LMFDB - Embedded newform 60.3.c.a.31.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,3,Mod(31,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("60.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	60.c (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:	$1.63488158616$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.85100625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + x^{5} + 3x^{4} + 2x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + x^5 + 3x^4 + 2x^3 - 8x^2 - 8*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			31.6
Root			$-0.600040 + 1.28061i$ of defining polynomial
Character	$\chi$	$=$	60.31
Dual form			60.3.c.a.31.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.67986 + 1.08539i) q^{2} -1.73205i q^{3} +(1.64388 + 3.64660i) q^{4} +2.23607 q^{5} +(1.87994 - 2.90961i) q^{6} -0.596540i q^{7} +(-1.19648 + 7.91002i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(1.67986 + 1.08539i) q^{2} -1.73205i q^{3} +(1.64388 + 3.64660i) q^{4} +2.23607 q^{5} +(1.87994 - 2.90961i) q^{6} -0.596540i q^{7} +(-1.19648 + 7.91002i) q^{8} -3.00000 q^{9} +(3.75629 + 2.42700i) q^{10} -9.27963i q^{11} +(6.31609 - 2.84728i) q^{12} -23.5117 q^{13} +(0.647476 - 1.00210i) q^{14} -3.87298i q^{15} +(-10.5953 + 11.9891i) q^{16} +3.97751 q^{17} +(-5.03959 - 3.25616i) q^{18} +7.04756i q^{19} +(3.67582 + 8.15404i) q^{20} -1.03324 q^{21} +(10.0720 - 15.5885i) q^{22} -32.0793i q^{23} +(13.7006 + 2.07237i) q^{24} +5.00000 q^{25} +(-39.4964 - 25.5192i) q^{26} +5.19615i q^{27} +(2.17534 - 0.980637i) q^{28} +35.6734 q^{29} +(4.20368 - 6.50608i) q^{30} +59.2585i q^{31} +(-30.8115 + 8.64000i) q^{32} -16.0728 q^{33} +(6.68167 + 4.31713i) q^{34} -1.33390i q^{35} +(-4.93163 - 10.9398i) q^{36} -5.38761 q^{37} +(-7.64932 + 11.8389i) q^{38} +40.7234i q^{39} +(-2.67541 + 17.6873i) q^{40} +40.0791 q^{41} +(-1.73570 - 1.12146i) q^{42} -36.1157i q^{43} +(33.8391 - 15.2545i) q^{44} -6.70820 q^{45} +(34.8184 - 53.8888i) q^{46} +74.0131i q^{47} +(20.7657 + 18.3517i) q^{48} +48.6441 q^{49} +(8.39931 + 5.42693i) q^{50} -6.88925i q^{51} +(-38.6503 - 85.7376i) q^{52} -2.55123 q^{53} +(-5.63983 + 8.72882i) q^{54} -20.7499i q^{55} +(4.71864 + 0.713748i) q^{56} +12.2067 q^{57} +(59.9265 + 38.7194i) q^{58} -36.4026i q^{59} +(14.1232 - 6.36670i) q^{60} -8.73223 q^{61} +(-64.3183 + 99.5461i) q^{62} +1.78962i q^{63} +(-61.1369 - 18.9284i) q^{64} -52.5737 q^{65} +(-27.0001 - 17.4452i) q^{66} -69.7379i q^{67} +(6.53853 + 14.5044i) q^{68} -55.5630 q^{69} +(1.44780 - 2.24077i) q^{70} +59.2170i q^{71} +(3.58944 - 23.7301i) q^{72} -83.0019 q^{73} +(-9.05044 - 5.84763i) q^{74} -8.66025i q^{75} +(-25.6996 + 11.5853i) q^{76} -5.53566 q^{77} +(-44.2006 + 68.4098i) q^{78} -65.8705i q^{79} +(-23.6919 + 26.8085i) q^{80} +9.00000 q^{81} +(67.3274 + 43.5013i) q^{82} -129.909i q^{83} +(-1.69851 - 3.76780i) q^{84} +8.89398 q^{85} +(39.1995 - 60.6695i) q^{86} -61.7882i q^{87} +(73.4020 + 11.1029i) q^{88} -130.466 q^{89} +(-11.2689 - 7.28099i) q^{90} +14.0256i q^{91} +(116.980 - 52.7344i) q^{92} +102.639 q^{93} +(-80.3327 + 124.332i) q^{94} +15.7588i q^{95} +(14.9649 + 53.3671i) q^{96} +93.1113 q^{97} +(81.7155 + 52.7977i) q^{98} +27.8389i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 10 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + 10 * q^4 - 6 * q^6 - 20 * q^8 - 24 * q^9	$ 8 q + 4 q^{2} + 10 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9} + 10 q^{10} + 16 q^{13} - 20 q^{14} + 34 q^{16} - 12 q^{18} - 40 q^{20} - 48 q^{21} + 68 q^{22} + 18 q^{24} + 40 q^{25} - 36 q^{26} + 28 q^{28} + 64 q^{29} - 76 q^{32} - 92 q^{34} - 30 q^{36} - 112 q^{37} - 40 q^{38} - 10 q^{40} - 16 q^{41} + 108 q^{42} + 172 q^{44} + 152 q^{46} + 48 q^{48} - 56 q^{49} + 20 q^{50} - 128 q^{52} + 352 q^{53} + 18 q^{54} + 116 q^{56} + 144 q^{57} - 204 q^{58} + 30 q^{60} - 176 q^{61} - 56 q^{62} - 110 q^{64} - 80 q^{65} + 108 q^{66} - 184 q^{68} - 96 q^{69} - 60 q^{70} + 60 q^{72} - 240 q^{73} + 132 q^{74} - 24 q^{76} - 288 q^{77} - 240 q^{78} - 80 q^{80} + 72 q^{81} + 40 q^{82} - 36 q^{84} + 160 q^{85} - 200 q^{86} + 140 q^{88} + 80 q^{89} - 30 q^{90} + 144 q^{92} + 144 q^{93} - 96 q^{94} - 174 q^{96} + 432 q^{97} + 660 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 + 10 * q^4 - 6 * q^6 - 20 * q^8 - 24 * q^9 + 10 * q^10 + 16 * q^13 - 20 * q^14 + 34 * q^16 - 12 * q^18 - 40 * q^20 - 48 * q^21 + 68 * q^22 + 18 * q^24 + 40 * q^25 - 36 * q^26 + 28 * q^28 + 64 * q^29 - 76 * q^32 - 92 * q^34 - 30 * q^36 - 112 * q^37 - 40 * q^38 - 10 * q^40 - 16 * q^41 + 108 * q^42 + 172 * q^44 + 152 * q^46 + 48 * q^48 - 56 * q^49 + 20 * q^50 - 128 * q^52 + 352 * q^53 + 18 * q^54 + 116 * q^56 + 144 * q^57 - 204 * q^58 + 30 * q^60 - 176 * q^61 - 56 * q^62 - 110 * q^64 - 80 * q^65 + 108 * q^66 - 184 * q^68 - 96 * q^69 - 60 * q^70 + 60 * q^72 - 240 * q^73 + 132 * q^74 - 24 * q^76 - 288 * q^77 - 240 * q^78 - 80 * q^80 + 72 * q^81 + 40 * q^82 - 36 * q^84 + 160 * q^85 - 200 * q^86 + 140 * q^88 + 80 * q^89 - 30 * q^90 + 144 * q^92 + 144 * q^93 - 96 * q^94 - 174 * q^96 + 432 * q^97 + 660 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	1.67986	+	1.08539i	0.839931	+	0.542693i
$2$	1.67986	+	1.08539i	0.839931	+	0.542693i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	1.64388	+	3.64660i	0.410969	+	0.911649i
$5$	2.23607			0.447214
$5$	2.23607			0.447214
$6$	1.87994	−	2.90961i	0.313324	−	0.484935i
$7$		−	0.596540i		−	0.0852199i	−0.999092	−	0.0426100i	$-0.986433\pi$
$7$		−	0.596540i		−	0.0852199i	0.999092	−	0.0426100i	$-0.0135673\pi$
$8$	−1.19648	+	7.91002i	−0.149560	+	0.988753i
$9$	−3.00000			−0.333333
$10$	3.75629	+	2.42700i	0.375629	+	0.242700i
$11$		−	9.27963i		−	0.843602i	−0.906688	−	0.421801i	$-0.861398\pi$
$11$		−	9.27963i		−	0.843602i	0.906688	−	0.421801i	$-0.138602\pi$
$12$	6.31609	−	2.84728i	0.526341	−	0.237273i
$13$	−23.5117			−1.80859			−0.904295	−	0.426907i	$-0.859603\pi$
$13$	−23.5117			−1.80859			−0.904295	+	0.426907i	$0.859603\pi$
$14$	0.647476	−	1.00210i	0.0462483	−	0.0715789i
$15$		−	3.87298i		−	0.258199i
$16$	−10.5953	+	11.9891i	−0.662209	+	0.749319i
$17$	3.97751			0.233971			0.116986	−	0.993134i	$-0.462677\pi$
$17$	3.97751			0.233971			0.116986	+	0.993134i	$0.462677\pi$
$18$	−5.03959	−	3.25616i	−0.279977	−	0.180898i
$19$			7.04756i			0.370924i	0.982651	+	0.185462i	$0.0593782\pi$
$19$			7.04756i			0.370924i	−0.982651	+	0.185462i	$0.940622\pi$
$20$	3.67582	+	8.15404i	0.183791	+	0.407702i
$21$	−1.03324			−0.0492018
$22$	10.0720	−	15.5885i	0.457817	−	0.708568i
$23$		−	32.0793i		−	1.39475i	−0.716705	−	0.697376i	$-0.754351\pi$
$23$		−	32.0793i		−	1.39475i	0.716705	−	0.697376i	$-0.245649\pi$
$24$	13.7006	+	2.07237i	0.570857	+	0.0863486i
$25$	5.00000			0.200000
$26$	−39.4964	−	25.5192i	−1.51909	−	0.981509i
$27$			5.19615i			0.192450i
$28$	2.17534	−	0.980637i	0.0776907	−	0.0350227i
$29$	35.6734			1.23012			0.615059	−	0.788481i	$-0.289132\pi$
$29$	35.6734			1.23012			0.615059	+	0.788481i	$0.289132\pi$
$30$	4.20368	−	6.50608i	0.140123	−	0.216869i
$31$			59.2585i			1.91156i	0.294076	+	0.955782i	$0.404988\pi$
$31$			59.2585i			1.91156i	−0.294076	+	0.955782i	$0.595012\pi$
$32$	−30.8115	+	8.64000i	−0.962860	+	0.270000i
$33$	−16.0728			−0.487054
$34$	6.68167	+	4.31713i	0.196520	+	0.126974i
$35$		−	1.33390i		−	0.0381115i
$36$	−4.93163	−	10.9398i	−0.136990	−	0.303883i
$37$	−5.38761			−0.145611			−0.0728055	−	0.997346i	$-0.523195\pi$
$37$	−5.38761			−0.145611			−0.0728055	+	0.997346i	$0.523195\pi$
$38$	−7.64932	+	11.8389i	−0.201298	+	0.311551i
$39$			40.7234i			1.04419i
$40$	−2.67541	+	17.6873i	−0.0668853	+	0.442184i
$41$	40.0791			0.977539			0.488769	−	0.872413i	$-0.337446\pi$
$41$	40.0791			0.977539			0.488769	+	0.872413i	$0.337446\pi$
$42$	−1.73570	−	1.12146i	−0.0413261	−	0.0267014i
$43$		−	36.1157i		−	0.839901i	−0.907547	−	0.419950i	$-0.862047\pi$
$43$		−	36.1157i		−	0.839901i	0.907547	−	0.419950i	$-0.137953\pi$
$44$	33.8391	−	15.2545i	0.769070	−	0.346694i
$45$	−6.70820			−0.149071
$46$	34.8184	−	53.8888i	0.756922	−	1.17150i
$47$			74.0131i			1.57475i	0.616477	+	0.787373i	$0.288559\pi$
$47$			74.0131i			1.57475i	−0.616477	+	0.787373i	$0.711441\pi$
$48$	20.7657	+	18.3517i	0.432620	+	0.382327i
$49$	48.6441			0.992738
$50$	8.39931	+	5.42693i	0.167986	+	0.108539i
$51$		−	6.88925i		−	0.135083i
