LMFDB - Embedded newform 605.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(1,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("605.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.2525.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 5x + 5 $ x^4 - 2x^3 - 4x^2 + 5*x + 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.777484$ of defining polynomial
Character	$\chi$	$=$	605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.87603 q^{2} -1.77748 q^{3} +1.51949 q^{4} +1.00000 q^{5} +3.33461 q^{6} +4.25800 q^{7} +0.901454 q^{8} +0.159450 q^{9} +O(q^{10})$	\(q-1.87603 q^{2} -1.77748 q^{3} +1.51949 q^{4} +1.00000 q^{5} +3.33461 q^{6} +4.25800 q^{7} +0.901454 q^{8} +0.159450 q^{9} -1.87603 q^{10} -2.70087 q^{12} +1.36004 q^{13} -7.98813 q^{14} -1.77748 q^{15} -4.73013 q^{16} +2.09855 q^{17} -0.299133 q^{18} +0.604482 q^{19} +1.51949 q^{20} -7.56852 q^{21} -4.39768 q^{23} -1.60232 q^{24} +1.00000 q^{25} -2.55147 q^{26} +5.04903 q^{27} +6.46998 q^{28} -6.63159 q^{29} +3.33461 q^{30} -2.19493 q^{31} +7.07096 q^{32} -3.93693 q^{34} +4.25800 q^{35} +0.242283 q^{36} +6.16951 q^{37} -1.13403 q^{38} -2.41745 q^{39} +0.901454 q^{40} +7.40557 q^{41} +14.1988 q^{42} +12.6671 q^{43} +0.159450 q^{45} +8.25018 q^{46} -3.07446 q^{47} +8.40773 q^{48} +11.1305 q^{49} -1.87603 q^{50} -3.73013 q^{51} +2.06656 q^{52} -6.65351 q^{53} -9.47214 q^{54} +3.83839 q^{56} -1.07446 q^{57} +12.4411 q^{58} +12.0372 q^{59} -2.70087 q^{60} -5.68899 q^{61} +4.11776 q^{62} +0.678939 q^{63} -3.80507 q^{64} +1.36004 q^{65} +9.86416 q^{67} +3.18872 q^{68} +7.81681 q^{69} -7.98813 q^{70} -5.23879 q^{71} +0.143737 q^{72} -0.722795 q^{73} -11.5742 q^{74} -1.77748 q^{75} +0.918503 q^{76} +4.53520 q^{78} +5.67056 q^{79} -4.73013 q^{80} -9.45293 q^{81} -13.8931 q^{82} -0.952648 q^{83} -11.5003 q^{84} +2.09855 q^{85} -23.7638 q^{86} +11.7875 q^{87} +1.24095 q^{89} -0.299133 q^{90} +5.79104 q^{91} -6.68222 q^{92} +3.90145 q^{93} +5.76777 q^{94} +0.604482 q^{95} -12.5685 q^{96} +11.5431 q^{97} -20.8812 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 2 q^{3} + 7 q^{4} + 4 q^{5} - q^{6} + 11 q^{7} + 9 q^{8}+O(q^{10}) $ 4 * q + 3 * q^2 - 2 * q^3 + 7 * q^4 + 4 * q^5 - q^6 + 11 * q^7 + 9 * q^8	$ 4 q + 3 q^{2} - 2 q^{3} + 7 q^{4} + 4 q^{5} - q^{6} + 11 q^{7} + 9 q^{8} + 3 q^{10} - 14 q^{12} + 7 q^{13} - 2 q^{14} - 2 q^{15} + 5 q^{16} + 3 q^{17} + 2 q^{18} + 12 q^{19} + 7 q^{20} - 6 q^{21} - 9 q^{23} - 15 q^{24} + 4 q^{25} + 13 q^{26} - 5 q^{27} + 7 q^{28} - 8 q^{29} - q^{30} + 3 q^{31} + 6 q^{32} - 10 q^{34} + 11 q^{35} + 8 q^{36} - 3 q^{37} + 12 q^{38} - 3 q^{39} + 9 q^{40} - 7 q^{41} + 2 q^{42} + 21 q^{43} + 12 q^{46} - 3 q^{47} - 2 q^{48} + 15 q^{49} + 3 q^{50} + 9 q^{51} + 27 q^{52} - 11 q^{53} - 20 q^{54} + 15 q^{56} + 5 q^{57} + 2 q^{58} - 7 q^{59} - 14 q^{60} + 4 q^{61} + 11 q^{62} + 3 q^{63} - 27 q^{64} + 7 q^{65} - q^{67} - 15 q^{68} - 28 q^{69} - 2 q^{70} - 15 q^{71} + 13 q^{72} - 9 q^{73} - 36 q^{74} - 2 q^{75} + 8 q^{76} + 6 q^{78} + 6 q^{79} + 5 q^{80} - 20 q^{81} - 44 q^{82} + 15 q^{83} - 47 q^{84} + 3 q^{85} - 3 q^{86} + 15 q^{87} + 2 q^{90} + 4 q^{91} + 18 q^{92} + 21 q^{93} - 11 q^{94} + 12 q^{95} - 26 q^{96} + 6 q^{97} - 42 q^{98}+O(q^{100}) $ 4 * q + 3 * q^2 - 2 * q^3 + 7 * q^4 + 4 * q^5 - q^6 + 11 * q^7 + 9 * q^8 + 3 * q^10 - 14 * q^12 + 7 * q^13 - 2 * q^14 - 2 * q^15 + 5 * q^16 + 3 * q^17 + 2 * q^18 + 12 * q^19 + 7 * q^20 - 6 * q^21 - 9 * q^23 - 15 * q^24 + 4 * q^25 + 13 * q^26 - 5 * q^27 + 7 * q^28 - 8 * q^29 - q^30 + 3 * q^31 + 6 * q^32 - 10 * q^34 + 11 * q^35 + 8 * q^36 - 3 * q^37 + 12 * q^38 - 3 * q^39 + 9 * q^40 - 7 * q^41 + 2 * q^42 + 21 * q^43 + 12 * q^46 - 3 * q^47 - 2 * q^48 + 15 * q^49 + 3 * q^50 + 9 * q^51 + 27 * q^52 - 11 * q^53 - 20 * q^54 + 15 * q^56 + 5 * q^57 + 2 * q^58 - 7 * q^59 - 14 * q^60 + 4 * q^61 + 11 * q^62 + 3 * q^63 - 27 * q^64 + 7 * q^65 - q^67 - 15 * q^68 - 28 * q^69 - 2 * q^70 - 15 * q^71 + 13 * q^72 - 9 * q^73 - 36 * q^74 - 2 * q^75 + 8 * q^76 + 6 * q^78 + 6 * q^79 + 5 * q^80 - 20 * q^81 - 44 * q^82 + 15 * q^83 - 47 * q^84 + 3 * q^85 - 3 * q^86 + 15 * q^87 + 2 * q^90 + 4 * q^91 + 18 * q^92 + 21 * q^93 - 11 * q^94 + 12 * q^95 - 26 * q^96 + 6 * q^97 - 42 * q^98

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 $

$2$	−1.87603	−1.32655	−0.663277	−	0.748374i	$-0.730835\pi$
$2$	−1.87603	−1.32655	−0.663277	+	0.748374i	$0.730835\pi$
$3$	−1.77748	−1.02623	−0.513116	−	0.858320i	$-0.671509\pi$
$3$	−1.77748	−1.02623	−0.513116	+	0.858320i	$0.671509\pi$
$4$	1.51949	0.759744
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.33461	1.36135
$7$	4.25800	1.60937	0.804686	−	0.593701i	$-0.202334\pi$
$7$	4.25800	1.60937	0.804686	+	0.593701i	$0.202334\pi$
$8$	0.901454	0.318712
$9$	0.159450	0.0531501
$10$	−1.87603	−0.593253
$11$	0	0
$11$	0	0
$12$	−2.70087	−0.779673
$13$	1.36004	0.377207	0.188603	−	0.982053i	$-0.439604\pi$
$13$	1.36004	0.377207	0.188603	+	0.982053i	$0.439604\pi$
$14$	−7.98813	−2.13492
$15$	−1.77748	−0.458944
$16$	−4.73013	−1.18253
$17$	2.09855	0.508972	0.254486	−	0.967076i	$-0.418094\pi$
$17$	2.09855	0.508972	0.254486	+	0.967076i	$0.418094\pi$
$18$	−0.299133	−0.0705064
$19$	0.604482	0.138678	0.0693388	−	0.997593i	$-0.477911\pi$
$19$	0.604482	0.138678	0.0693388	+	0.997593i	$0.477911\pi$
$20$	1.51949	0.339768
$21$	−7.56852	−1.65159
$22$	0	0
$23$	−4.39768	−0.916979	−0.458490	−	0.888700i	$-0.651609\pi$
$23$	−4.39768	−0.916979	−0.458490	+	0.888700i	$0.651609\pi$
$24$	−1.60232	−0.327072
$25$	1.00000	0.200000
$26$	−2.55147	−0.500385
$27$	5.04903	0.971687
$28$	6.46998	1.22271
$29$	−6.63159	−1.23145	−0.615727	−	0.787959i	$-0.711138\pi$
$29$	−6.63159	−1.23145	−0.615727	+	0.787959i	$0.711138\pi$
$30$	3.33461	0.608814
$31$	−2.19493	−0.394221	−0.197111	−	0.980381i	$-0.563156\pi$
$31$	−2.19493	−0.394221	−0.197111	+	0.980381i	$0.563156\pi$
$32$	7.07096	1.24998
$33$	0	0
$34$	−3.93693	−0.675179
$35$	4.25800	0.719733
$36$	0.242283	0.0403805
$37$	6.16951	1.01426	0.507130	−	0.861869i	$-0.330706\pi$
$37$	6.16951	1.01426	0.507130	+	0.861869i	$0.330706\pi$
$38$	−1.13403	−0.183963
$39$	−2.41745	−0.387101
$40$	0.901454	0.142532
