LMFDB - Embedded newform 370.2.h.d.253.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(117,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("370.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.h (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 3x^{8} - 8x^{7} - 26x^{6} + 12x^{5} + 24x^{4} + 166x^{3} + 113x^{2} - 152x + 160 $ x^10 + 3x^8 - 8x^7 - 26x^6 + 12x^5 + 24x^4 + 166x^3 + 113x^2 - 152x + 160
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.3
Root			$-0.551861 + 1.73844i$ of defining polynomial
Character	$\chi$	$=$	370.253
Dual form			370.2.h.d.117.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.215231 + 0.215231i) q^{3} +1.00000 q^{4} +(2.21058 - 0.336630i) q^{5} +(-0.215231 + 0.215231i) q^{6} +(-0.673260 + 0.673260i) q^{7} +1.00000 q^{8} +2.90735i q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.215231 + 0.215231i) q^{3} +1.00000 q^{4} +(2.21058 - 0.336630i) q^{5} +(-0.215231 + 0.215231i) q^{6} +(-0.673260 + 0.673260i) q^{7} +1.00000 q^{8} +2.90735i q^{9} +(2.21058 - 0.336630i) q^{10} -1.69991i q^{11} +(-0.215231 + 0.215231i) q^{12} +2.06054 q^{13} +(-0.673260 + 0.673260i) q^{14} +(-0.403333 + 0.548239i) q^{15} +1.00000 q^{16} -2.58061i q^{17} +2.90735i q^{18} +(0.312630 + 0.312630i) q^{19} +(2.21058 - 0.336630i) q^{20} -0.289813i q^{21} -1.69991i q^{22} -3.40706 q^{23} +(-0.215231 + 0.215231i) q^{24} +(4.77336 - 1.48830i) q^{25} +2.06054 q^{26} +(-1.27145 - 1.27145i) q^{27} +(-0.673260 + 0.673260i) q^{28} +(-2.85460 + 2.85460i) q^{29} +(-0.403333 + 0.548239i) q^{30} +(-0.382954 - 0.382954i) q^{31} +1.00000 q^{32} +(0.365873 + 0.365873i) q^{33} -2.58061i q^{34} +(-1.26166 + 1.71494i) q^{35} +2.90735i q^{36} +(1.45024 - 5.90735i) q^{37} +(0.312630 + 0.312630i) q^{38} +(-0.443492 + 0.443492i) q^{39} +(2.21058 - 0.336630i) q^{40} +3.11626i q^{41} -0.289813i q^{42} -7.38424 q^{43} -1.69991i q^{44} +(0.978702 + 6.42694i) q^{45} -3.40706 q^{46} +(1.26620 - 1.26620i) q^{47} +(-0.215231 + 0.215231i) q^{48} +6.09344i q^{49} +(4.77336 - 1.48830i) q^{50} +(0.555428 + 0.555428i) q^{51} +2.06054 q^{52} +(-2.69991 - 2.69991i) q^{53} +(-1.27145 - 1.27145i) q^{54} +(-0.572240 - 3.75779i) q^{55} +(-0.673260 + 0.673260i) q^{56} -0.134575 q^{57} +(-2.85460 + 2.85460i) q^{58} +(-3.61030 - 3.61030i) q^{59} +(-0.403333 + 0.548239i) q^{60} +(-4.54721 - 4.54721i) q^{61} +(-0.382954 - 0.382954i) q^{62} +(-1.95740 - 1.95740i) q^{63} +1.00000 q^{64} +(4.55499 - 0.693639i) q^{65} +(0.365873 + 0.365873i) q^{66} +(-8.19766 - 8.19766i) q^{67} -2.58061i q^{68} +(0.733305 - 0.733305i) q^{69} +(-1.26166 + 1.71494i) q^{70} -8.12107 q^{71} +2.90735i q^{72} +(-3.81038 + 3.81038i) q^{73} +(1.45024 - 5.90735i) q^{74} +(-0.707048 + 1.34770i) q^{75} +(0.312630 + 0.312630i) q^{76} +(1.14448 + 1.14448i) q^{77} +(-0.443492 + 0.443492i) q^{78} +(3.33149 + 3.33149i) q^{79} +(2.21058 - 0.336630i) q^{80} -8.17474 q^{81} +3.11626i q^{82} +(-6.48170 - 6.48170i) q^{83} -0.289813i q^{84} +(-0.868711 - 5.70466i) q^{85} -7.38424 q^{86} -1.22880i q^{87} -1.69991i q^{88} +(0.486184 - 0.486184i) q^{89} +(0.978702 + 6.42694i) q^{90} +(-1.38728 + 1.38728i) q^{91} -3.40706 q^{92} +0.164847 q^{93} +(1.26620 - 1.26620i) q^{94} +(0.796335 + 0.585854i) q^{95} +(-0.215231 + 0.215231i) q^{96} -0.430462i q^{97} +6.09344i q^{98} +4.94223 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 10 q^{8}+O(q^{10}) $ 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + 10 * q^8	$ 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 10 q^{8} + 2 q^{10} + 2 q^{12} - 12 q^{13} - 4 q^{14} - 14 q^{15} + 10 q^{16} + 8 q^{19} + 2 q^{20} + 4 q^{23} + 2 q^{24} + 28 q^{25} - 12 q^{26} - 28 q^{27} - 4 q^{28} - 32 q^{29} - 14 q^{30} - 26 q^{31} + 10 q^{32} - 24 q^{33} + 22 q^{35} - 2 q^{37} + 8 q^{38} + 6 q^{39} + 2 q^{40} + 12 q^{43} - 10 q^{45} + 4 q^{46} + 48 q^{47} + 2 q^{48} + 28 q^{50} + 16 q^{51} - 12 q^{52} - 2 q^{53} - 28 q^{54} + 12 q^{55} - 4 q^{56} + 76 q^{57} - 32 q^{58} - 20 q^{59} - 14 q^{60} - 24 q^{61} - 26 q^{62} + 20 q^{63} + 10 q^{64} + 28 q^{65} - 24 q^{66} - 10 q^{67} - 46 q^{69} + 22 q^{70} - 16 q^{71} + 4 q^{73} - 2 q^{74} - 48 q^{75} + 8 q^{76} - 24 q^{77} + 6 q^{78} - 2 q^{79} + 2 q^{80} + 2 q^{81} + 8 q^{83} - 10 q^{85} + 12 q^{86} - 2 q^{89} - 10 q^{90} + 16 q^{91} + 4 q^{92} - 60 q^{93} + 48 q^{94} - 28 q^{95} + 2 q^{96} + 28 q^{99}+O(q^{100}) $ 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + 10 * q^8 + 2 * q^10 + 2 * q^12 - 12 * q^13 - 4 * q^14 - 14 * q^15 + 10 * q^16 + 8 * q^19 + 2 * q^20 + 4 * q^23 + 2 * q^24 + 28 * q^25 - 12 * q^26 - 28 * q^27 - 4 * q^28 - 32 * q^29 - 14 * q^30 - 26 * q^31 + 10 * q^32 - 24 * q^33 + 22 * q^35 - 2 * q^37 + 8 * q^38 + 6 * q^39 + 2 * q^40 + 12 * q^43 - 10 * q^45 + 4 * q^46 + 48 * q^47 + 2 * q^48 + 28 * q^50 + 16 * q^51 - 12 * q^52 - 2 * q^53 - 28 * q^54 + 12 * q^55 - 4 * q^56 + 76 * q^57 - 32 * q^58 - 20 * q^59 - 14 * q^60 - 24 * q^61 - 26 * q^62 + 20 * q^63 + 10 * q^64 + 28 * q^65 - 24 * q^66 - 10 * q^67 - 46 * q^69 + 22 * q^70 - 16 * q^71 + 4 * q^73 - 2 * q^74 - 48 * q^75 + 8 * q^76 - 24 * q^77 + 6 * q^78 - 2 * q^79 + 2 * q^80 + 2 * q^81 + 8 * q^83 - 10 * q^85 + 12 * q^86 - 2 * q^89 - 10 * q^90 + 16 * q^91 + 4 * q^92 - 60 * q^93 + 48 * q^94 - 28 * q^95 + 2 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.215231	+	0.215231i	−0.124264	+	0.124264i	−0.766504	−	0.642240i	$-0.778005\pi$
$3$	−0.215231	+	0.215231i	−0.124264	+	0.124264i	0.642240	+	0.766504i	$0.278005\pi$
$4$	1.00000			0.500000
$5$	2.21058	−	0.336630i	0.988603	−	0.150546i
$5$	2.21058	−	0.336630i	0.988603	−	0.150546i
$6$	−0.215231	+	0.215231i	−0.0878677	+	0.0878677i
$7$	−0.673260	+	0.673260i	−0.254468	+	0.254468i	−0.822800	−	0.568331i	$-0.807589\pi$
$7$	−0.673260	+	0.673260i	−0.254468	+	0.254468i	0.568331	+	0.822800i	$0.307589\pi$
$8$	1.00000			0.353553
$9$			2.90735i			0.969117i
$10$	2.21058	−	0.336630i	0.699048	−	0.106452i
$11$		−	1.69991i		−	0.512541i	−0.966605	−	0.256271i	$-0.917506\pi$
$11$		−	1.69991i		−	0.512541i	0.966605	−	0.256271i	$-0.0824938\pi$
$12$	−0.215231	+	0.215231i	−0.0621319	+	0.0621319i
$13$	2.06054			0.571490			0.285745	−	0.958306i	$-0.407759\pi$
$13$	2.06054			0.571490			0.285745	+	0.958306i	$0.407759\pi$
$14$	−0.673260	+	0.673260i	−0.179936	+	0.179936i
$15$	−0.403333	+	0.548239i	−0.104140	+	0.141555i
$16$	1.00000			0.250000
$17$		−	2.58061i		−	0.625890i	−0.949771	−	0.312945i	$-0.898684\pi$
$17$		−	2.58061i		−	0.625890i	0.949771	−	0.312945i	$-0.101316\pi$
$18$			2.90735i			0.685269i
$19$	0.312630	+	0.312630i	0.0717222	+	0.0717222i	0.742058	−	0.670336i	$-0.233850\pi$
$19$	0.312630	+	0.312630i	0.0717222	+	0.0717222i	−0.670336	+	0.742058i	$0.733850\pi$
$20$	2.21058	−	0.336630i	0.494302	−	0.0752728i
$21$		−	0.289813i		−	0.0632424i
$22$		−	1.69991i		−	0.362421i
$23$	−3.40706			−0.710421			−0.355210	−	0.934786i	$-0.615591\pi$
$23$	−3.40706			−0.710421			−0.355210	+	0.934786i	$0.615591\pi$
$24$	−0.215231	+	0.215231i	−0.0439339	+	0.0439339i
$25$	4.77336	−	1.48830i	0.954672	−	0.297660i
$26$	2.06054			0.404105
$27$	−1.27145	−	1.27145i	−0.244690	−	0.244690i
$28$	−0.673260	+	0.673260i	−0.127234	+	0.127234i
$29$	−2.85460	+	2.85460i	−0.530086	+	0.530086i	−0.920598	−	0.390512i	$-0.872298\pi$
$29$	−2.85460	+	2.85460i	−0.530086	+	0.530086i	0.390512	+	0.920598i	$0.372298\pi$
$30$	−0.403333	+	0.548239i	−0.0736382	+	0.100094i
$31$	−0.382954	−	0.382954i	−0.0687806	−	0.0687806i	0.671880	−	0.740660i	$-0.265487\pi$
$31$	−0.382954	−	0.382954i	−0.0687806	−	0.0687806i	−0.740660	+	0.671880i	$0.765487\pi$
$32$	1.00000			0.176777
$33$	0.365873	+	0.365873i	0.0636903	+	0.0636903i
$34$		−	2.58061i		−	0.442571i
$35$	−1.26166	+	1.71494i	−0.213259	+	0.289877i
$36$			2.90735i			0.484559i
$37$	1.45024	−	5.90735i	0.238418	−	0.971163i
$37$	1.45024	−	5.90735i	0.238418	−	0.971163i
$38$	0.312630	+	0.312630i	0.0507152	+	0.0507152i
$39$	−0.443492	+	0.443492i	−0.0710155	+	0.0710155i
$40$	2.21058	−	0.336630i	0.349524	−	0.0532259i
$41$			3.11626i			0.486678i	0.969941	+	0.243339i	$0.0782427\pi$
$41$			3.11626i			0.486678i	−0.969941	+	0.243339i	$0.921757\pi$
$42$		−	0.289813i		−	0.0447191i
$43$	−7.38424			−1.12609			−0.563043	−	0.826428i	$-0.690369\pi$
$43$	−7.38424			−1.12609			−0.563043	+	0.826428i	$0.690369\pi$
$44$		−	1.69991i		−	0.256271i
$45$	0.978702	+	6.42694i	0.145896	+	0.958072i
$46$	−3.40706			−0.502343
$47$	1.26620	−	1.26620i	0.184695	−	0.184695i	−0.608703	−	0.793398i	$-0.708310\pi$
$47$	1.26620	−	1.26620i	0.184695	−	0.184695i	0.793398	+	0.608703i	$0.208310\pi$
$48$	−0.215231	+	0.215231i	−0.0310659	+	0.0310659i
$49$			6.09344i			0.870492i
$50$	4.77336	−	1.48830i	0.675055	−	0.210477i
$51$	0.555428	+	0.555428i	0.0777754	+	0.0777754i
$52$	2.06054			0.285745
