LMFDB - Embedded newform 930.2.e.a.929.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(929,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("930.929");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			929.7
Character	$\chi$	$=$	930.929
Dual form			930.2.e.a.929.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.36636 - 1.06445i) q^{3} +1.00000 q^{4} +(-2.16820 + 0.546716i) q^{5} +(1.36636 + 1.06445i) q^{6} -1.97405i q^{7} -1.00000 q^{8} +(0.733873 + 2.90885i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.36636 - 1.06445i) q^{3} +1.00000 q^{4} +(-2.16820 + 0.546716i) q^{5} +(1.36636 + 1.06445i) q^{6} -1.97405i q^{7} -1.00000 q^{8} +(0.733873 + 2.90885i) q^{9} +(2.16820 - 0.546716i) q^{10} +0.980092 q^{11} +(-1.36636 - 1.06445i) q^{12} +4.39735 q^{13} +1.97405i q^{14} +(3.54450 + 1.56094i) q^{15} +1.00000 q^{16} +2.02195i q^{17} +(-0.733873 - 2.90885i) q^{18} -3.72763 q^{19} +(-2.16820 + 0.546716i) q^{20} +(-2.10129 + 2.69726i) q^{21} -0.980092 q^{22} +6.09578i q^{23} +(1.36636 + 1.06445i) q^{24} +(4.40220 - 2.37078i) q^{25} -4.39735 q^{26} +(2.09361 - 4.75571i) q^{27} -1.97405i q^{28} +2.54734 q^{29} +(-3.54450 - 1.56094i) q^{30} +(-1.90121 - 5.23311i) q^{31} -1.00000 q^{32} +(-1.33916 - 1.04326i) q^{33} -2.02195i q^{34} +(1.07925 + 4.28014i) q^{35} +(0.733873 + 2.90885i) q^{36} +9.44453 q^{37} +3.72763 q^{38} +(-6.00835 - 4.68078i) q^{39} +(2.16820 - 0.546716i) q^{40} -12.5007i q^{41} +(2.10129 - 2.69726i) q^{42} -3.33266 q^{43} +0.980092 q^{44} +(-3.18150 - 5.90576i) q^{45} -6.09578i q^{46} -11.6412 q^{47} +(-1.36636 - 1.06445i) q^{48} +3.10312 q^{49} +(-4.40220 + 2.37078i) q^{50} +(2.15228 - 2.76271i) q^{51} +4.39735 q^{52} -7.67233i q^{53} +(-2.09361 + 4.75571i) q^{54} +(-2.12504 + 0.535832i) q^{55} +1.97405i q^{56} +(5.09328 + 3.96789i) q^{57} -2.54734 q^{58} -0.348160i q^{59} +(3.54450 + 1.56094i) q^{60} +5.15035i q^{61} +(1.90121 + 5.23311i) q^{62} +(5.74223 - 1.44870i) q^{63} +1.00000 q^{64} +(-9.53434 + 2.40410i) q^{65} +(1.33916 + 1.04326i) q^{66} -1.03734i q^{67} +2.02195i q^{68} +(6.48868 - 8.32902i) q^{69} +(-1.07925 - 4.28014i) q^{70} -8.70746i q^{71} +(-0.733873 - 2.90885i) q^{72} -5.88000 q^{73} -9.44453 q^{74} +(-8.53858 - 1.44660i) q^{75} -3.72763 q^{76} -1.93475i q^{77} +(6.00835 + 4.68078i) q^{78} -8.91713i q^{79} +(-2.16820 + 0.546716i) q^{80} +(-7.92286 + 4.26946i) q^{81} +12.5007i q^{82} -8.99302i q^{83} +(-2.10129 + 2.69726i) q^{84} +(-1.10543 - 4.38400i) q^{85} +3.33266 q^{86} +(-3.48058 - 2.71153i) q^{87} -0.980092 q^{88} +10.3304 q^{89} +(3.18150 + 5.90576i) q^{90} -8.68059i q^{91} +6.09578i q^{92} +(-2.97267 + 9.17405i) q^{93} +11.6412 q^{94} +(8.08225 - 2.03795i) q^{95} +(1.36636 + 1.06445i) q^{96} -17.1380i q^{97} -3.10312 q^{98} +(0.719263 + 2.85094i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{2} + 32 q^{4} + 2 q^{5} - 32 q^{8} + 4 q^{9}+O(q^{10}) $ 32 * q - 32 * q^2 + 32 * q^4 + 2 * q^5 - 32 * q^8 + 4 * q^9	$ 32 q - 32 q^{2} + 32 q^{4} + 2 q^{5} - 32 q^{8} + 4 q^{9} - 2 q^{10} + 32 q^{16} - 4 q^{18} + 8 q^{19} + 2 q^{20} + 10 q^{25} - 12 q^{31} - 32 q^{32} - 8 q^{33} + 16 q^{35} + 4 q^{36} - 8 q^{38} - 4 q^{39} - 2 q^{40} + 10 q^{45} - 4 q^{47} - 36 q^{49} - 10 q^{50} - 4 q^{51} + 12 q^{62} - 24 q^{63} + 32 q^{64} + 8 q^{66} - 8 q^{69} - 16 q^{70} - 4 q^{72} + 8 q^{76} + 4 q^{78} + 2 q^{80} + 24 q^{81} - 4 q^{87} - 10 q^{90} + 24 q^{93} + 4 q^{94} - 26 q^{95} + 36 q^{98}+O(q^{100}) $ 32 * q - 32 * q^2 + 32 * q^4 + 2 * q^5 - 32 * q^8 + 4 * q^9 - 2 * q^10 + 32 * q^16 - 4 * q^18 + 8 * q^19 + 2 * q^20 + 10 * q^25 - 12 * q^31 - 32 * q^32 - 8 * q^33 + 16 * q^35 + 4 * q^36 - 8 * q^38 - 4 * q^39 - 2 * q^40 + 10 * q^45 - 4 * q^47 - 36 * q^49 - 10 * q^50 - 4 * q^51 + 12 * q^62 - 24 * q^63 + 32 * q^64 + 8 * q^66 - 8 * q^69 - 16 * q^70 - 4 * q^72 + 8 * q^76 + 4 * q^78 + 2 * q^80 + 24 * q^81 - 4 * q^87 - 10 * q^90 + 24 * q^93 + 4 * q^94 - 26 * q^95 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.36636	−	1.06445i	−0.788868	−	0.614563i
$3$	−1.36636	−	1.06445i	−0.788868	−	0.614563i
$4$	1.00000			0.500000
$5$	−2.16820	+	0.546716i	−0.969650	+	0.244499i
$5$	−2.16820	+	0.546716i	−0.969650	+	0.244499i
$6$	1.36636	+	1.06445i	0.557814	+	0.434562i
$7$		−	1.97405i		−	0.746121i	−0.927807	−	0.373061i	$-0.878308\pi$
$7$		−	1.97405i		−	0.746121i	0.927807	−	0.373061i	$-0.121692\pi$
$8$	−1.00000			−0.353553
$9$	0.733873	+	2.90885i	0.244624	+	0.969618i
$10$	2.16820	−	0.546716i	0.685646	−	0.172887i
$11$	0.980092			0.295509			0.147754	−	0.989024i	$-0.452795\pi$
$11$	0.980092			0.295509			0.147754	+	0.989024i	$0.452795\pi$
$12$	−1.36636	−	1.06445i	−0.394434	−	0.307282i
$13$	4.39735			1.21960			0.609802	−	0.792554i	$-0.291249\pi$
$13$	4.39735			1.21960			0.609802	+	0.792554i	$0.291249\pi$
$14$			1.97405i			0.527587i
$15$	3.54450	+	1.56094i	0.915185	+	0.403034i
$16$	1.00000			0.250000
$17$			2.02195i			0.490395i	0.969473	+	0.245198i	$0.0788529\pi$
$17$			2.02195i			0.490395i	−0.969473	+	0.245198i	$0.921147\pi$
$18$	−0.733873	−	2.90885i	−0.172975	−	0.685623i
$19$	−3.72763			−0.855176			−0.427588	−	0.903974i	$-0.640637\pi$
$19$	−3.72763			−0.855176			−0.427588	+	0.903974i	$0.640637\pi$
$20$	−2.16820	+	0.546716i	−0.484825	+	0.122249i
$21$	−2.10129	+	2.69726i	−0.458539	+	0.588591i
$22$	−0.980092			−0.208956
$23$			6.09578i			1.27106i	0.772077	+	0.635529i	$0.219218\pi$
$23$			6.09578i			1.27106i	−0.772077	+	0.635529i	$0.780782\pi$
$24$	1.36636	+	1.06445i	0.278907	+	0.217281i
$25$	4.40220	−	2.37078i	0.880440	−	0.474157i
$26$	−4.39735			−0.862391
$27$	2.09361	−	4.75571i	0.402915	−	0.915237i
$28$		−	1.97405i		−	0.373061i
$29$	2.54734			0.473029			0.236515	−	0.971628i	$-0.423995\pi$
$29$	2.54734			0.473029			0.236515	+	0.971628i	$0.423995\pi$
$30$	−3.54450	−	1.56094i	−0.647134	−	0.284988i
$31$	−1.90121	−	5.23311i	−0.341467	−	0.939894i
$31$	−1.90121	−	5.23311i	−0.341467	−	0.939894i
$32$	−1.00000			−0.176777
$33$	−1.33916	−	1.04326i	−0.233117	−	0.181609i
$34$		−	2.02195i		−	0.346762i
$35$	1.07925	+	4.28014i	0.182426	+	0.723476i
$36$	0.733873	+	2.90885i	0.122312	+	0.484809i
$37$	9.44453			1.55267			0.776336	−	0.630320i	$-0.217076\pi$
$37$	9.44453			1.55267			0.776336	+	0.630320i	$0.217076\pi$
$38$	3.72763			0.604701
$39$	−6.00835	−	4.68078i	−0.962107	−	0.749524i
$40$	2.16820	−	0.546716i	0.342823	−	0.0864434i
$41$		−	12.5007i		−	1.95228i	−0.217138	−	0.976141i	$-0.569672\pi$
$41$		−	12.5007i		−	1.95228i	0.217138	−	0.976141i	$-0.430328\pi$
$42$	2.10129	−	2.69726i	0.324236	−	0.416197i
$43$	−3.33266			−0.508226			−0.254113	−	0.967175i	$-0.581784\pi$
$43$	−3.33266			−0.508226			−0.254113	+	0.967175i	$0.581784\pi$
$44$	0.980092			0.147754
$45$	−3.18150	−	5.90576i	−0.474270	−	0.880379i
$46$		−	6.09578i		−	0.898774i
$47$	−11.6412			−1.69805			−0.849023	−	0.528356i	$-0.822808\pi$
$47$	−11.6412			−1.69805			−0.849023	+	0.528356i	$0.822808\pi$
$48$	−1.36636	−	1.06445i	−0.197217	−	0.153641i
$49$	3.10312			0.443303
$50$	−4.40220	+	2.37078i	−0.622565	+	0.335279i
$51$	2.15228	−	2.76271i	0.301379	−	0.386857i
$52$	4.39735			0.609802
$53$		−	7.67233i		−	1.05388i	−0.849904	−	0.526938i	$-0.823340\pi$
$53$		−	7.67233i		−	1.05388i	0.849904	−	0.526938i	$-0.176660\pi$
$54$	−2.09361	+	4.75571i	−0.284904	+	0.647170i
$55$	−2.12504	+	0.535832i	−0.286540	+	0.0722516i
$56$			1.97405i			0.263794i
$57$	5.09328	+	3.96789i	0.674621	+	0.525560i
$58$	−2.54734			−0.334482
$59$		−	0.348160i		−	0.0453265i	−0.999743	−	0.0226633i	$-0.992785\pi$
$59$		−	0.348160i		−	0.0453265i	0.999743	−	0.0226633i	$-0.00721456\pi$
$60$	3.54450	+	1.56094i	0.457593	+	0.201517i
$61$			5.15035i			0.659435i	0.944080	+	0.329717i	$0.106953\pi$
$61$			5.15035i			0.659435i	−0.944080	+	0.329717i	$0.893047\pi$
$62$	1.90121	+	5.23311i	0.241454	+	0.664605i
$63$	5.74223	−	1.44870i	0.723452	−	0.182519i
$64$	1.00000			0.125000
$65$	−9.53434	+	2.40410i	−1.18259	+	0.298192i
