LMFDB - Embedded newform 8030.2.a.bl.1.11

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:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 9 x^{18} - x^{17} + 200 x^{16} - 263 x^{15} - 1900 x^{14} + 3165 x^{13} + 10217 x^{12} + \cdots + 1388 $ x^19 - 9x^18 - x^17 + 200x^16 - 263x^15 - 1900x^14 + 3165x^13 + 10217x^12 - 16393x^11 - 33875x^10 + 44043x^9 + 68537x^8 - 63620x^7 - 79890x^6 + 48388x^5 + 49353x^4 - 17806x^3 - 14287x^2 + 2436*x + 1388
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-0.328384$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.32838 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.32838 q^{6} -1.94037 q^{7} +1.00000 q^{8} -1.23540 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.32838 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.32838 q^{6} -1.94037 q^{7} +1.00000 q^{8} -1.23540 q^{9} +1.00000 q^{10} +1.00000 q^{11} +1.32838 q^{12} +5.40963 q^{13} -1.94037 q^{14} +1.32838 q^{15} +1.00000 q^{16} +4.71107 q^{17} -1.23540 q^{18} +8.23004 q^{19} +1.00000 q^{20} -2.57755 q^{21} +1.00000 q^{22} -3.83753 q^{23} +1.32838 q^{24} +1.00000 q^{25} +5.40963 q^{26} -5.62623 q^{27} -1.94037 q^{28} +6.15228 q^{29} +1.32838 q^{30} -8.39860 q^{31} +1.00000 q^{32} +1.32838 q^{33} +4.71107 q^{34} -1.94037 q^{35} -1.23540 q^{36} +8.81046 q^{37} +8.23004 q^{38} +7.18606 q^{39} +1.00000 q^{40} -8.97027 q^{41} -2.57755 q^{42} +3.33026 q^{43} +1.00000 q^{44} -1.23540 q^{45} -3.83753 q^{46} -9.62921 q^{47} +1.32838 q^{48} -3.23498 q^{49} +1.00000 q^{50} +6.25812 q^{51} +5.40963 q^{52} -5.28600 q^{53} -5.62623 q^{54} +1.00000 q^{55} -1.94037 q^{56} +10.9327 q^{57} +6.15228 q^{58} +10.2784 q^{59} +1.32838 q^{60} +12.2019 q^{61} -8.39860 q^{62} +2.39712 q^{63} +1.00000 q^{64} +5.40963 q^{65} +1.32838 q^{66} -4.77249 q^{67} +4.71107 q^{68} -5.09771 q^{69} -1.94037 q^{70} -5.01237 q^{71} -1.23540 q^{72} -1.00000 q^{73} +8.81046 q^{74} +1.32838 q^{75} +8.23004 q^{76} -1.94037 q^{77} +7.18606 q^{78} +7.78551 q^{79} +1.00000 q^{80} -3.76761 q^{81} -8.97027 q^{82} +16.3176 q^{83} -2.57755 q^{84} +4.71107 q^{85} +3.33026 q^{86} +8.17259 q^{87} +1.00000 q^{88} -7.58602 q^{89} -1.23540 q^{90} -10.4967 q^{91} -3.83753 q^{92} -11.1566 q^{93} -9.62921 q^{94} +8.23004 q^{95} +1.32838 q^{96} -10.3678 q^{97} -3.23498 q^{98} -1.23540 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 19 q^{2} + 10 q^{3} + 19 q^{4} + 19 q^{5} + 10 q^{6} + 8 q^{7} + 19 q^{8} + 27 q^{9}+O(q^{10}) $ 19 * q + 19 * q^2 + 10 * q^3 + 19 * q^4 + 19 * q^5 + 10 * q^6 + 8 * q^7 + 19 * q^8 + 27 * q^9	\( 19 q + 19 q^{2} + 10 q^{3} + 19 q^{4} + 19 q^{5} + 10 q^{6} + 8 q^{7} + 19 q^{8} + 27 q^{9} + 19 q^{10} + 19 q^{11} + 10 q^{12} + 16 q^{13} + 8 q^{14} + 10 q^{15} + 19 q^{16} + 12 q^{17} + 27 q^{18} + 12 q^{19} + 19 q^{20} + 3 q^{21} + 19 q^{22} + 26 q^{23} + 10 q^{24} + 19 q^{25} + 16 q^{26} + 25 q^{27} + 8 q^{28} + q^{29} + 10 q^{30} + 24 q^{31} + 19 q^{32} + 10 q^{33} + 12 q^{34} + 8 q^{35} + 27 q^{36} + 23 q^{37} + 12 q^{38} - 5 q^{39} + 19 q^{40} + 3 q^{42} + 8 q^{43} + 19 q^{44} + 27 q^{45} + 26 q^{46} + 34 q^{47} + 10 q^{48} + 27 q^{49} + 19 q^{50} + 15 q^{51} + 16 q^{52} + 25 q^{53} + 25 q^{54} + 19 q^{55} + 8 q^{56} + q^{57} + q^{58} + 24 q^{59} + 10 q^{60} + 31 q^{61} + 24 q^{62} + 15 q^{63} + 19 q^{64} + 16 q^{65} + 10 q^{66} + 24 q^{67} + 12 q^{68} + q^{69} + 8 q^{70} + 5 q^{71} + 27 q^{72} - 19 q^{73} + 23 q^{74} + 10 q^{75} + 12 q^{76} + 8 q^{77} - 5 q^{78} + 18 q^{79} + 19 q^{80} + 11 q^{81} + 12 q^{83} + 3 q^{84} + 12 q^{85} + 8 q^{86} + 12 q^{87} + 19 q^{88} + 27 q^{90} + 23 q^{91} + 26 q^{92} + 18 q^{93} + 34 q^{94} + 12 q^{95} + 10 q^{96} + 15 q^{97} + 27 q^{98} + 27 q^{99}+O(q^{100}) \) 19 * q + 19 * q^2 + 10 * q^3 + 19 * q^4 + 19 * q^5 + 10 * q^6 + 8 * q^7 + 19 * q^8 + 27 * q^9 + 19 * q^10 + 19 * q^11 + 10 * q^12 + 16 * q^13 + 8 * q^14 + 10 * q^15 + 19 * q^16 + 12 * q^17 + 27 * q^18 + 12 * q^19 + 19 * q^20 + 3 * q^21 + 19 * q^22 + 26 * q^23 + 10 * q^24 + 19 * q^25 + 16 * q^26 + 25 * q^27 + 8 * q^28 + q^29 + 10 * q^30 + 24 * q^31 + 19 * q^32 + 10 * q^33 + 12 * q^34 + 8 * q^35 + 27 * q^36 + 23 * q^37 + 12 * q^38 - 5 * q^39 + 19 * q^40 + 3 * q^42 + 8 * q^43 + 19 * q^44 + 27 * q^45 + 26 * q^46 + 34 * q^47 + 10 * q^48 + 27 * q^49 + 19 * q^50 + 15 * q^51 + 16 * q^52 + 25 * q^53 + 25 * q^54 + 19 * q^55 + 8 * q^56 + q^57 + q^58 + 24 * q^59 + 10 * q^60 + 31 * q^61 + 24 * q^62 + 15 * q^63 + 19 * q^64 + 16 * q^65 + 10 * q^66 + 24 * q^67 + 12 * q^68 + q^69 + 8 * q^70 + 5 * q^71 + 27 * q^72 - 19 * q^73 + 23 * q^74 + 10 * q^75 + 12 * q^76 + 8 * q^77 - 5 * q^78 + 18 * q^79 + 19 * q^80 + 11 * q^81 + 12 * q^83 + 3 * q^84 + 12 * q^85 + 8 * q^86 + 12 * q^87 + 19 * q^88 + 27 * q^90 + 23 * q^91 + 26 * q^92 + 18 * q^93 + 34 * q^94 + 12 * q^95 + 10 * q^96 + 15 * q^97 + 27 * q^98 + 27 * 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
$3$	1.32838	0.766943	0.383471	−	0.923553i	$-0.374728\pi$
$3$	1.32838	0.766943	0.383471	+	0.923553i	$0.374728\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.32838	0.542311
$7$	−1.94037	−0.733389	−0.366695	−	0.930341i	$-0.619511\pi$
$7$	−1.94037	−0.733389	−0.366695	+	0.930341i	$0.619511\pi$
$8$	1.00000	0.353553
$9$	−1.23540	−0.411798
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.32838	0.383471
$13$	5.40963	1.50036	0.750180	−	0.661234i	$-0.229967\pi$
$13$	5.40963	1.50036	0.750180	+	0.661234i	$0.229967\pi$
$14$	−1.94037	−0.518585
$15$	1.32838	0.342987
$16$	1.00000	0.250000
$17$	4.71107	1.14260	0.571302	−	0.820740i	$-0.306439\pi$
$17$	4.71107	1.14260	0.571302	+	0.820740i	$0.306439\pi$
$18$	−1.23540	−0.291185
$19$	8.23004	1.88810	0.944050	−	0.329802i	$-0.106982\pi$
$19$	8.23004	1.88810	0.944050	+	0.329802i	$0.106982\pi$
$20$	1.00000	0.223607
$21$	−2.57755	−0.562468
$22$	1.00000	0.213201
$23$	−3.83753	−0.800180	−0.400090	−	0.916476i	$-0.631021\pi$
$23$	−3.83753	−0.800180	−0.400090	+	0.916476i	$0.631021\pi$
$24$	1.32838	0.271155
$25$	1.00000	0.200000
$26$	5.40963	1.06091
$27$	−5.62623	−1.08277
$28$	−1.94037	−0.366695
$29$	6.15228	1.14245	0.571225	−	0.820794i	$-0.306468\pi$
$29$	6.15228	1.14245	0.571225	+	0.820794i	$0.306468\pi$
$30$	1.32838	0.242529
