LMFDB - Embedded newform 605.3.c.a.241.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,3,Mod(241,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.241"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	605.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$16.4850559938$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			241.4
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	605.241
Dual form			605.3.c.a.241.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.07768i q^{2} -4.00000 q^{3} -5.47214 q^{4} +2.23607 q^{5} -12.3107i q^{6} +8.05748i q^{7} -4.53077i q^{8} +7.00000 q^{9} +6.88191i q^{10} +21.8885 q^{12} +14.0413i q^{13} -24.7984 q^{14} -8.94427 q^{15} -7.94427 q^{16} +24.2784i q^{17} +21.5438i q^{18} -8.44100i q^{19} -12.2361 q^{20} -32.2299i q^{21} -25.3820 q^{23} +18.1231i q^{24} +5.00000 q^{25} -43.2148 q^{26} +8.00000 q^{27} -44.0916i q^{28} +36.5892i q^{29} -27.5276i q^{30} -10.3607 q^{31} -42.5730i q^{32} -74.7214 q^{34} +18.0171i q^{35} -38.3050 q^{36} -20.2705 q^{37} +25.9787 q^{38} -56.1653i q^{39} -10.1311i q^{40} -55.8473i q^{41} +99.1935 q^{42} -37.2752i q^{43} +15.6525 q^{45} -78.1177i q^{46} +85.5066 q^{47} +31.7771 q^{48} -15.9230 q^{49} +15.3884i q^{50} -97.1138i q^{51} -76.8361i q^{52} -54.5755 q^{53} +24.6215i q^{54} +36.5066 q^{56} +33.7640i q^{57} -112.610 q^{58} +59.2574 q^{59} +48.9443 q^{60} +36.7202i q^{61} -31.8869i q^{62} +56.4024i q^{63} +99.2492 q^{64} +31.3974i q^{65} +17.8197 q^{67} -132.855i q^{68} +101.528 q^{69} -55.4508 q^{70} +5.81966 q^{71} -31.7154i q^{72} +51.1701i q^{73} -62.3862i q^{74} -20.0000 q^{75} +46.1903i q^{76} +172.859 q^{78} -34.3190i q^{79} -17.7639 q^{80} -95.0000 q^{81} +171.880 q^{82} -145.852i q^{83} +176.367i q^{84} +54.2882i q^{85} +114.721 q^{86} -146.357i q^{87} -127.949 q^{89} +48.1734i q^{90} -113.138 q^{91} +138.894 q^{92} +41.4427 q^{93} +263.162i q^{94} -18.8746i q^{95} +170.292i q^{96} -90.3181 q^{97} -49.0059i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{3} - 4 q^{4} + 28 q^{9} + 16 q^{12} - 50 q^{14} + 4 q^{16} - 40 q^{20} - 106 q^{23} + 20 q^{25} - 70 q^{26} + 32 q^{27} + 48 q^{31} - 120 q^{34} - 28 q^{36} - 14 q^{37} + 10 q^{38} + 200 q^{42}+ \cdots - 84 q^{97}+O(q^{100}) $ 4 * q - 16 * q^3 - 4 * q^4 + 28 * q^9 + 16 * q^12 - 50 * q^14 + 4 * q^16 - 40 * q^20 - 106 * q^23 + 20 * q^25 - 70 * q^26 + 32 * q^27 + 48 * q^31 - 120 * q^34 - 28 * q^36 - 14 * q^37 + 10 * q^38 + 200 * q^42 + 266 * q^47 - 16 * q^48 + 66 * q^49 - 26 * q^53 + 70 * q^56 - 200 * q^58 + 322 * q^59 + 160 * q^60 + 236 * q^64 + 116 * q^67 + 424 * q^69 - 110 * q^70 + 68 * q^71 - 80 * q^75 + 280 * q^78 - 80 * q^80 - 380 * q^81 + 370 * q^82 + 280 * q^86 - 78 * q^89 - 220 * q^91 + 86 * q^92 - 192 * q^93 - 84 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$-1$

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 $

$2$	3.07768i	1.53884i	0.638742	+	0.769421i	$0.279455\pi$
$2$	3.07768i	1.53884i	−0.638742	+	0.769421i	$0.720545\pi$
$3$	−4.00000	−1.33333	−0.666667	−	0.745356i	$-0.732280\pi$
$3$	−4.00000	−1.33333	−0.666667	+	0.745356i	$0.732280\pi$
$4$	−5.47214	−1.36803
$5$	2.23607	0.447214
$5$	2.23607	0.447214
$6$	− 12.3107i	− 2.05179i
$7$	8.05748i	1.15107i	0.817778	+	0.575534i	$0.195206\pi$
$7$	8.05748i	1.15107i	−0.817778	+	0.575534i	$0.804794\pi$
$8$	− 4.53077i	− 0.566346i
$9$	7.00000	0.777778
$10$	6.88191i	0.688191i
$11$	0	0
$11$	0	0
$12$	21.8885	1.82405
$13$	14.0413i	1.08010i	0.841632	+	0.540051i	$0.181595\pi$
$13$	14.0413i	1.08010i	−0.841632	+	0.540051i	$0.818405\pi$
$14$	−24.7984	−1.77131
$15$	−8.94427	−0.596285
$16$	−7.94427	−0.496517
$17$	24.2784i	1.42814i	0.700072	+	0.714072i	$0.253151\pi$
$17$	24.2784i	1.42814i	−0.700072	+	0.714072i	$0.746849\pi$
$18$	21.5438i	1.19688i
$19$	− 8.44100i	− 0.444263i	−0.975017	−	0.222131i	$-0.928699\pi$
$19$	− 8.44100i	− 0.444263i	0.975017	−	0.222131i	$-0.0713014\pi$
$20$	−12.2361	−0.611803
$21$	− 32.2299i	− 1.53476i
$22$	0	0
$23$	−25.3820	−1.10356	−0.551782	−	0.833988i	$-0.686052\pi$
$23$	−25.3820	−1.10356	−0.551782	+	0.833988i	$0.686052\pi$
$24$	18.1231i	0.755128i
$25$	5.00000	0.200000
$26$	−43.2148	−1.66211
$27$	8.00000	0.296296
$28$	− 44.0916i	− 1.57470i
$29$	36.5892i	1.26170i	0.775907	+	0.630848i	$0.217293\pi$
$29$	36.5892i	1.26170i	−0.775907	+	0.630848i	$0.782707\pi$
$30$	− 27.5276i	− 0.917588i
$31$	−10.3607	−0.334215	−0.167108	−	0.985939i	$-0.553443\pi$
$31$	−10.3607	−0.334215	−0.167108	+	0.985939i	$0.553443\pi$
$32$	− 42.5730i	− 1.33041i
$33$	0	0
$34$	−74.7214	−2.19769
$35$	18.0171i	0.514774i
$36$	−38.3050	−1.06403
$37$	−20.2705	−0.547852	−0.273926	−	0.961751i	$-0.588322\pi$
$37$	−20.2705	−0.547852	−0.273926	+	0.961751i	$0.588322\pi$
$38$	25.9787	0.683650
$39$	− 56.1653i	− 1.44014i
$40$	− 10.1311i	− 0.253278i
$41$	− 55.8473i	− 1.36213i	−0.732223	−	0.681065i	$-0.761517\pi$
$41$	− 55.8473i	− 1.36213i	0.732223	−	0.681065i	$-0.238483\pi$
$42$	99.1935	2.36175
$43$	− 37.2752i	− 0.866866i	−0.901186	−	0.433433i	$-0.857302\pi$
$43$	− 37.2752i	− 0.866866i	0.901186	−	0.433433i	$-0.142698\pi$
$44$	0	0
$45$	15.6525	0.347833
$46$	− 78.1177i	− 1.69821i
$47$	85.5066	1.81929	0.909644	−	0.415388i	$-0.136354\pi$
$47$	85.5066	1.81929	0.909644	+	0.415388i	$0.136354\pi$
$48$	31.7771	0.662023
$49$	−15.9230	−0.324959
$50$	15.3884i	0.307768i
$51$	− 97.1138i	− 1.90419i
$52$	− 76.8361i	− 1.47762i
$53$	−54.5755	−1.02973	−0.514863	−	0.857273i	$-0.672157\pi$
$53$	−54.5755	−1.02973	−0.514863	+	0.857273i	$0.672157\pi$
$54$	24.6215i	0.455953i
$55$	0	0
$56$	36.5066	0.651903
$57$	33.7640i	0.592351i
$58$	−112.610	−1.94155
$59$	59.2574	1.00436	0.502181	−	0.864763i	$-0.332531\pi$
$59$	59.2574	1.00436	0.502181	+	0.864763i	$0.332531\pi$
$60$	48.9443	0.815738
$61$	36.7202i	0.601970i	0.953629	+	0.300985i	$0.0973155\pi$
$61$	36.7202i	0.601970i	−0.953629	+	0.300985i	$0.902685\pi$
