LMFDB - Embedded newform 975.2.k.b.307.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(307,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, 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("975.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.k (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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	975.307
Dual form			975.2.k.b.343.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41421i q^{2} +(-0.707107 + 0.707107i) q^{3} -3.82843 q^{4} +(1.70711 + 1.70711i) q^{6} +3.41421 q^{7} +4.41421i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-2.41421i q^{2} +(-0.707107 + 0.707107i) q^{3} -3.82843 q^{4} +(1.70711 + 1.70711i) q^{6} +3.41421 q^{7} +4.41421i q^{8} -1.00000i q^{9} +(-1.41421 + 1.41421i) q^{11} +(2.70711 - 2.70711i) q^{12} +(-0.707107 + 3.53553i) q^{13} -8.24264i q^{14} +3.00000 q^{16} +(-5.41421 + 5.41421i) q^{17} -2.41421 q^{18} +(-0.414214 + 0.414214i) q^{19} +(-2.41421 + 2.41421i) q^{21} +(3.41421 + 3.41421i) q^{22} +(4.82843 + 4.82843i) q^{23} +(-3.12132 - 3.12132i) q^{24} +(8.53553 + 1.70711i) q^{26} +(0.707107 + 0.707107i) q^{27} -13.0711 q^{28} +0.828427i q^{29} +(1.58579 + 1.58579i) q^{31} +1.58579i q^{32} -2.00000i q^{33} +(13.0711 + 13.0711i) q^{34} +3.82843i q^{36} +1.41421 q^{37} +(1.00000 + 1.00000i) q^{38} +(-2.00000 - 3.00000i) q^{39} +(-3.65685 - 3.65685i) q^{41} +(5.82843 + 5.82843i) q^{42} +(6.82843 + 6.82843i) q^{43} +(5.41421 - 5.41421i) q^{44} +(11.6569 - 11.6569i) q^{46} -4.82843 q^{47} +(-2.12132 + 2.12132i) q^{48} +4.65685 q^{49} -7.65685i q^{51} +(2.70711 - 13.5355i) q^{52} +(-4.58579 + 4.58579i) q^{53} +(1.70711 - 1.70711i) q^{54} +15.0711i q^{56} -0.585786i q^{57} +2.00000 q^{58} +(-0.585786 - 0.585786i) q^{59} +13.6569 q^{61} +(3.82843 - 3.82843i) q^{62} -3.41421i q^{63} +9.82843 q^{64} -4.82843 q^{66} -1.75736i q^{67} +(20.7279 - 20.7279i) q^{68} -6.82843 q^{69} +(-6.24264 - 6.24264i) q^{71} +4.41421 q^{72} -16.2426i q^{73} -3.41421i q^{74} +(1.58579 - 1.58579i) q^{76} +(-4.82843 + 4.82843i) q^{77} +(-7.24264 + 4.82843i) q^{78} -4.82843i q^{79} -1.00000 q^{81} +(-8.82843 + 8.82843i) q^{82} +9.31371 q^{83} +(9.24264 - 9.24264i) q^{84} +(16.4853 - 16.4853i) q^{86} +(-0.585786 - 0.585786i) q^{87} +(-6.24264 - 6.24264i) q^{88} +(-6.82843 - 6.82843i) q^{89} +(-2.41421 + 12.0711i) q^{91} +(-18.4853 - 18.4853i) q^{92} -2.24264 q^{93} +11.6569i q^{94} +(-1.12132 - 1.12132i) q^{96} +19.0711i q^{97} -11.2426i q^{98} +(1.41421 + 1.41421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{6} + 8 q^{7}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^6 + 8 * q^7	$ 4 q - 4 q^{4} + 4 q^{6} + 8 q^{7} + 8 q^{12} + 12 q^{16} - 16 q^{17} - 4 q^{18} + 4 q^{19} - 4 q^{21} + 8 q^{22} + 8 q^{23} - 4 q^{24} + 20 q^{26} - 24 q^{28} + 12 q^{31} + 24 q^{34} + 4 q^{38} - 8 q^{39} + 8 q^{41} + 12 q^{42} + 16 q^{43} + 16 q^{44} + 24 q^{46} - 8 q^{47} - 4 q^{49} + 8 q^{52} - 24 q^{53} + 4 q^{54} + 8 q^{58} - 8 q^{59} + 32 q^{61} + 4 q^{62} + 28 q^{64} - 8 q^{66} + 32 q^{68} - 16 q^{69} - 8 q^{71} + 12 q^{72} + 12 q^{76} - 8 q^{77} - 12 q^{78} - 4 q^{81} - 24 q^{82} - 8 q^{83} + 20 q^{84} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 16 q^{89} - 4 q^{91} - 40 q^{92} + 8 q^{93} + 4 q^{96}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^6 + 8 * q^7 + 8 * q^12 + 12 * q^16 - 16 * q^17 - 4 * q^18 + 4 * q^19 - 4 * q^21 + 8 * q^22 + 8 * q^23 - 4 * q^24 + 20 * q^26 - 24 * q^28 + 12 * q^31 + 24 * q^34 + 4 * q^38 - 8 * q^39 + 8 * q^41 + 12 * q^42 + 16 * q^43 + 16 * q^44 + 24 * q^46 - 8 * q^47 - 4 * q^49 + 8 * q^52 - 24 * q^53 + 4 * q^54 + 8 * q^58 - 8 * q^59 + 32 * q^61 + 4 * q^62 + 28 * q^64 - 8 * q^66 + 32 * q^68 - 16 * q^69 - 8 * q^71 + 12 * q^72 + 12 * q^76 - 8 * q^77 - 12 * q^78 - 4 * q^81 - 24 * q^82 - 8 * q^83 + 20 * q^84 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 16 * q^89 - 4 * q^91 - 40 * q^92 + 8 * q^93 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$		−	2.41421i		−	1.70711i	−0.521005	−	0.853553i	$-0.674443\pi$
$2$		−	2.41421i		−	1.70711i	0.521005	−	0.853553i	$-0.325557\pi$
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−3.82843			−1.91421
$5$		0			0
$5$		0			0
$6$	1.70711	+	1.70711i	0.696923	+	0.696923i
$7$	3.41421			1.29045			0.645226	−	0.763992i	$-0.276763\pi$
$7$	3.41421			1.29045			0.645226	+	0.763992i	$0.276763\pi$
$8$			4.41421i			1.56066i
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−1.41421	+	1.41421i	−0.426401	+	0.426401i	−0.887401	−	0.460999i	$-0.847491\pi$
$11$	−1.41421	+	1.41421i	−0.426401	+	0.426401i	0.460999	+	0.887401i	$0.347491\pi$
$12$	2.70711	−	2.70711i	0.781474	−	0.781474i
$13$	−0.707107	+	3.53553i	−0.196116	+	0.980581i
$13$	−0.707107	+	3.53553i	−0.196116	+	0.980581i
$14$		−	8.24264i		−	2.20294i
$15$		0			0
$16$	3.00000			0.750000
$17$	−5.41421	+	5.41421i	−1.31314	+	1.31314i	−0.394051	+	0.919089i	$0.628927\pi$
$17$	−5.41421	+	5.41421i	−1.31314	+	1.31314i	−0.919089	+	0.394051i	$0.871073\pi$
$18$	−2.41421			−0.569036
$19$	−0.414214	+	0.414214i	−0.0950271	+	0.0950271i	−0.753022	−	0.657995i	$-0.771405\pi$
$19$	−0.414214	+	0.414214i	−0.0950271	+	0.0950271i	0.657995	+	0.753022i	$0.271405\pi$
$20$		0			0
$21$	−2.41421	+	2.41421i	−0.526825	+	0.526825i
$22$	3.41421	+	3.41421i	0.727913	+	0.727913i
$23$	4.82843	+	4.82843i	1.00680	+	1.00680i	0.999977	+	0.00681991i	$0.00217086\pi$
$23$	4.82843	+	4.82843i	1.00680	+	1.00680i	0.00681991	+	0.999977i	$0.497829\pi$
$24$	−3.12132	−	3.12132i	−0.637137	−	0.637137i
$25$		0			0
$26$	8.53553	+	1.70711i	1.67396	+	0.334791i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−13.0711			−2.47020
$29$			0.828427i			0.153835i	0.997037	+	0.0769175i	$0.0245078\pi$
$29$			0.828427i			0.153835i	−0.997037	+	0.0769175i	$0.975492\pi$
$30$		0			0
$31$	1.58579	+	1.58579i	0.284816	+	0.284816i	0.835026	−	0.550210i	$-0.185452\pi$
$31$	1.58579	+	1.58579i	0.284816	+	0.284816i	−0.550210	+	0.835026i	$0.685452\pi$
$32$			1.58579i			0.280330i
$33$		−	2.00000i		−	0.348155i
$34$	13.0711	+	13.0711i	2.24167	+	2.24167i
$35$		0			0
$36$			3.82843i			0.638071i
$37$	1.41421			0.232495			0.116248	−	0.993220i	$-0.462913\pi$
$37$	1.41421			0.232495			0.116248	+	0.993220i	$0.462913\pi$
$38$	1.00000	+	1.00000i	0.162221	+	0.162221i
$39$	−2.00000	−	3.00000i	−0.320256	−	0.480384i
$40$		0			0
$41$	−3.65685	−	3.65685i	−0.571105	−	0.571105i	0.361332	−	0.932437i	$-0.382322\pi$
$41$	−3.65685	−	3.65685i	−0.571105	−	0.571105i	−0.932437	+	0.361332i	$0.882322\pi$
$42$	5.82843	+	5.82843i	0.899346	+	0.899346i
$43$	6.82843	+	6.82843i	1.04133	+	1.04133i	0.999108	+	0.0422169i	$0.0134421\pi$
$43$	6.82843	+	6.82843i	1.04133	+	1.04133i	0.0422169	+	0.999108i	$0.486558\pi$
$44$	5.41421	−	5.41421i	0.816223	−	0.816223i
$45$		0			0
$46$	11.6569	−	11.6569i	1.71871	−	1.71871i
$47$	−4.82843			−0.704298			−0.352149	−	0.935944i	$-0.614549\pi$
$47$	−4.82843			−0.704298			−0.352149	+	0.935944i	$0.614549\pi$
$48$	−2.12132	+	2.12132i	−0.306186	+	0.306186i
$49$	4.65685			0.665265
$50$		0			0
$51$		−	7.65685i		−	1.07217i
$52$	2.70711	−	13.5355i	0.375408	−	1.87704i
$53$	−4.58579	+	4.58579i	−0.629906	+	0.629906i	−0.948044	−	0.318138i	$-0.896942\pi$
$53$	−4.58579	+	4.58579i	−0.629906	+	0.629906i	0.318138	+	0.948044i	$0.396942\pi$
$54$	1.70711	−	1.70711i	0.232308	−	0.232308i
$55$		0			0
$56$			15.0711i			2.01396i
$57$		−	0.585786i		−	0.0775893i
$58$	2.00000			0.262613
$59$	−0.585786	−	0.585786i	−0.0762629	−	0.0762629i	0.667946	−	0.744209i	$-0.267174\pi$
