LMFDB - Embedded newform 6422.2.a.bm.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6422,2,Mod(1,6422)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6422, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6422.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6422 = 2 \cdot 13^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6422.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:	$51.2799281781$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} - 22 x^{12} + 98 x^{11} + 164 x^{10} - 912 x^{9} - 374 x^{8} + 3996 x^{7} - 817 x^{6} + \cdots + 358 $ x^14 - 4x^13 - 22x^12 + 98x^11 + 164x^10 - 912x^9 - 374x^8 + 3996x^7 - 817x^6 - 8194x^5 + 4418x^4 + 6430x^3 - 4327x^2 - 922*x + 358
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 494)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$1.57102$ of defining polynomial
Character	$\chi$	$=$	6422.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.57102 q^{3} +1.00000 q^{4} -2.81950 q^{5} -1.57102 q^{6} +4.61884 q^{7} -1.00000 q^{8} -0.531896 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.57102 q^{3} +1.00000 q^{4} -2.81950 q^{5} -1.57102 q^{6} +4.61884 q^{7} -1.00000 q^{8} -0.531896 q^{9} +2.81950 q^{10} -0.167488 q^{11} +1.57102 q^{12} -4.61884 q^{14} -4.42948 q^{15} +1.00000 q^{16} +2.12617 q^{17} +0.531896 q^{18} -1.00000 q^{19} -2.81950 q^{20} +7.25630 q^{21} +0.167488 q^{22} +3.77433 q^{23} -1.57102 q^{24} +2.94955 q^{25} -5.54868 q^{27} +4.61884 q^{28} +9.37867 q^{29} +4.42948 q^{30} -2.76469 q^{31} -1.00000 q^{32} -0.263126 q^{33} -2.12617 q^{34} -13.0228 q^{35} -0.531896 q^{36} -1.54011 q^{37} +1.00000 q^{38} +2.81950 q^{40} -0.466851 q^{41} -7.25630 q^{42} +9.52220 q^{43} -0.167488 q^{44} +1.49968 q^{45} -3.77433 q^{46} -4.35742 q^{47} +1.57102 q^{48} +14.3337 q^{49} -2.94955 q^{50} +3.34026 q^{51} -6.10204 q^{53} +5.54868 q^{54} +0.472231 q^{55} -4.61884 q^{56} -1.57102 q^{57} -9.37867 q^{58} -3.90192 q^{59} -4.42948 q^{60} +14.2893 q^{61} +2.76469 q^{62} -2.45674 q^{63} +1.00000 q^{64} +0.263126 q^{66} -1.24497 q^{67} +2.12617 q^{68} +5.92954 q^{69} +13.0228 q^{70} -16.1040 q^{71} +0.531896 q^{72} +12.6389 q^{73} +1.54011 q^{74} +4.63381 q^{75} -1.00000 q^{76} -0.773599 q^{77} -9.73309 q^{79} -2.81950 q^{80} -7.12140 q^{81} +0.466851 q^{82} -4.41971 q^{83} +7.25630 q^{84} -5.99473 q^{85} -9.52220 q^{86} +14.7341 q^{87} +0.167488 q^{88} +2.09120 q^{89} -1.49968 q^{90} +3.77433 q^{92} -4.34339 q^{93} +4.35742 q^{94} +2.81950 q^{95} -1.57102 q^{96} +16.1158 q^{97} -14.3337 q^{98} +0.0890860 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} + 4 q^{3} + 14 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 14 q^{8} + 18 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 + 4 * q^3 + 14 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 14 * q^8 + 18 * q^9	\( 14 q - 14 q^{2} + 4 q^{3} + 14 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 14 q^{8} + 18 q^{9} - 2 q^{10} - 10 q^{11} + 4 q^{12} + 2 q^{14} + 4 q^{15} + 14 q^{16} + 2 q^{17} - 18 q^{18} - 14 q^{19} + 2 q^{20} + 18 q^{21} + 10 q^{22} + 12 q^{23} - 4 q^{24} + 44 q^{25} + 10 q^{27} - 2 q^{28} + 4 q^{29} - 4 q^{30} - 4 q^{31} - 14 q^{32} - 12 q^{33} - 2 q^{34} + 14 q^{35} + 18 q^{36} - 18 q^{37} + 14 q^{38} - 2 q^{40} - 6 q^{41} - 18 q^{42} + 28 q^{43} - 10 q^{44} - 8 q^{45} - 12 q^{46} + 20 q^{47} + 4 q^{48} + 28 q^{49} - 44 q^{50} + 10 q^{51} + 12 q^{53} - 10 q^{54} - 2 q^{55} + 2 q^{56} - 4 q^{57} - 4 q^{58} - 16 q^{59} + 4 q^{60} + 30 q^{61} + 4 q^{62} - 28 q^{63} + 14 q^{64} + 12 q^{66} - 2 q^{67} + 2 q^{68} - 42 q^{69} - 14 q^{70} - 44 q^{71} - 18 q^{72} + 36 q^{73} + 18 q^{74} + 46 q^{75} - 14 q^{76} + 68 q^{77} + 34 q^{79} + 2 q^{80} - 6 q^{81} + 6 q^{82} - 2 q^{83} + 18 q^{84} + 30 q^{85} - 28 q^{86} + 52 q^{87} + 10 q^{88} - 42 q^{89} + 8 q^{90} + 12 q^{92} + 12 q^{93} - 20 q^{94} - 2 q^{95} - 4 q^{96} - 40 q^{97} - 28 q^{98} - 12 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 4 * q^3 + 14 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 14 * q^8 + 18 * q^9 - 2 * q^10 - 10 * q^11 + 4 * q^12 + 2 * q^14 + 4 * q^15 + 14 * q^16 + 2 * q^17 - 18 * q^18 - 14 * q^19 + 2 * q^20 + 18 * q^21 + 10 * q^22 + 12 * q^23 - 4 * q^24 + 44 * q^25 + 10 * q^27 - 2 * q^28 + 4 * q^29 - 4 * q^30 - 4 * q^31 - 14 * q^32 - 12 * q^33 - 2 * q^34 + 14 * q^35 + 18 * q^36 - 18 * q^37 + 14 * q^38 - 2 * q^40 - 6 * q^41 - 18 * q^42 + 28 * q^43 - 10 * q^44 - 8 * q^45 - 12 * q^46 + 20 * q^47 + 4 * q^48 + 28 * q^49 - 44 * q^50 + 10 * q^51 + 12 * q^53 - 10 * q^54 - 2 * q^55 + 2 * q^56 - 4 * q^57 - 4 * q^58 - 16 * q^59 + 4 * q^60 + 30 * q^61 + 4 * q^62 - 28 * q^63 + 14 * q^64 + 12 * q^66 - 2 * q^67 + 2 * q^68 - 42 * q^69 - 14 * q^70 - 44 * q^71 - 18 * q^72 + 36 * q^73 + 18 * q^74 + 46 * q^75 - 14 * q^76 + 68 * q^77 + 34 * q^79 + 2 * q^80 - 6 * q^81 + 6 * q^82 - 2 * q^83 + 18 * q^84 + 30 * q^85 - 28 * q^86 + 52 * q^87 + 10 * q^88 - 42 * q^89 + 8 * q^90 + 12 * q^92 + 12 * q^93 - 20 * q^94 - 2 * q^95 - 4 * q^96 - 40 * q^97 - 28 * q^98 - 12 * 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
$3$	1.57102	0.907029	0.453514	−	0.891249i	$-0.350170\pi$
$3$	1.57102	0.907029	0.453514	+	0.891249i	$0.350170\pi$
$4$	1.00000	0.500000
$5$	−2.81950	−1.26092	−0.630458	−	0.776223i	$-0.717133\pi$
$5$	−2.81950	−1.26092	−0.630458	+	0.776223i	$0.717133\pi$
$6$	−1.57102	−0.641366
$7$	4.61884	1.74576	0.872879	−	0.487936i	$-0.162250\pi$
$7$	4.61884	1.74576	0.872879	+	0.487936i	$0.162250\pi$
$8$	−1.00000	−0.353553
$9$	−0.531896	−0.177299
$10$	2.81950	0.891603
$11$	−0.167488	−0.0504994	−0.0252497	−	0.999681i	$-0.508038\pi$
$11$	−0.167488	−0.0504994	−0.0252497	+	0.999681i	$0.508038\pi$
$12$	1.57102	0.453514
$13$	0	0
$13$	0	0
$14$	−4.61884	−1.23444
$15$	−4.42948	−1.14369
$16$	1.00000	0.250000
$17$	2.12617	0.515672	0.257836	−	0.966189i	$-0.416990\pi$
$17$	2.12617	0.515672	0.257836	+	0.966189i	$0.416990\pi$
$18$	0.531896	0.125369
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.81950	−0.630458
$21$	7.25630	1.58345
$22$	0.167488	0.0357085
$23$	3.77433	0.787002	0.393501	−	0.919324i	$-0.371264\pi$
