LMFDB - Embedded newform 56.3.g.a.43.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,3,Mod(43,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("56.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	56.g (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:	$1.52588948042$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 6x^{2} + 16 $ x^4 + 6*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			43.4
Root			$0.707107 + 1.87083i$ of defining polynomial
Character	$\chi$	$=$	56.43
Dual form			56.3.g.a.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.87083i) q^{2} +3.41421 q^{3} +(-3.00000 + 2.64575i) q^{4} -1.54985i q^{5} +(2.41421 + 6.38741i) q^{6} -2.64575i q^{7} +(-7.07107 - 3.74166i) q^{8} +2.65685 q^{9} +O(q^{10})$	\(q+(0.707107 + 1.87083i) q^{2} +3.41421 q^{3} +(-3.00000 + 2.64575i) q^{4} -1.54985i q^{5} +(2.41421 + 6.38741i) q^{6} -2.64575i q^{7} +(-7.07107 - 3.74166i) q^{8} +2.65685 q^{9} +(2.89949 - 1.09591i) q^{10} -4.48528 q^{11} +(-10.2426 + 9.03316i) q^{12} +1.54985i q^{13} +(4.94975 - 1.87083i) q^{14} -5.29150i q^{15} +(2.00000 - 15.8745i) q^{16} +23.6569 q^{17} +(1.87868 + 4.97052i) q^{18} -24.8701 q^{19} +(4.10051 + 4.64954i) q^{20} -9.03316i q^{21} +(-3.17157 - 8.39119i) q^{22} -35.2248i q^{23} +(-24.1421 - 12.7748i) q^{24} +22.5980 q^{25} +(-2.89949 + 1.09591i) q^{26} -21.6569 q^{27} +(7.00000 + 7.93725i) q^{28} +22.4499i q^{29} +(9.89949 - 3.74166i) q^{30} +46.7156i q^{31} +(31.1127 - 7.48331i) q^{32} -15.3137 q^{33} +(16.7279 + 44.2579i) q^{34} -4.10051 q^{35} +(-7.97056 + 7.02938i) q^{36} +58.5826i q^{37} +(-17.5858 - 46.5276i) q^{38} +5.29150i q^{39} +(-5.79899 + 10.9591i) q^{40} -26.9706 q^{41} +(16.8995 - 6.38741i) q^{42} -17.1716 q^{43} +(13.4558 - 11.8669i) q^{44} -4.11771i q^{45} +(65.8995 - 24.9077i) q^{46} +36.1326i q^{47} +(6.82843 - 54.1990i) q^{48} -7.00000 q^{49} +(15.9792 + 42.2769i) q^{50} +80.7696 q^{51} +(-4.10051 - 4.64954i) q^{52} -97.8149i q^{53} +(-15.3137 - 40.5163i) q^{54} +6.95149i q^{55} +(-9.89949 + 18.7083i) q^{56} -84.9117 q^{57} +(-42.0000 + 15.8745i) q^{58} +61.5563 q^{59} +(14.0000 + 15.8745i) q^{60} +37.6825i q^{61} +(-87.3970 + 33.0329i) q^{62} -7.02938i q^{63} +(36.0000 + 52.9150i) q^{64} +2.40202 q^{65} +(-10.8284 - 28.6493i) q^{66} -33.3726 q^{67} +(-70.9706 + 62.5902i) q^{68} -120.265i q^{69} +(-2.89949 - 7.67134i) q^{70} -102.199i q^{71} +(-18.7868 - 9.94104i) q^{72} +69.3137 q^{73} +(-109.598 + 41.4241i) q^{74} +77.1543 q^{75} +(74.6102 - 65.8000i) q^{76} +11.8669i q^{77} +(-9.89949 + 3.74166i) q^{78} -38.7005i q^{79} +(-24.6030 - 3.09969i) q^{80} -97.8528 q^{81} +(-19.0711 - 50.4573i) q^{82} +3.61522 q^{83} +(23.8995 + 27.0995i) q^{84} -36.6645i q^{85} +(-12.1421 - 32.1251i) q^{86} +76.6489i q^{87} +(31.7157 + 16.7824i) q^{88} +44.0589 q^{89} +(7.70354 - 2.91166i) q^{90} +4.10051 q^{91} +(93.1960 + 105.674i) q^{92} +159.497i q^{93} +(-67.5980 + 25.5496i) q^{94} +38.5447i q^{95} +(106.225 - 25.5496i) q^{96} +96.1076 q^{97} +(-4.94975 - 13.0958i) q^{98} -11.9167 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{9}+O(q^{10}) $ 4 * q + 8 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^9	$ 4 q + 8 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{9} - 28 q^{10} + 16 q^{11} - 24 q^{12} + 8 q^{16} + 72 q^{17} + 16 q^{18} + 8 q^{19} + 56 q^{20} - 24 q^{22} - 40 q^{24} - 68 q^{25} + 28 q^{26} - 64 q^{27} + 28 q^{28} - 16 q^{33} + 16 q^{34} - 56 q^{35} + 36 q^{36} - 76 q^{38} + 56 q^{40} - 40 q^{41} + 28 q^{42} - 80 q^{43} - 48 q^{44} + 224 q^{46} + 16 q^{48} - 28 q^{49} + 112 q^{50} + 176 q^{51} - 56 q^{52} - 16 q^{54} - 136 q^{57} - 168 q^{58} + 184 q^{59} + 56 q^{60} - 112 q^{62} + 144 q^{64} + 168 q^{65} - 32 q^{66} - 224 q^{67} - 216 q^{68} + 28 q^{70} - 160 q^{72} + 232 q^{73} - 280 q^{74} + 88 q^{75} - 24 q^{76} - 336 q^{80} - 52 q^{81} - 48 q^{82} + 88 q^{83} + 56 q^{84} + 8 q^{86} + 240 q^{88} + 312 q^{89} + 308 q^{90} + 56 q^{91} + 56 q^{92} - 112 q^{94} + 176 q^{96} - 136 q^{97} - 240 q^{99}+O(q^{100}) $ 4 * q + 8 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^9 - 28 * q^10 + 16 * q^11 - 24 * q^12 + 8 * q^16 + 72 * q^17 + 16 * q^18 + 8 * q^19 + 56 * q^20 - 24 * q^22 - 40 * q^24 - 68 * q^25 + 28 * q^26 - 64 * q^27 + 28 * q^28 - 16 * q^33 + 16 * q^34 - 56 * q^35 + 36 * q^36 - 76 * q^38 + 56 * q^40 - 40 * q^41 + 28 * q^42 - 80 * q^43 - 48 * q^44 + 224 * q^46 + 16 * q^48 - 28 * q^49 + 112 * q^50 + 176 * q^51 - 56 * q^52 - 16 * q^54 - 136 * q^57 - 168 * q^58 + 184 * q^59 + 56 * q^60 - 112 * q^62 + 144 * q^64 + 168 * q^65 - 32 * q^66 - 224 * q^67 - 216 * q^68 + 28 * q^70 - 160 * q^72 + 232 * q^73 - 280 * q^74 + 88 * q^75 - 24 * q^76 - 336 * q^80 - 52 * q^81 - 48 * q^82 + 88 * q^83 + 56 * q^84 + 8 * q^86 + 240 * q^88 + 312 * q^89 + 308 * q^90 + 56 * q^91 + 56 * q^92 - 112 * q^94 + 176 * q^96 - 136 * q^97 - 240 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	0.707107	+	1.87083i	0.353553	+	0.935414i
$2$	0.707107	+	1.87083i	0.353553	+	0.935414i
$3$	3.41421			1.13807			0.569036	−	0.822313i	$-0.307317\pi$
$3$	3.41421			1.13807			0.569036	+	0.822313i	$0.307317\pi$
$4$	−3.00000	+	2.64575i	−0.750000	+	0.661438i
$5$		−	1.54985i		−	0.309969i	−0.987917	−	0.154985i	$-0.950467\pi$
$5$		−	1.54985i		−	0.309969i	0.987917	−	0.154985i	$-0.0495328\pi$
$6$	2.41421	+	6.38741i	0.402369	+	1.06457i
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	−7.07107	−	3.74166i	−0.883883	−	0.467707i
$9$	2.65685			0.295206
$10$	2.89949	−	1.09591i	0.289949	−	0.109591i
$11$	−4.48528			−0.407753			−0.203876	−	0.978997i	$-0.565354\pi$
$11$	−4.48528			−0.407753			−0.203876	+	0.978997i	$0.565354\pi$
$12$	−10.2426	+	9.03316i	−0.853553	+	0.752763i
$13$			1.54985i			0.119219i	0.998222	+	0.0596094i	$0.0189855\pi$
$13$			1.54985i			0.119219i	−0.998222	+	0.0596094i	$0.981014\pi$
$14$	4.94975	−	1.87083i	0.353553	−	0.133631i
$15$		−	5.29150i		−	0.352767i
$16$	2.00000	−	15.8745i	0.125000	−	0.992157i
$17$	23.6569			1.39158			0.695790	−	0.718245i	$-0.255055\pi$
$17$	23.6569			1.39158			0.695790	+	0.718245i	$0.255055\pi$
$18$	1.87868	+	4.97052i	0.104371	+	0.276140i
$19$	−24.8701			−1.30895			−0.654475	−	0.756083i	$-0.727110\pi$
$19$	−24.8701			−1.30895			−0.654475	+	0.756083i	$0.727110\pi$
$20$	4.10051	+	4.64954i	0.205025	+	0.232477i
$21$		−	9.03316i		−	0.430150i
$22$	−3.17157	−	8.39119i	−0.144162	−	0.381418i
$23$		−	35.2248i		−	1.53151i	−0.643132	−	0.765756i	$-0.722365\pi$
$23$		−	35.2248i		−	1.53151i	0.643132	−	0.765756i	$-0.277635\pi$
$24$	−24.1421	−	12.7748i	−1.00592	−	0.532284i
$25$	22.5980			0.903919
$26$	−2.89949	+	1.09591i	−0.111519	+	0.0421502i
$27$	−21.6569			−0.802106
$28$	7.00000	+	7.93725i	0.250000	+	0.283473i
$29$			22.4499i			0.774136i	0.922051	+	0.387068i	$0.126512\pi$
$29$			22.4499i			0.774136i	−0.922051	+	0.387068i	$0.873488\pi$
$30$	9.89949	−	3.74166i	0.329983	−	0.124722i
$31$			46.7156i			1.50696i	0.657473	+	0.753478i	$0.271625\pi$
$31$			46.7156i			1.50696i	−0.657473	+	0.753478i	$0.728375\pi$
$32$	31.1127	−	7.48331i	0.972272	−	0.233854i
$33$	−15.3137			−0.464052
$34$	16.7279	+	44.2579i	0.491998	+	1.30170i
$35$	−4.10051			−0.117157
$36$	−7.97056	+	7.02938i	−0.221405	+	0.195260i
$37$			58.5826i			1.58331i	0.610966	+	0.791657i	$0.290781\pi$
$37$			58.5826i			1.58331i	−0.610966	+	0.791657i	$0.709219\pi$
$38$	−17.5858	−	46.5276i	−0.462784	−	1.22441i
$39$			5.29150i			0.135680i
$40$	−5.79899	+	10.9591i	−0.144975	+	0.273977i
$41$	−26.9706			−0.657819			−0.328909	−	0.944362i	$-0.606681\pi$
$41$	−26.9706			−0.657819			−0.328909	+	0.944362i	$0.606681\pi$
$42$	16.8995	−	6.38741i	0.402369	−	0.152081i
$43$	−17.1716			−0.399339			−0.199669	−	0.979863i	$-0.563987\pi$
$43$	−17.1716			−0.399339			−0.199669	+	0.979863i	$0.563987\pi$
$44$	13.4558	−	11.8669i	0.305815	−	0.269703i
$45$		−	4.11771i		−	0.0915047i
$46$	65.8995	−	24.9077i	1.43260	−	0.541471i
$47$			36.1326i			0.768780i	0.923171	+	0.384390i	$0.125588\pi$
$47$			36.1326i			0.768780i	−0.923171	+	0.384390i	$0.874412\pi$
$48$	6.82843	−	54.1990i	0.142259	−	1.12915i
$49$	−7.00000			−0.142857
$50$	15.9792	+	42.2769i	0.319584	+	0.845539i
$51$	80.7696			1.58372
$52$	−4.10051	−	4.64954i	−0.0788559	−	0.0894141i
$53$		−	97.8149i		−	1.84556i	−0.385322	−	0.922782i	$-0.625910\pi$
