LMFDB - Embedded newform 6010.2.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 9 x^{14} + 75 x^{13} - 178 x^{12} - 232 x^{11} + 872 x^{10} + 228 x^{9} - 1986 x^{8} + \cdots - 10 $ x^16 - 8x^15 + 9x^14 + 75x^13 - 178x^12 - 232x^11 + 872x^10 + 228x^9 - 1986x^8 + 164x^7 + 2332x^6 - 440x^5 - 1344x^4 + 244x^3 + 295x^2 - 41*x - 10
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$2.75851$ of defining polynomial
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.75851 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.75851 q^{6} -0.115571 q^{7} +1.00000 q^{8} +0.0923708 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.75851 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.75851 q^{6} -0.115571 q^{7} +1.00000 q^{8} +0.0923708 q^{9} +1.00000 q^{10} -1.05946 q^{11} +1.75851 q^{12} -5.92506 q^{13} -0.115571 q^{14} +1.75851 q^{15} +1.00000 q^{16} -7.65454 q^{17} +0.0923708 q^{18} -6.01137 q^{19} +1.00000 q^{20} -0.203233 q^{21} -1.05946 q^{22} -0.155960 q^{23} +1.75851 q^{24} +1.00000 q^{25} -5.92506 q^{26} -5.11311 q^{27} -0.115571 q^{28} +3.22489 q^{29} +1.75851 q^{30} -3.14463 q^{31} +1.00000 q^{32} -1.86308 q^{33} -7.65454 q^{34} -0.115571 q^{35} +0.0923708 q^{36} +6.44860 q^{37} -6.01137 q^{38} -10.4193 q^{39} +1.00000 q^{40} -0.499853 q^{41} -0.203233 q^{42} -3.20309 q^{43} -1.05946 q^{44} +0.0923708 q^{45} -0.155960 q^{46} +5.42049 q^{47} +1.75851 q^{48} -6.98664 q^{49} +1.00000 q^{50} -13.4606 q^{51} -5.92506 q^{52} +4.44313 q^{53} -5.11311 q^{54} -1.05946 q^{55} -0.115571 q^{56} -10.5711 q^{57} +3.22489 q^{58} +2.13926 q^{59} +1.75851 q^{60} +5.01100 q^{61} -3.14463 q^{62} -0.0106754 q^{63} +1.00000 q^{64} -5.92506 q^{65} -1.86308 q^{66} -15.5059 q^{67} -7.65454 q^{68} -0.274258 q^{69} -0.115571 q^{70} +8.80287 q^{71} +0.0923708 q^{72} -11.1478 q^{73} +6.44860 q^{74} +1.75851 q^{75} -6.01137 q^{76} +0.122443 q^{77} -10.4193 q^{78} -2.78887 q^{79} +1.00000 q^{80} -9.26858 q^{81} -0.499853 q^{82} +5.34566 q^{83} -0.203233 q^{84} -7.65454 q^{85} -3.20309 q^{86} +5.67101 q^{87} -1.05946 q^{88} -3.18269 q^{89} +0.0923708 q^{90} +0.684765 q^{91} -0.155960 q^{92} -5.52987 q^{93} +5.42049 q^{94} -6.01137 q^{95} +1.75851 q^{96} -7.38623 q^{97} -6.98664 q^{98} -0.0978633 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9} + 16 q^{10} - 14 q^{11} - 8 q^{12} - 20 q^{13} - 10 q^{14} - 8 q^{15} + 16 q^{16} - 27 q^{17} - 2 q^{18} - 17 q^{19} + 16 q^{20} - 12 q^{21} - 14 q^{22} - 9 q^{23} - 8 q^{24} + 16 q^{25} - 20 q^{26} - 11 q^{27} - 10 q^{28} - 23 q^{29} - 8 q^{30} - 21 q^{31} + 16 q^{32} - 9 q^{33} - 27 q^{34} - 10 q^{35} - 2 q^{36} - 16 q^{37} - 17 q^{38} - 6 q^{39} + 16 q^{40} - 35 q^{41} - 12 q^{42} + 3 q^{43} - 14 q^{44} - 2 q^{45} - 9 q^{46} - 25 q^{47} - 8 q^{48} - 24 q^{49} + 16 q^{50} - q^{51} - 20 q^{52} - 39 q^{53} - 11 q^{54} - 14 q^{55} - 10 q^{56} - 6 q^{57} - 23 q^{58} - 32 q^{59} - 8 q^{60} - 38 q^{61} - 21 q^{62} + q^{63} + 16 q^{64} - 20 q^{65} - 9 q^{66} + 5 q^{67} - 27 q^{68} - 25 q^{69} - 10 q^{70} - 16 q^{71} - 2 q^{72} - 17 q^{73} - 16 q^{74} - 8 q^{75} - 17 q^{76} - 34 q^{77} - 6 q^{78} - 40 q^{79} + 16 q^{80} - 28 q^{81} - 35 q^{82} - 22 q^{83} - 12 q^{84} - 27 q^{85} + 3 q^{86} + 10 q^{87} - 14 q^{88} - 46 q^{89} - 2 q^{90} - q^{91} - 9 q^{92} + 14 q^{93} - 25 q^{94} - 17 q^{95} - 8 q^{96} - 21 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9 + 16 * q^10 - 14 * q^11 - 8 * q^12 - 20 * q^13 - 10 * q^14 - 8 * q^15 + 16 * q^16 - 27 * q^17 - 2 * q^18 - 17 * q^19 + 16 * q^20 - 12 * q^21 - 14 * q^22 - 9 * q^23 - 8 * q^24 + 16 * q^25 - 20 * q^26 - 11 * q^27 - 10 * q^28 - 23 * q^29 - 8 * q^30 - 21 * q^31 + 16 * q^32 - 9 * q^33 - 27 * q^34 - 10 * q^35 - 2 * q^36 - 16 * q^37 - 17 * q^38 - 6 * q^39 + 16 * q^40 - 35 * q^41 - 12 * q^42 + 3 * q^43 - 14 * q^44 - 2 * q^45 - 9 * q^46 - 25 * q^47 - 8 * q^48 - 24 * q^49 + 16 * q^50 - q^51 - 20 * q^52 - 39 * q^53 - 11 * q^54 - 14 * q^55 - 10 * q^56 - 6 * q^57 - 23 * q^58 - 32 * q^59 - 8 * q^60 - 38 * q^61 - 21 * q^62 + q^63 + 16 * q^64 - 20 * q^65 - 9 * q^66 + 5 * q^67 - 27 * q^68 - 25 * q^69 - 10 * q^70 - 16 * q^71 - 2 * q^72 - 17 * q^73 - 16 * q^74 - 8 * q^75 - 17 * q^76 - 34 * q^77 - 6 * q^78 - 40 * q^79 + 16 * q^80 - 28 * q^81 - 35 * q^82 - 22 * q^83 - 12 * q^84 - 27 * q^85 + 3 * q^86 + 10 * q^87 - 14 * q^88 - 46 * q^89 - 2 * q^90 - q^91 - 9 * q^92 + 14 * q^93 - 25 * q^94 - 17 * q^95 - 8 * q^96 - 21 * q^97 - 24 * q^98 + 15 * 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
$3$	1.75851	1.01528	0.507639	−	0.861570i	$-0.330518\pi$
$3$	1.75851	1.01528	0.507639	+	0.861570i	$0.330518\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.75851	0.717910
$7$	−0.115571	−0.0436818	−0.0218409	−	0.999761i	$-0.506953\pi$
$7$	−0.115571	−0.0436818	−0.0218409	+	0.999761i	$0.506953\pi$
$8$	1.00000	0.353553
$9$	0.0923708	0.0307903
$10$	1.00000	0.316228
$11$	−1.05946	−0.319440	−0.159720	−	0.987162i	$-0.551059\pi$
$11$	−1.05946	−0.319440	−0.159720	+	0.987162i	$0.551059\pi$
$12$	1.75851	0.507639
$13$	−5.92506	−1.64332	−0.821658	−	0.569981i	$-0.806950\pi$
$13$	−5.92506	−1.64332	−0.821658	+	0.569981i	$0.806950\pi$
$14$	−0.115571	−0.0308877
$15$	1.75851	0.454046
$16$	1.00000	0.250000
$17$	−7.65454	−1.85650	−0.928249	−	0.371960i	$-0.878686\pi$
$17$	−7.65454	−1.85650	−0.928249	+	0.371960i	$0.878686\pi$
$18$	0.0923708	0.0217720
$19$	−6.01137	−1.37910	−0.689551	−	0.724237i	$-0.742192\pi$
$19$	−6.01137	−1.37910	−0.689551	+	0.724237i	$0.742192\pi$
$20$	1.00000	0.223607
$21$	−0.203233	−0.0443491
$22$	−1.05946	−0.225878
$23$	−0.155960	−0.0325199	−0.0162600	−	0.999868i	$-0.505176\pi$
$23$	−0.155960	−0.0325199	−0.0162600	+	0.999868i	$0.505176\pi$
$24$	1.75851	0.358955
$25$	1.00000	0.200000
$26$	−5.92506	−1.16200
$27$	−5.11311	−0.984018
$28$	−0.115571	−0.0218409
$29$	3.22489	0.598847	0.299423	−	0.954120i	$-0.403206\pi$
$29$	3.22489	0.598847	0.299423	+	0.954120i	$0.403206\pi$
$30$	1.75851	0.321059
$31$	−3.14463	−0.564791	−0.282396	−	0.959298i	$-0.591129\pi$
$31$	−3.14463	−0.564791	−0.282396	+	0.959298i	$0.591129\pi$
$32$	1.00000	0.176777
$33$	−1.86308	−0.324320
$34$	−7.65454	−1.31274
$35$	−0.115571	−0.0195351
$36$	0.0923708	0.0153951