$31$	−8.39860	−1.50843	−0.754216	−	0.656626i	$-0.771983\pi$
$31$	−8.39860	−1.50843	−0.754216	+	0.656626i	$0.771983\pi$
$32$	1.00000	0.176777
$33$	1.32838	0.231242
$34$	4.71107	0.807942
$35$	−1.94037	−0.327982
$36$	−1.23540	−0.205899
$37$	8.81046	1.44843	0.724215	−	0.689574i	$-0.242202\pi$
$37$	8.81046	1.44843	0.724215	+	0.689574i	$0.242202\pi$
$38$	8.23004	1.33509
$39$	7.18606	1.15069
$40$	1.00000	0.158114
$41$	−8.97027	−1.40092	−0.700460	−	0.713691i	$-0.747022\pi$
$41$	−8.97027	−1.40092	−0.700460	+	0.713691i	$0.747022\pi$
$42$	−2.57755	−0.397725
$43$	3.33026	0.507860	0.253930	−	0.967223i	$-0.418277\pi$
$43$	3.33026	0.507860	0.253930	+	0.967223i	$0.418277\pi$
$44$	1.00000	0.150756
$45$	−1.23540	−0.184162
$46$	−3.83753	−0.565813
$47$	−9.62921	−1.40457	−0.702283	−	0.711898i	$-0.747836\pi$
$47$	−9.62921	−1.40457	−0.702283	+	0.711898i	$0.747836\pi$
$48$	1.32838	0.191736
$49$	−3.23498	−0.462140
$50$	1.00000	0.141421
$51$	6.25812	0.876311
$52$	5.40963	0.750180
$53$	−5.28600	−0.726088	−0.363044	−	0.931772i	$-0.618263\pi$
$53$	−5.28600	−0.726088	−0.363044	+	0.931772i	$0.618263\pi$
$54$	−5.62623	−0.765633
$55$	1.00000	0.134840
$56$	−1.94037	−0.259292
$57$	10.9327	1.44807
$58$	6.15228	0.807834
$59$	10.2784	1.33813	0.669066	−	0.743203i	$-0.266694\pi$
$59$	10.2784	1.33813	0.669066	+	0.743203i	$0.266694\pi$
$60$	1.32838	0.171494
$61$	12.2019	1.56229	0.781146	−	0.624348i	$-0.214635\pi$
$61$	12.2019	1.56229	0.781146	+	0.624348i	$0.214635\pi$
$62$	−8.39860	−1.06662
$63$	2.39712	0.302009
$64$	1.00000	0.125000
$65$	5.40963	0.670982
$66$	1.32838	0.163513
$67$	−4.77249	−0.583052	−0.291526	−	0.956563i	$-0.594163\pi$
$67$	−4.77249	−0.583052	−0.291526	+	0.956563i	$0.594163\pi$
$68$	4.71107	0.571302
$69$	−5.09771	−0.613693
$70$	−1.94037	−0.231918
$71$	−5.01237	−0.594858	−0.297429	−	0.954744i	$-0.596129\pi$
$71$	−5.01237	−0.594858	−0.297429	+	0.954744i	$0.596129\pi$
$72$	−1.23540	−0.145593
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	8.81046	1.02420
$75$	1.32838	0.153389
$76$	8.23004	0.944050
$77$	−1.94037	−0.221125
$78$	7.18606	0.813661
$79$	7.78551	0.875938	0.437969	−	0.898990i	$-0.355698\pi$
$79$	7.78551	0.875938	0.437969	+	0.898990i	$0.355698\pi$
$80$	1.00000	0.111803
$81$	−3.76761	−0.418624
$82$	−8.97027	−0.990600
$83$	16.3176	1.79109	0.895543	−	0.444975i	$-0.146787\pi$
$83$	16.3176	1.79109	0.895543	+	0.444975i	$0.146787\pi$
$84$	−2.57755	−0.281234
$85$	4.71107	0.510988
$86$	3.33026	0.359111
$87$	8.17259	0.876194
$88$	1.00000	0.106600
$89$	−7.58602	−0.804116	−0.402058	−	0.915614i	$-0.631705\pi$
$89$	−7.58602	−0.804116	−0.402058	+	0.915614i	$0.631705\pi$
$90$	−1.23540	−0.130222
$91$	−10.4967	−1.10035
$92$	−3.83753	−0.400090
$93$	−11.1566	−1.15688
$94$	−9.62921	−0.993177
$95$	8.23004	0.844384
$96$	1.32838	0.135578
$97$	−10.3678	−1.05269	−0.526347	−	0.850270i	$-0.676439\pi$
$97$	−10.3678	−1.05269	−0.526347	+	0.850270i	$0.676439\pi$
$98$	−3.23498	−0.326782
$99$	−1.23540	−0.124162
$100$	1.00000	0.100000
$101$	−11.8016	−1.17430	−0.587151	−	0.809477i	$-0.699751\pi$
$101$	−11.8016	−1.17430	−0.587151	+	0.809477i	$0.699751\pi$
$102$	6.25812	0.619646
$103$	18.8339	1.85576	0.927880	−	0.372880i	$-0.121630\pi$
$103$	18.8339	1.85576	0.927880	+	0.372880i	$0.121630\pi$
$104$	5.40963	0.530457
$105$	−2.57755	−0.251543
$106$	−5.28600	−0.513422
$107$	3.19957	0.309314	0.154657	−	0.987968i	$-0.450573\pi$
$107$	3.19957	0.309314	0.154657	+	0.987968i	$0.450573\pi$
$108$	−5.62623	−0.541384
$109$	−4.08604	−0.391372	−0.195686	−	0.980667i	$-0.562693\pi$
$109$	−4.08604	−0.391372	−0.195686	+	0.980667i	$0.562693\pi$
$110$	1.00000	0.0953463
$111$	11.7037	1.11086
$112$	−1.94037	−0.183347
$113$	−14.2904	−1.34433	−0.672164	−	0.740402i	$-0.734635\pi$
$113$	−14.2904	−1.34433	−0.672164	+	0.740402i	$0.734635\pi$
$114$	10.9327	1.02394
$115$	−3.83753	−0.357851
$116$	6.15228	0.571225
$117$	−6.68303	−0.617846
$118$	10.2784	0.946202
$119$	−9.14121	−0.837973
$120$	1.32838	0.121264
$121$	1.00000	0.0909091
$122$	12.2019	1.10471
$123$	−11.9160	−1.07443
$124$	−8.39860	−0.754216
$125$	1.00000	0.0894427
$126$	2.39712	0.213552
$127$	11.5512	1.02501	0.512504	−	0.858685i	$-0.328718\pi$
$127$	11.5512	1.02501	0.512504	+	0.858685i	$0.328718\pi$
$128$	1.00000	0.0883883
$129$	4.42387	0.389500
$130$	5.40963	0.474456
$131$	18.7042	1.63420	0.817098	−	0.576499i	$-0.195581\pi$
$131$	18.7042	1.63420	0.817098	+	0.576499i	$0.195581\pi$
$132$	1.32838	0.115621
$133$	−15.9693	−1.38471
$134$	−4.77249	−0.412280
$135$	−5.62623	−0.484229
$136$	4.71107	0.403971
$137$	−1.29076	−0.110277	−0.0551387	−	0.998479i	$-0.517560\pi$
$137$	−1.29076	−0.110277	−0.0551387	+	0.998479i	$0.517560\pi$
$138$	−5.09771	−0.433946
$139$	7.01585	0.595077	0.297538	−	0.954710i	$-0.403834\pi$
$139$	7.01585	0.595077	0.297538	+	0.954710i	$0.403834\pi$
$140$	−1.94037	−0.163991
$141$	−12.7913	−1.07722
$142$	−5.01237	−0.420628
$143$	5.40963	0.452376
$144$	−1.23540	−0.102950
$145$	6.15228	0.510919
$146$	−1.00000	−0.0827606
$147$	−4.29730	−0.354435
$148$	8.81046	0.724215
$149$	−10.8102	−0.885607	−0.442804	−	0.896619i	$-0.646016\pi$
$149$	−10.8102	−0.885607	−0.442804	+	0.896619i	$0.646016\pi$
$150$	1.32838	0.108462
$151$	7.04341	0.573185	0.286592	−	0.958053i	$-0.407477\pi$
$151$	7.04341	0.573185	0.286592	+	0.958053i	$0.407477\pi$
$152$	8.23004	0.667544
$153$	−5.82004	−0.470522
$154$	−1.94037	−0.156359
$155$	−8.39860	−0.674592
$156$	7.18606	0.575345
$157$	17.4666	1.39399	0.696994	−	0.717077i	$-0.254520\pi$
$157$	17.4666	1.39399	0.696994	+	0.717077i	$0.254520\pi$
$158$	7.78551	0.619382
$159$	−7.02184	−0.556868
$160$	1.00000	0.0790569
$161$	7.44621	0.586844
$162$	−3.76761	−0.296012
$163$	5.97134	0.467712	0.233856	−	0.972271i	$-0.424866\pi$
$163$	5.97134	0.467712	0.233856	+	0.972271i	$0.424866\pi$
$164$	−8.97027	−0.700460
$165$	1.32838	0.103415
$166$	16.3176	1.26649
$167$	21.5725	1.66933	0.834666	−	0.550756i	$-0.185661\pi$
$167$	21.5725	1.66933	0.834666	+	0.550756i	$0.185661\pi$
$168$	−2.57755	−0.198862
$169$	16.2641	1.25108
$170$	4.71107	0.361323
$171$	−10.1674	−0.777517
$172$	3.33026	0.253930
$173$	0.234620	0.0178378	0.00891891	−	0.999960i	$-0.497161\pi$
$173$	0.234620	0.0178378	0.00891891	+	0.999960i	$0.497161\pi$
