LMFDB - Embedded newform 912.2.u.a.229.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(229,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("912.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.u (of order $4$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			229.4
Character	$\chi$	$=$	912.229
Dual form			912.2.u.a.685.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33099 - 0.477978i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.54307 + 1.27237i) q^{4} +(2.04814 + 2.04814i) q^{5} +(1.27913 - 0.603171i) q^{6} -4.27873i q^{7} +(-1.44565 - 2.43107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.33099 - 0.477978i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.54307 + 1.27237i) q^{4} +(2.04814 + 2.04814i) q^{5} +(1.27913 - 0.603171i) q^{6} -4.27873i q^{7} +(-1.44565 - 2.43107i) q^{8} -1.00000i q^{9} +(-1.74709 - 3.70502i) q^{10} +(-2.85543 - 2.85543i) q^{11} +(-1.99082 + 0.191418i) q^{12} +(-2.38327 + 2.38327i) q^{13} +(-2.04514 + 5.69496i) q^{14} -2.89650 q^{15} +(0.762155 + 3.92672i) q^{16} -5.67010 q^{17} +(-0.477978 + 1.33099i) q^{18} +(0.707107 - 0.707107i) q^{19} +(0.554441 + 5.76641i) q^{20} +(3.02552 + 3.02552i) q^{21} +(2.43572 + 5.16538i) q^{22} +6.18292i q^{23} +(2.74126 + 0.696793i) q^{24} +3.38973i q^{25} +(4.31126 - 2.03296i) q^{26} +(0.707107 + 0.707107i) q^{27} +(5.44413 - 6.60240i) q^{28} +(-4.10672 + 4.10672i) q^{29} +(3.85522 + 1.38446i) q^{30} -8.78851 q^{31} +(0.862463 - 5.59072i) q^{32} +4.03819 q^{33} +(7.54685 + 2.71018i) q^{34} +(8.76343 - 8.76343i) q^{35} +(1.27237 - 1.54307i) q^{36} +(-2.04138 - 2.04138i) q^{37} +(-1.27913 + 0.603171i) q^{38} -3.37045i q^{39} +(2.01826 - 7.94005i) q^{40} +11.3706i q^{41} +(-2.58081 - 5.47308i) q^{42} +(0.355561 + 0.355561i) q^{43} +(-0.772980 - 8.03930i) q^{44} +(2.04814 - 2.04814i) q^{45} +(2.95530 - 8.22942i) q^{46} -9.68010 q^{47} +(-3.31553 - 2.23768i) q^{48} -11.3076 q^{49} +(1.62022 - 4.51170i) q^{50} +(4.00936 - 4.00936i) q^{51} +(-6.70996 + 0.645164i) q^{52} +(1.22503 + 1.22503i) q^{53} +(-0.603171 - 1.27913i) q^{54} -11.6966i q^{55} +(-10.4019 + 6.18557i) q^{56} +1.00000i q^{57} +(7.42892 - 3.50308i) q^{58} +(3.55701 + 3.55701i) q^{59} +(-4.46952 - 3.68542i) q^{60} +(6.48412 - 6.48412i) q^{61} +(11.6974 + 4.20071i) q^{62} -4.27873 q^{63} +(-3.82017 + 7.02896i) q^{64} -9.76253 q^{65} +(-5.37479 - 1.93017i) q^{66} +(-1.53219 + 1.53219i) q^{67} +(-8.74938 - 7.21445i) q^{68} +(-4.37199 - 4.37199i) q^{69} +(-15.8528 + 7.47532i) q^{70} +7.16709i q^{71} +(-2.43107 + 1.44565i) q^{72} -2.43337i q^{73} +(1.74132 + 3.69279i) q^{74} +(-2.39690 - 2.39690i) q^{75} +(1.99082 - 0.191418i) q^{76} +(-12.2176 + 12.2176i) q^{77} +(-1.61100 + 4.48604i) q^{78} +10.0716 q^{79} +(-6.48146 + 9.60345i) q^{80} -1.00000 q^{81} +(5.43491 - 15.1342i) q^{82} +(2.07736 - 2.07736i) q^{83} +(0.819025 + 8.51819i) q^{84} +(-11.6131 - 11.6131i) q^{85} +(-0.303298 - 0.643199i) q^{86} -5.80777i q^{87} +(-2.81378 + 11.0697i) q^{88} +2.59060i q^{89} +(-3.70502 + 1.74709i) q^{90} +(10.1974 + 10.1974i) q^{91} +(-7.86696 + 9.54071i) q^{92} +(6.21441 - 6.21441i) q^{93} +(12.8841 + 4.62688i) q^{94} +2.89650 q^{95} +(3.34338 + 4.56309i) q^{96} -16.6347 q^{97} +(15.0503 + 5.40477i) q^{98} +(-2.85543 + 2.85543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 4 q^{4}+O(q^{10}) $ 72 * q + 4 * q^4	$ 72 q + 4 q^{4} + 8 q^{11} - 8 q^{12} - 12 q^{14} - 4 q^{16} - 4 q^{18} - 44 q^{20} - 52 q^{26} + 52 q^{28} + 16 q^{29} + 8 q^{30} - 64 q^{31} + 40 q^{34} + 16 q^{37} + 4 q^{40} - 8 q^{42} + 8 q^{43} + 68 q^{44} + 104 q^{47} + 16 q^{48} - 72 q^{49} + 116 q^{50} - 8 q^{52} - 16 q^{53} - 28 q^{56} - 92 q^{58} - 32 q^{59} + 32 q^{60} + 24 q^{62} - 40 q^{63} + 28 q^{64} + 16 q^{65} + 28 q^{66} - 8 q^{67} - 100 q^{68} - 20 q^{70} + 4 q^{72} - 124 q^{74} - 16 q^{75} + 8 q^{76} - 16 q^{77} - 12 q^{78} + 48 q^{79} + 44 q^{80} - 72 q^{81} + 52 q^{82} - 8 q^{84} - 64 q^{85} + 48 q^{86} - 32 q^{88} + 8 q^{90} + 8 q^{91} + 96 q^{92} + 12 q^{94} - 20 q^{96} + 208 q^{98} + 8 q^{99}+O(q^{100}) $ 72 * q + 4 * q^4 + 8 * q^11 - 8 * q^12 - 12 * q^14 - 4 * q^16 - 4 * q^18 - 44 * q^20 - 52 * q^26 + 52 * q^28 + 16 * q^29 + 8 * q^30 - 64 * q^31 + 40 * q^34 + 16 * q^37 + 4 * q^40 - 8 * q^42 + 8 * q^43 + 68 * q^44 + 104 * q^47 + 16 * q^48 - 72 * q^49 + 116 * q^50 - 8 * q^52 - 16 * q^53 - 28 * q^56 - 92 * q^58 - 32 * q^59 + 32 * q^60 + 24 * q^62 - 40 * q^63 + 28 * q^64 + 16 * q^65 + 28 * q^66 - 8 * q^67 - 100 * q^68 - 20 * q^70 + 4 * q^72 - 124 * q^74 - 16 * q^75 + 8 * q^76 - 16 * q^77 - 12 * q^78 + 48 * q^79 + 44 * q^80 - 72 * q^81 + 52 * q^82 - 8 * q^84 - 64 * q^85 + 48 * q^86 - 32 * q^88 + 8 * q^90 + 8 * q^91 + 96 * q^92 + 12 * q^94 - 20 * q^96 + 208 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.33099	−	0.477978i	−0.941153	−	0.337981i
$2$	−1.33099	−	0.477978i	−0.941153	−	0.337981i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.54307	+	1.27237i	0.771537	+	0.636184i
$5$	2.04814	+	2.04814i	0.915955	+	0.915955i	0.996732	−	0.0807775i	$-0.0257403\pi$
$5$	2.04814	+	2.04814i	0.915955	+	0.915955i	−0.0807775	+	0.996732i	$0.525740\pi$
$6$	1.27913	−	0.603171i	0.522204	−	0.246244i
$7$		−	4.27873i		−	1.61721i	−0.588352	−	0.808605i	$-0.700223\pi$
$7$		−	4.27873i		−	1.61721i	0.588352	−	0.808605i	$-0.299777\pi$
$8$	−1.44565	−	2.43107i	−0.511116	−	0.859512i
$9$		−	1.00000i		−	0.333333i
$10$	−1.74709	−	3.70502i	−0.552478	−	1.17163i
$11$	−2.85543	−	2.85543i	−0.860945	−	0.860945i	0.130503	−	0.991448i	$-0.458341\pi$
$11$	−2.85543	−	2.85543i	−0.860945	−	0.860945i	−0.991448	+	0.130503i	$0.958341\pi$
$12$	−1.99082	+	0.191418i	−0.574700	+	0.0552575i
$13$	−2.38327	+	2.38327i	−0.661000	+	0.661000i	−0.955616	−	0.294615i	$-0.904808\pi$
$13$	−2.38327	+	2.38327i	−0.661000	+	0.661000i	0.294615	+	0.955616i	$0.404808\pi$
$14$	−2.04514	+	5.69496i	−0.546587	+	1.52204i
$15$	−2.89650			−0.747874
$16$	0.762155	+	3.92672i	0.190539	+	0.981680i
$17$	−5.67010			−1.37520			−0.687600	−	0.726090i	$-0.741336\pi$
$17$	−5.67010			−1.37520			−0.687600	+	0.726090i	$0.741336\pi$
$18$	−0.477978	+	1.33099i	−0.112660	+	0.313718i
$19$	0.707107	−	0.707107i	0.162221	−	0.162221i
$19$	0.707107	−	0.707107i	0.162221	−	0.162221i
$20$	0.554441	+	5.76641i	0.123977	+	1.28941i
$21$	3.02552	+	3.02552i	0.660223	+	0.660223i
$22$	2.43572	+	5.16538i	0.519297	+	1.10126i
$23$			6.18292i			1.28923i	0.764508	+	0.644614i	$0.222982\pi$
$23$			6.18292i			1.28923i	−0.764508	+	0.644614i	$0.777018\pi$
$24$	2.74126	+	0.696793i	0.559556	+	0.142232i
$25$			3.38973i			0.677946i
$26$	4.31126	−	2.03296i	0.845508	−	0.398696i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	5.44413	−	6.60240i	1.02884	−	1.24774i
$29$	−4.10672	+	4.10672i	−0.762598	+	0.762598i	−0.976791	−	0.214193i	$-0.931288\pi$
$29$	−4.10672	+	4.10672i	−0.762598	+	0.762598i	0.214193	+	0.976791i	$0.431288\pi$
$30$	3.85522	+	1.38446i	0.703864	+	0.252768i
$31$	−8.78851			−1.57846			−0.789231	−	0.614096i	$-0.789521\pi$
$31$	−8.78851			−1.57846			−0.789231	+	0.614096i	$0.789521\pi$
$32$	0.862463	−	5.59072i	0.152463	−	0.988309i
$33$	4.03819			0.702958
$34$	7.54685	+	2.71018i	1.29427	+	0.464792i
$35$	8.76343	−	8.76343i	1.48129	−	1.48129i
$36$	1.27237	−	1.54307i	0.212061	−	0.257179i
$37$	−2.04138	−	2.04138i	−0.335600	−	0.335600i	0.519108	−	0.854709i	$-0.326264\pi$
$37$	−2.04138	−	2.04138i	−0.335600	−	0.335600i	−0.854709	+	0.519108i	$0.826264\pi$
$38$	−1.27913	+	0.603171i	−0.207503	+	0.0978473i
$39$		−	3.37045i		−	0.539705i
$40$	2.01826	−	7.94005i	0.319115	−	1.25543i
$41$			11.3706i			1.77579i	0.460044	+	0.887896i	$0.347834\pi$
$41$			11.3706i			1.77579i	−0.460044	+	0.887896i	$0.652166\pi$
$42$	−2.58081	−	5.47308i	−0.398228	−	0.844514i
$43$	0.355561	+	0.355561i	0.0542226	+	0.0542226i	0.733698	−	0.679476i	$-0.237793\pi$
$43$	0.355561	+	0.355561i	0.0542226	+	0.0542226i	−0.679476	+	0.733698i	$0.737793\pi$
$44$	−0.772980	−	8.03930i	−0.116531	−	1.21197i
$45$	2.04814	−	2.04814i	0.305318	−	0.305318i
$46$	2.95530	−	8.22942i	0.435735	−	1.21336i
$47$	−9.68010			−1.41199			−0.705994	−	0.708218i	$-0.749499\pi$
$47$	−9.68010			−1.41199			−0.705994	+	0.708218i	$0.749499\pi$
$48$	−3.31553	−	2.23768i	−0.478556	−	0.322982i
$49$	−11.3076			−1.61537
$50$	1.62022	−	4.51170i	0.229133	−	0.638050i
$51$	4.00936	−	4.00936i	0.561423	−	0.561423i
$52$	−6.70996	+	0.645164i	−0.930504	+	0.0894681i
$53$	1.22503	+	1.22503i	0.168271	+	0.168271i	0.786219	−	0.617948i	$-0.212036\pi$
$53$	1.22503	+	1.22503i	0.168271	+	0.168271i	−0.617948	+	0.786219i	$0.712036\pi$
$54$	−0.603171	−	1.27913i	−0.0820812	−	0.174068i
$55$		−	11.6966i		−	1.57717i
$56$	−10.4019	+	6.18557i	−1.39001	+	0.826581i
$57$			1.00000i			0.132453i
$58$	7.42892	−	3.50308i	0.975465	−	0.459977i
$59$	3.55701	+	3.55701i	0.463083	+	0.463083i	0.899665	−	0.436581i	$-0.143811\pi$
$59$	3.55701	+	3.55701i	0.463083	+	0.463083i	−0.436581	+	0.899665i	$0.643811\pi$
