LMFDB - Embedded newform 299.2.i.b.231.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [299,2,Mod(231,299)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(299, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("299.231");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 299 = 13 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	299.i (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:	$2.38752702044$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			231.15
Character	$\chi$	$=$	299.231
Dual form			299.2.i.b.277.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.29353 - 1.32417i) q^{2} +(0.903971 + 1.56572i) q^{3} +(2.50685 - 4.34198i) q^{4} +4.10605i q^{5} +(4.14657 + 2.39402i) q^{6} +(-2.88094 - 1.66331i) q^{7} -7.98127i q^{8} +(-0.134328 + 0.232664i) q^{9} +O(q^{10})$	\(q+(2.29353 - 1.32417i) q^{2} +(0.903971 + 1.56572i) q^{3} +(2.50685 - 4.34198i) q^{4} +4.10605i q^{5} +(4.14657 + 2.39402i) q^{6} +(-2.88094 - 1.66331i) q^{7} -7.98127i q^{8} +(-0.134328 + 0.232664i) q^{9} +(5.43711 + 9.41734i) q^{10} +(-1.35139 + 0.780227i) q^{11} +9.06447 q^{12} +(-2.38585 - 2.70328i) q^{13} -8.81002 q^{14} +(-6.42895 + 3.71175i) q^{15} +(-5.55486 - 9.62130i) q^{16} +(1.55404 - 2.69167i) q^{17} +0.711494i q^{18} +(3.05027 + 1.76108i) q^{19} +(17.8284 + 10.2932i) q^{20} -6.01435i q^{21} +(-2.06630 + 3.57894i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(12.4965 - 7.21484i) q^{24} -11.8597 q^{25} +(-9.05161 - 3.04077i) q^{26} +4.93811 q^{27} +(-14.4441 + 8.33933i) q^{28} +(-2.15276 - 3.72869i) q^{29} +(-9.82998 + 17.0260i) q^{30} +6.31962i q^{31} +(-11.6565 - 6.72987i) q^{32} +(-2.44324 - 1.41061i) q^{33} -8.23124i q^{34} +(6.82965 - 11.8293i) q^{35} +(0.673481 + 1.16650i) q^{36} +(-4.07224 + 2.35111i) q^{37} +9.32785 q^{38} +(2.07584 - 6.17927i) q^{39} +32.7715 q^{40} +(-2.91221 + 1.68137i) q^{41} +(-7.96401 - 13.7941i) q^{42} +(0.470690 - 0.815258i) q^{43} +7.82364i q^{44} +(-0.955330 - 0.551560i) q^{45} +(-2.29353 - 1.32417i) q^{46} +4.23285i q^{47} +(10.0429 - 17.3948i) q^{48} +(2.03321 + 3.52163i) q^{49} +(-27.2005 + 15.7042i) q^{50} +5.61922 q^{51} +(-17.7185 + 3.58264i) q^{52} +5.00188 q^{53} +(11.3257 - 6.53889i) q^{54} +(-3.20365 - 5.54889i) q^{55} +(-13.2753 + 22.9936i) q^{56} +6.36785i q^{57} +(-9.87482 - 5.70123i) q^{58} +(7.13164 + 4.11746i) q^{59} +37.2192i q^{60} +(-6.45761 + 11.1849i) q^{61} +(8.36824 + 14.4942i) q^{62} +(0.773985 - 0.446860i) q^{63} -13.4265 q^{64} +(11.0998 - 9.79644i) q^{65} -7.47152 q^{66} +(4.45958 - 2.57474i) q^{67} +(-7.79147 - 13.4952i) q^{68} +(0.903971 - 1.56572i) q^{69} -36.1744i q^{70} +(13.9569 + 8.05801i) q^{71} +(1.85695 + 1.07211i) q^{72} -4.72019i q^{73} +(-6.22653 + 10.7847i) q^{74} +(-10.7208 - 18.5690i) q^{75} +(15.2931 - 8.82950i) q^{76} +5.19104 q^{77} +(-3.42140 - 16.9211i) q^{78} -4.47047 q^{79} +(39.5056 - 22.8085i) q^{80} +(4.86690 + 8.42971i) q^{81} +(-4.45283 + 7.71252i) q^{82} -9.35025i q^{83} +(-26.1142 - 15.0770i) q^{84} +(11.0522 + 6.38096i) q^{85} -2.49309i q^{86} +(3.89206 - 6.74125i) q^{87} +(6.22720 + 10.7858i) q^{88} +(-8.63318 + 4.98437i) q^{89} -2.92143 q^{90} +(2.37711 + 11.7564i) q^{91} -5.01369 q^{92} +(-9.89478 + 5.71275i) q^{93} +(5.60501 + 9.70817i) q^{94} +(-7.23107 + 12.5246i) q^{95} -24.3344i q^{96} +(4.45111 + 2.56985i) q^{97} +(9.32646 + 5.38464i) q^{98} -0.419227i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} + 16 q^{4} - 9 q^{6} - 3 q^{7} - 16 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 + 16 * q^4 - 9 * q^6 - 3 * q^7 - 16 * q^9	$ 30 q - 3 q^{3} + 16 q^{4} - 9 q^{6} - 3 q^{7} - 16 q^{9} + 23 q^{10} - 4 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} - 26 q^{16} + 13 q^{17} - 12 q^{19} + 6 q^{20} - 16 q^{22} - 15 q^{23} + 6 q^{24} - 52 q^{25} - 25 q^{26} + 54 q^{27} - 24 q^{28} - q^{29} + 20 q^{30} - 39 q^{32} - 18 q^{33} + 20 q^{35} + 23 q^{36} - 30 q^{37} + 18 q^{38} - 60 q^{39} + 124 q^{40} - 6 q^{41} - 12 q^{42} + 33 q^{43} + 18 q^{45} + 34 q^{48} + 48 q^{49} - 60 q^{50} + 20 q^{51} - 39 q^{52} + 62 q^{53} + 45 q^{54} - 16 q^{55} - 5 q^{56} - 66 q^{58} - 21 q^{59} - 18 q^{61} + 46 q^{62} - 117 q^{63} - 16 q^{64} - 4 q^{65} + 52 q^{66} + 24 q^{67} - 18 q^{68} - 3 q^{69} + 54 q^{71} - 54 q^{72} + 42 q^{74} + 4 q^{75} - 18 q^{76} - 20 q^{77} + 72 q^{79} + 114 q^{80} - 15 q^{81} + 14 q^{82} - 159 q^{84} - 39 q^{85} + 40 q^{87} + 93 q^{88} - 51 q^{89} - 78 q^{90} - 34 q^{91} - 32 q^{92} + 6 q^{93} + 8 q^{94} - 24 q^{95} - 6 q^{97} - 123 q^{98}+O(q^{100}) $ 30 * q - 3 * q^3 + 16 * q^4 - 9 * q^6 - 3 * q^7 - 16 * q^9 + 23 * q^10 - 4 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 - 26 * q^16 + 13 * q^17 - 12 * q^19 + 6 * q^20 - 16 * q^22 - 15 * q^23 + 6 * q^24 - 52 * q^25 - 25 * q^26 + 54 * q^27 - 24 * q^28 - q^29 + 20 * q^30 - 39 * q^32 - 18 * q^33 + 20 * q^35 + 23 * q^36 - 30 * q^37 + 18 * q^38 - 60 * q^39 + 124 * q^40 - 6 * q^41 - 12 * q^42 + 33 * q^43 + 18 * q^45 + 34 * q^48 + 48 * q^49 - 60 * q^50 + 20 * q^51 - 39 * q^52 + 62 * q^53 + 45 * q^54 - 16 * q^55 - 5 * q^56 - 66 * q^58 - 21 * q^59 - 18 * q^61 + 46 * q^62 - 117 * q^63 - 16 * q^64 - 4 * q^65 + 52 * q^66 + 24 * q^67 - 18 * q^68 - 3 * q^69 + 54 * q^71 - 54 * q^72 + 42 * q^74 + 4 * q^75 - 18 * q^76 - 20 * q^77 + 72 * q^79 + 114 * q^80 - 15 * q^81 + 14 * q^82 - 159 * q^84 - 39 * q^85 + 40 * q^87 + 93 * q^88 - 51 * q^89 - 78 * q^90 - 34 * q^91 - 32 * q^92 + 6 * q^93 + 8 * q^94 - 24 * q^95 - 6 * q^97 - 123 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/299\mathbb{Z}\right)^\times$.

$n$	$93$	$235$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	2.29353	−	1.32417i	1.62177	−	0.936329i	0.635322	−	0.772247i	$-0.280867\pi$
$2$	2.29353	−	1.32417i	1.62177	−	0.936329i	0.986447	−	0.164081i	$-0.0524660\pi$
$3$	0.903971	+	1.56572i	0.521908	+	0.903971i	0.999675	+	0.0254848i	$0.00811295\pi$
$3$	0.903971	+	1.56572i	0.521908	+	0.903971i	−0.477767	+	0.878487i	$0.658554\pi$
$4$	2.50685	−	4.34198i	1.25342	−	2.17099i
$5$			4.10605i			1.83628i	0.396253	+	0.918141i	$0.370310\pi$
$5$			4.10605i			1.83628i	−0.396253	+	0.918141i	$0.629690\pi$
$6$	4.14657	+	2.39402i	1.69283	+	0.977355i
$7$	−2.88094	−	1.66331i	−1.08889	−	0.628673i	−0.155612	−	0.987818i	$-0.549735\pi$
$7$	−2.88094	−	1.66331i	−1.08889	−	0.628673i	−0.933282	+	0.359145i	$0.883068\pi$
$8$		−	7.98127i		−	2.82181i
$9$	−0.134328	+	0.232664i	−0.0447762	+	0.0775546i
$10$	5.43711	+	9.41734i	1.71936	+	2.97803i
$11$	−1.35139	+	0.780227i	−0.407460	+	0.235247i	−0.689698	−	0.724097i	$-0.742257\pi$
$11$	−1.35139	+	0.780227i	−0.407460	+	0.235247i	0.282238	+	0.959345i	$0.408923\pi$
$12$	9.06447			2.61669
$13$	−2.38585	−	2.70328i	−0.661717	−	0.749754i
$13$	−2.38585	−	2.70328i	−0.661717	−	0.749754i
$14$	−8.81002			−2.35458
$15$	−6.42895	+	3.71175i	−1.65995	+	0.958371i
$16$	−5.55486	−	9.62130i	−1.38871	−	2.40532i
$17$	1.55404	−	2.69167i	0.376910	−	0.652827i	−0.613701	−	0.789538i	$-0.710320\pi$
$17$	1.55404	−	2.69167i	0.376910	−	0.652827i	0.990611	+	0.136712i	$0.0436534\pi$
$18$			0.711494i			0.167701i
$19$	3.05027	+	1.76108i	0.699781	+	0.404019i	0.807266	−	0.590188i	$-0.200946\pi$
$19$	3.05027	+	1.76108i	0.699781	+	0.404019i	−0.107485	+	0.994207i	$0.534280\pi$
$20$	17.8284	+	10.2932i	3.98655	+	2.30164i
$21$		−	6.01435i		−	1.31244i
$22$	−2.06630	+	3.57894i	−0.440538	+	0.763034i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	12.4965	−	7.21484i	2.55083	−	1.47272i
$25$	−11.8597			−2.37193
$26$	−9.05161	−	3.04077i	−1.77517	−	0.596344i
$27$	4.93811			0.950340
$28$	−14.4441	+	8.33933i	−2.72969	+	1.57599i
$29$	−2.15276	−	3.72869i	−0.399757	−	0.692400i	0.593939	−	0.804510i	$-0.297572\pi$
$29$	−2.15276	−	3.72869i	−0.399757	−	0.692400i	−0.993696	+	0.112111i	$0.964239\pi$
$30$	−9.82998	+	17.0260i	−1.79470	+	3.10851i
$31$			6.31962i			1.13504i	0.823361	+	0.567518i	$0.192096\pi$
$31$			6.31962i			1.13504i	−0.823361	+	0.567518i	$0.807904\pi$
$32$	−11.6565	−	6.72987i	−2.06059	−	1.18968i
$33$	−2.44324	−	1.41061i	−0.425314	−	0.245555i
$34$		−	8.23124i		−	1.41165i
$35$	6.82965	−	11.8293i	1.15442	−	1.99952i
$36$	0.673481	+	1.16650i	0.112247	+	0.194417i
$37$	−4.07224	+	2.35111i	−0.669472	+	0.386520i	−0.795876	−	0.605459i	$-0.792990\pi$
$37$	−4.07224	+	2.35111i	−0.669472	+	0.386520i	0.126405	+	0.991979i	$0.459656\pi$
$38$	9.32785			1.51318
$39$	2.07584	−	6.17927i	0.332401	−	0.989476i
$40$	32.7715			5.18163
$41$	−2.91221	+	1.68137i	−0.454811	+	0.262585i	−0.709860	−	0.704343i	$-0.751242\pi$
$41$	−2.91221	+	1.68137i	−0.454811	+	0.262585i	0.255049	+	0.966928i	$0.417908\pi$
$42$	−7.96401	−	13.7941i	−1.22887	−	2.12847i
$43$	0.470690	−	0.815258i	0.0717795	−	0.124326i	−0.827902	−	0.560873i	$-0.810466\pi$
$43$	0.470690	−	0.815258i	0.0717795	−	0.124326i	0.899681	+	0.436547i	$0.143799\pi$
$44$			7.82364i			1.17946i
$45$	−0.955330	−	0.551560i	−0.142412	−	0.0822217i
$46$	−2.29353	−	1.32417i	−0.338162	−	0.195238i
$47$			4.23285i			0.617425i	0.951155	+	0.308713i	$0.0998981\pi$
