323832
$66$	2.65270	0.326525
$67$	−1.40373	−0.171493	−0.0857467	−	0.996317i	$-0.527328\pi$
$67$	−1.40373	−0.171493	−0.0857467	+	0.996317i	$0.527328\pi$
$68$	2.38919	0.289731
$69$	5.75877	0.693274
$70$	10.1284	1.21057
$71$	−6.36959	−0.755931	−0.377965	−	0.925820i	$-0.623376\pi$
$71$	−6.36959	−0.755931	−0.377965	+	0.925820i	$0.623376\pi$
$72$	0.532089	0.0627073
$73$	−4.55943	−0.533641	−0.266820	−	0.963746i	$-0.585973\pi$
$73$	−4.55943	−0.533641	−0.266820	+	0.963746i	$0.585973\pi$
$74$	4.82295	0.560656
$75$	1.87939	0.217013
$76$	0	0
$77$	−7.14796	−0.814585
$78$	2.45336	0.277789
$79$	−2.24123	−0.252158	−0.126079	−	0.992020i	$-0.540239\pi$
$79$	−2.24123	−0.252158	−0.126079	+	0.992020i	$0.540239\pi$
$80$	2.00000	0.223607
$81$	−10.3131	−1.14591
$82$	−1.53209	−0.169191
$83$	−3.98545	−0.437460	−0.218730	−	0.975785i	$-0.570191\pi$
$83$	−3.98545	−0.437460	−0.218730	+	0.975785i	$0.570191\pi$
$84$	−9.51754	−1.03845
$85$	4.77837	0.518287
$86$	−0.758770	−0.0818203
$87$	−15.8871	−1.70328
$88$	−1.41147	−0.150464
$89$	−10.6459	−1.12846	−0.564231	−	0.825617i	$-0.690827\pi$
$89$	−10.6459	−1.12846	−0.564231	+	0.825617i	$0.690827\pi$
$90$	1.06418	0.112174
$91$	−6.61081	−0.693002
$92$	−3.06418	−0.319463
$93$	−0.694593	−0.0720259
$94$	−10.2121	−1.05330
$95$	0	0
$96$	−1.87939	−0.191814
$97$	−1.53209	−0.155560	−0.0777800	−	0.996971i	$-0.524783\pi$
$97$	−1.53209	−0.155560	−0.0777800	+	0.996971i	$0.524783\pi$
$98$	18.6459	1.88352
$99$	−0.751030	−0.0754813
$100$	−1.00000	−0.100000
$101$	8.82295	0.877916	0.438958	−	0.898508i	$-0.355348\pi$
$101$	8.82295	0.877916	0.438958	+	0.898508i	$0.355348\pi$
$102$	−4.49020	−0.444596
$103$	−7.14796	−0.704309	−0.352155	−	0.935942i	$-0.614551\pi$
$103$	−7.14796	−0.704309	−0.352155	+	0.935942i	$0.614551\pi$
$104$	−1.30541	−0.128006
$105$	−19.0351	−1.85763
$106$	1.67499	0.162690
$107$	−9.36959	−0.905792	−0.452896	−	0.891563i	$-0.649609\pi$
$107$	−9.36959	−0.905792	−0.452896	+	0.891563i	$0.649609\pi$
$108$	4.63816	0.446307
$109$	11.0642	1.05976	0.529878	−	0.848074i	$-0.322238\pi$
$109$	11.0642	1.05976	0.529878	+	0.848074i	$0.322238\pi$
$110$	−2.82295	−0.269158
$111$	−9.06418	−0.860334
$112$	5.06418	0.478520
$113$	−13.2986	−1.25103	−0.625514	−	0.780213i	$-0.715110\pi$
$113$	−13.2986	−1.25103	−0.625514	+	0.780213i	$0.715110\pi$
$114$	0	0
$115$	−6.12836	−0.571472
$116$	8.45336	0.784875
$117$	−0.694593	−0.0642151
$118$	0.716881	0.0659943
$119$	12.0993	1.10914
$120$	−3.75877	−0.343127
$121$	−9.00774	−0.818886
$122$	9.75877	0.883518
$123$	2.87939	0.259625
$124$	0.369585	0.0331897
$125$	−12.0000	−1.07331
$126$	2.69459	0.240053
$127$	−5.71419	−0.507053	−0.253526	−	0.967328i	$-0.581590\pi$
$127$	−5.71419	−0.507053	−0.253526	+	0.967328i	$0.581590\pi$
$128$	1.00000	0.0883883
$129$	1.42602	0.125554
$130$	−2.61081	−0.228984
$131$	−9.87939	−0.863166	−0.431583	−	0.902073i	$-0.642045\pi$
$131$	−9.87939	−0.863166	−0.431583	+	0.902073i	$0.642045\pi$
$132$	2.65270	0.230888
$133$	0	0
$134$	−1.40373	−0.121264
$135$	9.27631	0.798378
$136$	2.38919	0.204871
$137$	5.39693	0.461091	0.230545	−	0.973062i	$-0.425949\pi$
$137$	5.39693	0.461091	0.230545	+	0.973062i	$0.425949\pi$
$138$	5.75877	0.490219
$139$	−2.33956	−0.198439	−0.0992193	−	0.995066i	$-0.531635\pi$
$139$	−2.33956	−0.198439	−0.0992193	+	0.995066i	$0.531635\pi$
$140$	10.1284	0.856002
$141$	19.1925	1.61630
$142$	−6.36959	−0.534524
$143$	1.84255	0.154082
$144$	0.532089	0.0443407
$145$	16.9067	1.40403
$146$	−4.55943	−0.377341
$147$	−35.0428	−2.89028
$148$	4.82295	0.396444
$149$	−14.3696	−1.17720	−0.588601	−	0.808424i	$-0.700321\pi$
$149$	−14.3696	−1.17720	−0.588601	+	0.808424i	$0.700321\pi$
$150$	1.87939	0.153451
$151$	−20.8384	−1.69581	−0.847904	−	0.530150i	$-0.822135\pi$
$151$	−20.8384	−1.69581	−0.847904	+	0.530150i	$0.822135\pi$
$152$	0	0
$153$	1.27126	0.102775
$154$	−7.14796	−0.575999
$155$	0.739170	0.0593716
$156$	2.45336	0.196426
$157$	6.36959	0.508348	0.254174	−	0.967158i	$-0.418196\pi$
$157$	6.36959	0.508348	0.254174	+	0.967158i	$0.418196\pi$
$158$	−2.24123	−0.178303
$159$	−3.14796	−0.249649
$160$	2.00000	0.158114
$161$	−15.5175	−1.22295
$162$	−10.3131	−0.810277
$163$	4.73143	0.370594	0.185297	−	0.982683i	$-0.440675\pi$
$163$	4.73143	0.370594	0.185297	+	0.982683i	$0.440675\pi$
$164$	−1.53209	−0.119636
$165$	5.30541	0.413025
$166$	−3.98545	−0.309331
$167$	17.2763	1.33688	0.668441	−	0.743766i	$-0.266962\pi$
$167$	17.2763	1.33688	0.668441	+	0.743766i	$0.266962\pi$
$168$	−9.51754	−0.734294
$169$	−11.2959	−0.868916
$170$	4.77837	0.366484
$171$	0	0
$172$	−0.758770	−0.0578557
$173$	18.8229	1.43108	0.715541	−	0.698571i	$-0.246180\pi$
$173$	18.8229	1.43108	0.715541	+	0.698571i	$0.246180\pi$
$174$	−15.8871	−1.20440
$175$	−5.06418	−0.382816
$176$	−1.41147	−0.106394
$177$	−1.34730	−0.101269
$178$	−10.6459	−0.797944
$179$	−13.8280	−1.03355	−0.516777	−	0.856120i	$-0.672868\pi$
$179$	−13.8280	−1.03355	−0.516777	+	0.856120i	$0.672868\pi$
$180$	1.06418	0.0793191
$181$	12.2567	0.911034	0.455517	−	0.890227i	$-0.349454\pi$
$181$	12.2567	0.911034	0.455517	+	0.890227i	$0.349454\pi$
$182$	−6.61081	−0.490026
$183$	−18.3405	−1.35577
$184$	−3.06418	−0.225894
$185$	9.64590	0.709180
$186$	−0.694593	−0.0509300
$187$	−3.37227	−0.246605
$188$	−10.2121	−0.744796
$189$	23.4884	1.70853
$190$	0	0
$191$	−20.0993	−1.45433	−0.727166	−	0.686462i	$-0.759163\pi$
