LMFDB - Embedded newform 185.2.e.b.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [185,2,Mod(26,185)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(185, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("185.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.e (of order $3$, 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:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 13 x^{12} - 16 x^{11} + 98 x^{10} - 116 x^{9} + 378 x^{8} - 264 x^{7} + 795 x^{6} + \cdots + 9 $ x^14 - 2x^13 + 13x^12 - 16x^11 + 98x^10 - 116x^9 + 378x^8 - 264x^7 + 795x^6 - 520x^5 + 927x^4 - 71x^3 + 94x^2 - 3*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.2
Root			$-0.795055 - 1.37708i$ of defining polynomial
Character	$\chi$	$=$	185.121
Dual form			185.2.e.b.26.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.795055 + 1.37708i) q^{2} +(0.779300 + 1.34979i) q^{3} +(-0.264225 - 0.457651i) q^{4} +(0.500000 + 0.866025i) q^{5} -2.47835 q^{6} +(0.801138 + 1.38761i) q^{7} -2.33993 q^{8} +(0.285383 - 0.494298i) q^{9} +O(q^{10})$	\(q+(-0.795055 + 1.37708i) q^{2} +(0.779300 + 1.34979i) q^{3} +(-0.264225 - 0.457651i) q^{4} +(0.500000 + 0.866025i) q^{5} -2.47835 q^{6} +(0.801138 + 1.38761i) q^{7} -2.33993 q^{8} +(0.285383 - 0.494298i) q^{9} -1.59011 q^{10} +1.84299 q^{11} +(0.411821 - 0.713295i) q^{12} +(-0.521158 - 0.902672i) q^{13} -2.54779 q^{14} +(-0.779300 + 1.34979i) q^{15} +(2.38882 - 4.13756i) q^{16} +(-1.34466 + 2.32902i) q^{17} +(0.453790 + 0.785987i) q^{18} +(-2.81353 - 4.87317i) q^{19} +(0.264225 - 0.457651i) q^{20} +(-1.24865 + 2.16273i) q^{21} +(-1.46528 + 2.53793i) q^{22} -0.721350 q^{23} +(-1.82350 - 3.15840i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.65740 q^{26} +5.56540 q^{27} +(0.423361 - 0.733283i) q^{28} -6.48864 q^{29} +(-1.23917 - 2.14631i) q^{30} +5.95711 q^{31} +(1.45856 + 2.52630i) q^{32} +(1.43624 + 2.48764i) q^{33} +(-2.13816 - 3.70340i) q^{34} +(-0.801138 + 1.38761i) q^{35} -0.301621 q^{36} +(5.93568 - 1.32956i) q^{37} +8.94764 q^{38} +(0.812277 - 1.40690i) q^{39} +(-1.16996 - 2.02644i) q^{40} +(4.09082 + 7.08551i) q^{41} +(-1.98550 - 3.43898i) q^{42} +8.15587 q^{43} +(-0.486963 - 0.843445i) q^{44} +0.570766 q^{45} +(0.573513 - 0.993354i) q^{46} -1.59011 q^{47} +7.44643 q^{48} +(2.21636 - 3.83884i) q^{49} +(-0.795055 - 1.37708i) q^{50} -4.19158 q^{51} +(-0.275406 + 0.477017i) q^{52} +(-1.37677 + 2.38463i) q^{53} +(-4.42480 + 7.66397i) q^{54} +(0.921493 + 1.59607i) q^{55} +(-1.87460 - 3.24691i) q^{56} +(4.38517 - 7.59533i) q^{57} +(5.15882 - 8.93534i) q^{58} +(0.453742 - 0.785904i) q^{59} +0.823642 q^{60} +(0.661854 + 1.14637i) q^{61} +(-4.73623 + 8.20339i) q^{62} +0.914524 q^{63} +4.91674 q^{64} +(0.521158 - 0.902672i) q^{65} -4.56756 q^{66} +(-1.54372 - 2.67380i) q^{67} +1.42117 q^{68} +(-0.562148 - 0.973669i) q^{69} +(-1.27390 - 2.20645i) q^{70} +(-5.16020 - 8.93772i) q^{71} +(-0.667775 + 1.15662i) q^{72} -11.9279 q^{73} +(-2.88828 + 9.23095i) q^{74} -1.55860 q^{75} +(-1.48681 + 2.57523i) q^{76} +(1.47649 + 2.55735i) q^{77} +(1.29161 + 2.23713i) q^{78} +(-1.30379 - 2.25823i) q^{79} +4.77764 q^{80} +(3.48096 + 6.02921i) q^{81} -13.0097 q^{82} +(-1.03286 + 1.78896i) q^{83} +1.31970 q^{84} -2.68933 q^{85} +(-6.48437 + 11.2313i) q^{86} +(-5.05660 - 8.75828i) q^{87} -4.31245 q^{88} +(-1.93696 + 3.35491i) q^{89} +(-0.453790 + 0.785987i) q^{90} +(0.835038 - 1.44633i) q^{91} +(0.190599 + 0.330127i) q^{92} +(4.64238 + 8.04083i) q^{93} +(1.26422 - 2.18970i) q^{94} +(2.81353 - 4.87317i) q^{95} +(-2.27331 + 3.93749i) q^{96} -2.70551 q^{97} +(3.52425 + 6.10418i) q^{98} +(0.525957 - 0.910984i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 7 q^{5} + 4 q^{6} + 2 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) $ 14 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 7 * q^5 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 5 * q^9	\( 14 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 7 q^{5} + 4 q^{6} + 2 q^{7} - 6 q^{8} - 5 q^{9} + 4 q^{10} - 10 q^{11} - 8 q^{12} + 6 q^{13} - 36 q^{14} + 2 q^{15} - 14 q^{16} - q^{17} - 4 q^{18} + 6 q^{19} + 8 q^{20} + 13 q^{21} - q^{22} + 12 q^{23} - 21 q^{24} - 7 q^{25} + 2 q^{26} + 22 q^{27} + 13 q^{28} - 12 q^{29} + 2 q^{30} - 8 q^{31} + 18 q^{32} + q^{33} - 11 q^{34} - 2 q^{35} - 8 q^{36} + 12 q^{37} + 16 q^{38} + 23 q^{39} - 3 q^{40} - 3 q^{41} + 29 q^{42} - 38 q^{43} + 25 q^{44} - 10 q^{45} + 10 q^{46} + 4 q^{47} - 20 q^{48} - 7 q^{49} + 2 q^{50} - 14 q^{51} + 46 q^{52} - 2 q^{53} + 23 q^{54} - 5 q^{55} + 19 q^{56} + 22 q^{57} - 12 q^{58} - 18 q^{59} - 16 q^{60} - 20 q^{61} - 21 q^{62} + 46 q^{63} + 50 q^{64} - 6 q^{65} - 42 q^{66} - 20 q^{67} + 110 q^{68} + 17 q^{69} - 18 q^{70} - 11 q^{71} - 29 q^{72} - 36 q^{73} - 66 q^{74} + 4 q^{75} + 40 q^{76} - q^{77} + 6 q^{78} + 23 q^{79} - 28 q^{80} + 29 q^{81} - 24 q^{82} - 9 q^{83} + 8 q^{84} - 2 q^{85} - 3 q^{86} - 43 q^{87} - 116 q^{88} - 16 q^{89} + 4 q^{90} + 12 q^{91} - 33 q^{92} + 25 q^{93} + 22 q^{94} - 6 q^{95} - 67 q^{96} - 62 q^{97} - 24 q^{98} + 4 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 7 * q^5 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 5 * q^9 + 4 * q^10 - 10 * q^11 - 8 * q^12 + 6 * q^13 - 36 * q^14 + 2 * q^15 - 14 * q^16 - q^17 - 4 * q^18 + 6 * q^19 + 8 * q^20 + 13 * q^21 - q^22 + 12 * q^23 - 21 * q^24 - 7 * q^25 + 2 * q^26 + 22 * q^27 + 13 * q^28 - 12 * q^29 + 2 * q^30 - 8 * q^31 + 18 * q^32 + q^33 - 11 * q^34 - 2 * q^35 - 8 * q^36 + 12 * q^37 + 16 * q^38 + 23 * q^39 - 3 * q^40 - 3 * q^41 + 29 * q^42 - 38 * q^43 + 25 * q^44 - 10 * q^45 + 10 * q^46 + 4 * q^47 - 20 * q^48 - 7 * q^49 + 2 * q^50 - 14 * q^51 + 46 * q^52 - 2 * q^53 + 23 * q^54 - 5 * q^55 + 19 * q^56 + 22 * q^57 - 12 * q^58 - 18 * q^59 - 16 * q^60 - 20 * q^61 - 21 * q^62 + 46 * q^63 + 50 * q^64 - 6 * q^65 - 42 * q^66 - 20 * q^67 + 110 * q^68 + 17 * q^69 - 18 * q^70 - 11 * q^71 - 29 * q^72 - 36 * q^73 - 66 * q^74 + 4 * q^75 + 40 * q^76 - q^77 + 6 * q^78 + 23 * q^79 - 28 * q^80 + 29 * q^81 - 24 * q^82 - 9 * q^83 + 8 * q^84 - 2 * q^85 - 3 * q^86 - 43 * q^87 - 116 * q^88 - 16 * q^89 + 4 * q^90 + 12 * q^91 - 33 * q^92 + 25 * q^93 + 22 * q^94 - 6 * q^95 - 67 * q^96 - 62 * q^97 - 24 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.795055	+	1.37708i	−0.562189	+	0.973740i	0.435116	+	0.900374i	$0.356707\pi$
$2$	−0.795055	+	1.37708i	−0.562189	+	0.973740i	−0.997305	+	0.0733653i	$0.976626\pi$
$3$	0.779300	+	1.34979i	0.449929	+	0.779300i	0.998381	−	0.0568821i	$-0.0181159\pi$
$3$	0.779300	+	1.34979i	0.449929	+	0.779300i	−0.548452	+	0.836182i	$0.684783\pi$
$4$	−0.264225	−	0.457651i	−0.132112	−	0.228826i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−2.47835			−1.01178
$7$	0.801138	+	1.38761i	0.302802	+	0.524468i	0.976769	−	0.214293i	$-0.0687447\pi$
$7$	0.801138	+	1.38761i	0.302802	+	0.524468i	−0.673968	+	0.738761i	$0.735411\pi$
$8$	−2.33993			−0.827289
$9$	0.285383	−	0.494298i	0.0951276	−	0.164766i
$10$	−1.59011			−0.502837
$11$	1.84299			0.555681			0.277841	−	0.960627i	$-0.410381\pi$
$11$	1.84299			0.555681			0.277841	+	0.960627i	$0.410381\pi$
$12$	0.411821	−	0.713295i	0.118882	−	0.205911i
$13$	−0.521158	−	0.902672i	−0.144543	−	0.250356i	0.784659	−	0.619927i	$-0.212838\pi$
$13$	−0.521158	−	0.902672i	−0.144543	−	0.250356i	−0.929202	+	0.369571i	$0.879505\pi$
$14$	−2.54779			−0.680927
$15$	−0.779300	+	1.34979i	−0.201214	+	0.348514i
$16$	2.38882	−	4.13756i	0.597205	−	1.03439i
$17$	−1.34466	+	2.32902i	−0.326129	+	0.564871i	−0.981740	−	0.190227i	$-0.939078\pi$
$17$	−1.34466	+	2.32902i	−0.326129	+	0.564871i	0.655612	+	0.755098i	$0.272411\pi$
$18$	0.453790	+	0.785987i	0.106959	+	0.185259i
$19$	−2.81353	−	4.87317i	−0.645468	−	1.11798i	−0.984193	−	0.177097i	$-0.943329\pi$
$19$	−2.81353	−	4.87317i	−0.645468	−	1.11798i	0.338726	−	0.940885i	$-0.390004\pi$
$20$	0.264225	−	0.457651i	0.0590825	−	0.102334i
$21$	−1.24865	+	2.16273i	−0.272479	+	0.471947i
$22$	−1.46528	+	2.53793i	−0.312398	+	0.541089i
$23$	−0.721350			−0.150412			−0.0752060	−	0.997168i	$-0.523961\pi$
$23$	−0.721350			−0.150412			−0.0752060	+	0.997168i	$0.523961\pi$
$24$	−1.82350	−	3.15840i	−0.372221	−	0.644706i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.65740			0.325042
$27$	5.56540			1.07106
$28$	0.423361	−	0.733283i	0.0800077	−	0.138577i
$29$	−6.48864			−1.20491			−0.602455	−	0.798153i	$-0.705811\pi$
$29$	−6.48864			−1.20491			−0.602455	+	0.798153i	$0.705811\pi$
$30$	−1.23917	−	2.14631i	−0.226241	−	0.391861i
$31$	5.95711			1.06993			0.534964	−	0.844875i	$-0.320325\pi$
$31$	5.95711			1.06993			0.534964	+	0.844875i	$0.320325\pi$
$32$	1.45856	+	2.52630i	0.257840	+	0.446591i
$33$	1.43624	+	2.48764i	0.250017	+	0.433043i
$34$	−2.13816	−	3.70340i	−0.366692	−	0.635129i
$35$	−0.801138	+	1.38761i	−0.135417	+	0.234549i
$36$	−0.301621			−0.0502702
$37$	5.93568	−	1.32956i	0.975819	−	0.218579i
$37$	5.93568	−	1.32956i	0.975819	−	0.218579i
$38$	8.94764			1.45150
$39$	0.812277	−	1.40690i	0.130068	−	0.225285i
$40$	−1.16996	−	2.02644i	−0.184987	−	0.320408i
$41$	4.09082	+	7.08551i	0.638879	+	1.10657i	0.985679	+	0.168632i	$0.0539350\pi$
