LMFDB - Embedded newform 4030.2.a.k.1.7

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:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 18x^{6} + 12x^{5} + 98x^{4} - 18x^{3} - 173x^{2} - 48x + 32 $ x^8 - x^7 - 18x^6 + 12x^5 + 98x^4 - 18x^3 - 173x^2 - 48x + 32
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-1.98236$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.98236 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.98236 q^{6} +4.72598 q^{7} -1.00000 q^{8} +0.929744 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.98236 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.98236 q^{6} +4.72598 q^{7} -1.00000 q^{8} +0.929744 q^{9} +1.00000 q^{10} +5.18344 q^{11} +1.98236 q^{12} +1.00000 q^{13} -4.72598 q^{14} -1.98236 q^{15} +1.00000 q^{16} -0.225211 q^{17} -0.929744 q^{18} -5.61381 q^{19} -1.00000 q^{20} +9.36858 q^{21} -5.18344 q^{22} +7.15213 q^{23} -1.98236 q^{24} +1.00000 q^{25} -1.00000 q^{26} -4.10399 q^{27} +4.72598 q^{28} -6.80713 q^{29} +1.98236 q^{30} -1.00000 q^{31} -1.00000 q^{32} +10.2754 q^{33} +0.225211 q^{34} -4.72598 q^{35} +0.929744 q^{36} +7.00493 q^{37} +5.61381 q^{38} +1.98236 q^{39} +1.00000 q^{40} +8.16637 q^{41} -9.36858 q^{42} +1.31690 q^{43} +5.18344 q^{44} -0.929744 q^{45} -7.15213 q^{46} +6.13475 q^{47} +1.98236 q^{48} +15.3349 q^{49} -1.00000 q^{50} -0.446450 q^{51} +1.00000 q^{52} +8.49373 q^{53} +4.10399 q^{54} -5.18344 q^{55} -4.72598 q^{56} -11.1286 q^{57} +6.80713 q^{58} -0.602959 q^{59} -1.98236 q^{60} -9.42007 q^{61} +1.00000 q^{62} +4.39395 q^{63} +1.00000 q^{64} -1.00000 q^{65} -10.2754 q^{66} -15.5252 q^{67} -0.225211 q^{68} +14.1781 q^{69} +4.72598 q^{70} +0.727530 q^{71} -0.929744 q^{72} +2.54412 q^{73} -7.00493 q^{74} +1.98236 q^{75} -5.61381 q^{76} +24.4968 q^{77} -1.98236 q^{78} +13.4684 q^{79} -1.00000 q^{80} -10.9248 q^{81} -8.16637 q^{82} +15.4899 q^{83} +9.36858 q^{84} +0.225211 q^{85} -1.31690 q^{86} -13.4942 q^{87} -5.18344 q^{88} -5.08865 q^{89} +0.929744 q^{90} +4.72598 q^{91} +7.15213 q^{92} -1.98236 q^{93} -6.13475 q^{94} +5.61381 q^{95} -1.98236 q^{96} -15.6360 q^{97} -15.3349 q^{98} +4.81927 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - q^{3} + 8 q^{4} - 8 q^{5} + q^{6} - 8 q^{7} - 8 q^{8} + 13 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - q^3 + 8 * q^4 - 8 * q^5 + q^6 - 8 * q^7 - 8 * q^8 + 13 * q^9	\( 8 q - 8 q^{2} - q^{3} + 8 q^{4} - 8 q^{5} + q^{6} - 8 q^{7} - 8 q^{8} + 13 q^{9} + 8 q^{10} + 12 q^{11} - q^{12} + 8 q^{13} + 8 q^{14} + q^{15} + 8 q^{16} - 13 q^{18} - 3 q^{19} - 8 q^{20} + 27 q^{21} - 12 q^{22} + 17 q^{23} + q^{24} + 8 q^{25} - 8 q^{26} - 13 q^{27} - 8 q^{28} - 10 q^{29} - q^{30} - 8 q^{31} - 8 q^{32} + 4 q^{33} + 8 q^{35} + 13 q^{36} + 2 q^{37} + 3 q^{38} - q^{39} + 8 q^{40} + 14 q^{41} - 27 q^{42} - 19 q^{43} + 12 q^{44} - 13 q^{45} - 17 q^{46} + 8 q^{47} - q^{48} + 16 q^{49} - 8 q^{50} + 35 q^{51} + 8 q^{52} + 4 q^{53} + 13 q^{54} - 12 q^{55} + 8 q^{56} - 33 q^{57} + 10 q^{58} - 13 q^{59} + q^{60} + 11 q^{61} + 8 q^{62} - 27 q^{63} + 8 q^{64} - 8 q^{65} - 4 q^{66} - 34 q^{67} + 12 q^{69} - 8 q^{70} + 8 q^{71} - 13 q^{72} - 21 q^{73} - 2 q^{74} - q^{75} - 3 q^{76} + 19 q^{77} + q^{78} - 36 q^{79} - 8 q^{80} + 20 q^{81} - 14 q^{82} + 27 q^{84} + 19 q^{86} - 29 q^{87} - 12 q^{88} - 16 q^{89} + 13 q^{90} - 8 q^{91} + 17 q^{92} + q^{93} - 8 q^{94} + 3 q^{95} + q^{96} + q^{97} - 16 q^{98} + 65 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - q^3 + 8 * q^4 - 8 * q^5 + q^6 - 8 * q^7 - 8 * q^8 + 13 * q^9 + 8 * q^10 + 12 * q^11 - q^12 + 8 * q^13 + 8 * q^14 + q^15 + 8 * q^16 - 13 * q^18 - 3 * q^19 - 8 * q^20 + 27 * q^21 - 12 * q^22 + 17 * q^23 + q^24 + 8 * q^25 - 8 * q^26 - 13 * q^27 - 8 * q^28 - 10 * q^29 - q^30 - 8 * q^31 - 8 * q^32 + 4 * q^33 + 8 * q^35 + 13 * q^36 + 2 * q^37 + 3 * q^38 - q^39 + 8 * q^40 + 14 * q^41 - 27 * q^42 - 19 * q^43 + 12 * q^44 - 13 * q^45 - 17 * q^46 + 8 * q^47 - q^48 + 16 * q^49 - 8 * q^50 + 35 * q^51 + 8 * q^52 + 4 * q^53 + 13 * q^54 - 12 * q^55 + 8 * q^56 - 33 * q^57 + 10 * q^58 - 13 * q^59 + q^60 + 11 * q^61 + 8 * q^62 - 27 * q^63 + 8 * q^64 - 8 * q^65 - 4 * q^66 - 34 * q^67 + 12 * q^69 - 8 * q^70 + 8 * q^71 - 13 * q^72 - 21 * q^73 - 2 * q^74 - q^75 - 3 * q^76 + 19 * q^77 + q^78 - 36 * q^79 - 8 * q^80 + 20 * q^81 - 14 * q^82 + 27 * q^84 + 19 * q^86 - 29 * q^87 - 12 * q^88 - 16 * q^89 + 13 * q^90 - 8 * q^91 + 17 * q^92 + q^93 - 8 * q^94 + 3 * q^95 + q^96 + q^97 - 16 * q^98 + 65 * 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
$3$	1.98236	1.14451	0.572257	−	0.820074i	$-0.306068\pi$
$3$	1.98236	1.14451	0.572257	+	0.820074i	$0.306068\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.98236	−0.809294
$7$	4.72598	1.78625	0.893126	−	0.449806i	$-0.148507\pi$
$7$	4.72598	1.78625	0.893126	+	0.449806i	$0.148507\pi$
$8$	−1.00000	−0.353553
$9$	0.929744	0.309915
$10$	1.00000	0.316228
$11$	5.18344	1.56287	0.781433	−	0.623989i	$-0.214489\pi$
$11$	5.18344	1.56287	0.781433	+	0.623989i	$0.214489\pi$
$12$	1.98236	0.572257
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−4.72598	−1.26307
$15$	−1.98236	−0.511843
$16$	1.00000	0.250000
$17$	−0.225211	−0.0546218	−0.0273109	−	0.999627i	$-0.508694\pi$
$17$	−0.225211	−0.0546218	−0.0273109	+	0.999627i	$0.508694\pi$
$18$	−0.929744	−0.219143
$19$	−5.61381	−1.28790	−0.643948	−	0.765070i	$-0.722705\pi$
$19$	−5.61381	−1.28790	−0.643948	+	0.765070i	$0.722705\pi$
$20$	−1.00000	−0.223607
$21$	9.36858	2.04439
$22$	−5.18344	−1.10511
$23$	7.15213	1.49132	0.745661	−	0.666325i	$-0.232134\pi$
$23$	7.15213	1.49132	0.745661	+	0.666325i	$0.232134\pi$
$24$	−1.98236	−0.404647
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	−4.10399	−0.789813
$28$	4.72598	0.893126
$29$	−6.80713	−1.26405	−0.632026	−	0.774947i	$-0.717777\pi$
$29$	−6.80713	−1.26405	−0.632026	+	0.774947i	$0.717777\pi$
$30$	1.98236	0.361927
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	10.2754	1.78872
$34$	0.225211	0.0386234
$35$	−4.72598	−0.798836
$36$	0.929744	0.154957
$37$	7.00493	1.15160	0.575802	−	0.817589i	$-0.304690\pi$
$37$	7.00493	1.15160	0.575802	+	0.817589i	$0.304690\pi$
