LMFDB - Embedded newform 1805.2.a.t.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, 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("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 12x^{7} - 4x^{6} + 48x^{5} + 27x^{4} - 72x^{3} - 51x^{2} + 27x + 19 $ x^9 - 12x^7 - 4x^6 + 48x^5 + 27x^4 - 72x^3 - 51x^2 + 27*x + 19
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.593847$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.593847 q^{2} -1.93003 q^{3} -1.64735 q^{4} -1.00000 q^{5} +1.14614 q^{6} +1.06052 q^{7} +2.16596 q^{8} +0.725033 q^{9} +O(q^{10})$	\(q-0.593847 q^{2} -1.93003 q^{3} -1.64735 q^{4} -1.00000 q^{5} +1.14614 q^{6} +1.06052 q^{7} +2.16596 q^{8} +0.725033 q^{9} +0.593847 q^{10} +0.196653 q^{11} +3.17944 q^{12} -5.28245 q^{13} -0.629785 q^{14} +1.93003 q^{15} +2.00844 q^{16} +0.704965 q^{17} -0.430558 q^{18} +1.64735 q^{20} -2.04684 q^{21} -0.116781 q^{22} +6.62298 q^{23} -4.18038 q^{24} +1.00000 q^{25} +3.13697 q^{26} +4.39076 q^{27} -1.74704 q^{28} -3.38126 q^{29} -1.14614 q^{30} +7.91823 q^{31} -5.52463 q^{32} -0.379546 q^{33} -0.418641 q^{34} -1.06052 q^{35} -1.19438 q^{36} -1.09727 q^{37} +10.1953 q^{39} -2.16596 q^{40} -1.35463 q^{41} +1.21551 q^{42} +9.00810 q^{43} -0.323955 q^{44} -0.725033 q^{45} -3.93303 q^{46} +4.81938 q^{47} -3.87636 q^{48} -5.87530 q^{49} -0.593847 q^{50} -1.36061 q^{51} +8.70203 q^{52} -5.32420 q^{53} -2.60744 q^{54} -0.196653 q^{55} +2.29704 q^{56} +2.00795 q^{58} -10.9822 q^{59} -3.17944 q^{60} +11.7524 q^{61} -4.70221 q^{62} +0.768911 q^{63} -0.736100 q^{64} +5.28245 q^{65} +0.225392 q^{66} -3.05599 q^{67} -1.16132 q^{68} -12.7826 q^{69} +0.629785 q^{70} +2.50478 q^{71} +1.57040 q^{72} +6.55421 q^{73} +0.651609 q^{74} -1.93003 q^{75} +0.208554 q^{77} -6.05445 q^{78} -12.2632 q^{79} -2.00844 q^{80} -10.6494 q^{81} +0.804441 q^{82} -4.03175 q^{83} +3.37185 q^{84} -0.704965 q^{85} -5.34943 q^{86} +6.52596 q^{87} +0.425943 q^{88} +17.5253 q^{89} +0.430558 q^{90} -5.60214 q^{91} -10.9103 q^{92} -15.2825 q^{93} -2.86197 q^{94} +10.6627 q^{96} -1.33950 q^{97} +3.48903 q^{98} +0.142580 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} + 12 q^{8} + 6 q^{9}+O(q^{10}) $ 9 * q - 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 + 12 * q^8 + 6 * q^9	$ 9 q - 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} + 12 q^{8} + 6 q^{9} - 6 q^{12} + 3 q^{13} - 12 q^{14} + 3 q^{15} - 12 q^{16} - 9 q^{17} - 6 q^{18} - 6 q^{20} - 12 q^{21} - 12 q^{22} + 15 q^{24} + 9 q^{25} + 21 q^{26} - 6 q^{27} - 15 q^{28} - 15 q^{29} + 12 q^{30} - 30 q^{31} + 9 q^{32} - 9 q^{33} - 6 q^{36} - 30 q^{37} + 6 q^{39} - 12 q^{40} - 18 q^{41} + 36 q^{42} - 6 q^{43} - 24 q^{44} - 6 q^{45} - 21 q^{46} + 21 q^{47} - 15 q^{48} + 3 q^{49} - 18 q^{51} + 3 q^{52} + 9 q^{53} - 9 q^{54} - 36 q^{56} + 18 q^{58} - 27 q^{59} + 6 q^{60} + 12 q^{61} - 6 q^{62} - 15 q^{63} + 24 q^{64} - 3 q^{65} + 3 q^{66} - 36 q^{67} + 3 q^{68} - 27 q^{69} + 12 q^{70} + 6 q^{71} - 12 q^{72} - 9 q^{73} - 9 q^{74} - 3 q^{75} + 12 q^{77} - 54 q^{78} - 45 q^{79} + 12 q^{80} - 15 q^{81} - 48 q^{82} + 12 q^{84} + 9 q^{85} + 9 q^{86} + 45 q^{87} - 39 q^{88} + 9 q^{89} + 6 q^{90} - 51 q^{91} - 54 q^{92} + 9 q^{93} - 33 q^{94} - 9 q^{96} - 45 q^{97} - 33 q^{98} + 12 q^{99}+O(q^{100}) $ 9 * q - 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 + 12 * q^8 + 6 * q^9 - 6 * q^12 + 3 * q^13 - 12 * q^14 + 3 * q^15 - 12 * q^16 - 9 * q^17 - 6 * q^18 - 6 * q^20 - 12 * q^21 - 12 * q^22 + 15 * q^24 + 9 * q^25 + 21 * q^26 - 6 * q^27 - 15 * q^28 - 15 * q^29 + 12 * q^30 - 30 * q^31 + 9 * q^32 - 9 * q^33 - 6 * q^36 - 30 * q^37 + 6 * q^39 - 12 * q^40 - 18 * q^41 + 36 * q^42 - 6 * q^43 - 24 * q^44 - 6 * q^45 - 21 * q^46 + 21 * q^47 - 15 * q^48 + 3 * q^49 - 18 * q^51 + 3 * q^52 + 9 * q^53 - 9 * q^54 - 36 * q^56 + 18 * q^58 - 27 * q^59 + 6 * q^60 + 12 * q^61 - 6 * q^62 - 15 * q^63 + 24 * q^64 - 3 * q^65 + 3 * q^66 - 36 * q^67 + 3 * q^68 - 27 * q^69 + 12 * q^70 + 6 * q^71 - 12 * q^72 - 9 * q^73 - 9 * q^74 - 3 * q^75 + 12 * q^77 - 54 * q^78 - 45 * q^79 + 12 * q^80 - 15 * q^81 - 48 * q^82 + 12 * q^84 + 9 * q^85 + 9 * q^86 + 45 * q^87 - 39 * q^88 + 9 * q^89 + 6 * q^90 - 51 * q^91 - 54 * q^92 + 9 * q^93 - 33 * q^94 - 9 * q^96 - 45 * q^97 - 33 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.593847	−0.419913	−0.209956	−	0.977711i	$-0.567332\pi$
$2$	−0.593847	−0.419913	−0.209956	+	0.977711i	$0.567332\pi$
$3$	−1.93003	−1.11431	−0.557153	−	0.830410i	$-0.688106\pi$
$3$	−1.93003	−1.11431	−0.557153	+	0.830410i	$0.688106\pi$
$4$	−1.64735	−0.823673
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.14614	0.467911
$7$	1.06052	0.400838	0.200419	−	0.979710i	$-0.435770\pi$
$7$	1.06052	0.400838	0.200419	+	0.979710i	$0.435770\pi$
$8$	2.16596	0.765784
$9$	0.725033	0.241678
$10$	0.593847	0.187791
$11$	0.196653	0.0592930	0.0296465	−	0.999560i	$-0.490562\pi$
$11$	0.196653	0.0592930	0.0296465	+	0.999560i	$0.490562\pi$
$12$	3.17944	0.917824
$13$	−5.28245	−1.46509	−0.732544	−	0.680719i	$-0.761667\pi$
$13$	−5.28245	−1.46509	−0.732544	+	0.680719i	$0.761667\pi$
$14$	−0.629785	−0.168317
$15$	1.93003	0.498333
$16$	2.00844	0.502111
$17$	0.704965	0.170979	0.0854896	−	0.996339i	$-0.472755\pi$
$17$	0.704965	0.170979	0.0854896	+	0.996339i	$0.472755\pi$
$18$	−0.430558	−0.101484
$19$	0	0
$19$	0	0
$20$	1.64735	0.368358
$21$	−2.04684	−0.446656
$22$	−0.116781	−0.0248979
$23$	6.62298	1.38099	0.690493	−	0.723339i	$-0.257394\pi$
$23$	6.62298	1.38099	0.690493	+	0.723339i	$0.257394\pi$
$24$	−4.18038	−0.853318
$25$	1.00000	0.200000
$26$	3.13697	0.615210
$27$	4.39076	0.845003
$28$	−1.74704	−0.330160
$29$	−3.38126	−0.627885	−0.313942	−	0.949442i	$-0.601650\pi$
$29$	−3.38126	−0.627885	−0.313942	+	0.949442i	$0.601650\pi$
$30$	−1.14614	−0.209256
$31$	7.91823	1.42216	0.711078	−	0.703113i	$-0.248207\pi$
$31$	7.91823	1.42216	0.711078	+	0.703113i	$0.248207\pi$
$32$	−5.52463	−0.976627
$33$	−0.379546	−0.0660705
$34$	−0.418641	−0.0717964
$35$	−1.06052	−0.179260
$36$	−1.19438	−0.199063
$37$	−1.09727	−0.180390	−0.0901949	−	0.995924i	$-0.528749\pi$
$37$	−1.09727	−0.180390	−0.0901949	+	0.995924i	$0.528749\pi$
$38$	0	0
