LMFDB - Embedded newform 4030.2.a.h.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, 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("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.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:	$32.1797120146$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 12x^{5} + 10x^{4} + 26x^{3} - 6x^{2} - 17x - 4 $ x^7 - x^6 - 12x^5 + 10x^4 + 26x^3 - 6x^2 - 17*x - 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.854702$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.854702 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.854702 q^{6} +0.252640 q^{7} -1.00000 q^{8} -2.26949 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.854702 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.854702 q^{6} +0.252640 q^{7} -1.00000 q^{8} -2.26949 q^{9} -1.00000 q^{10} +2.77504 q^{11} +0.854702 q^{12} -1.00000 q^{13} -0.252640 q^{14} +0.854702 q^{15} +1.00000 q^{16} -6.26117 q^{17} +2.26949 q^{18} +5.36352 q^{19} +1.00000 q^{20} +0.215931 q^{21} -2.77504 q^{22} -9.02997 q^{23} -0.854702 q^{24} +1.00000 q^{25} +1.00000 q^{26} -4.50384 q^{27} +0.252640 q^{28} +0.739779 q^{29} -0.854702 q^{30} +1.00000 q^{31} -1.00000 q^{32} +2.37184 q^{33} +6.26117 q^{34} +0.252640 q^{35} -2.26949 q^{36} +1.20408 q^{37} -5.36352 q^{38} -0.854702 q^{39} -1.00000 q^{40} +3.51482 q^{41} -0.215931 q^{42} +1.65557 q^{43} +2.77504 q^{44} -2.26949 q^{45} +9.02997 q^{46} -9.56736 q^{47} +0.854702 q^{48} -6.93617 q^{49} -1.00000 q^{50} -5.35143 q^{51} -1.00000 q^{52} -1.77672 q^{53} +4.50384 q^{54} +2.77504 q^{55} -0.252640 q^{56} +4.58421 q^{57} -0.739779 q^{58} -12.6832 q^{59} +0.854702 q^{60} -2.52971 q^{61} -1.00000 q^{62} -0.573362 q^{63} +1.00000 q^{64} -1.00000 q^{65} -2.37184 q^{66} -5.00327 q^{67} -6.26117 q^{68} -7.71793 q^{69} -0.252640 q^{70} +3.84638 q^{71} +2.26949 q^{72} -0.875580 q^{73} -1.20408 q^{74} +0.854702 q^{75} +5.36352 q^{76} +0.701086 q^{77} +0.854702 q^{78} +0.848461 q^{79} +1.00000 q^{80} +2.95902 q^{81} -3.51482 q^{82} +5.40805 q^{83} +0.215931 q^{84} -6.26117 q^{85} -1.65557 q^{86} +0.632290 q^{87} -2.77504 q^{88} +7.15844 q^{89} +2.26949 q^{90} -0.252640 q^{91} -9.02997 q^{92} +0.854702 q^{93} +9.56736 q^{94} +5.36352 q^{95} -0.854702 q^{96} +4.06691 q^{97} +6.93617 q^{98} -6.29792 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + q^{6} - 4 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - q^3 + 7 * q^4 + 7 * q^5 + q^6 - 4 * q^7 - 7 * q^8 + 4 * q^9	\( 7 q - 7 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + q^{6} - 4 q^{7} - 7 q^{8} + 4 q^{9} - 7 q^{10} - 2 q^{11} - q^{12} - 7 q^{13} + 4 q^{14} - q^{15} + 7 q^{16} - 8 q^{17} - 4 q^{18} + q^{19} + 7 q^{20} - 11 q^{21} + 2 q^{22} - 5 q^{23} + q^{24} + 7 q^{25} + 7 q^{26} - q^{27} - 4 q^{28} - 4 q^{29} + q^{30} + 7 q^{31} - 7 q^{32} - 4 q^{33} + 8 q^{34} - 4 q^{35} + 4 q^{36} - 2 q^{37} - q^{38} + q^{39} - 7 q^{40} - 6 q^{41} + 11 q^{42} - 5 q^{43} - 2 q^{44} + 4 q^{45} + 5 q^{46} - 18 q^{47} - q^{48} - 9 q^{49} - 7 q^{50} - q^{51} - 7 q^{52} - 12 q^{53} + q^{54} - 2 q^{55} + 4 q^{56} - 31 q^{57} + 4 q^{58} + 3 q^{59} - q^{60} - 7 q^{61} - 7 q^{62} - 19 q^{63} + 7 q^{64} - 7 q^{65} + 4 q^{66} + 6 q^{67} - 8 q^{68} - 10 q^{69} + 4 q^{70} + 4 q^{71} - 4 q^{72} - 31 q^{73} + 2 q^{74} - q^{75} + q^{76} - 25 q^{77} - q^{78} - 2 q^{79} + 7 q^{80} + 31 q^{81} + 6 q^{82} - 40 q^{83} - 11 q^{84} - 8 q^{85} + 5 q^{86} - 5 q^{87} + 2 q^{88} - 4 q^{90} + 4 q^{91} - 5 q^{92} - q^{93} + 18 q^{94} + q^{95} + q^{96} - 21 q^{97} + 9 q^{98} - 23 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - q^3 + 7 * q^4 + 7 * q^5 + q^6 - 4 * q^7 - 7 * q^8 + 4 * q^9 - 7 * q^10 - 2 * q^11 - q^12 - 7 * q^13 + 4 * q^14 - q^15 + 7 * q^16 - 8 * q^17 - 4 * q^18 + q^19 + 7 * q^20 - 11 * q^21 + 2 * q^22 - 5 * q^23 + q^24 + 7 * q^25 + 7 * q^26 - q^27 - 4 * q^28 - 4 * q^29 + q^30 + 7 * q^31 - 7 * q^32 - 4 * q^33 + 8 * q^34 - 4 * q^35 + 4 * q^36 - 2 * q^37 - q^38 + q^39 - 7 * q^40 - 6 * q^41 + 11 * q^42 - 5 * q^43 - 2 * q^44 + 4 * q^45 + 5 * q^46 - 18 * q^47 - q^48 - 9 * q^49 - 7 * q^50 - q^51 - 7 * q^52 - 12 * q^53 + q^54 - 2 * q^55 + 4 * q^56 - 31 * q^57 + 4 * q^58 + 3 * q^59 - q^60 - 7 * q^61 - 7 * q^62 - 19 * q^63 + 7 * q^64 - 7 * q^65 + 4 * q^66 + 6 * q^67 - 8 * q^68 - 10 * q^69 + 4 * q^70 + 4 * q^71 - 4 * q^72 - 31 * q^73 + 2 * q^74 - q^75 + q^76 - 25 * q^77 - q^78 - 2 * q^79 + 7 * q^80 + 31 * q^81 + 6 * q^82 - 40 * q^83 - 11 * q^84 - 8 * q^85 + 5 * q^86 - 5 * q^87 + 2 * q^88 - 4 * q^90 + 4 * q^91 - 5 * q^92 - q^93 + 18 * q^94 + q^95 + q^96 - 21 * q^97 + 9 * q^98 - 23 * 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
$3$	0.854702	0.493462	0.246731	−	0.969084i	$-0.420644\pi$
$3$	0.854702	0.493462	0.246731	+	0.969084i	$0.420644\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.854702	−0.348930
$7$	0.252640	0.0954888	0.0477444	−	0.998860i	$-0.484797\pi$
$7$	0.252640	0.0954888	0.0477444	+	0.998860i	$0.484797\pi$
$8$	−1.00000	−0.353553
$9$	−2.26949	−0.756495
$10$	−1.00000	−0.316228
$11$	2.77504	0.836708	0.418354	−	0.908284i	$-0.362607\pi$
$11$	2.77504	0.836708	0.418354	+	0.908284i	$0.362607\pi$
$12$	0.854702	0.246731
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.252640	−0.0675208
$15$	0.854702	0.220683
$16$	1.00000	0.250000
$17$	−6.26117	−1.51856	−0.759278	−	0.650766i	$-0.774448\pi$
$17$	−6.26117	−1.51856	−0.759278	+	0.650766i	$0.774448\pi$
$18$	2.26949	0.534923
$19$	5.36352	1.23048	0.615238	−	0.788342i	$-0.289060\pi$
$19$	5.36352	1.23048	0.615238	+	0.788342i	$0.289060\pi$
$20$	1.00000	0.223607
$21$	0.215931	0.0471201
$22$	−2.77504	−0.591642
$23$	−9.02997	−1.88288	−0.941440	−	0.337181i	$-0.890526\pi$
$23$	−9.02997	−1.88288	−0.941440	+	0.337181i	$0.890526\pi$
$24$	−0.854702	−0.174465
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	−4.50384	−0.866764
$28$	0.252640	0.0477444
$29$	0.739779	0.137373	0.0686867	−	0.997638i	$-0.478119\pi$
$29$	0.739779	0.137373	0.0686867	+	0.997638i	$0.478119\pi$
$30$	−0.854702	−0.156046
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	2.37184	0.412884
$34$	6.26117	1.07378
$35$	0.252640	0.0427039
$36$	−2.26949	−0.378248