$47$			4.23285i			0.617425i	−0.951155	+	0.308713i	$0.900102\pi$
$48$	10.0429	−	17.3948i	1.44956	−	2.51072i
$49$	2.03321	+	3.52163i	0.290459	+	0.503090i
$50$	−27.2005	+	15.7042i	−3.84673	+	2.22091i
$51$	5.61922			0.786849
$52$	−17.7185	+	3.58264i	−2.45712	+	0.496823i
$53$	5.00188			0.687061			0.343530	−	0.939142i	$-0.388377\pi$
$53$	5.00188			0.687061			0.343530	+	0.939142i	$0.388377\pi$
$54$	11.3257	−	6.53889i	1.54123	−	0.889831i
$55$	−3.20365	−	5.54889i	−0.431981	−	0.748212i
$56$	−13.2753	+	22.9936i	−1.77399	+	3.07265i
$57$			6.36785i			0.843443i
$58$	−9.87482	−	5.70123i	−1.29663	−	0.748608i
$59$	7.13164	+	4.11746i	0.928461	+	0.536047i	0.886324	−	0.463065i	$-0.153250\pi$
$59$	7.13164	+	4.11746i	0.928461	+	0.536047i	0.0421363	+	0.999112i	$0.486584\pi$
$60$			37.2192i			4.80498i
$61$	−6.45761	+	11.1849i	−0.826813	+	1.43208i	0.0737136	+	0.997279i	$0.476515\pi$
$61$	−6.45761	+	11.1849i	−0.826813	+	1.43208i	−0.900526	+	0.434802i	$0.856818\pi$
$62$	8.36824	+	14.4942i	1.06277	+	1.84077i
$63$	0.773985	−	0.446860i	0.0975129	−	0.0562991i
$64$	−13.4265			−1.67831
$65$	11.0998	−	9.79644i	1.37676	−	1.21510i
$66$	−7.47152			−0.919681
$67$	4.45958	−	2.57474i	0.544825	−	0.314555i	−0.202207	−	0.979343i	$-0.564811\pi$
$67$	4.45958	−	2.57474i	0.544825	−	0.314555i	0.747032	+	0.664788i	$0.231478\pi$
$68$	−7.79147	−	13.4952i	−0.944854	−	1.63654i
$69$	0.903971	−	1.56572i	0.108825	−	0.188491i
$70$		−	36.1744i		−	4.32367i
$71$	13.9569	+	8.05801i	1.65638	+	0.956309i	0.974367	+	0.224966i	$0.0722272\pi$
$71$	13.9569	+	8.05801i	1.65638	+	0.956309i	0.682010	+	0.731343i	$0.261106\pi$
$72$	1.85695	+	1.07211i	0.218844	+	0.126350i
$73$		−	4.72019i		−	0.552457i	−0.961092	−	0.276228i	$-0.910915\pi$
$73$		−	4.72019i		−	0.552457i	0.961092	−	0.276228i	$-0.0890846\pi$
$74$	−6.22653	+	10.7847i	−0.723819	+	1.25369i
$75$	−10.7208	−	18.5690i	−1.23793	−	2.14416i
$76$	15.2931	−	8.82950i	1.75424	−	1.01281i
$77$	5.19104			0.591574
$78$	−3.42140	−	16.9211i	−0.387397	−	1.91594i
$79$	−4.47047			−0.502968			−0.251484	−	0.967862i	$-0.580919\pi$
$79$	−4.47047			−0.502968			−0.251484	+	0.967862i	$0.580919\pi$
$80$	39.5056	−	22.8085i	4.41686	−	2.55007i
$81$	4.86690	+	8.42971i	0.540766	+	0.936635i
$82$	−4.45283	+	7.71252i	−0.491733	+	0.851706i
$83$		−	9.35025i		−	1.02632i	−0.858292	−	0.513162i	$-0.828474\pi$
$83$		−	9.35025i		−	1.02632i	0.858292	−	0.513162i	$-0.171526\pi$
$84$	−26.1142	−	15.0770i	−2.84929	−	1.64504i
$85$	11.0522	+	6.38096i	1.19877	+	0.692113i
$86$		−	2.49309i		−	0.268837i
$87$	3.89206	−	6.74125i	0.417273	−	0.722738i
$88$	6.22720	+	10.7858i	0.663822	+	1.14977i
$89$	−8.63318	+	4.98437i	−0.915115	+	0.528342i	−0.882073	−	0.471112i	$-0.843853\pi$
$89$	−8.63318	+	4.98437i	−0.915115	+	0.528342i	−0.0330416	+	0.999454i	$0.510519\pi$
$90$	−2.92143			−0.307946
$91$	2.37711	+	11.7564i	0.249189	+	1.23241i
$92$	−5.01369			−0.522713
$93$	−9.89478	+	5.71275i	−1.02604	+	0.592385i
$94$	5.60501	+	9.70817i	0.578113	+	1.00132i
$95$	−7.23107	+	12.5246i	−0.741893	+	1.28500i
$96$		−	24.3344i		−	2.48362i
$97$	4.45111	+	2.56985i	0.451941	+	0.260928i	0.708650	−	0.705560i	$-0.249305\pi$
$97$	4.45111	+	2.56985i	0.451941	+	0.260928i	−0.256708	+	0.966489i	$0.582638\pi$
$98$	9.32646	+	5.38464i	0.942115	+	0.543930i
$99$		−	0.419227i		−	0.0421339i
$100$	−29.7304	+	51.4945i	−2.97304	+	5.14945i
$101$	−5.52660	−	9.57235i	−0.549917	−	0.952485i	−0.998280	−	0.0586327i	$-0.981326\pi$
$101$	−5.52660	−	9.57235i	−0.549917	−	0.952485i	0.448362	−	0.893852i	$-0.352007\pi$
$102$	12.8878	−	7.44080i	1.27609	−	0.736749i
$103$	−7.27599			−0.716925			−0.358463	−	0.933544i	$-0.616699\pi$
$103$	−7.27599			−0.716925			−0.358463	+	0.933544i	$0.616699\pi$
$104$	−21.5756	+	19.0421i	−2.11566	+	1.86724i
$105$	24.6952			2.41001
$106$	11.4719	−	6.62333i	1.11425	−	0.643314i
$107$	3.22328	+	5.58289i	0.311607	+	0.539718i	0.978710	−	0.205246i	$-0.0657996\pi$
$107$	3.22328	+	5.58289i	0.311607	+	0.539718i	−0.667104	+	0.744965i	$0.732466\pi$
$108$	12.3791	−	21.4412i	1.19118	−	2.06318i
$109$		−	10.5133i		−	1.00700i	−0.863997	−	0.503498i	$-0.832046\pi$
$109$		−	10.5133i		−	1.00700i	0.863997	−	0.503498i	$-0.167954\pi$
$110$	−14.6953	−	8.48436i	−1.40115	−	0.808952i
$111$	−7.36237	−	4.25067i	−0.698806	−	0.403456i
$112$			36.9579i			3.49219i
$113$	8.46655	−	14.6645i	0.796466	−	1.37952i	−0.125437	−	0.992102i	$-0.540033\pi$
$113$	8.46655	−	14.6645i	0.796466	−	1.37952i	0.921904	−	0.387419i	$-0.126633\pi$
$114$	8.43211	+	14.6048i	0.789740	+	1.36787i
$115$	3.55595	−	2.05303i	0.331594	−	0.191446i
$116$	−21.5865			−2.00426
$117$	0.949442	−	0.191974i	0.0877760	−	0.0177480i
$118$	21.8088			2.00766
$119$	−8.95419	+	5.16970i	−0.820829	+	0.473906i
$120$	29.6245	+	51.3112i	2.70434	+	4.68405i
$121$	−4.28249	+	7.41749i	−0.389317	+	0.674318i
$122$			34.2039i			3.09667i
$123$	−5.26512	−	3.03982i	−0.474739	−	0.274091i
$124$	27.4397	+	15.8423i	2.46416	+	1.42268i
$125$		−	28.1662i		−	2.51926i
$126$	1.18344	−	2.04977i	0.105429	−	0.182608i
$127$	5.78058	+	10.0123i	0.512944	+	0.888445i	0.999887	+	0.0150113i	$0.00477842\pi$
$127$	5.78058	+	10.0123i	0.512944	+	0.888445i	−0.486944	+	0.873433i	$0.661888\pi$
$128$	−7.48109	+	4.31921i	−0.661241	+	0.381768i
$129$	1.70196			0.149849
$130$	12.4856	−	37.1664i	1.09506	−	3.25971i
$131$	−10.9833			−0.959616			−0.479808	−	0.877374i	$-0.659294\pi$
$131$	−10.9833			−0.959616			−0.479808	+	0.877374i	$0.659294\pi$
$132$	−12.2497	+	7.07234i	−1.06620	+	0.615568i
$133$	−5.85844	−	10.1471i	−0.507991	−	0.879867i
$134$	6.81878	−	11.8105i	0.589053	−	1.02027i
$135$			20.2761i			1.74509i
$136$	−21.4830	−	12.4032i	−1.84215	−	1.06357i
$137$	−7.64262	−	4.41247i	−0.652953	−	0.376983i	0.136634	−	0.990622i	$-0.456372\pi$
$137$	−7.64262	−	4.41247i	−0.652953	−	0.376983i	−0.789587	+	0.613639i	$0.789705\pi$
$138$		−	4.78804i		−	0.407585i
$139$	6.44691	−	11.1664i	0.546820	−	0.947119i	−0.451670	−	0.892185i	$-0.649172\pi$
$139$	6.44691	−	11.1664i	0.546820	−	0.947119i	0.998490	−	0.0549344i	$-0.0174950\pi$
$140$	−34.2417	−	59.3084i	−2.89396	−	5.01248i
$141$	−6.62748	+	3.82638i	−0.558135	+	0.322239i
$142$	42.6806			3.58168
$143$	5.33339	+	1.79168i	0.446001	+	0.149828i
$144$	2.98470			0.248725
$145$	15.3102	−	8.83934i	1.27144	−	0.734067i
$146$	−6.25033	−	10.8259i	−0.517281	−	0.895957i
$147$	−3.67593	+	6.36690i	−0.303186	+	0.525133i
$148$			23.5755i			1.93789i
$149$	−18.3812	−	10.6124i	−1.50585	−	0.869401i	−0.999977	−	0.00679107i	$-0.997838\pi$
$149$	−18.3812	−	10.6124i	−1.50585	−	0.869401i	−0.505870	−	0.862610i	$-0.668828\pi$
$150$	−49.1769	−	28.3923i	−4.01528	−	2.31822i
$151$		−	8.83169i		−	0.718713i	−0.933200	−	0.359356i	$-0.882996\pi$
$151$		−	8.83169i		−	0.718713i	0.933200	−	0.359356i	$-0.117004\pi$
$152$	14.0556	−	24.3451i	1.14006	−	1.97465i
$153$	0.417503	+	0.723137i	0.0337531	+	0.0584621i
$154$	11.9058	−	6.87382i	0.959397	−	0.553908i
$155$	−25.9487			−2.08425
$156$	−21.6265	−	24.5038i	−1.73150	−	1.96187i
$157$	−10.1028			−0.806295			−0.403147	−	0.915135i	$-0.632084\pi$
$157$	−10.1028			−0.806295			−0.403147	+	0.915135i	$0.632084\pi$
$158$	−10.2532	+	5.91966i	−0.815697	+	0.470943i
$159$	4.52155	+	7.83156i	0.358582	+	0.621083i
$160$	27.6332	−	47.8621i	2.18460	−	3.78383i
$161$			3.32662i			0.262175i
$162$	22.3247	+	12.8892i	1.75400	+	1.01267i
$163$	10.2300	+	5.90632i	0.801279	+	0.462619i	0.843918	−	0.536472i	$-0.180243\pi$
$163$	10.2300	+	5.90632i	0.801279	+	0.462619i	−0.0426393	+	0.999091i	$0.513577\pi$
$164$			16.8597i			1.31652i
$165$	5.79202	−	10.0321i	0.450908	−	0.780996i
$166$	−12.3813	−	21.4451i	−0.960976	−	1.66446i
$167$	9.92973	−	5.73293i	0.768385	−	0.443627i	−0.0639130	−	0.997955i	$-0.520358\pi$
$167$	9.92973	−	5.73293i	0.768385	−	0.443627i	0.832298	+	0.554328i	$0.187025\pi$
$168$	−48.0021			−3.70344
$169$	−1.61541	+	12.8992i	−0.124262	+	0.992249i
$170$	33.7979			2.59218
$171$	−0.819477	+	0.473125i	−0.0626670	+	0.0361808i
$172$	−2.35989	−	4.08745i	−0.179940	−	0.311665i
$173$	6.91680	−	11.9803i	0.525875	−	0.910842i	−0.473671	−	0.880702i	$-0.657071\pi$
$173$	6.91680	−	11.9803i	0.525875	−	0.910842i	0.999546	−	0.0301399i	$-0.00959529\pi$
$174$		−	20.6150i		−	1.56282i
$175$	34.1670	+	19.7263i	2.58278	+	1.49117i
$176$	15.0136	+	8.66810i	1.13169	+	0.653383i
$177$			14.8882i			1.11907i
$178$	−13.2003	+	22.8636i	−0.989403	+	1.71370i
$179$	−7.16850	−	12.4162i	−0.535799	−	0.928031i	−0.999124	−	0.0418429i	$-0.986677\pi$
$179$	−7.16850	−	12.4162i	−0.535799	−	0.928031i	0.463325	−	0.886188i	$-0.346656\pi$
$180$	−4.78973	+	2.76535i	−0.357005	+	0.206117i
$181$	15.2888			1.13641			0.568204	−	0.822888i	$-0.307638\pi$
$181$	15.2888			1.13641			0.568204	+	0.822888i	$0.307638\pi$
$182$	21.0194	+	23.8159i	1.55806	+	1.76535i
$183$	−23.3500			−1.72608
$184$	−6.91198	+	3.99064i	−0.509558	+	0.294194i
$185$	−9.65377	−	16.7208i	−0.709759	−	1.22934i
$186$	−15.1293	+	26.2047i	−1.10933	+	1.92142i
$187$			4.85001i			0.354668i
$188$	18.3790	+	10.6111i	1.34043	+	0.773895i