$37$	6.44860	1.06014	0.530072	−	0.847953i	$-0.322165\pi$
$37$	6.44860	1.06014	0.530072	+	0.847953i	$0.322165\pi$
$38$	−6.01137	−0.975173
$39$	−10.4193	−1.66842
$40$	1.00000	0.158114
$41$	−0.499853	−0.0780639	−0.0390319	−	0.999238i	$-0.512427\pi$
$41$	−0.499853	−0.0780639	−0.0390319	+	0.999238i	$0.512427\pi$
$42$	−0.203233	−0.0313596
$43$	−3.20309	−0.488467	−0.244233	−	0.969716i	$-0.578536\pi$
$43$	−3.20309	−0.488467	−0.244233	+	0.969716i	$0.578536\pi$
$44$	−1.05946	−0.159720
$45$	0.0923708	0.0137698
$46$	−0.155960	−0.0229951
$47$	5.42049	0.790660	0.395330	−	0.918539i	$-0.370630\pi$
$47$	5.42049	0.790660	0.395330	+	0.918539i	$0.370630\pi$
$48$	1.75851	0.253820
$49$	−6.98664	−0.998092
$50$	1.00000	0.141421
$51$	−13.4606	−1.88486
$52$	−5.92506	−0.821658
$53$	4.44313	0.610311	0.305156	−	0.952303i	$-0.401292\pi$
$53$	4.44313	0.610311	0.305156	+	0.952303i	$0.401292\pi$
$54$	−5.11311	−0.695806
$55$	−1.05946	−0.142858
$56$	−0.115571	−0.0154438
$57$	−10.5711	−1.40017
$58$	3.22489	0.423449
$59$	2.13926	0.278508	0.139254	−	0.990257i	$-0.455530\pi$
$59$	2.13926	0.278508	0.139254	+	0.990257i	$0.455530\pi$
$60$	1.75851	0.227023
$61$	5.01100	0.641593	0.320796	−	0.947148i	$-0.396050\pi$
$61$	5.01100	0.641593	0.320796	+	0.947148i	$0.396050\pi$
$62$	−3.14463	−0.399368
$63$	−0.0106754	−0.00134497
$64$	1.00000	0.125000
$65$	−5.92506	−0.734913
$66$	−1.86308	−0.229329
$67$	−15.5059	−1.89434	−0.947171	−	0.320729i	$-0.896072\pi$
$67$	−15.5059	−1.89434	−0.947171	+	0.320729i	$0.896072\pi$
$68$	−7.65454	−0.928249
$69$	−0.274258	−0.0330168
$70$	−0.115571	−0.0138134
$71$	8.80287	1.04471	0.522354	−	0.852728i	$-0.325054\pi$
$71$	8.80287	1.04471	0.522354	+	0.852728i	$0.325054\pi$
$72$	0.0923708	0.0108860
$73$	−11.1478	−1.30475	−0.652376	−	0.757896i	$-0.726228\pi$
$73$	−11.1478	−1.30475	−0.652376	+	0.757896i	$0.726228\pi$
$74$	6.44860	0.749634
$75$	1.75851	0.203056
$76$	−6.01137	−0.689551
$77$	0.122443	0.0139537
$78$	−10.4193	−1.17975
$79$	−2.78887	−0.313773	−0.156886	−	0.987617i	$-0.550146\pi$
$79$	−2.78887	−0.313773	−0.156886	+	0.987617i	$0.550146\pi$
$80$	1.00000	0.111803
$81$	−9.26858	−1.02984
$82$	−0.499853	−0.0551995
$83$	5.34566	0.586762	0.293381	−	0.955996i	$-0.405220\pi$
$83$	5.34566	0.586762	0.293381	+	0.955996i	$0.405220\pi$
$84$	−0.203233	−0.0221746
$85$	−7.65454	−0.830251
$86$	−3.20309	−0.345398
$87$	5.67101	0.607996
$88$	−1.05946	−0.112939
$89$	−3.18269	−0.337364	−0.168682	−	0.985670i	$-0.553951\pi$
$89$	−3.18269	−0.337364	−0.168682	+	0.985670i	$0.553951\pi$
$90$	0.0923708	0.00973674
$91$	0.684765	0.0717829
$92$	−0.155960	−0.0162600
$93$	−5.52987	−0.573420
$94$	5.42049	0.559081
$95$	−6.01137	−0.616753
$96$	1.75851	0.179478
$97$	−7.38623	−0.749959	−0.374979	−	0.927033i	$-0.622350\pi$
$97$	−7.38623	−0.749959	−0.374979	+	0.927033i	$0.622350\pi$
$98$	−6.98664	−0.705758
$99$	−0.0978633	−0.00983564
$100$	1.00000	0.100000
$101$	−3.05060	−0.303546	−0.151773	−	0.988415i	$-0.548498\pi$
$101$	−3.05060	−0.303546	−0.151773	+	0.988415i	$0.548498\pi$
$102$	−13.4606	−1.33280
$103$	14.5891	1.43750	0.718752	−	0.695266i	$-0.244713\pi$
$103$	14.5891	1.43750	0.718752	+	0.695266i	$0.244713\pi$
$104$	−5.92506	−0.581000
$105$	−0.203233	−0.0198335
$106$	4.44313	0.431555
$107$	1.34607	0.130129	0.0650647	−	0.997881i	$-0.479275\pi$
$107$	1.34607	0.130129	0.0650647	+	0.997881i	$0.479275\pi$
$108$	−5.11311	−0.492009
$109$	−4.06826	−0.389669	−0.194834	−	0.980836i	$-0.562417\pi$
$109$	−4.06826	−0.389669	−0.194834	+	0.980836i	$0.562417\pi$
$110$	−1.05946	−0.101016
$111$	11.3399	1.07634
$112$	−0.115571	−0.0109204
$113$	−3.26230	−0.306891	−0.153446	−	0.988157i	$-0.549037\pi$
$113$	−3.26230	−0.306891	−0.153446	+	0.988157i	$0.549037\pi$
$114$	−10.5711	−0.990072
$115$	−0.155960	−0.0145434
$116$	3.22489	0.299423
$117$	−0.547303	−0.0505981
$118$	2.13926	0.196935
$119$	0.884643	0.0810951
$120$	1.75851	0.160530
$121$	−9.87754	−0.897958
$122$	5.01100	0.453674
$123$	−0.878998	−0.0792566
$124$	−3.14463	−0.282396
$125$	1.00000	0.0894427
$126$	−0.0106754	−0.000951040 0
$127$	6.50795	0.577487	0.288744	−	0.957406i	$-0.406762\pi$
$127$	6.50795	0.577487	0.288744	+	0.957406i	$0.406762\pi$
$128$	1.00000	0.0883883
$129$	−5.63268	−0.495930
$130$	−5.92506	−0.519662
$131$	−1.43515	−0.125390	−0.0626949	−	0.998033i	$-0.519970\pi$
$131$	−1.43515	−0.125390	−0.0626949	+	0.998033i	$0.519970\pi$
$132$	−1.86308	−0.162160
$133$	0.694740	0.0602416
$134$	−15.5059	−1.33950
$135$	−5.11311	−0.440066
$136$	−7.65454	−0.656371
$137$	13.7923	1.17836	0.589179	−	0.808002i	$-0.299451\pi$
$137$	13.7923	1.17836	0.589179	+	0.808002i	$0.299451\pi$
$138$	−0.274258	−0.0233464
$139$	3.68639	0.312675	0.156338	−	0.987704i	$-0.450031\pi$
$139$	3.68639	0.312675	0.156338	+	0.987704i	$0.450031\pi$
$140$	−0.115571	−0.00976754
$141$	9.53201	0.802740
$142$	8.80287	0.738721
$143$	6.27737	0.524940
$144$	0.0923708	0.00769757
$145$	3.22489	0.267812
$146$	−11.1478	−0.922599
$147$	−12.2861	−1.01334
$148$	6.44860	0.530072
$149$	−2.57210	−0.210714	−0.105357	−	0.994434i	$-0.533599\pi$
$149$	−2.57210	−0.210714	−0.105357	+	0.994434i	$0.533599\pi$
$150$	1.75851	0.143582
$151$	−3.91016	−0.318204	−0.159102	−	0.987262i	$-0.550860\pi$
$151$	−3.91016	−0.318204	−0.159102	+	0.987262i	$0.550860\pi$
$152$	−6.01137	−0.487586
$153$	−0.707056	−0.0571621
$154$	0.122443	0.00986674
$155$	−3.14463	−0.252582
$156$	−10.4193	−0.834211
$157$	12.1974	0.973461	0.486730	−	0.873552i	$-0.338189\pi$
$157$	12.1974	0.973461	0.486730	+	0.873552i	$0.338189\pi$
$158$	−2.78887	−0.221871
$159$	7.81331	0.619636
$160$	1.00000	0.0790569
$161$	0.0180245	0.00142053
$162$	−9.26858	−0.728208
$163$	4.00892	0.314003	0.157002	−	0.987598i	$-0.449817\pi$
$163$	4.00892	0.314003	0.157002	+	0.987598i	$0.449817\pi$
$164$	−0.499853	−0.0390319
$165$	−1.86308	−0.145040
$166$	5.34566	0.414904
$167$	8.33064	0.644644	0.322322	−	0.946630i	$-0.395537\pi$
$167$	8.33064	0.644644	0.322322	+	0.946630i	$0.395537\pi$
$168$	−0.203233	−0.0156798
$169$	22.1063	1.70048
$170$	−7.65454	−0.587076
$171$	−0.555275	−0.0424630
$172$	−3.20309	−0.244233
$173$	4.92679	0.374577	0.187289	−	0.982305i	$-0.440030\pi$
$173$	4.92679	0.374577	0.187289	+	0.982305i	$0.440030\pi$
$174$	5.67101	0.429918
