LMFDB - Embedded newform 525.2.n.c.106.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(106,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("525.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.n (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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			106.6
Character	$\chi$	$=$	525.106
Dual form			525.2.n.c.421.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.625840 + 1.92614i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.70029 + 1.23534i) q^{4} +(0.958238 + 2.02034i) q^{5} +(-1.63847 - 1.19042i) q^{6} +1.00000 q^{7} +(-0.166599 - 0.121041i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.625840 + 1.92614i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.70029 + 1.23534i) q^{4} +(0.958238 + 2.02034i) q^{5} +(-1.63847 - 1.19042i) q^{6} +1.00000 q^{7} +(-0.166599 - 0.121041i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-3.29175 + 3.11011i) q^{10} +(0.187958 + 0.578475i) q^{11} +(0.649455 - 1.99882i) q^{12} +(-1.19248 + 3.67009i) q^{13} +(0.625840 + 1.92614i) q^{14} +(-1.96276 - 1.07125i) q^{15} +(-1.17003 + 3.60099i) q^{16} +(-5.86368 - 4.26021i) q^{17} +2.02526 q^{18} +(5.96571 + 4.33434i) q^{19} +(-4.12509 - 2.25143i) q^{20} +(-0.809017 + 0.587785i) q^{21} +(-0.996591 + 0.724066i) q^{22} +(-1.55424 - 4.78347i) q^{23} +0.205928 q^{24} +(-3.16356 + 3.87194i) q^{25} -7.81540 q^{26} +(0.309017 + 0.951057i) q^{27} +(-1.70029 + 1.23534i) q^{28} +(8.37817 - 6.08710i) q^{29} +(0.835006 - 4.45097i) q^{30} +(-2.25899 - 1.64126i) q^{31} -8.08010 q^{32} +(-0.492081 - 0.357517i) q^{33} +(4.53603 - 13.9605i) q^{34} +(0.958238 + 2.02034i) q^{35} +(0.649455 + 1.99882i) q^{36} +(1.00193 - 3.08364i) q^{37} +(-4.61496 + 14.2034i) q^{38} +(-1.19248 - 3.67009i) q^{39} +(0.0849031 - 0.452573i) q^{40} +(-0.107012 + 0.329349i) q^{41} +(-1.63847 - 1.19042i) q^{42} -9.26017 q^{43} +(-1.03420 - 0.751387i) q^{44} +(2.21757 - 0.287019i) q^{45} +(8.24091 - 5.98737i) q^{46} +(3.04658 - 2.21347i) q^{47} +(-1.17003 - 3.60099i) q^{48} +1.00000 q^{49} +(-9.43776 - 3.67023i) q^{50} +7.24791 q^{51} +(-2.50622 - 7.71335i) q^{52} +(4.22617 - 3.07049i) q^{53} +(-1.63847 + 1.19042i) q^{54} +(-0.988609 + 0.934057i) q^{55} +(-0.166599 - 0.121041i) q^{56} -7.37402 q^{57} +(16.9680 + 12.3280i) q^{58} +(-1.77895 + 5.47504i) q^{59} +(4.66062 - 0.603222i) q^{60} +(3.17270 + 9.76455i) q^{61} +(1.74751 - 5.37830i) q^{62} +(0.309017 - 0.951057i) q^{63} +(-2.71679 - 8.36141i) q^{64} +(-8.55752 + 1.10760i) q^{65} +(0.380664 - 1.17156i) q^{66} +(12.1621 + 8.83630i) q^{67} +15.2328 q^{68} +(4.06906 + 2.95635i) q^{69} +(-3.29175 + 3.11011i) q^{70} +(-4.83159 + 3.51035i) q^{71} +(-0.166599 + 0.121041i) q^{72} +(0.498912 + 1.53549i) q^{73} +6.56656 q^{74} +(0.283505 - 4.99196i) q^{75} -15.4978 q^{76} +(0.187958 + 0.578475i) q^{77} +(6.32279 - 4.59378i) q^{78} +(11.2750 - 8.19175i) q^{79} +(-8.39639 + 1.08674i) q^{80} +(-0.809017 - 0.587785i) q^{81} -0.701344 q^{82} +(8.88497 + 6.45531i) q^{83} +(0.649455 - 1.99882i) q^{84} +(2.98828 - 15.9289i) q^{85} +(-5.79538 - 17.8363i) q^{86} +(-3.20018 + 9.84913i) q^{87} +(0.0387058 - 0.119124i) q^{88} +(0.243047 + 0.748022i) q^{89} +(1.94068 + 4.09172i) q^{90} +(-1.19248 + 3.67009i) q^{91} +(8.55186 + 6.21329i) q^{92} +2.79227 q^{93} +(6.17011 + 4.48285i) q^{94} +(-3.04028 + 16.2061i) q^{95} +(6.53694 - 4.74937i) q^{96} +(5.02301 - 3.64943i) q^{97} +(0.625840 + 1.92614i) q^{98} +0.608245 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9} - 16 q^{10} + 2 q^{11} + q^{12} + 8 q^{13} + q^{14} - 6 q^{15} + 13 q^{16} + 12 q^{17} - 4 q^{18} + 19 q^{19} + 11 q^{20} - 6 q^{21} - 19 q^{22} - 6 q^{24} + 9 q^{25} - 14 q^{26} - 6 q^{27} - 9 q^{28} + 5 q^{29} - 6 q^{30} + 17 q^{31} - 26 q^{32} + 7 q^{33} - 7 q^{34} - q^{35} + q^{36} + 22 q^{37} - 16 q^{38} + 8 q^{39} + 3 q^{40} + 37 q^{41} + q^{42} + 8 q^{43} + 13 q^{44} + 4 q^{45} + 24 q^{46} - 24 q^{47} + 13 q^{48} + 24 q^{49} - 21 q^{50} - 8 q^{51} + 23 q^{52} - 24 q^{53} + q^{54} - 55 q^{55} + 9 q^{56} - 26 q^{57} + 8 q^{58} - 39 q^{60} + 24 q^{62} - 6 q^{63} - q^{64} - 34 q^{65} + 16 q^{66} + 34 q^{67} + 22 q^{68} + 10 q^{69} - 16 q^{70} - 24 q^{71} + 9 q^{72} + 46 q^{73} + 10 q^{74} + 24 q^{75} - 20 q^{76} + 2 q^{77} - 14 q^{78} + 10 q^{79} + 6 q^{80} - 6 q^{81} - 78 q^{82} + 42 q^{83} + q^{84} - 22 q^{85} - 96 q^{86} - 10 q^{87} - 39 q^{88} + 29 q^{89} + 14 q^{90} + 8 q^{91} + 42 q^{92} - 58 q^{93} + 54 q^{94} - 42 q^{95} + 9 q^{96} - 32 q^{97} + q^{98} - 18 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9 - 16 * q^10 + 2 * q^11 + q^12 + 8 * q^13 + q^14 - 6 * q^15 + 13 * q^16 + 12 * q^17 - 4 * q^18 + 19 * q^19 + 11 * q^20 - 6 * q^21 - 19 * q^22 - 6 * q^24 + 9 * q^25 - 14 * q^26 - 6 * q^27 - 9 * q^28 + 5 * q^29 - 6 * q^30 + 17 * q^31 - 26 * q^32 + 7 * q^33 - 7 * q^34 - q^35 + q^36 + 22 * q^37 - 16 * q^38 + 8 * q^39 + 3 * q^40 + 37 * q^41 + q^42 + 8 * q^43 + 13 * q^44 + 4 * q^45 + 24 * q^46 - 24 * q^47 + 13 * q^48 + 24 * q^49 - 21 * q^50 - 8 * q^51 + 23 * q^52 - 24 * q^53 + q^54 - 55 * q^55 + 9 * q^56 - 26 * q^57 + 8 * q^58 - 39 * q^60 + 24 * q^62 - 6 * q^63 - q^64 - 34 * q^65 + 16 * q^66 + 34 * q^67 + 22 * q^68 + 10 * q^69 - 16 * q^70 - 24 * q^71 + 9 * q^72 + 46 * q^73 + 10 * q^74 + 24 * q^75 - 20 * q^76 + 2 * q^77 - 14 * q^78 + 10 * q^79 + 6 * q^80 - 6 * q^81 - 78 * q^82 + 42 * q^83 + q^84 - 22 * q^85 - 96 * q^86 - 10 * q^87 - 39 * q^88 + 29 * q^89 + 14 * q^90 + 8 * q^91 + 42 * q^92 - 58 * q^93 + 54 * q^94 - 42 * q^95 + 9 * q^96 - 32 * q^97 + q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.625840	+	1.92614i	0.442536	+	1.36198i	0.885164	+	0.465279i	$0.154046\pi$
$2$	0.625840	+	1.92614i	0.442536	+	1.36198i	−0.442628	+	0.896705i	$0.645954\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−1.70029	+	1.23534i	−0.850147	+	0.617668i
$5$	0.958238	+	2.02034i	0.428537	+	0.903524i
$5$	0.958238	+	2.02034i	0.428537	+	0.903524i
$6$	−1.63847	−	1.19042i	−0.668903	−	0.485986i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−0.166599	−	0.121041i	−0.0589017	−	0.0427946i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−3.29175	+	3.11011i	−1.04094	+	0.983503i
$11$	0.187958	+	0.578475i	0.0566715	+	0.174417i	0.975385	−	0.220507i	$-0.0707711\pi$
$11$	0.187958	+	0.578475i	0.0566715	+	0.174417i	−0.918714	+	0.394924i	$0.870771\pi$
$12$	0.649455	−	1.99882i	0.187481	−	0.577009i
$13$	−1.19248	+	3.67009i	−0.330736	+	1.01790i	0.638049	+	0.769996i	$0.279742\pi$
$13$	−1.19248	+	3.67009i	−0.330736	+	1.01790i	−0.968785	+	0.247904i	$0.920258\pi$
$14$	0.625840	+	1.92614i	0.167263	+	0.514782i
$15$	−1.96276	−	1.07125i	−0.506782	−	0.276596i
$16$	−1.17003	+	3.60099i	−0.292508	+	0.900247i
$17$	−5.86368	−	4.26021i	−1.42215	−	1.03325i	−0.991412	−	0.130777i	$-0.958253\pi$
$17$	−5.86368	−	4.26021i	−1.42215	−	1.03325i	−0.430740	−	0.902476i	$-0.641747\pi$
$18$	2.02526			0.477358
$19$	5.96571	+	4.33434i	1.36863	+	0.994366i	0.997843	+	0.0656472i	$0.0209112\pi$
$19$	5.96571	+	4.33434i	1.36863	+	0.994366i	0.370785	+	0.928719i	$0.379089\pi$
$20$	−4.12509	−	2.25143i	−0.922398	−	0.503435i
$21$	−0.809017	+	0.587785i	−0.176542	+	0.128265i
$22$	−0.996591	+	0.724066i	−0.212474	+	0.154371i
$23$	−1.55424	−	4.78347i	−0.324082	−	0.997422i	−0.971853	−	0.235587i	$-0.924299\pi$
$23$	−1.55424	−	4.78347i	−0.324082	−	0.997422i	0.647771	−	0.761835i	$-0.275701\pi$
$24$	0.205928			0.0420348
$25$	−3.16356	+	3.87194i	−0.632712	+	0.774388i
$26$	−7.81540			−1.53273
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−1.70029	+	1.23534i	−0.321325	+	0.233457i
$29$	8.37817	−	6.08710i	1.55579	−	1.13035i	0.616428	−	0.787411i	$-0.288579\pi$
$29$	8.37817	−	6.08710i	1.55579	−	1.13035i	0.939359	−	0.342934i	$-0.111421\pi$
$30$	0.835006	−	4.45097i	0.152451	−	0.812633i
$31$	−2.25899	−	1.64126i	−0.405727	−	0.294778i	0.366142	−	0.930559i	$-0.380678\pi$
$31$	−2.25899	−	1.64126i	−0.405727	−	0.294778i	−0.771870	+	0.635781i	$0.780678\pi$
$32$	−8.08010			−1.42837
$33$	−0.492081	−	0.357517i	−0.0856602	−	0.0622358i
$34$	4.53603	−	13.9605i	0.777923	−	2.39420i
$35$	0.958238	+	2.02034i	0.161972	+	0.341500i
$36$	0.649455	+	1.99882i	0.108242	+	0.333136i
$37$	1.00193	−	3.08364i	0.164717	−	0.506947i	−0.834298	−	0.551313i	$-0.814127\pi$
$37$	1.00193	−	3.08364i	0.164717	−	0.506947i	0.999015	+	0.0443663i	$0.0141269\pi$
$38$	−4.61496	+	14.2034i	−0.748645	+	2.30409i
$39$	−1.19248	−	3.67009i	−0.190950	−	0.587685i
$40$	0.0849031	−	0.452573i	0.0134244	−	0.0715581i
$41$	−0.107012	+	0.329349i	−0.0167125	+	0.0514357i	−0.959065	−	0.283186i	$-0.908609\pi$
$41$	−0.107012	+	0.329349i	−0.0167125	+	0.0514357i	0.942353	+	0.334622i	$0.108609\pi$
$42$	−1.63847	−	1.19042i	−0.252821	−	0.183686i
$43$	−9.26017			−1.41216			−0.706081	−	0.708131i	$-0.749539\pi$
$43$	−9.26017			−1.41216			−0.706081	+	0.708131i	$0.749539\pi$
$44$	−1.03420	−	0.751387i	−0.155911	−	0.113276i
$45$	2.21757	−	0.287019i	0.330576	−	0.0427863i
$46$	8.24091	−	5.98737i	1.21506	−	0.882790i
$47$	3.04658	−	2.21347i	0.444389	−	0.322868i	−0.342987	−	0.939340i	$-0.611439\pi$
$47$	3.04658	−	2.21347i	0.444389	−	0.322868i	0.787376	+	0.616472i	$0.211439\pi$
$48$	−1.17003	−	3.60099i	−0.168880	−	0.519758i
$49$	1.00000			0.142857
$50$	−9.43776	−	3.67023i	−1.33470	−	0.519049i
$51$	7.24791			1.01491
$52$	−2.50622	−	7.71335i	−0.347550	−	1.06965i
$53$	4.22617	−	3.07049i	0.580509	−	0.421765i	−0.258398	−	0.966038i	$-0.583195\pi$