$174$	8.17259	0.619562
$175$	−1.94037	−0.146678
$176$	1.00000	0.0753778
$177$	13.6536	1.02627
$178$	−7.58602	−0.568596
$179$	18.0652	1.35026	0.675128	−	0.737701i	$-0.264088\pi$
$179$	18.0652	1.35026	0.675128	+	0.737701i	$0.264088\pi$
$180$	−1.23540	−0.0920809
$181$	3.70514	0.275401	0.137701	−	0.990474i	$-0.456029\pi$
$181$	3.70514	0.275401	0.137701	+	0.990474i	$0.456029\pi$
$182$	−10.4967	−0.778064
$183$	16.2088	1.19819
$184$	−3.83753	−0.282906
$185$	8.81046	0.647758
$186$	−11.1566	−0.818039
$187$	4.71107	0.344508
$188$	−9.62921	−0.702283
$189$	10.9169	0.794091
$190$	8.23004	0.597070
$191$	−4.38714	−0.317442	−0.158721	−	0.987323i	$-0.550737\pi$
$191$	−4.38714	−0.317442	−0.158721	+	0.987323i	$0.550737\pi$
$192$	1.32838	0.0958679
$193$	−8.71694	−0.627459	−0.313729	−	0.949512i	$-0.601578\pi$
$193$	−8.71694	−0.627459	−0.313729	+	0.949512i	$0.601578\pi$
$194$	−10.3678	−0.744368
$195$	7.18606	0.514605
$196$	−3.23498	−0.231070
$197$	−14.7591	−1.05155	−0.525773	−	0.850625i	$-0.676224\pi$
$197$	−14.7591	−1.05155	−0.525773	+	0.850625i	$0.676224\pi$
$198$	−1.23540	−0.0877957
$199$	−6.02657	−0.427212	−0.213606	−	0.976920i	$-0.568521\pi$
$199$	−6.02657	−0.427212	−0.213606	+	0.976920i	$0.568521\pi$
$200$	1.00000	0.0707107
$201$	−6.33969	−0.447168
$202$	−11.8016	−0.830357
$203$	−11.9377	−0.837860
$204$	6.25812	0.438156
$205$	−8.97027	−0.626511
$206$	18.8339	1.31222
$207$	4.74087	0.329513
$208$	5.40963	0.375090
$209$	8.23004	0.569284
$210$	−2.57755	−0.177868
$211$	19.9965	1.37661	0.688307	−	0.725420i	$-0.258354\pi$
$211$	19.9965	1.37661	0.688307	+	0.725420i	$0.258354\pi$
$212$	−5.28600	−0.363044
$213$	−6.65835	−0.456223
$214$	3.19957	0.218718
$215$	3.33026	0.227122
$216$	−5.62623	−0.382817
$217$	16.2964	1.10627
$218$	−4.08604	−0.276742
$219$	−1.32838	−0.0897639
$220$	1.00000	0.0674200
$221$	25.4851	1.71432
$222$	11.7037	0.785499
$223$	18.9901	1.27167	0.635836	−	0.771824i	$-0.280655\pi$
$223$	18.9901	1.27167	0.635836	+	0.771824i	$0.280655\pi$
$224$	−1.94037	−0.129646
$225$	−1.23540	−0.0823597
$226$	−14.2904	−0.950583
$227$	−6.21279	−0.412357	−0.206179	−	0.978514i	$-0.566103\pi$
$227$	−6.21279	−0.412357	−0.206179	+	0.978514i	$0.566103\pi$
$228$	10.9327	0.724033
$229$	−7.65835	−0.506078	−0.253039	−	0.967456i	$-0.581430\pi$
$229$	−7.65835	−0.506078	−0.253039	+	0.967456i	$0.581430\pi$
$230$	−3.83753	−0.253039
$231$	−2.57755	−0.169590
$232$	6.15228	0.403917
$233$	−18.1944	−1.19195	−0.595976	−	0.803002i	$-0.703235\pi$
$233$	−18.1944	−1.19195	−0.595976	+	0.803002i	$0.703235\pi$
$234$	−6.68303	−0.436883
$235$	−9.62921	−0.628141
$236$	10.2784	0.669066
$237$	10.3421	0.671795
$238$	−9.14121	−0.592536
$239$	−10.0919	−0.652792	−0.326396	−	0.945233i	$-0.605834\pi$
$239$	−10.0919	−0.652792	−0.326396	+	0.945233i	$0.605834\pi$
$240$	1.32838	0.0857468
$241$	14.1146	0.909201	0.454601	−	0.890695i	$-0.349782\pi$
$241$	14.1146	0.909201	0.454601	+	0.890695i	$0.349782\pi$
$242$	1.00000	0.0642824
$243$	11.8739	0.761709
$244$	12.2019	0.781146
$245$	−3.23498	−0.206675
$246$	−11.9160	−0.759734
$247$	44.5214	2.83283
$248$	−8.39860	−0.533312
$249$	21.6760	1.37366
$250$	1.00000	0.0632456
$251$	−16.1337	−1.01835	−0.509174	−	0.860664i	$-0.670049\pi$
$251$	−16.1337	−1.01835	−0.509174	+	0.860664i	$0.670049\pi$
$252$	2.39712	0.151004
$253$	−3.83753	−0.241263
$254$	11.5512	0.724790
$255$	6.25812	0.391898
$256$	1.00000	0.0625000
$257$	−8.47773	−0.528826	−0.264413	−	0.964410i	$-0.585178\pi$
$257$	−8.47773	−0.528826	−0.264413	+	0.964410i	$0.585178\pi$
$258$	4.42387	0.275418
$259$	−17.0955	−1.06226
$260$	5.40963	0.335491
$261$	−7.60050	−0.470459
$262$	18.7042	1.15555
$263$	5.11333	0.315302	0.157651	−	0.987495i	$-0.449608\pi$
$263$	5.11333	0.315302	0.157651	+	0.987495i	$0.449608\pi$
$264$	1.32838	0.0817564
$265$	−5.28600	−0.324717
$266$	−15.9693	−0.979140
$267$	−10.0771	−0.616711
$268$	−4.77249	−0.291526
$269$	17.0652	1.04048	0.520242	−	0.854019i	$-0.325842\pi$
$269$	17.0652	1.04048	0.520242	+	0.854019i	$0.325842\pi$
$270$	−5.62623	−0.342402
$271$	−14.6412	−0.889390	−0.444695	−	0.895682i	$-0.646688\pi$
$271$	−14.6412	−0.889390	−0.444695	+	0.895682i	$0.646688\pi$
$272$	4.71107	0.285651
$273$	−13.9436	−0.843904
$274$	−1.29076	−0.0779780
$275$	1.00000	0.0603023
$276$	−5.09771	−0.306846
$277$	17.0511	1.02450	0.512250	−	0.858836i	$-0.328812\pi$
$277$	17.0511	1.02450	0.512250	+	0.858836i	$0.328812\pi$
$278$	7.01585	0.420783
$279$	10.3756	0.621170
$280$	−1.94037	−0.115959
$281$	21.4526	1.27975	0.639877	−	0.768478i	$-0.278985\pi$
$281$	21.4526	1.27975	0.639877	+	0.768478i	$0.278985\pi$
$282$	−12.7913	−0.761710
$283$	−25.7974	−1.53349	−0.766747	−	0.641950i	$-0.778126\pi$
$283$	−25.7974	−1.53349	−0.766747	+	0.641950i	$0.778126\pi$
$284$	−5.01237	−0.297429
$285$	10.9327	0.647594
$286$	5.40963	0.319878
$287$	17.4056	1.02742
$288$	−1.23540	−0.0727964
$289$	5.19421	0.305542
$290$	6.15228	0.361274
$291$	−13.7725	−0.807357
$292$	−1.00000	−0.0585206
$293$	−6.06161	−0.354123	−0.177061	−	0.984200i	$-0.556659\pi$
$293$	−6.06161	−0.354123	−0.177061	+	0.984200i	$0.556659\pi$
$294$	−4.29730	−0.250623
$295$	10.2784	0.598431
$296$	8.81046	0.512098
$297$	−5.62623	−0.326467
$298$	−10.8102	−0.626219
$299$	−20.7596	−1.20056
$300$	1.32838	0.0766943
$301$	−6.46193	−0.372459
$302$	7.04341	0.405303
$303$	−15.6771	−0.900623
$304$	8.23004	0.472025
$305$	12.2019	0.698678
$306$	−5.82004	−0.332709
$307$	−34.3351	−1.95961	−0.979804	−	0.199959i	$-0.935919\pi$
$307$	−34.3351	−1.95961	−0.979804	+	0.199959i	$0.935919\pi$
$308$	−1.94037	−0.110563
$309$	25.0187	1.42326
$310$	−8.39860	−0.477008
$311$	26.8801	1.52423	0.762116	−	0.647440i	$-0.224160\pi$
$311$	26.8801	1.52423	0.762116	+	0.647440i	$0.224160\pi$
$312$	7.18606	0.406831
$313$	−29.4990	−1.66738	−0.833691	−	0.552231i	$-0.813777\pi$
$313$	−29.4990	−1.66738	−0.833691	+	0.552231i	$0.813777\pi$
$314$	17.4666	0.985698
$315$	2.39712	0.135062
$316$	7.78551	0.437969
$317$	19.2551	1.08148	0.540738	−	0.841191i	$-0.318145\pi$
$317$	19.2551	1.08148	0.540738	+	0.841191i	$0.318145\pi$
$318$	−7.02184	−0.393765
$319$	6.15228	0.344461
$320$	1.00000	0.0559017
$321$	4.25026	0.237226
$322$	7.44621	0.414961
$323$	38.7723	2.15735
