LMFDB - Embedded newform 1850.2.d.i.1701.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1850,2,Mod(1701,1850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1850, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("1850.1701");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1850 = 2 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1850.d (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$14.7723243739$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 48 x^{18} + 878 x^{16} + 8102 x^{14} + 41081 x^{12} + 115688 x^{10} + 175041 x^{8} + 134990 x^{6} + \cdots + 1 $ x^20 + 48x^18 + 878x^16 + 8102x^14 + 41081x^12 + 115688x^10 + 175041x^8 + 134990x^6 + 49782x^4 + 6932*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 370)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1701.5
Root			$0.622139i$ of defining polynomial
Character	$\chi$	$=$	1850.1701
Dual form			1850.2.d.i.1701.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -0.377861 q^{3} -1.00000 q^{4} +0.377861i q^{6} +0.631751 q^{7} +1.00000i q^{8} -2.85722 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -0.377861 q^{3} -1.00000 q^{4} +0.377861i q^{6} +0.631751 q^{7} +1.00000i q^{8} -2.85722 q^{9} +1.24789 q^{11} +0.377861 q^{12} +3.34999i q^{13} -0.631751i q^{14} +1.00000 q^{16} -3.10511i q^{17} +2.85722i q^{18} +5.97327i q^{19} -0.238714 q^{21} -1.24789i q^{22} -7.60706i q^{23} -0.377861i q^{24} +3.34999 q^{26} +2.21322 q^{27} -0.631751 q^{28} -9.57629i q^{29} -7.26707i q^{31} -1.00000i q^{32} -0.471529 q^{33} -3.10511 q^{34} +2.85722 q^{36} +(4.48866 + 4.10511i) q^{37} +5.97327 q^{38} -1.26583i q^{39} -8.45510 q^{41} +0.238714i q^{42} -4.86640i q^{43} -1.24789 q^{44} -7.60706 q^{46} +13.1187 q^{47} -0.377861 q^{48} -6.60089 q^{49} +1.17330i q^{51} -3.34999i q^{52} +7.17340 q^{53} -2.21322i q^{54} +0.631751i q^{56} -2.25707i q^{57} -9.57629 q^{58} -4.36469i q^{59} +2.14666i q^{61} -7.26707 q^{62} -1.80505 q^{63} -1.00000 q^{64} +0.471529i q^{66} -11.3451 q^{67} +3.10511i q^{68} +2.87441i q^{69} -12.7183 q^{71} -2.85722i q^{72} +4.45836 q^{73} +(4.10511 - 4.48866i) q^{74} -5.97327i q^{76} +0.788355 q^{77} -1.26583 q^{78} -8.78679i q^{79} +7.73537 q^{81} +8.45510i q^{82} +6.63185 q^{83} +0.238714 q^{84} -4.86640 q^{86} +3.61851i q^{87} +1.24789i q^{88} -13.7784i q^{89} +2.11636i q^{91} +7.60706i q^{92} +2.74594i q^{93} -13.1187i q^{94} +0.377861i q^{96} -11.0583i q^{97} +6.60089i q^{98} -3.56550 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{4} + 16 q^{9}+O(q^{10}) $ 20 * q - 20 * q^4 + 16 * q^9	$ 20 q - 20 q^{4} + 16 q^{9} + 20 q^{16} - 24 q^{21} + 4 q^{26} + 36 q^{34} - 16 q^{36} - 8 q^{41} - 20 q^{46} + 16 q^{49} - 20 q^{64} - 40 q^{71} - 16 q^{74} + 116 q^{81} + 24 q^{84} + 20 q^{86} + 164 q^{99}+O(q^{100}) $ 20 * q - 20 * q^4 + 16 * q^9 + 20 * q^16 - 24 * q^21 + 4 * q^26 + 36 * q^34 - 16 * q^36 - 8 * q^41 - 20 * q^46 + 16 * q^49 - 20 * q^64 - 40 * q^71 - 16 * q^74 + 116 * q^81 + 24 * q^84 + 20 * q^86 + 164 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times$.

$n$	$1001$	$1777$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.377861			−0.218158			−0.109079	−	0.994033i	$-0.534790\pi$
$3$	−0.377861			−0.218158			−0.109079	+	0.994033i	$0.534790\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$			0.377861i			0.154261i
$7$	0.631751			0.238779			0.119390	−	0.992847i	$-0.461906\pi$
$7$	0.631751			0.238779			0.119390	+	0.992847i	$0.461906\pi$
$8$			1.00000i			0.353553i
$9$	−2.85722			−0.952407
$10$		0			0
$11$	1.24789			0.376253			0.188126	−	0.982145i	$-0.439759\pi$
$11$	1.24789			0.376253			0.188126	+	0.982145i	$0.439759\pi$
$12$	0.377861			0.109079
$13$			3.34999i			0.929120i	0.885542	+	0.464560i	$0.153788\pi$
$13$			3.34999i			0.929120i	−0.885542	+	0.464560i	$0.846212\pi$
$14$		−	0.631751i		−	0.168843i
$15$		0			0
$16$	1.00000			0.250000
$17$		−	3.10511i		−	0.753100i	−0.926396	−	0.376550i	$-0.877110\pi$
$17$		−	3.10511i		−	0.753100i	0.926396	−	0.376550i	$-0.122890\pi$
$18$			2.85722i			0.673453i
$19$			5.97327i			1.37036i	0.728373	+	0.685181i	$0.240277\pi$
$19$			5.97327i			1.37036i	−0.728373	+	0.685181i	$0.759723\pi$
$20$		0			0
$21$	−0.238714			−0.0520917
$22$		−	1.24789i		−	0.266051i
$23$		−	7.60706i		−	1.58618i	−0.609104	−	0.793090i	$-0.708471\pi$
$23$		−	7.60706i		−	1.58618i	0.609104	−	0.793090i	$-0.291529\pi$
$24$		−	0.377861i		−	0.0771306i
$25$		0			0
$26$	3.34999			0.656987
$27$	2.21322			0.425934
$28$	−0.631751			−0.119390
$29$		−	9.57629i		−	1.77827i	−0.457643	−	0.889136i	$-0.651306\pi$
$29$		−	9.57629i		−	1.77827i	0.457643	−	0.889136i	$-0.348694\pi$
$30$		0			0
$31$		−	7.26707i		−	1.30520i	−0.757701	−	0.652602i	$-0.773677\pi$
$31$		−	7.26707i		−	1.30520i	0.757701	−	0.652602i	$-0.226323\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.471529			−0.0820827
$34$	−3.10511			−0.532522
$35$		0			0
$36$	2.85722			0.476203
$37$	4.48866	+	4.10511i	0.737931	+	0.674876i
$37$	4.48866	+	4.10511i	0.737931	+	0.674876i
$38$	5.97327			0.968992
$39$		−	1.26583i		−	0.202695i
$40$		0			0
$41$	−8.45510			−1.32046			−0.660232	−	0.751061i	$-0.729542\pi$
$41$	−8.45510			−1.32046			−0.660232	+	0.751061i	$0.729542\pi$
$42$			0.238714i			0.0368344i
$43$		−	4.86640i		−	0.742119i	−0.928609	−	0.371059i	$-0.878995\pi$
$43$		−	4.86640i		−	0.742119i	0.928609	−	0.371059i	$-0.121005\pi$
$44$	−1.24789			−0.188126
$45$		0			0
$46$	−7.60706			−1.12160
$47$	13.1187			1.91356			0.956779	−	0.290815i	$-0.0939263\pi$
$47$	13.1187			1.91356			0.956779	+	0.290815i	$0.0939263\pi$
$48$	−0.377861			−0.0545396
$49$	−6.60089			−0.942984
$50$		0			0
$51$			1.17330i			0.164295i
$52$		−	3.34999i		−	0.464560i
$53$	7.17340			0.985343			0.492671	−	0.870215i	$-0.336020\pi$
$53$	7.17340			0.985343			0.492671	+	0.870215i	$0.336020\pi$
$54$		−	2.21322i		−	0.301181i
$55$		0			0
$56$			0.631751i			0.0844213i
$57$		−	2.25707i		−	0.298956i
$58$	−9.57629			−1.25743
$59$		−	4.36469i		−	0.568234i	−0.958790	−	0.284117i	$-0.908300\pi$
$59$		−	4.36469i		−	0.568234i	0.958790	−	0.284117i	$-0.0917004\pi$
$60$		0			0
$61$			2.14666i			0.274852i	0.990512	+	0.137426i	$0.0438829\pi$