$60$	−4.46952	−	3.68542i	−0.577012	−	0.475786i
$61$	6.48412	−	6.48412i	0.830207	−	0.830207i	−0.157338	−	0.987545i	$-0.550291\pi$
$61$	6.48412	−	6.48412i	0.830207	−	0.830207i	0.987545	+	0.157338i	$0.0502912\pi$
$62$	11.6974	+	4.20071i	1.48557	+	0.533491i
$63$	−4.27873			−0.539070
$64$	−3.82017	+	7.02896i	−0.477522	+	0.878620i
$65$	−9.76253			−1.21089
$66$	−5.37479	−	1.93017i	−0.661591	−	0.237587i
$67$	−1.53219	+	1.53219i	−0.187187	+	0.187187i	−0.794479	−	0.607292i	$-0.792256\pi$
$67$	−1.53219	+	1.53219i	−0.187187	+	0.187187i	0.607292	+	0.794479i	$0.292256\pi$
$68$	−8.74938	−	7.21445i	−1.06102	−	0.874881i
$69$	−4.37199	−	4.37199i	−0.526325	−	0.526325i
$70$	−15.8528	+	7.47532i	−1.89477	+	0.893472i
$71$			7.16709i			0.850577i	0.905058	+	0.425288i	$0.139827\pi$
$71$			7.16709i			0.850577i	−0.905058	+	0.425288i	$0.860173\pi$
$72$	−2.43107	+	1.44565i	−0.286504	+	0.170372i
$73$		−	2.43337i		−	0.284805i	−0.989809	−	0.142402i	$-0.954517\pi$
$73$		−	2.43337i		−	0.284805i	0.989809	−	0.142402i	$-0.0454827\pi$
$74$	1.74132	+	3.69279i	0.202425	+	0.429278i
$75$	−2.39690	−	2.39690i	−0.276770	−	0.276770i
$76$	1.99082	−	0.191418i	0.228363	−	0.0219571i
$77$	−12.2176	+	12.2176i	−1.39233	+	1.39233i
$78$	−1.61100	+	4.48604i	−0.182410	+	0.507944i
$79$	10.0716			1.13314			0.566570	−	0.824013i	$-0.308270\pi$
$79$	10.0716			1.13314			0.566570	+	0.824013i	$0.308270\pi$
$80$	−6.48146	+	9.60345i	−0.724649	+	1.07370i
$81$	−1.00000			−0.111111
$82$	5.43491	−	15.1342i	0.600185	−	1.67129i
$83$	2.07736	−	2.07736i	0.228020	−	0.228020i	−0.583845	−	0.811865i	$-0.698452\pi$
$83$	2.07736	−	2.07736i	0.228020	−	0.228020i	0.811865	+	0.583845i	$0.198452\pi$
$84$	0.819025	+	8.51819i	0.0893629	+	0.929410i
$85$	−11.6131	−	11.6131i	−1.25962	−	1.25962i
$86$	−0.303298	−	0.643199i	−0.0327055	−	0.0693580i
$87$		−	5.80777i		−	0.622659i
$88$	−2.81378	+	11.0697i	−0.299950	+	1.18003i
$89$			2.59060i			0.274603i	0.990529	+	0.137302i	$0.0438429\pi$
$89$			2.59060i			0.274603i	−0.990529	+	0.137302i	$0.956157\pi$
$90$	−3.70502	+	1.74709i	−0.390543	+	0.184159i
$91$	10.1974	+	10.1974i	1.06898	+	1.06898i
$92$	−7.86696	+	9.54071i	−0.820187	+	0.994688i
$93$	6.21441	−	6.21441i	0.644405	−	0.644405i
$94$	12.8841	+	4.62688i	1.32890	+	0.477226i
$95$	2.89650			0.297175
$96$	3.34338	+	4.56309i	0.341233	+	0.465718i
$97$	−16.6347			−1.68900			−0.844498	−	0.535559i	$-0.820101\pi$
$97$	−16.6347			−1.68900			−0.844498	+	0.535559i	$0.820101\pi$
$98$	15.0503	+	5.40477i	1.52031	+	0.545964i
$99$	−2.85543	+	2.85543i	−0.286982	+	0.286982i
$100$	−4.31298	+	5.23060i	−0.431298	+	0.523060i
$101$	4.68929	+	4.68929i	0.466602	+	0.466602i	0.900812	−	0.434210i	$-0.142972\pi$
$101$	4.68929	+	4.68929i	0.466602	+	0.466602i	−0.434210	+	0.900812i	$0.642972\pi$
$102$	−7.25281	+	3.42004i	−0.718136	+	0.338634i
$103$		−	10.7205i		−	1.05633i	−0.849143	−	0.528163i	$-0.822881\pi$
$103$		−	10.7205i		−	1.05633i	0.849143	−	0.528163i	$-0.177119\pi$
$104$	9.23927	+	2.34851i	0.905985	+	0.230290i
$105$			12.3934i			1.20947i
$106$	−1.04497	−	2.21604i	−0.101496	−	0.215241i
$107$	−4.85890	−	4.85890i	−0.469727	−	0.469727i	0.432099	−	0.901826i	$-0.357773\pi$
$107$	−4.85890	−	4.85890i	−0.469727	−	0.469727i	−0.901826	+	0.432099i	$0.857773\pi$
$108$	0.191418	+	1.99082i	0.0184192	+	0.191567i
$109$	−0.363695	+	0.363695i	−0.0348356	+	0.0348356i	−0.724310	−	0.689474i	$-0.757842\pi$
$109$	−0.363695	+	0.363695i	−0.0348356	+	0.0348356i	0.689474	+	0.724310i	$0.257842\pi$
$110$	−5.59073	+	15.5681i	−0.533055	+	1.48436i
$111$	2.88694			0.274017
$112$	16.8014	−	3.26106i	1.58758	−	0.308141i
$113$	−10.5495			−0.992414			−0.496207	−	0.868204i	$-0.665274\pi$
$113$	−10.5495			−0.992414			−0.496207	+	0.868204i	$0.665274\pi$
$114$	0.477978	−	1.33099i	0.0447667	−	0.124659i
$115$	−12.6635	+	12.6635i	−1.18087	+	1.18087i
$116$	−11.5622	+	1.11171i	−1.07353	+	0.103220i
$117$	2.38327	+	2.38327i	0.220333	+	0.220333i
$118$	−3.03418	−	6.43452i	−0.279319	−	0.592346i
$119$			24.2608i			2.22399i
$120$	4.18734	+	7.04159i	0.382250	+	0.642806i
$121$			5.30697i			0.482451i
$122$	−11.7296	+	5.53104i	−1.06195	+	0.500757i
$123$	−8.04024	−	8.04024i	−0.724964	−	0.724964i
$124$	−13.5613	−	11.1822i	−1.21784	−	1.00419i
$125$	3.29806	−	3.29806i	0.294987	−	0.294987i
$126$	5.69496	+	2.04514i	0.507347	+	0.182196i
$127$	−3.51739			−0.312117			−0.156059	−	0.987748i	$-0.549879\pi$
$127$	−3.51739			−0.312117			−0.156059	+	0.987748i	$0.549879\pi$
$128$	8.44430	−	7.52952i	0.746378	−	0.665522i
$129$	−0.502840			−0.0442726
$130$	12.9938	+	4.66627i	1.13964	+	0.409259i
$131$	5.53830	−	5.53830i	0.483883	−	0.483883i	−0.422486	−	0.906369i	$-0.638842\pi$
$131$	5.53830	−	5.53830i	0.483883	−	0.483883i	0.906369	+	0.422486i	$0.138842\pi$
$132$	6.23122	+	5.13806i	0.542358	+	0.447211i
$133$	−3.02552	−	3.02552i	−0.262346	−	0.262346i
$134$	2.77169	−	1.30698i	0.239438	−	0.112906i
$135$			2.89650i			0.249291i
$136$	8.19699	+	13.7844i	0.702886	+	1.18200i
$137$		−	18.4865i		−	1.57941i	−0.613487	−	0.789704i	$-0.710234\pi$
$137$		−	18.4865i		−	1.57941i	0.613487	−	0.789704i	$-0.289766\pi$
$138$	3.72936	+	7.90879i	0.317464	+	0.673241i
$139$	−6.43036	−	6.43036i	−0.545416	−	0.545416i	0.379696	−	0.925111i	$-0.376029\pi$
$139$	−6.43036	−	6.43036i	−0.545416	−	0.545416i	−0.925111	+	0.379696i	$0.876029\pi$
$140$	24.6729	−	2.37231i	2.08524	−	0.200497i
$141$	6.84487	−	6.84487i	0.576442	−	0.576442i
$142$	3.42571	−	9.53933i	0.287479	−	0.800523i
$143$	13.6105			1.13817
$144$	3.92672	−	0.762155i	0.327227	−	0.0635129i
$145$	−16.8222			−1.39701
$146$	−1.16310	+	3.23880i	−0.0962588	+	0.268045i
$147$	7.99566	−	7.99566i	0.659471	−	0.659471i
$148$	−0.552612	−	5.74738i	−0.0454244	−	0.472432i
$149$	−14.4807	−	14.4807i	−1.18630	−	1.18630i	−0.978082	−	0.208222i	$-0.933232\pi$
$149$	−14.4807	−	14.4807i	−1.18630	−	1.18630i	−0.208222	−	0.978082i	$-0.566768\pi$
$150$	2.04459	+	4.33592i	0.166940	+	0.354026i
$151$		−	0.964678i		−	0.0785044i	−0.999229	−	0.0392522i	$-0.987502\pi$
$151$		−	0.964678i		−	0.0785044i	0.999229	−	0.0392522i	$-0.0124976\pi$
$152$	−2.74126	−	0.696793i	−0.222345	−	0.0565173i
$153$			5.67010i			0.458400i
$154$	22.1013	−	10.4218i	1.78097	−	0.839812i
$155$	−18.0001	−	18.0001i	−1.44580	−	1.44580i
$156$	4.28846	−	5.20086i	0.343352	−	0.416402i
$157$	−5.13759	+	5.13759i	−0.410025	+	0.410025i	−0.881747	−	0.471722i	$-0.843632\pi$
$157$	−5.13759	+	5.13759i	−0.410025	+	0.410025i	0.471722	+	0.881747i	$0.343632\pi$
$158$	−13.4052	−	4.81399i	−1.06646	−	0.382981i
$159$	−1.73245			−0.137393
$160$	13.2170	−	9.68412i	1.04490	−	0.765597i
$161$	26.4551			2.08495
$162$	1.33099	+	0.477978i	0.104573	+	0.0375535i
$163$	14.2981	−	14.2981i	1.11991	−	1.11991i	0.128161	−	0.991753i	$-0.459093\pi$
$163$	14.2981	−	14.2981i	1.11991	−	1.11991i	0.991753	−	0.128161i	$-0.0409073\pi$
$164$	−14.4676	+	17.5457i	−1.12973	+	1.37009i
$165$	8.27076	+	8.27076i	0.643878	+	0.643878i
$166$	−3.75788	+	1.77202i	−0.291668	+	0.137535i
$167$		−	16.9460i		−	1.31132i	−0.755057	−	0.655659i	$-0.772391\pi$
$167$		−	16.9460i		−	1.31132i	0.755057	−	0.655659i	$-0.227609\pi$
$168$	2.98139	−	11.7291i	0.230019	−	0.904920i
$169$			1.64004i			0.126157i
$170$	9.90615	+	21.0078i	0.759767	+	1.61122i
$171$	−0.707107	−	0.707107i	−0.0540738	−	0.0540738i
$172$	0.0962523	+	1.00106i	0.00733917	+	0.0763303i
$173$	1.49280	−	1.49280i	0.113496	−	0.113496i	−0.648078	−	0.761574i	$-0.724427\pi$
$173$	1.49280	−	1.49280i	0.113496	−	0.113496i	0.761574	+	0.648078i	$0.224427\pi$
$174$	−2.77599	+	7.73010i	−0.210447	+	0.586017i
$175$	14.5037			1.09638
$176$	9.03619	−	13.3888i	0.681129	−	1.00922i
$177$	−5.03037			−0.378106
$178$	1.23825	−	3.44807i	0.0928107	−	0.258443i
$179$	−3.47869	+	3.47869i	−0.260009	+	0.260009i	−0.825058	−	0.565048i	$-0.808857\pi$
$179$	−3.47869	+	3.47869i	−0.260009	+	0.260009i	0.565048	+	0.825058i	$0.308857\pi$
$180$	5.76641	−	0.554441i	0.429803	−	0.0413256i
$181$	13.4591	+	13.4591i	1.00040	+	1.00040i	1.00000		0.000404395i	$0.000128723\pi$
$181$	13.4591	+	13.4591i	1.00040	+	1.00040i	0.000404395		1.00000i	$0.499871\pi$
$182$	−8.69850	−	18.4468i	−0.644776	−	1.36736i
$183$			9.16994i			0.677861i
$184$	15.0311	−	8.93836i	1.10811	−	0.658945i
$185$		−	8.36204i		−	0.614789i
$186$	−11.2417	+	5.30097i	−0.824280	+	0.388686i
$187$	16.1906	+	16.1906i	1.18397	+	1.18397i
$188$	−14.9371	−	12.3167i	−1.08940	−	0.898285i
$189$	3.02552	−	3.02552i	0.220074	−	0.220074i
$190$	−3.85522	−	1.38446i	−0.279687	−	0.100440i
$191$	−5.77772			−0.418061			−0.209031	−	0.977909i	$-0.567031\pi$
$191$	−5.77772			−0.418061			−0.209031	+	0.977909i	$0.567031\pi$
$192$	−2.26896	−	7.67150i	−0.163748	−	0.553642i
$193$	20.0776			1.44522			0.722608	−	0.691258i	$-0.242943\pi$
$193$	20.0776			1.44522			0.722608	+	0.691258i	$0.242943\pi$
$194$	22.1406	+	7.95101i	1.58960	+	0.570849i
$195$	6.90315	−	6.90315i	0.494345	−	0.494345i
$196$	−17.4484	−	14.3874i	−1.24632	−	1.02767i
