LMFDB - Embedded newform 4970.2.a.x.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4970,2,Mod(1,4970)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4970, 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("4970.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4970 = 2 \cdot 5 \cdot 7 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4970.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:	$39.6856498046$
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} - 11x^{5} + 9x^{4} + 35x^{3} - 24x^{2} - 33x + 22 $ x^7 - x^6 - 11x^5 + 9x^4 + 35x^3 - 24x^2 - 33*x + 22
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			1.3
Root			$-1.49310$ of defining polynomial
Character	$\chi$	$=$	4970.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.49310 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.49310 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.770660 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.49310 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.49310 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.770660 q^{9} -1.00000 q^{10} -3.24665 q^{11} -1.49310 q^{12} +5.86956 q^{13} -1.00000 q^{14} +1.49310 q^{15} +1.00000 q^{16} -5.04202 q^{17} -0.770660 q^{18} +1.12143 q^{19} -1.00000 q^{20} +1.49310 q^{21} -3.24665 q^{22} +6.84777 q^{23} -1.49310 q^{24} +1.00000 q^{25} +5.86956 q^{26} +5.62996 q^{27} -1.00000 q^{28} +4.15418 q^{29} +1.49310 q^{30} -1.02387 q^{31} +1.00000 q^{32} +4.84757 q^{33} -5.04202 q^{34} +1.00000 q^{35} -0.770660 q^{36} -6.05822 q^{37} +1.12143 q^{38} -8.76383 q^{39} -1.00000 q^{40} +5.54247 q^{41} +1.49310 q^{42} +2.89682 q^{43} -3.24665 q^{44} +0.770660 q^{45} +6.84777 q^{46} -7.93238 q^{47} -1.49310 q^{48} +1.00000 q^{49} +1.00000 q^{50} +7.52823 q^{51} +5.86956 q^{52} -8.35834 q^{53} +5.62996 q^{54} +3.24665 q^{55} -1.00000 q^{56} -1.67441 q^{57} +4.15418 q^{58} +2.72471 q^{59} +1.49310 q^{60} -5.61889 q^{61} -1.02387 q^{62} +0.770660 q^{63} +1.00000 q^{64} -5.86956 q^{65} +4.84757 q^{66} -8.43237 q^{67} -5.04202 q^{68} -10.2244 q^{69} +1.00000 q^{70} +1.00000 q^{71} -0.770660 q^{72} -4.54542 q^{73} -6.05822 q^{74} -1.49310 q^{75} +1.12143 q^{76} +3.24665 q^{77} -8.76383 q^{78} -11.8715 q^{79} -1.00000 q^{80} -6.09410 q^{81} +5.54247 q^{82} -5.16195 q^{83} +1.49310 q^{84} +5.04202 q^{85} +2.89682 q^{86} -6.20259 q^{87} -3.24665 q^{88} +15.1333 q^{89} +0.770660 q^{90} -5.86956 q^{91} +6.84777 q^{92} +1.52874 q^{93} -7.93238 q^{94} -1.12143 q^{95} -1.49310 q^{96} -13.2315 q^{97} +1.00000 q^{98} +2.50206 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} + q^{3} + 7 q^{4} - 7 q^{5} + q^{6} - 7 q^{7} + 7 q^{8} + 2 q^{9}+O(q^{10}) $ 7 * q + 7 * q^2 + q^3 + 7 * q^4 - 7 * q^5 + q^6 - 7 * q^7 + 7 * q^8 + 2 * q^9	$ 7 q + 7 q^{2} + q^{3} + 7 q^{4} - 7 q^{5} + q^{6} - 7 q^{7} + 7 q^{8} + 2 q^{9} - 7 q^{10} - 9 q^{11} + q^{12} - 7 q^{14} - q^{15} + 7 q^{16} - 5 q^{17} + 2 q^{18} + 2 q^{19} - 7 q^{20} - q^{21} - 9 q^{22} - 8 q^{23} + q^{24} + 7 q^{25} + q^{27} - 7 q^{28} - 19 q^{29} - q^{30} - 6 q^{31} + 7 q^{32} - 6 q^{33} - 5 q^{34} + 7 q^{35} + 2 q^{36} - 10 q^{37} + 2 q^{38} - 19 q^{39} - 7 q^{40} - 19 q^{41} - q^{42} - 22 q^{43} - 9 q^{44} - 2 q^{45} - 8 q^{46} + 2 q^{47} + q^{48} + 7 q^{49} + 7 q^{50} - 22 q^{51} - 3 q^{53} + q^{54} + 9 q^{55} - 7 q^{56} - 25 q^{57} - 19 q^{58} + 13 q^{59} - q^{60} - 4 q^{61} - 6 q^{62} - 2 q^{63} + 7 q^{64} - 6 q^{66} - 23 q^{67} - 5 q^{68} - 19 q^{69} + 7 q^{70} + 7 q^{71} + 2 q^{72} - 10 q^{74} + q^{75} + 2 q^{76} + 9 q^{77} - 19 q^{78} - 40 q^{79} - 7 q^{80} - 33 q^{81} - 19 q^{82} + 24 q^{83} - q^{84} + 5 q^{85} - 22 q^{86} - 6 q^{87} - 9 q^{88} - 4 q^{89} - 2 q^{90} - 8 q^{92} - 12 q^{93} + 2 q^{94} - 2 q^{95} + q^{96} - 35 q^{97} + 7 q^{98} - 24 q^{99}+O(q^{100}) $ 7 * q + 7 * q^2 + q^3 + 7 * q^4 - 7 * q^5 + q^6 - 7 * q^7 + 7 * q^8 + 2 * q^9 - 7 * q^10 - 9 * q^11 + q^12 - 7 * q^14 - q^15 + 7 * q^16 - 5 * q^17 + 2 * q^18 + 2 * q^19 - 7 * q^20 - q^21 - 9 * q^22 - 8 * q^23 + q^24 + 7 * q^25 + q^27 - 7 * q^28 - 19 * q^29 - q^30 - 6 * q^31 + 7 * q^32 - 6 * q^33 - 5 * q^34 + 7 * q^35 + 2 * q^36 - 10 * q^37 + 2 * q^38 - 19 * q^39 - 7 * q^40 - 19 * q^41 - q^42 - 22 * q^43 - 9 * q^44 - 2 * q^45 - 8 * q^46 + 2 * q^47 + q^48 + 7 * q^49 + 7 * q^50 - 22 * q^51 - 3 * q^53 + q^54 + 9 * q^55 - 7 * q^56 - 25 * q^57 - 19 * q^58 + 13 * q^59 - q^60 - 4 * q^61 - 6 * q^62 - 2 * q^63 + 7 * q^64 - 6 * q^66 - 23 * q^67 - 5 * q^68 - 19 * q^69 + 7 * q^70 + 7 * q^71 + 2 * q^72 - 10 * q^74 + q^75 + 2 * q^76 + 9 * q^77 - 19 * q^78 - 40 * q^79 - 7 * q^80 - 33 * q^81 - 19 * q^82 + 24 * q^83 - q^84 + 5 * q^85 - 22 * q^86 - 6 * q^87 - 9 * q^88 - 4 * q^89 - 2 * q^90 - 8 * q^92 - 12 * q^93 + 2 * q^94 - 2 * q^95 + q^96 - 35 * q^97 + 7 * q^98 - 24 * 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
$3$	−1.49310	−0.862040	−0.431020	−	0.902342i	$-0.641846\pi$
$3$	−1.49310	−0.862040	−0.431020	+	0.902342i	$0.641846\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.49310	−0.609554
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−0.770660	−0.256887
$10$	−1.00000	−0.316228
$11$	−3.24665	−0.978902	−0.489451	−	0.872031i	$-0.662803\pi$
$11$	−3.24665	−0.978902	−0.489451	+	0.872031i	$0.662803\pi$
$12$	−1.49310	−0.431020
$13$	5.86956	1.62792	0.813962	−	0.580919i	$-0.197307\pi$
$13$	5.86956	1.62792	0.813962	+	0.580919i	$0.197307\pi$
$14$	−1.00000	−0.267261
$15$	1.49310	0.385516
$16$	1.00000	0.250000
$17$	−5.04202	−1.22287	−0.611435	−	0.791295i	$-0.709407\pi$
$17$	−5.04202	−1.22287	−0.611435	+	0.791295i	$0.709407\pi$
$18$	−0.770660	−0.181646
$19$	1.12143	0.257274	0.128637	−	0.991692i	$-0.458940\pi$
$19$	1.12143	0.257274	0.128637	+	0.991692i	$0.458940\pi$
$20$	−1.00000	−0.223607
$21$	1.49310	0.325821
$22$	−3.24665	−0.692188
$23$	6.84777	1.42786	0.713930	−	0.700217i	$-0.246914\pi$
$23$	6.84777	1.42786	0.713930	+	0.700217i	$0.246914\pi$
$24$	−1.49310	−0.304777
$25$	1.00000	0.200000
$26$	5.86956	1.15112
$27$	5.62996	1.08349
$28$	−1.00000	−0.188982
$29$	4.15418	0.771411	0.385706	−	0.922622i	$-0.373958\pi$
$29$	4.15418	0.771411	0.385706	+	0.922622i	$0.373958\pi$
$30$	1.49310	0.272601
