LMFDB - Embedded newform 418.2.h.b.373.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(65,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("418.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.h (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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 41 x^{18} + 707 x^{16} + 6667 x^{14} + 37400 x^{12} + 126976 x^{10} + 253280 x^{8} + \cdots + 2304 $ x^20 + 41x^18 + 707x^16 + 6667x^14 + 37400x^12 + 126976x^10 + 253280x^8 + 273276x^6 + 137476x^4 + 30336*x^2 + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			373.10
Root			$2.97905i$ of defining polynomial
Character	$\chi$	$=$	418.373
Dual form			418.2.h.b.65.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(2.57993 - 1.48952i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.71710 + 2.97410i) q^{5} +(2.57993 + 1.48952i) q^{6} -4.12917i q^{7} -1.00000 q^{8} +(2.93737 - 5.08767i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(2.57993 - 1.48952i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.71710 + 2.97410i) q^{5} +(2.57993 + 1.48952i) q^{6} -4.12917i q^{7} -1.00000 q^{8} +(2.93737 - 5.08767i) q^{9} +(-1.71710 + 2.97410i) q^{10} +(-3.12139 + 1.12112i) q^{11} +2.97905i q^{12} +(0.367756 - 0.636973i) q^{13} +(3.57597 - 2.06459i) q^{14} +(8.86000 + 5.11532i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.549314 - 0.317147i) q^{17} +5.87473 q^{18} +(-3.57734 + 2.49051i) q^{19} -3.43420 q^{20} +(-6.15050 - 10.6530i) q^{21} +(-2.53161 - 2.14265i) q^{22} +(-2.44271 + 4.23090i) q^{23} +(-2.57993 + 1.48952i) q^{24} +(-3.39686 + 5.88354i) q^{25} +0.735513 q^{26} -8.56397i q^{27} +(3.57597 + 2.06459i) q^{28} +(-5.19100 + 8.99108i) q^{29} +10.2306i q^{30} -7.65537i q^{31} +(0.500000 - 0.866025i) q^{32} +(-6.38305 + 7.54180i) q^{33} +(0.549314 + 0.317147i) q^{34} +(12.2806 - 7.09020i) q^{35} +(2.93737 + 5.08767i) q^{36} -5.00167i q^{37} +(-3.94552 - 1.85281i) q^{38} -2.19113i q^{39} +(-1.71710 - 2.97410i) q^{40} +(4.69970 + 8.14011i) q^{41} +(6.15050 - 10.6530i) q^{42} +(6.93593 - 4.00446i) q^{43} +(0.589780 - 3.26376i) q^{44} +20.1750 q^{45} -4.88543 q^{46} +(0.102063 - 0.176779i) q^{47} +(-2.57993 - 1.48952i) q^{48} -10.0501 q^{49} -6.79373 q^{50} +(0.944795 - 1.63643i) q^{51} +(0.367756 + 0.636973i) q^{52} +(-5.92214 - 3.41915i) q^{53} +(7.41662 - 4.28199i) q^{54} +(-8.69406 - 7.35828i) q^{55} +4.12917i q^{56} +(-5.51961 + 11.7539i) q^{57} -10.3820 q^{58} +(1.83644 - 1.06027i) q^{59} +(-8.86000 + 5.11532i) q^{60} +(0.547594 + 0.316154i) q^{61} +(6.62974 - 3.82768i) q^{62} +(-21.0079 - 12.1289i) q^{63} +1.00000 q^{64} +2.52590 q^{65} +(-9.72291 - 1.75698i) q^{66} +(9.31419 + 5.37755i) q^{67} +0.634293i q^{68} +14.5539i q^{69} +(12.2806 + 7.09020i) q^{70} +(1.78588 - 1.03108i) q^{71} +(-2.93737 + 5.08767i) q^{72} +(-1.12051 + 0.646925i) q^{73} +(4.33157 - 2.50083i) q^{74} +20.2389i q^{75} +(-0.368179 - 4.34332i) q^{76} +(4.62929 + 12.8888i) q^{77} +(1.89757 - 1.09556i) q^{78} +(-8.45613 - 14.6465i) q^{79} +(1.71710 - 2.97410i) q^{80} +(-3.94415 - 6.83146i) q^{81} +(-4.69970 + 8.14011i) q^{82} -3.25643i q^{83} +12.3010 q^{84} +(1.88645 + 1.08915i) q^{85} +(6.93593 + 4.00446i) q^{86} +30.9285i q^{87} +(3.12139 - 1.12112i) q^{88} +(-9.59246 - 5.53821i) q^{89} +(10.0875 + 17.4721i) q^{90} +(-2.63017 - 1.51853i) q^{91} +(-2.44271 - 4.23090i) q^{92} +(-11.4029 - 19.7503i) q^{93} +0.204127 q^{94} +(-13.5497 - 6.36291i) q^{95} -2.97905i q^{96} +(0.135282 - 0.0781049i) q^{97} +(-5.02503 - 8.70360i) q^{98} +(-3.46480 + 19.1737i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9}+O(q^{10}) $ 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9	$ 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9} - 2 q^{10} + q^{11} + 5 q^{13} - 6 q^{14} + 12 q^{15} - 10 q^{16} + 6 q^{17} + 22 q^{18} - 18 q^{19} - 4 q^{20} - 14 q^{21} + 2 q^{22} - 4 q^{23} - 3 q^{24} - 20 q^{25} + 10 q^{26} - 6 q^{28} + 5 q^{29} + 10 q^{32} - 13 q^{33} + 6 q^{34} - 12 q^{35} + 11 q^{36} - 12 q^{38} - 2 q^{40} - q^{41} + 14 q^{42} + 3 q^{43} + q^{44} + 12 q^{45} - 8 q^{46} + q^{47} - 3 q^{48} + 8 q^{49} - 40 q^{50} - 12 q^{51} + 5 q^{52} - 24 q^{53} + 27 q^{54} - 2 q^{55} + 32 q^{57} + 10 q^{58} - 51 q^{59} - 12 q^{60} + 27 q^{61} + 12 q^{63} + 20 q^{64} - 8 q^{65} - 8 q^{66} + 27 q^{67} - 12 q^{70} + 33 q^{71} - 11 q^{72} - 9 q^{73} - 12 q^{74} + 6 q^{76} - 22 q^{77} - 24 q^{79} + 2 q^{80} + 12 q^{81} + q^{82} + 28 q^{84} - 12 q^{85} + 3 q^{86} - q^{88} + 21 q^{89} + 6 q^{90} + 12 q^{91} - 4 q^{92} - 10 q^{93} + 2 q^{94} - 24 q^{95} + 24 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) $ 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9 - 2 * q^10 + q^11 + 5 * q^13 - 6 * q^14 + 12 * q^15 - 10 * q^16 + 6 * q^17 + 22 * q^18 - 18 * q^19 - 4 * q^20 - 14 * q^21 + 2 * q^22 - 4 * q^23 - 3 * q^24 - 20 * q^25 + 10 * q^26 - 6 * q^28 + 5 * q^29 + 10 * q^32 - 13 * q^33 + 6 * q^34 - 12 * q^35 + 11 * q^36 - 12 * q^38 - 2 * q^40 - q^41 + 14 * q^42 + 3 * q^43 + q^44 + 12 * q^45 - 8 * q^46 + q^47 - 3 * q^48 + 8 * q^49 - 40 * q^50 - 12 * q^51 + 5 * q^52 - 24 * q^53 + 27 * q^54 - 2 * q^55 + 32 * q^57 + 10 * q^58 - 51 * q^59 - 12 * q^60 + 27 * q^61 + 12 * q^63 + 20 * q^64 - 8 * q^65 - 8 * q^66 + 27 * q^67 - 12 * q^70 + 33 * q^71 - 11 * q^72 - 9 * q^73 - 12 * q^74 + 6 * q^76 - 22 * q^77 - 24 * q^79 + 2 * q^80 + 12 * q^81 + q^82 + 28 * q^84 - 12 * q^85 + 3 * q^86 - q^88 + 21 * q^89 + 6 * q^90 + 12 * q^91 - 4 * q^92 - 10 * q^93 + 2 * q^94 - 24 * q^95 + 24 * q^97 + 4 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	2.57993	−	1.48952i	1.48952	−	0.859977i	0.489596	−	0.871949i	$-0.337144\pi$
$3$	2.57993	−	1.48952i	1.48952	−	0.859977i	0.999928	+	0.0119719i	$0.00381086\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.71710	+	2.97410i	0.767910	+	1.33006i	0.938694	+	0.344751i	$0.112037\pi$
$5$	1.71710	+	2.97410i	0.767910	+	1.33006i	−0.170784	+	0.985309i	$0.554630\pi$
$6$	2.57993	+	1.48952i	1.05325	+	0.608096i
$7$		−	4.12917i		−	1.56068i	−0.625356	−	0.780340i	$-0.715046\pi$
$7$		−	4.12917i		−	1.56068i	0.625356	−	0.780340i	$-0.284954\pi$
$8$	−1.00000			−0.353553
$9$	2.93737	−	5.08767i	0.979122	−	1.69589i
$10$	−1.71710	+	2.97410i	−0.542995	+	0.940494i
$11$	−3.12139	+	1.12112i	−0.941135	+	0.338030i
$11$	−3.12139	+	1.12112i	−0.941135	+	0.338030i
$12$			2.97905i			0.859977i
$13$	0.367756	−	0.636973i	0.101997	−	0.176664i	−0.810510	−	0.585725i	$-0.800810\pi$
$13$	0.367756	−	0.636973i	0.101997	−	0.176664i	0.912507	+	0.409060i	$0.134143\pi$
$14$	3.57597	−	2.06459i	0.955717	−	0.551784i
$15$	8.86000	+	5.11532i	2.28764	+	1.32077i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.549314	−	0.317147i	0.133228	−	0.0769194i	−0.431905	−	0.901919i	$-0.642158\pi$
$17$	0.549314	−	0.317147i	0.133228	−	0.0769194i	0.565133	+	0.825000i	$0.308825\pi$
$18$	5.87473			1.38469
$19$	−3.57734	+	2.49051i	−0.820698	+	0.571363i
$19$	−3.57734	+	2.49051i	−0.820698	+	0.571363i
$20$	−3.43420			−0.767910
$21$	−6.15050	−	10.6530i	−1.34215	−	2.32467i
$22$	−2.53161	−	2.14265i	−0.539742	−	0.456814i
$23$	−2.44271	+	4.23090i	−0.509341	+	0.882204i	0.490601	+	0.871385i	$0.336777\pi$
$23$	−2.44271	+	4.23090i	−0.509341	+	0.882204i	−0.999941	+	0.0108198i	$0.996556\pi$
$24$	−2.57993	+	1.48952i	−0.526626	+	0.304048i
$25$	−3.39686	+	5.88354i	−0.679373	+	1.17671i
$26$	0.735513			0.144246
$27$		−	8.56397i		−	1.64814i
$28$	3.57597	+	2.06459i	0.675794	+	0.390170i
$29$	−5.19100	+	8.99108i	−0.963945	+	1.66960i	−0.251522	+	0.967851i	$0.580931\pi$
$29$	−5.19100	+	8.99108i	−0.963945	+	1.66960i	−0.712423	+	0.701750i	$0.752402\pi$
$30$			10.2306i			1.86785i
$31$		−	7.65537i		−	1.37494i	−0.726211	−	0.687472i	$-0.758720\pi$
$31$		−	7.65537i		−	1.37494i	0.726211	−	0.687472i	$-0.241280\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−6.38305	+	7.54180i	−1.11115	+	1.31286i
$34$	0.549314	+	0.317147i	0.0942066	+	0.0543902i
$35$	12.2806	−	7.09020i	2.07580	−	1.19846i
$36$	2.93737	+	5.08767i	0.489561	+	0.847945i
$37$		−	5.00167i		−	0.822269i	−0.911575	−	0.411135i	$-0.865133\pi$
$37$		−	5.00167i		−	0.822269i	0.911575	−	0.411135i	$-0.134867\pi$
$38$	−3.94552	−	1.85281i	−0.640047	−	0.300565i
$39$		−	2.19113i		−	0.350861i
$40$	−1.71710	−	2.97410i	−0.271497	−	0.470247i
$41$	4.69970	+	8.14011i	0.733969	+	1.27127i	0.955174	+	0.296045i	$0.0956678\pi$
$41$	4.69970	+	8.14011i	0.733969	+	1.27127i	−0.221205	+	0.975227i	$0.570999\pi$
$42$	6.15050	−	10.6530i	0.949043	−	1.64379i
$43$	6.93593	−	4.00446i	1.05772	−	0.610675i	0.132919	−	0.991127i	$-0.457565\pi$
$43$	6.93593	−	4.00446i	1.05772	−	0.610675i	0.924801	+	0.380452i	$0.124232\pi$
$44$	0.589780	−	3.26376i	0.0889127	−	0.492031i
$45$	20.1750			3.00751
$46$	−4.88543			−0.720317
$47$	0.102063	−	0.176779i	0.0148875	−	0.0257858i	−0.858486	−	0.512838i	$-0.828594\pi$
$47$	0.102063	−	0.176779i	0.0148875	−	0.0257858i	0.873373	+	0.487052i	$0.161928\pi$
$48$	−2.57993	−	1.48952i	−0.372381	−	0.214994i
$49$	−10.0501			−1.43572
$50$	−6.79373			−0.960778