$189$	−14.2264	−	8.21362i	−1.03482	−	0.597453i
$190$			38.3006i			2.77862i
$191$	−0.659477	+	1.14225i	−0.0477181	+	0.0826501i	−0.888898	−	0.458105i	$-0.848528\pi$
$191$	−0.659477	+	1.14225i	−0.0477181	+	0.0826501i	0.841180	+	0.540755i	$0.181862\pi$
$192$	−12.1372	−	21.0222i	−0.875925	−	1.51715i
$193$	12.3492	−	7.12983i	0.888917	−	0.513217i	0.0153290	−	0.999883i	$-0.495120\pi$
$193$	12.3492	−	7.12983i	0.888917	−	0.513217i	0.873588	+	0.486666i	$0.161787\pi$
$194$	13.6116			0.977259
$195$	25.3724	+	8.52352i	1.81696	+	0.610382i
$196$	20.3878			1.45627
$197$	−1.58791	+	0.916782i	−0.113134	+	0.0653180i	−0.555499	−	0.831517i	$-0.687473\pi$
$197$	−1.58791	+	0.916782i	−0.113134	+	0.0653180i	0.442365	+	0.896835i	$0.354140\pi$
$198$	−0.555127	−	0.961508i	−0.0394512	−	0.0683314i
$199$	−0.802423	+	1.38984i	−0.0568823	+	0.0985230i	−0.893064	−	0.449929i	$-0.851449\pi$
$199$	−0.802423	+	1.38984i	−0.0568823	+	0.0985230i	0.836182	+	0.548452i	$0.184783\pi$
$200$			94.6552i			6.69314i
$201$	8.06267	+	4.65499i	0.568697	+	0.328337i
$202$	−25.3508	−	14.6363i	−1.78368	−	1.02981i
$203$			14.3228i			1.00527i
$204$	14.0865	−	24.3986i	0.986254	−	1.70824i
$205$	−6.90378	−	11.9577i	−0.482181	−	0.835162i
$206$	−16.6877	+	9.63464i	−1.16269	+	0.671278i
$207$	0.268657			0.0186729
$208$	−12.7560	+	37.9713i	−0.884466	+	2.63284i
$209$	−5.49616			−0.380177
$210$	56.6392	−	32.7006i	3.90847	−	2.25656i
$211$	−4.65419	−	8.06129i	−0.320408	−	0.554962i	0.660165	−	0.751121i	$-0.270487\pi$
$211$	−4.65419	−	8.06129i	−0.320408	−	0.554962i	−0.980572	+	0.196159i	$0.937153\pi$
$212$	12.5389	−	21.7181i	0.861177	−	1.49160i
$213$			29.1368i			1.99642i
$214$	14.7854	+	8.53634i	1.01071	+	0.583532i
$215$	3.34749	+	1.93268i	0.228297	+	0.131807i
$216$		−	39.4124i		−	2.68168i
$217$	10.5115	−	18.2064i	0.713567	−	1.23593i
$218$	−13.9214	−	24.1126i	−0.942879	−	1.63311i
$219$	7.39052	−	4.26692i	0.499405	−	0.288332i
$220$	−32.1243			−2.16582
$221$	−10.9840	+	2.22094i	−0.738867	+	0.149397i
$222$	−22.5144			−1.51107
$223$	−16.3940	+	9.46505i	−1.09782	+	0.633827i	−0.935648	−	0.352936i	$-0.885183\pi$
$223$	−16.3940	+	9.46505i	−1.09782	+	0.633827i	−0.162173	+	0.986762i	$0.551850\pi$
$224$	22.3877	+	38.7767i	1.49584	+	2.59088i
$225$	1.59309	−	2.75931i	0.106206	−	0.183954i
$226$		−	44.8446i		−	2.98302i
$227$	−0.741203	−	0.427934i	−0.0491954	−	0.0284030i	0.475201	−	0.879877i	$-0.342375\pi$
$227$	−0.741203	−	0.427934i	−0.0491954	−	0.0284030i	−0.524396	+	0.851475i	$0.675709\pi$
$228$	27.6491	+	15.9632i	1.83111	+	1.05719i
$229$		−	0.422468i		−	0.0279174i	−0.999903	−	0.0139587i	$-0.995557\pi$
$229$		−	0.422468i		−	0.0279174i	0.999903	−	0.0139587i	$-0.00444334\pi$
$230$	5.43711	−	9.41734i	0.358512	−	0.620961i
$231$	4.69256	+	8.12774i	0.308747	+	0.534766i
$232$	−29.7597	+	17.1817i	−1.95382	+	1.12804i
$233$	−7.20150			−0.471786			−0.235893	−	0.971779i	$-0.575801\pi$
$233$	−7.20150			−0.471786			−0.235893	+	0.971779i	$0.575801\pi$
$234$	1.92337	−	1.69752i	0.125734	−	0.110970i
$235$	−17.3803			−1.13377
$236$	35.7559	−	20.6436i	2.32751	−	1.34379i
$237$	−4.04118	−	6.99953i	−0.262503	−	0.454668i
$238$	−13.6911	+	23.7137i	−0.887463	+	1.53713i
$239$		−	4.38961i		−	0.283940i	−0.989871	−	0.141970i	$-0.954656\pi$
$239$		−	4.38961i		−	0.283940i	0.989871	−	0.141970i	$-0.0453437\pi$
$240$	71.4238	+	41.2365i	4.61039	+	2.66181i
$241$	6.23185	+	3.59796i	0.401429	+	0.231765i	0.687100	−	0.726563i	$-0.258883\pi$
$241$	6.23185	+	3.59796i	0.401429	+	0.231765i	−0.285671	+	0.958328i	$0.592217\pi$
$242$			22.6830i			1.45812i
$243$	−1.39190	+	2.41085i	−0.0892907	+	0.154656i
$244$	32.3765	+	56.0777i	2.07269	+	3.59001i
$245$	−14.4600	+	8.34848i	−0.923815	+	0.533365i
$246$	−16.1009			−1.02656
$247$	−2.51683	−	12.4474i	−0.160142	−	0.792010i
$248$	50.4386			3.20285
$249$	14.6399	−	8.45236i	0.927767	−	0.535647i
$250$	−37.2967	−	64.5999i	−2.35885	−	4.08565i
$251$	1.21096	−	2.09745i	0.0764354	−	0.132390i	−0.825274	−	0.564732i	$-0.808979\pi$
$251$	1.21096	−	2.09745i	0.0764354	−	0.132390i	0.901710	+	0.432342i	$0.142313\pi$
$252$		−	4.48084i		−	0.282266i
$253$	1.35139	+	0.780227i	0.0849613	+	0.0490525i
$254$	26.5159	+	15.3089i	1.66375	+	0.960568i
$255$			23.0728i			1.44488i
$256$	1.98778	−	3.44293i	0.124236	−	0.215183i
$257$	8.66551	+	15.0091i	0.540540	+	0.936243i	0.998873	+	0.0474621i	$0.0151133\pi$
$257$	8.66551	+	15.0091i	0.540540	+	0.936243i	−0.458333	+	0.888780i	$0.651553\pi$
$258$	3.90349	−	2.25368i	0.243021	−	0.140308i
$259$	15.6425			0.971978
$260$	−14.7105	−	72.7533i	−0.912307	−	4.51197i
$261$	1.15671			0.0715984
$262$	−25.1905	+	14.5437i	−1.55627	+	0.898516i
$263$	6.45613	+	11.1823i	0.398102	+	0.689533i	0.993492	−	0.113904i	$-0.0363357\pi$
$263$	6.45613	+	11.1823i	0.398102	+	0.689533i	−0.595390	+	0.803437i	$0.703002\pi$
$264$	−11.2584	+	19.5002i	−0.692908	+	1.20015i
$265$			20.5380i			1.26164i
$266$	−26.8730	−	15.5151i	−1.64769	−	0.951293i
$267$	−15.6083	−	9.01145i	−0.955212	−	0.551492i
$268$		−	25.8179i		−	1.57708i
$269$	5.02831	−	8.70929i	0.306582	−	0.531015i	−0.671031	−	0.741430i	$-0.734148\pi$
$269$	5.02831	−	8.70929i	0.306582	−	0.531015i	0.977612	+	0.210415i	$0.0674814\pi$
$270$	26.8490	+	46.5039i	1.63398	+	2.83014i
$271$	−6.21279	+	3.58696i	−0.377400	+	0.217892i	−0.676687	−	0.736271i	$-0.736585\pi$
$271$	−6.21279	+	3.58696i	−0.377400	+	0.217892i	0.299286	+	0.954163i	$0.403251\pi$
$272$	−34.5299			−2.09368
$273$	−16.2584	+	14.3493i	−0.984006	+	0.868462i
$274$	−23.3714			−1.41192
$275$	16.0271	−	9.25323i	0.966469	−	0.557991i
$276$	−4.53223	−	7.85006i	−0.272808	−	0.472518i
$277$	2.99146	−	5.18135i	0.179739	−	0.311317i	−0.762052	−	0.647516i	$-0.775808\pi$
$277$	2.99146	−	5.18135i	0.179739	−	0.311317i	0.941791	+	0.336198i	$0.109141\pi$
$278$		−	34.1472i		−	2.04801i
$279$	−1.47035	−	0.848904i	−0.0880273	−	0.0508226i
$280$	−94.4128	−	54.5093i	−5.64225	−	3.25755i
$281$			22.7057i			1.35451i	0.735749	+	0.677254i	$0.236830\pi$
$281$			22.7057i			1.35451i	−0.735749	+	0.677254i	$0.763170\pi$
$282$	−10.1335	+	17.5518i	−0.603444	+	1.04520i
$283$	9.24562	+	16.0139i	0.549595	+	0.951927i	0.998302	+	0.0582479i	$0.0185514\pi$
$283$	9.24562	+	16.0139i	0.549595	+	0.951927i	−0.448707	+	0.893679i	$0.648115\pi$
$284$	69.9755	−	40.4004i	4.15228	−	2.39732i
$285$	−26.1467			−1.54880
$286$	14.6048	−	2.95304i	0.863599	−	0.174617i
$287$	11.1866			0.660321
$288$	3.13159	−	1.80803i	0.184531	−	0.106539i
$289$	3.66993	+	6.35650i	0.215878	+	0.373912i
$290$	23.4096	−	40.5465i	1.37466	−	2.38097i
$291$			9.29227i			0.544723i
$292$	−20.4950	−	11.8328i	−1.19938	−	0.692462i
$293$	3.70845	+	2.14108i	0.216650	+	0.125083i	0.604398	−	0.796682i	$-0.293414\pi$
$293$	3.70845	+	2.14108i	0.216650	+	0.125083i	−0.387748	+	0.921765i	$0.626747\pi$
$294$			19.4702i			1.13553i
$295$	−16.9065	+	29.2829i	−0.984334	+	1.70492i
$296$	18.7648	+	32.5016i	1.09068	+	1.88912i
$297$	−6.67333	+	3.85285i	−0.387226	+	0.223565i
$298$	−56.2104			−3.25618
$299$	−1.14818	+	3.41785i	−0.0664009	+	0.197659i
$300$	−107.502			−6.20661
$301$	−2.71206	+	1.56581i	−0.156320	+	0.0902516i
$302$	−11.6946	−	20.2557i	−0.672951	−	1.16559i
$303$	9.99178	−	17.3063i	0.574013	−	0.994219i
$304$		−	39.1301i		−	2.24427i
$305$	−45.9258	−	26.5153i	−2.62971	−	1.51826i
$306$	1.91511	+	1.10569i	0.109480	+	0.0632081i
$307$		−	17.2594i		−	0.985047i	−0.870299	−	0.492524i	$-0.836075\pi$
$307$		−	17.2594i		−	0.985047i	0.870299	−	0.492524i	$-0.163925\pi$
$308$	13.0131	−	22.5394i	0.741493	−	1.28430i
$309$	−6.57729	−	11.3922i	−0.374169	−	0.648080i
$310$	−59.5140	+	34.3604i	−3.38017	+	1.95154i
$311$	−19.4363			−1.10213			−0.551065	−	0.834462i	$-0.685778\pi$
$311$	−19.4363			−1.10213			−0.551065	+	0.834462i	$0.685778\pi$
$312$	−49.3185	−	16.5679i	−2.79211	−	0.937971i
$313$	−7.66180			−0.433071			−0.216535	−	0.976275i	$-0.569476\pi$
$313$	−7.66180			−0.433071			−0.216535	+	0.976275i	$0.569476\pi$
$314$	−23.1712	+	13.3779i	−1.30762	+	0.754957i
$315$	1.83483	+	3.17802i	0.103381	+	0.179061i
$316$	−11.2068	+	19.4107i	−0.630431	+	1.09194i
$317$			14.4345i			0.810724i	0.914156	+	0.405362i	$0.132855\pi$
$317$			14.4345i			0.810724i	−0.914156	+	0.405362i	$0.867145\pi$
$318$	20.7406	+	11.9746i	1.16308	+	0.671502i
$319$	5.81844	+	3.35928i	0.325770	+	0.188084i
$320$		−	55.1299i		−	3.08186i
$321$	−5.82751	+	10.0935i	−0.325260	+	0.563367i
$322$	4.40501	+	7.62970i	0.245482	+	0.425187i
$323$	9.48049	−	5.47356i	0.527508	−	0.304557i
$324$	48.8022			2.71124
$325$	28.2954	+	32.0600i	1.56955	+	1.77837i
$326$	31.2838			1.73265
$327$	16.4610	−	9.50376i	0.910295	−	0.525559i
$328$	13.4194	+	23.2432i	0.740965	+	1.28339i
$329$	7.04056	−	12.1946i	0.388158	−	0.672310i
$330$		−	30.6785i		−	1.68879i
$331$	13.7701	+	7.95019i	0.756875	+	0.436982i	0.828173	−	0.560473i	$-0.189381\pi$
$331$	13.7701	+	7.95019i	0.756875	+	0.436982i	−0.0712978	+	0.997455i	$0.522714\pi$
$332$	−40.5986	−	23.4396i	−2.22814	−	1.28642i
$333$		−	1.26328i		−	0.0692275i
$334$	15.1827	−	26.2973i	0.830762	−	1.43892i