$62$	− 31.8869i	− 0.514305i
$63$	56.4024i	0.895276i
$64$	99.2492	1.55077
$65$	31.3974i	0.483037i
$66$	0	0
$67$	17.8197	0.265965	0.132983	−	0.991118i	$-0.457545\pi$
$67$	17.8197	0.265965	0.132983	+	0.991118i	$0.457545\pi$
$68$	− 132.855i	− 1.95375i
$69$	101.528	1.47142
$70$	−55.4508	−0.792155
$71$	5.81966	0.0819670	0.0409835	−	0.999160i	$-0.486951\pi$
$71$	5.81966	0.0819670	0.0409835	+	0.999160i	$0.486951\pi$
$72$	− 31.7154i	− 0.440491i
$73$	51.1701i	0.700960i	0.936570	+	0.350480i	$0.113982\pi$
$73$	51.1701i	0.700960i	−0.936570	+	0.350480i	$0.886018\pi$
$74$	− 62.3862i	− 0.843057i
$75$	−20.0000	−0.266667
$76$	46.1903i	0.607767i
$77$	0	0
$78$	172.859	2.21614
$79$	− 34.3190i	− 0.434418i	−0.976125	−	0.217209i	$-0.930305\pi$
$79$	− 34.3190i	− 0.434418i	0.976125	−	0.217209i	$-0.0696953\pi$
$80$	−17.7639	−0.222049
$81$	−95.0000	−1.17284
$82$	171.880	2.09610
$83$	− 145.852i	− 1.75725i	−0.477513	−	0.878625i	$-0.658462\pi$
$83$	− 145.852i	− 1.75725i	0.477513	−	0.878625i	$-0.341538\pi$
$84$	176.367i	2.09960i
$85$	54.2882i	0.638685i
$86$	114.721	1.33397
$87$	− 146.357i	− 1.68226i
$88$	0	0
$89$	−127.949	−1.43763	−0.718816	−	0.695200i	$-0.755316\pi$
$89$	−127.949	−1.43763	−0.718816	+	0.695200i	$0.755316\pi$
$90$	48.1734i	0.535260i
$91$	−113.138	−1.24327
$92$	138.894	1.50971
$93$	41.4427	0.445621
$94$	263.162i	2.79960i
$95$	− 18.8746i	− 0.198680i
$96$	170.292i	1.77388i
$97$	−90.3181	−0.931115	−0.465557	−	0.885018i	$-0.654146\pi$
$97$	−90.3181	−0.931115	−0.465557	+	0.885018i	$0.654146\pi$
$98$	− 49.0059i	− 0.500060i
$99$	0	0
$100$	−27.3607	−0.273607
$101$	− 107.890i	− 1.06822i	−0.845414	−	0.534111i	$-0.820646\pi$
$101$	− 107.890i	− 1.06822i	0.845414	−	0.534111i	$-0.179354\pi$
$102$	298.885	2.93025
$103$	−19.1722	−0.186138	−0.0930690	−	0.995660i	$-0.529668\pi$
$103$	−19.1722	−0.186138	−0.0930690	+	0.995660i	$0.529668\pi$
$104$	63.6180	0.611712
$105$	− 72.0683i	− 0.686365i
$106$	− 167.966i	− 1.58458i
$107$	96.2658i	0.899680i	0.893109	+	0.449840i	$0.148519\pi$
$107$	96.2658i	0.899680i	−0.893109	+	0.449840i	$0.851481\pi$
$108$	−43.7771	−0.405343
$109$	− 21.0793i	− 0.193388i	−0.995314	−	0.0966940i	$-0.969173\pi$
$109$	− 21.0793i	− 0.193388i	0.995314	−	0.0966940i	$-0.0308268\pi$
$110$	0	0
$111$	81.0820	0.730469
$112$	− 64.0108i	− 0.571525i
$113$	71.6231	0.633832	0.316916	−	0.948454i	$-0.397353\pi$
$113$	71.6231	0.633832	0.316916	+	0.948454i	$0.397353\pi$
$114$	−103.915	−0.911534
$115$	−56.7558	−0.493529
$116$	− 200.221i	− 1.72604i
$117$	98.2893i	0.840080i
$118$	182.375i	1.54555i
$119$	−195.623	−1.64389
$120$	40.5244i	0.337704i
$121$	0	0
$122$	−113.013	−0.926337
$123$	223.389i	1.81617i
$124$	56.6950	0.457218
$125$	11.1803	0.0894427
$126$	−173.589	−1.37769
$127$	− 26.9571i	− 0.212261i	−0.994352	−	0.106130i	$-0.966154\pi$
$127$	− 26.9571i	− 0.212261i	0.994352	−	0.106130i	$-0.0338461\pi$
$128$	135.166i	1.05598i
$129$	149.101i	1.15582i
$130$	−96.6312	−0.743317
$131$	88.8193i	0.678010i	0.940785	+	0.339005i	$0.110090\pi$
$131$	88.8193i	0.678010i	−0.940785	+	0.339005i	$0.889910\pi$
$132$	0	0
$133$	68.0132	0.511377
$134$	54.8433i	0.409278i
$135$	17.8885	0.132508
$136$	110.000	0.808824
$137$	−120.069	−0.876415	−0.438208	−	0.898874i	$-0.644387\pi$
$137$	−120.069	−0.876415	−0.438208	+	0.898874i	$0.644387\pi$
$138$	312.471i	2.26428i
$139$	3.51715i	0.0253033i	0.999920	+	0.0126516i	$0.00402725\pi$
$139$	3.51715i	0.0253033i	−0.999920	+	0.0126516i	$0.995973\pi$
$140$	− 98.5919i	− 0.704228i
$141$	−342.026	−2.42572
$142$	17.9111i	0.126134i
$143$	0	0
$144$	−55.6099	−0.386180
$145$	81.8159i	0.564247i
$146$	−157.485	−1.07867
$147$	63.6919	0.433279
$148$	110.923	0.749480
$149$	93.3095i	0.626239i	0.949714	+	0.313119i	$0.101374\pi$
$149$	93.3095i	0.626239i	−0.949714	+	0.313119i	$0.898626\pi$
$150$	− 61.5537i	− 0.410358i
$151$	− 98.0118i	− 0.649085i	−0.945871	−	0.324542i	$-0.894790\pi$
$151$	− 98.0118i	− 0.649085i	0.945871	−	0.324542i	$-0.105210\pi$
$152$	−38.2442	−0.251607
$153$	169.949i	1.11078i
$154$	0	0
$155$	−23.1672	−0.149466
$156$	307.344i	1.97016i
$157$	−172.257	−1.09718	−0.548590	−	0.836091i	$-0.684835\pi$
$157$	−172.257	−1.09718	−0.548590	+	0.836091i	$0.684835\pi$
$158$	105.623	0.668500
$159$	218.302	1.37297
$160$	− 95.1962i	− 0.594976i
$161$	− 204.515i	− 1.27028i
$162$	− 292.380i	− 1.80481i
$163$	253.177	1.55323	0.776617	−	0.629973i	$-0.216934\pi$
$163$	253.177	1.55323	0.776617	+	0.629973i	$0.216934\pi$
$164$	305.604i	1.86344i
$165$	0	0
$166$	448.885	2.70413
$167$	− 75.3830i	− 0.451395i	−0.974197	−	0.225698i	$-0.927534\pi$
$167$	− 75.3830i	− 0.451395i	0.974197	−	0.225698i	$-0.0724661\pi$
$168$	−146.026	−0.869204
$169$	−28.1591	−0.166622
$170$	−167.082	−0.982836
$171$	− 59.0870i	− 0.345538i
$172$	203.975i	1.18590i
$173$	− 112.063i	− 0.647761i	−0.946098	−	0.323881i	$-0.895012\pi$
$173$	− 112.063i	− 0.647761i	0.946098	−	0.323881i	$-0.104988\pi$
$174$	450.440	2.58873
$175$	40.2874i	0.230214i
$176$	0	0
$177$	−237.029	−1.33915
$178$	− 393.787i	− 2.21229i
$179$	−208.507	−1.16484	−0.582421	−	0.812888i	$-0.697894\pi$
$179$	−208.507	−1.16484	−0.582421	+	0.812888i	$0.697894\pi$
$180$	−85.6525	−0.475847
$181$	79.9837	0.441899	0.220950	−	0.975285i	$-0.429084\pi$
$181$	79.9837	0.441899	0.220950	+	0.975285i	$0.429084\pi$
$182$	− 348.202i	− 1.91320i
$183$	− 146.881i	− 0.802627i
$184$	115.000i	0.624999i
$185$	−45.3262	−0.245007
$186$	127.548i	0.685740i
$187$	0	0
$188$	−467.904	−2.48885
$189$	64.4598i	0.341057i
$190$	58.0902	0.305738
$191$	−87.1935	−0.456510	−0.228255	−	0.973601i	$-0.573302\pi$
$191$	−87.1935	−0.456510	−0.228255	+	0.973601i	$0.573302\pi$
$192$	−396.997	−2.06769
$193$	188.041i	0.974307i	0.873316	+	0.487153i	$0.161965\pi$
$193$	188.041i	0.974307i	−0.873316	+	0.487153i	$0.838035\pi$
$194$	− 277.971i	− 1.43284i
$195$	− 125.590i	− 0.644049i