$175$	−0.115571	−0.00873635
$176$	−1.05946	−0.0798599
$177$	3.76192	0.282763
$178$	−3.18269	−0.238553
$179$	−22.8285	−1.70628	−0.853140	−	0.521682i	$-0.825305\pi$
$179$	−22.8285	−1.70628	−0.853140	+	0.521682i	$0.825305\pi$
$180$	0.0923708	0.00688492
$181$	−2.34240	−0.174109	−0.0870545	−	0.996204i	$-0.527745\pi$
$181$	−2.34240	−0.174109	−0.0870545	+	0.996204i	$0.527745\pi$
$182$	0.684765	0.0507582
$183$	8.81191	0.651395
$184$	−0.155960	−0.0114975
$185$	6.44860	0.474110
$186$	−5.52987	−0.405470
$187$	8.10969	0.593039
$188$	5.42049	0.395330
$189$	0.590927	0.0429836
$190$	−6.01137	−0.436111
$191$	3.88368	0.281013	0.140507	−	0.990080i	$-0.455127\pi$
$191$	3.88368	0.281013	0.140507	+	0.990080i	$0.455127\pi$
$192$	1.75851	0.126910
$193$	9.37592	0.674894	0.337447	−	0.941345i	$-0.390437\pi$
$193$	9.37592	0.674894	0.337447	+	0.941345i	$0.390437\pi$
$194$	−7.38623	−0.530301
$195$	−10.4193	−0.746141
$196$	−6.98664	−0.499046
$197$	8.09795	0.576955	0.288478	−	0.957487i	$-0.406851\pi$
$197$	8.09795	0.576955	0.288478	+	0.957487i	$0.406851\pi$
$198$	−0.0978633	−0.00695485
$199$	−2.33970	−0.165857	−0.0829286	−	0.996555i	$-0.526427\pi$
$199$	−2.33970	−0.165857	−0.0829286	+	0.996555i	$0.526427\pi$
$200$	1.00000	0.0707107
$201$	−27.2673	−1.92328
$202$	−3.05060	−0.214640
$203$	−0.372704	−0.0261587
$204$	−13.4606	−0.942431
$205$	−0.499853	−0.0349112
$206$	14.5891	1.01647
$207$	−0.0144062	−0.00100130
$208$	−5.92506	−0.410829
$209$	6.36881	0.440540
$210$	−0.203233	−0.0140244
$211$	6.78067	0.466800	0.233400	−	0.972381i	$-0.425015\pi$
$211$	6.78067	0.466800	0.233400	+	0.972381i	$0.425015\pi$
$212$	4.44313	0.305156
$213$	15.4800	1.06067
$214$	1.34607	0.0920154
$215$	−3.20309	−0.218449
$216$	−5.11311	−0.347903
$217$	0.363428	0.0246711
$218$	−4.06826	−0.275538
$219$	−19.6036	−1.32469
$220$	−1.05946	−0.0714289
$221$	45.3536	3.05081
$222$	11.3399	0.761088
$223$	6.50219	0.435419	0.217709	−	0.976014i	$-0.430142\pi$
$223$	6.50219	0.435419	0.217709	+	0.976014i	$0.430142\pi$
$224$	−0.115571	−0.00772192
$225$	0.0923708	0.00615806
$226$	−3.26230	−0.217005
$227$	−10.9040	−0.723726	−0.361863	−	0.932231i	$-0.617859\pi$
$227$	−10.9040	−0.723726	−0.361863	+	0.932231i	$0.617859\pi$
$228$	−10.5711	−0.700087
$229$	4.98442	0.329380	0.164690	−	0.986345i	$-0.447338\pi$
$229$	4.98442	0.329380	0.164690	+	0.986345i	$0.447338\pi$
$230$	−0.155960	−0.0102837
$231$	0.215318	0.0141669
$232$	3.22489	0.211724
$233$	17.9641	1.17687	0.588435	−	0.808544i	$-0.299744\pi$
$233$	17.9641	1.17687	0.588435	+	0.808544i	$0.299744\pi$
$234$	−0.547303	−0.0357783
$235$	5.42049	0.353594
$236$	2.13926	0.139254
$237$	−4.90427	−0.318567
$238$	0.884643	0.0573429
$239$	−13.1816	−0.852645	−0.426322	−	0.904571i	$-0.640191\pi$
$239$	−13.1816	−0.852645	−0.426322	+	0.904571i	$0.640191\pi$
$240$	1.75851	0.113512
$241$	14.7855	0.952420	0.476210	−	0.879332i	$-0.342010\pi$
$241$	14.7855	0.952420	0.476210	+	0.879332i	$0.342010\pi$
$242$	−9.87754	−0.634952
$243$	−0.959608	−0.0615589
$244$	5.01100	0.320796
$245$	−6.98664	−0.446360
$246$	−0.878998	−0.0560429
$247$	35.6177	2.26630
$248$	−3.14463	−0.199684
$249$	9.40041	0.595727
$250$	1.00000	0.0632456
$251$	−7.44387	−0.469853	−0.234926	−	0.972013i	$-0.575485\pi$
$251$	−7.44387	−0.469853	−0.234926	+	0.972013i	$0.575485\pi$
$252$	−0.0106754	−0.000672487 0
$253$	0.165234	0.0103882
$254$	6.50795	0.408345
$255$	−13.4606	−0.842936
$256$	1.00000	0.0625000
$257$	3.60615	0.224945	0.112473	−	0.993655i	$-0.464123\pi$
$257$	3.60615	0.224945	0.112473	+	0.993655i	$0.464123\pi$
$258$	−5.63268	−0.350675
$259$	−0.745271	−0.0463089
$260$	−5.92506	−0.367456
$261$	0.297886	0.0184387
$262$	−1.43515	−0.0886640
$263$	−23.5575	−1.45262	−0.726308	−	0.687369i	$-0.758766\pi$
$263$	−23.5575	−1.45262	−0.726308	+	0.687369i	$0.758766\pi$
$264$	−1.86308	−0.114665
$265$	4.44313	0.272939
$266$	0.694740	0.0425973
$267$	−5.59680	−0.342519
$268$	−15.5059	−0.947171
$269$	−19.8168	−1.20825	−0.604126	−	0.796889i	$-0.706478\pi$
$269$	−19.8168	−1.20825	−0.604126	+	0.796889i	$0.706478\pi$
$270$	−5.11311	−0.311174
$271$	−22.7798	−1.38378	−0.691888	−	0.722005i	$-0.743221\pi$
$271$	−22.7798	−1.38378	−0.691888	+	0.722005i	$0.743221\pi$
$272$	−7.65454	−0.464124
$273$	1.20417	0.0728796
$274$	13.7923	0.833225
$275$	−1.05946	−0.0638879
$276$	−0.274258	−0.0165084
$277$	1.03363	0.0621049	0.0310524	−	0.999518i	$-0.490114\pi$
$277$	1.03363	0.0621049	0.0310524	+	0.999518i	$0.490114\pi$
$278$	3.68639	0.221095
$279$	−0.290472	−0.0173901
$280$	−0.115571	−0.00690669
$281$	4.30491	0.256810	0.128405	−	0.991722i	$-0.459014\pi$
$281$	4.30491	0.256810	0.128405	+	0.991722i	$0.459014\pi$
$282$	9.53201	0.567623
$283$	−18.7648	−1.11545	−0.557727	−	0.830025i	$-0.688326\pi$
$283$	−18.7648	−1.11545	−0.557727	+	0.830025i	$0.688326\pi$
$284$	8.80287	0.522354
$285$	−10.5711	−0.626176
$286$	6.27737	0.371189
$287$	0.0577685	0.00340997
$288$	0.0923708	0.00544300
$289$	41.5919	2.44658
$290$	3.22489	0.189372
$291$	−12.9888	−0.761417
$292$	−11.1478	−0.652376
$293$	10.7236	0.626480	0.313240	−	0.949674i	$-0.398586\pi$
$293$	10.7236	0.626480	0.313240	+	0.949674i	$0.398586\pi$
$294$	−12.2861	−0.716540
$295$	2.13926	0.124552
$296$	6.44860	0.374817
$297$	5.41714	0.314334
$298$	−2.57210	−0.148998
$299$	0.924073	0.0534405
$300$	1.75851	0.101528
$301$	0.370185	0.0213371
$302$	−3.91016	−0.225004
$303$	−5.36453	−0.308184
$304$	−6.01137	−0.344776
$305$	5.01100	0.286929
$306$	−0.707056	−0.0404197
$307$	7.68431	0.438567	0.219283	−	0.975661i	$-0.429628\pi$
$307$	7.68431	0.438567	0.219283	+	0.975661i	$0.429628\pi$
$308$	0.122443	0.00697684
$309$	25.6551	1.45947
$310$	−3.14463	−0.178603
$311$	23.6752	1.34250	0.671248	−	0.741233i	$-0.265759\pi$
$311$	23.6752	1.34250	0.671248	+	0.741233i	$0.265759\pi$
$312$	−10.4193	−0.589876
$313$	−27.7398	−1.56794	−0.783972	−	0.620796i	$-0.786810\pi$
$313$	−27.7398	−1.56794	−0.783972	+	0.620796i	$0.786810\pi$
$314$	12.1974	0.688341
$315$	−0.0106754	−0.000601490 0
$316$	−2.78887	−0.156886
$317$	−20.9930	−1.17908	−0.589541	−	0.807738i	$-0.700691\pi$
$317$	−20.9930	−1.17908	−0.589541	+	0.807738i	$0.700691\pi$
$318$	7.81331	0.438149
$319$	−3.41664	−0.191295
$320$	1.00000	0.0559017
$321$	2.36708	0.132118
