LMFDB - Embedded newform 1911.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1911,2,Mod(1,1911)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1911, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1911.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1911 = 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1911.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:	$15.2594118263$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.53209$ of defining polynomial
Character	$\chi$	$=$	1911.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.53209 q^{2} -1.00000 q^{3} +0.347296 q^{4} -0.532089 q^{5} +1.53209 q^{6} +2.53209 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.53209 q^{2} -1.00000 q^{3} +0.347296 q^{4} -0.532089 q^{5} +1.53209 q^{6} +2.53209 q^{8} +1.00000 q^{9} +0.815207 q^{10} -2.87939 q^{11} -0.347296 q^{12} +1.00000 q^{13} +0.532089 q^{15} -4.57398 q^{16} +3.34730 q^{17} -1.53209 q^{18} -2.06418 q^{19} -0.184793 q^{20} +4.41147 q^{22} +7.86484 q^{23} -2.53209 q^{24} -4.71688 q^{25} -1.53209 q^{26} -1.00000 q^{27} -7.04963 q^{29} -0.815207 q^{30} +6.22668 q^{31} +1.94356 q^{32} +2.87939 q^{33} -5.12836 q^{34} +0.347296 q^{36} -0.652704 q^{37} +3.16250 q^{38} -1.00000 q^{39} -1.34730 q^{40} -4.59627 q^{41} -6.10607 q^{43} -1.00000 q^{44} -0.532089 q^{45} -12.0496 q^{46} +9.51754 q^{47} +4.57398 q^{48} +7.22668 q^{50} -3.34730 q^{51} +0.347296 q^{52} +0.879385 q^{53} +1.53209 q^{54} +1.53209 q^{55} +2.06418 q^{57} +10.8007 q^{58} -2.24628 q^{59} +0.184793 q^{60} -8.29860 q^{61} -9.53983 q^{62} +6.17024 q^{64} -0.532089 q^{65} -4.41147 q^{66} -12.3969 q^{67} +1.16250 q^{68} -7.86484 q^{69} +10.6159 q^{71} +2.53209 q^{72} -0.551689 q^{73} +1.00000 q^{74} +4.71688 q^{75} -0.716881 q^{76} +1.53209 q^{78} -11.6159 q^{79} +2.43376 q^{80} +1.00000 q^{81} +7.04189 q^{82} -5.87939 q^{83} -1.78106 q^{85} +9.35504 q^{86} +7.04963 q^{87} -7.29086 q^{88} +5.49020 q^{89} +0.815207 q^{90} +2.73143 q^{92} -6.22668 q^{93} -14.5817 q^{94} +1.09833 q^{95} -1.94356 q^{96} +12.7811 q^{97} -2.87939 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3} + 3 q^{5} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^3 + 3 * q^5 + 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{3} + 3 q^{5} + 3 q^{8} + 3 q^{9} + 6 q^{10} - 3 q^{11} + 3 q^{13} - 3 q^{15} - 6 q^{16} + 9 q^{17} + 3 q^{19} + 3 q^{20} + 3 q^{22} - 3 q^{24} - 6 q^{25} - 3 q^{27} + 6 q^{29} - 6 q^{30} + 12 q^{31} - 9 q^{32} + 3 q^{33} + 3 q^{34} - 3 q^{37} + 12 q^{38} - 3 q^{39} - 3 q^{40} - 6 q^{43} - 3 q^{44} + 3 q^{45} - 9 q^{46} + 6 q^{47} + 6 q^{48} + 15 q^{50} - 9 q^{51} - 3 q^{53} - 3 q^{57} + 18 q^{58} - 3 q^{59} - 3 q^{60} + 15 q^{61} - 3 q^{64} + 3 q^{65} - 3 q^{66} - 9 q^{67} + 6 q^{68} + 21 q^{71} + 3 q^{72} + 3 q^{74} + 6 q^{75} + 6 q^{76} - 24 q^{79} - 9 q^{80} + 3 q^{81} + 18 q^{82} - 12 q^{83} + 12 q^{85} + 3 q^{86} - 6 q^{87} - 6 q^{88} + 15 q^{89} + 6 q^{90} + 18 q^{92} - 12 q^{93} - 12 q^{94} + 15 q^{95} + 9 q^{96} + 21 q^{97} - 3 q^{99}+O(q^{100}) $ 3 * q - 3 * q^3 + 3 * q^5 + 3 * q^8 + 3 * q^9 + 6 * q^10 - 3 * q^11 + 3 * q^13 - 3 * q^15 - 6 * q^16 + 9 * q^17 + 3 * q^19 + 3 * q^20 + 3 * q^22 - 3 * q^24 - 6 * q^25 - 3 * q^27 + 6 * q^29 - 6 * q^30 + 12 * q^31 - 9 * q^32 + 3 * q^33 + 3 * q^34 - 3 * q^37 + 12 * q^38 - 3 * q^39 - 3 * q^40 - 6 * q^43 - 3 * q^44 + 3 * q^45 - 9 * q^46 + 6 * q^47 + 6 * q^48 + 15 * q^50 - 9 * q^51 - 3 * q^53 - 3 * q^57 + 18 * q^58 - 3 * q^59 - 3 * q^60 + 15 * q^61 - 3 * q^64 + 3 * q^65 - 3 * q^66 - 9 * q^67 + 6 * q^68 + 21 * q^71 + 3 * q^72 + 3 * q^74 + 6 * q^75 + 6 * q^76 - 24 * q^79 - 9 * q^80 + 3 * q^81 + 18 * q^82 - 12 * q^83 + 12 * q^85 + 3 * q^86 - 6 * q^87 - 6 * q^88 + 15 * q^89 + 6 * q^90 + 18 * q^92 - 12 * q^93 - 12 * q^94 + 15 * q^95 + 9 * q^96 + 21 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.53209	−1.08335	−0.541675	−	0.840588i	$-0.682210\pi$
$2$	−1.53209	−1.08335	−0.541675	+	0.840588i	$0.682210\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.347296	0.173648
$5$	−0.532089	−0.237957	−0.118979	−	0.992897i	$-0.537962\pi$
$5$	−0.532089	−0.237957	−0.118979	+	0.992897i	$0.537962\pi$
$6$	1.53209	0.625473
$7$	0	0
$7$	0	0
$8$	2.53209	0.895229
$9$	1.00000	0.333333
$10$	0.815207	0.257791
$11$	−2.87939	−0.868167	−0.434084	−	0.900873i	$-0.642928\pi$
$11$	−2.87939	−0.868167	−0.434084	+	0.900873i	$0.642928\pi$
$12$	−0.347296	−0.100256
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	0.532089	0.137385
$16$	−4.57398	−1.14349
$17$	3.34730	0.811839	0.405919	−	0.913909i	$-0.366951\pi$
$17$	3.34730	0.811839	0.405919	+	0.913909i	$0.366951\pi$
$18$	−1.53209	−0.361117
$19$	−2.06418	−0.473555	−0.236777	−	0.971564i	$-0.576091\pi$
$19$	−2.06418	−0.473555	−0.236777	+	0.971564i	$0.576091\pi$
$20$	−0.184793	−0.0413209
$21$	0	0
$22$	4.41147	0.940529
$23$	7.86484	1.63993	0.819966	−	0.572412i	$-0.193992\pi$
$23$	7.86484	1.63993	0.819966	+	0.572412i	$0.193992\pi$
$24$	−2.53209	−0.516860
$25$	−4.71688	−0.943376
$26$	−1.53209	−0.300467
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−7.04963	−1.30908	−0.654542	−	0.756026i	$-0.727138\pi$
$29$	−7.04963	−1.30908	−0.654542	+	0.756026i	$0.727138\pi$
$30$	−0.815207	−0.148836
$31$	6.22668	1.11835	0.559173	−	0.829051i	$-0.311119\pi$
$31$	6.22668	1.11835	0.559173	+	0.829051i	$0.311119\pi$
$32$	1.94356	0.343577
$33$	2.87939	0.501237
$34$	−5.12836	−0.879506
$35$	0	0
$36$	0.347296	0.0578827
$37$	−0.652704	−0.107304	−0.0536519	−	0.998560i	$-0.517086\pi$
$37$	−0.652704	−0.107304	−0.0536519	+	0.998560i	$0.517086\pi$
$38$	3.16250	0.513026
$39$	−1.00000	−0.160128
$40$	−1.34730	−0.213026
$41$	−4.59627	−0.717816	−0.358908	−	0.933373i	$-0.616851\pi$
$41$	−4.59627	−0.717816	−0.358908	+	0.933373i	$0.616851\pi$
$42$	0	0
$43$	−6.10607	−0.931166	−0.465583	−	0.885004i	$-0.654155\pi$