$196$	87.1327	0.444555
$197$	10.5087i	0.0533437i	0.999644	+	0.0266719i	$0.00849093\pi$
$197$	10.5087i	0.0533437i	−0.999644	+	0.0266719i	$0.991509\pi$
$198$	0	0
$199$	8.30806	0.0417490	0.0208745	−	0.999782i	$-0.493355\pi$
$199$	8.30806	0.0417490	0.0208745	+	0.999782i	$0.493355\pi$
$200$	− 22.6538i	− 0.113269i
$201$	−71.2786	−0.354620
$202$	332.053	1.64382
$203$	−294.817	−1.45230
$204$	531.420i	2.60500i
$205$	− 124.878i	− 0.609163i
$206$	− 59.0060i	− 0.286437i
$207$	−177.674	−0.858327
$208$	− 111.548i	− 0.536289i
$209$	0	0
$210$	221.803	1.05621
$211$	76.6086i	0.363074i	0.983384	+	0.181537i	$0.0581072\pi$
$211$	76.6086i	0.363074i	−0.983384	+	0.181537i	$0.941893\pi$
$212$	298.644	1.40870
$213$	−23.2786	−0.109289
$214$	−296.276	−1.38447
$215$	− 83.3499i	− 0.387674i
$216$	− 36.2461i	− 0.167806i
$217$	− 83.4810i	− 0.384705i
$218$	64.8754	0.297594
$219$	− 204.680i	− 0.934613i
$220$	0	0
$221$	−340.902	−1.54254
$222$	249.545i	1.12408i
$223$	116.884	0.524141	0.262071	−	0.965049i	$-0.415595\pi$
$223$	116.884	0.524141	0.262071	+	0.965049i	$0.415595\pi$
$224$	343.031	1.53139
$225$	35.0000	0.155556
$226$	220.433i	0.975368i
$227$	387.738i	1.70810i	0.520193	+	0.854049i	$0.325860\pi$
$227$	387.738i	1.70810i	−0.520193	+	0.854049i	$0.674140\pi$
$228$	− 184.761i	− 0.810356i
$229$	138.652	0.605469	0.302735	−	0.953075i	$-0.402100\pi$
$229$	138.652	0.605469	0.302735	+	0.953075i	$0.402100\pi$
$230$	− 174.676i	− 0.759463i
$231$	0	0
$232$	165.777	0.714556
$233$	186.588i	0.800808i	0.916339	+	0.400404i	$0.131130\pi$
$233$	186.588i	0.800808i	−0.916339	+	0.400404i	$0.868870\pi$
$234$	−302.503	−1.29275
$235$	191.199	0.813611
$236$	−324.264	−1.37400
$237$	137.276i	0.579224i
$238$	− 602.066i	− 2.52969i
$239$	174.439i	0.729872i	0.931033	+	0.364936i	$0.118909\pi$
$239$	174.439i	0.729872i	−0.931033	+	0.364936i	$0.881091\pi$
$240$	71.0557	0.296066
$241$	229.308i	0.951484i	0.879585	+	0.475742i	$0.157820\pi$
$241$	229.308i	0.951484i	−0.879585	+	0.475742i	$0.842180\pi$
$242$	0	0
$243$	308.000	1.26749
$244$	− 200.938i	− 0.823516i
$245$	−35.6049	−0.145326
$246$	−687.522	−2.79480
$247$	118.523	0.479850
$248$	46.9418i	0.189282i
$249$	583.407i	2.34300i
$250$	34.4095i	0.137638i
$251$	−105.966	−0.422174	−0.211087	−	0.977467i	$-0.567700\pi$
$251$	−105.966	−0.422174	−0.211087	+	0.977467i	$0.567700\pi$
$252$	− 308.641i	− 1.22477i
$253$	0	0
$254$	82.9656	0.326636
$255$	− 217.153i	− 0.851580i
$256$	−19.0000	−0.0742188
$257$	−257.708	−1.00276	−0.501378	−	0.865228i	$-0.667173\pi$
$257$	−257.708	−1.00276	−0.501378	+	0.865228i	$0.667173\pi$
$258$	−458.885	−1.77863
$259$	− 163.329i	− 0.630615i
$260$	− 171.811i	− 0.660810i
$261$	256.124i	0.981319i
$262$	−273.358	−1.04335
$263$	− 290.347i	− 1.10398i	−0.833851	−	0.551990i	$-0.813869\pi$
$263$	− 290.347i	− 1.10398i	0.833851	−	0.551990i	$-0.186131\pi$
$264$	0	0
$265$	−122.034	−0.460507
$266$	209.323i	0.786928i
$267$	511.797	1.91684
$268$	−97.5116	−0.363849
$269$	−330.790	−1.22970	−0.614852	−	0.788643i	$-0.710784\pi$
$269$	−330.790	−1.22970	−0.614852	+	0.788643i	$0.710784\pi$
$270$	55.0553i	0.203908i
$271$	217.296i	0.801830i	0.916115	+	0.400915i	$0.131308\pi$
$271$	217.296i	0.801830i	−0.916115	+	0.400915i	$0.868692\pi$
$272$	− 192.875i	− 0.709098i
$273$	452.551	1.65770
$274$	− 369.534i	− 1.34866i
$275$	0	0
$276$	−555.574	−2.01295
$277$	448.631i	1.61961i	0.586702	+	0.809803i	$0.300426\pi$
$277$	448.631i	1.61961i	−0.586702	+	0.809803i	$0.699574\pi$
$278$	−10.8247	−0.0389377
$279$	−72.5248	−0.259945
$280$	81.6312	0.291540
$281$	93.6835i	0.333393i	0.986008	+	0.166697i	$0.0533100\pi$
$281$	93.6835i	0.333393i	−0.986008	+	0.166697i	$0.946690\pi$
$282$	− 1052.65i	− 3.73280i
$283$	292.309i	1.03289i	0.856320	+	0.516446i	$0.172745\pi$
$283$	292.309i	1.03289i	−0.856320	+	0.516446i	$0.827255\pi$
$284$	−31.8460	−0.112134
$285$	75.4986i	0.264907i
$286$	0	0
$287$	449.989	1.56791
$288$	− 298.011i	− 1.03476i
$289$	−300.443	−1.03959
$290$	−251.803	−0.868288
$291$	361.272	1.24149
$292$	− 280.010i	− 0.958937i
$293$	346.079i	1.18116i	0.806981	+	0.590578i	$0.201100\pi$
$293$	346.079i	1.18116i	−0.806981	+	0.590578i	$0.798900\pi$
$294$	196.024i	0.666747i
$295$	132.503	0.449164
$296$	91.8410i	0.310274i
$297$	0	0
$298$	−287.177	−0.963682
$299$	− 356.397i	− 1.19196i
$300$	109.443	0.364809
$301$	300.344	0.997822
$302$	301.649	0.998839
$303$	431.562i	1.42430i
$304$	67.0576i	0.220584i
$305$	82.1089i	0.269209i
$306$	−523.050	−1.70931
$307$	180.826i	0.589009i	0.955650	+	0.294505i	$0.0951546\pi$
$307$	180.826i	0.589009i	−0.955650	+	0.294505i	$0.904845\pi$
$308$	0	0
$309$	76.6888	0.248184
$310$	− 71.3013i	− 0.230004i
$311$	−373.161	−1.19987	−0.599937	−	0.800047i	$-0.704808\pi$
$311$	−373.161	−1.19987	−0.599937	+	0.800047i	$0.704808\pi$
$312$	−254.472	−0.815616
$313$	317.364	1.01394	0.506971	−	0.861963i	$-0.330765\pi$
$313$	317.364	1.01394	0.506971	+	0.861963i	$0.330765\pi$
$314$	− 530.154i	− 1.68839i
$315$	126.120i	0.400379i
$316$	187.798i	0.594298i
$317$	274.795	0.866862	0.433431	−	0.901187i	$-0.357303\pi$
$317$	274.795	0.866862	0.433431	+	0.901187i	$0.357303\pi$
$318$	671.864i	2.11278i
$319$	0	0
$320$	221.928	0.693525
$321$	− 385.063i	− 1.19957i
$322$	629.431	1.95476
$323$	204.934	0.634471
$324$	519.853	1.60448
$325$	70.2067i	0.216021i
$326$	779.199i	2.39018i
$327$	84.3172i	0.257851i
$328$	−253.031	−0.771437
$329$	688.968i	2.09413i
$330$	0	0
$331$	411.681	1.24375	0.621874	−	0.783117i	$-0.286372\pi$
$331$	411.681	1.24375	0.621874	+	0.783117i	$0.286372\pi$
$332$	798.120i	2.40398i
$333$	−141.894	−0.426107
$334$	232.005	0.694626
$335$	39.8460	0.118943
$336$	256.043i	0.762033i
$337$	− 463.075i	− 1.37411i	−0.726606	−	0.687054i	$-0.758903\pi$
$337$	− 463.075i	− 1.37411i	0.726606	−	0.687054i	$-0.241097\pi$
$338$	− 86.6647i	− 0.256404i
$339$	−286.492	−0.845110
$340$	− 297.073i	− 0.873743i
