LMFDB - Embedded newform 429.2.bi.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(5,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 8, 15]))

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

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

chi := DirichletCharacter("429.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bi (of order $20$, degree $8$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			5.1
Character	$\chi$	$=$	429.5
Dual form			429.2.bi.a.86.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23921 + 2.43208i) q^{2} +(0.596820 - 1.62598i) q^{3} +(-3.20380 - 4.40966i) q^{4} +(-2.41132 + 1.22863i) q^{5} +(3.21492 + 3.46643i) q^{6} +(3.29586 + 0.522013i) q^{7} +(9.30284 - 1.47343i) q^{8} +(-2.28761 - 1.94083i) q^{9} +O(q^{10})$	\(q+(-1.23921 + 2.43208i) q^{2} +(0.596820 - 1.62598i) q^{3} +(-3.20380 - 4.40966i) q^{4} +(-2.41132 + 1.22863i) q^{5} +(3.21492 + 3.46643i) q^{6} +(3.29586 + 0.522013i) q^{7} +(9.30284 - 1.47343i) q^{8} +(-2.28761 - 1.94083i) q^{9} -7.38704i q^{10} +(-1.52873 + 2.94329i) q^{11} +(-9.08210 + 2.57755i) q^{12} +(-3.59295 - 0.301176i) q^{13} +(-5.35383 + 7.36891i) q^{14} +(0.558601 + 4.65403i) q^{15} +(-4.57597 + 14.0834i) q^{16} +(0.113282 - 0.348646i) q^{17} +(7.55508 - 3.15856i) q^{18} +(-5.21046 + 0.825256i) q^{19} +(13.1432 + 6.69681i) q^{20} +(2.81582 - 5.04745i) q^{21} +(-5.26390 - 7.36535i) q^{22} -4.42950 q^{23} +(3.15636 - 16.0056i) q^{24} +(1.36601 - 1.88015i) q^{25} +(5.18489 - 8.36512i) q^{26} +(-4.52104 + 2.56128i) q^{27} +(-8.25739 - 16.2060i) q^{28} +(-1.45841 - 2.00733i) q^{29} +(-12.0112 - 4.40873i) q^{30} +(3.03175 + 1.54476i) q^{31} +(-15.2611 - 15.2611i) q^{32} +(3.87335 + 4.24230i) q^{33} +(0.707554 + 0.707554i) q^{34} +(-8.58874 + 2.79065i) q^{35} +(-1.22934 + 16.3056i) q^{36} +(-5.08538 - 0.805445i) q^{37} +(4.44974 - 13.6949i) q^{38} +(-2.63405 + 5.66231i) q^{39} +(-20.6218 + 14.9826i) q^{40} +(0.132540 + 0.836823i) q^{41} +(8.78643 + 13.1031i) q^{42} -3.67829i q^{43} +(17.8767 - 2.68853i) q^{44} +(7.90073 + 1.86934i) q^{45} +(5.48906 - 10.7729i) q^{46} +(-10.9586 + 1.73567i) q^{47} +(20.1683 + 15.8457i) q^{48} +(3.93282 + 1.27785i) q^{49} +(2.87991 + 5.65214i) q^{50} +(-0.499282 - 0.392272i) q^{51} +(10.1830 + 16.8086i) q^{52} +(-0.166632 + 0.0541421i) q^{53} +(-0.626739 - 14.1695i) q^{54} +(0.0700540 - 8.97547i) q^{55} +31.4300 q^{56} +(-1.76786 + 8.96462i) q^{57} +(6.68926 - 1.05947i) q^{58} +(0.0819982 - 0.517716i) q^{59} +(18.7330 - 17.3738i) q^{60} +(-1.97779 + 6.08701i) q^{61} +(-7.51393 + 5.45919i) q^{62} +(-6.52652 - 7.59088i) q^{63} +(27.8612 - 9.05265i) q^{64} +(9.03379 - 3.68817i) q^{65} +(-15.1175 + 4.16321i) q^{66} +(2.43659 - 2.43659i) q^{67} +(-1.90034 + 0.617458i) q^{68} +(-2.64361 + 7.20227i) q^{69} +(3.85614 - 24.3467i) q^{70} +(-0.471584 + 0.240284i) q^{71} +(-24.1410 - 14.6846i) q^{72} +(11.2551 + 1.78264i) q^{73} +(8.26074 - 11.3699i) q^{74} +(-2.24182 - 3.34321i) q^{75} +(20.3324 + 20.3324i) q^{76} +(-6.57494 + 8.90267i) q^{77} +(-10.5071 - 13.4230i) q^{78} +(3.48747 + 10.7333i) q^{79} +(-6.26913 - 39.5817i) q^{80} +(1.46634 + 8.87974i) q^{81} +(-2.19946 - 0.714649i) q^{82} +(-8.08074 + 4.11734i) q^{83} +(-31.2789 + 3.75426i) q^{84} +(0.155197 + 0.979878i) q^{85} +(8.94590 + 4.55816i) q^{86} +(-4.13428 + 1.17333i) q^{87} +(-9.88485 + 29.6335i) q^{88} +(-4.34177 + 4.34177i) q^{89} +(-14.3370 + 16.8987i) q^{90} +(-11.6847 - 2.86820i) q^{91} +(14.1913 + 19.5326i) q^{92} +(4.32115 - 4.00763i) q^{93} +(9.35864 - 28.8029i) q^{94} +(11.5502 - 8.39168i) q^{95} +(-33.9224 + 15.7061i) q^{96} +(-0.157839 - 0.0804229i) q^{97} +(-7.98140 + 7.98140i) q^{98} +(9.20959 - 3.76610i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) $ 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9	$ 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9} - 20 q^{13} - 30 q^{15} + 32 q^{16} + 2 q^{18} - 4 q^{19} - 12 q^{21} - 24 q^{22} - 78 q^{24} - 36 q^{27} - 84 q^{28} - 28 q^{31} - 44 q^{33} - 24 q^{34} - 12 q^{37} + 54 q^{39} + 88 q^{40} - 56 q^{42} + 8 q^{45} - 92 q^{46} + 40 q^{48} - 44 q^{52} - 176 q^{54} - 72 q^{55} - 6 q^{57} - 4 q^{58} + 12 q^{60} - 48 q^{61} - 46 q^{63} + 204 q^{66} - 64 q^{67} + 56 q^{70} - 66 q^{72} - 12 q^{73} - 104 q^{76} - 92 q^{78} + 104 q^{79} + 124 q^{81} + 16 q^{84} - 12 q^{85} - 24 q^{87} - 84 q^{91} - 124 q^{93} + 328 q^{94} - 152 q^{96} + 52 q^{97} - 142 q^{99}+O(q^{100}) $ 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9 - 20 * q^13 - 30 * q^15 + 32 * q^16 + 2 * q^18 - 4 * q^19 - 12 * q^21 - 24 * q^22 - 78 * q^24 - 36 * q^27 - 84 * q^28 - 28 * q^31 - 44 * q^33 - 24 * q^34 - 12 * q^37 + 54 * q^39 + 88 * q^40 - 56 * q^42 + 8 * q^45 - 92 * q^46 + 40 * q^48 - 44 * q^52 - 176 * q^54 - 72 * q^55 - 6 * q^57 - 4 * q^58 + 12 * q^60 - 48 * q^61 - 46 * q^63 + 204 * q^66 - 64 * q^67 + 56 * q^70 - 66 * q^72 - 12 * q^73 - 104 * q^76 - 92 * q^78 + 104 * q^79 + 124 * q^81 + 16 * q^84 - 12 * q^85 - 24 * q^87 - 84 * q^91 - 124 * q^93 + 328 * q^94 - 152 * q^96 + 52 * q^97 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{5}\right)$	$-1$

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 $

$2$	−1.23921	+	2.43208i	−0.876251	+	1.71974i	−0.204636	+	0.978838i	$0.565601\pi$
$2$	−1.23921	+	2.43208i	−0.876251	+	1.71974i	−0.671614	+	0.740901i	$0.734399\pi$
$3$	0.596820	−	1.62598i	0.344574	−	0.938759i
$3$	0.596820	−	1.62598i	0.344574	−	0.938759i
$4$	−3.20380	−	4.40966i	−1.60190	−	2.20483i
$5$	−2.41132	+	1.22863i	−1.07838	+	0.549460i	−0.900617	−	0.434614i	$-0.856885\pi$
$5$	−2.41132	+	1.22863i	−1.07838	+	0.549460i	−0.177759	+	0.984074i	$0.556885\pi$
$6$	3.21492	+	3.46643i	1.31249	+	1.41517i
$7$	3.29586	+	0.522013i	1.24572	+	0.197303i	0.744267	−	0.667883i	$-0.232799\pi$
$7$	3.29586	+	0.522013i	1.24572	+	0.197303i	0.501452	+	0.865185i	$0.332799\pi$
$8$	9.30284	−	1.47343i	3.28905	−	0.520935i
$9$	−2.28761	−	1.94083i	−0.762538	−	0.646944i
$10$		−	7.38704i		−	2.33599i
$11$	−1.52873	+	2.94329i	−0.460931	+	0.887436i
$11$	−1.52873	+	2.94329i	−0.460931	+	0.887436i
$12$	−9.08210	+	2.57755i	−2.62178	+	0.744073i
$13$	−3.59295	−	0.301176i	−0.996505	−	0.0835313i
$13$	−3.59295	−	0.301176i	−0.996505	−	0.0835313i
$14$	−5.35383	+	7.36891i	−1.43087	+	1.96943i
$15$	0.558601	+	4.65403i	0.144230	+	1.20166i
$16$	−4.57597	+	14.0834i	−1.14399	+	3.52085i
$17$	0.113282	−	0.348646i	0.0274749	−	0.0845590i	−0.936379	−	0.350991i	$-0.885845\pi$
$17$	0.113282	−	0.348646i	0.0274749	−	0.0845590i	0.963854	+	0.266432i	$0.0858448\pi$
$18$	7.55508	−	3.15856i	1.78075	−	0.744481i
$19$	−5.21046	+	0.825256i	−1.19536	+	0.189327i	−0.722222	−	0.691661i	$-0.756879\pi$
$19$	−5.21046	+	0.825256i	−1.19536	+	0.189327i	−0.473139	+	0.880988i	$0.656879\pi$
$20$	13.1432	+	6.69681i	2.93891	+	1.49745i
$21$	2.81582	−	5.04745i	0.614462	−	1.10144i
$22$	−5.26390	−	7.36535i	−1.12227	−	1.57030i
$23$	−4.42950			−0.923615			−0.461807	−	0.886980i	$-0.652799\pi$
$23$	−4.42950			−0.923615			−0.461807	+	0.886980i	$0.652799\pi$
$24$	3.15636	−	16.0056i	0.644289	−	3.26713i
$25$	1.36601	−	1.88015i	0.273202	−	0.376030i
$26$	5.18489	−	8.36512i	1.01684	−	1.64053i
$27$	−4.52104	+	2.56128i	−0.870075	+	0.492919i
$28$	−8.25739	−	16.2060i	−1.56050	−	3.06266i
$29$	−1.45841	−	2.00733i	−0.270820	−	0.372752i	0.651846	−	0.758351i	$-0.273995\pi$
$29$	−1.45841	−	2.00733i	−0.270820	−	0.372752i	−0.922666	+	0.385599i	$0.873995\pi$
$30$	−12.0112	−	4.40873i	−2.19293	−	0.804921i
$31$	3.03175	+	1.54476i	0.544519	+	0.277446i	0.704536	−	0.709668i	$-0.251155\pi$
$31$	3.03175	+	1.54476i	0.544519	+	0.277446i	−0.160017	+	0.987114i	$0.551155\pi$
$32$	−15.2611	−	15.2611i	−2.69781	−	2.69781i
$33$	3.87335	+	4.24230i	0.674264	+	0.738490i
$34$	0.707554	+	0.707554i	0.121345	+	0.121345i
$35$	−8.58874	+	2.79065i	−1.45176	+	0.471706i
$36$	−1.22934	+	16.3056i	−0.204890	+	2.71760i
$37$	−5.08538	−	0.805445i	−0.836031	−	0.132414i	−0.276282	−	0.961077i	$-0.589102\pi$
$37$	−5.08538	−	0.805445i	−0.836031	−	0.132414i	−0.559749	+	0.828662i	$0.689102\pi$
$38$	4.44974	−	13.6949i	0.721844	−	2.22161i
$39$	−2.63405	+	5.66231i	−0.421785	+	0.906696i
$40$	−20.6218	+	14.9826i	−3.26060	+	2.36896i
$41$	0.132540	+	0.836823i	0.0206992	+	0.130690i	0.995874	−	0.0907468i	$-0.0289254\pi$
$41$	0.132540	+	0.836823i	0.0206992	+	0.130690i	−0.975175	+	0.221437i	$0.928925\pi$
$42$	8.78643	+	13.1031i	1.35577	+	2.02186i
$43$		−	3.67829i		−	0.560935i	−0.959864	−	0.280467i	$-0.909511\pi$
$43$		−	3.67829i		−	0.560935i	0.959864	−	0.280467i	$-0.0904894\pi$
$44$	17.8767	−	2.68853i	2.69501	−	0.405312i
$45$	7.90073	+	1.86934i	1.17777	+	0.278665i
$46$	5.48906	−	10.7729i	0.809318	−	1.58838i
$47$	−10.9586	+	1.73567i	−1.59847	+	0.253173i	−0.891146	−	0.453716i	$-0.850098\pi$
$47$	−10.9586	+	1.73567i	−1.59847	+	0.253173i	−0.707324	+	0.706889i	$0.750098\pi$
$48$	20.1683	+	15.8457i	2.91104	+	2.28713i
$49$	3.93282	+	1.27785i	0.561831	+	0.182550i
$50$	2.87991	+	5.65214i	0.407281	+	0.799333i
$51$	−0.499282	−	0.392272i	−0.0699134	−	0.0549291i
$52$	10.1830	+	16.8086i	1.41213	+	2.33093i
$53$	−0.166632	+	0.0541421i	−0.0228887	+	0.00743699i	−0.320439	−	0.947269i	$-0.603830\pi$
$53$	−0.166632	+	0.0541421i	−0.0228887	+	0.00743699i	0.297550	+	0.954706i	$0.403830\pi$
$54$	−0.626739	−	14.1695i	−0.0852884	−	1.92822i
$55$	0.0700540	−	8.97547i	0.00944609	−	1.21025i
$56$	31.4300			4.20002
$57$	−1.76786	+	8.96462i	−0.234158	+	1.18739i
$58$	6.68926	−	1.05947i	0.878342	−	0.139116i
$59$	0.0819982	−	0.517716i	0.0106753	−	0.0674009i	−0.981776	−	0.190044i	$-0.939137\pi$
$59$	0.0819982	−	0.517716i	0.0106753	−	0.0674009i	0.992451	+	0.122643i	$0.0391370\pi$