$53$	4.22617	−	3.07049i	0.580509	−	0.421765i	0.838908	+	0.544274i	$0.183195\pi$
$54$	−1.63847	+	1.19042i	−0.222968	+	0.161995i
$55$	−0.988609	+	0.934057i	−0.133304	+	0.125948i
$56$	−0.166599	−	0.121041i	−0.0222627	−	0.0161748i
$57$	−7.37402			−0.976713
$58$	16.9680	+	12.3280i	2.22800	+	1.61874i
$59$	−1.77895	+	5.47504i	−0.231599	+	0.712789i	0.765955	+	0.642894i	$0.222266\pi$
$59$	−1.77895	+	5.47504i	−0.231599	+	0.712789i	−0.997554	+	0.0698951i	$0.977734\pi$
$60$	4.66062	−	0.603222i	0.601684	−	0.0778757i
$61$	3.17270	+	9.76455i	0.406222	+	1.25022i	0.919871	+	0.392222i	$0.128294\pi$
$61$	3.17270	+	9.76455i	0.406222	+	1.25022i	−0.513648	+	0.858001i	$0.671706\pi$
$62$	1.74751	−	5.37830i	0.221935	−	0.683044i
$63$	0.309017	−	0.951057i	0.0389325	−	0.119822i
$64$	−2.71679	−	8.36141i	−0.339598	−	1.04518i
$65$	−8.55752	+	1.10760i	−1.06143	+	0.137380i
$66$	0.380664	−	1.17156i	0.0468565	−	0.144209i
$67$	12.1621	+	8.83630i	1.48584	+	1.07953i	0.975616	+	0.219485i	$0.0704378\pi$
$67$	12.1621	+	8.83630i	1.48584	+	1.07953i	0.510225	+	0.860041i	$0.329562\pi$
$68$	15.2328			1.84725
$69$	4.06906	+	2.95635i	0.489857	+	0.355902i
$70$	−3.29175	+	3.11011i	−0.393439	+	0.371729i
$71$	−4.83159	+	3.51035i	−0.573404	+	0.416602i	−0.836340	−	0.548211i	$-0.815309\pi$
$71$	−4.83159	+	3.51035i	−0.573404	+	0.416602i	0.262936	+	0.964813i	$0.415309\pi$
$72$	−0.166599	+	0.121041i	−0.0196339	+	0.0142649i
$73$	0.498912	+	1.53549i	0.0583932	+	0.179716i	0.975999	−	0.217777i	$-0.0698805\pi$
$73$	0.498912	+	1.53549i	0.0583932	+	0.179716i	−0.917605	+	0.397493i	$0.869880\pi$
$74$	6.56656			0.763347
$75$	0.283505	−	4.99196i	0.0327363	−	0.576421i
$76$	−15.4978			−1.77772
$77$	0.187958	+	0.578475i	0.0214198	+	0.0659234i
$78$	6.32279	−	4.59378i	0.715915	−	0.520143i
$79$	11.2750	−	8.19175i	1.26853	−	0.921643i	0.269390	−	0.963031i	$-0.413178\pi$
$79$	11.2750	−	8.19175i	1.26853	−	0.921643i	0.999143	+	0.0413876i	$0.0131778\pi$
$80$	−8.39639	+	1.08674i	−0.938745	+	0.121501i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−0.701344			−0.0774504
$83$	8.88497	+	6.45531i	0.975252	+	0.708562i	0.956642	−	0.291265i	$-0.0940760\pi$
$83$	8.88497	+	6.45531i	0.975252	+	0.708562i	0.0186096	+	0.999827i	$0.494076\pi$
$84$	0.649455	−	1.99882i	0.0708613	−	0.218089i
$85$	2.98828	−	15.9289i	0.324125	−	1.72774i
$86$	−5.79538	−	17.8363i	−0.624932	−	1.92334i
$87$	−3.20018	+	9.84913i	−0.343095	+	1.05594i
$88$	0.0387058	−	0.119124i	0.00412605	−	0.0126987i
$89$	0.243047	+	0.748022i	0.0257630	+	0.0792902i	0.963111	−	0.269103i	$-0.0867273\pi$
$89$	0.243047	+	0.748022i	0.0257630	+	0.0792902i	−0.937348	+	0.348394i	$0.886727\pi$
$90$	1.94068	+	4.09172i	0.204566	+	0.431305i
$91$	−1.19248	+	3.67009i	−0.125006	+	0.384730i
$92$	8.55186	+	6.21329i	0.891593	+	0.647781i
$93$	2.79227			0.289545
$94$	6.17011	+	4.48285i	0.636399	+	0.462371i
$95$	−3.04028	+	16.2061i	−0.311926	+	1.66271i
$96$	6.53694	−	4.74937i	0.667174	−	0.484730i
$97$	5.02301	−	3.64943i	0.510010	−	0.370544i	−0.302817	−	0.953049i	$-0.597927\pi$
$97$	5.02301	−	3.64943i	0.510010	−	0.370544i	0.812827	+	0.582505i	$0.197927\pi$
$98$	0.625840	+	1.92614i	0.0632194	+	0.194569i
$99$	0.608245			0.0611309
$100$	0.595836	−	10.4915i	0.0595836	−	1.04915i
$101$	6.38288			0.635120			0.317560	−	0.948238i	$-0.397136\pi$
$101$	6.38288			0.635120			0.317560	+	0.948238i	$0.397136\pi$
$102$	4.53603	+	13.9605i	0.449134	+	1.38229i
$103$	−13.4222	+	9.75177i	−1.32252	+	0.960870i	−0.322627	+	0.946526i	$0.604566\pi$
$103$	−13.4222	+	9.75177i	−1.32252	+	0.960870i	−0.999897	+	0.0143440i	$0.995434\pi$
$104$	0.642899	−	0.467094i	0.0630415	−	0.0458023i
$105$	−1.96276	−	1.07125i	−0.191546	−	0.104543i
$106$	8.55910	+	6.21855i	0.831333	+	0.603999i
$107$	−0.915459			−0.0885008			−0.0442504	−	0.999020i	$-0.514090\pi$
$107$	−0.915459			−0.0885008			−0.0442504	+	0.999020i	$0.514090\pi$
$108$	−1.70029	−	1.23534i	−0.163611	−	0.118870i
$109$	5.78867	−	17.8157i	0.554454	−	1.70643i	−0.142927	−	0.989733i	$-0.545652\pi$
$109$	5.78867	−	17.8157i	0.554454	−	1.70643i	0.697381	−	0.716700i	$-0.254348\pi$
$110$	−2.41783	−	1.31963i	−0.230531	−	0.125821i
$111$	1.00193	+	3.08364i	0.0950995	+	0.292686i
$112$	−1.17003	+	3.60099i	−0.110558	+	0.340261i
$113$	4.71871	−	14.5227i	0.443899	−	1.36618i	−0.439787	−	0.898102i	$-0.644946\pi$
$113$	4.71871	−	14.5227i	0.443899	−	1.36618i	0.883687	−	0.468079i	$-0.155054\pi$
$114$	−4.61496	−	14.2034i	−0.432230	−	1.33027i
$115$	8.17490	−	7.72381i	0.762314	−	0.720249i
$116$	−6.72575	+	20.6997i	−0.624470	+	1.92192i
$117$	3.12197	+	2.26824i	0.288626	+	0.209699i
$118$	−11.6590			−1.07330
$119$	−5.86368	−	4.26021i	−0.537523	−	0.390533i
$120$	0.197328	+	0.416044i	0.0180135	+	0.0379795i
$121$	8.59988	−	6.24818i	0.781807	−	0.568016i
$122$	−16.8223	+	12.2221i	−1.52302	+	1.10654i
$123$	−0.107012	−	0.329349i	−0.00964894	−	0.0296964i
$124$	5.86846			0.527003
$125$	−10.8541	−	2.68123i	−0.970818	−	0.239816i
$126$	2.02526			0.180425
$127$	6.08065	+	18.7143i	0.539570	+	1.66063i	0.733561	+	0.679623i	$0.237857\pi$
$127$	6.08065	+	18.7143i	0.539570	+	1.66063i	−0.193991	+	0.981003i	$0.562143\pi$
$128$	1.33107	−	0.967079i	0.117651	−	0.0854785i
$129$	7.49163	−	5.44299i	0.659601	−	0.479228i
$130$	−7.48902	−	15.7898i	−0.656830	−	1.38486i
$131$	−2.11898	−	1.53953i	−0.185136	−	0.134509i	0.491357	−	0.870958i	$-0.336501\pi$
$131$	−2.11898	−	1.53953i	−0.185136	−	0.134509i	−0.676493	+	0.736449i	$0.736501\pi$
$132$	1.27834			0.111265
$133$	5.96571	+	4.33434i	0.517293	+	0.375835i
$134$	−9.40839	+	28.9560i	−0.812761	+	2.50142i
$135$	−1.62535	+	1.53566i	−0.139888	+	0.132168i
$136$	0.461222	+	1.41950i	0.0395495	+	0.121721i
$137$	2.72865	−	8.39792i	0.233124	−	0.717483i	−0.764240	−	0.644932i	$-0.776886\pi$
$137$	2.72865	−	8.39792i	0.233124	−	0.717483i	0.997365	−	0.0725515i	$-0.0231142\pi$
$138$	−3.14775	+	9.68777i	−0.267954	+	0.824678i
$139$	−2.15822	−	6.64233i	−0.183058	−	0.563395i	0.816851	−	0.576848i	$-0.195718\pi$
$139$	−2.15822	−	6.64233i	−0.183058	−	0.563395i	−0.999909	+	0.0134533i	$0.995718\pi$
$140$	−4.12509	−	2.25143i	−0.348634	−	0.190280i
$141$	−1.16369	+	3.58147i	−0.0980003	+	0.301614i
$142$	−9.78522	−	7.10938i	−0.821158	−	0.596606i
$143$	−2.34719			−0.196282
$144$	3.06318	+	2.22553i	0.255265	+	0.185461i
$145$	20.3263	+	11.0939i	1.68801	+	0.921296i
$146$	−2.64533	+	1.92195i	−0.218929	+	0.159061i
$147$	−0.809017	+	0.587785i	−0.0667266	+	0.0484797i
$148$	2.10575	+	6.48082i	0.173091	+	0.532720i
$149$	2.65431			0.217450			0.108725	−	0.994072i	$-0.465323\pi$
$149$	2.65431			0.217450			0.108725	+	0.994072i	$0.465323\pi$
$150$	9.79262	−	2.57810i	0.799564	−	0.210501i
$151$	−5.84121			−0.475351			−0.237675	−	0.971345i	$-0.576385\pi$
$151$	−5.84121			−0.475351			−0.237675	+	0.971345i	$0.576385\pi$
$152$	−0.469247	−	1.44419i	−0.0380610	−	0.117140i
$153$	−5.86368	+	4.26021i	−0.474051	+	0.344418i
$154$	−0.996591	+	0.724066i	−0.0803076	+	0.0583469i
$155$	1.15124	−	6.13665i	0.0924699	−	0.492908i
$156$	6.56137	+	4.76712i	0.525330	+	0.381675i
$157$	−14.4265			−1.15136			−0.575680	−	0.817675i	$-0.695263\pi$
$157$	−14.4265			−1.15136			−0.575680	+	0.817675i	$0.695263\pi$
$158$	22.8348	+	16.5904i	1.81664	+	1.31986i
$159$	−1.61425	+	4.96816i	−0.128019	+	0.394001i
$160$	−7.74267	−	16.3246i	−0.612111	−	1.29057i
$161$	−1.55424	−	4.78347i	−0.122492	−	0.376990i
$162$	0.625840	−	1.92614i	0.0491706	−	0.151332i
$163$	−3.19653	+	9.83789i	−0.250371	+	0.770563i	0.744335	+	0.667806i	$0.232766\pi$
$163$	−3.19653	+	9.83789i	−0.250371	+	0.770563i	−0.994706	+	0.102757i	$0.967234\pi$
$164$	−0.224905	−	0.692186i	−0.0175621	−	0.0540506i
$165$	0.250777	−	1.33676i	0.0195229	−	0.104066i
$166$	−6.87324	+	21.1537i	−0.533467	+	1.64184i
$167$	10.1442	+	7.37020i	0.784983	+	0.570323i	0.906470	−	0.422270i	$-0.138766\pi$
$167$	10.1442	+	7.37020i	0.784983	+	0.570323i	−0.121487	+	0.992593i	$0.538766\pi$
$168$	0.205928			0.0158877
$169$	−1.53032	−	1.11185i	−0.117717	−	0.0855266i
$170$	32.5515	−	4.21313i	2.49659	−	0.323132i
$171$	5.96571	−	4.33434i	0.456209	−	0.331455i
$172$	15.7450	−	11.4394i	1.20055	−	0.872247i
$173$	−1.65590	−	5.09635i	−0.125896	−	0.387468i	0.868167	−	0.496272i	$-0.165298\pi$
$173$	−1.65590	−	5.09635i	−0.125896	−	0.387468i	−0.994063	+	0.108803i	$0.965298\pi$
$174$	−20.9736			−1.59000
$175$	−3.16356	+	3.87194i	−0.239143	+	0.292691i
$176$	−2.30300			−0.173595
$177$	−1.77895	−	5.47504i	−0.133714	−	0.411529i
$178$	−1.28869	+	0.936285i	−0.0965910	+	0.0701775i
$179$	6.34785	−	4.61199i	0.474461	−	0.344716i	−0.324716	−	0.945811i	$-0.605269\pi$
$179$	6.34785	−	4.61199i	0.474461	−	0.344716i	0.799177	+	0.601095i	$0.205269\pi$
$180$	−3.41596	+	3.22746i	−0.254611	+	0.240561i
$181$	−7.16946	−	5.20892i	−0.532902	−	0.387176i	0.288540	−	0.957468i	$-0.406830\pi$
$181$	−7.16946	−	5.20892i	−0.532902	−	0.387176i	−0.821442	+	0.570292i	$0.806830\pi$
$182$	−7.81540			−0.579316
$183$	−8.30623	−	6.03483i	−0.614014	−	0.446107i
$184$	−0.320062	+	0.985049i	−0.0235953	+	0.0726188i
$185$	7.19009	−	0.930611i	0.528626	−	0.0684198i
$186$	1.74751	+	5.37830i	0.128134	+	0.394356i
$187$	1.36230	−	4.19274i	0.0996214	−	0.306603i
$188$	−2.44570	+	7.52710i	−0.178371	+	0.548970i
$189$	0.309017	+	0.951057i	0.0224777	+	0.0691792i
$190$	−33.1179	+	4.28643i	−2.40262	+	0.310971i
$191$	−1.31257	+	4.03966i	−0.0949739	+	0.292300i	−0.987247	−	0.159197i	$-0.949110\pi$
$191$	−1.31257	+	4.03966i	−0.0949739	+	0.292300i	0.892273	+	0.451496i	$0.149110\pi$
