LMFDB - Embedded newform 966.2.k.a.229.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(229,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("966.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.9
Character	$\chi$	$=$	966.229
Dual form			966.2.k.a.367.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.07087 + 3.58686i) q^{5} +1.00000i q^{6} +(-1.78719 + 1.95088i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.07087 + 3.58686i) q^{5} +1.00000i q^{6} +(-1.78719 + 1.95088i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.07087 - 3.58686i) q^{10} +(-2.94888 + 1.70253i) q^{11} +(-0.866025 - 0.500000i) q^{12} -0.0118794i q^{13} +(-0.795918 - 2.52320i) q^{14} +4.14174i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.74603 - 6.48831i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.10357 - 3.64349i) q^{19} +4.14174 q^{20} +(-0.572313 + 2.58311i) q^{21} -3.40507i q^{22} +(2.42611 + 4.13691i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-6.07702 - 10.5257i) q^{25} +(0.0102879 + 0.00593970i) q^{26} -1.00000i q^{27} +(2.58311 + 0.572313i) q^{28} -3.05566 q^{29} +(-3.58686 - 2.07087i) q^{30} +(5.66997 - 3.27356i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.70253 + 2.94888i) q^{33} +7.49206 q^{34} +(-3.29649 - 10.4504i) q^{35} -1.00000 q^{36} +(0.217789 + 0.125740i) q^{37} +(2.10357 + 3.64349i) q^{38} +(-0.00593970 - 0.0102879i) q^{39} +(-2.07087 + 3.58686i) q^{40} +7.42255i q^{41} +(-1.95088 - 1.78719i) q^{42} -6.14020i q^{43} +(2.94888 + 1.70253i) q^{44} +(2.07087 + 3.58686i) q^{45} +(-4.79572 + 0.0326186i) q^{46} +(1.66865 + 0.963394i) q^{47} +1.00000i q^{48} +(-0.611887 - 6.97321i) q^{49} +12.1540 q^{50} +(-6.48831 - 3.74603i) q^{51} +(-0.0102879 + 0.00593970i) q^{52} +(6.02910 - 3.48090i) q^{53} +(0.866025 + 0.500000i) q^{54} -14.1029i q^{55} +(-1.78719 + 1.95088i) q^{56} -4.20714i q^{57} +(1.52783 - 2.64628i) q^{58} +(-4.24307 + 2.44974i) q^{59} +(3.58686 - 2.07087i) q^{60} +(-1.73443 + 3.00412i) q^{61} +6.54712i q^{62} +(0.795918 + 2.52320i) q^{63} +1.00000 q^{64} +(0.0426097 + 0.0246007i) q^{65} +(-1.70253 - 2.94888i) q^{66} +(-5.67615 + 3.27713i) q^{67} +(-3.74603 + 6.48831i) q^{68} +(4.16953 + 2.36961i) q^{69} +(10.6986 + 2.37037i) q^{70} -14.7151 q^{71} +(0.500000 - 0.866025i) q^{72} +(-12.4835 + 7.20733i) q^{73} +(-0.217789 + 0.125740i) q^{74} +(-10.5257 - 6.07702i) q^{75} -4.20714 q^{76} +(1.94876 - 8.79567i) q^{77} +0.0118794 q^{78} +(-13.9139 - 8.03322i) q^{79} +(-2.07087 - 3.58686i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.42812 - 3.71128i) q^{82} +3.21985 q^{83} +(2.52320 - 0.795918i) q^{84} +31.0302 q^{85} +(5.31757 + 3.07010i) q^{86} +(-2.64628 + 1.52783i) q^{87} +(-2.94888 + 1.70253i) q^{88} +(-2.47304 + 4.28344i) q^{89} -4.14174 q^{90} +(0.0231753 + 0.0212308i) q^{91} +(2.36961 - 4.16953i) q^{92} +(3.27356 - 5.66997i) q^{93} +(-1.66865 + 0.963394i) q^{94} +(8.71244 + 15.0904i) q^{95} +(-0.866025 - 0.500000i) q^{96} -1.85846 q^{97} +(6.34492 + 2.95669i) q^{98} +3.40507i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 16 * q^9	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 16 q^{9} - 16 q^{16} + 16 q^{18} + 8 q^{23} - 24 q^{25} - 12 q^{26} - 8 q^{29} + 48 q^{31} - 16 q^{32} - 20 q^{35} - 32 q^{36} - 8 q^{39} + 8 q^{46} + 12 q^{47} + 24 q^{49} + 48 q^{50} + 12 q^{52} + 4 q^{58} - 12 q^{59} + 32 q^{64} + 64 q^{70} + 48 q^{71} + 16 q^{72} + 12 q^{73} + 36 q^{75} + 64 q^{77} + 16 q^{78} - 16 q^{81} - 12 q^{82} + 32 q^{85} - 24 q^{87} - 16 q^{92} - 12 q^{94} + 40 q^{95} - 24 q^{98}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 16 * q^9 - 16 * q^16 + 16 * q^18 + 8 * q^23 - 24 * q^25 - 12 * q^26 - 8 * q^29 + 48 * q^31 - 16 * q^32 - 20 * q^35 - 32 * q^36 - 8 * q^39 + 8 * q^46 + 12 * q^47 + 24 * q^49 + 48 * q^50 + 12 * q^52 + 4 * q^58 - 12 * q^59 + 32 * q^64 + 64 * q^70 + 48 * q^71 + 16 * q^72 + 12 * q^73 + 36 * q^75 + 64 * q^77 + 16 * q^78 - 16 * q^81 - 12 * q^82 + 32 * q^85 - 24 * q^87 - 16 * q^92 - 12 * q^94 + 40 * q^95 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.07087	+	3.58686i	−0.926122	+	1.60409i	−0.136376	+	0.990657i	$0.543545\pi$
$5$	−2.07087	+	3.58686i	−0.926122	+	1.60409i	−0.789747	+	0.613433i	$0.789788\pi$
$6$			1.00000i			0.408248i
$7$	−1.78719	+	1.95088i	−0.675495	+	0.737364i
$7$	−1.78719	+	1.95088i	−0.675495	+	0.737364i
$8$	1.00000			0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−2.07087	−	3.58686i	−0.654867	−	1.13426i
$11$	−2.94888	+	1.70253i	−0.889120	+	0.513334i	−0.873654	−	0.486547i	$-0.838256\pi$
$11$	−2.94888	+	1.70253i	−0.889120	+	0.513334i	−0.0154653	+	0.999880i	$0.504923\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$		−	0.0118794i		−	0.00329475i	−0.999999	−	0.00164738i	$-0.999476\pi$
$13$		−	0.0118794i		−	0.00329475i	0.999999	−	0.00164738i	$-0.000524376\pi$
$14$	−0.795918	−	2.52320i	−0.212718	−	0.674352i
$15$			4.14174i			1.06939i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.74603	−	6.48831i	−0.908545	−	1.57365i	−0.816086	−	0.577930i	$-0.803861\pi$
$17$	−3.74603	−	6.48831i	−0.908545	−	1.57365i	−0.0924590	−	0.995716i	$-0.529473\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	2.10357	−	3.64349i	0.482592	−	0.835873i	−0.517209	−	0.855859i	$-0.673029\pi$
$19$	2.10357	−	3.64349i	0.482592	−	0.835873i	0.999800	+	0.0199863i	$0.00636225\pi$
$20$	4.14174			0.926122
$21$	−0.572313	+	2.58311i	−0.124889	+	0.563681i
$22$		−	3.40507i		−	0.725963i
$23$	2.42611	+	4.13691i	0.505879	+	0.862605i
$23$	2.42611	+	4.13691i	0.505879	+	0.862605i
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	−6.07702	−	10.5257i	−1.21540	−	2.10514i
$26$	0.0102879	+	0.00593970i	0.00201762	+	0.00116487i
$27$		−	1.00000i		−	0.192450i
$28$	2.58311	+	0.572313i	0.488162	+	0.108157i
$29$	−3.05566			−0.567422			−0.283711	−	0.958910i	$-0.591566\pi$
$29$	−3.05566			−0.567422			−0.283711	+	0.958910i	$0.591566\pi$
$30$	−3.58686	−	2.07087i	−0.654867	−	0.378088i
$31$	5.66997	−	3.27356i	1.01836	−	0.587949i	0.104729	−	0.994501i	$-0.466602\pi$
$31$	5.66997	−	3.27356i	1.01836	−	0.587949i	0.913628	+	0.406552i	$0.133269\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.70253	+	2.94888i	−0.296373	+	0.513334i
$34$	7.49206			1.28488
$35$	−3.29649	−	10.4504i	−0.557208	−	1.76644i
$36$	−1.00000			−0.166667
$37$	0.217789	+	0.125740i	0.0358042	+	0.0206716i	0.517795	−	0.855505i	$-0.326753\pi$
$37$	0.217789	+	0.125740i	0.0358042	+	0.0206716i	−0.481991	+	0.876176i	$0.660086\pi$
$38$	2.10357	+	3.64349i	0.341244	+	0.591051i
$39$	−0.00593970	−	0.0102879i	−0.000951113	−	0.00164738i
$40$	−2.07087	+	3.58686i	−0.327434	+	0.567132i
$41$			7.42255i			1.15921i	0.814898	+	0.579604i	$0.196793\pi$
$41$			7.42255i			1.15921i	−0.814898	+	0.579604i	$0.803207\pi$
$42$	−1.95088	−	1.78719i	−0.301028	−	0.275770i
$43$		−	6.14020i		−	0.936372i	−0.883630	−	0.468186i	$-0.844908\pi$
$43$		−	6.14020i		−	0.936372i	0.883630	−	0.468186i	$-0.155092\pi$
$44$	2.94888	+	1.70253i	0.444560	+	0.256667i
$45$	2.07087	+	3.58686i	0.308707	+	0.534697i
$46$	−4.79572	+	0.0326186i	−0.707090	+	0.00480935i
$47$	1.66865	+	0.963394i	0.243397	+	0.140525i	0.616737	−	0.787169i	$-0.288454\pi$
$47$	1.66865	+	0.963394i	0.243397	+	0.140525i	−0.373340	+	0.927695i	$0.621788\pi$
$48$			1.00000i			0.144338i
$49$	−0.611887	−	6.97321i	−0.0874124	−	0.996172i
$50$	12.1540			1.71884
$51$	−6.48831	−	3.74603i	−0.908545	−	0.524549i
$52$	−0.0102879	+	0.00593970i	−0.00142667	+	0.000823688i
$53$	6.02910	−	3.48090i	0.828161	−	0.478139i	−0.0250616	−	0.999686i	$-0.507978\pi$
$53$	6.02910	−	3.48090i	0.828161	−	0.478139i	0.853223	+	0.521547i	$0.174645\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$		−	14.1029i		−	1.90164i
$56$	−1.78719	+	1.95088i	−0.238824	+	0.260698i
$57$		−	4.20714i		−	0.557249i
$58$	1.52783	−	2.64628i	0.200614	−	0.347474i
$59$	−4.24307	+	2.44974i	−0.552401	+	0.318929i	−0.750090	−	0.661336i	$-0.769990\pi$
$59$	−4.24307	+	2.44974i	−0.552401	+	0.318929i	0.197689	+	0.980265i	$0.436656\pi$
$60$	3.58686	−	2.07087i	0.463061	−	0.267348i
$61$	−1.73443	+	3.00412i	−0.222071	+	0.384639i	−0.955437	−	0.295196i	$-0.904615\pi$
$61$	−1.73443	+	3.00412i	−0.222071	+	0.384639i	0.733366	+	0.679834i	$0.237948\pi$
$62$			6.54712i			0.831485i
$63$	0.795918	+	2.52320i	0.100276	+	0.317893i
$64$	1.00000			0.125000
$65$	0.0426097	+	0.0246007i	0.00528508	+	0.00305134i
$66$	−1.70253	−	2.94888i	−0.209568	−	0.362982i
$67$	−5.67615	+	3.27713i	−0.693452	+	0.400365i	−0.804904	−	0.593405i	$-0.797783\pi$
$67$	−5.67615	+	3.27713i	−0.693452	+	0.400365i	0.111452	+	0.993770i	$0.464450\pi$
$68$	−3.74603	+	6.48831i	−0.454273	+	0.786823i
$69$	4.16953	+	2.36961i	0.501952	+	0.285268i
$70$	10.6986	+	2.37037i	1.27872	+	0.283314i
$71$	−14.7151			−1.74636			−0.873179	−	0.487400i	$-0.837945\pi$