$41$	7.40557	1.15656	0.578278	−	0.815840i	$-0.303725\pi$
$41$	7.40557	1.15656	0.578278	+	0.815840i	$0.303725\pi$
$42$	14.1988	2.19092
$43$	12.6671	1.93171	0.965855	−	0.259084i	$-0.0834207\pi$
$43$	12.6671	1.93171	0.965855	+	0.259084i	$0.0834207\pi$
$44$	0	0
$45$	0.159450	0.0237694
$46$	8.25018	1.21642
$47$	−3.07446	−0.448456	−0.224228	−	0.974537i	$-0.571986\pi$
$47$	−3.07446	−0.448456	−0.224228	+	0.974537i	$0.571986\pi$
$48$	8.40773	1.21355
$49$	11.1305	1.59008
$50$	−1.87603	−0.265311
$51$	−3.73013	−0.522323
$52$	2.06656	0.286581
$53$	−6.65351	−0.913930	−0.456965	−	0.889485i	$-0.651064\pi$
$53$	−6.65351	−0.913930	−0.456965	+	0.889485i	$0.651064\pi$
$54$	−9.47214	−1.28899
$55$	0	0
$56$	3.83839	0.512926
$57$	−1.07446	−0.142315
$58$	12.4411	1.63359
$59$	12.0372	1.56710	0.783552	−	0.621326i	$-0.213406\pi$
$59$	12.0372	1.56710	0.783552	+	0.621326i	$0.213406\pi$
$60$	−2.70087	−0.348680
$61$	−5.68899	−0.728401	−0.364201	−	0.931321i	$-0.618658\pi$
$61$	−5.68899	−0.728401	−0.364201	+	0.931321i	$0.618658\pi$
$62$	4.11776	0.522955
$63$	0.678939	0.0855382
$64$	−3.80507	−0.475634
$65$	1.36004	0.168692
$66$	0	0
$67$	9.86416	1.20510	0.602549	−	0.798082i	$-0.294152\pi$
$67$	9.86416	1.20510	0.602549	+	0.798082i	$0.294152\pi$
$68$	3.18872	0.386689
$69$	7.81681	0.941033
$70$	−7.98813	−0.954764
$71$	−5.23879	−0.621730	−0.310865	−	0.950454i	$-0.600619\pi$
$71$	−5.23879	−0.621730	−0.310865	+	0.950454i	$0.600619\pi$
$72$	0.143737	0.0169396
$73$	−0.722795	−0.0845967	−0.0422983	−	0.999105i	$-0.513468\pi$
$73$	−0.722795	−0.0845967	−0.0422983	+	0.999105i	$0.513468\pi$
$74$	−11.5742	−1.34547
$75$	−1.77748	−0.205246
$76$	0.918503	0.105360
$77$	0	0
$78$	4.53520	0.513510
$79$	5.67056	0.637988	0.318994	−	0.947757i	$-0.396655\pi$
$79$	5.67056	0.637988	0.318994	+	0.947757i	$0.396655\pi$
$80$	−4.73013	−0.528845
$81$	−9.45293	−1.05033
$82$	−13.8931	−1.53423
$83$	−0.952648	−0.104567	−0.0522833	−	0.998632i	$-0.516650\pi$
$83$	−0.952648	−0.104567	−0.0522833	+	0.998632i	$0.516650\pi$
$84$	−11.5003	−1.25478
$85$	2.09855	0.227619
$86$	−23.7638	−2.56252
$87$	11.7875	1.26376
$88$	0	0
$89$	1.24095	0.131540	0.0657701	−	0.997835i	$-0.479050\pi$
$89$	1.24095	0.131540	0.0657701	+	0.997835i	$0.479050\pi$
$90$	−0.299133	−0.0315314
$91$	5.79104	0.607066
$92$	−6.68222	−0.696670
$93$	3.90145	0.404562
$94$	5.76777	0.594900
$95$	0.604482	0.0620185
$96$	−12.5685	−1.28277
$97$	11.5431	1.17202	0.586012	−	0.810302i	$-0.300697\pi$
$97$	11.5431	1.17202	0.586012	+	0.810302i	$0.300697\pi$
$98$	−20.8812	−2.10932
$99$	0	0
$100$	1.51949	0.151949
$101$	2.80675	0.279282	0.139641	−	0.990202i	$-0.455405\pi$
$101$	2.80675	0.279282	0.139641	+	0.990202i	$0.455405\pi$
$102$	6.99784	0.692889
$103$	−0.406055	−0.0400098	−0.0200049	−	0.999800i	$-0.506368\pi$
$103$	−0.406055	−0.0400098	−0.0200049	+	0.999800i	$0.506368\pi$
$104$	1.22601	0.120220
$105$	−7.56852	−0.738612
$106$	12.4822	1.21238
$107$	15.3985	1.48863	0.744316	−	0.667827i	$-0.232776\pi$
$107$	15.3985	1.48863	0.744316	+	0.667827i	$0.232776\pi$
$108$	7.67195	0.738233
$109$	−3.07312	−0.294352	−0.147176	−	0.989110i	$-0.547018\pi$
$109$	−3.07312	−0.294352	−0.147176	+	0.989110i	$0.547018\pi$
$110$	0	0
$111$	−10.9662	−1.04087
$112$	−20.1409	−1.90313
$113$	−11.2646	−1.05968	−0.529840	−	0.848098i	$-0.677748\pi$
$113$	−11.2646	−1.05968	−0.529840	+	0.848098i	$0.677748\pi$
$114$	2.01571	0.188789
$115$	−4.39768	−0.410086
$116$	−10.0766	−0.935590
$117$	0.216858	0.0200486
$118$	−22.5821	−2.07885
$119$	8.93560	0.819125
$120$	−1.60232	−0.146271
$121$	0	0
$122$	10.6727	0.966263
$123$	−13.1633	−1.18689
$124$	−3.33517	−0.299507
$125$	1.00000	0.0894427
$126$	−1.27371	−0.113471
$127$	0.113136	0.0100392	0.00501961	−	0.999987i	$-0.498402\pi$
$127$	0.113136	0.0100392	0.00501961	+	0.999987i	$0.498402\pi$
$128$	−7.00350	−0.619027
$129$	−22.5155	−1.98238
$130$	−2.55147	−0.223779
$131$	0.474297	0.0414395	0.0207198	−	0.999785i	$-0.493404\pi$
$131$	0.474297	0.0414395	0.0207198	+	0.999785i	$0.493404\pi$
$132$	0	0
$133$	2.57388	0.223184
$134$	−18.5055	−1.59863
$135$	5.04903	0.434552
$136$	1.89174	0.162216
$137$	−0.868693	−0.0742174	−0.0371087	−	0.999311i	$-0.511815\pi$
$137$	−0.868693	−0.0742174	−0.0371087	+	0.999311i	$0.511815\pi$
$138$	−14.6646	−1.24833
$139$	19.3894	1.64459	0.822293	−	0.569065i	$-0.192695\pi$
$139$	19.3894	1.64459	0.822293	+	0.569065i	$0.192695\pi$
$140$	6.46998	0.546813
$141$	5.46480	0.460219
$142$	9.82812	0.824758
$143$	0	0
$144$	−0.754221	−0.0628517
$145$	−6.63159	−0.550723
$146$	1.35598	0.112222
$147$	−19.7843	−1.63178
$148$	9.37449	0.770579
$149$	−1.11258	−0.0911460	−0.0455730	−	0.998961i	$-0.514511\pi$
$149$	−1.11258	−0.0911460	−0.0455730	+	0.998961i	$0.514511\pi$
$150$	3.33461	0.272270
$151$	5.69465	0.463424	0.231712	−	0.972784i	$-0.425567\pi$
$151$	5.69465	0.463424	0.231712	+	0.972784i	$0.425567\pi$
$152$	0.544913	0.0441983
$153$	0.334614	0.0270519
$154$	0	0
$155$	−2.19493	−0.176301
$156$	−3.67328	−0.294098
$157$	1.04114	0.0830918	0.0415459	−	0.999137i	$-0.486772\pi$
$157$	1.04114	0.0830918	0.0415459	+	0.999137i	$0.486772\pi$
$158$	−10.6381	−0.846325
$159$	11.8265	0.937904
$160$	7.07096	0.559009
$161$	−18.7253	−1.47576
$162$	17.7340	1.39331
$163$	−12.9115	−1.01131	−0.505654	−	0.862737i	$-0.668749\pi$
$163$	−12.9115	−1.01131	−0.505654	+	0.862737i	$0.668749\pi$
$164$	11.2527	0.878687
$165$	0	0
$166$	1.78720	0.138713
$167$	4.22601	0.327019	0.163509	−	0.986542i	$-0.447719\pi$
$167$	4.22601	0.327019	0.163509	+	0.986542i	$0.447719\pi$
$168$	−6.82268	−0.526381
$169$	−11.1503	−0.857715
$170$	−3.93693	−0.301949
$171$	0.0963848	0.00737073
$172$	19.2475	1.46761
$173$	1.34571	0.102312	0.0511561	−	0.998691i	$-0.483709\pi$
$173$	1.34571	0.102312	0.0511561	+	0.998691i	$0.483709\pi$
$174$	−22.1138	−1.67644
$175$	4.25800	0.321874
$176$	0	0
$177$	−21.3959	−1.60821
$178$	−2.32805	−0.174495
$179$	12.4288	0.928975	0.464487	−	0.885580i	$-0.346239\pi$
$179$	12.4288	0.928975	0.464487	+	0.885580i	$0.346239\pi$
$180$	0.242283	0.0180587
$181$	17.3092	1.28658	0.643291	−	0.765622i	$-0.277569\pi$
$181$	17.3092	1.28658	0.643291	+	0.765622i	$0.277569\pi$
$182$	−10.8642	−0.805305
