LMFDB - Embedded newform 585.2.w.g.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(73,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, 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("585.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.w (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:	$4.67124851824$
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			73.2
Character	$\chi$	$=$	585.73
Dual form			585.2.w.g.577.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.21780 q^{2} +2.91862 q^{4} +(1.56243 - 1.59963i) q^{5} -4.11325i q^{7} -2.03732 q^{8} +O(q^{10})$	\(q-2.21780 q^{2} +2.91862 q^{4} +(1.56243 - 1.59963i) q^{5} -4.11325i q^{7} -2.03732 q^{8} +(-3.46515 + 3.54765i) q^{10} +(2.59303 - 2.59303i) q^{11} +(1.47066 - 3.29198i) q^{13} +9.12235i q^{14} -1.31889 q^{16} +(-1.98080 - 1.98080i) q^{17} +(-2.76089 + 2.76089i) q^{19} +(4.56015 - 4.66871i) q^{20} +(-5.75081 + 5.75081i) q^{22} +(-1.53954 + 1.53954i) q^{23} +(-0.117620 - 4.99862i) q^{25} +(-3.26162 + 7.30095i) q^{26} -12.0050i q^{28} +8.40712i q^{29} +(2.11332 + 2.11332i) q^{31} +6.99966 q^{32} +(4.39301 + 4.39301i) q^{34} +(-6.57967 - 6.42667i) q^{35} +7.83564i q^{37} +(6.12310 - 6.12310i) q^{38} +(-3.18317 + 3.25895i) q^{40} +(-1.65250 - 1.65250i) q^{41} +(1.27192 - 1.27192i) q^{43} +(7.56807 - 7.56807i) q^{44} +(3.41439 - 3.41439i) q^{46} -6.35092i q^{47} -9.91882 q^{49} +(0.260858 + 11.0859i) q^{50} +(4.29230 - 9.60806i) q^{52} +(-5.31987 - 5.31987i) q^{53} +(-0.0964538 - 8.19931i) q^{55} +8.38000i q^{56} -18.6453i q^{58} +(-6.51015 - 6.51015i) q^{59} +7.84876 q^{61} +(-4.68691 - 4.68691i) q^{62} -12.8861 q^{64} +(-2.96815 - 7.49601i) q^{65} -12.3496 q^{67} +(-5.78120 - 5.78120i) q^{68} +(14.5924 + 14.2530i) q^{70} +(7.75627 + 7.75627i) q^{71} +5.27944 q^{73} -17.3779i q^{74} +(-8.05801 + 8.05801i) q^{76} +(-10.6658 - 10.6658i) q^{77} -8.45538i q^{79} +(-2.06067 + 2.10973i) q^{80} +(3.66491 + 3.66491i) q^{82} -4.49388i q^{83} +(-6.26340 + 0.0736805i) q^{85} +(-2.82085 + 2.82085i) q^{86} +(-5.28283 + 5.28283i) q^{88} +(8.91884 + 8.91884i) q^{89} +(-13.5408 - 6.04919i) q^{91} +(-4.49334 + 4.49334i) q^{92} +14.0850i q^{94} +(0.102698 + 8.73011i) q^{95} +17.6029 q^{97} +21.9979 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} + 28 q^{4} + 4 q^{5} + 12 q^{8}+O(q^{10}) $ 28 * q + 4 * q^2 + 28 * q^4 + 4 * q^5 + 12 * q^8	$ 28 q + 