$52$	−38.6503	−	85.7376i	−0.743275	−	1.64880i
$53$	−2.55123			−0.0481364			−0.0240682	−	0.999710i	$-0.507662\pi$
$53$	−2.55123			−0.0481364			−0.0240682	+	0.999710i	$0.507662\pi$
$54$	−5.63983	+	8.72882i	−0.104441	+	0.161645i
$55$		−	20.7499i		−	0.377270i
$56$	4.71864	+	0.713748i	0.0842614	+	0.0127455i
$57$	12.2067			0.214153
$58$	59.9265	+	38.7194i	1.03321	+	0.667576i
$59$		−	36.4026i		−	0.616993i	−0.951225	−	0.308497i	$-0.900174\pi$
$59$		−	36.4026i		−	0.616993i	0.951225	−	0.308497i	$-0.0998259\pi$
$60$	14.1232	−	6.36670i	0.235387	−	0.106112i
$61$	−8.73223			−0.143151			−0.0715757	−	0.997435i	$-0.522803\pi$
$61$	−8.73223			−0.143151			−0.0715757	+	0.997435i	$0.522803\pi$
$62$	−64.3183	+	99.5461i	−1.03739	+	1.60558i
$63$			1.78962i			0.0284066i
$64$	−61.1369	−	18.9284i	−0.955264	−	0.295756i
$65$	−52.5737			−0.808826
$66$	−27.0001	−	17.4452i	−0.409092	−	0.264321i
$67$		−	69.7379i		−	1.04086i	−0.853903	−	0.520432i	$-0.825771\pi$
$67$		−	69.7379i		−	1.04086i	0.853903	−	0.520432i	$-0.174229\pi$
$68$	6.53853	+	14.5044i	0.0961548	+	0.213300i
$69$	−55.5630			−0.805261
$70$	1.44780	−	2.24077i	0.0206828	−	0.0320110i
$71$			59.2170i			0.834043i	0.908897	+	0.417021i	$0.136926\pi$
$71$			59.2170i			0.834043i	−0.908897	+	0.417021i	$0.863074\pi$
$72$	3.58944	−	23.7301i	0.0498534	−	0.329584i
$73$	−83.0019			−1.13701			−0.568506	−	0.822679i	$-0.692478\pi$
$73$	−83.0019			−1.13701			−0.568506	+	0.822679i	$0.692478\pi$
$74$	−9.05044	−	5.84763i	−0.122303	−	0.0790220i
$75$		−	8.66025i		−	0.115470i
$76$	−25.6996	+	11.5853i	−0.338153	+	0.152438i
$77$	−5.53566			−0.0718917
$78$	−44.2006	+	68.4098i	−0.566675	+	0.877048i
$79$		−	65.8705i		−	0.833804i	−0.908951	−	0.416902i	$-0.863116\pi$
$79$		−	65.8705i		−	0.833804i	0.908951	−	0.416902i	$-0.136884\pi$
$80$	−23.6919	+	26.8085i	−0.296149	+	0.335106i
$81$	9.00000			0.111111
$82$	67.3274	+	43.5013i	0.821065	+	0.530503i
$83$		−	129.909i		−	1.56517i	−0.622542	−	0.782586i	$-0.713900\pi$
$83$		−	129.909i		−	1.56517i	0.622542	−	0.782586i	$-0.286100\pi$
$84$	−1.69851	−	3.76780i	−0.0202204	−	0.0448547i
$85$	8.89398			0.104635
$86$	39.1995	−	60.6695i	0.455808	−	0.705459i
$87$		−	61.7882i		−	0.710209i
$88$	73.4020	+	11.1029i	0.834114	+	0.126169i
$89$	−130.466			−1.46591			−0.732956	−	0.680277i	$-0.761860\pi$
$89$	−130.466			−1.46591			−0.732956	+	0.680277i	$0.761860\pi$
$90$	−11.2689	−	7.28099i	−0.125210	−	0.0808999i
$91$			14.0256i			0.154128i
$92$	116.980	−	52.7344i	1.27152	−	0.573200i
$93$	102.639			1.10364
$94$	−80.3327	+	124.332i	−0.854603	+	1.32268i
$95$			15.7588i			0.165882i
$96$	14.9649	+	53.3671i	0.155885	+	0.555908i
$97$	93.1113			0.959911			0.479955	−	0.877293i	$-0.340653\pi$
$97$	93.1113			0.959911			0.479955	+	0.877293i	$0.340653\pi$
$98$	81.7155	+	52.7977i	0.833831	+	0.538752i
$99$			27.8389i			0.281201i
$100$	8.21938	+	18.2330i	0.0821938	+	0.182330i
$101$	−3.66081			−0.0362457			−0.0181228	−	0.999836i	$-0.505769\pi$
$101$	−3.66081			−0.0362457			−0.0181228	+	0.999836i	$0.505769\pi$
$102$	7.47749	−	11.5730i	0.0733087	−	0.113461i
$103$			151.417i			1.47007i	0.678032	+	0.735033i	$0.262833\pi$
$103$			151.417i			1.47007i	−0.678032	+	0.735033i	$0.737167\pi$
$104$	28.1313	−	185.978i	0.270493	−	1.78825i
$105$	−2.31039			−0.0220037
$106$	−4.28571	−	2.76907i	−0.0404313	−	0.0261233i
$107$			82.8092i			0.773918i	0.922097	+	0.386959i	$0.126474\pi$
$107$			82.8092i			0.773918i	−0.922097	+	0.386959i	$0.873526\pi$
$108$	−18.9483	+	8.54183i	−0.175447	+	0.0790910i
$109$	−7.36835			−0.0675996			−0.0337998	−	0.999429i	$-0.510761\pi$
$109$	−7.36835			−0.0675996			−0.0337998	+	0.999429i	$0.510761\pi$
$110$	22.5216	−	34.8569i	0.204742	−	0.316881i
$111$			9.33161i			0.0840685i
$112$	7.15197	+	6.32054i	0.0638569	+	0.0564334i
$113$	65.0370			0.575549			0.287774	−	0.957698i	$-0.407085\pi$
$113$	65.0370			0.575549			0.287774	+	0.957698i	$0.407085\pi$
$114$	20.5056	+	13.2490i	0.179874	+	0.116219i
$115$		−	71.7315i		−	0.623752i
$116$	58.6427	+	130.087i	0.505540	+	1.12144i
$117$	70.5350			0.602864
$118$	39.5109	−	61.1514i	0.334838	−	0.518232i
$119$		−	2.37274i		−	0.0199390i
$120$	30.6354	+	4.63395i	0.255295	+	0.0386163i
$121$	34.8885			0.288335
$122$	−14.6689	−	9.47784i	−0.120237	−	0.0776872i
$123$		−	69.4190i		−	0.564382i
$124$	−216.092	+	97.4136i	−1.74268	+	0.785593i
$125$	11.1803			0.0894427
$126$	−1.94243	+	3.00631i	−0.0154161	+	0.0238596i
$127$			139.469i			1.09818i	0.835763	+	0.549091i	$0.185026\pi$
$127$			139.469i			1.09818i	−0.835763	+	0.549091i	$0.814974\pi$
$128$	−82.1569	−	98.1542i	−0.641851	−	0.766829i
$129$	−62.5543			−0.484917
$130$	−88.3166	−	57.0628i	−0.679359	−	0.438944i
$131$		−	63.4856i		−	0.484623i	−0.970198	−	0.242312i	$-0.922094\pi$
$131$		−	63.4856i		−	0.484623i	0.970198	−	0.242312i	$-0.0779056\pi$
$132$	−26.4217	−	58.6110i	−0.200164	−	0.444023i
$133$	4.20415			0.0316101
$134$	75.6925	−	117.150i	0.564870	−	0.874254i
$135$			11.6190i			0.0860663i
$136$	−4.75901	+	31.4622i	−0.0349927	+	0.231340i
$137$	−138.157			−1.00845			−0.504223	−	0.863573i	$-0.668221\pi$
$137$	−138.157			−1.00845			−0.504223	+	0.863573i	$0.668221\pi$
$138$	−93.3382	−	60.3073i	−0.676363	−	0.437009i
$139$			29.9578i			0.215523i	0.994177	+	0.107762i	$0.0343684\pi$
$139$			29.9578i			0.215523i	−0.994177	+	0.107762i	$0.965632\pi$
$140$	4.86421	−	2.19277i	0.0347443	−	0.0156626i
$141$	128.194			0.909180
$142$	−64.2733	+	99.4765i	−0.452629	+	0.700539i
$143$			218.180i			1.52573i
$144$	31.7860	−	35.9673i	0.220736	−	0.249773i
$145$	79.7682			0.550126
$146$	−139.432	−	90.0891i	−0.955012	−	0.617048i
$147$		−	84.2541i		−	0.573157i
$148$	−8.85655	−	19.6464i	−0.0598416	−	0.132746i
$149$	−47.3823			−0.318002			−0.159001	−	0.987278i	$-0.550827\pi$
$149$	−47.3823			−0.318002			−0.159001	+	0.987278i	$0.550827\pi$
$150$	9.39972	−	14.5480i	0.0626648	−	0.0969869i
$151$		−	109.604i		−	0.725852i	−0.931818	−	0.362926i	$-0.881778\pi$
$151$		−	109.604i		−	0.725852i	0.931818	−	0.362926i	$-0.118222\pi$
$152$	−55.7463	−	8.43227i	−0.366752	−	0.0554755i
$153$	−11.9325			−0.0779904
$154$	−9.29915	−	6.00833i	−0.0603841	−	0.0390151i
$155$			132.506i			0.854877i
$156$	−148.502	+	66.9442i	−0.951936	+	0.429130i
$157$	−177.588			−1.13113			−0.565566	−	0.824703i	$-0.691342\pi$
$157$	−177.588			−1.13113			−0.565566	+	0.824703i	$0.691342\pi$
$158$	71.4950	−	110.653i	0.452500	−	0.700338i
$159$			4.41886i			0.0277916i
$160$	−68.8967	+	19.3196i	−0.430604	+	0.120748i
$161$	−19.1366			−0.118861
$162$	15.1188	+	9.76847i	0.0933257	+	0.0602992i
$163$			96.8778i			0.594342i	0.954824	+	0.297171i	$0.0960432\pi$
$163$			96.8778i			0.594342i	−0.954824	+	0.297171i	$0.903957\pi$
$164$	65.8850	+	146.152i	0.401738	+	0.891173i
$165$	−35.9398			−0.217817
$166$	141.002	−	218.230i	0.849408	−	1.31464i
$167$		−	152.605i		−	0.913801i	−0.889518	−	0.456901i	$-0.848960\pi$
$167$		−	152.605i		−	0.913801i	0.889518	−	0.456901i	$-0.151040\pi$
$168$	1.23625	−	8.17292i	0.00735862	−	0.0486484i
$169$	383.799			2.27100
$170$	14.9407	+	9.65340i	0.0878862	+	0.0567847i
$171$		−	21.1427i		−	0.123641i
$172$	131.700	−	59.3698i	0.765695	−	0.345173i
$173$	155.773			0.900422			0.450211	−	0.892922i	$-0.351349\pi$
$173$	155.773			0.900422			0.450211	+	0.892922i	$0.351349\pi$
$174$	67.0640	−	103.796i	0.385425	−	0.596527i
$175$		−	2.98270i		−	0.0170440i
$176$	111.254	+	98.3209i	0.632127	+	0.558641i
$177$	−63.0512			−0.356221
$178$	−219.165	−	141.606i	−1.23126	−	0.795540i
$179$			126.001i			0.703915i	0.936016	+	0.351957i	$0.114484\pi$
$179$			126.001i			0.703915i	−0.936016	+	0.351957i	$0.885516\pi$
$180$	−11.0275	−	24.4621i	−0.0612636	−	0.135901i
$181$	−346.725			−1.91561			−0.957803	−	0.287424i	$-0.907201\pi$
$181$	−346.725			−1.91561			−0.957803	+	0.287424i	$0.907201\pi$
$182$	−15.2232	+	23.5612i	−0.0836442	+	0.129457i
$183$			15.1247i			0.0826485i
$184$	253.748	+	38.3823i	1.37906	+	0.208599i
$185$	−12.0471			−0.0651192
$186$	172.419	+	111.403i	0.926983	+	0.598939i
$187$		−	36.9098i		−	0.197379i
$188$	−269.896	+	121.668i	−1.43562	+	0.647171i
$189$	3.09971			0.0164006
$190$	−17.1044	+	26.4727i	−0.0900232	+	0.139330i
$191$		−	133.159i		−	0.697167i	−0.937278	−	0.348584i	$-0.886663\pi$
$191$		−	133.159i		−	0.697167i	0.937278	−	0.348584i	$-0.113337\pi$
$192$	−32.7849	+	105.892i	−0.170755	+	0.551522i