$183$	10.1121	0.747508
$184$	−3.96431	−0.292253
$185$	6.16951	0.453591
$186$	−7.31925	−0.536673
$187$	0	0
$188$	−4.67160	−0.340712
$189$	21.4988	1.56380
$190$	−1.13403	−0.0822709
$191$	−19.6503	−1.42185	−0.710923	−	0.703269i	$-0.751723\pi$
$191$	−19.6503	−1.42185	−0.710923	+	0.703269i	$0.751723\pi$
$192$	6.76345	0.488110
$193$	10.1616	0.731449	0.365724	−	0.930723i	$-0.380821\pi$
$193$	10.1616	0.731449	0.365724	+	0.930723i	$0.380821\pi$
$194$	−21.6552	−1.55475
$195$	−2.41745	−0.173117
$196$	16.9127	1.20805
$197$	−8.45375	−0.602305	−0.301152	−	0.953576i	$-0.597371\pi$
$197$	−8.45375	−0.602305	−0.301152	+	0.953576i	$0.597371\pi$
$198$	0	0
$199$	−6.51033	−0.461505	−0.230753	−	0.973012i	$-0.574119\pi$
$199$	−6.51033	−0.461505	−0.230753	+	0.973012i	$0.574119\pi$
$200$	0.901454	0.0637424
$201$	−17.5334	−1.23671
$202$	−5.26555	−0.370483
$203$	−28.2373	−1.98187
$204$	−5.66789	−0.396832
$205$	7.40557	0.517228
$206$	0.761771	0.0530751
$207$	−0.701211	−0.0487375
$208$	−6.43316	−0.446059
$209$	0	0
$210$	14.1988	0.979808
$211$	4.01403	0.276337	0.138169	−	0.990409i	$-0.455878\pi$
$211$	4.01403	0.276337	0.138169	+	0.990409i	$0.455878\pi$
$212$	−10.1099	−0.694353
$213$	9.31186	0.638038
$214$	−28.8881	−1.97475
$215$	12.6671	0.863887
$216$	4.55147	0.309688
$217$	−9.34600	−0.634448
$218$	5.76527	0.390473
$219$	1.28476	0.0868158
$220$	0	0
$221$	2.85410	0.191988
$222$	20.5729	1.38076
$223$	15.3070	1.02503	0.512517	−	0.858677i	$-0.328713\pi$
$223$	15.3070	1.02503	0.512517	+	0.858677i	$0.328713\pi$
$224$	30.1081	2.01168
$225$	0.159450	0.0106300
$226$	21.1326	1.40572
$227$	11.5019	0.763407	0.381703	−	0.924285i	$-0.375338\pi$
$227$	11.5019	0.763407	0.381703	+	0.924285i	$0.375338\pi$
$228$	−1.63262	−0.108123
$229$	−27.5272	−1.81905	−0.909523	−	0.415653i	$-0.863553\pi$
$229$	−27.5272	−1.81905	−0.909523	+	0.415653i	$0.863553\pi$
$230$	8.25018	0.544001
$231$	0	0
$232$	−5.97807	−0.392480
$233$	9.20227	0.602861	0.301430	−	0.953488i	$-0.402536\pi$
$233$	9.20227	0.602861	0.301430	+	0.953488i	$0.402536\pi$
$234$	−0.406833	−0.0265955
$235$	−3.07446	−0.200555
$236$	18.2903	1.19060
$237$	−10.0793	−0.654723
$238$	−16.7635	−1.08661
$239$	12.6560	0.818647	0.409323	−	0.912389i	$-0.365765\pi$
$239$	12.6560	0.818647	0.409323	+	0.912389i	$0.365765\pi$
$240$	8.40773	0.542717
$241$	7.33167	0.472275	0.236137	−	0.971720i	$-0.424118\pi$
$241$	7.33167	0.472275	0.236137	+	0.971720i	$0.424118\pi$
$242$	0	0
$243$	1.65533	0.106190
$244$	−8.64436	−0.553398
$245$	11.1305	0.711103
$246$	24.6947	1.57448
$247$	0.822118	0.0523101
$248$	−1.97863	−0.125643
$249$	1.69332	0.107310
$250$	−1.87603	−0.118651
$251$	31.2579	1.97298	0.986489	−	0.163826i	$-0.0523835\pi$
$251$	31.2579	1.97298	0.986489	+	0.163826i	$0.0523835\pi$
$252$	1.03164	0.0649872
$253$	0	0
$254$	−0.212247	−0.0133176
$255$	−3.73013	−0.233590
$256$	20.7489	1.29681
$257$	−8.32028	−0.519005	−0.259503	−	0.965742i	$-0.583559\pi$
$257$	−8.32028	−0.519005	−0.259503	+	0.965742i	$0.583559\pi$
$258$	42.2398	2.62973
$259$	26.2697	1.63232
$260$	2.06656	0.128163
$261$	−1.05741	−0.0654519
$262$	−0.889795	−0.0549717
$263$	−2.87171	−0.177077	−0.0885386	−	0.996073i	$-0.528220\pi$
$263$	−2.87171	−0.177077	−0.0885386	+	0.996073i	$0.528220\pi$
$264$	0	0
$265$	−6.65351	−0.408722
$266$	−4.82868	−0.296065
$267$	−2.20576	−0.134991
$268$	14.9885	0.915567
$269$	−0.123970	−0.00755859	−0.00377929	−	0.999993i	$-0.501203\pi$
$269$	−0.123970	−0.00755859	−0.00377929	+	0.999993i	$0.501203\pi$
$270$	−9.47214	−0.576456
$271$	−17.0328	−1.03467	−0.517336	−	0.855783i	$-0.673076\pi$
$271$	−17.0328	−1.03467	−0.517336	+	0.855783i	$0.673076\pi$
$272$	−9.92640	−0.601876
$273$	−10.2935	−0.622990
$274$	1.62969	0.0984534
$275$	0	0
$276$	11.8775	0.714944
$277$	22.7411	1.36638	0.683190	−	0.730241i	$-0.260592\pi$
$277$	22.7411	1.36638	0.683190	+	0.730241i	$0.260592\pi$
$278$	−36.3751	−2.18163
$279$	−0.349982	−0.0209529
$280$	3.83839	0.229388
$281$	−12.9499	−0.772528	−0.386264	−	0.922388i	$-0.626235\pi$
$281$	−12.9499	−0.772528	−0.386264	+	0.922388i	$0.626235\pi$
$282$	−10.2521	−0.610505
$283$	15.8178	0.940273	0.470137	−	0.882594i	$-0.344205\pi$
$283$	15.8178	0.940273	0.470137	+	0.882594i	$0.344205\pi$
$284$	−7.96027	−0.472355
$285$	−1.07446	−0.0636453
$286$	0	0
$287$	31.5329	1.86133
$288$	1.12747	0.0664366
$289$	−12.5961	−0.740947
$290$	12.4411	0.730564
$291$	−20.5177	−1.20277
$292$	−1.09828	−0.0642718
$293$	−24.9306	−1.45646	−0.728230	−	0.685333i	$-0.759657\pi$
$293$	−24.9306	−1.45646	−0.728230	+	0.685333i	$0.759657\pi$
$294$	37.1160	2.16465
$295$	12.0372	0.700831
$296$	5.56153	0.323257
$297$	0	0
$298$	2.08723	0.120910
$299$	−5.98101	−0.345891
$300$	−2.70087	−0.155935
$301$	53.9363	3.10884
$302$	−10.6833	−0.614757
$303$	−4.98895	−0.286608
$304$	−2.85928	−0.163991
$305$	−5.68899	−0.325751
$306$	−0.627745	−0.0358858
$307$	−4.95566	−0.282835	−0.141417	−	0.989950i	$-0.545166\pi$
$307$	−4.95566	−0.282835	−0.141417	+	0.989950i	$0.545166\pi$
$308$	0	0
$309$	0.721756	0.0410593
$310$	4.11776	0.233873
$311$	−9.59477	−0.544070	−0.272035	−	0.962287i	$-0.587697\pi$
$311$	−9.59477	−0.544070	−0.272035	+	0.962287i	$0.587697\pi$
$312$	−2.17922	−0.123374
$313$	−26.9858	−1.52533	−0.762665	−	0.646794i	$-0.776109\pi$
$313$	−26.9858	−1.52533	−0.762665	+	0.646794i	$0.776109\pi$
$314$	−1.95321	−0.110226
$315$	0.678939	0.0382539
$316$	8.61635	0.484708
$317$	−14.2207	−0.798714	−0.399357	−	0.916795i	$-0.630767\pi$
$317$	−14.2207	−0.798714	−0.399357	+	0.916795i	$0.630767\pi$
$318$	−22.1869	−1.24418
$319$	0	0
$320$	−3.80507	−0.212710
$321$	−27.3707	−1.52768
$322$	35.1292	1.95768
$323$	1.26853	0.0705830
$324$	−14.3636	−0.797978
$325$	1.36004	0.0754413
$326$	24.2224	1.34155
$327$	5.46242	0.302073
$328$	6.67579	0.368609
$329$	−13.0910	−0.721732
$330$	0	0
$331$	−8.55985	−0.470492	−0.235246	−	0.971936i	$-0.575590\pi$
$331$	−8.55985	−0.470492	−0.235246	+	0.971936i	$0.575590\pi$
$332$	−1.44754	−0.0794439
$333$	0.983729	0.0539080
$334$	−7.92813	−0.433808
$335$	9.86416	0.538937
$336$	35.8001	1.95306
$337$	−15.6841	−0.854368	−0.427184	−	0.904165i	$-0.640494\pi$
$337$	−15.6841	−0.854368	−0.427184	+	0.904165i	$0.640494\pi$