$59$	−0.585786	−	0.585786i	−0.0762629	−	0.0762629i	−0.744209	+	0.667946i	$0.767174\pi$
$60$		0			0
$61$	13.6569			1.74858			0.874291	−	0.485403i	$-0.161327\pi$
$61$	13.6569			1.74858			0.874291	+	0.485403i	$0.161327\pi$
$62$	3.82843	−	3.82843i	0.486211	−	0.486211i
$63$		−	3.41421i		−	0.430150i
$64$	9.82843			1.22855
$65$		0			0
$66$	−4.82843			−0.594338
$67$		−	1.75736i		−	0.214696i	−0.994222	−	0.107348i	$-0.965764\pi$
$67$		−	1.75736i		−	0.214696i	0.994222	−	0.107348i	$-0.0342358\pi$
$68$	20.7279	−	20.7279i	2.51363	−	2.51363i
$69$	−6.82843			−0.822046
$70$		0			0
$71$	−6.24264	−	6.24264i	−0.740865	−	0.740865i	0.231879	−	0.972745i	$-0.425513\pi$
$71$	−6.24264	−	6.24264i	−0.740865	−	0.740865i	−0.972745	+	0.231879i	$0.925513\pi$
$72$	4.41421			0.520220
$73$		−	16.2426i		−	1.90106i	−0.310637	−	0.950529i	$-0.600542\pi$
$73$		−	16.2426i		−	1.90106i	0.310637	−	0.950529i	$-0.399458\pi$
$74$		−	3.41421i		−	0.396894i
$75$		0			0
$76$	1.58579	−	1.58579i	0.181902	−	0.181902i
$77$	−4.82843	+	4.82843i	−0.550250	+	0.550250i
$78$	−7.24264	+	4.82843i	−0.820068	+	0.546712i
$79$		−	4.82843i		−	0.543240i	−0.962405	−	0.271620i	$-0.912441\pi$
$79$		−	4.82843i		−	0.543240i	0.962405	−	0.271620i	$-0.0875595\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	−8.82843	+	8.82843i	−0.974937	+	0.974937i
$83$	9.31371			1.02231			0.511156	−	0.859488i	$-0.329217\pi$
$83$	9.31371			1.02231			0.511156	+	0.859488i	$0.329217\pi$
$84$	9.24264	−	9.24264i	1.00845	−	1.00845i
$85$		0			0
$86$	16.4853	−	16.4853i	1.77765	−	1.77765i
$87$	−0.585786	−	0.585786i	−0.0628029	−	0.0628029i
$88$	−6.24264	−	6.24264i	−0.665468	−	0.665468i
$89$	−6.82843	−	6.82843i	−0.723812	−	0.723812i	0.245568	−	0.969379i	$-0.421026\pi$
$89$	−6.82843	−	6.82843i	−0.723812	−	0.723812i	−0.969379	+	0.245568i	$0.921026\pi$
$90$		0			0
$91$	−2.41421	+	12.0711i	−0.253078	+	1.26539i
$92$	−18.4853	−	18.4853i	−1.92722	−	1.92722i
$93$	−2.24264			−0.232551
$94$			11.6569i			1.20231i
$95$		0			0
$96$	−1.12132	−	1.12132i	−0.114444	−	0.114444i
$97$			19.0711i			1.93637i	0.250229	+	0.968187i	$0.419494\pi$
$97$			19.0711i			1.93637i	−0.250229	+	0.968187i	$0.580506\pi$
$98$		−	11.2426i		−	1.13568i
$99$	1.41421	+	1.41421i	0.142134	+	0.142134i
$100$		0			0
$101$			17.3137i			1.72278i	0.507946	+	0.861389i	$0.330405\pi$
$101$			17.3137i			1.72278i	−0.507946	+	0.861389i	$0.669595\pi$
$102$	−18.4853			−1.83032
$103$	8.00000	+	8.00000i	0.788263	+	0.788263i	0.981209	−	0.192946i	$-0.0618042\pi$
$103$	8.00000	+	8.00000i	0.788263	+	0.788263i	−0.192946	+	0.981209i	$0.561804\pi$
$104$	−15.6066	−	3.12132i	−1.53035	−	0.306071i
$105$		0			0
$106$	11.0711	+	11.0711i	1.07532	+	1.07532i
$107$	7.17157	+	7.17157i	0.693302	+	0.693302i	0.962957	−	0.269655i	$-0.0869096\pi$
$107$	7.17157	+	7.17157i	0.693302	+	0.693302i	−0.269655	+	0.962957i	$0.586910\pi$
$108$	−2.70711	−	2.70711i	−0.260491	−	0.260491i
$109$	−1.82843	+	1.82843i	−0.175132	+	0.175132i	−0.789230	−	0.614098i	$-0.789520\pi$
$109$	−1.82843	+	1.82843i	−0.175132	+	0.175132i	0.614098	+	0.789230i	$0.289520\pi$
$110$		0			0
$111$	−1.00000	+	1.00000i	−0.0949158	+	0.0949158i
$112$	10.2426			0.967839
$113$	7.07107	−	7.07107i	0.665190	−	0.665190i	−0.291409	−	0.956599i	$-0.594124\pi$
$113$	7.07107	−	7.07107i	0.665190	−	0.665190i	0.956599	+	0.291409i	$0.0941239\pi$
$114$	−1.41421			−0.132453
$115$		0			0
$116$		−	3.17157i		−	0.294473i
$117$	3.53553	+	0.707107i	0.326860	+	0.0653720i
$118$	−1.41421	+	1.41421i	−0.130189	+	0.130189i
$119$	−18.4853	+	18.4853i	−1.69454	+	1.69454i
$120$		0			0
$121$			7.00000i			0.636364i
$122$		−	32.9706i		−	2.98501i
$123$	5.17157			0.466305
$124$	−6.07107	−	6.07107i	−0.545198	−	0.545198i
$125$		0			0
$126$	−8.24264			−0.734313
$127$	−7.41421	+	7.41421i	−0.657905	+	0.657905i	−0.954884	−	0.296979i	$-0.904021\pi$
$127$	−7.41421	+	7.41421i	−0.657905	+	0.657905i	0.296979	+	0.954884i	$0.404021\pi$
$128$		−	20.5563i		−	1.81694i
$129$	−9.65685			−0.850239
$130$		0			0
$131$	−13.1716			−1.15081			−0.575403	−	0.817870i	$-0.695155\pi$
$131$	−13.1716			−1.15081			−0.575403	+	0.817870i	$0.695155\pi$
$132$			7.65685i			0.666444i
$133$	−1.41421	+	1.41421i	−0.122628	+	0.122628i
$134$	−4.24264			−0.366508
$135$		0			0
$136$	−23.8995	−	23.8995i	−2.04936	−	2.04936i
$137$	18.8284			1.60862			0.804311	−	0.594209i	$-0.202535\pi$
$137$	18.8284			1.60862			0.804311	+	0.594209i	$0.202535\pi$
$138$			16.4853i			1.40332i
$139$		−	1.65685i		−	0.140533i	−0.997528	−	0.0702663i	$-0.977615\pi$
$139$		−	1.65685i		−	0.140533i	0.997528	−	0.0702663i	$-0.0223849\pi$
$140$		0			0
$141$	3.41421	−	3.41421i	0.287529	−	0.287529i
$142$	−15.0711	+	15.0711i	−1.26474	+	1.26474i
$143$	−4.00000	−	6.00000i	−0.334497	−	0.501745i
$144$		−	3.00000i		−	0.250000i
$145$		0			0
$146$	−39.2132			−3.24531
$147$	−3.29289	+	3.29289i	−0.271593	+	0.271593i
$148$	−5.41421			−0.445046
$149$	10.4853	−	10.4853i	0.858988	−	0.858988i	−0.132231	−	0.991219i	$-0.542214\pi$
$149$	10.4853	−	10.4853i	0.858988	−	0.858988i	0.991219	+	0.132231i	$0.0422141\pi$
$150$		0			0
$151$	−11.2426	+	11.2426i	−0.914913	+	0.914913i	−0.996654	−	0.0817405i	$-0.973952\pi$
$151$	−11.2426	+	11.2426i	−0.914913	+	0.914913i	0.0817405	+	0.996654i	$0.473952\pi$
$152$	−1.82843	−	1.82843i	−0.148305	−	0.148305i
$153$	5.41421	+	5.41421i	0.437713	+	0.437713i
$154$	11.6569	+	11.6569i	0.939336	+	0.939336i
$155$		0			0
$156$	7.65685	+	11.4853i	0.613039	+	0.919558i
$157$	−5.17157	−	5.17157i	−0.412736	−	0.412736i	0.469954	−	0.882691i	$-0.344270\pi$
$157$	−5.17157	−	5.17157i	−0.412736	−	0.412736i	−0.882691	+	0.469954i	$0.844270\pi$
$158$	−11.6569			−0.927370
$159$		−	6.48528i		−	0.514316i
$160$		0			0
$161$	16.4853	+	16.4853i	1.29922	+	1.29922i
$162$			2.41421i			0.189679i
$163$		−	19.4142i		−	1.52064i	−0.649550	−	0.760319i	$-0.725042\pi$
$163$		−	19.4142i		−	1.52064i	0.649550	−	0.760319i	$-0.274958\pi$
$164$	14.0000	+	14.0000i	1.09322	+	1.09322i
$165$		0			0
$166$		−	22.4853i		−	1.74520i
$167$	−16.1421			−1.24912			−0.624558	−	0.780978i	$-0.714721\pi$
$167$	−16.1421			−1.24912			−0.624558	+	0.780978i	$0.714721\pi$
$168$	−10.6569	−	10.6569i	−0.822194	−	0.822194i
$169$	−12.0000	−	5.00000i	−0.923077	−	0.384615i
$170$		0			0
$171$	0.414214	+	0.414214i	0.0316757	+	0.0316757i
$172$	−26.1421	−	26.1421i	−1.99332	−	1.99332i
$173$	1.07107	+	1.07107i	0.0814318	+	0.0814318i	0.746649	−	0.665218i	$-0.231661\pi$
$173$	1.07107	+	1.07107i	0.0814318	+	0.0814318i	−0.665218	+	0.746649i	$0.731661\pi$
$174$	−1.41421	+	1.41421i	−0.107211	+	0.107211i
$175$		0			0
$176$	−4.24264	+	4.24264i	−0.319801	+	0.319801i
$177$	0.828427			0.0622684
$178$	−16.4853	+	16.4853i	−1.23562	+	1.23562i
$179$	−16.0000			−1.19590			−0.597948	−	0.801535i	$-0.704017\pi$
$179$	−16.0000			−1.19590			−0.597948	+	0.801535i	$0.704017\pi$
$180$		0			0
$181$		−	5.65685i		−	0.420471i	−0.977651	−	0.210235i	$-0.932577\pi$
$181$		−	5.65685i		−	0.420471i	0.977651	−	0.210235i	$-0.0674230\pi$
$182$	29.1421	+	5.82843i	2.16016	+	0.432032i
$183$	−9.65685	+	9.65685i	−0.713855	+	0.713855i
$184$	−21.3137	+	21.3137i	−1.57127	+	1.57127i
$185$		0			0
$186$			5.41421i			0.396989i
$187$		−	15.3137i		−	1.11985i
$188$	18.4853			1.34818
$189$	2.41421	+	2.41421i	0.175608	+	0.175608i
$190$		0			0
$191$	3.31371			0.239772			0.119886	−	0.992788i	$-0.461747\pi$
$191$	3.31371			0.239772			0.119886	+	0.992788i	$0.461747\pi$
$192$	−6.94975	+	6.94975i	−0.501555	+	0.501555i
$193$			15.7574i			1.13424i	0.823635	+	0.567120i	$0.191942\pi$
$193$			15.7574i			1.13424i	−0.823635	+	0.567120i	$0.808058\pi$
$194$	46.0416			3.30560