$71$	−14.7151			−1.74636			−0.873179	+	0.487400i	$0.837945\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−12.4835	+	7.20733i	−1.46108	+	0.843554i	−0.999061	−	0.0433168i	$-0.986208\pi$
$73$	−12.4835	+	7.20733i	−1.46108	+	0.843554i	−0.462017	+	0.886871i	$0.652874\pi$
$74$	−0.217789	+	0.125740i	−0.0253174	+	0.0146170i
$75$	−10.5257	−	6.07702i	−1.21540	−	0.701714i
$76$	−4.20714			−0.482592
$77$	1.94876	−	8.79567i	0.222082	−	1.00236i
$78$	0.0118794			0.00134508
$79$	−13.9139	−	8.03322i	−1.56544	−	0.903808i	−0.996690	−	0.0812977i	$-0.974094\pi$
$79$	−13.9139	−	8.03322i	−1.56544	−	0.903808i	−0.568751	−	0.822510i	$-0.692573\pi$
$80$	−2.07087	−	3.58686i	−0.231531	−	0.401023i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.42812	−	3.71128i	−0.709867	−	0.409842i
$83$	3.21985			0.353424			0.176712	−	0.984263i	$-0.443454\pi$
$83$	3.21985			0.353424			0.176712	+	0.984263i	$0.443454\pi$
$84$	2.52320	−	0.795918i	0.275303	−	0.0868418i
$85$	31.0302			3.36570
$86$	5.31757	+	3.07010i	0.573408	+	0.331057i
$87$	−2.64628	+	1.52783i	−0.283711	+	0.163801i
$88$	−2.94888	+	1.70253i	−0.314351	+	0.181491i
$89$	−2.47304	+	4.28344i	−0.262142	+	0.454044i	−0.966811	−	0.255493i	$-0.917762\pi$
$89$	−2.47304	+	4.28344i	−0.262142	+	0.454044i	0.704669	+	0.709536i	$0.251096\pi$
$90$	−4.14174			−0.436578
$91$	0.0231753	+	0.0212308i	0.00242943	+	0.00222559i
$92$	2.36961	−	4.16953i	0.247049	−	0.434703i
$93$	3.27356	−	5.66997i	0.339452	−	0.587949i
$94$	−1.66865	+	0.963394i	−0.172108	+	0.0993665i
$95$	8.71244	+	15.0904i	0.893877	+	1.54824i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	−1.85846			−0.188698			−0.0943490	−	0.995539i	$-0.530077\pi$
$97$	−1.85846			−0.188698			−0.0943490	+	0.995539i	$0.530077\pi$
$98$	6.34492	+	2.95669i	0.640933	+	0.298671i
$99$			3.40507i			0.342222i
$100$	−6.07702	+	10.5257i	−0.607702	+	1.05257i
$101$	−4.95250	+	2.85933i	−0.492792	+	0.284513i	−0.725732	−	0.687978i	$-0.758499\pi$
$101$	−4.95250	+	2.85933i	−0.492792	+	0.284513i	0.232940	+	0.972491i	$0.425165\pi$
$102$	6.48831	−	3.74603i	0.642439	−	0.370912i
$103$	−8.11946	+	14.0633i	−0.800035	+	1.38570i	0.119558	+	0.992827i	$0.461852\pi$
$103$	−8.11946	+	14.0633i	−0.800035	+	1.38570i	−0.919593	+	0.392873i	$0.871481\pi$
$104$		−	0.0118794i		−	0.00116487i
$105$	−8.08006	−	7.40209i	−0.788533	−	0.722370i
$106$			6.96181i			0.676191i
$107$	−13.0748	−	7.54877i	−1.26399	−	0.729767i	−0.290149	−	0.956982i	$-0.593705\pi$
$107$	−13.0748	−	7.54877i	−1.26399	−	0.729767i	−0.973845	+	0.227215i	$0.927038\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	−4.60759	+	2.66020i	−0.441327	+	0.254801i	−0.704161	−	0.710041i	$-0.748676\pi$
$109$	−4.60759	+	2.66020i	−0.441327	+	0.254801i	0.262833	+	0.964841i	$0.415343\pi$
$110$	12.2135	+	7.05146i	1.16451	+	0.672331i
$111$	0.251481			0.0238695
$112$	−0.795918	−	2.52320i	−0.0752072	−	0.238420i
$113$		−	7.71714i		−	0.725968i	−0.931795	−	0.362984i	$-0.881758\pi$
$113$		−	7.71714i		−	0.725968i	0.931795	−	0.362984i	$-0.118242\pi$
$114$	3.64349	+	2.10357i	0.341244	+	0.197017i
$115$	−19.8626	+	0.135098i	−1.85220	+	0.0125980i
$116$	1.52783	+	2.64628i	0.141856	+	0.245701i
$117$	−0.0102879	−	0.00593970i	−0.000951113	−	0.000549125i
$118$		−	4.89948i		−	0.451033i
$119$	19.3528	+	4.28780i	1.77407	+	0.393062i
$120$			4.14174i			0.378088i
$121$	0.297250	−	0.514851i	0.0270227	−	0.0468047i
$122$	−1.73443	−	3.00412i	−0.157028	−	0.271980i
$123$	3.71128	+	6.42812i	0.334634	+	0.579604i
$124$	−5.66997	−	3.27356i	−0.509179	−	0.293974i
$125$	29.6302			2.65021
$126$	−2.58311	−	0.572313i	−0.230122	−	0.0509857i
$127$	3.73579			0.331498			0.165749	−	0.986168i	$-0.446996\pi$
$127$	3.73579			0.331498			0.165749	+	0.986168i	$0.446996\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−3.07010	−	5.31757i	−0.270307	−	0.468186i
$130$	−0.0426097	+	0.0246007i	−0.00373712	+	0.00215763i
$131$	9.86494	+	5.69552i	0.861904	+	0.497620i	0.864649	−	0.502376i	$-0.167541\pi$
$131$	9.86494	+	5.69552i	0.861904	+	0.497620i	−0.00274575	+	0.999996i	$0.500874\pi$
$132$	3.40507			0.296373
$133$	3.34853	+	10.6154i	0.290355	+	0.920474i
$134$		−	6.55425i		−	0.566201i
$135$	3.58686	+	2.07087i	0.308707	+	0.178232i
$136$	−3.74603	−	6.48831i	−0.321219	−	0.556368i
$137$	8.87797	−	5.12570i	0.758496	−	0.437918i	−0.0702592	−	0.997529i	$-0.522383\pi$
$137$	8.87797	−	5.12570i	0.758496	−	0.437918i	0.828756	+	0.559611i	$0.189049\pi$
$138$	−4.13691	+	2.42611i	−0.352157	+	0.206524i
$139$		−	3.82886i		−	0.324760i	−0.986728	−	0.162380i	$-0.948083\pi$
$139$		−	3.82886i		−	0.324760i	0.986728	−	0.162380i	$-0.0519170\pi$
$140$	−7.40209	+	8.08006i	−0.625591	+	0.682889i
$141$	1.92679			0.162265
$142$	7.35754	−	12.7436i	0.617431	−	1.06942i
$143$	0.0202251	+	0.0350309i	0.00169131	+	0.00292943i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	6.32789	−	10.9602i	0.525502	−	0.910197i
$146$		−	14.4147i		−	1.19297i
$147$	−4.01651	−	5.73303i	−0.331276	−	0.472852i
$148$		−	0.251481i		−	0.0206716i
$149$	0.189338	+	0.109314i	0.0155112	+	0.00895538i	0.507736	−	0.861513i	$-0.330483\pi$
$149$	0.189338	+	0.109314i	0.0155112	+	0.00895538i	−0.492224	+	0.870468i	$0.663816\pi$
$150$	10.5257	−	6.07702i	0.859421	−	0.496187i
$151$	−7.81998	−	13.5446i	−0.636381	−	1.10224i	−0.986221	−	0.165434i	$-0.947097\pi$
$151$	−7.81998	−	13.5446i	−0.636381	−	1.10224i	0.349840	−	0.936809i	$-0.386236\pi$
$152$	2.10357	−	3.64349i	0.170622	−	0.295526i
$153$	−7.49206			−0.605697
$154$	6.64289	+	6.08551i	0.535299	+	0.490385i
$155$			27.1165i			2.17805i
$156$	−0.00593970	+	0.0102879i	−0.000475557	+	0.000823688i
$157$	9.61479	+	16.6533i	0.767343	+	1.32908i	0.938999	+	0.343921i	$0.111755\pi$
$157$	9.61479	+	16.6533i	0.767343	+	1.32908i	−0.171655	+	0.985157i	$0.554911\pi$
$158$	13.9139	−	8.03322i	1.10693	−	0.639088i
$159$	3.48090	−	6.02910i	0.276054	−	0.478139i
$160$	4.14174			0.327434
$161$	−12.4065	−	2.66039i	−0.977773	−	0.209668i
$162$	1.00000			0.0785674
$163$	5.17329	−	8.96039i	0.405203	−	0.701832i	−0.589142	−	0.808029i	$-0.700534\pi$
$163$	5.17329	−	8.96039i	0.405203	−	0.701832i	0.994345	+	0.106197i	$0.0338675\pi$
$164$	6.42812	−	3.71128i	0.501952	−	0.289802i
$165$	−7.05146	−	12.2135i	−0.548956	−	0.950819i
$166$	−1.60992	+	2.78847i	−0.124954	+	0.216427i
$167$			1.64656i			0.127414i	0.997969	+	0.0637072i	$0.0202924\pi$
$167$			1.64656i			0.127414i	−0.997969	+	0.0637072i	$0.979708\pi$
$168$	−0.572313	+	2.58311i	−0.0441549	+	0.199291i
$169$	12.9999			0.999989
$170$	−15.5151	+	26.8729i	−1.18995	+	2.06106i
$171$	−2.10357	−	3.64349i	−0.160864	−	0.278624i
$172$	−5.31757	+	3.07010i	−0.405461	+	0.234093i
$173$	−8.50190	−	4.90858i	−0.646388	−	0.373192i	0.140683	−	0.990055i	$-0.455070\pi$
$173$	−8.50190	−	4.90858i	−0.646388	−	0.373192i	−0.787071	+	0.616863i	$0.788403\pi$
$174$		−	3.05566i		−	0.231649i
$175$	31.3952	+	6.95591i	2.37326	+	0.525818i
$176$		−	3.40507i		−	0.256667i
$177$	−2.44974	+	4.24307i	−0.184134	+	0.318929i
$178$	−2.47304	−	4.28344i	−0.185362	−	0.321057i
$179$	0.924798	+	1.60180i	0.0691226	+	0.119724i	0.898515	−	0.438942i	$-0.144647\pi$
$179$	0.924798	+	1.60180i	0.0691226	+	0.119724i	−0.829393	+	0.558666i	$0.811313\pi$
$180$	2.07087	−	3.58686i	0.154354	−	0.267348i
$181$	18.1838			1.35159			0.675795	−	0.737089i	$-0.263800\pi$
$181$	18.1838			1.35159			0.675795	+	0.737089i	$0.263800\pi$
$182$	−0.0299740	+	0.00945503i	−0.00222182	+	0.000700853i
$183$			3.46886i			0.256426i
$184$	2.42611	+	4.13691i	0.178855	+	0.304977i
$185$	−0.902025	+	0.520784i	−0.0663182	+	0.0382888i
$186$	3.27356	+	5.66997i	0.240029	+	0.415743i
$187$	22.0932	+	12.7555i	1.61561	+	0.932774i
$188$		−	1.92679i		−	0.140525i
$189$	1.95088	+	1.78719i	0.141906	+	0.129999i
$190$	−17.4249			−1.26413
$191$	−20.5685	−	11.8753i	−1.48829	−	0.859263i	−0.488377	−	0.872633i	$-0.662411\pi$
$191$	−20.5685	−	11.8753i	−1.48829	−	0.859263i	−0.999911	+	0.0133691i	$0.995744\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	5.19123	+	8.99148i	0.373673	+	0.647221i	0.990127	−	0.140170i	$-0.0447648\pi$
$193$	5.19123	+	8.99148i	0.373673	+	0.647221i	−0.616454	+	0.787391i	$0.711431\pi$
$194$	0.929230	−	1.60947i	0.0667148	−	0.115553i
$195$	0.0492014			0.00352339
$196$	−5.73303	+	4.01651i	−0.409502	+	0.286894i
$197$	−5.62319			−0.400636			−0.200318	−	0.979731i	$-0.564198\pi$
$197$	−5.62319			−0.400636			−0.200318	+	0.979731i	$0.564198\pi$
$198$	−2.94888	−	1.70253i	−0.209568	−	0.120994i
$199$	2.96979	+	5.14382i	0.210522	+	0.364636i	0.951878	−	0.306477i	$-0.0991501\pi$
$199$	2.96979	+	5.14382i	0.210522	+	0.364636i	−0.741356	+	0.671112i	$0.765817\pi$
$200$	−6.07702	−	10.5257i	−0.429710	−	0.744280i
$201$	−3.27713	+	5.67615i	−0.231151	+	0.400365i
$202$		−	5.71865i		−	0.402363i
$203$	5.46106	−	5.96124i	0.383291	−	0.418397i
$204$			7.49206i			0.524549i
