LMFDB - Embedded newform 975.2.t.d.268.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(268,975)]

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, 3, 1]))

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

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

chi := DirichletCharacter("975.268");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			268.14
Character	$\chi$	$=$	975.268
Dual form			975.2.t.d.382.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.73623 q^{2} +(0.707107 + 0.707107i) q^{3} +5.48694 q^{4} +(1.93480 + 1.93480i) q^{6} -2.18253i q^{7} +9.54105 q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+2.73623 q^{2} +(0.707107 + 0.707107i) q^{3} +5.48694 q^{4} +(1.93480 + 1.93480i) q^{6} -2.18253i q^{7} +9.54105 q^{8} +1.00000i q^{9} +(-0.403236 + 0.403236i) q^{11} +(3.87985 + 3.87985i) q^{12} +(-2.72201 + 2.36446i) q^{13} -5.97189i q^{14} +15.1326 q^{16} +(-4.22719 - 4.22719i) q^{17} +2.73623i q^{18} +(-0.462512 + 0.462512i) q^{19} +(1.54328 - 1.54328i) q^{21} +(-1.10334 + 1.10334i) q^{22} +(-4.43399 + 4.43399i) q^{23} +(6.74654 + 6.74654i) q^{24} +(-7.44802 + 6.46971i) q^{26} +(-0.707107 + 0.707107i) q^{27} -11.9754i q^{28} -4.40973i q^{29} +(-2.06316 - 2.06316i) q^{31} +22.3241 q^{32} -0.570261 q^{33} +(-11.5665 - 11.5665i) q^{34} +5.48694i q^{36} +4.58165i q^{37} +(-1.26554 + 1.26554i) q^{38} +(-3.59668 - 0.252821i) q^{39} +(6.83712 + 6.83712i) q^{41} +(4.22276 - 4.22276i) q^{42} +(-1.21836 + 1.21836i) q^{43} +(-2.21253 + 2.21253i) q^{44} +(-12.1324 + 12.1324i) q^{46} -5.28755i q^{47} +(10.7004 + 10.7004i) q^{48} +2.23658 q^{49} -5.97815i q^{51} +(-14.9355 + 12.9737i) q^{52} +(0.277932 + 0.277932i) q^{53} +(-1.93480 + 1.93480i) q^{54} -20.8236i q^{56} -0.654091 q^{57} -12.0660i q^{58} +(-2.41412 - 2.41412i) q^{59} -8.05723 q^{61} +(-5.64528 - 5.64528i) q^{62} +2.18253 q^{63} +30.8186 q^{64} -1.56036 q^{66} +6.48209 q^{67} +(-23.1943 - 23.1943i) q^{68} -6.27061 q^{69} +(2.32466 + 2.32466i) q^{71} +9.54105i q^{72} +2.98262 q^{73} +12.5364i q^{74} +(-2.53777 + 2.53777i) q^{76} +(0.880072 + 0.880072i) q^{77} +(-9.84132 - 0.691776i) q^{78} +12.7156i q^{79} -1.00000 q^{81} +(18.7079 + 18.7079i) q^{82} +0.553610i q^{83} +(8.46788 - 8.46788i) q^{84} +(-3.33370 + 3.33370i) q^{86} +(3.11815 - 3.11815i) q^{87} +(-3.84729 + 3.84729i) q^{88} +(-7.56032 - 7.56032i) q^{89} +(5.16050 + 5.94085i) q^{91} +(-24.3290 + 24.3290i) q^{92} -2.91775i q^{93} -14.4679i q^{94} +(15.7855 + 15.7855i) q^{96} -9.88577 q^{97} +6.11978 q^{98} +(-0.403236 - 0.403236i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} + 28 q^{4} + 12 q^{8}+O(q^{10}) $ 28 * q + 4 * q^2 + 28 * q^4 + 12 * q^8	$ 28 q + 4 q^{2} + 28 q^{4} + 12 q^{8} - 8 q^{11} + 8 q^{12} + 28 q^{16} - 28 q^{17} + 8 q^{21} + 32 q^{22} + 8 q^{23} - 16 q^{31} + 68 q^{32} + 8 q^{33} - 28 q^{34} - 8 q^{39} + 4 q^{41} - 40 q^{44} - 16 q^{46} + 16 q^{48} + 28 q^{49} - 48 q^{52} - 20 q^{53} - 32 q^{59} + 8 q^{61} + 72 q^{62} + 28 q^{64} + 16 q^{66} - 32 q^{67} - 60 q^{68} - 8 q^{69} + 40 q^{71} - 56 q^{73} - 40 q^{76} - 48 q^{77} - 40 q^{78} - 28 q^{81} + 4 q^{82} + 32 q^{84} + 16 q^{86} + 24 q^{87} + 72 q^{88} + 36 q^{89} - 56 q^{91} + 32 q^{92} - 48 q^{97} + 12 q^{98} - 8 q^{99}+O(q^{100}) $ 28 * q + 4 * q^2 + 28 * q^4 + 12 * q^8 - 8 * q^11 + 8 * q^12 + 28 * q^16 - 28 * q^17 + 8 * q^21 + 32 * q^22 + 8 * q^23 - 16 * q^31 + 68 * q^32 + 8 * q^33 - 28 * q^34 - 8 * q^39 + 4 * q^41 - 40 * q^44 - 16 * q^46 + 16 * q^48 + 28 * q^49 - 48 * q^52 - 20 * q^53 - 32 * q^59 + 8 * q^61 + 72 * q^62 + 28 * q^64 + 16 * q^66 - 32 * q^67 - 60 * q^68 - 8 * q^69 + 40 * q^71 - 56 * q^73 - 40 * q^76 - 48 * q^77 - 40 * q^78 - 28 * q^81 + 4 * q^82 + 32 * q^84 + 16 * q^86 + 24 * q^87 + 72 * q^88 + 36 * q^89 - 56 * q^91 + 32 * q^92 - 48 * q^97 + 12 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	2.73623			1.93480			0.967402	−	0.253245i	$-0.0814979\pi$
$2$	2.73623			1.93480			0.967402	+	0.253245i	$0.0814979\pi$
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	5.48694			2.74347
$5$		0			0
$5$		0			0
$6$	1.93480	+	1.93480i	0.789881	+	0.789881i
$7$		−	2.18253i		−	0.824918i	−0.910976	−	0.412459i	$-0.864670\pi$
$7$		−	2.18253i		−	0.824918i	0.910976	−	0.412459i	$-0.135330\pi$
$8$	9.54105			3.37327
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−0.403236	+	0.403236i	−0.121580	+	0.121580i	−0.765279	−	0.643699i	$-0.777399\pi$
$11$	−0.403236	+	0.403236i	−0.121580	+	0.121580i	0.643699	+	0.765279i	$0.277399\pi$
$12$	3.87985	+	3.87985i	1.12002	+	1.12002i
$13$	−2.72201	+	2.36446i	−0.754949	+	0.655784i
$13$	−2.72201	+	2.36446i	−0.754949	+	0.655784i
$14$		−	5.97189i		−	1.59605i
$15$		0			0
$16$	15.1326			3.78315
$17$	−4.22719	−	4.22719i	−1.02524	−	1.02524i	−0.999673	−	0.0255708i	$-0.991860\pi$
$17$	−4.22719	−	4.22719i	−1.02524	−	1.02524i	−0.0255708	−	0.999673i	$-0.508140\pi$
$18$			2.73623i			0.644935i
$19$	−0.462512	+	0.462512i	−0.106108	+	0.106108i	−0.758167	−	0.652060i	$-0.773905\pi$
$19$	−0.462512	+	0.462512i	−0.106108	+	0.106108i	0.652060	+	0.758167i	$0.273905\pi$
$20$		0			0
$21$	1.54328	−	1.54328i	0.336771	−	0.336771i
$22$	−1.10334	+	1.10334i	−0.235234	+	0.235234i
$23$	−4.43399	+	4.43399i	−0.924552	+	0.924552i	−0.997347	−	0.0727952i	$-0.976808\pi$
$23$	−4.43399	+	4.43399i	−0.924552	+	0.924552i	0.0727952	+	0.997347i	$0.476808\pi$
$24$	6.74654	+	6.74654i	1.37713	+	1.37713i
$25$		0			0
$26$	−7.44802	+	6.46971i	−1.46068	+	1.26881i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		−	11.9754i		−	2.26313i
$29$		−	4.40973i		−	0.818867i	−0.912340	−	0.409434i	$-0.865726\pi$
$29$		−	4.40973i		−	0.818867i	0.912340	−	0.409434i	$-0.134274\pi$
$30$		0			0
$31$	−2.06316	−	2.06316i	−0.370555	−	0.370555i	0.497124	−	0.867679i	$-0.334389\pi$
$31$	−2.06316	−	2.06316i	−0.370555	−	0.370555i	−0.867679	+	0.497124i	$0.834389\pi$
$32$	22.3241			3.94638
$33$	−0.570261			−0.0992697
$34$	−11.5665	−	11.5665i	−1.98365	−	1.98365i
$35$		0			0
$36$			5.48694i			0.914489i
$37$			4.58165i			0.753219i	0.926372	+	0.376609i	$0.122910\pi$
$37$			4.58165i			0.753219i	−0.926372	+	0.376609i	$0.877090\pi$
$38$	−1.26554	+	1.26554i	−0.205297	+	0.205297i
$39$	−3.59668	−	0.252821i	−0.575929	−	0.0404838i
$40$		0			0
$41$	6.83712	+	6.83712i	1.06778	+	1.06778i	0.997529	+	0.0702494i	$0.0223795\pi$
$41$	6.83712	+	6.83712i	1.06778	+	1.06778i	0.0702494	+	0.997529i	$0.477620\pi$
$42$	4.22276	−	4.22276i	0.651586	−	0.651586i
$43$	−1.21836	+	1.21836i	−0.185798	+	0.185798i	−0.793877	−	0.608079i	$-0.791940\pi$
$43$	−1.21836	+	1.21836i	−0.185798	+	0.185798i	0.608079	+	0.793877i	$0.291940\pi$
$44$	−2.21253	+	2.21253i	−0.333551	+	0.333551i
$45$		0			0
$46$	−12.1324	+	12.1324i	−1.78883	+	1.78883i
$47$		−	5.28755i		−	0.771268i	−0.922652	−	0.385634i	$-0.873983\pi$
$47$		−	5.28755i		−	0.771268i	0.922652	−	0.385634i	$-0.126017\pi$
$48$	10.7004	+	10.7004i	1.54446	+	1.54446i
$49$	2.23658			0.319511
$50$		0			0
$51$		−	5.97815i		−	0.837108i
$52$	−14.9355	+	12.9737i	−2.07118	+	1.79912i
$53$	0.277932	+	0.277932i	0.0381769	+	0.0381769i	0.725938	−	0.687761i	$-0.241406\pi$
$53$	0.277932	+	0.277932i	0.0381769	+	0.0381769i	−0.687761	+	0.725938i	$0.741406\pi$
$54$	−1.93480	+	1.93480i	−0.263294	+	0.263294i
$55$		0			0
$56$		−	20.8236i		−	2.78267i
$57$	−0.654091			−0.0866364
$58$		−	12.0660i		−	1.58435i
$59$	−2.41412	−	2.41412i	−0.314291	−	0.314291i	0.532278	−	0.846569i	$-0.321336\pi$
$59$	−2.41412	−	2.41412i	−0.314291	−	0.314291i	−0.846569	+	0.532278i	$0.821336\pi$
$60$		0			0
$61$	−8.05723			−1.03162			−0.515811	−	0.856702i	$-0.672509\pi$
