LMFDB - Embedded newform 8030.2.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.30278$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.30278 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.30278 q^{6} +0.302776 q^{7} -1.00000 q^{8} +2.30278 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.30278 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.30278 q^{6} +0.302776 q^{7} -1.00000 q^{8} +2.30278 q^{9} +1.00000 q^{10} +1.00000 q^{11} +2.30278 q^{12} +5.90833 q^{13} -0.302776 q^{14} -2.30278 q^{15} +1.00000 q^{16} -3.90833 q^{17} -2.30278 q^{18} -4.00000 q^{19} -1.00000 q^{20} +0.697224 q^{21} -1.00000 q^{22} +1.30278 q^{23} -2.30278 q^{24} +1.00000 q^{25} -5.90833 q^{26} -1.60555 q^{27} +0.302776 q^{28} -1.69722 q^{29} +2.30278 q^{30} -6.60555 q^{31} -1.00000 q^{32} +2.30278 q^{33} +3.90833 q^{34} -0.302776 q^{35} +2.30278 q^{36} -1.90833 q^{37} +4.00000 q^{38} +13.6056 q^{39} +1.00000 q^{40} -6.00000 q^{41} -0.697224 q^{42} -9.21110 q^{43} +1.00000 q^{44} -2.30278 q^{45} -1.30278 q^{46} -11.2111 q^{47} +2.30278 q^{48} -6.90833 q^{49} -1.00000 q^{50} -9.00000 q^{51} +5.90833 q^{52} +1.60555 q^{54} -1.00000 q^{55} -0.302776 q^{56} -9.21110 q^{57} +1.69722 q^{58} +7.81665 q^{59} -2.30278 q^{60} -0.605551 q^{61} +6.60555 q^{62} +0.697224 q^{63} +1.00000 q^{64} -5.90833 q^{65} -2.30278 q^{66} -2.30278 q^{67} -3.90833 q^{68} +3.00000 q^{69} +0.302776 q^{70} -3.51388 q^{71} -2.30278 q^{72} +1.00000 q^{73} +1.90833 q^{74} +2.30278 q^{75} -4.00000 q^{76} +0.302776 q^{77} -13.6056 q^{78} -3.21110 q^{79} -1.00000 q^{80} -10.6056 q^{81} +6.00000 q^{82} +10.3028 q^{83} +0.697224 q^{84} +3.90833 q^{85} +9.21110 q^{86} -3.90833 q^{87} -1.00000 q^{88} +17.7250 q^{89} +2.30278 q^{90} +1.78890 q^{91} +1.30278 q^{92} -15.2111 q^{93} +11.2111 q^{94} +4.00000 q^{95} -2.30278 q^{96} -19.5139 q^{97} +6.90833 q^{98} +2.30278 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} - q^{6} - 3 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 - q^6 - 3 * q^7 - 2 * q^8 + q^9	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} - q^{6} - 3 q^{7} - 2 q^{8} + q^{9} + 2 q^{10} + 2 q^{11} + q^{12} + q^{13} + 3 q^{14} - q^{15} + 2 q^{16} + 3 q^{17} - q^{18} - 8 q^{19} - 2 q^{20} + 5 q^{21} - 2 q^{22} - q^{23} - q^{24} + 2 q^{25} - q^{26} + 4 q^{27} - 3 q^{28} - 7 q^{29} + q^{30} - 6 q^{31} - 2 q^{32} + q^{33} - 3 q^{34} + 3 q^{35} + q^{36} + 7 q^{37} + 8 q^{38} + 20 q^{39} + 2 q^{40} - 12 q^{41} - 5 q^{42} - 4 q^{43} + 2 q^{44} - q^{45} + q^{46} - 8 q^{47} + q^{48} - 3 q^{49} - 2 q^{50} - 18 q^{51} + q^{52} - 4 q^{54} - 2 q^{55} + 3 q^{56} - 4 q^{57} + 7 q^{58} - 6 q^{59} - q^{60} + 6 q^{61} + 6 q^{62} + 5 q^{63} + 2 q^{64} - q^{65} - q^{66} - q^{67} + 3 q^{68} + 6 q^{69} - 3 q^{70} + 11 q^{71} - q^{72} + 2 q^{73} - 7 q^{74} + q^{75} - 8 q^{76} - 3 q^{77} - 20 q^{78} + 8 q^{79} - 2 q^{80} - 14 q^{81} + 12 q^{82} + 17 q^{83} + 5 q^{84} - 3 q^{85} + 4 q^{86} + 3 q^{87} - 2 q^{88} + 3 q^{89} + q^{90} + 18 q^{91} - q^{92} - 16 q^{93} + 8 q^{94} + 8 q^{95} - q^{96} - 21 q^{97} + 3 q^{98} + q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 - q^6 - 3 * q^7 - 2 * q^8 + q^9 + 2 * q^10 + 2 * q^11 + q^12 + q^13 + 3 * q^14 - q^15 + 2 * q^16 + 3 * q^17 - q^18 - 8 * q^19 - 2 * q^20 + 5 * q^21 - 2 * q^22 - q^23 - q^24 + 2 * q^25 - q^26 + 4 * q^27 - 3 * q^28 - 7 * q^29 + q^30 - 6 * q^31 - 2 * q^32 + q^33 - 3 * q^34 + 3 * q^35 + q^36 + 7 * q^37 + 8 * q^38 + 20 * q^39 + 2 * q^40 - 12 * q^41 - 5 * q^42 - 4 * q^43 + 2 * q^44 - q^45 + q^46 - 8 * q^47 + q^48 - 3 * q^49 - 2 * q^50 - 18 * q^51 + q^52 - 4 * q^54 - 2 * q^55 + 3 * q^56 - 4 * q^57 + 7 * q^58 - 6 * q^59 - q^60 + 6 * q^61 + 6 * q^62 + 5 * q^63 + 2 * q^64 - q^65 - q^66 - q^67 + 3 * q^68 + 6 * q^69 - 3 * q^70 + 11 * q^71 - q^72 + 2 * q^73 - 7 * q^74 + q^75 - 8 * q^76 - 3 * q^77 - 20 * q^78 + 8 * q^79 - 2 * q^80 - 14 * q^81 + 12 * q^82 + 17 * q^83 + 5 * q^84 - 3 * q^85 + 4 * q^86 + 3 * q^87 - 2 * q^88 + 3 * q^89 + q^90 + 18 * q^91 - q^92 - 16 * q^93 + 8 * q^94 + 8 * q^95 - q^96 - 21 * q^97 + 3 * q^98 + 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
$3$	2.30278	1.32951	0.664754	−	0.747062i	$-0.268536\pi$
$3$	2.30278	1.32951	0.664754	+	0.747062i	$0.268536\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.30278	−0.940104
$7$	0.302776	0.114438	0.0572192	−	0.998362i	$-0.481777\pi$
$7$	0.302776	0.114438	0.0572192	+	0.998362i	$0.481777\pi$
$8$	−1.00000	−0.353553
$9$	2.30278	0.767592
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.30278	0.664754
$13$	5.90833	1.63868	0.819338	−	0.573311i	$-0.194341\pi$
$13$	5.90833	1.63868	0.819338	+	0.573311i	$0.194341\pi$
$14$	−0.302776	−0.0809202
$15$	−2.30278	−0.594574
$16$	1.00000	0.250000
$17$	−3.90833	−0.947909	−0.473954	−	0.880549i	$-0.657174\pi$
$17$	−3.90833	−0.947909	−0.473954	+	0.880549i	$0.657174\pi$
$18$	−2.30278	−0.542769
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	−1.00000	−0.223607
$21$	0.697224	0.152147
$22$	−1.00000	−0.213201
$23$	1.30278	0.271647	0.135824	−	0.990733i	$-0.456632\pi$
$23$	1.30278	0.271647	0.135824	+	0.990733i	$0.456632\pi$
$24$	−2.30278	−0.470052
$25$	1.00000	0.200000
$26$	−5.90833	−1.15872
$27$	−1.60555	−0.308988
$28$	0.302776	0.0572192
$29$	−1.69722	−0.315167	−0.157583	−	0.987506i	$-0.550370\pi$
$29$	−1.69722	−0.315167	−0.157583	+	0.987506i	$0.550370\pi$
$30$	2.30278	0.420427
$31$	−6.60555	−1.18639	−0.593196	−	0.805058i	$-0.702134\pi$
$31$	−6.60555	−1.18639	−0.593196	+	0.805058i	$0.702134\pi$
$32$	−1.00000	−0.176777
$33$	2.30278	0.400862
$34$	3.90833	0.670273
$35$	−0.302776	−0.0511784
$36$	2.30278	0.383796
$37$	−1.90833	−0.313727	−0.156864	−	0.987620i	$-0.550138\pi$
$37$	−1.90833	−0.313727	−0.156864	+	0.987620i	$0.550138\pi$
$38$	4.00000	0.648886
$39$	13.6056	2.17863
$40$	1.00000	0.158114
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	−0.697224	−0.107584
$43$	−9.21110	−1.40468	−0.702340	−	0.711842i	$-0.747861\pi$
$43$	−9.21110	−1.40468	−0.702340	+	0.711842i	$0.747861\pi$