$37$	1.20408	0.197949	0.0989745	−	0.995090i	$-0.468444\pi$
$37$	1.20408	0.197949	0.0989745	+	0.995090i	$0.468444\pi$
$38$	−5.36352	−0.870078
$39$	−0.854702	−0.136862
$40$	−1.00000	−0.158114
$41$	3.51482	0.548923	0.274462	−	0.961598i	$-0.411500\pi$
$41$	3.51482	0.548923	0.274462	+	0.961598i	$0.411500\pi$
$42$	−0.215931	−0.0333189
$43$	1.65557	0.252472	0.126236	−	0.992000i	$-0.459710\pi$
$43$	1.65557	0.252472	0.126236	+	0.992000i	$0.459710\pi$
$44$	2.77504	0.418354
$45$	−2.26949	−0.338315
$46$	9.02997	1.33140
$47$	−9.56736	−1.39554	−0.697772	−	0.716320i	$-0.745825\pi$
$47$	−9.56736	−1.39554	−0.697772	+	0.716320i	$0.745825\pi$
$48$	0.854702	0.123366
$49$	−6.93617	−0.990882
$50$	−1.00000	−0.141421
$51$	−5.35143	−0.749350
$52$	−1.00000	−0.138675
$53$	−1.77672	−0.244051	−0.122026	−	0.992527i	$-0.538939\pi$
$53$	−1.77672	−0.244051	−0.122026	+	0.992527i	$0.538939\pi$
$54$	4.50384	0.612895
$55$	2.77504	0.374187
$56$	−0.252640	−0.0337604
$57$	4.58421	0.607193
$58$	−0.739779	−0.0971377
$59$	−12.6832	−1.65122	−0.825608	−	0.564244i	$-0.809168\pi$
$59$	−12.6832	−1.65122	−0.825608	+	0.564244i	$0.809168\pi$
$60$	0.854702	0.110341
$61$	−2.52971	−0.323896	−0.161948	−	0.986799i	$-0.551778\pi$
$61$	−2.52971	−0.323896	−0.161948	+	0.986799i	$0.551778\pi$
$62$	−1.00000	−0.127000
$63$	−0.573362	−0.0722368
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	−2.37184	−0.291953
$67$	−5.00327	−0.611247	−0.305623	−	0.952153i	$-0.598865\pi$
$67$	−5.00327	−0.611247	−0.305623	+	0.952153i	$0.598865\pi$
$68$	−6.26117	−0.759278
$69$	−7.71793	−0.929130
$70$	−0.252640	−0.0301962
$71$	3.84638	0.456482	0.228241	−	0.973605i	$-0.426703\pi$
$71$	3.84638	0.456482	0.228241	+	0.973605i	$0.426703\pi$
$72$	2.26949	0.267461
$73$	−0.875580	−0.102479	−0.0512394	−	0.998686i	$-0.516317\pi$
$73$	−0.875580	−0.102479	−0.0512394	+	0.998686i	$0.516317\pi$
$74$	−1.20408	−0.139971
$75$	0.854702	0.0986924
$76$	5.36352	0.615238
$77$	0.701086	0.0798962
$78$	0.854702	0.0967759
$79$	0.848461	0.0954593	0.0477297	−	0.998860i	$-0.484801\pi$
$79$	0.848461	0.0954593	0.0477297	+	0.998860i	$0.484801\pi$
$80$	1.00000	0.111803
$81$	2.95902	0.328780
$82$	−3.51482	−0.388147
$83$	5.40805	0.593610	0.296805	−	0.954938i	$-0.404079\pi$
$83$	5.40805	0.593610	0.296805	+	0.954938i	$0.404079\pi$
$84$	0.215931	0.0235600
$85$	−6.26117	−0.679119
$86$	−1.65557	−0.178525
$87$	0.632290	0.0677886
$88$	−2.77504	−0.295821
$89$	7.15844	0.758793	0.379396	−	0.925234i	$-0.376132\pi$
$89$	7.15844	0.758793	0.379396	+	0.925234i	$0.376132\pi$
$90$	2.26949	0.239225
$91$	−0.252640	−0.0264838
$92$	−9.02997	−0.941440
$93$	0.854702	0.0886284
$94$	9.56736	0.986798
$95$	5.36352	0.550285
$96$	−0.854702	−0.0872326
$97$	4.06691	0.412933	0.206466	−	0.978454i	$-0.433804\pi$
$97$	4.06691	0.412933	0.206466	+	0.978454i	$0.433804\pi$
$98$	6.93617	0.700659
$99$	−6.29792	−0.632965
$100$	1.00000	0.100000
$101$	−2.18067	−0.216984	−0.108492	−	0.994097i	$-0.534602\pi$
$101$	−2.18067	−0.216984	−0.108492	+	0.994097i	$0.534602\pi$
$102$	5.35143	0.529871
$103$	−7.90552	−0.778954	−0.389477	−	0.921036i	$-0.627344\pi$
$103$	−7.90552	−0.778954	−0.389477	+	0.921036i	$0.627344\pi$
$104$	1.00000	0.0980581
$105$	0.215931	0.0210727
$106$	1.77672	0.172570
$107$	−1.52337	−0.147270	−0.0736351	−	0.997285i	$-0.523460\pi$
$107$	−1.52337	−0.147270	−0.0736351	+	0.997285i	$0.523460\pi$
$108$	−4.50384	−0.433382
$109$	5.03852	0.482603	0.241301	−	0.970450i	$-0.422426\pi$
$109$	5.03852	0.482603	0.241301	+	0.970450i	$0.422426\pi$
$110$	−2.77504	−0.264590
$111$	1.02913	0.0976803
$112$	0.252640	0.0238722
$113$	−14.0491	−1.32163	−0.660816	−	0.750548i	$-0.729790\pi$
$113$	−14.0491	−1.32163	−0.660816	+	0.750548i	$0.729790\pi$
$114$	−4.58421	−0.429350
$115$	−9.02997	−0.842049
$116$	0.739779	0.0686867
$117$	2.26949	0.209814
$118$	12.6832	1.16759
$119$	−1.58182	−0.145005
$120$	−0.854702	−0.0780232
$121$	−3.29913	−0.299921
$122$	2.52971	0.229029
$123$	3.00413	0.270873
$124$	1.00000	0.0898027
$125$	1.00000	0.0894427
$126$	0.573362	0.0510791
$127$	0.262036	0.0232520	0.0116260	−	0.999932i	$-0.496299\pi$
$127$	0.262036	0.0232520	0.0116260	+	0.999932i	$0.496299\pi$
$128$	−1.00000	−0.0883883
$129$	1.41502	0.124585
$130$	1.00000	0.0877058
$131$	−12.7270	−1.11197	−0.555984	−	0.831193i	$-0.687658\pi$
$131$	−12.7270	−1.11197	−0.555984	+	0.831193i	$0.687658\pi$
$132$	2.37184	0.206442
$133$	1.35504	0.117497
$134$	5.00327	0.432217
$135$	−4.50384	−0.387629
$136$	6.26117	0.536891
$137$	−18.0944	−1.54591	−0.772953	−	0.634463i	$-0.781221\pi$
$137$	−18.0944	−1.54591	−0.772953	+	0.634463i	$0.781221\pi$
$138$	7.71793	0.656994
$139$	−16.6218	−1.40984	−0.704920	−	0.709287i	$-0.749017\pi$
$139$	−16.6218	−1.40984	−0.704920	+	0.709287i	$0.749017\pi$
$140$	0.252640	0.0213519
$141$	−8.17724	−0.688648
$142$	−3.84638	−0.322781
$143$	−2.77504	−0.232061
$144$	−2.26949	−0.189124
$145$	0.739779	0.0614353
$146$	0.875580	0.0724635
$147$	−5.92836	−0.488963
$148$	1.20408	0.0989745
$149$	1.97714	0.161974	0.0809869	−	0.996715i	$-0.474193\pi$
$149$	1.97714	0.161974	0.0809869	+	0.996715i	$0.474193\pi$
$150$	−0.854702	−0.0697861
$151$	−20.3331	−1.65468	−0.827341	−	0.561700i	$-0.810148\pi$
$151$	−20.3331	−1.65468	−0.827341	+	0.561700i	$0.810148\pi$
$152$	−5.36352	−0.435039
$153$	14.2096	1.14878
$154$	−0.701086	−0.0564951
$155$	1.00000	0.0803219
$156$	−0.854702	−0.0684309
$157$	0.238194	0.0190100	0.00950498	−	0.999955i	$-0.496974\pi$
$157$	0.238194	0.0190100	0.00950498	+	0.999955i	$0.496974\pi$
$158$	−0.848461	−0.0674999
$159$	−1.51857	−0.120430
$160$	−1.00000	−0.0790569
$161$	−2.28133	−0.179794
$162$	−2.95902	−0.232482
$163$	21.4564	1.68060	0.840298	−	0.542125i	$-0.182380\pi$
$163$	21.4564	1.68060	0.840298	+	0.542125i	$0.182380\pi$
$164$	3.51482	0.274462
$165$	2.37184	0.184647
$166$	−5.40805	−0.419746
$167$	10.5973	0.820046	0.410023	−	0.912075i	$-0.365521\pi$
$167$	10.5973	0.820046	0.410023	+	0.912075i	$0.365521\pi$
$168$	−0.215931	−0.0166595
$169$	1.00000	0.0769231
$170$	6.26117	0.480210
$171$	−12.1724	−0.930849
$172$	1.65557	0.126236
$173$	−1.86070	−0.141466	−0.0707331	−	0.997495i	$-0.522534\pi$
$173$	−1.86070	−0.141466	−0.0707331	+	0.997495i	$0.522534\pi$
$174$	−0.632290	−0.0479338
$175$	0.252640	0.0190978