$335$	10.5720	+	18.3113i	0.577611	+	1.00045i
$336$	−57.8658	+	33.4088i	−3.15684	+	1.82260i
$337$	−1.03822			−0.0565557			−0.0282778	−	0.999600i	$-0.509002\pi$
$337$	−1.03822			−0.0565557			−0.0282778	+	0.999600i	$0.509002\pi$
$338$	13.3758	+	31.7238i	0.727547	+	1.72555i
$339$	30.6141			1.66273
$340$	55.4121	−	31.9922i	3.00514	−	1.73502i
$341$	−4.93074	−	8.54028i	−0.267014	−	0.462482i
$342$	−1.25300	+	2.17025i	−0.0677543	+	0.117354i
$343$			9.75889i			0.526931i
$344$	−6.50680	−	3.75670i	−0.350823	−	0.202548i
$345$	6.42895	+	3.71175i	0.346123	+	0.199834i
$346$		−	36.6361i		−	1.96957i
$347$	−1.83943	+	3.18598i	−0.0987456	+	0.171032i	−0.911166	−	0.412040i	$-0.864816\pi$
$347$	−1.83943	+	3.18598i	−0.0987456	+	0.171032i	0.812420	+	0.583073i	$0.198150\pi$
$348$	−19.5136	−	33.7986i	−1.04604	−	1.81179i
$349$	−16.3074	+	9.41506i	−0.872913	+	0.503977i	−0.868315	−	0.496013i	$-0.834797\pi$
$349$	−16.3074	+	9.41506i	−0.872913	+	0.503977i	−0.00459780	+	0.999989i	$0.501464\pi$
$350$	104.484			5.58490
$351$	−11.7816	−	13.3491i	−0.628856	−	0.712521i
$352$	21.0033			1.11948
$353$	−23.0202	+	13.2907i	−1.22524	+	0.707394i	−0.966031	−	0.258427i	$-0.916796\pi$
$353$	−23.0202	+	13.2907i	−1.22524	+	0.707394i	−0.259211	+	0.965821i	$0.583462\pi$
$354$	19.7146	+	34.1466i	1.04782	+	1.81487i
$355$	−33.0866	+	57.3077i	−1.75605	+	3.04157i
$356$			49.9802i			2.64894i
$357$	−16.1887	−	9.34652i	−0.856794	−	0.494671i
$358$	−32.8823	−	18.9846i	−1.73788	−	1.00337i
$359$		−	14.7266i		−	0.777241i	−0.921398	−	0.388621i	$-0.872952\pi$
$359$		−	14.7266i		−	0.777241i	0.921398	−	0.388621i	$-0.127048\pi$
$360$	−4.40215	+	7.62474i	−0.232014	+	0.401859i
$361$	−3.29722	−	5.71095i	−0.173538	−	0.300576i
$362$	35.0653	−	20.2450i	1.84299	−	1.06405i
$363$	−15.4850			−0.812752
$364$	57.0051	+	19.1501i	2.98788	+	1.00374i
$365$	19.3814			1.01447
$366$	−53.5538	+	30.9193i	−2.79930	+	1.61618i
$367$	−7.15734	−	12.3969i	−0.373610	−	0.647112i	0.616508	−	0.787349i	$-0.288547\pi$
$367$	−7.15734	−	12.3969i	−0.373610	−	0.647112i	−0.990118	+	0.140237i	$0.955214\pi$
$368$	−5.55486	+	9.62130i	−0.289567	+	0.501545i
$369$		−	0.903422i		−	0.0470303i
$370$	−44.2824	−	25.5664i	−2.30213	−	1.32914i
$371$	−14.4101	−	8.31968i	−0.748136	−	0.431936i
$372$			57.2840i			2.97003i
$373$	−1.93191	+	3.34616i	−0.100030	+	0.173258i	−0.911697	−	0.410863i	$-0.865227\pi$
$373$	−1.93191	+	3.34616i	−0.100030	+	0.173258i	0.811667	+	0.584121i	$0.198561\pi$
$374$	6.42223	+	11.1236i	0.332086	+	0.575189i
$375$	44.1004	−	25.4614i	2.27734	−	1.31482i
$376$	33.7836			1.74225
$377$	−4.94351	+	14.7156i	−0.254604	+	0.757892i
$378$	−43.5049			−2.23765
$379$	−30.8842	+	17.8310i	−1.58641	+	0.915916i	−0.592521	+	0.805555i	$0.701867\pi$
$379$	−30.8842	+	17.8310i	−1.58641	+	0.915916i	−0.993892	+	0.110361i	$0.964799\pi$
$380$	36.2544	+	62.7944i	1.85981	+	3.22129i
$381$	−10.4510	+	18.1016i	−0.535419	+	0.927373i
$382$			3.49303i			0.178719i
$383$	28.3203	+	16.3507i	1.44710	+	0.835484i	0.998308	−	0.0581520i	$-0.0185208\pi$
$383$	28.3203	+	16.3507i	1.44710	+	0.835484i	0.448793	+	0.893636i	$0.351854\pi$
$384$	−13.5254	−	7.80888i	−0.690214	−	0.398495i
$385$			21.3147i			1.08630i
$386$	18.8822	−	32.7049i	0.961079	−	1.66464i
$387$	0.126454	+	0.219025i	0.00642802	+	0.0111337i
$388$	22.3165	−	12.8844i	1.13295	−	0.654107i
$389$	−5.59750			−0.283804			−0.141902	−	0.989881i	$-0.545322\pi$
$389$	−5.59750			−0.283804			−0.141902	+	0.989881i	$0.545322\pi$
$390$	69.4789	−	14.0484i	3.51820	−	0.711370i
$391$	−3.10808			−0.157182
$392$	28.1071	−	16.2276i	1.41962	−	0.819619i
$393$	−9.92859	−	17.1968i	−0.500831	−	0.867465i
$394$	−2.42795	+	4.20533i	−0.122318	+	0.211861i
$395$		−	18.3560i		−	0.923591i
$396$	−1.82028	−	1.05094i	−0.0914723	−	0.0528116i
$397$	2.60512	+	1.50407i	0.130747	+	0.0754870i	0.563947	−	0.825811i	$-0.309282\pi$
$397$	2.60512	+	1.50407i	0.130747	+	0.0754870i	−0.433200	+	0.901298i	$0.642616\pi$
$398$			4.25018i			0.213042i
$399$	10.5917	−	18.3454i	0.530249	−	0.918419i
$400$	65.8788	+	114.105i	3.29394	+	5.70527i
$401$	3.62936	−	2.09541i	0.181242	−	0.104640i	−0.406634	−	0.913591i	$-0.633298\pi$
$401$	3.62936	−	2.09541i	0.181242	−	0.104640i	0.587876	+	0.808951i	$0.299964\pi$
$402$	24.6559			1.22973
$403$	17.0837	−	15.0777i	0.850998	−	0.751073i
$404$	−55.4173			−2.75712
$405$	−34.6128	+	19.9837i	−1.71993	+	0.993000i
$406$	18.9658	+	32.8498i	0.941259	+	1.63031i
$407$	3.66880	−	6.35454i	0.181855	−	0.314983i
$408$		−	44.8486i		−	2.22033i
$409$	3.36151	+	1.94077i	0.166216	+	0.0959648i	0.580800	−	0.814046i	$-0.302740\pi$
$409$	3.36151	+	1.94077i	0.166216	+	0.0959648i	−0.414584	+	0.910011i	$0.636073\pi$
$410$	−31.6680	−	18.2835i	−1.56397	−	0.902960i
$411$		−	15.9550i		−	0.787001i
$412$	−18.2398	+	31.5923i	−0.898610	+	1.55644i
$413$	−13.6972	−	23.7243i	−0.673996	−	1.16740i
$414$	0.616172	−	0.355747i	0.0302832	−	0.0174840i
$415$	38.3926			1.88462
$416$	9.61794	+	47.5672i	0.471558	+	2.33217i
$417$	23.3113			1.14156
$418$	−12.6056	+	7.27784i	−0.616560	+	0.355971i
$419$	1.74363	+	3.02005i	0.0851817	+	0.147539i	0.905469	−	0.424413i	$-0.139520\pi$
$419$	1.74363	+	3.02005i	0.0851817	+	0.147539i	−0.820287	+	0.571952i	$0.806186\pi$
$420$	61.9071	−	107.226i	3.02076	−	5.23211i
$421$		−	33.1849i		−	1.61733i	−0.588268	−	0.808666i	$-0.700190\pi$
$421$		−	33.1849i		−	1.61733i	0.588268	−	0.808666i	$-0.299810\pi$
$422$	−21.3490	−	12.3259i	−1.03925	−	0.600014i
$423$	−0.984832	−	0.568593i	−0.0478842	−	0.0276459i
$424$		−	39.9213i		−	1.93875i
$425$	−18.4304	+	31.9224i	−0.894005	+	1.54846i
$426$	38.5821	+	66.8261i	1.86931	+	3.23774i
$427$	37.2080	−	21.4820i	1.80062	−	1.03959i
$428$	32.3211			1.56230
$429$	2.01596	+	9.97025i	0.0973313	+	0.481368i
$430$	10.2368			0.493660
$431$	−25.4896	+	14.7164i	−1.22779	+	0.708865i	−0.966567	−	0.256413i	$-0.917459\pi$
$431$	−25.4896	+	14.7164i	−1.22779	+	0.708865i	−0.261223	+	0.965278i	$0.584126\pi$
$432$	−27.4305	−	47.5110i	−1.31975	−	2.28588i
$433$	9.00135	−	15.5908i	0.432577	−	0.749246i	−0.564517	−	0.825421i	$-0.690938\pi$
$433$	9.00135	−	15.5908i	0.432577	−	0.749246i	0.997094	+	0.0761754i	$0.0242709\pi$
$434$		−	55.6760i		−	2.67253i
$435$	27.6799	+	15.9810i	1.32715	+	0.766231i
$436$	−45.6488	−	26.3553i	−2.18618	−	1.26219i
$437$		−	3.52215i		−	0.168487i
$438$	11.3002	−	19.5726i	0.539947	−	0.935215i
$439$	4.87008	+	8.43523i	0.232436	+	0.402592i	0.958525	−	0.285010i	$-0.0919969\pi$
$439$	4.87008	+	8.43523i	0.232436	+	0.402592i	−0.726088	+	0.687602i	$0.758664\pi$
$440$	−44.2872	+	25.5692i	−2.11131	+	1.21897i
$441$	−1.09247			−0.0520226
$442$	−22.2513	+	19.6385i	−1.05839	+	0.934109i
$443$	26.1460			1.24223			0.621117	−	0.783718i	$-0.286679\pi$
$443$	26.1460			1.24223			0.621117	+	0.783718i	$0.286679\pi$
$444$	−36.9127	+	21.3115i	−1.75180	+	1.01140i
$445$	−20.4661	−	35.4483i	−0.970185	−	1.68041i
$446$	−25.0667	+	43.4167i	−1.18694	+	2.05584i
$447$		−	38.3732i		−	1.81499i
$448$	38.6809	+	22.3325i	1.82750	+	1.05511i
$449$	−29.2949	−	16.9134i	−1.38251	−	0.798194i	−0.390056	−	0.920791i	$-0.627544\pi$
$449$	−29.2949	−	16.9134i	−1.38251	−	0.798194i	−0.992457	+	0.122597i	$0.960878\pi$
$450$		−	8.43809i		−	0.397775i
$451$	2.62370	−	4.54438i	0.123545	−	0.213986i
$452$	−42.4487	−	73.5233i	−1.99662	−	3.45824i
$453$	13.8280	−	7.98359i	0.649696	−	0.375102i
$454$	−2.26663			−0.106378
$455$	−48.2724	+	9.76054i	−2.26304	+	0.457581i
$456$	50.8236			2.38003
$457$	10.9141	−	6.30125i	0.510540	−	0.294760i	−0.222516	−	0.974929i	$-0.571427\pi$
$457$	10.9141	−	6.30125i	0.510540	−	0.294760i	0.733055	+	0.680169i	$0.238094\pi$
$458$	−0.559418	−	0.968941i	−0.0261399	−	0.0452756i
$459$	7.67402	−	13.2918i	0.358192	−	0.620407i
$460$		−	20.5865i		−	0.959850i
$461$	2.48053	+	1.43214i	0.115530	+	0.0667013i	0.556652	−	0.830746i	$-0.312086\pi$
$461$	2.48053	+	1.43214i	0.115530	+	0.0667013i	−0.441121	+	0.897447i	$0.645419\pi$
$462$	21.5250	+	12.4275i	1.00143	+	0.578178i
$463$			23.9782i			1.11436i	0.830392	+	0.557180i	$0.188117\pi$
$463$			23.9782i			1.11436i	−0.830392	+	0.557180i	$0.811883\pi$
$464$	−23.9165	+	41.4247i	−1.11030	+	1.92309i
$465$	−23.4569	−	40.6285i	−1.08779	−	1.88410i
$466$	−16.5168	+	9.53600i	−0.765128	+	0.441747i
$467$	35.0215			1.62060			0.810302	−	0.586013i	$-0.199303\pi$
$467$	35.0215			1.62060			0.810302	+	0.586013i	$0.199303\pi$
$468$	1.54656	−	4.60371i	0.0714896	−	0.212807i
$469$	−17.1304			−0.791008
$470$	−39.8622	+	23.0145i	−1.83871	+	1.06158i
$471$	−9.13268	−	15.8183i	−0.420812	−	0.728867i
$472$	32.8625	−	56.9196i	1.51262	−	2.61994i
$473$			1.46898i			0.0675437i
$474$	−18.5371	−	10.7024i	−0.851438	−	0.491578i
$475$	−36.1752	−	20.8858i	−1.65983	−	0.958306i
$476$			51.8386i			2.37602i
$477$	−0.671894	+	1.16376i	−0.0307639	+	0.0532847i
$478$	−5.81259	−	10.0677i	−0.265862	−	0.460486i
$479$	1.93547	−	1.11745i	0.0884340	−	0.0510574i	−0.455131	−	0.890425i	$-0.650408\pi$
$479$	1.93547	−	1.11745i	0.0884340	−	0.0510574i	0.543565	+	0.839367i	$0.317074\pi$
$480$	99.9185			4.56063