$61$	−8.05723			−1.03162			−0.515811	+	0.856702i	$0.672509\pi$
$62$	−5.64528	−	5.64528i	−0.716951	−	0.716951i
$63$	2.18253			0.274973
$64$	30.8186			3.85233
$65$		0			0
$66$	−1.56036			−0.192068
$67$	6.48209			0.791914			0.395957	−	0.918269i	$-0.370413\pi$
$67$	6.48209			0.791914			0.395957	+	0.918269i	$0.370413\pi$
$68$	−23.1943	−	23.1943i	−2.81272	−	2.81272i
$69$	−6.27061			−0.754893
$70$		0			0
$71$	2.32466	+	2.32466i	0.275887	+	0.275887i	0.831465	−	0.555578i	$-0.187503\pi$
$71$	2.32466	+	2.32466i	0.275887	+	0.275887i	−0.555578	+	0.831465i	$0.687503\pi$
$72$			9.54105i			1.12442i
$73$	2.98262			0.349089			0.174545	−	0.984649i	$-0.444155\pi$
$73$	2.98262			0.349089			0.174545	+	0.984649i	$0.444155\pi$
$74$			12.5364i			1.45733i
$75$		0			0
$76$	−2.53777	+	2.53777i	−0.291103	+	0.291103i
$77$	0.880072	+	0.880072i	0.100294	+	0.100294i
$78$	−9.84132	−	0.691776i	−1.11431	−	0.0783282i
$79$			12.7156i			1.43062i	0.698810	+	0.715308i	$0.253713\pi$
$79$			12.7156i			1.43062i	−0.698810	+	0.715308i	$0.746287\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	18.7079	+	18.7079i	2.06594	+	2.06594i
$83$			0.553610i			0.0607666i	0.999538	+	0.0303833i	$0.00967279\pi$
$83$			0.553610i			0.0607666i	−0.999538	+	0.0303833i	$0.990327\pi$
$84$	8.46788	−	8.46788i	0.923921	−	0.923921i
$85$		0			0
$86$	−3.33370	+	3.33370i	−0.359482	+	0.359482i
$87$	3.11815	−	3.11815i	0.334301	−	0.334301i
$88$	−3.84729	+	3.84729i	−0.410122	+	0.410122i
$89$	−7.56032	−	7.56032i	−0.801393	−	0.801393i	0.181920	−	0.983313i	$-0.441769\pi$
$89$	−7.56032	−	7.56032i	−0.801393	−	0.801393i	−0.983313	+	0.181920i	$0.941769\pi$
$90$		0			0
$91$	5.16050	+	5.94085i	0.540968	+	0.622770i
$92$	−24.3290	+	24.3290i	−2.53648	+	2.53648i
$93$		−	2.91775i		−	0.302557i
$94$		−	14.4679i		−	1.49225i
$95$		0			0
$96$	15.7855	+	15.7855i	1.61110	+	1.61110i
$97$	−9.88577			−1.00375			−0.501874	−	0.864941i	$-0.667356\pi$
$97$	−9.88577			−1.00375			−0.501874	+	0.864941i	$0.667356\pi$
$98$	6.11978			0.618191
$99$	−0.403236	−	0.403236i	−0.0405267	−	0.0405267i
$100$		0			0
$101$		−	6.83452i		−	0.680060i	−0.940415	−	0.340030i	$-0.889563\pi$
$101$		−	6.83452i		−	0.680060i	0.940415	−	0.340030i	$-0.110437\pi$
$102$		−	16.3576i		−	1.61964i
$103$	8.57596	−	8.57596i	0.845014	−	0.845014i	−0.144492	−	0.989506i	$-0.546155\pi$
$103$	8.57596	−	8.57596i	0.845014	−	0.845014i	0.989506	+	0.144492i	$0.0461547\pi$
$104$	−25.9708	+	22.5594i	−2.54664	+	2.21214i
$105$		0			0
$106$	0.760484	+	0.760484i	0.0738648	+	0.0738648i
$107$	10.1957	−	10.1957i	0.985655	−	0.985655i	−0.0142431	−	0.999899i	$-0.504534\pi$
$107$	10.1957	−	10.1957i	0.985655	−	0.985655i	0.999899	+	0.0142431i	$0.00453387\pi$
$108$	−3.87985	+	3.87985i	−0.373339	+	0.373339i
$109$	−3.71769	+	3.71769i	−0.356090	+	0.356090i	−0.862369	−	0.506280i	$-0.831020\pi$
$109$	−3.71769	+	3.71769i	−0.356090	+	0.356090i	0.506280	+	0.862369i	$0.331020\pi$
$110$		0			0
$111$	−3.23972	+	3.23972i	−0.307500	+	0.307500i
$112$		−	33.0273i		−	3.12079i
$113$	6.07606	+	6.07606i	0.571587	+	0.571587i	0.932572	−	0.360985i	$-0.117559\pi$
$113$	6.07606	+	6.07606i	0.571587	+	0.571587i	−0.360985	+	0.932572i	$0.617559\pi$
$114$	−1.78974			−0.167625
$115$		0			0
$116$		−	24.1959i		−	2.24654i
$117$	−2.36446	−	2.72201i	−0.218595	−	0.251650i
$118$	−6.60557	−	6.60557i	−0.608092	−	0.608092i
$119$	−9.22595	+	9.22595i	−0.845742	+	0.845742i
$120$		0			0
$121$			10.6748i			0.970437i
$122$	−22.0464			−1.99599
$123$			9.66915i			0.871838i
$124$	−11.3204	−	11.3204i	−1.01661	−	1.01661i
$125$		0			0
$126$	5.97189			0.532018
$127$	−6.69689	−	6.69689i	−0.594253	−	0.594253i	0.344524	−	0.938777i	$-0.388040\pi$
$127$	−6.69689	−	6.69689i	−0.594253	−	0.594253i	−0.938777	+	0.344524i	$0.888040\pi$
$128$	39.6785			3.50712
$129$	−1.72302			−0.151703
$130$		0			0
$131$	−11.8946			−1.03923			−0.519617	−	0.854400i	$-0.673925\pi$
$131$	−11.8946			−1.03923			−0.519617	+	0.854400i	$0.673925\pi$
$132$	−3.12899			−0.272343
$133$	1.00944	+	1.00944i	0.0875300	+	0.0875300i
$134$	17.7365			1.53220
$135$		0			0
$136$	−40.3318	−	40.3318i	−3.45842	−	3.45842i
$137$		−	20.1238i		−	1.71929i	−0.510892	−	0.859645i	$-0.670685\pi$
$137$		−	20.1238i		−	1.71929i	0.510892	−	0.859645i	$-0.329315\pi$
$138$	−17.1578			−1.46057
$139$		−	1.95472i		−	0.165797i	−0.996558	−	0.0828985i	$-0.973582\pi$
$139$		−	1.95472i		−	0.165797i	0.996558	−	0.0828985i	$-0.0264177\pi$
$140$		0			0
$141$	3.73886	−	3.73886i	0.314869	−	0.314869i
$142$	6.36081	+	6.36081i	0.533787	+	0.533787i
$143$	0.144174	−	2.05105i	0.0120564	−	0.171517i
$144$			15.1326i			1.26105i
$145$		0			0
$146$	8.16112			0.675419
$147$	1.58150	+	1.58150i	0.130440	+	0.130440i
$148$			25.1392i			2.06643i
$149$	8.07404	−	8.07404i	0.661451	−	0.661451i	−0.294271	−	0.955722i	$-0.595077\pi$
$149$	8.07404	−	8.07404i	0.661451	−	0.661451i	0.955722	+	0.294271i	$0.0950769\pi$
$150$		0			0
$151$	6.07785	−	6.07785i	0.494608	−	0.494608i	−0.415146	−	0.909755i	$-0.636270\pi$
$151$	6.07785	−	6.07785i	0.494608	−	0.494608i	0.909755	+	0.415146i	$0.136270\pi$
$152$	−4.41285	+	4.41285i	−0.357929	+	0.357929i
$153$	4.22719	−	4.22719i	0.341748	−	0.341748i
$154$	2.40808	+	2.40808i	0.194048	+	0.194048i
$155$		0			0
$156$	−19.7347	−	1.38721i	−1.58004	−	0.111066i
$157$	6.06202	−	6.06202i	0.483802	−	0.483802i	−0.422542	−	0.906343i	$-0.638862\pi$
$157$	6.06202	−	6.06202i	0.483802	−	0.483802i	0.906343	+	0.422542i	$0.138862\pi$
$158$			34.7927i			2.76796i
$159$			0.393055i			0.0311713i
$160$		0			0
$161$	9.67731	+	9.67731i	0.762679	+	0.762679i
$162$	−2.73623			−0.214978
$163$	1.10175			0.0862953			0.0431477	−	0.999069i	$-0.486261\pi$
$163$	1.10175			0.0862953			0.0431477	+	0.999069i	$0.486261\pi$
$164$	37.5148	+	37.5148i	2.92942	+	2.92942i
$165$		0			0
$166$			1.51480i			0.117571i
$167$			19.4106i			1.50204i	0.660280	+	0.751020i	$0.270438\pi$
$167$			19.4106i			1.50204i	−0.660280	+	0.751020i	$0.729562\pi$
$168$	14.7245	−	14.7245i	1.13602	−	1.13602i
$169$	1.81863	−	12.8722i	0.139895	−	0.990166i
$170$		0			0
$171$	−0.462512	−	0.462512i	−0.0353692	−	0.0353692i
$172$	−6.68505	+	6.68505i	−0.509730	+	0.509730i
$173$	12.9851	−	12.9851i	0.987237	−	0.987237i	−0.0126824	−	0.999920i	$-0.504037\pi$
$173$	12.9851	−	12.9851i	0.987237	−	0.987237i	0.999920	+	0.0126824i	$0.00403703\pi$
$174$	8.53197	−	8.53197i	0.646807	−	0.646807i
$175$		0			0
$176$	−6.10200	+	6.10200i	−0.459956	+	0.459956i
$177$		−	3.41407i		−	0.256618i
$178$	−20.6868	−	20.6868i	−1.55054	−	1.55054i
$179$	6.05315			0.452433			0.226217	−	0.974077i	$-0.427364\pi$
$179$	6.05315			0.452433			0.226217	+	0.974077i	$0.427364\pi$
$180$		0			0
$181$			0.642386i			0.0477482i	0.999715	+	0.0238741i	$0.00760009\pi$
$181$			0.642386i			0.0477482i	−0.999715	+	0.0238741i	$0.992400\pi$
$182$	14.1203	+	16.2555i	1.04667	+	1.20494i
$183$	−5.69732	−	5.69732i	−0.421158	−	0.421158i
$184$	−42.3049	+	42.3049i	−3.11876	+	3.11876i
$185$		0			0
$186$		−	7.98363i		−	0.585388i
$187$	3.40911			0.249298
$188$		−	29.0124i		−	2.11595i
$189$	1.54328	+	1.54328i	0.112257	+	0.112257i
$190$		0			0
$191$	−24.0434			−1.73972			−0.869861	−	0.493298i	$-0.835791\pi$
$191$	−24.0434			−1.73972			−0.869861	+	0.493298i	$0.835791\pi$
$192$	21.7921	+	21.7921i	1.57271	+	1.57271i
$193$	15.5465			1.11906			0.559531	−	0.828810i	$-0.310981\pi$
$193$	15.5465			1.11906			0.559531	+	0.828810i	$0.310981\pi$
$194$	−27.0497			−1.94206
$195$		0			0
$196$	12.2720			0.876568
$197$	3.65831			0.260644			0.130322	−	0.991472i	$-0.458399\pi$
$197$	3.65831			0.260644			0.130322	+	0.991472i	$0.458399\pi$