$176$	2.77504	0.209177
$177$	−10.8404	−0.814813
$178$	−7.15844	−0.536548
$179$	−12.8047	−0.957071	−0.478535	−	0.878068i	$-0.658832\pi$
$179$	−12.8047	−0.957071	−0.478535	+	0.878068i	$0.658832\pi$
$180$	−2.26949	−0.169157
$181$	24.9434	1.85403	0.927013	−	0.375030i	$-0.122368\pi$
$181$	24.9434	1.85403	0.927013	+	0.375030i	$0.122368\pi$
$182$	0.252640	0.0187269
$183$	−2.16214	−0.159830
$184$	9.02997	0.665698
$185$	1.20408	0.0885255
$186$	−0.854702	−0.0626698
$187$	−17.3750	−1.27059
$188$	−9.56736	−0.697772
$189$	−1.13785	−0.0827662
$190$	−5.36352	−0.389111
$191$	12.6009	0.911772	0.455886	−	0.890038i	$-0.349322\pi$
$191$	12.6009	0.911772	0.455886	+	0.890038i	$0.349322\pi$
$192$	0.854702	0.0616828
$193$	4.94213	0.355743	0.177871	−	0.984054i	$-0.443079\pi$
$193$	4.94213	0.355743	0.177871	+	0.984054i	$0.443079\pi$
$194$	−4.06691	−0.291987
$195$	−0.854702	−0.0612064
$196$	−6.93617	−0.495441
$197$	8.67326	0.617944	0.308972	−	0.951071i	$-0.400015\pi$
$197$	8.67326	0.617944	0.308972	+	0.951071i	$0.400015\pi$
$198$	6.29792	0.447574
$199$	−13.4685	−0.954755	−0.477378	−	0.878698i	$-0.658413\pi$
$199$	−13.4685	−0.954755	−0.477378	+	0.878698i	$0.658413\pi$
$200$	−1.00000	−0.0707107
$201$	−4.27630	−0.301627
$202$	2.18067	0.153431
$203$	0.186897	0.0131176
$204$	−5.35143	−0.374675
$205$	3.51482	0.245486
$206$	7.90552	0.550803
$207$	20.4934	1.42439
$208$	−1.00000	−0.0693375
$209$	14.8840	1.02955
$210$	−0.215931	−0.0149007
$211$	−14.5221	−0.999742	−0.499871	−	0.866100i	$-0.666619\pi$
$211$	−14.5221	−0.999742	−0.499871	+	0.866100i	$0.666619\pi$
$212$	−1.77672	−0.122026
$213$	3.28751	0.225257
$214$	1.52337	0.104136
$215$	1.65557	0.112909
$216$	4.50384	0.306447
$217$	0.252640	0.0171503
$218$	−5.03852	−0.341252
$219$	−0.748359	−0.0505694
$220$	2.77504	0.187093
$221$	6.26117	0.421172
$222$	−1.02913	−0.0690704
$223$	11.5556	0.773821	0.386910	−	0.922117i	$-0.373542\pi$
$223$	11.5556	0.773821	0.386910	+	0.922117i	$0.373542\pi$
$224$	−0.252640	−0.0168802
$225$	−2.26949	−0.151299
$226$	14.0491	0.934535
$227$	2.66505	0.176886	0.0884428	−	0.996081i	$-0.471811\pi$
$227$	2.66505	0.176886	0.0884428	+	0.996081i	$0.471811\pi$
$228$	4.58421	0.303597
$229$	0.496010	0.0327773	0.0163886	−	0.999866i	$-0.494783\pi$
$229$	0.496010	0.0327773	0.0163886	+	0.999866i	$0.494783\pi$
$230$	9.02997	0.595419
$231$	0.599219	0.0394257
$232$	−0.739779	−0.0485688
$233$	15.6475	1.02510	0.512550	−	0.858657i	$-0.328701\pi$
$233$	15.6475	1.02510	0.512550	+	0.858657i	$0.328701\pi$
$234$	−2.26949	−0.148361
$235$	−9.56736	−0.624106
$236$	−12.6832	−0.825608
$237$	0.725181	0.0471056
$238$	1.58182	0.102534
$239$	−12.1947	−0.788807	−0.394404	−	0.918937i	$-0.629049\pi$
$239$	−12.1947	−0.788807	−0.394404	+	0.918937i	$0.629049\pi$
$240$	0.854702	0.0551707
$241$	−6.42484	−0.413860	−0.206930	−	0.978356i	$-0.566347\pi$
$241$	−6.42484	−0.413860	−0.206930	+	0.978356i	$0.566347\pi$
$242$	3.29913	0.212076
$243$	16.0406	1.02900
$244$	−2.52971	−0.161948
$245$	−6.93617	−0.443136
$246$	−3.00413	−0.191536
$247$	−5.36352	−0.341272
$248$	−1.00000	−0.0635001
$249$	4.62227	0.292924
$250$	−1.00000	−0.0632456
$251$	7.15100	0.451367	0.225684	−	0.974201i	$-0.427538\pi$
$251$	7.15100	0.451367	0.225684	+	0.974201i	$0.427538\pi$
$252$	−0.573362	−0.0361184
$253$	−25.0586	−1.57542
$254$	−0.262036	−0.0164416
$255$	−5.35143	−0.335120
$256$	1.00000	0.0625000
$257$	−8.76447	−0.546713	−0.273356	−	0.961913i	$-0.588134\pi$
$257$	−8.76447	−0.546713	−0.273356	+	0.961913i	$0.588134\pi$
$258$	−1.41502	−0.0880951
$259$	0.304197	0.0189019
$260$	−1.00000	−0.0620174
$261$	−1.67892	−0.103922
$262$	12.7270	0.786280
$263$	7.02555	0.433214	0.216607	−	0.976259i	$-0.430501\pi$
$263$	7.02555	0.433214	0.216607	+	0.976259i	$0.430501\pi$
$264$	−2.37184	−0.145976
$265$	−1.77672	−0.109143
$266$	−1.35504	−0.0830826
$267$	6.11833	0.374436
$268$	−5.00327	−0.305623
$269$	−9.03180	−0.550678	−0.275339	−	0.961347i	$-0.588790\pi$
$269$	−9.03180	−0.550678	−0.275339	+	0.961347i	$0.588790\pi$
$270$	4.50384	0.274095
$271$	17.0654	1.03665	0.518326	−	0.855183i	$-0.326556\pi$
$271$	17.0654	1.03665	0.518326	+	0.855183i	$0.326556\pi$
$272$	−6.26117	−0.379639
$273$	−0.215931	−0.0130688
$274$	18.0944	1.09312
$275$	2.77504	0.167342
$276$	−7.71793	−0.464565
$277$	−8.29251	−0.498249	−0.249124	−	0.968471i	$-0.580143\pi$
$277$	−8.29251	−0.498249	−0.249124	+	0.968471i	$0.580143\pi$
$278$	16.6218	0.996907
$279$	−2.26949	−0.135871
$280$	−0.252640	−0.0150981
$281$	21.9638	1.31025	0.655126	−	0.755520i	$-0.272615\pi$
$281$	21.9638	1.31025	0.655126	+	0.755520i	$0.272615\pi$
$282$	8.17724	0.486947
$283$	−1.95901	−0.116451	−0.0582257	−	0.998303i	$-0.518544\pi$
$283$	−1.95901	−0.116451	−0.0582257	+	0.998303i	$0.518544\pi$
$284$	3.84638	0.228241
$285$	4.58421	0.271545
$286$	2.77504	0.164092
$287$	0.887983	0.0524160
$288$	2.26949	0.133731
$289$	22.2022	1.30601
$290$	−0.739779	−0.0434413
$291$	3.47600	0.203767
$292$	−0.875580	−0.0512394
$293$	−22.5800	−1.31914	−0.659569	−	0.751644i	$-0.729261\pi$
$293$	−22.5800	−1.31914	−0.659569	+	0.751644i	$0.729261\pi$
$294$	5.92836	0.345749
$295$	−12.6832	−0.738446
$296$	−1.20408	−0.0699855
$297$	−12.4984	−0.725228
$298$	−1.97714	−0.114533
$299$	9.02997	0.522217
$300$	0.854702	0.0493462
$301$	0.418262	0.0241082
$302$	20.3331	1.17004
$303$	−1.86382	−0.107074
$304$	5.36352	0.307619
$305$	−2.52971	−0.144851
$306$	−14.2096	−0.812310
$307$	−11.0615	−0.631315	−0.315657	−	0.948873i	$-0.602225\pi$
$307$	−11.0615	−0.631315	−0.315657	+	0.948873i	$0.602225\pi$
$308$	0.701086	0.0399481
$309$	−6.75686	−0.384384
$310$	−1.00000	−0.0567962
$311$	32.6276	1.85014	0.925071	−	0.379794i	$-0.124005\pi$
$311$	32.6276	1.85014	0.925071	+	0.379794i	$0.124005\pi$
$312$	0.854702	0.0483879
$313$	−8.85235	−0.500365	−0.250182	−	0.968199i	$-0.580491\pi$
$313$	−8.85235	−0.500365	−0.250182	+	0.968199i	$0.580491\pi$
$314$	−0.238194	−0.0134421
$315$	−0.573362	−0.0323053
$316$	0.848461	0.0477297
$317$	−21.1108	−1.18570	−0.592851	−	0.805312i	$-0.701998\pi$
$317$	−21.1108	−1.18570	−0.592851	+	0.805312i	$0.701998\pi$
$318$	1.51857	0.0851569
$319$	2.05292	0.114941
$320$	1.00000	0.0559017
$321$	−1.30203	−0.0726722
$322$	2.28133	0.127133
$323$	−33.5819	−1.86855