$195$		0			0
$196$	−17.8284			−1.27346
$197$		−	2.34315i		−	0.166942i	−0.996510	−	0.0834711i	$-0.973399\pi$
$197$		−	2.34315i		−	0.166942i	0.996510	−	0.0834711i	$-0.0266006\pi$
$198$	3.41421	−	3.41421i	0.242638	−	0.242638i
$199$	−8.00000			−0.567105			−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000			−0.567105			−0.283552	+	0.958957i	$0.591513\pi$
$200$		0			0
$201$	1.24264	+	1.24264i	0.0876491	+	0.0876491i
$202$	41.7990			2.94097
$203$			2.82843i			0.198517i
$204$			29.3137i			2.05237i
$205$		0			0
$206$	19.3137	−	19.3137i	1.34565	−	1.34565i
$207$	4.82843	−	4.82843i	0.335599	−	0.335599i
$208$	−2.12132	+	10.6066i	−0.147087	+	0.735436i
$209$		−	1.17157i		−	0.0810394i
$210$		0			0
$211$	13.7990			0.949962			0.474981	−	0.879996i	$-0.342455\pi$
$211$	13.7990			0.949962			0.474981	+	0.879996i	$0.342455\pi$
$212$	17.5563	−	17.5563i	1.20578	−	1.20578i
$213$	8.82843			0.604914
$214$	17.3137	−	17.3137i	1.18354	−	1.18354i
$215$		0			0
$216$	−3.12132	+	3.12132i	−0.212379	+	0.212379i
$217$	5.41421	+	5.41421i	0.367541	+	0.367541i
$218$	4.41421	+	4.41421i	0.298968	+	0.298968i
$219$	11.4853	+	11.4853i	0.776103	+	0.776103i
$220$		0			0
$221$	−15.3137	−	22.9706i	−1.03011	−	1.54517i
$222$	2.41421	+	2.41421i	0.162031	+	0.162031i
$223$	−22.0416			−1.47602			−0.738008	−	0.674792i	$-0.764234\pi$
$223$	−22.0416			−1.47602			−0.738008	+	0.674792i	$0.764234\pi$
$224$			5.41421i			0.361752i
$225$		0			0
$226$	−17.0711	−	17.0711i	−1.13555	−	1.13555i
$227$		−	10.4853i		−	0.695933i	−0.937507	−	0.347966i	$-0.886872\pi$
$227$		−	10.4853i		−	0.695933i	0.937507	−	0.347966i	$-0.113128\pi$
$228$			2.24264i			0.148523i
$229$	17.4853	+	17.4853i	1.15546	+	1.15546i	0.985441	+	0.170019i	$0.0543830\pi$
$229$	17.4853	+	17.4853i	1.15546	+	1.15546i	0.170019	+	0.985441i	$0.445617\pi$
$230$		0			0
$231$		−	6.82843i		−	0.449278i
$232$	−3.65685			−0.240084
$233$	7.41421	+	7.41421i	0.485721	+	0.485721i	0.906953	−	0.421232i	$-0.138402\pi$
$233$	7.41421	+	7.41421i	0.485721	+	0.485721i	−0.421232	+	0.906953i	$0.638402\pi$
$234$	1.70711	−	8.53553i	0.111597	−	0.557985i
$235$		0			0
$236$	2.24264	+	2.24264i	0.145983	+	0.145983i
$237$	3.41421	+	3.41421i	0.221777	+	0.221777i
$238$	44.6274	+	44.6274i	2.89277	+	2.89277i
$239$	7.89949	−	7.89949i	0.510976	−	0.510976i	−0.403850	−	0.914825i	$-0.632328\pi$
$239$	7.89949	−	7.89949i	0.510976	−	0.510976i	0.914825	+	0.403850i	$0.132328\pi$
$240$		0			0
$241$	−6.65685	+	6.65685i	−0.428806	+	0.428806i	−0.888221	−	0.459416i	$-0.848059\pi$
$241$	−6.65685	+	6.65685i	−0.428806	+	0.428806i	0.459416	+	0.888221i	$0.348059\pi$
$242$	16.8995			1.08634
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−52.2843			−3.34716
$245$		0			0
$246$		−	12.4853i		−	0.796032i
$247$	−1.17157	−	1.75736i	−0.0745454	−	0.111818i
$248$	−7.00000	+	7.00000i	−0.444500	+	0.444500i
$249$	−6.58579	+	6.58579i	−0.417357	+	0.417357i
$250$		0			0
$251$		−	20.4853i		−	1.29302i	−0.762906	−	0.646510i	$-0.776228\pi$
$251$		−	20.4853i		−	1.29302i	0.762906	−	0.646510i	$-0.223772\pi$
$252$			13.0711i			0.823400i
$253$	−13.6569			−0.858599
$254$	17.8995	+	17.8995i	1.12311	+	1.12311i
$255$		0			0
$256$	−29.9706			−1.87316
$257$	−18.7279	+	18.7279i	−1.16822	+	1.16822i	−0.185588	+	0.982628i	$0.559419\pi$
$257$	−18.7279	+	18.7279i	−1.16822	+	1.16822i	−0.982628	+	0.185588i	$0.940581\pi$
$258$			23.3137i			1.45145i
$259$	4.82843			0.300024
$260$		0			0
$261$	0.828427			0.0512784
$262$			31.7990i			1.96455i
$263$	−11.1716	+	11.1716i	−0.688869	+	0.688869i	−0.961982	−	0.273113i	$-0.911947\pi$
$263$	−11.1716	+	11.1716i	−0.688869	+	0.688869i	0.273113	+	0.961982i	$0.411947\pi$
$264$	8.82843			0.543352
$265$		0			0
$266$	3.41421	+	3.41421i	0.209339	+	0.209339i
$267$	9.65685			0.590990
$268$			6.72792i			0.410973i
$269$		−	8.82843i		−	0.538279i	−0.963101	−	0.269139i	$-0.913261\pi$
$269$		−	8.82843i		−	0.538279i	0.963101	−	0.269139i	$-0.0867392\pi$
$270$		0			0
$271$	−8.41421	+	8.41421i	−0.511127	+	0.511127i	−0.914872	−	0.403745i	$-0.867708\pi$
$271$	−8.41421	+	8.41421i	−0.511127	+	0.511127i	0.403745	+	0.914872i	$0.367708\pi$
$272$	−16.2426	+	16.2426i	−0.984855	+	0.984855i
$273$	−6.82843	−	10.2426i	−0.413275	−	0.619913i
$274$		−	45.4558i		−	2.74609i
$275$		0			0
$276$	26.1421			1.57357
$277$	7.07107	−	7.07107i	0.424859	−	0.424859i	−0.462014	−	0.886873i	$-0.652873\pi$
$277$	7.07107	−	7.07107i	0.424859	−	0.424859i	0.886873	+	0.462014i	$0.152873\pi$
$278$	−4.00000			−0.239904
$279$	1.58579	−	1.58579i	0.0949386	−	0.0949386i
$280$		0			0
$281$	12.1421	−	12.1421i	0.724339	−	0.724339i	−0.245147	−	0.969486i	$-0.578836\pi$
$281$	12.1421	−	12.1421i	0.724339	−	0.724339i	0.969486	+	0.245147i	$0.0788362\pi$
$282$	−8.24264	−	8.24264i	−0.490842	−	0.490842i
$283$	−3.41421	−	3.41421i	−0.202954	−	0.202954i	0.598310	−	0.801264i	$-0.295839\pi$
$283$	−3.41421	−	3.41421i	−0.202954	−	0.202954i	−0.801264	+	0.598310i	$0.795839\pi$
$284$	23.8995	+	23.8995i	1.41817	+	1.41817i
$285$		0			0
$286$	−14.4853	+	9.65685i	−0.856533	+	0.571022i
$287$	−12.4853	−	12.4853i	−0.736983	−	0.736983i
$288$	1.58579			0.0934434
$289$		−	41.6274i		−	2.44867i
$290$		0			0
$291$	−13.4853	−	13.4853i	−0.790521	−	0.790521i
$292$			62.1838i			3.63903i
$293$			19.7990i			1.15667i	0.815800	+	0.578335i	$0.196297\pi$
$293$			19.7990i			1.15667i	−0.815800	+	0.578335i	$0.803703\pi$
$294$	7.94975	+	7.94975i	0.463639	+	0.463639i
$295$		0			0
$296$			6.24264i			0.362846i
$297$	−2.00000			−0.116052
$298$	−25.3137	−	25.3137i	−1.46638	−	1.46638i
$299$	−20.4853	+	13.6569i	−1.18469	+	0.789796i
$300$		0			0
$301$	23.3137	+	23.3137i	1.34378	+	1.34378i
$302$	27.1421	+	27.1421i	1.56185	+	1.56185i
$303$	−12.2426	−	12.2426i	−0.703321	−	0.703321i
$304$	−1.24264	+	1.24264i	−0.0712703	+	0.0712703i
$305$		0			0
$306$	13.0711	−	13.0711i	0.747223	−	0.747223i
$307$	9.55635			0.545410			0.272705	−	0.962098i	$-0.412082\pi$
$307$	9.55635			0.545410			0.272705	+	0.962098i	$0.412082\pi$
$308$	18.4853	−	18.4853i	1.05330	−	1.05330i
$309$	−11.3137			−0.643614
$310$		0			0
$311$			2.14214i			0.121469i	0.998154	+	0.0607347i	$0.0193444\pi$
$311$			2.14214i			0.121469i	−0.998154	+	0.0607347i	$0.980656\pi$
$312$	13.2426	−	8.82843i	0.749717	−	0.499811i
$313$	20.7279	−	20.7279i	1.17161	−	1.17161i	0.189786	−	0.981825i	$-0.439221\pi$
$313$	20.7279	−	20.7279i	1.17161	−	1.17161i	0.981825	−	0.189786i	$-0.0607794\pi$
$314$	−12.4853	+	12.4853i	−0.704585	+	0.704585i
$315$		0			0
$316$			18.4853i			1.03988i
$317$			11.3137i			0.635441i	0.948184	+	0.317721i	$0.102917\pi$
$317$			11.3137i			0.635441i	−0.948184	+	0.317721i	$0.897083\pi$
$318$	−15.6569			−0.877993
$319$	−1.17157	−	1.17157i	−0.0655955	−	0.0655955i
$320$		0			0
$321$	−10.1421			−0.566079
$322$	39.7990	−	39.7990i	2.21791	−	2.21791i
$323$		−	4.48528i		−	0.249568i
$324$	3.82843			0.212690
$325$		0			0
$326$	−46.8701			−2.59589
$327$		−	2.58579i		−	0.142994i
$328$	16.1421	−	16.1421i	0.891300	−	0.891300i
$329$	−16.4853			−0.908863
$330$		0			0
$331$	13.7279	+	13.7279i	0.754555	+	0.754555i	0.975326	−	0.220771i	$-0.0708573\pi$
$331$	13.7279	+	13.7279i	0.754555	+	0.754555i	−0.220771	+	0.975326i	$0.570857\pi$
$332$	−35.6569			−1.95692
$333$		−	1.41421i		−	0.0774984i
$334$			38.9706i			2.13237i
$335$		0			0
$336$	−7.24264	+	7.24264i	−0.395118	+	0.395118i
$337$	6.34315	−	6.34315i	0.345533	−	0.345533i	−0.512910	−	0.858443i	$-0.671432\pi$
$337$	6.34315	−	6.34315i	0.345533	−	0.345533i	0.858443	+	0.512910i	$0.171432\pi$
$338$	−12.0711	+	28.9706i	−0.656580	+	1.57579i
$339$			10.0000i			0.543125i
$340$		0			0