$66$	1.33916	+	1.04326i	0.164839	+	0.128417i
$67$		−	1.03734i		−	0.126731i	−0.997990	−	0.0633653i	$-0.979817\pi$
$67$		−	1.03734i		−	0.126731i	0.997990	−	0.0633653i	$-0.0201833\pi$
$68$			2.02195i			0.245198i
$69$	6.48868	−	8.32902i	0.781145	−	1.00270i
$70$	−1.07925	−	4.28014i	−0.128995	−	0.511575i
$71$		−	8.70746i		−	1.03339i	−0.856171	−	0.516693i	$-0.827163\pi$
$71$		−	8.70746i		−	1.03339i	0.856171	−	0.516693i	$-0.172837\pi$
$72$	−0.733873	−	2.90885i	−0.0864877	−	0.342812i
$73$	−5.88000			−0.688202			−0.344101	−	0.938933i	$-0.611816\pi$
$73$	−5.88000			−0.688202			−0.344101	+	0.938933i	$0.611816\pi$
$74$	−9.44453			−1.09790
$75$	−8.53858	−	1.44660i	−0.985950	−	0.167039i
$76$	−3.72763			−0.427588
$77$		−	1.93475i		−	0.220485i
$78$	6.00835	+	4.68078i	0.680312	+	0.529994i
$79$		−	8.91713i		−	1.00326i	−0.865084	−	0.501628i	$-0.832735\pi$
$79$		−	8.91713i		−	1.00326i	0.865084	−	0.501628i	$-0.167265\pi$
$80$	−2.16820	+	0.546716i	−0.242412	+	0.0611247i
$81$	−7.92286	+	4.26946i	−0.880318	+	0.474384i
$82$			12.5007i			1.38047i
$83$		−	8.99302i		−	0.987113i	−0.869714	−	0.493556i	$-0.835697\pi$
$83$		−	8.99302i		−	0.987113i	0.869714	−	0.493556i	$-0.164303\pi$
$84$	−2.10129	+	2.69726i	−0.229269	+	0.294295i
$85$	−1.10543	−	4.38400i	−0.119901	−	0.475512i
$86$	3.33266			0.359370
$87$	−3.48058	−	2.71153i	−0.373158	−	0.290706i
$88$	−0.980092			−0.104478
$89$	10.3304			1.09502			0.547511	−	0.836798i	$-0.315575\pi$
$89$	10.3304			1.09502			0.547511	+	0.836798i	$0.315575\pi$
$90$	3.18150	+	5.90576i	0.335360	+	0.622522i
$91$		−	8.68059i		−	0.909973i
$92$			6.09578i			0.635529i
$93$	−2.97267	+	9.17405i	−0.308252	+	0.951305i
$94$	11.6412			1.20070
$95$	8.08225	−	2.03795i	0.829221	−	0.209090i
$96$	1.36636	+	1.06445i	0.139453	+	0.108640i
$97$		−	17.1380i		−	1.74010i	−0.492965	−	0.870049i	$-0.664087\pi$
$97$		−	17.1380i		−	1.74010i	0.492965	−	0.870049i	$-0.335913\pi$
$98$	−3.10312			−0.313463
$99$	0.719263	+	2.85094i	0.0722886	+	0.286531i
$100$	4.40220	−	2.37078i	0.440220	−	0.237078i
$101$			1.71289i			0.170439i	0.996362	+	0.0852194i	$0.0271591\pi$
$101$			1.71289i			0.170439i	−0.996362	+	0.0852194i	$0.972841\pi$
$102$	−2.15228	+	2.76271i	−0.213107	+	0.273549i
$103$		−	5.24855i		−	0.517155i	−0.965991	−	0.258577i	$-0.916746\pi$
$103$		−	5.24855i		−	0.517155i	0.965991	−	0.258577i	$-0.0832537\pi$
$104$	−4.39735			−0.431195
$105$	3.08138	−	6.99702i	0.300712	−	0.682839i
$106$			7.67233i			0.745202i
$107$	6.91333			0.668337			0.334168	−	0.942513i	$-0.391545\pi$
$107$	6.91333			0.668337			0.334168	+	0.942513i	$0.391545\pi$
$108$	2.09361	−	4.75571i	0.201458	−	0.457619i
$109$	−4.14606			−0.397121			−0.198560	−	0.980089i	$-0.563627\pi$
$109$	−4.14606			−0.397121			−0.198560	+	0.980089i	$0.563627\pi$
$110$	2.12504	−	0.535832i	0.202614	−	0.0510896i
$111$	−12.9046	−	10.0533i	−1.22485	−	0.954214i
$112$		−	1.97405i		−	0.186530i
$113$	4.54452			0.427513			0.213756	−	0.976887i	$-0.431430\pi$
$113$	4.54452			0.427513			0.213756	+	0.976887i	$0.431430\pi$
$114$	−5.09328	−	3.96789i	−0.477029	−	0.371627i
$115$	−3.33266	−	13.2169i	−0.310772	−	1.23248i
$116$	2.54734			0.236515
$117$	3.22709	+	12.7912i	0.298345	+	1.18255i
$118$			0.348160i			0.0320507i
$119$	3.99144			0.365894
$120$	−3.54450	−	1.56094i	−0.323567	−	0.142494i
$121$	−10.0394			−0.912675
$122$		−	5.15035i		−	0.466291i
$123$	−13.3064	+	17.0804i	−1.19980	+	1.54009i
$124$	−1.90121	−	5.23311i	−0.170734	−	0.469947i
$125$	−8.24872	+	7.54709i	−0.737788	+	0.675033i
$126$	−5.74223	+	1.44870i	−0.511558	+	0.129061i
$127$	10.5533			0.936458			0.468229	−	0.883607i	$-0.344892\pi$
$127$	10.5533			0.936458			0.468229	+	0.883607i	$0.344892\pi$
$128$	−1.00000			−0.0883883
$129$	4.55361	+	3.54747i	0.400923	+	0.312337i
$130$	9.53434	−	2.40410i	0.836217	−	0.210854i
$131$		−	12.1698i		−	1.06328i	−0.846969	−	0.531642i	$-0.821575\pi$
$131$		−	12.1698i		−	1.06328i	0.846969	−	0.531642i	$-0.178425\pi$
$132$	−1.33916	−	1.04326i	−0.116559	−	0.0908044i
$133$			7.35853i			0.638065i
$134$			1.03734i			0.0896121i
$135$	−1.93934	+	11.4560i	−0.166912	+	0.985972i
$136$		−	2.02195i		−	0.173381i
$137$		−	10.9229i		−	0.933208i	−0.884466	−	0.466604i	$-0.845477\pi$
$137$		−	10.9229i		−	0.933208i	0.884466	−	0.466604i	$-0.154523\pi$
$138$	−6.48868	+	8.32902i	−0.552353	+	0.709013i
$139$			19.3296i			1.63952i	0.572709	+	0.819759i	$0.305892\pi$
$139$			19.3296i			1.63952i	−0.572709	+	0.819759i	$0.694108\pi$
$140$	1.07925	+	4.28014i	0.0912129	+	0.361738i
$141$	15.9061	+	12.3915i	1.33953	+	1.04356i
$142$			8.70746i			0.730714i
$143$	4.30980			0.360404
$144$	0.733873	+	2.90885i	0.0611560	+	0.242404i
$145$	−5.52315	+	1.39267i	−0.458673	+	0.115655i
$146$	5.88000			0.486633
$147$	−4.23998	−	3.30313i	−0.349708	−	0.272438i
$148$	9.44453			0.776336
$149$			11.7905i			0.965917i	0.875643	+	0.482958i	$0.160438\pi$
$149$			11.7905i			0.965917i	−0.875643	+	0.482958i	$0.839562\pi$
$150$	8.53858	+	1.44660i	0.697172	+	0.118115i
$151$		−	20.0515i		−	1.63177i	−0.578217	−	0.815883i	$-0.696251\pi$
$151$		−	20.0515i		−	1.63177i	0.578217	−	0.815883i	$-0.303749\pi$
$152$	3.72763			0.302350
$153$	−5.88156	+	1.48385i	−0.475496	+	0.119963i
$154$			1.93475i			0.155907i
$155$	6.98323	+	10.3070i	0.560907	+	0.827879i
$156$	−6.00835	−	4.68078i	−0.481053	−	0.374762i
$157$			4.18221i			0.333777i	0.985976	+	0.166888i	$0.0533719\pi$
$157$			4.18221i			0.333777i	−0.985976	+	0.166888i	$0.946628\pi$
$158$			8.91713i			0.709408i
$159$	−8.16685	+	10.4832i	−0.647673	+	0.831368i
$160$	2.16820	−	0.546716i	0.171411	−	0.0432217i
$161$	12.0334			0.948363
$162$	7.92286	−	4.26946i	0.622479	−	0.335440i
$163$			22.8065i			1.78634i	0.449716	+	0.893171i	$0.351525\pi$
$163$			22.8065i			1.78634i	−0.449716	+	0.893171i	$0.648475\pi$
$164$		−	12.5007i		−	0.976141i
$165$	3.47393	+	1.52987i	0.270445	+	0.119100i
$166$			8.99302i			0.697994i
$167$		−	0.934127i		−	0.0722849i	−0.999347	−	0.0361424i	$-0.988493\pi$
$167$		−	0.934127i		−	0.0722849i	0.999347	−	0.0361424i	$-0.0115070\pi$
$168$	2.10129	−	2.69726i	0.162118	−	0.208098i
$169$	6.33666			0.487435
$170$	1.10543	+	4.38400i	0.0847829	+	0.336237i
$171$	−2.73560	−	10.8431i	−0.209197	−	0.829194i
$172$	−3.33266			−0.254113
$173$	15.1657			1.15303			0.576513	−	0.817088i	$-0.304413\pi$
$173$	15.1657			1.15303			0.576513	+	0.817088i	$0.304413\pi$
$174$	3.48058	+	2.71153i	0.263862	+	0.205561i
$175$	−4.68005	−	8.69017i	−0.353778	−	0.656915i
$176$	0.980092			0.0738772
$177$	−0.370600	+	0.475711i	−0.0278560	+	0.0357566i
$178$	−10.3304			−0.774298
$179$	17.0117			1.27151			0.635756	−	0.771890i	$-0.280689\pi$
$179$	17.0117			1.27151			0.635756	+	0.771890i	$0.280689\pi$
$180$	−3.18150	−	5.90576i	−0.237135	−	0.440190i
$181$		−	15.1867i		−	1.12882i	−0.825496	−	0.564408i	$-0.809104\pi$
$181$		−	15.1867i		−	1.12882i	0.825496	−	0.564408i	$-0.190896\pi$
$182$			8.68059i			0.643448i
$183$	5.48231	−	7.03723i	0.405264	−	0.520207i
$184$		−	6.09578i		−	0.449387i
$185$	−20.4777	+	5.16348i	−1.50555	+	0.379627i
$186$	2.97267	−	9.17405i	0.217967	−	0.672674i
$187$			1.98170i			0.144916i
$188$	−11.6412			−0.849023
$189$	−9.38802	−	4.13289i	−0.682878	−	0.300624i
$190$	−8.08225	+	2.03795i	−0.586348	+	0.147849i
$191$		−	5.27760i		−	0.381874i	−0.981602	−	0.190937i	$-0.938847\pi$
$191$		−	5.27760i		−	0.381874i	0.981602	−	0.190937i	$-0.0611526\pi$
$192$	−1.36636	−	1.06445i	−0.0986085	−	0.0768204i
$193$			14.8854i			1.07147i	0.844386	+	0.535736i	$0.179966\pi$
$193$			14.8854i			1.07147i	−0.844386	+	0.535736i	$0.820034\pi$
$194$			17.1380i			1.23044i
$195$	15.5864	+	6.86401i	1.11616	+	0.491542i
$196$	3.10312			0.221652
$197$		−	9.91445i		−	0.706375i	−0.935553	−	0.353187i	$-0.885098\pi$
$197$		−	9.91445i		−	0.706375i	0.935553	−	0.353187i	$-0.114902\pi$
$198$	−0.719263	−	2.85094i	−0.0511158	−	0.202608i
$199$			5.87620i			0.416553i	0.978070	+	0.208276i	$0.0667853\pi$
$199$			5.87620i			0.416553i	−0.978070	+	0.208276i	$0.933215\pi$