$61$			2.14666i			0.274852i	−0.990512	+	0.137426i	$0.956117\pi$
$62$	−7.26707			−0.922919
$63$	−1.80505			−0.227415
$64$	−1.00000			−0.125000
$65$		0			0
$66$			0.471529i			0.0580412i
$67$	−11.3451			−1.38602			−0.693012	−	0.720926i	$-0.743717\pi$
$67$	−11.3451			−1.38602			−0.693012	+	0.720926i	$0.743717\pi$
$68$			3.10511i			0.376550i
$69$			2.87441i			0.346038i
$70$		0			0
$71$	−12.7183			−1.50939			−0.754694	−	0.656077i	$-0.772215\pi$
$71$	−12.7183			−1.50939			−0.754694	+	0.656077i	$0.772215\pi$
$72$		−	2.85722i		−	0.336727i
$73$	4.45836			0.521811			0.260906	−	0.965364i	$-0.415979\pi$
$73$	4.45836			0.521811			0.260906	+	0.965364i	$0.415979\pi$
$74$	4.10511	−	4.48866i	0.477209	−	0.521796i
$75$		0			0
$76$		−	5.97327i		−	0.685181i
$77$	0.788355			0.0898414
$78$	−1.26583			−0.143327
$79$		−	8.78679i		−	0.988592i	−0.869294	−	0.494296i	$-0.835426\pi$
$79$		−	8.78679i		−	0.988592i	0.869294	−	0.494296i	$-0.164574\pi$
$80$		0			0
$81$	7.73537			0.859486
$82$			8.45510i			0.933710i
$83$	6.63185			0.727941			0.363970	−	0.931411i	$-0.381421\pi$
$83$	6.63185			0.727941			0.363970	+	0.931411i	$0.381421\pi$
$84$	0.238714			0.0260458
$85$		0			0
$86$	−4.86640			−0.524757
$87$			3.61851i			0.387945i
$88$			1.24789i			0.133026i
$89$		−	13.7784i		−	1.46051i	−0.683175	−	0.730255i	$-0.739401\pi$
$89$		−	13.7784i		−	1.46051i	0.683175	−	0.730255i	$-0.260599\pi$
$90$		0			0
$91$			2.11636i			0.221855i
$92$			7.60706i			0.793090i
$93$			2.74594i			0.284741i
$94$		−	13.1187i		−	1.35309i
$95$		0			0
$96$			0.377861i			0.0385653i
$97$		−	11.0583i		−	1.12280i	−0.827546	−	0.561398i	$-0.810264\pi$
$97$		−	11.0583i		−	1.12280i	0.827546	−	0.561398i	$-0.189736\pi$
$98$			6.60089i			0.666791i
$99$	−3.56550			−0.358346
$100$		0			0
$101$	8.65314			0.861019			0.430510	−	0.902586i	$-0.358334\pi$
$101$	8.65314			0.861019			0.430510	+	0.902586i	$0.358334\pi$
$102$	1.17330			0.116174
$103$		−	4.57336i		−	0.450627i	−0.974286	−	0.225313i	$-0.927659\pi$
$103$		−	4.57336i		−	0.450627i	0.974286	−	0.225313i	$-0.0723406\pi$
$104$	−3.34999			−0.328494
$105$		0			0
$106$		−	7.17340i		−	0.696743i
$107$	−11.4715			−1.10900			−0.554498	−	0.832185i	$-0.687090\pi$
$107$	−11.4715			−1.10900			−0.554498	+	0.832185i	$0.687090\pi$
$108$	−2.21322			−0.212967
$109$			0.727748i			0.0697057i	0.999392	+	0.0348528i	$0.0110962\pi$
$109$			0.727748i			0.0697057i	−0.999392	+	0.0348528i	$0.988904\pi$
$110$		0			0
$111$	−1.69609	−	1.55116i	−0.160986	−	0.147230i
$112$	0.631751			0.0596948
$113$		−	17.9970i		−	1.69301i	−0.532379	−	0.846506i	$-0.678702\pi$
$113$		−	17.9970i		−	1.69301i	0.532379	−	0.846506i	$-0.321298\pi$
$114$	−2.25707			−0.211394
$115$		0			0
$116$			9.57629i			0.889136i
$117$		−	9.57166i		−	0.884901i
$118$	−4.36469			−0.401802
$119$		−	1.96166i		−	0.179825i
$120$		0			0
$121$	−9.44277			−0.858434
$122$	2.14666			0.194350
$123$	3.19485			0.288070
$124$			7.26707i			0.652602i
$125$		0			0
$126$			1.80505i			0.160807i
$127$	15.4830			1.37389			0.686947	−	0.726707i	$-0.258950\pi$
$127$	15.4830			1.37389			0.686947	+	0.726707i	$0.258950\pi$
$128$			1.00000i			0.0883883i
$129$			1.83882i			0.161899i
$130$		0			0
$131$			6.22121i			0.543550i	0.962361	+	0.271775i	$0.0876106\pi$
$131$			6.22121i			0.543550i	−0.962361	+	0.271775i	$0.912389\pi$
$132$	0.471529			0.0410413
$133$			3.77362i			0.327214i
$134$			11.3451i			0.980066i
$135$		0			0
$136$	3.10511			0.266261
$137$	−14.1258			−1.20685			−0.603426	−	0.797419i	$-0.706198\pi$
$137$	−14.1258			−1.20685			−0.603426	+	0.797419i	$0.706198\pi$
$138$	2.87441			0.244686
$139$	−8.43675			−0.715596			−0.357798	−	0.933799i	$-0.616472\pi$
$139$	−8.43675			−0.715596			−0.357798	+	0.933799i	$0.616472\pi$
$140$		0			0
$141$	−4.95705			−0.417459
$142$			12.7183i			1.06730i
$143$			4.18042i			0.349584i
$144$	−2.85722			−0.238102
$145$		0			0
$146$		−	4.45836i		−	0.368976i
$147$	2.49422			0.205720
$148$	−4.48866	−	4.10511i	−0.368966	−	0.337438i
$149$	−13.6447			−1.11782			−0.558909	−	0.829229i	$-0.688780\pi$
$149$	−13.6447			−1.11782			−0.558909	+	0.829229i	$0.688780\pi$
$150$		0			0
$151$	−3.17741			−0.258574			−0.129287	−	0.991607i	$-0.541269\pi$
$151$	−3.17741			−0.258574			−0.129287	+	0.991607i	$0.541269\pi$
$152$	−5.97327			−0.484496
$153$			8.87199i			0.717258i
$154$		−	0.788355i		−	0.0635275i
$155$		0			0
$156$			1.26583i			0.101348i
$157$	0.215310			0.0171836			0.00859180	−	0.999963i	$-0.497265\pi$
$157$	0.215310			0.0171836			0.00859180	+	0.999963i	$0.497265\pi$
$158$	−8.78679			−0.699040
$159$	−2.71055			−0.214961
$160$		0			0
$161$		−	4.80576i		−	0.378747i
$162$		−	7.73537i		−	0.607748i
$163$			1.66609i			0.130498i	0.997869	+	0.0652490i	$0.0207842\pi$
$163$			1.66609i			0.130498i	−0.997869	+	0.0652490i	$0.979216\pi$
$164$	8.45510			0.660232
$165$		0			0
$166$		−	6.63185i		−	0.514732i
$167$			5.92242i			0.458290i	0.973392	+	0.229145i	$0.0735931\pi$
$167$			5.92242i			0.458290i	−0.973392	+	0.229145i	$0.926407\pi$
$168$		−	0.238714i		−	0.0184172i
$169$	1.77756			0.136736
$170$		0			0
$171$		−	17.0669i		−	1.30514i
$172$			4.86640i			0.371059i
$173$	2.88008			0.218968			0.109484	−	0.993989i	$-0.465080\pi$
$173$	2.88008			0.218968			0.109484	+	0.993989i	$0.465080\pi$
$174$	3.61851			0.274318
$175$		0			0
$176$	1.24789			0.0940632
$177$			1.64925i			0.123965i
$178$	−13.7784			−1.03274
$179$			4.46182i			0.333492i	0.986000	+	0.166746i	$0.0533260\pi$
$179$			4.46182i			0.333492i	−0.986000	+	0.166746i	$0.946674\pi$
$180$		0			0
$181$	3.93480			0.292472			0.146236	−	0.989250i	$-0.453284\pi$
$181$	3.93480			0.292472			0.146236	+	0.989250i	$0.453284\pi$
$182$	2.11636			0.156875
$183$		−	0.811140i		−	0.0599612i
$184$	7.60706			0.560800
$185$		0			0
$186$	2.74594			0.201342
$187$		−	3.87484i		−	0.283356i
$188$	−13.1187			−0.956779
$189$	1.39820			0.101704
$190$		0			0
$191$		−	7.76296i		−	0.561708i	−0.959751	−	0.280854i	$-0.909382\pi$
$191$		−	7.76296i		−	0.561708i	0.959751	−	0.280854i	$-0.0906177\pi$
$192$	0.377861			0.0272698
$193$			3.49189i			0.251352i	0.992071	+	0.125676i	$0.0401099\pi$
$193$			3.49189i			0.251352i	−0.992071	+	0.125676i	$0.959890\pi$
$194$	−11.0583			−0.793937