$191$	−20.0993	−1.45433	−0.727166	+	0.686462i	$0.759163\pi$
$192$	−1.87939	−0.135633
$193$	16.6851	1.20102	0.600510	−	0.799617i	$-0.294964\pi$
$193$	16.6851	1.20102	0.600510	+	0.799617i	$0.294964\pi$
$194$	−1.53209	−0.109998
$195$	4.90673	0.351378
$196$	18.6459	1.33185
$197$	12.9905	0.925535	0.462768	−	0.886480i	$-0.346856\pi$
$197$	12.9905	0.925535	0.462768	+	0.886480i	$0.346856\pi$
$198$	−0.751030	−0.0533734
$199$	17.1925	1.21875	0.609373	−	0.792884i	$-0.291421\pi$
$199$	17.1925	1.21875	0.609373	+	0.792884i	$0.291421\pi$
$200$	−1.00000	−0.0707107
$201$	2.63816	0.186081
$202$	8.82295	0.620780
$203$	42.8093	3.00463
$204$	−4.49020	−0.314377
$205$	−3.06418	−0.214011
$206$	−7.14796	−0.498022
$207$	−1.63041	−0.113322
$208$	−1.30541	−0.0905137
$209$	0	0
$210$	−19.0351	−1.31355
$211$	−16.1088	−1.10897	−0.554486	−	0.832193i	$-0.687085\pi$
$211$	−16.1088	−1.10897	−0.554486	+	0.832193i	$0.687085\pi$
$212$	1.67499	0.115039
$213$	11.9709	0.820233
$214$	−9.36959	−0.640492
$215$	−1.51754	−0.103495
$216$	4.63816	0.315587
$217$	1.87164	0.127056
$218$	11.0642	0.749361
$219$	8.56893	0.579034
$220$	−2.82295	−0.190323
$221$	−3.11886	−0.209797
$222$	−9.06418	−0.608348
$223$	4.08378	0.273470	0.136735	−	0.990608i	$-0.456339\pi$
$223$	4.08378	0.273470	0.136735	+	0.990608i	$0.456339\pi$
$224$	5.06418	0.338365
$225$	−0.532089	−0.0354726
$226$	−13.2986	−0.884610
$227$	13.6604	0.906676	0.453338	−	0.891339i	$-0.350233\pi$
$227$	13.6604	0.906676	0.453338	+	0.891339i	$0.350233\pi$
$228$	0	0
$229$	−5.22163	−0.345055	−0.172527	−	0.985005i	$-0.555193\pi$
$229$	−5.22163	−0.345055	−0.172527	+	0.985005i	$0.555193\pi$
$230$	−6.12836	−0.404092
$231$	13.4338	0.883877
$232$	8.45336	0.554990
$233$	−27.0428	−1.77163	−0.885817	−	0.464035i	$-0.846401\pi$
$233$	−27.0428	−1.77163	−0.885817	+	0.464035i	$0.846401\pi$
$234$	−0.694593	−0.0454069
$235$	−20.4243	−1.33233
$236$	0.716881	0.0466650
$237$	4.21213	0.273607
$238$	12.0993	0.784279
$239$	−0.285807	−0.0184873	−0.00924366	−	0.999957i	$-0.502942\pi$
$239$	−0.285807	−0.0184873	−0.00924366	+	0.999957i	$0.502942\pi$
$240$	−3.75877	−0.242628
$241$	3.10101	0.199754	0.0998769	−	0.995000i	$-0.468155\pi$
$241$	3.10101	0.199754	0.0998769	+	0.995000i	$0.468155\pi$
$242$	−9.00774	−0.579040
$243$	5.46791	0.350767
$244$	9.75877	0.624741
$245$	37.2918	2.38249
$246$	2.87939	0.183583
$247$	0	0
$248$	0.369585	0.0234687
$249$	7.49020	0.474672
$250$	−12.0000	−0.758947
$251$	−12.6578	−0.798950	−0.399475	−	0.916744i	$-0.630808\pi$
$251$	−12.6578	−0.798950	−0.399475	+	0.916744i	$0.630808\pi$
$252$	2.69459	0.169743
$253$	4.32501	0.271911
$254$	−5.71419	−0.358540
$255$	−8.98040	−0.562374
$256$	1.00000	0.0625000
$257$	−30.3928	−1.89585	−0.947926	−	0.318492i	$-0.896824\pi$
$257$	−30.3928	−1.89585	−0.947926	+	0.318492i	$0.896824\pi$
$258$	1.42602	0.0887803
$259$	24.4243	1.51765
$260$	−2.61081	−0.161916
$261$	4.49794	0.278416
$262$	−9.87939	−0.610350
$263$	21.9026	1.35057	0.675286	−	0.737556i	$-0.264020\pi$
$263$	21.9026	1.35057	0.675286	+	0.737556i	$0.264020\pi$
$264$	2.65270	0.163263
$265$	3.34998	0.205788
$266$	0	0
$267$	20.0077	1.22445
$268$	−1.40373	−0.0857467
$269$	−1.43376	−0.0874181	−0.0437090	−	0.999044i	$-0.513917\pi$
$269$	−1.43376	−0.0874181	−0.0437090	+	0.999044i	$0.513917\pi$
$270$	9.27631	0.564538
$271$	16.1729	0.982436	0.491218	−	0.871037i	$-0.336552\pi$
$271$	16.1729	0.982436	0.491218	+	0.871037i	$0.336552\pi$
$272$	2.38919	0.144866
$273$	12.4243	0.751951
$274$	5.39693	0.326040
$275$	1.41147	0.0851151
$276$	5.75877	0.346637
$277$	11.1088	0.667460	0.333730	−	0.942669i	$-0.391693\pi$
$277$	11.1088	0.667460	0.333730	+	0.942669i	$0.391693\pi$
$278$	−2.33956	−0.140317
$279$	0.196652	0.0117733
$280$	10.1284	0.605285
$281$	4.24897	0.253472	0.126736	−	0.991936i	$-0.459550\pi$
$281$	4.24897	0.253472	0.126736	+	0.991936i	$0.459550\pi$
$282$	19.1925	1.14290
$283$	−5.45605	−0.324329	−0.162164	−	0.986764i	$-0.551847\pi$
$283$	−5.45605	−0.324329	−0.162164	+	0.986764i	$0.551847\pi$
$284$	−6.36959	−0.377965
$285$	0	0
$286$	1.84255	0.108952
$287$	−7.75877	−0.457986
$288$	0.532089	0.0313536
$289$	−11.2918	−0.664223
$290$	16.9067	0.992797
$291$	2.87939	0.168793
$292$	−4.55943	−0.266820
$293$	17.8135	1.04067	0.520337	−	0.853961i	$-0.325807\pi$
$293$	17.8135	1.04067	0.520337	+	0.853961i	$0.325807\pi$
$294$	−35.0428	−2.04374
$295$	1.43376	0.0834769
$296$	4.82295	0.280328
$297$	−6.54664	−0.379874
$298$	−14.3696	−0.832408
$299$	4.00000	0.231326
$300$	1.87939	0.108506
$301$	−3.84255	−0.221481
$302$	−20.8384	−1.19912
$303$	−16.5817	−0.952595
$304$	0	0
$305$	19.5175	1.11757
$306$	1.27126	0.0726730
$307$	−28.6587	−1.63564	−0.817819	−	0.575476i	$-0.804817\pi$
$307$	−28.6587	−1.63564	−0.817819	+	0.575476i	$0.804817\pi$
$308$	−7.14796	−0.407293
$309$	13.4338	0.764220
$310$	0.739170	0.0419820
$311$	15.8135	0.896699	0.448349	−	0.893858i	$-0.352012\pi$
$311$	15.8135	0.896699	0.448349	+	0.893858i	$0.352012\pi$
$312$	2.45336	0.138894
$313$	13.1402	0.742729	0.371364	−	0.928487i	$-0.378890\pi$
$313$	13.1402	0.742729	0.371364	+	0.928487i	$0.378890\pi$
$314$	6.36959	0.359456
$315$	5.38919	0.303646
$316$	−2.24123	−0.126079
$317$	−21.4047	−1.20221	−0.601103	−	0.799172i	$-0.705272\pi$
$317$	−21.4047	−1.20221	−0.601103	+	0.799172i	$0.705272\pi$
$318$	−3.14796	−0.176529