$197$	−0.144337	−	0.144337i	−0.0102836	−	0.0102836i	0.701946	−	0.712230i	$-0.252315\pi$
$197$	−0.144337	−	0.144337i	−0.0102836	−	0.0102836i	−0.712230	+	0.701946i	$0.752315\pi$
$198$	5.16538	−	2.43572i	0.367088	−	0.173099i
$199$		−	2.68476i		−	0.190317i	−0.995462	−	0.0951587i	$-0.969664\pi$
$199$		−	2.68476i		−	0.190317i	0.995462	−	0.0951587i	$-0.0303359\pi$
$200$	8.24066	−	4.90037i	0.582702	−	0.346509i
$201$		−	2.16685i		−	0.152838i
$202$	−4.00003	−	8.48278i	−0.281441	−	0.596847i
$203$	17.5716	+	17.5716i	1.23328	+	1.23328i
$204$	11.2881	−	1.08536i	0.790327	−	0.0759901i
$205$	−23.2886	+	23.2886i	−1.62655	+	1.62655i
$206$	−5.12418	+	14.2689i	−0.357019	+	0.994165i
$207$	6.18292			0.429743
$208$	−11.1749	−	7.54201i	−0.774837	−	0.522944i
$209$	−4.03819			−0.279327
$210$	5.92376	−	16.4955i	0.408778	−	1.13829i
$211$	−7.72121	+	7.72121i	−0.531550	+	0.531550i	−0.921034	−	0.389483i	$-0.872654\pi$
$211$	−7.72121	+	7.72121i	−0.531550	+	0.531550i	0.389483	+	0.921034i	$0.372654\pi$
$212$	0.331622	+	3.44900i	0.0227759	+	0.236878i
$213$	−5.06790	−	5.06790i	−0.347246	−	0.347246i
$214$	4.14470	+	8.78960i	0.283326	+	0.600844i
$215$			1.45648i			0.0993309i
$216$	0.696793	−	2.74126i	0.0474107	−	0.186519i
$217$			37.6037i			2.55270i
$218$	0.657912	−	0.310236i	0.0445594	−	0.0210118i
$219$	1.72065	+	1.72065i	0.116271	+	0.116271i
$220$	14.8824	−	18.0488i	1.00337	−	1.21685i
$221$	13.5134	−	13.5134i	0.909008	−	0.909008i
$222$	−3.84250	−	1.37990i	−0.257891	−	0.0926125i
$223$	−6.22827			−0.417076			−0.208538	−	0.978014i	$-0.566870\pi$
$223$	−6.22827			−0.417076			−0.208538	+	0.978014i	$0.566870\pi$
$224$	−23.9212	−	3.69025i	−1.59830	−	0.246565i
$225$	3.38973			0.225982
$226$	14.0413	+	5.04243i	0.934013	+	0.335417i
$227$	−4.70898	+	4.70898i	−0.312546	+	0.312546i	−0.845895	−	0.533349i	$-0.820933\pi$
$227$	−4.70898	+	4.70898i	−0.312546	+	0.312546i	0.533349	+	0.845895i	$0.320933\pi$
$228$	−1.27237	+	1.54307i	−0.0842647	+	0.102193i
$229$	14.2755	+	14.2755i	0.943350	+	0.943350i	0.998479	−	0.0551292i	$-0.0175571\pi$
$229$	14.2755	+	14.2755i	0.943350	+	0.943350i	−0.0551292	+	0.998479i	$0.517557\pi$
$230$	22.9078	−	10.8021i	1.51050	−	0.712270i
$231$		−	17.2783i		−	1.13683i
$232$	15.9206	+	4.04681i	1.04524	+	0.265686i
$233$		−	7.58374i		−	0.496828i	−0.968654	−	0.248414i	$-0.920091\pi$
$233$		−	7.58374i		−	0.496828i	0.968654	−	0.248414i	$-0.0799093\pi$
$234$	−2.03296	−	4.31126i	−0.132899	−	0.281836i
$235$	−19.8262	−	19.8262i	−1.29332	−	1.29332i
$236$	0.962901	+	10.0146i	0.0626795	+	0.651892i
$237$	−7.12168	+	7.12168i	−0.462603	+	0.462603i
$238$	11.5961	−	32.2910i	0.751666	−	2.09311i
$239$	17.7525			1.14832			0.574158	−	0.818745i	$-0.305330\pi$
$239$	17.7525			1.14832			0.574158	+	0.818745i	$0.305330\pi$
$240$	−2.20758	−	11.3738i	−0.142499	−	0.734173i
$241$	18.6100			1.19877			0.599387	−	0.800459i	$-0.295411\pi$
$241$	18.6100			1.19877			0.599387	+	0.800459i	$0.295411\pi$
$242$	2.53661	−	7.06352i	0.163060	−	0.454060i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	18.2557	−	1.75529i	1.16870	−	0.112371i
$245$	−23.1594	−	23.1594i	−1.47960	−	1.47960i
$246$	6.85843	+	14.5445i	0.437278	+	0.927327i
$247$			3.37045i			0.214457i
$248$	12.7051	+	21.3654i	0.806777	+	1.35671i
$249$			2.93783i			0.186178i
$250$	−5.96608	+	2.81328i	−0.377328	+	0.177928i
$251$	−19.5354	−	19.5354i	−1.23307	−	1.23307i	−0.962780	−	0.270285i	$-0.912882\pi$
$251$	−19.5354	−	19.5354i	−1.23307	−	1.23307i	−0.270285	−	0.962780i	$-0.587118\pi$
$252$	−6.60240	−	5.44413i	−0.415912	−	0.342948i
$253$	17.6549	−	17.6549i	1.10995	−	1.10995i
$254$	4.68161	+	1.68123i	0.293750	+	0.105490i
$255$	16.4234			1.02848
$256$	−14.8382	+	5.98554i	−0.927390	+	0.374096i
$257$	−17.1406			−1.06920			−0.534601	−	0.845105i	$-0.679538\pi$
$257$	−17.1406			−1.06920			−0.534601	+	0.845105i	$0.679538\pi$
$258$	0.669275	+	0.240346i	0.0416672	+	0.0149633i
$259$	−8.73451	+	8.73451i	−0.542736	+	0.542736i
$260$	−15.0643	−	12.4215i	−0.934249	−	0.770351i
$261$	4.10672	+	4.10672i	0.254199	+	0.254199i
$262$	−10.0186	+	4.72424i	−0.618952	+	0.291865i
$263$			20.0312i			1.23518i	0.786500	+	0.617590i	$0.211891\pi$
$263$			20.0312i			1.23518i	−0.786500	+	0.617590i	$0.788109\pi$
$264$	−5.83782	−	9.81711i	−0.359293	−	0.604201i
$265$			5.01806i			0.308257i
$266$	2.58081	+	5.47308i	0.158240	+	0.335576i
$267$	−1.83183	−	1.83183i	−0.112106	−	0.112106i
$268$	−4.31381	+	0.414773i	−0.263508	+	0.0253363i
$269$	6.83094	−	6.83094i	0.416490	−	0.416490i	−0.467502	−	0.883992i	$-0.654846\pi$
$269$	6.83094	−	6.83094i	0.416490	−	0.416490i	0.883992	+	0.467502i	$0.154846\pi$
$270$	1.38446	−	3.85522i	0.0842558	−	0.234621i
$271$	−6.12025			−0.371779			−0.185889	−	0.982571i	$-0.559517\pi$
$271$	−6.12025			−0.371779			−0.185889	+	0.982571i	$0.559517\pi$
$272$	−4.32149	−	22.2649i	−0.262029	−	1.35001i
$273$	−14.4213			−0.872815
$274$	−8.83614	+	24.6054i	−0.533811	+	1.48647i
$275$	9.67913	−	9.67913i	0.583674	−	0.583674i
$276$	−1.18352	−	12.3091i	−0.0712395	−	0.740920i
$277$	16.6547	+	16.6547i	1.00069	+	1.00069i	1.00000		0.000685623i	$0.000218241\pi$
$277$	16.6547	+	16.6547i	1.00069	+	1.00069i	0.000685623		1.00000i	$0.499782\pi$
$278$	5.48518	+	11.6323i	0.328979	+	0.697660i
$279$			8.78851i			0.526154i
$280$	−33.9734	−	8.63561i	−2.03030	−	0.516076i
$281$			1.36377i			0.0813554i	0.999172	+	0.0406777i	$0.0129517\pi$
$281$			1.36377i			0.0813554i	−0.999172	+	0.0406777i	$0.987048\pi$
$282$	−12.3821	+	5.83876i	−0.737346	+	0.347693i
$283$	−13.6400	−	13.6400i	−0.810817	−	0.810817i	0.173940	−	0.984756i	$-0.444350\pi$
$283$	−13.6400	−	13.6400i	−0.810817	−	0.810817i	−0.984756	+	0.173940i	$0.944350\pi$
$284$	−9.11918	+	11.0593i	−0.541124	+	0.656251i
$285$	−2.04814	+	2.04814i	−0.121321	+	0.121321i
$286$	−18.1155	−	6.50553i	−1.07119	−	0.384680i
$287$	48.6519			2.87183
$288$	−5.59072	−	0.862463i	−0.329436	−	0.0508211i
$289$	15.1500			0.891176
$290$	22.3902	+	8.04066i	1.31480	+	0.472164i
$291$	11.7625	−	11.7625i	0.689529	−	0.689529i
$292$	3.09615	−	3.75488i	0.181188	−	0.219737i
$293$	4.57996	+	4.57996i	0.267564	+	0.267564i	0.828118	−	0.560554i	$-0.189412\pi$
$293$	4.57996	+	4.57996i	0.267564	+	0.267564i	−0.560554	+	0.828118i	$0.689412\pi$
$294$	−14.4639	+	6.82040i	−0.843552	+	0.397774i
$295$			14.5705i			0.848326i
$296$	−2.01160	+	7.91385i	−0.116922	+	0.459983i
$297$		−	4.03819i		−	0.234319i
$298$	12.3522	+	26.1951i	0.715544	+	1.51744i
$299$	−14.7356	−	14.7356i	−0.852181	−	0.852181i
$300$	−0.648853	−	6.74834i	−0.0374616	−	0.389615i
$301$	1.52135	−	1.52135i	0.0876893	−	0.0876893i
$302$	−0.461095	+	1.28398i	−0.0265330	+	0.0738846i
$303$	−6.63166			−0.380979
$304$	3.31553	+	2.23768i	0.190159	+	0.128340i
$305$	26.5607			1.52086
$306$	2.71018	−	7.54685i	0.154931	−	0.431425i
$307$	−8.89020	+	8.89020i	−0.507391	+	0.507391i	−0.913725	−	0.406334i	$-0.866807\pi$
$307$	−8.89020	+	8.89020i	−0.507391	+	0.507391i	0.406334	+	0.913725i	$0.366807\pi$
$308$	−34.3980	+	3.30738i	−1.96001	+	0.188455i
$309$	7.58057	+	7.58057i	0.431244	+	0.431244i
$310$	15.3543	+	32.5616i	0.872065	+	1.84937i
$311$			31.7912i			1.80271i	0.433079	+	0.901356i	$0.357427\pi$
$311$			31.7912i			1.80271i	−0.433079	+	0.901356i	$0.642573\pi$
$312$	−8.19380	+	4.87251i	−0.463883	+	0.275851i
$313$			24.1857i			1.36705i	0.729925	+	0.683527i	$0.239555\pi$
$313$			24.1857i			1.36705i	−0.729925	+	0.683527i	$0.760445\pi$
$314$	9.29375	−	4.38243i	0.524477	−	0.247315i
$315$	−8.76343	−	8.76343i	−0.493764	−	0.493764i
$316$	15.5412	+	12.8148i	0.874260	+	0.720887i
$317$	20.6900	−	20.6900i	1.16207	−	1.16207i	0.178045	−	0.984022i	$-0.443023\pi$
$317$	20.6900	−	20.6900i	1.16207	−	1.16207i	0.984022	−	0.178045i	$-0.0569772\pi$
$318$	2.30588	+	0.828075i	0.129307	+	0.0464361i
$319$	23.4529			1.31311
$320$	−22.2205	+	6.57204i	−1.24216	+	0.367388i
$321$	6.87152			0.383531
$322$	−35.2115	−	12.6449i	−1.96226	−	0.704675i
$323$	−4.00936	+	4.00936i	−0.223087	+	0.223087i
$324$	−1.54307	−	1.27237i	−0.0857263	−	0.0706872i
$325$	−8.07864	−	8.07864i	−0.448122	−	0.448122i
$326$	−25.8648	+	12.1965i	−1.43252	+	0.675500i
$327$		−	0.514342i		−	0.0284432i
$328$	27.6427	−	16.4380i	1.52631	−	0.907635i
$329$			41.4186i			2.28348i
$330$	−7.05507	−	14.9616i	−0.388369	−	0.823606i
$331$	5.33155	+	5.33155i	0.293049	+	0.293049i	0.838283	−	0.545235i	$-0.183560\pi$
$331$	5.33155	+	5.33155i	0.293049	+	0.293049i	−0.545235	+	0.838283i	$0.683560\pi$
$332$	5.84869	−	0.562353i	0.320989	−	0.0308631i
$333$	−2.04138	+	2.04138i	−0.111867	+	0.111867i
$334$	−8.09980	+	22.5549i	−0.443201	+	1.23415i
$335$	−6.27629			−0.342910
$336$	−9.57446	+	14.1863i	−0.522329	+	0.773926i
$337$	−26.1476			−1.42435			−0.712175	−	0.702002i	$-0.752290\pi$
$337$	−26.1476			−1.42435			−0.712175	+	0.702002i	$0.752290\pi$
$338$	0.783903	−	2.18288i	0.0426387	−	0.118733i
$339$	7.45962	−	7.45962i	0.405151	−	0.405151i
$340$	−3.14374	−	32.6961i	−0.170493	−	1.77320i