$322$	0.0180245	0.00100447
$323$	46.0142	2.56030
$324$	−9.26858	−0.514921
$325$	−5.92506	−0.328663
$326$	4.00892	0.222034
$327$	−7.15410	−0.395622
$328$	−0.499853	−0.0275997
$329$	−0.626452	−0.0345374
$330$	−1.86308	−0.102559
$331$	−30.1815	−1.65892	−0.829462	−	0.558563i	$-0.811353\pi$
$331$	−30.1815	−1.65892	−0.829462	+	0.558563i	$0.811353\pi$
$332$	5.34566	0.293381
$333$	0.595662	0.0326421
$334$	8.33064	0.455832
$335$	−15.5059	−0.847175
$336$	−0.203233	−0.0110873
$337$	−10.3899	−0.565975	−0.282988	−	0.959124i	$-0.591326\pi$
$337$	−10.3899	−0.565975	−0.282988	+	0.959124i	$0.591326\pi$
$338$	22.1063	1.20242
$339$	−5.73680	−0.311580
$340$	−7.65454	−0.415126
$341$	3.33161	0.180417
$342$	−0.555275	−0.0300258
$343$	1.61645	0.0872802
$344$	−3.20309	−0.172699
$345$	−0.274258	−0.0147656
$346$	4.92679	0.264866
$347$	−3.12197	−0.167596	−0.0837980	−	0.996483i	$-0.526705\pi$
$347$	−3.12197	−0.167596	−0.0837980	+	0.996483i	$0.526705\pi$
$348$	5.67101	0.303998
$349$	−19.8255	−1.06123	−0.530617	−	0.847612i	$-0.678040\pi$
$349$	−19.8255	−1.06123	−0.530617	+	0.847612i	$0.678040\pi$
$350$	−0.115571	−0.00617753
$351$	30.2954	1.61705
$352$	−1.05946	−0.0564695
$353$	−27.2823	−1.45209	−0.726045	−	0.687648i	$-0.758643\pi$
$353$	−27.2823	−1.45209	−0.726045	+	0.687648i	$0.758643\pi$
$354$	3.76192	0.199944
$355$	8.80287	0.467208
$356$	−3.18269	−0.168682
$357$	1.55566	0.0823341
$358$	−22.8285	−1.20652
$359$	−25.2933	−1.33493	−0.667466	−	0.744641i	$-0.732621\pi$
$359$	−25.2933	−1.33493	−0.667466	+	0.744641i	$0.732621\pi$
$360$	0.0923708	0.00486837
$361$	17.1366	0.901924
$362$	−2.34240	−0.123114
$363$	−17.3698	−0.911678
$364$	0.684765	0.0358914
$365$	−11.1478	−0.583503
$366$	8.81191	0.460606
$367$	−32.2471	−1.68329	−0.841644	−	0.540033i	$-0.818412\pi$
$367$	−32.2471	−1.68329	−0.841644	+	0.540033i	$0.818412\pi$
$368$	−0.155960	−0.00812999
$369$	−0.0461718	−0.00240361
$370$	6.44860	0.335247
$371$	−0.513497	−0.0266595
$372$	−5.52987	−0.286710
$373$	17.7463	0.918868	0.459434	−	0.888212i	$-0.348052\pi$
$373$	17.7463	0.918868	0.459434	+	0.888212i	$0.348052\pi$
$374$	8.10969	0.419342
$375$	1.75851	0.0908093
$376$	5.42049	0.279540
$377$	−19.1076	−0.984094
$378$	0.590927	0.0303940
$379$	8.59889	0.441695	0.220848	−	0.975308i	$-0.429118\pi$
$379$	8.59889	0.441695	0.220848	+	0.975308i	$0.429118\pi$
$380$	−6.01137	−0.308377
$381$	11.4443	0.586310
$382$	3.88368	0.198706
$383$	29.4587	1.50527	0.752636	−	0.658437i	$-0.228782\pi$
$383$	29.4587	1.50527	0.752636	+	0.658437i	$0.228782\pi$
$384$	1.75851	0.0897388
$385$	0.122443	0.00624028
$386$	9.37592	0.477222
$387$	−0.295872	−0.0150400
$388$	−7.38623	−0.374979
$389$	0.0800026	0.00405629	0.00202815	−	0.999998i	$-0.499354\pi$
$389$	0.0800026	0.00405629	0.00202815	+	0.999998i	$0.499354\pi$
$390$	−10.4193	−0.527602
$391$	1.19380	0.0603732
$392$	−6.98664	−0.352879
$393$	−2.52373	−0.127306
$394$	8.09795	0.407969
$395$	−2.78887	−0.140323
$396$	−0.0978633	−0.00491782
$397$	−9.52087	−0.477839	−0.238919	−	0.971039i	$-0.576793\pi$
$397$	−9.52087	−0.477839	−0.238919	+	0.971039i	$0.576793\pi$
$398$	−2.33970	−0.117279
$399$	1.22171	0.0611620
$400$	1.00000	0.0500000
$401$	38.3647	1.91584	0.957921	−	0.287034i	$-0.0926691\pi$
$401$	38.3647	1.91584	0.957921	+	0.287034i	$0.0926691\pi$
$402$	−27.2673	−1.35997
$403$	18.6321	0.928130
$404$	−3.05060	−0.151773
$405$	−9.26858	−0.460559
$406$	−0.372704	−0.0184970
$407$	−6.83204	−0.338652
$408$	−13.4606	−0.666399
$409$	−22.0031	−1.08798	−0.543991	−	0.839091i	$-0.683087\pi$
$409$	−22.0031	−1.08798	−0.543991	+	0.839091i	$0.683087\pi$
$410$	−0.499853	−0.0246860
$411$	24.2540	1.19636
$412$	14.5891	0.718752
$413$	−0.247236	−0.0121657
$414$	−0.0144062	−0.000708025 0
$415$	5.34566	0.262408
$416$	−5.92506	−0.290500
$417$	6.48257	0.317453
$418$	6.36881	0.311509
$419$	−16.8407	−0.822723	−0.411362	−	0.911472i	$-0.634947\pi$
$419$	−16.8407	−0.822723	−0.411362	+	0.911472i	$0.634947\pi$
$420$	−0.203233	−0.00991677
$421$	34.2753	1.67047	0.835237	−	0.549890i	$-0.185330\pi$
$421$	34.2753	1.67047	0.835237	+	0.549890i	$0.185330\pi$
$422$	6.78067	0.330078
$423$	0.500695	0.0243446
$424$	4.44313	0.215778
$425$	−7.65454	−0.371300
$426$	15.4800	0.750007
$427$	−0.579126	−0.0280259
$428$	1.34607	0.0650647
$429$	11.0388	0.532960
$430$	−3.20309	−0.154467
$431$	−35.8069	−1.72476	−0.862379	−	0.506263i	$-0.831026\pi$
$431$	−35.8069	−1.72476	−0.862379	+	0.506263i	$0.831026\pi$
$432$	−5.11311	−0.246004
$433$	−9.67497	−0.464949	−0.232475	−	0.972602i	$-0.574682\pi$
$433$	−9.67497	−0.464949	−0.232475	+	0.972602i	$0.574682\pi$
$434$	0.363428	0.0174451
$435$	5.67101	0.271904
$436$	−4.06826	−0.194834
$437$	0.937534	0.0448483
$438$	−19.6036	−0.936694
$439$	−14.6670	−0.700020	−0.350010	−	0.936746i	$-0.613822\pi$
$439$	−14.6670	−0.700020	−0.350010	+	0.936746i	$0.613822\pi$
$440$	−1.05946	−0.0505078
$441$	−0.645362	−0.0307315
$442$	45.3536	2.15725
$443$	13.3396	0.633783	0.316891	−	0.948462i	$-0.397361\pi$
$443$	13.3396	0.633783	0.316891	+	0.948462i	$0.397361\pi$
$444$	11.3399	0.538170
$445$	−3.18269	−0.150874
$446$	6.50219	0.307887
$447$	−4.52307	−0.213934
$448$	−0.115571	−0.00546022
$449$	18.3476	0.865878	0.432939	−	0.901423i	$-0.357476\pi$
$449$	18.3476	0.865878	0.432939	+	0.901423i	$0.357476\pi$
$450$	0.0923708	0.00435440
$451$	0.529575	0.0249367
$452$	−3.26230	−0.153446
$453$	−6.87607	−0.323066
$454$	−10.9040	−0.511752
$455$	0.684765	0.0321023
$456$	−10.5711	−0.495036
$457$	−37.0376	−1.73254	−0.866272	−	0.499573i	$-0.833490\pi$
$457$	−37.0376	−1.73254	−0.866272	+	0.499573i	$0.833490\pi$
$458$	4.98442	0.232907
$459$	39.1385	1.82683
$460$	−0.155960	−0.00727168
$461$	−3.57261	−0.166393	−0.0831965	−	0.996533i	$-0.526513\pi$
$461$	−3.57261	−0.166393	−0.0831965	+	0.996533i	$0.526513\pi$
$462$	0.215318	0.0100175
$463$	−17.6931	−0.822267	−0.411134	−	0.911575i	$-0.634867\pi$
$463$	−17.6931	−0.822267	−0.411134	+	0.911575i	$0.634867\pi$
$464$	3.22489	0.149712
$465$	−5.52987	−0.256441
$466$	17.9641	0.832173
$467$	−32.7445	−1.51523	−0.757617	−	0.652699i	$-0.773637\pi$
$467$	−32.7445	−1.51523	−0.757617	+	0.652699i	$0.773637\pi$
$468$	−0.547303	−0.0252991
$469$	1.79203	0.0827482
$470$	5.42049	0.250029
$471$	21.4493	0.988334
