LMFDB - Embedded newform 950.2.h.e.191.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(191,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("950.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.3
Character	$\chi$	$=$	950.191
Dual form			950.2.h.e.761.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.457139 - 1.40693i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.65863 - 1.49965i) q^{5} +(0.457139 - 1.40693i) q^{6} +0.448991 q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.656575 - 0.477030i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.457139 - 1.40693i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.65863 - 1.49965i) q^{5} +(0.457139 - 1.40693i) q^{6} +0.448991 q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.656575 - 0.477030i) q^{9} +(2.22333 - 0.238322i) q^{10} +(2.18297 + 1.58602i) q^{11} +(1.19681 - 0.869531i) q^{12} +(0.731543 - 0.531497i) q^{13} +(0.363242 + 0.263911i) q^{14} +(-2.86813 - 1.64803i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.924105 + 2.84410i) q^{17} +0.811572 q^{18} +(0.309017 - 0.951057i) q^{19} +(1.93880 + 1.11403i) q^{20} +(-0.205252 - 0.631699i) q^{21} +(0.833819 + 2.56623i) q^{22} +(3.84716 + 2.79512i) q^{23} +1.47933 q^{24} +(0.502110 - 4.97472i) q^{25} +0.904237 q^{26} +(-4.56171 - 3.31428i) q^{27} +(0.138746 + 0.427016i) q^{28} +(-2.40708 - 7.40823i) q^{29} +(-1.35168 - 3.01913i) q^{30} +(0.996490 - 3.06688i) q^{31} -1.00000 q^{32} +(1.23350 - 3.79631i) q^{33} +(-2.41934 + 1.75775i) q^{34} +(0.744711 - 0.673329i) q^{35} +(0.656575 + 0.477030i) q^{36} +(-1.61485 + 1.17326i) q^{37} +(0.809017 - 0.587785i) q^{38} +(-1.08220 - 0.786262i) q^{39} +(0.913705 + 2.04087i) q^{40} +(3.00813 - 2.18553i) q^{41} +(0.205252 - 0.631699i) q^{42} +5.17715 q^{43} +(-0.833819 + 2.56623i) q^{44} +(0.373639 - 1.77585i) q^{45} +(1.46948 + 4.52260i) q^{46} +(3.04324 + 9.36612i) q^{47} +(1.19681 + 0.869531i) q^{48} -6.79841 q^{49} +(3.33029 - 3.72950i) q^{50} +4.42390 q^{51} +(0.731543 + 0.531497i) q^{52} +(-1.33760 - 4.11671i) q^{53} +(-1.74242 - 5.36261i) q^{54} +(5.99920 - 0.643064i) q^{55} +(-0.138746 + 0.427016i) q^{56} -1.47933 q^{57} +(2.40708 - 7.40823i) q^{58} +(-0.561467 + 0.407930i) q^{59} +(0.681069 - 3.23702i) q^{60} +(-0.326366 - 0.237119i) q^{61} +(2.60884 - 1.89544i) q^{62} +(0.294797 - 0.214182i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.416301 - 1.97862i) q^{65} +(3.22934 - 2.34625i) q^{66} +(-1.03261 + 3.17805i) q^{67} -2.99047 q^{68} +(2.17386 - 6.69044i) q^{69} +(0.998257 - 0.107005i) q^{70} +(-1.48848 - 4.58107i) q^{71} +(0.250789 + 0.771850i) q^{72} +(2.79239 + 2.02879i) q^{73} -1.99606 q^{74} +(-7.22862 + 1.56771i) q^{75} +1.00000 q^{76} +(0.980133 + 0.712108i) q^{77} +(-0.413362 - 1.27220i) q^{78} +(-1.51357 - 4.65830i) q^{79} +(-0.460389 + 2.18816i) q^{80} +(-1.82525 + 5.61755i) q^{81} +3.71825 q^{82} +(-1.24950 + 3.84557i) q^{83} +(0.537356 - 0.390412i) q^{84} +(2.73240 + 6.10315i) q^{85} +(4.18840 + 3.04305i) q^{86} +(-9.32249 + 6.77319i) q^{87} +(-2.18297 + 1.58602i) q^{88} +(5.17467 + 3.75962i) q^{89} +(1.34610 - 1.21707i) q^{90} +(0.328457 - 0.238638i) q^{91} +(-1.46948 + 4.52260i) q^{92} -4.77042 q^{93} +(-3.04324 + 9.36612i) q^{94} +(-0.913705 - 2.04087i) q^{95} +(0.457139 + 1.40693i) q^{96} +(-0.242727 - 0.747037i) q^{97} +(-5.50003 - 3.99600i) q^{98} +2.18986 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9}+O(q^{10}) $ 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 5 * q^5 + q^6 + 28 * q^7 + 11 * q^8 - 8 * q^9	$ 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9} + 5 q^{10} - 6 q^{12} - 10 q^{13} + 12 q^{14} - 11 q^{16} - 20 q^{17} - 42 q^{18} - 11 q^{19} + 5 q^{20} - 3 q^{21} - 10 q^{22} - 6 q^{23} - 14 q^{24} - 15 q^{25} - 40 q^{26} + 5 q^{27} - 2 q^{28} + 6 q^{29} - 5 q^{31} - 44 q^{32} - 36 q^{33} - 10 q^{34} - 8 q^{36} - 10 q^{37} + 11 q^{38} + 39 q^{39} - 22 q^{41} + 3 q^{42} + 68 q^{43} + 10 q^{44} + 20 q^{45} + 6 q^{46} + 19 q^{47} - 6 q^{48} + 40 q^{49} - 30 q^{50} + 86 q^{51} - 10 q^{52} + 30 q^{54} + 2 q^{56} + 14 q^{57} - 6 q^{58} - 4 q^{59} + 15 q^{60} + 26 q^{61} - 15 q^{62} - 41 q^{63} - 11 q^{64} + 30 q^{65} - 4 q^{66} - 59 q^{67} + 20 q^{68} - 59 q^{69} - 25 q^{70} + 30 q^{71} + 13 q^{72} - 38 q^{73} - 50 q^{74} - 15 q^{75} + 44 q^{76} + 29 q^{77} + 16 q^{78} + 3 q^{79} + 5 q^{80} - 54 q^{81} - 8 q^{82} + 9 q^{83} + 7 q^{84} + 12 q^{86} - 43 q^{87} + 33 q^{89} - 6 q^{91} - 6 q^{92} + 84 q^{93} - 19 q^{94} + q^{96} + 30 q^{97} - 15 q^{98} - 54 q^{99}+O(q^{100}) $ 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 5 * q^5 + q^6 + 28 * q^7 + 11 * q^8 - 8 * q^9 + 5 * q^10 - 6 * q^12 - 10 * q^13 + 12 * q^14 - 11 * q^16 - 20 * q^17 - 42 * q^18 - 11 * q^19 + 5 * q^20 - 3 * q^21 - 10 * q^22 - 6 * q^23 - 14 * q^24 - 15 * q^25 - 40 * q^26 + 5 * q^27 - 2 * q^28 + 6 * q^29 - 5 * q^31 - 44 * q^32 - 36 * q^33 - 10 * q^34 - 8 * q^36 - 10 * q^37 + 11 * q^38 + 39 * q^39 - 22 * q^41 + 3 * q^42 + 68 * q^43 + 10 * q^44 + 20 * q^45 + 6 * q^46 + 19 * q^47 - 6 * q^48 + 40 * q^49 - 30 * q^50 + 86 * q^51 - 10 * q^52 + 30 * q^54 + 2 * q^56 + 14 * q^57 - 6 * q^58 - 4 * q^59 + 15 * q^60 + 26 * q^61 - 15 * q^62 - 41 * q^63 - 11 * q^64 + 30 * q^65 - 4 * q^66 - 59 * q^67 + 20 * q^68 - 59 * q^69 - 25 * q^70 + 30 * q^71 + 13 * q^72 - 38 * q^73 - 50 * q^74 - 15 * q^75 + 44 * q^76 + 29 * q^77 + 16 * q^78 + 3 * q^79 + 5 * q^80 - 54 * q^81 - 8 * q^82 + 9 * q^83 + 7 * q^84 + 12 * q^86 - 43 * q^87 + 33 * q^89 - 6 * q^91 - 6 * q^92 + 84 * q^93 - 19 * q^94 + q^96 + 30 * q^97 - 15 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−0.457139	−	1.40693i	−0.263929	−	0.812291i	−0.991938	−	0.126723i	$-0.959554\pi$
$3$	−0.457139	−	1.40693i	−0.263929	−	0.812291i	0.728009	−	0.685568i	$-0.240446\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.65863	−	1.49965i	0.741762	−	0.670663i
$5$	1.65863	−	1.49965i	0.741762	−	0.670663i
$6$	0.457139	−	1.40693i	0.186626	−	0.574377i
$7$	0.448991			0.169703			0.0848514	−	0.996394i	$-0.472958\pi$
$7$	0.448991			0.169703			0.0848514	+	0.996394i	$0.472958\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.656575	−	0.477030i	0.218858	−	0.159010i
$10$	2.22333	−	0.238322i	0.703079	−	0.0753642i
$11$	2.18297	+	1.58602i	0.658189	+	0.478202i	0.866051	−	0.499956i	$-0.166650\pi$
$11$	2.18297	+	1.58602i	0.658189	+	0.478202i	−0.207862	+	0.978158i	$0.566650\pi$
$12$	1.19681	−	0.869531i	0.345488	−	0.251012i
$13$	0.731543	−	0.531497i	0.202894	−	0.147411i	−0.481699	−	0.876337i	$-0.659980\pi$
$13$	0.731543	−	0.531497i	0.202894	−	0.147411i	0.684593	+	0.728926i	$0.259980\pi$
$14$	0.363242	+	0.263911i	0.0970804	+	0.0705331i
$15$	−2.86813	−	1.64803i	−0.740547	−	0.425519i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.924105	+	2.84410i	−0.224128	+	0.689796i	0.774251	+	0.632879i	$0.218127\pi$
$17$	−0.924105	+	2.84410i	−0.224128	+	0.689796i	−0.998379	+	0.0569170i	$0.981873\pi$
$18$	0.811572			0.191289
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$20$	1.93880	+	1.11403i	0.433528	+	0.249106i
$21$	−0.205252	−	0.631699i	−0.0447896	−	0.137848i
$22$	0.833819	+	2.56623i	0.177771	+	0.547122i
$23$	3.84716	+	2.79512i	0.802188	+	0.582824i	0.911555	−	0.411178i	$-0.134882\pi$
$23$	3.84716	+	2.79512i	0.802188	+	0.582824i	−0.109367	+	0.994001i	$0.534882\pi$
$24$	1.47933			0.301968
$25$	0.502110	−	4.97472i	0.100422	−	0.994945i
$26$	0.904237			0.177336
$27$	−4.56171	−	3.31428i	−0.877902	−	0.637833i
$28$	0.138746	+	0.427016i	0.0262205	+	0.0806985i
$29$	−2.40708	−	7.40823i	−0.446984	−	1.37567i	−0.880294	−	0.474429i	$-0.842655\pi$
$29$	−2.40708	−	7.40823i	−0.446984	−	1.37567i	0.433310	−	0.901245i	$-0.357345\pi$
$30$	−1.35168	−	3.01913i	−0.246781	−	0.551214i
$31$	0.996490	−	3.06688i	0.178975	−	0.550828i	−0.820818	−	0.571190i	$-0.806482\pi$
$31$	0.996490	−	3.06688i	0.178975	−	0.550828i	0.999793	+	0.0203622i	$0.00648194\pi$
$32$	−1.00000			−0.176777
$33$	1.23350	−	3.79631i	0.214724	−	0.660853i
$34$	−2.41934	+	1.75775i	−0.414913	+	0.301452i
$35$	0.744711	−	0.673329i	0.125879	−	0.113813i
$36$	0.656575	+	0.477030i	0.109429	+	0.0795050i
$37$	−1.61485	+	1.17326i	−0.265480	+	0.192882i	−0.712559	−	0.701612i	$-0.752464\pi$
$37$	−1.61485	+	1.17326i	−0.265480	+	0.192882i	0.447080	+	0.894494i	$0.352464\pi$
$38$	0.809017	−	0.587785i	0.131240	−	0.0953514i
$39$	−1.08220	−	0.786262i	−0.173290	−	0.125903i
$40$	0.913705	+	2.04087i	0.144469	+	0.322690i
$41$	3.00813	−	2.18553i	0.469790	−	0.341323i	−0.327569	−	0.944827i	$-0.606229\pi$
$41$	3.00813	−	2.18553i	0.469790	−	0.341323i	0.797360	+	0.603504i	$0.206229\pi$
$42$	0.205252	−	0.631699i	0.0316710	−	0.0974733i
$43$	5.17715			0.789507			0.394754	−	0.918787i	$-0.370830\pi$
$43$	5.17715			0.789507			0.394754	+	0.918787i	$0.370830\pi$
$44$	−0.833819	+	2.56623i	−0.125703	+	0.386874i
$45$	0.373639	−	1.77585i	0.0556988	−	0.264728i
$46$	1.46948	+	4.52260i	0.216663	+	0.666822i
$47$	3.04324	+	9.36612i	0.443902	+	1.36619i	0.883684	+	0.468084i	$0.155056\pi$
$47$	3.04324	+	9.36612i	0.443902	+	1.36619i	−0.439782	+	0.898105i	$0.644944\pi$
$48$	1.19681	+	0.869531i	0.172744	+	0.125506i
$49$	−6.79841			−0.971201
$50$	3.33029	−	3.72950i	0.470973	−	0.527432i
$51$	4.42390			0.619470
$52$	0.731543	+	0.531497i	0.101447	+	0.0737054i
$53$	−1.33760	−	4.11671i	−0.183734	−	0.565474i	0.816191	−	0.577783i	$-0.196082\pi$
$53$	−1.33760	−	4.11671i	−0.183734	−	0.565474i	−0.999924	+	0.0123088i	$0.996082\pi$
$54$	−1.74242	−	5.36261i	−0.237113	−	0.729759i
