LMFDB - Embedded newform 6018.2.a.ba.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 31 x^{10} + 111 x^{9} + 381 x^{8} - 1101 x^{7} - 2301 x^{6} + 4690 x^{5} + \cdots + 5653 $ x^12 - 4x^11 - 31x^10 + 111x^9 + 381x^8 - 1101x^7 - 2301x^6 + 4690x^5 + 6915x^4 - 8325x^3 - 10082x^2 + 5149*x + 5653
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$4.06325$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.06325 q^{5} +1.00000 q^{6} +1.90874 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.06325 q^{5} +1.00000 q^{6} +1.90874 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.06325 q^{10} -1.86510 q^{11} +1.00000 q^{12} +3.17193 q^{13} +1.90874 q^{14} -3.06325 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -7.26767 q^{19} -3.06325 q^{20} +1.90874 q^{21} -1.86510 q^{22} +8.51270 q^{23} +1.00000 q^{24} +4.38353 q^{25} +3.17193 q^{26} +1.00000 q^{27} +1.90874 q^{28} +8.04952 q^{29} -3.06325 q^{30} -9.13791 q^{31} +1.00000 q^{32} -1.86510 q^{33} -1.00000 q^{34} -5.84695 q^{35} +1.00000 q^{36} -1.54836 q^{37} -7.26767 q^{38} +3.17193 q^{39} -3.06325 q^{40} +1.93990 q^{41} +1.90874 q^{42} +11.8934 q^{43} -1.86510 q^{44} -3.06325 q^{45} +8.51270 q^{46} +6.99942 q^{47} +1.00000 q^{48} -3.35672 q^{49} +4.38353 q^{50} -1.00000 q^{51} +3.17193 q^{52} +9.22153 q^{53} +1.00000 q^{54} +5.71329 q^{55} +1.90874 q^{56} -7.26767 q^{57} +8.04952 q^{58} +1.00000 q^{59} -3.06325 q^{60} +12.5988 q^{61} -9.13791 q^{62} +1.90874 q^{63} +1.00000 q^{64} -9.71644 q^{65} -1.86510 q^{66} -14.4822 q^{67} -1.00000 q^{68} +8.51270 q^{69} -5.84695 q^{70} -15.5923 q^{71} +1.00000 q^{72} +14.1170 q^{73} -1.54836 q^{74} +4.38353 q^{75} -7.26767 q^{76} -3.56000 q^{77} +3.17193 q^{78} +11.5528 q^{79} -3.06325 q^{80} +1.00000 q^{81} +1.93990 q^{82} -5.03094 q^{83} +1.90874 q^{84} +3.06325 q^{85} +11.8934 q^{86} +8.04952 q^{87} -1.86510 q^{88} +9.15169 q^{89} -3.06325 q^{90} +6.05439 q^{91} +8.51270 q^{92} -9.13791 q^{93} +6.99942 q^{94} +22.2627 q^{95} +1.00000 q^{96} -10.4576 q^{97} -3.35672 q^{98} -1.86510 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9} + 8 q^{10} + 11 q^{11} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 8 q^{15} + 12 q^{16} - 12 q^{17} + 12 q^{18} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 11 q^{22} + 22 q^{23} + 12 q^{24} + 22 q^{25} + 6 q^{26} + 12 q^{27} + 5 q^{28} + 26 q^{29} + 8 q^{30} + q^{31} + 12 q^{32} + 11 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} + 10 q^{37} + 3 q^{38} + 6 q^{39} + 8 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 11 q^{44} + 8 q^{45} + 22 q^{46} + 6 q^{47} + 12 q^{48} + 11 q^{49} + 22 q^{50} - 12 q^{51} + 6 q^{52} + 10 q^{53} + 12 q^{54} + 15 q^{55} + 5 q^{56} + 3 q^{57} + 26 q^{58} + 12 q^{59} + 8 q^{60} + 15 q^{61} + q^{62} + 5 q^{63} + 12 q^{64} + 4 q^{65} + 11 q^{66} + 4 q^{67} - 12 q^{68} + 22 q^{69} + 24 q^{70} + 10 q^{71} + 12 q^{72} + 24 q^{73} + 10 q^{74} + 22 q^{75} + 3 q^{76} + 24 q^{77} + 6 q^{78} + 23 q^{79} + 8 q^{80} + 12 q^{81} + 16 q^{82} + 5 q^{84} - 8 q^{85} + 23 q^{86} + 26 q^{87} + 11 q^{88} + 13 q^{89} + 8 q^{90} + 3 q^{91} + 22 q^{92} + q^{93} + 6 q^{94} + 11 q^{95} + 12 q^{96} + 13 q^{97} + 11 q^{98} + 11 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9 + 8 * q^10 + 11 * q^11 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 8 * q^15 + 12 * q^16 - 12 * q^17 + 12 * q^18 + 3 * q^19 + 8 * q^20 + 5 * q^21 + 11 * q^22 + 22 * q^23 + 12 * q^24 + 22 * q^25 + 6 * q^26 + 12 * q^27 + 5 * q^28 + 26 * q^29 + 8 * q^30 + q^31 + 12 * q^32 + 11 * q^33 - 12 * q^34 + 24 * q^35 + 12 * q^36 + 10 * q^37 + 3 * q^38 + 6 * q^39 + 8 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 11 * q^44 + 8 * q^45 + 22 * q^46 + 6 * q^47 + 12 * q^48 + 11 * q^49 + 22 * q^50 - 12 * q^51 + 6 * q^52 + 10 * q^53 + 12 * q^54 + 15 * q^55 + 5 * q^56 + 3 * q^57 + 26 * q^58 + 12 * q^59 + 8 * q^60 + 15 * q^61 + q^62 + 5 * q^63 + 12 * q^64 + 4 * q^65 + 11 * q^66 + 4 * q^67 - 12 * q^68 + 22 * q^69 + 24 * q^70 + 10 * q^71 + 12 * q^72 + 24 * q^73 + 10 * q^74 + 22 * q^75 + 3 * q^76 + 24 * q^77 + 6 * q^78 + 23 * q^79 + 8 * q^80 + 12 * q^81 + 16 * q^82 + 5 * q^84 - 8 * q^85 + 23 * q^86 + 26 * q^87 + 11 * q^88 + 13 * q^89 + 8 * q^90 + 3 * q^91 + 22 * q^92 + q^93 + 6 * q^94 + 11 * q^95 + 12 * q^96 + 13 * q^97 + 11 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−3.06325	−1.36993	−0.684964	−	0.728576i	$-0.740182\pi$
$5$	−3.06325	−1.36993	−0.684964	+	0.728576i	$0.740182\pi$
$6$	1.00000	0.408248
$7$	1.90874	0.721435	0.360718	−	0.932675i	$-0.382532\pi$
$7$	1.90874	0.721435	0.360718	+	0.932675i	$0.382532\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.06325	−0.968686
$11$	−1.86510	−0.562350	−0.281175	−	0.959657i	$-0.590724\pi$
$11$	−1.86510	−0.562350	−0.281175	+	0.959657i	$0.590724\pi$
$12$	1.00000	0.288675
$13$	3.17193	0.879736	0.439868	−	0.898062i	$-0.355025\pi$
$13$	3.17193	0.879736	0.439868	+	0.898062i	$0.355025\pi$
$14$	1.90874	0.510132
$15$	−3.06325	−0.790929
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−7.26767	−1.66732	−0.833659	−	0.552280i	$-0.813758\pi$
$19$	−7.26767	−1.66732	−0.833659	+	0.552280i	$0.813758\pi$
$20$	−3.06325	−0.684964
$21$	1.90874	0.416521
$22$	−1.86510	−0.397641
$23$	8.51270	1.77502	0.887510	−	0.460788i	$-0.152433\pi$
$23$	8.51270	1.77502	0.887510	+	0.460788i	$0.152433\pi$
$24$	1.00000	0.204124
$25$	4.38353	0.876705
$26$	3.17193	0.622067
$27$	1.00000	0.192450
$28$	1.90874	0.360718
$29$	8.04952	1.49476	0.747380	−	0.664397i	$-0.231312\pi$
$29$	8.04952	1.49476	0.747380	+	0.664397i	$0.231312\pi$
$30$	−3.06325	−0.559271
$31$	−9.13791	−1.64122	−0.820608	−	0.571491i	$-0.806365\pi$
$31$	−9.13791	−1.64122	−0.820608	+	0.571491i	$0.806365\pi$
$32$	1.00000	0.176777
$33$	−1.86510	−0.324673
$34$	−1.00000	−0.171499
$35$	−5.84695	−0.988315
$36$	1.00000	0.166667
$37$	−1.54836	−0.254550	−0.127275	−	0.991867i	$-0.540623\pi$
$37$	−1.54836	−0.254550	−0.127275	+	0.991867i	$0.540623\pi$
$38$	−7.26767	−1.17897
$39$	3.17193	0.507916
$40$	−3.06325	−0.484343
$41$	1.93990	0.302962	0.151481	−	0.988460i	$-0.451596\pi$
