LMFDB - Embedded newform 4034.2.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.74374 q^{3} +1.00000 q^{4} -3.34943 q^{5} +1.74374 q^{6} +0.122108 q^{7} -1.00000 q^{8} +0.0406325 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.74374 q^{3} +1.00000 q^{4} -3.34943 q^{5} +1.74374 q^{6} +0.122108 q^{7} -1.00000 q^{8} +0.0406325 q^{9} +3.34943 q^{10} +1.72175 q^{11} -1.74374 q^{12} -1.02966 q^{13} -0.122108 q^{14} +5.84054 q^{15} +1.00000 q^{16} -6.37870 q^{17} -0.0406325 q^{18} -2.12780 q^{19} -3.34943 q^{20} -0.212925 q^{21} -1.72175 q^{22} +7.03300 q^{23} +1.74374 q^{24} +6.21869 q^{25} +1.02966 q^{26} +5.16037 q^{27} +0.122108 q^{28} +0.875497 q^{29} -5.84054 q^{30} -4.15574 q^{31} -1.00000 q^{32} -3.00229 q^{33} +6.37870 q^{34} -0.408992 q^{35} +0.0406325 q^{36} -2.57112 q^{37} +2.12780 q^{38} +1.79546 q^{39} +3.34943 q^{40} +10.8105 q^{41} +0.212925 q^{42} +4.99130 q^{43} +1.72175 q^{44} -0.136096 q^{45} -7.03300 q^{46} -3.61198 q^{47} -1.74374 q^{48} -6.98509 q^{49} -6.21869 q^{50} +11.1228 q^{51} -1.02966 q^{52} +10.6186 q^{53} -5.16037 q^{54} -5.76688 q^{55} -0.122108 q^{56} +3.71033 q^{57} -0.875497 q^{58} +0.822013 q^{59} +5.84054 q^{60} -9.50820 q^{61} +4.15574 q^{62} +0.00496155 q^{63} +1.00000 q^{64} +3.44877 q^{65} +3.00229 q^{66} +6.68694 q^{67} -6.37870 q^{68} -12.2637 q^{69} +0.408992 q^{70} +5.18582 q^{71} -0.0406325 q^{72} -13.6457 q^{73} +2.57112 q^{74} -10.8438 q^{75} -2.12780 q^{76} +0.210239 q^{77} -1.79546 q^{78} +14.0942 q^{79} -3.34943 q^{80} -9.12025 q^{81} -10.8105 q^{82} +12.7496 q^{83} -0.212925 q^{84} +21.3650 q^{85} -4.99130 q^{86} -1.52664 q^{87} -1.72175 q^{88} +2.97427 q^{89} +0.136096 q^{90} -0.125730 q^{91} +7.03300 q^{92} +7.24654 q^{93} +3.61198 q^{94} +7.12692 q^{95} +1.74374 q^{96} +9.20804 q^{97} +6.98509 q^{98} +0.0699591 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) $ 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * 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
$3$	−1.74374	−1.00675	−0.503375	−	0.864068i	$-0.667908\pi$
$3$	−1.74374	−1.00675	−0.503375	+	0.864068i	$0.667908\pi$
$4$	1.00000	0.500000
$5$	−3.34943	−1.49791	−0.748956	−	0.662620i	$-0.769444\pi$
$5$	−3.34943	−1.49791	−0.748956	+	0.662620i	$0.769444\pi$
$6$	1.74374	0.711879
$7$	0.122108	0.0461524	0.0230762	−	0.999734i	$-0.492654\pi$
$7$	0.122108	0.0461524	0.0230762	+	0.999734i	$0.492654\pi$
$8$	−1.00000	−0.353553
$9$	0.0406325	0.0135442
$10$	3.34943	1.05918
$11$	1.72175	0.519127	0.259564	−	0.965726i	$-0.416421\pi$
$11$	1.72175	0.519127	0.259564	+	0.965726i	$0.416421\pi$
$12$	−1.74374	−0.503375
$13$	−1.02966	−0.285576	−0.142788	−	0.989753i	$-0.545607\pi$
$13$	−1.02966	−0.285576	−0.142788	+	0.989753i	$0.545607\pi$
$14$	−0.122108	−0.0326347
$15$	5.84054	1.50802
$16$	1.00000	0.250000
$17$	−6.37870	−1.54706	−0.773531	−	0.633758i	$-0.781512\pi$
$17$	−6.37870	−1.54706	−0.773531	+	0.633758i	$0.781512\pi$
$18$	−0.0406325	−0.00957718
$19$	−2.12780	−0.488151	−0.244076	−	0.969756i	$-0.578485\pi$
$19$	−2.12780	−0.488151	−0.244076	+	0.969756i	$0.578485\pi$
$20$	−3.34943	−0.748956
$21$	−0.212925	−0.0464639
$22$	−1.72175	−0.367078
$23$	7.03300	1.46648	0.733241	−	0.679969i	$-0.238007\pi$
$23$	7.03300	1.46648	0.733241	+	0.679969i	$0.238007\pi$
$24$	1.74374	0.355940
$25$	6.21869	1.24374
$26$	1.02966	0.201933
$27$	5.16037	0.993114
$28$	0.122108	0.0230762
$29$	0.875497	0.162576	0.0812879	−	0.996691i	$-0.474097\pi$
$29$	0.875497	0.162576	0.0812879	+	0.996691i	$0.474097\pi$
$30$	−5.84054	−1.06633
$31$	−4.15574	−0.746393	−0.373197	−	0.927752i	$-0.621738\pi$
$31$	−4.15574	−0.746393	−0.373197	+	0.927752i	$0.621738\pi$
$32$	−1.00000	−0.176777
$33$	−3.00229	−0.522631
$34$	6.37870	1.09394
$35$	−0.408992	−0.0691323
$36$	0.0406325	0.00677209
$37$	−2.57112	−0.422689	−0.211345	−	0.977412i	$-0.567784\pi$
$37$	−2.57112	−0.422689	−0.211345	+	0.977412i	$0.567784\pi$
$38$	2.12780	0.345175
$39$	1.79546	0.287504
$40$	3.34943	0.529592
$41$	10.8105	1.68832	0.844162	−	0.536089i	$-0.180099\pi$
$41$	10.8105	1.68832	0.844162	+	0.536089i	$0.180099\pi$
$42$	0.212925	0.0328550
$43$	4.99130	0.761167	0.380583	−	0.924747i	$-0.375723\pi$
$43$	4.99130	0.761167	0.380583	+	0.924747i	$0.375723\pi$
$44$	1.72175	0.259564
$45$	−0.136096	−0.0202880
$46$	−7.03300	−1.03696
$47$	−3.61198	−0.526861	−0.263430	−	0.964678i	$-0.584854\pi$
$47$	−3.61198	−0.526861	−0.263430	+	0.964678i	$0.584854\pi$
$48$	−1.74374	−0.251687
$49$	−6.98509	−0.997870
$50$	−6.21869	−0.879455
$51$	11.1228	1.55750
$52$	−1.02966	−0.142788
$53$	10.6186	1.45858	0.729292	−	0.684203i	$-0.239850\pi$
$53$	10.6186	1.45858	0.729292	+	0.684203i	$0.239850\pi$
$54$	−5.16037	−0.702237
$55$	−5.76688	−0.777606
$56$	−0.122108	−0.0163174
$57$	3.71033	0.491446
$58$	−0.875497	−0.114958
$59$	0.822013	0.107017	0.0535085	−	0.998567i	$-0.482960\pi$
$59$	0.822013	0.107017	0.0535085	+	0.998567i	$0.482960\pi$
$60$	5.84054	0.754010
$61$	−9.50820	−1.21740	−0.608700	−	0.793400i	$-0.708309\pi$
$61$	−9.50820	−1.21740	−0.608700	+	0.793400i	$0.708309\pi$
$62$	4.15574	0.527780
$63$	0.00496155	0.000625097 0
$64$	1.00000	0.125000
$65$	3.44877	0.427768
$66$	3.00229	0.369556
$67$	6.68694	0.816940	0.408470	−	0.912772i	$-0.366062\pi$
$67$	6.68694	0.816940	0.408470	+	0.912772i	$0.366062\pi$
$68$	−6.37870	−0.773531
$69$	−12.2637	−1.47638
$70$	0.408992	0.0488839
$71$	5.18582	0.615443	0.307722	−	0.951476i	$-0.400433\pi$
$71$	5.18582	0.615443	0.307722	+	0.951476i	$0.400433\pi$
$72$	−0.0406325	−0.00478859
$73$	−13.6457	−1.59711	−0.798557	−	0.601919i	$-0.794403\pi$
$73$	−13.6457	−1.59711	−0.798557	+	0.601919i	$0.794403\pi$