$31$	−1.02387	−0.183893	−0.0919464	−	0.995764i	$-0.529309\pi$
$31$	−1.02387	−0.183893	−0.0919464	+	0.995764i	$0.529309\pi$
$32$	1.00000	0.176777
$33$	4.84757	0.843853
$34$	−5.04202	−0.864699
$35$	1.00000	0.169031
$36$	−0.770660	−0.128443
$37$	−6.05822	−0.995966	−0.497983	−	0.867187i	$-0.665926\pi$
$37$	−6.05822	−0.995966	−0.497983	+	0.867187i	$0.665926\pi$
$38$	1.12143	0.181920
$39$	−8.76383	−1.40334
$40$	−1.00000	−0.158114
$41$	5.54247	0.865588	0.432794	−	0.901493i	$-0.357528\pi$
$41$	5.54247	0.865588	0.432794	+	0.901493i	$0.357528\pi$
$42$	1.49310	0.230390
$43$	2.89682	0.441761	0.220881	−	0.975301i	$-0.429107\pi$
$43$	2.89682	0.441761	0.220881	+	0.975301i	$0.429107\pi$
$44$	−3.24665	−0.489451
$45$	0.770660	0.114883
$46$	6.84777	1.00965
$47$	−7.93238	−1.15706	−0.578528	−	0.815662i	$-0.696373\pi$
$47$	−7.93238	−1.15706	−0.578528	+	0.815662i	$0.696373\pi$
$48$	−1.49310	−0.215510
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	7.52823	1.05416
$52$	5.86956	0.813962
$53$	−8.35834	−1.14811	−0.574053	−	0.818818i	$-0.694630\pi$
$53$	−8.35834	−1.14811	−0.574053	+	0.818818i	$0.694630\pi$
$54$	5.62996	0.766141
$55$	3.24665	0.437778
$56$	−1.00000	−0.133631
$57$	−1.67441	−0.221781
$58$	4.15418	0.545470
$59$	2.72471	0.354727	0.177364	−	0.984145i	$-0.443243\pi$
$59$	2.72471	0.354727	0.177364	+	0.984145i	$0.443243\pi$
$60$	1.49310	0.192758
$61$	−5.61889	−0.719425	−0.359712	−	0.933063i	$-0.617125\pi$
$61$	−5.61889	−0.719425	−0.359712	+	0.933063i	$0.617125\pi$
$62$	−1.02387	−0.130032
$63$	0.770660	0.0970940
$64$	1.00000	0.125000
$65$	−5.86956	−0.728029
$66$	4.84757	0.596694
$67$	−8.43237	−1.03018	−0.515089	−	0.857137i	$-0.672241\pi$
$67$	−8.43237	−1.03018	−0.515089	+	0.857137i	$0.672241\pi$
$68$	−5.04202	−0.611435
$69$	−10.2244	−1.23087
$70$	1.00000	0.119523
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	−0.770660	−0.0908231
$73$	−4.54542	−0.532001	−0.266001	−	0.963973i	$-0.585702\pi$
$73$	−4.54542	−0.532001	−0.266001	+	0.963973i	$0.585702\pi$
$74$	−6.05822	−0.704254
$75$	−1.49310	−0.172408
$76$	1.12143	0.128637
$77$	3.24665	0.369990
$78$	−8.76383	−0.992308
$79$	−11.8715	−1.33565	−0.667824	−	0.744319i	$-0.732774\pi$
$79$	−11.8715	−1.33565	−0.667824	+	0.744319i	$0.732774\pi$
$80$	−1.00000	−0.111803
$81$	−6.09410	−0.677123
$82$	5.54247	0.612063
$83$	−5.16195	−0.566598	−0.283299	−	0.959032i	$-0.591429\pi$
$83$	−5.16195	−0.566598	−0.283299	+	0.959032i	$0.591429\pi$
$84$	1.49310	0.162910
$85$	5.04202	0.546884
$86$	2.89682	0.312373
$87$	−6.20259	−0.664988
$88$	−3.24665	−0.346094
$89$	15.1333	1.60413	0.802063	−	0.597240i	$-0.203736\pi$
$89$	15.1333	1.60413	0.802063	+	0.597240i	$0.203736\pi$
$90$	0.770660	0.0812347
$91$	−5.86956	−0.615297
$92$	6.84777	0.713930
$93$	1.52874	0.158523
$94$	−7.93238	−0.818163
$95$	−1.12143	−0.115056
$96$	−1.49310	−0.152389
$97$	−13.2315	−1.34345	−0.671726	−	0.740799i	$-0.734447\pi$
$97$	−13.2315	−1.34345	−0.671726	+	0.740799i	$0.734447\pi$
$98$	1.00000	0.101015
$99$	2.50206	0.251467
$100$	1.00000	0.100000
$101$	−3.61003	−0.359211	−0.179606	−	0.983739i	$-0.557482\pi$
$101$	−3.61003	−0.359211	−0.179606	+	0.983739i	$0.557482\pi$
$102$	7.52823	0.745405
$103$	13.0962	1.29041	0.645203	−	0.764011i	$-0.276773\pi$
$103$	13.0962	1.29041	0.645203	+	0.764011i	$0.276773\pi$
$104$	5.86956	0.575558
$105$	−1.49310	−0.145711
$106$	−8.35834	−0.811834
$107$	−0.259232	−0.0250609	−0.0125304	−	0.999921i	$-0.503989\pi$
$107$	−0.259232	−0.0250609	−0.0125304	+	0.999921i	$0.503989\pi$
$108$	5.62996	0.541743
$109$	−17.9608	−1.72033	−0.860165	−	0.510016i	$-0.829639\pi$
$109$	−17.9608	−1.72033	−0.860165	+	0.510016i	$0.829639\pi$
$110$	3.24665	0.309556
$111$	9.04552	0.858563
$112$	−1.00000	−0.0944911
$113$	−18.5790	−1.74776	−0.873882	−	0.486138i	$-0.838405\pi$
$113$	−18.5790	−1.74776	−0.873882	+	0.486138i	$0.838405\pi$
$114$	−1.67441	−0.156823
$115$	−6.84777	−0.638558
$116$	4.15418	0.385706
$117$	−4.52344	−0.418192
$118$	2.72471	0.250830
$119$	5.04202	0.462201
$120$	1.49310	0.136301
$121$	−0.459253	−0.0417502
$122$	−5.61889	−0.508710
$123$	−8.27545	−0.746172
$124$	−1.02387	−0.0919464
$125$	−1.00000	−0.0894427
$126$	0.770660	0.0686558
$127$	6.92393	0.614399	0.307200	−	0.951645i	$-0.400608\pi$
$127$	6.92393	0.614399	0.307200	+	0.951645i	$0.400608\pi$
$128$	1.00000	0.0883883
$129$	−4.32524	−0.380816
$130$	−5.86956	−0.514795
$131$	5.15416	0.450321	0.225161	−	0.974322i	$-0.427709\pi$
$131$	5.15416	0.450321	0.225161	+	0.974322i	$0.427709\pi$
$132$	4.84757	0.421927
$133$	−1.12143	−0.0972405
$134$	−8.43237	−0.728446
$135$	−5.62996	−0.484550
$136$	−5.04202	−0.432350
$137$	−7.46788	−0.638024	−0.319012	−	0.947751i	$-0.603351\pi$
$137$	−7.46788	−0.638024	−0.319012	+	0.947751i	$0.603351\pi$
$138$	−10.2244	−0.870358
$139$	−18.9516	−1.60746	−0.803728	−	0.594997i	$-0.797153\pi$
$139$	−18.9516	−1.60746	−0.803728	+	0.594997i	$0.797153\pi$
$140$	1.00000	0.0845154
$141$	11.8438	0.997429
$142$	1.00000	0.0839181
$143$	−19.0564	−1.59358
$144$	−0.770660	−0.0642217
$145$	−4.15418	−0.344986
$146$	−4.54542	−0.376182
$147$	−1.49310	−0.123149
$148$	−6.05822	−0.497983
$149$	−7.44038	−0.609540	−0.304770	−	0.952426i	$-0.598580\pi$
$149$	−7.44038	−0.609540	−0.304770	+	0.952426i	$0.598580\pi$
$150$	−1.49310	−0.121911
$151$	−4.90314	−0.399012	−0.199506	−	0.979897i	$-0.563934\pi$
$151$	−4.90314	−0.399012	−0.199506	+	0.979897i	$0.563934\pi$
$152$	1.12143	0.0909601
$153$	3.88568	0.314139
$154$	3.24665	0.261623
$155$	1.02387	0.0822393
$156$	−8.76383	−0.701668
$157$	−2.18799	−0.174620	−0.0873101	−	0.996181i	$-0.527827\pi$
$157$	−2.18799	−0.174620	−0.0873101	+	0.996181i	$0.527827\pi$
$158$	−11.8715	−0.944446
$159$	12.4798	0.989714
$160$	−1.00000	−0.0790569
$161$	−6.84777	−0.539680
$162$	−6.09410	−0.478798
$163$	−10.7473	−0.841793	−0.420896	−	0.907109i	$-0.638284\pi$
$163$	−10.7473	−0.841793	−0.420896	+	0.907109i	$0.638284\pi$
$164$	5.54247	0.432794
$165$	−4.84757	−0.377383
$166$	−5.16195	−0.400645
$167$	21.6788	1.67756	0.838778	−	0.544473i	$-0.183270\pi$
$167$	21.6788	1.67756	0.838778	+	0.544473i	$0.183270\pi$
$168$	1.49310	0.115195
$169$	21.4517	1.65013
$170$	5.04202	0.386705
$171$	−0.864242	−0.0660903
$172$	2.89682	0.220881
$173$	11.3328	0.861616	0.430808	−	0.902444i	$-0.358229\pi$