$200$	−4.40220	+	2.37078i	−0.311283	+	0.167640i
$201$	−1.10420	+	1.41737i	−0.0778840	+	0.0999737i
$202$		−	1.71289i		−	0.120518i
$203$		−	5.02858i		−	0.352937i
$204$	2.15228	−	2.76271i	0.150689	−	0.193428i
$205$	6.83434	+	27.1041i	0.477331	+	1.89303i
$206$			5.24855i			0.365684i
$207$	−17.7317	+	4.47353i	−1.23244	+	0.310931i
$208$	4.39735			0.304901
$209$	−3.65342			−0.252712
$210$	−3.08138	+	6.99702i	−0.212635	+	0.482840i
$211$	−12.3770			−0.852068			−0.426034	−	0.904707i	$-0.640090\pi$
$211$	−12.3770			−0.852068			−0.426034	+	0.904707i	$0.640090\pi$
$212$		−	7.67233i		−	0.526938i
$213$	−9.26870	+	11.8975i	−0.635081	+	0.815205i
$214$	−6.91333			−0.472585
$215$	7.22589	−	1.82202i	0.492801	−	0.124261i
$216$	−2.09361	+	4.75571i	−0.142452	+	0.323585i
$217$	−10.3304	+	3.75308i	−0.701275	+	0.254776i
$218$	4.14606			0.280807
$219$	8.03419	+	6.25900i	0.542901	+	0.422944i
$220$	−2.12504	+	0.535832i	−0.143270	+	0.0361258i
$221$			8.89122i			0.598088i
$222$	12.9046	+	10.0533i	0.866101	+	0.674732i
$223$	4.34309			0.290835			0.145417	−	0.989370i	$-0.453548\pi$
$223$	4.34309			0.290835			0.145417	+	0.989370i	$0.453548\pi$
$224$			1.97405i			0.131897i
$225$	10.1269	+	11.0655i	0.675128	+	0.737701i
$226$	−4.54452			−0.302297
$227$	24.1073			1.60006			0.800030	−	0.599960i	$-0.204817\pi$
$227$	24.1073			1.60006			0.800030	+	0.599960i	$0.204817\pi$
$228$	5.09328	+	3.96789i	0.337310	+	0.262780i
$229$			10.5199i			0.695177i	0.937647	+	0.347588i	$0.112999\pi$
$229$			10.5199i			0.695177i	−0.937647	+	0.347588i	$0.887001\pi$
$230$	3.33266	+	13.2169i	0.219749	+	0.871495i
$231$	−2.05946	+	2.64357i	−0.135502	+	0.173934i
$232$	−2.54734			−0.167241
$233$	23.0937			1.51292			0.756460	−	0.654040i	$-0.226927\pi$
$233$	23.0937			1.51292			0.756460	+	0.654040i	$0.226927\pi$
$234$	−3.22709	−	12.7912i	−0.210962	−	0.836189i
$235$	25.2405	−	6.36444i	1.64651	−	0.415170i
$236$		−	0.348160i		−	0.0226633i
$237$	−9.49188	+	12.1840i	−0.616564	+	0.791435i
$238$	−3.99144			−0.258726
$239$	−7.76373			−0.502194			−0.251097	−	0.967962i	$-0.580791\pi$
$239$	−7.76373			−0.502194			−0.251097	+	0.967962i	$0.580791\pi$
$240$	3.54450	+	1.56094i	0.228796	+	0.100758i
$241$		−	9.81525i		−	0.632256i	−0.948717	−	0.316128i	$-0.897617\pi$
$241$		−	9.81525i		−	0.632256i	0.948717	−	0.316128i	$-0.102383\pi$
$242$	10.0394			0.645358
$243$	15.3701	+	2.59992i	0.985993	+	0.166785i
$244$			5.15035i			0.329717i
$245$	−6.72820	+	1.69653i	−0.429849	+	0.108387i
$246$	13.3064	−	17.0804i	0.848387	−	1.08901i
$247$	−16.3917			−1.04298
$248$	1.90121	+	5.23311i	0.120727	+	0.332303i
$249$	−9.57267	+	12.2877i	−0.606643	+	0.778701i
$250$	8.24872	−	7.54709i	0.521695	−	0.477320i
$251$	−4.09502			−0.258475			−0.129238	−	0.991614i	$-0.541253\pi$
$251$	−4.09502			−0.258475			−0.129238	+	0.991614i	$0.541253\pi$
$252$	5.74223	−	1.44870i	0.361726	−	0.0912596i
$253$			5.97442i			0.375609i
$254$	−10.5533			−0.662176
$255$	−3.15615	+	7.16680i	−0.197646	+	0.448803i
$256$	1.00000			0.0625000
$257$	−8.41466			−0.524892			−0.262446	−	0.964947i	$-0.584529\pi$
$257$	−8.41466			−0.524892			−0.262446	+	0.964947i	$0.584529\pi$
$258$	−4.55361	−	3.54747i	−0.283496	−	0.220856i
$259$		−	18.6440i		−	1.15848i
$260$	−9.53434	+	2.40410i	−0.591295	+	0.149096i
$261$	1.86942	+	7.40984i	0.115714	+	0.458658i
$262$			12.1698i			0.751855i
$263$		−	8.26340i		−	0.509543i	−0.967001	−	0.254772i	$-0.918000\pi$
$263$		−	8.26340i		−	0.509543i	0.967001	−	0.254772i	$-0.0820003\pi$
$264$	1.33916	+	1.04326i	0.0824194	+	0.0642084i
$265$	4.19459	+	16.6352i	0.257671	+	1.02189i
$266$		−	7.35853i		−	0.451180i
$267$	−14.1151	−	10.9963i	−0.863828	−	0.672960i
$268$		−	1.03734i		−	0.0633653i
$269$	−32.7206			−1.99501			−0.997504	−	0.0706157i	$-0.977504\pi$
$269$	−32.7206			−1.99501			−0.997504	+	0.0706157i	$0.977504\pi$
$270$	1.93934	−	11.4560i	0.118025	−	0.697187i
$271$			6.39946i			0.388740i	0.980928	+	0.194370i	$0.0622662\pi$
$271$			6.39946i			0.388740i	−0.980928	+	0.194370i	$0.937734\pi$
$272$			2.02195i			0.122599i
$273$	−9.24009	+	11.8608i	−0.559236	+	0.717848i
$274$			10.9229i			0.659878i
$275$	4.31456	−	2.32359i	0.260178	−	0.140118i
$276$	6.48868	−	8.32902i	0.390573	−	0.501348i
$277$	10.2009			0.612912			0.306456	−	0.951885i	$-0.400857\pi$
$277$	10.2009			0.612912			0.306456	+	0.951885i	$0.400857\pi$
$278$		−	19.3296i		−	1.15931i
$279$	13.8271	−	9.37077i	0.827807	−	0.561013i
$280$	−1.07925	−	4.28014i	−0.0644973	−	0.255787i
$281$			17.4750i			1.04247i	0.853412	+	0.521236i	$0.174529\pi$
$281$			17.4750i			1.04247i	−0.853412	+	0.521236i	$0.825471\pi$
$282$	−15.9061	−	12.3915i	−0.947193	−	0.737906i
$283$			4.53813i			0.269764i	0.990862	+	0.134882i	$0.0430655\pi$
$283$			4.53813i			0.269764i	−0.990862	+	0.134882i	$0.956935\pi$
$284$		−	8.70746i		−	0.516693i
$285$	−13.2126	−	5.81861i	−0.782645	−	0.344665i
$286$	−4.30980			−0.254844
$287$	−24.6770			−1.45664
$288$	−0.733873	−	2.90885i	−0.0432439	−	0.171406i
$289$	12.9117			0.759512
$290$	5.52315	−	1.39267i	0.324331	−	0.0817806i
$291$	−18.2426	+	23.4166i	−1.06940	+	1.37271i
$292$	−5.88000			−0.344101
$293$	−7.62185			−0.445273			−0.222637	−	0.974902i	$-0.571466\pi$
$293$	−7.62185			−0.445273			−0.222637	+	0.974902i	$0.571466\pi$
$294$	4.23998	+	3.30313i	0.247281	+	0.192643i
$295$	0.190345	+	0.754881i	0.0110823	+	0.0439509i
$296$	−9.44453			−0.548952
$297$	2.05193	−	4.66104i	0.119065	−	0.270461i
$298$		−	11.7905i		−	0.683006i
$299$			26.8053i			1.55019i
$300$	−8.53858	−	1.44660i	−0.492975	−	0.0835197i
$301$			6.57885i			0.379198i
$302$			20.0515i			1.15383i
$303$	1.82329	−	2.34042i	0.104745	−	0.134454i
$304$	−3.72763			−0.213794
$305$	−2.81578	−	11.1670i	−0.161231	−	0.639421i
$306$	5.88156	−	1.48385i	0.336227	−	0.0848263i
$307$		−	13.5784i		−	0.774961i	−0.921878	−	0.387480i	$-0.873345\pi$
$307$		−	13.5784i		−	0.774961i	0.921878	−	0.387480i	$-0.126655\pi$
$308$		−	1.93475i		−	0.110243i
$309$	−5.58684	+	7.17140i	−0.317824	+	0.407967i
$310$	−6.98323	−	10.3070i	−0.396621	−	0.585399i
$311$		−	16.6305i		−	0.943027i	−0.881859	−	0.471513i	$-0.843708\pi$
$311$		−	16.6305i		−	0.943027i	0.881859	−	0.471513i	$-0.156292\pi$
$312$	6.00835	+	4.68078i	0.340156	+	0.264997i
$313$	21.9447			1.24039			0.620194	−	0.784449i	$-0.287054\pi$
$313$	21.9447			1.24039			0.620194	+	0.784449i	$0.287054\pi$
$314$		−	4.18221i		−	0.236016i
$315$	−11.6583	+	6.28045i	−0.656870	+	0.353863i
$316$		−	8.91713i		−	0.501628i
$317$	−9.19464			−0.516422			−0.258211	−	0.966088i	$-0.583133\pi$
$317$	−9.19464			−0.516422			−0.258211	+	0.966088i	$0.583133\pi$
$318$	8.16685	−	10.4832i	0.457974	−	0.587866i
$319$	2.49663			0.139784
$320$	−2.16820	+	0.546716i	−0.121206	+	0.0305624i
$321$	−9.44609	−	7.35893i	−0.527229	−	0.410735i
$322$	−12.0334			−0.670594
$323$		−	7.53708i		−	0.419374i
$324$	−7.92286	+	4.26946i	−0.440159	+	0.237192i
$325$	19.3580	−	10.4252i	1.07379	−	0.578284i
$326$		−	22.8065i		−	1.26314i
$327$	5.66501	+	4.41329i	0.313276	+	0.244056i
$328$			12.5007i			0.690236i
$329$			22.9803i			1.26695i
$330$	−3.47393	−	1.52987i	−0.191234	−	0.0842164i
$331$		−	12.1158i		−	0.665943i	−0.942937	−	0.332972i	$-0.891949\pi$
$331$		−	12.1158i		−	0.665943i	0.942937	−	0.332972i	$-0.108051\pi$
$332$		−	8.99302i		−	0.493556i
$333$	6.93108	+	27.4728i	0.379821	+	1.50550i
$334$			0.934127i			0.0511131i
$335$	0.567128	+	2.24915i	0.0309855	+	0.122884i
$336$	−2.10129	+	2.69726i	−0.114635	+	0.147148i
$337$	−11.5825			−0.630938			−0.315469	−	0.948936i	$-0.602162\pi$
$337$	−11.5825			−0.630938			−0.315469	+	0.948936i	$0.602162\pi$
$338$	−6.33666			−0.344669
$339$	−6.20945	−	4.83744i	−0.337251	−	0.262734i
$340$	−1.10543	−	4.38400i	−0.0599506	−	0.237756i
$341$	−1.86336	−	5.12893i	−0.100907	−	0.277747i
$342$	2.73560	+	10.8431i	0.147924	+	0.586329i
$343$		−	19.9441i		−	1.07688i
$344$	3.33266			0.179685
$345$	−9.51516	+	21.6065i	−0.512279	+	1.16325i