$51$	0.944795	−	1.63643i	0.132298	−	0.229147i
$52$	0.367756	+	0.636973i	0.0509986	+	0.0883322i
$53$	−5.92214	−	3.41915i	−0.813468	−	0.469656i	0.0346908	−	0.999398i	$-0.488955\pi$
$53$	−5.92214	−	3.41915i	−0.813468	−	0.469656i	−0.848159	+	0.529742i	$0.822289\pi$
$54$	7.41662	−	4.28199i	1.00927	−	0.582704i
$55$	−8.69406	−	7.35828i	−1.17231	−	0.992190i
$56$			4.12917i			0.551784i
$57$	−5.51961	+	11.7539i	−0.731090	+	1.55684i
$58$	−10.3820			−1.36322
$59$	1.83644	−	1.06027i	0.239084	−	0.138035i	−0.375672	−	0.926753i	$-0.622588\pi$
$59$	1.83644	−	1.06027i	0.239084	−	0.138035i	0.614756	+	0.788718i	$0.289255\pi$
$60$	−8.86000	+	5.11532i	−1.14382	+	0.660386i
$61$	0.547594	+	0.316154i	0.0701122	+	0.0404793i	0.534646	−	0.845076i	$-0.320445\pi$
$61$	0.547594	+	0.316154i	0.0701122	+	0.0404793i	−0.464534	+	0.885555i	$0.653778\pi$
$62$	6.62974	−	3.82768i	0.841978	−	0.486116i
$63$	−21.0079	−	12.1289i	−2.64674	−	1.52810i
$64$	1.00000			0.125000
$65$	2.52590			0.313299
$66$	−9.72291	−	1.75698i	−1.19681	−	0.216270i
$67$	9.31419	+	5.37755i	1.13791	+	0.656972i	0.945912	−	0.324423i	$-0.105170\pi$
$67$	9.31419	+	5.37755i	1.13791	+	0.656972i	0.191997	+	0.981395i	$0.438503\pi$
$68$			0.634293i			0.0769194i
$69$			14.5539i			1.75209i
$70$	12.2806	+	7.09020i	1.46781	+	0.847441i
$71$	1.78588	−	1.03108i	0.211944	−	0.122366i	−0.390270	−	0.920700i	$-0.627618\pi$
$71$	1.78588	−	1.03108i	0.211944	−	0.122366i	0.602215	+	0.798334i	$0.294285\pi$
$72$	−2.93737	+	5.08767i	−0.346172	+	0.599587i
$73$	−1.12051	+	0.646925i	−0.131145	+	0.0757168i	−0.564137	−	0.825681i	$-0.690791\pi$
$73$	−1.12051	+	0.646925i	−0.131145	+	0.0757168i	0.432992	+	0.901398i	$0.357458\pi$
$74$	4.33157	−	2.50083i	0.503535	−	0.290716i
$75$			20.2389i			2.33698i
$76$	−0.368179	−	4.34332i	−0.0422330	−	0.498213i
$77$	4.62929	+	12.8888i	0.527556	+	1.46881i
$78$	1.89757	−	1.09556i	0.214858	−	0.124048i
$79$	−8.45613	−	14.6465i	−0.951389	−	1.64785i	−0.742423	−	0.669932i	$-0.766323\pi$
$79$	−8.45613	−	14.6465i	−0.951389	−	1.64785i	−0.208966	−	0.977923i	$-0.567010\pi$
$80$	1.71710	−	2.97410i	0.191978	−	0.332515i
$81$	−3.94415	−	6.83146i	−0.438238	−	0.759051i
$82$	−4.69970	+	8.14011i	−0.518995	+	0.898925i
$83$		−	3.25643i		−	0.357439i	−0.983900	−	0.178720i	$-0.942804\pi$
$83$		−	3.25643i		−	0.357439i	0.983900	−	0.178720i	$-0.0571955\pi$
$84$	12.3010			1.34215
$85$	1.88645	+	1.08915i	0.204615	+	0.118134i
$86$	6.93593	+	4.00446i	0.747921	+	0.431812i
$87$			30.9285i			3.31588i
$88$	3.12139	−	1.12112i	0.332742	−	0.119512i
$89$	−9.59246	−	5.53821i	−1.01680	−	0.587049i	−0.103624	−	0.994617i	$-0.533044\pi$
$89$	−9.59246	−	5.53821i	−1.01680	−	0.587049i	−0.913175	+	0.407568i	$0.866377\pi$
$90$	10.0875	+	17.4721i	1.06332	+	1.84172i
$91$	−2.63017	−	1.51853i	−0.275717	−	0.159185i
$92$	−2.44271	−	4.23090i	−0.254670	−	0.441102i
$93$	−11.4029	−	19.7503i	−1.18242	−	2.04801i
$94$	0.204127			0.0210541
$95$	−13.5497	−	6.36291i	−1.39017	−	0.652821i
$96$		−	2.97905i		−	0.304048i
$97$	0.135282	−	0.0781049i	0.0137358	−	0.00793035i	−0.493116	−	0.869963i	$-0.664142\pi$
$97$	0.135282	−	0.0781049i	0.0137358	−	0.00793035i	0.506852	+	0.862033i	$0.330809\pi$
$98$	−5.02503	−	8.70360i	−0.507604	−	0.879196i
$99$	−3.46480	+	19.1737i	−0.348226	+	1.92703i
$100$	−3.39686	−	5.88354i	−0.339686	−	0.588354i
$101$	−6.12946	−	3.53884i	−0.609904	−	0.352128i	0.163024	−	0.986622i	$-0.447875\pi$
$101$	−6.12946	−	3.53884i	−0.609904	−	0.352128i	−0.772928	+	0.634494i	$0.781209\pi$
$102$	1.88959			0.187097
$103$			11.9269i			1.17520i	0.809153	+	0.587598i	$0.199926\pi$
$103$			11.9269i			1.17520i	−0.809153	+	0.587598i	$0.800074\pi$
$104$	−0.367756	+	0.636973i	−0.0360615	+	0.0624603i
$105$	21.1221	−	36.5845i	2.06130	−	3.57028i
$106$		−	6.83829i		−	0.664194i
$107$	7.06672			0.683166			0.341583	−	0.939852i	$-0.389037\pi$
$107$	7.06672			0.683166			0.341583	+	0.939852i	$0.389037\pi$
$108$	7.41662	+	4.28199i	0.713664	+	0.412034i
$109$	2.35983	+	4.08734i	0.226030	+	0.391496i	0.956628	−	0.291312i	$-0.0940918\pi$
$109$	2.35983	+	4.08734i	0.226030	+	0.391496i	−0.730598	+	0.682808i	$0.760758\pi$
$110$	2.02542	−	11.2084i	0.193117	−	1.06868i
$111$	−7.45011	−	12.9040i	−0.707133	−	1.22479i
$112$	−3.57597	+	2.06459i	−0.337897	+	0.195085i
$113$		−	4.61349i		−	0.434000i	−0.976172	−	0.217000i	$-0.930373\pi$
$113$		−	4.61349i		−	0.434000i	0.976172	−	0.217000i	$-0.0696272\pi$
$114$	−12.9390	+	1.09682i	−1.21185	+	0.102727i
$115$	−16.7775			−1.56451
$116$	−5.19100	−	8.99108i	−0.481973	−	0.834801i
$117$	−2.16047	−	3.74204i	−0.199736	−	0.345952i
$118$	1.83644	+	1.06027i	0.169058	+	0.0976055i
$119$	−1.30955	−	2.26821i	−0.120047	−	0.207927i
$120$	−8.86000	−	5.11532i	−0.808804	−	0.466963i
$121$	8.48619	−	6.99890i	0.771472	−	0.636263i
$122$			0.632307i			0.0572464i
$123$	24.2498	+	14.0006i	2.18653	+	1.26239i
$124$	6.62974	+	3.82768i	0.595368	+	0.343736i
$125$	−6.16002			−0.550969
$126$		−	24.2578i		−	2.16105i
$127$	5.66328	−	9.80908i	0.502535	−	0.870415i	−0.497461	−	0.867486i	$-0.665734\pi$
$127$	5.66328	−	9.80908i	0.502535	−	0.870415i	0.999996	−	0.00292914i	$-0.000932375\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	11.9295	−	20.6625i	1.05033	−	1.81923i
$130$	1.26295	+	2.18749i	0.110768	+	0.191856i
$131$	0.135724	−	0.0783602i	0.0118583	−	0.00684637i	−0.494059	−	0.869428i	$-0.664487\pi$
$131$	0.135724	−	0.0783602i	0.0118583	−	0.00684637i	0.505917	+	0.862582i	$0.331154\pi$
$132$	−3.33986	−	9.29878i	−0.290698	−	0.809355i
$133$	10.2838	+	14.7714i	0.891715	+	1.28085i
$134$			10.7551i			0.929099i
$135$	25.4701	−	14.7052i	2.19212	−	1.26562i
$136$	−0.549314	+	0.317147i	−0.0471033	+	0.0271951i
$137$	2.40597	−	4.16727i	0.205556	−	0.356034i	−0.744754	−	0.667339i	$-0.767433\pi$
$137$	2.40597	−	4.16727i	0.205556	−	0.356034i	0.950310	+	0.311306i	$0.100766\pi$
$138$	−12.6041	+	7.27696i	−1.07293	+	0.619456i
$139$	−7.55586	−	4.36238i	−0.640880	−	0.370012i	0.144074	−	0.989567i	$-0.453980\pi$
$139$	−7.55586	−	4.36238i	−0.640880	−	0.370012i	−0.784953	+	0.619555i	$0.787313\pi$
$140$			14.1804i			1.19846i
$141$		−	0.608103i		−	0.0512115i
$142$	1.78588	+	1.03108i	0.149867	+	0.0865260i
$143$	−0.433791	+	2.40054i	−0.0362754	+	0.200743i
$144$	−5.87473			−0.489561
$145$	−35.6539			−2.96089
$146$	−1.12051	−	0.646925i	−0.0927337	−	0.0535399i
$147$	−25.9285	+	14.9698i	−2.13854	+	1.23469i
$148$	4.33157	+	2.50083i	0.356053	+	0.205567i
$149$	−3.98778	+	2.30235i	−0.326692	+	0.188615i	−0.654371	−	0.756173i	$-0.727067\pi$
$149$	−3.98778	+	2.30235i	−0.326692	+	0.188615i	0.327680	+	0.944789i	$0.393733\pi$
$150$	−17.5274	+	10.1194i	−1.43110	+	0.826248i
$151$	12.2697			0.998491			0.499246	−	0.866461i	$-0.333611\pi$
$151$	12.2697			0.998491			0.499246	+	0.866461i	$0.333611\pi$
$152$	3.57734	−	2.49051i	0.290160	−	0.202007i
$153$		−	3.72630i		−	0.301254i
$154$	−8.84736	+	10.4535i	−0.712940	+	0.842364i
$155$	22.7679	−	13.1450i	1.82876	−	1.05583i
$156$	1.89757	+	1.09556i	0.151927	+	0.0877153i
$157$	7.64537	+	13.2422i	0.610167	+	1.05684i	0.991212	+	0.132284i	$0.0422311\pi$
$157$	7.64537	+	13.2422i	0.610167	+	1.05684i	−0.381045	+	0.924557i	$0.624436\pi$
$158$	8.45613	−	14.6465i	0.672734	−	1.16521i
$159$	−20.3716			−1.61557
$160$	3.43420			0.271497
$161$	17.4701	+	10.0864i	1.37684	+	0.794918i
$162$	3.94415	−	6.83146i	0.309881	−	0.536730i
$163$	7.53928			0.590522			0.295261	−	0.955417i	$-0.404593\pi$
$163$	7.53928			0.590522			0.295261	+	0.955417i	$0.404593\pi$
$164$	−9.39939			−0.733969
$165$	−33.3904	−	6.03384i	−2.59944	−	0.469734i
$166$	2.82015	−	1.62821i	0.218886	−	0.126374i
$167$	2.58916	−	4.48456i	0.200355	−	0.347025i	−0.748288	−	0.663374i	$-0.769124\pi$
$167$	2.58916	−	4.48456i	0.200355	−	0.347025i	0.948643	+	0.316349i	$0.102457\pi$
$168$	6.15050	+	10.6530i	0.474521	+	0.821895i
$169$	6.22951	+	10.7898i	0.479193	+	0.829987i
$170$			2.17829i			0.167067i
$171$	2.16295	+	25.5159i	0.165405	+	1.95125i
$172$			8.00892i			0.610675i
$173$	−3.21632	−	5.57082i	−0.244532	−	0.423542i	0.717468	−	0.696592i	$-0.245301\pi$
$173$	−3.21632	−	5.57082i	−0.244532	−	0.423542i	−0.962000	+	0.273050i	$0.911968\pi$
$174$	−26.7849	+	15.4643i	−2.03056	+	1.17234i
$175$	24.2941	+	14.0262i	1.83647	+	1.06028i
$176$	2.53161	+	2.14265i	0.190827	+	0.161508i
$177$	3.15859	−	5.47084i	0.237414	−	0.411213i
$178$		−	11.0764i		−	0.830213i
$179$		−	16.6994i		−	1.24817i	−0.781355	−	0.624087i	$-0.785471\pi$
$179$		−	16.6994i		−	1.24817i	0.781355	−	0.624087i	$-0.214529\pi$
$180$	−10.0875	+	17.4721i	−0.751878	+	1.30229i
$181$	−1.02910	−	0.594151i	−0.0764924	−	0.0441629i	0.461266	−	0.887262i	$-0.347395\pi$
$181$	−1.02910	−	0.594151i	−0.0764924	−	0.0441629i	−0.537758	+	0.843099i	$0.680729\pi$
$182$		−	3.03706i		−	0.225122i
$183$	1.88367			0.139245
$184$	2.44271	−	4.23090i	0.180079	−	0.311906i
$185$	14.8755	−	8.58836i	1.09367	−	0.631429i
$186$	11.4029	−	19.7503i	0.836098	−	1.44816i
$187$	−1.35907	+	1.60579i	−0.0993848	+	0.117427i
$188$	0.102063	+	0.176779i	0.00744373	+	0.0128929i
$189$	−35.3621			−2.57221