$38$	5.61381	0.910679
$39$	1.98236	0.317431
$40$	1.00000	0.158114
$41$	8.16637	1.27537	0.637686	−	0.770296i	$-0.279892\pi$
$41$	8.16637	1.27537	0.637686	+	0.770296i	$0.279892\pi$
$42$	−9.36858	−1.44560
$43$	1.31690	0.200826	0.100413	−	0.994946i	$-0.467984\pi$
$43$	1.31690	0.200826	0.100413	+	0.994946i	$0.467984\pi$
$44$	5.18344	0.781433
$45$	−0.929744	−0.138598
$46$	−7.15213	−1.05452
$47$	6.13475	0.894845	0.447423	−	0.894323i	$-0.352342\pi$
$47$	6.13475	0.894845	0.447423	+	0.894323i	$0.352342\pi$
$48$	1.98236	0.286129
$49$	15.3349	2.19070
$50$	−1.00000	−0.141421
$51$	−0.446450	−0.0625154
$52$	1.00000	0.138675
$53$	8.49373	1.16670	0.583352	−	0.812220i	$-0.301741\pi$
$53$	8.49373	1.16670	0.583352	+	0.812220i	$0.301741\pi$
$54$	4.10399	0.558482
$55$	−5.18344	−0.698935
$56$	−4.72598	−0.631536
$57$	−11.1286	−1.47402
$58$	6.80713	0.893820
$59$	−0.602959	−0.0784986	−0.0392493	−	0.999229i	$-0.512497\pi$
$59$	−0.602959	−0.0784986	−0.0392493	+	0.999229i	$0.512497\pi$
$60$	−1.98236	−0.255921
$61$	−9.42007	−1.20612	−0.603058	−	0.797697i	$-0.706051\pi$
$61$	−9.42007	−1.20612	−0.603058	+	0.797697i	$0.706051\pi$
$62$	1.00000	0.127000
$63$	4.39395	0.553586
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	−10.2754	−1.26482
$67$	−15.5252	−1.89670	−0.948352	−	0.317221i	$-0.897250\pi$
$67$	−15.5252	−1.89670	−0.948352	+	0.317221i	$0.897250\pi$
$68$	−0.225211	−0.0273109
$69$	14.1781	1.70684
$70$	4.72598	0.564863
$71$	0.727530	0.0863419	0.0431710	−	0.999068i	$-0.486254\pi$
$71$	0.727530	0.0863419	0.0431710	+	0.999068i	$0.486254\pi$
$72$	−0.929744	−0.109571
$73$	2.54412	0.297766	0.148883	−	0.988855i	$-0.452432\pi$
$73$	2.54412	0.297766	0.148883	+	0.988855i	$0.452432\pi$
$74$	−7.00493	−0.814307
$75$	1.98236	0.228903
$76$	−5.61381	−0.643948
$77$	24.4968	2.79167
$78$	−1.98236	−0.224458
$79$	13.4684	1.51531	0.757654	−	0.652656i	$-0.226345\pi$
$79$	13.4684	1.51531	0.757654	+	0.652656i	$0.226345\pi$
$80$	−1.00000	−0.111803
$81$	−10.9248	−1.21387
$82$	−8.16637	−0.901825
$83$	15.4899	1.70024	0.850119	−	0.526591i	$-0.176530\pi$
$83$	15.4899	1.70024	0.850119	+	0.526591i	$0.176530\pi$
$84$	9.36858	1.02220
$85$	0.225211	0.0244276
$86$	−1.31690	−0.142005
$87$	−13.4942	−1.44673
$88$	−5.18344	−0.552557
$89$	−5.08865	−0.539396	−0.269698	−	0.962945i	$-0.586924\pi$
$89$	−5.08865	−0.539396	−0.269698	+	0.962945i	$0.586924\pi$
$90$	0.929744	0.0980036
$91$	4.72598	0.495417
$92$	7.15213	0.745661
$93$	−1.98236	−0.205561
$94$	−6.13475	−0.632751
$95$	5.61381	0.575964
$96$	−1.98236	−0.202324
$97$	−15.6360	−1.58759	−0.793796	−	0.608184i	$-0.791898\pi$
$97$	−15.6360	−1.58759	−0.793796	+	0.608184i	$0.791898\pi$
$98$	−15.3349	−1.54906
$99$	4.81927	0.484355
$100$	1.00000	0.100000
$101$	−8.47951	−0.843743	−0.421872	−	0.906656i	$-0.638627\pi$
$101$	−8.47951	−0.843743	−0.421872	+	0.906656i	$0.638627\pi$
$102$	0.446450	0.0442051
$103$	−8.49788	−0.837321	−0.418660	−	0.908143i	$-0.637500\pi$
$103$	−8.49788	−0.837321	−0.418660	+	0.908143i	$0.637500\pi$
$104$	−1.00000	−0.0980581
$105$	−9.36858	−0.914280
$106$	−8.49373	−0.824984
$107$	5.46241	0.528071	0.264036	−	0.964513i	$-0.414946\pi$
$107$	5.46241	0.528071	0.264036	+	0.964513i	$0.414946\pi$
$108$	−4.10399	−0.394907
$109$	−16.2855	−1.55987	−0.779934	−	0.625862i	$-0.784747\pi$
$109$	−16.2855	−1.55987	−0.779934	+	0.625862i	$0.784747\pi$
$110$	5.18344	0.494222
$111$	13.8863	1.31803
$112$	4.72598	0.446563
$113$	−5.64814	−0.531332	−0.265666	−	0.964065i	$-0.585592\pi$
$113$	−5.64814	−0.531332	−0.265666	+	0.964065i	$0.585592\pi$
$114$	11.1286	1.04229
$115$	−7.15213	−0.666940
$116$	−6.80713	−0.632026
$117$	0.929744	0.0859548
$118$	0.602959	0.0555069
$119$	−1.06434	−0.0975683
$120$	1.98236	0.180964
$121$	15.8681	1.44255
$122$	9.42007	0.852853
$123$	16.1887	1.45968
$124$	−1.00000	−0.0898027
$125$	−1.00000	−0.0894427
$126$	−4.39395	−0.391444
$127$	−2.90379	−0.257669	−0.128835	−	0.991666i	$-0.541124\pi$
$127$	−2.90379	−0.257669	−0.128835	+	0.991666i	$0.541124\pi$
$128$	−1.00000	−0.0883883
$129$	2.61057	0.229848
$130$	1.00000	0.0877058
$131$	−2.89987	−0.253363	−0.126681	−	0.991943i	$-0.540433\pi$
$131$	−2.89987	−0.253363	−0.126681	+	0.991943i	$0.540433\pi$
$132$	10.2754	0.894362
$133$	−26.5307	−2.30051
$134$	15.5252	1.34117
$135$	4.10399	0.353215
$136$	0.225211	0.0193117
$137$	−11.3322	−0.968173	−0.484086	−	0.875020i	$-0.660848\pi$
$137$	−11.3322	−0.968173	−0.484086	+	0.875020i	$0.660848\pi$
$138$	−14.1781	−1.20692
$139$	2.93479	0.248926	0.124463	−	0.992224i	$-0.460279\pi$
$139$	2.93479	0.248926	0.124463	+	0.992224i	$0.460279\pi$
$140$	−4.72598	−0.399418
$141$	12.1613	1.02416
$142$	−0.727530	−0.0610530
$143$	5.18344	0.433461
$144$	0.929744	0.0774786
$145$	6.80713	0.565301
$146$	−2.54412	−0.210553
$147$	30.3992	2.50729
$148$	7.00493	0.575802
$149$	−17.1975	−1.40888	−0.704438	−	0.709766i	$-0.748801\pi$
$149$	−17.1975	−1.40888	−0.704438	+	0.709766i	$0.748801\pi$
$150$	−1.98236	−0.161859
$151$	2.52760	0.205694	0.102847	−	0.994697i	$-0.467205\pi$
$151$	2.52760	0.205694	0.102847	+	0.994697i	$0.467205\pi$
$152$	5.61381	0.455340
$153$	−0.209389	−0.0169281
$154$	−24.4968	−1.97401
$155$	1.00000	0.0803219
$156$	1.98236	0.158716
$157$	6.80115	0.542791	0.271395	−	0.962468i	$-0.412515\pi$
$157$	6.80115	0.542791	0.271395	+	0.962468i	$0.412515\pi$
$158$	−13.4684	−1.07148
$159$	16.8376	1.33531
$160$	1.00000	0.0790569
$161$	33.8008	2.66388
$162$	10.9248	0.858334
$163$	22.6988	1.77791	0.888953	−	0.457998i	$-0.151433\pi$
$163$	22.6988	1.77791	0.888953	+	0.457998i	$0.151433\pi$
$164$	8.16637	0.637686
$165$	−10.2754	−0.799942
$166$	−15.4899	−1.20225
$167$	13.3921	1.03631	0.518156	−	0.855286i	$-0.326619\pi$
$167$	13.3921	1.03631	0.518156	+	0.855286i	$0.326619\pi$
$168$	−9.36858	−0.722802
$169$	1.00000	0.0769231
$170$	−0.225211	−0.0172729
$171$	−5.21940	−0.399137
$172$	1.31690	0.100413
$173$	6.10456	0.464121	0.232061	−	0.972701i	$-0.425453\pi$
$173$	6.10456	0.464121	0.232061	+	0.972701i	$0.425453\pi$
$174$	13.4942	1.02299
$175$	4.72598	0.357250
$176$	5.18344	0.390717
$177$	−1.19528	−0.0898428
$178$	5.08865	0.381410
$179$	−15.2388	−1.13900	−0.569501	−	0.821990i	$-0.692864\pi$