$44$	1.00000	0.150756
$45$	−2.30278	−0.343278
$46$	−1.30278	−0.192084
$47$	−11.2111	−1.63531	−0.817654	−	0.575710i	$-0.804726\pi$
$47$	−11.2111	−1.63531	−0.817654	+	0.575710i	$0.804726\pi$
$48$	2.30278	0.332377
$49$	−6.90833	−0.986904
$50$	−1.00000	−0.141421
$51$	−9.00000	−1.26025
$52$	5.90833	0.819338
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	1.60555	0.218488
$55$	−1.00000	−0.134840
$56$	−0.302776	−0.0404601
$57$	−9.21110	−1.22004
$58$	1.69722	0.222856
$59$	7.81665	1.01764	0.508821	−	0.860872i	$-0.330082\pi$
$59$	7.81665	1.01764	0.508821	+	0.860872i	$0.330082\pi$
$60$	−2.30278	−0.297287
$61$	−0.605551	−0.0775329	−0.0387664	−	0.999248i	$-0.512343\pi$
$61$	−0.605551	−0.0775329	−0.0387664	+	0.999248i	$0.512343\pi$
$62$	6.60555	0.838906
$63$	0.697224	0.0878420
$64$	1.00000	0.125000
$65$	−5.90833	−0.732838
$66$	−2.30278	−0.283452
$67$	−2.30278	−0.281329	−0.140664	−	0.990057i	$-0.544924\pi$
$67$	−2.30278	−0.281329	−0.140664	+	0.990057i	$0.544924\pi$
$68$	−3.90833	−0.473954
$69$	3.00000	0.361158
$70$	0.302776	0.0361886
$71$	−3.51388	−0.417021	−0.208510	−	0.978020i	$-0.566861\pi$
$71$	−3.51388	−0.417021	−0.208510	+	0.978020i	$0.566861\pi$
$72$	−2.30278	−0.271385
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	1.90833	0.221838
$75$	2.30278	0.265902
$76$	−4.00000	−0.458831
$77$	0.302776	0.0345045
$78$	−13.6056	−1.54053
$79$	−3.21110	−0.361277	−0.180639	−	0.983550i	$-0.557816\pi$
$79$	−3.21110	−0.361277	−0.180639	+	0.983550i	$0.557816\pi$
$80$	−1.00000	−0.111803
$81$	−10.6056	−1.17839
$82$	6.00000	0.662589
$83$	10.3028	1.13088	0.565438	−	0.824791i	$-0.308707\pi$
$83$	10.3028	1.13088	0.565438	+	0.824791i	$0.308707\pi$
$84$	0.697224	0.0760734
$85$	3.90833	0.423918
$86$	9.21110	0.993259
$87$	−3.90833	−0.419017
$88$	−1.00000	−0.106600
$89$	17.7250	1.87884	0.939422	−	0.342762i	$-0.111363\pi$
$89$	17.7250	1.87884	0.939422	+	0.342762i	$0.111363\pi$
$90$	2.30278	0.242734
$91$	1.78890	0.187527
$92$	1.30278	0.135824
$93$	−15.2111	−1.57732
$94$	11.2111	1.15634
$95$	4.00000	0.410391
$96$	−2.30278	−0.235026
$97$	−19.5139	−1.98133	−0.990667	−	0.136304i	$-0.956478\pi$
$97$	−19.5139	−1.98133	−0.990667	+	0.136304i	$0.956478\pi$
$98$	6.90833	0.697846
$99$	2.30278	0.231438
$100$	1.00000	0.100000
$101$	1.69722	0.168880	0.0844401	−	0.996429i	$-0.473090\pi$
$101$	1.69722	0.168880	0.0844401	+	0.996429i	$0.473090\pi$
$102$	9.00000	0.891133
$103$	−18.6056	−1.83326	−0.916630	−	0.399737i	$-0.869101\pi$
$103$	−18.6056	−1.83326	−0.916630	+	0.399737i	$0.869101\pi$
$104$	−5.90833	−0.579359
$105$	−0.697224	−0.0680421
$106$	0	0
$107$	−0.513878	−0.0496785	−0.0248392	−	0.999691i	$-0.507907\pi$
$107$	−0.513878	−0.0496785	−0.0248392	+	0.999691i	$0.507907\pi$
$108$	−1.60555	−0.154494
$109$	−14.4222	−1.38140	−0.690698	−	0.723143i	$-0.742697\pi$
$109$	−14.4222	−1.38140	−0.690698	+	0.723143i	$0.742697\pi$
$110$	1.00000	0.0953463
$111$	−4.39445	−0.417103
$112$	0.302776	0.0286096
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	9.21110	0.862699
$115$	−1.30278	−0.121484
$116$	−1.69722	−0.157583
$117$	13.6056	1.25783
$118$	−7.81665	−0.719581
$119$	−1.18335	−0.108477
$120$	2.30278	0.210214
$121$	1.00000	0.0909091
$122$	0.605551	0.0548240
$123$	−13.8167	−1.24581
$124$	−6.60555	−0.593196
$125$	−1.00000	−0.0894427
$126$	−0.697224	−0.0621137
$127$	5.39445	0.478680	0.239340	−	0.970936i	$-0.423069\pi$
$127$	5.39445	0.478680	0.239340	+	0.970936i	$0.423069\pi$
$128$	−1.00000	−0.0883883
$129$	−21.2111	−1.86753
$130$	5.90833	0.518195
$131$	18.5139	1.61757	0.808783	−	0.588108i	$-0.200127\pi$
$131$	18.5139	1.61757	0.808783	+	0.588108i	$0.200127\pi$
$132$	2.30278	0.200431
$133$	−1.21110	−0.105016
$134$	2.30278	0.198930
$135$	1.60555	0.138184
$136$	3.90833	0.335136
$137$	6.90833	0.590218	0.295109	−	0.955464i	$-0.404644\pi$
$137$	6.90833	0.590218	0.295109	+	0.955464i	$0.404644\pi$
$138$	−3.00000	−0.255377
$139$	−0.0916731	−0.00777561	−0.00388780	−	0.999992i	$-0.501238\pi$
$139$	−0.0916731	−0.00777561	−0.00388780	+	0.999992i	$0.501238\pi$
$140$	−0.302776	−0.0255892
$141$	−25.8167	−2.17415
$142$	3.51388	0.294878
$143$	5.90833	0.494079
$144$	2.30278	0.191898
$145$	1.69722	0.140947
$146$	−1.00000	−0.0827606
$147$	−15.9083	−1.31210
$148$	−1.90833	−0.156864
$149$	−8.60555	−0.704994	−0.352497	−	0.935813i	$-0.614667\pi$
$149$	−8.60555	−0.704994	−0.352497	+	0.935813i	$0.614667\pi$
$150$	−2.30278	−0.188021
$151$	5.90833	0.480813	0.240406	−	0.970672i	$-0.422719\pi$
$151$	5.90833	0.480813	0.240406	+	0.970672i	$0.422719\pi$
$152$	4.00000	0.324443
$153$	−9.00000	−0.727607
$154$	−0.302776	−0.0243984
$155$	6.60555	0.530571
$156$	13.6056	1.08932
$157$	−21.2111	−1.69283	−0.846415	−	0.532524i	$-0.821244\pi$
$157$	−21.2111	−1.69283	−0.846415	+	0.532524i	$0.821244\pi$
$158$	3.21110	0.255462
$159$	0	0
$160$	1.00000	0.0790569
$161$	0.394449	0.0310869
$162$	10.6056	0.833251
$163$	8.00000	0.626608	0.313304	−	0.949653i	$-0.398564\pi$
$163$	8.00000	0.626608	0.313304	+	0.949653i	$0.398564\pi$
$164$	−6.00000	−0.468521
$165$	−2.30278	−0.179271
$166$	−10.3028	−0.799650
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	−0.697224	−0.0537920
$169$	21.9083	1.68526
$170$	−3.90833	−0.299755
$171$	−9.21110	−0.704391
$172$	−9.21110	−0.702340
$173$	11.2111	0.852364	0.426182	−	0.904637i	$-0.359858\pi$
$173$	11.2111	0.852364	0.426182	+	0.904637i	$0.359858\pi$
$174$	3.90833	0.296289
$175$	0.302776	0.0228877
$176$	1.00000	0.0753778
$177$	18.0000	1.35296
$178$	−17.7250	−1.32854
$179$	11.2111	0.837957	0.418979	−	0.907996i	$-0.362388\pi$
$179$	11.2111	0.837957	0.418979	+	0.907996i	$0.362388\pi$
$180$	−2.30278	−0.171639
$181$	2.90833	0.216174	0.108087	−	0.994141i	$-0.465527\pi$
$181$	2.90833	0.216174	0.108087	+	0.994141i	$0.465527\pi$
$182$	−1.78890	−0.132602
$183$	−1.39445	−0.103081
$184$	−1.30278	−0.0960419
$185$	1.90833	0.140303
$186$	15.2111	1.11533
$187$	−3.90833	−0.285805
$188$	−11.2111	−0.817654
$189$	−0.486122	−0.0353602
$190$	−4.00000	−0.290191