$205$	−26.6236	−	15.3712i	−1.85947	−	1.07357i
$206$	−8.11946	−	14.0633i	−0.565710	−	0.979838i
$207$	4.79572	−	0.0326186i	0.333326	−	0.00226715i
$208$	0.0102879	+	0.00593970i	0.000713335	+	0.000411844i
$209$			14.3256i			0.990922i
$210$	10.4504	−	3.29649i	0.721148	−	0.227479i
$211$	−22.8207			−1.57104			−0.785520	−	0.618836i	$-0.787604\pi$
$211$	−22.8207			−1.57104			−0.785520	+	0.618836i	$0.787604\pi$
$212$	−6.02910	−	3.48090i	−0.414080	−	0.239069i
$213$	−12.7436	+	7.35754i	−0.873179	+	0.504130i
$214$	13.0748	−	7.54877i	0.893778	−	0.516023i
$215$	22.0240	+	12.7156i	1.50202	+	0.867194i
$216$		−	1.00000i		−	0.0680414i
$217$	−3.74700	+	16.9119i	−0.254363	+	1.14806i
$218$		−	5.32039i		−	0.360342i
$219$	−7.20733	+	12.4835i	−0.487026	+	0.843554i
$220$	−12.2135	+	7.05146i	−0.823433	+	0.475410i
$221$	−0.0770772	+	0.0445006i	−0.00518478	+	0.00299343i
$222$	−0.125740	+	0.217789i	−0.00843914	+	0.0146170i
$223$		−	6.89129i		−	0.461475i	−0.973016	−	0.230737i	$-0.925886\pi$
$223$		−	6.89129i		−	0.461475i	0.973016	−	0.230737i	$-0.0741138\pi$
$224$	2.58311	+	0.572313i	0.172591	+	0.0382392i
$225$	−12.1540			−0.810269
$226$	6.68324	+	3.85857i	0.444563	+	0.256668i
$227$	12.3496	+	21.3901i	0.819670	+	1.41971i	0.905925	+	0.423437i	$0.139177\pi$
$227$	12.3496	+	21.3901i	0.819670	+	1.41971i	−0.0862551	+	0.996273i	$0.527490\pi$
$228$	−3.64349	+	2.10357i	−0.241296	+	0.139312i
$229$	−1.02737	+	1.77946i	−0.0678905	+	0.117590i	−0.897973	−	0.440052i	$-0.854960\pi$
$229$	−1.02737	+	1.77946i	−0.0678905	+	0.117590i	0.830082	+	0.557641i	$0.188294\pi$
$230$	9.81432	−	17.2691i	0.647137	−	1.13869i
$231$	−2.71016	−	8.59166i	−0.178315	−	0.565289i
$232$	−3.05566			−0.200614
$233$	−13.9172	+	24.1053i	−0.911748	+	1.57919i	−0.100154	+	0.994972i	$0.531933\pi$
$233$	−13.9172	+	24.1053i	−0.911748	+	1.57919i	−0.811594	+	0.584222i	$0.801400\pi$
$234$	0.0102879	−	0.00593970i	0.000672539	−	0.000388290i
$235$	−6.91111	+	3.99013i	−0.450831	+	0.260287i
$236$	4.24307	+	2.44974i	0.276200	+	0.159464i
$237$	−16.0664			−1.04363
$238$	−13.3897	+	14.6161i	−0.867928	+	0.947423i
$239$	−14.9101			−0.964457			−0.482229	−	0.876045i	$-0.660173\pi$
$239$	−14.9101			−0.964457			−0.482229	+	0.876045i	$0.660173\pi$
$240$	−3.58686	−	2.07087i	−0.231531	−	0.133674i
$241$	1.57716	+	2.73172i	0.101594	+	0.175966i	0.912341	−	0.409430i	$-0.134272\pi$
$241$	1.57716	+	2.73172i	0.101594	+	0.175966i	−0.810748	+	0.585396i	$0.800939\pi$
$242$	0.297250	+	0.514851i	0.0191079	+	0.0330959i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	3.46886			0.222071
$245$	26.2790	+	12.2459i	1.67890	+	0.782360i
$246$	−7.42255			−0.473245
$247$	−0.0432824	−	0.0249891i	−0.00275400	−	0.00159002i
$248$	5.66997	−	3.27356i	0.360044	−	0.207871i
$249$	2.78847	−	1.60992i	0.176712	−	0.102025i
$250$	−14.8151	+	25.6605i	−0.936990	+	1.62291i
$251$	−13.1734			−0.831501			−0.415750	−	0.909479i	$-0.636481\pi$
$251$	−13.1734			−0.831501			−0.415750	+	0.909479i	$0.636481\pi$
$252$	1.78719	−	1.95088i	0.112583	−	0.122894i
$253$	−14.1975	−	8.06869i	−0.892591	−	0.507274i
$254$	−1.86789	+	3.23529i	−0.117202	+	0.203000i
$255$	26.8729	−	15.5151i	1.68285	−	0.971593i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.5759	+	6.68336i	0.722086	+	0.416897i	0.815520	−	0.578729i	$-0.196451\pi$
$257$	11.5759	+	6.68336i	0.722086	+	0.416897i	−0.0934339	+	0.995625i	$0.529784\pi$
$258$	6.14020			0.382272
$259$	−0.634535	+	0.200158i	−0.0394281	+	0.0124372i
$260$		−	0.0492014i		−	0.00305134i
$261$	−1.52783	+	2.64628i	−0.0945704	+	0.163801i
$262$	−9.86494	+	5.69552i	−0.609458	+	0.351871i
$263$	−12.0907	+	6.98055i	−0.745543	+	0.430439i	−0.824081	−	0.566472i	$-0.808308\pi$
$263$	−12.0907	+	6.98055i	−0.745543	+	0.430439i	0.0785382	+	0.996911i	$0.474975\pi$
$264$	−1.70253	+	2.94888i	−0.104784	+	0.181491i
$265$			28.8340i			1.77126i
$266$	−10.8675	−	2.40780i	−0.666329	−	0.147631i
$267$			4.94609i			0.302696i
$268$	5.67615	+	3.27713i	0.346726	+	0.200182i
$269$	20.6740	−	11.9362i	1.26052	−	0.727760i	0.287343	−	0.957828i	$-0.407228\pi$
$269$	20.6740	−	11.9362i	1.26052	−	0.727760i	0.973175	+	0.230067i	$0.0738946\pi$
$270$	−3.58686	+	2.07087i	−0.218289	+	0.126029i
$271$	−21.6821	−	12.5182i	−1.31710	−	0.760426i	−0.333836	−	0.942631i	$-0.608343\pi$
$271$	−21.6821	−	12.5182i	−1.31710	−	0.760426i	−0.983260	+	0.182205i	$0.941676\pi$
$272$	7.49206			0.454273
$273$	0.0306858	+	0.00679873i	0.00185719	+	0.000411478i
$274$			10.2514i			0.619310i
$275$	35.8408	+	20.6927i	2.16128	+	1.24782i
$276$	−0.0326186	−	4.79572i	−0.00196341	−	0.288668i
$277$	11.6494	+	20.1774i	0.699946	+	1.21234i	0.968485	+	0.249073i	$0.0801258\pi$
$277$	11.6494	+	20.1774i	0.699946	+	1.21234i	−0.268539	+	0.963269i	$0.586541\pi$
$278$	3.31589	+	1.91443i	0.198874	+	0.114820i
$279$		−	6.54712i		−	0.391966i
$280$	−3.29649	−	10.4504i	−0.197003	−	0.624533i
$281$			2.63661i			0.157287i	0.996903	+	0.0786434i	$0.0250588\pi$
$281$			2.63661i			0.157287i	−0.996903	+	0.0786434i	$0.974941\pi$
$282$	−0.963394	+	1.66865i	−0.0573692	+	0.0993665i
$283$	−3.03221	−	5.25194i	−0.180246	−	0.312195i	0.761718	−	0.647908i	$-0.224356\pi$
$283$	−3.03221	−	5.25194i	−0.180246	−	0.312195i	−0.941964	+	0.335713i	$0.891023\pi$
$284$	7.35754	+	12.7436i	0.436589	+	0.756195i
$285$	15.0904	+	8.71244i	0.893877	+	0.516080i
$286$	−0.0404502			−0.00239187
$287$	−14.4805	−	13.2655i	−0.854759	−	0.783039i
$288$	−1.00000			−0.0589256
$289$	−19.5655	+	33.8884i	−1.15091	+	1.99343i
$290$	6.32789	+	10.9602i	0.371586	+	0.643606i
$291$	−1.60947	+	0.929230i	−0.0943490	+	0.0544724i
$292$	12.4835	+	7.20733i	0.730539	+	0.421777i
$293$	9.39019			0.548580			0.274290	−	0.961647i	$-0.411557\pi$
$293$	9.39019			0.548580			0.274290	+	0.961647i	$0.411557\pi$
$294$	6.97321	−	0.611887i	0.406686	−	0.0356860i
$295$		−	20.2924i		−	1.18147i
$296$	0.217789	+	0.125740i	0.0126587	+	0.00730851i
$297$	1.70253	+	2.94888i	0.0987911	+	0.171111i
$298$	−0.189338	+	0.109314i	−0.0109680	+	0.00633241i
$299$	0.0491440	−	0.0288207i	0.00284207	−	0.00166675i
$300$			12.1540i			0.701714i
$301$	11.9788	+	10.9737i	0.690447	+	0.632515i
$302$	15.6400			0.899978
$303$	−2.85933	+	4.95250i	−0.164264	+	0.284513i
$304$	2.10357	+	3.64349i	0.120648	+	0.208968i
$305$	−7.18357	−	12.4423i	−0.411330	−	0.712444i
$306$	3.74603	−	6.48831i	0.214146	−	0.370912i
$307$		−	16.7506i		−	0.956008i	−0.878358	−	0.478004i	$-0.841360\pi$
$307$		−	16.7506i		−	0.956008i	0.878358	−	0.478004i	$-0.158640\pi$
$308$	−8.59166	+	2.71016i	−0.489555	+	0.154425i
$309$			16.2389i			0.923800i
$310$	−23.4836	−	13.5582i	−1.33378	−	0.770057i
$311$	−15.0287	+	8.67684i	−0.852201	+	0.492019i	−0.861393	−	0.507939i	$-0.830407\pi$
$311$	−15.0287	+	8.67684i	−0.852201	+	0.492019i	0.00919180	+	0.999958i	$0.497074\pi$
$312$	−0.00593970	−	0.0102879i	−0.000336269	−	0.000582436i
$313$	12.2439	−	21.2070i	0.692065	−	1.19869i	−0.279095	−	0.960263i	$-0.590034\pi$
$313$	12.2439	−	21.2070i	0.692065	−	1.19869i	0.971160	−	0.238428i	$-0.0766322\pi$
$314$	−19.2296			−1.08519
$315$	−10.6986	−	2.37037i	−0.602797	−	0.133555i
$316$			16.0664i			0.903808i
$317$	12.0930	−	20.9457i	0.679209	−	1.17643i	−0.296010	−	0.955185i	$-0.595656\pi$
$317$	12.0930	−	20.9457i	0.679209	−	1.17643i	0.975219	−	0.221240i	$-0.0710105\pi$
$318$	3.48090	+	6.02910i	0.195199	+	0.338095i
$319$	9.01077	−	5.20237i	0.504507	−	0.291277i
$320$	−2.07087	+	3.58686i	−0.115765	+	0.200511i
$321$	−15.0975			−0.842662
$322$	8.50724	−	9.41418i	0.474090	−	0.524632i
$323$	−31.5201			−1.75382
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−0.125039	+	0.0721914i	−0.00693592	+	0.00400446i
$326$	5.17329	+	8.96039i	0.286522	+	0.496270i
$327$	−2.66020	+	4.60759i	−0.147109	+	0.254801i
$328$			7.42255i			0.409842i
$329$	−4.86166	+	1.53356i	−0.268032	+	0.0845481i
$330$	14.1029			0.776341
$331$	10.8867	−	18.8563i	0.598387	−	1.03644i	−0.394672	−	0.918822i	$-0.629142\pi$
$331$	10.8867	−	18.8563i	0.598387	−	1.03644i	0.993059	−	0.117615i	$-0.0375250\pi$
$332$	−1.60992	−	2.78847i	−0.0883561	−	0.153037i
$333$	0.217789	−	0.125740i	0.0119347	−	0.00689053i
$334$	−1.42596	−	0.823279i	−0.0780251	−	0.0450478i
$335$		−	27.1460i		−	1.48315i
$336$	−1.95088	−	1.78719i	−0.106429	−	0.0974993i
$337$		−	3.42043i		−	0.186323i	−0.995651	−	0.0931613i	$-0.970303\pi$
$337$		−	3.42043i		−	0.186323i	0.995651	−	0.0931613i	$-0.0296972\pi$
$338$	−6.49993	+	11.2582i	−0.353550	+	0.612366i
$339$	−3.85857	−	6.68324i	−0.209569	−	0.362984i
$340$	−15.5151	−	26.8729i	−0.841424	−	1.45739i
$341$	−11.1467	+	19.3066i	−0.603628	+	1.04551i
$342$	4.20714			0.227496
$343$	14.6975	+	11.2687i	0.793589	+	0.608455i
$344$		−	6.14020i		−	0.331057i
$345$	−17.1340	+	10.0483i	−0.922464	+	0.540983i
$346$	8.50190	−	4.90858i	0.457065	−	0.263887i
$347$	5.32191	+	9.21782i	0.285695	+	0.494838i	0.972778	−	0.231741i	$-0.0744422\pi$