$190$	−1.26440	−	14.9158i	−0.0917292	−	1.08211i
$191$	−9.52305			−0.689064			−0.344532	−	0.938775i	$-0.611962\pi$
$191$	−9.52305			−0.689064			−0.344532	+	0.938775i	$0.611962\pi$
$192$	2.57993	−	1.48952i	0.186191	−	0.107497i
$193$	1.58290	+	2.74166i	0.113939	+	0.197349i	0.917355	−	0.398070i	$-0.130320\pi$
$193$	1.58290	+	2.74166i	0.113939	+	0.197349i	−0.803416	+	0.595418i	$0.796986\pi$
$194$	0.135282	+	0.0781049i	0.00971266	+	0.00560761i
$195$	6.51665	−	3.76239i	0.466667	−	0.269430i
$196$	5.02503	−	8.70360i	0.358930	−	0.621686i
$197$			13.0048i			0.926553i	0.886214	+	0.463277i	$0.153326\pi$
$197$			13.0048i			0.926553i	−0.886214	+	0.463277i	$0.846674\pi$
$198$	−18.3374	+	6.58627i	−1.30318	+	0.468066i
$199$	−10.1712	+	17.6170i	−0.721017	+	1.24884i	0.239576	+	0.970878i	$0.422992\pi$
$199$	−10.1712	+	17.6170i	−0.721017	+	1.24884i	−0.960593	+	0.277960i	$0.910342\pi$
$200$	3.39686	−	5.88354i	0.240195	−	0.416029i
$201$	32.0400			2.25993
$202$		−	7.07769i		−	0.497984i
$203$	37.1257	+	21.4345i	2.60571	+	1.50441i
$204$	0.944795	+	1.63643i	0.0661489	+	0.114573i
$205$	−16.1397	+	27.9548i	−1.12725	+	1.95245i
$206$	−10.3290	+	5.96347i	−0.719658	+	0.415495i
$207$	14.3503	+	24.8554i	0.997414	+	1.72757i
$208$	−0.735513			−0.0509986
$209$	8.37412	−	11.7845i	0.579250	−	0.815150i
$210$	42.2441			2.91512
$211$	8.84798	+	15.3252i	0.609120	+	1.05503i	0.991386	+	0.130975i	$0.0418106\pi$
$211$	8.84798	+	15.3252i	0.609120	+	1.05503i	−0.382266	+	0.924053i	$0.624856\pi$
$212$	5.92214	−	3.41915i	0.406734	−	0.234828i
$213$	3.07163	−	5.32021i	0.210464	−	0.364535i
$214$	3.53336	+	6.11996i	0.241536	+	0.418352i
$215$	23.8194	+	13.7521i	1.62447	+	0.937887i
$216$			8.56397i			0.582704i
$217$	−31.6103			−2.14585
$218$	−2.35983	+	4.08734i	−0.159828	+	0.276829i
$219$	−1.92722	+	3.33804i	−0.130229	+	0.225564i
$220$	10.7195	−	3.85014i	0.722708	−	0.259576i
$221$		−	0.466531i		−	0.0313823i
$222$	7.45011	−	12.9040i	0.500019	−	0.866057i
$223$	−14.6912	+	8.48197i	−0.983796	+	0.567995i	−0.903414	−	0.428769i	$-0.858947\pi$
$223$	−14.6912	+	8.48197i	−0.983796	+	0.567995i	−0.0803821	+	0.996764i	$0.525614\pi$
$224$	−3.57597	−	2.06459i	−0.238929	−	0.137946i
$225$	19.9557	+	34.5642i	1.33038	+	2.30428i
$226$	3.99540	−	2.30674i	0.265770	−	0.153442i
$227$	19.9304			1.32283			0.661414	−	0.750021i	$-0.269957\pi$
$227$	19.9304			1.32283			0.661414	+	0.750021i	$0.269957\pi$
$228$	−7.41936	−	10.6571i	−0.491359	−	0.705781i
$229$	9.97573			0.659215			0.329607	−	0.944118i	$-0.393084\pi$
$229$	9.97573			0.659215			0.329607	+	0.944118i	$0.393084\pi$
$230$	−8.38877	−	14.5298i	−0.553139	−	0.958065i
$231$	31.1414	+	26.3567i	2.04895	+	1.73414i
$232$	5.19100	−	8.99108i	0.340806	−	0.590293i
$233$	1.73815	−	1.00352i	0.113870	−	0.0657430i	−0.441983	−	0.897023i	$-0.645725\pi$
$233$	1.73815	−	1.00352i	0.113870	−	0.0657430i	0.555853	+	0.831280i	$0.312392\pi$
$234$	2.16047	−	3.74204i	0.141234	−	0.244625i
$235$	0.701012			0.0457290
$236$			2.12054i			0.138035i
$237$	−43.6325	−	25.1912i	−2.83424	−	1.63635i
$238$	1.30955	−	2.26821i	0.0848857	−	0.147026i
$239$		−	5.79560i		−	0.374886i	−0.982275	−	0.187443i	$-0.939980\pi$
$239$		−	5.79560i		−	0.374886i	0.982275	−	0.187443i	$-0.0600200\pi$
$240$		−	10.2306i		−	0.660386i
$241$	7.17589	−	12.4290i	0.462240	−	0.800623i	−0.536832	−	0.843689i	$-0.680379\pi$
$241$	7.17589	−	12.4290i	0.462240	−	0.800623i	0.999072	+	0.0430661i	$0.0137126\pi$
$242$	10.3043	+	3.84981i	0.662387	+	0.247475i
$243$	1.89859	+	1.09615i	0.121795	+	0.0703183i
$244$	−0.547594	+	0.316154i	−0.0350561	+	0.0202397i
$245$	−17.2569	−	29.8899i	−1.10251	−	1.90960i
$246$			28.0013i			1.78529i
$247$	0.270800	+	3.19457i	0.0172306	+	0.203266i
$248$			7.65537i			0.486116i
$249$	−4.85053	−	8.40137i	−0.307390	−	0.532415i
$250$	−3.08001	−	5.33474i	−0.194797	−	0.337398i
$251$	3.25298	−	5.63433i	0.205327	−	0.355636i	−0.744910	−	0.667165i	$-0.767508\pi$
$251$	3.25298	−	5.63433i	0.205327	−	0.355636i	0.950237	+	0.311529i	$0.100841\pi$
$252$	21.0079	−	12.1289i	1.32337	−	0.764048i
$253$	2.88133	−	15.9449i	0.181148	−	1.00245i
$254$	11.3266			0.710691
$255$	6.48923			0.406372
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.57841	−	3.79805i	−0.410350	−	0.236916i	0.280590	−	0.959828i	$-0.409470\pi$
$257$	−6.57841	−	3.79805i	−0.410350	−	0.236916i	−0.690940	+	0.722912i	$0.742803\pi$
$258$	23.8590			1.48539
$259$	−20.6527			−1.28330
$260$	−1.26295	+	2.18749i	−0.0783248	+	0.135662i
$261$	30.4958	+	52.8202i	1.88764	+	3.26949i
$262$	0.135724	+	0.0783602i	0.00838505	+	0.00484111i
$263$	−7.88375	+	4.55169i	−0.486133	+	0.280669i	−0.722969	−	0.690881i	$-0.757223\pi$
$263$	−7.88375	+	4.55169i	−0.486133	+	0.280669i	0.236836	+	0.971550i	$0.423890\pi$
$264$	6.38305	−	7.54180i	0.392850	−	0.464166i
$265$		−	23.4841i		−	1.44261i
$266$	−7.65056	+	16.2917i	−0.469086	+	0.998909i
$267$	−32.9972			−2.01940
$268$	−9.31419	+	5.37755i	−0.568955	+	0.328486i
$269$	−18.7841	+	10.8450i	−1.14529	+	0.661233i	−0.947735	−	0.319059i	$-0.896633\pi$
$269$	−18.7841	+	10.8450i	−1.14529	+	0.661233i	−0.197554	+	0.980292i	$0.563300\pi$
$270$	25.4701	+	14.7052i	1.55006	+	0.894930i
$271$	−9.41317	+	5.43470i	−0.571809	+	0.330134i	−0.757872	−	0.652404i	$-0.773761\pi$
$271$	−9.41317	+	5.43470i	−0.571809	+	0.330134i	0.186062	+	0.982538i	$0.440427\pi$
$272$	−0.549314	−	0.317147i	−0.0333071	−	0.0192298i
$273$	−9.04754			−0.547582
$274$	4.81195			0.290700
$275$	4.00681	−	22.1731i	0.241620	−	1.33709i
$276$	−12.6041	−	7.27696i	−0.758676	−	0.438022i
$277$		−	23.4666i		−	1.40997i	−0.709221	−	0.704987i	$-0.750953\pi$
$277$		−	23.4666i		−	1.40997i	0.709221	−	0.704987i	$-0.249047\pi$
$278$		−	8.72476i		−	0.523276i
$279$	−38.9480	−	22.4866i	−2.33175	−	1.34624i
$280$	−12.2806	+	7.09020i	−0.733905	+	0.423720i
$281$	5.68146	−	9.84059i	0.338928	−	0.587040i	−0.645304	−	0.763926i	$-0.723269\pi$
$281$	5.68146	−	9.84059i	0.338928	−	0.587040i	0.984231	+	0.176886i	$0.0566024\pi$
$282$	0.526633	−	0.304052i	0.0313605	−	0.0181060i
$283$	10.8002	−	6.23551i	0.642006	−	0.370663i	−0.143381	−	0.989668i	$-0.545797\pi$
$283$	10.8002	−	6.23551i	0.642006	−	0.370663i	0.785387	+	0.619005i	$0.212464\pi$
$284$			2.06215i			0.122366i
$285$	−44.4350	+	3.76671i	−2.63210	+	0.223121i
$286$	−2.29582	+	0.824596i	−0.135755	+	0.0487594i
$287$	33.6119	−	19.4059i	1.98405	−	1.14549i
$288$	−2.93737	−	5.08767i	−0.173086	−	0.299794i
$289$	−8.29884	+	14.3740i	−0.488167	+	0.845530i
$290$	−17.8269	−	30.8772i	−1.04683	−	1.81317i
$291$	0.232678	−	0.403011i	0.0136398	−	0.0236249i
$292$		−	1.29385i		−	0.0757168i
$293$	27.0106			1.57797			0.788987	−	0.614410i	$-0.210606\pi$
$293$	27.0106			1.57797			0.788987	+	0.614410i	$0.210606\pi$
$294$	−25.9285	−	14.9698i	−1.51218	−	0.873056i
$295$	6.30669	+	3.64117i	0.367190	+	0.211997i
$296$			5.00167i			0.290716i
$297$	9.60122	+	26.7315i	0.557119	+	1.55112i
$298$	−3.98778	−	2.30235i	−0.231006	−	0.133371i
$299$	1.79665	+	3.11188i	0.103903	+	0.179965i
$300$	−17.5274	−	10.1194i	−1.01194	−	0.584245i
$301$	−16.5351	−	28.6396i	−0.953068	−	1.65076i
$302$	6.13483	+	10.6258i	0.353020	+	0.611448i
$303$	−21.0848			−1.21129
$304$	3.94552	+	1.85281i	0.226291	+	0.106266i
$305$			2.17147i			0.124338i
$306$	3.22707	−	1.86315i	0.184480	−	0.106509i
$307$	7.21450	+	12.4959i	0.411753	+	0.713177i	0.995082	−	0.0990590i	$-0.0315833\pi$
$307$	7.21450	+	12.4959i	0.411753	+	0.713177i	−0.583328	+	0.812236i	$0.698250\pi$
$308$	−13.4766	−	2.43530i	−0.767903	−	0.138764i
$309$	17.7655	+	30.7707i	1.01064	+	1.75048i
$310$	22.7679	+	13.1450i	1.29313	+	0.746587i
$311$	−11.7789			−0.667922			−0.333961	−	0.942587i	$-0.608385\pi$
$311$	−11.7789			−0.667922			−0.333961	+	0.942587i	$0.608385\pi$
$312$			2.19113i			0.124048i
$313$	1.20940	−	2.09474i	0.0683593	−	0.118402i	−0.829820	−	0.558031i	$-0.811557\pi$
$313$	1.20940	−	2.09474i	0.0683593	−	0.118402i	0.898179	+	0.439629i	$0.144890\pi$
$314$	−7.64537	+	13.2422i	−0.431453	+	0.747299i
$315$		−	83.3061i		−	4.69376i
$316$	16.9123			0.951389
$317$	21.0959	+	12.1797i	1.18486	+	0.684080i	0.957134	−	0.289645i	$-0.0935371\pi$
$317$	21.0959	+	12.1797i	1.18486	+	0.684080i	0.227728	+	0.973725i	$0.426870\pi$
$318$	−10.1858	−	17.6423i	−0.571192	−	0.989333i
$319$	6.12310	−	33.8844i	0.342828	−	1.89716i
$320$	1.71710	+	2.97410i	0.0959888	+	0.166257i
$321$	18.2317	−	10.5261i	1.01759	−	0.587507i
$322$			20.1728i			1.12418i
$323$	−1.17522	+	2.50261i	−0.0653912	+	0.139249i
$324$	7.88829			0.438238
$325$	2.49844	+	4.32742i	0.138588	+	0.240042i
$326$	3.76964	+	6.52921i	0.208781	+	0.361619i
$327$	12.1764	+	7.03004i	0.673355	+	0.388762i
$328$	−4.69970	−	8.14011i	−0.259497	−	0.449463i
$329$	−0.729950	−	0.421437i	−0.0402434	−	0.0232346i
$330$	−11.4698	−	31.9339i	−0.631390	−	1.75790i
$331$		−	3.41474i		−	0.187691i	−0.995587	−	0.0938456i	$-0.970084\pi$
$331$		−	3.41474i		−	0.187691i	0.995587	−	0.0938456i	$-0.0299160\pi$
$332$	2.82015	+	1.62821i	0.154776	+	0.0893599i
$333$	−25.4468	−	14.6917i	−1.39448	−	0.805102i
$334$	5.17832			0.283345
$335$			36.9352i			2.01798i