$346$	−15.1657			−0.815312
$347$			6.59046i			0.353795i	0.984229	+	0.176897i	$0.0566060\pi$
$347$			6.59046i			0.353795i	−0.984229	+	0.176897i	$0.943394\pi$
$348$	−3.48058	−	2.71153i	−0.186579	−	0.145353i
$349$	18.6042			0.995858			0.497929	−	0.867218i	$-0.334094\pi$
$349$	18.6042			0.995858			0.497929	+	0.867218i	$0.334094\pi$
$350$	4.68005	+	8.69017i	0.250159	+	0.464509i
$351$	9.20633	−	20.9125i	0.491397	−	1.11623i
$352$	−0.980092			−0.0522391
$353$		−	30.0655i		−	1.60022i	−0.599851	−	0.800112i	$-0.704774\pi$
$353$		−	30.0655i		−	1.60022i	0.599851	−	0.800112i	$-0.295226\pi$
$354$	0.370600	−	0.475711i	0.0196972	−	0.0252838i
$355$	4.76051	+	18.8795i	0.252662	+	1.00202i
$356$	10.3304			0.547511
$357$	−5.45373	−	4.24870i	−0.288642	−	0.224865i
$358$	−17.0117			−0.899095
$359$		−	22.8551i		−	1.20624i	−0.797649	−	0.603122i	$-0.793923\pi$
$359$		−	22.8551i		−	1.20624i	0.797649	−	0.603122i	$-0.206077\pi$
$360$	3.18150	+	5.90576i	0.167680	+	0.311261i
$361$	−5.10480			−0.268673
$362$			15.1867i			0.798194i
$363$	13.7174	+	10.6865i	0.719979	+	0.560896i
$364$		−	8.68059i		−	0.454986i
$365$	12.7490	−	3.21469i	0.667315	−	0.168265i
$366$	−5.48231	+	7.03723i	−0.286565	+	0.367842i
$367$	24.2108			1.26379			0.631896	−	0.775053i	$-0.282277\pi$
$367$	24.2108			1.26379			0.631896	+	0.775053i	$0.282277\pi$
$368$			6.09578i			0.317764i
$369$	36.3627	−	9.17392i	1.89297	−	0.477575i
$370$	20.4777	−	5.16348i	1.06458	−	0.268436i
$371$	−15.1456			−0.786319
$372$	−2.97267	+	9.17405i	−0.154126	+	0.475652i
$373$		−	24.0008i		−	1.24271i	−0.783528	−	0.621356i	$-0.786582\pi$
$373$		−	24.0008i		−	1.24271i	0.783528	−	0.621356i	$-0.213418\pi$
$374$		−	1.98170i		−	0.102471i
$375$	19.3042	−	1.53165i	0.996867	−	0.0790941i
$376$	11.6412			0.600350
$377$	11.2015			0.576909
$378$	9.38802	+	4.13289i	0.482868	+	0.212573i
$379$	−16.0776			−0.825849			−0.412925	−	0.910765i	$-0.635493\pi$
$379$	−16.0776			−0.825849			−0.412925	+	0.910765i	$0.635493\pi$
$380$	8.08225	−	2.03795i	0.414611	−	0.104545i
$381$	−14.4197	−	11.2336i	−0.738741	−	0.575513i
$382$			5.27760i			0.270026i
$383$		−	9.88187i		−	0.504940i	−0.967605	−	0.252470i	$-0.918757\pi$
$383$		−	9.88187i		−	0.504940i	0.967605	−	0.252470i	$-0.0812429\pi$
$384$	1.36636	+	1.06445i	0.0697267	+	0.0543202i
$385$	1.05776	+	4.19493i	0.0539085	+	0.213794i
$386$		−	14.8854i		−	0.757645i
$387$	−2.44575	−	9.69423i	−0.124324	−	0.492785i
$388$		−	17.1380i		−	0.870049i
$389$	16.2850			0.825683			0.412841	−	0.910803i	$-0.364536\pi$
$389$	16.2850			0.825683			0.412841	+	0.910803i	$0.364536\pi$
$390$	−15.5864	−	6.86401i	−0.789247	−	0.347572i
$391$	−12.3254			−0.623321
$392$	−3.10312			−0.156731
$393$	−12.9542	+	16.6284i	−0.653455	+	0.838790i
$394$			9.91445i			0.499483i
$395$	4.87514	+	19.3341i	0.245295	+	0.972806i
$396$	0.719263	+	2.85094i	0.0361443	+	0.143265i
$397$		−	18.5220i		−	0.929593i	−0.885418	−	0.464796i	$-0.846128\pi$
$397$		−	18.5220i		−	0.929593i	0.885418	−	0.464796i	$-0.153872\pi$
$398$		−	5.87620i		−	0.294547i
$399$	7.83282	−	10.0544i	0.392131	−	0.503349i
$400$	4.40220	−	2.37078i	0.220110	−	0.118539i
$401$	12.1940			0.608940			0.304470	−	0.952522i	$-0.401521\pi$
$401$	12.1940			0.608940			0.304470	+	0.952522i	$0.401521\pi$
$402$	1.10420	−	1.41737i	0.0550723	−	0.0706921i
$403$	−8.36027	−	23.0118i	−0.416455	−	1.14630i
$404$			1.71289i			0.0852194i
$405$	14.8442	−	13.5886i	0.737614	−	0.675223i
$406$			5.02858i			0.249564i
$407$	9.25651			0.458828
$408$	−2.15228	+	2.76271i	−0.106554	+	0.136775i
$409$			33.1466i			1.63899i	0.573084	+	0.819497i	$0.305747\pi$
$409$			33.1466i			1.63899i	−0.573084	+	0.819497i	$0.694253\pi$
$410$	−6.83434	−	27.1041i	−0.337524	−	1.33857i
$411$	−11.6270	+	14.9246i	−0.573515	+	0.736177i
$412$		−	5.24855i		−	0.258577i
$413$	−0.687285			−0.0338191
$414$	17.7317	−	4.47353i	0.871467	−	0.219862i
$415$	4.91663	+	19.4987i	0.241348	+	0.957153i
$416$	−4.39735			−0.215598
$417$	20.5755	−	26.4112i	1.00759	−	1.29336i
$418$	3.65342			0.178695
$419$			0.754572i			0.0368633i	0.999830	+	0.0184316i	$0.00586730\pi$
$419$			0.754572i			0.0368633i	−0.999830	+	0.0184316i	$0.994133\pi$
$420$	3.08138	−	6.99702i	0.150356	−	0.341420i
$421$	5.31618			0.259095			0.129547	−	0.991573i	$-0.458648\pi$
$421$	5.31618			0.259095			0.129547	+	0.991573i	$0.458648\pi$
$422$	12.3770			0.602503
$423$	−8.54317	−	33.8626i	−0.415383	−	1.64646i
$424$			7.67233i			0.372601i
$425$	4.79361	+	8.90104i	0.232524	+	0.431764i
$426$	9.26870	−	11.8975i	0.449070	−	0.576437i
$427$	10.1671			0.492018
$428$	6.91333			0.334168
$429$	−5.88874	−	4.58759i	−0.284311	−	0.221491i
$430$	−7.22589	+	1.82202i	−0.348463	+	0.0878656i
$431$		−	15.4872i		−	0.745993i	−0.927833	−	0.372996i	$-0.878330\pi$
$431$		−	15.4872i		−	0.745993i	0.927833	−	0.372996i	$-0.121670\pi$
$432$	2.09361	−	4.75571i	0.100729	−	0.228809i
$433$	−28.9497			−1.39123			−0.695616	−	0.718414i	$-0.744868\pi$
$433$	−28.9497			−1.39123			−0.695616	+	0.718414i	$0.744868\pi$
$434$	10.3304	−	3.75308i	0.495876	−	0.180154i
$435$	9.02904	+	3.97625i	0.432910	+	0.190647i
$436$	−4.14606			−0.198560
$437$		−	22.7228i		−	1.08698i
$438$	−8.03419	−	6.25900i	−0.383889	−	0.299066i
$439$	−3.14632			−0.150165			−0.0750827	−	0.997177i	$-0.523922\pi$
$439$	−3.14632			−0.150165			−0.0750827	+	0.997177i	$0.523922\pi$
$440$	2.12504	−	0.535832i	0.101307	−	0.0255448i
$441$	2.27730	+	9.02653i	0.108443	+	0.429835i
$442$		−	8.89122i		−	0.422912i
$443$	−11.9046			−0.565603			−0.282801	−	0.959179i	$-0.591264\pi$
$443$	−11.9046			−0.565603			−0.282801	+	0.959179i	$0.591264\pi$
$444$	−12.9046	−	10.0533i	−0.612426	−	0.477107i
$445$	−22.3984	+	5.64781i	−1.06179	+	0.267732i
$446$	−4.34309			−0.205651
$447$	12.5505	−	16.1101i	0.593617	−	0.761980i
$448$		−	1.97405i		−	0.0932651i
$449$	11.2069			0.528888			0.264444	−	0.964401i	$-0.414812\pi$
$449$	11.2069			0.528888			0.264444	+	0.964401i	$0.414812\pi$
$450$	−10.1269	−	11.0655i	−0.477387	−	0.521633i
$451$		−	12.2518i		−	0.576917i
$452$	4.54452			0.213756
$453$	−21.3439	+	27.3975i	−1.00282	+	1.28725i
$454$	−24.1073			−1.13141
$455$	4.74582	+	18.8213i	0.222487	+	0.882355i
$456$	−5.09328	−	3.96789i	−0.238515	−	0.185813i
$457$	−40.6055			−1.89944			−0.949722	−	0.313094i	$-0.898634\pi$
$457$	−40.6055			−1.89944			−0.949722	+	0.313094i	$0.898634\pi$
$458$		−	10.5199i		−	0.491564i
$459$	9.61582	+	4.23318i	0.448828	+	0.197588i
$460$	−3.33266	−	13.2169i	−0.155386	−	0.616240i
$461$	27.9308			1.30087			0.650433	−	0.759563i	$-0.274587\pi$
$461$	27.9308			1.30087			0.650433	+	0.759563i	$0.274587\pi$
$462$	2.05946	−	2.64357i	0.0958145	−	0.122990i
$463$	29.6880			1.37972			0.689858	−	0.723945i	$-0.257673\pi$
$463$	29.6880			1.37972			0.689858	+	0.723945i	$0.257673\pi$
$464$	2.54734			0.118257
$465$	1.42975	−	21.5164i	0.0663030	−	0.997800i
$466$	−23.0937			−1.06980
$467$	−37.9512			−1.75617			−0.878087	−	0.478502i	$-0.841180\pi$
$467$	−37.9512			−1.75617			−0.878087	+	0.478502i	$0.841180\pi$
$468$	3.22709	+	12.7912i	0.149172	+	0.591275i
$469$	−2.04775			−0.0945564
$470$	−25.2405	+	6.36444i	−1.16426	+	0.293570i
$471$	4.45177	−	5.71440i	0.205127	−	0.263306i
$472$			0.348160i			0.0160254i
$473$	−3.26632			−0.150185
$474$	9.49188	−	12.1840i	0.435976	−	0.559629i
$475$	−16.4098	+	8.83740i	−0.752932	+	0.405488i
$476$	3.99144			0.182947
$477$	22.3177	−	5.63051i	1.02186	−	0.257803i
$478$	7.76373			0.355105
$479$		−	28.5738i		−	1.30557i	−0.757543	−	0.652785i	$-0.773601\pi$
$479$		−	28.5738i		−	1.30557i	0.757543	−	0.652785i	$-0.226399\pi$
$480$	−3.54450	−	1.56094i	−0.161783	−	0.0712469i
$481$	41.5309			1.89364
$482$			9.81525i			0.447072i
$483$	−16.4419	−	12.8090i	−0.748133	−	0.582829i
$484$	−10.0394			−0.456337
$485$	9.36961	+	37.1586i	0.425452	+	1.68729i
$486$	−15.3701	−	2.59992i	−0.697203	−	0.117935i
$487$	−14.7351			−0.667712			−0.333856	−	0.942624i	$-0.608350\pi$
$487$	−14.7351			−0.667712			−0.333856	+	0.942624i	$0.608350\pi$
