LMFDB - Embedded newform 104.2.b.c.53.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [104,2,Mod(53,104)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("104.53"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(104, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 104 = 2^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	104.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.830444181021$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.399424.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			53.2
Root			$1.40680 - 0.144584i$ of defining polynomial
Character	$\chi$	$=$	104.53
Dual form			104.2.b.c.53.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40680 + 0.144584i) q^{2} +2.10278i q^{3} +(1.95819 - 0.406803i) q^{4} +1.00000i q^{5} +(-0.304028 - 2.95819i) q^{6} -2.10278 q^{7} +(-2.69597 + 0.855416i) q^{8} -1.42166 q^{9} +(-0.144584 - 1.40680i) q^{10} +5.62721i q^{11} +(0.855416 + 4.11763i) q^{12} -1.00000i q^{13} +(2.95819 - 0.304028i) q^{14} -2.10278 q^{15} +(3.66902 - 1.59320i) q^{16} +1.00000 q^{17} +(2.00000 - 0.205550i) q^{18} -4.00000i q^{19} +(0.406803 + 1.95819i) q^{20} -4.42166i q^{21} +(-0.813607 - 7.91638i) q^{22} +1.62721 q^{23} +(-1.79875 - 5.66902i) q^{24} +4.00000 q^{25} +(0.144584 + 1.40680i) q^{26} +3.31889i q^{27} +(-4.11763 + 0.855416i) q^{28} -7.83276i q^{29} +(2.95819 - 0.304028i) q^{30} +9.62721 q^{31} +(-4.93124 + 2.77180i) q^{32} -11.8328 q^{33} +(-1.40680 + 0.144584i) q^{34} -2.10278i q^{35} +(-2.78389 + 0.578337i) q^{36} +0.421663i q^{37} +(0.578337 + 5.62721i) q^{38} +2.10278 q^{39} +(-0.855416 - 2.69597i) q^{40} +5.83276 q^{41} +(0.639303 + 6.22041i) q^{42} +0.475562i q^{43} +(2.28917 + 11.0192i) q^{44} -1.42166i q^{45} +(-2.28917 + 0.235269i) q^{46} -4.68111 q^{47} +(3.35013 + 7.71513i) q^{48} -2.57834 q^{49} +(-5.62721 + 0.578337i) q^{50} +2.10278i q^{51} +(-0.406803 - 1.95819i) q^{52} +4.57834i q^{53} +(-0.479859 - 4.66902i) q^{54} -5.62721 q^{55} +(5.66902 - 1.79875i) q^{56} +8.41110 q^{57} +(1.13249 + 11.0192i) q^{58} -8.67609i q^{59} +(-4.11763 + 0.855416i) q^{60} +12.6761i q^{61} +(-13.5436 + 1.39194i) q^{62} +2.98944 q^{63} +(6.53653 - 4.61235i) q^{64} +1.00000 q^{65} +(16.6464 - 1.71083i) q^{66} -12.2056i q^{67} +(1.95819 - 0.406803i) q^{68} +3.42166i q^{69} +(0.304028 + 2.95819i) q^{70} -9.15165 q^{71} +(3.83276 - 1.21611i) q^{72} -2.57834 q^{73} +(-0.0609658 - 0.593197i) q^{74} +8.41110i q^{75} +(-1.62721 - 7.83276i) q^{76} -11.8328i q^{77} +(-2.95819 + 0.304028i) q^{78} -14.3033 q^{79} +(1.59320 + 3.66902i) q^{80} -11.2439 q^{81} +(-8.20555 + 0.843326i) q^{82} -8.20555i q^{83} +(-1.79875 - 8.65846i) q^{84} +1.00000i q^{85} +(-0.0687588 - 0.669022i) q^{86} +16.4705 q^{87} +(-4.81361 - 15.1708i) q^{88} +11.2544 q^{89} +(0.205550 + 2.00000i) q^{90} +2.10278i q^{91} +(3.18639 - 0.661956i) q^{92} +20.2439i q^{93} +(6.58540 - 0.676815i) q^{94} +4.00000 q^{95} +(-5.82847 - 10.3693i) q^{96} +10.6761 q^{97} +(3.62721 - 0.372787i) q^{98} -8.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 2 q^{4} - 10 q^{6} + 2 q^{7} - 8 q^{8} - 12 q^{9} + 6 q^{12} + 4 q^{14} + 2 q^{15} + 10 q^{16} + 6 q^{17} + 12 q^{18} - 4 q^{20} + 8 q^{22} - 16 q^{23} + 12 q^{24} + 24 q^{25} - 20 q^{28}+ \cdots - 4 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 - 2 * q^4 - 10 * q^6 + 2 * q^7 - 8 * q^8 - 12 * q^9 + 6 * q^12 + 4 * q^14 + 2 * q^15 + 10 * q^16 + 6 * q^17 + 12 * q^18 - 4 * q^20 + 8 * q^22 - 16 * q^23 + 12 * q^24 + 24 * q^25 - 20 * q^28 + 4 * q^30 + 32 * q^31 - 12 * q^32 - 16 * q^33 - 2 * q^34 + 16 * q^36 - 2 * q^39 - 6 * q^40 - 20 * q^41 - 28 * q^42 + 12 * q^44 - 12 * q^46 - 10 * q^47 - 10 * q^48 - 12 * q^49 - 8 * q^50 + 4 * q^52 + 38 * q^54 - 8 * q^55 + 22 * q^56 - 8 * q^57 + 12 * q^58 - 20 * q^60 - 28 * q^62 - 44 * q^63 + 22 * q^64 + 6 * q^65 + 32 * q^66 - 2 * q^68 + 10 * q^70 - 18 * q^71 - 32 * q^72 - 12 * q^73 + 28 * q^74 + 16 * q^76 - 4 * q^78 - 12 * q^79 + 16 * q^80 + 46 * q^81 - 20 * q^82 + 12 * q^84 - 18 * q^86 + 80 * q^87 - 16 * q^88 + 16 * q^89 - 28 * q^90 + 32 * q^92 + 24 * q^95 - 32 * q^96 + 16 * q^97 - 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$.

$n$	$41$	$53$	$79$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−1.40680	+	0.144584i	−0.994760	+	0.102237i
$2$	−1.40680	+	0.144584i	−0.994760	+	0.102237i
$3$			2.10278i			1.21404i	0.794687	+	0.607019i	$0.207635\pi$
$3$			2.10278i			1.21404i	−0.794687	+	0.607019i	$0.792365\pi$
$4$	1.95819	−	0.406803i	0.979095	−	0.203402i
$5$			1.00000i			0.447214i	0.974679	+	0.223607i	$0.0717831\pi$
$5$			1.00000i			0.447214i	−0.974679	+	0.223607i	$0.928217\pi$
$6$	−0.304028	−	2.95819i	−0.124119	−	1.20768i
$7$	−2.10278			−0.794774			−0.397387	−	0.917651i	$-0.630083\pi$
$7$	−2.10278			−0.794774			−0.397387	+	0.917651i	$0.630083\pi$
$8$	−2.69597	+	0.855416i	−0.953170	+	0.302435i
$9$	−1.42166			−0.473888
$10$	−0.144584	−	1.40680i	−0.0457216	−	0.444870i
$11$			5.62721i			1.69667i	0.529461	+	0.848334i	$0.322394\pi$
$11$			5.62721i			1.69667i	−0.529461	+	0.848334i	$0.677606\pi$
$12$	0.855416	+	4.11763i	0.246937	+	1.18866i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	2.95819	−	0.304028i	0.790610	−	0.0812550i
$15$	−2.10278			−0.542934
$16$	3.66902	−	1.59320i	0.917256	−	0.398299i
$17$	1.00000			0.242536			0.121268	−	0.992620i	$-0.461304\pi$
$17$	1.00000			0.242536			0.121268	+	0.992620i	$0.461304\pi$
$18$	2.00000	−	0.205550i	0.471405	−	0.0484486i
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$	0.406803	+	1.95819i	0.0909640	+	0.437865i
$21$		−	4.42166i		−	0.964886i
$22$	−0.813607	−	7.91638i	−0.173461	−	1.68778i
$23$	1.62721			0.339297			0.169649	−	0.985505i	$-0.445737\pi$
$23$	1.62721			0.339297			0.169649	+	0.985505i	$0.445737\pi$
$24$	−1.79875	−	5.66902i	−0.367168	−	1.15718i
$25$	4.00000			0.800000
$26$	0.144584	+	1.40680i	0.0283553	+	0.275897i
$27$			3.31889i			0.638720i
$28$	−4.11763	+	0.855416i	−0.778160	+	0.161658i
$29$		−	7.83276i		−	1.45451i	−0.686369	−	0.727254i	$-0.740796\pi$
$29$		−	7.83276i		−	1.45451i	0.686369	−	0.727254i	$-0.259204\pi$
$30$	2.95819	−	0.304028i	0.540089	−	0.0555077i
$31$	9.62721			1.72910			0.864549	−	0.502548i	$-0.167604\pi$
$31$	9.62721			1.72910			0.864549	+	0.502548i	$0.167604\pi$
$32$	−4.93124	+	2.77180i	−0.871729	+	0.489989i
$33$	−11.8328			−2.05982
$34$	−1.40680	+	0.144584i	−0.241265	+	0.0247960i
$35$		−	2.10278i		−	0.355434i
$36$	−2.78389	+	0.578337i	−0.463981	+	0.0963895i
$37$			0.421663i			0.0693210i	0.999399	+	0.0346605i	$0.0110350\pi$
$37$			0.421663i			0.0693210i	−0.999399	+	0.0346605i	$0.988965\pi$
$38$	0.578337	+	5.62721i	0.0938187	+	0.912854i
$39$	2.10278			0.336713
$40$	−0.855416	−	2.69597i	−0.135253	−	0.426271i
$41$	5.83276			0.910925			0.455462	−	0.890255i	$-0.349474\pi$
$41$	5.83276			0.910925			0.455462	+	0.890255i	$0.349474\pi$
$42$	0.639303	+	6.22041i	0.0986466	+	0.959830i
$43$			0.475562i			0.0725225i	0.999342	+	0.0362613i	$0.0115449\pi$
$43$			0.475562i			0.0725225i	−0.999342	+	0.0362613i	$0.988455\pi$
$44$	2.28917	+	11.0192i	0.345105	+	1.66120i
$45$		−	1.42166i		−	0.211929i
$46$	−2.28917	+	0.235269i	−0.337519	+	0.0346886i
$47$	−4.68111			−0.682810			−0.341405	−	0.939916i	$-0.610903\pi$
$47$	−4.68111			−0.682810			−0.341405	+	0.939916i	$0.610903\pi$
$48$	3.35013	+	7.71513i	0.483550	+	1.11358i
$49$	−2.57834			−0.368334
$50$	−5.62721	+	0.578337i	−0.795808	+	0.0817892i
$51$			2.10278i			0.294447i
$52$	−0.406803	−	1.95819i	−0.0564135	−	0.271552i
$53$			4.57834i			0.628883i	0.949277	+	0.314441i	$0.101817\pi$
$53$			4.57834i			0.628883i	−0.949277	+	0.314441i	$0.898183\pi$
$54$	−0.479859	−	4.66902i	−0.0653005	−	0.635373i
$55$	−5.62721			−0.758773
$56$	5.66902	−	1.79875i	0.757555	−	0.240368i
$57$	8.41110			1.11408
$58$	1.13249	+	11.0192i	0.148704	+	1.44689i
$59$		−	8.67609i		−	1.12953i	−0.825252	−	0.564765i	$-0.808967\pi$
$59$		−	8.67609i		−	1.12953i	0.825252	−	0.564765i	$-0.191033\pi$
$60$	−4.11763	+	0.855416i	−0.531584	+	0.110434i