$324$	−3.76761	−0.209312
$325$	5.40963	0.300072
$326$	5.97134	0.330722
$327$	−5.42783	−0.300160
$328$	−8.97027	−0.495300
$329$	18.6842	1.03009
$330$	1.32838	0.0731251
$331$	−1.55417	−0.0854252	−0.0427126	−	0.999087i	$-0.513600\pi$
$331$	−1.55417	−0.0854252	−0.0427126	+	0.999087i	$0.513600\pi$
$332$	16.3176	0.895543
$333$	−10.8844	−0.596462
$334$	21.5725	1.18040
$335$	−4.77249	−0.260749
$336$	−2.57755	−0.140617
$337$	3.09685	0.168696	0.0843482	−	0.996436i	$-0.473119\pi$
$337$	3.09685	0.168696	0.0843482	+	0.996436i	$0.473119\pi$
$338$	16.2641	0.884648
$339$	−18.9831	−1.03102
$340$	4.71107	0.255494
$341$	−8.39860	−0.454810
$342$	−10.1674	−0.549787
$343$	19.8596	1.07232
$344$	3.33026	0.179556
$345$	−5.09771	−0.274452
$346$	0.234620	0.0126132
$347$	26.3630	1.41524	0.707620	−	0.706593i	$-0.249769\pi$
$347$	26.3630	1.41524	0.707620	+	0.706593i	$0.249769\pi$
$348$	8.17259	0.438097
$349$	18.4102	0.985474	0.492737	−	0.870178i	$-0.335997\pi$
$349$	18.4102	0.985474	0.492737	+	0.870178i	$0.335997\pi$
$350$	−1.94037	−0.103717
$351$	−30.4358	−1.62454
$352$	1.00000	0.0533002
$353$	−27.2876	−1.45237	−0.726185	−	0.687499i	$-0.758709\pi$
$353$	−27.2876	−1.45237	−0.726185	+	0.687499i	$0.758709\pi$
$354$	13.6536	0.725683
$355$	−5.01237	−0.266029
$356$	−7.58602	−0.402058
$357$	−12.1430	−0.642678
$358$	18.0652	0.954775
$359$	−31.4908	−1.66202	−0.831010	−	0.556258i	$-0.812237\pi$
$359$	−31.4908	−1.66202	−0.831010	+	0.556258i	$0.812237\pi$
$360$	−1.23540	−0.0651111
$361$	48.7335	2.56492
$362$	3.70514	0.194738
$363$	1.32838	0.0697221
$364$	−10.4967	−0.550174
$365$	−1.00000	−0.0523424
$366$	16.2088	0.847248
$367$	28.5922	1.49250	0.746251	−	0.665665i	$-0.231852\pi$
$367$	28.5922	1.49250	0.746251	+	0.665665i	$0.231852\pi$
$368$	−3.83753	−0.200045
$369$	11.0818	0.576897
$370$	8.81046	0.458034
$371$	10.2568	0.532505
$372$	−11.1566	−0.578441
$373$	−20.5244	−1.06271	−0.531356	−	0.847148i	$-0.678317\pi$
$373$	−20.5244	−1.06271	−0.531356	+	0.847148i	$0.678317\pi$
$374$	4.71107	0.243604
$375$	1.32838	0.0685975
$376$	−9.62921	−0.496589
$377$	33.2815	1.71409
$378$	10.9169	0.561507
$379$	−8.17694	−0.420021	−0.210011	−	0.977699i	$-0.567350\pi$
$379$	−8.17694	−0.420021	−0.210011	+	0.977699i	$0.567350\pi$
$380$	8.23004	0.422192
$381$	15.3445	0.786122
$382$	−4.38714	−0.224465
$383$	−0.647037	−0.0330621	−0.0165310	−	0.999863i	$-0.505262\pi$
$383$	−0.647037	−0.0330621	−0.0165310	+	0.999863i	$0.505262\pi$
$384$	1.32838	0.0677888
$385$	−1.94037	−0.0988902
$386$	−8.71694	−0.443680
$387$	−4.11419	−0.209136
$388$	−10.3678	−0.526347
$389$	−31.8163	−1.61315	−0.806574	−	0.591133i	$-0.798681\pi$
$389$	−31.8163	−1.61315	−0.806574	+	0.591133i	$0.798681\pi$
$390$	7.18606	0.363880
$391$	−18.0789	−0.914288
$392$	−3.23498	−0.163391
$393$	24.8464	1.25334
$394$	−14.7591	−0.743555
$395$	7.78551	0.391732
$396$	−1.23540	−0.0620810
$397$	−15.8036	−0.793162	−0.396581	−	0.918000i	$-0.629803\pi$
$397$	−15.8036	−0.793162	−0.396581	+	0.918000i	$0.629803\pi$
$398$	−6.02657	−0.302085
$399$	−21.2133	−1.06200
$400$	1.00000	0.0500000
$401$	−19.9554	−0.996526	−0.498263	−	0.867026i	$-0.666029\pi$
$401$	−19.9554	−0.996526	−0.498263	+	0.867026i	$0.666029\pi$
$402$	−6.33969	−0.316195
$403$	−45.4333	−2.26319
$404$	−11.8016	−0.587151
$405$	−3.76761	−0.187214
$406$	−11.9377	−0.592457
$407$	8.81046	0.436718
$408$	6.25812	0.309823
$409$	−14.4243	−0.713235	−0.356618	−	0.934250i	$-0.616070\pi$
$409$	−14.4243	−0.713235	−0.356618	+	0.934250i	$0.616070\pi$
$410$	−8.97027	−0.443010
$411$	−1.71463	−0.0845766
$412$	18.8339	0.927880
$413$	−19.9438	−0.981372
$414$	4.74087	0.233001
$415$	16.3176	0.800998
$416$	5.40963	0.265229
$417$	9.31975	0.456390
$418$	8.23004	0.402544
$419$	5.83409	0.285014	0.142507	−	0.989794i	$-0.454484\pi$
$419$	5.83409	0.285014	0.142507	+	0.989794i	$0.454484\pi$
$420$	−2.57755	−0.125772
$421$	−26.7327	−1.30287	−0.651437	−	0.758703i	$-0.725833\pi$
$421$	−26.7327	−1.30287	−0.651437	+	0.758703i	$0.725833\pi$
$422$	19.9965	0.973413
$423$	11.8959	0.578398
$424$	−5.28600	−0.256711
$425$	4.71107	0.228521
$426$	−6.65835	−0.322598
$427$	−23.6761	−1.14577
$428$	3.19957	0.154657
$429$	7.18606	0.346946
$430$	3.33026	0.160599
$431$	0.0835868	0.00402623	0.00201312	−	0.999998i	$-0.499359\pi$
$431$	0.0835868	0.00402623	0.00201312	+	0.999998i	$0.499359\pi$
$432$	−5.62623	−0.270692
$433$	−17.2719	−0.830033	−0.415017	−	0.909814i	$-0.636224\pi$
$433$	−17.2719	−0.830033	−0.415017	+	0.909814i	$0.636224\pi$
$434$	16.2964	0.782250
$435$	8.17259	0.391846
$436$	−4.08604	−0.195686
$437$	−31.5830	−1.51082
$438$	−1.32838	−0.0634727
$439$	5.21826	0.249054	0.124527	−	0.992216i	$-0.460259\pi$
$439$	5.21826	0.249054	0.124527	+	0.992216i	$0.460259\pi$
$440$	1.00000	0.0476731
$441$	3.99648	0.190309
$442$	25.4851	1.21220
$443$	−5.64220	−0.268069	−0.134035	−	0.990977i	$-0.542793\pi$
$443$	−5.64220	−0.268069	−0.134035	+	0.990977i	$0.542793\pi$
$444$	11.7037	0.555432
$445$	−7.58602	−0.359612
$446$	18.9901	0.899208
$447$	−14.3601	−0.679210
$448$	−1.94037	−0.0916737
$449$	−13.9433	−0.658027	−0.329014	−	0.944325i	$-0.606716\pi$
$449$	−13.9433	−0.658027	−0.329014	+	0.944325i	$0.606716\pi$
$450$	−1.23540	−0.0582371
$451$	−8.97027	−0.422393
$452$	−14.2904	−0.672164
$453$	9.35636	0.439600
$454$	−6.21279	−0.291581
$455$	−10.4967	−0.492091
$456$	10.9327	0.511968
$457$	−21.6792	−1.01411	−0.507055	−	0.861914i	$-0.669266\pi$
$457$	−21.6792	−1.01411	−0.507055	+	0.861914i	$0.669266\pi$
$458$	−7.65835	−0.357851
$459$	−26.5056	−1.23718
$460$	−3.83753	−0.178926
$461$	−23.2735	−1.08396	−0.541978	−	0.840393i	$-0.682324\pi$
$461$	−23.2735	−1.08396	−0.541978	+	0.840393i	$0.682324\pi$
$462$	−2.57755	−0.119919
$463$	−13.8489	−0.643614	−0.321807	−	0.946805i	$-0.604290\pi$
$463$	−13.8489	−0.643614	−0.321807	+	0.946805i	$0.604290\pi$
$464$	6.15228	0.285612
$465$	−11.1566	−0.517373
$466$	−18.1944	−0.842837
$467$	−39.8083	−1.84211	−0.921055	−	0.389433i	$-0.872671\pi$
$467$	−39.8083	−1.84211	−0.921055	+	0.389433i	$0.872671\pi$
$468$	−6.68303	−0.308923
$469$	9.26037	0.427604
$470$	−9.62921	−0.444162
$471$	23.2024	1.06911
$472$	10.2784	0.473101
$473$	3.33026	0.153126
$474$	10.3421	0.475031
$475$	8.23004	0.377620