$192$	7.11264	+	5.16764i	0.513311	+	0.372942i
$193$	0.361099			0.0259925			0.0129963	−	0.999916i	$-0.495863\pi$
$193$	0.361099			0.0259925			0.0129963	+	0.999916i	$0.495863\pi$
$194$	10.1729	+	7.39105i	0.730373	+	0.530647i
$195$	6.27215	−	5.92605i	0.449158	−	0.424373i
$196$	−1.70029	+	1.23534i	−0.121450	+	0.0882383i
$197$	−5.17671	+	3.76110i	−0.368826	+	0.267967i	−0.756724	−	0.653735i	$-0.773201\pi$
$197$	−5.17671	+	3.76110i	−0.368826	+	0.267967i	0.387898	+	0.921702i	$0.373201\pi$
$198$	0.380664	+	1.17156i	0.0270526	+	0.0832594i
$199$	2.43150			0.172364			0.0861822	−	0.996279i	$-0.472533\pi$
$199$	2.43150			0.172364			0.0861822	+	0.996279i	$0.472533\pi$
$200$	0.995710	−	0.262140i	0.0704074	−	0.0185361i
$201$	−15.0332			−1.06036
$202$	3.99466	+	12.2943i	0.281063	+	0.865024i
$203$	8.37817	−	6.08710i	0.588032	−	0.427231i
$204$	−12.3236	+	8.95360i	−0.862823	+	0.626878i
$205$	−0.767940	+	0.0993941i	−0.0536353	+	0.00694199i
$206$	−27.1834	−	19.7499i	−1.89395	−	1.37604i
$207$	−5.02964			−0.349584
$208$	−11.8207	−	8.58824i	−0.819618	−	0.595488i
$209$	−1.38601	+	4.26569i	−0.0958721	+	0.295064i
$210$	0.835006	−	4.45097i	0.0576209	−	0.307146i
$211$	1.70267	+	5.24029i	0.117217	+	0.360756i	0.992403	−	0.123030i	$-0.0392612\pi$
$211$	1.70267	+	5.24029i	0.117217	+	0.360756i	−0.875186	+	0.483786i	$0.839261\pi$
$212$	−3.39265	+	10.4415i	−0.233008	+	0.717124i
$213$	1.84550	−	5.67987i	0.126452	−	0.389178i
$214$	−0.572931	−	1.76330i	−0.0391647	−	0.120537i
$215$	−8.87345	−	18.7087i	−0.605164	−	1.27592i
$216$	0.0636352	−	0.195849i	0.00432983	−	0.0133258i
$217$	−2.25899	−	1.64126i	−0.153351	−	0.111416i
$218$	37.9382			2.56950
$219$	−1.30617	−	0.948987i	−0.0882627	−	0.0641266i
$220$	0.527052	−	2.80944i	0.0355339	−	0.189412i
$221$	22.6277	−	16.4400i	1.52211	−	1.10587i
$222$	−5.31246	+	3.85973i	−0.356549	+	0.259048i
$223$	−7.32235	−	22.5359i	−0.490341	−	1.50911i	−0.824094	−	0.566454i	$-0.808315\pi$
$223$	−7.32235	−	22.5359i	−0.490341	−	1.50911i	0.333753	−	0.942661i	$-0.391685\pi$
$224$	−8.08010			−0.539875
$225$	2.70484	+	4.20522i	0.180323	+	0.280348i
$226$	30.9259			2.05716
$227$	−6.41352	−	19.7388i	−0.425680	−	1.31011i	−0.902342	−	0.431022i	$-0.858153\pi$
$227$	−6.41352	−	19.7388i	−0.425680	−	1.31011i	0.476662	−	0.879087i	$-0.341847\pi$
$228$	12.5380	−	9.10940i	0.830350	−	0.603285i
$229$	1.61826	−	1.17574i	0.106938	−	0.0776948i	−0.533031	−	0.846096i	$-0.678947\pi$
$229$	1.61826	−	1.17574i	0.106938	−	0.0776948i	0.639969	+	0.768401i	$0.278947\pi$
$230$	19.9933	+	10.9121i	1.31832	+	0.719524i
$231$	−0.492081	−	0.357517i	−0.0323765	−	0.0235229i
$232$	−2.13259			−0.140011
$233$	−14.6973	−	10.6782i	−0.962853	−	0.699553i	−0.00904109	−	0.999959i	$-0.502878\pi$
$233$	−14.6973	−	10.6782i	−0.962853	−	0.699553i	−0.953811	+	0.300406i	$0.902878\pi$
$234$	−2.41509	+	7.43289i	−0.157880	+	0.485903i
$235$	7.39131	+	4.03410i	0.482156	+	0.263155i
$236$	−3.73878	−	11.5068i	−0.243374	−	0.749027i
$237$	−4.30666	+	13.2545i	−0.279747	+	0.860974i
$238$	4.53603	−	13.9605i	0.294027	−	0.904923i
$239$	−2.65619	−	8.17490i	−0.171814	−	0.528790i	0.827659	−	0.561231i	$-0.189672\pi$
$239$	−2.65619	−	8.17490i	−0.171814	−	0.528790i	−0.999474	+	0.0324406i	$0.989672\pi$
$240$	6.15405	−	5.81447i	0.397242	−	0.375322i
$241$	4.80532	−	14.7893i	0.309538	−	0.952660i	−0.668407	−	0.743796i	$-0.733023\pi$
$241$	4.80532	−	14.7893i	0.309538	−	0.952660i	0.977945	−	0.208864i	$-0.0669766\pi$
$242$	17.4170	+	12.6542i	1.11961	+	0.813442i
$243$	1.00000			0.0641500
$244$	−17.4570	−	12.6833i	−1.11757	−	0.811963i
$245$	0.958238	+	2.02034i	0.0612196	+	0.129075i
$246$	0.567399	−	0.412239i	0.0361760	−	0.0262834i
$247$	−23.0214	+	16.7261i	−1.46482	+	1.06425i
$248$	0.177687	+	0.546863i	0.0112831	+	0.0347259i
$249$	−10.9824			−0.695983
$250$	−1.62850	−	22.5845i	−0.102996	−	1.42837i
$251$	−17.6762			−1.11571			−0.557857	−	0.829937i	$-0.688376\pi$
$251$	−17.6762			−1.11571			−0.557857	+	0.829937i	$0.688376\pi$
$252$	0.649455	+	1.99882i	0.0409118	+	0.125914i
$253$	2.47499	−	1.79818i	0.155601	−	0.113051i
$254$	−32.2408	+	23.4243i	−2.02297	+	1.46977i
$255$	6.94522	+	14.6432i	0.434927	+	0.916996i
$256$	−11.5295	−	8.37669i	−0.720595	−	0.523543i
$257$	20.7645			1.29526			0.647628	−	0.761956i	$-0.275761\pi$
$257$	20.7645			1.29526			0.647628	+	0.761956i	$0.275761\pi$
$258$	15.1725	+	11.0235i	0.944599	+	0.686291i
$259$	1.00193	−	3.08364i	0.0622572	−	0.191608i
$260$	13.1821	−	12.4547i	0.817516	−	0.772405i
$261$	−3.20018	−	9.84913i	−0.198086	−	0.609646i
$262$	1.63920	−	5.04494i	0.101270	−	0.311678i
$263$	3.21041	−	9.88063i	0.197962	−	0.609266i	−0.801967	−	0.597369i	$-0.796213\pi$
$263$	3.21041	−	9.88063i	0.197962	−	0.609266i	0.999929	−	0.0118971i	$-0.00378706\pi$
$264$	0.0387058	+	0.119124i	0.00238218	+	0.00733159i
$265$	10.2531	+	5.59605i	0.629845	+	0.343762i
$266$	−4.61496	+	14.2034i	−0.282961	+	0.870865i
$267$	−0.636306	−	0.462303i	−0.0389413	−	0.0282925i
$268$	−31.5950			−1.92997
$269$	15.8440	+	11.5114i	0.966028	+	0.701860i	0.954543	−	0.298074i	$-0.0963441\pi$
$269$	15.8440	+	11.5114i	0.966028	+	0.701860i	0.0114852	+	0.999934i	$0.496344\pi$
$270$	−3.97510	−	2.16956i	−0.241917	−	0.132035i
$271$	−2.98050	+	2.16546i	−0.181052	+	0.131542i	−0.674620	−	0.738165i	$-0.735693\pi$
$271$	−2.98050	+	2.16546i	−0.181052	+	0.131542i	0.493568	+	0.869707i	$0.335693\pi$
$272$	22.2017	−	16.1305i	1.34617	−	0.978052i
$273$	−1.19248	−	3.67009i	−0.0721725	−	0.222124i
$274$	17.8833			1.08037
$275$	−2.83444	−	1.10228i	−0.170923	−	0.0664699i
$276$	−10.5707			−0.636280
$277$	−6.95228	−	21.3969i	−0.417722	−	1.28562i	−0.909793	−	0.415061i	$-0.863760\pi$
$277$	−6.95228	−	21.3969i	−0.417722	−	1.28562i	0.492071	−	0.870555i	$-0.336240\pi$
$278$	11.4433	−	8.31406i	0.686325	−	0.498644i
$279$	−2.25899	+	1.64126i	−0.135242	+	0.0982594i
$280$	0.0849031	−	0.452573i	0.00507393	−	0.0270464i
$281$	−4.12441	−	2.99656i	−0.246042	−	0.178760i	0.457929	−	0.888989i	$-0.348591\pi$
$281$	−4.12441	−	2.99656i	−0.246042	−	0.178760i	−0.703971	+	0.710229i	$0.748591\pi$
$282$	−7.62668			−0.454162
$283$	6.09722	+	4.42989i	0.362442	+	0.263329i	0.754070	−	0.656794i	$-0.228088\pi$
$283$	6.09722	+	4.42989i	0.362442	+	0.263329i	−0.391628	+	0.920124i	$0.628088\pi$
$284$	3.87865	−	11.9373i	0.230156	−	0.708347i
$285$	−7.06607	−	14.8980i	−0.418558	−	0.882484i
$286$	−1.46897	−	4.52102i	−0.0868619	−	0.267333i
$287$	−0.107012	+	0.329349i	−0.00631672	+	0.0194409i
$288$	−2.49689	+	7.68463i	−0.147131	+	0.452821i
$289$	10.9800	+	33.7931i	0.645885	+	1.98783i
$290$	−8.64731	+	46.0942i	−0.507788	+	2.70675i
$291$	−1.91862	+	5.90491i	−0.112472	+	0.346152i
$292$	−2.74515	−	1.99447i	−0.160648	−	0.116717i
$293$	−26.7122			−1.56054			−0.780271	−	0.625442i	$-0.784919\pi$
$293$	−26.7122			−1.56054			−0.780271	+	0.625442i	$0.784919\pi$
$294$	−1.63847	−	1.19042i	−0.0955575	−	0.0694266i
$295$	−12.7661	+	1.65231i	−0.743271	+	0.0962012i
$296$	−0.540169	+	0.392456i	−0.0313967	+	0.0228110i
$297$	−0.492081	+	0.357517i	−0.0285534	+	0.0207453i
$298$	1.66117	+	5.11257i	0.0962292	+	0.296163i
$299$	19.4092			1.12246
$300$	5.68470	+	8.83802i	0.328207	+	0.510263i
$301$	−9.26017			−0.533747
$302$	−3.65566	−	11.2510i	−0.210360	−	0.647420i
$303$	−5.16386	+	3.75176i	−0.296656	+	0.215533i
$304$	−22.5880	+	16.4111i	−1.29551	+	0.941243i
$305$	−16.6875	+	15.7667i	−0.955525	+	0.902799i
$306$	−11.8755	−	8.62804i	−0.678876	−	0.493232i
$307$	−9.38398			−0.535572			−0.267786	−	0.963478i	$-0.586292\pi$
$307$	−9.38398			−0.535572			−0.267786	+	0.963478i	$0.586292\pi$
$308$	−1.03420	−	0.751387i	−0.0589288	−	0.0428143i
$309$	5.12681	−	15.7787i	0.291654	−	0.897618i
$310$	12.5405	−	1.62311i	0.712254	−	0.0921867i
$311$	−4.05071	−	12.4668i	−0.229695	−	0.706927i	−0.997781	−	0.0665810i	$-0.978791\pi$
$311$	−4.05071	−	12.4668i	−0.229695	−	0.706927i	0.768086	−	0.640346i	$-0.221209\pi$
$312$	−0.245566	+	0.755774i	−0.0139024	+	0.0427873i
$313$	5.46894	−	16.8317i	0.309123	−	0.951383i	−0.668983	−	0.743277i	$-0.733270\pi$
$313$	5.46894	−	16.8317i	0.309123	−	0.951383i	0.978106	−	0.208105i	$-0.0667297\pi$
$314$	−9.02867	−	27.7874i	−0.509518	−	1.56813i
$315$	2.21757	−	0.287019i	0.124946	−	0.0161717i
$316$	−9.05121	+	27.8568i	−0.509170	+	1.56707i
$317$	2.93810	+	2.13466i	0.165020	+	0.119894i	0.667230	−	0.744851i	$-0.267480\pi$
$317$	2.93810	+	2.13466i	0.165020	+	0.119894i	−0.502210	+	0.864746i	$0.667480\pi$
$318$	−10.5796			−0.593276
$319$	5.09598	+	3.70245i	0.285320	+	0.207297i
$320$	14.2896	−	13.5011i	0.798812	−	0.754732i
$321$	0.740622	−	0.538093i	0.0413375	−	0.0300334i
$322$	8.24091	−	5.98737i	0.459248	−	0.333663i
$323$	−16.5158	−	50.8304i	−0.918963	−	2.82828i
$324$	2.10168			0.116760
$325$	−10.4379	−	16.2278i	−0.578989	−	0.900155i
$326$	−20.9496			−1.16029
$327$	5.78867	+	17.8157i	0.320114	+	0.985210i
$328$	0.0576929	−	0.0419164i	0.00318556	−	0.00231444i
$329$	3.04658	−	2.21347i	0.167963	−	0.122032i
$330$	2.73172	−	0.353566i	0.150377	−	0.0194632i
$331$	−6.41167	−	4.65835i	−0.352417	−	0.256046i	0.397465	−	0.917617i	$-0.369890\pi$
$331$	−6.41167	−	4.65835i	−0.352417	−	0.256046i	−0.749882	+	0.661571i	$0.769890\pi$
$332$	−23.0815			−1.26676
$333$	−2.62310	−	1.90579i	−0.143745	−	0.104437i
$334$	−7.84737	+	24.1517i	−0.429389	+	1.32152i
$335$	−6.19813	+	33.0389i	−0.338640	+	1.80511i
$336$	−1.17003	−	3.60099i	−0.0638305	−	0.196450i
$337$	2.11444	−	6.50756i	0.115181	−	0.354490i	−0.876804	−	0.480848i	$-0.840329\pi$