$43$	−6.10607	−0.931166	−0.465583	+	0.885004i	$0.654155\pi$
$44$	−1.00000	−0.150756
$45$	−0.532089	−0.0793191
$46$	−12.0496	−1.77662
$47$	9.51754	1.38828	0.694138	−	0.719842i	$-0.255786\pi$
$47$	9.51754	1.38828	0.694138	+	0.719842i	$0.255786\pi$
$48$	4.57398	0.660197
$49$	0	0
$50$	7.22668	1.02201
$51$	−3.34730	−0.468715
$52$	0.347296	0.0481613
$53$	0.879385	0.120793	0.0603964	−	0.998174i	$-0.480764\pi$
$53$	0.879385	0.120793	0.0603964	+	0.998174i	$0.480764\pi$
$54$	1.53209	0.208491
$55$	1.53209	0.206587
$56$	0	0
$57$	2.06418	0.273407
$58$	10.8007	1.41820
$59$	−2.24628	−0.292441	−0.146221	−	0.989252i	$-0.546711\pi$
$59$	−2.24628	−0.292441	−0.146221	+	0.989252i	$0.546711\pi$
$60$	0.184793	0.0238566
$61$	−8.29860	−1.06253	−0.531263	−	0.847207i	$-0.678283\pi$
$61$	−8.29860	−1.06253	−0.531263	+	0.847207i	$0.678283\pi$
$62$	−9.53983	−1.21156
$63$	0	0
$64$	6.17024	0.771281
$65$	−0.532089	−0.0659975
$66$	−4.41147	−0.543015
$67$	−12.3969	−1.51453	−0.757263	−	0.653110i	$-0.773464\pi$
$67$	−12.3969	−1.51453	−0.757263	+	0.653110i	$0.773464\pi$
$68$	1.16250	0.140974
$69$	−7.86484	−0.946815
$70$	0	0
$71$	10.6159	1.25987	0.629936	−	0.776647i	$-0.283081\pi$
$71$	10.6159	1.25987	0.629936	+	0.776647i	$0.283081\pi$
$72$	2.53209	0.298410
$73$	−0.551689	−0.0645703	−0.0322852	−	0.999479i	$-0.510278\pi$
$73$	−0.551689	−0.0645703	−0.0322852	+	0.999479i	$0.510278\pi$
$74$	1.00000	0.116248
$75$	4.71688	0.544659
$76$	−0.716881	−0.0822319
$77$	0	0
$78$	1.53209	0.173475
$79$	−11.6159	−1.30689	−0.653444	−	0.756975i	$-0.726676\pi$
$79$	−11.6159	−1.30689	−0.653444	+	0.756975i	$0.726676\pi$
$80$	2.43376	0.272103
$81$	1.00000	0.111111
$82$	7.04189	0.777647
$83$	−5.87939	−0.645346	−0.322673	−	0.946510i	$-0.604581\pi$
$83$	−5.87939	−0.645346	−0.322673	+	0.946510i	$0.604581\pi$
$84$	0	0
$85$	−1.78106	−0.193183
$86$	9.35504	1.00878
$87$	7.04963	0.755800
$88$	−7.29086	−0.777208
$89$	5.49020	0.581960	0.290980	−	0.956729i	$-0.406019\pi$
$89$	5.49020	0.581960	0.290980	+	0.956729i	$0.406019\pi$
$90$	0.815207	0.0859304
$91$	0	0
$92$	2.73143	0.284771
$93$	−6.22668	−0.645677
$94$	−14.5817	−1.50399
$95$	1.09833	0.112686
$96$	−1.94356	−0.198364
$97$	12.7811	1.29772	0.648860	−	0.760908i	$-0.275246\pi$
$97$	12.7811	1.29772	0.648860	+	0.760908i	$0.275246\pi$
$98$	0	0
$99$	−2.87939	−0.289389
$100$	−1.63816	−0.163816
$101$	14.5321	1.44600	0.722998	−	0.690850i	$-0.242763\pi$
$101$	14.5321	1.44600	0.722998	+	0.690850i	$0.242763\pi$
$102$	5.12836	0.507783
$103$	11.6946	1.15230	0.576151	−	0.817343i	$-0.304554\pi$
$103$	11.6946	1.15230	0.576151	+	0.817343i	$0.304554\pi$
$104$	2.53209	0.248292
$105$	0	0
$106$	−1.34730	−0.130861
$107$	−2.58853	−0.250242	−0.125121	−	0.992141i	$-0.539932\pi$
$107$	−2.58853	−0.250242	−0.125121	+	0.992141i	$0.539932\pi$
$108$	−0.347296	−0.0334186
$109$	15.5449	1.48893	0.744465	−	0.667662i	$-0.232705\pi$
$109$	15.5449	1.48893	0.744465	+	0.667662i	$0.232705\pi$
$110$	−2.34730	−0.223806
$111$	0.652704	0.0619519
$112$	0	0
$113$	20.9736	1.97303	0.986515	−	0.163672i	$-0.0523339\pi$
$113$	20.9736	1.97303	0.986515	+	0.163672i	$0.0523339\pi$
$114$	−3.16250	−0.296196
$115$	−4.18479	−0.390234
$116$	−2.44831	−0.227320
$117$	1.00000	0.0924500
$118$	3.44150	0.316816
$119$	0	0
$120$	1.34730	0.122991
$121$	−2.70914	−0.246286
$122$	12.7142	1.15109
$123$	4.59627	0.414431
$124$	2.16250	0.194199
$125$	5.17024	0.462441
$126$	0	0
$127$	−14.0719	−1.24868	−0.624340	−	0.781152i	$-0.714632\pi$
$127$	−14.0719	−1.24868	−0.624340	+	0.781152i	$0.714632\pi$
$128$	−13.3405	−1.17914
$129$	6.10607	0.537609
$130$	0.815207	0.0714984
$131$	4.69728	0.410403	0.205202	−	0.978720i	$-0.434215\pi$
$131$	4.69728	0.410403	0.205202	+	0.978720i	$0.434215\pi$
$132$	1.00000	0.0870388
$133$	0	0
$134$	18.9932	1.64076
$135$	0.532089	0.0457949
$136$	8.47565	0.726781
$137$	10.3473	0.884029	0.442015	−	0.897008i	$-0.354264\pi$
$137$	10.3473	0.884029	0.442015	+	0.897008i	$0.354264\pi$
$138$	12.0496	1.02573
$139$	5.64496	0.478800	0.239400	−	0.970921i	$-0.423049\pi$
$139$	5.64496	0.478800	0.239400	+	0.970921i	$0.423049\pi$
$140$	0	0
$141$	−9.51754	−0.801522
$142$	−16.2645	−1.36488
$143$	−2.87939	−0.240786
$144$	−4.57398	−0.381165
$145$	3.75103	0.311506
$146$	0.845237	0.0699523
$147$	0	0
$148$	−0.226682	−0.0186331
$149$	5.78787	0.474160	0.237080	−	0.971490i	$-0.423810\pi$
$149$	5.78787	0.474160	0.237080	+	0.971490i	$0.423810\pi$
$150$	−7.22668	−0.590056
$151$	−0.739170	−0.0601528	−0.0300764	−	0.999548i	$-0.509575\pi$
$151$	−0.739170	−0.0601528	−0.0300764	+	0.999548i	$0.509575\pi$
$152$	−5.22668	−0.423940
$153$	3.34730	0.270613
$154$	0	0
$155$	−3.31315	−0.266118
$156$	−0.347296	−0.0278060
$157$	21.5672	1.72125	0.860624	−	0.509241i	$-0.170074\pi$
$157$	21.5672	1.72125	0.860624	+	0.509241i	$0.170074\pi$
$158$	17.7965	1.41582
$159$	−0.879385	−0.0697398
$160$	−1.03415	−0.0817566
$161$	0	0
$162$	−1.53209	−0.120372
$163$	−1.58079	−0.123817	−0.0619083	−	0.998082i	$-0.519719\pi$
$163$	−1.58079	−0.123817	−0.0619083	+	0.998082i	$0.519719\pi$
$164$	−1.59627	−0.124647
$165$	−1.53209	−0.119273
$166$	9.00774	0.699136
$167$	11.3405	0.877553	0.438777	−	0.898596i	$-0.355412\pi$
$167$	11.3405	0.877553	0.438777	+	0.898596i	$0.355412\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	2.72874	0.209285
$171$	−2.06418	−0.157852
$172$	−2.12061	−0.161695
$173$	2.34998	0.178666	0.0893330	−	0.996002i	$-0.471526\pi$
$173$	2.34998	0.178666	0.0893330	+	0.996002i	$0.471526\pi$
$174$	−10.8007	−0.818796
$175$	0	0
$176$	13.1702	0.992745
$177$	2.24628	0.168841
$178$	−8.41147	−0.630467
$179$	−11.8057	−0.882400	−0.441200	−	0.897409i	$-0.645447\pi$
$179$	−11.8057	−0.882400	−0.441200	+	0.897409i	$0.645447\pi$
$180$	−0.184793	−0.0137736
$181$	19.8111	1.47255	0.736273	−	0.676684i	$-0.236584\pi$