$488$		−	5.15035i		−	0.233145i
$489$	24.2765	−	31.1619i	1.09782	−	1.40919i
$490$	6.72820	−	1.69653i	0.303949	−	0.0766413i
$491$	23.1610			1.04524			0.522620	−	0.852566i	$-0.324955\pi$
$491$	23.1610			1.04524			0.522620	+	0.852566i	$0.324955\pi$
$492$	−13.3064	+	17.0804i	−0.599900	+	0.770046i
$493$			5.15060i			0.231971i
$494$	16.3917			0.737496
$495$	−3.11817	−	5.78819i	−0.140151	−	0.260160i
$496$	−1.90121	−	5.23311i	−0.0853668	−	0.234973i
$497$	−17.1890			−0.771031
$498$	9.57267	−	12.2877i	0.428961	−	0.550625i
$499$			18.6530i			0.835025i	0.908671	+	0.417512i	$0.137098\pi$
$499$			18.6530i			0.835025i	−0.908671	+	0.417512i	$0.862902\pi$
$500$	−8.24872	+	7.54709i	−0.368894	+	0.337516i
$501$	−0.994336	+	1.27635i	−0.0444236	+	0.0570232i
$502$	4.09502			0.182770
$503$	14.0028			0.624355			0.312177	−	0.950024i	$-0.398942\pi$
$503$	14.0028			0.624355			0.312177	+	0.950024i	$0.398942\pi$
$504$	−5.74223	+	1.44870i	−0.255779	+	0.0645303i
$505$	−0.936464	−	3.71389i	−0.0416721	−	0.165266i
$506$		−	5.97442i		−	0.265596i
$507$	−8.65815	−	6.74509i	−0.384522	−	0.299560i
$508$	10.5533			0.468229
$509$	−26.9945			−1.19651			−0.598255	−	0.801306i	$-0.704139\pi$
$509$	−26.9945			−1.19651			−0.598255	+	0.801306i	$0.704139\pi$
$510$	3.15615	−	7.16680i	0.139757	−	0.317351i
$511$			11.6074i			0.513482i
$512$	−1.00000			−0.0441942
$513$	−7.80420	+	17.7275i	−0.344564	+	0.782689i
$514$	8.41466			0.371155
$515$	2.86947	+	11.3799i	0.126444	+	0.501459i
$516$	4.55361	+	3.54747i	0.200462	+	0.156169i
$517$	−11.4095			−0.501787
$518$			18.6440i			0.819170i
$519$	−20.7218	−	16.1432i	−0.909584	−	0.708607i
$520$	9.53434	−	2.40410i	0.418108	−	0.105427i
$521$			43.5321i			1.90718i	0.301113	+	0.953589i	$0.402642\pi$
$521$			43.5321i			1.90718i	−0.301113	+	0.953589i	$0.597358\pi$
$522$	−1.86942	−	7.40984i	−0.0818225	−	0.324320i
$523$	35.6612			1.55936			0.779678	−	0.626181i	$-0.215383\pi$
$523$	35.6612			1.55936			0.779678	+	0.626181i	$0.215383\pi$
$524$		−	12.1698i		−	0.531642i
$525$	−2.85567	+	16.8556i	−0.124632	+	0.735638i
$526$			8.26340i			0.360301i
$527$	10.5811	−	3.84415i	0.460919	−	0.167454i
$528$	−1.33916	−	1.04326i	−0.0582793	−	0.0454022i
$529$	−14.1585			−0.615588
$530$	−4.19459	−	16.6352i	−0.182201	−	0.722585i
$531$	1.01275	−	0.255505i	0.0439494	−	0.0110880i
$532$			7.35853i			0.319033i
$533$		−	54.9699i		−	2.38101i
$534$	14.1151	+	10.9963i	0.610818	+	0.475855i
$535$	−14.9895	+	3.77963i	−0.648052	+	0.163408i
$536$			1.03734i			0.0448061i
$537$	−23.2440	−	18.1081i	−1.00305	−	0.781424i
$538$	32.7206			1.41068
$539$	3.04135			0.131000
$540$	−1.93934	+	11.4560i	−0.0834561	+	0.492986i
$541$	10.0862			0.433638			0.216819	−	0.976212i	$-0.430432\pi$
$541$	10.0862			0.433638			0.216819	+	0.976212i	$0.430432\pi$
$542$		−	6.39946i		−	0.274881i
$543$	−16.1655	+	20.7504i	−0.693729	+	0.890487i
$544$		−	2.02195i		−	0.0866905i
$545$	8.98950	−	2.26672i	0.385068	−	0.0970956i
$546$	9.24009	−	11.8608i	0.395439	−	0.507595i
$547$			13.9210i			0.595217i	0.954688	+	0.297609i	$0.0961891\pi$
$547$			13.9210i			0.595217i	−0.954688	+	0.297609i	$0.903811\pi$
$548$		−	10.9229i		−	0.466604i
$549$	−14.9816	+	3.77970i	−0.639400	+	0.161314i
$550$	−4.31456	+	2.32359i	−0.183974	+	0.0990780i
$551$	−9.49554			−0.404524
$552$	−6.48868	+	8.32902i	−0.276177	+	0.354507i
$553$	−17.6029			−0.748550
$554$	−10.2009			−0.433395
$555$	33.4761	+	14.7424i	1.42098	+	0.625779i
$556$			19.3296i			0.819759i
$557$			14.0790i			0.596547i	0.954480	+	0.298273i	$0.0964107\pi$
$557$			14.0790i			0.596547i	−0.954480	+	0.298273i	$0.903589\pi$
$558$	−13.8271	+	9.37077i	−0.585348	+	0.396696i
$559$	−14.6549			−0.619835
$560$	1.07925	+	4.28014i	0.0456065	+	0.180869i
$561$	2.10943	−	2.70771i	0.0890601	−	0.114320i
$562$		−	17.4750i		−	0.737139i
$563$	−32.9081			−1.38691			−0.693456	−	0.720499i	$-0.743913\pi$
$563$	−32.9081			−1.38691			−0.693456	+	0.720499i	$0.743913\pi$
$564$	15.9061	+	12.3915i	0.669766	+	0.521778i
$565$	−9.85345	+	2.48457i	−0.414538	+	0.104526i
$566$		−	4.53813i		−	0.190752i
$567$	8.42812	+	15.6401i	0.353948	+	0.656824i
$568$			8.70746i			0.365357i
$569$	−22.2225			−0.931617			−0.465808	−	0.884886i	$-0.654236\pi$
$569$	−22.2225			−0.931617			−0.465808	+	0.884886i	$0.654236\pi$
$570$	13.2126	+	5.81861i	0.553413	+	0.243715i
$571$			12.1969i			0.510422i	0.966885	+	0.255211i	$0.0821450\pi$
$571$			12.1969i			0.510422i	−0.966885	+	0.255211i	$0.917855\pi$
$572$	4.30980			0.180202
$573$	−5.61777	+	7.21110i	−0.234686	+	0.301248i
$574$	24.6770			1.03000
$575$	14.4518	+	26.8349i	0.602681	+	1.11909i
$576$	0.733873	+	2.90885i	0.0305780	+	0.121202i
$577$		−	24.0355i		−	1.00061i	−0.865849	−	0.500306i	$-0.833221\pi$
$577$		−	24.0355i		−	1.00061i	0.865849	−	0.500306i	$-0.166779\pi$
$578$	−12.9117			−0.537056
$579$	15.8448	−	20.3387i	0.658487	−	0.845249i
$580$	−5.52315	+	1.39267i	−0.229336	+	0.0578276i
$581$	−17.7527			−0.736506
$582$	18.2426	−	23.4166i	0.756180	−	0.970651i
$583$		−	7.51959i		−	0.311430i
$584$	5.88000			0.243316
$585$	−13.9902	−	25.9697i	−0.578422	−	1.07371i
$586$	7.62185			0.314856
$587$			9.02705i			0.372586i	0.982494	+	0.186293i	$0.0596474\pi$
$587$			9.02705i			0.372586i	−0.982494	+	0.186293i	$0.940353\pi$
$588$	−4.23998	−	3.30313i	−0.174854	−	0.136219i
$589$	7.08700	+	19.5071i	0.292015	+	0.803775i
$590$	−0.190345	−	0.754881i	−0.00783637	−	0.0310780i
$591$	−10.5535	+	13.5467i	−0.434112	+	0.557236i
$592$	9.44453			0.388168
$593$	−17.2015			−0.706383			−0.353191	−	0.935551i	$-0.614904\pi$
$593$	−17.2015			−0.706383			−0.353191	+	0.935551i	$0.614904\pi$
$594$	−2.05193	+	4.66104i	−0.0841917	+	0.191245i
$595$	−8.65424	+	2.18218i	−0.354789	+	0.0894608i
$596$			11.7905i			0.482958i
$597$	6.25495	−	8.02900i	0.255998	−	0.328605i
$598$		−	26.8053i		−	1.09615i
$599$		−	7.15936i		−	0.292523i	−0.989246	−	0.146262i	$-0.953276\pi$
$599$		−	7.15936i		−	0.292523i	0.989246	−	0.146262i	$-0.0467242\pi$
$600$	8.53858	+	1.44660i	0.348586	+	0.0590574i
$601$			4.27513i			0.174386i	0.996191	+	0.0871930i	$0.0277897\pi$
$601$			4.27513i			0.174386i	−0.996191	+	0.0871930i	$0.972210\pi$
$602$		−	6.57885i		−	0.268134i
$603$	3.01746	−	0.761272i	0.122880	−	0.0310014i
$604$		−	20.0515i		−	0.815883i
$605$	21.7675	−	5.48871i	0.884974	−	0.223148i
$606$	−1.82329	+	2.34042i	−0.0740662	+	0.0950731i
$607$		−	18.5102i		−	0.751306i	−0.926760	−	0.375653i	$-0.877418\pi$
$607$		−	18.5102i		−	0.751306i	0.926760	−	0.375653i	$-0.122582\pi$
$608$	3.72763			0.151175
$609$	−5.35270	+	6.87085i	−0.216902	+	0.278421i
$610$	2.81578	+	11.1670i	0.114008	+	0.452139i
$611$	−51.1904			−2.07094
$612$	−5.88156	+	1.48385i	−0.237748	+	0.0599813i
$613$	22.7495			0.918845			0.459422	−	0.888218i	$-0.348056\pi$
$613$	22.7495			0.918845			0.459422	+	0.888218i	$0.348056\pi$
$614$			13.5784i			0.547980i
$615$	19.5129	−	44.3087i	0.786835	−	1.78670i
$616$			1.93475i			0.0779534i
$617$	−20.4952			−0.825106			−0.412553	−	0.910934i	$-0.635363\pi$
$617$	−20.4952			−0.825106			−0.412553	+	0.910934i	$0.635363\pi$
$618$	5.58684	−	7.17140i	0.224736	−	0.288476i
$619$			33.1395i			1.33199i	0.745957	+	0.665994i	$0.231992\pi$
$619$			33.1395i			1.33199i	−0.745957	+	0.665994i	$0.768008\pi$
$620$	6.98323	+	10.3070i	0.280453	+	0.413940i
$621$	28.9898	+	12.7622i	1.16332	+	0.512129i
$622$			16.6305i			0.666821i
$623$		−	20.3928i		−	0.817019i
$624$	−6.00835	−	4.68078i	−0.240527	−	0.187381i
$625$	13.7588	−	20.8733i	0.550351	−	0.834933i
$626$	−21.9447			−0.877087
$627$	4.99188	+	3.88890i	0.199356	+	0.155308i
$628$			4.18221i			0.166888i
$629$			19.0964i			0.761423i
$630$	11.6583	−	6.28045i	0.464477	−	0.250219i
$631$			26.9085i			1.07121i	0.844468	+	0.535606i	$0.179917\pi$
$631$			26.9085i			1.07121i	−0.844468	+	0.535606i	$0.820083\pi$
$632$			8.91713i			0.354704i
$633$	16.9114	+	13.1748i	0.672169	+	0.523650i
$634$	9.19464			0.365166
$635$	−22.8818	+	5.76969i	−0.908036	+	0.228963i
