LMFDB - Embedded newform 390.2.t.a.343.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(307,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("390.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.t (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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 6x^{10} - 24x^{9} + 18x^{8} + 40x^{7} - 82x^{6} + 12x^{5} + 228x^{4} - 284x^{3} + 124x^{2} - 16x + 2 $ x^12 + 6x^10 - 24x^9 + 18x^8 + 40x^7 - 82x^6 + 12x^5 + 228x^4 - 284x^3 + 124x^2 - 16x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			343.3
Root			$-1.32833 - 3.20687i$ of defining polynomial
Character	$\chi$	$=$	390.343
Dual form			390.2.t.a.307.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.57013 - 1.59207i) q^{5} +(0.707107 - 0.707107i) q^{6} -1.24244 q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.57013 - 1.59207i) q^{5} +(0.707107 - 0.707107i) q^{6} -1.24244 q^{7} -1.00000i q^{8} +1.00000i q^{9} +(1.59207 + 1.57013i) q^{10} +(-2.63471 - 2.63471i) q^{11} +(0.707107 + 0.707107i) q^{12} +(2.42064 - 2.67217i) q^{13} -1.24244i q^{14} +(-2.23601 + 0.0155164i) q^{15} +1.00000 q^{16} +(0.658041 + 0.658041i) q^{17} -1.00000 q^{18} +(-5.37251 - 5.37251i) q^{19} +(-1.57013 + 1.59207i) q^{20} +(0.878539 + 0.878539i) q^{21} +(2.63471 - 2.63471i) q^{22} +(6.45495 - 6.45495i) q^{23} +(-0.707107 + 0.707107i) q^{24} +(-0.0693897 - 4.99952i) q^{25} +(2.67217 + 2.42064i) q^{26} +(0.707107 - 0.707107i) q^{27} +1.24244 q^{28} +8.74193i q^{29} +(-0.0155164 - 2.23601i) q^{30} +(1.00000 - 1.00000i) q^{31} +1.00000i q^{32} +3.72604i q^{33} +(-0.658041 + 0.658041i) q^{34} +(-1.95079 + 1.97806i) q^{35} -1.00000i q^{36} -1.70787 q^{37} +(5.37251 - 5.37251i) q^{38} +(-3.60116 + 0.177859i) q^{39} +(-1.59207 - 1.57013i) q^{40} +(6.86630 - 6.86630i) q^{41} +(-0.878539 + 0.878539i) q^{42} +(-1.99043 + 1.99043i) q^{43} +(2.63471 + 2.63471i) q^{44} +(1.59207 + 1.57013i) q^{45} +(6.45495 + 6.45495i) q^{46} +10.2601 q^{47} +(-0.707107 - 0.707107i) q^{48} -5.45634 q^{49} +(4.99952 - 0.0693897i) q^{50} -0.930610i q^{51} +(-2.42064 + 2.67217i) q^{52} +(2.99952 + 2.99952i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-8.33149 + 0.0578147i) q^{55} +1.24244i q^{56} +7.59788i q^{57} -8.74193 q^{58} +(-5.35343 + 5.35343i) q^{59} +(2.23601 - 0.0155164i) q^{60} -5.64048 q^{61} +(1.00000 + 1.00000i) q^{62} -1.24244i q^{63} -1.00000 q^{64} +(-0.453572 - 8.04949i) q^{65} -3.72604 q^{66} +6.45566i q^{67} +(-0.658041 - 0.658041i) q^{68} -9.12868 q^{69} +(-1.97806 - 1.95079i) q^{70} +(-8.57216 + 8.57216i) q^{71} +1.00000 q^{72} +6.74415i q^{73} -1.70787i q^{74} +(-3.48613 + 3.58426i) q^{75} +(5.37251 + 5.37251i) q^{76} +(3.27347 + 3.27347i) q^{77} +(-0.177859 - 3.60116i) q^{78} -6.92304i q^{79} +(1.57013 - 1.59207i) q^{80} -1.00000 q^{81} +(6.86630 + 6.86630i) q^{82} -1.95051 q^{83} +(-0.878539 - 0.878539i) q^{84} +(2.08086 - 0.0144397i) q^{85} +(-1.99043 - 1.99043i) q^{86} +(6.18148 - 6.18148i) q^{87} +(-2.63471 + 2.63471i) q^{88} +(7.93497 - 7.93497i) q^{89} +(-1.57013 + 1.59207i) q^{90} +(-3.00750 + 3.32002i) q^{91} +(-6.45495 + 6.45495i) q^{92} -1.41421 q^{93} +10.2601i q^{94} +(-16.9890 + 0.117892i) q^{95} +(0.707107 - 0.707107i) q^{96} -14.3492i q^{97} -5.45634i q^{98} +(2.63471 - 2.63471i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} - 4 q^{5}+O(q^{10}) $ 12 * q - 12 * q^4 - 4 * q^5	$ 12 q - 12 q^{4} - 4 q^{5} + 4 q^{11} + 20 q^{13} - 4 q^{15} + 12 q^{16} + 8 q^{17} - 12 q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{25} - 4 q^{26} + 4 q^{30} + 12 q^{31} - 8 q^{34} + 12 q^{35} - 16 q^{37} + 4 q^{38} - 12 q^{39} + 8 q^{41} + 8 q^{42} + 16 q^{43} - 4 q^{44} + 32 q^{47} - 20 q^{49} + 8 q^{50} - 20 q^{52} - 16 q^{53} - 12 q^{55} - 40 q^{58} + 20 q^{59} + 4 q^{60} + 16 q^{61} + 12 q^{62} - 12 q^{64} - 32 q^{65} - 16 q^{66} - 8 q^{68} - 32 q^{69} - 20 q^{70} - 32 q^{71} + 12 q^{72} + 4 q^{76} + 16 q^{77} - 4 q^{80} - 12 q^{81} + 8 q^{82} + 32 q^{83} + 8 q^{84} + 12 q^{85} + 16 q^{86} + 20 q^{87} + 4 q^{88} + 16 q^{89} + 4 q^{90} - 28 q^{91} - 8 q^{95} - 4 q^{99}+O(q^{100}) $ 12 * q - 12 * q^4 - 4 * q^5 + 4 * q^11 + 20 * q^13 - 4 * q^15 + 12 * q^16 + 8 * q^17 - 12 * q^18 - 4 * q^19 + 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^25 - 4 * q^26 + 4 * q^30 + 12 * q^31 - 8 * q^34 + 12 * q^35 - 16 * q^37 + 4 * q^38 - 12 * q^39 + 8 * q^41 + 8 * q^42 + 16 * q^43 - 4 * q^44 + 32 * q^47 - 20 * q^49 + 8 * q^50 - 20 * q^52 - 16 * q^53 - 12 * q^55 - 40 * q^58 + 20 * q^59 + 4 * q^60 + 16 * q^61 + 12 * q^62 - 12 * q^64 - 32 * q^65 - 16 * q^66 - 8 * q^68 - 32 * q^69 - 20 * q^70 - 32 * q^71 + 12 * q^72 + 4 * q^76 + 16 * q^77 - 4 * q^80 - 12 * q^81 + 8 * q^82 + 32 * q^83 + 8 * q^84 + 12 * q^85 + 16 * q^86 + 20 * q^87 + 4 * q^88 + 16 * q^89 + 4 * q^90 - 28 * q^91 - 8 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	1.57013	−	1.59207i	0.702183	−	0.711996i
$5$	1.57013	−	1.59207i	0.702183	−	0.711996i
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	−1.24244			−0.469599			−0.234799	−	0.972044i	$-0.575443\pi$
$7$	−1.24244			−0.469599			−0.234799	+	0.972044i	$0.575443\pi$
$8$		−	1.00000i		−	0.353553i
$9$			1.00000i			0.333333i
$10$	1.59207	+	1.57013i	0.503458	+	0.496518i
$11$	−2.63471	−	2.63471i	−0.794395	−	0.794395i	0.187810	−	0.982205i	$-0.439861\pi$
$11$	−2.63471	−	2.63471i	−0.794395	−	0.794395i	−0.982205	+	0.187810i	$0.939861\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	2.42064	−	2.67217i	0.671365	−	0.741127i
$13$	2.42064	−	2.67217i	0.671365	−	0.741127i
$14$		−	1.24244i		−	0.332056i
$15$	−2.23601	+	0.0155164i	−0.577336	+	0.00400631i
$16$	1.00000			0.250000
$17$	0.658041	+	0.658041i	0.159598	+	0.159598i	0.782389	−	0.622790i	$-0.214001\pi$
$17$	0.658041	+	0.658041i	0.159598	+	0.159598i	−0.622790	+	0.782389i	$0.714001\pi$
$18$	−1.00000			−0.235702
$19$	−5.37251	−	5.37251i	−1.23254	−	1.23254i	−0.962986	−	0.269553i	$-0.913124\pi$
$19$	−5.37251	−	5.37251i	−1.23254	−	1.23254i	−0.269553	−	0.962986i	$-0.586876\pi$
$20$	−1.57013	+	1.59207i	−0.351092	+	0.355998i
$21$	0.878539	+	0.878539i	0.191713	+	0.191713i
$22$	2.63471	−	2.63471i	0.561722	−	0.561722i
$23$	6.45495	−	6.45495i	1.34595	−	1.34595i	0.455941	−	0.890010i	$-0.349303\pi$
$23$	6.45495	−	6.45495i	1.34595	−	1.34595i	0.890010	−	0.455941i	$-0.150697\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$	−0.0693897	−	4.99952i	−0.0138779	−	0.999904i
$26$	2.67217	+	2.42064i	0.524056	+	0.474727i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	1.24244			0.234799
$29$			8.74193i			1.62334i	0.584119	+	0.811668i	$0.301440\pi$
$29$			8.74193i			1.62334i	−0.584119	+	0.811668i	$0.698560\pi$
$30$	−0.0155164	−	2.23601i	−0.00283289	−	0.408238i
$31$	1.00000	−	1.00000i	0.179605	−	0.179605i	−0.611578	−	0.791184i	$-0.709465\pi$
$31$	1.00000	−	1.00000i	0.179605	−	0.179605i	0.791184	+	0.611578i	$0.209465\pi$
$32$			1.00000i			0.176777i
$33$			3.72604i			0.648621i
$34$	−0.658041	+	0.658041i	−0.112853	+	0.112853i
$35$	−1.95079	+	1.97806i	−0.329744	+	0.334353i
$36$		−	1.00000i		−	0.166667i
$37$	−1.70787			−0.280771			−0.140386	−	0.990097i	$-0.544834\pi$
$37$	−1.70787			−0.280771			−0.140386	+	0.990097i	$0.544834\pi$
$38$	5.37251	−	5.37251i	0.871536	−	0.871536i
$39$	−3.60116	+	0.177859i	−0.576647	+	0.0284802i
$40$	−1.59207	−	1.57013i	−0.251729	−	0.248259i
$41$	6.86630	−	6.86630i	1.07234	−	1.07234i	0.0751652	−	0.997171i	$-0.476052\pi$
$41$	6.86630	−	6.86630i	1.07234	−	1.07234i	0.997171	−	0.0751652i	$-0.0239484\pi$
$42$	−0.878539	+	0.878539i	−0.135561	+	0.135561i
$43$	−1.99043	+	1.99043i	−0.303538	+	0.303538i	−0.842396	−	0.538859i	$-0.818856\pi$
$43$	−1.99043	+	1.99043i	−0.303538	+	0.303538i	0.538859	+	0.842396i	$0.318856\pi$
$44$	2.63471	+	2.63471i	0.397198	+	0.397198i
$45$	1.59207	+	1.57013i	0.237332	+	0.234061i
$46$	6.45495	+	6.45495i	0.951731	+	0.951731i
$47$	10.2601			1.49659			0.748297	−	0.663363i	$-0.230872\pi$
$47$	10.2601			1.49659			0.748297	+	0.663363i	$0.230872\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$	−5.45634			−0.779477
$50$	4.99952	−	0.0693897i	0.707039	−	0.00981318i
$51$		−	0.930610i		−	0.130312i
$52$	−2.42064	+	2.67217i	−0.335682	+	0.370563i
$53$	2.99952	+	2.99952i	0.412016	+	0.412016i	0.882440	−	0.470425i	$-0.155899\pi$
$53$	2.99952	+	2.99952i	0.412016	+	0.412016i	−0.470425	+	0.882440i	$0.655899\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	−8.33149	+	0.0578147i	−1.12342	+	0.00779574i
$56$			1.24244i			0.166028i
$57$			7.59788i			1.00636i
$58$	−8.74193			−1.14787
$59$	−5.35343	+	5.35343i	−0.696957	+	0.696957i	−0.963753	−	0.266796i	$-0.914035\pi$
$59$	−5.35343	+	5.35343i	−0.696957	+	0.696957i	0.266796	+	0.963753i	$0.414035\pi$