$41$	4.09082	+	7.08551i	0.638879	+	1.10657i	−0.346800	+	0.937939i	$0.612732\pi$
$42$	−1.98550	−	3.43898i	−0.306369	−	0.530646i
$43$	8.15587			1.24376			0.621879	−	0.783113i	$-0.286369\pi$
$43$	8.15587			1.24376			0.621879	+	0.783113i	$0.286369\pi$
$44$	−0.486963	−	0.843445i	−0.0734124	−	0.127154i
$45$	0.570766			0.0850847
$46$	0.573513	−	0.993354i	0.0845599	−	0.146462i
$47$	−1.59011			−0.231941			−0.115971	−	0.993253i	$-0.536998\pi$
$47$	−1.59011			−0.231941			−0.115971	+	0.993253i	$0.536998\pi$
$48$	7.44643			1.07480
$49$	2.21636	−	3.83884i	0.316622	−	0.548406i
$50$	−0.795055	−	1.37708i	−0.112438	−	0.194748i
$51$	−4.19158			−0.586939
$52$	−0.275406	+	0.477017i	−0.0381919	+	0.0661503i
$53$	−1.37677	+	2.38463i	−0.189114	+	0.327554i	−0.944955	−	0.327200i	$-0.893895\pi$
$53$	−1.37677	+	2.38463i	−0.189114	+	0.327554i	0.755841	+	0.654755i	$0.227228\pi$
$54$	−4.42480	+	7.66397i	−0.602138	+	1.04293i
$55$	0.921493	+	1.59607i	0.124254	+	0.215214i
$56$	−1.87460	−	3.24691i	−0.250504	−	0.433886i
$57$	4.38517	−	7.59533i	0.580829	−	1.00603i
$58$	5.15882	−	8.93534i	0.677387	−	1.17327i
$59$	0.453742	−	0.785904i	0.0590722	−	0.102316i	−0.834977	−	0.550285i	$-0.814519\pi$
$59$	0.453742	−	0.785904i	0.0590722	−	0.102316i	0.894049	+	0.447969i	$0.147852\pi$
$60$	0.823642			0.106332
$61$	0.661854	+	1.14637i	0.0847417	+	0.146777i	0.905281	−	0.424813i	$-0.139660\pi$
$61$	0.661854	+	1.14637i	0.0847417	+	0.146777i	−0.820539	+	0.571590i	$0.806327\pi$
$62$	−4.73623	+	8.20339i	−0.601502	+	1.04183i
$63$	0.914524			0.115219
$64$	4.91674			0.614592
$65$	0.521158	−	0.902672i	0.0646417	−	0.111963i
$66$	−4.56756			−0.562227
$67$	−1.54372	−	2.67380i	−0.188595	−	0.326656i	0.756187	−	0.654356i	$-0.227060\pi$
$67$	−1.54372	−	2.67380i	−0.188595	−	0.326656i	−0.944782	+	0.327699i	$0.893727\pi$
$68$	1.42117			0.172343
$69$	−0.562148	−	0.973669i	−0.0676747	−	0.117216i
$70$	−1.27390	−	2.20645i	−0.152260	−	0.263722i
$71$	−5.16020	−	8.93772i	−0.612403	−	1.06071i	−0.990834	−	0.135083i	$-0.956870\pi$
$71$	−5.16020	−	8.93772i	−0.612403	−	1.06071i	0.378432	−	0.925629i	$-0.376463\pi$
$72$	−0.667775	+	1.15662i	−0.0786980	+	0.136309i
$73$	−11.9279			−1.39606			−0.698029	−	0.716070i	$-0.745939\pi$
$73$	−11.9279			−1.39606			−0.698029	+	0.716070i	$0.745939\pi$
$74$	−2.88828	+	9.23095i	−0.335756	+	1.07308i
$75$	−1.55860			−0.179972
$76$	−1.48681	+	2.57523i	−0.170549	+	0.295399i
$77$	1.47649	+	2.55735i	0.168261	+	0.291437i
$78$	1.29161	+	2.23713i	0.146246	+	0.253305i
$79$	−1.30379	−	2.25823i	−0.146688	−	0.254071i	0.783314	−	0.621627i	$-0.213528\pi$
$79$	−1.30379	−	2.25823i	−0.146688	−	0.254071i	−0.930001	+	0.367556i	$0.880195\pi$
$80$	4.77764			0.534156
$81$	3.48096	+	6.02921i	0.386774	+	0.669912i
$82$	−13.0097			−1.43668
$83$	−1.03286	+	1.78896i	−0.113371	+	0.196364i	−0.917127	−	0.398594i	$-0.869498\pi$
$83$	−1.03286	+	1.78896i	−0.113371	+	0.196364i	0.803757	+	0.594958i	$0.202831\pi$
$84$	1.31970			0.143991
$85$	−2.68933			−0.291698
$86$	−6.48437	+	11.2313i	−0.699227	+	1.21110i
$87$	−5.05660	−	8.75828i	−0.542124	−	0.938986i
$88$	−4.31245			−0.459709
$89$	−1.93696	+	3.35491i	−0.205317	+	0.355620i	−0.950234	−	0.311538i	$-0.899156\pi$
$89$	−1.93696	+	3.35491i	−0.205317	+	0.355620i	0.744916	+	0.667158i	$0.232489\pi$
$90$	−0.453790	+	0.785987i	−0.0478337	+	0.0828504i
$91$	0.835038	−	1.44633i	0.0875358	−	0.151616i
$92$	0.190599	+	0.330127i	0.0198713	+	0.0344181i
$93$	4.64238	+	8.04083i	0.481392	+	0.833795i
$94$	1.26422	−	2.18970i	0.130395	−	0.225851i
$95$	2.81353	−	4.87317i	0.288662	−	0.499977i
$96$	−2.27331	+	3.93749i	−0.232019	+	0.401869i
$97$	−2.70551			−0.274703			−0.137351	−	0.990522i	$-0.543859\pi$
$97$	−2.70551			−0.274703			−0.137351	+	0.990522i	$0.543859\pi$
$98$	3.52425	+	6.10418i	0.356003	+	0.616615i
$99$	0.525957	−	0.910984i	0.0528606	−	0.0915573i
$100$	0.528450			0.0528450
$101$	3.47043			0.345321			0.172660	−	0.984981i	$-0.444764\pi$
$101$	3.47043			0.345321			0.172660	+	0.984981i	$0.444764\pi$
$102$	3.33254	−	5.77213i	0.329971	−	0.571526i
$103$	−19.6105			−1.93228			−0.966142	−	0.258011i	$-0.916933\pi$
$103$	−19.6105			−1.93228			−0.966142	+	0.258011i	$0.916933\pi$
$104$	1.21947	+	2.11219i	0.119579	+	0.207117i
$105$	−2.49731			−0.243712
$106$	−2.18921	−	3.79183i	−0.212635	−	0.368295i
$107$	−2.92895	−	5.07309i	−0.283152	−	0.490434i	0.689007	−	0.724754i	$-0.258047\pi$
$107$	−2.92895	−	5.07309i	−0.283152	−	0.490434i	−0.972159	+	0.234321i	$0.924713\pi$
$108$	−1.47052	−	2.54701i	−0.141501	−	0.245086i
$109$	−9.39783	+	16.2775i	−0.900149	+	1.55910i	−0.0728485	+	0.997343i	$0.523209\pi$
$109$	−9.39783	+	16.2775i	−0.900149	+	1.55910i	−0.827300	+	0.561760i	$0.810124\pi$
$110$	−2.93055			−0.279417
$111$	6.42030	+	6.97577i	0.609388	+	0.662111i
$112$	7.65510			0.723339
$113$	8.44276	−	14.6233i	0.794228	−	1.37564i	−0.129100	−	0.991632i	$-0.541209\pi$
$113$	8.44276	−	14.6233i	0.794228	−	1.37564i	0.923328	−	0.384012i	$-0.125458\pi$
$114$	6.97289	+	12.0774i	0.653071	+	1.13115i
$115$	−0.360675	−	0.624708i	−0.0336331	−	0.0582543i
$116$	1.71446	+	2.96953i	0.159184	+	0.275714i
$117$	−0.594918			−0.0550002
$118$	0.721500	+	1.24967i	0.0664195	+	0.115042i
$119$	−4.30904			−0.395009
$120$	1.82350	−	3.15840i	0.166462	−	0.288321i
$121$	−7.60340			−0.691218
$122$	−2.10484			−0.190563
$123$	−6.37596	+	11.0435i	−0.574901	+	0.995757i
$124$	−1.57402	−	2.72628i	−0.141351	−	0.244827i
$125$	−1.00000			−0.0894427
$126$	−0.727097	+	1.25937i	−0.0647749	+	0.112193i
$127$	4.76328	−	8.25024i	0.422673	−	0.732091i	−0.573527	−	0.819186i	$-0.694425\pi$
$127$	4.76328	−	8.25024i	0.422673	−	0.732091i	0.996200	+	0.0870959i	$0.0277587\pi$
$128$	−6.82620	+	11.8233i	−0.603356	+	1.04504i
$129$	6.35587	+	11.0087i	0.559603	+	0.969261i
$130$	0.828698	+	1.43535i	0.0726817	+	0.125888i
$131$	9.55811	−	16.5551i	0.835096	−	1.44643i	−0.0588557	−	0.998267i	$-0.518745\pi$
$131$	9.55811	−	16.5551i	0.835096	−	1.44643i	0.893952	−	0.448163i	$-0.147921\pi$
$132$	0.758981	−	1.31459i	0.0660608	−	0.114421i
$133$	4.50805	−	7.80817i	0.390897	−	0.677054i
$134$	4.90936			0.424104
$135$	2.78270	+	4.81977i	0.239497	+	0.414820i
$136$	3.14641	−	5.44975i	0.269803	−	0.467312i
$137$	−10.0988			−0.862802			−0.431401	−	0.902160i	$-0.641981\pi$
$137$	−10.0988			−0.862802			−0.431401	+	0.902160i	$0.641981\pi$
$138$	1.78776			0.152184
$139$	8.40420	−	14.5565i	0.712835	−	1.23467i	−0.250954	−	0.967999i	$-0.580744\pi$
$139$	8.40420	−	14.5565i	0.712835	−	1.23467i	0.963789	−	0.266667i	$-0.0859224\pi$
$140$	0.846722			0.0715611
$141$	−1.23917	−	2.14631i	−0.104357	−	0.180752i
$142$	16.4106			1.37714
$143$	−0.960487	−	1.66361i	−0.0803199	−	0.139118i
$144$	−1.36346	−	2.36158i	−0.113621	−	0.196798i
$145$	−3.24432	−	5.61932i	−0.269426	−	0.466659i
$146$	9.48336	−	16.4257i	0.784848	−	1.35940i
$147$	6.90883			0.569830
$148$	−2.17683	−	2.36517i	−0.178934	−	0.194415i
$149$	2.25525			0.184757			0.0923787	−	0.995724i	$-0.470553\pi$
$149$	2.25525			0.184757			0.0923787	+	0.995724i	$0.470553\pi$
$150$	1.23917	−	2.14631i	0.101178	−	0.175246i
$151$	5.34111	+	9.25107i	0.434653	+	0.752842i	0.997267	−	0.0738780i	$-0.0235375\pi$
$151$	5.34111	+	9.25107i	0.434653	+	0.752842i	−0.562614	+	0.826720i	$0.690204\pi$
$152$	6.58345	+	11.4029i	0.533988	+	0.924895i
$153$	0.767487	+	1.32933i	0.0620477	+	0.107470i
$154$	−4.69555			−0.378378
$155$	2.97856	+	5.15901i	0.239243	+	0.414382i
$156$	−0.858495			−0.0687346
$157$	3.84116	−	6.65309i	0.306558	−	0.530974i	−0.671049	−	0.741413i	$-0.734156\pi$
$157$	3.84116	−	6.65309i	0.306558	−	0.530974i	0.977607	+	0.210439i	$0.0674893\pi$
$158$	4.14634			0.329865
$159$	−4.29166			−0.340351
$160$	−1.45856	+	2.52630i	−0.115309	+	0.199722i
$161$	−0.577901	−	1.00095i	−0.0455450	−	0.0788862i
$162$	−11.0702			−0.869760
$163$	−2.31262	+	4.00558i	−0.181139	+	0.313741i	−0.942269	−	0.334858i	$-0.891312\pi$
$163$	−2.31262	+	4.00558i	−0.181139	+	0.313741i	0.761130	+	0.648599i	$0.224645\pi$
$164$	2.16180	−	3.74434i	0.168808	−	0.292384i
$165$	−1.43624	+	2.48764i	−0.111811	+	0.193662i
$166$	−1.64236	−	2.84464i	−0.127471	−	0.220787i
$167$	−3.29702	−	5.71060i	−0.255131	−	0.441900i	0.709800	−	0.704403i	$-0.248785\pi$
$167$	−3.29702	−	5.71060i	−0.255131	−	0.441900i	−0.964931	+	0.262503i	$0.915452\pi$
$168$	2.92176	−	5.06063i	0.225418	−	0.390436i
$169$	5.95679	−	10.3175i	0.458215	−	0.793651i
$170$	2.13816	−	3.70340i	0.163990	−	0.284038i
$171$	−3.21173			−0.245607
$172$	−2.15499	−	3.73254i	−0.164316	−	0.284604i
$173$	−5.20073	+	9.00792i	−0.395404	+	0.684860i	−0.993153	−	0.116824i	$-0.962729\pi$
$173$	−5.20073	+	9.00792i	−0.395404	+	0.684860i	0.597749	+	0.801684i	$0.296062\pi$
$174$	16.0811			1.21910
$175$	−1.60228			−0.121121
$176$	4.40256	−	7.62546i	0.331856	−	0.574791i
$177$	1.41441			0.106313
$178$	−3.07998	−	5.33468i	−0.230854	−	0.399851i
$179$	14.8927			1.11313			0.556567	−	0.830803i	$-0.312118\pi$
$179$	14.8927			1.11313			0.556567	+	0.830803i	$0.312118\pi$
$180$	−0.150811	−	0.261211i	−0.0112408	−	0.0194696i
$181$	10.8274	+	18.7536i	0.804793	+	1.39394i	0.916431	+	0.400193i	$0.131057\pi$
$181$	10.8274	+	18.7536i	0.804793	+	1.39394i	−0.111638	+	0.993749i	$0.535610\pi$