4 q^{2} + 28 q^{4} + 4 q^{5} + 12 q^{8} + 8 q^{11} + 28 q^{16} - 28 q^{17} - 12 q^{20} - 32 q^{22} + 8 q^{23} + 4 q^{25} - 16 q^{31} + 68 q^{32} - 28 q^{34} - 48 q^{40} - 4 q^{41} + 40 q^{44} - 16 q^{46} + 28 q^{49} - 4 q^{50} + 48 q^{52} - 20 q^{53} - 8 q^{55} + 32 q^{59} + 8 q^{61} + 72 q^{62} + 28 q^{64} - 64 q^{65} + 32 q^{67} - 60 q^{68} - 16 q^{70} - 40 q^{71} + 56 q^{73} - 40 q^{76} - 48 q^{77} + 12 q^{80} - 4 q^{82} + 44 q^{85} - 16 q^{86} - 72 q^{88} - 36 q^{89} - 56 q^{91} + 32 q^{92} + 56 q^{95} + 48 q^{97} + 12 q^{98}+O(q^{100}) $ 28 * q + 4 * q^2 + 28 * q^4 + 4 * q^5 + 12 * q^8 + 8 * q^11 + 28 * q^16 - 28 * q^17 - 12 * q^20 - 32 * q^22 + 8 * q^23 + 4 * q^25 - 16 * q^31 + 68 * q^32 - 28 * q^34 - 48 * q^40 - 4 * q^41 + 40 * q^44 - 16 * q^46 + 28 * q^49 - 4 * q^50 + 48 * q^52 - 20 * q^53 - 8 * q^55 + 32 * q^59 + 8 * q^61 + 72 * q^62 + 28 * q^64 - 64 * q^65 + 32 * q^67 - 60 * q^68 - 16 * q^70 - 40 * q^71 + 56 * q^73 - 40 * q^76 - 48 * q^77 + 12 * q^80 - 4 * q^82 + 44 * q^85 - 16 * q^86 - 72 * q^88 - 36 * q^89 - 56 * q^91 + 32 * q^92 + 56 * q^95 + 48 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−2.21780			−1.56822			−0.784110	−	0.620622i	$-0.786880\pi$
$2$	−2.21780			−1.56822			−0.784110	+	0.620622i	$0.786880\pi$
$3$		0			0
$3$		0			0
$4$	2.91862			1.45931
$5$	1.56243	−	1.59963i	0.698740	−	0.715375i
$5$	1.56243	−	1.59963i	0.698740	−	0.715375i
$6$		0			0
$7$		−	4.11325i		−	1.55466i	−0.629092	−	0.777331i	$-0.716573\pi$
$7$		−	4.11325i		−	1.55466i	0.629092	−	0.777331i	$-0.283427\pi$
$8$	−2.03732			−0.720301
$9$		0			0
$10$	−3.46515	+	3.54765i	−1.09578	+	1.12187i
$11$	2.59303	−	2.59303i	0.781827	−	0.781827i	−0.198312	−	0.980139i	$-0.563546\pi$
$11$	2.59303	−	2.59303i	0.781827	−	0.781827i	0.980139	+	0.198312i	$0.0635458\pi$
$12$		0			0
$13$	1.47066	−	3.29198i	0.407887	−	0.913032i
$13$	1.47066	−	3.29198i	0.407887	−	0.913032i
$14$			9.12235i			2.43805i
$15$		0			0
$16$	−1.31889			−0.329721
$17$	−1.98080	−	1.98080i	−0.480414	−	0.480414i	0.424850	−	0.905264i	$-0.360327\pi$
$17$	−1.98080	−	1.98080i	−0.480414	−	0.480414i	−0.905264	+	0.424850i	$0.860327\pi$
$18$		0			0
$19$	−2.76089	+	2.76089i	−0.633393	+	0.633393i	−0.948917	−	0.315525i	$-0.897819\pi$
$19$	−2.76089	+	2.76089i	−0.633393	+	0.633393i	0.315525	+	0.948917i	$0.397819\pi$
$20$	4.56015	−	4.66871i	1.01968	−	1.04396i
$21$		0			0
$22$	−5.75081	+	5.75081i	−1.22608	+	1.22608i