$55$	5.99920	−	0.643064i	0.808932	−	0.0867107i
$56$	−0.138746	+	0.427016i	−0.0185407	+	0.0570624i
$57$	−1.47933			−0.195943
$58$	2.40708	−	7.40823i	0.316065	−	0.972748i
$59$	−0.561467	+	0.407930i	−0.0730968	+	0.0531080i	−0.623734	−	0.781637i	$-0.714385\pi$
$59$	−0.561467	+	0.407930i	−0.0730968	+	0.0531080i	0.550637	+	0.834745i	$0.314385\pi$
$60$	0.681069	−	3.23702i	0.0879256	−	0.417897i
$61$	−0.326366	−	0.237119i	−0.0417869	−	0.0303600i	0.566696	−	0.823927i	$-0.308222\pi$
$61$	−0.326366	−	0.237119i	−0.0417869	−	0.0303600i	−0.608483	+	0.793567i	$0.708222\pi$
$62$	2.60884	−	1.89544i	0.331323	−	0.240721i
$63$	0.294797	−	0.214182i	0.0371409	−	0.0269844i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.416301	−	1.97862i	0.0516358	−	0.245417i
$66$	3.22934	−	2.34625i	0.397504	−	0.288803i
$67$	−1.03261	+	3.17805i	−0.126153	+	0.388260i	−0.994109	−	0.108381i	$-0.965433\pi$
$67$	−1.03261	+	3.17805i	−0.126153	+	0.388260i	0.867956	+	0.496641i	$0.165433\pi$
$68$	−2.99047			−0.362647
$69$	2.17386	−	6.69044i	0.261702	−	0.805435i
$70$	0.998257	−	0.107005i	0.119314	−	0.0127895i
$71$	−1.48848	−	4.58107i	−0.176650	−	0.543672i	0.823055	−	0.567962i	$-0.192268\pi$
$71$	−1.48848	−	4.58107i	−0.176650	−	0.543672i	−0.999705	+	0.0242891i	$0.992268\pi$
$72$	0.250789	+	0.771850i	0.0295558	+	0.0909634i
$73$	2.79239	+	2.02879i	0.326824	+	0.237452i	0.739082	−	0.673616i	$-0.235260\pi$
$73$	2.79239	+	2.02879i	0.326824	+	0.237452i	−0.412258	+	0.911067i	$0.635260\pi$
$74$	−1.99606			−0.232038
$75$	−7.22862	+	1.56771i	−0.834690	+	0.181023i
$76$	1.00000			0.114708
$77$	0.980133	+	0.712108i	0.111697	+	0.0811523i
$78$	−0.413362	−	1.27220i	−0.0468041	−	0.144048i
$79$	−1.51357	−	4.65830i	−0.170290	−	0.524100i	0.829097	−	0.559105i	$-0.188855\pi$
$79$	−1.51357	−	4.65830i	−0.170290	−	0.524100i	−0.999387	+	0.0350051i	$0.988855\pi$
$80$	−0.460389	+	2.18816i	−0.0514731	+	0.244644i
$81$	−1.82525	+	5.61755i	−0.202806	+	0.624172i
$82$	3.71825			0.410612
$83$	−1.24950	+	3.84557i	−0.137151	+	0.422106i	−0.995918	−	0.0902590i	$-0.971231\pi$
$83$	−1.24950	+	3.84557i	−0.137151	+	0.422106i	0.858768	+	0.512365i	$0.171231\pi$
$84$	0.537356	−	0.390412i	0.0586303	−	0.0425974i
$85$	2.73240	+	6.10315i	0.296371	+	0.661979i
$86$	4.18840	+	3.04305i	0.451647	+	0.328141i
$87$	−9.32249	+	6.77319i	−0.999476	+	0.726162i
$88$	−2.18297	+	1.58602i	−0.232705	+	0.169070i
$89$	5.17467	+	3.75962i	0.548514	+	0.398519i	0.827237	−	0.561853i	$-0.189911\pi$
$89$	5.17467	+	3.75962i	0.548514	+	0.398519i	−0.278723	+	0.960372i	$0.589911\pi$
$90$	1.34610	−	1.21707i	0.141891	−	0.128291i
$91$	0.328457	−	0.238638i	0.0344316	−	0.0250160i
$92$	−1.46948	+	4.52260i	−0.153204	+	0.471514i
$93$	−4.77042			−0.494669
$94$	−3.04324	+	9.36612i	−0.313886	+	0.966041i
$95$	−0.913705	−	2.04087i	−0.0937442	−	0.209389i
$96$	0.457139	+	1.40693i	0.0466566	+	0.143594i
$97$	−0.242727	−	0.747037i	−0.0246452	−	0.0758501i	0.937977	−	0.346696i	$-0.112697\pi$
$97$	−0.242727	−	0.747037i	−0.0246452	−	0.0758501i	−0.962623	+	0.270846i	$0.912697\pi$
$98$	−5.50003	−	3.99600i	−0.555587	−	0.403657i
$99$	2.18986			0.220089
$100$	4.88640	−	1.05974i	0.488640	−	0.105974i
$101$	−2.19115			−0.218027			−0.109014	−	0.994040i	$-0.534769\pi$
$101$	−2.19115			−0.218027			−0.109014	+	0.994040i	$0.534769\pi$
$102$	3.57901	+	2.60030i	0.354375	+	0.257468i
$103$	4.37526	+	13.4657i	0.431107	+	1.32681i	0.897024	+	0.441982i	$0.145724\pi$
$103$	4.37526	+	13.4657i	0.431107	+	1.32681i	−0.465917	+	0.884828i	$0.654276\pi$
$104$	0.279425	+	0.859981i	0.0273998	+	0.0843281i
$105$	−1.28776	−	0.739951i	−0.125673	−	0.0722118i
$106$	1.33760	−	4.11671i	0.129919	−	0.399850i
$107$	−8.28527			−0.800967			−0.400483	−	0.916304i	$-0.631158\pi$
$107$	−8.28527			−0.800967			−0.400483	+	0.916304i	$0.631158\pi$
$108$	1.74242	−	5.36261i	0.167664	−	0.516018i
$109$	−9.05280	+	6.57725i	−0.867101	+	0.629986i	−0.929808	−	0.368046i	$-0.880027\pi$
$109$	−9.05280	+	6.57725i	−0.867101	+	0.629986i	0.0627063	+	0.998032i	$0.480027\pi$
$110$	5.23144	+	3.00599i	0.498798	+	0.286610i
$111$	2.38890	+	1.73564i	0.226745	+	0.164740i
$112$	−0.363242	+	0.263911i	−0.0343231	+	0.0249372i
$113$	4.95030	−	3.59660i	0.465685	−	0.338340i	−0.330072	−	0.943956i	$-0.607073\pi$
$113$	4.95030	−	3.59660i	0.465685	−	0.338340i	0.795757	+	0.605616i	$0.207073\pi$
$114$	−1.19681	−	0.869531i	−0.112091	−	0.0814390i
$115$	10.5727	−	1.13331i	0.985911	−	0.105681i
$116$	6.30182	−	4.57854i	0.585109	−	0.425107i
$117$	0.226773	−	0.697936i	0.0209652	−	0.0645242i
$118$	−0.694012			−0.0638890
$119$	−0.414915	+	1.27698i	−0.0380352	+	0.117060i
$120$	2.45367	−	2.21848i	0.223988	−	0.202519i
$121$	−1.14930	−	3.53718i	−0.104482	−	0.321562i
$122$	−0.124661	−	0.383667i	−0.0112863	−	0.0347356i
$123$	−4.45002	−	3.23313i	−0.401245	−	0.291522i
$124$	3.22471			0.289587
$125$	−6.62752	−	9.00422i	−0.592784	−	0.805362i
$126$	0.364389			0.0324623
$127$	8.40855	+	6.10917i	0.746138	+	0.542101i	0.894627	−	0.446813i	$-0.147441\pi$
$127$	8.40855	+	6.10917i	0.746138	+	0.542101i	−0.148489	+	0.988914i	$0.547441\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−2.36668	−	7.28388i	−0.208374	−	0.641310i
$130$	1.49980	−	1.35604i	0.131541	−	0.118932i
$131$	−4.09579	+	12.6055i	−0.357851	+	1.10135i	0.596487	+	0.802622i	$0.296563\pi$
$131$	−4.09579	+	12.6055i	−0.357851	+	1.10135i	−0.954338	+	0.298729i	$0.903437\pi$
$132$	3.99168			0.347431
$133$	0.138746	−	0.427016i	0.0120308	−	0.0370270i
$134$	−2.70341	+	1.96414i	−0.233539	+	0.169676i
$135$	−12.5364	+	1.34380i	−1.07897	+	0.115656i
$136$	−2.41934	−	1.75775i	−0.207457	−	0.150726i
$137$	−9.29153	+	6.75069i	−0.793829	+	0.576750i	−0.909097	−	0.416584i	$-0.863227\pi$
$137$	−9.29153	+	6.75069i	−0.793829	+	0.576750i	0.115268	+	0.993334i	$0.463227\pi$
$138$	5.69123	−	4.13492i	0.484470	−	0.351988i
$139$	7.83478	+	5.69230i	0.664538	+	0.482815i	0.868192	−	0.496228i	$-0.165282\pi$
$139$	7.83478	+	5.69230i	0.664538	+	0.482815i	−0.203655	+	0.979043i	$0.565282\pi$
$140$	0.870502	+	0.500192i	0.0735709	+	0.0422739i
$141$	11.7863	−	8.56324i	0.992585	−	0.721155i
$142$	1.48848	−	4.58107i	0.124910	−	0.384434i
$143$	2.43990			0.204035
$144$	−0.250789	+	0.771850i	−0.0208991	+	0.0643209i
$145$	−15.1022	−	8.67774i	−1.25417	−	0.720647i
$146$	1.06660	+	3.28265i	0.0882722	+	0.271674i
$147$	3.10782	+	9.56488i	0.256329	+	0.788898i
$148$	−1.61485	−	1.17326i	−0.132740	−	0.0964411i
$149$	−22.8692			−1.87352			−0.936758	−	0.349977i	$-0.886189\pi$
$149$	−22.8692			−1.87352			−0.936758	+	0.349977i	$0.886189\pi$
$150$	−6.76956	−	2.98058i	−0.552732	−	0.243363i
$151$	6.56470			0.534228			0.267114	−	0.963665i	$-0.413930\pi$
$151$	6.56470			0.534228			0.267114	+	0.963665i	$0.413930\pi$
$152$	0.809017	+	0.587785i	0.0656199	+	0.0476757i
$153$	0.749977	+	2.30819i	0.0606321	+	0.186606i
$154$	0.374377	+	1.15222i	0.0301682	+	0.0928482i
$155$	−2.94643	−	6.58120i	−0.236663	−	0.528615i
$156$	0.413362	−	1.27220i	0.0330955	−	0.101857i
$157$	0.228247			0.0182161			0.00910805	−	0.999959i	$-0.497101\pi$
$157$	0.228247			0.0182161			0.00910805	+	0.999959i	$0.497101\pi$
$158$	1.51357	−	4.65830i	0.120414	−	0.370595i
$159$	−5.18046	+	3.76382i	−0.410837	+	0.298490i
$160$	−1.65863	+	1.49965i	−0.131126	+	0.118558i
$161$	1.72734	+	1.25499i	0.136134	+	0.0989068i
$162$	−4.77857	+	3.47183i	−0.375440	+	0.272773i
$163$	−17.4186	+	12.6554i	−1.36433	+	0.991246i	−0.366177	+	0.930545i	$0.619334\pi$
$163$	−17.4186	+	12.6554i	−1.36433	+	0.991246i	−0.998156	+	0.0607012i	$0.980666\pi$
$164$	3.00813	+	2.18553i	0.234895	+	0.170661i
$165$	−3.64722	−	8.14649i	−0.283935	−	0.634203i
$166$	−3.27124	+	2.37669i	−0.253897	+	0.184467i
$167$	−3.11973	+	9.60155i	−0.241412	+	0.742990i	0.754794	+	0.655962i	$0.227737\pi$
$167$	−3.11973	+	9.60155i	−0.241412	+	0.742990i	−0.996206	+	0.0870281i	$0.972263\pi$
$168$	0.664208			0.0512448
$169$	−3.76455	+	11.5861i	−0.289581	+	0.891239i
$170$	−1.37678	+	6.54362i	−0.105594	+	0.501873i
$171$	−0.250789	−	0.771850i	−0.0191783	−	0.0590249i
$172$	1.59983	+	4.92376i	0.121986	+	0.375433i
$173$	9.47240	+	6.88210i	0.720173	+	0.523237i	0.886440	−	0.462844i	$-0.153171\pi$
$173$	9.47240	+	6.88210i	0.720173	+	0.523237i	−0.166266	+	0.986081i	$0.553171\pi$
$174$	−11.5232			−0.873574
$175$	0.225443	−	2.23361i	0.0170419	−	0.168845i
$176$	−2.69829			−0.203392
$177$	0.830598	+	0.603464i	0.0624315	+	0.0453592i
$178$	1.97655	+	6.08319i	0.148149	+	0.455955i
$179$	−0.844572	−	2.59933i	−0.0631263	−	0.194283i	0.914519	−	0.404542i	$-0.132569\pi$
$179$	−0.844572	−	2.59933i	−0.0631263	−	0.194283i	−0.977646	+	0.210259i	$0.932569\pi$
$180$	1.80439	−	0.193416i	0.134491	−	0.0144164i
$181$	−3.90341	+	12.0135i	−0.290138	+	0.892954i	0.694673	+	0.719326i	$0.255549\pi$
$181$	−3.90341	+	12.0135i	−0.290138	+	0.892954i	−0.984811	+	0.173628i	$0.944451\pi$
$182$	0.405995			0.0300943
$183$	−0.184415	+	0.567571i	−0.0136324	+	0.0419561i
$184$	−3.84716	+	2.79512i	−0.283616	+	0.206059i
$185$	−0.918966	+	4.36771i	−0.0675637	+	0.321120i
$186$	−3.85935	−	2.80398i	−0.282981	−	0.205598i
$187$	−6.52809	+	4.74293i	−0.477381	+	0.346838i
$188$	−7.96730	+	5.78858i	−0.581075	+	0.422176i
$189$	−2.04817	−	1.48808i	−0.148982	−	0.108242i
$190$	0.460389	−	2.18816i	0.0334001	−	0.158746i
$191$	9.96122	−	7.23725i	0.720768	−	0.523669i	−0.165861	−	0.986149i	$-0.553040\pi$
$191$	9.96122	−	7.23725i	0.720768	−	0.523669i	0.886630	+	0.462480i	$0.153040\pi$
$192$	−0.457139	+	1.40693i	−0.0329912	+	0.101536i
$193$	−16.7136			−1.20307			−0.601535	−	0.798847i	$-0.705444\pi$