$60$	2.23601	−	0.0155164i	0.288668	−	0.00200316i
$61$	−5.64048			−0.722190			−0.361095	−	0.932529i	$-0.617597\pi$
$61$	−5.64048			−0.722190			−0.361095	+	0.932529i	$0.617597\pi$
$62$	1.00000	+	1.00000i	0.127000	+	0.127000i
$63$		−	1.24244i		−	0.156533i
$64$	−1.00000			−0.125000
$65$	−0.453572	−	8.04949i	−0.0562587	−	0.998416i
$66$	−3.72604			−0.458644
$67$			6.45566i			0.788684i	0.918964	+	0.394342i	$0.129028\pi$
$67$			6.45566i			0.788684i	−0.918964	+	0.394342i	$0.870972\pi$
$68$	−0.658041	−	0.658041i	−0.0797992	−	0.0797992i
$69$	−9.12868			−1.09896
$70$	−1.97806	−	1.95079i	−0.236423	−	0.233164i
$71$	−8.57216	+	8.57216i	−1.01733	+	1.01733i	−0.0174815	+	0.999847i	$0.505565\pi$
$71$	−8.57216	+	8.57216i	−1.01733	+	1.01733i	−0.999847	+	0.0174815i	$0.994435\pi$
$72$	1.00000			0.117851
$73$			6.74415i			0.789343i	0.918822	+	0.394671i	$0.129142\pi$
$73$			6.74415i			0.789343i	−0.918822	+	0.394671i	$0.870858\pi$
$74$		−	1.70787i		−	0.198535i
$75$	−3.48613	+	3.58426i	−0.402543	+	0.413875i
$76$	5.37251	+	5.37251i	0.616269	+	0.616269i
$77$	3.27347	+	3.27347i	0.373047	+	0.373047i
$78$	−0.177859	−	3.60116i	−0.0201386	−	0.407751i
$79$		−	6.92304i		−	0.778903i	−0.921047	−	0.389452i	$-0.872665\pi$
$79$		−	6.92304i		−	0.778903i	0.921047	−	0.389452i	$-0.127335\pi$
$80$	1.57013	−	1.59207i	0.175546	−	0.177999i
$81$	−1.00000			−0.111111
$82$	6.86630	+	6.86630i	0.758256	+	0.758256i
$83$	−1.95051			−0.214096			−0.107048	−	0.994254i	$-0.534140\pi$
$83$	−1.95051			−0.214096			−0.107048	+	0.994254i	$0.534140\pi$
$84$	−0.878539	−	0.878539i	−0.0958564	−	0.0958564i
$85$	2.08086	−	0.0144397i	0.225701	−	0.00156621i
$86$	−1.99043	−	1.99043i	−0.214634	−	0.214634i
$87$	6.18148	−	6.18148i	0.662724	−	0.662724i
$88$	−2.63471	+	2.63471i	−0.280861	+	0.280861i
$89$	7.93497	−	7.93497i	0.841105	−	0.841105i	−0.147898	−	0.989003i	$-0.547251\pi$
$89$	7.93497	−	7.93497i	0.841105	−	0.841105i	0.989003	+	0.147898i	$0.0472507\pi$
$90$	−1.57013	+	1.59207i	−0.165506	+	0.167819i
$91$	−3.00750	+	3.32002i	−0.315272	+	0.348032i
$92$	−6.45495	+	6.45495i	−0.672975	+	0.672975i
$93$	−1.41421			−0.146647
$94$			10.2601i			1.05825i
$95$	−16.9890	+	0.117892i	−1.74303	+	0.0120954i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$		−	14.3492i		−	1.45694i	−0.685078	−	0.728470i	$-0.740232\pi$
$97$		−	14.3492i		−	1.45694i	0.685078	−	0.728470i	$-0.259768\pi$
$98$		−	5.45634i		−	0.551174i
$99$	2.63471	−	2.63471i	0.264798	−	0.264798i
$100$	0.0693897	+	4.99952i	0.00693897	+	0.499952i
$101$			19.1723i			1.90771i	0.300261	+	0.953857i	$0.402926\pi$
$101$			19.1723i			1.90771i	−0.300261	+	0.953857i	$0.597074\pi$
$102$	0.930610			0.0921442
$103$	3.82647	−	3.82647i	0.377033	−	0.377033i	−0.492998	−	0.870031i	$-0.664099\pi$
$103$	3.82647	−	3.82647i	0.377033	−	0.377033i	0.870031	+	0.492998i	$0.164099\pi$
$104$	−2.67217	−	2.42064i	−0.262028	−	0.237363i
$105$	2.77812	−	0.0192782i	0.271116	−	0.00188136i
$106$	−2.99952	+	2.99952i	−0.291339	+	0.291339i
$107$	−0.643120	+	0.643120i	−0.0621727	+	0.0621727i	−0.737509	−	0.675337i	$-0.763998\pi$
$107$	−0.643120	+	0.643120i	−0.0621727	+	0.0621727i	0.675337	+	0.737509i	$0.263998\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	3.54428	+	3.54428i	0.339481	+	0.339481i	0.856172	−	0.516691i	$-0.172836\pi$
$109$	3.54428	+	3.54428i	0.339481	+	0.339481i	−0.516691	+	0.856172i	$0.672836\pi$
$110$	−0.0578147	−	8.33149i	−0.00551242	−	0.794376i
$111$	1.20764	+	1.20764i	0.114624	+	0.114624i
$112$	−1.24244			−0.117400
$113$	7.01631	+	7.01631i	0.660039	+	0.660039i	0.955389	−	0.295350i	$-0.0954363\pi$
$113$	7.01631	+	7.01631i	0.660039	+	0.660039i	−0.295350	+	0.955389i	$0.595436\pi$
$114$	−7.59788			−0.711606
$115$	−0.141644	−	20.4119i	−0.0132084	−	1.90342i
$116$		−	8.74193i		−	0.811668i
$117$	2.67217	+	2.42064i	0.247042	+	0.223788i
$118$	−5.35343	−	5.35343i	−0.492823	−	0.492823i
$119$	−0.817577	−	0.817577i	−0.0749472	−	0.0749472i
$120$	0.0155164	+	2.23601i	0.00141645	+	0.204119i
$121$			2.88341i			0.262128i
$122$		−	5.64048i		−	0.510665i
$123$	−9.71042			−0.875559
$124$	−1.00000	+	1.00000i	−0.0898027	+	0.0898027i
$125$	−8.06855	−	7.73942i	−0.721673	−	0.692234i
$126$	1.24244			0.110685
$127$	2.43952	+	2.43952i	0.216472	+	0.216472i	0.807010	−	0.590538i	$-0.201084\pi$
$127$	2.43952	+	2.43952i	0.216472	+	0.216472i	−0.590538	+	0.807010i	$0.701084\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	2.81489			0.247837
$130$	8.04949	−	0.453572i	0.705987	−	0.0397809i
$131$	13.7684			1.20295			0.601477	−	0.798890i	$-0.294579\pi$
$131$	13.7684			1.20295			0.601477	+	0.798890i	$0.294579\pi$
$132$		−	3.72604i		−	0.324311i
$133$	6.67503	+	6.67503i	0.578798	+	0.578798i
$134$	−6.45566			−0.557684
$135$	−0.0155164	−	2.23601i	−0.00133544	−	0.192445i
$136$	0.658041	−	0.658041i	0.0564265	−	0.0564265i
$137$	10.3216			0.881836			0.440918	−	0.897547i	$-0.354653\pi$
$137$	10.3216			0.881836			0.440918	+	0.897547i	$0.354653\pi$
$138$		−	9.12868i		−	0.777085i
$139$			17.6837i			1.49992i	0.661486	+	0.749958i	$0.269926\pi$
$139$			17.6837i			1.49992i	−0.661486	+	0.749958i	$0.730074\pi$
$140$	1.95079	−	1.97806i	0.164872	−	0.167176i
$141$	−7.25501	−	7.25501i	−0.610982	−	0.610982i
$142$	−8.57216	−	8.57216i	−0.719360	−	0.719360i
$143$	−13.4181	+	0.662710i	−1.12208	+	0.0554186i
$144$			1.00000i			0.0833333i
$145$	13.9178	+	13.7260i	1.15581	+	1.13988i
$146$	−6.74415			−0.558150
$147$	3.85821	+	3.85821i	0.318220	+	0.318220i
$148$	1.70787			0.140386
$149$	−1.57025	−	1.57025i	−0.128640	−	0.128640i	0.639856	−	0.768495i	$-0.278994\pi$
$149$	−1.57025	−	1.57025i	−0.128640	−	0.128640i	−0.768495	+	0.639856i	$0.778994\pi$
$150$	−3.58426	−	3.48613i	−0.292654	−	0.284641i
$151$	−0.254890	−	0.254890i	−0.0207427	−	0.0207427i	0.696659	−	0.717402i	$-0.254669\pi$
$151$	−0.254890	−	0.254890i	−0.0207427	−	0.0207427i	−0.717402	+	0.696659i	$0.754669\pi$
$152$	−5.37251	+	5.37251i	−0.435768	+	0.435768i
$153$	−0.658041	+	0.658041i	−0.0531995	+	0.0531995i
$154$	−3.27347	+	3.27347i	−0.263784	+	0.263784i
$155$	−0.0219435	−	3.16220i	−0.00176254	−	0.253994i
$156$	3.60116	−	0.177859i	0.288324	−	0.0142401i
$157$	−1.55691	+	1.55691i	−0.124255	+	0.124255i	−0.766500	−	0.642245i	$-0.778003\pi$
$157$	−1.55691	+	1.55691i	−0.124255	+	0.124255i	0.642245	+	0.766500i	$0.278003\pi$
$158$	6.92304			0.550768
$159$		−	4.24196i		−	0.336409i
$160$	1.59207	+	1.57013i	0.125864	+	0.124130i
$161$	−8.01990	+	8.01990i	−0.632057	+	0.632057i
$162$		−	1.00000i		−	0.0785674i
$163$			14.2344i			1.11493i	0.830201	+	0.557464i	$0.188225\pi$
$163$			14.2344i			1.11493i	−0.830201	+	0.557464i	$0.811775\pi$
$164$	−6.86630	+	6.86630i	−0.536168	+	0.536168i
$165$	5.93213	+	5.85037i	0.461816	+	0.455451i
$166$		−	1.95051i		−	0.151389i
$167$	15.4187			1.19313			0.596567	−	0.802563i	$-0.296531\pi$
$167$	15.4187			1.19313			0.596567	+	0.802563i	$0.296531\pi$
$168$	0.878539	−	0.878539i	0.0677807	−	0.0677807i
$169$	−1.28100	−	12.9367i	−0.0985383	−	0.995133i
$170$	0.0144397	+	2.08086i	0.00110747	+	0.159595i
$171$	5.37251	−	5.37251i	0.410846	−	0.410846i
$172$	1.99043	−	1.99043i	0.151769	−	0.151769i
$173$	12.4283	−	12.4283i	0.944903	−	0.944903i	−0.0536560	−	0.998559i	$-0.517087\pi$
$173$	12.4283	−	12.4283i	0.944903	−	0.944903i	0.998559	+	0.0536560i	$0.0170875\pi$
$174$	6.18148	+	6.18148i	0.468617	+	0.468617i
$175$	0.0862126	+	6.21161i	0.00651706	+	0.469553i
$176$	−2.63471	−	2.63471i	−0.198599	−	0.198599i
$177$	7.57090			0.569063
$178$	7.93497	+	7.93497i	0.594751	+	0.594751i
$179$	−3.56872			−0.266739			−0.133369	−	0.991066i	$-0.542580\pi$
$179$	−3.56872			−0.266739			−0.133369	+	0.991066i	$0.542580\pi$
$180$	−1.59207	−	1.57013i	−0.118666	−	0.117031i
$181$		−	3.22773i		−	0.239916i	−0.992779	−	0.119958i	$-0.961724\pi$
$181$		−	3.22773i		−	0.239916i	0.992779	−	0.119958i	$-0.0382759\pi$
$182$	−3.32002	−	3.00750i	−0.246096	−	0.222931i
$183$	3.98843	+	3.98843i	0.294833	+	0.294833i
$184$	−6.45495	−	6.45495i	−0.475866	−	0.475866i
$185$	−2.68157	+	2.71905i	−0.197153	+	0.199908i
$186$		−	1.41421i		−	0.103695i
$187$		−	3.46750i		−	0.253568i
$188$	−10.2601			−0.748297
$189$	−0.878539	+	0.878539i	−0.0639043	+	0.0639043i
$190$	−0.117892	−	16.9890i	−0.00855275	−	1.23251i
$191$	−4.46490			−0.323069			−0.161535	−	0.986867i	$-0.551644\pi$
$191$	−4.46490			−0.323069			−0.161535	+	0.986867i	$0.551644\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$		−	2.88820i		−	0.207897i	−0.994583	−	0.103948i	$-0.966852\pi$
$193$		−	2.88820i		−	0.207897i	0.994583	−	0.103948i	$-0.0331477\pi$
$194$	14.3492			1.03021
$195$	−5.37112	+	6.01257i	−0.384634	+	0.430569i
$196$	5.45634			0.389739
$197$		−	13.4960i		−	0.961548i	−0.876844	−	0.480774i	$-0.840356\pi$