$173$	11.3328	0.861616	0.430808	+	0.902444i	$0.358229\pi$
$174$	−6.20259	−0.470217
$175$	−1.00000	−0.0755929
$176$	−3.24665	−0.244726
$177$	−4.06826	−0.305789
$178$	15.1333	1.13429
$179$	20.8813	1.56074	0.780369	−	0.625319i	$-0.215031\pi$
$179$	20.8813	1.56074	0.780369	+	0.625319i	$0.215031\pi$
$180$	0.770660	0.0574416
$181$	7.82735	0.581802	0.290901	−	0.956753i	$-0.406045\pi$
$181$	7.82735	0.581802	0.290901	+	0.956753i	$0.406045\pi$
$182$	−5.86956	−0.435081
$183$	8.38955	0.620173
$184$	6.84777	0.504825
$185$	6.05822	0.445409
$186$	1.52874	0.112093
$187$	16.3697	1.19707
$188$	−7.93238	−0.578528
$189$	−5.62996	−0.409520
$190$	−1.12143	−0.0813572
$191$	−18.3531	−1.32798	−0.663992	−	0.747740i	$-0.731139\pi$
$191$	−18.3531	−1.32798	−0.663992	+	0.747740i	$0.731139\pi$
$192$	−1.49310	−0.107755
$193$	−25.2248	−1.81572	−0.907860	−	0.419274i	$-0.862285\pi$
$193$	−25.2248	−1.81572	−0.907860	+	0.419274i	$0.862285\pi$
$194$	−13.2315	−0.949964
$195$	8.76383	0.627591
$196$	1.00000	0.0714286
$197$	12.2121	0.870077	0.435038	−	0.900412i	$-0.356735\pi$
$197$	12.2121	0.870077	0.435038	+	0.900412i	$0.356735\pi$
$198$	2.50206	0.177814
$199$	−6.12915	−0.434484	−0.217242	−	0.976118i	$-0.569706\pi$
$199$	−6.12915	−0.434484	−0.217242	+	0.976118i	$0.569706\pi$
$200$	1.00000	0.0707107
$201$	12.5903	0.888055
$202$	−3.61003	−0.254001
$203$	−4.15418	−0.291566
$204$	7.52823	0.527081
$205$	−5.54247	−0.387103
$206$	13.0962	0.912455
$207$	−5.27730	−0.366798
$208$	5.86956	0.406981
$209$	−3.64090	−0.251846
$210$	−1.49310	−0.103034
$211$	−14.8959	−1.02547	−0.512737	−	0.858546i	$-0.671368\pi$
$211$	−14.8959	−1.02547	−0.512737	+	0.858546i	$0.671368\pi$
$212$	−8.35834	−0.574053
$213$	−1.49310	−0.102305
$214$	−0.259232	−0.0177207
$215$	−2.89682	−0.197562
$216$	5.62996	0.383070
$217$	1.02387	0.0695049
$218$	−17.9608	−1.21646
$219$	6.78676	0.458606
$220$	3.24665	0.218889
$221$	−29.5944	−1.99074
$222$	9.04552	0.607095
$223$	12.3684	0.828248	0.414124	−	0.910220i	$-0.364088\pi$
$223$	12.3684	0.828248	0.414124	+	0.910220i	$0.364088\pi$
$224$	−1.00000	−0.0668153
$225$	−0.770660	−0.0513773
$226$	−18.5790	−1.23586
$227$	17.3065	1.14867	0.574336	−	0.818619i	$-0.305260\pi$
$227$	17.3065	1.14867	0.574336	+	0.818619i	$0.305260\pi$
$228$	−1.67441	−0.110890
$229$	−21.8071	−1.44105	−0.720527	−	0.693427i	$-0.756100\pi$
$229$	−21.8071	−1.44105	−0.720527	+	0.693427i	$0.756100\pi$
$230$	−6.84777	−0.451529
$231$	−4.84757	−0.318947
$232$	4.15418	0.272735
$233$	25.5433	1.67340	0.836698	−	0.547664i	$-0.184483\pi$
$233$	25.5433	1.67340	0.836698	+	0.547664i	$0.184483\pi$
$234$	−4.52344	−0.295706
$235$	7.93238	0.517452
$236$	2.72471	0.177364
$237$	17.7253	1.15138
$238$	5.04202	0.326826
$239$	−9.36635	−0.605859	−0.302929	−	0.953013i	$-0.597965\pi$
$239$	−9.36635	−0.605859	−0.302929	+	0.953013i	$0.597965\pi$
$240$	1.49310	0.0963790
$241$	−0.921156	−0.0593369	−0.0296684	−	0.999560i	$-0.509445\pi$
$241$	−0.921156	−0.0593369	−0.0296684	+	0.999560i	$0.509445\pi$
$242$	−0.459253	−0.0295219
$243$	−7.79080	−0.499780
$244$	−5.61889	−0.359712
$245$	−1.00000	−0.0638877
$246$	−8.27545	−0.527623
$247$	6.58231	0.418822
$248$	−1.02387	−0.0650159
$249$	7.70730	0.488430
$250$	−1.00000	−0.0632456
$251$	−19.3511	−1.22143	−0.610717	−	0.791849i	$-0.709119\pi$
$251$	−19.3511	−1.22143	−0.610717	+	0.791849i	$0.709119\pi$
$252$	0.770660	0.0485470
$253$	−22.2323	−1.39773
$254$	6.92393	0.434446
$255$	−7.52823	−0.471436
$256$	1.00000	0.0625000
$257$	−14.8453	−0.926024	−0.463012	−	0.886352i	$-0.653231\pi$
$257$	−14.8453	−0.926024	−0.463012	+	0.886352i	$0.653231\pi$
$258$	−4.32524	−0.269278
$259$	6.05822	0.376440
$260$	−5.86956	−0.364015
$261$	−3.20146	−0.198165
$262$	5.15416	0.318425
$263$	31.9615	1.97083	0.985414	−	0.170173i	$-0.0544327\pi$
$263$	31.9615	1.97083	0.985414	+	0.170173i	$0.0544327\pi$
$264$	4.84757	0.298347
$265$	8.35834	0.513449
$266$	−1.12143	−0.0687594
$267$	−22.5955	−1.38282
$268$	−8.43237	−0.515089
$269$	−5.82312	−0.355042	−0.177521	−	0.984117i	$-0.556808\pi$
$269$	−5.82312	−0.355042	−0.177521	+	0.984117i	$0.556808\pi$
$270$	−5.62996	−0.342629
$271$	−21.8815	−1.32920	−0.664602	−	0.747198i	$-0.731399\pi$
$271$	−21.8815	−1.32920	−0.664602	+	0.747198i	$0.731399\pi$
$272$	−5.04202	−0.305717
$273$	8.76383	0.530411
$274$	−7.46788	−0.451151
$275$	−3.24665	−0.195780
$276$	−10.2244	−0.615436
$277$	−17.1327	−1.02941	−0.514703	−	0.857368i	$-0.672098\pi$
$277$	−17.1327	−1.02941	−0.514703	+	0.857368i	$0.672098\pi$
$278$	−18.9516	−1.13664
$279$	0.789057	0.0472396
$280$	1.00000	0.0597614
$281$	−15.7231	−0.937961	−0.468981	−	0.883208i	$-0.655379\pi$
$281$	−15.7231	−0.937961	−0.468981	+	0.883208i	$0.655379\pi$
$282$	11.8438	0.705289
$283$	−10.0317	−0.596322	−0.298161	−	0.954516i	$-0.596373\pi$
$283$	−10.0317	−0.596322	−0.298161	+	0.954516i	$0.596373\pi$
$284$	1.00000	0.0593391
$285$	1.67441	0.0991833
$286$	−19.0564	−1.12683
$287$	−5.54247	−0.327162
$288$	−0.770660	−0.0454116
$289$	8.42196	0.495409
$290$	−4.15418	−0.243942
$291$	19.7559	1.15811
$292$	−4.54542	−0.266001
$293$	−1.53907	−0.0899135	−0.0449568	−	0.998989i	$-0.514315\pi$
$293$	−1.53907	−0.0899135	−0.0449568	+	0.998989i	$0.514315\pi$
$294$	−1.49310	−0.0870792
$295$	−2.72471	−0.158639
$296$	−6.05822	−0.352127
$297$	−18.2785	−1.06063
$298$	−7.44038	−0.431010
$299$	40.1934	2.32445
$300$	−1.49310	−0.0862040
$301$	−2.89682	−0.166970
$302$	−4.90314	−0.282144
$303$	5.39013	0.309655
$304$	1.12143	0.0643185
$305$	5.61889	0.321737
$306$	3.88568	0.222130
$307$	−3.14440	−0.179460	−0.0897301	−	0.995966i	$-0.528600\pi$
$307$	−3.14440	−0.179460	−0.0897301	+	0.995966i	$0.528600\pi$
$308$	3.24665	0.184995
$309$	−19.5539	−1.11238
$310$	1.02387	0.0581520
$311$	−7.90616	−0.448317	−0.224159	−	0.974553i	$-0.571963\pi$
$311$	−7.90616	−0.448317	−0.224159	+	0.974553i	$0.571963\pi$
$312$	−8.76383	−0.496154
$313$	−17.9615	−1.01524	−0.507622	−	0.861580i	$-0.669475\pi$
$313$	−17.9615	−1.01524	−0.507622	+	0.861580i	$0.669475\pi$
$314$	−2.18799	−0.123475
$315$	−0.770660	−0.0434218
$316$	−11.8715	−0.667824
$317$	23.1100	1.29799	0.648995	−	0.760793i	$-0.275190\pi$
$317$	23.1100	1.29799	0.648995	+	0.760793i	$0.275190\pi$
$318$	12.4798	0.699833