$193$	−16.7136			−1.20307			−0.601535	+	0.798847i	$0.705444\pi$
$194$	0.242727	−	0.747037i	0.0174268	−	0.0536341i
$195$	−2.97408	+	0.318797i	−0.212978	+	0.0228295i
$196$	−2.10082	−	6.46567i	−0.150059	−	0.461834i
$197$	−3.89083	−	11.9747i	−0.277210	−	0.853165i	−0.988626	−	0.150394i	$-0.951946\pi$
$197$	−3.89083	−	11.9747i	−0.277210	−	0.853165i	0.711416	−	0.702771i	$-0.248054\pi$
$198$	1.77163	+	1.28717i	0.125904	+	0.0914750i
$199$	−12.2206			−0.866297			−0.433149	−	0.901323i	$-0.642597\pi$
$199$	−12.2206			−0.866297			−0.433149	+	0.901323i	$0.642597\pi$
$200$	4.57608	+	2.01481i	0.323578	+	0.142469i
$201$	4.94333			0.348676
$202$	−1.77268	−	1.28792i	−0.124725	−	0.0906180i
$203$	−1.08076	−	3.32623i	−0.0758544	−	0.233456i
$204$	1.36706	+	4.20738i	0.0957133	+	0.294575i
$205$	1.71184	−	8.13612i	0.119560	−	0.568251i
$206$	−4.37526	+	13.4657i	−0.304839	+	0.938197i
$207$	3.85930			0.268240
$208$	−0.279425	+	0.859981i	−0.0193746	+	0.0596289i
$209$	2.18297	−	1.58602i	0.150999	−	0.109707i
$210$	−0.606891	−	1.35556i	−0.0418794	−	0.0935426i
$211$	−0.903284	−	0.656275i	−0.0621847	−	0.0451798i	0.556259	−	0.831009i	$-0.312236\pi$
$211$	−0.903284	−	0.656275i	−0.0621847	−	0.0451798i	−0.618443	+	0.785829i	$0.712236\pi$
$212$	3.50188	−	2.54427i	0.240510	−	0.174741i
$213$	−5.76480	+	4.18837i	−0.394997	+	0.286982i
$214$	−6.70292	−	4.86996i	−0.458202	−	0.332903i
$215$	8.58697	−	7.76390i	0.585627	−	0.529493i
$216$	4.56171	−	3.31428i	0.310385	−	0.225508i
$217$	0.447415	−	1.37700i	0.0303725	−	0.0934770i
$218$	−11.1899			−0.757874
$219$	1.57785	−	4.85613i	0.106621	−	0.328147i
$220$	2.46545	+	5.50686i	0.166220	+	0.371273i
$221$	0.835610	+	2.57174i	0.0562092	+	0.172994i
$222$	0.912479	+	2.80832i	0.0612416	+	0.188482i
$223$	8.87618	+	6.44892i	0.594393	+	0.431852i	0.843884	−	0.536525i	$-0.180263\pi$
$223$	8.87618	+	6.44892i	0.594393	+	0.431852i	−0.249491	+	0.968377i	$0.580263\pi$
$224$	−0.448991			−0.0299995
$225$	−2.04342	−	3.50580i	−0.136228	−	0.233720i
$226$	6.11890			0.407023
$227$	4.77298	+	3.46777i	0.316794	+	0.230164i	0.734806	−	0.678277i	$-0.237273\pi$
$227$	4.77298	+	3.46777i	0.316794	+	0.230164i	−0.418012	+	0.908441i	$0.637273\pi$
$228$	−0.457139	−	1.40693i	−0.0302748	−	0.0931762i
$229$	−2.94885	−	9.07562i	−0.194865	−	0.599734i	−0.999978	−	0.00661204i	$-0.997895\pi$
$229$	−2.94885	−	9.07562i	−0.194865	−	0.599734i	0.805113	−	0.593122i	$-0.202105\pi$
$230$	9.21965	+	5.29762i	0.607925	+	0.349315i
$231$	0.553829	−	1.70451i	0.0364393	−	0.112149i
$232$	7.78947			0.511404
$233$	−4.83684	+	14.8863i	−0.316872	+	0.975231i	0.658105	+	0.752926i	$0.271358\pi$
$233$	−4.83684	+	14.8863i	−0.316872	+	0.975231i	−0.974977	+	0.222305i	$0.928642\pi$
$234$	0.593700	−	0.431348i	0.0388114	−	0.0281981i
$235$	19.0935	+	10.9711i	1.24552	+	0.715679i
$236$	−0.561467	−	0.407930i	−0.0365484	−	0.0265540i
$237$	−5.86199	+	4.25899i	−0.380777	+	0.276651i
$238$	−1.08626	+	0.789216i	−0.0704119	+	0.0511572i
$239$	−11.9056	−	8.64992i	−0.770109	−	0.559517i	0.131886	−	0.991265i	$-0.457897\pi$
$239$	−11.9056	−	8.64992i	−0.770109	−	0.559517i	−0.901994	+	0.431748i	$0.857897\pi$
$240$	3.28905	−	0.352558i	0.212307	−	0.0227575i
$241$	4.46804	−	3.24622i	0.287812	−	0.209107i	−0.434506	−	0.900669i	$-0.643077\pi$
$241$	4.46804	−	3.24622i	0.287812	−	0.209107i	0.722317	+	0.691562i	$0.243077\pi$
$242$	1.14930	−	3.53718i	0.0738797	−	0.227378i
$243$	−8.17787			−0.524611
$244$	0.124661	−	0.383667i	0.00798060	−	0.0245617i
$245$	−11.2760	+	10.1952i	−0.720400	+	0.651349i
$246$	−1.69976	−	5.23132i	−0.108373	−	0.333537i
$247$	−0.279425	−	0.859981i	−0.0177794	−	0.0547193i
$248$	2.60884	+	1.89544i	0.165662	+	0.120360i
$249$	5.98164			0.379071
$250$	−0.0692317	−	11.1801i	−0.00437860	−	0.707093i
$251$	17.4154			1.09925			0.549625	−	0.835412i	$-0.314771\pi$
$251$	17.4154			1.09925			0.549625	+	0.835412i	$0.314771\pi$
$252$	0.294797	+	0.214182i	0.0185704	+	0.0134922i
$253$	3.96510	+	12.2033i	0.249284	+	0.767216i
$254$	3.21178	+	9.88485i	0.201525	+	0.620230i
$255$	7.33761	−	6.63429i	0.459499	−	0.415455i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	26.2131			1.63513			0.817565	−	0.575837i	$-0.195324\pi$
$257$	26.2131			1.63513			0.817565	+	0.575837i	$0.195324\pi$
$258$	2.36668	−	7.28388i	0.147343	−	0.453475i
$259$	−0.725054	+	0.526782i	−0.0450526	+	0.0327327i
$260$	2.01042	−	0.215500i	0.124681	−	0.0133647i
$261$	−5.11438	−	3.71581i	−0.316572	−	0.230003i
$262$	−10.7229	+	7.79065i	−0.662464	+	0.481308i
$263$	−14.7727	+	10.7330i	−0.910925	+	0.661826i	−0.941249	−	0.337715i	$-0.890346\pi$
$263$	−14.7727	+	10.7330i	−0.910925	+	0.661826i	0.0303238	+	0.999540i	$0.490346\pi$
$264$	3.22934	+	2.34625i	0.198752	+	0.144402i
$265$	−8.39220	−	4.82217i	−0.515529	−	0.296224i
$266$	0.363242	−	0.263911i	0.0222718	−	0.0161814i
$267$	2.92398	−	8.99907i	0.178944	−	0.550734i
$268$	−3.34159			−0.204120
$269$	3.27727	−	10.0864i	0.199819	−	0.614979i	−0.800068	−	0.599910i	$-0.795203\pi$
$269$	3.27727	−	10.0864i	0.199819	−	0.614979i	0.999886	−	0.0150692i	$-0.00479686\pi$
$270$	−10.9321	−	6.28158i	−0.665304	−	0.382285i
$271$	3.79749	+	11.6875i	0.230681	+	0.709963i	0.997665	+	0.0682967i	$0.0217564\pi$
$271$	3.79749	+	11.6875i	0.230681	+	0.709963i	−0.766984	+	0.641666i	$0.778244\pi$
$272$	−0.924105	−	2.84410i	−0.0560321	−	0.172449i
$273$	−0.485897	−	0.353025i	−0.0294078	−	0.0213660i
$274$	−11.4850			−0.693832
$275$	8.98609	−	10.0633i	0.541882	−	0.606840i
$276$	7.03475			0.423442
$277$	−24.4370	−	17.7545i	−1.46828	−	1.06677i	−0.981109	−	0.193456i	$-0.938030\pi$
$277$	−24.4370	−	17.7545i	−1.46828	−	1.06677i	−0.487167	−	0.873309i	$-0.661970\pi$
$278$	2.99262	+	9.21034i	0.179485	+	0.552399i
$279$	−0.808723	−	2.48899i	−0.0484170	−	0.149012i
$280$	0.410246	+	0.916332i	0.0245169	+	0.0547613i
$281$	7.16390	−	22.0482i	0.427362	−	1.31529i	−0.473352	−	0.880874i	$-0.656956\pi$
$281$	7.16390	−	22.0482i	0.427362	−	1.31529i	0.900714	−	0.434412i	$-0.143044\pi$
$282$	14.5687			0.867551
$283$	−0.359156	+	1.10537i	−0.0213496	+	0.0657074i	−0.961164	−	0.275979i	$-0.910998\pi$
$283$	−0.359156	+	1.10537i	−0.0213496	+	0.0657074i	0.939814	+	0.341686i	$0.110998\pi$
$284$	3.89689	−	2.83125i	0.231238	−	0.168004i
$285$	−2.45367	+	2.21848i	−0.145343	+	0.131411i
$286$	1.97392	+	1.43414i	0.116720	+	0.0848023i
$287$	1.35062	−	0.981285i	0.0797247	−	0.0579234i
$288$	−0.656575	+	0.477030i	−0.0386891	+	0.0281092i
$289$	6.51834	+	4.73585i	0.383432	+	0.278579i
$290$	−7.11728	−	15.8973i	−0.417941	−	0.933521i
$291$	−0.940068	+	0.683000i	−0.0551078	+	0.0400382i
$292$	−1.06660	+	3.28265i	−0.0624179	+	0.192103i
$293$	−10.9435			−0.639327			−0.319664	−	0.947531i	$-0.603570\pi$
$293$	−10.9435			−0.639327			−0.319664	+	0.947531i	$0.603570\pi$
$294$	−3.10782	+	9.56488i	−0.181252	+	0.557835i
$295$	−0.319515	+	1.51861i	−0.0186029	+	0.0884168i
$296$	−0.616818	−	1.89837i	−0.0358518	−	0.110340i
$297$	−4.70156	−	14.4699i	−0.272812	−	0.839629i
$298$	−18.5016	−	13.4422i	−1.07177	−	0.778684i
$299$	4.29996			0.248673
$300$	−3.72475	−	6.39038i	−0.215048	−	0.368949i
$301$	2.32449			0.133982
$302$	5.31095	+	3.85863i	0.305611	+	0.222039i
$303$	1.00166	+	3.08279i	0.0575438	+	0.177102i
$304$	0.309017	+	0.951057i	0.0177233	+	0.0545468i
$305$	−0.896917	+	0.0961419i	−0.0513573	+	0.00550507i
$306$	−0.749977	+	2.30819i	−0.0428733	+	0.131951i
$307$	3.99941			0.228258			0.114129	−	0.993466i	$-0.463592\pi$
$307$	3.99941			0.228258			0.114129	+	0.993466i	$0.463592\pi$
$308$	−0.374377	+	1.15222i	−0.0213321	+	0.0656536i
$309$	16.9451	−	12.3114i	0.963975	−	0.700369i
$310$	1.48462	−	7.05618i	0.0843208	−	0.400764i
$311$	26.2143	+	19.0458i	1.48648	+	1.07999i	0.975396	+	0.220458i	$0.0707553\pi$
$311$	26.2143	+	19.0458i	1.48648	+	1.07999i	0.511082	+	0.859532i	$0.329245\pi$
$312$	1.08220	−	0.786262i	0.0612673	−	0.0445133i
$313$	−4.41837	+	3.21014i	−0.249741	+	0.181448i	−0.705612	−	0.708598i	$-0.749328\pi$
$313$	−4.41837	+	3.21014i	−0.249741	+	0.181448i	0.455871	+	0.890046i	$0.349328\pi$
$314$	0.184656	+	0.134160i	0.0104207	+	0.00757110i
$315$	0.167761	−	0.797340i	0.00945224	−	0.0449250i
$316$	3.96259	−	2.87899i	0.222913	−	0.161956i
$317$	5.69851	−	17.5382i	0.320060	−	0.985045i	−0.653561	−	0.756874i	$-0.726726\pi$
$317$	5.69851	−	17.5382i	0.320060	−	0.985045i	0.973621	−	0.228171i	$-0.0732744\pi$
$318$	−6.40340			−0.359085
$319$	6.49501	−	19.9896i	0.363651	−	1.11920i
$320$	−2.22333	+	0.238322i	−0.124288	+	0.0133226i
$321$	3.78752	+	11.6568i	0.211399	+	0.650619i
$322$	0.659785	+	2.03061i	0.0367684	+	0.113162i
$323$	2.41934	+	1.75775i	0.134616	+	0.0978039i
$324$	−5.90664			−0.328147
$325$	−2.27674	−	3.90610i	−0.126291	−	0.216671i
$326$	−21.5306			−1.19247
$327$	13.3921	+	9.72994i	0.740586	+	0.538067i
$328$	1.14900	+	3.53626i	0.0634430	+	0.195258i
$329$	1.36639	+	4.20531i	0.0753314	+	0.231846i
$330$	1.83772	−	8.73443i	0.101163	−	0.480814i
$331$	−4.17145	+	12.8384i	−0.229283	+	0.705662i	0.768545	+	0.639796i	$0.220981\pi$
$331$	−4.17145	+	12.8384i	−0.229283	+	0.705662i	−0.997828	+	0.0658662i	$0.979019\pi$
$332$	−4.04347			−0.221914
$333$	−0.500592	+	1.54066i	−0.0274323	+	0.0844278i
$334$	−8.16757	+	5.93409i	−0.446909	+	0.324699i
$335$	3.05323	+	6.81975i	0.166816	+	0.372603i
$336$	0.537356	+	0.390412i	0.0293152	+	0.0212987i
$337$	−16.6972	+	12.1312i	−0.909556	+	0.660831i	−0.940903	−	0.338677i	$-0.890020\pi$
$337$	−16.6972	+	12.1312i	−0.909556	+	0.660831i	0.0313465	+	0.999509i	$0.490020\pi$
$338$	−9.85573	+	7.16061i	−0.536081	+	0.389486i