$324$	2.95902	0.164390
$325$	−1.00000	−0.0554700
$326$	−21.4564	−1.18836
$327$	4.30643	0.238146
$328$	−3.51482	−0.194074
$329$	−2.41709	−0.133259
$330$	−2.37184	−0.130565
$331$	1.76978	0.0972762	0.0486381	−	0.998816i	$-0.484512\pi$
$331$	1.76978	0.0972762	0.0486381	+	0.998816i	$0.484512\pi$
$332$	5.40805	0.296805
$333$	−2.73263	−0.149747
$334$	−10.5973	−0.579860
$335$	−5.00327	−0.273358
$336$	0.215931	0.0117800
$337$	−10.5361	−0.573938	−0.286969	−	0.957940i	$-0.592648\pi$
$337$	−10.5361	−0.573938	−0.286969	+	0.957940i	$0.592648\pi$
$338$	−1.00000	−0.0543928
$339$	−12.0078	−0.652175
$340$	−6.26117	−0.339560
$341$	2.77504	0.150277
$342$	12.1724	0.658209
$343$	−3.52083	−0.190107
$344$	−1.65557	−0.0892623
$345$	−7.71793	−0.415519
$346$	1.86070	0.100032
$347$	−17.1607	−0.921237	−0.460618	−	0.887598i	$-0.652372\pi$
$347$	−17.1607	−0.921237	−0.460618	+	0.887598i	$0.652372\pi$
$348$	0.632290	0.0338943
$349$	−6.91043	−0.369907	−0.184953	−	0.982747i	$-0.559213\pi$
$349$	−6.91043	−0.369907	−0.184953	+	0.982747i	$0.559213\pi$
$350$	−0.252640	−0.0135042
$351$	4.50384	0.240397
$352$	−2.77504	−0.147910
$353$	−7.32260	−0.389743	−0.194871	−	0.980829i	$-0.562429\pi$
$353$	−7.32260	−0.389743	−0.194871	+	0.980829i	$0.562429\pi$
$354$	10.8404	0.576160
$355$	3.84638	0.204145
$356$	7.15844	0.379396
$357$	−1.35198	−0.0715545
$358$	12.8047	0.676751
$359$	3.05654	0.161318	0.0806591	−	0.996742i	$-0.474297\pi$
$359$	3.05654	0.161318	0.0806591	+	0.996742i	$0.474297\pi$
$360$	2.26949	0.119612
$361$	9.76733	0.514070
$362$	−24.9434	−1.31099
$363$	−2.81977	−0.147999
$364$	−0.252640	−0.0132419
$365$	−0.875580	−0.0458299
$366$	2.16214	0.113017
$367$	−2.68234	−0.140017	−0.0700084	−	0.997546i	$-0.522303\pi$
$367$	−2.68234	−0.140017	−0.0700084	+	0.997546i	$0.522303\pi$
$368$	−9.02997	−0.470720
$369$	−7.97684	−0.415258
$370$	−1.20408	−0.0625970
$371$	−0.448870	−0.0233042
$372$	0.854702	0.0443142
$373$	10.3187	0.534280	0.267140	−	0.963658i	$-0.413921\pi$
$373$	10.3187	0.534280	0.267140	+	0.963658i	$0.413921\pi$
$374$	17.3750	0.898441
$375$	0.854702	0.0441366
$376$	9.56736	0.493399
$377$	−0.739779	−0.0381005
$378$	1.13785	0.0585246
$379$	−34.7305	−1.78399	−0.891993	−	0.452049i	$-0.850693\pi$
$379$	−34.7305	−1.78399	−0.891993	+	0.452049i	$0.850693\pi$
$380$	5.36352	0.275143
$381$	0.223963	0.0114740
$382$	−12.6009	−0.644720
$383$	−32.3820	−1.65464	−0.827321	−	0.561729i	$-0.810136\pi$
$383$	−32.3820	−1.65464	−0.827321	+	0.561729i	$0.810136\pi$
$384$	−0.854702	−0.0436163
$385$	0.701086	0.0357307
$386$	−4.94213	−0.251548
$387$	−3.75729	−0.190994
$388$	4.06691	0.206466
$389$	−15.9301	−0.807689	−0.403844	−	0.914828i	$-0.632326\pi$
$389$	−15.9301	−0.807689	−0.403844	+	0.914828i	$0.632326\pi$
$390$	0.854702	0.0432795
$391$	56.5382	2.85926
$392$	6.93617	0.350330
$393$	−10.8778	−0.548714
$394$	−8.67326	−0.436953
$395$	0.848461	0.0426907
$396$	−6.29792	−0.316483
$397$	−1.53874	−0.0772273	−0.0386137	−	0.999254i	$-0.512294\pi$
$397$	−1.53874	−0.0772273	−0.0386137	+	0.999254i	$0.512294\pi$
$398$	13.4685	0.675114
$399$	1.15815	0.0579801
$400$	1.00000	0.0500000
$401$	−6.80286	−0.339719	−0.169859	−	0.985468i	$-0.554331\pi$
$401$	−6.80286	−0.339719	−0.169859	+	0.985468i	$0.554331\pi$
$402$	4.27630	0.213283
$403$	−1.00000	−0.0498135
$404$	−2.18067	−0.108492
$405$	2.95902	0.147035
$406$	−0.186897	−0.00927556
$407$	3.34137	0.165625
$408$	5.35143	0.264935
$409$	4.05462	0.200488	0.100244	−	0.994963i	$-0.468038\pi$
$409$	4.05462	0.200488	0.100244	+	0.994963i	$0.468038\pi$
$410$	−3.51482	−0.173585
$411$	−15.4653	−0.762847
$412$	−7.90552	−0.389477
$413$	−3.20429	−0.157673
$414$	−20.4934	−1.00720
$415$	5.40805	0.265471
$416$	1.00000	0.0490290
$417$	−14.2066	−0.695702
$418$	−14.8840	−0.728000
$419$	7.06085	0.344945	0.172472	−	0.985014i	$-0.444824\pi$
$419$	7.06085	0.344945	0.172472	+	0.985014i	$0.444824\pi$
$420$	0.215931	0.0105364
$421$	−28.6585	−1.39673	−0.698366	−	0.715741i	$-0.746089\pi$
$421$	−28.6585	−1.39673	−0.698366	+	0.715741i	$0.746089\pi$
$422$	14.5221	0.706925
$423$	21.7130	1.05572
$424$	1.77672	0.0862852
$425$	−6.26117	−0.303711
$426$	−3.28751	−0.159280
$427$	−0.639104	−0.0309284
$428$	−1.52337	−0.0736351
$429$	−2.37184	−0.114513
$430$	−1.65557	−0.0798386
$431$	36.1851	1.74297	0.871487	−	0.490418i	$-0.163156\pi$
$431$	36.1851	1.74297	0.871487	+	0.490418i	$0.163156\pi$
$432$	−4.50384	−0.216691
$433$	17.6993	0.850573	0.425286	−	0.905059i	$-0.360173\pi$
$433$	17.6993	0.850573	0.425286	+	0.905059i	$0.360173\pi$
$434$	−0.252640	−0.0121271
$435$	0.632290	0.0303160
$436$	5.03852	0.241301
$437$	−48.4324	−2.31684
$438$	0.748359	0.0357580
$439$	5.07915	0.242415	0.121207	−	0.992627i	$-0.461323\pi$
$439$	5.07915	0.242415	0.121207	+	0.992627i	$0.461323\pi$
$440$	−2.77504	−0.132295
$441$	15.7415	0.749597
$442$	−6.26117	−0.297813
$443$	−4.62872	−0.219917	−0.109959	−	0.993936i	$-0.535072\pi$
$443$	−4.62872	−0.219917	−0.109959	+	0.993936i	$0.535072\pi$
$444$	1.02913	0.0488402
$445$	7.15844	0.339342
$446$	−11.5556	−0.547174
$447$	1.68987	0.0799280
$448$	0.252640	0.0119361
$449$	−39.0834	−1.84446	−0.922229	−	0.386643i	$-0.873634\pi$
$449$	−39.0834	−1.84446	−0.922229	+	0.386643i	$0.873634\pi$
$450$	2.26949	0.106985
$451$	9.75379	0.459288
$452$	−14.0491	−0.660816
$453$	−17.3787	−0.816523
$454$	−2.66505	−0.125077
$455$	−0.252640	−0.0118439
$456$	−4.58421	−0.214675
$457$	24.9193	1.16567	0.582837	−	0.812589i	$-0.301943\pi$
$457$	24.9193	1.16567	0.582837	+	0.812589i	$0.301943\pi$
$458$	−0.496010	−0.0231770
$459$	28.1993	1.31623
$460$	−9.02997	−0.421025
$461$	−21.0973	−0.982601	−0.491301	−	0.870990i	$-0.663478\pi$
$461$	−21.0973	−0.982601	−0.491301	+	0.870990i	$0.663478\pi$
$462$	−0.599219	−0.0278782
$463$	0.295245	0.0137212	0.00686061	−	0.999976i	$-0.497816\pi$
$463$	0.295245	0.0137212	0.00686061	+	0.999976i	$0.497816\pi$
$464$	0.739779	0.0343434
$465$	0.854702	0.0396358
$466$	−15.6475	−0.724855
$467$	14.4843	0.670255	0.335128	−	0.942173i	$-0.391221\pi$
$467$	14.4843	0.670255	0.335128	+	0.942173i	$0.391221\pi$
$468$	2.26949	0.104907
$469$	−1.26402	−0.0583672
$470$	9.56736	0.441309
$471$	0.203585	0.00938070
$472$	12.6832	0.583793
$473$	4.59428	0.211245