$53$		−	97.8149i		−	1.84556i	0.385322	−	0.922782i	$-0.374090\pi$
$54$	−15.3137	−	40.5163i	−0.283587	−	0.750301i
$55$			6.95149i			0.126391i
$56$	−9.89949	+	18.7083i	−0.176777	+	0.334077i
$57$	−84.9117			−1.48968
$58$	−42.0000	+	15.8745i	−0.724138	+	0.273698i
$59$	61.5563			1.04333			0.521664	−	0.853151i	$-0.325311\pi$
$59$	61.5563			1.04333			0.521664	+	0.853151i	$0.325311\pi$
$60$	14.0000	+	15.8745i	0.233333	+	0.264575i
$61$			37.6825i			0.617746i	0.951103	+	0.308873i	$0.0999518\pi$
$61$			37.6825i			0.617746i	−0.951103	+	0.308873i	$0.900048\pi$
$62$	−87.3970	+	33.0329i	−1.40963	+	0.532790i
$63$		−	7.02938i		−	0.111577i
$64$	36.0000	+	52.9150i	0.562500	+	0.826797i
$65$	2.40202			0.0369542
$66$	−10.8284	−	28.6493i	−0.164067	−	0.434081i
$67$	−33.3726			−0.498098			−0.249049	−	0.968491i	$-0.580118\pi$
$67$	−33.3726			−0.498098			−0.249049	+	0.968491i	$0.580118\pi$
$68$	−70.9706	+	62.5902i	−1.04368	+	0.920443i
$69$		−	120.265i		−	1.74297i
$70$	−2.89949	−	7.67134i	−0.0414214	−	0.109591i
$71$		−	102.199i		−	1.43942i	−0.694277	−	0.719708i	$-0.744276\pi$
$71$		−	102.199i		−	1.43942i	0.694277	−	0.719708i	$-0.255724\pi$
$72$	−18.7868	−	9.94104i	−0.260928	−	0.138070i
$73$	69.3137			0.949503			0.474751	−	0.880120i	$-0.342538\pi$
$73$	69.3137			0.949503			0.474751	+	0.880120i	$0.342538\pi$
$74$	−109.598	+	41.4241i	−1.48105	+	0.559786i
$75$	77.1543			1.02872
$76$	74.6102	−	65.8000i	0.981713	−	0.865789i
$77$			11.8669i			0.154116i
$78$	−9.89949	+	3.74166i	−0.126917	+	0.0479700i
$79$		−	38.7005i		−	0.489880i	−0.969538	−	0.244940i	$-0.921232\pi$
$79$		−	38.7005i		−	0.489880i	0.969538	−	0.244940i	$-0.0787682\pi$
$80$	−24.6030	−	3.09969i	−0.307538	−	0.0387461i
$81$	−97.8528			−1.20806
$82$	−19.0711	−	50.4573i	−0.232574	−	0.615333i
$83$	3.61522			0.0435569			0.0217785	−	0.999763i	$-0.493067\pi$
$83$	3.61522			0.0435569			0.0217785	+	0.999763i	$0.493067\pi$
$84$	23.8995	+	27.0995i	0.284518	+	0.322613i
$85$		−	36.6645i		−	0.431347i
$86$	−12.1421	−	32.1251i	−0.141188	−	0.373547i
$87$			76.6489i			0.881022i
$88$	31.7157	+	16.7824i	0.360406	+	0.190709i
$89$	44.0589			0.495044			0.247522	−	0.968882i	$-0.420384\pi$
$89$	44.0589			0.495044			0.247522	+	0.968882i	$0.420384\pi$
$90$	7.70354	−	2.91166i	0.0855948	−	0.0323518i
$91$	4.10051			0.0450605
$92$	93.1960	+	105.674i	1.01300	+	1.14863i
$93$			159.497i			1.71502i
$94$	−67.5980	+	25.5496i	−0.719127	+	0.271805i
$95$			38.5447i			0.405734i
$96$	106.225	−	25.5496i	1.10651	−	0.266142i
$97$	96.1076			0.990800			0.495400	−	0.868665i	$-0.335021\pi$
$97$	96.1076			0.990800			0.495400	+	0.868665i	$0.335021\pi$
$98$	−4.94975	−	13.0958i	−0.0505076	−	0.133631i
$99$	−11.9167			−0.120371
$100$	−67.7939	+	59.7886i	−0.677939	+	0.597886i
$101$		−	19.6162i		−	0.194219i	−0.995274	−	0.0971097i	$-0.969040\pi$
$101$		−	19.6162i		−	0.194219i	0.995274	−	0.0971097i	$-0.0309598\pi$
$102$	57.1127	+	151.106i	0.559928	+	1.48143i
$103$		−	43.0841i		−	0.418293i	−0.977884	−	0.209146i	$-0.932932\pi$
$103$		−	43.0841i		−	0.418293i	0.977884	−	0.209146i	$-0.0670685\pi$
$104$	5.79899	−	10.9591i	0.0557595	−	0.105376i
$105$	−14.0000			−0.133333
$106$	182.995	−	69.1656i	1.72637	−	0.652506i
$107$	15.5980			0.145776			0.0728878	−	0.997340i	$-0.476779\pi$
$107$	15.5980			0.145776			0.0728878	+	0.997340i	$0.476779\pi$
$108$	64.9706	−	57.2987i	0.601579	−	0.530543i
$109$		−	3.85180i		−	0.0353376i	−0.999844	−	0.0176688i	$-0.994376\pi$
$109$		−	3.85180i		−	0.0353376i	0.999844	−	0.0176688i	$-0.00562445\pi$
$110$	−13.0051	+	4.91545i	−0.118228	+	0.0446859i
$111$			200.013i			1.80192i
$112$	−42.0000	−	5.29150i	−0.375000	−	0.0472456i
$113$	−13.7746			−0.121899			−0.0609496	−	0.998141i	$-0.519413\pi$
$113$	−13.7746			−0.121899			−0.0609496	+	0.998141i	$0.519413\pi$
$114$	−60.0416	−	158.855i	−0.526681	−	1.39347i
$115$	−54.5929			−0.474721
$116$	−59.3970	−	67.3498i	−0.512043	−	0.580602i
$117$			4.11771i			0.0351941i
$118$	43.5269	+	115.161i	0.368872	+	0.975944i
$119$		−	62.5902i		−	0.525968i
$120$	−19.7990	+	37.4166i	−0.164992	+	0.311805i
$121$	−100.882			−0.833738
$122$	−70.4975	+	26.6455i	−0.577848	+	0.218406i
$123$	−92.0833			−0.748644
$124$	−123.598	−	140.147i	−0.996758	−	1.13022i
$125$		−	73.7695i		−	0.590156i
$126$	13.1508	−	4.97052i	0.104371	−	0.0394486i
$127$		−	125.025i		−	0.984445i	−0.870469	−	0.492223i	$-0.836185\pi$
$127$		−	125.025i		−	0.984445i	0.870469	−	0.492223i	$-0.163815\pi$
$128$	−73.5391	+	104.766i	−0.574524	+	0.818488i
$129$	−58.6274			−0.454476
$130$	1.69848	+	4.49377i	0.0130653	+	0.0345674i
$131$	100.350			0.766033			0.383016	−	0.923742i	$-0.374885\pi$
$131$	100.350			0.766033			0.383016	+	0.923742i	$0.374885\pi$
$132$	45.9411	−	40.5163i	0.348039	−	0.306941i
$133$			65.8000i			0.494737i
$134$	−23.5980	−	62.4344i	−0.176104	−	0.465928i
$135$			33.5648i			0.248628i
$136$	−167.279	−	88.5158i	−1.22999	−	0.650852i
$137$	57.3137			0.418348			0.209174	−	0.977878i	$-0.432922\pi$
$137$	57.3137			0.418348			0.209174	+	0.977878i	$0.432922\pi$
$138$	224.995	−	85.0401i	1.63040	−	0.616233i
$139$	−183.664			−1.32132			−0.660662	−	0.750684i	$-0.729724\pi$
$139$	−183.664			−1.32132			−0.660662	+	0.750684i	$0.729724\pi$
$140$	12.3015	−	10.8489i	0.0878680	−	0.0774923i
$141$			123.365i			0.874926i
$142$	191.196	−	72.2653i	1.34645	−	0.508910i
$143$		−	6.95149i		−	0.0486118i
$144$	5.31371	−	42.1763i	0.0369008	−	0.292891i
$145$	34.7939			0.239958
$146$	49.0122	+	129.674i	0.335700	+	0.888179i
$147$	−23.8995			−0.162582
$148$	−154.995	−	175.748i	−1.04726	−	1.18748i
$149$		−	192.310i		−	1.29067i	−0.763900	−	0.645335i	$-0.776718\pi$
$149$		−	192.310i		−	1.29067i	0.763900	−	0.645335i	$-0.223282\pi$
$150$	54.5563	+	144.343i	0.363709	+	0.962284i
$151$			114.753i			0.759954i	0.924996	+	0.379977i	$0.124068\pi$
$151$			114.753i			0.759954i	−0.924996	+	0.379977i	$0.875932\pi$
$152$	175.858	+	93.0552i	1.15696	+	0.612205i
$153$	62.8528			0.410803
$154$	−22.2010	+	8.39119i	−0.144162	+	0.0544883i
$155$	72.4020			0.467110
$156$	−14.0000	−	15.8745i	−0.0897436	−	0.101760i
$157$			212.146i			1.35125i	0.737245	+	0.675625i	$0.236126\pi$
$157$			212.146i			1.35125i	−0.737245	+	0.675625i	$0.763874\pi$
$158$	72.4020	−	27.3654i	0.458241	−	0.173199i
$159$		−	333.961i		−	2.10038i
$160$	−11.5980	−	48.2199i	−0.0724874	−	0.301374i
$161$	−93.1960			−0.578857
$162$	−69.1924	−	183.066i	−0.427114	−	1.13004i
$163$	−240.534			−1.47567			−0.737835	−	0.674982i	$-0.764152\pi$
$163$	−240.534			−1.47567			−0.737835	+	0.674982i	$0.764152\pi$
$164$	80.9117	−	71.3574i	0.493364	−	0.435106i
$165$			23.7339i			0.143842i
$166$	2.55635	+	6.76346i	0.0153997	+	0.0407438i
$167$			212.101i			1.27006i	0.772486	+	0.635032i	$0.219013\pi$
$167$			212.101i			1.27006i	−0.772486	+	0.635032i	$0.780987\pi$
$168$	−33.7990	+	63.8741i	−0.201184	+	0.380203i
$169$	166.598			0.985787
$170$	68.5929	−	25.9257i	0.403488	−	0.152504i
$171$	−66.0761			−0.386410
$172$	51.5147	−	45.4317i	0.299504	−	0.264138i
$173$			182.213i			1.05325i	0.850096	+	0.526627i	$0.176544\pi$
$173$			182.213i			1.05325i	−0.850096	+	0.526627i	$0.823456\pi$
$174$	−143.397	+	54.1990i	−0.824121	+	0.311488i
$175$		−	59.7886i		−	0.341649i
$176$	−8.97056	+	71.2016i	−0.0509691	+	0.404555i
$177$	210.167			1.18738
$178$	31.1543	+	82.4266i	0.175024	+	0.463071i
$179$	57.2061			0.319587			0.159793	−	0.987150i	$-0.448917\pi$
$179$	57.2061			0.319587			0.159793	+	0.987150i	$0.448917\pi$
$180$	10.8944	+	12.3531i	0.0605247	+	0.0686285i
$181$		−	326.212i		−	1.80228i	−0.433533	−	0.901138i	$-0.642733\pi$
$181$		−	326.212i		−	1.80228i	0.433533	−	0.901138i	$-0.357267\pi$
$182$	2.89949	+	7.67134i	0.0159313	+	0.0421502i
$183$			128.656i			0.703039i
$184$	−131.799	+	249.077i	−0.716299	+	1.35368i
$185$	90.7939			0.490778
$186$	−298.392	+	112.782i	−1.60426	+	0.606352i
$187$	−106.108			−0.567421
$188$	−95.5980	−	108.398i	−0.508500	−	0.576585i
$189$			57.2987i			0.303167i
$190$	−72.1106	+	27.2552i	−0.379530	+	0.143449i
$191$		−	97.0628i		−	0.508182i	−0.967180	−	0.254091i	$-0.918224\pi$
$191$		−	97.0628i		−	0.508182i	0.967180	−	0.254091i	$-0.0817763\pi$
$192$	122.912	+	180.663i	0.640165	+	0.940954i
$193$	157.304			0.815045			0.407522	−	0.913195i	$-0.366393\pi$
$193$	157.304			0.815045			0.407522	+	0.913195i	$0.366393\pi$
$194$	67.9584	+	179.801i	0.350301	+	0.926809i