$481$	16.0715	+	5.39899i	0.732795	+	0.246173i
$482$	19.0572			0.868033
$483$	−5.20858	+	3.00717i	−0.236998	+	0.136831i
$484$	21.4711	+	37.1890i	0.975959	+	1.69041i
$485$	−10.5519	+	18.2765i	−0.479138	+	0.829892i
$486$			7.37246i			0.334422i
$487$	6.03509	+	3.48436i	0.273476	+	0.157891i	0.630466	−	0.776217i	$-0.282864\pi$
$487$	6.03509	+	3.48436i	0.273476	+	0.157891i	−0.356990	+	0.934108i	$0.616197\pi$
$488$	89.2698	+	51.5400i	4.04106	+	2.33310i
$489$			21.3566i			0.965777i
$490$	−22.1096	+	38.2949i	−0.998810	+	1.72999i
$491$	8.83360	+	15.3002i	0.398655	+	0.690490i	0.993560	−	0.113305i	$-0.0361438\pi$
$491$	8.83360	+	15.3002i	0.398655	+	0.690490i	−0.594905	+	0.803796i	$0.702810\pi$
$492$	−26.3977	+	15.2407i	−1.19010	+	0.687104i
$493$	−13.3819			−0.602689
$494$	−22.2549	−	25.2158i	−1.00129	−	1.13451i
$495$	1.72137			0.0773697
$496$	60.8029	−	35.1046i	2.73013	−	1.57624i
$497$	−26.8060	−	46.4293i	−1.20241	−	2.08264i
$498$	22.3847	−	38.7714i	1.00308	−	1.73739i
$499$			8.92181i			0.399395i	0.979858	+	0.199698i	$0.0639960\pi$
$499$			8.92181i			0.399395i	−0.979858	+	0.199698i	$0.936004\pi$
$500$	−122.297	−	70.6082i	−5.46929	−	3.15770i
$501$	17.9524	+	10.3648i	0.802053	+	0.463066i
$502$		−	6.41408i		−	0.286274i
$503$	−13.0316	+	22.5714i	−0.581051	+	1.00641i	0.414304	+	0.910139i	$0.364025\pi$
$503$	−13.0316	+	22.5714i	−0.581051	+	1.00641i	−0.995355	+	0.0962715i	$0.969308\pi$
$504$	−3.56651	−	6.17738i	−0.158865	−	0.275162i
$505$	39.3046	−	22.6925i	1.74903	−	1.00980i
$506$	4.13261			0.183717
$507$	−21.6569	+	9.13126i	−0.961819	+	0.405533i
$508$	57.9641			2.57174
$509$	27.1416	−	15.6702i	1.20303	−	0.694570i	0.241803	−	0.970325i	$-0.422261\pi$
$509$	27.1416	−	15.6702i	1.20303	−	0.694570i	0.961228	+	0.275755i	$0.0889278\pi$
$510$	30.5523	+	52.9182i	1.35288	+	2.34326i
$511$	−7.85116	+	13.5986i	−0.347315	+	0.601567i
$512$		−	27.8054i		−	1.22884i
$513$	15.0626	+	8.69639i	0.665030	+	0.383955i
$514$	39.7492	+	22.9492i	1.75326	+	1.01225i
$515$		−	29.8756i		−	1.31648i
$516$	4.26655	−	7.38988i	0.187824	−	0.325321i
$517$	−3.30259	−	5.72025i	−0.145248	−	0.251576i
$518$	35.8765	−	20.7133i	1.57632	−	0.910091i
$519$	25.0104			1.09783
$520$	−78.1880	−	88.5905i	−3.42877	−	3.88495i
$521$	33.4361			1.46486			0.732430	−	0.680842i	$-0.238386\pi$
$521$	33.4361			1.46486			0.732430	+	0.680842i	$0.238386\pi$
$522$	2.65294	−	1.53168i	0.116116	−	0.0670396i
$523$	−9.66261	−	16.7361i	−0.422516	−	0.731820i	0.573668	−	0.819088i	$-0.305520\pi$
$523$	−9.66261	−	16.7361i	−0.422516	−	0.731820i	−0.996185	+	0.0872676i	$0.972186\pi$
$524$	−27.5334	+	47.6893i	−1.20280	+	2.08332i
$525$			71.3281i			3.11302i
$526$	29.6146	+	17.0980i	1.29126	+	0.745509i
$527$	17.0103	+	9.82093i	0.740982	+	0.427806i
$528$			31.3429i			1.36402i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	27.1957	+	47.1044i	1.18131	+	2.04608i
$531$	−1.91596	+	1.10618i	−0.0831458	+	0.0480042i
$532$	−58.7448			−2.54691
$533$	11.4933	+	3.86102i	0.497831	+	0.167239i
$534$	−47.7307			−2.06551
$535$	−22.9236	+	13.2350i	−0.991075	+	0.572198i
$536$	−20.5497	−	35.5931i	−0.887612	−	1.53739i
$537$	12.9602	−	22.4478i	0.559276	−	0.968694i
$538$		−	26.6333i		−	1.14824i
$539$	−5.49534	−	3.17274i	−0.236701	−	0.136659i
$540$	88.0387	+	50.8292i	3.78858	+	2.18734i
$541$			1.51775i			0.0652530i	0.999468	+	0.0326265i	$0.0103872\pi$
$541$			1.51775i			0.0652530i	−0.999468	+	0.0326265i	$0.989613\pi$
$542$	−9.49947	+	16.4536i	−0.408037	+	0.706741i
$543$	13.8206	+	23.9381i	0.593101	+	1.02728i
$544$	−36.2292	+	20.9170i	−1.55332	+	0.896807i
$545$	43.1683			1.84913
$546$	−18.2882	+	54.4395i	−0.782664	+	2.32980i
$547$	−23.3521			−0.998462			−0.499231	−	0.866469i	$-0.666384\pi$
$547$	−23.3521			−0.998462			−0.499231	+	0.866469i	$0.666384\pi$
$548$	−38.3177	+	22.1228i	−1.63685	+	0.945038i
$549$	−1.73488	−	3.00490i	−0.0740430	−	0.128246i
$550$	24.5057	−	42.4451i	1.04493	−	1.80986i
$551$		−	15.1647i		−	0.646038i
$552$	−12.4965	−	7.21484i	−0.531885	−	0.307084i
$553$	12.8792	+	7.43579i	0.547678	+	0.316202i
$554$		−	15.8448i		−	0.673180i
$555$	17.4535	−	30.2303i	0.740858	−	1.28320i
$556$	−32.3228	−	55.9847i	−1.37079	−	2.37428i
$557$	−4.39672	+	2.53845i	−0.186295	+	0.107558i	−0.590247	−	0.807223i	$-0.700970\pi$
$557$	−4.39672	+	2.53845i	−0.186295	+	0.107558i	0.403952	+	0.914780i	$0.367636\pi$
$558$	−4.49637			−0.190347
$559$	−3.32687	+	0.672682i	−0.140711	+	0.0284514i
$560$	−151.751			−6.41265
$561$	−7.59378	+	4.38427i	−0.320610	+	0.185104i
$562$	30.0662	+	52.0762i	1.26827	+	2.19670i
$563$	21.8109	−	37.7776i	0.919219	−	1.59213i	0.118616	−	0.992940i	$-0.462154\pi$
$563$	21.8109	−	37.7776i	0.919219	−	1.59213i	0.800604	−	0.599194i	$-0.204512\pi$
$564$			38.3686i			1.61561i
$565$	60.2132	+	34.7641i	2.53319	+	1.46254i
$566$	42.4102	+	24.4855i	1.78263	+	1.02920i
$567$		−	32.3807i		−	1.35986i
$568$	64.3131	−	111.394i	2.69852	−	4.67397i
$569$	−19.5297	−	33.8264i	−0.818728	−	1.41808i	−0.906620	−	0.421948i	$-0.861347\pi$
$569$	−19.5297	−	33.8264i	−0.818728	−	1.41808i	0.0878926	−	0.996130i	$-0.471987\pi$
$570$	−59.9683	+	34.6227i	−2.51179	+	1.45018i
$571$	6.51727			0.272739			0.136370	−	0.990658i	$-0.456457\pi$
$571$	6.51727			0.272739			0.136370	+	0.990658i	$0.456457\pi$
$572$	21.1495	−	18.6660i	0.884303	−	0.780467i
$573$	−2.38459			−0.0996178
$574$	25.6567	−	14.8129i	1.07089	−	0.618278i
$575$	5.92983	+	10.2708i	0.247291	+	0.428321i
$576$	1.80356	−	3.12386i	0.0751484	−	0.130161i
$577$		−	38.5406i		−	1.60447i	−0.597010	−	0.802234i	$-0.703645\pi$
$577$		−	38.5406i		−	1.60447i	0.597010	−	0.802234i	$-0.296355\pi$
$578$	16.8342	+	9.71921i	0.700209	+	0.404266i
$579$	22.3267	+	12.8903i	0.927866	+	0.535704i
$580$		−	88.6354i		−	3.68039i
$581$	−15.5524	+	26.9375i	−0.645222	+	1.11756i
$582$	12.3045	+	21.3121i	0.510040	+	0.883414i
$583$	−6.75950	+	3.90260i	−0.279950	+	0.161629i
$584$	−37.6732			−1.55893
$585$	0.788257	+	3.89846i	0.0325904	+	0.161182i
$586$	11.3406			0.468475
$587$	10.1033	−	5.83316i	0.417009	−	0.240760i	−0.276788	−	0.960931i	$-0.589270\pi$
$587$	10.1033	−	5.83316i	0.417009	−	0.240760i	0.693797	+	0.720171i	$0.255937\pi$
$588$	18.4300	+	31.9217i	0.760040	+	1.31643i
$589$	−11.1293	+	19.2766i	−0.458576	+	0.794277i
$590$			89.5482i			3.68664i
$591$	−2.87086	−	1.65749i	−0.118091	−	0.0681800i
$592$	45.2414	+	26.1201i	1.85941	+	1.07353i
$593$			46.4773i			1.90860i	0.298857	+	0.954298i	$0.403395\pi$
$593$			46.4773i			1.90860i	−0.298857	+	0.954298i	$0.596605\pi$
$594$	−10.2036	+	17.6732i	−0.418661	+	0.725141i
$595$	−21.2271	−	36.7664i	−0.870225	−	1.50727i
$596$	−92.1577	+	53.2073i	−3.77493	+	2.17945i
$597$	−2.90147			−0.118749
$598$	1.89243	+	9.35931i	0.0773870	+	0.382731i
$599$	−0.235237			−0.00961154			−0.00480577	−	0.999988i	$-0.501530\pi$
$599$	−0.235237			−0.00961154			−0.00480577	+	0.999988i	$0.501530\pi$
$600$	−148.204	+	85.5656i	−6.05040	+	3.49320i
$601$	23.6319	+	40.9317i	0.963966	+	1.66964i	0.712368	+	0.701806i	$0.247623\pi$
$601$	23.6319	+	40.9317i	0.963966	+	1.66964i	0.251598	+	0.967832i	$0.419044\pi$
$602$	−4.14679	+	7.18244i	−0.169010	+	0.292735i
$603$			1.38344i			0.0563382i
$604$	−38.3471	−	22.1397i	−1.56032	−	0.900851i
$605$	−30.4566	−	17.5841i	−1.23824	−	0.714897i
$606$		−	52.9232i		−	2.14986i
$607$	−1.88943	+	3.27258i	−0.0766895	+	0.132830i	−0.901820	−	0.432112i	$-0.857768\pi$
$607$	−1.88943	+	3.27258i	−0.0766895	+	0.132830i	0.825130	+	0.564943i	$0.191102\pi$
$608$	−23.7036	−	41.0559i	−0.961309	−	1.66504i
$609$	−22.4256	+	12.9474i	−0.908732	+	0.524656i
$610$	−140.443			−5.68637
$611$	11.4426	−	10.0990i	0.462917	−	0.408561i
$612$	4.18646			0.169228
$613$	−4.42736	+	2.55614i	−0.178819	+	0.103241i	−0.586738	−	0.809777i	$-0.699588\pi$
$613$	−4.42736	+	2.55614i	−0.178819	+	0.103241i	0.407919	+	0.913018i	$0.366255\pi$
$614$	−22.8544	−	39.5850i	−0.922328	−	1.59752i
$615$	12.4816	−	21.6188i	0.503308	−	0.871756i
$616$		−	41.4311i		−	1.66931i
$617$	−27.8430	−	16.0752i	−1.12092	−	0.647163i	−0.179283	−	0.983798i	$-0.557378\pi$
$617$	−27.8430	−	16.0752i	−1.12092	−	0.647163i	−0.941635	+	0.336635i	$0.890711\pi$
$618$	−30.1704	−	17.4189i	−1.21363	−	0.700690i
$619$		−	19.7991i		−	0.795793i	−0.917430	−	0.397896i	$-0.869740\pi$
$619$		−	19.7991i		−	0.795793i	0.917430	−	0.397896i	$-0.130260\pi$
$620$	−65.0493	+	112.669i	−2.61244	+	4.52489i
$621$	−2.46906	−	4.27653i	−0.0990798	−	0.171611i
$622$	−44.5776	+	25.7369i	−1.78740	+	1.03196i
$623$	33.1622			1.32862
$624$	−70.9836	+	14.3527i	−2.84162	+	0.574567i
$625$	56.3534			2.25414
$626$	−17.5726	+	10.1455i	−0.702341	+	0.405496i
$627$	−4.96837	−	8.60547i	−0.198418	−	0.343669i
$628$	−25.3263	+	43.8664i	−1.01063	+	1.75046i
$629$			14.6148i			0.582732i
$630$	8.41647	+	4.85925i	0.335320	+	0.193597i
$631$	−35.2877	−	20.3734i	−1.40478	−	0.811051i	−0.409903	−	0.912129i	$-0.634438\pi$
$631$	−35.2877	−	20.3734i	−1.40478	−	0.811051i	−0.994879	+	0.101078i	$0.967771\pi$
$632$			35.6801i			1.41928i
$633$	8.41451	−	14.5744i	0.334447	−	0.579278i