$179$	−15.2388	−1.13900	−0.569501	+	0.821990i	$0.692864\pi$
$180$	−0.929744	−0.0692990
$181$	−8.09219	−0.601488	−0.300744	−	0.953705i	$-0.597235\pi$
$181$	−8.09219	−0.601488	−0.300744	+	0.953705i	$0.597235\pi$
$182$	−4.72598	−0.350313
$183$	−18.6740	−1.38042
$184$	−7.15213	−0.527262
$185$	−7.00493	−0.515013
$186$	1.98236	0.145354
$187$	−1.16737	−0.0853666
$188$	6.13475	0.447423
$189$	−19.3954	−1.41081
$190$	−5.61381	−0.407268
$191$	15.1985	1.09973	0.549864	−	0.835254i	$-0.314679\pi$
$191$	15.1985	1.09973	0.549864	+	0.835254i	$0.314679\pi$
$192$	1.98236	0.143064
$193$	−11.7296	−0.844316	−0.422158	−	0.906522i	$-0.638727\pi$
$193$	−11.7296	−0.844316	−0.422158	+	0.906522i	$0.638727\pi$
$194$	15.6360	1.12260
$195$	−1.98236	−0.141960
$196$	15.3349	1.09535
$197$	19.9617	1.42221	0.711105	−	0.703085i	$-0.248195\pi$
$197$	19.9617	1.42221	0.711105	+	0.703085i	$0.248195\pi$
$198$	−4.81927	−0.342491
$199$	17.7015	1.25483	0.627413	−	0.778687i	$-0.284114\pi$
$199$	17.7015	1.25483	0.627413	+	0.778687i	$0.284114\pi$
$200$	−1.00000	−0.0707107
$201$	−30.7765	−2.17081
$202$	8.47951	0.596617
$203$	−32.1704	−2.25792
$204$	−0.446450	−0.0312577
$205$	−8.16637	−0.570364
$206$	8.49788	0.592075
$207$	6.64965	0.462182
$208$	1.00000	0.0693375
$209$	−29.0988	−2.01281
$210$	9.36858	0.646494
$211$	1.85349	0.127600	0.0637998	−	0.997963i	$-0.479678\pi$
$211$	1.85349	0.127600	0.0637998	+	0.997963i	$0.479678\pi$
$212$	8.49373	0.583352
$213$	1.44223	0.0988196
$214$	−5.46241	−0.373403
$215$	−1.31690	−0.0898120
$216$	4.10399	0.279241
$217$	−4.72598	−0.320820
$218$	16.2855	1.10299
$219$	5.04335	0.340798
$220$	−5.18344	−0.349468
$221$	−0.225211	−0.0151494
$222$	−13.8863	−0.931987
$223$	−7.73463	−0.517949	−0.258975	−	0.965884i	$-0.583385\pi$
$223$	−7.73463	−0.517949	−0.258975	+	0.965884i	$0.583385\pi$
$224$	−4.72598	−0.315768
$225$	0.929744	0.0619829
$226$	5.64814	0.375709
$227$	1.25981	0.0836165	0.0418083	−	0.999126i	$-0.486688\pi$
$227$	1.25981	0.0836165	0.0418083	+	0.999126i	$0.486688\pi$
$228$	−11.1286	−0.737008
$229$	−11.2258	−0.741820	−0.370910	−	0.928669i	$-0.620954\pi$
$229$	−11.2258	−0.741820	−0.370910	+	0.928669i	$0.620954\pi$
$230$	7.15213	0.471597
$231$	48.5615	3.19511
$232$	6.80713	0.446910
$233$	19.6530	1.28751	0.643756	−	0.765231i	$-0.277375\pi$
$233$	19.6530	1.28751	0.643756	+	0.765231i	$0.277375\pi$
$234$	−0.929744	−0.0607792
$235$	−6.13475	−0.400187
$236$	−0.602959	−0.0392493
$237$	26.6991	1.73429
$238$	1.06434	0.0689912
$239$	15.2068	0.983643	0.491822	−	0.870696i	$-0.336331\pi$
$239$	15.2068	0.983643	0.491822	+	0.870696i	$0.336331\pi$
$240$	−1.98236	−0.127961
$241$	16.1309	1.03908	0.519542	−	0.854445i	$-0.326103\pi$
$241$	16.1309	1.03908	0.519542	+	0.854445i	$0.326103\pi$
$242$	−15.8681	−1.02004
$243$	−9.34491	−0.599476
$244$	−9.42007	−0.603058
$245$	−15.3349	−0.979710
$246$	−16.1887	−1.03215
$247$	−5.61381	−0.357198
$248$	1.00000	0.0635001
$249$	30.7065	1.94595
$250$	1.00000	0.0632456
$251$	6.26128	0.395209	0.197604	−	0.980282i	$-0.436684\pi$
$251$	6.26128	0.395209	0.197604	+	0.980282i	$0.436684\pi$
$252$	4.39395	0.276793
$253$	37.0727	2.33074
$254$	2.90379	0.182200
$255$	0.446450	0.0279578
$256$	1.00000	0.0625000
$257$	8.68486	0.541747	0.270873	−	0.962615i	$-0.412688\pi$
$257$	8.68486	0.541747	0.270873	+	0.962615i	$0.412688\pi$
$258$	−2.61057	−0.162527
$259$	33.1052	2.05706
$260$	−1.00000	−0.0620174
$261$	−6.32889	−0.391748
$262$	2.89987	0.179154
$263$	27.3685	1.68761	0.843807	−	0.536647i	$-0.180309\pi$
$263$	27.3685	1.68761	0.843807	+	0.536647i	$0.180309\pi$
$264$	−10.2754	−0.632410
$265$	−8.49373	−0.521766
$266$	26.5307	1.62670
$267$	−10.0875	−0.617346
$268$	−15.5252	−0.948352
$269$	1.40971	0.0859515	0.0429757	−	0.999076i	$-0.486316\pi$
$269$	1.40971	0.0859515	0.0429757	+	0.999076i	$0.486316\pi$
$270$	−4.10399	−0.249761
$271$	−3.94317	−0.239531	−0.119765	−	0.992802i	$-0.538214\pi$
$271$	−3.94317	−0.239531	−0.119765	+	0.992802i	$0.538214\pi$
$272$	−0.225211	−0.0136554
$273$	9.36858	0.567012
$274$	11.3322	0.684601
$275$	5.18344	0.312573
$276$	14.1781	0.853420
$277$	−11.8670	−0.713020	−0.356510	−	0.934292i	$-0.616033\pi$
$277$	−11.8670	−0.713020	−0.356510	+	0.934292i	$0.616033\pi$
$278$	−2.93479	−0.176017
$279$	−0.929744	−0.0556623
$280$	4.72598	0.282431
$281$	−6.09277	−0.363464	−0.181732	−	0.983348i	$-0.558170\pi$
$281$	−6.09277	−0.363464	−0.181732	+	0.983348i	$0.558170\pi$
$282$	−12.1613	−0.724193
$283$	−27.8598	−1.65610	−0.828048	−	0.560658i	$-0.810548\pi$
$283$	−27.8598	−1.65610	−0.828048	+	0.560658i	$0.810548\pi$
$284$	0.727530	0.0431710
$285$	11.1286	0.659200
$286$	−5.18344	−0.306503
$287$	38.5941	2.27814
$288$	−0.929744	−0.0547857
$289$	−16.9493	−0.997016
$290$	−6.80713	−0.399728
$291$	−30.9961	−1.81702
$292$	2.54412	0.148883
$293$	−33.4668	−1.95515	−0.977575	−	0.210586i	$-0.932463\pi$
$293$	−33.4668	−1.95515	−0.977575	+	0.210586i	$0.932463\pi$
$294$	−30.3992	−1.77292
$295$	0.602959	0.0351056
$296$	−7.00493	−0.407154
$297$	−21.2728	−1.23437
$298$	17.1975	0.996226
$299$	7.15213	0.413618
$300$	1.98236	0.114451
$301$	6.22365	0.358725
$302$	−2.52760	−0.145447
$303$	−16.8094	−0.965677
$304$	−5.61381	−0.321974
$305$	9.42007	0.539392
$306$	0.209389	0.0119700
$307$	11.8967	0.678983	0.339491	−	0.940609i	$-0.389745\pi$
$307$	11.8967	0.678983	0.339491	+	0.940609i	$0.389745\pi$
$308$	24.4968	1.39584
$309$	−16.8458	−0.958326
$310$	−1.00000	−0.0567962
$311$	30.3242	1.71953	0.859765	−	0.510690i	$-0.170610\pi$
$311$	30.3242	1.71953	0.859765	+	0.510690i	$0.170610\pi$
$312$	−1.98236	−0.112229
$313$	29.2723	1.65457	0.827284	−	0.561784i	$-0.189885\pi$
$313$	29.2723	1.65457	0.827284	+	0.561784i	$0.189885\pi$
$314$	−6.80115	−0.383811
$315$	−4.39395	−0.247571
$316$	13.4684	0.757654
$317$	−21.5224	−1.20882	−0.604408	−	0.796675i	$-0.706590\pi$
$317$	−21.5224	−1.20882	−0.604408	+	0.796675i	$0.706590\pi$
$318$	−16.8376	−0.944206
$319$	−35.2844	−1.97555
$320$	−1.00000	−0.0559017
$321$	10.8285	0.604385
$322$	−33.8008	−1.88365
$323$	1.26429	0.0703471
$324$	−10.9248	−0.606934
$325$	1.00000	0.0554700
$326$	−22.6988	−1.25717
$327$	−32.2837	−1.78529
$328$	−8.16637	−0.450912