$341$	−4.48528			−0.242892
$342$	1.00000	−	1.00000i	0.0540738	−	0.0540738i
$343$	−8.00000			−0.431959
$344$	−30.1421	+	30.1421i	−1.62516	+	1.62516i
$345$		0			0
$346$	2.58579	−	2.58579i	0.139013	−	0.139013i
$347$	−5.65685	−	5.65685i	−0.303676	−	0.303676i	0.538774	−	0.842450i	$-0.318888\pi$
$347$	−5.65685	−	5.65685i	−0.303676	−	0.303676i	−0.842450	+	0.538774i	$0.818888\pi$
$348$	2.24264	+	2.24264i	0.120218	+	0.120218i
$349$	−11.8284	−	11.8284i	−0.633161	−	0.633161i	0.315698	−	0.948860i	$-0.397761\pi$
$349$	−11.8284	−	11.8284i	−0.633161	−	0.633161i	−0.948860	+	0.315698i	$0.897761\pi$
$350$		0			0
$351$	−3.00000	+	2.00000i	−0.160128	+	0.106752i
$352$	−2.24264	−	2.24264i	−0.119533	−	0.119533i
$353$	−13.4558			−0.716182			−0.358091	−	0.933687i	$-0.616572\pi$
$353$	−13.4558			−0.716182			−0.358091	+	0.933687i	$0.616572\pi$
$354$		−	2.00000i		−	0.106299i
$355$		0			0
$356$	26.1421	+	26.1421i	1.38553	+	1.38553i
$357$		−	26.1421i		−	1.38359i
$358$			38.6274i			2.04152i
$359$	−7.55635	−	7.55635i	−0.398809	−	0.398809i	0.479004	−	0.877813i	$-0.340998\pi$
$359$	−7.55635	−	7.55635i	−0.398809	−	0.398809i	−0.877813	+	0.479004i	$0.840998\pi$
$360$		0			0
$361$			18.6569i			0.981940i
$362$	−13.6569			−0.717788
$363$	−4.94975	−	4.94975i	−0.259794	−	0.259794i
$364$	9.24264	−	46.2132i	0.484446	−	2.42223i
$365$		0			0
$366$	23.3137	+	23.3137i	1.21863	+	1.21863i
$367$	−22.0416	−	22.0416i	−1.15056	−	1.15056i	−0.986440	−	0.164124i	$-0.947520\pi$
$367$	−22.0416	−	22.0416i	−1.15056	−	1.15056i	−0.164124	−	0.986440i	$-0.552480\pi$
$368$	14.4853	+	14.4853i	0.755097	+	0.755097i
$369$	−3.65685	+	3.65685i	−0.190368	+	0.190368i
$370$		0			0
$371$	−15.6569	+	15.6569i	−0.812863	+	0.812863i
$372$	8.58579			0.445152
$373$	1.89949	−	1.89949i	0.0983521	−	0.0983521i	−0.656219	−	0.754571i	$-0.727845\pi$
$373$	1.89949	−	1.89949i	0.0983521	−	0.0983521i	0.754571	+	0.656219i	$0.227845\pi$
$374$	−36.9706			−1.91170
$375$		0			0
$376$		−	21.3137i		−	1.09917i
$377$	−2.92893	−	0.585786i	−0.150848	−	0.0301695i
$378$	5.82843	−	5.82843i	0.299782	−	0.299782i
$379$	11.7279	−	11.7279i	0.602423	−	0.602423i	−0.338532	−	0.940955i	$-0.609930\pi$
$379$	11.7279	−	11.7279i	0.602423	−	0.602423i	0.940955	+	0.338532i	$0.109930\pi$
$380$		0			0
$381$		−	10.4853i		−	0.537177i
$382$		−	8.00000i		−	0.409316i
$383$	3.17157			0.162060			0.0810299	−	0.996712i	$-0.474179\pi$
$383$	3.17157			0.162060			0.0810299	+	0.996712i	$0.474179\pi$
$384$	14.5355	+	14.5355i	0.741763	+	0.741763i
$385$		0			0
$386$	38.0416			1.93627
$387$	6.82843	−	6.82843i	0.347108	−	0.347108i
$388$		−	73.0122i		−	3.70663i
$389$	28.8284			1.46166			0.730830	−	0.682560i	$-0.239133\pi$
$389$	28.8284			1.46166			0.730830	+	0.682560i	$0.239133\pi$
$390$		0			0
$391$	−52.2843			−2.64413
$392$			20.5563i			1.03825i
$393$	9.31371	−	9.31371i	0.469814	−	0.469814i
$394$	−5.65685			−0.284988
$395$		0			0
$396$	−5.41421	−	5.41421i	−0.272074	−	0.272074i
$397$	−0.928932			−0.0466218			−0.0233109	−	0.999728i	$-0.507421\pi$
$397$	−0.928932			−0.0466218			−0.0233109	+	0.999728i	$0.507421\pi$
$398$			19.3137i			0.968109i
$399$		−	2.00000i		−	0.100125i
$400$		0			0
$401$	20.0000	−	20.0000i	0.998752	−	0.998752i	−0.00124688	−	0.999999i	$-0.500397\pi$
$401$	20.0000	−	20.0000i	0.998752	−	0.998752i	0.999999	+	0.00124688i	$0.000396896\pi$
$402$	3.00000	−	3.00000i	0.149626	−	0.149626i
$403$	−6.72792	+	4.48528i	−0.335142	+	0.223428i
$404$		−	66.2843i		−	3.29777i
$405$		0			0
$406$	6.82843			0.338889
$407$	−2.00000	+	2.00000i	−0.0991363	+	0.0991363i
$408$	33.7990			1.67330
$409$	3.68629	−	3.68629i	0.182275	−	0.182275i	−0.610071	−	0.792347i	$-0.708859\pi$
$409$	3.68629	−	3.68629i	0.182275	−	0.182275i	0.792347	+	0.610071i	$0.208859\pi$
$410$		0			0
$411$	−13.3137	+	13.3137i	−0.656717	+	0.656717i
$412$	−30.6274	−	30.6274i	−1.50890	−	1.50890i
$413$	−2.00000	−	2.00000i	−0.0984136	−	0.0984136i
$414$	−11.6569	−	11.6569i	−0.572903	−	0.572903i
$415$		0			0
$416$	−5.60660	−	1.12132i	−0.274886	−	0.0549773i
$417$	1.17157	+	1.17157i	0.0573722	+	0.0573722i
$418$	−2.82843			−0.138343
$419$			29.4558i			1.43901i	0.694486	+	0.719506i	$0.255632\pi$
$419$			29.4558i			1.43901i	−0.694486	+	0.719506i	$0.744368\pi$
$420$		0			0
$421$	21.8284	+	21.8284i	1.06385	+	1.06385i	0.997817	+	0.0660351i	$0.0210349\pi$
$421$	21.8284	+	21.8284i	1.06385	+	1.06385i	0.0660351	+	0.997817i	$0.478965\pi$
$422$		−	33.3137i		−	1.62169i
$423$			4.82843i			0.234766i
$424$	−20.2426	−	20.2426i	−0.983070	−	0.983070i
$425$		0			0
$426$		−	21.3137i		−	1.03265i
$427$	46.6274			2.25646
$428$	−27.4558	−	27.4558i	−1.32713	−	1.32713i
$429$	7.07107	+	1.41421i	0.341394	+	0.0682789i
$430$		0			0
$431$	9.41421	+	9.41421i	0.453467	+	0.453467i	0.896503	−	0.443037i	$-0.146099\pi$
$431$	9.41421	+	9.41421i	0.453467	+	0.453467i	−0.443037	+	0.896503i	$0.646099\pi$
$432$	2.12132	+	2.12132i	0.102062	+	0.102062i
$433$	2.14214	+	2.14214i	0.102944	+	0.102944i	0.756703	−	0.653759i	$-0.226809\pi$
$433$	2.14214	+	2.14214i	0.102944	+	0.102944i	−0.653759	+	0.756703i	$0.726809\pi$
$434$	13.0711	−	13.0711i	0.627431	−	0.627431i
$435$		0			0
$436$	7.00000	−	7.00000i	0.335239	−	0.335239i
$437$	−4.00000			−0.191346
$438$	27.7279	−	27.7279i	1.32489	−	1.32489i
$439$	22.4853			1.07316			0.536582	−	0.843848i	$-0.319715\pi$
$439$	22.4853			1.07316			0.536582	+	0.843848i	$0.319715\pi$
$440$		0			0
$441$		−	4.65685i		−	0.221755i
$442$	−55.4558	+	36.9706i	−2.63777	+	1.75851i
$443$	10.0000	−	10.0000i	0.475114	−	0.475114i	−0.428451	−	0.903565i	$-0.640940\pi$
$443$	10.0000	−	10.0000i	0.475114	−	0.475114i	0.903565	+	0.428451i	$0.140940\pi$
$444$	3.82843	−	3.82843i	0.181689	−	0.181689i
$445$		0			0
$446$			53.2132i			2.51972i
$447$			14.8284i			0.701361i
$448$	33.5563			1.58539
$449$	−4.68629	−	4.68629i	−0.221160	−	0.221160i	0.587827	−	0.808987i	$-0.299984\pi$
$449$	−4.68629	−	4.68629i	−0.221160	−	0.221160i	−0.808987	+	0.587827i	$0.799984\pi$
$450$		0			0
$451$	10.3431			0.487040
$452$	−27.0711	+	27.0711i	−1.27332	+	1.27332i
$453$		−	15.8995i		−	0.747023i
$454$	−25.3137			−1.18803
$455$		0			0
$456$	2.58579			0.121091
$457$		−	33.2132i		−	1.55365i	−0.629718	−	0.776824i	$-0.716829\pi$
$457$		−	33.2132i		−	1.55365i	0.629718	−	0.776824i	$-0.283171\pi$
$458$	42.2132	−	42.2132i	1.97249	−	1.97249i
$459$	−7.65685			−0.357391
$460$		0			0
$461$	−15.7990	−	15.7990i	−0.735832	−	0.735832i	0.235936	−	0.971769i	$-0.424184\pi$
$461$	−15.7990	−	15.7990i	−0.735832	−	0.735832i	−0.971769	+	0.235936i	$0.924184\pi$
$462$	−16.4853			−0.766965
$463$			5.75736i			0.267567i	0.991011	+	0.133784i	$0.0427127\pi$
$463$			5.75736i			0.267567i	−0.991011	+	0.133784i	$0.957287\pi$
$464$			2.48528i			0.115376i
$465$		0			0
$466$	17.8995	−	17.8995i	0.829178	−	0.829178i
$467$	−12.1421	+	12.1421i	−0.561871	+	0.561871i	−0.929839	−	0.367968i	$-0.880054\pi$
$467$	−12.1421	+	12.1421i	−0.561871	+	0.561871i	0.367968	+	0.929839i	$0.380054\pi$
$468$	−13.5355	−	2.70711i	−0.625680	−	0.125136i
$469$		−	6.00000i		−	0.277054i
$470$		0			0
$471$	7.31371			0.336998
$472$	2.58579	−	2.58579i	0.119020	−	0.119020i
$473$	−19.3137			−0.888045
$474$	8.24264	−	8.24264i	0.378597	−	0.378597i
$475$		0			0
$476$	70.7696	−	70.7696i	3.24372	−	3.24372i
$477$	4.58579	+	4.58579i	0.209969	+	0.209969i
$478$	−19.0711	−	19.0711i	−0.872290	−	0.872290i
$479$	16.5858	+	16.5858i	0.757824	+	0.757824i	0.975926	−	0.218102i	$-0.0699866\pi$
$479$	16.5858	+	16.5858i	0.757824	+	0.757824i	−0.218102	+	0.975926i	$0.569987\pi$
$480$		0			0
$481$	−1.00000	+	5.00000i	−0.0455961	+	0.227980i