$39$	10.1953	1.63256
$40$	−2.16596	−0.342469
$41$	−1.35463	−0.211557	−0.105779	−	0.994390i	$-0.533733\pi$
$41$	−1.35463	−0.211557	−0.105779	+	0.994390i	$0.533733\pi$
$42$	1.21551	0.187557
$43$	9.00810	1.37372	0.686861	−	0.726789i	$-0.258988\pi$
$43$	9.00810	1.37372	0.686861	+	0.726789i	$0.258988\pi$
$44$	−0.323955	−0.0488381
$45$	−0.725033	−0.108082
$46$	−3.93303	−0.579894
$47$	4.81938	0.702978	0.351489	−	0.936192i	$-0.385675\pi$
$47$	4.81938	0.702978	0.351489	+	0.936192i	$0.385675\pi$
$48$	−3.87636	−0.559505
$49$	−5.87530	−0.839329
$50$	−0.593847	−0.0839826
$51$	−1.36061	−0.190523
$52$	8.70203	1.20675
$53$	−5.32420	−0.731335	−0.365668	−	0.930746i	$-0.619159\pi$
$53$	−5.32420	−0.731335	−0.365668	+	0.930746i	$0.619159\pi$
$54$	−2.60744	−0.354828
$55$	−0.196653	−0.0265166
$56$	2.29704	0.306955
$57$	0	0
$58$	2.00795	0.263657
$59$	−10.9822	−1.42976	−0.714878	−	0.699250i	$-0.753518\pi$
$59$	−10.9822	−1.42976	−0.714878	+	0.699250i	$0.753518\pi$
$60$	−3.17944	−0.410463
$61$	11.7524	1.50475	0.752373	−	0.658737i	$-0.228909\pi$
$61$	11.7524	1.50475	0.752373	+	0.658737i	$0.228909\pi$
$62$	−4.70221	−0.597182
$63$	0.768911	0.0968737
$64$	−0.736100	−0.0920125
$65$	5.28245	0.655208
$66$	0.225392	0.0277439
$67$	−3.05599	−0.373349	−0.186674	−	0.982422i	$-0.559771\pi$
$67$	−3.05599	−0.373349	−0.186674	+	0.982422i	$0.559771\pi$
$68$	−1.16132	−0.140831
$69$	−12.7826	−1.53884
$70$	0.629785	0.0752737
$71$	2.50478	0.297262	0.148631	−	0.988893i	$-0.452513\pi$
$71$	2.50478	0.297262	0.148631	+	0.988893i	$0.452513\pi$
$72$	1.57040	0.185073
$73$	6.55421	0.767112	0.383556	−	0.923518i	$-0.374699\pi$
$73$	6.55421	0.767112	0.383556	+	0.923518i	$0.374699\pi$
$74$	0.651609	0.0757480
$75$	−1.93003	−0.222861
$76$	0	0
$77$	0.208554	0.0237669
$78$	−6.05445	−0.685532
$79$	−12.2632	−1.37972	−0.689859	−	0.723944i	$-0.742328\pi$
$79$	−12.2632	−1.37972	−0.689859	+	0.723944i	$0.742328\pi$
$80$	−2.00844	−0.224551
$81$	−10.6494	−1.18327
$82$	0.804441	0.0888356
$83$	−4.03175	−0.442542	−0.221271	−	0.975212i	$-0.571021\pi$
$83$	−4.03175	−0.442542	−0.221271	+	0.975212i	$0.571021\pi$
$84$	3.37185	0.367899
$85$	−0.704965	−0.0764642
$86$	−5.34943	−0.576844
$87$	6.52596	0.699656
$88$	0.425943	0.0454056
$89$	17.5253	1.85768	0.928840	−	0.370482i	$-0.120807\pi$
$89$	17.5253	1.85768	0.928840	+	0.370482i	$0.120807\pi$
$90$	0.430558	0.0453848
$91$	−5.60214	−0.587264
$92$	−10.9103	−1.13748
$93$	−15.2825	−1.58472
$94$	−2.86197	−0.295190
$95$	0	0
$96$	10.6627	1.08826
$97$	−1.33950	−0.136006	−0.0680028	−	0.997685i	$-0.521663\pi$
$97$	−1.33950	−0.136006	−0.0680028	+	0.997685i	$0.521663\pi$
$98$	3.48903	0.352445
$99$	0.142580	0.0143298
$100$	−1.64735	−0.164735
$101$	−17.9348	−1.78458	−0.892288	−	0.451467i	$-0.850901\pi$
$101$	−17.9348	−1.78458	−0.892288	+	0.451467i	$0.850901\pi$
$102$	0.807992	0.0800031
$103$	−11.6234	−1.14528	−0.572641	−	0.819806i	$-0.694081\pi$
$103$	−11.6234	−1.14528	−0.572641	+	0.819806i	$0.694081\pi$
$104$	−11.4416	−1.12194
$105$	2.04684	0.199751
$106$	3.16176	0.307097
$107$	2.49645	0.241341	0.120671	−	0.992693i	$-0.461496\pi$
$107$	2.49645	0.241341	0.120671	+	0.992693i	$0.461496\pi$
$108$	−7.23311	−0.696006
$109$	−2.07673	−0.198915	−0.0994574	−	0.995042i	$-0.531711\pi$
$109$	−2.07673	−0.198915	−0.0994574	+	0.995042i	$0.531711\pi$
$110$	0.116781	0.0111347
$111$	2.11776	0.201009
$112$	2.12999	0.201265
$113$	−15.3786	−1.44669	−0.723347	−	0.690484i	$-0.757397\pi$
$113$	−15.3786	−1.44669	−0.723347	+	0.690484i	$0.757397\pi$
$114$	0	0
$115$	−6.62298	−0.617596
$116$	5.57011	0.517172
$117$	−3.82995	−0.354079
$118$	6.52172	0.600373
$119$	0.747628	0.0685350
$120$	4.18038	0.381615
$121$	−10.9613	−0.996484
$122$	−6.97915	−0.631863
$123$	2.61448	0.235740
$124$	−13.0441	−1.17139
$125$	−1.00000	−0.0894427
$126$	−0.456615	−0.0406785
$127$	−7.60725	−0.675035	−0.337517	−	0.941319i	$-0.609587\pi$
$127$	−7.60725	−0.675035	−0.337517	+	0.941319i	$0.609587\pi$
$128$	11.4864	1.01526
$129$	−17.3859	−1.53075
$130$	−3.13697	−0.275130
$131$	−20.8602	−1.82256	−0.911281	−	0.411784i	$-0.864906\pi$
$131$	−20.8602	−1.82256	−0.911281	+	0.411784i	$0.864906\pi$
$132$	0.625244	0.0544205
$133$	0	0
$134$	1.81479	0.156774
$135$	−4.39076	−0.377897
$136$	1.52693	0.130933
$137$	19.2161	1.64174	0.820869	−	0.571116i	$-0.193489\pi$
$137$	19.2161	1.64174	0.820869	+	0.571116i	$0.193489\pi$
$138$	7.59089	0.646179
$139$	−19.6484	−1.66656	−0.833279	−	0.552852i	$-0.813539\pi$
$139$	−19.6484	−1.66656	−0.833279	+	0.552852i	$0.813539\pi$
$140$	1.74704	0.147652
$141$	−9.30156	−0.783333
$142$	−1.48745	−0.124824
$143$	−1.03881	−0.0868695
$144$	1.45619	0.121349
$145$	3.38126	0.280799
$146$	−3.89219	−0.322120
$147$	11.3395	0.935269
$148$	1.80758	0.148582
$149$	−8.65464	−0.709016	−0.354508	−	0.935053i	$-0.615352\pi$
$149$	−8.65464	−0.709016	−0.354508	+	0.935053i	$0.615352\pi$
$150$	1.14614	0.0935823
$151$	−4.95316	−0.403083	−0.201541	−	0.979480i	$-0.564595\pi$
$151$	−4.95316	−0.403083	−0.201541	+	0.979480i	$0.564595\pi$
$152$	0	0
$153$	0.511123	0.0413218
$154$	−0.123849	−0.00998003
$155$	−7.91823	−0.636008
$156$	−16.7952	−1.34469
$157$	−13.8649	−1.10654	−0.553269	−	0.833003i	$-0.686620\pi$
$157$	−13.8649	−1.10654	−0.553269	+	0.833003i	$0.686620\pi$
$158$	7.28246	0.579362
$159$	10.2759	0.814931
$160$	5.52463	0.436761
$161$	7.02379	0.553552
$162$	6.32412	0.496870
$163$	−6.35093	−0.497444	−0.248722	−	0.968575i	$-0.580010\pi$
$163$	−6.35093	−0.497444	−0.248722	+	0.968575i	$0.580010\pi$
$164$	2.23154	0.174254
$165$	0.379546	0.0295476
$166$	2.39424	0.185829
$167$	19.7001	1.52444	0.762220	−	0.647318i	$-0.224110\pi$
$167$	19.7001	1.52444	0.762220	+	0.647318i	$0.224110\pi$
$168$	−4.43337	−0.342042
$169$	14.9043	1.14648
$170$	0.418641	0.0321083
$171$	0	0
$172$	−14.8395	−1.13150
$173$	8.91767	0.677998	0.338999	−	0.940787i	$-0.389912\pi$
$173$	8.91767	0.677998	0.338999	+	0.940787i	$0.389912\pi$
$174$	−3.87542	−0.293795
$175$	1.06052	0.0801676
$176$	0.394966	0.0297716
$177$	21.1959	1.59318
$178$	−10.4073	−0.780064
$179$	1.77208	0.132451	0.0662257	−	0.997805i	$-0.478904\pi$
$179$	1.77208	0.132451	0.0662257	+	0.997805i	$0.478904\pi$
$180$	1.19438	0.0890239