$338$	20.9183	1.13780
$339$	20.0226	1.08748
$340$	3.18872	0.172932
$341$	0	0
$342$	−0.180821	−0.00977766
$343$	17.5878	0.949651
$344$	11.4188	0.615659
$345$	7.81681	0.420843
$346$	−2.52459	−0.135723
$347$	7.45509	0.400210	0.200105	−	0.979774i	$-0.435872\pi$
$347$	7.45509	0.400210	0.200105	+	0.979774i	$0.435872\pi$
$348$	17.9110	0.960132
$349$	−30.4733	−1.63120	−0.815600	−	0.578616i	$-0.803593\pi$
$349$	−30.4733	−1.63120	−0.815600	+	0.578616i	$0.803593\pi$
$350$	−7.98813	−0.426983
$351$	6.86688	0.366527
$352$	0	0
$353$	−17.5379	−0.933449	−0.466725	−	0.884403i	$-0.654566\pi$
$353$	−17.5379	−0.933449	−0.466725	+	0.884403i	$0.654566\pi$
$354$	40.1393	2.13338
$355$	−5.23879	−0.278046
$356$	1.88560	0.0999369
$357$	−15.8829	−0.840611
$358$	−23.3169	−1.23233
$359$	−3.00432	−0.158562	−0.0792810	−	0.996852i	$-0.525262\pi$
$359$	−3.00432	−0.158562	−0.0792810	+	0.996852i	$0.525262\pi$
$360$	0.143737	0.00757561
$361$	−18.6346	−0.980769
$362$	−32.4726	−1.70672
$363$	0	0
$364$	8.79941	0.461215
$365$	−0.722795	−0.0378328
$366$	−18.9706	−0.991609
$367$	6.18319	0.322760	0.161380	−	0.986892i	$-0.448406\pi$
$367$	6.18319	0.322760	0.161380	+	0.986892i	$0.448406\pi$
$368$	20.8016	1.08436
$369$	1.18082	0.0614711
$370$	−11.5742	−0.601713
$371$	−28.3306	−1.47085
$372$	5.92821	0.307364
$373$	20.8707	1.08064	0.540321	−	0.841459i	$-0.318303\pi$
$373$	20.8707	1.08064	0.540321	+	0.841459i	$0.318303\pi$
$374$	0	0
$375$	−1.77748	−0.0917889
$376$	−2.77148	−0.142928
$377$	−9.01921	−0.464513
$378$	−40.3323	−2.07447
$379$	−2.46424	−0.126580	−0.0632898	−	0.997995i	$-0.520159\pi$
$379$	−2.46424	−0.126580	−0.0632898	+	0.997995i	$0.520159\pi$
$380$	0.918503	0.0471182
$381$	−0.201098	−0.0103026
$382$	36.8646	1.88616
$383$	17.2036	0.879063	0.439532	−	0.898227i	$-0.355144\pi$
$383$	17.2036	0.879063	0.439532	+	0.898227i	$0.355144\pi$
$384$	12.4486	0.635265
$385$	0	0
$386$	−19.0635	−0.970306
$387$	2.01977	0.102671
$388$	17.5396	0.890438
$389$	−18.0548	−0.915413	−0.457706	−	0.889103i	$-0.651329\pi$
$389$	−18.0548	−0.915413	−0.457706	+	0.889103i	$0.651329\pi$
$390$	4.53520	0.229649
$391$	−9.22873	−0.466717
$392$	10.0337	0.506777
$393$	−0.843055	−0.0425265
$394$	15.8595	0.798990
$395$	5.67056	0.285317
$396$	0	0
$397$	−16.7432	−0.840317	−0.420159	−	0.907451i	$-0.638026\pi$
$397$	−16.7432	−0.840317	−0.420159	+	0.907451i	$0.638026\pi$
$398$	12.2136	0.612212
$399$	−4.57503	−0.229038
$400$	−4.73013	−0.236507
$401$	28.9395	1.44517	0.722584	−	0.691283i	$-0.242954\pi$
$401$	28.9395	1.44517	0.722584	+	0.691283i	$0.242954\pi$
$402$	32.8932	1.64056
$403$	−2.98519	−0.148703
$404$	4.26482	0.212183
$405$	−9.45293	−0.469720
$406$	52.9740	2.62905
$407$	0	0
$408$	−3.36254	−0.166471
$409$	−29.8733	−1.47714	−0.738569	−	0.674178i	$-0.764498\pi$
$409$	−29.8733	−1.47714	−0.738569	+	0.674178i	$0.764498\pi$
$410$	−13.8931	−0.686130
$411$	1.54409	0.0761642
$412$	−0.616996	−0.0303972
$413$	51.2542	2.52205
$414$	1.31549	0.0646530
$415$	−0.952648	−0.0467636
$416$	9.61678	0.471501
$417$	−34.4643	−1.68772
$418$	0	0
$419$	−8.29831	−0.405399	−0.202699	−	0.979241i	$-0.564971\pi$
$419$	−8.29831	−0.405399	−0.202699	+	0.979241i	$0.564971\pi$
$420$	−11.5003	−0.561156
$421$	−22.8672	−1.11448	−0.557239	−	0.830352i	$-0.688139\pi$
$421$	−22.8672	−1.11448	−0.557239	+	0.830352i	$0.688139\pi$
$422$	−7.53045	−0.366576
$423$	−0.490223	−0.0238355
$424$	−5.99784	−0.291281
$425$	2.09855	0.101794
$426$	−17.4693	−0.846392
$427$	−24.2237	−1.17227
$428$	23.3979	1.13098
$429$	0	0
$430$	−23.7638	−1.14599
$431$	−20.3617	−0.980789	−0.490395	−	0.871500i	$-0.663147\pi$
$431$	−20.3617	−0.980789	−0.490395	+	0.871500i	$0.663147\pi$
$432$	−23.8826	−1.14905
$433$	21.3889	1.02788	0.513942	−	0.857825i	$-0.328185\pi$
$433$	21.3889	1.02788	0.513942	+	0.857825i	$0.328185\pi$
$434$	17.5334	0.841629
$435$	11.7875	0.565169
$436$	−4.66957	−0.223632
$437$	−2.65832	−0.127165
$438$	−2.41024	−0.115166
$439$	−35.2311	−1.68149	−0.840744	−	0.541432i	$-0.817882\pi$
$439$	−35.2311	−1.68149	−0.840744	+	0.541432i	$0.817882\pi$
$440$	0	0
$441$	1.77477	0.0845127
$442$	−5.35438	−0.254682
$443$	23.2623	1.10523	0.552613	−	0.833438i	$-0.313631\pi$
$443$	23.2623	1.10523	0.552613	+	0.833438i	$0.313631\pi$
$444$	−16.6630	−0.790792
$445$	1.24095	0.0588265
$446$	−28.7164	−1.35976
$447$	1.97759	0.0935369
$448$	−16.2020	−0.765471
$449$	24.8518	1.17283	0.586415	−	0.810011i	$-0.300539\pi$
$449$	24.8518	1.17283	0.586415	+	0.810011i	$0.300539\pi$
$450$	−0.299133	−0.0141013
$451$	0	0
$452$	−17.1164	−0.805086
$453$	−10.1222	−0.475580
$454$	−21.5779	−1.01270
$455$	5.79104	0.271488
$456$	−0.968574	−0.0453576
$457$	5.90831	0.276379	0.138190	−	0.990406i	$-0.455872\pi$
$457$	5.90831	0.276379	0.138190	+	0.990406i	$0.455872\pi$
$458$	51.6418	2.41306
$459$	10.5956	0.494561
$460$	−6.68222	−0.311560
$461$	−17.3587	−0.808475	−0.404238	−	0.914654i	$-0.632463\pi$
$461$	−17.3587	−0.808475	−0.404238	+	0.914654i	$0.632463\pi$
$462$	0	0
$463$	34.6937	1.61235	0.806176	−	0.591675i	$-0.201533\pi$
$463$	34.6937	1.61235	0.806176	+	0.591675i	$0.201533\pi$
$464$	31.3683	1.45624
$465$	3.90145	0.180926
$466$	−17.2637	−0.799727
$467$	9.16601	0.424152	0.212076	−	0.977253i	$-0.431978\pi$
$467$	9.16601	0.424152	0.212076	+	0.977253i	$0.431978\pi$
$468$	0.329514	0.0152318
$469$	42.0015	1.93945
$470$	5.76777	0.266048
$471$	−1.85061	−0.0852714
$472$	10.8510	0.499455
$473$	0	0
$474$	18.9091	0.868525
$475$	0.604482	0.0277355
$476$	13.5775	0.622325
$477$	−1.06090	−0.0485755
$478$	−23.7430	−1.08598
$479$	−40.8320	−1.86566	−0.932831	−	0.360315i	$-0.882669\pi$
$479$	−40.8320	−1.86566	−0.932831	+	0.360315i	$0.882669\pi$
$480$	−12.5685	−0.573672
$481$	8.39076	0.382586
$482$	−13.7544	−0.626498
$483$	33.2839	1.51447
$484$	0	0
$485$	11.5431	0.524145
$486$	−3.10545	−0.140866
$487$	−26.1598	−1.18541	−0.592707	−	0.805418i	$-0.701941\pi$
$487$	−26.1598	−1.18541	−0.592707	+	0.805418i	$0.701941\pi$
$488$	−5.12837	−0.232150
$489$	22.9500	1.03784
$490$	−20.8812	−0.943317
$491$	23.0012	1.03803	0.519015	−	0.854765i	$-0.326299\pi$
$491$	23.0012	1.03803	0.519015	+	0.854765i	$0.326299\pi$
$492$	−20.0015	−0.901736