$341$	25.0950	+	25.0950i	1.35897	+	1.35897i
$342$	0.603171	+	1.27913i	0.0326158	+	0.0691677i
$343$			18.4309i			0.995178i
$344$	0.350375	−	1.37841i	0.0188910	−	0.0743190i
$345$		−	17.9089i		−	0.964180i
$346$	−2.70043	+	1.27338i	−0.145176	+	0.0684573i
$347$	−20.6635	−	20.6635i	−1.10928	−	1.10928i	−0.993246	−	0.116031i	$-0.962983\pi$
$347$	−20.6635	−	20.6635i	−1.10928	−	1.10928i	−0.116031	−	0.993246i	$-0.537017\pi$
$348$	7.38963	−	8.96183i	0.396126	−	0.480404i
$349$	21.9762	−	21.9762i	1.17636	−	1.17636i	0.195691	−	0.980666i	$-0.437305\pi$
$349$	21.9762	−	21.9762i	1.17636	−	1.17636i	0.980666	−	0.195691i	$-0.0626951\pi$
$350$	−19.3044	−	6.93247i	−1.03186	−	0.370556i
$351$	−3.37045			−0.179902
$352$	−18.4266	+	13.5012i	−0.982142	+	0.719617i
$353$	9.24360			0.491987			0.245994	−	0.969271i	$-0.420886\pi$
$353$	9.24360			0.491987			0.245994	+	0.969271i	$0.420886\pi$
$354$	6.69538	+	2.40441i	0.355855	+	0.127793i
$355$	−14.6792	+	14.6792i	−0.779090	+	0.779090i
$356$	−3.29620	+	3.99749i	−0.174698	+	0.211866i
$357$	−17.1550	−	17.1550i	−0.907939	−	0.907939i
$358$	6.29284	−	2.96737i	0.332587	−	0.156830i
$359$		−	36.2525i		−	1.91334i	−0.291182	−	0.956668i	$-0.594048\pi$
$359$		−	36.2525i		−	1.91334i	0.291182	−	0.956668i	$-0.405952\pi$
$360$	−7.94005	−	2.01826i	−0.418478	−	0.106372i
$361$		−	1.00000i		−	0.0526316i
$362$	−11.4808	−	24.3470i	−0.603415	−	1.27965i
$363$	−3.75259	−	3.75259i	−0.196960	−	0.196960i
$364$	2.76049	+	28.7102i	0.144689	+	1.50482i
$365$	4.98388	−	4.98388i	0.260868	−	0.260868i
$366$	4.38303	−	12.2051i	0.229105	−	0.637971i
$367$	−16.2698			−0.849278			−0.424639	−	0.905363i	$-0.639599\pi$
$367$	−16.2698			−0.849278			−0.424639	+	0.905363i	$0.639599\pi$
$368$	−24.2786	+	4.71235i	−1.26561	+	0.245648i
$369$	11.3706			0.591931
$370$	−3.99687	+	11.1298i	−0.207787	+	0.578611i
$371$	5.24158	−	5.24158i	0.272129	−	0.272129i
$372$	17.4963	−	1.68227i	0.907142	−	0.0872219i
$373$	5.62251	+	5.62251i	0.291123	+	0.291123i	0.837524	−	0.546401i	$-0.184003\pi$
$373$	5.62251	+	5.62251i	0.291123	+	0.291123i	−0.546401	+	0.837524i	$0.684003\pi$
$374$	−13.8108	−	29.2882i	−0.714137	−	1.51446i
$375$			4.66416i			0.240856i
$376$	13.9941	+	23.5330i	0.721689	+	1.21362i
$377$		−	19.5748i		−	1.00816i
$378$	−5.47308	+	2.58081i	−0.281505	+	0.132743i
$379$	−16.6244	−	16.6244i	−0.853936	−	0.853936i	0.136679	−	0.990615i	$-0.456357\pi$
$379$	−16.6244	−	16.6244i	−0.853936	−	0.853936i	−0.990615	+	0.136679i	$0.956357\pi$
$380$	4.46952	+	3.68542i	0.229281	+	0.189058i
$381$	2.48717	−	2.48717i	0.127421	−	0.127421i
$382$	7.69010	+	2.76162i	0.393460	+	0.141297i
$383$	33.4351			1.70845			0.854227	−	0.519901i	$-0.174031\pi$
$383$	33.4351			1.70845			0.854227	+	0.519901i	$0.174031\pi$
$384$	−0.646847	+	11.2952i	−0.0330093	+	0.576406i
$385$	−50.0467			−2.55062
$386$	−26.7231	−	9.59664i	−1.36017	−	0.488456i
$387$	0.355561	−	0.355561i	0.0180742	−	0.0180742i
$388$	−25.6685	−	21.1654i	−1.30312	−	1.07451i
$389$	11.7765	+	11.7765i	0.597093	+	0.597093i	0.939538	−	0.342445i	$-0.111255\pi$
$389$	11.7765	+	11.7765i	0.597093	+	0.597093i	−0.342445	+	0.939538i	$0.611255\pi$
$390$	−12.4876	+	5.88848i	−0.632334	+	0.298175i
$391$		−	35.0578i		−	1.77295i
$392$	16.3468	+	27.4895i	0.825639	+	1.38843i
$393$			7.83234i			0.395089i
$394$	0.123121	+	0.261100i	0.00620275	+	0.0131541i
$395$	20.6280	+	20.6280i	1.03791	+	1.03791i
$396$	−8.03930	+	0.772980i	−0.403990	+	0.0388437i
$397$	−0.463753	+	0.463753i	−0.0232751	+	0.0232751i	−0.718649	−	0.695373i	$-0.755239\pi$
$397$	−0.463753	+	0.463753i	−0.0232751	+	0.0232751i	0.695373	+	0.718649i	$0.255239\pi$
$398$	−1.28325	+	3.57339i	−0.0643237	+	0.179118i
$399$	4.27873			0.214205
$400$	−13.3105	+	2.58350i	−0.665526	+	0.129175i
$401$	7.65657			0.382351			0.191175	−	0.981556i	$-0.438770\pi$
$401$	7.65657			0.382351			0.191175	+	0.981556i	$0.438770\pi$
$402$	−1.03571	+	2.88406i	−0.0516563	+	0.143844i
$403$	20.9454	−	20.9454i	1.04336	−	1.04336i
$404$	1.26942	+	13.2024i	0.0631558	+	0.656846i
$405$	−2.04814	−	2.04814i	−0.101773	−	0.101773i
$406$	−14.9888	−	31.7864i	−0.743880	−	1.57753i
$407$			11.6580i			0.577867i
$408$	−15.5432	−	3.95088i	−0.769502	−	0.195598i
$409$			38.0072i			1.87933i	0.342092	+	0.939666i	$0.388865\pi$
$409$			38.0072i			1.87933i	−0.342092	+	0.939666i	$0.611135\pi$
$410$	42.1283	−	19.8655i	2.08057	−	0.981085i
$411$	13.0719	+	13.0719i	0.644791	+	0.644791i
$412$	13.6405	−	16.5426i	0.672019	−	0.814995i
$413$	15.2195	−	15.2195i	0.748903	−	0.748903i
$414$	−8.22942	−	2.95530i	−0.404454	−	0.145245i
$415$	8.50944			0.417712
$416$	11.2687	+	15.3797i	0.552494	+	0.754051i
$417$	9.09390			0.445330
$418$	5.37479	+	1.93017i	0.262890	+	0.0944075i
$419$	−17.7349	+	17.7349i	−0.866406	+	0.866406i	−0.992072	−	0.125667i	$-0.959893\pi$
$419$	−17.7349	+	17.7349i	−0.866406	+	0.866406i	0.125667	+	0.992072i	$0.459893\pi$
$420$	−15.7689	+	19.1239i	−0.769445	+	0.933150i
$421$	−18.1747	−	18.1747i	−0.885780	−	0.885780i	0.108335	−	0.994114i	$-0.465448\pi$
$421$	−18.1747	−	18.1747i	−0.885780	−	0.885780i	−0.994114	+	0.108335i	$0.965448\pi$
$422$	13.9674	−	6.58629i	0.679924	−	0.320616i
$423$			9.68010i			0.470663i
$424$	1.20716	−	4.74910i	0.0586249	−	0.230637i
$425$		−	19.2201i		−	0.932311i
$426$	4.32298	+	9.16767i	0.209449	+	0.444175i
$427$	−27.7438	−	27.7438i	−1.34262	−	1.34262i
$428$	−1.31533	−	13.6800i	−0.0635788	−	0.661245i
$429$	−9.62410	+	9.62410i	−0.464656	+	0.464656i
$430$	0.696164	−	1.93856i	0.0335720	−	0.0934855i
$431$	−15.5473			−0.748886			−0.374443	−	0.927250i	$-0.622166\pi$
$431$	−15.5473			−0.748886			−0.374443	+	0.927250i	$0.622166\pi$
$432$	−2.23768	+	3.31553i	−0.107661	+	0.159519i
$433$	−30.3909			−1.46049			−0.730246	−	0.683185i	$-0.760594\pi$
$433$	−30.3909			−1.46049			−0.730246	+	0.683185i	$0.760594\pi$
$434$	17.9737	−	50.0502i	0.862767	−	2.40249i
$435$	11.8951	−	11.8951i	0.570327	−	0.570327i
$436$	−1.02396	+	0.0984540i	−0.0490389	+	0.00471509i
$437$	4.37199	+	4.37199i	0.209140	+	0.209140i
$438$	−1.46774	−	3.11261i	−0.0701314	−	0.148726i
$439$			21.1175i			1.00788i	0.863738	+	0.503941i	$0.168117\pi$
$439$			21.1175i			1.00788i	−0.863738	+	0.503941i	$0.831883\pi$
$440$	−28.4353	+	16.9093i	−1.35560	+	0.806118i
$441$			11.3076i			0.538456i
$442$	−24.4453	+	11.5271i	−1.16274	+	0.548288i
$443$	6.71469	+	6.71469i	0.319024	+	0.319024i	0.848392	−	0.529368i	$-0.177571\pi$
$443$	6.71469	+	6.71469i	0.319024	+	0.319024i	−0.529368	+	0.848392i	$0.677571\pi$
$444$	4.45477	+	3.67326i	0.211414	+	0.174325i
$445$	−5.30590	+	5.30590i	−0.251524	+	0.251524i
$446$	8.28977	+	2.97697i	0.392532	+	0.140964i
$447$	20.4788			0.968613
$448$	30.0751	+	16.3455i	1.42091	+	0.772252i
$449$	−24.7986			−1.17032			−0.585159	−	0.810919i	$-0.698968\pi$
$449$	−24.7986			−1.17032			−0.585159	+	0.810919i	$0.698968\pi$
$450$	−4.51170	−	1.62022i	−0.212683	−	0.0763777i
$451$	32.4680	−	32.4680i	1.52886	−	1.52886i
$452$	−16.2787	−	13.4229i	−0.765684	−	0.631358i
$453$	0.682130	+	0.682130i	0.0320493	+	0.0320493i
$454$	8.51840	−	4.01682i	0.399788	−	0.188519i
$455$			41.7713i			1.95827i
$456$	2.43107	−	1.44565i	0.113845	−	0.0676989i
$457$			3.07017i			0.143616i	0.997418	+	0.0718082i	$0.0228770\pi$
$457$			3.07017i			0.143616i	−0.997418	+	0.0718082i	$0.977123\pi$
$458$	−12.1772	−	25.8239i	−0.569002	−	1.20667i
$459$	−4.00936	−	4.00936i	−0.187141	−	0.187141i
$460$	−35.6533	+	3.42807i	−1.66234	+	0.159835i
$461$	−10.5409	+	10.5409i	−0.490937	+	0.490937i	−0.908601	−	0.417665i	$-0.862849\pi$
$461$	−10.5409	+	10.5409i	−0.490937	+	0.490937i	0.417665	+	0.908601i	$0.362849\pi$
$462$	−8.25866	+	22.9973i	−0.384228	+	1.06993i
$463$	−23.0860			−1.07290			−0.536449	−	0.843933i	$-0.680235\pi$
$463$	−23.0860			−1.07290			−0.536449	+	0.843933i	$0.680235\pi$
$464$	−19.2559	−	12.9960i	−0.893932	−	0.603323i
$465$	25.4559			1.18049
$466$	−3.62486	+	10.0939i	−0.167919	+	0.467591i
$467$	−27.6502	+	27.6502i	−1.27950	+	1.27950i	−0.338547	+	0.940949i	$0.609935\pi$
$467$	−27.6502	+	27.6502i	−1.27950	+	1.27950i	−0.940949	+	0.338547i	$0.890065\pi$
$468$	0.645164	+	6.70996i	0.0298227	+	0.310168i
$469$	6.55585	+	6.55585i	0.302721	+	0.302721i
$470$	16.9120	+	35.8649i	0.780092	+	1.65433i
$471$		−	7.26566i		−	0.334784i
$472$	3.50513	−	13.7895i	0.161336	−	0.634715i
$473$		−	2.03056i		−	0.0933653i
$474$	12.8829	−	6.07489i	0.591731	−	0.279029i
$475$	2.39690	+	2.39690i	0.109977	+	0.109977i
$476$	−30.8687	+	37.4363i	−1.41487	+	1.71589i
$477$	1.22503	−	1.22503i	0.0560903	−	0.0560903i
$478$	−23.6285	−	8.48532i	−1.08074	−	0.388109i
$479$	−12.2146			−0.558097			−0.279049	−	0.960277i	$-0.590019\pi$
$479$	−12.2146			−0.558097			−0.279049	+	0.960277i	$0.590019\pi$
$480$	−2.49813	+	16.1935i	−0.114023	+	0.739131i
$481$	9.73031			0.443664
$482$	−24.7697	−	8.89516i	−1.12823	−	0.405164i
$483$	−18.7066	+	18.7066i	−0.851178	+	0.851178i
$484$	−6.75242	+	8.18904i	−0.306928	+	0.372229i