$182$	1.32780	+	2.29982i	0.0984233	+	0.170474i
$183$	−1.03157	+	1.78672i	−0.0762556	+	0.132078i
$184$	1.68791			0.124434
$185$	4.11927	+	4.47567i	0.302855	+	0.329058i
$186$	−14.7638			−1.08253
$187$	−2.47820	+	4.29236i	−0.181224	+	0.313888i
$188$	0.420147	+	0.727716i	0.0306424	+	0.0530741i
$189$	4.45865	+	7.72261i	0.324319	+	0.561737i
$190$	4.47382	+	7.74888i	0.324565	+	0.562163i
$191$	−22.3271			−1.61553			−0.807767	−	0.589501i	$-0.799324\pi$
$191$	−22.3271			−1.61553			−0.807767	+	0.589501i	$0.799324\pi$
$192$	3.83161	+	6.63655i	0.276523	+	0.478952i
$193$	−19.8631			−1.42978			−0.714889	−	0.699238i	$-0.753523\pi$
$193$	−19.8631			−1.42978			−0.714889	+	0.699238i	$0.753523\pi$
$194$	2.15103	−	3.72569i	0.154435	−	0.267489i
$195$	1.62455			0.116337
$196$	−2.34247			−0.167319
$197$	−5.36347	+	9.28980i	−0.382131	+	0.661871i	−0.991367	−	0.131119i	$-0.958143\pi$
$197$	−5.36347	+	9.28980i	−0.382131	+	0.661871i	0.609235	+	0.792989i	$0.291476\pi$
$198$	0.836329	+	1.44856i	0.0594353	+	0.102945i
$199$	4.23810			0.300431			0.150215	−	0.988653i	$-0.452003\pi$
$199$	4.23810			0.300431			0.150215	+	0.988653i	$0.452003\pi$
$200$	1.16996	−	2.02644i	0.0827289	−	0.143291i
$201$	2.40604	−	4.16738i	0.169709	−	0.293944i
$202$	−2.75918	+	4.77905i	−0.194135	+	0.336252i
$203$	−5.19829	−	9.00371i	−0.364849	−	0.631936i
$204$	1.10752	+	1.91828i	0.0775420	+	0.134307i
$205$	−4.09082	+	7.08551i	−0.285715	+	0.494874i
$206$	15.5915	−	27.0052i	1.08631	−	1.88154i
$207$	−0.205861	+	0.356562i	−0.0143083	+	0.0247827i
$208$	−4.97981			−0.345288
$209$	−5.18529	−	8.98119i	−0.358674	−	0.621242i
$210$	1.98550	−	3.43898i	0.137012	−	0.237312i
$211$	−17.4674			−1.20251			−0.601253	−	0.799059i	$-0.705332\pi$
$211$	−17.4674			−1.20251			−0.601253	+	0.799059i	$0.705332\pi$
$212$	1.45511			0.0999371
$213$	8.04268	−	13.9303i	0.551075	−	0.954491i
$214$	9.31470			0.636740
$215$	4.07794	+	7.06319i	0.278113	+	0.481706i
$216$	−13.0226			−0.886077
$217$	4.77247	+	8.26615i	0.323976	+	0.561143i
$218$	−14.9436	−	25.8830i	−1.01211	−	1.75302i
$219$	−9.29543	−	16.1002i	−0.628127	−	1.08795i
$220$	0.486963	−	0.843445i	0.0328310	−	0.0568650i
$221$	2.80313			0.188559
$222$	−14.7107	+	3.29511i	−0.987315	+	0.221154i
$223$	−17.2281			−1.15368			−0.576840	−	0.816857i	$-0.695714\pi$
$223$	−17.2281			−1.15368			−0.576840	+	0.816857i	$0.695714\pi$
$224$	−2.33702	+	4.04783i	−0.156148	+	0.270457i
$225$	0.285383	+	0.494298i	0.0190255	+	0.0329532i
$226$	13.4249	+	23.2526i	0.893012	+	1.54674i
$227$	−9.63418	−	16.6869i	−0.639443	−	1.10755i	−0.985555	−	0.169354i	$-0.945832\pi$
$227$	−9.63418	−	16.6869i	−0.639443	−	1.10755i	0.346112	−	0.938193i	$-0.387502\pi$
$228$	−4.63468			−0.306939
$229$	12.9109	+	22.3623i	0.853175	+	1.47774i	0.878328	+	0.478059i	$0.158659\pi$
$229$	12.9109	+	22.3623i	0.853175	+	1.47774i	−0.0251529	+	0.999684i	$0.508007\pi$
$230$	1.14703			0.0756327
$231$	−2.30125	+	3.98588i	−0.151411	+	0.262252i
$232$	15.1829			0.996808
$233$	22.1076			1.44832			0.724158	−	0.689634i	$-0.242228\pi$
$233$	22.1076			1.44832			0.724158	+	0.689634i	$0.242228\pi$
$234$	0.472992	−	0.819247i	0.0309205	−	0.0535559i
$235$	−0.795055	−	1.37708i	−0.0518637	−	0.0898305i
$236$	−0.479560			−0.0312167
$237$	2.03209	−	3.51968i	0.131998	−	0.228628i
$238$	3.42592	−	5.93387i	0.222070	−	0.384636i
$239$	9.49957	−	16.4537i	0.614476	−	1.06430i	−0.376000	−	0.926620i	$-0.622701\pi$
$239$	9.49957	−	16.4537i	0.614476	−	1.06430i	0.990476	−	0.137684i	$-0.0439658\pi$
$240$	3.72322	+	6.44880i	0.240333	+	0.416268i
$241$	−2.03802	−	3.52995i	−0.131280	−	0.227384i	0.792890	−	0.609365i	$-0.208575\pi$
$241$	−2.03802	−	3.52995i	−0.131280	−	0.227384i	−0.924170	+	0.381981i	$0.875242\pi$
$242$	6.04512	−	10.4705i	0.388595	−	0.673067i
$243$	2.92266	−	5.06220i	0.187489	−	0.324740i
$244$	0.349757	−	0.605797i	0.0223909	−	0.0387821i
$245$	4.43271			0.283196
$246$	−10.1385	−	17.5604i	−0.646405	−	1.11961i
$247$	−2.93258	+	5.07939i	−0.186596	+	0.323194i
$248$	−13.9392			−0.885140
$249$	−3.21962			−0.204035
$250$	0.795055	−	1.37708i	0.0502837	−	0.0870939i
$251$	10.3091			0.650707			0.325354	−	0.945592i	$-0.394517\pi$
$251$	10.3091			0.650707			0.325354	+	0.945592i	$0.394517\pi$
$252$	−0.241640	−	0.418533i	−0.0152219	−	0.0263651i
$253$	−1.32944			−0.0835811
$254$	7.57414	+	13.1188i	0.475244	+	0.823146i
$255$	−2.09579	−	3.63002i	−0.131244	−	0.227321i
$256$	−5.93767	−	10.2843i	−0.371104	−	0.642771i
$257$	−14.4749	+	25.0713i	−0.902922	+	1.56391i	−0.0792388	+	0.996856i	$0.525249\pi$
$257$	−14.4749	+	25.0713i	−0.902922	+	1.56391i	−0.823683	+	0.567051i	$0.808084\pi$
$258$	−20.2131			−1.25841
$259$	6.60021	+	7.17125i	0.410117	+	0.445600i
$260$	−0.550812			−0.0341599
$261$	−1.85175	+	3.20732i	−0.114620	+	0.198528i
$262$	15.1985	+	26.3245i	0.938964	+	1.62633i
$263$	−3.88221	−	6.72419i	−0.239387	−	0.414631i	0.721151	−	0.692778i	$-0.243613\pi$
$263$	−3.88221	−	6.72419i	−0.239387	−	0.414631i	−0.960539	+	0.278146i	$0.910280\pi$
$264$	−3.36070	−	5.82089i	−0.206836	−	0.358251i
$265$	−2.75354			−0.169148
$266$	7.16829	+	12.4158i	0.439516	+	0.761264i
$267$	−6.03789			−0.369513
$268$	−0.815777	+	1.41297i	−0.0498315	+	0.0863107i
$269$	−14.9432			−0.911106			−0.455553	−	0.890209i	$-0.650558\pi$
$269$	−14.9432			−0.911106			−0.455553	+	0.890209i	$0.650558\pi$
$270$	−8.84959			−0.538569
$271$	−13.8617	+	24.0092i	−0.842039	+	1.45845i	0.0461285	+	0.998936i	$0.485312\pi$
$271$	−13.8617	+	24.0092i	−0.842039	+	1.45845i	−0.888168	+	0.459519i	$0.848022\pi$
$272$	6.42432	+	11.1272i	0.389531	+	0.674688i
$273$	2.60298			0.157540
$274$	8.02913	−	13.9069i	0.485058	−	0.840145i
$275$	−0.921493	+	1.59607i	−0.0555681	+	0.0962468i
$276$	−0.297067	+	0.514536i	−0.0178813	+	0.0309714i
$277$	−2.61426	−	4.52804i	−0.157076	−	0.272063i	0.776737	−	0.629825i	$-0.216873\pi$
$277$	−2.61426	−	4.52804i	−0.157076	−	0.272063i	−0.933813	+	0.357762i	$0.883540\pi$
$278$	13.3636	+	23.1464i	0.801495	+	1.38823i
$279$	1.70006	−	2.94458i	0.101780	−	0.176288i
$280$	1.87460	−	3.24691i	0.112029	−	0.194040i
$281$	−7.52004	+	13.0251i	−0.448608	+	0.777011i	−0.998296	−	0.0583587i	$-0.981413\pi$
$281$	−7.52004	+	13.0251i	−0.448608	+	0.777011i	0.549688	+	0.835370i	$0.314747\pi$
$282$	3.94084			0.234674
$283$	9.34068	+	16.1785i	0.555246	+	0.961714i	0.997884	+	0.0650136i	$0.0207091\pi$
$283$	9.34068	+	16.1785i	0.555246	+	0.961714i	−0.442639	+	0.896700i	$0.645958\pi$
$284$	−2.72691	+	4.72314i	−0.161812	+	0.280267i
$285$	8.77033			0.519510
$286$	3.05456			0.180620
$287$	−6.55463	+	11.3529i	−0.386907	+	0.670143i
$288$	1.66499			0.0981106
$289$	4.88376	+	8.45893i	0.287280	+	0.497584i
$290$	10.3176			0.605873
$291$	−2.10840	−	3.65186i	−0.123597	−	0.214076i
$292$	3.15166	+	5.45883i	0.184437	+	0.319454i
$293$	−0.631698	−	1.09413i	−0.0369042	−	0.0639199i	0.846983	−	0.531619i	$-0.178416\pi$
$293$	−0.631698	−	1.09413i	−0.0369042	−	0.0639199i	−0.883888	+	0.467699i	$0.845083\pi$
$294$	−5.49290	+	9.51398i	−0.320352	+	0.554866i
$295$	0.907484			0.0528358
$296$	−13.8890	+	3.11108i	−0.807285	+	0.180828i
$297$	10.2569			0.595169
$298$	−1.79305	+	3.10565i	−0.103869	+	0.179906i
$299$	0.375937	+	0.651143i	0.0217410	+	0.0376565i
$300$	0.411821	+	0.713295i	0.0237765	+	0.0411821i
$301$	6.53398	+	11.3172i	0.376612	+	0.652311i
$302$	−16.9859			−0.977429
$303$	2.70451	+	4.68434i	0.155370	+	0.269109i
$304$	−26.8841			−1.54191
$305$	−0.661854	+	1.14637i	−0.0378977	+	0.0656407i
$306$	−2.44078			−0.139530
$307$	23.4192			1.33660			0.668302	−	0.743890i	$-0.267021\pi$
$307$	23.4192			1.33660			0.668302	+	0.743890i	$0.267021\pi$
$308$	0.780249	−	1.35143i	0.0444588	−	0.0770049i
$309$	−15.2825	−	26.4701i	−0.869391	−	1.50583i
$310$	−9.47246			−0.538000
$311$	4.91264	−	8.50894i	0.278570	−	0.482498i	−0.692459	−	0.721457i	$-0.743473\pi$
$311$	4.91264	−	8.50894i	0.278570	−	0.482498i	0.971030	+	0.238959i	$0.0768062\pi$
$312$	−1.90067	+	3.29205i	−0.107604	+	0.186376i
$313$	11.2102	−	19.4167i	0.633639	−	1.09750i	−0.353163	−	0.935562i	$-0.614894\pi$
$313$	11.2102	−	19.4167i	0.633639	−	1.09750i	0.986802	−	0.161933i	$-0.0517729\pi$
$314$	6.10787	+	10.5791i	0.344687	+	0.597015i
$315$	0.457262	+	0.792001i	0.0257638	+	0.0446242i
$316$	−0.688988	+	1.19336i	−0.0387586	+	0.0671318i
$317$	7.93132	−	13.7374i	0.445467	−	0.771572i	−0.552617	−	0.833435i	$-0.686371\pi$
$317$	7.93132	−	13.7374i	0.445467	−	0.771572i	0.998085	+	0.0618631i	$0.0197042\pi$
$318$	3.41211	−	5.90994i	0.191341	−	0.331413i
$319$	−11.9585			−0.669546
$320$	2.45837	+	4.25802i	0.137427	+	0.238031i
$321$	4.56506	−	7.90691i	0.254797	−	0.441321i
$322$	1.83785			0.102419
$323$	15.1330			0.842022
$324$	1.83952	−	3.18613i	0.102195	−	0.177007i
$325$	1.04232			0.0578173
$326$	−3.67733	−	6.36931i	−0.203668	−	0.352764i
$327$	−29.2949			−1.62001
$328$	−9.57223	−	16.5796i	−0.528538	−	0.915454i
$329$	−1.27390	−	2.20645i	−0.0702322	−	0.121646i
$330$	−2.28378	−	3.95562i	−0.125718	−	0.217750i
$331$	−0.768861	+	1.33171i	−0.0422604	+	0.0731972i	−0.886382	−	0.462955i	$-0.846789\pi$
$331$	−0.768861	+	1.33171i	−0.0422604	+	0.0731972i	0.844122	+	0.536152i	$0.180123\pi$
$332$	1.09163			0.0599107