$181$	8.54886	0.635432	0.317716	−	0.948186i	$-0.397084\pi$
$181$	8.54886	0.635432	0.317716	+	0.948186i	$0.397084\pi$
$182$	3.32681	0.246600
$183$	−22.6826	−1.67675
$184$	14.3451	1.05754
$185$	1.09727	0.0806727
$186$	9.07544	0.665443
$187$	0.138633	0.0101379
$188$	−7.93918	−0.579024
$189$	4.65649	0.338710
$190$	0	0
$191$	−12.3918	−0.896636	−0.448318	−	0.893874i	$-0.647977\pi$
$191$	−12.3918	−0.896636	−0.448318	+	0.893874i	$0.647977\pi$
$192$	1.42070	0.102530
$193$	1.52571	0.109823	0.0549115	−	0.998491i	$-0.482512\pi$
$193$	1.52571	0.109823	0.0549115	+	0.998491i	$0.482512\pi$
$194$	0.795457	0.0571105
$195$	−10.1953	−0.730102
$196$	9.67866	0.691333
$197$	13.7625	0.980538	0.490269	−	0.871571i	$-0.336899\pi$
$197$	13.7625	0.980538	0.490269	+	0.871571i	$0.336899\pi$
$198$	−0.0846704	−0.00601727
$199$	−14.2917	−1.01311	−0.506556	−	0.862207i	$-0.669082\pi$
$199$	−14.2917	−1.01311	−0.506556	+	0.862207i	$0.669082\pi$
$200$	2.16596	0.153157
$201$	5.89817	0.416025
$202$	10.6505	0.749366
$203$	−3.58589	−0.251680
$204$	2.24139	0.156929
$205$	1.35463	0.0946113
$206$	6.90249	0.480919
$207$	4.80188	0.333754
$208$	−10.6095	−0.735637
$209$	0	0
$210$	−1.21551	−0.0838779
$211$	1.75603	0.120890	0.0604452	−	0.998172i	$-0.480748\pi$
$211$	1.75603	0.120890	0.0604452	+	0.998172i	$0.480748\pi$
$212$	8.77080	0.602381
$213$	−4.83430	−0.331241
$214$	−1.48251	−0.101342
$215$	−9.00810	−0.614347
$216$	9.51024	0.647090
$217$	8.39743	0.570055
$218$	1.23326	0.0835269
$219$	−12.6498	−0.854797
$220$	0.323955	0.0218410
$221$	−3.72394	−0.250500
$222$	−1.25763	−0.0844064
$223$	−16.7418	−1.12111	−0.560557	−	0.828116i	$-0.689413\pi$
$223$	−16.7418	−1.12111	−0.560557	+	0.828116i	$0.689413\pi$
$224$	−5.85898	−0.391469
$225$	0.725033	0.0483355
$226$	9.13251	0.607486
$227$	16.3212	1.08328	0.541638	−	0.840612i	$-0.317804\pi$
$227$	16.3212	1.08328	0.541638	+	0.840612i	$0.317804\pi$
$228$	0	0
$229$	10.0335	0.663033	0.331517	−	0.943449i	$-0.392440\pi$
$229$	10.0335	0.663033	0.331517	+	0.943449i	$0.392440\pi$
$230$	3.93303	0.259336
$231$	−0.402516	−0.0264836
$232$	−7.32370	−0.480824
$233$	10.9230	0.715589	0.357794	−	0.933800i	$-0.383529\pi$
$233$	10.9230	0.715589	0.357794	+	0.933800i	$0.383529\pi$
$234$	2.27440	0.148682
$235$	−4.81938	−0.314381
$236$	18.0914	1.17765
$237$	23.6684	1.53743
$238$	−0.443977	−0.0287787
$239$	−11.8665	−0.767581	−0.383790	−	0.923420i	$-0.625382\pi$
$239$	−11.8665	−0.767581	−0.383790	+	0.923420i	$0.625382\pi$
$240$	3.87636	0.250218
$241$	3.22626	0.207821	0.103911	−	0.994587i	$-0.466864\pi$
$241$	3.22626	0.207821	0.103911	+	0.994587i	$0.466864\pi$
$242$	6.50935	0.418437
$243$	7.38147	0.473521
$244$	−19.3604	−1.23942
$245$	5.87530	0.375359
$246$	−1.55260	−0.0989901
$247$	0	0
$248$	17.1506	1.08906
$249$	7.78142	0.493127
$250$	0.593847	0.0375582
$251$	−1.75483	−0.110764	−0.0553820	−	0.998465i	$-0.517638\pi$
$251$	−1.75483	−0.110764	−0.0553820	+	0.998465i	$0.517638\pi$
$252$	−1.26666	−0.0797922
$253$	1.30243	0.0818828
$254$	4.51754	0.283456
$255$	1.36061	0.0852045
$256$	−5.34896	−0.334310
$257$	24.2332	1.51163	0.755814	−	0.654787i	$-0.227241\pi$
$257$	24.2332	1.51163	0.755814	+	0.654787i	$0.227241\pi$
$258$	10.3246	0.642780
$259$	−1.16367	−0.0723071
$260$	−8.70203	−0.539677
$261$	−2.45153	−0.151746
$262$	12.3877	0.765318
$263$	12.6925	0.782651	0.391325	−	0.920252i	$-0.372017\pi$
$263$	12.6925	0.782651	0.391325	+	0.920252i	$0.372017\pi$
$264$	−0.822084	−0.0505958
$265$	5.32420	0.327063
$266$	0	0
$267$	−33.8245	−2.07002
$268$	5.03428	0.307517
$269$	28.2663	1.72342	0.861712	−	0.507398i	$-0.169392\pi$
$269$	28.2663	1.72342	0.861712	+	0.507398i	$0.169392\pi$
$270$	2.60744	0.158684
$271$	8.18674	0.497309	0.248654	−	0.968592i	$-0.420012\pi$
$271$	8.18674	0.497309	0.248654	+	0.968592i	$0.420012\pi$
$272$	1.41588	0.0858505
$273$	10.8123	0.654391
$274$	−11.4114	−0.689387
$275$	0.196653	0.0118586
$276$	21.0573	1.26750
$277$	−25.0575	−1.50556	−0.752779	−	0.658273i	$-0.771287\pi$
$277$	−25.0575	−1.50556	−0.752779	+	0.658273i	$0.771287\pi$
$278$	11.6682	0.699810
$279$	5.74098	0.343703
$280$	−2.29704	−0.137275
$281$	−24.5418	−1.46404	−0.732019	−	0.681284i	$-0.761422\pi$
$281$	−24.5418	−1.46404	−0.732019	+	0.681284i	$0.761422\pi$
$282$	5.52370	0.328932
$283$	25.7298	1.52948	0.764739	−	0.644340i	$-0.222868\pi$
$283$	25.7298	1.52948	0.764739	+	0.644340i	$0.222868\pi$
$284$	−4.12623	−0.244847
$285$	0	0
$286$	0.616893	0.0364776
$287$	−1.43661	−0.0848002
$288$	−4.00554	−0.236029
$289$	−16.5030	−0.970766
$290$	−2.00795	−0.117911
$291$	2.58528	0.151552
$292$	−10.7970	−0.631849
$293$	−5.45848	−0.318888	−0.159444	−	0.987207i	$-0.550970\pi$
$293$	−5.45848	−0.318888	−0.159444	+	0.987207i	$0.550970\pi$
$294$	−6.73394	−0.392731
$295$	10.9822	0.639406
$296$	−2.37664	−0.138140
$297$	0.863455	0.0501028
$298$	5.13953	0.297725
$299$	−34.9856	−2.02327
$300$	3.17944	0.183565
$301$	9.55325	0.550640
$302$	2.94142	0.169260
$303$	34.6147	1.98856
$304$	0	0
$305$	−11.7524	−0.672943
$306$	−0.303529	−0.0173516
$307$	−3.70644	−0.211538	−0.105769	−	0.994391i	$-0.533730\pi$
$307$	−3.70644	−0.211538	−0.105769	+	0.994391i	$0.533730\pi$
$308$	−0.343560	−0.0195762
$309$	22.4335	1.27620
$310$	4.70221	0.267068
$311$	−1.73452	−0.0983555	−0.0491777	−	0.998790i	$-0.515660\pi$
$311$	−1.73452	−0.0983555	−0.0491777	+	0.998790i	$0.515660\pi$
$312$	22.0827	1.25019
$313$	3.96847	0.224311	0.112156	−	0.993691i	$-0.464224\pi$
$313$	3.96847	0.224311	0.112156	+	0.993691i	$0.464224\pi$
$314$	8.23361	0.464650
$315$	−0.768911	−0.0433232
$316$	20.2017	1.13644
$317$	−26.7159	−1.50052	−0.750258	−	0.661146i	$-0.770071\pi$
$317$	−26.7159	−1.50052	−0.750258	+	0.661146i	$0.770071\pi$
$318$	−6.10230	−0.342200
$319$	−0.664935	−0.0372292
$320$	0.736100	0.0411493
$321$	−4.81824	−0.268928
$322$	−4.17105	−0.232444
$323$	0	0
$324$	17.5433	0.974627
$325$	−5.28245	−0.293018
$326$	3.77148	0.208883
$327$	4.00817	0.221652
$328$	−2.93407	−0.162007
$329$	5.11104	0.281781
$330$	−0.225392	−0.0124074
$331$	−19.1145	−1.05063	−0.525314	−	0.850908i	$-0.676052\pi$
$331$	−19.1145	−1.05063	−0.525314	+	0.850908i	$0.676052\pi$
$332$	6.64169	0.364510
$333$	−0.795555	−0.0435962