$485$	−34.0701	−	34.0701i	−1.54704	−	1.54704i
$486$	−1.27913	+	0.603171i	−0.0580227	+	0.0273604i
$487$		−	36.2707i		−	1.64358i	−0.569788	−	0.821792i	$-0.692975\pi$
$487$		−	36.2707i		−	1.64358i	0.569788	−	0.821792i	$-0.307025\pi$
$488$	−25.1371	−	6.38954i	−1.13790	−	0.289241i
$489$			20.2206i			0.914406i
$490$	19.7553	+	41.8947i	0.892454	+	1.89261i
$491$	−16.0960	−	16.0960i	−0.726401	−	0.726401i	0.243500	−	0.969901i	$-0.421705\pi$
$491$	−16.0960	−	16.0960i	−0.726401	−	0.726401i	−0.969901	+	0.243500i	$0.921705\pi$
$492$	−2.17654	−	22.6368i	−0.0981258	−	1.02055i
$493$	23.2855	−	23.2855i	1.04873	−	1.04873i
$494$	1.61100	−	4.48604i	0.0724824	−	0.201837i
$495$	−11.6966			−0.525724
$496$	−6.69821	−	34.5100i	−0.300758	−	1.54954i
$497$	30.6661			1.37556
$498$	1.40422	−	3.91023i	0.0629246	−	0.175222i
$499$	−13.5203	+	13.5203i	−0.605251	+	0.605251i	−0.941701	−	0.336451i	$-0.890774\pi$
$499$	−13.5203	+	13.5203i	−0.605251	+	0.605251i	0.336451	+	0.941701i	$0.390774\pi$
$500$	9.28549	−	0.892801i	0.415260	−	0.0399273i
$501$	11.9826	+	11.9826i	0.535344	+	0.535344i
$502$	16.6640	+	35.3390i	0.743750	+	1.57726i
$503$			25.3227i			1.12908i	0.825405	+	0.564541i	$0.190947\pi$
$503$			25.3227i			1.12908i	−0.825405	+	0.564541i	$0.809053\pi$
$504$	6.18557	+	10.4019i	0.275527	+	0.463337i
$505$			19.2086i			0.854772i
$506$	−31.9372	+	15.0599i	−1.41978	+	0.669493i
$507$	−1.15968	−	1.15968i	−0.0515033	−	0.0515033i
$508$	−5.42759	−	4.47541i	−0.240810	−	0.198564i
$509$	−17.1308	+	17.1308i	−0.759311	+	0.759311i	−0.976197	−	0.216886i	$-0.930410\pi$
$509$	−17.1308	+	17.1308i	−0.759311	+	0.759311i	0.216886	+	0.976197i	$0.430410\pi$
$510$	−21.8595	−	7.85005i	−0.967953	−	0.347606i
$511$	−10.4118			−0.460589
$512$	22.6105	−	0.874345i	0.999253	−	0.0386410i
$513$	1.00000			0.0441511
$514$	22.8140	+	8.19283i	1.00628	+	0.361370i
$515$	21.9571	−	21.9571i	0.967547	−	0.967547i
$516$	−0.775919	−	0.639798i	−0.0341579	−	0.0281655i
$517$	27.6409	+	27.6409i	1.21564	+	1.21564i
$518$	15.8005	−	7.45065i	0.694232	−	0.327363i
$519$			2.11114i			0.0926687i
$520$	14.1132	+	23.7334i	0.618906	+	1.04078i
$521$			2.78286i			0.121919i	0.998140	+	0.0609597i	$0.0194161\pi$
$521$			2.78286i			0.121919i	−0.998140	+	0.0609597i	$0.980584\pi$
$522$	−3.50308	−	7.42892i	−0.153326	−	0.325155i
$523$	26.0063	+	26.0063i	1.13718	+	1.13718i	0.988954	+	0.148224i	$0.0473557\pi$
$523$	26.0063	+	26.0063i	1.13718	+	1.13718i	0.148224	+	0.988954i	$0.452644\pi$
$524$	15.5928	−	1.49925i	0.681173	−	0.0654949i
$525$	−10.2557	+	10.2557i	−0.447595	+	0.447595i
$526$	9.57450	−	26.6614i	0.417468	−	1.16249i
$527$	49.8317			2.17070
$528$	3.07773	+	15.8568i	0.133941	+	0.690080i
$529$	−15.2285			−0.662110
$530$	2.39852	−	6.67899i	0.104185	−	0.290117i
$531$	3.55701	−	3.55701i	0.154361	−	0.154361i
$532$	−0.819025	−	8.51819i	−0.0355092	−	0.369310i
$533$	−27.0993	−	27.0993i	−1.17380	−	1.17380i
$534$	1.56258	+	3.31373i	0.0676193	+	0.143399i
$535$		−	19.9034i		−	0.860498i
$536$	5.93989	+	1.50984i	0.256564	+	0.0652154i
$537$		−	4.91961i		−	0.212297i
$538$	−12.3570	+	5.82688i	−0.532746	+	0.251215i
$539$	32.2880	+	32.2880i	1.39074	+	1.39074i
$540$	−3.68542	+	4.46952i	−0.158595	+	0.192337i
$541$	−9.00510	+	9.00510i	−0.387159	+	0.387159i	−0.873673	−	0.486514i	$-0.838268\pi$
$541$	−9.00510	+	9.00510i	−0.387159	+	0.387159i	0.486514	+	0.873673i	$0.338268\pi$
$542$	8.14600	+	2.92534i	0.349900	+	0.125654i
$543$	−19.0340			−0.816827
$544$	−4.89025	+	31.6999i	−0.209668	+	1.35912i
$545$	−1.48979			−0.0638157
$546$	19.1946	+	6.89305i	0.821453	+	0.294995i
$547$	5.49186	−	5.49186i	0.234815	−	0.234815i	−0.579884	−	0.814699i	$-0.696902\pi$
$547$	5.49186	−	5.49186i	0.234815	−	0.234815i	0.814699	+	0.579884i	$0.196902\pi$
$548$	23.5217	−	28.5260i	1.00480	−	1.21857i
$549$	−6.48412	−	6.48412i	−0.276736	−	0.276736i
$550$	−17.5093	+	8.25643i	−0.746597	+	0.352055i
$551$			5.80777i			0.247420i
$552$	−4.30821	+	16.9490i	−0.183370	+	0.721396i
$553$		−	43.0936i		−	1.83253i
$554$	−14.2067	−	30.1279i	−0.603585	−	1.28001i
$555$	5.91286	+	5.91286i	0.250987	+	0.250987i
$556$	−1.74073	−	18.1043i	−0.0738234	−	0.767793i
$557$	−2.41328	+	2.41328i	−0.102254	+	0.102254i	−0.756383	−	0.654129i	$-0.773035\pi$
$557$	−2.41328	+	2.41328i	−0.102254	+	0.102254i	0.654129	+	0.756383i	$0.273035\pi$
$558$	4.20071	−	11.6974i	0.177830	−	0.495191i
$559$	−1.69480			−0.0716823
$560$	41.0906	+	27.7324i	1.73640	+	1.17191i
$561$	−22.8969			−0.966709
$562$	0.651850	−	1.81516i	0.0274966	−	0.0765679i
$563$	−23.3849	+	23.3849i	−0.985556	+	0.985556i	−0.999897	−	0.0143410i	$-0.995435\pi$
$563$	−23.3849	+	23.3849i	−0.985556	+	0.985556i	0.0143410	+	0.999897i	$0.495435\pi$
$564$	19.2713	−	1.85294i	0.811469	−	0.0780229i
$565$	−21.6068	−	21.6068i	−0.909006	−	0.909006i
$566$	11.6351	+	24.6744i	0.489061	+	1.03714i
$567$			4.27873i			0.179690i
$568$	17.4237	−	10.3611i	0.731081	−	0.434743i
$569$		−	22.4629i		−	0.941692i	−0.882215	−	0.470846i	$-0.843949\pi$
$569$		−	22.4629i		−	0.941692i	0.882215	−	0.470846i	$-0.156051\pi$
$570$	3.70502	−	1.74709i	0.155186	−	0.0731774i
$571$	18.6631	+	18.6631i	0.781025	+	0.781025i	0.980004	−	0.198979i	$-0.0637625\pi$
$571$	18.6631	+	18.6631i	0.781025	+	0.781025i	−0.198979	+	0.980004i	$0.563763\pi$
$572$	21.0021	+	17.3176i	0.878140	+	0.724086i
$573$	4.08547	−	4.08547i	0.170673	−	0.170673i
$574$	−64.7552	−	23.2545i	−2.70283	−	0.970625i
$575$	−20.9584			−0.874027
$576$	7.02896	+	3.82017i	0.292873	+	0.159174i
$577$	−30.8602			−1.28473			−0.642364	−	0.766399i	$-0.722046\pi$
$577$	−30.8602			−1.28473			−0.642364	+	0.766399i	$0.722046\pi$
$578$	−20.1645	−	7.24136i	−0.838733	−	0.301201i
$579$	−14.1970	+	14.1970i	−0.590007	+	0.590007i
$580$	−25.9580	−	21.4041i	−1.07785	−	0.888756i
$581$	−8.88848	−	8.88848i	−0.368756	−	0.368756i
$582$	−21.2780	+	10.0336i	−0.882001	+	0.415904i
$583$		−	6.99598i		−	0.289744i
$584$	−5.91569	+	3.51781i	−0.244793	+	0.145568i
$585$			9.76253i			0.403631i
$586$	−3.90677	−	8.28501i	−0.161387	−	0.342251i
$587$	24.0862	+	24.0862i	0.994144	+	0.994144i	0.999983	−	0.00583867i	$-0.00185852\pi$
$587$	24.0862	+	24.0862i	0.994144	+	0.994144i	−0.00583867	+	0.999983i	$0.501859\pi$
$588$	22.5113	−	2.16447i	0.928351	−	0.0892611i
$589$	−6.21441	+	6.21441i	−0.256060	+	0.256060i
$590$	6.96437	−	19.3932i	0.286719	−	0.798405i
$591$	0.204123			0.00839649
$592$	6.46007	−	9.57176i	0.265507	−	0.393397i
$593$	−4.11124			−0.168828			−0.0844142	−	0.996431i	$-0.526902\pi$
$593$	−4.11124			−0.168828			−0.0844142	+	0.996431i	$0.526902\pi$
$594$	−1.93017	+	5.37479i	−0.0791956	+	0.220530i
$595$	−49.6895	+	49.6895i	−2.03707	+	2.03707i
$596$	−3.92000	−	40.7695i	−0.160569	−	1.66998i
$597$	1.89841	+	1.89841i	0.0776967	+	0.0776967i
$598$	12.5696	+	26.6562i	0.514011	+	1.09005i
$599$		−	34.0950i		−	1.39308i	−0.717516	−	0.696542i	$-0.754721\pi$
$599$		−	34.0950i		−	1.39308i	0.717516	−	0.696542i	$-0.245279\pi$
$600$	−2.36194	+	9.29211i	−0.0964257	+	0.379349i
$601$		−	6.49930i		−	0.265112i	−0.991176	−	0.132556i	$-0.957682\pi$
$601$		−	6.49930i		−	0.265112i	0.991176	−	0.132556i	$-0.0423184\pi$
$602$	−2.75208	+	1.29773i	−0.112166	+	0.0528917i
$603$	1.53219	+	1.53219i	0.0623958	+	0.0623958i
$604$	1.22743	−	1.48857i	0.0499432	−	0.0605690i
$605$	−10.8694	+	10.8694i	−0.441904	+	0.441904i
$606$	8.82668	+	3.16979i	0.358559	+	0.128764i
$607$	1.41898			0.0575945			0.0287972	−	0.999585i	$-0.490832\pi$
$607$	1.41898			0.0575945			0.0287972	+	0.999585i	$0.490832\pi$
$608$	−3.34338	−	4.56309i	−0.135592	−	0.185058i
$609$	−24.8499			−1.00697
$610$	−35.3521	−	12.6955i	−1.43137	−	0.514024i
$611$	23.0703	−	23.0703i	0.933325	−	0.933325i
$612$	−7.21445	+	8.74938i	−0.291627	+	0.353673i
$613$	33.8820	+	33.8820i	1.36848	+	1.36848i	0.862607	+	0.505875i	$0.168830\pi$
$613$	33.8820	+	33.8820i	1.36848	+	1.36848i	0.505875	+	0.862607i	$0.331170\pi$
$614$	16.0821	−	7.58346i	0.649021	−	0.306044i
$615$		−	32.9350i		−	1.32807i
$616$	47.3643	+	12.0394i	1.90836	+	0.485082i
$617$			16.1395i			0.649751i	0.945757	+	0.324876i	$0.105322\pi$
$617$			16.1395i			0.649751i	−0.945757	+	0.324876i	$0.894678\pi$
$618$	−6.46632	−	13.7130i	−0.260114	−	0.551618i
$619$	10.1483	+	10.1483i	0.407893	+	0.407893i	0.881003	−	0.473110i	$-0.156869\pi$
$619$	10.1483	+	10.1483i	0.407893	+	0.407893i	−0.473110	+	0.881003i	$0.656869\pi$
$620$	−4.87271	−	50.6782i	−0.195693	−	2.03528i
$621$	−4.37199	+	4.37199i	−0.175442	+	0.175442i
$622$	15.1955	−	42.3138i	0.609283	−	1.69663i
$623$	11.0845			0.444091
$624$	13.2348	−	2.56881i	0.529817	−	0.102835i
$625$	30.4584			1.21834
$626$	11.5602	−	32.1909i	0.462039	−	1.28661i
$627$	2.85543	−	2.85543i	0.114035	−	0.114035i
$628$	−14.4646	+	1.39077i	−0.577201	+	0.0554979i
$629$	11.5748	+	11.5748i	0.461518	+	0.461518i
$630$	7.47532	+	15.8528i	0.297824	+	0.631590i
$631$			18.2633i			0.727051i	0.931584	+	0.363525i	$0.118427\pi$
$631$			18.2633i			0.727051i	−0.931584	+	0.363525i	$0.881573\pi$