$319$	−13.4872	−0.755136
$320$	−1.00000	−0.0559017
$321$	0.387058	0.0216035
$322$	−6.84777	−0.381611
$323$	−5.65428	−0.314613
$324$	−6.09410	−0.338561
$325$	5.86956	0.325585
$326$	−10.7473	−0.595237
$327$	26.8172	1.48299
$328$	5.54247	0.306032
$329$	7.93238	0.437326
$330$	−4.84757	−0.266850
$331$	−5.04091	−0.277073	−0.138537	−	0.990357i	$-0.544240\pi$
$331$	−5.04091	−0.277073	−0.138537	+	0.990357i	$0.544240\pi$
$332$	−5.16195	−0.283299
$333$	4.66883	0.255850
$334$	21.6788	1.18621
$335$	8.43237	0.460710
$336$	1.49310	0.0814551
$337$	−25.9236	−1.41215	−0.706073	−	0.708139i	$-0.749535\pi$
$337$	−25.9236	−1.41215	−0.706073	+	0.708139i	$0.749535\pi$
$338$	21.4517	1.16682
$339$	27.7402	1.50664
$340$	5.04202	0.273442
$341$	3.32415	0.180013
$342$	−0.864242	−0.0467329
$343$	−1.00000	−0.0539949
$344$	2.89682	0.156186
$345$	10.2244	0.550463
$346$	11.3328	0.609255
$347$	−2.51173	−0.134837	−0.0674183	−	0.997725i	$-0.521476\pi$
$347$	−2.51173	−0.134837	−0.0674183	+	0.997725i	$0.521476\pi$
$348$	−6.20259	−0.332494
$349$	28.2910	1.51438	0.757191	−	0.653193i	$-0.226571\pi$
$349$	28.2910	1.51438	0.757191	+	0.653193i	$0.226571\pi$
$350$	−1.00000	−0.0534522
$351$	33.0454	1.76383
$352$	−3.24665	−0.173047
$353$	21.9558	1.16859	0.584295	−	0.811541i	$-0.301371\pi$
$353$	21.9558	1.16859	0.584295	+	0.811541i	$0.301371\pi$
$354$	−4.06826	−0.216226
$355$	−1.00000	−0.0530745
$356$	15.1333	0.802063
$357$	−7.52823	−0.398436
$358$	20.8813	1.10361
$359$	−26.5421	−1.40084	−0.700420	−	0.713731i	$-0.747004\pi$
$359$	−26.5421	−1.40084	−0.700420	+	0.713731i	$0.747004\pi$
$360$	0.770660	0.0406173
$361$	−17.7424	−0.933810
$362$	7.82735	0.411396
$363$	0.685709	0.0359904
$364$	−5.86956	−0.307649
$365$	4.54542	0.237918
$366$	8.38955	0.438529
$367$	18.6534	0.973697	0.486849	−	0.873486i	$-0.338146\pi$
$367$	18.6534	0.973697	0.486849	+	0.873486i	$0.338146\pi$
$368$	6.84777	0.356965
$369$	−4.27136	−0.222358
$370$	6.05822	0.314952
$371$	8.35834	0.433943
$372$	1.52874	0.0792615
$373$	−28.3509	−1.46796	−0.733978	−	0.679174i	$-0.762338\pi$
$373$	−28.3509	−1.46796	−0.733978	+	0.679174i	$0.762338\pi$
$374$	16.3697	0.846456
$375$	1.49310	0.0771032
$376$	−7.93238	−0.409081
$377$	24.3832	1.25580
$378$	−5.62996	−0.289574
$379$	−4.57059	−0.234776	−0.117388	−	0.993086i	$-0.537452\pi$
$379$	−4.57059	−0.234776	−0.117388	+	0.993086i	$0.537452\pi$
$380$	−1.12143	−0.0575282
$381$	−10.3381	−0.529637
$382$	−18.3531	−0.939026
$383$	20.9227	1.06910	0.534550	−	0.845137i	$-0.320481\pi$
$383$	20.9227	1.06910	0.534550	+	0.845137i	$0.320481\pi$
$384$	−1.49310	−0.0761943
$385$	−3.24665	−0.165465
$386$	−25.2248	−1.28391
$387$	−2.23247	−0.113483
$388$	−13.2315	−0.671726
$389$	16.6437	0.843870	0.421935	−	0.906626i	$-0.361351\pi$
$389$	16.6437	0.843870	0.421935	+	0.906626i	$0.361351\pi$
$390$	8.76383	0.443774
$391$	−34.5266	−1.74609
$392$	1.00000	0.0505076
$393$	−7.69567	−0.388195
$394$	12.2121	0.615237
$395$	11.8715	0.597320
$396$	2.50206	0.125733
$397$	−22.3322	−1.12082	−0.560410	−	0.828216i	$-0.689356\pi$
$397$	−22.3322	−1.12082	−0.560410	+	0.828216i	$0.689356\pi$
$398$	−6.12915	−0.307227
$399$	1.67441	0.0838252
$400$	1.00000	0.0500000
$401$	−36.0314	−1.79932	−0.899662	−	0.436588i	$-0.856187\pi$
$401$	−36.0314	−1.79932	−0.899662	+	0.436588i	$0.856187\pi$
$402$	12.5903	0.627950
$403$	−6.00968	−0.299363
$404$	−3.61003	−0.179606
$405$	6.09410	0.302818
$406$	−4.15418	−0.206168
$407$	19.6689	0.974953
$408$	7.52823	0.372703
$409$	31.3817	1.55172	0.775861	−	0.630903i	$-0.217316\pi$
$409$	31.3817	1.55172	0.775861	+	0.630903i	$0.217316\pi$
$410$	−5.54247	−0.273723
$411$	11.1503	0.550002
$412$	13.0962	0.645203
$413$	−2.72471	−0.134074
$414$	−5.27730	−0.259365
$415$	5.16195	0.253390
$416$	5.86956	0.287779
$417$	28.2966	1.38569
$418$	−3.64090	−0.178082
$419$	−27.9417	−1.36504	−0.682520	−	0.730867i	$-0.739116\pi$
$419$	−27.9417	−1.36504	−0.682520	+	0.730867i	$0.739116\pi$
$420$	−1.49310	−0.0728557
$421$	18.8496	0.918675	0.459337	−	0.888262i	$-0.348087\pi$
$421$	18.8496	0.918675	0.459337	+	0.888262i	$0.348087\pi$
$422$	−14.8959	−0.725120
$423$	6.11317	0.297232
$424$	−8.35834	−0.405917
$425$	−5.04202	−0.244574
$426$	−1.49310	−0.0723408
$427$	5.61889	0.271917
$428$	−0.259232	−0.0125304
$429$	28.4531	1.37373
$430$	−2.89682	−0.139697
$431$	31.8766	1.53544	0.767720	−	0.640786i	$-0.221391\pi$
$431$	31.8766	1.53544	0.767720	+	0.640786i	$0.221391\pi$
$432$	5.62996	0.270872
$433$	3.33801	0.160414	0.0802072	−	0.996778i	$-0.474442\pi$
$433$	3.33801	0.160414	0.0802072	+	0.996778i	$0.474442\pi$
$434$	1.02387	0.0491474
$435$	6.20259	0.297391
$436$	−17.9608	−0.860165
$437$	7.67931	0.367351
$438$	6.78676	0.324284
$439$	−12.2581	−0.585050	−0.292525	−	0.956258i	$-0.594495\pi$
$439$	−12.2581	−0.585050	−0.292525	+	0.956258i	$0.594495\pi$
$440$	3.24665	0.154778
$441$	−0.770660	−0.0366981
$442$	−29.5944	−1.40766
$443$	15.8390	0.752534	0.376267	−	0.926511i	$-0.377207\pi$
$443$	15.8390	0.752534	0.376267	+	0.926511i	$0.377207\pi$
$444$	9.04552	0.429281
$445$	−15.1333	−0.717387
$446$	12.3684	0.585660
$447$	11.1092	0.525448
$448$	−1.00000	−0.0472456
$449$	−35.2165	−1.66197	−0.830984	−	0.556297i	$-0.812222\pi$
$449$	−35.2165	−1.66197	−0.830984	+	0.556297i	$0.812222\pi$
$450$	−0.770660	−0.0363293
$451$	−17.9945	−0.847326
$452$	−18.5790	−0.873882
$453$	7.32087	0.343964
$454$	17.3065	0.812234
$455$	5.86956	0.275169
$456$	−1.67441	−0.0784113
$457$	15.4710	0.723701	0.361851	−	0.932236i	$-0.382145\pi$
$457$	15.4710	0.723701	0.361851	+	0.932236i	$0.382145\pi$
$458$	−21.8071	−1.01898
$459$	−28.3864	−1.32496
$460$	−6.84777	−0.319279
$461$	−35.0992	−1.63473	−0.817367	−	0.576117i	$-0.804567\pi$
$461$	−35.0992	−1.63473	−0.817367	+	0.576117i	$0.804567\pi$
$462$	−4.84757	−0.225529
$463$	−16.7054	−0.776367	−0.388183	−	0.921582i	$-0.626897\pi$
$463$	−16.7054	−0.776367	−0.388183	+	0.921582i	$0.626897\pi$
$464$	4.15418	0.192853
$465$	−1.52874	−0.0708936
$466$	25.5433	1.18327
$467$	36.9080	1.70790	0.853949	−	0.520357i	$-0.174201\pi$
$467$	36.9080	1.70790	0.853949	+	0.520357i	$0.174201\pi$
$468$	−4.52344	−0.209096
$469$	8.43237	0.389371
$470$	7.93238	0.365893
$471$	3.26687	0.150530
$472$	2.72471	0.125415