$191$	19.0278	1.37680	0.688400	−	0.725331i	$-0.258313\pi$
$191$	19.0278	1.37680	0.688400	+	0.725331i	$0.258313\pi$
$192$	2.30278	0.166189
$193$	11.9083	0.857180	0.428590	−	0.903499i	$-0.359010\pi$
$193$	11.9083	0.857180	0.428590	+	0.903499i	$0.359010\pi$
$194$	19.5139	1.40101
$195$	−13.6056	−0.974314
$196$	−6.90833	−0.493452
$197$	16.3028	1.16152	0.580762	−	0.814073i	$-0.302755\pi$
$197$	16.3028	1.16152	0.580762	+	0.814073i	$0.302755\pi$
$198$	−2.30278	−0.163651
$199$	−17.8167	−1.26299	−0.631495	−	0.775380i	$-0.717558\pi$
$199$	−17.8167	−1.26299	−0.631495	+	0.775380i	$0.717558\pi$
$200$	−1.00000	−0.0707107
$201$	−5.30278	−0.374029
$202$	−1.69722	−0.119416
$203$	−0.513878	−0.0360672
$204$	−9.00000	−0.630126
$205$	6.00000	0.419058
$206$	18.6056	1.29631
$207$	3.00000	0.208514
$208$	5.90833	0.409669
$209$	−4.00000	−0.276686
$210$	0.697224	0.0481131
$211$	1.21110	0.0833757	0.0416879	−	0.999131i	$-0.486726\pi$
$211$	1.21110	0.0833757	0.0416879	+	0.999131i	$0.486726\pi$
$212$	0	0
$213$	−8.09167	−0.554432
$214$	0.513878	0.0351280
$215$	9.21110	0.628192
$216$	1.60555	0.109244
$217$	−2.00000	−0.135769
$218$	14.4222	0.976795
$219$	2.30278	0.155607
$220$	−1.00000	−0.0674200
$221$	−23.0917	−1.55331
$222$	4.39445	0.294936
$223$	23.9083	1.60102	0.800510	−	0.599319i	$-0.204562\pi$
$223$	23.9083	1.60102	0.800510	+	0.599319i	$0.204562\pi$
$224$	−0.302776	−0.0202300
$225$	2.30278	0.153518
$226$	−6.00000	−0.399114
$227$	−25.8167	−1.71351	−0.856756	−	0.515722i	$-0.827524\pi$
$227$	−25.8167	−1.71351	−0.856756	+	0.515722i	$0.827524\pi$
$228$	−9.21110	−0.610020
$229$	−13.3944	−0.885130	−0.442565	−	0.896736i	$-0.645931\pi$
$229$	−13.3944	−0.885130	−0.442565	+	0.896736i	$0.645931\pi$
$230$	1.30278	0.0859025
$231$	0.697224	0.0458740
$232$	1.69722	0.111428
$233$	−28.4222	−1.86200	−0.931000	−	0.365018i	$-0.881063\pi$
$233$	−28.4222	−1.86200	−0.931000	+	0.365018i	$0.881063\pi$
$234$	−13.6056	−0.889423
$235$	11.2111	0.731332
$236$	7.81665	0.508821
$237$	−7.39445	−0.480321
$238$	1.18335	0.0767049
$239$	16.6972	1.08005	0.540027	−	0.841648i	$-0.318414\pi$
$239$	16.6972	1.08005	0.540027	+	0.841648i	$0.318414\pi$
$240$	−2.30278	−0.148644
$241$	14.0000	0.901819	0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000	0.901819	0.450910	+	0.892570i	$0.351100\pi$
$242$	−1.00000	−0.0642824
$243$	−19.6056	−1.25770
$244$	−0.605551	−0.0387664
$245$	6.90833	0.441357
$246$	13.8167	0.880918
$247$	−23.6333	−1.50375
$248$	6.60555	0.419453
$249$	23.7250	1.50351
$250$	1.00000	0.0632456
$251$	−28.5416	−1.80153	−0.900766	−	0.434305i	$-0.856994\pi$
$251$	−28.5416	−1.80153	−0.900766	+	0.434305i	$0.856994\pi$
$252$	0.697224	0.0439210
$253$	1.30278	0.0819048
$254$	−5.39445	−0.338478
$255$	9.00000	0.563602
$256$	1.00000	0.0625000
$257$	21.6333	1.34945	0.674724	−	0.738070i	$-0.264263\pi$
$257$	21.6333	1.34945	0.674724	+	0.738070i	$0.264263\pi$
$258$	21.2111	1.32055
$259$	−0.577795	−0.0359024
$260$	−5.90833	−0.366419
$261$	−3.90833	−0.241919
$262$	−18.5139	−1.14379
$263$	−4.30278	−0.265321	−0.132660	−	0.991162i	$-0.542352\pi$
$263$	−4.30278	−0.265321	−0.132660	+	0.991162i	$0.542352\pi$
$264$	−2.30278	−0.141726
$265$	0	0
$266$	1.21110	0.0742575
$267$	40.8167	2.49794
$268$	−2.30278	−0.140664
$269$	−8.48612	−0.517408	−0.258704	−	0.965957i	$-0.583295\pi$
$269$	−8.48612	−0.517408	−0.258704	+	0.965957i	$0.583295\pi$
$270$	−1.60555	−0.0977107
$271$	−17.6972	−1.07503	−0.537515	−	0.843254i	$-0.680637\pi$
$271$	−17.6972	−1.07503	−0.537515	+	0.843254i	$0.680637\pi$
$272$	−3.90833	−0.236977
$273$	4.11943	0.249319
$274$	−6.90833	−0.417347
$275$	1.00000	0.0603023
$276$	3.00000	0.180579
$277$	−16.9083	−1.01592	−0.507961	−	0.861380i	$-0.669601\pi$
$277$	−16.9083	−1.01592	−0.507961	+	0.861380i	$0.669601\pi$
$278$	0.0916731	0.00549819
$279$	−15.2111	−0.910665
$280$	0.302776	0.0180943
$281$	−14.0917	−0.840639	−0.420319	−	0.907376i	$-0.638082\pi$
$281$	−14.0917	−0.840639	−0.420319	+	0.907376i	$0.638082\pi$
$282$	25.8167	1.53736
$283$	12.4222	0.738423	0.369212	−	0.929345i	$-0.379628\pi$
$283$	12.4222	0.738423	0.369212	+	0.929345i	$0.379628\pi$
$284$	−3.51388	−0.208510
$285$	9.21110	0.545619
$286$	−5.90833	−0.349367
$287$	−1.81665	−0.107234
$288$	−2.30278	−0.135692
$289$	−1.72498	−0.101469
$290$	−1.69722	−0.0996644
$291$	−44.9361	−2.63420
$292$	1.00000	0.0585206
$293$	−15.6333	−0.913308	−0.456654	−	0.889644i	$-0.650952\pi$
$293$	−15.6333	−0.913308	−0.456654	+	0.889644i	$0.650952\pi$
$294$	15.9083	0.927792
$295$	−7.81665	−0.455103
$296$	1.90833	0.110919
$297$	−1.60555	−0.0931635
$298$	8.60555	0.498506
$299$	7.69722	0.445142
$300$	2.30278	0.132951
$301$	−2.78890	−0.160749
$302$	−5.90833	−0.339986
$303$	3.90833	0.224528
$304$	−4.00000	−0.229416
$305$	0.605551	0.0346738
$306$	9.00000	0.514496
$307$	−2.30278	−0.131426	−0.0657132	−	0.997839i	$-0.520932\pi$
$307$	−2.30278	−0.131426	−0.0657132	+	0.997839i	$0.520932\pi$
$308$	0.302776	0.0172522
$309$	−42.8444	−2.43733
$310$	−6.60555	−0.375170
$311$	−24.0000	−1.36092	−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000	−1.36092	−0.680458	+	0.732787i	$0.738219\pi$
$312$	−13.6056	−0.770263
$313$	−26.4222	−1.49347	−0.746736	−	0.665121i	$-0.768380\pi$
$313$	−26.4222	−1.49347	−0.746736	+	0.665121i	$0.768380\pi$
$314$	21.2111	1.19701
$315$	−0.697224	−0.0392841
$316$	−3.21110	−0.180639
$317$	−29.7250	−1.66952	−0.834761	−	0.550613i	$-0.814394\pi$
$317$	−29.7250	−1.66952	−0.834761	+	0.550613i	$0.814394\pi$
$318$	0	0
$319$	−1.69722	−0.0950263
$320$	−1.00000	−0.0559017
$321$	−1.18335	−0.0660479
$322$	−0.394449	−0.0219818
$323$	15.6333	0.869861
$324$	−10.6056	−0.589197
$325$	5.90833	0.327735
$326$	−8.00000	−0.443079
$327$	−33.2111	−1.83658
$328$	6.00000	0.331295
$329$	−3.39445	−0.187142
$330$	2.30278	0.126764
$331$	−25.6333	−1.40893	−0.704467	−	0.709737i	$-0.748814\pi$
$331$	−25.6333	−1.40893	−0.704467	+	0.709737i	$0.748814\pi$
$332$	10.3028	0.565438
$333$	−4.39445	−0.240814
$334$	−12.0000	−0.656611
$335$	2.30278	0.125814
$336$	0.697224	0.0380367
