LMFDB - Embedded newform 525.2.n.c.421.2

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			421.2
Character	$\chi$	$=$	525.421
Dual form			525.2.n.c.106.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.612004 + 1.88356i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.55520 - 1.12992i) q^{4} +(-2.21075 - 0.335565i) q^{5} +(1.60225 - 1.16410i) q^{6} +1.00000 q^{7} +(-0.124444 + 0.0904141i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.612004 + 1.88356i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.55520 - 1.12992i) q^{4} +(-2.21075 - 0.335565i) q^{5} +(1.60225 - 1.16410i) q^{6} +1.00000 q^{7} +(-0.124444 + 0.0904141i) q^{8} +(0.309017 + 0.951057i) q^{9} +(1.98504 - 3.95870i) q^{10} +(0.881334 - 2.71247i) q^{11} +(0.594033 + 1.82825i) q^{12} +(-0.350788 - 1.07961i) q^{13} +(-0.612004 + 1.88356i) q^{14} +(1.59129 + 1.57092i) q^{15} +(-1.28221 - 3.94622i) q^{16} +(2.41492 - 1.75455i) q^{17} -1.98049 q^{18} +(2.80892 - 2.04080i) q^{19} +(3.05899 + 3.01983i) q^{20} +(-0.809017 - 0.587785i) q^{21} +(4.56970 + 3.32008i) q^{22} +(-1.55205 + 4.77671i) q^{23} +0.153822 q^{24} +(4.77479 + 1.48370i) q^{25} +2.24820 q^{26} +(0.309017 - 0.951057i) q^{27} +(-1.55520 - 1.12992i) q^{28} +(2.78726 + 2.02506i) q^{29} +(-3.93279 + 2.03587i) q^{30} +(6.54839 - 4.75768i) q^{31} +7.91000 q^{32} +(-2.30736 + 1.67640i) q^{33} +(1.82684 + 5.62244i) q^{34} +(-2.21075 - 0.335565i) q^{35} +(0.594033 - 1.82825i) q^{36} +(0.435621 + 1.34070i) q^{37} +(2.12489 + 6.53973i) q^{38} +(-0.350788 + 1.07961i) q^{39} +(0.305455 - 0.158123i) q^{40} +(0.479594 + 1.47604i) q^{41} +(1.60225 - 1.16410i) q^{42} +10.2413 q^{43} +(-4.43552 + 3.22259i) q^{44} +(-0.364017 - 2.20624i) q^{45} +(-8.04734 - 5.84673i) q^{46} +(0.590852 + 0.429279i) q^{47} +(-1.28221 + 3.94622i) q^{48} +1.00000 q^{49} +(-5.71682 + 8.08556i) q^{50} -2.98501 q^{51} +(-0.674331 + 2.07538i) q^{52} +(-6.44055 - 4.67933i) q^{53} +(1.60225 + 1.16410i) q^{54} +(-2.85862 + 5.70083i) q^{55} +(-0.124444 + 0.0904141i) q^{56} -3.47201 q^{57} +(-5.52013 + 4.01061i) q^{58} +(-2.09061 - 6.43423i) q^{59} +(-0.699760 - 4.24112i) q^{60} +(4.53235 - 13.9491i) q^{61} +(4.95372 + 15.2460i) q^{62} +(0.309017 + 0.951057i) q^{63} +(-2.27655 + 7.00649i) q^{64} +(0.413222 + 2.50447i) q^{65} +(-1.74547 - 5.37201i) q^{66} +(-4.17169 + 3.03091i) q^{67} -5.73818 q^{68} +(4.06331 - 2.95217i) q^{69} +(1.98504 - 3.95870i) q^{70} +(-4.85521 - 3.52751i) q^{71} +(-0.124444 - 0.0904141i) q^{72} +(-1.43772 + 4.42485i) q^{73} -2.79189 q^{74} +(-2.99079 - 4.00689i) q^{75} -6.67436 q^{76} +(0.881334 - 2.71247i) q^{77} +(-1.81883 - 1.32146i) q^{78} +(-2.04567 - 1.48626i) q^{79} +(1.51042 + 9.15436i) q^{80} +(-0.809017 + 0.587785i) q^{81} -3.07372 q^{82} +(6.21079 - 4.51240i) q^{83} +(0.594033 + 1.82825i) q^{84} +(-5.92755 + 3.06849i) q^{85} +(-6.26773 + 19.2901i) q^{86} +(-1.06464 - 3.27662i) q^{87} +(0.135568 + 0.417236i) q^{88} +(1.27004 - 3.90879i) q^{89} +(4.37835 + 0.664583i) q^{90} +(-0.350788 - 1.07961i) q^{91} +(7.81103 - 5.67505i) q^{92} -8.09425 q^{93} +(-1.17017 + 0.850182i) q^{94} +(-6.89462 + 3.56911i) q^{95} +(-6.39933 - 4.64938i) q^{96} +(-1.95369 - 1.41944i) q^{97} +(-0.612004 + 1.88356i) q^{98} +2.85206 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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

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 $

$2$	−0.612004	+	1.88356i	−0.432752	+	1.33188i	0.462620	+	0.886557i	$0.346909\pi$
$2$	−0.612004	+	1.88356i	−0.432752	+	1.33188i	−0.895372	+	0.445318i	$0.853091\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	−1.55520	−	1.12992i	−0.777599	−	0.564959i
$5$	−2.21075	−	0.335565i	−0.988675	−	0.150069i
$5$	−2.21075	−	0.335565i	−0.988675	−	0.150069i
$6$	1.60225	−	1.16410i	0.654115	−	0.475242i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−0.124444	+	0.0904141i	−0.0439977	+	0.0319662i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	1.98504	−	3.95870i	0.627725	−	1.25185i
$11$	0.881334	−	2.71247i	0.265732	−	0.817840i	−0.725792	−	0.687915i	$-0.758526\pi$
$11$	0.881334	−	2.71247i	0.265732	−	0.817840i	0.991524	−	0.129925i	$-0.0414737\pi$
$12$	0.594033	+	1.82825i	0.171483	+	0.527769i
$13$	−0.350788	−	1.07961i	−0.0972911	−	0.299431i	0.890553	−	0.454880i	$-0.150318\pi$
$13$	−0.350788	−	1.07961i	−0.0972911	−	0.299431i	−0.987844	+	0.155448i	$0.950318\pi$
$14$	−0.612004	+	1.88356i	−0.163565	+	0.503401i
$15$	1.59129	+	1.57092i	0.410869	+	0.405610i
$16$	−1.28221	−	3.94622i	−0.320551	−	0.986556i
$17$	2.41492	−	1.75455i	0.585705	−	0.425540i	−0.255071	−	0.966922i	$-0.582099\pi$
$17$	2.41492	−	1.75455i	0.585705	−	0.425540i	0.840776	+	0.541382i	$0.182099\pi$
$18$	−1.98049			−0.466805
$19$	2.80892	−	2.04080i	0.644409	−	0.468191i	−0.216953	−	0.976182i	$-0.569612\pi$
$19$	2.80892	−	2.04080i	0.644409	−	0.468191i	0.861362	+	0.507991i	$0.169612\pi$
$20$	3.05899	+	3.01983i	0.684010	+	0.675255i
$21$	−0.809017	−	0.587785i	−0.176542	−	0.128265i
$22$	4.56970	+	3.32008i	0.974264	+	0.707844i
$23$	−1.55205	+	4.77671i	−0.323624	+	0.996013i	0.648434	+	0.761271i	$0.275424\pi$
$23$	−1.55205	+	4.77671i	−0.323624	+	0.996013i	−0.972058	+	0.234742i	$0.924576\pi$
$24$	0.153822			0.0313987
$25$	4.77479	+	1.48370i	0.954958	+	0.296740i
$26$	2.24820			0.440908
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−1.55520	−	1.12992i	−0.293905	−	0.213534i
$29$	2.78726	+	2.02506i	0.517580	+	0.376044i	0.815692	−	0.578487i	$-0.196357\pi$
$29$	2.78726	+	2.02506i	0.517580	+	0.376044i	−0.298111	+	0.954531i	$0.596357\pi$
$30$	−3.93279	+	2.03587i	−0.718027	+	0.371698i
$31$	6.54839	−	4.75768i	1.17613	−	0.854505i	0.184396	−	0.982852i	$-0.440967\pi$
$31$	6.54839	−	4.75768i	1.17613	−	0.854505i	0.991729	+	0.128347i	$0.0409672\pi$
$32$	7.91000			1.39830
$33$	−2.30736	+	1.67640i	−0.401660	+	0.291823i
$34$	1.82684	+	5.62244i	0.313300	+	0.964240i
$35$	−2.21075	−	0.335565i	−0.373684	−	0.0567209i
$36$	0.594033	−	1.82825i	0.0990055	−	0.304708i
$37$	0.435621	+	1.34070i	0.0716157	+	0.220410i	0.980458	−	0.196730i	$-0.0630323\pi$
$37$	0.435621	+	1.34070i	0.0716157	+	0.220410i	−0.908842	+	0.417141i	$0.863032\pi$
$38$	2.12489	+	6.53973i	0.344702	+	1.06088i
$39$	−0.350788	+	1.07961i	−0.0561710	+	0.172877i
$40$	0.305455	−	0.158123i	0.0482966	−	0.0250015i
$41$	0.479594	+	1.47604i	0.0749001	+	0.230519i	0.981497	−	0.191480i	$-0.0613287\pi$
$41$	0.479594	+	1.47604i	0.0749001	+	0.230519i	−0.906596	+	0.421999i	$0.861329\pi$
$42$	1.60225	−	1.16410i	0.247232	−	0.179625i
$43$	10.2413			1.56179			0.780893	−	0.624664i	$-0.214764\pi$
$43$	10.2413			1.56179			0.780893	+	0.624664i	$0.214764\pi$
$44$	−4.43552	+	3.22259i	−0.668679	+	0.485824i
$45$	−0.364017	−	2.20624i	−0.0542644	−	0.328887i
$46$	−8.04734	−	5.84673i	−1.18652	−	0.862054i
$47$	0.590852	+	0.429279i	0.0861846	+	0.0626168i	0.630043	−	0.776560i	$-0.283037\pi$
$47$	0.590852	+	0.429279i	0.0861846	+	0.0626168i	−0.543859	+	0.839177i	$0.683037\pi$
$48$	−1.28221	+	3.94622i	−0.185070	+	0.569588i
$49$	1.00000			0.142857
$50$	−5.71682	+	8.08556i	−0.808481	+	1.14347i
$51$	−2.98501			−0.417985
$52$	−0.674331	+	2.07538i	−0.0935129	+	0.287803i
$53$	−6.44055	−	4.67933i	−0.884678	−	0.642756i	0.0498071	−	0.998759i	$-0.484139\pi$
$53$	−6.44055	−	4.67933i	−0.884678	−	0.642756i	−0.934485	+	0.356003i	$0.884139\pi$
$54$	1.60225	+	1.16410i	0.218038	+	0.158414i
$55$	−2.85862	+	5.70083i	−0.385456	+	0.768700i
$56$	−0.124444	+	0.0904141i	−0.0166296	+	0.0120821i
$57$	−3.47201			−0.459879
$58$	−5.52013	+	4.01061i	−0.724828	+	0.526618i
$59$	−2.09061	−	6.43423i	−0.272174	−	0.837665i	−0.989953	−	0.141394i	$-0.954841\pi$
$59$	−2.09061	−	6.43423i	−0.272174	−	0.837665i	0.717780	−	0.696270i	$-0.245159\pi$
$60$	−0.699760	−	4.24112i	−0.0903387	−	0.547527i
$61$	4.53235	−	13.9491i	0.580308	−	1.78600i	−0.0370396	−	0.999314i	$-0.511793\pi$
$61$	4.53235	−	13.9491i	0.580308	−	1.78600i	0.617348	−	0.786691i	$-0.288207\pi$
$62$	4.95372	+	15.2460i	0.629123	+	1.93624i
$63$	0.309017	+	0.951057i	0.0389325	+	0.119822i
$64$	−2.27655	+	7.00649i	−0.284568	+	0.875811i
$65$	0.413222	+	2.50447i	0.0512539	+	0.310641i
$66$	−1.74547	−	5.37201i	−0.214853	−	0.661249i
$67$	−4.17169	+	3.03091i	−0.509653	+	0.370284i	−0.812692	−	0.582694i	$-0.801999\pi$
$67$	−4.17169	+	3.03091i	−0.509653	+	0.370284i	0.303039	+	0.952978i	$0.401999\pi$
$68$	−5.73818			−0.695857
$69$	4.06331	−	2.95217i	0.489165	−	0.355399i
$70$	1.98504	−	3.95870i	0.237258	−	0.473155i
$71$	−4.85521	−	3.52751i	−0.576207	−	0.418639i	0.261148	−	0.965299i	$-0.415899\pi$
$71$	−4.85521	−	3.52751i	−0.576207	−	0.418639i	−0.837355	+	0.546660i	$0.815899\pi$
$72$	−0.124444	−	0.0904141i	−0.0146659	−	0.0106554i
$73$	−1.43772	+	4.42485i	−0.168273	+	0.517890i	−0.999263	−	0.0383976i	$-0.987775\pi$
$73$	−1.43772	+	4.42485i	−0.168273	+	0.517890i	0.830990	+	0.556287i	$0.187775\pi$
$74$	−2.79189			−0.324551