$23$	3.77433	0.787002	0.393501	+	0.919324i	$0.371264\pi$
$24$	−1.57102	−0.320683
$25$	2.94955	0.589911
$26$	0	0
$27$	−5.54868	−1.06784
$28$	4.61884	0.872879
$29$	9.37867	1.74158	0.870788	−	0.491659i	$-0.163609\pi$
$29$	9.37867	1.74158	0.870788	+	0.491659i	$0.163609\pi$
$30$	4.42948	0.808709
$31$	−2.76469	−0.496554	−0.248277	−	0.968689i	$-0.579864\pi$
$31$	−2.76469	−0.496554	−0.248277	+	0.968689i	$0.579864\pi$
$32$	−1.00000	−0.176777
$33$	−0.263126	−0.0458044
$34$	−2.12617	−0.364636
$35$	−13.0228	−2.20126
$36$	−0.531896	−0.0886493
$37$	−1.54011	−0.253193	−0.126596	−	0.991954i	$-0.540405\pi$
$37$	−1.54011	−0.253193	−0.126596	+	0.991954i	$0.540405\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	2.81950	0.445801
$41$	−0.466851	−0.0729099	−0.0364550	−	0.999335i	$-0.511607\pi$
$41$	−0.466851	−0.0729099	−0.0364550	+	0.999335i	$0.511607\pi$
$42$	−7.25630	−1.11967
$43$	9.52220	1.45212	0.726061	−	0.687631i	$-0.241349\pi$
$43$	9.52220	1.45212	0.726061	+	0.687631i	$0.241349\pi$
$44$	−0.167488	−0.0252497
$45$	1.49968	0.223559
$46$	−3.77433	−0.556494
$47$	−4.35742	−0.635595	−0.317797	−	0.948159i	$-0.602943\pi$
$47$	−4.35742	−0.635595	−0.317797	+	0.948159i	$0.602943\pi$
$48$	1.57102	0.226757
$49$	14.3337	2.04767
$50$	−2.94955	−0.417130
$51$	3.34026	0.467730
$52$	0	0
$53$	−6.10204	−0.838179	−0.419090	−	0.907945i	$-0.637651\pi$
$53$	−6.10204	−0.838179	−0.419090	+	0.907945i	$0.637651\pi$
$54$	5.54868	0.755080
$55$	0.472231	0.0636756
$56$	−4.61884	−0.617219
$57$	−1.57102	−0.208087
$58$	−9.37867	−1.23148
$59$	−3.90192	−0.507987	−0.253993	−	0.967206i	$-0.581744\pi$
$59$	−3.90192	−0.507987	−0.253993	+	0.967206i	$0.581744\pi$
$60$	−4.42948	−0.571844
$61$	14.2893	1.82956	0.914779	−	0.403954i	$-0.132364\pi$
$61$	14.2893	1.82956	0.914779	+	0.403954i	$0.132364\pi$
$62$	2.76469	0.351116
$63$	−2.45674	−0.309521
$64$	1.00000	0.125000
$65$	0	0
$66$	0.263126	0.0323886
$67$	−1.24497	−0.152098	−0.0760488	−	0.997104i	$-0.524230\pi$
$67$	−1.24497	−0.152098	−0.0760488	+	0.997104i	$0.524230\pi$
$68$	2.12617	0.257836
$69$	5.92954	0.713833
$70$	13.0228	1.55652
$71$	−16.1040	−1.91119	−0.955594	−	0.294688i	$-0.904784\pi$
$71$	−16.1040	−1.91119	−0.955594	+	0.294688i	$0.904784\pi$
$72$	0.531896	0.0626845
$73$	12.6389	1.47927	0.739637	−	0.673006i	$-0.234997\pi$
$73$	12.6389	1.47927	0.739637	+	0.673006i	$0.234997\pi$
$74$	1.54011	0.179034
$75$	4.63381	0.535066
$76$	−1.00000	−0.114708
$77$	−0.773599	−0.0881598
$78$	0	0
$79$	−9.73309	−1.09506	−0.547529	−	0.836787i	$-0.684431\pi$
$79$	−9.73309	−1.09506	−0.547529	+	0.836787i	$0.684431\pi$
$80$	−2.81950	−0.315229
$81$	−7.12140	−0.791267
$82$	0.466851	0.0515551
$83$	−4.41971	−0.485126	−0.242563	−	0.970136i	$-0.577988\pi$
$83$	−4.41971	−0.485126	−0.242563	+	0.970136i	$0.577988\pi$
$84$	7.25630	0.791727
$85$	−5.99473	−0.650220
$86$	−9.52220	−1.02680
$87$	14.7341	1.57966
$88$	0.167488	0.0178542
$89$	2.09120	0.221666	0.110833	−	0.993839i	$-0.464648\pi$
$89$	2.09120	0.221666	0.110833	+	0.993839i	$0.464648\pi$
$90$	−1.49968	−0.158080
$91$	0	0
$92$	3.77433	0.393501
$93$	−4.34339	−0.450388
$94$	4.35742	0.449433
$95$	2.81950	0.289274
$96$	−1.57102	−0.160342
$97$	16.1158	1.63631	0.818155	−	0.574998i	$-0.194997\pi$
$97$	16.1158	1.63631	0.818155	+	0.574998i	$0.194997\pi$
$98$	−14.3337	−1.44792
$99$	0.0890860	0.00895348
$100$	2.94955	0.294955
$101$	0.215522	0.0214453	0.0107226	−	0.999943i	$-0.496587\pi$
$101$	0.215522	0.0214453	0.0107226	+	0.999943i	$0.496587\pi$
$102$	−3.34026	−0.330735
$103$	4.81809	0.474741	0.237370	−	0.971419i	$-0.423715\pi$
$103$	4.81809	0.474741	0.237370	+	0.971419i	$0.423715\pi$
$104$	0	0
$105$	−20.4591	−1.99660
$106$	6.10204	0.592682
$107$	−2.18368	−0.211104	−0.105552	−	0.994414i	$-0.533661\pi$
$107$	−2.18368	−0.211104	−0.105552	+	0.994414i	$0.533661\pi$
$108$	−5.54868	−0.533922
$109$	11.7354	1.12405	0.562024	−	0.827121i	$-0.310023\pi$
$109$	11.7354	1.12405	0.562024	+	0.827121i	$0.310023\pi$
$110$	−0.472231	−0.0450254
$111$	−2.41955	−0.229653
$112$	4.61884	0.436440
$113$	5.40877	0.508815	0.254407	−	0.967097i	$-0.418120\pi$
$113$	5.40877	0.508815	0.254407	+	0.967097i	$0.418120\pi$
$114$	1.57102	0.147140
$115$	−10.6417	−0.992343
$116$	9.37867	0.870788
$117$	0	0
$118$	3.90192	0.359201
$119$	9.82046	0.900240
$120$	4.42948	0.404355
$121$	−10.9719	−0.997450
$122$	−14.2893	−1.29369
$123$	−0.733433	−0.0661314
$124$	−2.76469	−0.248277
$125$	5.78122	0.517088
$126$	2.45674	0.218864
$127$	17.1672	1.52334	0.761672	−	0.647963i	$-0.224379\pi$
$127$	17.1672	1.52334	0.761672	+	0.647963i	$0.224379\pi$
$128$	−1.00000	−0.0883883
$129$	14.9596	1.31712
$130$	0	0
$131$	15.5641	1.35984	0.679920	−	0.733286i	$-0.262014\pi$
$131$	15.5641	1.35984	0.679920	+	0.733286i	$0.262014\pi$
$132$	−0.263126	−0.0229022
$133$	−4.61884	−0.400505
$134$	1.24497	0.107549
$135$	15.6445	1.34646
$136$	−2.12617	−0.182318
$137$	5.71387	0.488169	0.244084	−	0.969754i	$-0.421513\pi$
$137$	5.71387	0.488169	0.244084	+	0.969754i	$0.421513\pi$
$138$	−5.92954	−0.504756
$139$	−9.21480	−0.781589	−0.390795	−	0.920478i	$-0.627800\pi$
$139$	−9.21480	−0.781589	−0.390795	+	0.920478i	$0.627800\pi$
$140$	−13.0228	−1.10063
$141$	−6.84559	−0.576503
$142$	16.1040	1.35141
$143$	0	0
$144$	−0.531896	−0.0443246
$145$	−26.4431	−2.19598
$146$	−12.6389	−1.04601
$147$	22.5186	1.85730
$148$	−1.54011	−0.126596
$149$	18.6829	1.53057	0.765283	−	0.643694i	$-0.222599\pi$
$149$	18.6829	1.53057	0.765283	+	0.643694i	$0.222599\pi$
$150$	−4.63381	−0.378349
$151$	−13.3473	−1.08619	−0.543094	−	0.839672i	$-0.682747\pi$
$151$	−13.3473	−1.08619	−0.543094	+	0.839672i	$0.682747\pi$
$152$	1.00000	0.0811107
$153$	−1.13090	−0.0914280
$154$	0.773599	0.0623384
$155$	7.79504	0.626113
$156$	0	0
$157$	16.2275	1.29510	0.647549	−	0.762024i	$-0.275794\pi$
$157$	16.2275	1.29510	0.647549	+	0.762024i	$0.275794\pi$
$158$	9.73309	0.774323
$159$	−9.58643	−0.760253
$160$	2.81950	0.222901
$161$	17.4330	1.37391
$162$	7.12140	0.559510
$163$	5.76297	0.451391	0.225695	−	0.974198i	$-0.427535\pi$
$163$	5.76297	0.451391	0.225695	+	0.974198i	$0.427535\pi$
$164$	−0.466851	−0.0364550
$165$	0.741884	0.0577556
$166$	4.41971	0.343036
$167$	−14.2595	−1.10343	−0.551715	−	0.834032i	$-0.686027\pi$