$41$	1.93990	0.302962	0.151481	+	0.988460i	$0.451596\pi$
$42$	1.90874	0.294525
$43$	11.8934	1.81372	0.906862	−	0.421428i	$-0.138471\pi$
$43$	11.8934	1.81372	0.906862	+	0.421428i	$0.138471\pi$
$44$	−1.86510	−0.281175
$45$	−3.06325	−0.456643
$46$	8.51270	1.25513
$47$	6.99942	1.02097	0.510485	−	0.859887i	$-0.329466\pi$
$47$	6.99942	1.02097	0.510485	+	0.859887i	$0.329466\pi$
$48$	1.00000	0.144338
$49$	−3.35672	−0.479531
$50$	4.38353	0.619924
$51$	−1.00000	−0.140028
$52$	3.17193	0.439868
$53$	9.22153	1.26668	0.633338	−	0.773876i	$-0.281684\pi$
$53$	9.22153	1.26668	0.633338	+	0.773876i	$0.281684\pi$
$54$	1.00000	0.136083
$55$	5.71329	0.770379
$56$	1.90874	0.255066
$57$	−7.26767	−0.962626
$58$	8.04952	1.05695
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−3.06325	−0.395464
$61$	12.5988	1.61312	0.806558	−	0.591155i	$-0.201328\pi$
$61$	12.5988	1.61312	0.806558	+	0.591155i	$0.201328\pi$
$62$	−9.13791	−1.16052
$63$	1.90874	0.240478
$64$	1.00000	0.125000
$65$	−9.71644	−1.20518
$66$	−1.86510	−0.229578
$67$	−14.4822	−1.76928	−0.884640	−	0.466274i	$-0.845596\pi$
$67$	−14.4822	−1.76928	−0.884640	+	0.466274i	$0.845596\pi$
$68$	−1.00000	−0.121268
$69$	8.51270	1.02481
$70$	−5.84695	−0.698844
$71$	−15.5923	−1.85047	−0.925236	−	0.379393i	$-0.876133\pi$
$71$	−15.5923	−1.85047	−0.925236	+	0.379393i	$0.876133\pi$
$72$	1.00000	0.117851
$73$	14.1170	1.65227	0.826135	−	0.563473i	$-0.190535\pi$
$73$	14.1170	1.65227	0.826135	+	0.563473i	$0.190535\pi$
$74$	−1.54836	−0.179994
$75$	4.38353	0.506166
$76$	−7.26767	−0.833659
$77$	−3.56000	−0.405699
$78$	3.17193	0.359151
$79$	11.5528	1.29980	0.649898	−	0.760021i	$-0.274812\pi$
$79$	11.5528	1.29980	0.649898	+	0.760021i	$0.274812\pi$
$80$	−3.06325	−0.342482
$81$	1.00000	0.111111
$82$	1.93990	0.214227
$83$	−5.03094	−0.552217	−0.276109	−	0.961126i	$-0.589045\pi$
$83$	−5.03094	−0.552217	−0.276109	+	0.961126i	$0.589045\pi$
$84$	1.90874	0.208260
$85$	3.06325	0.332257
$86$	11.8934	1.28250
$87$	8.04952	0.863000
$88$	−1.86510	−0.198821
$89$	9.15169	0.970077	0.485038	−	0.874493i	$-0.338806\pi$
$89$	9.15169	0.970077	0.485038	+	0.874493i	$0.338806\pi$
$90$	−3.06325	−0.322895
$91$	6.05439	0.634673
$92$	8.51270	0.887510
$93$	−9.13791	−0.947557
$94$	6.99942	0.721935
$95$	22.2627	2.28411
$96$	1.00000	0.102062
$97$	−10.4576	−1.06181	−0.530906	−	0.847431i	$-0.678148\pi$
$97$	−10.4576	−1.06181	−0.530906	+	0.847431i	$0.678148\pi$
$98$	−3.35672	−0.339080
$99$	−1.86510	−0.187450
$100$	4.38353	0.438353
$101$	13.0126	1.29480	0.647399	−	0.762152i	$-0.275857\pi$
$101$	13.0126	1.29480	0.647399	+	0.762152i	$0.275857\pi$
$102$	−1.00000	−0.0990148
$103$	−1.32085	−0.130148	−0.0650739	−	0.997880i	$-0.520728\pi$
$103$	−1.32085	−0.130148	−0.0650739	+	0.997880i	$0.520728\pi$
$104$	3.17193	0.311034
$105$	−5.84695	−0.570604
$106$	9.22153	0.895675
$107$	5.96565	0.576721	0.288360	−	0.957522i	$-0.406890\pi$
$107$	5.96565	0.576721	0.288360	+	0.957522i	$0.406890\pi$
$108$	1.00000	0.0962250
$109$	6.59962	0.632129	0.316065	−	0.948738i	$-0.397638\pi$
$109$	6.59962	0.632129	0.316065	+	0.948738i	$0.397638\pi$
$110$	5.71329	0.544741
$111$	−1.54836	−0.146964
$112$	1.90874	0.180359
$113$	5.50149	0.517537	0.258768	−	0.965939i	$-0.416683\pi$
$113$	5.50149	0.517537	0.258768	+	0.965939i	$0.416683\pi$
$114$	−7.26767	−0.680679
$115$	−26.0766	−2.43165
$116$	8.04952	0.747380
$117$	3.17193	0.293245
$118$	1.00000	0.0920575
$119$	−1.90874	−0.174974
$120$	−3.06325	−0.279636
$121$	−7.52139	−0.683763
$122$	12.5988	1.14065
$123$	1.93990	0.174915
$124$	−9.13791	−0.820608
$125$	1.88842	0.168905
$126$	1.90874	0.170044
$127$	−2.64239	−0.234474	−0.117237	−	0.993104i	$-0.537404\pi$
$127$	−2.64239	−0.234474	−0.117237	+	0.993104i	$0.537404\pi$
$128$	1.00000	0.0883883
$129$	11.8934	1.04715
$130$	−9.71644	−0.852188
$131$	−12.1740	−1.06365	−0.531825	−	0.846854i	$-0.678494\pi$
$131$	−12.1740	−1.06365	−0.531825	+	0.846854i	$0.678494\pi$
$132$	−1.86510	−0.162336
$133$	−13.8721	−1.20286
$134$	−14.4822	−1.25107
$135$	−3.06325	−0.263643
$136$	−1.00000	−0.0857493
$137$	15.4018	1.31587	0.657934	−	0.753075i	$-0.271431\pi$
$137$	15.4018	1.31587	0.657934	+	0.753075i	$0.271431\pi$
$138$	8.51270	0.724649
$139$	−1.33885	−0.113560	−0.0567800	−	0.998387i	$-0.518083\pi$
$139$	−1.33885	−0.113560	−0.0567800	+	0.998387i	$0.518083\pi$
$140$	−5.84695	−0.494158
$141$	6.99942	0.589457
$142$	−15.5923	−1.30848
$143$	−5.91599	−0.494720
$144$	1.00000	0.0833333
$145$	−24.6577	−2.04771
$146$	14.1170	1.16833
$147$	−3.35672	−0.276857
$148$	−1.54836	−0.127275
$149$	11.0669	0.906638	0.453319	−	0.891348i	$-0.350240\pi$
$149$	11.0669	0.906638	0.453319	+	0.891348i	$0.350240\pi$
$150$	4.38353	0.357913
$151$	2.11510	0.172124	0.0860621	−	0.996290i	$-0.472572\pi$
$151$	2.11510	0.172124	0.0860621	+	0.996290i	$0.472572\pi$
$152$	−7.26767	−0.589486
$153$	−1.00000	−0.0808452
$154$	−3.56000	−0.286873
$155$	27.9917	2.24835
$156$	3.17193	0.253958
$157$	−1.46492	−0.116913	−0.0584566	−	0.998290i	$-0.518618\pi$
$157$	−1.46492	−0.116913	−0.0584566	+	0.998290i	$0.518618\pi$
$158$	11.5528	0.919095
$159$	9.22153	0.731315
$160$	−3.06325	−0.242172
$161$	16.2485	1.28056
$162$	1.00000	0.0785674
$163$	17.7396	1.38947	0.694735	−	0.719266i	$-0.255522\pi$
$163$	17.7396	1.38947	0.694735	+	0.719266i	$0.255522\pi$
$164$	1.93990	0.151481
$165$	5.71329	0.444779
$166$	−5.03094	−0.390476
$167$	−10.7470	−0.831629	−0.415815	−	0.909449i	$-0.636503\pi$
$167$	−10.7470	−0.831629	−0.415815	+	0.909449i	$0.636503\pi$
$168$	1.90874	0.147262
$169$	−2.93884	−0.226064
$170$	3.06325	0.234941
$171$	−7.26767	−0.555772
$172$	11.8934	0.906862
$173$	20.1069	1.52870	0.764350	−	0.644801i	$-0.223060\pi$
$173$	20.1069	1.52870	0.764350	+	0.644801i	$0.223060\pi$
$174$	8.04952	0.610233
$175$	8.36700	0.632486
$176$	−1.86510	−0.140587
$177$	1.00000	0.0751646
$178$	9.15169	0.685948
$179$	19.3908	1.44934	0.724668	−	0.689098i	$-0.241993\pi$
$179$	19.3908	1.44934	0.724668	+	0.689098i	$0.241993\pi$
$180$	−3.06325	−0.228321
$181$	−5.23378	−0.389024	−0.194512	−	0.980900i	$-0.562312\pi$