$53$	−2.69991	−	2.69991i	−0.370861	−	0.370861i	0.496930	−	0.867791i	$-0.334461\pi$
$53$	−2.69991	−	2.69991i	−0.370861	−	0.370861i	−0.867791	+	0.496930i	$0.834461\pi$
$54$	−1.27145	−	1.27145i	−0.173022	−	0.173022i
$55$	−0.572240	−	3.75779i	−0.0771608	−	0.506700i
$56$	−0.673260	+	0.673260i	−0.0899681	+	0.0899681i
$57$	−0.134575			−0.0178249
$58$	−2.85460	+	2.85460i	−0.374827	+	0.374827i
$59$	−3.61030	−	3.61030i	−0.470020	−	0.470020i	0.431901	−	0.901921i	$-0.357843\pi$
$59$	−3.61030	−	3.61030i	−0.470020	−	0.470020i	−0.901921	+	0.431901i	$0.857843\pi$
$60$	−0.403333	+	0.548239i	−0.0520701	+	0.0707774i
$61$	−4.54721	−	4.54721i	−0.582211	−	0.582211i	0.353299	−	0.935510i	$-0.385060\pi$
$61$	−4.54721	−	4.54721i	−0.582211	−	0.582211i	−0.935510	+	0.353299i	$0.885060\pi$
$62$	−0.382954	−	0.382954i	−0.0486353	−	0.0486353i
$63$	−1.95740	−	1.95740i	−0.246610	−	0.246610i
$64$	1.00000			0.125000
$65$	4.55499	−	0.693639i	0.564977	−	0.0860353i
$66$	0.365873	+	0.365873i	0.0450358	+	0.0450358i
$67$	−8.19766	−	8.19766i	−1.00150	−	1.00150i	−0.999999	−	0.00150430i	$-0.999521\pi$
$67$	−8.19766	−	8.19766i	−1.00150	−	1.00150i	−0.00150430	−	0.999999i	$-0.500479\pi$
$68$		−	2.58061i		−	0.312945i
$69$	0.733305	−	0.733305i	0.0882795	−	0.0882795i
$70$	−1.26166	+	1.71494i	−0.150797	+	0.204974i
$71$	−8.12107			−0.963794			−0.481897	−	0.876228i	$-0.660052\pi$
$71$	−8.12107			−0.963794			−0.481897	+	0.876228i	$0.660052\pi$
$72$			2.90735i			0.342635i
$73$	−3.81038	+	3.81038i	−0.445971	+	0.445971i	−0.894013	−	0.448042i	$-0.852122\pi$
$73$	−3.81038	+	3.81038i	−0.445971	+	0.445971i	0.448042	+	0.894013i	$0.352122\pi$
$74$	1.45024	−	5.90735i	0.168587	−	0.686716i
$75$	−0.707048	+	1.34770i	−0.0816428	+	0.155619i
$76$	0.312630	+	0.312630i	0.0358611	+	0.0358611i
$77$	1.14448	+	1.14448i	0.130426	+	0.130426i
$78$	−0.443492	+	0.443492i	−0.0502155	+	0.0502155i
$79$	3.33149	+	3.33149i	0.374822	+	0.374822i	0.869230	−	0.494408i	$-0.164615\pi$
$79$	3.33149	+	3.33149i	0.374822	+	0.374822i	−0.494408	+	0.869230i	$0.664615\pi$
$80$	2.21058	−	0.336630i	0.247151	−	0.0376364i
$81$	−8.17474			−0.908305
$82$			3.11626i			0.344133i
$83$	−6.48170	−	6.48170i	−0.711460	−	0.711460i	0.255381	−	0.966840i	$-0.417799\pi$
$83$	−6.48170	−	6.48170i	−0.711460	−	0.711460i	−0.966840	+	0.255381i	$0.917799\pi$
$84$		−	0.289813i		−	0.0316212i
$85$	−0.868711	−	5.70466i	−0.0942249	−	0.618757i
$86$	−7.38424			−0.796263
$87$		−	1.22880i		−	0.131741i
$88$		−	1.69991i		−	0.181211i
$89$	0.486184	−	0.486184i	0.0515354	−	0.0515354i	−0.680869	−	0.732405i	$-0.738398\pi$
$89$	0.486184	−	0.486184i	0.0515354	−	0.0515354i	0.732405	+	0.680869i	$0.238398\pi$
$90$	0.978702	+	6.42694i	0.103164	+	0.677459i
$91$	−1.38728	+	1.38728i	−0.145426	+	0.145426i
$92$	−3.40706			−0.355210
$93$	0.164847			0.0170939
$94$	1.26620	−	1.26620i	0.130599	−	0.130599i
$95$	0.796335	+	0.585854i	0.0817022	+	0.0601073i
$96$	−0.215231	+	0.215231i	−0.0219669	+	0.0219669i
$97$		−	0.430462i		−	0.0437068i	−0.999761	−	0.0218534i	$-0.993043\pi$
$97$		−	0.430462i		−	0.0437068i	0.999761	−	0.0218534i	$-0.00695671\pi$
$98$			6.09344i			0.615531i
$99$	4.94223			0.496712
$100$	4.77336	−	1.48830i	0.477336	−	0.148830i
$101$			2.72028i			0.270677i	0.990799	+	0.135339i	$0.0432123\pi$
$101$			2.72028i			0.270677i	−0.990799	+	0.135339i	$0.956788\pi$
$102$	0.555428	+	0.555428i	0.0549955	+	0.0549955i
$103$			13.5156i			1.33173i	0.746072	+	0.665866i	$0.231938\pi$
$103$			13.5156i			1.33173i	−0.746072	+	0.665866i	$0.768062\pi$
$104$	2.06054			0.202052
$105$	−0.0975597	−	0.640656i	−0.00952085	−	0.0625216i
$106$	−2.69991	−	2.69991i	−0.262238	−	0.262238i
$107$	12.0332	−	12.0332i	1.16329	−	1.16329i	0.179540	−	0.983751i	$-0.442539\pi$
$107$	12.0332	−	12.0332i	1.16329	−	1.16329i	0.983751	−	0.179540i	$-0.0574611\pi$
$108$	−1.27145	−	1.27145i	−0.122345	−	0.122345i
$109$	12.8690	+	12.8690i	1.23262	+	1.23262i	0.962952	+	0.269673i	$0.0869156\pi$
$109$	12.8690	+	12.8690i	1.23262	+	1.23262i	0.269673	+	0.962952i	$0.413084\pi$
$110$	−0.572240	−	3.75779i	−0.0545609	−	0.358291i
$111$	0.959308	+	1.58358i	0.0910535	+	0.150307i
$112$	−0.673260	+	0.673260i	−0.0636171	+	0.0636171i
$113$		−	4.08335i		−	0.384130i	−0.981382	−	0.192065i	$-0.938482\pi$
$113$		−	4.08335i		−	0.384130i	0.981382	−	0.192065i	$-0.0615184\pi$
$114$	−0.134575			−0.0126041
$115$	−7.53158	+	1.14692i	−0.702324	+	0.106951i
$116$	−2.85460	+	2.85460i	−0.265043	+	0.265043i
$117$			5.99071i			0.553841i
$118$	−3.61030	−	3.61030i	−0.332355	−	0.332355i
$119$	1.73742	+	1.73742i	0.159269	+	0.159269i
$120$	−0.403333	+	0.548239i	−0.0368191	+	0.0500472i
$121$	8.11032			0.737301
$122$	−4.54721	−	4.54721i	−0.411685	−	0.411685i
$123$	−0.670716	−	0.670716i	−0.0604764	−	0.0604764i
$124$	−0.382954	−	0.382954i	−0.0343903	−	0.0343903i
$125$	10.0509	−	4.89686i	0.898980	−	0.437989i
$126$	−1.95740	−	1.95740i	−0.174379	−	0.174379i
$127$	−2.18226	+	2.18226i	−0.193644	+	0.193644i	−0.797269	−	0.603624i	$-0.793723\pi$
$127$	−2.18226	+	2.18226i	−0.193644	+	0.193644i	0.603624	+	0.797269i	$0.293723\pi$
$128$	1.00000			0.0883883
$129$	1.58932	−	1.58932i	0.139932	−	0.139932i
$130$	4.55499	−	0.693639i	0.399499	−	0.0608361i
$131$	13.2125	+	13.2125i	1.15438	+	1.15438i	0.985665	+	0.168713i	$0.0539612\pi$
$131$	13.2125	+	13.2125i	1.15438	+	1.15438i	0.168713	+	0.985665i	$0.446039\pi$
$132$	0.365873	+	0.365873i	0.0318451	+	0.0318451i
$133$	−0.420962			−0.0365021
$134$	−8.19766	−	8.19766i	−0.708170	−	0.708170i
$135$	−3.23864	−	2.38263i	−0.278738	−	0.205064i
$136$		−	2.58061i		−	0.221286i
$137$	8.89131	−	8.89131i	0.759636	−	0.759636i	−0.216620	−	0.976256i	$-0.569503\pi$
$137$	8.89131	−	8.89131i	0.759636	−	0.759636i	0.976256	+	0.216620i	$0.0695034\pi$
$138$	0.733305	−	0.733305i	0.0624230	−	0.0624230i
$139$	5.78423			0.490612			0.245306	−	0.969446i	$-0.421112\pi$
$139$	5.78423			0.490612			0.245306	+	0.969446i	$0.421112\pi$
$140$	−1.26166	+	1.71494i	−0.106630	+	0.144939i
$141$			0.545052i			0.0459017i
$142$	−8.12107			−0.681505
$143$		−	3.50272i		−	0.292912i
$144$			2.90735i			0.242279i
$145$	−5.34939	+	7.27128i	−0.444243	+	0.603847i
$146$	−3.81038	+	3.81038i	−0.315349	+	0.315349i
$147$	−1.31150	−	1.31150i	−0.108171	−	0.108171i
$148$	1.45024	−	5.90735i	0.119209	−	0.485581i
$149$		−	8.17437i		−	0.669670i	−0.942277	−	0.334835i	$-0.891319\pi$
$149$		−	8.17437i		−	0.669670i	0.942277	−	0.334835i	$-0.108681\pi$
$150$	−0.707048	+	1.34770i	−0.0577302	+	0.110040i
$151$			11.8313i			0.962814i	0.876497	+	0.481407i	$0.159874\pi$
$151$			11.8313i			0.962814i	−0.876497	+	0.481407i	$0.840126\pi$
$152$	0.312630	+	0.312630i	0.0253576	+	0.0253576i
$153$	7.50274			0.606561
$154$	1.14448	+	1.14448i	0.0922248	+	0.0922248i
$155$	−0.975467	−	0.717639i	−0.0783514	−	0.0576421i
$156$	−0.443492	+	0.443492i	−0.0355077	+	0.0355077i
$157$	−2.88552	+	2.88552i	−0.230290	+	0.230290i	−0.812814	−	0.582524i	$-0.802065\pi$
$157$	−2.88552	+	2.88552i	−0.230290	+	0.230290i	0.582524	+	0.812814i	$0.302065\pi$
$158$	3.33149	+	3.33149i	0.265039	+	0.265039i
$159$	1.16221			0.0921691
$160$	2.21058	−	0.336630i	0.174762	−	0.0266129i
$161$	2.29384	−	2.29384i	0.180780	−	0.180780i
$162$	−8.17474			−0.642269
$163$			11.0884i			0.868507i	0.900791	+	0.434253i	$0.142988\pi$
$163$			11.0884i			0.868507i	−0.900791	+	0.434253i	$0.857012\pi$
$164$			3.11626i			0.243339i
$165$	0.931956	+	0.685629i	0.0725527	+	0.0533761i
$166$	−6.48170	−	6.48170i	−0.503078	−	0.503078i
$167$		−	7.75419i		−	0.600037i	−0.953933	−	0.300018i	$-0.903007\pi$
$167$		−	7.75419i		−	0.600037i	0.953933	−	0.300018i	$-0.0969929\pi$
$168$		−	0.289813i		−	0.0223596i
$169$	−8.75419			−0.673399
$170$	−0.868711	−	5.70466i	−0.0666271	−	0.437527i
$171$	−0.908925	+	0.908925i	−0.0695072	+	0.0695072i
$172$	−7.38424			−0.563043
$173$	−1.45954	+	1.45954i	−0.110967	+	0.110967i	−0.760410	−	0.649443i	$-0.775002\pi$
$173$	−1.45954	+	1.45954i	−0.110967	+	0.110967i	0.649443	+	0.760410i	$0.275002\pi$
$174$		−	1.22880i		−	0.0931549i
$175$	−2.21170	+	4.21572i	−0.167189	+	0.318679i
$176$		−	1.69991i		−	0.128135i
$177$	1.55410			0.116813
$178$	0.486184	−	0.486184i	0.0364410	−	0.0364410i
$179$	−4.31587	+	4.31587i	−0.322583	+	0.322583i	−0.849757	−	0.527174i	$-0.823252\pi$
$179$	−4.31587	+	4.31587i	−0.322583	+	0.322583i	0.527174	+	0.849757i	$0.323252\pi$
$180$	0.978702	+	6.42694i	0.0729481	+	0.479036i
$181$	11.8012			0.877176			0.438588	−	0.898688i	$-0.355479\pi$
$181$	11.8012			0.877176			0.438588	+	0.898688i	$0.355479\pi$
$182$	−1.38728	+	1.38728i	−0.102832	+	0.102832i
$183$	1.95740			0.144695
$184$	−3.40706			−0.251172
$185$	1.21729	−	13.5469i	0.0894969	−	0.995987i
$186$	0.164847			0.0120872
$187$	−4.38680			−0.320795
$188$	1.26620	−	1.26620i	0.0923473	−	0.0923473i
$189$	1.71203			0.124532
$190$	0.796335	+	0.585854i	0.0577722	+	0.0425023i