$23$	−1.53954	+	1.53954i	−0.321017	+	0.321017i	−0.849157	−	0.528140i	$-0.822890\pi$
$23$	−1.53954	+	1.53954i	−0.321017	+	0.321017i	0.528140	+	0.849157i	$0.322890\pi$
$24$		0			0
$25$	−0.117620	−	4.99862i	−0.0235241	−	0.999723i
$26$	−3.26162	+	7.30095i	−0.639657	+	1.43183i
$27$		0			0
$28$		−	12.0050i		−	2.26874i
$29$			8.40712i			1.56116i	0.625054	+	0.780582i	$0.285077\pi$
$29$			8.40712i			1.56116i	−0.625054	+	0.780582i	$0.714923\pi$
$30$		0			0
$31$	2.11332	+	2.11332i	0.379563	+	0.379563i	0.870944	−	0.491381i	$-0.163508\pi$
$31$	2.11332	+	2.11332i	0.379563	+	0.379563i	−0.491381	+	0.870944i	$0.663508\pi$
$32$	6.99966			1.23738
$33$		0			0
$34$	4.39301	+	4.39301i	0.753395	+	0.753395i
$35$	−6.57967	−	6.42667i	−1.11217	−	1.08631i
$36$		0			0
$37$			7.83564i			1.28817i	0.764953	+	0.644086i	$0.222762\pi$
$37$			7.83564i			1.28817i	−0.764953	+	0.644086i	$0.777238\pi$
$38$	6.12310	−	6.12310i	0.993299	−	0.993299i
$39$		0			0
$40$	−3.18317	+	3.25895i	−0.503304	+	0.515286i
$41$	−1.65250	−	1.65250i	−0.258077	−	0.258077i	0.566195	−	0.824272i	$-0.308415\pi$
$41$	−1.65250	−	1.65250i	−0.258077	−	0.258077i	−0.824272	+	0.566195i	$0.808415\pi$
$42$		0			0
$43$	1.27192	−	1.27192i	0.193965	−	0.193965i	−0.603442	−	0.797407i	$-0.706204\pi$
$43$	1.27192	−	1.27192i	0.193965	−	0.193965i	0.797407	+	0.603442i	$0.206204\pi$
$44$	7.56807	−	7.56807i	1.14093	−	1.14093i
$45$		0			0
$46$	3.41439	−	3.41439i	0.503425	−	0.503425i
$47$		−	6.35092i		−	0.926376i	−0.886260	−	0.463188i	$-0.846705\pi$
$47$		−	6.35092i		−	0.926376i	0.886260	−	0.463188i	$-0.153295\pi$
$48$		0			0
$49$	−9.91882			−1.41697
$50$	0.260858	+	11.0859i	0.0368909	+	1.56779i
$51$		0			0
$52$	4.29230	−	9.60806i	0.595235	−	1.33240i
$53$	−5.31987	−	5.31987i	−0.730740	−	0.730740i	0.240027	−	0.970766i	$-0.422844\pi$
$53$	−5.31987	−	5.31987i	−0.730740	−	0.730740i	−0.970766	+	0.240027i	$0.922844\pi$
$54$		0			0
$55$	−0.0964538	−	8.19931i	−0.0130058	−	1.10559i
$56$			8.38000i			1.11983i
$57$		0			0
$58$		−	18.6453i		−	2.44825i
$59$	−6.51015	−	6.51015i	−0.847550	−	0.847550i	0.142277	−	0.989827i	$-0.454558\pi$
$59$	−6.51015	−	6.51015i	−0.847550	−	0.847550i	−0.989827	+	0.142277i	$0.954558\pi$
$60$		0			0
$61$	7.84876			1.00493			0.502465	−	0.864597i	$-0.332426\pi$
$61$	7.84876			1.00493			0.502465	+	0.864597i	$0.332426\pi$
$62$	−4.68691	−	4.68691i	−0.595238	−	0.595238i
$63$		0			0