$347$	5.32191	+	9.21782i	0.285695	+	0.494838i	−0.687082	+	0.726580i	$0.741109\pi$
$348$	2.64628	+	1.52783i	0.141856	+	0.0819004i
$349$			15.1249i			0.809617i	0.914401	+	0.404809i	$0.132662\pi$
$349$			15.1249i			0.809617i	−0.914401	+	0.404809i	$0.867338\pi$
$350$	−21.7216	+	23.7111i	−1.16107	+	1.26741i
$351$	−0.0118794			−0.000634076
$352$	2.94888	+	1.70253i	0.157176	+	0.0907454i
$353$	−3.33838	+	1.92741i	−0.177684	+	0.102586i	−0.586204	−	0.810163i	$-0.699378\pi$
$353$	−3.33838	+	1.92741i	−0.177684	+	0.102586i	0.408520	+	0.912749i	$0.366045\pi$
$354$	−2.44974	−	4.24307i	−0.130202	−	0.225517i
$355$	30.4730	−	52.7808i	1.61734	−	2.80132i
$356$	4.94609			0.262142
$357$	18.9039	−	5.96306i	1.00050	−	0.315599i
$358$	−1.84960			−0.0977542
$359$	−5.60508	−	3.23609i	−0.295825	−	0.170794i	0.344741	−	0.938698i	$-0.387967\pi$
$359$	−5.60508	−	3.23609i	−0.295825	−	0.170794i	−0.640566	+	0.767903i	$0.721300\pi$
$360$	2.07087	+	3.58686i	0.109145	+	0.189044i
$361$	0.650006	+	1.12584i	0.0342109	+	0.0592549i
$362$	−9.09190	+	15.7476i	−0.477860	+	0.827677i
$363$		−	0.594499i		−	0.0312031i
$364$	0.00679873	−	0.0306858i	0.000356350	−	0.00160837i
$365$		−	59.7018i		−	3.12494i
$366$	−3.00412	−	1.73443i	−0.157028	−	0.0906602i
$367$	−13.2604	−	22.9677i	−0.692187	−	1.19890i	−0.971120	−	0.238592i	$-0.923314\pi$
$367$	−13.2604	−	22.9677i	−0.692187	−	1.19890i	0.278933	−	0.960310i	$-0.410019\pi$
$368$	−4.79572	+	0.0326186i	−0.249994	+	0.00170036i
$369$	6.42812	+	3.71128i	0.334634	+	0.193201i
$370$		−	1.04157i		−	0.0541486i
$371$	−3.98433	+	17.9831i	−0.206856	+	0.933637i
$372$	−6.54712			−0.339452
$373$	−27.8367	−	16.0715i	−1.44133	−	0.832151i	−0.443389	−	0.896329i	$-0.646224\pi$
$373$	−27.8367	−	16.0715i	−1.44133	−	0.832151i	−0.997938	+	0.0641781i	$0.979557\pi$
$374$	−22.0932	+	12.7555i	−1.14241	+	0.659570i
$375$	25.6605	−	14.8151i	1.32510	−	0.765049i
$376$	1.66865	+	0.963394i	0.0860539	+	0.0496832i
$377$			0.0362994i			0.00186952i
$378$	−2.52320	+	0.795918i	−0.129779	+	0.0409376i
$379$			8.96195i			0.460345i	0.973150	+	0.230172i	$0.0739290\pi$
$379$			8.96195i			0.460345i	−0.973150	+	0.230172i	$0.926071\pi$
$380$	8.71244	−	15.0904i	0.446939	−	0.774120i
$381$	3.23529	−	1.86789i	0.165749	−	0.0956951i
$382$	20.5685	−	11.8753i	1.05238	−	0.607591i
$383$	−10.8746	+	18.8354i	−0.555667	+	0.962444i	0.442184	+	0.896924i	$0.354204\pi$
$383$	−10.8746	+	18.8354i	−0.555667	+	0.962444i	−0.997851	+	0.0655195i	$0.979130\pi$
$384$			1.00000i			0.0510310i
$385$	27.5132	+	25.2046i	1.40220	+	1.28455i
$386$	−10.3825			−0.528454
$387$	−5.31757	−	3.07010i	−0.270307	−	0.156062i
$388$	0.929230	+	1.60947i	0.0471745	+	0.0817086i
$389$	14.3560	−	8.28843i	0.727878	−	0.420240i	−0.0897677	−	0.995963i	$-0.528612\pi$
$389$	14.3560	−	8.28843i	0.727878	−	0.420240i	0.817645	+	0.575722i	$0.195279\pi$
$390$	−0.0246007	+	0.0426097i	−0.00124571	+	0.00215763i
$391$	17.7533	−	31.2383i	0.897821	−	1.57979i
$392$	−0.611887	−	6.97321i	−0.0309050	−	0.352200i
$393$	11.3910			0.574602
$394$	2.81160	−	4.86983i	0.141646	−	0.245338i
$395$	57.6280	−	33.2715i	2.89958	−	1.67407i
$396$	2.94888	−	1.70253i	0.148187	−	0.0855556i
$397$	14.8886	+	8.59593i	0.747237	+	0.431417i	0.824695	−	0.565578i	$-0.191347\pi$
$397$	14.8886	+	8.59593i	0.747237	+	0.431417i	−0.0774578	+	0.996996i	$0.524680\pi$
$398$	−5.93957			−0.297724
$399$	8.20763	+	7.51896i	0.410895	+	0.376419i
$400$	12.1540			0.607702
$401$	−25.9597	−	14.9878i	−1.29636	−	0.748456i	−0.316589	−	0.948563i	$-0.602538\pi$
$401$	−25.9597	−	14.9878i	−1.29636	−	0.748456i	−0.979774	+	0.200107i	$0.935871\pi$
$402$	−3.27713	−	5.67615i	−0.163448	−	0.283101i
$403$	−0.0388879	−	0.0673559i	−0.00193715	−	0.00335523i
$404$	4.95250	+	2.85933i	0.246396	+	0.142257i
$405$	4.14174			0.205805
$406$	2.43206	+	7.71004i	0.120701	+	0.382643i
$407$	−0.856309			−0.0424457
$408$	−6.48831	−	3.74603i	−0.321219	−	0.185456i
$409$	7.61386	−	4.39586i	0.376481	−	0.217361i	−0.299805	−	0.954000i	$-0.596922\pi$
$409$	7.61386	−	4.39586i	0.376481	−	0.217361i	0.676286	+	0.736639i	$0.263588\pi$
$410$	26.6236	−	15.3712i	1.31485	−	0.759127i
$411$	5.12570	−	8.87797i	0.252832	−	0.437918i
$412$	16.2389			0.800035
$413$	2.80403	−	12.6559i	0.137977	−	0.622756i
$414$	−2.36961	+	4.16953i	−0.116460	+	0.204921i
$415$	−6.66789	+	11.5491i	−0.327314	+	0.566925i
$416$	−0.0102879	+	0.00593970i	−0.000504404	+	0.000291218i
$417$	−1.91443	−	3.31589i	−0.0937501	−	0.162380i
$418$	−12.4063	−	7.16279i	−0.606813	−	0.350344i
$419$	−19.4537			−0.950376			−0.475188	−	0.879884i	$-0.657620\pi$
$419$	−19.4537			−0.950376			−0.475188	+	0.879884i	$0.657620\pi$
$420$	−2.37037	+	10.6986i	−0.115662	+	0.522037i
$421$			29.0638i			1.41648i	0.705970	+	0.708242i	$0.250511\pi$
$421$			29.0638i			1.41648i	−0.705970	+	0.708242i	$0.749489\pi$
$422$	11.4103	−	19.7633i	0.555447	−	0.962062i
$423$	1.66865	−	0.963394i	0.0811324	−	0.0468418i
$424$	6.02910	−	3.48090i	0.292799	−	0.169048i
$425$	−45.5294	+	78.8592i	−2.20850	+	3.82523i
$426$		−	14.7151i		−	0.712947i
$427$	−2.76093	−	8.75262i	−0.133611	−	0.423569i
$428$			15.0975i			0.729767i
$429$	0.0350309	+	0.0202251i	0.00169131	+	0.000976477i
$430$	−22.0240	+	12.7156i	−1.06209	+	0.613199i
$431$	4.05180	−	2.33931i	0.195169	−	0.112681i	−0.399231	−	0.916850i	$-0.630723\pi$
$431$	4.05180	−	2.33931i	0.195169	−	0.112681i	0.594400	+	0.804170i	$0.297390\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	3.61273			0.173617			0.0868083	−	0.996225i	$-0.472333\pi$
$433$	3.61273			0.173617			0.0868083	+	0.996225i	$0.472333\pi$
$434$	−12.7727	−	11.7010i	−0.613107	−	0.561664i
$435$		−	12.6558i		−	0.606798i
$436$	4.60759	+	2.66020i	0.220664	+	0.127400i
$437$	20.1762	−	0.137231i	0.965161	−	0.00656465i
$438$	−7.20733	−	12.4835i	−0.344380	−	0.596483i
$439$	8.12548	+	4.69125i	0.387808	+	0.223901i	0.681210	−	0.732088i	$-0.261454\pi$
$439$	8.12548	+	4.69125i	0.387808	+	0.223901i	−0.293402	+	0.955989i	$0.594787\pi$
$440$		−	14.1029i		−	0.672331i
$441$	−6.34492	−	2.95669i	−0.302139	−	0.140795i
$442$		−	0.0890011i		−	0.00423335i
$443$	15.7665	−	27.3083i	0.749087	−	1.29746i	−0.199174	−	0.979964i	$-0.563826\pi$
$443$	15.7665	−	27.3083i	0.749087	−	1.29746i	0.948261	−	0.317492i	$-0.102841\pi$
$444$	−0.125740	−	0.217789i	−0.00596737	−	0.0103358i
$445$	−10.2427	−	17.7409i	−0.485551	−	0.840999i
$446$	5.96803	+	3.44564i	0.282594	+	0.163156i
$447$	0.218629			0.0103408
$448$	−1.78719	+	1.95088i	−0.0844369	+	0.0921705i
$449$	−30.9475			−1.46050			−0.730251	−	0.683179i	$-0.760597\pi$
$449$	−30.9475			−1.46050			−0.730251	+	0.683179i	$0.760597\pi$
$450$	6.07702	−	10.5257i	0.286474	−	0.496187i
$451$	−12.6372	−	21.8882i	−0.595060	−	1.03067i
$452$	−6.68324	+	3.85857i	−0.314353	+	0.181492i
$453$	−13.5446	−	7.81998i	−0.636381	−	0.367415i
$454$	−24.6992			−1.15919
$455$	−0.124145	+	0.0391603i	−0.00582000	+	0.00183586i
$456$		−	4.20714i		−	0.197017i
$457$	10.1142	+	5.83943i	0.473122	+	0.273157i	0.717546	−	0.696512i	$-0.245265\pi$
$457$	10.1142	+	5.83943i	0.473122	+	0.273157i	−0.244424	+	0.969668i	$0.578599\pi$
$458$	−1.02737	−	1.77946i	−0.0480058	−	0.0831485i
$459$	−6.48831	+	3.74603i	−0.302848	+	0.174850i
$460$	10.0483	+	17.1340i	0.468505	+	0.798877i
$461$			24.3030i			1.13191i	0.824438	+	0.565953i	$0.191492\pi$
$461$			24.3030i			1.13191i	−0.824438	+	0.565953i	$0.808508\pi$
$462$	8.79567	+	1.94876i	0.409212	+	0.0906647i
$463$	22.9252			1.06542			0.532712	−	0.846297i	$-0.321173\pi$
$463$	22.9252			1.06542			0.532712	+	0.846297i	$0.321173\pi$
$464$	1.52783	−	2.64628i	0.0709278	−	0.122851i
$465$	13.5582	+	23.4836i	0.628749	+	1.08902i
$466$	−13.9172	−	24.1053i	−0.644703	−	1.11666i
$467$	10.9483	−	18.9630i	0.506627	−	0.877503i	−0.493344	−	0.869834i	$-0.664226\pi$
$467$	10.9483	−	18.9630i	0.506627	−	0.877503i	0.999971	−	0.00766879i	$-0.00244107\pi$
$468$			0.0118794i			0.000549125i
$469$	3.75108	−	16.9304i	0.173209	−	0.781772i
$470$		−	7.98026i		−	0.368102i
$471$	16.6533	+	9.61479i	0.767343	+	0.443026i
$472$	−4.24307	+	2.44974i	−0.195303	+	0.112758i
$473$	10.4539	+	18.1067i	0.480671	+	0.832546i
$474$	8.03322	−	13.9139i	0.368978	−	0.639088i
$475$	−51.1337			−2.34618
$476$	−5.96306	−	18.9039i	−0.273316	−	0.866460i
$477$		−	6.96181i		−	0.318759i
$478$	7.45507	−	12.9126i	0.340987	−	0.590607i
$479$	−6.05009	−	10.4791i	−0.276436	−	0.478801i	0.694061	−	0.719917i	$-0.255820\pi$
$479$	−6.05009	−	10.4791i	−0.276436	−	0.478801i	−0.970496	+	0.241116i	$0.922487\pi$
$480$	3.58686	−	2.07087i	0.163717	−	0.0945219i
$481$	0.00149372	−	0.00258720i	6.81078e−5	−	0.000117966i
$482$	−3.15432			−0.143675
$483$	−12.0746	+	3.89930i	−0.549412	+	0.177424i
$484$	−0.594499			−0.0270227
$485$	3.84863	−	6.66603i	0.174757	−	0.302689i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	19.9371	+	34.5321i	0.903438	+	1.56480i	0.823000	+	0.568041i	$0.192299\pi$