$61$			12.6761i			1.62301i	0.584348	+	0.811503i	$0.301350\pi$
$61$			12.6761i			1.62301i	−0.584348	+	0.811503i	$0.698650\pi$
$62$	−13.5436	+	1.39194i	−1.72004	+	0.176777i
$63$	2.98944			0.376634
$64$	6.53653	−	4.61235i	0.817066	−	0.576544i
$65$	1.00000			0.124035
$66$	16.6464	−	1.71083i	2.04903	−	0.210589i
$67$		−	12.2056i		−	1.49115i	−0.666424	−	0.745573i	$-0.732176\pi$
$67$		−	12.2056i		−	1.49115i	0.666424	−	0.745573i	$-0.267824\pi$
$68$	1.95819	−	0.406803i	0.237466	−	0.0493321i
$69$			3.42166i			0.411920i
$70$	0.304028	+	2.95819i	0.0363383	+	0.353571i
$71$	−9.15165			−1.08610			−0.543051	−	0.839700i	$-0.682731\pi$
$71$	−9.15165			−1.08610			−0.543051	+	0.839700i	$0.682731\pi$
$72$	3.83276	−	1.21611i	0.451695	−	0.143320i
$73$	−2.57834			−0.301772			−0.150886	−	0.988551i	$-0.548213\pi$
$73$	−2.57834			−0.301772			−0.150886	+	0.988551i	$0.548213\pi$
$74$	−0.0609658	−	0.593197i	−0.00708713	−	0.0689577i
$75$			8.41110i			0.971230i
$76$	−1.62721	−	7.83276i	−0.186654	−	0.898480i
$77$		−	11.8328i		−	1.34847i
$78$	−2.95819	+	0.304028i	−0.334949	+	0.0344244i
$79$	−14.3033			−1.60925			−0.804624	−	0.593785i	$-0.797633\pi$
$79$	−14.3033			−1.60925			−0.804624	+	0.593785i	$0.797633\pi$
$80$	1.59320	+	3.66902i	0.178125	+	0.410209i
$81$	−11.2439			−1.24932
$82$	−8.20555	+	0.843326i	−0.906151	+	0.0931298i
$83$		−	8.20555i		−	0.900676i	−0.892858	−	0.450338i	$-0.851303\pi$
$83$		−	8.20555i		−	0.900676i	0.892858	−	0.450338i	$-0.148697\pi$
$84$	−1.79875	−	8.65846i	−0.196259	−	0.944715i
$85$			1.00000i			0.108465i
$86$	−0.0687588	−	0.669022i	−0.00741445	−	0.0721425i
$87$	16.4705			1.76583
$88$	−4.81361	−	15.1708i	−0.513132	−	1.61721i
$89$	11.2544			1.19297			0.596483	−	0.802625i	$-0.296564\pi$
$89$	11.2544			1.19297			0.596483	+	0.802625i	$0.296564\pi$
$90$	0.205550	+	2.00000i	0.0216669	+	0.210819i
$91$			2.10278i			0.220431i
$92$	3.18639	−	0.661956i	0.332204	−	0.0690136i
$93$			20.2439i			2.09919i
$94$	6.58540	−	0.676815i	0.679233	−	0.0698082i
$95$	4.00000			0.410391
$96$	−5.82847	−	10.3693i	−0.594865	−	1.05831i
$97$	10.6761			1.08399			0.541996	−	0.840381i	$-0.317669\pi$
$97$	10.6761			1.08399			0.541996	+	0.840381i	$0.317669\pi$
$98$	3.62721	−	0.372787i	0.366404	−	0.0376572i
$99$		−	8.00000i		−	0.804030i
$100$	7.83276	−	1.62721i	0.783276	−	0.162721i
$101$		−	9.15667i		−	0.911123i	−0.890204	−	0.455562i	$-0.849438\pi$
$101$		−	9.15667i		−	0.911123i	0.890204	−	0.455562i	$-0.150562\pi$
$102$	−0.304028	−	2.95819i	−0.0301033	−	0.292905i
$103$	5.36222			0.528356			0.264178	−	0.964474i	$-0.414899\pi$
$103$	5.36222			0.528356			0.264178	+	0.964474i	$0.414899\pi$
$104$	0.855416	+	2.69597i	0.0838804	+	0.264362i
$105$	4.42166			0.431510
$106$	−0.661956	−	6.44082i	−0.0642948	−	0.625588i
$107$			6.37279i			0.616081i	0.951373	+	0.308040i	$0.0996732\pi$
$107$			6.37279i			0.616081i	−0.951373	+	0.308040i	$0.900327\pi$
$108$	1.35013	+	6.49902i	0.129917	+	0.625368i
$109$			14.0872i			1.34931i	0.738134	+	0.674654i	$0.235707\pi$
$109$			14.0872i			1.34931i	−0.738134	+	0.674654i	$0.764293\pi$
$110$	7.91638	−	0.813607i	0.754797	−	0.0775743i
$111$	−0.886662			−0.0841583
$112$	−7.71513	+	3.35013i	−0.729011	+	0.316558i
$113$	−4.84333			−0.455622			−0.227811	−	0.973705i	$-0.573157\pi$
$113$	−4.84333			−0.455622			−0.227811	+	0.973705i	$0.573157\pi$
$114$	−11.8328	+	1.21611i	−1.10824	+	0.113899i
$115$			1.62721i			0.151738i
$116$	−3.18639	−	15.3380i	−0.295849	−	1.42410i
$117$			1.42166i			0.131433i
$118$	1.25443	+	12.2056i	0.115479	+	1.12361i
$119$	−2.10278			−0.192761
$120$	5.66902	−	1.79875i	0.517509	−	0.164202i
$121$	−20.6655			−1.87868
$122$	−1.83276	−	17.8328i	−0.165931	−	1.61450i
$123$			12.2650i			1.10590i
$124$	18.8519	−	3.91638i	1.69295	−	0.351701i
$125$			9.00000i			0.804984i
$126$	−4.20555	+	0.432226i	−0.374660	+	0.0385057i
$127$	10.0383			0.890756			0.445378	−	0.895343i	$-0.353069\pi$
$127$	10.0383			0.890756			0.445378	+	0.895343i	$0.353069\pi$
$128$	−8.52873	+	7.43375i	−0.753841	+	0.657057i
$129$	−1.00000			−0.0880451
$130$	−1.40680	+	0.144584i	−0.123385	+	0.0126809i
$131$		−	8.47556i		−	0.740513i	−0.928929	−	0.370257i	$-0.879270\pi$
$131$		−	8.47556i		−	0.740513i	0.928929	−	0.370257i	$-0.120730\pi$
$132$	−23.1708	+	4.81361i	−2.01676	+	0.418971i
$133$			8.41110i			0.729335i
$134$	1.76473	+	17.1708i	0.152450	+	1.48333i
$135$	−3.31889			−0.285644
$136$	−2.69597	+	0.855416i	−0.231178	+	0.0733513i
$137$	−19.0872			−1.63073			−0.815364	−	0.578948i	$-0.803463\pi$
$137$	−19.0872			−1.63073			−0.815364	+	0.578948i	$0.803463\pi$
$138$	−0.494719	−	4.81361i	−0.0421132	−	0.409761i
$139$		−	3.99498i		−	0.338850i	−0.985543	−	0.169425i	$-0.945809\pi$
$139$		−	3.99498i		−	0.338850i	0.985543	−	0.169425i	$-0.0541910\pi$
$140$	−0.855416	−	4.11763i	−0.0722958	−	0.348004i
$141$		−	9.84333i		−	0.828958i
$142$	12.8746	−	1.32318i	1.08041	−	0.111039i
$143$	5.62721			0.470571
$144$	−5.21611	+	2.26499i	−0.434676	+	0.188749i
$145$	7.83276			0.650476
$146$	3.62721	−	0.372787i	0.300190	−	0.0308521i
$147$		−	5.42166i		−	0.447171i
$148$	0.171534	+	0.825696i	0.0141000	+	0.0678718i
$149$			3.15667i			0.258605i	0.991605	+	0.129302i	$0.0412738\pi$
$149$			3.15667i			0.258605i	−0.991605	+	0.129302i	$0.958726\pi$
$150$	−1.21611	−	11.8328i	−0.0992952	−	0.966141i
$151$	−2.36776			−0.192686			−0.0963429	−	0.995348i	$-0.530715\pi$
$151$	−2.36776			−0.192686			−0.0963429	+	0.995348i	$0.530715\pi$
$152$	3.42166	+	10.7839i	0.277534	+	0.874689i
$153$	−1.42166			−0.114935
$154$	1.71083	+	16.6464i	0.137863	+	1.34140i
$155$			9.62721i			0.773276i
$156$	4.11763	−	0.855416i	0.329675	−	0.0684881i
$157$		−	15.9305i		−	1.27139i	−0.771939	−	0.635697i	$-0.780713\pi$
$157$		−	15.9305i		−	1.27139i	0.771939	−	0.635697i	$-0.219287\pi$
$158$	20.1219	−	2.06803i	1.60081	−	0.164524i
$159$	−9.62721			−0.763488
$160$	−2.77180	−	4.93124i	−0.219130	−	0.389849i
$161$	−3.42166			−0.269665
$162$	15.8179	−	1.62569i	1.24277	−	0.127726i
$163$			3.52946i			0.276449i	0.990401	+	0.138224i	$0.0441395\pi$
$163$			3.52946i			0.276449i	−0.990401	+	0.138224i	$0.955860\pi$
$164$	11.4217	−	2.37279i	0.891882	−	0.185284i
$165$		−	11.8328i		−	0.921179i
$166$	1.18639	+	11.5436i	0.0920820	+	0.895957i
$167$	15.7250			1.21683			0.608417	−	0.793617i	$-0.291805\pi$
$167$	15.7250			1.21683			0.608417	+	0.793617i	$0.291805\pi$
$168$	3.78236	+	11.9207i	0.291815	+	0.919700i
$169$	−1.00000			−0.0769231
$170$	−0.144584	−	1.40680i	−0.0110891	−	0.107897i
$171$			5.68665i			0.434869i
$172$	0.193460	+	0.931241i	0.0147512	+	0.0710065i
$173$		−	14.4111i		−	1.09566i	−0.836591	−	0.547828i	$-0.815455\pi$
$173$		−	14.4111i		−	1.09566i	0.836591	−	0.547828i	$-0.184545\pi$
$174$	−23.1708	+	2.38138i	−1.75657	+	0.180532i
$175$	−8.41110			−0.635819
$176$	8.96526	+	20.6464i	0.675782	+	1.55628i
$177$	18.2439			1.37129
$178$	−15.8328	+	1.62721i	−1.18672	+	0.121965i
$179$		−	1.69167i		−	0.126442i	−0.998000	−	0.0632209i	$-0.979863\pi$
$179$		−	1.69167i		−	0.126442i	0.998000	−	0.0632209i	$-0.0201373\pi$
$180$	−0.578337	−	2.78389i	−0.0431067	−	0.207499i
$181$			17.2544i			1.28251i	0.767327	+	0.641256i	$0.221586\pi$
$181$			17.2544i			1.28251i	−0.767327	+	0.641256i	$0.778414\pi$
$182$	−0.304028	−	2.95819i	−0.0225361	−	0.219276i
$183$	−26.6550			−1.97039
$184$	−4.38692	+	1.39194i	−0.323408	+	0.102615i
$185$	−0.421663			−0.0310013
$186$	−2.92694	−	28.4791i	−0.214614	−	2.08819i
$187$			5.62721i			0.411503i
$188$	−9.16651	+	1.90429i	−0.668536	+	0.138885i
$189$		−	6.97887i		−	0.507638i
$190$	−5.62721	+	0.578337i	−0.408241	+	0.0419570i
$191$	6.03831			0.436917			0.218459	−	0.975846i	$-0.429897\pi$
$191$	6.03831			0.436917			0.218459	+	0.975846i	$0.429897\pi$
$192$	9.69874	+	13.7448i	0.699946	+	0.991949i
$193$	13.2544			0.954074			0.477037	−	0.878883i	$-0.341711\pi$
$193$	13.2544			0.954074			0.477037	+	0.878883i	$0.341711\pi$
$194$	−15.0192	+	1.54359i	−1.07831	+	0.110824i
$195$			2.10278i			0.150583i
$196$	−5.04888	+	1.04888i	−0.360634	+	0.0749197i
$197$		−	22.9305i		−	1.63373i	−0.576828	−	0.816866i	$-0.695710\pi$