$195$	8.20101			0.0420565
$196$	21.0000	−	18.5203i	0.107143	−	0.0944911i
$197$			124.117i			0.630034i	0.949086	+	0.315017i	$0.102010\pi$
$197$			124.117i			0.630034i	−0.949086	+	0.315017i	$0.897990\pi$
$198$	−8.42641	−	22.2942i	−0.0425576	−	0.112597i
$199$		−	180.975i		−	0.909421i	−0.890639	−	0.454710i	$-0.849743\pi$
$199$		−	180.975i		−	0.909421i	0.890639	−	0.454710i	$-0.150257\pi$
$200$	−159.792	−	84.5539i	−0.798959	−	0.422769i
$201$	−113.941			−0.566871
$202$	36.6985	−	13.8707i	0.181676	−	0.0686669i
$203$	59.3970			0.292596
$204$	−242.309	+	213.696i	−1.18779	+	1.04753i
$205$			41.8002i			0.203903i
$206$	80.6030	−	30.4651i	0.391277	−	0.147889i
$207$		−	93.5871i		−	0.452111i
$208$	24.6030	+	3.09969i	0.118284	+	0.0149024i
$209$	111.549			0.533728
$210$	−9.89949	−	26.1916i	−0.0471405	−	0.124722i
$211$	164.049			0.777482			0.388741	−	0.921347i	$-0.372910\pi$
$211$	164.049			0.777482			0.388741	+	0.921347i	$0.372910\pi$
$212$	258.794	+	293.445i	1.22073	+	1.38417i
$213$		−	348.928i		−	1.63816i
$214$	11.0294	+	29.1811i	0.0515394	+	0.136361i
$215$			26.6133i			0.123783i
$216$	153.137	+	81.0325i	0.708968	+	0.375151i
$217$	123.598			0.569576
$218$	7.20606	−	2.72363i	0.0330553	−	0.0124937i
$219$	236.652			1.08060
$220$	−18.3919	−	20.8545i	−0.0835996	−	0.0947931i
$221$			36.6645i			0.165903i
$222$	−374.191	+	141.431i	−1.68554	+	0.637076i
$223$		−	10.5830i		−	0.0474574i	−0.999718	−	0.0237287i	$-0.992446\pi$
$223$		−	10.5830i		−	0.0474574i	0.999718	−	0.0237287i	$-0.00755379\pi$
$224$	−19.7990	−	82.3165i	−0.0883883	−	0.367484i
$225$	60.0395			0.266842
$226$	−9.74012	−	25.7699i	−0.0430979	−	0.114026i
$227$	105.806			0.466106			0.233053	−	0.972464i	$-0.425128\pi$
$227$	105.806			0.466106			0.233053	+	0.972464i	$0.425128\pi$
$228$	254.735	−	224.655i	1.11726	−	0.985330i
$229$		−	74.8788i		−	0.326982i	−0.986545	−	0.163491i	$-0.947725\pi$
$229$		−	74.8788i		−	0.326982i	0.986545	−	0.163491i	$-0.0522754\pi$
$230$	−38.6030	−	102.134i	−0.167839	−	0.444061i
$231$			40.5163i			0.175395i
$232$	84.0000	−	158.745i	0.362069	−	0.684246i
$233$	−419.137			−1.79887			−0.899436	−	0.437053i	$-0.856022\pi$
$233$	−419.137			−1.79887			−0.899436	+	0.437053i	$0.856022\pi$
$234$	−7.70354	+	2.91166i	−0.0329211	+	0.0124430i
$235$	56.0000			0.238298
$236$	−184.669	+	162.863i	−0.782496	+	0.690097i
$237$		−	132.132i		−	0.557518i
$238$	117.095	−	44.2579i	0.491998	−	0.185958i
$239$			148.318i			0.620577i	0.950642	+	0.310288i	$0.100426\pi$
$239$			148.318i			0.620577i	−0.950642	+	0.310288i	$0.899574\pi$
$240$	−84.0000	−	10.5830i	−0.350000	−	0.0440959i
$241$	−459.872			−1.90818			−0.954092	−	0.299515i	$-0.903175\pi$
$241$	−459.872			−1.90818			−0.954092	+	0.299515i	$0.903175\pi$
$242$	−71.3345	−	188.733i	−0.294771	−	0.779890i
$243$	−139.179			−0.572752
$244$	−99.6985	−	113.047i	−0.408600	−	0.463309i
$245$			10.8489i			0.0442813i
$246$	−65.1127	−	172.272i	−0.264686	−	0.700293i
$247$		−	38.5447i		−	0.156052i
$248$	174.794	−	330.329i	0.704814	−	1.33197i
$249$	12.3431			0.0495709
$250$	138.010	−	52.1629i	0.552040	−	0.208652i
$251$	124.919			0.497685			0.248842	−	0.968544i	$-0.419950\pi$
$251$	124.919			0.497685			0.248842	+	0.968544i	$0.419950\pi$
$252$	18.5980	+	21.0881i	0.0738015	+	0.0836830i
$253$			157.993i			0.624478i
$254$	233.899	−	88.4057i	0.920864	−	0.348054i
$255$		−	125.180i		−	0.490903i
$256$	−248.000	−	63.4980i	−0.968750	−	0.248039i
$257$	−427.352			−1.66285			−0.831425	−	0.555637i	$-0.812474\pi$
$257$	−427.352			−1.66285			−0.831425	+	0.555637i	$0.812474\pi$
$258$	−41.4558	−	109.682i	−0.160682	−	0.425123i
$259$	154.995			0.598436
$260$	−7.20606	+	6.35515i	−0.0277156	+	0.0244429i
$261$			59.6462i			0.228530i
$262$	70.9584	+	187.738i	0.270833	+	0.716558i
$263$			257.624i			0.979558i	0.871847	+	0.489779i	$0.162922\pi$
$263$			257.624i			0.979558i	−0.871847	+	0.489779i	$0.837078\pi$
$264$	108.284	+	57.2987i	0.410168	+	0.217040i
$265$	−151.598			−0.572068
$266$	−123.101	+	46.5276i	−0.462784	+	0.174916i
$267$	150.426			0.563395
$268$	100.118	−	88.2956i	0.373574	−	0.329461i
$269$		−	215.246i		−	0.800171i	−0.916478	−	0.400085i	$-0.868980\pi$
$269$		−	215.246i		−	0.800171i	0.916478	−	0.400085i	$-0.131020\pi$
$270$	−62.7939	+	23.7339i	−0.232570	+	0.0879033i
$271$			378.549i			1.39686i	0.715678	+	0.698431i	$0.246118\pi$
$271$			378.549i			1.39686i	−0.715678	+	0.698431i	$0.753882\pi$
$272$	47.3137	−	375.541i	0.173947	−	1.38067i
$273$	14.0000			0.0512821
$274$	40.5269	+	107.224i	0.147908	+	0.391329i
$275$	−101.358			−0.368576
$276$	318.191	+	360.795i	1.15287	+	1.30723i
$277$		−	166.449i		−	0.600898i	−0.953798	−	0.300449i	$-0.902864\pi$
$277$		−	166.449i		−	0.600898i	0.953798	−	0.300449i	$-0.0971365\pi$
$278$	−129.870	−	343.604i	−0.467158	−	1.23599i
$279$			124.117i			0.444863i
$280$	28.9949	+	15.3427i	0.103553	+	0.0547953i
$281$	−421.765			−1.50094			−0.750471	−	0.660904i	$-0.770173\pi$
$281$	−421.765			−1.50094			−0.750471	+	0.660904i	$0.770173\pi$
$282$	−230.794	+	87.2319i	−0.818418	+	0.309333i
$283$	−345.439			−1.22063			−0.610316	−	0.792158i	$-0.708957\pi$
$283$	−345.439			−1.22063			−0.610316	+	0.792158i	$0.708957\pi$
$284$	270.392	+	306.596i	0.952084	+	1.07956i
$285$			131.600i			0.461754i
$286$	13.0051	−	4.91545i	0.0454722	−	0.0171869i
$287$			71.3574i			0.248632i
$288$	82.6619	−	19.8821i	0.287021	−	0.0690350i
$289$	270.647			0.936494
$290$	24.6030	+	65.0935i	0.0848380	+	0.224460i
$291$	328.132			1.12760
$292$	−207.941	+	183.387i	−0.712127	+	0.628037i
$293$			511.038i			1.74416i	0.489365	+	0.872079i	$0.337229\pi$
$293$			511.038i			1.74416i	−0.489365	+	0.872079i	$0.662771\pi$
$294$	−16.8995	−	44.7119i	−0.0574813	−	0.152081i
$295$		−	95.4028i		−	0.323399i
$296$	219.196	−	414.241i	0.740527	−	1.39946i
$297$	97.1371			0.327061
$298$	359.779	−	135.984i	1.20731	−	0.456321i
$299$	54.5929			0.182585
$300$	−231.463	+	204.131i	−0.771543	+	0.680437i
$301$			45.4317i			0.150936i
$302$	−214.683	+	81.1427i	−0.710872	+	0.268684i
$303$		−	66.9738i		−	0.221036i
$304$	−49.7401	+	394.800i	−0.163619	+	1.29868i
$305$	58.4020			0.191482
$306$	44.4437	+	117.587i	0.145241	+	0.384271i
$307$	223.331			0.727462			0.363731	−	0.931504i	$-0.381503\pi$
$307$	223.331			0.727462			0.363731	+	0.931504i	$0.381503\pi$
$308$	−31.3970	−	35.6008i	−0.101938	−	0.115587i
$309$		−	147.098i		−	0.476047i
$310$	51.1960	+	135.452i	0.165148	+	0.436941i
$311$		−	12.3988i		−	0.0398674i	−0.999801	−	0.0199337i	$-0.993654\pi$
$311$		−	12.3988i		−	0.0398674i	0.999801	−	0.0199337i	$-0.00634551\pi$
$312$	19.7990	−	37.4166i	0.0634583	−	0.119925i
$313$	410.049			1.31006			0.655030	−	0.755603i	$-0.272656\pi$
$313$	410.049			1.31006			0.655030	+	0.755603i	$0.272656\pi$
$314$	−396.889	+	150.010i	−1.26398	+	0.477739i
$315$	−10.8944			−0.0345855
$316$	102.392	+	116.102i	0.324025	+	0.367410i
$317$		−	130.316i		−	0.411092i	−0.978647	−	0.205546i	$-0.934103\pi$
$317$		−	130.316i		−	0.411092i	0.978647	−	0.205546i	$-0.0658970\pi$
$318$	624.784	−	236.146i	1.96473	−	0.742598i
$319$		−	100.694i		−	0.315656i
$320$	82.0101	−	55.7944i	0.256282	−	0.174358i
$321$	53.2548			0.165903
$322$	−65.8995	−	174.354i	−0.204657	−	0.541471i
$323$	−588.347			−1.82151
$324$	293.558	−	258.894i	0.906045	−	0.799056i
$325$			35.0234i			0.107764i
$326$	−170.083	−	449.998i	−0.521728	−	1.38036i
$327$		−	13.1509i		−	0.0402167i
$328$	190.711	+	100.915i	0.581435	+	0.307666i
$329$	95.5980			0.290571
$330$	−44.4020	+	16.7824i	−0.134552	+	0.0508557i
$331$	214.260			0.647311			0.323655	−	0.946175i	$-0.395088\pi$
$331$	214.260			0.647311			0.323655	+	0.946175i	$0.395088\pi$
$332$	−10.8457	+	9.56498i	−0.0326677	+	0.0288102i
$333$			155.645i			0.467404i
$334$	−396.804	+	149.978i	−1.18804	+	0.449035i
$335$			51.7223i			0.154395i
$336$	−143.397	−	18.0663i	−0.426777	−	0.0537688i
$337$	164.049			0.486792			0.243396	−	0.969927i	$-0.421739\pi$
$337$	164.049			0.486792			0.243396	+	0.969927i	$0.421739\pi$
$338$	117.803	+	311.676i	0.348528	+	0.922119i
$339$	−47.0294			−0.138730
$340$	97.0051	+	109.993i	0.285309	+	0.323510i
$341$		−	209.533i		−	0.614466i
$342$	−46.7229	−	123.617i	−0.136617	−	0.361454i
$343$			18.5203i			0.0539949i
$344$	121.421	+	64.2501i	0.352969	+	0.186774i
$345$	−186.392			−0.540266
$346$	−340.889	+	128.844i	−0.985229	+	0.372382i