$195$		0			0
$196$	6.60089			0.471492
$197$	1.07617			0.0766736			0.0383368	−	0.999265i	$-0.487794\pi$
$197$	1.07617			0.0766736			0.0383368	+	0.999265i	$0.487794\pi$
$198$			3.56550i			0.253389i
$199$		−	5.71343i		−	0.405014i	−0.979281	−	0.202507i	$-0.935091\pi$
$199$		−	5.71343i		−	0.405014i	0.979281	−	0.202507i	$-0.0649090\pi$
$200$		0			0
$201$	4.28687			0.302372
$202$		−	8.65314i		−	0.608833i
$203$		−	6.04983i		−	0.424615i
$204$		−	1.17330i		−	0.0821475i
$205$		0			0
$206$	−4.57336			−0.318641
$207$			21.7350i			1.51069i
$208$			3.34999i			0.232280i
$209$			7.45398i			0.515603i
$210$		0			0
$211$	22.8397			1.57235			0.786176	−	0.618003i	$-0.212058\pi$
$211$	22.8397			1.57235			0.786176	+	0.618003i	$0.212058\pi$
$212$	−7.17340			−0.492671
$213$	4.80576			0.329286
$214$			11.4715i			0.784178i
$215$		0			0
$216$			2.21322i			0.150590i
$217$		−	4.59098i		−	0.311656i
$218$	0.727748			0.0492893
$219$	−1.68464			−0.113837
$220$		0			0
$221$	10.4021			0.699720
$222$	−1.55116	+	1.69609i	−0.104107	+	0.113834i
$223$	3.32116			0.222401			0.111201	−	0.993798i	$-0.464530\pi$
$223$	3.32116			0.222401			0.111201	+	0.993798i	$0.464530\pi$
$224$		−	0.631751i		−	0.0422106i
$225$		0			0
$226$	−17.9970			−1.19714
$227$			5.62938i			0.373635i	0.982395	+	0.186818i	$0.0598174\pi$
$227$			5.62938i			0.373635i	−0.982395	+	0.186818i	$0.940183\pi$
$228$			2.25707i			0.149478i
$229$	0.973208			0.0643114			0.0321557	−	0.999483i	$-0.489763\pi$
$229$	0.973208			0.0643114			0.0321557	+	0.999483i	$0.489763\pi$
$230$		0			0
$231$	−0.297889			−0.0195997
$232$	9.57629			0.628714
$233$	14.4150			0.944357			0.472178	−	0.881503i	$-0.343468\pi$
$233$	14.4150			0.944357			0.472178	+	0.881503i	$0.343468\pi$
$234$	−9.57166			−0.625719
$235$		0			0
$236$			4.36469i			0.284117i
$237$			3.32019i			0.215669i
$238$	−1.96166			−0.127155
$239$			8.43344i			0.545514i	0.962083	+	0.272757i	$0.0879355\pi$
$239$			8.43344i			0.545514i	−0.962083	+	0.272757i	$0.912065\pi$
$240$		0			0
$241$		−	18.6567i		−	1.20178i	−0.799331	−	0.600891i	$-0.794812\pi$
$241$		−	18.6567i		−	1.20178i	0.799331	−	0.600891i	$-0.205188\pi$
$242$			9.44277i			0.607004i
$243$	−9.56255			−0.613438
$244$		−	2.14666i		−	0.137426i
$245$		0			0
$246$		−	3.19485i		−	0.203696i
$247$	−20.0104			−1.27323
$248$	7.26707			0.461460
$249$	−2.50592			−0.158806
$250$		0			0
$251$			25.1189i			1.58549i	0.609553	+	0.792746i	$0.291349\pi$
$251$			25.1189i			1.58549i	−0.609553	+	0.792746i	$0.708651\pi$
$252$	1.80505			0.113708
$253$		−	9.49277i		−	0.596805i
$254$		−	15.4830i		−	0.971490i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	20.3552i		−	1.26973i	−0.772625	−	0.634863i	$-0.781057\pi$
$257$		−	20.3552i		−	1.26973i	0.772625	−	0.634863i	$-0.218943\pi$
$258$	1.83882			0.114480
$259$	2.83571	+	2.59341i	0.176203	+	0.161146i
$260$		0			0
$261$			27.3616i			1.69364i
$262$	6.22121			0.384348
$263$	−22.2211			−1.37021			−0.685107	−	0.728443i	$-0.740244\pi$
$263$	−22.2211			−1.37021			−0.685107	+	0.728443i	$0.740244\pi$
$264$		−	0.471529i		−	0.0290206i
$265$		0			0
$266$	3.77362			0.231375
$267$			5.20633i			0.318622i
$268$	11.3451			0.693012
$269$	15.8411			0.965850			0.482925	−	0.875662i	$-0.339574\pi$
$269$	15.8411			0.965850			0.482925	+	0.875662i	$0.339574\pi$
$270$		0			0
$271$	−2.00602			−0.121857			−0.0609285	−	0.998142i	$-0.519406\pi$
$271$	−2.00602			−0.121857			−0.0609285	+	0.998142i	$0.519406\pi$
$272$		−	3.10511i		−	0.188275i
$273$		−	0.799690i		−	0.0483994i
$274$			14.1258i			0.853373i
$275$		0			0
$276$		−	2.87441i		−	0.173019i
$277$		−	11.5671i		−	0.695000i	−0.937680	−	0.347500i	$-0.887031\pi$
$277$		−	11.5671i		−	0.695000i	0.937680	−	0.347500i	$-0.112969\pi$
$278$			8.43675i			0.506003i
$279$			20.7636i			1.24309i
$280$		0			0
$281$			14.2909i			0.852521i	0.904600	+	0.426261i	$0.140169\pi$
$281$			14.2909i			0.852521i	−0.904600	+	0.426261i	$0.859831\pi$
$282$			4.95705i			0.295188i
$283$			12.3837i			0.736137i	0.929799	+	0.368068i	$0.119981\pi$
$283$			12.3837i			0.736137i	−0.929799	+	0.368068i	$0.880019\pi$
$284$	12.7183			0.754694
$285$		0			0
$286$	4.18042			0.247193
$287$	−5.34152			−0.315300
$288$			2.85722i			0.168363i
$289$	7.35829			0.432840
$290$		0			0
$291$			4.17849i			0.244947i
$292$	−4.45836			−0.260906
$293$	27.8374			1.62628			0.813140	−	0.582068i	$-0.197756\pi$
$293$	27.8374			1.62628			0.813140	+	0.582068i	$0.197756\pi$
$294$		−	2.49422i		−	0.145466i
$295$		0			0
$296$	−4.10511	+	4.48866i	−0.238605	+	0.260898i
$297$	2.76185			0.160259
$298$			13.6447i			0.790416i
$299$	25.4836			1.47375
$300$		0			0
$301$		−	3.07435i		−	0.177203i
$302$			3.17741i			0.182839i
$303$	−3.26968			−0.187838
$304$			5.97327i			0.342590i
$305$		0			0
$306$	8.87199			0.507178
$307$	−19.9411			−1.13810			−0.569049	−	0.822304i	$-0.692688\pi$
$307$	−19.9411			−1.13810			−0.569049	+	0.822304i	$0.692688\pi$
$308$	−0.788355			−0.0449207
$309$			1.72810i			0.0983080i
$310$		0			0
$311$			4.96832i			0.281727i	0.990029	+	0.140864i	$0.0449879\pi$
$311$			4.96832i			0.281727i	−0.990029	+	0.140864i	$0.955012\pi$
$312$	1.26583			0.0716636
$313$			10.0000i			0.565233i	0.959233	+	0.282617i	$0.0912024\pi$
$313$			10.0000i			0.565233i	−0.959233	+	0.282617i	$0.908798\pi$
$314$		−	0.215310i		−	0.0121506i
$315$		0			0
$316$			8.78679i			0.494296i
$317$	22.9198			1.28730			0.643651	−	0.765319i	$-0.277419\pi$
$317$	22.9198			1.28730			0.643651	+	0.765319i	$0.277419\pi$
$318$			2.71055i			0.152000i
$319$		−	11.9502i		−	0.669080i
$320$		0			0
$321$	4.33465			0.241937
$322$	−4.80576			−0.267815
$323$	18.5477			1.03202
$324$	−7.73537			−0.429743
$325$		0			0
$326$	1.66609			0.0922760
$327$		−	0.274988i		−	0.0152069i
$328$		−	8.45510i		−	0.466855i
$329$	8.28775			0.456918
$330$		0			0
$331$		−	5.54265i		−	0.304651i	−0.988330	−	0.152326i	$-0.951324\pi$
$331$		−	5.54265i		−	0.304651i	0.988330	−	0.152326i	$-0.0486763\pi$
$332$	−6.63185			−0.363970
$333$	−12.8251	−	11.7292i	−0.702811	−	0.642757i
$334$	5.92242			0.324060
$335$		0			0
$336$	−0.238714			−0.0130229
$337$	25.6348			1.39642			0.698209	−	0.715894i	$-0.253981\pi$
$337$	25.6348			1.39642			0.698209	+	0.715894i	$0.253981\pi$