$197$		−	22.9305i		−	1.63373i	0.576828	−	0.816866i	$-0.304290\pi$
$198$	1.15667	+	11.2544i	0.0822013	+	0.799817i
$199$	−0.951124			−0.0674234			−0.0337117	−	0.999432i	$-0.510733\pi$
$199$	−0.951124			−0.0674234			−0.0337117	+	0.999432i	$0.510733\pi$
$200$	−10.7839	+	3.42166i	−0.762536	+	0.241948i
$201$	25.6655			1.81031
$202$	1.32391	+	12.8816i	0.0931501	+	0.906349i
$203$			16.4705i			1.15601i
$204$	0.855416	+	4.11763i	0.0598911	+	0.288292i
$205$			5.83276i			0.407378i
$206$	−7.54359	+	0.775293i	−0.525587	+	0.0540172i
$207$	−2.31335			−0.160789
$208$	−1.59320	−	3.66902i	−0.110468	−	0.254401i
$209$	22.5089			1.55697
$210$	−6.22041	+	0.639303i	−0.429249	+	0.0441161i
$211$		−	11.7300i		−	0.807526i	−0.914864	−	0.403763i	$-0.867702\pi$
$211$		−	11.7300i		−	0.807526i	0.914864	−	0.403763i	$-0.132298\pi$
$212$	1.86248	+	8.96526i	0.127916	+	0.615736i
$213$		−	19.2439i		−	1.31857i
$214$	−0.921405	−	8.96526i	−0.0629859	−	0.612852i
$215$	−0.475562			−0.0324331
$216$	−2.83903	−	8.94763i	−0.193171	−	0.608809i
$217$	−20.2439			−1.37424
$218$	−2.03679	−	19.8179i	−0.137949	−	1.34224i
$219$		−	5.42166i		−	0.366362i
$220$	−11.0192	+	2.28917i	−0.742911	+	0.154336i
$221$		−	1.00000i		−	0.0672673i
$222$	1.24736	−	0.128197i	0.0837173	−	0.00860405i
$223$	4.68111			0.313470			0.156735	−	0.987641i	$-0.449903\pi$
$223$	4.68111			0.313470			0.156735	+	0.987641i	$0.449903\pi$
$224$	10.3693	−	5.82847i	0.692827	−	0.389431i
$225$	−5.68665			−0.379110
$226$	6.81361	−	0.700269i	0.453234	−	0.0465812i
$227$		−	11.7350i		−	0.778880i	−0.921052	−	0.389440i	$-0.872669\pi$
$227$		−	11.7350i		−	0.778880i	0.921052	−	0.389440i	$-0.127331\pi$
$228$	16.4705	−	3.42166i	1.09079	−	0.226605i
$229$			5.84333i			0.386138i	0.981185	+	0.193069i	$0.0618441\pi$
$229$			5.84333i			0.386138i	−0.981185	+	0.193069i	$0.938156\pi$
$230$	−0.235269	−	2.28917i	−0.0155132	−	0.150943i
$231$	24.8816			1.63709
$232$	6.70027	+	21.1169i	0.439894	+	1.38639i
$233$	−25.2439			−1.65378			−0.826890	−	0.562363i	$-0.809892\pi$
$233$	−25.2439			−1.65378			−0.826890	+	0.562363i	$0.809892\pi$
$234$	−0.205550	−	2.00000i	−0.0134372	−	0.130744i
$235$		−	4.68111i		−	0.305362i
$236$	−3.52946	−	16.9894i	−0.229748	−	1.10592i
$237$		−	30.0766i		−	1.95369i
$238$	2.95819	−	0.304028i	0.191751	−	0.0197072i
$239$	−11.4650			−0.741609			−0.370805	−	0.928711i	$-0.620918\pi$
$239$	−11.4650			−0.741609			−0.370805	+	0.928711i	$0.620918\pi$
$240$	−7.71513	+	3.35013i	−0.498009	+	0.216250i
$241$	−2.09775			−0.135128			−0.0675640	−	0.997715i	$-0.521523\pi$
$241$	−2.09775			−0.135128			−0.0675640	+	0.997715i	$0.521523\pi$
$242$	29.0723	−	2.98791i	1.86884	−	0.192070i
$243$		−	13.6867i		−	0.877999i
$244$	5.15667	+	24.8222i	0.330122	+	1.58908i
$245$		−	2.57834i		−	0.164724i
$246$	−1.77332	−	17.2544i	−0.113063	−	1.10010i
$247$	−4.00000			−0.254514
$248$	−25.9547	+	8.23527i	−1.64812	+	0.522940i
$249$	17.2544			1.09345
$250$	−1.30126	−	12.6612i	−0.0822988	−	0.800766i
$251$			14.7839i			0.933151i	0.884481	+	0.466575i	$0.154512\pi$
$251$			14.7839i			0.933151i	−0.884481	+	0.466575i	$0.845488\pi$
$252$	5.85389	−	1.21611i	0.368760	−	0.0766079i
$253$			9.15667i			0.575675i
$254$	−14.1219	+	1.45138i	−0.886089	+	0.0910678i
$255$	−2.10278			−0.131681
$256$	10.9234	−	11.6909i	0.682716	−	0.730684i
$257$	3.31335			0.206681			0.103340	−	0.994646i	$-0.467047\pi$
$257$	3.31335			0.206681			0.103340	+	0.994646i	$0.467047\pi$
$258$	1.40680	−	0.144584i	0.0875837	−	0.00900142i
$259$		−	0.886662i		−	0.0550945i
$260$	1.95819	−	0.406803i	0.121442	−	0.0252289i
$261$			11.1355i			0.689273i
$262$	1.22543	+	11.9234i	0.0757075	+	0.736633i
$263$	17.4217			1.07427			0.537133	−	0.843498i	$-0.319507\pi$
$263$	17.4217			1.07427			0.537133	+	0.843498i	$0.319507\pi$
$264$	31.9008	−	10.1219i	1.96336	−	0.622962i
$265$	−4.57834			−0.281245
$266$	−1.21611	−	11.8328i	−0.0745647	−	0.725513i
$267$			23.6655i			1.44831i
$268$	−4.96526	−	23.9008i	−0.303301	−	1.45997i
$269$		−	3.32391i		−	0.202662i	−0.994853	−	0.101331i	$-0.967690\pi$
$269$		−	3.32391i		−	0.202662i	0.994853	−	0.101331i	$-0.0323102\pi$
$270$	4.66902	−	0.479859i	0.284148	−	0.0292033i
$271$	−14.0333			−0.852462			−0.426231	−	0.904614i	$-0.640159\pi$
$271$	−14.0333			−0.852462			−0.426231	+	0.904614i	$0.640159\pi$
$272$	3.66902	−	1.59320i	0.222467	−	0.0966017i
$273$	−4.42166			−0.267611
$274$	26.8519	−	2.75971i	1.62218	−	0.166720i
$275$			22.5089i			1.35733i
$276$	1.39194	+	6.70027i	0.0837852	+	0.403309i
$277$		−	1.01056i		−	0.0607188i	−0.999539	−	0.0303594i	$-0.990335\pi$
$277$		−	1.01056i		−	0.0607188i	0.999539	−	0.0303594i	$-0.00966519\pi$
$278$	0.577611	+	5.62015i	0.0346428	+	0.337074i
$279$	−13.6867			−0.819398
$280$	1.79875	+	5.66902i	0.107496	+	0.338789i
$281$	3.58890			0.214096			0.107048	−	0.994254i	$-0.465860\pi$
$281$	3.58890			0.214096			0.107048	+	0.994254i	$0.465860\pi$
$282$	1.42319	+	13.8476i	0.0847497	+	0.824614i
$283$		−	13.2927i		−	0.790171i	−0.918644	−	0.395086i	$-0.870715\pi$
$283$		−	13.2927i		−	0.790171i	0.918644	−	0.395086i	$-0.129285\pi$
$284$	−17.9207	+	3.72292i	−1.06340	+	0.220915i
$285$			8.41110i			0.498231i
$286$	−7.91638	+	0.813607i	−0.468105	+	0.0481096i
$287$	−12.2650			−0.723979
$288$	7.01056	−	3.94056i	0.413101	−	0.232200i
$289$	−16.0000			−0.941176
$290$	−11.0192	+	1.13249i	−0.647067	+	0.0665024i
$291$			22.4494i			1.31601i
$292$	−5.04888	+	1.04888i	−0.295463	+	0.0613808i
$293$			9.24386i			0.540032i	0.962856	+	0.270016i	$0.0870290\pi$
$293$			9.24386i			0.540032i	−0.962856	+	0.270016i	$0.912971\pi$
$294$	0.783887	+	7.62721i	0.0457172	+	0.444828i
$295$	8.67609			0.505141
$296$	−0.360697	−	1.13679i	−0.0209651	−	0.0660747i
$297$	−18.6761			−1.08370
$298$	−0.456405	−	4.44082i	−0.0264389	−	0.257250i
$299$		−	1.62721i		−	0.0941042i
$300$	3.42166	+	16.4705i	0.197550	+	0.950927i
$301$		−	1.00000i		−	0.0576390i
$302$	3.33098	−	0.342341i	0.191676	−	0.0196995i
$303$	19.2544			1.10614
$304$	−6.37279	−	14.6761i	−0.365504	−	0.841731i
$305$	−12.6761			−0.725831
$306$	2.00000	−	0.205550i	0.114332	−	0.0117505i
$307$			8.26499i			0.471708i	0.971789	+	0.235854i	$0.0757887\pi$
$307$			8.26499i			0.471708i	−0.971789	+	0.235854i	$0.924211\pi$
$308$	−4.81361	−	23.1708i	−0.274281	−	1.32028i
$309$			11.2756i			0.641444i
$310$	−1.39194	−	13.5436i	−0.0790571	−	0.769224i
$311$	−23.6655			−1.34195			−0.670974	−	0.741480i	$-0.734124\pi$
$311$	−23.6655			−1.34195			−0.670974	+	0.741480i	$0.734124\pi$
$312$	−5.66902	+	1.79875i	−0.320945	+	0.101834i
$313$	−0.735011			−0.0415453			−0.0207726	−	0.999784i	$-0.506613\pi$
$313$	−0.735011			−0.0415453			−0.0207726	+	0.999784i	$0.506613\pi$
$314$	2.30330	+	22.4111i	0.129983	+	1.26473i
$315$			2.98944i			0.168436i
$316$	−28.0086	+	5.81863i	−1.57561	+	0.327323i
$317$			11.1567i			0.626621i	0.949651	+	0.313311i	$0.101438\pi$
$317$			11.1567i			0.626621i	−0.949651	+	0.313311i	$0.898562\pi$
$318$	13.5436	−	1.39194i	0.759487	−	0.0780563i
$319$	44.0766			2.46782
$320$	4.61235	+	6.53653i	0.257838	+	0.365403i
$321$	−13.4005			−0.747945
$322$	4.81361	−	0.494719i	0.268252	−	0.0275696i
$323$		−	4.00000i		−	0.222566i
$324$	−22.0176	+	4.57404i	−1.22320	+	0.254113i
$325$		−	4.00000i		−	0.221880i
$326$	−0.510305	−	4.96526i	−0.0282632	−	0.275000i
$327$	−29.6222			−1.63811
$328$	−15.7250	+	4.98944i	−0.868266	+	0.275496i
$329$	9.84333			0.542680
$330$	1.71083	+	16.6464i	0.0941782	+	0.916352i
$331$		−	7.79445i		−	0.428422i	−0.976787	−	0.214211i	$-0.931282\pi$
$331$		−	7.79445i		−	0.428422i	0.976787	−	0.214211i	$-0.0687180\pi$
$332$	−3.33804	−	16.0680i	−0.183199	−	0.881848i
$333$		−	0.599463i		−	0.0328503i
$334$	−22.1219	+	2.27358i	−1.21046	+	0.124405i
$335$	12.2056			0.666860
$336$	−7.04458	−	16.2232i	−0.384313	−	0.885047i
$337$	19.2439			1.04828			0.524140	−	0.851632i	$-0.324387\pi$
$337$	19.2439			1.04828			0.524140	+	0.851632i	$0.324387\pi$
$338$	1.40680	−	0.144584i	0.0765200	−	0.00786435i
$339$		−	10.1844i		−	0.553142i
$340$	0.406803	+	1.95819i	0.0220620	+	0.106198i
$341$			54.1744i			2.93371i