$472$	2.13926	0.0984674
$473$	3.39355	0.156036
$474$	−4.90427	−0.225261
$475$	−6.01137	−0.275821
$476$	0.884643	0.0405475
$477$	0.410416	0.0187917
$478$	−13.1816	−0.602911
$479$	−5.78661	−0.264397	−0.132198	−	0.991223i	$-0.542204\pi$
$479$	−5.78661	−0.264397	−0.132198	+	0.991223i	$0.542204\pi$
$480$	1.75851	0.0802648
$481$	−38.2083	−1.74215
$482$	14.7855	0.673462
$483$	0.0316963	0.00144223
$484$	−9.87754	−0.448979
$485$	−7.38623	−0.335392
$486$	−0.959608	−0.0435287
$487$	23.4387	1.06211	0.531055	−	0.847338i	$-0.321796\pi$
$487$	23.4387	1.06211	0.531055	+	0.847338i	$0.321796\pi$
$488$	5.01100	0.226837
$489$	7.04975	0.318801
$490$	−6.98664	−0.315624
$491$	−4.03449	−0.182074	−0.0910369	−	0.995848i	$-0.529018\pi$
$491$	−4.03449	−0.182074	−0.0910369	+	0.995848i	$0.529018\pi$
$492$	−0.878998	−0.0396283
$493$	−24.6850	−1.11176
$494$	35.6177	1.60252
$495$	−0.0978633	−0.00439863
$496$	−3.14463	−0.141198
$497$	−1.01736	−0.0456347
$498$	9.40041	0.421243
$499$	−3.14365	−0.140729	−0.0703646	−	0.997521i	$-0.522416\pi$
$499$	−3.14365	−0.140729	−0.0703646	+	0.997521i	$0.522416\pi$
$500$	1.00000	0.0447214
$501$	14.6495	0.654493
$502$	−7.44387	−0.332236
$503$	17.0587	0.760612	0.380306	−	0.924861i	$-0.375819\pi$
$503$	17.0587	0.760612	0.380306	+	0.924861i	$0.375819\pi$
$504$	−0.0106754	−0.000475520 0
$505$	−3.05060	−0.135750
$506$	0.165234	0.00734554
$507$	38.8742	1.72647
$508$	6.50795	0.288744
$509$	11.4905	0.509307	0.254653	−	0.967032i	$-0.418039\pi$
$509$	11.4905	0.509307	0.254653	+	0.967032i	$0.418039\pi$
$510$	−13.4606	−0.596046
$511$	1.28836	0.0569938
$512$	1.00000	0.0441942
$513$	30.7368	1.35706
$514$	3.60615	0.159060
$515$	14.5891	0.642872
$516$	−5.63268	−0.247965
$517$	−5.74280	−0.252568
$518$	−0.745271	−0.0327453
$519$	8.66383	0.380300
$520$	−5.92506	−0.259831
$521$	13.6864	0.599614	0.299807	−	0.954000i	$-0.403078\pi$
$521$	13.6864	0.599614	0.299807	+	0.954000i	$0.403078\pi$
$522$	0.297886	0.0130381
$523$	38.3083	1.67511	0.837553	−	0.546356i	$-0.183985\pi$
$523$	38.3083	1.67511	0.837553	+	0.546356i	$0.183985\pi$
$524$	−1.43515	−0.0626949
$525$	−0.203233	−0.00886983
$526$	−23.5575	−1.02716
$527$	24.0706	1.04853
$528$	−1.86308	−0.0810800
$529$	−22.9757	−0.998942
$530$	4.44313	0.192997
$531$	0.197605	0.00857533
$532$	0.694740	0.0301208
$533$	2.96166	0.128284
$534$	−5.59680	−0.242197
$535$	1.34607	0.0581956
$536$	−15.5059	−0.669751
$537$	−40.1442	−1.73235
$538$	−19.8168	−0.854363
$539$	7.40208	0.318830
$540$	−5.11311	−0.220033
$541$	−43.4449	−1.86784	−0.933922	−	0.357477i	$-0.883637\pi$
$541$	−43.4449	−1.86784	−0.933922	+	0.357477i	$0.883637\pi$
$542$	−22.7798	−0.978477
$543$	−4.11914	−0.176769
$544$	−7.65454	−0.328186
$545$	−4.06826	−0.174265
$546$	1.20417	0.0515337
$547$	39.8275	1.70290	0.851450	−	0.524437i	$-0.175724\pi$
$547$	39.8275	1.70290	0.851450	+	0.524437i	$0.175724\pi$
$548$	13.7923	0.589179
$549$	0.462870	0.0197548
$550$	−1.05946	−0.0451756
$551$	−19.3860	−0.825871
$552$	−0.274258	−0.0116732
$553$	0.322313	0.0137061
$554$	1.03363	0.0439148
$555$	11.3399	0.481354
$556$	3.68639	0.156338
$557$	16.3993	0.694863	0.347431	−	0.937705i	$-0.387054\pi$
$557$	16.3993	0.694863	0.347431	+	0.937705i	$0.387054\pi$
$558$	−0.290472	−0.0122966
$559$	18.9785	0.802705
$560$	−0.115571	−0.00488377
$561$	14.2610	0.602100
$562$	4.30491	0.181592
$563$	−25.7493	−1.08520	−0.542602	−	0.839990i	$-0.682561\pi$
$563$	−25.7493	−1.08520	−0.542602	+	0.839990i	$0.682561\pi$
$564$	9.53201	0.401370
$565$	−3.26230	−0.137246
$566$	−18.7648	−0.788745
$567$	1.07118	0.0449853
$568$	8.80287	0.369360
$569$	16.2960	0.683163	0.341582	−	0.939852i	$-0.389037\pi$
$569$	16.2960	0.683163	0.341582	+	0.939852i	$0.389037\pi$
$570$	−10.5711	−0.442774
$571$	5.28775	0.221286	0.110643	−	0.993860i	$-0.464709\pi$
$571$	5.28775	0.221286	0.110643	+	0.993860i	$0.464709\pi$
$572$	6.27737	0.262470
$573$	6.82950	0.285307
$574$	0.0577685	0.00241121
$575$	−0.155960	−0.00650399
$576$	0.0923708	0.00384878
$577$	22.6166	0.941540	0.470770	−	0.882256i	$-0.343976\pi$
$577$	22.6166	0.941540	0.470770	+	0.882256i	$0.343976\pi$
$578$	41.5919	1.73000
$579$	16.4877	0.685205
$580$	3.22489	0.133906
$581$	−0.617803	−0.0256308
$582$	−12.9888	−0.538403
$583$	−4.70733	−0.194958
$584$	−11.1478	−0.461299
$585$	−0.547303	−0.0226282
$586$	10.7236	0.442988
$587$	17.5749	0.725392	0.362696	−	0.931907i	$-0.381856\pi$
$587$	17.5749	0.725392	0.362696	+	0.931907i	$0.381856\pi$
$588$	−12.2861	−0.506671
$589$	18.9035	0.778905
$590$	2.13926	0.0880719
$591$	14.2404	0.585770
$592$	6.44860	0.265036
$593$	−33.9525	−1.39426	−0.697132	−	0.716943i	$-0.745541\pi$
$593$	−33.9525	−1.39426	−0.697132	+	0.716943i	$0.745541\pi$
$594$	5.41714	0.222268
$595$	0.884643	0.0362668
$596$	−2.57210	−0.105357
$597$	−4.11440	−0.168391
$598$	0.924073	0.0377882
$599$	−10.5128	−0.429540	−0.214770	−	0.976665i	$-0.568900\pi$
$599$	−10.5128	−0.429540	−0.214770	+	0.976665i	$0.568900\pi$
$600$	1.75851	0.0717910
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	0.370185	0.0150876
$603$	−1.43229	−0.0583273
$604$	−3.91016	−0.159102
$605$	−9.87754	−0.401579
$606$	−5.36453	−0.217919
$607$	0.0255091	0.00103538	0.000517691	−	1.00000i	$-0.499835\pi$
$607$	0.0255091	0.00103538	0.000517691		1.00000i	$0.499835\pi$
$608$	−6.01137	−0.243793
$609$	−0.655405	−0.0265583
$610$	5.01100	0.202889
$611$	−32.1167	−1.29930
$612$	−0.707056	−0.0285810
$613$	−24.0389	−0.970924	−0.485462	−	0.874258i	$-0.661349\pi$
$613$	−24.0389	−0.970924	−0.485462	+	0.874258i	$0.661349\pi$
$614$	7.68431	0.310113
$615$	−0.878998	−0.0354446
$616$	0.122443	0.00493337
$617$	−16.0653	−0.646767	−0.323383	−	0.946268i	$-0.604820\pi$
$617$	−16.0653	−0.646767	−0.323383	+	0.946268i	$0.604820\pi$
$618$	25.6551	1.03200
$619$	−11.7331	−0.471593	−0.235797	−	0.971802i	$-0.575770\pi$
$619$	−11.7331	−0.471593	−0.235797	+	0.971802i	$0.575770\pi$
$620$	−3.14463	−0.126291
$621$	0.797441	0.0320002
$622$	23.6752	0.949287
$623$	0.367827	0.0147367
$624$	−10.4193	−0.417106
$625$	1.00000	0.0400000
$626$	−27.7398	−1.10870
$627$	11.1996	0.447271
$628$	12.1974	0.486730
$629$	−49.3610	−1.96815
$630$	−0.0106754	−0.000425318 0
$631$	33.0265	1.31477	0.657383	−	0.753557i	$-0.271663\pi$
