LMFDB - Embedded newform 74.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,2,Mod(1,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, 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("74.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.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:	$0.590892974957$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
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			1.1
Root			$-1.30278$ of defining polynomial
Character	$\chi$	$=$	74.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.302776 q^{3} +1.00000 q^{4} +1.30278 q^{5} +0.302776 q^{6} +4.60555 q^{7} -1.00000 q^{8} -2.90833 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.302776 q^{3} +1.00000 q^{4} +1.30278 q^{5} +0.302776 q^{6} +4.60555 q^{7} -1.00000 q^{8} -2.90833 q^{9} -1.30278 q^{10} +1.30278 q^{11} -0.302776 q^{12} -2.30278 q^{13} -4.60555 q^{14} -0.394449 q^{15} +1.00000 q^{16} -6.00000 q^{17} +2.90833 q^{18} +2.00000 q^{19} +1.30278 q^{20} -1.39445 q^{21} -1.30278 q^{22} -6.90833 q^{23} +0.302776 q^{24} -3.30278 q^{25} +2.30278 q^{26} +1.78890 q^{27} +4.60555 q^{28} +6.90833 q^{29} +0.394449 q^{30} +3.30278 q^{31} -1.00000 q^{32} -0.394449 q^{33} +6.00000 q^{34} +6.00000 q^{35} -2.90833 q^{36} +1.00000 q^{37} -2.00000 q^{38} +0.697224 q^{39} -1.30278 q^{40} -0.908327 q^{41} +1.39445 q^{42} -6.60555 q^{43} +1.30278 q^{44} -3.78890 q^{45} +6.90833 q^{46} -2.60555 q^{47} -0.302776 q^{48} +14.2111 q^{49} +3.30278 q^{50} +1.81665 q^{51} -2.30278 q^{52} -6.00000 q^{53} -1.78890 q^{54} +1.69722 q^{55} -4.60555 q^{56} -0.605551 q^{57} -6.90833 q^{58} +3.39445 q^{59} -0.394449 q^{60} -10.5139 q^{61} -3.30278 q^{62} -13.3944 q^{63} +1.00000 q^{64} -3.00000 q^{65} +0.394449 q^{66} +14.5139 q^{67} -6.00000 q^{68} +2.09167 q^{69} -6.00000 q^{70} +6.00000 q^{71} +2.90833 q^{72} -8.69722 q^{73} -1.00000 q^{74} +1.00000 q^{75} +2.00000 q^{76} +6.00000 q^{77} -0.697224 q^{78} -16.1194 q^{79} +1.30278 q^{80} +8.18335 q^{81} +0.908327 q^{82} +17.2111 q^{83} -1.39445 q^{84} -7.81665 q^{85} +6.60555 q^{86} -2.09167 q^{87} -1.30278 q^{88} +5.21110 q^{89} +3.78890 q^{90} -10.6056 q^{91} -6.90833 q^{92} -1.00000 q^{93} +2.60555 q^{94} +2.60555 q^{95} +0.302776 q^{96} +12.4222 q^{97} -14.2111 q^{98} -3.78890 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 3 q^{3} + 2 q^{4} - q^{5} - 3 q^{6} + 2 q^{7} - 2 q^{8} + 5 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 - q^5 - 3 * q^6 + 2 * q^7 - 2 * q^8 + 5 * q^9	\( 2 q - 2 q^{2} + 3 q^{3} + 2 q^{4} - q^{5} - 3 q^{6} + 2 q^{7} - 2 q^{8} + 5 q^{9} + q^{10} - q^{11} + 3 q^{12} - q^{13} - 2 q^{14} - 8 q^{15} + 2 q^{16} - 12 q^{17} - 5 q^{18} + 4 q^{19} - q^{20} - 10 q^{21} + q^{22} - 3 q^{23} - 3 q^{24} - 3 q^{25} + q^{26} + 18 q^{27} + 2 q^{28} + 3 q^{29} + 8 q^{30} + 3 q^{31} - 2 q^{32} - 8 q^{33} + 12 q^{34} + 12 q^{35} + 5 q^{36} + 2 q^{37} - 4 q^{38} + 5 q^{39} + q^{40} + 9 q^{41} + 10 q^{42} - 6 q^{43} - q^{44} - 22 q^{45} + 3 q^{46} + 2 q^{47} + 3 q^{48} + 14 q^{49} + 3 q^{50} - 18 q^{51} - q^{52} - 12 q^{53} - 18 q^{54} + 7 q^{55} - 2 q^{56} + 6 q^{57} - 3 q^{58} + 14 q^{59} - 8 q^{60} - 3 q^{61} - 3 q^{62} - 34 q^{63} + 2 q^{64} - 6 q^{65} + 8 q^{66} + 11 q^{67} - 12 q^{68} + 15 q^{69} - 12 q^{70} + 12 q^{71} - 5 q^{72} - 21 q^{73} - 2 q^{74} + 2 q^{75} + 4 q^{76} + 12 q^{77} - 5 q^{78} - 7 q^{79} - q^{80} + 38 q^{81} - 9 q^{82} + 20 q^{83} - 10 q^{84} + 6 q^{85} + 6 q^{86} - 15 q^{87} + q^{88} - 4 q^{89} + 22 q^{90} - 14 q^{91} - 3 q^{92} - 2 q^{93} - 2 q^{94} - 2 q^{95} - 3 q^{96} - 4 q^{97} - 14 q^{98} - 22 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 - q^5 - 3 * q^6 + 2 * q^7 - 2 * q^8 + 5 * q^9 + q^10 - q^11 + 3 * q^12 - q^13 - 2 * q^14 - 8 * q^15 + 2 * q^16 - 12 * q^17 - 5 * q^18 + 4 * q^19 - q^20 - 10 * q^21 + q^22 - 3 * q^23 - 3 * q^24 - 3 * q^25 + q^26 + 18 * q^27 + 2 * q^28 + 3 * q^29 + 8 * q^30 + 3 * q^31 - 2 * q^32 - 8 * q^33 + 12 * q^34 + 12 * q^35 + 5 * q^36 + 2 * q^37 - 4 * q^38 + 5 * q^39 + q^40 + 9 * q^41 + 10 * q^42 - 6 * q^43 - q^44 - 22 * q^45 + 3 * q^46 + 2 * q^47 + 3 * q^48 + 14 * q^49 + 3 * q^50 - 18 * q^51 - q^52 - 12 * q^53 - 18 * q^54 + 7 * q^55 - 2 * q^56 + 6 * q^57 - 3 * q^58 + 14 * q^59 - 8 * q^60 - 3 * q^61 - 3 * q^62 - 34 * q^63 + 2 * q^64 - 6 * q^65 + 8 * q^66 + 11 * q^67 - 12 * q^68 + 15 * q^69 - 12 * q^70 + 12 * q^71 - 5 * q^72 - 21 * q^73 - 2 * q^74 + 2 * q^75 + 4 * q^76 + 12 * q^77 - 5 * q^78 - 7 * q^79 - q^80 + 38 * q^81 - 9 * q^82 + 20 * q^83 - 10 * q^84 + 6 * q^85 + 6 * q^86 - 15 * q^87 + q^88 - 4 * q^89 + 22 * q^90 - 14 * q^91 - 3 * q^92 - 2 * q^93 - 2 * q^94 - 2 * q^95 - 3 * q^96 - 4 * q^97 - 14 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.302776	−0.174808	−0.0874038	−	0.996173i	$-0.527857\pi$
$3$	−0.302776	−0.174808	−0.0874038	+	0.996173i	$0.527857\pi$
$4$	1.00000	0.500000
$5$	1.30278	0.582619	0.291309	−	0.956629i	$-0.405909\pi$
$5$	1.30278	0.582619	0.291309	+	0.956629i	$0.405909\pi$
$6$	0.302776	0.123608
$7$	4.60555	1.74073	0.870367	−	0.492403i	$-0.163881\pi$
$7$	4.60555	1.74073	0.870367	+	0.492403i	$0.163881\pi$
$8$	−1.00000	−0.353553
$9$	−2.90833	−0.969442
$10$	−1.30278	−0.411974
$11$	1.30278	0.392802	0.196401	−	0.980524i	$-0.437075\pi$
$11$	1.30278	0.392802	0.196401	+	0.980524i	$0.437075\pi$
$12$	−0.302776	−0.0874038
$13$	−2.30278	−0.638675	−0.319338	−	0.947641i	$-0.603460\pi$
$13$	−2.30278	−0.638675	−0.319338	+	0.947641i	$0.603460\pi$
$14$	−4.60555	−1.23089
$15$	−0.394449	−0.101846
$16$	1.00000	0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	2.90833	0.685499
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	1.30278	0.291309
$21$	−1.39445	−0.304294
$22$	−1.30278	−0.277753
$23$	−6.90833	−1.44049	−0.720243	−	0.693722i	$-0.755970\pi$
$23$	−6.90833	−1.44049	−0.720243	+	0.693722i	$0.755970\pi$
$24$	0.302776	0.0618038
$25$	−3.30278	−0.660555
$26$	2.30278	0.451611
$27$	1.78890	0.344273
$28$	4.60555	0.870367
$29$	6.90833	1.28284	0.641422	−	0.767188i	$-0.278345\pi$
$29$	6.90833	1.28284	0.641422	+	0.767188i	$0.278345\pi$
$30$	0.394449	0.0720162
$31$	3.30278	0.593196	0.296598	−	0.955002i	$-0.404148\pi$
$31$	3.30278	0.593196	0.296598	+	0.955002i	$0.404148\pi$