$482$	16.0711	+	16.0711i	0.732017	+	0.732017i
$483$	−23.3137			−1.06081
$484$		−	26.7990i		−	1.21814i
$485$		0			0
$486$	−1.70711	−	1.70711i	−0.0774359	−	0.0774359i
$487$		−	13.0711i		−	0.592307i	−0.955140	−	0.296153i	$-0.904296\pi$
$487$		−	13.0711i		−	0.592307i	0.955140	−	0.296153i	$-0.0957039\pi$
$488$			60.2843i			2.72894i
$489$	13.7279	+	13.7279i	0.620798	+	0.620798i
$490$		0			0
$491$			9.17157i			0.413907i	0.978351	+	0.206954i	$0.0663549\pi$
$491$			9.17157i			0.413907i	−0.978351	+	0.206954i	$0.933645\pi$
$492$	−19.7990			−0.892607
$493$	−4.48528	−	4.48528i	−0.202007	−	0.202007i
$494$	−4.24264	+	2.82843i	−0.190885	+	0.127257i
$495$		0			0
$496$	4.75736	+	4.75736i	0.213612	+	0.213612i
$497$	−21.3137	−	21.3137i	−0.956050	−	0.956050i
$498$	15.8995	+	15.8995i	0.712473	+	0.712473i
$499$	7.24264	−	7.24264i	0.324225	−	0.324225i	−0.526160	−	0.850385i	$-0.676369\pi$
$499$	7.24264	−	7.24264i	0.324225	−	0.324225i	0.850385	+	0.526160i	$0.176369\pi$
$500$		0			0
$501$	11.4142	−	11.4142i	0.509949	−	0.509949i
$502$	−49.4558			−2.20732
$503$	11.6569	−	11.6569i	0.519753	−	0.519753i	−0.397743	−	0.917497i	$-0.630207\pi$
$503$	11.6569	−	11.6569i	0.519753	−	0.519753i	0.917497	+	0.397743i	$0.130207\pi$
$504$	15.0711			0.671319
$505$		0			0
$506$			32.9706i			1.46572i
$507$	12.0208	−	4.94975i	0.533863	−	0.219826i
$508$	28.3848	−	28.3848i	1.25937	−	1.25937i
$509$	16.0000	−	16.0000i	0.709188	−	0.709188i	−0.257177	−	0.966364i	$-0.582792\pi$
$509$	16.0000	−	16.0000i	0.709188	−	0.709188i	0.966364	+	0.257177i	$0.0827923\pi$
$510$		0			0
$511$		−	55.4558i		−	2.45322i
$512$			31.2426i			1.38074i
$513$	−0.585786			−0.0258631
$514$	45.2132	+	45.2132i	1.99427	+	1.99427i
$515$		0			0
$516$	36.9706			1.62754
$517$	6.82843	−	6.82843i	0.300314	−	0.300314i
$518$		−	11.6569i		−	0.512173i
$519$	−1.51472			−0.0664888
$520$		0			0
$521$	19.1716			0.839922			0.419961	−	0.907542i	$-0.362044\pi$
$521$	19.1716			0.839922			0.419961	+	0.907542i	$0.362044\pi$
$522$		−	2.00000i		−	0.0875376i
$523$	−18.2426	+	18.2426i	−0.797695	+	0.797695i	−0.982732	−	0.185037i	$-0.940760\pi$
$523$	−18.2426	+	18.2426i	−0.797695	+	0.797695i	0.185037	+	0.982732i	$0.440760\pi$
$524$	50.4264			2.20289
$525$		0			0
$526$	26.9706	+	26.9706i	1.17597	+	1.17597i
$527$	−17.1716			−0.748005
$528$		−	6.00000i		−	0.261116i
$529$			23.6274i			1.02728i
$530$		0			0
$531$	−0.585786	+	0.585786i	−0.0254210	+	0.0254210i
$532$	5.41421	−	5.41421i	0.234736	−	0.234736i
$533$	15.5147	−	10.3431i	0.672017	−	0.448011i
$534$		−	23.3137i		−	1.00888i
$535$		0			0
$536$	7.75736			0.335067
$537$	11.3137	−	11.3137i	0.488223	−	0.488223i
$538$	−21.3137			−0.918899
$539$	−6.58579	+	6.58579i	−0.283670	+	0.283670i
$540$		0			0
$541$	−3.48528	+	3.48528i	−0.149844	+	0.149844i	−0.778048	−	0.628204i	$-0.783790\pi$
$541$	−3.48528	+	3.48528i	−0.149844	+	0.149844i	0.628204	+	0.778048i	$0.283790\pi$
$542$	20.3137	+	20.3137i	0.872548	+	0.872548i
$543$	4.00000	+	4.00000i	0.171656	+	0.171656i
$544$	−8.58579	−	8.58579i	−0.368113	−	0.368113i
$545$		0			0
$546$	−24.7279	+	16.4853i	−1.05826	+	0.705505i
$547$	30.2426	+	30.2426i	1.29308	+	1.29308i	0.932871	+	0.360211i	$0.117295\pi$
$547$	30.2426	+	30.2426i	1.29308	+	1.29308i	0.360211	+	0.932871i	$0.382705\pi$
$548$	−72.0833			−3.07924
$549$		−	13.6569i		−	0.582860i
$550$		0			0
$551$	−0.343146	−	0.343146i	−0.0146185	−	0.0146185i
$552$		−	30.1421i		−	1.28293i
$553$		−	16.4853i		−	0.701025i
$554$	−17.0711	−	17.0711i	−0.725280	−	0.725280i
$555$		0			0
$556$			6.34315i			0.269009i
$557$	11.5147			0.487894			0.243947	−	0.969789i	$-0.421558\pi$
$557$	11.5147			0.487894			0.243947	+	0.969789i	$0.421558\pi$
$558$	−3.82843	−	3.82843i	−0.162070	−	0.162070i
$559$	−28.9706	+	19.3137i	−1.22532	+	0.816883i
$560$		0			0
$561$	10.8284	+	10.8284i	0.457177	+	0.457177i
$562$	−29.3137	−	29.3137i	−1.23652	−	1.23652i
$563$	2.14214	+	2.14214i	0.0902803	+	0.0902803i	0.750805	−	0.660524i	$-0.229666\pi$
$563$	2.14214	+	2.14214i	0.0902803	+	0.0902803i	−0.660524	+	0.750805i	$0.729666\pi$
$564$	−13.0711	+	13.0711i	−0.550391	+	0.550391i
$565$		0			0
$566$	−8.24264	+	8.24264i	−0.346464	+	0.346464i
$567$	−3.41421			−0.143383
$568$	27.5563	−	27.5563i	1.15624	−	1.15624i
$569$	14.9706			0.627599			0.313799	−	0.949489i	$-0.398398\pi$
$569$	14.9706			0.627599			0.313799	+	0.949489i	$0.398398\pi$
$570$		0			0
$571$		−	32.2843i		−	1.35105i	−0.737335	−	0.675527i	$-0.763916\pi$
$571$		−	32.2843i		−	1.35105i	0.737335	−	0.675527i	$-0.236084\pi$
$572$	15.3137	+	22.9706i	0.640298	+	0.960447i
$573$	−2.34315	+	2.34315i	−0.0978863	+	0.0978863i
$574$	−30.1421	+	30.1421i	−1.25811	+	1.25811i
$575$		0			0
$576$		−	9.82843i		−	0.409518i
$577$		−	17.2132i		−	0.716595i	−0.933607	−	0.358298i	$-0.883357\pi$
$577$		−	17.2132i		−	0.716595i	0.933607	−	0.358298i	$-0.116643\pi$
$578$	−100.497			−4.18014
$579$	−11.1421	−	11.1421i	−0.463051	−	0.463051i
$580$		0			0
$581$	31.7990			1.31924
$582$	−32.5563	+	32.5563i	−1.34950	+	1.34950i
$583$		−	12.9706i		−	0.537186i
$584$	71.6985			2.96690
$585$		0			0
$586$	47.7990			1.97456
$587$		−	26.0000i		−	1.07313i	−0.843857	−	0.536567i	$-0.819721\pi$
$587$		−	26.0000i		−	1.07313i	0.843857	−	0.536567i	$-0.180279\pi$
$588$	12.6066	−	12.6066i	0.519887	−	0.519887i
$589$	−1.31371			−0.0541304
$590$		0			0
$591$	1.65685	+	1.65685i	0.0681539	+	0.0681539i
$592$	4.24264			0.174371
$593$			20.2843i			0.832975i	0.909141	+	0.416488i	$0.136739\pi$
$593$			20.2843i			0.832975i	−0.909141	+	0.416488i	$0.863261\pi$
$594$			4.82843i			0.198113i
$595$		0			0
$596$	−40.1421	+	40.1421i	−1.64429	+	1.64429i
$597$	5.65685	−	5.65685i	0.231520	−	0.231520i
$598$	32.9706	+	49.4558i	1.34827	+	2.02240i
$599$		−	1.17157i		−	0.0478692i	−0.999714	−	0.0239346i	$-0.992381\pi$
$599$		−	1.17157i		−	0.0478692i	0.999714	−	0.0239346i	$-0.00761934\pi$
$600$		0			0
$601$	−10.6274			−0.433501			−0.216751	−	0.976227i	$-0.569546\pi$
$601$	−10.6274			−0.433501			−0.216751	+	0.976227i	$0.569546\pi$
$602$	56.2843	−	56.2843i	2.29398	−	2.29398i
$603$	−1.75736			−0.0715652
$604$	43.0416	−	43.0416i	1.75134	−	1.75134i
$605$		0			0
$606$	−29.5563	+	29.5563i	−1.20064	+	1.20064i
$607$	2.72792	+	2.72792i	0.110723	+	0.110723i	0.760298	−	0.649575i	$-0.225053\pi$
$607$	2.72792	+	2.72792i	0.110723	+	0.110723i	−0.649575	+	0.760298i	$0.725053\pi$
$608$	−0.656854	−	0.656854i	−0.0266390	−	0.0266390i
$609$	−2.00000	−	2.00000i	−0.0810441	−	0.0810441i
$610$		0			0
$611$	3.41421	−	17.0711i	0.138124	−	0.690621i
$612$	−20.7279	−	20.7279i	−0.837877	−	0.837877i
$613$	30.5858			1.23535			0.617674	−	0.786434i	$-0.288075\pi$
$613$	30.5858			1.23535			0.617674	+	0.786434i	$0.288075\pi$
$614$		−	23.0711i		−	0.931073i
$615$		0			0
$616$	−21.3137	−	21.3137i	−0.858754	−	0.858754i
$617$		−	11.5147i		−	0.463565i	−0.972768	−	0.231783i	$-0.925544\pi$
$617$		−	11.5147i		−	0.463565i	0.972768	−	0.231783i	$-0.0744558\pi$
$618$			27.3137i			1.09872i
$619$	16.0711	+	16.0711i	0.645951	+	0.645951i	0.952012	−	0.306061i	$-0.0990112\pi$
$619$	16.0711	+	16.0711i	0.645951	+	0.645951i	−0.306061	+	0.952012i	$0.599011\pi$
$620$		0			0
$621$			6.82843i			0.274015i
$622$	5.17157			0.207361
$623$	−23.3137	−	23.3137i	−0.934044	−	0.934044i
$624$	−6.00000	−	9.00000i	−0.240192	−	0.360288i
$625$		0			0
$626$	−50.0416	−	50.0416i	−2.00007	−	2.00007i
$627$	0.828427	+	0.828427i	0.0330842	+	0.0330842i
$628$	19.7990	+	19.7990i	0.790066	+	0.790066i
$629$	−7.65685	+	7.65685i	−0.305299	+	0.305299i
$630$		0			0
$631$	4.07107	−	4.07107i	0.162067	−	0.162067i	−0.621415	−	0.783482i	$-0.713442\pi$