$167$	−14.2595	−1.10343	−0.551715	+	0.834032i	$0.686027\pi$
$168$	−7.25630	−0.559835
$169$	0	0
$170$	5.99473	0.459775
$171$	0.531896	0.0406751
$172$	9.52220	0.726061
$173$	−19.1532	−1.45619	−0.728097	−	0.685474i	$-0.759595\pi$
$173$	−19.1532	−1.45619	−0.728097	+	0.685474i	$0.759595\pi$
$174$	−14.7341	−1.11699
$175$	13.6235	1.02984
$176$	−0.167488	−0.0126249
$177$	−6.13000	−0.460759
$178$	−2.09120	−0.156742
$179$	10.6419	0.795410	0.397705	−	0.917513i	$-0.369807\pi$
$179$	10.6419	0.795410	0.397705	+	0.917513i	$0.369807\pi$
$180$	1.49968	0.111779
$181$	0.786741	0.0584780	0.0292390	−	0.999572i	$-0.490692\pi$
$181$	0.786741	0.0584780	0.0292390	+	0.999572i	$0.490692\pi$
$182$	0	0
$183$	22.4488	1.65946
$184$	−3.77433	−0.278247
$185$	4.34234	0.319255
$186$	4.34339	0.318473
$187$	−0.356108	−0.0260412
$188$	−4.35742	−0.317797
$189$	−25.6285	−1.86420
$190$	−2.81950	−0.204548
$191$	2.78680	0.201645	0.100823	−	0.994904i	$-0.467853\pi$
$191$	2.78680	0.201645	0.100823	+	0.994904i	$0.467853\pi$
$192$	1.57102	0.113379
$193$	−21.1970	−1.52580	−0.762898	−	0.646519i	$-0.776224\pi$
$193$	−21.1970	−1.52580	−0.762898	+	0.646519i	$0.776224\pi$
$194$	−16.1158	−1.15705
$195$	0	0
$196$	14.3337	1.02384
$197$	−5.79314	−0.412744	−0.206372	−	0.978474i	$-0.566166\pi$
$197$	−5.79314	−0.412744	−0.206372	+	0.978474i	$0.566166\pi$
$198$	−0.0890860	−0.00633106
$199$	−10.0509	−0.712487	−0.356243	−	0.934393i	$-0.615943\pi$
$199$	−10.0509	−0.712487	−0.356243	+	0.934393i	$0.615943\pi$
$200$	−2.94955	−0.208565
$201$	−1.95588	−0.137957
$202$	−0.215522	−0.0151641
$203$	43.3186	3.04037
$204$	3.34026	0.233865
$205$	1.31628	0.0919333
$206$	−4.81809	−0.335692
$207$	−2.00755	−0.139534
$208$	0	0
$209$	0.167488	0.0115854
$210$	20.4591	1.41181
$211$	−6.15840	−0.423962	−0.211981	−	0.977274i	$-0.567992\pi$
$211$	−6.15840	−0.423962	−0.211981	+	0.977274i	$0.567992\pi$
$212$	−6.10204	−0.419090
$213$	−25.2996	−1.73350
$214$	2.18368	0.149273
$215$	−26.8478	−1.83100
$216$	5.54868	0.377540
$217$	−12.7697	−0.866863
$218$	−11.7354	−0.794822
$219$	19.8560	1.34175
$220$	0.472231	0.0318378
$221$	0	0
$222$	2.41955	0.162389
$223$	17.5794	1.17720	0.588602	−	0.808423i	$-0.299678\pi$
$223$	17.5794	1.17720	0.588602	+	0.808423i	$0.299678\pi$
$224$	−4.61884	−0.308610
$225$	−1.56886	−0.104590
$226$	−5.40877	−0.359786
$227$	−13.5375	−0.898512	−0.449256	−	0.893403i	$-0.648311\pi$
$227$	−13.5375	−0.898512	−0.449256	+	0.893403i	$0.648311\pi$
$228$	−1.57102	−0.104043
$229$	28.1954	1.86320	0.931602	−	0.363480i	$-0.118411\pi$
$229$	28.1954	1.86320	0.931602	+	0.363480i	$0.118411\pi$
$230$	10.6417	0.701693
$231$	−1.21534	−0.0799635
$232$	−9.37867	−0.615740
$233$	16.5004	1.08097	0.540487	−	0.841352i	$-0.318240\pi$
$233$	16.5004	1.08097	0.540487	+	0.841352i	$0.318240\pi$
$234$	0	0
$235$	12.2857	0.801432
$236$	−3.90192	−0.253993
$237$	−15.2909	−0.993249
$238$	−9.82046	−0.636566
$239$	3.54175	0.229096	0.114548	−	0.993418i	$-0.463458\pi$
$239$	3.54175	0.229096	0.114548	+	0.993418i	$0.463458\pi$
$240$	−4.42948	−0.285922
$241$	17.1321	1.10358	0.551789	−	0.833984i	$-0.313945\pi$
$241$	17.1321	1.10358	0.551789	+	0.833984i	$0.313945\pi$
$242$	10.9719	0.705304
$243$	5.45818	0.350142
$244$	14.2893	0.914779
$245$	−40.4139	−2.58195
$246$	0.733433	0.0467620
$247$	0	0
$248$	2.76469	0.175558
$249$	−6.94345	−0.440023
$250$	−5.78122	−0.365637
$251$	−11.8327	−0.746873	−0.373436	−	0.927656i	$-0.621821\pi$
$251$	−11.8327	−0.746873	−0.373436	+	0.927656i	$0.621821\pi$
$252$	−2.45674	−0.154760
$253$	−0.632153	−0.0397431
$254$	−17.1672	−1.07717
$255$	−9.41785	−0.589768
$256$	1.00000	0.0625000
$257$	17.3536	1.08249	0.541243	−	0.840866i	$-0.317954\pi$
$257$	17.3536	1.08249	0.541243	+	0.840866i	$0.317954\pi$
$258$	−14.9596	−0.931342
$259$	−7.11354	−0.442014
$260$	0	0
$261$	−4.98847	−0.308779
$262$	−15.5641	−0.961553
$263$	−1.56178	−0.0963032	−0.0481516	−	0.998840i	$-0.515333\pi$
$263$	−1.56178	−0.0963032	−0.0481516	+	0.998840i	$0.515333\pi$
$264$	0.263126	0.0161943
$265$	17.2047	1.05687
$266$	4.61884	0.283200
$267$	3.28531	0.201058
$268$	−1.24497	−0.0760488
$269$	−2.74547	−0.167394	−0.0836971	−	0.996491i	$-0.526673\pi$
$269$	−2.74547	−0.167394	−0.0836971	+	0.996491i	$0.526673\pi$
$270$	−15.6445	−0.952093
$271$	16.8840	1.02563	0.512816	−	0.858499i	$-0.328602\pi$
$271$	16.8840	1.02563	0.512816	+	0.858499i	$0.328602\pi$
$272$	2.12617	0.128918
$273$	0	0
$274$	−5.71387	−0.345187
$275$	−0.494014	−0.0297902
$276$	5.92954	0.356917
$277$	−5.58477	−0.335557	−0.167778	−	0.985825i	$-0.553659\pi$
$277$	−5.58477	−0.335557	−0.167778	+	0.985825i	$0.553659\pi$
$278$	9.21480	0.552667
$279$	1.47053	0.0880382
$280$	13.0228	0.778262
$281$	24.2016	1.44375	0.721874	−	0.692024i	$-0.243281\pi$
$281$	24.2016	1.44375	0.721874	+	0.692024i	$0.243281\pi$
$282$	6.84559	0.407649
$283$	−25.9475	−1.54242	−0.771209	−	0.636582i	$-0.780348\pi$
$283$	−25.9475	−1.54242	−0.771209	+	0.636582i	$0.780348\pi$
$284$	−16.1040	−0.955594
$285$	4.42948	0.262380
$286$	0	0
$287$	−2.15631	−0.127283
$288$	0.531896	0.0313423
$289$	−12.4794	−0.734082
$290$	26.4431	1.55279
$291$	25.3182	1.48418
$292$	12.6389	0.739637
$293$	14.4299	0.843002	0.421501	−	0.906828i	$-0.361503\pi$
$293$	14.4299	0.843002	0.421501	+	0.906828i	$0.361503\pi$
$294$	−22.5186	−1.31331
$295$	11.0014	0.640529
$296$	1.54011	0.0895172
$297$	0.929335	0.0539255
$298$	−18.6829	−1.08227
$299$	0	0
$300$	4.63381	0.267533
$301$	43.9815	2.53505
$302$	13.3473	0.768051
$303$	0.338590	0.0194515
$304$	−1.00000	−0.0573539
$305$	−40.2886	−2.30692
$306$	1.13090	0.0646494
$307$	1.27895	0.0729934	0.0364967	−	0.999334i	$-0.488380\pi$
$307$	1.27895	0.0729934	0.0364967	+	0.999334i	$0.488380\pi$
$308$	−0.773599	−0.0440799
$309$	7.56932	0.430603
$310$	−7.79504	−0.442729
$311$	8.19033	0.464431	0.232215	−	0.972664i	$-0.425403\pi$
$311$	8.19033	0.464431	0.232215	+	0.972664i	$0.425403\pi$
$312$	0	0
$313$	−3.25848	−0.184180	−0.0920901	−	0.995751i	$-0.529355\pi$
$313$	−3.25848	−0.184180	−0.0920901	+	0.995751i	$0.529355\pi$
$314$	−16.2275	−0.915772
$315$	6.92678	0.390280
$316$	−9.73309	−0.547529
$317$	−17.4705	−0.981242	−0.490621	−	0.871373i	$-0.663230\pi$