$336$	−6.15050	+	10.6530i	−0.335537	+	0.581168i
$337$	7.30904	+	12.6596i	0.398149	+	0.689614i	0.993498	−	0.113853i	$-0.0363194\pi$
$337$	7.30904	+	12.6596i	0.398149	+	0.689614i	−0.595349	+	0.803467i	$0.702986\pi$
$338$	−6.22951	+	10.7898i	−0.338841	+	0.586889i
$339$	−6.87190	−	11.9025i	−0.373231	−	0.646454i
$340$	−1.88645	+	1.08915i	−0.102307	+	0.0590672i
$341$	8.58256	+	23.8954i	0.464772	+	1.29401i
$342$	−21.0159	+	14.6311i	−1.13641	+	0.791159i
$343$			12.5942i			0.680022i
$344$	−6.93593	+	4.00446i	−0.373960	+	0.215906i
$345$	−43.2849	+	24.9905i	−2.33038	+	1.34545i
$346$	3.21632	−	5.57082i	0.172910	−	0.299489i
$347$	12.1315	−	7.00412i	0.651253	−	0.376001i	−0.137683	−	0.990476i	$-0.543966\pi$
$347$	12.1315	−	7.00412i	0.651253	−	0.376001i	0.788936	+	0.614475i	$0.210632\pi$
$348$	−26.7849	−	15.4643i	−1.43582	−	0.828971i
$349$			25.2310i			1.35059i	0.737549	+	0.675293i	$0.235983\pi$
$349$			25.2310i			1.35059i	−0.737549	+	0.675293i	$0.764017\pi$
$350$			28.0525i			1.49947i
$351$	−5.45502	−	3.14946i	−0.291167	−	0.168105i
$352$	−0.589780	+	3.26376i	−0.0314354	+	0.173959i
$353$	−4.82356			−0.256732			−0.128366	−	0.991727i	$-0.540973\pi$
$353$	−4.82356			−0.256732			−0.128366	+	0.991727i	$0.540973\pi$
$354$	6.31718			0.335754
$355$	6.13305	+	3.54092i	0.325509	+	0.187933i
$356$	9.59246	−	5.53821i	0.508399	−	0.293524i
$357$	−6.75711	−	3.90122i	−0.357624	−	0.206475i
$358$	14.4621	−	8.34972i	0.764348	−	0.441296i
$359$	−20.1597	+	11.6392i	−1.06399	+	0.614293i	−0.926532	−	0.376215i	$-0.877225\pi$
$359$	−20.1597	+	11.6392i	−1.06399	+	0.614293i	−0.137454	+	0.990508i	$0.543892\pi$
$360$	−20.1750			−1.06332
$361$	6.59469	−	17.8188i	0.347089	−	0.937832i
$362$		−	1.18830i		−	0.0624558i
$363$	11.4688	−	30.6971i	0.601954	−	1.61118i
$364$	2.63017	−	1.51853i	0.137858	−	0.0795925i
$365$	−3.84804	−	2.22167i	−0.201416	−	0.116287i
$366$	0.941837	+	1.63131i	0.0492306	+	0.0852699i
$367$	8.81137	−	15.2617i	0.459950	−	0.796657i	−0.539008	−	0.842301i	$-0.681201\pi$
$367$	8.81137	−	15.2617i	0.459950	−	0.796657i	0.998958	+	0.0456442i	$0.0145340\pi$
$368$	4.88543			0.254670
$369$	55.2189			2.87458
$370$	14.8755	+	8.58836i	0.773340	+	0.446488i
$371$	−14.1182	+	24.4535i	−0.732983	+	1.26956i
$372$	22.8057			1.18242
$373$	−22.3578			−1.15764			−0.578821	−	0.815455i	$-0.696487\pi$
$373$	−22.3578			−1.15764			−0.578821	+	0.815455i	$0.696487\pi$
$374$	−2.07018	−	0.374094i	−0.107047	−	0.0193439i
$375$	−15.8924	+	9.17551i	−0.820682	+	0.473821i
$376$	−0.102063	+	0.176779i	−0.00526351	+	0.00911667i
$377$	3.81805	+	6.61306i	0.196640	+	0.340590i
$378$	−17.6811	−	30.6245i	−0.909415	−	1.57515i
$379$		−	8.03980i		−	0.412977i	−0.978449	−	0.206489i	$-0.933796\pi$
$379$		−	8.03980i		−	0.412977i	0.978449	−	0.206489i	$-0.0662036\pi$
$380$	12.2853	−	8.55292i	0.630222	−	0.438756i
$381$		−	33.7424i		−	1.72867i
$382$	−4.76153	−	8.24720i	−0.243621	−	0.421964i
$383$	−1.35811	+	0.784105i	−0.0693962	+	0.0400659i	−0.534297	−	0.845297i	$-0.679423\pi$
$383$	−1.35811	+	0.784105i	−0.0693962	+	0.0400659i	0.464900	+	0.885363i	$0.346090\pi$
$384$	2.57993	+	1.48952i	0.131657	+	0.0760120i
$385$	−30.3836	+	35.8993i	−1.54849	+	1.82960i
$386$	−1.58290	+	2.74166i	−0.0805672	+	0.139547i
$387$		−	47.0503i		−	2.39170i
$388$			0.156210i			0.00793035i
$389$	7.27802	−	12.6059i	0.369010	−	0.639144i	−0.620401	−	0.784285i	$-0.713030\pi$
$389$	7.27802	−	12.6059i	0.369010	−	0.639144i	0.989411	+	0.145141i	$0.0463634\pi$
$390$	6.51665	+	3.76239i	0.329983	+	0.190516i
$391$			3.09879i			0.156713i
$392$	10.0501			0.507604
$393$	0.233439	−	0.404328i	0.0117754	−	0.0203957i
$394$	−11.2625	+	6.50240i	−0.567396	+	0.327586i
$395$	29.0400	−	50.2988i	1.46116	−	2.53081i
$396$	−14.8726	−	12.5875i	−0.747374	−	0.632545i
$397$	−14.6884	−	25.4411i	−0.737190	−	1.27685i	−0.953756	−	0.300583i	$-0.902819\pi$
$397$	−14.6884	−	25.4411i	−0.737190	−	1.27685i	0.216566	−	0.976268i	$-0.430514\pi$
$398$	−20.3424			−1.01967
$399$	48.5338	+	22.7914i	2.42973	+	1.14100i
$400$	6.79373			0.339686
$401$	23.3032	−	13.4541i	1.16371	−	0.671865i	0.211516	−	0.977375i	$-0.432160\pi$
$401$	23.3032	−	13.4541i	1.16371	−	0.671865i	0.952189	+	0.305509i	$0.0988266\pi$
$402$	16.0200	+	27.7474i	0.799004	+	1.38392i
$403$	−4.87626	−	2.81531i	−0.242904	−	0.140241i
$404$	6.12946	−	3.53884i	0.304952	−	0.176064i
$405$	13.5450	−	23.4606i	0.673056	−	1.16577i
$406$			42.8691i			2.12756i
$407$	5.60746	+	15.6122i	0.277951	+	0.773867i
$408$	−0.944795	+	1.63643i	−0.0467743	+	0.0810155i
$409$	−3.80335	+	6.58759i	−0.188063	+	0.325735i	−0.944605	−	0.328211i	$-0.893554\pi$
$409$	−3.80335	+	6.58759i	−0.188063	+	0.325735i	0.756541	+	0.653946i	$0.226888\pi$
$410$	−32.2794			−1.59417
$411$		−	14.3350i		−	0.707095i
$412$	−10.3290	−	5.96347i	−0.508875	−	0.293799i
$413$	−4.37803	−	7.58296i	−0.215429	−	0.373133i
$414$	−14.3503	+	24.8554i	−0.705278	+	1.22158i
$415$	9.68496	−	5.59161i	0.475416	−	0.274482i
$416$	−0.367756	−	0.636973i	−0.0180307	−	0.0312302i
$417$	−25.9915			−1.27281
$418$	14.3927	+	1.35996i	0.703971	+	0.0665177i
$419$	0.944008			0.0461178			0.0230589	−	0.999734i	$-0.492659\pi$
$419$	0.944008			0.0461178			0.0230589	+	0.999734i	$0.492659\pi$
$420$	21.1221	+	36.5845i	1.03065	+	1.78514i
$421$	−2.12809	+	1.22866i	−0.103717	+	0.0598810i	−0.550961	−	0.834531i	$-0.685739\pi$
$421$	−2.12809	+	1.22866i	−0.103717	+	0.0598810i	0.447244	+	0.894412i	$0.352405\pi$
$422$	−8.84798	+	15.3252i	−0.430713	+	0.746017i
$423$	−0.599595	−	1.03853i	−0.0291533	−	0.0504950i
$424$	5.92214	+	3.41915i	0.287604	+	0.166048i
$425$			4.30922i			0.209028i
$426$	6.14325			0.297641
$427$	1.30545	−	2.26111i	0.0631753	−	0.109423i
$428$	−3.53336	+	6.11996i	−0.170792	+	0.295820i
$429$	2.45651	+	6.83937i	0.118602	+	0.330208i
$430$			27.5042i			1.32637i
$431$	5.91070	−	10.2376i	0.284708	−	0.493130i	−0.687830	−	0.725872i	$-0.741437\pi$
$431$	5.91070	−	10.2376i	0.284708	−	0.493130i	0.972538	+	0.232742i	$0.0747699\pi$
$432$	−7.41662	+	4.28199i	−0.356832	+	0.206017i
$433$	1.30372	+	0.752706i	0.0626530	+	0.0361727i	0.530999	−	0.847372i	$-0.321817\pi$
$433$	1.30372	+	0.752706i	0.0626530	+	0.0361727i	−0.468346	+	0.883545i	$0.655150\pi$
$434$	−15.8052	−	27.3753i	−0.758672	−	1.31406i
$435$	−91.9846	+	53.1073i	−4.41032	+	2.54630i
$436$	−4.71965			−0.226030
$437$	−1.79871	−	21.2190i	−0.0860440	−	1.01504i
$438$	−3.85444			−0.184172
$439$	16.0679	+	27.8305i	0.766881	+	1.32828i	0.939246	+	0.343244i	$0.111526\pi$
$439$	16.0679	+	27.8305i	0.766881	+	1.32828i	−0.172365	+	0.985033i	$0.555141\pi$
$440$	8.69406	+	7.35828i	0.414473	+	0.350792i
$441$	−29.5207	+	51.1313i	−1.40575	+	2.43483i
$442$	0.404028	−	0.233265i	0.0192176	−	0.0110953i
$443$	−20.5472	+	35.5888i	−0.976228	+	1.69088i	−0.300407	+	0.953811i	$0.597123\pi$
$443$	−20.5472	+	35.5888i	−0.976228	+	1.69088i	−0.675821	+	0.737066i	$0.736211\pi$
$444$	14.9002			0.707133
$445$		−	38.0386i		−	1.80320i
$446$	−14.6912	−	8.48197i	−0.695649	−	0.401633i
$447$	−6.85880	+	11.8798i	−0.324410	+	0.561895i
$448$		−	4.12917i		−	0.195085i
$449$			8.43791i			0.398210i	0.979978	+	0.199105i	$0.0638034\pi$
$449$			8.43791i			0.398210i	−0.979978	+	0.199105i	$0.936197\pi$
$450$	−19.9557	+	34.5642i	−0.940719	+	1.62937i
$451$	−23.7956	−	20.1396i	−1.12049	−	0.948336i
$452$	3.99540	+	2.30674i	0.187928	+	0.108500i
$453$	31.6549	−	18.2760i	1.48728	−	0.858680i
$454$	9.96521	+	17.2602i	0.467690	+	0.810064i
$455$		−	10.4299i		−	0.488960i
$456$	5.51961	−	11.7539i	0.258479	−	0.550426i
$457$			37.1348i			1.73709i	0.495608	+	0.868546i	$0.334945\pi$
$457$			37.1348i			1.73709i	−0.495608	+	0.868546i	$0.665055\pi$
$458$	4.98787	+	8.63924i	0.233068	+	0.403685i
$459$	−2.71604	−	4.70431i	−0.126774	−	0.219578i
$460$	8.38877	−	14.5298i	0.391128	−	0.677454i
$461$	−3.51316	+	2.02833i	−0.163624	+	0.0944686i	−0.579576	−	0.814918i	$-0.696782\pi$
$461$	−3.51316	+	2.02833i	−0.163624	+	0.0944686i	0.415952	+	0.909387i	$0.363449\pi$
$462$	−7.25489	+	40.1476i	−0.337528	+	1.86783i
$463$	−22.7991			−1.05957			−0.529783	−	0.848134i	$-0.677726\pi$
$463$	−22.7991			−1.05957			−0.529783	+	0.848134i	$0.677726\pi$
$464$	10.3820			0.481973
$465$	39.1597	−	67.8266i	1.81599	−	3.14538i
$466$	1.73815	+	1.00352i	0.0805184	+	0.0464873i
$467$	−32.2303			−1.49144			−0.745719	−	0.666260i	$-0.767894\pi$
$467$	−32.2303			−1.49144			−0.745719	+	0.666260i	$0.767894\pi$
$468$	4.32094			0.199736
$469$	22.2048	−	38.4599i	1.02532	−	1.77591i
$470$	0.350506	+	0.607094i	0.0161676	+	0.0280032i
$471$	39.4491	+	22.7759i	1.81772	+	1.04946i
$472$	−1.83644	+	1.06027i	−0.0845289	+	0.0488028i
$473$	−17.1603	+	20.2755i	−0.789031	+	0.932268i
$474$		−	50.3825i		−	2.31414i
$475$	−2.50131	−	29.5074i	−0.114768	−	1.35389i
$476$	2.61911			0.120047
$477$	−34.7910	+	20.0866i	−1.59297	+	0.919701i
$478$	5.01914	−	2.89780i	0.229570	−	0.132542i
$479$	−31.3786	−	18.1165i	−1.43373	−	0.827762i	−0.436323	−	0.899790i	$-0.643719\pi$
$479$	−31.3786	−	18.1165i	−1.43373	−	0.827762i	−0.997403	+	0.0720284i	$0.977053\pi$
$480$	8.86000	−	5.11532i	0.404402	−	0.233482i