$337$	28.7250	1.56475	0.782375	−	0.622808i	$-0.214008\pi$
$337$	28.7250	1.56475	0.782375	+	0.622808i	$0.214008\pi$
$338$	−21.9083	−1.19166
$339$	13.8167	0.750418
$340$	3.90833	0.211959
$341$	−6.60555	−0.357711
$342$	9.21110	0.498079
$343$	−4.21110	−0.227378
$344$	9.21110	0.496629
$345$	−3.00000	−0.161515
$346$	−11.2111	−0.602713
$347$	−21.6333	−1.16134	−0.580668	−	0.814140i	$-0.697209\pi$
$347$	−21.6333	−1.16134	−0.580668	+	0.814140i	$0.697209\pi$
$348$	−3.90833	−0.209508
$349$	19.2111	1.02835	0.514173	−	0.857686i	$-0.328099\pi$
$349$	19.2111	1.02835	0.514173	+	0.857686i	$0.328099\pi$
$350$	−0.302776	−0.0161840
$351$	−9.48612	−0.506332
$352$	−1.00000	−0.0533002
$353$	5.09167	0.271002	0.135501	−	0.990777i	$-0.456736\pi$
$353$	5.09167	0.271002	0.135501	+	0.990777i	$0.456736\pi$
$354$	−18.0000	−0.956689
$355$	3.51388	0.186497
$356$	17.7250	0.939422
$357$	−2.72498	−0.144221
$358$	−11.2111	−0.592525
$359$	19.0278	1.00425	0.502123	−	0.864796i	$-0.332552\pi$
$359$	19.0278	1.00425	0.502123	+	0.864796i	$0.332552\pi$
$360$	2.30278	0.121367
$361$	−3.00000	−0.157895
$362$	−2.90833	−0.152858
$363$	2.30278	0.120864
$364$	1.78890	0.0937637
$365$	−1.00000	−0.0523424
$366$	1.39445	0.0728890
$367$	32.7527	1.70968	0.854839	−	0.518893i	$-0.173656\pi$
$367$	32.7527	1.70968	0.854839	+	0.518893i	$0.173656\pi$
$368$	1.30278	0.0679119
$369$	−13.8167	−0.719266
$370$	−1.90833	−0.0992092
$371$	0	0
$372$	−15.2111	−0.788659
$373$	−24.6056	−1.27403	−0.637014	−	0.770853i	$-0.719830\pi$
$373$	−24.6056	−1.27403	−0.637014	+	0.770853i	$0.719830\pi$
$374$	3.90833	0.202095
$375$	−2.30278	−0.118915
$376$	11.2111	0.578168
$377$	−10.0278	−0.516456
$378$	0.486122	0.0250034
$379$	−14.4222	−0.740819	−0.370409	−	0.928869i	$-0.620783\pi$
$379$	−14.4222	−0.740819	−0.370409	+	0.928869i	$0.620783\pi$
$380$	4.00000	0.205196
$381$	12.4222	0.636409
$382$	−19.0278	−0.973545
$383$	5.21110	0.266275	0.133137	−	0.991098i	$-0.457495\pi$
$383$	5.21110	0.266275	0.133137	+	0.991098i	$0.457495\pi$
$384$	−2.30278	−0.117513
$385$	−0.302776	−0.0154309
$386$	−11.9083	−0.606118
$387$	−21.2111	−1.07822
$388$	−19.5139	−0.990667
$389$	8.09167	0.410264	0.205132	−	0.978734i	$-0.434238\pi$
$389$	8.09167	0.410264	0.205132	+	0.978734i	$0.434238\pi$
$390$	13.6056	0.688944
$391$	−5.09167	−0.257497
$392$	6.90833	0.348923
$393$	42.6333	2.15057
$394$	−16.3028	−0.821322
$395$	3.21110	0.161568
$396$	2.30278	0.115719
$397$	−13.9083	−0.698039	−0.349019	−	0.937115i	$-0.613485\pi$
$397$	−13.9083	−0.698039	−0.349019	+	0.937115i	$0.613485\pi$
$398$	17.8167	0.893068
$399$	−2.78890	−0.139620
$400$	1.00000	0.0500000
$401$	−28.3028	−1.41337	−0.706687	−	0.707527i	$-0.749811\pi$
$401$	−28.3028	−1.41337	−0.706687	+	0.707527i	$0.749811\pi$
$402$	5.30278	0.264478
$403$	−39.0278	−1.94411
$404$	1.69722	0.0844401
$405$	10.6056	0.526994
$406$	0.513878	0.0255033
$407$	−1.90833	−0.0945923
$408$	9.00000	0.445566
$409$	−27.3305	−1.35141	−0.675704	−	0.737173i	$-0.736160\pi$
$409$	−27.3305	−1.35141	−0.675704	+	0.737173i	$0.736160\pi$
$410$	−6.00000	−0.296319
$411$	15.9083	0.784700
$412$	−18.6056	−0.916630
$413$	2.36669	0.116457
$414$	−3.00000	−0.147442
$415$	−10.3028	−0.505743
$416$	−5.90833	−0.289680
$417$	−0.211103	−0.0103377
$418$	4.00000	0.195646
$419$	19.6972	0.962272	0.481136	−	0.876646i	$-0.340224\pi$
$419$	19.6972	0.962272	0.481136	+	0.876646i	$0.340224\pi$
$420$	−0.697224	−0.0340211
$421$	8.00000	0.389896	0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000	0.389896	0.194948	+	0.980814i	$0.437546\pi$
$422$	−1.21110	−0.0589555
$423$	−25.8167	−1.25525
$424$	0	0
$425$	−3.90833	−0.189582
$426$	8.09167	0.392043
$427$	−0.183346	−0.00887274
$428$	−0.513878	−0.0248392
$429$	13.6056	0.656882
$430$	−9.21110	−0.444199
$431$	−4.69722	−0.226257	−0.113129	−	0.993580i	$-0.536087\pi$
$431$	−4.69722	−0.226257	−0.113129	+	0.993580i	$0.536087\pi$
$432$	−1.60555	−0.0772471
$433$	0.183346	0.00881105	0.00440553	−	0.999990i	$-0.498598\pi$
$433$	0.183346	0.00881105	0.00440553	+	0.999990i	$0.498598\pi$
$434$	2.00000	0.0960031
$435$	3.90833	0.187390
$436$	−14.4222	−0.690698
$437$	−5.21110	−0.249281
$438$	−2.30278	−0.110031
$439$	26.7889	1.27856	0.639282	−	0.768972i	$-0.279232\pi$
$439$	26.7889	1.27856	0.639282	+	0.768972i	$0.279232\pi$
$440$	1.00000	0.0476731
$441$	−15.9083	−0.757539
$442$	23.0917	1.09836
$443$	7.02776	0.333899	0.166949	−	0.985965i	$-0.446608\pi$
$443$	7.02776	0.333899	0.166949	+	0.985965i	$0.446608\pi$
$444$	−4.39445	−0.208551
$445$	−17.7250	−0.840245
$446$	−23.9083	−1.13209
$447$	−19.8167	−0.937296
$448$	0.302776	0.0143048
$449$	−12.0000	−0.566315	−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000	−0.566315	−0.283158	+	0.959073i	$0.591382\pi$
$450$	−2.30278	−0.108554
$451$	−6.00000	−0.282529
$452$	6.00000	0.282216
$453$	13.6056	0.639245
$454$	25.8167	1.21164
$455$	−1.78890	−0.0838648
$456$	9.21110	0.431349
$457$	5.63331	0.263515	0.131758	−	0.991282i	$-0.457938\pi$
$457$	5.63331	0.263515	0.131758	+	0.991282i	$0.457938\pi$
$458$	13.3944	0.625881
$459$	6.27502	0.292893
$460$	−1.30278	−0.0607422
$461$	6.00000	0.279448	0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000	0.279448	0.139724	+	0.990190i	$0.455378\pi$
$462$	−0.697224	−0.0324378
$463$	36.9361	1.71657	0.858283	−	0.513177i	$-0.171532\pi$
$463$	36.9361	1.71657	0.858283	+	0.513177i	$0.171532\pi$
$464$	−1.69722	−0.0787917
$465$	15.2111	0.705398
$466$	28.4222	1.31663
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	13.6056	0.628917
$469$	−0.697224	−0.0321948
$470$	−11.2111	−0.517130
$471$	−48.8444	−2.25063
$472$	−7.81665	−0.359791
$473$	−9.21110	−0.423527
$474$	7.39445	0.339638
$475$	−4.00000	−0.183533
$476$	−1.18335	−0.0542386
$477$	0	0
$478$	−16.6972	−0.763713
$479$	18.7889	0.858487	0.429243	−	0.903189i	$-0.358780\pi$
$479$	18.7889	0.858487	0.429243	+	0.903189i	$0.358780\pi$
$480$	2.30278	0.105107
$481$	−11.2750	−0.514097
$482$	−14.0000	−0.637683
$483$	0.908327	0.0413303
$484$	1.00000	0.0454545
$485$	19.5139	0.886080