$319$	−11.9317	−0.668047
$320$	2.00000	0.111803
$321$	17.6091	0.982842
$322$	−15.5175	−0.864759
$323$	0	0
$324$	−10.3131	−0.572953
$325$	1.30541	0.0724110
$326$	4.73143	0.262050
$327$	−20.7939	−1.14990
$328$	−1.53209	−0.0845955
$329$	−51.7161	−2.85120
$330$	5.30541	0.292053
$331$	−25.3979	−1.39599	−0.697996	−	0.716101i	$-0.745925\pi$
$331$	−25.3979	−1.39599	−0.697996	+	0.716101i	$0.745925\pi$
$332$	−3.98545	−0.218730
$333$	2.56624	0.140629
$334$	17.2763	0.945318
$335$	−2.80747	−0.153388
$336$	−9.51754	−0.519224
$337$	26.3773	1.43686	0.718432	−	0.695597i	$-0.244860\pi$
$337$	26.3773	1.43686	0.718432	+	0.695597i	$0.244860\pi$
$338$	−11.2959	−0.614417
$339$	24.9932	1.35744
$340$	4.77837	0.259144
$341$	−0.521660	−0.0282495
$342$	0	0
$343$	58.9769	3.18445
$344$	−0.758770	−0.0409102
$345$	11.5175	0.620084
$346$	18.8229	1.01193
$347$	−25.6313	−1.37596	−0.687981	−	0.725728i	$-0.741503\pi$
$347$	−25.6313	−1.37596	−0.687981	+	0.725728i	$0.741503\pi$
$348$	−15.8871	−0.851639
$349$	−5.84255	−0.312744	−0.156372	−	0.987698i	$-0.549980\pi$
$349$	−5.84255	−0.312744	−0.156372	+	0.987698i	$0.549980\pi$
$350$	−5.06418	−0.270692
$351$	−6.05468	−0.323175
$352$	−1.41147	−0.0752318
$353$	−22.4097	−1.19275	−0.596375	−	0.802706i	$-0.703393\pi$
$353$	−22.4097	−1.19275	−0.596375	+	0.802706i	$0.703393\pi$
$354$	−1.34730	−0.0716080
$355$	−12.7392	−0.676125
$356$	−10.6459	−0.564231
$357$	−22.7392	−1.20348
$358$	−13.8280	−0.730833
$359$	9.61680	0.507555	0.253778	−	0.967263i	$-0.418327\pi$
$359$	9.61680	0.507555	0.253778	+	0.967263i	$0.418327\pi$
$360$	1.06418	0.0560871
$361$	0	0
$362$	12.2567	0.644198
$363$	16.9290	0.888543
$364$	−6.61081	−0.346501
$365$	−9.11886	−0.477303
$366$	−18.3405	−0.958673
$367$	23.3601	1.21939	0.609693	−	0.792637i	$-0.291293\pi$
$367$	23.3601	1.21939	0.609693	+	0.792637i	$0.291293\pi$
$368$	−3.06418	−0.159731
$369$	−0.815207	−0.0424380
$370$	9.64590	0.501466
$371$	8.48246	0.440387
$372$	−0.694593	−0.0360130
$373$	−25.9418	−1.34322	−0.671608	−	0.740907i	$-0.734396\pi$
$373$	−25.9418	−1.34322	−0.671608	+	0.740907i	$0.734396\pi$
$374$	−3.37227	−0.174376
$375$	22.5526	1.16461
$376$	−10.2121	−0.526651
$377$	−11.0351	−0.568336
$378$	23.4884	1.20812
$379$	9.47834	0.486870	0.243435	−	0.969917i	$-0.421726\pi$
$379$	9.47834	0.486870	0.243435	+	0.969917i	$0.421726\pi$
$380$	0	0
$381$	10.7392	0.550184
$382$	−20.0993	−1.02837
$383$	−13.4884	−0.689227	−0.344614	−	0.938745i	$-0.611990\pi$
$383$	−13.4884	−0.689227	−0.344614	+	0.938745i	$0.611990\pi$
$384$	−1.87939	−0.0959070
$385$	−14.2959	−0.728587
$386$	16.6851	0.849249
$387$	−0.403733	−0.0205229
$388$	−1.53209	−0.0777800
$389$	−25.1480	−1.27505	−0.637526	−	0.770429i	$-0.720042\pi$
$389$	−25.1480	−1.27505	−0.637526	+	0.770429i	$0.720042\pi$
$390$	4.90673	0.248462
$391$	−7.32089	−0.370233
$392$	18.6459	0.941760
$393$	18.5672	0.936590
$394$	12.9905	0.654452
$395$	−4.48246	−0.225537
$396$	−0.751030	−0.0377407
$397$	6.56624	0.329550	0.164775	−	0.986331i	$-0.447310\pi$
$397$	6.56624	0.329550	0.164775	+	0.986331i	$0.447310\pi$
$398$	17.1925	0.861784
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	−29.5107	−1.47370	−0.736848	−	0.676059i	$-0.763687\pi$
$401$	−29.5107	−1.47370	−0.736848	+	0.676059i	$0.763687\pi$
$402$	2.63816	0.131579
$403$	−0.482459	−0.0240330
$404$	8.82295	0.438958
$405$	−20.6263	−1.02493
$406$	42.8093	2.12459
$407$	−6.80747	−0.337434
$408$	−4.49020	−0.222298
$409$	21.1310	1.04486	0.522431	−	0.852681i	$-0.325025\pi$
$409$	21.1310	1.04486	0.522431	+	0.852681i	$0.325025\pi$
$410$	−3.06418	−0.151329
$411$	−10.1429	−0.500313
$412$	−7.14796	−0.352155
$413$	3.63041	0.178641
$414$	−1.63041	−0.0801305
$415$	−7.97090	−0.391276
$416$	−1.30541	−0.0640029
$417$	4.39693	0.215318
$418$	0	0
$419$	−27.8830	−1.36217	−0.681087	−	0.732202i	$-0.738492\pi$
$419$	−27.8830	−1.36217	−0.681087	+	0.732202i	$0.738492\pi$
$420$	−19.0351	−0.928817
$421$	−0.0445774	−0.00217257	−0.00108629	−	0.999999i	$-0.500346\pi$
$421$	−0.0445774	−0.00217257	−0.00108629	+	0.999999i	$0.500346\pi$
$422$	−16.1088	−0.784162
$423$	−5.43376	−0.264199
$424$	1.67499	0.0813448
$425$	−2.38919	−0.115893
$426$	11.9709	0.579992
$427$	49.4201	2.39161
$428$	−9.36959	−0.452896
$429$	−3.46286	−0.167188
$430$	−1.51754	−0.0731823
$431$	−11.7879	−0.567802	−0.283901	−	0.958854i	$-0.591629\pi$
$431$	−11.7879	−0.567802	−0.283901	+	0.958854i	$0.591629\pi$
$432$	4.63816	0.223153
$433$	27.6459	1.32858	0.664289	−	0.747476i	$-0.268735\pi$
$433$	27.6459	1.32858	0.664289	+	0.747476i	$0.268735\pi$
$434$	1.87164	0.0898418
$435$	−31.7743	−1.52346
$436$	11.0642	0.529878
$437$	0	0
$438$	8.56893	0.409439
$439$	37.4492	1.78735	0.893677	−	0.448710i	$-0.148116\pi$
$439$	37.4492	1.78735	0.893677	+	0.448710i	$0.148116\pi$
$440$	−2.82295	−0.134579
$441$	9.92127	0.472442
$442$	−3.11886	−0.148349
$443$	20.9881	0.997177	0.498588	−	0.866839i	$-0.333852\pi$
$443$	20.9881	0.997177	0.498588	+	0.866839i	$0.333852\pi$
$444$	−9.06418	−0.430167
$445$	−21.2918	−1.00933
$446$	4.08378	0.193372
$447$	27.0060	1.27734
$448$	5.06418	0.239260
$449$	−21.8949	−1.03328	−0.516641	−	0.856202i	$-0.672818\pi$
$449$	−21.8949	−1.03328	−0.516641	+	0.856202i	$0.672818\pi$
$450$	−0.532089	−0.0250829
$451$	2.16250	0.101828
$452$	−13.2986	−0.625514
$453$	39.1634	1.84006
$454$	13.6604	0.641116
$455$	−13.2216	−0.619840