$634$	19.1138	+	33.1060i	0.759104	+	1.31481i
$635$	−41.1109	+	23.7354i	−1.63144	+	0.941910i
$636$	45.3393			1.79782
$637$	4.66899	−	13.8984i	0.184992	−	0.550676i
$638$	17.7930			0.704432
$639$	−3.74961	+	2.16484i	−0.148332	+	0.0856397i
$640$	−17.7349	−	30.7177i	−0.701033	−	1.21423i
$641$	16.9770	−	29.4051i	0.670553	−	1.16143i	−0.307195	−	0.951647i	$-0.599390\pi$
$641$	16.9770	−	29.4051i	0.670553	−	1.16143i	0.977748	−	0.209785i	$-0.0672763\pi$
$642$			30.8664i			1.21820i
$643$	2.57813	+	1.48849i	0.101672	+	0.0587001i	0.549974	−	0.835182i	$-0.314638\pi$
$643$	2.57813	+	1.48849i	0.101672	+	0.0587001i	−0.448302	+	0.893882i	$0.647971\pi$
$644$	14.4441	+	8.33933i	0.569179	+	0.328616i
$645$			6.98834i			0.275165i
$646$	14.4958	−	25.1075i	0.570331	−	0.987843i
$647$	−17.8621	−	30.9381i	−0.702233	−	1.21630i	−0.967681	−	0.252178i	$-0.918853\pi$
$647$	−17.8621	−	30.9381i	−0.702233	−	1.21630i	0.265448	−	0.964125i	$-0.414480\pi$
$648$	67.2798	−	38.8440i	2.64300	−	1.52594i
$649$	−12.8502			−0.504414
$650$	107.349	+	36.0625i	4.21058	+	1.41449i
$651$	38.0084			1.48966
$652$	51.2903	−	29.6125i	2.00868	−	1.15971i
$653$	−1.66394	−	2.88203i	−0.0651151	−	0.112783i	0.831630	−	0.555330i	$-0.187408\pi$
$653$	−1.66394	−	2.88203i	−0.0651151	−	0.112783i	−0.896745	+	0.442548i	$0.854075\pi$
$654$	25.1692	−	43.5943i	0.984192	−	1.70467i
$655$		−	45.0980i		−	1.76213i
$656$	32.3539	+	18.6795i	1.26321	+	0.729313i
$657$	1.09822	+	0.634056i	0.0428456	+	0.0247369i
$658$		−	37.2915i		−	1.45378i
$659$	−4.40501	+	7.62970i	−0.171595	+	0.297211i	−0.938978	−	0.343978i	$-0.888225\pi$
$659$	−4.40501	+	7.62970i	−0.171595	+	0.297211i	0.767383	+	0.641189i	$0.221559\pi$
$660$	−29.0394	−	50.2977i	−1.13036	−	1.95784i
$661$	−28.3048	+	16.3418i	−1.10093	+	0.635621i	−0.936465	−	0.350762i	$-0.885922\pi$
$661$	−28.3048	+	16.3418i	−1.10093	+	0.635621i	−0.164463	+	0.986383i	$0.552589\pi$
$662$	42.1096			1.63663
$663$	−13.4066	−	15.1903i	−0.520671	−	0.589943i
$664$	−74.6269			−2.89609
$665$	41.6646	−	24.0551i	1.61568	−	0.932815i
$666$	−1.67280	−	2.89737i	−0.0648197	−	0.112271i
$667$	−2.15276	+	3.72869i	−0.0833551	+	0.144375i
$668$		−	57.4863i		−	2.22421i
$669$	−29.6393	−	17.1123i	−1.14592	−	0.661599i
$670$	48.4945	+	27.9983i	1.87350	+	1.08167i
$671$		−	20.1536i		−	0.778022i
$672$	−40.4758	+	70.1061i	−1.56139	+	2.70440i
$673$	−0.575256	−	0.996373i	−0.0221745	−	0.0384074i	0.854725	−	0.519081i	$-0.173726\pi$
$673$	−0.575256	−	0.996373i	−0.0221745	−	0.0384074i	−0.876900	+	0.480673i	$0.840392\pi$
$674$	−2.38120	+	1.37478i	−0.0917203	+	0.0529547i
$675$	−58.5644			−2.25414
$676$	51.9587	+	39.3505i	1.99841	+	1.51348i
$677$	−10.3156			−0.396460			−0.198230	−	0.980156i	$-0.563519\pi$
$677$	−10.3156			−0.396460			−0.198230	+	0.980156i	$0.563519\pi$
$678$	70.2143	−	40.5382i	2.69656	−	1.55686i
$679$	−8.54892	−	14.8072i	−0.328077	−	0.568247i
$680$	50.9282	−	88.2102i	1.95301	−	3.38271i
$681$		−	1.54736i		−	0.0592949i
$682$	−22.6176	−	13.0583i	−0.866071	−	0.500026i
$683$	−20.5144	−	11.8440i	−0.784963	−	0.453199i	0.0532233	−	0.998583i	$-0.483050\pi$
$683$	−20.5144	−	11.8440i	−0.784963	−	0.453199i	−0.838186	+	0.545384i	$0.816384\pi$
$684$			4.74421i			0.181399i
$685$	18.1178	−	31.3810i	0.692247	−	1.19901i
$686$	12.9224	+	22.3823i	0.493380	+	0.854560i
$687$	0.661468	−	0.381899i	0.0252366	−	0.0145703i
$688$	−10.4585			−0.398725
$689$	−11.9337	−	13.5215i	−0.454639	−	0.515126i
$690$	19.6600			0.748442
$691$	−20.2551	+	11.6943i	−0.770539	+	0.444871i	−0.833067	−	0.553173i	$-0.813417\pi$
$691$	−20.2551	+	11.6943i	−0.770539	+	0.444871i	0.0625282	+	0.998043i	$0.480084\pi$
$692$	−34.6787	−	60.0653i	−1.31829	−	2.28334i
$693$	−0.697305	+	1.20777i	−0.0264884	+	0.0458793i
$694$			9.74285i			0.369833i
$695$	45.8497	+	26.4713i	1.73918	+	1.00412i
$696$	−53.8038	−	31.0636i	−2.03943	−	1.17746i
$697$			10.4516i			0.395884i
$698$	−24.9343	+	43.1874i	−0.943775	+	1.63467i
$699$	−6.50995	−	11.2756i	−0.246229	−	0.426481i
$700$	171.303	−	98.9017i	6.47464	−	3.73813i
$701$	36.1569			1.36563			0.682813	−	0.730593i	$-0.260756\pi$
$701$	36.1569			1.36563			0.682813	+	0.730593i	$0.260756\pi$
$702$	−44.6979	−	15.0156i	−1.68701	−	0.566729i
$703$	−16.5619			−0.624645
$704$	18.1445	−	10.4757i	0.683846	−	0.394818i
$705$	−15.7113	−	27.2128i	−0.591722	−	1.02489i
$706$	−35.1983	+	60.9653i	−1.32471	+	2.29446i
$707$			36.7698i			1.38287i
$708$	64.6445	+	37.3225i	2.42949	+	1.40267i
$709$	3.32825	+	1.92157i	0.124995	+	0.0721659i	0.561194	−	0.827684i	$-0.310342\pi$
$709$	3.32825	+	1.92157i	0.124995	+	0.0721659i	−0.436199	+	0.899850i	$0.643676\pi$
$710$			175.249i			6.57698i
$711$	0.600512	−	1.04012i	0.0225210	−	0.0390074i
$712$	39.7816	+	68.9037i	1.49088	+	2.58228i
$713$	5.47295	−	3.15981i	0.204964	−	0.118336i
$714$	−49.5055			−1.85270
$715$	−7.35674	+	21.8992i	−0.275126	+	0.818984i
$716$	−71.8813			−2.68633
$717$	6.87292	−	3.96808i	0.256674	−	0.148191i
$718$	−19.5005	−	33.7759i	−0.727753	−	1.26051i
$719$	−12.2107	+	21.1495i	−0.455382	+	0.788745i	−0.998710	−	0.0507757i	$-0.983831\pi$
$719$	−12.2107	+	21.1495i	−0.455382	+	0.788745i	0.543328	+	0.839520i	$0.317164\pi$
$720$			12.2553i			0.456730i
$721$	20.9617	+	12.1022i	0.780655	+	0.450711i
$722$	−15.1245	−	8.73214i	−0.562876	−	0.324977i
$723$			13.0098i			0.483840i
$724$	38.3267	−	66.3838i	1.42440	−	2.46713i
$725$	25.5310	+	44.2210i	0.948197	+	1.64233i
$726$	−35.5153	+	20.5048i	−1.31810	+	0.761003i
$727$	−7.15656			−0.265422			−0.132711	−	0.991155i	$-0.542368\pi$
$727$	−7.15656			−0.265422			−0.132711	+	0.991155i	$0.542368\pi$
$728$	93.8310	−	18.9724i	3.47761	−	0.703162i
$729$	24.1684			0.895127
$730$	44.4517	−	25.6642i	1.64523	−	0.949875i
$731$	−1.46294	−	2.53389i	−0.0541088	−	0.0937191i
$732$	−58.5348	+	101.385i	−2.16351	+	3.74731i
$733$			30.8323i			1.13882i	0.822055	+	0.569408i	$0.192827\pi$
$733$			30.8323i			1.13882i	−0.822055	+	0.569408i	$0.807173\pi$
$734$	−32.8311	−	18.9551i	−1.21182	−	0.699644i
$735$	−26.1428	−	15.0936i	−0.964293	−	0.556735i
$736$			13.4597i			0.496133i
$737$	−4.01777	+	6.95897i	−0.147996	+	0.256337i
$738$	−1.19628	−	2.07202i	−0.0440358	−	0.0762722i
$739$	−15.8532	+	9.15286i	−0.583170	+	0.336693i	−0.762392	−	0.647115i	$-0.775975\pi$
$739$	−15.8532	+	9.15286i	−0.583170	+	0.336693i	0.179222	+	0.983809i	$0.442642\pi$
$740$	−96.8021			−3.55851
$741$	17.2141	−	15.1928i	0.632375	−	0.558120i
$742$	−44.0666			−1.61774
$743$	−7.59422	+	4.38453i	−0.278605	+	0.160853i	−0.632792	−	0.774322i	$-0.718091\pi$
$743$	−7.59422	+	4.38453i	−0.278605	+	0.160853i	0.354187	+	0.935175i	$0.384758\pi$
$744$	45.5950	+	78.9729i	1.67159	+	2.89529i
$745$	43.5750	−	75.4742i	1.59647	−	2.76516i
$746$			10.2327i			0.374645i
$747$	2.17546	+	1.25601i	0.0795961	+	0.0459548i
$748$	21.0587	+	12.1582i	0.769981	+	0.444549i
$749$		−	21.4453i		−	0.783594i
$750$	67.4304	−	116.793i	2.46221	−	4.26467i
$751$	−15.4771	−	26.8072i	−0.564769	−	0.978208i	−0.997071	−	0.0764794i	$-0.975632\pi$
$751$	−15.4771	−	26.8072i	−0.564769	−	0.978208i	0.432302	−	0.901729i	$-0.357701\pi$
$752$	40.7256	−	23.5129i	1.48511	−	0.857428i
$753$	4.37871			0.159569
$754$	8.14787	+	40.2967i	0.296728	+	1.46752i
$755$	36.2634			1.31976
$756$	−71.3268	+	41.1806i	−2.59413	+	1.49772i
$757$	8.81812	+	15.2734i	0.320500	+	0.555122i	0.980591	−	0.196063i	$-0.0628158\pi$
$757$	8.81812	+	15.2734i	0.320500	+	0.555122i	−0.660091	+	0.751185i	$0.729482\pi$
$758$	−47.2225	+	81.7917i	−1.71520	+	2.97081i
$759$			2.82121i			0.102403i
$760$	99.9621	+	57.7132i	3.62601	+	2.09348i
$761$	−39.8502	−	23.0075i	−1.44457	−	0.834021i	−0.446417	−	0.894825i	$-0.647300\pi$
$761$	−39.8502	−	23.0075i	−1.44457	−	0.834021i	−0.998150	+	0.0608036i	$0.980634\pi$
$762$			55.3554i			2.00531i
$763$	−17.4870	+	30.2883i	−0.633071	+	1.09651i
$764$	3.30641	+	5.72687i	0.119622	+	0.207191i
$765$	−2.96924	+	1.71429i	−0.107353	+	0.0619803i
$766$	86.6046			3.12915
$767$	−5.88443	−	29.1024i	−0.212474	−	1.05083i
$768$	7.18758			0.259359
$769$	−32.0181	+	18.4856i	−1.15460	+	0.666609i	−0.950004	−	0.312237i	$-0.898922\pi$
$769$	−32.0181	+	18.4856i	−1.15460	+	0.666609i	−0.204597	+	0.978846i	$0.565588\pi$
$770$	28.2243	+	48.8859i	1.01713	+	1.76172i
$771$	−15.6668	+	27.1356i	−0.564224	+	0.977265i
$772$		−	71.4936i		−	2.57311i
$773$	−3.82456	−	2.20811i	−0.137560	−	0.0794203i	0.429641	−	0.903000i	$-0.358640\pi$
$773$	−3.82456	−	2.20811i	−0.137560	−	0.0794203i	−0.567201	+	0.823580i	$0.691974\pi$
$774$	0.580052	+	0.334893i	0.0208495	+	0.0120375i
$775$		−	74.9486i		−	2.69223i
$776$	20.5107	−	35.5255i	0.736290	−	1.27529i
$777$	14.1404	+	24.4918i	0.507283	+	0.878640i
$778$	−12.8380	+	7.41203i	−0.460265	+	0.265734i
$779$	−11.8441			−0.424358
$780$	100.614	−	88.7995i	3.60255	−	3.17953i
$781$	−25.1483			−0.899877
$782$	−7.12846	+	4.11562i	−0.254913	+	0.147174i
$783$	−10.6306	−	18.4127i	−0.379905	−	0.658015i
$784$	22.5884	−	39.1243i	0.806730	−	1.39730i
$785$		−	41.4828i		−	1.48059i
$786$	−45.5430	−	26.2943i	−1.62446	−	0.937885i