$197$		−	13.4960i		−	0.961548i	0.876844	−	0.480774i	$-0.159644\pi$
$198$	2.63471	+	2.63471i	0.187241	+	0.187241i
$199$	18.2097			1.29085			0.645425	−	0.763824i	$-0.276680\pi$
$199$	18.2097			1.29085			0.645425	+	0.763824i	$0.276680\pi$
$200$	−4.99952	+	0.0693897i	−0.353519	+	0.00490659i
$201$	4.56484	−	4.56484i	0.321979	−	0.321979i
$202$	−19.1723			−1.34896
$203$		−	10.8613i		−	0.762316i
$204$			0.930610i			0.0651558i
$205$	−0.150671	−	21.7126i	−0.0105233	−	1.51648i
$206$	3.82647	+	3.82647i	0.266603	+	0.266603i
$207$	6.45495	+	6.45495i	0.448650	+	0.448650i
$208$	2.42064	−	2.67217i	0.167841	−	0.185282i
$209$			28.3100i			1.95825i
$210$	0.0192782	+	2.77812i	0.00133032	+	0.191708i
$211$	9.57746			0.659339			0.329670	−	0.944096i	$-0.393063\pi$
$211$	9.57746			0.659339			0.329670	+	0.944096i	$0.393063\pi$
$212$	−2.99952	−	2.99952i	−0.206008	−	0.206008i
$213$	12.1229			0.830645
$214$	−0.643120	−	0.643120i	−0.0439628	−	0.0439628i
$215$	0.0436769	+	6.29414i	0.00297874	+	0.429257i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−1.24244	+	1.24244i	−0.0843424	+	0.0843424i
$218$	−3.54428	+	3.54428i	−0.240049	+	0.240049i
$219$	4.76883	−	4.76883i	0.322248	−	0.322248i
$220$	8.33149	−	0.0578147i	0.561709	−	0.00389787i
$221$	3.35128	−	0.165517i	0.225431	−	0.0111339i
$222$	−1.20764	+	1.20764i	−0.0810517	+	0.0810517i
$223$	9.61384			0.643790			0.321895	−	0.946775i	$-0.395680\pi$
$223$	9.61384			0.643790			0.321895	+	0.946775i	$0.395680\pi$
$224$		−	1.24244i		−	0.0830141i
$225$	4.99952	−	0.0693897i	0.333301	−	0.00462598i
$226$	−7.01631	+	7.01631i	−0.466718	+	0.466718i
$227$		−	19.1670i		−	1.27216i	−0.771624	−	0.636079i	$-0.780555\pi$
$227$		−	19.1670i		−	1.27216i	0.771624	−	0.636079i	$-0.219445\pi$
$228$		−	7.59788i		−	0.503182i
$229$	19.1000	−	19.1000i	1.26216	−	1.26216i	0.312116	−	0.950044i	$-0.398962\pi$
$229$	19.1000	−	19.1000i	1.26216	−	1.26216i	0.950044	−	0.312116i	$-0.101038\pi$
$230$	20.4119	−	0.141644i	1.34592	−	0.00933974i
$231$		−	4.62939i		−	0.304592i
$232$	8.74193			0.573936
$233$	−7.14541	+	7.14541i	−0.468112	+	0.468112i	−0.901302	−	0.433191i	$-0.857388\pi$
$233$	−7.14541	+	7.14541i	−0.468112	+	0.468112i	0.433191	+	0.901302i	$0.357388\pi$
$234$	−2.42064	+	2.67217i	−0.158242	+	0.174685i
$235$	16.1097	−	16.3349i	1.05088	−	1.06557i
$236$	5.35343	−	5.35343i	0.348479	−	0.348479i
$237$	−4.89533	+	4.89533i	−0.317986	+	0.317986i
$238$	0.817577	−	0.817577i	0.0529957	−	0.0529957i
$239$	−14.7651	−	14.7651i	−0.955076	−	0.955076i	0.0439574	−	0.999033i	$-0.486003\pi$
$239$	−14.7651	−	14.7651i	−0.955076	−	0.955076i	−0.999033	+	0.0439574i	$0.986003\pi$
$240$	−2.23601	+	0.0155164i	−0.144334	+	0.00100158i
$241$	12.0956	+	12.0956i	0.779143	+	0.779143i	0.979685	−	0.200542i	$-0.0642702\pi$
$241$	12.0956	+	12.0956i	0.779143	+	0.779143i	−0.200542	+	0.979685i	$0.564270\pi$
$242$	−2.88341			−0.185352
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	5.64048			0.361095
$245$	−8.56716	+	8.68689i	−0.547336	+	0.554985i
$246$		−	9.71042i		−	0.619114i
$247$	−27.3612	+	1.35135i	−1.74095	+	0.0859844i
$248$	−1.00000	−	1.00000i	−0.0635001	−	0.0635001i
$249$	1.37922	+	1.37922i	0.0874043	+	0.0874043i
$250$	7.73942	−	8.06855i	0.489484	−	0.510300i
$251$		−	14.7406i		−	0.930420i	−0.885200	−	0.465210i	$-0.845979\pi$
$251$		−	14.7406i		−	0.930420i	0.885200	−	0.465210i	$-0.154021\pi$
$252$			1.24244i			0.0782664i
$253$	−34.0139			−2.13843
$254$	−2.43952	+	2.43952i	−0.153069	+	0.153069i
$255$	−1.48160	−	1.46118i	−0.0927813	−	0.0915025i
$256$	1.00000			0.0625000
$257$	2.62072	+	2.62072i	0.163476	+	0.163476i	0.784105	−	0.620629i	$-0.213123\pi$
$257$	2.62072	+	2.62072i	0.163476	+	0.163476i	−0.620629	+	0.784105i	$0.713123\pi$
$258$			2.81489i			0.175248i
$259$	2.12192			0.131850
$260$	0.453572	+	8.04949i	0.0281293	+	0.499208i
$261$	−8.74193			−0.541112
$262$			13.7684i			0.850617i
$263$	5.88735	+	5.88735i	0.363029	+	0.363029i	0.864927	−	0.501898i	$-0.167365\pi$
$263$	5.88735	+	5.88735i	0.363029	+	0.363029i	−0.501898	+	0.864927i	$0.667365\pi$
$264$	3.72604			0.229322
$265$	9.48508	−	0.0658199i	0.582664	−	0.00404328i
$266$	−6.67503	+	6.67503i	−0.409272	+	0.409272i
$267$	−11.2217			−0.686759
$268$		−	6.45566i		−	0.394342i
$269$			8.94934i			0.545651i	0.962064	+	0.272826i	$0.0879582\pi$
$269$			8.94934i			0.545651i	−0.962064	+	0.272826i	$0.912042\pi$
$270$	2.23601	−	0.0155164i	0.136079	−	0.000944297i
$271$	−12.3970	−	12.3970i	−0.753066	−	0.753066i	0.221984	−	0.975050i	$-0.428747\pi$
$271$	−12.3970	−	12.3970i	−0.753066	−	0.753066i	−0.975050	+	0.221984i	$0.928747\pi$
$272$	0.658041	+	0.658041i	0.0398996	+	0.0398996i
$273$	4.47423	−	0.220979i	0.270793	−	0.0133743i
$274$			10.3216i			0.623553i
$275$	−12.9895	+	13.3551i	−0.783294	+	0.805343i
$276$	9.12868			0.549482
$277$	−15.0750	−	15.0750i	−0.905771	−	0.905771i	0.0901568	−	0.995928i	$-0.471263\pi$
$277$	−15.0750	−	15.0750i	−0.905771	−	0.905771i	−0.995928	+	0.0901568i	$0.971263\pi$
$278$	−17.6837			−1.06060
$279$	1.00000	+	1.00000i	0.0598684	+	0.0598684i
$280$	1.97806	+	1.95079i	0.118211	+	0.116582i
$281$	0.279475	+	0.279475i	0.0166721	+	0.0166721i	0.715394	−	0.698722i	$-0.246247\pi$
$281$	0.279475	+	0.279475i	0.0166721	+	0.0166721i	−0.698722	+	0.715394i	$0.746247\pi$
$282$	7.25501	−	7.25501i	0.432030	−	0.432030i
$283$	−20.8023	+	20.8023i	−1.23657	+	1.23657i	−0.275171	+	0.961395i	$0.588735\pi$
$283$	−20.8023	+	20.8023i	−1.23657	+	1.23657i	−0.961395	+	0.275171i	$0.911265\pi$
$284$	8.57216	−	8.57216i	0.508664	−	0.508664i
$285$	12.0964	+	11.9296i	0.716527	+	0.706651i
$286$	−0.662710	−	13.4181i	−0.0391869	−	0.793428i
$287$	−8.53098	+	8.53098i	−0.503568	+	0.503568i
$288$	−1.00000			−0.0589256
$289$		−	16.1340i		−	0.949057i
$290$	−13.7260	+	13.9178i	−0.806016	+	0.817281i
$291$	−10.1464	+	10.1464i	−0.594793	+	0.594793i
$292$		−	6.74415i		−	0.394671i
$293$			14.0996i			0.823707i	0.911250	+	0.411854i	$0.135119\pi$
$293$			14.0996i			0.823707i	−0.911250	+	0.411854i	$0.864881\pi$
$294$	−3.85821	+	3.85821i	−0.225016	+	0.225016i
$295$	0.117473	+	16.9286i	0.00683954	+	0.985623i
$296$			1.70787i			0.0992677i
$297$	−3.72604			−0.216207
$298$	1.57025	−	1.57025i	0.0909620	−	0.0909620i
$299$	−1.62362	−	32.8739i	−0.0938962	−	1.90114i
$300$	3.48613	−	3.58426i	0.201272	−	0.206937i
$301$	2.47299	−	2.47299i	0.142541	−	0.142541i
$302$	0.254890	−	0.254890i	0.0146673	−	0.0146673i
$303$	13.5569	−	13.5569i	0.778821	−	0.778821i
$304$	−5.37251	−	5.37251i	−0.308135	−	0.308135i
$305$	−8.85629	+	8.98006i	−0.507110	+	0.514197i
$306$	−0.658041	−	0.658041i	−0.0376177	−	0.0376177i
$307$	−11.4693			−0.654585			−0.327293	−	0.944923i	$-0.606136\pi$
$307$	−11.4693			−0.654585			−0.327293	+	0.944923i	$0.606136\pi$
$308$	−3.27347	−	3.27347i	−0.186523	−	0.186523i
$309$	−5.41144			−0.307846
$310$	3.16220	−	0.0219435i	0.179601	−	0.00124631i
$311$			7.46653i			0.423388i	0.977336	+	0.211694i	$0.0678981\pi$
$311$			7.46653i			0.423388i	−0.977336	+	0.211694i	$0.932102\pi$
$312$	0.177859	+	3.60116i	0.0100693	+	0.203876i
$313$	5.35015	+	5.35015i	0.302408	+	0.302408i	0.841955	−	0.539547i	$-0.181405\pi$
$313$	5.35015	+	5.35015i	0.302408	+	0.302408i	−0.539547	+	0.841955i	$0.681405\pi$
$314$	−1.55691	−	1.55691i	−0.0878617	−	0.0878617i
$315$	−1.97806	−	1.95079i	−0.111451	−	0.109915i
$316$			6.92304i			0.389452i
$317$		−	12.7940i		−	0.718583i	−0.933225	−	0.359291i	$-0.883018\pi$
$317$		−	12.7940i		−	0.718583i	0.933225	−	0.359291i	$-0.116982\pi$
$318$	4.24196			0.237877
$319$	23.0325	−	23.0325i	1.28957	−	1.28957i
$320$	−1.57013	+	1.59207i	−0.0877729	+	0.0889996i
$321$	0.909509			0.0507638
$322$	−8.01990	−	8.01990i	−0.446932	−	0.446932i
$323$		−	7.07066i		−	0.393422i
$324$	1.00000			0.0555556
$325$	−13.5275	−	11.9166i	−0.750373	−	0.661015i
$326$	−14.2344			−0.788373
$327$		−	5.01237i		−	0.277185i
$328$	−6.86630	−	6.86630i	−0.379128	−	0.379128i
$329$	−12.7476			−0.702799
$330$	−5.85037	+	5.93213i	−0.322052	+	0.326553i
$331$	3.70065	−	3.70065i	0.203406	−	0.203406i	−0.598052	−	0.801458i	$-0.704058\pi$
$331$	3.70065	−	3.70065i	0.203406	−	0.203406i	0.801458	+	0.598052i	$0.204058\pi$
$332$	1.95051			0.107048
$333$		−	1.70787i		−	0.0935905i
$334$			15.4187i			0.843674i
$335$	10.2779	+	10.1362i	0.561540	+	0.553801i
$336$	0.878539	+	0.878539i	0.0479282	+	0.0479282i
$337$	4.31081	+	4.31081i	0.234825	+	0.234825i	0.814703	−	0.579878i	$-0.196900\pi$
$337$	4.31081	+	4.31081i	0.234825	+	0.234825i	−0.579878	+	0.814703i	$0.696900\pi$
$338$	12.9367	−	1.28100i	0.703665	−	0.0696771i
$339$		−	9.92256i		−	0.538920i
$340$	−2.08086	+	0.0144397i	−0.112850	+	0.000783103i
$341$	−5.26942			−0.285355
$342$	5.37251	+	5.37251i	0.290512	+	0.290512i
$343$	15.4763			0.835640
$344$	1.99043	+	1.99043i	0.107317	+	0.107317i