$339$	−7.32314	−	5.32057i	−0.397738	−	0.288974i
$340$	−4.96008	+	4.48465i	−0.268998	+	0.243214i
$341$	7.03943	−	5.11444i	0.381206	−	0.276963i
$342$	0.250789	−	0.771850i	0.0135611	−	0.0417369i
$343$	−6.19537			−0.334518
$344$	−1.59983	+	4.92376i	−0.0862568	+	0.265471i
$345$	−6.42769	−	14.3570i	−0.346055	−	0.772954i
$346$	3.61814	+	11.1355i	0.194512	+	0.598647i
$347$	−3.63137	−	11.1762i	−0.194942	−	0.599971i	−0.999977	−	0.00674335i	$-0.997854\pi$
$347$	−3.63137	−	11.1762i	−0.194942	−	0.599971i	0.805035	−	0.593227i	$-0.202146\pi$
$348$	−9.32249	−	6.77319i	−0.499738	−	0.363081i
$349$	20.2240			1.08257			0.541283	−	0.840841i	$-0.317939\pi$
$349$	20.2240			1.08257			0.541283	+	0.840841i	$0.317939\pi$
$350$	1.49527	−	1.67452i	0.0799255	−	0.0895066i
$351$	−5.09862			−0.272144
$352$	−2.18297	−	1.58602i	−0.116352	−	0.0845350i
$353$	−5.27899	−	16.2471i	−0.280972	−	0.864743i	−0.987577	−	0.157135i	$-0.949774\pi$
$353$	−5.27899	−	16.2471i	−0.280972	−	0.864743i	0.706605	−	0.707608i	$-0.250226\pi$
$354$	0.317260	+	0.976426i	0.0168622	+	0.0518965i
$355$	−9.33882	−	5.36610i	−0.495653	−	0.284803i
$356$	−1.97655	+	6.08319i	−0.104757	+	0.322409i
$357$	1.98629			0.105126
$358$	0.844572	−	2.59933i	0.0446370	−	0.137379i
$359$	28.3198	−	20.5755i	1.49466	−	1.08594i	0.522214	−	0.852815i	$-0.325106\pi$
$359$	28.3198	−	20.5755i	1.49466	−	1.08594i	0.972448	−	0.233121i	$-0.0748937\pi$
$360$	1.57347	+	0.904119i	0.0829292	+	0.0476512i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	−10.2193	+	7.42473i	−0.537113	+	0.390235i
$363$	−4.45117	+	3.23397i	−0.233626	+	0.169739i
$364$	0.328457	+	0.238638i	0.0172158	+	0.0125080i
$365$	7.67401	−	0.822590i	0.401676	−	0.0430563i
$366$	−0.482805	+	0.350778i	−0.0252366	+	0.0183355i
$367$	−4.06693	+	12.5167i	−0.212292	+	0.653368i	0.787043	+	0.616899i	$0.211611\pi$
$367$	−4.06693	+	12.5167i	−0.212292	+	0.653368i	−0.999335	+	0.0364696i	$0.988389\pi$
$368$	−4.75535			−0.247890
$369$	0.932497	−	2.86993i	0.0485439	−	0.149403i
$370$	−3.31073	+	2.99339i	−0.172117	+	0.155619i
$371$	−0.600571	−	1.84837i	−0.0311801	−	0.0959625i
$372$	−1.47414	−	4.53694i	−0.0764306	−	0.235229i
$373$	15.8398	+	11.5083i	0.820153	+	0.595876i	0.916756	−	0.399447i	$-0.130798\pi$
$373$	15.8398	+	11.5083i	0.820153	+	0.595876i	−0.0966033	+	0.995323i	$0.530798\pi$
$374$	−8.06916			−0.417246
$375$	−9.63860	+	13.4406i	−0.497735	+	0.694072i
$376$	−9.84812			−0.507878
$377$	−5.69834	−	4.14009i	−0.293479	−	0.213225i
$378$	−0.782331	−	2.40777i	−0.0402388	−	0.123842i
$379$	−4.17338	−	12.8443i	−0.214372	−	0.659769i	−0.999198	−	0.0400523i	$-0.987248\pi$
$379$	−4.17338	−	12.8443i	−0.214372	−	0.659769i	0.784826	−	0.619717i	$-0.212752\pi$
$380$	1.65863	−	1.49965i	0.0850859	−	0.0769303i
$381$	4.75130	−	14.6230i	0.243416	−	0.749158i
$382$	12.3127			0.629975
$383$	1.41043	−	4.34086i	0.0720697	−	0.221808i	−0.908533	−	0.417813i	$-0.862797\pi$
$383$	1.41043	−	4.34086i	0.0720697	−	0.221808i	0.980603	+	0.196005i	$0.0627969\pi$
$384$	−1.19681	+	0.869531i	−0.0610743	+	0.0443730i
$385$	2.69359	−	0.288730i	0.137278	−	0.0147151i
$386$	−13.5216	−	9.82399i	−0.688229	−	0.500028i
$387$	3.39919	−	2.46965i	0.172790	−	0.125540i
$388$	0.635467	−	0.461694i	0.0322610	−	0.0234390i
$389$	21.0483	+	15.2925i	1.06719	+	0.775359i	0.975405	−	0.220420i	$-0.0707427\pi$
$389$	21.0483	+	15.2925i	1.06719	+	0.775359i	0.0917851	+	0.995779i	$0.470743\pi$
$390$	−2.59347	−	1.49021i	−0.131325	−	0.0754597i
$391$	−11.5048	+	8.35872i	−0.581822	+	0.422719i
$392$	2.10082	−	6.46567i	0.106108	−	0.326566i
$393$	19.6075			0.989065
$394$	3.89083	−	11.9747i	0.196017	−	0.603279i
$395$	−9.49628	−	5.45658i	−0.477810	−	0.274550i
$396$	0.676704	+	2.08268i	0.0340056	+	0.104659i
$397$	4.56375	+	14.0458i	0.229048	+	0.704937i	0.997855	+	0.0654566i	$0.0208504\pi$
$397$	4.56375	+	14.0458i	0.229048	+	0.704937i	−0.768808	+	0.639480i	$0.779150\pi$
$398$	−9.88669	−	7.18310i	−0.495575	−	0.360056i
$399$	−0.664208			−0.0332520
$400$	2.51785	+	4.31977i	0.125893	+	0.215988i
$401$	20.8982			1.04361			0.521804	−	0.853066i	$-0.325259\pi$
$401$	20.8982			1.04361			0.521804	+	0.853066i	$0.325259\pi$
$402$	3.99924	+	2.90562i	0.199464	+	0.144919i
$403$	−0.901063	−	2.77319i	−0.0448851	−	0.138142i
$404$	−0.677102	−	2.08391i	−0.0336871	−	0.103678i
$405$	5.39693	+	12.0547i	0.268175	+	0.599001i
$406$	1.08076	−	3.32623i	0.0536371	−	0.165078i
$407$	−5.38597			−0.266973
$408$	−1.36706	+	4.20738i	−0.0676795	+	0.208296i
$409$	−21.4352	+	15.5736i	−1.05990	+	0.770065i	−0.974070	−	0.226245i	$-0.927355\pi$
$409$	−21.4352	+	15.5736i	−1.05990	+	0.770065i	−0.0858326	+	0.996310i	$0.527355\pi$
$410$	6.16720	−	5.57607i	0.304576	−	0.275382i
$411$	13.7453	+	9.98652i	0.678004	+	0.492599i
$412$	−11.4546	+	8.32223i	−0.564326	+	0.410007i
$413$	−0.252094	+	0.183157i	−0.0124047	+	0.00901257i
$414$	3.12224	+	2.26844i	0.153450	+	0.111488i
$415$	3.69454	+	8.25219i	0.181358	+	0.405084i
$416$	−0.731543	+	0.531497i	−0.0358669	+	0.0260588i
$417$	4.42708	−	13.6252i	0.216795	−	0.667227i
$418$	2.69829			0.131978
$419$	8.86482	−	27.2831i	0.433075	−	1.33287i	−0.461972	−	0.886894i	$-0.652858\pi$
$419$	8.86482	−	27.2831i	0.433075	−	1.33287i	0.895047	−	0.445972i	$-0.147142\pi$
$420$	0.305794	−	1.45339i	0.0149212	−	0.0709183i
$421$	−5.63844	−	17.3533i	−0.274801	−	0.845749i	−0.989272	−	0.146085i	$-0.953333\pi$
$421$	−5.63844	−	17.3533i	−0.274801	−	0.845749i	0.714471	−	0.699665i	$-0.246667\pi$
$422$	−0.345024	−	1.06187i	−0.0167955	−	0.0516912i
$423$	6.46603	+	4.69785i	0.314389	+	0.228417i
$424$	4.32857			0.210214
$425$	13.6846	+	6.02522i	0.663802	+	0.292266i
$426$	−7.12568			−0.345240
$427$	−0.146536	−	0.106464i	−0.00709136	−	0.00515218i
$428$	−2.56029	−	7.87976i	−0.123756	−	0.380882i
$429$	−1.11537	−	3.43277i	−0.0538507	−	0.165736i
$430$	11.5105	−	1.23383i	0.555086	−	0.0595006i
$431$	2.29956	−	7.07733i	0.110766	−	0.340903i	−0.880274	−	0.474465i	$-0.842642\pi$
$431$	2.29956	−	7.07733i	0.110766	−	0.340903i	0.991040	+	0.133562i	$0.0426415\pi$
$432$	5.63859			0.271287
$433$	1.01714	−	3.13044i	0.0488807	−	0.150439i	−0.923637	−	0.383269i	$-0.874798\pi$
$433$	1.01714	−	3.13044i	0.0488807	−	0.150439i	0.972518	+	0.232829i	$0.0747983\pi$
$434$	1.17135	−	0.851034i	0.0562265	−	0.0408510i
$435$	−5.30517	+	25.2147i	−0.254363	+	1.20895i
$436$	−9.05280	−	6.57725i	−0.433551	−	0.314993i
$437$	3.84716	−	2.79512i	0.184034	−	0.133709i
$438$	4.13088	−	3.00126i	0.197381	−	0.143406i
$439$	−13.8964	−	10.0963i	−0.663239	−	0.481872i	0.204516	−	0.978863i	$-0.434438\pi$
$439$	−13.8964	−	10.0963i	−0.663239	−	0.481872i	−0.867755	+	0.496992i	$0.834438\pi$
$440$	−1.24227	+	5.90430i	−0.0592227	+	0.281476i
$441$	−4.46366	+	3.24304i	−0.212555	+	0.154431i
$442$	−0.835610	+	2.57174i	−0.0397459	+	0.122325i
$443$	−26.9588			−1.28085			−0.640425	−	0.768021i	$-0.721242\pi$
$443$	−26.9588			−1.28085			−0.640425	+	0.768021i	$0.721242\pi$
$444$	−0.912479	+	2.80832i	−0.0433043	+	0.133277i
$445$	14.2210	−	1.52437i	0.674139	−	0.0722620i
$446$	3.39040	+	10.4346i	0.160540	+	0.494091i
$447$	10.4544	+	32.1753i	0.494476	+	1.52184i
$448$	−0.363242	−	0.263911i	−0.0171616	−	0.0124686i
$449$	−17.2692			−0.814984			−0.407492	−	0.913209i	$-0.633597\pi$
$449$	−17.2692			−0.814984			−0.407492	+	0.913209i	$0.633597\pi$
$450$	0.407498	−	4.03734i	0.0192096	−	0.190322i
$451$	10.0329			0.472432
$452$	4.95030	+	3.59660i	0.232842	+	0.169170i
$453$	−3.00098	−	9.23607i	−0.140998	−	0.433949i
$454$	1.82312	+	5.61098i	0.0855631	+	0.263336i
$455$	0.186916	−	0.888381i	0.00876274	−	0.0416480i
$456$	0.457139	−	1.40693i	0.0214075	−	0.0658855i
$457$	4.75909			0.222621			0.111310	−	0.993786i	$-0.464495\pi$
$457$	4.75909			0.222621			0.111310	+	0.993786i	$0.464495\pi$
$458$	2.94885	−	9.07562i	0.137791	−	0.424076i
$459$	13.6416	−	9.91124i	0.636738	−	0.462617i
$460$	4.34499	+	9.70504i	0.202586	+	0.452500i
$461$	20.9135	+	15.1946i	0.974041	+	0.707682i	0.956369	−	0.292162i	$-0.0943745\pi$
$461$	20.9135	+	15.1946i	0.974041	+	0.707682i	0.0176720	+	0.999844i	$0.494375\pi$
$462$	1.44994	−	1.05345i	0.0674575	−	0.0490107i
$463$	−30.4703	+	22.1380i	−1.41608	+	1.02884i	−0.423672	+	0.905815i	$0.639259\pi$
$463$	−30.4703	+	22.1380i	−1.41608	+	1.02884i	−0.992404	+	0.123024i	$0.960741\pi$
$464$	6.30182	+	4.57854i	0.292555	+	0.212553i
$465$	−7.91236	+	7.15395i	−0.366927	+	0.331757i
$466$	−12.6630	+	9.20021i	−0.586602	+	0.426192i
$467$	11.5640	−	35.5902i	0.535116	−	1.64692i	−0.208282	−	0.978069i	$-0.566787\pi$
$467$	11.5640	−	35.5902i	0.535116	−	1.64692i	0.743398	−	0.668849i	$-0.233213\pi$
$468$	0.733853			0.0339224
$469$	−0.463633	+	1.42692i	−0.0214086	+	0.0658888i
$470$	8.99828	+	20.0987i	0.415060	+	0.927085i
$471$	−0.104341	−	0.321128i	−0.00480777	−	0.0147968i
$472$	−0.214461	−	0.660044i	−0.00987139	−	0.0303810i
$473$	11.3015	+	8.21104i	0.519645	+	0.377544i
$474$	−7.24582			−0.332812
$475$	−4.57608	−	2.01481i	−0.209965	−	0.0924458i
$476$	−1.34269			−0.0615423
$477$	−2.84203	−	2.06486i	−0.130128	−	0.0945432i
$478$	−4.54753	−	13.9959i	−0.207999	−	0.640156i
$479$	8.70043	+	26.7772i	0.397533	+	1.22348i	0.926971	+	0.375132i	$0.122403\pi$
$479$	8.70043	+	26.7772i	0.397533	+	1.22348i	−0.529438	+	0.848348i	$0.677597\pi$
$480$	2.86813	+	1.64803i	0.130911	+	0.0752219i
$481$	−0.557750	+	1.71658i	−0.0254312	+	0.0782692i
$482$	5.52280			0.251557
$483$	0.976043	−	3.00395i	0.0444115	−	0.136684i
$484$	3.00890	−	2.18610i	0.136768	−	0.0993680i
$485$	−1.52289	−	0.875053i	−0.0691507	−	0.0397341i