$181$	−5.23378	−0.389024	−0.194512	+	0.980900i	$0.562312\pi$
$182$	6.05439	0.448781
$183$	12.5988	0.931333
$184$	8.51270	0.627564
$185$	4.74303	0.348715
$186$	−9.13791	−0.670024
$187$	1.86510	0.136390
$188$	6.99942	0.510485
$189$	1.90874	0.138840
$190$	22.2627	1.61511
$191$	−21.1946	−1.53359	−0.766795	−	0.641893i	$-0.778149\pi$
$191$	−21.1946	−1.53359	−0.766795	+	0.641893i	$0.778149\pi$
$192$	1.00000	0.0721688
$193$	−3.99110	−0.287286	−0.143643	−	0.989630i	$-0.545882\pi$
$193$	−3.99110	−0.287286	−0.143643	+	0.989630i	$0.545882\pi$
$194$	−10.4576	−0.750814
$195$	−9.71644	−0.695809
$196$	−3.35672	−0.239766
$197$	10.4179	0.742241	0.371121	−	0.928585i	$-0.378974\pi$
$197$	10.4179	0.742241	0.371121	+	0.928585i	$0.378974\pi$
$198$	−1.86510	−0.132547
$199$	10.9130	0.773602	0.386801	−	0.922163i	$-0.373580\pi$
$199$	10.9130	0.773602	0.386801	+	0.922163i	$0.373580\pi$
$200$	4.38353	0.309962
$201$	−14.4822	−1.02149
$202$	13.0126	0.915560
$203$	15.3644	1.07837
$204$	−1.00000	−0.0700140
$205$	−5.94242	−0.415037
$206$	−1.32085	−0.0920283
$207$	8.51270	0.591673
$208$	3.17193	0.219934
$209$	13.5550	0.937616
$210$	−5.84695	−0.403478
$211$	−16.5806	−1.14146	−0.570728	−	0.821139i	$-0.693339\pi$
$211$	−16.5806	−1.14146	−0.570728	+	0.821139i	$0.693339\pi$
$212$	9.22153	0.633338
$213$	−15.5923	−1.06837
$214$	5.96565	0.407803
$215$	−36.4324	−2.48467
$216$	1.00000	0.0680414
$217$	−17.4419	−1.18403
$218$	6.59962	0.446983
$219$	14.1170	0.953938
$220$	5.71329	0.385190
$221$	−3.17193	−0.213367
$222$	−1.54836	−0.103919
$223$	5.86384	0.392672	0.196336	−	0.980537i	$-0.437096\pi$
$223$	5.86384	0.392672	0.196336	+	0.980537i	$0.437096\pi$
$224$	1.90874	0.127533
$225$	4.38353	0.292235
$226$	5.50149	0.365954
$227$	−21.7352	−1.44262	−0.721308	−	0.692615i	$-0.756459\pi$
$227$	−21.7352	−1.44262	−0.721308	+	0.692615i	$0.756459\pi$
$228$	−7.26767	−0.481313
$229$	−25.5909	−1.69109	−0.845546	−	0.533903i	$-0.820725\pi$
$229$	−25.5909	−1.69109	−0.845546	+	0.533903i	$0.820725\pi$
$230$	−26.0766	−1.71944
$231$	−3.56000	−0.234230
$232$	8.04952	0.528477
$233$	−12.8470	−0.841633	−0.420817	−	0.907146i	$-0.638256\pi$
$233$	−12.8470	−0.841633	−0.420817	+	0.907146i	$0.638256\pi$
$234$	3.17193	0.207356
$235$	−21.4410	−1.39866
$236$	1.00000	0.0650945
$237$	11.5528	0.750438
$238$	−1.90874	−0.123725
$239$	26.6205	1.72193	0.860967	−	0.508661i	$-0.169859\pi$
$239$	26.6205	1.72193	0.860967	+	0.508661i	$0.169859\pi$
$240$	−3.06325	−0.197732
$241$	20.0065	1.28874	0.644368	−	0.764716i	$-0.277121\pi$
$241$	20.0065	1.28874	0.644368	+	0.764716i	$0.277121\pi$
$242$	−7.52139	−0.483493
$243$	1.00000	0.0641500
$244$	12.5988	0.806558
$245$	10.2825	0.656924
$246$	1.93990	0.123684
$247$	−23.0526	−1.46680
$248$	−9.13791	−0.580258
$249$	−5.03094	−0.318823
$250$	1.88842	0.119434
$251$	−17.5243	−1.10612	−0.553061	−	0.833141i	$-0.686540\pi$
$251$	−17.5243	−1.10612	−0.553061	+	0.833141i	$0.686540\pi$
$252$	1.90874	0.120239
$253$	−15.8771	−0.998182
$254$	−2.64239	−0.165798
$255$	3.06325	0.191828
$256$	1.00000	0.0625000
$257$	3.69893	0.230733	0.115367	−	0.993323i	$-0.463196\pi$
$257$	3.69893	0.230733	0.115367	+	0.993323i	$0.463196\pi$
$258$	11.8934	0.740449
$259$	−2.95542	−0.183641
$260$	−9.71644	−0.602588
$261$	8.04952	0.498253
$262$	−12.1740	−0.752114
$263$	8.40891	0.518515	0.259258	−	0.965808i	$-0.416522\pi$
$263$	8.40891	0.518515	0.259258	+	0.965808i	$0.416522\pi$
$264$	−1.86510	−0.114789
$265$	−28.2479	−1.73525
$266$	−13.8721	−0.850552
$267$	9.15169	0.560074
$268$	−14.4822	−0.884640
$269$	19.2461	1.17345	0.586726	−	0.809785i	$-0.300416\pi$
$269$	19.2461	1.17345	0.586726	+	0.809785i	$0.300416\pi$
$270$	−3.06325	−0.186424
$271$	8.81278	0.535339	0.267669	−	0.963511i	$-0.413747\pi$
$271$	8.81278	0.535339	0.267669	+	0.963511i	$0.413747\pi$
$272$	−1.00000	−0.0606339
$273$	6.05439	0.366428
$274$	15.4018	0.930459
$275$	−8.17573	−0.493015
$276$	8.51270	0.512404
$277$	−4.47388	−0.268809	−0.134405	−	0.990927i	$-0.542912\pi$
$277$	−4.47388	−0.268809	−0.134405	+	0.990927i	$0.542912\pi$
$278$	−1.33885	−0.0802990
$279$	−9.13791	−0.547072
$280$	−5.84695	−0.349422
$281$	9.57633	0.571276	0.285638	−	0.958338i	$-0.407795\pi$
$281$	9.57633	0.571276	0.285638	+	0.958338i	$0.407795\pi$
$282$	6.99942	0.416809
$283$	26.1820	1.55636	0.778180	−	0.628041i	$-0.216143\pi$
$283$	26.1820	1.55636	0.778180	+	0.628041i	$0.216143\pi$
$284$	−15.5923	−0.925236
$285$	22.2627	1.31873
$286$	−5.91599	−0.349820
$287$	3.70277	0.218568
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−24.6577	−1.44795
$291$	−10.4576	−0.613037
$292$	14.1170	0.826135
$293$	−17.1574	−1.00235	−0.501173	−	0.865347i	$-0.667098\pi$
$293$	−17.1574	−1.00235	−0.501173	+	0.865347i	$0.667098\pi$
$294$	−3.35672	−0.195768
$295$	−3.06325	−0.178350
$296$	−1.54836	−0.0899969
$297$	−1.86510	−0.108224
$298$	11.0669	0.641090
$299$	27.0017	1.56155
$300$	4.38353	0.253083
$301$	22.7014	1.30848
$302$	2.11510	0.121710
$303$	13.0126	0.747552
$304$	−7.26767	−0.416829
$305$	−38.5934	−2.20985
$306$	−1.00000	−0.0571662
$307$	−31.2650	−1.78439	−0.892193	−	0.451655i	$-0.850834\pi$
$307$	−31.2650	−1.78439	−0.892193	+	0.451655i	$0.850834\pi$
$308$	−3.56000	−0.202850
$309$	−1.32085	−0.0751408
$310$	27.9917	1.58982
$311$	10.2754	0.582664	0.291332	−	0.956622i	$-0.405902\pi$
$311$	10.2754	0.582664	0.291332	+	0.956622i	$0.405902\pi$
$312$	3.17193	0.179575
$313$	−8.31687	−0.470097	−0.235049	−	0.971984i	$-0.575525\pi$
$313$	−8.31687	−0.470097	−0.235049	+	0.971984i	$0.575525\pi$
$314$	−1.46492	−0.0826702
$315$	−5.84695	−0.329438
$316$	11.5528	0.649898
$317$	34.6589	1.94664	0.973319	−	0.229454i	$-0.0736941\pi$
$317$	34.6589	1.94664	0.973319	+	0.229454i	$0.0736941\pi$
$318$	9.22153	0.517118
$319$	−15.0132	−0.840578
$320$	−3.06325	−0.171241
$321$	5.96565	0.332970
$322$	16.2485	0.905494
$323$	7.26767	0.404384
$324$	1.00000	0.0555556
$325$	13.9043	0.771269
$326$	17.7396	0.982504
$327$	6.59962	0.364960
$328$	1.93990	0.107113
$329$	13.3601	0.736564
$330$	5.71329	0.314506
$331$	20.9961	1.15405	0.577024	−	0.816727i	$-0.304214\pi$