$787$	17.2854	+	9.97973i	0.616158	+	0.355739i	0.775372	−	0.631505i	$-0.217563\pi$
$787$	17.2854	+	9.97973i	0.616158	+	0.355739i	−0.159214	+	0.987244i	$0.550896\pi$
$788$			9.19292i			0.327484i
$789$	−11.6723	+	20.2170i	−0.415545	+	0.719745i
$790$	−24.3064	−	42.1000i	−0.864784	−	1.49785i
$791$	−48.7833	+	28.1650i	−1.73453	+	1.00143i
$792$	−3.34596			−0.118894
$793$	45.6428	−	9.22885i	1.62082	−	0.327726i
$794$	7.96656			0.282723
$795$	−32.1568	+	18.5657i	−1.14048	+	0.658459i
$796$	4.02310	+	6.96822i	0.142595	+	0.246982i
$797$	22.5130	−	38.9936i	0.797450	−	1.38122i	−0.123822	−	0.992304i	$-0.539515\pi$
$797$	22.5130	−	38.9936i	0.797450	−	1.38122i	0.921272	−	0.388919i	$-0.127151\pi$
$798$		−	56.1009i		−	1.98595i
$799$	11.3935	+	6.57802i	0.403072	+	0.232714i
$800$	138.242	+	79.8140i	4.88759	+	2.82185i
$801$		−	2.67817i		−	0.0946285i
$802$	5.54936	−	9.61177i	0.195955	−	0.339404i
$803$	3.68282	+	6.37884i	0.129964	+	0.225104i
$804$	40.4237	−	23.3387i	1.42564	−	0.823091i
$805$	−13.6593			−0.481427
$806$	19.2165	−	57.2027i	0.676872	−	2.01488i
$807$	18.1818			0.640030
$808$	−76.3995	+	44.1093i	−2.68773	+	1.55176i
$809$	−7.44743	−	12.8993i	−0.261838	−	0.453516i	0.704892	−	0.709314i	$-0.250995\pi$
$809$	−7.44743	−	12.8993i	−0.261838	−	0.453516i	−0.966730	+	0.255798i	$0.917662\pi$
$810$	−52.9237	+	91.6665i	−1.85955	+	3.22083i
$811$			33.1853i			1.16529i	0.812726	+	0.582647i	$0.197983\pi$
$811$			33.1853i			1.16529i	−0.812726	+	0.582647i	$0.802017\pi$
$812$	62.1895	+	35.9051i	2.18242	+	1.26002i
$813$	−11.2324	−	6.48501i	−0.393937	−	0.227439i
$814$		−	19.4324i		−	0.681106i
$815$	−24.2517	+	42.0051i	−0.849498	+	1.47137i
$816$	−31.2140	−	54.0642i	−1.09271	−	1.89263i
$817$	2.87147	−	1.65784i	0.100460	−	0.0580005i
$818$	10.2796			0.359418
$819$	−3.05460	−	1.02615i	−0.106736	−	0.0358566i
$820$	−69.2269			−2.41751
$821$	1.53445	−	0.885914i	0.0535526	−	0.0309186i	−0.472985	−	0.881071i	$-0.656823\pi$
$821$	1.53445	−	0.885914i	0.0535526	−	0.0309186i	0.526537	+	0.850152i	$0.323490\pi$
$822$	−21.1271	−	36.5932i	−0.736892	−	1.27633i
$823$	−23.9265	+	41.4419i	−0.834025	+	1.44457i	0.0607968	+	0.998150i	$0.480636\pi$
$823$	−23.9265	+	41.4419i	−0.834025	+	1.44457i	−0.894822	+	0.446424i	$0.852697\pi$
$824$			58.0717i			2.02302i
$825$	28.9760	+	16.7293i	1.00882	+	0.582440i
$826$	−62.8299	−	36.2749i	−2.18613	−	1.26216i
$827$		−	11.4818i		−	0.399261i	−0.979871	−	0.199630i	$-0.936026\pi$
$827$		−	11.4818i		−	0.399261i	0.979871	−	0.199630i	$-0.0639741\pi$
$828$	0.673481	−	1.16650i	0.0234051	−	0.0405388i
$829$	16.6474	+	28.8341i	0.578187	+	1.00145i	0.995687	+	0.0927731i	$0.0295731\pi$
$829$	16.6474	+	28.8341i	0.578187	+	1.00145i	−0.417500	+	0.908677i	$0.637094\pi$
$830$	88.0546	−	50.8383i	3.05642	−	1.76462i
$831$	10.8168			0.375229
$832$	32.0336	+	36.2955i	1.11057	+	1.25832i
$833$	12.6388			0.437907
$834$	53.4651	−	30.8681i	1.85134	−	1.06887i
$835$	23.5397	+	40.7720i	0.814625	+	1.41097i
$836$	−13.7780	+	23.8642i	−0.476523	+	0.825362i
$837$			31.2070i			1.07867i
$838$	7.99811	+	4.61771i	0.276290	+	0.159516i
$839$	38.4305	+	22.1879i	1.32677	+	0.766011i	0.984799	−	0.173699i	$-0.0555721\pi$
$839$	38.4305	+	22.1879i	1.32677	+	0.766011i	0.341971	+	0.939710i	$0.388905\pi$
$840$		−	197.099i		−	6.80057i
$841$	5.23126	−	9.06082i	0.180388	−	0.312442i
$842$	−43.9424	−	76.1104i	−1.51435	−	2.62294i
$843$	−35.5509	+	20.5253i	−1.22444	+	0.706929i
$844$	−46.6693			−1.60642
$845$	−52.9650	−	6.63296i	−1.82205	−	0.228181i
$846$	−3.01165			−0.103543
$847$	24.6752	−	14.2462i	0.847850	−	0.489507i
$848$	−27.7847	−	48.1245i	−0.954131	−	1.65260i
$849$	−16.7156	+	28.9522i	−0.573676	+	0.993637i
$850$			97.6197i			3.34833i
$851$	4.07224	+	2.35111i	0.139595	+	0.0805949i
$852$	126.512	+	73.0415i	4.33422	+	2.50236i
$853$			36.4816i			1.24911i	0.780982	+	0.624553i	$0.214719\pi$
$853$			36.4816i			1.24911i	−0.780982	+	0.624553i	$0.785281\pi$
$854$	56.8917	−	98.5393i	1.94679	−	3.37195i
$855$	−1.94268	−	3.36482i	−0.0664382	−	0.115074i
$856$	44.5586	−	25.7259i	1.52298	−	0.879293i
$857$	0.0224839			0.000768037			0.000384018	−	1.00000i	$-0.499878\pi$
$857$	0.0224839			0.000768037			0.000384018		1.00000i	$0.499878\pi$
$858$	17.8260	+	20.1976i	0.608568	+	0.689534i
$859$	−0.135914			−0.00463733			−0.00231867	−	0.999997i	$-0.500738\pi$
$859$	−0.135914			−0.00463733			−0.00231867	+	0.999997i	$0.500738\pi$
$860$	16.7833	−	9.68984i	0.572306	−	0.330421i
$861$	10.1123	+	17.5151i	0.344627	+	0.596912i
$862$	−38.9741	+	67.5051i	−1.32746	+	2.29923i
$863$		−	19.9389i		−	0.678729i	−0.940655	−	0.339364i	$-0.889788\pi$
$863$		−	19.9389i		−	0.678729i	0.940655	−	0.339364i	$-0.110212\pi$
$864$	−57.5610	−	33.2329i	−1.95826	−	1.13060i
$865$	49.1916	+	28.4008i	1.67256	+	0.965655i
$866$		−	47.6772i		−	1.62014i
$867$	−6.63502	+	11.4922i	−0.225337	+	0.390295i
$868$	−52.7014	−	91.2815i	−1.78880	−	3.09830i
$869$	6.04137	−	3.48798i	0.204939	−	0.118322i
$870$	84.6463			2.86978
$871$	−17.6001	−	5.91253i	−0.596358	−	0.200338i
$872$	−83.9098			−2.84155
$873$	−1.19582	+	0.690407i	−0.0404724	+	0.0233667i
$874$	−4.66393	−	8.07816i	−0.157760	−	0.273248i
$875$	−46.8491	+	81.1450i	−1.58379	+	2.74320i
$876$		−	42.7860i		−	1.44561i
$877$	−15.3248	−	8.84780i	−0.517483	−	0.298769i	0.218421	−	0.975855i	$-0.429909\pi$
$877$	−15.3248	−	8.84780i	−0.517483	−	0.298769i	−0.735904	+	0.677086i	$0.763243\pi$
$878$	22.3393	+	12.8976i	0.753916	+	0.435274i
$879$			7.74189i			0.261127i
$880$	−35.5917	+	61.6466i	−1.19980	+	2.07811i
$881$	7.91987	+	13.7176i	0.266827	+	0.462158i	0.968041	−	0.250793i	$-0.0806914\pi$
$881$	7.91987	+	13.7176i	0.266827	+	0.462158i	−0.701214	+	0.712951i	$0.747358\pi$
$882$	−2.50562	+	1.44662i	−0.0843686	+	0.0487102i
$883$	11.1007			0.373570			0.186785	−	0.982401i	$-0.440193\pi$
$883$	11.1007			0.373570			0.186785	+	0.982401i	$0.440193\pi$
$884$	−17.8920	+	53.2601i	−0.601774	+	1.79133i
$885$	−61.1319			−2.05493
$886$	59.9665	−	34.6217i	2.01462	−	1.16314i
$887$	4.58604	+	7.94326i	0.153984	+	0.266708i	0.932689	−	0.360682i	$-0.117456\pi$
$887$	4.58604	+	7.94326i	0.153984	+	0.266708i	−0.778704	+	0.627391i	$0.784123\pi$
$888$	−33.9257	+	58.7611i	−1.13847	+	1.97189i
$889$		−	38.4597i		−	1.28990i
$890$	−93.8790	−	54.2011i	−3.14683	−	1.81682i
$891$	−13.1542	−	7.59457i	−0.440682	−	0.254428i
$892$			94.9097i			3.17781i
$893$	−7.45438	+	12.9114i	−0.249451	+	0.432062i
$894$	−50.8126	−	88.0100i	−1.69943	−	2.94349i
$895$	50.9816	−	29.4343i	1.70413	−	0.983879i
$896$	28.7368			0.960028
$897$	−6.38933	+	1.29190i	−0.213333	+	0.0431354i
$898$	−89.5849			−2.98949
$899$	23.5639	−	13.6046i	0.785899	−	0.453739i
$900$	−7.98727	−	13.8344i	−0.266242	−	0.461145i
$901$	7.77311	−	13.4634i	0.258960	−	0.448531i
$902$		−	13.8969i		−	0.462715i
$903$	−4.90325	−	2.83089i	−0.163170	−	0.0942061i
$904$	−117.041	−	67.5739i	−3.89274	−	2.24747i
$905$			62.7767i			2.08677i
$906$	21.1433	−	36.6212i	0.702438	−	1.21666i
$907$	9.99091	+	17.3048i	0.331743	+	0.574595i	0.982854	−	0.184387i	$-0.0590301\pi$
$907$	9.99091	+	17.3048i	0.331743	+	0.574595i	−0.651111	+	0.758983i	$0.725697\pi$
$908$	−3.71616	+	2.14553i	−0.123325	+	0.0712018i
$909$	2.96952			0.0984927
$910$	−97.7895	+	86.3068i	−3.24169	+	2.86104i
$911$	−34.2341			−1.13423			−0.567113	−	0.823640i	$-0.691940\pi$
$911$	−34.2341			−1.13423			−0.567113	+	0.823640i	$0.691940\pi$
$912$	61.2670	−	35.3725i	2.02875	−	1.17130i
$913$	7.29532	+	12.6359i	0.241440	+	0.418186i
$914$	16.6878	−	28.9042i	0.551985	−	0.956066i
$915$		−	95.8763i		−	3.16957i
$916$	−1.83435	−	1.05906i	−0.0606085	−	0.0349924i
$917$	31.6422	+	18.2687i	1.04492	+	0.603284i
$918$		−	40.6468i		−	1.34154i
$919$	1.81708	−	3.14727i	0.0599398	−	0.103819i	−0.834498	−	0.551010i	$-0.814242\pi$
$919$	1.81708	−	3.14727i	0.0599398	−	0.103819i	0.894438	+	0.447192i	$0.147576\pi$
$920$	−16.3858	−	28.3810i	−0.540223	−	0.935693i
$921$	27.0235	−	15.6020i	0.890454	−	0.514104i
$922$	7.58557			0.249817
$923$	−11.5160	−	56.9545i	−0.379055	−	1.87468i
$924$	47.0540			1.54796
$925$	48.2954	−	27.8834i	1.58794	−	0.916799i
$926$	31.7512	+	54.9946i	1.04341	+	1.80724i
$927$	0.977373	−	1.69286i	0.0321011	−	0.0556008i
$928$			57.9511i			1.90234i
$929$	20.3496	+	11.7489i	0.667650	+	0.385468i	0.795185	−	0.606366i	$-0.207373\pi$
$929$	20.3496	+	11.7489i	0.667650	+	0.385468i	−0.127536	+	0.991834i	$0.540707\pi$
$930$	−107.598	−	62.1217i	−3.52827	−	2.03705i
$931$			14.3226i			0.469404i
$932$	−18.0530	+	31.2688i	−0.591347	+	1.02424i
$933$	−17.5698	−	30.4319i	−0.575211	−	0.996294i
$934$	80.3228	−	46.3744i	2.62824	−	1.51742i
$935$	−19.9144			−0.651271
$936$	−1.53220	−	7.57776i	−0.0500815	−	0.247687i
$937$	47.4371			1.54970			0.774851	−	0.632144i	$-0.217825\pi$
$937$	47.4371			1.54970			0.774851	+	0.632144i	$0.217825\pi$
$938$	−39.2890	+	22.6835i	−1.28283	+	0.740644i
$939$	−6.92605	−	11.9963i	−0.226023	−	0.391483i
$940$	−43.5698	+	75.4651i	−1.42109	+	2.46140i
$941$			37.6499i			1.22735i	0.789558	+	0.613675i	$0.210310\pi$