$493$	−13.9167	−0.626776
$494$	−1.54232	−0.0693922
$495$	0	0
$496$	10.3823	0.466180
$497$	−22.3067	−1.00059
$498$	−3.17671	−0.142352
$499$	−26.2140	−1.17350	−0.586750	−	0.809768i	$-0.699593\pi$
$499$	−26.2140	−1.17350	−0.586750	+	0.809768i	$0.699593\pi$
$500$	1.51949	0.0679536
$501$	−7.51167	−0.335597
$502$	−58.6407	−2.61726
$503$	1.68460	0.0751124	0.0375562	−	0.999295i	$-0.488043\pi$
$503$	1.68460	0.0751124	0.0375562	+	0.999295i	$0.488043\pi$
$504$	0.612032	0.0272621
$505$	2.80675	0.124899
$506$	0	0
$507$	19.8195	0.880214
$508$	0.171909	0.00762724
$509$	17.8483	0.791112	0.395556	−	0.918442i	$-0.370552\pi$
$509$	17.8483	0.791112	0.395556	+	0.918442i	$0.370552\pi$
$510$	6.99784	0.309870
$511$	−3.07766	−0.136147
$512$	−24.9186	−1.10126
$513$	3.05205	0.134751
$514$	15.6091	0.688488
$515$	−0.406055	−0.0178929
$516$	−34.2121	−1.50610
$517$	0	0
$518$	−49.2828	−2.16536
$519$	−2.39197	−0.104996
$520$	1.22601	0.0537642
$521$	−9.54339	−0.418104	−0.209052	−	0.977905i	$-0.567038\pi$
$521$	−9.54339	−0.418104	−0.209052	+	0.977905i	$0.567038\pi$
$522$	1.98373	0.0868255
$523$	−21.7454	−0.950862	−0.475431	−	0.879753i	$-0.657708\pi$
$523$	−21.7454	−0.950862	−0.475431	+	0.879753i	$0.657708\pi$
$524$	0.720689	0.0314834
$525$	−7.56852	−0.330317
$526$	5.38741	0.234902
$527$	−4.60616	−0.200648
$528$	0	0
$529$	−3.66042	−0.159149
$530$	12.4822	0.542192
$531$	1.91933	0.0832918
$532$	3.91098	0.169563
$533$	10.0719	0.436261
$534$	4.13808	0.179072
$535$	15.3985	0.665737
$536$	8.89209	0.384080
$537$	−22.0921	−0.953343
$538$	0.232572	0.0100269
$539$	0	0
$540$	7.67195	0.330148
$541$	13.4876	0.579876	0.289938	−	0.957045i	$-0.406365\pi$
$541$	13.4876	0.579876	0.289938	+	0.957045i	$0.406365\pi$
$542$	31.9541	1.37255
$543$	−30.7668	−1.32033
$544$	14.8387	0.636205
$545$	−3.07312	−0.131638
$546$	19.3109	0.826429
$547$	−24.4217	−1.04419	−0.522097	−	0.852886i	$-0.674850\pi$
$547$	−24.4217	−1.04419	−0.522097	+	0.852886i	$0.674850\pi$
$548$	−1.31997	−0.0563862
$549$	−0.907112	−0.0387146
$550$	0	0
$551$	−4.00867	−0.170775
$552$	7.04649	0.299919
$553$	24.1452	1.02676
$554$	−42.6630	−1.81258
$555$	−10.9662	−0.465489
$556$	29.4619	1.24946
$557$	−25.7940	−1.09293	−0.546464	−	0.837483i	$-0.684026\pi$
$557$	−25.7940	−1.09293	−0.546464	+	0.837483i	$0.684026\pi$
$558$	0.656577	0.0277951
$559$	17.2277	0.728654
$560$	−20.1409	−0.851108
$561$	0	0
$562$	24.2945	1.02480
$563$	−40.3703	−1.70140	−0.850702	−	0.525649i	$-0.823823\pi$
$563$	−40.3703	−1.70140	−0.850702	+	0.525649i	$0.823823\pi$
$564$	8.30370	0.349649
$565$	−11.2646	−0.473903
$566$	−29.6747	−1.24732
$567$	−40.2505	−1.69036
$568$	−4.72253	−0.198153
$569$	−10.5541	−0.442453	−0.221226	−	0.975222i	$-0.571006\pi$
$569$	−10.5541	−0.442453	−0.221226	+	0.975222i	$0.571006\pi$
$570$	2.01571	0.0844289
$571$	−9.77700	−0.409155	−0.204577	−	0.978850i	$-0.565582\pi$
$571$	−9.77700	−0.409155	−0.204577	+	0.978850i	$0.565582\pi$
$572$	0	0
$573$	34.9281	1.45914
$574$	−59.1567	−2.46915
$575$	−4.39768	−0.183396
$576$	−0.606719	−0.0252800
$577$	−16.2960	−0.678411	−0.339205	−	0.940712i	$-0.610158\pi$
$577$	−16.2960	−0.678411	−0.339205	+	0.940712i	$0.610158\pi$
$578$	23.6307	0.982906
$579$	−18.0621	−0.750635
$580$	−10.0766	−0.418409
$581$	−4.05637	−0.168287
$582$	38.4918	1.59554
$583$	0	0
$584$	−0.651566	−0.0269620
$585$	0.216858	0.00896599
$586$	46.7705	1.93207
$587$	33.6827	1.39023	0.695117	−	0.718896i	$-0.255352\pi$
$587$	33.6827	1.39023	0.695117	+	0.718896i	$0.255352\pi$
$588$	−30.0621	−1.23974
$589$	−1.32680	−0.0546697
$590$	−22.5821	−0.929689
$591$	15.0264	0.618104
$592$	−29.1826	−1.19940
$593$	−21.3355	−0.876143	−0.438071	−	0.898940i	$-0.644338\pi$
$593$	−21.3355	−0.876143	−0.438071	+	0.898940i	$0.644338\pi$
$594$	0	0
$595$	8.93560	0.366324
$596$	−1.69055	−0.0692476
$597$	11.5720	0.473611
$598$	11.2206	0.458843
$599$	−16.4096	−0.670476	−0.335238	−	0.942133i	$-0.608817\pi$
$599$	−16.4096	−0.670476	−0.335238	+	0.942133i	$0.608817\pi$
$600$	−1.60232	−0.0654145
$601$	−13.7954	−0.562726	−0.281363	−	0.959601i	$-0.590787\pi$
$601$	−13.7954	−0.562726	−0.281363	+	0.959601i	$0.590787\pi$
$602$	−101.186	−4.12404
$603$	1.57284	0.0640511
$604$	8.65296	0.352084
$605$	0	0
$606$	9.35943	0.380201
$607$	−5.64351	−0.229063	−0.114531	−	0.993420i	$-0.536537\pi$
$607$	−5.64351	−0.229063	−0.114531	+	0.993420i	$0.536537\pi$
$608$	4.27427	0.173344
$609$	50.1913	2.03385
$610$	10.6727	0.432126
$611$	−4.18138	−0.169160
$612$	0.508442	0.0205525
$613$	−3.33104	−0.134539	−0.0672697	−	0.997735i	$-0.521429\pi$
$613$	−3.33104	−0.134539	−0.0672697	+	0.997735i	$0.521429\pi$
$614$	9.29697	0.375195
$615$	−13.1633	−0.530795
$616$	0	0
$617$	−9.45854	−0.380786	−0.190393	−	0.981708i	$-0.560976\pi$
$617$	−9.45854	−0.380786	−0.190393	+	0.981708i	$0.560976\pi$
$618$	−1.35404	−0.0544673
$619$	−27.2070	−1.09354	−0.546771	−	0.837282i	$-0.684143\pi$
$619$	−27.2070	−1.09354	−0.546771	+	0.837282i	$0.684143\pi$
$620$	−3.33517	−0.133944
$621$	−22.2040	−0.891017
$622$	18.0001	0.721737
$623$	5.28395	0.211697
$624$	11.4348	0.457760
$625$	1.00000	0.0400000
$626$	50.6262	2.02343
$627$	0	0
$628$	1.58200	0.0631285
$629$	12.9470	0.516230
$630$	−1.27371	−0.0507458
$631$	−30.3287	−1.20737	−0.603683	−	0.797224i	$-0.706301\pi$
$631$	−30.3287	−1.20737	−0.603683	+	0.797224i	$0.706301\pi$
$632$	5.11175	0.203335
$633$	−7.13488	−0.283586
$634$	26.6785	1.05954
$635$	0.113136	0.00448968
$636$	17.9703	0.712567
$637$	15.1379	0.599787
$638$	0	0
$639$	−0.835326	−0.0330450
$640$	−7.00350	−0.276838
$641$	39.8313	1.57324	0.786620	−	0.617437i	$-0.211829\pi$
$641$	39.8313	1.57324	0.786620	+	0.617437i	$0.211829\pi$
$642$	51.3482	2.02655
$643$	−27.3517	−1.07864	−0.539322	−	0.842100i	$-0.681319\pi$
$643$	−27.3517	−1.07864	−0.539322	+	0.842100i	$0.681319\pi$
$644$	−28.4529	−1.12120
$645$	−22.5155	−0.886547
$646$	−2.37981	−0.0936322
$647$	22.2738	0.875675	0.437837	−	0.899054i	$-0.355745\pi$
$647$	22.2738	0.875675	0.437837	+	0.899054i	$0.355745\pi$
$648$	−8.52138	−0.334751
$649$	0	0
$650$	−2.55147	−0.100077
$651$	16.6124	0.651090
$652$	−19.6189	−0.768335
$653$	29.3913	1.15017	0.575085	−	0.818094i	$-0.304969\pi$