$342$	−0.822200	−	8.00000i	−0.0444595	−	0.432590i
$343$	20.1411			1.08752
$344$	−0.406803	−	1.28210i	−0.0219334	−	0.0691263i
$345$	−3.42166			−0.184216
$346$	2.08362	+	20.2736i	0.112016	+	1.08991i
$347$			32.6116i			1.75068i	0.483504	+	0.875342i	$0.339364\pi$
$347$			32.6116i			1.75068i	−0.483504	+	0.875342i	$0.660636\pi$
$348$	32.2525	−	6.70027i	1.72891	−	0.359172i
$349$			31.8222i			1.70340i	0.524027	+	0.851702i	$0.324429\pi$
$349$			31.8222i			1.70340i	−0.524027	+	0.851702i	$0.675571\pi$
$350$	11.8328	−	1.21611i	0.632488	−	0.0650040i
$351$	3.31889			0.177149
$352$	−15.5975	−	27.7491i	−0.831349	−	1.47903i
$353$	20.0978			1.06970			0.534848	−	0.844948i	$-0.320369\pi$
$353$	20.0978			1.06970			0.534848	+	0.844948i	$0.320369\pi$
$354$	−25.6655	+	2.63778i	−1.36411	+	0.140196i
$355$		−	9.15165i		−	0.485719i
$356$	22.0383	−	4.57834i	1.16803	−	0.242651i
$357$		−	4.42166i		−	0.234019i
$358$	0.244590	+	2.37985i	0.0129270	+	0.125779i
$359$	8.68614			0.458437			0.229218	−	0.973375i	$-0.426383\pi$
$359$	8.68614			0.458437			0.229218	+	0.973375i	$0.426383\pi$
$360$	1.21611	+	3.83276i	0.0640948	+	0.202004i
$361$	3.00000			0.157895
$362$	−2.49472	−	24.2736i	−0.131120	−	1.27579i
$363$		−	43.4550i		−	2.28079i
$364$	0.855416	+	4.11763i	0.0448360	+	0.215823i
$365$		−	2.57834i		−	0.134956i
$366$	37.4983	−	3.85389i	1.96007	−	0.201446i
$367$	−9.36222			−0.488704			−0.244352	−	0.969687i	$-0.578575\pi$
$367$	−9.36222			−0.488704			−0.244352	+	0.969687i	$0.578575\pi$
$368$	5.97028	−	2.59247i	0.311222	−	0.135142i
$369$	−8.29222			−0.431676
$370$	0.593197	−	0.0609658i	0.0308388	−	0.00316946i
$371$		−	9.62721i		−	0.499820i
$372$	8.23527	+	39.6413i	0.426979	+	2.05531i
$373$		−	21.9789i		−	1.13802i	−0.822330	−	0.569011i	$-0.807326\pi$
$373$		−	21.9789i		−	1.13802i	0.822330	−	0.569011i	$-0.192674\pi$
$374$	−0.813607	−	7.91638i	−0.0420706	−	0.409346i
$375$	−18.9250			−0.977282
$376$	12.6201	−	4.00430i	0.650834	−	0.206506i
$377$	−7.83276			−0.403408
$378$	1.00904	+	9.81790i	0.0518992	+	0.504978i
$379$		−	4.05944i		−	0.208519i	−0.994550	−	0.104260i	$-0.966753\pi$
$379$		−	4.05944i		−	0.208519i	0.994550	−	0.104260i	$-0.0332473\pi$
$380$	7.83276	−	1.62721i	0.401812	−	0.0834743i
$381$			21.1083i			1.08141i
$382$	−8.49472	+	0.873045i	−0.434628	+	0.0446689i
$383$	−7.39551			−0.377893			−0.188947	−	0.981987i	$-0.560507\pi$
$383$	−7.39551			−0.377893			−0.188947	+	0.981987i	$0.560507\pi$
$384$	−15.6315	−	17.9340i	−0.797692	−	0.915191i
$385$	11.8328			0.603053
$386$	−18.6464	+	1.91638i	−0.949075	+	0.0975413i
$387$		−	0.676089i		−	0.0343675i
$388$	20.9058	−	4.34307i	1.06133	−	0.220486i
$389$		−	13.4217i		−	0.680505i	−0.940334	−	0.340253i	$-0.889487\pi$
$389$		−	13.4217i		−	0.680505i	0.940334	−	0.340253i	$-0.110513\pi$
$390$	−0.304028	−	2.95819i	−0.0153951	−	0.149794i
$391$	1.62721			0.0822917
$392$	6.95112	−	2.20555i	0.351085	−	0.111397i
$393$	17.8222			0.899011
$394$	3.31539	+	32.2587i	0.167027	+	1.62517i
$395$		−	14.3033i		−	0.719677i
$396$	−3.25443	−	15.6655i	−0.163541	−	0.787222i
$397$		−	33.1355i		−	1.66303i	−0.555506	−	0.831513i	$-0.687475\pi$
$397$		−	33.1355i		−	1.66303i	0.555506	−	0.831513i	$-0.312525\pi$
$398$	1.33804	−	0.137518i	0.0670701	−	0.00689313i
$399$	−17.6867			−0.885440
$400$	14.6761	−	6.37279i	0.733804	−	0.318639i
$401$	−14.2650			−0.712360			−0.356180	−	0.934417i	$-0.615921\pi$
$401$	−14.2650			−0.712360			−0.356180	+	0.934417i	$0.615921\pi$
$402$	−36.1063	+	3.71083i	−1.80082	+	0.185079i
$403$		−	9.62721i		−	0.479566i
$404$	−3.72496	−	17.9305i	−0.185324	−	0.892076i
$405$		−	11.2439i		−	0.558712i
$406$	−2.38138	−	23.1708i	−0.118186	−	1.14995i
$407$	−2.37279			−0.117615
$408$	−1.79875	−	5.66902i	−0.0890512	−	0.280658i
$409$	5.93051			0.293245			0.146623	−	0.989193i	$-0.453160\pi$
$409$	5.93051			0.293245			0.146623	+	0.989193i	$0.453160\pi$
$410$	−0.843326	−	8.20555i	−0.0416489	−	0.405243i
$411$		−	40.1361i		−	1.97977i
$412$	10.5003	−	2.18137i	0.517311	−	0.107468i
$413$			18.2439i			0.897722i
$414$	3.25443	−	0.334474i	0.159946	−	0.0164385i
$415$	8.20555			0.402795
$416$	2.77180	+	4.93124i	0.135899	+	0.241774i
$417$	8.40054			0.411376
$418$	−31.6655	+	3.25443i	−1.54881	+	0.159179i
$419$		−	25.5628i		−	1.24882i	−0.781096	−	0.624411i	$-0.785339\pi$
$419$		−	25.5628i		−	1.24882i	0.781096	−	0.624411i	$-0.214661\pi$
$420$	8.65846	−	1.79875i	0.422490	−	0.0877699i
$421$		−	26.6655i		−	1.29960i	−0.760106	−	0.649799i	$-0.774853\pi$
$421$		−	26.6655i		−	1.29960i	0.760106	−	0.649799i	$-0.225147\pi$
$422$	1.69597	+	16.5018i	0.0825586	+	0.803294i
$423$	6.65496			0.323575
$424$	−3.91638	−	12.3431i	−0.190196	−	0.599432i
$425$	4.00000			0.194029
$426$	2.78236	+	27.0723i	0.134806	+	1.31166i
$427$		−	26.6550i		−	1.28992i
$428$	2.59247	+	12.4791i	0.125312	+	0.603202i
$429$			11.8328i			0.571291i
$430$	0.669022	−	0.0687588i	0.0322631	−	0.00331584i
$431$	−12.4061			−0.597580			−0.298790	−	0.954319i	$-0.596583\pi$
$431$	−12.4061			−0.597580			−0.298790	+	0.954319i	$0.596583\pi$
$432$	5.28764	+	12.1771i	0.254402	+	0.585870i
$433$	0.108315			0.00520526			0.00260263	−	0.999997i	$-0.499172\pi$
$433$	0.108315			0.00520526			0.00260263	+	0.999997i	$0.499172\pi$
$434$	28.4791	−	2.92694i	1.36704	−	0.140498i
$435$			16.4705i			0.789702i
$436$	5.73071	+	27.5854i	0.274451	+	1.32110i
$437$		−	6.50885i		−	0.311361i
$438$	0.783887	+	7.62721i	0.0374556	+	0.364442i
$439$	−6.24386			−0.298003			−0.149002	−	0.988837i	$-0.547606\pi$
$439$	−6.24386			−0.298003			−0.149002	+	0.988837i	$0.547606\pi$
$440$	15.1708	−	4.81361i	0.723240	−	0.229480i
$441$	3.66553			0.174549
$442$	0.144584	+	1.40680i	0.00687717	+	0.0669148i
$443$			14.0333i			0.666742i	0.942796	+	0.333371i	$0.108186\pi$
$443$			14.0333i			0.666742i	−0.942796	+	0.333371i	$0.891814\pi$
$444$	−1.73625	+	0.360697i	−0.0823990	+	0.0171179i
$445$			11.2544i			0.533511i
$446$	−6.58540	+	0.676815i	−0.311828	+	0.0320481i
$447$	−6.63778			−0.313956
$448$	−13.7448	+	9.69874i	−0.649383	+	0.458222i
$449$	5.51941			0.260477			0.130239	−	0.991483i	$-0.458426\pi$
$449$	5.51941			0.260477			0.130239	+	0.991483i	$0.458426\pi$
$450$	8.00000	−	0.822200i	0.377124	−	0.0387589i
$451$			32.8222i			1.54554i
$452$	−9.48416	+	1.97028i	−0.446097	+	0.0926742i
$453$		−	4.97887i		−	0.233928i
$454$	1.69670	+	16.5089i	0.0796300	+	0.774799i
$455$	−2.10278			−0.0985796
$456$	−22.6761	+	7.19499i	−1.06191	+	0.336936i
$457$	−20.0766			−0.939145			−0.469572	−	0.882894i	$-0.655592\pi$
$457$	−20.0766			−0.939145			−0.469572	+	0.882894i	$0.655592\pi$
$458$	−0.844853	−	8.22041i	−0.0394774	−	0.384115i
$459$			3.31889i			0.154912i
$460$	0.661956	+	3.18639i	0.0308638	+	0.148566i
$461$		−	12.4217i		−	0.578535i	−0.957248	−	0.289267i	$-0.906588\pi$
$461$		−	12.4217i		−	0.578535i	0.957248	−	0.289267i	$-0.0934116\pi$
$462$	−35.0036	+	3.59749i	−1.62851	+	0.167371i
$463$	−11.1184			−0.516714			−0.258357	−	0.966050i	$-0.583181\pi$
$463$	−11.1184			−0.516714			−0.258357	+	0.966050i	$0.583181\pi$
$464$	−12.4791	−	28.7386i	−0.579329	−	1.33416i
$465$	−20.2439			−0.938787
$466$	35.5131	−	3.64987i	1.64511	−	0.169077i
$467$			1.09724i			0.0507740i	0.999678	+	0.0253870i	$0.00808180\pi$
$467$			1.09724i			0.0507740i	−0.999678	+	0.0253870i	$0.991918\pi$
$468$	0.578337	+	2.78389i	0.0267336	+	0.128685i
$469$			25.6655i			1.18512i
$470$	0.676815	+	6.58540i	0.0312192	+	0.303762i
$471$	33.4983			1.54352
$472$	7.42166	+	23.3905i	0.341610	+	1.07663i
$473$	−2.67609			−0.123047
$474$	4.34861	+	42.3119i	0.199738	+	1.94345i
$475$		−	16.0000i		−	0.734130i
$476$	−4.11763	+	0.855416i	−0.188731	+	0.0392079i
$477$		−	6.50885i		−	0.298020i
$478$	16.1290	−	1.65766i	0.737723	−	0.0758195i
$479$	14.9844			0.684655			0.342328	−	0.939581i	$-0.388785\pi$
$479$	14.9844			0.684655			0.342328	+	0.939581i	$0.388785\pi$
$480$	10.3693	−	5.82847i	0.473291	−	0.266032i
$481$	0.421663			0.0192262
$482$	2.95112	−	0.303302i	0.134420	−	0.0138150i
$483$		−	7.19499i		−	0.327383i
$484$	−40.4670	+	8.40680i	−1.83941	+	0.382127i