$32$	−1.00000	−0.176777
$33$	−0.394449	−0.0686647
$34$	6.00000	1.02899
$35$	6.00000	1.01419
$36$	−2.90833	−0.484721
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−2.00000	−0.324443
$39$	0.697224	0.111645
$40$	−1.30278	−0.205987
$41$	−0.908327	−0.141857	−0.0709284	−	0.997481i	$-0.522596\pi$
$41$	−0.908327	−0.141857	−0.0709284	+	0.997481i	$0.522596\pi$
$42$	1.39445	0.215168
$43$	−6.60555	−1.00734	−0.503669	−	0.863897i	$-0.668017\pi$
$43$	−6.60555	−1.00734	−0.503669	+	0.863897i	$0.668017\pi$
$44$	1.30278	0.196401
$45$	−3.78890	−0.564815
$46$	6.90833	1.01858
$47$	−2.60555	−0.380059	−0.190029	−	0.981778i	$-0.560858\pi$
$47$	−2.60555	−0.380059	−0.190029	+	0.981778i	$0.560858\pi$
$48$	−0.302776	−0.0437019
$49$	14.2111	2.03016
$50$	3.30278	0.467083
$51$	1.81665	0.254382
$52$	−2.30278	−0.319338
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	−1.78890	−0.243438
$55$	1.69722	0.228854
$56$	−4.60555	−0.615443
$57$	−0.605551	−0.0802072
$58$	−6.90833	−0.907108
$59$	3.39445	0.441920	0.220960	−	0.975283i	$-0.429081\pi$
$59$	3.39445	0.441920	0.220960	+	0.975283i	$0.429081\pi$
$60$	−0.394449	−0.0509231
$61$	−10.5139	−1.34616	−0.673082	−	0.739568i	$-0.735030\pi$
$61$	−10.5139	−1.34616	−0.673082	+	0.739568i	$0.735030\pi$
$62$	−3.30278	−0.419453
$63$	−13.3944	−1.68754
$64$	1.00000	0.125000
$65$	−3.00000	−0.372104
$66$	0.394449	0.0485533
$67$	14.5139	1.77315	0.886576	−	0.462583i	$-0.153077\pi$
$67$	14.5139	1.77315	0.886576	+	0.462583i	$0.153077\pi$
$68$	−6.00000	−0.727607
$69$	2.09167	0.251808
$70$	−6.00000	−0.717137
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	2.90833	0.342750
$73$	−8.69722	−1.01793	−0.508967	−	0.860786i	$-0.669972\pi$
$73$	−8.69722	−1.01793	−0.508967	+	0.860786i	$0.669972\pi$
$74$	−1.00000	−0.116248
$75$	1.00000	0.115470
$76$	2.00000	0.229416
$77$	6.00000	0.683763
$78$	−0.697224	−0.0789451
$79$	−16.1194	−1.81358	−0.906789	−	0.421585i	$-0.861474\pi$
$79$	−16.1194	−1.81358	−0.906789	+	0.421585i	$0.861474\pi$
$80$	1.30278	0.145655
$81$	8.18335	0.909261
$82$	0.908327	0.100308
$83$	17.2111	1.88916	0.944582	−	0.328276i	$-0.106467\pi$
$83$	17.2111	1.88916	0.944582	+	0.328276i	$0.106467\pi$
$84$	−1.39445	−0.152147
$85$	−7.81665	−0.847835
$86$	6.60555	0.712295
$87$	−2.09167	−0.224251
$88$	−1.30278	−0.138876
$89$	5.21110	0.552376	0.276188	−	0.961104i	$-0.410929\pi$
$89$	5.21110	0.552376	0.276188	+	0.961104i	$0.410929\pi$
$90$	3.78890	0.399385
$91$	−10.6056	−1.11176
$92$	−6.90833	−0.720243
$93$	−1.00000	−0.103695
$94$	2.60555	0.268742
$95$	2.60555	0.267324
$96$	0.302776	0.0309019
$97$	12.4222	1.26128	0.630642	−	0.776074i	$-0.282792\pi$
$97$	12.4222	1.26128	0.630642	+	0.776074i	$0.282792\pi$
$98$	−14.2111	−1.43554
$99$	−3.78890	−0.380799
$100$	−3.30278	−0.330278
$101$	16.4222	1.63407	0.817035	−	0.576588i	$-0.195616\pi$
$101$	16.4222	1.63407	0.817035	+	0.576588i	$0.195616\pi$
$102$	−1.81665	−0.179876
$103$	3.30278	0.325432	0.162716	−	0.986673i	$-0.447975\pi$
$103$	3.30278	0.325432	0.162716	+	0.986673i	$0.447975\pi$
$104$	2.30278	0.225806
$105$	−1.81665	−0.177287
$106$	6.00000	0.582772
$107$	4.30278	0.415965	0.207983	−	0.978133i	$-0.433310\pi$
$107$	4.30278	0.415965	0.207983	+	0.978133i	$0.433310\pi$
$108$	1.78890	0.172137
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	−1.69722	−0.161824
$111$	−0.302776	−0.0287382
$112$	4.60555	0.435184
$113$	11.2111	1.05465	0.527326	−	0.849663i	$-0.323195\pi$
$113$	11.2111	1.05465	0.527326	+	0.849663i	$0.323195\pi$
$114$	0.605551	0.0567151
$115$	−9.00000	−0.839254
$116$	6.90833	0.641422
$117$	6.69722	0.619159
$118$	−3.39445	−0.312484
$119$	−27.6333	−2.53314
$120$	0.394449	0.0360081
$121$	−9.30278	−0.845707
$122$	10.5139	0.951882
$123$	0.275019	0.0247977
$124$	3.30278	0.296598
$125$	−10.8167	−0.967471
$126$	13.3944	1.19327
$127$	−4.78890	−0.424946	−0.212473	−	0.977167i	$-0.568152\pi$
$127$	−4.78890	−0.424946	−0.212473	+	0.977167i	$0.568152\pi$
$128$	−1.00000	−0.0883883
$129$	2.00000	0.176090
$130$	3.00000	0.263117
$131$	3.39445	0.296574	0.148287	−	0.988944i	$-0.452624\pi$
$131$	3.39445	0.296574	0.148287	+	0.988944i	$0.452624\pi$
$132$	−0.394449	−0.0343324
$133$	9.21110	0.798704
$134$	−14.5139	−1.25381
$135$	2.33053	0.200580
$136$	6.00000	0.514496
$137$	−9.90833	−0.846525	−0.423263	−	0.906007i	$-0.639115\pi$
$137$	−9.90833	−0.846525	−0.423263	+	0.906007i	$0.639115\pi$
$138$	−2.09167	−0.178055
$139$	8.90833	0.755594	0.377797	−	0.925888i	$-0.376682\pi$
$139$	8.90833	0.755594	0.377797	+	0.925888i	$0.376682\pi$
$140$	6.00000	0.507093
$141$	0.788897	0.0664372
$142$	−6.00000	−0.503509
$143$	−3.00000	−0.250873
$144$	−2.90833	−0.242361
$145$	9.00000	0.747409
$146$	8.69722	0.719787
$147$	−4.30278	−0.354887
$148$	1.00000	0.0821995
$149$	−1.81665	−0.148826	−0.0744130	−	0.997228i	$-0.523708\pi$
$149$	−1.81665	−0.148826	−0.0744130	+	0.997228i	$0.523708\pi$
$150$	−1.00000	−0.0816497
$151$	−13.3944	−1.09002	−0.545012	−	0.838428i	$-0.683475\pi$
$151$	−13.3944	−1.09002	−0.545012	+	0.838428i	$0.683475\pi$
$152$	−2.00000	−0.162221
$153$	17.4500	1.41075
$154$	−6.00000	−0.483494
$155$	4.30278	0.345607
$156$	0.697224	0.0558226
$157$	7.21110	0.575509	0.287754	−	0.957704i	$-0.407091\pi$
$157$	7.21110	0.575509	0.287754	+	0.957704i	$0.407091\pi$
$158$	16.1194	1.28239
$159$	1.81665	0.144070
$160$	−1.30278	−0.102993
$161$	−31.8167	−2.50750
$162$	−8.18335	−0.642944
$163$	−20.4222	−1.59959	−0.799795	−	0.600273i	$-0.795059\pi$
$163$	−20.4222	−1.59959	−0.799795	+	0.600273i	$0.795059\pi$
$164$	−0.908327	−0.0709284
$165$	−0.513878	−0.0400054
$166$	−17.2111	−1.33584
$167$	12.5139	0.968353	0.484176	−	0.874970i	$-0.339119\pi$
$167$	12.5139	0.968353	0.484176	+	0.874970i	$0.339119\pi$
$168$	1.39445	0.107584
$169$	−7.69722	−0.592094
$170$	7.81665	0.599510
$171$	−5.81665	−0.444811
$172$	−6.60555	−0.503669
$173$	−23.2111	−1.76471	−0.882354	−	0.470587i	$-0.844042\pi$
$173$	−23.2111	−1.76471	−0.882354	+	0.470587i	$0.844042\pi$
$174$	2.09167	0.158569
$175$	−15.2111	−1.14985
$176$	1.30278	0.0982004
$177$	−1.02776	−0.0772509
$178$	−5.21110	−0.390589
$179$	7.81665	0.584244	0.292122	−	0.956381i	$-0.405639\pi$
$179$	7.81665	0.584244	0.292122	+	0.956381i	$0.405639\pi$
$180$	−3.78890	−0.282408