$333$	1.03674	−	3.31342i	0.0568131	−	0.181575i
$334$	10.4852			0.573727
$335$	1.54372	−	2.67380i	0.0843423	−	0.146085i
$336$	5.96562	+	10.3328i	0.325451	+	0.563698i
$337$	−11.9440	−	20.6875i	−0.650629	−	1.12692i	−0.982971	−	0.183763i	$-0.941172\pi$
$337$	−11.9440	−	20.6875i	−0.650629	−	1.12692i	0.332342	−	0.943159i	$-0.392161\pi$
$338$	9.47195	+	16.4059i	0.515206	+	0.892363i
$339$	26.3178			1.42939
$340$	0.710587	+	1.23077i	0.0385370	+	0.0667480i
$341$	10.9789			0.594539
$342$	2.55350	−	4.42280i	0.138078	−	0.239157i
$343$	18.3184			0.989098
$344$	−19.0841			−1.02895
$345$	0.562148	−	0.973669i	0.0302650	−	0.0524206i
$346$	−8.26973	−	14.3236i	−0.444583	−	0.770041i
$347$	−2.47704			−0.132974			−0.0664872	−	0.997787i	$-0.521179\pi$
$347$	−2.47704			−0.132974			−0.0664872	+	0.997787i	$0.521179\pi$
$348$	−2.67216	+	4.62831i	−0.143243	+	0.248104i
$349$	−14.2014	+	24.5975i	−0.760181	+	1.31667i	0.182576	+	0.983192i	$0.441557\pi$
$349$	−14.2014	+	24.5975i	−0.760181	+	1.31667i	−0.942757	+	0.333481i	$0.891777\pi$
$350$	1.27390	−	2.20645i	0.0680927	−	0.117940i
$351$	−2.90045	−	5.02373i	−0.154815	−	0.268147i
$352$	2.68811	+	4.65594i	0.143277	+	0.248162i
$353$	11.2659	−	19.5131i	0.599624	−	1.03858i	−0.393252	−	0.919431i	$-0.628650\pi$
$353$	11.2659	−	19.5131i	0.599624	−	1.03858i	0.992876	−	0.119149i	$-0.0380167\pi$
$354$	−1.12453	+	1.94774i	−0.0597681	+	0.103521i
$355$	5.16020	−	8.93772i	0.273875	−	0.474365i
$356$	2.04717			0.108500
$357$	−3.35804	−	5.81629i	−0.177726	−	0.307831i
$358$	−11.8405	+	20.5084i	−0.625791	+	1.08390i
$359$	−4.60068			−0.242814			−0.121407	−	0.992603i	$-0.538741\pi$
$359$	−4.60068			−0.242814			−0.121407	+	0.992603i	$0.538741\pi$
$360$	−1.33555			−0.0703896
$361$	−6.33188	+	10.9671i	−0.333257	+	0.577218i
$362$	−34.4334			−1.80978
$363$	−5.92533	−	10.2630i	−0.310999	−	0.538666i
$364$	−0.882552			−0.0462583
$365$	−5.96396	−	10.3299i	−0.312168	−	0.540691i
$366$	−1.64030	−	2.84109i	−0.0857400	−	0.148506i
$367$	−5.35749	−	9.27945i	−0.279659	−	0.484383i	0.691641	−	0.722241i	$-0.256888\pi$
$367$	−5.35749	−	9.27945i	−0.279659	−	0.484383i	−0.971300	+	0.237858i	$0.923555\pi$
$368$	−1.72318	+	2.98463i	−0.0898268	+	0.155585i
$369$	4.66980			0.243100
$370$	−9.43838	+	2.11415i	−0.490678	+	0.109909i
$371$	−4.41192			−0.229056
$372$	2.45326	−	4.24918i	0.127196	−	0.220310i
$373$	−3.22237	−	5.58130i	−0.166848	−	0.288989i	0.770462	−	0.637486i	$-0.220026\pi$
$373$	−3.22237	−	5.58130i	−0.166848	−	0.288989i	−0.937310	+	0.348497i	$0.886692\pi$
$374$	−3.94060	−	6.82533i	−0.203764	−	0.352929i
$375$	−0.779300	−	1.34979i	−0.0402429	−	0.0697027i
$376$	3.72074			0.191883
$377$	3.38160	+	5.85711i	0.174161	+	0.301657i
$378$	−14.1795			−0.729314
$379$	−0.944650	+	1.63618i	−0.0485234	+	0.0840450i	−0.889267	−	0.457389i	$-0.848785\pi$
$379$	−0.944650	+	1.63618i	−0.0485234	+	0.0840450i	0.840744	+	0.541434i	$0.182118\pi$
$380$	−2.97362			−0.152543
$381$	14.8481			0.760691
$382$	17.7513	−	30.7462i	0.908236	−	1.57311i
$383$	18.0470	+	31.2583i	0.922157	+	1.59722i	0.796072	+	0.605203i	$0.206908\pi$
$383$	18.0470	+	31.2583i	0.922157	+	1.59722i	0.126085	+	0.992019i	$0.459759\pi$
$384$	−21.2786			−1.08587
$385$	−1.47649	+	2.55735i	−0.0752487	+	0.130335i
$386$	15.7923	−	27.3530i	0.803805	−	1.39223i
$387$	2.32755	−	4.03143i	0.118316	−	0.204929i
$388$	0.714863	+	1.23818i	0.0362917	+	0.0628590i
$389$	−2.17230	−	3.76254i	−0.110140	−	0.190768i	0.805687	−	0.592342i	$-0.201797\pi$
$389$	−2.17230	−	3.76254i	−0.110140	−	0.190768i	−0.915827	+	0.401574i	$0.868463\pi$
$390$	−1.29161	+	2.23713i	−0.0654032	+	0.113282i
$391$	0.969973	−	1.68004i	0.0490536	−	0.0849634i
$392$	−5.18611	+	8.98261i	−0.261938	+	0.453690i
$393$	29.7946			1.50294
$394$	−8.52851	−	14.7718i	−0.429660	−	0.744193i
$395$	1.30379	−	2.25823i	0.0656008	−	0.113624i
$396$	−0.555884			−0.0279342
$397$	−0.927448			−0.0465473			−0.0232736	−	0.999729i	$-0.507409\pi$
$397$	−0.927448			−0.0465473			−0.0232736	+	0.999729i	$0.507409\pi$
$398$	−3.36952	+	5.83618i	−0.168899	+	0.292541i
$399$	14.0525			0.703504
$400$	2.38882	+	4.13756i	0.119441	+	0.206878i
$401$	−14.2105			−0.709638			−0.354819	−	0.934935i	$-0.615457\pi$
$401$	−14.2105			−0.709638			−0.354819	+	0.934935i	$0.615457\pi$
$402$	3.82586	+	6.62659i	0.190817	+	0.330504i
$403$	−3.10459	−	5.37732i	−0.154651	−	0.267863i
$404$	−0.916974	−	1.58825i	−0.0456212	−	0.0790182i
$405$	−3.48096	+	6.02921i	−0.172971	+	0.299594i
$406$	16.5317			0.820455
$407$	10.9394	−	2.45036i	0.542245	−	0.121460i
$408$	9.80800			0.485568
$409$	−3.70415	+	6.41578i	−0.183159	+	0.317240i	−0.942954	−	0.332922i	$-0.891965\pi$
$409$	−3.70415	+	6.41578i	−0.183159	+	0.317240i	0.759796	+	0.650162i	$0.225299\pi$
$410$	−6.50486	−	11.2667i	−0.321252	−	0.556425i
$411$	−7.87003	−	13.6313i	−0.388200	−	0.672382i
$412$	5.18159	+	8.97478i	0.255279	+	0.442156i
$413$	1.45404			0.0715486
$414$	−0.327342	−	0.566972i	−0.0160880	−	0.0278652i
$415$	−2.06571			−0.101402
$416$	1.52028	−	2.63320i	0.0745379	−	0.129103i
$417$	26.1976			1.28290
$418$	16.4904			0.806571
$419$	16.4640	−	28.5165i	0.804319	−	1.39312i	−0.112432	−	0.993659i	$-0.535864\pi$
$419$	16.4640	−	28.5165i	0.804319	−	1.39312i	0.916750	−	0.399461i	$-0.130803\pi$
$420$	0.659851	+	1.14290i	0.0321974	+	0.0557676i
$421$	19.2409			0.937745			0.468873	−	0.883266i	$-0.344660\pi$
$421$	19.2409			0.937745			0.468873	+	0.883266i	$0.344660\pi$
$422$	13.8876	−	24.0540i	0.676036	−	1.17093i
$423$	−0.453790	+	0.785987i	−0.0220640	+	0.0382160i
$424$	3.22154	−	5.57986i	0.156452	−	0.270982i
$425$	−1.34466	−	2.32902i	−0.0652257	−	0.112974i
$426$	12.7887	+	22.1508i	0.619617	+	1.07321i
$427$	−1.06047	+	1.83679i	−0.0513199	+	0.0888886i
$428$	−1.54780	+	2.68087i	−0.0748158	+	0.129585i
$429$	1.49702	−	2.59291i	0.0722766	−	0.125187i
$430$	−12.9687			−0.625408
$431$	11.1323	+	19.2816i	0.536222	+	0.928764i	0.999103	+	0.0423434i	$0.0134824\pi$
$431$	11.1323	+	19.2816i	0.536222	+	0.928764i	−0.462881	+	0.886420i	$0.653184\pi$
$432$	13.2947	−	23.0271i	0.639643	−	1.10789i
$433$	−4.16115			−0.199972			−0.0999860	−	0.994989i	$-0.531880\pi$
$433$	−4.16115			−0.199972			−0.0999860	+	0.994989i	$0.531880\pi$
$434$	−15.1775			−0.728543
$435$	5.05660	−	8.75828i	0.242445	−	0.419927i
$436$	9.93256			0.475683
$437$	2.02954	+	3.51526i	0.0970860	+	0.168158i
$438$	29.5615			1.41250
$439$	14.8329	+	25.6913i	0.707935	+	1.22618i	0.965622	+	0.259951i	$0.0837064\pi$
$439$	14.8329	+	25.6913i	0.707935	+	1.22618i	−0.257687	+	0.966229i	$0.582960\pi$
$440$	−2.15623	−	3.73469i	−0.102794	−	0.178045i
$441$	−1.26502	−	2.19108i	−0.0602391	−	0.104337i
$442$	−2.22864	+	3.86012i	−0.106006	+	0.183607i
$443$	−41.0483			−1.95027			−0.975133	−	0.221622i	$-0.928865\pi$
$443$	−41.0483			−1.95027			−0.975133	+	0.221622i	$0.928865\pi$
$444$	1.49607	−	4.78143i	0.0710002	−	0.226917i
$445$	−3.87392			−0.183641
$446$	13.6973	−	23.7244i	0.648586	−	1.12338i
$447$	1.75752	+	3.04411i	0.0831278	+	0.143982i
$448$	3.93898	+	6.82252i	0.186100	+	0.322334i
$449$	−3.87973	−	6.71989i	−0.183096	−	0.317131i	0.759837	−	0.650113i	$-0.225279\pi$
$449$	−3.87973	−	6.71989i	−0.183096	−	0.317131i	−0.942933	+	0.332982i	$0.891945\pi$
$450$	−0.907580			−0.0427837
$451$	7.53933	+	13.0585i	0.355013	+	0.614901i
$452$	−8.92315			−0.419710
$453$	−8.32466	+	14.4187i	−0.391126	+	0.677451i
$454$	30.6388			1.43795
$455$	1.67008			0.0782944
$456$	−10.2610	+	17.7725i	−0.480514	+	0.832274i
$457$	−14.7662	−	25.5758i	−0.690734	−	1.19639i	−0.971598	−	0.236639i	$-0.923954\pi$
$457$	−14.7662	−	25.5758i	−0.690734	−	1.19639i	0.280863	−	0.959748i	$-0.409379\pi$
$458$	−41.0594			−1.91858
$459$	−7.48358	+	12.9619i	−0.349304	+	0.605012i
$460$	−0.190599	+	0.330127i	−0.00888671	+	0.0153922i
$461$	4.43872	−	7.68809i	0.206732	−	0.358070i	−0.743951	−	0.668234i	$-0.767051\pi$
$461$	4.43872	−	7.68809i	0.206732	−	0.358070i	0.950683	+	0.310164i	$0.100384\pi$
$462$	−3.65924	−	6.33799i	−0.170243	−	0.294870i
$463$	12.2403	+	21.2008i	0.568854	+	0.985284i	0.996680	+	0.0814224i	$0.0259463\pi$
$463$	12.2403	+	21.2008i	0.568854	+	0.985284i	−0.427826	+	0.903861i	$0.640720\pi$
$464$	−15.5002	+	26.8471i	−0.719578	+	1.24635i
$465$	−4.64238	+	8.04083i	−0.215285	+	0.372885i
$466$	−17.5768	+	30.4438i	−0.814227	+	1.41028i
$467$	8.22805			0.380749			0.190374	−	0.981712i	$-0.439030\pi$
$467$	8.22805			0.380749			0.190374	+	0.981712i	$0.439030\pi$
$468$	0.157192	+	0.272265i	0.00726621	+	0.0125854i
$469$	2.47346	−	4.28416i	0.114214	−	0.197824i
$470$	2.52845			0.116629
$471$	11.9737			0.551717
$472$	−1.06172	+	1.83896i	−0.0488698	+	0.0846449i
$473$	15.0312			0.691134
$474$	3.23124	+	5.59668i	0.148416	+	0.257064i
$475$	5.62706			0.258187
$476$	1.13856	+	1.97204i	0.0521856	+	0.0903882i
$477$	0.785812	+	1.36107i	0.0359798	+	0.0623189i
$478$	15.1054	+	26.1632i	0.690903	+	1.19668i
$479$	−8.71590	+	15.0964i	−0.398240	+	0.689771i	−0.993509	−	0.113755i	$-0.963712\pi$
$479$	−8.71590	+	15.0964i	−0.398240	+	0.689771i	0.595269	+	0.803526i	$0.297045\pi$
$480$	−4.54663			−0.207524
$481$	−4.29358	−	4.66506i	−0.195771	−	0.212708i
$482$	6.48135			0.295217
$483$	0.900716	−	1.56009i	0.0409840	−	0.0709864i