$486$	−6.61604	−	4.80683i	−0.300110	−	0.218042i
$487$	−10.5751	+	7.68326i	−0.479204	+	0.348162i	−0.801017	−	0.598641i	$-0.795708\pi$
$487$	−10.5751	+	7.68326i	−0.479204	+	0.348162i	0.321814	+	0.946803i	$0.395708\pi$
$488$	0.326366	−	0.237119i	0.0147739	−	0.0107339i
$489$	25.7680	+	18.7215i	1.16527	+	0.846617i
$490$	−15.1151	+	1.62021i	−0.682831	+	0.0731938i
$491$	−2.44245	+	1.77455i	−0.110226	+	0.0800842i	−0.641533	−	0.767095i	$-0.721701\pi$
$491$	−2.44245	+	1.77455i	−0.110226	+	0.0800842i	0.531307	+	0.847180i	$0.321701\pi$
$492$	1.69976	−	5.23132i	0.0766310	−	0.235846i
$493$	23.2942			1.04912
$494$	0.279425	−	0.859981i	0.0125719	−	0.0386924i
$495$	3.63217	−	3.28402i	0.163254	−	0.147606i
$496$	0.996490	+	3.06688i	0.0447437	+	0.137707i
$497$	−0.668314	−	2.05686i	−0.0299780	−	0.0922627i
$498$	4.83925	+	3.51592i	0.216852	+	0.157552i
$499$	−27.0510			−1.21097			−0.605484	−	0.795858i	$-0.707020\pi$
$499$	−27.0510			−1.21097			−0.605484	+	0.795858i	$0.707020\pi$
$500$	6.51550	−	9.08560i	0.291382	−	0.406321i
$501$	14.9349			0.667241
$502$	14.0893	+	10.2365i	0.628838	+	0.456878i
$503$	8.27837	+	25.4782i	0.369114	+	1.13602i	0.947364	+	0.320157i	$0.103736\pi$
$503$	8.27837	+	25.4782i	0.369114	+	1.13602i	−0.578250	+	0.815859i	$0.696264\pi$
$504$	0.112602	+	0.346554i	0.00501570	+	0.0154368i
$505$	−3.63430	+	3.28595i	−0.161724	+	0.146223i
$506$	−3.96510	+	12.2033i	−0.176270	+	0.542504i
$507$	18.0218			0.800375
$508$	−3.21178	+	9.88485i	−0.142500	+	0.438569i
$509$	30.6610	−	22.2765i	1.35902	−	0.987389i	0.360518	−	0.932752i	$-0.382600\pi$
$509$	30.6610	−	22.2765i	1.35902	−	0.987389i	0.998506	−	0.0546364i	$-0.0174000\pi$
$510$	9.83579	−	1.05431i	0.435536	−	0.0466858i
$511$	1.25376	+	0.910909i	0.0554630	+	0.0402962i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−4.56171	+	3.31428i	−0.201405	+	0.146329i
$514$	21.2069	+	15.4077i	0.935394	+	0.679604i
$515$	27.4507	+	15.7732i	1.20962	+	0.695050i
$516$	6.19604	−	4.50169i	0.272765	−	0.198176i
$517$	−8.21155	+	25.2725i	−0.361143	+	1.11149i
$518$	−0.896216			−0.0393774
$519$	5.35243	−	16.4731i	0.234946	−	0.723088i
$520$	1.75313	+	1.00735i	0.0768799	+	0.0441753i
$521$	−0.340279	−	1.04727i	−0.0149079	−	0.0458818i	0.943326	−	0.331868i	$-0.107679\pi$
$521$	−0.340279	−	1.04727i	−0.0149079	−	0.0458818i	−0.958234	+	0.285986i	$0.907679\pi$
$522$	−1.95352	−	6.01231i	−0.0855031	−	0.263152i
$523$	21.4370	+	15.5749i	0.937373	+	0.681042i	0.947787	−	0.318904i	$-0.103315\pi$
$523$	21.4370	+	15.5749i	0.937373	+	0.681042i	−0.0104137	+	0.999946i	$0.503315\pi$
$524$	−13.2542			−0.579015
$525$	−3.24559	+	0.703888i	−0.141649	+	0.0307202i
$526$	−18.2601			−0.796177
$527$	7.80166	+	5.66824i	0.339846	+	0.246912i
$528$	1.23350	+	3.79631i	0.0536810	+	0.165213i
$529$	−0.119487	−	0.367742i	−0.00519507	−	0.0159888i
$530$	−3.95503	−	8.83403i	−0.171796	−	0.383726i
$531$	−0.174051	+	0.535673i	−0.00755316	+	0.0232462i
$532$	0.448991			0.0194662
$533$	1.03897	−	3.19762i	0.0450028	−	0.138504i
$534$	7.65507	−	5.56173i	0.331267	−	0.240680i
$535$	−13.7422	+	12.4250i	−0.594127	+	0.537179i
$536$	−2.70341	−	1.96414i	−0.116769	−	0.0848379i
$537$	−3.27098	+	2.37651i	−0.141153	+	0.102554i
$538$	8.58001	−	6.23374i	0.369910	−	0.268756i
$539$	−14.8407	−	10.7824i	−0.639234	−	0.464431i
$540$	−5.15201	−	11.5076i	−0.221707	−	0.495209i
$541$	10.2946	−	7.47944i	0.442598	−	0.321566i	−0.344068	−	0.938945i	$-0.611805\pi$
$541$	10.2946	−	7.47944i	0.442598	−	0.321566i	0.786666	+	0.617378i	$0.211805\pi$
$542$	−3.79749	+	11.6875i	−0.163116	+	0.502019i
$543$	18.6865			0.801915
$544$	0.924105	−	2.84410i	0.0396207	−	0.121940i
$545$	−5.15170	+	24.4852i	−0.220675	+	1.04883i
$546$	−0.185596	−	0.571206i	−0.00794278	−	0.0244454i
$547$	−4.53197	−	13.9480i	−0.193773	−	0.596372i	−0.999989	−	0.00475033i	$-0.998488\pi$
$547$	−4.53197	−	13.9480i	−0.193773	−	0.596372i	0.806216	−	0.591622i	$-0.201512\pi$
$548$	−9.29153	−	6.75069i	−0.396914	−	0.288375i
$549$	−0.327397			−0.0139730
$550$	13.1850	−	2.85949i	0.562208	−	0.121929i
$551$	−7.78947			−0.331843
$552$	5.69123	+	4.13492i	0.242235	+	0.175994i
$553$	−0.679582	−	2.09154i	−0.0288988	−	0.0889413i
$554$	−9.33410	−	28.7274i	−0.396568	−	1.22051i
$555$	6.56515	−	0.703729i	0.278675	−	0.0298716i
$556$	−2.99262	+	9.21034i	−0.126915	+	0.390605i
$557$	29.6213			1.25509			0.627546	−	0.778579i	$-0.284059\pi$
$557$	29.6213			1.25509			0.627546	+	0.778579i	$0.284059\pi$
$558$	0.808723	−	2.48899i	0.0342360	−	0.105367i
$559$	3.78731	−	2.75164i	0.160186	−	0.116382i
$560$	−0.206711	+	0.982465i	−0.00873512	+	0.0415167i
$561$	9.65722	+	7.01638i	0.407728	+	0.296232i
$562$	18.7553	−	13.6265i	0.791146	−	0.574801i
$563$	−16.6779	+	12.1172i	−0.702889	+	0.510679i	−0.880872	−	0.473355i	$-0.843043\pi$
$563$	−16.6779	+	12.1172i	−0.702889	+	0.510679i	0.177983	+	0.984034i	$0.443043\pi$
$564$	11.7863	+	8.56324i	0.496292	+	0.360578i
$565$	2.81708	−	13.3891i	0.118515	−	0.563285i
$566$	−0.940284	+	0.683156i	−0.0395231	+	0.0287152i
$567$	−0.819522	+	2.52223i	−0.0344167	+	0.105924i
$568$	4.81682			0.202109
$569$	5.80021	−	17.8512i	0.243157	−	0.748362i	−0.752777	−	0.658276i	$-0.771286\pi$
$569$	5.80021	−	17.8512i	0.243157	−	0.748362i	0.995934	−	0.0900856i	$-0.0287141\pi$
$570$	−3.28905	+	0.352558i	−0.137763	+	0.0147670i
$571$	−7.09279	−	21.8294i	−0.296824	−	0.913531i	−0.982603	−	0.185720i	$-0.940538\pi$
$571$	−7.09279	−	21.8294i	−0.296824	−	0.913531i	0.685779	−	0.727810i	$-0.259462\pi$
$572$	0.753970	+	2.32048i	0.0315251	+	0.0970242i
$573$	−14.7360	−	10.7063i	−0.615604	−	0.447262i
$574$	1.66946			0.0696820
$575$	15.8367	−	17.7351i	0.660435	−	0.739604i
$576$	−0.811572			−0.0338155
$577$	−10.4718	−	7.60819i	−0.435946	−	0.316733i	0.348076	−	0.937466i	$-0.386835\pi$
$577$	−10.4718	−	7.60819i	−0.435946	−	0.316733i	−0.784022	+	0.620733i	$0.786835\pi$
$578$	2.48978	+	7.66277i	0.103561	+	0.318729i
$579$	7.64043	+	23.5148i	0.317525	+	0.977243i
$580$	3.58619	−	17.0446i	0.148908	−	0.707739i
$581$	−0.561015	+	1.72663i	−0.0232748	+	0.0716326i
$582$	−1.16199			−0.0481660
$583$	3.60924	−	11.1081i	0.149479	−	0.460050i
$584$	−2.79239	+	2.02879i	−0.115550	+	0.0839519i
$585$	−0.670526	−	1.49770i	−0.0277228	−	0.0619222i
$586$	−8.85350	−	6.43244i	−0.365735	−	0.265722i
$587$	15.9266	−	11.5714i	0.657361	−	0.477601i	−0.208410	−	0.978042i	$-0.566829\pi$
$587$	15.9266	−	11.5714i	0.657361	−	0.477601i	0.865771	+	0.500441i	$0.166829\pi$
$588$	−8.13638	+	5.91142i	−0.335538	+	0.243783i
$589$	−2.60884	−	1.89544i	−0.107496	−	0.0781001i
$590$	−1.15111	+	1.04077i	−0.0473904	+	0.0428480i
$591$	−15.0690	+	10.9483i	−0.619855	+	0.450351i
$592$	0.616818	−	1.89837i	0.0253510	−	0.0780225i
$593$	2.31437			0.0950398			0.0475199	−	0.998870i	$-0.484868\pi$
$593$	2.31437			0.0950398			0.0475199	+	0.998870i	$0.484868\pi$
$594$	4.70156	−	14.4699i	0.192907	−	0.593708i
$595$	1.22683	+	2.74026i	0.0502950	+	0.112340i
$596$	−7.06697	−	21.7499i	−0.289474	−	0.890910i
$597$	5.58653	+	17.1936i	0.228641	+	0.703686i
$598$	3.47874	+	2.52745i	0.142256	+	0.103355i
$599$	−38.6605			−1.57962			−0.789812	−	0.613349i	$-0.789822\pi$
$599$	−38.6605			−1.57962			−0.789812	+	0.613349i	$0.789822\pi$
$600$	0.742788	−	7.35928i	0.0303242	−	0.300441i
$601$	−43.7720			−1.78550			−0.892748	−	0.450557i	$-0.851225\pi$
$601$	−43.7720			−1.78550			−0.892748	+	0.450557i	$0.851225\pi$
$602$	1.88056	+	1.36630i	0.0766457	+	0.0556864i
$603$	0.838036	+	2.57921i	0.0341275	+	0.105034i
$604$	2.02860	+	6.24340i	0.0825427	+	0.254040i
$605$	−7.21078	−	4.14333i	−0.293160	−	0.168450i
$606$	−1.00166	+	3.08279i	−0.0406896	+	0.125230i
$607$	9.94820			0.403785			0.201892	−	0.979408i	$-0.435291\pi$
$607$	9.94820			0.403785			0.201892	+	0.979408i	$0.435291\pi$
$608$	−0.309017	+	0.951057i	−0.0125323	+	0.0385704i
$609$	−4.18572	+	3.04110i	−0.169614	+	0.123232i
$610$	−0.782132	−	0.449414i	−0.0316676	−	0.0181962i
$611$	7.20433	+	5.23425i	0.291456	+	0.211755i
$612$	−1.96347	+	1.42654i	−0.0793684	+	0.0576645i
$613$	11.0073	−	7.99731i	0.444583	−	0.323008i	−0.342871	−	0.939383i	$-0.611399\pi$
$613$	11.0073	−	7.99731i	0.444583	−	0.323008i	0.787453	+	0.616375i	$0.211399\pi$
$614$	3.23559	+	2.35079i	0.130578	+	0.0948702i
$615$	−12.2295	+	1.31090i	−0.493141	+	0.0528606i
$616$	−0.980133	+	0.712108i	−0.0394907	+	0.0286917i
$617$	11.0101	−	33.8855i	0.443249	−	1.36418i	−0.441144	−	0.897436i	$-0.645427\pi$
$617$	11.0101	−	33.8855i	0.443249	−	1.36418i	0.884393	−	0.466743i	$-0.154573\pi$
$618$	20.9453			0.842545
$619$	3.67822	−	11.3204i	0.147840	−	0.455005i	−0.849525	−	0.527548i	$-0.823112\pi$
$619$	3.67822	−	11.3204i	0.147840	−	0.455005i	0.997365	+	0.0725432i	$0.0231115\pi$
$620$	5.34860	−	4.83593i	0.214805	−	0.194216i
$621$	−8.28581	−	25.5011i	−0.332498	−	1.02332i
$622$	10.0130	+	30.8168i	0.401484	+	1.23564i
$623$	2.32338	+	1.68804i	0.0930844	+	0.0676298i
$624$	1.33767			0.0535496
$625$	−24.4958	−	4.99572i	−0.979831	−	0.199829i
$626$	−5.46141			−0.218282
$627$	−3.22934	−	2.34625i	−0.128967	−	0.0937002i
$628$	0.0705323	+	0.217076i	0.00281454	+	0.00866227i
$629$	−1.84457	−	5.67701i	−0.0735479	−	0.226357i
$630$	0.604386	−	0.546455i	0.0240793	−	0.0217713i
$631$	−1.87142	+	5.75962i	−0.0744999	+	0.229287i	−0.981371	−	0.192120i	$-0.938464\pi$
$631$	−1.87142	+	5.75962i	−0.0744999	+	0.229287i	0.906872	+	0.421407i	$0.138464\pi$
$632$	4.89803			0.194833
$633$	−0.510406	+	1.57087i	−0.0202868	+	0.0624364i
$634$	14.9189	−	10.8392i	0.592505	−	0.430480i
$635$	23.1083	−	2.47701i	0.917025	−	0.0982973i