$347$	−109.691			−0.316113			−0.158057	−	0.987430i	$-0.550523\pi$
$347$	−109.691			−0.316113			−0.158057	+	0.987430i	$0.550523\pi$
$348$	−202.794	−	229.947i	−0.582741	−	0.660766i
$349$			463.479i			1.32802i	0.747723	+	0.664010i	$0.231147\pi$
$349$			463.479i			1.32802i	−0.747723	+	0.664010i	$0.768853\pi$
$350$	111.854	−	42.2769i	0.319584	−	0.120791i
$351$		−	33.5648i		−	0.0956261i
$352$	−139.549	+	33.5648i	−0.396447	+	0.0953545i
$353$	78.0975			0.221240			0.110620	−	0.993863i	$-0.464716\pi$
$353$	78.0975			0.221240			0.110620	+	0.993863i	$0.464716\pi$
$354$	148.610	+	393.186i	0.419803	+	1.11069i
$355$	−158.392			−0.446174
$356$	−132.177	+	116.569i	−0.371283	+	0.327441i
$357$		−	213.696i		−	0.598589i
$358$	40.4508	+	107.023i	0.112991	+	0.298946i
$359$		−	365.114i		−	1.01703i	−0.861053	−	0.508515i	$-0.830195\pi$
$359$		−	365.114i		−	1.01703i	0.861053	−	0.508515i	$-0.169805\pi$
$360$	−15.4071	+	29.1166i	−0.0427974	+	0.0808795i
$361$	257.520			0.713351
$362$	610.286	−	230.667i	1.68587	−	0.637200i
$363$	−344.434			−0.948853
$364$	−12.3015	+	10.8489i	−0.0337954	+	0.0298047i
$365$		−	107.426i		−	0.294316i
$366$	−240.693	+	90.9736i	−0.657632	+	0.248562i
$367$			220.739i			0.601468i	0.953708	+	0.300734i	$0.0972317\pi$
$367$			220.739i			0.601468i	−0.953708	+	0.300734i	$0.902768\pi$
$368$	−559.176	−	70.4495i	−1.51950	−	0.191439i
$369$	−71.6569			−0.194192
$370$	64.2010	+	169.860i	0.173516	+	0.459081i
$371$	−258.794			−0.697558
$372$	−421.990	−	478.492i	−1.13438	−	1.28627i
$373$			251.553i			0.674406i	0.941432	+	0.337203i	$0.109481\pi$
$373$			251.553i			0.674406i	−0.941432	+	0.337203i	$0.890519\pi$
$374$	−75.0294	−	198.509i	−0.200613	−	0.530773i
$375$		−	251.865i		−	0.671640i
$376$	135.196	−	255.496i	0.359564	−	0.679512i
$377$	−34.7939			−0.0922916
$378$	−107.196	+	40.5163i	−0.283587	+	0.107186i
$379$	286.024			0.754682			0.377341	−	0.926074i	$-0.376839\pi$
$379$	286.024			0.754682			0.377341	+	0.926074i	$0.376839\pi$
$380$	−101.980	−	115.634i	−0.268368	−	0.304301i
$381$		−	426.860i		−	1.12037i
$382$	181.588	−	68.6338i	0.475361	−	0.179670i
$383$		−	106.894i		−	0.279096i	−0.990215	−	0.139548i	$-0.955435\pi$
$383$		−	106.894i		−	0.279096i	0.990215	−	0.139548i	$-0.0445649\pi$
$384$	−251.078	+	357.695i	−0.653850	+	0.931497i
$385$	18.3919			0.0477712
$386$	111.230	+	294.288i	0.288162	+	0.762404i
$387$	−45.6224			−0.117887
$388$	−288.323	+	254.277i	−0.743100	+	0.655353i
$389$			77.1807i			0.198408i	0.995067	+	0.0992040i	$0.0316296\pi$
$389$			77.1807i			0.198408i	−0.995067	+	0.0992040i	$0.968370\pi$
$390$	5.79899	+	15.3427i	0.0148692	+	0.0393402i
$391$		−	833.307i		−	2.13122i
$392$	49.4975	+	26.1916i	0.126269	+	0.0668153i
$393$	342.617			0.871800
$394$	−232.201	+	87.7637i	−0.589343	+	0.222751i
$395$	−59.9798			−0.151848
$396$	35.7502	−	31.5287i	0.0902783	−	0.0796180i
$397$		−	657.514i		−	1.65621i	−0.560576	−	0.828103i	$-0.689420\pi$
$397$		−	657.514i		−	1.65621i	0.560576	−	0.828103i	$-0.310580\pi$
$398$	338.573	−	127.968i	0.850685	−	0.321529i
$399$			224.655i			0.563046i
$400$	45.1960	−	358.732i	0.112990	−	0.896830i
$401$	318.794			0.794997			0.397499	−	0.917603i	$-0.369878\pi$
$401$	318.794			0.794997			0.397499	+	0.917603i	$0.369878\pi$
$402$	−80.5685	−	213.164i	−0.200419	−	0.530260i
$403$	−72.4020			−0.179658
$404$	51.8995	+	58.8485i	0.128464	+	0.145665i
$405$			151.657i			0.374461i
$406$	42.0000	+	111.122i	0.103448	+	0.273698i
$407$		−	262.759i		−	0.645600i
$408$	−571.127	−	302.212i	−1.39982	−	0.740716i
$409$	145.265			0.355171			0.177585	−	0.984105i	$-0.443171\pi$
$409$	145.265			0.355171			0.177585	+	0.984105i	$0.443171\pi$
$410$	−78.2010	+	29.5572i	−0.190734	+	0.0720907i
$411$	195.681			0.476110
$412$	113.990	+	129.252i	0.276675	+	0.313719i
$413$		−	162.863i		−	0.394341i
$414$	175.085	−	66.1760i	0.422911	−	0.159846i
$415$		−	5.60304i		−	0.0135013i
$416$	11.5980	+	48.2199i	0.0278798	+	0.115913i
$417$	−627.068			−1.50376
$418$	78.8772	+	208.689i	0.188701	+	0.499257i
$419$	707.012			1.68738			0.843690	−	0.536831i	$-0.180379\pi$
$419$	707.012			1.68738			0.843690	+	0.536831i	$0.180379\pi$
$420$	42.0000	−	37.0405i	0.100000	−	0.0881917i
$421$		−	121.989i		−	0.289761i	−0.989449	−	0.144880i	$-0.953720\pi$
$421$		−	121.989i		−	0.289761i	0.989449	−	0.144880i	$-0.0462798\pi$
$422$	116.000	+	306.907i	0.274882	+	0.727268i
$423$			95.9992i			0.226948i
$424$	−365.990	+	691.656i	−0.863184	+	1.63126i
$425$	534.597			1.25788
$426$	652.784	−	246.729i	1.53236	−	0.579176i
$427$	99.6985			0.233486
$428$	−46.7939	+	41.2684i	−0.109332	+	0.0964214i
$429$		−	23.7339i		−	0.0553237i
$430$	−49.7889	+	18.8184i	−0.115788	+	0.0437638i
$431$			588.861i			1.36627i	0.730294	+	0.683133i	$0.239383\pi$
$431$			588.861i			1.36627i	−0.730294	+	0.683133i	$0.760617\pi$
$432$	−43.3137	+	343.792i	−0.100263	+	0.795815i
$433$	137.696			0.318004			0.159002	−	0.987278i	$-0.449172\pi$
$433$	137.696			0.318004			0.159002	+	0.987278i	$0.449172\pi$
$434$	87.3970	+	231.231i	0.201376	+	0.532790i
$435$	118.794			0.273090
$436$	10.1909	+	11.5554i	0.0233736	+	0.0265032i
$437$			876.042i			2.00467i
$438$	167.338	+	442.735i	0.382050	+	1.01081i
$439$			440.543i			1.00352i	0.865008	+	0.501758i	$0.167313\pi$
$439$			440.543i			1.00352i	−0.865008	+	0.501758i	$0.832687\pi$
$440$	26.0101	−	49.1545i	0.0591139	−	0.111715i
$441$	−18.5980			−0.0421723
$442$	−68.5929	+	25.9257i	−0.155188	+	0.0586554i
$443$	−487.058			−1.09945			−0.549727	−	0.835344i	$-0.685268\pi$
$443$	−487.058			−1.09945			−0.549727	+	0.835344i	$0.685268\pi$
$444$	−529.186	−	600.040i	−1.19186	−	1.35144i
$445$		−	68.2844i		−	0.153448i
$446$	19.7990	−	7.48331i	0.0443924	−	0.0167787i
$447$		−	656.587i		−	1.46887i
$448$	140.000	−	95.2470i	0.312500	−	0.212605i
$449$	264.039			0.588059			0.294030	−	0.955796i	$-0.405004\pi$
$449$	264.039			0.588059			0.294030	+	0.955796i	$0.405004\pi$
$450$	42.4544	+	112.324i	0.0943430	+	0.249608i
$451$	120.971			0.268227
$452$	41.3238	−	36.4442i	0.0914244	−	0.0806287i
$453$			391.791i			0.864882i
$454$	74.8162	+	197.945i	0.164793	+	0.436003i
$455$		−	6.35515i		−	0.0139674i
$456$	600.416	+	317.710i	1.31670	+	0.696733i
$457$	−514.323			−1.12543			−0.562717	−	0.826650i	$-0.690244\pi$
$457$	−514.323			−1.12543			−0.562717	+	0.826650i	$0.690244\pi$
$458$	140.085	−	52.9473i	0.305863	−	0.115605i
$459$	−512.333			−1.11619
$460$	163.779	−	144.439i	0.356041	−	0.313999i
$461$			202.224i			0.438664i	0.975650	+	0.219332i	$0.0703878\pi$
$461$			202.224i			0.438664i	−0.975650	+	0.219332i	$0.929612\pi$
$462$	−75.7990	+	28.6493i	−0.164067	+	0.0620115i
$463$			722.653i			1.56081i	0.625277	+	0.780403i	$0.284986\pi$
$463$			722.653i			1.56081i	−0.625277	+	0.780403i	$0.715014\pi$
$464$	356.382	+	44.8999i	0.768064	+	0.0967670i
$465$	247.196			0.531604
$466$	−296.375	−	784.134i	−0.635997	−	1.68269i
$467$	−347.282			−0.743645			−0.371822	−	0.928304i	$-0.621267\pi$
$467$	−347.282			−0.743645			−0.371822	+	0.928304i	$0.621267\pi$
$468$	−10.8944	−	12.3531i	−0.0232787	−	0.0263956i
$469$			88.2956i			0.188263i
$470$	39.5980	+	104.766i	0.0842510	+	0.222907i
$471$			724.313i			1.53782i
$472$	−435.269	−	230.323i	−0.922180	−	0.487972i
$473$	77.0193			0.162832
$474$	247.196	−	93.4313i	0.521510	−	0.197112i
$475$	−562.013			−1.18319
$476$	165.598	+	187.770i	0.347895	+	0.394476i
$477$		−	259.880i		−	0.544822i
$478$	−277.477	+	104.877i	−0.580496	+	0.219407i
$479$		−	29.1811i		−	0.0609210i	−0.999536	−	0.0304605i	$-0.990303\pi$
$479$		−	29.1811i		−	0.0609210i	0.999536	−	0.0304605i	$-0.00969737\pi$
$480$	−39.5980	−	164.633i	−0.0824958	−	0.342985i
$481$	−90.7939			−0.188761
$482$	−325.179	−	860.342i	−0.674645	−	1.78494i
$483$	−318.191			−0.658780
$484$	302.647	−	266.909i	0.625303	−	0.551466i
$485$		−	148.952i		−	0.307117i
$486$	−98.4142	−	260.380i	−0.202498	−	0.535760i
$487$		−	701.643i		−	1.44074i	−0.693588	−	0.720372i	$-0.743971\pi$
$487$		−	701.643i		−	1.44074i	0.693588	−	0.720372i	$-0.256029\pi$
$488$	140.995	−	266.455i	0.288924	−	0.546015i
$489$	−821.235			−1.67942
$490$	−20.2965	+	7.67134i	−0.0414214	+	0.0156558i
$491$	−59.9512			−0.122100			−0.0610501	−	0.998135i	$-0.519445\pi$
$491$	−59.9512			−0.122100			−0.0610501	+	0.998135i	$0.519445\pi$
$492$	276.250	−	243.629i	0.561483	−	0.495182i
$493$			531.095i			1.07727i
$494$	72.1106	−	27.2552i	0.145973	−	0.0551726i