$181$	19.8111	1.47255	0.736273	+	0.676684i	$0.236584\pi$
$182$	0	0
$183$	8.29860	0.613450
$184$	19.9145	1.46811
$185$	0.347296	0.0255337
$186$	9.53983	0.699494
$187$	−9.63816	−0.704812
$188$	3.30541	0.241072
$189$	0	0
$190$	−1.68273	−0.122078
$191$	11.6408	0.842302	0.421151	−	0.906991i	$-0.361626\pi$
$191$	11.6408	0.842302	0.421151	+	0.906991i	$0.361626\pi$
$192$	−6.17024	−0.445299
$193$	−0.593578	−0.0427267	−0.0213634	−	0.999772i	$-0.506801\pi$
$193$	−0.593578	−0.0427267	−0.0213634	+	0.999772i	$0.506801\pi$
$194$	−19.5817	−1.40589
$195$	0.532089	0.0381037
$196$	0	0
$197$	7.07873	0.504338	0.252169	−	0.967683i	$-0.418856\pi$
$197$	7.07873	0.504338	0.252169	+	0.967683i	$0.418856\pi$
$198$	4.41147	0.313510
$199$	−3.75103	−0.265903	−0.132952	−	0.991123i	$-0.542446\pi$
$199$	−3.75103	−0.265903	−0.132952	+	0.991123i	$0.542446\pi$
$200$	−11.9436	−0.844537
$201$	12.3969	0.874412
$202$	−22.2645	−1.56652
$203$	0	0
$204$	−1.16250	−0.0813915
$205$	2.44562	0.170810
$206$	−17.9172	−1.24835
$207$	7.86484	0.546644
$208$	−4.57398	−0.317148
$209$	5.94356	0.411125
$210$	0	0
$211$	−10.3500	−0.712522	−0.356261	−	0.934386i	$-0.615949\pi$
$211$	−10.3500	−0.712522	−0.356261	+	0.934386i	$0.615949\pi$
$212$	0.305407	0.0209755
$213$	−10.6159	−0.727387
$214$	3.96585	0.271100
$215$	3.24897	0.221578
$216$	−2.53209	−0.172287
$217$	0	0
$218$	−23.8161	−1.61303
$219$	0.551689	0.0372797
$220$	0.532089	0.0358734
$221$	3.34730	0.225164
$222$	−1.00000	−0.0671156
$223$	20.6955	1.38587	0.692937	−	0.720998i	$-0.256316\pi$
$223$	20.6955	1.38587	0.692937	+	0.720998i	$0.256316\pi$
$224$	0	0
$225$	−4.71688	−0.314459
$226$	−32.1334	−2.13748
$227$	−17.4047	−1.15519	−0.577594	−	0.816324i	$-0.696008\pi$
$227$	−17.4047	−1.15519	−0.577594	+	0.816324i	$0.696008\pi$
$228$	0.716881	0.0474766
$229$	1.90673	0.126000	0.0630000	−	0.998014i	$-0.479933\pi$
$229$	1.90673	0.126000	0.0630000	+	0.998014i	$0.479933\pi$
$230$	6.41147	0.422760
$231$	0	0
$232$	−17.8503	−1.17193
$233$	−10.9932	−0.720188	−0.360094	−	0.932916i	$-0.617255\pi$
$233$	−10.9932	−0.720188	−0.360094	+	0.932916i	$0.617255\pi$
$234$	−1.53209	−0.100156
$235$	−5.06418	−0.330351
$236$	−0.780126	−0.0507818
$237$	11.6159	0.754532
$238$	0	0
$239$	11.9736	0.774507	0.387254	−	0.921973i	$-0.373424\pi$
$239$	11.9736	0.774507	0.387254	+	0.921973i	$0.373424\pi$
$240$	−2.43376	−0.157099
$241$	24.0205	1.54730	0.773649	−	0.633614i	$-0.218429\pi$
$241$	24.0205	1.54730	0.773649	+	0.633614i	$0.218429\pi$
$242$	4.15064	0.266814
$243$	−1.00000	−0.0641500
$244$	−2.88207	−0.184506
$245$	0	0
$246$	−7.04189	−0.448974
$247$	−2.06418	−0.131340
$248$	15.7665	1.00117
$249$	5.87939	0.372591
$250$	−7.92127	−0.500985
$251$	10.8280	0.683457	0.341729	−	0.939799i	$-0.388988\pi$
$251$	10.8280	0.683457	0.341729	+	0.939799i	$0.388988\pi$
$252$	0	0
$253$	−22.6459	−1.42374
$254$	21.5594	1.35276
$255$	1.78106	0.111534
$256$	8.09833	0.506145
$257$	27.3233	1.70438	0.852189	−	0.523234i	$-0.175275\pi$
$257$	27.3233	1.70438	0.852189	+	0.523234i	$0.175275\pi$
$258$	−9.35504	−0.582419
$259$	0	0
$260$	−0.184793	−0.0114603
$261$	−7.04963	−0.436361
$262$	−7.19665	−0.444611
$263$	14.1702	0.873775	0.436887	−	0.899516i	$-0.356081\pi$
$263$	14.1702	0.873775	0.436887	+	0.899516i	$0.356081\pi$
$264$	7.29086	0.448721
$265$	−0.467911	−0.0287436
$266$	0	0
$267$	−5.49020	−0.335995
$268$	−4.30541	−0.262995
$269$	29.5895	1.80410	0.902051	−	0.431630i	$-0.142061\pi$
$269$	29.5895	1.80410	0.902051	+	0.431630i	$0.142061\pi$
$270$	−0.815207	−0.0496119
$271$	5.31315	0.322751	0.161375	−	0.986893i	$-0.448407\pi$
$271$	5.31315	0.322751	0.161375	+	0.986893i	$0.448407\pi$
$272$	−15.3105	−0.928333
$273$	0	0
$274$	−15.8530	−0.957713
$275$	13.5817	0.819008
$276$	−2.73143	−0.164413
$277$	−5.36690	−0.322466	−0.161233	−	0.986916i	$-0.551547\pi$
$277$	−5.36690	−0.322466	−0.161233	+	0.986916i	$0.551547\pi$
$278$	−8.64858	−0.518708
$279$	6.22668	0.372782
$280$	0	0
$281$	14.6432	0.873541	0.436770	−	0.899573i	$-0.356122\pi$
$281$	14.6432	0.873541	0.436770	+	0.899573i	$0.356122\pi$
$282$	14.5817	0.868329
$283$	−30.2550	−1.79847	−0.899235	−	0.437465i	$-0.855876\pi$
$283$	−30.2550	−1.79847	−0.899235	+	0.437465i	$0.855876\pi$
$284$	3.68685	0.218774
$285$	−1.09833	−0.0650592
$286$	4.41147	0.260856
$287$	0	0
$288$	1.94356	0.114526
$289$	−5.79561	−0.340918
$290$	−5.74691	−0.337470
$291$	−12.7811	−0.749239
$292$	−0.191600	−0.0112125
$293$	−8.32594	−0.486407	−0.243203	−	0.969975i	$-0.578198\pi$
$293$	−8.32594	−0.486407	−0.243203	+	0.969975i	$0.578198\pi$
$294$	0	0
$295$	1.19522	0.0695885
$296$	−1.65270	−0.0960614
$297$	2.87939	0.167079
$298$	−8.86753	−0.513682
$299$	7.86484	0.454835
$300$	1.63816	0.0945790
$301$	0	0
$302$	1.13247	0.0651666
$303$	−14.5321	−0.834847
$304$	9.44150	0.541507
$305$	4.41559	0.252836
$306$	−5.12836	−0.293169
$307$	−22.9486	−1.30975	−0.654873	−	0.755739i	$-0.727278\pi$
$307$	−22.9486	−1.30975	−0.654873	+	0.755739i	$0.727278\pi$
$308$	0	0
$309$	−11.6946	−0.665282
$310$	5.07604	0.288300
$311$	1.18479	0.0671834	0.0335917	−	0.999436i	$-0.489305\pi$
$311$	1.18479	0.0671834	0.0335917	+	0.999436i	$0.489305\pi$
$312$	−2.53209	−0.143351
$313$	−4.38650	−0.247939	−0.123970	−	0.992286i	$-0.539563\pi$
$313$	−4.38650	−0.247939	−0.123970	+	0.992286i	$0.539563\pi$
$314$	−33.0428	−1.86471
$315$	0	0
$316$	−4.03415	−0.226939
$317$	1.80066	0.101135	0.0505676	−	0.998721i	$-0.483897\pi$
$317$	1.80066	0.101135	0.0505676	+	0.998721i	$0.483897\pi$
$318$	1.34730	0.0755526
$319$	20.2986	1.13650
$320$	−3.28312	−0.183532
$321$	2.58853	0.144477
$322$	0	0
$323$	−6.90941	−0.384450
$324$	0.347296	0.0192942
$325$	−4.71688	−0.261646
$326$	2.42190	0.134137
$327$	−15.5449	−0.859634
$328$	−11.6382	−0.642610
$329$	0	0
$330$	2.34730	0.129214
$331$	25.1807	1.38406	0.692028	−	0.721871i	$-0.256718\pi$