$456$	0	0
$457$	−13.0496	−0.610436	−0.305218	−	0.952283i	$-0.598729\pi$
$457$	−13.0496	−0.610436	−0.305218	+	0.952283i	$0.598729\pi$
$458$	−5.22163	−0.243991
$459$	11.0814	0.517236
$460$	−6.12836	−0.285736
$461$	4.40879	0.205338	0.102669	−	0.994716i	$-0.467262\pi$
$461$	4.40879	0.205338	0.102669	+	0.994716i	$0.467262\pi$
$462$	13.4338	0.624995
$463$	26.6655	1.23925	0.619625	−	0.784898i	$-0.287285\pi$
$463$	26.6655	1.23925	0.619625	+	0.784898i	$0.287285\pi$
$464$	8.45336	0.392438
$465$	−1.38919	−0.0644219
$466$	−27.0428	−1.25273
$467$	30.1138	1.39350	0.696750	−	0.717314i	$-0.254629\pi$
$467$	30.1138	1.39350	0.696750	+	0.717314i	$0.254629\pi$
$468$	−0.694593	−0.0321076
$469$	−7.10876	−0.328252
$470$	−20.4243	−0.942101
$471$	−11.9709	−0.551590
$472$	0.716881	0.0329971
$473$	1.07098	0.0492439
$474$	4.21213	0.193470
$475$	0	0
$476$	12.0993	0.554569
$477$	0.891245	0.0408073
$478$	−0.285807	−0.0130725
$479$	8.16756	0.373185	0.186593	−	0.982437i	$-0.440256\pi$
$479$	8.16756	0.373185	0.186593	+	0.982437i	$0.440256\pi$
$480$	−3.75877	−0.171564
$481$	−6.29591	−0.287069
$482$	3.10101	0.141247
$483$	29.1634	1.32698
$484$	−9.00774	−0.409443
$485$	−3.06418	−0.139137
$486$	5.46791	0.248029
$487$	26.5871	1.20478	0.602388	−	0.798203i	$-0.294216\pi$
$487$	26.5871	1.20478	0.602388	+	0.798203i	$0.294216\pi$
$488$	9.75877	0.441759
$489$	−8.89218	−0.402118
$490$	37.2918	1.68467
$491$	38.8289	1.75233	0.876163	−	0.482016i	$-0.160095\pi$
$491$	38.8289	1.75233	0.876163	+	0.482016i	$0.160095\pi$
$492$	2.87939	0.129813
$493$	20.1967	0.909611
$494$	0	0
$495$	−1.50206	−0.0675125
$496$	0.369585	0.0165949
$497$	−32.2567	−1.44691
$498$	7.49020	0.335644
$499$	20.6587	0.924810	0.462405	−	0.886669i	$-0.346987\pi$
$499$	20.6587	0.924810	0.462405	+	0.886669i	$0.346987\pi$
$500$	−12.0000	−0.536656
$501$	−32.4688	−1.45060
$502$	−12.6578	−0.564943
$503$	0.0736733	0.00328493	0.00164246	−	0.999999i	$-0.499477\pi$
$503$	0.0736733	0.00328493	0.00164246	+	0.999999i	$0.499477\pi$
$504$	2.69459	0.120027
$505$	17.6459	0.785232
$506$	4.32501	0.192270
$507$	21.2294	0.942829
$508$	−5.71419	−0.253526
$509$	15.0196	0.665732	0.332866	−	0.942974i	$-0.391984\pi$
$509$	15.0196	0.665732	0.332866	+	0.942974i	$0.391984\pi$
$510$	−8.98040	−0.397659
$511$	−23.0898	−1.02143
$512$	1.00000	0.0441942
$513$	0	0
$514$	−30.3928	−1.34057
$515$	−14.2959	−0.629953
$516$	1.42602	0.0627771
$517$	14.4142	0.633934
$518$	24.4243	1.07314
$519$	−35.3756	−1.55282
$520$	−2.61081	−0.114492
$521$	45.1712	1.97899	0.989493	−	0.144583i	$-0.0461842\pi$
$521$	45.1712	1.97899	0.989493	+	0.144583i	$0.0461842\pi$
$522$	4.49794	0.196870
$523$	0.167556	0.00732672	0.00366336	−	0.999993i	$-0.498834\pi$
$523$	0.167556	0.00732672	0.00366336	+	0.999993i	$0.498834\pi$
$524$	−9.87939	−0.431583
$525$	9.51754	0.415380
$526$	21.9026	0.954999
$527$	0.883007	0.0384644
$528$	2.65270	0.115444
$529$	−13.6108	−0.591775
$530$	3.34998	0.145514
$531$	0.381445	0.0165533
$532$	0	0
$533$	2.00000	0.0866296
$534$	20.0077	0.865820
$535$	−18.7392	−0.810165
$536$	−1.40373	−0.0606320
$537$	25.9881	1.12147
$538$	−1.43376	−0.0618139
$539$	−26.3182	−1.13361
$540$	9.27631	0.399189
$541$	−0.980400	−0.0421507	−0.0210753	−	0.999778i	$-0.506709\pi$
$541$	−0.980400	−0.0421507	−0.0210753	+	0.999778i	$0.506709\pi$
$542$	16.1729	0.694687
$543$	−23.0351	−0.988530
$544$	2.38919	0.102435
$545$	22.1284	0.947875
$546$	12.4243	0.531710
$547$	28.4047	1.21450	0.607248	−	0.794512i	$-0.292273\pi$
$547$	28.4047	1.21450	0.607248	+	0.794512i	$0.292273\pi$
$548$	5.39693	0.230545
$549$	5.19253	0.221612
$550$	1.41147	0.0601855
$551$	0	0
$552$	5.75877	0.245110
$553$	−11.3500	−0.482650
$554$	11.1088	0.471966
$555$	−18.1284	−0.769506
$556$	−2.33956	−0.0992193
$557$	35.6323	1.50979	0.754894	−	0.655847i	$-0.227688\pi$
$557$	35.6323	1.50979	0.754894	+	0.655847i	$0.227688\pi$
$558$	0.196652	0.00832495
$559$	0.990505	0.0418939
$560$	10.1284	0.428001
$561$	6.33780	0.267582
$562$	4.24897	0.179232
$563$	8.62773	0.363615	0.181808	−	0.983334i	$-0.441805\pi$
$563$	8.62773	0.363615	0.181808	+	0.983334i	$0.441805\pi$
$564$	19.1925	0.808151
$565$	−26.5972	−1.11895
$566$	−5.45605	−0.229335
$567$	−52.2276	−2.19335
$568$	−6.36959	−0.267262
$569$	22.3310	0.936164	0.468082	−	0.883685i	$-0.344945\pi$
$569$	22.3310	0.936164	0.468082	+	0.883685i	$0.344945\pi$
$570$	0	0
$571$	−9.56448	−0.400261	−0.200131	−	0.979769i	$-0.564137\pi$
$571$	−9.56448	−0.400261	−0.200131	+	0.979769i	$0.564137\pi$
$572$	1.84255	0.0770408
$573$	37.7743	1.57804
$574$	−7.75877	−0.323845
$575$	3.06418	0.127785
$576$	0.532089	0.0221704
$577$	22.4757	0.935674	0.467837	−	0.883815i	$-0.345033\pi$
$577$	22.4757	0.935674	0.467837	+	0.883815i	$0.345033\pi$
$578$	−11.2918	−0.469677
$579$	−31.3577	−1.30318
$580$	16.9067	0.702014
$581$	−20.1830	−0.837334
$582$	2.87939	0.119354
$583$	−2.36421	−0.0979155
$584$	−4.55943	−0.188671
$585$	−1.38919	−0.0574357
$586$	17.8135	0.735867
$587$	4.14796	0.171204	0.0856022	−	0.996329i	$-0.472719\pi$
$587$	4.14796	0.171204	0.0856022	+	0.996329i	$0.472719\pi$
$588$	−35.0428	−1.44514
$589$	0	0
$590$	1.43376	0.0590271
$591$	−24.4142	−1.00426
$592$	4.82295	0.198222
$593$	10.4175	0.427794	0.213897	−	0.976856i	$-0.431384\pi$
$593$	10.4175	0.427794	0.213897	+	0.976856i	$0.431384\pi$
$594$	−6.54664	−0.268612