$191$	−0.707267	+	0.707267i	−0.0511760	+	0.0511760i	−0.732232	−	0.681056i	$-0.761521\pi$
$191$	−0.707267	+	0.707267i	−0.0511760	+	0.0511760i	0.681056	+	0.732232i	$0.261521\pi$
$192$	−0.215231	+	0.215231i	−0.0155330	+	0.0155330i
$193$	8.39923			0.604590			0.302295	−	0.953214i	$-0.402247\pi$
$193$	8.39923			0.604590			0.302295	+	0.953214i	$0.402247\pi$
$194$		−	0.430462i		−	0.0309054i
$195$	−0.831083	+	1.12967i	−0.0595151	+	0.0808972i
$196$			6.09344i			0.435246i
$197$	15.0419	−	15.0419i	1.07169	−	1.07169i	0.0744696	−	0.997223i	$-0.476274\pi$
$197$	15.0419	−	15.0419i	1.07169	−	1.07169i	0.997223	−	0.0744696i	$-0.0237264\pi$
$198$	4.94223			0.351229
$199$	1.52878	−	1.52878i	0.108372	−	0.108372i	−0.650841	−	0.759214i	$-0.725584\pi$
$199$	1.52878	−	1.52878i	0.108372	−	0.108372i	0.759214	+	0.650841i	$0.225584\pi$
$200$	4.77336	−	1.48830i	0.337528	−	0.105239i
$201$	3.52878			0.248901
$202$			2.72028i			0.191398i
$203$		−	3.84378i		−	0.269780i
$204$	0.555428	+	0.555428i	0.0388877	+	0.0388877i
$205$	1.04903	+	6.88875i	0.0732672	+	0.481131i
$206$			13.5156i			0.941676i
$207$		−	9.90551i		−	0.688481i
$208$	2.06054			0.142873
$209$	0.531442	−	0.531442i	0.0367606	−	0.0367606i
$210$	−0.0975597	−	0.640656i	−0.00673226	−	0.0442094i
$211$	24.1444			1.66217			0.831085	−	0.556146i	$-0.187720\pi$
$211$	24.1444			1.66217			0.831085	+	0.556146i	$0.187720\pi$
$212$	−2.69991	−	2.69991i	−0.185430	−	0.185430i
$213$	1.74791	−	1.74791i	0.119765	−	0.119765i
$214$	12.0332	−	12.0332i	0.822571	−	0.822571i
$215$	−16.3235	+	2.48576i	−1.11325	+	0.169527i
$216$	−1.27145	−	1.27145i	−0.0865109	−	0.0865109i
$217$	0.515656			0.0350050
$218$	12.8690	+	12.8690i	0.871597	+	0.871597i
$219$		−	1.64022i		−	0.110836i
$220$	−0.572240	−	3.75779i	−0.0385804	−	0.253350i
$221$		−	5.31745i		−	0.357690i
$222$	0.959308	+	1.58358i	0.0643846	+	0.106283i
$223$	−10.0159	−	10.0159i	−0.670714	−	0.670714i	0.287167	−	0.957881i	$-0.407287\pi$
$223$	−10.0159	−	10.0159i	−0.670714	−	0.670714i	−0.957881	+	0.287167i	$0.907287\pi$
$224$	−0.673260	+	0.673260i	−0.0449841	+	0.0449841i
$225$	4.32700	+	13.8778i	0.288467	+	0.925189i
$226$		−	4.08335i		−	0.271621i
$227$			3.05788i			0.202959i	0.994838	+	0.101479i	$0.0323576\pi$
$227$			3.05788i			0.202959i	−0.994838	+	0.101479i	$0.967642\pi$
$228$	−0.134575			−0.00891247
$229$			26.8791i			1.77622i	0.459632	+	0.888109i	$0.347981\pi$
$229$			26.8791i			1.77622i	−0.459632	+	0.888109i	$0.652019\pi$
$230$	−7.53158	+	1.14692i	−0.496618	+	0.0756255i
$231$	−0.492655			−0.0324143
$232$	−2.85460	+	2.85460i	−0.187414	+	0.187414i
$233$	0.315711	−	0.315711i	0.0206829	−	0.0206829i	−0.696690	−	0.717373i	$-0.745345\pi$
$233$	0.315711	−	0.315711i	0.0206829	−	0.0206829i	0.717373	+	0.696690i	$0.245345\pi$
$234$			5.99071i			0.391625i
$235$	2.37281	−	3.22529i	0.154785	−	0.210395i
$236$	−3.61030	−	3.61030i	−0.235010	−	0.235010i
$237$	−1.43408			−0.0931535
$238$	1.73742	+	1.73742i	0.112620	+	0.112620i
$239$	−7.59846	−	7.59846i	−0.491503	−	0.491503i	0.417276	−	0.908780i	$-0.362985\pi$
$239$	−7.59846	−	7.59846i	−0.491503	−	0.491503i	−0.908780	+	0.417276i	$0.862985\pi$
$240$	−0.403333	+	0.548239i	−0.0260350	+	0.0353887i
$241$	3.57132	−	3.57132i	0.230049	−	0.230049i	−0.582664	−	0.812713i	$-0.697990\pi$
$241$	3.57132	−	3.57132i	0.230049	−	0.230049i	0.812713	+	0.582664i	$0.197990\pi$
$242$	8.11032			0.521351
$243$	5.57380	−	5.57380i	0.357559	−	0.357559i
$244$	−4.54721	−	4.54721i	−0.291106	−	0.291106i
$245$	2.05124	+	13.4701i	0.131049	+	0.860571i
$246$	−0.670716	−	0.670716i	−0.0427633	−	0.0427633i
$247$	0.644185	+	0.644185i	0.0409885	+	0.0409885i
$248$	−0.382954	−	0.382954i	−0.0243176	−	0.0243176i
$249$	2.79013			0.176817
$250$	10.0509	−	4.89686i	0.635675	−	0.309705i
$251$	19.0270	+	19.0270i	1.20097	+	1.20097i	0.973872	+	0.227100i	$0.0729243\pi$
$251$	19.0270	+	19.0270i	1.20097	+	1.20097i	0.227100	+	0.973872i	$0.427076\pi$
$252$	−1.95740	−	1.95740i	−0.123305	−	0.123305i
$253$			5.79168i			0.364120i
$254$	−2.18226	+	2.18226i	−0.136927	+	0.136927i
$255$	1.41479	+	1.04085i	0.0885978	+	0.0651803i
$256$	1.00000			0.0625000
$257$			24.5612i			1.53208i	0.642791	+	0.766042i	$0.277776\pi$
$257$			24.5612i			1.53208i	−0.642791	+	0.766042i	$0.722224\pi$
$258$	1.58932	−	1.58932i	0.0989466	−	0.0989466i
$259$	3.00079	+	4.95357i	0.186460	+	0.307800i
$260$	4.55499	−	0.693639i	0.282488	−	0.0430176i
$261$	−8.29933	−	8.29933i	−0.513715	−	0.513715i
$262$	13.2125	+	13.2125i	0.816269	+	0.816269i
$263$	15.9933	−	15.9933i	0.986188	−	0.986188i	−0.0137182	−	0.999906i	$-0.504367\pi$
$263$	15.9933	−	15.9933i	0.986188	−	0.986188i	0.999906	+	0.0137182i	$0.00436677\pi$
$264$	0.365873	+	0.365873i	0.0225179	+	0.0225179i
$265$	−6.87724	−	5.05950i	−0.422466	−	0.310803i
$266$	−0.420962			−0.0258109
$267$			0.209284i			0.0128080i
$268$	−8.19766	−	8.19766i	−0.500752	−	0.500752i
$269$			8.06679i			0.491841i	0.969290	+	0.245921i	$0.0790902\pi$
$269$			8.06679i			0.491841i	−0.969290	+	0.245921i	$0.920910\pi$
$270$	−3.23864	−	2.38263i	−0.197098	−	0.145002i
$271$	−24.2256			−1.47160			−0.735800	−	0.677199i	$-0.763194\pi$
$271$	−24.2256			−1.47160			−0.735800	+	0.677199i	$0.763194\pi$
$272$		−	2.58061i		−	0.156473i
$273$		−	0.597170i		−	0.0361424i
$274$	8.89131	−	8.89131i	0.537143	−	0.537143i
$275$	−2.52997	−	8.11427i	−0.152563	−	0.489309i
$276$	0.733305	−	0.733305i	0.0441397	−	0.0441397i
$277$	−18.8030			−1.12976			−0.564881	−	0.825173i	$-0.691078\pi$
$277$	−18.8030			−1.12976			−0.564881	+	0.825173i	$0.691078\pi$
$278$	5.78423			0.346915
$279$	1.11338	−	1.11338i	0.0666565	−	0.0666565i
$280$	−1.26166	+	1.71494i	−0.0753985	+	0.102487i
$281$	14.2311	−	14.2311i	0.848954	−	0.848954i	−0.141049	−	0.990003i	$-0.545048\pi$
$281$	14.2311	−	14.2311i	0.848954	−	0.848954i	0.990003	+	0.141049i	$0.0450475\pi$
$282$			0.545052i			0.0324574i
$283$		−	0.905573i		−	0.0538307i	−0.999638	−	0.0269154i	$-0.991432\pi$
$283$		−	0.905573i		−	0.0538307i	0.999638	−	0.0269154i	$-0.00856846\pi$
$284$	−8.12107			−0.481897
$285$	−0.297490	+	0.0453021i	−0.0176218	+	0.00268346i
$286$		−	3.50272i		−	0.207120i
$287$	−2.09805	−	2.09805i	−0.123844	−	0.123844i
$288$			2.90735i			0.171317i
$289$	10.3404			0.608262
$290$	−5.34939	+	7.27128i	−0.314127	+	0.426984i
$291$	0.0926488	+	0.0926488i	0.00543117	+	0.00543117i
$292$	−3.81038	+	3.81038i	−0.222986	+	0.222986i
$293$	−14.1364	−	14.1364i	−0.825855	−	0.825855i	0.161086	−	0.986940i	$-0.448500\pi$
$293$	−14.1364	−	14.1364i	−0.825855	−	0.825855i	−0.986940	+	0.161086i	$0.948500\pi$
$294$	−1.31150	−	1.31150i	−0.0764881	−	0.0764881i
$295$	−9.19619	−	6.76553i	−0.535423	−	0.393904i
$296$	1.45024	−	5.90735i	0.0842936	−	0.343358i
$297$	−2.16134	+	2.16134i	−0.125414	+	0.125414i
$298$		−	8.17437i		−	0.473528i
$299$	−7.02037			−0.405998
$300$	−0.707048	+	1.34770i	−0.0408214	+	0.0778097i
$301$	4.97151	−	4.97151i	0.286553	−	0.286553i
$302$			11.8313i			0.680813i
$303$	−0.585488	−	0.585488i	−0.0336354	−	0.0336354i
$304$	0.312630	+	0.312630i	0.0179305	+	0.0179305i
$305$	−11.5827	−	8.52127i	−0.663225	−	0.487926i
$306$	7.50274			0.428903
$307$	22.5470	+	22.5470i	1.28682	+	1.28682i	0.936705	+	0.350120i	$0.113859\pi$
$307$	22.5470	+	22.5470i	1.28682	+	1.28682i	0.350120	+	0.936705i	$0.386141\pi$
$308$	1.14448	+	1.14448i	0.0652128	+	0.0652128i
$309$	−2.90898	−	2.90898i	−0.165486	−	0.165486i
$310$	−0.975467	−	0.717639i	−0.0554028	−	0.0407591i
$311$	−18.8440	−	18.8440i	−1.06855	−	1.06855i	−0.997471	−	0.0710771i	$-0.977356\pi$
$311$	−18.8440	−	18.8440i	−1.06855	−	1.06855i	−0.0710771	−	0.997471i	$-0.522644\pi$
$312$	−0.443492	+	0.443492i	−0.0251078	+	0.0251078i
$313$	−13.8468			−0.782669			−0.391335	−	0.920248i	$-0.627987\pi$
$313$	−13.8468			−0.782669			−0.391335	+	0.920248i	$0.627987\pi$
$314$	−2.88552	+	2.88552i	−0.162839	+	0.162839i
$315$	−4.98592	−	3.66808i	−0.280925	−	0.206673i
$316$	3.33149	+	3.33149i	0.187411	+	0.187411i
$317$	9.84958	+	9.84958i	0.553207	+	0.553207i	0.927365	−	0.374158i	$-0.122068\pi$
$317$	9.84958	+	9.84958i	0.553207	+	0.553207i	−0.374158	+	0.927365i	$0.622068\pi$
$318$	1.16221			0.0651734
$319$	4.85256	+	4.85256i	0.271691	+	0.271691i
$320$	2.21058	−	0.336630i	0.123575	−	0.0188182i
$321$			5.17983i			0.289110i
$322$	2.29384	−	2.29384i	0.127830	−	0.127830i
$323$	0.806776	−	0.806776i	0.0448902	−	0.0448902i
$324$	−8.17474			−0.454152
$325$	9.83569	−	3.06669i	0.545586	−	0.170109i
$326$			11.0884i			0.614127i
$327$	−5.53961			−0.306341
$328$			3.11626i			0.172067i
$329$			1.70497i			0.0939979i
$330$	0.931956	+	0.685629i	0.0513025	+	0.0377426i
$331$	−11.7035	+	11.7035i	−0.643281	+	0.643281i	−0.951360	−	0.308080i	$-0.900314\pi$
$331$	−11.7035	+	11.7035i	−0.643281	+	0.643281i	0.308080	+	0.951360i	$0.400314\pi$
$332$	−6.48170	−	6.48170i	−0.355730	−	0.355730i