$337$	2.11444	−	6.50756i	0.115181	−	0.354490i	0.991985	+	0.126358i	$0.0403289\pi$
$338$	1.18383	−	3.64345i	0.0643918	−	0.198178i
$339$	4.71871	+	14.5227i	0.256285	+	0.788765i
$340$	14.5966	+	30.7754i	0.791614	+	1.66903i
$341$	0.524830	−	1.61526i	0.0284211	−	0.0874712i
$342$	12.0821	+	8.77817i	0.653326	+	0.474669i
$343$	1.00000			0.0539949
$344$	1.54274	+	1.12086i	0.0831787	+	0.0604329i
$345$	−2.07370	+	11.0538i	−0.111644	+	0.595115i
$346$	8.77994	−	6.37900i	0.472012	−	0.342937i
$347$	−12.6322	+	9.17784i	−0.678132	+	0.492692i	−0.872738	−	0.488190i	$-0.837657\pi$
$347$	−12.6322	+	9.17784i	−0.678132	+	0.492692i	0.194605	+	0.980882i	$0.437657\pi$
$348$	−6.72575	−	20.6997i	−0.360538	−	1.10962i
$349$	9.25516			0.495417			0.247709	−	0.968835i	$-0.420322\pi$
$349$	9.25516			0.495417			0.247709	+	0.968835i	$0.420322\pi$
$350$	−9.43776	−	3.67023i	−0.504470	−	0.196182i
$351$	−3.85896			−0.205976
$352$	−1.51872	−	4.67414i	−0.0809481	−	0.249133i
$353$	−2.25611	+	1.63916i	−0.120081	+	0.0872438i	−0.646205	−	0.763164i	$-0.723645\pi$
$353$	−2.25611	+	1.63916i	−0.120081	+	0.0872438i	0.526124	+	0.850408i	$0.323645\pi$
$354$	9.43234	−	6.85299i	0.501323	−	0.364232i
$355$	−11.7219	−	6.39770i	−0.622135	−	0.339555i
$356$	−1.33731	−	0.971613i	−0.0708774	−	0.0514954i
$357$	7.24791			0.383600
$358$	12.8561	+	9.34047i	0.679464	+	0.493659i
$359$	−7.39397	+	22.7563i	−0.390239	+	1.20103i	0.542369	+	0.840141i	$0.317528\pi$
$359$	−7.39397	+	22.7563i	−0.390239	+	1.20103i	−0.932608	+	0.360892i	$0.882472\pi$
$360$	−0.404186	−	0.220601i	−0.0213025	−	0.0116267i
$361$	10.9318	+	33.6448i	0.575360	+	1.77078i
$362$	5.54616	−	17.0693i	0.291500	−	0.897144i
$363$	−3.28486	+	10.1098i	−0.172411	+	0.530625i
$364$	−2.50622	−	7.71335i	−0.131362	−	0.404290i
$365$	−2.62414	+	2.47934i	−0.137354	+	0.129775i
$366$	6.42553	−	19.7758i	0.335868	−	1.03370i
$367$	18.1510	+	13.1875i	0.947475	+	0.688381i	0.950208	−	0.311616i	$-0.100870\pi$
$367$	18.1510	+	13.1875i	0.947475	+	0.688381i	−0.00273356	+	0.999996i	$0.500870\pi$
$368$	19.0437			0.992723
$369$	0.280161	+	0.203549i	0.0145846	+	0.0105963i
$370$	6.29233	+	13.2667i	0.327123	+	0.689703i
$371$	4.22617	−	3.07049i	0.219412	−	0.159412i
$372$	−4.74768	+	3.44939i	−0.246156	+	0.178843i
$373$	7.76949	+	23.9120i	0.402289	+	1.23812i	0.923138	+	0.384470i	$0.125616\pi$
$373$	7.76949	+	23.9120i	0.402289	+	1.23812i	−0.520849	+	0.853649i	$0.674384\pi$
$374$	8.92837			0.461675
$375$	10.3571	−	4.21071i	0.534839	−	0.217440i
$376$	−0.775478			−0.0399922
$377$	12.3494	+	38.0074i	0.636024	+	1.95748i
$378$	−1.63847	+	1.19042i	−0.0842738	+	0.0612285i
$379$	−25.7469	+	18.7062i	−1.32253	+	0.960872i	−0.322630	+	0.946525i	$0.604567\pi$
$379$	−25.7469	+	18.7062i	−1.32253	+	0.960872i	−0.999897	+	0.0143473i	$0.995433\pi$
$380$	−14.8506	−	31.3109i	−0.761821	−	1.60622i
$381$	−15.9193	−	11.5661i	−0.815573	−	0.592548i
$382$	−8.60240			−0.440137
$383$	6.03845	+	4.38719i	0.308551	+	0.224175i	0.731274	−	0.682084i	$-0.238926\pi$
$383$	6.03845	+	4.38719i	0.308551	+	0.224175i	−0.422724	+	0.906259i	$0.638926\pi$
$384$	−0.508424	+	1.56477i	−0.0259454	+	0.0798517i
$385$	−0.988609	+	0.934057i	−0.0503842	+	0.0476039i
$386$	0.225990	+	0.695527i	0.0115026	+	0.0354014i
$387$	−2.86155	+	8.80694i	−0.145461	+	0.447682i
$388$	−4.03233	+	12.4102i	−0.204710	+	0.630034i
$389$	−1.39207	−	4.28435i	−0.0705807	−	0.217225i	0.909544	−	0.415608i	$-0.136431\pi$
$389$	−1.39207	−	4.28435i	−0.0705807	−	0.217225i	−0.980125	+	0.198383i	$0.936431\pi$
$390$	15.3397	+	8.37227i	0.776758	+	0.423946i
$391$	−11.2650	+	34.6701i	−0.569696	+	1.75334i
$392$	−0.166599	−	0.121041i	−0.00841452	−	0.00611351i
$393$	2.61920			0.132121
$394$	−10.4842	−	7.61721i	−0.528186	−	0.383750i
$395$	27.3542	+	14.9296i	1.37634	+	0.751192i
$396$	−1.03420	+	0.751387i	−0.0519703	+	0.0377586i
$397$	−16.4090	+	11.9218i	−0.823543	+	0.598339i	−0.917725	−	0.397216i	$-0.869976\pi$
$397$	−16.4090	+	11.9218i	−0.823543	+	0.598339i	0.0941819	+	0.995555i	$0.469976\pi$
$398$	1.52173	+	4.68340i	0.0762774	+	0.234758i
$399$	−7.37402			−0.369163
$400$	−10.2413	−	15.9222i	−0.512067	−	0.796111i
$401$	−14.3204			−0.715125			−0.357563	−	0.933889i	$-0.616392\pi$
$401$	−14.3204			−0.715125			−0.357563	+	0.933889i	$0.616392\pi$
$402$	−9.40839	−	28.9560i	−0.469248	−	1.44420i
$403$	8.71737	−	6.33354i	0.434243	−	0.315496i
$404$	−10.8528	+	7.88500i	−0.539946	+	0.392293i
$405$	0.412296	−	2.19773i	0.0204871	−	0.109206i
$406$	16.9680	+	12.3280i	0.842107	+	0.611826i
$407$	1.97213			0.0977549
$408$	−1.20749	−	0.877296i	−0.0597799	−	0.0434326i
$409$	7.26328	−	22.3541i	0.359146	−	1.10534i	−0.594420	−	0.804155i	$-0.702618\pi$
$409$	7.26328	−	22.3541i	0.359146	−	1.10534i	0.953566	−	0.301184i	$-0.0973817\pi$
$410$	−0.672054	−	1.41695i	−0.0331904	−	0.0699783i
$411$	2.72865	+	8.39792i	0.134594	+	0.414239i
$412$	10.7749	−	33.1618i	0.530842	−	1.63376i
$413$	−1.77895	+	5.47504i	−0.0875363	+	0.269409i
$414$	−3.14775	−	9.68777i	−0.154703	−	0.476128i
$415$	−4.52801	+	24.1364i	−0.222271	+	1.18481i
$416$	9.63540	−	29.6547i	0.472414	−	1.45394i
$417$	5.65030	+	4.10518i	0.276696	+	0.201032i
$418$	−9.08372			−0.444299
$419$	6.93487	+	5.03847i	0.338790	+	0.246146i	0.744151	−	0.668011i	$-0.232854\pi$
$419$	6.93487	+	5.03847i	0.338790	+	0.246146i	−0.405361	+	0.914157i	$0.632854\pi$
$420$	4.66062	−	0.603222i	0.227415	−	0.0294342i
$421$	4.39957	−	3.19648i	0.214422	−	0.155787i	−0.475390	−	0.879775i	$-0.657693\pi$
$421$	4.39957	−	3.19648i	0.214422	−	0.155787i	0.689812	+	0.723988i	$0.257693\pi$
$422$	−9.02791	+	6.55916i	−0.439472	+	0.319295i
$423$	−1.16369	−	3.58147i	−0.0565805	−	0.174137i
$424$	−1.07573			−0.0522422
$425$	35.0454	−	9.22637i	1.69995	−	0.447545i
$426$	12.0952			0.586014
$427$	3.17270	+	9.76455i	0.153538	+	0.472540i
$428$	1.55655	−	1.13090i	0.0752387	−	0.0546641i
$429$	1.89892	−	1.37965i	0.0916807	−	0.0666099i
$430$	30.4822	−	28.8001i	1.46998	−	1.38887i
$431$	−14.7455	−	10.7132i	−0.710266	−	0.516038i	0.172994	−	0.984923i	$-0.444656\pi$
$431$	−14.7455	−	10.7132i	−0.710266	−	0.516038i	−0.883259	+	0.468885i	$0.844656\pi$
$432$	−3.78630			−0.182169
$433$	7.94241	+	5.77050i	0.381688	+	0.277313i	0.762041	−	0.647529i	$-0.224197\pi$
$433$	7.94241	+	5.77050i	0.381688	+	0.277313i	−0.380353	+	0.924841i	$0.624197\pi$
$434$	1.74751	−	5.37830i	0.0838834	−	0.258166i
$435$	−22.9651	+	2.97237i	−1.10109	+	0.142514i
$436$	12.1659	+	37.4429i	0.582642	+	1.79319i
$437$	11.4610	−	35.2734i	0.548255	−	1.68736i
$438$	1.01043	−	3.10977i	0.0482800	−	0.148591i
$439$	3.57611	+	11.0061i	0.170678	+	0.525294i	0.999410	−	0.0343525i	$-0.0109369\pi$
$439$	3.57611	+	11.0061i	0.170678	+	0.525294i	−0.828731	+	0.559647i	$0.810937\pi$
$440$	0.277761	−	0.0359505i	0.0132417	−	0.00171387i
$441$	0.309017	−	0.951057i	0.0147151	−	0.0452884i
$442$	45.8270	+	33.2953i	2.17977	+	1.58370i
$443$	18.1759			0.863565			0.431782	−	0.901978i	$-0.357885\pi$
$443$	18.1759			0.863565			0.431782	+	0.901978i	$0.357885\pi$
$444$	−5.51292	−	4.00537i	−0.261631	−	0.190086i
$445$	−1.27836	+	1.20782i	−0.0606002	+	0.0572563i
$446$	38.8246	−	28.2077i	1.83840	−	1.33567i
$447$	−2.14738	+	1.56016i	−0.101568	+	0.0737933i
$448$	−2.71679	−	8.36141i	−0.128356	−	0.395040i
$449$	−32.3106			−1.52483			−0.762415	−	0.647089i	$-0.775986\pi$
$449$	−32.3106			−1.52483			−0.762415	+	0.647089i	$0.775986\pi$
$450$	−6.40703	+	7.84168i	−0.302030	+	0.369660i
$451$	−0.210634			−0.00991837
$452$	9.91722	+	30.5221i	0.466467	+	1.43564i
$453$	4.72563	−	3.43337i	0.222030	−	0.161314i
$454$	34.0057	−	24.7066i	1.59597	−	1.15954i
$455$	−8.55752	+	1.10760i	−0.401183	+	0.0519249i
$456$	1.22851	+	0.892561i	0.0575300	+	0.0417980i
$457$	−4.39198			−0.205448			−0.102724	−	0.994710i	$-0.532756\pi$
$457$	−4.39198			−0.205448			−0.102724	+	0.994710i	$0.532756\pi$
$458$	3.27740	+	2.38117i	0.153143	+	0.111265i
$459$	2.23973	−	6.89317i	0.104541	−	0.321746i
$460$	−4.35825	+	23.2315i	−0.203204	+	1.08317i
$461$	−4.99086	−	15.3603i	−0.232447	−	0.715400i	−0.997450	−	0.0713722i	$-0.977262\pi$
$461$	−4.99086	−	15.3603i	−0.232447	−	0.715400i	0.765002	−	0.644028i	$-0.222738\pi$
$462$	0.380664	−	1.17156i	0.0177101	−	0.0545061i
$463$	−1.47511	+	4.53993i	−0.0685544	+	0.210989i	−0.979465	−	0.201616i	$-0.935381\pi$
$463$	−1.47511	+	4.53993i	−0.0685544	+	0.210989i	0.910910	+	0.412604i	$0.135381\pi$
$464$	12.1168	+	37.2918i	0.562510	+	1.73123i
$465$	2.67566	+	5.64134i	0.124081	+	0.261611i
$466$	11.3696	−	34.9919i	0.526684	−	1.62097i
$467$	−30.8939	−	22.4457i	−1.42960	−	1.03866i	−0.990091	−	0.140425i	$-0.955153\pi$
$467$	−30.8939	−	22.4457i	−1.42960	−	1.03866i	−0.439508	−	0.898239i	$-0.644847\pi$
$468$	−8.11030			−0.374899
$469$	12.1621	+	8.83630i	0.561595	+	0.408023i
$470$	−3.14445	+	16.7614i	−0.145043	+	0.773144i
$471$	11.6713	−	8.47968i	0.537784	−	0.390723i
$472$	0.959077	−	0.696810i	0.0441451	−	0.0320733i
$473$	−1.74052	−	5.35678i	−0.0800293	−	0.246305i
$474$	−28.2253			−1.29643
$475$	−35.6552	+	9.38691i	−1.63597	+	0.430701i
$476$	15.2328			0.698193
$477$	−1.61425	−	4.96816i	−0.0739116	−	0.227477i
$478$	14.0836	−	10.2324i	0.644170	−	0.468017i
$479$	13.3654	−	9.71053i	0.610681	−	0.443686i	−0.238973	−	0.971026i	$-0.576811\pi$
$479$	13.3654	−	9.71053i	0.610681	−	0.443686i	0.849654	+	0.527341i	$0.176811\pi$
$480$	15.8593	+	8.65583i	0.723874	+	0.395083i
$481$	10.1224	+	7.35438i	0.461544	+	0.335331i
$482$	31.4935			1.43449