$595$	24.1985	0.992043
$596$	−14.3696	−0.588601
$597$	−32.3114	−1.32242
$598$	4.00000	0.163572
$599$	−39.6560	−1.62030	−0.810150	−	0.586222i	$-0.800614\pi$
$599$	−39.6560	−1.62030	−0.810150	+	0.586222i	$0.800614\pi$
$600$	1.87939	0.0767256
$601$	23.8648	0.973467	0.486734	−	0.873551i	$-0.338188\pi$
$601$	23.8648	0.973467	0.486734	+	0.873551i	$0.338188\pi$
$602$	−3.84255	−0.156611
$603$	−0.746911	−0.0304166
$604$	−20.8384	−0.847904
$605$	−18.0155	−0.732433
$606$	−16.5817	−0.673586
$607$	−29.9317	−1.21489	−0.607445	−	0.794362i	$-0.707806\pi$
$607$	−29.9317	−1.21489	−0.607445	+	0.794362i	$0.707806\pi$
$608$	0	0
$609$	−80.4552	−3.26021
$610$	19.5175	0.790242
$611$	13.3310	0.539314
$612$	1.27126	0.0513876
$613$	−35.5776	−1.43697	−0.718483	−	0.695545i	$-0.755163\pi$
$613$	−35.5776	−1.43697	−0.718483	+	0.695545i	$0.755163\pi$
$614$	−28.6587	−1.15657
$615$	5.75877	0.232216
$616$	−7.14796	−0.287999
$617$	12.0324	0.484406	0.242203	−	0.970226i	$-0.422130\pi$
$617$	12.0324	0.484406	0.242203	+	0.970226i	$0.422130\pi$
$618$	13.4338	0.540385
$619$	−17.1129	−0.687824	−0.343912	−	0.939002i	$-0.611752\pi$
$619$	−17.1129	−0.687824	−0.343912	+	0.939002i	$0.611752\pi$
$620$	0.739170	0.0296858
$621$	−14.2121	−0.570313
$622$	15.8135	0.634062
$623$	−53.9127	−2.15997
$624$	2.45336	0.0982131
$625$	−19.0000	−0.760000
$626$	13.1402	0.525189
$627$	0	0
$628$	6.36959	0.254174
$629$	11.5229	0.459449
$630$	5.38919	0.214710
$631$	18.3405	0.730123	0.365062	−	0.930983i	$-0.381048\pi$
$631$	18.3405	0.730123	0.365062	+	0.930983i	$0.381048\pi$
$632$	−2.24123	−0.0891513
$633$	30.2746	1.20331
$634$	−21.4047	−0.850088
$635$	−11.4284	−0.453522
$636$	−3.14796	−0.124825
$637$	−24.3405	−0.964405
$638$	−11.9317	−0.472381
$639$	−3.38919	−0.134074
$640$	2.00000	0.0790569
$641$	−31.1780	−1.23146	−0.615728	−	0.787959i	$-0.711138\pi$
$641$	−31.1780	−1.23146	−0.615728	+	0.787959i	$0.711138\pi$
$642$	17.6091	0.694974
$643$	−31.9495	−1.25997	−0.629984	−	0.776608i	$-0.716938\pi$
$643$	−31.9495	−1.25997	−0.629984	+	0.776608i	$0.716938\pi$
$644$	−15.5175	−0.611477
$645$	2.85204	0.112299
$646$	0	0
$647$	2.99588	0.117780	0.0588901	−	0.998264i	$-0.481244\pi$
$647$	2.99588	0.117780	0.0588901	+	0.998264i	$0.481244\pi$
$648$	−10.3131	−0.405139
$649$	−1.01186	−0.0397190
$650$	1.30541	0.0512023
$651$	−3.51754	−0.137863
$652$	4.73143	0.185297
$653$	0.935822	0.0366216	0.0183108	−	0.999832i	$-0.494171\pi$
$653$	0.935822	0.0366216	0.0183108	+	0.999832i	$0.494171\pi$
$654$	−20.7939	−0.813104
$655$	−19.7588	−0.772039
$656$	−1.53209	−0.0598180
$657$	−2.42602	−0.0946481
$658$	−51.7161	−2.01610
$659$	−12.2371	−0.476690	−0.238345	−	0.971181i	$-0.576605\pi$
$659$	−12.2371	−0.476690	−0.238345	+	0.971181i	$0.576605\pi$
$660$	5.30541	0.206513
$661$	−11.9554	−0.465012	−0.232506	−	0.972595i	$-0.574693\pi$
$661$	−11.9554	−0.465012	−0.232506	+	0.972595i	$0.574693\pi$
$662$	−25.3979	−0.987116
$663$	5.86154	0.227643
$664$	−3.98545	−0.154666
$665$	0	0
$666$	2.56624	0.0994397
$667$	−25.9026	−1.00295
$668$	17.2763	0.668441
$669$	−7.67499	−0.296732
$670$	−2.80747	−0.108462
$671$	−13.7743	−0.531749
$672$	−9.51754	−0.367147
$673$	44.8634	1.72936	0.864679	−	0.502325i	$-0.167522\pi$
$673$	44.8634	1.72936	0.864679	+	0.502325i	$0.167522\pi$
$674$	26.3773	1.01602
$675$	−4.63816	−0.178523
$676$	−11.2959	−0.434458
$677$	0.945927	0.0363549	0.0181775	−	0.999835i	$-0.494214\pi$
$677$	0.945927	0.0363549	0.0181775	+	0.999835i	$0.494214\pi$
$678$	24.9932	0.959858
$679$	−7.75877	−0.297754
$680$	4.77837	0.183242
$681$	−25.6732	−0.983801
$682$	−0.521660	−0.0199754
$683$	−5.92221	−0.226607	−0.113303	−	0.993560i	$-0.536143\pi$
$683$	−5.92221	−0.226607	−0.113303	+	0.993560i	$0.536143\pi$
$684$	0	0
$685$	10.7939	0.412412
$686$	58.9769	2.25175
$687$	9.81345	0.374407
$688$	−0.758770	−0.0289279
$689$	−2.18655	−0.0833008
$690$	11.5175	0.438465
$691$	0.206148	0.00784222	0.00392111	−	0.999992i	$-0.498752\pi$
$691$	0.206148	0.00784222	0.00392111	+	0.999992i	$0.498752\pi$
$692$	18.8229	0.715541
$693$	−3.80335	−0.144477
$694$	−25.6313	−0.972953
$695$	−4.67911	−0.177489
$696$	−15.8871	−0.602200
$697$	−3.66044	−0.138649
$698$	−5.84255	−0.221144
$699$	50.8239	1.92234
$700$	−5.06418	−0.191408
$701$	4.36959	0.165037	0.0825185	−	0.996590i	$-0.473704\pi$
$701$	4.36959	0.165037	0.0825185	+	0.996590i	$0.473704\pi$
$702$	−6.05468	−0.228519
$703$	0	0
$704$	−1.41147	−0.0531969
$705$	38.3851	1.44567
$706$	−22.4097	−0.843401
$707$	44.6810	1.68040
$708$	−1.34730	−0.0506345
$709$	8.75465	0.328788	0.164394	−	0.986395i	$-0.447433\pi$
$709$	8.75465	0.328788	0.164394	+	0.986395i	$0.447433\pi$
$710$	−12.7392	−0.478093
$711$	−1.19253	−0.0447235
$712$	−10.6459	−0.398972
$713$	−1.13247	−0.0424115
$714$	−22.7392	−0.850992
$715$	3.68510	0.137815
$716$	−13.8280	−0.516777
$717$	0.537141	0.0200599
$718$	9.61680	0.358896
$719$	−27.6067	−1.02956	−0.514778	−	0.857324i	$-0.672126\pi$
$719$	−27.6067	−1.02956	−0.514778	+	0.857324i	$0.672126\pi$
$720$	1.06418	0.0396596
$721$	−36.1985	−1.34810
$722$	0	0
$723$	−5.82800	−0.216746
$724$	12.2567	0.455517
$725$	−8.45336	−0.313950
$726$	16.9290	0.628295
$727$	28.6364	1.06207	0.531033	−	0.847351i	$-0.321804\pi$
$727$	28.6364	1.06207	0.531033	+	0.847351i	$0.321804\pi$
$728$	−6.61081	−0.245013
$729$	20.6631	0.765301
$730$	−9.11886	−0.337504
$731$	−1.81284	−0.0670504