$473$	−9.40498	−0.432441
$474$	17.7253	0.814150
$475$	1.12143	0.0514548
$476$	5.04202	0.231101
$477$	6.44144	0.294933
$478$	−9.36635	−0.428407
$479$	15.8176	0.722723	0.361362	−	0.932426i	$-0.382312\pi$
$479$	15.8176	0.722723	0.361362	+	0.932426i	$0.382312\pi$
$480$	1.49310	0.0681503
$481$	−35.5591	−1.62136
$482$	−0.921156	−0.0419575
$483$	10.2244	0.465226
$484$	−0.459253	−0.0208751
$485$	13.2315	0.600810
$486$	−7.79080	−0.353398
$487$	26.1498	1.18496	0.592480	−	0.805585i	$-0.298149\pi$
$487$	26.1498	1.18496	0.592480	+	0.805585i	$0.298149\pi$
$488$	−5.61889	−0.254355
$489$	16.0467	0.725659
$490$	−1.00000	−0.0451754
$491$	−4.53765	−0.204781	−0.102391	−	0.994744i	$-0.532649\pi$
$491$	−4.53765	−0.204781	−0.102391	+	0.994744i	$0.532649\pi$
$492$	−8.27545	−0.373086
$493$	−20.9454	−0.943335
$494$	6.58231	0.296152
$495$	−2.50206	−0.112459
$496$	−1.02387	−0.0459732
$497$	−1.00000	−0.0448561
$498$	7.70730	0.345372
$499$	9.19046	0.411422	0.205711	−	0.978613i	$-0.434049\pi$
$499$	9.19046	0.411422	0.205711	+	0.978613i	$0.434049\pi$
$500$	−1.00000	−0.0447214
$501$	−32.3686	−1.44612
$502$	−19.3511	−0.863684
$503$	20.1371	0.897868	0.448934	−	0.893565i	$-0.351804\pi$
$503$	20.1371	0.897868	0.448934	+	0.893565i	$0.351804\pi$
$504$	0.770660	0.0343279
$505$	3.61003	0.160644
$506$	−22.2323	−0.988348
$507$	−32.0296	−1.42248
$508$	6.92393	0.307200
$509$	41.2725	1.82937	0.914686	−	0.404166i	$-0.132438\pi$
$509$	41.2725	1.82937	0.914686	+	0.404166i	$0.132438\pi$
$510$	−7.52823	−0.333355
$511$	4.54542	0.201078
$512$	1.00000	0.0441942
$513$	6.31362	0.278753
$514$	−14.8453	−0.654798
$515$	−13.0962	−0.577087
$516$	−4.32524	−0.190408
$517$	25.7537	1.13265
$518$	6.05822	0.266183
$519$	−16.9210	−0.742748
$520$	−5.86956	−0.257397
$521$	−21.0692	−0.923057	−0.461529	−	0.887125i	$-0.652699\pi$
$521$	−21.0692	−0.923057	−0.461529	+	0.887125i	$0.652699\pi$
$522$	−3.20146	−0.140124
$523$	−22.8940	−1.00109	−0.500543	−	0.865712i	$-0.666866\pi$
$523$	−22.8940	−1.00109	−0.500543	+	0.865712i	$0.666866\pi$
$524$	5.15416	0.225161
$525$	1.49310	0.0651641
$526$	31.9615	1.39359
$527$	5.16238	0.224877
$528$	4.84757	0.210963
$529$	23.8920	1.03878
$530$	8.35834	0.363063
$531$	−2.09983	−0.0911247
$532$	−1.12143	−0.0486202
$533$	32.5319	1.40911
$534$	−22.5955	−0.977802
$535$	0.259232	0.0112076
$536$	−8.43237	−0.364223
$537$	−31.1778	−1.34542
$538$	−5.82312	−0.251052
$539$	−3.24665	−0.139843
$540$	−5.62996	−0.242275
$541$	−41.1602	−1.76962	−0.884808	−	0.465956i	$-0.845710\pi$
$541$	−41.1602	−1.76962	−0.884808	+	0.465956i	$0.845710\pi$
$542$	−21.8815	−0.939889
$543$	−11.6870	−0.501537
$544$	−5.04202	−0.216175
$545$	17.9608	0.769355
$546$	8.76383	0.375057
$547$	11.1895	0.478428	0.239214	−	0.970967i	$-0.423110\pi$
$547$	11.1895	0.478428	0.239214	+	0.970967i	$0.423110\pi$
$548$	−7.46788	−0.319012
$549$	4.33025	0.184811
$550$	−3.24665	−0.138438
$551$	4.65863	0.198464
$552$	−10.2244	−0.435179
$553$	11.8715	0.504827
$554$	−17.1327	−0.727901
$555$	−9.04552	−0.383961
$556$	−18.9516	−0.803728
$557$	−5.02753	−0.213023	−0.106512	−	0.994311i	$-0.533968\pi$
$557$	−5.02753	−0.213023	−0.106512	+	0.994311i	$0.533968\pi$
$558$	0.789057	0.0334034
$559$	17.0031	0.719154
$560$	1.00000	0.0422577
$561$	−24.4415	−1.03192
$562$	−15.7231	−0.663239
$563$	−6.18330	−0.260595	−0.130298	−	0.991475i	$-0.541593\pi$
$563$	−6.18330	−0.260595	−0.130298	+	0.991475i	$0.541593\pi$
$564$	11.8438	0.498715
$565$	18.5790	0.781624
$566$	−10.0317	−0.421664
$567$	6.09410	0.255928
$568$	1.00000	0.0419591
$569$	−24.0902	−1.00992	−0.504958	−	0.863144i	$-0.668492\pi$
$569$	−24.0902	−1.00992	−0.504958	+	0.863144i	$0.668492\pi$
$570$	1.67441	0.0701332
$571$	8.19818	0.343083	0.171542	−	0.985177i	$-0.445125\pi$
$571$	8.19818	0.343083	0.171542	+	0.985177i	$0.445125\pi$
$572$	−19.0564	−0.796789
$573$	27.4030	1.14478
$574$	−5.54247	−0.231338
$575$	6.84777	0.285572
$576$	−0.770660	−0.0321108
$577$	−5.47175	−0.227792	−0.113896	−	0.993493i	$-0.536333\pi$
$577$	−5.47175	−0.227792	−0.113896	+	0.993493i	$0.536333\pi$
$578$	8.42196	0.350307
$579$	37.6631	1.56522
$580$	−4.15418	−0.172493
$581$	5.16195	0.214154
$582$	19.7559	0.818908
$583$	27.1366	1.12388
$584$	−4.54542	−0.188091
$585$	4.52344	0.187021
$586$	−1.53907	−0.0635785
$587$	37.7454	1.55792	0.778960	−	0.627074i	$-0.215748\pi$
$587$	37.7454	1.55792	0.778960	+	0.627074i	$0.215748\pi$
$588$	−1.49310	−0.0615743
$589$	−1.14820	−0.0473108
$590$	−2.72471	−0.112175
$591$	−18.2339	−0.750041
$592$	−6.05822	−0.248991
$593$	−12.1465	−0.498796	−0.249398	−	0.968401i	$-0.580233\pi$
$593$	−12.1465	−0.498796	−0.249398	+	0.968401i	$0.580233\pi$
$594$	−18.2785	−0.749977
$595$	−5.04202	−0.206703
$596$	−7.44038	−0.304770
$597$	9.15142	0.374543
$598$	40.1934	1.64363
$599$	14.0415	0.573720	0.286860	−	0.957973i	$-0.407389\pi$
$599$	14.0415	0.573720	0.286860	+	0.957973i	$0.407389\pi$
$600$	−1.49310	−0.0609554
$601$	−18.9912	−0.774666	−0.387333	−	0.921940i	$-0.626604\pi$
$601$	−18.9912	−0.774666	−0.387333	+	0.921940i	$0.626604\pi$
$602$	−2.89682	−0.118066
$603$	6.49849	0.264639
$604$	−4.90314	−0.199506
$605$	0.459253	0.0186713
$606$	5.39013	0.218959
$607$	22.6123	0.917806	0.458903	−	0.888486i	$-0.348243\pi$
$607$	22.6123	0.917806	0.458903	+	0.888486i	$0.348243\pi$
$608$	1.12143	0.0454801
$609$	6.20259	0.251342
$610$	5.61889	0.227502
$611$	−46.5596	−1.88360
$612$	3.88568	0.157069
$613$	21.4846	0.867757	0.433878	−	0.900971i	$-0.357145\pi$
$613$	21.4846	0.867757	0.433878	+	0.900971i	$0.357145\pi$
$614$	−3.14440	−0.126897
$615$	8.27545	0.333698
$616$	3.24665	0.130811
$617$	−20.0238	−0.806129	−0.403064	−	0.915172i	$-0.632055\pi$
$617$	−20.0238	−0.806129	−0.403064	+	0.915172i	$0.632055\pi$
$618$	−19.5539	−0.786573
$619$	−14.4457	−0.580621	−0.290310	−	0.956933i	$-0.593759\pi$
$619$	−14.4457	−0.580621	−0.290310	+	0.956933i	$0.593759\pi$
$620$	1.02387	0.0411197
$621$	38.5527	1.54707
$622$	−7.90616	−0.317008
$623$	−15.1333	−0.606302
$624$	−8.76383	−0.350834
$625$	1.00000	0.0400000
$626$	−17.9615	−0.717886
$627$	5.43622	0.217102
$628$	−2.18799	−0.0873101
$629$	30.5457	1.21794
$630$	−0.770660	−0.0307038
$631$	−9.53188	−0.379458	−0.189729	−	0.981836i	$-0.560761\pi$