$75$	−2.99079	−	4.00689i	−0.345347	−	0.462676i
$76$	−6.67436			−0.765601
$77$	0.881334	−	2.71247i	0.100437	−	0.309114i
$78$	−1.81883	−	1.32146i	−0.205942	−	0.149626i
$79$	−2.04567	−	1.48626i	−0.230156	−	0.167218i	0.466731	−	0.884400i	$-0.345432\pi$
$79$	−2.04567	−	1.48626i	−0.230156	−	0.167218i	−0.696886	+	0.717182i	$0.745432\pi$
$80$	1.51042	+	9.15436i	0.168870	+	1.02349i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−3.07372			−0.339435
$83$	6.21079	−	4.51240i	0.681722	−	0.495300i	−0.192206	−	0.981355i	$-0.561564\pi$
$83$	6.21079	−	4.51240i	0.681722	−	0.495300i	0.873929	+	0.486054i	$0.161564\pi$
$84$	0.594033	+	1.82825i	0.0648143	+	0.199478i
$85$	−5.92755	+	3.06849i	−0.642933	+	0.332824i
$86$	−6.26773	+	19.2901i	−0.675867	+	2.08010i
$87$	−1.06464	−	3.27662i	−0.114141	−	0.351290i
$88$	0.135568	+	0.417236i	0.0144516	+	0.0444775i
$89$	1.27004	−	3.90879i	0.134624	−	0.414331i	−0.860907	−	0.508762i	$-0.830103\pi$
$89$	1.27004	−	3.90879i	0.134624	−	0.414331i	0.995531	+	0.0944311i	$0.0301032\pi$
$90$	4.37835	+	0.664583i	0.461519	+	0.0700532i
$91$	−0.350788	−	1.07961i	−0.0367726	−	0.113174i
$92$	7.81103	−	5.67505i	0.814357	−	0.591665i
$93$	−8.09425			−0.839335
$94$	−1.17017	+	0.850182i	−0.120694	+	0.0876896i
$95$	−6.89462	+	3.56911i	−0.707373	+	0.366183i
$96$	−6.39933	−	4.64938i	−0.653129	−	0.474526i
$97$	−1.95369	−	1.41944i	−0.198367	−	0.144122i	0.484168	−	0.874975i	$-0.339122\pi$
$97$	−1.95369	−	1.41944i	−0.198367	−	0.144122i	−0.682535	+	0.730853i	$0.739122\pi$
$98$	−0.612004	+	1.88356i	−0.0618218	+	0.190268i
$99$	2.85206			0.286643
$100$	−5.74929	−	7.70257i	−0.574929	−	0.770257i
$101$	9.64080			0.959295			0.479648	−	0.877461i	$-0.340764\pi$
$101$	9.64080			0.959295			0.479648	+	0.877461i	$0.340764\pi$
$102$	1.82684	−	5.62244i	0.180884	−	0.556704i
$103$	−9.30756	−	6.76234i	−0.917101	−	0.666313i	0.0256996	−	0.999670i	$-0.491819\pi$
$103$	−9.30756	−	6.76234i	−0.917101	−	0.666313i	−0.942801	+	0.333357i	$0.891819\pi$
$104$	0.141266	+	0.102636i	0.0138523	+	0.0100643i
$105$	1.59129	+	1.57092i	0.155294	+	0.153306i
$106$	12.7554	−	9.26736i	1.23892	−	0.900126i
$107$	14.5522			1.40682			0.703408	−	0.710786i	$-0.251661\pi$
$107$	14.5522			1.40682			0.703408	+	0.710786i	$0.251661\pi$
$108$	−1.55520	+	1.12992i	−0.149649	+	0.108726i
$109$	−3.04567	−	9.37360i	−0.291722	−	0.897828i	−0.984303	−	0.176488i	$-0.943526\pi$
$109$	−3.04567	−	9.37360i	−0.291722	−	0.897828i	0.692581	−	0.721340i	$-0.256474\pi$
$110$	−8.98835	−	8.87329i	−0.857005	−	0.846035i
$111$	0.435621	−	1.34070i	0.0413474	−	0.127254i
$112$	−1.28221	−	3.94622i	−0.121157	−	0.372883i
$113$	−0.570886	−	1.75701i	−0.0537045	−	0.165285i	0.920607	−	0.390491i	$-0.127695\pi$
$113$	−0.570886	−	1.75701i	−0.0537045	−	0.165285i	−0.974311	+	0.225205i	$0.927695\pi$
$114$	2.12489	−	6.53973i	0.199014	−	0.612501i
$115$	5.03408	−	10.0393i	0.469430	−	0.936168i
$116$	−2.04658	−	6.29874i	−0.190021	−	0.584823i
$117$	0.918375	−	0.667238i	0.0849038	−	0.0616862i
$118$	13.3987			1.23345
$119$	2.41492	−	1.75455i	0.221376	−	0.160839i
$120$	−0.340061	−	0.0516172i	−0.0310431	−	0.00471198i
$121$	2.31846	+	1.68446i	0.210769	+	0.153132i
$122$	23.5002	+	17.0739i	2.12760	+	1.54580i
$123$	0.479594	−	1.47604i	0.0432436	−	0.133090i
$124$	−15.5598			−1.39731
$125$	−10.0580	−	4.88233i	−0.899612	−	0.436689i
$126$	−1.98049			−0.176436
$127$	−4.48204	+	13.7943i	−0.397716	+	1.22405i	0.529109	+	0.848554i	$0.322526\pi$
$127$	−4.48204	+	13.7943i	−0.397716	+	1.22405i	−0.926826	+	0.375492i	$0.877474\pi$
$128$	0.994804	+	0.722767i	0.0879291	+	0.0638842i
$129$	−8.28540	−	6.01970i	−0.729489	−	0.530005i
$130$	−4.97019	−	0.754417i	−0.435915	−	0.0661667i
$131$	12.6650	−	9.20163i	1.10654	−	0.803950i	0.124427	−	0.992229i	$-0.460291\pi$
$131$	12.6650	−	9.20163i	1.10654	−	0.803950i	0.982116	+	0.188278i	$0.0602907\pi$
$132$	5.48260			0.477199
$133$	2.80892	−	2.04080i	0.243564	−	0.176960i
$134$	−3.15579	−	9.71253i	−0.272619	−	0.839035i
$135$	−1.00230	+	1.99885i	−0.0862642	+	0.172034i
$136$	−0.141888	+	0.436687i	−0.0121668	+	0.0374456i
$137$	−3.03613	−	9.34425i	−0.259394	−	0.798333i	−0.992932	−	0.118685i	$-0.962132\pi$
$137$	−3.03613	−	9.34425i	−0.259394	−	0.798333i	0.733538	−	0.679649i	$-0.237868\pi$
$138$	3.07381	+	9.46022i	0.261660	+	0.805307i
$139$	−5.58741	+	17.1963i	−0.473918	+	1.45857i	0.373493	+	0.927633i	$0.378160\pi$
$139$	−5.58741	+	17.1963i	−0.473918	+	1.45857i	−0.847411	+	0.530937i	$0.821840\pi$
$140$	3.05899	+	3.01983i	0.258532	+	0.255222i
$141$	−0.225685	−	0.694588i	−0.0190061	−	0.0584949i
$142$	9.61568	−	6.98620i	0.806930	−	0.586269i
$143$	−3.23758			−0.270740
$144$	3.35686	−	2.43890i	0.279738	−	0.203242i
$145$	−5.48237	−	5.41220i	−0.455286	−	0.449459i
$146$	−7.45457	−	5.41606i	−0.616944	−	0.448236i
$147$	−0.809017	−	0.587785i	−0.0667266	−	0.0484797i
$148$	0.837409	−	2.57728i	0.0688346	−	0.211851i
$149$	−4.07119			−0.333525			−0.166762	−	0.985997i	$-0.553331\pi$
$149$	−4.07119			−0.333525			−0.166762	+	0.985997i	$0.553331\pi$
$150$	9.37758	−	3.18109i	0.765676	−	0.259735i
$151$	−12.5875			−1.02436			−0.512180	−	0.858878i	$-0.671162\pi$
$151$	−12.5875			−1.02436			−0.512180	+	0.858878i	$0.671162\pi$
$152$	−0.165037	+	0.507931i	−0.0133863	+	0.0411987i
$153$	2.41492	+	1.75455i	0.195235	+	0.141847i
$154$	4.56970	+	3.32008i	0.368237	+	0.267540i
$155$	−16.0733	+	8.32061i	−1.29104	+	0.668328i
$156$	1.76542	−	1.28265i	0.141347	−	0.102694i
$157$	−16.8866			−1.34770			−0.673851	−	0.738868i	$-0.735361\pi$
$157$	−16.8866			−1.34770			−0.673851	+	0.738868i	$0.735361\pi$
$158$	4.05142	−	2.94353i	0.322314	−	0.234175i
$159$	2.46007	+	7.57132i	0.195096	+	0.600445i
$160$	−17.4870	−	2.65432i	−1.38247	−	0.209843i
$161$	−1.55205	+	4.77671i	−0.122318	+	0.376458i
$162$	−0.612004	−	1.88356i	−0.0480836	−	0.147986i
$163$	2.95173	+	9.08450i	0.231198	+	0.711553i	0.997603	+	0.0691959i	$0.0220433\pi$
$163$	2.95173	+	9.08450i	0.231198	+	0.711553i	−0.766406	+	0.642357i	$0.777957\pi$
$164$	0.921939	−	2.83744i	0.0719914	−	0.221567i
$165$	5.66353	−	2.93182i	0.440905	−	0.228242i
$166$	4.69833	+	14.4600i	0.364661	+	1.12231i
$167$	17.9608	−	13.0493i	1.38985	−	1.00979i	0.393969	−	0.919124i	$-0.371102\pi$
$167$	17.9608	−	13.0493i	1.38985	−	1.00979i	0.995882	−	0.0906615i	$-0.0288981\pi$
$168$	0.153822			0.0118676
$169$	9.47471	−	6.88378i	0.728824	−	0.529521i
$170$	−2.15199	−	13.0428i	−0.165050	−	1.00034i
$171$	2.80892	+	2.04080i	0.214803	+	0.156064i
$172$	−15.9273	−	11.5719i	−1.21444	−	0.882345i
$173$	2.59485	−	7.98614i	0.197283	−	0.607175i	−0.802659	−	0.596438i	$-0.796582\pi$
$173$	2.59485	−	7.98614i	0.197283	−	0.607175i	0.999942	−	0.0107370i	$-0.00341776\pi$
$174$	6.82325			0.517269
$175$	4.77479	+	1.48370i	0.360940	+	0.112157i
$176$	−11.8341			−0.892025
$177$	−2.09061	+	6.43423i	−0.157140	+	0.483626i
$178$	6.58516	+	4.78440i	0.493578	+	0.358606i
$179$	−10.0374	−	7.29259i	−0.750230	−	0.545074i	0.145668	−	0.989334i	$-0.453467\pi$
$179$	−10.0374	−	7.29259i	−0.750230	−	0.545074i	−0.895898	+	0.444260i	$0.853467\pi$
$180$	−1.92675	+	3.84245i	−0.143612	+	0.286399i
$181$	12.0940	−	8.78683i	0.898942	−	0.653120i	−0.0392518	−	0.999229i	$-0.512497\pi$
$181$	12.0940	−	8.78683i	0.898942	−	0.653120i	0.938194	+	0.346110i	$0.112497\pi$
$182$	2.24820			0.166648
$183$	−11.8658	+	8.62104i	−0.877149	+	0.637286i
$184$	−0.238739	−	0.734762i	−0.0176000	−	0.0541673i
$185$	−0.513154	−	3.11014i	−0.0377279	−	0.228662i
$186$	4.95372	−	15.2460i	0.363224	−	1.11789i
$187$	−2.63079	−	8.09675i	−0.192383	−	0.592093i
$188$	−0.433842	−	1.33523i	−0.0316412	−	0.0973815i
$189$	0.309017	−	0.951057i	0.0224777	−	0.0691792i
$190$	−2.50308	−	15.1707i	−0.181592	−	1.10060i
$191$	8.46576	+	26.0549i	0.612561	+	1.88527i	0.432572	+	0.901600i	$0.357606\pi$
$191$	8.46576	+	26.0549i	0.612561	+	1.88527i	0.179989	+	0.983669i	$0.442394\pi$
$192$	5.96007	−	4.33025i	0.430131	−	0.312509i
$193$	15.7052			1.13049			0.565243	−	0.824925i	$-0.308783\pi$
$193$	15.7052			1.13049			0.565243	+	0.824925i	$0.308783\pi$
$194$	3.86925	−	2.81118i	0.277796	−	0.201831i
$195$	1.13778	−	2.26904i	0.0814784	−	0.162489i
$196$	−1.55520	−	1.12992i	−0.111086	−	0.0807084i
$197$	−14.1160	−	10.2559i	−1.00573	−	0.730703i	−0.0424184	−	0.999100i	$-0.513506\pi$
$197$	−14.1160	−	10.2559i	−1.00573	−	0.730703i	−0.963309	+	0.268397i	$0.913506\pi$
$198$	−1.74547	+	5.37201i	−0.124045	+	0.381772i
$199$	−23.8504			−1.69071			−0.845354	−	0.534207i	$-0.820610\pi$
$199$	−23.8504			−1.69071			−0.845354	+	0.534207i	$0.820610\pi$
$200$	−0.728343	+	0.247071i	−0.0515016	+	0.0174705i
$201$	5.15649			0.363711
$202$	−5.90021	+	18.1590i	−0.415137	+	1.27766i
$203$	2.78726	+	2.02506i	0.195627	+	0.142131i
$204$	4.64229	+	3.37282i	0.325025	+	0.236145i
$205$	−0.564954	−	3.42408i	−0.0394581	−	0.239148i
$206$	18.4335	−	13.3927i	1.28432	−	0.933116i
$207$	−5.02253			−0.349090
$208$	−3.81062	+	2.76858i	−0.264219	+	0.191966i