$481$	−3.18593	−	1.83940i	−0.145266	−	0.0838692i
$482$	14.3518			0.653706
$483$	60.0956			2.73445
$484$	1.81813	+	10.8487i	0.0826421	+	0.493123i
$485$	0.464584	+	0.268228i	0.0210957	+	0.0121796i
$486$			2.19231i			0.0994451i
$487$		−	12.9021i		−	0.584651i	−0.956319	−	0.292326i	$-0.905571\pi$
$487$		−	12.9021i		−	0.584651i	0.956319	−	0.292326i	$-0.0944291\pi$
$488$	−0.547594	−	0.316154i	−0.0247884	−	0.0143116i
$489$	19.4508	−	11.2299i	0.879597	−	0.507836i
$490$	17.2569	−	29.8899i	0.779589	−	1.35029i
$491$	−20.6492	+	11.9218i	−0.931886	+	0.538025i	−0.887408	−	0.460986i	$-0.847496\pi$
$491$	−20.6492	+	11.9218i	−0.931886	+	0.538025i	−0.0444785	+	0.999010i	$0.514163\pi$
$492$	−24.2498	+	14.0006i	−1.09327	+	0.631197i
$493$			6.58524i			0.296584i
$494$	−2.63118	+	1.83180i	−0.118382	+	0.0824168i
$495$	−62.9741	+	22.6186i	−2.83048	+	1.01663i
$496$	−6.62974	+	3.82768i	−0.297684	+	0.171868i
$497$	−4.25749	−	7.37419i	−0.190974	−	0.330777i
$498$	4.85053	−	8.40137i	0.217357	−	0.376474i
$499$	15.5326	+	26.9032i	0.695333	+	1.20435i	0.970068	+	0.242832i	$0.0780763\pi$
$499$	15.5326	+	26.9032i	0.695333	+	1.20435i	−0.274736	+	0.961520i	$0.588590\pi$
$500$	3.08001	−	5.33474i	0.137742	−	0.238577i
$501$		−	15.4265i		−	0.689204i
$502$	6.50597			0.290376
$503$	−34.4433	−	19.8858i	−1.53575	−	0.886665i	−0.999081	−	0.0428721i	$-0.986349\pi$
$503$	−34.4433	−	19.8858i	−1.53575	−	0.886665i	−0.536669	−	0.843793i	$-0.680317\pi$
$504$	21.0079	+	12.1289i	0.935764	+	0.540264i
$505$		−	24.3062i		−	1.08161i
$506$	15.2493	−	5.47714i	0.677916	−	0.243488i
$507$	32.1434	+	18.5580i	1.42754	+	0.824190i
$508$	5.66328	+	9.80908i	0.251267	+	0.435208i
$509$	10.9259	+	6.30810i	0.484284	+	0.279602i	0.722200	−	0.691684i	$-0.243131\pi$
$509$	10.9259	+	6.30810i	0.484284	+	0.279602i	−0.237916	+	0.971286i	$0.576464\pi$
$510$	3.24462	+	5.61984i	0.143674	+	0.248851i
$511$	2.67126	+	4.62676i	0.118170	+	0.204676i
$512$	−1.00000			−0.0441942
$513$	21.3287	+	30.6362i	0.941684	+	1.35262i
$514$		−	7.59610i		−	0.335050i
$515$	−35.4720	+	20.4798i	−1.56308	+	0.902446i
$516$	11.9295	+	20.6625i	0.525166	+	0.909615i
$517$	−0.120390	+	0.666221i	−0.00529474	+	0.0293004i
$518$	−10.3264	−	17.8858i	−0.453715	−	0.785857i
$519$	−16.5958	−	9.58156i	−0.728473	−	0.420584i
$520$	−2.52590			−0.110768
$521$		−	13.9715i		−	0.612102i	−0.952015	−	0.306051i	$-0.900992\pi$
$521$		−	13.9715i		−	0.612102i	0.952015	−	0.306051i	$-0.0990078\pi$
$522$	−30.4958	+	52.8202i	−1.33476	+	2.31188i
$523$	7.25617	−	12.5681i	0.317290	−	0.549563i	−0.662632	−	0.748946i	$-0.730560\pi$
$523$	7.25617	−	12.5681i	0.317290	−	0.549563i	0.979922	+	0.199383i	$0.0638938\pi$
$524$			0.156720i			0.00684637i
$525$	83.5697			3.64728
$526$	−7.88375	−	4.55169i	−0.343748	−	0.198463i
$527$	−2.42787	−	4.20520i	−0.105760	−	0.183181i
$528$	9.72291	+	1.75698i	0.423136	+	0.0764630i
$529$	−0.433698	−	0.751187i	−0.0188564	−	0.0326603i
$530$	20.3378	−	11.7420i	0.883417	−	0.510041i
$531$		−	12.4576i		−	0.540613i
$532$	−17.9343	+	1.52027i	−0.777551	+	0.0659122i
$533$	6.91337			0.299451
$534$	−16.4986	−	28.5764i	−0.713964	−	1.23662i
$535$	12.1343	+	21.0172i	0.524610	+	0.908652i
$536$	−9.31419	−	5.37755i	−0.402312	−	0.232275i
$537$	−24.8742	−	43.0834i	−1.07340	−	1.85919i
$538$	−18.7841	−	10.8450i	−0.809841	−	0.467562i
$539$	31.3702	−	11.2673i	1.35121	−	0.485316i
$540$			29.4104i			1.26562i
$541$	−4.91487	−	2.83760i	−0.211307	−	0.121998i	0.390612	−	0.920556i	$-0.372264\pi$
$541$	−4.91487	−	2.83760i	−0.211307	−	0.121998i	−0.601919	+	0.798557i	$0.705597\pi$
$542$	−9.41317	−	5.43470i	−0.404330	−	0.233440i
$543$	−3.54001			−0.151916
$544$		−	0.634293i		−	0.0271951i
$545$	−8.10411	+	14.0367i	−0.347142	+	0.601268i
$546$	−4.52377	−	7.83540i	−0.193600	−	0.335324i
$547$	−18.1766	+	31.4828i	−0.777176	+	1.34611i	0.156388	+	0.987696i	$0.450015\pi$
$547$	−18.1766	+	31.4828i	−0.777176	+	1.34611i	−0.933564	+	0.358412i	$0.883318\pi$
$548$	2.40597	+	4.16727i	0.102778	+	0.178017i
$549$	3.21697	−	1.85732i	0.137297	−	0.0792684i
$550$	21.2059	−	7.61657i	0.904223	−	0.324772i
$551$	−3.82244	−	45.0924i	−0.162841	−	1.92100i
$552$		−	14.5539i		−	0.619456i
$553$	−60.4777	+	34.9168i	−2.57177	+	1.48481i
$554$	20.3227	−	11.7333i	0.863429	−	0.498501i
$555$	25.5852	−	44.3148i	1.08603	−	1.88106i
$556$	7.55586	−	4.36238i	0.320440	−	0.185006i
$557$	−28.3779	−	16.3840i	−1.20241	−	0.694212i	−0.241321	−	0.970445i	$-0.577581\pi$
$557$	−28.3779	−	16.3840i	−1.20241	−	0.694212i	−0.961091	+	0.276233i	$0.910914\pi$
$558$		−	44.9732i		−	1.90387i
$559$		−	5.89066i		−	0.249149i
$560$	−12.2806	−	7.09020i	−0.518949	−	0.299616i
$561$	−1.11444	+	6.16718i	−0.0470519	+	0.260379i
$562$	11.3629			0.479316
$563$	−0.410088			−0.0172832			−0.00864158	−	0.999963i	$-0.502751\pi$
$563$	−0.410088			−0.0172832			−0.00864158	+	0.999963i	$0.502751\pi$
$564$	0.526633	+	0.304052i	0.0221752	+	0.0128029i
$565$	13.7210	−	7.92182i	0.577247	−	0.333273i
$566$	10.8002	+	6.23551i	0.453967	+	0.262098i
$567$	−28.2083	+	16.2861i	−1.18464	+	0.683950i
$568$	−1.78588	+	1.03108i	−0.0749337	+	0.0432630i
$569$	−19.7430			−0.827669			−0.413834	−	0.910352i	$-0.635811\pi$
$569$	−19.7430			−0.827669			−0.413834	+	0.910352i	$0.635811\pi$
$570$	−25.4796	−	36.5985i	−1.06722	−	1.53294i
$571$		−	31.9660i		−	1.33773i	−0.743382	−	0.668867i	$-0.766779\pi$
$571$		−	31.9660i		−	1.33773i	0.743382	−	0.668867i	$-0.233221\pi$
$572$	−1.86203	−	1.57594i	−0.0778555	−	0.0658935i
$573$	−24.5688	+	14.1848i	−1.02638	+	0.592579i
$574$	33.6119	+	19.4059i	1.40293	+	0.809985i
$575$	−16.5951	−	28.7436i	−0.692065	−	1.19869i
$576$	2.93737	−	5.08767i	0.122390	−	0.211986i
$577$	−16.6632			−0.693697			−0.346848	−	0.937921i	$-0.612748\pi$
$577$	−16.6632			−0.693697			−0.346848	+	0.937921i	$0.612748\pi$
$578$	−16.5977			−0.690372
$579$	8.16753	+	4.71552i	0.339431	+	0.195970i
$580$	17.8269	−	30.8772i	0.740224	−	1.28210i
$581$	−13.4464			−0.557849
$582$	0.465357			0.0192897
$583$	22.3186	+	4.03309i	0.924341	+	0.167034i
$584$	1.12051	−	0.646925i	0.0463669	−	0.0267699i
$585$	7.41949	−	12.8509i	0.306758	−	0.531321i
$586$	13.5053	+	23.3918i	0.557898	+	0.966308i
$587$	2.70860	+	4.69142i	0.111796	+	0.193636i	0.916494	−	0.400048i	$-0.131006\pi$
$587$	2.70860	+	4.69142i	0.111796	+	0.193636i	−0.804699	+	0.593684i	$0.797673\pi$
$588$		−	29.9396i		−	1.23469i
$589$	19.0658	+	27.3858i	0.785592	+	1.12841i
$590$			7.28234i			0.299809i
$591$	19.3710	+	33.5515i	0.796815	+	1.38012i
$592$	−4.33157	+	2.50083i	−0.178027	+	0.102784i
$593$	−2.17337	−	1.25479i	−0.0892494	−	0.0515282i	0.454711	−	0.890639i	$-0.349743\pi$
$593$	−2.17337	−	1.25479i	−0.0892494	−	0.0515282i	−0.543960	+	0.839111i	$0.683076\pi$
$594$	−18.3496	+	21.6807i	−0.752892	+	0.889568i
$595$	4.49727	−	7.78949i	0.184370	−	0.319338i
$596$		−	4.60469i		−	0.188615i
$597$			60.6010i			2.48023i
$598$	−1.79665	+	3.11188i	−0.0734704	+	0.127254i
$599$	−32.4401	−	18.7293i	−1.32546	−	0.765257i	−0.340870	−	0.940110i	$-0.610722\pi$
$599$	−32.4401	−	18.7293i	−1.32546	−	0.765257i	−0.984595	+	0.174853i	$0.944055\pi$
$600$		−	20.2389i		−	0.826248i
$601$	15.4119			0.628665			0.314333	−	0.949313i	$-0.398219\pi$
$601$	15.4119			0.628665			0.314333	+	0.949313i	$0.398219\pi$
$602$	16.5351	−	28.6396i	0.673921	−	1.16726i
$603$	54.7184	−	31.5917i	2.22830	−	1.28651i
$604$	−6.13483	+	10.6258i	−0.249623	+	0.432359i
$605$	35.3871	+	13.2210i	1.43869	+	0.537511i
$606$	−10.5424	−	18.2600i	−0.428255	−	0.741760i
$607$	−35.9601			−1.45958			−0.729788	−	0.683674i	$-0.760381\pi$
$607$	−35.9601			−1.45958			−0.729788	+	0.683674i	$0.760381\pi$
$608$	0.368179	+	4.34332i	0.0149316	+	0.176145i
$609$	127.709			5.17503
$610$	−1.88055	+	1.08573i	−0.0761411	+	0.0439601i
$611$	−0.0750689	−	0.130023i	−0.00303696	−	0.00526017i
$612$	3.22707	+	1.86315i	0.130447	+	0.0753135i
$613$	−21.3094	+	12.3030i	−0.860678	+	0.496913i	−0.864239	−	0.503081i	$-0.832200\pi$
$613$	−21.3094	+	12.3030i	−0.860678	+	0.496913i	0.00356133	+	0.999994i	$0.498866\pi$
$614$	−7.21450	+	12.4959i	−0.291153	+	0.504293i
$615$			96.1619i			3.87762i
$616$	−4.62929	−	12.8888i	−0.186519	−	0.519303i
$617$	23.3744	−	40.4856i	0.941017	−	1.62989i	0.177482	−	0.984124i	$-0.443205\pi$
$617$	23.3744	−	40.4856i	0.941017	−	1.62989i	0.763536	−	0.645766i	$-0.223462\pi$
$618$	−17.7655	+	30.7707i	−0.714632	+	1.23778i
$619$	18.1190			0.728263			0.364132	−	0.931347i	$-0.381366\pi$
$619$	18.1190			0.728263			0.364132	+	0.931347i	$0.381366\pi$
$620$			26.2901i			1.05583i
$621$	36.2333	+	20.9193i	1.45399	+	0.839464i
$622$	−5.88946	−	10.2009i	−0.236146	−	0.409017i
$623$	−22.8682	+	39.6089i	−0.916196	+	1.58690i
$624$	−1.89757	+	1.09556i	−0.0759637	+	0.0438577i
$625$	6.40695	+	11.0972i	0.256278	+	0.443886i
$626$	2.41880			0.0966747
$627$	4.05138	−	42.8766i	0.161796	−	1.71233i
$628$	−15.2907			−0.610167
$629$	−1.58626	−	2.74749i	−0.0632484	−	0.109549i
$630$	72.1452	−	41.6530i	2.87433	−	1.65950i
$631$	20.6881	−	35.8328i	0.823578	−	1.42648i	−0.0794225	−	0.996841i	$-0.525308\pi$
$631$	20.6881	−	35.8328i	0.823578	−	1.42648i	0.903001	−	0.429639i	$-0.141359\pi$