$631$	−9.53188	−0.379458	−0.189729	+	0.981836i	$0.560761\pi$
$632$	−11.8715	−0.472223
$633$	22.2410	0.884000
$634$	23.1100	0.917817
$635$	−6.92393	−0.274768
$636$	12.4798	0.494857
$637$	5.86956	0.232560
$638$	−13.4872	−0.533962
$639$	−0.770660	−0.0304868
$640$	−1.00000	−0.0395285
$641$	−24.5379	−0.969190	−0.484595	−	0.874739i	$-0.661033\pi$
$641$	−24.5379	−0.969190	−0.484595	+	0.874739i	$0.661033\pi$
$642$	0.387058	0.0152760
$643$	19.9947	0.788516	0.394258	−	0.919000i	$-0.371002\pi$
$643$	19.9947	0.788516	0.394258	+	0.919000i	$0.371002\pi$
$644$	−6.84777	−0.269840
$645$	4.32524	0.170306
$646$	−5.65428	−0.222465
$647$	11.4777	0.451233	0.225617	−	0.974216i	$-0.427560\pi$
$647$	11.4777	0.451233	0.225617	+	0.974216i	$0.427560\pi$
$648$	−6.09410	−0.239399
$649$	−8.84619	−0.347244
$650$	5.86956	0.230223
$651$	−1.52874	−0.0599161
$652$	−10.7473	−0.420896
$653$	−38.1728	−1.49382	−0.746909	−	0.664926i	$-0.768463\pi$
$653$	−38.1728	−1.49382	−0.746909	+	0.664926i	$0.768463\pi$
$654$	26.8172	1.04863
$655$	−5.15416	−0.201390
$656$	5.54247	0.216397
$657$	3.50297	0.136664
$658$	7.93238	0.309236
$659$	−41.8516	−1.63031	−0.815154	−	0.579245i	$-0.803348\pi$
$659$	−41.8516	−1.63031	−0.815154	+	0.579245i	$0.803348\pi$
$660$	−4.84757	−0.188691
$661$	15.7436	0.612356	0.306178	−	0.951974i	$-0.400950\pi$
$661$	15.7436	0.612356	0.306178	+	0.951974i	$0.400950\pi$
$662$	−5.04091	−0.195920
$663$	44.1874	1.71610
$664$	−5.16195	−0.200323
$665$	1.12143	0.0434873
$666$	4.66883	0.180913
$667$	28.4469	1.10147
$668$	21.6788	0.838778
$669$	−18.4672	−0.713983
$670$	8.43237	0.325771
$671$	18.2426	0.704247
$672$	1.49310	0.0575975
$673$	17.7872	0.685648	0.342824	−	0.939400i	$-0.388617\pi$
$673$	17.7872	0.685648	0.342824	+	0.939400i	$0.388617\pi$
$674$	−25.9236	−0.998538
$675$	5.62996	0.216697
$676$	21.4517	0.825067
$677$	−2.06543	−0.0793810	−0.0396905	−	0.999212i	$-0.512637\pi$
$677$	−2.06543	−0.0793810	−0.0396905	+	0.999212i	$0.512637\pi$
$678$	27.7402	1.06536
$679$	13.2315	0.507777
$680$	5.04202	0.193353
$681$	−25.8403	−0.990202
$682$	3.32415	0.127288
$683$	0.281357	0.0107658	0.00538291	−	0.999986i	$-0.498287\pi$
$683$	0.281357	0.0107658	0.00538291	+	0.999986i	$0.498287\pi$
$684$	−0.864242	−0.0330451
$685$	7.46788	0.285333
$686$	−1.00000	−0.0381802
$687$	32.5601	1.24225
$688$	2.89682	0.110440
$689$	−49.0598	−1.86903
$690$	10.2244	0.389236
$691$	12.7123	0.483598	0.241799	−	0.970326i	$-0.422263\pi$
$691$	12.7123	0.483598	0.241799	+	0.970326i	$0.422263\pi$
$692$	11.3328	0.430808
$693$	−2.50206	−0.0950456
$694$	−2.51173	−0.0953438
$695$	18.9516	0.718876
$696$	−6.20259	−0.235109
$697$	−27.9452	−1.05850
$698$	28.2910	1.07083
$699$	−38.1386	−1.44254
$700$	−1.00000	−0.0377964
$701$	22.1158	0.835303	0.417652	−	0.908607i	$-0.362853\pi$
$701$	22.1158	0.835303	0.417652	+	0.908607i	$0.362853\pi$
$702$	33.0454	1.24722
$703$	−6.79388	−0.256236
$704$	−3.24665	−0.122363
$705$	−11.8438	−0.446064
$706$	21.9558	0.826318
$707$	3.61003	0.135769
$708$	−4.06826	−0.152895
$709$	21.6602	0.813465	0.406733	−	0.913547i	$-0.366668\pi$
$709$	21.6602	0.813465	0.406733	+	0.913547i	$0.366668\pi$
$710$	−1.00000	−0.0375293
$711$	9.14889	0.343110
$712$	15.1333	0.567144
$713$	−7.01124	−0.262573
$714$	−7.52823	−0.281737
$715$	19.0564	0.712670
$716$	20.8813	0.780369
$717$	13.9849	0.522275
$718$	−26.5421	−0.990543
$719$	−10.8235	−0.403647	−0.201823	−	0.979422i	$-0.564687\pi$
$719$	−10.8235	−0.403647	−0.201823	+	0.979422i	$0.564687\pi$
$720$	0.770660	0.0287208
$721$	−13.0962	−0.487728
$722$	−17.7424	−0.660303
$723$	1.37538	0.0511508
$724$	7.82735	0.290901
$725$	4.15418	0.154282
$726$	0.685709	0.0254490
$727$	17.9519	0.665798	0.332899	−	0.942962i	$-0.391973\pi$
$727$	17.9519	0.665798	0.332899	+	0.942962i	$0.391973\pi$
$728$	−5.86956	−0.217540
$729$	29.9147	1.10795
$730$	4.54542	0.168234
$731$	−14.6058	−0.540217
$732$	8.38955	0.310087
$733$	3.82209	0.141172	0.0705861	−	0.997506i	$-0.477513\pi$
$733$	3.82209	0.141172	0.0705861	+	0.997506i	$0.477513\pi$
$734$	18.6534	0.688508
$735$	1.49310	0.0550737
$736$	6.84777	0.252412
$737$	27.3770	1.00844
$738$	−4.27136	−0.157231
$739$	−11.5440	−0.424653	−0.212327	−	0.977199i	$-0.568104\pi$
$739$	−11.5440	−0.424653	−0.212327	+	0.977199i	$0.568104\pi$
$740$	6.05822	0.222705
$741$	−9.82803	−0.361042
$742$	8.35834	0.306844
$743$	−42.1636	−1.54683	−0.773417	−	0.633897i	$-0.781454\pi$
$743$	−42.1636	−1.54683	−0.773417	+	0.633897i	$0.781454\pi$
$744$	1.52874	0.0560463
$745$	7.44038	0.272595
$746$	−28.3509	−1.03800
$747$	3.97811	0.145552
$748$	16.3697	0.598535
$749$	0.259232	0.00947211
$750$	1.49310	0.0545202
$751$	32.2954	1.17848	0.589238	−	0.807960i	$-0.299428\pi$
$751$	32.2954	1.17848	0.589238	+	0.807960i	$0.299428\pi$
$752$	−7.93238	−0.289264
$753$	28.8931	1.05292
$754$	24.3832	0.887984
$755$	4.90314	0.178444
$756$	−5.62996	−0.204760
$757$	11.1628	0.405717	0.202859	−	0.979208i	$-0.434977\pi$
$757$	11.1628	0.405717	0.202859	+	0.979208i	$0.434977\pi$
$758$	−4.57059	−0.166011
$759$	33.1950	1.20490
$760$	−1.12143	−0.0406786
$761$	−12.0586	−0.437123	−0.218561	−	0.975823i	$-0.570136\pi$
$761$	−12.0586	−0.437123	−0.218561	+	0.975823i	$0.570136\pi$
$762$	−10.3381	−0.374510
$763$	17.9608	0.650223
$764$	−18.3531	−0.663992
$765$	−3.88568	−0.140487
$766$	20.9227	0.755968
$767$	15.9929	0.577469
$768$	−1.49310	−0.0538775
$769$	1.65346	0.0596252	0.0298126	−	0.999556i	$-0.490509\pi$
$769$	1.65346	0.0596252	0.0298126	+	0.999556i	$0.490509\pi$
$770$	−3.24665	−0.117001
$771$	22.1655	0.798270
$772$	−25.2248	−0.907860
$773$	26.4948	0.952952	0.476476	−	0.879187i	$-0.341914\pi$
$773$	26.4948	0.952952	0.476476	+	0.879187i	$0.341914\pi$
$774$	−2.23247	−0.0802443
$775$	−1.02387	−0.0367786
$776$	−13.2315	−0.474982
$777$	−9.04552	−0.324506
$778$	16.6437	0.596706
$779$	6.21550	0.222693
$780$	8.76383	0.313795
$781$	−3.24665	−0.116174
$782$	−34.5266	−1.23467
$783$	23.3879	0.835814
$784$	1.00000	0.0357143
$785$	2.18799	0.0780925
$786$	−7.69567	−0.274495
$787$	3.00546	0.107133	0.0535666	−	0.998564i	$-0.482941\pi$
$787$	3.00546	0.107133	0.0535666	+	0.998564i	$0.482941\pi$
$788$	12.2121	0.435038
$789$	−47.7216	−1.69893
$790$	11.8715	0.422369
$791$	18.5790	0.660593
$792$	2.50206	0.0889070