$476$	−9.14121	−0.418987
$477$	6.53030	0.299002
$478$	−10.0919	−0.461593
$479$	−40.1201	−1.83314	−0.916568	−	0.399880i	$-0.869052\pi$
$479$	−40.1201	−1.83314	−0.916568	+	0.399880i	$0.869052\pi$
$480$	1.32838	0.0606322
$481$	47.6613	2.17317
$482$	14.1146	0.642902
$483$	9.89143	0.450076
$484$	1.00000	0.0454545
$485$	−10.3678	−0.470779
$486$	11.8739	0.538609
$487$	−5.75491	−0.260780	−0.130390	−	0.991463i	$-0.541623\pi$
$487$	−5.75491	−0.260780	−0.130390	+	0.991463i	$0.541623\pi$
$488$	12.2019	0.552354
$489$	7.93224	0.358708
$490$	−3.23498	−0.146142
$491$	−1.95489	−0.0882229	−0.0441114	−	0.999027i	$-0.514046\pi$
$491$	−1.95489	−0.0882229	−0.0441114	+	0.999027i	$0.514046\pi$
$492$	−11.9160	−0.537213
$493$	28.9838	1.30537
$494$	44.5214	2.00311
$495$	−1.23540	−0.0555269
$496$	−8.39860	−0.377108
$497$	9.72583	0.436263
$498$	21.6760	0.971325
$499$	−17.6766	−0.791312	−0.395656	−	0.918399i	$-0.629483\pi$
$499$	−17.6766	−0.791312	−0.395656	+	0.918399i	$0.629483\pi$
$500$	1.00000	0.0447214
$501$	28.6566	1.28028
$502$	−16.1337	−0.720080
$503$	−31.2044	−1.39134	−0.695668	−	0.718363i	$-0.744891\pi$
$503$	−31.2044	−1.39134	−0.695668	+	0.718363i	$0.744891\pi$
$504$	2.39712	0.106776
$505$	−11.8016	−0.525164
$506$	−3.83753	−0.170599
$507$	21.6049	0.959508
$508$	11.5512	0.512504
$509$	−15.4012	−0.682644	−0.341322	−	0.939946i	$-0.610875\pi$
$509$	−15.4012	−0.682644	−0.341322	+	0.939946i	$0.610875\pi$
$510$	6.25812	0.277114
$511$	1.94037	0.0858367
$512$	1.00000	0.0441942
$513$	−46.3041	−2.04438
$514$	−8.47773	−0.373937
$515$	18.8339	0.829921
$516$	4.42387	0.194750
$517$	−9.62921	−0.423492
$518$	−17.0955	−0.751134
$519$	0.311665	0.0136806
$520$	5.40963	0.237228
$521$	−7.70578	−0.337596	−0.168798	−	0.985651i	$-0.553989\pi$
$521$	−7.70578	−0.337596	−0.168798	+	0.985651i	$0.553989\pi$
$522$	−7.60050	−0.332665
$523$	9.98238	0.436499	0.218250	−	0.975893i	$-0.429965\pi$
$523$	9.98238	0.436499	0.218250	+	0.975893i	$0.429965\pi$
$524$	18.7042	0.817098
$525$	−2.57755	−0.112494
$526$	5.11333	0.222952
$527$	−39.5664	−1.72354
$528$	1.32838	0.0578105
$529$	−8.27337	−0.359712
$530$	−5.28600	−0.229609
$531$	−12.6979	−0.551041
$532$	−15.9693	−0.692356
$533$	−48.5258	−2.10189
$534$	−10.0771	−0.436081
$535$	3.19957	0.138330
$536$	−4.77249	−0.206140
$537$	23.9975	1.03557
$538$	17.0652	0.735733
$539$	−3.23498	−0.139340
$540$	−5.62623	−0.242114
$541$	−3.11725	−0.134021	−0.0670105	−	0.997752i	$-0.521346\pi$
$541$	−3.11725	−0.134021	−0.0670105	+	0.997752i	$0.521346\pi$
$542$	−14.6412	−0.628894
$543$	4.92185	0.211217
$544$	4.71107	0.201986
$545$	−4.08604	−0.175027
$546$	−13.9436	−0.596731
$547$	−30.0550	−1.28506	−0.642528	−	0.766262i	$-0.722115\pi$
$547$	−30.0550	−1.28506	−0.642528	+	0.766262i	$0.722115\pi$
$548$	−1.29076	−0.0551387
$549$	−15.0742	−0.643350
$550$	1.00000	0.0426401
$551$	50.6335	2.15706
$552$	−5.09771	−0.216973
$553$	−15.1067	−0.642404
$554$	17.0511	0.724431
$555$	11.7037	0.496793
$556$	7.01585	0.297538
$557$	17.4640	0.739973	0.369986	−	0.929037i	$-0.379362\pi$
$557$	17.4640	0.739973	0.369986	+	0.929037i	$0.379362\pi$
$558$	10.3756	0.439234
$559$	18.0155	0.761973
$560$	−1.94037	−0.0819954
$561$	6.25812	0.264218
$562$	21.4526	0.904922
$563$	12.6585	0.533493	0.266746	−	0.963767i	$-0.414051\pi$
$563$	12.6585	0.533493	0.266746	+	0.963767i	$0.414051\pi$
$564$	−12.7913	−0.538611
$565$	−14.2904	−0.601202
$566$	−25.7974	−1.08434
$567$	7.31055	0.307014
$568$	−5.01237	−0.210314
$569$	−7.14909	−0.299706	−0.149853	−	0.988708i	$-0.547880\pi$
$569$	−7.14909	−0.299706	−0.149853	+	0.988708i	$0.547880\pi$
$570$	10.9327	0.457918
$571$	−3.17896	−0.133035	−0.0665176	−	0.997785i	$-0.521189\pi$
$571$	−3.17896	−0.133035	−0.0665176	+	0.997785i	$0.521189\pi$
$572$	5.40963	0.226188
$573$	−5.82780	−0.243460
$574$	17.4056	0.726496
$575$	−3.83753	−0.160036
$576$	−1.23540	−0.0514748
$577$	−25.9755	−1.08137	−0.540687	−	0.841224i	$-0.681836\pi$
$577$	−25.9755	−1.08137	−0.540687	+	0.841224i	$0.681836\pi$
$578$	5.19421	0.216051
$579$	−11.5794	−0.481225
$580$	6.15228	0.255459
$581$	−31.6621	−1.31356
$582$	−13.7725	−0.570888
$583$	−5.28600	−0.218924
$584$	−1.00000	−0.0413803
$585$	−6.68303	−0.276309
$586$	−6.06161	−0.250403
$587$	12.9383	0.534022	0.267011	−	0.963693i	$-0.413964\pi$
$587$	12.9383	0.534022	0.267011	+	0.963693i	$0.413964\pi$
$588$	−4.29730	−0.177218
$589$	−69.1208	−2.84807
$590$	10.2784	0.423154
$591$	−19.6058	−0.806475
$592$	8.81046	0.362108
$593$	23.8162	0.978012	0.489006	−	0.872280i	$-0.337360\pi$
$593$	23.8162	0.978012	0.489006	+	0.872280i	$0.337360\pi$
$594$	−5.62623	−0.230847
$595$	−9.14121	−0.374753
$596$	−10.8102	−0.442804
$597$	−8.00560	−0.327647
$598$	−20.7596	−0.848923
$599$	11.7206	0.478889	0.239445	−	0.970910i	$-0.423035\pi$
$599$	11.7206	0.478889	0.239445	+	0.970910i	$0.423035\pi$
$600$	1.32838	0.0542311
$601$	−21.3111	−0.869299	−0.434649	−	0.900600i	$-0.643128\pi$
$601$	−21.3111	−0.869299	−0.434649	+	0.900600i	$0.643128\pi$
$602$	−6.46193	−0.263368
$603$	5.89591	0.240100
$604$	7.04341	0.286592
$605$	1.00000	0.0406558
$606$	−15.6771	−0.636837
$607$	35.3812	1.43608	0.718040	−	0.696002i	$-0.245039\pi$
$607$	35.3812	1.43608	0.718040	+	0.696002i	$0.245039\pi$
$608$	8.23004	0.333772
$609$	−15.8578	−0.642591
$610$	12.2019	0.494040
$611$	−52.0904	−2.10735
$612$	−5.82004	−0.235261
$613$	41.5357	1.67761	0.838806	−	0.544431i	$-0.183254\pi$
$613$	41.5357	1.67761	0.838806	+	0.544431i	$0.183254\pi$
$614$	−34.3351	−1.38565
$615$	−11.9160	−0.480498
$616$	−1.94037	−0.0781796
$617$	26.6811	1.07414	0.537071	−	0.843537i	$-0.319531\pi$
$617$	26.6811	1.07414	0.537071	+	0.843537i	$0.319531\pi$
$618$	25.0187	1.00640
$619$	19.9041	0.800014	0.400007	−	0.916512i	$-0.369008\pi$
$619$	19.9041	0.800014	0.400007	+	0.916512i	$0.369008\pi$
$620$	−8.39860	−0.337296
$621$	21.5908	0.866410
$622$	26.8801	1.07780
$623$	14.7197	0.589730
$624$	7.18606	0.287673
$625$	1.00000	0.0400000
$626$	−29.4990	−1.17902
$627$	10.9327	0.436608
$628$	17.4666	0.696994
$629$	41.5067	1.65498
$630$	2.39712	0.0955035
$631$	−37.0575	−1.47524	−0.737618	−	0.675218i	$-0.764050\pi$
$631$	−37.0575	−1.47524	−0.737618	+	0.675218i	$0.764050\pi$
$632$	7.78551	0.309691
$633$	26.5630	1.05578