$181$	20.0000	1.48659	0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000	1.48659	0.743294	+	0.668965i	$0.233262\pi$
$182$	10.6056	0.786136
$183$	3.18335	0.235320
$184$	6.90833	0.509289
$185$	1.30278	0.0957820
$186$	1.00000	0.0733236
$187$	−7.81665	−0.571610
$188$	−2.60555	−0.190029
$189$	8.23886	0.599289
$190$	−2.60555	−0.189027
$191$	12.5139	0.905472	0.452736	−	0.891644i	$-0.350448\pi$
$191$	12.5139	0.905472	0.452736	+	0.891644i	$0.350448\pi$
$192$	−0.302776	−0.0218509
$193$	−4.00000	−0.287926	−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000	−0.287926	−0.143963	+	0.989583i	$0.545985\pi$
$194$	−12.4222	−0.891862
$195$	0.908327	0.0650466
$196$	14.2111	1.01508
$197$	−6.00000	−0.427482	−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000	−0.427482	−0.213741	+	0.976890i	$0.568565\pi$
$198$	3.78890	0.269265
$199$	−2.42221	−0.171706	−0.0858528	−	0.996308i	$-0.527361\pi$
$199$	−2.42221	−0.171706	−0.0858528	+	0.996308i	$0.527361\pi$
$200$	3.30278	0.233542
$201$	−4.39445	−0.309961
$202$	−16.4222	−1.15546
$203$	31.8167	2.23309
$204$	1.81665	0.127191
$205$	−1.18335	−0.0826485
$206$	−3.30278	−0.230115
$207$	20.0917	1.39647
$208$	−2.30278	−0.159669
$209$	2.60555	0.180230
$210$	1.81665	0.125361
$211$	6.69722	0.461056	0.230528	−	0.973066i	$-0.425955\pi$
$211$	6.69722	0.461056	0.230528	+	0.973066i	$0.425955\pi$
$212$	−6.00000	−0.412082
$213$	−1.81665	−0.124475
$214$	−4.30278	−0.294132
$215$	−8.60555	−0.586894
$216$	−1.78890	−0.121719
$217$	15.2111	1.03260
$218$	−2.00000	−0.135457
$219$	2.63331	0.177942
$220$	1.69722	0.114427
$221$	13.8167	0.929409
$222$	0.302776	0.0203210
$223$	15.8167	1.05916	0.529581	−	0.848260i	$-0.322349\pi$
$223$	15.8167	1.05916	0.529581	+	0.848260i	$0.322349\pi$
$224$	−4.60555	−0.307721
$225$	9.60555	0.640370
$226$	−11.2111	−0.745751
$227$	−7.81665	−0.518810	−0.259405	−	0.965769i	$-0.583526\pi$
$227$	−7.81665	−0.518810	−0.259405	+	0.965769i	$0.583526\pi$
$228$	−0.605551	−0.0401036
$229$	17.3944	1.14946	0.574729	−	0.818344i	$-0.305108\pi$
$229$	17.3944	1.14946	0.574729	+	0.818344i	$0.305108\pi$
$230$	9.00000	0.593442
$231$	−1.81665	−0.119527
$232$	−6.90833	−0.453554
$233$	−9.51388	−0.623275	−0.311637	−	0.950201i	$-0.600877\pi$
$233$	−9.51388	−0.623275	−0.311637	+	0.950201i	$0.600877\pi$
$234$	−6.69722	−0.437811
$235$	−3.39445	−0.221429
$236$	3.39445	0.220960
$237$	4.88057	0.317027
$238$	27.6333	1.79120
$239$	0.513878	0.0332400	0.0166200	−	0.999862i	$-0.494709\pi$
$239$	0.513878	0.0332400	0.0166200	+	0.999862i	$0.494709\pi$
$240$	−0.394449	−0.0254616
$241$	8.00000	0.515325	0.257663	−	0.966235i	$-0.417048\pi$
$241$	8.00000	0.515325	0.257663	+	0.966235i	$0.417048\pi$
$242$	9.30278	0.598005
$243$	−7.84441	−0.503219
$244$	−10.5139	−0.673082
$245$	18.5139	1.18281
$246$	−0.275019	−0.0175346
$247$	−4.60555	−0.293044
$248$	−3.30278	−0.209726
$249$	−5.21110	−0.330240
$250$	10.8167	0.684105
$251$	−6.78890	−0.428511	−0.214256	−	0.976778i	$-0.568733\pi$
$251$	−6.78890	−0.428511	−0.214256	+	0.976778i	$0.568733\pi$
$252$	−13.3944	−0.843771
$253$	−9.00000	−0.565825
$254$	4.78890	0.300482
$255$	2.36669	0.148208
$256$	1.00000	0.0625000
$257$	−11.2111	−0.699329	−0.349665	−	0.936875i	$-0.613704\pi$
$257$	−11.2111	−0.699329	−0.349665	+	0.936875i	$0.613704\pi$
$258$	−2.00000	−0.124515
$259$	4.60555	0.286175
$260$	−3.00000	−0.186052
$261$	−20.0917	−1.24364
$262$	−3.39445	−0.209710
$263$	−7.81665	−0.481996	−0.240998	−	0.970526i	$-0.577475\pi$
$263$	−7.81665	−0.481996	−0.240998	+	0.970526i	$0.577475\pi$
$264$	0.394449	0.0242766
$265$	−7.81665	−0.480173
$266$	−9.21110	−0.564769
$267$	−1.57779	−0.0965595
$268$	14.5139	0.886576
$269$	−6.78890	−0.413926	−0.206963	−	0.978349i	$-0.566358\pi$
$269$	−6.78890	−0.413926	−0.206963	+	0.978349i	$0.566358\pi$
$270$	−2.33053	−0.141832
$271$	6.42221	0.390121	0.195061	−	0.980791i	$-0.437510\pi$
$271$	6.42221	0.390121	0.195061	+	0.980791i	$0.437510\pi$
$272$	−6.00000	−0.363803
$273$	3.21110	0.194345
$274$	9.90833	0.598584
$275$	−4.30278	−0.259467
$276$	2.09167	0.125904
$277$	−25.1194	−1.50928	−0.754640	−	0.656139i	$-0.772189\pi$
$277$	−25.1194	−1.50928	−0.754640	+	0.656139i	$0.772189\pi$
$278$	−8.90833	−0.534286
$279$	−9.60555	−0.575069
$280$	−6.00000	−0.358569
$281$	−12.0000	−0.715860	−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000	−0.715860	−0.357930	+	0.933748i	$0.616517\pi$
$282$	−0.788897	−0.0469782
$283$	17.3944	1.03399	0.516996	−	0.855988i	$-0.327050\pi$
$283$	17.3944	1.03399	0.516996	+	0.855988i	$0.327050\pi$
$284$	6.00000	0.356034
$285$	−0.788897	−0.0467303
$286$	3.00000	0.177394
$287$	−4.18335	−0.246935
$288$	2.90833	0.171375
$289$	19.0000	1.11765
$290$	−9.00000	−0.528498
$291$	−3.76114	−0.220482
$292$	−8.69722	−0.508967
$293$	−25.0278	−1.46214	−0.731069	−	0.682304i	$-0.760978\pi$
$293$	−25.0278	−1.46214	−0.731069	+	0.682304i	$0.760978\pi$
$294$	4.30278	0.250943
$295$	4.42221	0.257471
$296$	−1.00000	−0.0581238
$297$	2.33053	0.135231
$298$	1.81665	0.105236
$299$	15.9083	0.920002
$300$	1.00000	0.0577350
$301$	−30.4222	−1.75351
$302$	13.3944	0.770764
$303$	−4.97224	−0.285648
$304$	2.00000	0.114708
$305$	−13.6972	−0.784301
$306$	−17.4500	−0.997548
$307$	7.09167	0.404743	0.202372	−	0.979309i	$-0.435135\pi$
$307$	7.09167	0.404743	0.202372	+	0.979309i	$0.435135\pi$
$308$	6.00000	0.341882
$309$	−1.00000	−0.0568880
$310$	−4.30278	−0.244381
$311$	5.09167	0.288722	0.144361	−	0.989525i	$-0.453887\pi$
$311$	5.09167	0.288722	0.144361	+	0.989525i	$0.453887\pi$
$312$	−0.697224	−0.0394726
$313$	27.0278	1.52770	0.763850	−	0.645394i	$-0.223307\pi$
$313$	27.0278	1.52770	0.763850	+	0.645394i	$0.223307\pi$
$314$	−7.21110	−0.406946
$315$	−17.4500	−0.983194
$316$	−16.1194	−0.906789
$317$	−5.21110	−0.292685	−0.146342	−	0.989234i	$-0.546750\pi$
$317$	−5.21110	−0.292685	−0.146342	+	0.989234i	$0.546750\pi$
$318$	−1.81665	−0.101873
$319$	9.00000	0.503903
$320$	1.30278	0.0728274
$321$	−1.30278	−0.0727138
$322$	31.8167	1.77307
$323$	−12.0000	−0.667698
$324$	8.18335	0.454630
$325$	7.60555	0.421880
$326$	20.4222	1.13108
$327$	−0.605551	−0.0334871
$328$	0.908327	0.0501540
$329$	−12.0000	−0.661581
$330$	0.513878	0.0282881
$331$	1.21110	0.0665682	0.0332841	−	0.999446i	$-0.489403\pi$
$331$	1.21110	0.0665682	0.0332841	+	0.999446i	$0.489403\pi$