$331$	20.9961	1.15405	0.577024	+	0.816727i	$0.304214\pi$
$332$	−5.03094	−0.276109
$333$	−1.54836	−0.0848499
$334$	−10.7470	−0.588051
$335$	44.3626	2.42379
$336$	1.90874	0.104130
$337$	−21.2365	−1.15682	−0.578412	−	0.815745i	$-0.696327\pi$
$337$	−21.2365	−1.15682	−0.578412	+	0.815745i	$0.696327\pi$
$338$	−2.93884	−0.159852
$339$	5.50149	0.298800
$340$	3.06325	0.166128
$341$	17.0431	0.922938
$342$	−7.26767	−0.392990
$343$	−19.7683	−1.06739
$344$	11.8934	0.641248
$345$	−26.0766	−1.40391
$346$	20.1069	1.08095
$347$	−28.0313	−1.50480	−0.752398	−	0.658708i	$-0.771103\pi$
$347$	−28.0313	−1.50480	−0.752398	+	0.658708i	$0.771103\pi$
$348$	8.04952	0.431500
$349$	−19.9217	−1.06638	−0.533191	−	0.845995i	$-0.679007\pi$
$349$	−19.9217	−1.06638	−0.533191	+	0.845995i	$0.679007\pi$
$350$	8.36700	0.447235
$351$	3.17193	0.169305
$352$	−1.86510	−0.0994104
$353$	−8.78498	−0.467577	−0.233789	−	0.972287i	$-0.575112\pi$
$353$	−8.78498	−0.467577	−0.233789	+	0.972287i	$0.575112\pi$
$354$	1.00000	0.0531494
$355$	47.7633	2.53501
$356$	9.15169	0.485038
$357$	−1.90874	−0.101021
$358$	19.3908	1.02484
$359$	20.7914	1.09733	0.548665	−	0.836042i	$-0.315136\pi$
$359$	20.7914	1.09733	0.548665	+	0.836042i	$0.315136\pi$
$360$	−3.06325	−0.161448
$361$	33.8190	1.77995
$362$	−5.23378	−0.275082
$363$	−7.52139	−0.394770
$364$	6.05439	0.317336
$365$	−43.2439	−2.26349
$366$	12.5988	0.658552
$367$	9.01517	0.470588	0.235294	−	0.971924i	$-0.424395\pi$
$367$	9.01517	0.470588	0.235294	+	0.971924i	$0.424395\pi$
$368$	8.51270	0.443755
$369$	1.93990	0.100987
$370$	4.74303	0.246579
$371$	17.6015	0.913824
$372$	−9.13791	−0.473778
$373$	−3.64578	−0.188771	−0.0943856	−	0.995536i	$-0.530089\pi$
$373$	−3.64578	−0.188771	−0.0943856	+	0.995536i	$0.530089\pi$
$374$	1.86510	0.0964422
$375$	1.88842	0.0975174
$376$	6.99942	0.360967
$377$	25.5326	1.31499
$378$	1.90874	0.0981749
$379$	19.0418	0.978113	0.489056	−	0.872252i	$-0.337341\pi$
$379$	19.0418	0.978113	0.489056	+	0.872252i	$0.337341\pi$
$380$	22.2627	1.14205
$381$	−2.64239	−0.135374
$382$	−21.1946	−1.08441
$383$	4.07572	0.208260	0.104130	−	0.994564i	$-0.466794\pi$
$383$	4.07572	0.208260	0.104130	+	0.994564i	$0.466794\pi$
$384$	1.00000	0.0510310
$385$	10.9052	0.555779
$386$	−3.99110	−0.203142
$387$	11.8934	0.604574
$388$	−10.4576	−0.530906
$389$	−9.04696	−0.458699	−0.229350	−	0.973344i	$-0.573660\pi$
$389$	−9.04696	−0.458699	−0.229350	+	0.973344i	$0.573660\pi$
$390$	−9.71644	−0.492011
$391$	−8.51270	−0.430506
$392$	−3.35672	−0.169540
$393$	−12.1740	−0.614099
$394$	10.4179	0.524844
$395$	−35.3893	−1.78063
$396$	−1.86510	−0.0937250
$397$	12.3610	0.620382	0.310191	−	0.950674i	$-0.399607\pi$
$397$	12.3610	0.620382	0.310191	+	0.950674i	$0.399607\pi$
$398$	10.9130	0.547019
$399$	−13.8721	−0.694472
$400$	4.38353	0.219176
$401$	7.16909	0.358007	0.179004	−	0.983848i	$-0.442713\pi$
$401$	7.16909	0.358007	0.179004	+	0.983848i	$0.442713\pi$
$402$	−14.4822	−0.722306
$403$	−28.9848	−1.44384
$404$	13.0126	0.647399
$405$	−3.06325	−0.152214
$406$	15.3644	0.762524
$407$	2.88786	0.143146
$408$	−1.00000	−0.0495074
$409$	−13.0294	−0.644261	−0.322130	−	0.946695i	$-0.604399\pi$
$409$	−13.0294	−0.644261	−0.322130	+	0.946695i	$0.604399\pi$
$410$	−5.94242	−0.293475
$411$	15.4018	0.759717
$412$	−1.32085	−0.0650739
$413$	1.90874	0.0939229
$414$	8.51270	0.418376
$415$	15.4110	0.756498
$416$	3.17193	0.155517
$417$	−1.33885	−0.0655638
$418$	13.5550	0.662995
$419$	11.8905	0.580888	0.290444	−	0.956892i	$-0.406197\pi$
$419$	11.8905	0.580888	0.290444	+	0.956892i	$0.406197\pi$
$420$	−5.84695	−0.285302
$421$	9.57765	0.466786	0.233393	−	0.972382i	$-0.425017\pi$
$421$	9.57765	0.466786	0.233393	+	0.972382i	$0.425017\pi$
$422$	−16.5806	−0.807131
$423$	6.99942	0.340323
$424$	9.22153	0.447837
$425$	−4.38353	−0.212632
$426$	−15.5923	−0.755452
$427$	24.0479	1.16376
$428$	5.96565	0.288360
$429$	−5.91599	−0.285626
$430$	−36.4324	−1.75693
$431$	−5.99714	−0.288872	−0.144436	−	0.989514i	$-0.546137\pi$
$431$	−5.99714	−0.288872	−0.144436	+	0.989514i	$0.546137\pi$
$432$	1.00000	0.0481125
$433$	−15.4325	−0.741640	−0.370820	−	0.928705i	$-0.620923\pi$
$433$	−15.4325	−0.741640	−0.370820	+	0.928705i	$0.620923\pi$
$434$	−17.4419	−0.837237
$435$	−24.6577	−1.18225
$436$	6.59962	0.316065
$437$	−61.8675	−2.95952
$438$	14.1170	0.674536
$439$	−7.60496	−0.362965	−0.181482	−	0.983394i	$-0.558090\pi$
$439$	−7.60496	−0.362965	−0.181482	+	0.983394i	$0.558090\pi$
$440$	5.71329	0.272370
$441$	−3.35672	−0.159844
$442$	−3.17193	−0.150873
$443$	24.2563	1.15245	0.576226	−	0.817291i	$-0.304525\pi$
$443$	24.2563	1.15245	0.576226	+	0.817291i	$0.304525\pi$
$444$	−1.54836	−0.0734821
$445$	−28.0339	−1.32894
$446$	5.86384	0.277661
$447$	11.0669	0.523448
$448$	1.90874	0.0901794
$449$	15.2162	0.718095	0.359048	−	0.933319i	$-0.383102\pi$
$449$	15.2162	0.718095	0.359048	+	0.933319i	$0.383102\pi$
$450$	4.38353	0.206641
$451$	−3.61812	−0.170371
$452$	5.50149	0.258768
$453$	2.11510	0.0993759
$454$	−21.7352	−1.02008
$455$	−18.5461	−0.869456
$456$	−7.26767	−0.340340
$457$	−16.3434	−0.764512	−0.382256	−	0.924056i	$-0.624853\pi$
$457$	−16.3434	−0.764512	−0.382256	+	0.924056i	$0.624853\pi$
$458$	−25.5909	−1.19578
$459$	−1.00000	−0.0466760
$460$	−26.0766	−1.21583
$461$	−7.03044	−0.327440	−0.163720	−	0.986507i	$-0.552349\pi$
$461$	−7.03044	−0.327440	−0.163720	+	0.986507i	$0.552349\pi$
$462$	−3.56000	−0.165626
$463$	−12.4715	−0.579597	−0.289799	−	0.957088i	$-0.593588\pi$
$463$	−12.4715	−0.579597	−0.289799	+	0.957088i	$0.593588\pi$
$464$	8.04952	0.373690
$465$	27.9917	1.29809
$466$	−12.8470	−0.595125
$467$	2.99402	0.138547	0.0692733	−	0.997598i	$-0.477932\pi$
$467$	2.99402	0.138547	0.0692733	+	0.997598i	$0.477932\pi$
$468$	3.17193	0.146623
$469$	−27.6427	−1.27642
$470$	−21.4410	−0.988999
$471$	−1.46492	−0.0674999
$472$	1.00000	0.0460287
$473$	−22.1824	−1.01995
$474$	11.5528	0.530640
$475$	−31.8580	−1.46175
$476$	−1.90874	−0.0874869
$477$	9.22153	0.422225
$478$	26.6205	1.21759
$479$	−23.9778	−1.09557	−0.547786	−	0.836619i	$-0.684529\pi$
$479$	−23.9778	−1.09557	−0.547786	+	0.836619i	$0.684529\pi$