$483$	4.06906	+	2.95635i	0.185149	+	0.134518i
$484$	−6.90373	+	21.2475i	−0.313806	+	0.965795i
$485$	12.1863	+	6.65118i	0.553354	+	0.302014i
$486$	0.625840	+	1.92614i	0.0283887	+	0.0873714i
$487$	5.28961	−	16.2797i	0.239695	−	0.737705i	−0.756769	−	0.653683i	$-0.773223\pi$
$487$	5.28961	−	16.2797i	0.239695	−	0.737705i	0.996464	−	0.0840227i	$-0.0267768\pi$
$488$	0.653346	−	2.01079i	0.0295756	−	0.0910243i
$489$	−3.19653	−	9.83789i	−0.144552	−	0.444885i
$490$	−3.29175	+	3.11011i	−0.148706	+	0.140500i
$491$	−6.54472	+	20.1426i	−0.295359	+	0.909021i	0.687742	+	0.725955i	$0.258602\pi$
$491$	−6.54472	+	20.1426i	−0.295359	+	0.909021i	−0.983101	+	0.183066i	$0.941398\pi$
$492$	0.588809	+	0.427794i	0.0265455	+	0.0192865i
$493$	−75.0593			−3.38050
$494$	−46.6244	−	33.8746i	−2.09773	−	1.52409i
$495$	0.582844	+	1.22886i	0.0261969	+	0.0552333i
$496$	8.55323	−	6.21429i	0.384052	−	0.279030i
$497$	−4.83159	+	3.51035i	−0.216726	+	0.157461i
$498$	−6.87324	−	21.1537i	−0.307997	−	0.947918i
$499$	−5.36882			−0.240342			−0.120171	−	0.992753i	$-0.538344\pi$
$499$	−5.36882			−0.240342			−0.120171	+	0.992753i	$0.538344\pi$
$500$	21.7673	−	8.84956i	0.973465	−	0.395764i
$501$	−12.5389			−0.560198
$502$	−11.0625	−	34.0469i	−0.493744	−	1.51959i
$503$	13.7217	−	9.96938i	0.611819	−	0.444513i	−0.238235	−	0.971207i	$-0.576569\pi$
$503$	13.7217	−	9.96938i	0.611819	−	0.444513i	0.850054	+	0.526695i	$0.176569\pi$
$504$	−0.166599	+	0.121041i	−0.00742091	+	0.00539161i
$505$	6.11632	+	12.8956i	0.272173	+	0.573846i
$506$	5.01249	+	3.64179i	0.222832	+	0.161897i
$507$	1.89158			0.0840082
$508$	−33.4574	−	24.3082i	−1.48443	−	1.07850i
$509$	5.36726	−	16.5187i	0.237900	−	0.732180i	−0.758824	−	0.651296i	$-0.774226\pi$
$509$	5.36726	−	16.5187i	0.237900	−	0.732180i	0.996724	−	0.0808841i	$-0.0257744\pi$
$510$	−23.8583	+	22.5418i	−1.05646	+	0.998167i
$511$	0.498912	+	1.53549i	0.0220706	+	0.0679262i
$512$	9.93586	−	30.5794i	0.439107	−	1.35143i
$513$	−2.27870	+	7.01311i	−0.100607	+	0.309636i
$514$	12.9953	+	39.9954i	0.573197	+	1.76412i
$515$	−32.5635	−	17.7728i	−1.43492	−	0.783164i
$516$	−6.01406	+	18.5094i	−0.264754	+	0.814829i
$517$	1.85307	+	1.34633i	0.0814977	+	0.0592116i
$518$	6.56656			0.288518
$519$	4.33522	+	3.14972i	0.190295	+	0.138257i
$520$	1.55974	+	0.851289i	0.0683991	+	0.0373315i
$521$	−2.74720	+	1.99596i	−0.120357	+	0.0874446i	−0.646335	−	0.763053i	$-0.723699\pi$
$521$	−2.74720	+	1.99596i	−0.120357	+	0.0874446i	0.525978	+	0.850498i	$0.323699\pi$
$522$	16.9680	−	12.3280i	0.742668	−	0.539580i
$523$	0.816056	+	2.51156i	0.0356837	+	0.109823i	0.967312	−	0.253590i	$-0.0816114\pi$
$523$	0.816056	+	2.51156i	0.0356837	+	0.109823i	−0.931628	+	0.363413i	$0.881611\pi$
$524$	5.50473			0.240475
$525$	0.283505	−	4.99196i	0.0123732	−	0.217867i
$526$	21.0407			0.917416
$527$	6.25392	+	19.2476i	0.272425	+	0.838438i
$528$	1.86317	−	1.35367i	0.0810839	−	0.0589109i
$529$	−1.85851	+	1.35029i	−0.0808048	+	0.0587081i
$530$	−4.36194	+	23.2512i	−0.189470	+	1.00997i
$531$	4.65734	+	3.38376i	0.202112	+	0.146843i
$532$	−15.4978			−0.671916
$533$	−1.08113	−	0.785487i	−0.0468290	−	0.0340232i
$534$	0.492234	−	1.51494i	0.0213010	−	0.0655579i
$535$	−0.877228	−	1.84954i	−0.0379259	−	0.0799626i
$536$	−0.956642	−	2.94424i	−0.0413206	−	0.127172i
$537$	−2.42466	+	7.46235i	−0.104632	+	0.322024i
$538$	−12.2566	+	37.7221i	−0.528421	+	1.62631i
$539$	0.187958	+	0.578475i	0.00809593	+	0.0249167i
$540$	0.866513	−	4.61892i	0.0372888	−	0.198767i
$541$	−9.86738	+	30.3687i	−0.424232	+	1.30565i	0.479496	+	0.877544i	$0.340819\pi$
$541$	−9.86738	+	30.3687i	−0.424232	+	1.30565i	−0.903728	+	0.428107i	$0.859181\pi$
$542$	−6.03629	−	4.38562i	−0.259281	−	0.188378i
$543$	8.86195			0.380302
$544$	47.3791	+	34.4230i	2.03136	+	1.47587i
$545$	41.5407	−	5.37659i	1.77941	−	0.230308i
$546$	6.32279	−	4.59378i	0.270591	−	0.196596i
$547$	1.64645	−	1.19622i	0.0703973	−	0.0511466i	−0.552030	−	0.833824i	$-0.686147\pi$
$547$	1.64645	−	1.19622i	0.0703973	−	0.0511466i	0.622427	+	0.782678i	$0.286147\pi$
$548$	5.73475	+	17.6497i	0.244976	+	0.753960i
$549$	10.2671			0.438187
$550$	0.349236	−	6.14936i	0.0148915	−	0.262210i
$551$	76.3653			3.25327
$552$	−0.320062	−	0.985049i	−0.0136227	−	0.0419265i
$553$	11.2750	−	8.19175i	0.479461	−	0.348348i
$554$	36.8624	−	26.7821i	1.56613	−	1.13786i
$555$	−5.26991	+	4.97911i	−0.223695	+	0.211352i
$556$	11.8751	+	8.62778i	0.503617	+	0.365899i
$557$	13.7373			0.582068			0.291034	−	0.956713i	$-0.406001\pi$
$557$	13.7373			0.582068			0.291034	+	0.956713i	$0.406001\pi$
$558$	−4.57505	−	3.32397i	−0.193677	−	0.140715i
$559$	11.0426	−	33.9856i	0.467052	−	1.43744i
$560$	−8.39639	+	1.08674i	−0.354812	+	0.0459232i
$561$	1.36230	+	4.19274i	0.0575165	+	0.177017i
$562$	3.19056	−	9.81955i	0.134586	−	0.414213i
$563$	−4.10909	+	12.6465i	−0.173177	+	0.532985i	−0.999546	−	0.0301452i	$-0.990403\pi$
$563$	−4.10909	+	12.6465i	−0.173177	+	0.532985i	0.826368	+	0.563130i	$0.190403\pi$
$564$	−2.44570	−	7.52710i	−0.102983	−	0.316948i
$565$	33.8625	−	4.38280i	1.42460	−	0.184386i
$566$	−4.71669	+	14.5165i	−0.198257	+	0.610173i
$567$	−0.809017	−	0.587785i	−0.0339755	−	0.0246847i
$568$	1.22984			0.0516028
$569$	−17.3701	−	12.6201i	−0.728192	−	0.529062i	0.160799	−	0.986987i	$-0.448593\pi$
$569$	−17.3701	−	12.6201i	−0.728192	−	0.529062i	−0.888991	+	0.457925i	$0.848593\pi$
$570$	24.2734	−	22.9340i	1.01670	−	0.960600i
$571$	8.49304	−	6.17055i	0.355423	−	0.258230i	−0.395718	−	0.918372i	$-0.629504\pi$
$571$	8.49304	−	6.17055i	0.355423	−	0.258230i	0.751140	+	0.660143i	$0.229504\pi$
$572$	3.99092	−	2.89957i	0.166869	−	0.121237i
$573$	−1.31257	−	4.03966i	−0.0548332	−	0.168759i
$574$	−0.701344			−0.0292735
$575$	23.4382	+	9.11485i	0.977442	+	0.380115i
$576$	−8.79171			−0.366321
$577$	−13.6011	−	41.8600i	−0.566222	−	1.74265i	−0.664292	−	0.747473i	$-0.731267\pi$
$577$	−13.6011	−	41.8600i	−0.566222	−	1.74265i	0.0980700	−	0.995180i	$-0.468733\pi$
$578$	−58.2184	+	42.2981i	−2.42157	+	1.75937i
$579$	−0.292136	+	0.212249i	−0.0121407	+	0.00882077i
$580$	−48.2654	+	6.24696i	−2.00411	+	0.259391i
$581$	8.88497	+	6.45531i	0.368611	+	0.267811i
$582$	−12.5744			−0.521226
$583$	2.57055	+	1.86761i	0.106461	+	0.0773486i
$584$	0.102740	−	0.316201i	0.00425140	−	0.0130845i
$585$	−1.59103	+	8.48095i	−0.0657811	+	0.350644i
$586$	−16.7175	−	51.4513i	−0.690595	−	2.12543i
$587$	3.82528	−	11.7730i	0.157886	−	0.485923i	−0.840556	−	0.541725i	$-0.817771\pi$
$587$	3.82528	−	11.7730i	0.157886	−	0.485923i	0.998442	+	0.0558017i	$0.0177715\pi$
$588$	0.649455	−	1.99882i	0.0267831	−	0.0824298i
$589$	−6.36274	−	19.5825i	−0.262172	−	0.806883i
$590$	−11.1721	−	23.5552i	−0.459949	−	0.969751i
$591$	1.97733	−	6.08559i	0.0813364	−	0.250328i
$592$	9.93185	+	7.21591i	0.408196	+	0.296572i
$593$	−29.5676			−1.21420			−0.607098	−	0.794627i	$-0.707666\pi$
$593$	−29.5676			−1.21420			−0.607098	+	0.794627i	$0.707666\pi$
$594$	−0.996591	−	0.724066i	−0.0408906	−	0.0297088i
$595$	2.98828	−	15.9289i	0.122508	−	0.653023i
$596$	−4.51311	+	3.27897i	−0.184864	+	0.134312i
$597$	−1.96712	+	1.42920i	−0.0805090	+	0.0584932i
$598$	12.1470	+	37.3847i	0.496729	+	1.52878i
$599$	−26.0685			−1.06513			−0.532565	−	0.846389i	$-0.678772\pi$
$599$	−26.0685			−1.06513			−0.532565	+	0.846389i	$0.678772\pi$
$600$	−0.651465	+	0.797340i	−0.0265959	+	0.0325513i
$601$	−4.18435			−0.170683			−0.0853416	−	0.996352i	$-0.527198\pi$
$601$	−4.18435			−0.170683			−0.0853416	+	0.996352i	$0.527198\pi$
$602$	−5.79538	−	17.8363i	−0.236202	−	0.726955i
$603$	12.1621	−	8.83630i	0.495280	−	0.359842i
$604$	9.93177	−	7.21585i	0.404118	−	0.293609i
$605$	20.8642	+	11.3874i	0.848250	+	0.462966i
$606$	−10.4582	−	7.59829i	−0.424834	−	0.308660i
$607$	−7.70406			−0.312698			−0.156349	−	0.987702i	$-0.549972\pi$
$607$	−7.70406			−0.312698			−0.156349	+	0.987702i	$0.549972\pi$
$608$	−48.2035	−	35.0219i	−1.95491	−	1.42033i
$609$	−3.20018	+	9.84913i	−0.129678	+	0.399107i
$610$	−40.8125	−	22.2750i	−1.65245	−	0.901890i
$611$	4.49063	+	13.8207i	0.181672	+	0.559127i
$612$	4.70719	−	14.4872i	0.190277	−	0.585612i
$613$	0.923069	−	2.84091i	0.0372824	−	0.114743i	−0.930683	−	0.365826i	$-0.880787\pi$
$613$	0.923069	−	2.84091i	0.0372824	−	0.114743i	0.967966	+	0.251083i	$0.0807866\pi$
$614$	−5.87287	−	18.0748i	−0.237010	−	0.729441i
$615$	0.562854	−	0.531795i	0.0226965	−	0.0214441i
$616$	0.0387058	−	0.119124i	0.00155950	−	0.00479965i
$617$	7.17055	+	5.20971i	0.288676	+	0.209735i	0.722693	−	0.691170i	$-0.242904\pi$
$617$	7.17055	+	5.20971i	0.288676	+	0.209735i	−0.434017	+	0.900905i	$0.642904\pi$
$618$	33.6005			1.35161
$619$	1.51983	+	1.10422i	0.0610873	+	0.0443825i	0.617910	−	0.786249i	$-0.287980\pi$
$619$	1.51983	+	1.10422i	0.0610873	+	0.0443825i	−0.556823	+	0.830631i	$0.687980\pi$
$620$	5.62338	+	11.8563i	0.225840	+	0.476160i
$621$	4.06906	−	2.95635i	0.163286	−	0.118634i
$622$	21.4777	−	15.6044i	0.861176	−	0.625681i
$623$	0.243047	+	0.748022i	0.00973748	+	0.0299689i
$624$	14.6112			0.584916
$625$	−4.98380	−	24.4982i	−0.199352	−	0.979928i
$626$	35.8428			1.43257
$627$	−1.38601	−	4.26569i	−0.0553518	−	0.170355i
$628$	24.5293	−	17.8216i	0.978825	−	0.711158i
$629$	−19.0120	+	13.8130i	−0.758057	+	0.550761i
$630$	1.94068	+	4.09172i	0.0773186	+	0.163018i
$631$	21.3347	+	15.5006i	0.849320	+	0.617067i	0.924959	−	0.380068i	$-0.124099\pi$
$631$	21.3347	+	15.5006i	0.849320	+	0.617067i	−0.0756383	+	0.997135i	$0.524099\pi$
$632$	−2.86994			−0.114160