$331$	25.1807	1.38406	0.692028	+	0.721871i	$0.256718\pi$
$332$	−2.04189	−0.112063
$333$	−0.652704	−0.0357679
$334$	−17.3746	−0.950698
$335$	6.59627	0.360393
$336$	0	0
$337$	−19.5963	−1.06748	−0.533738	−	0.845650i	$-0.679213\pi$
$337$	−19.5963	−1.06748	−0.533738	+	0.845650i	$0.679213\pi$
$338$	−1.53209	−0.0833346
$339$	−20.9736	−1.13913
$340$	−0.618555	−0.0335459
$341$	−17.9290	−0.970911
$342$	3.16250	0.171009
$343$	0	0
$344$	−15.4611	−0.833607
$345$	4.18479	0.225302
$346$	−3.60039	−0.193558
$347$	11.2935	0.606269	0.303135	−	0.952948i	$-0.401967\pi$
$347$	11.2935	0.606269	0.303135	+	0.952948i	$0.401967\pi$
$348$	2.44831	0.131243
$349$	14.1848	0.759295	0.379647	−	0.925131i	$-0.376045\pi$
$349$	14.1848	0.759295	0.379647	+	0.925131i	$0.376045\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	−5.59627	−0.298282
$353$	22.5672	1.20113	0.600565	−	0.799576i	$-0.294943\pi$
$353$	22.5672	1.20113	0.600565	+	0.799576i	$0.294943\pi$
$354$	−3.44150	−0.182914
$355$	−5.64858	−0.299796
$356$	1.90673	0.101056
$357$	0	0
$358$	18.0874	0.955949
$359$	−22.1111	−1.16698	−0.583490	−	0.812120i	$-0.698313\pi$
$359$	−22.1111	−1.16698	−0.583490	+	0.812120i	$0.698313\pi$
$360$	−1.34730	−0.0710088
$361$	−14.7392	−0.775746
$362$	−30.3523	−1.59528
$363$	2.70914	0.142193
$364$	0	0
$365$	0.293548	0.0153650
$366$	−12.7142	−0.664582
$367$	−30.9617	−1.61619	−0.808095	−	0.589053i	$-0.799501\pi$
$367$	−30.9617	−1.61619	−0.808095	+	0.589053i	$0.799501\pi$
$368$	−35.9736	−1.87525
$369$	−4.59627	−0.239272
$370$	−0.532089	−0.0276620
$371$	0	0
$372$	−2.16250	−0.112121
$373$	29.3405	1.51919	0.759596	−	0.650395i	$-0.225396\pi$
$373$	29.3405	1.51919	0.759596	+	0.650395i	$0.225396\pi$
$374$	14.7665	0.763558
$375$	−5.17024	−0.266990
$376$	24.0993	1.24282
$377$	−7.04963	−0.363074
$378$	0	0
$379$	37.2208	1.91190	0.955952	−	0.293522i	$-0.0948275\pi$
$379$	37.2208	1.91190	0.955952	+	0.293522i	$0.0948275\pi$
$380$	0.381445	0.0195677
$381$	14.0719	0.720926
$382$	−17.8348	−0.912508
$383$	−14.8452	−0.758556	−0.379278	−	0.925283i	$-0.623828\pi$
$383$	−14.8452	−0.758556	−0.379278	+	0.925283i	$0.623828\pi$
$384$	13.3405	0.680779
$385$	0	0
$386$	0.909415	0.0462880
$387$	−6.10607	−0.310389
$388$	4.43882	0.225347
$389$	8.70233	0.441226	0.220613	−	0.975361i	$-0.429194\pi$
$389$	8.70233	0.441226	0.220613	+	0.975361i	$0.429194\pi$
$390$	−0.815207	−0.0412796
$391$	26.3259	1.33136
$392$	0	0
$393$	−4.69728	−0.236946
$394$	−10.8452	−0.546375
$395$	6.18067	0.310983
$396$	−1.00000	−0.0502519
$397$	−8.36453	−0.419804	−0.209902	−	0.977722i	$-0.567314\pi$
$397$	−8.36453	−0.419804	−0.209902	+	0.977722i	$0.567314\pi$
$398$	5.74691	0.288067
$399$	0	0
$400$	21.5749	1.07875
$401$	3.76827	0.188178	0.0940891	−	0.995564i	$-0.470006\pi$
$401$	3.76827	0.188178	0.0940891	+	0.995564i	$0.470006\pi$
$402$	−18.9932	−0.947294
$403$	6.22668	0.310173
$404$	5.04694	0.251095
$405$	−0.532089	−0.0264397
$406$	0	0
$407$	1.87939	0.0931577
$408$	−8.47565	−0.419607
$409$	−3.04189	−0.150412	−0.0752059	−	0.997168i	$-0.523961\pi$
$409$	−3.04189	−0.150412	−0.0752059	+	0.997168i	$0.523961\pi$
$410$	−3.74691	−0.185047
$411$	−10.3473	−0.510394
$412$	4.06149	0.200095
$413$	0	0
$414$	−12.0496	−0.592207
$415$	3.12836	0.153565
$416$	1.94356	0.0952910
$417$	−5.64496	−0.276435
$418$	−9.10607	−0.445392
$419$	−26.6168	−1.30032	−0.650158	−	0.759799i	$-0.725297\pi$
$419$	−26.6168	−1.30032	−0.650158	+	0.759799i	$0.725297\pi$
$420$	0	0
$421$	22.0506	1.07468	0.537339	−	0.843366i	$-0.319429\pi$
$421$	22.0506	1.07468	0.537339	+	0.843366i	$0.319429\pi$
$422$	15.8571	0.771911
$423$	9.51754	0.462759
$424$	2.22668	0.108137
$425$	−15.7888	−0.765869
$426$	16.2645	0.788015
$427$	0	0
$428$	−0.898986	−0.0434541
$429$	2.87939	0.139018
$430$	−4.97771	−0.240047
$431$	11.5321	0.555481	0.277741	−	0.960656i	$-0.410414\pi$
$431$	11.5321	0.555481	0.277741	+	0.960656i	$0.410414\pi$
$432$	4.57398	0.220066
$433$	−26.4911	−1.27308	−0.636541	−	0.771243i	$-0.719636\pi$
$433$	−26.4911	−1.27308	−0.636541	+	0.771243i	$0.719636\pi$
$434$	0	0
$435$	−3.75103	−0.179848
$436$	5.39868	0.258550
$437$	−16.2344	−0.776598
$438$	−0.845237	−0.0403870
$439$	−31.5800	−1.50723	−0.753615	−	0.657316i	$-0.771692\pi$
$439$	−31.5800	−1.50723	−0.753615	+	0.657316i	$0.771692\pi$
$440$	3.87939	0.184942
$441$	0	0
$442$	−5.12836	−0.243931
$443$	−15.9240	−0.756570	−0.378285	−	0.925689i	$-0.623486\pi$
$443$	−15.9240	−0.756570	−0.378285	+	0.925689i	$0.623486\pi$
$444$	0.226682	0.0107578
$445$	−2.92127	−0.138482
$446$	−31.7074	−1.50139
$447$	−5.78787	−0.273757
$448$	0	0
$449$	−34.1462	−1.61146	−0.805729	−	0.592284i	$-0.798226\pi$
$449$	−34.1462	−1.61146	−0.805729	+	0.592284i	$0.798226\pi$
$450$	7.22668	0.340669
$451$	13.2344	0.623185
$452$	7.28405	0.342613
$453$	0.739170	0.0347292
$454$	26.6655	1.25147
$455$	0	0
$456$	5.22668	0.244762
$457$	3.66994	0.171673	0.0858363	−	0.996309i	$-0.472644\pi$
$457$	3.66994	0.171673	0.0858363	+	0.996309i	$0.472644\pi$
$458$	−2.92127	−0.136502
$459$	−3.34730	−0.156238
$460$	−1.45336	−0.0677634
$461$	18.0077	0.838704	0.419352	−	0.907824i	$-0.362257\pi$
$461$	18.0077	0.838704	0.419352	+	0.907824i	$0.362257\pi$
$462$	0	0
$463$	−8.73648	−0.406019	−0.203009	−	0.979177i	$-0.565072\pi$
$463$	−8.73648	−0.406019	−0.203009	+	0.979177i	$0.565072\pi$
$464$	32.2449	1.49693
$465$	3.31315	0.153644
$466$	16.8425	0.780216
$467$	10.3901	0.480797	0.240399	−	0.970674i	$-0.422722\pi$
$467$	10.3901	0.480797	0.240399	+	0.970674i	$0.422722\pi$
$468$	0.347296	0.0160538
$469$	0	0
$470$	7.75877	0.357885
$471$	−21.5672	−0.993763
$472$	−5.68779	−0.261802
$473$	17.5817	0.808408
$474$	−17.7965	−0.817422
$475$	9.73648	0.446740
$476$	0	0
$477$	0.879385	0.0402643
$478$	−18.3446	−0.839063
$479$	−16.6135	−0.759090	−0.379545	−	0.925173i	$-0.623920\pi$
$479$	−16.6135	−0.759090	−0.379545	+	0.925173i	$0.623920\pi$