$480$	−3.06325	−0.139818
$481$	−4.91131	−0.223936
$482$	20.0065	0.911273
$483$	16.2485	0.739333
$484$	−7.52139	−0.341881
$485$	32.0344	1.45461
$486$	1.00000	0.0453609
$487$	2.69053	0.121920	0.0609598	−	0.998140i	$-0.480584\pi$
$487$	2.69053	0.121920	0.0609598	+	0.998140i	$0.480584\pi$
$488$	12.5988	0.570323
$489$	17.7396	0.802211
$490$	10.2825	0.464515
$491$	8.74203	0.394522	0.197261	−	0.980351i	$-0.436795\pi$
$491$	8.74203	0.394522	0.197261	+	0.980351i	$0.436795\pi$
$492$	1.93990	0.0874576
$493$	−8.04952	−0.362532
$494$	−23.0526	−1.03718
$495$	5.71329	0.256793
$496$	−9.13791	−0.410304
$497$	−29.7617	−1.33500
$498$	−5.03094	−0.225442
$499$	2.07913	0.0930748	0.0465374	−	0.998917i	$-0.485181\pi$
$499$	2.07913	0.0930748	0.0465374	+	0.998917i	$0.485181\pi$
$500$	1.88842	0.0844525
$501$	−10.7470	−0.480141
$502$	−17.5243	−0.782146
$503$	−34.9928	−1.56025	−0.780125	−	0.625624i	$-0.784844\pi$
$503$	−34.9928	−1.56025	−0.780125	+	0.625624i	$0.784844\pi$
$504$	1.90874	0.0850220
$505$	−39.8608	−1.77378
$506$	−15.8771	−0.705822
$507$	−2.93884	−0.130518
$508$	−2.64239	−0.117237
$509$	−13.0253	−0.577337	−0.288668	−	0.957429i	$-0.593212\pi$
$509$	−13.0253	−0.577337	−0.288668	+	0.957429i	$0.593212\pi$
$510$	3.06325	0.135643
$511$	26.9456	1.19201
$512$	1.00000	0.0441942
$513$	−7.26767	−0.320875
$514$	3.69893	0.163153
$515$	4.04611	0.178293
$516$	11.8934	0.523577
$517$	−13.0546	−0.574142
$518$	−2.95542	−0.129854
$519$	20.1069	0.882596
$520$	−9.71644	−0.426094
$521$	−10.8944	−0.477293	−0.238647	−	0.971106i	$-0.576704\pi$
$521$	−10.8944	−0.477293	−0.238647	+	0.971106i	$0.576704\pi$
$522$	8.04952	0.352318
$523$	−5.13190	−0.224402	−0.112201	−	0.993686i	$-0.535790\pi$
$523$	−5.13190	−0.224402	−0.112201	+	0.993686i	$0.535790\pi$
$524$	−12.1740	−0.531825
$525$	8.36700	0.365166
$526$	8.40891	0.366646
$527$	9.13791	0.398053
$528$	−1.86510	−0.0811682
$529$	49.4660	2.15070
$530$	−28.2479	−1.22701
$531$	1.00000	0.0433963
$532$	−13.8721	−0.601431
$533$	6.15325	0.266527
$534$	9.15169	0.396032
$535$	−18.2743	−0.790066
$536$	−14.4822	−0.625535
$537$	19.3908	0.836775
$538$	19.2461	0.829756
$539$	6.26063	0.269664
$540$	−3.06325	−0.131821
$541$	−15.7222	−0.675950	−0.337975	−	0.941155i	$-0.609742\pi$
$541$	−15.7222	−0.675950	−0.337975	+	0.941155i	$0.609742\pi$
$542$	8.81278	0.378542
$543$	−5.23378	−0.224603
$544$	−1.00000	−0.0428746
$545$	−20.2163	−0.865972
$546$	6.05439	0.259104
$547$	9.70798	0.415083	0.207542	−	0.978226i	$-0.433454\pi$
$547$	9.70798	0.415083	0.207542	+	0.978226i	$0.433454\pi$
$548$	15.4018	0.657934
$549$	12.5988	0.537705
$550$	−8.17573	−0.348614
$551$	−58.5013	−2.49224
$552$	8.51270	0.362324
$553$	22.0513	0.937719
$554$	−4.47388	−0.190077
$555$	4.74303	0.201331
$556$	−1.33885	−0.0567800
$557$	−17.8758	−0.757424	−0.378712	−	0.925515i	$-0.623633\pi$
$557$	−17.8758	−0.757424	−0.378712	+	0.925515i	$0.623633\pi$
$558$	−9.13791	−0.386838
$559$	37.7250	1.59560
$560$	−5.84695	−0.247079
$561$	1.86510	0.0787447
$562$	9.57633	0.403953
$563$	−16.8911	−0.711875	−0.355937	−	0.934510i	$-0.615838\pi$
$563$	−16.8911	−0.711875	−0.355937	+	0.934510i	$0.615838\pi$
$564$	6.99942	0.294729
$565$	−16.8525	−0.708989
$566$	26.1820	1.10051
$567$	1.90874	0.0801595
$568$	−15.5923	−0.654240
$569$	−36.3197	−1.52260	−0.761300	−	0.648400i	$-0.775438\pi$
$569$	−36.3197	−1.52260	−0.761300	+	0.648400i	$0.775438\pi$
$570$	22.2627	0.932482
$571$	8.23907	0.344794	0.172397	−	0.985028i	$-0.444849\pi$
$571$	8.23907	0.344794	0.172397	+	0.985028i	$0.444849\pi$
$572$	−5.91599	−0.247360
$573$	−21.1946	−0.885418
$574$	3.70277	0.154551
$575$	37.3156	1.55617
$576$	1.00000	0.0416667
$577$	−32.7436	−1.36313	−0.681566	−	0.731757i	$-0.738701\pi$
$577$	−32.7436	−1.36313	−0.681566	+	0.731757i	$0.738701\pi$
$578$	1.00000	0.0415945
$579$	−3.99110	−0.165864
$580$	−24.6577	−1.02386
$581$	−9.60274	−0.398389
$582$	−10.4576	−0.433483
$583$	−17.1991	−0.712315
$584$	14.1170	0.584165
$585$	−9.71644	−0.401725
$586$	−17.1574	−0.708766
$587$	−1.60250	−0.0661421	−0.0330710	−	0.999453i	$-0.510529\pi$
$587$	−1.60250	−0.0661421	−0.0330710	+	0.999453i	$0.510529\pi$
$588$	−3.35672	−0.138429
$589$	66.4113	2.73643
$590$	−3.06325	−0.126112
$591$	10.4179	0.428533
$592$	−1.54836	−0.0636374
$593$	−8.75560	−0.359549	−0.179775	−	0.983708i	$-0.557537\pi$
$593$	−8.75560	−0.359549	−0.179775	+	0.983708i	$0.557537\pi$
$594$	−1.86510	−0.0765261
$595$	5.84695	0.239702
$596$	11.0669	0.453319
$597$	10.9130	0.446640
$598$	27.0017	1.10418
$599$	−30.0494	−1.22779	−0.613893	−	0.789390i	$-0.710397\pi$
$599$	−30.0494	−1.22779	−0.613893	+	0.789390i	$0.710397\pi$
$600$	4.38353	0.178957
$601$	−7.72781	−0.315224	−0.157612	−	0.987501i	$-0.550379\pi$
$601$	−7.72781	−0.315224	−0.157612	+	0.987501i	$0.550379\pi$
$602$	22.7014	0.925238
$603$	−14.4822	−0.589760
$604$	2.11510	0.0860621
$605$	23.0399	0.936706
$606$	13.0126	0.528599
$607$	−37.9302	−1.53954	−0.769769	−	0.638322i	$-0.779629\pi$
$607$	−37.9302	−1.53954	−0.769769	+	0.638322i	$0.779629\pi$
$608$	−7.26767	−0.294743
$609$	15.3644	0.622598
$610$	−38.5934	−1.56260
$611$	22.2017	0.898184
$612$	−1.00000	−0.0404226
$613$	−27.5552	−1.11294	−0.556472	−	0.830866i	$-0.687845\pi$
$613$	−27.5552	−1.11294	−0.556472	+	0.830866i	$0.687845\pi$
$614$	−31.2650	−1.26175
$615$	−5.94242	−0.239621
$616$	−3.56000	−0.143436
$617$	−3.16898	−0.127578	−0.0637892	−	0.997963i	$-0.520319\pi$
$617$	−3.16898	−0.127578	−0.0637892	+	0.997963i	$0.520319\pi$
$618$	−1.32085	−0.0531326
$619$	26.1464	1.05091	0.525456	−	0.850821i	$-0.323895\pi$
$619$	26.1464	1.05091	0.525456	+	0.850821i	$0.323895\pi$
$620$	27.9917	1.12417
$621$	8.51270	0.341603
$622$	10.2754	0.412006
$623$	17.4682	0.699848
$624$	3.17193	0.126979
$625$	−27.7023	−1.10809
$626$	−8.31687	−0.332409
$627$	13.5550	0.541333
$628$	−1.46492	−0.0584566
$629$	1.54836	0.0617373
$630$	−5.84695	−0.232948
$631$	−45.9720	−1.83012	−0.915059	−	0.403321i	$-0.867856\pi$
$631$	−45.9720	−1.83012	−0.915059	+	0.403321i	$0.867856\pi$
$632$	11.5528	0.459547
$633$	−16.5806	−0.659020
$634$	34.6589	1.37648
$635$	8.09432	0.321213