$193$	−136.246			−0.705940			−0.352970	−	0.935635i	$-0.614828\pi$
$193$	−136.246			−0.705940			−0.352970	+	0.935635i	$0.614828\pi$
$194$	156.414	+	101.062i	0.806259	+	0.520937i
$195$			91.0604i			0.466976i
$196$	79.9649	+	177.386i	0.407984	+	0.905029i
$197$	74.8945			0.380175			0.190087	−	0.981767i	$-0.439123\pi$
$197$	74.8945			0.380175			0.190087	+	0.981767i	$0.439123\pi$
$198$	−30.2159	+	46.7655i	−0.152606	+	0.236189i
$199$		−	251.605i		−	1.26434i	−0.774828	−	0.632172i	$-0.782164\pi$
$199$		−	251.605i		−	1.26434i	0.774828	−	0.632172i	$-0.217836\pi$
$200$	−5.98240	+	39.5501i	−0.0299120	+	0.197751i
$201$	−120.790			−0.600943
$202$	−6.14966	−	3.97339i	−0.0304439	−	0.0196703i
$203$		−	21.2806i		−	0.104831i
$204$	25.1223	−	11.3251i	0.123149	−	0.0555150i
$205$	89.6196			0.437169
$206$	−164.346	+	254.359i	−0.797794	+	1.23475i
$207$			96.2379i			0.464917i
$208$	249.114	−	281.884i	1.19767	−	1.35521i
$209$	65.3987			0.312913
$210$	−3.88113	−	2.50766i	−0.0184816	−	0.0119412i
$211$		−	228.203i		−	1.08153i	−0.841173	−	0.540766i	$-0.818135\pi$
$211$		−	228.203i		−	1.08153i	0.841173	−	0.540766i	$-0.181865\pi$
$212$	−4.19390	−	9.30331i	−0.0197826	−	0.0438835i
$213$	102.567			0.481535
$214$	−89.8799	+	139.108i	−0.420000	+	0.650038i
$215$		−	80.7573i		−	0.375615i
$216$	−41.1017	−	6.21710i	−0.190286	−	0.0287829i
$217$	35.3500			0.162903
$218$	−12.3778	−	7.99751i	−0.0567790	−	0.0366858i
$219$			143.763i			0.656454i
$220$	75.6664	−	34.1102i	0.343938	−	0.155046i
$221$	−93.5179			−0.423158
$222$	−10.1284	+	15.6758i	−0.0456234	+	0.0706118i
$223$			85.9549i			0.385448i	0.981253	+	0.192724i	$0.0617322\pi$
$223$			85.9549i			0.385448i	−0.981253	+	0.192724i	$0.938268\pi$
$224$	5.15410	+	18.3803i	0.0230094	+	0.0820549i
$225$	−15.0000			−0.0666667
$226$	109.253	+	70.5902i	0.483421	+	0.312346i
$227$		−	282.357i		−	1.24386i	−0.783071	−	0.621932i	$-0.786348\pi$
$227$		−	282.357i		−	1.24386i	0.783071	−	0.621932i	$-0.213652\pi$
$228$	20.0663	+	44.5130i	0.0880103	+	0.195233i
$229$	138.263			0.603768			0.301884	−	0.953345i	$-0.402385\pi$
$229$	138.263			0.603768			0.301884	+	0.953345i	$0.402385\pi$
$230$	77.8563	−	120.499i	0.338506	−	0.523909i
$231$			9.58805i			0.0415067i
$232$	−42.6826	+	282.178i	−0.183977	+	1.21628i
$233$	−0.522939			−0.00224438			−0.00112219	−	0.999999i	$-0.500357\pi$
$233$	−0.522939			−0.00224438			−0.00112219	+	0.999999i	$0.500357\pi$
$234$	118.489	+	76.5577i	0.506364	+	0.327170i
$235$			165.498i			0.704248i
$236$	132.746	−	59.8413i	0.562482	−	0.253565i
$237$	−114.091			−0.481397
$238$	2.57534	−	3.98588i	0.0108208	−	0.0167474i
$239$		−	73.6928i		−	0.308338i	−0.988044	−	0.154169i	$-0.950730\pi$
$239$		−	73.6928i		−	0.308338i	0.988044	−	0.154169i	$-0.0492700\pi$
$240$	46.4336	+	41.0356i	0.193473	+	0.170982i
$241$	31.3705			0.130168			0.0650840	−	0.997880i	$-0.479268\pi$
$241$	31.3705			0.130168			0.0650840	+	0.997880i	$0.479268\pi$
$242$	58.6080	+	37.8675i	0.242182	+	0.156477i
$243$		−	15.5885i		−	0.0641500i
$244$	−14.3547	−	31.8429i	−0.0588307	−	0.130504i
$245$	108.772			0.443966
$246$	75.3464	−	116.614i	0.306286	−	0.474042i
$247$		−	165.700i		−	0.670850i
$248$	−468.736	−	70.9016i	−1.89006	−	0.285894i
$249$	−225.010			−0.903653
$250$	18.7814	+	12.1350i	0.0751257	+	0.0485399i
$251$		−	78.7478i		−	0.313736i	−0.987620	−	0.156868i	$-0.949860\pi$
$251$		−	78.7478i		−	0.313736i	0.987620	−	0.156868i	$-0.0501398\pi$
$252$	−6.52602	+	2.94191i	−0.0258969	+	0.0116742i
$253$	−297.684			−1.17662
$254$	−151.378	+	234.289i	−0.595975	+	0.922397i
$255$		−	15.4048i		−	0.0604111i
$256$	−31.4772	−	254.057i	−0.122958	−	0.992412i
$257$	243.954			0.949236			0.474618	−	0.880192i	$-0.342586\pi$
$257$	243.954			0.949236			0.474618	+	0.880192i	$0.342586\pi$
$258$	−105.083	−	67.8956i	−0.407297	−	0.263161i
$259$			3.21392i			0.0124090i
$260$	−86.4246	−	191.715i	−0.332402	−	0.737366i
$261$	−107.020			−0.410039
$262$	68.9064	−	106.647i	0.263002	−	0.407050i
$263$		−	102.737i		−	0.390635i	−0.980740	−	0.195317i	$-0.937426\pi$
$263$		−	102.737i		−	0.390635i	0.980740	−	0.195317i	$-0.0625737\pi$
$264$	19.2308	−	127.136i	0.0728439	−	0.481576i
$265$	−5.70472			−0.0215273
$266$	7.06239	+	4.56312i	0.0265503	+	0.0171546i
$267$			225.974i			0.846344i
$268$	254.306	−	114.640i	0.948903	−	0.427763i
$269$	−123.646			−0.459651			−0.229825	−	0.973232i	$-0.573816\pi$
$269$	−123.646			−0.459651			−0.229825	+	0.973232i	$0.573816\pi$
$270$	−12.6110	+	19.5182i	−0.0467076	+	0.0722898i
$271$			332.371i			1.22646i	0.789904	+	0.613230i	$0.210130\pi$
$271$			332.371i			1.22646i	−0.789904	+	0.613230i	$0.789870\pi$
$272$	−42.1431	+	47.6868i	−0.154938	+	0.175319i
$273$	24.2931			0.0889858
$274$	−232.085	−	149.954i	−0.847026	−	0.547277i
$275$		−	46.3981i		−	0.168720i
$276$	−91.3386	−	202.616i	−0.330937	−	0.734115i
$277$	−125.916			−0.454571			−0.227286	−	0.973828i	$-0.572985\pi$
$277$	−125.916			−0.454571			−0.227286	+	0.973828i	$0.572985\pi$
$278$	−32.5157	+	50.3249i	−0.116963	+	0.181025i
$279$		−	177.775i		−	0.637188i
$280$	10.5512	+	1.59599i	0.0376829	+	0.00569996i
$281$	52.5628			0.187056			0.0935281	−	0.995617i	$-0.470186\pi$
$281$	52.5628			0.187056			0.0935281	+	0.995617i	$0.470186\pi$
$282$	215.349	+	139.140i	0.763649	+	0.493405i
$283$			199.288i			0.704199i	0.935963	+	0.352100i	$0.114532\pi$
$283$			199.288i			0.704199i	−0.935963	+	0.352100i	$0.885468\pi$
$284$	−215.941	+	97.3454i	−0.760355	+	0.342766i
$285$	27.2951			0.0957722
$286$	−236.809	+	366.512i	−0.828004	+	1.28151i
$287$		−	23.9088i		−	0.0833058i
$288$	92.4346	−	25.9200i	0.320953	−	0.0900001i
$289$	−273.179			−0.945258
$290$	134.000	+	86.5793i	0.462068	+	0.298549i
$291$		−	161.274i		−	0.554205i
$292$	−136.445	−	302.674i	−0.467276	−	1.03656i
$293$	102.161			0.348672			0.174336	−	0.984686i	$-0.444222\pi$
$293$	102.161			0.348672			0.174336	+	0.984686i	$0.444222\pi$
$294$	91.4482	−	141.535i	0.311048	−	0.481413i
$295$		−	81.3987i		−	0.275928i
$296$	6.44617	−	42.6161i	0.0217776	−	0.143973i
$297$	48.2184			0.162351
$298$	−79.5957	−	51.4281i	−0.267100	−	0.172577i
$299$			754.238i			2.52254i
$300$	31.5805	−	14.2364i	0.105268	−	0.0474546i
$301$	−21.5445			−0.0715763
$302$	118.962	−	184.119i	0.393915	−	0.609666i
$303$			6.34071i			0.0209264i
$304$	−84.4939	−	74.6713i	−0.277941	−	0.245629i
$305$	−19.5259			−0.0640192
$306$	−20.0450	−	12.9514i	−0.0655065	−	0.0423248i
$307$			328.391i			1.06968i	0.844954	+	0.534839i	$0.179628\pi$
$307$			328.391i			1.06968i	−0.844954	+	0.534839i	$0.820372\pi$
$308$	−9.09994	−	20.1863i	−0.0295453	−	0.0655401i
$309$	262.262			0.848743
$310$	−143.820	+	222.592i	−0.463936	+	0.718038i
$311$			95.4377i			0.306874i	0.988158	+	0.153437i	$0.0490342\pi$
$311$			95.4377i			0.306874i	−0.988158	+	0.153437i	$0.950966\pi$
$312$	−322.123	−	48.7248i	−1.03245	−	0.156169i
$313$	550.408			1.75849			0.879246	−	0.476368i	$-0.158047\pi$
$313$	550.408			1.75849			0.879246	+	0.476368i	$0.158047\pi$
$314$	−298.323	−	192.751i	−0.950073	−	0.613858i
$315$			4.00171i			0.0127038i
$316$	240.203	−	108.283i	0.760137	−	0.342668i
$317$	439.394			1.38610			0.693051	−	0.720889i	$-0.256266\pi$
$317$	439.394			1.38610			0.693051	+	0.720889i	$0.256266\pi$
$318$	−4.79617	+	7.42307i	−0.0150823	+	0.0233430i
$319$		−	331.036i		−	1.03773i
$320$	−136.706	−	42.3251i	−0.427207	−	0.132266i
$321$	143.430			0.446822
$322$	−32.1468	−	20.7706i	−0.0998348	−	0.0645048i
$323$			28.0317i			0.0867855i
$324$	14.7949	+	32.8194i	0.0456632	+	0.101294i
$325$	−117.558			−0.361718
$326$	−105.150	+	162.741i	−0.322545	+	0.499206i
$327$			12.7624i			0.0390286i
$328$	−47.9539	+	317.026i	−0.146201	+	0.966544i
$329$	44.1517			0.134200
$330$	−60.3740	−	39.0086i	−0.182951	−	0.118208i
$331$			479.922i			1.44992i	0.688794	+	0.724958i	$0.258141\pi$
$331$			479.922i			1.44992i	−0.688794	+	0.724958i	$0.741859\pi$
$332$	473.727	−	213.555i	1.42689	−	0.643237i
$333$	16.1628			0.0485370
$334$	165.635	−	256.355i	0.495913	−	0.767530i
$335$		−	155.939i		−	0.465489i
$336$	10.9475	−	12.3876i	0.0325819	−	0.0368678i
$337$	58.8437			0.174610			0.0873052	−	0.996182i	$-0.472174\pi$
$337$	58.8437			0.174610			0.0873052	+	0.996182i	$0.472174\pi$
$338$	644.730	+	416.570i	1.90748	+	1.23246i
$339$		−	112.647i		−	0.332293i
$340$	14.6206	+	32.4328i	0.0430017	+	0.0953905i
$341$	549.897			1.61260