$485$			10.6761i			0.484776i
$486$	1.97887	+	19.2544i	0.0897636	+	0.873399i
$487$	−23.1950			−1.05107			−0.525533	−	0.850773i	$-0.676134\pi$
$487$	−23.1950			−1.05107			−0.525533	+	0.850773i	$0.676134\pi$
$488$	−10.8433	−	34.1744i	−0.490854	−	1.54700i
$489$	−7.42166			−0.335619
$490$	0.372787	+	3.62721i	0.0168408	+	0.163861i
$491$			22.9844i			1.03727i	0.854995	+	0.518636i	$0.173560\pi$
$491$			22.9844i			1.03727i	−0.854995	+	0.518636i	$0.826440\pi$
$492$	4.98944	+	24.0172i	0.224941	+	1.08278i
$493$		−	7.83276i		−	0.352770i
$494$	5.62721	−	0.578337i	0.253180	−	0.0260206i
$495$	8.00000			0.359573
$496$	35.3225	−	15.3380i	1.58603	−	0.688699i
$497$	19.2439			0.863205
$498$	−24.2736	+	2.49472i	−1.08773	+	0.111791i
$499$		−	13.4983i		−	0.604266i	−0.953266	−	0.302133i	$-0.902301\pi$
$499$		−	13.4983i		−	0.604266i	0.953266	−	0.302133i	$-0.0976987\pi$
$500$	3.66123	+	17.6237i	0.163735	+	0.788157i
$501$			33.0661i			1.47728i
$502$	−2.13752	−	20.7980i	−0.0954021	−	0.928261i
$503$	17.5678			0.783308			0.391654	−	0.920112i	$-0.371903\pi$
$503$	17.5678			0.783308			0.391654	+	0.920112i	$0.371903\pi$
$504$	−8.05944	+	2.55721i	−0.358996	+	0.113907i
$505$	9.15667			0.407467
$506$	−1.32391	−	12.8816i	−0.0588550	−	0.572659i
$507$		−	2.10278i		−	0.0933875i
$508$	19.6569	−	4.08362i	0.872135	−	0.181181i
$509$			8.31335i			0.368483i	0.982881	+	0.184241i	$0.0589828\pi$
$509$			8.31335i			0.368483i	−0.982881	+	0.184241i	$0.941017\pi$
$510$	2.95819	−	0.304028i	0.130991	−	0.0134626i
$511$	5.42166			0.239840
$512$	−13.6768	+	18.0262i	−0.604436	+	0.796654i
$513$	13.2756			0.586130
$514$	−4.66123	+	0.479058i	−0.205598	+	0.0211303i
$515$			5.36222i			0.236288i
$516$	−1.95819	+	0.406803i	−0.0862045	+	0.0179085i
$517$		−	26.3416i		−	1.15850i
$518$	0.128197	+	1.24736i	0.00563267	+	0.0548058i
$519$	30.3033			1.33017
$520$	−2.69597	+	0.855416i	−0.118226	+	0.0375125i
$521$	16.0872			0.704793			0.352396	−	0.935851i	$-0.385367\pi$
$521$	16.0872			0.704793			0.352396	+	0.935851i	$0.385367\pi$
$522$	−1.61003	−	15.6655i	−0.0704689	−	0.685661i
$523$		−	9.09724i		−	0.397794i	−0.980020	−	0.198897i	$-0.936264\pi$
$523$		−	9.09724i		−	0.397794i	0.980020	−	0.198897i	$-0.0637360\pi$
$524$	−3.44789	−	16.5968i	−0.150622	−	0.725033i
$525$		−	17.6867i		−	0.771909i
$526$	−24.5089	+	2.51890i	−1.06864	+	0.109829i
$527$	9.62721			0.419368
$528$	−43.4147	+	18.8519i	−1.88938	+	0.820424i
$529$	−20.3522			−0.884877
$530$	6.44082	−	0.661956i	0.279771	−	0.0287535i
$531$			12.3345i			0.535271i
$532$	3.42166	+	16.4705i	0.148348	+	0.714088i
$533$		−	5.83276i		−	0.252645i
$534$	−3.42166	−	33.2927i	−0.148070	−	1.44072i
$535$	−6.37279			−0.275520
$536$	10.4408	+	32.9058i	0.450975	+	1.42131i
$537$	3.55721			0.153505
$538$	0.480585	+	4.67609i	0.0207195	+	0.201601i
$539$		−	14.5089i		−	0.624940i
$540$	−6.49902	+	1.35013i	−0.279673	+	0.0581005i
$541$		−	22.0872i		−	0.949602i	−0.880093	−	0.474801i	$-0.842520\pi$
$541$		−	22.0872i		−	0.949602i	0.880093	−	0.474801i	$-0.157480\pi$
$542$	19.7421	−	2.02899i	0.847995	−	0.0871527i
$543$	−36.2822			−1.55702
$544$	−4.93124	+	2.77180i	−0.211425	+	0.118840i
$545$	−14.0872			−0.603429
$546$	6.22041	−	0.639303i	0.266209	−	0.0273596i
$547$			44.2772i			1.89315i	0.322477	+	0.946577i	$0.395484\pi$
$547$			44.2772i			1.89315i	−0.322477	+	0.946577i	$0.604516\pi$
$548$	−37.3764	+	7.76473i	−1.59664	+	0.331693i
$549$		−	18.0211i		−	0.769123i
$550$	−3.25443	−	31.6655i	−0.138769	−	1.35022i
$551$	−31.3311			−1.33475
$552$	−2.92694	−	9.22471i	−0.124579	−	0.392630i
$553$	30.0766			1.27899
$554$	0.146111	+	1.42166i	0.00620768	+	0.0604007i
$555$		−	0.886662i		−	0.0376367i
$556$	−1.62517	−	7.82293i	−0.0689225	−	0.331766i
$557$			36.9094i			1.56390i	0.623341	+	0.781951i	$0.285775\pi$
$557$			36.9094i			1.56390i	−0.623341	+	0.781951i	$0.714225\pi$
$558$	19.2544	−	1.97887i	0.815105	−	0.0837724i
$559$	0.475562			0.0201141
$560$	−3.35013	−	7.71513i	−0.141569	−	0.326024i
$561$	−11.8328			−0.499580
$562$	−5.04888	+	0.518898i	−0.212974	+	0.0218884i
$563$		−	1.28057i		−	0.0539698i	−0.999636	−	0.0269849i	$-0.991409\pi$
$563$		−	1.28057i		−	0.0539698i	0.999636	−	0.0269849i	$-0.00859060\pi$
$564$	−4.00430	−	19.2751i	−0.168611	−	0.811629i
$565$		−	4.84333i		−	0.203760i
$566$	1.92192	+	18.7003i	0.0807844	+	0.786031i
$567$	23.6433			0.992926
$568$	24.6726	−	7.82847i	1.03524	−	0.328475i
$569$	−37.5089			−1.57245			−0.786226	−	0.617938i	$-0.787968\pi$
$569$	−37.5089			−1.57245			−0.786226	+	0.617938i	$0.787968\pi$
$570$	−1.21611	−	11.8328i	−0.0509374	−	0.495620i
$571$			29.7583i			1.24534i	0.782483	+	0.622672i	$0.213953\pi$
$571$			29.7583i			1.24534i	−0.782483	+	0.622672i	$0.786047\pi$
$572$	11.0192	−	2.28917i	0.460734	−	0.0957149i
$573$			12.6972i			0.530434i
$574$	17.2544	−	1.77332i	0.720186	−	0.0740171i
$575$	6.50885			0.271438
$576$	−9.29274	+	6.55721i	−0.387197	+	0.273217i
$577$	−20.4605			−0.851781			−0.425891	−	0.904775i	$-0.640039\pi$
$577$	−20.4605			−0.851781			−0.425891	+	0.904775i	$0.640039\pi$
$578$	22.5089	−	2.31335i	0.936245	−	0.0962226i
$579$			27.8711i			1.15828i
$580$	15.3380	−	3.18639i	0.636878	−	0.132308i
$581$			17.2544i			0.715834i
$582$	−3.24583	−	31.5819i	−0.134544	−	1.30911i
$583$	−25.7633			−1.06701
$584$	6.95112	−	2.20555i	0.287640	−	0.0912663i
$585$	−1.42166			−0.0587785
$586$	−1.33652	−	13.0043i	−0.0552110	−	0.537203i
$587$		−	9.62721i		−	0.397358i	−0.980065	−	0.198679i	$-0.936335\pi$
$587$		−	9.62721i		−	0.397358i	0.980065	−	0.198679i	$-0.0636651\pi$
$588$	−2.20555	−	10.6167i	−0.0909554	−	0.437823i
$589$		−	38.5089i		−	1.58673i
$590$	−12.2056	+	1.25443i	−0.502495	+	0.0516439i
$591$	48.2177			1.98341
$592$	0.671792	+	1.54709i	0.0276105	+	0.0635850i
$593$	−28.6550			−1.17672			−0.588359	−	0.808600i	$-0.700226\pi$
$593$	−28.6550			−1.17672			−0.588359	+	0.808600i	$0.700226\pi$
$594$	26.2736	−	2.70027i	1.07802	−	0.110793i
$595$		−	2.10278i		−	0.0862054i
$596$	1.28415	+	6.18137i	0.0526006	+	0.253199i
$597$		−	2.00000i		−	0.0818546i
$598$	0.235269	+	2.28917i	0.00962088	+	0.0936111i
$599$	39.0661			1.59620			0.798098	−	0.602528i	$-0.205840\pi$
$599$	39.0661			1.59620			0.798098	+	0.602528i	$0.205840\pi$
$600$	−7.19499	−	22.6761i	−0.293734	−	0.925747i
$601$	19.8222			0.808564			0.404282	−	0.914634i	$-0.367521\pi$
$601$	19.8222			0.808564			0.404282	+	0.914634i	$0.367521\pi$
$602$	0.144584	+	1.40680i	0.00589282	+	0.0573370i
$603$			17.3522i			0.706635i
$604$	−4.63653	+	0.963214i	−0.188658	+	0.0391926i
$605$		−	20.6655i		−	0.840173i
$606$	−27.0872	+	2.78389i	−1.10034	+	0.113088i
$607$	−12.8917			−0.523257			−0.261629	−	0.965169i	$-0.584260\pi$
$607$	−12.8917			−0.523257			−0.261629	+	0.965169i	$0.584260\pi$
$608$	11.0872	+	19.7250i	0.449645	+	0.799953i
$609$	−34.6338			−1.40343
$610$	17.8328	−	1.83276i	0.722027	−	0.0742064i
$611$			4.68111i			0.189378i
$612$	−2.78389	+	0.578337i	−0.112532	+	0.0233779i
$613$		−	0.313348i		−	0.0126560i	−0.999980	−	0.00632801i	$-0.997986\pi$
$613$		−	0.313348i		−	0.0126560i	0.999980	−	0.00632801i	$-0.00201428\pi$
$614$	−1.19499	−	11.6272i	−0.0482258	−	0.469236i
$615$	−12.2650			−0.494572
$616$	10.1219	+	31.9008i	0.407824	+	1.28532i
$617$	6.31335			0.254166			0.127083	−	0.991892i	$-0.459439\pi$
$617$	6.31335			0.254166			0.127083	+	0.991892i	$0.459439\pi$
$618$	−1.63027	−	15.8625i	−0.0655790	−	0.638083i
$619$			33.1638i			1.33297i	0.745520	+	0.666483i	$0.232201\pi$
$619$			33.1638i			1.33297i	−0.745520	+	0.666483i	$0.767799\pi$
$620$	3.91638	+	18.8519i	0.157286	+	0.757111i
$621$			5.40054i			0.216716i
$622$	33.2927	−	3.42166i	1.33492	−	0.137196i
$623$	−23.6655			−0.948139
$624$	7.71513	−	3.35013i	0.308852	−	0.134113i
$625$	11.0000			0.440000
$626$	1.03402	−	0.106271i	0.0413276	−	0.00424745i
$627$			47.3311i			1.89022i
$628$	−6.48059	−	31.1950i	−0.258604	−	1.24482i
$629$			0.421663i			0.0168128i
$630$	−0.432226	−	4.20555i	−0.0172203	−	0.167553i
$631$	−9.42669			−0.375270			−0.187635	−	0.982239i	$-0.560082\pi$
$631$	−9.42669			−0.375270			−0.187635	+	0.982239i	$0.560082\pi$