$333$	17.1747	+	4.21636i	0.941170	+	0.231055i
$334$		−	7.75419i		−	0.424290i
$335$	−20.8812	−	15.3620i	−1.14086	−	0.839317i
$336$		−	0.289813i		−	0.0158106i
$337$	2.42851	+	2.42851i	0.132289	+	0.132289i	0.770151	−	0.637862i	$-0.220181\pi$
$337$	2.42851	+	2.42851i	0.132289	+	0.132289i	−0.637862	+	0.770151i	$0.720181\pi$
$338$	−8.75419			−0.476165
$339$	0.878865	+	0.878865i	0.0477334	+	0.0477334i
$340$	−0.868711	−	5.70466i	−0.0471125	−	0.309378i
$341$	−0.650987	+	0.650987i	−0.0352529	+	0.0352529i
$342$	−0.908925	+	0.908925i	−0.0491490	+	0.0491490i
$343$	−8.81529	−	8.81529i	−0.475981	−	0.475981i
$344$	−7.38424			−0.398132
$345$	1.37418	−	1.86788i	0.0739833	−	0.100563i
$346$	−1.45954	+	1.45954i	−0.0784652	+	0.0784652i
$347$	−6.68904			−0.359086			−0.179543	−	0.983750i	$-0.557462\pi$
$347$	−6.68904			−0.359086			−0.179543	+	0.983750i	$0.557462\pi$
$348$		−	1.22880i		−	0.0658705i
$349$		−	18.6205i		−	0.996732i	−0.866967	−	0.498366i	$-0.833934\pi$
$349$		−	18.6205i		−	0.996732i	0.866967	−	0.498366i	$-0.166066\pi$
$350$	−2.21170	+	4.21572i	−0.118220	+	0.225340i
$351$	−2.61986	−	2.61986i	−0.139838	−	0.139838i
$352$		−	1.69991i		−	0.0906053i
$353$			4.81726i			0.256397i	0.991749	+	0.128198i	$0.0409195\pi$
$353$			4.81726i			0.256397i	−0.991749	+	0.128198i	$0.959081\pi$
$354$	1.55410			0.0825992
$355$	−17.9523	+	2.73380i	−0.952810	+	0.145095i
$356$	0.486184	−	0.486184i	0.0257677	−	0.0257677i
$357$	−0.747894			−0.0395828
$358$	−4.31587	+	4.31587i	−0.228101	+	0.228101i
$359$		−	9.55311i		−	0.504194i	−0.967702	−	0.252097i	$-0.918880\pi$
$359$		−	9.55311i		−	0.504194i	0.967702	−	0.252097i	$-0.0811202\pi$
$360$	0.978702	+	6.42694i	0.0515821	+	0.338730i
$361$		−	18.8045i		−	0.989712i
$362$	11.8012			0.620257
$363$	−1.74559	+	1.74559i	−0.0916198	+	0.0916198i
$364$	−1.38728	+	1.38728i	−0.0727131	+	0.0727131i
$365$	−7.14047	+	9.70585i	−0.373750	+	0.508027i
$366$	1.95740			0.102315
$367$	−22.7113	+	22.7113i	−1.18552	+	1.18552i	−0.207229	+	0.978293i	$0.566444\pi$
$367$	−22.7113	+	22.7113i	−1.18552	+	1.18552i	−0.978293	+	0.207229i	$0.933556\pi$
$368$	−3.40706			−0.177605
$369$	−9.06006			−0.471648
$370$	1.21729	−	13.5469i	0.0632839	−	0.704269i
$371$	3.63548			0.188745
$372$	0.164847			0.00854694
$373$	−22.7358	+	22.7358i	−1.17721	+	1.17721i	−0.196763	+	0.980451i	$0.563043\pi$
$373$	−22.7358	+	22.7358i	−1.17721	+	1.17721i	−0.980451	+	0.196763i	$0.936957\pi$
$374$	−4.38680			−0.226836
$375$	−1.10931	+	3.21722i	−0.0572845	+	0.166137i
$376$	1.26620	−	1.26620i	0.0652994	−	0.0652994i
$377$	−5.88201	+	5.88201i	−0.302939	+	0.302939i
$378$	1.71203			0.0880571
$379$			3.70695i			0.190413i	0.995458	+	0.0952065i	$0.0303511\pi$
$379$			3.70695i			0.190413i	−0.995458	+	0.0952065i	$0.969649\pi$
$380$	0.796335	+	0.585854i	0.0408511	+	0.0300537i
$381$		−	0.939381i		−	0.0481259i
$382$	−0.707267	+	0.707267i	−0.0361869	+	0.0361869i
$383$	23.3542			1.19334			0.596671	−	0.802486i	$-0.296490\pi$
$383$	23.3542			1.19334			0.596671	+	0.802486i	$0.296490\pi$
$384$	−0.215231	+	0.215231i	−0.0109835	+	0.0109835i
$385$	2.91523	+	2.14470i	0.148574	+	0.109304i
$386$	8.39923			0.427509
$387$		−	21.4686i		−	1.09131i
$388$		−	0.430462i		−	0.0218534i
$389$	−16.1783	−	16.1783i	−0.820273	−	0.820273i	0.165874	−	0.986147i	$-0.446955\pi$
$389$	−16.1783	−	16.1783i	−0.820273	−	0.820273i	−0.986147	+	0.165874i	$0.946955\pi$
$390$	−0.831083	+	1.12967i	−0.0420835	+	0.0572030i
$391$			8.79229i			0.444645i
$392$			6.09344i			0.307765i
$393$	−5.68747			−0.286895
$394$	15.0419	−	15.0419i	0.757801	−	0.757801i
$395$	8.48602	+	6.24306i	0.426978	+	0.314122i
$396$	4.94223			0.248356
$397$	14.6564	+	14.6564i	0.735586	+	0.735586i	0.971720	−	0.236134i	$-0.0758805\pi$
$397$	14.6564	+	14.6564i	0.735586	+	0.735586i	−0.236134	+	0.971720i	$0.575881\pi$
$398$	1.52878	−	1.52878i	0.0766308	−	0.0766308i
$399$	0.0906042	−	0.0906042i	0.00453588	−	0.00453588i
$400$	4.77336	−	1.48830i	0.238668	−	0.0744149i
$401$	−14.9949	−	14.9949i	−0.748810	−	0.748810i	0.225446	−	0.974256i	$-0.427616\pi$
$401$	−14.9949	−	14.9949i	−0.748810	−	0.748810i	−0.974256	+	0.225446i	$0.927616\pi$
$402$	3.52878			0.176000
$403$	−0.789092	−	0.789092i	−0.0393075	−	0.0393075i
$404$			2.72028i			0.135339i
$405$	−18.0710	+	2.75186i	−0.897953	+	0.136741i
$406$		−	3.84378i		−	0.190763i
$407$	−10.0419	−	2.46528i	−0.497761	−	0.122199i
$408$	0.555428	+	0.555428i	0.0274978	+	0.0274978i
$409$	−10.9013	+	10.9013i	−0.539035	+	0.539035i	−0.923245	−	0.384211i	$-0.874474\pi$
$409$	−10.9013	+	10.9013i	−0.539035	+	0.539035i	0.384211	+	0.923245i	$0.374474\pi$
$410$	1.04903	+	6.88875i	0.0518077	+	0.340211i
$411$			3.82737i			0.188790i
$412$			13.5156i			0.665866i
$413$	4.86133			0.239211
$414$		−	9.90551i		−	0.486829i
$415$	−16.5103	−	12.1464i	−0.810458	−	0.596244i
$416$	2.06054			0.101026
$417$	−1.24494	+	1.24494i	−0.0609652	+	0.0609652i
$418$	0.531442	−	0.531442i	0.0259937	−	0.0259937i
$419$		−	13.2565i		−	0.647621i	−0.946122	−	0.323810i	$-0.895036\pi$
$419$		−	13.2565i		−	0.647621i	0.946122	−	0.323810i	$-0.104964\pi$
$420$	−0.0975597	−	0.640656i	−0.00476043	−	0.0312608i
$421$	−23.9484	−	23.9484i	−1.16717	−	1.16717i	−0.982870	−	0.184302i	$-0.940998\pi$
$421$	−23.9484	−	23.9484i	−1.16717	−	1.16717i	−0.184302	−	0.982870i	$-0.559002\pi$
$422$	24.1444			1.17533
$423$	3.68130	+	3.68130i	0.178991	+	0.178991i
$424$	−2.69991	−	2.69991i	−0.131119	−	0.131119i
$425$	−3.84072	−	12.3182i	−0.186302	−	0.597520i
$426$	1.74791	−	1.74791i	0.0846864	−	0.0846864i
$427$	6.12291			0.296309
$428$	12.0332	−	12.0332i	0.581645	−	0.581645i
$429$	0.753894	+	0.753894i	0.0363984	+	0.0363984i
$430$	−16.3235	+	2.48576i	−0.787188	+	0.119874i
$431$	−10.5581	−	10.5581i	−0.508567	−	0.508567i	0.405519	−	0.914087i	$-0.367091\pi$
$431$	−10.5581	−	10.5581i	−0.508567	−	0.508567i	−0.914087	+	0.405519i	$0.867091\pi$
$432$	−1.27145	−	1.27145i	−0.0611724	−	0.0611724i
$433$	4.00718	+	4.00718i	0.192573	+	0.192573i	0.796807	−	0.604234i	$-0.206521\pi$
$433$	4.00718	+	4.00718i	0.192573	+	0.192573i	−0.604234	+	0.796807i	$0.706521\pi$
$434$	0.515656			0.0247523
$435$	−0.413650	−	2.71636i	−0.0198330	−	0.130239i
$436$	12.8690	+	12.8690i	0.616312	+	0.616312i
$437$	−1.06515	−	1.06515i	−0.0509529	−	0.0509529i
$438$		−	1.64022i		−	0.0783729i
$439$	−16.2656	+	16.2656i	−0.776315	+	0.776315i	−0.979202	−	0.202887i	$-0.934967\pi$
$439$	−16.2656	+	16.2656i	−0.776315	+	0.776315i	0.202887	+	0.979202i	$0.434967\pi$
$440$	−0.572240	−	3.75779i	−0.0272805	−	0.179145i
$441$	−17.7158			−0.843608
$442$		−	5.31745i		−	0.252925i
$443$	8.83849	−	8.83849i	0.419929	−	0.419929i	−0.465250	−	0.885179i	$-0.654036\pi$
$443$	8.83849	−	8.83849i	0.419929	−	0.419929i	0.885179	+	0.465250i	$0.154036\pi$
$444$	0.959308	+	1.58358i	0.0455268	+	0.0751535i
$445$	0.911086	−	1.23841i	0.0431896	−	0.0587065i
$446$	−10.0159	−	10.0159i	−0.474266	−	0.474266i
$447$	1.75938	+	1.75938i	0.0832157	+	0.0832157i
$448$	−0.673260	+	0.673260i	−0.0318085	+	0.0318085i
$449$	−23.1025	−	23.1025i	−1.09027	−	1.09027i	−0.995499	−	0.0947738i	$-0.969787\pi$
$449$	−23.1025	−	23.1025i	−1.09027	−	1.09027i	−0.0947738	−	0.995499i	$-0.530213\pi$
$450$	4.32700	+	13.8778i	0.203977	+	0.654207i
$451$	5.29735			0.249442
$452$		−	4.08335i		−	0.192065i
$453$	−2.54645	−	2.54645i	−0.119643	−	0.119643i
$454$			3.05788i			0.143514i
$455$	−2.59969	+	3.53369i	−0.121876	+	0.165662i
$456$	−0.134575			−0.00630206
$457$		−	7.81169i		−	0.365415i	−0.983167	−	0.182708i	$-0.941514\pi$
$457$		−	7.81169i		−	0.365415i	0.983167	−	0.182708i	$-0.0584862\pi$
$458$			26.8791i			1.25598i
$459$	−3.28111	+	3.28111i	−0.153149	+	0.153149i
$460$	−7.53158	+	1.14692i	−0.351162	+	0.0534753i
$461$	5.55252	−	5.55252i	0.258607	−	0.258607i	−0.565881	−	0.824487i	$-0.691464\pi$
$461$	5.55252	−	5.55252i	0.258607	−	0.258607i	0.824487	+	0.565881i	$0.191464\pi$
$462$	−0.492655			−0.0229204
$463$	27.6492			1.28497			0.642484	−	0.766299i	$-0.277904\pi$
$463$	27.6492			1.28497			0.642484	+	0.766299i	$0.277904\pi$
$464$	−2.85460	+	2.85460i	−0.132522	+	0.132522i
$465$	0.364409	−	0.0554926i	0.0168991	−	0.00257341i
$466$	0.315711	−	0.315711i	0.0146250	−	0.0146250i
$467$			36.0724i			1.66923i	0.550832	+	0.834616i	$0.314311\pi$
$467$			36.0724i			1.66923i	−0.550832	+	0.834616i	$0.685689\pi$
$468$			5.99071i			0.276920i
$469$	11.0383			0.509702
$470$	2.37281	−	3.22529i	0.109449	−	0.148771i
$471$		−	1.24211i		−	0.0572333i
$472$	−3.61030	−	3.61030i	−0.166177	−	0.166177i
$473$			12.5525i			0.577166i
$474$	−1.43408			−0.0658695
$475$	1.95758	+	1.02701i	0.0898200	+	0.0471224i
$476$	1.73742	+	1.73742i	0.0796346	+	0.0796346i
$477$	7.84958	−	7.84958i	0.359407	−	0.359407i
$478$	−7.59846	−	7.59846i	−0.347545	−	0.347545i
$479$	15.5362	+	15.5362i	0.709869	+	0.709869i	0.966507	−	0.256639i	$-0.0826151\pi$