$332$	17.2111	0.944582
$333$	−2.90833	−0.159375
$334$	−12.5139	−0.684729
$335$	18.9083	1.03307
$336$	−1.39445	−0.0760734
$337$	−19.1194	−1.04150	−0.520751	−	0.853709i	$-0.674348\pi$
$337$	−19.1194	−1.04150	−0.520751	+	0.853709i	$0.674348\pi$
$338$	7.69722	0.418674
$339$	−3.39445	−0.184361
$340$	−7.81665	−0.423918
$341$	4.30278	0.233008
$342$	5.81665	0.314529
$343$	33.2111	1.79323
$344$	6.60555	0.356147
$345$	2.72498	0.146708
$346$	23.2111	1.24784
$347$	31.8167	1.70801	0.854004	−	0.520267i	$-0.174168\pi$
$347$	31.8167	1.70801	0.854004	+	0.520267i	$0.174168\pi$
$348$	−2.09167	−0.112125
$349$	−22.2389	−1.19042	−0.595209	−	0.803571i	$-0.702931\pi$
$349$	−22.2389	−1.19042	−0.595209	+	0.803571i	$0.702931\pi$
$350$	15.2111	0.813068
$351$	−4.11943	−0.219879
$352$	−1.30278	−0.0694382
$353$	31.8167	1.69343	0.846715	−	0.532047i	$-0.178577\pi$
$353$	31.8167	1.69343	0.846715	+	0.532047i	$0.178577\pi$
$354$	1.02776	0.0546246
$355$	7.81665	0.414865
$356$	5.21110	0.276188
$357$	8.36669	0.442812
$358$	−7.81665	−0.413123
$359$	−11.2111	−0.591699	−0.295850	−	0.955235i	$-0.595603\pi$
$359$	−11.2111	−0.591699	−0.295850	+	0.955235i	$0.595603\pi$
$360$	3.78890	0.199692
$361$	−15.0000	−0.789474
$362$	−20.0000	−1.05118
$363$	2.81665	0.147836
$364$	−10.6056	−0.555882
$365$	−11.3305	−0.593067
$366$	−3.18335	−0.166396
$367$	−17.8167	−0.930022	−0.465011	−	0.885305i	$-0.653950\pi$
$367$	−17.8167	−0.930022	−0.465011	+	0.885305i	$0.653950\pi$
$368$	−6.90833	−0.360121
$369$	2.64171	0.137522
$370$	−1.30278	−0.0677281
$371$	−27.6333	−1.43465
$372$	−1.00000	−0.0518476
$373$	3.81665	0.197619	0.0988094	−	0.995106i	$-0.468497\pi$
$373$	3.81665	0.197619	0.0988094	+	0.995106i	$0.468497\pi$
$374$	7.81665	0.404190
$375$	3.27502	0.169121
$376$	2.60555	0.134371
$377$	−15.9083	−0.819321
$378$	−8.23886	−0.423761
$379$	−15.3305	−0.787477	−0.393738	−	0.919223i	$-0.628818\pi$
$379$	−15.3305	−0.787477	−0.393738	+	0.919223i	$0.628818\pi$
$380$	2.60555	0.133662
$381$	1.44996	0.0742838
$382$	−12.5139	−0.640266
$383$	20.8444	1.06510	0.532550	−	0.846399i	$-0.321234\pi$
$383$	20.8444	1.06510	0.532550	+	0.846399i	$0.321234\pi$
$384$	0.302776	0.0154510
$385$	7.81665	0.398374
$386$	4.00000	0.203595
$387$	19.2111	0.976555
$388$	12.4222	0.630642
$389$	−11.8806	−0.602369	−0.301184	−	0.953566i	$-0.597382\pi$
$389$	−11.8806	−0.602369	−0.301184	+	0.953566i	$0.597382\pi$
$390$	−0.908327	−0.0459949
$391$	41.4500	2.09621
$392$	−14.2111	−0.717769
$393$	−1.02776	−0.0518435
$394$	6.00000	0.302276
$395$	−21.0000	−1.05662
$396$	−3.78890	−0.190399
$397$	27.8167	1.39608	0.698039	−	0.716060i	$-0.254056\pi$
$397$	27.8167	1.39608	0.698039	+	0.716060i	$0.254056\pi$
$398$	2.42221	0.121414
$399$	−2.78890	−0.139620
$400$	−3.30278	−0.165139
$401$	13.8167	0.689971	0.344985	−	0.938608i	$-0.387884\pi$
$401$	13.8167	0.689971	0.344985	+	0.938608i	$0.387884\pi$
$402$	4.39445	0.219175
$403$	−7.60555	−0.378859
$404$	16.4222	0.817035
$405$	10.6611	0.529753
$406$	−31.8167	−1.57903
$407$	1.30278	0.0645762
$408$	−1.81665	−0.0899378
$409$	−5.02776	−0.248607	−0.124303	−	0.992244i	$-0.539670\pi$
$409$	−5.02776	−0.248607	−0.124303	+	0.992244i	$0.539670\pi$
$410$	1.18335	0.0584413
$411$	3.00000	0.147979
$412$	3.30278	0.162716
$413$	15.6333	0.769265
$414$	−20.0917	−0.987452
$415$	22.4222	1.10066
$416$	2.30278	0.112903
$417$	−2.69722	−0.132084
$418$	−2.60555	−0.127442
$419$	−25.1472	−1.22852	−0.614260	−	0.789104i	$-0.710545\pi$
$419$	−25.1472	−1.22852	−0.614260	+	0.789104i	$0.710545\pi$
$420$	−1.81665	−0.0886436
$421$	28.7250	1.39997	0.699985	−	0.714158i	$-0.253190\pi$
$421$	28.7250	1.39997	0.699985	+	0.714158i	$0.253190\pi$
$422$	−6.69722	−0.326016
$423$	7.57779	0.368445
$424$	6.00000	0.291386
$425$	19.8167	0.961249
$426$	1.81665	0.0880172
$427$	−48.4222	−2.34331
$428$	4.30278	0.207983
$429$	0.908327	0.0438544
$430$	8.60555	0.414997
$431$	−5.21110	−0.251010	−0.125505	−	0.992093i	$-0.540055\pi$
$431$	−5.21110	−0.251010	−0.125505	+	0.992093i	$0.540055\pi$
$432$	1.78890	0.0860684
$433$	−11.9361	−0.573612	−0.286806	−	0.957989i	$-0.592593\pi$
$433$	−11.9361	−0.573612	−0.286806	+	0.957989i	$0.592593\pi$
$434$	−15.2111	−0.730156
$435$	−2.72498	−0.130653
$436$	2.00000	0.0957826
$437$	−13.8167	−0.660940
$438$	−2.63331	−0.125824
$439$	−9.33053	−0.445322	−0.222661	−	0.974896i	$-0.571474\pi$
$439$	−9.33053	−0.445322	−0.222661	+	0.974896i	$0.571474\pi$
$440$	−1.69722	−0.0809120
$441$	−41.3305	−1.96812
$442$	−13.8167	−0.657191
$443$	0.275019	0.0130666	0.00653328	−	0.999979i	$-0.497920\pi$
$443$	0.275019	0.0130666	0.00653328	+	0.999979i	$0.497920\pi$
$444$	−0.302776	−0.0143691
$445$	6.78890	0.321825
$446$	−15.8167	−0.748940
$447$	0.550039	0.0260159
$448$	4.60555	0.217592
$449$	−0.788897	−0.0372304	−0.0186152	−	0.999827i	$-0.505926\pi$
$449$	−0.788897	−0.0372304	−0.0186152	+	0.999827i	$0.505926\pi$
$450$	−9.60555	−0.452810
$451$	−1.18335	−0.0557216
$452$	11.2111	0.527326
$453$	4.05551	0.190545
$454$	7.81665	0.366854
$455$	−13.8167	−0.647735
$456$	0.605551	0.0283575
$457$	4.60555	0.215439	0.107719	−	0.994181i	$-0.465645\pi$
$457$	4.60555	0.215439	0.107719	+	0.994181i	$0.465645\pi$
$458$	−17.3944	−0.812789
$459$	−10.7334	−0.500991
$460$	−9.00000	−0.419627
$461$	−16.4222	−0.764858	−0.382429	−	0.923985i	$-0.624912\pi$
$461$	−16.4222	−0.764858	−0.382429	+	0.923985i	$0.624912\pi$
$462$	1.81665	0.0845184
$463$	30.3028	1.40829	0.704145	−	0.710056i	$-0.251331\pi$
$463$	30.3028	1.40829	0.704145	+	0.710056i	$0.251331\pi$
$464$	6.90833	0.320711
$465$	−1.30278	−0.0604148
$466$	9.51388	0.440722
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	6.69722	0.309579
$469$	66.8444	3.08659
$470$	3.39445	0.156574
$471$	−2.18335	−0.100603
$472$	−3.39445	−0.156242
$473$	−8.60555	−0.395684
$474$	−4.88057	−0.224172
$475$	−6.60555	−0.303083
$476$	−27.6333	−1.26657
$477$	17.4500	0.798979
$478$	−0.513878	−0.0235042
$479$	12.1194	0.553751	0.276875	−	0.960906i	$-0.410701\pi$
$479$	12.1194	0.553751	0.276875	+	0.960906i	$0.410701\pi$
$480$	0.394449	0.0180040
$481$	−2.30278	−0.104998
$482$	−8.00000	−0.364390
$483$	9.63331	0.438331
$484$	−9.30278	−0.422853
$485$	16.1833	0.734848
$486$	7.84441	0.355830