$487$	19.9371	+	34.5321i	0.903438	+	1.56480i	0.0804383	+	0.996760i	$0.474368\pi$
$488$	−1.73443	+	3.00412i	−0.0785140	+	0.135990i
$489$		−	10.3466i		−	0.467888i
$490$	−23.7447	+	16.6354i	−1.07268	+	0.751509i
$491$	19.0618			0.860248			0.430124	−	0.902770i	$-0.358470\pi$
$491$	19.0618			0.860248			0.430124	+	0.902770i	$0.358470\pi$
$492$	3.71128	−	6.42812i	0.167317	−	0.289802i
$493$	11.4466	+	19.8261i	0.515529	+	0.892922i
$494$	0.0432824	−	0.0249891i	0.00194737	−	0.00112431i
$495$	−12.2135	−	7.05146i	−0.548956	−	0.316940i
$496$			6.54712i			0.293974i
$497$	26.2987	−	28.7074i	1.17966	−	1.28770i
$498$			3.21985i			0.144285i
$499$	5.53289	−	9.58324i	0.247686	−	0.429005i	−0.715197	−	0.698923i	$-0.753663\pi$
$499$	5.53289	−	9.58324i	0.247686	−	0.429005i	0.962883	+	0.269918i	$0.0869965\pi$
$500$	−14.8151	−	25.6605i	−0.662552	−	1.14757i
$501$	0.823279	+	1.42596i	0.0367814	+	0.0637072i
$502$	6.58672	−	11.4085i	0.293980	−	0.509188i
$503$	18.6027			0.829455			0.414727	−	0.909946i	$-0.363877\pi$
$503$	18.6027			0.829455			0.414727	+	0.909946i	$0.363877\pi$
$504$	0.795918	+	2.52320i	0.0354530	+	0.112392i
$505$		−	23.6852i		−	1.05398i
$506$	14.0865	−	8.26107i	0.626219	−	0.367249i
$507$	11.2582	−	6.49993i	0.499995	−	0.288672i
$508$	−1.86789	−	3.23529i	−0.0828744	−	0.143543i
$509$	−38.6617	−	22.3214i	−1.71365	−	0.989377i	−0.929512	−	0.368793i	$-0.879771\pi$
$509$	−38.6617	−	22.3214i	−1.71365	−	0.989377i	−0.784140	−	0.620584i	$-0.786896\pi$
$510$			31.0302i			1.37404i
$511$	8.24969	−	37.2347i	0.364945	−	1.64716i
$512$	1.00000			0.0441942
$513$	−3.64349	−	2.10357i	−0.160864	−	0.0928748i
$514$	−11.5759	+	6.68336i	−0.510592	+	0.294790i
$515$	−33.6287	−	58.2467i	−1.48186	−	2.56666i
$516$	−3.07010	+	5.31757i	−0.135154	+	0.234093i
$517$	−6.56084			−0.288546
$518$	0.143926	−	0.649602i	0.00632373	−	0.0285419i
$519$	−9.81715			−0.430925
$520$	0.0426097	+	0.0246007i	0.00186856	+	0.00107881i
$521$	4.40981	+	7.63802i	0.193197	+	0.334628i	0.946308	−	0.323266i	$-0.104781\pi$
$521$	4.40981	+	7.63802i	0.193197	+	0.334628i	−0.753111	+	0.657894i	$0.771448\pi$
$522$	−1.52783	−	2.64628i	−0.0668714	−	0.115825i
$523$	−19.7779	+	34.2563i	−0.864827	+	1.49792i	0.00239200	+	0.999997i	$0.499239\pi$
$523$	−19.7779	+	34.2563i	−0.864827	+	1.49792i	−0.867219	+	0.497927i	$0.834095\pi$
$524$		−	11.3910i		−	0.497620i
$525$	30.6670	−	9.67362i	1.33842	−	0.422191i
$526$		−	13.9611i		−	0.608733i
$527$	−42.4797	−	24.5257i	−1.85045	−	1.06836i
$528$	−1.70253	−	2.94888i	−0.0740933	−	0.128333i
$529$	−11.2280	+	20.0732i	−0.488174	+	0.872747i
$530$	−24.9710	−	14.4170i	−1.08467	−	0.626235i
$531$			4.89948i			0.212619i
$532$	7.51896	−	8.20763i	0.325988	−	0.355846i
$533$	0.0881755			0.00381930
$534$	−4.28344	−	2.47304i	−0.185362	−	0.107019i
$535$	54.1527	−	31.2651i	2.34122	−	1.35171i
$536$	−5.67615	+	3.27713i	−0.245172	+	0.141550i
$537$	1.60180	+	0.924798i	0.0691226	+	0.0399080i
$538$			23.8723i			1.02921i
$539$	13.6765	+	19.5214i	0.589089	+	0.840845i
$540$		−	4.14174i		−	0.178232i
$541$	−6.52010	+	11.2931i	−0.280321	+	0.485530i	−0.971464	−	0.237188i	$-0.923774\pi$
$541$	−6.52010	+	11.2931i	−0.280321	+	0.485530i	0.691143	+	0.722718i	$0.257108\pi$
$542$	21.6821	−	12.5182i	0.931328	−	0.537702i
$543$	15.7476	−	9.09190i	0.675795	−	0.390171i
$544$	−3.74603	+	6.48831i	−0.160610	+	0.278184i
$545$		−	22.0357i		−	0.943906i
$546$	−0.0212308	+	0.0231753i	−0.000908593	+	0.000991812i
$547$	2.21359			0.0946461			0.0473230	−	0.998880i	$-0.484931\pi$
$547$	2.21359			0.0946461			0.0473230	+	0.998880i	$0.484931\pi$
$548$	−8.87797	−	5.12570i	−0.379248	−	0.218959i
$549$	1.73443	+	3.00412i	0.0740237	+	0.128213i
$550$	−35.8408	+	20.6927i	−1.52826	+	0.882339i
$551$	−6.42779	+	11.1333i	−0.273833	+	0.474293i
$552$	4.16953	+	2.36961i	0.177467	+	0.100857i
$553$	40.5388	−	12.7876i	1.72388	−	0.543782i
$554$	−23.2988			−0.989873
$555$	−0.520784	+	0.902025i	−0.0221061	+	0.0382888i
$556$	−3.31589	+	1.91443i	−0.140625	+	0.0811900i
$557$	−11.4538	+	6.61285i	−0.485313	+	0.280195i	−0.722628	−	0.691237i	$-0.757066\pi$
$557$	−11.4538	+	6.61285i	−0.485313	+	0.280195i	0.237315	+	0.971433i	$0.423733\pi$
$558$	5.66997	+	3.27356i	0.240029	+	0.138581i
$559$	−0.0729419			−0.00308511
$560$	10.6986	+	2.37037i	0.452098	+	0.100167i
$561$	25.5110			1.07707
$562$	−2.28337	−	1.31830i	−0.0963181	−	0.0556093i
$563$	6.92727	+	11.9984i	0.291950	+	0.505672i	0.974271	−	0.225381i	$-0.0723627\pi$
$563$	6.92727	+	11.9984i	0.291950	+	0.505672i	−0.682321	+	0.731053i	$0.739029\pi$
$564$	−0.963394	−	1.66865i	−0.0405662	−	0.0702627i
$565$	27.6803	+	15.9812i	1.16452	+	0.672335i
$566$	6.06441			0.254906
$567$	2.58311	+	0.572313i	0.108480	+	0.0240349i
$568$	−14.7151			−0.617431
$569$	10.6379	+	6.14177i	0.445962	+	0.257476i	0.706123	−	0.708089i	$-0.250442\pi$
$569$	10.6379	+	6.14177i	0.445962	+	0.257476i	−0.260161	+	0.965565i	$0.583776\pi$
$570$	−15.0904	+	8.71244i	−0.632067	+	0.364924i
$571$	−3.25436	+	1.87891i	−0.136191	+	0.0786298i	−0.566547	−	0.824029i	$-0.691721\pi$
$571$	−3.25436	+	1.87891i	−0.136191	+	0.0786298i	0.430357	+	0.902659i	$0.358388\pi$
$572$	0.0202251	−	0.0350309i	0.000845654	−	0.00146472i
$573$	−23.7505			−0.992192
$574$	18.7285	−	5.90774i	0.781714	−	0.246584i
$575$	28.8004	−	50.6766i	1.20106	−	2.11336i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−22.2088	+	12.8223i	−0.924566	+	0.533798i	−0.885089	−	0.465422i	$-0.845903\pi$
$577$	−22.2088	+	12.8223i	−0.924566	+	0.533798i	−0.0394771	+	0.999220i	$0.512569\pi$
$578$	−19.5655	−	33.8884i	−0.813816	−	1.40957i
$579$	8.99148	+	5.19123i	0.373673	+	0.215740i
$580$	−12.6558			−0.525502
$581$	−5.75449	+	6.28155i	−0.238736	+	0.260602i
$582$		−	1.85846i		−	0.0770357i
$583$	−11.8527	+	20.5295i	−0.490890	+	0.850246i
$584$	−12.4835	+	7.20733i	−0.516569	+	0.298241i
$585$	0.0426097	−	0.0246007i	0.00176169	−	0.00101711i
$586$	−4.69509	+	8.13214i	−0.193952	+	0.335936i
$587$			5.66839i			0.233959i	0.993134	+	0.116980i	$0.0373212\pi$
$587$			5.66839i			0.233959i	−0.993134	+	0.116980i	$0.962679\pi$
$588$	−2.95669	+	6.34492i	−0.121932	+	0.261660i
$589$		−	27.5446i		−	1.13496i
$590$	17.5737	+	10.1462i	0.723499	+	0.417712i
$591$	−4.86983	+	2.81160i	−0.200318	+	0.115654i
$592$	−0.217789	+	0.125740i	−0.00895106	+	0.00516790i
$593$	−10.3112	−	5.95320i	−0.423432	−	0.244469i	0.273113	−	0.961982i	$-0.411947\pi$
$593$	−10.3112	−	5.95320i	−0.423432	−	0.244469i	−0.696545	+	0.717513i	$0.745280\pi$
$594$	−3.40507			−0.139712
$595$	−55.4569	+	60.5362i	−2.27351	+	2.48174i
$596$		−	0.218629i		−	0.00895538i
$597$	5.14382	+	2.96979i	0.210522	+	0.121545i
$598$	0.000387490		0.0569703i	1.58456e−5		0.00232969i
$599$	−14.1893	−	24.5766i	−0.579758	−	1.00417i	−0.995507	−	0.0946913i	$-0.969814\pi$
$599$	−14.1893	−	24.5766i	−0.579758	−	1.00417i	0.415748	−	0.909480i	$-0.363520\pi$
$600$	−10.5257	−	6.07702i	−0.429710	−	0.248093i
$601$		−	8.33218i		−	0.339877i	−0.985455	−	0.169938i	$-0.945643\pi$
$601$		−	8.33218i		−	0.339877i	0.985455	−	0.169938i	$-0.0543569\pi$
$602$	−15.4929	+	4.88709i	−0.631444	+	0.199183i
$603$			6.55425i			0.266910i
$604$	−7.81998	+	13.5446i	−0.318190	+	0.551122i
$605$	1.23113	+	2.13238i	0.0500526	+	0.0866937i
$606$	−2.85933	−	4.95250i	−0.116152	−	0.201181i
$607$	6.49459	+	3.74965i	0.263607	+	0.152194i	0.625979	−	0.779840i	$-0.284700\pi$
$607$	6.49459	+	3.74965i	0.263607	+	0.152194i	−0.362372	+	0.932034i	$0.618033\pi$
$608$	−4.20714			−0.170622
$609$	1.74879	−	7.89311i	0.0708647	−	0.319845i
$610$	14.3671			0.581708
$611$	0.0114445	−	0.0198225i	0.000462996	−	0.000801933i
$612$	3.74603	+	6.48831i	0.151424	+	0.262274i
$613$	8.46312	−	4.88618i	0.341822	−	0.197351i	−0.319255	−	0.947669i	$-0.603433\pi$
$613$	8.46312	−	4.88618i	0.341822	−	0.197351i	0.661077	+	0.750318i	$0.270099\pi$
$614$	14.5065	+	8.37530i	0.585433	+	0.338000i
$615$	−30.7423			−1.23965
$616$	1.94876	−	8.79567i	0.0785180	−	0.354388i
$617$		−	27.1140i		−	1.09157i	−0.837925	−	0.545785i	$-0.816232\pi$
$617$		−	27.1140i		−	1.09157i	0.837925	−	0.545785i	$-0.183768\pi$
$618$	−14.0633	−	8.11946i	−0.565710	−	0.326613i
$619$	13.2336	+	22.9213i	0.531904	+	0.921284i	0.999306	+	0.0372395i	$0.0118565\pi$
$619$	13.2336	+	22.9213i	0.531904	+	0.921284i	−0.467403	+	0.884044i	$0.654810\pi$
$620$	23.4836	−	13.5582i	0.943123	−	0.544512i
$621$	4.13691	−	2.42611i	0.166008	−	0.0973564i
$622$		−	17.3537i		−	0.695819i
$623$	−3.93668	−	12.4799i	−0.157720	−	0.499999i
$624$	0.0118794			0.000475557
$625$	−30.9753	+	53.6507i	−1.23901	+	2.14603i
$626$	12.2439	+	21.2070i	0.489364	+	0.847603i
$627$	7.16279	+	12.4063i	0.286054	+	0.495461i
$628$	9.61479	−	16.6533i	0.383672	−	0.664539i
$629$		−	1.88411i		−	0.0751243i
$630$	7.40209	−	8.08006i	0.294906	−	0.321917i