$480$	1.03415	0.0472022
$481$	−0.652704	−0.0297607
$482$	−36.8016	−1.67627
$483$	0	0
$484$	−0.940875	−0.0427670
$485$	−6.80066	−0.308802
$486$	1.53209	0.0694970
$487$	19.0547	0.863450	0.431725	−	0.902005i	$-0.357905\pi$
$487$	19.0547	0.863450	0.431725	+	0.902005i	$0.357905\pi$
$488$	−21.0128	−0.951204
$489$	1.58079	0.0714856
$490$	0	0
$491$	−21.0036	−0.947880	−0.473940	−	0.880557i	$-0.657169\pi$
$491$	−21.0036	−0.947880	−0.473940	+	0.880557i	$0.657169\pi$
$492$	1.59627	0.0719653
$493$	−23.5972	−1.06276
$494$	3.16250	0.142288
$495$	1.53209	0.0688623
$496$	−28.4807	−1.27882
$497$	0	0
$498$	−9.00774	−0.403647
$499$	14.6810	0.657211	0.328605	−	0.944467i	$-0.393421\pi$
$499$	14.6810	0.657211	0.328605	+	0.944467i	$0.393421\pi$
$500$	1.79561	0.0803020
$501$	−11.3405	−0.506656
$502$	−16.5895	−0.740424
$503$	−34.1566	−1.52297	−0.761484	−	0.648183i	$-0.775529\pi$
$503$	−34.1566	−1.52297	−0.761484	+	0.648183i	$0.775529\pi$
$504$	0	0
$505$	−7.73236	−0.344086
$506$	34.6955	1.54240
$507$	−1.00000	−0.0444116
$508$	−4.88713	−0.216831
$509$	−21.5871	−0.956831	−0.478416	−	0.878134i	$-0.658789\pi$
$509$	−21.5871	−0.956831	−0.478416	+	0.878134i	$0.658789\pi$
$510$	−2.72874	−0.120831
$511$	0	0
$512$	14.2736	0.630811
$513$	2.06418	0.0911357
$514$	−41.8617	−1.84644
$515$	−6.22256	−0.274199
$516$	2.12061	0.0933549
$517$	−27.4047	−1.20526
$518$	0	0
$519$	−2.34998	−0.103153
$520$	−1.34730	−0.0590829
$521$	−26.1566	−1.14594	−0.572971	−	0.819575i	$-0.694209\pi$
$521$	−26.1566	−1.14594	−0.572971	+	0.819575i	$0.694209\pi$
$522$	10.8007	0.472732
$523$	34.6810	1.51649	0.758247	−	0.651968i	$-0.226056\pi$
$523$	34.6810	1.51649	0.758247	+	0.651968i	$0.226056\pi$
$524$	1.63135	0.0712658
$525$	0	0
$526$	−21.7101	−0.946604
$527$	20.8425	0.907916
$528$	−13.1702	−0.573161
$529$	38.8557	1.68938
$530$	0.716881	0.0311393
$531$	−2.24628	−0.0974803
$532$	0	0
$533$	−4.59627	−0.199086
$534$	8.41147	0.364000
$535$	1.37733	0.0595470
$536$	−31.3901	−1.35585
$537$	11.8057	0.509454
$538$	−45.3337	−1.95447
$539$	0	0
$540$	0.184793	0.00795220
$541$	37.5526	1.61451	0.807257	−	0.590201i	$-0.200951\pi$
$541$	37.5526	1.61451	0.807257	+	0.590201i	$0.200951\pi$
$542$	−8.14022	−0.349652
$543$	−19.8111	−0.850175
$544$	6.50568	0.278929
$545$	−8.27126	−0.354302
$546$	0	0
$547$	−7.61856	−0.325746	−0.162873	−	0.986647i	$-0.552076\pi$
$547$	−7.61856	−0.325746	−0.162873	+	0.986647i	$0.552076\pi$
$548$	3.59358	0.153510
$549$	−8.29860	−0.354176
$550$	−20.8084	−0.887273
$551$	14.5517	0.619923
$552$	−19.9145	−0.847616
$553$	0	0
$554$	8.22256	0.349343
$555$	−0.347296	−0.0147419
$556$	1.96048	0.0831427
$557$	−18.5039	−0.784037	−0.392018	−	0.919957i	$-0.628223\pi$
$557$	−18.5039	−0.784037	−0.392018	+	0.919957i	$0.628223\pi$
$558$	−9.53983	−0.403853
$559$	−6.10607	−0.258259
$560$	0	0
$561$	9.63816	0.406923
$562$	−22.4347	−0.946351
$563$	18.1361	0.764345	0.382173	−	0.924091i	$-0.375176\pi$
$563$	18.1361	0.764345	0.382173	+	0.924091i	$0.375176\pi$
$564$	−3.30541	−0.139183
$565$	−11.1598	−0.469497
$566$	46.3533	1.94837
$567$	0	0
$568$	26.8803	1.12787
$569$	−25.8976	−1.08568	−0.542841	−	0.839835i	$-0.682651\pi$
$569$	−25.8976	−1.08568	−0.542841	+	0.839835i	$0.682651\pi$
$570$	1.68273	0.0704819
$571$	26.0104	1.08850	0.544251	−	0.838922i	$-0.316814\pi$
$571$	26.0104	1.08850	0.544251	+	0.838922i	$0.316814\pi$
$572$	−1.00000	−0.0418121
$573$	−11.6408	−0.486303
$574$	0	0
$575$	−37.0975	−1.54707
$576$	6.17024	0.257094
$577$	1.21389	0.0505348	0.0252674	−	0.999681i	$-0.491956\pi$
$577$	1.21389	0.0505348	0.0252674	+	0.999681i	$0.491956\pi$
$578$	8.87939	0.369334
$579$	0.593578	0.0246683
$580$	1.30272	0.0540925
$581$	0	0
$582$	19.5817	0.811688
$583$	−2.53209	−0.104868
$584$	−1.39693	−0.0578052
$585$	−0.532089	−0.0219992
$586$	12.7561	0.526949
$587$	−27.9881	−1.15519	−0.577597	−	0.816322i	$-0.696010\pi$
$587$	−27.9881	−1.15519	−0.577597	+	0.816322i	$0.696010\pi$
$588$	0	0
$589$	−12.8530	−0.529598
$590$	−1.83119	−0.0753887
$591$	−7.07873	−0.291180
$592$	2.98545	0.122701
$593$	−19.8631	−0.815679	−0.407840	−	0.913054i	$-0.633718\pi$
$593$	−19.8631	−0.815679	−0.407840	+	0.913054i	$0.633718\pi$
$594$	−4.41147	−0.181005
$595$	0	0
$596$	2.01010	0.0823371
$597$	3.75103	0.153519
$598$	−12.0496	−0.492746
$599$	9.19160	0.375559	0.187779	−	0.982211i	$-0.439871\pi$
$599$	9.19160	0.375559	0.187779	+	0.982211i	$0.439871\pi$
$600$	11.9436	0.487594
$601$	19.2317	0.784479	0.392239	−	0.919863i	$-0.371700\pi$
$601$	19.2317	0.784479	0.392239	+	0.919863i	$0.371700\pi$
$602$	0	0
$603$	−12.3969	−0.504842
$604$	−0.256711	−0.0104454
$605$	1.44150	0.0586055
$606$	22.2645	0.904432
$607$	18.6587	0.757333	0.378666	−	0.925533i	$-0.376383\pi$
$607$	18.6587	0.757333	0.378666	+	0.925533i	$0.376383\pi$
$608$	−4.01186	−0.162702
$609$	0	0
$610$	−6.76508	−0.273910
$611$	9.51754	0.385038
$612$	1.16250	0.0469914
$613$	15.9932	0.645959	0.322979	−	0.946406i	$-0.395316\pi$
$613$	15.9932	0.645959	0.322979	+	0.946406i	$0.395316\pi$
$614$	35.1593	1.41891
$615$	−2.44562	−0.0986170
$616$	0	0
$617$	39.4056	1.58641	0.793205	−	0.608955i	$-0.208411\pi$
$617$	39.4056	1.58641	0.793205	+	0.608955i	$0.208411\pi$
$618$	17.9172	0.720734
$619$	30.7056	1.23416	0.617082	−	0.786899i	$-0.288315\pi$
$619$	30.7056	1.23416	0.617082	+	0.786899i	$0.288315\pi$
$620$	−1.15064	−0.0462110
$621$	−7.86484	−0.315605
$622$	−1.81521	−0.0727832
$623$	0	0
$624$	4.57398	0.183106
$625$	20.8334	0.833335
$626$	6.72050	0.268605
$627$	−5.94356	−0.237363
$628$	7.49020	0.298892
$629$	−2.18479	−0.0871134
$630$	0	0
$631$	21.4270	0.852994	0.426497	−	0.904489i	$-0.359748\pi$
$631$	21.4270	0.852994	0.426497	+	0.904489i	$0.359748\pi$
$632$	−29.4124	−1.16996
$633$	10.3500	0.411375
$634$	−2.75877	−0.109565
$635$	7.48751	0.297133
$636$	−0.305407	−0.0121102
$637$	0	0