$941$			37.6499i			1.22735i	−0.789558	+	0.613675i	$0.789690\pi$
$942$	−41.8921	−	24.1864i	−1.36492	−	0.788036i
$943$	2.91221	+	1.68137i	0.0948347	+	0.0547529i
$944$		−	91.4875i		−	2.97767i
$945$	33.7256	−	58.4144i	1.09709	−	1.90022i
$946$	1.94518	+	3.36914i	0.0632431	+	0.109540i
$947$	14.3555	−	8.28818i	0.466493	−	0.269330i	−0.248278	−	0.968689i	$-0.579865\pi$
$947$	14.3555	−	8.28818i	0.466493	−	0.269330i	0.714770	+	0.699359i	$0.246531\pi$
$948$	−40.5225			−1.31611
$949$	−12.7600	+	11.2617i	−0.414207	+	0.365570i
$950$	−110.625			−3.58916
$951$	−22.6005	+	13.0484i	−0.732871	+	0.423123i
$952$	41.2608	+	71.4658i	1.33727	+	2.31622i
$953$	11.7835	−	20.4096i	0.381705	−	0.661132i	−0.609601	−	0.792708i	$-0.708671\pi$
$953$	11.7835	−	20.4096i	0.381705	−	0.661132i	0.991306	+	0.131576i	$0.0420038\pi$
$954$			3.55881i			0.115221i
$955$	−4.69013	−	2.70785i	−0.151769	−	0.0876238i
$956$	−19.0596	−	11.0041i	−0.616432	−	0.355897i
$957$			12.1468i			0.392649i
$958$	2.95937	−	5.12578i	0.0956130	−	0.165607i
$959$	14.6786	+	25.4241i	0.473998	+	0.820988i
$960$	86.3182	−	49.8359i	2.78591	−	1.60845i
$961$	−8.93755			−0.288308
$962$	44.0095	−	8.89859i	1.41892	−	0.286902i
$963$	−1.73191			−0.0558102
$964$	31.2446	−	18.0391i	1.00632	−	0.580999i
$965$	29.2755	+	50.7066i	0.942411	+	1.63230i
$966$	−7.96401	+	13.7941i	−0.256238	+	0.443817i
$967$			40.2726i			1.29508i	0.762031	+	0.647541i	$0.224202\pi$
$967$			40.2726i			1.29508i	−0.762031	+	0.647541i	$0.775798\pi$
$968$	59.2010	+	34.1797i	1.90279	+	1.09858i
$969$	17.1402	+	9.89589i	0.550622	+	0.317902i
$970$			55.8901i			1.79452i
$971$	−8.17658	+	14.1623i	−0.262399	+	0.454489i	−0.966879	−	0.255235i	$-0.917847\pi$
$971$	−8.17658	+	14.1623i	−0.262399	+	0.454489i	0.704480	+	0.709724i	$0.251180\pi$
$972$	6.97857	+	12.0872i	0.223838	+	0.387699i
$973$	−37.1463	+	21.4464i	−1.19086	+	0.687541i
$974$	18.4555			0.591353
$975$	−24.6188	+	73.2841i	−0.788433	+	2.34697i
$976$	143.485			4.59283
$977$	−18.3317	+	10.5838i	−0.586484	+	0.338607i	−0.763706	−	0.645564i	$-0.776622\pi$
$977$	−18.3317	+	10.5838i	−0.586484	+	0.338607i	0.177222	+	0.984171i	$0.443289\pi$
$978$	28.2797	+	48.9819i	0.904285	+	1.56627i
$979$	7.77788	−	13.4717i	0.248582	−	0.430557i
$980$			83.7134i			2.67413i
$981$	2.44607	+	1.41224i	0.0780971	+	0.0450894i
$982$	40.5202	+	23.3944i	1.29305	+	0.746544i
$983$		−	38.4832i		−	1.22742i	−0.789530	−	0.613712i	$-0.789676\pi$
$983$		−	38.4832i		−	1.22742i	0.789530	−	0.613712i	$-0.210324\pi$
$984$	−24.2616	+	42.0223i	−0.773431	+	1.33962i
$985$	−3.76435	−	6.52005i	−0.119942	−	0.207746i
$986$	−30.6917	+	17.7199i	−0.977423	+	0.564315i
$987$	25.4578			0.810332
$988$	−60.3557	−	20.2757i	−1.92017	−	0.645056i
$989$	−0.941379			−0.0299341
$990$	3.94800	−	2.27938i	0.125476	−	0.0724435i
$991$	15.4434	+	26.7487i	0.490574	+	0.849699i	0.999941	−	0.0108500i	$-0.00345373\pi$
$991$	15.4434	+	26.7487i	0.490574	+	0.849699i	−0.509367	+	0.860549i	$0.670120\pi$
$992$	42.5302	−	73.6645i	1.35034	−	2.33885i
$993$			28.7470i			0.912257i
$994$	−122.960	−	70.9912i	−3.90007	−	2.25170i
$995$	−5.70675	−	3.29479i	−0.180916	−	0.104452i
$996$		−	84.7551i		−	2.68557i
$997$	−3.43540	+	5.95028i	−0.108800	+	0.188447i	−0.915284	−	0.402808i	$-0.868034\pi$
$997$	−3.43540	+	5.95028i	−0.108800	+	0.188447i	0.806484	+	0.591255i	$0.201368\pi$
$998$	11.8140	+	20.4624i	0.373965	+	0.647727i
$999$	−20.1092	+	11.6100i	−0.636226	+	0.367325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	299.2.i.b.231.15	✓	30
13.2	odd	12		3887.2.a.u.1.29		30
13.4	even	6	inner	299.2.i.b.277.15	yes	30
13.11	odd	12		3887.2.a.u.1.2		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
299.2.i.b.231.15	✓	30	1.1	even	1	trivial
299.2.i.b.277.15	yes	30	13.4	even	6	inner
3887.2.a.u.1.2		30	13.11	odd	12
3887.2.a.u.1.29		30	13.2	odd	12

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:	\( N \)	\(=\)	\( 299 = 13 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	299.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.29353 - 1.32417i) q^{2} +(0.903971 + 1.56572i) q^{3} +(2.50685 - 4.34198i) q^{4} +4.10605i q^{5} +(4.14657 + 2.39402i) q^{6} +(-2.88094 - 1.66331i) q^{7} -7.98127i q^{8} +(-0.134328 + 0.232664i) q^{9} +O(q^{10})\)	\(q+(2.29353 - 1.32417i) q^{2} +(0.903971 + 1.56572i) q^{3} +(2.50685 - 4.34198i) q^{4} +4.10605i q^{5} +(4.14657 + 2.39402i) q^{6} +(-2.88094 - 1.66331i) q^{7} -7.98127i q^{8} +(-0.134328 + 0.232664i) q^{9} +(5.43711 + 9.41734i) q^{10} +(-1.35139 + 0.780227i) q^{11} +9.06447 q^{12} +(-2.38585 - 2.70328i) q^{13} -8.81002 q^{14} +(-6.42895 + 3.71175i) q^{15} +(-5.55486 - 9.62130i) q^{16} +(1.55404 - 2.69167i) q^{17} +0.711494i q^{18} +(3.05027 + 1.76108i) q^{19} +(17.8284 + 10.2932i) q^{20} -6.01435i q^{21} +(-2.06630 + 3.57894i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(12.4965 - 7.21484i) q^{24} -11.8597 q^{25} +(-9.05161 - 3.04077i) q^{26} +4.93811 q^{27} +(-14.4441 + 8.33933i) q^{28} +(-2.15276 - 3.72869i) q^{29} +(-9.82998 + 17.0260i) q^{30} +6.31962i q^{31} +(-11.6565 - 6.72987i) q^{32} +(-2.44324 - 1.41061i) q^{33} -8.23124i q^{34} +(6.82965 - 11.8293i) q^{35} +(0.673481 + 1.16650i) q^{36} +(-4.07224 + 2.35111i) q^{37} +9.32785 q^{38} +(2.07584 - 6.17927i) q^{39} +32.7715 q^{40} +(-2.91221 + 1.68137i) q^{41} +(-7.96401 - 13.7941i) q^{42} +(0.470690 - 0.815258i) q^{43} +7.82364i q^{44} +(-0.955330 - 0.551560i) q^{45} +(-2.29353 - 1.32417i) q^{46} +4.23285i q^{47} +(10.0429 - 17.3948i) q^{48} +(2.03321 + 3.52163i) q^{49} +(-27.2005 + 15.7042i) q^{50} +5.61922 q^{51} +(-17.7185 + 3.58264i) q^{52} +5.00188 q^{53} +(11.3257 - 6.53889i) q^{54} +(-3.20365 - 5.54889i) q^{55} +(-13.2753 + 22.9936i) q^{56} +6.36785i q^{57} +(-9.87482 - 5.70123i) q^{58} +(7.13164 + 4.11746i) q^{59} +37.2192i q^{60} +(-6.45761 + 11.1849i) q^{61} +(8.36824 + 14.4942i) q^{62} +(0.773985 - 0.446860i) q^{63} -13.4265 q^{64} +(11.0998 - 9.79644i) q^{65} -7.47152 q^{66} +(4.45958 - 2.57474i) q^{67} +(-7.79147 - 13.4952i) q^{68} +(0.903971 - 1.56572i) q^{69} -36.1744i q^{70} +(13.9569 + 8.05801i) q^{71} +(1.85695 + 1.07211i) q^{72} -4.72019i q^{73} +(-6.22653 + 10.7847i) q^{74} +(-10.7208 - 18.5690i) q^{75} +(15.2931 - 8.82950i) q^{76} +5.19104 q^{77} +(-3.42140 - 16.9211i) q^{78} -4.47047 q^{79} +(39.5056 - 22.8085i) q^{80} +(4.86690 + 8.42971i) q^{81} +(-4.45283 + 7.71252i) q^{82} -9.35025i q^{83} +(-26.1142 - 15.0770i) q^{84} +(11.0522 + 6.38096i) q^{85} -2.49309i q^{86} +(3.89206 - 6.74125i) q^{87} +(6.22720 + 10.7858i) q^{88} +(-8.63318 + 4.98437i) q^{89} -2.92143 q^{90} +(2.37711 + 11.7564i) q^{91} -5.01369 q^{92} +(-9.89478 + 5.71275i) q^{93} +(5.60501 + 9.70817i) q^{94} +(-7.23107 + 12.5246i) q^{95} -24.3344i q^{96} +(4.45111 + 2.56985i) q^{97} +(9.32646 + 5.38464i) q^{98} -0.419227i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} + 16 q^{4} - 9 q^{6} - 3 q^{7} - 16 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 + 16 * q^4 - 9 * q^6 - 3 * q^7 - 16 * q^9	\( 30 q - 3 q^{3} + 16 q^{4} - 9 q^{6} - 3 q^{7} - 16 q^{9} + 23 q^{10} - 4 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} - 26 q^{16} + 13 q^{17} - 12 q^{19} + 6 q^{20} - 16 q^{22} - 15 q^{23} + 6 q^{24} - 52 q^{25} - 25 q^{26} + 54 q^{27} - 24 q^{28} - q^{29} + 20 q^{30} - 39 q^{32} - 18 q^{33} + 20 q^{35} + 23 q^{36} - 30 q^{37} + 18 q^{38} - 60 q^{39} + 124 q^{40} - 6 q^{41} - 12 q^{42} + 33 q^{43} + 18 q^{45} + 34 q^{48} + 48 q^{49} - 60 q^{50} + 20 q^{51} - 39 q^{52} + 62 q^{53} + 45 q^{54} - 16 q^{55} - 5 q^{56} - 66 q^{58} - 21 q^{59} - 18 q^{61} + 46 q^{62} - 117 q^{63} - 16 q^{64} - 4 q^{65} + 52 q^{66} + 24 q^{67} - 18 q^{68} - 3 q^{69} + 54 q^{71} - 54 q^{72} + 42 q^{74} + 4 q^{75} - 18 q^{76} - 20 q^{77} + 72 q^{79} + 114 q^{80} - 15 q^{81} + 14 q^{82} - 159 q^{84} - 39 q^{85} + 40 q^{87} + 93 q^{88} - 51 q^{89} - 78 q^{90} - 34 q^{91} - 32 q^{92} + 6 q^{93} + 8 q^{94} - 24 q^{95} - 6 q^{97} - 123 q^{98}+O(q^{100}) \) 30 * q - 3 * q^3 + 16 * q^4 - 9 * q^6 - 3 * q^7 - 16 * q^9 + 23 * q^10 - 4 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 - 26 * q^16 + 13 * q^17 - 12 * q^19 + 6 * q^20 - 16 * q^22 - 15 * q^23 + 6 * q^24 - 52 * q^25 - 25 * q^26 + 54 * q^27 - 24 * q^28 - q^29 + 20 * q^30 - 39 * q^32 - 18 * q^33 + 20 * q^35 + 23 * q^36 - 30 * q^37 + 18 * q^38 - 60 * q^39 + 124 * q^40 - 6 * q^41 - 12 * q^42 + 33 * q^43 + 18 * q^45 + 34 * q^48 + 48 * q^49 - 60 * q^50 + 20 * q^51 - 39 * q^52 + 62 * q^53 + 45 * q^54 - 16 * q^55 - 5 * q^56 - 66 * q^58 - 21 * q^59 - 18 * q^61 + 46 * q^62 - 117 * q^63 - 16 * q^64 - 4 * q^65 + 52 * q^66 + 24 * q^67 - 18 * q^68 - 3 * q^69 + 54 * q^71 - 54 * q^72 + 42 * q^74 + 4 * q^75 - 18 * q^76 - 20 * q^77 + 72 * q^79 + 114 * q^80 - 15 * q^81 + 14 * q^82 - 159 * q^84 - 39 * q^85 + 40 * q^87 + 93 * q^88 - 51 * q^89 - 78 * q^90 - 34 * q^91 - 32 * q^92 + 6 * q^93 + 8 * q^94 - 24 * q^95 - 6 * q^97 - 123 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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