$636$	−5.18046	−	3.76382i	−0.205418	−	0.149245i
$637$	−4.97333	+	3.61334i	−0.197050	+	0.143166i
$638$	17.0042	−	12.3542i	0.673201	−	0.489109i
$639$	−3.16260	−	2.29777i	−0.125111	−	0.0908982i
$640$	−1.93880	−	1.11403i	−0.0766376	−	0.0440361i
$641$	3.85546	−	2.80116i	0.152282	−	0.110639i	−0.509035	−	0.860746i	$-0.669998\pi$
$641$	3.85546	−	2.80116i	0.152282	−	0.110639i	0.661317	+	0.750106i	$0.269998\pi$
$642$	−3.78752	+	11.6568i	−0.149482	+	0.460057i
$643$	9.38280			0.370022			0.185011	−	0.982736i	$-0.440768\pi$
$643$	9.38280			0.370022			0.185011	+	0.982736i	$0.440768\pi$
$644$	−0.659785	+	2.03061i	−0.0259992	+	0.0800173i
$645$	−14.8487	−	8.53209i	−0.584667	−	0.335951i
$646$	0.924105	+	2.84410i	0.0363584	+	0.111900i
$647$	−9.74400	−	29.9890i	−0.383076	−	1.17899i	−0.937866	−	0.346997i	$-0.887201\pi$
$647$	−9.74400	−	29.9890i	−0.383076	−	1.17899i	0.554790	−	0.831991i	$-0.312799\pi$
$648$	−4.77857	−	3.47183i	−0.187720	−	0.136387i
$649$	−1.87265			−0.0735079
$650$	0.454027	−	4.49833i	0.0178084	−	0.176439i
$651$	−2.14188			−0.0839468
$652$	−17.4186	−	12.6554i	−0.682167	−	0.495623i
$653$	−9.79974	−	30.1605i	−0.383493	−	1.18027i	−0.937567	−	0.347804i	$-0.886928\pi$
$653$	−9.79974	−	30.1605i	−0.383493	−	1.18027i	0.554074	−	0.832467i	$-0.313072\pi$
$654$	5.11533	+	15.7434i	0.200025	+	0.615615i
$655$	12.1105	+	27.0502i	0.473196	+	1.05694i
$656$	−1.14900	+	3.53626i	−0.0448610	+	0.138068i
$657$	2.80121			0.109285
$658$	−1.36639	+	4.20531i	−0.0532673	+	0.163940i
$659$	−19.2202	+	13.9643i	−0.748712	+	0.543971i	−0.895427	−	0.445208i	$-0.853130\pi$
$659$	−19.2202	+	13.9643i	−0.748712	+	0.543971i	0.146715	+	0.989179i	$0.453130\pi$
$660$	6.62072	−	5.98611i	0.257711	−	0.233009i
$661$	−17.5750	−	12.7690i	−0.683588	−	0.496656i	0.190958	−	0.981598i	$-0.438841\pi$
$661$	−17.5750	−	12.7690i	−0.683588	−	0.496656i	−0.874546	+	0.484942i	$0.838841\pi$
$662$	−10.9210	+	7.93456i	−0.424456	+	0.308386i
$663$	3.23627	−	2.35129i	0.125686	−	0.0913165i
$664$	−3.27124	−	2.37669i	−0.126949	−	0.0922336i
$665$	−0.410246	−	0.916332i	−0.0159087	−	0.0355338i
$666$	−1.31057	+	0.952182i	−0.0507834	+	0.0368963i
$667$	11.4465	−	35.2287i	0.443210	−	1.36406i
$668$	−10.0957			−0.390613
$669$	5.01553	−	15.4362i	0.193912	−	0.596799i
$670$	−1.53843	+	7.31194i	−0.0594349	+	0.282485i
$671$	−0.336372	−	1.03525i	−0.0129855	−	0.0399652i
$672$	0.205252	+	0.631699i	0.00791775	+	0.0243683i
$673$	20.8265	+	15.1313i	0.802803	+	0.583270i	0.911735	−	0.410779i	$-0.134743\pi$
$673$	20.8265	+	15.1313i	0.802803	+	0.583270i	−0.108932	+	0.994049i	$0.534743\pi$
$674$	−20.6389			−0.794981
$675$	−18.7781	+	21.0291i	−0.722769	+	0.809412i
$676$	−12.1824			−0.468552
$677$	−14.1875	−	10.3078i	−0.545268	−	0.396161i	0.280770	−	0.959775i	$-0.409410\pi$
$677$	−14.1875	−	10.3078i	−0.545268	−	0.396161i	−0.826038	+	0.563615i	$0.809410\pi$
$678$	−2.79719	−	8.60887i	−0.107425	−	0.330622i
$679$	−0.108982	−	0.335413i	−0.00418236	−	0.0128720i
$680$	−6.64880	+	0.712695i	−0.254970	+	0.0273306i
$681$	2.69700	−	8.30051i	0.103349	−	0.318076i
$682$	8.70121			0.333187
$683$	5.67975	−	17.4805i	0.217330	−	0.668872i	−0.781650	−	0.623717i	$-0.785622\pi$
$683$	5.67975	−	17.4805i	0.217330	−	0.668872i	0.998980	−	0.0451549i	$-0.0143781\pi$
$684$	0.656575	−	0.477030i	0.0251048	−	0.0182397i
$685$	−5.28755	+	25.1309i	−0.202027	+	0.960203i
$686$	−5.01216	−	3.64154i	−0.191365	−	0.139035i
$687$	−11.4207	+	8.29764i	−0.435728	+	0.316575i
$688$	−4.18840	+	3.04305i	−0.159681	+	0.116015i
$689$	−3.16653	−	2.30062i	−0.120635	−	0.0876467i
$690$	3.23872	−	15.3931i	0.123296	−	0.586007i
$691$	31.9654	−	23.2243i	1.21602	−	0.883492i	0.220259	−	0.975441i	$-0.429310\pi$
$691$	31.9654	−	23.2243i	1.21602	−	0.883492i	0.995764	+	0.0919493i	$0.0293098\pi$
$692$	−3.61814	+	11.1355i	−0.137541	+	0.423307i
$693$	0.983228			0.0373497
$694$	3.63137	−	11.1762i	0.137845	−	0.424243i
$695$	21.5315	−	2.30799i	0.816735	−	0.0875471i
$696$	−3.56087	−	10.9592i	−0.134975	−	0.415409i
$697$	3.43605	+	10.5751i	0.130150	+	0.400560i
$698$	16.3615	+	11.8874i	0.619294	+	0.449943i
$699$	23.1550			0.875804
$700$	2.19395	−	0.475814i	0.0829237	−	0.0179841i
$701$	32.7970			1.23872			0.619362	−	0.785105i	$-0.287391\pi$
$701$	32.7970			1.23872			0.619362	+	0.785105i	$0.287391\pi$
$702$	−4.12487	−	2.99689i	−0.155683	−	0.113110i
$703$	0.616818	+	1.89837i	0.0232637	+	0.0715984i
$704$	−0.833819	−	2.56623i	−0.0314257	−	0.0967184i
$705$	6.70725	−	31.8785i	0.252610	−	1.20062i
$706$	5.27899	−	16.2471i	0.198677	−	0.611466i
$707$	−0.983806			−0.0369998
$708$	−0.317260	+	0.976426i	−0.0119234	+	0.0366963i
$709$	−13.3900	+	9.72838i	−0.502871	+	0.365357i	−0.810112	−	0.586275i	$-0.800594\pi$
$709$	−13.3900	+	9.72838i	−0.502871	+	0.365357i	0.307242	+	0.951632i	$0.400594\pi$
$710$	−4.40115	−	9.83049i	−0.165172	−	0.368932i
$711$	−3.21593	−	2.33651i	−0.120607	−	0.0876258i
$712$	−5.17467	+	3.75962i	−0.193929	+	0.140898i
$713$	12.4060	−	9.01346i	0.464607	−	0.337557i
$714$	1.60694	+	1.16751i	0.0601384	+	0.0436931i
$715$	4.04689	−	3.65899i	0.151345	−	0.136838i
$716$	2.21112	−	1.60647i	0.0826334	−	0.0600367i
$717$	−6.72732	+	20.7045i	−0.251236	+	0.773226i
$718$	35.0052			1.30638
$719$	2.46883	−	7.59829i	0.0920719	−	0.283368i	−0.894408	−	0.447253i	$-0.852402\pi$
$719$	2.46883	−	7.59829i	0.0920719	−	0.283368i	0.986480	+	0.163884i	$0.0524024\pi$
$720$	0.741537	+	1.65631i	0.0276355	+	0.0617270i
$721$	1.96445	+	6.04596i	0.0731600	+	0.225163i
$722$	−0.309017	−	0.951057i	−0.0115004	−	0.0353947i
$723$	−6.60972	−	4.80224i	−0.245818	−	0.178597i
$724$	−12.6317			−0.469454
$725$	−38.0625	+	8.25481i	−1.41361	+	0.306576i
$726$	−5.50195			−0.204197
$727$	−7.29370	−	5.29918i	−0.270508	−	0.196536i	0.444258	−	0.895899i	$-0.353467\pi$
$727$	−7.29370	−	5.29918i	−0.270508	−	0.196536i	−0.714767	+	0.699363i	$0.753467\pi$
$728$	0.125459	+	0.386124i	0.00464983	+	0.0143107i
$729$	9.21418	+	28.3583i	0.341266	+	1.05031i
$730$	6.69191	+	3.84518i	0.247679	+	0.142317i
$731$	−4.78423	+	14.7243i	−0.176951	+	0.544599i
$732$	−0.596780			−0.0220576
$733$	14.0847	−	43.3482i	0.520229	−	1.60110i	−0.253332	−	0.967380i	$-0.581526\pi$
$733$	14.0847	−	43.3482i	0.520229	−	1.60110i	0.773561	−	0.633722i	$-0.218474\pi$
$734$	−10.6474	+	7.73577i	−0.393002	+	0.285532i
$735$	19.4987	+	11.2040i	0.719220	+	0.413265i
$736$	−3.84716	−	2.79512i	−0.141808	−	0.103030i
$737$	−7.29459	+	5.29983i	−0.268700	+	0.195222i
$738$	2.44131	−	1.77372i	0.0898659	−	0.0652914i
$739$	−7.12376	−	5.17572i	−0.262052	−	0.190392i	0.448999	−	0.893532i	$-0.351781\pi$
$739$	−7.12376	−	5.17572i	−0.262052	−	0.190392i	−0.711051	+	0.703140i	$0.751781\pi$
$740$	−4.43791	+	0.475707i	−0.163141	+	0.0174873i
$741$	−1.08220	+	0.786262i	−0.0397555	+	0.0288841i
$742$	0.600571	−	1.84837i	0.0220477	−	0.0678557i
$743$	−31.4614			−1.15421			−0.577103	−	0.816672i	$-0.695817\pi$
$743$	−31.4614			−1.15421			−0.577103	+	0.816672i	$0.695817\pi$
$744$	1.47414	−	4.53694i	0.0540446	−	0.166332i
$745$	−37.9315	+	34.2957i	−1.38970	+	1.25650i
$746$	6.05026	+	18.6208i	0.221516	+	0.681755i
$747$	1.01406	+	3.12095i	0.0371025	+	0.114190i
$748$	−6.52809	−	4.74293i	−0.238690	−	0.173419i
$749$	−3.72001			−0.135926
$750$	−15.6980	+	5.20828i	−0.573210	+	0.190179i
$751$	−38.8156			−1.41640			−0.708201	−	0.706011i	$-0.750493\pi$
$751$	−38.8156			−1.41640			−0.708201	+	0.706011i	$0.750493\pi$
$752$	−7.96730	−	5.78858i	−0.290537	−	0.211088i
$753$	−7.96126	−	24.5022i	−0.290124	−	0.892911i
$754$	−2.17657	−	6.69880i	−0.0792661	−	0.243956i
$755$	10.8884	−	9.84474i	0.396270	−	0.358287i
$756$	0.782331	−	2.40777i	0.0284531	−	0.0875697i
$757$	38.0759			1.38389			0.691945	−	0.721950i	$-0.256754\pi$
$757$	38.0759			1.38389			0.691945	+	0.721950i	$0.256754\pi$
$758$	4.17338	−	12.8443i	0.151584	−	0.466527i
$759$	15.3566	−	11.1572i	0.557410	−	0.404982i
$760$	2.22333	−	0.238322i	0.0806487	−	0.00864486i
$761$	−21.7993	−	15.8381i	−0.790224	−	0.574131i	0.117806	−	0.993037i	$-0.462414\pi$
$761$	−21.7993	−	15.8381i	−0.790224	−	0.574131i	−0.908030	+	0.418905i	$0.862414\pi$
$762$	12.4391	−	9.03750i	0.450619	−	0.327394i
$763$	−4.06463	+	2.95313i	−0.147150	+	0.106910i
$764$	9.96122	+	7.23725i	0.360384	+	0.261834i
$765$	4.70541	+	2.70374i	0.170125	+	0.0977538i
$766$	3.69256	−	2.68280i	0.133418	−	0.0969335i
$767$	−0.193924	+	0.596837i	−0.00700219	+	0.0215505i
$768$	−1.47933			−0.0533809
$769$	−0.710784	+	2.18757i	−0.0256315	+	0.0788857i	−0.963054	−	0.269308i	$-0.913205\pi$
$769$	−0.710784	+	2.18757i	−0.0256315	+	0.0788857i	0.937422	+	0.348194i	$0.113205\pi$
$770$	2.34887	+	1.34966i	0.0846475	+	0.0486385i
$771$	−11.9830	−	36.8800i	−0.431559	−	1.32820i
$772$	−5.16478	−	15.8956i	−0.185884	−	0.572093i
$773$	−18.0433	−	13.1093i	−0.648974	−	0.471507i	0.213948	−	0.976845i	$-0.431368\pi$
$773$	−18.0433	−	13.1093i	−0.648974	−	0.471507i	−0.862922	+	0.505338i	$0.831368\pi$
$774$	4.20162			0.151024
$775$	−14.7565	−	6.49717i	−0.530070	−	0.233385i
$776$	0.785481			0.0281971
$777$	1.07260	+	0.779287i	0.0384792	+	0.0279568i
$778$	8.03973	+	24.7437i	0.288238	+	0.887106i
$779$	−1.14900	−	3.53626i	−0.0411673	−	0.126700i
$780$	−1.22224	−	2.73001i	−0.0437630	−	0.0977499i
$781$	4.01635	−	12.3611i	0.143716	−	0.442314i
$782$	−14.2207			−0.508531
$783$	−13.5725	+	41.7720i	−0.485043	+	1.49281i
$784$	5.50003	−	3.99600i	0.196430	−	0.142714i
$785$	0.378578	−	0.342290i	0.0135120	−	0.0122169i
$786$	15.8628	+	11.5250i	0.565806	+	0.411082i
$787$	−32.9017	+	23.9045i	−1.17282	+	0.852104i	−0.991344	−	0.131292i	$-0.958088\pi$