$636$	−8.16685	+	10.4832i	−0.323836	+	0.415684i
$637$	13.6455			0.540655
$638$	−2.49663			−0.0988425
$639$	25.3287	−	6.39017i	1.00199	−	0.252791i
$640$	2.16820	−	0.546716i	0.0857057	−	0.0216109i
$641$	49.3752			1.95021			0.975103	−	0.221755i	$-0.0711784\pi$
$641$	49.3752			1.95021			0.975103	+	0.221755i	$0.0711784\pi$
$642$	9.44609	+	7.35893i	0.372807	+	0.290434i
$643$	−28.2228			−1.11300			−0.556499	−	0.830849i	$-0.687856\pi$
$643$	−28.2228			−1.11300			−0.556499	+	0.830849i	$0.687856\pi$
$644$	12.0334			0.474182
$645$	−11.8126	−	5.20209i	−0.465121	−	0.204832i
$646$			7.53708i			0.296543i
$647$			32.6979i			1.28549i	0.766082	+	0.642743i	$0.222204\pi$
$647$			32.6979i			1.28549i	−0.766082	+	0.642743i	$0.777796\pi$
$648$	7.92286	−	4.26946i	0.311239	−	0.167720i
$649$		−	0.341229i		−	0.0133944i
$650$	−19.3580	+	10.4252i	−0.759284	+	0.408908i
$651$	18.1100	+	5.86821i	0.709789	+	0.229993i
$652$			22.8065i			0.893171i
$653$	20.9406			0.819468			0.409734	−	0.912205i	$-0.365622\pi$
$653$	20.9406			0.819468			0.409734	+	0.912205i	$0.365622\pi$
$654$	−5.66501	−	4.41329i	−0.221519	−	0.172573i
$655$	6.65345	+	26.3867i	0.259972	+	1.03101i
$656$		−	12.5007i		−	0.488070i
$657$	−4.31517	−	17.1041i	−0.168351	−	0.667293i
$658$		−	22.9803i		−	0.895867i
$659$		−	18.8086i		−	0.732679i	−0.930481	−	0.366340i	$-0.880611\pi$
$659$		−	18.8086i		−	0.732679i	0.930481	−	0.366340i	$-0.119389\pi$
$660$	3.47393	+	1.52987i	0.135223	+	0.0595500i
$661$	−5.76127			−0.224088			−0.112044	−	0.993703i	$-0.535740\pi$
$661$	−5.76127			−0.224088			−0.112044	+	0.993703i	$0.535740\pi$
$662$			12.1158i			0.470893i
$663$	9.46430	−	12.1486i	0.367563	−	0.471813i
$664$			8.99302i			0.348997i
$665$	−4.02303	−	15.9548i	−0.156006	−	0.618700i
$666$	−6.93108	−	27.4728i	−0.268574	−	1.06455i
$667$			15.5280i			0.601248i
$668$		−	0.934127i		−	0.0361424i
$669$	−5.93421	−	4.62302i	−0.229430	−	0.178736i
$670$	−0.567128	−	2.24915i	−0.0219101	−	0.0868924i
$671$			5.04782i			0.194869i
$672$	2.10129	−	2.69726i	0.0810589	−	0.104049i
$673$	−30.8816			−1.19040			−0.595198	−	0.803579i	$-0.702926\pi$
$673$	−30.8816			−1.19040			−0.595198	+	0.803579i	$0.702926\pi$
$674$	11.5825			0.446141
$675$	−2.05827	−	25.8991i	−0.0792228	−	0.996857i
$676$	6.33666			0.243718
$677$		−	8.66218i		−	0.332915i	−0.986049	−	0.166457i	$-0.946767\pi$
$677$		−	8.66218i		−	0.332915i	0.986049	−	0.166457i	$-0.0532328\pi$
$678$	6.20945	+	4.83744i	0.238472	+	0.185781i
$679$	−33.8312			−1.29832
$680$	1.10543	+	4.38400i	0.0423915	+	0.168119i
$681$	−32.9393	−	25.6612i	−1.26224	−	0.983338i
$682$	1.86336	+	5.12893i	0.0713517	+	0.196397i
$683$	−2.72934			−0.104435			−0.0522176	−	0.998636i	$-0.516629\pi$
$683$	−2.72934			−0.104435			−0.0522176	+	0.998636i	$0.516629\pi$
$684$	−2.73560	−	10.8431i	−0.104598	−	0.414597i
$685$	5.97174	+	23.6831i	0.228168	+	0.904885i
$686$			19.9441i			0.761468i
$687$	11.1980	−	14.3740i	0.427230	−	0.548402i
$688$	−3.33266			−0.127057
$689$		−	33.7379i		−	1.28531i
$690$	9.51516	−	21.6065i	0.362236	−	0.822544i
$691$	26.4423			1.00591			0.502956	−	0.864312i	$-0.332246\pi$
$691$	26.4423			1.00591			0.502956	+	0.864312i	$0.332246\pi$
$692$	15.1657			0.576513
$693$	5.62791	−	1.41986i	0.213787	−	0.0539361i
$694$		−	6.59046i		−	0.250171i
$695$	−10.5678	−	41.9105i	−0.400860	−	1.58976i
$696$	3.48058	+	2.71153i	0.131931	+	0.102780i
$697$	25.2758			0.957390
$698$	−18.6042			−0.704178
$699$	−31.5543	−	24.5822i	−1.19349	−	0.929785i
$700$	−4.68005	−	8.69017i	−0.176889	−	0.328458i
$701$		−	12.6266i		−	0.476899i	−0.971155	−	0.238449i	$-0.923361\pi$
$701$		−	12.6266i		−	0.476899i	0.971155	−	0.238449i	$-0.0766391\pi$
$702$	−9.20633	+	20.9125i	−0.347470	+	0.789292i
$703$	−35.2057			−1.32781
$704$	0.980092			0.0369386
$705$	−41.2622	−	18.1713i	−1.55403	−	0.684369i
$706$			30.0655i			1.13153i
$707$	3.38133			0.127168
$708$	−0.370600	+	0.475711i	−0.0139280	+	0.0178783i
$709$		−	4.52667i		−	0.170003i	−0.996381	−	0.0850013i	$-0.972911\pi$
$709$		−	4.52667i		−	0.170003i	0.996381	−	0.0850013i	$-0.0270894\pi$
$710$	−4.76051	−	18.8795i	−0.178659	−	0.708537i
$711$	25.9386	−	6.54403i	0.972774	−	0.245420i
$712$	−10.3304			−0.387149
$713$	31.8999	−	11.5893i	1.19466	−	0.434025i
$714$	5.45373	+	4.24870i	0.204101	+	0.159004i
$715$	−9.34453	+	2.35624i	−0.349466	+	0.0881184i
$716$	17.0117			0.635756
$717$	10.6080	+	8.26414i	0.396165	+	0.308630i
$718$			22.8551i			0.852944i
$719$	−12.3702			−0.461331			−0.230665	−	0.973033i	$-0.574090\pi$
$719$	−12.3702			−0.461331			−0.230665	+	0.973033i	$0.574090\pi$
$720$	−3.18150	−	5.90576i	−0.118568	−	0.220095i
$721$	−10.3609			−0.385860
$722$	5.10480			0.189981
$723$	−10.4479	+	13.4112i	−0.388561	+	0.498766i
$724$		−	15.1867i		−	0.564408i
$725$	11.2139	−	6.03919i	0.416474	−	0.224290i
$726$	−13.7174	−	10.6865i	−0.509102	−	0.396613i
$727$		−	22.9460i		−	0.851022i	−0.904953	−	0.425511i	$-0.860094\pi$
$727$		−	22.9460i		−	0.851022i	0.904953	−	0.425511i	$-0.139906\pi$
$728$			8.68059i			0.321724i
$729$	−18.2336	−	19.9132i	−0.675318	−	0.737526i
$730$	−12.7490	+	3.21469i	−0.471863	+	0.118981i
$731$		−	6.73848i		−	0.249232i
$732$	5.48231	−	7.03723i	0.202632	−	0.260103i
$733$		−	3.20540i		−	0.118394i	−0.998246	−	0.0591971i	$-0.981146\pi$
$733$		−	3.20540i		−	0.118394i	0.998246	−	0.0591971i	$-0.0188541\pi$
$734$	−24.2108			−0.893637
$735$	10.9990	+	4.84380i	0.405705	+	0.178666i
$736$		−	6.09578i		−	0.224693i
$737$		−	1.01668i		−	0.0374500i
$738$	−36.3627	+	9.17392i	−1.33853	+	0.337697i
$739$			17.2107i			0.633106i	0.948575	+	0.316553i	$0.102526\pi$
$739$			17.2107i			0.633106i	−0.948575	+	0.316553i	$0.897474\pi$
$740$	−20.4777	+	5.16348i	−0.752773	+	0.189813i
$741$	22.3969	+	17.4482i	0.822771	+	0.640975i
$742$	15.1456			0.556011
$743$			47.4219i			1.73974i	0.493280	+	0.869871i	$0.335798\pi$
$743$			47.4219i			1.73974i	−0.493280	+	0.869871i	$0.664202\pi$
$744$	2.97267	−	9.17405i	0.108983	−	0.336337i
$745$	−6.44607	−	25.5642i	−0.236166	−	0.936601i
$746$			24.0008i			0.878731i
$747$	26.1594	−	6.59973i	0.957122	−	0.241472i
$748$			1.98170i			0.0724581i
$749$		−	13.6473i		−	0.498660i
$750$	−19.3042	+	1.53165i	−0.704892	+	0.0559280i
$751$	−3.68943			−0.134629			−0.0673146	−	0.997732i	$-0.521443\pi$
$751$	−3.68943			−0.134629			−0.0673146	+	0.997732i	$0.521443\pi$
$752$	−11.6412			−0.424511
$753$	5.59527	+	4.35896i	0.203903	+	0.158849i
$754$	−11.2015			−0.407936
$755$	10.9625	+	43.4757i	0.398965	+	1.58224i
$756$	−9.38802	−	4.13289i	−0.341439	−	0.150312i
$757$	16.9932			0.617627			0.308813	−	0.951123i	$-0.400068\pi$
$757$	16.9932			0.617627			0.308813	+	0.951123i	$0.400068\pi$
$758$	16.0776			0.583964
$759$	6.35950	−	8.16321i	0.230835	−	0.296306i
$760$	−8.08225	+	2.03795i	−0.293174	+	0.0739244i
$761$	−36.5468			−1.32482			−0.662411	−	0.749141i	$-0.730467\pi$
$761$	−36.5468			−1.32482			−0.662411	+	0.749141i	$0.730467\pi$
$762$	14.4197	+	11.2336i	0.522369	+	0.406949i
$763$			8.18453i			0.296300i
$764$		−	5.27760i		−	0.190937i
$765$	11.9412	−	6.43284i	0.431734	−	0.232580i
$766$			9.88187i			0.357046i
$767$		−	1.53098i		−	0.0552805i
$768$	−1.36636	−	1.06445i	−0.0493042	−	0.0384102i
$769$	−15.4077			−0.555614			−0.277807	−	0.960637i	$-0.589608\pi$
$769$	−15.4077			−0.555614			−0.277807	+	0.960637i	$0.589608\pi$
$770$	−1.05776	−	4.19493i	−0.0381190	−	0.151175i
$771$	11.4974	+	8.95702i	0.414070	+	0.322579i
$772$			14.8854i			0.535736i
$773$		−	9.20090i		−	0.330933i	−0.986215	−	0.165467i	$-0.947087\pi$
$773$		−	9.20090i		−	0.330933i	0.986215	−	0.165467i	$-0.0529130\pi$
$774$	2.44575	+	9.69423i	0.0879106	+	0.348452i
$775$	−20.7761	−	18.5298i	−0.746298	−	0.665612i
$776$			17.1380i			0.615218i
$777$	−19.8457	+	25.4744i	−0.711960	+	0.913888i
$778$	−16.2850			−0.583846
$779$			46.5980i			1.66955i
$780$	15.5864	+	6.86401i	0.558082	+	0.245771i
$781$		−	8.53412i		−	0.305375i
$782$	12.3254			0.440754
$783$	5.33314	−	12.1144i	0.190591	−	0.432934i