$317$	−17.4705	−0.981242	−0.490621	+	0.871373i	$0.663230\pi$
$318$	9.58643	0.537580
$319$	−1.57081	−0.0879486
$320$	−2.81950	−0.157615
$321$	−3.43060	−0.191478
$322$	−17.4330	−0.971505
$323$	−2.12617	−0.118303
$324$	−7.12140	−0.395633
$325$	0	0
$326$	−5.76297	−0.319181
$327$	18.4366	1.01954
$328$	0.466851	0.0257775
$329$	−20.1262	−1.10959
$330$	−0.741884	−0.0408394
$331$	26.8209	1.47421	0.737105	−	0.675779i	$-0.236192\pi$
$331$	26.8209	1.47421	0.737105	+	0.675779i	$0.236192\pi$
$332$	−4.41971	−0.242563
$333$	0.819179	0.0448907
$334$	14.2595	0.780243
$335$	3.51019	0.191782
$336$	7.25630	0.395863
$337$	9.26426	0.504656	0.252328	−	0.967642i	$-0.418804\pi$
$337$	9.26426	0.504656	0.252328	+	0.967642i	$0.418804\pi$
$338$	0	0
$339$	8.49729	0.461510
$340$	−5.99473	−0.325110
$341$	0.463052	0.0250757
$342$	−0.531896	−0.0287616
$343$	33.8733	1.82899
$344$	−9.52220	−0.513402
$345$	−16.7183	−0.900084
$346$	19.1532	1.02968
$347$	30.1115	1.61647	0.808234	−	0.588862i	$-0.200424\pi$
$347$	30.1115	1.61647	0.808234	+	0.588862i	$0.200424\pi$
$348$	14.7341	0.789830
$349$	8.11747	0.434518	0.217259	−	0.976114i	$-0.430288\pi$
$349$	8.11747	0.434518	0.217259	+	0.976114i	$0.430288\pi$
$350$	−13.6235	−0.728208
$351$	0	0
$352$	0.167488	0.00892712
$353$	−18.3490	−0.976617	−0.488308	−	0.872671i	$-0.662386\pi$
$353$	−18.3490	−0.976617	−0.488308	+	0.872671i	$0.662386\pi$
$354$	6.13000	0.325806
$355$	45.4050	2.40985
$356$	2.09120	0.110833
$357$	15.4281	0.816544
$358$	−10.6419	−0.562439
$359$	−18.1510	−0.957973	−0.478987	−	0.877822i	$-0.658996\pi$
$359$	−18.1510	−0.957973	−0.478987	+	0.877822i	$0.658996\pi$
$360$	−1.49968	−0.0790399
$361$	1.00000	0.0526316
$362$	−0.786741	−0.0413502
$363$	−17.2372	−0.904716
$364$	0	0
$365$	−35.6354	−1.86524
$366$	−22.4488	−1.17342
$367$	23.7794	1.24127	0.620637	−	0.784098i	$-0.286874\pi$
$367$	23.7794	1.24127	0.620637	+	0.784098i	$0.286874\pi$
$368$	3.77433	0.196750
$369$	0.248316	0.0129268
$370$	−4.34234	−0.225748
$371$	−28.1844	−1.46326
$372$	−4.34339	−0.225194
$373$	−12.0839	−0.625678	−0.312839	−	0.949806i	$-0.601280\pi$
$373$	−12.0839	−0.625678	−0.312839	+	0.949806i	$0.601280\pi$
$374$	0.356108	0.0184139
$375$	9.08241	0.469014
$376$	4.35742	0.224717
$377$	0	0
$378$	25.6285	1.31819
$379$	1.27737	0.0656141	0.0328071	−	0.999462i	$-0.489555\pi$
$379$	1.27737	0.0656141	0.0328071	+	0.999462i	$0.489555\pi$
$380$	2.81950	0.144637
$381$	26.9700	1.38172
$382$	−2.78680	−0.142585
$383$	17.5663	0.897596	0.448798	−	0.893633i	$-0.351852\pi$
$383$	17.5663	0.897596	0.448798	+	0.893633i	$0.351852\pi$
$384$	−1.57102	−0.0801708
$385$	2.18116	0.111162
$386$	21.1970	1.07890
$387$	−5.06481	−0.257459
$388$	16.1158	0.818155
$389$	0.0492487	0.00249701	0.00124850	−	0.999999i	$-0.499603\pi$
$389$	0.0492487	0.00249701	0.00124850	+	0.999999i	$0.499603\pi$
$390$	0	0
$391$	8.02487	0.405835
$392$	−14.3337	−0.723962
$393$	24.4515	1.23341
$394$	5.79314	0.291854
$395$	27.4424	1.38078
$396$	0.0890860	0.00447674
$397$	33.8454	1.69865	0.849326	−	0.527869i	$-0.177009\pi$
$397$	33.8454	1.69865	0.849326	+	0.527869i	$0.177009\pi$
$398$	10.0509	0.503804
$399$	−7.25630	−0.363269
$400$	2.94955	0.147478
$401$	25.3595	1.26639	0.633196	−	0.773991i	$-0.281743\pi$
$401$	25.3595	1.26639	0.633196	+	0.773991i	$0.281743\pi$
$402$	1.95588	0.0975502
$403$	0	0
$404$	0.215522	0.0107226
$405$	20.0788	0.997721
$406$	−43.3186	−2.14987
$407$	0.257950	0.0127861
$408$	−3.34026	−0.165367
$409$	25.9468	1.28299	0.641495	−	0.767128i	$-0.278315\pi$
$409$	25.9468	1.28299	0.641495	+	0.767128i	$0.278315\pi$
$410$	−1.31628	−0.0650067
$411$	8.97660	0.442783
$412$	4.81809	0.237370
$413$	−18.0224	−0.886822
$414$	2.00755	0.0986656
$415$	12.4613	0.611703
$416$	0	0
$417$	−14.4766	−0.708924
$418$	−0.167488	−0.00819209
$419$	−34.4082	−1.68095	−0.840475	−	0.541850i	$-0.817724\pi$
$419$	−34.4082	−1.68095	−0.840475	+	0.541850i	$0.817724\pi$
$420$	−20.4591	−0.998302
$421$	23.3518	1.13809	0.569047	−	0.822305i	$-0.307312\pi$
$421$	23.3518	1.13809	0.569047	+	0.822305i	$0.307312\pi$
$422$	6.15840	0.299786
$423$	2.31769	0.112690
$424$	6.10204	0.296341
$425$	6.27126	0.304201
$426$	25.2996	1.22577
$427$	66.0001	3.19397
$428$	−2.18368	−0.105552
$429$	0	0
$430$	26.8478	1.29472
$431$	−20.5460	−0.989664	−0.494832	−	0.868989i	$-0.664770\pi$
$431$	−20.5460	−0.989664	−0.494832	+	0.868989i	$0.664770\pi$
$432$	−5.54868	−0.266961
$433$	−20.4768	−0.984052	−0.492026	−	0.870580i	$-0.663744\pi$
$433$	−20.4768	−0.984052	−0.492026	+	0.870580i	$0.663744\pi$
$434$	12.7697	0.612965
$435$	−41.5427	−1.99182
$436$	11.7354	0.562024
$437$	−3.77433	−0.180551
$438$	−19.8560	−0.948757
$439$	−1.50234	−0.0717026	−0.0358513	−	0.999357i	$-0.511414\pi$
$439$	−1.50234	−0.0717026	−0.0358513	+	0.999357i	$0.511414\pi$
$440$	−0.472231	−0.0225127
$441$	−7.62404	−0.363050
$442$	0	0
$443$	19.6984	0.935899	0.467949	−	0.883755i	$-0.344993\pi$
$443$	19.6984	0.935899	0.467949	+	0.883755i	$0.344993\pi$
$444$	−2.41955	−0.114827
$445$	−5.89612	−0.279503
$446$	−17.5794	−0.832409
$447$	29.3513	1.38827
$448$	4.61884	0.218220
$449$	−19.3450	−0.912945	−0.456473	−	0.889738i	$-0.650887\pi$
$449$	−19.3450	−0.912945	−0.456473	+	0.889738i	$0.650887\pi$
$450$	1.56886	0.0739566
$451$	0.0781918	0.00368191
$452$	5.40877	0.254407
$453$	−20.9689	−0.985204
$454$	13.5375	0.635344
$455$	0	0
$456$	1.57102	0.0735698
$457$	−11.6864	−0.546669	−0.273334	−	0.961919i	$-0.588127\pi$
$457$	−11.6864	−0.546669	−0.273334	+	0.961919i	$0.588127\pi$
$458$	−28.1954	−1.31748
$459$	−11.7974	−0.550658
$460$	−10.6417	−0.496172
$461$	−20.4857	−0.954114	−0.477057	−	0.878872i	$-0.658296\pi$
$461$	−20.4857	−0.954114	−0.477057	+	0.878872i	$0.658296\pi$
$462$	1.21534	0.0565427
$463$	−0.112903	−0.00524706	−0.00262353	−	0.999997i	$-0.500835\pi$
$463$	−0.112903	−0.00524706	−0.00262353	+	0.999997i	$0.500835\pi$
$464$	9.37867	0.435394
$465$	12.2462	0.567902
$466$	−16.5004	−0.764364
$467$	41.2449	1.90859	0.954293	−	0.298871i	$-0.0966102\pi$
$467$	41.2449	1.90859	0.954293	+	0.298871i	$0.0966102\pi$
$468$	0	0
$469$	−5.75033	−0.265526
$470$	−12.2857	−0.566698
$471$	25.4938	1.17469
$472$	3.90192	0.179600
$473$	−1.59485	−0.0733313