$653$	29.3913	1.15017	0.575085	+	0.818094i	$0.304969\pi$
$654$	−10.2477	−0.400716
$655$	0.474297	0.0185323
$656$	−35.0293	−1.36767
$657$	−0.115250	−0.00449632
$658$	24.5592	0.957416
$659$	22.8429	0.889832	0.444916	−	0.895572i	$-0.353234\pi$
$659$	22.8429	0.889832	0.444916	+	0.895572i	$0.353234\pi$
$660$	0	0
$661$	32.0302	1.24583	0.622916	−	0.782289i	$-0.285948\pi$
$661$	32.0302	1.24583	0.622916	+	0.782289i	$0.285948\pi$
$662$	16.0585	0.624133
$663$	−5.07312	−0.197024
$664$	−0.858768	−0.0333267
$665$	2.57388	0.0998108
$666$	−1.84551	−0.0715119
$667$	29.1636	1.12922
$668$	6.42138	0.248450
$669$	−27.2080	−1.05192
$670$	−18.5055	−0.714928
$671$	0	0
$672$	−53.5167	−2.06445
$673$	13.5740	0.523238	0.261619	−	0.965171i	$-0.415744\pi$
$673$	13.5740	0.523238	0.261619	+	0.965171i	$0.415744\pi$
$674$	29.4239	1.13337
$675$	5.04903	0.194337
$676$	−16.9427	−0.651644
$677$	1.58263	0.0608254	0.0304127	−	0.999537i	$-0.490318\pi$
$677$	1.58263	0.0608254	0.0304127	+	0.999537i	$0.490318\pi$
$678$	−37.5629	−1.44260
$679$	49.1505	1.88622
$680$	1.89174	0.0725450
$681$	−20.4444	−0.783432
$682$	0	0
$683$	33.8348	1.29465	0.647325	−	0.762214i	$-0.275887\pi$
$683$	33.8348	1.29465	0.647325	+	0.762214i	$0.275887\pi$
$684$	0.146456	0.00559987
$685$	−0.868693	−0.0331910
$686$	−32.9952	−1.25976
$687$	48.9291	1.86676
$688$	−59.9169	−2.28431
$689$	−9.04903	−0.344741
$690$	−14.6646	−0.558270
$691$	−33.7446	−1.28371	−0.641853	−	0.766828i	$-0.721834\pi$
$691$	−33.7446	−1.28371	−0.641853	+	0.766828i	$0.721834\pi$
$692$	2.04479	0.0777311
$693$	0	0
$694$	−13.9860	−0.530900
$695$	19.3894	0.735481
$696$	10.6259	0.402775
$697$	15.5409	0.588655
$698$	57.1689	2.16387
$699$	−16.3569	−0.618674
$700$	6.46998	0.244542
$701$	1.88737	0.0712851	0.0356426	−	0.999365i	$-0.488652\pi$
$701$	1.88737	0.0712851	0.0356426	+	0.999365i	$0.488652\pi$
$702$	−12.8825	−0.486217
$703$	3.72935	0.140655
$704$	0	0
$705$	5.46480	0.205816
$706$	32.9017	1.23827
$707$	11.9511	0.449468
$708$	−32.5108	−1.22183
$709$	−7.03820	−0.264325	−0.132163	−	0.991228i	$-0.542192\pi$
$709$	−7.03820	−0.264325	−0.132163	+	0.991228i	$0.542192\pi$
$710$	9.82812	0.368843
$711$	0.904173	0.0339091
$712$	1.11866	0.0419235
$713$	9.65260	0.361493
$714$	29.7968	1.11512
$715$	0	0
$716$	18.8855	0.705783
$717$	−22.4958	−0.840121
$718$	5.63620	0.210341
$719$	8.02849	0.299412	0.149706	−	0.988731i	$-0.452167\pi$
$719$	8.02849	0.299412	0.149706	+	0.988731i	$0.452167\pi$
$720$	−0.754221	−0.0281081
$721$	−1.72898	−0.0643906
$722$	34.9591	1.30104
$723$	−13.0319	−0.484663
$724$	26.3011	0.977473
$725$	−6.63159	−0.246291
$726$	0	0
$727$	−29.8123	−1.10568	−0.552838	−	0.833289i	$-0.686455\pi$
$727$	−29.8123	−1.10568	−0.552838	+	0.833289i	$0.686455\pi$
$728$	5.22035	0.193479
$729$	25.4165	0.941350
$730$	1.35598	0.0501872
$731$	26.5824	0.983186
$732$	15.3652	0.567915
$733$	40.9187	1.51137	0.755683	−	0.654938i	$-0.227305\pi$
$733$	40.9187	1.51137	0.755683	+	0.654938i	$0.227305\pi$
$734$	−11.5999	−0.428159
$735$	−19.7843	−0.729756
$736$	−31.0958	−1.14621
$737$	0	0
$738$	−2.21526	−0.0815447
$739$	−4.36478	−0.160561	−0.0802805	−	0.996772i	$-0.525582\pi$
$739$	−4.36478	−0.160561	−0.0802805	+	0.996772i	$0.525582\pi$
$740$	9.37449	0.344613
$741$	−1.46130	−0.0536823
$742$	53.1491	1.95117
$743$	19.7055	0.722926	0.361463	−	0.932386i	$-0.382277\pi$
$743$	19.7055	0.722926	0.361463	+	0.932386i	$0.382277\pi$
$744$	3.51698	0.128939
$745$	−1.11258	−0.0407617
$746$	−39.1540	−1.43353
$747$	−0.151900	−0.00555773
$748$	0	0
$749$	65.5669	2.39576
$750$	3.33461	0.121763
$751$	−38.9543	−1.42146	−0.710731	−	0.703464i	$-0.751636\pi$
$751$	−38.9543	−1.42146	−0.710731	+	0.703464i	$0.751636\pi$
$752$	14.5426	0.530314
$753$	−55.5604	−2.02473
$754$	16.9203	0.616201
$755$	5.69465	0.207250
$756$	32.6671	1.18809
$757$	53.1675	1.93241	0.966203	−	0.257783i	$-0.0829918\pi$
$757$	53.1675	1.93241	0.966203	+	0.257783i	$0.0829918\pi$
$758$	4.62299	0.167915
$759$	0	0
$760$	0.544913	0.0197661
$761$	51.2783	1.85884	0.929418	−	0.369029i	$-0.120310\pi$
$761$	51.2783	1.85884	0.929418	+	0.369029i	$0.120310\pi$
$762$	0.377266	0.0136669
$763$	−13.0853	−0.473721
$764$	−29.8584	−1.08024
$765$	0.334614	0.0120980
$766$	−32.2745	−1.16612
$767$	16.3710	0.591122
$768$	−36.8809	−1.33082
$769$	45.0332	1.62394	0.811970	−	0.583699i	$-0.198395\pi$
$769$	45.0332	1.62394	0.811970	+	0.583699i	$0.198395\pi$
$770$	0	0
$771$	14.7892	0.532619
$772$	15.4404	0.555714
$773$	−49.9436	−1.79635	−0.898173	−	0.439641i	$-0.855106\pi$
$773$	−49.9436	−1.79635	−0.898173	+	0.439641i	$0.855106\pi$
$774$	−3.78914	−0.136198
$775$	−2.19493	−0.0788442
$776$	10.4056	0.373538
$777$	−46.6940	−1.67514
$778$	33.8713	1.21434
$779$	4.47653	0.160388
$780$	−3.67328	−0.131525
$781$	0	0
$782$	17.3134	0.619125
$783$	−33.4831	−1.19659
$784$	−52.6489	−1.88032
$785$	1.04114	0.0371598
$786$	1.58160	0.0564137
$787$	9.78526	0.348807	0.174403	−	0.984674i	$-0.444200\pi$
$787$	9.78526	0.348807	0.174403	+	0.984674i	$0.444200\pi$
$788$	−12.8454	−0.457598
$789$	5.10442	0.181722
$790$	−10.6381	−0.378488
$791$	−47.9644	−1.70542
$792$	0	0
$793$	−7.73725	−0.274758
$794$	31.4108	1.11473
$795$	11.8265	0.419443
$796$	−9.89238	−0.350626
$797$	36.1647	1.28102	0.640509	−	0.767950i	$-0.278723\pi$
$797$	36.1647	1.28102	0.640509	+	0.767950i	$0.278723\pi$
$798$	8.58290	0.303831
$799$	−6.45189	−0.228251
$800$	7.07096	0.249996
$801$	0.197869	0.00699137
$802$	−54.2913	−1.91709
$803$	0	0
$804$	−26.6418	−0.939583
$805$	−18.7253	−0.659980
$806$	5.60030	0.197262
$807$	0.220355	0.00775686
$808$	2.53016	0.0890106
$809$	16.3357	0.574332	0.287166	−	0.957881i	$-0.407287\pi$
$809$	16.3357	0.574332	0.287166	+	0.957881i	$0.407287\pi$
$810$	17.7340	0.623108
$811$	51.6959	1.81529	0.907643	−	0.419742i	$-0.137879\pi$
$811$	51.6959	1.81529	0.907643	+	0.419742i	$0.137879\pi$
$812$	−42.9062	−1.50571
$813$	30.2756	1.06181
$814$	0	0
$815$	−12.9115	−0.452270
$816$	17.6440	0.617664
$817$	7.65701	0.267885
$818$	56.0431	1.95950
$819$	0.923382	0.0322656
$820$	11.2527	0.392961
$821$	38.6713	1.34964	0.674819	−	0.737983i	$-0.264222\pi$
$821$	38.6713	1.34964	0.674819	+	0.737983i	$0.264222\pi$
$822$	−2.89675	−0.101036