$342$	22.9480	−	35.5168i	0.0670993	−	0.103850i
$343$		−	58.2486i		−	0.169821i
$344$	285.676	+	43.2118i	0.830454	+	0.125616i
$345$	−124.243			−0.360123
$346$	261.677	+	169.074i	0.756293	+	0.488653i
$347$		−	12.1484i		−	0.0350099i	−0.999847	−	0.0175049i	$-0.994428\pi$
$347$		−	12.1484i		−	0.0350099i	0.999847	−	0.0175049i	$-0.00557228\pi$
$348$	225.317	−	101.572i	0.647462	−	0.291874i
$349$	−30.9277			−0.0886180			−0.0443090	−	0.999018i	$-0.514109\pi$
$349$	−30.9277			−0.0886180			−0.0443090	+	0.999018i	$0.514109\pi$
$350$	3.23738	−	5.01052i	0.00924965	−	0.0143158i
$351$		−	122.170i		−	0.348063i
$352$	80.1760	+	285.919i	0.227773	+	0.812271i
$353$	−288.065			−0.816048			−0.408024	−	0.912971i	$-0.633782\pi$
$353$	−288.065			−0.816048			−0.408024	+	0.912971i	$0.633782\pi$
$354$	−105.917	−	68.4348i	−0.299201	−	0.193319i
$355$			132.413i			0.372995i
$356$	−214.470	−	475.757i	−0.602444	−	1.33640i
$357$	−4.10971			−0.0115118
$358$	−136.759	+	211.664i	−0.382010	+	0.591240i
$359$		−	663.911i		−	1.84933i	−0.380776	−	0.924667i	$-0.624343\pi$
$359$		−	663.911i		−	1.84933i	0.380776	−	0.924667i	$-0.375657\pi$
$360$	8.02624	−	53.0620i	0.0222951	−	0.147395i
$361$	311.332			0.862415
$362$	−582.450	−	376.330i	−1.60898	−	1.03959i
$363$		−	60.4287i		−	0.166470i
$364$	−51.1459	+	23.0564i	−0.140511	+	0.0633418i
$365$	−185.598			−0.508487
$366$	−16.4161	+	25.4074i	−0.0448527	+	0.0694190i
$367$		−	6.08529i		−	0.0165812i	−0.999966	−	0.00829059i	$-0.997361\pi$
$367$		−	6.08529i		−	0.0165812i	0.999966	−	0.00829059i	$-0.00263901\pi$
$368$	384.602	+	339.891i	1.04511	+	0.923618i
$369$	−120.237			−0.325846
$370$	−20.2374	−	13.0757i	−0.0546957	−	0.0353397i
$371$			1.52191i			0.00410218i
$372$	168.725	+	374.282i	0.453562	+	1.00613i
$373$	−204.741			−0.548903			−0.274451	−	0.961601i	$-0.588496\pi$
$373$	−204.741			−0.548903			−0.274451	+	0.961601i	$0.588496\pi$
$374$	40.0614	−	62.0034i	0.107116	−	0.165784i
$375$		−	19.3649i		−	0.0516398i
$376$	−585.445	−	88.5552i	−1.55703	−	0.235519i
$377$	−838.742			−2.22478
$378$	5.20709	+	3.36438i	0.0137754	+	0.00890048i
$379$			402.331i			1.06156i	0.847510	+	0.530780i	$0.178101\pi$
$379$			402.331i			1.06156i	−0.847510	+	0.530780i	$0.821899\pi$
$380$	−57.4661	+	25.9055i	−0.151227	+	0.0681725i
$381$	241.568			0.634036
$382$	144.529	−	223.689i	0.378348	−	0.585573i
$383$			331.751i			0.866191i	0.901348	+	0.433096i	$0.142579\pi$
$383$			331.751i			0.866191i	−0.901348	+	0.433096i	$0.857421\pi$
$384$	−170.008	+	142.300i	−0.442729	+	0.370573i
$385$	−12.3781			−0.0321510
$386$	−228.875	−	147.880i	−0.592941	−	0.383109i
$387$			108.347i			0.279967i
$388$	153.063	+	339.540i	0.394493	+	0.875102i
$389$	−623.310			−1.60234			−0.801169	−	0.598438i	$-0.795788\pi$
$389$	−623.310			−1.60234			−0.801169	+	0.598438i	$0.795788\pi$
$390$	−98.8356	+	152.969i	−0.253425	+	0.392228i
$391$		−	127.596i		−	0.326332i
$392$	−58.2018	+	384.776i	−0.148474	+	0.981572i
$393$	−109.960			−0.279797
$394$	125.812	+	81.2894i	0.319321	+	0.206318i
$395$		−	147.291i		−	0.372889i
$396$	−101.517	+	45.7636i	−0.256357	+	0.115565i
$397$	−355.449			−0.895338			−0.447669	−	0.894199i	$-0.647746\pi$
$397$	−355.449			−0.895338			−0.447669	+	0.894199i	$0.647746\pi$
$398$	273.088	−	422.661i	0.686151	−	1.06196i
$399$		−	7.28180i		−	0.0182501i
$400$	−52.9767	+	59.9455i	−0.132442	+	0.149864i
$401$	−542.927			−1.35393			−0.676966	−	0.736014i	$-0.736706\pi$
$401$	−542.927			−1.35393			−0.676966	+	0.736014i	$0.736706\pi$
$402$	−202.910	−	131.103i	−0.504751	−	0.326128i
$403$		−	1393.27i		−	3.45724i
$404$	−6.01792	−	13.3495i	−0.0148958	−	0.0330433i
$405$	20.1246			0.0496904
$406$	23.0977	−	35.7485i	0.0568908	−	0.0880505i
$407$			49.9950i			0.122838i
$408$	54.4941	+	8.24285i	0.133564	+	0.0202031i
$409$	−108.497			−0.265273			−0.132636	−	0.991165i	$-0.542344\pi$
$409$	−108.497			−0.265273			−0.132636	+	0.991165i	$0.542344\pi$
$410$	150.549	+	97.2718i	0.367192	+	0.237248i
$411$			239.295i			0.582227i
$412$	−552.156	+	248.910i	−1.34018	+	0.604151i
$413$	−21.7156			−0.0525801
$414$	−104.455	+	161.666i	−0.252307	+	0.390499i
$415$		−	290.486i		−	0.699966i
$416$	724.431	−	203.141i	1.74142	−	0.488320i
$417$	51.8884			0.124433
$418$	109.861	+	70.9828i	0.262825	+	0.169815i
$419$			172.176i			0.410921i	0.978665	+	0.205460i	$0.0658691\pi$
$419$			172.176i			0.410921i	−0.978665	+	0.205460i	$0.934131\pi$
$420$	−3.79799	−	8.42505i	−0.00904283	−	0.0200597i
$421$	478.522			1.13663			0.568316	−	0.822810i	$-0.307595\pi$
$421$	478.522			1.13663			0.568316	+	0.822810i	$0.307595\pi$
$422$	247.688	−	383.350i	0.586940	−	0.908412i
$423$		−	222.039i		−	0.524915i
$424$	3.05250	−	20.1803i	0.00719929	−	0.0475950i
$425$	19.8875			0.0467942
$426$	172.298	+	111.325i	0.404456	+	0.261326i
$427$			5.20912i			0.0121993i
$428$	−301.972	+	136.128i	−0.705541	+	0.318056i
$429$	377.898			0.880882
$430$	87.6528	−	135.661i	0.203844	−	0.315491i
$431$			290.722i			0.674530i	0.941410	+	0.337265i	$0.109502\pi$
$431$			290.722i			0.674530i	−0.941410	+	0.337265i	$0.890498\pi$
$432$	−62.2972	−	55.0550i	−0.144207	−	0.127442i
$433$	53.7726			0.124186			0.0620931	−	0.998070i	$-0.480222\pi$
$433$	53.7726			0.124186			0.0620931	+	0.998070i	$0.480222\pi$
$434$	59.3832	+	38.3684i	0.136828	+	0.0884065i
$435$		−	138.163i		−	0.317615i
$436$	−12.1127	−	26.8694i	−0.0277813	−	0.0616271i
$437$	226.081			0.517347
$438$	−156.039	+	241.503i	−0.356253	+	0.551376i
$439$		−	328.657i		−	0.748650i	−0.927298	−	0.374325i	$-0.877874\pi$
$439$		−	328.657i		−	0.748650i	0.927298	−	0.374325i	$-0.122126\pi$
$440$	164.132	+	24.8268i	0.373027	+	0.0564246i
$441$	−145.932			−0.330913
$442$	−157.097	−	101.503i	−0.355424	−	0.229645i
$443$		−	428.910i		−	0.968194i	−0.875014	−	0.484097i	$-0.839148\pi$
$443$		−	428.910i		−	0.968194i	0.875014	−	0.484097i	$-0.160852\pi$
$444$	−34.0286	+	15.3400i	−0.0766410	+	0.0345496i
$445$	−291.731			−0.655575
$446$	−93.2942	+	144.392i	−0.209180	+	0.323750i
$447$			82.0685i			0.183599i
$448$	−11.2915	+	36.4706i	−0.0252043	+	0.0814075i
$449$	409.229			0.911423			0.455711	−	0.890128i	$-0.349385\pi$
$449$	409.229			0.911423			0.455711	+	0.890128i	$0.349385\pi$
$450$	−25.1979	−	16.2808i	−0.0559954	−	0.0361795i
$451$		−	371.919i		−	0.824654i
$452$	106.913	+	237.164i	0.236533	+	0.524698i
$453$	−189.839			−0.419071
$454$	306.466	−	474.321i	0.675036	−	1.04476i
$455$			31.3623i			0.0689281i
$456$	−14.6051	+	96.5555i	−0.0320288	+	0.211745i
$457$	768.561			1.68175			0.840876	−	0.541228i	$-0.182040\pi$
$457$	768.561			1.68175			0.840876	+	0.541228i	$0.182040\pi$
$458$	232.262	+	150.068i	0.507123	+	0.327660i
$459$			20.6677i			0.0450278i
$460$	261.576	−	117.918i	0.568643	−	0.256343i
$461$	−316.563			−0.686687			−0.343343	−	0.939210i	$-0.611559\pi$
$461$	−316.563			−0.686687			−0.343343	+	0.939210i	$0.611559\pi$
$462$	−10.4067	+	16.1066i	−0.0225254	+	0.0348628i
$463$			491.208i			1.06093i	0.847708	+	0.530463i	$0.177982\pi$
$463$			491.208i			1.06093i	−0.847708	+	0.530463i	$0.822018\pi$
$464$	−377.972	+	427.692i	−0.814596	+	0.921751i
$465$	229.507			0.493564
$466$	−0.878466	−	0.567591i	−0.00188512	−	0.00121801i
$467$			410.393i			0.878785i	0.898295	+	0.439393i	$0.144806\pi$
$467$			410.393i			0.878785i	−0.898295	+	0.439393i	$0.855194\pi$
$468$	115.951	+	257.213i	0.247758	+	0.549600i
$469$	−41.6014			−0.0887024
$470$	−179.629	+	278.014i	−0.382190	+	0.591520i
$471$			307.591i			0.653060i
$472$	287.945	+	43.5550i	0.610054	+	0.0922776i
$473$	−335.141			−0.708542
$474$	−191.657	−	123.833i	−0.404341	−	0.261251i
$475$			35.2378i			0.0741848i
$476$	8.65243	−	3.90049i	0.0181774	−	0.00819431i
$477$	7.65369			0.0160455
$478$	79.9851	−	123.794i	0.167333	−	0.258983i
$479$			198.918i			0.415277i	0.978206	+	0.207638i	$0.0665778\pi$
$479$			198.918i			0.415277i	−0.978206	+	0.207638i	$0.933422\pi$
$480$	33.4626	+	119.333i	0.0697137	+	0.248609i
$481$	126.672			0.263351
$482$	52.6981	+	34.0491i	0.109332	+	0.0706413i
$483$			33.1455i			0.0686242i
$484$	57.3524	+	127.224i	0.118497	+	0.262860i
$485$	208.203			0.429285
$486$	16.9195	−	26.1865i	0.0348138	−	0.0538816i
$487$		−	204.762i		−	0.420456i	−0.977652	−	0.210228i	$-0.932579\pi$
$487$		−	204.762i		−	0.420456i	0.977652	−	0.210228i	$-0.0674206\pi$
$488$	10.4479	−	69.0721i	0.0214097	−	0.141541i
$489$	167.797			0.343144