$334$	−11.6988	−0.640132
$335$	3.05599	0.166967
$336$	−4.11095	−0.224271
$337$	−12.2171	−0.665510	−0.332755	−	0.943013i	$-0.607978\pi$
$337$	−12.2171	−0.665510	−0.332755	+	0.943013i	$0.607978\pi$
$338$	−8.85087	−0.481424
$339$	29.6812	1.61206
$340$	1.16132	0.0629815
$341$	1.55714	0.0843239
$342$	0	0
$343$	−13.6545	−0.737273
$344$	19.5112	1.05197
$345$	12.7826	0.688191
$346$	−5.29573	−0.284700
$347$	−3.96425	−0.212812	−0.106406	−	0.994323i	$-0.533934\pi$
$347$	−3.96425	−0.212812	−0.106406	+	0.994323i	$0.533934\pi$
$348$	−10.7505	−0.576288
$349$	−24.8326	−1.32926	−0.664628	−	0.747174i	$-0.731410\pi$
$349$	−24.8326	−1.32926	−0.664628	+	0.747174i	$0.731410\pi$
$350$	−0.629785	−0.0336634
$351$	−23.1940	−1.23800
$352$	−1.08643	−0.0579071
$353$	14.0216	0.746297	0.373148	−	0.927772i	$-0.378278\pi$
$353$	14.0216	0.746297	0.373148	+	0.927772i	$0.378278\pi$
$354$	−12.5871	−0.668999
$355$	−2.50478	−0.132940
$356$	−28.8703	−1.53012
$357$	−1.44295	−0.0763689
$358$	−1.05234	−0.0556180
$359$	−17.5130	−0.924301	−0.462151	−	0.886801i	$-0.652922\pi$
$359$	−17.5130	−0.924301	−0.462151	+	0.886801i	$0.652922\pi$
$360$	−1.57040	−0.0827671
$361$	0	0
$362$	−5.07671	−0.266826
$363$	21.1557	1.11039
$364$	9.22866	0.483713
$365$	−6.55421	−0.343063
$366$	13.4700	0.704088
$367$	18.2965	0.955068	0.477534	−	0.878613i	$-0.341531\pi$
$367$	18.2965	0.955068	0.477534	+	0.878613i	$0.341531\pi$
$368$	13.3019	0.693408
$369$	−0.982150	−0.0511287
$370$	−0.651609	−0.0338755
$371$	−5.64641	−0.293147
$372$	25.1755	1.30529
$373$	7.71339	0.399384	0.199692	−	0.979859i	$-0.436006\pi$
$373$	7.71339	0.399384	0.199692	+	0.979859i	$0.436006\pi$
$374$	−0.0823269	−0.00425702
$375$	1.93003	0.0996666
$376$	10.4386	0.538329
$377$	17.8614	0.919907
$378$	−2.76524	−0.142228
$379$	−12.7900	−0.656977	−0.328488	−	0.944508i	$-0.606539\pi$
$379$	−12.7900	−0.656977	−0.328488	+	0.944508i	$0.606539\pi$
$380$	0	0
$381$	14.6823	0.752195
$382$	7.35880	0.376509
$383$	16.1868	0.827106	0.413553	−	0.910480i	$-0.364288\pi$
$383$	16.1868	0.827106	0.413553	+	0.910480i	$0.364288\pi$
$384$	−22.1691	−1.13131
$385$	−0.208554	−0.0106289
$386$	−0.906038	−0.0461161
$387$	6.53117	0.331998
$388$	2.20662	0.112024
$389$	−2.77039	−0.140465	−0.0702323	−	0.997531i	$-0.522374\pi$
$389$	−2.77039	−0.140465	−0.0702323	+	0.997531i	$0.522374\pi$
$390$	6.05445	0.306579
$391$	4.66897	0.236120
$392$	−12.7257	−0.642744
$393$	40.2609	2.03089
$394$	−8.17282	−0.411741
$395$	12.2632	0.617029
$396$	−0.234878	−0.0118031
$397$	27.1420	1.36222	0.681109	−	0.732182i	$-0.261498\pi$
$397$	27.1420	1.36222	0.681109	+	0.732182i	$0.261498\pi$
$398$	8.48707	0.425418
$399$	0	0
$400$	2.00844	0.100422
$401$	−11.9676	−0.597632	−0.298816	−	0.954311i	$-0.596592\pi$
$401$	−11.9676	−0.597632	−0.298816	+	0.954311i	$0.596592\pi$
$402$	−3.50261	−0.174694
$403$	−41.8277	−2.08359
$404$	29.5448	1.46991
$405$	10.6494	0.529174
$406$	2.12947	0.105684
$407$	−0.215781	−0.0106958
$408$	−2.94703	−0.145900
$409$	−29.4536	−1.45639	−0.728193	−	0.685372i	$-0.759640\pi$
$409$	−29.4536	−1.45639	−0.728193	+	0.685372i	$0.759640\pi$
$410$	−0.804441	−0.0397285
$411$	−37.0877	−1.82940
$412$	19.1477	0.943339
$413$	−11.6468	−0.573101
$414$	−2.85158	−0.140147
$415$	4.03175	0.197911
$416$	29.1836	1.43084
$417$	37.9222	1.85706
$418$	0	0
$419$	19.9013	0.972243	0.486121	−	0.873891i	$-0.338411\pi$
$419$	19.9013	0.972243	0.486121	+	0.873891i	$0.338411\pi$
$420$	−3.37185	−0.164529
$421$	−16.1432	−0.786773	−0.393386	−	0.919373i	$-0.628697\pi$
$421$	−16.1432	−0.786773	−0.393386	+	0.919373i	$0.628697\pi$
$422$	−1.04281	−0.0507634
$423$	3.49421	0.169894
$424$	−11.5320	−0.560045
$425$	0.704965	0.0341958
$426$	2.87084	0.139092
$427$	12.4637	0.603160
$428$	−4.11252	−0.198786
$429$	2.00494	0.0967992
$430$	5.34943	0.257972
$431$	14.3829	0.692801	0.346401	−	0.938087i	$-0.387404\pi$
$431$	14.3829	0.692801	0.346401	+	0.938087i	$0.387404\pi$
$432$	8.81860	0.424285
$433$	−31.2784	−1.50315	−0.751573	−	0.659650i	$-0.770705\pi$
$433$	−31.2784	−1.50315	−0.751573	+	0.659650i	$0.770705\pi$
$434$	−4.98678	−0.239373
$435$	−6.52596	−0.312896
$436$	3.42110	0.163841
$437$	0	0
$438$	7.51207	0.358940
$439$	−3.11511	−0.148676	−0.0743382	−	0.997233i	$-0.523684\pi$
$439$	−3.11511	−0.148676	−0.0743382	+	0.997233i	$0.523684\pi$
$440$	−0.425943	−0.0203060
$441$	−4.25979	−0.202847
$442$	2.21145	0.105188
$443$	−20.7826	−0.987411	−0.493706	−	0.869629i	$-0.664358\pi$
$443$	−20.7826	−0.987411	−0.493706	+	0.869629i	$0.664358\pi$
$444$	−3.48869	−0.165566
$445$	−17.5253	−0.830780
$446$	9.94205	0.470770
$447$	16.7038	0.790061
$448$	−0.780648	−0.0368821
$449$	−15.7733	−0.744388	−0.372194	−	0.928155i	$-0.621394\pi$
$449$	−15.7733	−0.744388	−0.372194	+	0.928155i	$0.621394\pi$
$450$	−0.430558	−0.0202967
$451$	−0.266391	−0.0125439
$452$	25.3338	1.19160
$453$	9.55977	0.449157
$454$	−9.69228	−0.454881
$455$	5.60214	0.262632
$456$	0	0
$457$	−26.9899	−1.26254	−0.631268	−	0.775565i	$-0.717465\pi$
$457$	−26.9899	−1.26254	−0.631268	+	0.775565i	$0.717465\pi$
$458$	−5.95837	−0.278416
$459$	3.09534	0.144478
$460$	10.9103	0.508697
$461$	−7.28234	−0.339172	−0.169586	−	0.985515i	$-0.554243\pi$
$461$	−7.28234	−0.339172	−0.169586	+	0.985515i	$0.554243\pi$
$462$	0.239033	0.0111208
$463$	12.2146	0.567660	0.283830	−	0.958875i	$-0.408395\pi$
$463$	12.2146	0.567660	0.283830	+	0.958875i	$0.408395\pi$
$464$	−6.79107	−0.315268
$465$	15.2825	0.708707
$466$	−6.48658	−0.300485
$467$	−10.5737	−0.489293	−0.244646	−	0.969612i	$-0.578672\pi$
$467$	−10.5737	−0.489293	−0.244646	+	0.969612i	$0.578672\pi$
$468$	6.30926	0.291646
$469$	−3.24094	−0.149652
$470$	2.86197	0.132013
$471$	26.7597	1.23302
$472$	−23.7870	−1.09488
$473$	1.77147	0.0814521
$474$	−14.0554	−0.645586
$475$	0	0
$476$	−1.23160	−0.0564504
$477$	−3.86022	−0.176747
$478$	7.04689	0.322317
$479$	1.52234	0.0695576	0.0347788	−	0.999395i	$-0.488927\pi$
$479$	1.52234	0.0695576	0.0347788	+	0.999395i	$0.488927\pi$
$480$	−10.6627	−0.486685
$481$	5.79626	0.264287
$482$	−1.91590	−0.0872669
$483$	−13.5562	−0.616826
$484$	18.0571	0.820777
$485$	1.33950	0.0608236
$486$	−4.38346	−0.198838
$487$	28.9305	1.31096	0.655482	−	0.755211i	$-0.272465\pi$