$638$	−31.0993	−1.23123
$639$	10.6159	0.419957
$640$	7.09833	0.280586
$641$	−37.2790	−1.47243	−0.736216	−	0.676747i	$-0.763389\pi$
$641$	−37.2790	−1.47243	−0.736216	+	0.676747i	$0.763389\pi$
$642$	−3.96585	−0.156520
$643$	23.7169	0.935303	0.467651	−	0.883913i	$-0.345100\pi$
$643$	23.7169	0.935303	0.467651	+	0.883913i	$0.345100\pi$
$644$	0	0
$645$	−3.24897	−0.127928
$646$	10.5858	0.416494
$647$	10.0692	0.395862	0.197931	−	0.980216i	$-0.436578\pi$
$647$	10.0692	0.395862	0.197931	+	0.980216i	$0.436578\pi$
$648$	2.53209	0.0994698
$649$	6.46791	0.253888
$650$	7.22668	0.283454
$651$	0	0
$652$	−0.549001	−0.0215005
$653$	−19.7496	−0.772862	−0.386431	−	0.922318i	$-0.626292\pi$
$653$	−19.7496	−0.772862	−0.386431	+	0.922318i	$0.626292\pi$
$654$	23.8161	0.931285
$655$	−2.49937	−0.0976585
$656$	21.0232	0.820819
$657$	−0.551689	−0.0215234
$658$	0	0
$659$	12.8075	0.498908	0.249454	−	0.968387i	$-0.419749\pi$
$659$	12.8075	0.498908	0.249454	+	0.968387i	$0.419749\pi$
$660$	−0.532089	−0.0207115
$661$	−34.7648	−1.35219	−0.676096	−	0.736813i	$-0.736330\pi$
$661$	−34.7648	−1.35219	−0.676096	+	0.736813i	$0.736330\pi$
$662$	−38.5790	−1.49942
$663$	−3.34730	−0.129998
$664$	−14.8871	−0.577733
$665$	0	0
$666$	1.00000	0.0387492
$667$	−55.4442	−2.14681
$668$	3.93851	0.152386
$669$	−20.6955	−0.800135
$670$	−10.1061	−0.390431
$671$	23.8949	0.922451
$672$	0	0
$673$	12.8479	0.495251	0.247626	−	0.968856i	$-0.420350\pi$
$673$	12.8479	0.495251	0.247626	+	0.968856i	$0.420350\pi$
$674$	30.0232	1.15645
$675$	4.71688	0.181553
$676$	0.347296	0.0133576
$677$	9.73143	0.374009	0.187005	−	0.982359i	$-0.440122\pi$
$677$	9.73143	0.374009	0.187005	+	0.982359i	$0.440122\pi$
$678$	32.1334	1.23408
$679$	0	0
$680$	−4.50980	−0.172943
$681$	17.4047	0.666948
$682$	27.4688	1.05184
$683$	42.2249	1.61569	0.807846	−	0.589394i	$-0.200633\pi$
$683$	42.2249	1.61569	0.807846	+	0.589394i	$0.200633\pi$
$684$	−0.716881	−0.0274106
$685$	−5.50568	−0.210361
$686$	0	0
$687$	−1.90673	−0.0727461
$688$	27.9290	1.06478
$689$	0.879385	0.0335019
$690$	−6.41147	−0.244081
$691$	7.02229	0.267140	0.133570	−	0.991039i	$-0.457356\pi$
$691$	7.02229	0.267140	0.133570	+	0.991039i	$0.457356\pi$
$692$	0.816141	0.0310250
$693$	0	0
$694$	−17.3027	−0.656802
$695$	−3.00362	−0.113934
$696$	17.8503	0.676613
$697$	−15.3851	−0.582751
$698$	−21.7324	−0.822582
$699$	10.9932	0.415801
$700$	0	0
$701$	−7.47834	−0.282453	−0.141227	−	0.989977i	$-0.545105\pi$
$701$	−7.47834	−0.282453	−0.141227	+	0.989977i	$0.545105\pi$
$702$	1.53209	0.0578250
$703$	1.34730	0.0508142
$704$	−17.7665	−0.669601
$705$	5.06418	0.190728
$706$	−34.5749	−1.30124
$707$	0	0
$708$	0.780126	0.0293189
$709$	−16.1002	−0.604655	−0.302328	−	0.953204i	$-0.597764\pi$
$709$	−16.1002	−0.604655	−0.302328	+	0.953204i	$0.597764\pi$
$710$	8.65413	0.324784
$711$	−11.6159	−0.435629
$712$	13.9017	0.520987
$713$	48.9718	1.83401
$714$	0	0
$715$	1.53209	0.0572969
$716$	−4.10008	−0.153227
$717$	−11.9736	−0.447162
$718$	33.8762	1.26425
$719$	27.7169	1.03367	0.516833	−	0.856086i	$-0.327111\pi$
$719$	27.7169	1.03367	0.516833	+	0.856086i	$0.327111\pi$
$720$	2.43376	0.0907010
$721$	0	0
$722$	22.5817	0.840405
$723$	−24.0205	−0.893333
$724$	6.88032	0.255705
$725$	33.2523	1.23496
$726$	−4.15064	−0.154045
$727$	−19.4543	−0.721520	−0.360760	−	0.932659i	$-0.617483\pi$
$727$	−19.4543	−0.721520	−0.360760	+	0.932659i	$0.617483\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−0.449741	−0.0166457
$731$	−20.4388	−0.755957
$732$	2.88207	0.106525
$733$	41.7410	1.54174	0.770870	−	0.636992i	$-0.219822\pi$
$733$	41.7410	1.54174	0.770870	+	0.636992i	$0.219822\pi$
$734$	47.4361	1.75090
$735$	0	0
$736$	15.2858	0.563442
$737$	35.6955	1.31486
$738$	7.04189	0.259216
$739$	20.4347	0.751702	0.375851	−	0.926680i	$-0.377350\pi$
$739$	20.4347	0.751702	0.375851	+	0.926680i	$0.377350\pi$
$740$	0.120615	0.00443389
$741$	2.06418	0.0758295
$742$	0	0
$743$	42.7965	1.57005	0.785026	−	0.619462i	$-0.212649\pi$
$743$	42.7965	1.57005	0.785026	+	0.619462i	$0.212649\pi$
$744$	−15.7665	−0.578028
$745$	−3.07966	−0.112830
$746$	−44.9522	−1.64582
$747$	−5.87939	−0.215115
$748$	−3.34730	−0.122389
$749$	0	0
$750$	7.92127	0.289244
$751$	−44.0951	−1.60905	−0.804527	−	0.593916i	$-0.797581\pi$
$751$	−44.0951	−1.60905	−0.804527	+	0.593916i	$0.797581\pi$
$752$	−43.5330	−1.58749
$753$	−10.8280	−0.394594
$754$	10.8007	0.393337
$755$	0.393304	0.0143138
$756$	0	0
$757$	−3.65951	−0.133007	−0.0665036	−	0.997786i	$-0.521184\pi$
$757$	−3.65951	−0.133007	−0.0665036	+	0.997786i	$0.521184\pi$
$758$	−57.0256	−2.07126
$759$	22.6459	0.821994
$760$	2.78106	0.100880
$761$	−8.67829	−0.314588	−0.157294	−	0.987552i	$-0.550277\pi$
$761$	−8.67829	−0.314588	−0.157294	+	0.987552i	$0.550277\pi$
$762$	−21.5594	−0.781016
$763$	0	0
$764$	4.04282	0.146264
$765$	−1.78106	−0.0643943
$766$	22.7442	0.821782
$767$	−2.24628	−0.0811085
$768$	−8.09833	−0.292223
$769$	35.8939	1.29437	0.647184	−	0.762334i	$-0.275946\pi$
$769$	35.8939	1.29437	0.647184	+	0.762334i	$0.275946\pi$
$770$	0	0
$771$	−27.3233	−0.984023
$772$	−0.206148	−0.00741941
$773$	34.2077	1.23037	0.615183	−	0.788385i	$-0.289082\pi$
$773$	34.2077	1.23037	0.615183	+	0.788385i	$0.289082\pi$
$774$	9.35504	0.336260
$775$	−29.3705	−1.05502
$776$	32.3628	1.16176
$777$	0	0
$778$	−13.3327	−0.478002
$779$	9.48751	0.339925
$780$	0.184793	0.00661663
$781$	−30.5672	−1.09378
$782$	−40.3337	−1.44233
$783$	7.04963	0.251933
$784$	0	0
$785$	−11.4757	−0.409584
$786$	7.19665	0.256696
$787$	−46.9736	−1.67443	−0.837214	−	0.546876i	$-0.815817\pi$
$787$	−46.9736	−1.67443	−0.837214	+	0.546876i	$0.815817\pi$
$788$	2.45842	0.0875774
$789$	−14.1702	−0.504474
$790$	−9.46934	−0.336904
$791$	0	0
$792$	−7.29086	−0.259069
$793$	−8.29860	−0.294692
$794$	12.8152	0.454795
$795$	0.467911	0.0165951
$796$	−1.30272	−0.0461736