$60$	18.7330	−	17.3738i	2.41842	−	2.24295i
$61$	−1.97779	+	6.08701i	−0.253230	+	0.779362i	0.740943	+	0.671568i	$0.234379\pi$
$61$	−1.97779	+	6.08701i	−0.253230	+	0.779362i	−0.994173	+	0.107794i	$0.965621\pi$
$62$	−7.51393	+	5.45919i	−0.954270	+	0.693318i
$63$	−6.52652	−	7.59088i	−0.822264	−	0.956361i
$64$	27.8612	−	9.05265i	3.48265	−	1.13158i
$65$	9.03379	−	3.68817i	1.12050	−	0.457461i
$66$	−15.1175	+	4.16321i	−1.86084	+	0.512455i
$67$	2.43659	−	2.43659i	0.297677	−	0.297677i	−0.542426	−	0.840104i	$-0.682494\pi$
$67$	2.43659	−	2.43659i	0.297677	−	0.297677i	0.840104	+	0.542426i	$0.182494\pi$
$68$	−1.90034	+	0.617458i	−0.230450	+	0.0748778i
$69$	−2.64361	+	7.20227i	−0.318254	+	0.867052i
$70$	3.85614	−	24.3467i	0.460896	−	2.90999i
$71$	−0.471584	+	0.240284i	−0.0559667	+	0.0285164i	−0.481750	−	0.876309i	$-0.659999\pi$
$71$	−0.471584	+	0.240284i	−0.0559667	+	0.0285164i	0.425783	+	0.904825i	$0.359999\pi$
$72$	−24.1410	−	14.6846i	−2.84504	−	1.73060i
$73$	11.2551	+	1.78264i	1.31732	+	0.208642i	0.775229	−	0.631680i	$-0.217635\pi$
$73$	11.2551	+	1.78264i	1.31732	+	0.208642i	0.542086	+	0.840323i	$0.317635\pi$
$74$	8.26074	−	11.3699i	0.960291	−	1.32173i
$75$	−2.24182	−	3.34321i	−0.258864	−	0.386041i
$76$	20.3324	+	20.3324i	2.33228	+	2.33228i
$77$	−6.57494	+	8.90267i	−0.749284	+	1.01455i
$78$	−10.5071	−	13.4230i	−1.18969	−	1.51985i
$79$	3.48747	+	10.7333i	0.392371	+	1.20759i	0.930990	+	0.365044i	$0.118946\pi$
$79$	3.48747	+	10.7333i	0.392371	+	1.20759i	−0.538620	+	0.842549i	$0.681054\pi$
$80$	−6.26913	−	39.5817i	−0.700910	−	4.42537i
$81$	1.46634	+	8.87974i	0.162927	+	0.986638i
$82$	−2.19946	−	0.714649i	−0.242890	−	0.0789197i
$83$	−8.08074	+	4.11734i	−0.886976	+	0.451937i	−0.837246	−	0.546826i	$-0.815836\pi$
$83$	−8.08074	+	4.11734i	−0.886976	+	0.451937i	−0.0497296	+	0.998763i	$0.515836\pi$
$84$	−31.2789	+	3.75426i	−3.41280	+	0.409623i
$85$	0.155197	+	0.979878i	0.0168335	+	0.106283i
$86$	8.94590	+	4.55816i	0.964661	+	0.491519i
$87$	−4.13428	+	1.17333i	−0.443242	+	0.125794i
$88$	−9.88485	+	29.6335i	−1.05373	+	3.15894i
$89$	−4.34177	+	4.34177i	−0.460226	+	0.460226i	−0.898730	−	0.438503i	$-0.855509\pi$
$89$	−4.34177	+	4.34177i	−0.460226	+	0.460226i	0.438503	+	0.898730i	$0.355509\pi$
$90$	−14.3370	+	16.8987i	−1.51125	+	1.78128i
$91$	−11.6847	−	2.86820i	−1.22488	−	0.300670i
$92$	14.1913	+	19.5326i	1.47954	+	2.03641i
$93$	4.32115	−	4.00763i	0.448082	−	0.415571i
$94$	9.35864	−	28.8029i	0.965270	−	2.97080i
$95$	11.5502	−	8.39168i	1.18502	−	0.860968i
$96$	−33.9224	+	15.7061i	−3.46219	+	1.60300i
$97$	−0.157839	−	0.0804229i	−0.0160261	−	0.00816570i	0.445959	−	0.895053i	$-0.352863\pi$
$97$	−0.157839	−	0.0804229i	−0.0160261	−	0.00816570i	−0.461985	+	0.886888i	$0.652863\pi$
$98$	−7.98140	+	7.98140i	−0.806243	+	0.806243i
$99$	9.20959	−	3.76610i	0.925598	−	0.378507i
$100$	−12.6672			−1.26672
$101$	−4.61946	−	14.2172i	−0.459653	−	1.41467i	−0.865584	−	0.500763i	$-0.833053\pi$
$101$	−4.61946	−	14.2172i	−0.459653	−	1.41467i	0.405931	−	0.913904i	$-0.366947\pi$
$102$	1.57275	−	0.728186i	0.155725	−	0.0721011i
$103$	10.2223	+	14.0698i	1.00723	+	1.38633i	0.920782	+	0.390078i	$0.127552\pi$
$103$	10.2223	+	14.0698i	1.00723	+	1.38633i	0.0864489	+	0.996256i	$0.472448\pi$
$104$	−33.8684	+	2.49215i	−3.32107	+	0.244375i
$105$	−0.588390	+	15.6306i	−0.0574209	+	1.52539i
$106$	0.0748138	−	0.472356i	0.00726656	−	0.0458792i
$107$	1.20624	−	1.66025i	0.116612	−	0.160502i	−0.746721	−	0.665137i	$-0.768373\pi$
$107$	1.20624	−	1.66025i	0.116612	−	0.160502i	0.863333	+	0.504635i	$0.168373\pi$
$108$	25.7789	+	11.7304i	2.48058	+	1.12876i
$109$	−5.98682	+	5.98682i	−0.573434	+	0.573434i	−0.933086	−	0.359653i	$-0.882895\pi$
$109$	−5.98682	+	5.98682i	−0.573434	+	0.573434i	0.359653	+	0.933086i	$0.382895\pi$
$110$	21.7422	+	11.2928i	2.07304	+	1.07673i
$111$	−4.34469	+	7.78801i	−0.412380	+	0.739205i
$112$	−22.4335	+	44.0282i	−2.11977	+	4.16027i
$113$	9.13865	−	12.5783i	0.859692	−	1.18326i	−0.121951	−	0.992536i	$-0.538915\pi$
$113$	9.13865	−	12.5783i	0.859692	−	1.18326i	0.981643	−	0.190728i	$-0.0610850\pi$
$114$	−19.6119	−	15.4086i	−1.83683	−	1.44315i
$115$	10.6809	−	5.44221i	0.996003	−	0.507489i
$116$	−4.17918	+	12.8622i	−0.388027	+	1.19422i
$117$	7.63475	+	7.66229i	0.705833	+	0.708379i
$118$	1.15751	+	0.840983i	0.106558	+	0.0774188i
$119$	0.555359	−	1.08995i	0.0509097	−	0.0999159i
$120$	12.0539	+	42.4726i	1.10037	+	3.87720i
$121$	−6.32594	−	8.99903i	−0.575086	−	0.818093i
$122$	−12.3532	−	12.3532i	−1.11841	−	1.11841i
$123$	1.43976	+	0.283925i	0.129819	+	0.0256007i
$124$	−2.90130	−	18.3181i	−0.260544	−	1.64501i
$125$	1.13290	−	7.15288i	0.101330	−	0.639773i
$126$	26.5493	−	6.46634i	2.36520	−	0.576067i
$127$	−8.91165	−	2.89557i	−0.790781	−	0.256940i	−0.114344	−	0.993441i	$-0.536477\pi$
$127$	−8.91165	−	2.89557i	−0.790781	−	0.256940i	−0.676436	+	0.736501i	$0.736477\pi$
$128$	−5.75650	+	36.3451i	−0.508808	+	3.21248i
$129$	−5.98083	−	2.19528i	−0.526583	−	0.193283i
$130$	−2.22480	+	26.5413i	−0.195128	+	2.32782i
$131$		−	9.84438i		−	0.860108i	−0.902803	−	0.430054i	$-0.858495\pi$
$131$		−	9.84438i		−	0.860108i	0.902803	−	0.430054i	$-0.141505\pi$
$132$	6.29765	−	30.6717i	0.548140	−	2.66963i
$133$	−17.6038			−1.52644
$134$	2.90655	+	8.94543i	0.251087	+	0.772768i
$135$	7.75482	−	11.7308i	0.667428	−	1.00962i
$136$	0.540140	−	3.41031i	0.0463166	−	0.292431i
$137$	7.38817	+	14.5001i	0.631214	+	1.23883i	0.956091	+	0.293070i	$0.0946770\pi$
$137$	7.38817	+	14.5001i	0.631214	+	1.23883i	−0.324877	+	0.945756i	$0.605323\pi$
$138$	−14.2405	−	15.3546i	−1.21223	−	1.30707i
$139$	10.6813	−	7.76039i	0.905972	−	0.658228i	−0.0340206	−	0.999421i	$-0.510831\pi$
$139$	10.6813	−	7.76039i	0.905972	−	0.658228i	0.939993	+	0.341194i	$0.110831\pi$
$140$	39.8224	+	28.9327i	3.36561	+	2.44526i
$141$	−3.71813	+	18.8543i	−0.313123	+	1.58782i
$142$		−	1.44469i		−	0.121236i
$143$	6.37912	−	10.1147i	0.533449	−	0.845832i
$144$	37.8015	−	23.3362i	3.15013	−	1.94468i
$145$	5.98296	+	3.04847i	0.496858	+	0.253162i
$146$	−18.2830	+	25.1643i	−1.51311	+	2.08262i
$147$	4.42494	−	5.63203i	0.364963	−	0.464522i
$148$	12.7408	+	25.0053i	1.04729	+	2.05542i
$149$	5.13488	−	2.61635i	0.420666	−	0.214340i	−0.230827	−	0.972995i	$-0.574143\pi$
$149$	5.13488	−	2.61635i	0.420666	−	0.214340i	0.651493	+	0.758655i	$0.274143\pi$
$150$	10.9090	−	1.30936i	0.890719	−	0.106909i
$151$	−1.92708	−	12.1671i	−0.156824	−	0.990146i	−0.933064	−	0.359709i	$-0.882876\pi$
$151$	−1.92708	−	12.1671i	−0.156824	−	0.990146i	0.776241	−	0.630437i	$-0.217124\pi$
$152$	−47.2561	+	15.3544i	−3.83298	+	1.24541i
$153$	−0.935808	+	0.577705i	−0.0756556	+	0.0467047i
$154$	−13.5043	−	27.0230i	−1.08821	−	2.17758i
$155$	−9.20846			−0.739641
$156$	33.4078	−	6.52568i	2.67477	−	0.522473i
$157$	3.30110	+	2.39839i	0.263456	+	0.191412i	0.711669	−	0.702515i	$-0.247939\pi$
$157$	3.30110	+	2.39839i	0.263456	+	0.191412i	−0.448213	+	0.893927i	$0.647939\pi$
$158$	−30.4260	−	4.81900i	−2.42056	−	0.383379i
$159$	−0.0114155	+	0.303253i	−0.000905307	+	0.0240496i
$160$	55.5498	+	18.0492i	4.39160	+	1.42692i
$161$	−14.5990	−	2.31226i	−1.15056	−	0.182232i
$162$	−23.4133	−	7.43756i	−1.83953	−	0.584350i
$163$	4.53815	−	8.90662i	0.355455	−	0.697621i	−0.642165	−	0.766566i	$-0.721964\pi$
$163$	4.53815	−	8.90662i	0.355455	−	0.697621i	0.997620	+	0.0689459i	$0.0219636\pi$
$164$	3.26547	−	3.26547i	0.254990	−	0.254990i
$165$	−14.5521	−	5.47064i	−1.13288	−	0.425889i
$166$		−	24.7552i		−	1.92138i
$167$	15.8821	+	8.09232i	1.22899	+	0.626202i	0.943243	−	0.332103i	$-0.107758\pi$
$167$	15.8821	+	8.09232i	1.22899	+	0.626202i	0.285748	+	0.958305i	$0.407758\pi$
$168$	18.7581	−	51.1046i	1.44722	−	3.94280i
$169$	12.8186	+	2.16422i	0.986045	+	0.166479i
$170$	−2.57546	−	0.836818i	−0.197529	−	0.0641810i
$171$	13.5212	+	8.22476i	1.03399	+	0.628963i
$172$	−16.2200	+	11.7845i	−1.23676	+	0.898562i
$173$	6.37936	+	4.63488i	0.485014	+	0.352383i	0.803264	−	0.595624i	$-0.203095\pi$
$173$	6.37936	+	4.63488i	0.485014	+	0.352383i	−0.318250	+	0.948007i	$0.603095\pi$
$174$	2.26960	−	11.5089i	0.172058	−	0.872488i
$175$	5.48365	−	5.48365i	0.414525	−	0.414525i
$176$	−34.4561	−	34.9982i	−2.59723	−	2.63809i
$177$	−0.792858	−	0.442311i	−0.0595948	−	0.0332461i
$178$	−5.17917	−	15.9399i	−0.388195	−	1.19474i
$179$	5.37925	+	3.90825i	0.402064	+	0.292117i	0.770381	−	0.637584i	$-0.220066\pi$
$179$	5.37925	+	3.90825i	0.402064	+	0.292117i	−0.368317	+	0.929700i	$0.620066\pi$
$180$	−17.0692	−	40.8285i	−1.27227	−	3.04318i
$181$	−14.7570	−	4.79483i	−1.09688	−	0.356397i	−0.295977	−	0.955195i	$-0.595645\pi$
$181$	−14.7570	−	4.79483i	−1.09688	−	0.356397i	−0.800900	+	0.598798i	$0.795645\pi$
$182$	21.4554	−	24.8637i	1.59038	−	1.84302i
$183$	8.71697	+	6.84869i	0.644377	+	0.506270i
$184$	−41.2070	+	6.52654i	−3.03782	+	0.481143i
$185$	13.2521	−	4.30586i	0.974312	−	0.316573i
$186$	4.39207	+	15.4756i	0.322042	+	1.13473i
$187$	0.852988	+	0.866408i	0.0623767	+	0.0633580i
$188$	42.7628	+	42.7628i	3.11880	+	3.11880i
$189$	−16.2378	+	6.08159i	−1.18112	+	0.442371i
$190$	6.09620	+	38.4899i	0.442265	+	2.79235i
$191$	2.93671	+	4.04204i	0.212493	+	0.292472i	0.901937	−	0.431867i	$-0.142145\pi$
$191$	2.93671	+	4.04204i	0.212493	+	0.292472i	−0.689444	+	0.724339i	$0.742145\pi$
$192$	1.90869	−	50.7045i	0.137748	−	3.65928i
$193$	−16.9237	+	8.62303i	−1.21819	+	0.620699i	−0.940442	−	0.339954i	$-0.889588\pi$
$193$	−16.9237	+	8.62303i	−1.21819	+	0.620699i	−0.277749	+	0.960654i	$0.589588\pi$
$194$	0.391189	−	0.284216i	0.0280858	−	0.0204055i
$195$	−0.605344	−	16.8899i	−0.0433496	−	1.20951i
$196$	−6.96509	−	21.4363i	−0.497507	−	1.53117i