$631$			49.1912i			1.95827i	0.203213	+	0.979135i	$0.434862\pi$
$631$			49.1912i			1.95827i	−0.203213	+	0.979135i	$0.565138\pi$
$632$	−13.9139	−	8.03322i	−0.553467	−	0.319544i
$633$	−19.7633	+	11.4103i	−0.785520	+	0.453520i
$634$	12.0930	+	20.9457i	0.480274	+	0.831858i
$635$	−7.73634	+	13.3997i	−0.307007	+	0.531752i
$636$	−6.96181			−0.276054
$637$	−0.0828375	+	0.00726885i	−0.00328214	+	0.000288002i
$638$			10.4047i			0.411928i
$639$	−7.35754	+	12.7436i	−0.291060	+	0.504130i
$640$	−2.07087	−	3.58686i	−0.0818584	−	0.141783i
$641$	−33.5754	+	19.3847i	−1.32615	+	0.765651i	−0.984701	−	0.174250i	$-0.944250\pi$
$641$	−33.5754	+	19.3847i	−1.32615	+	0.765651i	−0.341446	+	0.939901i	$0.610917\pi$
$642$	7.54877	−	13.0748i	0.297926	−	0.516023i
$643$	5.75691			0.227030			0.113515	−	0.993536i	$-0.463789\pi$
$643$	5.75691			0.227030			0.113515	+	0.993536i	$0.463789\pi$
$644$	3.89930	+	12.0746i	0.153654	+	0.475805i
$645$	25.4311			1.00135
$646$	15.7600	−	27.2972i	0.620071	−	1.07399i
$647$	−20.9855	+	12.1160i	−0.825024	+	0.476328i	−0.852146	−	0.523304i	$-0.824699\pi$
$647$	−20.9855	+	12.1160i	−0.825024	+	0.476328i	0.0271219	+	0.999632i	$0.491366\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	8.34153	−	14.4480i	0.327434	−	0.567132i
$650$		−	0.144383i		−	0.00566316i
$651$	5.21097	+	16.5197i	0.204234	+	0.647457i
$652$	−10.3466			−0.405203
$653$	−13.2641	+	22.9741i	−0.519065	+	0.899048i	0.480689	+	0.876891i	$0.340387\pi$
$653$	−13.2641	+	22.9741i	−0.519065	+	0.899048i	−0.999755	+	0.0221565i	$0.992947\pi$
$654$	−2.66020	−	4.60759i	−0.104022	−	0.180171i
$655$	−40.8580	+	23.5894i	−1.59646	+	0.921714i
$656$	−6.42812	−	3.71128i	−0.250976	−	0.144901i
$657$			14.4147i			0.562369i
$658$	1.10272	−	4.97710i	0.0429887	−	0.194028i
$659$		−	28.9246i		−	1.12674i	−0.826204	−	0.563372i	$-0.809504\pi$
$659$		−	28.9246i		−	1.12674i	0.826204	−	0.563372i	$-0.190496\pi$
$660$	−7.05146	+	12.2135i	−0.274478	+	0.475410i
$661$	7.26785	+	12.5883i	0.282686	+	0.489627i	0.972046	−	0.234793i	$-0.0754411\pi$
$661$	7.26785	+	12.5883i	0.282686	+	0.489627i	−0.689359	+	0.724420i	$0.742108\pi$
$662$	10.8867	+	18.8563i	0.423124	+	0.732872i
$663$	−0.0445006	+	0.0770772i	−0.00172826	+	0.00299343i
$664$	3.21985			0.124954
$665$	−45.0104	−	9.97248i	−1.74543	−	0.386716i
$666$			0.251481i			0.00974468i
$667$	−7.41337	−	12.6410i	−0.287047	−	0.489461i
$668$	1.42596	−	0.823279i	0.0551721	−	0.0318536i
$669$	−3.44564	−	5.96803i	−0.133216	−	0.230737i
$670$	23.5092	+	13.5730i	0.908238	+	0.524372i
$671$		−	11.8117i		−	0.455986i
$672$	2.52320	−	0.795918i	0.0973344	−	0.0307032i
$673$	16.1673			0.623204			0.311602	−	0.950213i	$-0.399134\pi$
$673$	16.1673			0.623204			0.311602	+	0.950213i	$0.399134\pi$
$674$	2.96218	+	1.71021i	0.114099	+	0.0658750i
$675$	−10.5257	+	6.07702i	−0.405135	+	0.233905i
$676$	−6.49993	−	11.2582i	−0.249997	−	0.433008i
$677$	6.09267	−	10.5528i	0.234160	−	0.405578i	−0.724868	−	0.688888i	$-0.758099\pi$
$677$	6.09267	−	10.5528i	0.234160	−	0.405578i	0.959028	+	0.283310i	$0.0914326\pi$
$678$	7.71714			0.296375
$679$	3.32143	−	3.62564i	0.127465	−	0.139139i
$680$	31.0302			1.18995
$681$	21.3901	+	12.3496i	0.819670	+	0.473237i
$682$	−11.1467	−	19.3066i	−0.426829	−	0.739290i
$683$	2.73869	+	4.74356i	0.104793	+	0.181507i	0.913654	−	0.406493i	$-0.133249\pi$
$683$	2.73869	+	4.74356i	0.104793	+	0.181507i	−0.808861	+	0.588001i	$0.799915\pi$
$684$	−2.10357	+	3.64349i	−0.0804319	+	0.139312i
$685$			42.4587i			1.62226i
$686$	−17.1077	+	7.09401i	−0.653177	+	0.270850i
$687$			2.05474i			0.0783932i
$688$	5.31757	+	3.07010i	0.202730	+	0.117046i
$689$	−0.0413511	−	0.0716221i	−0.00157535	−	0.00272859i
$690$	−0.135098	−	19.8626i	−0.00514309	−	0.756158i
$691$	−15.9845	−	9.22868i	−0.608081	−	0.351076i	0.164133	−	0.986438i	$-0.447517\pi$
$691$	−15.9845	−	9.22868i	−0.608081	−	0.351076i	−0.772214	+	0.635363i	$0.780851\pi$
$692$			9.81715i			0.373192i
$693$	−6.64289	−	6.08551i	−0.252343	−	0.231170i
$694$	−10.6438			−0.404034
$695$	13.7336	+	7.92909i	0.520944	+	0.300767i
$696$	−2.64628	+	1.52783i	−0.100307	+	0.0579123i
$697$	48.1598	−	27.8051i	1.82418	−	1.05319i
$698$	−13.0985	−	7.56245i	−0.495787	−	0.286243i
$699$			27.8345i			1.05280i
$700$	−9.67362	−	30.6670i	−0.365628	−	1.15910i
$701$		−	5.95869i		−	0.225057i	−0.993649	−	0.112528i	$-0.964105\pi$
$701$		−	5.95869i		−	0.225057i	0.993649	−	0.112528i	$-0.0358949\pi$
$702$	0.00593970	−	0.0102879i	0.000224180	−	0.000388290i
$703$	0.916266	−	0.529007i	0.0345576	−	0.0199519i
$704$	−2.94888	+	1.70253i	−0.111140	+	0.0641667i
$705$	−3.99013	+	6.91111i	−0.150277	+	0.260287i
$706$		−	3.85483i		−	0.145078i
$707$	3.27286	−	14.7719i	0.123088	−	0.555555i
$708$	4.89948			0.184134
$709$	41.1190	+	23.7400i	1.54425	+	0.891576i	0.998563	+	0.0535899i	$0.0170664\pi$
$709$	41.1190	+	23.7400i	1.54425	+	0.891576i	0.545692	+	0.837986i	$0.316267\pi$
$710$	30.4730	+	52.7808i	1.14363	+	1.98083i
$711$	−13.9139	+	8.03322i	−0.521814	+	0.301269i
$712$	−2.47304	+	4.28344i	−0.0926812	+	0.160529i
$713$	27.2984	+	15.5141i	1.02233	+	0.581009i
$714$	−4.28780	+	19.3528i	−0.160467	+	0.724261i
$715$	−0.167534			−0.00626543
$716$	0.924798	−	1.60180i	0.0345613	−	0.0598620i
$717$	−12.9126	+	7.45507i	−0.482229	+	0.278415i
$718$	5.60508	−	3.23609i	0.209180	−	0.120770i
$719$	1.39863	+	0.807497i	0.0521599	+	0.0301146i	0.525853	−	0.850575i	$-0.323746\pi$
$719$	1.39863	+	0.807497i	0.0521599	+	0.0301146i	−0.473693	+	0.880690i	$0.657079\pi$
$720$	−4.14174			−0.154354
$721$	−12.9249	−	40.9740i	−0.481347	−	1.52595i
$722$	−1.30001			−0.0483815
$723$	2.73172	+	1.57716i	0.101594	+	0.0586552i
$724$	−9.09190	−	15.7476i	−0.337898	−	0.585256i
$725$	18.5693	+	32.1630i	0.689648	+	1.19450i
$726$	0.514851	+	0.297250i	0.0191079	+	0.0110320i
$727$	−5.21471			−0.193403			−0.0967014	−	0.995313i	$-0.530829\pi$
$727$	−5.21471			−0.193403			−0.0967014	+	0.995313i	$0.530829\pi$
$728$	0.0231753	+	0.0212308i	0.000858934	+	0.000786865i
$729$	−1.00000			−0.0370370
$730$	51.7033	+	29.8509i	1.91362	+	1.10483i
$731$	−39.8395	+	23.0014i	−1.47352	+	0.850736i
$732$	3.00412	−	1.73443i	0.111036	−	0.0641064i
$733$	1.29724	−	2.24689i	0.0479147	−	0.0829907i	−0.841073	−	0.540921i	$-0.818076\pi$
$733$	1.29724	−	2.24689i	0.0479147	−	0.0829907i	0.888988	+	0.457930i	$0.151409\pi$
$734$	26.5208			0.978900
$735$	28.8812	−	2.53428i	1.06530	−	0.0934783i
$736$	2.36961	−	4.16953i	0.0873450	−	0.153691i
$737$	11.1588	−	19.3277i	0.411041	−	0.711945i
$738$	−6.42812	+	3.71128i	−0.236622	+	0.136614i
$739$	−18.8050	−	32.5712i	−0.691752	−	1.19815i	−0.971263	−	0.238007i	$-0.923506\pi$
$739$	−18.8050	−	32.5712i	−0.691752	−	1.19815i	0.279512	−	0.960142i	$-0.409827\pi$
$740$	0.902025	+	0.520784i	0.0331591	+	0.0191444i
$741$	−0.0499782			−0.00183600
$742$	−13.5817	−	12.4421i	−0.498599	−	0.456764i
$743$			4.60969i			0.169113i	0.996419	+	0.0845565i	$0.0269473\pi$
$743$			4.60969i			0.169113i	−0.996419	+	0.0845565i	$0.973053\pi$
$744$	3.27356	−	5.66997i	0.120015	−	0.207871i
$745$	−0.784189	+	0.452752i	−0.0287305	+	0.0165875i
$746$	27.8367	−	16.0715i	1.01917	−	0.588420i
$747$	1.60992	−	2.78847i	0.0589040	−	0.102025i
$748$		−	25.5110i		−	0.932774i
$749$	38.0940	−	12.0164i	1.39193	−	0.439070i
$750$			29.6302i			1.08194i
$751$	31.3229	+	18.0843i	1.14299	+	0.659905i	0.947169	−	0.320735i	$-0.103930\pi$
$751$	31.3229	+	18.0843i	1.14299	+	0.659905i	0.195820	+	0.980640i	$0.437263\pi$
$752$	−1.66865	+	0.963394i	−0.0608493	+	0.0351313i
$753$	−11.4085	+	6.58672i	−0.415750	+	0.240034i
$754$	−0.0314362	−	0.0181497i	−0.00114484	−	0.000660974i
$755$	64.7767			2.35747
$756$	0.572313	−	2.58311i	0.0208148	−	0.0939468i
$757$		−	18.0602i		−	0.656410i	−0.944607	−	0.328205i	$-0.893556\pi$
$757$		−	18.0602i		−	0.656410i	0.944607	−	0.328205i	$-0.106444\pi$
$758$	−7.76128	−	4.48098i	−0.281902	−	0.162756i
$759$	−16.3298	+	0.111069i	−0.592733	+	0.00403154i
$760$	8.71244	+	15.0904i	0.316033	+	0.547386i
$761$	−16.1393	−	9.31800i	−0.585048	−	0.337777i	0.178089	−	0.984014i	$-0.443008\pi$
$761$	−16.1393	−	9.31800i	−0.585048	−	0.337777i	−0.763137	+	0.646237i	$0.776342\pi$
$762$			3.73579i			0.135333i
$763$	3.04493	−	13.7432i	0.110234	−	0.497536i
$764$			23.7505i			0.859263i
$765$	15.5151	−	26.8729i	0.560949	−	0.971593i
$766$	−10.8746	−	18.8354i	−0.392916	−	0.680551i
$767$	0.0291014	+	0.0504052i	0.00105079	+	0.00182002i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	18.7231			0.675172			0.337586	−	0.941295i	$-0.390390\pi$
$769$	18.7231			0.675172			0.337586	+	0.941295i	$0.390390\pi$
$770$	−35.5844	+	11.2248i	−1.28237	+	0.404513i
$771$	13.3667			0.481391
$772$	5.19123	−	8.99148i	0.186837	−	0.323610i
$773$	1.90468	+	3.29900i	0.0685065	+	0.118657i	0.898244	−	0.439497i	$-0.144843\pi$
$773$	1.90468	+	3.29900i	0.0685065	+	0.118657i	−0.829738	+	0.558154i	$0.811510\pi$