$209$	−3.06000	−	9.41772i	−0.211665	−	0.651437i
$210$	−3.93279	+	2.03587i	−0.271389	+	0.140489i
$211$	−6.01634	+	18.5164i	−0.414182	+	1.27472i	0.498799	+	0.866718i	$0.333775\pi$
$211$	−6.01634	+	18.5164i	−0.414182	+	1.27472i	−0.912981	+	0.408003i	$0.866225\pi$
$212$	4.72907	+	14.5546i	0.324794	+	0.999613i
$213$	1.85452	+	5.70764i	0.127070	+	0.391081i
$214$	−8.90602	+	27.4099i	−0.608803	+	1.87370i
$215$	−22.6410	−	3.43663i	−1.54410	−	0.234376i
$216$	0.0475335	+	0.146293i	0.00323425	+	0.00995399i
$217$	6.54839	−	4.75768i	0.444533	−	0.322972i
$218$	19.5197			1.32204
$219$	3.76401	−	2.73471i	0.254348	−	0.184795i
$220$	10.8872	−	5.63592i	0.734014	−	0.379974i
$221$	−2.74136	−	1.99171i	−0.184404	−	0.133977i
$222$	2.25869	+	1.64103i	0.151593	+	0.110139i
$223$	−3.48752	+	10.7335i	−0.233541	+	0.718767i	0.763770	+	0.645488i	$0.223346\pi$
$223$	−3.48752	+	10.7335i	−0.233541	+	0.718767i	−0.997312	+	0.0732783i	$0.976654\pi$
$224$	7.91000			0.528509
$225$	0.0644109	+	4.99959i	0.00429406	+	0.333306i
$226$	3.65881			0.243380
$227$	−0.208288	+	0.641045i	−0.0138246	+	0.0425476i	−0.957731	−	0.287666i	$-0.907121\pi$
$227$	−0.208288	+	0.641045i	−0.0138246	+	0.0425476i	0.943906	+	0.330213i	$0.107121\pi$
$228$	5.39967	+	3.92309i	0.357602	+	0.259813i
$229$	17.4408	+	12.6715i	1.15252	+	0.837357i	0.988814	−	0.149151i	$-0.0476541\pi$
$229$	17.4408	+	12.6715i	1.15252	+	0.837357i	0.163709	+	0.986509i	$0.447654\pi$
$230$	15.8287	+	15.6261i	1.04371	+	1.03035i
$231$	−2.30736	+	1.67640i	−0.151813	+	0.110299i
$232$	−0.529952			−0.0347931
$233$	−2.90098	+	2.10769i	−0.190050	+	0.138079i	−0.678741	−	0.734377i	$-0.737474\pi$
$233$	−2.90098	+	2.10769i	−0.190050	+	0.138079i	0.488692	+	0.872457i	$0.337474\pi$
$234$	0.694731	+	2.13816i	0.0454160	+	0.139776i
$235$	−1.16217	−	1.14730i	−0.0758118	−	0.0748413i
$236$	−4.01884	+	12.3687i	−0.261604	+	0.805135i
$237$	0.781376	+	2.40483i	0.0507558	+	0.156210i
$238$	1.82684	+	5.62244i	0.118416	+	0.364448i
$239$	−6.75116	+	20.7779i	−0.436696	+	1.34401i	0.454642	+	0.890674i	$0.349767\pi$
$239$	−6.75116	+	20.7779i	−0.436696	+	1.34401i	−0.891339	+	0.453338i	$0.850233\pi$
$240$	4.15885	−	8.29383i	0.268452	−	0.535365i
$241$	6.01077	+	18.4993i	0.387188	+	1.19164i	0.934881	+	0.354963i	$0.115506\pi$
$241$	6.01077	+	18.4993i	0.387188	+	1.19164i	−0.547693	+	0.836680i	$0.684494\pi$
$242$	−4.59167	+	3.33605i	−0.295164	+	0.214449i
$243$	1.00000			0.0641500
$244$	−22.8101	+	16.5725i	−1.46027	+	1.06095i
$245$	−2.21075	−	0.335565i	−0.141239	−	0.0214385i
$246$	2.48669	+	1.80669i	0.158546	+	0.115190i
$247$	−3.18861	−	2.31666i	−0.202886	−	0.147405i
$248$	−0.384748	+	1.18413i	−0.0244315	+	0.0751925i
$249$	−7.67695			−0.486507
$250$	15.3517	−	15.9567i	0.970925	−	1.00919i
$251$	4.73675			0.298981			0.149491	−	0.988763i	$-0.452237\pi$
$251$	4.73675			0.298981			0.149491	+	0.988763i	$0.452237\pi$
$252$	0.594033	−	1.82825i	0.0374206	−	0.115169i
$253$	11.5888	+	8.41976i	0.728582	+	0.529346i
$254$	−23.2393	−	16.8843i	−1.45816	−	1.05942i
$255$	6.59910	+	1.00167i	0.413252	+	0.0627267i
$256$	−13.8903	+	10.0919i	−0.868146	+	0.630745i
$257$	−7.37369			−0.459958			−0.229979	−	0.973196i	$-0.573866\pi$
$257$	−7.37369			−0.459958			−0.229979	+	0.973196i	$0.573866\pi$
$258$	16.4091	−	11.9219i	1.02159	−	0.742227i
$259$	0.435621	+	1.34070i	0.0270682	+	0.0833073i
$260$	2.18720	−	4.36185i	0.135644	−	0.270510i
$261$	−1.06464	+	3.27662i	−0.0658994	+	0.202817i
$262$	9.58078	+	29.4866i	0.591902	+	1.82169i
$263$	6.51075	+	20.0380i	0.401470	+	1.23560i	0.923807	+	0.382859i	$0.125061\pi$
$263$	6.51075	+	20.0380i	0.401470	+	1.23560i	−0.522336	+	0.852739i	$0.674939\pi$
$264$	0.135568	−	0.417236i	0.00834365	−	0.0256791i
$265$	12.6682	+	12.5060i	0.778201	+	0.768240i
$266$	2.12489	+	6.53973i	0.130285	+	0.400976i
$267$	−3.32502	+	2.41577i	−0.203488	+	0.147843i
$268$	9.91248			0.605501
$269$	−16.4374	+	11.9425i	−1.00220	+	0.728144i	−0.962560	−	0.271070i	$-0.912623\pi$
$269$	−16.4374	+	11.9425i	−1.00220	+	0.728144i	−0.0396448	+	0.999214i	$0.512623\pi$
$270$	−3.15153	−	3.11119i	−0.191796	−	0.189341i
$271$	22.6865	+	16.4827i	1.37811	+	1.00125i	0.997054	+	0.0767012i	$0.0244388\pi$
$271$	22.6865	+	16.4827i	1.37811	+	1.00125i	0.381054	+	0.924553i	$0.375561\pi$
$272$	−10.0203	−	7.28014i	−0.607567	−	0.441424i
$273$	−0.350788	+	1.07961i	−0.0212307	+	0.0653412i
$274$	19.4585			1.17553
$275$	8.23267	−	11.6438i	0.496449	−	0.702150i
$276$	−9.65497			−0.581161
$277$	7.21506	−	22.2057i	0.433511	−	1.33421i	−0.461094	−	0.887351i	$-0.652543\pi$
$277$	7.21506	−	22.2057i	0.433511	−	1.33421i	0.894605	−	0.446858i	$-0.147457\pi$
$278$	−28.9706	−	21.0484i	−1.73754	−	1.26240i
$279$	6.54839	+	4.75768i	0.392042	+	0.284835i
$280$	0.305455	−	0.158123i	0.0182544	−	0.00944968i
$281$	12.4621	−	9.05428i	0.743429	−	0.540133i	−0.150354	−	0.988632i	$-0.548041\pi$
$281$	12.4621	−	9.05428i	0.743429	−	0.540133i	0.893783	+	0.448499i	$0.148041\pi$
$282$	1.44642			0.0861328
$283$	−22.7130	+	16.5019i	−1.35015	+	0.980939i	−0.351143	+	0.936322i	$0.614207\pi$
$283$	−22.7130	+	16.5019i	−1.35015	+	0.980939i	−0.999004	+	0.0446170i	$0.985793\pi$
$284$	3.56501	+	10.9720i	0.211544	+	0.651067i
$285$	7.67573	+	1.16509i	0.454671	+	0.0690137i
$286$	1.98141	−	6.09816i	0.117163	−	0.360592i
$287$	0.479594	+	1.47604i	0.0283096	+	0.0871279i
$288$	2.44433	+	7.52286i	0.144033	+	0.443289i
$289$	−2.49986	+	7.69377i	−0.147050	+	0.452575i
$290$	13.5494	−	7.01407i	0.795649	−	0.411880i
$291$	0.746242	+	2.29670i	0.0437455	+	0.134635i
$292$	7.23567	−	5.25702i	0.423435	−	0.307644i
$293$	17.4517			1.01954			0.509769	−	0.860311i	$-0.329731\pi$
$293$	17.4517			1.01954			0.509769	+	0.860311i	$0.329731\pi$
$294$	1.60225	−	1.16410i	0.0934450	−	0.0678918i
$295$	2.46270	+	14.9260i	0.143384	+	0.869024i
$296$	−0.175429	−	0.127457i	−0.0101966	−	0.00740828i
$297$	−2.30736	−	1.67640i	−0.133887	−	0.0972744i
$298$	2.49159	−	7.66831i	0.144334	−	0.444213i
$299$	5.70145			0.329723
$300$	0.123819	+	9.61086i	0.00714870	+	0.554883i
$301$	10.2413			0.590300
$302$	7.70363	−	23.7093i	0.443294	−	1.36432i
$303$	−7.79957	−	5.66672i	−0.448074	−	0.325545i
$304$	−11.6550	−	8.46789i	−0.668463	−	0.485667i
$305$	−14.7007	+	29.3171i	−0.841761	+	1.67869i
$306$	−4.78273	+	3.47486i	−0.273410	+	0.198644i
$307$	−20.0674			−1.14530			−0.572652	−	0.819798i	$-0.694086\pi$
$307$	−20.0674			−1.14530			−0.572652	+	0.819798i	$0.694086\pi$
$308$	−4.43552	+	3.22259i	−0.252737	+	0.183624i
$309$	3.55517	+	10.9417i	0.202247	+	0.622451i
$310$	−5.83539	−	35.3673i	−0.331428	−	2.00873i
$311$	−1.53814	+	4.73391i	−0.0872199	+	0.268435i	−0.985148	−	0.171707i	$-0.945072\pi$
$311$	−1.53814	+	4.73391i	−0.0872199	+	0.268435i	0.897928	+	0.440142i	$0.145072\pi$
$312$	−0.0539588	−	0.166068i	−0.00305482	−	0.00940176i
$313$	−2.64744	−	8.14799i	−0.149642	−	0.460552i	0.847936	−	0.530098i	$-0.177845\pi$
$313$	−2.64744	−	8.14799i	−0.149642	−	0.460552i	−0.997579	+	0.0695462i	$0.977845\pi$
$314$	10.3347	−	31.8069i	0.583221	−	1.79497i
$315$	−0.364017	−	2.20624i	−0.0205100	−	0.124308i
$316$	1.50206	+	4.62287i	0.0844976	+	0.260057i
$317$	13.2771	−	9.64641i	0.745719	−	0.541796i	−0.148778	−	0.988871i	$-0.547534\pi$
$317$	13.2771	−	9.64641i	0.745719	−	0.541796i	0.894497	+	0.447074i	$0.147534\pi$
$318$	−15.7666			−0.884146
$319$	7.94941	−	5.77559i	0.445082	−	0.323371i
$320$	7.38399	−	14.7256i	0.412778	−	0.823188i
$321$	−11.7730	−	8.55358i	−0.657104	−	0.477414i
$322$	−8.04734	−	5.84673i	−0.448461	−	0.325826i
$323$	3.20265	−	9.85674i	0.178200	−	0.548444i
$324$	1.92233			0.106796
$325$	−0.0731176	−	5.67540i	−0.00405584	−	0.314814i
$326$	−18.9176			−1.04775
$327$	−3.04567	+	9.37360i	−0.168426	+	0.518361i
$328$	−0.193138	−	0.140323i	−0.0106642	−	0.00774802i
$329$	0.590852	+	0.429279i	0.0325747	+	0.0236669i
$330$	2.05613	+	12.4619i	0.113186	+	0.686003i
$331$	26.7755	−	19.4536i	1.47172	−	1.06926i	0.491604	−	0.870819i	$-0.336411\pi$
$331$	26.7755	−	19.4536i	1.47172	−	1.06926i	0.980112	−	0.198445i	$-0.0635892\pi$
$332$	−14.7576			−0.809931
$333$	−1.14047	+	0.828601i	−0.0624975	+	0.0454071i
$334$	13.5870	+	41.8164i	0.743447	+	2.28809i
$335$	10.2396	−	5.30069i	0.559449	−	0.289608i
$336$	−1.28221	+	3.94622i	−0.0699501	+	0.215284i
$337$	−10.5328	−	32.4167i	−0.573760	−	1.76585i	−0.640364	−	0.768071i	$-0.721217\pi$
$337$	−10.5328	−	32.4167i	−0.573760	−	1.76585i	0.0666047	−	0.997779i	$-0.478783\pi$
$338$	7.16742	+	22.0590i	0.389856	+	1.19985i
$339$	−0.570886	+	1.75701i	−0.0310063	+	0.0954275i
$340$	12.6857	+	1.92553i	0.687976	+	0.104427i
$341$	−7.13374	−	21.9554i	−0.386314	−	1.18895i
$342$	−5.56302	+	4.04177i	−0.300814	+	0.218554i
$343$	1.00000			0.0539949
$344$	−1.27447	+	0.925960i	−0.0687151	+	0.0499244i
$345$	−9.97360	+	5.16299i	−0.536960	+	0.277966i
$346$	13.4543	+	9.77510i	0.723306	+	0.525513i
$347$	2.13183	+	1.54887i	0.114443	+	0.0831476i	0.643535	−	0.765417i	$-0.277467\pi$