$631$	4.07107	−	4.07107i	0.162067	−	0.162067i	0.783482	+	0.621415i	$0.213442\pi$
$632$	21.3137			0.847814
$633$	−9.75736	+	9.75736i	−0.387820	+	0.387820i
$634$	27.3137			1.08477
$635$		0			0
$636$			24.8284i			0.984511i
$637$	−3.29289	+	16.4645i	−0.130469	+	0.652346i
$638$	−2.82843	+	2.82843i	−0.111979	+	0.111979i
$639$	−6.24264	+	6.24264i	−0.246955	+	0.246955i
$640$		0			0
$641$		−	3.17157i		−	0.125270i	−0.998037	−	0.0626348i	$-0.980050\pi$
$641$		−	3.17157i		−	0.125270i	0.998037	−	0.0626348i	$-0.0199503\pi$
$642$			24.4853i			0.966357i
$643$	1.55635			0.0613764			0.0306882	−	0.999529i	$-0.490230\pi$
$643$	1.55635			0.0613764			0.0306882	+	0.999529i	$0.490230\pi$
$644$	−63.1127	−	63.1127i	−2.48699	−	2.48699i
$645$		0			0
$646$	−10.8284			−0.426039
$647$	11.5147	−	11.5147i	0.452690	−	0.452690i	−0.443556	−	0.896247i	$-0.646283\pi$
$647$	11.5147	−	11.5147i	0.452690	−	0.452690i	0.896247	+	0.443556i	$0.146283\pi$
$648$		−	4.41421i		−	0.173407i
$649$	1.65685			0.0650372
$650$		0			0
$651$	−7.65685			−0.300096
$652$			74.3259i			2.91083i
$653$	−5.41421	+	5.41421i	−0.211875	+	0.211875i	−0.805063	−	0.593189i	$-0.797869\pi$
$653$	−5.41421	+	5.41421i	−0.211875	+	0.211875i	0.593189	+	0.805063i	$0.297869\pi$
$654$	−6.24264			−0.244107
$655$		0			0
$656$	−10.9706	−	10.9706i	−0.428329	−	0.428329i
$657$	−16.2426			−0.633686
$658$			39.7990i			1.55153i
$659$		−	27.3137i		−	1.06399i	−0.846747	−	0.531996i	$-0.821442\pi$
$659$		−	27.3137i		−	1.06399i	0.846747	−	0.531996i	$-0.178558\pi$
$660$		0			0
$661$	8.17157	−	8.17157i	0.317837	−	0.317837i	−0.530099	−	0.847936i	$-0.677845\pi$
$661$	8.17157	−	8.17157i	0.317837	−	0.317837i	0.847936	+	0.530099i	$0.177845\pi$
$662$	33.1421	−	33.1421i	1.28811	−	1.28811i
$663$	27.0711	+	5.41421i	1.05135	+	0.210271i
$664$			41.1127i			1.59548i
$665$		0			0
$666$	−3.41421			−0.132298
$667$	−4.00000	+	4.00000i	−0.154881	+	0.154881i
$668$	61.7990			2.39107
$669$	15.5858	−	15.5858i	0.602581	−	0.602581i
$670$		0			0
$671$	−19.3137	+	19.3137i	−0.745597	+	0.745597i
$672$	−3.82843	−	3.82843i	−0.147685	−	0.147685i
$673$	−23.5563	−	23.5563i	−0.908031	−	0.908031i	0.0880826	−	0.996113i	$-0.471926\pi$
$673$	−23.5563	−	23.5563i	−0.908031	−	0.908031i	−0.996113	+	0.0880826i	$0.971926\pi$
$674$	−15.3137	−	15.3137i	−0.589862	−	0.589862i
$675$		0			0
$676$	45.9411	+	19.1421i	1.76697	+	0.736236i
$677$	33.5563	+	33.5563i	1.28968	+	1.28968i	0.934983	+	0.354692i	$0.115414\pi$
$677$	33.5563	+	33.5563i	1.28968	+	1.28968i	0.354692	+	0.934983i	$0.384586\pi$
$678$	24.1421			0.927173
$679$			65.1127i			2.49880i
$680$		0			0
$681$	7.41421	+	7.41421i	0.284113	+	0.284113i
$682$			10.8284i			0.414642i
$683$			50.7696i			1.94264i	0.237770	+	0.971321i	$0.423584\pi$
$683$			50.7696i			1.94264i	−0.237770	+	0.971321i	$0.576416\pi$
$684$	−1.58579	−	1.58579i	−0.0606341	−	0.0606341i
$685$		0			0
$686$			19.3137i			0.737401i
$687$	−24.7279			−0.943429
$688$	20.4853	+	20.4853i	0.780994	+	0.780994i
$689$	−12.9706	−	19.4558i	−0.494139	−	0.741209i
$690$		0			0
$691$	−9.58579	−	9.58579i	−0.364661	−	0.364661i	0.500865	−	0.865525i	$-0.333015\pi$
$691$	−9.58579	−	9.58579i	−0.364661	−	0.364661i	−0.865525	+	0.500865i	$0.833015\pi$
$692$	−4.10051	−	4.10051i	−0.155878	−	0.155878i
$693$	4.82843	+	4.82843i	0.183417	+	0.183417i
$694$	−13.6569	+	13.6569i	−0.518407	+	0.518407i
$695$		0			0
$696$	2.58579	−	2.58579i	0.0980140	−	0.0980140i
$697$	39.5980			1.49988
$698$	−28.5563	+	28.5563i	−1.08087	+	1.08087i
$699$	−10.4853			−0.396590
$700$		0			0
$701$			13.1127i			0.495260i	0.968855	+	0.247630i	$0.0796517\pi$
$701$			13.1127i			0.495260i	−0.968855	+	0.247630i	$0.920348\pi$
$702$	4.82843	+	7.24264i	0.182237	+	0.273356i
$703$	−0.585786	+	0.585786i	−0.0220934	+	0.0220934i
$704$	−13.8995	+	13.8995i	−0.523857	+	0.523857i
$705$		0			0
$706$			32.4853i			1.22260i
$707$			59.1127i			2.22316i
$708$	−3.17157			−0.119195
$709$	−14.4558	−	14.4558i	−0.542901	−	0.542901i	0.381478	−	0.924378i	$-0.375415\pi$
$709$	−14.4558	−	14.4558i	−0.542901	−	0.542901i	−0.924378	+	0.381478i	$0.875415\pi$
$710$		0			0
$711$	−4.82843			−0.181080
$712$	30.1421	−	30.1421i	1.12962	−	1.12962i
$713$			15.3137i			0.573503i
$714$	−63.1127			−2.36193
$715$		0			0
$716$	61.2548			2.28920
$717$			11.1716i			0.417210i
$718$	−18.2426	+	18.2426i	−0.680809	+	0.680809i
$719$	−20.4853			−0.763972			−0.381986	−	0.924168i	$-0.624760\pi$
$719$	−20.4853			−0.763972			−0.381986	+	0.924168i	$0.624760\pi$
$720$		0			0
$721$	27.3137	+	27.3137i	1.01722	+	1.01722i
$722$	45.0416			1.67628
$723$		−	9.41421i		−	0.350118i
$724$			21.6569i			0.804871i
$725$		0			0
$726$	−11.9497	+	11.9497i	−0.443497	+	0.443497i
$727$	−32.8701	+	32.8701i	−1.21908	+	1.21908i	−0.251129	+	0.967954i	$0.580802\pi$
$727$	−32.8701	+	32.8701i	−1.21908	+	1.21908i	−0.967954	+	0.251129i	$0.919198\pi$
$728$	−53.2843	−	10.6569i	−1.97485	−	0.394969i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−73.9411			−2.73481
$732$	36.9706	−	36.9706i	1.36647	−	1.36647i
$733$	32.5269			1.20141			0.600704	−	0.799471i	$-0.294887\pi$
$733$	32.5269			1.20141			0.600704	+	0.799471i	$0.294887\pi$
$734$	−53.2132	+	53.2132i	−1.96414	+	1.96414i
$735$		0			0
$736$	−7.65685	+	7.65685i	−0.282235	+	0.282235i
$737$	2.48528	+	2.48528i	0.0915465	+	0.0915465i
$738$	8.82843	+	8.82843i	0.324979	+	0.324979i
$739$	5.58579	+	5.58579i	0.205476	+	0.205476i	0.802342	−	0.596865i	$-0.203587\pi$
$739$	5.58579	+	5.58579i	0.205476	+	0.205476i	−0.596865	+	0.802342i	$0.703587\pi$
$740$		0			0
$741$	2.07107	+	0.414214i	0.0760826	+	0.0152165i
$742$	37.7990	+	37.7990i	1.38764	+	1.38764i
$743$	43.6569			1.60161			0.800807	−	0.598922i	$-0.204404\pi$
$743$	43.6569			1.60161			0.800807	+	0.598922i	$0.204404\pi$
$744$		−	9.89949i		−	0.362933i
$745$		0			0
$746$	−4.58579	−	4.58579i	−0.167898	−	0.167898i
$747$		−	9.31371i		−	0.340771i
$748$			58.6274i			2.14363i
$749$	24.4853	+	24.4853i	0.894673	+	0.894673i
$750$		0			0
$751$			7.45584i			0.272068i	0.990704	+	0.136034i	$0.0434356\pi$
$751$			7.45584i			0.272068i	−0.990704	+	0.136034i	$0.956564\pi$
$752$	−14.4853			−0.528224
$753$	14.4853	+	14.4853i	0.527873	+	0.527873i
$754$	−1.41421	+	7.07107i	−0.0515026	+	0.257513i
$755$		0			0
$756$	−9.24264	−	9.24264i	−0.336152	−	0.336152i
$757$	−33.6985	−	33.6985i	−1.22479	−	1.22479i	−0.965908	−	0.258884i	$-0.916645\pi$
$757$	−33.6985	−	33.6985i	−1.22479	−	1.22479i	−0.258884	−	0.965908i	$-0.583355\pi$
$758$	−28.3137	−	28.3137i	−1.02840	−	1.02840i
$759$	9.65685	−	9.65685i	0.350522	−	0.350522i
$760$		0			0
$761$	−1.51472	+	1.51472i	−0.0549085	+	0.0549085i	−0.734028	−	0.679119i	$-0.762362\pi$
$761$	−1.51472	+	1.51472i	−0.0549085	+	0.0549085i	0.679119	+	0.734028i	$0.262362\pi$
$762$	−25.3137			−0.917019
$763$	−6.24264	+	6.24264i	−0.225999	+	0.225999i
$764$	−12.6863			−0.458974
$765$		0			0
$766$		−	7.65685i		−	0.276653i
$767$	2.48528	−	1.65685i	0.0897383	−	0.0598255i
$768$	21.1924	−	21.1924i	0.764714	−	0.764714i
$769$	13.9706	−	13.9706i	0.503791	−	0.503791i	−0.408823	−	0.912614i	$-0.634060\pi$
$769$	13.9706	−	13.9706i	0.503791	−	0.503791i	0.912614	+	0.408823i	$0.134060\pi$
$770$		0			0
$771$		−	26.4853i		−	0.953844i
$772$		−	60.3259i		−	2.17118i
$773$	−27.1127			−0.975176			−0.487588	−	0.873074i	$-0.662123\pi$
$773$	−27.1127			−0.975176			−0.487588	+	0.873074i	$0.662123\pi$
$774$	−16.4853	−	16.4853i	−0.592551	−	0.592551i
$775$		0			0
$776$	−84.1838			−3.02202
$777$	−3.41421	+	3.41421i	−0.122484	+	0.122484i
$778$		−	69.5980i		−	2.49521i
$779$	3.02944			0.108541
$780$		0			0