$487$	−22.7889	−1.03266	−0.516332	−	0.856389i	$-0.672703\pi$
$487$	−22.7889	−1.03266	−0.516332	+	0.856389i	$0.672703\pi$
$488$	10.5139	0.475941
$489$	6.18335	0.279621
$490$	−18.5139	−0.836372
$491$	−14.7250	−0.664529	−0.332265	−	0.943186i	$-0.607813\pi$
$491$	−14.7250	−0.664529	−0.332265	+	0.943186i	$0.607813\pi$
$492$	0.275019	0.0123988
$493$	−41.4500	−1.86681
$494$	4.60555	0.207214
$495$	−4.93608	−0.221860
$496$	3.30278	0.148299
$497$	27.6333	1.23952
$498$	5.21110	0.233515
$499$	8.23886	0.368822	0.184411	−	0.982849i	$-0.440962\pi$
$499$	8.23886	0.368822	0.184411	+	0.982849i	$0.440962\pi$
$500$	−10.8167	−0.483735
$501$	−3.78890	−0.169275
$502$	6.78890	0.303003
$503$	−24.5139	−1.09302	−0.546510	−	0.837453i	$-0.684044\pi$
$503$	−24.5139	−1.09302	−0.546510	+	0.837453i	$0.684044\pi$
$504$	13.3944	0.596636
$505$	21.3944	0.952040
$506$	9.00000	0.400099
$507$	2.33053	0.103503
$508$	−4.78890	−0.212473
$509$	−25.8167	−1.14430	−0.572152	−	0.820148i	$-0.693891\pi$
$509$	−25.8167	−1.14430	−0.572152	+	0.820148i	$0.693891\pi$
$510$	−2.36669	−0.104799
$511$	−40.0555	−1.77195
$512$	−1.00000	−0.0441942
$513$	3.57779	0.157964
$514$	11.2111	0.494501
$515$	4.30278	0.189603
$516$	2.00000	0.0880451
$517$	−3.39445	−0.149288
$518$	−4.60555	−0.202356
$519$	7.02776	0.308484
$520$	3.00000	0.131559
$521$	−9.63331	−0.422043	−0.211021	−	0.977481i	$-0.567679\pi$
$521$	−9.63331	−0.422043	−0.211021	+	0.977481i	$0.567679\pi$
$522$	20.0917	0.879389
$523$	32.2389	1.40971	0.704853	−	0.709353i	$-0.251013\pi$
$523$	32.2389	1.40971	0.704853	+	0.709353i	$0.251013\pi$
$524$	3.39445	0.148287
$525$	4.60555	0.201003
$526$	7.81665	0.340822
$527$	−19.8167	−0.863227
$528$	−0.394449	−0.0171662
$529$	24.7250	1.07500
$530$	7.81665	0.339534
$531$	−9.87217	−0.428416
$532$	9.21110	0.399352
$533$	2.09167	0.0906004
$534$	1.57779	0.0682779
$535$	5.60555	0.242349
$536$	−14.5139	−0.626904
$537$	−2.36669	−0.102130
$538$	6.78890	0.292690
$539$	18.5139	0.797449
$540$	2.33053	0.100290
$541$	−20.9361	−0.900113	−0.450056	−	0.893000i	$-0.648596\pi$
$541$	−20.9361	−0.900113	−0.450056	+	0.893000i	$0.648596\pi$
$542$	−6.42221	−0.275857
$543$	−6.05551	−0.259867
$544$	6.00000	0.257248
$545$	2.60555	0.111610
$546$	−3.21110	−0.137423
$547$	−13.3944	−0.572705	−0.286353	−	0.958124i	$-0.592443\pi$
$547$	−13.3944	−0.572705	−0.286353	+	0.958124i	$0.592443\pi$
$548$	−9.90833	−0.423263
$549$	30.5778	1.30503
$550$	4.30278	0.183471
$551$	13.8167	0.588609
$552$	−2.09167	−0.0890275
$553$	−74.2389	−3.15696
$554$	25.1194	1.06722
$555$	−0.394449	−0.0167434
$556$	8.90833	0.377797
$557$	−6.51388	−0.276002	−0.138001	−	0.990432i	$-0.544068\pi$
$557$	−6.51388	−0.276002	−0.138001	+	0.990432i	$0.544068\pi$
$558$	9.60555	0.406635
$559$	15.2111	0.643361
$560$	6.00000	0.253546
$561$	2.36669	0.0999218
$562$	12.0000	0.506189
$563$	44.0555	1.85672	0.928359	−	0.371684i	$-0.121220\pi$
$563$	44.0555	1.85672	0.928359	+	0.371684i	$0.121220\pi$
$564$	0.788897	0.0332186
$565$	14.6056	0.614460
$566$	−17.3944	−0.731143
$567$	37.6888	1.58278
$568$	−6.00000	−0.251754
$569$	−10.4222	−0.436922	−0.218461	−	0.975846i	$-0.570104\pi$
$569$	−10.4222	−0.436922	−0.218461	+	0.975846i	$0.570104\pi$
$570$	0.788897	0.0330433
$571$	−20.3028	−0.849645	−0.424822	−	0.905277i	$-0.639663\pi$
$571$	−20.3028	−0.849645	−0.424822	+	0.905277i	$0.639663\pi$
$572$	−3.00000	−0.125436
$573$	−3.78890	−0.158283
$574$	4.18335	0.174609
$575$	22.8167	0.951520
$576$	−2.90833	−0.121180
$577$	−28.2389	−1.17560	−0.587800	−	0.809007i	$-0.700006\pi$
$577$	−28.2389	−1.17560	−0.587800	+	0.809007i	$0.700006\pi$
$578$	−19.0000	−0.790296
$579$	1.21110	0.0503317
$580$	9.00000	0.373705
$581$	79.2666	3.28853
$582$	3.76114	0.155904
$583$	−7.81665	−0.323733
$584$	8.69722	0.359894
$585$	8.72498	0.360734
$586$	25.0278	1.03389
$587$	−2.36669	−0.0976838	−0.0488419	−	0.998807i	$-0.515553\pi$
$587$	−2.36669	−0.0976838	−0.0488419	+	0.998807i	$0.515553\pi$
$588$	−4.30278	−0.177443
$589$	6.60555	0.272177
$590$	−4.42221	−0.182059
$591$	1.81665	0.0747272
$592$	1.00000	0.0410997
$593$	36.5139	1.49945	0.749723	−	0.661752i	$-0.230187\pi$
$593$	36.5139	1.49945	0.749723	+	0.661752i	$0.230187\pi$
$594$	−2.33053	−0.0956229
$595$	−36.0000	−1.47586
$596$	−1.81665	−0.0744130
$597$	0.733385	0.0300154
$598$	−15.9083	−0.650540
$599$	−35.2111	−1.43869	−0.719343	−	0.694655i	$-0.755557\pi$
$599$	−35.2111	−1.43869	−0.719343	+	0.694655i	$0.755557\pi$
$600$	−1.00000	−0.0408248
$601$	−20.6972	−0.844257	−0.422129	−	0.906536i	$-0.638717\pi$
$601$	−20.6972	−0.844257	−0.422129	+	0.906536i	$0.638717\pi$
$602$	30.4222	1.23992
$603$	−42.2111	−1.71897
$604$	−13.3944	−0.545012
$605$	−12.1194	−0.492725
$606$	4.97224	0.201984
$607$	−31.5139	−1.27911	−0.639554	−	0.768746i	$-0.720881\pi$
$607$	−31.5139	−1.27911	−0.639554	+	0.768746i	$0.720881\pi$
$608$	−2.00000	−0.0811107
$609$	−9.63331	−0.390361
$610$	13.6972	0.554584
$611$	6.00000	0.242734
$612$	17.4500	0.705373
$613$	−8.18335	−0.330522	−0.165261	−	0.986250i	$-0.552847\pi$
$613$	−8.18335	−0.330522	−0.165261	+	0.986250i	$0.552847\pi$
$614$	−7.09167	−0.286197
$615$	0.358288	0.0144476
$616$	−6.00000	−0.241747
$617$	47.5694	1.91507	0.957536	−	0.288314i	$-0.0930948\pi$
$617$	47.5694	1.91507	0.957536	+	0.288314i	$0.0930948\pi$
$618$	1.00000	0.0402259
$619$	−2.69722	−0.108411	−0.0542053	−	0.998530i	$-0.517263\pi$
$619$	−2.69722	−0.108411	−0.0542053	+	0.998530i	$0.517263\pi$
$620$	4.30278	0.172804
$621$	−12.3583	−0.495921
$622$	−5.09167	−0.204157
$623$	24.0000	0.961540
$624$	0.697224	0.0279113
$625$	2.42221	0.0968882
$626$	−27.0278	−1.08025
$627$	−0.788897	−0.0315055
$628$	7.21110	0.287754
$629$	−6.00000	−0.239236
$630$	17.4500	0.695223
$631$	18.3028	0.728622	0.364311	−	0.931277i	$-0.381305\pi$
$631$	18.3028	0.728622	0.364311	+	0.931277i	$0.381305\pi$
$632$	16.1194	0.641196
$633$	−2.02776	−0.0805961
$634$	5.21110	0.206959
$635$	−6.23886	−0.247582
$636$	1.81665	0.0720350
$637$	−32.7250	−1.29661
$638$	−9.00000	−0.356313
$639$	−17.4500	−0.690310
$640$	−1.30278	−0.0514967
$641$	−2.48612	−0.0981959	−0.0490980	−	0.998794i	$-0.515635\pi$
$641$	−2.48612	−0.0981959	−0.0490980	+	0.998794i	$0.515635\pi$
$642$	1.30278	0.0514165
$643$	−29.8167	−1.17585	−0.587927	−	0.808914i	$-0.700056\pi$