$797$	−50.7169	−1.79648	−0.898242	−	0.439501i	$-0.855155\pi$
$797$	−50.7169	−1.79648	−0.898242	+	0.439501i	$0.855155\pi$
$798$	0	0
$799$	31.8580	1.12706
$800$	−9.16756	−0.324122
$801$	5.49020	0.193987
$802$	−5.77332	−0.203863
$803$	1.58853	0.0560579
$804$	4.30541	0.151840
$805$	0	0
$806$	−9.53983	−0.336026
$807$	−29.5895	−1.04160
$808$	36.7965	1.29450
$809$	27.0752	0.951914	0.475957	−	0.879469i	$-0.342102\pi$
$809$	27.0752	0.951914	0.475957	+	0.879469i	$0.342102\pi$
$810$	0.815207	0.0286435
$811$	−36.9240	−1.29658	−0.648288	−	0.761395i	$-0.724515\pi$
$811$	−36.9240	−1.29658	−0.648288	+	0.761395i	$0.724515\pi$
$812$	0	0
$813$	−5.31315	−0.186340
$814$	−2.87939	−0.100922
$815$	0.841118	0.0294631
$816$	15.3105	0.535973
$817$	12.6040	0.440958
$818$	4.66044	0.162949
$819$	0	0
$820$	0.849356	0.0296608
$821$	18.6527	0.650984	0.325492	−	0.945545i	$-0.394470\pi$
$821$	18.6527	0.650984	0.325492	+	0.945545i	$0.394470\pi$
$822$	15.8530	0.552936
$823$	45.4175	1.58315	0.791577	−	0.611070i	$-0.209261\pi$
$823$	45.4175	1.58315	0.791577	+	0.611070i	$0.209261\pi$
$824$	29.6117	1.03157
$825$	−13.5817	−0.472855
$826$	0	0
$827$	9.81109	0.341165	0.170582	−	0.985343i	$-0.445435\pi$
$827$	9.81109	0.341165	0.170582	+	0.985343i	$0.445435\pi$
$828$	2.73143	0.0949237
$829$	29.8990	1.03843	0.519217	−	0.854642i	$-0.326224\pi$
$829$	29.8990	1.03843	0.519217	+	0.854642i	$0.326224\pi$
$830$	−4.79292	−0.166365
$831$	5.36690	0.186176
$832$	6.17024	0.213915
$833$	0	0
$834$	8.64858	0.299476
$835$	−6.03415	−0.208820
$836$	2.06418	0.0713911
$837$	−6.22668	−0.215226
$838$	40.7793	1.40870
$839$	45.3655	1.56619	0.783095	−	0.621902i	$-0.213640\pi$
$839$	45.3655	1.56619	0.783095	+	0.621902i	$0.213640\pi$
$840$	0	0
$841$	20.6973	0.713699
$842$	−33.7834	−1.16425
$843$	−14.6432	−0.504339
$844$	−3.59451	−0.123728
$845$	−0.532089	−0.0183044
$846$	−14.5817	−0.501330
$847$	0	0
$848$	−4.02229	−0.138126
$849$	30.2550	1.03835
$850$	24.1898	0.829705
$851$	−5.13341	−0.175971
$852$	−3.68685	−0.126309
$853$	52.8744	1.81039	0.905193	−	0.425000i	$-0.139726\pi$
$853$	52.8744	1.81039	0.905193	+	0.425000i	$0.139726\pi$
$854$	0	0
$855$	1.09833	0.0375620
$856$	−6.55438	−0.224024
$857$	−38.5066	−1.31536	−0.657680	−	0.753297i	$-0.728462\pi$
$857$	−38.5066	−1.31536	−0.657680	+	0.753297i	$0.728462\pi$
$858$	−4.41147	−0.150605
$859$	25.8990	0.883662	0.441831	−	0.897098i	$-0.354329\pi$
$859$	25.8990	0.883662	0.441831	+	0.897098i	$0.354329\pi$
$860$	1.12836	0.0384766
$861$	0	0
$862$	−17.6682	−0.601781
$863$	−48.6067	−1.65459	−0.827296	−	0.561767i	$-0.810122\pi$
$863$	−48.6067	−1.65459	−0.827296	+	0.561767i	$0.810122\pi$
$864$	−1.94356	−0.0661214
$865$	−1.25040	−0.0425149
$866$	40.5868	1.37919
$867$	5.79561	0.196829
$868$	0	0
$869$	33.4466	1.13460
$870$	5.74691	0.194839
$871$	−12.3969	−0.420054
$872$	39.3610	1.33293
$873$	12.7811	0.432573
$874$	24.8726	0.841328
$875$	0	0
$876$	0.191600	0.00647355
$877$	32.5348	1.09862	0.549311	−	0.835618i	$-0.314890\pi$
$877$	32.5348	1.09862	0.549311	+	0.835618i	$0.314890\pi$
$878$	48.3833	1.63286
$879$	8.32594	0.280827
$880$	−7.00774	−0.236231
$881$	−4.95273	−0.166862	−0.0834309	−	0.996514i	$-0.526588\pi$
$881$	−4.95273	−0.166862	−0.0834309	+	0.996514i	$0.526588\pi$
$882$	0	0
$883$	−9.20439	−0.309752	−0.154876	−	0.987934i	$-0.549498\pi$
$883$	−9.20439	−0.309752	−0.154876	+	0.987934i	$0.549498\pi$
$884$	1.16250	0.0390992
$885$	−1.19522	−0.0401769
$886$	24.3969	0.819631
$887$	−12.1489	−0.407920	−0.203960	−	0.978979i	$-0.565381\pi$
$887$	−12.1489	−0.407920	−0.203960	+	0.978979i	$0.565381\pi$
$888$	1.65270	0.0554611
$889$	0	0
$890$	4.47565	0.150024
$891$	−2.87939	−0.0964630
$892$	7.18748	0.240655
$893$	−19.6459	−0.657425
$894$	8.86753	0.296574
$895$	6.28169	0.209974
$896$	0	0
$897$	−7.86484	−0.262599
$898$	52.3150	1.74577
$899$	−43.8958	−1.46401
$900$	−1.63816	−0.0546052
$901$	2.94356	0.0980643
$902$	−20.2763	−0.675127
$903$	0	0
$904$	53.1070	1.76631
$905$	−10.5413	−0.350403
$906$	−1.13247	−0.0376239
$907$	−34.8060	−1.15572	−0.577858	−	0.816138i	$-0.696111\pi$
$907$	−34.8060	−1.15572	−0.577858	+	0.816138i	$0.696111\pi$
$908$	−6.04458	−0.200596
$909$	14.5321	0.481999
$910$	0	0
$911$	−37.5280	−1.24336	−0.621679	−	0.783272i	$-0.713549\pi$
$911$	−37.5280	−1.24336	−0.621679	+	0.783272i	$0.713549\pi$
$912$	−9.44150	−0.312639
$913$	16.9290	0.560269
$914$	−5.62267	−0.185982
$915$	−4.41559	−0.145975
$916$	0.662199	0.0218797
$917$	0	0
$918$	5.12836	0.169261
$919$	−16.1780	−0.533662	−0.266831	−	0.963743i	$-0.585977\pi$
$919$	−16.1780	−0.533662	−0.266831	+	0.963743i	$0.585977\pi$
$920$	−10.5963	−0.349349
$921$	22.9486	0.756183
$922$	−27.5895	−0.908610
$923$	10.6159	0.349426
$924$	0	0
$925$	3.07873	0.101228
$926$	13.3851	0.439861
$927$	11.6946	0.384101
$928$	−13.7014	−0.449770
$929$	−0.941808	−0.0308997	−0.0154499	−	0.999881i	$-0.504918\pi$
$929$	−0.941808	−0.0308997	−0.0154499	+	0.999881i	$0.504918\pi$
$930$	−5.07604	−0.166450
$931$	0	0
$932$	−3.81790	−0.125059
$933$	−1.18479	−0.0387884
$934$	−15.9186	−0.520872
$935$	5.12836	0.167715
$936$	2.53209	0.0827639
$937$	−6.47203	−0.211432	−0.105716	−	0.994396i	$-0.533713\pi$
$937$	−6.47203	−0.211432	−0.105716	+	0.994396i	$0.533713\pi$
$938$	0	0
$939$	4.38650	0.143148
$940$	−1.75877	−0.0573648
$941$	55.5672	1.81144	0.905719	−	0.423879i	$-0.139332\pi$
$941$	55.5672	1.81144	0.905719	+	0.423879i	$0.139332\pi$
$942$	33.0428	1.07659
$943$	−36.1489	−1.17717
$944$	10.2744	0.334405
$945$	0	0
$946$	−26.9368	−0.875789
$947$	−29.2431	−0.950273	−0.475136	−	0.879912i	$-0.657601\pi$
$947$	−29.2431	−0.950273	−0.475136	+	0.879912i	$0.657601\pi$
$948$	4.03415	0.131023
$949$	−0.551689	−0.0179086
$950$	−14.9172	−0.483976
$951$	−1.80066	−0.0583904
$952$	0	0
$953$	28.2668	0.915652	0.457826	−	0.889042i	$-0.348628\pi$