$198$	−1.10334	−	1.10334i	−0.0784112	−	0.0784112i
$199$	16.5387			1.17240			0.586199	−	0.810167i	$-0.300624\pi$
$199$	16.5387			1.17240			0.586199	+	0.810167i	$0.300624\pi$
$200$		0			0
$201$	4.58353	+	4.58353i	0.323297	+	0.323297i
$202$		−	18.7008i		−	1.31578i
$203$	−9.62436			−0.675498
$204$		−	32.8017i		−	2.29658i
$205$		0			0
$206$	23.4658	−	23.4658i	1.63494	−	1.63494i
$207$	−4.43399	−	4.43399i	−0.308184	−	0.308184i
$208$	−41.1910	+	35.7805i	−2.85608	+	2.48093i
$209$		−	0.373003i		−	0.0258011i
$210$		0			0
$211$	6.29230			0.433180			0.216590	−	0.976263i	$-0.430507\pi$
$211$	6.29230			0.433180			0.216590	+	0.976263i	$0.430507\pi$
$212$	1.52499	+	1.52499i	0.104737	+	0.104737i
$213$			3.28757i			0.225261i
$214$	27.8977	−	27.8977i	1.90705	−	1.90705i
$215$		0			0
$216$	−6.74654	+	6.74654i	−0.459044	+	0.459044i
$217$	−4.50291	+	4.50291i	−0.305677	+	0.305677i
$218$	−10.1724	+	10.1724i	−0.688964	+	0.688964i
$219$	2.10903	+	2.10903i	0.142515	+	0.142515i
$220$		0			0
$221$	21.5015	+	1.51140i	1.44634	+	0.101668i
$222$	−8.86460	+	8.86460i	−0.594953	+	0.594953i
$223$			26.7096i			1.78861i	0.447459	+	0.894304i	$0.352329\pi$
$223$			26.7096i			1.78861i	−0.447459	+	0.894304i	$0.647671\pi$
$224$		−	48.7230i		−	3.25544i
$225$		0			0
$226$	16.6255	+	16.6255i	1.10591	+	1.10591i
$227$	−15.1974			−1.00869			−0.504343	−	0.863503i	$-0.668265\pi$
$227$	−15.1974			−1.00869			−0.504343	+	0.863503i	$0.668265\pi$
$228$	−3.58895			−0.237684
$229$	2.32027	+	2.32027i	0.153328	+	0.153328i	0.779602	−	0.626275i	$-0.215421\pi$
$229$	2.32027	+	2.32027i	0.153328	+	0.153328i	−0.626275	+	0.779602i	$0.715421\pi$
$230$		0			0
$231$			1.24461i			0.0818893i
$232$		−	42.0735i		−	2.76226i
$233$	−3.25148	+	3.25148i	−0.213011	+	0.213011i	−0.805545	−	0.592534i	$-0.798128\pi$
$233$	−3.25148	+	3.25148i	−0.213011	+	0.213011i	0.592534	+	0.805545i	$0.298128\pi$
$234$	−6.46971	−	7.44802i	−0.422938	−	0.486893i
$235$		0			0
$236$	−13.2461	−	13.2461i	−0.862247	−	0.862247i
$237$	−8.99128	+	8.99128i	−0.584046	+	0.584046i
$238$	−25.2443	+	25.2443i	−1.63634	+	1.63634i
$239$	−10.0778	+	10.0778i	−0.651877	+	0.651877i	−0.953445	−	0.301567i	$-0.902490\pi$
$239$	−10.0778	+	10.0778i	−0.651877	+	0.651877i	0.301567	+	0.953445i	$0.402490\pi$
$240$		0			0
$241$	−1.54296	+	1.54296i	−0.0993911	+	0.0993911i	−0.755054	−	0.655663i	$-0.772389\pi$
$241$	−1.54296	+	1.54296i	−0.0993911	+	0.0993911i	0.655663	+	0.755054i	$0.272389\pi$
$242$			29.2087i			1.87760i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−44.2095			−2.83022
$245$		0			0
$246$			26.4570i			1.68684i
$247$	0.165368	−	2.35255i	0.0105221	−	0.149689i
$248$	−19.6847	−	19.6847i	−1.24998	−	1.24998i
$249$	−0.391461	+	0.391461i	−0.0248078	+	0.0248078i
$250$		0			0
$251$		−	17.9493i		−	1.13295i	−0.824078	−	0.566476i	$-0.808306\pi$
$251$		−	17.9493i		−	1.13295i	0.824078	−	0.566476i	$-0.191694\pi$
$252$	11.9754			0.754378
$253$		−	3.57589i		−	0.224814i
$254$	−18.3242	−	18.3242i	−1.14976	−	1.14976i
$255$		0			0
$256$	46.9322			2.93326
$257$	6.15242	+	6.15242i	0.383778	+	0.383778i	0.872461	−	0.488684i	$-0.162523\pi$
$257$	6.15242	+	6.15242i	0.383778	+	0.383778i	−0.488684	+	0.872461i	$0.662523\pi$
$258$	−4.71457			−0.293516
$259$	9.99958			0.621344
$260$		0			0
$261$	4.40973			0.272956
$262$	−32.5462			−2.01071
$263$	7.67855	+	7.67855i	0.473480	+	0.473480i	0.903039	−	0.429559i	$-0.141331\pi$
$263$	7.67855	+	7.67855i	0.473480	+	0.473480i	−0.429559	+	0.903039i	$0.641331\pi$
$264$	−5.44089			−0.334864
$265$		0			0
$266$	2.76207	+	2.76207i	0.169353	+	0.169353i
$267$		−	10.6919i		−	0.654334i
$268$	35.5668			2.17259
$269$			15.3699i			0.937121i	0.883431	+	0.468561i	$0.155227\pi$
$269$			15.3699i			0.937121i	−0.883431	+	0.468561i	$0.844773\pi$
$270$		0			0
$271$	−14.9961	+	14.9961i	−0.910946	+	0.910946i	−0.996347	−	0.0854010i	$-0.972783\pi$
$271$	−14.9961	+	14.9961i	−0.910946	+	0.910946i	0.0854010	+	0.996347i	$0.472783\pi$
$272$	−63.9683	−	63.9683i	−3.87865	−	3.87865i
$273$	−0.551789	+	7.84984i	−0.0333958	+	0.475094i
$274$		−	55.0632i		−	3.32649i
$275$		0			0
$276$	−34.4065			−2.07103
$277$	21.1916	+	21.1916i	1.27328	+	1.27328i	0.944358	+	0.328920i	$0.106685\pi$
$277$	21.1916	+	21.1916i	1.27328	+	1.27328i	0.328920	+	0.944358i	$0.393315\pi$
$278$		−	5.34855i		−	0.320785i
$279$	2.06316	−	2.06316i	0.123518	−	0.123518i
$280$		0			0
$281$	−5.73727	+	5.73727i	−0.342257	+	0.342257i	−0.857215	−	0.514958i	$-0.827807\pi$
$281$	−5.73727	+	5.73727i	−0.342257	+	0.342257i	0.514958	+	0.857215i	$0.327807\pi$
$282$	10.2304	−	10.2304i	0.609210	−	0.609210i
$283$	11.7247	−	11.7247i	0.696964	−	0.696964i	−0.266791	−	0.963754i	$-0.585963\pi$
$283$	11.7247	−	11.7247i	0.696964	−	0.696964i	0.963754	+	0.266791i	$0.0859633\pi$
$284$	12.7553	+	12.7553i	0.756886	+	0.756886i
$285$		0			0
$286$	0.394493	−	5.61212i	0.0233269	−	0.331852i
$287$	14.9222	−	14.9222i	0.880830	−	0.880830i
$288$			22.3241i			1.31546i
$289$			18.7382i			1.10225i
$290$		0			0
$291$	−6.99029	−	6.99029i	−0.409778	−	0.409778i
$292$	16.3654			0.957715
$293$	−24.9122			−1.45539			−0.727693	−	0.685903i	$-0.759408\pi$
$293$	−24.9122			−1.45539			−0.727693	+	0.685903i	$0.759408\pi$
$294$	4.32734	+	4.32734i	0.252376	+	0.252376i
$295$		0			0
$296$			43.7137i			2.54081i
$297$		−	0.570261i		−	0.0330899i
$298$	22.0924	−	22.0924i	1.27978	−	1.27978i
$299$	1.58534	−	22.5534i	0.0916829	−	1.30430i
$300$		0			0
$301$	2.65910	+	2.65910i	0.153268	+	0.153268i
$302$	16.6304	−	16.6304i	0.956971	−	0.956971i
$303$	4.83274	−	4.83274i	0.277633	−	0.277633i
$304$	−6.99901	+	6.99901i	−0.401420	+	0.401420i
$305$		0			0
$306$	11.5665	−	11.5665i	0.661215	−	0.661215i
$307$			17.4397i			0.995334i	0.867368	+	0.497667i	$0.165810\pi$
$307$			17.4397i			0.995334i	−0.867368	+	0.497667i	$0.834190\pi$
$308$	4.82890	+	4.82890i	0.275152	+	0.275152i
$309$	12.1282			0.689951
$310$		0			0
$311$		−	17.2745i		−	0.979549i	−0.871849	−	0.489774i	$-0.837079\pi$
$311$		−	17.2745i		−	0.979549i	0.871849	−	0.489774i	$-0.162921\pi$
$312$	−34.3161	−	2.41218i	−1.94276	−	0.136563i
$313$	4.81994	+	4.81994i	0.272439	+	0.272439i	0.830081	−	0.557642i	$-0.188294\pi$
$313$	4.81994	+	4.81994i	0.272439	+	0.272439i	−0.557642	+	0.830081i	$0.688294\pi$
$314$	16.5870	−	16.5870i	0.936061	−	0.936061i
$315$		0			0
$316$			69.7696i			3.92485i
$317$	−6.98466			−0.392298			−0.196149	−	0.980574i	$-0.562844\pi$
$317$	−6.98466			−0.392298			−0.196149	+	0.980574i	$0.562844\pi$
$318$			1.07549i			0.0603103i
$319$	1.77816	+	1.77816i	0.0995579	+	0.0995579i
$320$		0			0
$321$	14.4189			0.804784
$322$	26.4793	+	26.4793i	1.47563	+	1.47563i
$323$	3.91025			0.217572
$324$	−5.48694			−0.304830
$325$		0			0
$326$	3.01462			0.166965
$327$	−5.25760			−0.290746
$328$	65.2333	+	65.2333i	3.60191	+	3.60191i
$329$	−11.5402			−0.636232
$330$		0			0
$331$	−2.71466	−	2.71466i	−0.149211	−	0.149211i	0.628554	−	0.777766i	$-0.283647\pi$
$331$	−2.71466	−	2.71466i	−0.149211	−	0.149211i	−0.777766	+	0.628554i	$0.783647\pi$
$332$			3.03762i			0.166711i
$333$	−4.58165			−0.251073
$334$			53.1119i			2.90615i
$335$		0			0
$336$	23.3538	−	23.3538i	1.27406	−	1.27406i
$337$	24.3781	+	24.3781i	1.32796	+	1.32796i	0.907150	+	0.420808i	$0.138253\pi$
$337$	24.3781	+	24.3781i	1.32796	+	1.32796i	0.420808	+	0.907150i	$0.361747\pi$
$338$	4.97619	−	35.2212i	0.270669	−	1.91578i
$339$			8.59284i			0.466699i
$340$		0			0
$341$	1.66388			0.0901042
$342$	−1.26554	−	1.26554i	−0.0684324	−	0.0684324i
$343$		−	20.1591i		−	1.08849i
$344$	−11.6244	+	11.6244i	−0.626746	+	0.626746i