$787$	−32.9017	+	23.9045i	−1.17282	+	0.852104i	−0.181476	+	0.983395i	$0.558088\pi$
$788$	10.1863	−	7.40080i	0.362873	−	0.263643i
$789$	21.8538	+	15.8777i	0.778015	+	0.565261i
$790$	−4.47536	−	9.99623i	−0.159226	−	0.355650i
$791$	2.22264	−	1.61484i	0.0790280	−	0.0574172i
$792$	−0.676704	+	2.08268i	−0.0240456	+	0.0740048i
$793$	−0.364779			−0.0129537
$794$	−4.56375	+	14.0458i	−0.161961	+	0.498466i
$795$	−2.94805	+	14.0116i	−0.104557	+	0.496942i
$796$	−3.77638	−	11.6225i	−0.133850	−	0.411949i
$797$	−14.6515	−	45.0927i	−0.518983	−	1.59727i	−0.775915	−	0.630837i	$-0.782712\pi$
$797$	−14.6515	−	45.0927i	−0.518983	−	1.59727i	0.256932	−	0.966430i	$-0.417288\pi$
$798$	−0.537356	−	0.390412i	−0.0190222	−	0.0138204i
$799$	−29.4505			−1.04188
$800$	−0.502110	+	4.97472i	−0.0177523	+	0.175883i
$801$	5.19101			0.183415
$802$	16.9070	+	12.2837i	0.597008	+	0.433751i
$803$	2.87799	+	8.85756i	0.101562	+	0.312576i
$804$	1.52757	+	4.70139i	0.0538734	+	0.165805i
$805$	4.74706	−	0.508845i	0.167312	−	0.0179344i
$806$	0.901063	−	2.77319i	0.0317386	−	0.0976813i
$807$	−15.6890			−0.552280
$808$	0.677102	−	2.08391i	0.0238204	−	0.0733115i
$809$	−16.7743	+	12.1872i	−0.589752	+	0.428480i	−0.842227	−	0.539124i	$-0.818756\pi$
$809$	−16.7743	+	12.1872i	−0.589752	+	0.428480i	0.252475	+	0.967603i	$0.418756\pi$
$810$	−2.71935	+	12.9247i	−0.0955483	+	0.454126i
$811$	−25.4375	−	18.4814i	−0.893230	−	0.648970i	0.0434879	−	0.999054i	$-0.486153\pi$
$811$	−25.4375	−	18.4814i	−0.893230	−	0.648970i	−0.936718	+	0.350084i	$0.886153\pi$
$812$	2.82946	−	2.05572i	0.0992946	−	0.0721418i
$813$	14.7075	−	10.6856i	0.515813	−	0.374760i
$814$	−4.35734	−	3.16579i	−0.152725	−	0.110961i
$815$	−9.91247	+	47.1124i	−0.347219	+	1.65028i
$816$	−3.57901	+	2.60030i	−0.125290	+	0.0910288i
$817$	1.59983	−	4.92376i	0.0559708	−	0.172261i
$818$	−26.4954			−0.926389
$819$	0.101819	−	0.313367i	0.00355785	−	0.0109499i
$820$	8.26690	−	0.886142i	0.288693	−	0.0309454i
$821$	−7.08744	−	21.8129i	−0.247353	−	0.761275i	−0.995241	−	0.0974492i	$-0.968932\pi$
$821$	−7.08744	−	21.8129i	−0.247353	−	0.761275i	0.747887	−	0.663826i	$-0.231068\pi$
$822$	5.25023	+	16.1585i	0.183123	+	0.563594i
$823$	45.5991	+	33.1297i	1.58948	+	1.15483i	0.904672	+	0.426109i	$0.140116\pi$
$823$	45.5991	+	33.1297i	1.58948	+	1.15483i	0.684813	+	0.728719i	$0.259884\pi$
$824$	−14.1586			−0.493239
$825$	−18.2663	−	8.04247i	−0.635949	−	0.280003i
$826$	−0.311605			−0.0108421
$827$	−13.3326	−	9.68670i	−0.463620	−	0.336839i	0.331330	−	0.943515i	$-0.392503\pi$
$827$	−13.3326	−	9.68670i	−0.463620	−	0.336839i	−0.794950	+	0.606676i	$0.792503\pi$
$828$	1.19259	+	3.67042i	0.0414454	+	0.127556i
$829$	15.8750	+	48.8582i	0.551362	+	1.69692i	0.705363	+	0.708846i	$0.250784\pi$
$829$	15.8750	+	48.8582i	0.551362	+	1.69692i	−0.154002	+	0.988071i	$0.549216\pi$
$830$	−1.86157	+	8.84776i	−0.0646160	+	0.307110i
$831$	−13.8082	+	42.4974i	−0.479003	+	1.47422i
$832$	−0.904237			−0.0313488
$833$	6.28244	−	19.3354i	0.217674	−	0.669931i
$834$	11.5903	−	8.42082i	0.401338	−	0.291589i
$835$	9.22447	+	20.6039i	0.319226	+	0.713028i
$836$	2.18297	+	1.58602i	0.0754995	+	0.0548536i
$837$	−14.7102	+	10.6876i	−0.508459	+	0.369417i
$838$	23.2084	−	16.8619i	0.801721	−	0.582484i
$839$	23.0097	+	16.7175i	0.794384	+	0.577154i	0.909261	−	0.416226i	$-0.136647\pi$
$839$	23.0097	+	16.7175i	0.794384	+	0.577154i	−0.114877	+	0.993380i	$0.536647\pi$
$840$	1.10168	−	0.996079i	0.0380114	−	0.0343680i
$841$	−25.6264	+	18.6186i	−0.883667	+	0.642022i
$842$	5.63844	−	17.3533i	0.194313	−	0.598035i
$843$	−34.2952			−1.18119
$844$	0.345024	−	1.06187i	0.0118762	−	0.0365512i
$845$	11.1311	+	24.8626i	0.382921	+	0.855299i
$846$	2.46980	+	7.60128i	0.0849136	+	0.261337i
$847$	−0.516025	−	1.58816i	−0.0177308	−	0.0545699i
$848$	3.50188	+	2.54427i	0.120255	+	0.0873705i
$849$	1.71936			0.0590084
$850$	7.52956	+	12.9181i	0.258262	+	0.443088i
$851$	−9.49198			−0.325381
$852$	−5.76480	−	4.18837i	−0.197499	−	0.143491i
$853$	10.1523	+	31.2455i	0.347607	+	1.06982i	0.960173	+	0.279405i	$0.0901372\pi$
$853$	10.1523	+	31.2455i	0.347607	+	1.06982i	−0.612566	+	0.790419i	$0.709863\pi$
$854$	−0.0559717	−	0.172263i	−0.00191531	−	0.00589472i
$855$	−1.57347	−	0.904119i	−0.0538116	−	0.0309202i
$856$	2.56029	−	7.87976i	0.0875089	−	0.269325i
$857$	−19.3492			−0.660957			−0.330478	−	0.943814i	$-0.607210\pi$
$857$	−19.3492			−0.660957			−0.330478	+	0.943814i	$0.607210\pi$
$858$	1.11537	−	3.43277i	0.0380782	−	0.117193i
$859$	−13.3470	+	9.69713i	−0.455392	+	0.330862i	−0.791721	−	0.610883i	$-0.790815\pi$
$859$	−13.3470	+	9.69713i	−0.455392	+	0.330862i	0.336329	+	0.941745i	$0.390815\pi$
$860$	10.0374	+	5.76752i	0.342273	+	0.196671i
$861$	−1.99802	−	1.45165i	−0.0680924	−	0.0494720i
$862$	6.02034	−	4.37403i	0.205053	−	0.148980i
$863$	15.2023	−	11.0452i	0.517494	−	0.375981i	−0.298165	−	0.954514i	$-0.596375\pi$
$863$	15.2023	−	11.0452i	0.517494	−	0.375981i	0.815659	+	0.578533i	$0.196375\pi$
$864$	4.56171	+	3.31428i	0.155193	+	0.112754i
$865$	26.0320	−	2.79041i	0.885113	−	0.0948767i
$866$	2.66291	−	1.93472i	0.0904895	−	0.0657444i
$867$	3.68322	−	11.3358i	0.125089	−	0.384984i
$868$	1.44787			0.0491438
$869$	4.08407	−	12.5695i	0.138543	−	0.426390i
$870$	−19.1128	+	17.2808i	−0.647984	+	0.585874i
$871$	0.933724	+	2.87371i	0.0316380	+	0.0973719i
$872$	−3.45786	−	10.6422i	−0.117098	−	0.360391i
$873$	−0.515727	−	0.374698i	−0.0174547	−	0.0126816i
$874$	4.75535			0.160852
$875$	−2.97570	−	4.04282i	−0.100597	−	0.136672i
$876$	5.10604			0.172517
$877$	0.901908	+	0.655274i	0.0304553	+	0.0221270i	0.602909	−	0.797810i	$-0.294008\pi$
$877$	0.901908	+	0.655274i	0.0304553	+	0.0221270i	−0.572453	+	0.819937i	$0.694008\pi$
$878$	−5.30796	−	16.3362i	−0.179135	−	0.551320i
$879$	5.00271	+	15.3968i	0.168737	+	0.519320i
$880$	−4.47547	+	4.04649i	−0.150868	+	0.136407i
$881$	−5.23757	+	16.1196i	−0.176458	+	0.543083i	−0.999697	−	0.0246126i	$-0.992165\pi$
$881$	−5.23757	+	16.1196i	−0.176458	+	0.543083i	0.823239	+	0.567695i	$0.192165\pi$
$882$	−5.51739			−0.185780
$883$	−10.7879	+	33.2018i	−0.363043	+	1.11733i	0.588155	+	0.808748i	$0.299854\pi$
$883$	−10.7879	+	33.2018i	−0.363043	+	1.11733i	−0.951198	+	0.308582i	$0.900146\pi$
$884$	−2.18766	+	1.58943i	−0.0735788	+	0.0534581i
$885$	2.28264	−	0.244680i	0.0767301	−	0.00822482i
$886$	−21.8101	−	15.8460i	−0.732724	−	0.532355i
$887$	−3.12195	+	2.26823i	−0.104825	+	0.0761598i	−0.638963	−	0.769238i	$-0.720636\pi$
$887$	−3.12195	+	2.26823i	−0.104825	+	0.0761598i	0.534138	+	0.845397i	$0.320636\pi$
$888$	−2.38890	+	1.73564i	−0.0801663	+	0.0582442i
$889$	3.77537	+	2.74297i	0.126622	+	0.0919961i
$890$	12.4010	+	7.12564i	0.415683	+	0.238852i
$891$	−12.8940	+	9.36803i	−0.431965	+	0.313841i
$892$	−3.39040	+	10.4346i	−0.113519	+	0.349375i
$893$	9.84812			0.329555
$894$	−10.4544	+	32.1753i	−0.349647	+	1.07610i
$895$	−5.29891	−	3.04476i	−0.177123	−	0.101775i
$896$	−0.138746	−	0.427016i	−0.00463518	−	0.0142656i
$897$	−1.96568	−	6.04975i	−0.0656322	−	0.201995i
$898$	−13.9711	−	10.1506i	−0.466221	−	0.338729i
$899$	−25.1188			−0.837758
$900$	2.70276	−	3.02676i	0.0900922	−	0.100892i
$901$	12.9444			0.431242
$902$	8.11681	+	5.89721i	0.270260	+	0.196356i
$903$	−1.06262	−	3.27040i	−0.0353617	−	0.108832i
$904$	1.89085	+	5.81942i	0.0628886	+	0.193551i
$905$	11.5417	+	25.7797i	0.383658	+	0.856945i
$906$	3.00098	−	9.23607i	0.0997009	−	0.306848i
$907$	3.76472			0.125006			0.0625028	−	0.998045i	$-0.480092\pi$
$907$	3.76472			0.125006			0.0625028	+	0.998045i	$0.480092\pi$
$908$	−1.82312	+	5.61098i	−0.0605023	+	0.186207i
$909$	−1.43865	+	1.04524i	−0.0477171	+	0.0346685i
$910$	0.673395	−	0.608849i	0.0223228	−	0.0201832i
$911$	−1.80171	−	1.30902i	−0.0596932	−	0.0433697i	0.557538	−	0.830151i	$-0.311746\pi$
$911$	−1.80171	−	1.30902i	−0.0596932	−	0.0433697i	−0.617232	+	0.786781i	$0.711746\pi$
$912$	1.19681	−	0.869531i	0.0396302	−	0.0287930i
$913$	−8.82676	+	6.41302i	−0.292123	+	0.212240i
$914$	3.85018	+	2.79732i	0.127353	+	0.0925271i
$915$	0.545281	+	1.21795i	0.0180264	+	0.0402641i
$916$	7.72018	−	5.60904i	0.255082	−	0.185328i
$917$	−1.83897	+	5.65978i	−0.0607283	+	0.186902i
$918$	16.8620			0.556529
$919$	16.7701	−	51.6129i	0.553193	−	1.70255i	−0.147475	−	0.989066i	$-0.547115\pi$
$919$	16.7701	−	51.6129i	0.553193	−	1.70255i	0.700668	−	0.713487i	$-0.252885\pi$
$920$	−2.18931	+	10.4055i	−0.0721794	+	0.343058i
$921$	−1.82829	−	5.62689i	−0.0602441	−	0.185412i
$922$	7.98826	+	24.5853i	0.263079	+	0.809675i
$923$	−3.52371	−	2.56013i	−0.115984	−	0.0842676i
$924$	1.79223			0.0589600
$925$	5.02580	+	8.62254i	0.165247	+	0.283507i
$926$	−37.6634			−1.23770
$927$	9.29620	+	6.75409i	0.305327	+	0.221833i
$928$	2.40708	+	7.40823i	0.0790163	+	0.243187i
$929$	7.01959	+	21.6041i	0.230305	+	0.708806i	0.997710	+	0.0676430i	$0.0215479\pi$
$929$	7.01959	+	21.6041i	0.230305	+	0.708806i	−0.767404	+	0.641163i	$0.778452\pi$
$930$	−10.6062	+	1.13690i	−0.347792	+	0.0372804i
$931$	−2.10082	+	6.46567i	−0.0688517	+	0.211904i
$932$	−15.6523			−0.512709
$933$	14.8125	−	45.5883i	0.484941	−	1.49250i
$934$	30.2748	−	21.9960i	0.990623	−	0.719730i
$935$	−3.71495	+	17.6566i	−0.121492	+	0.577433i
$936$	0.593700	+	0.431348i	0.0194057	+	0.0140991i
$937$	−30.1272	+	21.8887i	−0.984214	+	0.715073i	−0.958646	−	0.284600i	$-0.908139\pi$
$937$	−30.1272	+	21.8887i	−0.984214	+	0.715073i	−0.0255672	+	0.999673i	$0.508139\pi$
$938$	−1.21381	+	0.881882i	−0.0396322	+	0.0287945i
$939$	6.53625	+	4.74886i	0.213302	+	0.154973i