$634$	19.2551	0.764718
$635$	11.5512	0.458397
$636$	−7.02184	−0.278434
$637$	−17.5000	−0.693377
$638$	6.15228	0.243571
$639$	6.19226	0.244962
$640$	1.00000	0.0395285
$641$	−3.09227	−0.122137	−0.0610686	−	0.998134i	$-0.519451\pi$
$641$	−3.09227	−0.122137	−0.0610686	+	0.998134i	$0.519451\pi$
$642$	4.25026	0.167744
$643$	−37.6559	−1.48501	−0.742503	−	0.669843i	$-0.766361\pi$
$643$	−37.6559	−1.48501	−0.742503	+	0.669843i	$0.766361\pi$
$644$	7.44621	0.293422
$645$	4.42387	0.174190
$646$	38.7723	1.52548
$647$	−1.06645	−0.0419263	−0.0209632	−	0.999780i	$-0.506673\pi$
$647$	−1.06645	−0.0419263	−0.0209632	+	0.999780i	$0.506673\pi$
$648$	−3.76761	−0.148006
$649$	10.2784	0.403462
$650$	5.40963	0.212183
$651$	21.6478	0.848445
$652$	5.97134	0.233856
$653$	−47.1868	−1.84656	−0.923281	−	0.384125i	$-0.874503\pi$
$653$	−47.1868	−1.84656	−0.923281	+	0.384125i	$0.874503\pi$
$654$	−5.42783	−0.212245
$655$	18.7042	0.730835
$656$	−8.97027	−0.350230
$657$	1.23540	0.0481974
$658$	18.6842	0.728386
$659$	29.2693	1.14017	0.570084	−	0.821586i	$-0.306911\pi$
$659$	29.2693	1.14017	0.570084	+	0.821586i	$0.306911\pi$
$660$	1.32838	0.0517073
$661$	−23.1794	−0.901575	−0.450787	−	0.892631i	$-0.648857\pi$
$661$	−23.1794	−0.901575	−0.450787	+	0.892631i	$0.648857\pi$
$662$	−1.55417	−0.0604047
$663$	33.8541	1.31478
$664$	16.3176	0.633245
$665$	−15.9693	−0.619262
$666$	−10.8844	−0.421762
$667$	−23.6095	−0.914165
$668$	21.5725	0.834666
$669$	25.2262	0.975300
$670$	−4.77249	−0.184377
$671$	12.2019	0.471049
$672$	−2.57755	−0.0994312
$673$	43.1071	1.66166	0.830828	−	0.556530i	$-0.187868\pi$
$673$	43.1071	1.66166	0.830828	+	0.556530i	$0.187868\pi$
$674$	3.09685	0.119286
$675$	−5.62623	−0.216554
$676$	16.2641	0.625540
$677$	−38.6255	−1.48450	−0.742250	−	0.670124i	$-0.766241\pi$
$677$	−38.6255	−1.48450	−0.742250	+	0.670124i	$0.766241\pi$
$678$	−18.9831	−0.729043
$679$	20.1174	0.772035
$680$	4.71107	0.180661
$681$	−8.25297	−0.316255
$682$	−8.39860	−0.321599
$683$	−25.9028	−0.991143	−0.495572	−	0.868567i	$-0.665041\pi$
$683$	−25.9028	−0.991143	−0.495572	+	0.868567i	$0.665041\pi$
$684$	−10.1674	−0.388758
$685$	−1.29076	−0.0493176
$686$	19.8596	0.758243
$687$	−10.1732	−0.388133
$688$	3.33026	0.126965
$689$	−28.5953	−1.08939
$690$	−5.09771	−0.194067
$691$	50.3083	1.91382	0.956909	−	0.290388i	$-0.0937843\pi$
$691$	50.3083	1.91382	0.956909	+	0.290388i	$0.0937843\pi$
$692$	0.234620	0.00891891
$693$	2.39712	0.0910590
$694$	26.3630	1.00073
$695$	7.01585	0.266126
$696$	8.17259	0.309781
$697$	−42.2596	−1.60070
$698$	18.4102	0.696835
$699$	−24.1691	−0.914159
$700$	−1.94037	−0.0733389
$701$	48.3150	1.82483	0.912416	−	0.409264i	$-0.134214\pi$
$701$	48.3150	1.82483	0.912416	+	0.409264i	$0.134214\pi$
$702$	−30.4358	−1.14873
$703$	72.5104	2.73478
$704$	1.00000	0.0376889
$705$	−12.7913	−0.481748
$706$	−27.2876	−1.02698
$707$	22.8994	0.861221
$708$	13.6536	0.513135
$709$	26.7745	1.00554	0.502769	−	0.864421i	$-0.332315\pi$
$709$	26.7745	1.00554	0.502769	+	0.864421i	$0.332315\pi$
$710$	−5.01237	−0.188111
$711$	−9.61818	−0.360710
$712$	−7.58602	−0.284298
$713$	32.2299	1.20702
$714$	−12.1430	−0.454442
$715$	5.40963	0.202309
$716$	18.0652	0.675128
$717$	−13.4059	−0.500654
$718$	−31.4908	−1.17523
$719$	−19.3451	−0.721450	−0.360725	−	0.932672i	$-0.617471\pi$
$719$	−19.3451	−0.721450	−0.360725	+	0.932672i	$0.617471\pi$
$720$	−1.23540	−0.0460405
$721$	−36.5447	−1.36099
$722$	48.7335	1.81367
$723$	18.7496	0.697306
$724$	3.70514	0.137701
$725$	6.15228	0.228490
$726$	1.32838	0.0493010
$727$	−32.2791	−1.19717	−0.598583	−	0.801061i	$-0.704269\pi$
$727$	−32.2791	−1.19717	−0.598583	+	0.801061i	$0.704269\pi$
$728$	−10.4967	−0.389032
$729$	27.0759	1.00281
$730$	−1.00000	−0.0370117
$731$	15.6891	0.580283
$732$	16.2088	0.599095
$733$	−32.9166	−1.21580	−0.607902	−	0.794012i	$-0.707988\pi$
$733$	−32.9166	−1.21580	−0.607902	+	0.794012i	$0.707988\pi$
$734$	28.5922	1.05536
$735$	−4.29730	−0.158508
$736$	−3.83753	−0.141453
$737$	−4.77249	−0.175797
$738$	11.0818	0.407928
$739$	−28.0518	−1.03190	−0.515950	−	0.856618i	$-0.672561\pi$
$739$	−28.0518	−1.03190	−0.515950	+	0.856618i	$0.672561\pi$
$740$	8.81046	0.323879
$741$	59.1416	2.17262
$742$	10.2568	0.376538
$743$	26.3756	0.967627	0.483813	−	0.875171i	$-0.339251\pi$
$743$	26.3756	0.967627	0.483813	+	0.875171i	$0.339251\pi$
$744$	−11.1566	−0.409020
$745$	−10.8102	−0.396056
$746$	−20.5244	−0.751451
$747$	−20.1587	−0.737567
$748$	4.71107	0.172254
$749$	−6.20834	−0.226848
$750$	1.32838	0.0485057
$751$	−23.1261	−0.843883	−0.421942	−	0.906623i	$-0.638651\pi$
$751$	−23.1261	−0.843883	−0.421942	+	0.906623i	$0.638651\pi$
$752$	−9.62921	−0.351141
$753$	−21.4317	−0.781014
$754$	33.2815	1.21204
$755$	7.04341	0.256336
$756$	10.9169	0.397046
$757$	21.2256	0.771457	0.385729	−	0.922612i	$-0.373950\pi$
$757$	21.2256	0.771457	0.385729	+	0.922612i	$0.373950\pi$
$758$	−8.17694	−0.297000
$759$	−5.09771	−0.185035
$760$	8.23004	0.298535
$761$	−27.8431	−1.00931	−0.504656	−	0.863320i	$-0.668381\pi$
$761$	−27.8431	−1.00931	−0.504656	+	0.863320i	$0.668381\pi$
$762$	15.3445	0.555872
$763$	7.92842	0.287028
$764$	−4.38714	−0.158721
$765$	−5.82004	−0.210424
$766$	−0.647037	−0.0233784
$767$	55.6022	2.00768
$768$	1.32838	0.0479339
$769$	1.11486	0.0402030	0.0201015	−	0.999798i	$-0.493601\pi$
$769$	1.11486	0.0402030	0.0201015	+	0.999798i	$0.493601\pi$
$770$	−1.94037	−0.0699259
$771$	−11.2617	−0.405580
$772$	−8.71694	−0.313729
$773$	−24.6668	−0.887205	−0.443602	−	0.896224i	$-0.646300\pi$
$773$	−24.6668	−0.887205	−0.443602	+	0.896224i	$0.646300\pi$
$774$	−4.11419	−0.147882
$775$	−8.39860	−0.301687
$776$	−10.3678	−0.372184
$777$	−22.7094	−0.814696
$778$	−31.8163	−1.14067
$779$	−73.8256	−2.64508
$780$	7.18606	0.257302
$781$	−5.01237	−0.179357
$782$	−18.0789	−0.646499
$783$	−34.6141	−1.23701
$784$	−3.23498	−0.115535
$785$	17.4666	0.623410
$786$	24.8464	0.886242
$787$	−16.4577	−0.586654	−0.293327	−	0.956012i	$-0.594762\pi$
$787$	−16.4577	−0.586654	−0.293327	+	0.956012i	$0.594762\pi$
$788$	−14.7591	−0.525773
$789$	6.79247	0.241818
$790$	7.78551	0.276996
$791$	27.7286	0.985916
$792$	−1.23540	−0.0438979
$793$	66.0077	2.34400
$794$	−15.8036	−0.560850
$795$	−7.02184	−0.249039