$632$	38.5613	−	12.2353i	1.53389	−	0.486693i
$633$	24.6655			0.980367
$634$	−1.61308	−	15.6952i	−0.0640636	−	0.623338i
$635$			10.0383i			0.398358i
$636$	−18.8519	+	3.91638i	−0.747527	+	0.155295i
$637$			2.57834i			0.102157i
$638$	−62.0071	+	6.37279i	−2.45489	+	0.252301i
$639$	13.0106			0.514690
$640$	−7.43375	−	8.52873i	−0.293845	−	0.337128i
$641$	−3.68665			−0.145614			−0.0728070	−	0.997346i	$-0.523196\pi$
$641$	−3.68665			−0.145614			−0.0728070	+	0.997346i	$0.523196\pi$
$642$	18.8519	−	1.93751i	0.744026	−	0.0764673i
$643$		−	10.3033i		−	0.406323i	−0.979145	−	0.203161i	$-0.934878\pi$
$643$		−	10.3033i		−	0.406323i	0.979145	−	0.203161i	$-0.0651216\pi$
$644$	−6.70027	+	1.39194i	−0.264028	+	0.0548503i
$645$		−	1.00000i		−	0.0393750i
$646$	0.578337	+	5.62721i	0.0227544	+	0.221400i
$647$	−29.8328			−1.17285			−0.586423	−	0.810005i	$-0.699465\pi$
$647$	−29.8328			−1.17285			−0.586423	+	0.810005i	$0.699465\pi$
$648$	30.3131	−	9.61818i	1.19081	−	0.377838i
$649$	48.8222			1.91644
$650$	0.578337	+	5.62721i	0.0226842	+	0.220717i
$651$		−	42.5683i		−	1.66838i
$652$	1.43580	+	6.91136i	0.0562301	+	0.270670i
$653$		−	7.47002i		−	0.292325i	−0.989261	−	0.146162i	$-0.953308\pi$
$653$		−	7.47002i		−	0.292325i	0.989261	−	0.146162i	$-0.0466922\pi$
$654$	41.6726	−	4.28290i	1.62953	−	0.167475i
$655$	8.47556			0.331168
$656$	21.4005	−	9.29274i	0.835551	−	0.362821i
$657$	3.66553			0.143006
$658$	−13.8476	+	1.42319i	−0.539837	+	0.0554817i
$659$		−	9.09724i		−	0.354378i	−0.984177	−	0.177189i	$-0.943300\pi$
$659$		−	9.09724i		−	0.354378i	0.984177	−	0.177189i	$-0.0567004\pi$
$660$	−4.81361	−	23.1708i	−0.187369	−	0.901922i
$661$		−	42.6832i		−	1.66019i	−0.557626	−	0.830093i	$-0.688287\pi$
$661$		−	42.6832i		−	1.66019i	0.557626	−	0.830093i	$-0.311713\pi$
$662$	1.12695	+	10.9653i	0.0438003	+	0.426177i
$663$	2.10278			0.0816650
$664$	7.01916	+	22.1219i	0.272396	+	0.858497i
$665$	−8.41110			−0.326168
$666$	0.0866729	+	0.843326i	0.00335850	+	0.0326782i
$667$		−	12.7456i		−	0.493511i
$668$	30.7925	−	6.39697i	1.19140	−	0.247506i
$669$			9.84333i			0.380565i
$670$	−17.1708	+	1.76473i	−0.663366	+	0.0681775i
$671$	−71.3311			−2.75370
$672$	12.2560	+	21.8043i	0.472784	+	0.841119i
$673$	−18.6655			−0.719503			−0.359752	−	0.933048i	$-0.617139\pi$
$673$	−18.6655			−0.719503			−0.359752	+	0.933048i	$0.617139\pi$
$674$	−27.0723	+	2.78236i	−1.04279	+	0.107173i
$675$			13.2756i			0.510976i
$676$	−1.95819	+	0.406803i	−0.0753150	+	0.0156463i
$677$		−	11.9022i		−	0.457441i	−0.973492	−	0.228720i	$-0.926546\pi$
$677$		−	11.9022i		−	0.457441i	0.973492	−	0.228720i	$-0.0734541\pi$
$678$	1.47251	+	14.3275i	0.0565513	+	0.550244i
$679$	−22.4494			−0.861529
$680$	−0.855416	−	2.69597i	−0.0328037	−	0.103386i
$681$	24.6761			0.945590
$682$	−7.83276	−	76.2127i	−0.299932	−	2.91833i
$683$		−	4.95112i		−	0.189449i	−0.995504	−	0.0947247i	$-0.969803\pi$
$683$		−	4.95112i		−	0.189449i	0.995504	−	0.0947247i	$-0.0301971\pi$
$684$	2.31335	+	11.1355i	0.0884531	+	0.425778i
$685$		−	19.0872i		−	0.729284i
$686$	−28.3345	+	2.91208i	−1.08182	+	0.111184i
$687$	−12.2872			−0.468786
$688$	0.757664	+	1.74485i	0.0288857	+	0.0665217i
$689$	4.57834			0.174421
$690$	4.81361	−	0.494719i	0.183251	−	0.0188336i
$691$			34.7244i			1.32098i	0.750835	+	0.660490i	$0.229651\pi$
$691$			34.7244i			1.32098i	−0.750835	+	0.660490i	$0.770349\pi$
$692$	−5.86248	−	28.2197i	−0.222858	−	1.07275i
$693$			16.8222i			0.639023i
$694$	−4.71513	−	45.8781i	−0.178984	−	1.74151i
$695$	3.99498			0.151538
$696$	−44.4041	+	14.0892i	−1.68313	+	0.534048i
$697$	5.83276			0.220932
$698$	−4.60099	−	44.7676i	−0.174150	−	1.69448i
$699$		−	53.0822i		−	2.00775i
$700$	−16.4705	+	3.42166i	−0.622528	+	0.129327i
$701$			30.2650i			1.14309i	0.820570	+	0.571546i	$0.193656\pi$
$701$			30.2650i			1.14309i	−0.820570	+	0.571546i	$0.806344\pi$
$702$	−4.66902	+	0.479859i	−0.176221	+	0.0181111i
$703$	1.68665			0.0636133
$704$	25.9547	+	36.7824i	0.978204	+	1.38629i
$705$	9.84333			0.370721
$706$	−28.2736	+	2.90582i	−1.06409	+	0.109362i
$707$			19.2544i			0.724137i
$708$	35.7250	−	7.42166i	1.34263	−	0.278923i
$709$			49.3311i			1.85267i	0.376705	+	0.926333i	$0.377057\pi$
$709$			49.3311i			1.85267i	−0.376705	+	0.926333i	$0.622943\pi$
$710$	1.32318	+	12.8746i	0.0496582	+	0.483174i
$711$	20.3345			0.762602
$712$	−30.3416	+	9.62721i	−1.13710	+	0.360795i
$713$	15.6655			0.586679
$714$	0.639303	+	6.22041i	0.0239253	+	0.232793i
$715$			5.62721i			0.210446i
$716$	−0.688179	−	3.31262i	−0.0257185	−	0.123799i
$717$		−	24.1083i		−	0.900342i
$718$	−12.2197	+	1.25588i	−0.456035	+	0.0468690i
$719$	39.3411			1.46718			0.733588	−	0.679595i	$-0.237844\pi$
$719$	39.3411			1.46718			0.733588	+	0.679595i	$0.237844\pi$
$720$	−2.26499	−	5.21611i	−0.0844111	−	0.194393i
$721$	−11.2756			−0.419923
$722$	−4.22041	+	0.433753i	−0.157067	+	0.0161426i
$723$		−	4.41110i		−	0.164051i
$724$	7.01916	+	33.7875i	0.260865	+	1.25570i
$725$		−	31.3311i		−	1.16361i
$726$	6.28290	+	61.1326i	0.233180	+	2.26884i
$727$	38.4494			1.42601			0.713005	−	0.701159i	$-0.247334\pi$
$727$	38.4494			1.42601			0.713005	+	0.701159i	$0.247334\pi$
$728$	−1.79875	−	5.66902i	−0.0666660	−	0.210108i
$729$	−4.95164			−0.183394
$730$	0.372787	+	3.62721i	0.0137975	+	0.134249i
$731$			0.475562i			0.0175893i
$732$	−52.1955	+	10.8433i	−1.92920	+	0.400781i
$733$			42.3522i			1.56431i	0.623082	+	0.782157i	$0.285880\pi$
$733$			42.3522i			1.56431i	−0.623082	+	0.782157i	$0.714120\pi$
$734$	13.1708	−	1.35363i	0.486143	−	0.0499634i
$735$	5.42166			0.199981
$736$	−8.02418	+	4.51030i	−0.295775	+	0.166252i
$737$	68.6832			2.52998
$738$	11.6655	−	1.19893i	0.429414	−	0.0441330i
$739$			14.5783i			0.536273i	0.963381	+	0.268136i	$0.0864078\pi$
$739$			14.5783i			0.536273i	−0.963381	+	0.268136i	$0.913592\pi$
$740$	−0.825696	+	0.171534i	−0.0303532	+	0.00630571i
$741$		−	8.41110i		−	0.308989i
$742$	1.39194	+	13.5436i	0.0510999	+	0.497201i
$743$	−2.78891			−0.102315			−0.0511576	−	0.998691i	$-0.516291\pi$
$743$	−2.78891			−0.102315			−0.0511576	+	0.998691i	$0.516291\pi$
$744$	−17.3169	−	54.5769i	−0.634869	−	2.00089i
$745$	−3.15667			−0.115652
$746$	3.17780	+	30.9200i	0.116348	+	1.13206i
$747$			11.6655i			0.426819i
$748$	2.28917	+	11.0192i	0.0837003	+	0.402900i
$749$		−	13.4005i		−	0.489645i
$750$	26.6237	−	2.73625i	0.972161	−	0.0999139i
$751$	−34.2439			−1.24958			−0.624788	−	0.780794i	$-0.714815\pi$
$751$	−34.2439			−1.24958			−0.624788	+	0.780794i	$0.714815\pi$
$752$	−17.1751	+	7.45793i	−0.626312	+	0.271963i
$753$	−31.0872			−1.13288
$754$	11.0192	−	1.13249i	0.401294	−	0.0412430i
$755$		−	2.36776i		−	0.0861717i
$756$	−2.83903	−	13.6660i	−0.103254	−	0.497026i
$757$		−	18.4605i		−	0.670958i	−0.942048	−	0.335479i	$-0.891102\pi$
$757$		−	18.4605i		−	0.670958i	0.942048	−	0.335479i	$-0.108898\pi$
$758$	0.586931	+	5.71083i	0.0213183	+	0.207427i
$759$	−19.2544			−0.698891
$760$	−10.7839	+	3.42166i	−0.391173	+	0.124117i
$761$	17.6172			0.638622			0.319311	−	0.947650i	$-0.396549\pi$
$761$	17.6172			0.638622			0.319311	+	0.947650i	$0.396549\pi$
$762$	−3.05193	−	29.6952i	−0.110560	−	1.07575i
$763$		−	29.6222i		−	1.07240i
$764$	11.8242	−	2.45641i	0.427783	−	0.0888696i
$765$		−	1.42166i		−	0.0514003i
$766$	10.4040	−	1.06928i	0.375913	−	0.0386345i
$767$	−8.67609			−0.313275
$768$	24.5834	+	22.9696i	0.887078	+	0.828842i
$769$	−41.3522			−1.49120			−0.745599	−	0.666395i	$-0.767836\pi$
$769$	−41.3522			−1.49120			−0.745599	+	0.666395i	$0.767836\pi$
$770$	−16.6464	+	1.71083i	−0.599894	+	0.0616541i
$771$			6.96723i			0.250919i
$772$	25.9547	−	5.39194i	0.934130	−	0.194060i
$773$			22.6867i			0.815982i	0.912986	+	0.407991i	$0.133771\pi$
$773$			22.6867i			0.815982i	−0.912986	+	0.407991i	$0.866229\pi$
$774$	0.0977518	+	0.951124i	0.00351362	+	0.0341874i
$775$	38.5089			1.38328
$776$	−28.7824	+	9.13249i	−1.03323	+	0.327837i
$777$	1.86445			0.0668868
$778$	1.94056	+	18.8816i	0.0695725	+	0.676940i
$779$		−	23.3311i		−	0.835922i
$780$	0.855416	+	4.11763i	0.0306288	+	0.147435i