$732$	−18.3405	−0.677884
$733$	36.9614	1.36520	0.682600	−	0.730792i	$-0.260849\pi$
$733$	36.9614	1.36520	0.682600	+	0.730792i	$0.260849\pi$
$734$	23.3601	0.862237
$735$	−70.0856	−2.58515
$736$	−3.06418	−0.112947
$737$	1.98133	0.0729833
$738$	−0.815207	−0.0300082
$739$	46.0265	1.69311	0.846556	−	0.532299i	$-0.178672\pi$
$739$	46.0265	1.69311	0.846556	+	0.532299i	$0.178672\pi$
$740$	9.64590	0.354590
$741$	0	0
$742$	8.48246	0.311401
$743$	26.4107	0.968913	0.484456	−	0.874815i	$-0.339017\pi$
$743$	26.4107	0.968913	0.484456	+	0.874815i	$0.339017\pi$
$744$	−0.694593	−0.0254650
$745$	−28.7392	−1.05292
$746$	−25.9418	−0.949797
$747$	−2.12061	−0.0775892
$748$	−3.37227	−0.123303
$749$	−47.4492	−1.73376
$750$	22.5526	0.823505
$751$	−27.1771	−0.991705	−0.495852	−	0.868407i	$-0.665144\pi$
$751$	−27.1771	−0.991705	−0.495852	+	0.868407i	$0.665144\pi$
$752$	−10.2121	−0.372398
$753$	23.7888	0.866912
$754$	−11.0351	−0.401874
$755$	−41.6769	−1.51678
$756$	23.4884	0.854266
$757$	19.4047	0.705275	0.352637	−	0.935760i	$-0.385285\pi$
$757$	19.4047	0.705275	0.352637	+	0.935760i	$0.385285\pi$
$758$	9.47834	0.344269
$759$	−8.12836	−0.295041
$760$	0	0
$761$	40.2645	1.45959	0.729793	−	0.683669i	$-0.239617\pi$
$761$	40.2645	1.45959	0.729793	+	0.683669i	$0.239617\pi$
$762$	10.7392	0.389039
$763$	56.0310	2.02846
$764$	−20.0993	−0.727166
$765$	2.54252	0.0919249
$766$	−13.4884	−0.487357
$767$	−0.935822	−0.0337906
$768$	−1.87939	−0.0678165
$769$	−38.9418	−1.40428	−0.702139	−	0.712040i	$-0.747771\pi$
$769$	−38.9418	−1.40428	−0.702139	+	0.712040i	$0.747771\pi$
$770$	−14.2959	−0.515189
$771$	57.1198	2.05712
$772$	16.6851	0.600510
$773$	−6.76289	−0.243244	−0.121622	−	0.992576i	$-0.538810\pi$
$773$	−6.76289	−0.243244	−0.121622	+	0.992576i	$0.538810\pi$
$774$	−0.403733	−0.0145119
$775$	−0.369585	−0.0132759
$776$	−1.53209	−0.0549988
$777$	−45.9026	−1.64675
$778$	−25.1480	−0.901598
$779$	0	0
$780$	4.90673	0.175689
$781$	8.99050	0.321706
$782$	−7.32089	−0.261794
$783$	39.2080	1.40118
$784$	18.6459	0.665925
$785$	12.7392	0.454680
$786$	18.5672	0.662269
$787$	5.80478	0.206918	0.103459	−	0.994634i	$-0.467009\pi$
$787$	5.80478	0.206918	0.103459	+	0.994634i	$0.467009\pi$
$788$	12.9905	0.462768
$789$	−41.1634	−1.46546
$790$	−4.48246	−0.159479
$791$	−67.3465	−2.39456
$792$	−0.751030	−0.0266867
$793$	−12.7392	−0.452381
$794$	6.56624	0.233027
$795$	−6.29591	−0.223293
$796$	17.1925	0.609373
$797$	−39.2181	−1.38918	−0.694589	−	0.719407i	$-0.744414\pi$
$797$	−39.2181	−1.38918	−0.694589	+	0.719407i	$0.744414\pi$
$798$	0	0
$799$	−24.3987	−0.863163
$800$	−1.00000	−0.0353553
$801$	−5.66456	−0.200148
$802$	−29.5107	−1.04206
$803$	6.43552	0.227104
$804$	2.63816	0.0930406
$805$	−31.0351	−1.09384
$806$	−0.482459	−0.0169939
$807$	2.69459	0.0948542
$808$	8.82295	0.310390
$809$	7.00269	0.246201	0.123101	−	0.992394i	$-0.460716\pi$
$809$	7.00269	0.246201	0.123101	+	0.992394i	$0.460716\pi$
$810$	−20.6263	−0.724734
$811$	43.6851	1.53399	0.766996	−	0.641652i	$-0.221751\pi$
$811$	43.6851	1.53399	0.766996	+	0.641652i	$0.221751\pi$
$812$	42.8093	1.50231
$813$	−30.3952	−1.06601
$814$	−6.80747	−0.238602
$815$	9.46286	0.331469
$816$	−4.49020	−0.157188
$817$	0	0
$818$	21.1310	0.738830
$819$	−3.51754	−0.122913
$820$	−3.06418	−0.107006
$821$	12.3851	0.432242	0.216121	−	0.976367i	$-0.430659\pi$
$821$	12.3851	0.432242	0.216121	+	0.976367i	$0.430659\pi$
$822$	−10.1429	−0.353774
$823$	−12.8283	−0.447167	−0.223584	−	0.974685i	$-0.571776\pi$
$823$	−12.8283	−0.447167	−0.223584	+	0.974685i	$0.571776\pi$
$824$	−7.14796	−0.249011
$825$	−2.65270	−0.0923553
$826$	3.63041	0.126318
$827$	25.0966	0.872693	0.436347	−	0.899779i	$-0.356272\pi$
$827$	25.0966	0.872693	0.436347	+	0.899779i	$0.356272\pi$
$828$	−1.63041	−0.0566608
$829$	28.3269	0.983833	0.491917	−	0.870642i	$-0.336297\pi$
$829$	28.3269	0.983833	0.491917	+	0.870642i	$0.336297\pi$
$830$	−7.97090	−0.276674
$831$	−20.8776	−0.724237
$832$	−1.30541	−0.0452569
$833$	44.5485	1.54351
$834$	4.39693	0.152253
$835$	34.5526	1.19574
$836$	0	0
$837$	1.71419	0.0592512
$838$	−27.8830	−0.963203
$839$	−30.3304	−1.04712	−0.523561	−	0.851988i	$-0.675397\pi$
$839$	−30.3304	−1.04712	−0.523561	+	0.851988i	$0.675397\pi$
$840$	−19.0351	−0.656773
$841$	42.4593	1.46412
$842$	−0.0445774	−0.00153624
$843$	−7.98545	−0.275034
$844$	−16.1088	−0.554486
$845$	−22.5918	−0.777182
$846$	−5.43376	−0.186817
$847$	−45.6168	−1.56741
$848$	1.67499	0.0575195
$849$	10.2540	0.351917
$850$	−2.38919	−0.0819484
$851$	−14.7784	−0.506596
$852$	11.9709	0.410116
$853$	−43.6323	−1.49394	−0.746970	−	0.664857i	$-0.768492\pi$
$853$	−43.6323	−1.49394	−0.746970	+	0.664857i	$0.768492\pi$
$854$	49.4201	1.69112
$855$	0	0
$856$	−9.36959	−0.320246
$857$	−31.5098	−1.07635	−0.538177	−	0.842832i	$-0.680887\pi$
$857$	−31.5098	−1.07635	−0.538177	+	0.842832i	$0.680887\pi$
$858$	−3.46286	−0.118220
$859$	−18.6979	−0.637964	−0.318982	−	0.947761i	$-0.603341\pi$
$859$	−18.6979	−0.637964	−0.318982	+	0.947761i	$0.603341\pi$
$860$	−1.51754	−0.0517477
$861$	14.5817	0.496944
$862$	−11.7879	−0.401496
$863$	10.6263	0.361723	0.180862	−	0.983509i	$-0.442111\pi$
$863$	10.6263	0.361723	0.180862	+	0.983509i	$0.442111\pi$
$864$	4.63816	0.157793
$865$	37.6459	1.28000
$866$	27.6459	0.939446
$867$	21.2216	0.720724
$868$	1.87164	0.0635278
$869$	3.16344	0.107312