$823$	−5.30457	−0.184906	−0.0924528	−	0.995717i	$-0.529471\pi$
$823$	−5.30457	−0.184906	−0.0924528	+	0.995717i	$0.529471\pi$
$824$	−0.366040	−0.0127516
$825$	0	0
$826$	−96.1544	−3.34564
$827$	−11.8642	−0.412558	−0.206279	−	0.978493i	$-0.566135\pi$
$827$	−11.8642	−0.412558	−0.206279	+	0.978493i	$0.566135\pi$
$828$	−1.06548	−0.0370281
$829$	−49.3457	−1.71385	−0.856923	−	0.515445i	$-0.827627\pi$
$829$	−49.3457	−1.71385	−0.856923	+	0.515445i	$0.827627\pi$
$830$	1.78720	0.0620345
$831$	−40.4219	−1.40222
$832$	−5.17504	−0.179412
$833$	23.3579	0.809304
$834$	64.6561	2.23886
$835$	4.22601	0.146247
$836$	0	0
$837$	−11.0823	−0.383059
$838$	15.5679	0.537783
$839$	−21.4081	−0.739089	−0.369544	−	0.929213i	$-0.620486\pi$
$839$	−21.4081	−0.739089	−0.369544	+	0.929213i	$0.620486\pi$
$840$	−6.82268	−0.235405
$841$	14.9779	0.516481
$842$	42.8995	1.47841
$843$	23.0183	0.792792
$844$	6.09928	0.209946
$845$	−11.1503	−0.383582
$846$	0.919673	0.0316190
$847$	0	0
$848$	31.4720	1.08075
$849$	−28.1160	−0.964938
$850$	−3.93693	−0.135036
$851$	−27.1315	−0.930056
$852$	14.1493	0.484746
$853$	31.0811	1.06420	0.532098	−	0.846683i	$-0.321404\pi$
$853$	31.0811	1.06420	0.532098	+	0.846683i	$0.321404\pi$
$854$	45.4444	1.55508
$855$	0.0963848	0.00329629
$856$	13.8811	0.474445
$857$	33.2665	1.13636	0.568181	−	0.822904i	$-0.307647\pi$
$857$	33.2665	1.13636	0.568181	+	0.822904i	$0.307647\pi$
$858$	0	0
$859$	−18.9045	−0.645012	−0.322506	−	0.946567i	$-0.604525\pi$
$859$	−18.9045	−0.645012	−0.322506	+	0.946567i	$0.604525\pi$
$860$	19.2475	0.656333
$861$	−56.0492	−1.91015
$862$	38.1992	1.30107
$863$	13.8324	0.470862	0.235431	−	0.971891i	$-0.424350\pi$
$863$	13.8324	0.470862	0.235431	+	0.971891i	$0.424350\pi$
$864$	35.7015	1.21459
$865$	1.34571	0.0457554
$866$	−40.1262	−1.36354
$867$	22.3894	0.760383
$868$	−14.2011	−0.482018
$869$	0	0
$870$	−22.1138	−0.749727
$871$	13.4156	0.454571
$872$	−2.77028	−0.0938135
$873$	1.84055	0.0622932
$874$	4.98708	0.168691
$875$	4.25800	0.143947
$876$	1.95217	0.0659578
$877$	−48.3403	−1.63233	−0.816167	−	0.577816i	$-0.803905\pi$
$877$	−48.3403	−1.63233	−0.816167	+	0.577816i	$0.803905\pi$
$878$	66.0946	2.23058
$879$	44.3137	1.49466
$880$	0	0
$881$	−33.4457	−1.12682	−0.563408	−	0.826179i	$-0.690510\pi$
$881$	−33.4457	−1.12682	−0.563408	+	0.826179i	$0.690510\pi$
$882$	−3.32951	−0.112111
$883$	18.2657	0.614689	0.307345	−	0.951598i	$-0.400560\pi$
$883$	18.2657	0.614689	0.307345	+	0.951598i	$0.400560\pi$
$884$	4.33677	0.145862
$885$	−21.3959	−0.719214
$886$	−43.6408	−1.46614
$887$	−15.6871	−0.526721	−0.263361	−	0.964697i	$-0.584831\pi$
$887$	−15.6871	−0.526721	−0.263361	+	0.964697i	$0.584831\pi$
$888$	−9.88553	−0.331737
$889$	0.481734	0.0161568
$890$	−2.32805	−0.0780366
$891$	0	0
$892$	23.2589	0.778764
$893$	−1.85845	−0.0621908
$894$	−3.71002	−0.124082
$895$	12.4288	0.415450
$896$	−29.8209	−0.996245
$897$	10.6312	0.354964
$898$	−46.6227	−1.55582
$899$	14.5559	0.485465
$900$	0.242283	0.00807609
$901$	−13.9627	−0.465165
$902$	0	0
$903$	−95.8710	−3.19039
$904$	−10.1545	−0.337733
$905$	17.3092	0.575377
$906$	18.9895	0.630883
$907$	−25.8952	−0.859835	−0.429918	−	0.902868i	$-0.641457\pi$
$907$	−25.8952	−0.859835	−0.429918	+	0.902868i	$0.641457\pi$
$908$	17.4770	0.579994
$909$	0.447537	0.0148439
$910$	−10.8642	−0.360143
$911$	15.4526	0.511967	0.255983	−	0.966681i	$-0.417601\pi$
$911$	15.4526	0.511967	0.255983	+	0.966681i	$0.417601\pi$
$912$	5.08232	0.168293
$913$	0	0
$914$	−11.0842	−0.366632
$915$	10.1121	0.334296
$916$	−41.8272	−1.38201
$917$	2.01955	0.0666916
$918$	−19.8777	−0.656062
$919$	47.7134	1.57392	0.786959	−	0.617005i	$-0.211654\pi$
$919$	47.7134	1.57392	0.786959	+	0.617005i	$0.211654\pi$
$920$	−3.96431	−0.130699
$921$	8.80861	0.290254
$922$	32.5654	1.07249
$923$	−7.12495	−0.234521
$924$	0	0
$925$	6.16951	0.202852
$926$	−65.0864	−2.13887
$927$	−0.0647456	−0.00212652
$928$	−46.8917	−1.53929
$929$	−37.7533	−1.23865	−0.619323	−	0.785136i	$-0.712593\pi$
$929$	−37.7533	−1.23865	−0.619323	+	0.785136i	$0.712593\pi$
$930$	−7.31925	−0.240008
$931$	6.72820	0.220508
$932$	13.9827	0.458020
$933$	17.0546	0.558341
$934$	−17.1957	−0.562661
$935$	0	0
$936$	0.195488	0.00638972
$937$	−49.6382	−1.62161	−0.810805	−	0.585316i	$-0.800970\pi$
$937$	−49.6382	−1.62161	−0.810805	+	0.585316i	$0.800970\pi$
$938$	−78.7962	−2.57279
$939$	47.9669	1.56534
$940$	−4.67160	−0.152371
$941$	33.3188	1.08616	0.543081	−	0.839680i	$-0.317258\pi$
$941$	33.3188	1.08616	0.543081	+	0.839680i	$0.317258\pi$
$942$	3.47179	0.113117
$943$	−32.5673	−1.06054
$944$	−56.9374	−1.85315
$945$	21.4988	0.699355
$946$	0	0
$947$	−22.6463	−0.735907	−0.367954	−	0.929844i	$-0.619941\pi$
$947$	−22.6463	−0.735907	−0.367954	+	0.929844i	$0.619941\pi$
$948$	−15.3154	−0.497422
$949$	−0.983028	−0.0319104
$950$	−1.13403	−0.0367927
$951$	25.2771	0.819665
$952$	8.05503	0.261065
$953$	48.5378	1.57229	0.786147	−	0.618040i	$-0.212073\pi$
$953$	48.5378	1.57229	0.786147	+	0.618040i	$0.212073\pi$
$954$	1.99029	0.0644380
$955$	−19.6503	−0.635869
$956$	19.2306	0.621962
$957$	0	0
$958$	76.6020	2.47490
$959$	−3.69889	−0.119443
$960$	6.76345	0.218289
$961$	−26.1823	−0.844590
$962$	−15.7413	−0.507521
$963$	2.45530	0.0791209
$964$	11.1404	0.358808
$965$	10.1616	0.327114
$966$	−62.4416	−2.00903
$967$	−47.2983	−1.52101	−0.760505	−	0.649332i	$-0.775048\pi$
$967$	−47.2983	−1.52101	−0.760505	+	0.649332i	$0.775048\pi$
$968$	0	0
$969$	−2.25480	−0.0724345
$970$	−21.6552	−0.695306
$971$	19.2817	0.618780	0.309390	−	0.950935i	$-0.399875\pi$
$971$	19.2817	0.618780	0.309390	+	0.950935i	$0.399875\pi$
$972$	2.51526	0.0806769
$973$	82.5599	2.64675
$974$	49.0766	1.57251
$975$	−2.41745	−0.0774202
$976$	26.9097	0.861358
$977$	31.8772	1.01984	0.509920	−	0.860222i	$-0.329675\pi$
$977$	31.8772	1.01984	0.509920	+	0.860222i	$0.329675\pi$
$978$	−43.0549	−1.37674
$979$	0	0
$980$	16.9127	0.540257
$981$	−0.490010	−0.0156448
$982$	−43.1509	−1.37700
$983$	1.60184	0.0510908	0.0255454	−	0.999674i	$-0.491868\pi$
$983$	1.60184	0.0510908	0.0255454	+	0.999674i	$0.491868\pi$
$984$	−11.8661	−0.378278
$985$	−8.45375	−0.269359
$986$	26.1081	0.831452