$74$	2.57112	0.298886
$75$	−10.8438	−1.25213
$76$	−2.12780	−0.244076
$77$	0.210239	0.0239590
$78$	−1.79546	−0.203296
$79$	14.0942	1.58572	0.792861	−	0.609403i	$-0.208591\pi$
$79$	14.0942	1.58572	0.792861	+	0.609403i	$0.208591\pi$
$80$	−3.34943	−0.374478
$81$	−9.12025	−1.01336
$82$	−10.8105	−1.19382
$83$	12.7496	1.39945	0.699723	−	0.714414i	$-0.253307\pi$
$83$	12.7496	1.39945	0.699723	+	0.714414i	$0.253307\pi$
$84$	−0.212925	−0.0232320
$85$	21.3650	2.31736
$86$	−4.99130	−0.538226
$87$	−1.52664	−0.163673
$88$	−1.72175	−0.183539
$89$	2.97427	0.315272	0.157636	−	0.987497i	$-0.449613\pi$
$89$	2.97427	0.315272	0.157636	+	0.987497i	$0.449613\pi$
$90$	0.136096	0.0143458
$91$	−0.125730	−0.0131800
$92$	7.03300	0.733241
$93$	7.24654	0.751431
$94$	3.61198	0.372547
$95$	7.12692	0.731207
$96$	1.74374	0.177970
$97$	9.20804	0.934935	0.467467	−	0.884010i	$-0.345167\pi$
$97$	9.20804	0.934935	0.467467	+	0.884010i	$0.345167\pi$
$98$	6.98509	0.705601
$99$	0.0699591	0.00703115
$100$	6.21869	0.621869
$101$	−3.14195	−0.312636	−0.156318	−	0.987707i	$-0.549962\pi$
$101$	−3.14195	−0.312636	−0.156318	+	0.987707i	$0.549962\pi$
$102$	−11.1228	−1.10132
$103$	4.19063	0.412915	0.206458	−	0.978456i	$-0.433806\pi$
$103$	4.19063	0.412915	0.206458	+	0.978456i	$0.433806\pi$
$104$	1.02966	0.100966
$105$	0.713176	0.0695988
$106$	−10.6186	−1.03137
$107$	10.0952	0.975941	0.487971	−	0.872860i	$-0.337737\pi$
$107$	10.0952	0.975941	0.487971	+	0.872860i	$0.337737\pi$
$108$	5.16037	0.496557
$109$	−11.0150	−1.05504	−0.527521	−	0.849542i	$-0.676879\pi$
$109$	−11.0150	−1.05504	−0.527521	+	0.849542i	$0.676879\pi$
$110$	5.76688	0.549851
$111$	4.48336	0.425542
$112$	0.122108	0.0115381
$113$	11.0822	1.04253	0.521265	−	0.853395i	$-0.325460\pi$
$113$	11.0822	1.04253	0.521265	+	0.853395i	$0.325460\pi$
$114$	−3.71033	−0.347505
$115$	−23.5566	−2.19666
$116$	0.875497	0.0812879
$117$	−0.0418377	−0.00386789
$118$	−0.822013	−0.0756725
$119$	−0.778890	−0.0714007
$120$	−5.84054	−0.533166
$121$	−8.03558	−0.730507
$122$	9.50820	0.860832
$123$	−18.8508	−1.69972
$124$	−4.15574	−0.373197
$125$	−4.08191	−0.365097
$126$	−0.00496155	−0.000442010 0
$127$	−5.79094	−0.513863	−0.256931	−	0.966430i	$-0.582711\pi$
$127$	−5.79094	−0.513863	−0.256931	+	0.966430i	$0.582711\pi$
$128$	−1.00000	−0.0883883
$129$	−8.70354	−0.766304
$130$	−3.44877	−0.302477
$131$	12.4786	1.09026	0.545131	−	0.838351i	$-0.316480\pi$
$131$	12.4786	1.09026	0.545131	+	0.838351i	$0.316480\pi$
$132$	−3.00229	−0.261315
$133$	−0.259821	−0.0225294
$134$	−6.68694	−0.577664
$135$	−17.2843	−1.48760
$136$	6.37870	0.546969
$137$	−11.8821	−1.01516	−0.507580	−	0.861605i	$-0.669460\pi$
$137$	−11.8821	−1.01516	−0.507580	+	0.861605i	$0.669460\pi$
$138$	12.2637	1.04396
$139$	−8.37342	−0.710224	−0.355112	−	0.934824i	$-0.615557\pi$
$139$	−8.37342	−0.710224	−0.355112	+	0.934824i	$0.615557\pi$
$140$	−0.408992	−0.0345661
$141$	6.29835	0.530417
$142$	−5.18582	−0.435184
$143$	−1.77282	−0.148250
$144$	0.0406325	0.00338605
$145$	−2.93242	−0.243524
$146$	13.6457	1.12933
$147$	12.1802	1.00460
$148$	−2.57112	−0.211345
$149$	2.33335	0.191155	0.0955776	−	0.995422i	$-0.469530\pi$
$149$	2.33335	0.191155	0.0955776	+	0.995422i	$0.469530\pi$
$150$	10.8438	0.885391
$151$	−3.75934	−0.305931	−0.152965	−	0.988232i	$-0.548882\pi$
$151$	−3.75934	−0.305931	−0.152965	+	0.988232i	$0.548882\pi$
$152$	2.12780	0.172588
$153$	−0.259183	−0.0209537
$154$	−0.210239	−0.0169416
$155$	13.9194	1.11803
$156$	1.79546	0.143752
$157$	7.41489	0.591773	0.295886	−	0.955223i	$-0.404385\pi$
$157$	7.41489	0.591773	0.295886	+	0.955223i	$0.404385\pi$
$158$	−14.0942	−1.12127
$159$	−18.5162	−1.46843
$160$	3.34943	0.264796
$161$	0.858785	0.0676817
$162$	9.12025	0.716554
$163$	17.6351	1.38129	0.690643	−	0.723196i	$-0.257328\pi$
$163$	17.6351	1.38129	0.690643	+	0.723196i	$0.257328\pi$
$164$	10.8105	0.844162
$165$	10.0560	0.782855
$166$	−12.7496	−0.989558
$167$	7.63781	0.591031	0.295516	−	0.955338i	$-0.404509\pi$
$167$	7.63781	0.591031	0.295516	+	0.955338i	$0.404509\pi$
$168$	0.212925	0.0164275
$169$	−11.9398	−0.918446
$170$	−21.3650	−1.63862
$171$	−0.0864580	−0.00661161
$172$	4.99130	0.380583
$173$	−7.79749	−0.592832	−0.296416	−	0.955059i	$-0.595791\pi$
$173$	−7.79749	−0.592832	−0.296416	+	0.955059i	$0.595791\pi$
$174$	1.52664	0.115734
$175$	0.759351	0.0574015
$176$	1.72175	0.129782
$177$	−1.43338	−0.107739
$178$	−2.97427	−0.222931
$179$	−20.3178	−1.51862	−0.759312	−	0.650727i	$-0.774464\pi$
$179$	−20.3178	−1.51862	−0.759312	+	0.650727i	$0.774464\pi$
$180$	−0.136096	−0.0101440
$181$	−5.90074	−0.438598	−0.219299	−	0.975658i	$-0.570377\pi$
$181$	−5.90074	−0.438598	−0.219299	+	0.975658i	$0.570377\pi$
$182$	0.125730	0.00931969
$183$	16.5798	1.22562
$184$	−7.03300	−0.518480
$185$	8.61178	0.633151
$186$	−7.24654	−0.531342
$187$	−10.9825	−0.803122
$188$	−3.61198	−0.263430
$189$	0.630122	0.0458346
$190$	−7.12692	−0.517041
$191$	1.60202	0.115918	0.0579590	−	0.998319i	$-0.481541\pi$
$191$	1.60202	0.115918	0.0579590	+	0.998319i	$0.481541\pi$
$192$	−1.74374	−0.125844
$193$	7.78584	0.560437	0.280219	−	0.959936i	$-0.409593\pi$
$193$	7.78584	0.560437	0.280219	+	0.959936i	$0.409593\pi$
$194$	−9.20804	−0.661099
$195$	−6.01377	−0.430655
$196$	−6.98509	−0.498935
$197$	−13.8985	−0.990224	−0.495112	−	0.868829i	$-0.664873\pi$
$197$	−13.8985	−0.990224	−0.495112	+	0.868829i	$0.664873\pi$
$198$	−0.0699591	−0.00497178
$199$	−8.58538	−0.608602	−0.304301	−	0.952576i	$-0.598423\pi$
$199$	−8.58538	−0.608602	−0.304301	+	0.952576i	$0.598423\pi$
$200$	−6.21869	−0.439728
$201$	−11.6603	−0.822454
$202$	3.14195	0.221067
$203$	0.106905	0.00750327