$940$	−4.53397	+	21.5493i	−0.147882	+	0.702859i
$941$	−14.6706	+	10.6588i	−0.478248	+	0.347467i	−0.800647	−	0.599137i	$-0.795511\pi$
$941$	−14.6706	+	10.6588i	−0.478248	+	0.347467i	0.322399	+	0.946604i	$0.395511\pi$
$942$	0.104341	−	0.321128i	0.00339961	−	0.0104629i
$943$	17.6816			0.575791
$944$	0.214461	−	0.660044i	0.00698013	−	0.0214826i
$945$	−5.62876	+	0.603355i	−0.183103	+	0.0196272i
$946$	4.31680	+	13.2857i	0.140351	+	0.431957i
$947$	−4.98009	−	15.3271i	−0.161831	−	0.498065i	0.836958	−	0.547268i	$-0.184332\pi$
$947$	−4.98009	−	15.3271i	−0.161831	−	0.498065i	−0.998789	+	0.0492025i	$0.984332\pi$
$948$	−5.86199	−	4.25899i	−0.190389	−	0.138325i
$949$	3.12105			0.101314
$950$	−2.51785	−	4.31977i	−0.0816900	−	0.140152i
$951$	−27.2801			−0.884617
$952$	−1.08626	−	0.789216i	−0.0352060	−	0.0255786i
$953$	−7.49672	−	23.0725i	−0.242843	−	0.747393i	−0.995984	−	0.0895339i	$-0.971462\pi$
$953$	−7.49672	−	23.0725i	−0.242843	−	0.747393i	0.753141	−	0.657859i	$-0.228538\pi$
$954$	−1.08556	−	3.34101i	−0.0351463	−	0.108169i
$955$	5.66865	−	26.9422i	0.183433	−	0.871831i
$956$	4.54753	−	13.9959i	0.147078	−	0.452658i
$957$	−31.0931			−1.00510
$958$	−8.70043	+	26.7772i	−0.281098	+	0.865131i
$959$	−4.17182	+	3.03100i	−0.134715	+	0.0978761i
$960$	1.35168	+	3.01913i	0.0436251	+	0.0974418i
$961$	16.6668	+	12.1091i	0.537638	+	0.390617i
$962$	−1.46021	+	1.06090i	−0.0470790	+	0.0342049i
$963$	−5.43990	+	3.95232i	−0.175298	+	0.127362i
$964$	4.46804	+	3.24622i	0.143906	+	0.104554i
$965$	−27.7216	+	25.0645i	−0.892391	+	0.806854i
$966$	2.55531	−	1.85654i	0.0822159	−	0.0597333i
$967$	−1.33390	+	4.10532i	−0.0428953	+	0.132018i	−0.970211	−	0.242263i	$-0.922110\pi$
$967$	−1.33390	+	4.10532i	−0.0428953	+	0.132018i	0.927315	+	0.374281i	$0.122110\pi$
$968$	3.71921			0.119540
$969$	1.36706	−	4.20738i	0.0439163	−	0.135160i
$970$	−0.717698	−	1.60306i	−0.0230439	−	0.0514713i
$971$	−2.12831	−	6.55025i	−0.0683006	−	0.210208i	0.911081	−	0.412228i	$-0.135249\pi$
$971$	−2.12831	−	6.55025i	−0.0683006	−	0.210208i	−0.979381	+	0.202020i	$0.935249\pi$
$972$	−2.52710	−	7.77762i	−0.0810568	−	0.249467i
$973$	3.51775	+	2.55579i	0.112774	+	0.0819350i
$974$	−13.0715			−0.418839
$975$	−4.45482	+	4.98884i	−0.142668	+	0.159771i
$976$	0.403411			0.0129129
$977$	1.15449	+	0.838788i	0.0369355	+	0.0268352i	0.606100	−	0.795389i	$-0.292733\pi$
$977$	1.15449	+	0.838788i	0.0369355	+	0.0268352i	−0.569164	+	0.822224i	$0.692733\pi$
$978$	9.84250	+	30.2921i	0.314728	+	0.968634i
$979$	5.33331	+	16.4142i	0.170453	+	0.524602i
$980$	−13.1807	−	7.57366i	−0.421043	−	0.241932i
$981$	−2.80630	+	8.63691i	−0.0895984	+	0.275755i
$982$	−3.01904			−0.0963414
$983$	10.5258	−	32.3952i	0.335722	−	1.03325i	−0.630643	−	0.776073i	$-0.717209\pi$
$983$	10.5258	−	32.3952i	0.335722	−	1.03325i	0.966365	−	0.257174i	$-0.0827913\pi$
$984$	4.45002	−	3.23313i	0.141862	−	0.103068i
$985$	−24.4114	−	14.0268i	−0.777811	−	0.446931i
$986$	18.8454	+	13.6920i	0.600159	+	0.436041i
$987$	5.29194	−	3.84482i	0.168444	−	0.122382i
$988$	0.731543	−	0.531497i	0.0232735	−	0.0169092i
$989$	19.9173	+	14.4708i	0.633333	+	0.460143i
$990$	4.86878	−	0.521892i	0.154740	−	0.0165868i
$991$	16.6078	−	12.0663i	0.527564	−	0.383298i	−0.291882	−	0.956454i	$-0.594281\pi$
$991$	16.6078	−	12.0663i	0.527564	−	0.383298i	0.819446	+	0.573157i	$0.194281\pi$
$992$	−0.996490	+	3.06688i	−0.0316386	+	0.0973735i
$993$	19.9697			0.633718
$994$	0.668314	−	2.05686i	0.0211976	−	0.0652396i
$995$	−20.2695	+	18.3266i	−0.642586	+	0.580993i
$996$	1.84843	+	5.68888i	0.0585697	+	0.180259i
$997$	−9.53645	−	29.3502i	−0.302022	−	0.929529i	−0.980772	−	0.195159i	$-0.937478\pi$
$997$	−9.53645	−	29.3502i	−0.302022	−	0.929529i	0.678749	−	0.734370i	$-0.262522\pi$
$998$	−21.8847	−	15.9002i	−0.692748	−	0.503311i
$999$	11.2550			0.356092

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.h.e.191.3	✓	44
25.11	even	5	inner	950.2.h.e.761.3	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.h.e.191.3	✓	44	1.1	even	1	trivial
950.2.h.e.761.3	yes	44	25.11	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.457139 - 1.40693i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.65863 - 1.49965i) q^{5} +(0.457139 - 1.40693i) q^{6} +0.448991 q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.656575 - 0.477030i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.457139 - 1.40693i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.65863 - 1.49965i) q^{5} +(0.457139 - 1.40693i) q^{6} +0.448991 q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.656575 - 0.477030i) q^{9} +(2.22333 - 0.238322i) q^{10} +(2.18297 + 1.58602i) q^{11} +(1.19681 - 0.869531i) q^{12} +(0.731543 - 0.531497i) q^{13} +(0.363242 + 0.263911i) q^{14} +(-2.86813 - 1.64803i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.924105 + 2.84410i) q^{17} +0.811572 q^{18} +(0.309017 - 0.951057i) q^{19} +(1.93880 + 1.11403i) q^{20} +(-0.205252 - 0.631699i) q^{21} +(0.833819 + 2.56623i) q^{22} +(3.84716 + 2.79512i) q^{23} +1.47933 q^{24} +(0.502110 - 4.97472i) q^{25} +0.904237 q^{26} +(-4.56171 - 3.31428i) q^{27} +(0.138746 + 0.427016i) q^{28} +(-2.40708 - 7.40823i) q^{29} +(-1.35168 - 3.01913i) q^{30} +(0.996490 - 3.06688i) q^{31} -1.00000 q^{32} +(1.23350 - 3.79631i) q^{33} +(-2.41934 + 1.75775i) q^{34} +(0.744711 - 0.673329i) q^{35} +(0.656575 + 0.477030i) q^{36} +(-1.61485 + 1.17326i) q^{37} +(0.809017 - 0.587785i) q^{38} +(-1.08220 - 0.786262i) q^{39} +(0.913705 + 2.04087i) q^{40} +(3.00813 - 2.18553i) q^{41} +(0.205252 - 0.631699i) q^{42} +5.17715 q^{43} +(-0.833819 + 2.56623i) q^{44} +(0.373639 - 1.77585i) q^{45} +(1.46948 + 4.52260i) q^{46} +(3.04324 + 9.36612i) q^{47} +(1.19681 + 0.869531i) q^{48} -6.79841 q^{49} +(3.33029 - 3.72950i) q^{50} +4.42390 q^{51} +(0.731543 + 0.531497i) q^{52} +(-1.33760 - 4.11671i) q^{53} +(-1.74242 - 5.36261i) q^{54} +(5.99920 - 0.643064i) q^{55} +(-0.138746 + 0.427016i) q^{56} -1.47933 q^{57} +(2.40708 - 7.40823i) q^{58} +(-0.561467 + 0.407930i) q^{59} +(0.681069 - 3.23702i) q^{60} +(-0.326366 - 0.237119i) q^{61} +(2.60884 - 1.89544i) q^{62} +(0.294797 - 0.214182i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.416301 - 1.97862i) q^{65} +(3.22934 - 2.34625i) q^{66} +(-1.03261 + 3.17805i) q^{67} -2.99047 q^{68} +(2.17386 - 6.69044i) q^{69} +(0.998257 - 0.107005i) q^{70} +(-1.48848 - 4.58107i) q^{71} +(0.250789 + 0.771850i) q^{72} +(2.79239 + 2.02879i) q^{73} -1.99606 q^{74} +(-7.22862 + 1.56771i) q^{75} +1.00000 q^{76} +(0.980133 + 0.712108i) q^{77} +(-0.413362 - 1.27220i) q^{78} +(-1.51357 - 4.65830i) q^{79} +(-0.460389 + 2.18816i) q^{80} +(-1.82525 + 5.61755i) q^{81} +3.71825 q^{82} +(-1.24950 + 3.84557i) q^{83} +(0.537356 - 0.390412i) q^{84} +(2.73240 + 6.10315i) q^{85} +(4.18840 + 3.04305i) q^{86} +(-9.32249 + 6.77319i) q^{87} +(-2.18297 + 1.58602i) q^{88} +(5.17467 + 3.75962i) q^{89} +(1.34610 - 1.21707i) q^{90} +(0.328457 - 0.238638i) q^{91} +(-1.46948 + 4.52260i) q^{92} -4.77042 q^{93} +(-3.04324 + 9.36612i) q^{94} +(-0.913705 - 2.04087i) q^{95} +(0.457139 + 1.40693i) q^{96} +(-0.242727 - 0.747037i) q^{97} +(-5.50003 - 3.99600i) q^{98} +2.18986 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9}+O(q^{10}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 5 * q^5 + q^6 + 28 * q^7 + 11 * q^8 - 8 * q^9	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 5 q^{5} + q^{6} + 28 q^{7} + 11 q^{8} - 8 q^{9} + 5 q^{10} - 6 q^{12} - 10 q^{13} + 12 q^{14} - 11 q^{16} - 20 q^{17} - 42 q^{18} - 11 q^{19} + 5 q^{20} - 3 q^{21} - 10 q^{22} - 6 q^{23} - 14 q^{24} - 15 q^{25} - 40 q^{26} + 5 q^{27} - 2 q^{28} + 6 q^{29} - 5 q^{31} - 44 q^{32} - 36 q^{33} - 10 q^{34} - 8 q^{36} - 10 q^{37} + 11 q^{38} + 39 q^{39} - 22 q^{41} + 3 q^{42} + 68 q^{43} + 10 q^{44} + 20 q^{45} + 6 q^{46} + 19 q^{47} - 6 q^{48} + 40 q^{49} - 30 q^{50} + 86 q^{51} - 10 q^{52} + 30 q^{54} + 2 q^{56} + 14 q^{57} - 6 q^{58} - 4 q^{59} + 15 q^{60} + 26 q^{61} - 15 q^{62} - 41 q^{63} - 11 q^{64} + 30 q^{65} - 4 q^{66} - 59 q^{67} + 20 q^{68} - 59 q^{69} - 25 q^{70} + 30 q^{71} + 13 q^{72} - 38 q^{73} - 50 q^{74} - 15 q^{75} + 44 q^{76} + 29 q^{77} + 16 q^{78} + 3 q^{79} + 5 q^{80} - 54 q^{81} - 8 q^{82} + 9 q^{83} + 7 q^{84} + 12 q^{86} - 43 q^{87} + 33 q^{89} - 6 q^{91} - 6 q^{92} + 84 q^{93} - 19 q^{94} + q^{96} + 30 q^{97} - 15 q^{98} - 54 q^{99}+O(q^{100}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 5 * q^5 + q^6 + 28 * q^7 + 11 * q^8 - 8 * q^9 + 5 * q^10 - 6 * q^12 - 10 * q^13 + 12 * q^14 - 11 * q^16 - 20 * q^17 - 42 * q^18 - 11 * q^19 + 5 * q^20 - 3 * q^21 - 10 * q^22 - 6 * q^23 - 14 * q^24 - 15 * q^25 - 40 * q^26 + 5 * q^27 - 2 * q^28 + 6 * q^29 - 5 * q^31 - 44 * q^32 - 36 * q^33 - 10 * q^34 - 8 * q^36 - 10 * q^37 + 11 * q^38 + 39 * q^39 - 22 * q^41 + 3 * q^42 + 68 * q^43 + 10 * q^44 + 20 * q^45 + 6 * q^46 + 19 * q^47 - 6 * q^48 + 40 * q^49 - 30 * q^50 + 86 * q^51 - 10 * q^52 + 30 * q^54 + 2 * q^56 + 14 * q^57 - 6 * q^58 - 4 * q^59 + 15 * q^60 + 26 * q^61 - 15 * q^62 - 41 * q^63 - 11 * q^64 + 30 * q^65 - 4 * q^66 - 59 * q^67 + 20 * q^68 - 59 * q^69 - 25 * q^70 + 30 * q^71 + 13 * q^72 - 38 * q^73 - 50 * q^74 - 15 * q^75 + 44 * q^76 + 29 * q^77 + 16 * q^78 + 3 * q^79 + 5 * q^80 - 54 * q^81 - 8 * q^82 + 9 * q^83 + 7 * q^84 + 12 * q^86 - 43 * q^87 + 33 * q^89 - 6 * q^91 - 6 * q^92 + 84 * q^93 - 19 * q^94 + q^96 + 30 * q^97 - 15 * q^98 - 54 * q^99

Introduction

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