$495$			18.4691i			0.0373113i
$496$	741.588	+	93.4313i	1.49514	+	0.188370i
$497$	−270.392			−0.544048
$498$	8.72792	+	23.0919i	0.0175259	+	0.0463693i
$499$	−84.2843			−0.168906			−0.0844532	−	0.996427i	$-0.526914\pi$
$499$	−84.2843			−0.168906			−0.0844532	+	0.996427i	$0.526914\pi$
$500$	195.176	+	221.309i	0.390352	+	0.442617i
$501$			724.157i			1.44542i
$502$	88.3310	+	233.702i	0.175958	+	0.465541i
$503$		−	409.987i		−	0.815083i	−0.913187	−	0.407542i	$-0.866386\pi$
$503$		−	409.987i		−	0.815083i	0.913187	−	0.407542i	$-0.133614\pi$
$504$	−26.3015	+	49.7052i	−0.0521855	+	0.0986214i
$505$	−30.4020			−0.0602020
$506$	−295.578	+	111.718i	−0.584146	+	0.220786i
$507$	568.801			1.12190
$508$	330.784	+	375.074i	0.651149	+	0.738334i
$509$		−	477.033i		−	0.937196i	−0.883411	−	0.468598i	$-0.844759\pi$
$509$		−	477.033i		−	0.937196i	0.883411	−	0.468598i	$-0.155241\pi$
$510$	234.191	−	88.5158i	0.459198	−	0.173560i
$511$		−	183.387i		−	0.358878i
$512$	−56.5685	−	508.865i	−0.110485	−	0.993878i
$513$	538.607			1.04992
$514$	−302.184	−	799.503i	−0.587906	−	1.55545i
$515$	−66.7737			−0.129658
$516$	175.882	−	155.114i	0.340857	−	0.300608i
$517$		−	162.065i		−	0.313472i
$518$	109.598	+	289.969i	0.211579	+	0.559786i
$519$			622.114i			1.19868i
$520$	−16.9848	−	8.98754i	−0.0326632	−	0.0172837i
$521$	210.873			0.404747			0.202373	−	0.979308i	$-0.435135\pi$
$521$	210.873			0.404747			0.202373	+	0.979308i	$0.435135\pi$
$522$	−111.588	+	42.1763i	−0.213770	+	0.0807974i
$523$	511.566			0.978139			0.489069	−	0.872245i	$-0.337337\pi$
$523$	511.566			0.978139			0.489069	+	0.872245i	$0.337337\pi$
$524$	−301.051	+	265.502i	−0.574525	+	0.506683i
$525$		−	204.131i		−	0.388821i
$526$	−481.970	+	182.167i	−0.916292	+	0.346326i
$527$			1105.15i			2.09705i
$528$	−30.6274	+	243.098i	−0.0580065	+	0.460412i
$529$	−711.784			−1.34553
$530$	−107.196	−	283.614i	−0.202257	−	0.535120i
$531$	163.546			0.307997
$532$	−174.090	−	197.400i	−0.327238	−	0.371053i
$533$		−	41.8002i		−	0.0784244i
$534$	106.368	+	281.422i	0.199190	+	0.527008i
$535$		−	24.1745i		−	0.0451859i
$536$	235.980	+	124.869i	0.440261	+	0.232964i
$537$	195.314			0.363713
$538$	402.688	−	152.202i	0.748491	−	0.282903i
$539$	31.3970			0.0582504
$540$	−88.8040	−	100.694i	−0.164452	−	0.186471i
$541$		−	342.417i		−	0.632933i	−0.948604	−	0.316466i	$-0.897504\pi$
$541$		−	342.417i		−	0.632933i	0.948604	−	0.316466i	$-0.102496\pi$
$542$	−708.201	+	267.675i	−1.30664	+	0.493865i
$543$		−	1113.76i		−	2.05112i
$544$	736.029	−	177.032i	1.35299	−	0.325426i
$545$	−5.96970			−0.0109536
$546$	9.89949	+	26.1916i	0.0181309	+	0.0479700i
$547$	−441.976			−0.807999			−0.404000	−	0.914759i	$-0.632380\pi$
$547$	−441.976			−0.807999			−0.404000	+	0.914759i	$0.632380\pi$
$548$	−171.941	+	151.638i	−0.313761	+	0.276711i
$549$			100.117i			0.182362i
$550$	−71.6711	−	189.624i	−0.130311	−	0.344771i
$551$		−	558.331i		−	1.01331i
$552$	−449.990	+	850.401i	−0.815199	+	1.54058i
$553$	−102.392			−0.185157
$554$	311.397	−	117.697i	0.562088	−	0.212449i
$555$	309.990			0.558540
$556$	550.992	−	485.929i	0.990993	−	0.873973i
$557$		−	365.710i		−	0.656571i	−0.944579	−	0.328285i	$-0.893529\pi$
$557$		−	365.710i		−	0.656571i	0.944579	−	0.328285i	$-0.106471\pi$
$558$	−232.201	+	87.7637i	−0.416131	+	0.157283i
$559$		−	26.6133i		−	0.0476087i
$560$	−8.20101	+	65.0935i	−0.0146447	+	0.116238i
$561$	−362.274			−0.645765
$562$	−298.233	−	789.049i	−0.530663	−	1.40400i
$563$	806.389			1.43231			0.716154	−	0.697943i	$-0.245901\pi$
$563$	806.389			1.43231			0.716154	+	0.697943i	$0.245901\pi$
$564$	−326.392	−	370.094i	−0.578709	−	0.656194i
$565$			21.3485i			0.0377850i
$566$	−244.262	−	646.256i	−0.431558	−	1.14180i
$567$			258.894i			0.456604i
$568$	−382.392	+	722.653i	−0.673225	+	1.27228i
$569$	222.891			0.391725			0.195862	−	0.980631i	$-0.437249\pi$
$569$	222.891			0.391725			0.195862	+	0.980631i	$0.437249\pi$
$570$	−246.201	+	93.0552i	−0.431932	+	0.163255i
$571$	573.082			1.00365			0.501823	−	0.864970i	$-0.332663\pi$
$571$	573.082			1.00365			0.501823	+	0.864970i	$0.332663\pi$
$572$	18.3919	+	20.8545i	0.0321537	+	0.0364589i
$573$		−	331.393i		−	0.578348i
$574$	−133.497	+	50.4573i	−0.232574	+	0.0879047i
$575$		−	796.008i		−	1.38436i
$576$	95.6468	+	140.588i	0.166053	+	0.244076i
$577$	−723.901			−1.25459			−0.627297	−	0.778780i	$-0.715839\pi$
$577$	−723.901			−1.25459			−0.627297	+	0.778780i	$0.715839\pi$
$578$	191.376	+	506.334i	0.331101	+	0.876010i
$579$	537.068			0.927579
$580$	−104.382	+	92.0561i	−0.179969	+	0.158717i
$581$		−	9.56498i		−	0.0164630i
$582$	232.024	+	613.879i	0.398667	+	1.05477i
$583$			438.727i			0.752534i
$584$	−490.122	−	259.348i	−0.839250	−	0.444089i
$585$	6.38182			0.0109091
$586$	−956.065	+	361.359i	−1.63151	+	0.616653i
$587$	21.1198			0.0359793			0.0179896	−	0.999838i	$-0.494273\pi$
$587$	21.1198			0.0359793			0.0179896	+	0.999838i	$0.494273\pi$
$588$	71.6985	−	63.2321i	0.121936	−	0.107538i
$589$		−	1161.82i		−	1.97253i
$590$	178.482	−	67.4600i	0.302512	−	0.114339i
$591$			423.761i			0.717023i
$592$	929.970	+	117.165i	1.57089	+	0.197914i
$593$	−128.745			−0.217108			−0.108554	−	0.994091i	$-0.534622\pi$
$593$	−128.745			−0.217108			−0.108554	+	0.994091i	$0.534622\pi$
$594$	68.6863	+	181.727i	0.115633	+	0.305937i
$595$	−97.0051			−0.163034
$596$	508.804	+	576.930i	0.853698	+	0.968003i
$597$		−	617.886i		−	1.03499i
$598$	38.6030	+	102.134i	0.0645536	+	0.170793i
$599$			324.130i			0.541119i	0.962703	+	0.270559i	$0.0872086\pi$
$599$			324.130i			0.541119i	−0.962703	+	0.270559i	$0.912791\pi$
$600$	−545.563	−	288.685i	−0.909272	−	0.481142i
$601$	−721.862			−1.20110			−0.600551	−	0.799587i	$-0.705052\pi$
$601$	−721.862			−1.20110			−0.600551	+	0.799587i	$0.705052\pi$
$602$	−84.9949	+	32.1251i	−0.141188	+	0.0533639i
$603$	−88.6661			−0.147042
$604$	−303.608	−	344.259i	−0.502662	−	0.569966i
$605$			156.352i			0.258433i
$606$	125.296	−	47.3576i	0.206760	−	0.0781479i
$607$			705.999i			1.16310i	0.813512	+	0.581548i	$0.197553\pi$
$607$			705.999i			1.16310i	−0.813512	+	0.581548i	$0.802447\pi$
$608$	−773.775	+	186.110i	−1.27266	+	0.306103i
$609$	202.794			0.332995
$610$	41.2965	+	109.260i	0.0676991	+	0.179115i
$611$	−56.0000			−0.0916530
$612$	−188.558	+	166.293i	−0.308102	+	0.271720i
$613$			21.8269i			0.0356066i	0.999842	+	0.0178033i	$0.00566727\pi$
$613$			21.8269i			0.0356066i	−0.999842	+	0.0178033i	$0.994333\pi$
$614$	157.919	+	417.814i	0.257197	+	0.680479i
$615$			142.715i			0.232057i
$616$	44.4020	−	83.9119i	0.0720812	−	0.136221i
$617$	−699.578			−1.13384			−0.566919	−	0.823774i	$-0.691865\pi$
$617$	−699.578			−1.13384			−0.566919	+	0.823774i	$0.691865\pi$
$618$	275.196	−	104.014i	0.445301	−	0.168308i
$619$	96.1981			0.155409			0.0777044	−	0.996976i	$-0.475241\pi$
$619$	96.1981			0.155409			0.0777044	+	0.996976i	$0.475241\pi$
$620$	−217.206	+	191.558i	−0.350332	+	0.308964i
$621$			762.858i			1.22843i
$622$	23.1960	−	8.76725i	0.0372925	−	0.0140953i
$623$		−	116.569i		−	0.187109i
$624$	84.0000	+	10.5830i	0.134615	+	0.0169599i
$625$	450.618			0.720989
$626$	289.948	+	767.131i	0.463176	+	1.22545i
$627$	380.853			0.607421
$628$	−561.286	−	636.439i	−0.893768	−	1.01344i
$629$			1385.88i			2.20331i
$630$	−7.70354	−	20.3816i	−0.0122278	−	0.0323518i
$631$			269.399i			0.426940i	0.976950	+	0.213470i	$0.0684766\pi$
$631$			269.399i			0.426940i	−0.976950	+	0.213470i	$0.931523\pi$
$632$	−144.804	+	273.654i	−0.229120	+	0.432997i
$633$	560.098			0.884830
$634$	243.799	−	92.1474i	0.384541	−	0.145343i
$635$	−193.769			−0.305148
$636$	883.578	+	1001.88i	1.38927	+	1.57529i
$637$		−	10.8489i		−	0.0170313i
$638$	188.382	−	71.2016i	0.295269	−	0.111601i
$639$		−	271.527i		−	0.424924i
$640$	162.372	+	113.974i	0.253706	+	0.178085i
$641$	635.813			0.991908			0.495954	−	0.868349i	$-0.334818\pi$
$641$	635.813			0.991908			0.495954	+	0.868349i	$0.334818\pi$
$642$	37.6569	+	99.6307i	0.0586555	+	0.155188i
$643$	1281.70			1.99332			0.996658	−	0.0816828i	$-0.0260295\pi$
$643$	1281.70			1.99332			0.996658	+	0.0816828i	$0.0260295\pi$
$644$	279.588	−	246.573i	0.434143	−	0.382878i
$645$			90.8634i			0.140874i
$646$	−416.024	−	1100.70i	−0.644001	−	1.70387i
$647$		−	260.761i		−	0.403031i	−0.979485	−	0.201516i	$-0.935413\pi$