$204$	11.1228	0.778752
$205$	−36.2092	−2.52896
$206$	−4.19063	−0.291975
$207$	0.285769	0.0198623
$208$	−1.02966	−0.0713940
$209$	−3.66354	−0.253413
$210$	−0.713176	−0.0492138
$211$	−8.90945	−0.613352	−0.306676	−	0.951814i	$-0.599217\pi$
$211$	−8.90945	−0.613352	−0.306676	+	0.951814i	$0.599217\pi$
$212$	10.6186	0.729292
$213$	−9.04272	−0.619597
$214$	−10.0952	−0.690095
$215$	−16.7180	−1.14016
$216$	−5.16037	−0.351119
$217$	−0.507449	−0.0344479
$218$	11.0150	0.746028
$219$	23.7946	1.60789
$220$	−5.76688	−0.388803
$221$	6.56789	0.441804
$222$	−4.48336	−0.300904
$223$	−0.795272	−0.0532553	−0.0266277	−	0.999645i	$-0.508477\pi$
$223$	−0.795272	−0.0532553	−0.0266277	+	0.999645i	$0.508477\pi$
$224$	−0.122108	−0.00815868
$225$	0.252681	0.0168454
$226$	−11.0822	−0.737180
$227$	−1.24510	−0.0826401	−0.0413201	−	0.999146i	$-0.513156\pi$
$227$	−1.24510	−0.0826401	−0.0413201	+	0.999146i	$0.513156\pi$
$228$	3.71033	0.245723
$229$	−20.8718	−1.37924	−0.689622	−	0.724169i	$-0.742223\pi$
$229$	−20.8718	−1.37924	−0.689622	+	0.724169i	$0.742223\pi$
$230$	23.5566	1.55327
$231$	−0.366603	−0.0241207
$232$	−0.875497	−0.0574792
$233$	−3.62464	−0.237458	−0.118729	−	0.992927i	$-0.537882\pi$
$233$	−3.62464	−0.237458	−0.118729	+	0.992927i	$0.537882\pi$
$234$	0.0418377	0.00273501
$235$	12.0981	0.789191
$236$	0.822013	0.0535085
$237$	−24.5766	−1.59642
$238$	0.778890	0.0504879
$239$	−17.1694	−1.11060	−0.555300	−	0.831650i	$-0.687396\pi$
$239$	−17.1694	−1.11060	−0.555300	+	0.831650i	$0.687396\pi$
$240$	5.84054	0.377005
$241$	−1.97373	−0.127139	−0.0635695	−	0.997977i	$-0.520248\pi$
$241$	−1.97373	−0.127139	−0.0635695	+	0.997977i	$0.520248\pi$
$242$	8.03558	0.516546
$243$	0.422237	0.0270865
$244$	−9.50820	−0.608700
$245$	23.3961	1.49472
$246$	18.8508	1.20188
$247$	2.19091	0.139404
$248$	4.15574	0.263890
$249$	−22.2319	−1.40889
$250$	4.08191	0.258163
$251$	−18.0732	−1.14077	−0.570386	−	0.821377i	$-0.693206\pi$
$251$	−18.0732	−1.14077	−0.570386	+	0.821377i	$0.693206\pi$
$252$	0.00496155	0.000312549 0
$253$	12.1091	0.761291
$254$	5.79094	0.363356
$255$	−37.2551	−2.33300
$256$	1.00000	0.0625000
$257$	−1.40966	−0.0879324	−0.0439662	−	0.999033i	$-0.513999\pi$
$257$	−1.40966	−0.0879324	−0.0439662	+	0.999033i	$0.513999\pi$
$258$	8.70354	0.541859
$259$	−0.313954	−0.0195081
$260$	3.44877	0.213884
$261$	0.0355737	0.00220196
$262$	−12.4786	−0.770932
$263$	−15.5258	−0.957359	−0.478679	−	0.877990i	$-0.658884\pi$
$263$	−15.5258	−0.957359	−0.478679	+	0.877990i	$0.658884\pi$
$264$	3.00229	0.184778
$265$	−35.5664	−2.18483
$266$	0.259821	0.0159307
$267$	−5.18636	−0.317400
$268$	6.68694	0.408470
$269$	20.3160	1.23869	0.619345	−	0.785119i	$-0.287398\pi$
$269$	20.3160	1.23869	0.619345	+	0.785119i	$0.287398\pi$
$270$	17.2843	1.05189
$271$	15.9774	0.970559	0.485280	−	0.874359i	$-0.338718\pi$
$271$	15.9774	0.970559	0.485280	+	0.874359i	$0.338718\pi$
$272$	−6.37870	−0.386766
$273$	0.219240	0.0132690
$274$	11.8821	0.717826
$275$	10.7070	0.645658
$276$	−12.2637	−0.738190
$277$	−15.3406	−0.921725	−0.460863	−	0.887472i	$-0.652460\pi$
$277$	−15.3406	−0.921725	−0.460863	+	0.887472i	$0.652460\pi$
$278$	8.37342	0.502204
$279$	−0.168858	−0.0101093
$280$	0.408992	0.0244419
$281$	−10.9448	−0.652910	−0.326455	−	0.945213i	$-0.605854\pi$
$281$	−10.9448	−0.652910	−0.326455	+	0.945213i	$0.605854\pi$
$282$	−6.29835	−0.375061
$283$	−2.91543	−0.173305	−0.0866523	−	0.996239i	$-0.527617\pi$
$283$	−2.91543	−0.173305	−0.0866523	+	0.996239i	$0.527617\pi$
$284$	5.18582	0.307722
$285$	−12.4275	−0.736142
$286$	1.77282	0.104829
$287$	1.32005	0.0779202
$288$	−0.0406325	−0.00239430
$289$	23.6879	1.39340
$290$	2.93242	0.172197
$291$	−16.0564	−0.941245
$292$	−13.6457	−0.798557
$293$	−5.93962	−0.346997	−0.173498	−	0.984834i	$-0.555507\pi$
$293$	−5.93962	−0.346997	−0.173498	+	0.984834i	$0.555507\pi$
$294$	−12.1802	−0.710363
$295$	−2.75328	−0.160302
$296$	2.57112	0.149443
$297$	8.88487	0.515552
$298$	−2.33335	−0.135167
$299$	−7.24159	−0.418792
$300$	−10.8438	−0.626066
$301$	0.609478	0.0351297
$302$	3.75934	0.216326
$303$	5.47875	0.314746
$304$	−2.12780	−0.122038
$305$	31.8471	1.82356
$306$	0.259183	0.0148165
$307$	−27.9902	−1.59749	−0.798743	−	0.601673i	$-0.794501\pi$
$307$	−27.9902	−1.59749	−0.798743	+	0.601673i	$0.794501\pi$
$308$	0.210239	0.0119795
$309$	−7.30738	−0.415702
$310$	−13.9194	−0.790567
$311$	−22.8809	−1.29746	−0.648729	−	0.761019i	$-0.724699\pi$
$311$	−22.8809	−1.29746	−0.648729	+	0.761019i	$0.724699\pi$
$312$	−1.79546	−0.101648
$313$	−16.2145	−0.916495	−0.458248	−	0.888825i	$-0.651523\pi$
$313$	−16.2145	−0.916495	−0.458248	+	0.888825i	$0.651523\pi$
$314$	−7.41489	−0.418447
$315$	−0.0166184	−0.000936340 0
$316$	14.0942	0.792861
$317$	31.3679	1.76179	0.880897	−	0.473308i	$-0.156940\pi$
$317$	31.3679	1.76179	0.880897	+	0.473308i	$0.156940\pi$
$318$	18.5162	1.03834
$319$	1.50739	0.0843975
$320$	−3.34943	−0.187239
$321$	−17.6034	−0.982528
$322$	−0.858785	−0.0478582
$323$	13.5726	0.755201
$324$	−9.12025	−0.506680
$325$	−6.40313	−0.355182
$326$	−17.6351	−0.976716
$327$	19.2073	1.06216
$328$	−10.8105	−0.596912
$329$	−0.441051	−0.0243159
$330$	−10.0560	−0.553562
$331$	28.3797	1.55989	0.779945	−	0.625848i	$-0.215247\pi$
$331$	28.3797	1.55989	0.779945	+	0.625848i	$0.215247\pi$
$332$	12.7496	0.699723
$333$	−0.104471	−0.00572498
$334$	−7.63781	−0.417922
$335$	−22.3974	−1.22370
$336$	−0.212925	−0.0116160
$337$	3.98983	0.217340	0.108670	−	0.994078i	$-0.465341\pi$
$337$	3.98983	0.217340	0.108670	+	0.994078i	$0.465341\pi$
$338$	11.9398	0.649440
$339$	−19.3246	−1.04957
$340$	21.3650	1.15868
$341$	−7.15515	−0.387473