$632$	−14.5600	−	24.4847i	−0.579166	−	0.973948i
$633$		−	10.9194i		−	0.434009i
$634$	−37.4276	+	17.6489i	−1.48644	+	0.700925i
$635$	−7.20409	−	7.20409i	−0.285885	−	0.285885i
$636$	−2.67331	−	2.20432i	−0.106003	−	0.0874070i
$637$	26.9490	−	26.9490i	1.06776	−	1.06776i
$638$	−31.2156	−	11.2100i	−1.23584	−	0.443807i
$639$	7.16709			0.283526
$640$	32.7166	+	1.87359i	1.29324	+	0.0740603i
$641$	−32.1734			−1.27077			−0.635387	−	0.772194i	$-0.719159\pi$
$641$	−32.1734			−1.27077			−0.635387	+	0.772194i	$0.719159\pi$
$642$	−9.14593	−	3.28444i	−0.360961	−	0.129626i
$643$	−6.61702	+	6.61702i	−0.260950	+	0.260950i	−0.825440	−	0.564490i	$-0.809073\pi$
$643$	−6.61702	+	6.61702i	−0.260950	+	0.260950i	0.564490	+	0.825440i	$0.309073\pi$
$644$	40.8222	+	33.6606i	1.60862	+	1.32641i
$645$	−1.02988	−	1.02988i	−0.0405517	−	0.0405517i
$646$	7.25281	−	3.42004i	0.285358	−	0.134560i
$647$			8.50466i			0.334353i	0.985927	+	0.167176i	$0.0534649\pi$
$647$			8.50466i			0.334353i	−0.985927	+	0.167176i	$0.946535\pi$
$648$	1.44565	+	2.43107i	0.0567906	+	0.0955013i
$649$		−	20.3136i		−	0.797378i
$650$	6.89119	+	14.6140i	0.270295	+	0.573209i
$651$	−26.5898	−	26.5898i	−1.04214	−	1.04214i
$652$	40.2555	−	3.87057i	1.57653	−	0.151583i
$653$	25.3451	−	25.3451i	0.991832	−	0.991832i	−0.00813466	−	0.999967i	$-0.502589\pi$
$653$	25.3451	−	25.3451i	0.991832	−	0.991832i	0.999967	+	0.00813466i	$0.00258937\pi$
$654$	−0.245844	+	0.684584i	−0.00961326	+	0.0267694i
$655$	22.6864			0.886430
$656$	−44.6492	+	8.66618i	−1.74326	+	0.338357i
$657$	−2.43337			−0.0949349
$658$	19.7972	−	55.1278i	0.771774	−	2.14910i
$659$	−12.6483	+	12.6483i	−0.492708	+	0.492708i	−0.909159	−	0.416450i	$-0.863274\pi$
$659$	−12.6483	+	12.6483i	−0.492708	+	0.492708i	0.416450	+	0.909159i	$0.363274\pi$
$660$	2.23894	+	23.2859i	0.0871506	+	0.906401i
$661$	3.65273	+	3.65273i	0.142075	+	0.142075i	0.774567	−	0.632492i	$-0.217968\pi$
$661$	3.65273	+	3.65273i	0.142075	+	0.142075i	−0.632492	+	0.774567i	$0.717968\pi$
$662$	−4.54788	−	9.64461i	−0.176758	−	0.374848i
$663$			19.1108i			0.742202i
$664$	−8.05335	−	2.04706i	−0.312531	−	0.0794413i
$665$		−	12.3934i		−	0.480594i
$666$	3.69279	−	1.74132i	0.143093	−	0.0674748i
$667$	−25.3915	−	25.3915i	−0.983163	−	0.983163i
$668$	21.5615	−	26.1489i	0.834240	−	1.01173i
$669$	4.40405	−	4.40405i	0.170270	−	0.170270i
$670$	8.35368	+	2.99993i	0.322731	+	0.115897i
$671$	−37.0299			−1.42952
$672$	19.5243	−	14.3054i	0.753164	−	0.551845i
$673$	−21.1399			−0.814884			−0.407442	−	0.913231i	$-0.633579\pi$
$673$	−21.1399			−0.814884			−0.407442	+	0.913231i	$0.633579\pi$
$674$	34.8022	+	12.4980i	1.34053	+	0.481404i
$675$	−2.39690	+	2.39690i	−0.0922567	+	0.0922567i
$676$	−2.08673	+	2.53070i	−0.0802590	+	0.0973347i
$677$	−28.0342	−	28.0342i	−1.07744	−	1.07744i	−0.996738	−	0.0807033i	$-0.974283\pi$
$677$	−28.0342	−	28.0342i	−1.07744	−	1.07744i	−0.0807033	−	0.996738i	$-0.525717\pi$
$678$	−13.4942	+	6.36316i	−0.518243	+	0.244376i
$679$			71.1754i			2.73146i
$680$	−11.4437	+	45.0209i	−0.438847	+	1.72647i
$681$		−	6.65950i		−	0.255193i
$682$	−21.4063	−	45.3960i	−0.819691	−	1.73830i
$683$	26.2512	+	26.2512i	1.00447	+	1.00447i	0.999990	+	0.00448379i	$0.00142724\pi$
$683$	26.2512	+	26.2512i	1.00447	+	1.00447i	0.00448379	+	0.999990i	$0.498573\pi$
$684$	−0.191418	−	1.99082i	−0.00731903	−	0.0761209i
$685$	37.8629	−	37.8629i	1.44667	−	1.44667i
$686$	8.80959	−	24.5314i	0.336352	−	0.936614i
$687$	−20.1886			−0.770242
$688$	−1.12520	+	1.66718i	−0.0428977	+	0.0635607i
$689$	−5.83916			−0.222454
$690$	−8.56004	+	23.8365i	−0.325875	+	0.907441i
$691$	9.92656	−	9.92656i	0.377624	−	0.377624i	−0.492620	−	0.870244i	$-0.663961\pi$
$691$	9.92656	−	9.92656i	0.377624	−	0.377624i	0.870244	+	0.492620i	$0.163961\pi$
$692$	4.20290	−	0.404109i	0.159770	−	0.0153619i
$693$	12.2176	+	12.2176i	0.464109	+	0.464109i
$694$	17.6263	+	37.3797i	0.669084	+	1.41891i
$695$		−	26.3405i		−	0.999152i
$696$	−14.1191	+	8.39603i	−0.535183	+	0.318251i
$697$		−	64.4725i		−	2.44207i
$698$	−39.7542	+	18.7460i	−1.50472	+	0.709545i
$699$	5.36252	+	5.36252i	0.202829	+	0.202829i
$700$	22.3804	+	18.4541i	0.845898	+	0.697500i
$701$	6.55602	−	6.55602i	0.247617	−	0.247617i	−0.572375	−	0.819992i	$-0.693978\pi$
$701$	6.55602	−	6.55602i	0.247617	−	0.247617i	0.819992	+	0.572375i	$0.193978\pi$
$702$	4.48604	+	1.61100i	0.169315	+	0.0608034i
$703$	−2.88694			−0.108883
$704$	30.9789	−	9.16247i	1.16756	−	0.345324i
$705$	28.0384			1.05599
$706$	−12.3032	−	4.41824i	−0.463035	−	0.166283i
$707$	20.0642	−	20.0642i	0.754593	−	0.754593i
$708$	−7.76224	−	6.40049i	−0.291723	−	0.240545i
$709$	36.6217	+	36.6217i	1.37536	+	1.37536i	0.852294	+	0.523063i	$0.175211\pi$
$709$	36.6217	+	36.6217i	1.37536	+	1.37536i	0.523063	+	0.852294i	$0.324789\pi$
$710$	26.5542	−	12.5215i	0.996560	−	0.469925i
$711$		−	10.0716i		−	0.377714i
$712$	6.29792	−	3.74511i	0.236025	−	0.140354i
$713$		−	54.3387i		−	2.03500i
$714$	14.6334	+	31.0329i	0.547643	+	1.16138i
$715$	27.8762	+	27.8762i	1.04251	+	1.04251i
$716$	−9.79405	+	0.941699i	−0.366021	+	0.0351929i
$717$	−12.5529	+	12.5529i	−0.468798	+	0.468798i
$718$	−17.3279	+	48.2518i	−0.646672	+	1.80074i
$719$	−36.1138			−1.34682			−0.673409	−	0.739270i	$-0.735171\pi$
$719$	−36.1138			−1.34682			−0.673409	+	0.739270i	$0.735171\pi$
$720$	9.60345	+	6.48146i	0.357900	+	0.241550i
$721$	−45.8704			−1.70830
$722$	−0.477978	+	1.33099i	−0.0177885	+	0.0495344i
$723$	−13.1592	+	13.1592i	−0.489398	+	0.489398i
$724$	3.64344	+	37.8932i	0.135407	+	1.40829i
$725$	−13.9207	−	13.9207i	−0.517000	−	0.517000i
$726$	3.20101	+	6.78832i	0.118801	+	0.251938i
$727$		−	4.79346i		−	0.177780i	−0.996041	−	0.0888899i	$-0.971668\pi$
$727$		−	4.79346i		−	0.177780i	0.996041	−	0.0888899i	$-0.0283319\pi$
$728$	10.0486	−	39.5324i	0.372427	−	1.46517i
$729$			1.00000i			0.0370370i
$730$	−9.01569	+	4.25132i	−0.333686	+	0.157348i
$731$	−2.01607	−	2.01607i	−0.0745669	−	0.0745669i
$732$	−11.6675	+	14.1499i	−0.431245	+	0.522995i
$733$	5.55803	−	5.55803i	0.205291	−	0.205291i	−0.596972	−	0.802262i	$-0.703630\pi$
$733$	5.55803	−	5.55803i	0.205291	−	0.205291i	0.802262	+	0.596972i	$0.203630\pi$
$734$	21.6550	+	7.77662i	0.799300	+	0.287040i
$735$	32.7524			1.20809
$736$	34.5670	+	5.33255i	1.27416	+	0.196560i
$737$	8.75015			0.322316
$738$	−15.1342	−	5.43491i	−0.557097	−	0.200062i
$739$	1.86956	−	1.86956i	0.0687728	−	0.0687728i	−0.671884	−	0.740657i	$-0.734515\pi$
$739$	1.86956	−	1.86956i	0.0687728	−	0.0687728i	0.740657	+	0.671884i	$0.234515\pi$
$740$	10.6396	−	12.9032i	0.391119	−	0.474333i
$741$	−2.38327	−	2.38327i	−0.0875516	−	0.0875516i
$742$	−9.48185	+	4.47114i	−0.348090	+	0.164141i
$743$		−	28.2471i		−	1.03629i	−0.855294	−	0.518143i	$-0.826624\pi$
$743$		−	28.2471i		−	1.03629i	0.855294	−	0.518143i	$-0.173376\pi$
$744$	−24.0915	−	6.12377i	−0.883239	−	0.224508i
$745$		−	59.3168i		−	2.17320i
$746$	−4.79608	−	10.1710i	−0.175597	−	0.372385i
$747$	−2.07736	−	2.07736i	−0.0760067	−	0.0760067i
$748$	4.38287	+	45.5836i	0.160254	+	1.66670i
$749$	−20.7899	+	20.7899i	−0.759648	+	0.759648i
$750$	2.22936	−	6.20795i	0.0814049	−	0.226682i
$751$	−40.1456			−1.46494			−0.732468	−	0.680802i	$-0.761631\pi$
$751$	−40.1456			−1.46494			−0.732468	+	0.680802i	$0.761631\pi$
$752$	−7.37774	−	38.0110i	−0.269038	−	1.38612i
$753$	27.6273			1.00679
$754$	−9.35634	+	26.0539i	−0.340738	+	0.948828i
$755$	1.97579	−	1.97579i	0.0719064	−	0.0719064i
$756$	8.51819	−	0.819025i	0.309803	−	0.0297876i
$757$	−1.07075	−	1.07075i	−0.0389171	−	0.0389171i	0.687380	−	0.726298i	$-0.258761\pi$
$757$	−1.07075	−	1.07075i	−0.0389171	−	0.0389171i	−0.726298	+	0.687380i	$0.758761\pi$
$758$	14.1808	+	30.0730i	0.515070	+	1.09230i
$759$			24.9678i			0.906274i
$760$	−4.18734	−	7.04159i	−0.151891	−	0.255425i
$761$			18.7934i			0.681260i	0.940197	+	0.340630i	$0.110640\pi$
$761$			18.7934i			0.681260i	−0.940197	+	0.340630i	$0.889360\pi$
$762$	−4.49921	+	2.12159i	−0.162989	+	0.0768569i
$763$	1.55615	+	1.55615i	0.0563365	+	0.0563365i
$764$	−8.91545	−	7.35139i	−0.322550	−	0.265964i
$765$	−11.6131	+	11.6131i	−0.419874	+	0.419874i
$766$	−44.5018	−	15.9812i	−1.60792	−	0.577426i
$767$	−16.9546			−0.612196
$768$	6.25981	−	14.7246i	0.225881	−	0.531329i
$769$	39.1195			1.41068			0.705342	−	0.708867i	$-0.250793\pi$
$769$	39.1195			1.41068			0.705342	+	0.708867i	$0.250793\pi$
$770$	66.6118	+	23.9212i	2.40052	+	0.862062i
$771$	12.1202	−	12.1202i	0.436500	−	0.436500i
$772$	30.9812	+	25.5461i	1.11504	+	0.919424i
$773$	−1.25779	−	1.25779i	−0.0452397	−	0.0452397i	0.684125	−	0.729365i	$-0.260184\pi$
$773$	−1.25779	−	1.25779i	−0.0452397	−	0.0452397i	−0.729365	+	0.684125i	$0.760184\pi$
$774$	−0.643199	+	0.303298i	−0.0231193	+	0.0109018i
$775$		−	29.7907i		−	1.07011i
$776$	24.0480	+	40.4400i	0.863272	+	1.45171i
$777$		−	12.3525i		−	0.443142i
$778$	−10.0455	−	21.3033i	−0.360149	−	0.763762i