$341$	0	0
$342$	181.851	0.531728
$343$	266.517i	0.777019i
$344$	−168.885	−0.490946
$345$	227.023	0.658038
$346$	344.894	0.996802
$347$	− 170.978i	− 0.492732i	−0.969177	−	0.246366i	$-0.920763\pi$
$347$	− 170.978i	− 0.492732i	0.969177	−	0.246366i	$-0.0792366\pi$
$348$	800.884i	2.30139i
$349$	172.743i	0.494967i	0.968892	+	0.247483i	$0.0796035\pi$
$349$	172.743i	0.494967i	−0.968892	+	0.247483i	$0.920396\pi$
$350$	−123.992	−0.354262
$351$	112.331i	0.320030i
$352$	0	0
$353$	−494.535	−1.40095	−0.700474	−	0.713678i	$-0.747028\pi$
$353$	−494.535	−1.40095	−0.700474	+	0.713678i	$0.747028\pi$
$354$	− 729.502i	− 2.06074i
$355$	13.0132	0.0366568
$356$	700.156	1.96673
$357$	782.492	2.19186
$358$	− 641.717i	− 1.79251i
$359$	153.953i	0.428839i	0.976742	+	0.214420i	$0.0687860\pi$
$359$	153.953i	0.428839i	−0.976742	+	0.214420i	$0.931214\pi$
$360$	− 70.9177i	− 0.196994i
$361$	289.750	0.802630
$362$	246.165i	0.680013i
$363$	0	0
$364$	619.105	1.70084
$365$	114.420i	0.313479i
$366$	452.053	1.23512
$367$	−185.692	−0.505973	−0.252986	−	0.967470i	$-0.581413\pi$
$367$	−185.692	−0.505973	−0.252986	+	0.967470i	$0.581413\pi$
$368$	201.641	0.547938
$369$	− 390.931i	− 1.05943i
$370$	− 139.500i	− 0.377027i
$371$	− 439.741i	− 1.18528i
$372$	−226.780	−0.609624
$373$	268.844i	0.720760i	0.932806	+	0.360380i	$0.117353\pi$
$373$	268.844i	0.720760i	−0.932806	+	0.360380i	$0.882647\pi$
$374$	0	0
$375$	−44.7214	−0.119257
$376$	− 387.411i	− 1.03035i
$377$	−513.761	−1.36276
$378$	−198.387	−0.524833
$379$	−301.520	−0.795567	−0.397783	−	0.917479i	$-0.630220\pi$
$379$	−301.520	−0.795567	−0.397783	+	0.917479i	$0.630220\pi$
$380$	103.285i	0.271802i
$381$	107.829i	0.283015i
$382$	− 268.354i	− 0.702497i
$383$	−486.877	−1.27122	−0.635610	−	0.772010i	$-0.719251\pi$
$383$	−486.877	−1.27122	−0.635610	+	0.772010i	$0.719251\pi$
$384$	− 540.662i	− 1.40797i
$385$	0	0
$386$	−578.731	−1.49930
$387$	− 260.927i	− 0.674229i
$388$	494.233	1.27380
$389$	382.105	0.982276	0.491138	−	0.871082i	$-0.336581\pi$
$389$	382.105	0.982276	0.491138	+	0.871082i	$0.336581\pi$
$390$	386.525	0.991089
$391$	− 616.235i	− 1.57605i
$392$	72.1434i	0.184039i
$393$	− 355.277i	− 0.904013i
$394$	−32.3425	−0.0820876
$395$	− 76.7396i	− 0.194278i
$396$	0	0
$397$	668.123	1.68293	0.841465	−	0.540311i	$-0.181693\pi$
$397$	668.123	1.68293	0.841465	+	0.540311i	$0.181693\pi$
$398$	25.5696i	0.0642452i
$399$	−272.053	−0.681836
$400$	−39.7214	−0.0993034
$401$	360.068	0.897924	0.448962	−	0.893551i	$-0.351794\pi$
$401$	360.068	0.897924	0.448962	+	0.893551i	$0.351794\pi$
$402$	− 219.373i	− 0.545704i
$403$	− 145.478i	− 0.360987i
$404$	590.391i	1.46136i
$405$	−212.426	−0.524510
$406$	− 907.352i	− 2.23486i
$407$	0	0
$408$	−440.000	−1.07843
$409$	36.2116i	0.0885368i	0.999020	+	0.0442684i	$0.0140957\pi$
$409$	36.2116i	0.0885368i	−0.999020	+	0.0442684i	$0.985904\pi$
$410$	384.336	0.937406
$411$	480.276	1.16855
$412$	104.913	0.254643
$413$	477.465i	1.15609i
$414$	− 546.824i	− 1.32083i
$415$	− 326.134i	− 0.785866i
$416$	597.782	1.43698
$417$	− 14.0686i	− 0.0337377i
$418$	0	0
$419$	−423.543	−1.01084	−0.505421	−	0.862873i	$-0.668663\pi$
$419$	−423.543	−1.01084	−0.505421	+	0.862873i	$0.668663\pi$
$420$	394.367i	0.938970i
$421$	683.745	1.62410	0.812048	−	0.583590i	$-0.198353\pi$
$421$	683.745	1.62410	0.812048	+	0.583590i	$0.198353\pi$
$422$	−235.777	−0.558713
$423$	598.546	1.41500
$424$	247.269i	0.583181i
$425$	121.392i	0.285629i
$426$	− 71.6443i	− 0.168179i
$427$	−295.872	−0.692909
$428$	− 526.779i	− 1.23079i
$429$	0	0
$430$	256.525	0.596569
$431$	− 129.070i	− 0.299466i	−0.988726	−	0.149733i	$-0.952159\pi$
$431$	− 129.070i	− 0.299466i	0.988726	−	0.149733i	$-0.0478414\pi$
$432$	−63.5542	−0.147116
$433$	−551.368	−1.27337	−0.636683	−	0.771126i	$-0.719694\pi$
$433$	−551.368	−1.27337	−0.636683	+	0.771126i	$0.719694\pi$
$434$	256.928	0.592000
$435$	− 327.264i	− 0.752330i
$436$	115.349i	0.264561i
$437$	214.249i	0.490272i
$438$	629.941	1.43822
$439$	− 470.583i	− 1.07194i	−0.844236	−	0.535972i	$-0.819945\pi$
$439$	− 470.583i	− 1.07194i	0.844236	−	0.535972i	$-0.180055\pi$
$440$	0	0
$441$	−111.461	−0.252746
$442$	− 1049.19i	− 2.37373i
$443$	99.2624	0.224069	0.112034	−	0.993704i	$-0.464263\pi$
$443$	99.2624	0.224069	0.112034	+	0.993704i	$0.464263\pi$
$444$	−443.692	−0.999306
$445$	−286.103	−0.642929
$446$	359.730i	0.806571i
$447$	− 373.238i	− 0.834985i
$448$	799.699i	1.78504i
$449$	136.303	0.303570	0.151785	−	0.988414i	$-0.451498\pi$
$449$	136.303	0.303570	0.151785	+	0.988414i	$0.451498\pi$
$450$	107.719i	0.239375i
$451$	0	0
$452$	−391.931	−0.867104
$453$	392.047i	0.865447i
$454$	−1193.34	−2.62849
$455$	−252.984	−0.556008
$456$	152.977	0.335475
$457$	− 30.7960i	− 0.0673872i	−0.999432	−	0.0336936i	$-0.989273\pi$
$457$	− 30.7960i	− 0.0673872i	0.999432	−	0.0336936i	$-0.0107270\pi$
$458$	426.728i	0.931721i
$459$	194.228i	0.423154i
$460$	310.575	0.675164
$461$	− 142.653i	− 0.309442i	−0.987958	−	0.154721i	$-0.950552\pi$
$461$	− 142.653i	− 0.309442i	0.987958	−	0.154721i	$-0.0494478\pi$
$462$	0	0
$463$	490.864	1.06018	0.530091	−	0.847941i	$-0.322158\pi$
$463$	490.864	1.06018	0.530091	+	0.847941i	$0.322158\pi$
$464$	− 290.674i	− 0.626453i
$465$	92.6687	0.199288
$466$	−574.259	−1.23232
$467$	−757.935	−1.62299	−0.811494	−	0.584361i	$-0.801345\pi$
$467$	−757.935	−1.62299	−0.811494	+	0.584361i	$0.801345\pi$
$468$	− 537.853i	− 1.14926i
$469$	143.582i	0.306144i
$470$	588.449i	1.25202i
$471$	689.029	1.46291
$472$	− 268.481i	− 0.568816i
$473$	0	0
$474$	−422.492	−0.891334
$475$	− 42.2050i	− 0.0888526i
$476$	1070.48	2.24890
$477$	−382.028	−0.800898
$478$	−536.869	−1.12316
$479$	− 620.956i	− 1.29636i	−0.761488	−	0.648180i	$-0.775531\pi$
$479$	− 620.956i	− 1.29636i	0.761488	−	0.648180i	$-0.224469\pi$
$480$	380.785i	0.793302i
$481$	− 284.625i	− 0.591736i
$482$	−705.736	−1.46418