$474$	−0.725181	−0.0333087
$475$	5.36352	0.246095
$476$	−1.58182	−0.0725025
$477$	4.03224	0.184624
$478$	12.1947	0.557771
$479$	6.48163	0.296153	0.148077	−	0.988976i	$-0.452692\pi$
$479$	6.48163	0.296153	0.148077	+	0.988976i	$0.452692\pi$
$480$	−0.854702	−0.0390116
$481$	−1.20408	−0.0549012
$482$	6.42484	0.292643
$483$	−1.94985	−0.0887215
$484$	−3.29913	−0.149960
$485$	4.06691	0.184669
$486$	−16.0406	−0.727616
$487$	−33.2298	−1.50578	−0.752892	−	0.658144i	$-0.771342\pi$
$487$	−33.2298	−1.50578	−0.752892	+	0.658144i	$0.771342\pi$
$488$	2.52971	0.114514
$489$	18.3388	0.829310
$490$	6.93617	0.313344
$491$	24.1218	1.08860	0.544300	−	0.838890i	$-0.316795\pi$
$491$	24.1218	1.08860	0.544300	+	0.838890i	$0.316795\pi$
$492$	3.00413	0.135436
$493$	−4.63188	−0.208609
$494$	5.36352	0.241316
$495$	−6.29792	−0.283071
$496$	1.00000	0.0449013
$497$	0.971749	0.0435889
$498$	−4.62227	−0.207129
$499$	23.2895	1.04258	0.521291	−	0.853379i	$-0.325451\pi$
$499$	23.2895	1.04258	0.521291	+	0.853379i	$0.325451\pi$
$500$	1.00000	0.0447214
$501$	9.05756	0.404662
$502$	−7.15100	−0.319165
$503$	−21.4067	−0.954479	−0.477239	−	0.878773i	$-0.658363\pi$
$503$	−21.4067	−0.954479	−0.477239	+	0.878773i	$0.658363\pi$
$504$	0.573362	0.0255396
$505$	−2.18067	−0.0970383
$506$	25.0586	1.11399
$507$	0.854702	0.0379586
$508$	0.262036	0.0116260
$509$	−30.6898	−1.36030	−0.680151	−	0.733072i	$-0.738086\pi$
$509$	−30.6898	−1.36030	−0.680151	+	0.733072i	$0.738086\pi$
$510$	5.35143	0.236965
$511$	−0.221206	−0.00978558
$512$	−1.00000	−0.0441942
$513$	−24.1564	−1.06653
$514$	8.76447	0.386584
$515$	−7.90552	−0.348359
$516$	1.41502	0.0622927
$517$	−26.5499	−1.16766
$518$	−0.304197	−0.0133657
$519$	−1.59034	−0.0698082
$520$	1.00000	0.0438529
$521$	2.80638	0.122950	0.0614748	−	0.998109i	$-0.480420\pi$
$521$	2.80638	0.122950	0.0614748	+	0.998109i	$0.480420\pi$
$522$	1.67892	0.0734842
$523$	9.06829	0.396529	0.198264	−	0.980149i	$-0.436470\pi$
$523$	9.06829	0.396529	0.198264	+	0.980149i	$0.436470\pi$
$524$	−12.7270	−0.555984
$525$	0.215931	0.00942402
$526$	−7.02555	−0.306329
$527$	−6.26117	−0.272741
$528$	2.37184	0.103221
$529$	58.5404	2.54524
$530$	1.77672	0.0771758
$531$	28.7844	1.24914
$532$	1.35504	0.0587483
$533$	−3.51482	−0.152244
$534$	−6.11833	−0.264766
$535$	−1.52337	−0.0658612
$536$	5.00327	0.216108
$537$	−10.9442	−0.472278
$538$	9.03180	0.389388
$539$	−19.2482	−0.829078
$540$	−4.50384	−0.193814
$541$	−1.42948	−0.0614582	−0.0307291	−	0.999528i	$-0.509783\pi$
$541$	−1.42948	−0.0614582	−0.0307291	+	0.999528i	$0.509783\pi$
$542$	−17.0654	−0.733023
$543$	21.3191	0.914891
$544$	6.26117	0.268445
$545$	5.03852	0.215827
$546$	0.215931	0.00924101
$547$	−22.6017	−0.966379	−0.483189	−	0.875516i	$-0.660522\pi$
$547$	−22.6017	−0.966379	−0.483189	+	0.875516i	$0.660522\pi$
$548$	−18.0944	−0.772953
$549$	5.74113	0.245026
$550$	−2.77504	−0.118328
$551$	3.96782	0.169035
$552$	7.71793	0.328497
$553$	0.214355	0.00911530
$554$	8.29251	0.352315
$555$	1.02913	0.0436840
$556$	−16.6218	−0.704920
$557$	−43.9733	−1.86321	−0.931604	−	0.363475i	$-0.881590\pi$
$557$	−43.9733	−1.86321	−0.931604	+	0.363475i	$0.881590\pi$
$558$	2.26949	0.0960750
$559$	−1.65557	−0.0700231
$560$	0.252640	0.0106760
$561$	−14.8505	−0.626987
$562$	−21.9638	−0.926488
$563$	18.4947	0.779458	0.389729	−	0.920929i	$-0.372569\pi$
$563$	18.4947	0.779458	0.389729	+	0.920929i	$0.372569\pi$
$564$	−8.17724	−0.344324
$565$	−14.0491	−0.591052
$566$	1.95901	0.0823435
$567$	0.747565	0.0313948
$568$	−3.84638	−0.161391
$569$	6.67085	0.279657	0.139828	−	0.990176i	$-0.455345\pi$
$569$	6.67085	0.279657	0.139828	+	0.990176i	$0.455345\pi$
$570$	−4.58421	−0.192011
$571$	−34.9761	−1.46371	−0.731853	−	0.681463i	$-0.761344\pi$
$571$	−34.9761	−1.46371	−0.731853	+	0.681463i	$0.761344\pi$
$572$	−2.77504	−0.116030
$573$	10.7700	0.449925
$574$	−0.887983	−0.0370637
$575$	−9.02997	−0.376576
$576$	−2.26949	−0.0945619
$577$	8.60281	0.358140	0.179070	−	0.983836i	$-0.442691\pi$
$577$	8.60281	0.358140	0.179070	+	0.983836i	$0.442691\pi$
$578$	−22.2022	−0.923491
$579$	4.22405	0.175545
$580$	0.739779	0.0307176
$581$	1.36629	0.0566831
$582$	−3.47600	−0.144085
$583$	−4.93048	−0.204200
$584$	0.875580	0.0362318
$585$	2.26949	0.0938317
$586$	22.5800	0.932771
$587$	4.35616	0.179798	0.0898990	−	0.995951i	$-0.471346\pi$
$587$	4.35616	0.179798	0.0898990	+	0.995951i	$0.471346\pi$
$588$	−5.92836	−0.244481
$589$	5.36352	0.221000
$590$	12.6832	0.522160
$591$	7.41305	0.304932
$592$	1.20408	0.0494873
$593$	−20.1696	−0.828266	−0.414133	−	0.910216i	$-0.635915\pi$
$593$	−20.1696	−0.828266	−0.414133	+	0.910216i	$0.635915\pi$
$594$	12.4984	0.512814
$595$	−1.58182	−0.0648482
$596$	1.97714	0.0809869
$597$	−11.5115	−0.471136
$598$	−9.02997	−0.369263
$599$	6.00618	0.245406	0.122703	−	0.992443i	$-0.460844\pi$
$599$	6.00618	0.245406	0.122703	+	0.992443i	$0.460844\pi$
$600$	−0.854702	−0.0348930
$601$	−19.9028	−0.811852	−0.405926	−	0.913906i	$-0.633051\pi$
$601$	−19.9028	−0.811852	−0.405926	+	0.913906i	$0.633051\pi$
$602$	−0.418262	−0.0170471
$603$	11.3548	0.462405
$604$	−20.3331	−0.827341
$605$	−3.29913	−0.134129
$606$	1.86382	0.0757124
$607$	42.5166	1.72569	0.862847	−	0.505464i	$-0.168679\pi$
$607$	42.5166	1.72569	0.862847	+	0.505464i	$0.168679\pi$
$608$	−5.36352	−0.217519
$609$	0.159741	0.00647305
$610$	2.52971	0.102425
$611$	9.56736	0.387054
$612$	14.2096	0.574390
$613$	39.5840	1.59878	0.799392	−	0.600810i	$-0.205155\pi$
$613$	39.5840	1.59878	0.799392	+	0.600810i	$0.205155\pi$
$614$	11.0615	0.446407
$615$	3.00413	0.121138
$616$	−0.701086	−0.0282476
$617$	−21.7961	−0.877476	−0.438738	−	0.898615i	$-0.644574\pi$
$617$	−21.7961	−0.877476	−0.438738	+	0.898615i	$0.644574\pi$
$618$	6.75686	0.271801
$619$	−46.6157	−1.87364	−0.936822	−	0.349807i	$-0.886247\pi$
$619$	−46.6157	−1.87364	−0.936822	+	0.349807i	$0.886247\pi$
$620$	1.00000	0.0401610
$621$	40.6695	1.63201
$622$	−32.6276	−1.30825
$623$	1.80850	0.0724562
$624$	−0.854702	−0.0342154
$625$	1.00000	0.0400000
$626$	8.85235	0.353811
$627$	12.7214	0.508043
$628$	0.238194	0.00950498
$629$	−7.53893	−0.300597
$630$	0.573362	0.0228433
$631$	39.5637	1.57501	0.787503	−	0.616311i	$-0.211374\pi$
$631$	39.5637	1.57501	0.787503	+	0.616311i	$0.211374\pi$