$636$	9.22153	0.365658
$637$	−10.6473	−0.421861
$638$	−15.0132	−0.594378
$639$	−15.5923	−0.616824
$640$	−3.06325	−0.121086
$641$	44.2790	1.74891	0.874457	−	0.485103i	$-0.161218\pi$
$641$	44.2790	1.74891	0.874457	+	0.485103i	$0.161218\pi$
$642$	5.96565	0.235445
$643$	−8.20490	−0.323570	−0.161785	−	0.986826i	$-0.551725\pi$
$643$	−8.20490	−0.323570	−0.161785	+	0.986826i	$0.551725\pi$
$644$	16.2485	0.640281
$645$	−36.4324	−1.43453
$646$	7.26767	0.285943
$647$	30.3114	1.19166	0.595832	−	0.803109i	$-0.296822\pi$
$647$	30.3114	1.19166	0.595832	+	0.803109i	$0.296822\pi$
$648$	1.00000	0.0392837
$649$	−1.86510	−0.0732117
$650$	13.9043	0.545370
$651$	−17.4419	−0.683601
$652$	17.7396	0.694735
$653$	−37.7781	−1.47837	−0.739186	−	0.673501i	$-0.764790\pi$
$653$	−37.7781	−1.47837	−0.739186	+	0.673501i	$0.764790\pi$
$654$	6.59962	0.258066
$655$	37.2922	1.45713
$656$	1.93990	0.0757405
$657$	14.1170	0.550756
$658$	13.3601	0.520829
$659$	−38.9939	−1.51899	−0.759493	−	0.650516i	$-0.774553\pi$
$659$	−38.9939	−1.51899	−0.759493	+	0.650516i	$0.774553\pi$
$660$	5.71329	0.222389
$661$	−42.0262	−1.63463	−0.817314	−	0.576192i	$-0.804538\pi$
$661$	−42.0262	−1.63463	−0.817314	+	0.576192i	$0.804538\pi$
$662$	20.9961	0.816036
$663$	−3.17193	−0.123188
$664$	−5.03094	−0.195238
$665$	42.4937	1.64783
$666$	−1.54836	−0.0599979
$667$	68.5232	2.65323
$668$	−10.7470	−0.415815
$669$	5.86384	0.226709
$670$	44.3626	1.71388
$671$	−23.4981	−0.907136
$672$	1.90874	0.0736312
$673$	−3.94772	−0.152173	−0.0760866	−	0.997101i	$-0.524243\pi$
$673$	−3.94772	−0.152173	−0.0760866	+	0.997101i	$0.524243\pi$
$674$	−21.2365	−0.817998
$675$	4.38353	0.168722
$676$	−2.93884	−0.113032
$677$	27.8433	1.07011	0.535053	−	0.844819i	$-0.320292\pi$
$677$	27.8433	1.07011	0.535053	+	0.844819i	$0.320292\pi$
$678$	5.50149	0.211283
$679$	−19.9609	−0.766028
$680$	3.06325	0.117470
$681$	−21.7352	−0.832895
$682$	17.0431	0.652616
$683$	13.5382	0.518026	0.259013	−	0.965874i	$-0.416603\pi$
$683$	13.5382	0.518026	0.259013	+	0.965874i	$0.416603\pi$
$684$	−7.26767	−0.277886
$685$	−47.1798	−1.80265
$686$	−19.7683	−0.754756
$687$	−25.5909	−0.976352
$688$	11.8934	0.453431
$689$	29.2501	1.11434
$690$	−26.0766	−0.992717
$691$	27.8888	1.06094	0.530470	−	0.847704i	$-0.322016\pi$
$691$	27.8888	1.06094	0.530470	+	0.847704i	$0.322016\pi$
$692$	20.1069	0.764350
$693$	−3.56000	−0.135233
$694$	−28.0313	−1.06405
$695$	4.10124	0.155569
$696$	8.04952	0.305116
$697$	−1.93990	−0.0734791
$698$	−19.9217	−0.754046
$699$	−12.8470	−0.485917
$700$	8.36700	0.316243
$701$	2.30297	0.0869821	0.0434911	−	0.999054i	$-0.486152\pi$
$701$	2.30297	0.0869821	0.0434911	+	0.999054i	$0.486152\pi$
$702$	3.17193	0.119717
$703$	11.2530	0.424415
$704$	−1.86510	−0.0702937
$705$	−21.4410	−0.807514
$706$	−8.78498	−0.330627
$707$	24.8376	0.934112
$708$	1.00000	0.0375823
$709$	−14.7690	−0.554661	−0.277330	−	0.960775i	$-0.589450\pi$
$709$	−14.7690	−0.554661	−0.277330	+	0.960775i	$0.589450\pi$
$710$	47.7633	1.79253
$711$	11.5528	0.433265
$712$	9.15169	0.342974
$713$	−77.7882	−2.91319
$714$	−1.90874	−0.0714327
$715$	18.1222	0.677731
$716$	19.3908	0.724668
$717$	26.6205	0.994159
$718$	20.7914	0.775930
$719$	10.3287	0.385194	0.192597	−	0.981278i	$-0.438309\pi$
$719$	10.3287	0.385194	0.192597	+	0.981278i	$0.438309\pi$
$720$	−3.06325	−0.114161
$721$	−2.52117	−0.0938931
$722$	33.8190	1.25861
$723$	20.0065	0.744052
$724$	−5.23378	−0.194512
$725$	35.2853	1.31046
$726$	−7.52139	−0.279145
$727$	−22.3603	−0.829298	−0.414649	−	0.909982i	$-0.636096\pi$
$727$	−22.3603	−0.829298	−0.414649	+	0.909982i	$0.636096\pi$
$728$	6.05439	0.224391
$729$	1.00000	0.0370370
$730$	−43.2439	−1.60053
$731$	−11.8934	−0.439893
$732$	12.5988	0.465667
$733$	−21.7256	−0.802454	−0.401227	−	0.915979i	$-0.631416\pi$
$733$	−21.7256	−0.802454	−0.401227	+	0.915979i	$0.631416\pi$
$734$	9.01517	0.332756
$735$	10.2825	0.379275
$736$	8.51270	0.313782
$737$	27.0108	0.994955
$738$	1.93990	0.0714089
$739$	18.8916	0.694939	0.347470	−	0.937691i	$-0.387041\pi$
$739$	18.8916	0.694939	0.347470	+	0.937691i	$0.387041\pi$
$740$	4.74303	0.174357
$741$	−23.0526	−0.846857
$742$	17.6015	0.646171
$743$	−6.77385	−0.248508	−0.124254	−	0.992250i	$-0.539654\pi$
$743$	−6.77385	−0.248508	−0.124254	+	0.992250i	$0.539654\pi$
$744$	−9.13791	−0.335012
$745$	−33.9008	−1.24203
$746$	−3.64578	−0.133481
$747$	−5.03094	−0.184072
$748$	1.86510	0.0681949
$749$	11.3869	0.416067
$750$	1.88842	0.0689552
$751$	−32.4461	−1.18397	−0.591987	−	0.805948i	$-0.701656\pi$
$751$	−32.4461	−1.18397	−0.591987	+	0.805948i	$0.701656\pi$
$752$	6.99942	0.255242
$753$	−17.5243	−0.638620
$754$	25.5326	0.929841
$755$	−6.47908	−0.235798
$756$	1.90874	0.0694201
$757$	−30.6033	−1.11229	−0.556147	−	0.831084i	$-0.687721\pi$
$757$	−30.6033	−1.11229	−0.556147	+	0.831084i	$0.687721\pi$
$758$	19.0418	0.691630
$759$	−15.8771	−0.576301
$760$	22.2627	0.807554
$761$	−29.1318	−1.05603	−0.528014	−	0.849236i	$-0.677063\pi$
$761$	−29.1318	−1.05603	−0.528014	+	0.849236i	$0.677063\pi$
$762$	−2.64239	−0.0957237
$763$	12.5970	0.456040
$764$	−21.1946	−0.766795
$765$	3.06325	0.110752
$766$	4.07572	0.147262
$767$	3.17193	0.114532
$768$	1.00000	0.0360844
$769$	5.57669	0.201101	0.100550	−	0.994932i	$-0.467940\pi$
$769$	5.57669	0.201101	0.100550	+	0.994932i	$0.467940\pi$
$770$	10.9052	0.392995
$771$	3.69893	0.133214
$772$	−3.99110	−0.143643
$773$	39.0021	1.40281	0.701404	−	0.712764i	$-0.252557\pi$
$773$	39.0021	1.40281	0.701404	+	0.712764i	$0.252557\pi$
$774$	11.8934	0.427499
$775$	−40.0562	−1.43886
$776$	−10.4576	−0.375407
$777$	−2.95542	−0.106025
$778$	−9.04696	−0.324349
$779$	−14.0986	−0.505134
$780$	−9.71644	−0.347904
$781$	29.0813	1.04061
$782$	−8.51270	−0.304413
$783$	8.04952	0.287667
$784$	−3.35672	−0.119883
$785$	4.48742	0.160163
$786$	−12.1740	−0.434233
$787$	11.5788	0.412738	0.206369	−	0.978474i	$-0.433835\pi$
$787$	11.5788	0.412738	0.206369	+	0.978474i	$0.433835\pi$
$788$	10.4179	0.371121
$789$	8.40891	0.299365
$790$	−35.3893	−1.25909
$791$	10.5009	0.373369
$792$	−1.86510	−0.0662736
$793$	39.9627	1.41912