$870$	−31.7743	−1.07725
$871$	1.83244	0.0620900
$872$	11.0642	0.374680
$873$	−0.815207	−0.0275906
$874$	0	0
$875$	−60.7701	−2.05441
$876$	8.56893	0.289517
$877$	44.8985	1.51611	0.758057	−	0.652188i	$-0.226149\pi$
$877$	44.8985	1.51611	0.758057	+	0.652188i	$0.226149\pi$
$878$	37.4492	1.26385
$879$	−33.4783	−1.12920
$880$	−2.82295	−0.0951616
$881$	−18.0164	−0.606988	−0.303494	−	0.952833i	$-0.598153\pi$
$881$	−18.0164	−0.606988	−0.303494	+	0.952833i	$0.598153\pi$
$882$	9.92127	0.334067
$883$	−46.5981	−1.56815	−0.784076	−	0.620665i	$-0.786863\pi$
$883$	−46.5981	−1.56815	−0.784076	+	0.620665i	$0.786863\pi$
$884$	−3.11886	−0.104899
$885$	−2.69459	−0.0905777
$886$	20.9881	0.705110
$887$	7.07966	0.237712	0.118856	−	0.992912i	$-0.462077\pi$
$887$	7.07966	0.237712	0.118856	+	0.992912i	$0.462077\pi$
$888$	−9.06418	−0.304174
$889$	−28.9377	−0.970539
$890$	−21.2918	−0.713703
$891$	14.5567	0.487669
$892$	4.08378	0.136735
$893$	0	0
$894$	27.0060	0.903215
$895$	−27.6560	−0.924438
$896$	5.06418	0.169182
$897$	−7.51754	−0.251003
$898$	−21.8949	−0.730641
$899$	3.12424	0.104199
$900$	−0.532089	−0.0177363
$901$	4.00187	0.133322
$902$	2.16250	0.0720035
$903$	7.22163	0.240321
$904$	−13.2986	−0.442305
$905$	24.5134	0.814854
$906$	39.1634	1.30112
$907$	15.1156	0.501904	0.250952	−	0.968000i	$-0.419256\pi$
$907$	15.1156	0.501904	0.250952	+	0.968000i	$0.419256\pi$
$908$	13.6604	0.453338
$909$	4.69459	0.155710
$910$	−13.2216	−0.438293
$911$	−12.8366	−0.425294	−0.212647	−	0.977129i	$-0.568208\pi$
$911$	−12.8366	−0.425294	−0.212647	+	0.977129i	$0.568208\pi$
$912$	0	0
$913$	5.62536	0.186172
$914$	−13.0496	−0.431643
$915$	−36.6810	−1.21264
$916$	−5.22163	−0.172527
$917$	−50.0310	−1.65217
$918$	11.0814	0.365741
$919$	−20.6791	−0.682141	−0.341070	−	0.940038i	$-0.610789\pi$
$919$	−20.6791	−0.682141	−0.341070	+	0.940038i	$0.610789\pi$
$920$	−6.12836	−0.202046
$921$	53.8607	1.77477
$922$	4.40879	0.145196
$923$	8.31490	0.273688
$924$	13.4338	0.441938
$925$	−4.82295	−0.158578
$926$	26.6655	0.876283
$927$	−3.80335	−0.124918
$928$	8.45336	0.277495
$929$	−18.2499	−0.598760	−0.299380	−	0.954134i	$-0.596780\pi$
$929$	−18.2499	−0.598760	−0.299380	+	0.954134i	$0.596780\pi$
$930$	−1.38919	−0.0455532
$931$	0	0
$932$	−27.0428	−0.885817
$933$	−29.7196	−0.972975
$934$	30.1138	0.985354
$935$	−6.74455	−0.220570
$936$	−0.694593	−0.0227035
$937$	−4.74691	−0.155075	−0.0775374	−	0.996989i	$-0.524706\pi$
$937$	−4.74691	−0.155075	−0.0775374	+	0.996989i	$0.524706\pi$
$938$	−7.10876	−0.232109
$939$	−24.6955	−0.805908
$940$	−20.4243	−0.666166
$941$	47.0215	1.53286	0.766428	−	0.642330i	$-0.222032\pi$
$941$	47.0215	1.53286	0.766428	+	0.642330i	$0.222032\pi$
$942$	−11.9709	−0.390033
$943$	4.69459	0.152877
$944$	0.716881	0.0233325
$945$	46.9769	1.52816
$946$	1.07098	0.0348207
$947$	36.9959	1.20220	0.601102	−	0.799172i	$-0.294728\pi$
$947$	36.9959	1.20220	0.601102	+	0.799172i	$0.294728\pi$
$948$	4.21213	0.136804
$949$	5.95191	0.193207
$950$	0	0
$951$	40.2276	1.30447
$952$	12.0993	0.392139
$953$	−37.7093	−1.22152	−0.610761	−	0.791815i	$-0.709136\pi$
$953$	−37.7093	−1.22152	−0.610761	+	0.791815i	$0.709136\pi$
$954$	0.891245	0.0288551
$955$	−40.1985	−1.30079
$956$	−0.285807	−0.00924366
$957$	22.4243	0.724874
$958$	8.16756	0.263882
$959$	27.3310	0.882564
$960$	−3.75877	−0.121314
$961$	−30.8634	−0.995594
$962$	−6.29591	−0.202988
$963$	−4.98545	−0.160654
$964$	3.10101	0.0998769
$965$	33.3702	1.07422
$966$	29.1634	0.938318
$967$	40.5134	1.30282	0.651412	−	0.758724i	$-0.274177\pi$
$967$	40.5134	1.30282	0.651412	+	0.758724i	$0.274177\pi$
$968$	−9.00774	−0.289520
$969$	0	0
$970$	−3.06418	−0.0983848
$971$	−14.0779	−0.451781	−0.225891	−	0.974153i	$-0.572529\pi$
$971$	−14.0779	−0.451781	−0.225891	+	0.974153i	$0.572529\pi$
$972$	5.46791	0.175383
$973$	−11.8479	−0.379827
$974$	26.5871	0.851905
$975$	−2.45336	−0.0785705
$976$	9.75877	0.312371
$977$	−35.2057	−1.12633	−0.563164	−	0.826345i	$-0.690416\pi$
$977$	−35.2057	−1.12633	−0.563164	+	0.826345i	$0.690416\pi$
$978$	−8.89218	−0.284341
$979$	15.0264	0.480246
$980$	37.2918	1.19124
$981$	5.88713	0.187961
$982$	38.8289	1.23908
$983$	22.4397	0.715717	0.357858	−	0.933776i	$-0.383507\pi$
$983$	22.4397	0.715717	0.357858	+	0.933776i	$0.383507\pi$
$984$	2.87939	0.0917914
$985$	25.9810	0.827824
$986$	20.1967	0.643192
$987$	97.1944	3.09373
$988$	0	0
$989$	2.32501	0.0739309
$990$	−1.50206	−0.0477386
$991$	27.1034	0.860967	0.430484	−	0.902598i	$-0.358343\pi$
$991$	27.1034	0.860967	0.430484	+	0.902598i	$0.358343\pi$
$992$	0.369585	0.0117343
$993$	47.7324	1.51474
$994$	−32.2567	−1.02312
$995$	34.3851	1.09008
$996$	7.49020	0.237336
$997$	27.9472	0.885096	0.442548	−	0.896745i	$-0.354075\pi$
$997$	27.9472	0.885096	0.442548	+	0.896745i	$0.354075\pi$
$998$	20.6587	0.653939
$999$	22.3696	0.707742

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.a.l.1.1		3
3.2	odd	2		6498.2.a.bl.1.3		3
4.3	odd	2		5776.2.a.bn.1.3		3
19.2	odd	18		722.2.e.k.99.1		6
19.3	odd	18		722.2.e.l.389.1		6
19.4	even	9		722.2.e.m.415.1		6
19.5	even	9		722.2.e.m.595.1		6
19.6	even	9		722.2.e.b.245.1		6
19.7	even	3		722.2.c.k.429.3		6
19.8	odd	6		722.2.c.l.653.1		6
19.9	even	9		38.2.e.a.5.1	✓	6
19.10	odd	18		722.2.e.k.423.1		6
19.11	even	3		722.2.c.k.653.3		6
19.12	odd	6		722.2.c.l.429.1		6
19.13	odd	18		722.2.e.l.245.1		6