$64$	−12.8861			−1.61076
$65$	−2.96815	−	7.49601i	−0.368154	−	0.929765i
$66$		0			0
$67$	−12.3496			−1.50874			−0.754372	−	0.656447i	$-0.772058\pi$
$67$	−12.3496			−1.50874			−0.754372	+	0.656447i	$0.772058\pi$
$68$	−5.78120	−	5.78120i	−0.701074	−	0.701074i
$69$		0			0
$70$	14.5924	+	14.2530i	1.74412	+	1.70356i
$71$	7.75627	+	7.75627i	0.920500	+	0.920500i	0.997065	−	0.0765650i	$-0.0243953\pi$
$71$	7.75627	+	7.75627i	0.920500	+	0.920500i	−0.0765650	+	0.997065i	$0.524395\pi$
$72$		0			0
$73$	5.27944			0.617912			0.308956	−	0.951076i	$-0.400020\pi$
$73$	5.27944			0.617912			0.308956	+	0.951076i	$0.400020\pi$
$74$		−	17.3779i		−	2.02014i
$75$		0			0
$76$	−8.05801	+	8.05801i	−0.924317	+	0.924317i
$77$	−10.6658	−	10.6658i	−1.21548	−	1.21548i
$78$		0			0
$79$		−	8.45538i		−	0.951305i	−0.879633	−	0.475653i	$-0.842212\pi$
$79$		−	8.45538i		−	0.951305i	0.879633	−	0.475653i	$-0.157788\pi$
$80$	−2.06067	+	2.10973i	−0.230390	+	0.235874i
$81$		0			0
$82$	3.66491	+	3.66491i	0.404722	+	0.404722i
$83$		−	4.49388i		−	0.493267i	−0.969109	−	0.246634i	$-0.920676\pi$
$83$		−	4.49388i		−	0.493267i	0.969109	−	0.246634i	$-0.0793244\pi$
$84$		0			0
$85$	−6.26340	+	0.0736805i	−0.679361	+	0.00799177i
$86$	−2.82085	+	2.82085i	−0.304180	+	0.304180i
$87$		0			0
$88$	−5.28283	+	5.28283i	−0.563151	+	0.563151i
$89$	8.91884	+	8.91884i	0.945395	+	0.945395i	0.998584	−	0.0531890i	$-0.0169386\pi$
$89$	8.91884	+	8.91884i	0.945395	+	0.945395i	−0.0531890	+	0.998584i	$0.516939\pi$
$90$		0			0
$91$	−13.5408	−	6.04919i	−1.41946	−	0.634127i
$92$	−4.49334	+	4.49334i	−0.468464	+	0.468464i
$93$		0			0
$94$			14.0850i			1.45276i
$95$	0.102698	+	8.73011i	0.0105366	+	0.895691i
$96$		0			0
$97$	17.6029			1.78730			0.893650	−	0.448765i	$-0.148136\pi$
$97$	17.6029			1.78730			0.893650	+	0.448765i	$0.148136\pi$
$98$	21.9979			2.22213
$99$		0			0
$100$	−0.343289	−	14.5891i	−0.0343289	−	1.45891i
$101$		−	4.66632i		−	0.464316i	−0.972678	−	0.232158i	$-0.925421\pi$
$101$		−	4.66632i		−	0.464316i	0.972678	−	0.232158i	$-0.0745787\pi$
$102$		0			0
$103$	−2.08089	+	2.08089i	−0.205036	+	0.205036i	−0.802154	−	0.597118i	$-0.796313\pi$
$103$	−2.08089	+	2.08089i	−0.205036	+	0.205036i	0.597118	+	0.802154i	$0.296313\pi$
$104$	−2.99620	+	6.70683i	−0.293802	+	0.657658i
$105$		0			0
$106$	11.7984	+	11.7984i	1.14596	+	1.14596i
$107$	−1.71214	+	1.71214i	−0.165519	+	0.165519i	−0.785006	−	0.619488i	$-0.787340\pi$