$779$	8.04024	+	8.04024i	0.288072	+	0.288072i
$780$	19.4354	−	1.86872i	0.695900	−	0.0669109i
$781$	20.4651	−	20.4651i	0.732299	−	0.732299i
$782$	−16.7568	+	46.6616i	−0.599223	+	1.66861i
$783$	−5.80777			−0.207553
$784$	−8.61812	−	44.4016i	−0.307790	−	1.58577i
$785$	−21.0450			−0.751128
$786$	3.74368	−	10.4248i	0.133533	−	0.371839i
$787$	−27.7268	+	27.7268i	−0.988355	+	0.988355i	−0.999933	−	0.0115775i	$-0.996315\pi$
$787$	−27.7268	+	27.7268i	−0.988355	+	0.988355i	0.0115775	+	0.999933i	$0.496315\pi$
$788$	−0.0390727	−	0.406372i	−0.00139191	−	0.0144764i
$789$	−14.1642	−	14.1642i	−0.504260	−	0.504260i
$790$	−17.5959	−	37.3153i	−0.626035	−	1.32762i
$791$			45.1385i			1.60494i
$792$	11.0697	+	2.81378i	0.393345	+	0.0999833i
$793$			30.9068i			1.09753i
$794$	0.838914	−	0.395587i	0.0297719	−	0.0140389i
$795$	−3.54830	−	3.54830i	−0.125845	−	0.125845i
$796$	3.41600	−	4.14278i	0.121077	−	0.146837i
$797$	38.4057	−	38.4057i	1.36040	−	1.36040i	0.486998	−	0.873403i	$-0.338092\pi$
$797$	38.4057	−	38.4057i	1.36040	−	1.36040i	0.873403	−	0.486998i	$-0.161908\pi$
$798$	−5.69496	−	2.04514i	−0.201599	−	0.0723972i
$799$	54.8871			1.94177
$800$	18.9510	+	2.92352i	0.670020	+	0.103362i
$801$	2.59060			0.0915343
$802$	−10.1908	−	3.65967i	−0.359851	−	0.129228i
$803$	−6.94833	+	6.94833i	−0.245201	+	0.245201i
$804$	2.75703	−	3.34361i	0.0972330	−	0.117920i
$805$	54.1836	+	54.1836i	1.90972	+	1.90972i
$806$	−37.8896	+	17.8667i	−1.33460	+	0.629327i
$807$			9.66041i			0.340062i
$808$	4.62089	−	18.1791i	0.162562	−	0.639537i
$809$		−	16.0827i		−	0.565439i	−0.959203	−	0.282720i	$-0.908763\pi$
$809$		−	16.0827i		−	0.565439i	0.959203	−	0.282720i	$-0.0912366\pi$
$810$	1.74709	+	3.70502i	0.0613864	+	0.130181i
$811$	−20.7348	−	20.7348i	−0.728096	−	0.728096i	0.242144	−	0.970240i	$-0.422149\pi$
$811$	−20.7348	−	20.7348i	−0.728096	−	0.728096i	−0.970240	+	0.242144i	$0.922149\pi$
$812$	4.75671	+	49.4717i	0.166928	+	1.73612i
$813$	4.32767	−	4.32767i	0.151778	−	0.151778i
$814$	5.57228	−	15.5167i	0.195308	−	0.543861i
$815$	58.5689			2.05158
$816$	18.7994	+	12.6879i	0.658111	+	0.444165i
$817$	0.502840			0.0175921
$818$	18.1666	−	50.5872i	0.635180	−	1.76874i
$819$	10.1974	−	10.1974i	0.356325	−	0.356325i
$820$	−65.5677	+	6.30434i	−2.28972	+	0.220157i
$821$	−9.07532	−	9.07532i	−0.316731	−	0.316731i	0.530779	−	0.847510i	$-0.321899\pi$
$821$	−9.07532	−	9.07532i	−0.316731	−	0.316731i	−0.847510	+	0.530779i	$0.821899\pi$
$822$	−11.1505	−	23.6467i	−0.388919	−	0.824774i
$823$		−	32.4782i		−	1.13212i	−0.824364	−	0.566060i	$-0.808467\pi$
$823$		−	32.4782i		−	1.13212i	0.824364	−	0.566060i	$-0.191533\pi$
$824$	−26.0624	+	15.4982i	−0.907925	+	0.539905i
$825$			13.6884i			0.476568i
$826$	−27.5316	+	12.9824i	−0.957947	+	0.451717i
$827$	5.11117	+	5.11117i	0.177733	+	0.177733i	0.790367	−	0.612634i	$-0.209890\pi$
$827$	5.11117	+	5.11117i	0.177733	+	0.177733i	−0.612634	+	0.790367i	$0.709890\pi$
$828$	9.54071	+	7.86696i	0.331563	+	0.273396i
$829$	−13.5868	+	13.5868i	−0.471888	+	0.471888i	−0.902525	−	0.430637i	$-0.858289\pi$
$829$	−13.5868	+	13.5868i	−0.471888	+	0.471888i	0.430637	+	0.902525i	$0.358289\pi$
$830$	−11.3260	−	4.06733i	−0.393131	−	0.141179i
$831$	−23.5533			−0.817056
$832$	−7.64741	−	25.8564i	−0.265126	−	0.896410i
$833$	64.1150			2.22145
$834$	−12.1039	−	4.34668i	−0.419124	−	0.150513i
$835$	34.7077	−	34.7077i	1.20111	−	1.20111i
$836$	−6.23122	−	5.13806i	−0.215511	−	0.177704i
$837$	−6.21441	−	6.21441i	−0.214802	−	0.214802i
$838$	32.0818	−	15.1281i	1.10825	−	0.522591i
$839$			23.3943i			0.807659i	0.914834	+	0.403830i	$0.132321\pi$
$839$			23.3943i			0.807659i	−0.914834	+	0.403830i	$0.867679\pi$
$840$	30.1291	−	17.9165i	1.03955	−	0.618178i
$841$		−	4.73024i		−	0.163112i
$842$	15.5032	+	32.8774i	0.534277	+	1.13303i
$843$	−0.964328	−	0.964328i	−0.0332132	−	0.0332132i
$844$	−21.7386	+	2.09017i	−0.748275	+	0.0719467i
$845$	−3.35902	+	3.35902i	−0.115554	+	0.115554i
$846$	4.62688	−	12.8841i	0.159075	−	0.442965i
$847$	22.7071			0.780225
$848$	−3.87669	+	5.74401i	−0.133126	+	0.197250i
$849$	19.2899			0.662029
$850$	−9.18678	+	25.5818i	−0.315104	+	0.877447i
$851$	12.6217	−	12.6217i	0.432666	−	0.432666i
$852$	−1.37191	−	14.2684i	−0.0470007	−	0.488826i
$853$	10.4050	+	10.4050i	0.356259	+	0.356259i	0.862432	−	0.506173i	$-0.168940\pi$
$853$	10.4050	+	10.4050i	0.356259	+	0.356259i	−0.506173	+	0.862432i	$0.668940\pi$
$854$	23.6659	+	50.1878i	0.809829	+	1.71739i
$855$		−	2.89650i		−	0.0990583i
$856$	−4.78802	+	18.8366i	−0.163651	+	0.643821i
$857$		−	1.18978i		−	0.0406420i	−0.999794	−	0.0203210i	$-0.993531\pi$
$857$		−	1.18978i		−	0.0406420i	0.999794	−	0.0203210i	$-0.00646882\pi$
$858$	17.4097	−	8.20948i	0.594357	−	0.280267i
$859$	18.2372	+	18.2372i	0.622245	+	0.622245i	0.946105	−	0.323860i	$-0.104981\pi$
$859$	18.2372	+	18.2372i	0.622245	+	0.622245i	−0.323860	+	0.946105i	$0.604981\pi$
$860$	−1.85318	+	2.24745i	−0.0631928	+	0.0766374i
$861$	−34.4021	+	34.4021i	−1.17242	+	1.17242i
$862$	20.6933	+	7.43126i	0.704816	+	0.253110i
$863$	−2.24564			−0.0764423			−0.0382212	−	0.999269i	$-0.512169\pi$
$863$	−2.24564			−0.0764423			−0.0382212	+	0.999269i	$0.512169\pi$
$864$	4.56309	−	3.34338i	0.155239	−	0.113744i
$865$	6.11492			0.207914
$866$	40.4499	+	14.5262i	1.37455	+	0.493619i
$867$	−10.7127	+	10.7127i	−0.363821	+	0.363821i
$868$	−47.8458	+	58.0253i	−1.62399	+	1.96951i
$869$	−28.7587	−	28.7587i	−0.975572	−	0.975572i
$870$	−21.5179	+	10.1467i	−0.729525	+	0.344005i
$871$		−	7.30327i		−	0.247462i
$872$	1.40994	+	0.358390i	0.0477467	+	0.0121366i
$873$			16.6347i			0.562998i
$874$	−3.72936	−	7.90879i	−0.126148	−	0.267519i
$875$	−14.1115	−	14.1115i	−0.477056	−	0.477056i
$876$	0.465790	+	4.84441i	0.0157376	+	0.163677i
$877$	−6.61162	+	6.61162i	−0.223258	+	0.223258i	−0.809869	−	0.586611i	$-0.800462\pi$
$877$	−6.61162	+	6.61162i	−0.223258	+	0.223258i	0.586611	+	0.809869i	$0.300462\pi$
$878$	10.0937	−	28.1071i	0.340645	−	0.948570i
$879$	−6.47704			−0.218465
$880$	45.9294	−	8.91464i	1.54828	−	0.300513i
$881$	20.7368			0.698641			0.349320	−	0.937003i	$-0.386413\pi$
$881$	20.7368			0.698641			0.349320	+	0.937003i	$0.386413\pi$
$882$	5.40477	−	15.0503i	0.181988	−	0.506769i
$883$	−16.5010	+	16.5010i	−0.555303	+	0.555303i	−0.927966	−	0.372664i	$-0.878445\pi$
$883$	−16.5010	+	16.5010i	−0.555303	+	0.555303i	0.372664	+	0.927966i	$0.378445\pi$
$884$	38.0461	−	3.65814i	1.27963	−	0.123037i
$885$	−10.3029	−	10.3029i	−0.346328	−	0.346328i
$886$	−5.72771	−	12.1467i	−0.192426	−	0.408075i
$887$		−	42.7798i		−	1.43641i	−0.695833	−	0.718203i	$-0.744965\pi$
$887$		−	42.7798i		−	1.43641i	0.695833	−	0.718203i	$-0.255035\pi$
$888$	−4.17352	−	7.01835i	−0.140054	−	0.235521i
$889$			15.0500i			0.504759i
$890$	9.59821	−	4.52600i	0.321733	−	0.151712i
$891$	2.85543	+	2.85543i	0.0956605	+	0.0956605i
$892$	−9.61068	−	7.92465i	−0.321789	−	0.265337i
$893$	−6.84487	+	6.84487i	−0.229055	+	0.229055i
$894$	−27.2571	−	9.78840i	−0.911612	−	0.327373i
$895$	−14.2497			−0.476313
$896$	−32.2168	−	36.1309i	−1.07629	−	1.20705i
$897$	20.8393			0.695803
$898$	33.0067	+	11.8532i	1.10145	+	0.395546i
$899$	36.0919	−	36.0919i	1.20373	−	1.20373i
$900$	5.23060	+	4.31298i	0.174353	+	0.143766i
$901$	−6.94604	−	6.94604i	−0.231406	−	0.231406i
$902$	−58.7336	+	27.6956i	−1.95562	+	0.922164i
$903$			2.15152i			0.0715980i
$904$	15.2509	+	25.6465i	0.507238	+	0.852991i
$905$			55.1320i			1.83265i
$906$	−0.581866	−	1.23395i	−0.0193312	−	0.0409953i
$907$	−31.0395	−	31.0395i	−1.03065	−	1.03065i	−0.999515	−	0.0311351i	$-0.990088\pi$
$907$	−31.0395	−	31.0395i	−1.03065	−	1.03065i	−0.0311351	−	0.999515i	$-0.509912\pi$
$908$	−13.2579	+	1.27475i	−0.439978	+	0.0423039i
$909$	4.68929	−	4.68929i	0.155534	−	0.155534i
$910$	19.9658	−	55.5972i	0.661858	−	1.84303i
$911$	−13.5819			−0.449988			−0.224994	−	0.974360i	$-0.572236\pi$
$911$	−13.5819			−0.449988			−0.224994	+	0.974360i	$0.572236\pi$
$912$	−3.92672	+	0.762155i	−0.130027	+	0.0252375i
$913$	−11.8635			−0.392625
$914$	1.46747	−	4.08637i	0.0485397	−	0.135165i
$915$	−18.7813	+	18.7813i	−0.620890	+	0.620890i
$916$	3.86445	+	40.1918i	0.127685	+	1.32797i
$917$	−23.6969	−	23.6969i	−0.782541	−	0.782541i
$918$	3.42004	+	7.25281i	0.112878	+	0.239379i
$919$		−	42.5647i		−	1.40408i	−0.712138	−	0.702040i	$-0.752273\pi$
$919$		−	42.5647i		−	1.40408i	0.712138	−	0.702040i	$-0.247727\pi$
$920$	49.0927	+	12.4788i	1.61854	+	0.411412i
$921$		−	12.5726i		−	0.414283i
$922$	19.0681	−	8.99149i	0.627974	−	0.296119i
$923$	−17.0811	−	17.0811i	−0.562232	−	0.562232i
$924$	21.9844	−	26.6618i	0.723234	−	0.877107i
$925$	6.91972	−	6.91972i	0.227519	−	0.227519i
$926$	30.7273	+	11.0346i	1.00976	+	0.362619i
$927$	−10.7205			−0.352109
$928$	19.4176	+	26.5014i	0.637414	+	0.869951i
$929$	26.6404			0.874044			0.437022	−	0.899451i	$-0.356033\pi$
$929$	26.6404			0.874044			0.437022	+	0.899451i	$0.356033\pi$
$930$	−33.8816	−	12.1674i	−1.11102	−	0.398984i