$490$	182.721	+	118.059i	0.372901	+	0.240937i
$491$			788.598i			1.60611i	0.595908	+	0.803053i	$0.296792\pi$
$491$			788.598i			1.60611i	−0.595908	+	0.803053i	$0.703208\pi$
$492$	253.143	−	114.116i	0.514519	−	0.231944i
$493$	141.891			0.287812
$494$	179.848	−	278.353i	0.364066	−	0.563468i
$495$			62.2496i			0.125757i
$496$	−710.456	−	627.864i	−1.43237	−	1.26586i
$497$	35.3253			0.0710771
$498$	−377.985	−	244.222i	−0.759006	−	0.490406i
$499$			740.385i			1.48374i	0.670545	+	0.741869i	$0.266060\pi$
$499$			740.385i			1.48374i	−0.670545	+	0.741869i	$0.733940\pi$
$500$	18.3791	+	40.7702i	0.0367582	+	0.0815404i
$501$	−264.319			−0.527583
$502$	85.4717	−	132.285i	0.170262	−	0.263517i
$503$			70.8800i			0.140914i	0.997515	+	0.0704572i	$0.0224458\pi$
$503$			70.8800i			0.140914i	−0.997515	+	0.0704572i	$0.977554\pi$
$504$	−14.1559	−	2.14124i	−0.0280871	−	0.00424850i
$505$	−8.18582			−0.0162095
$506$	−500.068	−	323.102i	−0.988277	−	0.638541i
$507$		−	664.760i		−	1.31116i
$508$	−508.588	+	229.270i	−1.00116	+	0.451318i
$509$	522.642			1.02680			0.513400	−	0.858149i	$-0.328386\pi$
$509$	522.642			1.02680			0.513400	+	0.858149i	$0.328386\pi$
$510$	16.7202	−	25.8780i	0.0327847	−	0.0507411i
$511$			49.5139i			0.0968961i
$512$	222.873	−	460.946i	0.435299	−	0.900286i
$513$	−36.6202			−0.0713844
$514$	409.809	+	264.784i	0.797293	+	0.515144i
$515$			338.578i			0.657433i
$516$	−102.831	−	228.110i	−0.199286	−	0.442074i
$517$	686.813			1.32846
$518$	−3.48834	+	5.39894i	−0.00673425	+	0.0104227i
$519$		−	269.807i		−	0.519859i
$520$	62.9034	−	415.859i	0.120968	−	0.799729i
$521$	304.082			0.583650			0.291825	−	0.956472i	$-0.405738\pi$
$521$	304.082			0.583650			0.291825	+	0.956472i	$0.405738\pi$
$522$	−179.779	−	116.158i	−0.344405	−	0.222525i
$523$		−	174.416i		−	0.333491i	−0.986000	−	0.166746i	$-0.946674\pi$
$523$		−	174.416i		−	0.333491i	0.986000	−	0.166746i	$-0.0533259\pi$
$524$	231.507	−	104.362i	0.441806	−	0.199165i
$525$	−5.16618			−0.00984035
$526$	111.509	−	172.584i	0.211995	−	0.328106i
$527$			235.701i			0.447251i
$528$	170.297	−	192.698i	0.322532	−	0.364959i
$529$	−500.081			−0.945333
$530$	−9.58315	−	6.19182i	−0.0180814	−	0.0116827i
$531$			109.208i			0.205664i
$532$	6.91109	+	15.3308i	0.0129908	+	0.0288174i
$533$	−942.327			−1.76797
$534$	−245.269	+	379.605i	−0.459305	+	0.710871i
$535$			185.167i			0.346106i
$536$	551.628	+	83.4401i	1.02916	+	0.155672i
$537$	218.240			0.406405
$538$	−207.708	−	134.204i	−0.386075	−	0.249449i
$539$		−	451.399i		−	0.837476i
$540$	−42.3696	+	19.1001i	−0.0784623	+	0.0353706i
$541$	−262.199			−0.484655			−0.242328	−	0.970194i	$-0.577911\pi$
$541$	−262.199			−0.484655			−0.242328	+	0.970194i	$0.577911\pi$
$542$	−360.750	+	558.337i	−0.665591	+	1.03014i
$543$			600.545i			1.10598i
$544$	−122.553	+	34.3657i	−0.225281	+	0.0631722i
$545$	−16.4761			−0.0302314
$546$	40.8091	+	26.3674i	0.0747420	+	0.0482920i
$547$			146.179i			0.267237i	0.991033	+	0.133619i	$0.0426598\pi$
$547$			146.179i			0.267237i	−0.991033	+	0.133619i	$0.957340\pi$
$548$	−227.113	−	503.804i	−0.414440	−	0.919350i
$549$	26.1967			0.0477171
$550$	50.3599	−	77.9425i	0.0915634	−	0.141714i
$551$			251.411i			0.456281i
$552$	66.4800	−	439.504i	0.120435	−	0.796203i
$553$	−39.2944			−0.0710568
$554$	−211.522	−	136.668i	−0.381809	−	0.246693i
$555$			20.8661i			0.0375966i
$556$	−109.244	+	49.2468i	−0.196482	+	0.0885734i
$557$	187.700			0.336984			0.168492	−	0.985703i	$-0.446110\pi$
$557$	187.700			0.336984			0.168492	+	0.985703i	$0.446110\pi$
$558$	192.955	−	298.638i	0.345797	−	0.535194i
$559$			849.142i			1.51904i
$560$	15.9923	+	14.1332i	0.0285577	+	0.0252378i
$561$	−63.9296			−0.113957
$562$	88.2982	+	57.0509i	0.157114	+	0.101514i
$563$		−	447.848i		−	0.795467i	−0.917501	−	0.397734i	$-0.869797\pi$
$563$		−	447.848i		−	0.795467i	0.917501	−	0.397734i	$-0.130203\pi$
$564$	210.736	+	467.473i	0.373645	+	0.828853i
$565$	145.427			0.257393
$566$	−216.305	+	334.777i	−0.382164	+	0.591479i
$567$		−	5.36886i		−	0.00946888i
$568$	−468.408	−	70.8520i	−0.824662	−	0.124740i
$569$	1078.91			1.89615			0.948077	−	0.318042i	$-0.103025\pi$
$569$	1078.91			1.89615			0.948077	+	0.318042i	$0.103025\pi$
$570$	45.8520	+	29.6257i	0.0804421	+	0.0519749i
$571$		−	936.324i		−	1.63980i	−0.572509	−	0.819899i	$-0.694030\pi$
$571$		−	936.324i		−	1.63980i	0.572509	−	0.819899i	$-0.305970\pi$
$572$	−795.613	+	358.660i	−1.39093	+	0.627028i
$573$	−230.638			−0.402510
$574$	25.9502	−	40.1634i	0.0452095	−	0.0699711i
$575$		−	160.396i		−	0.278950i
$576$	183.411	+	56.7851i	0.318421	+	0.0985853i
$577$	−544.832			−0.944250			−0.472125	−	0.881532i	$-0.656513\pi$
$577$	−544.832			−0.944250			−0.472125	+	0.881532i	$0.656513\pi$
$578$	−458.904	−	296.505i	−0.793951	−	0.512985i
$579$			235.986i			0.407575i
$580$	131.129	+	290.883i	0.226084	+	0.501522i
$581$	−77.4960			−0.133384
$582$	175.044	−	270.917i	0.300763	−	0.465494i
$583$			23.6745i			0.0406080i
$584$	99.3101	−	656.547i	0.170052	−	1.12422i
$585$	157.721			0.269609
$586$	171.616	+	110.884i	0.292861	+	0.189222i
$587$		−	337.889i		−	0.575619i	−0.957688	−	0.287810i	$-0.907073\pi$
$587$		−	337.889i		−	0.575619i	0.957688	−	0.287810i	$-0.0929271\pi$
$588$	307.241	−	138.503i	0.522519	−	0.235550i
$589$	−417.628			−0.709045
$590$	88.3490	−	136.739i	0.149744	−	0.231760i
$591$		−	129.721i		−	0.219494i
$592$	57.0836	−	64.5926i	0.0964249	−	0.109109i
$593$	567.269			0.956608			0.478304	−	0.878194i	$-0.341252\pi$
$593$	567.269			0.956608			0.478304	+	0.878194i	$0.341252\pi$
$594$	81.0002	+	52.3355i	0.136364	+	0.0881069i
$595$		−	5.30561i		−	0.00891699i
$596$	−77.8906	−	172.784i	−0.130689	−	0.289906i
$597$	−435.792			−0.729969
$598$	−818.640	+	1267.02i	−1.36896	+	2.11876i
$599$		−	762.966i		−	1.27373i	−0.770974	−	0.636867i	$-0.780230\pi$
$599$		−	762.966i		−	1.27373i	0.770974	−	0.636867i	$-0.219770\pi$
$600$	68.5028	+	10.3618i	0.114171	+	0.0172697i
$601$	−790.102			−1.31464			−0.657322	−	0.753609i	$-0.728311\pi$
$601$	−790.102			−1.31464			−0.657322	+	0.753609i	$0.728311\pi$
$602$	−36.1917	−	23.3841i	−0.0601192	−	0.0388440i
$603$			209.214i			0.346955i
$604$	399.680	−	180.175i	0.661722	−	0.298302i
$605$	78.0132			0.128947
$606$	−6.88212	+	10.6515i	−0.0113566	+	0.0175768i
$607$			522.994i			0.861605i	0.902446	+	0.430802i	$0.141769\pi$
$607$			522.994i			0.861605i	−0.902446	+	0.430802i	$0.858231\pi$
$608$	−60.8909	−	217.146i	−0.100150	−	0.357148i
$609$	−36.8591			−0.0605240
$610$	−32.8008	−	21.1931i	−0.0537717	−	0.0347428i
$611$		−	1740.17i		−	2.84807i
$612$	−19.6156	−	43.5131i	−0.0320516	−	0.0710999i
$613$	1026.91			1.67522			0.837609	−	0.546270i	$-0.183953\pi$
$613$	1026.91			1.67522			0.837609	+	0.546270i	$0.183953\pi$
$614$	−356.431	+	551.652i	−0.580506	+	0.898455i
$615$		−	155.226i		−	0.252399i
$616$	6.62332	−	43.7872i	0.0107521	−	0.0710831i
$617$	−479.223			−0.776698			−0.388349	−	0.921512i	$-0.626954\pi$
$617$	−479.223			−0.776698			−0.388349	+	0.921512i	$0.626954\pi$
$618$	440.563	+	284.655i	0.712886	+	0.460607i
$619$			507.654i			0.820119i	0.912059	+	0.410059i	$0.134492\pi$
$619$			507.654i			0.820119i	−0.912059	+	0.410059i	$0.865508\pi$
$620$	−483.196	+	217.823i	−0.779348	+	0.351328i
$621$	166.689			0.268420
$622$	−103.587	+	160.322i	−0.166538	+	0.257753i
$623$			77.8282i			0.124925i
$624$	−488.237	−	431.479i	−0.782432	−	0.691473i
$625$	25.0000			0.0400000
$626$	924.609	+	597.405i	1.47701	+	0.954321i
$627$		−	113.274i		−	0.180660i
$628$	−291.932	−	647.591i	−0.464860	−	1.03120i
$629$	−21.4293			−0.0340688
$630$	−4.34340	+	6.72232i	−0.00689428	+	0.0106703i
$631$			460.186i			0.729297i	0.931145	+	0.364648i	$0.118811\pi$
$631$			460.186i			0.729297i	−0.931145	+	0.364648i	$0.881189\pi$
$632$	521.037	+	78.8128i	0.824426	+	0.124704i
$633$	−395.259			−0.624423
$634$	738.122	+	476.912i	1.16423	+	0.752228i
$635$			311.862i			0.491122i
$636$	−16.1138	+	7.26405i	−0.0253362	+	0.0114215i
$637$	−1143.71			−1.79546
$638$	359.302	−	556.095i	0.563169	−	0.871622i
$639$		−	177.651i		−	0.278014i
$640$	−183.708	−	219.479i	−0.287045	−	0.342937i
$641$	250.774			0.391223			0.195612	−	0.980681i	$-0.437331\pi$
$641$	250.774			0.391223			0.195612	+	0.980681i	$0.437331\pi$
$642$	240.942	+	155.677i	0.375299	+	0.242487i
$643$			590.355i			0.918126i	0.888404	+	0.459063i	$0.151815\pi$