$631$	33.0265	1.31477	0.657383	+	0.753557i	$0.271663\pi$
$632$	−2.78887	−0.110935
$633$	11.9239	0.473932
$634$	−20.9930	−0.833737
$635$	6.50795	0.258260
$636$	7.81331	0.309818
$637$	41.3963	1.64018
$638$	−3.41664	−0.135266
$639$	0.813129	0.0321669
$640$	1.00000	0.0395285
$641$	37.7607	1.49146	0.745729	−	0.666250i	$-0.232102\pi$
$641$	37.7607	1.49146	0.745729	+	0.666250i	$0.232102\pi$
$642$	2.36708	0.0934212
$643$	−13.2655	−0.523142	−0.261571	−	0.965184i	$-0.584241\pi$
$643$	−13.2655	−0.523142	−0.261571	+	0.965184i	$0.584241\pi$
$644$	0.0180245	0.000710264 0
$645$	−5.63268	−0.221787
$646$	46.0142	1.81041
$647$	−12.3466	−0.485396	−0.242698	−	0.970102i	$-0.578032\pi$
$647$	−12.3466	−0.485396	−0.242698	+	0.970102i	$0.578032\pi$
$648$	−9.26858	−0.364104
$649$	−2.26646	−0.0889665
$650$	−5.92506	−0.232400
$651$	0.639093	0.0250480
$652$	4.00892	0.157002
$653$	−7.03367	−0.275249	−0.137624	−	0.990485i	$-0.543947\pi$
$653$	−7.03367	−0.275249	−0.137624	+	0.990485i	$0.543947\pi$
$654$	−7.15410	−0.279747
$655$	−1.43515	−0.0560760
$656$	−0.499853	−0.0195160
$657$	−1.02973	−0.0401737
$658$	−0.626452	−0.0244216
$659$	−7.03423	−0.274015	−0.137007	−	0.990570i	$-0.543748\pi$
$659$	−7.03423	−0.274015	−0.137007	+	0.990570i	$0.543748\pi$
$660$	−1.86308	−0.0725202
$661$	−0.591861	−0.0230207	−0.0115104	−	0.999934i	$-0.503664\pi$
$661$	−0.591861	−0.0230207	−0.0115104	+	0.999934i	$0.503664\pi$
$662$	−30.1815	−1.17304
$663$	79.7549	3.09742
$664$	5.34566	0.207452
$665$	0.694740	0.0269409
$666$	0.595662	0.0230815
$667$	−0.502954	−0.0194745
$668$	8.33064	0.322322
$669$	11.4342	0.442071
$670$	−15.5059	−0.599044
$671$	−5.30896	−0.204950
$672$	−0.203233	−0.00783989
$673$	−17.6471	−0.680246	−0.340123	−	0.940381i	$-0.610469\pi$
$673$	−17.6471	−0.680246	−0.340123	+	0.940381i	$0.610469\pi$
$674$	−10.3899	−0.400205
$675$	−5.11311	−0.196804
$676$	22.1063	0.850242
$677$	11.5061	0.442216	0.221108	−	0.975249i	$-0.429033\pi$
$677$	11.5061	0.442216	0.221108	+	0.975249i	$0.429033\pi$
$678$	−5.73680	−0.220320
$679$	0.853635	0.0327595
$680$	−7.65454	−0.293538
$681$	−19.1749	−0.734783
$682$	3.33161	0.127574
$683$	−25.1718	−0.963171	−0.481586	−	0.876399i	$-0.659939\pi$
$683$	−25.1718	−0.963171	−0.481586	+	0.876399i	$0.659939\pi$
$684$	−0.555275	−0.0212315
$685$	13.7923	0.526978
$686$	1.61645	0.0617164
$687$	8.76517	0.334412
$688$	−3.20309	−0.122117
$689$	−26.3258	−1.00293
$690$	−0.274258	−0.0104408
$691$	1.02855	0.0391278	0.0195639	−	0.999809i	$-0.493772\pi$
$691$	1.02855	0.0391278	0.0195639	+	0.999809i	$0.493772\pi$
$692$	4.92679	0.187289
$693$	0.0113102	0.000429638 0
$694$	−3.12197	−0.118508
$695$	3.68639	0.139833
$696$	5.67101	0.214959
$697$	3.82614	0.144925
$698$	−19.8255	−0.750406
$699$	31.5902	1.19485
$700$	−0.115571	−0.00436818
$701$	−7.99077	−0.301807	−0.150904	−	0.988548i	$-0.548218\pi$
$701$	−7.99077	−0.301807	−0.150904	+	0.988548i	$0.548218\pi$
$702$	30.2954	1.14343
$703$	−38.7649	−1.46205
$704$	−1.05946	−0.0399300
$705$	9.53201	0.358996
$706$	−27.2823	−1.02678
$707$	0.352561	0.0132594
$708$	3.76192	0.141382
$709$	−27.5073	−1.03306	−0.516529	−	0.856270i	$-0.672776\pi$
$709$	−27.5073	−1.03306	−0.516529	+	0.856270i	$0.672776\pi$
$710$	8.80287	0.330366
$711$	−0.257611	−0.00966115
$712$	−3.18269	−0.119276
$713$	0.490436	0.0183670
$714$	1.55566	0.0582190
$715$	6.27737	0.234760
$716$	−22.8285	−0.853140
$717$	−23.1800	−0.865672
$718$	−25.2933	−0.943939
$719$	−25.5509	−0.952889	−0.476444	−	0.879205i	$-0.658075\pi$
$719$	−25.5509	−0.952889	−0.476444	+	0.879205i	$0.658075\pi$
$720$	0.0923708	0.00344246
$721$	−1.68608	−0.0627927
$722$	17.1366	0.637757
$723$	26.0006	0.966971
$724$	−2.34240	−0.0870545
$725$	3.22489	0.119769
$726$	−17.3698	−0.644653
$727$	−11.7504	−0.435800	−0.217900	−	0.975971i	$-0.569921\pi$
$727$	−11.7504	−0.435800	−0.217900	+	0.975971i	$0.569921\pi$
$728$	0.684765	0.0253791
$729$	26.1183	0.967343
$730$	−11.1478	−0.412599
$731$	24.5182	0.906837
$732$	8.81191	0.325698
$733$	3.36788	0.124396	0.0621978	−	0.998064i	$-0.480189\pi$
$733$	3.36788	0.124396	0.0621978	+	0.998064i	$0.480189\pi$
$734$	−32.2471	−1.19026
$735$	−12.2861	−0.453180
$736$	−0.155960	−0.00574877
$737$	16.4279	0.605128
$738$	−0.0461718	−0.00169961
$739$	11.1562	0.410389	0.205195	−	0.978721i	$-0.434217\pi$
$739$	11.1562	0.410389	0.205195	+	0.978721i	$0.434217\pi$
$740$	6.44860	0.237055
$741$	62.6342	2.30093
$742$	−0.513497	−0.0188511
$743$	12.9513	0.475139	0.237569	−	0.971371i	$-0.423649\pi$
$743$	12.9513	0.475139	0.237569	+	0.971371i	$0.423649\pi$
$744$	−5.52987	−0.202735
$745$	−2.57210	−0.0942343
$746$	17.7463	0.649738
$747$	0.493783	0.0180666
$748$	8.10969	0.296520
$749$	−0.155567	−0.00568428
$750$	1.75851	0.0642118
$751$	−38.3680	−1.40007	−0.700035	−	0.714109i	$-0.746832\pi$
$751$	−38.3680	−1.40007	−0.700035	+	0.714109i	$0.746832\pi$
$752$	5.42049	0.197665
$753$	−13.0901	−0.477032
$754$	−19.1076	−0.695859
$755$	−3.91016	−0.142305
$756$	0.590927	0.0214918
$757$	4.16306	0.151309	0.0756545	−	0.997134i	$-0.475895\pi$
$757$	4.16306	0.151309	0.0756545	+	0.997134i	$0.475895\pi$
$758$	8.59889	0.312326
$759$	0.290566	0.0105469
$760$	−6.01137	−0.218055
$761$	21.9747	0.796581	0.398291	−	0.917259i	$-0.369604\pi$
$761$	21.9747	0.796581	0.398291	+	0.917259i	$0.369604\pi$
$762$	11.4443	0.414584
$763$	0.470173	0.0170214
$764$	3.88368	0.140507
$765$	−0.707056	−0.0255637
$766$	29.4587	1.06439
$767$	−12.6752	−0.457676
$768$	1.75851	0.0634549
$769$	16.8733	0.608468	0.304234	−	0.952597i	$-0.401599\pi$
$769$	16.8733	0.608468	0.304234	+	0.952597i	$0.401599\pi$
$770$	0.122443	0.00441254
$771$	6.34146	0.228382
$772$	9.37592	0.337447
$773$	−31.9352	−1.14863	−0.574315	−	0.818634i	$-0.694732\pi$
$773$	−31.9352	−1.14863	−0.574315	+	0.818634i	$0.694732\pi$
$774$	−0.295872	−0.0106349
$775$	−3.14463	−0.112958
$776$	−7.38623	−0.265150
$777$	−1.31057	−0.0470164
$778$	0.0800026	0.00286823
$779$	3.00480	0.107658
$780$	−10.4193	−0.373071
$781$	−9.32631	−0.333721
$782$	1.19380	0.0426903
$783$	−16.4892	−0.589276
$784$	−6.98664	−0.249523
$785$	12.1974	0.435345
$786$	−2.52373	−0.0900186
$787$	6.04218	0.215380	0.107690	−	0.994184i	$-0.465655\pi$
$787$	6.04218	0.215380	0.107690	+	0.994184i	$0.465655\pi$