$345$		0			0
$346$	35.5301	−	35.5301i	1.91011	−	1.91011i
$347$	13.2149	−	13.2149i	0.709412	−	0.709412i	−0.257000	−	0.966411i	$-0.582734\pi$
$347$	13.2149	−	13.2149i	0.709412	−	0.709412i	0.966411	+	0.257000i	$0.0827340\pi$
$348$	17.1091	−	17.1091i	0.917144	−	0.917144i
$349$	23.3899	+	23.3899i	1.25203	+	1.25203i	0.954807	+	0.297228i	$0.0960621\pi$
$349$	23.3899	+	23.3899i	1.25203	+	1.25203i	0.297228	+	0.954807i	$0.403938\pi$
$350$		0			0
$351$	0.252821	−	3.59668i	0.0134946	−	0.191976i
$352$	−9.00187	+	9.00187i	−0.479802	+	0.479802i
$353$		−	7.41087i		−	0.394441i	−0.980359	−	0.197220i	$-0.936809\pi$
$353$		−	7.41087i		−	0.394441i	0.980359	−	0.197220i	$-0.0631914\pi$
$354$		−	9.34168i		−	0.496505i
$355$		0			0
$356$	−41.4830	−	41.4830i	−2.19860	−	2.19860i
$357$	−13.0475			−0.690545
$358$	16.5628			0.875370
$359$	−10.9837	−	10.9837i	−0.579700	−	0.579700i	0.355120	−	0.934821i	$-0.384440\pi$
$359$	−10.9837	−	10.9837i	−0.579700	−	0.579700i	−0.934821	+	0.355120i	$0.884440\pi$
$360$		0			0
$361$			18.5722i			0.977482i
$362$			1.75771i			0.0923834i
$363$	−7.54822	+	7.54822i	−0.396179	+	0.396179i
$364$	28.3153	+	32.5971i	1.48413	+	1.70855i
$365$		0			0
$366$	−15.5892	−	15.5892i	−0.814858	−	0.814858i
$367$	−10.6094	+	10.6094i	−0.553807	+	0.553807i	−0.927537	−	0.373730i	$-0.878079\pi$
$367$	−10.6094	+	10.6094i	−0.553807	+	0.553807i	0.373730	+	0.927537i	$0.378079\pi$
$368$	−67.0978	+	67.0978i	−3.49772	+	3.49772i
$369$	−6.83712	+	6.83712i	−0.355926	+	0.355926i
$370$		0			0
$371$	0.606593	−	0.606593i	0.0314928	−	0.0314928i
$372$		−	16.0095i		−	0.830055i
$373$	2.17179	+	2.17179i	0.112451	+	0.112451i	0.761093	−	0.648642i	$-0.224663\pi$
$373$	2.17179	+	2.17179i	0.112451	+	0.112451i	−0.648642	+	0.761093i	$0.724663\pi$
$374$	9.32808			0.482344
$375$		0			0
$376$		−	50.4487i		−	2.60169i
$377$	10.4267	+	12.0033i	0.537000	+	0.618203i
$378$	4.22276	+	4.22276i	0.217195	+	0.217195i
$379$	−18.8444	+	18.8444i	−0.967974	+	0.967974i	−0.999503	−	0.0315286i	$-0.989962\pi$
$379$	−18.8444	+	18.8444i	−0.967974	+	0.967974i	0.0315286	+	0.999503i	$0.489962\pi$
$380$		0			0
$381$		−	9.47083i		−	0.485205i
$382$	−65.7883			−3.36602
$383$			13.3355i			0.681410i	0.940170	+	0.340705i	$0.110666\pi$
$383$			13.3355i			0.681410i	−0.940170	+	0.340705i	$0.889334\pi$
$384$	28.0570	+	28.0570i	1.43178	+	1.43178i
$385$		0			0
$386$	42.5388			2.16517
$387$	−1.21836	−	1.21836i	−0.0619326	−	0.0619326i
$388$	−54.2426			−2.75375
$389$	14.5958			0.740038			0.370019	−	0.929024i	$-0.379351\pi$
$389$	14.5958			0.740038			0.370019	+	0.929024i	$0.379351\pi$
$390$		0			0
$391$	37.4867			1.89578
$392$	21.3393			1.07780
$393$	−8.41073	−	8.41073i	−0.424265	−	0.424265i
$394$	10.0100			0.504295
$395$		0			0
$396$	−2.21253	−	2.21253i	−0.111184	−	0.111184i
$397$		−	2.66580i		−	0.133793i	−0.997760	−	0.0668963i	$-0.978690\pi$
$397$		−	2.66580i		−	0.133793i	0.997760	−	0.0668963i	$-0.0213097\pi$
$398$	45.2537			2.26836
$399$			1.42757i			0.0714679i
$400$		0			0
$401$	−3.94441	+	3.94441i	−0.196974	+	0.196974i	−0.798702	−	0.601727i	$-0.794479\pi$
$401$	−3.94441	+	3.94441i	−0.196974	+	0.196974i	0.601727	+	0.798702i	$0.294479\pi$
$402$	12.5416	+	12.5416i	0.625517	+	0.625517i
$403$	10.4942	+	0.737670i	0.522754	+	0.0367459i
$404$		−	37.5006i		−	1.86572i
$405$		0			0
$406$	−26.3344			−1.30696
$407$	−1.84748	−	1.84748i	−0.0915764	−	0.0915764i
$408$		−	57.0378i		−	2.82379i
$409$	−6.46298	+	6.46298i	−0.319574	+	0.319574i	−0.848603	−	0.529030i	$-0.822556\pi$
$409$	−6.46298	+	6.46298i	−0.319574	+	0.319574i	0.529030	+	0.848603i	$0.322556\pi$
$410$		0			0
$411$	14.2297	−	14.2297i	0.701897	−	0.701897i
$412$	47.0557	−	47.0557i	2.31827	−	2.31827i
$413$	−5.26887	+	5.26887i	−0.259264	+	0.259264i
$414$	−12.1324	−	12.1324i	−0.596276	−	0.596276i
$415$		0			0
$416$	−60.7664	+	52.7845i	−2.97932	+	2.58797i
$417$	1.38219	−	1.38219i	0.0676864	−	0.0676864i
$418$		−	1.02062i		−	0.0499201i
$419$		−	4.68103i		−	0.228683i	−0.993441	−	0.114342i	$-0.963524\pi$
$419$		−	4.68103i		−	0.228683i	0.993441	−	0.114342i	$-0.0364759\pi$
$420$		0			0
$421$	−14.8900	−	14.8900i	−0.725692	−	0.725692i	0.244066	−	0.969759i	$-0.421519\pi$
$421$	−14.8900	−	14.8900i	−0.725692	−	0.725692i	−0.969759	+	0.244066i	$0.921519\pi$
$422$	17.2171			0.838118
$423$	5.28755			0.257089
$424$	2.65176	+	2.65176i	0.128781	+	0.128781i
$425$		0			0
$426$			8.99554i			0.435835i
$427$			17.5851i			0.851003i
$428$	55.9431	−	55.9431i	2.70411	−	2.70411i
$429$	1.55225	−	1.34836i	0.0749435	−	0.0650995i
$430$		0			0
$431$	−8.23888	−	8.23888i	−0.396853	−	0.396853i	0.480269	−	0.877122i	$-0.340539\pi$
$431$	−8.23888	−	8.23888i	−0.396853	−	0.396853i	−0.877122	+	0.480269i	$0.840539\pi$
$432$	−10.7004	+	10.7004i	−0.514821	+	0.514821i
$433$	20.2068	−	20.2068i	0.971076	−	0.971076i	−0.0285175	−	0.999593i	$-0.509079\pi$
$433$	20.2068	−	20.2068i	0.971076	−	0.971076i	0.999593	+	0.0285175i	$0.00907864\pi$
$434$	−12.3210	+	12.3210i	−0.591425	+	0.591425i
$435$		0			0
$436$	−20.3987	+	20.3987i	−0.976921	+	0.976921i
$437$		−	4.10155i		−	0.196204i
$438$	5.77078	+	5.77078i	0.275739	+	0.275739i
$439$	14.1906			0.677282			0.338641	−	0.940916i	$-0.390033\pi$
$439$	14.1906			0.677282			0.338641	+	0.940916i	$0.390033\pi$
$440$		0			0
$441$			2.23658i			0.106504i
$442$	58.8329	+	4.13554i	2.79839	+	0.196708i
$443$	−7.40061	−	7.40061i	−0.351613	−	0.351613i	0.509096	−	0.860710i	$-0.329980\pi$
$443$	−7.40061	−	7.40061i	−0.351613	−	0.351613i	−0.860710	+	0.509096i	$0.829980\pi$
$444$	−17.7761	+	17.7761i	−0.843617	+	0.843617i
$445$		0			0
$446$			73.0836i			3.46061i
$447$	11.4184			0.540072
$448$		−	67.2625i		−	3.17785i
$449$	14.0038	+	14.0038i	0.660879	+	0.660879i	0.955587	−	0.294709i	$-0.0952226\pi$
$449$	14.0038	+	14.0038i	0.660879	+	0.660879i	−0.294709	+	0.955587i	$0.595223\pi$
$450$		0			0
$451$	−5.51394			−0.259641
$452$	33.3389	+	33.3389i	1.56813	+	1.56813i
$453$	8.59538			0.403846
$454$	−41.5835			−1.95161
$455$		0			0
$456$	−6.24071			−0.292248
$457$	10.1902			0.476680			0.238340	−	0.971182i	$-0.423397\pi$
$457$	10.1902			0.476680			0.238340	+	0.971182i	$0.423397\pi$
$458$	6.34879	+	6.34879i	0.296659	+	0.296659i
$459$	5.97815			0.279036
$460$		0			0
$461$	−8.03629	−	8.03629i	−0.374288	−	0.374288i	0.494749	−	0.869036i	$-0.335260\pi$
$461$	−8.03629	−	8.03629i	−0.374288	−	0.374288i	−0.869036	+	0.494749i	$0.835260\pi$
$462$			3.40554i			0.158440i
$463$	−14.2791			−0.663606			−0.331803	−	0.943349i	$-0.607657\pi$
$463$	−14.2791			−0.663606			−0.331803	+	0.943349i	$0.607657\pi$
$464$		−	66.7307i		−	3.09790i
$465$		0			0
$466$	−8.89678	+	8.89678i	−0.412135	+	0.412135i
$467$	−25.6127	−	25.6127i	−1.18521	−	1.18521i	−0.978375	−	0.206840i	$-0.933682\pi$
$467$	−25.6127	−	25.6127i	−1.18521	−	1.18521i	−0.206840	−	0.978375i	$-0.566318\pi$
$468$	−12.9737	−	14.9355i	−0.599707	−	0.690392i
$469$		−	14.1473i		−	0.653263i
$470$		0			0
$471$	8.57299			0.395022
$472$	−23.0332	−	23.0332i	−1.06019	−	1.06019i
$473$		−	0.982570i		−	0.0451786i
$474$	−24.6022	+	24.6022i	−1.13002	+	1.13002i
$475$		0			0
$476$	−50.6222	+	50.6222i	−2.32027	+	2.32027i
$477$	−0.277932	+	0.277932i	−0.0127256	+	0.0127256i
$478$	−27.5751	+	27.5751i	−1.26126	+	1.26126i
$479$	−6.00774	−	6.00774i	−0.274500	−	0.274500i	0.556408	−	0.830909i	$-0.312179\pi$
$479$	−6.00774	−	6.00774i	−0.274500	−	0.274500i	−0.830909	+	0.556408i	$0.812179\pi$
$480$		0			0
$481$	−10.8331	−	12.4713i	−0.493949	−	0.568642i
$482$	−4.22190	+	4.22190i	−0.192302	+	0.192302i
$483$			13.6858i			0.622725i
$484$			58.5720i			2.66236i
$485$		0			0