$329$	28.9927	1.59842
$330$	10.2754	0.565644
$331$	−21.3067	−1.17112	−0.585561	−	0.810629i	$-0.699126\pi$
$331$	−21.3067	−1.17112	−0.585561	+	0.810629i	$0.699126\pi$
$332$	15.4899	0.850119
$333$	6.51279	0.356899
$334$	−13.3921	−0.732784
$335$	15.5252	0.848232
$336$	9.36858	0.511098
$337$	−13.4535	−0.732858	−0.366429	−	0.930446i	$-0.619420\pi$
$337$	−13.4535	−0.732858	−0.366429	+	0.930446i	$0.619420\pi$
$338$	−1.00000	−0.0543928
$339$	−11.1966	−0.608118
$340$	0.225211	0.0122138
$341$	−5.18344	−0.280699
$342$	5.21940	0.282233
$343$	39.3905	2.12689
$344$	−1.31690	−0.0710026
$345$	−14.1781	−0.763322
$346$	−6.10456	−0.328183
$347$	1.62372	0.0871656	0.0435828	−	0.999050i	$-0.486123\pi$
$347$	1.62372	0.0871656	0.0435828	+	0.999050i	$0.486123\pi$
$348$	−13.4942	−0.723363
$349$	19.6038	1.04937	0.524684	−	0.851297i	$-0.324184\pi$
$349$	19.6038	1.04937	0.524684	+	0.851297i	$0.324184\pi$
$350$	−4.72598	−0.252614
$351$	−4.10399	−0.219055
$352$	−5.18344	−0.276278
$353$	−7.35671	−0.391558	−0.195779	−	0.980648i	$-0.562724\pi$
$353$	−7.35671	−0.391558	−0.195779	+	0.980648i	$0.562724\pi$
$354$	1.19528	0.0635285
$355$	−0.727530	−0.0386133
$356$	−5.08865	−0.269698
$357$	−2.10991	−0.111668
$358$	15.2388	0.805397
$359$	−1.56320	−0.0825023	−0.0412512	−	0.999149i	$-0.513134\pi$
$359$	−1.56320	−0.0825023	−0.0412512	+	0.999149i	$0.513134\pi$
$360$	0.929744	0.0490018
$361$	12.5148	0.658674
$362$	8.09219	0.425316
$363$	31.4562	1.65102
$364$	4.72598	0.247709
$365$	−2.54412	−0.133165
$366$	18.6740	0.976103
$367$	1.91107	0.0997571	0.0498786	−	0.998755i	$-0.484117\pi$
$367$	1.91107	0.0997571	0.0498786	+	0.998755i	$0.484117\pi$
$368$	7.15213	0.372831
$369$	7.59263	0.395257
$370$	7.00493	0.364169
$371$	40.1412	2.08403
$372$	−1.98236	−0.102780
$373$	−11.0569	−0.572503	−0.286251	−	0.958155i	$-0.592409\pi$
$373$	−11.0569	−0.572503	−0.286251	+	0.958155i	$0.592409\pi$
$374$	1.16737	0.0603633
$375$	−1.98236	−0.102369
$376$	−6.13475	−0.316376
$377$	−6.80713	−0.350585
$378$	19.3954	0.997590
$379$	−37.0148	−1.90132	−0.950661	−	0.310232i	$-0.899593\pi$
$379$	−37.0148	−1.90132	−0.950661	+	0.310232i	$0.899593\pi$
$380$	5.61381	0.287982
$381$	−5.75634	−0.294906
$382$	−15.1985	−0.777625
$383$	−22.2741	−1.13815	−0.569076	−	0.822285i	$-0.692699\pi$
$383$	−22.2741	−1.13815	−0.569076	+	0.822285i	$0.692699\pi$
$384$	−1.98236	−0.101162
$385$	−24.4968	−1.24847
$386$	11.7296	0.597022
$387$	1.22438	0.0622388
$388$	−15.6360	−0.793796
$389$	−4.21626	−0.213773	−0.106886	−	0.994271i	$-0.534088\pi$
$389$	−4.21626	−0.213773	−0.106886	+	0.994271i	$0.534088\pi$
$390$	1.98236	0.100381
$391$	−1.61074	−0.0814587
$392$	−15.3349	−0.774528
$393$	−5.74858	−0.289977
$394$	−19.9617	−1.00565
$395$	−13.4684	−0.677667
$396$	4.81927	0.242178
$397$	−17.5120	−0.878903	−0.439452	−	0.898266i	$-0.644827\pi$
$397$	−17.5120	−0.878903	−0.439452	+	0.898266i	$0.644827\pi$
$398$	−17.7015	−0.887296
$399$	−52.5934	−2.63296
$400$	1.00000	0.0500000
$401$	−29.7433	−1.48531	−0.742655	−	0.669674i	$-0.766434\pi$
$401$	−29.7433	−1.48531	−0.742655	+	0.669674i	$0.766434\pi$
$402$	30.7765	1.53499
$403$	−1.00000	−0.0498135
$404$	−8.47951	−0.421872
$405$	10.9248	0.542858
$406$	32.1704	1.59659
$407$	36.3097	1.79980
$408$	0.446450	0.0221025
$409$	2.55853	0.126511	0.0632556	−	0.997997i	$-0.479852\pi$
$409$	2.55853	0.126511	0.0632556	+	0.997997i	$0.479852\pi$
$410$	8.16637	0.403308
$411$	−22.4644	−1.10809
$412$	−8.49788	−0.418660
$413$	−2.84957	−0.140218
$414$	−6.64965	−0.326812
$415$	−15.4899	−0.760369
$416$	−1.00000	−0.0490290
$417$	5.81781	0.284899
$418$	29.0988	1.42327
$419$	35.5840	1.73839	0.869195	−	0.494469i	$-0.164637\pi$
$419$	35.5840	1.73839	0.869195	+	0.494469i	$0.164637\pi$
$420$	−9.36858	−0.457140
$421$	−6.91456	−0.336995	−0.168497	−	0.985702i	$-0.553891\pi$
$421$	−6.91456	−0.336995	−0.168497	+	0.985702i	$0.553891\pi$
$422$	−1.85349	−0.0902266
$423$	5.70375	0.277326
$424$	−8.49373	−0.412492
$425$	−0.225211	−0.0109244
$426$	−1.44223	−0.0698760
$427$	−44.5191	−2.15443
$428$	5.46241	0.264036
$429$	10.2754	0.496103
$430$	1.31690	0.0635067
$431$	24.9390	1.20127	0.600635	−	0.799523i	$-0.294915\pi$
$431$	24.9390	1.20127	0.600635	+	0.799523i	$0.294915\pi$
$432$	−4.10399	−0.197453
$433$	12.8446	0.617272	0.308636	−	0.951180i	$-0.400128\pi$
$433$	12.8446	0.617272	0.308636	+	0.951180i	$0.400128\pi$
$434$	4.72598	0.226854
$435$	13.4942	0.646996
$436$	−16.2855	−0.779934
$437$	−40.1507	−1.92067
$438$	−5.04335	−0.240981
$439$	−22.8333	−1.08978	−0.544888	−	0.838509i	$-0.683428\pi$
$439$	−22.8333	−1.08978	−0.544888	+	0.838509i	$0.683428\pi$
$440$	5.18344	0.247111
$441$	14.2575	0.678929
$442$	0.225211	0.0107122
$443$	15.1659	0.720556	0.360278	−	0.932845i	$-0.382682\pi$
$443$	15.1659	0.720556	0.360278	+	0.932845i	$0.382682\pi$
$444$	13.8863	0.659014
$445$	5.08865	0.241225
$446$	7.73463	0.366245
$447$	−34.0916	−1.61248
$448$	4.72598	0.223282
$449$	15.1599	0.715442	0.357721	−	0.933828i	$-0.383554\pi$
$449$	15.1599	0.715442	0.357721	+	0.933828i	$0.383554\pi$
$450$	−0.929744	−0.0438285
$451$	42.3299	1.99324
$452$	−5.64814	−0.265666
$453$	5.01062	0.235419
$454$	−1.25981	−0.0591258
$455$	−4.72598	−0.221557
$456$	11.1286	0.521143
$457$	−2.42160	−0.113278	−0.0566389	−	0.998395i	$-0.518038\pi$
$457$	−2.42160	−0.113278	−0.0566389	+	0.998395i	$0.518038\pi$
$458$	11.2258	0.524546
$459$	0.924265	0.0431410
$460$	−7.15213	−0.333470
$461$	−0.521661	−0.0242962	−0.0121481	−	0.999926i	$-0.503867\pi$
$461$	−0.521661	−0.0242962	−0.0121481	+	0.999926i	$0.503867\pi$
$462$	−48.5615	−2.25929
$463$	−1.50484	−0.0699360	−0.0349680	−	0.999388i	$-0.511133\pi$
$463$	−1.50484	−0.0699360	−0.0349680	+	0.999388i	$0.511133\pi$
$464$	−6.80713	−0.316013
$465$	1.98236	0.0919297
$466$	−19.6530	−0.910409
$467$	−1.90792	−0.0882879	−0.0441440	−	0.999025i	$-0.514056\pi$
$467$	−1.90792	−0.0882879	−0.0441440	+	0.999025i	$0.514056\pi$
$468$	0.929744	0.0429774
$469$	−73.3717	−3.38799
$470$	6.13475	0.282975
$471$	13.4823	0.621232
$472$	0.602959	0.0277534
$473$	6.82609	0.313864
$474$	−26.6991	−1.22633
$475$	−5.61381	−0.257579
$476$	−1.06434	−0.0487841
$477$	7.89699	0.361578
$478$	−15.2068	−0.695541