$784$	3.10312			0.110826
$785$	−2.28648	−	9.06787i	−0.0816080	−	0.323646i
$786$	12.9542	−	16.6284i	0.462062	−	0.593114i
$787$	40.9564			1.45994			0.729969	−	0.683481i	$-0.239535\pi$
$787$	40.9564			1.45994			0.729969	+	0.683481i	$0.239535\pi$
$788$		−	9.91445i		−	0.353187i
$789$	−8.79602	+	11.2908i	−0.313147	+	0.401962i
$790$	−4.87514	−	19.3341i	−0.173450	−	0.687878i
$791$		−	8.97112i		−	0.318976i
$792$	−0.719263	−	2.85094i	−0.0255579	−	0.101304i
$793$			22.6479i			0.804250i
$794$			18.5220i			0.657321i
$795$	11.9761	−	27.1945i	0.424747	−	0.964491i
$796$			5.87620i			0.208276i
$797$			44.8728i			1.58948i	0.606953	+	0.794738i	$0.292392\pi$
$797$			44.8728i			1.58948i	−0.606953	+	0.794738i	$0.707608\pi$
$798$	−7.83282	+	10.0544i	−0.277279	+	0.355921i
$799$		−	23.5380i		−	0.832713i
$800$	−4.40220	+	2.37078i	−0.155641	+	0.0838198i
$801$	7.58121	+	30.0497i	0.267869	+	1.06175i
$802$	−12.1940			−0.430585
$803$	−5.76294			−0.203370
$804$	−1.10420	+	1.41737i	−0.0389420	+	0.0499869i
$805$	−26.0908	+	6.57885i	−0.919580	+	0.231874i
$806$	8.36027	+	23.0118i	0.294478	+	0.810556i
$807$	44.7080	+	34.8295i	1.57380	+	1.22606i
$808$		−	1.71289i		−	0.0602592i
$809$	2.70729			0.0951831			0.0475915	−	0.998867i	$-0.484845\pi$
$809$	2.70729			0.0951831			0.0475915	+	0.998867i	$0.484845\pi$
$810$	−14.8442	+	13.5886i	−0.521572	+	0.477455i
$811$	42.5385			1.49373			0.746865	−	0.664976i	$-0.231558\pi$
$811$	42.5385			1.49373			0.746865	+	0.664976i	$0.231558\pi$
$812$		−	5.02858i		−	0.176469i
$813$	6.81194	−	8.74396i	0.238905	−	0.306664i
$814$	−9.25651			−0.324440
$815$	−12.4687	−	49.4491i	−0.436759	−	1.73213i
$816$	2.15228	−	2.76271i	0.0753447	−	0.0967142i
$817$	12.4229			0.434623
$818$		−	33.1466i		−	1.15894i
$819$	25.2506	−	6.37044i	0.882326	−	0.222601i
$820$	6.83434	+	27.1041i	0.238665	+	0.946515i
$821$	17.9562			0.626675			0.313338	−	0.949642i	$-0.398553\pi$
$821$	17.9562			0.626675			0.313338	+	0.949642i	$0.398553\pi$
$822$	11.6270	−	14.9246i	0.405536	−	0.520556i
$823$	−36.9861			−1.28925			−0.644627	−	0.764497i	$-0.722987\pi$
$823$	−36.9861			−1.28925			−0.644627	+	0.764497i	$0.722987\pi$
$824$			5.24855i			0.182842i
$825$	−8.36859	−	1.41781i	−0.291357	−	0.0493616i
$826$	0.687285			0.0239137
$827$			47.7088i			1.65900i	0.558508	+	0.829499i	$0.311374\pi$
$827$			47.7088i			1.65900i	−0.558508	+	0.829499i	$0.688626\pi$
$828$	−17.7317	+	4.47353i	−0.616220	+	0.155466i
$829$		−	43.5833i		−	1.51371i	−0.653583	−	0.756855i	$-0.726735\pi$
$829$		−	43.5833i		−	1.51371i	0.653583	−	0.756855i	$-0.273265\pi$
$830$	−4.91663	−	19.4987i	−0.170659	−	0.676810i
$831$	−13.9381	−	10.8584i	−0.483507	−	0.376673i
$832$	4.39735			0.152451
$833$			6.27436i			0.217394i
$834$	−20.5755	+	26.4112i	−0.712471	+	0.914545i
$835$	0.510702	+	2.02538i	0.0176736	+	0.0700910i
$836$	−3.65342			−0.126356
$837$	−28.8675	−	1.91448i	−0.997808	−	0.0661742i
$838$		−	0.754572i		−	0.0260663i
$839$			2.32033i			0.0801066i	0.999198	+	0.0400533i	$0.0127528\pi$
$839$			2.32033i			0.0801066i	−0.999198	+	0.0400533i	$0.987247\pi$
$840$	−3.08138	+	6.99702i	−0.106318	+	0.241420i
$841$	−22.5111			−0.776243
$842$	−5.31618			−0.183208
$843$	18.6014	−	23.8772i	0.640665	−	0.822373i
$844$	−12.3770			−0.426034
$845$	−13.7392	+	3.46436i	−0.472641	+	0.119177i
$846$	8.54317	+	33.8626i	0.293720	+	1.16422i
$847$			19.8183i			0.680966i
$848$		−	7.67233i		−	0.263469i
$849$	4.83063	−	6.20071i	0.165787	−	0.212808i
$850$	−4.79361	−	8.90104i	−0.164419	−	0.305303i
$851$			57.5718i			1.97353i
$852$	−9.26870	+	11.8975i	−0.317540	+	0.407602i
$853$			15.1244i			0.517850i	0.965897	+	0.258925i	$0.0833683\pi$
$853$			15.1244i			0.517850i	−0.965897	+	0.258925i	$0.916632\pi$
$854$	−10.1671			−0.347909
$855$	11.8595	+	22.0145i	0.405585	+	0.752879i
$856$	−6.91333			−0.236293
$857$	−17.1494			−0.585813			−0.292907	−	0.956141i	$-0.594623\pi$
$857$	−17.1494			−0.585813			−0.292907	+	0.956141i	$0.594623\pi$
$858$	5.88874	+	4.58759i	0.201038	+	0.156618i
$859$			48.7995i			1.66502i	0.554013	+	0.832508i	$0.313096\pi$
$859$			48.7995i			1.66502i	−0.554013	+	0.832508i	$0.686904\pi$
$860$	7.22589	−	1.82202i	0.246401	−	0.0621304i
$861$	33.7177	+	26.2676i	1.14910	+	0.895197i
$862$			15.4872i			0.527496i
$863$			24.5424i			0.835432i	0.908578	+	0.417716i	$0.137169\pi$
$863$			24.5424i			0.835432i	−0.908578	+	0.417716i	$0.862831\pi$
$864$	−2.09361	+	4.75571i	−0.0712261	+	0.161793i
$865$	−32.8823	+	8.29132i	−1.11803	+	0.281913i
$866$	28.9497			0.983749
$867$	−17.6420	−	13.7439i	−0.599155	−	0.466768i
$868$	−10.3304	+	3.75308i	−0.350637	+	0.127388i
$869$		−	8.73960i		−	0.296471i
$870$	−9.02904	−	3.97625i	−0.306113	−	0.134808i
$871$		−	4.56152i		−	0.154561i
$872$	4.14606			0.140403
$873$	49.8519	−	12.5771i	1.68723	−	0.425670i
$874$			22.7228i			0.768610i
$875$	14.8983	+	16.2834i	0.503656	+	0.550479i
$876$	8.03419	+	6.25900i	0.271450	+	0.211472i
$877$			38.1302i			1.28756i	0.765209	+	0.643782i	$0.222636\pi$
$877$			38.1302i			1.28756i	−0.765209	+	0.643782i	$0.777364\pi$
$878$	3.14632			0.106183
$879$	10.4142	+	8.11311i	0.351262	+	0.273649i
$880$	−2.12504	+	0.535832i	−0.0716350	+	0.0180629i
$881$	−30.8392			−1.03900			−0.519499	−	0.854471i	$-0.673881\pi$
$881$	−30.8392			−1.03900			−0.519499	+	0.854471i	$0.673881\pi$
$882$	−2.27730	−	9.02653i	−0.0766806	−	0.303939i
$883$	−50.7217			−1.70692			−0.853460	−	0.521158i	$-0.825500\pi$
$883$	−50.7217			−1.70692			−0.853460	+	0.521158i	$0.825500\pi$
$884$			8.89122i			0.299044i
$885$	0.543457	−	1.23405i	0.0182681	−	0.0414822i
$886$	11.9046			0.399941
$887$	39.6617			1.33171			0.665855	−	0.746081i	$-0.268067\pi$
$887$	39.6617			1.33171			0.665855	+	0.746081i	$0.268067\pi$
$888$	12.9046	+	10.0533i	0.433051	+	0.337366i
$889$		−	20.8328i		−	0.698711i
$890$	22.3984	−	5.64781i	0.750797	−	0.189315i
$891$	−7.76513	+	4.18446i	−0.260142	+	0.140185i
$892$	4.34309			0.145417
$893$	43.3941			1.45213
$894$	−12.5505	+	16.1101i	−0.419751	+	0.538802i
$895$	−36.8847	+	9.30056i	−1.23292	+	0.310883i
$896$			1.97405i			0.0659484i
$897$	28.5330	−	36.6256i	0.952688	−	1.22289i
$898$	−11.2069			−0.373980
$899$	−4.84303	−	13.3305i	−0.161524	−	0.444597i
$900$	10.1269	+	11.0655i	0.337564	+	0.368850i
$901$	15.5131			0.516816
$902$			12.2518i			0.407942i
$903$	7.00288	−	8.98906i	0.233041	−	0.299137i
$904$	−4.54452			−0.151149
$905$	8.30280	+	32.9278i	0.275994	+	1.09456i
$906$	21.3439	−	27.3975i	0.709103	−	0.910221i
$907$			22.3172i			0.741029i	0.928827	+	0.370515i	$0.120819\pi$
$907$			22.3172i			0.741029i	−0.928827	+	0.370515i	$0.879181\pi$
$908$	24.1073			0.800030
$909$	−4.98254	+	1.25704i	−0.165261	+	0.0416935i
$910$	−4.74582	−	18.8213i	−0.157322	−	0.623919i
$911$	20.1057			0.666133			0.333066	−	0.942903i	$-0.391917\pi$
$911$	20.1057			0.666133			0.333066	+	0.942903i	$0.391917\pi$
$912$	5.09328	+	3.96789i	0.168655	+	0.131390i
$913$		−	8.81399i		−	0.291701i
$914$	40.6055			1.34311
$915$	−8.03940	+	18.2554i	−0.265774	+	0.603505i
$916$			10.5199i			0.347588i
$917$	−24.0239			−0.793338
$918$	−9.61582	−	4.23318i	−0.317369	−	0.139716i
$919$	19.7019			0.649904			0.324952	−	0.945730i	$-0.394652\pi$
$919$	19.7019			0.649904			0.324952	+	0.945730i	$0.394652\pi$
$920$	3.33266	+	13.2169i	0.109875	+	0.435748i
$921$	−14.4536	+	18.5530i	−0.476262	+	0.611341i
$922$	−27.9308			−0.919852
$923$		−	38.2897i		−	1.26032i
$924$	−2.05946	+	2.64357i	−0.0677511	+	0.0869669i
$925$	41.5767	−	22.3909i	1.36703	−	0.736209i
$926$	−29.6880			−0.975607
$927$	15.2673	−	3.85176i	0.501442	−	0.126509i
$928$	−2.54734			−0.0836206
$929$	4.02752			0.132139			0.0660694	−	0.997815i	$-0.478954\pi$
$929$	4.02752			0.132139			0.0660694	+	0.997815i	$0.478954\pi$
$930$	−1.42975	+	21.5164i	−0.0468833	+	0.705551i
$931$	−11.5673			−0.379102
$932$	23.0937			0.756460
$933$	−17.7024	+	22.7232i	−0.579550	+	0.743923i
$934$	37.9512			1.24180
$935$	−1.08343	−	4.29672i	−0.0354319	−	0.140518i