$484$	2.00901	+	3.47970i	0.0913186	+	0.158168i
$485$	−1.35275	−	2.34304i	−0.0614254	−	0.106392i
$486$	4.64735	+	8.04945i	0.210808	+	0.365131i
$487$	−10.9881			−0.497917			−0.248958	−	0.968514i	$-0.580088\pi$
$487$	−10.9881			−0.497917			−0.248958	+	0.968514i	$0.580088\pi$
$488$	−1.54869	−	2.68241i	−0.0701059	−	0.121427i
$489$	−7.20891			−0.325998
$490$	−3.52425	+	6.10418i	−0.159209	+	0.275759i
$491$	−3.11047			−0.140373			−0.0701867	−	0.997534i	$-0.522360\pi$
$491$	−3.11047			−0.140373			−0.0701867	+	0.997534i	$0.522360\pi$
$492$	6.73875			0.303806
$493$	8.72503	−	15.1122i	0.392956	−	0.680619i
$494$	−4.66313	−	8.07678i	−0.209804	−	0.363392i
$495$	1.05191			0.0472800
$496$	14.2305	−	24.6479i	0.638967	−	1.10672i
$497$	8.26806	−	14.3207i	0.370873	−	0.642371i
$498$	2.55978	−	4.43366i	0.114706	−	0.198677i
$499$	18.5186	+	32.0751i	0.829004	+	1.43588i	0.898820	+	0.438318i	$0.144425\pi$
$499$	18.5186	+	32.0751i	0.829004	+	1.43588i	−0.0698159	+	0.997560i	$0.522241\pi$
$500$	0.264225	+	0.457651i	0.0118165	+	0.0204668i
$501$	5.13873	−	8.90055i	0.229582	−	0.397647i
$502$	−8.19634	+	14.1965i	−0.365820	+	0.633619i
$503$	−13.2457	+	22.9423i	−0.590598	+	1.02295i	0.403554	+	0.914956i	$0.367775\pi$
$503$	−13.2457	+	22.9423i	−0.590598	+	1.02295i	−0.994152	+	0.107990i	$0.965558\pi$
$504$	−2.13992			−0.0953195
$505$	1.73522	+	3.00548i	0.0772161	+	0.133742i
$506$	1.05698	−	1.83074i	0.0469884	−	0.0813862i
$507$	18.5685			0.824656
$508$	−5.03431			−0.223361
$509$	−16.7216	+	28.9627i	−0.741173	+	1.28375i	0.210788	+	0.977532i	$0.432397\pi$
$509$	−16.7216	+	28.9627i	−0.741173	+	1.28375i	−0.951961	+	0.306218i	$0.900936\pi$
$510$	6.66508			0.295135
$511$	−9.55591	−	16.5513i	−0.422729	−	0.732187i
$512$	−8.42170			−0.372190
$513$	−15.6584	−	27.1211i	−0.691335	−	1.19743i
$514$	−23.0167	−	39.8662i	−1.01522	−	1.75842i
$515$	−9.80527	−	16.9832i	−0.432072	−	0.748370i
$516$	3.35876	−	5.81754i	0.147861	−	0.256103i
$517$	−2.93055			−0.128886
$518$	−15.1229	+	3.38745i	−0.664461	+	0.148836i
$519$	−16.2117			−0.711615
$520$	−1.21947	+	2.11219i	−0.0534773	+	0.0926255i
$521$	−1.00711	−	1.74437i	−0.0441225	−	0.0764223i	0.843121	−	0.537724i	$-0.180716\pi$
$521$	−1.00711	−	1.74437i	−0.0441225	−	0.0764223i	−0.887243	+	0.461302i	$0.847383\pi$
$522$	−2.94448	−	5.09999i	−0.128876	−	0.223220i
$523$	10.4943	+	18.1766i	0.458883	+	0.794809i	0.998902	−	0.0468439i	$-0.0149163\pi$
$523$	10.4943	+	18.1766i	0.458883	+	0.794809i	−0.540019	+	0.841653i	$0.681583\pi$
$524$	−10.1020			−0.441307
$525$	−1.24865	−	2.16273i	−0.0544957	−	0.0943893i
$526$	12.3463			0.538324
$527$	−8.01030	+	13.8743i	−0.348934	+	0.604372i
$528$	13.7237			0.597246
$529$	−22.4797			−0.977376
$530$	2.18921	−	3.79183i	0.0950933	−	0.164706i
$531$	−0.258980	−	0.448567i	−0.0112388	−	0.0194662i
$532$	−4.76455			−0.206570
$533$	4.26393	−	7.38534i	0.184691	−	0.319895i
$534$	4.80046	−	8.31464i	0.207736	−	0.359810i
$535$	2.92895	−	5.07309i	0.126629	−	0.219329i
$536$	3.61218	+	6.25649i	0.156023	+	0.270239i
$537$	11.6059	+	20.1020i	0.500831	+	0.867465i
$538$	11.8807	−	20.5780i	0.512213	−	0.887180i
$539$	4.08472	−	7.07493i	0.175941	−	0.304739i
$540$	1.47052	−	2.54701i	0.0632810	−	0.109606i
$541$	−43.9888			−1.89123			−0.945613	−	0.325293i	$-0.894537\pi$
$541$	−43.9888			−1.89123			−0.945613	+	0.325293i	$0.894537\pi$
$542$	−22.0417	−	38.1773i	−0.946770	−	1.63985i
$543$	−16.8756	+	29.2293i	−0.724199	+	1.25435i
$544$	−7.84509			−0.336355
$545$	−18.7957			−0.805117
$546$	−2.06951	+	3.58450i	−0.0885670	+	0.153403i
$547$	8.24396			0.352486			0.176243	−	0.984347i	$-0.443605\pi$
$547$	8.24396			0.352486			0.176243	+	0.984347i	$0.443605\pi$
$548$	2.66837	+	4.62175i	0.113987	+	0.197431i
$549$	0.755527			0.0322451
$550$	−1.46528	−	2.53793i	−0.0624796	−	0.108218i
$551$	18.2560	+	31.6203i	0.777730	+	1.34707i
$552$	1.31539	+	2.27831i	0.0559865	+	0.0969715i
$553$	2.08903	−	3.61831i	0.0888346	−	0.153866i
$554$	8.31394			0.353225
$555$	−2.83105	+	9.04803i	−0.120171	+	0.384067i
$556$	−8.88239			−0.376697
$557$	1.46427	−	2.53619i	0.0620431	−	0.107462i	−0.833335	−	0.552768i	$-0.813572\pi$
$557$	1.46427	−	2.53619i	0.0620431	−	0.107462i	0.895379	+	0.445306i	$0.146905\pi$
$558$	2.70328	+	4.68221i	0.114439	+	0.198214i
$559$	−4.25050	−	7.36208i	−0.179777	−	0.311383i
$560$	3.82755	+	6.62951i	0.161743	+	0.280148i
$561$	−7.72503			−0.326151
$562$	−11.9577	−	20.7113i	−0.504404	−	0.873654i
$563$	19.8548			0.836782			0.418391	−	0.908267i	$-0.362594\pi$
$563$	19.8548			0.836782			0.418391	+	0.908267i	$0.362594\pi$
$564$	−0.654841	+	1.13422i	−0.0275738	+	0.0477592i
$565$	16.8855			0.710379
$566$	−29.7054			−1.24861
$567$	−5.57746	+	9.66045i	−0.234232	+	0.405701i
$568$	12.0745	+	20.9136i	0.506634	+	0.877516i
$569$	−38.6284			−1.61939			−0.809693	−	0.586854i	$-0.800366\pi$
$569$	−38.6284			−1.61939			−0.809693	+	0.586854i	$0.800366\pi$
$570$	−6.97289	+	12.0774i	−0.292062	+	0.505867i
$571$	−0.0924866	+	0.160192i	−0.00387045	+	0.00670381i	−0.867954	−	0.496644i	$-0.834565\pi$
$571$	−0.0924866	+	0.160192i	−0.00387045	+	0.00670381i	0.864084	+	0.503348i	$0.167899\pi$
$572$	−0.507569	+	0.879136i	−0.0212225	+	0.0367585i
$573$	−17.3995	−	30.1369i	−0.726876	−	1.25899i
$574$	−10.4226	−	18.0524i	−0.435030	−	0.753494i
$575$	0.360675	−	0.624708i	0.0150412	−	0.0260521i
$576$	1.40315	−	2.43033i	0.0584647	−	0.101264i
$577$	−22.6857	+	39.2928i	−0.944419	+	1.63578i	−0.187508	+	0.982263i	$0.560041\pi$
$577$	−22.6857	+	39.2928i	−0.944419	+	1.63578i	−0.756911	+	0.653518i	$0.773292\pi$
$578$	−15.5314			−0.646023
$579$	−15.4793	−	26.8110i	−0.643299	−	1.11423i
$580$	−1.71446	+	2.96953i	−0.0711891	+	0.123303i
$581$	−3.30984			−0.137315
$582$	6.70518			0.277939
$583$	−2.53736	+	4.39484i	−0.105087	+	0.182016i
$584$	27.9105			1.15494
$585$	−0.297459	−	0.515214i	−0.0122984	−	0.0213015i
$586$	2.00894			0.0829884
$587$	19.0331	+	32.9662i	0.785579	+	1.36066i	0.928653	+	0.370950i	$0.120968\pi$
$587$	19.0331	+	32.9662i	0.785579	+	1.36066i	−0.143074	+	0.989712i	$0.545699\pi$
$588$	−1.82548	−	3.16183i	−0.0752817	−	0.130392i
$589$	−16.7605	−	29.0300i	−0.690604	−	1.19616i
$590$	−0.721500	+	1.24967i	−0.0297037	+	0.0514483i
$591$	−16.7190			−0.687728
$592$	8.67813	−	27.7353i	0.356669	−	1.13991i
$593$	47.4147			1.94709			0.973544	−	0.228499i	$-0.0733818\pi$
$593$	47.4147			1.94709			0.973544	+	0.228499i	$0.0733818\pi$
$594$	−8.15484	+	14.1246i	−0.334597	+	0.579539i
$595$	−2.15452	−	3.73174i	−0.0883267	−	0.152986i
$596$	−0.595894	−	1.03212i	−0.0244088	−	0.0422772i
$597$	3.30275	+	5.72053i	0.135173	+	0.234126i
$598$	−1.19556			−0.0488902
$599$	−6.57165	−	11.3824i	−0.268510	−	0.465074i	0.699967	−	0.714175i	$-0.253198\pi$
$599$	−6.57165	−	11.3824i	−0.268510	−	0.465074i	−0.968477	+	0.249102i	$0.919865\pi$
$600$	3.64701			0.148889
$601$	−6.56439	+	11.3699i	−0.267767	+	0.463786i	−0.968285	−	0.249849i	$-0.919619\pi$
$601$	−6.56439	+	11.3699i	−0.267767	+	0.463786i	0.700518	+	0.713635i	$0.252952\pi$
$602$	−20.7795			−0.846909
$603$	−1.76220			−0.0717624
$604$	2.82251	−	4.88873i	0.114846	−	0.198920i
$605$	−3.80170	−	6.58474i	−0.154561	−	0.267708i
$606$	−8.60093			−0.349389
$607$	2.70662	−	4.68800i	0.109858	−	0.190280i	−0.805854	−	0.592114i	$-0.798294\pi$
$607$	2.70662	−	4.68800i	0.109858	−	0.190280i	0.915713	+	0.401834i	$0.131627\pi$
$608$	8.20740	−	14.2156i	0.332854	−	0.576520i
$609$	8.10206	−	14.0332i	0.328312	−	0.568653i
$610$	−1.05242	−	1.82285i	−0.0426113	−	0.0738049i
$611$	0.828698	+	1.43535i	0.0335255	+	0.0580679i
$612$	0.405579	−	0.702483i	0.0163945	−	0.0283962i
$613$	−19.1223	+	33.1208i	−0.772342	+	1.33774i	0.163934	+	0.986471i	$0.447582\pi$
$613$	−19.1223	+	33.1208i	−0.772342	+	1.33774i	−0.936276	+	0.351265i	$0.885752\pi$
$614$	−18.6195	+	32.2500i	−0.751424	+	1.30150i
$615$	−12.7519			−0.514207
$616$	−3.45487	−	5.98401i	−0.139201	−	0.241103i
$617$	−19.7548	+	34.2163i	−0.795297	+	1.37749i	0.127354	+	0.991857i	$0.459352\pi$
$617$	−19.7548	+	34.2163i	−0.795297	+	1.37749i	−0.922650	+	0.385637i	$0.873982\pi$
$618$	48.6017			1.95505
$619$	11.9126			0.478809			0.239405	−	0.970920i	$-0.423048\pi$
$619$	11.9126			0.478809			0.239405	+	0.970920i	$0.423048\pi$
$620$	1.57402	−	2.72628i	0.0632141	−	0.109490i
$621$	−4.01460			−0.161100
$622$	7.81164	+	13.5302i	0.313218	+	0.542510i
$623$	−6.20709			−0.248682
$624$	−3.88077	−	6.72168i	−0.155355	−	0.269083i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	17.8255	+	30.8746i	0.712450	+	1.23400i
$627$	8.08180	−	13.9981i	0.322756	−	0.559030i
$628$	−4.05972			−0.162001
$629$	−4.88490	+	15.6121i	−0.194774	+	0.622497i
$630$	−1.45419			−0.0579365
$631$	7.43981	−	12.8861i	0.296174	−	0.512988i	−0.679083	−	0.734061i	$-0.737622\pi$
$631$	7.43981	−	12.8861i	0.296174	−	0.512988i	0.975257	+	0.221073i	$0.0709558\pi$
$632$	3.05077	+	5.28409i	0.121353	+	0.210190i
$633$	−13.6124	−	23.5773i	−0.541043	−	0.937113i
$634$	12.6117	+	21.8441i	0.500873	+	0.867538i
$635$	9.52656			0.378050
$636$	1.13396	+	1.96408i	0.0449646	+	0.0778810i
$637$	−4.62029			−0.183062
$638$	9.50764	−	16.4677i	0.376411	−	0.651963i
$639$	−5.89052			−0.233026
$640$	−13.6524			−0.539658