$632$	−0.848461	−0.0337500
$633$	−12.4121	−0.493335
$634$	21.1108	0.838418
$635$	0.262036	0.0103986
$636$	−1.51857	−0.0602150
$637$	6.93617	0.274821
$638$	−2.05292	−0.0812758
$639$	−8.72931	−0.345326
$640$	−1.00000	−0.0395285
$641$	14.1301	0.558105	0.279052	−	0.960276i	$-0.409980\pi$
$641$	14.1301	0.558105	0.279052	+	0.960276i	$0.409980\pi$
$642$	1.30203	0.0513870
$643$	−3.82587	−0.150877	−0.0754387	−	0.997150i	$-0.524036\pi$
$643$	−3.82587	−0.150877	−0.0754387	+	0.997150i	$0.524036\pi$
$644$	−2.28133	−0.0898969
$645$	1.41502	0.0557162
$646$	33.5819	1.32126
$647$	−8.87700	−0.348991	−0.174495	−	0.984658i	$-0.555829\pi$
$647$	−8.87700	−0.348991	−0.174495	+	0.984658i	$0.555829\pi$
$648$	−2.95902	−0.116241
$649$	−35.1965	−1.38158
$650$	1.00000	0.0392232
$651$	0.215931	0.00846302
$652$	21.4564	0.840298
$653$	16.5237	0.646622	0.323311	−	0.946293i	$-0.395204\pi$
$653$	16.5237	0.646622	0.323311	+	0.946293i	$0.395204\pi$
$654$	−4.30643	−0.168395
$655$	−12.7270	−0.497287
$656$	3.51482	0.137231
$657$	1.98712	0.0775248
$658$	2.41709	0.0942281
$659$	−6.85037	−0.266853	−0.133426	−	0.991059i	$-0.542598\pi$
$659$	−6.85037	−0.266853	−0.133426	+	0.991059i	$0.542598\pi$
$660$	2.37184	0.0923236
$661$	−17.5542	−0.682781	−0.341391	−	0.939922i	$-0.610898\pi$
$661$	−17.5542	−0.682781	−0.341391	+	0.939922i	$0.610898\pi$
$662$	−1.76978	−0.0687846
$663$	5.35143	0.207832
$664$	−5.40805	−0.209873
$665$	1.35504	0.0525461
$666$	2.73263	0.105887
$667$	−6.68018	−0.258658
$668$	10.5973	0.410023
$669$	9.87660	0.381851
$670$	5.00327	0.193293
$671$	−7.02005	−0.271006
$672$	−0.215931	−0.00832973
$673$	11.0697	0.426706	0.213353	−	0.976975i	$-0.431561\pi$
$673$	11.0697	0.426706	0.213353	+	0.976975i	$0.431561\pi$
$674$	10.5361	0.405835
$675$	−4.50384	−0.173353
$676$	1.00000	0.0384615
$677$	−44.1992	−1.69871	−0.849357	−	0.527819i	$-0.823010\pi$
$677$	−44.1992	−1.69871	−0.849357	+	0.527819i	$0.823010\pi$
$678$	12.0078	0.461158
$679$	1.02746	0.0394304
$680$	6.26117	0.240105
$681$	2.27782	0.0872863
$682$	−2.77504	−0.106262
$683$	−2.35228	−0.0900076	−0.0450038	−	0.998987i	$-0.514330\pi$
$683$	−2.35228	−0.0900076	−0.0450038	+	0.998987i	$0.514330\pi$
$684$	−12.1724	−0.465424
$685$	−18.0944	−0.691351
$686$	3.52083	0.134426
$687$	0.423941	0.0161743
$688$	1.65557	0.0631180
$689$	1.77672	0.0676876
$690$	7.71793	0.293817
$691$	46.7565	1.77870	0.889350	−	0.457226i	$-0.151157\pi$
$691$	46.7565	1.77870	0.889350	+	0.457226i	$0.151157\pi$
$692$	−1.86070	−0.0707331
$693$	−1.59110	−0.0604411
$694$	17.1607	0.651413
$695$	−16.6218	−0.630499
$696$	−0.632290	−0.0239669
$697$	−22.0069	−0.833571
$698$	6.91043	0.261563
$699$	13.3739	0.505848
$700$	0.252640	0.00954888
$701$	−7.03422	−0.265679	−0.132839	−	0.991138i	$-0.542409\pi$
$701$	−7.03422	−0.265679	−0.132839	+	0.991138i	$0.542409\pi$
$702$	−4.50384	−0.169986
$703$	6.45809	0.243571
$704$	2.77504	0.104588
$705$	−8.17724	−0.307973
$706$	7.32260	0.275590
$707$	−0.550922	−0.0207196
$708$	−10.8404	−0.407406
$709$	−17.1974	−0.645862	−0.322931	−	0.946422i	$-0.604668\pi$
$709$	−17.1974	−0.645862	−0.322931	+	0.946422i	$0.604668\pi$
$710$	−3.84638	−0.144352
$711$	−1.92557	−0.0722145
$712$	−7.15844	−0.268274
$713$	−9.02997	−0.338175
$714$	1.35198	0.0505967
$715$	−2.77504	−0.103781
$716$	−12.8047	−0.478535
$717$	−10.4228	−0.389246
$718$	−3.05654	−0.114069
$719$	38.9665	1.45321	0.726603	−	0.687058i	$-0.241098\pi$
$719$	38.9665	1.45321	0.726603	+	0.687058i	$0.241098\pi$
$720$	−2.26949	−0.0845787
$721$	−1.99725	−0.0743813
$722$	−9.76733	−0.363502
$723$	−5.49132	−0.204224
$724$	24.9434	0.927013
$725$	0.739779	0.0274747
$726$	2.81977	0.104651
$727$	19.8734	0.737065	0.368533	−	0.929615i	$-0.379860\pi$
$727$	19.8734	0.737065	0.368533	+	0.929615i	$0.379860\pi$
$728$	0.252640	0.00936344
$729$	4.83286	0.178995
$730$	0.875580	0.0324067
$731$	−10.3658	−0.383393
$732$	−2.16214	−0.0799151
$733$	33.8880	1.25168	0.625842	−	0.779950i	$-0.284756\pi$
$733$	33.8880	1.25168	0.625842	+	0.779950i	$0.284756\pi$
$734$	2.68234	0.0990069
$735$	−5.92836	−0.218671
$736$	9.02997	0.332849
$737$	−13.8843	−0.511435
$738$	7.97684	0.293632
$739$	28.1132	1.03416	0.517080	−	0.855937i	$-0.327019\pi$
$739$	28.1132	1.03416	0.517080	+	0.855937i	$0.327019\pi$
$740$	1.20408	0.0442627
$741$	−4.58421	−0.168405
$742$	0.448870	0.0164785
$743$	10.6972	0.392443	0.196221	−	0.980560i	$-0.437133\pi$
$743$	10.6972	0.392443	0.196221	+	0.980560i	$0.437133\pi$
$744$	−0.854702	−0.0313349
$745$	1.97714	0.0724369
$746$	−10.3187	−0.377793
$747$	−12.2735	−0.449063
$748$	−17.3750	−0.635294
$749$	−0.384865	−0.0140626
$750$	−0.854702	−0.0312093
$751$	29.0571	1.06031	0.530154	−	0.847901i	$-0.322134\pi$
$751$	29.0571	1.06031	0.530154	+	0.847901i	$0.322134\pi$
$752$	−9.56736	−0.348886
$753$	6.11197	0.222733
$754$	0.739779	0.0269411
$755$	−20.3331	−0.739997
$756$	−1.13785	−0.0413831
$757$	28.0714	1.02027	0.510137	−	0.860093i	$-0.329595\pi$
$757$	28.0714	1.02027	0.510137	+	0.860093i	$0.329595\pi$
$758$	34.7305	1.26147
$759$	−21.4176	−0.777410
$760$	−5.36352	−0.194555
$761$	8.95723	0.324699	0.162350	−	0.986733i	$-0.448093\pi$
$761$	8.95723	0.324699	0.162350	+	0.986733i	$0.448093\pi$
$762$	−0.223963	−0.00811332
$763$	1.27293	0.0460832
$764$	12.6009	0.455886
$765$	14.2096	0.513750
$766$	32.3820	1.17001
$767$	12.6832	0.457965
$768$	0.854702	0.0308414
$769$	3.85590	0.139047	0.0695237	−	0.997580i	$-0.477852\pi$
$769$	3.85590	0.139047	0.0695237	+	0.997580i	$0.477852\pi$
$770$	−0.701086	−0.0252654
$771$	−7.49101	−0.269782
$772$	4.94213	0.177871
$773$	8.13682	0.292661	0.146331	−	0.989236i	$-0.453254\pi$
$773$	8.13682	0.292661	0.146331	+	0.989236i	$0.453254\pi$
$774$	3.75729	0.135053
$775$	1.00000	0.0359211
$776$	−4.06691	−0.145994
$777$	0.259998	0.00932738
$778$	15.9301	0.571122
$779$	18.8518	0.675437
$780$	−0.854702	−0.0306032
$781$	10.6739	0.381942
$782$	−56.5382	−2.02180
$783$	−3.33184	−0.119070
$784$	−6.93617	−0.247720
$785$	0.238194	0.00850152
$786$	10.8778	0.387999
$787$	−3.98152	−0.141926	−0.0709630	−	0.997479i	$-0.522607\pi$
$787$	−3.98152	−0.141926	−0.0709630	+	0.997479i	$0.522607\pi$
$788$	8.67326	0.308972
$789$	6.00475	0.213775
$790$	−0.848461	−0.0301869