$474$	15.2909	0.702333
$475$	−2.94955	−0.135335
$476$	9.82046	0.450120
$477$	3.24565	0.148608
$478$	−3.54175	−0.161996
$479$	16.0438	0.733060	0.366530	−	0.930406i	$-0.380546\pi$
$479$	16.0438	0.733060	0.366530	+	0.930406i	$0.380546\pi$
$480$	4.42948	0.202177
$481$	0	0
$482$	−17.1321	−0.780347
$483$	27.3876	1.24618
$484$	−10.9719	−0.498725
$485$	−45.4384	−2.06325
$486$	−5.45818	−0.247588
$487$	−40.7552	−1.84679	−0.923397	−	0.383847i	$-0.874599\pi$
$487$	−40.7552	−1.84679	−0.923397	+	0.383847i	$0.874599\pi$
$488$	−14.2893	−0.646847
$489$	9.05374	0.409424
$490$	40.4139	1.82571
$491$	6.31252	0.284880	0.142440	−	0.989803i	$-0.454505\pi$
$491$	6.31252	0.284880	0.142440	+	0.989803i	$0.454505\pi$
$492$	−0.733433	−0.0330657
$493$	19.9407	0.898083
$494$	0	0
$495$	−0.251177	−0.0112896
$496$	−2.76469	−0.124138
$497$	−74.3816	−3.33647
$498$	6.94345	0.311143
$499$	21.5861	0.966325	0.483163	−	0.875531i	$-0.339488\pi$
$499$	21.5861	0.966325	0.483163	+	0.875531i	$0.339488\pi$
$500$	5.78122	0.258544
$501$	−22.4019	−1.00084
$502$	11.8327	0.528119
$503$	−41.8928	−1.86791	−0.933955	−	0.357392i	$-0.883666\pi$
$503$	−41.8928	−1.86791	−0.933955	+	0.357392i	$0.883666\pi$
$504$	2.45674	0.109432
$505$	−0.607664	−0.0270407
$506$	0.632153	0.0281026
$507$	0	0
$508$	17.1672	0.761672
$509$	34.5124	1.52974	0.764868	−	0.644187i	$-0.222804\pi$
$509$	34.5124	1.52974	0.764868	+	0.644187i	$0.222804\pi$
$510$	9.41785	0.417029
$511$	58.3773	2.58246
$512$	−1.00000	−0.0441942
$513$	5.54868	0.244980
$514$	−17.3536	−0.765433
$515$	−13.5846	−0.598608
$516$	14.9596	0.658558
$517$	0.729813	0.0320972
$518$	7.11354	0.312551
$519$	−30.0901	−1.32081
$520$	0	0
$521$	−19.8718	−0.870600	−0.435300	−	0.900285i	$-0.643358\pi$
$521$	−19.8718	−0.870600	−0.435300	+	0.900285i	$0.643358\pi$
$522$	4.98847	0.218340
$523$	1.29121	0.0564608	0.0282304	−	0.999601i	$-0.491013\pi$
$523$	1.29121	0.0564608	0.0282304	+	0.999601i	$0.491013\pi$
$524$	15.5641	0.679920
$525$	21.4028	0.934097
$526$	1.56178	0.0680967
$527$	−5.87821	−0.256059
$528$	−0.263126	−0.0114511
$529$	−8.75446	−0.380629
$530$	−17.2047	−0.747323
$531$	2.07541	0.0900653
$532$	−4.61884	−0.200252
$533$	0	0
$534$	−3.28531	−0.142169
$535$	6.15687	0.266185
$536$	1.24497	0.0537746
$537$	16.7186	0.721459
$538$	2.74547	0.118366
$539$	−2.40072	−0.103406
$540$	15.6445	0.673231
$541$	−0.428319	−0.0184149	−0.00920744	−	0.999958i	$-0.502931\pi$
$541$	−0.428319	−0.0184149	−0.00920744	+	0.999958i	$0.502931\pi$
$542$	−16.8840	−0.725231
$543$	1.23599	0.0530412
$544$	−2.12617	−0.0911589
$545$	−33.0879	−1.41733
$546$	0	0
$547$	−44.0511	−1.88349	−0.941745	−	0.336328i	$-0.890815\pi$
$547$	−44.0511	−1.88349	−0.941745	+	0.336328i	$0.890815\pi$
$548$	5.71387	0.244084
$549$	−7.60042	−0.324378
$550$	0.494014	0.0210648
$551$	−9.37867	−0.399545
$552$	−5.92954	−0.252378
$553$	−44.9556	−1.91171
$554$	5.58477	0.237274
$555$	6.82190	0.289574
$556$	−9.21480	−0.390795
$557$	−21.7089	−0.919834	−0.459917	−	0.887962i	$-0.652121\pi$
$557$	−21.7089	−0.919834	−0.459917	+	0.887962i	$0.652121\pi$
$558$	−1.47053	−0.0622524
$559$	0	0
$560$	−13.0228	−0.550314
$561$	−0.559452	−0.0236201
$562$	−24.2016	−1.02088
$563$	18.3842	0.774802	0.387401	−	0.921911i	$-0.373373\pi$
$563$	18.3842	0.774802	0.387401	+	0.921911i	$0.373373\pi$
$564$	−6.84559	−0.288251
$565$	−15.2500	−0.641573
$566$	25.9475	1.09065
$567$	−32.8926	−1.38136
$568$	16.1040	0.675707
$569$	32.1189	1.34650	0.673248	−	0.739417i	$-0.264899\pi$
$569$	32.1189	1.34650	0.673248	+	0.739417i	$0.264899\pi$
$570$	−4.42948	−0.185531
$571$	15.2549	0.638396	0.319198	−	0.947688i	$-0.396586\pi$
$571$	15.2549	0.638396	0.319198	+	0.947688i	$0.396586\pi$
$572$	0	0
$573$	4.37811	0.182898
$574$	2.15631	0.0900028
$575$	11.1326	0.464261
$576$	−0.531896	−0.0221623
$577$	−26.9122	−1.12037	−0.560185	−	0.828367i	$-0.689270\pi$
$577$	−26.9122	−1.12037	−0.560185	+	0.828367i	$0.689270\pi$
$578$	12.4794	0.519074
$579$	−33.3010	−1.38394
$580$	−26.4431	−1.09799
$581$	−20.4139	−0.846913
$582$	−25.3182	−1.04947
$583$	1.02202	0.0423276
$584$	−12.6389	−0.523003
$585$	0	0
$586$	−14.4299	−0.596092
$587$	−34.4954	−1.42378	−0.711889	−	0.702292i	$-0.752160\pi$
$587$	−34.4954	−1.42378	−0.711889	+	0.702292i	$0.752160\pi$
$588$	22.5186	0.928650
$589$	2.76469	0.113917
$590$	−11.0014	−0.452922
$591$	−9.10114	−0.374371
$592$	−1.54011	−0.0632982
$593$	−3.67243	−0.150808	−0.0754042	−	0.997153i	$-0.524025\pi$
$593$	−3.67243	−0.150808	−0.0754042	+	0.997153i	$0.524025\pi$
$594$	−0.929335	−0.0381311
$595$	−27.6887	−1.13513
$596$	18.6829	0.765283
$597$	−15.7901	−0.646246
$598$	0	0
$599$	−3.02725	−0.123690	−0.0618451	−	0.998086i	$-0.519698\pi$
$599$	−3.02725	−0.123690	−0.0618451	+	0.998086i	$0.519698\pi$
$600$	−4.63381	−0.189174
$601$	35.7063	1.45649	0.728246	−	0.685316i	$-0.240336\pi$
$601$	35.7063	1.45649	0.728246	+	0.685316i	$0.240336\pi$
$602$	−43.9815	−1.79255
$603$	0.662195	0.0269667
$604$	−13.3473	−0.543094
$605$	30.9354	1.25770
$606$	−0.338590	−0.0137543
$607$	−36.6068	−1.48582	−0.742912	−	0.669389i	$-0.766556\pi$
$607$	−36.6068	−1.48582	−0.742912	+	0.669389i	$0.766556\pi$
$608$	1.00000	0.0405554
$609$	68.0544	2.75770
$610$	40.2886	1.63124
$611$	0	0
$612$	−1.13090	−0.0457140
$613$	24.9214	1.00657	0.503283	−	0.864122i	$-0.332125\pi$
$613$	24.9214	1.00657	0.503283	+	0.864122i	$0.332125\pi$
$614$	−1.27895	−0.0516141
$615$	2.06791	0.0833862
$616$	0.773599	0.0311692
$617$	−15.8458	−0.637926	−0.318963	−	0.947767i	$-0.603335\pi$
$617$	−15.8458	−0.637926	−0.318963	+	0.947767i	$0.603335\pi$
$618$	−7.56932	−0.304483
$619$	22.1605	0.890706	0.445353	−	0.895355i	$-0.353078\pi$
$619$	22.1605	0.890706	0.445353	+	0.895355i	$0.353078\pi$
$620$	7.79504	0.313056
$621$	−20.9425	−0.840395
$622$	−8.19033	−0.328402
$623$	9.65891	0.386976
$624$	0	0
$625$	−31.0479	−1.24192
$626$	3.25848	0.130235
$627$	0.263126	0.0105083
$628$	16.2275	0.647549
$629$	−3.27454	−0.130565
$630$	−6.92678	−0.275969
$631$	47.9728	1.90977	0.954883	−	0.296983i	$-0.0959804\pi$
$631$	47.9728	1.90977	0.954883	+	0.296983i	$0.0959804\pi$
$632$	9.73309	0.387161
$633$	−9.67498	−0.384546
$634$	17.4705	0.693843
$635$	−48.4029	−1.92081