$342$	0.0864580	0.00467511
$343$	−1.70769	−0.0922066
$344$	−4.99130	−0.269113
$345$	41.0765	2.21149
$346$	7.79749	0.419196
$347$	8.63356	0.463474	0.231737	−	0.972779i	$-0.425559\pi$
$347$	8.63356	0.463474	0.231737	+	0.972779i	$0.425559\pi$
$348$	−1.52664	−0.0818365
$349$	6.20747	0.332278	0.166139	−	0.986102i	$-0.446870\pi$
$349$	6.20747	0.332278	0.166139	+	0.986102i	$0.446870\pi$
$350$	−0.759351	−0.0405890
$351$	−5.31342	−0.283610
$352$	−1.72175	−0.0917696
$353$	−21.4732	−1.14290	−0.571452	−	0.820636i	$-0.693620\pi$
$353$	−21.4732	−1.14290	−0.571452	+	0.820636i	$0.693620\pi$
$354$	1.43338	0.0761832
$355$	−17.3695	−0.921879
$356$	2.97427	0.157636
$357$	1.35818	0.0718826
$358$	20.3178	1.07383
$359$	6.50837	0.343499	0.171749	−	0.985141i	$-0.445058\pi$
$359$	6.50837	0.343499	0.171749	+	0.985141i	$0.445058\pi$
$360$	0.136096	0.00717288
$361$	−14.4725	−0.761708
$362$	5.90074	0.310136
$363$	14.0120	0.735437
$364$	−0.125730	−0.00659002
$365$	45.7055	2.39233
$366$	−16.5798	−0.866642
$367$	−34.0300	−1.77635	−0.888175	−	0.459506i	$-0.848026\pi$
$367$	−34.0300	−1.77635	−0.888175	+	0.459506i	$0.848026\pi$
$368$	7.03300	0.366621
$369$	0.439260	0.0228670
$370$	−8.61178	−0.447705
$371$	1.29662	0.0673172
$372$	7.24654	0.375715
$373$	35.7238	1.84971	0.924855	−	0.380321i	$-0.124186\pi$
$373$	35.7238	1.84971	0.924855	+	0.380321i	$0.124186\pi$
$374$	10.9825	0.567893
$375$	7.11780	0.367561
$376$	3.61198	0.186273
$377$	−0.901464	−0.0464277
$378$	−0.630122	−0.0324100
$379$	13.5267	0.694819	0.347410	−	0.937713i	$-0.387061\pi$
$379$	13.5267	0.694819	0.347410	+	0.937713i	$0.387061\pi$
$380$	7.12692	0.365604
$381$	10.0979	0.517331
$382$	−1.60202	−0.0819664
$383$	10.5862	0.540928	0.270464	−	0.962730i	$-0.412823\pi$
$383$	10.5862	0.540928	0.270464	+	0.962730i	$0.412823\pi$
$384$	1.74374	0.0889849
$385$	−0.704182	−0.0358884
$386$	−7.78584	−0.396289
$387$	0.202809	0.0103094
$388$	9.20804	0.467467
$389$	−9.75110	−0.494401	−0.247200	−	0.968964i	$-0.579511\pi$
$389$	−9.75110	−0.494401	−0.247200	+	0.968964i	$0.579511\pi$
$390$	6.01377	0.304519
$391$	−44.8614	−2.26874
$392$	6.98509	0.352800
$393$	−21.7595	−1.09762
$394$	13.8985	0.700194
$395$	−47.2075	−2.37527
$396$	0.0699591	0.00351558
$397$	−15.6958	−0.787748	−0.393874	−	0.919164i	$-0.628865\pi$
$397$	−15.6958	−0.787748	−0.393874	+	0.919164i	$0.628865\pi$
$398$	8.58538	0.430346
$399$	0.453061	0.0226814
$400$	6.21869	0.310934
$401$	24.7273	1.23482	0.617411	−	0.786641i	$-0.288181\pi$
$401$	24.7273	1.23482	0.617411	+	0.786641i	$0.288181\pi$
$402$	11.6603	0.581563
$403$	4.27900	0.213152
$404$	−3.14195	−0.156318
$405$	30.5476	1.51792
$406$	−0.106905	−0.00530561
$407$	−4.42682	−0.219429
$408$	−11.1228	−0.550661
$409$	16.8425	0.832810	0.416405	−	0.909179i	$-0.363290\pi$
$409$	16.8425	0.832810	0.416405	+	0.909179i	$0.363290\pi$
$410$	36.2092	1.78824
$411$	20.7194	1.02201
$412$	4.19063	0.206458
$413$	0.100374	0.00493910
$414$	−0.285769	−0.0140448
$415$	−42.7038	−2.09625
$416$	1.02966	0.0504832
$417$	14.6011	0.715018
$418$	3.66354	0.179190
$419$	11.1892	0.546627	0.273313	−	0.961925i	$-0.411880\pi$
$419$	11.1892	0.546627	0.273313	+	0.961925i	$0.411880\pi$
$420$	0.713176	0.0347994
$421$	13.1983	0.643248	0.321624	−	0.946867i	$-0.395771\pi$
$421$	13.1983	0.643248	0.321624	+	0.946867i	$0.395771\pi$
$422$	8.90945	0.433705
$423$	−0.146764	−0.00713590
$424$	−10.6186	−0.515687
$425$	−39.6672	−1.92414
$426$	9.04272	0.438121
$427$	−1.16103	−0.0561860
$428$	10.0952	0.487971
$429$	3.09133	0.149251
$430$	16.7180	0.806215
$431$	−27.8634	−1.34213	−0.671066	−	0.741398i	$-0.734163\pi$
$431$	−27.8634	−1.34213	−0.671066	+	0.741398i	$0.734163\pi$
$432$	5.16037	0.248278
$433$	24.5389	1.17926	0.589632	−	0.807672i	$-0.299273\pi$
$433$	24.5389	1.17926	0.589632	+	0.807672i	$0.299273\pi$
$434$	0.507449	0.0243583
$435$	5.11338	0.245168
$436$	−11.0150	−0.527521
$437$	−14.9648	−0.715865
$438$	−23.7946	−1.13695
$439$	16.5660	0.790651	0.395326	−	0.918541i	$-0.370632\pi$
$439$	16.5660	0.790651	0.395326	+	0.918541i	$0.370632\pi$
$440$	5.76688	0.274925
$441$	−0.283822	−0.0135153
$442$	−6.56789	−0.312403
$443$	−39.0755	−1.85653	−0.928267	−	0.371915i	$-0.878701\pi$
$443$	−39.0755	−1.85653	−0.928267	+	0.371915i	$0.878701\pi$
$444$	4.48336	0.212771
$445$	−9.96211	−0.472249
$446$	0.795272	0.0376572
$447$	−4.06875	−0.192445
$448$	0.122108	0.00576905
$449$	−38.6736	−1.82512	−0.912559	−	0.408945i	$-0.865897\pi$
$449$	−38.6736	−1.82512	−0.912559	+	0.408945i	$0.865897\pi$
$450$	−0.252681	−0.0119115
$451$	18.6131	0.876455
$452$	11.0822	0.521265
$453$	6.55531	0.307995
$454$	1.24510	0.0584354
$455$	0.421122	0.0197425
$456$	−3.71033	−0.173752
$457$	−0.613254	−0.0286868	−0.0143434	−	0.999897i	$-0.504566\pi$
$457$	−0.613254	−0.0286868	−0.0143434	+	0.999897i	$0.504566\pi$
$458$	20.8718	0.975273
$459$	−32.9165	−1.53641
$460$	−23.5566	−1.09833
$461$	9.07992	0.422894	0.211447	−	0.977389i	$-0.432182\pi$
$461$	9.07992	0.422894	0.211447	+	0.977389i	$0.432182\pi$
$462$	0.366603	0.0170559
$463$	−9.28590	−0.431553	−0.215776	−	0.976443i	$-0.569228\pi$
$463$	−9.28590	−0.431553	−0.215776	+	0.976443i	$0.569228\pi$
$464$	0.875497	0.0406439
$465$	−24.2718	−1.12558
$466$	3.62464	0.167908
$467$	−10.0387	−0.464536	−0.232268	−	0.972652i	$-0.574615\pi$
$467$	−10.0387	−0.464536	−0.232268	+	0.972652i	$0.574615\pi$
$468$	−0.0418377	−0.00193395
$469$	0.816528	0.0377038
$470$	−12.0981	−0.558042
$471$	−12.9297	−0.595767
$472$	−0.822013	−0.0378362
$473$	8.59378	0.395142
$474$	24.5766	1.12884
$475$	−13.2321	−0.607132
$476$	−0.778890	−0.0357004
$477$	0.431463	0.0197553