$338$		−	1.77756i		−	0.0966867i
$339$			6.80035i			0.369344i
$340$		0			0
$341$		−	9.06851i		−	0.491087i
$342$	−17.0669			−0.922875
$343$	−8.59237			−0.463945
$344$	4.86640			0.262379
$345$		0			0
$346$		−	2.88008i		−	0.154834i
$347$			19.6225i			1.05339i	0.850054	+	0.526696i	$0.176569\pi$
$347$			19.6225i			1.05339i	−0.850054	+	0.526696i	$0.823431\pi$
$348$		−	3.61851i		−	0.193972i
$349$	15.6263			0.836459			0.418230	−	0.908341i	$-0.362651\pi$
$349$	15.6263			0.836459			0.418230	+	0.908341i	$0.362651\pi$
$350$		0			0
$351$			7.41425i			0.395744i
$352$		−	1.24789i		−	0.0665128i
$353$		−	23.5724i		−	1.25463i	−0.778765	−	0.627316i	$-0.784153\pi$
$353$		−	23.5724i		−	1.25463i	0.778765	−	0.627316i	$-0.215847\pi$
$354$	1.64925			0.0876564
$355$		0			0
$356$			13.7784i			0.730255i
$357$			0.741234i			0.0392302i
$358$	4.46182			0.235815
$359$	9.34905			0.493424			0.246712	−	0.969089i	$-0.420650\pi$
$359$	9.34905			0.493424			0.246712	+	0.969089i	$0.420650\pi$
$360$		0			0
$361$	−16.6799			−0.877891
$362$		−	3.93480i		−	0.206809i
$363$	3.56806			0.187274
$364$		−	2.11636i		−	0.110927i
$365$		0			0
$366$	−0.811140			−0.0423990
$367$	−12.2379			−0.638811			−0.319406	−	0.947618i	$-0.603483\pi$
$367$	−12.2379			−0.638811			−0.319406	+	0.947618i	$0.603483\pi$
$368$		−	7.60706i		−	0.396545i
$369$	24.1581			1.25762
$370$		0			0
$371$	4.53180			0.235280
$372$		−	2.74594i		−	0.142371i
$373$	−10.1918			−0.527712			−0.263856	−	0.964562i	$-0.584994\pi$
$373$	−10.1918			−0.527712			−0.263856	+	0.964562i	$0.584994\pi$
$374$	−3.87484			−0.200363
$375$		0			0
$376$			13.1187i			0.676545i
$377$	32.0805			1.65223
$378$		−	1.39820i		−	0.0719157i
$379$	−20.7538			−1.06605			−0.533025	−	0.846099i	$-0.678945\pi$
$379$	−20.7538			−1.06605			−0.533025	+	0.846099i	$0.678945\pi$
$380$		0			0
$381$	−5.85042			−0.299726
$382$	−7.76296			−0.397188
$383$		−	17.7328i		−	0.906103i	−0.891484	−	0.453052i	$-0.850335\pi$
$383$		−	17.7328i		−	0.906103i	0.891484	−	0.453052i	$-0.149665\pi$
$384$		−	0.377861i		−	0.0192826i
$385$		0			0
$386$	3.49189			0.177732
$387$			13.9044i			0.706799i
$388$			11.0583i			0.561398i
$389$			10.9054i			0.552923i	0.961025	+	0.276462i	$0.0891619\pi$
$389$			10.9054i			0.552923i	−0.961025	+	0.276462i	$0.910838\pi$
$390$		0			0
$391$	−23.6208			−1.19455
$392$		−	6.60089i		−	0.333395i
$393$		−	2.35075i		−	0.118580i
$394$		−	1.07617i		−	0.0542164i
$395$		0			0
$396$	3.56550			0.179173
$397$	−23.0106			−1.15487			−0.577435	−	0.816437i	$-0.695946\pi$
$397$	−23.0106			−1.15487			−0.577435	+	0.816437i	$0.695946\pi$
$398$	−5.71343			−0.286388
$399$		−	1.42590i		−	0.0713844i
$400$		0			0
$401$			16.5769i			0.827809i	0.910320	+	0.413904i	$0.135835\pi$
$401$			16.5769i			0.827809i	−0.910320	+	0.413904i	$0.864165\pi$
$402$		−	4.28687i		−	0.213810i
$403$	24.3446			1.21269
$404$	−8.65314			−0.430510
$405$		0			0
$406$	−6.04983			−0.300248
$407$	5.60135	+	5.12273i	0.277649	+	0.253924i
$408$	−1.17330			−0.0580870
$409$			5.05401i			0.249905i	0.992163	+	0.124952i	$0.0398778\pi$
$409$			5.05401i			0.249905i	−0.992163	+	0.124952i	$0.960122\pi$
$410$		0			0
$411$	5.33760			0.263285
$412$			4.57336i			0.225313i
$413$		−	2.75740i		−	0.135683i
$414$	21.7350			1.06822
$415$		0			0
$416$	3.34999			0.164247
$417$	3.18792			0.156113
$418$	7.45398			0.364586
$419$	24.2194			1.18319			0.591597	−	0.806234i	$-0.298498\pi$
$419$	24.2194			1.18319			0.591597	+	0.806234i	$0.298498\pi$
$420$		0			0
$421$		−	20.8487i		−	1.01611i	−0.861326	−	0.508053i	$-0.830365\pi$
$421$		−	20.8487i		−	1.01611i	0.861326	−	0.508053i	$-0.169635\pi$
$422$		−	22.8397i		−	1.11182i
$423$	−37.4830			−1.82249
$424$			7.17340i			0.348371i
$425$		0			0
$426$		−	4.80576i		−	0.232840i
$427$			1.35616i			0.0656290i
$428$	11.4715			0.554498
$429$		−	1.57962i		−	0.0762647i
$430$		0			0
$431$		−	28.2298i		−	1.35978i	−0.733314	−	0.679890i	$-0.762027\pi$
$431$		−	28.2298i		−	1.35978i	0.733314	−	0.679890i	$-0.237973\pi$
$432$	2.21322			0.106483
$433$	30.3997			1.46091			0.730457	−	0.682958i	$-0.239307\pi$
$433$	30.3997			1.46091			0.730457	+	0.682958i	$0.239307\pi$
$434$	−4.59098			−0.220374
$435$		0			0
$436$		−	0.727748i		−	0.0348528i
$437$	45.4390			2.17364
$438$			1.68464i			0.0804952i
$439$			33.7591i			1.61123i	0.592438	+	0.805616i	$0.298166\pi$
$439$			33.7591i			1.61123i	−0.592438	+	0.805616i	$0.701834\pi$
$440$		0			0
$441$	18.8602			0.898105
$442$		−	10.4021i		−	0.494777i
$443$	−15.5413			−0.738388			−0.369194	−	0.929352i	$-0.620366\pi$
$443$	−15.5413			−0.738388			−0.369194	+	0.929352i	$0.620366\pi$
$444$	1.69609	+	1.55116i	0.0804929	+	0.0736149i
$445$		0			0
$446$		−	3.32116i		−	0.157261i
$447$	5.15580			0.243861
$448$	−0.631751			−0.0298474
$449$			14.2184i			0.671006i	0.942039	+	0.335503i	$0.108906\pi$
$449$			14.2184i			0.671006i	−0.942039	+	0.335503i	$0.891094\pi$
$450$		0			0
$451$	−10.5510			−0.496829
$452$			17.9970i			0.846506i
$453$	1.20062			0.0564100
$454$	5.62938			0.264200
$455$		0			0
$456$	2.25707			0.105697
$457$			9.17031i			0.428969i	0.976727	+	0.214484i	$0.0688071\pi$
$457$			9.17031i			0.428969i	−0.976727	+	0.214484i	$0.931193\pi$
$458$		−	0.973208i		−	0.0454750i
$459$		−	6.87228i		−	0.320771i
$460$		0			0
$461$		−	10.3300i		−	0.481114i	−0.970635	−	0.240557i	$-0.922670\pi$
$461$		−	10.3300i		−	0.481114i	0.970635	−	0.240557i	$-0.0773301\pi$
$462$			0.297889i			0.0138590i
$463$			25.8049i			1.19926i	0.800278	+	0.599629i	$0.204685\pi$
$463$			25.8049i			1.19926i	−0.800278	+	0.599629i	$0.795315\pi$
$464$		−	9.57629i		−	0.444568i
$465$		0			0
$466$		−	14.4150i		−	0.667761i
$467$		−	34.4582i		−	1.59454i	−0.603625	−	0.797268i	$-0.706278\pi$
$467$		−	34.4582i		−	1.59454i	0.603625	−	0.797268i	$-0.293722\pi$
$468$			9.57166i			0.442450i
$469$	−7.16727			−0.330954
$470$		0			0
$471$	−0.0813572			−0.00374874
$472$	4.36469			0.200901
$473$		−	6.07273i		−	0.279224i
$474$	3.32019			0.152501
$475$		0			0
$476$			1.96166i			0.0899124i
$477$	−20.4960			−0.938448
$478$	8.43344			0.385737
$479$			29.6039i			1.35264i	0.736610	+	0.676318i	$0.236426\pi$
$479$			29.6039i			1.35264i	−0.736610	+	0.676318i	$0.763574\pi$