$345$	−14.3332	+	14.5335i	−0.771674	+	0.782459i
$346$	12.4283	+	12.4283i	0.668148	+	0.668148i
$347$	−0.634599	+	0.634599i	−0.0340671	+	0.0340671i	−0.723935	−	0.689868i	$-0.757669\pi$
$347$	−0.634599	+	0.634599i	−0.0340671	+	0.0340671i	0.689868	+	0.723935i	$0.257669\pi$
$348$	−6.18148	+	6.18148i	−0.331362	+	0.331362i
$349$	−19.7728	+	19.7728i	−1.05841	+	1.05841i	−0.0602300	+	0.998185i	$0.519183\pi$
$349$	−19.7728	+	19.7728i	−1.05841	+	1.05841i	−0.998185	+	0.0602300i	$0.980817\pi$
$350$	−6.21161	+	0.0862126i	−0.332024	+	0.00460826i
$351$	−0.177859	−	3.60116i	−0.00949341	−	0.192216i
$352$	2.63471	−	2.63471i	0.140431	−	0.140431i
$353$	−18.6883			−0.994679			−0.497340	−	0.867556i	$-0.665690\pi$
$353$	−18.6883			−0.994679			−0.497340	+	0.867556i	$0.665690\pi$
$354$			7.57090i			0.402389i
$355$	0.188103	+	27.1069i	0.00998347	+	1.43869i
$356$	−7.93497	+	7.93497i	−0.420552	+	0.420552i
$357$			1.15623i			0.0611941i
$358$		−	3.56872i		−	0.188613i
$359$	0.228745	−	0.228745i	0.0120727	−	0.0120727i	−0.701045	−	0.713117i	$-0.747283\pi$
$359$	0.228745	−	0.228745i	0.0120727	−	0.0120727i	0.713117	+	0.701045i	$0.247283\pi$
$360$	1.57013	−	1.59207i	0.0827531	−	0.0839096i
$361$			38.7277i			2.03830i
$362$	3.22773			0.169646
$363$	2.03888	−	2.03888i	0.107013	−	0.107013i
$364$	3.00750	−	3.32002i	0.157636	−	0.174016i
$365$	10.7372	+	10.5892i	0.562009	+	0.554263i
$366$	−3.98843	+	3.98843i	−0.208478	+	0.208478i
$367$	−1.17022	+	1.17022i	−0.0610848	+	0.0610848i	−0.736989	−	0.675904i	$-0.763753\pi$
$367$	−1.17022	+	1.17022i	−0.0610848	+	0.0610848i	0.675904	+	0.736989i	$0.263753\pi$
$368$	6.45495	−	6.45495i	0.336488	−	0.336488i
$369$	6.86630	+	6.86630i	0.357445	+	0.357445i
$370$	−2.71905	−	2.68157i	−0.141356	−	0.139408i
$371$	−3.72673	−	3.72673i	−0.193482	−	0.193482i
$372$	1.41421			0.0733236
$373$	0.230351	+	0.230351i	0.0119271	+	0.0119271i	0.713045	−	0.701118i	$-0.247315\pi$
$373$	0.230351	+	0.230351i	0.0119271	+	0.0119271i	−0.701118	+	0.713045i	$0.747315\pi$
$374$	3.46750			0.179300
$375$	0.232731	+	11.1779i	0.0120182	+	0.577225i
$376$		−	10.2601i		−	0.529126i
$377$	23.3599	+	21.1611i	1.20310	+	1.08985i
$378$	−0.878539	−	0.878539i	−0.0451872	−	0.0451872i
$379$	19.8037	+	19.8037i	1.01725	+	1.01725i	0.999849	+	0.0173990i	$0.00553854\pi$
$379$	19.8037	+	19.8037i	1.01725	+	1.01725i	0.0173990	+	0.999849i	$0.494461\pi$
$380$	16.9890	−	0.117892i	0.871515	−	0.00604771i
$381$		−	3.45000i		−	0.176749i
$382$		−	4.46490i		−	0.228444i
$383$	−14.1230			−0.721651			−0.360826	−	0.932633i	$-0.617505\pi$
$383$	−14.1230			−0.721651			−0.360826	+	0.932633i	$0.617505\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	10.3514	−	0.0718314i	0.527555	−	0.00366087i
$386$	2.88820			0.147005
$387$	−1.99043	−	1.99043i	−0.101179	−	0.101179i
$388$			14.3492i			0.728470i
$389$	8.73801			0.443035			0.221517	−	0.975156i	$-0.428899\pi$
$389$	8.73801			0.443035			0.221517	+	0.975156i	$0.428899\pi$
$390$	−6.01257	−	5.37112i	−0.304458	−	0.271977i
$391$	8.49525			0.429623
$392$			5.45634i			0.275587i
$393$	−9.73575	−	9.73575i	−0.491104	−	0.491104i
$394$	13.4960			0.679917
$395$	−11.0220	−	10.8701i	−0.554576	−	0.546933i
$396$	−2.63471	+	2.63471i	−0.132399	+	0.132399i
$397$	−8.96140			−0.449760			−0.224880	−	0.974386i	$-0.572199\pi$
$397$	−8.96140			−0.449760			−0.224880	+	0.974386i	$0.572199\pi$
$398$			18.2097i			0.912769i
$399$		−	9.43992i		−	0.472587i
$400$	−0.0693897	−	4.99952i	−0.00346948	−	0.249976i
$401$	−19.2434	−	19.2434i	−0.960971	−	0.960971i	0.0382953	−	0.999266i	$-0.487807\pi$
$401$	−19.2434	−	19.2434i	−0.960971	−	0.960971i	−0.999266	+	0.0382953i	$0.987807\pi$
$402$	4.56484	+	4.56484i	0.227674	+	0.227674i
$403$	−0.251531	−	5.09281i	−0.0125296	−	0.253691i
$404$		−	19.1723i		−	0.953857i
$405$	−1.57013	+	1.59207i	−0.0780203	+	0.0791107i
$406$	10.8613			0.539039
$407$	4.49973	+	4.49973i	0.223044	+	0.223044i
$408$	−0.930610			−0.0460721
$409$	10.3171	+	10.3171i	0.510147	+	0.510147i	0.914571	−	0.404425i	$-0.132528\pi$
$409$	10.3171	+	10.3171i	0.510147	+	0.510147i	−0.404425	+	0.914571i	$0.632528\pi$
$410$	21.7126	−	0.150671i	1.07231	−	0.00744109i
$411$	−7.29850	−	7.29850i	−0.360008	−	0.360008i
$412$	−3.82647	+	3.82647i	−0.188516	+	0.188516i
$413$	6.65132	−	6.65132i	0.327290	−	0.327290i
$414$	−6.45495	+	6.45495i	−0.317244	+	0.317244i
$415$	−3.06255	+	3.10535i	−0.150335	+	0.152436i
$416$	2.67217	+	2.42064i	0.131014	+	0.118682i
$417$	12.5043	−	12.5043i	0.612338	−	0.612338i
$418$	−28.3100			−1.38469
$419$			32.5361i			1.58949i	0.606942	+	0.794746i	$0.292396\pi$
$419$			32.5361i			1.58949i	−0.606942	+	0.794746i	$0.707604\pi$
$420$	−2.77812	+	0.0192782i	−0.135558	+	0.000940679i
$421$	16.1077	−	16.1077i	0.785041	−	0.785041i	−0.195636	−	0.980677i	$-0.562677\pi$
$421$	16.1077	−	16.1077i	0.785041	−	0.785041i	0.980677	+	0.195636i	$0.0626771\pi$
$422$			9.57746i			0.466223i
$423$			10.2601i			0.498865i
$424$	2.99952	−	2.99952i	0.145669	−	0.145669i
$425$	3.24423	−	3.33555i	0.157368	−	0.161798i
$426$			12.1229i			0.587355i
$427$	7.00797			0.339139
$428$	0.643120	−	0.643120i	0.0310864	−	0.0310864i
$429$	9.95663	+	9.01941i	0.480711	+	0.435461i
$430$	−6.29414	+	0.0436769i	−0.303530	+	0.00210629i
$431$	11.4172	−	11.4172i	0.549946	−	0.549946i	−0.376479	−	0.926425i	$-0.622865\pi$
$431$	11.4172	−	11.4172i	0.549946	−	0.549946i	0.926425	+	0.376479i	$0.122865\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	7.47995	−	7.47995i	0.359463	−	0.359463i	−0.504152	−	0.863615i	$-0.668195\pi$
$433$	7.47995	−	7.47995i	0.359463	−	0.359463i	0.863615	+	0.504152i	$0.168195\pi$
$434$	−1.24244	−	1.24244i	−0.0596391	−	0.0596391i
$435$	−0.135643	−	19.5471i	−0.00650359	−	0.937211i
$436$	−3.54428	−	3.54428i	−0.169740	−	0.169740i
$437$	−69.3586			−3.31787
$438$	4.76883	+	4.76883i	0.227864	+	0.227864i
$439$	−32.8415			−1.56744			−0.783721	−	0.621113i	$-0.786681\pi$
$439$	−32.8415			−1.56744			−0.783721	+	0.621113i	$0.786681\pi$
$440$	0.0578147	+	8.33149i	0.00275621	+	0.397188i
$441$		−	5.45634i		−	0.259826i
$442$	0.165517	+	3.35128i	0.00787286	+	0.159404i
$443$	1.29541	+	1.29541i	0.0615466	+	0.0615466i	0.737210	−	0.675664i	$-0.236143\pi$
$443$	1.29541	+	1.29541i	0.0615466	+	0.0615466i	−0.675664	+	0.737210i	$0.736143\pi$
$444$	−1.20764	−	1.20764i	−0.0573122	−	0.0573122i
$445$	−0.174121	−	25.0920i	−0.00825412	−	1.18947i
$446$			9.61384i			0.455229i
$447$			2.22066i			0.105034i
$448$	1.24244			0.0586998
$449$	7.46259	−	7.46259i	0.352182	−	0.352182i	−0.508739	−	0.860921i	$-0.669888\pi$
$449$	7.46259	−	7.46259i	0.352182	−	0.352182i	0.860921	+	0.508739i	$0.169888\pi$
$450$	0.0693897	+	4.99952i	0.00327106	+	0.235680i
$451$	−36.1815			−1.70372
$452$	−7.01631	−	7.01631i	−0.330020	−	0.330020i
$453$			0.360469i			0.0169363i
$454$	19.1670			0.899552
$455$	0.563537	+	10.0010i	0.0264190	+	0.468855i
$456$	7.59788			0.355803
$457$		−	18.6585i		−	0.872809i	−0.899751	−	0.436404i	$-0.856252\pi$
$457$		−	18.6585i		−	0.872809i	0.899751	−	0.436404i	$-0.143748\pi$
$458$	19.1000	+	19.1000i	0.892482	+	0.892482i
$459$	0.930610			0.0434372
$460$	0.141644	+	20.4119i	0.00660419	+	0.951708i
$461$	−5.51836	+	5.51836i	−0.257016	+	0.257016i	−0.823839	−	0.566824i	$-0.808172\pi$
$461$	−5.51836	+	5.51836i	−0.257016	+	0.257016i	0.566824	+	0.823839i	$0.308172\pi$
$462$	4.62939			0.215379
$463$			7.00926i			0.325748i	0.986647	+	0.162874i	$0.0520764\pi$
$463$			7.00926i			0.325748i	−0.986647	+	0.162874i	$0.947924\pi$
$464$			8.74193i			0.405834i
$465$	−2.22050	+	2.25153i	−0.102973	+	0.104412i
$466$	−7.14541	−	7.14541i	−0.331005	−	0.331005i
$467$	21.7877	+	21.7877i	1.00821	+	1.00821i	0.999966	+	0.00824840i	$0.00262558\pi$
$467$	21.7877	+	21.7877i	1.00821	+	1.00821i	0.00824840	+	0.999966i	$0.497374\pi$
$468$	−2.67217	−	2.42064i	−0.123521	−	0.111894i
$469$		−	8.02078i		−	0.370365i
$470$	16.3349	+	16.1097i	0.753472	+	0.743087i
$471$	2.20181			0.101454
$472$	5.35343	+	5.35343i	0.246412	+	0.246412i
$473$	10.4884			0.482258
$474$	−4.89533	−	4.89533i	−0.224850	−	0.224850i
$475$	−26.4872	+	27.2328i	−1.21531	+	1.24952i
$476$	0.817577	+	0.817577i	0.0374736	+	0.0374736i
$477$	−2.99952	+	2.99952i	−0.137339	+	0.137339i
$478$	14.7651	−	14.7651i	0.675341	−	0.675341i
$479$	3.07248	−	3.07248i	0.140385	−	0.140385i	−0.633422	−	0.773807i	$-0.718350\pi$
$479$	3.07248	−	3.07248i	0.140385	−	0.140385i	0.773807	+	0.633422i	$0.218350\pi$
$480$	−0.0155164	−	2.23601i	−0.000708223	−	0.102060i
$481$	−4.13413	+	4.56371i	−0.188500	+	0.208087i
$482$	−12.0956	+	12.0956i	−0.550938	+	0.550938i
$483$	11.3419			0.516072
$484$		−	2.88341i		−	0.131064i
$485$	−22.8449	−	22.5301i	−1.03734	−	1.02304i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$			15.5332i			0.703877i	0.936023	+	0.351938i	$0.114477\pi$