$479$	−8.98843	−0.410692	−0.205346	−	0.978689i	$-0.565832\pi$
$479$	−8.98843	−0.410692	−0.205346	+	0.978689i	$0.565832\pi$
$480$	1.98236	0.0904819
$481$	7.00493	0.319397
$482$	−16.1309	−0.734743
$483$	67.0053	3.04885
$484$	15.8681	0.721276
$485$	15.6360	0.709993
$486$	9.34491	0.423894
$487$	−15.6032	−0.707049	−0.353525	−	0.935425i	$-0.615017\pi$
$487$	−15.6032	−0.707049	−0.353525	+	0.935425i	$0.615017\pi$
$488$	9.42007	0.426426
$489$	44.9971	2.03484
$490$	15.3349	0.692759
$491$	34.1741	1.54225	0.771127	−	0.636681i	$-0.219693\pi$
$491$	34.1741	1.54225	0.771127	+	0.636681i	$0.219693\pi$
$492$	16.1887	0.729842
$493$	1.53304	0.0690448
$494$	5.61381	0.252577
$495$	−4.81927	−0.216610
$496$	−1.00000	−0.0449013
$497$	3.43829	0.154228
$498$	−30.7065	−1.37599
$499$	8.36370	0.374411	0.187205	−	0.982321i	$-0.440057\pi$
$499$	8.36370	0.374411	0.187205	+	0.982321i	$0.440057\pi$
$500$	−1.00000	−0.0447214
$501$	26.5480	1.18608
$502$	−6.26128	−0.279455
$503$	−12.0646	−0.537933	−0.268966	−	0.963150i	$-0.586682\pi$
$503$	−12.0646	−0.537933	−0.268966	+	0.963150i	$0.586682\pi$
$504$	−4.39395	−0.195722
$505$	8.47951	0.377333
$506$	−37.0727	−1.64808
$507$	1.98236	0.0880396
$508$	−2.90379	−0.128835
$509$	−9.39247	−0.416314	−0.208157	−	0.978095i	$-0.566746\pi$
$509$	−9.39247	−0.416314	−0.208157	+	0.978095i	$0.566746\pi$
$510$	−0.446450	−0.0197691
$511$	12.0234	0.531886
$512$	−1.00000	−0.0441942
$513$	23.0390	1.01720
$514$	−8.68486	−0.383073
$515$	8.49788	0.374461
$516$	2.61057	0.114924
$517$	31.7991	1.39852
$518$	−33.1052	−1.45456
$519$	12.1014	0.531194
$520$	1.00000	0.0438529
$521$	−9.47187	−0.414970	−0.207485	−	0.978238i	$-0.566528\pi$
$521$	−9.47187	−0.414970	−0.207485	+	0.978238i	$0.566528\pi$
$522$	6.32889	0.277008
$523$	−25.1260	−1.09868	−0.549341	−	0.835598i	$-0.685121\pi$
$523$	−25.1260	−1.09868	−0.549341	+	0.835598i	$0.685121\pi$
$524$	−2.89987	−0.126681
$525$	9.36858	0.408879
$526$	−27.3685	−1.19332
$527$	0.225211	0.00981036
$528$	10.2754	0.447181
$529$	28.1530	1.22404
$530$	8.49373	0.368944
$531$	−0.560597	−0.0243279
$532$	−26.5307	−1.15025
$533$	8.16637	0.353725
$534$	10.0875	0.436530
$535$	−5.46241	−0.236161
$536$	15.5252	0.670586
$537$	−30.2088	−1.30361
$538$	−1.40971	−0.0607769
$539$	79.4875	3.42377
$540$	4.10399	0.176608
$541$	−39.2324	−1.68673	−0.843366	−	0.537339i	$-0.819430\pi$
$541$	−39.2324	−1.68673	−0.843366	+	0.537339i	$0.819430\pi$
$542$	3.94317	0.169374
$543$	−16.0416	−0.688412
$544$	0.225211	0.00965586
$545$	16.2855	0.697594
$546$	−9.36858	−0.400938
$547$	39.3128	1.68089	0.840446	−	0.541895i	$-0.182293\pi$
$547$	39.3128	1.68089	0.840446	+	0.541895i	$0.182293\pi$
$548$	−11.3322	−0.484086
$549$	−8.75825	−0.373793
$550$	−5.18344	−0.221023
$551$	38.2139	1.62797
$552$	−14.1781	−0.603459
$553$	63.6512	2.70672
$554$	11.8670	0.504181
$555$	−13.8863	−0.589440
$556$	2.93479	0.124463
$557$	16.9213	0.716978	0.358489	−	0.933534i	$-0.383292\pi$
$557$	16.9213	0.716978	0.358489	+	0.933534i	$0.383292\pi$
$558$	0.929744	0.0393592
$559$	1.31690	0.0556990
$560$	−4.72598	−0.199709
$561$	−2.31415	−0.0977033
$562$	6.09277	0.257008
$563$	−21.6426	−0.912126	−0.456063	−	0.889947i	$-0.650741\pi$
$563$	−21.6426	−0.912126	−0.456063	+	0.889947i	$0.650741\pi$
$564$	12.1613	0.512082
$565$	5.64814	0.237619
$566$	27.8598	1.17104
$567$	−51.6304	−2.16827
$568$	−0.727530	−0.0305265
$569$	5.15056	0.215923	0.107961	−	0.994155i	$-0.465568\pi$
$569$	5.15056	0.215923	0.107961	+	0.994155i	$0.465568\pi$
$570$	−11.1286	−0.466125
$571$	10.5506	0.441527	0.220764	−	0.975327i	$-0.429145\pi$
$571$	10.5506	0.441527	0.220764	+	0.975327i	$0.429145\pi$
$572$	5.18344	0.216731
$573$	30.1290	1.25866
$574$	−38.5941	−1.61089
$575$	7.15213	0.298264
$576$	0.929744	0.0387393
$577$	−13.4717	−0.560836	−0.280418	−	0.959878i	$-0.590473\pi$
$577$	−13.4717	−0.560836	−0.280418	+	0.959878i	$0.590473\pi$
$578$	16.9493	0.704997
$579$	−23.2523	−0.966333
$580$	6.80713	0.282651
$581$	73.2050	3.03705
$582$	30.9961	1.28483
$583$	44.0268	1.82340
$584$	−2.54412	−0.105276
$585$	−0.929744	−0.0384402
$586$	33.4668	1.38250
$587$	−35.6813	−1.47272	−0.736362	−	0.676588i	$-0.763458\pi$
$587$	−35.6813	−1.47272	−0.736362	+	0.676588i	$0.763458\pi$
$588$	30.3992	1.25364
$589$	5.61381	0.231313
$590$	−0.602959	−0.0248234
$591$	39.5712	1.62774
$592$	7.00493	0.287901
$593$	−23.9923	−0.985247	−0.492623	−	0.870243i	$-0.663962\pi$
$593$	−23.9923	−0.985247	−0.492623	+	0.870243i	$0.663962\pi$
$594$	21.2728	0.872833
$595$	1.06434	0.0436339
$596$	−17.1975	−0.704438
$597$	35.0907	1.43617
$598$	−7.15213	−0.292472
$599$	40.2096	1.64292	0.821461	−	0.570265i	$-0.193160\pi$
$599$	40.2096	1.64292	0.821461	+	0.570265i	$0.193160\pi$
$600$	−1.98236	−0.0809294
$601$	35.6909	1.45586	0.727930	−	0.685651i	$-0.240482\pi$
$601$	35.6909	1.45586	0.727930	+	0.685651i	$0.240482\pi$
$602$	−6.22365	−0.253657
$603$	−14.4344	−0.587816
$604$	2.52760	0.102847
$605$	−15.8681	−0.645129
$606$	16.8094	0.682837
$607$	−20.4998	−0.832061	−0.416031	−	0.909351i	$-0.636579\pi$
$607$	−20.4998	−0.832061	−0.416031	+	0.909351i	$0.636579\pi$
$608$	5.61381	0.227670
$609$	−63.7732	−2.58422
$610$	−9.42007	−0.381407
$611$	6.13475	0.248185
$612$	−0.209389	−0.00846404
$613$	10.9500	0.442266	0.221133	−	0.975244i	$-0.429024\pi$
$613$	10.9500	0.442266	0.221133	+	0.975244i	$0.429024\pi$
$614$	−11.8967	−0.480113
$615$	−16.1887	−0.652790
$616$	−24.4968	−0.987006
$617$	−43.2699	−1.74198	−0.870991	−	0.491300i	$-0.836522\pi$
$617$	−43.2699	−1.74198	−0.870991	+	0.491300i	$0.836522\pi$
$618$	16.8458	0.677639
$619$	43.1134	1.73287	0.866437	−	0.499286i	$-0.166404\pi$
$619$	43.1134	1.73287	0.866437	+	0.499286i	$0.166404\pi$
$620$	1.00000	0.0401610
$621$	−29.3523	−1.17787
$622$	−30.3242	−1.21589
$623$	−24.0488	−0.963497
$624$	1.98236	0.0793578
$625$	1.00000	0.0400000
$626$	−29.2723	−1.16996
$627$	−57.6843	−2.30369
$628$	6.80115	0.271395
$629$	−1.57759	−0.0629027
$630$	4.39395	0.175059
$631$	12.1695	0.484459	0.242229	−	0.970219i	$-0.422121\pi$
$631$	12.1695	0.484459	0.242229	+	0.970219i	$0.422121\pi$
$632$	−13.4684	−0.535742
$633$	3.67429	0.146040
$634$	21.5224	0.854762
$635$	2.90379	0.115233