$632$	8.45613	+	14.6465i	0.336367	+	0.582605i
$633$	45.6544	+	26.3586i	1.81460	+	1.04766i
$634$			24.3594i			0.967436i
$635$	38.8976			1.54361
$636$	10.1858	−	17.6423i	0.403893	−	0.699564i
$637$	−3.69597	+	6.40161i	−0.146440	+	0.253641i
$638$	32.4063	−	11.6394i	1.28298	−	0.460810i
$639$		−	12.1146i		−	0.479246i
$640$	−1.71710	+	2.97410i	−0.0678743	+	0.117562i
$641$	−33.7828	+	19.5045i	−1.33434	+	0.770382i	−0.985962	−	0.166972i	$-0.946601\pi$
$641$	−33.7828	+	19.5045i	−1.33434	+	0.770382i	−0.348379	+	0.937354i	$0.613268\pi$
$642$	18.2317	+	10.5261i	0.719547	+	0.415430i
$643$	−9.51128	−	16.4740i	−0.375088	−	0.649672i	0.615252	−	0.788331i	$-0.289054\pi$
$643$	−9.51128	−	16.4740i	−0.375088	−	0.649672i	−0.990340	+	0.138658i	$0.955721\pi$
$644$	−17.4701	+	10.0864i	−0.688419	+	0.397459i
$645$	81.9365			3.22625
$646$	−2.75494	+	0.233533i	−0.108392	+	0.00918825i
$647$	−31.4269			−1.23552			−0.617759	−	0.786368i	$-0.711959\pi$
$647$	−31.4269			−1.23552			−0.617759	+	0.786368i	$0.711959\pi$
$648$	3.94415	+	6.83146i	0.154941	+	0.268365i
$649$	−4.54356	+	5.36837i	−0.178350	+	0.210727i
$650$	−2.49844	+	4.32742i	−0.0979968	+	0.169735i
$651$	−81.5525	+	47.0843i	−3.19629	+	1.84538i
$652$	−3.76964	+	6.52921i	−0.147630	+	0.255704i
$653$	−13.4292			−0.525524			−0.262762	−	0.964861i	$-0.584633\pi$
$653$	−13.4292			−0.525524			−0.262762	+	0.964861i	$0.584633\pi$
$654$			14.0601i			0.549792i
$655$	0.466103	+	0.269105i	0.0182122	+	0.0105148i
$656$	4.69970	−	8.14011i	0.183492	−	0.317818i
$657$			7.60102i			0.296544i
$658$		−	0.842874i		−	0.0328586i
$659$	−12.1545	+	21.0522i	−0.473473	+	0.820079i	−0.999539	−	0.0303646i	$-0.990333\pi$
$659$	−12.1545	+	21.0522i	−0.473473	+	0.820079i	0.526066	+	0.850444i	$0.323666\pi$
$660$	21.9207	−	25.9000i	0.853261	−	1.00816i
$661$	39.3706	+	22.7306i	1.53134	+	0.884119i	0.999300	+	0.0373979i	$0.0119069\pi$
$661$	39.3706	+	22.7306i	1.53134	+	0.884119i	0.532038	+	0.846721i	$0.321426\pi$
$662$	2.95725	−	1.70737i	0.114937	−	0.0663588i
$663$	−0.694909	−	1.20362i	−0.0269880	−	0.0467446i
$664$			3.25643i			0.126374i
$665$	−26.2736	+	55.9490i	−1.01885	+	2.16961i
$666$		−	29.3835i		−	1.13859i
$667$	−25.3603	−	43.9253i	−0.981953	−	1.70079i
$668$	2.58916	+	4.48456i	0.100178	+	0.173513i
$669$	−25.2682	+	43.7658i	−0.976926	+	1.69209i
$670$	−31.9868	+	18.4676i	−1.23576	+	0.713465i
$671$	−2.06370	−	0.372922i	−0.0796683	−	0.0143965i
$672$	−12.3010			−0.474521
$673$	−3.32009			−0.127980			−0.0639901	−	0.997951i	$-0.520383\pi$
$673$	−3.32009			−0.127980			−0.0639901	+	0.997951i	$0.520383\pi$
$674$	−7.30904	+	12.6596i	−0.281534	+	0.487631i
$675$	50.3865	+	29.0907i	1.93938	+	1.11970i
$676$	−12.4590			−0.479193
$677$	26.3040			1.01095			0.505473	−	0.862842i	$-0.331318\pi$
$677$	26.3040			1.01095			0.505473	+	0.862842i	$0.331318\pi$
$678$	6.87190	−	11.9025i	0.263914	−	0.457112i
$679$	−0.322509	−	0.558601i	−0.0123767	−	0.0214371i
$680$	−1.88645	−	1.08915i	−0.0723422	−	0.0417668i
$681$	51.4191	−	29.6868i	1.97039	−	1.13760i
$682$	−16.4027	+	19.3804i	−0.628094	+	0.742115i
$683$			40.9395i			1.56651i	0.621703	+	0.783253i	$0.286441\pi$
$683$			40.9395i			1.56651i	−0.621703	+	0.783253i	$0.713559\pi$
$684$	−23.1789	−	10.8848i	−0.886266	−	0.416189i
$685$	16.5252			0.631395
$686$	−10.9069	+	6.29709i	−0.416427	+	0.240424i
$687$	25.7367	−	14.8591i	0.981917	−	0.566910i
$688$	−6.93593	−	4.00446i	−0.264430	−	0.152669i
$689$	−4.35581	+	2.51483i	−0.165943	+	0.0958072i
$690$	−43.2849	−	24.9905i	−1.64783	−	0.951374i
$691$	16.5403			0.629222			0.314611	−	0.949221i	$-0.398126\pi$
$691$	16.5403			0.629222			0.314611	+	0.949221i	$0.398126\pi$
$692$	6.43263			0.244532
$693$	79.1717	+	14.3068i	3.00748	+	0.543469i
$694$	12.1315	+	7.00412i	0.460505	+	0.265873i
$695$		−	29.9626i		−	1.13654i
$696$		−	30.9285i		−	1.17234i
$697$	5.16322	+	2.98099i	0.195571	+	0.112913i
$698$	−21.8507	+	12.6155i	−0.827062	+	0.477504i
$699$	2.98955	−	5.17805i	0.113075	−	0.195852i
$700$	−24.2941	+	14.0262i	−0.918233	+	0.530142i
$701$	23.5769	−	13.6121i	0.890488	−	0.514123i	0.0163858	−	0.999866i	$-0.494784\pi$
$701$	23.5769	−	13.6121i	0.890488	−	0.514123i	0.874102	+	0.485742i	$0.161451\pi$
$702$		−	6.29891i		−	0.237737i
$703$	12.4567	+	17.8927i	0.469814	+	0.674834i
$704$	−3.12139	+	1.12112i	−0.117642	+	0.0422537i
$705$	1.80856	−	1.04417i	0.0681144	−	0.0393259i
$706$	−2.41178	−	4.17732i	−0.0907685	−	0.157216i
$707$	−14.6125	+	25.3096i	−0.549559	+	0.951865i
$708$	3.15859	+	5.47084i	0.118707	+	0.205607i
$709$	−11.9147	+	20.6368i	−0.447465	+	0.775033i	−0.998220	−	0.0596342i	$-0.981007\pi$
$709$	−11.9147	+	20.6368i	−0.447465	+	0.775033i	0.550755	+	0.834667i	$0.314340\pi$
$710$			7.08184i			0.265777i
$711$	−99.3550			−3.72611
$712$	9.59246	+	5.53821i	0.359493	+	0.207553i
$713$	32.3891	+	18.6999i	1.21298	+	0.700315i
$714$		−	7.80244i		−	0.291999i
$715$	−7.88432	+	2.83183i	−0.294857	+	0.105904i
$716$	14.4621	+	8.34972i	0.540475	+	0.312044i
$717$	−8.63269	−	14.9523i	−0.322394	−	0.558402i
$718$	−20.1597	−	11.6392i	−0.752352	−	0.434371i
$719$	13.1560	+	22.7868i	0.490635	+	0.849806i	0.999942	−	0.0107797i	$-0.00343135\pi$
$719$	13.1560	+	22.7868i	0.490635	+	0.849806i	−0.509306	+	0.860585i	$0.670098\pi$
$720$	−10.0875	−	17.4721i	−0.375939	−	0.651146i
$721$	49.2484			1.83411
$722$	18.7289	−	3.19824i	0.697017	−	0.119026i
$723$		−	42.7547i		−	1.59006i
$724$	1.02910	−	0.594151i	0.0382462	−	0.0220815i
$725$	−35.2663	−	61.0830i	−1.30976	−	2.26856i
$726$	32.3188	−	5.41629i	1.19946	−	0.201017i
$727$	9.14811	+	15.8450i	0.339285	+	0.587658i	0.984298	−	0.176513i	$-0.0564817\pi$
$727$	9.14811	+	15.8450i	0.339285	+	0.587658i	−0.645014	+	0.764171i	$0.723148\pi$
$728$	2.63017	+	1.51853i	0.0974806	+	0.0562804i
$729$	30.1959			1.11837
$730$		−	4.44334i		−	0.164455i
$731$	2.54000	−	4.39941i	0.0939454	−	0.162718i
$732$	−0.941837	+	1.63131i	−0.0348113	+	0.0602949i
$733$		−	18.1630i		−	0.670864i	−0.942064	−	0.335432i	$-0.891118\pi$
$733$		−	18.1630i		−	0.670864i	0.942064	−	0.335432i	$-0.108882\pi$
$734$	17.6227			0.650467
$735$	−89.0435	−	51.4093i	−3.28442	−	1.89626i
$736$	2.44271	+	4.23090i	0.0900396	+	0.155953i
$737$	−35.1021	−	6.34315i	−1.29300	−	0.233653i
$738$	27.6095	+	47.8210i	1.01632	+	1.76032i
$739$	36.5704	−	21.1140i	1.34527	−	0.776689i	0.357691	−	0.933840i	$-0.383564\pi$
$739$	36.5704	−	21.1140i	1.34527	−	0.776689i	0.987575	+	0.157151i	$0.0502308\pi$
$740$			17.1767i			0.631429i
$741$	5.45703	+	7.83841i	0.200469	+	0.287951i
$742$	−28.2365			−1.03659
$743$	6.55547	+	11.3544i	0.240497	+	0.416553i	0.960856	−	0.277049i	$-0.0893563\pi$
$743$	6.55547	+	11.3544i	0.240497	+	0.416553i	−0.720359	+	0.693601i	$0.756023\pi$
$744$	11.4029	+	19.7503i	0.418049	+	0.724082i
$745$	−13.6948	−	7.90671i	−0.501740	−	0.289680i
$746$	−11.1789	−	19.3624i	−0.409288	−	0.708908i
$747$	−16.5676	−	9.56533i	−0.606178	−	0.349977i
$748$	−0.711117	−	1.97988i	−0.0260010	−	0.0723915i
$749$		−	29.1797i		−	1.06620i
$750$	−15.8924	−	9.17551i	−0.580310	−	0.335042i
$751$	−8.72509	−	5.03743i	−0.318383	−	0.183819i	0.332289	−	0.943178i	$-0.392179\pi$
$751$	−8.72509	−	5.03743i	−0.318383	−	0.183819i	−0.650672	+	0.759359i	$0.725513\pi$
$752$	−0.204127			−0.00744373
$753$		−	19.3816i		−	0.706305i
$754$	−3.81805	+	6.61306i	−0.139045	+	0.240833i
$755$	21.0682	+	36.4913i	0.766752	+	1.32805i
$756$	17.6811	−	30.6245i	0.643054	−	1.11380i
$757$	−11.2096	−	19.4156i	−0.407419	−	0.705670i	0.587181	−	0.809456i	$-0.300238\pi$
$757$	−11.2096	−	19.4156i	−0.407419	−	0.705670i	−0.994600	+	0.103785i	$0.966904\pi$
$758$	6.96267	−	4.01990i	0.252896	−	0.146009i
$759$	−16.3167	−	45.4285i	−0.592257	−	1.64895i
$760$	13.5497	+	6.36291i	0.491499	+	0.230807i
$761$			16.8910i			0.612298i	0.951984	+	0.306149i	$0.0990406\pi$
$761$			16.8910i			0.612298i	−0.951984	+	0.306149i	$0.900959\pi$
$762$	29.2217	−	16.8712i	1.05859	−	0.611178i
$763$	16.8773	−	9.74412i	0.611000	−	0.352761i
$764$	4.76153	−	8.24720i	0.172266	−	0.298373i
$765$	11.0824	−	6.39844i	0.400686	−	0.231336i
$766$	−1.35811	−	0.784105i	−0.0490705	−	0.0283309i
$767$		−	1.55968i		−	0.0563168i
$768$			2.97905i			0.107497i
$769$	−39.0784	−	22.5619i	−1.40920	−	0.813604i	−0.413892	−	0.910326i	$-0.635831\pi$
$769$	−39.0784	−	22.5619i	−1.40920	−	0.813604i	−0.995311	+	0.0967223i	$0.969164\pi$
$770$	−46.2815	−	8.36332i	−1.66787	−	0.301393i
$771$	−22.6292			−0.814969
$772$	−3.16579			−0.113939
$773$	17.1073	+	9.87688i	0.615305	+	0.355247i	0.775039	−	0.631913i	$-0.217730\pi$
$773$	17.1073	+	9.87688i	0.615305	+	0.355247i	−0.159734	+	0.987160i	$0.551064\pi$
$774$	40.7467	−	23.5251i	1.46461	−	0.845594i
$775$	45.0407	+	26.0042i	1.61791	+	0.934100i
$776$	−0.135282	+	0.0781049i	−0.00485633	+	0.00280380i
$777$	−53.2827	+	30.7628i	−1.91151	+	1.10361i
$778$	14.5560			0.521859
$779$	−37.0855	−	17.4153i	−1.32872	−	0.623967i
$780$			7.52477i			0.269430i
$781$	−4.41846	+	5.22057i	−0.158105	+	0.186807i
$782$	−2.68363	+	1.54940i	−0.0959666	+	0.0554063i
$783$	76.9994	+	44.4556i	2.75173	+	1.58871i