$791$	−3.54937	−0.126201
$792$	6.29792	0.223787
$793$	2.52971	0.0898325
$794$	1.53874	0.0546080
$795$	−1.51857	−0.0538580
$796$	−13.4685	−0.477378
$797$	38.5512	1.36556	0.682778	−	0.730626i	$-0.260772\pi$
$797$	38.5512	1.36556	0.682778	+	0.730626i	$0.260772\pi$
$798$	−1.15815	−0.0409981
$799$	59.9029	2.11921
$800$	−1.00000	−0.0353553
$801$	−16.2460	−0.574023
$802$	6.80286	0.240217
$803$	−2.42977	−0.0857448
$804$	−4.27630	−0.150814
$805$	−2.28133	−0.0804063
$806$	1.00000	0.0352235
$807$	−7.71949	−0.271739
$808$	2.18067	0.0767155
$809$	30.6685	1.07825	0.539124	−	0.842226i	$-0.318755\pi$
$809$	30.6685	1.07825	0.539124	+	0.842226i	$0.318755\pi$
$810$	−2.95902	−0.103969
$811$	47.9016	1.68205	0.841026	−	0.540995i	$-0.181952\pi$
$811$	47.9016	1.68205	0.841026	+	0.540995i	$0.181952\pi$
$812$	0.186897	0.00655881
$813$	14.5858	0.511548
$814$	−3.34137	−0.117115
$815$	21.4564	0.751585
$816$	−5.35143	−0.187338
$817$	8.87967	0.310660
$818$	−4.05462	−0.141767
$819$	0.573362	0.0200349
$820$	3.51482	0.122743
$821$	44.3861	1.54908	0.774542	−	0.632522i	$-0.217980\pi$
$821$	44.3861	1.54908	0.774542	+	0.632522i	$0.217980\pi$
$822$	15.4653	0.539414
$823$	29.1950	1.01767	0.508836	−	0.860863i	$-0.330076\pi$
$823$	29.1950	1.01767	0.508836	+	0.860863i	$0.330076\pi$
$824$	7.90552	0.275402
$825$	2.37184	0.0825767
$826$	3.20429	0.111491
$827$	−27.1783	−0.945083	−0.472541	−	0.881308i	$-0.656663\pi$
$827$	−27.1783	−0.945083	−0.472541	+	0.881308i	$0.656663\pi$
$828$	20.4934	0.712195
$829$	6.67745	0.231917	0.115959	−	0.993254i	$-0.463006\pi$
$829$	6.67745	0.231917	0.115959	+	0.993254i	$0.463006\pi$
$830$	−5.40805	−0.187716
$831$	−7.08762	−0.245867
$832$	−1.00000	−0.0346688
$833$	43.4285	1.50471
$834$	14.2066	0.491936
$835$	10.5973	0.366736
$836$	14.8840	0.514774
$837$	−4.50384	−0.155675
$838$	−7.06085	−0.243913
$839$	38.2803	1.32158	0.660792	−	0.750569i	$-0.270220\pi$
$839$	38.2803	1.32158	0.660792	+	0.750569i	$0.270220\pi$
$840$	−0.215931	−0.00745034
$841$	−28.4527	−0.981129
$842$	28.6585	0.987639
$843$	18.7725	0.646560
$844$	−14.5221	−0.499871
$845$	1.00000	0.0344010
$846$	−21.7130	−0.746508
$847$	−0.833490	−0.0286390
$848$	−1.77672	−0.0610128
$849$	−1.67437	−0.0574643
$850$	6.26117	0.214756
$851$	−10.8728	−0.372714
$852$	3.28751	0.112628
$853$	18.8269	0.644619	0.322310	−	0.946634i	$-0.395541\pi$
$853$	18.8269	0.644619	0.322310	+	0.946634i	$0.395541\pi$
$854$	0.639104	0.0218697
$855$	−12.1724	−0.416288
$856$	1.52337	0.0520679
$857$	−8.56259	−0.292493	−0.146246	−	0.989248i	$-0.546719\pi$
$857$	−8.56259	−0.292493	−0.146246	+	0.989248i	$0.546719\pi$
$858$	2.37184	0.0809731
$859$	30.4453	1.03878	0.519390	−	0.854537i	$-0.326159\pi$
$859$	30.4453	1.03878	0.519390	+	0.854537i	$0.326159\pi$
$860$	1.65557	0.0564544
$861$	0.758961	0.0258653
$862$	−36.1851	−1.23247
$863$	27.6250	0.940366	0.470183	−	0.882569i	$-0.344188\pi$
$863$	27.6250	0.940366	0.470183	+	0.882569i	$0.344188\pi$
$864$	4.50384	0.153224
$865$	−1.86070	−0.0632656
$866$	−17.6993	−0.601446
$867$	18.9763	0.644468
$868$	0.252640	0.00857514
$869$	2.35452	0.0798716
$870$	−0.632290	−0.0214366
$871$	5.00327	0.169529
$872$	−5.03852	−0.170626
$873$	−9.22980	−0.312381
$874$	48.4324	1.63825
$875$	0.252640	0.00854078
$876$	−0.748359	−0.0252847
$877$	26.5109	0.895209	0.447605	−	0.894232i	$-0.352277\pi$
$877$	26.5109	0.895209	0.447605	+	0.894232i	$0.352277\pi$
$878$	−5.07915	−0.171413
$879$	−19.2992	−0.650944
$880$	2.77504	0.0935467
$881$	−54.0118	−1.81970	−0.909852	−	0.414934i	$-0.863805\pi$
$881$	−54.0118	−1.81970	−0.909852	+	0.414934i	$0.863805\pi$
$882$	−15.7415	−0.530045
$883$	39.0960	1.31569	0.657843	−	0.753155i	$-0.271469\pi$
$883$	39.0960	1.31569	0.657843	+	0.753155i	$0.271469\pi$
$884$	6.26117	0.210586
$885$	−10.8404	−0.364395
$886$	4.62872	0.155505
$887$	−35.1007	−1.17856	−0.589282	−	0.807927i	$-0.700589\pi$
$887$	−35.1007	−1.17856	−0.589282	+	0.807927i	$0.700589\pi$
$888$	−1.02913	−0.0345352
$889$	0.0662008	0.00222030
$890$	−7.15844	−0.239951
$891$	8.21141	0.275093
$892$	11.5556	0.386910
$893$	−51.3147	−1.71718
$894$	−1.68987	−0.0565176
$895$	−12.8047	−0.428015
$896$	−0.252640	−0.00844009
$897$	7.71793	0.257694
$898$	39.0834	1.30423
$899$	0.739779	0.0246730
$900$	−2.26949	−0.0756495
$901$	11.1243	0.370606
$902$	−9.75379	−0.324766
$903$	0.357489	0.0118965
$904$	14.0491	0.467267
$905$	24.9434	0.829145
$906$	17.3787	0.577369
$907$	38.1636	1.26720	0.633600	−	0.773661i	$-0.281576\pi$
$907$	38.1636	1.26720	0.633600	+	0.773661i	$0.281576\pi$
$908$	2.66505	0.0884428
$909$	4.94899	0.164148
$910$	0.252640	0.00837492
$911$	−39.0220	−1.29286	−0.646428	−	0.762975i	$-0.723738\pi$
$911$	−39.0220	−1.29286	−0.646428	+	0.762975i	$0.723738\pi$
$912$	4.58421	0.151798
$913$	15.0076	0.496678
$914$	−24.9193	−0.824256
$915$	−2.16214	−0.0714783
$916$	0.496010	0.0163886
$917$	−3.21536	−0.106180
$918$	−28.1993	−0.930715
$919$	53.5990	1.76807	0.884034	−	0.467423i	$-0.154817\pi$
$919$	53.5990	1.76807	0.884034	+	0.467423i	$0.154817\pi$
$920$	9.02997	0.297709
$921$	−9.45431	−0.311530
$922$	21.0973	0.694804
$923$	−3.84638	−0.126605
$924$	0.599219	0.0197129
$925$	1.20408	0.0395898
$926$	−0.295245	−0.00970237
$927$	17.9415	0.589275
$928$	−0.739779	−0.0242844
$929$	−6.26217	−0.205455	−0.102728	−	0.994710i	$-0.532757\pi$
$929$	−6.26217	−0.205455	−0.102728	+	0.994710i	$0.532757\pi$
$930$	−0.854702	−0.0280268
$931$	−37.2023	−1.21926
$932$	15.6475	0.512550
$933$	27.8869	0.912975
$934$	−14.4843	−0.473942
$935$	−17.3750	−0.568224
$936$	−2.26949	−0.0741804
$937$	−23.8631	−0.779574	−0.389787	−	0.920905i	$-0.627451\pi$
$937$	−23.8631	−0.779574	−0.389787	+	0.920905i	$0.627451\pi$
$938$	1.26402	0.0412718
$939$	−7.56612	−0.246911
$940$	−9.56736	−0.312053
$941$	1.21153	0.0394948	0.0197474	−	0.999805i	$-0.493714\pi$
$941$	1.21153	0.0394948	0.0197474	+	0.999805i	$0.493714\pi$
$942$	−0.203585	−0.00663316
$943$	−31.7388	−1.03356
$944$	−12.6832	−0.412804
$945$	−1.13785	−0.0370142
$946$	−4.59428	−0.149373
$947$	8.09640	0.263098	0.131549	−	0.991310i	$-0.458005\pi$
$947$	8.09640	0.263098	0.131549	+	0.991310i	$0.458005\pi$
$948$	0.725181	0.0235528
$949$	0.875580	0.0284225
$950$	−5.36352	−0.174016
$951$	−18.0435	−0.585099