$480$		0			0
$481$	−13.7521	+	15.0370i	−0.627041	+	0.685627i
$482$	−18.6567			−0.849789
$483$			1.81591i			0.0826268i
$484$	9.44277			0.429217
$485$		0			0
$486$			9.56255i			0.433766i
$487$		−	27.0961i		−	1.22784i	−0.789369	−	0.613920i	$-0.789592\pi$
$487$		−	27.0961i		−	1.22784i	0.789369	−	0.613920i	$-0.210408\pi$
$488$	−2.14666			−0.0971749
$489$		−	0.629549i		−	0.0284692i
$490$		0			0
$491$	2.46033			0.111033			0.0555166	−	0.998458i	$-0.482319\pi$
$491$	2.46033			0.111033			0.0555166	+	0.998458i	$0.482319\pi$
$492$	−3.19485			−0.144035
$493$	−29.7354			−1.33922
$494$			20.0104i			0.900310i
$495$		0			0
$496$		−	7.26707i		−	0.326301i
$497$	−8.03482			−0.360411
$498$			2.50592i			0.112293i
$499$		−	31.4091i		−	1.40606i	−0.711158	−	0.703032i	$-0.751829\pi$
$499$		−	31.4091i		−	1.40606i	0.711158	−	0.703032i	$-0.248171\pi$
$500$		0			0
$501$		−	2.23785i		−	0.0999798i
$502$	25.1189			1.12111
$503$		−	1.78145i		−	0.0794311i	−0.999211	−	0.0397156i	$-0.987355\pi$
$503$		−	1.78145i		−	0.0794311i	0.999211	−	0.0397156i	$-0.0126452\pi$
$504$		−	1.80505i		−	0.0804034i
$505$		0			0
$506$	−9.49277			−0.422005
$507$	−0.671672			−0.0298300
$508$	−15.4830			−0.686947
$509$	−21.2370			−0.941314			−0.470657	−	0.882316i	$-0.655983\pi$
$509$	−21.2370			−0.941314			−0.470657	+	0.882316i	$0.655983\pi$
$510$		0			0
$511$	2.81657			0.124598
$512$		−	1.00000i		−	0.0441942i
$513$			13.2201i			0.583683i
$514$	−20.3552			−0.897831
$515$		0			0
$516$		−	1.83882i		−	0.0809496i
$517$	16.3707			0.719982
$518$	2.59341	−	2.83571i	0.113948	−	0.124594i
$519$	−1.08827			−0.0477698
$520$		0			0
$521$	2.52950			0.110819			0.0554097	−	0.998464i	$-0.482354\pi$
$521$	2.52950			0.110819			0.0554097	+	0.998464i	$0.482354\pi$
$522$	27.3616			1.19758
$523$			1.60848i			0.0703338i	0.999381	+	0.0351669i	$0.0111963\pi$
$523$			1.60848i			0.0703338i	−0.999381	+	0.0351669i	$0.988804\pi$
$524$		−	6.22121i		−	0.271775i
$525$		0			0
$526$			22.2211i			0.968887i
$527$	−22.5651			−0.982950
$528$	−0.471529			−0.0205207
$529$	−34.8673			−1.51597
$530$		0			0
$531$			12.4709i			0.541190i
$532$		−	3.77362i		−	0.163607i
$533$		−	28.3245i		−	1.22687i
$534$	5.20633			0.225300
$535$		0			0
$536$		−	11.3451i		−	0.490033i
$537$		−	1.68595i		−	0.0727541i
$538$		−	15.8411i		−	0.682959i
$539$	−8.23719			−0.354801
$540$		0			0
$541$			3.12463i			0.134338i	0.997742	+	0.0671692i	$0.0213967\pi$
$541$			3.12463i			0.134338i	−0.997742	+	0.0671692i	$0.978603\pi$
$542$			2.00602i			0.0861660i
$543$	−1.48681			−0.0638051
$544$	−3.10511			−0.133131
$545$		0			0
$546$	−0.799690			−0.0342236
$547$			5.44201i			0.232683i	0.993209	+	0.116342i	$0.0371168\pi$
$547$			5.44201i			0.232683i	−0.993209	+	0.116342i	$0.962883\pi$
$548$	14.1258			0.603426
$549$		−	6.13349i		−	0.261771i
$550$		0			0
$551$	57.2017			2.43688
$552$	−2.87441			−0.122343
$553$		−	5.55106i		−	0.236055i
$554$	−11.5671			−0.491440
$555$		0			0
$556$	8.43675			0.357798
$557$		−	36.3451i		−	1.53999i	−0.638050	−	0.769995i	$-0.720259\pi$
$557$		−	36.3451i		−	1.53999i	0.638050	−	0.769995i	$-0.279741\pi$
$558$	20.7636			0.878995
$559$	16.3024			0.689517
$560$		0			0
$561$			1.46415i			0.0618165i
$562$	14.2909			0.602824
$563$			38.4949i			1.62237i	0.584791	+	0.811184i	$0.301177\pi$
$563$			38.4949i			1.62237i	−0.584791	+	0.811184i	$0.698823\pi$
$564$	4.95705			0.208729
$565$		0			0
$566$	12.3837			0.520527
$567$	4.88683			0.205228
$568$		−	12.7183i		−	0.533649i
$569$			41.2793i			1.73052i	0.501324	+	0.865260i	$0.332846\pi$
$569$			41.2793i			1.73052i	−0.501324	+	0.865260i	$0.667154\pi$
$570$		0			0
$571$	−26.0635			−1.09072			−0.545362	−	0.838200i	$-0.683608\pi$
$571$	−26.0635			−1.09072			−0.545362	+	0.838200i	$0.683608\pi$
$572$		−	4.18042i		−	0.174792i
$573$			2.93332i			0.122541i
$574$			5.34152i			0.222951i
$575$		0			0
$576$	2.85722			0.119051
$577$			11.8411i			0.492952i	0.969149	+	0.246476i	$0.0792727\pi$
$577$			11.8411i			0.492952i	−0.969149	+	0.246476i	$0.920727\pi$
$578$		−	7.35829i		−	0.306064i
$579$		−	1.31945i		−	0.0548344i
$580$		0			0
$581$	4.18968			0.173817
$582$	4.17849			0.173204
$583$	8.95162			0.370738
$584$			4.45836i			0.184488i
$585$		0			0
$586$		−	27.8374i		−	1.14995i
$587$		−	26.7315i		−	1.10333i	−0.834067	−	0.551663i	$-0.813994\pi$
$587$		−	26.7315i		−	1.10333i	0.834067	−	0.551663i	$-0.186006\pi$
$588$	−2.49422			−0.102860
$589$	43.4082			1.78860
$590$		0			0
$591$	−0.406641			−0.0167270
$592$	4.48866	+	4.10511i	0.184483	+	0.168719i
$593$	22.6119			0.928560			0.464280	−	0.885688i	$-0.346313\pi$
$593$	22.6119			0.928560			0.464280	+	0.885688i	$0.346313\pi$
$594$		−	2.76185i		−	0.113320i
$595$		0			0
$596$	13.6447			0.558909
$597$			2.15888i			0.0883572i
$598$		−	25.4836i		−	1.04210i
$599$	−14.3406			−0.585942			−0.292971	−	0.956121i	$-0.594644\pi$
$599$	−14.3406			−0.585942			−0.292971	+	0.956121i	$0.594644\pi$
$600$		0			0
$601$	15.0845			0.615308			0.307654	−	0.951498i	$-0.400456\pi$
$601$	15.0845			0.615308			0.307654	+	0.951498i	$0.400456\pi$
$602$	−3.07435			−0.125301
$603$	32.4154			1.32006
$604$	3.17741			0.129287
$605$		0			0
$606$			3.26968i			0.132822i
$607$			41.5964i			1.68835i	0.536070	+	0.844174i	$0.319908\pi$
$607$			41.5964i			1.68835i	−0.536070	+	0.844174i	$0.680092\pi$
$608$	5.97327			0.242248
$609$			2.28599i			0.0926332i
$610$		0			0
$611$			43.9475i			1.77793i
$612$		−	8.87199i		−	0.358629i
$613$	−30.4369			−1.22934			−0.614668	−	0.788786i	$-0.710710\pi$
$613$	−30.4369			−1.22934			−0.614668	+	0.788786i	$0.710710\pi$
$614$			19.9411i			0.804756i
$615$		0			0
$616$			0.788355i			0.0317637i
$617$	39.8195			1.60307			0.801536	−	0.597946i	$-0.204016\pi$
$617$	39.8195			1.60307			0.801536	+	0.597946i	$0.204016\pi$
$618$	1.72810			0.0695142
$619$	−39.4011			−1.58367			−0.791833	−	0.610738i	$-0.790873\pi$
$619$	−39.4011			−1.58367			−0.791833	+	0.610738i	$0.790873\pi$
$620$		0			0
$621$		−	16.8361i		−	0.675608i
$622$	4.96832			0.199211
$623$		−	8.70453i		−	0.348740i
$624$		−	1.26583i		−	0.0506738i
$625$		0			0
$626$	10.0000			0.399680
$627$		−	2.81657i		−	0.112483i
$628$	−0.215310			−0.00859180