$641$	16.2983	−	28.2295i	0.643745	−	1.11500i	−0.340845	−	0.940120i	$-0.610713\pi$
$641$	16.2983	−	28.2295i	0.643745	−	1.11500i	0.984590	−	0.174880i	$-0.0559536\pi$
$642$	7.25894	+	12.5729i	0.286488	+	0.496211i
$643$	32.4234			1.27865			0.639327	−	0.768935i	$-0.279213\pi$
$643$	32.4234			1.27865			0.639327	+	0.768935i	$0.279213\pi$
$644$	−0.305392	+	0.528954i	−0.0120341	+	0.0208437i
$645$	−6.35587	+	11.0087i	−0.250262	+	0.433467i
$646$	−12.0316	+	20.8393i	−0.473375	+	0.819910i
$647$	9.00984	+	15.6055i	0.354213	+	0.613515i	0.986983	−	0.160825i	$-0.0514154\pi$
$647$	9.00984	+	15.6055i	0.354213	+	0.613515i	−0.632770	+	0.774340i	$0.718082\pi$
$648$	−8.14520	−	14.1079i	−0.319974	−	0.554211i
$649$	0.836241	−	1.44841i	0.0328253	−	0.0568551i
$650$	−0.828698	+	1.43535i	−0.0325042	+	0.0562990i
$651$	−7.43837	+	12.8836i	−0.291533	+	0.504949i
$652$	2.44421			0.0957227
$653$	4.35463	+	7.54244i	0.170410	+	0.295158i	0.938563	−	0.345107i	$-0.112158\pi$
$653$	4.35463	+	7.54244i	0.170410	+	0.295158i	−0.768153	+	0.640266i	$0.778824\pi$
$654$	23.2911	−	40.3413i	0.910753	−	1.57747i
$655$	19.1162			0.746933
$656$	39.0890			1.52617
$657$	−3.40402	+	5.89594i	−0.132804	+	0.230023i
$658$	4.05127			0.157935
$659$	−7.58833	−	13.1434i	−0.295599	−	0.511993i	0.679525	−	0.733653i	$-0.262186\pi$
$659$	−7.58833	−	13.1434i	−0.295599	−	0.511993i	−0.975124	+	0.221659i	$0.928853\pi$
$660$	1.51796			0.0590866
$661$	−3.64179	−	6.30777i	−0.141649	−	0.245344i	0.786469	−	0.617630i	$-0.211907\pi$
$661$	−3.64179	−	6.30777i	−0.141649	−	0.245344i	−0.928118	+	0.372287i	$0.878574\pi$
$662$	−1.22257	−	2.11756i	−0.0475167	−	0.0823013i
$663$	2.18448	+	3.78362i	0.0848380	+	0.146944i
$664$	2.41681	−	4.18603i	0.0937903	−	0.162450i
$665$	9.01609			0.349629
$666$	3.73857	+	4.06203i	0.144867	+	0.157400i
$667$	4.68058			0.181233
$668$	−1.74231	+	3.01777i	−0.0674120	+	0.116761i
$669$	−13.4259	−	23.2543i	−0.519074	−	0.899063i
$670$	2.45468	+	4.25163i	0.0948325	+	0.164255i
$671$	1.21979	+	2.11274i	0.0470894	+	0.0815612i
$672$	−7.28495			−0.281023
$673$	4.40697	+	7.63309i	0.169876	+	0.294234i	0.938376	−	0.345616i	$-0.112330\pi$
$673$	4.40697	+	7.63309i	0.169876	+	0.294234i	−0.768500	+	0.639850i	$0.778997\pi$
$674$	37.9844			1.46310
$675$	−2.78270	+	4.81977i	−0.107106	+	0.185513i
$676$	−6.29573			−0.242143
$677$	15.4074			0.592154			0.296077	−	0.955164i	$-0.404321\pi$
$677$	15.4074			0.592154			0.296077	+	0.955164i	$0.404321\pi$
$678$	−20.9241	+	36.2416i	−0.803584	+	1.39185i
$679$	−2.16748	−	3.75419i	−0.0831804	−	0.144073i
$680$	6.29282			0.241319
$681$	15.0158	−	26.0082i	0.575408	−	0.996636i
$682$	−8.72881	+	15.1187i	−0.334243	+	0.578927i
$683$	14.8703	−	25.7560i	0.568994	−	0.985527i	−0.427671	−	0.903934i	$-0.640666\pi$
$683$	14.8703	−	25.7560i	0.568994	−	0.985527i	0.996666	−	0.0815930i	$-0.0260008\pi$
$684$	0.848619	+	1.46985i	0.0324478	+	0.0562012i
$685$	−5.04942	−	8.74585i	−0.192928	−	0.334162i
$686$	−14.5641	+	25.2258i	−0.556060	+	0.963124i
$687$	−20.1229	+	34.8539i	−0.767737	+	1.32976i
$688$	19.4829	−	33.7454i	0.742779	−	1.28653i
$689$	2.87005			0.109340
$690$	0.893878	+	1.54824i	0.0340293	+	0.0589405i
$691$	14.3719	−	24.8929i	0.546733	−	0.946969i	−0.451763	−	0.892138i	$-0.649205\pi$
$691$	14.3719	−	24.8929i	0.546733	−	0.946969i	0.998496	−	0.0548311i	$-0.0174620\pi$
$692$	5.49665			0.208951
$693$	1.68545			0.0640251
$694$	1.96938	−	3.41107i	0.0747567	−	0.129482i
$695$	16.8084			0.637579
$696$	11.8321	+	20.4937i	0.448493	+	0.776813i
$697$	−22.0031			−0.833427
$698$	−22.5817	−	39.1127i	−0.854731	−	1.48044i
$699$	17.2284	+	29.8406i	0.651640	+	1.12867i
$700$	0.423361	+	0.733283i	0.0160015	+	0.0277155i
$701$	25.6269	−	44.3871i	0.967915	−	1.67648i	0.266344	−	0.963878i	$-0.414184\pi$
$701$	25.6269	−	44.3871i	0.967915	−	1.67648i	0.701571	−	0.712600i	$-0.252482\pi$
$702$	9.22407			0.348140
$703$	−23.1794	−	25.1848i	−0.874227	−	0.949864i
$704$	9.06148			0.341517
$705$	1.23917	−	2.14631i	0.0466699	−	0.0808347i
$706$	17.9141	+	31.0281i	0.674204	+	1.16776i
$707$	2.78029	+	4.81561i	0.104564	+	0.181110i
$708$	−0.373721	−	0.647304i	−0.0140453	−	0.0243272i
$709$	1.16264			0.0436639			0.0218320	−	0.999762i	$-0.493050\pi$
$709$	1.16264			0.0436639			0.0218320	+	0.999762i	$0.493050\pi$
$710$	8.20528	+	14.2120i	0.307939	+	0.533365i
$711$	−1.48832			−0.0558162
$712$	4.53235	−	7.85025i	0.169857	−	0.294201i
$713$	−4.29716			−0.160930
$714$	10.6793			0.399662
$715$	0.960487	−	1.66361i	0.0359202	−	0.0622156i
$716$	−3.93503	−	6.81566i	−0.147059	−	0.254713i
$717$	29.6121			1.10588
$718$	3.65779	−	6.33548i	0.136508	−	0.236438i
$719$	−17.0365	+	29.5080i	−0.635353	+	1.10046i	0.351087	+	0.936343i	$0.385812\pi$
$719$	−17.0365	+	29.5080i	−0.635353	+	1.10046i	−0.986440	+	0.164121i	$0.947521\pi$
$720$	1.36346	−	2.36158i	0.0508130	−	0.0880107i
$721$	−15.7107	−	27.2118i	−0.585099	−	1.01342i
$722$	−10.0684	−	17.4390i	−0.374706	−	0.649011i
$723$	3.17646	−	5.50178i	0.118134	−	0.204614i
$724$	5.72173	−	9.91032i	0.212646	−	0.368314i
$725$	3.24432	−	5.61932i	0.120491	−	0.208696i
$726$	18.8439			0.699361
$727$	14.7942	+	25.6243i	0.548687	+	0.950354i	0.998365	+	0.0571630i	$0.0182055\pi$
$727$	14.7942	+	25.6243i	0.548687	+	0.950354i	−0.449678	+	0.893191i	$0.648461\pi$
$728$	−1.95393	+	3.38430i	−0.0724174	+	0.125431i
$729$	29.9963			1.11097
$730$	18.9667			0.701990
$731$	−10.9669	+	18.9952i	−0.405625	+	0.702564i
$732$	1.09026			0.0402972
$733$	−16.0500	−	27.7994i	−0.592820	−	1.02679i	−0.993851	−	0.110730i	$-0.964681\pi$
$733$	−16.0500	−	27.7994i	−0.592820	−	1.02679i	0.401031	−	0.916065i	$-0.368652\pi$
$734$	17.0380			0.628884
$735$	3.45441	+	5.98322i	0.127418	+	0.220694i
$736$	−1.05213	−	1.82235i	−0.0387821	−	0.0671726i
$737$	−2.84505	−	4.92777i	−0.104799	−	0.181517i
$738$	−3.71275	+	6.43067i	−0.136668	+	0.236716i
$739$	50.9263			1.87335			0.936677	−	0.350194i	$-0.113884\pi$
$739$	50.9263			1.87335			0.936677	+	0.350194i	$0.113884\pi$
$740$	0.959879	−	3.06777i	0.0352858	−	0.112774i
$741$	−9.14145			−0.335820
$742$	3.50772	−	6.07555i	0.128773	−	0.223041i
$743$	−22.4664	−	38.9130i	−0.824213	−	1.42758i	−0.902520	−	0.430649i	$-0.858285\pi$
$743$	−22.4664	−	38.9130i	−0.824213	−	1.42758i	0.0783070	−	0.996929i	$-0.475049\pi$
$744$	−10.8628	−	18.8150i	−0.398250	−	0.689790i
$745$	1.12763	+	1.95311i	0.0413130	+	0.0715563i
$746$	10.2478			0.375200
$747$	0.589519	+	1.02108i	0.0215694	+	0.0373592i
$748$	2.61920			0.0957676
$749$	4.69298	−	8.12848i	0.171478	−	0.297008i
$750$	2.47835			0.0904964
$751$	−40.8902			−1.49210			−0.746052	−	0.665888i	$-0.768053\pi$
$751$	−40.8902			−1.49210			−0.746052	+	0.665888i	$0.768053\pi$
$752$	−3.79849	+	6.57917i	−0.138517	+	0.239918i
$753$	8.03392	+	13.9151i	0.292772	+	0.507096i
$754$	−10.7542			−0.391646
$755$	−5.34111	+	9.25107i	−0.194383	+	0.336681i
$756$	2.35617	−	4.08101i	0.0856932	−	0.148425i
$757$	22.8219	−	39.5287i	0.829477	−	1.43670i	−0.0689721	−	0.997619i	$-0.521972\pi$
$757$	22.8219	−	39.5287i	0.829477	−	1.43670i	0.898449	−	0.439078i	$-0.144695\pi$
$758$	−1.50210	−	2.60171i	−0.0545586	−	0.0944983i
$759$	−1.03603	−	1.79446i	−0.0376056	−	0.0651348i
$760$	−6.58345	+	11.4029i	−0.238807	+	0.413625i
$761$	22.8898	−	39.6464i	0.829756	−	1.43718i	−0.0684730	−	0.997653i	$-0.521813\pi$
$761$	22.8898	−	39.6464i	0.829756	−	1.43718i	0.898229	−	0.439527i	$-0.144854\pi$
$762$	−11.8051	+	20.4470i	−0.427652	+	0.740715i
$763$	−30.1158			−1.09027
$764$	5.89939	+	10.2180i	0.213432	+	0.369676i
$765$	−0.767487	+	1.32933i	−0.0277486	+	0.0480619i
$766$	−57.3933			−2.07370
$767$	−0.945885			−0.0341539
$768$	9.25445	−	16.0292i	0.333941	−	0.578403i
$769$	−3.44133			−0.124097			−0.0620487	−	0.998073i	$-0.519763\pi$
$769$	−3.44133			−0.124097			−0.0620487	+	0.998073i	$0.519763\pi$
$770$	−2.34778	−	4.06647i	−0.0846079	−	0.146545i
$771$	−45.1213			−1.62500
$772$	5.24833	+	9.09038i	0.188892	+	0.327170i
$773$	11.4732	+	19.8722i	0.412662	+	0.714752i	0.995180	−	0.0980661i	$-0.0312656\pi$
$773$	11.4732	+	19.8722i	0.412662	+	0.714752i	−0.582518	+	0.812818i	$0.697932\pi$
$774$	3.70105	+	6.41041i	0.133032	+	0.230418i
$775$	−2.97856	+	5.15901i	−0.106993	+	0.185317i
$776$	6.33069			0.227259
$777$	−4.53612	+	14.4974i	−0.162732	+	0.520093i
$778$	6.90840			0.247678
$779$	23.0193	−	39.8706i	0.824752	−	1.42851i
$780$	−0.429248	−	0.743479i	−0.0153695	−	0.0266208i
$781$	−9.51017	−	16.4721i	−0.340301	−	0.589418i
$782$	1.54236	+	2.67145i	0.0551548	+	0.0955309i
$783$	−36.1118			−1.29053
$784$	−10.5890	−	18.3406i	−0.378177	−	0.655022i
$785$	7.68232			0.274194
$786$	−23.6883	+	41.0294i	−0.844934	+	1.46347i
$787$	−1.93194			−0.0688664			−0.0344332	−	0.999407i	$-0.510963\pi$
$787$	−1.93194			−0.0688664			−0.0344332	+	0.999407i	$0.510963\pi$
$788$	5.66865			0.201937
$789$	6.05082	−	10.4803i	0.215415	−	0.373109i
$790$	2.07317	+	3.59084i	0.0737601	+	0.127756i
$791$	27.0553			0.961974
$792$	−1.23070	+	2.13163i	−0.0437310	+	0.0757443i
$793$	0.689861	−	1.19487i	0.0244977	−	0.0424312i
$794$	0.737372	−	1.27717i	0.0261683	−	0.0453249i
$795$	−2.14583	−	3.71669i	−0.0761048	−	0.131817i
$796$	−1.11981	−	1.93957i	−0.0396906	−	0.0687462i