$953$	28.2668	0.915652	0.457826	+	0.889042i	$0.348628\pi$
$954$	−1.34730	−0.0436203
$955$	−6.19396	−0.200432
$956$	4.15839	0.134492
$957$	−20.2986	−0.656161
$958$	25.4534	0.822361
$959$	0	0
$960$	3.28312	0.105962
$961$	7.77156	0.250696
$962$	1.00000	0.0322413
$963$	−2.58853	−0.0834141
$964$	8.34224	0.268686
$965$	0.315836	0.0101671
$966$	0	0
$967$	17.2662	0.555244	0.277622	−	0.960690i	$-0.410454\pi$
$967$	17.2662	0.555244	0.277622	+	0.960690i	$0.410454\pi$
$968$	−6.85978	−0.220482
$969$	6.90941	0.221962
$970$	10.4192	0.334541
$971$	28.9573	0.929284	0.464642	−	0.885499i	$-0.346183\pi$
$971$	28.9573	0.929284	0.464642	+	0.885499i	$0.346183\pi$
$972$	−0.347296	−0.0111395
$973$	0	0
$974$	−29.1935	−0.935419
$975$	4.71688	0.151061
$976$	37.9576	1.21499
$977$	−27.7929	−0.889174	−0.444587	−	0.895736i	$-0.646650\pi$
$977$	−27.7929	−0.889174	−0.444587	+	0.895736i	$0.646650\pi$
$978$	−2.42190	−0.0774439
$979$	−15.8084	−0.505239
$980$	0	0
$981$	15.5449	0.496310
$982$	32.1794	1.02689
$983$	−42.3105	−1.34949	−0.674747	−	0.738049i	$-0.735747\pi$
$983$	−42.3105	−1.34949	−0.674747	+	0.738049i	$0.735747\pi$
$984$	11.6382	0.371011
$985$	−3.76651	−0.120011
$986$	36.1530	1.15135
$987$	0	0
$988$	−0.716881	−0.0228070
$989$	−48.0232	−1.52705
$990$	−2.34730	−0.0746020
$991$	−56.6965	−1.80102	−0.900511	−	0.434833i	$-0.856807\pi$
$991$	−56.6965	−1.80102	−0.900511	+	0.434833i	$0.856807\pi$
$992$	12.1019	0.384237
$993$	−25.1807	−0.799085
$994$	0	0
$995$	1.99588	0.0632737
$996$	2.04189	0.0646997
$997$	−52.0069	−1.64708	−0.823538	−	0.567261i	$-0.808003\pi$
$997$	−52.0069	−1.64708	−0.823538	+	0.567261i	$0.808003\pi$
$998$	−22.4926	−0.711990
$999$	0.652704	0.0206506

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1911.2.a.o.1.1		3
3.2	odd	2		5733.2.a.y.1.3		3
7.2	even	3		273.2.i.b.235.3	yes	6
7.4	even	3		273.2.i.b.79.3	✓	6
7.6	odd	2		1911.2.a.p.1.1		3
21.2	odd	6		819.2.j.e.235.1		6
21.11	odd	6		819.2.j.e.352.1		6
21.20	even	2		5733.2.a.z.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.i.b.79.3	✓	6	7.4	even	3
273.2.i.b.235.3	yes	6	7.2	even	3
819.2.j.e.235.1		6	21.2	odd	6
819.2.j.e.352.1		6	21.11	odd	6
1911.2.a.o.1.1		3	1.1	even	1	trivial
1911.2.a.p.1.1		3	7.6	odd	2
5733.2.a.y.1.3		3	3.2	odd	2
5733.2.a.z.1.3		3	21.20	even	2

Overview	Random
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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:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1911.a (trivial)

\(f(q)\)	\(=\)	\(q-1.53209 q^{2} -1.00000 q^{3} +0.347296 q^{4} -0.532089 q^{5} +1.53209 q^{6} +2.53209 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.53209 q^{2} -1.00000 q^{3} +0.347296 q^{4} -0.532089 q^{5} +1.53209 q^{6} +2.53209 q^{8} +1.00000 q^{9} +0.815207 q^{10} -2.87939 q^{11} -0.347296 q^{12} +1.00000 q^{13} +0.532089 q^{15} -4.57398 q^{16} +3.34730 q^{17} -1.53209 q^{18} -2.06418 q^{19} -0.184793 q^{20} +4.41147 q^{22} +7.86484 q^{23} -2.53209 q^{24} -4.71688 q^{25} -1.53209 q^{26} -1.00000 q^{27} -7.04963 q^{29} -0.815207 q^{30} +6.22668 q^{31} +1.94356 q^{32} +2.87939 q^{33} -5.12836 q^{34} +0.347296 q^{36} -0.652704 q^{37} +3.16250 q^{38} -1.00000 q^{39} -1.34730 q^{40} -4.59627 q^{41} -6.10607 q^{43} -1.00000 q^{44} -0.532089 q^{45} -12.0496 q^{46} +9.51754 q^{47} +4.57398 q^{48} +7.22668 q^{50} -3.34730 q^{51} +0.347296 q^{52} +0.879385 q^{53} +1.53209 q^{54} +1.53209 q^{55} +2.06418 q^{57} +10.8007 q^{58} -2.24628 q^{59} +0.184793 q^{60} -8.29860 q^{61} -9.53983 q^{62} +6.17024 q^{64} -0.532089 q^{65} -4.41147 q^{66} -12.3969 q^{67} +1.16250 q^{68} -7.86484 q^{69} +10.6159 q^{71} +2.53209 q^{72} -0.551689 q^{73} +1.00000 q^{74} +4.71688 q^{75} -0.716881 q^{76} +1.53209 q^{78} -11.6159 q^{79} +2.43376 q^{80} +1.00000 q^{81} +7.04189 q^{82} -5.87939 q^{83} -1.78106 q^{85} +9.35504 q^{86} +7.04963 q^{87} -7.29086 q^{88} +5.49020 q^{89} +0.815207 q^{90} +2.73143 q^{92} -6.22668 q^{93} -14.5817 q^{94} +1.09833 q^{95} -1.94356 q^{96} +12.7811 q^{97} -2.87939 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} + 3 q^{5} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^3 + 3 * q^5 + 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{3} + 3 q^{5} + 3 q^{8} + 3 q^{9} + 6 q^{10} - 3 q^{11} + 3 q^{13} - 3 q^{15} - 6 q^{16} + 9 q^{17} + 3 q^{19} + 3 q^{20} + 3 q^{22} - 3 q^{24} - 6 q^{25} - 3 q^{27} + 6 q^{29} - 6 q^{30} + 12 q^{31} - 9 q^{32} + 3 q^{33} + 3 q^{34} - 3 q^{37} + 12 q^{38} - 3 q^{39} - 3 q^{40} - 6 q^{43} - 3 q^{44} + 3 q^{45} - 9 q^{46} + 6 q^{47} + 6 q^{48} + 15 q^{50} - 9 q^{51} - 3 q^{53} - 3 q^{57} + 18 q^{58} - 3 q^{59} - 3 q^{60} + 15 q^{61} - 3 q^{64} + 3 q^{65} - 3 q^{66} - 9 q^{67} + 6 q^{68} + 21 q^{71} + 3 q^{72} + 3 q^{74} + 6 q^{75} + 6 q^{76} - 24 q^{79} - 9 q^{80} + 3 q^{81} + 18 q^{82} - 12 q^{83} + 12 q^{85} + 3 q^{86} - 6 q^{87} - 6 q^{88} + 15 q^{89} + 6 q^{90} + 18 q^{92} - 12 q^{93} - 12 q^{94} + 15 q^{95} + 9 q^{96} + 21 q^{97} - 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^3 + 3 * q^5 + 3 * q^8 + 3 * q^9 + 6 * q^10 - 3 * q^11 + 3 * q^13 - 3 * q^15 - 6 * q^16 + 9 * q^17 + 3 * q^19 + 3 * q^20 + 3 * q^22 - 3 * q^24 - 6 * q^25 - 3 * q^27 + 6 * q^29 - 6 * q^30 + 12 * q^31 - 9 * q^32 + 3 * q^33 + 3 * q^34 - 3 * q^37 + 12 * q^38 - 3 * q^39 - 3 * q^40 - 6 * q^43 - 3 * q^44 + 3 * q^45 - 9 * q^46 + 6 * q^47 + 6 * q^48 + 15 * q^50 - 9 * q^51 - 3 * q^53 - 3 * q^57 + 18 * q^58 - 3 * q^59 - 3 * q^60 + 15 * q^61 - 3 * q^64 + 3 * q^65 - 3 * q^66 - 9 * q^67 + 6 * q^68 + 21 * q^71 + 3 * q^72 + 3 * q^74 + 6 * q^75 + 6 * q^76 - 24 * q^79 - 9 * q^80 + 3 * q^81 + 18 * q^82 - 12 * q^83 + 12 * q^85 + 3 * q^86 - 6 * q^87 - 6 * q^88 + 15 * q^89 + 6 * q^90 + 18 * q^92 - 12 * q^93 - 12 * q^94 + 15 * q^95 + 9 * q^96 + 21 * q^97 - 3 * q^99

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