$478$	17.1694	0.785312
$479$	−30.8229	−1.40833	−0.704167	−	0.710034i	$-0.748680\pi$
$479$	−30.8229	−1.40833	−0.704167	+	0.710034i	$0.748680\pi$
$480$	−5.84054	−0.266583
$481$	2.64737	0.120710
$482$	1.97373	0.0899008
$483$	−1.49750	−0.0681385
$484$	−8.03558	−0.365253
$485$	−30.8417	−1.40045
$486$	−0.422237	−0.0191531
$487$	−28.2921	−1.28204	−0.641018	−	0.767526i	$-0.721488\pi$
$487$	−28.2921	−1.28204	−0.641018	+	0.767526i	$0.721488\pi$
$488$	9.50820	0.430416
$489$	−30.7510	−1.39061
$490$	−23.3961	−1.05693
$491$	−27.5916	−1.24519	−0.622596	−	0.782544i	$-0.713922\pi$
$491$	−27.5916	−1.24519	−0.622596	+	0.782544i	$0.713922\pi$
$492$	−18.8508	−0.849859
$493$	−5.58454	−0.251515
$494$	−2.19091	−0.0985737
$495$	−0.234323	−0.0105320
$496$	−4.15574	−0.186598
$497$	0.633229	0.0284042
$498$	22.2319	0.996237
$499$	−19.7517	−0.884207	−0.442103	−	0.896964i	$-0.645768\pi$
$499$	−19.7517	−0.884207	−0.442103	+	0.896964i	$0.645768\pi$
$500$	−4.08191	−0.182549
$501$	−13.3184	−0.595020
$502$	18.0732	0.806647
$503$	10.2704	0.457934	0.228967	−	0.973434i	$-0.426465\pi$
$503$	10.2704	0.457934	0.228967	+	0.973434i	$0.426465\pi$
$504$	−0.00496155	−0.000221005 0
$505$	10.5238	0.468301
$506$	−12.1091	−0.538314
$507$	20.8199	0.924645
$508$	−5.79094	−0.256931
$509$	6.92139	0.306785	0.153393	−	0.988165i	$-0.450980\pi$
$509$	6.92139	0.306785	0.153393	+	0.988165i	$0.450980\pi$
$510$	37.2551	1.64968
$511$	−1.66625	−0.0737107
$512$	−1.00000	−0.0441942
$513$	−10.9802	−0.484790
$514$	1.40966	0.0621776
$515$	−14.0362	−0.618510
$516$	−8.70354	−0.383152
$517$	−6.21892	−0.273508
$518$	0.313954	0.0137943
$519$	13.5968	0.596833
$520$	−3.44877	−0.151239
$521$	−41.3344	−1.81089	−0.905447	−	0.424459i	$-0.860464\pi$
$521$	−41.3344	−1.81089	−0.905447	+	0.424459i	$0.860464\pi$
$522$	−0.0355737	−0.00155702
$523$	−24.2538	−1.06055	−0.530273	−	0.847827i	$-0.677911\pi$
$523$	−24.2538	−1.06055	−0.530273	+	0.847827i	$0.677911\pi$
$524$	12.4786	0.545131
$525$	−1.32411	−0.0577889
$526$	15.5258	0.676955
$527$	26.5082	1.15472
$528$	−3.00229	−0.130658
$529$	26.4631	1.15057
$530$	35.5664	1.54491
$531$	0.0334005	0.00144946
$532$	−0.259821	−0.0112647
$533$	−11.1312	−0.482145
$534$	5.18636	0.224436
$535$	−33.8132	−1.46187
$536$	−6.68694	−0.288832
$537$	35.4290	1.52887
$538$	−20.3160	−0.875886
$539$	−12.0266	−0.518021
$540$	−17.2843	−0.743798
$541$	39.4720	1.69703	0.848517	−	0.529167i	$-0.177496\pi$
$541$	39.4720	1.69703	0.848517	+	0.529167i	$0.177496\pi$
$542$	−15.9774	−0.686289
$543$	10.2894	0.441559
$544$	6.37870	0.273485
$545$	36.8939	1.58036
$546$	−0.219240	−0.00938259
$547$	0.868282	0.0371250	0.0185625	−	0.999828i	$-0.494091\pi$
$547$	0.868282	0.0371250	0.0185625	+	0.999828i	$0.494091\pi$
$548$	−11.8821	−0.507580
$549$	−0.386342	−0.0164887
$550$	−10.7070	−0.456549
$551$	−1.86288	−0.0793615
$552$	12.2637	0.521979
$553$	1.72101	0.0731849
$554$	15.3406	0.651758
$555$	−15.0167	−0.637424
$556$	−8.37342	−0.355112
$557$	43.0232	1.82295	0.911477	−	0.411352i	$-0.134943\pi$
$557$	43.0232	1.82295	0.911477	+	0.411352i	$0.134943\pi$
$558$	0.168858	0.00714834
$559$	−5.13934	−0.217371
$560$	−0.408992	−0.0172831
$561$	19.1507	0.808543
$562$	10.9448	0.461677
$563$	27.5692	1.16190	0.580952	−	0.813938i	$-0.302680\pi$
$563$	27.5692	1.16190	0.580952	+	0.813938i	$0.302680\pi$
$564$	6.29835	0.265208
$565$	−37.1192	−1.56162
$566$	2.91543	0.122545
$567$	−1.11365	−0.0467691
$568$	−5.18582	−0.217592
$569$	3.29944	0.138320	0.0691599	−	0.997606i	$-0.477968\pi$
$569$	3.29944	0.138320	0.0691599	+	0.997606i	$0.477968\pi$
$570$	12.4275	0.520531
$571$	−7.50363	−0.314017	−0.157009	−	0.987597i	$-0.550185\pi$
$571$	−7.50363	−0.314017	−0.157009	+	0.987597i	$0.550185\pi$
$572$	−1.77282	−0.0741252
$573$	−2.79350	−0.116700
$574$	−1.32005	−0.0550979
$575$	43.7360	1.82392
$576$	0.0406325	0.00169302
$577$	−24.8241	−1.03344	−0.516720	−	0.856154i	$-0.672847\pi$
$577$	−24.8241	−1.03344	−0.516720	+	0.856154i	$0.672847\pi$
$578$	−23.6879	−0.985285
$579$	−13.5765	−0.564220
$580$	−2.93242	−0.121762
$581$	1.55682	0.0645879
$582$	16.0564	0.665561
$583$	18.2827	0.757190
$584$	13.6457	0.564665
$585$	0.140132	0.00579376
$586$	5.93962	0.245364
$587$	4.63171	0.191171	0.0955855	−	0.995421i	$-0.469528\pi$
$587$	4.63171	0.191171	0.0955855	+	0.995421i	$0.469528\pi$
$588$	12.1802	0.502302
$589$	8.84259	0.364353
$590$	2.75328	0.113351
$591$	24.2353	0.996907
$592$	−2.57112	−0.105672
$593$	11.2743	0.462982	0.231491	−	0.972837i	$-0.425640\pi$
$593$	11.2743	0.462982	0.231491	+	0.972837i	$0.425640\pi$
$594$	−8.88487	−0.364551
$595$	2.60884	0.106952
$596$	2.33335	0.0955776
$597$	14.9707	0.612709
$598$	7.24159	0.296131
$599$	−26.2975	−1.07449	−0.537243	−	0.843427i	$-0.680534\pi$
$599$	−26.2975	−1.07449	−0.537243	+	0.843427i	$0.680534\pi$
$600$	10.8438	0.442696
$601$	−25.2278	−1.02906	−0.514531	−	0.857472i	$-0.672034\pi$
$601$	−25.2278	−1.02906	−0.514531	+	0.857472i	$0.672034\pi$
$602$	−0.609478	−0.0248405
$603$	0.271707	0.0110648
$604$	−3.75934	−0.152965
$605$	26.9146	1.09423
$606$	−5.47875	−0.222559
$607$	5.46666	0.221885	0.110942	−	0.993827i	$-0.464613\pi$
$607$	5.46666	0.221885	0.110942	+	0.993827i	$0.464613\pi$
$608$	2.12780	0.0862938
$609$	−0.186415	−0.00755391
$610$	−31.8471	−1.28945
$611$	3.71910	0.150459
$612$	−0.259183	−0.0104768
$613$	29.8892	1.20721	0.603606	−	0.797283i	$-0.293730\pi$
$613$	29.8892	1.20721	0.603606	+	0.797283i	$0.293730\pi$
$614$	27.9902	1.12959
$615$	63.1394	2.54603
$616$	−0.210239	−0.00847078
$617$	7.98407	0.321427	0.160713	−	0.987001i	$-0.448621\pi$
$617$	7.98407	0.321427	0.160713	+	0.987001i	$0.448621\pi$
$618$	7.30738	0.293946