$636$	16.8376	0.667655
$637$	15.3349	0.607590
$638$	35.2844	1.39692
$639$	0.676416	0.0267586
$640$	1.00000	0.0395285
$641$	21.7262	0.858132	0.429066	−	0.903273i	$-0.358843\pi$
$641$	21.7262	0.858132	0.429066	+	0.903273i	$0.358843\pi$
$642$	−10.8285	−0.427365
$643$	−21.9621	−0.866103	−0.433051	−	0.901369i	$-0.642563\pi$
$643$	−21.9621	−0.866103	−0.433051	+	0.901369i	$0.642563\pi$
$644$	33.8008	1.33194
$645$	−2.61057	−0.102791
$646$	−1.26429	−0.0497429
$647$	−36.2865	−1.42657	−0.713284	−	0.700875i	$-0.752793\pi$
$647$	−36.2865	−1.42657	−0.713284	+	0.700875i	$0.752793\pi$
$648$	10.9248	0.429167
$649$	−3.12540	−0.122683
$650$	−1.00000	−0.0392232
$651$	−9.36858	−0.367184
$652$	22.6988	0.888953
$653$	−4.69811	−0.183851	−0.0919256	−	0.995766i	$-0.529302\pi$
$653$	−4.69811	−0.183851	−0.0919256	+	0.995766i	$0.529302\pi$
$654$	32.2837	1.26239
$655$	2.89987	0.113307
$656$	8.16637	0.318843
$657$	2.36538	0.0922822
$658$	−28.9927	−1.13025
$659$	38.0707	1.48302	0.741511	−	0.670940i	$-0.234109\pi$
$659$	38.0707	1.48302	0.741511	+	0.670940i	$0.234109\pi$
$660$	−10.2754	−0.399971
$661$	−22.4767	−0.874241	−0.437120	−	0.899403i	$-0.644002\pi$
$661$	−22.4767	−0.874241	−0.437120	+	0.899403i	$0.644002\pi$
$662$	21.3067	0.828108
$663$	−0.446450	−0.0173387
$664$	−15.4899	−0.601125
$665$	26.5307	1.02882
$666$	−6.51279	−0.252366
$667$	−48.6855	−1.88511
$668$	13.3921	0.518156
$669$	−15.3328	−0.592800
$670$	−15.5252	−0.599790
$671$	−48.8284	−1.88500
$672$	−9.36858	−0.361401
$673$	−1.12762	−0.0434666	−0.0217333	−	0.999764i	$-0.506918\pi$
$673$	−1.12762	−0.0434666	−0.0217333	+	0.999764i	$0.506918\pi$
$674$	13.4535	0.518209
$675$	−4.10399	−0.157963
$676$	1.00000	0.0384615
$677$	36.2191	1.39201	0.696007	−	0.718035i	$-0.254958\pi$
$677$	36.2191	1.39201	0.696007	+	0.718035i	$0.254958\pi$
$678$	11.1966	0.430004
$679$	−73.8953	−2.83584
$680$	−0.225211	−0.00863646
$681$	2.49739	0.0957004
$682$	5.18344	0.198484
$683$	−17.5757	−0.672517	−0.336259	−	0.941770i	$-0.609162\pi$
$683$	−17.5757	−0.672517	−0.336259	+	0.941770i	$0.609162\pi$
$684$	−5.21940	−0.199569
$685$	11.3322	0.432980
$686$	−39.3905	−1.50394
$687$	−22.2535	−0.849024
$688$	1.31690	0.0502064
$689$	8.49373	0.323585
$690$	14.1781	0.539750
$691$	29.0136	1.10373	0.551864	−	0.833934i	$-0.313917\pi$
$691$	29.0136	1.10373	0.551864	+	0.833934i	$0.313917\pi$
$692$	6.10456	0.232061
$693$	22.7758	0.865181
$694$	−1.62372	−0.0616354
$695$	−2.93479	−0.111323
$696$	13.4942	0.511495
$697$	−1.83916	−0.0696631
$698$	−19.6038	−0.742015
$699$	38.9593	1.47358
$700$	4.72598	0.178625
$701$	−50.4905	−1.90700	−0.953500	−	0.301393i	$-0.902549\pi$
$701$	−50.4905	−1.90700	−0.953500	+	0.301393i	$0.902549\pi$
$702$	4.10399	0.154895
$703$	−39.3243	−1.48315
$704$	5.18344	0.195358
$705$	−12.1613	−0.458020
$706$	7.35671	0.276874
$707$	−40.0740	−1.50714
$708$	−1.19528	−0.0449214
$709$	30.8595	1.15895	0.579476	−	0.814989i	$-0.303257\pi$
$709$	30.8595	1.15895	0.579476	+	0.814989i	$0.303257\pi$
$710$	0.727530	0.0273037
$711$	12.5221	0.469616
$712$	5.08865	0.190705
$713$	−7.15213	−0.267849
$714$	2.10991	0.0789615
$715$	−5.18344	−0.193850
$716$	−15.2388	−0.569501
$717$	30.1452	1.12579
$718$	1.56320	0.0583380
$719$	−12.8825	−0.480436	−0.240218	−	0.970719i	$-0.577219\pi$
$719$	−12.8825	−0.480436	−0.240218	+	0.970719i	$0.577219\pi$
$720$	−0.929744	−0.0346495
$721$	−40.1608	−1.49567
$722$	−12.5148	−0.465753
$723$	31.9772	1.18925
$724$	−8.09219	−0.300744
$725$	−6.80713	−0.252810
$726$	−31.4562	−1.16745
$727$	32.7953	1.21631	0.608156	−	0.793818i	$-0.291910\pi$
$727$	32.7953	1.21631	0.608156	+	0.793818i	$0.291910\pi$
$728$	−4.72598	−0.175156
$729$	14.2495	0.527758
$730$	2.54412	0.0941620
$731$	−0.296581	−0.0109695
$732$	−18.6740	−0.690209
$733$	−32.4778	−1.19960	−0.599798	−	0.800151i	$-0.704753\pi$
$733$	−32.4778	−1.19960	−0.599798	+	0.800151i	$0.704753\pi$
$734$	−1.91107	−0.0705390
$735$	−30.3992	−1.12129
$736$	−7.15213	−0.263631
$737$	−80.4739	−2.96430
$738$	−7.59263	−0.279489
$739$	24.1886	0.889791	0.444896	−	0.895582i	$-0.353241\pi$
$739$	24.1886	0.889791	0.444896	+	0.895582i	$0.353241\pi$
$740$	−7.00493	−0.257506
$741$	−11.1286	−0.408818
$742$	−40.1412	−1.47363
$743$	−34.2733	−1.25737	−0.628683	−	0.777661i	$-0.716406\pi$
$743$	−34.2733	−1.25737	−0.628683	+	0.777661i	$0.716406\pi$
$744$	1.98236	0.0726768
$745$	17.1975	0.630068
$746$	11.0569	0.404821
$747$	14.4016	0.526928
$748$	−1.16737	−0.0426833
$749$	25.8152	0.943268
$750$	1.98236	0.0723855
$751$	−20.1554	−0.735482	−0.367741	−	0.929928i	$-0.619869\pi$
$751$	−20.1554	−0.735482	−0.367741	+	0.929928i	$0.619869\pi$
$752$	6.13475	0.223711
$753$	12.4121	0.452322
$754$	6.80713	0.247901
$755$	−2.52760	−0.0919889
$756$	−19.3954	−0.705403
$757$	−34.9897	−1.27172	−0.635861	−	0.771804i	$-0.719355\pi$
$757$	−34.9897	−1.27172	−0.635861	+	0.771804i	$0.719355\pi$
$758$	37.0148	1.34444
$759$	73.4913	2.66756
$760$	−5.61381	−0.203634
$761$	40.0043	1.45015	0.725077	−	0.688668i	$-0.241804\pi$
$761$	40.0043	1.45015	0.725077	+	0.688668i	$0.241804\pi$
$762$	5.75634	0.208530
$763$	−76.9650	−2.78632
$764$	15.1985	0.549864
$765$	0.209389	0.00757047
$766$	22.2741	0.804795
$767$	−0.602959	−0.0217716
$768$	1.98236	0.0715322
$769$	−20.4838	−0.738666	−0.369333	−	0.929297i	$-0.620414\pi$
$769$	−20.4838	−0.738666	−0.369333	+	0.929297i	$0.620414\pi$
$770$	24.4968	0.882805
$771$	17.2165	0.620037
$772$	−11.7296	−0.422158
$773$	9.22324	0.331737	0.165868	−	0.986148i	$-0.446957\pi$
$773$	9.22324	0.331737	0.165868	+	0.986148i	$0.446957\pi$
$774$	−1.22438	−0.0440095
$775$	−1.00000	−0.0359211
$776$	15.6360	0.561299
$777$	65.6263	2.35433
$778$	4.21626	0.151160
$779$	−45.8444	−1.64255
$780$	−1.98236	−0.0709798
$781$	3.77111	0.134941
$782$	1.61074	0.0576000
$783$	27.9364	0.998365
$784$	15.3349	0.547674
$785$	−6.80115	−0.242743
$786$	5.74858	0.205045
$787$	−32.5797	−1.16134	−0.580670	−	0.814139i	$-0.697209\pi$
$787$	−32.5797	−1.16134	−0.580670	+	0.814139i	$0.697209\pi$
$788$	19.9617	0.711105
$789$	54.2542	1.93150
$790$	13.4684	0.479183
$791$	−26.6930	−0.949094
$792$	−4.81927	−0.171245
$793$	−9.42007	−0.334516
$794$	17.5120	0.621478