$647$		−	260.761i		−	0.403031i	0.979485	−	0.201516i	$-0.0645867\pi$
$648$	691.924	+	366.132i	1.06778	+	0.565018i
$649$	−276.098			−0.425420
$650$	−65.5227	+	24.7653i	−0.100804	+	0.0381004i
$651$	421.990			0.648218
$652$	721.602	−	636.393i	1.10675	−	0.976063i
$653$		−	1090.58i		−	1.67011i	−0.550167	−	0.835055i	$-0.685436\pi$
$653$		−	1090.58i		−	1.67011i	0.550167	−	0.835055i	$-0.314564\pi$
$654$	24.6030	−	9.29907i	0.0376193	−	0.0142188i
$655$		−	155.527i		−	0.237446i
$656$	−53.9411	+	428.144i	−0.0822273	+	0.652659i
$657$	184.156			0.280299
$658$	67.5980	+	178.847i	0.102732	+	0.271805i
$659$	−362.780			−0.550500			−0.275250	−	0.961373i	$-0.588761\pi$
$659$	−362.780			−0.550500			−0.275250	+	0.961373i	$0.588761\pi$
$660$	−62.7939	−	71.2016i	−0.0951423	−	0.107881i
$661$			117.834i			0.178266i	0.996020	+	0.0891330i	$0.0284096\pi$
$661$			117.834i			0.178266i	−0.996020	+	0.0891330i	$0.971590\pi$
$662$	151.505	+	400.844i	0.228859	+	0.605504i
$663$			125.180i			0.188809i
$664$	−25.5635	−	13.5269i	−0.0384992	−	0.0203719i
$665$	101.980			0.153353
$666$	−291.186	+	110.058i	−0.437216	+	0.165252i
$667$	790.794			1.18560
$668$	−561.166	−	636.302i	−0.840068	−	0.952548i
$669$		−	36.1326i		−	0.0540099i
$670$	−96.7636	+	36.5732i	−0.144423	+	0.0545869i
$671$		−	169.017i		−	0.251888i
$672$	−67.5980	−	281.046i	−0.100592	−	0.418223i
$673$	−6.56854			−0.00976009			−0.00488005	−	0.999988i	$-0.501553\pi$
$673$	−6.56854			−0.00976009			−0.00488005	+	0.999988i	$0.501553\pi$
$674$	116.000	+	306.907i	0.172107	+	0.455352i
$675$	−489.401			−0.725039
$676$	−499.794	+	440.777i	−0.739340	+	0.652037i
$677$			125.796i			0.185813i	0.995675	+	0.0929066i	$0.0296158\pi$
$677$			125.796i			0.185813i	−0.995675	+	0.0929066i	$0.970384\pi$
$678$	−33.2548	−	87.9840i	−0.0490484	−	0.129770i
$679$		−	254.277i		−	0.374487i
$680$	−137.186	+	259.257i	−0.201744	+	0.381260i
$681$	361.245			0.530462
$682$	392.000	−	148.162i	0.574780	−	0.217246i
$683$	−553.775			−0.810797			−0.405399	−	0.914140i	$-0.632867\pi$
$683$	−553.775			−0.810797			−0.405399	+	0.914140i	$0.632867\pi$
$684$	198.228	−	174.821i	0.289808	−	0.255586i
$685$		−	88.8274i		−	0.129675i
$686$	−34.6482	+	13.0958i	−0.0505076	+	0.0190901i
$687$		−	255.652i		−	0.372128i
$688$	−34.3431	+	272.590i	−0.0499174	+	0.396207i
$689$	151.598			0.220026
$690$	−131.799	−	348.707i	−0.191013	−	0.505373i
$691$	−1046.83			−1.51494			−0.757471	−	0.652868i	$-0.773565\pi$
$691$	−1046.83			−1.51494			−0.757471	+	0.652868i	$0.773565\pi$
$692$	−482.090	−	546.639i	−0.696662	−	0.789941i
$693$			31.5287i			0.0454960i
$694$	−77.5635	−	205.214i	−0.111763	−	0.295697i
$695$			284.651i			0.409569i
$696$	286.794	−	541.990i	0.412060	−	0.778721i
$697$	−638.039			−0.915407
$698$	−867.090	+	327.729i	−1.24225	+	0.469526i
$699$	−1431.02			−2.04724
$700$	158.186	+	179.366i	0.225980	+	0.256237i
$701$		−	625.993i		−	0.893000i	−0.894784	−	0.446500i	$-0.852670\pi$
$701$		−	625.993i		−	0.893000i	0.894784	−	0.446500i	$-0.147330\pi$
$702$	62.7939	−	23.7339i	0.0894501	−	0.0338089i
$703$		−	1456.95i		−	2.07248i
$704$	−161.470	−	237.339i	−0.229361	−	0.337129i
$705$	191.196			0.271200
$706$	55.2233	+	146.107i	0.0782200	+	0.206951i
$707$	−51.8995			−0.0734081
$708$	−630.500	+	556.048i	−0.890536	+	0.785379i
$709$			593.492i			0.837083i	0.908198	+	0.418541i	$0.137459\pi$
$709$			593.492i			0.837083i	−0.908198	+	0.418541i	$0.862541\pi$
$710$	−112.000	−	296.324i	−0.157746	−	0.417358i
$711$		−	102.822i		−	0.144615i
$712$	−311.543	−	164.853i	−0.437561	−	0.231535i
$713$	1645.55			2.30792
$714$	399.789	−	151.106i	0.559928	−	0.211633i
$715$	−10.7737			−0.0150682
$716$	−171.618	+	151.353i	−0.239690	+	0.211387i
$717$			506.389i			0.706261i
$718$	683.065	−	258.174i	0.951344	−	0.359574i
$719$		−	611.505i		−	0.850493i	−0.905078	−	0.425247i	$-0.860187\pi$
$719$		−	611.505i		−	0.850493i	0.905078	−	0.425247i	$-0.139813\pi$
$720$	−65.3667	−	8.23543i	−0.0907870	−	0.0114381i
$721$	−113.990			−0.158100
$722$	182.094	+	481.775i	0.252208	+	0.667279i
$723$	−1570.10			−2.17165
$724$	863.075	+	978.635i	1.19209	+	1.35171i
$725$			507.323i			0.699756i
$726$	−243.551	−	644.376i	−0.335470	−	0.887570i
$727$			944.144i			1.29868i	0.760496	+	0.649342i	$0.224956\pi$
$727$			944.144i			1.29868i	−0.760496	+	0.649342i	$0.775044\pi$
$728$	−28.9949	−	15.3427i	−0.0398282	−	0.0210751i
$729$	405.489			0.556227
$730$	200.975	−	75.9613i	0.275308	−	0.104057i
$731$	−406.225			−0.555712
$732$	−340.392	−	385.968i	−0.465016	−	0.527279i
$733$		−	218.254i		−	0.297755i	−0.988856	−	0.148878i	$-0.952434\pi$
$733$		−	218.254i		−	0.297755i	0.988856	−	0.148878i	$-0.0475660\pi$
$734$	−412.965	+	156.086i	−0.562622	+	0.212651i
$735$			37.0405i			0.0503953i
$736$	−263.598	−	1095.94i	−0.358149	−	1.48905i
$737$	149.685			0.203101
$738$	−50.6690	−	134.058i	−0.0686572	−	0.181650i
$739$	−7.29942			−0.00987743			−0.00493872	−	0.999988i	$-0.501572\pi$
$739$	−7.29942			−0.00987743			−0.00493872	+	0.999988i	$0.501572\pi$
$740$	−272.382	+	240.218i	−0.368084	+	0.324619i
$741$		−	131.600i		−	0.177598i
$742$	−182.995	−	484.159i	−0.246624	−	0.652506i
$743$		−	106.867i		−	0.143832i	−0.997411	−	0.0719159i	$-0.977089\pi$
$743$		−	106.867i		−	0.143832i	0.997411	−	0.0719159i	$-0.0229113\pi$
$744$	596.784	−	1127.82i	0.802129	−	1.51588i
$745$	−298.051			−0.400068
$746$	−470.613	+	177.875i	−0.630849	+	0.238438i
$747$	9.60512			0.0128583
$748$	318.323	−	280.734i	0.425565	−	0.375313i
$749$		−	41.2684i		−	0.0550980i
$750$	471.196	−	178.095i	0.628261	−	0.237460i
$751$			127.463i			0.169725i	0.996393	+	0.0848624i	$0.0270451\pi$
$751$			127.463i			0.169725i	−0.996393	+	0.0848624i	$0.972955\pi$
$752$	573.588	+	72.2653i	0.762750	+	0.0960974i
$753$	426.500			0.566400
$754$	−24.6030	−	65.0935i	−0.0326300	−	0.0863309i
$755$	177.849			0.235562
$756$	−151.598	−	171.896i	−0.200526	−	0.227376i
$757$			704.275i			0.930350i	0.885219	+	0.465175i	$0.154009\pi$
$757$			704.275i			0.930350i	−0.885219	+	0.465175i	$0.845991\pi$
$758$	202.250	+	535.103i	0.266820	+	0.705940i
$759$			539.422i			0.710701i
$760$	144.221	−	272.552i	0.189765	−	0.358622i
$761$	−1002.93			−1.31791			−0.658955	−	0.752182i	$-0.729001\pi$
$761$	−1002.93			−1.31791			−0.658955	+	0.752182i	$0.729001\pi$
$762$	798.583	−	301.836i	1.04801	−	0.396110i
$763$	−10.1909			−0.0133564
$764$	256.804	+	291.188i	0.336131	+	0.381137i
$765$		−	97.4121i		−	0.127336i
$766$	199.980	−	75.5853i	0.261070	−	0.0986753i
$767$			95.4028i			0.124384i
$768$	−846.725	−	216.796i	−1.10251	−	0.282286i
$769$	−646.950			−0.841288			−0.420644	−	0.907226i	$-0.638196\pi$
$769$	−646.950			−0.841288			−0.420644	+	0.907226i	$0.638196\pi$
$770$	13.0051	+	34.4081i	0.0168897	+	0.0446859i
$771$	−1459.07			−1.89244
$772$	−471.911	+	416.186i	−0.611283	+	0.539101i
$773$		−	564.265i		−	0.729968i	−0.931014	−	0.364984i	$-0.881075\pi$
$773$		−	564.265i		−	0.729968i	0.931014	−	0.364984i	$-0.118925\pi$
$774$	−32.2599	−	85.3516i	−0.0416794	−	0.110273i
$775$			1055.68i			1.36217i
$776$	−679.584	−	359.602i	−0.875752	−	0.463404i
$777$	529.186			0.681063
$778$	−144.392	+	54.5750i	−0.185594	+	0.0701478i
$779$	670.759			0.861052
$780$	−24.6030	+	21.6978i	−0.0315423	+	0.0278177i
$781$			458.389i			0.586926i
$782$	1558.97	−	589.237i	1.99357	−	0.753500i
$783$		−	486.195i		−	0.620939i
$784$	−14.0000	+	111.122i	−0.0178571	+	0.141737i
$785$	328.794			0.418846
$786$	242.267	+	640.978i	0.308228	+	0.815494i
$787$	923.345			1.17325			0.586623	−	0.809860i	$-0.300457\pi$
$787$	923.345			1.17325			0.586623	+	0.809860i	$0.300457\pi$
$788$	−328.382	−	372.350i	−0.416728	−	0.472525i
$789$			879.582i			1.11481i
$790$	−42.4121	−	112.212i	−0.0536862	−	0.142040i
$791$			36.4442i			0.0460735i
$792$	84.2641	+	44.5884i	0.106394	+	0.0562984i
$793$	−58.4020			−0.0736469
$794$	1230.10	−	464.932i	1.54924	−	0.585557i
$795$	−517.588			−0.651054
$796$	478.814	+	542.924i	0.601525	+	0.682066i
$797$		−	207.983i		−	0.260957i	−0.991451	−	0.130479i	$-0.958349\pi$
$797$		−	207.983i		−	0.260957i	0.991451	−	0.130479i	$-0.0416514\pi$
$798$	−420.291	+	158.855i	−0.526681	+	0.199067i
$799$			854.785i			1.06982i
$800$	703.084	−	169.108i	0.878855	−	0.211385i
$801$	117.058			0.146140
$802$	225.421	+	596.409i	0.281074	+	0.743652i
$803$	−310.891			−0.387162
$804$	341.823	−	301.460i	0.425153	−	0.374950i