$483$	818.059i	1.69370i
$484$	0	0
$485$	−201.957	−0.416407
$486$	947.927i	1.95047i
$487$	−393.712	−0.808444	−0.404222	−	0.914661i	$-0.632458\pi$
$487$	−393.712	−0.808444	−0.404222	+	0.914661i	$0.632458\pi$
$488$	166.371	0.340924
$489$	−1012.71	−2.07098
$490$	− 109.581i	− 0.223634i
$491$	− 648.692i	− 1.32116i	−0.750754	−	0.660582i	$-0.770309\pi$
$491$	− 648.692i	− 1.32116i	0.750754	−	0.660582i	$-0.229691\pi$
$492$	− 1222.42i	− 2.48459i
$493$	−888.328	−1.80188
$494$	364.776i	0.738413i
$495$	0	0
$496$	82.3081	0.165944
$497$	46.8918i	0.0943497i
$498$	−1795.54	−3.60551
$499$	−717.025	−1.43692	−0.718462	−	0.695566i	$-0.755154\pi$
$499$	−717.025	−1.43692	−0.718462	+	0.695566i	$0.755154\pi$
$500$	−61.1803	−0.122361
$501$	301.532i	0.601860i
$502$	− 326.128i	− 0.649658i
$503$	− 627.339i	− 1.24719i	−0.781746	−	0.623597i	$-0.785671\pi$
$503$	− 627.339i	− 1.24719i	0.781746	−	0.623597i	$-0.214329\pi$
$504$	255.546	0.507036
$505$	− 241.250i	− 0.477723i
$506$	0	0
$507$	112.636	0.222162
$508$	147.513i	0.290380i
$509$	−258.312	−0.507489	−0.253744	−	0.967271i	$-0.581662\pi$
$509$	−258.312	−0.507489	−0.253744	+	0.967271i	$0.581662\pi$
$510$	668.328	1.31045
$511$	−412.302	−0.806853
$512$	482.186i	0.941770i
$513$	− 67.5280i	− 0.131633i
$514$	− 793.144i	− 1.54308i
$515$	−42.8704	−0.0832434
$516$	− 815.900i	− 1.58120i
$517$	0	0
$518$	502.676	0.970416
$519$	448.251i	0.863682i
$520$	142.254	0.273566
$521$	300.500	0.576776	0.288388	−	0.957514i	$-0.406881\pi$
$521$	300.500	0.576776	0.288388	+	0.957514i	$0.406881\pi$
$522$	−788.269	−1.51009
$523$	421.066i	0.805098i	0.915398	+	0.402549i	$0.131876\pi$
$523$	421.066i	0.805098i	−0.915398	+	0.402549i	$0.868124\pi$
$524$	− 486.031i	− 0.927540i
$525$	− 161.150i	− 0.306952i
$526$	893.596	1.69885
$527$	− 251.541i	− 0.477308i
$528$	0	0
$529$	115.244	0.217853
$530$	− 375.583i	− 0.708648i
$531$	414.801	0.781170
$532$	−372.177	−0.699581
$533$	784.171	1.47124
$534$	1575.15i	2.94972i
$535$	215.257i	0.402349i
$536$	− 80.7368i	− 0.150628i
$537$	834.026	1.55312
$538$	− 1018.07i	− 1.89232i
$539$	0	0
$540$	−97.8885	−0.181275
$541$	− 191.845i	− 0.354613i	−0.984156	−	0.177306i	$-0.943262\pi$
$541$	− 191.845i	− 0.354613i	0.984156	−	0.177306i	$-0.0567383\pi$
$542$	−668.768	−1.23389
$543$	−319.935	−0.589199
$544$	1033.61	1.90001
$545$	− 47.1347i	− 0.0864857i
$546$	1392.81i	2.55093i
$547$	− 199.292i	− 0.364336i	−0.983267	−	0.182168i	$-0.941688\pi$
$547$	− 199.292i	− 0.364336i	0.983267	−	0.182168i	$-0.0583115\pi$
$548$	657.033	1.19897
$549$	257.041i	0.468199i
$550$	0	0
$551$	308.849	0.560525
$552$	− 459.999i	− 0.833332i
$553$	276.525	0.500045
$554$	−1380.74	−2.49232
$555$	181.305	0.326676
$556$	− 19.2463i	− 0.0346157i
$557$	757.488i	1.35994i	0.733239	+	0.679971i	$0.238008\pi$
$557$	757.488i	1.35994i	−0.733239	+	0.679971i	$0.761992\pi$
$558$	− 223.208i	− 0.400015i
$559$	523.394	0.936304
$560$	− 143.133i	− 0.255594i
$561$	0	0
$562$	−288.328	−0.513039
$563$	− 151.564i	− 0.269208i	−0.990899	−	0.134604i	$-0.957024\pi$
$563$	− 151.564i	− 0.269208i	0.990899	−	0.134604i	$-0.0429762\pi$
$564$	1871.61	3.31847
$565$	160.154	0.283458
$566$	−899.633	−1.58946
$567$	− 765.461i	− 1.35002i
$568$	− 26.3675i	− 0.0464217i
$569$	− 879.194i	− 1.54516i	−0.634919	−	0.772578i	$-0.718967\pi$
$569$	− 879.194i	− 1.54516i	0.634919	−	0.772578i	$-0.281033\pi$
$570$	−232.361	−0.407650
$571$	− 324.644i	− 0.568554i	−0.958742	−	0.284277i	$-0.908246\pi$
$571$	− 324.644i	− 0.568554i	0.958742	−	0.284277i	$-0.0917536\pi$
$572$	0	0
$573$	348.774	0.608681
$574$	1384.92i	2.41276i
$575$	−126.910	−0.220713
$576$	694.745	1.20615
$577$	−520.604	−0.902259	−0.451130	−	0.892458i	$-0.648979\pi$
$577$	−520.604	−0.902259	−0.451130	+	0.892458i	$0.648979\pi$
$578$	− 924.668i	− 1.59977i
$579$	− 752.165i	− 1.29908i
$580$	− 447.708i	− 0.771910i
$581$	1175.20	2.02271
$582$	1111.88i	1.91045i
$583$	0	0
$584$	231.840	0.396986
$585$	219.782i	0.375695i
$586$	−1065.12	−1.81761
$587$	−990.105	−1.68672	−0.843361	−	0.537348i	$-0.819426\pi$
$587$	−990.105	−1.68672	−0.843361	+	0.537348i	$0.819426\pi$
$588$	−348.531	−0.592740
$589$	87.4545i	0.148480i
$590$	407.804i	0.691193i
$591$	− 42.0349i	− 0.0711250i
$592$	161.034	0.272018
$593$	289.152i	0.487609i	0.969824	+	0.243804i	$0.0783955\pi$
$593$	289.152i	0.487609i	−0.969824	+	0.243804i	$0.921604\pi$
$594$	0	0
$595$	−437.426	−0.735171
$596$	− 510.602i	− 0.856716i
$597$	−33.2322	−0.0556654
$598$	1096.88	1.83424
$599$	833.220	1.39102	0.695509	−	0.718517i	$-0.255179\pi$
$599$	833.220	1.39102	0.695509	+	0.718517i	$0.255179\pi$
$600$	90.6154i	0.151026i
$601$	− 94.6043i	− 0.157412i	−0.996898	−	0.0787058i	$-0.974921\pi$
$601$	− 94.6043i	− 0.157412i	0.996898	−	0.0787058i	$-0.0250788\pi$
$602$	924.365i	1.53549i
$603$	124.738	0.206862
$604$	536.334i	0.887970i
$605$	0	0
$606$	−1328.21	−2.19177
$607$	212.389i	0.349899i	0.984577	+	0.174950i	$0.0559763\pi$
$607$	212.389i	0.349899i	−0.984577	+	0.174950i	$0.944024\pi$
$608$	−359.359	−0.591051
$609$	1179.27	1.93640
$610$	−252.705	−0.414271
$611$	1200.63i	1.96502i
$612$	− 929.985i	− 1.51958i
$613$	789.121i	1.28731i	0.765316	+	0.643655i	$0.222583\pi$
$613$	789.121i	1.28731i	−0.765316	+	0.643655i	$0.777417\pi$
$614$	−556.525	−0.906392
$615$	499.514i	0.812217i
$616$	0	0
$617$	181.544	0.294237	0.147118	−	0.989119i	$-0.453000\pi$
$617$	181.544	0.294237	0.147118	+	0.989119i	$0.453000\pi$
$618$	236.024i	0.381916i
$619$	−36.1165	−0.0583465	−0.0291732	−	0.999574i	$-0.509287\pi$
$619$	−36.1165	−0.0583465	−0.0291732	+	0.999574i	$0.509287\pi$
$620$	126.774	0.204474
$621$	−203.056	−0.326982
$622$	− 1148.47i	− 1.84642i
$623$	− 1030.95i	− 1.65481i
$624$	446.193i	0.715052i
$625$	25.0000	0.0400000
$626$	976.745i	1.56030i
$627$	0	0
$628$	942.616	1.50098
$629$	− 492.136i	− 0.782411i
$630$	−388.156	−0.616121