$479$	15.5362	+	15.5362i	0.709869	+	0.709869i	−0.256639	+	0.966507i	$0.582615\pi$
$480$	−0.403333	+	0.548239i	−0.0184095	+	0.0250236i
$481$	2.98828	−	12.1723i	0.136254	−	0.555010i
$482$	3.57132	−	3.57132i	0.162669	−	0.162669i
$483$			0.987409i			0.0449287i
$484$	8.11032			0.368651
$485$	−0.144906	−	0.951573i	−0.00657986	−	0.0432087i
$486$	5.57380	−	5.57380i	0.252832	−	0.252832i
$487$			28.9759i			1.31302i	0.754315	+	0.656512i	$0.227969\pi$
$487$			28.9759i			1.31302i	−0.754315	+	0.656512i	$0.772031\pi$
$488$	−4.54721	−	4.54721i	−0.205843	−	0.205843i
$489$	−2.38656	−	2.38656i	−0.107924	−	0.107924i
$490$	2.05124	+	13.4701i	0.0926654	+	0.608515i
$491$	42.0592			1.89810			0.949052	−	0.315118i	$-0.102044\pi$
$491$	42.0592			1.89810			0.949052	+	0.315118i	$0.102044\pi$
$492$	−0.670716	−	0.670716i	−0.0302382	−	0.0302382i
$493$	7.36661	+	7.36661i	0.331776	+	0.331776i
$494$	0.644185	+	0.644185i	0.0289833	+	0.0289833i
$495$	10.9252	−	1.66370i	0.491051	−	0.0747778i
$496$	−0.382954	−	0.382954i	−0.0171952	−	0.0171952i
$497$	5.46759	−	5.46759i	0.245255	−	0.245255i
$498$	2.79013			0.125029
$499$	9.34143	−	9.34143i	0.418180	−	0.418180i	−0.466396	−	0.884576i	$-0.654448\pi$
$499$	9.34143	−	9.34143i	0.418180	−	0.418180i	0.884576	+	0.466396i	$0.154448\pi$
$500$	10.0509	−	4.89686i	0.449490	−	0.218994i
$501$	1.66894	+	1.66894i	0.0745628	+	0.0745628i
$502$	19.0270	+	19.0270i	0.849215	+	0.849215i
$503$	17.7689			0.792274			0.396137	−	0.918191i	$-0.370350\pi$
$503$	17.7689			0.792274			0.396137	+	0.918191i	$0.370350\pi$
$504$	−1.95740	−	1.95740i	−0.0871897	−	0.0871897i
$505$	0.915726	+	6.01340i	0.0407493	+	0.267593i
$506$			5.79168i			0.257472i
$507$	1.88417	−	1.88417i	0.0836791	−	0.0836791i
$508$	−2.18226	+	2.18226i	−0.0968222	+	0.0968222i
$509$	−18.7841			−0.832592			−0.416296	−	0.909229i	$-0.636672\pi$
$509$	−18.7841			−0.832592			−0.416296	+	0.909229i	$0.636672\pi$
$510$	1.41479	+	1.04085i	0.0626481	+	0.0460894i
$511$		−	5.13075i		−	0.226971i
$512$	1.00000			0.0441942
$513$		−	0.794983i		−	0.0350994i
$514$			24.5612i			1.08335i
$515$	4.54975	+	29.8774i	0.200486	+	1.31655i
$516$	1.58932	−	1.58932i	0.0699658	−	0.0699658i
$517$	−2.15243	−	2.15243i	−0.0946636	−	0.0946636i
$518$	3.00079	+	4.95357i	0.131847	+	0.217648i
$519$		−	0.628275i		−	0.0275782i
$520$	4.55499	−	0.693639i	0.199750	−	0.0304181i
$521$			16.1307i			0.706699i	0.935491	+	0.353350i	$0.114957\pi$
$521$			16.1307i			0.706699i	−0.935491	+	0.353350i	$0.885043\pi$
$522$	−8.29933	−	8.29933i	−0.363252	−	0.363252i
$523$	5.32902			0.233022			0.116511	−	0.993189i	$-0.462829\pi$
$523$	5.32902			0.233022			0.116511	+	0.993189i	$0.462829\pi$
$524$	13.2125	+	13.2125i	0.577189	+	0.577189i
$525$	−0.431328	−	1.38338i	−0.0188247	−	0.0603757i
$526$	15.9933	−	15.9933i	0.697340	−	0.697340i
$527$	−0.988256	+	0.988256i	−0.0430491	+	0.0430491i
$528$	0.365873	+	0.365873i	0.0159226	+	0.0159226i
$529$	−11.3920			−0.495303
$530$	−6.87724	−	5.05950i	−0.298728	−	0.219771i
$531$	10.4964	−	10.4964i	0.455505	−	0.455505i
$532$	−0.420962			−0.0182510
$533$			6.42117i			0.278132i
$534$			0.209284i			0.00905659i
$535$	22.5496	−	30.6511i	0.974905	−	1.32516i
$536$	−8.19766	−	8.19766i	−0.354085	−	0.354085i
$537$		−	1.85782i		−	0.0801708i
$538$			8.06679i			0.347784i
$539$	10.3583			0.446163
$540$	−3.23864	−	2.38263i	−0.139369	−	0.102532i
$541$	15.5936	−	15.5936i	0.670423	−	0.670423i	−0.287391	−	0.957813i	$-0.592788\pi$
$541$	15.5936	−	15.5936i	0.670423	−	0.670423i	0.957813	+	0.287391i	$0.0927877\pi$
$542$	−24.2256			−1.04058
$543$	−2.53999	+	2.53999i	−0.109001	+	0.109001i
$544$		−	2.58061i		−	0.110643i
$545$	32.7800	+	24.1159i	1.40414	+	1.03301i
$546$		−	0.597170i		−	0.0255565i
$547$	45.2269			1.93376			0.966880	−	0.255230i	$-0.0821513\pi$
$547$	45.2269			1.93376			0.966880	+	0.255230i	$0.0821513\pi$
$548$	8.89131	−	8.89131i	0.379818	−	0.379818i
$549$	13.2203	−	13.2203i	0.564231	−	0.564231i
$550$	−2.52997	−	8.11427i	−0.107878	−	0.345994i
$551$	−1.78487			−0.0760379
$552$	0.733305	−	0.733305i	0.0312115	−	0.0312115i
$553$	−4.48592			−0.190761
$554$	−18.8030			−0.798862
$555$	2.65371	+	3.17771i	0.112644	+	0.134886i
$556$	5.78423			0.245306
$557$	−11.9401			−0.505919			−0.252959	−	0.967477i	$-0.581404\pi$
$557$	−11.9401			−0.505919			−0.252959	+	0.967477i	$0.581404\pi$
$558$	1.11338	−	1.11338i	0.0471333	−	0.0471333i
$559$	−15.2155			−0.643547
$560$	−1.26166	+	1.71494i	−0.0533148	+	0.0724693i
$561$	0.944175	−	0.944175i	0.0398631	−	0.0398631i
$562$	14.2311	−	14.2311i	0.600301	−	0.600301i
$563$	5.67895			0.239339			0.119670	−	0.992814i	$-0.461816\pi$
$563$	5.67895			0.239339			0.119670	+	0.992814i	$0.461816\pi$
$564$			0.545052i			0.0229508i
$565$	−1.37458	−	9.02660i	−0.0578290	−	0.379752i
$566$		−	0.905573i		−	0.0380641i
$567$	5.50373	−	5.50373i	0.231135	−	0.231135i
$568$	−8.12107			−0.340753
$569$	−5.85876	+	5.85876i	−0.245612	+	0.245612i	−0.819167	−	0.573555i	$-0.805564\pi$
$569$	−5.85876	+	5.85876i	−0.245612	+	0.245612i	0.573555	+	0.819167i	$0.305564\pi$
$570$	−0.297490	+	0.0453021i	−0.0124605	+	0.00189750i
$571$	35.6191			1.49061			0.745307	−	0.666721i	$-0.232303\pi$
$571$	35.6191			1.49061			0.745307	+	0.666721i	$0.232303\pi$
$572$		−	3.50272i		−	0.146456i
$573$		−	0.304452i		−	0.0127186i
$574$	−2.09805	−	2.09805i	−0.0875710	−	0.0875710i
$575$	−16.2631	+	5.07071i	−0.678219	+	0.211463i
$576$			2.90735i			0.121140i
$577$			10.6524i			0.443464i	0.975108	+	0.221732i	$0.0711710\pi$
$577$			10.6524i			0.443464i	−0.975108	+	0.221732i	$0.928829\pi$
$578$	10.3404			0.430106
$579$	−1.80777	+	1.80777i	−0.0751285	+	0.0751285i
$580$	−5.34939	+	7.27128i	−0.222121	+	0.301923i
$581$	8.72774			0.362088
$582$	0.0926488	+	0.0926488i	0.00384042	+	0.00384042i
$583$	−4.58959	+	4.58959i	−0.190081	+	0.190081i
$584$	−3.81038	+	3.81038i	−0.157675	+	0.157675i
$585$	2.01665	+	13.2430i	0.0833783	+	0.547529i
$586$	−14.1364	−	14.1364i	−0.583967	−	0.583967i
$587$	−4.99347			−0.206103			−0.103051	−	0.994676i	$-0.532861\pi$
$587$	−4.99347			−0.206103			−0.103051	+	0.994676i	$0.532861\pi$
$588$	−1.31150	−	1.31150i	−0.0540853	−	0.0540853i
$589$		−	0.239446i		−	0.00986620i
$590$	−9.19619	−	6.76553i	−0.378601	−	0.278532i
$591$			6.47498i			0.266345i
$592$	1.45024	−	5.90735i	0.0596046	−	0.242791i
$593$	7.45193	+	7.45193i	0.306014	+	0.306014i	0.843361	−	0.537347i	$-0.180573\pi$
$593$	7.45193	+	7.45193i	0.306014	+	0.306014i	−0.537347	+	0.843361i	$0.680573\pi$
$594$	−2.16134	+	2.16134i	−0.0886808	+	0.0886808i
$595$	4.42559	+	3.25585i	0.181431	+	0.133477i
$596$		−	8.17437i		−	0.334835i
$597$			0.658082i			0.0269335i
$598$	−7.02037			−0.287084
$599$			9.88045i			0.403704i	0.979416	+	0.201852i	$0.0646961\pi$
$599$			9.88045i			0.403704i	−0.979416	+	0.201852i	$0.935304\pi$
$600$	−0.707048	+	1.34770i	−0.0288651	+	0.0550198i
$601$	1.44426			0.0589125			0.0294562	−	0.999566i	$-0.490622\pi$
$601$	1.44426			0.0589125			0.0294562	+	0.999566i	$0.490622\pi$
$602$	4.97151	−	4.97151i	0.202624	−	0.202624i
$603$	23.8335	−	23.8335i	0.970574	−	0.970574i
$604$			11.8313i			0.481407i
$605$	17.9285	−	2.73018i	0.728899	−	0.110997i
$606$	−0.585488	−	0.585488i	−0.0237838	−	0.0237838i
$607$	−28.7523			−1.16702			−0.583510	−	0.812106i	$-0.698321\pi$
$607$	−28.7523			−1.16702			−0.583510	+	0.812106i	$0.698321\pi$
$608$	0.312630	+	0.312630i	0.0126788	+	0.0126788i
$609$	0.827300	+	0.827300i	0.0335239	+	0.0335239i
$610$	−11.5827	−	8.52127i	−0.468971	−	0.345016i
$611$	2.60906	−	2.60906i	0.105551	−	0.105551i
$612$	7.50274			0.303280
$613$	−33.5232	+	33.5232i	−1.35399	+	1.35399i	−0.472841	+	0.881148i	$0.656772\pi$
$613$	−33.5232	+	33.5232i	−1.35399	+	1.35399i	−0.881148	+	0.472841i	$0.843228\pi$
$614$	22.5470	+	22.5470i	0.909923	+	0.909923i
$615$	−1.70846	−	1.25689i	−0.0688916	−	0.0506827i
$616$	1.14448	+	1.14448i	0.0461124	+	0.0461124i
$617$	9.02064	+	9.02064i	0.363157	+	0.363157i	0.864974	−	0.501817i	$-0.167335\pi$
$617$	9.02064	+	9.02064i	0.363157	+	0.363157i	−0.501817	+	0.864974i	$0.667335\pi$
$618$	−2.90898	−	2.90898i	−0.117016	−	0.117016i
$619$	41.8727			1.68301			0.841504	−	0.540251i	$-0.181671\pi$
$619$	41.8727			1.68301			0.841504	+	0.540251i	$0.181671\pi$
$620$	−0.975467	−	0.717639i	−0.0391757	−	0.0288211i
$621$	4.33189	+	4.33189i	0.173833	+	0.173833i
$622$	−18.8440	−	18.8440i	−0.755577	−	0.755577i
$623$			0.654656i			0.0262282i
$624$	−0.443492	+	0.443492i	−0.0177539	+	0.0177539i
$625$	20.5699	−	14.2084i	0.822798	−	0.568334i
$626$	−13.8468			−0.553431
$627$			0.228765i			0.00913601i
$628$	−2.88552	+	2.88552i	−0.115145	+	0.115145i
$629$	−15.2446	−	3.74251i	−0.607841	−	0.149224i
$630$	−4.98592	−	3.66808i	−0.198644	−	0.146140i
$631$	−4.63219	−	4.63219i	−0.184405	−	0.184405i	0.608867	−	0.793272i	$-0.291624\pi$