$936$	−3.22709	−	12.7912i	−0.105481	−	0.418095i
$937$			58.9267i			1.92505i	0.271189	+	0.962526i	$0.412583\pi$
$937$			58.9267i			1.92505i	−0.271189	+	0.962526i	$0.587417\pi$
$938$	2.04775			0.0668615
$939$	−29.9843	−	23.3591i	−0.978502	−	0.762297i
$940$	25.2405	−	6.36444i	0.823254	−	0.207585i
$941$	8.33254			0.271633			0.135817	−	0.990734i	$-0.456634\pi$
$941$	8.33254			0.271633			0.135817	+	0.990734i	$0.456634\pi$
$942$	−4.45177	+	5.71440i	−0.145047	+	0.186185i
$943$	76.2015			2.48146
$944$		−	0.348160i		−	0.0113316i
$945$	22.6146	+	3.82836i	0.735654	+	0.124537i
$946$	3.26632			0.106197
$947$			17.2118i			0.559310i	0.960101	+	0.279655i	$0.0902200\pi$
$947$			17.2118i			0.559310i	−0.960101	+	0.279655i	$0.909780\pi$
$948$	−9.49188	+	12.1840i	−0.308282	+	0.395718i
$949$	−25.8564			−0.839335
$950$	16.4098	−	8.83740i	0.532403	−	0.286723i
$951$	12.5632	+	9.78728i	0.407389	+	0.317374i
$952$	−3.99144			−0.129363
$953$			38.6364i			1.25155i	0.780002	+	0.625777i	$0.215218\pi$
$953$			38.6364i			1.25155i	−0.780002	+	0.625777i	$0.784782\pi$
$954$	−22.3177	+	5.63051i	−0.722562	+	0.182295i
$955$	2.88535	+	11.4429i	0.0933678	+	0.370284i
$956$	−7.76373			−0.251097
$957$	−3.41129	−	2.65755i	−0.110271	−	0.0859063i
$958$			28.5738i			0.923177i
$959$	−21.5624			−0.696286
$960$	3.54450	+	1.56094i	0.114398	+	0.0503792i
$961$	−23.7708	+	19.8985i	−0.766800	+	0.641886i
$962$	−41.5309			−1.33901
$963$	5.07350	+	20.1099i	0.163491	+	0.648031i
$964$		−	9.81525i		−	0.316128i
$965$	−8.13807	−	32.2745i	−0.261974	−	1.03895i
$966$	16.4419	+	12.8090i	0.529010	+	0.412122i
$967$	18.5194			0.595544			0.297772	−	0.954637i	$-0.403756\pi$
$967$	18.5194			0.595544			0.297772	+	0.954637i	$0.403756\pi$
$968$	10.0394			0.322679
$969$	−8.02288	+	10.2984i	−0.257732	+	0.330831i
$970$	−9.36961	−	37.1586i	−0.300840	−	1.19309i
$971$			20.4044i			0.654810i	0.944884	+	0.327405i	$0.106174\pi$
$971$			20.4044i			0.654810i	−0.944884	+	0.327405i	$0.893826\pi$
$972$	15.3701	+	2.59992i	0.492997	+	0.0833924i
$973$	38.1577			1.22328
$974$	14.7351			0.472144
$975$	−37.5471	−	6.36122i	−1.20247	−	0.203722i
$976$			5.15035i			0.164859i
$977$	−0.505552			−0.0161741			−0.00808703	−	0.999967i	$-0.502574\pi$
$977$	−0.505552			−0.0161741			−0.00808703	+	0.999967i	$0.502574\pi$
$978$	−24.2765	+	31.1619i	−0.776276	+	0.996446i
$979$	10.1248			0.323589
$980$	−6.72820	+	1.69653i	−0.214924	+	0.0541936i
$981$	−3.04268	−	12.0603i	−0.0971453	−	0.385055i
$982$	−23.1610			−0.739096
$983$		−	18.2196i		−	0.581113i	−0.956858	−	0.290557i	$-0.906160\pi$
$983$		−	18.2196i		−	0.581113i	0.956858	−	0.290557i	$-0.0938405\pi$
$984$	13.3064	−	17.0804i	0.424194	−	0.544505i
$985$	5.42039	+	21.4965i	0.172708	+	0.684936i
$986$		−	5.15060i		−	0.164029i
$987$	24.4615	−	31.3994i	0.778619	−	0.999454i
$988$	−16.3917			−0.521488
$989$		−	20.3152i		−	0.645985i
$990$	3.11817	+	5.78819i	0.0991018	+	0.183961i
$991$		−	54.7506i		−	1.73921i	−0.493747	−	0.869605i	$-0.664373\pi$
$991$		−	54.7506i		−	1.73921i	0.493747	−	0.869605i	$-0.335627\pi$
$992$	1.90121	+	5.23311i	0.0603634	+	0.166151i
$993$	−12.8967	+	16.5545i	−0.409264	+	0.525341i
$994$	17.1890			0.545201
$995$	−3.21261	−	12.7408i	−0.101847	−	0.403910i
$996$	−9.57267	+	12.2877i	−0.303322	+	0.389351i
$997$		−	56.6089i		−	1.79282i	−0.443222	−	0.896412i	$-0.646165\pi$
$997$		−	56.6089i		−	1.79282i	0.443222	−	0.896412i	$-0.353835\pi$
$998$		−	18.6530i		−	0.590452i
$999$	19.7732	−	44.9155i	0.625595	−	1.42106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.e.a.929.7	✓	32
3.2	odd	2		930.2.e.b.929.8	yes	32
5.4	even	2		930.2.e.b.929.26	yes	32
15.14	odd	2	inner	930.2.e.a.929.25	yes	32
31.30	odd	2	inner	930.2.e.a.929.26	yes	32
93.92	even	2		930.2.e.b.929.25	yes	32
155.154	odd	2		930.2.e.b.929.7	yes	32
465.464	even	2	inner	930.2.e.a.929.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.e.a.929.7	✓	32	1.1	even	1	trivial
930.2.e.a.929.8	yes	32	465.464	even	2	inner
930.2.e.a.929.25	yes	32	15.14	odd	2	inner
930.2.e.a.929.26	yes	32	31.30	odd	2	inner
930.2.e.b.929.7	yes	32	155.154	odd	2
930.2.e.b.929.8	yes	32	3.2	odd	2
930.2.e.b.929.25	yes	32	93.92	even	2
930.2.e.b.929.26	yes	32	5.4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.36636 - 1.06445i) q^{3} +1.00000 q^{4} +(-2.16820 + 0.546716i) q^{5} +(1.36636 + 1.06445i) q^{6} -1.97405i q^{7} -1.00000 q^{8} +(0.733873 + 2.90885i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.36636 - 1.06445i) q^{3} +1.00000 q^{4} +(-2.16820 + 0.546716i) q^{5} +(1.36636 + 1.06445i) q^{6} -1.97405i q^{7} -1.00000 q^{8} +(0.733873 + 2.90885i) q^{9} +(2.16820 - 0.546716i) q^{10} +0.980092 q^{11} +(-1.36636 - 1.06445i) q^{12} +4.39735 q^{13} +1.97405i q^{14} +(3.54450 + 1.56094i) q^{15} +1.00000 q^{16} +2.02195i q^{17} +(-0.733873 - 2.90885i) q^{18} -3.72763 q^{19} +(-2.16820 + 0.546716i) q^{20} +(-2.10129 + 2.69726i) q^{21} -0.980092 q^{22} +6.09578i q^{23} +(1.36636 + 1.06445i) q^{24} +(4.40220 - 2.37078i) q^{25} -4.39735 q^{26} +(2.09361 - 4.75571i) q^{27} -1.97405i q^{28} +2.54734 q^{29} +(-3.54450 - 1.56094i) q^{30} +(-1.90121 - 5.23311i) q^{31} -1.00000 q^{32} +(-1.33916 - 1.04326i) q^{33} -2.02195i q^{34} +(1.07925 + 4.28014i) q^{35} +(0.733873 + 2.90885i) q^{36} +9.44453 q^{37} +3.72763 q^{38} +(-6.00835 - 4.68078i) q^{39} +(2.16820 - 0.546716i) q^{40} -12.5007i q^{41} +(2.10129 - 2.69726i) q^{42} -3.33266 q^{43} +0.980092 q^{44} +(-3.18150 - 5.90576i) q^{45} -6.09578i q^{46} -11.6412 q^{47} +(-1.36636 - 1.06445i) q^{48} +3.10312 q^{49} +(-4.40220 + 2.37078i) q^{50} +(2.15228 - 2.76271i) q^{51} +4.39735 q^{52} -7.67233i q^{53} +(-2.09361 + 4.75571i) q^{54} +(-2.12504 + 0.535832i) q^{55} +1.97405i q^{56} +(5.09328 + 3.96789i) q^{57} -2.54734 q^{58} -0.348160i q^{59} +(3.54450 + 1.56094i) q^{60} +5.15035i q^{61} +(1.90121 + 5.23311i) q^{62} +(5.74223 - 1.44870i) q^{63} +1.00000 q^{64} +(-9.53434 + 2.40410i) q^{65} +(1.33916 + 1.04326i) q^{66} -1.03734i q^{67} +2.02195i q^{68} +(6.48868 - 8.32902i) q^{69} +(-1.07925 - 4.28014i) q^{70} -8.70746i q^{71} +(-0.733873 - 2.90885i) q^{72} -5.88000 q^{73} -9.44453 q^{74} +(-8.53858 - 1.44660i) q^{75} -3.72763 q^{76} -1.93475i q^{77} +(6.00835 + 4.68078i) q^{78} -8.91713i q^{79} +(-2.16820 + 0.546716i) q^{80} +(-7.92286 + 4.26946i) q^{81} +12.5007i q^{82} -8.99302i q^{83} +(-2.10129 + 2.69726i) q^{84} +(-1.10543 - 4.38400i) q^{85} +3.33266 q^{86} +(-3.48058 - 2.71153i) q^{87} -0.980092 q^{88} +10.3304 q^{89} +(3.18150 + 5.90576i) q^{90} -8.68059i q^{91} +6.09578i q^{92} +(-2.97267 + 9.17405i) q^{93} +11.6412 q^{94} +(8.08225 - 2.03795i) q^{95} +(1.36636 + 1.06445i) q^{96} -17.1380i q^{97} -3.10312 q^{98} +(0.719263 + 2.85094i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{2} + 32 q^{4} + 2 q^{5} - 32 q^{8} + 4 q^{9}+O(q^{10}) \) 32 * q - 32 * q^2 + 32 * q^4 + 2 * q^5 - 32 * q^8 + 4 * q^9	\( 32 q - 32 q^{2} + 32 q^{4} + 2 q^{5} - 32 q^{8} + 4 q^{9} - 2 q^{10} + 32 q^{16} - 4 q^{18} + 8 q^{19} + 2 q^{20} + 10 q^{25} - 12 q^{31} - 32 q^{32} - 8 q^{33} + 16 q^{35} + 4 q^{36} - 8 q^{38} - 4 q^{39} - 2 q^{40} + 10 q^{45} - 4 q^{47} - 36 q^{49} - 10 q^{50} - 4 q^{51} + 12 q^{62} - 24 q^{63} + 32 q^{64} + 8 q^{66} - 8 q^{69} - 16 q^{70} - 4 q^{72} + 8 q^{76} + 4 q^{78} + 2 q^{80} + 24 q^{81} - 4 q^{87} - 10 q^{90} + 24 q^{93} + 4 q^{94} - 26 q^{95} + 36 q^{98}+O(q^{100}) \) 32 * q - 32 * q^2 + 32 * q^4 + 2 * q^5 - 32 * q^8 + 4 * q^9 - 2 * q^10 + 32 * q^16 - 4 * q^18 + 8 * q^19 + 2 * q^20 + 10 * q^25 - 12 * q^31 - 32 * q^32 - 8 * q^33 + 16 * q^35 + 4 * q^36 - 8 * q^38 - 4 * q^39 - 2 * q^40 + 10 * q^45 - 4 * q^47 - 36 * q^49 - 10 * q^50 - 4 * q^51 + 12 * q^62 - 24 * q^63 + 32 * q^64 + 8 * q^66 - 8 * q^69 - 16 * q^70 - 4 * q^72 + 8 * q^76 + 4 * q^78 + 2 * q^80 + 24 * q^81 - 4 * q^87 - 10 * q^90 + 24 * q^93 + 4 * q^94 - 26 * q^95 + 36 * q^98

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