$197$	9.83696	+	9.83696i	0.700854	+	0.700854i	0.964594	−	0.263740i	$-0.0849560\pi$
$197$	9.83696	+	9.83696i	0.700854	+	0.700854i	−0.263740	+	0.964594i	$0.584956\pi$
$198$	−2.25313	+	27.0654i	−0.160123	+	1.92345i
$199$			10.3508i			0.733747i	0.930271	+	0.366873i	$0.119572\pi$
$199$			10.3508i			0.733747i	−0.930271	+	0.366873i	$0.880428\pi$
$200$	9.93751	−	19.5035i	0.702688	−	1.37910i
$201$	−2.50764	−	5.41606i	−0.176876	−	0.382019i
$202$	40.3019	+	6.38319i	2.83563	+	0.449119i
$203$	−3.75887	−	7.37720i	−0.263821	−	0.517778i
$204$	−0.130187	+	3.45842i	−0.00911490	+	0.242138i
$205$	−1.34774	−	1.85501i	−0.0941303	−	0.129559i
$206$	−46.8862	+	7.42605i	−3.26672	+	0.517398i
$207$	10.1330	+	8.59692i	0.704291	+	0.597527i
$208$	20.6828	−	49.2228i	1.43410	−	3.41298i
$209$	5.53644	−	16.5975i	0.382964	−	1.14807i
$210$	−37.2858	−	20.8006i	−2.57296	−	1.43538i
$211$	−3.30784	−	10.1805i	−0.227721	−	0.700854i	−0.998004	−	0.0631517i	$-0.979885\pi$
$211$	−3.30784	−	10.1805i	−0.227721	−	0.700854i	0.770283	−	0.637703i	$-0.220115\pi$
$212$	0.772605	+	0.561330i	0.0530627	+	0.0385523i
$213$	0.109246	+	0.910191i	0.00748542	+	0.0623652i
$214$	2.54308	+	4.99107i	0.173841	+	0.341182i
$215$	4.51926	+	8.86955i	0.308211	+	0.604898i
$216$	−38.2847	+	30.4886i	−2.60494	+	2.07449i
$217$	9.18586	+	6.67392i	0.623577	+	0.453055i
$218$	−7.14152	−	21.9793i	−0.483685	−	1.48863i
$219$	9.61583	−	17.2367i	0.649777	−	1.16475i
$220$	−39.8032	+	28.4467i	−2.68353	+	1.91788i
$221$	−0.512020	+	1.21855i	−0.0344422	+	0.0819685i
$222$	−13.5571	−	20.2176i	−0.909892	−	1.35691i
$223$	−2.03140	+	0.321741i	−0.136032	+	0.0215454i	−0.224079	−	0.974571i	$-0.571937\pi$
$223$	−2.03140	+	0.321741i	−0.136032	+	0.0215454i	0.0880470	+	0.996116i	$0.471937\pi$
$224$	−42.3321	−	58.2651i	−2.82843	−	3.89300i
$225$	−6.77396	+	1.64986i	−0.451597	+	0.109991i
$226$	19.2667	+	37.8130i	1.28160	+	2.51528i
$227$	0.555316	+	0.0879534i	0.0368576	+	0.00583767i	0.174836	−	0.984598i	$-0.444060\pi$
$227$	0.555316	+	0.0879534i	0.0368576	+	0.00583767i	−0.137978	+	0.990435i	$0.544060\pi$
$228$	45.1948	−	20.9252i	2.99310	−	1.38581i
$229$	−3.19674	+	6.27396i	−0.211247	+	0.414595i	−0.972180	−	0.234235i	$-0.924741\pi$
$229$	−3.19674	+	6.27396i	−0.211247	+	0.414595i	0.760933	+	0.648830i	$0.224741\pi$
$230$			32.7209i			2.15755i
$231$	10.5515	+	16.0040i	0.694237	+	1.05299i
$232$	−16.5250	−	16.5250i	−1.08492	−	1.08492i
$233$	−4.74846	−	14.6143i	−0.311082	−	0.957412i	−0.977337	−	0.211688i	$-0.932104\pi$
$233$	−4.74846	−	14.6143i	−0.311082	−	0.957412i	0.666255	−	0.745724i	$-0.267896\pi$
$234$	−28.0963	+	9.07315i	−1.83671	+	0.593130i
$235$	24.2921	−	17.6493i	1.58464	−	1.15131i
$236$	−2.54566	+	1.29708i	−0.165708	+	0.0844325i
$237$	19.5335	+	0.735308i	1.26884	+	0.0477634i
$238$	1.96265	+	2.70135i	0.127220	+	0.175103i
$239$	−0.372021	−	2.34885i	−0.0240640	−	0.151934i	0.972731	−	0.231938i	$-0.0745067\pi$
$239$	−0.372021	−	2.34885i	−0.0240640	−	0.151934i	−0.996795	+	0.0800040i	$0.974507\pi$
$240$	−68.1006	−	13.4297i	−4.39587	−	0.866882i
$241$	−18.3708	−	18.3708i	−1.18336	−	1.18336i	−0.978867	−	0.204498i	$-0.934444\pi$
$241$	−18.3708	−	18.3708i	−1.18336	−	1.18336i	−0.204498	−	0.978867i	$-0.565556\pi$
$242$	29.7255	−	4.23354i	1.91083	−	0.272142i
$243$	15.3134	+	2.91536i	0.982356	+	0.187020i
$244$	33.1781	−	10.7802i	2.12401	−	0.690132i
$245$	−11.0533	+	1.75067i	−0.706168	+	0.111846i
$246$	−2.47469	+	3.14976i	−0.157780	+	0.200822i
$247$	18.9695	−	1.39583i	1.20700	−	0.0888148i
$248$	30.4800	+	9.90355i	1.93548	+	0.628876i
$249$	1.87197	+	15.5964i	0.118631	+	0.988382i
$250$	15.9925	+	11.6192i	1.01145	+	0.734863i
$251$	−4.18396	−	12.8769i	−0.264089	−	0.812782i	−0.991902	−	0.127006i	$-0.959463\pi$
$251$	−4.18396	−	12.8769i	−0.264089	−	0.812782i	0.727813	−	0.685776i	$-0.240537\pi$
$252$	−12.5635	+	53.0994i	−0.791426	+	3.34495i
$253$	6.77153	−	13.0373i	0.425723	−	0.819649i
$254$	18.0856	−	18.0856i	1.13479	−	1.13479i
$255$	1.68589	+	0.332463i	0.105574	+	0.0208196i
$256$	−33.8604	−	24.6010i	−2.11627	−	1.53756i
$257$	−16.6569	+	12.1019i	−1.03903	+	0.754898i	−0.970095	−	0.242724i	$-0.921959\pi$
$257$	−16.6569	+	12.1019i	−1.03903	+	0.754898i	−0.0689322	+	0.997621i	$0.521959\pi$
$258$	12.7506	−	11.8254i	0.793816	−	0.736220i
$259$	−16.3403	−	5.30927i	−1.01533	−	0.329902i
$260$	−45.2060	−	28.0197i	−2.80356	−	1.73771i
$261$	−0.559611	+	7.42252i	−0.0346390	+	0.459443i
$262$	23.9423	+	12.1992i	1.47916	+	0.753670i
$263$			8.58287i			0.529242i	0.964352	+	0.264621i	$0.0852469\pi$
$263$			8.58287i			0.529242i	−0.964352	+	0.264621i	$0.914753\pi$
$264$	42.2839	+	33.7584i	2.60239	+	2.07769i
$265$	0.335283	−	0.335283i	0.0205963	−	0.0205963i
$266$	21.8147	−	42.8137i	1.33754	−	2.62508i
$267$	4.46837	+	9.65087i	0.273460	+	0.590624i
$268$	−18.5509	−	2.93818i	−1.13318	−	0.179478i
$269$	0.591971	+	0.192343i	0.0360931	+	0.0117274i	0.327008	−	0.945022i	$-0.393960\pi$
$269$	0.591971	+	0.192343i	0.0360931	+	0.0117274i	−0.290915	+	0.956749i	$0.593960\pi$
$270$	18.9203	+	33.3971i	1.15145	+	2.03249i
$271$	14.8731	+	2.35567i	0.903477	+	0.143097i	0.590852	−	0.806780i	$-0.298792\pi$
$271$	14.8731	+	2.35567i	0.903477	+	0.143097i	0.312625	+	0.949877i	$0.398792\pi$
$272$	4.39174	+	3.19078i	0.266288	+	0.193470i
$273$	−11.6373	+	17.2872i	−0.704320	+	1.04627i
$274$	−44.4208			−2.68356
$275$	3.44557	+	6.89482i	0.207776	+	0.415773i
$276$	40.2292	−	11.4172i	2.42151	−	0.687237i
$277$	9.90074	−	3.21694i	0.594878	−	0.193287i	0.00392308	−	0.999992i	$-0.498751\pi$
$277$	9.90074	−	3.21694i	0.594878	−	0.193287i	0.590955	+	0.806705i	$0.298751\pi$
$278$	5.63759	+	35.5944i	0.338120	+	2.13481i
$279$	−3.93737	−	9.41792i	−0.235724	−	0.563836i
$280$	−75.7879	+	38.6159i	−4.52919	+	2.30774i
$281$	−7.20828	−	14.1470i	−0.430010	−	0.843942i	−0.999755	−	0.0221206i	$-0.992958\pi$
$281$	−7.20828	−	14.1470i	−0.430010	−	0.843942i	0.569746	−	0.821821i	$-0.307042\pi$
$282$	−41.2475	−	32.4071i	−2.45625	−	1.92981i
$283$	−18.6645	+	25.6895i	−1.10949	+	1.52708i	−0.287324	+	0.957833i	$0.592766\pi$
$283$	−18.6645	+	25.6895i	−1.10949	+	1.52708i	−0.822165	+	0.569249i	$0.807234\pi$
$284$	2.57043	+	1.30970i	0.152527	+	0.0777164i
$285$	−6.75133	−	23.7886i	−0.399914	−	1.40912i
$286$	16.6947	+	28.0487i	0.987176	+	1.65855i
$287$			2.82724i			0.166887i
$288$	5.29228	+	64.5309i	0.311850	+	3.80252i
$289$	13.6446	+	9.91336i	0.802622	+	0.583139i
$290$	−14.8282	+	10.7733i	−0.870744	+	0.632633i
$291$	−0.224967	+	0.208645i	−0.0131878	+	0.0122310i
$292$	−28.1984	−	55.3426i	−1.65019	−	3.23868i
$293$	−1.04651	+	6.60741i	−0.0611378	+	0.386009i	0.938078	+	0.346423i	$0.112604\pi$
$293$	−1.04651	+	6.60741i	−0.0611378	+	0.386009i	−0.999216	+	0.0395858i	$0.987396\pi$
$294$	8.21413	+	17.7410i	0.479058	+	1.03468i
$295$	0.438357	+	1.34913i	0.0255222	+	0.0785491i
$296$	−48.4952			−2.81873
$297$	−0.627131	−	17.2223i	−0.0363898	−	0.999338i
$298$			15.7306i			0.911251i
$299$	15.9150	+	1.33406i	0.920387	+	0.0771508i
$300$	−7.56006	+	20.5967i	−0.436480	+	1.18915i
$301$	1.92012	−	12.1232i	0.110674	−	0.698767i
$302$	31.9794	+	10.3907i	1.84021	+	0.597920i
$303$	−25.8739	−	0.973980i	−1.48642	−	0.0559537i
$304$	12.2205	−	77.1573i	0.700894	−	4.42527i
$305$	−2.70959	−	17.1077i	−0.155151	−	0.979584i
$306$	−0.245366	−	2.99185i	−0.0140267	−	0.171033i
$307$	−4.43654	−	4.43654i	−0.253207	−	0.253207i	0.569077	−	0.822284i	$-0.307300\pi$
$307$	−4.43654	−	4.43654i	−0.253207	−	0.253207i	−0.822284	+	0.569077i	$0.807300\pi$
$308$	60.3225	+	0.470821i	3.43719	+	0.0268275i
$309$	28.9780	−	8.22410i	1.64850	−	0.467852i
$310$	11.4112	−	22.3957i	0.648111	−	1.27199i
$311$	7.76221	+	5.63957i	0.440154	+	0.319791i	0.785696	−	0.618612i	$-0.212305\pi$
$311$	7.76221	+	5.63957i	0.440154	+	0.319791i	−0.345542	+	0.938403i	$0.612305\pi$
$312$	−16.1612	+	56.5567i	−0.914945	+	3.20189i
$313$	0.284653	−	0.876071i	0.0160895	−	0.0495185i	−0.942689	−	0.333671i	$-0.891712\pi$
$313$	0.284653	−	0.876071i	0.0160895	−	0.0495185i	0.958779	+	0.284153i	$0.0917124\pi$
$314$	−9.92380	+	5.05643i	−0.560032	+	0.285351i
$315$	25.0639	+	10.2854i	1.41219	+	0.579515i
$316$	36.1571	−	49.7660i	2.03400	−	2.79955i
$317$	−7.09358	+	13.9219i	−0.398415	+	0.781934i	−0.999856	−	0.0169835i	$-0.994594\pi$
$317$	−7.09358	+	13.9219i	−0.398415	+	0.781934i	0.601440	+	0.798918i	$0.294594\pi$
$318$	−0.723390	−	0.403557i	−0.0405657	−	0.0226303i
$319$	8.13768	−	1.22385i	0.455623	−	0.0685227i
$320$	−56.0599	+	56.0599i	−3.13384	+	3.13384i
$321$	−1.97962	−	2.95219i	−0.110492	−	0.164775i
$322$	23.7148	−	32.6406i	1.32157	−	1.81899i
$323$	−0.302529	+	1.91009i	−0.0168331	+	0.106280i
$324$	34.4587	−	34.9150i	1.91437	−	1.93972i
$325$	−5.47426	+	6.34388i	−0.303658	+	0.351895i
$326$	16.0379	+	22.0743i	0.888257	+	1.22258i
$327$	6.16139	+	13.3075i	0.340726	+	0.735906i
$328$	2.46599	+	7.58954i	0.136162	+	0.419062i
$329$	−37.0240			−2.04120
$330$	31.3381	−	28.6126i	1.72510	−	1.57507i
$331$	−3.23887	+	3.23887i	−0.178024	+	0.178024i	−0.790494	−	0.612470i	$-0.790176\pi$
$331$	−3.23887	+	3.23887i	−0.178024	+	0.178024i	0.612470	+	0.790494i	$0.290176\pi$
$332$	44.0451	+	22.4421i	2.41729	+	1.23167i
$333$	10.0701	+	11.7124i	0.551841	+	0.641836i
$334$	−39.3623	+	28.5984i	−2.15381	+	1.56483i
$335$	−2.88174	+	8.86908i	−0.157446	+	0.484570i
$336$	58.2002	+	62.7533i	3.17508	+	3.42347i
$337$	−9.97566	−	13.7303i	−0.543409	−	0.747938i	0.445691	−	0.895187i	$-0.352958\pi$
$337$	−9.97566	−	13.7303i	−0.543409	−	0.747938i	−0.989099	+	0.147249i	$0.952958\pi$
$338$	−21.1484	+	28.4939i	−1.15032	+	1.54986i
$339$	−14.9979	−	22.3662i	−0.814573	−	1.21477i
$340$	3.82370	−	3.82370i	0.207369	−	0.207369i