$793$	−32.9804	−1.17117
$794$	−22.3322	−0.792539
$795$	−12.4798	−0.442613
$796$	−6.12915	−0.217242
$797$	−39.5197	−1.39986	−0.699930	−	0.714212i	$-0.746785\pi$
$797$	−39.5197	−1.39986	−0.699930	+	0.714212i	$0.746785\pi$
$798$	1.67441	0.0592734
$799$	39.9952	1.41493
$800$	1.00000	0.0353553
$801$	−11.6626	−0.412078
$802$	−36.0314	−1.27231
$803$	14.7574	0.520777
$804$	12.5903	0.444027
$805$	6.84777	0.241352
$806$	−6.00968	−0.211682
$807$	8.69448	0.306060
$808$	−3.61003	−0.127000
$809$	−5.70462	−0.200564	−0.100282	−	0.994959i	$-0.531974\pi$
$809$	−5.70462	−0.200564	−0.100282	+	0.994959i	$0.531974\pi$
$810$	6.09410	0.214125
$811$	46.8696	1.64581	0.822907	−	0.568176i	$-0.192351\pi$
$811$	46.8696	1.64581	0.822907	+	0.568176i	$0.192351\pi$
$812$	−4.15418	−0.145783
$813$	32.6711	1.14583
$814$	19.6689	0.689396
$815$	10.7473	0.376461
$816$	7.52823	0.263541
$817$	3.24859	0.113654
$818$	31.3817	1.09723
$819$	4.52344	0.158062
$820$	−5.54247	−0.193551
$821$	−28.0353	−0.978440	−0.489220	−	0.872160i	$-0.662719\pi$
$821$	−28.0353	−0.978440	−0.489220	+	0.872160i	$0.662719\pi$
$822$	11.1503	0.388910
$823$	−24.1012	−0.840115	−0.420058	−	0.907497i	$-0.637990\pi$
$823$	−24.1012	−0.840115	−0.420058	+	0.907497i	$0.637990\pi$
$824$	13.0962	0.456227
$825$	4.84757	0.168771
$826$	−2.72471	−0.0948049
$827$	−16.4382	−0.571613	−0.285807	−	0.958287i	$-0.592262\pi$
$827$	−16.4382	−0.571613	−0.285807	+	0.958287i	$0.592262\pi$
$828$	−5.27730	−0.183399
$829$	29.1390	1.01204	0.506020	−	0.862522i	$-0.331116\pi$
$829$	29.1390	1.01204	0.506020	+	0.862522i	$0.331116\pi$
$830$	5.16195	0.179174
$831$	25.5809	0.887390
$832$	5.86956	0.203490
$833$	−5.04202	−0.174696
$834$	28.2966	0.979832
$835$	−21.6788	−0.750226
$836$	−3.64090	−0.125923
$837$	−5.76436	−0.199245
$838$	−27.9417	−0.965229
$839$	−28.2376	−0.974872	−0.487436	−	0.873159i	$-0.662068\pi$
$839$	−28.2376	−0.974872	−0.487436	+	0.873159i	$0.662068\pi$
$840$	−1.49310	−0.0515168
$841$	−11.7428	−0.404925
$842$	18.8496	0.649601
$843$	23.4761	0.808560
$844$	−14.8959	−0.512737
$845$	−21.4517	−0.737963
$846$	6.11317	0.210175
$847$	0.459253	0.0157801
$848$	−8.35834	−0.287027
$849$	14.9783	0.514054
$850$	−5.04202	−0.172940
$851$	−41.4853	−1.42210
$852$	−1.49310	−0.0511527
$853$	57.0057	1.95184	0.975918	−	0.218137i	$-0.0699979\pi$
$853$	57.0057	1.95184	0.975918	+	0.218137i	$0.0699979\pi$
$854$	5.61889	0.192274
$855$	0.864242	0.0295565
$856$	−0.259232	−0.00886035
$857$	8.76128	0.299280	0.149640	−	0.988741i	$-0.452189\pi$
$857$	8.76128	0.299280	0.149640	+	0.988741i	$0.452189\pi$
$858$	28.4531	0.971373
$859$	−45.0664	−1.53765	−0.768823	−	0.639461i	$-0.779157\pi$
$859$	−45.0664	−1.53765	−0.768823	+	0.639461i	$0.779157\pi$
$860$	−2.89682	−0.0987809
$861$	8.27545	0.282026
$862$	31.8766	1.08572
$863$	−21.4756	−0.731039	−0.365520	−	0.930804i	$-0.619109\pi$
$863$	−21.4756	−0.731039	−0.365520	+	0.930804i	$0.619109\pi$
$864$	5.62996	0.191535
$865$	−11.3328	−0.385326
$866$	3.33801	0.113430
$867$	−12.5748	−0.427063
$868$	1.02387	0.0347525
$869$	38.5426	1.30747
$870$	6.20259	0.210288
$871$	−49.4943	−1.67705
$872$	−17.9608	−0.608228
$873$	10.1970	0.345115
$874$	7.67931	0.259757
$875$	1.00000	0.0338062
$876$	6.78676	0.229303
$877$	34.1339	1.15262	0.576311	−	0.817231i	$-0.304492\pi$
$877$	34.1339	1.15262	0.576311	+	0.817231i	$0.304492\pi$
$878$	−12.2581	−0.413692
$879$	2.29798	0.0775091
$880$	3.24665	0.109445
$881$	−24.6801	−0.831495	−0.415747	−	0.909480i	$-0.636480\pi$
$881$	−24.6801	−0.831495	−0.415747	+	0.909480i	$0.636480\pi$
$882$	−0.770660	−0.0259495
$883$	12.7174	0.427976	0.213988	−	0.976836i	$-0.431355\pi$
$883$	12.7174	0.427976	0.213988	+	0.976836i	$0.431355\pi$
$884$	−29.5944	−0.995369
$885$	4.06826	0.136753
$886$	15.8390	0.532122
$887$	18.6228	0.625292	0.312646	−	0.949870i	$-0.398785\pi$
$887$	18.6228	0.625292	0.312646	+	0.949870i	$0.398785\pi$
$888$	9.04552	0.303548
$889$	−6.92393	−0.232221
$890$	−15.1333	−0.507269
$891$	19.7854	0.662837
$892$	12.3684	0.414124
$893$	−8.89562	−0.297681
$894$	11.1092	0.371548
$895$	−20.8813	−0.697983
$896$	−1.00000	−0.0334077
$897$	−60.0127	−2.00377
$898$	−35.2165	−1.17519
$899$	−4.25334	−0.141857
$900$	−0.770660	−0.0256887
$901$	42.1429	1.40398
$902$	−17.9945	−0.599150
$903$	4.32524	0.143935
$904$	−18.5790	−0.617928
$905$	−7.82735	−0.260190
$906$	7.32087	0.243220
$907$	−25.7846	−0.856165	−0.428082	−	0.903740i	$-0.640811\pi$
$907$	−25.7846	−0.856165	−0.428082	+	0.903740i	$0.640811\pi$
$908$	17.3065	0.574336
$909$	2.78211	0.0922766
$910$	5.86956	0.194574
$911$	−13.4307	−0.444981	−0.222490	−	0.974935i	$-0.571419\pi$
$911$	−13.4307	−0.444981	−0.222490	+	0.974935i	$0.571419\pi$
$912$	−1.67441	−0.0554451
$913$	16.7591	0.554644
$914$	15.4710	0.511734
$915$	−8.38955	−0.277350
$916$	−21.8071	−0.720527
$917$	−5.15416	−0.170205
$918$	−28.3864	−0.936890
$919$	19.5733	0.645662	0.322831	−	0.946457i	$-0.395365\pi$
$919$	19.5733	0.645662	0.322831	+	0.946457i	$0.395365\pi$
$920$	−6.84777	−0.225764
$921$	4.69489	0.154702
$922$	−35.0992	−1.15593
$923$	5.86956	0.193199
$924$	−4.84757	−0.159473
$925$	−6.05822	−0.199193
$926$	−16.7054	−0.548974
$927$	−10.0927	−0.331488
$928$	4.15418	0.136368
$929$	32.8787	1.07871	0.539357	−	0.842077i	$-0.318667\pi$
$929$	32.8787	1.07871	0.539357	+	0.842077i	$0.318667\pi$
$930$	−1.52874	−0.0501294
$931$	1.12143	0.0367534
$932$	25.5433	0.836698
$933$	11.8047	0.386467
$934$	36.9080	1.20767
$935$	−16.3697	−0.535346
$936$	−4.52344	−0.147853
$937$	41.0083	1.33968	0.669841	−	0.742504i	$-0.266362\pi$
$937$	41.0083	1.33968	0.669841	+	0.742504i	$0.266362\pi$
$938$	8.43237	0.275327
$939$	26.8183	0.875182
$940$	7.93238	0.258726
$941$	1.18697	0.0386940	0.0193470	−	0.999813i	$-0.493841\pi$
$941$	1.18697	0.0386940	0.0193470	+	0.999813i	$0.493841\pi$
$942$	3.26687	0.106441
$943$	37.9536	1.23594
$944$	2.72471	0.0886819
$945$	5.62996	0.183143
$946$	−9.40498	−0.305782
$947$	20.9651	0.681275	0.340638	−	0.940195i	$-0.389357\pi$
$947$	20.9651	0.681275	0.340638	+	0.940195i	$0.389357\pi$
$948$	17.7253	0.575691
$949$	−26.6796	−0.866057
$950$	1.12143	0.0363840
$951$	−34.5055	−1.11892
$952$	5.04202	0.163413
$953$	10.0215	0.324628	0.162314	−	0.986739i	$-0.448104\pi$