$619$	1.79550	0.0721671	0.0360835	−	0.999349i	$-0.488512\pi$
$619$	1.79550	0.0721671	0.0360835	+	0.999349i	$0.488512\pi$
$620$	13.9194	0.559015
$621$	36.2929	1.45638
$622$	22.8809	0.917442
$623$	0.363182	0.0145506
$624$	1.79546	0.0718759
$625$	−17.4214	−0.696854
$626$	16.2145	0.648060
$627$	6.38827	0.255123
$628$	7.41489	0.295886
$629$	16.4004	0.653927
$630$	0.0166184	0.000662092 0
$631$	−25.0203	−0.996041	−0.498020	−	0.867165i	$-0.665940\pi$
$631$	−25.0203	−0.996041	−0.498020	+	0.867165i	$0.665940\pi$
$632$	−14.0942	−0.560637
$633$	15.5358	0.617491
$634$	−31.3679	−1.24578
$635$	19.3964	0.769721
$636$	−18.5162	−0.734214
$637$	7.19226	0.284968
$638$	−1.50739	−0.0596780
$639$	0.210713	0.00833568
$640$	3.34943	0.132398
$641$	−3.48592	−0.137686	−0.0688428	−	0.997628i	$-0.521931\pi$
$641$	−3.48592	−0.137686	−0.0688428	+	0.997628i	$0.521931\pi$
$642$	17.6034	0.694753
$643$	9.25185	0.364857	0.182429	−	0.983219i	$-0.441604\pi$
$643$	9.25185	0.364857	0.182429	+	0.983219i	$0.441604\pi$
$644$	0.858785	0.0338409
$645$	29.1519	1.14786
$646$	−13.5726	−0.534007
$647$	6.34993	0.249642	0.124821	−	0.992179i	$-0.460164\pi$
$647$	6.34993	0.249642	0.124821	+	0.992179i	$0.460164\pi$
$648$	9.12025	0.358277
$649$	1.41530	0.0555554
$650$	6.40313	0.251151
$651$	0.884859	0.0346804
$652$	17.6351	0.690643
$653$	17.8013	0.696618	0.348309	−	0.937380i	$-0.386756\pi$
$653$	17.8013	0.696618	0.348309	+	0.937380i	$0.386756\pi$
$654$	−19.2073	−0.751063
$655$	−41.7963	−1.63312
$656$	10.8105	0.422081
$657$	−0.554461	−0.0216316
$658$	0.441051	0.0171939
$659$	2.49281	0.0971061	0.0485531	−	0.998821i	$-0.484539\pi$
$659$	2.49281	0.0971061	0.0485531	+	0.998821i	$0.484539\pi$
$660$	10.0560	0.391427
$661$	13.2545	0.515541	0.257771	−	0.966206i	$-0.417012\pi$
$661$	13.2545	0.515541	0.257771	+	0.966206i	$0.417012\pi$
$662$	−28.3797	−1.10301
$663$	−11.4527	−0.444786
$664$	−12.7496	−0.494779
$665$	0.870254	0.0337470
$666$	0.104471	0.00404817
$667$	6.15737	0.238414
$668$	7.63781	0.295516
$669$	1.38675	0.0536148
$670$	22.3974	0.865289
$671$	−16.3708	−0.631986
$672$	0.212925	0.00821374
$673$	0.592522	0.0228401	0.0114200	−	0.999935i	$-0.496365\pi$
$673$	0.592522	0.0228401	0.0114200	+	0.999935i	$0.496365\pi$
$674$	−3.98983	−0.153683
$675$	32.0907	1.23517
$676$	−11.9398	−0.459223
$677$	7.34019	0.282106	0.141053	−	0.990002i	$-0.454951\pi$
$677$	7.34019	0.282106	0.141053	+	0.990002i	$0.454951\pi$
$678$	19.3246	0.742155
$679$	1.12437	0.0431495
$680$	−21.3650	−0.819311
$681$	2.17113	0.0831979
$682$	7.15515	0.273985
$683$	30.7210	1.17551	0.587753	−	0.809041i	$-0.300013\pi$
$683$	30.7210	1.17551	0.587753	+	0.809041i	$0.300013\pi$
$684$	−0.0864580	−0.00330580
$685$	39.7984	1.52062
$686$	1.70769	0.0651999
$687$	36.3949	1.38855
$688$	4.99130	0.190292
$689$	−10.9336	−0.416537
$690$	−41.0765	−1.56376
$691$	−5.22869	−0.198909	−0.0994544	−	0.995042i	$-0.531710\pi$
$691$	−5.22869	−0.198909	−0.0994544	+	0.995042i	$0.531710\pi$
$692$	−7.79749	−0.296416
$693$	0.00854256	0.000324505 0
$694$	−8.63356	−0.327725
$695$	28.0462	1.06385
$696$	1.52664	0.0578672
$697$	−68.9573	−2.61194
$698$	−6.20747	−0.234956
$699$	6.32043	0.239061
$700$	0.759351	0.0287008
$701$	39.5689	1.49450	0.747249	−	0.664544i	$-0.231374\pi$
$701$	39.5689	1.49450	0.747249	+	0.664544i	$0.231374\pi$
$702$	5.31342	0.200542
$703$	5.47083	0.206336
$704$	1.72175	0.0648909
$705$	−21.0959	−0.794517
$706$	21.4732	0.808155
$707$	−0.383657	−0.0144289
$708$	−1.43338	−0.0538697
$709$	−41.2676	−1.54984	−0.774919	−	0.632060i	$-0.782210\pi$
$709$	−41.2676	−1.54984	−0.774919	+	0.632060i	$0.782210\pi$
$710$	17.3695	0.651867
$711$	0.572683	0.0214773
$712$	−2.97427	−0.111465
$713$	−29.2273	−1.09457
$714$	−1.35818	−0.0508287
$715$	5.93793	0.222066
$716$	−20.3178	−0.759312
$717$	29.9391	1.11809
$718$	−6.50837	−0.242890
$719$	42.9941	1.60341	0.801704	−	0.597721i	$-0.203927\pi$
$719$	42.9941	1.60341	0.801704	+	0.597721i	$0.203927\pi$
$720$	−0.136096	−0.00507199
$721$	0.511709	0.0190570
$722$	14.4725	0.538609
$723$	3.44167	0.127997
$724$	−5.90074	−0.219299
$725$	5.44444	0.202202
$726$	−14.0120	−0.520033
$727$	−8.88142	−0.329394	−0.164697	−	0.986344i	$-0.552665\pi$
$727$	−8.88142	−0.329394	−0.164697	+	0.986344i	$0.552665\pi$
$728$	0.125730	0.00465985
$729$	26.6245	0.986091
$730$	−45.7055	−1.69164
$731$	−31.8380	−1.17757
$732$	16.5798	0.612809
$733$	−13.9701	−0.515998	−0.257999	−	0.966145i	$-0.583063\pi$
$733$	−13.9701	−0.515998	−0.257999	+	0.966145i	$0.583063\pi$
$734$	34.0300	1.25607
$735$	−40.7967	−1.50481
$736$	−7.03300	−0.259240
$737$	11.5132	0.424096
$738$	−0.439260	−0.0161694
$739$	38.9677	1.43345	0.716726	−	0.697355i	$-0.245640\pi$
$739$	38.9677	1.43345	0.716726	+	0.697355i	$0.245640\pi$
$740$	8.61178	0.316575
$741$	−3.82038	−0.140345
$742$	−1.29662	−0.0476004
$743$	−48.7528	−1.78857	−0.894283	−	0.447503i	$-0.852313\pi$
$743$	−48.7528	−1.78857	−0.894283	+	0.447503i	$0.852313\pi$
$744$	−7.24654	−0.265671
$745$	−7.81538	−0.286333
$746$	−35.7238	−1.30794
$747$	0.518047	0.0189544
$748$	−10.9825	−0.401561
$749$	1.23271	0.0450421
$750$	−7.11780	−0.259905
$751$	14.2271	0.519154	0.259577	−	0.965722i	$-0.416417\pi$
$751$	14.2271	0.519154	0.259577	+	0.965722i	$0.416417\pi$
$752$	−3.61198	−0.131715
$753$	31.5150	1.14847
$754$	0.901464	0.0328294
$755$	12.5916	0.458257
$756$	0.630122	0.0229173
$757$	−4.54453	−0.165174	−0.0825868	−	0.996584i	$-0.526318\pi$
$757$	−4.54453	−0.165174	−0.0825868	+	0.996584i	$0.526318\pi$
$758$	−13.5267	−0.491311
$759$	−21.1151	−0.766429
$760$	−7.12692	−0.258521
$761$	−32.9728	−1.19526	−0.597632	−	0.801771i	$-0.703891\pi$