$486$	19.6056	0.889326
$487$	−3.33053	−0.150921	−0.0754604	−	0.997149i	$-0.524043\pi$
$487$	−3.33053	−0.150921	−0.0754604	+	0.997149i	$0.524043\pi$
$488$	0.605551	0.0274120
$489$	18.4222	0.833081
$490$	−6.90833	−0.312086
$491$	−14.7250	−0.664529	−0.332265	−	0.943186i	$-0.607813\pi$
$491$	−14.7250	−0.664529	−0.332265	+	0.943186i	$0.607813\pi$
$492$	−13.8167	−0.622903
$493$	6.63331	0.298749
$494$	23.6333	1.06331
$495$	−2.30278	−0.103502
$496$	−6.60555	−0.296598
$497$	−1.06392	−0.0477232
$498$	−23.7250	−1.06314
$499$	−6.33053	−0.283394	−0.141697	−	0.989910i	$-0.545256\pi$
$499$	−6.33053	−0.283394	−0.141697	+	0.989910i	$0.545256\pi$
$500$	−1.00000	−0.0447214
$501$	27.6333	1.23457
$502$	28.5416	1.27388
$503$	−30.0000	−1.33763	−0.668817	−	0.743427i	$-0.733199\pi$
$503$	−30.0000	−1.33763	−0.668817	+	0.743427i	$0.733199\pi$
$504$	−0.697224	−0.0310568
$505$	−1.69722	−0.0755255
$506$	−1.30278	−0.0579154
$507$	50.4500	2.24056
$508$	5.39445	0.239340
$509$	13.3028	0.589635	0.294818	−	0.955554i	$-0.404741\pi$
$509$	13.3028	0.589635	0.294818	+	0.955554i	$0.404741\pi$
$510$	−9.00000	−0.398527
$511$	0.302776	0.0133940
$512$	−1.00000	−0.0441942
$513$	6.42221	0.283547
$514$	−21.6333	−0.954204
$515$	18.6056	0.819859
$516$	−21.2111	−0.933767
$517$	−11.2111	−0.493064
$518$	0.577795	0.0253869
$519$	25.8167	1.13323
$520$	5.90833	0.259097
$521$	31.8167	1.39391	0.696956	−	0.717113i	$-0.254537\pi$
$521$	31.8167	1.39391	0.696956	+	0.717113i	$0.254537\pi$
$522$	3.90833	0.171063
$523$	17.6333	0.771051	0.385525	−	0.922697i	$-0.374020\pi$
$523$	17.6333	0.771051	0.385525	+	0.922697i	$0.374020\pi$
$524$	18.5139	0.808783
$525$	0.697224	0.0304294
$526$	4.30278	0.187610
$527$	25.8167	1.12459
$528$	2.30278	0.100215
$529$	−21.3028	−0.926208
$530$	0	0
$531$	18.0000	0.781133
$532$	−1.21110	−0.0525080
$533$	−35.4500	−1.53551
$534$	−40.8167	−1.76631
$535$	0.513878	0.0222169
$536$	2.30278	0.0994648
$537$	25.8167	1.11407
$538$	8.48612	0.365863
$539$	−6.90833	−0.297563
$540$	1.60555	0.0690919
$541$	35.5139	1.52686	0.763430	−	0.645890i	$-0.223514\pi$
$541$	35.5139	1.52686	0.763430	+	0.645890i	$0.223514\pi$
$542$	17.6972	0.760161
$543$	6.69722	0.287405
$544$	3.90833	0.167568
$545$	14.4222	0.617779
$546$	−4.11943	−0.176295
$547$	23.6333	1.01049	0.505244	−	0.862977i	$-0.331403\pi$
$547$	23.6333	1.01049	0.505244	+	0.862977i	$0.331403\pi$
$548$	6.90833	0.295109
$549$	−1.39445	−0.0595136
$550$	−1.00000	−0.0426401
$551$	6.78890	0.289217
$552$	−3.00000	−0.127688
$553$	−0.972244	−0.0413440
$554$	16.9083	0.718366
$555$	4.39445	0.186534
$556$	−0.0916731	−0.00388780
$557$	9.63331	0.408176	0.204088	−	0.978953i	$-0.434577\pi$
$557$	9.63331	0.408176	0.204088	+	0.978953i	$0.434577\pi$
$558$	15.2111	0.643937
$559$	−54.4222	−2.30181
$560$	−0.302776	−0.0127946
$561$	−9.00000	−0.379980
$562$	14.0917	0.594421
$563$	12.1194	0.510773	0.255387	−	0.966839i	$-0.417797\pi$
$563$	12.1194	0.510773	0.255387	+	0.966839i	$0.417797\pi$
$564$	−25.8167	−1.08708
$565$	−6.00000	−0.252422
$566$	−12.4222	−0.522144
$567$	−3.21110	−0.134854
$568$	3.51388	0.147439
$569$	−2.48612	−0.104224	−0.0521118	−	0.998641i	$-0.516595\pi$
$569$	−2.48612	−0.104224	−0.0521118	+	0.998641i	$0.516595\pi$
$570$	−9.21110	−0.385811
$571$	−10.5139	−0.439992	−0.219996	−	0.975501i	$-0.570604\pi$
$571$	−10.5139	−0.439992	−0.219996	+	0.975501i	$0.570604\pi$
$572$	5.90833	0.247040
$573$	43.8167	1.83047
$574$	1.81665	0.0758257
$575$	1.30278	0.0543295
$576$	2.30278	0.0959490
$577$	12.4222	0.517143	0.258572	−	0.965992i	$-0.416748\pi$
$577$	12.4222	0.517143	0.258572	+	0.965992i	$0.416748\pi$
$578$	1.72498	0.0717497
$579$	27.4222	1.13963
$580$	1.69722	0.0704734
$581$	3.11943	0.129416
$582$	44.9361	1.86266
$583$	0	0
$584$	−1.00000	−0.0413803
$585$	−13.6056	−0.562520
$586$	15.6333	0.645806
$587$	−15.5139	−0.640326	−0.320163	−	0.947362i	$-0.603738\pi$
$587$	−15.5139	−0.640326	−0.320163	+	0.947362i	$0.603738\pi$
$588$	−15.9083	−0.656048
$589$	26.4222	1.08871
$590$	7.81665	0.321807
$591$	37.5416	1.54426
$592$	−1.90833	−0.0784318
$593$	31.8167	1.30655	0.653277	−	0.757119i	$-0.273394\pi$
$593$	31.8167	1.30655	0.653277	+	0.757119i	$0.273394\pi$
$594$	1.60555	0.0658766
$595$	1.18335	0.0485125
$596$	−8.60555	−0.352497
$597$	−41.0278	−1.67915
$598$	−7.69722	−0.314763
$599$	−4.18335	−0.170927	−0.0854634	−	0.996341i	$-0.527237\pi$
$599$	−4.18335	−0.170927	−0.0854634	+	0.996341i	$0.527237\pi$
$600$	−2.30278	−0.0940104
$601$	−6.09167	−0.248485	−0.124242	−	0.992252i	$-0.539650\pi$
$601$	−6.09167	−0.248485	−0.124242	+	0.992252i	$0.539650\pi$
$602$	2.78890	0.113667
$603$	−5.30278	−0.215946
$604$	5.90833	0.240406
$605$	−1.00000	−0.0406558
$606$	−3.90833	−0.158765
$607$	−22.0000	−0.892952	−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000	−0.892952	−0.446476	+	0.894795i	$0.647321\pi$
$608$	4.00000	0.162221
$609$	−1.18335	−0.0479516
$610$	−0.605551	−0.0245181
$611$	−66.2389	−2.67974
$612$	−9.00000	−0.363803
$613$	13.7250	0.554347	0.277173	−	0.960820i	$-0.410602\pi$
$613$	13.7250	0.554347	0.277173	+	0.960820i	$0.410602\pi$
$614$	2.30278	0.0929325
$615$	13.8167	0.557141
$616$	−0.302776	−0.0121992
$617$	−21.3944	−0.861308	−0.430654	−	0.902517i	$-0.641717\pi$
$617$	−21.3944	−0.861308	−0.430654	+	0.902517i	$0.641717\pi$
$618$	42.8444	1.72345
$619$	−26.6972	−1.07305	−0.536526	−	0.843884i	$-0.680264\pi$
$619$	−26.6972	−1.07305	−0.536526	+	0.843884i	$0.680264\pi$
$620$	6.60555	0.265285
$621$	−2.09167	−0.0839359
$622$	24.0000	0.962312
$623$	5.36669	0.215012
$624$	13.6056	0.544658
$625$	1.00000	0.0400000
$626$	26.4222	1.05604
$627$	−9.21110	−0.367856
$628$	−21.2111	−0.846415
$629$	7.45837	0.297385
$630$	0.697224	0.0277781
$631$	−47.8167	−1.90355	−0.951775	−	0.306795i	$-0.900743\pi$
$631$	−47.8167	−1.90355	−0.951775	+	0.306795i	$0.900743\pi$
$632$	3.21110	0.127731
$633$	2.78890	0.110849
$634$	29.7250	1.18053
$635$	−5.39445	−0.214072
$636$	0	0
$637$	−40.8167	−1.61721
$638$	1.69722	0.0671938
$639$	−8.09167	−0.320102
$640$	1.00000	0.0395285