$347$	2.13183	+	1.54887i	0.114443	+	0.0831476i	−0.529092	+	0.848565i	$0.677467\pi$
$348$	−2.04658	+	6.29874i	−0.109708	+	0.337648i
$349$	−12.5449			−0.671514			−0.335757	−	0.941949i	$-0.608992\pi$
$349$	−12.5449			−0.671514			−0.335757	+	0.941949i	$0.608992\pi$
$350$	−5.71682	+	8.08556i	−0.305577	+	0.432191i
$351$	−1.13517			−0.0605911
$352$	6.97136	−	21.4556i	0.371575	−	1.14359i
$353$	−4.08386	−	2.96710i	−0.217362	−	0.157923i	0.473776	−	0.880645i	$-0.342891\pi$
$353$	−4.08386	−	2.96710i	−0.217362	−	0.157923i	−0.691138	+	0.722722i	$0.742891\pi$
$354$	−10.8398	−	7.87555i	−0.576127	−	0.418581i
$355$	9.54992	+	9.42768i	0.506857	+	0.500369i
$356$	−6.39178	+	4.64390i	−0.338764	+	0.246126i
$357$	−2.98501			−0.157984
$358$	19.8789	−	14.4429i	1.05063	−	0.763330i
$359$	−8.86265	−	27.2764i	−0.467753	−	1.43959i	−0.855487	−	0.517824i	$-0.826742\pi$
$359$	−8.86265	−	27.2764i	−0.467753	−	1.43959i	0.387735	−	0.921771i	$-0.373258\pi$
$360$	0.244775	+	0.241642i	0.0129008	+	0.0127356i
$361$	−2.14617	+	6.60522i	−0.112956	+	0.347643i
$362$	9.14888	+	28.1574i	0.480854	+	1.47992i
$363$	−0.885571	−	2.72551i	−0.0464804	−	0.143052i
$364$	−0.674331	+	2.07538i	−0.0353445	+	0.108779i
$365$	4.66326	−	9.29978i	0.244086	−	0.486773i
$366$	−8.97626	−	27.6261i	−0.469197	−	1.44404i
$367$	−8.13328	+	5.90917i	−0.424554	+	0.308456i	−0.779467	−	0.626443i	$-0.784510\pi$
$367$	−8.13328	+	5.90917i	−0.424554	+	0.308456i	0.354914	+	0.934899i	$0.384510\pi$
$368$	20.8400			1.08636
$369$	−1.25559	+	0.912243i	−0.0653636	+	0.0474895i
$370$	6.17217	+	0.936862i	0.320876	+	0.0487052i
$371$	−6.44055	−	4.67933i	−0.334377	−	0.242939i
$372$	12.5882	+	9.14584i	0.652666	+	0.474190i
$373$	8.48119	−	26.1024i	0.439140	−	1.35153i	−0.449645	−	0.893207i	$-0.648450\pi$
$373$	8.48119	−	26.1024i	0.439140	−	1.35153i	0.888785	−	0.458325i	$-0.151550\pi$
$374$	16.8607			0.871848
$375$	5.26731	+	9.86182i	0.272003	+	0.509262i
$376$	−0.112341			−0.00579355
$377$	1.20855	−	3.71953i	0.0622434	−	0.191565i
$378$	1.60225	+	1.16410i	0.0824108	+	0.0598749i
$379$	20.8951	+	15.1812i	1.07331	+	0.779807i	0.976505	−	0.215497i	$-0.0691370\pi$
$379$	20.8951	+	15.1812i	1.07331	+	0.779807i	0.0968071	+	0.995303i	$0.469137\pi$
$380$	14.7553	+	2.23968i	0.756931	+	0.114893i
$381$	11.7341	−	8.52534i	0.601157	−	0.436766i
$382$	−54.2570			−2.77603
$383$	−11.6117	+	8.43641i	−0.593331	+	0.431080i	−0.843506	−	0.537120i	$-0.819512\pi$
$383$	−11.6117	+	8.43641i	−0.593331	+	0.431080i	0.250174	+	0.968201i	$0.419512\pi$
$384$	−0.379981	−	1.16946i	−0.0193908	−	0.0596789i
$385$	−2.85862	+	5.70083i	−0.145689	+	0.290541i
$386$	−9.61165	+	29.5816i	−0.489220	+	1.50566i
$387$	3.16474	+	9.74007i	0.160873	+	0.495116i
$388$	1.43452	+	4.41501i	0.0728269	+	0.224138i
$389$	−3.40753	+	10.4873i	−0.172768	+	0.531727i	−0.999525	−	0.0308339i	$-0.990184\pi$
$389$	−3.40753	+	10.4873i	−0.172768	+	0.531727i	0.826756	+	0.562561i	$0.190184\pi$
$390$	3.57754	+	3.53174i	0.181156	+	0.178837i
$391$	4.63288	+	14.2585i	0.234295	+	0.721085i
$392$	−0.124444	+	0.0904141i	−0.00628539	+	0.00456660i
$393$	−15.6548			−0.789678
$394$	27.9567	−	20.3117i	1.40844	−	1.02329i
$395$	4.02371	+	3.97221i	0.202455	+	0.199863i
$396$	−4.43552	−	3.22259i	−0.222893	−	0.161941i
$397$	−17.1123	−	12.4328i	−0.858843	−	0.623986i	0.0687271	−	0.997636i	$-0.478106\pi$
$397$	−17.1123	−	12.4328i	−0.858843	−	0.623986i	−0.927570	+	0.373650i	$0.878106\pi$
$398$	14.5965	−	44.9235i	0.731658	−	2.25181i
$399$	−3.47201			−0.173818
$400$	−0.267261	−	20.7448i	−0.0133630	−	1.03724i
$401$	0.812104			0.0405546			0.0202773	−	0.999794i	$-0.493545\pi$
$401$	0.812104			0.0405546			0.0202773	+	0.999794i	$0.493545\pi$
$402$	−3.15579	+	9.71253i	−0.157397	+	0.484417i
$403$	−7.43356	−	5.40080i	−0.370292	−	0.269033i
$404$	−14.9934	−	10.8933i	−0.745948	−	0.541963i
$405$	1.98577	−	1.02797i	0.0986738	−	0.0510800i
$406$	−5.52013	+	4.01061i	−0.273959	+	0.199043i
$407$	4.02055			0.199291
$408$	0.371468	−	0.269887i	0.0183904	−	0.0133614i
$409$	−6.38826	−	19.6611i	−0.315879	−	0.972176i	−0.975391	−	0.220482i	$-0.929237\pi$
$409$	−6.38826	−	19.6611i	−0.315879	−	0.972176i	0.659512	−	0.751694i	$-0.270763\pi$
$410$	6.79521	+	1.03143i	0.335591	+	0.0509388i
$411$	−3.03613	+	9.34425i	−0.149761	+	0.460918i
$412$	6.83422	+	21.0336i	0.336698	+	1.03625i
$413$	−2.09061	−	6.43423i	−0.102872	−	0.316608i
$414$	3.07381	−	9.46022i	0.151070	−	0.464944i
$415$	−15.2447	+	7.89165i	−0.748332	+	0.387386i
$416$	−2.77473	−	8.53975i	−0.136043	−	0.418696i
$417$	14.6280	−	10.6279i	0.716338	−	0.520450i
$418$	19.6115			0.959231
$419$	−12.8657	+	9.34746i	−0.628529	+	0.456653i	−0.855890	−	0.517157i	$-0.826990\pi$
$419$	−12.8657	+	9.34746i	−0.628529	+	0.456653i	0.227361	+	0.973811i	$0.426990\pi$
$420$	−0.699760	−	4.24112i	−0.0341448	−	0.206946i
$421$	1.00381	+	0.729314i	0.0489229	+	0.0355446i	0.611978	−	0.790875i	$-0.290374\pi$
$421$	1.00381	+	0.729314i	0.0489229	+	0.0355446i	−0.563055	+	0.826419i	$0.690374\pi$
$422$	−31.1946	−	22.6642i	−1.51853	−	1.10328i
$423$	−0.225685	+	0.694588i	−0.0109732	+	0.0337720i
$424$	1.22457			0.0594703
$425$	14.1340	−	4.79457i	0.685599	−	0.232571i
$426$	−11.8856			−0.575861
$427$	4.53235	−	13.9491i	0.219336	−	0.675046i
$428$	−22.6316	−	16.4428i	−1.09394	−	0.794793i
$429$	2.61926	+	1.90300i	0.126459	+	0.0918778i
$430$	20.3294	−	40.5423i	0.980373	−	1.95512i
$431$	7.50955	−	5.45600i	0.361722	−	0.262806i	−0.392048	−	0.919945i	$-0.628233\pi$
$431$	7.50955	−	5.45600i	0.361722	−	0.262806i	0.753770	+	0.657138i	$0.228233\pi$
$432$	−4.14930			−0.199634
$433$	14.1251	−	10.2625i	0.678809	−	0.493184i	−0.194153	−	0.980971i	$-0.562196\pi$
$433$	14.1251	−	10.2625i	0.678809	−	0.493184i	0.872962	+	0.487787i	$0.162196\pi$
$434$	4.95372	+	15.2460i	0.237786	+	0.731830i
$435$	1.25412	+	7.60102i	0.0601306	+	0.364441i
$436$	−5.85478	+	18.0192i	−0.280393	+	0.862961i
$437$	5.38872	+	16.5848i	0.257778	+	0.793358i
$438$	2.84739	+	8.76337i	0.136054	+	0.418730i
$439$	−2.71187	+	8.34627i	−0.129430	+	0.398346i	−0.994682	−	0.102992i	$-0.967158\pi$
$439$	−2.71187	+	8.34627i	−0.129430	+	0.398346i	0.865252	+	0.501337i	$0.167158\pi$
$440$	−0.159697	−	0.967895i	−0.00761326	−	0.0461426i
$441$	0.309017	+	0.951057i	0.0147151	+	0.0452884i
$442$	5.42923	−	3.94457i	0.258242	−	0.187624i
$443$	−0.981770			−0.0466453			−0.0233226	−	0.999728i	$-0.507425\pi$
$443$	−0.981770			−0.0466453			−0.0233226	+	0.999728i	$0.507425\pi$
$444$	−2.19236	+	1.59285i	−0.104045	+	0.0755931i
$445$	−4.11940	+	8.21516i	−0.195278	+	0.389436i
$446$	−18.0827	−	13.1379i	−0.856242	−	0.622096i
$447$	3.29366	+	2.39299i	0.155785	+	0.113184i
$448$	−2.27655	+	7.00649i	−0.107557	+	0.331025i
$449$	14.2518			0.672583			0.336292	−	0.941758i	$-0.390827\pi$
$449$	14.2518			0.672583			0.336292	+	0.941758i	$0.390827\pi$
$450$	−9.45642	−	2.93845i	−0.445780	−	0.138520i
$451$	4.42639			0.208431
$452$	−1.09743	+	3.37755i	−0.0516189	+	0.158867i
$453$	10.1835	+	7.39877i	0.478464	+	0.347625i
$454$	−1.07997	−	0.784644i	−0.0506855	−	0.0368252i
$455$	0.413222	+	2.50447i	0.0193721	+	0.117411i
$456$	0.432072	−	0.313919i	0.0202336	−	0.0147006i
$457$	−3.95335			−0.184930			−0.0924650	−	0.995716i	$-0.529475\pi$
$457$	−3.95335			−0.184930			−0.0924650	+	0.995716i	$0.529475\pi$
$458$	−34.5414	+	25.0958i	−1.61401	+	1.17265i
$459$	−0.922419	−	2.83891i	−0.0430548	−	0.132509i
$460$	−19.1726	+	9.92498i	−0.893925	+	0.462754i
$461$	−6.72436	+	20.6955i	−0.313185	+	0.963884i	0.663310	+	0.748344i	$0.269151\pi$
$461$	−6.72436	+	20.6955i	−0.313185	+	0.963884i	−0.976495	+	0.215539i	$0.930849\pi$
$462$	−1.74547	−	5.37201i	−0.0812067	−	0.249928i
$463$	−4.68252	−	14.4113i	−0.217615	−	0.669751i	−0.998958	−	0.0456480i	$-0.985465\pi$
$463$	−4.68252	−	14.4113i	−0.217615	−	0.669751i	0.781342	−	0.624103i	$-0.214535\pi$
$464$	4.41750	−	13.5957i	0.205077	−	0.631163i
$465$	17.8943	+	2.71615i	0.829830	+	0.125958i
$466$	−2.19453	−	6.75408i	−0.101660	−	0.312877i
$467$	15.5930	−	11.3290i	0.721557	−	0.524242i	−0.165325	−	0.986239i	$-0.552867\pi$
$467$	15.5930	−	11.3290i	0.721557	−	0.524242i	0.886881	+	0.461998i	$0.152867\pi$
$468$	−2.18218			−0.100871
$469$	−4.17169	+	3.03091i	−0.192631	+	0.139954i
$470$	2.87225	−	1.48687i	0.132487	−	0.0685840i
$471$	13.6616	+	9.92572i	0.629493	+	0.457353i
$472$	0.841909	+	0.611683i	0.0387520	+	0.0281550i
$473$	9.02603	−	27.7792i	0.415017	−	1.27729i
$474$	−5.00783			−0.230017
$475$	16.4399	−	5.57680i	0.754315	−	0.255881i
$476$	−5.73818			−0.263009
$477$	2.46007	−	7.57132i	0.112639	−	0.346667i
$478$	−35.0046	−	25.4324i	−1.60108	−	1.16325i
$479$	−8.92027	−	6.48096i	−0.407578	−	0.296122i	0.365043	−	0.930991i	$-0.381054\pi$
$479$	−8.92027	−	6.48096i	−0.407578	−	0.296122i	−0.772620	+	0.634868i	$0.781054\pi$
$480$	12.5871	+	12.4260i	0.574521	+	0.567166i
$481$	1.29463	−	0.940606i	0.0590302	−	0.0428880i
$482$	−38.5230			−1.75468
$483$	4.06331	−	2.95217i	0.184887	−	0.134328i