$631$	−4.63219	−	4.63219i	−0.184405	−	0.184405i	−0.793272	+	0.608867i	$0.791624\pi$
$632$	3.33149	+	3.33149i	0.132520	+	0.132520i
$633$	−5.19663	+	5.19663i	−0.206547	+	0.206547i
$634$	9.84958	+	9.84958i	0.391177	+	0.391177i
$635$	−4.08946	+	5.55868i	−0.162285	+	0.220590i
$636$	1.16221			0.0460845
$637$			12.5558i			0.497477i
$638$	4.85256	+	4.85256i	0.192115	+	0.192115i
$639$		−	23.6108i		−	0.934029i
$640$	2.21058	−	0.336630i	0.0873810	−	0.0133065i
$641$	1.32847			0.0524714			0.0262357	−	0.999656i	$-0.491648\pi$
$641$	1.32847			0.0524714			0.0262357	+	0.999656i	$0.491648\pi$
$642$			5.17983i			0.204431i
$643$		−	3.72617i		−	0.146946i	−0.997297	−	0.0734729i	$-0.976592\pi$
$643$		−	3.72617i		−	0.146946i	0.997297	−	0.0734729i	$-0.0234083\pi$
$644$	2.29384	−	2.29384i	0.0903898	−	0.0903898i
$645$	2.97831	−	4.04833i	0.117271	−	0.159403i
$646$	0.806776	−	0.806776i	0.0317422	−	0.0317422i
$647$	−31.4105			−1.23487			−0.617437	−	0.786621i	$-0.711829\pi$
$647$	−31.4105			−1.23487			−0.617437	+	0.786621i	$0.711829\pi$
$648$	−8.17474			−0.321134
$649$	−6.13717	+	6.13717i	−0.240905	+	0.240905i
$650$	9.83569	−	3.06669i	0.385787	−	0.120286i
$651$	−0.110985	+	0.110985i	−0.00434985	+	0.00434985i
$652$			11.0884i			0.434253i
$653$			3.85917i			0.151021i	0.997145	+	0.0755104i	$0.0240586\pi$
$653$			3.85917i			0.151021i	−0.997145	+	0.0755104i	$0.975941\pi$
$654$	−5.53961			−0.216616
$655$	33.6550	+	24.7595i	1.31501	+	0.967436i
$656$			3.11626i			0.121669i
$657$	−11.0781	−	11.0781i	−0.432198	−	0.432198i
$658$			1.70497i			0.0664665i
$659$	20.7025			0.806457			0.403228	−	0.915099i	$-0.367888\pi$
$659$	20.7025			0.806457			0.403228	+	0.915099i	$0.367888\pi$
$660$	0.931956	+	0.685629i	0.0362763	+	0.0266881i
$661$	−18.0647	−	18.0647i	−0.702635	−	0.702635i	0.262340	−	0.964975i	$-0.415506\pi$
$661$	−18.0647	−	18.0647i	−0.702635	−	0.702635i	−0.964975	+	0.262340i	$0.915506\pi$
$662$	−11.7035	+	11.7035i	−0.454868	+	0.454868i
$663$	1.14448	+	1.14448i	0.0444479	+	0.0444479i
$664$	−6.48170	−	6.48170i	−0.251539	−	0.251539i
$665$	−0.930572	+	0.141709i	−0.0360860	+	0.00549522i
$666$	17.1747	+	4.21636i	0.665508	+	0.163381i
$667$	9.72579	−	9.72579i	0.376584	−	0.376584i
$668$		−	7.75419i		−	0.300018i
$669$	4.31146			0.166691
$670$	−20.8812	−	15.3620i	−0.806710	−	0.593487i
$671$	−7.72984	+	7.72984i	−0.298407	+	0.298407i
$672$		−	0.289813i		−	0.0111798i
$673$	−18.6183	−	18.6183i	−0.717681	−	0.717681i	0.250449	−	0.968130i	$-0.419422\pi$
$673$	−18.6183	−	18.6183i	−0.717681	−	0.717681i	−0.968130	+	0.250449i	$0.919422\pi$
$674$	2.42851	+	2.42851i	0.0935426	+	0.0935426i
$675$	−7.96136	−	4.17678i	−0.306433	−	0.160764i
$676$	−8.75419			−0.336699
$677$	22.0917	+	22.0917i	0.849054	+	0.849054i	0.990015	−	0.140961i	$-0.0450193\pi$
$677$	22.0917	+	22.0917i	0.849054	+	0.849054i	−0.140961	+	0.990015i	$0.545019\pi$
$678$	0.878865	+	0.878865i	0.0337526	+	0.0337526i
$679$	0.289813	+	0.289813i	0.0111220	+	0.0111220i
$680$	−0.868711	−	5.70466i	−0.0333136	−	0.218764i
$681$	−0.658151	−	0.658151i	−0.0252204	−	0.0252204i
$682$	−0.650987	+	0.650987i	−0.0249276	+	0.0249276i
$683$	−4.05946			−0.155331			−0.0776654	−	0.996979i	$-0.524747\pi$
$683$	−4.05946			−0.155331			−0.0776654	+	0.996979i	$0.524747\pi$
$684$	−0.908925	+	0.908925i	−0.0347536	+	0.0347536i
$685$	16.6619	−	22.6481i	0.636618	−	0.865338i
$686$	−8.81529	−	8.81529i	−0.336569	−	0.336569i
$687$	−5.78521	−	5.78521i	−0.220720	−	0.220720i
$688$	−7.38424			−0.281522
$689$	−5.56326	−	5.56326i	−0.211943	−	0.211943i
$690$	1.37418	−	1.86788i	0.0523141	−	0.0711091i
$691$			19.1786i			0.729590i	0.931088	+	0.364795i	$0.118861\pi$
$691$			19.1786i			0.729590i	−0.931088	+	0.364795i	$0.881139\pi$
$692$	−1.45954	+	1.45954i	−0.0554833	+	0.0554833i
$693$	−3.32740	+	3.32740i	−0.126398	+	0.126398i
$694$	−6.68904			−0.253912
$695$	12.7865	−	1.94714i	0.485020	−	0.0738594i
$696$		−	1.22880i		−	0.0465774i
$697$	8.04185			0.304607
$698$		−	18.6205i		−	0.704796i
$699$			0.135902i			0.00514027i
$700$	−2.21170	+	4.21572i	−0.0835945	+	0.159339i
$701$	−24.6018	+	24.6018i	−0.929198	+	0.929198i	−0.997654	−	0.0684559i	$-0.978193\pi$
$701$	−24.6018	+	24.6018i	−0.929198	+	0.929198i	0.0684559	+	0.997654i	$0.478193\pi$
$702$	−2.61986	−	2.61986i	−0.0988803	−	0.0988803i
$703$	2.30020	−	1.39343i	0.0867538	−	0.0525540i
$704$		−	1.69991i		−	0.0640677i
$705$	0.183481	+	1.20488i	0.00691029	+	0.0453785i
$706$			4.81726i			0.181300i
$707$	−1.83145	−	1.83145i	−0.0688789	−	0.0688789i
$708$	1.55410			0.0584065
$709$	−33.2828	−	33.2828i	−1.24996	−	1.24996i	−0.955736	−	0.294227i	$-0.904938\pi$
$709$	−33.2828	−	33.2828i	−1.24996	−	1.24996i	−0.294227	−	0.955736i	$-0.595062\pi$
$710$	−17.9523	+	2.73380i	−0.673738	+	0.102598i
$711$	−9.68581	+	9.68581i	−0.363246	+	0.363246i
$712$	0.486184	−	0.486184i	0.0182205	−	0.0182205i
$713$	1.30475	+	1.30475i	0.0488632	+	0.0488632i
$714$	−0.747894			−0.0279892
$715$	−1.17912	−	7.74306i	−0.0440966	−	0.289574i
$716$	−4.31587	+	4.31587i	−0.161292	+	0.161292i
$717$	3.27085			0.122152
$718$		−	9.55311i		−	0.356519i
$719$		−	30.9253i		−	1.15332i	−0.816984	−	0.576660i	$-0.804356\pi$
$719$		−	30.9253i		−	1.15332i	0.816984	−	0.576660i	$-0.195644\pi$
$720$	0.978702	+	6.42694i	0.0364741	+	0.239518i
$721$	−9.09951	−	9.09951i	−0.338883	−	0.338883i
$722$		−	18.8045i		−	0.699832i
$723$			1.53732i			0.0571734i
$724$	11.8012			0.438588
$725$	−9.37754	+	17.8745i	−0.348273	+	0.663844i
$726$	−1.74559	+	1.74559i	−0.0647850	+	0.0647850i
$727$	−44.0653			−1.63429			−0.817146	−	0.576431i	$-0.804445\pi$
$727$	−44.0653			−1.63429			−0.817146	+	0.576431i	$0.804445\pi$
$728$	−1.38728	+	1.38728i	−0.0514159	+	0.0514159i
$729$		−	22.1249i		−	0.819442i
$730$	−7.14047	+	9.70585i	−0.264281	+	0.359230i
$731$			19.0559i			0.704806i
$732$	1.95740			0.0723477
$733$	4.94476	−	4.94476i	0.182639	−	0.182639i	−0.609866	−	0.792505i	$-0.708777\pi$
$733$	4.94476	−	4.94476i	0.182639	−	0.182639i	0.792505	+	0.609866i	$0.208777\pi$
$734$	−22.7113	+	22.7113i	−0.838290	+	0.838290i
$735$	−3.34067	−	2.45769i	−0.123222	−	0.0906531i
$736$	−3.40706			−0.125586
$737$	−13.9353	+	13.9353i	−0.513312	+	0.513312i
$738$	−9.06006			−0.333505
$739$	19.8515			0.730251			0.365125	−	0.930958i	$-0.381026\pi$
$739$	19.8515			0.730251			0.365125	+	0.930958i	$0.381026\pi$
$740$	1.21729	−	13.5469i	0.0447485	−	0.497994i
$741$	−0.277297			−0.0101868
$742$	3.63548			0.133463
$743$	10.5608	−	10.5608i	0.387439	−	0.387439i	−0.486334	−	0.873773i	$-0.661666\pi$
$743$	10.5608	−	10.5608i	0.387439	−	0.387439i	0.873773	+	0.486334i	$0.161666\pi$
$744$	0.164847			0.00604360
$745$	−2.75174	−	18.0701i	−0.100816	−	0.662038i
$746$	−22.7358	+	22.7358i	−0.832416	+	0.832416i
$747$	18.8446	−	18.8446i	0.689488	−	0.689488i
$748$	−4.38680			−0.160397
$749$			16.2029i			0.592041i
$750$	−1.10931	+	3.21722i	−0.0405063	+	0.117476i
$751$			30.0307i			1.09583i	0.836533	+	0.547917i	$0.184579\pi$
$751$			30.0307i			1.09583i	−0.836533	+	0.547917i	$0.815421\pi$
$752$	1.26620	−	1.26620i	0.0461737	−	0.0461737i
$753$	−8.19039			−0.298474
$754$	−5.88201	+	5.88201i	−0.214210	+	0.214210i
$755$	3.98276	+	26.1540i	0.144947	+	0.951841i
$756$	1.71203			0.0622658
$757$		−	45.2685i		−	1.64531i	−0.568541	−	0.822655i	$-0.692492\pi$
$757$		−	45.2685i		−	1.64531i	0.568541	−	0.822655i	$-0.307508\pi$
$758$			3.70695i			0.134642i
$759$	−1.24655	−	1.24655i	−0.0452469	−	0.0452469i
$760$	0.796335	+	0.585854i	0.0288861	+	0.0212511i
$761$			48.5501i			1.75994i	0.475029	+	0.879970i	$0.342437\pi$
$761$			48.5501i			1.75994i	−0.475029	+	0.879970i	$0.657563\pi$
$762$		−	0.939381i		−	0.0340302i
$763$	−17.3283			−0.627328
$764$	−0.707267	+	0.707267i	−0.0255880	+	0.0255880i
$765$	16.5854	−	2.52565i	0.599648	−	0.0913150i
$766$	23.3542			0.843821
$767$	−7.43915	−	7.43915i	−0.268612	−	0.268612i
$768$	−0.215231	+	0.215231i	−0.00776648	+	0.00776648i
$769$	20.0854	−	20.0854i	0.724300	−	0.724300i	−0.245178	−	0.969478i	$-0.578846\pi$
$769$	20.0854	−	20.0854i	0.724300	−	0.724300i	0.969478	+	0.245178i	$0.0788465\pi$
$770$	2.91523	+	2.14470i	0.105058	+	0.0772897i
$771$	−5.28633	−	5.28633i	−0.190382	−	0.190382i
$772$	8.39923			0.302295
$773$	−22.9236	−	22.9236i	−0.824504	−	0.824504i	0.162247	−	0.986750i	$-0.448126\pi$
$773$	−22.9236	−	22.9236i	−0.824504	−	0.824504i	−0.986750	+	0.162247i	$0.948126\pi$
$774$		−	21.4686i		−	0.771672i
$775$	−2.39793	−	1.25803i	−0.0861362	−	0.0451897i
$776$		−	0.430462i		−	0.0154527i
$777$	−1.71203	−	0.420299i	−0.0614186	−	0.0150781i
$778$	−16.1783	−	16.1783i	−0.580020	−	0.580020i
$779$	−0.974235	+	0.974235i	−0.0349056	+	0.0349056i
$780$	−0.831083	+	1.12967i	−0.0297575	+	0.0404486i
$781$			13.8051i			0.493984i
$782$			8.79229i			0.314412i
$783$	7.25894			0.259413
$784$			6.09344i			0.217623i