$643$			590.355i			0.918126i	−0.888404	+	0.459063i	$0.848185\pi$
$644$	−31.4581	−	69.7834i	−0.0488480	−	0.108359i
$645$	−139.876			−0.216862
$646$	−30.4252	+	47.0894i	−0.0470979	+	0.0728939i
$647$			319.341i			0.493572i	0.969070	+	0.246786i	$0.0793744\pi$
$647$			319.341i			0.493572i	−0.969070	+	0.246786i	$0.920626\pi$
$648$	−10.7683	+	71.1902i	−0.0166178	+	0.109861i
$649$	−337.803			−0.520497
$650$	−197.482	−	127.596i	−0.303818	−	0.196302i
$651$		−	61.2280i		−	0.0940523i
$652$	−353.274	+	159.255i	−0.541832	+	0.244256i
$653$	88.5949			0.135674			0.0678369	−	0.997696i	$-0.478390\pi$
$653$	88.5949			0.135674			0.0678369	+	0.997696i	$0.478390\pi$
$654$	−13.8521	+	21.4390i	−0.0211806	+	0.0327814i
$655$		−	141.958i		−	0.216730i
$656$	−424.652	+	480.512i	−0.647335	+	0.732488i
$657$	249.006			0.379004
$658$	74.1688	+	47.9216i	0.112719	+	0.0728292i
$659$		−	758.423i		−	1.15087i	−0.817847	−	0.575435i	$-0.804833\pi$
$659$		−	758.423i		−	1.15087i	0.817847	−	0.575435i	$-0.195167\pi$
$660$	−59.0806	−	131.058i	−0.0895161	−	0.198573i
$661$	527.327			0.797771			0.398885	−	0.917001i	$-0.369397\pi$
$661$	527.327			0.797771			0.398885	+	0.917001i	$0.369397\pi$
$662$	−520.900	+	806.203i	−0.786859	+	1.21783i
$663$			161.978i			0.244310i
$664$	1027.59	+	155.434i	1.54757	+	0.234087i
$665$	9.40076			0.0141365
$666$	27.1513	+	17.5429i	0.0407677	+	0.0263407i
$667$		−	1144.38i		−	1.71571i
$668$	556.488	−	250.863i	0.833066	−	0.375544i
$669$	148.878			0.222538
$670$	169.254	−	261.956i	0.252617	−	0.390978i
$671$			81.0318i			0.120763i
$672$	31.8356	−	8.92717i	0.0473744	−	0.0132845i
$673$	120.657			0.179283			0.0896415	−	0.995974i	$-0.471428\pi$
$673$	120.657			0.179283			0.0896415	+	0.995974i	$0.471428\pi$
$674$	98.8493	+	63.8681i	0.146661	+	0.0947598i
$675$			25.9808i			0.0384900i
$676$	630.918	+	1399.56i	0.933311	+	2.07036i
$677$	−219.196			−0.323776			−0.161888	−	0.986809i	$-0.551758\pi$
$677$	−219.196			−0.323776			−0.161888	+	0.986809i	$0.551758\pi$
$678$	122.266	−	189.232i	0.180333	−	0.279103i
$679$		−	55.5446i		−	0.0818035i
$680$	−10.6415	+	70.3516i	−0.0156492	+	0.103458i
$681$	−489.057			−0.718145
$682$	923.751	+	596.850i	1.35447	+	0.875146i
$683$			205.502i			0.300881i	0.988619	+	0.150441i	$0.0480693\pi$
$683$			205.502i			0.300881i	−0.988619	+	0.150441i	$0.951931\pi$
$684$	77.0988	−	34.7559i	0.112718	−	0.0508128i
$685$	−308.929			−0.450991
$686$	63.2222	−	97.8496i	0.0921606	−	0.142638i
$687$		−	239.478i		−	0.348585i
$688$	432.995	+	382.659i	0.629354	+	0.556190i
$689$	59.9837			0.0870591
$690$	−208.710	−	134.851i	−0.302479	−	0.195436i
$691$			109.536i			0.158519i	0.996854	+	0.0792593i	$0.0252555\pi$
$691$			109.536i			0.158519i	−0.996854	+	0.0792593i	$0.974744\pi$
$692$	256.071	+	568.042i	0.370045	+	0.820869i
$693$	16.6070			0.0239639
$694$	13.1857	−	20.4077i	0.0189996	−	0.0294059i
$695$			66.9876i			0.0963850i
$696$	488.746	+	73.9284i	0.702221	+	0.106219i
$697$	159.415			0.228716
$698$	−51.9543	−	33.5685i	−0.0744331	−	0.0480924i
$699$			0.905758i			0.00129579i
$700$	10.8767	−	4.90318i	0.0155381	−	0.00700455i
$701$	168.847			0.240865			0.120433	−	0.992721i	$-0.461572\pi$
$701$	168.847			0.240865			0.120433	+	0.992721i	$0.461572\pi$
$702$	132.602	−	205.229i	0.188892	−	0.292349i
$703$		−	37.9695i		−	0.0540106i
$704$	−175.648	+	567.327i	−0.249500	+	0.805863i
$705$	286.651			0.406598
$706$	−483.909	−	312.661i	−0.685424	−	0.442863i
$707$			2.18382i			0.00308885i
$708$	−103.648	−	229.922i	−0.146396	−	0.324749i
$709$	−554.846			−0.782576			−0.391288	−	0.920268i	$-0.627970\pi$
$709$	−554.846			−0.782576			−0.391288	+	0.920268i	$0.627970\pi$
$710$	−143.720	+	222.436i	−0.202422	+	0.313290i
$711$			197.612i			0.277935i
$712$	156.100	−	1031.99i	0.219242	−	1.44942i
$713$	1900.97			2.66616
$714$	−6.90374	−	4.46062i	−0.00966911	−	0.00624737i
$715$			487.864i			0.682328i
$716$	−459.474	+	207.130i	−0.641723	+	0.289287i
$717$	−127.640			−0.178019
$718$	720.600	−	1115.28i	1.00362	−	1.55331i
$719$		−	377.485i		−	0.525014i	−0.964930	−	0.262507i	$-0.915451\pi$
$719$		−	377.485i		−	0.525014i	0.964930	−	0.262507i	$-0.0845494\pi$
$720$	71.0758	−	80.4254i	0.0987163	−	0.111702i
$721$	90.3261			0.125279
$722$	522.995	+	337.915i	0.724369	+	0.468027i
$723$		−	54.3353i		−	0.0751525i
$724$	−569.972	−	1264.37i	−0.787255	−	1.74636i
$725$	178.367			0.246024
$726$	65.5885	−	101.512i	0.0903423	−	0.139824i
$727$		−	173.183i		−	0.238216i	−0.992881	−	0.119108i	$-0.961997\pi$
$727$		−	173.183i		−	0.238216i	0.992881	−	0.119108i	$-0.0380035\pi$
$728$	−110.943	−	16.7814i	−0.152394	−	0.0230514i
$729$	−27.0000			−0.0370370
$730$	−311.779	−	201.445i	−0.427094	−	0.275952i
$731$		−	143.651i		−	0.196513i
$732$	−55.1536	+	24.8631i	−0.0753464	+	0.0339659i
$733$	278.722			0.380249			0.190124	−	0.981760i	$-0.439111\pi$
$733$	278.722			0.380249			0.190124	+	0.981760i	$0.439111\pi$
$734$	6.60489	−	10.2225i	0.00899849	−	0.0139270i
$735$		−	188.398i		−	0.256324i
$736$	277.165	+	988.412i	0.376583	+	1.34295i
$737$	−647.142			−0.878075
$738$	−201.982	−	130.504i	−0.273688	−	0.176834i
$739$		−	521.363i		−	0.705498i	−0.935718	−	0.352749i	$-0.885247\pi$
$739$		−	521.363i		−	0.705498i	0.935718	−	0.352749i	$-0.114753\pi$
$740$	−19.8039	−	43.9308i	−0.0267620	−	0.0593659i
$741$	−287.001			−0.387315
$742$	−1.65186	+	2.55660i	−0.00222622	+	0.00344555i
$743$			1277.93i			1.71996i	0.510326	+	0.859981i	$0.329525\pi$
$743$			1277.93i			1.71996i	−0.510326	+	0.859981i	$0.670475\pi$
$744$	−122.805	+	811.874i	−0.165061	+	1.09123i
$745$	−105.950			−0.142215
$746$	−343.936	−	222.223i	−0.461041	−	0.297886i
$747$			389.728i			0.521724i
$748$	134.595	−	60.6751i	0.179940	−	0.0811164i
$749$	49.3989			0.0659532
$750$	21.0184	−	32.5304i	0.0280245	−	0.0433739i
$751$		−	1165.31i		−	1.55168i	−0.630930	−	0.775840i	$-0.717327\pi$
$751$		−	1165.31i		−	1.55168i	0.630930	−	0.775840i	$-0.282673\pi$
$752$	−887.350	−	784.194i	−1.17999	−	1.04281i
$753$	−136.395			−0.181136
$754$	−1408.97	−	910.359i	−1.86866	−	1.20737i
$755$		−	245.081i		−	0.324611i
$756$	5.09554	+	11.3034i	0.00674013	+	0.0149516i
$757$	1063.75			1.40522			0.702611	−	0.711574i	$-0.252017\pi$
$757$	1063.75			1.40522			0.702611	+	0.711574i	$0.252017\pi$
$758$	−436.685	+	675.861i	−0.576101	+	0.891638i
$759$			515.604i			0.679320i
$760$	−124.653	−	18.8551i	−0.164017	−	0.0248094i
$761$	−677.847			−0.890732			−0.445366	−	0.895349i	$-0.646926\pi$
$761$	−677.847			−0.890732			−0.445366	+	0.895349i	$0.646926\pi$
$762$	405.800	+	262.194i	0.532546	+	0.344087i
$763$			4.39551i			0.00576083i
$764$	485.577	−	218.897i	0.635572	−	0.286514i
$765$	−26.6819			−0.0348784
$766$	−360.078	+	557.296i	−0.470076	+	0.727541i
$767$			855.887i			1.11589i
$768$	−440.040	+	54.5201i	−0.572969	+	0.0709898i
$769$	−1289.59			−1.67697			−0.838486	−	0.544922i	$-0.816559\pi$
$769$	−1289.59			−1.67697			−0.838486	+	0.544922i	$0.816559\pi$
$770$	−20.7935	−	13.4350i	−0.0270046	−	0.0174481i
$771$		−	422.540i		−	0.548042i
$772$	−223.972	−	496.836i	−0.290119	−	0.643570i
$773$	−750.339			−0.970684			−0.485342	−	0.874324i	$-0.661305\pi$
$773$	−750.339			−0.970684			−0.485342	+	0.874324i	$0.661305\pi$
$774$	−117.599	+	182.008i	−0.151936	+	0.235153i
$775$			296.292i			0.382313i
$776$	−111.406	+	736.513i	−0.143564	+	0.949114i
$777$	5.56667			0.00716432
$778$	−1047.07	−	676.532i	−1.34585	−	0.869578i
$779$			282.460i			0.362593i
$780$	−332.060	+	149.692i	−0.425719	+	0.191913i
$781$	549.512			0.703600
$782$	138.491	−	214.343i	0.177098	−	0.274096i
$783$			185.365i			0.236736i
$784$	−515.402	+	583.200i	−0.657400	+	0.743877i
$785$	−397.098			−0.505858
$786$	−184.718	−	119.349i	−0.235011	−	0.151844i
$787$		−	825.185i		−	1.04852i	−0.851558	−	0.524260i	$-0.824342\pi$
$787$		−	825.185i		−	1.04852i	0.851558	−	0.524260i	$-0.175658\pi$
$788$	123.117	+	273.110i	0.156240	+	0.346586i
$789$	−177.946			−0.225533
$790$	159.868	−	247.429i	0.202364	−	0.313201i
$791$		−	38.7971i		−	0.0490482i
$792$	−220.206	−	33.3087i	−0.278038	−	0.0420564i
$793$	205.309			0.258902
$794$	−597.106	−	385.799i	−0.752022	−	0.485893i
$795$			9.88087i			0.0124288i
$796$	917.500	−	413.606i	1.15264	−	0.519606i
$797$	1113.70			1.39737			0.698684	−	0.715430i	$-0.253769\pi$
$797$	1113.70			1.39737			0.698684	+	0.715430i	$0.253769\pi$
$798$	7.90356	−	12.2324i	0.00990421	−	0.0153288i