$781$	17.6569			0.631812
$782$			126.225i			4.51381i
$783$	−0.585786	+	0.585786i	−0.0209343	+	0.0209343i
$784$	13.9706			0.498949
$785$		0			0
$786$	−22.4853	−	22.4853i	−0.802023	−	0.802023i
$787$	−34.9289			−1.24508			−0.622541	−	0.782587i	$-0.713900\pi$
$787$	−34.9289			−1.24508			−0.622541	+	0.782587i	$0.713900\pi$
$788$			8.97056i			0.319563i
$789$		−	15.7990i		−	0.562459i
$790$		0			0
$791$	24.1421	−	24.1421i	0.858396	−	0.858396i
$792$	−6.24264	+	6.24264i	−0.221823	+	0.221823i
$793$	−9.65685	+	48.2843i	−0.342925	+	1.71462i
$794$			2.24264i			0.0795883i
$795$		0			0
$796$	30.6274			1.08556
$797$	16.2426	−	16.2426i	0.575344	−	0.575344i	−0.358273	−	0.933617i	$-0.616634\pi$
$797$	16.2426	−	16.2426i	0.575344	−	0.575344i	0.933617	+	0.358273i	$0.116634\pi$
$798$	−4.82843			−0.170924
$799$	26.1421	−	26.1421i	0.924842	−	0.924842i
$800$		0			0
$801$	−6.82843	+	6.82843i	−0.241271	+	0.241271i
$802$	−48.2843	−	48.2843i	−1.70498	−	1.70498i
$803$	22.9706	+	22.9706i	0.810614	+	0.810614i
$804$	−4.75736	−	4.75736i	−0.167779	−	0.167779i
$805$		0			0
$806$	10.8284	+	16.2426i	0.381415	+	0.572123i
$807$	6.24264	+	6.24264i	0.219751	+	0.219751i
$808$	−76.4264			−2.68867
$809$		−	26.4853i		−	0.931173i	−0.885002	−	0.465586i	$-0.845843\pi$
$809$		−	26.4853i		−	0.931173i	0.885002	−	0.465586i	$-0.154157\pi$
$810$		0			0
$811$	−22.7574	−	22.7574i	−0.799119	−	0.799119i	0.183838	−	0.982957i	$-0.441148\pi$
$811$	−22.7574	−	22.7574i	−0.799119	−	0.799119i	−0.982957	+	0.183838i	$0.941148\pi$
$812$		−	10.8284i		−	0.380003i
$813$		−	11.8995i		−	0.417334i
$814$	4.82843	+	4.82843i	0.169236	+	0.169236i
$815$		0			0
$816$		−	22.9706i		−	0.804131i
$817$	−5.65685			−0.197908
$818$	−8.89949	−	8.89949i	−0.311164	−	0.311164i
$819$	12.0711	+	2.41421i	0.421797	+	0.0843594i
$820$		0			0
$821$	7.65685	+	7.65685i	0.267226	+	0.267226i	0.827981	−	0.560755i	$-0.189489\pi$
$821$	7.65685	+	7.65685i	0.267226	+	0.267226i	−0.560755	+	0.827981i	$0.689489\pi$
$822$	32.1421	+	32.1421i	1.12109	+	1.12109i
$823$	−8.68629	−	8.68629i	−0.302785	−	0.302785i	0.539317	−	0.842103i	$-0.318682\pi$
$823$	−8.68629	−	8.68629i	−0.302785	−	0.302785i	−0.842103	+	0.539317i	$0.818682\pi$
$824$	−35.3137	+	35.3137i	−1.23021	+	1.23021i
$825$		0			0
$826$	−4.82843	+	4.82843i	−0.168002	+	0.168002i
$827$	21.7990			0.758025			0.379013	−	0.925392i	$-0.376264\pi$
$827$	21.7990			0.758025			0.379013	+	0.925392i	$0.376264\pi$
$828$	−18.4853	+	18.4853i	−0.642408	+	0.642408i
$829$	30.6863			1.06578			0.532889	−	0.846185i	$-0.321106\pi$
$829$	30.6863			1.06578			0.532889	+	0.846185i	$0.321106\pi$
$830$		0			0
$831$			10.0000i			0.346896i
$832$	−6.94975	+	34.7487i	−0.240939	+	1.20470i
$833$	−25.2132	+	25.2132i	−0.873586	+	0.873586i
$834$	2.82843	−	2.82843i	0.0979404	−	0.0979404i
$835$		0			0
$836$			4.48528i			0.155127i
$837$			2.24264i			0.0775170i
$838$	71.1127			2.45655
$839$	10.7279	+	10.7279i	0.370369	+	0.370369i	0.867612	−	0.497243i	$-0.165654\pi$
$839$	10.7279	+	10.7279i	0.370369	+	0.370369i	−0.497243	+	0.867612i	$0.665654\pi$
$840$		0			0
$841$	28.3137			0.976335
$842$	52.6985	−	52.6985i	1.81611	−	1.81611i
$843$			17.1716i			0.591420i
$844$	−52.8284			−1.81843
$845$		0			0
$846$	11.6569			0.400771
$847$			23.8995i			0.821196i
$848$	−13.7574	+	13.7574i	−0.472430	+	0.472430i
$849$	4.82843			0.165711
$850$		0			0
$851$	6.82843	+	6.82843i	0.234075	+	0.234075i
$852$	−33.7990			−1.15793
$853$			9.41421i			0.322337i	0.986927	+	0.161168i	$0.0515262\pi$
$853$			9.41421i			0.322337i	−0.986927	+	0.161168i	$0.948474\pi$
$854$		−	112.569i		−	3.85202i
$855$		0			0
$856$	−31.6569	+	31.6569i	−1.08201	+	1.08201i
$857$	−1.55635	+	1.55635i	−0.0531639	+	0.0531639i	−0.733189	−	0.680025i	$-0.761969\pi$
$857$	−1.55635	+	1.55635i	−0.0531639	+	0.0531639i	0.680025	+	0.733189i	$0.261969\pi$
$858$	3.41421	−	17.0711i	0.116559	−	0.582797i
$859$			35.1716i			1.20004i	0.799986	+	0.600019i	$0.204840\pi$
$859$			35.1716i			1.20004i	−0.799986	+	0.600019i	$0.795160\pi$
$860$		0			0
$861$	17.6569			0.601744
$862$	22.7279	−	22.7279i	0.774116	−	0.774116i
$863$	9.79899			0.333561			0.166781	−	0.985994i	$-0.446663\pi$
$863$	9.79899			0.333561			0.166781	+	0.985994i	$0.446663\pi$
$864$	−1.12132	+	1.12132i	−0.0381481	+	0.0381481i
$865$		0			0
$866$	5.17157	−	5.17157i	0.175737	−	0.175737i
$867$	29.4350	+	29.4350i	0.999666	+	0.999666i
$868$	−20.7279	−	20.7279i	−0.703552	−	0.703552i
$869$	6.82843	+	6.82843i	0.231639	+	0.231639i
$870$		0			0
$871$	6.21320	+	1.24264i	0.210526	+	0.0421053i
$872$	−8.07107	−	8.07107i	−0.273321	−	0.273321i
$873$	19.0711			0.645458
$874$			9.65685i			0.326648i
$875$		0			0
$876$	−43.9706	−	43.9706i	−1.48563	−	1.48563i
$877$			5.21320i			0.176037i	0.996119	+	0.0880187i	$0.0280535\pi$
$877$			5.21320i			0.176037i	−0.996119	+	0.0880187i	$0.971946\pi$
$878$		−	54.2843i		−	1.83201i
$879$	−14.0000	−	14.0000i	−0.472208	−	0.472208i
$880$		0			0
$881$			24.3431i			0.820141i	0.912054	+	0.410071i	$0.134496\pi$
$881$			24.3431i			0.820141i	−0.912054	+	0.410071i	$0.865504\pi$
$882$	−11.2426			−0.378559
$883$	−15.8995	−	15.8995i	−0.535061	−	0.535061i	0.387013	−	0.922074i	$-0.373507\pi$
$883$	−15.8995	−	15.8995i	−0.535061	−	0.535061i	−0.922074	+	0.387013i	$0.873507\pi$
$884$	58.6274	+	87.9411i	1.97185	+	2.95778i
$885$		0			0
$886$	−24.1421	−	24.1421i	−0.811071	−	0.811071i
$887$	−15.3137	−	15.3137i	−0.514184	−	0.514184i	0.401622	−	0.915806i	$-0.368447\pi$
$887$	−15.3137	−	15.3137i	−0.514184	−	0.514184i	−0.915806	+	0.401622i	$0.868447\pi$
$888$	−4.41421	−	4.41421i	−0.148131	−	0.148131i
$889$	−25.3137	+	25.3137i	−0.848995	+	0.848995i
$890$		0			0
$891$	1.41421	−	1.41421i	0.0473779	−	0.0473779i
$892$	84.3848			2.82541
$893$	2.00000	−	2.00000i	0.0669274	−	0.0669274i
$894$	35.7990			1.19730
$895$		0			0
$896$		−	70.1838i		−	2.34468i
$897$	4.82843	−	24.1421i	0.161216	−	0.806082i
$898$	−11.3137	+	11.3137i	−0.377543	+	0.377543i
$899$	−1.31371	+	1.31371i	−0.0438146	+	0.0438146i
$900$		0			0
$901$		−	49.6569i		−	1.65431i
$902$		−	24.9706i		−	0.831429i
$903$	−32.9706			−1.09719
$904$	31.2132	+	31.2132i	1.03814	+	1.03814i
$905$		0			0
$906$	−38.3848			−1.27525
$907$	10.7279	−	10.7279i	0.356215	−	0.356215i	−0.506201	−	0.862416i	$-0.668951\pi$
$907$	10.7279	−	10.7279i	0.356215	−	0.356215i	0.862416	+	0.506201i	$0.168951\pi$
$908$			40.1421i			1.33216i
$909$	17.3137			0.574259
$910$		0			0
$911$	−20.0000			−0.662630			−0.331315	−	0.943520i	$-0.607492\pi$
$911$	−20.0000			−0.662630			−0.331315	+	0.943520i	$0.607492\pi$
$912$		−	1.75736i		−	0.0581920i
$913$	−13.1716	+	13.1716i	−0.435915	+	0.435915i
$914$	−80.1838			−2.65224
$915$		0			0
$916$	−66.9411	−	66.9411i	−2.21180	−	2.21180i
$917$	−44.9706			−1.48506
$918$			18.4853i			0.610105i
$919$		−	1.79899i		−	0.0593432i	−0.999560	−	0.0296716i	$-0.990554\pi$
$919$		−	1.79899i		−	0.0593432i	0.999560	−	0.0296716i	$-0.00944615\pi$
$920$		0			0
$921$	−6.75736	+	6.75736i	−0.222663	+	0.222663i
$922$	−38.1421	+	38.1421i	−1.25614	+	1.25614i
$923$	26.4853	−	17.6569i	0.871774	−	0.581182i
$924$			26.1421i			0.860013i
$925$		0			0
$926$	13.8995			0.456766
$927$	8.00000	−	8.00000i	0.262754	−	0.262754i
$928$	−1.31371			−0.0431246
$929$	8.62742	−	8.62742i	0.283056	−	0.283056i	−0.551270	−	0.834327i	$-0.685857\pi$
$929$	8.62742	−	8.62742i	0.283056	−	0.283056i	0.834327	+	0.551270i	$0.185857\pi$
$930$		0			0
$931$	−1.92893	+	1.92893i	−0.0632182	+	0.0632182i
$932$	−28.3848	−	28.3848i	−0.929774	−	0.929774i
$933$	−1.51472	−	1.51472i	−0.0495897	−	0.0495897i
$934$	29.3137	+	29.3137i	0.959174	+	0.959174i