$629$	12.7468	−	13.9378i	0.508249	−	0.555736i
$630$		0			0
$631$			0.114985i			0.00457750i	0.999997	+	0.00228875i	$0.000728532\pi$
$631$			0.114985i			0.00457750i	−0.999997	+	0.00228875i	$0.999271\pi$
$632$	8.78679			0.349520
$633$	−8.63024			−0.343021
$634$		−	22.9198i		−	0.910260i
$635$		0			0
$636$	2.71055			0.107480
$637$		−	22.1129i		−	0.876146i
$638$	−11.9502			−0.473111
$639$	36.3391			1.43755
$640$		0			0
$641$	34.9774			1.38153			0.690763	−	0.723081i	$-0.257275\pi$
$641$	34.9774			1.38153			0.690763	+	0.723081i	$0.257275\pi$
$642$		−	4.33465i		−	0.171075i
$643$			25.2868i			0.997216i	0.866828	+	0.498608i	$0.166155\pi$
$643$			25.2868i			0.997216i	−0.866828	+	0.498608i	$0.833845\pi$
$644$			4.80576i			0.189374i
$645$		0			0
$646$		−	18.5477i		−	0.729748i
$647$			23.5824i			0.927120i	0.886066	+	0.463560i	$0.153428\pi$
$647$			23.5824i			0.927120i	−0.886066	+	0.463560i	$0.846572\pi$
$648$			7.73537i			0.303874i
$649$		−	5.44665i		−	0.213800i
$650$		0			0
$651$			1.73475i			0.0679903i
$652$		−	1.66609i		−	0.0652490i
$653$			9.89261i			0.387128i	0.981088	+	0.193564i	$0.0620047\pi$
$653$			9.89261i			0.387128i	−0.981088	+	0.193564i	$0.937995\pi$
$654$	−0.274988			−0.0107529
$655$		0			0
$656$	−8.45510			−0.330116
$657$	−12.7385			−0.496977
$658$		−	8.28775i		−	0.323090i
$659$	25.4137			0.989976			0.494988	−	0.868900i	$-0.335173\pi$
$659$	25.4137			0.989976			0.494988	+	0.868900i	$0.335173\pi$
$660$		0			0
$661$		−	28.4574i		−	1.10687i	−0.832894	−	0.553433i	$-0.813318\pi$
$661$		−	28.4574i		−	1.10687i	0.832894	−	0.553433i	$-0.186682\pi$
$662$	−5.54265			−0.215421
$663$	−3.93055			−0.152650
$664$			6.63185i			0.257366i
$665$		0			0
$666$	−11.7292	+	12.8251i	−0.454498	+	0.496962i
$667$	−72.8474			−2.82066
$668$		−	5.92242i		−	0.229145i
$669$	−1.25494			−0.0485186
$670$		0			0
$671$			2.67880i			0.103414i
$672$			0.238714i			0.00920860i
$673$	−20.4187			−0.787082			−0.393541	−	0.919307i	$-0.628750\pi$
$673$	−20.4187			−0.787082			−0.393541	+	0.919307i	$0.628750\pi$
$674$		−	25.6348i		−	0.987416i
$675$		0			0
$676$	−1.77756			−0.0683678
$677$	−18.5163			−0.711641			−0.355821	−	0.934554i	$-0.615799\pi$
$677$	−18.5163			−0.711641			−0.355821	+	0.934554i	$0.615799\pi$
$678$	6.80035			0.261166
$679$		−	6.98607i		−	0.268101i
$680$		0			0
$681$		−	2.12713i		−	0.0815116i
$682$	−9.06851			−0.347251
$683$			32.0667i			1.22700i	0.789695	+	0.613499i	$0.210239\pi$
$683$			32.0667i			1.22700i	−0.789695	+	0.613499i	$0.789761\pi$
$684$			17.0669i			0.652571i
$685$		0			0
$686$			8.59237i			0.328058i
$687$	−0.367738			−0.0140301
$688$		−	4.86640i		−	0.185530i
$689$			24.0308i			0.915502i
$690$		0			0
$691$	−6.57629			−0.250174			−0.125087	−	0.992146i	$-0.539921\pi$
$691$	−6.57629			−0.250174			−0.125087	+	0.992146i	$0.539921\pi$
$692$	−2.88008			−0.109484
$693$	−2.25251			−0.0855656
$694$	19.6225			0.744860
$695$		0			0
$696$	−3.61851			−0.137159
$697$			26.2540i			0.994442i
$698$		−	15.6263i		−	0.591466i
$699$	−5.44686			−0.206019
$700$		0			0
$701$			9.62168i			0.363406i	0.983353	+	0.181703i	$0.0581609\pi$
$701$			9.62168i			0.363406i	−0.983353	+	0.181703i	$0.941839\pi$
$702$	7.41425			0.279833
$703$	−24.5209	+	26.8120i	−0.924824	+	1.01123i
$704$	−1.24789			−0.0470316
$705$		0			0
$706$	−23.5724			−0.887159
$707$	5.46663			0.205594
$708$		−	1.64925i		−	0.0619825i
$709$		−	8.65759i		−	0.325142i	−0.986697	−	0.162571i	$-0.948021\pi$
$709$		−	8.65759i		−	0.325142i	0.986697	−	0.162571i	$-0.0519787\pi$
$710$		0			0
$711$			25.1058i			0.941541i
$712$	13.7784			0.516368
$713$	−55.2810			−2.07029
$714$	0.741234			0.0277400
$715$		0			0
$716$		−	4.46182i		−	0.166746i
$717$		−	3.18667i		−	0.119008i
$718$		−	9.34905i		−	0.348904i
$719$	−51.5303			−1.92176			−0.960878	−	0.276972i	$-0.910669\pi$
$719$	−51.5303			−1.92176			−0.960878	+	0.276972i	$0.910669\pi$
$720$		0			0
$721$		−	2.88923i		−	0.107600i
$722$			16.6799i			0.620763i
$723$			7.04964i			0.262179i
$724$	−3.93480			−0.146236
$725$		0			0
$726$		−	3.56806i		−	0.132423i
$727$			11.3224i			0.419924i	0.977710	+	0.209962i	$0.0673340\pi$
$727$			11.3224i			0.419924i	−0.977710	+	0.209962i	$0.932666\pi$
$728$	−2.11636			−0.0784375
$729$	−19.5928			−0.725660
$730$		0			0
$731$	−15.1107			−0.558890
$732$			0.811140i			0.0299806i
$733$	2.74231			0.101290			0.0506448	−	0.998717i	$-0.483872\pi$
$733$	2.74231			0.101290			0.0506448	+	0.998717i	$0.483872\pi$
$734$			12.2379i			0.451708i
$735$		0			0
$736$	−7.60706			−0.280400
$737$	−14.1574			−0.521495
$738$		−	24.1581i		−	0.889272i
$739$	−8.18878			−0.301229			−0.150614	−	0.988593i	$-0.548125\pi$
$739$	−8.18878			−0.301229			−0.150614	+	0.988593i	$0.548125\pi$
$740$		0			0
$741$	7.56115			0.277766
$742$		−	4.53180i		−	0.166368i
$743$	−22.1217			−0.811567			−0.405784	−	0.913969i	$-0.633001\pi$
$743$	−22.1217			−0.811567			−0.405784	+	0.913969i	$0.633001\pi$
$744$	−2.74594			−0.100671
$745$		0			0
$746$			10.1918i			0.373149i
$747$	−18.9487			−0.693296
$748$			3.87484i			0.141678i
$749$	−7.24715			−0.264805
$750$		0			0
$751$	−19.0818			−0.696306			−0.348153	−	0.937438i	$-0.613191\pi$
$751$	−19.0818			−0.696306			−0.348153	+	0.937438i	$0.613191\pi$
$752$	13.1187			0.478390
$753$		−	9.49146i		−	0.345888i
$754$		−	32.0805i		−	1.16830i
$755$		0			0
$756$	−1.39820			−0.0508521
$757$			31.2209i			1.13474i	0.823462	+	0.567372i	$0.192040\pi$
$757$			31.2209i			1.13474i	−0.823462	+	0.567372i	$0.807960\pi$
$758$			20.7538i			0.753811i
$759$			3.58695i			0.130198i
$760$		0			0
$761$	−29.3163			−1.06271			−0.531357	−	0.847148i	$-0.678318\pi$
$761$	−29.3163			−1.06271			−0.531357	+	0.847148i	$0.678318\pi$
$762$			5.85042i			0.211939i
$763$			0.459756i			0.0166443i
$764$			7.76296i			0.280854i
$765$		0			0
$766$	−17.7328			−0.640712
$767$	14.6217			0.527958
$768$	−0.377861			−0.0136349
$769$		−	29.0289i		−	1.04681i	−0.852084	−	0.523404i	$-0.824662\pi$
$769$		−	29.0289i		−	1.04681i	0.852084	−	0.523404i	$-0.175338\pi$
$770$		0			0
$771$			7.69146i			0.277001i
$772$		−	3.49189i		−	0.125676i
$773$	43.4153			1.56154			0.780769	−	0.624819i	$-0.214827\pi$
$773$	43.4153			1.56154			0.780769	+	0.624819i	$0.214827\pi$