$805$			144.439i			0.179428i
$806$	−51.1960	−	135.452i	−0.0635186	−	0.168054i
$807$		−	734.896i		−	0.910652i
$808$	−73.3970	+	138.707i	−0.0908378	+	0.171667i
$809$	340.540			0.420939			0.210470	−	0.977600i	$-0.432501\pi$
$809$	340.540			0.420939			0.210470	+	0.977600i	$0.432501\pi$
$810$	−283.724	+	107.237i	−0.350276	+	0.132392i
$811$	−907.380			−1.11884			−0.559420	−	0.828884i	$-0.688976\pi$
$811$	−907.380			−1.11884			−0.559420	+	0.828884i	$0.688976\pi$
$812$	−178.191	+	157.150i	−0.219447	+	0.193534i
$813$			1292.45i			1.58973i
$814$	491.578	−	185.799i	0.603904	−	0.228254i
$815$			372.791i			0.457412i
$816$	161.539	−	1282.18i	0.197965	−	1.57130i
$817$	427.058			0.522715
$818$	102.718	+	271.766i	0.125572	+	0.332232i
$819$	10.8944			0.0133021
$820$	−110.593	−	125.401i	−0.134869	−	0.152928i
$821$			633.423i			0.771526i	0.922598	+	0.385763i	$0.126062\pi$
$821$			633.423i			0.771526i	−0.922598	+	0.385763i	$0.873938\pi$
$822$	138.368	+	366.086i	0.168330	+	0.445360i
$823$		−	143.649i		−	0.174544i	−0.996185	−	0.0872718i	$-0.972185\pi$
$823$		−	143.649i		−	0.174544i	0.996185	−	0.0872718i	$-0.0278149\pi$
$824$	−161.206	+	304.651i	−0.195638	+	0.369722i
$825$	−346.059			−0.419465
$826$	304.688	−	115.161i	0.368872	−	0.139421i
$827$	1545.57			1.86888			0.934442	−	0.356114i	$-0.115899\pi$
$827$	1545.57			1.86888			0.934442	+	0.356114i	$0.115899\pi$
$828$	247.608	+	280.761i	0.299044	+	0.339084i
$829$		−	743.956i		−	0.897413i	−0.893679	−	0.448707i	$-0.851885\pi$
$829$		−	743.956i		−	0.897413i	0.893679	−	0.448707i	$-0.148115\pi$
$830$	10.4823	−	3.96195i	0.0126293	−	0.00477343i
$831$		−	568.291i		−	0.683864i
$832$	−82.0101	+	55.7944i	−0.0985698	+	0.0670606i
$833$	−165.598			−0.198797
$834$	−443.404	−	1173.14i	−0.531660	−	1.40664i
$835$	328.723			0.393681
$836$	−334.648	+	295.131i	−0.400296	+	0.353028i
$837$		−	1011.71i		−	1.20874i
$838$	499.933	+	1322.70i	0.596579	+	1.57840i
$839$			96.3107i			0.114792i	0.998351	+	0.0573961i	$0.0182798\pi$
$839$			96.3107i			0.114792i	−0.998351	+	0.0573961i	$0.981720\pi$
$840$	98.9949	+	52.3832i	0.117851	+	0.0623610i
$841$	337.000			0.400713
$842$	228.221	−	86.2595i	0.271047	−	0.102446i
$843$	−1439.99			−1.70818
$844$	−492.146	+	434.032i	−0.583112	+	0.514256i
$845$		−	258.201i		−	0.305563i
$846$	−179.598	+	67.8817i	−0.212291	+	0.0802384i
$847$			266.909i			0.315123i
$848$	−1552.76	−	195.630i	−1.83109	−	0.230696i
$849$	−1179.40			−1.38917
$850$	378.017	+	1000.14i	0.444726	+	1.17663i
$851$	2063.56			2.42486
$852$	923.176	+	1046.78i	1.08354	+	1.22862i
$853$		−	904.866i		−	1.06080i	−0.847746	−	0.530402i	$-0.822041\pi$
$853$		−	904.866i		−	1.06080i	0.847746	−	0.530402i	$-0.177959\pi$
$854$	70.4975	+	186.519i	0.0825497	+	0.218406i
$855$			102.408i			0.119775i
$856$	−110.294	−	58.3623i	−0.128849	−	0.0681803i
$857$	160.932			0.187785			0.0938926	−	0.995582i	$-0.470069\pi$
$857$	160.932			0.187785			0.0938926	+	0.995582i	$0.470069\pi$
$858$	44.4020	−	16.7824i	0.0517506	−	0.0195599i
$859$	231.693			0.269724			0.134862	−	0.990864i	$-0.456941\pi$
$859$	231.693			0.269724			0.134862	+	0.990864i	$0.456941\pi$
$860$	−70.4121	−	79.8398i	−0.0818746	−	0.0928370i
$861$			243.629i			0.282961i
$862$	−1101.66	+	416.388i	−1.27803	+	0.483048i
$863$		−	1337.35i		−	1.54965i	−0.632176	−	0.774825i	$-0.717838\pi$
$863$		−	1337.35i		−	1.54965i	0.632176	−	0.774825i	$-0.282162\pi$
$864$	−673.803	+	162.065i	−0.779865	+	0.187575i
$865$	282.402			0.326476
$866$	97.3654	+	257.605i	0.112431	+	0.297465i
$867$	924.046			1.06580
$868$	−370.794	+	327.010i	−0.427182	+	0.376739i
$869$			173.583i			0.199750i
$870$	84.0000	+	222.243i	0.0965517	+	0.255452i
$871$		−	51.7223i		−	0.0593827i
$872$	−14.4121	+	27.2363i	−0.0165277	+	0.0312343i
$873$	255.344			0.292490
$874$	−1638.92	+	619.455i	−1.87520	+	0.708759i
$875$	−195.176			−0.223058
$876$	−709.955	+	626.122i	−0.810451	+	0.714751i
$877$			1436.14i			1.63755i	0.574111	+	0.818777i	$0.305348\pi$
$877$			1436.14i			1.63755i	−0.574111	+	0.818777i	$0.694652\pi$
$878$	−824.181	+	311.511i	−0.938703	+	0.354796i
$879$			1744.79i			1.98498i
$880$	110.352	+	13.9030i	0.125399	+	0.0157988i
$881$	−186.706			−0.211926			−0.105963	−	0.994370i	$-0.533792\pi$
$881$	−186.706			−0.211926			−0.105963	+	0.994370i	$0.533792\pi$
$882$	−13.1508	−	34.7936i	−0.0149102	−	0.0394486i
$883$	1277.99			1.44733			0.723664	−	0.690153i	$-0.242457\pi$
$883$	1277.99			1.44733			0.723664	+	0.690153i	$0.242457\pi$
$884$	−97.0051	−	109.993i	−0.109734	−	0.124427i
$885$		−	325.726i		−	0.368052i
$886$	−344.402	−	911.202i	−0.388716	−	1.02844i
$887$		−	980.717i		−	1.10566i	−0.833295	−	0.552828i	$-0.813549\pi$
$887$		−	980.717i		−	1.10566i	0.833295	−	0.552828i	$-0.186451\pi$
$888$	748.382	−	1414.31i	0.842772	−	1.59269i
$889$	−330.784			−0.372085
$890$	127.748	−	48.2844i	0.143538	−	0.0542521i
$891$	438.897			0.492590
$892$	28.0000	+	31.7490i	0.0313901	+	0.0355931i
$893$		−	898.621i		−	1.00629i
$894$	1228.36	−	464.277i	1.37401	−	0.519326i
$895$		−	88.6605i		−	0.0990621i
$896$	277.186	+	194.566i	0.309359	+	0.217150i
$897$	186.392			0.207795
$898$	186.704	+	493.971i	0.207910	+	0.550079i
$899$	−1048.76			−1.16659
$900$	−180.119	+	158.850i	−0.200132	+	0.176500i
$901$		−	2313.99i		−	2.56825i
$902$	85.5391	+	226.315i	0.0948327	+	0.250904i
$903$			155.114i			0.171776i
$904$	97.4012	+	51.5398i	0.107745	+	0.0570131i
$905$	−505.578			−0.558649
$906$	−732.975	+	277.038i	−0.809023	+	0.305782i
$907$	−658.372			−0.725878			−0.362939	−	0.931813i	$-0.618227\pi$
$907$	−658.372			−0.725878			−0.362939	+	0.931813i	$0.618227\pi$
$908$	−317.418	+	279.937i	−0.349580	+	0.308300i
$909$		−	52.1173i		−	0.0573348i
$910$	11.8894	−	4.49377i	0.0130653	−	0.00493821i
$911$		−	276.507i		−	0.303520i	−0.988417	−	0.151760i	$-0.951506\pi$
$911$		−	276.507i		−	0.303520i	0.988417	−	0.151760i	$-0.0484941\pi$
$912$	−169.823	+	1347.93i	−0.186210	+	1.47799i
$913$	−16.2153			−0.0177605
$914$	−363.681	−	962.210i	−0.397901	−	1.05275i
$915$	199.397			0.217920
$916$	198.111	+	224.636i	0.216278	+	0.245236i
$917$		−	265.502i		−	0.289533i
$918$	−362.274	−	958.487i	−0.394634	−	1.04410i
$919$		−	1339.73i		−	1.45782i	−0.684611	−	0.728908i	$-0.740028\pi$
$919$		−	1339.73i		−	1.45782i	0.684611	−	0.728908i	$-0.259972\pi$
$920$	386.030	+	204.268i	0.419598	+	0.222030i
$921$	762.500			0.827904
$922$	−378.327	+	142.994i	−0.410333	+	0.155091i
$923$	158.392			0.171606
$924$	−107.196	−	121.549i	−0.116013	−	0.131546i
$925$			1323.85i			1.43119i
$926$	−1351.96	+	510.993i	−1.46000	+	0.551828i
$927$		−	114.468i		−	0.123482i
$928$	168.000	+	698.478i	0.181034	+	0.752671i
$929$	35.4012			0.0381067			0.0190534	−	0.999818i	$-0.493935\pi$
$929$	35.4012			0.0381067			0.0190534	+	0.999818i	$0.493935\pi$
$930$	174.794	+	462.461i	0.187950	+	0.497270i
$931$	174.090			0.186993
$932$	1257.41	−	1108.93i	1.34915	−	1.18984i
$933$		−	42.3320i		−	0.0453719i
$934$	−245.566	−	649.705i	−0.262918	−	0.695616i
$935$			164.450i			0.175883i
$936$	15.4071	−	29.1166i	0.0164605	−	0.0311075i
$937$	610.235			0.651265			0.325633	−	0.945496i	$-0.394423\pi$
$937$	610.235			0.651265			0.325633	+	0.945496i	$0.394423\pi$
$938$	−165.186	+	62.4344i	−0.176104	+	0.0665612i
$939$	1399.99			1.49094
$940$	−168.000	+	148.162i	−0.178723	+	0.157619i
$941$		−	1852.90i		−	1.96907i	−0.175175	−	0.984537i	$-0.556049\pi$
$941$		−	1852.90i		−	1.96907i	0.175175	−	0.984537i	$-0.443951\pi$
$942$	−1355.07	+	512.166i	−1.43850	+	0.543701i
$943$			950.032i			1.00746i
$944$	123.113	−	977.177i	0.130416	−	1.03514i
$945$	88.8040			0.0939725
$946$	54.4609	+	144.090i	0.0575697	+	0.152315i
$947$	−1832.90			−1.93548			−0.967738	−	0.251959i	$-0.918925\pi$
$947$	−1832.90			−1.93548			−0.967738	+	0.251959i	$0.918925\pi$
$948$	349.588	+	396.395i	0.368764	+	0.418139i
$949$			107.426i			0.113199i
$950$	−397.403	−	1051.43i	−0.418319	−	1.10677i
$951$		−	444.927i		−	0.467852i
$952$	−234.191	+	442.579i	−0.245999	+	0.464894i
$953$	349.687			0.366933			0.183467	−	0.983026i	$-0.441268\pi$
$953$	349.687			0.366933			0.183467	+	0.983026i	$0.441268\pi$
$954$	486.191	−	183.763i	0.509634	−	0.192624i
$955$	−150.432			−0.157521
$956$	−392.412	−	444.954i	−0.410473	−	0.465433i
$957$		−	343.792i		−	0.359239i
$958$	54.5929	−	20.6342i	0.0569864	−	0.0215388i
$959$		−	151.638i		−	0.158121i