$486$	−1.93480	−	1.93480i	−0.0877645	−	0.0877645i
$487$	−43.1824			−1.95678			−0.978391	−	0.206761i	$-0.933708\pi$
$487$	−43.1824			−1.95678			−0.978391	+	0.206761i	$0.933708\pi$
$488$	−76.8744			−3.47994
$489$	0.779051	+	0.779051i	0.0352299	+	0.0352299i
$490$		0			0
$491$		−	35.5626i		−	1.60492i	−0.596706	−	0.802460i	$-0.703524\pi$
$491$		−	35.5626i		−	1.60492i	0.596706	−	0.802460i	$-0.296476\pi$
$492$			53.0540i			2.39186i
$493$	−18.6408	+	18.6408i	−0.839538	+	0.839538i
$494$	0.452484	−	6.43712i	0.0203582	−	0.289620i
$495$		0			0
$496$	−31.2210	−	31.2210i	−1.40186	−	1.40186i
$497$	5.07364	−	5.07364i	0.227584	−	0.227584i
$498$	−1.07113	+	1.07113i	−0.0479983	+	0.0479983i
$499$	8.05960	−	8.05960i	0.360797	−	0.360797i	−0.503309	−	0.864106i	$-0.667884\pi$
$499$	8.05960	−	8.05960i	0.360797	−	0.360797i	0.864106	+	0.503309i	$0.167884\pi$
$500$		0			0
$501$	−13.7254	+	13.7254i	−0.613205	+	0.613205i
$502$		−	49.1134i		−	2.19204i
$503$	0.598343	+	0.598343i	0.0266788	+	0.0266788i	0.720320	−	0.693642i	$-0.243995\pi$
$503$	0.598343	+	0.598343i	0.0266788	+	0.0266788i	−0.693642	+	0.720320i	$0.743995\pi$
$504$	20.8236			0.927556
$505$		0			0
$506$		−	9.78444i		−	0.434971i
$507$	10.3880	−	7.81603i	0.461346	−	0.347122i
$508$	−36.7454	−	36.7454i	−1.63031	−	1.63031i
$509$	10.1171	−	10.1171i	0.448434	−	0.448434i	−0.446400	−	0.894834i	$-0.647294\pi$
$509$	10.1171	−	10.1171i	0.448434	−	0.448434i	0.894834	+	0.446400i	$0.147294\pi$
$510$		0			0
$511$		−	6.50964i		−	0.287970i
$512$	49.0601			2.16817
$513$		−	0.654091i		−	0.0288788i
$514$	16.8344	+	16.8344i	0.742534	+	0.742534i
$515$		0			0
$516$	−9.45409			−0.416193
$517$	2.13213	+	2.13213i	0.0937708	+	0.0937708i
$518$	27.3611			1.20218
$519$	18.3637			0.806076
$520$		0			0
$521$	−17.8118			−0.780350			−0.390175	−	0.920741i	$-0.627586\pi$
$521$	−17.8118			−0.780350			−0.390175	+	0.920741i	$0.627586\pi$
$522$	12.0660			0.528116
$523$	−8.40927	−	8.40927i	−0.367712	−	0.367712i	0.498930	−	0.866642i	$-0.333726\pi$
$523$	−8.40927	−	8.40927i	−0.367712	−	0.367712i	−0.866642	+	0.498930i	$0.833726\pi$
$524$	−65.2647			−2.85110
$525$		0			0
$526$	21.0103	+	21.0103i	0.916091	+	0.916091i
$527$			17.4427i			0.759818i
$528$	−8.62953			−0.375552
$529$		−	16.3206i		−	0.709592i
$530$		0			0
$531$	2.41412	−	2.41412i	0.104764	−	0.104764i
$532$	5.53876	+	5.53876i	0.240136	+	0.240136i
$533$	−34.7768	−	2.44457i	−1.50635	−	0.105886i
$534$		−	29.2555i		−	1.26601i
$535$		0			0
$536$	61.8459			2.67134
$537$	4.28022	+	4.28022i	0.184705	+	0.184705i
$538$			42.0556i			1.81315i
$539$	−0.901867	+	0.901867i	−0.0388462	+	0.0388462i
$540$		0			0
$541$	7.53385	−	7.53385i	0.323906	−	0.323906i	−0.526358	−	0.850263i	$-0.676443\pi$
$541$	7.53385	−	7.53385i	0.323906	−	0.323906i	0.850263	+	0.526358i	$0.176443\pi$
$542$	−41.0326	+	41.0326i	−1.76250	+	1.76250i
$543$	−0.454236	+	0.454236i	−0.0194931	+	0.0194931i
$544$	−94.3682	−	94.3682i	−4.04600	−	4.04600i
$545$		0			0
$546$	−1.50982	+	21.4789i	−0.0646143	+	0.919214i
$547$	−2.00219	+	2.00219i	−0.0856074	+	0.0856074i	−0.748614	−	0.663006i	$-0.769280\pi$
$547$	−2.00219	+	2.00219i	−0.0856074	+	0.0856074i	0.663006	+	0.748614i	$0.269280\pi$
$548$		−	110.418i		−	4.71682i
$549$		−	8.05723i		−	0.343874i
$550$		0			0
$551$	2.03955	+	2.03955i	0.0868880	+	0.0868880i
$552$	−59.8282			−2.54646
$553$	27.7521			1.18014
$554$	57.9849	+	57.9849i	2.46354	+	2.46354i
$555$		0			0
$556$		−	10.7254i		−	0.454859i
$557$			10.8795i			0.460977i	0.973075	+	0.230489i	$0.0740325\pi$
$557$			10.8795i			0.460977i	−0.973075	+	0.230489i	$0.925968\pi$
$558$	5.64528	−	5.64528i	0.238984	−	0.238984i
$559$	0.435616	−	6.19714i	0.0184246	−	0.262111i
$560$		0			0
$561$	2.41060	+	2.41060i	0.101776	+	0.101776i
$562$	−15.6985	+	15.6985i	−0.662200	+	0.662200i
$563$	7.54907	−	7.54907i	0.318155	−	0.318155i	−0.529903	−	0.848058i	$-0.677772\pi$
$563$	7.54907	−	7.54907i	0.318155	−	0.318155i	0.848058	+	0.529903i	$0.177772\pi$
$564$	20.5149	−	20.5149i	0.863832	−	0.863832i
$565$		0			0
$566$	32.0816	−	32.0816i	1.34849	−	1.34849i
$567$			2.18253i			0.0916575i
$568$	22.1797	+	22.1797i	0.930640	+	0.930640i
$569$	18.9891			0.796063			0.398031	−	0.917372i	$-0.369693\pi$
$569$	18.9891			0.796063			0.398031	+	0.917372i	$0.369693\pi$
$570$		0			0
$571$		−	11.6537i		−	0.487690i	−0.969814	−	0.243845i	$-0.921591\pi$
$571$		−	11.6537i		−	0.487690i	0.969814	−	0.243845i	$-0.0784089\pi$
$572$	0.791074	−	11.2540i	0.0330765	−	0.470551i
$573$	−17.0013	−	17.0013i	−0.710238	−	0.710238i
$574$	40.8305	−	40.8305i	1.70423	−	1.70423i
$575$		0			0
$576$			30.8186i			1.28411i
$577$	44.8098			1.86545			0.932727	−	0.360583i	$-0.117422\pi$
$577$	44.8098			1.86545			0.932727	+	0.360583i	$0.117422\pi$
$578$			51.2721i			2.13264i
$579$	10.9930	+	10.9930i	0.456855	+	0.456855i
$580$		0			0
$581$	1.20827			0.0501274
$582$	−19.1270	−	19.1270i	−0.792841	−	0.792841i
$583$	−0.224144			−0.00928309
$584$	28.4573			1.17757
$585$		0			0
$586$	−68.1654			−2.81589
$587$	−40.6108			−1.67619			−0.838094	−	0.545526i	$-0.816330\pi$
$587$	−40.6108			−1.67619			−0.838094	+	0.545526i	$0.816330\pi$
$588$	8.67758	+	8.67758i	0.357857	+	0.357857i
$589$	1.90847			0.0786373
$590$		0			0
$591$	2.58682	+	2.58682i	0.106407	+	0.106407i
$592$			69.3323i			2.84954i
$593$	37.0717			1.52235			0.761177	−	0.648544i	$-0.224622\pi$
$593$	37.0717			1.52235			0.761177	+	0.648544i	$0.224622\pi$
$594$		−	1.56036i		−	0.0640225i
$595$		0			0
$596$	44.3017	−	44.3017i	1.81467	−	1.81467i
$597$	11.6946	+	11.6946i	0.478630	+	0.478630i
$598$	4.33786	−	61.7111i	0.177388	−	2.52356i
$599$			17.5005i			0.715052i	0.933903	+	0.357526i	$0.116380\pi$
$599$			17.5005i			0.715052i	−0.933903	+	0.357526i	$0.883620\pi$
$600$		0			0
$601$	12.1303			0.494806			0.247403	−	0.968913i	$-0.420423\pi$
$601$	12.1303			0.494806			0.247403	+	0.968913i	$0.420423\pi$
$602$	7.27590	+	7.27590i	0.296543	+	0.296543i
$603$			6.48209i			0.263971i
$604$	33.3488	−	33.3488i	1.35694	−	1.35694i
$605$		0			0
$606$	13.2235	−	13.2235i	0.537166	−	0.537166i
$607$	−21.4794	+	21.4794i	−0.871823	+	0.871823i	−0.992671	−	0.120848i	$-0.961439\pi$
$607$	−21.4794	+	21.4794i	−0.871823	+	0.871823i	0.120848	+	0.992671i	$0.461439\pi$
$608$	−10.3252	+	10.3252i	−0.418741	+	0.418741i
$609$	−6.80545	−	6.80545i	−0.275771	−	0.275771i
$610$		0			0
$611$	12.5022	+	14.3927i	0.505785	+	0.582268i
$612$	23.1943	−	23.1943i	0.937574	−	0.937574i
$613$		−	0.726110i		−	0.0293273i	−0.999892	−	0.0146637i	$-0.995332\pi$
$613$		−	0.726110i		−	0.0293273i	0.999892	−	0.0146637i	$-0.00466775\pi$
$614$			47.7188i			1.92578i
$615$		0			0
$616$	8.39681	+	8.39681i	0.338317	+	0.338317i
$617$	−5.15654			−0.207595			−0.103797	−	0.994598i	$-0.533099\pi$
$617$	−5.15654			−0.207595			−0.103797	+	0.994598i	$0.533099\pi$
$618$	33.1856			1.33492
$619$	−9.30732	−	9.30732i	−0.374093	−	0.374093i	0.494873	−	0.868966i	$-0.335215\pi$
$619$	−9.30732	−	9.30732i	−0.374093	−	0.374093i	−0.868966	+	0.494873i	$0.835215\pi$
$620$		0			0
$621$		−	6.27061i		−	0.251631i
$622$		−	47.2670i		−	1.89524i
$623$	−16.5006	+	16.5006i	−0.661083	+	0.661083i
$624$	−54.4270	−	3.82584i	−2.17883	−	0.153156i
$625$		0			0
$626$	13.1885	+	13.1885i	0.527117	+	0.527117i
$627$	0.263753	−	0.263753i	0.0105333	−	0.0105333i
$628$	33.2619	−	33.2619i	1.32729	−	1.32729i
$629$	19.3675	−	19.3675i	0.772233	−	0.772233i
$630$		0			0
$631$	12.6202	−	12.6202i	0.502401	−	0.502401i	−0.409783	−	0.912183i	$-0.634395\pi$
$631$	12.6202	−	12.6202i	0.502401	−	0.502401i	0.912183	+	0.409783i	$0.134395\pi$
$632$			121.320i			4.82585i