$487$			15.5332i			0.703877i	−0.936023	+	0.351938i	$0.885523\pi$
$488$			5.64048i			0.255333i
$489$	10.0653	−	10.0653i	0.455167	−	0.455167i
$490$	−8.68689	−	8.56716i	−0.392434	−	0.387025i
$491$		−	28.7710i		−	1.29842i	−0.760610	−	0.649209i	$-0.775100\pi$
$491$		−	28.7710i		−	1.29842i	0.760610	−	0.649209i	$-0.224900\pi$
$492$	9.71042			0.437779
$493$	−5.75255	+	5.75255i	−0.259082	+	0.259082i
$494$	−1.35135	−	27.3612i	−0.0608001	−	1.23104i
$495$	−0.0578147	−	8.33149i	−0.00259858	−	0.374473i
$496$	1.00000	−	1.00000i	0.0449013	−	0.0449013i
$497$	10.6504	−	10.6504i	0.477736	−	0.477736i
$498$	−1.37922	+	1.37922i	−0.0618042	+	0.0618042i
$499$	8.49652	+	8.49652i	0.380357	+	0.380357i	0.871231	−	0.490874i	$-0.163322\pi$
$499$	8.49652	+	8.49652i	0.380357	+	0.380357i	−0.490874	+	0.871231i	$0.663322\pi$
$500$	8.06855	+	7.73942i	0.360836	+	0.346117i
$501$	−10.9027	−	10.9027i	−0.487095	−	0.487095i
$502$	14.7406			0.657907
$503$	8.18812	+	8.18812i	0.365090	+	0.365090i	0.865683	−	0.500593i	$-0.166885\pi$
$503$	8.18812	+	8.18812i	0.365090	+	0.365090i	−0.500593	+	0.865683i	$0.666885\pi$
$504$	−1.24244			−0.0553427
$505$	30.5237	+	30.1030i	1.35829	+	1.33956i
$506$		−	34.0139i		−	1.51210i
$507$	−8.24185	+	10.0535i	−0.366033	+	0.446490i
$508$	−2.43952	−	2.43952i	−0.108236	−	0.108236i
$509$	0.509282	+	0.509282i	0.0225735	+	0.0225735i	0.718303	−	0.695730i	$-0.244919\pi$
$509$	0.509282	+	0.509282i	0.0225735	+	0.0225735i	−0.695730	+	0.718303i	$0.744919\pi$
$510$	1.46118	−	1.48160i	0.0647021	−	0.0656063i
$511$		−	8.37921i		−	0.370674i
$512$			1.00000i			0.0441942i
$513$	−7.59788			−0.335454
$514$	−2.62072	+	2.62072i	−0.115595	+	0.115595i
$515$	−0.0839660	−	12.1001i	−0.00369998	−	0.533192i
$516$	−2.81489			−0.123919
$517$	−27.0325	−	27.0325i	−1.18889	−	1.18889i
$518$			2.12192i			0.0932319i
$519$	−17.5762			−0.771510
$520$	−8.04949	+	0.453572i	−0.352993	+	0.0198905i
$521$	−2.55725			−0.112035			−0.0560176	−	0.998430i	$-0.517840\pi$
$521$	−2.55725			−0.112035			−0.0560176	+	0.998430i	$0.517840\pi$
$522$		−	8.74193i		−	0.382624i
$523$	23.9232	+	23.9232i	1.04609	+	1.04609i	0.998885	+	0.0472039i	$0.0150310\pi$
$523$	23.9232	+	23.9232i	1.04609	+	1.04609i	0.0472039	+	0.998885i	$0.484969\pi$
$524$	−13.7684			−0.601477
$525$	4.33131	−	4.45323i	0.189034	−	0.194355i
$526$	−5.88735	+	5.88735i	−0.256700	+	0.256700i
$527$	1.31608			0.0573294
$528$			3.72604i			0.162155i
$529$		−	60.3329i		−	2.62317i
$530$	0.0658199	+	9.48508i	0.00285903	+	0.412006i
$531$	−5.35343	−	5.35343i	−0.232319	−	0.232319i
$532$	−6.67503	−	6.67503i	−0.289399	−	0.289399i
$533$	−1.72708	−	34.9688i	−0.0748083	−	1.51467i
$534$		−	11.2217i		−	0.485612i
$535$	0.0141123	+	2.03367i	0.000610127	+	0.0879234i
$536$	6.45566			0.278842
$537$	2.52347	+	2.52347i	0.108896	+	0.108896i
$538$	−8.94934			−0.385834
$539$	14.3759	+	14.3759i	0.619213	+	0.619213i
$540$	0.0155164	+	2.23601i	0.000667719	+	0.0962227i
$541$	11.2496	+	11.2496i	0.483658	+	0.483658i	0.906298	−	0.422640i	$-0.138897\pi$
$541$	11.2496	+	11.2496i	0.483658	+	0.483658i	−0.422640	+	0.906298i	$0.638897\pi$
$542$	12.3970	−	12.3970i	0.532498	−	0.532498i
$543$	−2.28235	+	2.28235i	−0.0979452	+	0.0979452i
$544$	−0.658041	+	0.658041i	−0.0282133	+	0.0282133i
$545$	11.2077	−	0.0777739i	0.480087	−	0.00333147i
$546$	0.220979	+	4.47423i	0.00945704	+	0.191479i
$547$	−23.5606	+	23.5606i	−1.00738	+	1.00738i	−0.00740567	+	0.999973i	$0.502357\pi$
$547$	−23.5606	+	23.5606i	−1.00738	+	1.00738i	−0.999973	+	0.00740567i	$0.997643\pi$
$548$	−10.3216			−0.440918
$549$		−	5.64048i		−	0.240730i
$550$	−13.3551	−	12.9895i	−0.569464	−	0.553873i
$551$	46.9661	−	46.9661i	2.00082	−	2.00082i
$552$			9.12868i			0.388543i
$553$			8.60147i			0.365772i
$554$	15.0750	−	15.0750i	0.640477	−	0.640477i
$555$	3.81881	−	0.0264999i	0.162100	−	0.00112486i
$556$		−	17.6837i		−	0.749958i
$557$	13.9488			0.591028			0.295514	−	0.955338i	$-0.404509\pi$
$557$	13.9488			0.591028			0.295514	+	0.955338i	$0.404509\pi$
$558$	−1.00000	+	1.00000i	−0.0423334	+	0.0423334i
$559$	0.500654	+	10.1369i	0.0211754	+	0.428744i
$560$	−1.95079	+	1.97806i	−0.0824361	+	0.0835881i
$561$	−2.45189	+	2.45189i	−0.103519	+	0.103519i
$562$	−0.279475	+	0.279475i	−0.0117889	+	0.0117889i
$563$	23.1339	−	23.1339i	0.974977	−	0.974977i	−0.0247178	−	0.999694i	$-0.507869\pi$
$563$	23.1339	−	23.1339i	0.974977	−	0.974977i	0.999694	+	0.0247178i	$0.00786873\pi$
$564$	7.25501	+	7.25501i	0.305491	+	0.305491i
$565$	22.1870	−	0.153962i	0.933414	−	0.00647724i
$566$	−20.8023	−	20.8023i	−0.874384	−	0.874384i
$567$	1.24244			0.0521776
$568$	8.57216	+	8.57216i	0.359680	+	0.359680i
$569$	23.2671			0.975409			0.487705	−	0.873009i	$-0.337834\pi$
$569$	23.2671			0.975409			0.487705	+	0.873009i	$0.337834\pi$
$570$	−11.9296	+	12.0964i	−0.499678	+	0.506661i
$571$			16.7988i			0.703007i	0.936186	+	0.351504i	$0.114330\pi$
$571$			16.7988i			0.703007i	−0.936186	+	0.351504i	$0.885670\pi$
$572$	13.4181	−	0.662710i	0.561038	−	0.0277093i
$573$	3.15716	+	3.15716i	0.131892	+	0.131892i
$574$	−8.53098	−	8.53098i	−0.356076	−	0.356076i
$575$	−32.7196	−	31.8238i	−1.36450	−	1.32714i
$576$		−	1.00000i		−	0.0416667i
$577$		−	7.17858i		−	0.298848i	−0.988773	−	0.149424i	$-0.952258\pi$
$577$		−	7.17858i		−	0.298848i	0.988773	−	0.149424i	$-0.0477419\pi$
$578$	16.1340			0.671084
$579$	−2.04226	+	2.04226i	−0.0848735	+	0.0848735i
$580$	−13.9178	−	13.7260i	−0.577905	−	0.569940i
$581$	2.42339			0.100539
$582$	−10.1464	−	10.1464i	−0.420582	−	0.420582i
$583$		−	15.8057i		−	0.654606i
$584$	6.74415			0.279075
$585$	8.04949	−	0.453572i	0.332805	−	0.0187529i
$586$	−14.0996			−0.582449
$587$		−	7.60633i		−	0.313947i	−0.987603	−	0.156973i	$-0.949826\pi$
$587$		−	7.60633i		−	0.313947i	0.987603	−	0.156973i	$-0.0501737\pi$
$588$	−3.85821	−	3.85821i	−0.159110	−	0.159110i
$589$	−10.7450			−0.442741
$590$	−16.9286	+	0.117473i	−0.696941	+	0.00483628i
$591$	−9.54310	+	9.54310i	−0.392551	+	0.392551i
$592$	−1.70787			−0.0701929
$593$			42.3981i			1.74108i	0.492097	+	0.870540i	$0.336231\pi$
$593$			42.3981i			1.74108i	−0.492097	+	0.870540i	$0.663769\pi$
$594$		−	3.72604i		−	0.152881i
$595$	−2.58534	+	0.0179405i	−0.105989	+	0.000735488i
$596$	1.57025	+	1.57025i	0.0643198	+	0.0643198i
$597$	−12.8762	−	12.8762i	−0.526987	−	0.526987i
$598$	32.8739	−	1.62362i	1.34431	−	0.0663947i
$599$			13.5731i			0.554581i	0.960786	+	0.277291i	$0.0894365\pi$
$599$			13.5731i			0.554581i	−0.960786	+	0.277291i	$0.910563\pi$
$600$	3.58426	+	3.48613i	0.146327	+	0.142321i
$601$	−26.6588			−1.08743			−0.543717	−	0.839269i	$-0.682984\pi$
$601$	−26.6588			−1.08743			−0.543717	+	0.839269i	$0.682984\pi$
$602$	2.47299	+	2.47299i	0.100792	+	0.100792i
$603$	−6.45566			−0.262895
$604$	0.254890	+	0.254890i	0.0103713	+	0.0103713i
$605$	4.59059	+	4.52732i	0.186634	+	0.184062i
$606$	13.5569	+	13.5569i	0.550710	+	0.550710i
$607$	1.74990	−	1.74990i	0.0710264	−	0.0710264i	−0.670701	−	0.741728i	$-0.734007\pi$
$607$	1.74990	−	1.74990i	0.0710264	−	0.0710264i	0.741728	+	0.670701i	$0.234007\pi$
$608$	5.37251	−	5.37251i	0.217884	−	0.217884i
$609$	−7.68013	+	7.68013i	−0.311214	+	0.311214i
$610$	−8.98006	−	8.85629i	−0.363592	−	0.358581i
$611$	24.8361	−	27.4168i	1.00476	−	1.10917i
$612$	0.658041	−	0.658041i	0.0265997	−	0.0265997i
$613$	−29.7886			−1.20315			−0.601576	−	0.798816i	$-0.705460\pi$
$613$	−29.7886			−1.20315			−0.601576	+	0.798816i	$0.705460\pi$
$614$		−	11.4693i		−	0.462862i
$615$	−15.2466	+	15.4597i	−0.614803	+	0.623395i
$616$	3.27347	−	3.27347i	0.131892	−	0.131892i
$617$		−	14.9125i		−	0.600355i	−0.953883	−	0.300177i	$-0.902954\pi$
$617$		−	14.9125i		−	0.600355i	0.953883	−	0.300177i	$-0.0970459\pi$
$618$		−	5.41144i		−	0.217680i
$619$	6.96418	−	6.96418i	0.279914	−	0.279914i	−0.553161	−	0.833075i	$-0.686578\pi$
$619$	6.96418	−	6.96418i	0.279914	−	0.279914i	0.833075	+	0.553161i	$0.186578\pi$
$620$	0.0219435	+	3.16220i	0.000881271	+	0.126997i
$621$		−	9.12868i		−	0.366321i
$622$	−7.46653			−0.299381
$623$	−9.85873	+	9.85873i	−0.394982	+	0.394982i
$624$	−3.60116	+	0.177859i	−0.144162	+	0.00712006i
$625$	−24.9904	+	0.693830i	−0.999615	+	0.0277532i
$626$	−5.35015	+	5.35015i	−0.213835	+	0.213835i
$627$	20.0182	−	20.0182i	0.799450	−	0.799450i
$628$	1.55691	−	1.55691i	0.0621276	−	0.0621276i
$629$	−1.12385	−	1.12385i	−0.0448107	−	0.0448107i
$630$	1.95079	−	1.97806i	0.0777215	−	0.0788077i
$631$	18.3113	+	18.3113i	0.728962	+	0.728962i	0.970413	−	0.241451i	$-0.0776233\pi$
$631$	18.3113	+	18.3113i	0.728962	+	0.728962i	−0.241451	+	0.970413i	$0.577623\pi$
$632$	−6.92304			−0.275384
$633$	−6.77228	−	6.77228i	−0.269174	−	0.269174i
$634$	12.7940			0.508115
$635$	7.71424	−	0.0535315i	0.306130	−	0.00212433i