$935$		0			0
$936$	−3.12132	+	15.6066i	−0.102024	+	0.510118i
$937$	−7.07107	−	7.07107i	−0.231002	−	0.231002i	0.582109	−	0.813111i	$-0.302228\pi$
$937$	−7.07107	−	7.07107i	−0.231002	−	0.231002i	−0.813111	+	0.582109i	$0.802228\pi$
$938$	−14.4853			−0.472961
$939$			29.3137i			0.956617i
$940$		0			0
$941$	−0.343146	−	0.343146i	−0.0111862	−	0.0111862i	0.701492	−	0.712678i	$-0.252518\pi$
$941$	−0.343146	−	0.343146i	−0.0111862	−	0.0111862i	−0.712678	+	0.701492i	$0.752518\pi$
$942$		−	17.6569i		−	0.575291i
$943$		−	35.3137i		−	1.14997i
$944$	−1.75736	−	1.75736i	−0.0571972	−	0.0571972i
$945$		0			0
$946$			46.6274i			1.51599i
$947$	−51.9411			−1.68786			−0.843930	−	0.536453i	$-0.819764\pi$
$947$	−51.9411			−1.68786			−0.843930	+	0.536453i	$0.819764\pi$
$948$	−13.0711	−	13.0711i	−0.424529	−	0.424529i
$949$	57.4264	+	11.4853i	1.86414	+	0.372828i
$950$		0			0
$951$	−8.00000	−	8.00000i	−0.259418	−	0.259418i
$952$	−81.5980	−	81.5980i	−2.64461	−	2.64461i
$953$	18.2426	+	18.2426i	0.590937	+	0.590937i	0.937885	−	0.346947i	$-0.112782\pi$
$953$	18.2426	+	18.2426i	0.590937	+	0.590937i	−0.346947	+	0.937885i	$0.612782\pi$
$954$	11.0711	−	11.0711i	0.358439	−	0.358439i
$955$		0			0
$956$	−30.2426	+	30.2426i	−0.978117	+	0.978117i
$957$	1.65685			0.0535585
$958$	40.0416	−	40.0416i	1.29369	−	1.29369i
$959$	64.2843			2.07585
$960$		0			0
$961$		−	25.9706i		−	0.837760i
$962$	12.0711	+	2.41421i	0.389187	+	0.0778374i
$963$	7.17157	−	7.17157i	0.231101	−	0.231101i
$964$	25.4853	−	25.4853i	0.820826	−	0.820826i
$965$		0			0
$966$			56.2843i			1.81092i
$967$			7.21320i			0.231961i	0.993251	+	0.115980i	$0.0370010\pi$
$967$			7.21320i			0.231961i	−0.993251	+	0.115980i	$0.962999\pi$
$968$	−30.8995			−0.993147
$969$	3.17157	+	3.17157i	0.101886	+	0.101886i
$970$		0			0
$971$	16.2843			0.522587			0.261294	−	0.965259i	$-0.415851\pi$
$971$	16.2843			0.522587			0.261294	+	0.965259i	$0.415851\pi$
$972$	−2.70711	+	2.70711i	−0.0868305	+	0.0868305i
$973$		−	5.65685i		−	0.181350i
$974$	−31.5563			−1.01113
$975$		0			0
$976$	40.9706			1.31144
$977$			21.6569i			0.692864i	0.938075	+	0.346432i	$0.112607\pi$
$977$			21.6569i			0.692864i	−0.938075	+	0.346432i	$0.887393\pi$
$978$	33.1421	−	33.1421i	1.05977	−	1.05977i
$979$	19.3137			0.617269
$980$		0			0
$981$	1.82843	+	1.82843i	0.0583772	+	0.0583772i
$982$	22.1421			0.706584
$983$		−	16.6274i		−	0.530332i	−0.964203	−	0.265166i	$-0.914573\pi$
$983$		−	16.6274i		−	0.530332i	0.964203	−	0.265166i	$-0.0854268\pi$
$984$			22.8284i			0.727744i
$985$		0			0
$986$	−10.8284	+	10.8284i	−0.344847	+	0.344847i
$987$	11.6569	−	11.6569i	0.371042	−	0.371042i
$988$	4.48528	+	6.72792i	0.142696	+	0.214044i
$989$			65.9411i			2.09681i
$990$		0			0
$991$	−35.3137			−1.12178			−0.560888	−	0.827891i	$-0.689540\pi$
$991$	−35.3137			−1.12178			−0.560888	+	0.827891i	$0.689540\pi$
$992$	−2.51472	+	2.51472i	−0.0798424	+	0.0798424i
$993$	−19.4142			−0.616091
$994$	−51.4558	+	51.4558i	−1.63208	+	1.63208i
$995$		0			0
$996$	25.2132	−	25.2132i	0.798911	−	0.798911i
$997$	25.1716	+	25.1716i	0.797192	+	0.797192i	0.982652	−	0.185460i	$-0.0593775\pi$
$997$	25.1716	+	25.1716i	0.797192	+	0.797192i	−0.185460	+	0.982652i	$0.559378\pi$
$998$	−17.4853	−	17.4853i	−0.553487	−	0.553487i
$999$	1.00000	+	1.00000i	0.0316386	+	0.0316386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.k.b.307.1	yes	4
5.2	odd	4		975.2.t.b.268.2	yes	4
5.3	odd	4		975.2.t.a.268.1	yes	4
5.4	even	2		975.2.k.a.307.2	✓	4
13.5	odd	4		975.2.t.a.382.1	yes	4
65.18	even	4	inner	975.2.k.b.343.2	yes	4
65.44	odd	4		975.2.t.b.382.2	yes	4
65.57	even	4		975.2.k.a.343.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.k.a.307.2	✓	4	5.4	even	2
975.2.k.a.343.1	yes	4	65.57	even	4
975.2.k.b.307.1	yes	4	1.1	even	1	trivial
975.2.k.b.343.2	yes	4	65.18	even	4	inner
975.2.t.a.268.1	yes	4	5.3	odd	4
975.2.t.a.382.1	yes	4	13.5	odd	4
975.2.t.b.268.2	yes	4	5.2	odd	4
975.2.t.b.382.2	yes	4	65.44	odd	4

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.41421i q^{2} +(-0.707107 + 0.707107i) q^{3} -3.82843 q^{4} +(1.70711 + 1.70711i) q^{6} +3.41421 q^{7} +4.41421i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-2.41421i q^{2} +(-0.707107 + 0.707107i) q^{3} -3.82843 q^{4} +(1.70711 + 1.70711i) q^{6} +3.41421 q^{7} +4.41421i q^{8} -1.00000i q^{9} +(-1.41421 + 1.41421i) q^{11} +(2.70711 - 2.70711i) q^{12} +(-0.707107 + 3.53553i) q^{13} -8.24264i q^{14} +3.00000 q^{16} +(-5.41421 + 5.41421i) q^{17} -2.41421 q^{18} +(-0.414214 + 0.414214i) q^{19} +(-2.41421 + 2.41421i) q^{21} +(3.41421 + 3.41421i) q^{22} +(4.82843 + 4.82843i) q^{23} +(-3.12132 - 3.12132i) q^{24} +(8.53553 + 1.70711i) q^{26} +(0.707107 + 0.707107i) q^{27} -13.0711 q^{28} +0.828427i q^{29} +(1.58579 + 1.58579i) q^{31} +1.58579i q^{32} -2.00000i q^{33} +(13.0711 + 13.0711i) q^{34} +3.82843i q^{36} +1.41421 q^{37} +(1.00000 + 1.00000i) q^{38} +(-2.00000 - 3.00000i) q^{39} +(-3.65685 - 3.65685i) q^{41} +(5.82843 + 5.82843i) q^{42} +(6.82843 + 6.82843i) q^{43} +(5.41421 - 5.41421i) q^{44} +(11.6569 - 11.6569i) q^{46} -4.82843 q^{47} +(-2.12132 + 2.12132i) q^{48} +4.65685 q^{49} -7.65685i q^{51} +(2.70711 - 13.5355i) q^{52} +(-4.58579 + 4.58579i) q^{53} +(1.70711 - 1.70711i) q^{54} +15.0711i q^{56} -0.585786i q^{57} +2.00000 q^{58} +(-0.585786 - 0.585786i) q^{59} +13.6569 q^{61} +(3.82843 - 3.82843i) q^{62} -3.41421i q^{63} +9.82843 q^{64} -4.82843 q^{66} -1.75736i q^{67} +(20.7279 - 20.7279i) q^{68} -6.82843 q^{69} +(-6.24264 - 6.24264i) q^{71} +4.41421 q^{72} -16.2426i q^{73} -3.41421i q^{74} +(1.58579 - 1.58579i) q^{76} +(-4.82843 + 4.82843i) q^{77} +(-7.24264 + 4.82843i) q^{78} -4.82843i q^{79} -1.00000 q^{81} +(-8.82843 + 8.82843i) q^{82} +9.31371 q^{83} +(9.24264 - 9.24264i) q^{84} +(16.4853 - 16.4853i) q^{86} +(-0.585786 - 0.585786i) q^{87} +(-6.24264 - 6.24264i) q^{88} +(-6.82843 - 6.82843i) q^{89} +(-2.41421 + 12.0711i) q^{91} +(-18.4853 - 18.4853i) q^{92} -2.24264 q^{93} +11.6569i q^{94} +(-1.12132 - 1.12132i) q^{96} +19.0711i q^{97} -11.2426i q^{98} +(1.41421 + 1.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{6} + 8 q^{7}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^6 + 8 * q^7	\( 4 q - 4 q^{4} + 4 q^{6} + 8 q^{7} + 8 q^{12} + 12 q^{16} - 16 q^{17} - 4 q^{18} + 4 q^{19} - 4 q^{21} + 8 q^{22} + 8 q^{23} - 4 q^{24} + 20 q^{26} - 24 q^{28} + 12 q^{31} + 24 q^{34} + 4 q^{38} - 8 q^{39} + 8 q^{41} + 12 q^{42} + 16 q^{43} + 16 q^{44} + 24 q^{46} - 8 q^{47} - 4 q^{49} + 8 q^{52} - 24 q^{53} + 4 q^{54} + 8 q^{58} - 8 q^{59} + 32 q^{61} + 4 q^{62} + 28 q^{64} - 8 q^{66} + 32 q^{68} - 16 q^{69} - 8 q^{71} + 12 q^{72} + 12 q^{76} - 8 q^{77} - 12 q^{78} - 4 q^{81} - 24 q^{82} - 8 q^{83} + 20 q^{84} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 16 q^{89} - 4 q^{91} - 40 q^{92} + 8 q^{93} + 4 q^{96}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^6 + 8 * q^7 + 8 * q^12 + 12 * q^16 - 16 * q^17 - 4 * q^18 + 4 * q^19 - 4 * q^21 + 8 * q^22 + 8 * q^23 - 4 * q^24 + 20 * q^26 - 24 * q^28 + 12 * q^31 + 24 * q^34 + 4 * q^38 - 8 * q^39 + 8 * q^41 + 12 * q^42 + 16 * q^43 + 16 * q^44 + 24 * q^46 - 8 * q^47 - 4 * q^49 + 8 * q^52 - 24 * q^53 + 4 * q^54 + 8 * q^58 - 8 * q^59 + 32 * q^61 + 4 * q^62 + 28 * q^64 - 8 * q^66 + 32 * q^68 - 16 * q^69 - 8 * q^71 + 12 * q^72 + 12 * q^76 - 8 * q^77 - 12 * q^78 - 4 * q^81 - 24 * q^82 - 8 * q^83 + 20 * q^84 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 16 * q^89 - 4 * q^91 - 40 * q^92 + 8 * q^93 + 4 * q^96

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