$987$	23.2691	0.740663
$988$	1.24920	0.0397423
$989$	−55.7057	−1.77134
$990$	0	0
$991$	48.3005	1.53432	0.767158	−	0.641458i	$-0.221670\pi$
$991$	48.3005	1.53432	0.767158	+	0.641458i	$0.221670\pi$
$992$	−15.5203	−0.492769
$993$	15.2150	0.482833
$994$	41.8481	1.32734
$995$	−6.51033	−0.206391
$996$	2.57297	0.0815278
$997$	−22.8677	−0.724228	−0.362114	−	0.932134i	$-0.617945\pi$
$997$	−22.8677	−0.724228	−0.362114	+	0.932134i	$0.617945\pi$
$998$	49.1783	1.55671
$999$	31.1500	0.985544

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.a.l.1.1		4
3.2	odd	2		5445.2.a.bg.1.4		4
4.3	odd	2		9680.2.a.cs.1.3		4
5.4	even	2		3025.2.a.v.1.4		4
11.2	odd	10		605.2.g.g.81.1		8
11.3	even	5		55.2.g.a.31.1	yes	8
11.4	even	5		55.2.g.a.16.1	✓	8
11.5	even	5		605.2.g.j.366.2		8
11.6	odd	10		605.2.g.g.366.1		8
11.7	odd	10		605.2.g.n.511.2		8
11.8	odd	10		605.2.g.n.251.2		8
11.9	even	5		605.2.g.j.81.2		8
11.10	odd	2		605.2.a.i.1.4		4
33.14	odd	10		495.2.n.f.361.2		8
33.26	odd	10		495.2.n.f.181.2		8
33.32	even	2		5445.2.a.bu.1.1		4
44.3	odd	10		880.2.bo.e.801.1		8
44.15	odd	10		880.2.bo.e.401.1		8
44.43	even	2		9680.2.a.cv.1.3		4
55.3	odd	20		275.2.z.b.174.3		16
55.4	even	10		275.2.h.b.126.2		8
55.14	even	10		275.2.h.b.251.2		8
55.37	odd	20		275.2.z.b.49.3		16
55.47	odd	20		275.2.z.b.174.2		16
55.48	odd	20		275.2.z.b.49.2		16
55.54	odd	2		3025.2.a.be.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.16.1	✓	8	11.4	even	5
55.2.g.a.31.1	yes	8	11.3	even	5
275.2.h.b.126.2		8	55.4	even	10
275.2.h.b.251.2		8	55.14	even	10
275.2.z.b.49.2		16	55.48	odd	20
275.2.z.b.49.3		16	55.37	odd	20
275.2.z.b.174.2		16	55.47	odd	20
275.2.z.b.174.3		16	55.3	odd	20
495.2.n.f.181.2		8	33.26	odd	10
495.2.n.f.361.2		8	33.14	odd	10
605.2.a.i.1.4		4	11.10	odd	2
605.2.a.l.1.1		4	1.1	even	1	trivial
605.2.g.g.81.1		8	11.2	odd	10
605.2.g.g.366.1		8	11.6	odd	10
605.2.g.j.81.2		8	11.9	even	5
605.2.g.j.366.2		8	11.5	even	5
605.2.g.n.251.2		8	11.8	odd	10
605.2.g.n.511.2		8	11.7	odd	10
880.2.bo.e.401.1		8	44.15	odd	10
880.2.bo.e.801.1		8	44.3	odd	10
3025.2.a.v.1.4		4	5.4	even	2
3025.2.a.be.1.1		4	55.54	odd	2
5445.2.a.bg.1.4		4	3.2	odd	2
5445.2.a.bu.1.1		4	33.32	even	2
9680.2.a.cs.1.3		4	4.3	odd	2
9680.2.a.cv.1.3		4	44.43	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.a (trivial)

\(f(q)\)	\(=\)	\(q-1.87603 q^{2} -1.77748 q^{3} +1.51949 q^{4} +1.00000 q^{5} +3.33461 q^{6} +4.25800 q^{7} +0.901454 q^{8} +0.159450 q^{9} +O(q^{10})\)	\(q-1.87603 q^{2} -1.77748 q^{3} +1.51949 q^{4} +1.00000 q^{5} +3.33461 q^{6} +4.25800 q^{7} +0.901454 q^{8} +0.159450 q^{9} -1.87603 q^{10} -2.70087 q^{12} +1.36004 q^{13} -7.98813 q^{14} -1.77748 q^{15} -4.73013 q^{16} +2.09855 q^{17} -0.299133 q^{18} +0.604482 q^{19} +1.51949 q^{20} -7.56852 q^{21} -4.39768 q^{23} -1.60232 q^{24} +1.00000 q^{25} -2.55147 q^{26} +5.04903 q^{27} +6.46998 q^{28} -6.63159 q^{29} +3.33461 q^{30} -2.19493 q^{31} +7.07096 q^{32} -3.93693 q^{34} +4.25800 q^{35} +0.242283 q^{36} +6.16951 q^{37} -1.13403 q^{38} -2.41745 q^{39} +0.901454 q^{40} +7.40557 q^{41} +14.1988 q^{42} +12.6671 q^{43} +0.159450 q^{45} +8.25018 q^{46} -3.07446 q^{47} +8.40773 q^{48} +11.1305 q^{49} -1.87603 q^{50} -3.73013 q^{51} +2.06656 q^{52} -6.65351 q^{53} -9.47214 q^{54} +3.83839 q^{56} -1.07446 q^{57} +12.4411 q^{58} +12.0372 q^{59} -2.70087 q^{60} -5.68899 q^{61} +4.11776 q^{62} +0.678939 q^{63} -3.80507 q^{64} +1.36004 q^{65} +9.86416 q^{67} +3.18872 q^{68} +7.81681 q^{69} -7.98813 q^{70} -5.23879 q^{71} +0.143737 q^{72} -0.722795 q^{73} -11.5742 q^{74} -1.77748 q^{75} +0.918503 q^{76} +4.53520 q^{78} +5.67056 q^{79} -4.73013 q^{80} -9.45293 q^{81} -13.8931 q^{82} -0.952648 q^{83} -11.5003 q^{84} +2.09855 q^{85} -23.7638 q^{86} +11.7875 q^{87} +1.24095 q^{89} -0.299133 q^{90} +5.79104 q^{91} -6.68222 q^{92} +3.90145 q^{93} +5.76777 q^{94} +0.604482 q^{95} -12.5685 q^{96} +11.5431 q^{97} -20.8812 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 2 q^{3} + 7 q^{4} + 4 q^{5} - q^{6} + 11 q^{7} + 9 q^{8}+O(q^{10}) \) 4 * q + 3 * q^2 - 2 * q^3 + 7 * q^4 + 4 * q^5 - q^6 + 11 * q^7 + 9 * q^8	\( 4 q + 3 q^{2} - 2 q^{3} + 7 q^{4} + 4 q^{5} - q^{6} + 11 q^{7} + 9 q^{8} + 3 q^{10} - 14 q^{12} + 7 q^{13} - 2 q^{14} - 2 q^{15} + 5 q^{16} + 3 q^{17} + 2 q^{18} + 12 q^{19} + 7 q^{20} - 6 q^{21} - 9 q^{23} - 15 q^{24} + 4 q^{25} + 13 q^{26} - 5 q^{27} + 7 q^{28} - 8 q^{29} - q^{30} + 3 q^{31} + 6 q^{32} - 10 q^{34} + 11 q^{35} + 8 q^{36} - 3 q^{37} + 12 q^{38} - 3 q^{39} + 9 q^{40} - 7 q^{41} + 2 q^{42} + 21 q^{43} + 12 q^{46} - 3 q^{47} - 2 q^{48} + 15 q^{49} + 3 q^{50} + 9 q^{51} + 27 q^{52} - 11 q^{53} - 20 q^{54} + 15 q^{56} + 5 q^{57} + 2 q^{58} - 7 q^{59} - 14 q^{60} + 4 q^{61} + 11 q^{62} + 3 q^{63} - 27 q^{64} + 7 q^{65} - q^{67} - 15 q^{68} - 28 q^{69} - 2 q^{70} - 15 q^{71} + 13 q^{72} - 9 q^{73} - 36 q^{74} - 2 q^{75} + 8 q^{76} + 6 q^{78} + 6 q^{79} + 5 q^{80} - 20 q^{81} - 44 q^{82} + 15 q^{83} - 47 q^{84} + 3 q^{85} - 3 q^{86} + 15 q^{87} + 2 q^{90} + 4 q^{91} + 18 q^{92} + 21 q^{93} - 11 q^{94} + 12 q^{95} - 26 q^{96} + 6 q^{97} - 42 q^{98}+O(q^{100}) \) 4 * q + 3 * q^2 - 2 * q^3 + 7 * q^4 + 4 * q^5 - q^6 + 11 * q^7 + 9 * q^8 + 3 * q^10 - 14 * q^12 + 7 * q^13 - 2 * q^14 - 2 * q^15 + 5 * q^16 + 3 * q^17 + 2 * q^18 + 12 * q^19 + 7 * q^20 - 6 * q^21 - 9 * q^23 - 15 * q^24 + 4 * q^25 + 13 * q^26 - 5 * q^27 + 7 * q^28 - 8 * q^29 - q^30 + 3 * q^31 + 6 * q^32 - 10 * q^34 + 11 * q^35 + 8 * q^36 - 3 * q^37 + 12 * q^38 - 3 * q^39 + 9 * q^40 - 7 * q^41 + 2 * q^42 + 21 * q^43 + 12 * q^46 - 3 * q^47 - 2 * q^48 + 15 * q^49 + 3 * q^50 + 9 * q^51 + 27 * q^52 - 11 * q^53 - 20 * q^54 + 15 * q^56 + 5 * q^57 + 2 * q^58 - 7 * q^59 - 14 * q^60 + 4 * q^61 + 11 * q^62 + 3 * q^63 - 27 * q^64 + 7 * q^65 - q^67 - 15 * q^68 - 28 * q^69 - 2 * q^70 - 15 * q^71 + 13 * q^72 - 9 * q^73 - 36 * q^74 - 2 * q^75 + 8 * q^76 + 6 * q^78 + 6 * q^79 + 5 * q^80 - 20 * q^81 - 44 * q^82 + 15 * q^83 - 47 * q^84 + 3 * q^85 - 3 * q^86 + 15 * q^87 + 2 * q^90 + 4 * q^91 + 18 * q^92 + 21 * q^93 - 11 * q^94 + 12 * q^95 - 26 * q^96 + 6 * q^97 - 42 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more