$952$	1.58182	0.0512670
$953$	−16.8558	−0.546014	−0.273007	−	0.962012i	$-0.588018\pi$
$953$	−16.8558	−0.546014	−0.273007	+	0.962012i	$0.588018\pi$
$954$	−4.03224	−0.130549
$955$	12.6009	0.407757
$956$	−12.1947	−0.394404
$957$	1.75463	0.0567192
$958$	−6.48163	−0.209412
$959$	−4.57136	−0.147617
$960$	0.854702	0.0275854
$961$	1.00000	0.0322581
$962$	1.20408	0.0388210
$963$	3.45727	0.111409
$964$	−6.42484	−0.206930
$965$	4.94213	0.159093
$966$	1.94985	0.0627355
$967$	−38.9978	−1.25408	−0.627042	−	0.778986i	$-0.715735\pi$
$967$	−38.9978	−1.25408	−0.627042	+	0.778986i	$0.715735\pi$
$968$	3.29913	0.106038
$969$	−28.7025	−0.922057
$970$	−4.06691	−0.130581
$971$	−6.60936	−0.212105	−0.106052	−	0.994361i	$-0.533821\pi$
$971$	−6.60936	−0.212105	−0.106052	+	0.994361i	$0.533821\pi$
$972$	16.0406	0.514502
$973$	−4.19931	−0.134624
$974$	33.2298	1.06475
$975$	−0.854702	−0.0273724
$976$	−2.52971	−0.0809739
$977$	38.0147	1.21620	0.608098	−	0.793862i	$-0.291933\pi$
$977$	38.0147	1.21620	0.608098	+	0.793862i	$0.291933\pi$
$978$	−18.3388	−0.586411
$979$	19.8650	0.634888
$980$	−6.93617	−0.221568
$981$	−11.4349	−0.365087
$982$	−24.1218	−0.769757
$983$	−6.48566	−0.206860	−0.103430	−	0.994637i	$-0.532982\pi$
$983$	−6.48566	−0.206860	−0.103430	+	0.994637i	$0.532982\pi$
$984$	−3.00413	−0.0957680
$985$	8.67326	0.276353
$986$	4.63188	0.147509
$987$	−2.06589	−0.0657581
$988$	−5.36352	−0.170636
$989$	−14.9497	−0.475374
$990$	6.29792	0.200161
$991$	0.0571247	0.00181463	0.000907313	−	1.00000i	$-0.499711\pi$
$991$	0.0571247	0.00181463	0.000907313		1.00000i	$0.499711\pi$
$992$	−1.00000	−0.0317500
$993$	1.51264	0.0480021
$994$	−0.971749	−0.0308220
$995$	−13.4685	−0.426979
$996$	4.62227	0.146462
$997$	−16.3608	−0.518153	−0.259076	−	0.965857i	$-0.583418\pi$
$997$	−16.3608	−0.518153	−0.259076	+	0.965857i	$0.583418\pi$
$998$	−23.2895	−0.737216
$999$	−5.42297	−0.171575

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.h.1.6	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.h.1.6	✓	7	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.854702 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.854702 q^{6} +0.252640 q^{7} -1.00000 q^{8} -2.26949 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.854702 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.854702 q^{6} +0.252640 q^{7} -1.00000 q^{8} -2.26949 q^{9} -1.00000 q^{10} +2.77504 q^{11} +0.854702 q^{12} -1.00000 q^{13} -0.252640 q^{14} +0.854702 q^{15} +1.00000 q^{16} -6.26117 q^{17} +2.26949 q^{18} +5.36352 q^{19} +1.00000 q^{20} +0.215931 q^{21} -2.77504 q^{22} -9.02997 q^{23} -0.854702 q^{24} +1.00000 q^{25} +1.00000 q^{26} -4.50384 q^{27} +0.252640 q^{28} +0.739779 q^{29} -0.854702 q^{30} +1.00000 q^{31} -1.00000 q^{32} +2.37184 q^{33} +6.26117 q^{34} +0.252640 q^{35} -2.26949 q^{36} +1.20408 q^{37} -5.36352 q^{38} -0.854702 q^{39} -1.00000 q^{40} +3.51482 q^{41} -0.215931 q^{42} +1.65557 q^{43} +2.77504 q^{44} -2.26949 q^{45} +9.02997 q^{46} -9.56736 q^{47} +0.854702 q^{48} -6.93617 q^{49} -1.00000 q^{50} -5.35143 q^{51} -1.00000 q^{52} -1.77672 q^{53} +4.50384 q^{54} +2.77504 q^{55} -0.252640 q^{56} +4.58421 q^{57} -0.739779 q^{58} -12.6832 q^{59} +0.854702 q^{60} -2.52971 q^{61} -1.00000 q^{62} -0.573362 q^{63} +1.00000 q^{64} -1.00000 q^{65} -2.37184 q^{66} -5.00327 q^{67} -6.26117 q^{68} -7.71793 q^{69} -0.252640 q^{70} +3.84638 q^{71} +2.26949 q^{72} -0.875580 q^{73} -1.20408 q^{74} +0.854702 q^{75} +5.36352 q^{76} +0.701086 q^{77} +0.854702 q^{78} +0.848461 q^{79} +1.00000 q^{80} +2.95902 q^{81} -3.51482 q^{82} +5.40805 q^{83} +0.215931 q^{84} -6.26117 q^{85} -1.65557 q^{86} +0.632290 q^{87} -2.77504 q^{88} +7.15844 q^{89} +2.26949 q^{90} -0.252640 q^{91} -9.02997 q^{92} +0.854702 q^{93} +9.56736 q^{94} +5.36352 q^{95} -0.854702 q^{96} +4.06691 q^{97} +6.93617 q^{98} -6.29792 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + q^{6} - 4 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - q^3 + 7 * q^4 + 7 * q^5 + q^6 - 4 * q^7 - 7 * q^8 + 4 * q^9	\( 7 q - 7 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + q^{6} - 4 q^{7} - 7 q^{8} + 4 q^{9} - 7 q^{10} - 2 q^{11} - q^{12} - 7 q^{13} + 4 q^{14} - q^{15} + 7 q^{16} - 8 q^{17} - 4 q^{18} + q^{19} + 7 q^{20} - 11 q^{21} + 2 q^{22} - 5 q^{23} + q^{24} + 7 q^{25} + 7 q^{26} - q^{27} - 4 q^{28} - 4 q^{29} + q^{30} + 7 q^{31} - 7 q^{32} - 4 q^{33} + 8 q^{34} - 4 q^{35} + 4 q^{36} - 2 q^{37} - q^{38} + q^{39} - 7 q^{40} - 6 q^{41} + 11 q^{42} - 5 q^{43} - 2 q^{44} + 4 q^{45} + 5 q^{46} - 18 q^{47} - q^{48} - 9 q^{49} - 7 q^{50} - q^{51} - 7 q^{52} - 12 q^{53} + q^{54} - 2 q^{55} + 4 q^{56} - 31 q^{57} + 4 q^{58} + 3 q^{59} - q^{60} - 7 q^{61} - 7 q^{62} - 19 q^{63} + 7 q^{64} - 7 q^{65} + 4 q^{66} + 6 q^{67} - 8 q^{68} - 10 q^{69} + 4 q^{70} + 4 q^{71} - 4 q^{72} - 31 q^{73} + 2 q^{74} - q^{75} + q^{76} - 25 q^{77} - q^{78} - 2 q^{79} + 7 q^{80} + 31 q^{81} + 6 q^{82} - 40 q^{83} - 11 q^{84} - 8 q^{85} + 5 q^{86} - 5 q^{87} + 2 q^{88} - 4 q^{90} + 4 q^{91} - 5 q^{92} - q^{93} + 18 q^{94} + q^{95} + q^{96} - 21 q^{97} + 9 q^{98} - 23 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - q^3 + 7 * q^4 + 7 * q^5 + q^6 - 4 * q^7 - 7 * q^8 + 4 * q^9 - 7 * q^10 - 2 * q^11 - q^12 - 7 * q^13 + 4 * q^14 - q^15 + 7 * q^16 - 8 * q^17 - 4 * q^18 + q^19 + 7 * q^20 - 11 * q^21 + 2 * q^22 - 5 * q^23 + q^24 + 7 * q^25 + 7 * q^26 - q^27 - 4 * q^28 - 4 * q^29 + q^30 + 7 * q^31 - 7 * q^32 - 4 * q^33 + 8 * q^34 - 4 * q^35 + 4 * q^36 - 2 * q^37 - q^38 + q^39 - 7 * q^40 - 6 * q^41 + 11 * q^42 - 5 * q^43 - 2 * q^44 + 4 * q^45 + 5 * q^46 - 18 * q^47 - q^48 - 9 * q^49 - 7 * q^50 - q^51 - 7 * q^52 - 12 * q^53 + q^54 - 2 * q^55 + 4 * q^56 - 31 * q^57 + 4 * q^58 + 3 * q^59 - q^60 - 7 * q^61 - 7 * q^62 - 19 * q^63 + 7 * q^64 - 7 * q^65 + 4 * q^66 + 6 * q^67 - 8 * q^68 - 10 * q^69 + 4 * q^70 + 4 * q^71 - 4 * q^72 - 31 * q^73 + 2 * q^74 - q^75 + q^76 - 25 * q^77 - q^78 - 2 * q^79 + 7 * q^80 + 31 * q^81 + 6 * q^82 - 40 * q^83 - 11 * q^84 - 8 * q^85 + 5 * q^86 - 5 * q^87 + 2 * q^88 - 4 * q^90 + 4 * q^91 - 5 * q^92 - q^93 + 18 * q^94 + q^95 + q^96 - 21 * q^97 + 9 * q^98 - 23 * q^99

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