$781$		−	51.4983i		−	1.84275i
$782$	−2.28917	+	0.235269i	−0.0818605	+	0.00841322i
$783$	25.9961			0.929023
$784$	−9.45998	+	4.10780i	−0.337856	+	0.146707i
$785$	15.9305			0.568584
$786$	−25.0723	+	2.57681i	−0.894300	+	0.0919118i
$787$			15.5194i			0.553207i	0.960984	+	0.276604i	$0.0892089\pi$
$787$			15.5194i			0.553207i	−0.960984	+	0.276604i	$0.910791\pi$
$788$	−9.32821	−	44.9023i	−0.332304	−	1.59958i
$789$			36.6338i			1.30420i
$790$	2.06803	+	20.1219i	0.0735773	+	0.715906i
$791$	10.1844			0.362116
$792$	6.84333	+	21.5678i	0.243167	+	0.766377i
$793$	12.6761			0.450141
$794$	4.79088	+	46.6152i	0.170022	+	1.65431i
$795$		−	9.62721i		−	0.341442i
$796$	−1.86248	+	0.386920i	−0.0660139	+	0.0137140i
$797$			1.56777i			0.0555334i	0.999614	+	0.0277667i	$0.00883955\pi$
$797$			1.56777i			0.0555334i	−0.999614	+	0.0277667i	$0.991160\pi$
$798$	24.8816	−	2.55721i	0.880800	−	0.0905243i
$799$	−4.68111			−0.165606
$800$	−19.7250	+	11.0872i	−0.697383	+	0.391991i
$801$	−16.0000			−0.565332
$802$	20.0680	−	2.06249i	0.708627	−	0.0728292i
$803$		−	14.5089i		−	0.512006i
$804$	50.2580	−	10.4408i	1.77246	−	0.368219i
$805$		−	3.42166i		−	0.120598i
$806$	1.39194	+	13.5436i	0.0490291	+	0.477053i
$807$	6.98944			0.246040
$808$	7.83276	+	24.6861i	0.275556	+	0.868455i
$809$	−44.4005			−1.56104			−0.780520	−	0.625131i	$-0.785046\pi$
$809$	−44.4005			−1.56104			−0.780520	+	0.625131i	$0.785046\pi$
$810$	1.62569	+	15.8179i	0.0571208	+	0.555784i
$811$		−	32.9411i		−	1.15672i	−0.815782	−	0.578359i	$-0.803693\pi$
$811$		−	32.9411i		−	1.15672i	0.815782	−	0.578359i	$-0.196307\pi$
$812$	6.70027	+	32.2525i	0.235133	+	1.13184i
$813$		−	29.5089i		−	1.03492i
$814$	3.33804	−	0.343068i	0.116998	−	0.0120245i
$815$	−3.52946			−0.123632
$816$	3.35013	+	7.71513i	0.117278	+	0.270084i
$817$	1.90225			0.0665512
$818$	−8.34307	+	0.857459i	−0.291709	+	0.0299804i
$819$		−	2.98944i		−	0.104459i
$820$	2.37279	+	11.4217i	0.0828613	+	0.398862i
$821$			30.3522i			1.05930i	0.848217	+	0.529649i	$0.177676\pi$
$821$			30.3522i			1.05930i	−0.848217	+	0.529649i	$0.822324\pi$
$822$	5.80304	+	56.4635i	0.202404	+	1.96939i
$823$	−34.5783			−1.20533			−0.602663	−	0.797996i	$-0.705893\pi$
$823$	−34.5783			−1.20533			−0.602663	+	0.797996i	$0.705893\pi$
$824$	−14.4564	+	4.58693i	−0.503613	+	0.159793i
$825$	−47.3311			−1.64786
$826$	−2.63778	−	25.6655i	−0.0917800	−	0.893018i
$827$		−	14.1744i		−	0.492891i	−0.969157	−	0.246446i	$-0.920737\pi$
$827$		−	14.1744i		−	0.492891i	0.969157	−	0.246446i	$-0.0792627\pi$
$828$	−4.52998	+	0.941078i	−0.157428	+	0.0327047i
$829$			33.1355i			1.15085i	0.817856	+	0.575423i	$0.195162\pi$
$829$			33.1355i			1.15085i	−0.817856	+	0.575423i	$0.804838\pi$
$830$	−11.5436	+	1.18639i	−0.400684	+	0.0411803i
$831$	2.12499			0.0737149
$832$	−4.61235	−	6.53653i	−0.159905	−	0.226613i
$833$	−2.57834			−0.0893341
$834$	−11.8179	+	1.21459i	−0.409221	+	0.0420577i
$835$			15.7250i			0.544185i
$836$	44.0766	−	9.15667i	1.52442	−	0.316690i
$837$			31.9516i			1.10441i
$838$	3.69597	+	35.9618i	0.127675	+	1.24228i
$839$	−34.4494			−1.18933			−0.594663	−	0.803975i	$-0.702714\pi$
$839$	−34.4494			−1.18933			−0.594663	+	0.803975i	$0.702714\pi$
$840$	−11.9207	+	3.78236i	−0.411302	+	0.130504i
$841$	−32.3522			−1.11559
$842$	3.85542	+	37.5131i	0.132866	+	1.29279i
$843$			7.54665i			0.259920i
$844$	−4.77180	−	22.9696i	−0.164252	−	0.790645i
$845$		−	1.00000i		−	0.0344010i
$846$	−9.36222	+	0.962203i	−0.321880	+	0.0330812i
$847$	43.4550			1.49313
$848$	7.29419	+	16.7980i	0.250484	+	0.576846i
$849$	27.9516			0.959298
$850$	−5.62721	+	0.578337i	−0.193012	+	0.0198368i
$851$			0.686135i			0.0235204i
$852$	−7.82847	−	37.6832i	−0.268199	−	1.29100i
$853$			17.1744i			0.588040i	0.955799	+	0.294020i	$0.0949931\pi$
$853$			17.1744i			0.588040i	−0.955799	+	0.294020i	$0.905007\pi$
$854$	3.85389	+	37.4983i	0.131877	+	1.28317i
$855$	−5.68665			−0.194479
$856$	−5.45138	−	17.1809i	−0.186324	−	0.587230i
$857$	−34.4877			−1.17808			−0.589039	−	0.808104i	$-0.700494\pi$
$857$	−34.4877			−1.17808			−0.589039	+	0.808104i	$0.700494\pi$
$858$	−1.71083	−	16.6464i	−0.0584068	−	0.568298i
$859$		−	5.29274i		−	0.180586i	−0.995915	−	0.0902930i	$-0.971220\pi$
$859$		−	5.29274i		−	0.180586i	0.995915	−	0.0902930i	$-0.0287803\pi$
$860$	−0.931241	+	0.193460i	−0.0317551	+	0.00659694i
$861$		−	25.7905i		−	0.878938i
$862$	17.4529	−	1.79372i	0.594448	−	0.0610945i
$863$	11.5939			0.394662			0.197331	−	0.980337i	$-0.436773\pi$
$863$	11.5939			0.394662			0.197331	+	0.980337i	$0.436773\pi$
$864$	−9.19928	−	16.3662i	−0.312966	−	0.556791i
$865$	14.4111			0.489992
$866$	−0.152377	+	0.0156606i	−0.00517799	+	0.000532168i
$867$		−	33.6444i		−	1.14262i
$868$	−39.6413	+	8.23527i	−1.34551	+	0.279523i
$869$		−	80.4877i		−	2.73036i
$870$	−2.38138	−	23.1708i	−0.0807364	−	0.785564i
$871$	−12.2056			−0.413569
$872$	−12.0504	−	37.9787i	−0.408078	−	1.28612i
$873$	−15.1778			−0.513691
$874$	0.941078	+	9.15667i	0.0318324	+	0.309729i
$875$		−	18.9250i		−	0.639781i
$876$	−2.20555	−	10.6167i	−0.0745186	−	0.358703i
$877$			10.3522i			0.349568i	0.984607	+	0.174784i	$0.0559227\pi$
$877$			10.3522i			0.349568i	−0.984607	+	0.174784i	$0.944077\pi$
$878$	8.78389	−	0.902764i	0.296442	−	0.0304668i
$879$	−19.4378			−0.655620
$880$	−20.6464	+	8.96526i	−0.695989	+	0.302219i
$881$	39.7044			1.33767			0.668837	−	0.743409i	$-0.266792\pi$
$881$	39.7044			1.33767			0.668837	+	0.743409i	$0.266792\pi$
$882$	−5.15667	+	0.529977i	−0.173634	+	0.0178453i
$883$			42.2388i			1.42145i	0.703470	+	0.710725i	$0.251633\pi$
$883$			42.2388i			1.42145i	−0.703470	+	0.710725i	$0.748367\pi$
$884$	−0.406803	−	1.95819i	−0.0136823	−	0.0658611i
$885$			18.2439i			0.613261i
$886$	−2.02899	−	19.7421i	−0.0681654	−	0.663248i
$887$	36.1461			1.21367			0.606834	−	0.794829i	$-0.292439\pi$
$887$	36.1461			1.21367			0.606834	+	0.794829i	$0.292439\pi$
$888$	2.39042	−	0.758465i	0.0802171	−	0.0254524i
$889$	−21.1083			−0.707950
$890$	−1.62721	−	15.8328i	−0.0545443	−	0.530715i
$891$		−	63.2716i		−	2.11968i
$892$	9.16651	−	1.90429i	0.306917	−	0.0637604i
$893$			18.7244i			0.626590i
$894$	9.33804	−	0.959718i	0.312311	−	0.0320978i
$895$	1.69167			0.0565465
$896$	17.9340	−	15.6315i	0.599133	−	0.522212i
$897$	3.42166			0.114246
$898$	−7.76473	+	0.798021i	−0.259112	+	0.0266303i
$899$		−	75.4077i		−	2.51499i
$900$	−11.1355	+	2.31335i	−0.371185	+	0.0771116i
$901$			4.57834i			0.152527i
$902$	−4.74557	−	46.1744i	−0.158010	−	1.53744i
$903$	2.10278			0.0699760
$904$	13.0575	−	4.14306i	0.434285	−	0.137796i
$905$	−17.2544			−0.573557
$906$	0.719867	+	7.00430i	0.0239160	+	0.232702i
$907$			43.5910i			1.44742i	0.690106	+	0.723708i	$0.257564\pi$
$907$			43.5910i			1.44742i	−0.690106	+	0.723708i	$0.742436\pi$
$908$	−4.77384	−	22.9794i	−0.158425	−	0.762598i
$909$			13.0177i			0.431770i
$910$	2.95819	−	0.304028i	0.0980631	−	0.0100784i
$911$	53.8993			1.78576			0.892882	−	0.450290i	$-0.148679\pi$
$911$	53.8993			1.78576			0.892882	+	0.450290i	$0.148679\pi$
$912$	30.8605	−	13.4005i	1.02189	−	0.443736i
$913$	46.1744			1.52815
$914$	28.2439	−	2.90276i	0.934224	−	0.0960149i
$915$		−	26.6550i		−	0.881186i
$916$	2.37708	+	11.4423i	0.0785411	+	0.378066i
$917$			17.8222i			0.588541i
$918$	−0.479859	−	4.66902i	−0.0158377	−	0.154101i
$919$	6.64782			0.219291			0.109646	−	0.993971i	$-0.465028\pi$
$919$	6.64782			0.219291			0.109646	+	0.993971i	$0.465028\pi$
$920$	−1.39194	−	4.38692i	−0.0458910	−	0.144632i
$921$	−17.3794			−0.572671
$922$	1.79598	+	17.4748i	0.0591474	+	0.575503i
$923$			9.15165i			0.301230i
$924$	48.7230	−	10.1219i	1.60287	−	0.332987i
$925$			1.68665i			0.0554568i
$926$	15.6413	−	1.60754i	0.514007	−	0.0528270i
$927$	−7.62328			−0.250381
$928$	21.7108	+	38.6252i	0.712693	+	1.26794i
$929$	−17.9789			−0.589868			−0.294934	−	0.955518i	$-0.595298\pi$
$929$	−17.9789			−0.589868			−0.294934	+	0.955518i	$0.595298\pi$
$930$	28.4791	−	2.92694i	0.933868	−	0.0959783i
$931$			10.3133i			0.338006i
$932$	−49.4323	+	10.2693i	−1.61921	+	0.336382i