$643$	−29.8167	−1.17585	−0.587927	+	0.808914i	$0.700056\pi$
$644$	−31.8167	−1.25375
$645$	2.60555	0.102593
$646$	12.0000	0.472134
$647$	−25.9361	−1.01965	−0.509826	−	0.860277i	$-0.670290\pi$
$647$	−25.9361	−1.01965	−0.509826	+	0.860277i	$0.670290\pi$
$648$	−8.18335	−0.321472
$649$	4.42221	0.173587
$650$	−7.60555	−0.298314
$651$	−4.60555	−0.180506
$652$	−20.4222	−0.799795
$653$	6.90833	0.270344	0.135172	−	0.990822i	$-0.456841\pi$
$653$	6.90833	0.270344	0.135172	+	0.990822i	$0.456841\pi$
$654$	0.605551	0.0236789
$655$	4.42221	0.172790
$656$	−0.908327	−0.0354642
$657$	25.2944	0.986827
$658$	12.0000	0.467809
$659$	−42.1194	−1.64074	−0.820370	−	0.571833i	$-0.806233\pi$
$659$	−42.1194	−1.64074	−0.820370	+	0.571833i	$0.806233\pi$
$660$	−0.513878	−0.0200027
$661$	−12.4861	−0.485654	−0.242827	−	0.970070i	$-0.578075\pi$
$661$	−12.4861	−0.485654	−0.242827	+	0.970070i	$0.578075\pi$
$662$	−1.21110	−0.0470708
$663$	−4.18335	−0.162468
$664$	−17.2111	−0.667920
$665$	12.0000	0.465340
$666$	2.90833	0.112695
$667$	−47.7250	−1.84792
$668$	12.5139	0.484176
$669$	−4.78890	−0.185149
$670$	−18.9083	−0.730492
$671$	−13.6972	−0.528775
$672$	1.39445	0.0537920
$673$	24.3028	0.936803	0.468402	−	0.883516i	$-0.344830\pi$
$673$	24.3028	0.936803	0.468402	+	0.883516i	$0.344830\pi$
$674$	19.1194	0.736453
$675$	−5.90833	−0.227412
$676$	−7.69722	−0.296047
$677$	−36.2389	−1.39277	−0.696386	−	0.717667i	$-0.745210\pi$
$677$	−36.2389	−1.39277	−0.696386	+	0.717667i	$0.745210\pi$
$678$	3.39445	0.130363
$679$	57.2111	2.19556
$680$	7.81665	0.299755
$681$	2.36669	0.0906918
$682$	−4.30278	−0.164762
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	−5.81665	−0.222405
$685$	−12.9083	−0.493202
$686$	−33.2111	−1.26801
$687$	−5.26662	−0.200934
$688$	−6.60555	−0.251834
$689$	13.8167	0.526373
$690$	−2.72498	−0.103738
$691$	8.00000	0.304334	0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000	0.304334	0.152167	+	0.988355i	$0.451375\pi$
$692$	−23.2111	−0.882354
$693$	−17.4500	−0.662869
$694$	−31.8167	−1.20774
$695$	11.6056	0.440224
$696$	2.09167	0.0792847
$697$	5.44996	0.206432
$698$	22.2389	0.841753
$699$	2.88057	0.108953
$700$	−15.2111	−0.574926
$701$	14.8806	0.562031	0.281016	−	0.959703i	$-0.409329\pi$
$701$	14.8806	0.562031	0.281016	+	0.959703i	$0.409329\pi$
$702$	4.11943	0.155478
$703$	2.00000	0.0754314
$704$	1.30278	0.0491002
$705$	1.02776	0.0387075
$706$	−31.8167	−1.19744
$707$	75.6333	2.84448
$708$	−1.02776	−0.0386254
$709$	−1.66947	−0.0626982	−0.0313491	−	0.999508i	$-0.509980\pi$
$709$	−1.66947	−0.0626982	−0.0313491	+	0.999508i	$0.509980\pi$
$710$	−7.81665	−0.293354
$711$	46.8806	1.75816
$712$	−5.21110	−0.195294
$713$	−22.8167	−0.854490
$714$	−8.36669	−0.313116
$715$	−3.90833	−0.146163
$716$	7.81665	0.292122
$717$	−0.155590	−0.00581061
$718$	11.2111	0.418395
$719$	−8.36669	−0.312025	−0.156012	−	0.987755i	$-0.549864\pi$
$719$	−8.36669	−0.312025	−0.156012	+	0.987755i	$0.549864\pi$
$720$	−3.78890	−0.141204
$721$	15.2111	0.566491
$722$	15.0000	0.558242
$723$	−2.42221	−0.0900828
$724$	20.0000	0.743294
$725$	−22.8167	−0.847389
$726$	−2.81665	−0.104536
$727$	29.9083	1.10924	0.554619	−	0.832104i	$-0.312864\pi$
$727$	29.9083	1.10924	0.554619	+	0.832104i	$0.312864\pi$
$728$	10.6056	0.393068
$729$	−22.1749	−0.821294
$730$	11.3305	0.419362
$731$	39.6333	1.46589
$732$	3.18335	0.117660
$733$	29.6333	1.09453	0.547266	−	0.836959i	$-0.315669\pi$
$733$	29.6333	1.09453	0.547266	+	0.836959i	$0.315669\pi$
$734$	17.8167	0.657625
$735$	−5.60555	−0.206764
$736$	6.90833	0.254644
$737$	18.9083	0.696497
$738$	−2.64171	−0.0972427
$739$	−42.3305	−1.55715	−0.778577	−	0.627549i	$-0.784058\pi$
$739$	−42.3305	−1.55715	−0.778577	+	0.627549i	$0.784058\pi$
$740$	1.30278	0.0478910
$741$	1.39445	0.0512264
$742$	27.6333	1.01445
$743$	35.4500	1.30053	0.650266	−	0.759706i	$-0.274657\pi$
$743$	35.4500	1.30053	0.650266	+	0.759706i	$0.274657\pi$
$744$	1.00000	0.0366618
$745$	−2.36669	−0.0867089
$746$	−3.81665	−0.139738
$747$	−50.0555	−1.83144
$748$	−7.81665	−0.285805
$749$	19.8167	0.724085
$750$	−3.27502	−0.119587
$751$	14.0000	0.510867	0.255434	−	0.966827i	$-0.417782\pi$
$751$	14.0000	0.510867	0.255434	+	0.966827i	$0.417782\pi$
$752$	−2.60555	−0.0950147
$753$	2.05551	0.0749070
$754$	15.9083	0.579347
$755$	−17.4500	−0.635069
$756$	8.23886	0.299644
$757$	9.30278	0.338115	0.169058	−	0.985606i	$-0.445928\pi$
$757$	9.30278	0.338115	0.169058	+	0.985606i	$0.445928\pi$
$758$	15.3305	0.556830
$759$	2.72498	0.0989105
$760$	−2.60555	−0.0945133
$761$	42.1194	1.52683	0.763414	−	0.645909i	$-0.223522\pi$
$761$	42.1194	1.52683	0.763414	+	0.645909i	$0.223522\pi$
$762$	−1.44996	−0.0525266
$763$	9.21110	0.333464
$764$	12.5139	0.452736
$765$	22.7334	0.821927
$766$	−20.8444	−0.753139
$767$	−7.81665	−0.282243
$768$	−0.302776	−0.0109255
$769$	−22.0000	−0.793340	−0.396670	−	0.917961i	$-0.629834\pi$
$769$	−22.0000	−0.793340	−0.396670	+	0.917961i	$0.629834\pi$
$770$	−7.81665	−0.281693
$771$	3.39445	0.122248
$772$	−4.00000	−0.143963
$773$	−50.0555	−1.80037	−0.900186	−	0.435506i	$-0.856569\pi$
$773$	−50.0555	−1.80037	−0.900186	+	0.435506i	$0.856569\pi$
$774$	−19.2111	−0.690529
$775$	−10.9083	−0.391839
$776$	−12.4222	−0.445931
$777$	−1.39445	−0.0500256
$778$	11.8806	0.425939
$779$	−1.81665	−0.0650884
$780$	0.908327	0.0325233
$781$	7.81665	0.279702
$782$	−41.4500	−1.48225
$783$	12.3583	0.441649
$784$	14.2111	0.507539
$785$	9.39445	0.335302
$786$	1.02776	0.0366589
$787$	25.2111	0.898679	0.449339	−	0.893361i	$-0.351659\pi$
$787$	25.2111	0.898679	0.449339	+	0.893361i	$0.351659\pi$
$788$	−6.00000	−0.213741
$789$	2.36669	0.0842565
$790$	21.0000	0.747146
$791$	51.6333	1.83587
$792$	3.78890	0.134633
$793$	24.2111	0.859761
$794$	−27.8167	−0.987176
$795$	2.36669	0.0839379
$796$	−2.42221	−0.0858528
$797$	−17.3305	−0.613879	−0.306939	−	0.951729i	$-0.599305\pi$
$797$	−17.3305	−0.613879	−0.306939	+	0.951729i	$0.599305\pi$
$798$	2.78890	0.0987259
$799$	15.6333	0.553067
$800$	3.30278	0.116771
$801$	−15.1556	−0.535496
$802$	−13.8167	−0.487883
$803$	−11.3305	−0.399846
$804$	−4.39445	−0.154980
$805$	−41.4500	−1.46092
$806$	7.60555	0.267894
$807$	2.05551	0.0723575
$808$	−16.4222	−0.577731
$809$	29.4500	1.03541	0.517703	−	0.855561i	$-0.326787\pi$