$794$	12.3610	0.438677
$795$	−28.2479	−1.00185
$796$	10.9130	0.386801
$797$	−40.3721	−1.43005	−0.715026	−	0.699098i	$-0.753585\pi$
$797$	−40.3721	−1.43005	−0.715026	+	0.699098i	$0.753585\pi$
$798$	−13.8721	−0.491066
$799$	−6.99942	−0.247622
$800$	4.38353	0.154981
$801$	9.15169	0.323359
$802$	7.16909	0.253149
$803$	−26.3297	−0.929153
$804$	−14.4822	−0.510747
$805$	−49.7733	−1.75428
$806$	−28.9848	−1.02095
$807$	19.2461	0.677493
$808$	13.0126	0.457780
$809$	−42.5447	−1.49579	−0.747895	−	0.663817i	$-0.768935\pi$
$809$	−42.5447	−1.49579	−0.747895	+	0.663817i	$0.768935\pi$
$810$	−3.06325	−0.107632
$811$	22.2322	0.780679	0.390340	−	0.920671i	$-0.372358\pi$
$811$	22.2322	0.780679	0.390340	+	0.920671i	$0.372358\pi$
$812$	15.3644	0.539186
$813$	8.81278	0.309078
$814$	2.88786	0.101219
$815$	−54.3408	−1.90348
$816$	−1.00000	−0.0350070
$817$	−86.4371	−3.02405
$818$	−13.0294	−0.455561
$819$	6.05439	0.211558
$820$	−5.94242	−0.207518
$821$	−7.35165	−0.256574	−0.128287	−	0.991737i	$-0.540948\pi$
$821$	−7.35165	−0.256574	−0.128287	+	0.991737i	$0.540948\pi$
$822$	15.4018	0.537201
$823$	36.5597	1.27439	0.637195	−	0.770703i	$-0.280095\pi$
$823$	36.5597	1.27439	0.637195	+	0.770703i	$0.280095\pi$
$824$	−1.32085	−0.0460142
$825$	−8.17573	−0.284642
$826$	1.90874	0.0664135
$827$	−1.71120	−0.0595044	−0.0297522	−	0.999557i	$-0.509472\pi$
$827$	−1.71120	−0.0595044	−0.0297522	+	0.999557i	$0.509472\pi$
$828$	8.51270	0.295837
$829$	26.8063	0.931022	0.465511	−	0.885042i	$-0.345871\pi$
$829$	26.8063	0.931022	0.465511	+	0.885042i	$0.345871\pi$
$830$	15.4110	0.534925
$831$	−4.47388	−0.155197
$832$	3.17193	0.109967
$833$	3.35672	0.116303
$834$	−1.33885	−0.0463606
$835$	32.9209	1.13927
$836$	13.5550	0.468808
$837$	−9.13791	−0.315852
$838$	11.8905	0.410750
$839$	−27.5070	−0.949649	−0.474824	−	0.880081i	$-0.657488\pi$
$839$	−27.5070	−0.949649	−0.474824	+	0.880081i	$0.657488\pi$
$840$	−5.84695	−0.201739
$841$	35.7948	1.23431
$842$	9.57765	0.330068
$843$	9.57633	0.329826
$844$	−16.5806	−0.570728
$845$	9.00241	0.309692
$846$	6.99942	0.240645
$847$	−14.3564	−0.493290
$848$	9.22153	0.316669
$849$	26.1820	0.898565
$850$	−4.38353	−0.150354
$851$	−13.1808	−0.451831
$852$	−15.5923	−0.534185
$853$	7.82933	0.268071	0.134036	−	0.990977i	$-0.457206\pi$
$853$	7.82933	0.268071	0.134036	+	0.990977i	$0.457206\pi$
$854$	24.0479	0.822902
$855$	22.2627	0.761369
$856$	5.96565	0.203902
$857$	34.5907	1.18159	0.590797	−	0.806820i	$-0.298813\pi$
$857$	34.5907	1.18159	0.590797	+	0.806820i	$0.298813\pi$
$858$	−5.91599	−0.201968
$859$	−35.3940	−1.20763	−0.603814	−	0.797125i	$-0.706353\pi$
$859$	−35.3940	−1.20763	−0.603814	+	0.797125i	$0.706353\pi$
$860$	−36.4324	−1.24234
$861$	3.70277	0.126190
$862$	−5.99714	−0.204264
$863$	28.0992	0.956507	0.478254	−	0.878222i	$-0.341270\pi$
$863$	28.0992	0.956507	0.478254	+	0.878222i	$0.341270\pi$
$864$	1.00000	0.0340207
$865$	−61.5926	−2.09421
$866$	−15.4325	−0.524418
$867$	1.00000	0.0339618
$868$	−17.4419	−0.592016
$869$	−21.5472	−0.730940
$870$	−24.6577	−0.835976
$871$	−45.9365	−1.55650
$872$	6.59962	0.223491
$873$	−10.4576	−0.353937
$874$	−61.8675	−2.09270
$875$	3.60449	0.121854
$876$	14.1170	0.476969
$877$	23.4088	0.790461	0.395230	−	0.918582i	$-0.370665\pi$
$877$	23.4088	0.790461	0.395230	+	0.918582i	$0.370665\pi$
$878$	−7.60496	−0.256655
$879$	−17.1574	−0.578705
$880$	5.71329	0.192595
$881$	39.0906	1.31700	0.658498	−	0.752583i	$-0.271192\pi$
$881$	39.0906	1.31700	0.658498	+	0.752583i	$0.271192\pi$
$882$	−3.35672	−0.113027
$883$	−19.3219	−0.650234	−0.325117	−	0.945674i	$-0.605404\pi$
$883$	−19.3219	−0.650234	−0.325117	+	0.945674i	$0.605404\pi$
$884$	−3.17193	−0.106684
$885$	−3.06325	−0.102970
$886$	24.2563	0.814906
$887$	−5.93270	−0.199201	−0.0996003	−	0.995028i	$-0.531756\pi$
$887$	−5.93270	−0.199201	−0.0996003	+	0.995028i	$0.531756\pi$
$888$	−1.54836	−0.0519597
$889$	−5.04363	−0.169158
$890$	−28.0339	−0.939700
$891$	−1.86510	−0.0624833
$892$	5.86384	0.196336
$893$	−50.8694	−1.70228
$894$	11.0669	0.370134
$895$	−59.3989	−1.98549
$896$	1.90874	0.0637665
$897$	27.0017	0.901561
$898$	15.2162	0.507770
$899$	−73.5558	−2.45322
$900$	4.38353	0.146118
$901$	−9.22153	−0.307214
$902$	−3.61812	−0.120470
$903$	22.7014	0.755454
$904$	5.50149	0.182977
$905$	16.0324	0.532935
$906$	2.11510	0.0702694
$907$	−21.0407	−0.698644	−0.349322	−	0.937003i	$-0.613588\pi$
$907$	−21.0407	−0.698644	−0.349322	+	0.937003i	$0.613588\pi$
$908$	−21.7352	−0.721308
$909$	13.0126	0.431599
$910$	−18.5461	−0.614799
$911$	1.94418	0.0644136	0.0322068	−	0.999481i	$-0.489746\pi$
$911$	1.94418	0.0644136	0.0322068	+	0.999481i	$0.489746\pi$
$912$	−7.26767	−0.240657
$913$	9.38322	0.310539
$914$	−16.3434	−0.540592
$915$	−38.5934	−1.27586
$916$	−25.5909	−0.845546
$917$	−23.2370	−0.767355
$918$	−1.00000	−0.0330049
$919$	39.4867	1.30254	0.651272	−	0.758844i	$-0.274236\pi$
$919$	39.4867	1.30254	0.651272	+	0.758844i	$0.274236\pi$
$920$	−26.0766	−0.859719
$921$	−31.2650	−1.03022
$922$	−7.03044	−0.231535
$923$	−49.4579	−1.62793
$924$	−3.56000	−0.117115
$925$	−6.78730	−0.223165
$926$	−12.4715	−0.409837
$927$	−1.32085	−0.0433826
$928$	8.04952	0.264239
$929$	−38.0744	−1.24918	−0.624590	−	0.780953i	$-0.714734\pi$
$929$	−38.0744	−1.24918	−0.624590	+	0.780953i	$0.714734\pi$
$930$	27.9917	0.917885
$931$	24.3955	0.799531
$932$	−12.8470	−0.420817
$933$	10.2754	0.336401
$934$	2.99402	0.0979673
$935$	−5.71329	−0.186844
$936$	3.17193	0.103678
$937$	−15.6410	−0.510969	−0.255485	−	0.966813i	$-0.582235\pi$
$937$	−15.6410	−0.510969	−0.255485	+	0.966813i	$0.582235\pi$
$938$	−27.6427	−0.902566
$939$	−8.31687	−0.271411
$940$	−21.4410	−0.699328
$941$	−25.0973	−0.818149	−0.409074	−	0.912501i	$-0.634148\pi$
$941$	−25.0973	−0.818149	−0.409074	+	0.912501i	$0.634148\pi$
$942$	−1.46492	−0.0477296
$943$	16.5138	0.537764
$944$	1.00000	0.0325472
$945$	−5.84695	−0.190201
$946$	−22.1824	−0.721212
$947$	45.9428	1.49294	0.746470	−	0.665419i	$-0.231747\pi$
$947$	45.9428	1.49294	0.746470	+	0.665419i	$0.231747\pi$
$948$	11.5528	0.375219
$949$	44.7782	1.45356