$933$		−	49.7633i		−	1.62918i
$934$	−0.158643	−	1.54359i	−0.00519096	−	0.0505080i
$935$	−5.62721			−0.184030
$936$	−1.21611	−	3.83276i	−0.0397499	−	0.125278i
$937$	−22.4877			−0.734642			−0.367321	−	0.930094i	$-0.619725\pi$
$937$	−22.4877			−0.734642			−0.367321	+	0.930094i	$0.619725\pi$
$938$	−3.71083	−	36.1063i	−0.121163	−	1.17891i
$939$		−	1.54556i		−	0.0504376i
$940$	−1.90429	−	9.16651i	−0.0621111	−	0.298979i
$941$		−	15.1955i		−	0.495359i	−0.968842	−	0.247680i	$-0.920332\pi$
$941$		−	15.1955i		−	0.495359i	0.968842	−	0.247680i	$-0.0796680\pi$
$942$	−47.1255	+	4.84333i	−1.53543	+	0.157804i
$943$	9.49115			0.309074
$944$	−13.8227	−	31.8328i	−0.449891	−	1.03607i
$945$	6.97887			0.227023
$946$	3.76473	−	0.386920i	0.122402	−	0.0125799i
$947$		−	32.0594i		−	1.04179i	−0.853620	−	0.520896i	$-0.825598\pi$
$947$		−	32.0594i		−	1.04179i	0.853620	−	0.520896i	$-0.174402\pi$
$948$	−12.2353	−	58.8958i	−0.397383	−	1.91285i
$949$			2.57834i			0.0836964i
$950$	2.31335	+	22.5089i	0.0750549	+	0.730284i
$951$	−23.4600			−0.760742
$952$	5.66902	−	1.79875i	0.183734	−	0.0582977i
$953$	31.5089			1.02067			0.510336	−	0.859975i	$-0.329521\pi$
$953$	31.5089			1.02067			0.510336	+	0.859975i	$0.329521\pi$
$954$	0.941078	+	9.15667i	0.0304685	+	0.296458i
$955$			6.03831i			0.195395i
$956$	−22.4507	+	4.66400i	−0.726106	+	0.150845i
$957$			92.6832i			2.99602i
$958$	−21.0801	+	2.16651i	−0.681068	+	0.0699968i
$959$	40.1361			1.29606
$960$	−13.7448	+	9.69874i	−0.443613	+	0.313026i
$961$	61.6832			1.98978
$962$	−0.593197	+	0.0609658i	−0.0191254	+	0.00196562i
$963$		−	9.05995i		−	0.291953i
$964$	−4.10780	+	0.853372i	−0.132303	+	0.0274853i
$965$			13.2544i			0.426675i
$966$	1.04028	+	10.1219i	0.0334705	+	0.325668i
$967$	44.3960			1.42768			0.713840	−	0.700309i	$-0.246954\pi$
$967$	44.3960			1.42768			0.713840	+	0.700309i	$0.246954\pi$
$968$	55.7137	−	17.6776i	1.79071	−	0.568180i
$969$	8.41110			0.270203
$970$	−1.54359	−	15.0192i	−0.0495618	−	0.482236i
$971$		−	49.2978i		−	1.58204i	−0.611790	−	0.791020i	$-0.709550\pi$
$971$		−	49.2978i		−	1.58204i	0.611790	−	0.791020i	$-0.290450\pi$
$972$	−5.56777	−	26.8011i	−0.178586	−	0.859645i
$973$			8.40054i			0.269309i
$974$	32.6308	−	3.35363i	1.04556	−	0.107457i
$975$	8.41110			0.269371
$976$	20.1955	+	46.5089i	0.646442	+	1.48871i
$977$	−3.35218			−0.107246			−0.0536228	−	0.998561i	$-0.517077\pi$
$977$	−3.35218			−0.107246			−0.0536228	+	0.998561i	$0.517077\pi$
$978$	10.4408	−	1.07306i	0.333861	−	0.0343125i
$979$			63.3311i			2.02407i
$980$	−1.04888	−	5.04888i	−0.0335051	−	0.161280i
$981$		−	20.0272i		−	0.639420i
$982$	−3.32318	−	32.3345i	−0.106047	−	1.03184i
$983$	21.8972			0.698413			0.349207	−	0.937046i	$-0.386451\pi$
$983$	21.8972			0.698413			0.349207	+	0.937046i	$0.386451\pi$
$984$	−10.4917	−	33.0661i	−0.334462	−	1.05411i
$985$	22.9305			0.730627
$986$	1.13249	+	11.0192i	0.0360660	+	0.350921i
$987$			20.6983i			0.658834i
$988$	−7.83276	+	1.62721i	−0.249193	+	0.0517685i
$989$			0.773841i			0.0246067i
$990$	−11.2544	+	1.15667i	−0.357689	+	0.0367615i
$991$	−59.7422			−1.89777			−0.948886	−	0.315619i	$-0.897788\pi$
$991$	−59.7422			−1.89777			−0.948886	+	0.315619i	$0.897788\pi$
$992$	−47.4741	+	26.6847i	−1.50730	+	0.847240i
$993$	16.3900			0.520120
$994$	−27.0723	+	2.78236i	−0.858682	+	0.0882511i
$995$		−	0.951124i		−	0.0301527i
$996$	33.7875	−	7.01916i	1.07060	−	0.222410i
$997$			38.3416i			1.21429i	0.794591	+	0.607146i	$0.207686\pi$
$997$			38.3416i			1.21429i	−0.794591	+	0.607146i	$0.792314\pi$
$998$	1.95164	+	18.9894i	0.0617781	+	0.601100i
$999$	−1.39945			−0.0442767

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	104.2.b.c.53.2	yes	6
3.2	odd	2		936.2.g.c.469.5		6
4.3	odd	2		416.2.b.c.209.2		6
8.3	odd	2		416.2.b.c.209.5		6
8.5	even	2	inner	104.2.b.c.53.1	✓	6
12.11	even	2		3744.2.g.c.1873.3		6
16.3	odd	4		3328.2.a.bf.1.3		3
16.5	even	4		3328.2.a.be.1.3		3
16.11	odd	4		3328.2.a.bg.1.1		3
16.13	even	4		3328.2.a.bh.1.1		3
24.5	odd	2		936.2.g.c.469.6		6
24.11	even	2		3744.2.g.c.1873.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.b.c.53.1	✓	6	8.5	even	2	inner
104.2.b.c.53.2	yes	6	1.1	even	1	trivial
416.2.b.c.209.2		6	4.3	odd	2
416.2.b.c.209.5		6	8.3	odd	2
936.2.g.c.469.5		6	3.2	odd	2
936.2.g.c.469.6		6	24.5	odd	2
3328.2.a.be.1.3		3	16.5	even	4
3328.2.a.bf.1.3		3	16.3	odd	4
3328.2.a.bg.1.1		3	16.11	odd	4
3328.2.a.bh.1.1		3	16.13	even	4
3744.2.g.c.1873.3		6	12.11	even	2
3744.2.g.c.1873.6		6	24.11	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40680 + 0.144584i) q^{2} +2.10278i q^{3} +(1.95819 - 0.406803i) q^{4} +1.00000i q^{5} +(-0.304028 - 2.95819i) q^{6} -2.10278 q^{7} +(-2.69597 + 0.855416i) q^{8} -1.42166 q^{9} +(-0.144584 - 1.40680i) q^{10} +5.62721i q^{11} +(0.855416 + 4.11763i) q^{12} -1.00000i q^{13} +(2.95819 - 0.304028i) q^{14} -2.10278 q^{15} +(3.66902 - 1.59320i) q^{16} +1.00000 q^{17} +(2.00000 - 0.205550i) q^{18} -4.00000i q^{19} +(0.406803 + 1.95819i) q^{20} -4.42166i q^{21} +(-0.813607 - 7.91638i) q^{22} +1.62721 q^{23} +(-1.79875 - 5.66902i) q^{24} +4.00000 q^{25} +(0.144584 + 1.40680i) q^{26} +3.31889i q^{27} +(-4.11763 + 0.855416i) q^{28} -7.83276i q^{29} +(2.95819 - 0.304028i) q^{30} +9.62721 q^{31} +(-4.93124 + 2.77180i) q^{32} -11.8328 q^{33} +(-1.40680 + 0.144584i) q^{34} -2.10278i q^{35} +(-2.78389 + 0.578337i) q^{36} +0.421663i q^{37} +(0.578337 + 5.62721i) q^{38} +2.10278 q^{39} +(-0.855416 - 2.69597i) q^{40} +5.83276 q^{41} +(0.639303 + 6.22041i) q^{42} +0.475562i q^{43} +(2.28917 + 11.0192i) q^{44} -1.42166i q^{45} +(-2.28917 + 0.235269i) q^{46} -4.68111 q^{47} +(3.35013 + 7.71513i) q^{48} -2.57834 q^{49} +(-5.62721 + 0.578337i) q^{50} +2.10278i q^{51} +(-0.406803 - 1.95819i) q^{52} +4.57834i q^{53} +(-0.479859 - 4.66902i) q^{54} -5.62721 q^{55} +(5.66902 - 1.79875i) q^{56} +8.41110 q^{57} +(1.13249 + 11.0192i) q^{58} -8.67609i q^{59} +(-4.11763 + 0.855416i) q^{60} +12.6761i q^{61} +(-13.5436 + 1.39194i) q^{62} +2.98944 q^{63} +(6.53653 - 4.61235i) q^{64} +1.00000 q^{65} +(16.6464 - 1.71083i) q^{66} -12.2056i q^{67} +(1.95819 - 0.406803i) q^{68} +3.42166i q^{69} +(0.304028 + 2.95819i) q^{70} -9.15165 q^{71} +(3.83276 - 1.21611i) q^{72} -2.57834 q^{73} +(-0.0609658 - 0.593197i) q^{74} +8.41110i q^{75} +(-1.62721 - 7.83276i) q^{76} -11.8328i q^{77} +(-2.95819 + 0.304028i) q^{78} -14.3033 q^{79} +(1.59320 + 3.66902i) q^{80} -11.2439 q^{81} +(-8.20555 + 0.843326i) q^{82} -8.20555i q^{83} +(-1.79875 - 8.65846i) q^{84} +1.00000i q^{85} +(-0.0687588 - 0.669022i) q^{86} +16.4705 q^{87} +(-4.81361 - 15.1708i) q^{88} +11.2544 q^{89} +(0.205550 + 2.00000i) q^{90} +2.10278i q^{91} +(3.18639 - 0.661956i) q^{92} +20.2439i q^{93} +(6.58540 - 0.676815i) q^{94} +4.00000 q^{95} +(-5.82847 - 10.3693i) q^{96} +10.6761 q^{97} +(3.62721 - 0.372787i) q^{98} -8.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 2 q^{4} - 10 q^{6} + 2 q^{7} - 8 q^{8} - 12 q^{9} + 6 q^{12} + 4 q^{14} + 2 q^{15} + 10 q^{16} + 6 q^{17} + 12 q^{18} - 4 q^{20} + 8 q^{22} - 16 q^{23} + 12 q^{24} + 24 q^{25} - 20 q^{28}+ \cdots - 4 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 - 2 * q^4 - 10 * q^6 + 2 * q^7 - 8 * q^8 - 12 * q^9 + 6 * q^12 + 4 * q^14 + 2 * q^15 + 10 * q^16 + 6 * q^17 + 12 * q^18 - 4 * q^20 + 8 * q^22 - 16 * q^23 + 12 * q^24 + 24 * q^25 - 20 * q^28 + 4 * q^30 + 32 * q^31 - 12 * q^32 - 16 * q^33 - 2 * q^34 + 16 * q^36 - 2 * q^39 - 6 * q^40 - 20 * q^41 - 28 * q^42 + 12 * q^44 - 12 * q^46 - 10 * q^47 - 10 * q^48 - 12 * q^49 - 8 * q^50 + 4 * q^52 + 38 * q^54 - 8 * q^55 + 22 * q^56 - 8 * q^57 + 12 * q^58 - 20 * q^60 - 28 * q^62 - 44 * q^63 + 22 * q^64 + 6 * q^65 + 32 * q^66 - 2 * q^68 + 10 * q^70 - 18 * q^71 - 32 * q^72 - 12 * q^73 + 28 * q^74 + 16 * q^76 - 4 * q^78 - 12 * q^79 + 16 * q^80 + 46 * q^81 - 20 * q^82 + 12 * q^84 - 18 * q^86 + 80 * q^87 - 16 * q^88 + 16 * q^89 - 28 * q^90 + 32 * q^92 + 24 * q^95 - 32 * q^96 + 16 * q^97 - 4 * q^98

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