19.14	odd	18		722.2.e.a.595.1		6
19.15	odd	18		722.2.e.a.415.1		6
19.16	even	9		722.2.e.b.389.1		6
19.17	even	9		38.2.e.a.23.1	yes	6
19.18	odd	2		722.2.a.k.1.3		3
57.17	odd	18		342.2.u.c.289.1		6
57.47	odd	18		342.2.u.c.271.1		6
57.56	even	2		6498.2.a.bq.1.3		3
76.47	odd	18		304.2.u.c.81.1		6
76.55	odd	18		304.2.u.c.289.1		6
76.75	even	2		5776.2.a.bo.1.1		3
95.9	even	18		950.2.l.d.651.1		6
95.17	odd	36		950.2.u.b.99.2		12
95.28	odd	36		950.2.u.b.499.2		12
95.47	odd	36		950.2.u.b.499.1		12
95.74	even	18		950.2.l.d.251.1		6
95.93	odd	36		950.2.u.b.99.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.e.a.5.1	✓	6	19.9	even	9
38.2.e.a.23.1	yes	6	19.17	even	9
304.2.u.c.81.1		6	76.47	odd	18
304.2.u.c.289.1		6	76.55	odd	18
342.2.u.c.271.1		6	57.47	odd	18
342.2.u.c.289.1		6	57.17	odd	18
722.2.a.k.1.3		3	19.18	odd	2
722.2.a.l.1.1		3	1.1	even	1	trivial
722.2.c.k.429.3		6	19.7	even	3
722.2.c.k.653.3		6	19.11	even	3
722.2.c.l.429.1		6	19.12	odd	6
722.2.c.l.653.1		6	19.8	odd	6
722.2.e.a.415.1		6	19.15	odd	18
722.2.e.a.595.1		6	19.14	odd	18
722.2.e.b.245.1		6	19.6	even	9
722.2.e.b.389.1		6	19.16	even	9
722.2.e.k.99.1		6	19.2	odd	18
722.2.e.k.423.1		6	19.10	odd	18
722.2.e.l.245.1		6	19.13	odd	18
722.2.e.l.389.1		6	19.3	odd	18
722.2.e.m.415.1		6	19.4	even	9
722.2.e.m.595.1		6	19.5	even	9
950.2.l.d.251.1		6	95.74	even	18
950.2.l.d.651.1		6	95.9	even	18
950.2.u.b.99.1		12	95.93	odd	36
950.2.u.b.99.2		12	95.17	odd	36
950.2.u.b.499.1		12	95.47	odd	36
950.2.u.b.499.2		12	95.28	odd	36
5776.2.a.bn.1.3		3	4.3	odd	2
5776.2.a.bo.1.1		3	76.75	even	2
6498.2.a.bl.1.3		3	3.2	odd	2
6498.2.a.bq.1.3		3	57.56	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.87939 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.87939 q^{6} +5.06418 q^{7} +1.00000 q^{8} +0.532089 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.87939 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.87939 q^{6} +5.06418 q^{7} +1.00000 q^{8} +0.532089 q^{9} +2.00000 q^{10} -1.41147 q^{11} -1.87939 q^{12} -1.30541 q^{13} +5.06418 q^{14} -3.75877 q^{15} +1.00000 q^{16} +2.38919 q^{17} +0.532089 q^{18} +2.00000 q^{20} -9.51754 q^{21} -1.41147 q^{22} -3.06418 q^{23} -1.87939 q^{24} -1.00000 q^{25} -1.30541 q^{26} +4.63816 q^{27} +5.06418 q^{28} +8.45336 q^{29} -3.75877 q^{30} +0.369585 q^{31} +1.00000 q^{32} +2.65270 q^{33} +2.38919 q^{34} +10.1284 q^{35} +0.532089 q^{36} +4.82295 q^{37} +2.45336 q^{39} +2.00000 q^{40} -1.53209 q^{41} -9.51754 q^{42} -0.758770 q^{43} -1.41147 q^{44} +1.06418 q^{45} -3.06418 q^{46} -10.2121 q^{47} -1.87939 q^{48} +18.6459 q^{49} -1.00000 q^{50} -4.49020 q^{51} -1.30541 q^{52} +1.67499 q^{53} +4.63816 q^{54} -2.82295 q^{55} +5.06418 q^{56} +8.45336 q^{58} +0.716881 q^{59} -3.75877 q^{60} +9.75877 q^{61} +0.369585 q^{62} +2.69459 q^{63} +1.00000 q^{64} -2.61081 q^{65} +2.65270 q^{66} -1.40373 q^{67} +2.38919 q^{68} +5.75877 q^{69} +10.1284 q^{70} -6.36959 q^{71} +0.532089 q^{72} -4.55943 q^{73} +4.82295 q^{74} +1.87939 q^{75} -7.14796 q^{77} +2.45336 q^{78} -2.24123 q^{79} +2.00000 q^{80} -10.3131 q^{81} -1.53209 q^{82} -3.98545 q^{83} -9.51754 q^{84} +4.77837 q^{85} -0.758770 q^{86} -15.8871 q^{87} -1.41147 q^{88} -10.6459 q^{89} +1.06418 q^{90} -6.61081 q^{91} -3.06418 q^{92} -0.694593 q^{93} -10.2121 q^{94} -1.87939 q^{96} -1.53209 q^{97} +18.6459 q^{98} -0.751030 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{4} + 6 q^{5} + 6 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 + 6 * q^7 + 3 * q^8 - 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{4} + 6 q^{5} + 6 q^{7} + 3 q^{8} - 3 q^{9} + 6 q^{10} + 6 q^{11} - 6 q^{13} + 6 q^{14} + 3 q^{16} + 3 q^{17} - 3 q^{18} + 6 q^{20} - 6 q^{21} + 6 q^{22} - 3 q^{25} - 6 q^{26} - 3 q^{27} + 6 q^{28} + 12 q^{29} - 6 q^{31} + 3 q^{32} + 9 q^{33} + 3 q^{34} + 12 q^{35} - 3 q^{36} - 6 q^{37} - 6 q^{39} + 6 q^{40} - 6 q^{42} + 9 q^{43} + 6 q^{44} - 6 q^{45} - 6 q^{47} + 15 q^{49} - 3 q^{50} - 12 q^{51} - 6 q^{52} - 3 q^{54} + 12 q^{55} + 6 q^{56} + 12 q^{58} - 6 q^{59} + 18 q^{61} - 6 q^{62} + 6 q^{63} + 3 q^{64} - 12 q^{65} + 9 q^{66} - 18 q^{67} + 3 q^{68} + 6 q^{69} + 12 q^{70} - 12 q^{71} - 3 q^{72} + 12 q^{73} - 6 q^{74} - 6 q^{77} - 6 q^{78} - 18 q^{79} + 6 q^{80} - 9 q^{81} + 6 q^{83} - 6 q^{84} + 6 q^{85} + 9 q^{86} - 18 q^{87} + 6 q^{88} + 9 q^{89} - 6 q^{90} - 24 q^{91} - 6 q^{94} + 15 q^{98} - 15 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 + 6 * q^7 + 3 * q^8 - 3 * q^9 + 6 * q^10 + 6 * q^11 - 6 * q^13 + 6 * q^14 + 3 * q^16 + 3 * q^17 - 3 * q^18 + 6 * q^20 - 6 * q^21 + 6 * q^22 - 3 * q^25 - 6 * q^26 - 3 * q^27 + 6 * q^28 + 12 * q^29 - 6 * q^31 + 3 * q^32 + 9 * q^33 + 3 * q^34 + 12 * q^35 - 3 * q^36 - 6 * q^37 - 6 * q^39 + 6 * q^40 - 6 * q^42 + 9 * q^43 + 6 * q^44 - 6 * q^45 - 6 * q^47 + 15 * q^49 - 3 * q^50 - 12 * q^51 - 6 * q^52 - 3 * q^54 + 12 * q^55 + 6 * q^56 + 12 * q^58 - 6 * q^59 + 18 * q^61 - 6 * q^62 + 6 * q^63 + 3 * q^64 - 12 * q^65 + 9 * q^66 - 18 * q^67 + 3 * q^68 + 6 * q^69 + 12 * q^70 - 12 * q^71 - 3 * q^72 + 12 * q^73 - 6 * q^74 - 6 * q^77 - 6 * q^78 - 18 * q^79 + 6 * q^80 - 9 * q^81 + 6 * q^83 - 6 * q^84 + 6 * q^85 + 9 * q^86 - 18 * q^87 + 6 * q^88 + 9 * q^89 - 6 * q^90 - 24 * q^91 - 6 * q^94 + 15 * q^98 - 15 * q^99

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