$785$	−5.40733	+	7.35004i	−0.192996	+	0.262334i
$786$	−5.68747			−0.202865
$787$	22.0858	−	22.0858i	0.787274	−	0.787274i	−0.193772	−	0.981047i	$-0.562072\pi$
$787$	22.0858	−	22.0858i	0.787274	−	0.787274i	0.981047	+	0.193772i	$0.0620723\pi$
$788$	15.0419	−	15.0419i	0.535846	−	0.535846i
$789$			6.88450i			0.245095i
$790$	8.48602	+	6.24306i	0.301919	+	0.222118i
$791$	2.74916	+	2.74916i	0.0977488	+	0.0977488i
$792$	4.94223			0.175614
$793$	−9.36970	−	9.36970i	−0.332728	−	0.332728i
$794$	14.6564	+	14.6564i	0.520138	+	0.520138i
$795$	2.56916	−	0.391234i	0.0911186	−	0.0138756i
$796$	1.52878	−	1.52878i	0.0541862	−	0.0541862i
$797$	−3.09119			−0.109495			−0.0547477	−	0.998500i	$-0.517435\pi$
$797$	−3.09119			−0.109495			−0.0547477	+	0.998500i	$0.517435\pi$
$798$	0.0906042	−	0.0906042i	0.00320735	−	0.00320735i
$799$	−3.26758	−	3.26758i	−0.115599	−	0.115599i
$800$	4.77336	−	1.48830i	0.168764	−	0.0526193i
$801$	1.41351	+	1.41351i	0.0499438	+	0.0499438i
$802$	−14.9949	−	14.9949i	−0.529489	−	0.529489i
$803$	6.47729	+	6.47729i	0.228579	+	0.228579i
$804$	3.52878			0.124450
$805$	4.29854	−	5.84289i	0.151504	−	0.205935i
$806$	−0.789092	−	0.789092i	−0.0277946	−	0.0277946i
$807$	−1.73622	−	1.73622i	−0.0611180	−	0.0611180i
$808$			2.72028i			0.0956989i
$809$	−32.0623	+	32.0623i	−1.12725	+	1.12725i	−0.136629	+	0.990622i	$0.543627\pi$
$809$	−32.0623	+	32.0623i	−1.12725	+	1.12725i	−0.990622	+	0.136629i	$0.956373\pi$
$810$	−18.0710	+	2.75186i	−0.634949	+	0.0966906i
$811$	−48.8130			−1.71406			−0.857029	−	0.515269i	$-0.827692\pi$
$811$	−48.8130			−1.71406			−0.857029	+	0.515269i	$0.827692\pi$
$812$		−	3.84378i		−	0.134890i
$813$	5.21410	−	5.21410i	0.182866	−	0.182866i
$814$	−10.0419	−	2.46528i	−0.351970	−	0.0864079i
$815$	3.73267	+	24.5117i	0.130750	+	0.858609i
$816$	0.555428	+	0.555428i	0.0194439	+	0.0194439i
$817$	−2.30853	−	2.30853i	−0.0807654	−	0.0807654i
$818$	−10.9013	+	10.9013i	−0.381155	+	0.381155i
$819$	−4.03330	−	4.03330i	−0.140935	−	0.140935i
$820$	1.04903	+	6.88875i	0.0366336	+	0.240566i
$821$	−28.2934			−0.987445			−0.493723	−	0.869619i	$-0.664364\pi$
$821$	−28.2934			−0.987445			−0.493723	+	0.869619i	$0.664364\pi$
$822$			3.82737i			0.133495i
$823$	15.4120	+	15.4120i	0.537229	+	0.537229i	0.922714	−	0.385485i	$-0.125966\pi$
$823$	15.4120	+	15.4120i	0.537229	+	0.537229i	−0.385485	+	0.922714i	$0.625966\pi$
$824$			13.5156i			0.470838i
$825$	2.29097	+	1.20192i	0.0797613	+	0.0418453i
$826$	4.86133			0.169147
$827$		−	9.92069i		−	0.344976i	−0.985012	−	0.172488i	$-0.944819\pi$
$827$		−	9.92069i		−	0.344976i	0.985012	−	0.172488i	$-0.0551806\pi$
$828$		−	9.90551i		−	0.344240i
$829$	−6.35906	+	6.35906i	−0.220859	+	0.220859i	−0.808860	−	0.588001i	$-0.799915\pi$
$829$	−6.35906	+	6.35906i	−0.220859	+	0.220859i	0.588001	+	0.808860i	$0.299915\pi$
$830$	−16.5103	−	12.1464i	−0.573080	−	0.421608i
$831$	4.04699	−	4.04699i	0.140388	−	0.140388i
$832$	2.06054			0.0714363
$833$	15.7248			0.544832
$834$	−1.24494	+	1.24494i	−0.0431089	+	0.0431089i
$835$	−2.61029	−	17.1413i	−0.0903329	−	0.593198i
$836$	0.531442	−	0.531442i	0.0183803	−	0.0183803i
$837$			0.973811i			0.0336598i
$838$		−	13.2565i		−	0.457937i
$839$	12.9249			0.446218			0.223109	−	0.974793i	$-0.428379\pi$
$839$	12.9249			0.446218			0.223109	+	0.974793i	$0.428379\pi$
$840$	−0.0975597	−	0.640656i	−0.00336613	−	0.0221047i
$841$			12.7025i			0.438018i
$842$	−23.9484	−	23.9484i	−0.825315	−	0.825315i
$843$			6.12593i			0.210988i
$844$	24.1444			0.831085
$845$	−19.3519	+	2.94692i	−0.665724	+	0.101377i
$846$	3.68130	+	3.68130i	0.126566	+	0.126566i
$847$	−5.46035	+	5.46035i	−0.187620	+	0.187620i
$848$	−2.69991	−	2.69991i	−0.0927152	−	0.0927152i
$849$	0.194907	+	0.194907i	0.00668920	+	0.00668920i
$850$	−3.84072	−	12.3182i	−0.131736	−	0.422510i
$851$	−4.94106	+	20.1267i	−0.169377	+	0.689934i
$852$	1.74791	−	1.74791i	0.0598823	−	0.0598823i
$853$			14.2055i			0.486387i	0.969978	+	0.243193i	$0.0781949\pi$
$853$			14.2055i			0.486387i	−0.969978	+	0.243193i	$0.921805\pi$
$854$	6.12291			0.209522
$855$	−1.70328	+	2.31523i	−0.0582510	+	0.0791790i
$856$	12.0332	−	12.0332i	0.411285	−	0.411285i
$857$			25.8639i			0.883494i	0.897140	+	0.441747i	$0.145641\pi$
$857$			25.8639i			0.883494i	−0.897140	+	0.441747i	$0.854359\pi$
$858$	0.753894	+	0.753894i	0.0257375	+	0.0257375i
$859$	30.1371	+	30.1371i	1.02827	+	1.02827i	0.999589	+	0.0286775i	$0.00912957\pi$
$859$	30.1371	+	30.1371i	1.02827	+	1.02827i	0.0286775	+	0.999589i	$0.490870\pi$
$860$	−16.3235	+	2.48576i	−0.556626	+	0.0847636i
$861$	0.903132			0.0307787
$862$	−10.5581	−	10.5581i	−0.359611	−	0.359611i
$863$	−23.5513	−	23.5513i	−0.801695	−	0.801695i	0.181665	−	0.983360i	$-0.441851\pi$
$863$	−23.5513	−	23.5513i	−0.801695	−	0.801695i	−0.983360	+	0.181665i	$0.941851\pi$
$864$	−1.27145	−	1.27145i	−0.0432555	−	0.0432555i
$865$	−2.73510	+	3.71775i	−0.0929963	+	0.126407i
$866$	4.00718	+	4.00718i	0.136169	+	0.136169i
$867$	−2.22559	+	2.22559i	−0.0755848	+	0.0755848i
$868$	0.515656			0.0175025
$869$	5.66322	−	5.66322i	0.192112	−	0.192112i
$870$	−0.413650	−	2.71636i	−0.0140241	−	0.0920932i
$871$	−16.8916	−	16.8916i	−0.572349	−	0.572349i
$872$	12.8690	+	12.8690i	0.435799	+	0.435799i
$873$	1.25150			0.0423570
$874$	−1.06515	−	1.06515i	−0.0360292	−	0.0360292i
$875$	−3.47001	+	10.0637i	−0.117308	+	0.340216i
$876$		−	1.64022i		−	0.0554180i
$877$	23.0266	−	23.0266i	0.777553	−	0.777553i	−0.201862	−	0.979414i	$-0.564699\pi$
$877$	23.0266	−	23.0266i	0.777553	−	0.777553i	0.979414	+	0.201862i	$0.0646991\pi$
$878$	−16.2656	+	16.2656i	−0.548937	+	0.548937i
$879$	6.08516			0.205248
$880$	−0.572240	−	3.75779i	−0.0192902	−	0.126675i
$881$		−	27.1213i		−	0.913741i	−0.889533	−	0.456870i	$-0.848970\pi$
$881$		−	27.1213i		−	0.913741i	0.889533	−	0.456870i	$-0.151030\pi$
$882$	−17.7158			−0.596521
$883$		−	49.1920i		−	1.65544i	−0.561139	−	0.827722i	$-0.689637\pi$
$883$		−	49.1920i		−	1.65544i	0.561139	−	0.827722i	$-0.310363\pi$
$884$		−	5.31745i		−	0.178845i
$885$	3.43546	−	0.523155i	0.115482	−	0.0175857i
$886$	8.83849	−	8.83849i	0.296935	−	0.296935i
$887$	5.87709	+	5.87709i	0.197333	+	0.197333i	0.798856	−	0.601523i	$-0.205439\pi$
$887$	5.87709	+	5.87709i	0.197333	+	0.197333i	−0.601523	+	0.798856i	$0.705439\pi$
$888$	0.959308	+	1.58358i	0.0321923	+	0.0531416i
$889$		−	2.93846i		−	0.0985527i
$890$	0.911086	−	1.23841i	0.0305397	−	0.0415117i
$891$			13.8963i			0.465544i
$892$	−10.0159	−	10.0159i	−0.335357	−	0.335357i
$893$	0.791705			0.0264934
$894$	1.75938	+	1.75938i	0.0588424	+	0.0588424i
$895$	−8.08774	+	10.9934i	−0.270343	+	0.367470i
$896$	−0.673260	+	0.673260i	−0.0224920	+	0.0224920i
$897$	1.51100	−	1.51100i	0.0504509	−	0.0504509i
$898$	−23.1025	−	23.1025i	−0.770939	−	0.770939i
$899$	2.18636			0.0729193
$900$	4.32700	+	13.8778i	0.144233	+	0.462595i
$901$	−6.96741	+	6.96741i	−0.232118	+	0.232118i
$902$	5.29735			0.176382
$903$			2.14005i			0.0712163i
$904$		−	4.08335i		−	0.135810i
$905$	26.0875	−	3.97264i	0.867179	−	0.132055i
$906$	−2.54645	−	2.54645i	−0.0846003	−	0.0846003i
$907$			1.31786i			0.0437587i	0.999761	+	0.0218793i	$0.00696497\pi$
$907$			1.31786i			0.0437587i	−0.999761	+	0.0218793i	$0.993035\pi$
$908$			3.05788i			0.101479i
$909$	−7.90879			−0.262318
$910$	−2.59969	+	3.53369i	−0.0861790	+	0.117141i
$911$	−14.9006	+	14.9006i	−0.493679	+	0.493679i	−0.909463	−	0.415784i	$-0.863507\pi$
$911$	−14.9006	+	14.9006i	−0.493679	+	0.493679i	0.415784	+	0.909463i	$0.363507\pi$
$912$	−0.134575			−0.00445623
$913$	−11.0183	+	11.0183i	−0.364652	+	0.364652i
$914$		−	7.81169i		−	0.258388i
$915$	4.32700	−	0.658921i	0.143046	−	0.0217832i
$916$			26.8791i			0.888109i
$917$	−17.7908			−0.587506
$918$	−3.28111	+	3.28111i	−0.108293	+	0.108293i
$919$	34.2859	−	34.2859i	1.13099	−	1.13099i	0.140975	−	0.990013i	$-0.454976\pi$
$919$	34.2859	−	34.2859i	1.13099	−	1.13099i	0.990013	−	0.140975i	$-0.0450237\pi$
$920$	−7.53158	+	1.14692i	−0.248309	+	0.0378128i
$921$	−9.70563			−0.319811
$922$	5.55252	−	5.55252i	0.182863	−	0.182863i
$923$	−16.7338			−0.550799
$924$	−0.492655			−0.0162072
$925$	−1.86937	−	30.3563i	−0.0614644	−	0.998109i
$926$	27.6492			0.908609
$927$	−39.2946			−1.29060
$928$	−2.85460	+	2.85460i	−0.0937069	+	0.0937069i
$929$	36.4095			1.19456			0.597278	−	0.802034i	$-0.296249\pi$
$929$	36.4095			1.19456			0.597278	+	0.802034i	$0.296249\pi$
$930$	0.364409	−	0.0554926i	0.0119494	−	0.00181967i
$931$	−1.90499	+	1.90499i	−0.0624336	+	0.0624336i
$932$	0.315711	−	0.315711i	0.0103415	−	0.0103415i
$933$	8.11165			0.265563
$934$			36.0724i			1.18033i
$935$	−9.69739	+	1.47673i	−0.317138	+	0.0482942i
$936$			5.99071i			0.195812i
$937$	35.9882	−	35.9882i	1.17568	−	1.17568i	0.194848	−	0.980833i	$-0.437579\pi$
$937$	35.9882	−	35.9882i	1.17568	−	1.17568i	0.980833	−	0.194848i	$-0.0624214\pi$