$761$	−32.9728	−1.19526	−0.597632	+	0.801771i	$0.703891\pi$
$762$	−10.0979	−0.365808
$763$	−1.34501	−0.0486928
$764$	1.60202	0.0579590
$765$	0.868115	0.0313868
$766$	−10.5862	−0.382494
$767$	−0.846394	−0.0305615
$768$	−1.74374	−0.0629218
$769$	5.10640	0.184142	0.0920708	−	0.995752i	$-0.470651\pi$
$769$	5.10640	0.184142	0.0920708	+	0.995752i	$0.470651\pi$
$770$	0.704182	0.0253770
$771$	2.45809	0.0885259
$772$	7.78584	0.280219
$773$	19.2899	0.693811	0.346906	−	0.937900i	$-0.387232\pi$
$773$	19.2899	0.693811	0.346906	+	0.937900i	$0.387232\pi$
$774$	−0.202809	−0.00728983
$775$	−25.8433	−0.928317
$776$	−9.20804	−0.330549
$777$	0.547454	0.0196398
$778$	9.75110	0.349594
$779$	−23.0027	−0.824157
$780$	−6.01377	−0.215327
$781$	8.92868	0.319493
$782$	44.8614	1.60424
$783$	4.51789	0.161456
$784$	−6.98509	−0.249467
$785$	−24.8357	−0.886423
$786$	21.7595	0.776135
$787$	−11.7742	−0.419704	−0.209852	−	0.977733i	$-0.567298\pi$
$787$	−11.7742	−0.419704	−0.209852	+	0.977733i	$0.567298\pi$
$788$	−13.8985	−0.495112
$789$	27.0729	0.963821
$790$	47.2075	1.67957
$791$	1.35323	0.0481153
$792$	−0.0699591	−0.00248589
$793$	9.79021	0.347661
$794$	15.6958	0.557022
$795$	62.0186	2.19957
$796$	−8.58538	−0.304301
$797$	14.2879	0.506102	0.253051	−	0.967453i	$-0.418566\pi$
$797$	14.2879	0.506102	0.253051	+	0.967453i	$0.418566\pi$
$798$	−0.453061	−0.0160382
$799$	23.0397	0.815087
$800$	−6.21869	−0.219864
$801$	0.120852	0.00427010
$802$	−24.7273	−0.873151
$803$	−23.4946	−0.829105
$804$	−11.6603	−0.411227
$805$	−2.87644	−0.101381
$806$	−4.27900	−0.150721
$807$	−35.4259	−1.24705
$808$	3.14195	0.110534
$809$	16.1641	0.568298	0.284149	−	0.958780i	$-0.408289\pi$
$809$	16.1641	0.568298	0.284149	+	0.958780i	$0.408289\pi$
$810$	−30.5476	−1.07333
$811$	49.3892	1.73429	0.867144	−	0.498058i	$-0.165953\pi$
$811$	49.3892	1.73429	0.867144	+	0.498058i	$0.165953\pi$
$812$	0.106905	0.00375163
$813$	−27.8605	−0.977110
$814$	4.42682	0.155160
$815$	−59.0674	−2.06904
$816$	11.1228	0.389376
$817$	−10.6205	−0.371564
$818$	−16.8425	−0.588886
$819$	−0.00510871	−0.000178513 0
$820$	−36.2092	−1.26448
$821$	−32.3844	−1.13022	−0.565111	−	0.825015i	$-0.691167\pi$
$821$	−32.3844	−1.13022	−0.565111	+	0.825015i	$0.691167\pi$
$822$	−20.7194	−0.722671
$823$	−3.32998	−0.116076	−0.0580380	−	0.998314i	$-0.518484\pi$
$823$	−3.32998	−0.116076	−0.0580380	+	0.998314i	$0.518484\pi$
$824$	−4.19063	−0.145988
$825$	−18.6703	−0.650016
$826$	−0.100374	−0.00349247
$827$	31.4987	1.09532	0.547659	−	0.836702i	$-0.315519\pi$
$827$	31.4987	1.09532	0.547659	+	0.836702i	$0.315519\pi$
$828$	0.285769	0.00993115
$829$	−38.6051	−1.34081	−0.670406	−	0.741994i	$-0.733880\pi$
$829$	−38.6051	−1.34081	−0.670406	+	0.741994i	$0.733880\pi$
$830$	42.7038	1.48227
$831$	26.7500	0.927946
$832$	−1.02966	−0.0356970
$833$	44.5558	1.54377
$834$	−14.6011	−0.505594
$835$	−25.5823	−0.885312
$836$	−3.66354	−0.126706
$837$	−21.4452	−0.741253
$838$	−11.1892	−0.386524
$839$	−3.52621	−0.121738	−0.0608691	−	0.998146i	$-0.519387\pi$
$839$	−3.52621	−0.121738	−0.0608691	+	0.998146i	$0.519387\pi$
$840$	−0.713176	−0.0246069
$841$	−28.2335	−0.973569
$842$	−13.1983	−0.454845
$843$	19.0848	0.657317
$844$	−8.90945	−0.306676
$845$	39.9915	1.37575
$846$	0.146764	0.00504584
$847$	−0.981207	−0.0337147
$848$	10.6186	0.364646
$849$	5.08376	0.174474
$850$	39.6672	1.36057
$851$	−18.0827	−0.619866
$852$	−9.04272	−0.309799
$853$	47.9182	1.64069	0.820344	−	0.571871i	$-0.193782\pi$
$853$	47.9182	1.64069	0.820344	+	0.571871i	$0.193782\pi$
$854$	1.16103	0.0397295
$855$	0.289585	0.00990360
$856$	−10.0952	−0.345047
$857$	55.2985	1.88896	0.944481	−	0.328567i	$-0.106566\pi$
$857$	55.2985	1.88896	0.944481	+	0.328567i	$0.106566\pi$
$858$	−3.09133	−0.105536
$859$	40.4918	1.38156	0.690781	−	0.723064i	$-0.257267\pi$
$859$	40.4918	1.38156	0.690781	+	0.723064i	$0.257267\pi$
$860$	−16.7180	−0.570080
$861$	−2.30183	−0.0784462
$862$	27.8634	0.949030
$863$	−13.5317	−0.460626	−0.230313	−	0.973117i	$-0.573975\pi$
$863$	−13.5317	−0.460626	−0.230313	+	0.973117i	$0.573975\pi$
$864$	−5.16037	−0.175559
$865$	26.1172	0.888010
$866$	−24.5389	−0.833866
$867$	−41.3055	−1.40281
$868$	−0.507449	−0.0172239
$869$	24.2667	0.823191
$870$	−5.11338	−0.173360
$871$	−6.88527	−0.233298
$872$	11.0150	0.373014
$873$	0.374146	0.0126629
$874$	14.9648	0.506193
$875$	−0.498434	−0.0168501
$876$	23.7946	0.803947
$877$	33.7401	1.13932	0.569661	−	0.821880i	$-0.307074\pi$
$877$	33.7401	1.13932	0.569661	+	0.821880i	$0.307074\pi$
$878$	−16.5660	−0.559075
$879$	10.3572	0.349338
$880$	−5.76688	−0.194402
$881$	20.5674	0.692933	0.346467	−	0.938062i	$-0.387381\pi$
$881$	20.5674	0.692933	0.346467	+	0.938062i	$0.387381\pi$
$882$	0.283822	0.00955678
$883$	−32.0730	−1.07934	−0.539671	−	0.841876i	$-0.681452\pi$
$883$	−32.0730	−1.07934	−0.539671	+	0.841876i	$0.681452\pi$
$884$	6.56789	0.220902
$885$	4.80100	0.161384
$886$	39.0755	1.31277
$887$	−23.0529	−0.774039	−0.387020	−	0.922071i	$-0.626495\pi$
$887$	−23.0529	−0.774039	−0.387020	+	0.922071i	$0.626495\pi$
$888$	−4.48336	−0.150452
$889$	−0.707119	−0.0237160
$890$	9.96211	0.333931
$891$	−15.7028	−0.526063
$892$	−0.795272	−0.0266277
$893$	7.68557	0.257188
$894$	4.06875	0.136079
$895$	68.0530	2.27476
$896$	−0.122108	−0.00407934
$897$	12.6275	0.421619
$898$	38.6736	1.29055
$899$	−3.63834	−0.121345
$900$	0.252681	0.00842270
$901$	−67.7332	−2.25652
$902$	−18.6131	−0.619747
$903$	−1.06277	−0.0353668
$904$	−11.0822	−0.368590
$905$	19.7641	0.656981
$906$	−6.55531	−0.217786
$907$	39.2458	1.30313	0.651567	−	0.758591i	$-0.274112\pi$
$907$	39.2458	1.30313	0.651567	+	0.758591i	$0.274112\pi$