$809$	29.4500	1.03541	0.517703	+	0.855561i	$0.326787\pi$
$810$	−10.6611	−0.374592
$811$	54.1472	1.90136	0.950682	−	0.310166i	$-0.100385\pi$
$811$	54.1472	1.90136	0.950682	+	0.310166i	$0.100385\pi$
$812$	31.8167	1.11655
$813$	−1.94449	−0.0681961
$814$	−1.30278	−0.0456623
$815$	−26.6056	−0.931952
$816$	1.81665	0.0635956
$817$	−13.2111	−0.462198
$818$	5.02776	0.175791
$819$	30.8444	1.07779
$820$	−1.18335	−0.0413242
$821$	11.2111	0.391270	0.195635	−	0.980677i	$-0.437323\pi$
$821$	11.2111	0.391270	0.195635	+	0.980677i	$0.437323\pi$
$822$	−3.00000	−0.104637
$823$	−12.8444	−0.447728	−0.223864	−	0.974620i	$-0.571867\pi$
$823$	−12.8444	−0.447728	−0.223864	+	0.974620i	$0.571867\pi$
$824$	−3.30278	−0.115058
$825$	1.30278	0.0453568
$826$	−15.6333	−0.543952
$827$	27.3944	0.952598	0.476299	−	0.879283i	$-0.341978\pi$
$827$	27.3944	0.952598	0.476299	+	0.879283i	$0.341978\pi$
$828$	20.0917	0.698234
$829$	4.72498	0.164105	0.0820527	−	0.996628i	$-0.473852\pi$
$829$	4.72498	0.164105	0.0820527	+	0.996628i	$0.473852\pi$
$830$	−22.4222	−0.778286
$831$	7.60555	0.263834
$832$	−2.30278	−0.0798344
$833$	−85.2666	−2.95431
$834$	2.69722	0.0933972
$835$	16.3028	0.564181
$836$	2.60555	0.0901149
$837$	5.90833	0.204222
$838$	25.1472	0.868695
$839$	−49.0278	−1.69263	−0.846313	−	0.532686i	$-0.821183\pi$
$839$	−49.0278	−1.69263	−0.846313	+	0.532686i	$0.821183\pi$
$840$	1.81665	0.0626805
$841$	18.7250	0.645689
$842$	−28.7250	−0.989928
$843$	3.63331	0.125138
$844$	6.69722	0.230528
$845$	−10.0278	−0.344965
$846$	−7.57779	−0.260530
$847$	−42.8444	−1.47215
$848$	−6.00000	−0.206041
$849$	−5.26662	−0.180750
$850$	−19.8167	−0.679706
$851$	−6.90833	−0.236814
$852$	−1.81665	−0.0622375
$853$	−11.5416	−0.395178	−0.197589	−	0.980285i	$-0.563311\pi$
$853$	−11.5416	−0.395178	−0.197589	+	0.980285i	$0.563311\pi$
$854$	48.4222	1.65697
$855$	−7.57779	−0.259155
$856$	−4.30278	−0.147066
$857$	−14.8444	−0.507075	−0.253538	−	0.967326i	$-0.581594\pi$
$857$	−14.8444	−0.507075	−0.253538	+	0.967326i	$0.581594\pi$
$858$	−0.908327	−0.0310098
$859$	−24.0555	−0.820764	−0.410382	−	0.911914i	$-0.634605\pi$
$859$	−24.0555	−0.820764	−0.410382	+	0.911914i	$0.634605\pi$
$860$	−8.60555	−0.293447
$861$	1.26662	0.0431661
$862$	5.21110	0.177491
$863$	12.0000	0.408485	0.204242	−	0.978920i	$-0.434527\pi$
$863$	12.0000	0.408485	0.204242	+	0.978920i	$0.434527\pi$
$864$	−1.78890	−0.0608595
$865$	−30.2389	−1.02815
$866$	11.9361	0.405605
$867$	−5.75274	−0.195373
$868$	15.2111	0.516298
$869$	−21.0000	−0.712376
$870$	2.72498	0.0923855
$871$	−33.4222	−1.13247
$872$	−2.00000	−0.0677285
$873$	−36.1278	−1.22274
$874$	13.8167	0.467355
$875$	−49.8167	−1.68411
$876$	2.63331	0.0889712
$877$	7.21110	0.243502	0.121751	−	0.992561i	$-0.461149\pi$
$877$	7.21110	0.243502	0.121751	+	0.992561i	$0.461149\pi$
$878$	9.33053	0.314890
$879$	7.57779	0.255593
$880$	1.69722	0.0572134
$881$	25.5416	0.860520	0.430260	−	0.902705i	$-0.358422\pi$
$881$	25.5416	0.860520	0.430260	+	0.902705i	$0.358422\pi$
$882$	41.3305	1.39167
$883$	−2.42221	−0.0815137	−0.0407568	−	0.999169i	$-0.512977\pi$
$883$	−2.42221	−0.0815137	−0.0407568	+	0.999169i	$0.512977\pi$
$884$	13.8167	0.464704
$885$	−1.33894	−0.0450078
$886$	−0.275019	−0.00923945
$887$	28.4222	0.954324	0.477162	−	0.878815i	$-0.341665\pi$
$887$	28.4222	0.954324	0.477162	+	0.878815i	$0.341665\pi$
$888$	0.302776	0.0101605
$889$	−22.0555	−0.739718
$890$	−6.78890	−0.227564
$891$	10.6611	0.357159
$892$	15.8167	0.529581
$893$	−5.21110	−0.174383
$894$	−0.550039	−0.0183960
$895$	10.1833	0.340392
$896$	−4.60555	−0.153861
$897$	−4.81665	−0.160823
$898$	0.788897	0.0263258
$899$	22.8167	0.760978
$900$	9.60555	0.320185
$901$	36.0000	1.19933
$902$	1.18335	0.0394011
$903$	9.21110	0.306526
$904$	−11.2111	−0.372876
$905$	26.0555	0.866115
$906$	−4.05551	−0.134735
$907$	26.0000	0.863316	0.431658	−	0.902037i	$-0.357929\pi$
$907$	26.0000	0.863316	0.431658	+	0.902037i	$0.357929\pi$
$908$	−7.81665	−0.259405
$909$	−47.7611	−1.58414
$910$	13.8167	0.458018
$911$	−46.4222	−1.53804	−0.769018	−	0.639227i	$-0.779254\pi$
$911$	−46.4222	−1.53804	−0.769018	+	0.639227i	$0.779254\pi$
$912$	−0.605551	−0.0200518
$913$	22.4222	0.742067
$914$	−4.60555	−0.152338
$915$	4.14719	0.137102
$916$	17.3944	0.574729
$917$	15.6333	0.516257
$918$	10.7334	0.354254
$919$	−38.4222	−1.26743	−0.633716	−	0.773566i	$-0.718471\pi$
$919$	−38.4222	−1.26743	−0.633716	+	0.773566i	$0.718471\pi$
$920$	9.00000	0.296721
$921$	−2.14719	−0.0707522
$922$	16.4222	0.540837
$923$	−13.8167	−0.454781
$924$	−1.81665	−0.0597635
$925$	−3.30278	−0.108595
$926$	−30.3028	−0.995811
$927$	−9.60555	−0.315488
$928$	−6.90833	−0.226777
$929$	−36.5139	−1.19798	−0.598991	−	0.800756i	$-0.704431\pi$
$929$	−36.5139	−1.19798	−0.598991	+	0.800756i	$0.704431\pi$
$930$	1.30278	0.0427197
$931$	28.4222	0.931500
$932$	−9.51388	−0.311637
$933$	−1.54163	−0.0504708
$934$	0	0
$935$	−10.1833	−0.333031
$936$	−6.69722	−0.218906
$937$	−28.9083	−0.944394	−0.472197	−	0.881493i	$-0.656539\pi$
$937$	−28.9083	−0.944394	−0.472197	+	0.881493i	$0.656539\pi$
$938$	−66.8444	−2.18255
$939$	−8.18335	−0.267053
$940$	−3.39445	−0.110715
$941$	−7.81665	−0.254816	−0.127408	−	0.991850i	$-0.540666\pi$
$941$	−7.81665	−0.254816	−0.127408	+	0.991850i	$0.540666\pi$
$942$	2.18335	0.0711373
$943$	6.27502	0.204343
$944$	3.39445	0.110480
$945$	10.7334	0.349157
$946$	8.60555	0.279791
$947$	39.6333	1.28791	0.643955	−	0.765064i	$-0.277293\pi$
$947$	39.6333	1.28791	0.643955	+	0.765064i	$0.277293\pi$
$948$	4.88057	0.158514
$949$	20.0278	0.650128
$950$	6.60555	0.214312
$951$	1.57779	0.0511635
$952$	27.6333	0.895601
$953$	−18.7527	−0.607461	−0.303730	−	0.952758i	$-0.598232\pi$
$953$	−18.7527	−0.607461	−0.303730	+	0.952758i	$0.598232\pi$
$954$	−17.4500	−0.564963
$955$	16.3028	0.527545
$956$	0.513878	0.0166200
$957$	−2.72498	−0.0880861
$958$	−12.1194	−0.391561
$959$	−45.6333	−1.47358
$960$	−0.394449	−0.0127308
$961$	−20.0917	−0.648118
$962$	2.30278	0.0742445
$963$	−12.5139	−0.403254
$964$	8.00000	0.257663
$965$	−5.21110	−0.167751
$966$	−9.63331	−0.309947
$967$	25.7250	0.827260	0.413630	−	0.910445i	$-0.364261\pi$
$967$	25.7250	0.827260	0.413630	+	0.910445i	$0.364261\pi$
$968$	9.30278	0.299003
$969$	3.63331	0.116719