$487$	28.9305	1.31096	0.655482	+	0.755211i	$0.272465\pi$
$488$	25.4554	1.15231
$489$	12.2575	0.554304
$490$	−3.48903	−0.157618
$491$	−14.7582	−0.666027	−0.333013	−	0.942922i	$-0.608065\pi$
$491$	−14.7582	−0.666027	−0.333013	+	0.942922i	$0.608065\pi$
$492$	−4.30695	−0.194172
$493$	−2.38367	−0.107355
$494$	0	0
$495$	−0.142580	−0.00640848
$496$	15.9033	0.714080
$497$	2.65636	0.119154
$498$	−4.62097	−0.207071
$499$	22.4539	1.00518	0.502588	−	0.864526i	$-0.332381\pi$
$499$	22.4539	1.00518	0.502588	+	0.864526i	$0.332381\pi$
$500$	1.64735	0.0736716
$501$	−38.0219	−1.69869
$502$	1.04210	0.0465112
$503$	−43.9991	−1.96182	−0.980912	−	0.194455i	$-0.937706\pi$
$503$	−43.9991	−1.96182	−0.980912	+	0.194455i	$0.937706\pi$
$504$	1.66543	0.0741843
$505$	17.9348	0.798086
$506$	−0.773441	−0.0343837
$507$	−28.7658	−1.27753
$508$	12.5318	0.556008
$509$	−13.9423	−0.617981	−0.308990	−	0.951065i	$-0.599991\pi$
$509$	−13.9423	−0.617981	−0.308990	+	0.951065i	$0.599991\pi$
$510$	−0.807992	−0.0357785
$511$	6.95086	0.307488
$512$	−19.7963	−0.874883
$513$	0	0
$514$	−14.3908	−0.634752
$515$	11.6234	0.512186
$516$	28.6407	1.26084
$517$	0.947743	0.0416817
$518$	0.691043	0.0303627
$519$	−17.2114	−0.755497
$520$	11.4416	0.501747
$521$	25.7694	1.12898	0.564489	−	0.825440i	$-0.309073\pi$
$521$	25.7694	1.12898	0.564489	+	0.825440i	$0.309073\pi$
$522$	1.45583	0.0637200
$523$	−20.9485	−0.916015	−0.458008	−	0.888948i	$-0.651437\pi$
$523$	−20.9485	−0.916015	−0.458008	+	0.888948i	$0.651437\pi$
$524$	34.3639	1.50120
$525$	−2.04684	−0.0893313
$526$	−7.53737	−0.328645
$527$	5.58208	0.243159
$528$	−0.762297	−0.0331747
$529$	20.8638	0.907124
$530$	−3.16176	−0.137338
$531$	−7.96243	−0.345540
$532$	0	0
$533$	7.15575	0.309950
$534$	20.0865	0.869230
$535$	−2.49645	−0.107931
$536$	−6.61917	−0.285905
$537$	−3.42017	−0.147591
$538$	−16.7858	−0.723688
$539$	−1.15539	−0.0497663
$540$	7.23311	0.311263
$541$	9.53234	0.409827	0.204914	−	0.978780i	$-0.434309\pi$
$541$	9.53234	0.409827	0.204914	+	0.978780i	$0.434309\pi$
$542$	−4.86167	−0.208826
$543$	−16.4996	−0.708065
$544$	−3.89467	−0.166983
$545$	2.07673	0.0889574
$546$	−6.42086	−0.274787
$547$	13.6538	0.583793	0.291896	−	0.956450i	$-0.405714\pi$
$547$	13.6538	0.583793	0.291896	+	0.956450i	$0.405714\pi$
$548$	−31.6555	−1.35226
$549$	8.52091	0.363664
$550$	−0.116781	−0.00497958
$551$	0	0
$552$	−27.6866	−1.17842
$553$	−13.0054	−0.553044
$554$	14.8803	0.632203
$555$	−2.11776	−0.0898941
$556$	32.3678	1.37270
$557$	8.56312	0.362831	0.181416	−	0.983407i	$-0.441932\pi$
$557$	8.56312	0.362831	0.181416	+	0.983407i	$0.441932\pi$
$558$	−3.40926	−0.144326
$559$	−47.5849	−2.01263
$560$	−2.12999	−0.0900085
$561$	−0.267567	−0.0112967
$562$	14.5740	0.614769
$563$	−14.2191	−0.599263	−0.299631	−	0.954055i	$-0.596864\pi$
$563$	−14.2191	−0.599263	−0.299631	+	0.954055i	$0.596864\pi$
$564$	15.3229	0.645210
$565$	15.3786	0.646981
$566$	−15.2795	−0.642247
$567$	−11.2939	−0.474300
$568$	5.42526	0.227639
$569$	30.2404	1.26774	0.633872	−	0.773438i	$-0.281465\pi$
$569$	30.2404	1.26774	0.633872	+	0.773438i	$0.281465\pi$
$570$	0	0
$571$	−32.2109	−1.34798	−0.673992	−	0.738739i	$-0.735422\pi$
$571$	−32.2109	−1.34798	−0.673992	+	0.738739i	$0.735422\pi$
$572$	1.71128	0.0715521
$573$	23.9165	0.999127
$574$	0.853124	0.0356087
$575$	6.62298	0.276197
$576$	−0.533697	−0.0222374
$577$	−44.7931	−1.86476	−0.932381	−	0.361478i	$-0.882272\pi$
$577$	−44.7931	−1.86476	−0.932381	+	0.361478i	$0.882272\pi$
$578$	9.80026	0.407637
$579$	−2.94467	−0.122377
$580$	−5.57011	−0.231286
$581$	−4.27575	−0.177388
$582$	−1.53526	−0.0636386
$583$	−1.04702	−0.0433630
$584$	14.1962	0.587442
$585$	3.82995	0.158349
$586$	3.24150	0.133905
$587$	−8.76880	−0.361927	−0.180964	−	0.983490i	$-0.557922\pi$
$587$	−8.76880	−0.361927	−0.180964	+	0.983490i	$0.557922\pi$
$588$	−18.6801	−0.770356
$589$	0	0
$590$	−6.52172	−0.268495
$591$	−26.5621	−1.09262
$592$	−2.20380	−0.0905756
$593$	10.4206	0.427924	0.213962	−	0.976842i	$-0.431363\pi$
$593$	10.4206	0.427924	0.213962	+	0.976842i	$0.431363\pi$
$594$	−0.512760	−0.0210388
$595$	−0.747628	−0.0306498
$596$	14.2572	0.583997
$597$	27.5835	1.12892
$598$	20.7761	0.849596
$599$	18.9458	0.774104	0.387052	−	0.922058i	$-0.373493\pi$
$599$	18.9458	0.774104	0.387052	+	0.922058i	$0.373493\pi$
$600$	−4.18038	−0.170664
$601$	−4.83652	−0.197286	−0.0986429	−	0.995123i	$-0.531450\pi$
$601$	−4.83652	−0.197286	−0.0986429	+	0.995123i	$0.531450\pi$
$602$	−5.67317	−0.231221
$603$	−2.21570	−0.0902301
$604$	8.15957	0.332008
$605$	10.9613	0.445641
$606$	−20.5558	−0.835023
$607$	−19.4767	−0.790537	−0.395268	−	0.918566i	$-0.629348\pi$
$607$	−19.4767	−0.790537	−0.395268	+	0.918566i	$0.629348\pi$
$608$	0	0
$609$	6.92090	0.280449
$610$	6.97915	0.282578
$611$	−25.4581	−1.02993
$612$	−0.841997	−0.0340357
$613$	−37.1623	−1.50097	−0.750485	−	0.660887i	$-0.770180\pi$
$613$	−37.1623	−1.50097	−0.750485	+	0.660887i	$0.770180\pi$
$614$	2.20106	0.0888274
$615$	−2.61448	−0.105426
$616$	0.451720	0.0182003
$617$	−14.1365	−0.569116	−0.284558	−	0.958659i	$-0.591847\pi$
$617$	−14.1365	−0.569116	−0.284558	+	0.958659i	$0.591847\pi$
$618$	−13.3220	−0.535891
$619$	31.9110	1.28261	0.641306	−	0.767286i	$-0.278393\pi$
$619$	31.9110	1.28261	0.641306	+	0.767286i	$0.278393\pi$
$620$	13.0441	0.523862
$621$	29.0799	1.16694
$622$	1.03004	0.0413007
$623$	18.5859	0.744629
$624$	20.4767	0.819724
$625$	1.00000	0.0400000
$626$	−2.35666	−0.0941912
$627$	0	0
$628$	22.8403	0.911426
$629$	−0.773535	−0.0308429
$630$	0.456615	0.0181920
$631$	4.30611	0.171424	0.0857118	−	0.996320i	$-0.472684\pi$
$631$	4.30611	0.171424	0.0857118	+	0.996320i	$0.472684\pi$
$632$	−26.5617	−1.05657
$633$	−3.38921	−0.134709
$634$	15.8652	0.630086
$635$	7.60725	0.301885
$636$	−16.9279	−0.671237
$637$	31.0360	1.22969
$638$	0.394869	0.0156330
$639$	1.81605	0.0718417
$640$	−11.4864	−0.454040
$641$	32.0886	1.26742	0.633711	−	0.773570i	$-0.281531\pi$
$641$	32.0886	1.26742	0.633711	+	0.773570i	$0.281531\pi$
$642$	2.86129	0.112926
$643$	−19.2873	−0.760618	−0.380309	−	0.924859i	$-0.624182\pi$
$643$	−19.2873	−0.760618	−0.380309	+	0.924859i	$0.624182\pi$