$484$	−1.70236	−	5.23933i	−0.0773801	−	0.238151i
$485$	3.84279	+	3.79360i	0.174492	+	0.172259i
$486$	−0.612004	+	1.88356i	−0.0277611	+	0.0854398i
$487$	2.61904	+	8.06057i	0.118680	+	0.365259i	0.992697	−	0.120636i	$-0.0384935\pi$
$487$	2.61904	+	8.06057i	0.118680	+	0.365259i	−0.874017	+	0.485896i	$0.838493\pi$
$488$	0.697174	+	2.14568i	0.0315596	+	0.0971304i
$489$	2.95173	−	9.08450i	0.133482	−	0.410815i
$490$	1.98504	−	3.95870i	0.0896750	−	0.178836i
$491$	−1.06397	−	3.27456i	−0.0480162	−	0.147779i	0.924174	−	0.381972i	$-0.124755\pi$
$491$	−1.06397	−	3.27456i	−0.0480162	−	0.147779i	−0.972190	+	0.234194i	$0.924755\pi$
$492$	−2.41367	+	1.75363i	−0.108817	+	0.0790599i
$493$	10.2841			0.463171
$494$	6.31500	−	4.58811i	0.284125	−	0.206429i
$495$	−6.30517	−	0.957051i	−0.283396	−	0.0430162i
$496$	−27.1713	−	19.7411i	−1.22003	−	0.886400i
$497$	−4.85521	−	3.52751i	−0.217786	−	0.158231i
$498$	4.69833	−	14.4600i	0.210537	−	0.647967i
$499$	12.7167			0.569276			0.284638	−	0.958635i	$-0.408127\pi$
$499$	12.7167			0.569276			0.284638	+	0.958635i	$0.408127\pi$
$500$	10.1255	+	18.9577i	0.452827	+	0.847813i
$501$	−22.2008			−0.991859
$502$	−2.89891	+	8.92194i	−0.129385	+	0.398206i
$503$	12.6466	+	9.18832i	0.563885	+	0.409687i	0.832879	−	0.553455i	$-0.186691\pi$
$503$	12.6466	+	9.18832i	0.563885	+	0.409687i	−0.268993	+	0.963142i	$0.586691\pi$
$504$	−0.124444	−	0.0904141i	−0.00554319	−	0.00402736i
$505$	−21.3134	−	3.23512i	−0.948432	−	0.143961i
$506$	−22.9515	+	16.6752i	−1.02032	+	0.741304i
$507$	−11.7114			−0.520121
$508$	22.5569	−	16.3885i	1.00080	−	0.727123i
$509$	−1.50353	−	4.62740i	−0.0666429	−	0.205106i	0.912190	−	0.409768i	$-0.134390\pi$
$509$	−1.50353	−	4.62740i	−0.0666429	−	0.205106i	−0.978833	+	0.204662i	$0.934390\pi$
$510$	−5.92537	+	11.8168i	−0.262380	+	0.523254i
$511$	−1.43772	+	4.42485i	−0.0636011	+	0.195744i
$512$	−9.74779	−	30.0006i	−0.430796	−	1.32585i
$513$	−1.07291	−	3.30208i	−0.0473701	−	0.145790i
$514$	4.51273	−	13.8887i	0.199048	−	0.612606i
$515$	18.3074	+	18.0731i	0.806722	+	0.796396i
$516$	6.08368	+	18.7236i	0.267819	+	0.824263i
$517$	1.68514	−	1.22433i	0.0741125	−	0.0538459i
$518$	−2.79189			−0.122669
$519$	−6.79341	+	4.93570i	−0.298198	+	0.216653i
$520$	−0.277862	−	0.274305i	−0.0121851	−	0.0120291i
$521$	−2.36309	−	1.71688i	−0.103529	−	0.0752181i	0.534816	−	0.844968i	$-0.320381\pi$
$521$	−2.36309	−	1.71688i	−0.103529	−	0.0752181i	−0.638345	+	0.769750i	$0.720381\pi$
$522$	−5.52013	−	4.01061i	−0.241609	−	0.175539i
$523$	−7.34721	+	22.6124i	−0.321271	+	0.988771i	0.651825	+	0.758370i	$0.274004\pi$
$523$	−7.34721	+	22.6124i	−0.321271	+	0.988771i	−0.973096	+	0.230401i	$0.925996\pi$
$524$	−30.0936			−1.31465
$525$	−2.99079	−	4.00689i	−0.130529	−	0.174875i
$526$	−41.7274			−1.81940
$527$	7.46629	−	22.9789i	0.325237	−	1.00098i
$528$	9.57395	+	6.95588i	0.416653	+	0.302716i
$529$	−1.80072	−	1.30830i	−0.0782922	−	0.0568826i
$530$	−31.3088	+	16.2075i	−1.35997	+	0.704009i
$531$	5.47328	−	3.97657i	0.237520	−	0.172568i
$532$	−6.67436			−0.289370
$533$	1.42532	−	1.03555i	0.0617374	−	0.0448548i
$534$	−2.51531	−	7.74131i	−0.108848	−	0.334999i
$535$	−32.1712	−	4.88322i	−1.39088	−	0.211120i
$536$	0.245106	−	0.754359i	0.0105870	−	0.0325833i
$537$	3.83394	+	11.7997i	0.165447	+	0.509193i
$538$	−12.4345	−	38.2695i	−0.536091	−	1.64992i
$539$	0.881334	−	2.71247i	0.0379618	−	0.116834i
$540$	3.81731	−	1.97609i	0.164271	−	0.0850374i
$541$	8.39943	+	25.8508i	0.361120	+	1.11141i	0.952375	+	0.304928i	$0.0986325\pi$
$541$	8.39943	+	25.8508i	0.361120	+	1.11141i	−0.591256	+	0.806484i	$0.701368\pi$
$542$	−44.9304	+	32.6438i	−1.92992	+	1.40217i
$543$	−14.9490			−0.641525
$544$	19.1021	−	13.8785i	0.818994	−	0.595034i
$545$	3.58774	+	21.7447i	0.153682	+	0.931439i
$546$	−1.81883	−	1.32146i	−0.0778387	−	0.0565532i
$547$	34.1496	+	24.8111i	1.46013	+	1.06085i	0.983329	+	0.181837i	$0.0582043\pi$
$547$	34.1496	+	24.8111i	1.46013	+	1.06085i	0.476803	+	0.879010i	$0.341796\pi$
$548$	−5.83645	+	17.9627i	−0.249321	+	0.767330i
$549$	14.6670			0.625972
$550$	16.8934	+	22.6328i	0.720336	+	0.965065i
$551$	11.9619			0.509594
$552$	−0.238739	+	0.734762i	−0.0101614	+	0.0312735i
$553$	−2.04567	−	1.48626i	−0.0869907	−	0.0632024i
$554$	37.4099	+	27.1799i	1.58940	+	1.15476i
$555$	−1.41294	+	2.81778i	−0.0599760	+	0.119608i
$556$	28.1199	−	20.4303i	1.19255	−	0.866439i
$557$	22.1557			0.938768			0.469384	−	0.882994i	$-0.344476\pi$
$557$	22.1557			0.938768			0.469384	+	0.882994i	$0.344476\pi$
$558$	−12.9690	+	9.42253i	−0.549022	+	0.398887i
$559$	−3.59253	−	11.0567i	−0.151948	−	0.467648i
$560$	1.51042	+	9.15436i	0.0638267	+	0.386842i
$561$	−2.63079	+	8.09675i	−0.111072	+	0.341845i
$562$	9.42735	+	29.0144i	0.397669	+	1.22390i
$563$	−11.7413	−	36.1360i	−0.494836	−	1.52295i	−0.817212	−	0.576337i	$-0.804481\pi$
$563$	−11.7413	−	36.1360i	−0.494836	−	1.52295i	0.322376	−	0.946612i	$-0.395519\pi$
$564$	−0.433842	+	1.33523i	−0.0182680	+	0.0562233i
$565$	0.672494	+	4.07586i	0.0282920	+	0.171473i
$566$	−17.1819	−	52.8804i	−0.722209	−	2.22273i
$567$	−0.809017	+	0.587785i	−0.0339755	+	0.0246847i
$568$	0.923140			0.0387341
$569$	−24.1626	+	17.5551i	−1.01295	+	0.735950i	−0.964825	−	0.262891i	$-0.915324\pi$
$569$	−24.1626	+	17.5551i	−1.01295	+	0.735950i	−0.0481228	+	0.998841i	$0.515324\pi$
$570$	−6.89209	+	13.7446i	−0.288678	+	0.575699i
$571$	15.8927	+	11.5467i	0.665088	+	0.483215i	0.868377	−	0.495904i	$-0.165163\pi$
$571$	15.8927	+	11.5467i	0.665088	+	0.483215i	−0.203290	+	0.979119i	$0.565163\pi$
$572$	5.03508	+	3.65820i	0.210527	+	0.152957i
$573$	8.46576	−	26.0549i	0.353662	−	1.08846i
$574$	−3.07372			−0.128294
$575$	−14.4979	+	20.5050i	−0.604604	+	0.855119i
$576$	−7.36706			−0.306961
$577$	−4.60499	+	14.1727i	−0.191708	+	0.590018i	0.808291	+	0.588783i	$0.200393\pi$
$577$	−4.60499	+	14.1727i	−0.191708	+	0.590018i	−0.999999	+	0.00123426i	$0.999607\pi$
$578$	−12.9617	−	9.41724i	−0.539136	−	0.391706i
$579$	−12.7058	−	9.23129i	−0.528034	−	0.383639i
$580$	2.41084	+	14.6117i	0.100105	+	0.606717i
$581$	6.21079	−	4.51240i	0.257667	−	0.187206i
$582$	−4.78266			−0.198248
$583$	−18.3688	+	13.3457i	−0.760759	+	0.552724i
$584$	−0.221153	−	0.680638i	−0.00915137	−	0.0281650i
$585$	−2.25420	+	1.16692i	−0.0931995	+	0.0482462i
$586$	−10.6805	+	32.8712i	−0.441208	+	1.35790i
$587$	2.57964	+	7.93931i	0.106473	+	0.327691i	0.990073	−	0.140551i	$-0.0448875\pi$
$587$	2.57964	+	7.93931i	0.106473	+	0.327691i	−0.883600	+	0.468242i	$0.844888\pi$
$588$	0.594033	+	1.82825i	0.0244975	+	0.0753956i
$589$	8.68441	−	26.7279i	0.357835	−	1.10130i
$590$	−29.6211	−	4.49613i	−1.21948	−	0.185103i
$591$	5.39185	+	16.5944i	0.221791	+	0.682603i
$592$	4.73216	−	3.43812i	0.194491	−	0.141306i
$593$	−41.8505			−1.71859			−0.859296	−	0.511478i	$-0.829098\pi$
$593$	−41.8505			−1.71859			−0.859296	+	0.511478i	$0.829098\pi$
$594$	4.56970	−	3.32008i	0.187497	−	0.136225i
$595$	−5.92755	+	3.06849i	−0.243006	+	0.125796i
$596$	6.33151	+	4.60011i	0.259349	+	0.188428i
$597$	19.2954	+	14.0189i	0.789706	+	0.573755i
$598$	−3.48931	+	10.7390i	−0.142688	+	0.439150i
$599$	35.2440			1.44003			0.720016	−	0.693957i	$-0.244134\pi$
$599$	35.2440			1.44003			0.720016	+	0.693957i	$0.244134\pi$
$600$	0.734467	+	0.228225i	0.0299845	+	0.00931725i
$601$	15.2798			0.623275			0.311638	−	0.950201i	$-0.399122\pi$
$601$	15.2798			0.623275			0.311638	+	0.950201i	$0.399122\pi$
$602$	−6.26773	+	19.2901i	−0.255454	+	0.786206i
$603$	−4.17169	−	3.03091i	−0.169884	−	0.123428i
$604$	19.5761	+	14.2229i	0.796542	+	0.578721i
$605$	−4.56027	−	4.50190i	−0.185401	−	0.183028i
$606$	15.4470	−	11.2229i	0.627490	−	0.455898i
$607$	−24.9492			−1.01266			−0.506328	−	0.862341i	$-0.668997\pi$
$607$	−24.9492			−1.01266			−0.506328	+	0.862341i	$0.668997\pi$
$608$	22.2185	−	16.1427i	0.901080	−	0.654673i
$609$	−1.06464	−	3.27662i	−0.0431413	−	0.132775i
$610$	−46.2235	−	45.6318i	−1.87153	−	1.84758i
$611$	0.256192	−	0.788478i	0.0103644	−	0.0318984i
$612$	−1.77320	−	5.45733i	−0.0716772	−	0.220600i
$613$	−7.21083	−	22.1927i	−0.291243	−	0.896353i	−0.984458	−	0.175622i	$-0.943806\pi$
$613$	−7.21083	−	22.1927i	−0.291243	−	0.896353i	0.693215	−	0.720731i	$-0.256194\pi$
$614$	12.2813	−	37.7980i	0.495633	−	1.52540i
$615$	−1.55557	+	3.10221i	−0.0627266	+	0.125093i
$616$	0.135568	+	0.417236i	0.00546220	+	0.0168109i
$617$	2.87967	−	2.09220i	0.115931	−	0.0842290i	−0.528309	−	0.849052i	$-0.677174\pi$
$617$	2.87967	−	2.09220i	0.115931	−	0.0842290i	0.644240	+	0.764823i	$0.277174\pi$
$618$	−22.7851			−0.916550
$619$	−4.60643	+	3.34677i	−0.185148	+	0.134518i	−0.676498	−	0.736444i	$-0.736503\pi$
$619$	−4.60643	+	3.34677i	−0.185148	+	0.134518i	0.491350	+	0.870962i	$0.336503\pi$
$620$	34.3988	+	5.22134i	1.38149	+	0.209694i
$621$	4.06331	+	2.95217i	0.163055	+	0.118466i
$622$	−7.97523	−	5.79434i	−0.319777	−	0.232332i
$623$	1.27004	−	3.90879i	0.0508832	−	0.156602i
$624$	4.71018			0.188558