$633$	−4.45765	−	3.23868i	−0.177176	−	0.128726i
$634$	−2.27286	+	6.99514i	−0.0902667	+	0.277812i
$635$	−31.9826	+	30.2178i	−1.26919	+	1.19916i
$636$	−3.39265	−	10.4415i	−0.134527	−	0.414032i
$637$	−1.19248	+	3.67009i	−0.0472480	+	0.145414i
$638$	−3.94215	+	12.1327i	−0.156071	+	0.480338i
$639$	1.84550	+	5.67987i	0.0730069	+	0.224692i
$640$	3.22931	+	1.76252i	0.127650	+	0.0696699i
$641$	−6.89294	+	21.2143i	−0.272255	+	0.837914i	0.717678	+	0.696375i	$0.245205\pi$
$641$	−6.89294	+	21.2143i	−0.272255	+	0.837914i	−0.989933	+	0.141539i	$0.954795\pi$
$642$	1.49995	+	1.08978i	0.0591984	+	0.0430101i
$643$	3.78979			0.149455			0.0747274	−	0.997204i	$-0.476191\pi$
$643$	3.78979			0.149455			0.0747274	+	0.997204i	$0.476191\pi$
$644$	8.55186	+	6.21329i	0.336991	+	0.244838i
$645$	18.1755	+	9.91997i	0.715658	+	0.390598i
$646$	87.5701	−	63.6234i	3.44540	−	2.50323i
$647$	0.968521	−	0.703672i	0.0380765	−	0.0276642i	−0.568584	−	0.822625i	$-0.692509\pi$
$647$	0.968521	−	0.703672i	0.0380765	−	0.0276642i	0.606661	+	0.794961i	$0.292509\pi$
$648$	0.0636352	+	0.195849i	0.00249983	+	0.00769367i
$649$	−3.50154			−0.137448
$650$	24.7245	−	30.2607i	0.969774	−	1.18692i
$651$	2.79227			0.109438
$652$	−6.71807	−	20.6761i	−0.263100	−	0.809739i
$653$	−19.4632	+	14.1408i	−0.761652	+	0.553373i	−0.899417	−	0.437092i	$-0.856008\pi$
$653$	−19.4632	+	14.1408i	−0.761652	+	0.553373i	0.137765	+	0.990465i	$0.456008\pi$
$654$	−30.6927	+	22.2995i	−1.20018	+	0.871981i
$655$	1.07989	−	5.75630i	0.0421946	−	0.224917i
$656$	−1.06077	−	0.770697i	−0.0414163	−	0.0300907i
$657$	1.61451			0.0629881
$658$	6.17011	+	4.48285i	0.240536	+	0.174760i
$659$	3.16115	−	9.72903i	0.123141	−	0.378989i	−0.870417	−	0.492316i	$-0.836151\pi$
$659$	3.16115	−	9.72903i	0.123141	−	0.378989i	0.993558	+	0.113326i	$0.0361506\pi$
$660$	1.22495	+	2.58268i	0.0476812	+	0.100531i
$661$	−15.1028	−	46.4816i	−0.587430	−	1.80792i	−0.589285	−	0.807925i	$-0.700590\pi$
$661$	−15.1028	−	46.4816i	−0.587430	−	1.80792i	0.00185467	−	0.999998i	$-0.499410\pi$
$662$	4.95994	−	15.2651i	0.192774	−	0.593296i
$663$	−8.64302	+	26.6005i	−0.335667	+	1.03308i
$664$	−0.698869	−	2.15090i	−0.0271214	−	0.0834710i
$665$	−3.04028	+	16.2061i	−0.117897	+	0.628446i
$666$	2.02918	−	6.24517i	0.0786291	−	0.241995i
$667$	−42.1392	−	30.6159i	−1.63163	−	1.18545i
$668$	−26.3528			−1.01962
$669$	19.1702	+	13.9279i	0.741161	+	0.538485i
$670$	−67.5166	+	8.73864i	−2.60839	+	0.337603i
$671$	−5.05222	+	3.67065i	−0.195039	+	0.141704i
$672$	6.53694	−	4.74937i	0.252168	−	0.183211i
$673$	10.7136	+	32.9730i	0.412978	+	1.27102i	0.914047	+	0.405609i	$0.132940\pi$
$673$	10.7136	+	32.9730i	0.412978	+	1.27102i	−0.501069	+	0.865408i	$0.667060\pi$
$674$	13.8578			0.533781
$675$	−4.66002	−	1.81223i	−0.179364	−	0.0697527i
$676$	3.97550			0.152904
$677$	3.37627	+	10.3911i	0.129760	+	0.399362i	0.994738	−	0.102448i	$-0.0326676\pi$
$677$	3.37627	+	10.3911i	0.129760	+	0.399362i	−0.864978	+	0.501810i	$0.832668\pi$
$678$	−25.0196	+	18.1778i	−0.960870	+	0.698113i
$679$	5.02301	−	3.64943i	0.192766	−	0.140052i
$680$	−2.42590	+	2.29204i	−0.0930292	+	0.0878958i
$681$	16.7908	+	12.1992i	0.643425	+	0.467476i
$682$	3.43967			0.131712
$683$	−22.3292	−	16.2231i	−0.854405	−	0.620762i	0.0719521	−	0.997408i	$-0.477077\pi$
$683$	−22.3292	−	16.2231i	−0.854405	−	0.620762i	−0.926357	+	0.376647i	$0.877077\pi$
$684$	−4.78909	+	14.7393i	−0.183116	+	0.563572i
$685$	19.5814	−	2.53441i	0.748166	−	0.0968347i
$686$	0.625840	+	1.92614i	0.0238947	+	0.0735403i
$687$	−0.618121	+	1.90238i	−0.0235828	+	0.0725803i
$688$	10.8347	−	33.3457i	0.413069	−	1.27129i
$689$	6.22935	+	19.1720i	0.237319	+	0.730393i
$690$	−22.5889	+	2.92367i	−0.859945	+	0.111302i
$691$	−4.62944	+	14.2479i	−0.176112	+	0.542017i	−0.999683	−	0.0251968i	$-0.991979\pi$
$691$	−4.62944	+	14.2479i	−0.176112	+	0.542017i	0.823570	+	0.567214i	$0.191979\pi$
$692$	9.11123	+	6.61970i	0.346357	+	0.251643i
$693$	0.608245			0.0231053
$694$	−25.5835	−	18.5875i	−0.971137	−	0.705572i
$695$	11.3517	−	10.7253i	0.430594	−	0.406833i
$696$	1.72530	−	1.25350i	0.0653973	−	0.0475139i
$697$	2.03058	−	1.47530i	0.0769137	−	0.0558811i
$698$	5.79225	+	17.8267i	0.219240	+	0.674751i
$699$	18.1669			0.687134
$700$	0.595836	−	10.4915i	0.0225205	−	0.396541i
$701$	42.7662			1.61526			0.807629	−	0.589691i	$-0.200750\pi$
$701$	42.7662			1.61526			0.807629	+	0.589691i	$0.200750\pi$
$702$	−2.41509	−	7.43289i	−0.0911518	−	0.280536i
$703$	19.3428	−	14.0534i	0.729527	−	0.530033i
$704$	4.32623	−	3.14319i	0.163051	−	0.118463i
$705$	−8.35088	+	1.08085i	−0.314512	+	0.0407072i
$706$	−4.56922	−	3.31973i	−0.171965	−	0.124940i
$707$	6.38288			0.240053
$708$	9.78825	+	7.11158i	0.367865	+	0.267269i
$709$	−0.574590	+	1.76841i	−0.0215792	+	0.0664139i	−0.961266	−	0.275622i	$-0.911116\pi$
$709$	−0.574590	+	1.76841i	−0.0215792	+	0.0664139i	0.939687	+	0.342036i	$0.111116\pi$
$710$	4.98680	−	26.5820i	0.187151	−	0.997604i
$711$	−4.30666	−	13.2545i	−0.161512	−	0.497083i
$712$	0.0500502	−	0.154039i	0.00187571	−	0.00577284i
$713$	−4.33987	+	13.3567i	−0.162529	+	0.500214i
$714$	4.53603	+	13.9605i	0.169757	+	0.522457i
$715$	−2.24917	−	4.74213i	−0.0841143	−	0.177346i
$716$	−5.09587	+	15.6835i	−0.190442	+	0.586119i
$717$	6.95398	+	5.05237i	0.259701	+	0.188684i
$718$	−48.4592			−1.80848
$719$	−19.4131	−	14.1044i	−0.723986	−	0.526007i	0.163669	−	0.986515i	$-0.447667\pi$
$719$	−19.4131	−	14.1044i	−0.723986	−	0.526007i	−0.887655	+	0.460509i	$0.847667\pi$
$720$	−1.56108	+	8.32127i	−0.0581779	+	0.310115i
$721$	−13.4222	+	9.75177i	−0.499867	+	0.363175i
$722$	−57.9628	+	42.1125i	−2.15715	+	1.56726i
$723$	4.80532	+	14.7893i	0.178712	+	0.550019i
$724$	18.6250			0.692192
$725$	−2.93597	+	51.6966i	−0.109039	+	1.91997i
$726$	−21.5286			−0.799001
$727$	4.26658	+	13.1312i	0.158239	+	0.487009i	0.998475	−	0.0552121i	$-0.0175835\pi$
$727$	4.26658	+	13.1312i	0.158239	+	0.487009i	−0.840236	+	0.542221i	$0.817583\pi$
$728$	0.642899	−	0.467094i	0.0238274	−	0.0173116i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−6.41784	−	3.50279i	−0.237535	−	0.129644i
$731$	54.2987	+	39.4503i	2.00831	+	1.45912i
$732$	21.5781			0.797548
$733$	−3.74681	−	2.72222i	−0.138392	−	0.100547i	0.516435	−	0.856326i	$-0.327259\pi$
$733$	−3.74681	−	2.72222i	−0.138392	−	0.100547i	−0.654827	+	0.755779i	$0.727259\pi$
$734$	−14.0413	+	43.2146i	−0.518273	+	1.59508i
$735$	−1.96276	−	1.07125i	−0.0723974	−	0.0395137i
$736$	12.5584	+	38.6509i	0.462910	+	1.42469i
$737$	−2.82561	+	8.69635i	−0.104083	+	0.320334i
$738$	−0.216727	+	0.667017i	−0.00797783	+	0.0245532i
$739$	−1.44417	−	4.44470i	−0.0531246	−	0.163501i	0.920974	−	0.389624i	$-0.127395\pi$
$739$	−1.44417	−	4.44470i	−0.0531246	−	0.163501i	−0.974099	+	0.226123i	$0.927395\pi$
$740$	−11.0757	+	10.4645i	−0.407149	+	0.384683i
$741$	8.79341	−	27.0633i	0.323034	−	0.994196i
$742$	8.55910	+	6.21855i	0.314214	+	0.228290i
$743$	−19.5785			−0.718267			−0.359134	−	0.933286i	$-0.616928\pi$
$743$	−19.5785			−0.718267			−0.359134	+	0.933286i	$0.616928\pi$
$744$	−0.465190	−	0.337980i	−0.0170547	−	0.0123910i
$745$	2.54346	+	5.36261i	0.0931853	+	0.196471i
$746$	−41.1954	+	29.9302i	−1.50827	+	1.09582i
$747$	8.88497	−	6.45531i	0.325084	−	0.236187i
$748$	2.86312	+	8.81179i	0.104686	+	0.322191i
$749$	−0.915459			−0.0334501
$750$	14.5923	+	17.3140i	0.532835	+	0.632218i
$751$	−29.2964			−1.06904			−0.534521	−	0.845155i	$-0.679508\pi$
$751$	−29.2964			−1.06904			−0.534521	+	0.845155i	$0.679508\pi$
$752$	4.40608	+	13.5605i	0.160673	+	0.494501i
$753$	14.3004	−	10.3898i	0.521135	−	0.378627i
$754$	−65.4788	+	47.5731i	−2.38460	+	1.73251i
$755$	−5.59727	−	11.8012i	−0.203705	−	0.429491i
$756$	−1.70029	−	1.23534i	−0.0618391	−	0.0449287i
$757$	−14.6032			−0.530764			−0.265382	−	0.964143i	$-0.585498\pi$
$757$	−14.6032			−0.530764			−0.265382	+	0.964143i	$0.585498\pi$
$758$	−52.1441	−	37.8849i	−1.89396	−	1.37604i
$759$	−0.945361	+	2.90952i	−0.0343144	+	0.105609i
$760$	2.46812	−	2.33192i	0.0895279	−	0.0845877i
$761$	7.04881	+	21.6940i	0.255519	+	0.786407i	0.993727	+	0.111833i	$0.0356723\pi$
$761$	7.04881	+	21.6940i	0.255519	+	0.786407i	−0.738208	+	0.674573i	$0.764328\pi$
$762$	12.3149	−	37.9014i	0.446122	−	1.37302i
$763$	5.78867	−	17.8157i	0.209564	−	0.644971i
$764$	−2.75859	−	8.49008i	−0.0998024	−	0.307160i
$765$	−14.2259	−	7.76434i	−0.514338	−	0.280720i
$766$	−4.67123	+	14.3766i	−0.168778	+	0.519447i
$767$	−17.9725	−	13.0578i	−0.648950	−	0.471490i
$768$	14.2513			0.514248
$769$	−36.8856	−	26.7990i	−1.33013	−	0.966396i	−0.999746	−	0.0225490i	$-0.992822\pi$
$769$	−36.8856	−	26.7990i	−1.33013	−	0.966396i	−0.330384	−	0.943847i	$-0.607178\pi$
$770$	−2.41783	−	1.31963i	−0.0871326	−	0.0475560i
$771$	−16.7989	+	12.2051i	−0.604996	+	0.439556i
$772$	−0.613975	+	0.446079i	−0.0220975	+	0.0160547i
$773$	15.4084	+	47.4221i	0.554201	+	1.70566i	0.698044	+	0.716055i	$0.254054\pi$
$773$	15.4084	+	47.4221i	0.554201	+	1.70566i	−0.143843	+	0.989601i	$0.545946\pi$
$774$	−18.7542			−0.674107
$775$	13.5013	−	3.55448i	0.484981	−	0.127681i
$776$	−1.27856			−0.0458977
$777$	1.00193	+	3.08364i	0.0359442	+	0.110625i
$778$	7.38103	−	5.36263i	0.264623	−	0.192260i
$779$	−2.06591	+	1.50097i	−0.0740190	+	0.0537780i
$780$	−3.34384	+	17.8242i	−0.119729	+	0.638210i
$781$	−2.93879	−	2.13516i	−0.105158	−	0.0764019i
$782$	−73.8295			−2.64014
$783$	8.37817	+	6.08710i	0.299411	+	0.217535i
$784$	−1.17003	+	3.60099i	−0.0417868	+	0.128607i