$644$	−11.5706	−0.455946
$645$	17.3859	0.684571
$646$	0	0
$647$	7.19470	0.282853	0.141426	−	0.989949i	$-0.454831\pi$
$647$	7.19470	0.282853	0.141426	+	0.989949i	$0.454831\pi$
$648$	−23.0663	−0.906129
$649$	−2.15967	−0.0847745
$650$	3.13697	0.123042
$651$	−16.2073	−0.635215
$652$	10.4622	0.409731
$653$	−44.8697	−1.75589	−0.877944	−	0.478763i	$-0.841085\pi$
$653$	−44.8697	−1.75589	−0.877944	+	0.478763i	$0.841085\pi$
$654$	−2.38023	−0.0930746
$655$	20.8602	0.815075
$656$	−2.72069	−0.106225
$657$	4.75202	0.185394
$658$	−3.03517	−0.118323
$659$	−4.96593	−0.193445	−0.0967226	−	0.995311i	$-0.530836\pi$
$659$	−4.96593	−0.193445	−0.0967226	+	0.995311i	$0.530836\pi$
$660$	−0.625244	−0.0243376
$661$	−1.68450	−0.0655195	−0.0327598	−	0.999463i	$-0.510430\pi$
$661$	−1.68450	−0.0655195	−0.0327598	+	0.999463i	$0.510430\pi$
$662$	11.3511	0.441172
$663$	7.18734	0.279133
$664$	−8.73263	−0.338892
$665$	0	0
$666$	0.472438	0.0183066
$667$	−22.3940	−0.867101
$668$	−32.4529	−1.25564
$669$	32.3122	1.24926
$670$	−1.81479	−0.0701115
$671$	2.31115	0.0892209
$672$	11.3080	0.436217
$673$	−0.429596	−0.0165597	−0.00827986	−	0.999966i	$-0.502636\pi$
$673$	−0.429596	−0.0165597	−0.00827986	+	0.999966i	$0.502636\pi$
$674$	7.25511	0.279456
$675$	4.39076	0.169001
$676$	−24.5525	−0.944329
$677$	13.9059	0.534447	0.267223	−	0.963635i	$-0.413894\pi$
$677$	13.9059	0.534447	0.267223	+	0.963635i	$0.413894\pi$
$678$	−17.6261	−0.676925
$679$	−1.42056	−0.0545163
$680$	−1.52693	−0.0585551
$681$	−31.5005	−1.20710
$682$	−0.924703	−0.0354087
$683$	19.7531	0.755831	0.377916	−	0.925840i	$-0.376641\pi$
$683$	19.7531	0.755831	0.377916	+	0.925840i	$0.376641\pi$
$684$	0	0
$685$	−19.2161	−0.734208
$686$	8.10867	0.309591
$687$	−19.3650	−0.738822
$688$	18.0923	0.689761
$689$	28.1248	1.07147
$690$	−7.59089	−0.288980
$691$	12.1130	0.460800	0.230400	−	0.973096i	$-0.425997\pi$
$691$	12.1130	0.460800	0.230400	+	0.973096i	$0.425997\pi$
$692$	−14.6905	−0.558449
$693$	0.151208	0.00574393
$694$	2.35415	0.0893625
$695$	19.6484	0.745308
$696$	14.1350	0.535785
$697$	−0.954965	−0.0361719
$698$	14.7467	0.558172
$699$	−21.0817	−0.797385
$700$	−1.74704	−0.0660319
$701$	−20.3516	−0.768670	−0.384335	−	0.923194i	$-0.625569\pi$
$701$	−20.3516	−0.768670	−0.384335	+	0.923194i	$0.625569\pi$
$702$	13.7737	0.519854
$703$	0	0
$704$	−0.144756	−0.00545570
$705$	9.30156	0.350317
$706$	−8.32670	−0.313380
$707$	−19.0201	−0.715326
$708$	−34.9171	−1.31226
$709$	39.8887	1.49805	0.749027	−	0.662540i	$-0.230522\pi$
$709$	39.8887	1.49805	0.749027	+	0.662540i	$0.230522\pi$
$710$	1.48745	0.0558231
$711$	−8.89123	−0.333447
$712$	37.9592	1.42258
$713$	52.4423	1.96398
$714$	0.856890	0.0320683
$715$	1.03881	0.0388492
$716$	−2.91923	−0.109097
$717$	22.9028	0.855320
$718$	10.4000	0.388126
$719$	24.1535	0.900772	0.450386	−	0.892834i	$-0.351286\pi$
$719$	24.1535	0.900772	0.450386	+	0.892834i	$0.351286\pi$
$720$	−1.45619	−0.0542689
$721$	−12.3268	−0.459073
$722$	0	0
$723$	−6.22679	−0.231577
$724$	−14.0829	−0.523388
$725$	−3.38126	−0.125577
$726$	−12.5633	−0.466266
$727$	−33.1287	−1.22868	−0.614338	−	0.789043i	$-0.710577\pi$
$727$	−33.1287	−1.22868	−0.614338	+	0.789043i	$0.710577\pi$
$728$	−12.1340	−0.449717
$729$	17.7018	0.655622
$730$	3.89219	0.144057
$731$	6.35040	0.234878
$732$	37.3661	1.38109
$733$	−20.2774	−0.748962	−0.374481	−	0.927235i	$-0.622179\pi$
$733$	−20.2774	−0.748962	−0.374481	+	0.927235i	$0.622179\pi$
$734$	−10.8653	−0.401045
$735$	−11.3395	−0.418265
$736$	−36.5895	−1.34871
$737$	−0.600969	−0.0221370
$738$	0.583246	0.0214696
$739$	−25.6142	−0.942232	−0.471116	−	0.882071i	$-0.656149\pi$
$739$	−25.6142	−0.942232	−0.471116	+	0.882071i	$0.656149\pi$
$740$	−1.80758	−0.0664480
$741$	0	0
$742$	3.35310	0.123096
$743$	23.8850	0.876255	0.438127	−	0.898913i	$-0.355642\pi$
$743$	23.8850	0.876255	0.438127	+	0.898913i	$0.355642\pi$
$744$	−33.1013	−1.21355
$745$	8.65464	0.317082
$746$	−4.58057	−0.167707
$747$	−2.92315	−0.106953
$748$	−0.228377	−0.00835029
$749$	2.64753	0.0967387
$750$	−1.14614	−0.0418513
$751$	−49.1093	−1.79203	−0.896013	−	0.444029i	$-0.853549\pi$
$751$	−49.1093	−1.79203	−0.896013	+	0.444029i	$0.853549\pi$
$752$	9.67944	0.352973
$753$	3.38688	0.123425
$754$	−10.6069	−0.386281
$755$	4.95316	0.180264
$756$	−7.67085	−0.278986
$757$	−21.3259	−0.775104	−0.387552	−	0.921848i	$-0.626679\pi$
$757$	−21.3259	−0.775104	−0.387552	+	0.921848i	$0.626679\pi$
$758$	7.59528	0.275873
$759$	−2.51373	−0.0912425
$760$	0	0
$761$	11.4807	0.416176	0.208088	−	0.978110i	$-0.433276\pi$
$761$	11.4807	0.416176	0.208088	+	0.978110i	$0.433276\pi$
$762$	−8.71901	−0.315856
$763$	−2.20241	−0.0797327
$764$	20.4135	0.738535
$765$	−0.511123	−0.0184797
$766$	−9.61247	−0.347313
$767$	58.0127	2.09472
$768$	10.3237	0.372523
$769$	0.115723	0.00417309	0.00208655	−	0.999998i	$-0.499336\pi$
$769$	0.115723	0.00417309	0.00208655	+	0.999998i	$0.499336\pi$
$770$	0.123849	0.00446320
$771$	−46.7710	−1.68442
$772$	−2.51337	−0.0904583
$773$	34.3645	1.23600	0.618002	−	0.786177i	$-0.287942\pi$
$773$	34.3645	1.23600	0.618002	+	0.786177i	$0.287942\pi$
$774$	−3.87851	−0.139410
$775$	7.91823	0.284431
$776$	−2.90131	−0.104151
$777$	2.24593	0.0805722
$778$	1.64519	0.0589829
$779$	0	0
$780$	16.7952	0.601365
$781$	0.492571	0.0176256
$782$	−2.77265	−0.0991498
$783$	−14.8463	−0.530565
$784$	−11.8002	−0.421436
$785$	13.8649	0.494859
$786$	−23.9088	−0.852798
$787$	5.70731	0.203444	0.101722	−	0.994813i	$-0.467565\pi$
$787$	5.70731	0.203444	0.101722	+	0.994813i	$0.467565\pi$
$788$	−22.6716	−0.807643
$789$	−24.4969	−0.872112
$790$	−7.28246	−0.259098
$791$	−16.3093	−0.579890
$792$	0.308822	0.0109735
$793$	−62.0817	−2.20459
$794$	−16.1182	−0.572013
$795$	−10.2759	−0.364448
$796$	23.5434	0.834473
$797$	−39.6776	−1.40545	−0.702726	−	0.711461i	$-0.748034\pi$
$797$	−39.6776	−1.40545	−0.702726	+	0.711461i	$0.748034\pi$
$798$	0	0
$799$	3.39749	0.120195
$800$	−5.52463	−0.195325
$801$	12.7064	0.448960
$802$	7.10690	0.250953
$803$	1.28890	0.0454844
$804$	−9.71633	−0.342669
$805$	−7.02379	−0.247556
$806$	24.8392	0.874924
$807$	−54.5549	−1.92042
$808$	−38.8460	−1.36660
$809$	−23.7933	−0.836528	−0.418264	−	0.908325i	$-0.637361\pi$