$931$	−7.99566	+	7.99566i	−0.262047	+	0.262047i
$932$	9.64932	−	11.7023i	0.316074	−	0.383321i
$933$	−22.4798	−	22.4798i	−0.735954	−	0.735954i
$934$	50.0183	−	23.5859i	1.63665	−	0.771756i
$935$			66.3210i			2.16893i
$936$	2.34851	−	9.23927i	0.0767634	−	0.301995i
$937$			21.4842i			0.701857i	0.936402	+	0.350928i	$0.114134\pi$
$937$			21.4842i			0.701857i	−0.936402	+	0.350928i	$0.885866\pi$
$938$	−5.59223	−	11.8593i	−0.182593	−	0.387221i
$939$	−17.1019	−	17.1019i	−0.558098	−	0.558098i
$940$	−5.36705	−	55.8195i	−0.175054	−	1.82063i
$941$	31.2741	−	31.2741i	1.01951	−	1.01951i	0.0196997	−	0.999806i	$-0.493729\pi$
$941$	31.2741	−	31.2741i	1.01951	−	1.01951i	0.999806	−	0.0196997i	$-0.00627102\pi$
$942$	−3.47282	+	9.67052i	−0.113151	+	0.315083i
$943$	−70.3037			−2.28940
$944$	−11.2564	+	16.6784i	−0.366364	+	0.542835i
$945$	12.3934			0.403156
$946$	−0.970564	+	2.70266i	−0.0315557	+	0.0878710i
$947$	−8.03326	+	8.03326i	−0.261046	+	0.261046i	−0.825479	−	0.564433i	$-0.809095\pi$
$947$	−8.03326	+	8.03326i	−0.261046	+	0.261046i	0.564433	+	0.825479i	$0.309095\pi$
$948$	−20.0507	+	1.92788i	−0.651216	+	0.0626145i
$949$	5.79939	+	5.79939i	0.188256	+	0.188256i
$950$	−2.04459	−	4.33592i	−0.0663352	−	0.140676i
$951$			29.2601i			0.948824i
$952$	58.9797	−	35.0728i	1.91154	−	1.13671i
$953$		−	9.19660i		−	0.297907i	−0.988844	−	0.148954i	$-0.952409\pi$
$953$		−	9.19660i		−	0.297907i	0.988844	−	0.148954i	$-0.0475905\pi$
$954$	−2.21604	+	1.04497i	−0.0717470	+	0.0338320i
$955$	−11.8336	−	11.8336i	−0.382925	−	0.382925i
$956$	27.3935	+	22.5878i	0.885968	+	0.730540i
$957$	−16.5837	+	16.5837i	−0.536075	+	0.536075i
$958$	16.2575	+	5.83829i	0.525255	+	0.188627i
$959$	−79.0989			−2.55424
$960$	11.0651	−	20.3594i	0.357126	−	0.657097i
$961$	46.2379			1.49154
$962$	−12.9510	−	4.65087i	−0.417556	−	0.149950i
$963$	−4.85890	+	4.85890i	−0.156576	+	0.156576i
$964$	28.7166	+	23.6788i	0.924899	+	0.762642i
$965$	41.1216	+	41.1216i	1.32375	+	1.32375i
$966$	33.8396	−	15.9569i	1.08877	−	0.513406i
$967$			34.2837i			1.10249i	0.834344	+	0.551244i	$0.185847\pi$
$967$			34.2837i			1.10249i	−0.834344	+	0.551244i	$0.814153\pi$
$968$	12.9016	−	7.67203i	0.414673	−	0.246588i
$969$		−	5.67010i		−	0.182150i
$970$	29.0622	+	61.6317i	0.933132	+	1.97888i
$971$	2.29237	+	2.29237i	0.0735655	+	0.0735655i	0.742932	−	0.669367i	$-0.233434\pi$
$971$	2.29237	+	2.29237i	0.0735655	+	0.0735655i	−0.669367	+	0.742932i	$0.733434\pi$
$972$	1.99082	−	0.191418i	0.0638555	−	0.00613972i
$973$	−27.5138	+	27.5138i	−0.882051	+	0.882051i
$974$	−17.3366	+	48.2760i	−0.555501	+	1.54686i
$975$	11.4249			0.365890
$976$	30.4032	+	20.5194i	0.973184	+	0.656811i
$977$	−12.8563			−0.411310			−0.205655	−	0.978625i	$-0.565933\pi$
$977$	−12.8563			−0.411310			−0.205655	+	0.978625i	$0.565933\pi$
$978$	9.66499	−	26.9134i	0.309052	−	0.860596i
$979$	7.39728	−	7.39728i	0.236418	−	0.236418i
$980$	−6.26938	−	65.2041i	−0.200268	−	2.08287i
$981$	0.363695	+	0.363695i	0.0116119	+	0.0116119i
$982$	13.7301	+	29.1171i	0.438144	+	0.929165i
$983$			53.4367i			1.70437i	0.523244	+	0.852183i	$0.324722\pi$
$983$			53.4367i			1.70437i	−0.523244	+	0.852183i	$0.675278\pi$
$984$	−7.92296	+	31.1698i	−0.252575	+	0.993656i
$985$		−	0.591242i		−	0.0188385i
$986$	−42.1227	+	19.8628i	−1.34146	+	0.632561i
$987$	−29.2874	−	29.2874i	−0.932227	−	0.932227i
$988$	−4.28846	+	5.20086i	−0.136434	+	0.165461i
$989$	−2.19841	+	2.19841i	−0.0699053	+	0.0699053i
$990$	15.5681	+	5.59073i	0.494787	+	0.177685i
$991$	36.3748			1.15549			0.577743	−	0.816219i	$-0.303934\pi$
$991$	36.3748			1.15549			0.577743	+	0.816219i	$0.303934\pi$
$992$	−7.57977	+	49.1341i	−0.240658	+	1.56001i
$993$	−7.53995			−0.239273
$994$	−40.8163	−	14.6577i	−1.29461	−	0.464914i
$995$	5.49875	−	5.49875i	0.174322	−	0.174322i
$996$	−3.73801	+	4.53329i	−0.118443	+	0.143643i
$997$	−1.66497	−	1.66497i	−0.0527302	−	0.0527302i	0.680250	−	0.732980i	$-0.261871\pi$
$997$	−1.66497	−	1.66497i	−0.0527302	−	0.0527302i	−0.732980	+	0.680250i	$0.761871\pi$
$998$	24.4578	−	11.5330i	0.774197	−	0.365070i
$999$		−	2.88694i		−	0.0913389i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.u.a.229.4	✓	72
16.13	even	4	inner	912.2.u.a.685.4	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.u.a.229.4	✓	72	1.1	even	1	trivial
912.2.u.a.685.4	yes	72	16.13	even	4	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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33099 - 0.477978i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.54307 + 1.27237i) q^{4} +(2.04814 + 2.04814i) q^{5} +(1.27913 - 0.603171i) q^{6} -4.27873i q^{7} +(-1.44565 - 2.43107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.33099 - 0.477978i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.54307 + 1.27237i) q^{4} +(2.04814 + 2.04814i) q^{5} +(1.27913 - 0.603171i) q^{6} -4.27873i q^{7} +(-1.44565 - 2.43107i) q^{8} -1.00000i q^{9} +(-1.74709 - 3.70502i) q^{10} +(-2.85543 - 2.85543i) q^{11} +(-1.99082 + 0.191418i) q^{12} +(-2.38327 + 2.38327i) q^{13} +(-2.04514 + 5.69496i) q^{14} -2.89650 q^{15} +(0.762155 + 3.92672i) q^{16} -5.67010 q^{17} +(-0.477978 + 1.33099i) q^{18} +(0.707107 - 0.707107i) q^{19} +(0.554441 + 5.76641i) q^{20} +(3.02552 + 3.02552i) q^{21} +(2.43572 + 5.16538i) q^{22} +6.18292i q^{23} +(2.74126 + 0.696793i) q^{24} +3.38973i q^{25} +(4.31126 - 2.03296i) q^{26} +(0.707107 + 0.707107i) q^{27} +(5.44413 - 6.60240i) q^{28} +(-4.10672 + 4.10672i) q^{29} +(3.85522 + 1.38446i) q^{30} -8.78851 q^{31} +(0.862463 - 5.59072i) q^{32} +4.03819 q^{33} +(7.54685 + 2.71018i) q^{34} +(8.76343 - 8.76343i) q^{35} +(1.27237 - 1.54307i) q^{36} +(-2.04138 - 2.04138i) q^{37} +(-1.27913 + 0.603171i) q^{38} -3.37045i q^{39} +(2.01826 - 7.94005i) q^{40} +11.3706i q^{41} +(-2.58081 - 5.47308i) q^{42} +(0.355561 + 0.355561i) q^{43} +(-0.772980 - 8.03930i) q^{44} +(2.04814 - 2.04814i) q^{45} +(2.95530 - 8.22942i) q^{46} -9.68010 q^{47} +(-3.31553 - 2.23768i) q^{48} -11.3076 q^{49} +(1.62022 - 4.51170i) q^{50} +(4.00936 - 4.00936i) q^{51} +(-6.70996 + 0.645164i) q^{52} +(1.22503 + 1.22503i) q^{53} +(-0.603171 - 1.27913i) q^{54} -11.6966i q^{55} +(-10.4019 + 6.18557i) q^{56} +1.00000i q^{57} +(7.42892 - 3.50308i) q^{58} +(3.55701 + 3.55701i) q^{59} +(-4.46952 - 3.68542i) q^{60} +(6.48412 - 6.48412i) q^{61} +(11.6974 + 4.20071i) q^{62} -4.27873 q^{63} +(-3.82017 + 7.02896i) q^{64} -9.76253 q^{65} +(-5.37479 - 1.93017i) q^{66} +(-1.53219 + 1.53219i) q^{67} +(-8.74938 - 7.21445i) q^{68} +(-4.37199 - 4.37199i) q^{69} +(-15.8528 + 7.47532i) q^{70} +7.16709i q^{71} +(-2.43107 + 1.44565i) q^{72} -2.43337i q^{73} +(1.74132 + 3.69279i) q^{74} +(-2.39690 - 2.39690i) q^{75} +(1.99082 - 0.191418i) q^{76} +(-12.2176 + 12.2176i) q^{77} +(-1.61100 + 4.48604i) q^{78} +10.0716 q^{79} +(-6.48146 + 9.60345i) q^{80} -1.00000 q^{81} +(5.43491 - 15.1342i) q^{82} +(2.07736 - 2.07736i) q^{83} +(0.819025 + 8.51819i) q^{84} +(-11.6131 - 11.6131i) q^{85} +(-0.303298 - 0.643199i) q^{86} -5.80777i q^{87} +(-2.81378 + 11.0697i) q^{88} +2.59060i q^{89} +(-3.70502 + 1.74709i) q^{90} +(10.1974 + 10.1974i) q^{91} +(-7.86696 + 9.54071i) q^{92} +(6.21441 - 6.21441i) q^{93} +(12.8841 + 4.62688i) q^{94} +2.89650 q^{95} +(3.34338 + 4.56309i) q^{96} -16.6347 q^{97} +(15.0503 + 5.40477i) q^{98} +(-2.85543 + 2.85543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 4 q^{4}+O(q^{10}) \) 72 * q + 4 * q^4	\( 72 q + 4 q^{4} + 8 q^{11} - 8 q^{12} - 12 q^{14} - 4 q^{16} - 4 q^{18} - 44 q^{20} - 52 q^{26} + 52 q^{28} + 16 q^{29} + 8 q^{30} - 64 q^{31} + 40 q^{34} + 16 q^{37} + 4 q^{40} - 8 q^{42} + 8 q^{43} + 68 q^{44} + 104 q^{47} + 16 q^{48} - 72 q^{49} + 116 q^{50} - 8 q^{52} - 16 q^{53} - 28 q^{56} - 92 q^{58} - 32 q^{59} + 32 q^{60} + 24 q^{62} - 40 q^{63} + 28 q^{64} + 16 q^{65} + 28 q^{66} - 8 q^{67} - 100 q^{68} - 20 q^{70} + 4 q^{72} - 124 q^{74} - 16 q^{75} + 8 q^{76} - 16 q^{77} - 12 q^{78} + 48 q^{79} + 44 q^{80} - 72 q^{81} + 52 q^{82} - 8 q^{84} - 64 q^{85} + 48 q^{86} - 32 q^{88} + 8 q^{90} + 8 q^{91} + 96 q^{92} + 12 q^{94} - 20 q^{96} + 208 q^{98} + 8 q^{99}+O(q^{100}) \) 72 * q + 4 * q^4 + 8 * q^11 - 8 * q^12 - 12 * q^14 - 4 * q^16 - 4 * q^18 - 44 * q^20 - 52 * q^26 + 52 * q^28 + 16 * q^29 + 8 * q^30 - 64 * q^31 + 40 * q^34 + 16 * q^37 + 4 * q^40 - 8 * q^42 + 8 * q^43 + 68 * q^44 + 104 * q^47 + 16 * q^48 - 72 * q^49 + 116 * q^50 - 8 * q^52 - 16 * q^53 - 28 * q^56 - 92 * q^58 - 32 * q^59 + 32 * q^60 + 24 * q^62 - 40 * q^63 + 28 * q^64 + 16 * q^65 + 28 * q^66 - 8 * q^67 - 100 * q^68 - 20 * q^70 + 4 * q^72 - 124 * q^74 - 16 * q^75 + 8 * q^76 - 16 * q^77 - 12 * q^78 + 48 * q^79 + 44 * q^80 - 72 * q^81 + 52 * q^82 - 8 * q^84 - 64 * q^85 + 48 * q^86 - 32 * q^88 + 8 * q^90 + 8 * q^91 + 96 * q^92 + 12 * q^94 - 20 * q^96 + 208 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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