$795$	−16.8376	−0.597168
$796$	17.7015	0.627413
$797$	3.35459	0.118826	0.0594129	−	0.998233i	$-0.481077\pi$
$797$	3.35459	0.118826	0.0594129	+	0.998233i	$0.481077\pi$
$798$	52.5934	1.86179
$799$	−1.38162	−0.0488780
$800$	−1.00000	−0.0353553
$801$	−4.73114	−0.167167
$802$	29.7433	1.05027
$803$	13.1873	0.465369
$804$	−30.7765	−1.08540
$805$	−33.8008	−1.19132
$806$	1.00000	0.0352235
$807$	2.79455	0.0983728
$808$	8.47951	0.298308
$809$	−54.1842	−1.90501	−0.952507	−	0.304517i	$-0.901505\pi$
$809$	−54.1842	−1.90501	−0.952507	+	0.304517i	$0.901505\pi$
$810$	−10.9248	−0.383859
$811$	26.8417	0.942539	0.471269	−	0.881989i	$-0.343796\pi$
$811$	26.8417	0.942539	0.471269	+	0.881989i	$0.343796\pi$
$812$	−32.1704	−1.12896
$813$	−7.81678	−0.274147
$814$	−36.3097	−1.27265
$815$	−22.6988	−0.795104
$816$	−0.446450	−0.0156289
$817$	−7.39283	−0.258642
$818$	−2.55853	−0.0894570
$819$	4.39395	0.153537
$820$	−8.16637	−0.285182
$821$	4.44849	0.155253	0.0776266	−	0.996983i	$-0.475266\pi$
$821$	4.44849	0.155253	0.0776266	+	0.996983i	$0.475266\pi$
$822$	22.4644	0.783537
$823$	−22.1160	−0.770916	−0.385458	−	0.922725i	$-0.625956\pi$
$823$	−22.1160	−0.770916	−0.385458	+	0.922725i	$0.625956\pi$
$824$	8.49788	0.296038
$825$	10.2754	0.357745
$826$	2.84957	0.0991493
$827$	−10.9162	−0.379595	−0.189797	−	0.981823i	$-0.560783\pi$
$827$	−10.9162	−0.379595	−0.189797	+	0.981823i	$0.560783\pi$
$828$	6.64965	0.231091
$829$	16.2638	0.564864	0.282432	−	0.959287i	$-0.408859\pi$
$829$	16.2638	0.564864	0.282432	+	0.959287i	$0.408859\pi$
$830$	15.4899	0.537662
$831$	−23.5247	−0.816062
$832$	1.00000	0.0346688
$833$	−3.45359	−0.119660
$834$	−5.81781	−0.201454
$835$	−13.3921	−0.463453
$836$	−29.0988	−1.00640
$837$	4.10399	0.141855
$838$	−35.5840	−1.22923
$839$	−52.3888	−1.80866	−0.904331	−	0.426832i	$-0.859630\pi$
$839$	−52.3888	−1.80866	−0.904331	+	0.426832i	$0.859630\pi$
$840$	9.36858	0.323247
$841$	17.3370	0.597829
$842$	6.91456	0.238291
$843$	−12.0780	−0.415990
$844$	1.85349	0.0637998
$845$	−1.00000	−0.0344010
$846$	−5.70375	−0.196099
$847$	74.9922	2.57676
$848$	8.49373	0.291676
$849$	−55.2282	−1.89543
$850$	0.225211	0.00772469
$851$	50.1002	1.71741
$852$	1.44223	0.0494098
$853$	−35.5907	−1.21860	−0.609301	−	0.792939i	$-0.708550\pi$
$853$	−35.5907	−1.21860	−0.609301	+	0.792939i	$0.708550\pi$
$854$	44.5191	1.52341
$855$	5.21940	0.178500
$856$	−5.46241	−0.186701
$857$	−27.5100	−0.939725	−0.469863	−	0.882740i	$-0.655697\pi$
$857$	−27.5100	−0.939725	−0.469863	+	0.882740i	$0.655697\pi$
$858$	−10.2754	−0.350798
$859$	−16.5065	−0.563193	−0.281597	−	0.959533i	$-0.590864\pi$
$859$	−16.5065	−0.563193	−0.281597	+	0.959533i	$0.590864\pi$
$860$	−1.31690	−0.0449060
$861$	76.5073	2.60736
$862$	−24.9390	−0.849426
$863$	15.8180	0.538451	0.269225	−	0.963077i	$-0.413232\pi$
$863$	15.8180	0.538451	0.269225	+	0.963077i	$0.413232\pi$
$864$	4.10399	0.139621
$865$	−6.10456	−0.207561
$866$	−12.8446	−0.436477
$867$	−33.5995	−1.14110
$868$	−4.72598	−0.160410
$869$	69.8125	2.36823
$870$	−13.4942	−0.457495
$871$	−15.5252	−0.526051
$872$	16.2855	0.551497
$873$	−14.5374	−0.492018
$874$	40.1507	1.35812
$875$	−4.72598	−0.159767
$876$	5.04335	0.170399
$877$	10.8792	0.367365	0.183682	−	0.982986i	$-0.441198\pi$
$877$	10.8792	0.367365	0.183682	+	0.982986i	$0.441198\pi$
$878$	22.8333	0.770587
$879$	−66.3432	−2.23770
$880$	−5.18344	−0.174734
$881$	−38.3352	−1.29154	−0.645772	−	0.763530i	$-0.723464\pi$
$881$	−38.3352	−1.29154	−0.645772	+	0.763530i	$0.723464\pi$
$882$	−14.2575	−0.480075
$883$	35.7628	1.20351	0.601756	−	0.798680i	$-0.294468\pi$
$883$	35.7628	1.20351	0.601756	+	0.798680i	$0.294468\pi$
$884$	−0.225211	−0.00757468
$885$	1.19528	0.0401789
$886$	−15.1659	−0.509510
$887$	−47.9891	−1.61132	−0.805658	−	0.592381i	$-0.798188\pi$
$887$	−47.9891	−1.61132	−0.805658	+	0.592381i	$0.798188\pi$
$888$	−13.8863	−0.465993
$889$	−13.7232	−0.460263
$890$	−5.08865	−0.170572
$891$	−56.6281	−1.89711
$892$	−7.73463	−0.258975
$893$	−34.4393	−1.15247
$894$	34.0916	1.14020
$895$	15.2388	0.509377
$896$	−4.72598	−0.157884
$897$	14.1781	0.473392
$898$	−15.1599	−0.505894
$899$	6.80713	0.227031
$900$	0.929744	0.0309915
$901$	−1.91288	−0.0637274
$902$	−42.3299	−1.40943
$903$	12.3375	0.410567
$904$	5.64814	0.187854
$905$	8.09219	0.268994
$906$	−5.01062	−0.166467
$907$	2.70394	0.0897827	0.0448914	−	0.998992i	$-0.485706\pi$
$907$	2.70394	0.0897827	0.0448914	+	0.998992i	$0.485706\pi$
$908$	1.25981	0.0418083
$909$	−7.88377	−0.261488
$910$	4.72598	0.156665
$911$	16.5407	0.548017	0.274008	−	0.961727i	$-0.411650\pi$
$911$	16.5407	0.548017	0.274008	+	0.961727i	$0.411650\pi$
$912$	−11.1286	−0.368504
$913$	80.2910	2.65725
$914$	2.42160	0.0800996
$915$	18.6740	0.617342
$916$	−11.2258	−0.370910
$917$	−13.7047	−0.452570
$918$	−0.924265	−0.0305053
$919$	22.8636	0.754199	0.377100	−	0.926173i	$-0.376921\pi$
$919$	22.8636	0.754199	0.377100	+	0.926173i	$0.376921\pi$
$920$	7.15213	0.235799
$921$	23.5836	0.777106
$922$	0.521661	0.0171800
$923$	0.727530	0.0239469
$924$	48.5615	1.59756
$925$	7.00493	0.230321
$926$	1.50484	0.0494522
$927$	−7.90085	−0.259498
$928$	6.80713	0.223455
$929$	−52.8956	−1.73545	−0.867724	−	0.497047i	$-0.834418\pi$
$929$	−52.8956	−1.73545	−0.867724	+	0.497047i	$0.834418\pi$
$930$	−1.98236	−0.0650041
$931$	−86.0870	−2.82139
$932$	19.6530	0.643756
$933$	60.1135	1.96803
$934$	1.90792	0.0624290
$935$	1.16737	0.0381771
$936$	−0.929744	−0.0303896
$937$	−0.434790	−0.0142040	−0.00710199	−	0.999975i	$-0.502261\pi$
$937$	−0.434790	−0.0142040	−0.00710199	+	0.999975i	$0.502261\pi$
$938$	73.3717	2.39567
$939$	58.0282	1.89368
$940$	−6.13475	−0.200093
$941$	−30.9433	−1.00872	−0.504361	−	0.863493i	$-0.668272\pi$
$941$	−30.9433	−1.00872	−0.504361	+	0.863493i	$0.668272\pi$
$942$	−13.4823	−0.439278
$943$	58.4069	1.90199
$944$	−0.602959	−0.0196246
$945$	19.3954	0.630931
$946$	−6.82609	−0.221935
$947$	39.8988	1.29654	0.648269	−	0.761411i	$-0.275493\pi$
$947$	39.8988	1.29654	0.648269	+	0.761411i	$0.275493\pi$
$948$	26.6991	0.867147
$949$	2.54412	0.0825856
$950$	5.61381	0.182136
$951$	−42.6650	−1.38351
$952$	1.06434	0.0344956
$953$	−42.4455	−1.37494	−0.687472	−	0.726211i	$-0.741280\pi$