$625$	20.5973	+	14.1687i	0.823891	+	0.566748i
$626$	16.9674			0.678156
$627$	−3.06000	+	9.41772i	−0.122205	+	0.376107i
$628$	26.2621	+	19.0805i	1.04797	+	0.761396i
$629$	3.40432	+	2.47338i	0.135739	+	0.0986203i
$630$	4.37835	+	0.664583i	0.174438	+	0.0264776i
$631$	−20.6438	+	14.9986i	−0.821817	+	0.597085i	−0.917232	−	0.398353i	$-0.869582\pi$
$631$	−20.6438	+	14.9986i	−0.821817	+	0.597085i	0.0954155	+	0.995438i	$0.469582\pi$
$632$	0.388951			0.0154716
$633$	15.7510	−	11.4438i	0.626045	−	0.454849i
$634$	10.0439	+	30.9119i	0.398893	+	1.22767i
$635$	14.5375	−	28.9917i	0.576904	−	1.15050i
$636$	4.72907	−	14.5546i	0.187520	−	0.577127i
$637$	−0.350788	−	1.07961i	−0.0138987	−	0.0427759i
$638$	6.01356	+	18.5078i	0.238079	+	0.732733i
$639$	1.85452	−	5.70764i	0.0733638	−	0.225791i
$640$	−1.95672	−	1.93168i	−0.0773463	−	0.0763562i
$641$	−10.4167	−	32.0593i	−0.411435	−	1.26627i	−0.915401	−	0.402543i	$-0.868126\pi$
$641$	−10.4167	−	32.0593i	−0.411435	−	1.26627i	0.503966	−	0.863723i	$-0.331874\pi$
$642$	23.3163	−	16.9403i	0.920219	−	0.668579i
$643$	−8.89206			−0.350669			−0.175334	−	0.984509i	$-0.556101\pi$
$643$	−8.89206			−0.350669			−0.175334	+	0.984509i	$0.556101\pi$
$644$	7.81103	−	5.67505i	0.307798	−	0.223628i
$645$	16.2969	+	16.0883i	0.641690	+	0.633477i
$646$	16.6057	+	12.0647i	0.653342	+	0.474681i
$647$	30.8319	+	22.4007i	1.21213	+	0.880662i	0.995422	−	0.0955755i	$-0.0304691\pi$
$647$	30.8319	+	22.4007i	1.21213	+	0.880662i	0.216705	+	0.976237i	$0.430469\pi$
$648$	0.0475335	−	0.146293i	0.00186729	−	0.00574694i
$649$	−19.2952			−0.757401
$650$	10.7347	+	3.33565i	0.421049	+	0.130835i
$651$	−8.09425			−0.317239
$652$	5.67421	−	17.4634i	0.222219	−	0.683920i
$653$	36.5685	+	26.5686i	1.43104	+	1.03971i	0.989823	+	0.142306i	$0.0454517\pi$
$653$	36.5685	+	26.5686i	1.43104	+	1.03971i	0.441213	+	0.897402i	$0.354548\pi$
$654$	−15.7917	−	11.4734i	−0.617506	−	0.448644i
$655$	−31.0868	+	16.0925i	−1.21466	+	0.628788i
$656$	5.20984	−	3.78517i	0.203410	−	0.147786i
$657$	−4.65257			−0.181514
$658$	−1.17017	+	0.850182i	−0.0456182	+	0.0331435i
$659$	2.50010	+	7.69452i	0.0973902	+	0.299736i	0.987869	−	0.155288i	$-0.0496306\pi$
$659$	2.50010	+	7.69452i	0.0973902	+	0.299736i	−0.890479	+	0.455024i	$0.849631\pi$
$660$	−12.1206	−	1.83977i	−0.471795	−	0.0716129i
$661$	−7.54007	+	23.2059i	−0.293275	+	0.902607i	0.690521	+	0.723313i	$0.257381\pi$
$661$	−7.54007	+	23.2059i	−0.293275	+	0.902607i	−0.983796	+	0.179294i	$0.942619\pi$
$662$	20.2551	+	62.3389i	0.787238	+	2.42287i
$663$	1.04711	+	3.22266i	0.0406662	+	0.125158i
$664$	−0.364913	+	1.12309i	−0.0141614	+	0.0435842i
$665$	−6.89462	+	3.56911i	−0.267362	+	0.138404i
$666$	−0.862743	−	2.65525i	−0.0334306	−	0.102889i
$667$	−13.9991	+	10.1709i	−0.542046	+	0.393820i
$668$	−42.6773			−1.65123
$669$	9.13044	−	6.63365i	0.353003	−	0.256472i
$670$	3.71747	+	22.5309i	0.143618	+	0.870445i
$671$	−33.8421	−	24.5877i	−1.30646	−	0.949198i
$672$	−6.39933	−	4.64938i	−0.246859	−	0.179354i
$673$	−8.68977	+	26.7443i	−0.334966	+	1.03092i	0.631773	+	0.775153i	$0.282327\pi$
$673$	−8.68977	+	26.7443i	−0.334966	+	1.03092i	−0.966739	+	0.255765i	$0.917673\pi$
$674$	67.5048			2.60019
$675$	2.88657	−	4.08261i	0.111104	−	0.157140i
$676$	−22.5132			−0.865891
$677$	−2.34629	+	7.22113i	−0.0901751	+	0.277530i	−0.985966	−	0.166945i	$-0.946610\pi$
$677$	−2.34629	+	7.22113i	−0.0901751	+	0.277530i	0.895791	+	0.444475i	$0.146610\pi$
$678$	−2.96004	−	2.15059i	−0.113679	−	0.0825930i
$679$	−1.95369	−	1.41944i	−0.0749756	−	0.0544730i
$680$	0.460215	−	0.917790i	0.0176484	−	0.0351957i
$681$	0.545305	−	0.396187i	0.0208961	−	0.0151819i
$682$	45.7201			1.75071
$683$	−21.8736	+	15.8921i	−0.836972	+	0.608096i	−0.921523	−	0.388324i	$-0.873054\pi$
$683$	−21.8736	+	15.8921i	−0.836972	+	0.608096i	0.0845514	+	0.996419i	$0.473054\pi$
$684$	−2.06249	−	6.34769i	−0.0788612	−	0.242710i
$685$	3.57651	+	21.6766i	0.136651	+	0.828219i
$686$	−0.612004	+	1.88356i	−0.0233664	+	0.0719145i
$687$	−6.66181	−	20.5029i	−0.254164	−	0.782236i
$688$	−13.1315	−	40.4145i	−0.500633	−	1.54079i
$689$	−2.79261	+	8.59477i	−0.106390	+	0.327435i
$690$	−3.62089	−	21.9456i	−0.137845	−	0.835454i
$691$	−4.66982	−	14.3722i	−0.177648	−	0.546746i	0.822096	−	0.569349i	$-0.192805\pi$
$691$	−4.66982	−	14.3722i	−0.177648	−	0.546746i	−0.999745	+	0.0226031i	$0.992805\pi$
$692$	−13.0592	+	9.48806i	−0.496436	+	0.360682i
$693$	2.85206			0.108341
$694$	−4.22207	+	3.06751i	−0.160268	+	0.116441i
$695$	18.1228	−	36.1417i	0.687438	−	1.37093i
$696$	0.428740	+	0.311498i	0.0162514	+	0.0118073i
$697$	3.74796	+	2.72305i	0.141964	+	0.103143i
$698$	7.67754	−	23.6290i	0.290599	−	0.894373i
$699$	3.58581			0.135628
$700$	−5.74929	−	7.70257i	−0.217303	−	0.291130i
$701$	−40.5129			−1.53015			−0.765076	−	0.643940i	$-0.777299\pi$
$701$	−40.5129			−1.53015			−0.765076	+	0.643940i	$0.777299\pi$
$702$	0.694731	−	2.13816i	0.0262209	−	0.0806998i
$703$	3.95973	+	2.87691i	0.149344	+	0.108505i
$704$	16.9985	+	12.3501i	0.640654	+	0.465462i
$705$	0.265853	+	1.61129i	0.0100126	+	0.0606847i
$706$	8.08804	−	5.87630i	0.304397	−	0.221158i
$707$	9.64080			0.362580
$708$	10.5215	−	7.64429i	0.395421	−	0.287290i
$709$	−6.25474	−	19.2501i	−0.234902	−	0.722953i	−0.997134	−	0.0756501i	$-0.975897\pi$
$709$	−6.25474	−	19.2501i	−0.234902	−	0.722953i	0.762233	−	0.647303i	$-0.224103\pi$
$710$	−23.6021	+	12.2180i	−0.885773	+	0.458534i
$711$	0.781376	−	2.40483i	0.0293039	−	0.0901881i
$712$	0.195360	+	0.601257i	0.00732143	+	0.0225331i
$713$	12.5627	+	38.6639i	0.470475	+	1.44797i
$714$	1.82684	−	5.62244i	0.0683678	−	0.210414i
$715$	7.15747	+	1.08642i	0.267674	+	0.0406298i
$716$	7.37011	+	22.6829i	0.275434	+	0.847698i
$717$	17.6748	−	12.8415i	0.660076	−	0.479573i
$718$	56.8006			2.11978
$719$	23.3948	−	16.9973i	0.872480	−	0.633894i	−0.0587709	−	0.998271i	$-0.518718\pi$
$719$	23.3948	−	16.9973i	0.872480	−	0.633894i	0.931251	+	0.364377i	$0.118718\pi$
$720$	−8.23957	+	4.26534i	−0.307071	+	0.158960i
$721$	−9.30756	−	6.76234i	−0.346632	−	0.251843i
$722$	−11.1278	−	8.08485i	−0.414135	−	0.300887i
$723$	6.01077	−	18.4993i	0.223543	−	0.687995i
$724$	−28.7370			−1.06800
$725$	10.3040	+	13.8047i	0.382681	+	0.512693i
$726$	5.67562			0.210642
$727$	−4.24174	+	13.0547i	−0.157318	+	0.484174i	−0.998388	−	0.0567514i	$-0.981926\pi$
$727$	−4.24174	+	13.0547i	−0.157318	+	0.484174i	0.841071	+	0.540925i	$0.181926\pi$
$728$	0.141266	+	0.102636i	0.00523567	+	0.00380393i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	14.6627	+	14.4750i	0.542691	+	0.535745i
$731$	24.7320	−	17.9689i	0.914747	−	0.664602i
$732$	28.1948			1.04211
$733$	−18.4313	+	13.3911i	−0.680776	+	0.494612i	−0.873615	−	0.486618i	$-0.838230\pi$
$733$	−18.4313	+	13.3911i	−0.680776	+	0.494612i	0.192839	+	0.981230i	$0.438230\pi$
$734$	−6.15265	−	18.9359i	−0.227099	−	0.698937i
$735$	1.59129	+	1.57092i	0.0586956	+	0.0579443i
$736$	−12.2767	+	37.7838i	−0.452525	+	1.39273i
$737$	4.54459	+	13.9868i	0.167402	+	0.515211i
$738$	−0.949831	−	2.92328i	−0.0349638	−	0.107607i
$739$	4.82141	−	14.8388i	0.177358	−	0.545853i	−0.822375	−	0.568946i	$-0.807351\pi$
$739$	4.82141	−	14.8388i	0.177358	−	0.545853i	0.999733	+	0.0230930i	$0.00735140\pi$
$740$	−2.71614	+	5.41670i	−0.0998474	+	0.199122i
$741$	1.21794	+	3.74843i	0.0447421	+	0.137702i
$742$	12.7554	−	9.26736i	0.468267	−	0.340216i
$743$	−49.6425			−1.82121			−0.910604	−	0.413281i	$-0.864383\pi$
$743$	−49.6425			−1.82121			−0.910604	+	0.413281i	$0.864383\pi$
$744$	1.00728	−	0.731835i	0.0369288	−	0.0268304i
$745$	9.00036	+	1.36615i	0.329748	+	0.0500518i
$746$	43.9749	+	31.9496i	1.61003	+	1.16976i
$747$	6.21079	+	4.51240i	0.227241	+	0.165100i
$748$	−5.05726	+	15.5646i	−0.184912	+	0.569099i
$749$	14.5522			0.531726
$750$	−21.7989	+	3.88579i	−0.795983	+	0.141889i
$751$	5.65090			0.206204			0.103102	−	0.994671i	$-0.467123\pi$
$751$	5.65090			0.206204			0.103102	+	0.994671i	$0.467123\pi$
$752$	0.936437	−	2.88206i	0.0341484	−	0.105098i
$753$	−3.83211	−	2.78419i	−0.139650	−	0.101462i
$754$	6.26630	+	4.55273i	0.228205	+	0.165801i
$755$	27.8279	+	4.22394i	1.01276	+	0.153725i
$756$	−1.55520	+	1.12992i	−0.0565620	+	0.0410947i
$757$	−14.7116			−0.534704			−0.267352	−	0.963599i	$-0.586149\pi$
$757$	−14.7116			−0.534704			−0.267352	+	0.963599i	$0.586149\pi$
$758$	−41.3826	+	30.0662i	−1.50308	+	1.09205i
$759$	−4.42653	−	13.6235i	−0.160673	−	0.494500i
$760$	0.535299	−	1.06753i	0.0194173	−	0.0387232i
$761$	14.0707	−	43.3051i	0.510062	−	1.56981i	−0.282029	−	0.959406i	$-0.591008\pi$
$761$	14.0707	−	43.3051i	0.510062	−	1.56981i	0.792091	−	0.610403i	$-0.208992\pi$
$762$	8.87662	+	27.3194i	0.321566	+	0.989678i
$763$	−3.04567	−	9.37360i	−0.110261	−	0.339347i
$764$	16.2740	−	50.0862i	0.588772	−	1.81206i
$765$	−4.75002	−	4.68922i	−0.171737	−	0.169539i
$766$	−8.78402	−	27.0344i	−0.317380	−	0.976794i
$767$	−6.21312	+	4.51410i	−0.224343	+	0.162995i