$784$	5.02503	+	8.70360i	0.179465	+	0.310843i
$785$	−26.2557	+	45.4763i	−0.937108	+	1.62312i
$786$	0.466878			0.0166530
$787$	−27.7256			−0.988312			−0.494156	−	0.869373i	$-0.664523\pi$
$787$	−27.7256			−0.988312			−0.494156	+	0.869373i	$0.664523\pi$
$788$	−11.2625	−	6.50240i	−0.401209	−	0.231638i
$789$	−13.5597	+	23.4861i	−0.482738	+	0.836127i
$790$	58.0801			2.06640
$791$	−19.0499			−0.677336
$792$	3.46480	−	19.1737i	0.123116	−	0.681309i
$793$	0.402762	−	0.232535i	0.0143025	−	0.00825756i
$794$	14.6884	−	25.4411i	0.521272	−	0.902870i
$795$	−34.9801	−	60.5873i	−1.24062	−	2.14881i
$796$	−10.1712	−	17.6170i	−0.360508	−	0.624419i
$797$			10.0338i			0.355417i	0.984083	+	0.177709i	$0.0568684\pi$
$797$			10.0338i			0.355417i	−0.984083	+	0.177709i	$0.943132\pi$
$798$	4.52897	+	53.4272i	0.160324	+	1.89130i
$799$		−	0.129476i		−	0.00458054i
$800$	3.39686	+	5.88354i	0.120097	+	0.208015i
$801$	−56.3531	+	32.5355i	−1.99114	+	1.14959i
$802$	23.3032	+	13.4541i	0.822864	+	0.475081i
$803$	2.77226	−	3.27552i	0.0978310	−	0.115591i
$804$	−16.0200	+	27.7474i	−0.564981	+	0.978576i
$805$			69.2773i			2.44170i
$806$		−	5.63062i		−	0.198330i
$807$	−32.3079	+	55.9588i	−1.13729	+	1.96984i
$808$	6.12946	+	3.53884i	0.215634	+	0.124496i
$809$			27.0058i			0.949473i	0.880128	+	0.474736i	$0.157457\pi$
$809$			27.0058i			0.949473i	−0.880128	+	0.474736i	$0.842543\pi$
$810$	27.0900			0.951845
$811$	11.5563	−	20.0161i	0.405797	−	0.702861i	−0.588617	−	0.808412i	$-0.700327\pi$
$811$	11.5563	−	20.0161i	0.405797	−	0.702861i	0.994414	+	0.105551i	$0.0336606\pi$
$812$	−37.1257	+	21.4345i	−1.30286	+	0.752205i
$813$	−16.1902	+	28.0423i	−0.567816	+	0.983486i
$814$	−10.7168	+	12.6623i	−0.375624	+	0.443813i
$815$	12.9457	+	22.4226i	0.453468	+	0.785430i
$816$	−1.88959			−0.0661489
$817$	−14.8390	+	31.5993i	−0.519151	+	1.10552i
$818$	−7.60669			−0.265962
$819$	−15.4515	+	8.92095i	−0.539921	+	0.311723i
$820$	−16.1397	−	27.9548i	−0.563623	−	0.976223i
$821$	−3.39258	−	1.95871i	−0.118402	−	0.0683594i	0.439629	−	0.898179i	$-0.355110\pi$
$821$	−3.39258	−	1.95871i	−0.118402	−	0.0683594i	−0.558031	+	0.829820i	$0.688443\pi$
$822$	12.4145	−	7.16751i	0.433005	−	0.249996i
$823$	−2.98812	+	5.17557i	−0.104159	+	0.180409i	−0.913394	−	0.407076i	$-0.866548\pi$
$823$	−2.98812	+	5.17557i	−0.104159	+	0.180409i	0.809235	+	0.587485i	$0.199882\pi$
$824$		−	11.9269i		−	0.415495i
$825$	−22.6901	−	63.1734i	−0.789969	−	2.19942i
$826$	4.37803	−	7.58296i	0.152331	−	0.263845i
$827$	−0.687493	+	1.19077i	−0.0239065	+	0.0414073i	−0.877731	−	0.479153i	$-0.840944\pi$
$827$	−0.687493	+	1.19077i	−0.0239065	+	0.0414073i	0.853825	+	0.520561i	$0.174277\pi$
$828$	−28.7006			−0.997414
$829$		−	26.3859i		−	0.916419i	−0.888844	−	0.458210i	$-0.848491\pi$
$829$		−	26.3859i		−	0.916419i	0.888844	−	0.458210i	$-0.151509\pi$
$830$	9.68496	+	5.59161i	0.336170	+	0.194088i
$831$	−34.9541	−	60.5423i	−1.21255	−	2.10019i
$832$	0.367756	−	0.636973i	0.0127497	−	0.0220831i
$833$	−5.52064	+	3.18734i	−0.191279	+	0.110435i
$834$	−12.9957	−	22.5093i	−0.450006	−	0.779433i
$835$	17.7834			0.615419
$836$	6.01861	+	13.1444i	0.208158	+	0.454610i
$837$	−65.5603			−2.26610
$838$	0.472004	+	0.817535i	0.0163051	+	0.0282413i
$839$	12.1495	−	7.01452i	0.419448	−	0.242168i	−0.275393	−	0.961332i	$-0.588808\pi$
$839$	12.1495	−	7.01452i	0.419448	−	0.242168i	0.694841	+	0.719163i	$0.255475\pi$
$840$	−21.1221	+	36.5845i	−0.728780	+	1.26228i
$841$	−39.3930	−	68.2307i	−1.35838	−	2.35278i
$842$	−2.12809	−	1.22866i	−0.0733390	−	0.0423423i
$843$		−	33.8507i		−	1.16588i
$844$	−17.6960			−0.609120
$845$	−21.3934	+	37.0544i	−0.735955	+	1.27471i
$846$	0.599595	−	1.03853i	0.0206145	−	0.0357053i
$847$	−28.8996	−	35.0409i	−0.993003	−	1.20402i
$848$			6.83829i			0.234828i
$849$	18.5759	−	32.1744i	0.637523	−	1.10422i
$850$	−3.73189	+	2.15461i	−0.128003	+	0.0739025i
$851$	21.1616	+	12.2176i	0.725410	+	0.418815i
$852$	3.07163	+	5.32021i	0.105232	+	0.182267i
$853$	−18.5660	+	10.7191i	−0.635689	+	0.367015i	−0.782952	−	0.622082i	$-0.786287\pi$
$853$	−18.5660	+	10.7191i	−0.635689	+	0.367015i	0.147263	+	0.989097i	$0.452954\pi$
$854$	2.61090			0.0893433
$855$	−72.1728	+	50.2461i	−2.46826	+	1.71838i
$856$	−7.06672			−0.241536
$857$	4.06824	+	7.04639i	0.138968	+	0.240700i	0.927106	−	0.374798i	$-0.122288\pi$
$857$	4.06824	+	7.04639i	0.138968	+	0.240700i	−0.788138	+	0.615499i	$0.788955\pi$
$858$	−4.69482	+	5.54709i	−0.160278	+	0.189375i
$859$	−4.87037	+	8.43573i	−0.166175	+	0.287823i	−0.937072	−	0.349136i	$-0.886475\pi$
$859$	−4.87037	+	8.43573i	−0.166175	+	0.287823i	0.770897	+	0.636960i	$0.219808\pi$
$860$	−23.8194	+	13.7521i	−0.812234	+	0.468943i
$861$	57.8110	−	100.132i	1.97019	−	3.41247i
$862$	11.8214			0.402639
$863$		−	13.0390i		−	0.443852i	−0.975063	−	0.221926i	$-0.928766\pi$
$863$		−	13.0390i		−	0.443852i	0.975063	−	0.221926i	$-0.0712344\pi$
$864$	−7.41662	−	4.28199i	−0.252318	−	0.145676i
$865$	11.0455	−	19.1313i	0.375557	−	0.650484i
$866$			1.50541i			0.0511560i
$867$			49.4453i			1.67925i
$868$	15.8052	−	27.3753i	0.536462	−	0.929179i
$869$	42.8153	+	36.2370i	1.45241	+	1.22926i
$870$	−91.9846	−	53.1073i	−3.11857	−	1.80051i
$871$	6.85071	−	3.95526i	0.232127	−	0.134019i
$872$	−2.35983	−	4.08734i	−0.0799138	−	0.138415i
$873$		−	0.917691i		−	0.0310591i
$874$	17.4768	−	12.1672i	0.591162	−	0.411562i
$875$			25.4358i			0.859887i
$876$	−1.92722	−	3.33804i	−0.0651147	−	0.112782i
$877$	8.53286	+	14.7794i	0.288134	+	0.499063i	0.973364	−	0.229263i	$-0.0736317\pi$
$877$	8.53286	+	14.7794i	0.288134	+	0.499063i	−0.685230	+	0.728327i	$0.740298\pi$
$878$	−16.0679	+	27.8305i	−0.542267	+	0.939234i
$879$	69.6854	−	40.2329i	2.35043	−	1.35702i
$880$	−2.02542	+	11.2084i	−0.0682770	+	0.377836i
$881$	−5.88549			−0.198287			−0.0991437	−	0.995073i	$-0.531610\pi$
$881$	−5.88549			−0.198287			−0.0991437	+	0.995073i	$0.531610\pi$
$882$	−59.0414			−1.98803
$883$	23.8598	−	41.3263i	0.802945	−	1.39074i	−0.114725	−	0.993397i	$-0.536599\pi$
$883$	23.8598	−	41.3263i	0.802945	−	1.39074i	0.917670	−	0.397344i	$-0.130068\pi$
$884$	0.404028	+	0.233265i	0.0135889	+	0.00784557i
$885$	21.6945			0.729251
$886$	−41.0945			−1.38060
$887$	7.07336	−	12.2514i	0.237500	−	0.411362i	−0.722496	−	0.691375i	$-0.757005\pi$
$887$	7.07336	−	12.2514i	0.237500	−	0.411362i	0.959996	+	0.280012i	$0.0903386\pi$
$888$	7.45011	+	12.9040i	0.250009	+	0.433029i
$889$	−40.5034	−	23.3846i	−1.35844	−	0.784296i
$890$	32.9424	−	19.0193i	1.10423	−	0.637529i
$891$	19.9701	+	16.9018i	0.669024	+	0.566232i
$892$		−	16.9639i		−	0.567995i
$893$	0.0751551	+	0.886588i	0.00251497	+	0.0296685i
$894$	−13.7176			−0.458785
$895$	49.6659	−	28.6746i	1.66015	−	0.958486i
$896$	3.57597	−	2.06459i	0.119465	−	0.0689730i
$897$	9.27045	+	5.35230i	0.309531	+	0.178708i
$898$	−7.30745	+	4.21896i	−0.243853	+	0.140788i
$899$	68.8300	+	39.7390i	2.29561	+	1.32537i
$900$	−39.9113			−1.33038
$901$	−4.33748			−0.144503
$902$	5.54358	−	30.6774i	0.184581	−	1.02145i
$903$	−85.3189	−	49.2589i	−2.83924	−	1.63923i
$904$			4.61349i			0.153442i
$905$		−	4.08087i		−	0.135653i
$906$	31.6549	+	18.2760i	1.05166	+	0.607178i
$907$	−22.5638	+	13.0272i	−0.749219	+	0.432562i	−0.825412	−	0.564531i	$-0.809057\pi$
$907$	−22.5638	+	13.0272i	−0.749219	+	0.432562i	0.0761925	+	0.997093i	$0.475724\pi$
$908$	−9.96521	+	17.2602i	−0.330707	+	0.572801i
$909$	−36.0089	+	20.7898i	−1.19434	+	0.689553i
$910$	9.03253	−	5.21493i	0.299425	−	0.172873i
$911$			9.90289i			0.328097i	0.986452	+	0.164049i	$0.0524554\pi$
$911$			9.90289i			0.328097i	−0.986452	+	0.164049i	$0.947545\pi$
$912$	12.9390	−	1.09682i	0.428452	−	0.0363194i
$913$	3.65084	+	10.1646i	0.120825	+	0.336399i
$914$	−32.1597	+	18.5674i	−1.06375	+	0.614155i
$915$	3.23446	+	5.60224i	0.106928	+	0.185204i
$916$	−4.98787	+	8.63924i	−0.164804	+	0.285448i
$917$	−0.323563	−	0.560427i	−0.0106850	−	0.0185069i
$918$	2.71604	−	4.70431i	0.0896425	−	0.155265i
$919$		−	15.2439i		−	0.502849i	−0.967877	−	0.251425i	$-0.919101\pi$
$919$		−	15.2439i		−	0.502849i	0.967877	−	0.251425i	$-0.0808991\pi$
$920$	16.7775			0.553139
$921$	37.2258	+	21.4923i	1.22663	+	0.708197i
$922$	−3.51316	−	2.02833i	−0.115700	−	0.0667994i
$923$		−	1.51674i		−	0.0499241i
$924$	−38.3963	+	13.7909i	−1.26314	+	0.453686i
$925$	29.4275	+	16.9900i	0.967571	+	0.558627i
$926$	−11.3996	−	19.7446i	−0.374613	−	0.648848i
$927$	60.6803	+	35.0338i	1.99300	+	1.15066i
$928$	5.19100	+	8.99108i	0.170403	+	0.295147i
$929$	−0.0461593	−	0.0799502i	−0.00151444	−	0.00262308i	0.865267	−	0.501311i	$-0.167149\pi$
$929$	−0.0461593	−	0.0799502i	−0.00151444	−	0.00262308i	−0.866782	+	0.498688i	$0.833815\pi$
$930$	78.3194			2.56819
$931$	35.9524	−	25.0298i	1.17829	−	0.820318i
$932$			2.00705i			0.0657430i
$933$	−30.3888	+	17.5450i	−0.994886	+	0.574398i
$934$	−16.1151	−	27.9122i	−0.527303	−	0.913316i
$935$	−7.10943	−	1.28471i	−0.232503	−	0.0420146i
$936$	2.16047	+	3.74204i	0.0706172	+	0.122313i
$937$	−20.6527	−	11.9238i	−0.674694	−	0.389535i	0.123159	−	0.992387i	$-0.460697\pi$