$341$	−9.18141	+	6.56181i	−0.497201	+	0.355342i
$342$	−36.7588	+	22.6924i	−1.98769	+	1.22707i
$343$	−8.51772	−	4.33999i	−0.459913	−	0.234338i
$344$	−5.41969	−	34.2186i	−0.292210	−	1.84494i
$345$	−2.47433	−	20.6150i	−0.133213	−	1.10987i
$346$	−19.1777	+	9.77154i	−1.03100	+	0.525321i
$347$	−23.5136	−	7.64002i	−1.26227	−	0.410138i	−0.399970	−	0.916528i	$-0.630979\pi$
$347$	−23.5136	−	7.64002i	−1.26227	−	0.410138i	−0.862304	+	0.506391i	$0.830979\pi$
$348$	18.4194	+	14.4717i	0.987385	+	0.775762i
$349$	3.89482	+	24.5909i	0.208485	+	1.31632i	0.840688	+	0.541519i	$0.182151\pi$
$349$	3.89482	+	24.5909i	0.208485	+	1.31632i	−0.632204	+	0.774802i	$0.717849\pi$
$350$	6.54129	+	20.1320i	0.349647	+	1.07610i
$351$	17.0153	−	7.84093i	0.908209	−	0.418518i
$352$	68.2482	−	21.5878i	3.63764	−	1.15063i
$353$	17.1275	+	17.1275i	0.911607	+	0.911607i	0.996399	−	0.0847915i	$-0.0270224\pi$
$353$	17.1275	+	17.1275i	0.911607	+	0.911607i	−0.0847915	+	0.996399i	$0.527022\pi$
$354$	2.05825	−	1.38018i	0.109395	−	0.0733556i
$355$	0.841919	−	1.15880i	0.0446844	−	0.0615028i
$356$	33.0559	+	5.23553i	1.75196	+	0.277483i
$357$	−1.44079	−	1.55351i	−0.0762548	−	0.0822203i
$358$	−16.1712	+	8.23963i	−0.854673	+	0.435478i
$359$	3.38917	−	21.3983i	0.178873	−	1.12936i	−0.720911	−	0.693027i	$-0.756277\pi$
$359$	3.38917	−	21.3983i	0.178873	−	1.12936i	0.899785	−	0.436334i	$-0.143723\pi$
$360$	76.2536	+	5.74903i	4.01892	+	0.303001i
$361$	8.39776	−	2.72860i	0.441987	−	0.143610i
$362$	29.9483	−	29.9483i	1.57405	−	1.57405i
$363$	−18.4077	+	4.91505i	−0.966152	+	0.257973i
$364$	24.7875	+	60.7145i	1.29922	+	3.18230i
$365$	−29.3300	+	9.52988i	−1.53520	+	0.498817i
$366$	−27.4587	+	12.7134i	−1.43529	+	0.664540i
$367$	−30.2873	+	22.0050i	−1.58098	+	1.14865i	−0.665424	+	0.746466i	$0.731749\pi$
$367$	−30.2873	+	22.0050i	−1.58098	+	1.14865i	−0.915558	+	0.402185i	$0.868251\pi$
$368$	20.2693	−	62.3824i	1.05661	−	3.25191i
$369$	1.32093	−	2.17156i	0.0687650	−	0.113047i
$370$	−5.94986	+	37.5659i	−0.309318	+	1.95296i
$371$	−0.577460	+	0.0914606i	−0.0299802	+	0.00474840i
$372$	−31.5164	−	6.21514i	−1.63405	−	0.322240i
$373$	−31.3491			−1.62319			−0.811597	−	0.584217i	$-0.801402\pi$
$373$	−31.3491			−1.62319			−0.811597	+	0.584217i	$0.801402\pi$
$374$	−3.16420	+	1.00088i	−0.163617	+	0.0517541i
$375$	−10.9543	−	6.11106i	−0.565677	−	0.315574i
$376$	−99.3884	+	32.2932i	−5.12557	+	1.66540i
$377$	4.63544	+	7.65148i	0.238737	+	0.394071i
$378$	5.33102	−	47.0278i	0.274198	−	2.41885i
$379$	2.39289	+	4.69631i	0.122915	+	0.241233i	0.944262	−	0.329195i	$-0.106777\pi$
$379$	2.39289	+	4.69631i	0.122915	+	0.241233i	−0.821347	+	0.570428i	$0.806777\pi$
$380$	−74.0088	−	24.0469i	−3.79657	−	1.23358i
$381$	−10.0268	+	12.7620i	−0.513687	+	0.653818i
$382$	−13.4697	+	2.13340i	−0.689172	+	0.109154i
$383$	−7.89698	+	15.4987i	−0.403517	+	0.791946i	−0.999943	−	0.0107221i	$-0.996587\pi$
$383$	−7.89698	+	15.4987i	−0.403517	+	0.791946i	0.596426	+	0.802668i	$0.296587\pi$
$384$	55.6608	+	31.0514i	2.84043	+	1.58459i
$385$	4.91620	−	29.5453i	0.250553	−	1.50577i
$386$		−	51.8454i		−	2.63886i
$387$	−7.13895	+	8.41451i	−0.362893	+	0.427734i
$388$	0.151047	+	0.953674i	0.00766825	+	0.0484154i
$389$	−20.1560	+	14.6442i	−1.02195	+	0.742490i	−0.966682	−	0.255982i	$-0.917601\pi$
$389$	−20.1560	+	14.6442i	−1.02195	+	0.742490i	−0.0552681	+	0.998472i	$0.517601\pi$
$390$	41.8278	+	19.4578i	2.11803	+	0.985286i
$391$	−0.501782	+	1.54433i	−0.0253762	+	0.0780999i
$392$	38.4692	+	6.09292i	1.94299	+	0.307739i
$393$	−16.0068	−	5.87532i	−0.807434	−	0.296371i
$394$	−36.1143	+	11.7342i	−1.81941	+	0.591162i
$395$	−21.5967	−	21.5967i	−1.08665	−	1.08665i
$396$	−46.1129	−	28.5453i	−2.31726	−	1.43445i
$397$	−6.65423	−	6.65423i	−0.333966	−	0.333966i	0.520124	−	0.854091i	$-0.325886\pi$
$397$	−6.65423	−	6.65423i	−0.333966	−	0.333966i	−0.854091	+	0.520124i	$0.825886\pi$
$398$	−25.1739	−	12.8267i	−1.26185	−	0.642946i
$399$	−10.5063	+	28.6233i	−0.525971	+	1.43296i
$400$	20.2281	+	27.8416i	1.01140	+	1.39208i
$401$	−0.168061	−	0.329839i	−0.00839258	−	0.0164714i	0.886772	−	0.462207i	$-0.152942\pi$
$401$	−0.168061	−	0.329839i	−0.00839258	−	0.0164714i	−0.895165	+	0.445735i	$0.852942\pi$
$402$	16.2798	+	0.612825i	0.811961	+	0.0305650i
$403$	−10.4277	−	6.46332i	−0.519440	−	0.321961i
$404$	−47.8932	+	65.9194i	−2.38278	+	3.27961i
$405$	−14.4457	−	19.6103i	−0.717814	−	0.974444i
$406$	22.5999			1.12162
$407$	10.1449	−	13.7364i	0.502862	−	0.680890i
$408$	−5.22272	−	2.91359i	−0.258563	−	0.144244i
$409$	8.55247	+	4.35770i	0.422893	+	0.215475i	0.652468	−	0.757816i	$-0.273734\pi$
$409$	8.55247	+	4.35770i	0.422893	+	0.215475i	−0.229575	+	0.973291i	$0.573734\pi$
$410$	6.18165	−	0.979077i	0.305290	−	0.0483531i
$411$	27.9862	−	3.35906i	1.38046	−	0.165690i
$412$	29.2926	−	90.1534i	1.44314	−	4.44154i
$413$	0.540510	−	1.66352i	0.0265967	−	0.0818564i
$414$	−33.4652	+	13.9909i	−1.64473	+	0.687613i
$415$	14.4266	−	19.8565i	0.708172	−	0.974715i
$416$	50.2362	+	59.4288i	2.46303	+	2.91374i
$417$	−6.24344	−	21.9990i	−0.305743	−	1.07730i
$418$	33.5056	+	34.0328i	1.63881	+	1.66460i
$419$			19.7983i			0.967213i	0.875286	+	0.483606i	$0.160673\pi$
$419$			19.7983i			0.967213i	−0.875286	+	0.483606i	$0.839327\pi$
$420$	70.8108	−	47.4828i	3.45521	−	2.31693i
$421$	−35.0726	+	5.55496i	−1.70933	+	0.270732i	−0.933075	−	0.359682i	$-0.882885\pi$
$421$	−35.0726	+	5.55496i	−1.70933	+	0.270732i	−0.776259	+	0.630414i	$0.782885\pi$
$422$	28.8589	+	4.57080i	1.40483	+	0.222503i
$423$	28.4376	+	17.2982i	1.38268	+	0.841067i
$424$	−1.47038	+	0.749195i	−0.0714079	+	0.0363841i
$425$	−0.500763	−	0.689240i	−0.0242906	−	0.0334331i
$426$	−2.34903	−	0.862219i	−0.113811	−	0.0417746i
$427$	−9.69603	+	19.0295i	−0.469224	+	0.920903i
$428$	−11.1857			−0.540681
$429$	−12.6391	−	16.4090i	−0.610220	−	0.792232i
$430$	−27.1717			−1.31034
$431$	9.40549	−	18.4593i	0.453047	−	0.889154i	−0.545645	−	0.838016i	$-0.683715\pi$
$431$	9.40549	−	18.4593i	0.453047	−	0.889154i	0.998692	−	0.0511377i	$-0.0162847\pi$
$432$	−15.3834	−	75.3920i	−0.740134	−	3.62730i
$433$	−7.72442	−	10.6317i	−0.371212	−	0.510929i	0.582018	−	0.813176i	$-0.302263\pi$
$433$	−7.72442	−	10.6317i	−0.371212	−	0.510929i	−0.953230	+	0.302247i	$0.902263\pi$
$434$	−27.6147	+	14.0704i	−1.32555	+	0.675399i
$435$	8.52750	−	7.90878i	0.408862	−	0.379197i
$436$	45.5804	+	7.21923i	2.18291	+	0.345738i
$437$	23.0797	−	3.65547i	1.10405	−	0.174865i
$438$	30.0050	+	44.7463i	1.43370	+	2.13806i
$439$		−	6.76393i		−	0.322825i	−0.986887	−	0.161412i	$-0.948395\pi$
$439$		−	6.76393i		−	0.322825i	0.986887	−	0.161412i	$-0.0516049\pi$
$440$	−12.5730	−	83.6006i	−0.599393	−	3.98550i
$441$	−6.51667	−	10.5562i	−0.310318	−	0.502674i
$442$	−2.32911	−	2.75531i	−0.110784	−	0.131056i
$443$	17.5841	−	24.2024i	0.835444	−	1.14989i	−0.151441	−	0.988466i	$-0.548391\pi$
$443$	17.5841	−	24.2024i	0.835444	−	1.14989i	0.986885	−	0.161424i	$-0.0516086\pi$
$444$	48.2620	−	5.79267i	2.29041	−	0.274908i
$445$	5.13497	−	15.8038i	0.243421	−	0.749172i
$446$	1.73482	−	5.33922i	0.0821459	−	0.252819i
$447$	−1.18954	−	9.91070i	−0.0562631	−	0.468760i
$448$	96.5523	−	15.2924i	4.56167	−	0.722497i
$449$	−16.2170	−	8.26299i	−0.765329	−	0.389955i	0.0273245	−	0.999627i	$-0.491301\pi$
$449$	−16.2170	−	8.26299i	−0.765329	−	0.389955i	−0.792654	+	0.609672i	$0.791301\pi$
$450$	4.38173	−	18.5193i	0.206557	−	0.873009i
$451$	−2.66563	−	0.889177i	−0.125520	−	0.0418697i
$452$	−84.7443			−3.98604
$453$	−20.9336	−	4.12818i	−0.983546	−	0.193959i
$454$	−0.902060	+	1.24158i	−0.0423358	+	0.0582702i
$455$	31.6994	−	7.43994i	1.48609	−	0.348790i
$456$	−3.23738	+	86.0013i	−0.151604	+	4.02738i
$457$	5.76786	+	11.3201i	0.269809	+	0.529531i	0.985664	−	0.168718i	$-0.0539629\pi$
$457$	5.76786	+	11.3201i	0.269809	+	0.529531i	−0.715855	+	0.698249i	$0.753963\pi$
$458$	−11.2973	−	15.5495i	−0.527890	−	0.726578i
$459$	0.380828	+	1.86639i	0.0177755	+	0.0871156i
$460$	−58.2179	−	29.6635i	−2.71443	−	1.38307i
$461$	3.47244	+	3.47244i	0.161728	+	0.161728i	0.783332	−	0.621604i	$-0.213519\pi$
$461$	3.47244	+	3.47244i	0.161728	+	0.161728i	−0.621604	+	0.783332i	$0.713519\pi$
$462$	−51.9984	+	5.82982i	−2.41919	+	0.271228i
$463$	−0.836021	−	0.836021i	−0.0388532	−	0.0388532i	0.687413	−	0.726266i	$-0.258746\pi$
$463$	−0.836021	−	0.836021i	−0.0388532	−	0.0388532i	−0.726266	+	0.687413i	$0.758746\pi$
$464$	34.9437	−	11.3539i	1.62222	−	0.527091i
$465$	−5.49579	+	14.9728i	−0.254861	+	0.694345i
$466$	41.4273	+	6.56144i	1.91908	+	0.303953i
$467$	−7.91623	+	24.3637i	−0.366320	+	1.12742i	0.582831	+	0.812593i	$0.301945\pi$
$467$	−7.91623	+	24.3637i	−0.366320	+	1.12742i	−0.949151	+	0.314823i	$0.898055\pi$
$468$	9.32783	−	58.2151i	0.431179	−	2.69099i
$469$	9.30262	−	6.75875i	0.429555	−	0.312090i
$470$	12.8214	+	80.9514i	0.591409	+	3.73401i
$471$	5.86988	−	3.93611i	0.270470	−	0.181366i
$472$		−	4.93705i		−	0.227246i
$473$	10.8263	+	5.62314i	0.497794	+	0.258552i
$474$	−25.9944	+	46.5959i	−1.19396	+	2.14022i
$475$	−5.56593	+	10.9238i	−0.255383	+	0.501216i
$476$	−6.58558	+	1.04305i	−0.301850	+	0.0478083i
$477$	0.486271	+	0.199549i	0.0222648	+	0.00913672i
$478$	6.17359	+	2.00592i	0.282373	+	0.0917486i
$479$	−5.76383	−	11.3122i	−0.263356	−	0.516866i	0.721026	−	0.692908i	$-0.243671\pi$
$479$	−5.76383	−	11.3122i	−0.263356	−	0.516866i	−0.984383	+	0.176042i	$0.943671\pi$
$480$	62.5008	−	79.5506i	2.85276	−	3.63097i
$481$	18.0289	+	4.42552i	0.822049	+	0.201786i
$482$	67.4443	−	21.9140i	3.07200	−	0.998154i
$483$	−12.4727	+	22.3577i	−0.567526	+	1.01731i
$484$	−19.4155	+	56.7263i	−0.882525	+	2.57847i
$485$	0.479410			0.0217689
$486$	−26.0669	+	33.6307i	−1.18242	+	1.52552i