$799$			294.388i			0.368445i
$800$	−154.058	+	43.2000i	−0.192572	+	0.0540000i
$801$	391.398			0.488637
$802$	−912.043	−	589.285i	−1.13721	−	0.734770i
$803$			770.226i			0.959186i
$804$	−198.563	−	440.471i	−0.246969	−	0.547849i
$805$	−42.7907			−0.0531561
$806$	1512.23	−	2340.50i	1.87622	−	2.90384i
$807$			214.161i			0.265379i
$808$	4.38009	−	28.9571i	0.00542090	−	0.0358380i
$809$	−1049.54			−1.29733			−0.648664	−	0.761075i	$-0.724672\pi$
$809$	−1049.54			−1.29733			−0.648664	+	0.761075i	$0.724672\pi$
$810$	33.8066	+	21.8430i	0.0417365	+	0.0269666i
$811$			424.482i			0.523406i	0.965148	+	0.261703i	$0.0842841\pi$
$811$			424.482i			0.523406i	−0.965148	+	0.261703i	$0.915716\pi$
$812$	77.6018	−	34.9827i	0.0955688	−	0.0430821i
$813$	575.683			0.708097
$814$	−54.2638	+	83.9847i	−0.0666632	+	0.103175i
$815$			216.625i			0.265798i
$816$	82.5959	+	72.9940i	0.101220	+	0.0894534i
$817$	254.528			0.311540
$818$	−182.259	−	117.761i	−0.222811	−	0.143962i
$819$		−	42.0769i		−	0.0513760i
$820$	147.323	+	326.807i	0.179663	+	0.398545i
$821$	−1257.98			−1.53225			−0.766126	−	0.642690i	$-0.777818\pi$
$821$	−1257.98			−1.53225			−0.766126	+	0.642690i	$0.777818\pi$
$822$	−259.728	+	401.983i	−0.315970	+	0.489031i
$823$			729.181i			0.886004i	0.896521	+	0.443002i	$0.146087\pi$
$823$			729.181i			0.886004i	−0.896521	+	0.443002i	$0.853913\pi$
$824$	−1197.71	−	181.167i	−1.45353	−	0.219863i
$825$	−80.3639			−0.0974108
$826$	−36.4792	−	23.5698i	−0.0441637	−	0.0285349i
$827$		−	72.5882i		−	0.0877729i	−0.999037	−	0.0438865i	$-0.986026\pi$
$827$		−	72.5882i		−	0.0877729i	0.999037	−	0.0438865i	$-0.0139740\pi$
$828$	−350.941	+	158.203i	−0.423842	+	0.191067i
$829$	900.257			1.08596			0.542978	−	0.839747i	$-0.317297\pi$
$829$	900.257			1.08596			0.542978	+	0.839747i	$0.317297\pi$
$830$	315.289	−	487.977i	0.379867	−	0.587924i
$831$			218.093i			0.262447i
$832$	1437.43	+	445.038i	1.72768	+	0.534901i
$833$	193.482			0.232272
$834$	87.1653	+	56.3189i	0.104515	+	0.0675286i
$835$		−	341.235i		−	0.408664i
$836$	107.507	+	238.483i	0.128597	+	0.285266i
$837$	−307.916			−0.367881
$838$	−186.877	+	289.232i	−0.223004	+	0.345145i
$839$			71.4721i			0.0851872i	0.999092	+	0.0425936i	$0.0135621\pi$
$839$			71.4721i			0.0851872i	−0.999092	+	0.0425936i	$0.986438\pi$
$840$	2.76433	−	18.2752i	0.00329087	−	0.0217562i
$841$	431.594			0.513191
$842$	803.851	+	519.381i	0.954693	+	0.616842i
$843$		−	91.0414i		−	0.107997i
$844$	832.165	−	375.138i	0.985978	−	0.444476i
$845$	858.201			1.01562
$846$	240.998	−	372.995i	0.284868	−	0.440893i
$847$		−	20.8124i		−	0.0245719i
$848$	27.0312	−	30.5870i	0.0318764	−	0.0360695i
$849$	345.178			0.406570
$850$	33.4083	+	21.5857i	0.0393039	+	0.0253949i
$851$			172.831i			0.203091i
$852$	168.607	+	374.020i	0.197896	+	0.438991i
$853$	882.349			1.03441			0.517203	−	0.855862i	$-0.326973\pi$
$853$	882.349			1.03441			0.517203	+	0.855862i	$0.326973\pi$
$854$	−5.65391	+	8.75061i	−0.00662050	+	0.0102466i
$855$		−	47.2765i		−	0.0552941i
$856$	−655.022	−	99.0796i	−0.765213	−	0.115747i
$857$	−370.111			−0.431868			−0.215934	−	0.976408i	$-0.569280\pi$
$857$	−370.111			−0.431868			−0.215934	+	0.976408i	$0.569280\pi$
$858$	634.817	+	410.165i	0.739880	+	0.478048i
$859$		−	1039.00i		−	1.20955i	−0.796397	−	0.604774i	$-0.793264\pi$
$859$		−	1039.00i		−	1.20955i	0.796397	−	0.604774i	$-0.206736\pi$
$860$	294.489	−	132.755i	0.342429	−	0.154366i
$861$	−41.4112			−0.0480966
$862$	−315.546	+	488.373i	−0.366062	+	0.566558i
$863$			72.0666i			0.0835071i	0.999128	+	0.0417535i	$0.0132944\pi$
$863$			72.0666i			0.0835071i	−0.999128	+	0.0417535i	$0.986706\pi$
$864$	−44.8948	−	160.101i	−0.0519616	−	0.185303i
$865$	348.319			0.402681
$866$	90.3306	+	58.3640i	0.104308	+	0.0673950i
$867$			473.161i			0.545745i
$868$	58.1110	+	128.907i	0.0669482	+	0.148511i
$869$	−611.254			−0.703399
$870$	149.960	−	232.094i	0.172368	−	0.266775i
$871$			1639.66i			1.88250i
$872$	8.81609	−	58.2838i	0.0101102	−	0.0668393i
$873$	−279.334			−0.319970
$874$	379.785	+	245.385i	0.434536	+	0.280761i
$875$		−	6.66951i		−	0.00762230i
$876$	−524.247	+	236.329i	−0.598456	+	0.269782i
$877$	14.4444			0.0164703			0.00823514	−	0.999966i	$-0.497379\pi$
$877$	14.4444			0.0164703			0.00823514	+	0.999966i	$0.497379\pi$
$878$	356.720	−	552.099i	0.406287	−	0.628815i
$879$		−	176.948i		−	0.201306i
$880$	248.772	+	219.852i	0.282696	+	0.249832i
$881$	1589.22			1.80388			0.901942	−	0.431858i	$-0.142142\pi$
$881$	1589.22			1.80388			0.901942	+	0.431858i	$0.142142\pi$
$882$	−245.146	−	158.393i	−0.277944	−	0.179584i
$883$		−	495.149i		−	0.560758i	−0.959889	−	0.280379i	$-0.909540\pi$
$883$		−	495.149i		−	0.560758i	0.959889	−	0.280379i	$-0.0904601\pi$
$884$	−153.732	−	341.022i	−0.173905	−	0.385772i
$885$	−140.987			−0.159307
$886$	465.533	−	720.510i	0.525432	−	0.813216i
$887$		−	1384.20i		−	1.56054i	−0.625440	−	0.780272i	$-0.715081\pi$
$887$		−	1384.20i		−	1.56054i	0.625440	−	0.780272i	$-0.284919\pi$
$888$	−73.8132	−	11.1651i	−0.0831230	−	0.0125733i
$889$	83.1988			0.0935870
$890$	−490.068	−	316.641i	−0.550638	−	0.355776i
$891$		−	83.5166i		−	0.0937336i
$892$	−313.443	+	141.299i	−0.351393	+	0.158407i
$893$	−521.611			−0.584111
$894$	−89.0760	+	137.864i	−0.0996376	+	0.154210i
$895$			281.746i			0.314800i
$896$	−58.5528	+	49.0099i	−0.0653491	+	0.0546985i
$897$	1306.38			1.45639
$898$	687.448	+	444.171i	0.765533	+	0.494623i
$899$			2113.95i			2.35145i
$900$	−24.6581	−	54.6990i	−0.0273979	−	0.0607766i
$901$	−10.1475			−0.0112625
$902$	403.676	−	624.773i	0.447534	−	0.692653i
$903$			37.3161i			0.0413246i
$904$	−77.8155	+	514.444i	−0.0860791	+	0.569075i
$905$	−775.300			−0.856685
$906$	−318.903	−	206.049i	−0.351991	−	0.227427i
$907$			957.750i			1.05595i	0.849259	+	0.527977i	$0.177049\pi$
$907$			957.750i			1.05595i	−0.849259	+	0.527977i	$0.822951\pi$
$908$	1029.64	−	464.160i	1.13397	−	0.511189i
$909$	10.9824			0.0120819
$910$	−34.0402	+	52.6844i	−0.0374068	+	0.0578949i
$911$		−	704.979i		−	0.773852i	−0.922111	−	0.386926i	$-0.873537\pi$
$911$		−	704.979i		−	0.773852i	0.922111	−	0.386926i	$-0.126463\pi$
$912$	−129.335	+	146.348i	−0.141814	+	0.160469i
$913$	−1205.51			−1.32038
$914$	1291.08	+	834.185i	1.41256	+	0.912675i
$915$			33.8198i			0.0369615i
$916$	227.287	+	504.189i	0.248130	+	0.550424i
$917$	−37.8717			−0.0412996
$918$	−22.4325	+	34.7190i	−0.0244362	+	0.0378202i
$919$		−	607.048i		−	0.660553i	−0.943884	−	0.330277i	$-0.892858\pi$
$919$		−	607.048i		−	0.660553i	0.943884	−	0.330277i	$-0.107142\pi$
$920$	567.398	+	85.8254i	0.616737	+	0.0932884i
$921$	568.790			0.617578
$922$	−531.782	−	343.593i	−0.576770	−	0.372660i
$923$		−	1392.29i		−	1.50844i
$924$	−34.9638	+	15.7616i	−0.0378396	+	0.0170580i
$925$	−26.9380			−0.0291222
$926$	−533.151	+	825.163i	−0.575757	+	0.891104i
$927$		−	454.250i		−	0.490022i
$928$	−1099.15	+	308.219i	−1.18443	+	0.332132i
$929$	1011.21			1.08849			0.544247	−	0.838925i	$-0.316815\pi$
$929$	1011.21			1.08849			0.544247	+	0.838925i	$0.316815\pi$
$930$	385.540	+	249.104i	0.414560	+	0.267854i
$931$			342.822i			0.368230i
$932$	−0.859647	−	1.90695i	−0.000922368	−	0.00204608i
$933$	165.303			0.177174
$934$	−445.434	+	689.403i	−0.476910	+	0.738119i
$935$		−	82.5328i		−	0.0882704i
$936$	−84.3938	+	557.934i	−0.0901643	+	0.596083i
$937$	−363.105			−0.387519			−0.193760	−	0.981049i	$-0.562068\pi$
$937$	−363.105			−0.387519			−0.193760	+	0.981049i	$0.562068\pi$
$938$	−69.8846	−	45.1536i	−0.0745039	−	0.0481381i
$939$		−	953.334i		−	1.01527i
$940$	−603.505	+	272.058i	−0.642027	+	0.289424i
$941$	−1106.51			−1.17588			−0.587942	−	0.808903i	$-0.700061\pi$
$941$	−1106.51			−1.17588			−0.587942	+	0.808903i	$0.700061\pi$
$942$	−333.855	+	516.711i	−0.354411	+	0.548525i
$943$		−	1285.71i		−	1.36342i
$944$	436.435	+	385.698i	0.462325	+	0.408579i
$945$	6.93116			0.00733456
$946$	−562.990	−	363.757i	−0.595127	−	0.384521i
$947$			553.561i			0.584541i	0.956336	+	0.292271i	$0.0944108\pi$
$947$			553.561i			0.584541i	−0.956336	+	0.292271i	$0.905589\pi$
$948$	−187.552	−	416.044i	−0.197839	−	0.438865i
$949$	1951.51			2.05639
$950$	−38.2466	+	59.1947i	−0.0402596	+	0.0623102i
$951$		−	761.053i		−	0.800266i
$952$	18.7684	+	2.83894i	0.0197147	+	0.00298208i
$953$	−1674.84			−1.75744			−0.878718	−	0.477342i	$-0.841600\pi$
$953$	−1674.84			−1.75744			−0.878718	+	0.477342i	$0.841600\pi$