$641$	−7.69722	−0.304022	−0.152011	−	0.988379i	$-0.548575\pi$
$641$	−7.69722	−0.304022	−0.152011	+	0.988379i	$0.548575\pi$
$642$	1.18335	0.0467029
$643$	10.6056	0.418242	0.209121	−	0.977890i	$-0.432940\pi$
$643$	10.6056	0.418242	0.209121	+	0.977890i	$0.432940\pi$
$644$	0.394449	0.0155435
$645$	21.2111	0.835186
$646$	−15.6333	−0.615084
$647$	−9.39445	−0.369334	−0.184667	−	0.982801i	$-0.559121\pi$
$647$	−9.39445	−0.369334	−0.184667	+	0.982801i	$0.559121\pi$
$648$	10.6056	0.416625
$649$	7.81665	0.306831
$650$	−5.90833	−0.231744
$651$	−4.60555	−0.180506
$652$	8.00000	0.313304
$653$	4.30278	0.168381	0.0841903	−	0.996450i	$-0.473170\pi$
$653$	4.30278	0.168381	0.0841903	+	0.996450i	$0.473170\pi$
$654$	33.2111	1.29866
$655$	−18.5139	−0.723397
$656$	−6.00000	−0.234261
$657$	2.30278	0.0898398
$658$	3.39445	0.132329
$659$	18.2389	0.710485	0.355243	−	0.934774i	$-0.384398\pi$
$659$	18.2389	0.710485	0.355243	+	0.934774i	$0.384398\pi$
$660$	−2.30278	−0.0896354
$661$	−37.1194	−1.44378	−0.721889	−	0.692009i	$-0.756726\pi$
$661$	−37.1194	−1.44378	−0.721889	+	0.692009i	$0.756726\pi$
$662$	25.6333	0.996267
$663$	−53.1749	−2.06514
$664$	−10.3028	−0.399825
$665$	1.21110	0.0469645
$666$	4.39445	0.170281
$667$	−2.21110	−0.0856142
$668$	12.0000	0.464294
$669$	55.0555	2.12857
$670$	−2.30278	−0.0889640
$671$	−0.605551	−0.0233770
$672$	−0.697224	−0.0268960
$673$	2.23886	0.0863017	0.0431508	−	0.999069i	$-0.486260\pi$
$673$	2.23886	0.0863017	0.0431508	+	0.999069i	$0.486260\pi$
$674$	−28.7250	−1.10644
$675$	−1.60555	−0.0617977
$676$	21.9083	0.842628
$677$	−34.9361	−1.34270	−0.671351	−	0.741139i	$-0.734286\pi$
$677$	−34.9361	−1.34270	−0.671351	+	0.741139i	$0.734286\pi$
$678$	−13.8167	−0.530625
$679$	−5.90833	−0.226741
$680$	−3.90833	−0.149877
$681$	−59.4500	−2.27813
$682$	6.60555	0.252940
$683$	6.78890	0.259770	0.129885	−	0.991529i	$-0.458539\pi$
$683$	6.78890	0.259770	0.129885	+	0.991529i	$0.458539\pi$
$684$	−9.21110	−0.352195
$685$	−6.90833	−0.263954
$686$	4.21110	0.160781
$687$	−30.8444	−1.17679
$688$	−9.21110	−0.351170
$689$	0	0
$690$	3.00000	0.114208
$691$	−24.6056	−0.936039	−0.468020	−	0.883718i	$-0.655032\pi$
$691$	−24.6056	−0.936039	−0.468020	+	0.883718i	$0.655032\pi$
$692$	11.2111	0.426182
$693$	0.697224	0.0264854
$694$	21.6333	0.821189
$695$	0.0916731	0.00347736
$696$	3.90833	0.148145
$697$	23.4500	0.888231
$698$	−19.2111	−0.727151
$699$	−65.4500	−2.47554
$700$	0.302776	0.0114438
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	9.48612	0.358031
$703$	7.63331	0.287896
$704$	1.00000	0.0376889
$705$	25.8167	0.972311
$706$	−5.09167	−0.191628
$707$	0.513878	0.0193264
$708$	18.0000	0.676481
$709$	28.8444	1.08327	0.541637	−	0.840612i	$-0.317805\pi$
$709$	28.8444	1.08327	0.541637	+	0.840612i	$0.317805\pi$
$710$	−3.51388	−0.131873
$711$	−7.39445	−0.277313
$712$	−17.7250	−0.664272
$713$	−8.60555	−0.322280
$714$	2.72498	0.101980
$715$	−5.90833	−0.220959
$716$	11.2111	0.418979
$717$	38.4500	1.43594
$718$	−19.0278	−0.710110
$719$	21.6333	0.806786	0.403393	−	0.915027i	$-0.367831\pi$
$719$	21.6333	0.806786	0.403393	+	0.915027i	$0.367831\pi$
$720$	−2.30278	−0.0858194
$721$	−5.63331	−0.209795
$722$	3.00000	0.111648
$723$	32.2389	1.19898
$724$	2.90833	0.108087
$725$	−1.69722	−0.0630333
$726$	−2.30278	−0.0854640
$727$	3.69722	0.137122	0.0685612	−	0.997647i	$-0.478159\pi$
$727$	3.69722	0.137122	0.0685612	+	0.997647i	$0.478159\pi$
$728$	−1.78890	−0.0663010
$729$	−13.3305	−0.493723
$730$	1.00000	0.0370117
$731$	36.0000	1.33151
$732$	−1.39445	−0.0515403
$733$	39.8167	1.47066	0.735331	−	0.677708i	$-0.237027\pi$
$733$	39.8167	1.47066	0.735331	+	0.677708i	$0.237027\pi$
$734$	−32.7527	−1.20893
$735$	15.9083	0.586787
$736$	−1.30278	−0.0480209
$737$	−2.30278	−0.0848238
$738$	13.8167	0.508598
$739$	−19.3944	−0.713436	−0.356718	−	0.934212i	$-0.616104\pi$
$739$	−19.3944	−0.713436	−0.356718	+	0.934212i	$0.616104\pi$
$740$	1.90833	0.0701515
$741$	−54.4222	−1.99925
$742$	0	0
$743$	11.0917	0.406914	0.203457	−	0.979084i	$-0.434782\pi$
$743$	11.0917	0.406914	0.203457	+	0.979084i	$0.434782\pi$
$744$	15.2111	0.557666
$745$	8.60555	0.315283
$746$	24.6056	0.900873
$747$	23.7250	0.868052
$748$	−3.90833	−0.142903
$749$	−0.155590	−0.00568513
$750$	2.30278	0.0840855
$751$	−15.2111	−0.555061	−0.277531	−	0.960717i	$-0.589516\pi$
$751$	−15.2111	−0.555061	−0.277531	+	0.960717i	$0.589516\pi$
$752$	−11.2111	−0.408827
$753$	−65.7250	−2.39515
$754$	10.0278	0.365189
$755$	−5.90833	−0.215026
$756$	−0.486122	−0.0176801
$757$	7.09167	0.257751	0.128876	−	0.991661i	$-0.458863\pi$
$757$	7.09167	0.257751	0.128876	+	0.991661i	$0.458863\pi$
$758$	14.4222	0.523838
$759$	3.00000	0.108893
$760$	−4.00000	−0.145095
$761$	40.1472	1.45533	0.727667	−	0.685930i	$-0.240605\pi$
$761$	40.1472	1.45533	0.727667	+	0.685930i	$0.240605\pi$
$762$	−12.4222	−0.450009
$763$	−4.36669	−0.158085
$764$	19.0278	0.688400
$765$	9.00000	0.325396
$766$	−5.21110	−0.188285
$767$	46.1833	1.66758
$768$	2.30278	0.0830943
$769$	6.93608	0.250122	0.125061	−	0.992149i	$-0.460087\pi$
$769$	6.93608	0.250122	0.125061	+	0.992149i	$0.460087\pi$
$770$	0.302776	0.0109113
$771$	49.8167	1.79410
$772$	11.9083	0.428590
$773$	−35.4500	−1.27505	−0.637523	−	0.770431i	$-0.720041\pi$
$773$	−35.4500	−1.27505	−0.637523	+	0.770431i	$0.720041\pi$
$774$	21.2111	0.762417
$775$	−6.60555	−0.237278
$776$	19.5139	0.700507
$777$	−1.33053	−0.0477326
$778$	−8.09167	−0.290101
$779$	24.0000	0.859889
$780$	−13.6056	−0.487157
$781$	−3.51388	−0.125736
$782$	5.09167	0.182078
$783$	2.72498	0.0973829
$784$	−6.90833	−0.246726
$785$	21.2111	0.757057
$786$	−42.6333	−1.52068
$787$	10.3667	0.369533	0.184766	−	0.982782i	$-0.440847\pi$
$787$	10.3667	0.369533	0.184766	+	0.982782i	$0.440847\pi$
$788$	16.3028	0.580762
$789$	−9.90833	−0.352746
$790$	−3.21110	−0.114246
$791$	1.81665	0.0645928
$792$	−2.30278	−0.0818256
$793$	−3.57779	−0.127051
$794$	13.9083	0.493588
$795$	0	0
$796$	−17.8167	−0.631495
$797$	45.3583	1.60667	0.803337	−	0.595525i	$-0.203056\pi$