$796$	−6.02657	−0.213606
$797$	18.2403	0.646105	0.323052	−	0.946381i	$-0.395291\pi$
$797$	18.2403	0.646105	0.323052	+	0.946381i	$0.395291\pi$
$798$	−21.2133	−0.750944
$799$	−45.3639	−1.60486
$800$	1.00000	0.0353553
$801$	9.37173	0.331134
$802$	−19.9554	−0.704651
$803$	−1.00000	−0.0352892
$804$	−6.33969	−0.223584
$805$	7.44621	0.262444
$806$	−45.4333	−1.60032
$807$	22.6691	0.797992
$808$	−11.8016	−0.415179
$809$	−6.14983	−0.216217	−0.108108	−	0.994139i	$-0.534479\pi$
$809$	−6.14983	−0.216217	−0.108108	+	0.994139i	$0.534479\pi$
$810$	−3.76761	−0.132380
$811$	−36.1824	−1.27053	−0.635267	−	0.772292i	$-0.719110\pi$
$811$	−36.1824	−1.27053	−0.635267	+	0.772292i	$0.719110\pi$
$812$	−11.9377	−0.418930
$813$	−19.4491	−0.682111
$814$	8.81046	0.308807
$815$	5.97134	0.209167
$816$	6.25812	0.219078
$817$	27.4082	0.958891
$818$	−14.4243	−0.504334
$819$	12.9675	0.453122
$820$	−8.97027	−0.313255
$821$	7.41661	0.258842	0.129421	−	0.991590i	$-0.458688\pi$
$821$	7.41661	0.258842	0.129421	+	0.991590i	$0.458688\pi$
$822$	−1.71463	−0.0598047
$823$	12.7103	0.443054	0.221527	−	0.975154i	$-0.428896\pi$
$823$	12.7103	0.443054	0.221527	+	0.975154i	$0.428896\pi$
$824$	18.8339	0.656110
$825$	1.32838	0.0462484
$826$	−19.9438	−0.693935
$827$	8.63958	0.300428	0.150214	−	0.988654i	$-0.452004\pi$
$827$	8.63958	0.300428	0.150214	+	0.988654i	$0.452004\pi$
$828$	4.74087	0.164756
$829$	−14.2528	−0.495022	−0.247511	−	0.968885i	$-0.579613\pi$
$829$	−14.2528	−0.495022	−0.247511	+	0.968885i	$0.579613\pi$
$830$	16.3176	0.566391
$831$	22.6504	0.785734
$832$	5.40963	0.187545
$833$	−15.2402	−0.528043
$834$	9.31975	0.322717
$835$	21.5725	0.746548
$836$	8.23004	0.284642
$837$	47.2525	1.63328
$838$	5.83409	0.201535
$839$	−38.9902	−1.34609	−0.673046	−	0.739601i	$-0.735014\pi$
$839$	−38.9902	−1.34609	−0.673046	+	0.739601i	$0.735014\pi$
$840$	−2.57755	−0.0889340
$841$	8.85053	0.305191
$842$	−26.7327	−0.921271
$843$	28.4973	0.981498
$844$	19.9965	0.688307
$845$	16.2641	0.559500
$846$	11.8959	0.408989
$847$	−1.94037	−0.0666718
$848$	−5.28600	−0.181522
$849$	−34.2688	−1.17610
$850$	4.71107	0.161588
$851$	−33.8104	−1.15901
$852$	−6.65835	−0.228111
$853$	20.0687	0.687140	0.343570	−	0.939127i	$-0.388364\pi$
$853$	20.0687	0.687140	0.343570	+	0.939127i	$0.388364\pi$
$854$	−23.6761	−0.810181
$855$	−10.1674	−0.347716
$856$	3.19957	0.109359
$857$	−26.8747	−0.918023	−0.459012	−	0.888430i	$-0.651796\pi$
$857$	−26.8747	−0.918023	−0.459012	+	0.888430i	$0.651796\pi$
$858$	7.18606	0.245328
$859$	20.7292	0.707271	0.353635	−	0.935383i	$-0.384945\pi$
$859$	20.7292	0.707271	0.353635	+	0.935383i	$0.384945\pi$
$860$	3.33026	0.113561
$861$	23.1213	0.787973
$862$	0.0835868	0.00284698
$863$	11.0054	0.374627	0.187314	−	0.982300i	$-0.440022\pi$
$863$	11.0054	0.374627	0.187314	+	0.982300i	$0.440022\pi$
$864$	−5.62623	−0.191408
$865$	0.234620	0.00797732
$866$	−17.2719	−0.586922
$867$	6.89991	0.234333
$868$	16.2964	0.553134
$869$	7.78551	0.264105
$870$	8.17259	0.277077
$871$	−25.8174	−0.874788
$872$	−4.08604	−0.138371
$873$	12.8084	0.433498
$874$	−31.5830	−1.06831
$875$	−1.94037	−0.0655963
$876$	−1.32838	−0.0448819
$877$	15.8074	0.533780	0.266890	−	0.963727i	$-0.414004\pi$
$877$	15.8074	0.533780	0.266890	+	0.963727i	$0.414004\pi$
$878$	5.21826	0.176108
$879$	−8.05214	−0.271592
$880$	1.00000	0.0337100
$881$	−13.1727	−0.443799	−0.221899	−	0.975070i	$-0.571226\pi$
$881$	−13.1727	−0.443799	−0.221899	+	0.975070i	$0.571226\pi$
$882$	3.99648	0.134568
$883$	−40.8582	−1.37499	−0.687494	−	0.726190i	$-0.741289\pi$
$883$	−40.8582	−1.37499	−0.687494	+	0.726190i	$0.741289\pi$
$884$	25.4851	0.857158
$885$	13.6536	0.458962
$886$	−5.64220	−0.189554
$887$	2.82096	0.0947185	0.0473592	−	0.998878i	$-0.484919\pi$
$887$	2.82096	0.0947185	0.0473592	+	0.998878i	$0.484919\pi$
$888$	11.7037	0.392750
$889$	−22.4136	−0.751729
$890$	−7.58602	−0.254284
$891$	−3.76761	−0.126220
$892$	18.9901	0.635836
$893$	−79.2488	−2.65196
$894$	−14.3601	−0.480274
$895$	18.0652	0.603853
$896$	−1.94037	−0.0648231
$897$	−27.5767	−0.920760
$898$	−13.9433	−0.465295
$899$	−51.6705	−1.72331
$900$	−1.23540	−0.0411798
$901$	−24.9027	−0.829631
$902$	−8.97027	−0.298677
$903$	−8.58392	−0.285655
$904$	−14.2904	−0.475292
$905$	3.70514	0.123163
$906$	9.35636	0.310844
$907$	37.9725	1.26085	0.630427	−	0.776248i	$-0.282880\pi$
$907$	37.9725	1.26085	0.630427	+	0.776248i	$0.282880\pi$
$908$	−6.21279	−0.206179
$909$	14.5796	0.483576
$910$	−10.4967	−0.347961
$911$	17.9428	0.594473	0.297236	−	0.954804i	$-0.403935\pi$
$911$	17.9428	0.594473	0.297236	+	0.954804i	$0.403935\pi$
$912$	10.9327	0.362016
$913$	16.3176	0.540033
$914$	−21.6792	−0.717083
$915$	16.2088	0.535846
$916$	−7.65835	−0.253039
$917$	−36.2931	−1.19850
$918$	−26.5056	−0.874815
$919$	−36.4052	−1.20090	−0.600449	−	0.799663i	$-0.705011\pi$
$919$	−36.4052	−1.20090	−0.600449	+	0.799663i	$0.705011\pi$
$920$	−3.83753	−0.126520
$921$	−45.6102	−1.50291
$922$	−23.2735	−0.766472
$923$	−27.1150	−0.892502
$924$	−2.57755	−0.0847952
$925$	8.81046	0.289686
$926$	−13.8489	−0.455104
$927$	−23.2673	−0.764199
$928$	6.15228	0.201958
$929$	−23.3674	−0.766661	−0.383330	−	0.923611i	$-0.625223\pi$
$929$	−23.3674	−0.766661	−0.383330	+	0.923611i	$0.625223\pi$
$930$	−11.1566	−0.365838
$931$	−26.6240	−0.872567
$932$	−18.1944	−0.595976
$933$	35.7071	1.16900
$934$	−39.8083	−1.30257
$935$	4.71107	0.154069
$936$	−6.68303	−0.218442
$937$	−19.5670	−0.639225	−0.319612	−	0.947548i	$-0.603553\pi$
$937$	−19.5670	−0.639225	−0.319612	+	0.947548i	$0.603553\pi$
$938$	9.26037	0.302362
$939$	−39.1860	−1.27879
$940$	−9.62921	−0.314070
$941$	57.7420	1.88233	0.941167	−	0.337942i	$-0.109731\pi$
$941$	57.7420	1.88233	0.941167	+	0.337942i	$0.109731\pi$
$942$	23.2024	0.755974
$943$	34.4237	1.12099
$944$	10.2784	0.334533
$945$	10.9169	0.355128
$946$	3.33026	0.108276
$947$	17.3636	0.564241	0.282120	−	0.959379i	$-0.408962\pi$
$947$	17.3636	0.564241	0.282120	+	0.959379i	$0.408962\pi$
$948$	10.3421	0.335897
$949$	−5.40963	−0.175604
$950$	8.23004	0.267018
$951$	25.5782	0.829430
$952$	−9.14121	−0.296268
$953$	52.3094	1.69447	0.847234	−	0.531220i	$-0.178266\pi$
$953$	52.3094	1.69447	0.847234	+	0.531220i	$0.178266\pi$