$636$			4.24196i			0.168205i
$637$	−13.2078	+	14.5803i	−0.523314	+	0.577691i
$638$	23.0325	+	23.0325i	0.911864	+	0.911864i
$639$	−8.57216	−	8.57216i	−0.339110	−	0.339110i
$640$	−1.59207	−	1.57013i	−0.0629322	−	0.0620648i
$641$			28.0194i			1.10670i	0.832949	+	0.553350i	$0.186651\pi$
$641$			28.0194i			1.10670i	−0.832949	+	0.553350i	$0.813349\pi$
$642$			0.909509i			0.0358954i
$643$	25.2580			0.996080			0.498040	−	0.867154i	$-0.334053\pi$
$643$	25.2580			0.996080			0.498040	+	0.867154i	$0.334053\pi$
$644$	8.01990	−	8.01990i	0.316028	−	0.316028i
$645$	4.41974	−	4.48151i	0.174027	−	0.176459i
$646$	7.07066			0.278192
$647$	21.1527	+	21.1527i	0.831598	+	0.831598i	0.987735	−	0.156137i	$-0.0499042\pi$
$647$	21.1527	+	21.1527i	0.831598	+	0.831598i	−0.156137	+	0.987735i	$0.549904\pi$
$648$			1.00000i			0.0392837i
$649$	28.2095			1.10732
$650$	11.9166	−	13.5275i	0.467408	−	0.530594i
$651$	1.75708			0.0688653
$652$		−	14.2344i		−	0.557464i
$653$	−27.6098	−	27.6098i	−1.08046	−	1.08046i	−0.996467	−	0.0839887i	$-0.973234\pi$
$653$	−27.6098	−	27.6098i	−1.08046	−	1.08046i	−0.0839887	−	0.996467i	$-0.526766\pi$
$654$	5.01237			0.195999
$655$	21.6182	−	21.9203i	0.844694	−	0.856499i
$656$	6.86630	−	6.86630i	0.268084	−	0.268084i
$657$	−6.74415			−0.263114
$658$		−	12.7476i		−	0.496954i
$659$			30.7147i			1.19647i	0.801319	+	0.598237i	$0.204132\pi$
$659$			30.7147i			1.19647i	−0.801319	+	0.598237i	$0.795868\pi$
$660$	−5.93213	−	5.85037i	−0.230908	−	0.227725i
$661$	−18.7791	−	18.7791i	−0.730421	−	0.730421i	0.240282	−	0.970703i	$-0.422760\pi$
$661$	−18.7791	−	18.7791i	−0.730421	−	0.730421i	−0.970703	+	0.240282i	$0.922760\pi$
$662$	3.70065	+	3.70065i	0.143830	+	0.143830i
$663$	−2.48675	−	2.25267i	−0.0965774	−	0.0874866i
$664$			1.95051i			0.0756943i
$665$	21.1078	−	0.146473i	0.818525	−	0.00567999i
$666$	1.70787			0.0661785
$667$	56.4288	+	56.4288i	2.18493	+	2.18493i
$668$	−15.4187			−0.596567
$669$	−6.79801	−	6.79801i	−0.262826	−	0.262826i
$670$	−10.1362	+	10.2779i	−0.391596	+	0.397069i
$671$	14.8610	+	14.8610i	0.573704	+	0.573704i
$672$	−0.878539	+	0.878539i	−0.0338904	+	0.0338904i
$673$	−17.4743	+	17.4743i	−0.673583	+	0.673583i	−0.958540	−	0.284957i	$-0.908021\pi$
$673$	−17.4743	+	17.4743i	−0.673583	+	0.673583i	0.284957	+	0.958540i	$0.408021\pi$
$674$	−4.31081	+	4.31081i	−0.166046	+	0.166046i
$675$	−3.58426	−	3.48613i	−0.137958	−	0.134181i
$676$	1.28100	+	12.9367i	0.0492691	+	0.497567i
$677$	−3.68324	+	3.68324i	−0.141559	+	0.141559i	−0.774335	−	0.632776i	$-0.781915\pi$
$677$	−3.68324	+	3.68324i	−0.141559	+	0.141559i	0.632776	+	0.774335i	$0.281915\pi$
$678$	9.92256			0.381074
$679$			17.8280i			0.684177i
$680$	−0.0144397	−	2.08086i	−0.000553737	−	0.0797973i
$681$	−13.5531	+	13.5531i	−0.519357	+	0.519357i
$682$		−	5.26942i		−	0.201777i
$683$		−	21.9478i		−	0.839808i	−0.907569	−	0.419904i	$-0.862064\pi$
$683$		−	21.9478i		−	0.839808i	0.907569	−	0.419904i	$-0.137936\pi$
$684$	−5.37251	+	5.37251i	−0.205423	+	0.205423i
$685$	16.2063	−	16.4328i	0.619211	−	0.627864i
$686$			15.4763i			0.590887i
$687$	−27.0114			−1.03055
$688$	−1.99043	+	1.99043i	−0.0758844	+	0.0758844i
$689$	15.2760	−	0.754470i	0.581969	−	0.0287430i
$690$	−14.5335	−	14.3332i	−0.553282	−	0.545656i
$691$	10.8503	−	10.8503i	0.412765	−	0.412765i	−0.469936	−	0.882701i	$-0.655723\pi$
$691$	10.8503	−	10.8503i	0.412765	−	0.412765i	0.882701	+	0.469936i	$0.155723\pi$
$692$	−12.4283	+	12.4283i	−0.472452	+	0.472452i
$693$	−3.27347	+	3.27347i	−0.124349	+	0.124349i
$694$	−0.634599	−	0.634599i	−0.0240890	−	0.0240890i
$695$	28.1538	+	27.7658i	1.06793	+	1.05322i
$696$	−6.18148	−	6.18148i	−0.234308	−	0.234308i
$697$	9.03662			0.342286
$698$	−19.7728	−	19.7728i	−0.748412	−	0.748412i
$699$	10.1051			0.382212
$700$	−0.0862126	−	6.21161i	−0.00325853	−	0.234777i
$701$		−	21.0611i		−	0.795465i	−0.917501	−	0.397733i	$-0.869797\pi$
$701$		−	21.0611i		−	0.795465i	0.917501	−	0.397733i	$-0.130203\pi$
$702$	3.60116	−	0.177859i	0.135917	−	0.00671285i
$703$	9.17553	+	9.17553i	0.346062	+	0.346062i
$704$	2.63471	+	2.63471i	0.0992994	+	0.0992994i
$705$	−22.9418	+	0.159200i	−0.864039	+	0.00599583i
$706$		−	18.6883i		−	0.703344i
$707$		−	23.8204i		−	0.895860i
$708$	−7.57090			−0.284532
$709$	−6.41268	+	6.41268i	−0.240833	+	0.240833i	−0.817195	−	0.576362i	$-0.804472\pi$
$709$	−6.41268	+	6.41268i	−0.240833	+	0.240833i	0.576362	+	0.817195i	$0.304472\pi$
$710$	−27.1069	+	0.188103i	−1.01730	+	0.00705938i
$711$	6.92304			0.259634
$712$	−7.93497	−	7.93497i	−0.297375	−	0.297375i
$713$		−	12.9099i		−	0.483480i
$714$	−1.15623			−0.0432708
$715$	−20.0130	+	22.4031i	−0.748446	+	0.837829i
$716$	3.56872			0.133369
$717$			20.8810i			0.779816i
$718$	0.228745	+	0.228745i	0.00853670	+	0.00853670i
$719$	−8.83953			−0.329659			−0.164829	−	0.986322i	$-0.552707\pi$
$719$	−8.83953			−0.329659			−0.164829	+	0.986322i	$0.552707\pi$
$720$	1.59207	+	1.57013i	0.0593330	+	0.0585153i
$721$	−4.75416	+	4.75416i	−0.177054	+	0.177054i
$722$	−38.7277			−1.44130
$723$		−	17.1057i		−	0.636168i
$724$			3.22773i			0.119958i
$725$	43.7055	−	0.606600i	1.62318	−	0.0225286i
$726$	2.03888	+	2.03888i	0.0756698	+	0.0756698i
$727$	−14.7695	−	14.7695i	−0.547771	−	0.547771i	0.378024	−	0.925796i	$-0.376604\pi$
$727$	−14.7695	−	14.7695i	−0.547771	−	0.547771i	−0.925796	+	0.378024i	$0.876604\pi$
$728$	3.32002	+	3.00750i	0.123048	+	0.111466i
$729$		−	1.00000i		−	0.0370370i
$730$	−10.5892	+	10.7372i	−0.391923	+	0.397401i
$731$	−2.61957			−0.0968882
$732$	−3.98843	−	3.98843i	−0.147416	−	0.147416i
$733$	−25.1707			−0.929700			−0.464850	−	0.885390i	$-0.653892\pi$
$733$	−25.1707			−0.929700			−0.464850	+	0.885390i	$0.653892\pi$
$734$	−1.17022	−	1.17022i	−0.0431935	−	0.0431935i
$735$	12.2005	−	0.0846626i	0.450020	−	0.00312283i
$736$	6.45495	+	6.45495i	0.237933	+	0.237933i
$737$	17.0088	−	17.0088i	0.626527	−	0.626527i
$738$	−6.86630	+	6.86630i	−0.252752	+	0.252752i
$739$	−16.6864	+	16.6864i	−0.613821	+	0.613821i	−0.943939	−	0.330119i	$-0.892911\pi$
$739$	−16.6864	+	16.6864i	−0.613821	+	0.613821i	0.330119	+	0.943939i	$0.392911\pi$
$740$	2.68157	−	2.71905i	0.0985765	−	0.0999541i
$741$	20.3028	+	18.3917i	0.745843	+	0.675637i
$742$	3.72673	−	3.72673i	0.136812	−	0.136812i
$743$	−20.7881			−0.762642			−0.381321	−	0.924443i	$-0.624531\pi$
$743$	−20.7881			−0.762642			−0.381321	+	0.924443i	$0.624531\pi$
$744$			1.41421i			0.0518476i
$745$	−4.96544	+	0.0344567i	−0.181920	+	0.00126239i
$746$	−0.230351	+	0.230351i	−0.00843374	+	0.00843374i
$747$		−	1.95051i		−	0.0713653i
$748$			3.46750i			0.126784i
$749$	0.799038	−	0.799038i	0.0291962	−	0.0291962i
$750$	−11.1779	+	0.232731i	−0.408160	+	0.00849813i
$751$		−	15.6232i		−	0.570097i	−0.958513	−	0.285048i	$-0.907990\pi$
$751$		−	15.6232i		−	0.570097i	0.958513	−	0.285048i	$-0.0920097\pi$
$752$	10.2601			0.374149
$753$	−10.4232	+	10.4232i	−0.379843	+	0.379843i
$754$	−21.1611	+	23.3599i	−0.770641	+	0.850719i
$755$	−0.806015	+	0.00559318i	−0.0293339	+	0.000203557i
$756$	0.878539	−	0.878539i	0.0319521	−	0.0319521i
$757$	−1.75414	+	1.75414i	−0.0637552	+	0.0637552i	−0.738265	−	0.674510i	$-0.764355\pi$
$757$	−1.75414	+	1.75414i	−0.0637552	+	0.0637552i	0.674510	+	0.738265i	$0.264355\pi$
$758$	−19.8037	+	19.8037i	−0.719303	+	0.719303i
$759$	24.0514	+	24.0514i	0.873012	+	0.873012i
$760$	0.117892	+	16.9890i	0.00427638	+	0.616254i
$761$	21.4809	+	21.4809i	0.778681	+	0.778681i	0.979607	−	0.200926i	$-0.0643949\pi$
$761$	21.4809	+	21.4809i	0.778681	+	0.778681i	−0.200926	+	0.979607i	$0.564395\pi$
$762$	3.45000			0.124980
$763$	−4.40356	−	4.40356i	−0.159420	−	0.159420i
$764$	4.46490			0.161535
$765$	0.0144397	+	2.08086i	0.000522069	+	0.0752336i
$766$		−	14.1230i		−	0.510285i
$767$	1.34655	+	27.2640i	0.0486212	+	0.984447i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−5.30354	−	5.30354i	−0.191251	−	0.191251i	0.604986	−	0.796236i	$-0.293179\pi$
$769$	−5.30354	−	5.30354i	−0.191251	−	0.191251i	−0.796236	+	0.604986i	$0.793179\pi$
$770$	0.0718314	+	10.3514i	0.00258862	+	0.373038i
$771$		−	3.70626i		−	0.133478i
$772$			2.88820i			0.103948i
$773$	52.4709			1.88725			0.943624	−	0.331019i	$-0.107392\pi$
$773$	52.4709			1.88725			0.943624	+	0.331019i	$0.107392\pi$
$774$	1.99043	−	1.99043i	0.0715445	−	0.0715445i
$775$	−5.06891	−	4.93013i	−0.182081	−	0.177095i
$776$	−14.3492			−0.515106
$777$	−1.50043	−	1.50043i	−0.0538275	−	0.0538275i
$778$			8.73801i			0.313273i
$779$	−73.7786			−2.64339
$780$	5.37112	−	6.01257i	0.192317	−	0.215285i
$781$	45.1704			1.61632
$782$			8.49525i			0.303789i
$783$	6.18148	+	6.18148i	0.220908	+	0.220908i
$784$	−5.45634			−0.194869
$785$	0.0341641	+	4.92327i	0.00121937	+	0.175719i
$786$	9.73575	−	9.73575i	0.347263	−	0.347263i