$797$	45.3583	1.60667	0.803337	+	0.595525i	$0.203056\pi$
$798$	2.78890	0.0987259
$799$	43.8167	1.55012
$800$	−1.00000	−0.0353553
$801$	40.8167	1.44219
$802$	28.3028	0.999406
$803$	1.00000	0.0352892
$804$	−5.30278	−0.187014
$805$	−0.394449	−0.0139025
$806$	39.0278	1.37469
$807$	−19.5416	−0.687898
$808$	−1.69722	−0.0597081
$809$	−30.2389	−1.06314	−0.531571	−	0.847014i	$-0.678398\pi$
$809$	−30.2389	−1.06314	−0.531571	+	0.847014i	$0.678398\pi$
$810$	−10.6056	−0.372641
$811$	13.2111	0.463905	0.231952	−	0.972727i	$-0.425489\pi$
$811$	13.2111	0.463905	0.231952	+	0.972727i	$0.425489\pi$
$812$	−0.513878	−0.0180336
$813$	−40.7527	−1.42926
$814$	1.90833	0.0668868
$815$	−8.00000	−0.280228
$816$	−9.00000	−0.315063
$817$	36.8444	1.28902
$818$	27.3305	0.955590
$819$	4.11943	0.143945
$820$	6.00000	0.209529
$821$	41.2111	1.43828	0.719139	−	0.694867i	$-0.244537\pi$
$821$	41.2111	1.43828	0.719139	+	0.694867i	$0.244537\pi$
$822$	−15.9083	−0.554867
$823$	9.02776	0.314688	0.157344	−	0.987544i	$-0.449707\pi$
$823$	9.02776	0.314688	0.157344	+	0.987544i	$0.449707\pi$
$824$	18.6056	0.648155
$825$	2.30278	0.0801724
$826$	−2.36669	−0.0823478
$827$	−3.63331	−0.126342	−0.0631712	−	0.998003i	$-0.520121\pi$
$827$	−3.63331	−0.126342	−0.0631712	+	0.998003i	$0.520121\pi$
$828$	3.00000	0.104257
$829$	3.02776	0.105158	0.0525792	−	0.998617i	$-0.483256\pi$
$829$	3.02776	0.105158	0.0525792	+	0.998617i	$0.483256\pi$
$830$	10.3028	0.357615
$831$	−38.9361	−1.35068
$832$	5.90833	0.204834
$833$	27.0000	0.935495
$834$	0.211103	0.00730988
$835$	−12.0000	−0.415277
$836$	−4.00000	−0.138343
$837$	10.6056	0.366581
$838$	−19.6972	−0.680429
$839$	8.36669	0.288850	0.144425	−	0.989516i	$-0.453867\pi$
$839$	8.36669	0.288850	0.144425	+	0.989516i	$0.453867\pi$
$840$	0.697224	0.0240565
$841$	−26.1194	−0.900670
$842$	−8.00000	−0.275698
$843$	−32.4500	−1.11764
$844$	1.21110	0.0416879
$845$	−21.9083	−0.753669
$846$	25.8167	0.887595
$847$	0.302776	0.0104035
$848$	0	0
$849$	28.6056	0.981740
$850$	3.90833	0.134055
$851$	−2.48612	−0.0852232
$852$	−8.09167	−0.277216
$853$	40.8444	1.39849	0.699243	−	0.714884i	$-0.253521\pi$
$853$	40.8444	1.39849	0.699243	+	0.714884i	$0.253521\pi$
$854$	0.183346	0.00627398
$855$	9.21110	0.315013
$856$	0.513878	0.0175640
$857$	−9.39445	−0.320908	−0.160454	−	0.987043i	$-0.551296\pi$
$857$	−9.39445	−0.320908	−0.160454	+	0.987043i	$0.551296\pi$
$858$	−13.6056	−0.464486
$859$	−41.0278	−1.39985	−0.699924	−	0.714217i	$-0.746783\pi$
$859$	−41.0278	−1.39985	−0.699924	+	0.714217i	$0.746783\pi$
$860$	9.21110	0.314096
$861$	−4.18335	−0.142568
$862$	4.69722	0.159988
$863$	−0.788897	−0.0268544	−0.0134272	−	0.999910i	$-0.504274\pi$
$863$	−0.788897	−0.0268544	−0.0134272	+	0.999910i	$0.504274\pi$
$864$	1.60555	0.0546220
$865$	−11.2111	−0.381189
$866$	−0.183346	−0.00623036
$867$	−3.97224	−0.134904
$868$	−2.00000	−0.0678844
$869$	−3.21110	−0.108929
$870$	−3.90833	−0.132505
$871$	−13.6056	−0.461007
$872$	14.4222	0.488397
$873$	−44.9361	−1.52086
$874$	5.21110	0.176268
$875$	−0.302776	−0.0102357
$876$	2.30278	0.0778036
$877$	15.5778	0.526025	0.263012	−	0.964792i	$-0.415284\pi$
$877$	15.5778	0.526025	0.263012	+	0.964792i	$0.415284\pi$
$878$	−26.7889	−0.904081
$879$	−36.0000	−1.21425
$880$	−1.00000	−0.0337100
$881$	−0.788897	−0.0265786	−0.0132893	−	0.999912i	$-0.504230\pi$
$881$	−0.788897	−0.0265786	−0.0132893	+	0.999912i	$0.504230\pi$
$882$	15.9083	0.535661
$883$	2.23886	0.0753436	0.0376718	−	0.999290i	$-0.488006\pi$
$883$	2.23886	0.0753436	0.0376718	+	0.999290i	$0.488006\pi$
$884$	−23.0917	−0.776657
$885$	−18.0000	−0.605063
$886$	−7.02776	−0.236102
$887$	23.3305	0.783363	0.391681	−	0.920101i	$-0.371894\pi$
$887$	23.3305	0.783363	0.391681	+	0.920101i	$0.371894\pi$
$888$	4.39445	0.147468
$889$	1.63331	0.0547794
$890$	17.7250	0.594143
$891$	−10.6056	−0.355299
$892$	23.9083	0.800510
$893$	44.8444	1.50066
$894$	19.8167	0.662768
$895$	−11.2111	−0.374746
$896$	−0.302776	−0.0101150
$897$	17.7250	0.591820
$898$	12.0000	0.400445
$899$	11.2111	0.373911
$900$	2.30278	0.0767592
$901$	0	0
$902$	6.00000	0.199778
$903$	−6.42221	−0.213718
$904$	−6.00000	−0.199557
$905$	−2.90833	−0.0966761
$906$	−13.6056	−0.452014
$907$	−28.0000	−0.929725	−0.464862	−	0.885383i	$-0.653896\pi$
$907$	−28.0000	−0.929725	−0.464862	+	0.885383i	$0.653896\pi$
$908$	−25.8167	−0.856756
$909$	3.90833	0.129631
$910$	1.78890	0.0593014
$911$	1.06392	0.0352491	0.0176246	−	0.999845i	$-0.494390\pi$
$911$	1.06392	0.0352491	0.0176246	+	0.999845i	$0.494390\pi$
$912$	−9.21110	−0.305010
$913$	10.3028	0.340972
$914$	−5.63331	−0.186333
$915$	1.39445	0.0460991
$916$	−13.3944	−0.442565
$917$	5.60555	0.185112
$918$	−6.27502	−0.207106
$919$	28.8444	0.951489	0.475745	−	0.879583i	$-0.342179\pi$
$919$	28.8444	0.951489	0.475745	+	0.879583i	$0.342179\pi$
$920$	1.30278	0.0429512
$921$	−5.30278	−0.174732
$922$	−6.00000	−0.197599
$923$	−20.7611	−0.683361
$924$	0.697224	0.0229370
$925$	−1.90833	−0.0627454
$926$	−36.9361	−1.21380
$927$	−42.8444	−1.40720
$928$	1.69722	0.0557141
$929$	−21.6333	−0.709766	−0.354883	−	0.934911i	$-0.615479\pi$
$929$	−21.6333	−0.709766	−0.354883	+	0.934911i	$0.615479\pi$
$930$	−15.2111	−0.498792
$931$	27.6333	0.905645
$932$	−28.4222	−0.931000
$933$	−55.2666	−1.80935
$934$	−12.0000	−0.392652
$935$	3.90833	0.127816
$936$	−13.6056	−0.444711
$937$	22.8444	0.746294	0.373147	−	0.927772i	$-0.378279\pi$
$937$	22.8444	0.746294	0.373147	+	0.927772i	$0.378279\pi$
$938$	0.697224	0.0227652
$939$	−60.8444	−1.98558
$940$	11.2111	0.365666
$941$	1.57779	0.0514346	0.0257173	−	0.999669i	$-0.491813\pi$
$941$	1.57779	0.0514346	0.0257173	+	0.999669i	$0.491813\pi$
$942$	48.8444	1.59144
$943$	−7.81665	−0.254545
$944$	7.81665	0.254410
$945$	0.486122	0.0158135
$946$	9.21110	0.299479
$947$	−18.7889	−0.610557	−0.305279	−	0.952263i	$-0.598750\pi$
$947$	−18.7889	−0.610557	−0.305279	+	0.952263i	$0.598750\pi$
$948$	−7.39445	−0.240161
$949$	5.90833	0.191792
$950$	4.00000	0.129777
$951$	−68.4500	−2.21964
$952$	1.18335	0.0383525