$797$	−4.45474	+	7.71583i	−0.157795	+	0.273309i	−0.934073	−	0.357082i	$-0.883772\pi$
$797$	−4.45474	+	7.71583i	−0.157795	+	0.273309i	0.776278	+	0.630390i	$0.217105\pi$
$798$	−11.1725	+	19.3513i	−0.395502	+	0.685030i
$799$	2.13816	−	3.70340i	0.0756427	−	0.131017i
$800$	−2.91712			−0.103136
$801$	1.10555	+	1.91487i	0.0390627	+	0.0676586i
$802$	11.2981	−	19.5689i	0.398950	−	0.691002i
$803$	−21.9830			−0.775763
$804$	−2.54294			−0.0896826
$805$	0.577901	−	1.00095i	0.0203683	−	0.0352790i
$806$	9.87329			0.347772
$807$	−11.6453	−	20.1702i	−0.409933	−	0.710025i
$808$	−8.12055			−0.285680
$809$	18.1178	+	31.3809i	0.636986	+	1.10329i	0.986091	+	0.166209i	$0.0531526\pi$
$809$	18.1178	+	31.3809i	0.636986	+	1.10329i	−0.349104	+	0.937084i	$0.613514\pi$
$810$	−5.53512	−	9.58710i	−0.194484	−	0.336857i
$811$	−0.0121930	−	0.0211188i	−0.000428153	−	0.000741583i	0.865811	−	0.500371i	$-0.166803\pi$
$811$	−0.0121930	−	0.0211188i	−0.000428153	−	0.000741583i	−0.866239	+	0.499629i	$0.833470\pi$
$812$	−2.74704	+	4.75801i	−0.0964021	+	0.166973i
$813$	−43.2097			−1.51543
$814$	−5.32307	+	17.0125i	−0.186573	+	0.596289i
$815$	−4.62525			−0.162015
$816$	−10.0129	+	17.3429i	−0.350523	+	0.607124i
$817$	−22.9468	−	39.7450i	−0.802806	−	1.39050i
$818$	−5.89001	−	10.2018i	−0.205939	−	0.356697i
$819$	−0.476611	−	0.825515i	−0.0166541	−	0.0288458i
$820$	4.32359			0.150986
$821$	−23.2070	−	40.1956i	−0.809929	−	1.40284i	−0.912913	−	0.408155i	$-0.866172\pi$
$821$	−23.2070	−	40.1956i	−0.809929	−	1.40284i	0.102984	−	0.994683i	$-0.467161\pi$
$822$	25.0284			0.872966
$823$	14.1118	−	24.4423i	0.491905	−	0.852004i	−0.508052	−	0.861327i	$-0.669634\pi$
$823$	14.1118	−	24.4423i	0.491905	−	0.852004i	0.999957	+	0.00932246i	$0.00296748\pi$
$824$	45.8872			1.59856
$825$	−2.87248			−0.100007
$826$	−1.15604	+	2.00232i	−0.0402238	+	0.0696697i
$827$	−1.80525	−	3.12679i	−0.0627747	−	0.108729i	0.832930	−	0.553378i	$-0.186662\pi$
$827$	−1.80525	−	3.12679i	−0.0627747	−	0.108729i	−0.895705	+	0.444649i	$0.853328\pi$
$828$	0.217574			0.00756123
$829$	−9.37520	+	16.2383i	−0.325614	+	0.563981i	−0.981636	−	0.190761i	$-0.938904\pi$
$829$	−9.37520	+	16.2383i	−0.325614	+	0.563981i	0.656022	+	0.754742i	$0.272238\pi$
$830$	1.64236	−	2.84464i	0.0570070	−	0.0987390i
$831$	4.07459	−	7.05740i	0.141346	−	0.244819i
$832$	−2.56240	−	4.43820i	−0.0888351	−	0.153867i
$833$	5.96050	+	10.3239i	0.206519	+	0.357702i
$834$	−20.8285	+	36.0760i	−0.721232	+	1.24921i
$835$	3.29702	−	5.71060i	0.114098	−	0.197624i
$836$	−2.74017	+	4.74611i	−0.0947707	+	0.164148i
$837$	33.1537			1.14596
$838$	26.1796	+	45.3443i	0.904358	+	1.56639i
$839$	2.44588	−	4.23639i	0.0844413	−	0.146257i	−0.820712	−	0.571343i	$-0.806423\pi$
$839$	2.44588	−	4.23639i	0.0844413	−	0.146257i	0.905153	+	0.425086i	$0.139756\pi$
$840$	5.84351			0.201620
$841$	13.1024			0.451807
$842$	−15.2976	+	26.4962i	−0.527190	+	0.913120i
$843$	−23.4415			−0.807367
$844$	4.61533	+	7.99398i	0.158866	+	0.275164i
$845$	11.9136			0.409840
$846$	−0.721576	−	1.24981i	−0.0248083	−	0.0429692i
$847$	−6.09137	−	10.5506i	−0.209302	−	0.362522i
$848$	6.57770	+	11.3929i	0.225879	+	0.391234i
$849$	−14.5584	+	25.2159i	−0.499642	+	0.865406i
$850$	4.27632			0.146677
$851$	−4.28170	+	0.959080i	−0.146775	+	0.0328768i
$852$	−8.50031			−0.291216
$853$	−6.36889	+	11.0312i	−0.218067	+	0.377702i	−0.954217	−	0.299116i	$-0.903308\pi$
$853$	−6.36889	+	11.0312i	−0.218067	+	0.377702i	0.736150	+	0.676818i	$0.236642\pi$
$854$	−1.68627	−	2.92070i	−0.0577029	−	0.0999444i
$855$	−1.60586	−	2.78144i	−0.0549194	−	0.0951232i
$856$	6.85352	+	11.8706i	0.234249	+	0.405730i
$857$	19.9351			0.680972			0.340486	−	0.940250i	$-0.389408\pi$
$857$	19.9351			0.680972			0.340486	+	0.940250i	$0.389408\pi$
$858$	2.38042	+	4.12301i	0.0812662	+	0.140757i
$859$	−31.3832			−1.07078			−0.535390	−	0.844605i	$-0.679836\pi$
$859$	−31.3832			−1.07078			−0.535390	+	0.844605i	$0.679836\pi$
$860$	2.15499	−	3.73254i	0.0734844	−	0.127279i
$861$	−20.4321			−0.696323
$862$	−35.4030			−1.20583
$863$	−10.5591	+	18.2889i	−0.359435	+	0.622560i	−0.987867	−	0.155305i	$-0.950364\pi$
$863$	−10.5591	+	18.2889i	−0.359435	+	0.622560i	0.628431	+	0.777865i	$0.283697\pi$
$864$	8.11747	+	14.0599i	0.276162	+	0.478326i
$865$	−10.4015			−0.353660
$866$	3.30834	−	5.73021i	0.112422	−	0.194721i
$867$	−7.61184	+	13.1841i	−0.258511	+	0.447755i
$868$	2.52201	−	4.36825i	0.0856026	−	0.148268i
$869$	−2.40287	−	4.16189i	−0.0815117	−	0.141182i
$870$	8.04054	+	13.9266i	0.272600	+	0.472157i
$871$	−1.60904	+	2.78694i	−0.0545202	+	0.0944318i
$872$	21.9902	−	38.0882i	0.744683	−	1.28983i
$873$	−0.772105	+	1.33733i	−0.0261318	+	0.0452616i
$874$	−6.45438			−0.218323
$875$	−0.801138	−	1.38761i	−0.0270834	−	0.0469098i
$876$	−4.91217	+	8.50813i	−0.165967	+	0.287463i
$877$	−20.4132			−0.689304			−0.344652	−	0.938730i	$-0.612003\pi$
$877$	−20.4132			−0.689304			−0.344652	+	0.938730i	$0.612003\pi$
$878$	−47.1718			−1.59197
$879$	0.984564	−	1.70531i	0.0332085	−	0.0575188i
$880$	8.80513			0.296821
$881$	23.5835	+	40.8479i	0.794549	+	1.37620i	0.923125	+	0.384500i	$0.125626\pi$
$881$	23.5835	+	40.8479i	0.794549	+	1.37620i	−0.128576	+	0.991700i	$0.541041\pi$
$882$	4.02304			0.135463
$883$	15.4192	+	26.7069i	0.518899	+	0.898759i	0.999759	+	0.0219616i	$0.00699117\pi$
$883$	15.4192	+	26.7069i	0.518899	+	0.898759i	−0.480860	+	0.876797i	$0.659676\pi$
$884$	−0.740656	−	1.28285i	−0.0249110	−	0.0431470i
$885$	0.707203	+	1.22491i	0.0237724	+	0.0411749i
$886$	32.6357	−	56.5267i	1.09642	−	1.89905i
$887$	−33.5473			−1.12641			−0.563204	−	0.826318i	$-0.690432\pi$
$887$	−33.5473			−1.12641			−0.563204	+	0.826318i	$0.690432\pi$
$888$	−15.0230	−	16.3228i	−0.504140	−	0.547757i
$889$	15.2642			0.511944
$890$	3.07998	−	5.33468i	0.103241	−	0.178819i
$891$	6.41537	+	11.1117i	0.214923	+	0.372258i
$892$	4.55210	+	7.88447i	0.152416	+	0.263991i
$893$	4.47382	+	7.74888i	0.149711	+	0.259306i
$894$	−5.58930			−0.186934
$895$	7.44635	+	12.8975i	0.248904	+	0.431115i
$896$	−21.8749			−0.730789
$897$	−0.585936	+	1.01487i	−0.0195638	+	0.0338856i
$898$	12.3384			0.411738
$899$	−38.6535			−1.28917
$900$	0.150811	−	0.261211i	0.00502702	−	0.00870705i
$901$	−3.70258	−	6.41305i	−0.123351	−	0.213650i
$902$	−23.9767			−0.798338
$903$	−10.1839	+	17.6390i	−0.338898	+	0.586988i
$904$	−19.7554	+	34.2174i	−0.657056	+	1.13805i
$905$	−10.8274	+	18.7536i	−0.359914	+	0.623390i
$906$	−13.2371	−	22.9274i	−0.439774	−	0.761711i
$907$	7.84462	+	13.5873i	0.260476	+	0.451158i	0.966369	−	0.257161i	$-0.0827871\pi$
$907$	7.84462	+	13.5873i	0.260476	+	0.451158i	−0.705892	+	0.708319i	$0.749454\pi$
$908$	−5.09118	+	8.81818i	−0.168957	+	0.292642i
$909$	0.990401	−	1.71543i	0.0328495	−	0.0568971i
$910$	−1.32780	+	2.29982i	−0.0440162	+	0.0762384i
$911$	38.6976			1.28211			0.641055	−	0.767495i	$-0.278497\pi$
$911$	38.6976			1.28211			0.641055	+	0.767495i	$0.278497\pi$
$912$	−20.9507	−	36.2877i	−0.693748	−	1.20161i
$913$	−1.90354	+	3.29703i	−0.0629980	+	0.109116i
$914$	46.9598			1.55329
$915$	−2.06313			−0.0682050
$916$	6.82275	−	11.8174i	0.225430	−	0.390456i
$917$	30.6295			1.01147
$918$	−11.8997	−	20.6109i	−0.392749	−	0.680262i
$919$	35.1580			1.15976			0.579878	−	0.814703i	$-0.303100\pi$
$919$	35.1580			1.15976			0.579878	+	0.814703i	$0.303100\pi$
$920$	0.843953	+	1.46177i	0.0278243	+	0.0481931i
$921$	18.2506	+	31.6109i	0.601377	+	1.04162i
$922$	7.05806	+	12.2249i	0.232445	+	0.402606i
$923$	−5.37855	+	9.31593i	−0.177037	+	0.306637i
$924$	2.43219			0.0800132
$925$	−1.81640	+	5.80523i	−0.0597230	+	0.190875i
$926$	−38.9268			−1.27921
$927$	−5.59651	+	9.69344i	−0.183814	+	0.318374i
$928$	−9.46407	−	16.3922i	−0.310673	−	0.538102i
$929$	7.47422	+	12.9457i	0.245221	+	0.424736i	0.962194	−	0.272366i	$-0.0878061\pi$
$929$	7.47422	+	12.9457i	0.245221	+	0.424736i	−0.716973	+	0.697101i	$0.754473\pi$
$930$	−7.38189	−	12.7858i	−0.242062	−	0.419263i
$931$	−24.9431			−0.817478
$932$	−5.84138	−	10.1176i	−0.191341	−	0.331412i
$933$	15.3137			0.501347
$934$	−6.54175	+	11.3306i	−0.214053	+	0.370750i
$935$	−4.95639			−0.162091
$936$	1.39206			0.0455010
$937$	1.69457	−	2.93508i	0.0553591	−	0.0958848i	−0.837018	−	0.547176i	$-0.815703\pi$
$937$	1.69457	−	2.93508i	0.0553591	−	0.0958848i	0.892377	+	0.451291i	$0.149036\pi$
$938$	3.93307	+	6.81228i	0.128419	+	0.222429i
$939$	34.9445			1.14037
$940$	−0.420147	+	0.727716i	−0.0137037	+	0.0237355i
$941$	2.52778	−	4.37825i	0.0824033	−	0.142727i	−0.821878	−	0.569663i	$-0.807074\pi$
$941$	2.52778	−	4.37825i	0.0824033	−	0.142727i	0.904282	+	0.426936i	$0.140407\pi$
$942$	−9.51972	+	16.4886i	−0.310169	+	0.537229i
$943$	−2.95092	−	5.11114i	−0.0960950	−	0.166442i
$944$	−2.16782	−	3.75477i	−0.0705564	−	0.122207i
$945$	−4.45865	+	7.72261i	−0.145040	+	0.251216i
$946$	−11.9506	+	20.6990i	−0.388548	+	0.672984i
$947$	18.5305	−	32.0957i	0.602159	−	1.04297i	−0.390334	−	0.920673i	$-0.627641\pi$
$947$	18.5305	−	32.0957i	0.602159	−	1.04297i	0.992494	−	0.122297i	$-0.0390260\pi$
$948$	−2.14771			−0.0697545
$949$	6.21633	+	10.7670i	0.201791	+	0.349512i
$950$	−4.47382	+	7.74888i	−0.145150	+	0.251407i
$951$	24.7235			0.801715
$952$	10.0828			0.326787