$487$	36.1342	−	5.72310i	1.63740	−	0.259338i	0.731190	−	0.682173i	$-0.238965\pi$
$487$	36.1342	−	5.72310i	1.63740	−	0.259338i	0.906207	+	0.422835i	$0.138965\pi$
$488$	−9.43031	+	59.5406i	−0.426890	+	2.69528i
$489$	−11.7735	−	12.6946i	−0.532417	−	0.574069i
$490$	9.43953	−	29.0519i	0.426435	−	1.31243i
$491$	27.2966	−	19.8322i	1.23188	−	0.895013i	0.234850	−	0.972032i	$-0.424540\pi$
$491$	27.2966	−	19.8322i	1.23188	−	0.895013i	0.997030	+	0.0770187i	$0.0245401\pi$
$492$	−3.36069	−	7.25848i	−0.151512	−	0.327238i
$493$	−0.865059	+	0.281075i	−0.0389603	+	0.0126590i
$494$	−20.1123	+	47.8650i	−0.904895	+	2.15355i
$495$	−17.5801	+	20.3964i	−0.790168	+	0.916752i
$496$	−35.6286	+	35.6286i	−1.59977	+	1.59977i
$497$	−1.67971	+	0.545770i	−0.0753451	+	0.0244811i
$498$	−40.2514	−	14.7744i	−1.80371	−	0.662056i
$499$	3.98385	−	25.1531i	0.178342	−	1.12601i	−0.722344	−	0.691534i	$-0.756935\pi$
$499$	3.98385	−	25.1531i	0.178342	−	1.12601i	0.900686	−	0.434471i	$-0.143065\pi$
$500$	−35.1713	+	17.9207i	−1.57291	+	0.801438i
$501$	22.6367	−	20.9942i	1.01133	−	0.937954i
$502$	36.5024	+	5.78141i	1.62918	+	0.258037i
$503$	23.6690	−	32.5776i	1.05535	−	1.45257i	0.171274	−	0.985223i	$-0.445212\pi$
$503$	23.6690	−	32.5776i	1.05535	−	1.45257i	0.884077	−	0.467342i	$-0.154788\pi$
$504$	−71.8998	−	61.0004i	−3.20267	−	2.71717i
$505$	28.6067	+	28.6067i	1.27298	+	1.27298i
$506$	23.3165	+	32.6248i	1.03654	+	1.45035i
$507$	11.1694	−	19.5511i	0.496049	−	0.868295i
$508$	15.7827	+	48.5741i	0.700244	+	2.15513i
$509$	0.277329	+	1.75099i	0.0122924	+	0.0776111i	0.993072	−	0.117508i	$-0.0374906\pi$
$509$	0.277329	+	1.75099i	0.0122924	+	0.0776111i	−0.980780	+	0.195119i	$0.937491\pi$
$510$	−2.89773	+	3.68821i	−0.128314	+	0.163317i
$511$	36.1649	+	11.7507i	1.59984	+	0.519819i
$512$	36.2167	−	18.4533i	1.60057	−	0.815530i
$513$	21.4430	−	17.0765i	0.946731	−	0.753945i
$514$	−8.79154	−	55.5076i	−0.387778	−	2.44834i
$515$	−41.9357	−	21.3673i	−1.84791	−	0.941556i
$516$	9.48097	+	33.4066i	0.417377	+	1.47065i
$517$	11.6442	−	34.9076i	0.512110	−	1.53524i
$518$	33.1615	−	33.1615i	1.45703	−	1.45703i
$519$	11.3435	−	7.60652i	0.497926	−	0.333889i
$520$	78.6057	−	47.6211i	3.44709	−	2.08832i
$521$	3.49746	+	4.81384i	0.153226	+	0.210898i	0.878729	−	0.477322i	$-0.158392\pi$
$521$	3.49746	+	4.81384i	0.153226	+	0.210898i	−0.725502	+	0.688220i	$0.758392\pi$
$522$	−17.3587	−	10.5591i	−0.759769	−	0.462157i
$523$	−3.97118	+	12.2220i	−0.173648	+	0.534433i	−0.999569	−	0.0293525i	$-0.990655\pi$
$523$	−3.97118	+	12.2220i	−0.173648	+	0.534433i	0.825921	+	0.563785i	$0.190655\pi$
$524$	−43.4104	+	31.5395i	−1.89639	+	1.37781i
$525$	−5.64354	−	12.1890i	−0.246304	−	0.531973i
$526$	−20.8742	−	10.6359i	−0.910159	−	0.463749i
$527$	0.882015	−	0.882015i	0.0384212	−	0.0384212i
$528$	−77.4704	+	35.1373i	−3.37147	+	1.52915i
$529$	−3.37952			−0.146935
$530$	0.399950	+	1.23092i	0.0173727	+	0.0534677i
$531$	−1.19238	+	1.02519i	−0.0517449	+	0.0444895i
$532$	56.3989	+	77.6265i	2.44520	+	3.36554i
$533$	−0.224177	−	3.04658i	−0.00971019	−	0.131962i
$534$	−29.0089	−	1.09199i	−1.25534	−	0.0472552i
$535$	−0.868805	+	5.48542i	−0.0375617	+	0.237155i
$536$	19.0771	−	26.2574i	0.824006	−	1.13415i
$537$	9.56518	−	6.41402i	0.412768	−	0.276786i
$538$	−1.20137	+	1.20137i	−0.0517946	+	0.0517946i
$539$	−9.77332	+	9.62194i	−0.420967	+	0.414446i
$540$	−76.5735	+	3.38697i	−3.29520	+	0.145752i
$541$	−6.11134	+	11.9942i	−0.262747	+	0.515670i	−0.984259	−	0.176732i	$-0.943448\pi$
$541$	−6.11134	+	11.9942i	−0.262747	+	0.515670i	0.721512	+	0.692402i	$0.243448\pi$
$542$	−24.1600	+	33.2534i	−1.03776	+	1.42836i
$543$	−16.6035	+	21.1329i	−0.712526	+	0.906898i
$544$	−7.04954	+	3.59192i	−0.302247	+	0.154002i
$545$	7.08056	−	21.7917i	0.303298	−	0.933455i
$546$	−27.6228	−	49.7251i	−1.18215	−	2.12804i
$547$	−20.5645	−	14.9410i	−0.879274	−	0.638830i	0.0537856	−	0.998553i	$-0.482871\pi$
$547$	−20.5645	−	14.9410i	−0.879274	−	0.638830i	−0.933059	+	0.359723i	$0.882871\pi$
$548$	40.2702	−	79.0347i	1.72026	−	3.37620i
$549$	16.3383	−	10.0862i	0.697301	−	0.430467i
$550$	−21.0385	−	0.164207i	−0.897085	−	0.00700180i
$551$	9.25555	+	9.25555i	0.394300	+	0.394300i
$552$	−13.9811	+	70.8968i	−0.595075	+	3.01757i
$553$	5.89127	+	37.1960i	0.250522	+	1.58174i
$554$	−4.44519	+	28.0658i	−0.188858	+	1.19240i
$555$	0.907861	−	24.1174i	0.0385365	−	1.02373i
$556$	−68.4413	−	22.2379i	−2.90256	−	0.943098i
$557$	−5.72495	+	36.1459i	−0.242574	+	1.53155i	0.502504	+	0.864575i	$0.332412\pi$
$557$	−5.72495	+	36.1459i	−0.242574	+	1.53155i	−0.745078	+	0.666977i	$0.767588\pi$
$558$	27.7843	+	2.09476i	1.17620	+	0.0886783i
$559$	−1.10782	+	13.2159i	−0.0468556	+	0.558974i
$560$		−	133.729i		−	5.65106i
$561$	1.91784	−	0.869851i	0.0809713	−	0.0367252i
$562$	43.3393			1.82816
$563$	9.66955	+	29.7598i	0.407523	+	1.25423i	0.918770	+	0.394793i	$0.129184\pi$
$563$	9.66955	+	29.7598i	0.407523	+	1.25423i	−0.511247	+	0.859434i	$0.670816\pi$
$564$	95.0530	−	44.0097i	4.00245	−	1.85314i
$565$	−6.58218	+	41.5583i	−0.276914	+	1.74837i
$566$	−39.3497	−	77.2281i	−1.65399	−	3.24614i
$567$	0.197527	+	30.0319i	0.00829536	+	1.26122i
$568$	−4.03303	+	2.93017i	−0.169222	+	0.122947i
$569$	2.21252	+	1.60749i	0.0927538	+	0.0673895i	0.633196	−	0.773992i	$-0.281743\pi$
$569$	2.21252	+	1.60749i	0.0927538	+	0.0673895i	−0.540442	+	0.841381i	$0.681743\pi$
$570$	66.2221	+	13.0592i	2.77374	+	0.546991i
$571$		−	20.9932i		−	0.878538i	−0.898356	−	0.439269i	$-0.855238\pi$
$571$		−	20.9932i		−	0.878538i	0.898356	−	0.439269i	$-0.144762\pi$
$572$	−65.0397	+	4.27574i	−2.71945	+	0.178778i
$573$	8.32495	−	2.36266i	0.347780	−	0.0987017i
$574$	−6.87607	−	3.50353i	−0.287002	−	0.146235i
$575$	−6.05074	+	8.32813i	−0.252333	+	0.347307i
$576$	−81.3053	−	33.3649i	−3.38772	−	1.39021i
$577$	−16.5740	−	32.5284i	−0.689986	−	1.35417i	−0.924170	−	0.381981i	$-0.875242\pi$
$577$	−16.5740	−	32.5284i	−0.689986	−	1.35417i	0.234184	−	0.972192i	$-0.424758\pi$
$578$	−41.0185	+	20.9000i	−1.70614	+	0.869324i
$579$	3.92050	+	32.6639i	0.162930	+	1.35747i
$580$	−5.72552	−	36.1495i	−0.237739	−	1.50103i
$581$	−28.7823	+	9.35194i	−1.19409	+	0.387984i
$582$	−0.228659	−	0.805691i	−0.00947823	−	0.0333970i
$583$	0.0953804	−	0.573216i	0.00395025	−	0.0237402i
$584$	107.331			4.44141
$585$	−27.8239	−	9.09596i	−1.15038	−	0.376072i
$586$	−14.7729	−	10.7331i	−0.610263	−	0.443382i
$587$	−46.5798	−	7.37752i	−1.92256	−	0.304503i	−0.925344	−	0.379129i	$-0.876224\pi$
$587$	−46.5798	−	7.37752i	−1.92256	−	0.304503i	−0.997212	+	0.0746262i	$0.976224\pi$
$588$	−39.0119	−	1.46854i	−1.60883	−	0.0605616i
$589$	−17.0716	−	5.54691i	−0.703425	−	0.228557i
$590$	−3.82439	−	0.605724i	−0.157448	−	0.0249373i
$591$	21.8656	−	10.1238i	0.899430	−	0.416437i
$592$	34.6139	−	67.9337i	1.42262	−	2.79206i
$593$	−9.59118	+	9.59118i	−0.393863	+	0.393863i	−0.876062	−	0.482199i	$-0.839838\pi$
$593$	−9.59118	+	9.59118i	−0.393863	+	0.393863i	0.482199	+	0.876062i	$0.339838\pi$
$594$	42.6631	+	19.8167i	1.75049	+	0.813089i
$595$			3.31056i			0.135720i
$596$	−27.9884	−	14.2608i	−1.14645	−	0.584144i
$597$	16.8301	+	6.17754i	0.688812	+	0.252830i
$598$	−22.9665	+	37.0533i	−0.939169	+	1.51522i
$599$	−30.1200	−	9.78657i	−1.23067	−	0.399869i	−0.379712	−	0.925105i	$-0.623977\pi$
$599$	−30.1200	−	9.78657i	−1.23067	−	0.399869i	−0.850957	+	0.525236i	$0.823977\pi$
$600$	−25.7813	−	27.7982i	−1.05252	−	1.13486i
$601$	−5.20148	+	3.77910i	−0.212173	+	0.154153i	−0.688796	−	0.724955i	$-0.741861\pi$
$601$	−5.20148	+	3.77910i	−0.212173	+	0.154153i	0.476623	+	0.879108i	$0.341861\pi$
$602$	27.1050	+	19.6930i	1.10472	+	0.802625i
$603$	−10.3030	+	0.844965i	−0.419571	+	0.0344096i
$604$	−47.4788	+	47.4788i	−1.93189	+	1.93189i
$605$	26.3103	+	13.9273i	1.06967	+	0.566225i
$606$	34.4319	−	61.7203i	1.39870	−	2.50722i
$607$	5.28125	+	16.2540i	0.214359	+	0.659730i	0.999198	+	0.0400306i	$0.0127455\pi$
$607$	5.28125	+	16.2540i	0.214359	+	0.659730i	−0.784839	+	0.619700i	$0.787254\pi$
$608$	92.1119	+	66.9232i	3.73563	+	2.71409i
$609$	−14.2385	+	1.70899i	−0.576974	+	0.0692516i
$610$	44.9650	+	14.6100i	1.82058	+	0.591543i
$611$	39.8963	−	2.93570i	1.61403	−	0.118766i
$612$	5.54562	+	2.27574i	0.224169	+	0.0919912i
$613$	17.6936	−	2.80239i	0.714639	−	0.113188i	0.211481	−	0.977382i	$-0.432171\pi$
$613$	17.6936	−	2.80239i	0.714639	−	0.113188i	0.503158	+	0.864194i	$0.332171\pi$
$614$	16.2878	−	5.29222i	0.657322	−	0.213577i
$615$	−3.82056	+	1.08429i	−0.154060	+	0.0437229i
$616$	−48.0482	+	92.5078i	−1.93592	+	3.72724i
$617$	9.56380	+	9.56380i	0.385024	+	0.385024i	0.872908	−	0.487884i	$-0.162231\pi$
$617$	9.56380	+	9.56380i	0.385024	+	0.385024i	−0.487884	+	0.872908i	$0.662231\pi$
$618$	−15.9080	+	80.6680i	−0.639915	+	3.24494i
$619$	3.16751	+	19.9989i	0.127313	+	0.803822i	0.965874	+	0.259014i	$0.0833975\pi$
$619$	3.16751	+	19.9989i	0.127313	+	0.803822i	−0.838561	+	0.544808i	$0.816602\pi$
$620$	29.5021	+	40.6061i	1.18483	+	1.63078i
$621$	20.0260	−	11.3452i	0.803614	−	0.455268i
$622$	−23.3349	+	11.8897i	−0.935642	+	0.476734i
$623$	−16.5763	+	12.0434i	−0.664116	+	0.482509i
$624$	−67.6912	−	63.0069i	−2.70982	−	2.52230i
$625$	9.64721	+	29.6911i	0.385888	+	1.18764i
$626$	1.77793	+	1.77793i	0.0710604	+	0.0710604i
$627$	−23.6829	−	18.9078i	−0.945805	−	0.755107i
$628$		−	22.2407i		−	0.887499i
$629$	−0.856896	+	1.68175i	−0.0341667	+	0.0670559i
$630$	−56.0742	+	48.2117i	−2.23405	+	1.92080i
$631$	−24.8525	−	3.93625i	−0.989364	−	0.156700i	−0.359282	−	0.933229i	$-0.616978\pi$
$631$	−24.8525	−	3.93625i	−0.989364	−	0.156700i	−0.630081	+	0.776529i	$0.716978\pi$
$632$	48.2581	+	94.7118i	1.91960	+	3.76743i