$788$	8.09795	0.288478
$789$	−41.4262	−1.47481
$790$	−2.78887	−0.0992237
$791$	0.377027	0.0134056
$792$	−0.0978633	−0.00347742
$793$	−29.6904	−1.05434
$794$	−9.52087	−0.337883
$795$	7.81331	0.277110
$796$	−2.33970	−0.0829286
$797$	−13.5925	−0.481473	−0.240736	−	0.970591i	$-0.577389\pi$
$797$	−13.5925	−0.481473	−0.240736	+	0.970591i	$0.577389\pi$
$798$	1.22171	0.0432481
$799$	−41.4913	−1.46786
$800$	1.00000	0.0353553
$801$	−0.293988	−0.0103875
$802$	38.3647	1.35470
$803$	11.8107	0.416789
$804$	−27.2673	−0.961642
$805$	0.0180245	0.000635280 0
$806$	18.6321	0.656287
$807$	−34.8481	−1.22671
$808$	−3.05060	−0.107320
$809$	49.6483	1.74554	0.872771	−	0.488130i	$-0.162321\pi$
$809$	49.6483	1.74554	0.872771	+	0.488130i	$0.162321\pi$
$810$	−9.26858	−0.325665
$811$	12.6727	0.444999	0.222499	−	0.974933i	$-0.428578\pi$
$811$	12.6727	0.444999	0.222499	+	0.974933i	$0.428578\pi$
$812$	−0.372704	−0.0130793
$813$	−40.0586	−1.40492
$814$	−6.83204	−0.239463
$815$	4.00892	0.140426
$816$	−13.4606	−0.471216
$817$	19.2550	0.673646
$818$	−22.0031	−0.769319
$819$	0.0632523	0.00221022
$820$	−0.499853	−0.0174556
$821$	31.7128	1.10678	0.553392	−	0.832921i	$-0.313333\pi$
$821$	31.7128	1.10678	0.553392	+	0.832921i	$0.313333\pi$
$822$	24.2540	0.845956
$823$	45.1045	1.57224	0.786122	−	0.618071i	$-0.212086\pi$
$823$	45.1045	1.57224	0.786122	+	0.618071i	$0.212086\pi$
$824$	14.5891	0.508235
$825$	−1.86308	−0.0648640
$826$	−0.247236	−0.00860246
$827$	10.0656	0.350016	0.175008	−	0.984567i	$-0.444005\pi$
$827$	10.0656	0.350016	0.175008	+	0.984567i	$0.444005\pi$
$828$	−0.0144062	−0.000500649 0
$829$	−15.2100	−0.528266	−0.264133	−	0.964486i	$-0.585086\pi$
$829$	−15.2100	−0.528266	−0.264133	+	0.964486i	$0.585086\pi$
$830$	5.34566	0.185550
$831$	1.81765	0.0630537
$832$	−5.92506	−0.205414
$833$	53.4795	1.85296
$834$	6.48257	0.224473
$835$	8.33064	0.288294
$836$	6.36881	0.220270
$837$	16.0788	0.555765
$838$	−16.8407	−0.581753
$839$	−28.1900	−0.973228	−0.486614	−	0.873617i	$-0.661768\pi$
$839$	−28.1900	−0.973228	−0.486614	+	0.873617i	$0.661768\pi$
$840$	−0.203233	−0.00701221
$841$	−18.6001	−0.641383
$842$	34.2753	1.18120
$843$	7.57025	0.260733
$844$	6.78067	0.233400
$845$	22.1063	0.760480
$846$	0.500695	0.0172143
$847$	1.14156	0.0392244
$848$	4.44313	0.152578
$849$	−32.9982	−1.13250
$850$	−7.65454	−0.262548
$851$	−1.00572	−0.0344758
$852$	15.4800	0.530335
$853$	−17.1029	−0.585591	−0.292796	−	0.956175i	$-0.594586\pi$
$853$	−17.1029	−0.585591	−0.292796	+	0.956175i	$0.594586\pi$
$854$	−0.579126	−0.0198173
$855$	−0.555275	−0.0189900
$856$	1.34607	0.0460077
$857$	−35.5869	−1.21563	−0.607813	−	0.794080i	$-0.707953\pi$
$857$	−35.5869	−1.21563	−0.607813	+	0.794080i	$0.707953\pi$
$858$	11.0388	0.376860
$859$	52.2232	1.78183	0.890916	−	0.454169i	$-0.150064\pi$
$859$	52.2232	1.78183	0.890916	+	0.454169i	$0.150064\pi$
$860$	−3.20309	−0.109224
$861$	0.101587	0.00346207
$862$	−35.8069	−1.21959
$863$	42.7203	1.45422	0.727108	−	0.686523i	$-0.240864\pi$
$863$	42.7203	1.45422	0.727108	+	0.686523i	$0.240864\pi$
$864$	−5.11311	−0.173951
$865$	4.92679	0.167516
$866$	−9.67497	−0.328769
$867$	73.1400	2.48396
$868$	0.363428	0.0123355
$869$	2.95470	0.100231
$870$	5.67101	0.192265
$871$	91.8731	3.11300
$872$	−4.06826	−0.137769
$873$	−0.682273	−0.0230914
$874$	0.937534	0.0317126
$875$	−0.115571	−0.00390701
$876$	−19.6036	−0.662343
$877$	−28.3762	−0.958198	−0.479099	−	0.877761i	$-0.659036\pi$
$877$	−28.3762	−0.958198	−0.479099	+	0.877761i	$0.659036\pi$
$878$	−14.6670	−0.494989
$879$	18.8576	0.636051
$880$	−1.05946	−0.0357144
$881$	−54.2295	−1.82704	−0.913519	−	0.406797i	$-0.866646\pi$
$881$	−54.2295	−1.82704	−0.913519	+	0.406797i	$0.866646\pi$
$882$	−0.645362	−0.0217305
$883$	16.0177	0.539038	0.269519	−	0.962995i	$-0.413135\pi$
$883$	16.0177	0.539038	0.269519	+	0.962995i	$0.413135\pi$
$884$	45.3536	1.52541
$885$	3.76192	0.126455
$886$	13.3396	0.448152
$887$	−34.0395	−1.14293	−0.571467	−	0.820625i	$-0.693625\pi$
$887$	−34.0395	−1.14293	−0.571467	+	0.820625i	$0.693625\pi$
$888$	11.3399	0.380544
$889$	−0.752131	−0.0252257
$890$	−3.18269	−0.106684
$891$	9.81970	0.328972
$892$	6.50219	0.217709
$893$	−32.5846	−1.09040
$894$	−4.52307	−0.151274
$895$	−22.8285	−0.763072
$896$	−0.115571	−0.00386096
$897$	1.62500	0.0542570
$898$	18.3476	0.612268
$899$	−10.1411	−0.338223
$900$	0.0923708	0.00307903
$901$	−34.0101	−1.13304
$902$	0.529575	0.0176329
$903$	0.650975	0.0216631
$904$	−3.26230	−0.108502
$905$	−2.34240	−0.0778639
$906$	−6.87607	−0.228442
$907$	2.37458	0.0788468	0.0394234	−	0.999223i	$-0.487448\pi$
$907$	2.37458	0.0788468	0.0394234	+	0.999223i	$0.487448\pi$
$908$	−10.9040	−0.361863
$909$	−0.281787	−0.00934627
$910$	0.684765	0.0226997
$911$	46.0411	1.52541	0.762705	−	0.646747i	$-0.223871\pi$
$911$	46.0411	1.52541	0.762705	+	0.646747i	$0.223871\pi$
$912$	−10.5711	−0.350043
$913$	−5.66352	−0.187435
$914$	−37.0376	−1.22509
$915$	8.81191	0.291313
$916$	4.98442	0.164690
$917$	0.165862	0.00547725
$918$	39.1385	1.29176
$919$	−43.1275	−1.42265	−0.711323	−	0.702866i	$-0.751904\pi$
$919$	−43.1275	−1.42265	−0.711323	+	0.702866i	$0.751904\pi$
$920$	−0.155960	−0.00514186
$921$	13.5130	0.445267
$922$	−3.57261	−0.117658
$923$	−52.1575	−1.71679
$924$	0.215318	0.00708344
$925$	6.44860	0.212029
$926$	−17.6931	−0.581431
$927$	1.34761	0.0442612
$928$	3.22489	0.105862
$929$	−53.0317	−1.73991	−0.869957	−	0.493128i	$-0.835853\pi$
$929$	−53.0317	−1.73991	−0.869957	+	0.493128i	$0.835853\pi$
$930$	−5.52987	−0.181331
$931$	41.9993	1.37647
$932$	17.9641	0.588435
$933$	41.6331	1.36301
$934$	−32.7445	−1.07143
$935$	8.10969	0.265215
$936$	−0.547303	−0.0178891
$937$	2.80676	0.0916929	0.0458464	−	0.998948i	$-0.485402\pi$
$937$	2.80676	0.0916929	0.0458464	+	0.998948i	$0.485402\pi$
$938$	1.79203	0.0585118
$939$	−48.7808	−1.59190
$940$	5.42049	0.176797
$941$	16.5716	0.540218	0.270109	−	0.962830i	$-0.412940\pi$
$941$	16.5716	0.540218	0.270109	+	0.962830i	$0.412940\pi$
$942$	21.4493	0.698858
$943$	0.0779571	0.00253863
$944$	2.13926	0.0696270
$945$	0.590927	0.0192229
$946$	3.39355	0.110334
$947$	−0.688425	−0.0223708	−0.0111854	−	0.999937i	$-0.503560\pi$
$947$	−0.688425	−0.0223708	−0.0111854	+	0.999937i	$0.503560\pi$