$768$	17.1694			0.619548
$769$	16.1648	−	11.7444i	0.582917	−	0.423514i	−0.256858	−	0.966449i	$-0.582687\pi$
$769$	16.1648	−	11.7444i	0.582917	−	0.423514i	0.839774	+	0.542936i	$0.182687\pi$
$770$	−8.98835	−	8.87329i	−0.323918	−	0.319771i
$771$	5.96544	+	4.33414i	0.214840	+	0.156090i
$772$	−24.4247	−	17.7456i	−0.879065	−	0.638678i
$773$	7.62370	−	23.4633i	0.274205	−	0.843918i	−0.715223	−	0.698896i	$-0.753675\pi$
$773$	7.62370	−	23.4633i	0.274205	−	0.843918i	0.989429	−	0.145021i	$-0.0463251\pi$
$774$	−20.2828			−0.729050
$775$	38.3262	−	13.0011i	1.37672	−	0.467014i
$776$	0.371462			0.0133347
$777$	0.435621	−	1.34070i	0.0156278	−	0.0480975i
$778$	−17.6680	−	12.8365i	−0.633428	−	0.460212i
$779$	4.35944	+	3.16732i	0.156193	+	0.113481i
$780$	−4.33331	+	2.24321i	−0.155157	+	0.0803197i
$781$	−13.8473	+	10.0607i	−0.495496	+	0.359999i
$782$	−29.6921			−1.06179
$783$	2.78726	−	2.02506i	0.0996084	−	0.0723697i
$784$	−1.28221	−	3.94622i	−0.0457931	−	0.140937i
$785$	37.3321	+	5.66657i	1.33244	+	0.202249i
$786$	9.58078	−	29.4866i	0.341735	−	1.05175i
$787$	−4.69592	−	14.4526i	−0.167391	−	0.515178i	0.831813	−	0.555056i	$-0.187303\pi$
$787$	−4.69592	−	14.4526i	−0.167391	−	0.515178i	−0.999205	+	0.0398779i	$0.987303\pi$
$788$	10.3649	+	31.9000i	0.369235	+	1.13639i
$789$	6.51075	−	20.0380i	0.231789	−	0.713373i
$790$	−9.94441	+	5.14788i	−0.353806	+	0.183153i
$791$	−0.570886	−	1.75701i	−0.0202984	−	0.0624720i
$792$	−0.354922	+	0.257866i	−0.0126116	+	0.00916288i
$793$	−16.6496			−0.591244
$794$	33.8907	−	24.6231i	1.20274	−	0.873840i
$795$	−2.89792	−	17.5638i	−0.102779	−	0.622923i
$796$	37.0921	+	26.9490i	1.31469	+	0.955181i
$797$	−24.5456	−	17.8334i	−0.869450	−	0.631692i	0.0609893	−	0.998138i	$-0.480574\pi$
$797$	−24.5456	−	17.8334i	−0.869450	−	0.631692i	−0.930439	+	0.366446i	$0.880574\pi$
$798$	2.12489	−	6.53973i	0.0752201	−	0.231504i
$799$	2.18005			0.0771247
$800$	37.7686	+	11.7361i	1.33532	+	0.414932i
$801$	4.10995			0.145218
$802$	−0.497011	+	1.52964i	−0.0175501	+	0.0540136i
$803$	10.7352	+	7.79955i	0.378836	+	0.275240i
$804$	−8.01936	−	5.82641i	−0.282821	−	0.205482i
$805$	5.03408	−	10.0393i	0.177428	−	0.353838i
$806$	14.7221	−	10.6962i	0.518563	−	0.376758i
$807$	20.3177			0.715217
$808$	−1.19974	+	0.871664i	−0.0422068	+	0.0306650i
$809$	13.4798	+	41.4866i	0.473925	+	1.45859i	0.847402	+	0.530952i	$0.178165\pi$
$809$	13.4798	+	41.4866i	0.473925	+	1.45859i	−0.373477	+	0.927639i	$0.621835\pi$
$810$	0.720930	+	4.36943i	0.0253309	+	0.153526i
$811$	14.2458	−	43.8441i	0.500238	−	1.53957i	−0.308394	−	0.951259i	$-0.599791\pi$
$811$	14.2458	−	43.8441i	0.500238	−	1.53957i	0.808632	−	0.588315i	$-0.200209\pi$
$812$	−2.04658	−	6.29874i	−0.0718211	−	0.221042i
$813$	−8.66548	−	26.6696i	−0.303912	−	0.935344i
$814$	−2.46059	+	7.57292i	−0.0862437	+	0.265431i
$815$	−3.47709	−	21.0740i	−0.121797	−	0.738191i
$816$	3.82740	+	11.7795i	0.133986	+	0.412366i
$817$	28.7670	−	20.9005i	1.00643	−	0.731214i
$818$	40.9423			1.43152
$819$	0.918375	−	0.667238i	0.0320906	−	0.0233152i
$820$	−2.99032	+	5.96348i	−0.104426	+	0.208254i
$821$	21.4140	+	15.5582i	0.747354	+	0.542984i	0.895005	−	0.446055i	$-0.147172\pi$
$821$	21.4140	+	15.5582i	0.747354	+	0.542984i	−0.147652	+	0.989039i	$0.547172\pi$
$822$	−15.7423	−	11.4374i	−0.549075	−	0.398927i
$823$	17.2011	−	52.9397i	0.599594	−	1.84536i	0.0692135	−	0.997602i	$-0.477951\pi$
$823$	17.2011	−	52.9397i	0.599594	−	1.84536i	0.530381	−	0.847760i	$-0.322049\pi$
$824$	1.76968			0.0616499
$825$	−13.5044	+	4.58102i	−0.470164	+	0.159491i
$826$	13.3987			0.466200
$827$	11.5083	−	35.4189i	0.400183	−	1.23164i	−0.524668	−	0.851307i	$-0.675811\pi$
$827$	11.5083	−	35.4189i	0.400183	−	1.23164i	0.924851	−	0.380330i	$-0.124189\pi$
$828$	7.81103	+	5.67505i	0.271452	+	0.197222i
$829$	−37.4573	−	27.2143i	−1.30095	−	0.945192i	−0.300981	−	0.953630i	$-0.597314\pi$
$829$	−37.4573	−	27.2143i	−1.30095	−	0.945192i	−0.999964	+	0.00843835i	$0.997314\pi$
$830$	−5.53455	−	33.5439i	−0.192107	−	1.16433i
$831$	−18.8893	+	13.7239i	−0.655261	+	0.476075i
$832$	8.36289			0.289931
$833$	2.41492	−	1.75455i	0.0836722	−	0.0607914i
$834$	11.0658	+	34.0570i	0.383177	+	1.17930i
$835$	−44.0857	+	22.8217i	−1.52565	+	0.789776i
$836$	−5.88234	+	18.1040i	−0.203445	+	0.626139i
$837$	−2.50126	−	7.69809i	−0.0864562	−	0.266085i
$838$	−9.73261	−	29.9539i	−0.336207	−	1.03474i
$839$	−17.8610	+	54.9706i	−0.616632	+	1.89780i	−0.244287	+	0.969703i	$0.578554\pi$
$839$	−17.8610	+	54.9706i	−0.616632	+	1.89780i	−0.372345	+	0.928094i	$0.621446\pi$
$840$	−0.340061	−	0.0516172i	−0.0117332	−	0.00178096i
$841$	−5.29357	−	16.2919i	−0.182537	−	0.561790i
$842$	−1.98804	+	1.44440i	−0.0685125	+	0.0497772i
$843$	−15.4041			−0.530544
$844$	30.2786	−	21.9987i	1.04223	−	0.757226i
$845$	−23.2561	+	12.0389i	−0.800035	+	0.414151i
$846$	−1.17017	−	0.850182i	−0.0402314	−	0.0292299i
$847$	2.31846	+	1.68446i	0.0796631	+	0.0578786i
$848$	−10.2076	+	31.4157i	−0.350530	+	1.07882i
$849$	28.0748			0.963524
$850$	0.380783	+	29.5564i	0.0130608	+	1.01378i
$851$	−7.08026			−0.242708
$852$	3.56501	−	10.9720i	0.122135	−	0.375894i
$853$	22.2525	+	16.1674i	0.761910	+	0.553560i	0.899496	−	0.436930i	$-0.143934\pi$
$853$	22.2525	+	16.1674i	0.761910	+	0.553560i	−0.137585	+	0.990490i	$0.543934\pi$
$854$	23.5002	+	17.0739i	0.804159	+	0.584256i
$855$	−5.52498	−	5.45426i	−0.188950	−	0.186532i
$856$	−1.81094	+	1.31573i	−0.0618967	+	0.0449706i
$857$	−9.61585			−0.328471			−0.164236	−	0.986421i	$-0.552516\pi$
$857$	−9.61585			−0.328471			−0.164236	+	0.986421i	$0.552516\pi$
$858$	−5.18741	+	3.76887i	−0.177095	+	0.128667i
$859$	−9.09868	−	28.0029i	−0.310443	−	0.955446i	−0.977590	−	0.210519i	$-0.932485\pi$
$859$	−9.09868	−	28.0029i	−0.310443	−	0.955446i	0.667147	−	0.744926i	$-0.267515\pi$
$860$	31.3281	+	30.9271i	1.06828	+	1.05460i
$861$	0.479594	−	1.47604i	0.0163445	−	0.0503033i
$862$	5.68081	+	17.4837i	0.193489	+	0.595499i
$863$	8.57352	+	26.3866i	0.291846	+	0.898210i	0.984263	+	0.176712i	$0.0565461\pi$
$863$	8.57352	+	26.3866i	0.291846	+	0.898210i	−0.692416	+	0.721498i	$0.743454\pi$
$864$	2.44433	−	7.52286i	0.0831576	−	0.255933i
$865$	−8.41643	+	16.7846i	−0.286167	+	0.570693i
$866$	10.6853	+	32.8861i	0.363103	+	1.11752i
$867$	6.54471	−	4.75501i	0.222270	−	0.161489i
$868$	−15.5598			−0.528135
$869$	−5.83436	+	4.23891i	−0.197917	+	0.143795i
$870$	−15.0845	−	2.28964i	−0.511411	−	0.0776262i
$871$	4.73559	+	3.44061i	0.160459	+	0.116581i
$872$	1.22652	+	0.891120i	0.0415353	+	0.0301771i
$873$	0.746242	−	2.29670i	0.0252565	−	0.0777314i
$874$	−34.5363			−1.16821
$875$	−10.0580	−	4.88233i	−0.340022	−	0.165053i
$876$	−8.94377			−0.302182
$877$	−7.46026	+	22.9603i	−0.251915	+	0.775315i	0.742507	+	0.669839i	$0.233637\pi$
$877$	−7.46026	+	22.9603i	−0.251915	+	0.775315i	−0.994422	+	0.105476i	$0.966363\pi$
$878$	−14.0610	−	10.2159i	−0.474535	−	0.344770i
$879$	−14.1187	−	10.2578i	−0.476212	−	0.345989i
$880$	26.1621	+	3.97110i	0.881924	+	0.133866i
$881$	−11.3288	+	8.23085i	−0.381677	+	0.277305i	−0.762036	−	0.647534i	$-0.775800\pi$
$881$	−11.3288	+	8.23085i	−0.381677	+	0.277305i	0.380359	+	0.924839i	$0.375800\pi$
$882$	−1.98049			−0.0666865
$883$	−24.4349	+	17.7530i	−0.822301	+	0.597437i	−0.917371	−	0.398034i	$-0.869693\pi$
$883$	−24.4349	+	17.7530i	−0.822301	+	0.597437i	0.0950694	+	0.995471i	$0.469693\pi$
$884$	2.01289	+	6.19502i	0.0677007	+	0.208361i
$885$	6.78090	−	13.5229i	0.227938	−	0.454567i
$886$	0.600847	−	1.84922i	0.0201859	−	0.0621257i
$887$	−2.95015	−	9.07963i	−0.0990564	−	0.304864i	0.889233	−	0.457454i	$-0.151239\pi$
$887$	−2.95015	−	9.07963i	−0.0990564	−	0.304864i	−0.988290	+	0.152590i	$0.951239\pi$
$888$	0.0670080	+	0.206229i	0.00224864	+	0.00692061i
$889$	−4.48204	+	13.7943i	−0.150323	+	0.462646i
$890$	−12.9526	−	12.7868i	−0.434173	−	0.428616i
$891$	0.881334	+	2.71247i	0.0295258	+	0.0908711i
$892$	17.5517	−	12.7521i	0.587675	−	0.426971i
$893$	2.53572			0.0848548
$894$	−6.52306	+	4.73928i	−0.218164	+	0.158505i
$895$	19.7430	+	19.4903i	0.659935	+	0.651488i
$896$	0.994804	+	0.722767i	0.0332341	+	0.0241460i
$897$	−4.61257	−	3.35123i	−0.154009	−	0.111894i
$898$	−8.72216	+	26.8440i	−0.291062	+	0.895797i
$899$	27.8866			0.930071
$900$	5.54895	−	7.84813i	0.184965	−	0.261604i
$901$	−23.7636			−0.791679
$902$	−2.70897	+	8.33736i	−0.0901989	+	0.277604i
$903$	−8.28540	−	6.01970i	−0.275721	−	0.200323i
$904$	0.229902	+	0.167033i	0.00764642	+	0.00555545i
$905$	−29.6854	+	15.3671i	−0.986775	+	0.510820i
$906$	−20.1684	+	14.6532i	−0.670049	+	0.486819i
$907$	13.6172			0.452153			0.226076	−	0.974110i	$-0.427410\pi$
$907$	13.6172			0.452153			0.226076	+	0.974110i	$0.427410\pi$
$908$	1.04826	−	0.761603i	0.0347876	−	0.0252747i
$909$	2.97917	+	9.16895i	0.0988129	+	0.304115i
$910$	−4.97019	−	0.754417i	−0.164760	−	0.0250087i
$911$	−9.32822	+	28.7093i	−0.309058	+	0.951182i	0.669074	+	0.743196i	$0.266691\pi$