$633$	−18.5275	−	0.697436i	−0.736400	−	0.0277206i
$634$	−25.0688	−	34.5043i	−0.995611	−	1.37034i
$635$	25.0464	−	3.96696i	0.993937	−	0.157424i
$636$	1.37382	−	0.921226i	0.0544754	−	0.0365290i
$637$	−13.7456	−	5.77572i	−0.544619	−	0.228842i
$638$	−7.10775	+	21.3081i	−0.281399	+	0.843595i
$639$	1.54515	+	0.365588i	0.0611252	+	0.0144624i
$640$	−30.7739	−	94.7123i	−1.21645	−	3.74383i
$641$	−8.50189	−	6.17698i	−0.335804	−	0.243976i	0.407085	−	0.913390i	$-0.366545\pi$
$641$	−8.50189	−	6.17698i	−0.335804	−	0.243976i	−0.742889	+	0.669414i	$0.766545\pi$
$642$	9.63312	−	1.15622i	0.380189	−	0.0456324i
$643$	3.72539	+	7.31150i	0.146915	+	0.288337i	0.952723	−	0.303840i	$-0.0982687\pi$
$643$	3.72539	+	7.31150i	0.146915	+	0.288337i	−0.805808	+	0.592177i	$0.798269\pi$
$644$	36.5761	+	71.7847i	1.44130	+	2.82871i
$645$	17.1189	−	2.05470i	0.674055	−	0.0809038i
$646$	−4.27059	−	3.10277i	−0.168024	−	0.122077i
$647$	−1.56253	−	4.80897i	−0.0614294	−	0.189060i	0.915632	−	0.402017i	$-0.131691\pi$
$647$	−1.56253	−	4.80897i	−0.0614294	−	0.189060i	−0.977062	+	0.212957i	$0.931691\pi$
$648$	26.7248	+	80.4463i	1.04985	+	3.16023i
$649$	1.39844	+	1.03280i	0.0548935	+	0.0405408i
$650$	−8.64508	−	21.1752i	−0.339088	−	0.830560i
$651$	16.3339	−	10.9529i	0.640178	−	0.429277i
$652$	−53.8145	+	8.52338i	−2.10754	+	0.333801i
$653$	24.2332	+	33.3541i	0.948317	+	1.30525i	0.952271	+	0.305255i	$0.0987416\pi$
$653$	24.2332	+	33.3541i	0.948317	+	1.30525i	−0.00395338	+	0.999992i	$0.501258\pi$
$654$	−40.0001	−	1.50574i	−1.56413	−	0.0588791i
$655$	12.0951	+	23.7380i	0.472595	+	0.927519i
$656$	−12.3918	−	1.96267i	−0.483819	−	0.0766293i
$657$	−22.2876	−	25.9223i	−0.869523	−	1.01133i
$658$	45.8803	−	90.0452i	1.78860	−	3.51033i
$659$		−	38.2215i		−	1.48890i	−0.667679	−	0.744449i	$-0.732712\pi$
$659$		−	38.2215i		−	1.48890i	0.667679	−	0.744449i	$-0.267288\pi$
$660$	22.4984	+	81.6967i	0.875751	+	3.18004i
$661$	31.2536	+	31.2536i	1.21562	+	1.21562i	0.969149	+	0.246475i	$0.0792722\pi$
$661$	31.2536	+	31.2536i	1.21562	+	1.21562i	0.246475	+	0.969149i	$0.420728\pi$
$662$	−3.86356	−	11.8908i	−0.150162	−	0.462150i
$663$	1.67575	+	1.55979i	0.0650808	+	0.0605771i
$664$	−69.1072	+	50.2093i	−2.68188	+	1.94850i
$665$	42.4483	−	21.6285i	1.64607	−	0.838716i
$666$	−40.9645	+	9.97729i	−1.58734	+	0.386612i
$667$	6.46003	+	8.89147i	0.250133	+	0.344279i
$668$	−15.1987	−	95.9606i	−0.588054	−	3.71283i
$669$	−0.689232	+	3.49503i	−0.0266472	+	0.135126i
$670$	−17.9992	−	17.9992i	−0.695371	−	0.695371i
$671$	−14.8923	−	15.1266i	−0.574912	−	0.583957i
$672$	−120.002	+	34.0573i	−4.62920	+	1.31379i
$673$	−2.77172	+	0.900585i	−0.106842	+	0.0347150i	−0.361950	−	0.932198i	$-0.617889\pi$
$673$	−2.77172	+	0.900585i	−0.106842	+	0.0347150i	0.255108	+	0.966913i	$0.417889\pi$
$674$	45.7551	−	7.24690i	1.76242	−	0.279140i
$675$	−1.36019	+	11.9990i	−0.0523537	+	0.461841i
$676$	−31.5247	−	63.4593i	−1.21249	−	2.44074i
$677$	14.0599	+	4.56835i	0.540367	+	0.175576i	0.566468	−	0.824084i	$-0.308309\pi$
$677$	14.0599	+	4.56835i	0.540367	+	0.175576i	−0.0261016	+	0.999659i	$0.508309\pi$
$678$	72.9818	−	8.75968i	2.80285	−	0.336413i
$679$	−0.478233	−	0.347457i	−0.0183529	−	0.0133342i
$680$	2.88755	+	8.88698i	0.110733	+	0.340800i
$681$	0.474434	−	0.850439i	0.0181803	−	0.0325889i
$682$	−4.58119	−	30.4613i	−0.175423	−	1.16643i
$683$	−20.6842	+	20.6842i	−0.791458	+	0.791458i	−0.981731	−	0.190273i	$-0.939063\pi$
$683$	−20.6842	+	20.6842i	−0.791458	+	0.791458i	0.190273	+	0.981731i	$0.439063\pi$
$684$	−7.05089	−	85.9743i	−0.269597	−	3.28731i
$685$	−35.6305	−	25.8871i	−1.36137	−	0.989093i
$686$	21.1104	−	15.3376i	0.805999	−	0.585593i
$687$	8.29345	+	8.94226i	0.316415	+	0.341168i
$688$	51.8029	+	16.8318i	1.97497	+	0.641705i
$689$	0.615008	−	0.144344i	0.0234299	−	0.00549907i
$690$	53.2035	+	19.5285i	2.02542	+	0.743437i
$691$	−38.9502	−	19.8461i	−1.48174	−	0.754982i	−0.488661	−	0.872474i	$-0.662515\pi$
$691$	−38.9502	−	19.8461i	−1.48174	−	0.754982i	−0.993074	+	0.117492i	$0.962515\pi$
$692$		−	42.9800i		−	1.63386i
$693$	32.3195	−	7.60501i	1.22772	−	0.288890i
$694$	47.7193	−	47.7193i	1.81140	−	1.81140i
$695$	−16.2213	+	31.8361i	−0.615309	+	1.20761i
$696$	−36.7318	+	17.0069i	−1.39231	+	0.644644i
$697$	0.306769	+	0.0485874i	0.0116197	+	0.00184038i
$698$	−64.6335	−	21.0007i	−2.44641	−	0.794888i
$699$	−26.5964	−	1.00118i	−1.00597	−	0.0378681i
$700$	−41.7495	−	6.61247i	−1.57798	−	0.249928i
$701$	34.3410	+	24.9502i	1.29704	+	0.942356i	0.999922	−	0.0124849i	$-0.00397418\pi$
$701$	34.3410	+	24.9502i	1.29704	+	0.942356i	0.297119	+	0.954840i	$0.403974\pi$
$702$	−2.01567	+	51.0990i	−0.0760767	+	1.92861i
$703$	27.1619			1.02443
$704$	−15.9478	+	95.8428i	−0.601054	+	3.61221i
$705$	−14.1993	−	50.0319i	−0.534777	−	1.88431i
$706$	−62.8801	+	20.4310i	−2.36652	+	0.768930i
$707$	−7.80351	−	49.2694i	−0.293481	−	1.85297i
$708$	0.589722	+	4.91331i	0.0221631	+	0.184653i
$709$	−21.7179	+	11.0658i	−0.815633	+	0.415586i	−0.811462	−	0.584405i	$-0.801328\pi$
$709$	−21.7179	+	11.0658i	−0.815633	+	0.415586i	−0.00417131	+	0.999991i	$0.501328\pi$
$710$	1.77499	+	3.48361i	0.0666141	+	0.130737i
$711$	12.8536	−	31.3223i	0.482047	−	1.17468i
$712$	−33.9935	+	46.7880i	−1.27396	+	1.75346i
$713$	−13.4292	−	6.84250i	−0.502926	−	0.256253i
$714$	5.56369	−	1.57900i	0.208216	−	0.0590927i
$715$	−2.95490	+	32.2273i	−0.110507	+	1.20523i
$716$		−	36.2419i		−	1.35442i
$717$	−4.04120	−	0.796939i	−0.150921	−	0.0297623i
$718$	47.8426	+	34.7597i	1.78547	+	1.29722i
$719$	−1.18813	+	0.863224i	−0.0443096	+	0.0321928i	−0.609720	−	0.792617i	$-0.708718\pi$
$719$	−1.18813	+	0.863224i	−0.0443096	+	0.0321928i	0.565410	+	0.824810i	$0.308718\pi$
$720$	−62.4801	+	102.715i	−2.32850	+	3.82796i
$721$	26.3466	+	51.7081i	0.981199	+	1.92571i
$722$	−3.77039	+	23.8053i	−0.140319	+	0.885941i
$723$	−40.8345	+	18.9064i	−1.51865	+	0.703138i
$724$	26.1349	+	80.4349i	0.971295	+	2.98934i
$725$	−5.76629			−0.214155
$726$	10.8571	−	50.8596i	0.402945	−	1.88758i
$727$			8.23670i			0.305482i	0.988266	+	0.152741i	$0.0488101\pi$
$727$			8.23670i			0.305482i	−0.988266	+	0.152741i	$0.951190\pi$
$728$	−112.927	−	9.46599i	−4.18534	−	0.350833i
$729$	13.8797	−	23.1593i	0.514061	−	0.857753i
$730$	13.1684	−	83.1423i	0.487386	−	3.07723i
$731$	−1.28242	−	0.416684i	−0.0474321	−	0.0154116i
$732$	2.27293	−	60.3807i	0.0840100	−	2.23173i
$733$	−4.53946	+	28.6611i	−0.167669	+	1.05862i	0.750047	+	0.661384i	$0.230031\pi$
$733$	−4.53946	+	28.6611i	−0.167669	+	1.05862i	−0.917716	+	0.397236i	$0.869969\pi$
$734$	−15.9857	−	100.930i	−0.590043	−	3.72538i
$735$	−3.75027	+	19.0172i	−0.138331	+	0.701461i
$736$	67.5992	+	67.5992i	2.49174	+	2.49174i
$737$	3.44670	+	10.8965i	0.126961	+	0.401378i
$738$	3.64451	+	5.90363i	0.134156	+	0.217315i
$739$	3.29720	−	6.47112i	0.121289	−	0.238044i	−0.822376	−	0.568944i	$-0.807352\pi$
$739$	3.29720	−	6.47112i	0.121289	−	0.238044i	0.943666	+	0.330900i	$0.107352\pi$
$740$	−61.4444	−	44.6420i	−2.25874	−	1.64107i
$741$	9.05175	−	31.6770i	0.332524	−	1.16368i
$742$	0.493152	−	1.51777i	0.0181042	−	0.0557189i
$743$	17.2816	−	8.80544i	0.634002	−	0.323040i	−0.107285	−	0.994228i	$-0.534216\pi$
$743$	17.2816	−	8.80544i	0.634002	−	0.323040i	0.741287	+	0.671188i	$0.234216\pi$
$744$	34.2940	−	43.6492i	1.25728	−	1.60026i
$745$	−9.16732	+	12.6177i	−0.335864	+	0.462278i
$746$	38.8480	−	76.2434i	1.42233	−	2.79147i
$747$	26.4767	+	6.26447i	0.968730	+	0.229205i
$748$	1.08776	−	6.53719i	0.0397723	−	0.239023i
$749$	4.84228	−	4.84228i	0.176933	−	0.176933i
$750$	28.4372	−	19.0688i	1.03838	−	0.696295i
$751$	1.19702	−	1.64756i	0.0436799	−	0.0601202i	−0.786618	−	0.617439i	$-0.788170\pi$
$751$	1.19702	−	1.64756i	0.0436799	−	0.0601202i	0.830298	+	0.557319i	$0.188170\pi$
$752$	25.7020	−	162.276i	0.937256	−	5.91760i
$753$	−23.4346	−	0.882158i	−0.854005	−	0.0321476i
$754$	−24.3533	+	1.79199i	−0.886893	+	0.0652605i
$755$	19.5957	+	26.9711i	0.713160	+	0.981580i
$756$	78.8403	+	52.1187i	2.86739	+	1.89554i
$757$	5.27549	+	16.2363i	0.191741	+	0.590118i	0.999999	+	0.00128978i	$0.000410550\pi$
$757$	5.27549	+	16.2363i	0.191741	+	0.590118i	−0.808258	+	0.588828i	$0.799589\pi$
$758$	−14.3871			−0.522562
$759$	−17.1570	−	18.7913i	−0.622760	−	0.682081i
$760$	95.0847	−	95.0847i	3.44909	−	3.44909i
$761$	−21.8010	−	11.1082i	−0.790287	−	0.402671i	0.0117613	−	0.999931i	$-0.496256\pi$
$761$	−21.8010	−	11.1082i	−0.790287	−	0.402671i	−0.802048	+	0.597260i	$0.796256\pi$
$762$	−18.6130	−	40.2007i	−0.674277	−	1.45632i
$763$	−22.8569	+	16.6065i	−0.827477	+	0.601197i
$764$	8.41535	−	25.8998i	0.304457	−	0.937021i
$765$	1.54675	−	2.54279i	0.0559227	−	0.0919349i
$766$	−27.9080	−	38.4121i	−1.00836	−	1.38789i
$767$	−0.450540	+	1.83543i	−0.0162680	+	0.0662737i
$768$	−60.2092	+	40.3739i	−2.17261	+	1.45687i
$769$	−1.09699	+	1.09699i	−0.0395586	+	0.0395586i	−0.726609	−	0.687051i	$-0.758905\pi$
$769$	−1.09699	+	1.09699i	−0.0395586	+	0.0395586i	0.687051	+	0.726609i	$0.258905\pi$
$770$	65.7644	+	48.5693i	2.36998	+	1.75032i
$771$	9.73633	+	34.3064i	0.350645	+	1.23551i
$772$	92.2447	+	47.0010i	3.31996	+	1.69160i
$773$	1.43673	+	9.07116i	0.0516756	+	0.326267i	0.999961	+	0.00884751i	$0.00281629\pi$
$773$	1.43673	+	9.07116i	0.0516756	+	0.326267i	−0.948285	+	0.317419i	$0.897184\pi$
$774$	−11.6181	−	27.7898i	−0.417605	−	0.998884i
$775$	7.04578	−	3.59000i	0.253092	−	0.128957i
$776$	−1.58685	−	0.515598i	−0.0569645	−	0.0185089i
$777$	−18.3849	+	23.4002i	−0.659556	+	0.839479i
$778$	−10.6384	−	67.1681i	−0.381405	−	2.40809i
$779$	−1.38119	−	4.25085i	−0.0494861	−	0.152303i
$780$	−72.5393	+	56.7813i	−2.59732	+	2.03310i
$781$	0.0137005	−	1.75534i	0.000490243	−	0.0628109i