$774$	13.9044			0.499782
$775$		0			0
$776$	11.0583			0.396969
$777$	−1.07151	−	0.979948i	−0.0384401	−	0.0351554i
$778$	10.9054			0.390976
$779$		−	50.5046i		−	1.80951i
$780$		0			0
$781$	−15.8711			−0.567912
$782$			23.6208i			0.844676i
$783$		−	21.1944i		−	0.757426i
$784$	−6.60089			−0.235746
$785$		0			0
$786$	−2.35075			−0.0838486
$787$	−18.9119			−0.674136			−0.337068	−	0.941480i	$-0.609435\pi$
$787$	−18.9119			−0.674136			−0.337068	+	0.941480i	$0.609435\pi$
$788$	−1.07617			−0.0383368
$789$	8.39650			0.298923
$790$		0			0
$791$		−	11.3696i		−	0.404256i
$792$		−	3.56550i		−	0.126694i
$793$	−7.19130			−0.255371
$794$			23.0106i			0.816616i
$795$		0			0
$796$			5.71343i			0.202507i
$797$			6.65779i			0.235831i	0.993024	+	0.117916i	$0.0376212\pi$
$797$			6.65779i			0.235831i	−0.993024	+	0.117916i	$0.962379\pi$
$798$	−1.42590			−0.0504764
$799$		−	40.7350i		−	1.44110i
$800$		0			0
$801$			39.3680i			1.39100i
$802$	16.5769			0.585349
$803$	5.56354			0.196333
$804$	−4.28687			−0.151186
$805$		0			0
$806$		−	24.3446i		−	0.857503i
$807$	−5.98574			−0.210708
$808$			8.65314i			0.304416i
$809$		−	35.3855i		−	1.24409i	−0.782982	−	0.622044i	$-0.786302\pi$
$809$		−	35.3855i		−	1.24409i	0.782982	−	0.622044i	$-0.213698\pi$
$810$		0			0
$811$	34.1205			1.19813			0.599067	−	0.800699i	$-0.295538\pi$
$811$	34.1205			1.19813			0.599067	+	0.800699i	$0.295538\pi$
$812$			6.04983i			0.212307i
$813$	0.757997			0.0265841
$814$	5.12273	−	5.60135i	0.179551	−	0.196327i
$815$		0			0
$816$			1.17330i			0.0410737i
$817$	29.0683			1.01697
$818$	5.05401			0.176709
$819$		−	6.04691i		−	0.211296i
$820$		0			0
$821$	−50.1981			−1.75193			−0.875963	−	0.482378i	$-0.839773\pi$
$821$	−50.1981			−1.75193			−0.875963	+	0.482378i	$0.839773\pi$
$822$		−	5.33760i		−	0.186170i
$823$	47.6713			1.66172			0.830859	−	0.556483i	$-0.187850\pi$
$823$	47.6713			1.66172			0.830859	+	0.556483i	$0.187850\pi$
$824$	4.57336			0.159321
$825$		0			0
$826$	−2.75740			−0.0959420
$827$		−	3.77813i		−	0.131378i	−0.997840	−	0.0656892i	$-0.979075\pi$
$827$		−	3.77813i		−	0.131378i	0.997840	−	0.0656892i	$-0.0209246\pi$
$828$		−	21.7350i		−	0.755345i
$829$		−	11.9862i		−	0.416297i	−0.978097	−	0.208149i	$-0.933256\pi$
$829$		−	11.9862i		−	0.416297i	0.978097	−	0.208149i	$-0.0667438\pi$
$830$		0			0
$831$			4.37076i			0.151620i
$832$		−	3.34999i		−	0.116140i
$833$			20.4965i			0.710162i
$834$		−	3.18792i		−	0.110389i
$835$		0			0
$836$		−	7.45398i		−	0.257801i
$837$		−	16.0836i		−	0.555931i
$838$		−	24.2194i		−	0.836644i
$839$	54.1303			1.86879			0.934393	−	0.356243i	$-0.115942\pi$
$839$	54.1303			1.86879			0.934393	+	0.356243i	$0.115942\pi$
$840$		0			0
$841$	−62.7053			−2.16225
$842$	−20.8487			−0.718495
$843$		−	5.39996i		−	0.185985i
$844$	−22.8397			−0.786176
$845$		0			0
$846$			37.4830i			1.28869i
$847$	−5.96548			−0.204976
$848$	7.17340			0.246336
$849$		−	4.67933i		−	0.160594i
$850$		0			0
$851$	31.2278	−	34.1455i	1.07048	−	1.17049i
$852$	−4.80576			−0.164643
$853$		−	54.7590i		−	1.87491i	−0.348101	−	0.937457i	$-0.613173\pi$
$853$		−	54.7590i		−	1.87491i	0.348101	−	0.937457i	$-0.386827\pi$
$854$	1.35616			0.0464067
$855$		0			0
$856$		−	11.4715i		−	0.392089i
$857$		−	13.8273i		−	0.472331i	−0.971713	−	0.236165i	$-0.924109\pi$
$857$		−	13.8273i		−	0.472331i	0.971713	−	0.236165i	$-0.0758907\pi$
$858$	−1.57962			−0.0539273
$859$			27.9420i			0.953368i	0.879075	+	0.476684i	$0.158161\pi$
$859$			27.9420i			0.953368i	−0.879075	+	0.476684i	$0.841839\pi$
$860$		0			0
$861$	2.01835			0.0687852
$862$	−28.2298			−0.961510
$863$	−0.665448			−0.0226521			−0.0113261	−	0.999936i	$-0.503605\pi$
$863$	−0.665448			−0.0226521			−0.0113261	+	0.999936i	$0.503605\pi$
$864$		−	2.21322i		−	0.0752951i
$865$		0			0
$866$		−	30.3997i		−	1.03302i
$867$	−2.78041			−0.0944277
$868$			4.59098i			0.155828i
$869$		−	10.9650i		−	0.371961i
$870$		0			0
$871$		−	38.0059i		−	1.28778i
$872$	−0.727748			−0.0246447
$873$			31.5959i			1.06936i
$874$		−	45.4390i		−	1.53700i
$875$		0			0
$876$	1.68464			0.0569187
$877$	−2.04026			−0.0688948			−0.0344474	−	0.999407i	$-0.510967\pi$
$877$	−2.04026			−0.0688948			−0.0344474	+	0.999407i	$0.510967\pi$
$878$	33.7591			1.13931
$879$	−10.5187			−0.354786
$880$		0			0
$881$	19.5251			0.657816			0.328908	−	0.944362i	$-0.393319\pi$
$881$	19.5251			0.657816			0.328908	+	0.944362i	$0.393319\pi$
$882$		−	18.8602i		−	0.635056i
$883$		−	21.6799i		−	0.729586i	−0.931089	−	0.364793i	$-0.881140\pi$
$883$		−	21.6799i		−	0.729586i	0.931089	−	0.364793i	$-0.118860\pi$
$884$	−10.4021			−0.349860
$885$		0			0
$886$			15.5413i			0.522119i
$887$	−35.0252			−1.17603			−0.588015	−	0.808850i	$-0.700090\pi$
$887$	−35.0252			−1.17603			−0.588015	+	0.808850i	$0.700090\pi$
$888$	1.55116	−	1.69609i	0.0520536	−	0.0569171i
$889$	9.78140			0.328058
$890$		0			0
$891$	9.65290			0.323384
$892$	−3.32116			−0.111201
$893$			78.3615i			2.62227i
$894$		−	5.15580i		−	0.172436i
$895$		0			0
$896$			0.631751i			0.0211053i
$897$	−9.62925			−0.321511
$898$	14.2184			0.474473
$899$	−69.5916			−2.32101
$900$		0			0
$901$		−	22.2742i		−	0.742062i
$902$			10.5510i			0.351311i
$903$			1.16168i			0.0386582i
$904$	17.9970			0.598570
$905$		0			0
$906$		−	1.20062i		−	0.0398879i
$907$			19.4042i			0.644307i	0.946688	+	0.322153i	$0.104407\pi$
$907$			19.4042i			0.644307i	−0.946688	+	0.322153i	$0.895593\pi$
$908$		−	5.62938i		−	0.186818i
$909$	−24.7239			−0.820041
$910$		0			0
$911$			7.46474i			0.247318i	0.992325	+	0.123659i	$0.0394629\pi$
$911$			7.46474i			0.247318i	−0.992325	+	0.123659i	$0.960537\pi$
$912$		−	2.25707i		−	0.0747389i
$913$	8.27583			0.273890
$914$	9.17031			0.303327
$915$		0			0
$916$	−0.973208			−0.0321557
$917$			3.93025i			0.129788i
$918$	−6.87228			−0.226819
$919$		−	27.8014i		−	0.917083i	−0.888673	−	0.458541i	$-0.848372\pi$
$919$		−	27.8014i		−	0.917083i	0.888673	−	0.458541i	$-0.151628\pi$
$920$		0			0
$921$	7.53496			0.248285
$922$	−10.3300			−0.340199
$923$		−	42.6063i		−	1.40240i
$924$	0.297889			0.00979983
$925$		0			0
$926$	25.8049			0.848003
$927$			13.0671i			0.429180i
$928$	−9.57629			−0.314357