$809$	−23.7933	−0.836528	−0.418264	+	0.908325i	$0.637361\pi$
$810$	−6.32412	−0.222207
$811$	−15.5784	−0.547032	−0.273516	−	0.961868i	$-0.588187\pi$
$811$	−15.5784	−0.547032	−0.273516	+	0.961868i	$0.588187\pi$
$812$	5.90721	0.207302
$813$	−15.8007	−0.554154
$814$	0.128141	0.00449132
$815$	6.35093	0.222464
$816$	−2.73270	−0.0956637
$817$	0	0
$818$	17.4909	0.611555
$819$	−4.06173	−0.141928
$820$	−2.23154	−0.0779288
$821$	49.3819	1.72344	0.861720	−	0.507385i	$-0.169388\pi$
$821$	49.3819	1.72344	0.861720	+	0.507385i	$0.169388\pi$
$822$	22.0244	0.768188
$823$	7.56905	0.263840	0.131920	−	0.991260i	$-0.457886\pi$
$823$	7.56905	0.263840	0.131920	+	0.991260i	$0.457886\pi$
$824$	−25.1758	−0.877039
$825$	−0.379546	−0.0132141
$826$	6.91640	0.240652
$827$	−32.0613	−1.11488	−0.557440	−	0.830217i	$-0.688216\pi$
$827$	−32.0613	−1.11488	−0.557440	+	0.830217i	$0.688216\pi$
$828$	−7.91036	−0.274904
$829$	13.0362	0.452766	0.226383	−	0.974038i	$-0.427310\pi$
$829$	13.0362	0.452766	0.226383	+	0.974038i	$0.427310\pi$
$830$	−2.39424	−0.0831053
$831$	48.3618	1.67765
$832$	3.88841	0.134807
$833$	−4.14188	−0.143508
$834$	−22.5199	−0.779802
$835$	−19.7001	−0.681750
$836$	0	0
$837$	34.7671	1.20173
$838$	−11.8183	−0.408257
$839$	−9.00794	−0.310989	−0.155494	−	0.987837i	$-0.549697\pi$
$839$	−9.00794	−0.310989	−0.155494	+	0.987837i	$0.549697\pi$
$840$	4.43337	0.152966
$841$	−17.5671	−0.605760
$842$	9.58660	0.330376
$843$	47.3664	1.63139
$844$	−2.89280	−0.0995742
$845$	−14.9043	−0.512723
$846$	−2.07502	−0.0713408
$847$	−11.6247	−0.399429
$848$	−10.6933	−0.367211
$849$	−49.6594	−1.70431
$850$	−0.418641	−0.0143593
$851$	−7.26718	−0.249116
$852$	7.96377	0.272834
$853$	19.5224	0.668434	0.334217	−	0.942496i	$-0.391528\pi$
$853$	19.5224	0.668434	0.334217	+	0.942496i	$0.391528\pi$
$854$	−7.40152	−0.253275
$855$	0	0
$856$	5.40722	0.184815
$857$	−20.6184	−0.704311	−0.352155	−	0.935942i	$-0.614551\pi$
$857$	−20.6184	−0.704311	−0.352155	+	0.935942i	$0.614551\pi$
$858$	−1.19062	−0.0406472
$859$	16.9711	0.579046	0.289523	−	0.957171i	$-0.406503\pi$
$859$	16.9711	0.579046	0.289523	+	0.957171i	$0.406503\pi$
$860$	14.8395	0.506021
$861$	2.77270	0.0944934
$862$	−8.54125	−0.290916
$863$	−7.17739	−0.244321	−0.122161	−	0.992510i	$-0.538982\pi$
$863$	−7.17739	−0.244321	−0.122161	+	0.992510i	$0.538982\pi$
$864$	−24.2574	−0.825252
$865$	−8.91767	−0.303210
$866$	18.5746	0.631191
$867$	31.8514	1.08173
$868$	−13.8335	−0.469539
$869$	−2.41159	−0.0818077
$870$	3.87542	0.131389
$871$	16.1431	0.546989
$872$	−4.49813	−0.152326
$873$	−0.971182	−0.0328695
$874$	0	0
$875$	−1.06052	−0.0358521
$876$	20.8387	0.704074
$877$	−1.52300	−0.0514280	−0.0257140	−	0.999669i	$-0.508186\pi$
$877$	−1.52300	−0.0514280	−0.0257140	+	0.999669i	$0.508186\pi$
$878$	1.84990	0.0624311
$879$	10.5350	0.355338
$880$	−0.394966	−0.0133143
$881$	51.5139	1.73555	0.867774	−	0.496960i	$-0.165550\pi$
$881$	51.5139	1.73555	0.867774	+	0.496960i	$0.165550\pi$
$882$	2.52966	0.0851781
$883$	3.44935	0.116080	0.0580400	−	0.998314i	$-0.481515\pi$
$883$	3.44935	0.116080	0.0580400	+	0.998314i	$0.481515\pi$
$884$	6.13463	0.206330
$885$	−21.1959	−0.712494
$886$	12.3417	0.414627
$887$	−36.9520	−1.24073	−0.620364	−	0.784314i	$-0.713015\pi$
$887$	−36.9520	−1.24073	−0.620364	+	0.784314i	$0.713015\pi$
$888$	4.58700	0.153930
$889$	−8.06763	−0.270580
$890$	10.4073	0.348855
$891$	−2.09424	−0.0701596
$892$	27.5795	0.923431
$893$	0	0
$894$	−9.91947	−0.331757
$895$	−1.77208	−0.0592340
$896$	12.1815	0.406957
$897$	67.5233	2.25454
$898$	9.36692	0.312578
$899$	−26.7736	−0.892951
$900$	−1.19438	−0.0398127
$901$	−3.75337	−0.125043
$902$	0.158195	0.00526733
$903$	−18.4381	−0.613582
$904$	−33.3094	−1.10786
$905$	−8.54886	−0.284174
$906$	−5.67704	−0.188607
$907$	−23.0663	−0.765905	−0.382952	−	0.923768i	$-0.625093\pi$
$907$	−23.0663	−0.765905	−0.382952	+	0.923768i	$0.625093\pi$
$908$	−26.8867	−0.892265
$909$	−13.0033	−0.431292
$910$	−3.32681	−0.110283
$911$	22.8760	0.757915	0.378957	−	0.925414i	$-0.376283\pi$
$911$	22.8760	0.757915	0.378957	+	0.925414i	$0.376283\pi$
$912$	0	0
$913$	−0.792855	−0.0262397
$914$	16.0279	0.530155
$915$	22.6826	0.749865
$916$	−16.5287	−0.546123
$917$	−22.1226	−0.730553
$918$	−1.83815	−0.0606681
$919$	−12.9324	−0.426601	−0.213301	−	0.976987i	$-0.568421\pi$
$919$	−12.9324	−0.426601	−0.213301	+	0.976987i	$0.568421\pi$
$920$	−14.3451	−0.472945
$921$	7.15355	0.235718
$922$	4.32459	0.142423
$923$	−13.2314	−0.435516
$924$	0.663083	0.0218138
$925$	−1.09727	−0.0360779
$926$	−7.25359	−0.238368
$927$	−8.42731	−0.276789
$928$	18.6802	0.613209
$929$	−12.3880	−0.406437	−0.203219	−	0.979133i	$-0.565140\pi$
$929$	−12.3880	−0.406437	−0.203219	+	0.979133i	$0.565140\pi$
$930$	−9.07544	−0.297595
$931$	0	0
$932$	−17.9939	−0.589411
$933$	3.34768	0.109598
$934$	6.27916	0.205460
$935$	−0.138633	−0.00453379
$936$	−8.29554	−0.271148
$937$	−10.6696	−0.348561	−0.174280	−	0.984696i	$-0.555760\pi$
$937$	−10.6696	−0.348561	−0.174280	+	0.984696i	$0.555760\pi$
$938$	1.92462	0.0628410
$939$	−7.65929	−0.249951
$940$	7.93918	0.258948
$941$	12.7892	0.416917	0.208459	−	0.978031i	$-0.433155\pi$
$941$	12.7892	0.416917	0.208459	+	0.978031i	$0.433155\pi$
$942$	−15.8912	−0.517762
$943$	−8.97167	−0.292158
$944$	−22.0570	−0.717895
$945$	−4.65649	−0.151476
$946$	−1.05198	−0.0342028
$947$	14.1158	0.458703	0.229351	−	0.973344i	$-0.426339\pi$
$947$	14.1158	0.458703	0.229351	+	0.973344i	$0.426339\pi$
$948$	−38.9901	−1.26634
$949$	−34.6223	−1.12389
$950$	0	0
$951$	51.5626	1.67203
$952$	1.61934	0.0524830
$953$	−43.7008	−1.41561	−0.707803	−	0.706410i	$-0.750314\pi$
$953$	−43.7008	−1.41561	−0.707803	+	0.706410i	$0.750314\pi$
$954$	2.29238	0.0742185
$955$	12.3918	0.400988
$956$	19.5483	0.632236
$957$	1.28335	0.0414847
$958$	−0.904038	−0.0292081
$959$	20.3790	0.658072
$960$	−1.42070	−0.0458529
$961$	31.6984	1.02253
$962$	−3.44209	−0.110977
$963$	1.81001	0.0583268
$964$	−5.31476	−0.171177
$965$	−1.52571	−0.0491144
$966$	8.05028	0.259013
$967$	2.29371	0.0737606	0.0368803	−	0.999320i	$-0.488258\pi$
$967$	2.29371	0.0737606	0.0368803	+	0.999320i	$0.488258\pi$
$968$	−23.7418	−0.763092