$782$	−3.13411	−	3.13411i	−0.112076	−	0.112076i
$783$	11.7349	+	5.33982i	0.419370	+	0.190830i
$784$	−35.9929	+	49.5400i	−1.28546	+	1.76929i
$785$	−10.9067	−	1.72746i	−0.389278	−	0.0616555i
$786$	34.1249	−	31.6490i	1.21720	−	1.12888i
$787$	26.9594	−	13.7365i	0.961000	−	0.489654i	0.0981816	−	0.995169i	$-0.468697\pi$
$787$	26.9594	−	13.7365i	0.961000	−	0.489654i	0.862818	+	0.505515i	$0.168697\pi$
$788$	11.8619	−	74.8933i	0.422564	−	2.66796i
$789$	13.9556	+	5.12242i	0.496831	+	0.182363i
$790$	79.2875	−	25.7621i	2.82092	−	0.916573i
$791$	36.6858	−	36.6858i	1.30440	−	1.30440i
$792$	80.1263	−	48.6050i	2.84716	−	1.72711i
$793$	8.93937	−	21.2747i	0.317446	−	0.755486i
$794$	24.4296	−	7.93765i	0.866973	−	0.281697i
$795$	−0.345060	−	0.745267i	−0.0122380	−	0.0264319i
$796$	45.6434	−	33.1618i	1.61779	−	1.17539i
$797$	−10.9641	+	33.7440i	−0.388368	+	1.19527i	0.545639	+	0.838021i	$0.316287\pi$
$797$	−10.9641	+	33.7440i	−0.388368	+	1.19527i	−0.934007	+	0.357254i	$0.883713\pi$
$798$	−56.5947	−	61.0222i	−2.00343	−	2.16016i
$799$	−0.636274	+	4.01727i	−0.0225098	+	0.142121i
$800$	−49.5401	+	7.84639i	−1.75151	+	0.277412i
$801$	18.3589	−	1.50564i	0.648680	−	0.0531993i
$802$	1.01046			0.0356804
$803$	−22.4530	+	30.4020i	−0.792348	+	1.07286i
$804$	−15.8490	+	28.4098i	−0.558950	+	1.00194i
$805$	38.0438	−	12.3612i	1.34087	−	0.435675i
$806$	28.6414	−	17.3516i	1.00885	−	0.611183i
$807$	0.666046	−	0.847738i	0.0234459	−	0.0298418i
$808$	−63.9221	−	125.454i	−2.24877	−	4.41346i
$809$	23.6030	+	7.66909i	0.829838	+	0.269631i	0.692977	−	0.720959i	$-0.256299\pi$
$809$	23.6030	+	7.66909i	0.829838	+	0.269631i	0.136861	+	0.990590i	$0.456299\pi$
$810$	65.5950	−	10.8320i	2.30478	−	0.380596i
$811$	28.6532	−	4.53822i	1.00615	−	0.159358i	0.368453	−	0.929646i	$-0.379888\pi$
$811$	28.6532	−	4.53822i	1.00615	−	0.159358i	0.637696	+	0.770288i	$0.279888\pi$
$812$	−20.4882	+	40.2104i	−0.718996	+	1.41111i
$813$	12.7068	−	22.7775i	0.445648	−	0.798840i
$814$	20.8366	+	41.6954i	0.730321	+	1.46142i
$815$			27.0524i			0.947605i
$816$	7.80922	−	5.23655i	0.273378	−	0.183316i
$817$	3.03553	+	19.1656i	0.106200	+	0.670520i
$818$	−21.1966	+	15.4002i	−0.741120	+	0.538455i
$819$	21.1633	+	29.2393i	0.739504	+	1.02170i
$820$	−3.86204	+	11.8861i	−0.134868	+	0.415082i
$821$	21.4359	+	3.39512i	0.748120	+	0.118490i	0.518841	−	0.854870i	$-0.326363\pi$
$821$	21.4359	+	3.39512i	0.748120	+	0.118490i	0.229278	+	0.973361i	$0.426363\pi$
$822$	−26.5112	+	72.2273i	−0.924685	+	2.51922i
$823$	50.4408	−	16.3892i	1.75826	−	0.571292i	0.761238	−	0.648473i	$-0.224592\pi$
$823$	50.4408	−	16.3892i	1.75826	−	0.571292i	0.997017	+	0.0771809i	$0.0245919\pi$
$824$	115.827	+	115.827i	4.03502	+	4.03502i
$825$	13.2672	−	1.48746i	0.461905	−	0.0517867i
$826$	3.37600	+	3.37600i	0.117466	+	0.117466i
$827$	32.7192	+	16.6712i	1.13776	+	0.579716i	0.918292	−	0.395904i	$-0.129569\pi$
$827$	32.7192	+	16.6712i	1.13776	+	0.579716i	0.219465	+	0.975620i	$0.429569\pi$
$828$	5.44536	−	72.2258i	0.189239	−	2.51002i
$829$	22.9367	+	31.5696i	0.796624	+	1.09646i	0.993251	+	0.115981i	$0.0370011\pi$
$829$	22.9367	+	31.5696i	0.796624	+	1.09646i	−0.196627	+	0.980478i	$0.562999\pi$
$830$	30.4150	+	59.6927i	1.05572	+	2.07197i
$831$	0.678271	−	18.0183i	0.0235289	−	0.625049i
$832$	−102.830	+	24.1346i	−3.56500	+	0.836716i
$833$	0.891033	−	1.22640i	0.0308725	−	0.0424923i
$834$	61.2403	+	12.0768i	2.12058	+	0.418186i
$835$	−48.2392			−1.66939
$836$	−90.9269	+	28.7613i	−3.14477	+	0.994731i
$837$	−17.6632	+	0.781273i	−0.610531	+	0.0270048i
$838$	−48.1511	−	24.5342i	−1.66335	−	0.847521i
$839$	−11.9689	+	1.89569i	−0.413213	+	0.0654464i	−0.359580	−	0.933114i	$-0.617080\pi$
$839$	−11.9689	+	1.89569i	−0.413213	+	0.0654464i	−0.0536326	+	0.998561i	$0.517080\pi$
$840$	17.5569	+	146.276i	0.605769	+	5.04701i
$841$	7.05908	−	21.7256i	0.243417	−	0.749159i
$842$	29.9521	−	92.1831i	1.03222	−	3.17684i
$843$	−27.3048	+	3.27727i	−0.940428	+	0.112875i
$844$	−34.2948	+	47.2028i	−1.18048	+	1.62479i
$845$	−33.5687	+	10.5306i	−1.15480	+	0.362265i
$846$	−77.3106	+	47.7264i	−2.65799	+	1.64087i
$847$	−16.1518	−	32.9618i	−0.554983	−	1.13258i
$848$		−	2.59450i		−	0.0890955i
$849$	30.6312	+	45.6801i	1.05126	+	1.56774i
$850$	2.29683	−	0.363783i	0.0787808	−	0.0124776i
$851$	22.5257	+	3.56772i	0.772171	+	0.122300i
$852$	3.66363	−	3.39781i	0.125514	−	0.116407i
$853$	−12.9349	+	6.59066i	−0.442883	+	0.225660i	−0.661188	−	0.750221i	$-0.729947\pi$
$853$	−12.9349	+	6.59066i	−0.442883	+	0.225660i	0.218305	+	0.975881i	$0.429947\pi$
$854$	−34.2659	−	47.1630i	−1.17256	−	1.61388i
$855$	−42.7091	−	3.21999i	−1.46062	−	0.110121i
$856$	8.77523	−	17.2223i	0.299931	−	0.588648i
$857$	−4.10234			−0.140133			−0.0700667	−	0.997542i	$-0.522321\pi$
$857$	−4.10234			−0.140133			−0.0700667	+	0.997542i	$0.522321\pi$
$858$	55.5703	−	10.4052i	1.89714	−	0.355226i
$859$	11.8637			0.404785			0.202393	−	0.979304i	$-0.435128\pi$
$859$	11.8637			0.404785			0.202393	+	0.979304i	$0.435128\pi$
$860$	24.6328	−	48.3447i	0.839973	−	1.64854i
$861$	4.59703	+	1.68735i	0.156666	+	0.0575048i
$862$	33.2392	+	45.7498i	1.13213	+	1.55824i
$863$	−9.32543	+	4.75154i	−0.317441	+	0.161744i	−0.605450	−	0.795883i	$-0.707007\pi$
$863$	−9.32543	+	4.75154i	−0.317441	+	0.161744i	0.288009	+	0.957628i	$0.407007\pi$
$864$	108.084	+	29.9082i	3.67710	+	1.01750i
$865$	−21.0772	−	3.33831i	−0.716648	−	0.113506i
$866$	35.4294	−	5.61146i	1.20394	−	0.190685i
$867$	24.2623	−	16.2693i	0.823989	−	0.552534i
$868$		−	61.8884i		−	2.10063i
$869$	−36.9227	−	6.14376i	−1.25252	−	0.208413i
$870$	8.66745	+	30.5401i	0.293854	+	1.03541i
$871$	−9.48841	+	8.02072i	−0.321502	+	0.271772i
$872$	−46.8733	+	64.5156i	−1.58733	+	2.18477i
$873$	0.204987	+	0.490315i	0.00693775	+	0.0165946i
$874$	−19.7101	+	60.6616i	−0.666706	+	2.05191i
$875$	7.46780	−	22.9835i	0.252458	−	0.776985i
$876$	−106.815	+	12.8205i	−3.60895	+	0.433166i
$877$	−18.3340	+	2.90382i	−0.619095	+	0.0980550i	−0.458100	−	0.888900i	$-0.651470\pi$
$877$	−18.3340	+	2.90382i	−0.619095	+	0.0980550i	−0.160994	+	0.986955i	$0.551470\pi$
$878$	16.4504	+	8.38190i	0.555175	+	0.282876i
$879$	10.1189	+	5.64504i	0.341303	+	0.190402i
$880$	126.084	+	42.0581i	4.25031	+	1.41778i
$881$	−51.7467			−1.74339			−0.871695	−	0.490049i	$-0.836979\pi$
$881$	−51.7467			−1.74339			−0.871695	+	0.490049i	$0.836979\pi$
$882$	33.7489	−	2.76780i	1.13638	−	0.0931966i
$883$	−10.8746	+	14.9676i	−0.365960	+	0.503700i	−0.951797	−	0.306728i	$-0.900766\pi$
$883$	−10.8746	+	14.9676i	−0.365960	+	0.503700i	0.585837	+	0.810429i	$0.300766\pi$
$884$	7.01379	−	1.64616i	0.235899	−	0.0553663i
$885$	2.45527	+	0.0924246i	0.0825330	+	0.00310682i
$886$	37.0718	+	72.7576i	1.24545	+	2.44434i
$887$	−14.4953	−	19.9510i	−0.486703	−	0.669890i	0.493072	−	0.869988i	$-0.335874\pi$
$887$	−14.4953	−	19.9510i	−0.486703	−	0.669890i	−0.979776	+	0.200099i	$0.935874\pi$
$888$	−28.9429	+	78.8522i	−0.971260	+	2.64611i
$889$	−27.8600	−	14.1954i	−0.934396	−	0.476098i
$890$	32.0728	+	32.0728i	1.07508	+	1.07508i
$891$	−28.3773	−	9.25889i	−0.950676	−	0.310184i
$892$	7.92696	+	7.92696i	0.265414	+	0.265414i
$893$	55.6668	−	18.0872i	1.86282	−	0.605266i
$894$	25.5777	+	9.38835i	0.855445	+	0.313993i
$895$	−17.7729	−	2.81495i	−0.594082	−	0.0940934i
$896$	−37.9453	+	116.784i	−1.26766	+	3.90146i
$897$	11.6675	−	25.0812i	0.389567	−	0.837438i
$898$	40.1925	−	29.2016i	1.34124	−	0.974469i
$899$	−1.32071	−	8.33862i	−0.0440481	−	0.278108i
$900$	28.9778	+	24.5850i	0.965925	+	0.819500i
$901$			0.0642289i			0.00213978i
$902$	5.46581	−	5.38115i	0.181992	−	0.179173i
$903$	−18.5660	−	10.3574i	−0.617839	−	0.344673i
$904$	66.4823	−	130.479i	2.21117	−	4.33966i
$905$	41.4749	−	6.56897i	1.37867	−	0.218360i
$906$	35.9811	−	45.7965i	1.19539	−	1.52149i
$907$	0.113022	+	0.0367231i	0.00375283	+	0.00121937i	0.310893	−	0.950445i	$-0.399372\pi$
$907$	0.113022	+	0.0367231i	0.00375283	+	0.00121937i	−0.307140	+	0.951664i	$0.599372\pi$
$908$	−1.39128	−	2.73054i	−0.0461712	−	0.0906161i
$909$	−17.0257	+	41.4891i	−0.564707	+	1.37611i
$910$	−21.1876	+	86.3150i	−0.702360	+	2.86132i
$911$	−31.3176	+	10.1757i	−1.03760	+	0.337137i	−0.777791	−	0.628523i	$-0.783660\pi$
$911$	−31.3176	+	10.1757i	−1.03760	+	0.337137i	−0.259809	+	0.965660i	$0.583660\pi$
$912$	−118.163	−	65.9193i	−3.91276	−	2.18280i
$913$	0.234763	−	30.0783i	0.00776951	−	0.995446i
$914$	−34.6789			−1.14707
$915$	−29.4339	−	5.80447i	−0.973055	−	0.191890i
$916$	37.9077	−	6.00400i	1.25251	−	0.198378i
$917$	5.13890	−	32.4457i	0.169701	−	1.07145i
$918$	−5.01113	−	1.38664i	−0.165392	−	0.0457658i
$919$	7.41982	−	22.8359i	0.244757	−	0.753286i	−0.750919	−	0.660394i	$-0.770389\pi$
$919$	7.41982	−	22.8359i	0.244757	−	0.753286i	0.995676	−	0.0928912i	$-0.0296109\pi$
$920$	91.3445	−	66.3656i	3.01154	−	2.18801i
$921$	−9.86153	+	4.56590i	−0.324948	+	0.150452i
$922$	−12.7483	+	4.14218i	−0.419843	+	0.136415i
$923$	1.76674	−	0.721298i	0.0581531	−	0.0237418i
$924$	36.7672	−	97.8021i	1.20955	−	3.21745i
$925$	−8.46104	+	8.46104i	−0.278197	+	0.278197i
$926$	3.06927	−	0.997266i	0.100862	−	0.0327722i
$927$	3.92242	−	52.0259i	0.128829	−	1.70875i
$928$	−8.37714	+	52.8912i	−0.274993	+	1.73624i
$929$	52.6016	−	26.8018i	1.72580	−	0.879340i	0.749773	−	0.661695i	$-0.230163\pi$
$929$	52.6016	−	26.8018i	1.72580	−	0.879340i	0.976028	−	0.217645i	$-0.0698374\pi$
$930$	−29.6045	−	31.9205i	−0.970770	−	1.04671i
$931$	−21.5463	−	3.41260i	−0.706152	−	0.111844i
$932$	−49.2307	+	67.7603i	−1.61261	+	2.21956i
$933$	13.8025	−	9.25537i	0.451872	−	0.303007i
$934$	−49.4445	−	49.4445i	−1.61787	−	1.61787i
$935$	−3.12132	−	1.04118i	−0.102078	−	0.0340503i