$633$	4.44933	+	4.44933i	0.176845	+	0.176845i
$634$	−19.1116			−0.759019
$635$		0			0
$636$			2.15667i			0.0855174i
$637$	−6.08798	+	5.28830i	−0.241214	+	0.209530i
$638$	4.86545	+	4.86545i	0.192625	+	0.192625i
$639$	−2.32466	+	2.32466i	−0.0919623	+	0.0919623i
$640$		0			0
$641$			45.1788i			1.78445i	0.451586	+	0.892227i	$0.350858\pi$
$641$			45.1788i			1.78445i	−0.451586	+	0.892227i	$0.649142\pi$
$642$	39.4534			1.55710
$643$			4.62889i			0.182545i	0.995826	+	0.0912727i	$0.0290935\pi$
$643$			4.62889i			0.182545i	−0.995826	+	0.0912727i	$0.970906\pi$
$644$	53.0988	+	53.0988i	2.09239	+	2.09239i
$645$		0			0
$646$	10.6993			0.420960
$647$	−10.9090	−	10.9090i	−0.428875	−	0.428875i	0.459370	−	0.888245i	$-0.348075\pi$
$647$	−10.9090	−	10.9090i	−0.428875	−	0.428875i	−0.888245	+	0.459370i	$0.848075\pi$
$648$	−9.54105			−0.374808
$649$	1.94691			0.0764231
$650$		0			0
$651$	−6.36807			−0.249584
$652$	6.04520			0.236748
$653$	−12.5146	−	12.5146i	−0.489732	−	0.489732i	0.418489	−	0.908222i	$-0.362560\pi$
$653$	−12.5146	−	12.5146i	−0.489732	−	0.489732i	−0.908222	+	0.418489i	$0.862560\pi$
$654$	−14.3860			−0.562537
$655$		0			0
$656$	103.463	+	103.463i	4.03957	+	4.03957i
$657$			2.98262i			0.116363i
$658$	−31.5766			−1.23099
$659$		−	18.9250i		−	0.737212i	−0.929586	−	0.368606i	$-0.879835\pi$
$659$		−	18.9250i		−	0.737212i	0.929586	−	0.368606i	$-0.120165\pi$
$660$		0			0
$661$	−19.8468	+	19.8468i	−0.771950	+	0.771950i	−0.978447	−	0.206497i	$-0.933794\pi$
$661$	−19.8468	+	19.8468i	−0.771950	+	0.771950i	0.206497	+	0.978447i	$0.433794\pi$
$662$	−7.42793	−	7.42793i	−0.288695	−	0.288695i
$663$	14.1351	+	16.2726i	0.548962	+	0.631974i
$664$			5.28202i			0.204982i
$665$		0			0
$666$	−12.5364			−0.485777
$667$	19.5527	+	19.5527i	0.757085	+	0.757085i
$668$			106.505i			4.12080i
$669$	−18.8866	+	18.8866i	−0.730196	+	0.730196i
$670$		0			0
$671$	3.24896	−	3.24896i	0.125425	−	0.125425i
$672$	34.4523	−	34.4523i	1.32903	−	1.32903i
$673$	1.67376	−	1.67376i	0.0645189	−	0.0645189i	−0.674111	−	0.738630i	$-0.735473\pi$
$673$	1.67376	−	1.67376i	0.0645189	−	0.0645189i	0.738630	+	0.674111i	$0.235473\pi$
$674$	66.7039	+	66.7039i	2.56934	+	2.56934i
$675$		0			0
$676$	9.97872	−	70.6287i	0.383797	−	2.71649i
$677$	26.4518	−	26.4518i	1.01662	−	1.01662i	0.0167645	−	0.999859i	$-0.494663\pi$
$677$	26.4518	−	26.4518i	1.01662	−	1.01662i	0.999859	−	0.0167645i	$-0.00533657\pi$
$678$			23.5120i			0.902971i
$679$			21.5760i			0.828009i
$680$		0			0
$681$	−10.7462	−	10.7462i	−0.411794	−	0.411794i
$682$	4.55275			0.174334
$683$	7.05381			0.269906			0.134953	−	0.990852i	$-0.456912\pi$
$683$	7.05381			0.269906			0.134953	+	0.990852i	$0.456912\pi$
$684$	−2.53777	−	2.53777i	−0.0970342	−	0.0970342i
$685$		0			0
$686$		−	55.1598i		−	2.10601i
$687$			3.28136i			0.125192i
$688$	−18.4369	+	18.4369i	−0.702901	+	0.702901i
$689$	−1.41369	−	0.0993726i	−0.0538573	−	0.00378580i
$690$		0			0
$691$	2.82022	+	2.82022i	0.107286	+	0.107286i	0.758712	−	0.651426i	$-0.225829\pi$
$691$	2.82022	+	2.82022i	0.107286	+	0.107286i	−0.651426	+	0.758712i	$0.725829\pi$
$692$	71.2483	−	71.2483i	2.70845	−	2.70845i
$693$	−0.880072	+	0.880072i	−0.0334312	+	0.0334312i
$694$	36.1589	−	36.1589i	1.37257	−	1.37257i
$695$		0			0
$696$	29.7504	−	29.7504i	1.12769	−	1.12769i
$697$		−	57.8036i		−	2.18947i
$698$	64.0002	+	64.0002i	2.42244	+	2.42244i
$699$	−4.59828			−0.173923
$700$		0			0
$701$			34.2082i			1.29203i	0.763326	+	0.646013i	$0.223565\pi$
$701$			34.2082i			1.29203i	−0.763326	+	0.646013i	$0.776435\pi$
$702$	0.691776	−	9.84132i	0.0261094	−	0.371437i
$703$	−2.11907	−	2.11907i	−0.0799222	−	0.0799222i
$704$	−12.4272	+	12.4272i	−0.468367	+	0.468367i
$705$		0			0
$706$		−	20.2778i		−	0.763166i
$707$	−14.9165			−0.560994
$708$		−	18.7328i		−	0.704022i
$709$	−11.6794	−	11.6794i	−0.438629	−	0.438629i	0.452922	−	0.891550i	$-0.350382\pi$
$709$	−11.6794	−	11.6794i	−0.438629	−	0.438629i	−0.891550	+	0.452922i	$0.850382\pi$
$710$		0			0
$711$	−12.7156			−0.476872
$712$	−72.1334	−	72.1334i	−2.70331	−	2.70331i
$713$	18.2961			0.685194
$714$	−35.7008			−1.33607
$715$		0			0
$716$	33.2132			1.24124
$717$	−14.2521			−0.532256
$718$	−30.0540	−	30.0540i	−1.12161	−	1.12161i
$719$	5.64612			0.210565			0.105282	−	0.994442i	$-0.466425\pi$
$719$	5.64612			0.210565			0.105282	+	0.994442i	$0.466425\pi$
$720$		0			0
$721$	−18.7173	−	18.7173i	−0.697067	−	0.697067i
$722$			50.8177i			1.89124i
$723$	−2.18208			−0.0811525
$724$			3.52473i			0.130996i
$725$		0			0
$726$	−20.6537	+	20.6537i	−0.766529	+	0.766529i
$727$	−28.2805	−	28.2805i	−1.04887	−	1.04887i	−0.998743	−	0.0501220i	$-0.984039\pi$
$727$	−28.2805	−	28.2805i	−1.04887	−	1.04887i	−0.0501220	−	0.998743i	$-0.515961\pi$
$728$	49.2366	+	56.6819i	1.82483	+	2.10077i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	10.3005			0.380976
$732$	−31.2608	−	31.2608i	−1.15543	−	1.15543i
$733$			11.2999i			0.417371i	0.977983	+	0.208685i	$0.0669184\pi$
$733$			11.2999i			0.417371i	−0.977983	+	0.208685i	$0.933082\pi$
$734$	−29.0298	+	29.0298i	−1.07151	+	1.07151i
$735$		0			0
$736$	−98.9850	+	98.9850i	−3.64863	+	3.64863i
$737$	−2.61381	+	2.61381i	−0.0962809	+	0.0962809i
$738$	−18.7079	+	18.7079i	−0.688648	+	0.688648i
$739$	−29.7175	−	29.7175i	−1.09318	−	1.09318i	−0.995187	−	0.0979893i	$-0.968759\pi$
$739$	−29.7175	−	29.7175i	−1.09318	−	1.09318i	−0.0979893	−	0.995187i	$-0.531241\pi$
$740$		0			0
$741$	1.78044	−	1.54657i	0.0654061	−	0.0568148i
$742$	1.65978	−	1.65978i	0.0609323	−	0.0609323i
$743$			0.480200i			0.0176168i	0.999961	+	0.00880841i	$0.00280384\pi$
$743$			0.480200i			0.0176168i	−0.999961	+	0.00880841i	$0.997196\pi$
$744$		−	27.8384i		−	1.02061i
$745$		0			0
$746$	5.94252	+	5.94252i	0.217571	+	0.217571i
$747$	−0.553610			−0.0202555
$748$	18.7055			0.683942
$749$	−22.2524	−	22.2524i	−0.813085	−	0.813085i
$750$		0			0
$751$			14.4818i			0.528449i	0.964461	+	0.264224i	$0.0851160\pi$
$751$			14.4818i			0.528449i	−0.964461	+	0.264224i	$0.914884\pi$
$752$		−	80.0143i		−	2.91782i
$753$	12.6921	−	12.6921i	0.462526	−	0.462526i
$754$	28.5297	+	32.8438i	1.03899	+	1.19610i
$755$		0			0
$756$	8.46788	+	8.46788i	0.307974	+	0.307974i
$757$	−3.80569	+	3.80569i	−0.138320	+	0.138320i	−0.772877	−	0.634556i	$-0.781183\pi$
$757$	−3.80569	+	3.80569i	−0.138320	+	0.138320i	0.634556	+	0.772877i	$0.281183\pi$
$758$	−51.5627	+	51.5627i	−1.87284	+	1.87284i
$759$	2.52853	−	2.52853i	0.0917800	−	0.0917800i
$760$		0			0
$761$	−7.13165	+	7.13165i	−0.258522	+	0.258522i	−0.824453	−	0.565931i	$-0.808517\pi$
$761$	−7.13165	+	7.13165i	−0.258522	+	0.258522i	0.565931	+	0.824453i	$0.308517\pi$
$762$		−	25.9143i		−	0.938778i
$763$	8.11395	+	8.11395i	0.293745	+	0.293745i
$764$	−131.925			−4.77287
$765$		0			0
$766$			36.4888i			1.31840i
$767$	12.2793	+	0.863151i	0.443381	+	0.0311666i
$768$	33.1861	+	33.1861i	1.19750	+	1.19750i
$769$	−6.28641	+	6.28641i	−0.226694	+	0.226694i	−0.811310	−	0.584616i	$-0.801245\pi$
$769$	−6.28641	+	6.28641i	−0.226694	+	0.226694i	0.584616	+	0.811310i	$0.301245\pi$
$770$		0			0
$771$			8.70084i			0.313353i
$772$	85.3027			3.07011
$773$		−	24.2193i		−	0.871108i	−0.900163	−	0.435554i	$-0.856553\pi$
$773$		−	24.2193i		−	0.871108i	0.900163	−	0.435554i	$-0.143447\pi$
$774$	−3.33370	−	3.33370i	−0.119827	−	0.119827i
$775$		0			0
$776$	−94.3206			−3.38591
$777$	7.07077	+	7.07077i	0.253662	+	0.253662i
$778$	39.9375			1.43183
$779$	−6.32450			−0.226599
$780$		0			0
$781$	−1.87477			−0.0670847
$782$	102.572			3.66797
$783$	3.11815	+	3.11815i	0.111434	+	0.111434i
$784$	33.8452			1.20876
$785$		0			0