$636$	−9.58643	−0.380127
$637$	0	0
$638$	1.57081	0.0621890
$639$	8.56562	0.338851
$640$	2.81950	0.111450
$641$	20.1067	0.794168	0.397084	−	0.917782i	$-0.370022\pi$
$641$	20.1067	0.794168	0.397084	+	0.917782i	$0.370022\pi$
$642$	3.43060	0.135395
$643$	−8.98320	−0.354263	−0.177131	−	0.984187i	$-0.556682\pi$
$643$	−8.98320	−0.354263	−0.177131	+	0.984187i	$0.556682\pi$
$644$	17.4330	0.686957
$645$	−42.1784	−1.66077
$646$	2.12617	0.0836531
$647$	−4.99967	−0.196557	−0.0982786	−	0.995159i	$-0.531334\pi$
$647$	−4.99967	−0.196557	−0.0982786	+	0.995159i	$0.531334\pi$
$648$	7.12140	0.279755
$649$	0.653523	0.0256530
$650$	0	0
$651$	−20.0614	−0.786270
$652$	5.76297	0.225695
$653$	−13.8203	−0.540832	−0.270416	−	0.962744i	$-0.587161\pi$
$653$	−13.8203	−0.540832	−0.270416	+	0.962744i	$0.587161\pi$
$654$	−18.4366	−0.720927
$655$	−43.8829	−1.71465
$656$	−0.466851	−0.0182275
$657$	−6.72259	−0.262273
$658$	20.1262	0.784602
$659$	25.9102	1.00932	0.504660	−	0.863318i	$-0.331618\pi$
$659$	25.9102	1.00932	0.504660	+	0.863318i	$0.331618\pi$
$660$	0.741884	0.0288778
$661$	−13.7411	−0.534467	−0.267233	−	0.963632i	$-0.586109\pi$
$661$	−13.7411	−0.534467	−0.267233	+	0.963632i	$0.586109\pi$
$662$	−26.8209	−1.04242
$663$	0	0
$664$	4.41971	0.171518
$665$	13.0228	0.505003
$666$	−0.819179	−0.0317426
$667$	35.3982	1.37062
$668$	−14.2595	−0.551715
$669$	27.6176	1.06776
$670$	−3.51019	−0.135611
$671$	−2.39328	−0.0923917
$672$	−7.25630	−0.279918
$673$	−15.0069	−0.578474	−0.289237	−	0.957258i	$-0.593402\pi$
$673$	−15.0069	−0.578474	−0.289237	+	0.957258i	$0.593402\pi$
$674$	−9.26426	−0.356846
$675$	−16.3661	−0.629933
$676$	0	0
$677$	2.95246	0.113472	0.0567362	−	0.998389i	$-0.481931\pi$
$677$	2.95246	0.113472	0.0567362	+	0.998389i	$0.481931\pi$
$678$	−8.49729	−0.326337
$679$	74.4363	2.85660
$680$	5.99473	0.229888
$681$	−21.2676	−0.814977
$682$	−0.463052	−0.0177312
$683$	22.0617	0.844166	0.422083	−	0.906557i	$-0.361299\pi$
$683$	22.0617	0.844166	0.422083	+	0.906557i	$0.361299\pi$
$684$	0.531896	0.0203375
$685$	−16.1102	−0.615540
$686$	−33.8733	−1.29329
$687$	44.2955	1.68998
$688$	9.52220	0.363030
$689$	0	0
$690$	16.7183	0.636456
$691$	−30.0925	−1.14477	−0.572386	−	0.819984i	$-0.693982\pi$
$691$	−30.0925	−1.14477	−0.572386	+	0.819984i	$0.693982\pi$
$692$	−19.1532	−0.728097
$693$	0.411474	0.0156306
$694$	−30.1115	−1.14302
$695$	25.9811	0.985519
$696$	−14.7341	−0.558494
$697$	−0.992606	−0.0375976
$698$	−8.11747	−0.307251
$699$	25.9224	0.980475
$700$	13.6235	0.514921
$701$	31.1252	1.17558	0.587792	−	0.809012i	$-0.299997\pi$
$701$	31.1252	1.17558	0.587792	+	0.809012i	$0.299997\pi$
$702$	0	0
$703$	1.54011	0.0580864
$704$	−0.167488	−0.00631243
$705$	19.3011	0.726922
$706$	18.3490	0.690572
$707$	0.995464	0.0374383
$708$	−6.13000	−0.230379
$709$	2.64650	0.0993913	0.0496956	−	0.998764i	$-0.484175\pi$
$709$	2.64650	0.0993913	0.0496956	+	0.998764i	$0.484175\pi$
$710$	−45.4050	−1.70402
$711$	5.17699	0.194152
$712$	−2.09120	−0.0783709
$713$	−10.4349	−0.390788
$714$	−15.4281	−0.577384
$715$	0	0
$716$	10.6419	0.397705
$717$	5.56415	0.207797
$718$	18.1510	0.677389
$719$	9.18450	0.342524	0.171262	−	0.985226i	$-0.445216\pi$
$719$	9.18450	0.342524	0.171262	+	0.985226i	$0.445216\pi$
$720$	1.49968	0.0558897
$721$	22.2540	0.828783
$722$	−1.00000	−0.0372161
$723$	26.9149	1.00098
$724$	0.786741	0.0292390
$725$	27.6629	1.02737
$726$	17.2372	0.639731
$727$	22.2003	0.823365	0.411683	−	0.911327i	$-0.364941\pi$
$727$	22.2003	0.823365	0.411683	+	0.911327i	$0.364941\pi$
$728$	0	0
$729$	29.9391	1.10886
$730$	35.6354	1.31893
$731$	20.2458	0.748819
$732$	22.4488	0.829731
$733$	29.8331	1.10191	0.550955	−	0.834535i	$-0.314264\pi$
$733$	29.8331	1.10191	0.550955	+	0.834535i	$0.314264\pi$
$734$	−23.7794	−0.877713
$735$	−63.4910	−2.34190
$736$	−3.77433	−0.139124
$737$	0.208517	0.00768084
$738$	−0.248316	−0.00914064
$739$	10.9455	0.402639	0.201319	−	0.979526i	$-0.435477\pi$
$739$	10.9455	0.402639	0.201319	+	0.979526i	$0.435477\pi$
$740$	4.34234	0.159628
$741$	0	0
$742$	28.1844	1.03468
$743$	45.7381	1.67797	0.838984	−	0.544157i	$-0.183150\pi$
$743$	45.7381	1.67797	0.838984	+	0.544157i	$0.183150\pi$
$744$	4.34339	0.159236
$745$	−52.6765	−1.92992
$746$	12.0839	0.442421
$747$	2.35082	0.0860121
$748$	−0.356108	−0.0130206
$749$	−10.0861	−0.368537
$750$	−9.08241	−0.331643
$751$	15.4658	0.564355	0.282178	−	0.959362i	$-0.408943\pi$
$751$	15.4658	0.564355	0.282178	+	0.959362i	$0.408943\pi$
$752$	−4.35742	−0.158899
$753$	−18.5894	−0.677435
$754$	0	0
$755$	37.6326	1.36959
$756$	−25.6285	−0.932099
$757$	−25.1938	−0.915683	−0.457841	−	0.889034i	$-0.651377\pi$
$757$	−25.1938	−0.915683	−0.457841	+	0.889034i	$0.651377\pi$
$758$	−1.27737	−0.0463962
$759$	−0.993125	−0.0360482
$760$	−2.81950	−0.102274
$761$	3.16517	0.114737	0.0573687	−	0.998353i	$-0.481729\pi$
$761$	3.16517	0.114737	0.0573687	+	0.998353i	$0.481729\pi$
$762$	−26.9700	−0.977021
$763$	54.2040	1.96232
$764$	2.78680	0.100823
$765$	3.18857	0.115283
$766$	−17.5663	−0.634696
$767$	0	0
$768$	1.57102	0.0566893
$769$	−10.6587	−0.384364	−0.192182	−	0.981359i	$-0.561556\pi$
$769$	−10.6587	−0.384364	−0.192182	+	0.981359i	$0.561556\pi$
$770$	−2.18116	−0.0786035
$771$	27.2628	0.981846
$772$	−21.1970	−0.762898
$773$	−52.4684	−1.88716	−0.943578	−	0.331151i	$-0.892563\pi$
$773$	−52.4684	−1.88716	−0.943578	+	0.331151i	$0.892563\pi$
$774$	5.06481	0.182051
$775$	−8.15462	−0.292922
$776$	−16.1158	−0.578523
$777$	−11.1755	−0.400919
$778$	−0.0492487	−0.00176565
$779$	0.466851	0.0167267
$780$	0	0
$781$	2.69721	0.0965139
$782$	−8.02487	−0.286969
$783$	−52.0392	−1.85973
$784$	14.3337	0.511919
$785$	−45.7534	−1.63301
$786$	−24.4515	−0.872156
$787$	−22.8990	−0.816260	−0.408130	−	0.912924i	$-0.633819\pi$
$787$	−22.8990	−0.816260	−0.408130	+	0.912924i	$0.633819\pi$
$788$	−5.79314	−0.206372
$789$	−2.45358	−0.0873498
$790$	−27.4424	−0.976357
$791$	24.9823	0.888268
$792$	−0.0890860	−0.00316553
$793$	0	0
$794$	−33.8454	−1.20113
$795$	27.0289	0.958616
$796$	−10.0509	−0.356243
$797$	19.2440	0.681656	0.340828	−	0.940126i	$-0.389293\pi$
$797$	19.2440	0.681656	0.340828	+	0.940126i	$0.389293\pi$
$798$	7.25630	0.256870