$631$	1009.15	1.59929	0.799647	−	0.600470i	$-0.205020\pi$
$631$	1009.15	1.59929	0.799647	+	0.600470i	$0.205020\pi$
$632$	−155.492	−0.246031
$633$	− 306.434i	− 0.484099i
$634$	845.733i	1.33396i
$635$	− 60.2780i	− 0.0949260i
$636$	−1194.58	−1.87827
$637$	− 223.580i	− 0.350989i
$638$	0	0
$639$	40.7376	0.0637521
$640$	302.239i	0.472249i
$641$	−107.572	−0.167818	−0.0839092	−	0.996473i	$-0.526741\pi$
$641$	−107.572	−0.167818	−0.0839092	+	0.996473i	$0.526741\pi$
$642$	1185.10	1.84595
$643$	−27.0356	−0.0420461	−0.0210230	−	0.999779i	$-0.506692\pi$
$643$	−27.0356	−0.0420461	−0.0210230	+	0.999779i	$0.506692\pi$
$644$	1119.13i	1.73778i
$645$	333.400i	0.516899i
$646$	630.723i	0.976351i
$647$	−1116.32	−1.72538	−0.862691	−	0.505732i	$-0.831223\pi$
$647$	−1116.32	−1.72538	−0.862691	+	0.505732i	$0.831223\pi$
$648$	430.423i	0.664233i
$649$	0	0
$650$	−216.074	−0.332421
$651$	333.924i	0.512940i
$652$	−1385.42	−2.12488
$653$	−1093.80	−1.67504	−0.837518	−	0.546410i	$-0.815994\pi$
$653$	−1093.80	−1.67504	−0.837518	+	0.546410i	$0.815994\pi$
$654$	−259.502	−0.396791
$655$	198.606i	0.303215i
$656$	443.666i	0.676321i
$657$	358.191i	0.545191i
$658$	−2120.42	−3.22253
$659$	− 587.822i	− 0.891991i	−0.895035	−	0.445996i	$-0.852850\pi$
$659$	− 587.822i	− 0.891991i	0.895035	−	0.445996i	$-0.147150\pi$
$660$	0	0
$661$	389.155	0.588736	0.294368	−	0.955692i	$-0.404891\pi$
$661$	389.155	0.588736	0.294368	+	0.955692i	$0.404891\pi$
$662$	1267.02i	1.91393i
$663$	1363.61	2.05672
$664$	−660.820	−0.995211
$665$	152.082	0.228695
$666$	− 436.704i	− 0.655711i
$667$	− 928.705i	− 1.39236i
$668$	412.506i	0.617524i
$669$	−467.534	−0.698855
$670$	122.633i	0.183035i
$671$	0	0
$672$	−1372.13	−2.04185
$673$	− 1024.28i	− 1.52197i	−0.648770	−	0.760984i	$-0.724716\pi$
$673$	− 1024.28i	− 1.52197i	0.648770	−	0.760984i	$-0.275284\pi$
$674$	1425.20	2.11454
$675$	40.0000	0.0592593
$676$	154.090	0.227944
$677$	247.363i	0.365381i	0.983170	+	0.182691i	$0.0584806\pi$
$677$	247.363i	0.365381i	−0.983170	+	0.182691i	$0.941519\pi$
$678$	− 881.732i	− 1.30049i
$679$	− 727.736i	− 1.07178i
$680$	245.967	0.361717
$681$	− 1550.95i	− 2.27746i
$682$	0	0
$683$	−979.967	−1.43480	−0.717399	−	0.696662i	$-0.754668\pi$
$683$	−979.967	−1.43480	−0.717399	+	0.696662i	$0.754668\pi$
$684$	323.332i	0.472708i
$685$	−268.482	−0.391945
$686$	−820.256	−1.19571
$687$	−554.610	−0.807292
$688$	296.125i	0.430414i
$689$	− 766.312i	− 1.11221i
$690$	698.706i	1.01262i
$691$	−664.353	−0.961436	−0.480718	−	0.876875i	$-0.659624\pi$
$691$	−664.353	−0.961436	−0.480718	+	0.876875i	$0.659624\pi$
$692$	613.222i	0.886160i
$693$	0	0
$694$	526.217	0.758237
$695$	7.86459i	0.0113160i
$696$	−663.108	−0.952742
$697$	1355.89	1.94532
$698$	−531.649	−0.761675
$699$	− 746.353i	− 1.06774i
$700$	− 220.458i	− 0.314940i
$701$	1035.18i	1.47672i	0.674407	+	0.738360i	$0.264399\pi$
$701$	1035.18i	1.47672i	−0.674407	+	0.738360i	$0.735601\pi$
$702$	−345.718	−0.492476
$703$	171.103i	0.243390i
$704$	0	0
$705$	−764.794	−1.08481
$706$	− 1522.02i	− 2.15584i
$707$	869.325	1.22960
$708$	1297.06	1.83200
$709$	−1231.92	−1.73754	−0.868772	−	0.495212i	$-0.835090\pi$
$709$	−1231.92	−1.73754	−0.868772	+	0.495212i	$0.835090\pi$
$710$	40.0504i	0.0564090i
$711$	− 240.233i	− 0.337881i
$712$	579.709i	0.814198i
$713$	262.974	0.368828
$714$	2408.26i	3.37292i
$715$	0	0
$716$	1140.98	1.59354
$717$	− 697.757i	− 0.973162i
$718$	−473.820	−0.659916
$719$	743.125	1.03355	0.516777	−	0.856120i	$-0.327132\pi$
$719$	743.125	1.03355	0.516777	+	0.856120i	$0.327132\pi$
$720$	−124.348	−0.172705
$721$	− 154.480i	− 0.214258i
$722$	891.758i	1.23512i
$723$	− 917.231i	− 1.26865i
$724$	−437.682	−0.604533
$725$	182.946i	0.252339i
$726$	0	0
$727$	−10.4678	−0.0143987	−0.00719934	−	0.999974i	$-0.502292\pi$
$727$	−10.4678	−0.0143987	−0.00719934	+	0.999974i	$0.502292\pi$
$728$	512.601i	0.704122i
$729$	−377.000	−0.517147
$730$	−352.148	−0.482394
$731$	904.984	1.23801
$732$	803.752i	1.09802i
$733$	1010.61i	1.37874i	0.724411	+	0.689368i	$0.242112\pi$
$733$	1010.61i	1.37874i	−0.724411	+	0.689368i	$0.757888\pi$
$734$	− 571.501i	− 0.778612i
$735$	142.420	0.193768
$736$	1080.59i	1.46819i
$737$	0	0
$738$	1203.16	1.63030
$739$	576.872i	0.780611i	0.920685	+	0.390306i	$0.127631\pi$
$739$	576.872i	0.780611i	−0.920685	+	0.390306i	$0.872369\pi$
$740$	248.031	0.335177
$741$	−474.091	−0.639799
$742$	1353.38	1.82397
$743$	1153.39i	1.55234i	0.630521	+	0.776172i	$0.282841\pi$
$743$	1153.39i	1.55234i	−0.630521	+	0.776172i	$0.717159\pi$
$744$	− 187.767i	− 0.252375i
$745$	208.646i	0.280062i
$746$	−827.415	−1.10914
$747$	− 1020.96i	− 1.36675i
$748$	0	0
$749$	−775.659	−1.03559
$750$	− 137.638i	− 0.183518i
$751$	1447.83	1.92787	0.963933	−	0.266145i	$-0.0857500\pi$
$751$	1447.83	1.92787	0.963933	+	0.266145i	$0.0857500\pi$
$752$	−679.288	−0.903308
$753$	423.862	0.562898
$754$	− 1581.19i	− 2.09707i
$755$	− 219.161i	− 0.290280i
$756$	− 352.733i	− 0.466578i
$757$	528.438	0.698069	0.349035	−	0.937110i	$-0.386510\pi$
$757$	528.438	0.698069	0.349035	+	0.937110i	$0.386510\pi$
$758$	− 927.982i	− 1.22425i
$759$	0	0
$760$	−85.5166	−0.112522
$761$	− 218.749i	− 0.287449i	−0.989618	−	0.143725i	$-0.954092\pi$
$761$	− 218.749i	− 0.287449i	0.989618	−	0.143725i	$-0.0459080\pi$
$762$	−331.862	−0.435515
$763$	169.846	0.222603
$764$	477.135	0.624522
$765$	380.018i	0.496755i
$766$	− 1498.45i	− 1.95621i
$767$	832.052i	1.08481i
$768$	76.0000	0.0989583
$769$	162.687i	0.211557i	0.994390	+	0.105778i	$0.0337334\pi$
$769$	162.687i	0.211557i	−0.994390	+	0.105778i	$0.966267\pi$
$770$	0	0
$771$	1030.83	1.33701
$772$	− 1028.99i	− 1.33288i
$773$	326.458	0.422326	0.211163	−	0.977451i	$-0.432275\pi$
$773$	326.458	0.422326	0.211163	+	0.977451i	$0.432275\pi$
$774$	803.050	1.03753
$775$	−51.8034	−0.0668431
$776$	409.210i	0.527333i
$777$	653.317i	0.840820i
$778$	1176.00i	1.51157i