$785$	−13.8240	−	29.1464i	−0.493400	−	1.04028i
$786$	1.63920	+	5.04494i	0.0584684	+	0.179947i
$787$	5.71733	−	17.5961i	0.203801	−	0.627235i	−0.795960	−	0.605350i	$-0.793033\pi$
$787$	5.71733	−	17.5961i	0.203801	−	0.627235i	0.999760	−	0.0218849i	$-0.00696675\pi$
$788$	4.15571	−	12.7900i	0.148041	−	0.455624i
$789$	3.21041	+	9.88063i	0.114294	+	0.351760i
$790$	−11.6372	+	62.0316i	−0.414032	+	2.20698i
$791$	4.71871	−	14.5227i	0.167778	−	0.516368i
$792$	−0.101333	−	0.0736228i	−0.00360071	−	0.00261607i
$793$	−39.6202			−1.40695
$794$	−33.2325	−	24.1448i	−1.17938	−	0.856867i
$795$	−11.5842	+	1.49934i	−0.410850	+	0.0531761i
$796$	−4.13426	+	3.00372i	−0.146535	+	0.106464i
$797$	−21.9349	+	15.9366i	−0.776973	+	0.564504i	−0.904069	−	0.427387i	$-0.859434\pi$
$797$	−21.9349	+	15.9366i	−0.776973	+	0.564504i	0.127096	+	0.991890i	$0.459434\pi$
$798$	−4.61496	−	14.2034i	−0.163368	−	0.502794i
$799$	−27.2940			−0.965593
$800$	25.5619	−	31.2857i	0.903749	−	1.10611i
$801$	0.786517			0.0277902
$802$	−8.96226	−	27.5830i	−0.316468	−	0.973990i
$803$	−0.794470	+	0.577216i	−0.0280362	+	0.0203695i
$804$	25.5609	−	18.5711i	0.901463	−	0.654952i
$805$	8.17490	−	7.72381i	0.288128	−	0.272228i
$806$	17.6549	+	12.8271i	0.621869	+	0.451814i
$807$	−19.5843			−0.689400
$808$	−1.06338	−	0.772592i	−0.0374096	−	0.0271797i
$809$	8.35435	−	25.7121i	0.293723	−	0.903988i	−0.689924	−	0.723882i	$-0.742356\pi$
$809$	8.35435	−	25.7121i	0.293723	−	0.903988i	0.983647	−	0.180106i	$-0.0576440\pi$
$810$	4.49116	−	0.581288i	0.157803	−	0.0204244i
$811$	−0.924568	−	2.84553i	−0.0324660	−	0.0999200i	0.933510	−	0.358550i	$-0.116729\pi$
$811$	−0.924568	−	2.84553i	−0.0324660	−	0.0999200i	−0.965976	+	0.258630i	$0.916729\pi$
$812$	−6.72575	+	20.6997i	−0.236027	+	0.726418i
$813$	1.13845	−	3.50379i	0.0399272	−	0.122883i
$814$	1.23424	+	3.79859i	0.0432600	+	0.133141i
$815$	−22.9389	+	2.96898i	−0.803516	+	0.103999i
$816$	−8.48028	+	26.0996i	−0.296869	+	0.913670i
$817$	−55.2434	−	40.1367i	−1.93272	−	1.40421i
$818$	47.6027			1.66439
$819$	3.12197	+	2.26824i	0.109090	+	0.0792587i
$820$	1.18294	−	1.11766i	0.0413100	−	0.0390305i
$821$	−21.3248	+	15.4934i	−0.744241	+	0.540723i	−0.894037	−	0.447994i	$-0.852139\pi$
$821$	−21.3248	+	15.4934i	−0.744241	+	0.540723i	0.149795	+	0.988717i	$0.452139\pi$
$822$	−14.4679	+	10.5115i	−0.504624	+	0.366631i
$823$	14.0739	+	43.3149i	0.490584	+	1.50986i	0.823727	+	0.566986i	$0.191891\pi$
$823$	14.0739	+	43.3149i	0.490584	+	1.50986i	−0.333143	+	0.942876i	$0.608109\pi$
$824$	3.41649			0.119019
$825$	2.94101	−	0.774278i	0.102393	−	0.0269569i
$826$	−11.6590			−0.405669
$827$	3.73953	+	11.5091i	0.130036	+	0.400210i	0.994785	−	0.101995i	$-0.0325225\pi$
$827$	3.73953	+	11.5091i	0.130036	+	0.400210i	−0.864749	+	0.502205i	$0.832522\pi$
$828$	8.55186	−	6.21329i	0.297198	−	0.215927i
$829$	11.8761	−	8.62846i	0.412473	−	0.299679i	−0.362129	−	0.932128i	$-0.617950\pi$
$829$	11.8761	−	8.62846i	0.412473	−	0.299679i	0.774602	+	0.632449i	$0.217950\pi$
$830$	−49.3238	+	6.38396i	−1.71205	+	0.221590i
$831$	18.2013	+	13.2240i	0.631396	+	0.458736i
$832$	33.9269			1.17620
$833$	−5.86368	−	4.26021i	−0.203165	−	0.147608i
$834$	−4.37096	+	13.4524i	−0.151354	+	0.465820i
$835$	−5.16975	+	27.5572i	−0.178907	+	0.953656i
$836$	−2.91294	−	8.96511i	−0.100746	−	0.310065i
$837$	0.862859	−	2.65561i	0.0298248	−	0.0917912i
$838$	−5.36468	+	16.5108i	−0.185320	+	0.570355i
$839$	−10.8867	−	33.5058i	−0.375851	−	1.15675i	−0.942903	−	0.333068i	$-0.891916\pi$
$839$	−10.8867	−	33.5058i	−0.375851	−	1.15675i	0.567052	−	0.823682i	$-0.308084\pi$
$840$	0.197328	+	0.416044i	0.00680846	+	0.0143549i
$841$	24.1795	−	74.4169i	0.833776	−	2.56610i
$842$	8.91028	+	6.47369i	0.307068	+	0.223098i
$843$	5.09805			0.175586
$844$	−9.36856	−	6.80666i	−0.322479	−	0.234295i
$845$	0.779892	−	4.15719i	0.0268291	−	0.143012i
$846$	6.17011	−	4.48285i	0.212133	−	0.154124i
$847$	8.59988	−	6.24818i	0.295495	−	0.214690i
$848$	6.11205	+	18.8110i	0.209889	+	0.645971i
$849$	−7.53657			−0.258655
$850$	39.7041	+	61.7280i	1.36184	+	2.11725i
$851$	−16.3077			−0.559022
$852$	3.87865	+	11.9373i	0.132881	+	0.408964i
$853$	19.7586	−	14.3555i	0.676523	−	0.491523i	−0.195679	−	0.980668i	$-0.562691\pi$
$853$	19.7586	−	14.3555i	0.676523	−	0.491523i	0.872202	+	0.489145i	$0.162691\pi$
$854$	−16.8223	+	12.2221i	−0.575646	+	0.418231i
$855$	14.4734	+	7.89944i	0.494981	+	0.270155i
$856$	0.152515	+	0.110808i	0.00521284	+	0.00378735i
$857$	−52.5915			−1.79649			−0.898246	−	0.439494i	$-0.855158\pi$
$857$	−52.5915			−1.79649			−0.898246	+	0.439494i	$0.855158\pi$
$858$	3.84581	+	2.79414i	0.131294	+	0.0953905i
$859$	10.8018	−	33.2446i	0.368554	−	1.13429i	−0.579172	−	0.815205i	$-0.696624\pi$
$859$	10.8018	−	33.2446i	0.368554	−	1.13429i	0.947726	−	0.319086i	$-0.103376\pi$
$860$	38.1990	+	20.8486i	1.30258	+	0.710931i
$861$	−0.107012	−	0.329349i	−0.00364696	−	0.0112242i
$862$	11.4068	−	35.1066i	0.388518	−	1.19574i
$863$	10.5511	−	32.4731i	0.359165	−	1.10540i	−0.594390	−	0.804177i	$-0.702606\pi$
$863$	10.5511	−	32.4731i	0.359165	−	1.10540i	0.953555	−	0.301219i	$-0.0973936\pi$
$864$	−2.49689	−	7.68463i	−0.0849459	−	0.261437i
$865$	8.70962	−	8.22901i	0.296136	−	0.279795i
$866$	−6.14410	+	18.9096i	−0.208785	+	0.642574i
$867$	−28.7461	−	20.8853i	−0.976270	−	0.709302i
$868$	5.86846			0.199188
$869$	6.85795	+	4.98259i	0.232640	+	0.169023i
$870$	−20.0977	−	42.3738i	−0.681375	−	1.43661i
$871$	−46.9332	+	34.0990i	−1.59027	+	1.15540i
$872$	−3.12082	+	2.26741i	−0.105684	+	0.0767842i
$873$	−1.91862	−	5.90491i	−0.0649355	−	0.199851i
$874$	75.1142			2.54077
$875$	−10.8541	−	2.68123i	−0.366935	−	0.0906420i
$876$	3.39319			0.114645
$877$	−13.1609	−	40.5050i	−0.444411	−	1.36776i	−0.883129	−	0.469131i	$-0.844567\pi$
$877$	−13.1609	−	40.5050i	−0.444411	−	1.36776i	0.438718	−	0.898625i	$-0.355433\pi$
$878$	−18.9612	+	13.7762i	−0.639911	+	0.464923i
$879$	21.6106	−	15.7010i	0.728907	−	0.529582i
$880$	−2.20682	−	4.65285i	−0.0743920	−	0.156847i
$881$	7.72384	+	5.61170i	0.260223	+	0.189063i	0.710245	−	0.703954i	$-0.248584\pi$
$881$	7.72384	+	5.61170i	0.260223	+	0.189063i	−0.450023	+	0.893017i	$0.648584\pi$
$882$	2.02526			0.0681941
$883$	45.1255	+	32.7856i	1.51859	+	1.10332i	0.962179	+	0.272417i	$0.0878232\pi$
$883$	45.1255	+	32.7856i	1.51859	+	1.10332i	0.556414	+	0.830905i	$0.312177\pi$
$884$	−18.1649	+	55.9057i	−0.610950	+	1.88031i
$885$	9.35679	−	8.84047i	0.314525	−	0.297169i
$886$	11.3752	+	35.0093i	0.382158	+	1.17616i
$887$	−17.0728	+	52.5448i	−0.573250	+	1.76428i	0.0688119	+	0.997630i	$0.478079\pi$
$887$	−17.0728	+	52.5448i	−0.573250	+	1.76428i	−0.642062	+	0.766653i	$0.721921\pi$
$888$	0.206326	−	0.635007i	0.00692386	−	0.0213094i
$889$	6.08065	+	18.7143i	0.203938	+	0.627658i
$890$	−3.12648	−	1.70640i	−0.104800	−	0.0571987i
$891$	0.187958	−	0.578475i	0.00629683	−	0.0193797i
$892$	40.2895	+	29.2721i	1.34899	+	0.980101i
$893$	27.7689			0.929252
$894$	−4.34901	−	3.15974i	−0.145453	−	0.105678i
$895$	15.4005	+	8.40545i	0.514783	+	0.280963i
$896$	1.33107	−	0.967079i	0.0444679	−	0.0323078i
$897$	−15.7024	+	11.4084i	−0.524286	+	0.380916i
$898$	−20.2212	−	62.2346i	−0.674791	−	2.07679i
$899$	−28.9167			−0.964427
$900$	−9.79388	−	3.80872i	−0.326463	−	0.126957i
$901$	−37.8619			−1.26136
$902$	−0.131823	−	0.405710i	−0.00438923	−	0.0135087i
$903$	7.49163	−	5.44299i	0.249306	−	0.181131i
$904$	−2.54398	+	1.84831i	−0.0846115	+	0.0614739i
$905$	3.65374	−	19.4762i	0.121454	−	0.647409i
$906$	9.57064	+	6.95348i	0.317963	+	0.231014i
$907$	35.2659			1.17098			0.585492	−	0.810678i	$-0.300901\pi$
$907$	35.2659			1.17098			0.585492	+	0.810678i	$0.300901\pi$
$908$	35.2889	+	25.6389i	1.17110	+	0.850856i
$909$	1.97242	−	6.07048i	0.0654210	−	0.201345i
$910$	−7.48902	−	15.7898i	−0.248259	−	0.523426i
$911$	5.82806	+	17.9369i	0.193092	+	0.594277i	0.999994	+	0.00359068i	$0.00114295\pi$
$911$	5.82806	+	17.9369i	0.193092	+	0.594277i	−0.806901	+	0.590686i	$0.798857\pi$
$912$	8.62784	−	26.5538i	0.285696	−	0.879283i
$913$	−2.06424	+	6.35306i	−0.0683162	+	0.210256i
$914$	−2.74867	−	8.45955i	−0.0909181	−	0.279817i
$915$	4.23306	−	22.5642i	0.139941	−	0.745950i
$916$	−1.29909	+	3.99819i	−0.0429232	+	0.132104i
$917$	−2.11898	−	1.53953i	−0.0699749	−	0.0508397i
$918$	14.6789			0.484476
$919$	19.9817	+	14.5175i	0.659135	+	0.478890i	0.866371	−	0.499401i	$-0.166447\pi$
$919$	19.9817	+	14.5175i	0.659135	+	0.478890i	−0.207236	+	0.978291i	$0.566447\pi$
$920$	−2.29683	+	0.297278i	−0.0757243	+	0.00980096i
$921$	7.59180	−	5.51577i	0.250158	−	0.181751i
$922$	26.4625	−	19.2262i	0.871497	−	0.633180i
$923$	−7.12172	−	21.9184i	−0.234414	−	0.721453i
$924$	1.27834			0.0420542
$925$	8.76998	+	13.6347i	0.288355	+	0.448306i
$926$	−9.66772			−0.317701
$927$	5.12681	+	15.7787i	0.168386	+	0.518240i
$928$	−67.6965	+	49.1844i	−2.22225	+	1.61456i
$929$	26.4779	−	19.2373i	0.868713	−	0.631157i	−0.0615285	−	0.998105i	$-0.519598\pi$
$929$	26.4779	−	19.2373i	0.868713	−	0.631157i	0.930241	+	0.366949i	$0.119598\pi$
$930$	−9.19146	+	8.68427i	−0.301400	+	0.284768i
$931$	5.96571	+	4.33434i	0.195518	+	0.142052i
$932$	38.1809			1.25066
$933$	10.6049	+	7.70490i	0.347188	+	0.252247i
$934$	23.8989	−	73.5533i	0.781996	−	2.40674i
$935$	9.77617	−	1.26533i	0.319715	−	0.0413806i
$936$	−0.245566	−	0.755774i	−0.00802657	−	0.0247032i
$937$	−1.20049	+	3.69473i	−0.0392183	+	0.120702i	−0.968749	−	0.248043i	$-0.920212\pi$