$954$	6.53030	0.211426
$955$	−4.38714	−0.141964
$956$	−10.0919	−0.326396
$957$	8.17259	0.264182
$958$	−40.1201	−1.29622
$959$	2.50456	0.0808763
$960$	1.32838	0.0428734
$961$	39.5365	1.27537
$962$	47.6613	1.53666
$963$	−3.95274	−0.127375
$964$	14.1146	0.454601
$965$	−8.71694	−0.280608
$966$	9.89143	0.318251
$967$	55.2286	1.77603	0.888017	−	0.459812i	$-0.152083\pi$
$967$	55.2286	1.77603	0.888017	+	0.459812i	$0.152083\pi$
$968$	1.00000	0.0321412
$969$	51.5045	1.65456
$970$	−10.3678	−0.332891
$971$	−4.97788	−0.159748	−0.0798738	−	0.996805i	$-0.525452\pi$
$971$	−4.97788	−0.159748	−0.0798738	+	0.996805i	$0.525452\pi$
$972$	11.8739	0.380854
$973$	−13.6133	−0.436423
$974$	−5.75491	−0.184399
$975$	7.18606	0.230138
$976$	12.2019	0.390573
$977$	51.2515	1.63968	0.819840	−	0.572592i	$-0.194062\pi$
$977$	51.2515	1.63968	0.819840	+	0.572592i	$0.194062\pi$
$978$	7.93224	0.253645
$979$	−7.58602	−0.242450
$980$	−3.23498	−0.103338
$981$	5.04788	0.161166
$982$	−1.95489	−0.0623830
$983$	55.5027	1.77026	0.885130	−	0.465343i	$-0.154069\pi$
$983$	55.5027	1.77026	0.885130	+	0.465343i	$0.154069\pi$
$984$	−11.9160	−0.379867
$985$	−14.7591	−0.470265
$986$	28.9838	0.923033
$987$	24.8198	0.790023
$988$	44.5214	1.41642
$989$	−12.7800	−0.406380
$990$	−1.23540	−0.0392634
$991$	33.7590	1.07239	0.536195	−	0.844094i	$-0.319861\pi$
$991$	33.7590	1.07239	0.536195	+	0.844094i	$0.319861\pi$
$992$	−8.39860	−0.266656
$993$	−2.06454	−0.0655162
$994$	9.72583	0.308484
$995$	−6.02657	−0.191055
$996$	21.6760	0.686830
$997$	4.04520	0.128113	0.0640564	−	0.997946i	$-0.479596\pi$
$997$	4.04520	0.128113	0.0640564	+	0.997946i	$0.479596\pi$
$998$	−17.6766	−0.559542
$999$	−49.5697	−1.56832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bl.1.11	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bl.1.11	✓	19	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.32838 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.32838 q^{6} -1.94037 q^{7} +1.00000 q^{8} -1.23540 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.32838 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.32838 q^{6} -1.94037 q^{7} +1.00000 q^{8} -1.23540 q^{9} +1.00000 q^{10} +1.00000 q^{11} +1.32838 q^{12} +5.40963 q^{13} -1.94037 q^{14} +1.32838 q^{15} +1.00000 q^{16} +4.71107 q^{17} -1.23540 q^{18} +8.23004 q^{19} +1.00000 q^{20} -2.57755 q^{21} +1.00000 q^{22} -3.83753 q^{23} +1.32838 q^{24} +1.00000 q^{25} +5.40963 q^{26} -5.62623 q^{27} -1.94037 q^{28} +6.15228 q^{29} +1.32838 q^{30} -8.39860 q^{31} +1.00000 q^{32} +1.32838 q^{33} +4.71107 q^{34} -1.94037 q^{35} -1.23540 q^{36} +8.81046 q^{37} +8.23004 q^{38} +7.18606 q^{39} +1.00000 q^{40} -8.97027 q^{41} -2.57755 q^{42} +3.33026 q^{43} +1.00000 q^{44} -1.23540 q^{45} -3.83753 q^{46} -9.62921 q^{47} +1.32838 q^{48} -3.23498 q^{49} +1.00000 q^{50} +6.25812 q^{51} +5.40963 q^{52} -5.28600 q^{53} -5.62623 q^{54} +1.00000 q^{55} -1.94037 q^{56} +10.9327 q^{57} +6.15228 q^{58} +10.2784 q^{59} +1.32838 q^{60} +12.2019 q^{61} -8.39860 q^{62} +2.39712 q^{63} +1.00000 q^{64} +5.40963 q^{65} +1.32838 q^{66} -4.77249 q^{67} +4.71107 q^{68} -5.09771 q^{69} -1.94037 q^{70} -5.01237 q^{71} -1.23540 q^{72} -1.00000 q^{73} +8.81046 q^{74} +1.32838 q^{75} +8.23004 q^{76} -1.94037 q^{77} +7.18606 q^{78} +7.78551 q^{79} +1.00000 q^{80} -3.76761 q^{81} -8.97027 q^{82} +16.3176 q^{83} -2.57755 q^{84} +4.71107 q^{85} +3.33026 q^{86} +8.17259 q^{87} +1.00000 q^{88} -7.58602 q^{89} -1.23540 q^{90} -10.4967 q^{91} -3.83753 q^{92} -11.1566 q^{93} -9.62921 q^{94} +8.23004 q^{95} +1.32838 q^{96} -10.3678 q^{97} -3.23498 q^{98} -1.23540 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 19 q^{2} + 10 q^{3} + 19 q^{4} + 19 q^{5} + 10 q^{6} + 8 q^{7} + 19 q^{8} + 27 q^{9}+O(q^{10}) \) 19 * q + 19 * q^2 + 10 * q^3 + 19 * q^4 + 19 * q^5 + 10 * q^6 + 8 * q^7 + 19 * q^8 + 27 * q^9	\( 19 q + 19 q^{2} + 10 q^{3} + 19 q^{4} + 19 q^{5} + 10 q^{6} + 8 q^{7} + 19 q^{8} + 27 q^{9} + 19 q^{10} + 19 q^{11} + 10 q^{12} + 16 q^{13} + 8 q^{14} + 10 q^{15} + 19 q^{16} + 12 q^{17} + 27 q^{18} + 12 q^{19} + 19 q^{20} + 3 q^{21} + 19 q^{22} + 26 q^{23} + 10 q^{24} + 19 q^{25} + 16 q^{26} + 25 q^{27} + 8 q^{28} + q^{29} + 10 q^{30} + 24 q^{31} + 19 q^{32} + 10 q^{33} + 12 q^{34} + 8 q^{35} + 27 q^{36} + 23 q^{37} + 12 q^{38} - 5 q^{39} + 19 q^{40} + 3 q^{42} + 8 q^{43} + 19 q^{44} + 27 q^{45} + 26 q^{46} + 34 q^{47} + 10 q^{48} + 27 q^{49} + 19 q^{50} + 15 q^{51} + 16 q^{52} + 25 q^{53} + 25 q^{54} + 19 q^{55} + 8 q^{56} + q^{57} + q^{58} + 24 q^{59} + 10 q^{60} + 31 q^{61} + 24 q^{62} + 15 q^{63} + 19 q^{64} + 16 q^{65} + 10 q^{66} + 24 q^{67} + 12 q^{68} + q^{69} + 8 q^{70} + 5 q^{71} + 27 q^{72} - 19 q^{73} + 23 q^{74} + 10 q^{75} + 12 q^{76} + 8 q^{77} - 5 q^{78} + 18 q^{79} + 19 q^{80} + 11 q^{81} + 12 q^{83} + 3 q^{84} + 12 q^{85} + 8 q^{86} + 12 q^{87} + 19 q^{88} + 27 q^{90} + 23 q^{91} + 26 q^{92} + 18 q^{93} + 34 q^{94} + 12 q^{95} + 10 q^{96} + 15 q^{97} + 27 q^{98} + 27 q^{99}+O(q^{100}) \) 19 * q + 19 * q^2 + 10 * q^3 + 19 * q^4 + 19 * q^5 + 10 * q^6 + 8 * q^7 + 19 * q^8 + 27 * q^9 + 19 * q^10 + 19 * q^11 + 10 * q^12 + 16 * q^13 + 8 * q^14 + 10 * q^15 + 19 * q^16 + 12 * q^17 + 27 * q^18 + 12 * q^19 + 19 * q^20 + 3 * q^21 + 19 * q^22 + 26 * q^23 + 10 * q^24 + 19 * q^25 + 16 * q^26 + 25 * q^27 + 8 * q^28 + q^29 + 10 * q^30 + 24 * q^31 + 19 * q^32 + 10 * q^33 + 12 * q^34 + 8 * q^35 + 27 * q^36 + 23 * q^37 + 12 * q^38 - 5 * q^39 + 19 * q^40 + 3 * q^42 + 8 * q^43 + 19 * q^44 + 27 * q^45 + 26 * q^46 + 34 * q^47 + 10 * q^48 + 27 * q^49 + 19 * q^50 + 15 * q^51 + 16 * q^52 + 25 * q^53 + 25 * q^54 + 19 * q^55 + 8 * q^56 + q^57 + q^58 + 24 * q^59 + 10 * q^60 + 31 * q^61 + 24 * q^62 + 15 * q^63 + 19 * q^64 + 16 * q^65 + 10 * q^66 + 24 * q^67 + 12 * q^68 + q^69 + 8 * q^70 + 5 * q^71 + 27 * q^72 - 19 * q^73 + 23 * q^74 + 10 * q^75 + 12 * q^76 + 8 * q^77 - 5 * q^78 + 18 * q^79 + 19 * q^80 + 11 * q^81 + 12 * q^83 + 3 * q^84 + 12 * q^85 + 8 * q^86 + 12 * q^87 + 19 * q^88 + 27 * q^90 + 23 * q^91 + 26 * q^92 + 18 * q^93 + 34 * q^94 + 12 * q^95 + 10 * q^96 + 15 * q^97 + 27 * q^98 + 27 * q^99

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