$799$	−9.26462	−0.327759
$800$	−2.94955	−0.104283
$801$	−1.11230	−0.0393011
$802$	−25.3595	−0.895475
$803$	−2.11686	−0.0747025
$804$	−1.95588	−0.0689784
$805$	−49.1523	−1.73239
$806$	0	0
$807$	−4.31319	−0.151831
$808$	−0.215522	−0.00758205
$809$	16.8453	0.592249	0.296125	−	0.955149i	$-0.404306\pi$
$809$	16.8453	0.592249	0.296125	+	0.955149i	$0.404306\pi$
$810$	−20.0788	−0.705496
$811$	−3.83311	−0.134599	−0.0672994	−	0.997733i	$-0.521438\pi$
$811$	−3.83311	−0.134599	−0.0672994	+	0.997733i	$0.521438\pi$
$812$	43.3186	1.52019
$813$	26.5252	0.930278
$814$	−0.257950	−0.00904114
$815$	−16.2487	−0.569166
$816$	3.34026	0.116932
$817$	−9.52220	−0.333139
$818$	−25.9468	−0.907210
$819$	0	0
$820$	1.31628	0.0459667
$821$	−34.5387	−1.20541	−0.602705	−	0.797964i	$-0.705910\pi$
$821$	−34.5387	−1.20541	−0.602705	+	0.797964i	$0.705910\pi$
$822$	−8.97660	−0.313095
$823$	−4.63019	−0.161398	−0.0806992	−	0.996739i	$-0.525715\pi$
$823$	−4.63019	−0.161398	−0.0806992	+	0.996739i	$0.525715\pi$
$824$	−4.81809	−0.167846
$825$	−0.776106	−0.0270205
$826$	18.0224	0.627078
$827$	−22.7184	−0.789996	−0.394998	−	0.918682i	$-0.629255\pi$
$827$	−22.7184	−0.789996	−0.394998	+	0.918682i	$0.629255\pi$
$828$	−2.00755	−0.0697671
$829$	−45.2354	−1.57109	−0.785546	−	0.618804i	$-0.787618\pi$
$829$	−45.2354	−1.57109	−0.785546	+	0.618804i	$0.787618\pi$
$830$	−12.4613	−0.432539
$831$	−8.77379	−0.304359
$832$	0	0
$833$	30.4760	1.05593
$834$	14.4766	0.501285
$835$	40.2045	1.39133
$836$	0.167488	0.00579268
$837$	15.3404	0.530242
$838$	34.4082	1.18861
$839$	2.95597	0.102051	0.0510257	−	0.998697i	$-0.483751\pi$
$839$	2.95597	0.102051	0.0510257	+	0.998697i	$0.483751\pi$
$840$	20.4591	0.705906
$841$	58.9595	2.03309
$842$	−23.3518	−0.804754
$843$	38.0212	1.30952
$844$	−6.15840	−0.211981
$845$	0	0
$846$	−2.31769	−0.0796839
$847$	−50.6777	−1.74131
$848$	−6.10204	−0.209545
$849$	−40.7640	−1.39902
$850$	−6.27126	−0.215102
$851$	−5.81289	−0.199263
$852$	−25.2996	−0.866751
$853$	11.7157	0.401139	0.200570	−	0.979679i	$-0.435721\pi$
$853$	11.7157	0.401139	0.200570	+	0.979679i	$0.435721\pi$
$854$	−66.0001	−2.25848
$855$	−1.49968	−0.0512879
$856$	2.18368	0.0746366
$857$	2.91516	0.0995798	0.0497899	−	0.998760i	$-0.484145\pi$
$857$	2.91516	0.0995798	0.0497899	+	0.998760i	$0.484145\pi$
$858$	0	0
$859$	27.1979	0.927980	0.463990	−	0.885840i	$-0.346417\pi$
$859$	27.1979	0.927980	0.463990	+	0.885840i	$0.346417\pi$
$860$	−26.8478	−0.915502
$861$	−3.38761	−0.115449
$862$	20.5460	0.699798
$863$	−11.2008	−0.381279	−0.190640	−	0.981660i	$-0.561056\pi$
$863$	−11.2008	−0.381279	−0.190640	+	0.981660i	$0.561056\pi$
$864$	5.54868	0.188770
$865$	54.0025	1.83614
$866$	20.4768	0.695830
$867$	−19.6054	−0.665833
$868$	−12.7697	−0.433431
$869$	1.63017	0.0552998
$870$	41.5427	1.40843
$871$	0	0
$872$	−11.7354	−0.397411
$873$	−8.57192	−0.290115
$874$	3.77433	0.127669
$875$	26.7026	0.902711
$876$	19.8560	0.670873
$877$	34.9211	1.17920	0.589600	−	0.807695i	$-0.299285\pi$
$877$	34.9211	1.17920	0.589600	+	0.807695i	$0.299285\pi$
$878$	1.50234	0.0507014
$879$	22.6696	0.764627
$880$	0.472231	0.0159189
$881$	−1.96349	−0.0661517	−0.0330758	−	0.999453i	$-0.510530\pi$
$881$	−1.96349	−0.0661517	−0.0330758	+	0.999453i	$0.510530\pi$
$882$	7.62404	0.256715
$883$	−41.6115	−1.40034	−0.700169	−	0.713977i	$-0.746892\pi$
$883$	−41.6115	−1.40034	−0.700169	+	0.713977i	$0.746892\pi$
$884$	0	0
$885$	17.2835	0.580978
$886$	−19.6984	−0.661780
$887$	−45.6103	−1.53144	−0.765721	−	0.643173i	$-0.777618\pi$
$887$	−45.6103	−1.53144	−0.765721	+	0.643173i	$0.777618\pi$
$888$	2.41955	0.0811947
$889$	79.2927	2.65939
$890$	5.89612	0.197638
$891$	1.19275	0.0399585
$892$	17.5794	0.588602
$893$	4.35742	0.145815
$894$	−29.3513	−0.981654
$895$	−30.0047	−1.00295
$896$	−4.61884	−0.154305
$897$	0	0
$898$	19.3450	0.645550
$899$	−25.9292	−0.864786
$900$	−1.56886	−0.0522952
$901$	−12.9740	−0.432226
$902$	−0.0781918	−0.00260350
$903$	69.0959	2.29937
$904$	−5.40877	−0.179893
$905$	−2.21821	−0.0737359
$906$	20.9689	0.696644
$907$	−5.43696	−0.180531	−0.0902657	−	0.995918i	$-0.528772\pi$
$907$	−5.43696	−0.180531	−0.0902657	+	0.995918i	$0.528772\pi$
$908$	−13.5375	−0.449256
$909$	−0.114635	−0.00380222
$910$	0	0
$911$	−39.0965	−1.29532	−0.647662	−	0.761928i	$-0.724253\pi$
$911$	−39.0965	−1.29532	−0.647662	+	0.761928i	$0.724253\pi$
$912$	−1.57102	−0.0520217
$913$	0.740246	0.0244986
$914$	11.6864	0.386553
$915$	−63.2943	−2.09244
$916$	28.1954	0.931602
$917$	71.8881	2.37395
$918$	11.7974	0.389374
$919$	4.38363	0.144603	0.0723014	−	0.997383i	$-0.476966\pi$
$919$	4.38363	0.144603	0.0723014	+	0.997383i	$0.476966\pi$
$920$	10.6417	0.350846
$921$	2.00925	0.0662071
$922$	20.4857	0.674660
$923$	0	0
$924$	−1.21534	−0.0399818
$925$	−4.54265	−0.149361
$926$	0.112903	0.00371023
$927$	−2.56272	−0.0841708
$928$	−9.37867	−0.307870
$929$	−4.71783	−0.154787	−0.0773935	−	0.997001i	$-0.524660\pi$
$929$	−4.71783	−0.154787	−0.0773935	+	0.997001i	$0.524660\pi$
$930$	−12.2462	−0.401568
$931$	−14.3337	−0.469769
$932$	16.5004	0.540487
$933$	12.8672	0.421252
$934$	−41.2449	−1.34957
$935$	1.00404	0.0328357
$936$	0	0
$937$	43.0137	1.40520	0.702599	−	0.711586i	$-0.252023\pi$
$937$	43.0137	1.40520	0.702599	+	0.711586i	$0.252023\pi$
$938$	5.75033	0.187755
$939$	−5.11914	−0.167057
$940$	12.2857	0.400716
$941$	−44.9256	−1.46453	−0.732267	−	0.681018i	$-0.761538\pi$
$941$	−44.9256	−1.46453	−0.732267	+	0.681018i	$0.761538\pi$
$942$	−25.4938	−0.830632
$943$	−1.76205	−0.0573802
$944$	−3.90192	−0.126997
$945$	72.2594	2.35060
$946$	1.59485	0.0518531
$947$	26.6136	0.864827	0.432414	−	0.901675i	$-0.357662\pi$
$947$	26.6136	0.864827	0.432414	+	0.901675i	$0.357662\pi$
$948$	−15.2909	−0.496625
$949$	0	0
$950$	2.94955	0.0956962
$951$	−27.4465	−0.890015
$952$	−9.82046	−0.318283
$953$	19.2966	0.625080	0.312540	−	0.949905i	$-0.398820\pi$
$953$	19.2966	0.625080	0.312540	+	0.949905i	$0.398820\pi$
$954$	−3.24565	−0.105082
$955$	−7.85736	−0.254258
$956$	3.54175	0.114548
$957$	−2.46778	−0.0797719
$958$	−16.0438	−0.518352
$959$	26.3915	0.852225
$960$	−4.42948	−0.142961
$961$	−23.3565	−0.753434
$962$	0	0
$963$	1.16149	0.0374285
$964$	17.1321	0.551789