$953$	−13.7152	+	23.7554i	−0.444279	+	0.769513i	−0.998002	−	0.0631877i	$-0.979873\pi$
$953$	−13.7152	+	23.7554i	−0.444279	+	0.769513i	0.553723	+	0.832701i	$0.313207\pi$
$954$	−2.49905			−0.0809099
$955$	−11.1636	−	19.3359i	−0.361245	−	0.625694i
$956$	−10.0401			−0.324720
$957$	−9.31924	−	16.1414i	−0.301248	−	0.521777i
$958$	−13.8592	−	24.0049i	−0.447772	−	0.775563i
$959$	−8.09056	−	14.0133i	−0.261258	−	0.452512i
$960$	−3.83161	+	6.63655i	−0.123665	+	0.214194i
$961$	4.48716			0.144747
$962$	9.83777	−	2.20361i	0.317182	−	0.0710473i
$963$	−3.34348			−0.107742
$964$	−1.07699	+	1.86540i	−0.0346875	+	0.0600806i
$965$	−9.93156	−	17.2020i	−0.319708	−	0.553751i
$966$	1.43224	+	2.48071i	0.0460815	+	0.0798155i
$967$	−9.02200	−	15.6266i	−0.290128	−	0.502516i	0.683712	−	0.729752i	$-0.260365\pi$
$967$	−9.02200	−	15.6266i	−0.290128	−	0.502516i	−0.973840	+	0.227236i	$0.927031\pi$
$968$	17.7914			0.571837
$969$	11.7931	+	20.4263i	0.378850	+	0.656188i
$970$	4.30206			0.138131
$971$	−10.8135	+	18.7295i	−0.347020	+	0.601057i	−0.985719	−	0.168400i	$-0.946140\pi$
$971$	−10.8135	+	18.7295i	−0.347020	+	0.601057i	0.638698	+	0.769457i	$0.279473\pi$
$972$	−3.08896			−0.0990784
$973$	26.9317			0.863390
$974$	8.73612	−	15.1314i	0.279923	−	0.484841i
$975$	0.812277	+	1.40690i	0.0260137	+	0.0450570i
$976$	6.32420			0.202433
$977$	−9.00054	+	15.5894i	−0.287953	+	0.498749i	−0.973321	−	0.229448i	$-0.926308\pi$
$977$	−9.00054	+	15.5894i	−0.287953	+	0.498749i	0.685368	+	0.728197i	$0.259641\pi$
$978$	5.73148	−	9.92721i	0.183273	−	0.317437i
$979$	−3.56979	+	6.18306i	−0.114091	+	0.197612i
$980$	−1.17123	−	2.02864i	−0.0374137	−	0.0648024i
$981$	5.36396	+	9.29065i	0.171258	+	0.296627i
$982$	2.47299	−	4.28335i	0.0789164	−	0.136687i
$983$	−20.1472	+	34.8959i	−0.642595	+	1.11301i	0.342256	+	0.939607i	$0.388809\pi$
$983$	−20.1472	+	34.8959i	−0.642595	+	1.11301i	−0.984851	+	0.173401i	$0.944524\pi$
$984$	14.9193	−	25.8409i	0.475609	−	0.823779i
$985$	−10.7269			−0.341789
$986$	13.8738	+	24.0300i	0.441830	+	0.765273i
$987$	1.98550	−	3.43898i	0.0631990	−	0.109464i
$988$	3.09945			0.0986066
$989$	−5.88324			−0.187076
$990$	−0.836329	+	1.44856i	−0.0265803	+	0.0460384i
$991$	−30.8204			−0.979043			−0.489521	−	0.871991i	$-0.662829\pi$
$991$	−30.8204			−0.979043			−0.489521	+	0.871991i	$0.662829\pi$
$992$	8.68881	+	15.0495i	0.275870	+	0.477821i
$993$	−2.39669			−0.0760568
$994$	13.1471	+	22.7715i	0.417001	+	0.722267i
$995$	2.11905	+	3.67030i	0.0671783	+	0.116356i
$996$	0.850704	+	1.47346i	0.0269556	+	0.0466884i
$997$	25.5328	−	44.2240i	0.808630	−	1.40059i	−0.105182	−	0.994453i	$-0.533543\pi$
$997$	25.5328	−	44.2240i	0.808630	−	1.40059i	0.913813	−	0.406136i	$-0.133124\pi$
$998$	−58.8931			−1.86423
$999$	33.0344	−	7.39954i	1.04516	−	0.234111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.e.b.121.2	yes	14
5.2	odd	4		925.2.o.c.824.4		28
5.3	odd	4		925.2.o.c.824.11		28
5.4	even	2		925.2.e.b.676.6		14
37.10	even	3		6845.2.a.j.1.6		7
37.26	even	3	inner	185.2.e.b.26.2	✓	14
37.27	even	6		6845.2.a.m.1.2		7
185.63	odd	12		925.2.o.c.174.4		28
185.137	odd	12		925.2.o.c.174.11		28
185.174	even	6		925.2.e.b.26.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.e.b.26.2	✓	14	37.26	even	3	inner
185.2.e.b.121.2	yes	14	1.1	even	1	trivial
925.2.e.b.26.6		14	185.174	even	6
925.2.e.b.676.6		14	5.4	even	2
925.2.o.c.174.4		28	185.63	odd	12
925.2.o.c.174.11		28	185.137	odd	12
925.2.o.c.824.4		28	5.2	odd	4
925.2.o.c.824.11		28	5.3	odd	4
6845.2.a.j.1.6		7	37.10	even	3
6845.2.a.m.1.2		7	37.27	even	6

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:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.795055 + 1.37708i) q^{2} +(0.779300 + 1.34979i) q^{3} +(-0.264225 - 0.457651i) q^{4} +(0.500000 + 0.866025i) q^{5} -2.47835 q^{6} +(0.801138 + 1.38761i) q^{7} -2.33993 q^{8} +(0.285383 - 0.494298i) q^{9} +O(q^{10})\)	\(q+(-0.795055 + 1.37708i) q^{2} +(0.779300 + 1.34979i) q^{3} +(-0.264225 - 0.457651i) q^{4} +(0.500000 + 0.866025i) q^{5} -2.47835 q^{6} +(0.801138 + 1.38761i) q^{7} -2.33993 q^{8} +(0.285383 - 0.494298i) q^{9} -1.59011 q^{10} +1.84299 q^{11} +(0.411821 - 0.713295i) q^{12} +(-0.521158 - 0.902672i) q^{13} -2.54779 q^{14} +(-0.779300 + 1.34979i) q^{15} +(2.38882 - 4.13756i) q^{16} +(-1.34466 + 2.32902i) q^{17} +(0.453790 + 0.785987i) q^{18} +(-2.81353 - 4.87317i) q^{19} +(0.264225 - 0.457651i) q^{20} +(-1.24865 + 2.16273i) q^{21} +(-1.46528 + 2.53793i) q^{22} -0.721350 q^{23} +(-1.82350 - 3.15840i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.65740 q^{26} +5.56540 q^{27} +(0.423361 - 0.733283i) q^{28} -6.48864 q^{29} +(-1.23917 - 2.14631i) q^{30} +5.95711 q^{31} +(1.45856 + 2.52630i) q^{32} +(1.43624 + 2.48764i) q^{33} +(-2.13816 - 3.70340i) q^{34} +(-0.801138 + 1.38761i) q^{35} -0.301621 q^{36} +(5.93568 - 1.32956i) q^{37} +8.94764 q^{38} +(0.812277 - 1.40690i) q^{39} +(-1.16996 - 2.02644i) q^{40} +(4.09082 + 7.08551i) q^{41} +(-1.98550 - 3.43898i) q^{42} +8.15587 q^{43} +(-0.486963 - 0.843445i) q^{44} +0.570766 q^{45} +(0.573513 - 0.993354i) q^{46} -1.59011 q^{47} +7.44643 q^{48} +(2.21636 - 3.83884i) q^{49} +(-0.795055 - 1.37708i) q^{50} -4.19158 q^{51} +(-0.275406 + 0.477017i) q^{52} +(-1.37677 + 2.38463i) q^{53} +(-4.42480 + 7.66397i) q^{54} +(0.921493 + 1.59607i) q^{55} +(-1.87460 - 3.24691i) q^{56} +(4.38517 - 7.59533i) q^{57} +(5.15882 - 8.93534i) q^{58} +(0.453742 - 0.785904i) q^{59} +0.823642 q^{60} +(0.661854 + 1.14637i) q^{61} +(-4.73623 + 8.20339i) q^{62} +0.914524 q^{63} +4.91674 q^{64} +(0.521158 - 0.902672i) q^{65} -4.56756 q^{66} +(-1.54372 - 2.67380i) q^{67} +1.42117 q^{68} +(-0.562148 - 0.973669i) q^{69} +(-1.27390 - 2.20645i) q^{70} +(-5.16020 - 8.93772i) q^{71} +(-0.667775 + 1.15662i) q^{72} -11.9279 q^{73} +(-2.88828 + 9.23095i) q^{74} -1.55860 q^{75} +(-1.48681 + 2.57523i) q^{76} +(1.47649 + 2.55735i) q^{77} +(1.29161 + 2.23713i) q^{78} +(-1.30379 - 2.25823i) q^{79} +4.77764 q^{80} +(3.48096 + 6.02921i) q^{81} -13.0097 q^{82} +(-1.03286 + 1.78896i) q^{83} +1.31970 q^{84} -2.68933 q^{85} +(-6.48437 + 11.2313i) q^{86} +(-5.05660 - 8.75828i) q^{87} -4.31245 q^{88} +(-1.93696 + 3.35491i) q^{89} +(-0.453790 + 0.785987i) q^{90} +(0.835038 - 1.44633i) q^{91} +(0.190599 + 0.330127i) q^{92} +(4.64238 + 8.04083i) q^{93} +(1.26422 - 2.18970i) q^{94} +(2.81353 - 4.87317i) q^{95} +(-2.27331 + 3.93749i) q^{96} -2.70551 q^{97} +(3.52425 + 6.10418i) q^{98} +(0.525957 - 0.910984i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 7 q^{5} + 4 q^{6} + 2 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) \) 14 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 7 * q^5 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 5 * q^9	\( 14 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 7 q^{5} + 4 q^{6} + 2 q^{7} - 6 q^{8} - 5 q^{9} + 4 q^{10} - 10 q^{11} - 8 q^{12} + 6 q^{13} - 36 q^{14} + 2 q^{15} - 14 q^{16} - q^{17} - 4 q^{18} + 6 q^{19} + 8 q^{20} + 13 q^{21} - q^{22} + 12 q^{23} - 21 q^{24} - 7 q^{25} + 2 q^{26} + 22 q^{27} + 13 q^{28} - 12 q^{29} + 2 q^{30} - 8 q^{31} + 18 q^{32} + q^{33} - 11 q^{34} - 2 q^{35} - 8 q^{36} + 12 q^{37} + 16 q^{38} + 23 q^{39} - 3 q^{40} - 3 q^{41} + 29 q^{42} - 38 q^{43} + 25 q^{44} - 10 q^{45} + 10 q^{46} + 4 q^{47} - 20 q^{48} - 7 q^{49} + 2 q^{50} - 14 q^{51} + 46 q^{52} - 2 q^{53} + 23 q^{54} - 5 q^{55} + 19 q^{56} + 22 q^{57} - 12 q^{58} - 18 q^{59} - 16 q^{60} - 20 q^{61} - 21 q^{62} + 46 q^{63} + 50 q^{64} - 6 q^{65} - 42 q^{66} - 20 q^{67} + 110 q^{68} + 17 q^{69} - 18 q^{70} - 11 q^{71} - 29 q^{72} - 36 q^{73} - 66 q^{74} + 4 q^{75} + 40 q^{76} - q^{77} + 6 q^{78} + 23 q^{79} - 28 q^{80} + 29 q^{81} - 24 q^{82} - 9 q^{83} + 8 q^{84} - 2 q^{85} - 3 q^{86} - 43 q^{87} - 116 q^{88} - 16 q^{89} + 4 q^{90} + 12 q^{91} - 33 q^{92} + 25 q^{93} + 22 q^{94} - 6 q^{95} - 67 q^{96} - 62 q^{97} - 24 q^{98} + 4 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 7 * q^5 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 5 * q^9 + 4 * q^10 - 10 * q^11 - 8 * q^12 + 6 * q^13 - 36 * q^14 + 2 * q^15 - 14 * q^16 - q^17 - 4 * q^18 + 6 * q^19 + 8 * q^20 + 13 * q^21 - q^22 + 12 * q^23 - 21 * q^24 - 7 * q^25 + 2 * q^26 + 22 * q^27 + 13 * q^28 - 12 * q^29 + 2 * q^30 - 8 * q^31 + 18 * q^32 + q^33 - 11 * q^34 - 2 * q^35 - 8 * q^36 + 12 * q^37 + 16 * q^38 + 23 * q^39 - 3 * q^40 - 3 * q^41 + 29 * q^42 - 38 * q^43 + 25 * q^44 - 10 * q^45 + 10 * q^46 + 4 * q^47 - 20 * q^48 - 7 * q^49 + 2 * q^50 - 14 * q^51 + 46 * q^52 - 2 * q^53 + 23 * q^54 - 5 * q^55 + 19 * q^56 + 22 * q^57 - 12 * q^58 - 18 * q^59 - 16 * q^60 - 20 * q^61 - 21 * q^62 + 46 * q^63 + 50 * q^64 - 6 * q^65 - 42 * q^66 - 20 * q^67 + 110 * q^68 + 17 * q^69 - 18 * q^70 - 11 * q^71 - 29 * q^72 - 36 * q^73 - 66 * q^74 + 4 * q^75 + 40 * q^76 - q^77 + 6 * q^78 + 23 * q^79 - 28 * q^80 + 29 * q^81 - 24 * q^82 - 9 * q^83 + 8 * q^84 - 2 * q^85 - 3 * q^86 - 43 * q^87 - 116 * q^88 - 16 * q^89 + 4 * q^90 + 12 * q^91 - 33 * q^92 + 25 * q^93 + 22 * q^94 - 6 * q^95 - 67 * q^96 - 62 * q^97 - 24 * q^98 + 4 * q^99

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