$779$	−471.407	−0.605144
$780$	687.243i	0.881081i
$781$	0	0
$782$	1896.58	2.42529
$783$	292.713i	0.373836i
$784$	126.497	0.161348
$785$	−385.179	−0.490674
$786$	1093.43	1.39113
$787$	387.252i	0.492061i	0.969262	+	0.246031i	$0.0791264\pi$
$787$	387.252i	0.492061i	−0.969262	+	0.246031i	$0.920874\pi$
$788$	− 57.5051i	− 0.0729760i
$789$	1161.39i	1.47197i
$790$	236.180	0.298962
$791$	577.101i	0.729585i
$792$	0	0
$793$	−515.601	−0.650190
$794$	2056.27i	2.58976i
$795$	488.138	0.614010
$796$	−45.4628	−0.0571141
$797$	−21.9787	−0.0275768	−0.0137884	−	0.999905i	$-0.504389\pi$
$797$	−21.9787	−0.0275768	−0.0137884	+	0.999905i	$0.504389\pi$
$798$	− 837.292i	− 1.04924i
$799$	2075.97i	2.59821i
$800$	− 212.865i	− 0.266081i
$801$	−895.645	−1.11816
$802$	1108.17i	1.38176i
$803$	0	0
$804$	390.046	0.485132
$805$	− 457.309i	− 0.568085i
$806$	447.735	0.555502
$807$	1323.16	1.63960
$808$	−488.827	−0.604983
$809$	1019.89i	1.26068i	0.776319	+	0.630341i	$0.217085\pi$
$809$	1019.89i	1.26068i	−0.776319	+	0.630341i	$0.782915\pi$
$810$	− 653.781i	− 0.807138i
$811$	989.112i	1.21962i	0.792548	+	0.609810i	$0.208754\pi$
$811$	989.112i	1.21962i	−0.792548	+	0.609810i	$0.791246\pi$
$812$	1613.28	1.98679
$813$	− 869.183i	− 1.06911i
$814$	0	0
$815$	566.122	0.694628
$816$	771.498i	0.945463i
$817$	−314.640	−0.385116
$818$	−111.448	−0.136244
$819$	−791.964	−0.966989
$820$	683.352i	0.833356i
$821$	− 767.313i	− 0.934607i	−0.884097	−	0.467304i	$-0.845225\pi$
$821$	− 767.313i	− 0.934607i	0.884097	−	0.467304i	$-0.154775\pi$
$822$	1478.14i	1.79822i
$823$	834.303	1.01373	0.506867	−	0.862024i	$-0.330804\pi$
$823$	834.303	1.01373	0.506867	+	0.862024i	$0.330804\pi$
$824$	86.8648i	0.105418i
$825$	0	0
$826$	−1469.49	−1.77904
$827$	560.150i	0.677328i	0.940907	+	0.338664i	$0.109975\pi$
$827$	560.150i	0.677328i	−0.940907	+	0.338664i	$0.890025\pi$
$828$	972.255	1.17422
$829$	−1200.60	−1.44825	−0.724125	−	0.689668i	$-0.757756\pi$
$829$	−1200.60	−1.44825	−0.724125	+	0.689668i	$0.757756\pi$
$830$	1003.74	1.20932
$831$	− 1794.52i	− 2.15947i
$832$	1393.59i	1.67499i
$833$	− 386.585i	− 0.464088i
$834$	43.2987	0.0519170
$835$	− 168.562i	− 0.201870i
$836$	0	0
$837$	−82.8854	−0.0990268
$838$	− 1303.53i	− 1.55553i
$839$	525.440	0.626270	0.313135	−	0.949709i	$-0.398621\pi$
$839$	525.440	0.626270	0.313135	+	0.949709i	$0.398621\pi$
$840$	−326.525	−0.388720
$841$	−497.768	−0.591876
$842$	2104.35i	2.49923i
$843$	− 374.734i	− 0.444524i
$844$	− 419.213i	− 0.496698i
$845$	−62.9656	−0.0745155
$846$	1842.14i	2.17746i
$847$	0	0
$848$	433.562	0.511276
$849$	− 1169.23i	− 1.37719i
$850$	−373.607	−0.439537
$851$	514.505	0.604589
$852$	127.384	0.149512
$853$	958.373i	1.12353i	0.827296	+	0.561766i	$0.189878\pi$
$853$	958.373i	1.12353i	−0.827296	+	0.561766i	$0.810122\pi$
$854$	− 910.601i	− 1.06628i
$855$	− 132.122i	− 0.154529i
$856$	436.158	0.509530
$857$	56.2536i	0.0656402i	0.999461	+	0.0328201i	$0.0104488\pi$
$857$	56.2536i	0.0656402i	−0.999461	+	0.0328201i	$0.989551\pi$
$858$	0	0
$859$	−1517.29	−1.76634	−0.883171	−	0.469051i	$-0.844596\pi$
$859$	−1517.29	−1.76634	−0.883171	+	0.469051i	$0.844596\pi$
$860$	456.102i	0.530351i
$861$	−1799.96	−2.09054
$862$	397.236	0.460831
$863$	−1096.52	−1.27059	−0.635294	−	0.772270i	$-0.719121\pi$
$863$	−1096.52	−1.27059	−0.635294	+	0.772270i	$0.719121\pi$
$864$	− 340.584i	− 0.394195i
$865$	− 250.580i	− 0.289688i
$866$	− 1696.94i	− 1.95951i
$867$	1201.77	1.38613
$868$	456.819i	0.526289i
$869$	0	0
$870$	1007.21	1.15772
$871$	250.212i	0.287270i
$872$	−95.5054	−0.109525
$873$	−632.227	−0.724200
$874$	−659.391	−0.754452
$875$	90.0854i	0.102955i
$876$	1120.04i	1.27858i
$877$	1137.29i	1.29679i	0.761303	+	0.648396i	$0.224560\pi$
$877$	1137.29i	1.29679i	−0.761303	+	0.648396i	$0.775440\pi$
$878$	1448.31	1.64955
$879$	− 1384.31i	− 1.57487i
$880$	0	0
$881$	850.822	0.965746	0.482873	−	0.875690i	$-0.339593\pi$
$881$	850.822	0.965746	0.482873	+	0.875690i	$0.339593\pi$
$882$	− 343.041i	− 0.388936i
$883$	509.915	0.577480	0.288740	−	0.957408i	$-0.406764\pi$
$883$	509.915	0.577480	0.288740	+	0.957408i	$0.406764\pi$
$884$	1865.46	2.11025
$885$	−530.014	−0.598886
$886$	305.498i	0.344806i
$887$	− 583.506i	− 0.657842i	−0.944357	−	0.328921i	$-0.893315\pi$
$887$	− 583.506i	− 0.657842i	0.944357	−	0.328921i	$-0.106685\pi$
$888$	− 367.364i	− 0.413698i
$889$	217.207	0.244327
$890$	− 880.535i	− 0.989366i
$891$	0	0
$892$	−639.603	−0.717043
$893$	− 721.761i	− 0.808243i
$894$	1148.71	1.28491
$895$	−466.235	−0.520933
$896$	−1089.09	−1.21551
$897$	1425.59i	1.58928i
$898$	419.498i	0.467147i
$899$	− 379.089i	− 0.421678i
$900$	−191.525	−0.212805
$901$	− 1325.01i	− 1.47060i
$902$	0	0
$903$	−1201.38	−1.33043
$904$	− 324.508i	− 0.358968i
$905$	178.849	0.197623
$906$	−1206.60	−1.33179
$907$	640.502	0.706177	0.353088	−	0.935590i	$-0.385132\pi$
$907$	640.502	0.706177	0.353088	+	0.935590i	$0.385132\pi$
$908$	− 2121.76i	− 2.33674i
$909$	− 755.233i	− 0.830839i
$910$	− 778.604i	− 0.855609i
$911$	−1095.06	−1.20204	−0.601021	−	0.799234i	$-0.705239\pi$
$911$	−1095.06	−1.20204	−0.601021	+	0.799234i	$0.705239\pi$
$912$	− 268.230i	− 0.294112i
$913$	0	0
$914$	94.7802	0.103698
$915$	− 328.435i	− 0.358946i
$916$	−758.725	−0.828303
$917$	−715.659	−0.780436
$918$	−597.771	−0.651167
$919$	− 1240.93i	− 1.35031i	−0.737677	−	0.675154i	$-0.764077\pi$
$919$	− 1240.93i	− 1.35031i	0.737677	−	0.675154i	$-0.235923\pi$
$920$	257.147i	0.279508i
$921$	− 723.303i	− 0.785346i
$922$	439.039	0.476182
$923$	81.7158i	0.0885328i
$924$	0	0
$925$	−101.353	−0.109570
$926$	1510.72i	1.63145i
$927$	−134.205	−0.144774
$928$	1557.71	1.67857
$929$	1032.05	1.11093	0.555463	−	0.831541i	$-0.312541\pi$
$929$	1032.05	1.11093	0.555463	+	0.831541i	$0.312541\pi$
$930$	285.205i	0.306672i
$931$	134.406i	0.144367i
$932$	− 1021.04i	− 1.09553i
$933$	1492.64	1.59983
$934$	− 2332.68i	− 2.49752i