$948$	−4.90427	−0.159283
$949$	66.0514	2.14412
$950$	−6.01137	−0.195035
$951$	−36.9164	−1.19710
$952$	0.884643	0.0286714
$953$	−6.54144	−0.211898	−0.105949	−	0.994372i	$-0.533788\pi$
$953$	−6.54144	−0.211898	−0.105949	+	0.994372i	$0.533788\pi$
$954$	0.410416	0.0132877
$955$	3.88368	0.125673
$956$	−13.1816	−0.426322
$957$	−6.00822	−0.194218
$958$	−5.78661	−0.186957
$959$	−1.59399	−0.0514728
$960$	1.75851	0.0567558
$961$	−21.1113	−0.681011
$962$	−38.2083	−1.23189
$963$	0.124338	0.00400672
$964$	14.7855	0.476210
$965$	9.37592	0.301822
$966$	0.0316963	0.00101981
$967$	−25.4310	−0.817805	−0.408903	−	0.912578i	$-0.634088\pi$
$967$	−25.4310	−0.817805	−0.408903	+	0.912578i	$0.634088\pi$
$968$	−9.87754	−0.317476
$969$	80.9167	2.59942
$970$	−7.38623	−0.237158
$971$	25.4416	0.816460	0.408230	−	0.912879i	$-0.366146\pi$
$971$	25.4416	0.816460	0.408230	+	0.912879i	$0.366146\pi$
$972$	−0.959608	−0.0307794
$973$	−0.426040	−0.0136582
$974$	23.4387	0.751025
$975$	−10.4193	−0.333685
$976$	5.01100	0.160398
$977$	−43.9535	−1.40620	−0.703098	−	0.711093i	$-0.748200\pi$
$977$	−43.9535	−1.40620	−0.703098	+	0.711093i	$0.748200\pi$
$978$	7.04975	0.225426
$979$	3.37194	0.107768
$980$	−6.98664	−0.223180
$981$	−0.375789	−0.0119980
$982$	−4.03449	−0.128746
$983$	12.4179	0.396068	0.198034	−	0.980195i	$-0.436544\pi$
$983$	12.4179	0.396068	0.198034	+	0.980195i	$0.436544\pi$
$984$	−0.878998	−0.0280214
$985$	8.09795	0.258022
$986$	−24.6850	−0.786131
$987$	−1.10162	−0.0350651
$988$	35.6177	1.13315
$989$	0.499555	0.0158849
$990$	−0.0978633	−0.00311030
$991$	−4.64070	−0.147417	−0.0737084	−	0.997280i	$-0.523483\pi$
$991$	−4.64070	−0.147417	−0.0737084	+	0.997280i	$0.523483\pi$
$992$	−3.14463	−0.0998420
$993$	−53.0746	−1.68427
$994$	−1.01736	−0.0322686
$995$	−2.33970	−0.0741736
$996$	9.40041	0.297863
$997$	36.3901	1.15249	0.576243	−	0.817278i	$-0.304518\pi$
$997$	36.3901	1.15249	0.576243	+	0.817278i	$0.304518\pi$
$998$	−3.14365	−0.0995105
$999$	−32.9724	−1.04320

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.c.1.15	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.c.1.15	✓	16	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.75851 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.75851 q^{6} -0.115571 q^{7} +1.00000 q^{8} +0.0923708 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.75851 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.75851 q^{6} -0.115571 q^{7} +1.00000 q^{8} +0.0923708 q^{9} +1.00000 q^{10} -1.05946 q^{11} +1.75851 q^{12} -5.92506 q^{13} -0.115571 q^{14} +1.75851 q^{15} +1.00000 q^{16} -7.65454 q^{17} +0.0923708 q^{18} -6.01137 q^{19} +1.00000 q^{20} -0.203233 q^{21} -1.05946 q^{22} -0.155960 q^{23} +1.75851 q^{24} +1.00000 q^{25} -5.92506 q^{26} -5.11311 q^{27} -0.115571 q^{28} +3.22489 q^{29} +1.75851 q^{30} -3.14463 q^{31} +1.00000 q^{32} -1.86308 q^{33} -7.65454 q^{34} -0.115571 q^{35} +0.0923708 q^{36} +6.44860 q^{37} -6.01137 q^{38} -10.4193 q^{39} +1.00000 q^{40} -0.499853 q^{41} -0.203233 q^{42} -3.20309 q^{43} -1.05946 q^{44} +0.0923708 q^{45} -0.155960 q^{46} +5.42049 q^{47} +1.75851 q^{48} -6.98664 q^{49} +1.00000 q^{50} -13.4606 q^{51} -5.92506 q^{52} +4.44313 q^{53} -5.11311 q^{54} -1.05946 q^{55} -0.115571 q^{56} -10.5711 q^{57} +3.22489 q^{58} +2.13926 q^{59} +1.75851 q^{60} +5.01100 q^{61} -3.14463 q^{62} -0.0106754 q^{63} +1.00000 q^{64} -5.92506 q^{65} -1.86308 q^{66} -15.5059 q^{67} -7.65454 q^{68} -0.274258 q^{69} -0.115571 q^{70} +8.80287 q^{71} +0.0923708 q^{72} -11.1478 q^{73} +6.44860 q^{74} +1.75851 q^{75} -6.01137 q^{76} +0.122443 q^{77} -10.4193 q^{78} -2.78887 q^{79} +1.00000 q^{80} -9.26858 q^{81} -0.499853 q^{82} +5.34566 q^{83} -0.203233 q^{84} -7.65454 q^{85} -3.20309 q^{86} +5.67101 q^{87} -1.05946 q^{88} -3.18269 q^{89} +0.0923708 q^{90} +0.684765 q^{91} -0.155960 q^{92} -5.52987 q^{93} +5.42049 q^{94} -6.01137 q^{95} +1.75851 q^{96} -7.38623 q^{97} -6.98664 q^{98} -0.0978633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9} + 16 q^{10} - 14 q^{11} - 8 q^{12} - 20 q^{13} - 10 q^{14} - 8 q^{15} + 16 q^{16} - 27 q^{17} - 2 q^{18} - 17 q^{19} + 16 q^{20} - 12 q^{21} - 14 q^{22} - 9 q^{23} - 8 q^{24} + 16 q^{25} - 20 q^{26} - 11 q^{27} - 10 q^{28} - 23 q^{29} - 8 q^{30} - 21 q^{31} + 16 q^{32} - 9 q^{33} - 27 q^{34} - 10 q^{35} - 2 q^{36} - 16 q^{37} - 17 q^{38} - 6 q^{39} + 16 q^{40} - 35 q^{41} - 12 q^{42} + 3 q^{43} - 14 q^{44} - 2 q^{45} - 9 q^{46} - 25 q^{47} - 8 q^{48} - 24 q^{49} + 16 q^{50} - q^{51} - 20 q^{52} - 39 q^{53} - 11 q^{54} - 14 q^{55} - 10 q^{56} - 6 q^{57} - 23 q^{58} - 32 q^{59} - 8 q^{60} - 38 q^{61} - 21 q^{62} + q^{63} + 16 q^{64} - 20 q^{65} - 9 q^{66} + 5 q^{67} - 27 q^{68} - 25 q^{69} - 10 q^{70} - 16 q^{71} - 2 q^{72} - 17 q^{73} - 16 q^{74} - 8 q^{75} - 17 q^{76} - 34 q^{77} - 6 q^{78} - 40 q^{79} + 16 q^{80} - 28 q^{81} - 35 q^{82} - 22 q^{83} - 12 q^{84} - 27 q^{85} + 3 q^{86} + 10 q^{87} - 14 q^{88} - 46 q^{89} - 2 q^{90} - q^{91} - 9 q^{92} + 14 q^{93} - 25 q^{94} - 17 q^{95} - 8 q^{96} - 21 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9 + 16 * q^10 - 14 * q^11 - 8 * q^12 - 20 * q^13 - 10 * q^14 - 8 * q^15 + 16 * q^16 - 27 * q^17 - 2 * q^18 - 17 * q^19 + 16 * q^20 - 12 * q^21 - 14 * q^22 - 9 * q^23 - 8 * q^24 + 16 * q^25 - 20 * q^26 - 11 * q^27 - 10 * q^28 - 23 * q^29 - 8 * q^30 - 21 * q^31 + 16 * q^32 - 9 * q^33 - 27 * q^34 - 10 * q^35 - 2 * q^36 - 16 * q^37 - 17 * q^38 - 6 * q^39 + 16 * q^40 - 35 * q^41 - 12 * q^42 + 3 * q^43 - 14 * q^44 - 2 * q^45 - 9 * q^46 - 25 * q^47 - 8 * q^48 - 24 * q^49 + 16 * q^50 - q^51 - 20 * q^52 - 39 * q^53 - 11 * q^54 - 14 * q^55 - 10 * q^56 - 6 * q^57 - 23 * q^58 - 32 * q^59 - 8 * q^60 - 38 * q^61 - 21 * q^62 + q^63 + 16 * q^64 - 20 * q^65 - 9 * q^66 + 5 * q^67 - 27 * q^68 - 25 * q^69 - 10 * q^70 - 16 * q^71 - 2 * q^72 - 17 * q^73 - 16 * q^74 - 8 * q^75 - 17 * q^76 - 34 * q^77 - 6 * q^78 - 40 * q^79 + 16 * q^80 - 28 * q^81 - 35 * q^82 - 22 * q^83 - 12 * q^84 - 27 * q^85 + 3 * q^86 + 10 * q^87 - 14 * q^88 - 46 * q^89 - 2 * q^90 - q^91 - 9 * q^92 + 14 * q^93 - 25 * q^94 - 17 * q^95 - 8 * q^96 - 21 * q^97 - 24 * q^98 + 15 * q^99

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