$911$	−9.32822	+	28.7093i	−0.309058	+	0.951182i	−0.978132	+	0.207986i	$0.933309\pi$
$912$	4.45183	+	13.7013i	0.147415	+	0.453696i
$913$	−6.76596	−	20.8235i	−0.223921	−	0.689157i
$914$	2.41947	−	7.44636i	0.0800289	−	0.246304i
$915$	29.1253	−	15.0772i	0.962852	−	0.498436i
$916$	−12.8062	−	39.4135i	−0.423129	−	1.30226i
$917$	12.6650	−	9.20163i	0.418234	−	0.303865i
$918$	5.91178			0.195118
$919$	−26.3999	+	19.1806i	−0.870851	+	0.632710i	−0.930815	−	0.365490i	$-0.880901\pi$
$919$	−26.3999	+	19.1806i	−0.870851	+	0.632710i	0.0599640	+	0.998201i	$0.480901\pi$
$920$	0.281230	+	1.70448i	0.00927187	+	0.0561951i
$921$	16.2348	+	11.7953i	0.534956	+	0.388668i
$922$	−34.8657	−	25.3314i	−1.14824	−	0.834246i
$923$	−2.10521	+	6.47916i	−0.0692937	+	0.213264i
$924$	5.48260			0.180364
$925$	0.0908001	+	7.04792i	0.00298549	+	0.231734i
$926$	30.0102			0.986198
$927$	3.55517	−	10.9417i	0.116767	−	0.359372i
$928$	22.0472	+	16.0182i	0.723735	+	0.525824i
$929$	45.9314	+	33.3711i	1.50696	+	1.09487i	0.967503	+	0.252860i	$0.0813712\pi$
$929$	45.9314	+	33.3711i	1.50696	+	1.09487i	0.539459	+	0.842012i	$0.318629\pi$
$930$	−16.0674	+	32.0427i	−0.526872	+	1.05072i
$931$	2.80892	−	2.04080i	0.0920585	−	0.0668844i
$932$	6.89312			0.225792
$933$	4.02690	−	2.92571i	0.131835	−	0.0957836i
$934$	11.7958	+	36.3036i	0.385969	+	1.18789i
$935$	3.09903	+	18.7827i	0.101349	+	0.614258i
$936$	−0.0539588	+	0.166068i	−0.00176370	+	0.00542811i
$937$	5.22784	+	16.0896i	0.170786	+	0.525626i	0.999416	−	0.0341711i	$-0.0108791\pi$
$937$	5.22784	+	16.0896i	0.170786	+	0.525626i	−0.828630	+	0.559797i	$0.810879\pi$
$938$	−3.15579	−	9.71253i	−0.103040	−	0.317125i
$939$	−2.64744	+	8.14799i	−0.0863961	+	0.265900i
$940$	0.511058	+	3.09743i	0.0166689	+	0.101027i
$941$	−14.0615	−	43.2767i	−0.458391	−	1.41078i	−0.867108	−	0.498120i	$-0.834024\pi$
$941$	−14.0615	−	43.2767i	−0.458391	−	1.41078i	0.408717	−	0.912661i	$-0.365976\pi$
$942$	−27.0566	+	19.6578i	−0.881552	+	0.640485i
$943$	−7.79497			−0.253839
$944$	−22.7103	+	16.5000i	−0.739158	+	0.537029i
$945$	−1.00230	+	1.99885i	−0.0326048	+	0.0650226i
$946$	46.7998	+	34.0020i	1.52159	+	1.10550i
$947$	−14.1954	−	10.3136i	−0.461288	−	0.335145i	0.332748	−	0.943016i	$-0.392024\pi$
$947$	−14.1954	−	10.3136i	−0.461288	−	0.335145i	−0.794036	+	0.607870i	$0.792024\pi$
$948$	1.50206	−	4.62287i	0.0487847	−	0.150144i
$949$	5.28147			0.171444
$950$	0.442907	+	34.3785i	0.0143698	+	1.11539i
$951$	−16.4114			−0.532178
$952$	−0.141888	+	0.436687i	−0.00459862	+	0.0141531i
$953$	−4.24811	−	3.08643i	−0.137610	−	0.0999793i	0.516851	−	0.856075i	$-0.327104\pi$
$953$	−4.24811	−	3.08643i	−0.137610	−	0.0999793i	−0.654460	+	0.756096i	$0.727104\pi$
$954$	12.7554	+	9.26736i	0.412972	+	0.300042i
$955$	−9.97251	−	60.4416i	−0.322703	−	1.95585i
$956$	33.9767	−	24.6856i	1.09889	−	0.798388i
$957$	−9.82601			−0.317630
$958$	17.6665	−	12.8355i	0.570778	−	0.414695i
$959$	−3.03613	−	9.34425i	−0.0980418	−	0.301742i
$960$	−14.6293	+	7.57308i	−0.472158	+	0.244420i
$961$	10.6663	−	32.8275i	0.344075	−	1.05895i
$962$	0.979363	+	3.01417i	0.0315759	+	0.0971807i
$963$	4.49688	+	13.8400i	0.144910	+	0.445987i
$964$	11.5547	−	35.5617i	0.372152	−	1.14537i
$965$	−34.7202	−	5.27012i	−1.11768	−	0.169651i
$966$	3.07381	+	9.46022i	0.0988982	+	0.304377i
$967$	−39.6415	+	28.8013i	−1.27479	+	0.926186i	−0.999382	−	0.0351423i	$-0.988812\pi$
$967$	−39.6415	+	28.8013i	−1.27479	+	0.926186i	−0.275404	+	0.961329i	$0.588812\pi$
$968$	−0.440817			−0.0141684
$969$	−8.38465	+	6.09180i	−0.269354	+	0.195697i
$970$	−9.49726	+	4.91641i	−0.304939	+	0.157856i
$971$	−19.8624	−	14.4309i	−0.637414	−	0.463109i	0.221547	−	0.975150i	$-0.428890\pi$
$971$	−19.8624	−	14.4309i	−0.637414	−	0.463109i	−0.858961	+	0.512041i	$0.828890\pi$
$972$	−1.55520	−	1.12992i	−0.0498830	−	0.0362421i
$973$	−5.58741	+	17.1963i	−0.179124	+	0.551288i
$974$	−16.7854			−0.537839
$975$	−3.27676	+	4.63447i	−0.104940	+	0.148422i
$976$	−60.8578			−1.94801
$977$	−6.91064	+	21.2688i	−0.221091	+	0.680448i	0.777574	+	0.628791i	$0.216450\pi$
$977$	−6.91064	+	21.2688i	−0.221091	+	0.680448i	−0.998665	+	0.0516563i	$0.983550\pi$
$978$	15.3047	+	11.1195i	0.489390	+	0.355563i
$979$	−9.48314	−	6.88990i	−0.303082	−	0.220202i
$980$	3.05899	+	3.01983i	0.0977158	+	0.0964650i
$981$	7.97366	−	5.79320i	0.254579	−	0.184963i
$982$	6.81897			0.217602
$983$	19.3713	−	14.0740i	0.617847	−	0.448892i	−0.234322	−	0.972159i	$-0.575287\pi$
$983$	19.3713	−	14.0740i	0.617847	−	0.448892i	0.852169	+	0.523267i	$0.175287\pi$
$984$	0.0737720	+	0.227047i	0.00235177	+	0.00723799i
$985$	27.7655	+	27.4101i	0.884681	+	0.873357i
$986$	−6.29390	+	19.3706i	−0.200439	+	0.616886i
$987$	−0.225685	−	0.694588i	−0.00718364	−	0.0221090i
$988$	2.34128	+	7.20573i	0.0744862	+	0.229245i
$989$	−15.8950	+	48.9198i	−0.505432	+	1.55556i
$990$	5.66145	−	11.2904i	0.179933	−	0.358833i
$991$	−3.66264	−	11.2724i	−0.116347	−	0.358081i	0.875878	−	0.482532i	$-0.160283\pi$
$991$	−3.66264	−	11.2724i	−0.116347	−	0.358081i	−0.992226	+	0.124452i	$0.960283\pi$
$992$	51.7978	−	37.6333i	1.64458	−	1.19486i
$993$	−33.0964			−1.05028
$994$	9.61568	−	6.98620i	0.304991	−	0.221589i
$995$	52.7271	+	8.00335i	1.67156	+	0.253723i
$996$	11.9392	+	8.67433i	0.378308	+	0.274857i
$997$	−3.75173	−	2.72579i	−0.118819	−	0.0863268i	0.526789	−	0.849996i	$-0.323396\pi$
$997$	−3.75173	−	2.72579i	−0.118819	−	0.0863268i	−0.645608	+	0.763669i	$0.723396\pi$
$998$	−7.78266	+	23.9526i	−0.246356	+	0.758205i
$999$	1.40970			0.0446009

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.n.c.421.2	yes	24
25.6	even	5	inner	525.2.n.c.106.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.n.c.106.2	✓	24	25.6	even	5	inner
525.2.n.c.421.2	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.612004 + 1.88356i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.55520 - 1.12992i) q^{4} +(-2.21075 - 0.335565i) q^{5} +(1.60225 - 1.16410i) q^{6} +1.00000 q^{7} +(-0.124444 + 0.0904141i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.612004 + 1.88356i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-1.55520 - 1.12992i) q^{4} +(-2.21075 - 0.335565i) q^{5} +(1.60225 - 1.16410i) q^{6} +1.00000 q^{7} +(-0.124444 + 0.0904141i) q^{8} +(0.309017 + 0.951057i) q^{9} +(1.98504 - 3.95870i) q^{10} +(0.881334 - 2.71247i) q^{11} +(0.594033 + 1.82825i) q^{12} +(-0.350788 - 1.07961i) q^{13} +(-0.612004 + 1.88356i) q^{14} +(1.59129 + 1.57092i) q^{15} +(-1.28221 - 3.94622i) q^{16} +(2.41492 - 1.75455i) q^{17} -1.98049 q^{18} +(2.80892 - 2.04080i) q^{19} +(3.05899 + 3.01983i) q^{20} +(-0.809017 - 0.587785i) q^{21} +(4.56970 + 3.32008i) q^{22} +(-1.55205 + 4.77671i) q^{23} +0.153822 q^{24} +(4.77479 + 1.48370i) q^{25} +2.24820 q^{26} +(0.309017 - 0.951057i) q^{27} +(-1.55520 - 1.12992i) q^{28} +(2.78726 + 2.02506i) q^{29} +(-3.93279 + 2.03587i) q^{30} +(6.54839 - 4.75768i) q^{31} +7.91000 q^{32} +(-2.30736 + 1.67640i) q^{33} +(1.82684 + 5.62244i) q^{34} +(-2.21075 - 0.335565i) q^{35} +(0.594033 - 1.82825i) q^{36} +(0.435621 + 1.34070i) q^{37} +(2.12489 + 6.53973i) q^{38} +(-0.350788 + 1.07961i) q^{39} +(0.305455 - 0.158123i) q^{40} +(0.479594 + 1.47604i) q^{41} +(1.60225 - 1.16410i) q^{42} +10.2413 q^{43} +(-4.43552 + 3.22259i) q^{44} +(-0.364017 - 2.20624i) q^{45} +(-8.04734 - 5.84673i) q^{46} +(0.590852 + 0.429279i) q^{47} +(-1.28221 + 3.94622i) q^{48} +1.00000 q^{49} +(-5.71682 + 8.08556i) q^{50} -2.98501 q^{51} +(-0.674331 + 2.07538i) q^{52} +(-6.44055 - 4.67933i) q^{53} +(1.60225 + 1.16410i) q^{54} +(-2.85862 + 5.70083i) q^{55} +(-0.124444 + 0.0904141i) q^{56} -3.47201 q^{57} +(-5.52013 + 4.01061i) q^{58} +(-2.09061 - 6.43423i) q^{59} +(-0.699760 - 4.24112i) q^{60} +(4.53235 - 13.9491i) q^{61} +(4.95372 + 15.2460i) q^{62} +(0.309017 + 0.951057i) q^{63} +(-2.27655 + 7.00649i) q^{64} +(0.413222 + 2.50447i) q^{65} +(-1.74547 - 5.37201i) q^{66} +(-4.17169 + 3.03091i) q^{67} -5.73818 q^{68} +(4.06331 - 2.95217i) q^{69} +(1.98504 - 3.95870i) q^{70} +(-4.85521 - 3.52751i) q^{71} +(-0.124444 - 0.0904141i) q^{72} +(-1.43772 + 4.42485i) q^{73} -2.79189 q^{74} +(-2.99079 - 4.00689i) q^{75} -6.67436 q^{76} +(0.881334 - 2.71247i) q^{77} +(-1.81883 - 1.32146i) q^{78} +(-2.04567 - 1.48626i) q^{79} +(1.51042 + 9.15436i) q^{80} +(-0.809017 + 0.587785i) q^{81} -3.07372 q^{82} +(6.21079 - 4.51240i) q^{83} +(0.594033 + 1.82825i) q^{84} +(-5.92755 + 3.06849i) q^{85} +(-6.26773 + 19.2901i) q^{86} +(-1.06464 - 3.27662i) q^{87} +(0.135568 + 0.417236i) q^{88} +(1.27004 - 3.90879i) q^{89} +(4.37835 + 0.664583i) q^{90} +(-0.350788 - 1.07961i) q^{91} +(7.81103 - 5.67505i) q^{92} -8.09425 q^{93} +(-1.17017 + 0.850182i) q^{94} +(-6.89462 + 3.56911i) q^{95} +(-6.39933 - 4.64938i) q^{96} +(-1.95369 - 1.41944i) q^{97} +(-0.612004 + 1.88356i) q^{98} +2.85206 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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