$929$	−19.4503			−0.638145			−0.319072	−	0.947730i	$-0.603371\pi$
$929$	−19.4503			−0.638145			−0.319072	+	0.947730i	$0.603371\pi$
$930$		0			0
$931$		−	39.4289i		−	1.29223i
$932$	−14.4150			−0.472178
$933$		−	1.87733i		−	0.0614611i
$934$	−34.4582			−1.12751
$935$		0			0
$936$	9.57166			0.312860
$937$	14.2786			0.466463			0.233231	−	0.972421i	$-0.425070\pi$
$937$	14.2786			0.466463			0.233231	+	0.972421i	$0.425070\pi$
$938$			7.16727i			0.234020i
$939$		−	3.77861i		−	0.123310i
$940$		0			0
$941$	−18.0266			−0.587649			−0.293825	−	0.955859i	$-0.594928\pi$
$941$	−18.0266			−0.587649			−0.293825	+	0.955859i	$0.594928\pi$
$942$			0.0813572i			0.00265076i
$943$			64.3184i			2.09450i
$944$		−	4.36469i		−	0.142058i
$945$		0			0
$946$	−6.07273			−0.197441
$947$		−	20.7621i		−	0.674679i	−0.941383	−	0.337339i	$-0.890473\pi$
$947$		−	20.7621i		−	0.674679i	0.941383	−	0.337339i	$-0.109527\pi$
$948$		−	3.32019i		−	0.107835i
$949$			14.9354i			0.484825i
$950$		0			0
$951$	−8.66049			−0.280836
$952$	1.96166			0.0635776
$953$	−40.9858			−1.32766			−0.663831	−	0.747883i	$-0.731071\pi$
$953$	−40.9858			−1.32766			−0.663831	+	0.747883i	$0.731071\pi$
$954$			20.4960i			0.663583i
$955$		0			0
$956$		−	8.43344i		−	0.272757i
$957$			4.51550i			0.145965i
$958$	29.6039			0.956458
$959$	−8.92401			−0.288171
$960$		0			0
$961$	−21.8103			−0.703560
$962$	15.0370	+	13.7521i	0.484811	+	0.443385i
$963$	32.7767			1.05622
$964$			18.6567i			0.600891i
$965$		0			0
$966$	1.81591			0.0584260
$967$			25.1227i			0.807892i	0.914783	+	0.403946i	$0.132362\pi$
$967$			25.1227i			0.807892i	−0.914783	+	0.403946i	$0.867638\pi$
$968$		−	9.44277i		−	0.303502i
$969$	−7.00844			−0.225144
$970$		0			0
$971$	−10.0012			−0.320953			−0.160476	−	0.987040i	$-0.551303\pi$
$971$	−10.0012			−0.320953			−0.160476	+	0.987040i	$0.551303\pi$
$972$	9.56255			0.306719
$973$	−5.32992			−0.170869
$974$	−27.0961			−0.868214
$975$		0			0
$976$			2.14666i			0.0687130i
$977$		−	49.4636i		−	1.58248i	−0.611505	−	0.791240i	$-0.709436\pi$
$977$		−	49.4636i		−	1.58248i	0.611505	−	0.791240i	$-0.290564\pi$
$978$	−0.629549			−0.0201308
$979$		−	17.1940i		−	0.549521i
$980$		0			0
$981$		−	2.07934i		−	0.0663882i
$982$		−	2.46033i		−	0.0785123i
$983$	−36.4329			−1.16203			−0.581014	−	0.813894i	$-0.697344\pi$
$983$	−36.4329			−1.16203			−0.581014	+	0.813894i	$0.697344\pi$
$984$			3.19485i			0.101848i
$985$		0			0
$986$			29.7354i			0.946969i
$987$	−3.13162			−0.0996805
$988$	20.0104			0.636615
$989$	−37.0190			−1.17713
$990$		0			0
$991$			49.5991i			1.57557i	0.615953	+	0.787783i	$0.288771\pi$
$991$			49.5991i			1.57557i	−0.615953	+	0.787783i	$0.711229\pi$
$992$	−7.26707			−0.230730
$993$			2.09435i			0.0664622i
$994$			8.03482i			0.254849i
$995$		0			0
$996$	2.50592			0.0794031
$997$			3.21866i			0.101936i	0.998700	+	0.0509680i	$0.0162307\pi$
$997$			3.21866i			0.101936i	−0.998700	+	0.0509680i	$0.983769\pi$
$998$	−31.4091			−0.994238
$999$	9.93437	+	9.08550i	0.314310	+	0.287452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.d.i.1701.5		20
5.2	odd	4		370.2.c.b.369.6	yes	10
5.3	odd	4		370.2.c.a.369.5	✓	10
5.4	even	2	inner	1850.2.d.i.1701.16		20
15.2	even	4		3330.2.e.c.739.8		10
15.8	even	4		3330.2.e.d.739.4		10
37.36	even	2	inner	1850.2.d.i.1701.15		20
185.73	odd	4		370.2.c.b.369.5	yes	10
185.147	odd	4		370.2.c.a.369.6	yes	10
185.184	even	2	inner	1850.2.d.i.1701.6		20
555.332	even	4		3330.2.e.d.739.3		10
555.443	even	4		3330.2.e.c.739.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.c.a.369.5	✓	10	5.3	odd	4
370.2.c.a.369.6	yes	10	185.147	odd	4
370.2.c.b.369.5	yes	10	185.73	odd	4
370.2.c.b.369.6	yes	10	5.2	odd	4
1850.2.d.i.1701.5		20	1.1	even	1	trivial
1850.2.d.i.1701.6		20	185.184	even	2	inner
1850.2.d.i.1701.15		20	37.36	even	2	inner
1850.2.d.i.1701.16		20	5.4	even	2	inner
3330.2.e.c.739.7		10	555.443	even	4
3330.2.e.c.739.8		10	15.2	even	4
3330.2.e.d.739.3		10	555.332	even	4
3330.2.e.d.739.4		10	15.8	even	4

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:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -0.377861 q^{3} -1.00000 q^{4} +0.377861i q^{6} +0.631751 q^{7} +1.00000i q^{8} -2.85722 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -0.377861 q^{3} -1.00000 q^{4} +0.377861i q^{6} +0.631751 q^{7} +1.00000i q^{8} -2.85722 q^{9} +1.24789 q^{11} +0.377861 q^{12} +3.34999i q^{13} -0.631751i q^{14} +1.00000 q^{16} -3.10511i q^{17} +2.85722i q^{18} +5.97327i q^{19} -0.238714 q^{21} -1.24789i q^{22} -7.60706i q^{23} -0.377861i q^{24} +3.34999 q^{26} +2.21322 q^{27} -0.631751 q^{28} -9.57629i q^{29} -7.26707i q^{31} -1.00000i q^{32} -0.471529 q^{33} -3.10511 q^{34} +2.85722 q^{36} +(4.48866 + 4.10511i) q^{37} +5.97327 q^{38} -1.26583i q^{39} -8.45510 q^{41} +0.238714i q^{42} -4.86640i q^{43} -1.24789 q^{44} -7.60706 q^{46} +13.1187 q^{47} -0.377861 q^{48} -6.60089 q^{49} +1.17330i q^{51} -3.34999i q^{52} +7.17340 q^{53} -2.21322i q^{54} +0.631751i q^{56} -2.25707i q^{57} -9.57629 q^{58} -4.36469i q^{59} +2.14666i q^{61} -7.26707 q^{62} -1.80505 q^{63} -1.00000 q^{64} +0.471529i q^{66} -11.3451 q^{67} +3.10511i q^{68} +2.87441i q^{69} -12.7183 q^{71} -2.85722i q^{72} +4.45836 q^{73} +(4.10511 - 4.48866i) q^{74} -5.97327i q^{76} +0.788355 q^{77} -1.26583 q^{78} -8.78679i q^{79} +7.73537 q^{81} +8.45510i q^{82} +6.63185 q^{83} +0.238714 q^{84} -4.86640 q^{86} +3.61851i q^{87} +1.24789i q^{88} -13.7784i q^{89} +2.11636i q^{91} +7.60706i q^{92} +2.74594i q^{93} -13.1187i q^{94} +0.377861i q^{96} -11.0583i q^{97} +6.60089i q^{98} -3.56550 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{4} + 16 q^{9}+O(q^{10}) \) 20 * q - 20 * q^4 + 16 * q^9	\( 20 q - 20 q^{4} + 16 q^{9} + 20 q^{16} - 24 q^{21} + 4 q^{26} + 36 q^{34} - 16 q^{36} - 8 q^{41} - 20 q^{46} + 16 q^{49} - 20 q^{64} - 40 q^{71} - 16 q^{74} + 116 q^{81} + 24 q^{84} + 20 q^{86} + 164 q^{99}+O(q^{100}) \) 20 * q - 20 * q^4 + 16 * q^9 + 20 * q^16 - 24 * q^21 + 4 * q^26 + 36 * q^34 - 16 * q^36 - 8 * q^41 - 20 * q^46 + 16 * q^49 - 20 * q^64 - 40 * q^71 - 16 * q^74 + 116 * q^81 + 24 * q^84 + 20 * q^86 + 164 * q^99

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