$969$	0	0
$970$	−0.795457	−0.0255406
$971$	−29.5744	−0.949086	−0.474543	−	0.880232i	$-0.657387\pi$
$971$	−29.5744	−0.949086	−0.474543	+	0.880232i	$0.657387\pi$
$972$	−12.1598	−0.390027
$973$	−20.8375	−0.668020
$974$	−17.1803	−0.550491
$975$	10.1953	0.326511
$976$	23.6041	0.755549
$977$	16.3897	0.524354	0.262177	−	0.965020i	$-0.415560\pi$
$977$	16.3897	0.524354	0.262177	+	0.965020i	$0.415560\pi$
$978$	−7.27909	−0.232760
$979$	3.44640	0.110147
$980$	−9.67866	−0.309173
$981$	−1.50570	−0.0480733
$982$	8.76409	0.279673
$983$	51.3730	1.63854	0.819272	−	0.573404i	$-0.194378\pi$
$983$	51.3730	1.63854	0.819272	+	0.573404i	$0.194378\pi$
$984$	5.66286	0.180526
$985$	−13.7625	−0.438510
$986$	1.41554	0.0450799
$987$	−9.86448	−0.313990
$988$	0	0
$989$	59.6605	1.89709
$990$	0.0846704	0.00269100
$991$	−48.8793	−1.55270	−0.776351	−	0.630301i	$-0.782932\pi$
$991$	−48.8793	−1.55270	−0.776351	+	0.630301i	$0.782932\pi$
$992$	−43.7453	−1.38892
$993$	36.8916	1.17072
$994$	−1.57747	−0.0500343
$995$	14.2917	0.453077
$996$	−12.8187	−0.406176
$997$	19.2225	0.608783	0.304392	−	0.952547i	$-0.401547\pi$
$997$	19.2225	0.608783	0.304392	+	0.952547i	$0.401547\pi$
$998$	−13.3342	−0.422086
$999$	−4.81784	−0.152430

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.t.1.5		9
5.4	even	2		9025.2.a.ce.1.5		9
19.4	even	9		95.2.k.b.16.2	yes	18
19.5	even	9		95.2.k.b.6.2	✓	18
19.18	odd	2		1805.2.a.u.1.5		9
57.5	odd	18		855.2.bs.b.766.2		18
57.23	odd	18		855.2.bs.b.586.2		18
95.4	even	18		475.2.l.b.301.2		18
95.23	odd	36		475.2.u.c.149.3		36
95.24	even	18		475.2.l.b.101.2		18
95.42	odd	36		475.2.u.c.149.4		36
95.43	odd	36		475.2.u.c.424.4		36
95.62	odd	36		475.2.u.c.424.3		36
95.94	odd	2		9025.2.a.cd.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.6.2	✓	18	19.5	even	9
95.2.k.b.16.2	yes	18	19.4	even	9
475.2.l.b.101.2		18	95.24	even	18
475.2.l.b.301.2		18	95.4	even	18
475.2.u.c.149.3		36	95.23	odd	36
475.2.u.c.149.4		36	95.42	odd	36
475.2.u.c.424.3		36	95.62	odd	36
475.2.u.c.424.4		36	95.43	odd	36
855.2.bs.b.586.2		18	57.23	odd	18
855.2.bs.b.766.2		18	57.5	odd	18
1805.2.a.t.1.5		9	1.1	even	1	trivial
1805.2.a.u.1.5		9	19.18	odd	2
9025.2.a.cd.1.5		9	95.94	odd	2
9025.2.a.ce.1.5		9	5.4	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q-0.593847 q^{2} -1.93003 q^{3} -1.64735 q^{4} -1.00000 q^{5} +1.14614 q^{6} +1.06052 q^{7} +2.16596 q^{8} +0.725033 q^{9} +O(q^{10})\)	\(q-0.593847 q^{2} -1.93003 q^{3} -1.64735 q^{4} -1.00000 q^{5} +1.14614 q^{6} +1.06052 q^{7} +2.16596 q^{8} +0.725033 q^{9} +0.593847 q^{10} +0.196653 q^{11} +3.17944 q^{12} -5.28245 q^{13} -0.629785 q^{14} +1.93003 q^{15} +2.00844 q^{16} +0.704965 q^{17} -0.430558 q^{18} +1.64735 q^{20} -2.04684 q^{21} -0.116781 q^{22} +6.62298 q^{23} -4.18038 q^{24} +1.00000 q^{25} +3.13697 q^{26} +4.39076 q^{27} -1.74704 q^{28} -3.38126 q^{29} -1.14614 q^{30} +7.91823 q^{31} -5.52463 q^{32} -0.379546 q^{33} -0.418641 q^{34} -1.06052 q^{35} -1.19438 q^{36} -1.09727 q^{37} +10.1953 q^{39} -2.16596 q^{40} -1.35463 q^{41} +1.21551 q^{42} +9.00810 q^{43} -0.323955 q^{44} -0.725033 q^{45} -3.93303 q^{46} +4.81938 q^{47} -3.87636 q^{48} -5.87530 q^{49} -0.593847 q^{50} -1.36061 q^{51} +8.70203 q^{52} -5.32420 q^{53} -2.60744 q^{54} -0.196653 q^{55} +2.29704 q^{56} +2.00795 q^{58} -10.9822 q^{59} -3.17944 q^{60} +11.7524 q^{61} -4.70221 q^{62} +0.768911 q^{63} -0.736100 q^{64} +5.28245 q^{65} +0.225392 q^{66} -3.05599 q^{67} -1.16132 q^{68} -12.7826 q^{69} +0.629785 q^{70} +2.50478 q^{71} +1.57040 q^{72} +6.55421 q^{73} +0.651609 q^{74} -1.93003 q^{75} +0.208554 q^{77} -6.05445 q^{78} -12.2632 q^{79} -2.00844 q^{80} -10.6494 q^{81} +0.804441 q^{82} -4.03175 q^{83} +3.37185 q^{84} -0.704965 q^{85} -5.34943 q^{86} +6.52596 q^{87} +0.425943 q^{88} +17.5253 q^{89} +0.430558 q^{90} -5.60214 q^{91} -10.9103 q^{92} -15.2825 q^{93} -2.86197 q^{94} +10.6627 q^{96} -1.33950 q^{97} +3.48903 q^{98} +0.142580 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} + 12 q^{8} + 6 q^{9}+O(q^{10}) \) 9 * q - 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 + 12 * q^8 + 6 * q^9	\( 9 q - 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} + 12 q^{8} + 6 q^{9} - 6 q^{12} + 3 q^{13} - 12 q^{14} + 3 q^{15} - 12 q^{16} - 9 q^{17} - 6 q^{18} - 6 q^{20} - 12 q^{21} - 12 q^{22} + 15 q^{24} + 9 q^{25} + 21 q^{26} - 6 q^{27} - 15 q^{28} - 15 q^{29} + 12 q^{30} - 30 q^{31} + 9 q^{32} - 9 q^{33} - 6 q^{36} - 30 q^{37} + 6 q^{39} - 12 q^{40} - 18 q^{41} + 36 q^{42} - 6 q^{43} - 24 q^{44} - 6 q^{45} - 21 q^{46} + 21 q^{47} - 15 q^{48} + 3 q^{49} - 18 q^{51} + 3 q^{52} + 9 q^{53} - 9 q^{54} - 36 q^{56} + 18 q^{58} - 27 q^{59} + 6 q^{60} + 12 q^{61} - 6 q^{62} - 15 q^{63} + 24 q^{64} - 3 q^{65} + 3 q^{66} - 36 q^{67} + 3 q^{68} - 27 q^{69} + 12 q^{70} + 6 q^{71} - 12 q^{72} - 9 q^{73} - 9 q^{74} - 3 q^{75} + 12 q^{77} - 54 q^{78} - 45 q^{79} + 12 q^{80} - 15 q^{81} - 48 q^{82} + 12 q^{84} + 9 q^{85} + 9 q^{86} + 45 q^{87} - 39 q^{88} + 9 q^{89} + 6 q^{90} - 51 q^{91} - 54 q^{92} + 9 q^{93} - 33 q^{94} - 9 q^{96} - 45 q^{97} - 33 q^{98} + 12 q^{99}+O(q^{100}) \) 9 * q - 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 + 12 * q^8 + 6 * q^9 - 6 * q^12 + 3 * q^13 - 12 * q^14 + 3 * q^15 - 12 * q^16 - 9 * q^17 - 6 * q^18 - 6 * q^20 - 12 * q^21 - 12 * q^22 + 15 * q^24 + 9 * q^25 + 21 * q^26 - 6 * q^27 - 15 * q^28 - 15 * q^29 + 12 * q^30 - 30 * q^31 + 9 * q^32 - 9 * q^33 - 6 * q^36 - 30 * q^37 + 6 * q^39 - 12 * q^40 - 18 * q^41 + 36 * q^42 - 6 * q^43 - 24 * q^44 - 6 * q^45 - 21 * q^46 + 21 * q^47 - 15 * q^48 + 3 * q^49 - 18 * q^51 + 3 * q^52 + 9 * q^53 - 9 * q^54 - 36 * q^56 + 18 * q^58 - 27 * q^59 + 6 * q^60 + 12 * q^61 - 6 * q^62 - 15 * q^63 + 24 * q^64 - 3 * q^65 + 3 * q^66 - 36 * q^67 + 3 * q^68 - 27 * q^69 + 12 * q^70 + 6 * q^71 - 12 * q^72 - 9 * q^73 - 9 * q^74 - 3 * q^75 + 12 * q^77 - 54 * q^78 - 45 * q^79 + 12 * q^80 - 15 * q^81 - 48 * q^82 + 12 * q^84 + 9 * q^85 + 9 * q^86 + 45 * q^87 - 39 * q^88 + 9 * q^89 + 6 * q^90 - 51 * q^91 - 54 * q^92 + 9 * q^93 - 33 * q^94 - 9 * q^96 - 45 * q^97 - 33 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more