$936$	82.3146	+	60.0318i	2.69054	+	1.96220i
$937$	−6.21055	−	19.1141i	−0.202890	−	0.624431i	−0.999793	−	0.0203242i	$-0.993530\pi$
$937$	−6.21055	−	19.1141i	−0.202890	−	0.624431i	0.796904	−	0.604106i	$-0.206470\pi$
$938$	4.90994	+	31.0002i	0.160315	+	1.01219i
$939$	−1.25459	−	0.985695i	−0.0409419	−	0.0321670i
$940$	−155.654	−	50.5752i	−5.07688	−	1.64958i
$941$	−44.7460	+	22.7992i	−1.45868	+	0.743234i	−0.990123	−	0.140200i	$-0.955225\pi$
$941$	−44.7460	+	22.7992i	−1.45868	+	0.743234i	−0.468555	+	0.883434i	$0.655225\pi$
$942$	2.29893	+	19.1537i	0.0749031	+	0.624060i
$943$	−0.587085	−	3.70671i	−0.0191181	−	0.120707i
$944$	6.91598	+	3.52387i	0.225096	+	0.114692i
$945$	31.6824	−	34.6149i	1.03063	−	1.12602i
$946$	−27.0919	+	19.3622i	−0.880834	+	0.629519i
$947$	2.40514	−	2.40514i	0.0781567	−	0.0781567i	−0.666948	−	0.745104i	$-0.732400\pi$
$947$	2.40514	−	2.40514i	0.0781567	−	0.0781567i	0.745104	+	0.666948i	$0.232400\pi$
$948$	−59.3391	−	88.4920i	−1.92725	−	2.87409i
$949$	−39.9023	−	9.79472i	−1.29528	−	0.317950i
$950$	−19.6701	−	27.0736i	−0.638182	−	0.878383i
$951$	18.4032	+	19.8429i	0.596764	+	0.643450i
$952$	3.56045	−	10.9579i	0.115395	−	0.355149i
$953$	−5.45876	+	3.96602i	−0.176827	+	0.128472i	−0.672678	−	0.739935i	$-0.734856\pi$
$953$	−5.45876	+	3.96602i	−0.176827	+	0.128472i	0.495851	+	0.868407i	$0.334856\pi$
$954$	−1.08791	+	0.935366i	−0.0352223	+	0.0302836i
$955$	−12.0475	−	6.13852i	−0.389849	−	0.198638i
$956$	−9.16572	+	9.16572i	−0.296441	+	0.296441i
$957$	2.86677	−	13.9621i	0.0926694	−	0.451331i
$958$	34.6546			1.11964
$959$	16.7811	+	51.6470i	0.541891	+	1.66777i
$960$	57.6946	+	124.610i	1.86208	+	4.02177i
$961$	−11.4161	−	15.7129i	−0.368261	−	0.506868i
$962$	−33.1048	+	38.3636i	−1.06734	+	1.23689i
$963$	−5.98168	+	1.45690i	−0.192757	+	0.0469478i
$964$	−22.1524	+	139.865i	−0.713482	+	4.50475i
$965$	30.2138	−	41.5858i	0.972618	−	1.33869i
$966$	−38.9195	−	58.0403i	−1.25221	−	1.86742i
$967$	24.2671	−	24.2671i	0.780378	−	0.780378i	−0.199517	−	0.979894i	$-0.563937\pi$
$967$	24.2671	−	24.2671i	0.780378	−	0.780378i	0.979894	+	0.199517i	$0.0639372\pi$
$968$	−72.1086	−	74.3957i	−2.31766	−	2.39117i
$969$	2.92521	+	1.63188i	0.0939713	+	0.0524237i
$970$	−0.594087	+	1.16596i	−0.0190750	+	0.0374368i
$971$	11.7686	−	16.1980i	0.377671	−	0.519820i	−0.577294	−	0.816536i	$-0.695891\pi$
$971$	11.7686	−	16.1980i	0.377671	−	0.519820i	0.954966	+	0.296716i	$0.0958915\pi$
$972$	−36.2054	−	76.8671i	−1.16129	−	2.46551i
$973$	39.2550	−	20.0014i	1.25846	−	0.641216i
$974$	−30.8587	+	94.9733i	−0.988776	+	3.04314i
$975$	7.04787	+	12.6872i	0.225712	+	0.406315i
$976$	−76.6755	−	55.7080i	−2.45432	−	1.78317i
$977$	−21.8037	+	42.7921i	−0.697562	+	1.36904i	0.221591	+	0.975140i	$0.428875\pi$
$977$	−21.8037	+	42.7921i	−0.697562	+	1.36904i	−0.919152	+	0.393902i	$0.871125\pi$
$978$	45.4640	−	12.9029i	1.45378	−	0.412590i
$979$	−6.14168	−	19.4165i	−0.196289	−	0.620554i
$980$	43.1324	+	43.1324i	1.37781	+	1.37781i
$981$	25.3149	−	2.07612i	0.808244	−	0.0662853i
$982$	14.4072	+	90.9637i	0.459753	+	2.90277i
$983$	2.98399	−	18.8402i	0.0951745	−	0.600908i	−0.893293	−	0.449475i	$-0.851611\pi$
$983$	2.98399	−	18.8402i	0.0951745	−	0.600908i	0.988467	−	0.151433i	$-0.0483888\pi$
$984$	13.8122	+	0.519937i	0.440316	+	0.0165750i
$985$	−35.8060	−	11.6341i	−1.14088	−	0.370693i
$986$	0.388390	−	2.45220i	0.0123689	−	0.0780939i
$987$	−22.0966	+	60.2002i	−0.703343	+	1.91619i
$988$	−66.9296	−	79.1769i	−2.12931	−	2.51895i
$989$			16.2930i			0.518088i
$990$	−27.8203	−	68.0316i	−0.884188	−	2.16219i
$991$	−21.7826			−0.691948			−0.345974	−	0.938244i	$-0.612451\pi$
$991$	−21.7826			−0.691948			−0.345974	+	0.938244i	$0.612451\pi$
$992$	−22.6933	−	69.8427i	−0.720512	−	2.21751i
$993$	3.33331	+	7.19936i	0.105780	+	0.228465i
$994$	0.754147	−	4.76150i	0.0239201	−	0.151026i
$995$	−12.7173	−	24.9590i	−0.403164	−	0.791254i
$996$	62.7774	−	58.2226i	1.98918	−	1.84485i
$997$	−40.0285	+	29.0824i	−1.26772	+	0.921050i	−0.999109	−	0.0421996i	$-0.986563\pi$
$997$	−40.0285	+	29.0824i	−1.26772	+	0.921050i	−0.268607	+	0.963250i	$0.586563\pi$
$998$	56.2374	+	40.8589i	1.78016	+	1.29336i
$999$	25.0542	−	9.38365i	0.792679	−	0.296885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bi.a.5.1	✓	416
3.2	odd	2	inner	429.2.bi.a.5.52	yes	416
11.9	even	5	inner	429.2.bi.a.317.52	yes	416
13.8	odd	4	inner	429.2.bi.a.203.1	yes	416
33.20	odd	10	inner	429.2.bi.a.317.1	yes	416
39.8	even	4	inner	429.2.bi.a.203.52	yes	416
143.86	odd	20	inner	429.2.bi.a.86.52	yes	416
429.86	even	20	inner	429.2.bi.a.86.1	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bi.a.5.1	✓	416	1.1	even	1	trivial
429.2.bi.a.5.52	yes	416	3.2	odd	2	inner
429.2.bi.a.86.1	yes	416	429.86	even	20	inner
429.2.bi.a.86.52	yes	416	143.86	odd	20	inner
429.2.bi.a.203.1	yes	416	13.8	odd	4	inner
429.2.bi.a.203.52	yes	416	39.8	even	4	inner
429.2.bi.a.317.1	yes	416	33.20	odd	10	inner
429.2.bi.a.317.52	yes	416	11.9	even	5	inner

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23921 + 2.43208i) q^{2} +(0.596820 - 1.62598i) q^{3} +(-3.20380 - 4.40966i) q^{4} +(-2.41132 + 1.22863i) q^{5} +(3.21492 + 3.46643i) q^{6} +(3.29586 + 0.522013i) q^{7} +(9.30284 - 1.47343i) q^{8} +(-2.28761 - 1.94083i) q^{9} +O(q^{10})\)	\(q+(-1.23921 + 2.43208i) q^{2} +(0.596820 - 1.62598i) q^{3} +(-3.20380 - 4.40966i) q^{4} +(-2.41132 + 1.22863i) q^{5} +(3.21492 + 3.46643i) q^{6} +(3.29586 + 0.522013i) q^{7} +(9.30284 - 1.47343i) q^{8} +(-2.28761 - 1.94083i) q^{9} -7.38704i q^{10} +(-1.52873 + 2.94329i) q^{11} +(-9.08210 + 2.57755i) q^{12} +(-3.59295 - 0.301176i) q^{13} +(-5.35383 + 7.36891i) q^{14} +(0.558601 + 4.65403i) q^{15} +(-4.57597 + 14.0834i) q^{16} +(0.113282 - 0.348646i) q^{17} +(7.55508 - 3.15856i) q^{18} +(-5.21046 + 0.825256i) q^{19} +(13.1432 + 6.69681i) q^{20} +(2.81582 - 5.04745i) q^{21} +(-5.26390 - 7.36535i) q^{22} -4.42950 q^{23} +(3.15636 - 16.0056i) q^{24} +(1.36601 - 1.88015i) q^{25} +(5.18489 - 8.36512i) q^{26} +(-4.52104 + 2.56128i) q^{27} +(-8.25739 - 16.2060i) q^{28} +(-1.45841 - 2.00733i) q^{29} +(-12.0112 - 4.40873i) q^{30} +(3.03175 + 1.54476i) q^{31} +(-15.2611 - 15.2611i) q^{32} +(3.87335 + 4.24230i) q^{33} +(0.707554 + 0.707554i) q^{34} +(-8.58874 + 2.79065i) q^{35} +(-1.22934 + 16.3056i) q^{36} +(-5.08538 - 0.805445i) q^{37} +(4.44974 - 13.6949i) q^{38} +(-2.63405 + 5.66231i) q^{39} +(-20.6218 + 14.9826i) q^{40} +(0.132540 + 0.836823i) q^{41} +(8.78643 + 13.1031i) q^{42} -3.67829i q^{43} +(17.8767 - 2.68853i) q^{44} +(7.90073 + 1.86934i) q^{45} +(5.48906 - 10.7729i) q^{46} +(-10.9586 + 1.73567i) q^{47} +(20.1683 + 15.8457i) q^{48} +(3.93282 + 1.27785i) q^{49} +(2.87991 + 5.65214i) q^{50} +(-0.499282 - 0.392272i) q^{51} +(10.1830 + 16.8086i) q^{52} +(-0.166632 + 0.0541421i) q^{53} +(-0.626739 - 14.1695i) q^{54} +(0.0700540 - 8.97547i) q^{55} +31.4300 q^{56} +(-1.76786 + 8.96462i) q^{57} +(6.68926 - 1.05947i) q^{58} +(0.0819982 - 0.517716i) q^{59} +(18.7330 - 17.3738i) q^{60} +(-1.97779 + 6.08701i) q^{61} +(-7.51393 + 5.45919i) q^{62} +(-6.52652 - 7.59088i) q^{63} +(27.8612 - 9.05265i) q^{64} +(9.03379 - 3.68817i) q^{65} +(-15.1175 + 4.16321i) q^{66} +(2.43659 - 2.43659i) q^{67} +(-1.90034 + 0.617458i) q^{68} +(-2.64361 + 7.20227i) q^{69} +(3.85614 - 24.3467i) q^{70} +(-0.471584 + 0.240284i) q^{71} +(-24.1410 - 14.6846i) q^{72} +(11.2551 + 1.78264i) q^{73} +(8.26074 - 11.3699i) q^{74} +(-2.24182 - 3.34321i) q^{75} +(20.3324 + 20.3324i) q^{76} +(-6.57494 + 8.90267i) q^{77} +(-10.5071 - 13.4230i) q^{78} +(3.48747 + 10.7333i) q^{79} +(-6.26913 - 39.5817i) q^{80} +(1.46634 + 8.87974i) q^{81} +(-2.19946 - 0.714649i) q^{82} +(-8.08074 + 4.11734i) q^{83} +(-31.2789 + 3.75426i) q^{84} +(0.155197 + 0.979878i) q^{85} +(8.94590 + 4.55816i) q^{86} +(-4.13428 + 1.17333i) q^{87} +(-9.88485 + 29.6335i) q^{88} +(-4.34177 + 4.34177i) q^{89} +(-14.3370 + 16.8987i) q^{90} +(-11.6847 - 2.86820i) q^{91} +(14.1913 + 19.5326i) q^{92} +(4.32115 - 4.00763i) q^{93} +(9.35864 - 28.8029i) q^{94} +(11.5502 - 8.39168i) q^{95} +(-33.9224 + 15.7061i) q^{96} +(-0.157839 - 0.0804229i) q^{97} +(-7.98140 + 7.98140i) q^{98} +(9.20959 - 3.76610i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) \) 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9	\( 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9} - 20 q^{13} - 30 q^{15} + 32 q^{16} + 2 q^{18} - 4 q^{19} - 12 q^{21} - 24 q^{22} - 78 q^{24} - 36 q^{27} - 84 q^{28} - 28 q^{31} - 44 q^{33} - 24 q^{34} - 12 q^{37} + 54 q^{39} + 88 q^{40} - 56 q^{42} + 8 q^{45} - 92 q^{46} + 40 q^{48} - 44 q^{52} - 176 q^{54} - 72 q^{55} - 6 q^{57} - 4 q^{58} + 12 q^{60} - 48 q^{61} - 46 q^{63} + 204 q^{66} - 64 q^{67} + 56 q^{70} - 66 q^{72} - 12 q^{73} - 104 q^{76} - 92 q^{78} + 104 q^{79} + 124 q^{81} + 16 q^{84} - 12 q^{85} - 24 q^{87} - 84 q^{91} - 124 q^{93} + 328 q^{94} - 152 q^{96} + 52 q^{97} - 142 q^{99}+O(q^{100}) \) 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9 - 20 * q^13 - 30 * q^15 + 32 * q^16 + 2 * q^18 - 4 * q^19 - 12 * q^21 - 24 * q^22 - 78 * q^24 - 36 * q^27 - 84 * q^28 - 28 * q^31 - 44 * q^33 - 24 * q^34 - 12 * q^37 + 54 * q^39 + 88 * q^40 - 56 * q^42 + 8 * q^45 - 92 * q^46 + 40 * q^48 - 44 * q^52 - 176 * q^54 - 72 * q^55 - 6 * q^57 - 4 * q^58 + 12 * q^60 - 48 * q^61 - 46 * q^63 + 204 * q^66 - 64 * q^67 + 56 * q^70 - 66 * q^72 - 12 * q^73 - 104 * q^76 - 92 * q^78 + 104 * q^79 + 124 * q^81 + 16 * q^84 - 12 * q^85 - 24 * q^87 - 84 * q^91 - 124 * q^93 + 328 * q^94 - 152 * q^96 + 52 * q^97 - 142 * q^99

Introduction

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