$953$	−42.4455	−1.37494	−0.687472	+	0.726211i	$0.741280\pi$
$954$	−7.89699	−0.255674
$955$	−15.1985	−0.491814
$956$	15.2068	0.491822
$957$	−69.9463	−2.26104
$958$	8.98843	0.290403
$959$	−53.5556	−1.72940
$960$	−1.98236	−0.0639803
$961$	1.00000	0.0322581
$962$	−7.00493	−0.225848
$963$	5.07864	0.163657
$964$	16.1309	0.519542
$965$	11.7296	0.377590
$966$	−67.0053	−2.15586
$967$	−27.7470	−0.892283	−0.446142	−	0.894962i	$-0.647202\pi$
$967$	−27.7470	−0.892283	−0.446142	+	0.894962i	$0.647202\pi$
$968$	−15.8681	−0.510019
$969$	2.50628	0.0805133
$970$	−15.6360	−0.502041
$971$	−18.1376	−0.582063	−0.291032	−	0.956713i	$-0.593999\pi$
$971$	−18.1376	−0.582063	−0.291032	+	0.956713i	$0.593999\pi$
$972$	−9.34491	−0.299738
$973$	13.8698	0.444644
$974$	15.6032	0.499959
$975$	1.98236	0.0634863
$976$	−9.42007	−0.301529
$977$	7.84071	0.250847	0.125423	−	0.992103i	$-0.459971\pi$
$977$	7.84071	0.250847	0.125423	+	0.992103i	$0.459971\pi$
$978$	−44.9971	−1.43885
$979$	−26.3767	−0.843004
$980$	−15.3349	−0.489855
$981$	−15.1413	−0.483426
$982$	−34.1741	−1.09054
$983$	−37.4505	−1.19449	−0.597243	−	0.802060i	$-0.703737\pi$
$983$	−37.4505	−1.19449	−0.597243	+	0.802060i	$0.703737\pi$
$984$	−16.1887	−0.516076
$985$	−19.9617	−0.636032
$986$	−1.53304	−0.0488220
$987$	57.4739	1.82942
$988$	−5.61381	−0.178599
$989$	9.41865	0.299496
$990$	4.81927	0.153167
$991$	−12.3885	−0.393533	−0.196767	−	0.980450i	$-0.563044\pi$
$991$	−12.3885	−0.393533	−0.196767	+	0.980450i	$0.563044\pi$
$992$	1.00000	0.0317500
$993$	−42.2375	−1.34037
$994$	−3.43829	−0.109056
$995$	−17.7015	−0.561175
$996$	30.7065	0.972974
$997$	−51.2285	−1.62242	−0.811212	−	0.584752i	$-0.801192\pi$
$997$	−51.2285	−1.62242	−0.811212	+	0.584752i	$0.801192\pi$
$998$	−8.36370	−0.264748
$999$	−28.7482	−0.909552

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.k.1.7	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.k.1.7	✓	8	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.98236 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.98236 q^{6} +4.72598 q^{7} -1.00000 q^{8} +0.929744 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.98236 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.98236 q^{6} +4.72598 q^{7} -1.00000 q^{8} +0.929744 q^{9} +1.00000 q^{10} +5.18344 q^{11} +1.98236 q^{12} +1.00000 q^{13} -4.72598 q^{14} -1.98236 q^{15} +1.00000 q^{16} -0.225211 q^{17} -0.929744 q^{18} -5.61381 q^{19} -1.00000 q^{20} +9.36858 q^{21} -5.18344 q^{22} +7.15213 q^{23} -1.98236 q^{24} +1.00000 q^{25} -1.00000 q^{26} -4.10399 q^{27} +4.72598 q^{28} -6.80713 q^{29} +1.98236 q^{30} -1.00000 q^{31} -1.00000 q^{32} +10.2754 q^{33} +0.225211 q^{34} -4.72598 q^{35} +0.929744 q^{36} +7.00493 q^{37} +5.61381 q^{38} +1.98236 q^{39} +1.00000 q^{40} +8.16637 q^{41} -9.36858 q^{42} +1.31690 q^{43} +5.18344 q^{44} -0.929744 q^{45} -7.15213 q^{46} +6.13475 q^{47} +1.98236 q^{48} +15.3349 q^{49} -1.00000 q^{50} -0.446450 q^{51} +1.00000 q^{52} +8.49373 q^{53} +4.10399 q^{54} -5.18344 q^{55} -4.72598 q^{56} -11.1286 q^{57} +6.80713 q^{58} -0.602959 q^{59} -1.98236 q^{60} -9.42007 q^{61} +1.00000 q^{62} +4.39395 q^{63} +1.00000 q^{64} -1.00000 q^{65} -10.2754 q^{66} -15.5252 q^{67} -0.225211 q^{68} +14.1781 q^{69} +4.72598 q^{70} +0.727530 q^{71} -0.929744 q^{72} +2.54412 q^{73} -7.00493 q^{74} +1.98236 q^{75} -5.61381 q^{76} +24.4968 q^{77} -1.98236 q^{78} +13.4684 q^{79} -1.00000 q^{80} -10.9248 q^{81} -8.16637 q^{82} +15.4899 q^{83} +9.36858 q^{84} +0.225211 q^{85} -1.31690 q^{86} -13.4942 q^{87} -5.18344 q^{88} -5.08865 q^{89} +0.929744 q^{90} +4.72598 q^{91} +7.15213 q^{92} -1.98236 q^{93} -6.13475 q^{94} +5.61381 q^{95} -1.98236 q^{96} -15.6360 q^{97} -15.3349 q^{98} +4.81927 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - q^{3} + 8 q^{4} - 8 q^{5} + q^{6} - 8 q^{7} - 8 q^{8} + 13 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - q^3 + 8 * q^4 - 8 * q^5 + q^6 - 8 * q^7 - 8 * q^8 + 13 * q^9	\( 8 q - 8 q^{2} - q^{3} + 8 q^{4} - 8 q^{5} + q^{6} - 8 q^{7} - 8 q^{8} + 13 q^{9} + 8 q^{10} + 12 q^{11} - q^{12} + 8 q^{13} + 8 q^{14} + q^{15} + 8 q^{16} - 13 q^{18} - 3 q^{19} - 8 q^{20} + 27 q^{21} - 12 q^{22} + 17 q^{23} + q^{24} + 8 q^{25} - 8 q^{26} - 13 q^{27} - 8 q^{28} - 10 q^{29} - q^{30} - 8 q^{31} - 8 q^{32} + 4 q^{33} + 8 q^{35} + 13 q^{36} + 2 q^{37} + 3 q^{38} - q^{39} + 8 q^{40} + 14 q^{41} - 27 q^{42} - 19 q^{43} + 12 q^{44} - 13 q^{45} - 17 q^{46} + 8 q^{47} - q^{48} + 16 q^{49} - 8 q^{50} + 35 q^{51} + 8 q^{52} + 4 q^{53} + 13 q^{54} - 12 q^{55} + 8 q^{56} - 33 q^{57} + 10 q^{58} - 13 q^{59} + q^{60} + 11 q^{61} + 8 q^{62} - 27 q^{63} + 8 q^{64} - 8 q^{65} - 4 q^{66} - 34 q^{67} + 12 q^{69} - 8 q^{70} + 8 q^{71} - 13 q^{72} - 21 q^{73} - 2 q^{74} - q^{75} - 3 q^{76} + 19 q^{77} + q^{78} - 36 q^{79} - 8 q^{80} + 20 q^{81} - 14 q^{82} + 27 q^{84} + 19 q^{86} - 29 q^{87} - 12 q^{88} - 16 q^{89} + 13 q^{90} - 8 q^{91} + 17 q^{92} + q^{93} - 8 q^{94} + 3 q^{95} + q^{96} + q^{97} - 16 q^{98} + 65 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - q^3 + 8 * q^4 - 8 * q^5 + q^6 - 8 * q^7 - 8 * q^8 + 13 * q^9 + 8 * q^10 + 12 * q^11 - q^12 + 8 * q^13 + 8 * q^14 + q^15 + 8 * q^16 - 13 * q^18 - 3 * q^19 - 8 * q^20 + 27 * q^21 - 12 * q^22 + 17 * q^23 + q^24 + 8 * q^25 - 8 * q^26 - 13 * q^27 - 8 * q^28 - 10 * q^29 - q^30 - 8 * q^31 - 8 * q^32 + 4 * q^33 + 8 * q^35 + 13 * q^36 + 2 * q^37 + 3 * q^38 - q^39 + 8 * q^40 + 14 * q^41 - 27 * q^42 - 19 * q^43 + 12 * q^44 - 13 * q^45 - 17 * q^46 + 8 * q^47 - q^48 + 16 * q^49 - 8 * q^50 + 35 * q^51 + 8 * q^52 + 4 * q^53 + 13 * q^54 - 12 * q^55 + 8 * q^56 - 33 * q^57 + 10 * q^58 - 13 * q^59 + q^60 + 11 * q^61 + 8 * q^62 - 27 * q^63 + 8 * q^64 - 8 * q^65 - 4 * q^66 - 34 * q^67 + 12 * q^69 - 8 * q^70 + 8 * q^71 - 13 * q^72 - 21 * q^73 - 2 * q^74 - q^75 - 3 * q^76 + 19 * q^77 + q^78 - 36 * q^79 - 8 * q^80 + 20 * q^81 - 14 * q^82 + 27 * q^84 + 19 * q^86 - 29 * q^87 - 12 * q^88 - 16 * q^89 + 13 * q^90 - 8 * q^91 + 17 * q^92 + q^93 - 8 * q^94 + 3 * q^95 + q^96 + q^97 - 16 * q^98 + 65 * q^99

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