$965$	59.7649	1.92390
$966$	−27.3876	−0.881183
$967$	−17.2205	−0.553773	−0.276886	−	0.960903i	$-0.589303\pi$
$967$	−17.2205	−0.553773	−0.276886	+	0.960903i	$0.589303\pi$
$968$	10.9719	0.352652
$969$	−3.34026	−0.107305
$970$	45.4384	1.45894
$971$	60.4374	1.93953	0.969764	−	0.244046i	$-0.0784749\pi$
$971$	60.4374	1.93953	0.969764	+	0.244046i	$0.0784749\pi$
$972$	5.45818	0.175071
$973$	−42.5617	−1.36447
$974$	40.7552	1.30588
$975$	0	0
$976$	14.2893	0.457390
$977$	47.0685	1.50585	0.752927	−	0.658104i	$-0.228641\pi$
$977$	47.0685	1.50585	0.752927	+	0.658104i	$0.228641\pi$
$978$	−9.05374	−0.289507
$979$	−0.350249	−0.0111940
$980$	−40.4139	−1.29097
$981$	−6.24201	−0.199292
$982$	−6.31252	−0.201440
$983$	−43.8752	−1.39940	−0.699700	−	0.714436i	$-0.746683\pi$
$983$	−43.8752	−1.39940	−0.699700	+	0.714436i	$0.746683\pi$
$984$	0.733433	0.0233810
$985$	16.3337	0.520436
$986$	−19.9407	−0.635040
$987$	−31.6187	−1.00643
$988$	0	0
$989$	35.9399	1.14282
$990$	0.251177	0.00798294
$991$	16.7581	0.532338	0.266169	−	0.963926i	$-0.414242\pi$
$991$	16.7581	0.532338	0.266169	+	0.963926i	$0.414242\pi$
$992$	2.76469	0.0877791
$993$	42.1362	1.33715
$994$	74.3816	2.35924
$995$	28.3384	0.898386
$996$	−6.94345	−0.220012
$997$	−2.42268	−0.0767272	−0.0383636	−	0.999264i	$-0.512215\pi$
$997$	−2.42268	−0.0767272	−0.0383636	+	0.999264i	$0.512215\pi$
$998$	−21.5861	−0.683295
$999$	8.54559	0.270371

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6422.2.a.bm.1.10		14
13.2	odd	12		494.2.m.b.381.2	yes	28
13.7	odd	12		494.2.m.b.153.2	✓	28
13.12	even	2		6422.2.a.bn.1.10		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.m.b.153.2	✓	28	13.7	odd	12
494.2.m.b.381.2	yes	28	13.2	odd	12
6422.2.a.bm.1.10		14	1.1	even	1	trivial
6422.2.a.bn.1.10		14	13.12	even	2

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:	\( N \)	\(=\)	\( 6422 = 2 \cdot 13^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6422.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.57102 q^{3} +1.00000 q^{4} -2.81950 q^{5} -1.57102 q^{6} +4.61884 q^{7} -1.00000 q^{8} -0.531896 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.57102 q^{3} +1.00000 q^{4} -2.81950 q^{5} -1.57102 q^{6} +4.61884 q^{7} -1.00000 q^{8} -0.531896 q^{9} +2.81950 q^{10} -0.167488 q^{11} +1.57102 q^{12} -4.61884 q^{14} -4.42948 q^{15} +1.00000 q^{16} +2.12617 q^{17} +0.531896 q^{18} -1.00000 q^{19} -2.81950 q^{20} +7.25630 q^{21} +0.167488 q^{22} +3.77433 q^{23} -1.57102 q^{24} +2.94955 q^{25} -5.54868 q^{27} +4.61884 q^{28} +9.37867 q^{29} +4.42948 q^{30} -2.76469 q^{31} -1.00000 q^{32} -0.263126 q^{33} -2.12617 q^{34} -13.0228 q^{35} -0.531896 q^{36} -1.54011 q^{37} +1.00000 q^{38} +2.81950 q^{40} -0.466851 q^{41} -7.25630 q^{42} +9.52220 q^{43} -0.167488 q^{44} +1.49968 q^{45} -3.77433 q^{46} -4.35742 q^{47} +1.57102 q^{48} +14.3337 q^{49} -2.94955 q^{50} +3.34026 q^{51} -6.10204 q^{53} +5.54868 q^{54} +0.472231 q^{55} -4.61884 q^{56} -1.57102 q^{57} -9.37867 q^{58} -3.90192 q^{59} -4.42948 q^{60} +14.2893 q^{61} +2.76469 q^{62} -2.45674 q^{63} +1.00000 q^{64} +0.263126 q^{66} -1.24497 q^{67} +2.12617 q^{68} +5.92954 q^{69} +13.0228 q^{70} -16.1040 q^{71} +0.531896 q^{72} +12.6389 q^{73} +1.54011 q^{74} +4.63381 q^{75} -1.00000 q^{76} -0.773599 q^{77} -9.73309 q^{79} -2.81950 q^{80} -7.12140 q^{81} +0.466851 q^{82} -4.41971 q^{83} +7.25630 q^{84} -5.99473 q^{85} -9.52220 q^{86} +14.7341 q^{87} +0.167488 q^{88} +2.09120 q^{89} -1.49968 q^{90} +3.77433 q^{92} -4.34339 q^{93} +4.35742 q^{94} +2.81950 q^{95} -1.57102 q^{96} +16.1158 q^{97} -14.3337 q^{98} +0.0890860 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} + 4 q^{3} + 14 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 14 q^{8} + 18 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 + 4 * q^3 + 14 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 14 * q^8 + 18 * q^9	\( 14 q - 14 q^{2} + 4 q^{3} + 14 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 14 q^{8} + 18 q^{9} - 2 q^{10} - 10 q^{11} + 4 q^{12} + 2 q^{14} + 4 q^{15} + 14 q^{16} + 2 q^{17} - 18 q^{18} - 14 q^{19} + 2 q^{20} + 18 q^{21} + 10 q^{22} + 12 q^{23} - 4 q^{24} + 44 q^{25} + 10 q^{27} - 2 q^{28} + 4 q^{29} - 4 q^{30} - 4 q^{31} - 14 q^{32} - 12 q^{33} - 2 q^{34} + 14 q^{35} + 18 q^{36} - 18 q^{37} + 14 q^{38} - 2 q^{40} - 6 q^{41} - 18 q^{42} + 28 q^{43} - 10 q^{44} - 8 q^{45} - 12 q^{46} + 20 q^{47} + 4 q^{48} + 28 q^{49} - 44 q^{50} + 10 q^{51} + 12 q^{53} - 10 q^{54} - 2 q^{55} + 2 q^{56} - 4 q^{57} - 4 q^{58} - 16 q^{59} + 4 q^{60} + 30 q^{61} + 4 q^{62} - 28 q^{63} + 14 q^{64} + 12 q^{66} - 2 q^{67} + 2 q^{68} - 42 q^{69} - 14 q^{70} - 44 q^{71} - 18 q^{72} + 36 q^{73} + 18 q^{74} + 46 q^{75} - 14 q^{76} + 68 q^{77} + 34 q^{79} + 2 q^{80} - 6 q^{81} + 6 q^{82} - 2 q^{83} + 18 q^{84} + 30 q^{85} - 28 q^{86} + 52 q^{87} + 10 q^{88} - 42 q^{89} + 8 q^{90} + 12 q^{92} + 12 q^{93} - 20 q^{94} - 2 q^{95} - 4 q^{96} - 40 q^{97} - 28 q^{98} - 12 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 4 * q^3 + 14 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 14 * q^8 + 18 * q^9 - 2 * q^10 - 10 * q^11 + 4 * q^12 + 2 * q^14 + 4 * q^15 + 14 * q^16 + 2 * q^17 - 18 * q^18 - 14 * q^19 + 2 * q^20 + 18 * q^21 + 10 * q^22 + 12 * q^23 - 4 * q^24 + 44 * q^25 + 10 * q^27 - 2 * q^28 + 4 * q^29 - 4 * q^30 - 4 * q^31 - 14 * q^32 - 12 * q^33 - 2 * q^34 + 14 * q^35 + 18 * q^36 - 18 * q^37 + 14 * q^38 - 2 * q^40 - 6 * q^41 - 18 * q^42 + 28 * q^43 - 10 * q^44 - 8 * q^45 - 12 * q^46 + 20 * q^47 + 4 * q^48 + 28 * q^49 - 44 * q^50 + 10 * q^51 + 12 * q^53 - 10 * q^54 - 2 * q^55 + 2 * q^56 - 4 * q^57 - 4 * q^58 - 16 * q^59 + 4 * q^60 + 30 * q^61 + 4 * q^62 - 28 * q^63 + 14 * q^64 + 12 * q^66 - 2 * q^67 + 2 * q^68 - 42 * q^69 - 14 * q^70 - 44 * q^71 - 18 * q^72 + 36 * q^73 + 18 * q^74 + 46 * q^75 - 14 * q^76 + 68 * q^77 + 34 * q^79 + 2 * q^80 - 6 * q^81 + 6 * q^82 - 2 * q^83 + 18 * q^84 + 30 * q^85 - 28 * q^86 + 52 * q^87 + 10 * q^88 - 42 * q^89 + 8 * q^90 + 12 * q^92 + 12 * q^93 - 20 * q^94 - 2 * q^95 - 4 * q^96 - 40 * q^97 - 28 * q^98 - 12 * q^99

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