$953$	10.0215	0.324628	0.162314	+	0.986739i	$0.448104\pi$
$954$	6.44144	0.208549
$955$	18.3531	0.593892
$956$	−9.36635	−0.302929
$957$	20.1377	0.650958
$958$	15.8176	0.511042
$959$	7.46788	0.241150
$960$	1.49310	0.0481895
$961$	−29.9517	−0.966183
$962$	−35.5591	−1.14647
$963$	0.199779	0.00643780
$964$	−0.921156	−0.0296684
$965$	25.2248	0.812015
$966$	10.2244	0.328964
$967$	−55.1468	−1.77340	−0.886700	−	0.462345i	$-0.847008\pi$
$967$	−55.1468	−1.77340	−0.886700	+	0.462345i	$0.847008\pi$
$968$	−0.459253	−0.0147609
$969$	8.44239	0.271209
$970$	13.2315	0.424837
$971$	−15.2582	−0.489659	−0.244829	−	0.969566i	$-0.578732\pi$
$971$	−15.2582	−0.489659	−0.244829	+	0.969566i	$0.578732\pi$
$972$	−7.79080	−0.249890
$973$	18.9516	0.607561
$974$	26.1498	0.837894
$975$	−8.76383	−0.280667
$976$	−5.61889	−0.179856
$977$	−53.1466	−1.70031	−0.850156	−	0.526532i	$-0.823492\pi$
$977$	−53.1466	−1.70031	−0.850156	+	0.526532i	$0.823492\pi$
$978$	16.0467	0.513118
$979$	−49.1325	−1.57028
$980$	−1.00000	−0.0319438
$981$	13.8416	0.441930
$982$	−4.53765	−0.144802
$983$	15.2091	0.485095	0.242548	−	0.970140i	$-0.422017\pi$
$983$	15.2091	0.485095	0.242548	+	0.970140i	$0.422017\pi$
$984$	−8.27545	−0.263812
$985$	−12.2121	−0.389110
$986$	−20.9454	−0.667039
$987$	−11.8438	−0.376993
$988$	6.58231	0.209411
$989$	19.8368	0.630773
$990$	−2.50206	−0.0795208
$991$	7.21299	0.229128	0.114564	−	0.993416i	$-0.463453\pi$
$991$	7.21299	0.229128	0.114564	+	0.993416i	$0.463453\pi$
$992$	−1.02387	−0.0325080
$993$	7.52657	0.238848
$994$	−1.00000	−0.0317181
$995$	6.12915	0.194307
$996$	7.70730	0.244215
$997$	−14.1126	−0.446950	−0.223475	−	0.974710i	$-0.571740\pi$
$997$	−14.1126	−0.446950	−0.223475	+	0.974710i	$0.571740\pi$
$998$	9.19046	0.290919
$999$	−34.1076	−1.07912

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4970.2.a.x.1.3	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4970.2.a.x.1.3	✓	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:	\( N \)	\(=\)	\( 4970 = 2 \cdot 5 \cdot 7 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4970.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.49310 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.49310 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.770660 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.49310 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.49310 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.770660 q^{9} -1.00000 q^{10} -3.24665 q^{11} -1.49310 q^{12} +5.86956 q^{13} -1.00000 q^{14} +1.49310 q^{15} +1.00000 q^{16} -5.04202 q^{17} -0.770660 q^{18} +1.12143 q^{19} -1.00000 q^{20} +1.49310 q^{21} -3.24665 q^{22} +6.84777 q^{23} -1.49310 q^{24} +1.00000 q^{25} +5.86956 q^{26} +5.62996 q^{27} -1.00000 q^{28} +4.15418 q^{29} +1.49310 q^{30} -1.02387 q^{31} +1.00000 q^{32} +4.84757 q^{33} -5.04202 q^{34} +1.00000 q^{35} -0.770660 q^{36} -6.05822 q^{37} +1.12143 q^{38} -8.76383 q^{39} -1.00000 q^{40} +5.54247 q^{41} +1.49310 q^{42} +2.89682 q^{43} -3.24665 q^{44} +0.770660 q^{45} +6.84777 q^{46} -7.93238 q^{47} -1.49310 q^{48} +1.00000 q^{49} +1.00000 q^{50} +7.52823 q^{51} +5.86956 q^{52} -8.35834 q^{53} +5.62996 q^{54} +3.24665 q^{55} -1.00000 q^{56} -1.67441 q^{57} +4.15418 q^{58} +2.72471 q^{59} +1.49310 q^{60} -5.61889 q^{61} -1.02387 q^{62} +0.770660 q^{63} +1.00000 q^{64} -5.86956 q^{65} +4.84757 q^{66} -8.43237 q^{67} -5.04202 q^{68} -10.2244 q^{69} +1.00000 q^{70} +1.00000 q^{71} -0.770660 q^{72} -4.54542 q^{73} -6.05822 q^{74} -1.49310 q^{75} +1.12143 q^{76} +3.24665 q^{77} -8.76383 q^{78} -11.8715 q^{79} -1.00000 q^{80} -6.09410 q^{81} +5.54247 q^{82} -5.16195 q^{83} +1.49310 q^{84} +5.04202 q^{85} +2.89682 q^{86} -6.20259 q^{87} -3.24665 q^{88} +15.1333 q^{89} +0.770660 q^{90} -5.86956 q^{91} +6.84777 q^{92} +1.52874 q^{93} -7.93238 q^{94} -1.12143 q^{95} -1.49310 q^{96} -13.2315 q^{97} +1.00000 q^{98} +2.50206 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + q^{3} + 7 q^{4} - 7 q^{5} + q^{6} - 7 q^{7} + 7 q^{8} + 2 q^{9}+O(q^{10}) \) 7 * q + 7 * q^2 + q^3 + 7 * q^4 - 7 * q^5 + q^6 - 7 * q^7 + 7 * q^8 + 2 * q^9	\( 7 q + 7 q^{2} + q^{3} + 7 q^{4} - 7 q^{5} + q^{6} - 7 q^{7} + 7 q^{8} + 2 q^{9} - 7 q^{10} - 9 q^{11} + q^{12} - 7 q^{14} - q^{15} + 7 q^{16} - 5 q^{17} + 2 q^{18} + 2 q^{19} - 7 q^{20} - q^{21} - 9 q^{22} - 8 q^{23} + q^{24} + 7 q^{25} + q^{27} - 7 q^{28} - 19 q^{29} - q^{30} - 6 q^{31} + 7 q^{32} - 6 q^{33} - 5 q^{34} + 7 q^{35} + 2 q^{36} - 10 q^{37} + 2 q^{38} - 19 q^{39} - 7 q^{40} - 19 q^{41} - q^{42} - 22 q^{43} - 9 q^{44} - 2 q^{45} - 8 q^{46} + 2 q^{47} + q^{48} + 7 q^{49} + 7 q^{50} - 22 q^{51} - 3 q^{53} + q^{54} + 9 q^{55} - 7 q^{56} - 25 q^{57} - 19 q^{58} + 13 q^{59} - q^{60} - 4 q^{61} - 6 q^{62} - 2 q^{63} + 7 q^{64} - 6 q^{66} - 23 q^{67} - 5 q^{68} - 19 q^{69} + 7 q^{70} + 7 q^{71} + 2 q^{72} - 10 q^{74} + q^{75} + 2 q^{76} + 9 q^{77} - 19 q^{78} - 40 q^{79} - 7 q^{80} - 33 q^{81} - 19 q^{82} + 24 q^{83} - q^{84} + 5 q^{85} - 22 q^{86} - 6 q^{87} - 9 q^{88} - 4 q^{89} - 2 q^{90} - 8 q^{92} - 12 q^{93} + 2 q^{94} - 2 q^{95} + q^{96} - 35 q^{97} + 7 q^{98} - 24 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + q^3 + 7 * q^4 - 7 * q^5 + q^6 - 7 * q^7 + 7 * q^8 + 2 * q^9 - 7 * q^10 - 9 * q^11 + q^12 - 7 * q^14 - q^15 + 7 * q^16 - 5 * q^17 + 2 * q^18 + 2 * q^19 - 7 * q^20 - q^21 - 9 * q^22 - 8 * q^23 + q^24 + 7 * q^25 + q^27 - 7 * q^28 - 19 * q^29 - q^30 - 6 * q^31 + 7 * q^32 - 6 * q^33 - 5 * q^34 + 7 * q^35 + 2 * q^36 - 10 * q^37 + 2 * q^38 - 19 * q^39 - 7 * q^40 - 19 * q^41 - q^42 - 22 * q^43 - 9 * q^44 - 2 * q^45 - 8 * q^46 + 2 * q^47 + q^48 + 7 * q^49 + 7 * q^50 - 22 * q^51 - 3 * q^53 + q^54 + 9 * q^55 - 7 * q^56 - 25 * q^57 - 19 * q^58 + 13 * q^59 - q^60 - 4 * q^61 - 6 * q^62 - 2 * q^63 + 7 * q^64 - 6 * q^66 - 23 * q^67 - 5 * q^68 - 19 * q^69 + 7 * q^70 + 7 * q^71 + 2 * q^72 - 10 * q^74 + q^75 + 2 * q^76 + 9 * q^77 - 19 * q^78 - 40 * q^79 - 7 * q^80 - 33 * q^81 - 19 * q^82 + 24 * q^83 - q^84 + 5 * q^85 - 22 * q^86 - 6 * q^87 - 9 * q^88 - 4 * q^89 - 2 * q^90 - 8 * q^92 - 12 * q^93 + 2 * q^94 - 2 * q^95 + q^96 - 35 * q^97 + 7 * q^98 - 24 * q^99

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