$960$	280.000	−	190.494i	0.291667	−	0.198431i
$961$	−1221.35			−1.27092
$962$	−64.2010	−	169.860i	−0.0667370	−	0.176570i
$963$	41.4416			0.0430338
$964$	1379.62	−	1216.71i	1.43114	−	1.26214i
$965$		−	243.796i		−	0.252639i
$966$	−224.995	−	595.281i	−0.232914	−	0.616233i
$967$		−	632.128i		−	0.653700i	−0.945076	−	0.326850i	$-0.894013\pi$
$967$		−	632.128i		−	0.653700i	0.945076	−	0.326850i	$-0.105987\pi$
$968$	713.345	+	377.467i	0.736927	+	0.389945i
$969$	−2008.74			−2.07301
$970$	278.664	−	105.325i	0.287282	−	0.108582i
$971$	656.497			0.676104			0.338052	−	0.941128i	$-0.390232\pi$
$971$	656.497			0.676104			0.338052	+	0.941128i	$0.390232\pi$
$972$	417.536	−	368.232i	0.429564	−	0.378840i
$973$			485.929i			0.499413i
$974$	1312.65	−	496.136i	1.34769	−	0.509380i
$975$			119.577i			0.122643i
$976$	598.191	+	75.3650i	0.612901	+	0.0772182i
$977$	169.314			0.173300			0.0866498	−	0.996239i	$-0.472384\pi$
$977$	169.314			0.173300			0.0866498	+	0.996239i	$0.472384\pi$
$978$	−580.701	−	1536.39i	−0.593763	−	1.57095i
$979$	−197.616			−0.201855
$980$	−28.7035	−	32.5467i	−0.0292893	−	0.0332110i
$981$		−	10.2337i		−	0.0104319i
$982$	−42.3919	−	112.158i	−0.0431690	−	0.114214i
$983$			698.607i			0.710689i	0.934735	+	0.355345i	$0.115636\pi$
$983$			698.607i			0.710689i	−0.934735	+	0.355345i	$0.884364\pi$
$984$	651.127	+	344.544i	0.661714	+	0.350146i
$985$	192.362			0.195291
$986$	−993.588	+	375.541i	−1.00770	+	0.380873i
$987$	326.392			0.330691
$988$	101.980	+	115.634i	0.103218	+	0.117039i
$989$			604.865i			0.611592i
$990$	−34.5525	+	13.0596i	−0.0349015	+	0.0131915i
$991$			429.702i			0.433605i	0.976216	+	0.216802i	$0.0695627\pi$
$991$			429.702i			0.433605i	−0.976216	+	0.216802i	$0.930437\pi$
$992$	349.588	+	1453.45i	0.352407	+	1.46517i
$993$	731.529			0.736686
$994$	−191.196	−	505.857i	−0.192350	−	0.508910i
$995$	−280.483			−0.281892
$996$	−37.0294	+	32.6569i	−0.0371781	+	0.0327880i
$997$		−	52.3910i		−	0.0525487i	−0.999655	−	0.0262743i	$-0.991636\pi$
$997$		−	52.3910i		−	0.0525487i	0.999655	−	0.0262743i	$-0.00836434\pi$
$998$	−59.5980	−	157.681i	−0.0597174	−	0.157997i
$999$		−	1268.71i		−	1.26998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.3.g.a.43.4	yes	4
3.2	odd	2		504.3.g.a.379.1		4
4.3	odd	2		224.3.g.a.15.1		4
7.2	even	3		392.3.k.i.67.3		8
7.3	odd	6		392.3.k.j.275.1		8
7.4	even	3		392.3.k.i.275.1		8
7.5	odd	6		392.3.k.j.67.3		8
7.6	odd	2		392.3.g.h.99.4		4
8.3	odd	2	inner	56.3.g.a.43.3	✓	4
8.5	even	2		224.3.g.a.15.2		4
12.11	even	2		2016.3.g.a.1135.3		4
16.3	odd	4		1792.3.d.g.1023.1		8
16.5	even	4		1792.3.d.g.1023.2		8
16.11	odd	4		1792.3.d.g.1023.8		8
16.13	even	4		1792.3.d.g.1023.7		8
24.5	odd	2		2016.3.g.a.1135.2		4
24.11	even	2		504.3.g.a.379.2		4
28.27	even	2		1568.3.g.h.687.4		4
56.3	even	6		392.3.k.j.275.3		8
56.11	odd	6		392.3.k.i.275.3		8
56.13	odd	2		1568.3.g.h.687.3		4
56.19	even	6		392.3.k.j.67.1		8
56.27	even	2		392.3.g.h.99.3		4
56.51	odd	6		392.3.k.i.67.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.a.43.3	✓	4	8.3	odd	2	inner
56.3.g.a.43.4	yes	4	1.1	even	1	trivial
224.3.g.a.15.1		4	4.3	odd	2
224.3.g.a.15.2		4	8.5	even	2
392.3.g.h.99.3		4	56.27	even	2
392.3.g.h.99.4		4	7.6	odd	2
392.3.k.i.67.1		8	56.51	odd	6
392.3.k.i.67.3		8	7.2	even	3
392.3.k.i.275.1		8	7.4	even	3
392.3.k.i.275.3		8	56.11	odd	6
392.3.k.j.67.1		8	56.19	even	6
392.3.k.j.67.3		8	7.5	odd	6
392.3.k.j.275.1		8	7.3	odd	6
392.3.k.j.275.3		8	56.3	even	6
504.3.g.a.379.1		4	3.2	odd	2
504.3.g.a.379.2		4	24.11	even	2
1568.3.g.h.687.3		4	56.13	odd	2
1568.3.g.h.687.4		4	28.27	even	2
1792.3.d.g.1023.1		8	16.3	odd	4
1792.3.d.g.1023.2		8	16.5	even	4
1792.3.d.g.1023.7		8	16.13	even	4
1792.3.d.g.1023.8		8	16.11	odd	4
2016.3.g.a.1135.2		4	24.5	odd	2
2016.3.g.a.1135.3		4	12.11	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:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	56.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.87083i) q^{2} +3.41421 q^{3} +(-3.00000 + 2.64575i) q^{4} -1.54985i q^{5} +(2.41421 + 6.38741i) q^{6} -2.64575i q^{7} +(-7.07107 - 3.74166i) q^{8} +2.65685 q^{9} +O(q^{10})\)	\(q+(0.707107 + 1.87083i) q^{2} +3.41421 q^{3} +(-3.00000 + 2.64575i) q^{4} -1.54985i q^{5} +(2.41421 + 6.38741i) q^{6} -2.64575i q^{7} +(-7.07107 - 3.74166i) q^{8} +2.65685 q^{9} +(2.89949 - 1.09591i) q^{10} -4.48528 q^{11} +(-10.2426 + 9.03316i) q^{12} +1.54985i q^{13} +(4.94975 - 1.87083i) q^{14} -5.29150i q^{15} +(2.00000 - 15.8745i) q^{16} +23.6569 q^{17} +(1.87868 + 4.97052i) q^{18} -24.8701 q^{19} +(4.10051 + 4.64954i) q^{20} -9.03316i q^{21} +(-3.17157 - 8.39119i) q^{22} -35.2248i q^{23} +(-24.1421 - 12.7748i) q^{24} +22.5980 q^{25} +(-2.89949 + 1.09591i) q^{26} -21.6569 q^{27} +(7.00000 + 7.93725i) q^{28} +22.4499i q^{29} +(9.89949 - 3.74166i) q^{30} +46.7156i q^{31} +(31.1127 - 7.48331i) q^{32} -15.3137 q^{33} +(16.7279 + 44.2579i) q^{34} -4.10051 q^{35} +(-7.97056 + 7.02938i) q^{36} +58.5826i q^{37} +(-17.5858 - 46.5276i) q^{38} +5.29150i q^{39} +(-5.79899 + 10.9591i) q^{40} -26.9706 q^{41} +(16.8995 - 6.38741i) q^{42} -17.1716 q^{43} +(13.4558 - 11.8669i) q^{44} -4.11771i q^{45} +(65.8995 - 24.9077i) q^{46} +36.1326i q^{47} +(6.82843 - 54.1990i) q^{48} -7.00000 q^{49} +(15.9792 + 42.2769i) q^{50} +80.7696 q^{51} +(-4.10051 - 4.64954i) q^{52} -97.8149i q^{53} +(-15.3137 - 40.5163i) q^{54} +6.95149i q^{55} +(-9.89949 + 18.7083i) q^{56} -84.9117 q^{57} +(-42.0000 + 15.8745i) q^{58} +61.5563 q^{59} +(14.0000 + 15.8745i) q^{60} +37.6825i q^{61} +(-87.3970 + 33.0329i) q^{62} -7.02938i q^{63} +(36.0000 + 52.9150i) q^{64} +2.40202 q^{65} +(-10.8284 - 28.6493i) q^{66} -33.3726 q^{67} +(-70.9706 + 62.5902i) q^{68} -120.265i q^{69} +(-2.89949 - 7.67134i) q^{70} -102.199i q^{71} +(-18.7868 - 9.94104i) q^{72} +69.3137 q^{73} +(-109.598 + 41.4241i) q^{74} +77.1543 q^{75} +(74.6102 - 65.8000i) q^{76} +11.8669i q^{77} +(-9.89949 + 3.74166i) q^{78} -38.7005i q^{79} +(-24.6030 - 3.09969i) q^{80} -97.8528 q^{81} +(-19.0711 - 50.4573i) q^{82} +3.61522 q^{83} +(23.8995 + 27.0995i) q^{84} -36.6645i q^{85} +(-12.1421 - 32.1251i) q^{86} +76.6489i q^{87} +(31.7157 + 16.7824i) q^{88} +44.0589 q^{89} +(7.70354 - 2.91166i) q^{90} +4.10051 q^{91} +(93.1960 + 105.674i) q^{92} +159.497i q^{93} +(-67.5980 + 25.5496i) q^{94} +38.5447i q^{95} +(106.225 - 25.5496i) q^{96} +96.1076 q^{97} +(-4.94975 - 13.0958i) q^{98} -11.9167 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{9}+O(q^{10}) \) 4 * q + 8 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^9	\( 4 q + 8 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{9} - 28 q^{10} + 16 q^{11} - 24 q^{12} + 8 q^{16} + 72 q^{17} + 16 q^{18} + 8 q^{19} + 56 q^{20} - 24 q^{22} - 40 q^{24} - 68 q^{25} + 28 q^{26} - 64 q^{27} + 28 q^{28} - 16 q^{33} + 16 q^{34} - 56 q^{35} + 36 q^{36} - 76 q^{38} + 56 q^{40} - 40 q^{41} + 28 q^{42} - 80 q^{43} - 48 q^{44} + 224 q^{46} + 16 q^{48} - 28 q^{49} + 112 q^{50} + 176 q^{51} - 56 q^{52} - 16 q^{54} - 136 q^{57} - 168 q^{58} + 184 q^{59} + 56 q^{60} - 112 q^{62} + 144 q^{64} + 168 q^{65} - 32 q^{66} - 224 q^{67} - 216 q^{68} + 28 q^{70} - 160 q^{72} + 232 q^{73} - 280 q^{74} + 88 q^{75} - 24 q^{76} - 336 q^{80} - 52 q^{81} - 48 q^{82} + 88 q^{83} + 56 q^{84} + 8 q^{86} + 240 q^{88} + 312 q^{89} + 308 q^{90} + 56 q^{91} + 56 q^{92} - 112 q^{94} + 176 q^{96} - 136 q^{97} - 240 q^{99}+O(q^{100}) \) 4 * q + 8 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^9 - 28 * q^10 + 16 * q^11 - 24 * q^12 + 8 * q^16 + 72 * q^17 + 16 * q^18 + 8 * q^19 + 56 * q^20 - 24 * q^22 - 40 * q^24 - 68 * q^25 + 28 * q^26 - 64 * q^27 + 28 * q^28 - 16 * q^33 + 16 * q^34 - 56 * q^35 + 36 * q^36 - 76 * q^38 + 56 * q^40 - 40 * q^41 + 28 * q^42 - 80 * q^43 - 48 * q^44 + 224 * q^46 + 16 * q^48 - 28 * q^49 + 112 * q^50 + 176 * q^51 - 56 * q^52 - 16 * q^54 - 136 * q^57 - 168 * q^58 + 184 * q^59 + 56 * q^60 - 112 * q^62 + 144 * q^64 + 168 * q^65 - 32 * q^66 - 224 * q^67 - 216 * q^68 + 28 * q^70 - 160 * q^72 + 232 * q^73 - 280 * q^74 + 88 * q^75 - 24 * q^76 - 336 * q^80 - 52 * q^81 - 48 * q^82 + 88 * q^83 + 56 * q^84 + 8 * q^86 + 240 * q^88 + 312 * q^89 + 308 * q^90 + 56 * q^91 + 56 * q^92 - 112 * q^94 + 176 * q^96 - 136 * q^97 - 240 * q^99

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