$774$	5.31757	−	3.07010i	0.191136	−	0.110352i
$775$	−68.9131	−	39.7870i	−2.47543	−	1.42919i
$776$	−1.85846			−0.0667148
$777$	−0.449444	+	0.490609i	−0.0161237	+	0.0176005i
$778$			16.5769i			0.594310i
$779$	27.0440	+	15.6138i	0.968951	+	0.559424i
$780$	−0.0246007	−	0.0426097i	−0.000880847	−	0.00152567i
$781$	43.3929	−	25.0529i	1.55272	−	0.896464i
$782$	18.1765	+	30.9939i	0.649992	+	1.10834i
$783$			3.05566i			0.109200i
$784$	6.34492	+	2.95669i	0.226604	+	0.105596i
$785$	−79.6440			−2.84261
$786$	−5.69552	+	9.86494i	−0.203153	+	0.351871i
$787$	−7.63862	−	13.2305i	−0.272287	−	0.471616i	0.697160	−	0.716916i	$-0.254447\pi$
$787$	−7.63862	−	13.2305i	−0.272287	−	0.471616i	−0.969447	+	0.245300i	$0.921114\pi$
$788$	2.81160	+	4.86983i	0.100159	+	0.173480i
$789$	−6.98055	+	12.0907i	−0.248514	+	0.430439i
$790$			66.5431i			2.36750i
$791$	15.0552	+	13.7920i	0.535303	+	0.490388i
$792$			3.40507i			0.120994i
$793$	0.0356872	+	0.0206040i	0.00126729	+	0.000731670i
$794$	−14.8886	+	8.59593i	−0.528376	+	0.305058i
$795$	14.4170	+	24.9710i	0.511319	+	0.885630i
$796$	2.96979	−	5.14382i	0.105261	−	0.182318i
$797$	−35.9534			−1.27353			−0.636767	−	0.771056i	$-0.719729\pi$
$797$	−35.9534			−1.27353			−0.636767	+	0.771056i	$0.719729\pi$
$798$	−10.6154	+	3.34853i	−0.375782	+	0.118537i
$799$		−	14.4356i		−	0.510695i
$800$	−6.07702	+	10.5257i	−0.214855	+	0.372140i
$801$	2.47304	+	4.28344i	0.0873807	+	0.151348i
$802$	25.9597	−	14.9878i	0.916667	−	0.529238i
$803$	24.5415	−	42.5071i	0.866049	−	1.50004i
$804$	6.55425			0.231151
$805$	35.2348	−	38.9911i	1.24186	−	1.37426i
$806$	0.0777759			0.00273954
$807$	11.9362	−	20.6740i	0.420173	−	0.727760i
$808$	−4.95250	+	2.85933i	−0.174228	+	0.100591i
$809$	−27.8287	−	48.2008i	−0.978406	−	1.69465i	−0.668205	−	0.743977i	$-0.732937\pi$
$809$	−27.8287	−	48.2008i	−0.978406	−	1.69465i	−0.310201	−	0.950671i	$-0.600396\pi$
$810$	−2.07087	+	3.58686i	−0.0727630	+	0.126029i
$811$			46.4070i			1.62957i	0.579764	+	0.814784i	$0.303145\pi$
$811$			46.4070i			1.62957i	−0.579764	+	0.814784i	$0.696855\pi$
$812$	−7.89311	−	1.74879i	−0.276994	−	0.0613707i
$813$	−25.0364			−0.878064
$814$	0.428155	−	0.741586i	0.0150068	−	0.0259926i
$815$	21.4264	+	37.1117i	0.750535	+	1.29996i
$816$	6.48831	−	3.74603i	0.227136	−	0.131137i
$817$	−22.3717	−	12.9163i	−0.782688	−	0.451885i
$818$			8.79172i			0.307395i
$819$	0.0299740	−	0.00945503i	0.00104738	−	0.000330385i
$820$			30.7423i			1.07357i
$821$	7.39132	−	12.8021i	0.257959	−	0.446798i	−0.707736	−	0.706477i	$-0.750283\pi$
$821$	7.39132	−	12.8021i	0.257959	−	0.446798i	0.965695	+	0.259679i	$0.0836168\pi$
$822$	5.12570	+	8.87797i	0.178779	+	0.309655i
$823$	18.6894	+	32.3710i	0.651471	+	1.12838i	0.982766	+	0.184853i	$0.0591810\pi$
$823$	18.6894	+	32.3710i	0.651471	+	1.12838i	−0.331295	+	0.943527i	$0.607486\pi$
$824$	−8.11946	+	14.0633i	−0.282855	+	0.489919i
$825$	41.3854			1.44085
$826$	9.55831	+	8.75631i	0.332576	+	0.304671i
$827$		−	37.4564i		−	1.30249i	−0.758869	−	0.651243i	$-0.774248\pi$
$827$		−	37.4564i		−	1.30249i	0.758869	−	0.651243i	$-0.225752\pi$
$828$	−2.42611	−	4.13691i	−0.0843131	−	0.143767i
$829$	−21.5298	+	12.4302i	−0.747759	+	0.431719i	−0.824884	−	0.565302i	$-0.808759\pi$
$829$	−21.5298	+	12.4302i	−0.747759	+	0.431719i	0.0771244	+	0.997021i	$0.475426\pi$
$830$	−6.66789	−	11.5491i	−0.231446	−	0.400876i
$831$	20.1774	+	11.6494i	0.699946	+	0.404114i
$832$		−	0.0118794i		−	0.000411844i
$833$	−42.9522	+	30.0919i	−1.48820	+	1.04262i
$834$	3.82886			0.132583
$835$	−5.90596	−	3.40981i	−0.204384	−	0.118001i
$836$	12.4063	−	7.16279i	0.429082	−	0.247730i
$837$	−3.27356	−	5.66997i	−0.113151	−	0.195983i
$838$	9.72686	−	16.8474i	0.336009	−	0.581984i
$839$	−49.8140			−1.71977			−0.859884	−	0.510489i	$-0.829464\pi$
$839$	−49.8140			−1.71977			−0.859884	+	0.510489i	$0.829464\pi$
$840$	−8.08006	−	7.40209i	−0.278788	−	0.255396i
$841$	−19.6629			−0.678032
$842$	−25.1700	−	14.5319i	−0.867416	−	0.500803i
$843$	1.31830	+	2.28337i	0.0454048	+	0.0786434i
$844$	11.4103	+	19.7633i	0.392760	+	0.680280i
$845$	−26.9210	+	46.6286i	−0.926112	+	1.60407i
$846$			1.92679i			0.0662443i
$847$	0.473172	+	1.50004i	0.0162584	+	0.0515419i
$848$			6.96181i			0.239069i
$849$	−5.25194	−	3.03221i	−0.180246	−	0.104065i
$850$	−45.5294	−	78.8592i	−1.56164	−	2.70485i
$851$	0.00820296	+	1.20603i	0.000281194	+	0.0413422i
$852$	12.7436	+	7.35754i	0.436589	+	0.252065i
$853$		−	24.9380i		−	0.853860i	−0.904285	−	0.426930i	$-0.859595\pi$
$853$		−	24.9380i		−	0.853860i	0.904285	−	0.426930i	$-0.140405\pi$
$854$	8.96045	+	1.98527i	0.306620	+	0.0679347i
$855$	17.4249			0.595918
$856$	−13.0748	−	7.54877i	−0.446889	−	0.258012i
$857$	11.5553	−	6.67148i	0.394723	−	0.227893i	−0.289482	−	0.957184i	$-0.593483\pi$
$857$	11.5553	−	6.67148i	0.394723	−	0.227893i	0.684205	+	0.729290i	$0.260150\pi$
$858$	−0.0350309	+	0.0202251i	−0.00119593	+	0.000690473i
$859$	−24.3843	−	14.0783i	−0.831981	−	0.480344i	0.0225496	−	0.999746i	$-0.492822\pi$
$859$	−24.3843	−	14.0783i	−0.831981	−	0.480344i	−0.854530	+	0.519401i	$0.826155\pi$
$860$		−	25.4311i		−	0.867194i
$861$	−19.1733	−	4.24802i	−0.653423	−	0.144772i
$862$			4.67862i			0.159354i
$863$	7.99368	−	13.8455i	0.272108	−	0.471305i	−0.697293	−	0.716786i	$-0.745613\pi$
$863$	7.99368	−	13.8455i	0.272108	−	0.471305i	0.969401	+	0.245481i	$0.0789459\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	35.2127	−	20.3301i	1.19727	−	0.691243i
$866$	−1.80636	+	3.12871i	−0.0613827	+	0.106318i
$867$			39.1309i			1.32896i
$868$	16.5197	−	5.21097i	0.560714	−	0.176872i
$869$	54.7073			1.85582
$870$	10.9602	+	6.32789i	0.371586	+	0.214535i
$871$	0.0389303	+	0.0674293i	0.00131910	+	0.00228475i
$872$	−4.60759	+	2.66020i	−0.156033	+	0.0900856i
$873$	−0.929230	+	1.60947i	−0.0314497	+	0.0544724i
$874$	−9.96928	+	17.5418i	−0.337216	+	0.593359i
$875$	−52.9549	+	57.8051i	−1.79020	+	1.95417i
$876$	14.4147			0.487026
$877$	3.00817	−	5.21031i	0.101579	−	0.175940i	−0.810756	−	0.585384i	$-0.800944\pi$
$877$	3.00817	−	5.21031i	0.101579	−	0.175940i	0.912335	+	0.409444i	$0.134277\pi$
$878$	−8.12548	+	4.69125i	−0.274222	+	0.158322i
$879$	8.13214	−	4.69509i	0.274290	−	0.158362i
$880$	12.2135	+	7.05146i	0.411717	+	0.237705i
$881$	34.0526			1.14726			0.573631	−	0.819114i	$-0.305534\pi$
$881$	34.0526			1.14726			0.573631	+	0.819114i	$0.305534\pi$
$882$	5.73303	−	4.01651i	0.193041	−	0.135243i
$883$	7.04926			0.237226			0.118613	−	0.992941i	$-0.462155\pi$
$883$	7.04926			0.237226			0.118613	+	0.992941i	$0.462155\pi$
$884$	0.0770772	+	0.0445006i	0.00259239	+	0.00149672i
$885$	−10.1462	−	17.5737i	−0.341060	−	0.590734i
$886$	15.7665	+	27.3083i	0.529684	+	0.917440i
$887$	31.8605	+	18.3947i	1.06977	+	0.617632i	0.928119	−	0.372284i	$-0.121425\pi$
$887$	31.8605	+	18.3947i	1.06977	+	0.617632i	0.141652	+	0.989917i	$0.454759\pi$
$888$	0.251481			0.00843914
$889$	−6.67657	+	7.28808i	−0.223925	+	0.244434i
$890$	20.4854			0.686673
$891$	2.94888	+	1.70253i	0.0987911	+	0.0570371i
$892$	−5.96803	+	3.44564i	−0.199824	+	0.115369i
$893$	7.02022	−	4.05313i	0.234923	−	0.135633i
$894$	−0.109314	+	0.189338i	−0.00365602	+	0.00633241i
$895$	−7.66055			−0.256064
$896$	−0.795918	−	2.52320i	−0.0265897	−	0.0842940i
$897$	0.0281496	−	0.0495315i	0.000939887	−	0.00165381i
$898$	15.4737	−	26.8013i	0.516365	−	0.894371i
$899$	−17.3255	+	10.0029i	−0.577839	+	0.333615i
$900$	6.07702	+	10.5257i	0.202567	+	0.350857i
$901$	−45.1704	−	26.0791i	−1.50484	−	0.868822i
$902$	25.2743			0.841542
$903$	15.8608	+	3.51411i	0.527815	+	0.116942i
$904$		−	7.71714i		−	0.256668i
$905$	−37.6563	+	65.2226i	−1.25174	+	2.16807i
$906$	13.5446	−	7.81998i	0.449989	−	0.259801i
$907$	−7.66817	+	4.42722i	−0.254618	+	0.147004i	−0.621877	−	0.783115i	$-0.713630\pi$
$907$	−7.66817	+	4.42722i	−0.254618	+	0.147004i	0.367259	+	0.930119i	$0.380296\pi$
$908$	12.3496	−	21.3901i	0.409835	−	0.709855i
$909$			5.71865i			0.189676i
$910$	0.0281586	−	0.127093i	0.000933449	−	0.00421308i
$911$		−	5.06796i		−	0.167909i	−0.996470	−	0.0839546i	$-0.973245\pi$
$911$		−	5.06796i		−	0.167909i	0.996470	−	0.0839546i	$-0.0267551\pi$
$912$	3.64349	+	2.10357i	0.120648	+	0.0696561i
$913$	−9.49494	+	5.48190i	−0.314237	+	0.181425i
$914$	−10.1142	+	5.83943i	−0.334548	+	0.193151i
$915$	−12.4423	−	7.18357i	−0.411330	−	0.237481i
$916$	2.05474			0.0678905
$917$	−28.7418	+	9.06634i	−0.949139	+	0.299397i
$918$		−	7.49206i		−	0.247275i
$919$	−11.1742	−	6.45141i	−0.368602	−	0.212812i	0.304246	−	0.952594i	$-0.401596\pi$
$919$	−11.1742	−	6.45141i	−0.368602	−	0.212812i	−0.672847	+	0.739781i	$0.734929\pi$
$920$	−19.8626	+	0.135098i	−0.654852	+	0.00445405i
$921$	−8.37530	−	14.5065i	−0.275976	−	0.478004i
$922$	−21.0471	−	12.1515i	−0.693148	−	0.400189i
$923$			0.174806i			0.00575382i
$924$	−6.08551	+	6.64289i	−0.200199	+	0.218535i