$937$	−1.20049	+	3.69473i	−0.0392183	+	0.120702i	0.929531	+	0.368745i	$0.120212\pi$
$938$	−9.40839	+	28.9560i	−0.307195	+	0.945448i
$939$	5.46894	+	16.8317i	0.178472	+	0.549281i
$940$	−17.5509	+	2.27160i	−0.572446	+	0.0740914i
$941$	2.10426	−	6.47626i	0.0685971	−	0.211120i	−0.910882	−	0.412668i	$-0.864597\pi$
$941$	2.10426	−	6.47626i	0.0685971	−	0.211120i	0.979479	+	0.201548i	$0.0645971\pi$
$942$	23.6374	+	17.1736i	0.770147	+	0.559545i
$943$	1.74175			0.0567193
$944$	−17.6341	−	12.8119i	−0.573942	−	0.416993i
$945$	−1.62535	+	1.53566i	−0.0528725	+	0.0499550i
$946$	9.22860	−	6.70497i	0.300048	−	0.217997i
$947$	38.5191	−	27.9858i	1.25170	−	0.909415i	0.253383	−	0.967366i	$-0.418457\pi$
$947$	38.5191	−	27.9858i	1.25170	−	0.909415i	0.998319	+	0.0579507i	$0.0184566\pi$
$948$	−9.05121	−	27.8568i	−0.293970	−	0.904746i
$949$	−6.23034			−0.202245
$950$	−40.3949	−	62.8020i	−1.31058	−	2.03757i
$951$	−3.63169			−0.117766
$952$	0.461222	+	1.41950i	0.0149483	+	0.0460061i
$953$	10.4807	−	7.61468i	0.339503	−	0.246664i	−0.404949	−	0.914339i	$-0.632711\pi$
$953$	10.4807	−	7.61468i	0.339503	−	0.246664i	0.744452	+	0.667676i	$0.232711\pi$
$954$	8.55910	−	6.21855i	0.277111	−	0.201333i
$955$	−9.41925	+	1.21913i	−0.304800	+	0.0394501i
$956$	14.6150	+	10.6185i	0.472684	+	0.343425i
$957$	−6.29898			−0.203617
$958$	27.0684	+	19.6664i	0.874541	+	0.635391i
$959$	2.72865	−	8.39792i	0.0881127	−	0.271183i
$960$	−3.62478	+	19.3218i	−0.116989	+	0.623608i
$961$	−7.17019	−	22.0676i	−0.231296	−	0.711857i
$962$	−7.83052	+	24.0999i	−0.252466	+	0.777011i
$963$	−0.282892	+	0.870653i	−0.00911608	+	0.0280564i
$964$	10.0992	+	31.0823i	0.325275	+	1.00109i
$965$	0.346019	+	0.729544i	0.0111388	+	0.0234849i
$966$	−3.14775	+	9.68777i	−0.101277	+	0.311699i
$967$	27.1983	+	19.7607i	0.874638	+	0.635462i	0.931828	−	0.362901i	$-0.118214\pi$
$967$	27.1983	+	19.7607i	0.874638	+	0.635462i	−0.0571892	+	0.998363i	$0.518214\pi$
$968$	−2.18902			−0.0703578
$969$	43.2389	+	31.4149i	1.38903	+	1.00919i
$970$	−5.18438	+	27.6351i	−0.166460	+	0.887311i
$971$	28.8106	−	20.9321i	0.924575	−	0.671743i	−0.0200833	−	0.999798i	$-0.506393\pi$
$971$	28.8106	−	20.9321i	0.924575	−	0.671743i	0.944659	+	0.328055i	$0.106393\pi$
$972$	−1.70029	+	1.23534i	−0.0545370	+	0.0396234i
$973$	−2.15822	−	6.64233i	−0.0691894	−	0.212943i
$974$	34.6674			1.11082
$975$	17.9829	+	6.99332i	0.575912	+	0.223965i
$976$	−38.8742			−1.24433
$977$	−1.99787	−	6.14880i	−0.0639175	−	0.196718i	0.913998	−	0.405719i	$-0.132979\pi$
$977$	−1.99787	−	6.14880i	−0.0639175	−	0.196718i	−0.977915	+	0.209001i	$0.932979\pi$
$978$	16.9486	−	12.3139i	0.541957	−	0.393755i
$979$	−0.387030	+	0.281194i	−0.0123695	+	0.00898699i
$980$	−4.12509	−	2.25143i	−0.131771	−	0.0719192i
$981$	−15.1549	−	11.0107i	−0.483860	−	0.351545i
$982$	−42.8933			−1.36878
$983$	−33.1298	−	24.0702i	−1.05668	−	0.767720i	−0.0832055	−	0.996532i	$-0.526516\pi$
$983$	−33.1298	−	24.0702i	−1.05668	−	0.767720i	−0.973471	+	0.228812i	$0.926516\pi$
$984$	−0.0220367	+	0.0678221i	−0.000702505	+	0.00216209i
$985$	−12.5592	−	6.85470i	−0.400171	−	0.218409i
$986$	−46.9751	−	144.574i	−1.49599	−	4.60419i
$987$	−1.16369	+	3.58147i	−0.0370406	+	0.113999i
$988$	18.4809	−	56.8784i	0.587957	−	1.80954i
$989$	14.3925	+	44.2957i	0.457656	+	1.40852i
$990$	−2.00219	+	1.89171i	−0.0636338	+	0.0601224i
$991$	1.74388	−	5.36712i	0.0553963	−	0.170492i	−0.919530	−	0.393019i	$-0.871431\pi$
$991$	1.74388	−	5.36712i	0.0553963	−	0.170492i	0.974927	+	0.222527i	$0.0714305\pi$
$992$	18.2529	+	13.2615i	0.579530	+	0.421053i
$993$	7.92526			0.251500
$994$	−9.78522	−	7.10938i	−0.310368	−	0.225496i
$995$	2.32996	+	4.91246i	0.0738646	+	0.155735i
$996$	18.6734	−	13.5670i	0.591688	−	0.429887i
$997$	4.28980	−	3.11672i	0.135859	−	0.0987076i	−0.517780	−	0.855514i	$-0.673241\pi$
$997$	4.28980	−	3.11672i	0.135859	−	0.0987076i	0.653639	+	0.756806i	$0.273241\pi$
$998$	−3.36002	−	10.3411i	−0.106360	−	0.327341i
$999$	3.24233			0.102583

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.n.c.106.6	✓	24
25.21	even	5	inner	525.2.n.c.421.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.n.c.106.6	✓	24	1.1	even	1	trivial
525.2.n.c.421.6	yes	24	25.21	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.625840 + 1.92614i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.70029 + 1.23534i) q^{4} +(0.958238 + 2.02034i) q^{5} +(-1.63847 - 1.19042i) q^{6} +1.00000 q^{7} +(-0.166599 - 0.121041i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.625840 + 1.92614i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.70029 + 1.23534i) q^{4} +(0.958238 + 2.02034i) q^{5} +(-1.63847 - 1.19042i) q^{6} +1.00000 q^{7} +(-0.166599 - 0.121041i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-3.29175 + 3.11011i) q^{10} +(0.187958 + 0.578475i) q^{11} +(0.649455 - 1.99882i) q^{12} +(-1.19248 + 3.67009i) q^{13} +(0.625840 + 1.92614i) q^{14} +(-1.96276 - 1.07125i) q^{15} +(-1.17003 + 3.60099i) q^{16} +(-5.86368 - 4.26021i) q^{17} +2.02526 q^{18} +(5.96571 + 4.33434i) q^{19} +(-4.12509 - 2.25143i) q^{20} +(-0.809017 + 0.587785i) q^{21} +(-0.996591 + 0.724066i) q^{22} +(-1.55424 - 4.78347i) q^{23} +0.205928 q^{24} +(-3.16356 + 3.87194i) q^{25} -7.81540 q^{26} +(0.309017 + 0.951057i) q^{27} +(-1.70029 + 1.23534i) q^{28} +(8.37817 - 6.08710i) q^{29} +(0.835006 - 4.45097i) q^{30} +(-2.25899 - 1.64126i) q^{31} -8.08010 q^{32} +(-0.492081 - 0.357517i) q^{33} +(4.53603 - 13.9605i) q^{34} +(0.958238 + 2.02034i) q^{35} +(0.649455 + 1.99882i) q^{36} +(1.00193 - 3.08364i) q^{37} +(-4.61496 + 14.2034i) q^{38} +(-1.19248 - 3.67009i) q^{39} +(0.0849031 - 0.452573i) q^{40} +(-0.107012 + 0.329349i) q^{41} +(-1.63847 - 1.19042i) q^{42} -9.26017 q^{43} +(-1.03420 - 0.751387i) q^{44} +(2.21757 - 0.287019i) q^{45} +(8.24091 - 5.98737i) q^{46} +(3.04658 - 2.21347i) q^{47} +(-1.17003 - 3.60099i) q^{48} +1.00000 q^{49} +(-9.43776 - 3.67023i) q^{50} +7.24791 q^{51} +(-2.50622 - 7.71335i) q^{52} +(4.22617 - 3.07049i) q^{53} +(-1.63847 + 1.19042i) q^{54} +(-0.988609 + 0.934057i) q^{55} +(-0.166599 - 0.121041i) q^{56} -7.37402 q^{57} +(16.9680 + 12.3280i) q^{58} +(-1.77895 + 5.47504i) q^{59} +(4.66062 - 0.603222i) q^{60} +(3.17270 + 9.76455i) q^{61} +(1.74751 - 5.37830i) q^{62} +(0.309017 - 0.951057i) q^{63} +(-2.71679 - 8.36141i) q^{64} +(-8.55752 + 1.10760i) q^{65} +(0.380664 - 1.17156i) q^{66} +(12.1621 + 8.83630i) q^{67} +15.2328 q^{68} +(4.06906 + 2.95635i) q^{69} +(-3.29175 + 3.11011i) q^{70} +(-4.83159 + 3.51035i) q^{71} +(-0.166599 + 0.121041i) q^{72} +(0.498912 + 1.53549i) q^{73} +6.56656 q^{74} +(0.283505 - 4.99196i) q^{75} -15.4978 q^{76} +(0.187958 + 0.578475i) q^{77} +(6.32279 - 4.59378i) q^{78} +(11.2750 - 8.19175i) q^{79} +(-8.39639 + 1.08674i) q^{80} +(-0.809017 - 0.587785i) q^{81} -0.701344 q^{82} +(8.88497 + 6.45531i) q^{83} +(0.649455 - 1.99882i) q^{84} +(2.98828 - 15.9289i) q^{85} +(-5.79538 - 17.8363i) q^{86} +(-3.20018 + 9.84913i) q^{87} +(0.0387058 - 0.119124i) q^{88} +(0.243047 + 0.748022i) q^{89} +(1.94068 + 4.09172i) q^{90} +(-1.19248 + 3.67009i) q^{91} +(8.55186 + 6.21329i) q^{92} +2.79227 q^{93} +(6.17011 + 4.48285i) q^{94} +(-3.04028 + 16.2061i) q^{95} +(6.53694 - 4.74937i) q^{96} +(5.02301 - 3.64943i) q^{97} +(0.625840 + 1.92614i) q^{98} +0.608245 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9} - 16 q^{10} + 2 q^{11} + q^{12} + 8 q^{13} + q^{14} - 6 q^{15} + 13 q^{16} + 12 q^{17} - 4 q^{18} + 19 q^{19} + 11 q^{20} - 6 q^{21} - 19 q^{22} - 6 q^{24} + 9 q^{25} - 14 q^{26} - 6 q^{27} - 9 q^{28} + 5 q^{29} - 6 q^{30} + 17 q^{31} - 26 q^{32} + 7 q^{33} - 7 q^{34} - q^{35} + q^{36} + 22 q^{37} - 16 q^{38} + 8 q^{39} + 3 q^{40} + 37 q^{41} + q^{42} + 8 q^{43} + 13 q^{44} + 4 q^{45} + 24 q^{46} - 24 q^{47} + 13 q^{48} + 24 q^{49} - 21 q^{50} - 8 q^{51} + 23 q^{52} - 24 q^{53} + q^{54} - 55 q^{55} + 9 q^{56} - 26 q^{57} + 8 q^{58} - 39 q^{60} + 24 q^{62} - 6 q^{63} - q^{64} - 34 q^{65} + 16 q^{66} + 34 q^{67} + 22 q^{68} + 10 q^{69} - 16 q^{70} - 24 q^{71} + 9 q^{72} + 46 q^{73} + 10 q^{74} + 24 q^{75} - 20 q^{76} + 2 q^{77} - 14 q^{78} + 10 q^{79} + 6 q^{80} - 6 q^{81} - 78 q^{82} + 42 q^{83} + q^{84} - 22 q^{85} - 96 q^{86} - 10 q^{87} - 39 q^{88} + 29 q^{89} + 14 q^{90} + 8 q^{91} + 42 q^{92} - 58 q^{93} + 54 q^{94} - 42 q^{95} + 9 q^{96} - 32 q^{97} + q^{98} - 18 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9 - 16 * q^10 + 2 * q^11 + q^12 + 8 * q^13 + q^14 - 6 * q^15 + 13 * q^16 + 12 * q^17 - 4 * q^18 + 19 * q^19 + 11 * q^20 - 6 * q^21 - 19 * q^22 - 6 * q^24 + 9 * q^25 - 14 * q^26 - 6 * q^27 - 9 * q^28 + 5 * q^29 - 6 * q^30 + 17 * q^31 - 26 * q^32 + 7 * q^33 - 7 * q^34 - q^35 + q^36 + 22 * q^37 - 16 * q^38 + 8 * q^39 + 3 * q^40 + 37 * q^41 + q^42 + 8 * q^43 + 13 * q^44 + 4 * q^45 + 24 * q^46 - 24 * q^47 + 13 * q^48 + 24 * q^49 - 21 * q^50 - 8 * q^51 + 23 * q^52 - 24 * q^53 + q^54 - 55 * q^55 + 9 * q^56 - 26 * q^57 + 8 * q^58 - 39 * q^60 + 24 * q^62 - 6 * q^63 - q^64 - 34 * q^65 + 16 * q^66 + 34 * q^67 + 22 * q^68 + 10 * q^69 - 16 * q^70 - 24 * q^71 + 9 * q^72 + 46 * q^73 + 10 * q^74 + 24 * q^75 - 20 * q^76 + 2 * q^77 - 14 * q^78 + 10 * q^79 + 6 * q^80 - 6 * q^81 - 78 * q^82 + 42 * q^83 + q^84 - 22 * q^85 - 96 * q^86 - 10 * q^87 - 39 * q^88 + 29 * q^89 + 14 * q^90 + 8 * q^91 + 42 * q^92 - 58 * q^93 + 54 * q^94 - 42 * q^95 + 9 * q^96 - 32 * q^97 + q^98 - 18 * q^99

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