$787$	37.6588			1.34239			0.671196	−	0.741280i	$-0.265781\pi$
$787$	37.6588			1.34239			0.671196	+	0.741280i	$0.265781\pi$
$788$			13.4960i			0.480774i
$789$		−	8.32596i		−	0.296412i
$790$	10.8701	−	11.0220i	0.386740	−	0.392145i
$791$	−8.71735	−	8.71735i	−0.309953	−	0.309953i
$792$	−2.63471	−	2.63471i	−0.0936204	−	0.0936204i
$793$	−13.6536	+	15.0723i	−0.484853	+	0.535235i
$794$		−	8.96140i		−	0.318028i
$795$	−6.75351	−	6.66042i	−0.239522	−	0.236221i
$796$	−18.2097			−0.645425
$797$	−9.10912	−	9.10912i	−0.322662	−	0.322662i	0.527126	−	0.849787i	$-0.323270\pi$
$797$	−9.10912	−	9.10912i	−0.322662	−	0.322662i	−0.849787	+	0.527126i	$0.823270\pi$
$798$	9.43992			0.334169
$799$	6.75159	+	6.75159i	0.238854	+	0.238854i
$800$	4.99952	−	0.0693897i	0.176760	−	0.00245330i
$801$	7.93497	+	7.93497i	0.280368	+	0.280368i
$802$	19.2434	−	19.2434i	0.679509	−	0.679509i
$803$	17.7689	−	17.7689i	0.627050	−	0.627050i
$804$	−4.56484	+	4.56484i	−0.160989	+	0.160989i
$805$	0.175984	+	25.3605i	0.00620264	+	0.893842i
$806$	5.09281	−	0.251531i	0.179387	−	0.00885978i
$807$	6.32814	−	6.32814i	0.222761	−	0.222761i
$808$	19.1723			0.674479
$809$		−	0.566354i		−	0.0199119i	−0.999950	−	0.00995597i	$-0.996831\pi$
$809$		−	0.566354i		−	0.0199119i	0.999950	−	0.00995597i	$-0.00316914\pi$
$810$	−1.59207	−	1.57013i	−0.0559397	−	0.0551687i
$811$	−28.7336	+	28.7336i	−1.00897	+	1.00897i	−0.00901224	+	0.999959i	$0.502869\pi$
$811$	−28.7336	+	28.7336i	−1.00897	+	1.00897i	−0.999959	+	0.00901224i	$0.997131\pi$
$812$			10.8613i			0.381158i
$813$			17.5320i			0.614876i
$814$	−4.49973	+	4.49973i	−0.157716	+	0.157716i
$815$	22.6623	+	22.3499i	0.793824	+	0.782883i
$816$		−	0.930610i		−	0.0325779i
$817$	21.3872			0.748244
$818$	−10.3171	+	10.3171i	−0.360728	+	0.360728i
$819$	−3.32002	−	3.00750i	−0.116011	−	0.105091i
$820$	0.150671	+	21.7126i	0.00526164	+	0.758238i
$821$	−17.7943	+	17.7943i	−0.621025	+	0.621025i	−0.945794	−	0.324768i	$-0.894714\pi$
$821$	−17.7943	+	17.7943i	−0.621025	+	0.621025i	0.324768	+	0.945794i	$0.394714\pi$
$822$	7.29850	−	7.29850i	0.254564	−	0.254564i
$823$	20.4028	−	20.4028i	0.711195	−	0.711195i	−0.255590	−	0.966785i	$-0.582270\pi$
$823$	20.4028	−	20.4028i	0.711195	−	0.711195i	0.966785	+	0.255590i	$0.0822697\pi$
$824$	−3.82647	−	3.82647i	−0.133301	−	0.133301i
$825$	18.6284	−	0.258549i	0.648559	−	0.00900152i
$826$	6.65132	+	6.65132i	0.231429	+	0.231429i
$827$	−6.40080			−0.222578			−0.111289	−	0.993788i	$-0.535498\pi$
$827$	−6.40080			−0.222578			−0.111289	+	0.993788i	$0.535498\pi$
$828$	−6.45495	−	6.45495i	−0.224325	−	0.224325i
$829$	−38.0684			−1.32217			−0.661085	−	0.750311i	$-0.729904\pi$
$829$	−38.0684			−1.32217			−0.661085	+	0.750311i	$0.729904\pi$
$830$	−3.10535	−	3.06255i	−0.107788	−	0.106303i
$831$			21.3193i			0.739559i
$832$	−2.42064	+	2.67217i	−0.0839206	+	0.0926409i
$833$	−3.59049	−	3.59049i	−0.124403	−	0.124403i
$834$	12.5043	+	12.5043i	0.432988	+	0.432988i
$835$	24.2093	−	24.5477i	0.837799	−	0.849508i
$836$		−	28.3100i		−	0.979123i
$837$		−	1.41421i		−	0.0488824i
$838$	−32.5361			−1.12394
$839$	−1.91534	+	1.91534i	−0.0661249	+	0.0661249i	−0.739396	−	0.673271i	$-0.764889\pi$
$839$	−1.91534	+	1.91534i	−0.0661249	+	0.0661249i	0.673271	+	0.739396i	$0.264889\pi$
$840$	−0.0192782	−	2.77812i	−0.000665161	−	0.0958541i
$841$	−47.4214			−1.63522
$842$	16.1077	+	16.1077i	0.555108	+	0.555108i
$843$		−	0.395237i		−	0.0136127i
$844$	−9.57746			−0.329670
$845$	−22.6075	−	18.2729i	−0.777723	−	0.628607i
$846$	−10.2601			−0.352751
$847$		−	3.58246i		−	0.123095i
$848$	2.99952	+	2.99952i	0.103004	+	0.103004i
$849$	29.4188			1.00965
$850$	3.33555	+	3.24423i	0.114408	+	0.111276i
$851$	−11.0242	+	11.0242i	−0.377905	+	0.377905i
$852$	−12.1229			−0.415323
$853$			3.78212i			0.129497i	0.997902	+	0.0647486i	$0.0206246\pi$
$853$			3.78212i			0.129497i	−0.997902	+	0.0647486i	$0.979375\pi$
$854$			7.00797i			0.239808i
$855$	−0.117892	−	16.9890i	−0.00403181	−	0.581010i
$856$	0.643120	+	0.643120i	0.0219814	+	0.0219814i
$857$	20.4881	+	20.4881i	0.699860	+	0.699860i	0.964380	−	0.264520i	$-0.0852136\pi$
$857$	20.4881	+	20.4881i	0.699860	+	0.699860i	−0.264520	+	0.964380i	$0.585214\pi$
$858$	−9.01941	+	9.95663i	−0.307918	+	0.339914i
$859$		−	29.9195i		−	1.02084i	−0.859926	−	0.510419i	$-0.829490\pi$
$859$		−	29.9195i		−	1.02084i	0.859926	−	0.510419i	$-0.170510\pi$
$860$	−0.0436769	−	6.29414i	−0.00148937	−	0.214628i
$861$	12.0646			0.411161
$862$	11.4172	+	11.4172i	0.388870	+	0.388870i
$863$	−38.3891			−1.30678			−0.653390	−	0.757022i	$-0.726654\pi$
$863$	−38.3891			−1.30678			−0.653390	+	0.757022i	$0.726654\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	−0.272719	−	39.3007i	−0.00927273	−	1.33626i
$866$	7.47995	+	7.47995i	0.254179	+	0.254179i
$867$	−11.4084	+	11.4084i	−0.387451	+	0.387451i
$868$	1.24244	−	1.24244i	0.0421712	−	0.0421712i
$869$	−18.2402	+	18.2402i	−0.618757	+	0.618757i
$870$	19.5471	−	0.135643i	0.662708	−	0.00459873i
$871$	17.2506	+	15.6268i	0.584515	+	0.529495i
$872$	3.54428	−	3.54428i	0.120025	−	0.120025i
$873$	14.3492			0.485646
$874$		−	69.3586i		−	2.34609i
$875$	10.0247	+	9.61577i	0.338897	+	0.325072i
$876$	−4.76883	+	4.76883i	−0.161124	+	0.161124i
$877$		−	50.2908i		−	1.69820i	−0.528232	−	0.849100i	$-0.677145\pi$
$877$		−	50.2908i		−	1.69820i	0.528232	−	0.849100i	$-0.322855\pi$
$878$		−	32.8415i		−	1.10835i
$879$	9.96992	−	9.96992i	0.336277	−	0.336277i
$880$	−8.33149	+	0.0578147i	−0.280854	+	0.00194893i
$881$			51.7497i			1.74349i	0.489959	+	0.871745i	$0.337012\pi$
$881$			51.7497i			1.74349i	−0.489959	+	0.871745i	$0.662988\pi$
$882$	5.45634			0.183725
$883$	19.6067	−	19.6067i	0.659819	−	0.659819i	−0.295518	−	0.955337i	$-0.595492\pi$
$883$	19.6067	−	19.6067i	0.659819	−	0.659819i	0.955337	+	0.295518i	$0.0954922\pi$
$884$	−3.35128	+	0.165517i	−0.112716	+	0.00556695i
$885$	11.8873	−	12.0534i	0.399587	−	0.405171i
$886$	−1.29541	+	1.29541i	−0.0435200	+	0.0435200i
$887$	−25.7388	+	25.7388i	−0.864223	+	0.864223i	−0.991825	−	0.127602i	$-0.959272\pi$
$887$	−25.7388	+	25.7388i	−0.864223	+	0.864223i	0.127602	+	0.991825i	$0.459272\pi$
$888$	1.20764	−	1.20764i	0.0405259	−	0.0405259i
$889$	−3.03096	−	3.03096i	−0.101655	−	0.101655i
$890$	25.0920	−	0.174121i	0.841085	−	0.00583654i
$891$	2.63471	+	2.63471i	0.0882662	+	0.0882662i
$892$	−9.61384			−0.321895
$893$	−55.1227	−	55.1227i	−1.84461	−	1.84461i
$894$	−2.22066			−0.0742701
$895$	−5.60336	+	5.68167i	−0.187300	+	0.189917i
$896$			1.24244i			0.0415070i
$897$	−22.0973	+	24.3934i	−0.737806	+	0.814472i
$898$	7.46259	+	7.46259i	0.249030	+	0.249030i
$899$	8.74193	+	8.74193i	0.291560	+	0.291560i
$900$	−4.99952	+	0.0693897i	−0.166651	+	0.00231299i
$901$			3.94761i			0.131514i
$902$		−	36.1815i		−	1.20471i
$903$	−3.49734			−0.116384
$904$	7.01631	−	7.01631i	0.233359	−	0.233359i
$905$	−5.13879	−	5.06796i	−0.170819	−	0.168465i
$906$	−0.360469			−0.0119758
$907$	2.64304	+	2.64304i	0.0877608	+	0.0877608i	0.749624	−	0.661864i	$-0.230234\pi$
$907$	2.64304	+	2.64304i	0.0877608	+	0.0877608i	−0.661864	+	0.749624i	$0.730234\pi$
$908$			19.1670i			0.636079i
$909$	−19.1723			−0.635905
$910$	−10.0010	+	0.563537i	−0.331530	+	0.0186811i
$911$	−3.39791			−0.112578			−0.0562889	−	0.998415i	$-0.517927\pi$
$911$	−3.39791			−0.112578			−0.0562889	+	0.998415i	$0.517927\pi$
$912$			7.59788i			0.251591i
$913$	5.13902	+	5.13902i	0.170077	+	0.170077i
$914$	18.6585			0.617169
$915$	12.6122	−	0.0875199i	0.416947	−	0.00289332i
$916$	−19.1000	+	19.1000i	−0.631080	+	0.631080i
$917$	−17.1065			−0.564905
$918$			0.930610i			0.0307147i
$919$			7.42668i			0.244984i	0.992470	+	0.122492i	$0.0390885\pi$
$919$			7.42668i			0.244984i	−0.992470	+	0.122492i	$0.960911\pi$
$920$	−20.4119	+	0.141644i	−0.672959	+	0.00466987i
$921$	8.10999	+	8.10999i	0.267233	+	0.267233i
$922$	−5.51836	−	5.51836i	−0.181738	−	0.181738i
$923$	2.15616	+	43.6564i	0.0709709	+	1.43697i
$924$			4.62939i			0.152296i
$925$	0.118508	+	8.53851i	0.00389653	+	0.280744i
$926$	−7.00926			−0.230338
$927$	3.82647	+	3.82647i	0.125678	+	0.125678i
$928$	−8.74193			−0.286968
$929$	15.3355	+	15.3355i	0.503141	+	0.503141i	0.912413	−	0.409272i	$-0.134217\pi$
$929$	15.3355	+	15.3355i	0.503141	+	0.503141i	−0.409272	+	0.912413i	$0.634217\pi$
$930$	−2.25153	−	2.22050i	−0.0738306	−	0.0728130i
$931$	29.3142	+	29.3142i	0.960735	+	0.960735i
$932$	7.14541	−	7.14541i	0.234056	−	0.234056i
$933$	5.27964	−	5.27964i	0.172848	−	0.172848i
$934$	−21.7877	+	21.7877i	−0.712915	+	0.712915i
$935$	−5.52050	−	5.44442i	−0.180540	−	0.178051i
$936$	2.42064	−	2.67217i	0.0791211	−	0.0873426i
$937$	−13.6072	+	13.6072i	−0.444526	+	0.444526i	−0.893530	−	0.449004i	$-0.851779\pi$