$950$	−31.8580	−1.03361
$951$	34.6589	1.12389
$952$	−1.90874	−0.0618626
$953$	−24.7193	−0.800737	−0.400368	−	0.916354i	$-0.631118\pi$
$953$	−24.7193	−0.800737	−0.400368	+	0.916354i	$0.631118\pi$
$954$	9.22153	0.298558
$955$	64.9245	2.10091
$956$	26.6205	0.860967
$957$	−15.0132	−0.485308
$958$	−23.9778	−0.774686
$959$	29.3981	0.949314
$960$	−3.06325	−0.0988661
$961$	52.5013	1.69359
$962$	−4.91131	−0.158347
$963$	5.96565	0.192240
$964$	20.0065	0.644368
$965$	12.2258	0.393561
$966$	16.2485	0.522787
$967$	−37.3300	−1.20045	−0.600225	−	0.799831i	$-0.704922\pi$
$967$	−37.3300	−1.20045	−0.600225	+	0.799831i	$0.704922\pi$
$968$	−7.52139	−0.241747
$969$	7.26767	0.233471
$970$	32.0344	1.02856
$971$	−28.4071	−0.911626	−0.455813	−	0.890076i	$-0.650651\pi$
$971$	−28.4071	−0.911626	−0.455813	+	0.890076i	$0.650651\pi$
$972$	1.00000	0.0320750
$973$	−2.55552	−0.0819261
$974$	2.69053	0.0862101
$975$	13.9043	0.445292
$976$	12.5988	0.403279
$977$	−38.1947	−1.22196	−0.610978	−	0.791648i	$-0.709224\pi$
$977$	−38.1947	−1.22196	−0.610978	+	0.791648i	$0.709224\pi$
$978$	17.7396	0.567249
$979$	−17.0688	−0.545523
$980$	10.2825	0.328462
$981$	6.59962	0.210710
$982$	8.74203	0.278969
$983$	−29.5750	−0.943296	−0.471648	−	0.881787i	$-0.656341\pi$
$983$	−29.5750	−0.943296	−0.471648	+	0.881787i	$0.656341\pi$
$984$	1.93990	0.0618419
$985$	−31.9125	−1.01682
$986$	−8.04952	−0.256349
$987$	13.3601	0.425255
$988$	−23.0526	−0.733400
$989$	101.245	3.21940
$990$	5.71329	0.181580
$991$	−7.80301	−0.247871	−0.123935	−	0.992290i	$-0.539552\pi$
$991$	−7.80301	−0.247871	−0.123935	+	0.992290i	$0.539552\pi$
$992$	−9.13791	−0.290129
$993$	20.9961	0.666290
$994$	−29.7617	−0.943984
$995$	−33.4293	−1.05978
$996$	−5.03094	−0.159411
$997$	46.6413	1.47714	0.738572	−	0.674175i	$-0.235500\pi$
$997$	46.6413	1.47714	0.738572	+	0.674175i	$0.235500\pi$
$998$	2.07913	0.0658138
$999$	−1.54836	−0.0489881

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.ba.1.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.ba.1.2	✓	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.06325 q^{5} +1.00000 q^{6} +1.90874 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.06325 q^{5} +1.00000 q^{6} +1.90874 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.06325 q^{10} -1.86510 q^{11} +1.00000 q^{12} +3.17193 q^{13} +1.90874 q^{14} -3.06325 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -7.26767 q^{19} -3.06325 q^{20} +1.90874 q^{21} -1.86510 q^{22} +8.51270 q^{23} +1.00000 q^{24} +4.38353 q^{25} +3.17193 q^{26} +1.00000 q^{27} +1.90874 q^{28} +8.04952 q^{29} -3.06325 q^{30} -9.13791 q^{31} +1.00000 q^{32} -1.86510 q^{33} -1.00000 q^{34} -5.84695 q^{35} +1.00000 q^{36} -1.54836 q^{37} -7.26767 q^{38} +3.17193 q^{39} -3.06325 q^{40} +1.93990 q^{41} +1.90874 q^{42} +11.8934 q^{43} -1.86510 q^{44} -3.06325 q^{45} +8.51270 q^{46} +6.99942 q^{47} +1.00000 q^{48} -3.35672 q^{49} +4.38353 q^{50} -1.00000 q^{51} +3.17193 q^{52} +9.22153 q^{53} +1.00000 q^{54} +5.71329 q^{55} +1.90874 q^{56} -7.26767 q^{57} +8.04952 q^{58} +1.00000 q^{59} -3.06325 q^{60} +12.5988 q^{61} -9.13791 q^{62} +1.90874 q^{63} +1.00000 q^{64} -9.71644 q^{65} -1.86510 q^{66} -14.4822 q^{67} -1.00000 q^{68} +8.51270 q^{69} -5.84695 q^{70} -15.5923 q^{71} +1.00000 q^{72} +14.1170 q^{73} -1.54836 q^{74} +4.38353 q^{75} -7.26767 q^{76} -3.56000 q^{77} +3.17193 q^{78} +11.5528 q^{79} -3.06325 q^{80} +1.00000 q^{81} +1.93990 q^{82} -5.03094 q^{83} +1.90874 q^{84} +3.06325 q^{85} +11.8934 q^{86} +8.04952 q^{87} -1.86510 q^{88} +9.15169 q^{89} -3.06325 q^{90} +6.05439 q^{91} +8.51270 q^{92} -9.13791 q^{93} +6.99942 q^{94} +22.2627 q^{95} +1.00000 q^{96} -10.4576 q^{97} -3.35672 q^{98} -1.86510 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 8 q^{5} + 12 q^{6} + 5 q^{7} + 12 q^{8} + 12 q^{9} + 8 q^{10} + 11 q^{11} + 12 q^{12} + 6 q^{13} + 5 q^{14} + 8 q^{15} + 12 q^{16} - 12 q^{17} + 12 q^{18} + 3 q^{19} + 8 q^{20} + 5 q^{21} + 11 q^{22} + 22 q^{23} + 12 q^{24} + 22 q^{25} + 6 q^{26} + 12 q^{27} + 5 q^{28} + 26 q^{29} + 8 q^{30} + q^{31} + 12 q^{32} + 11 q^{33} - 12 q^{34} + 24 q^{35} + 12 q^{36} + 10 q^{37} + 3 q^{38} + 6 q^{39} + 8 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 11 q^{44} + 8 q^{45} + 22 q^{46} + 6 q^{47} + 12 q^{48} + 11 q^{49} + 22 q^{50} - 12 q^{51} + 6 q^{52} + 10 q^{53} + 12 q^{54} + 15 q^{55} + 5 q^{56} + 3 q^{57} + 26 q^{58} + 12 q^{59} + 8 q^{60} + 15 q^{61} + q^{62} + 5 q^{63} + 12 q^{64} + 4 q^{65} + 11 q^{66} + 4 q^{67} - 12 q^{68} + 22 q^{69} + 24 q^{70} + 10 q^{71} + 12 q^{72} + 24 q^{73} + 10 q^{74} + 22 q^{75} + 3 q^{76} + 24 q^{77} + 6 q^{78} + 23 q^{79} + 8 q^{80} + 12 q^{81} + 16 q^{82} + 5 q^{84} - 8 q^{85} + 23 q^{86} + 26 q^{87} + 11 q^{88} + 13 q^{89} + 8 q^{90} + 3 q^{91} + 22 q^{92} + q^{93} + 6 q^{94} + 11 q^{95} + 12 q^{96} + 13 q^{97} + 11 q^{98} + 11 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 8 * q^5 + 12 * q^6 + 5 * q^7 + 12 * q^8 + 12 * q^9 + 8 * q^10 + 11 * q^11 + 12 * q^12 + 6 * q^13 + 5 * q^14 + 8 * q^15 + 12 * q^16 - 12 * q^17 + 12 * q^18 + 3 * q^19 + 8 * q^20 + 5 * q^21 + 11 * q^22 + 22 * q^23 + 12 * q^24 + 22 * q^25 + 6 * q^26 + 12 * q^27 + 5 * q^28 + 26 * q^29 + 8 * q^30 + q^31 + 12 * q^32 + 11 * q^33 - 12 * q^34 + 24 * q^35 + 12 * q^36 + 10 * q^37 + 3 * q^38 + 6 * q^39 + 8 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 11 * q^44 + 8 * q^45 + 22 * q^46 + 6 * q^47 + 12 * q^48 + 11 * q^49 + 22 * q^50 - 12 * q^51 + 6 * q^52 + 10 * q^53 + 12 * q^54 + 15 * q^55 + 5 * q^56 + 3 * q^57 + 26 * q^58 + 12 * q^59 + 8 * q^60 + 15 * q^61 + q^62 + 5 * q^63 + 12 * q^64 + 4 * q^65 + 11 * q^66 + 4 * q^67 - 12 * q^68 + 22 * q^69 + 24 * q^70 + 10 * q^71 + 12 * q^72 + 24 * q^73 + 10 * q^74 + 22 * q^75 + 3 * q^76 + 24 * q^77 + 6 * q^78 + 23 * q^79 + 8 * q^80 + 12 * q^81 + 16 * q^82 + 5 * q^84 - 8 * q^85 + 23 * q^86 + 26 * q^87 + 11 * q^88 + 13 * q^89 + 8 * q^90 + 3 * q^91 + 22 * q^92 + q^93 + 6 * q^94 + 11 * q^95 + 12 * q^96 + 13 * q^97 + 11 * q^98 + 11 * q^99

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