$937$	−20.6527	−	11.9238i	−0.674694	−	0.389535i	−0.797853	+	0.602852i	$0.794031\pi$
$938$	44.4096			1.45003
$939$		−	7.20572i		−	0.235150i
$940$	−0.350506	+	0.607094i	−0.0114322	+	0.0198012i
$941$	24.7278	−	42.8298i	0.806103	−	1.39621i	−0.109440	−	0.993993i	$-0.534906\pi$
$941$	24.7278	−	42.8298i	0.806103	−	1.39621i	0.915544	−	0.402218i	$-0.131761\pi$
$942$			45.5519i			1.48416i
$943$	−45.9201			−1.49536
$944$	−1.83644	−	1.06027i	−0.0597709	−	0.0345088i
$945$	−60.7203	−	105.171i	−1.97523	−	3.42120i
$946$	−26.1392	−	4.72351i	−0.849860	−	0.153574i
$947$	−10.3059	−	17.8503i	−0.334896	−	0.580056i	0.648569	−	0.761156i	$-0.275368\pi$
$947$	−10.3059	−	17.8503i	−0.334896	−	0.580056i	−0.983465	+	0.181099i	$0.942034\pi$
$948$	43.6325	−	25.1912i	1.41712	−	0.818173i
$949$			0.951642i			0.0308916i
$950$	24.3035	−	16.9199i	0.788508	−	0.548953i
$951$	72.5679			2.35317
$952$	1.30955	+	2.26821i	0.0424428	+	0.0735132i
$953$	−9.64182	−	16.7001i	−0.312329	−	0.540970i	0.666537	−	0.745472i	$-0.267776\pi$
$953$	−9.64182	−	16.7001i	−0.312329	−	0.540970i	−0.978866	+	0.204502i	$0.934443\pi$
$954$	−34.7910	−	20.0866i	−1.12640	−	0.650327i
$955$	−16.3520	−	28.3226i	−0.529139	−	0.916496i
$956$	5.01914	+	2.89780i	0.162330	+	0.0937215i
$957$	−34.6745	−	96.5400i	−1.12087	−	3.12070i
$958$		−	36.2329i		−	1.17063i
$959$	−17.2074	−	9.93467i	−0.555655	−	0.320807i
$960$	8.86000	+	5.11532i	0.285955	+	0.165096i
$961$	−27.6046			−0.890472
$962$		−	3.67879i		−	0.118609i
$963$	20.7576	−	35.9531i	0.668903	−	1.15857i
$964$	7.17589	+	12.4290i	0.231120	+	0.400311i
$965$	−5.43598	+	9.41539i	−0.174990	+	0.303092i
$966$	30.0478	+	52.0444i	0.966773	+	1.67450i
$967$	13.6347	−	7.87200i	0.438463	−	0.253147i	−0.264483	−	0.964390i	$-0.585201\pi$
$967$	13.6347	−	7.87200i	0.438463	−	0.253147i	0.702945	+	0.711244i	$0.251868\pi$
$968$	−8.48619	+	6.99890i	−0.272757	+	0.224953i
$969$	0.695708	+	8.20710i	0.0223494	+	0.263650i
$970$			0.536456i			0.0172246i
$971$	42.3187	−	24.4327i	1.35807	−	0.784084i	0.368709	−	0.929545i	$-0.379800\pi$
$971$	42.3187	−	24.4327i	1.35807	−	0.784084i	0.989364	+	0.145461i	$0.0464666\pi$
$972$	−1.89859	+	1.09615i	−0.0608974	+	0.0351591i
$973$	−18.0130	+	31.1994i	−0.577470	+	1.00021i
$974$	11.1736	−	6.45106i	0.358024	−	0.206705i
$975$	12.8916	+	7.44297i	0.412862	+	0.238366i
$976$		−	0.632307i		−	0.0202397i
$977$			18.8540i			0.603192i	0.953436	+	0.301596i	$0.0975194\pi$
$977$			18.8540i			0.603192i	−0.953436	+	0.301596i	$0.902481\pi$
$978$	19.4508	+	11.2299i	0.621969	+	0.359094i
$979$	36.1508	+	6.53265i	1.15539	+	0.208785i
$980$	34.5139			1.10251
$981$	27.7267			0.885245
$982$	−20.6492	−	11.9218i	−0.658943	−	0.380441i
$983$	−0.516306	+	0.298089i	−0.0164676	+	0.00950757i	−0.508211	−	0.861232i	$-0.669693\pi$
$983$	−0.516306	+	0.298089i	−0.0164676	+	0.00950757i	0.491744	+	0.870740i	$0.336360\pi$
$984$	−24.2498	−	14.0006i	−0.773055	−	0.446324i
$985$	−38.6776	+	22.3305i	−1.23237	+	0.711510i
$986$	−5.70298	+	3.29262i	−0.181620	+	0.104858i
$987$	−2.51096			−0.0799248
$988$	−2.90198	−	1.36276i	−0.0923242	−	0.0433553i
$989$			39.1270i			1.24417i
$990$	−51.0753	−	43.2279i	−1.62328	−	1.37387i
$991$	−29.9960	+	17.3182i	−0.952853	+	0.550130i	−0.893966	−	0.448135i	$-0.852089\pi$
$991$	−29.9960	+	17.3182i	−0.952853	+	0.550130i	−0.0588870	+	0.998265i	$0.518755\pi$
$992$	−6.62974	−	3.82768i	−0.210494	−	0.121529i
$993$	−5.08634	−	8.80980i	−0.161410	−	0.279571i
$994$	4.25749	−	7.37419i	0.135039	−	0.233895i
$995$	−69.8598			−2.21471
$996$	9.70106			0.307390
$997$	−35.5996	−	20.5534i	−1.12745	−	0.650934i	−0.184158	−	0.982897i	$-0.558956\pi$
$997$	−35.5996	−	20.5534i	−1.12745	−	0.650934i	−0.943293	+	0.331962i	$0.892289\pi$
$998$	−15.5326	+	26.9032i	−0.491674	+	0.851605i
$999$	−42.8341			−1.35521

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.h.b.373.10	yes	20
11.10	odd	2		418.2.h.a.373.10	yes	20
19.8	odd	6		418.2.h.a.65.10	✓	20
209.65	even	6	inner	418.2.h.b.65.10	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.h.a.65.10	✓	20	19.8	odd	6
418.2.h.a.373.10	yes	20	11.10	odd	2
418.2.h.b.65.10	yes	20	209.65	even	6	inner
418.2.h.b.373.10	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(2.57993 - 1.48952i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.71710 + 2.97410i) q^{5} +(2.57993 + 1.48952i) q^{6} -4.12917i q^{7} -1.00000 q^{8} +(2.93737 - 5.08767i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(2.57993 - 1.48952i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.71710 + 2.97410i) q^{5} +(2.57993 + 1.48952i) q^{6} -4.12917i q^{7} -1.00000 q^{8} +(2.93737 - 5.08767i) q^{9} +(-1.71710 + 2.97410i) q^{10} +(-3.12139 + 1.12112i) q^{11} +2.97905i q^{12} +(0.367756 - 0.636973i) q^{13} +(3.57597 - 2.06459i) q^{14} +(8.86000 + 5.11532i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.549314 - 0.317147i) q^{17} +5.87473 q^{18} +(-3.57734 + 2.49051i) q^{19} -3.43420 q^{20} +(-6.15050 - 10.6530i) q^{21} +(-2.53161 - 2.14265i) q^{22} +(-2.44271 + 4.23090i) q^{23} +(-2.57993 + 1.48952i) q^{24} +(-3.39686 + 5.88354i) q^{25} +0.735513 q^{26} -8.56397i q^{27} +(3.57597 + 2.06459i) q^{28} +(-5.19100 + 8.99108i) q^{29} +10.2306i q^{30} -7.65537i q^{31} +(0.500000 - 0.866025i) q^{32} +(-6.38305 + 7.54180i) q^{33} +(0.549314 + 0.317147i) q^{34} +(12.2806 - 7.09020i) q^{35} +(2.93737 + 5.08767i) q^{36} -5.00167i q^{37} +(-3.94552 - 1.85281i) q^{38} -2.19113i q^{39} +(-1.71710 - 2.97410i) q^{40} +(4.69970 + 8.14011i) q^{41} +(6.15050 - 10.6530i) q^{42} +(6.93593 - 4.00446i) q^{43} +(0.589780 - 3.26376i) q^{44} +20.1750 q^{45} -4.88543 q^{46} +(0.102063 - 0.176779i) q^{47} +(-2.57993 - 1.48952i) q^{48} -10.0501 q^{49} -6.79373 q^{50} +(0.944795 - 1.63643i) q^{51} +(0.367756 + 0.636973i) q^{52} +(-5.92214 - 3.41915i) q^{53} +(7.41662 - 4.28199i) q^{54} +(-8.69406 - 7.35828i) q^{55} +4.12917i q^{56} +(-5.51961 + 11.7539i) q^{57} -10.3820 q^{58} +(1.83644 - 1.06027i) q^{59} +(-8.86000 + 5.11532i) q^{60} +(0.547594 + 0.316154i) q^{61} +(6.62974 - 3.82768i) q^{62} +(-21.0079 - 12.1289i) q^{63} +1.00000 q^{64} +2.52590 q^{65} +(-9.72291 - 1.75698i) q^{66} +(9.31419 + 5.37755i) q^{67} +0.634293i q^{68} +14.5539i q^{69} +(12.2806 + 7.09020i) q^{70} +(1.78588 - 1.03108i) q^{71} +(-2.93737 + 5.08767i) q^{72} +(-1.12051 + 0.646925i) q^{73} +(4.33157 - 2.50083i) q^{74} +20.2389i q^{75} +(-0.368179 - 4.34332i) q^{76} +(4.62929 + 12.8888i) q^{77} +(1.89757 - 1.09556i) q^{78} +(-8.45613 - 14.6465i) q^{79} +(1.71710 - 2.97410i) q^{80} +(-3.94415 - 6.83146i) q^{81} +(-4.69970 + 8.14011i) q^{82} -3.25643i q^{83} +12.3010 q^{84} +(1.88645 + 1.08915i) q^{85} +(6.93593 + 4.00446i) q^{86} +30.9285i q^{87} +(3.12139 - 1.12112i) q^{88} +(-9.59246 - 5.53821i) q^{89} +(10.0875 + 17.4721i) q^{90} +(-2.63017 - 1.51853i) q^{91} +(-2.44271 - 4.23090i) q^{92} +(-11.4029 - 19.7503i) q^{93} +0.204127 q^{94} +(-13.5497 - 6.36291i) q^{95} -2.97905i q^{96} +(0.135282 - 0.0781049i) q^{97} +(-5.02503 - 8.70360i) q^{98} +(-3.46480 + 19.1737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9}+O(q^{10}) \) 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9	\( 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9} - 2 q^{10} + q^{11} + 5 q^{13} - 6 q^{14} + 12 q^{15} - 10 q^{16} + 6 q^{17} + 22 q^{18} - 18 q^{19} - 4 q^{20} - 14 q^{21} + 2 q^{22} - 4 q^{23} - 3 q^{24} - 20 q^{25} + 10 q^{26} - 6 q^{28} + 5 q^{29} + 10 q^{32} - 13 q^{33} + 6 q^{34} - 12 q^{35} + 11 q^{36} - 12 q^{38} - 2 q^{40} - q^{41} + 14 q^{42} + 3 q^{43} + q^{44} + 12 q^{45} - 8 q^{46} + q^{47} - 3 q^{48} + 8 q^{49} - 40 q^{50} - 12 q^{51} + 5 q^{52} - 24 q^{53} + 27 q^{54} - 2 q^{55} + 32 q^{57} + 10 q^{58} - 51 q^{59} - 12 q^{60} + 27 q^{61} + 12 q^{63} + 20 q^{64} - 8 q^{65} - 8 q^{66} + 27 q^{67} - 12 q^{70} + 33 q^{71} - 11 q^{72} - 9 q^{73} - 12 q^{74} + 6 q^{76} - 22 q^{77} - 24 q^{79} + 2 q^{80} + 12 q^{81} + q^{82} + 28 q^{84} - 12 q^{85} + 3 q^{86} - q^{88} + 21 q^{89} + 6 q^{90} + 12 q^{91} - 4 q^{92} - 10 q^{93} + 2 q^{94} - 24 q^{95} + 24 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) \) 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9 - 2 * q^10 + q^11 + 5 * q^13 - 6 * q^14 + 12 * q^15 - 10 * q^16 + 6 * q^17 + 22 * q^18 - 18 * q^19 - 4 * q^20 - 14 * q^21 + 2 * q^22 - 4 * q^23 - 3 * q^24 - 20 * q^25 + 10 * q^26 - 6 * q^28 + 5 * q^29 + 10 * q^32 - 13 * q^33 + 6 * q^34 - 12 * q^35 + 11 * q^36 - 12 * q^38 - 2 * q^40 - q^41 + 14 * q^42 + 3 * q^43 + q^44 + 12 * q^45 - 8 * q^46 + q^47 - 3 * q^48 + 8 * q^49 - 40 * q^50 - 12 * q^51 + 5 * q^52 - 24 * q^53 + 27 * q^54 - 2 * q^55 + 32 * q^57 + 10 * q^58 - 51 * q^59 - 12 * q^60 + 27 * q^61 + 12 * q^63 + 20 * q^64 - 8 * q^65 - 8 * q^66 + 27 * q^67 - 12 * q^70 + 33 * q^71 - 11 * q^72 - 9 * q^73 - 12 * q^74 + 6 * q^76 - 22 * q^77 - 24 * q^79 + 2 * q^80 + 12 * q^81 + q^82 + 28 * q^84 - 12 * q^85 + 3 * q^86 - q^88 + 21 * q^89 + 6 * q^90 + 12 * q^91 - 4 * q^92 - 10 * q^93 + 2 * q^94 - 24 * q^95 + 24 * q^97 + 4 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more