$970$	−16.1833	−0.519616
$971$	31.5416	1.01222	0.506110	−	0.862469i	$-0.331083\pi$
$971$	31.5416	1.01222	0.506110	+	0.862469i	$0.331083\pi$
$972$	−7.84441	−0.251610
$973$	41.0278	1.31529
$974$	22.7889	0.730203
$975$	−2.30278	−0.0737478
$976$	−10.5139	−0.336541
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	−6.18335	−0.197722
$979$	6.78890	0.216974
$980$	18.5139	0.591404
$981$	−5.81665	−0.185711
$982$	14.7250	0.469893
$983$	−12.0000	−0.382741	−0.191370	−	0.981518i	$-0.561293\pi$
$983$	−12.0000	−0.382741	−0.191370	+	0.981518i	$0.561293\pi$
$984$	−0.275019	−0.00876729
$985$	−7.81665	−0.249059
$986$	41.4500	1.32004
$987$	3.63331	0.115649
$988$	−4.60555	−0.146522
$989$	45.6333	1.45105
$990$	4.93608	0.156879
$991$	54.3028	1.72498	0.862492	−	0.506070i	$-0.168902\pi$
$991$	54.3028	1.72498	0.862492	+	0.506070i	$0.168902\pi$
$992$	−3.30278	−0.104863
$993$	−0.366692	−0.0116366
$994$	−27.6333	−0.876475
$995$	−3.15559	−0.100039
$996$	−5.21110	−0.165120
$997$	−23.5778	−0.746716	−0.373358	−	0.927687i	$-0.621794\pi$
$997$	−23.5778	−0.746716	−0.373358	+	0.927687i	$0.621794\pi$
$998$	−8.23886	−0.260797
$999$	1.78890	0.0565982

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.2.a.a.1.1	✓	2
3.2	odd	2		666.2.a.j.1.1		2
4.3	odd	2		592.2.a.f.1.2		2
5.2	odd	4		1850.2.b.i.149.2		4
5.3	odd	4		1850.2.b.i.149.3		4
5.4	even	2		1850.2.a.u.1.2		2
7.6	odd	2		3626.2.a.a.1.2		2
8.3	odd	2		2368.2.a.ba.1.1		2
8.5	even	2		2368.2.a.s.1.2		2
11.10	odd	2		8954.2.a.p.1.1		2
12.11	even	2		5328.2.a.bf.1.1		2
37.36	even	2		2738.2.a.l.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.a.a.1.1	✓	2	1.1	even	1	trivial
592.2.a.f.1.2		2	4.3	odd	2
666.2.a.j.1.1		2	3.2	odd	2
1850.2.a.u.1.2		2	5.4	even	2
1850.2.b.i.149.2		4	5.2	odd	4
1850.2.b.i.149.3		4	5.3	odd	4
2368.2.a.s.1.2		2	8.5	even	2
2368.2.a.ba.1.1		2	8.3	odd	2
2738.2.a.l.1.1		2	37.36	even	2
3626.2.a.a.1.2		2	7.6	odd	2
5328.2.a.bf.1.1		2	12.11	even	2
8954.2.a.p.1.1		2	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.302776 q^{3} +1.00000 q^{4} +1.30278 q^{5} +0.302776 q^{6} +4.60555 q^{7} -1.00000 q^{8} -2.90833 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.302776 q^{3} +1.00000 q^{4} +1.30278 q^{5} +0.302776 q^{6} +4.60555 q^{7} -1.00000 q^{8} -2.90833 q^{9} -1.30278 q^{10} +1.30278 q^{11} -0.302776 q^{12} -2.30278 q^{13} -4.60555 q^{14} -0.394449 q^{15} +1.00000 q^{16} -6.00000 q^{17} +2.90833 q^{18} +2.00000 q^{19} +1.30278 q^{20} -1.39445 q^{21} -1.30278 q^{22} -6.90833 q^{23} +0.302776 q^{24} -3.30278 q^{25} +2.30278 q^{26} +1.78890 q^{27} +4.60555 q^{28} +6.90833 q^{29} +0.394449 q^{30} +3.30278 q^{31} -1.00000 q^{32} -0.394449 q^{33} +6.00000 q^{34} +6.00000 q^{35} -2.90833 q^{36} +1.00000 q^{37} -2.00000 q^{38} +0.697224 q^{39} -1.30278 q^{40} -0.908327 q^{41} +1.39445 q^{42} -6.60555 q^{43} +1.30278 q^{44} -3.78890 q^{45} +6.90833 q^{46} -2.60555 q^{47} -0.302776 q^{48} +14.2111 q^{49} +3.30278 q^{50} +1.81665 q^{51} -2.30278 q^{52} -6.00000 q^{53} -1.78890 q^{54} +1.69722 q^{55} -4.60555 q^{56} -0.605551 q^{57} -6.90833 q^{58} +3.39445 q^{59} -0.394449 q^{60} -10.5139 q^{61} -3.30278 q^{62} -13.3944 q^{63} +1.00000 q^{64} -3.00000 q^{65} +0.394449 q^{66} +14.5139 q^{67} -6.00000 q^{68} +2.09167 q^{69} -6.00000 q^{70} +6.00000 q^{71} +2.90833 q^{72} -8.69722 q^{73} -1.00000 q^{74} +1.00000 q^{75} +2.00000 q^{76} +6.00000 q^{77} -0.697224 q^{78} -16.1194 q^{79} +1.30278 q^{80} +8.18335 q^{81} +0.908327 q^{82} +17.2111 q^{83} -1.39445 q^{84} -7.81665 q^{85} +6.60555 q^{86} -2.09167 q^{87} -1.30278 q^{88} +5.21110 q^{89} +3.78890 q^{90} -10.6056 q^{91} -6.90833 q^{92} -1.00000 q^{93} +2.60555 q^{94} +2.60555 q^{95} +0.302776 q^{96} +12.4222 q^{97} -14.2111 q^{98} -3.78890 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 3 q^{3} + 2 q^{4} - q^{5} - 3 q^{6} + 2 q^{7} - 2 q^{8} + 5 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 - q^5 - 3 * q^6 + 2 * q^7 - 2 * q^8 + 5 * q^9	\( 2 q - 2 q^{2} + 3 q^{3} + 2 q^{4} - q^{5} - 3 q^{6} + 2 q^{7} - 2 q^{8} + 5 q^{9} + q^{10} - q^{11} + 3 q^{12} - q^{13} - 2 q^{14} - 8 q^{15} + 2 q^{16} - 12 q^{17} - 5 q^{18} + 4 q^{19} - q^{20} - 10 q^{21} + q^{22} - 3 q^{23} - 3 q^{24} - 3 q^{25} + q^{26} + 18 q^{27} + 2 q^{28} + 3 q^{29} + 8 q^{30} + 3 q^{31} - 2 q^{32} - 8 q^{33} + 12 q^{34} + 12 q^{35} + 5 q^{36} + 2 q^{37} - 4 q^{38} + 5 q^{39} + q^{40} + 9 q^{41} + 10 q^{42} - 6 q^{43} - q^{44} - 22 q^{45} + 3 q^{46} + 2 q^{47} + 3 q^{48} + 14 q^{49} + 3 q^{50} - 18 q^{51} - q^{52} - 12 q^{53} - 18 q^{54} + 7 q^{55} - 2 q^{56} + 6 q^{57} - 3 q^{58} + 14 q^{59} - 8 q^{60} - 3 q^{61} - 3 q^{62} - 34 q^{63} + 2 q^{64} - 6 q^{65} + 8 q^{66} + 11 q^{67} - 12 q^{68} + 15 q^{69} - 12 q^{70} + 12 q^{71} - 5 q^{72} - 21 q^{73} - 2 q^{74} + 2 q^{75} + 4 q^{76} + 12 q^{77} - 5 q^{78} - 7 q^{79} - q^{80} + 38 q^{81} - 9 q^{82} + 20 q^{83} - 10 q^{84} + 6 q^{85} + 6 q^{86} - 15 q^{87} + q^{88} - 4 q^{89} + 22 q^{90} - 14 q^{91} - 3 q^{92} - 2 q^{93} - 2 q^{94} - 2 q^{95} - 3 q^{96} - 4 q^{97} - 14 q^{98} - 22 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 3 * q^3 + 2 * q^4 - q^5 - 3 * q^6 + 2 * q^7 - 2 * q^8 + 5 * q^9 + q^10 - q^11 + 3 * q^12 - q^13 - 2 * q^14 - 8 * q^15 + 2 * q^16 - 12 * q^17 - 5 * q^18 + 4 * q^19 - q^20 - 10 * q^21 + q^22 - 3 * q^23 - 3 * q^24 - 3 * q^25 + q^26 + 18 * q^27 + 2 * q^28 + 3 * q^29 + 8 * q^30 + 3 * q^31 - 2 * q^32 - 8 * q^33 + 12 * q^34 + 12 * q^35 + 5 * q^36 + 2 * q^37 - 4 * q^38 + 5 * q^39 + q^40 + 9 * q^41 + 10 * q^42 - 6 * q^43 - q^44 - 22 * q^45 + 3 * q^46 + 2 * q^47 + 3 * q^48 + 14 * q^49 + 3 * q^50 - 18 * q^51 - q^52 - 12 * q^53 - 18 * q^54 + 7 * q^55 - 2 * q^56 + 6 * q^57 - 3 * q^58 + 14 * q^59 - 8 * q^60 - 3 * q^61 - 3 * q^62 - 34 * q^63 + 2 * q^64 - 6 * q^65 + 8 * q^66 + 11 * q^67 - 12 * q^68 + 15 * q^69 - 12 * q^70 + 12 * q^71 - 5 * q^72 - 21 * q^73 - 2 * q^74 + 2 * q^75 + 4 * q^76 + 12 * q^77 - 5 * q^78 - 7 * q^79 - q^80 + 38 * q^81 - 9 * q^82 + 20 * q^83 - 10 * q^84 + 6 * q^85 + 6 * q^86 - 15 * q^87 + q^88 - 4 * q^89 + 22 * q^90 - 14 * q^91 - 3 * q^92 - 2 * q^93 - 2 * q^94 - 2 * q^95 - 3 * q^96 - 4 * q^97 - 14 * q^98 - 22 * q^99

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