$938$	11.0383			0.360414
$939$	2.98027	−	2.98027i	0.0972574	−	0.0972574i
$940$	2.37281	−	3.22529i	0.0773924	−	0.105197i
$941$	31.5238			1.02765			0.513823	−	0.857896i	$-0.328229\pi$
$941$	31.5238			1.02765			0.513823	+	0.857896i	$0.328229\pi$
$942$		−	1.24211i		−	0.0404700i
$943$		−	10.6173i		−	0.345746i
$944$	−3.61030	−	3.61030i	−0.117505	−	0.117505i
$945$	3.78458	−	0.576320i	0.123112	−	0.0187477i
$946$			12.5525i			0.408118i
$947$		−	48.9752i		−	1.59148i	−0.605637	−	0.795741i	$-0.707082\pi$
$947$		−	48.9752i		−	1.59148i	0.605637	−	0.795741i	$-0.292918\pi$
$948$	−1.43408			−0.0465768
$949$	−7.85143	+	7.85143i	−0.254868	+	0.254868i
$950$	1.95758	+	1.02701i	0.0635123	+	0.0333206i
$951$	−4.23987			−0.137487
$952$	1.73742	+	1.73742i	0.0563102	+	0.0563102i
$953$	−9.58879	+	9.58879i	−0.310611	+	0.310611i	−0.845146	−	0.534535i	$-0.820487\pi$
$953$	−9.58879	+	9.58879i	−0.310611	+	0.310611i	0.534535	+	0.845146i	$0.320487\pi$
$954$	7.84958	−	7.84958i	0.254139	−	0.254139i
$955$	−1.32539	+	1.80156i	−0.0428885	+	0.0582971i
$956$	−7.59846	−	7.59846i	−0.245752	−	0.245752i
$957$	−2.08884			−0.0675227
$958$	15.5362	+	15.5362i	0.501953	+	0.501953i
$959$			11.9723i			0.386606i
$960$	−0.403333	+	0.548239i	−0.0130175	+	0.0176944i
$961$		−	30.7067i		−	0.990538i
$962$	2.98828	−	12.1723i	0.0963459	−	0.392451i
$963$	34.9847	+	34.9847i	1.12737	+	1.12737i
$964$	3.57132	−	3.57132i	0.115024	−	0.115024i
$965$	18.5672	−	2.82743i	0.597699	−	0.0910182i
$966$			0.987409i			0.0317694i
$967$			29.6562i			0.953681i	0.878990	+	0.476840i	$0.158218\pi$
$967$			29.6562i			0.953681i	−0.878990	+	0.476840i	$0.841782\pi$
$968$	8.11032			0.260675
$969$			0.347286i			0.0111564i
$970$	−0.144906	−	0.951573i	−0.00465267	−	0.0305532i
$971$	−23.8296			−0.764729			−0.382365	−	0.924012i	$-0.624890\pi$
$971$	−23.8296			−0.764729			−0.382365	+	0.924012i	$0.624890\pi$
$972$	5.57380	−	5.57380i	0.178780	−	0.178780i
$973$	−3.89429	+	3.89429i	−0.124845	+	0.124845i
$974$			28.9759i			0.928449i
$975$	−1.45690	+	2.77699i	−0.0466581	+	0.0889349i
$976$	−4.54721	−	4.54721i	−0.145553	−	0.145553i
$977$	−29.1322			−0.932023			−0.466011	−	0.884779i	$-0.654309\pi$
$977$	−29.1322			−0.932023			−0.466011	+	0.884779i	$0.654309\pi$
$978$	−2.38656	−	2.38656i	−0.0763137	−	0.0763137i
$979$	−0.826467	−	0.826467i	−0.0264140	−	0.0264140i
$980$	2.05124	+	13.4701i	0.0655243	+	0.430285i
$981$	−37.4146	+	37.4146i	−1.19456	+	1.19456i
$982$	42.0592			1.34216
$983$	7.65743	−	7.65743i	0.244234	−	0.244234i	−0.574365	−	0.818599i	$-0.694751\pi$
$983$	7.65743	−	7.65743i	0.244234	−	0.244234i	0.818599	+	0.574365i	$0.194751\pi$
$984$	−0.670716	−	0.670716i	−0.0213816	−	0.0213816i
$985$	28.1879	−	38.3150i	0.898140	−	1.22082i
$986$	7.36661	+	7.36661i	0.234601	+	0.234601i
$987$	−0.366962	−	0.366962i	−0.0116805	−	0.0116805i
$988$	0.644185	+	0.644185i	0.0204943	+	0.0204943i
$989$	25.1585			0.799995
$990$	10.9252	−	1.66370i	0.347226	−	0.0528759i
$991$	23.2373	+	23.2373i	0.738158	+	0.738158i	0.972221	−	0.234063i	$-0.0752023\pi$
$991$	23.2373	+	23.2373i	0.738158	+	0.738158i	−0.234063	+	0.972221i	$0.575202\pi$
$992$	−0.382954	−	0.382954i	−0.0121588	−	0.0121588i
$993$		−	5.03790i		−	0.159873i
$994$	5.46759	−	5.46759i	0.173422	−	0.173422i
$995$	2.86486	−	3.89413i	0.0908223	−	0.123452i
$996$	2.79013			0.0884086
$997$			4.12715i			0.130708i	0.997862	+	0.0653540i	$0.0208177\pi$
$997$			4.12715i			0.130708i	−0.997862	+	0.0653540i	$0.979182\pi$
$998$	9.34143	−	9.34143i	0.295698	−	0.295698i
$999$	−9.35478	+	5.66697i	−0.295972	+	0.179295i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.h.d.253.3	yes	10
5.2	odd	4		370.2.g.d.327.3	yes	10
37.6	odd	4		370.2.g.d.43.3	✓	10
185.117	even	4	inner	370.2.h.d.117.3	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.d.43.3	✓	10	37.6	odd	4
370.2.g.d.327.3	yes	10	5.2	odd	4
370.2.h.d.117.3	yes	10	185.117	even	4	inner
370.2.h.d.253.3	yes	10	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.h (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.215231 + 0.215231i) q^{3} +1.00000 q^{4} +(2.21058 - 0.336630i) q^{5} +(-0.215231 + 0.215231i) q^{6} +(-0.673260 + 0.673260i) q^{7} +1.00000 q^{8} +2.90735i q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.215231 + 0.215231i) q^{3} +1.00000 q^{4} +(2.21058 - 0.336630i) q^{5} +(-0.215231 + 0.215231i) q^{6} +(-0.673260 + 0.673260i) q^{7} +1.00000 q^{8} +2.90735i q^{9} +(2.21058 - 0.336630i) q^{10} -1.69991i q^{11} +(-0.215231 + 0.215231i) q^{12} +2.06054 q^{13} +(-0.673260 + 0.673260i) q^{14} +(-0.403333 + 0.548239i) q^{15} +1.00000 q^{16} -2.58061i q^{17} +2.90735i q^{18} +(0.312630 + 0.312630i) q^{19} +(2.21058 - 0.336630i) q^{20} -0.289813i q^{21} -1.69991i q^{22} -3.40706 q^{23} +(-0.215231 + 0.215231i) q^{24} +(4.77336 - 1.48830i) q^{25} +2.06054 q^{26} +(-1.27145 - 1.27145i) q^{27} +(-0.673260 + 0.673260i) q^{28} +(-2.85460 + 2.85460i) q^{29} +(-0.403333 + 0.548239i) q^{30} +(-0.382954 - 0.382954i) q^{31} +1.00000 q^{32} +(0.365873 + 0.365873i) q^{33} -2.58061i q^{34} +(-1.26166 + 1.71494i) q^{35} +2.90735i q^{36} +(1.45024 - 5.90735i) q^{37} +(0.312630 + 0.312630i) q^{38} +(-0.443492 + 0.443492i) q^{39} +(2.21058 - 0.336630i) q^{40} +3.11626i q^{41} -0.289813i q^{42} -7.38424 q^{43} -1.69991i q^{44} +(0.978702 + 6.42694i) q^{45} -3.40706 q^{46} +(1.26620 - 1.26620i) q^{47} +(-0.215231 + 0.215231i) q^{48} +6.09344i q^{49} +(4.77336 - 1.48830i) q^{50} +(0.555428 + 0.555428i) q^{51} +2.06054 q^{52} +(-2.69991 - 2.69991i) q^{53} +(-1.27145 - 1.27145i) q^{54} +(-0.572240 - 3.75779i) q^{55} +(-0.673260 + 0.673260i) q^{56} -0.134575 q^{57} +(-2.85460 + 2.85460i) q^{58} +(-3.61030 - 3.61030i) q^{59} +(-0.403333 + 0.548239i) q^{60} +(-4.54721 - 4.54721i) q^{61} +(-0.382954 - 0.382954i) q^{62} +(-1.95740 - 1.95740i) q^{63} +1.00000 q^{64} +(4.55499 - 0.693639i) q^{65} +(0.365873 + 0.365873i) q^{66} +(-8.19766 - 8.19766i) q^{67} -2.58061i q^{68} +(0.733305 - 0.733305i) q^{69} +(-1.26166 + 1.71494i) q^{70} -8.12107 q^{71} +2.90735i q^{72} +(-3.81038 + 3.81038i) q^{73} +(1.45024 - 5.90735i) q^{74} +(-0.707048 + 1.34770i) q^{75} +(0.312630 + 0.312630i) q^{76} +(1.14448 + 1.14448i) q^{77} +(-0.443492 + 0.443492i) q^{78} +(3.33149 + 3.33149i) q^{79} +(2.21058 - 0.336630i) q^{80} -8.17474 q^{81} +3.11626i q^{82} +(-6.48170 - 6.48170i) q^{83} -0.289813i q^{84} +(-0.868711 - 5.70466i) q^{85} -7.38424 q^{86} -1.22880i q^{87} -1.69991i q^{88} +(0.486184 - 0.486184i) q^{89} +(0.978702 + 6.42694i) q^{90} +(-1.38728 + 1.38728i) q^{91} -3.40706 q^{92} +0.164847 q^{93} +(1.26620 - 1.26620i) q^{94} +(0.796335 + 0.585854i) q^{95} +(-0.215231 + 0.215231i) q^{96} -0.430462i q^{97} +6.09344i q^{98} +4.94223 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 10 q^{8}+O(q^{10}) \) 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + 10 * q^8	\( 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 10 q^{8} + 2 q^{10} + 2 q^{12} - 12 q^{13} - 4 q^{14} - 14 q^{15} + 10 q^{16} + 8 q^{19} + 2 q^{20} + 4 q^{23} + 2 q^{24} + 28 q^{25} - 12 q^{26} - 28 q^{27} - 4 q^{28} - 32 q^{29} - 14 q^{30} - 26 q^{31} + 10 q^{32} - 24 q^{33} + 22 q^{35} - 2 q^{37} + 8 q^{38} + 6 q^{39} + 2 q^{40} + 12 q^{43} - 10 q^{45} + 4 q^{46} + 48 q^{47} + 2 q^{48} + 28 q^{50} + 16 q^{51} - 12 q^{52} - 2 q^{53} - 28 q^{54} + 12 q^{55} - 4 q^{56} + 76 q^{57} - 32 q^{58} - 20 q^{59} - 14 q^{60} - 24 q^{61} - 26 q^{62} + 20 q^{63} + 10 q^{64} + 28 q^{65} - 24 q^{66} - 10 q^{67} - 46 q^{69} + 22 q^{70} - 16 q^{71} + 4 q^{73} - 2 q^{74} - 48 q^{75} + 8 q^{76} - 24 q^{77} + 6 q^{78} - 2 q^{79} + 2 q^{80} + 2 q^{81} + 8 q^{83} - 10 q^{85} + 12 q^{86} - 2 q^{89} - 10 q^{90} + 16 q^{91} + 4 q^{92} - 60 q^{93} + 48 q^{94} - 28 q^{95} + 2 q^{96} + 28 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + 10 * q^8 + 2 * q^10 + 2 * q^12 - 12 * q^13 - 4 * q^14 - 14 * q^15 + 10 * q^16 + 8 * q^19 + 2 * q^20 + 4 * q^23 + 2 * q^24 + 28 * q^25 - 12 * q^26 - 28 * q^27 - 4 * q^28 - 32 * q^29 - 14 * q^30 - 26 * q^31 + 10 * q^32 - 24 * q^33 + 22 * q^35 - 2 * q^37 + 8 * q^38 + 6 * q^39 + 2 * q^40 + 12 * q^43 - 10 * q^45 + 4 * q^46 + 48 * q^47 + 2 * q^48 + 28 * q^50 + 16 * q^51 - 12 * q^52 - 2 * q^53 - 28 * q^54 + 12 * q^55 - 4 * q^56 + 76 * q^57 - 32 * q^58 - 20 * q^59 - 14 * q^60 - 24 * q^61 - 26 * q^62 + 20 * q^63 + 10 * q^64 + 28 * q^65 - 24 * q^66 - 10 * q^67 - 46 * q^69 + 22 * q^70 - 16 * q^71 + 4 * q^73 - 2 * q^74 - 48 * q^75 + 8 * q^76 - 24 * q^77 + 6 * q^78 - 2 * q^79 + 2 * q^80 + 2 * q^81 + 8 * q^83 - 10 * q^85 + 12 * q^86 - 2 * q^89 - 10 * q^90 + 16 * q^91 + 4 * q^92 - 60 * q^93 + 48 * q^94 - 28 * q^95 + 2 * q^96 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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