$786$	−23.0137	−	23.0137i	−0.820870	−	0.820870i
$787$			32.7945i			1.16900i	0.811394	+	0.584499i	$0.198709\pi$
$787$			32.7945i			1.16900i	−0.811394	+	0.584499i	$0.801291\pi$
$788$	20.0729			0.715069
$789$			10.8591i			0.386595i
$790$		0			0
$791$	13.2612	−	13.2612i	0.471512	−	0.471512i
$792$	−3.84729	−	3.84729i	−0.136707	−	0.136707i
$793$	21.9318	−	19.0510i	0.778822	−	0.676521i
$794$		−	7.29423i		−	0.258863i
$795$		0			0
$796$	90.7469			3.21644
$797$	3.08683	+	3.08683i	0.109341	+	0.109341i	0.759661	−	0.650320i	$-0.225365\pi$
$797$	3.08683	+	3.08683i	0.109341	+	0.109341i	−0.650320	+	0.759661i	$0.725365\pi$
$798$			3.90616i			0.138276i
$799$	−22.3515	+	22.3515i	−0.790738	+	0.790738i
$800$		0			0
$801$	7.56032	−	7.56032i	0.267131	−	0.267131i
$802$	−10.7928	+	10.7928i	−0.381107	+	0.381107i
$803$	−1.20270	+	1.20270i	−0.0424423	+	0.0424423i
$804$	25.1495	+	25.1495i	0.886956	+	0.886956i
$805$		0			0
$806$	28.7145	+	2.01843i	1.01143	+	0.0710962i
$807$	−10.8682	+	10.8682i	−0.382578	+	0.382578i
$808$		−	65.2085i		−	2.29403i
$809$		−	27.8780i		−	0.980140i	−0.871683	−	0.490070i	$-0.836971\pi$
$809$		−	27.8780i		−	0.980140i	0.871683	−	0.490070i	$-0.163029\pi$
$810$		0			0
$811$	26.2382	+	26.2382i	0.921347	+	0.921347i	0.997125	−	0.0757777i	$-0.0241439\pi$
$811$	26.2382	+	26.2382i	0.921347	+	0.921347i	−0.0757777	+	0.997125i	$0.524144\pi$
$812$	−52.8083			−1.85321
$813$	−21.2076			−0.743784
$814$	−5.05514	−	5.05514i	−0.177182	−	0.177182i
$815$		0			0
$816$		−	90.4649i		−	3.16690i
$817$		−	1.12701i		−	0.0394291i
$818$	−17.6842	+	17.6842i	−0.618313	+	0.618313i
$819$	−5.94085	+	5.16050i	−0.207590	+	0.180323i
$820$		0			0
$821$	23.4557	+	23.4557i	0.818609	+	0.818609i	0.985906	−	0.167298i	$-0.0535041\pi$
$821$	23.4557	+	23.4557i	0.818609	+	0.818609i	−0.167298	+	0.985906i	$0.553504\pi$
$822$	38.9356	−	38.9356i	1.35803	−	1.35803i
$823$	−21.2386	+	21.2386i	−0.740333	+	0.740333i	−0.972642	−	0.232309i	$-0.925372\pi$
$823$	−21.2386	+	21.2386i	−0.740333	+	0.740333i	0.232309	+	0.972642i	$0.425372\pi$
$824$	81.8236	−	81.8236i	2.85046	−	2.85046i
$825$		0			0
$826$	−14.4168	+	14.4168i	−0.501626	+	0.501626i
$827$		−	54.2245i		−	1.88557i	−0.333398	−	0.942786i	$-0.608195\pi$
$827$		−	54.2245i		−	1.88557i	0.333398	−	0.942786i	$-0.391805\pi$
$828$	−24.3290	−	24.3290i	−0.845493	−	0.845493i
$829$	−19.2741			−0.669416			−0.334708	−	0.942322i	$-0.608638\pi$
$829$	−19.2741			−0.669416			−0.334708	+	0.942322i	$0.608638\pi$
$830$		0			0
$831$			29.9694i			1.03963i
$832$	−83.8885	+	72.8695i	−2.90831	+	2.52630i
$833$	−9.45443	−	9.45443i	−0.327577	−	0.327577i
$834$	3.78200	−	3.78200i	0.130960	−	0.130960i
$835$		0			0
$836$		−	2.04664i		−	0.0707846i
$837$	2.91775			0.100852
$838$		−	12.8084i		−	0.442457i
$839$	−14.3455	−	14.3455i	−0.495261	−	0.495261i	0.414698	−	0.909959i	$-0.363887\pi$
$839$	−14.3455	−	14.3455i	−0.495261	−	0.495261i	−0.909959	+	0.414698i	$0.863887\pi$
$840$		0			0
$841$	9.55424			0.329457
$842$	−40.7423	−	40.7423i	−1.40407	−	1.40407i
$843$	−8.11373			−0.279452
$844$	34.5254			1.18841
$845$		0			0
$846$	14.4679			0.497417
$847$	23.2980			0.800530
$848$	4.20583	+	4.20583i	0.144429	+	0.144429i
$849$	16.5813			0.569068
$850$		0			0
$851$	−20.3150	−	20.3150i	−0.696390	−	0.696390i
$852$			18.0387i			0.617995i
$853$	−48.6784			−1.66672			−0.833358	−	0.552734i	$-0.813585\pi$
$853$	−48.6784			−1.66672			−0.833358	+	0.552734i	$0.813585\pi$
$854$			48.1169i			1.64652i
$855$		0			0
$856$	97.2776	−	97.2776i	3.32488	−	3.32488i
$857$	30.4034	+	30.4034i	1.03856	+	1.03856i	0.999226	+	0.0393345i	$0.0125238\pi$
$857$	30.4034	+	30.4034i	1.03856	+	1.03856i	0.0393345	+	0.999226i	$0.487476\pi$
$858$	4.24732	−	3.68942i	0.145001	−	0.125955i
$859$		−	41.7176i		−	1.42339i	−0.702490	−	0.711693i	$-0.747929\pi$
$859$		−	41.7176i		−	1.42339i	0.702490	−	0.711693i	$-0.252071\pi$
$860$		0			0
$861$	21.1032			0.719194
$862$	−22.5434	−	22.5434i	−0.767833	−	0.767833i
$863$		−	46.2439i		−	1.57416i	−0.616851	−	0.787080i	$-0.711592\pi$
$863$		−	46.2439i		−	1.57416i	0.616851	−	0.787080i	$-0.288408\pi$
$864$	−15.7855	+	15.7855i	−0.537035	+	0.537035i
$865$		0			0
$866$	55.2903	−	55.2903i	1.87884	−	1.87884i
$867$	−13.2499	+	13.2499i	−0.449992	+	0.449992i
$868$	−24.7072	+	24.7072i	−0.838615	+	0.838615i
$869$	−5.12738	−	5.12738i	−0.173934	−	0.173934i
$870$		0			0
$871$	−17.6443	+	15.3267i	−0.597854	+	0.519324i
$872$	−35.4706	+	35.4706i	−1.20119	+	1.20119i
$873$		−	9.88577i		−	0.334583i
$874$		−	11.2228i		−	0.379616i
$875$		0			0
$876$	11.5721	+	11.5721i	0.390985	+	0.390985i
$877$	43.7565			1.47755			0.738776	−	0.673951i	$-0.235404\pi$
$877$	43.7565			1.47755			0.738776	+	0.673951i	$0.235404\pi$
$878$	38.8288			1.31041
$879$	−17.6156	−	17.6156i	−0.594159	−	0.594159i
$880$		0			0
$881$		−	23.4781i		−	0.790998i	−0.918466	−	0.395499i	$-0.870572\pi$
$881$		−	23.4781i		−	0.790998i	0.918466	−	0.395499i	$-0.129428\pi$
$882$			6.11978i			0.206064i
$883$	32.6644	−	32.6644i	1.09925	−	1.09925i	0.104747	−	0.994499i	$-0.466597\pi$
$883$	32.6644	−	32.6644i	1.09925	−	1.09925i	0.994499	−	0.104747i	$-0.0334033\pi$
$884$	117.977	+	8.29297i	3.96800	+	0.278923i
$885$		0			0
$886$	−20.2497	−	20.2497i	−0.680303	−	0.680303i
$887$	−19.0826	+	19.0826i	−0.640732	+	0.640732i	−0.950735	−	0.310004i	$-0.899670\pi$
$887$	−19.0826	+	19.0826i	−0.640732	+	0.640732i	0.310004	+	0.950735i	$0.399670\pi$
$888$	−30.9103	+	30.9103i	−1.03728	+	1.03728i
$889$	−14.6161	+	14.6161i	−0.490210	+	0.490210i
$890$		0			0
$891$	0.403236	−	0.403236i	0.0135089	−	0.0135089i
$892$			146.554i			4.90699i
$893$	2.44555	+	2.44555i	0.0818373	+	0.0818373i
$894$	31.2434			1.04493
$895$		0			0
$896$		−	86.5995i		−	2.89309i
$897$	17.0686	−	14.8266i	0.569906	−	0.495047i
$898$	38.3175	+	38.3175i	1.27867	+	1.27867i
$899$	−9.09799	+	9.09799i	−0.303435	+	0.303435i
$900$		0			0
$901$		−	2.34974i		−	0.0782812i
$902$	−15.0874			−0.502355
$903$			3.76053i			0.125143i
$904$	57.9719	+	57.9719i	1.92812	+	1.92812i
$905$		0			0
$906$	23.5189			0.781363
$907$	−22.9031	−	22.9031i	−0.760486	−	0.760486i	0.215924	−	0.976410i	$-0.430724\pi$
$907$	−22.9031	−	22.9031i	−0.760486	−	0.760486i	−0.976410	+	0.215924i	$0.930724\pi$
$908$	−83.3871			−2.76730
$909$	6.83452			0.226687
$910$		0			0
$911$	−40.3959			−1.33838			−0.669188	−	0.743093i	$-0.733358\pi$
$911$	−40.3959			−1.33838			−0.669188	+	0.743093i	$0.733358\pi$
$912$	−9.89809			−0.327758
$913$	−0.223235	−	0.223235i	−0.00738800	−	0.00738800i
$914$	27.8828			0.922282
$915$		0			0
$916$	12.7312	+	12.7312i	0.420650	+	0.420650i
$917$			25.9602i			0.857282i
$918$	16.3576			0.539880
$919$		−	17.0001i		−	0.560783i	−0.959886	−	0.280391i	$-0.909536\pi$
$919$		−	17.0001i		−	0.560783i	0.959886	−	0.280391i	$-0.0904642\pi$
$920$		0			0
$921$	−12.3317	+	12.3317i	−0.406343	+	0.406343i
$922$	−21.9891	−	21.9891i	−0.724173	−	0.724173i
$923$	−11.8243	−	0.831168i	−0.389202	−	0.0273582i
$924$			6.82910i			0.224661i
$925$		0			0
$926$	−39.0709			−1.28395
$927$	8.57596	+	8.57596i	0.281671	+	0.281671i
$928$		−	98.4434i		−	3.23156i
$929$	−42.8153	+	42.8153i	−1.40473	+	1.40473i	−0.620594	+	0.784132i	$0.713108\pi$
$929$	−42.8153	+	42.8153i	−1.40473	+	1.40473i	−0.784132	+	0.620594i	$0.786892\pi$
$930$		0			0
$931$	−1.03444	+	1.03444i	−0.0339025	+	0.0339025i
$932$	−17.8406	+	17.8406i	−0.584390	+	0.584390i
$933$	12.2149	−	12.2149i	0.399899	−	0.399899i
$934$	−70.0821	−	70.0821i	−2.29316	−	2.29316i
$935$		0			0
$936$	−22.5594	−	25.9708i	−0.737379	−	0.848882i
$937$	3.27358	−	3.27358i	0.106943	−	0.106943i	−0.651610	−	0.758554i	$-0.725906\pi$