$908$	−1.24510	−0.0413201
$909$	−0.127666	−0.00423440
$910$	−0.421122	−0.0139601
$911$	−44.2838	−1.46719	−0.733594	−	0.679588i	$-0.762159\pi$
$911$	−44.2838	−1.46719	−0.733594	+	0.679588i	$0.762159\pi$
$912$	3.71033	0.122861
$913$	21.9516	0.726491
$914$	0.613254	0.0202846
$915$	−55.5330	−1.83587
$916$	−20.8718	−0.689622
$917$	1.52374	0.0503183
$918$	32.9165	1.08641
$919$	22.5560	0.744052	0.372026	−	0.928222i	$-0.378663\pi$
$919$	22.5560	0.744052	0.372026	+	0.928222i	$0.378663\pi$
$920$	23.5566	0.776637
$921$	48.8077	1.60827
$922$	−9.07992	−0.299031
$923$	−5.33962	−0.175756
$924$	−0.366603	−0.0120603
$925$	−15.9890	−0.525714
$926$	9.28590	0.305154
$927$	0.170276	0.00559260
$928$	−0.875497	−0.0287396
$929$	20.8104	0.682767	0.341384	−	0.939924i	$-0.389104\pi$
$929$	20.8104	0.682767	0.341384	+	0.939924i	$0.389104\pi$
$930$	24.2718	0.795903
$931$	14.8629	0.487111
$932$	−3.62464	−0.118729
$933$	39.8984	1.30622
$934$	10.0387	0.328477
$935$	36.7852	1.20301
$936$	0.0418377	0.00136751
$937$	−19.2858	−0.630038	−0.315019	−	0.949085i	$-0.602011\pi$
$937$	−19.2858	−0.630038	−0.315019	+	0.949085i	$0.602011\pi$
$938$	−0.816528	−0.0266606
$939$	28.2738	0.922681
$940$	12.0981	0.394595
$941$	19.4723	0.634777	0.317389	−	0.948296i	$-0.397194\pi$
$941$	19.4723	0.634777	0.317389	+	0.948296i	$0.397194\pi$
$942$	12.9297	0.421271
$943$	76.0306	2.47590
$944$	0.822013	0.0267543
$945$	−2.11055	−0.0686562
$946$	−8.59378	−0.279408
$947$	−2.57720	−0.0837478	−0.0418739	−	0.999123i	$-0.513333\pi$
$947$	−2.57720	−0.0837478	−0.0418739	+	0.999123i	$0.513333\pi$
$948$	−24.5766	−0.798212
$949$	14.0505	0.456098
$950$	13.2321	0.429307
$951$	−54.6974	−1.77369
$952$	0.778890	0.0252440
$953$	−29.7248	−0.962880	−0.481440	−	0.876479i	$-0.659886\pi$
$953$	−29.7248	−0.962880	−0.481440	+	0.876479i	$0.659886\pi$
$954$	−0.431463	−0.0139691
$955$	−5.36585	−0.173635
$956$	−17.1694	−0.555300
$957$	−2.62849	−0.0849671
$958$	30.8229	0.995843
$959$	−1.45090	−0.0468521
$960$	5.84054	0.188503
$961$	−13.7298	−0.442897
$962$	−2.64737	−0.0853548
$963$	0.410194	0.0132183
$964$	−1.97373	−0.0635695
$965$	−26.0781	−0.839485
$966$	1.49750	0.0481812
$967$	−3.38615	−0.108891	−0.0544456	−	0.998517i	$-0.517339\pi$
$967$	−3.38615	−0.108891	−0.0544456	+	0.998517i	$0.517339\pi$
$968$	8.03558	0.258273
$969$	−23.6671	−0.760298
$970$	30.8417	0.990267
$971$	−16.1107	−0.517016	−0.258508	−	0.966009i	$-0.583231\pi$
$971$	−16.1107	−0.517016	−0.258508	+	0.966009i	$0.583231\pi$
$972$	0.422237	0.0135433
$973$	−1.02246	−0.0327786
$974$	28.2921	0.906536
$975$	11.1654	0.357579
$976$	−9.50820	−0.304350
$977$	−3.77929	−0.120910	−0.0604551	−	0.998171i	$-0.519255\pi$
$977$	−3.77929	−0.120910	−0.0604551	+	0.998171i	$0.519255\pi$
$978$	30.7510	0.983308
$979$	5.12095	0.163666
$980$	23.3961	0.747360
$981$	−0.447566	−0.0142897
$982$	27.5916	0.880483
$983$	2.19521	0.0700165	0.0350082	−	0.999387i	$-0.488854\pi$
$983$	2.19521	0.0700165	0.0350082	+	0.999387i	$0.488854\pi$
$984$	18.8508	0.600941
$985$	46.5519	1.48327
$986$	5.58454	0.177848
$987$	0.769078	0.0244800
$988$	2.19091	0.0697022
$989$	35.1038	1.11624
$990$	0.234323	0.00744728
$991$	5.45383	0.173247	0.0866233	−	0.996241i	$-0.472392\pi$
$991$	5.45383	0.173247	0.0866233	+	0.996241i	$0.472392\pi$
$992$	4.15574	0.131945
$993$	−49.4868	−1.57042
$994$	−0.633229	−0.0200848
$995$	28.7561	0.911631
$996$	−22.2319	−0.704446
$997$	−10.5650	−0.334598	−0.167299	−	0.985906i	$-0.553505\pi$
$997$	−10.5650	−0.334598	−0.167299	+	0.985906i	$0.553505\pi$
$998$	19.7517	0.625228
$999$	−13.2679	−0.419778

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.b.1.11	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.b.1.11	✓	35	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.74374 q^{3} +1.00000 q^{4} -3.34943 q^{5} +1.74374 q^{6} +0.122108 q^{7} -1.00000 q^{8} +0.0406325 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.74374 q^{3} +1.00000 q^{4} -3.34943 q^{5} +1.74374 q^{6} +0.122108 q^{7} -1.00000 q^{8} +0.0406325 q^{9} +3.34943 q^{10} +1.72175 q^{11} -1.74374 q^{12} -1.02966 q^{13} -0.122108 q^{14} +5.84054 q^{15} +1.00000 q^{16} -6.37870 q^{17} -0.0406325 q^{18} -2.12780 q^{19} -3.34943 q^{20} -0.212925 q^{21} -1.72175 q^{22} +7.03300 q^{23} +1.74374 q^{24} +6.21869 q^{25} +1.02966 q^{26} +5.16037 q^{27} +0.122108 q^{28} +0.875497 q^{29} -5.84054 q^{30} -4.15574 q^{31} -1.00000 q^{32} -3.00229 q^{33} +6.37870 q^{34} -0.408992 q^{35} +0.0406325 q^{36} -2.57112 q^{37} +2.12780 q^{38} +1.79546 q^{39} +3.34943 q^{40} +10.8105 q^{41} +0.212925 q^{42} +4.99130 q^{43} +1.72175 q^{44} -0.136096 q^{45} -7.03300 q^{46} -3.61198 q^{47} -1.74374 q^{48} -6.98509 q^{49} -6.21869 q^{50} +11.1228 q^{51} -1.02966 q^{52} +10.6186 q^{53} -5.16037 q^{54} -5.76688 q^{55} -0.122108 q^{56} +3.71033 q^{57} -0.875497 q^{58} +0.822013 q^{59} +5.84054 q^{60} -9.50820 q^{61} +4.15574 q^{62} +0.00496155 q^{63} +1.00000 q^{64} +3.44877 q^{65} +3.00229 q^{66} +6.68694 q^{67} -6.37870 q^{68} -12.2637 q^{69} +0.408992 q^{70} +5.18582 q^{71} -0.0406325 q^{72} -13.6457 q^{73} +2.57112 q^{74} -10.8438 q^{75} -2.12780 q^{76} +0.210239 q^{77} -1.79546 q^{78} +14.0942 q^{79} -3.34943 q^{80} -9.12025 q^{81} -10.8105 q^{82} +12.7496 q^{83} -0.212925 q^{84} +21.3650 q^{85} -4.99130 q^{86} -1.52664 q^{87} -1.72175 q^{88} +2.97427 q^{89} +0.136096 q^{90} -0.125730 q^{91} +7.03300 q^{92} +7.24654 q^{93} +3.61198 q^{94} +7.12692 q^{95} +1.74374 q^{96} +9.20804 q^{97} +6.98509 q^{98} +0.0699591 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * q^99

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