$954$	12.8571	+	8.30720i	0.0134771	+	0.00870776i
$955$		−	297.753i		−	0.311783i
$956$	268.728	−	121.142i	0.281096	−	0.126717i
$957$	−573.371			−0.599134
$958$	−215.902	+	334.154i	−0.225368	+	0.348804i
$959$			82.4162i			0.0859398i
$960$	−73.3093	+	236.782i	−0.0763638	+	0.246648i
$961$	−2550.57			−2.65408
$962$	212.791	+	137.488i	0.221196	+	0.142919i
$963$		−	248.428i		−	0.257973i
$964$	51.5692	+	114.396i	0.0534950	+	0.118668i
$965$	−304.656			−0.315706
$966$	−35.9757	+	55.6799i	−0.0372419	+	0.0576396i
$967$		−	786.720i		−	0.813568i	−0.913524	−	0.406784i	$-0.866650\pi$
$967$		−	786.720i		−	0.813568i	0.913524	−	0.406784i	$-0.133350\pi$
$968$	−41.7435	+	275.969i	−0.0431234	+	0.285092i
$969$	48.5524			0.0501057
$970$	349.753	+	225.981i	0.360570	+	0.232970i
$971$			1289.75i			1.32827i	0.747612	+	0.664135i	$0.231200\pi$
$971$			1289.75i			1.32827i	−0.747612	+	0.664135i	$0.768800\pi$
$972$	56.8448	−	25.6255i	0.0584823	−	0.0263637i
$973$	17.8710			0.0183669
$974$	222.246	−	343.972i	0.228178	−	0.353154i
$975$			203.617i			0.208838i
$976$	92.5210	−	104.692i	0.0947961	−	0.107266i
$977$	495.847			0.507520			0.253760	−	0.967267i	$-0.418333\pi$
$977$	495.847			0.507520			0.253760	+	0.967267i	$0.418333\pi$
$978$	281.876	+	182.125i	0.288217	+	0.186222i
$979$			1210.68i			1.23665i
$980$	178.807	+	396.646i	0.182456	+	0.404741i
$981$	22.1051			0.0225332
$982$	−855.933	+	1324.74i	−0.871622	+	1.34902i
$983$		−	967.035i		−	0.983759i	−0.870663	−	0.491880i	$-0.836310\pi$
$983$		−	967.035i		−	0.983759i	0.870663	−	0.491880i	$-0.163690\pi$
$984$	549.106	+	83.0585i	0.558035	+	0.0844091i
$985$	167.469			0.170019
$986$	238.358	+	154.007i	0.241742	+	0.156194i
$987$		−	76.4730i		−	0.0774803i
$988$	604.241	−	272.390i	0.611580	−	0.275698i
$989$	−1158.57			−1.17145
$990$	−67.5649	+	104.571i	−0.0682473	+	0.105627i
$991$		−	1203.68i		−	1.21461i	−0.794469	−	0.607305i	$-0.792251\pi$
$991$		−	1203.68i		−	1.21461i	0.794469	−	0.607305i	$-0.207749\pi$
$992$	−511.994	−	1825.84i	−0.516123	−	1.84057i
$993$	831.249			0.837109
$994$	59.3417	+	38.3416i	0.0596999	+	0.0385730i
$995$		−	562.605i		−	0.565432i
$996$	−369.888	−	820.519i	−0.371373	−	0.823814i
$997$	−1274.55			−1.27838			−0.639192	−	0.769047i	$-0.720731\pi$
$997$	−1274.55			−1.27838			−0.639192	+	0.769047i	$0.720731\pi$
$998$	−803.603	+	1243.74i	−0.805214	+	1.24624i
$999$		−	27.9948i		−	0.0280228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.3.c.a.31.6	yes	8
3.2	odd	2		180.3.c.b.91.3		8
4.3	odd	2	inner	60.3.c.a.31.5	✓	8
5.2	odd	4		300.3.f.b.199.4		16
5.3	odd	4		300.3.f.b.199.13		16
5.4	even	2		300.3.c.d.151.3		8
8.3	odd	2		960.3.e.c.511.1		8
8.5	even	2		960.3.e.c.511.6		8
12.11	even	2		180.3.c.b.91.4		8
15.2	even	4		900.3.f.f.199.13		16
15.8	even	4		900.3.f.f.199.4		16
15.14	odd	2		900.3.c.u.451.6		8
20.3	even	4		300.3.f.b.199.3		16
20.7	even	4		300.3.f.b.199.14		16
20.19	odd	2		300.3.c.d.151.4		8
24.5	odd	2		2880.3.e.j.2431.6		8
24.11	even	2		2880.3.e.j.2431.7		8
60.23	odd	4		900.3.f.f.199.14		16
60.47	odd	4		900.3.f.f.199.3		16
60.59	even	2		900.3.c.u.451.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.c.a.31.5	✓	8	4.3	odd	2	inner
60.3.c.a.31.6	yes	8	1.1	even	1	trivial
180.3.c.b.91.3		8	3.2	odd	2
180.3.c.b.91.4		8	12.11	even	2
300.3.c.d.151.3		8	5.4	even	2
300.3.c.d.151.4		8	20.19	odd	2
300.3.f.b.199.3		16	20.3	even	4
300.3.f.b.199.4		16	5.2	odd	4
300.3.f.b.199.13		16	5.3	odd	4
300.3.f.b.199.14		16	20.7	even	4
900.3.c.u.451.5		8	60.59	even	2
900.3.c.u.451.6		8	15.14	odd	2
900.3.f.f.199.3		16	60.47	odd	4
900.3.f.f.199.4		16	15.8	even	4
900.3.f.f.199.13		16	15.2	even	4
900.3.f.f.199.14		16	60.23	odd	4
960.3.e.c.511.1		8	8.3	odd	2
960.3.e.c.511.6		8	8.5	even	2
2880.3.e.j.2431.6		8	24.5	odd	2
2880.3.e.j.2431.7		8	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	60.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.67986 + 1.08539i) q^{2} -1.73205i q^{3} +(1.64388 + 3.64660i) q^{4} +2.23607 q^{5} +(1.87994 - 2.90961i) q^{6} -0.596540i q^{7} +(-1.19648 + 7.91002i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(1.67986 + 1.08539i) q^{2} -1.73205i q^{3} +(1.64388 + 3.64660i) q^{4} +2.23607 q^{5} +(1.87994 - 2.90961i) q^{6} -0.596540i q^{7} +(-1.19648 + 7.91002i) q^{8} -3.00000 q^{9} +(3.75629 + 2.42700i) q^{10} -9.27963i q^{11} +(6.31609 - 2.84728i) q^{12} -23.5117 q^{13} +(0.647476 - 1.00210i) q^{14} -3.87298i q^{15} +(-10.5953 + 11.9891i) q^{16} +3.97751 q^{17} +(-5.03959 - 3.25616i) q^{18} +7.04756i q^{19} +(3.67582 + 8.15404i) q^{20} -1.03324 q^{21} +(10.0720 - 15.5885i) q^{22} -32.0793i q^{23} +(13.7006 + 2.07237i) q^{24} +5.00000 q^{25} +(-39.4964 - 25.5192i) q^{26} +5.19615i q^{27} +(2.17534 - 0.980637i) q^{28} +35.6734 q^{29} +(4.20368 - 6.50608i) q^{30} +59.2585i q^{31} +(-30.8115 + 8.64000i) q^{32} -16.0728 q^{33} +(6.68167 + 4.31713i) q^{34} -1.33390i q^{35} +(-4.93163 - 10.9398i) q^{36} -5.38761 q^{37} +(-7.64932 + 11.8389i) q^{38} +40.7234i q^{39} +(-2.67541 + 17.6873i) q^{40} +40.0791 q^{41} +(-1.73570 - 1.12146i) q^{42} -36.1157i q^{43} +(33.8391 - 15.2545i) q^{44} -6.70820 q^{45} +(34.8184 - 53.8888i) q^{46} +74.0131i q^{47} +(20.7657 + 18.3517i) q^{48} +48.6441 q^{49} +(8.39931 + 5.42693i) q^{50} -6.88925i q^{51} +(-38.6503 - 85.7376i) q^{52} -2.55123 q^{53} +(-5.63983 + 8.72882i) q^{54} -20.7499i q^{55} +(4.71864 + 0.713748i) q^{56} +12.2067 q^{57} +(59.9265 + 38.7194i) q^{58} -36.4026i q^{59} +(14.1232 - 6.36670i) q^{60} -8.73223 q^{61} +(-64.3183 + 99.5461i) q^{62} +1.78962i q^{63} +(-61.1369 - 18.9284i) q^{64} -52.5737 q^{65} +(-27.0001 - 17.4452i) q^{66} -69.7379i q^{67} +(6.53853 + 14.5044i) q^{68} -55.5630 q^{69} +(1.44780 - 2.24077i) q^{70} +59.2170i q^{71} +(3.58944 - 23.7301i) q^{72} -83.0019 q^{73} +(-9.05044 - 5.84763i) q^{74} -8.66025i q^{75} +(-25.6996 + 11.5853i) q^{76} -5.53566 q^{77} +(-44.2006 + 68.4098i) q^{78} -65.8705i q^{79} +(-23.6919 + 26.8085i) q^{80} +9.00000 q^{81} +(67.3274 + 43.5013i) q^{82} -129.909i q^{83} +(-1.69851 - 3.76780i) q^{84} +8.89398 q^{85} +(39.1995 - 60.6695i) q^{86} -61.7882i q^{87} +(73.4020 + 11.1029i) q^{88} -130.466 q^{89} +(-11.2689 - 7.28099i) q^{90} +14.0256i q^{91} +(116.980 - 52.7344i) q^{92} +102.639 q^{93} +(-80.3327 + 124.332i) q^{94} +15.7588i q^{95} +(14.9649 + 53.3671i) q^{96} +93.1113 q^{97} +(81.7155 + 52.7977i) q^{98} +27.8389i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 10 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + 10 * q^4 - 6 * q^6 - 20 * q^8 - 24 * q^9	\( 8 q + 4 q^{2} + 10 q^{4} - 6 q^{6} - 20 q^{8} - 24 q^{9} + 10 q^{10} + 16 q^{13} - 20 q^{14} + 34 q^{16} - 12 q^{18} - 40 q^{20} - 48 q^{21} + 68 q^{22} + 18 q^{24} + 40 q^{25} - 36 q^{26} + 28 q^{28} + 64 q^{29} - 76 q^{32} - 92 q^{34} - 30 q^{36} - 112 q^{37} - 40 q^{38} - 10 q^{40} - 16 q^{41} + 108 q^{42} + 172 q^{44} + 152 q^{46} + 48 q^{48} - 56 q^{49} + 20 q^{50} - 128 q^{52} + 352 q^{53} + 18 q^{54} + 116 q^{56} + 144 q^{57} - 204 q^{58} + 30 q^{60} - 176 q^{61} - 56 q^{62} - 110 q^{64} - 80 q^{65} + 108 q^{66} - 184 q^{68} - 96 q^{69} - 60 q^{70} + 60 q^{72} - 240 q^{73} + 132 q^{74} - 24 q^{76} - 288 q^{77} - 240 q^{78} - 80 q^{80} + 72 q^{81} + 40 q^{82} - 36 q^{84} + 160 q^{85} - 200 q^{86} + 140 q^{88} + 80 q^{89} - 30 q^{90} + 144 q^{92} + 144 q^{93} - 96 q^{94} - 174 q^{96} + 432 q^{97} + 660 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 + 10 * q^4 - 6 * q^6 - 20 * q^8 - 24 * q^9 + 10 * q^10 + 16 * q^13 - 20 * q^14 + 34 * q^16 - 12 * q^18 - 40 * q^20 - 48 * q^21 + 68 * q^22 + 18 * q^24 + 40 * q^25 - 36 * q^26 + 28 * q^28 + 64 * q^29 - 76 * q^32 - 92 * q^34 - 30 * q^36 - 112 * q^37 - 40 * q^38 - 10 * q^40 - 16 * q^41 + 108 * q^42 + 172 * q^44 + 152 * q^46 + 48 * q^48 - 56 * q^49 + 20 * q^50 - 128 * q^52 + 352 * q^53 + 18 * q^54 + 116 * q^56 + 144 * q^57 - 204 * q^58 + 30 * q^60 - 176 * q^61 - 56 * q^62 - 110 * q^64 - 80 * q^65 + 108 * q^66 - 184 * q^68 - 96 * q^69 - 60 * q^70 + 60 * q^72 - 240 * q^73 + 132 * q^74 - 24 * q^76 - 288 * q^77 - 240 * q^78 - 80 * q^80 + 72 * q^81 + 40 * q^82 - 36 * q^84 + 160 * q^85 - 200 * q^86 + 140 * q^88 + 80 * q^89 - 30 * q^90 + 144 * q^92 + 144 * q^93 - 96 * q^94 - 174 * q^96 + 432 * q^97 + 660 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more