$937$	3.27358	−	3.27358i	0.106943	−	0.106943i	0.758554	+	0.651610i	$0.225906\pi$
$938$		−	38.7103i		−	1.26394i
$939$			6.81643i			0.222446i
$940$		0			0
$941$	−1.51052	−	1.51052i	−0.0492416	−	0.0492416i	0.682057	−	0.731299i	$-0.261085\pi$
$941$	−1.51052	−	1.51052i	−0.0492416	−	0.0492416i	−0.731299	+	0.682057i	$0.761085\pi$
$942$	23.4576			0.764291
$943$	−60.6315			−1.97443
$944$	−36.5318	−	36.5318i	−1.18901	−	1.18901i
$945$		0			0
$946$		−	2.68854i		−	0.0874118i
$947$			3.23810i			0.105224i	0.998615	+	0.0526120i	$0.0167547\pi$
$947$			3.23810i			0.105224i	−0.998615	+	0.0526120i	$0.983245\pi$
$948$	−49.3346	+	49.3346i	−1.60231	+	1.60231i
$949$	−8.11871	+	7.05229i	−0.263544	+	0.228927i
$950$		0			0
$951$	−4.93890	−	4.93890i	−0.160155	−	0.160155i
$952$	−88.0252	+	88.0252i	−2.85291	+	2.85291i
$953$	13.8263	−	13.8263i	0.447879	−	0.447879i	−0.446770	−	0.894649i	$-0.647426\pi$
$953$	13.8263	−	13.8263i	0.447879	−	0.447879i	0.894649	+	0.446770i	$0.147426\pi$
$954$	−0.760484	+	0.760484i	−0.0246216	+	0.0246216i
$955$		0			0
$956$	−55.2961	+	55.2961i	−1.78840	+	1.78840i
$957$			2.51470i			0.0812887i
$958$	−16.4385	−	16.4385i	−0.531105	−	0.531105i
$959$	−43.9207			−1.41827
$960$		0			0
$961$		−	22.4867i		−	0.725378i
$962$	−29.6419	−	34.1243i	−0.955694	−	1.10021i
$963$	10.1957	+	10.1957i	0.328552	+	0.328552i
$964$	−8.46615	+	8.46615i	−0.272676	+	0.272676i
$965$		0			0
$966$			37.4474i			1.20485i
$967$	−30.3258			−0.975211			−0.487605	−	0.873064i	$-0.662129\pi$
$967$	−30.3258			−0.975211			−0.487605	+	0.873064i	$0.662129\pi$
$968$			101.849i			3.27354i
$969$	2.76496	+	2.76496i	0.0888235	+	0.0888235i
$970$		0			0
$971$	−48.6798			−1.56221			−0.781104	−	0.624401i	$-0.785343\pi$
$971$	−48.6798			−1.56221			−0.781104	+	0.624401i	$0.785343\pi$
$972$	−3.87985	−	3.87985i	−0.124446	−	0.124446i
$973$	−4.26623			−0.136769
$974$	−118.157			−3.78599
$975$		0			0
$976$	−121.927			−3.90278
$977$	27.4765			0.879051			0.439525	−	0.898230i	$-0.355147\pi$
$977$	27.4765			0.879051			0.439525	+	0.898230i	$0.355147\pi$
$978$	2.13166	+	2.13166i	0.0681630	+	0.0681630i
$979$	6.09718			0.194867
$980$		0			0
$981$	−3.71769	−	3.71769i	−0.118697	−	0.118697i
$982$		−	97.3075i		−	3.10521i
$983$	−25.7298			−0.820654			−0.410327	−	0.911938i	$-0.634585\pi$
$983$	−25.7298			−0.820654			−0.410327	+	0.911938i	$0.634585\pi$
$984$			92.2538i			2.94094i
$985$		0			0
$986$	−51.0054	+	51.0054i	−1.62434	+	1.62434i
$987$	−8.16016	−	8.16016i	−0.259741	−	0.259741i
$988$	0.907364	−	12.9083i	0.0288671	−	0.410668i
$989$		−	10.8044i		−	0.343559i
$990$		0			0
$991$	−32.9796			−1.04763			−0.523816	−	0.851831i	$-0.675492\pi$
$991$	−32.9796			−1.04763			−0.523816	+	0.851831i	$0.675492\pi$
$992$	−46.0582	−	46.0582i	−1.46235	−	1.46235i
$993$		−	3.83911i		−	0.121831i
$994$	13.8826	−	13.8826i	0.440330	−	0.440330i
$995$		0			0
$996$	−2.14792	+	2.14792i	−0.0680595	+	0.0680595i
$997$	−37.1254	+	37.1254i	−1.17577	+	1.17577i	−0.194961	+	0.980811i	$0.562458\pi$
$997$	−37.1254	+	37.1254i	−1.17577	+	1.17577i	−0.980811	+	0.194961i	$0.937542\pi$
$998$	22.0529	−	22.0529i	0.698072	−	0.698072i
$999$	−3.23972	−	3.23972i	−0.102500	−	0.102500i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.t.d.268.14		28
5.2	odd	4		975.2.k.d.307.14		28
5.3	odd	4		195.2.k.a.112.1	✓	28
5.4	even	2		195.2.t.a.73.1	yes	28
13.5	odd	4		975.2.k.d.343.1		28
15.8	even	4		585.2.n.g.307.14		28
15.14	odd	2		585.2.w.g.73.14		28
65.18	even	4		195.2.t.a.187.1	yes	28
65.44	odd	4		195.2.k.a.148.14	yes	28
65.57	even	4	inner	975.2.t.d.382.14		28
195.44	even	4		585.2.n.g.343.1		28
195.83	odd	4		585.2.w.g.577.14		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.k.a.112.1	✓	28	5.3	odd	4
195.2.k.a.148.14	yes	28	65.44	odd	4
195.2.t.a.73.1	yes	28	5.4	even	2
195.2.t.a.187.1	yes	28	65.18	even	4
585.2.n.g.307.14		28	15.8	even	4
585.2.n.g.343.1		28	195.44	even	4
585.2.w.g.73.14		28	15.14	odd	2
585.2.w.g.577.14		28	195.83	odd	4
975.2.k.d.307.14		28	5.2	odd	4
975.2.k.d.343.1		28	13.5	odd	4
975.2.t.d.268.14		28	1.1	even	1	trivial
975.2.t.d.382.14		28	65.57	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.73623 q^{2} +(0.707107 + 0.707107i) q^{3} +5.48694 q^{4} +(1.93480 + 1.93480i) q^{6} -2.18253i q^{7} +9.54105 q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+2.73623 q^{2} +(0.707107 + 0.707107i) q^{3} +5.48694 q^{4} +(1.93480 + 1.93480i) q^{6} -2.18253i q^{7} +9.54105 q^{8} +1.00000i q^{9} +(-0.403236 + 0.403236i) q^{11} +(3.87985 + 3.87985i) q^{12} +(-2.72201 + 2.36446i) q^{13} -5.97189i q^{14} +15.1326 q^{16} +(-4.22719 - 4.22719i) q^{17} +2.73623i q^{18} +(-0.462512 + 0.462512i) q^{19} +(1.54328 - 1.54328i) q^{21} +(-1.10334 + 1.10334i) q^{22} +(-4.43399 + 4.43399i) q^{23} +(6.74654 + 6.74654i) q^{24} +(-7.44802 + 6.46971i) q^{26} +(-0.707107 + 0.707107i) q^{27} -11.9754i q^{28} -4.40973i q^{29} +(-2.06316 - 2.06316i) q^{31} +22.3241 q^{32} -0.570261 q^{33} +(-11.5665 - 11.5665i) q^{34} +5.48694i q^{36} +4.58165i q^{37} +(-1.26554 + 1.26554i) q^{38} +(-3.59668 - 0.252821i) q^{39} +(6.83712 + 6.83712i) q^{41} +(4.22276 - 4.22276i) q^{42} +(-1.21836 + 1.21836i) q^{43} +(-2.21253 + 2.21253i) q^{44} +(-12.1324 + 12.1324i) q^{46} -5.28755i q^{47} +(10.7004 + 10.7004i) q^{48} +2.23658 q^{49} -5.97815i q^{51} +(-14.9355 + 12.9737i) q^{52} +(0.277932 + 0.277932i) q^{53} +(-1.93480 + 1.93480i) q^{54} -20.8236i q^{56} -0.654091 q^{57} -12.0660i q^{58} +(-2.41412 - 2.41412i) q^{59} -8.05723 q^{61} +(-5.64528 - 5.64528i) q^{62} +2.18253 q^{63} +30.8186 q^{64} -1.56036 q^{66} +6.48209 q^{67} +(-23.1943 - 23.1943i) q^{68} -6.27061 q^{69} +(2.32466 + 2.32466i) q^{71} +9.54105i q^{72} +2.98262 q^{73} +12.5364i q^{74} +(-2.53777 + 2.53777i) q^{76} +(0.880072 + 0.880072i) q^{77} +(-9.84132 - 0.691776i) q^{78} +12.7156i q^{79} -1.00000 q^{81} +(18.7079 + 18.7079i) q^{82} +0.553610i q^{83} +(8.46788 - 8.46788i) q^{84} +(-3.33370 + 3.33370i) q^{86} +(3.11815 - 3.11815i) q^{87} +(-3.84729 + 3.84729i) q^{88} +(-7.56032 - 7.56032i) q^{89} +(5.16050 + 5.94085i) q^{91} +(-24.3290 + 24.3290i) q^{92} -2.91775i q^{93} -14.4679i q^{94} +(15.7855 + 15.7855i) q^{96} -9.88577 q^{97} +6.11978 q^{98} +(-0.403236 - 0.403236i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} + 28 q^{4} + 12 q^{8}+O(q^{10}) \) 28 * q + 4 * q^2 + 28 * q^4 + 12 * q^8	\( 28 q + 4 q^{2} + 28 q^{4} + 12 q^{8} - 8 q^{11} + 8 q^{12} + 28 q^{16} - 28 q^{17} + 8 q^{21} + 32 q^{22} + 8 q^{23} - 16 q^{31} + 68 q^{32} + 8 q^{33} - 28 q^{34} - 8 q^{39} + 4 q^{41} - 40 q^{44} - 16 q^{46} + 16 q^{48} + 28 q^{49} - 48 q^{52} - 20 q^{53} - 32 q^{59} + 8 q^{61} + 72 q^{62} + 28 q^{64} + 16 q^{66} - 32 q^{67} - 60 q^{68} - 8 q^{69} + 40 q^{71} - 56 q^{73} - 40 q^{76} - 48 q^{77} - 40 q^{78} - 28 q^{81} + 4 q^{82} + 32 q^{84} + 16 q^{86} + 24 q^{87} + 72 q^{88} + 36 q^{89} - 56 q^{91} + 32 q^{92} - 48 q^{97} + 12 q^{98} - 8 q^{99}+O(q^{100}) \) 28 * q + 4 * q^2 + 28 * q^4 + 12 * q^8 - 8 * q^11 + 8 * q^12 + 28 * q^16 - 28 * q^17 + 8 * q^21 + 32 * q^22 + 8 * q^23 - 16 * q^31 + 68 * q^32 + 8 * q^33 - 28 * q^34 - 8 * q^39 + 4 * q^41 - 40 * q^44 - 16 * q^46 + 16 * q^48 + 28 * q^49 - 48 * q^52 - 20 * q^53 - 32 * q^59 + 8 * q^61 + 72 * q^62 + 28 * q^64 + 16 * q^66 - 32 * q^67 - 60 * q^68 - 8 * q^69 + 40 * q^71 - 56 * q^73 - 40 * q^76 - 48 * q^77 - 40 * q^78 - 28 * q^81 + 4 * q^82 + 32 * q^84 + 16 * q^86 + 24 * q^87 + 72 * q^88 + 36 * q^89 - 56 * q^91 + 32 * q^92 - 48 * q^97 + 12 * q^98 - 8 * q^99

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