$953$	−56.0555	−1.81582	−0.907908	−	0.419169i	$-0.862321\pi$
$953$	−56.0555	−1.81582	−0.907908	+	0.419169i	$0.862321\pi$
$954$	0	0
$955$	−19.0278	−0.615724
$956$	16.6972	0.540027
$957$	−3.90833	−0.126338
$958$	−18.7889	−0.607042
$959$	2.09167	0.0675436
$960$	−2.30278	−0.0743218
$961$	12.6333	0.407526
$962$	11.2750	0.363521
$963$	−1.18335	−0.0381328
$964$	14.0000	0.450910
$965$	−11.9083	−0.383343
$966$	−0.908327	−0.0292249
$967$	61.2111	1.96842	0.984208	−	0.177015i	$-0.0566441\pi$
$967$	61.2111	1.96842	0.984208	+	0.177015i	$0.0566441\pi$
$968$	−1.00000	−0.0321412
$969$	36.0000	1.15649
$970$	−19.5139	−0.626553
$971$	60.2389	1.93316	0.966578	−	0.256371i	$-0.0825268\pi$
$971$	60.2389	1.93316	0.966578	+	0.256371i	$0.0825268\pi$
$972$	−19.6056	−0.628848
$973$	−0.0277564	−0.000889829 0
$974$	3.33053	0.106717
$975$	13.6056	0.435726
$976$	−0.605551	−0.0193832
$977$	−3.39445	−0.108598	−0.0542990	−	0.998525i	$-0.517292\pi$
$977$	−3.39445	−0.108598	−0.0542990	+	0.998525i	$0.517292\pi$
$978$	−18.4222	−0.589077
$979$	17.7250	0.566493
$980$	6.90833	0.220678
$981$	−33.2111	−1.06035
$982$	14.7250	0.469893
$983$	−55.2666	−1.76273	−0.881366	−	0.472435i	$-0.843375\pi$
$983$	−55.2666	−1.76273	−0.881366	+	0.472435i	$0.843375\pi$
$984$	13.8167	0.440459
$985$	−16.3028	−0.519450
$986$	−6.63331	−0.211248
$987$	−7.81665	−0.248807
$988$	−23.6333	−0.751876
$989$	−12.0000	−0.381578
$990$	2.30278	0.0731870
$991$	46.0555	1.46300	0.731501	−	0.681841i	$-0.238820\pi$
$991$	46.0555	1.46300	0.731501	+	0.681841i	$0.238820\pi$
$992$	6.60555	0.209726
$993$	−59.0278	−1.87319
$994$	1.06392	0.0337454
$995$	17.8167	0.564826
$996$	23.7250	0.751755
$997$	−51.4500	−1.62944	−0.814718	−	0.579857i	$-0.803108\pi$
$997$	−51.4500	−1.62944	−0.814718	+	0.579857i	$0.803108\pi$
$998$	6.33053	0.200389
$999$	3.06392	0.0969380

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.l.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.l.1.2	✓	2	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.30278 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.30278 q^{6} +0.302776 q^{7} -1.00000 q^{8} +2.30278 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.30278 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.30278 q^{6} +0.302776 q^{7} -1.00000 q^{8} +2.30278 q^{9} +1.00000 q^{10} +1.00000 q^{11} +2.30278 q^{12} +5.90833 q^{13} -0.302776 q^{14} -2.30278 q^{15} +1.00000 q^{16} -3.90833 q^{17} -2.30278 q^{18} -4.00000 q^{19} -1.00000 q^{20} +0.697224 q^{21} -1.00000 q^{22} +1.30278 q^{23} -2.30278 q^{24} +1.00000 q^{25} -5.90833 q^{26} -1.60555 q^{27} +0.302776 q^{28} -1.69722 q^{29} +2.30278 q^{30} -6.60555 q^{31} -1.00000 q^{32} +2.30278 q^{33} +3.90833 q^{34} -0.302776 q^{35} +2.30278 q^{36} -1.90833 q^{37} +4.00000 q^{38} +13.6056 q^{39} +1.00000 q^{40} -6.00000 q^{41} -0.697224 q^{42} -9.21110 q^{43} +1.00000 q^{44} -2.30278 q^{45} -1.30278 q^{46} -11.2111 q^{47} +2.30278 q^{48} -6.90833 q^{49} -1.00000 q^{50} -9.00000 q^{51} +5.90833 q^{52} +1.60555 q^{54} -1.00000 q^{55} -0.302776 q^{56} -9.21110 q^{57} +1.69722 q^{58} +7.81665 q^{59} -2.30278 q^{60} -0.605551 q^{61} +6.60555 q^{62} +0.697224 q^{63} +1.00000 q^{64} -5.90833 q^{65} -2.30278 q^{66} -2.30278 q^{67} -3.90833 q^{68} +3.00000 q^{69} +0.302776 q^{70} -3.51388 q^{71} -2.30278 q^{72} +1.00000 q^{73} +1.90833 q^{74} +2.30278 q^{75} -4.00000 q^{76} +0.302776 q^{77} -13.6056 q^{78} -3.21110 q^{79} -1.00000 q^{80} -10.6056 q^{81} +6.00000 q^{82} +10.3028 q^{83} +0.697224 q^{84} +3.90833 q^{85} +9.21110 q^{86} -3.90833 q^{87} -1.00000 q^{88} +17.7250 q^{89} +2.30278 q^{90} +1.78890 q^{91} +1.30278 q^{92} -15.2111 q^{93} +11.2111 q^{94} +4.00000 q^{95} -2.30278 q^{96} -19.5139 q^{97} +6.90833 q^{98} +2.30278 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} - q^{6} - 3 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 - q^6 - 3 * q^7 - 2 * q^8 + q^9	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} - q^{6} - 3 q^{7} - 2 q^{8} + q^{9} + 2 q^{10} + 2 q^{11} + q^{12} + q^{13} + 3 q^{14} - q^{15} + 2 q^{16} + 3 q^{17} - q^{18} - 8 q^{19} - 2 q^{20} + 5 q^{21} - 2 q^{22} - q^{23} - q^{24} + 2 q^{25} - q^{26} + 4 q^{27} - 3 q^{28} - 7 q^{29} + q^{30} - 6 q^{31} - 2 q^{32} + q^{33} - 3 q^{34} + 3 q^{35} + q^{36} + 7 q^{37} + 8 q^{38} + 20 q^{39} + 2 q^{40} - 12 q^{41} - 5 q^{42} - 4 q^{43} + 2 q^{44} - q^{45} + q^{46} - 8 q^{47} + q^{48} - 3 q^{49} - 2 q^{50} - 18 q^{51} + q^{52} - 4 q^{54} - 2 q^{55} + 3 q^{56} - 4 q^{57} + 7 q^{58} - 6 q^{59} - q^{60} + 6 q^{61} + 6 q^{62} + 5 q^{63} + 2 q^{64} - q^{65} - q^{66} - q^{67} + 3 q^{68} + 6 q^{69} - 3 q^{70} + 11 q^{71} - q^{72} + 2 q^{73} - 7 q^{74} + q^{75} - 8 q^{76} - 3 q^{77} - 20 q^{78} + 8 q^{79} - 2 q^{80} - 14 q^{81} + 12 q^{82} + 17 q^{83} + 5 q^{84} - 3 q^{85} + 4 q^{86} + 3 q^{87} - 2 q^{88} + 3 q^{89} + q^{90} + 18 q^{91} - q^{92} - 16 q^{93} + 8 q^{94} + 8 q^{95} - q^{96} - 21 q^{97} + 3 q^{98} + q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 - q^6 - 3 * q^7 - 2 * q^8 + q^9 + 2 * q^10 + 2 * q^11 + q^12 + q^13 + 3 * q^14 - q^15 + 2 * q^16 + 3 * q^17 - q^18 - 8 * q^19 - 2 * q^20 + 5 * q^21 - 2 * q^22 - q^23 - q^24 + 2 * q^25 - q^26 + 4 * q^27 - 3 * q^28 - 7 * q^29 + q^30 - 6 * q^31 - 2 * q^32 + q^33 - 3 * q^34 + 3 * q^35 + q^36 + 7 * q^37 + 8 * q^38 + 20 * q^39 + 2 * q^40 - 12 * q^41 - 5 * q^42 - 4 * q^43 + 2 * q^44 - q^45 + q^46 - 8 * q^47 + q^48 - 3 * q^49 - 2 * q^50 - 18 * q^51 + q^52 - 4 * q^54 - 2 * q^55 + 3 * q^56 - 4 * q^57 + 7 * q^58 - 6 * q^59 - q^60 + 6 * q^61 + 6 * q^62 + 5 * q^63 + 2 * q^64 - q^65 - q^66 - q^67 + 3 * q^68 + 6 * q^69 - 3 * q^70 + 11 * q^71 - q^72 + 2 * q^73 - 7 * q^74 + q^75 - 8 * q^76 - 3 * q^77 - 20 * q^78 + 8 * q^79 - 2 * q^80 - 14 * q^81 + 12 * q^82 + 17 * q^83 + 5 * q^84 - 3 * q^85 + 4 * q^86 + 3 * q^87 - 2 * q^88 + 3 * q^89 + q^90 + 18 * q^91 - q^92 - 16 * q^93 + 8 * q^94 + 8 * q^95 - q^96 - 21 * q^97 + 3 * q^98 + q^99

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