$935$	0	0
$936$	445.326	0.475776
$937$	− 306.589i	− 0.327203i	−0.986527	−	0.163601i	$-0.947689\pi$
$937$	− 306.589i	− 0.327203i	0.986527	−	0.163601i	$-0.0523111\pi$
$938$	−441.899	−0.471107
$939$	−1269.46	−1.35192
$940$	−1046.26	−1.11305
$941$	19.0830i	0.0202795i	0.999949	+	0.0101397i	$0.00322763\pi$
$941$	19.0830i	0.0202795i	−0.999949	+	0.0101397i	$0.996772\pi$
$942$	2120.61i	2.25118i
$943$	1417.52i	1.50320i
$944$	−470.757	−0.498683
$945$	144.137i	0.152525i
$946$	0	0
$947$	−804.636	−0.849669	−0.424834	−	0.905271i	$-0.639668\pi$
$947$	−804.636	−0.849669	−0.424834	+	0.905271i	$0.639668\pi$
$948$	− 751.193i	− 0.792398i
$949$	−718.496	−0.757109
$950$	129.894	0.136730
$951$	−1099.18	−1.15582
$952$	886.323i	0.931011i
$953$	− 1854.14i	− 1.94559i	−0.231673	−	0.972794i	$-0.574420\pi$
$953$	− 1854.14i	− 1.94559i	0.231673	−	0.972794i	$-0.425580\pi$
$954$	− 1175.76i	− 1.23245i
$955$	−194.971	−0.204158
$956$	− 954.556i	− 0.998489i
$957$	0	0
$958$	1911.11	1.99489
$959$	− 967.453i	− 1.00881i
$960$	−887.712	−0.924700
$961$	−853.656	−0.888300
$962$	875.986	0.910588
$963$	673.860i	0.699751i
$964$	− 1254.80i	− 1.30166i
$965$	420.473i	0.435723i
$966$	−2517.73	−2.60634
$967$	660.803i	0.683353i	0.939818	+	0.341677i	$0.110995\pi$
$967$	660.803i	0.683353i	−0.939818	+	0.341677i	$0.889005\pi$
$968$	0	0
$969$	−819.737	−0.845962
$970$	− 621.561i	− 0.640785i
$971$	−538.861	−0.554955	−0.277477	−	0.960732i	$-0.589498\pi$
$971$	−538.861	−0.554955	−0.277477	+	0.960732i	$0.589498\pi$
$972$	−1685.42	−1.73397
$973$	−28.3394	−0.0291258
$974$	− 1211.72i	− 1.24407i
$975$	− 280.827i	− 0.288027i
$976$	− 291.715i	− 0.298889i
$977$	−301.388	−0.308483	−0.154241	−	0.988033i	$-0.549293\pi$
$977$	−301.388	−0.308483	−0.154241	+	0.988033i	$0.549293\pi$
$978$	− 3116.80i	− 3.18691i
$979$	0	0
$980$	194.835	0.198811
$981$	− 147.555i	− 0.150413i
$982$	1996.47	2.03306
$983$	−771.218	−0.784555	−0.392278	−	0.919847i	$-0.628313\pi$
$983$	−771.218	−0.784555	−0.392278	+	0.919847i	$0.628313\pi$
$984$	1012.13	1.02858
$985$	23.4982i	0.0238560i
$986$	− 2733.99i	− 2.77281i
$987$	− 2755.87i	− 2.79217i
$988$	−648.573	−0.656450
$989$	946.119i	0.956642i
$990$	0	0
$991$	118.312	0.119386	0.0596932	−	0.998217i	$-0.480988\pi$
$991$	118.312	0.119386	0.0596932	+	0.998217i	$0.480988\pi$
$992$	441.086i	0.444643i
$993$	−1646.72	−1.65833
$994$	−144.318	−0.145189
$995$	18.5774	0.0186707
$996$	− 3192.48i	− 3.20530i
$997$	37.8803i	0.0379943i	0.999820	+	0.0189971i	$0.00604734\pi$
$997$	37.8803i	0.0379943i	−0.999820	+	0.0189971i	$0.993953\pi$
$998$	− 2206.78i	− 2.21120i
$999$	−162.164	−0.162326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.3.c.a.241.4		4
11.2	odd	10		55.3.i.a.51.1	yes	4
11.5	even	5		55.3.i.a.41.1	✓	4
11.10	odd	2	inner	605.3.c.a.241.1		4
55.2	even	20		275.3.q.c.249.1		8
55.13	even	20		275.3.q.c.249.2		8
55.24	odd	10		275.3.x.d.51.1		4
55.27	odd	20		275.3.q.c.74.2		8
55.38	odd	20		275.3.q.c.74.1		8
55.49	even	10		275.3.x.d.151.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.i.a.41.1	✓	4	11.5	even	5
55.3.i.a.51.1	yes	4	11.2	odd	10
275.3.q.c.74.1		8	55.38	odd	20
275.3.q.c.74.2		8	55.27	odd	20
275.3.q.c.249.1		8	55.2	even	20
275.3.q.c.249.2		8	55.13	even	20
275.3.x.d.51.1		4	55.24	odd	10
275.3.x.d.151.1		4	55.49	even	10
605.3.c.a.241.1		4	11.10	odd	2	inner
605.3.c.a.241.4		4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	605.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.07768i q^{2} -4.00000 q^{3} -5.47214 q^{4} +2.23607 q^{5} -12.3107i q^{6} +8.05748i q^{7} -4.53077i q^{8} +7.00000 q^{9} +6.88191i q^{10} +21.8885 q^{12} +14.0413i q^{13} -24.7984 q^{14} -8.94427 q^{15} -7.94427 q^{16} +24.2784i q^{17} +21.5438i q^{18} -8.44100i q^{19} -12.2361 q^{20} -32.2299i q^{21} -25.3820 q^{23} +18.1231i q^{24} +5.00000 q^{25} -43.2148 q^{26} +8.00000 q^{27} -44.0916i q^{28} +36.5892i q^{29} -27.5276i q^{30} -10.3607 q^{31} -42.5730i q^{32} -74.7214 q^{34} +18.0171i q^{35} -38.3050 q^{36} -20.2705 q^{37} +25.9787 q^{38} -56.1653i q^{39} -10.1311i q^{40} -55.8473i q^{41} +99.1935 q^{42} -37.2752i q^{43} +15.6525 q^{45} -78.1177i q^{46} +85.5066 q^{47} +31.7771 q^{48} -15.9230 q^{49} +15.3884i q^{50} -97.1138i q^{51} -76.8361i q^{52} -54.5755 q^{53} +24.6215i q^{54} +36.5066 q^{56} +33.7640i q^{57} -112.610 q^{58} +59.2574 q^{59} +48.9443 q^{60} +36.7202i q^{61} -31.8869i q^{62} +56.4024i q^{63} +99.2492 q^{64} +31.3974i q^{65} +17.8197 q^{67} -132.855i q^{68} +101.528 q^{69} -55.4508 q^{70} +5.81966 q^{71} -31.7154i q^{72} +51.1701i q^{73} -62.3862i q^{74} -20.0000 q^{75} +46.1903i q^{76} +172.859 q^{78} -34.3190i q^{79} -17.7639 q^{80} -95.0000 q^{81} +171.880 q^{82} -145.852i q^{83} +176.367i q^{84} +54.2882i q^{85} +114.721 q^{86} -146.357i q^{87} -127.949 q^{89} +48.1734i q^{90} -113.138 q^{91} +138.894 q^{92} +41.4427 q^{93} +263.162i q^{94} -18.8746i q^{95} +170.292i q^{96} -90.3181 q^{97} -49.0059i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{3} - 4 q^{4} + 28 q^{9} + 16 q^{12} - 50 q^{14} + 4 q^{16} - 40 q^{20} - 106 q^{23} + 20 q^{25} - 70 q^{26} + 32 q^{27} + 48 q^{31} - 120 q^{34} - 28 q^{36} - 14 q^{37} + 10 q^{38} + 200 q^{42}+ \cdots - 84 q^{97}+O(q^{100}) \) 4 * q - 16 * q^3 - 4 * q^4 + 28 * q^9 + 16 * q^12 - 50 * q^14 + 4 * q^16 - 40 * q^20 - 106 * q^23 + 20 * q^25 - 70 * q^26 + 32 * q^27 + 48 * q^31 - 120 * q^34 - 28 * q^36 - 14 * q^37 + 10 * q^38 + 200 * q^42 + 266 * q^47 - 16 * q^48 + 66 * q^49 - 26 * q^53 + 70 * q^56 - 200 * q^58 + 322 * q^59 + 160 * q^60 + 236 * q^64 + 116 * q^67 + 424 * q^69 - 110 * q^70 + 68 * q^71 - 80 * q^75 + 280 * q^78 - 80 * q^80 - 380 * q^81 + 370 * q^82 + 280 * q^86 - 78 * q^89 - 220 * q^91 + 86 * q^92 - 192 * q^93 - 84 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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