$937$	−13.6072	+	13.6072i	−0.444526	+	0.444526i	0.449004	+	0.893530i	$0.351779\pi$
$938$	8.02078			0.261888
$939$		−	7.56625i		−	0.246915i
$940$	−16.1097	+	16.3349i	−0.525442	+	0.532785i
$941$	−42.3649	+	42.3649i	−1.38106	+	1.38106i	−0.538309	+	0.842747i	$0.680937\pi$
$941$	−42.3649	+	42.3649i	−1.38106	+	1.38106i	−0.842747	+	0.538309i	$0.819063\pi$
$942$			2.20181i			0.0717388i
$943$		−	88.6433i		−	2.88662i
$944$	−5.35343	+	5.35343i	−0.174239	+	0.174239i
$945$	0.0192782	+	2.77812i	0.000627120	+	0.0903721i
$946$			10.4884i			0.341008i
$947$	41.3451			1.34353			0.671767	−	0.740762i	$-0.265535\pi$
$947$	41.3451			1.34353			0.671767	+	0.740762i	$0.265535\pi$
$948$	4.89533	−	4.89533i	0.158993	−	0.158993i
$949$	18.0215	+	16.3252i	0.585003	+	0.529937i
$950$	−27.2328	−	26.4872i	−0.883547	−	0.859357i
$951$	−9.04673	+	9.04673i	−0.293360	+	0.293360i
$952$	−0.817577	+	0.817577i	−0.0264978	+	0.0264978i
$953$	−16.4217	+	16.4217i	−0.531952	+	0.531952i	−0.921153	−	0.389201i	$-0.872751\pi$
$953$	−16.4217	+	16.4217i	−0.531952	+	0.531952i	0.389201	+	0.921153i	$0.372751\pi$
$954$	−2.99952	−	2.99952i	−0.0971130	−	0.0971130i
$955$	−7.01047	+	7.10845i	−0.226854	+	0.230024i
$956$	14.7651	+	14.7651i	0.477538	+	0.477538i
$957$	−32.5728			−1.05293
$958$	3.07248	+	3.07248i	0.0992673	+	0.0992673i
$959$	−12.8240			−0.414109
$960$	2.23601	−	0.0155164i	0.0721670	−	0.000500789i
$961$			29.0000i			0.935484i
$962$	−4.56371	−	4.13413i	−0.147140	−	0.133290i
$963$	−0.643120	−	0.643120i	−0.0207242	−	0.0207242i
$964$	−12.0956	−	12.0956i	−0.389572	−	0.389572i
$965$	−4.59822	−	4.53484i	−0.148022	−	0.145982i
$966$			11.3419i			0.364918i
$967$			26.1072i			0.839550i	0.907628	+	0.419775i	$0.137891\pi$
$967$			26.1072i			0.839550i	−0.907628	+	0.419775i	$0.862109\pi$
$968$	2.88341			0.0926762
$969$	−4.99971	+	4.99971i	−0.160614	+	0.160614i
$970$	22.5301	−	22.8449i	0.723397	−	0.733507i
$971$	18.5254			0.594508			0.297254	−	0.954798i	$-0.403929\pi$
$971$	18.5254			0.594508			0.297254	+	0.954798i	$0.403929\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$		−	21.9710i		−	0.704358i
$974$	−15.5332			−0.497716
$975$	1.13909	+	17.9917i	0.0364802	+	0.576197i
$976$	−5.64048			−0.180548
$977$		−	32.0028i		−	1.02386i	−0.859027	−	0.511930i	$-0.828931\pi$
$977$		−	32.0028i		−	1.02386i	0.859027	−	0.511930i	$-0.171069\pi$
$978$	10.0653	+	10.0653i	0.321852	+	0.321852i
$979$	−41.8127			−1.33634
$980$	8.56716	−	8.68689i	0.273668	−	0.277492i
$981$	−3.54428	+	3.54428i	−0.113160	+	0.113160i
$982$	28.7710			0.918121
$983$			59.6220i			1.90165i	0.309736	+	0.950823i	$0.399759\pi$
$983$			59.6220i			1.90165i	−0.309736	+	0.950823i	$0.600241\pi$
$984$			9.71042i			0.309557i
$985$	−21.4866	−	21.1904i	−0.684619	−	0.675183i
$986$	−5.75255	−	5.75255i	−0.183198	−	0.183198i
$987$	9.01393	+	9.01393i	0.286916	+	0.286916i
$988$	27.3612	−	1.35135i	0.870475	−	0.0429922i
$989$			25.6963i			0.817093i
$990$	8.33149	−	0.0578147i	0.264792	−	0.00183747i
$991$	−35.8657			−1.13931			−0.569656	−	0.821883i	$-0.692924\pi$
$991$	−35.8657			−1.13931			−0.569656	+	0.821883i	$0.692924\pi$
$992$	1.00000	+	1.00000i	0.0317500	+	0.0317500i
$993$	−5.23351			−0.166080
$994$	10.6504	+	10.6504i	0.337811	+	0.337811i
$995$	28.5916	−	28.9911i	0.906413	−	0.919081i
$996$	−1.37922	−	1.37922i	−0.0437021	−	0.0437021i
$997$	34.3592	−	34.3592i	1.08817	−	1.08817i	0.0924486	−	0.995717i	$-0.470531\pi$
$997$	34.3592	−	34.3592i	1.08817	−	1.08817i	0.995717	−	0.0924486i	$-0.0294694\pi$
$998$	−8.49652	+	8.49652i	−0.268953	+	0.268953i
$999$	−1.20764	+	1.20764i	−0.0382082	+	0.0382082i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.t.a.343.3	yes	12
3.2	odd	2		1170.2.w.f.343.1		12
5.2	odd	4		390.2.j.a.187.3	yes	12
5.3	odd	4		1950.2.j.c.1357.6		12
5.4	even	2		1950.2.t.b.343.6		12
13.8	odd	4		390.2.j.a.73.3	✓	12
15.2	even	4		1170.2.m.f.577.2		12
39.8	even	4		1170.2.m.f.73.2		12
65.8	even	4		1950.2.t.b.307.6		12
65.34	odd	4		1950.2.j.c.1243.4		12
65.47	even	4	inner	390.2.t.a.307.3	yes	12
195.47	odd	4		1170.2.w.f.307.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.j.a.73.3	✓	12	13.8	odd	4
390.2.j.a.187.3	yes	12	5.2	odd	4
390.2.t.a.307.3	yes	12	65.47	even	4	inner
390.2.t.a.343.3	yes	12	1.1	even	1	trivial
1170.2.m.f.73.2		12	39.8	even	4
1170.2.m.f.577.2		12	15.2	even	4
1170.2.w.f.307.1		12	195.47	odd	4
1170.2.w.f.343.1		12	3.2	odd	2
1950.2.j.c.1243.4		12	65.34	odd	4
1950.2.j.c.1357.6		12	5.3	odd	4
1950.2.t.b.307.6		12	65.8	even	4
1950.2.t.b.343.6		12	5.4	even	2

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.57013 - 1.59207i) q^{5} +(0.707107 - 0.707107i) q^{6} -1.24244 q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.57013 - 1.59207i) q^{5} +(0.707107 - 0.707107i) q^{6} -1.24244 q^{7} -1.00000i q^{8} +1.00000i q^{9} +(1.59207 + 1.57013i) q^{10} +(-2.63471 - 2.63471i) q^{11} +(0.707107 + 0.707107i) q^{12} +(2.42064 - 2.67217i) q^{13} -1.24244i q^{14} +(-2.23601 + 0.0155164i) q^{15} +1.00000 q^{16} +(0.658041 + 0.658041i) q^{17} -1.00000 q^{18} +(-5.37251 - 5.37251i) q^{19} +(-1.57013 + 1.59207i) q^{20} +(0.878539 + 0.878539i) q^{21} +(2.63471 - 2.63471i) q^{22} +(6.45495 - 6.45495i) q^{23} +(-0.707107 + 0.707107i) q^{24} +(-0.0693897 - 4.99952i) q^{25} +(2.67217 + 2.42064i) q^{26} +(0.707107 - 0.707107i) q^{27} +1.24244 q^{28} +8.74193i q^{29} +(-0.0155164 - 2.23601i) q^{30} +(1.00000 - 1.00000i) q^{31} +1.00000i q^{32} +3.72604i q^{33} +(-0.658041 + 0.658041i) q^{34} +(-1.95079 + 1.97806i) q^{35} -1.00000i q^{36} -1.70787 q^{37} +(5.37251 - 5.37251i) q^{38} +(-3.60116 + 0.177859i) q^{39} +(-1.59207 - 1.57013i) q^{40} +(6.86630 - 6.86630i) q^{41} +(-0.878539 + 0.878539i) q^{42} +(-1.99043 + 1.99043i) q^{43} +(2.63471 + 2.63471i) q^{44} +(1.59207 + 1.57013i) q^{45} +(6.45495 + 6.45495i) q^{46} +10.2601 q^{47} +(-0.707107 - 0.707107i) q^{48} -5.45634 q^{49} +(4.99952 - 0.0693897i) q^{50} -0.930610i q^{51} +(-2.42064 + 2.67217i) q^{52} +(2.99952 + 2.99952i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-8.33149 + 0.0578147i) q^{55} +1.24244i q^{56} +7.59788i q^{57} -8.74193 q^{58} +(-5.35343 + 5.35343i) q^{59} +(2.23601 - 0.0155164i) q^{60} -5.64048 q^{61} +(1.00000 + 1.00000i) q^{62} -1.24244i q^{63} -1.00000 q^{64} +(-0.453572 - 8.04949i) q^{65} -3.72604 q^{66} +6.45566i q^{67} +(-0.658041 - 0.658041i) q^{68} -9.12868 q^{69} +(-1.97806 - 1.95079i) q^{70} +(-8.57216 + 8.57216i) q^{71} +1.00000 q^{72} +6.74415i q^{73} -1.70787i q^{74} +(-3.48613 + 3.58426i) q^{75} +(5.37251 + 5.37251i) q^{76} +(3.27347 + 3.27347i) q^{77} +(-0.177859 - 3.60116i) q^{78} -6.92304i q^{79} +(1.57013 - 1.59207i) q^{80} -1.00000 q^{81} +(6.86630 + 6.86630i) q^{82} -1.95051 q^{83} +(-0.878539 - 0.878539i) q^{84} +(2.08086 - 0.0144397i) q^{85} +(-1.99043 - 1.99043i) q^{86} +(6.18148 - 6.18148i) q^{87} +(-2.63471 + 2.63471i) q^{88} +(7.93497 - 7.93497i) q^{89} +(-1.57013 + 1.59207i) q^{90} +(-3.00750 + 3.32002i) q^{91} +(-6.45495 + 6.45495i) q^{92} -1.41421 q^{93} +10.2601i q^{94} +(-16.9890 + 0.117892i) q^{95} +(0.707107 - 0.707107i) q^{96} -14.3492i q^{97} -5.45634i q^{98} +(2.63471 - 2.63471i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} - 4 q^{5}+O(q^{10}) \) 12 * q - 12 * q^4 - 4 * q^5	\( 12 q - 12 q^{4} - 4 q^{5} + 4 q^{11} + 20 q^{13} - 4 q^{15} + 12 q^{16} + 8 q^{17} - 12 q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{25} - 4 q^{26} + 4 q^{30} + 12 q^{31} - 8 q^{34} + 12 q^{35} - 16 q^{37} + 4 q^{38} - 12 q^{39} + 8 q^{41} + 8 q^{42} + 16 q^{43} - 4 q^{44} + 32 q^{47} - 20 q^{49} + 8 q^{50} - 20 q^{52} - 16 q^{53} - 12 q^{55} - 40 q^{58} + 20 q^{59} + 4 q^{60} + 16 q^{61} + 12 q^{62} - 12 q^{64} - 32 q^{65} - 16 q^{66} - 8 q^{68} - 32 q^{69} - 20 q^{70} - 32 q^{71} + 12 q^{72} + 4 q^{76} + 16 q^{77} - 4 q^{80} - 12 q^{81} + 8 q^{82} + 32 q^{83} + 8 q^{84} + 12 q^{85} + 16 q^{86} + 20 q^{87} + 4 q^{88} + 16 q^{89} + 4 q^{90} - 28 q^{91} - 8 q^{95} - 4 q^{99}+O(q^{100}) \) 12 * q - 12 * q^4 - 4 * q^5 + 4 * q^11 + 20 * q^13 - 4 * q^15 + 12 * q^16 + 8 * q^17 - 12 * q^18 - 4 * q^19 + 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^25 - 4 * q^26 + 4 * q^30 + 12 * q^31 - 8 * q^34 + 12 * q^35 - 16 * q^37 + 4 * q^38 - 12 * q^39 + 8 * q^41 + 8 * q^42 + 16 * q^43 - 4 * q^44 + 32 * q^47 - 20 * q^49 + 8 * q^50 - 20 * q^52 - 16 * q^53 - 12 * q^55 - 40 * q^58 + 20 * q^59 + 4 * q^60 + 16 * q^61 + 12 * q^62 - 12 * q^64 - 32 * q^65 - 16 * q^66 - 8 * q^68 - 32 * q^69 - 20 * q^70 - 32 * q^71 + 12 * q^72 + 4 * q^76 + 16 * q^77 - 4 * q^80 - 12 * q^81 + 8 * q^82 + 32 * q^83 + 8 * q^84 + 12 * q^85 + 16 * q^86 + 20 * q^87 + 4 * q^88 + 16 * q^89 + 4 * q^90 - 28 * q^91 - 8 * q^95 - 4 * q^99

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