$925$		−	3.05651i		−	0.100497i
$926$	−11.4626	+	19.8538i	−0.376684	+	0.652436i
$927$	8.11946	+	14.0633i	0.266678	+	0.461900i
$928$	1.52783	+	2.64628i	0.0501535	+	0.0868685i
$929$	8.28958	+	4.78599i	0.271972	+	0.157023i	0.629784	−	0.776771i	$-0.283144\pi$
$929$	8.28958	+	4.78599i	0.271972	+	0.157023i	−0.357811	+	0.933794i	$0.616477\pi$
$930$	−27.1165			−0.889185
$931$	−26.6939	−	12.4392i	−0.874858	−	0.407679i
$932$	27.8345			0.911748
$933$	−8.67684	+	15.0287i	−0.284067	+	0.492019i
$934$	10.9483	+	18.9630i	0.358239	+	0.620488i
$935$	−91.5042	+	52.8300i	−2.99251	+	1.72772i
$936$	−0.0102879	−	0.00593970i	−0.000336269	−	0.000194145i
$937$	−31.7528			−1.03732			−0.518660	−	0.854981i	$-0.673569\pi$
$937$	−31.7528			−1.03732			−0.518660	+	0.854981i	$0.673569\pi$
$938$	12.7866	+	11.7137i	0.417497	+	0.382466i
$939$		−	24.4878i		−	0.799128i
$940$	6.91111	+	3.99013i	0.225415	+	0.130144i
$941$	25.5210	+	44.2036i	0.831960	+	1.44100i	0.896481	+	0.443081i	$0.146115\pi$
$941$	25.5210	+	44.2036i	0.831960	+	1.44100i	−0.0645211	+	0.997916i	$0.520552\pi$
$942$	−16.6533	+	9.61479i	−0.542594	+	0.313267i
$943$	−30.7064	+	18.0079i	−0.999938	+	0.586418i
$944$		−	4.89948i		−	0.159464i
$945$	−10.4504	+	3.29649i	−0.339952	+	0.107235i
$946$	−20.9078			−0.679771
$947$	8.34138	−	14.4477i	0.271058	−	0.469487i	−0.698075	−	0.716025i	$-0.745960\pi$
$947$	8.34138	−	14.4477i	0.271058	−	0.469487i	0.969133	+	0.246538i	$0.0792931\pi$
$948$	8.03322	+	13.9139i	0.260907	+	0.451904i
$949$	0.0856188	+	0.148296i	0.00277930	+	0.00481389i
$950$	25.5668	−	44.2831i	0.829498	−	1.43673i
$951$		−	24.1860i		−	0.784283i
$952$	19.3528	+	4.28780i	0.627228	+	0.138968i
$953$			29.0195i			0.940033i	0.882658	+	0.470017i	$0.155752\pi$
$953$			29.0195i			0.940033i	−0.882658	+	0.470017i	$0.844248\pi$
$954$	6.02910	+	3.48090i	0.195199	+	0.112698i
$955$	85.1897	−	49.1843i	2.75667	−	1.59157i
$956$	7.45507	+	12.9126i	0.241114	+	0.417622i
$957$	5.20237	−	9.01077i	0.168169	−	0.291277i
$958$	12.1002			0.390939
$959$	−5.86701	+	26.4805i	−0.189455	+	0.855100i
$960$			4.14174i			0.133674i
$961$	5.93239	−	10.2752i	0.191367	−	0.331458i
$962$	0.00149372	+	0.00258720i	4.81595e−5	+	8.34146e-5i
$963$	−13.0748	+	7.54877i	−0.421331	+	0.243256i
$964$	1.57716	−	2.73172i	0.0507969	−	0.0879828i
$965$	−43.0015			−1.38427
$966$	2.66039	−	12.4065i	0.0855968	−	0.399174i
$967$	−20.0795			−0.645712			−0.322856	−	0.946448i	$-0.604643\pi$
$967$	−20.0795			−0.645712			−0.322856	+	0.946448i	$0.604643\pi$
$968$	0.297250	−	0.514851i	0.00955396	−	0.0165479i
$969$	−27.2972	+	15.7600i	−0.876912	+	0.506286i
$970$	3.84863	+	6.66603i	0.123572	+	0.214033i
$971$	−3.86971	+	6.70254i	−0.124185	+	0.215095i	−0.921414	−	0.388582i	$-0.872965\pi$
$971$	−3.86971	+	6.70254i	−0.124185	+	0.215095i	0.797229	+	0.603677i	$0.206298\pi$
$972$			1.00000i			0.0320750i
$973$	7.46966	+	6.84291i	0.239466	+	0.219374i
$974$	−39.8743			−1.27765
$975$	−0.0721914	+	0.125039i	−0.00231197	+	0.00400446i
$976$	−1.73443	−	3.00412i	−0.0555178	−	0.0961596i
$977$	19.1625	−	11.0635i	0.613062	−	0.353951i	−0.161101	−	0.986938i	$-0.551505\pi$
$977$	19.1625	−	11.0635i	0.613062	−	0.353951i	0.774163	+	0.632987i	$0.218171\pi$
$978$	8.96039	+	5.17329i	0.286522	+	0.165423i
$979$		−	16.8418i		−	0.538265i
$980$	−2.53428	−	28.8812i	−0.0809546	−	0.922577i
$981$			5.32039i			0.169867i
$982$	−9.53091	+	16.5080i	−0.304144	+	0.526792i
$983$	−11.8131	−	20.4609i	−0.376779	−	0.652601i	0.613812	−	0.789452i	$-0.289635\pi$
$983$	−11.8131	−	20.4609i	−0.376779	−	0.652601i	−0.990592	+	0.136851i	$0.956302\pi$
$984$	3.71128	+	6.42812i	0.118311	+	0.204921i
$985$	11.6449	−	20.1696i	0.371038	−	0.642656i
$986$	−22.8932			−0.729068
$987$	−3.44354	+	3.75894i	−0.109609	+	0.119648i
$988$			0.0499782i			0.00159002i
$989$	25.4014	−	14.8968i	0.807718	−	0.473690i
$990$	12.2135	−	7.05146i	0.388170	−	0.224110i
$991$	23.7988	+	41.2207i	0.755993	+	1.30942i	0.944879	+	0.327419i	$0.106179\pi$
$991$	23.7988	+	41.2207i	0.755993	+	1.30942i	−0.188886	+	0.981999i	$0.560488\pi$
$992$	−5.66997	−	3.27356i	−0.180022	−	0.103936i
$993$		−	21.7734i		−	0.690958i
$994$	11.7120	+	37.1290i	0.371482	+	1.17766i
$995$	−24.6002			−0.779878
$996$	−2.78847	−	1.60992i	−0.0883561	−	0.0510124i
$997$	50.2275	−	28.9989i	1.59072	−	0.918403i	0.597537	−	0.801841i	$-0.296146\pi$
$997$	50.2275	−	28.9989i	1.59072	−	0.918403i	0.993183	−	0.116561i	$-0.0371872\pi$
$998$	5.53289	+	9.58324i	0.175141	+	0.303352i
$999$	0.125740	−	0.217789i	0.00397825	−	0.00689053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.k.a.229.9	✓	32
7.3	odd	6	inner	966.2.k.a.367.16	yes	32
23.22	odd	2	inner	966.2.k.a.229.16	yes	32
161.45	even	6	inner	966.2.k.a.367.9	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.k.a.229.9	✓	32	1.1	even	1	trivial
966.2.k.a.229.16	yes	32	23.22	odd	2	inner
966.2.k.a.367.9	yes	32	161.45	even	6	inner
966.2.k.a.367.16	yes	32	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.07087 + 3.58686i) q^{5} +1.00000i q^{6} +(-1.78719 + 1.95088i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.07087 + 3.58686i) q^{5} +1.00000i q^{6} +(-1.78719 + 1.95088i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.07087 - 3.58686i) q^{10} +(-2.94888 + 1.70253i) q^{11} +(-0.866025 - 0.500000i) q^{12} -0.0118794i q^{13} +(-0.795918 - 2.52320i) q^{14} +4.14174i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.74603 - 6.48831i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.10357 - 3.64349i) q^{19} +4.14174 q^{20} +(-0.572313 + 2.58311i) q^{21} -3.40507i q^{22} +(2.42611 + 4.13691i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-6.07702 - 10.5257i) q^{25} +(0.0102879 + 0.00593970i) q^{26} -1.00000i q^{27} +(2.58311 + 0.572313i) q^{28} -3.05566 q^{29} +(-3.58686 - 2.07087i) q^{30} +(5.66997 - 3.27356i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.70253 + 2.94888i) q^{33} +7.49206 q^{34} +(-3.29649 - 10.4504i) q^{35} -1.00000 q^{36} +(0.217789 + 0.125740i) q^{37} +(2.10357 + 3.64349i) q^{38} +(-0.00593970 - 0.0102879i) q^{39} +(-2.07087 + 3.58686i) q^{40} +7.42255i q^{41} +(-1.95088 - 1.78719i) q^{42} -6.14020i q^{43} +(2.94888 + 1.70253i) q^{44} +(2.07087 + 3.58686i) q^{45} +(-4.79572 + 0.0326186i) q^{46} +(1.66865 + 0.963394i) q^{47} +1.00000i q^{48} +(-0.611887 - 6.97321i) q^{49} +12.1540 q^{50} +(-6.48831 - 3.74603i) q^{51} +(-0.0102879 + 0.00593970i) q^{52} +(6.02910 - 3.48090i) q^{53} +(0.866025 + 0.500000i) q^{54} -14.1029i q^{55} +(-1.78719 + 1.95088i) q^{56} -4.20714i q^{57} +(1.52783 - 2.64628i) q^{58} +(-4.24307 + 2.44974i) q^{59} +(3.58686 - 2.07087i) q^{60} +(-1.73443 + 3.00412i) q^{61} +6.54712i q^{62} +(0.795918 + 2.52320i) q^{63} +1.00000 q^{64} +(0.0426097 + 0.0246007i) q^{65} +(-1.70253 - 2.94888i) q^{66} +(-5.67615 + 3.27713i) q^{67} +(-3.74603 + 6.48831i) q^{68} +(4.16953 + 2.36961i) q^{69} +(10.6986 + 2.37037i) q^{70} -14.7151 q^{71} +(0.500000 - 0.866025i) q^{72} +(-12.4835 + 7.20733i) q^{73} +(-0.217789 + 0.125740i) q^{74} +(-10.5257 - 6.07702i) q^{75} -4.20714 q^{76} +(1.94876 - 8.79567i) q^{77} +0.0118794 q^{78} +(-13.9139 - 8.03322i) q^{79} +(-2.07087 - 3.58686i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.42812 - 3.71128i) q^{82} +3.21985 q^{83} +(2.52320 - 0.795918i) q^{84} +31.0302 q^{85} +(5.31757 + 3.07010i) q^{86} +(-2.64628 + 1.52783i) q^{87} +(-2.94888 + 1.70253i) q^{88} +(-2.47304 + 4.28344i) q^{89} -4.14174 q^{90} +(0.0231753 + 0.0212308i) q^{91} +(2.36961 - 4.16953i) q^{92} +(3.27356 - 5.66997i) q^{93} +(-1.66865 + 0.963394i) q^{94} +(8.71244 + 15.0904i) q^{95} +(-0.866025 - 0.500000i) q^{96} -1.85846 q^{97} +(6.34492 + 2.95669i) q^{98} +3.40507i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 16 * q^9	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} + 16 q^{9} - 16 q^{16} + 16 q^{18} + 8 q^{23} - 24 q^{25} - 12 q^{26} - 8 q^{29} + 48 q^{31} - 16 q^{32} - 20 q^{35} - 32 q^{36} - 8 q^{39} + 8 q^{46} + 12 q^{47} + 24 q^{49} + 48 q^{50} + 12 q^{52} + 4 q^{58} - 12 q^{59} + 32 q^{64} + 64 q^{70} + 48 q^{71} + 16 q^{72} + 12 q^{73} + 36 q^{75} + 64 q^{77} + 16 q^{78} - 16 q^{81} - 12 q^{82} + 32 q^{85} - 24 q^{87} - 16 q^{92} - 12 q^{94} + 40 q^{95} - 24 q^{98}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 + 16 * q^9 - 16 * q^16 + 16 * q^18 + 8 * q^23 - 24 * q^25 - 12 * q^26 - 8 * q^29 + 48 * q^31 - 16 * q^32 - 20 * q^35 - 32 * q^36 - 8 * q^39 + 8 * q^46 + 12 * q^47 + 24 * q^49 + 48 * q^50 + 12 * q^52 + 4 * q^58 - 12 * q^59 + 32 * q^64 + 64 * q^70 + 48 * q^71 + 16 * q^72 + 12 * q^73 + 36 * q^75 + 64 * q^77 + 16 * q^78 - 16 * q^81 - 12 * q^82 + 32 * q^85 - 24 * q^87 - 16 * q^92 - 12 * q^94 + 40 * q^95 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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