$107$	−1.71214	+	1.71214i	−0.165519	+	0.165519i	0.619488	+	0.785006i	$0.287340\pi$
$108$		0			0
$109$	4.77725	−	4.77725i	0.457578	−	0.457578i	−0.440282	−	0.897860i	$-0.645121\pi$
$109$	4.77725	−	4.77725i	0.457578	−	0.457578i	0.897860	+	0.440282i	$0.145121\pi$
$110$	0.213915	+	18.1844i	0.0203960	+	1.73381i
$111$		0			0
$112$			5.42490i			0.512605i
$113$	1.95021	+	1.95021i	0.183460	+	0.183460i	0.792862	−	0.609402i	$-0.208590\pi$
$113$	1.95021	+	1.95021i	0.183460	+	0.183460i	−0.609402	+	0.792862i	$0.708590\pi$
$114$		0			0
$115$	0.0572669	+	4.86812i	0.00534017	+	0.453955i
$116$			24.5372i			2.27822i
$117$		0			0
$118$	14.4382	+	14.4382i	1.32914	+	1.32914i
$119$	−8.14752	+	8.14752i	−0.746882	+	0.746882i
$120$		0			0
$121$		−	2.44759i		−	0.222508i
$122$	−17.4070			−1.57595
$123$		0			0
$124$	6.16798	+	6.16798i	0.553901	+	0.553901i
$125$	−8.17970	−	7.62184i	−0.731615	−	0.681718i
$126$		0			0
$127$	−4.33250	−	4.33250i	−0.384447	−	0.384447i	0.488254	−	0.872701i	$-0.337634\pi$
$127$	−4.33250	−	4.33250i	−0.384447	−	0.384447i	−0.872701	+	0.488254i	$0.837634\pi$
$128$	14.5793			1.28864
$129$		0			0
$130$	6.58275	+	16.6246i	0.577345	+	1.45808i
$131$	11.7646			1.02788			0.513939	−	0.857827i	$-0.328186\pi$
$131$	11.7646			1.02788			0.513939	+	0.857827i	$0.328186\pi$
$132$		0			0
$133$	11.3562	+	11.3562i	0.984712	+	0.984712i
$134$	27.3889			2.36604
$135$		0			0
$136$	4.03552	+	4.03552i	0.346043	+	0.346043i
$137$			12.3668i			1.05657i	0.849067	+	0.528286i	$0.177165\pi$
$137$			12.3668i			1.05657i	−0.849067	+	0.528286i	$0.822835\pi$
$138$		0			0
$139$		−	15.1730i		−	1.28695i	−0.765466	−	0.643477i	$-0.777491\pi$
$139$		−	15.1730i		−	1.28695i	0.765466	−	0.643477i	$-0.222509\pi$
$140$	−19.2036	−	18.7570i	−1.62300	−	1.58526i
$141$		0			0
$142$	−17.2018	−	17.2018i	−1.44355	−	1.44355i
$143$	−4.72275	−	12.3497i	−0.394936	−	1.03273i
$144$		0			0
$145$	13.4483	+	13.1355i	1.11682	+	1.09085i
$146$	−11.7087			−0.969022
$147$		0			0
$148$			22.8693i			1.87984i
$149$	6.53739	−	6.53739i	0.535564	−	0.535564i	−0.386659	−	0.922223i	$-0.626371\pi$
$149$	6.53739	−	6.53739i	0.535564	−	0.535564i	0.922223	+	0.386659i	$0.126371\pi$
$150$		0			0
$151$	2.56165	−	2.56165i	0.208464	−	0.208464i	−0.595150	−	0.803614i	$-0.702907\pi$
$151$	2.56165	−	2.56165i	0.208464	−	0.208464i	0.803614	+	0.595150i	$0.202907\pi$
$152$	5.62483	−	5.62483i	0.456234	−	0.456234i
$153$		0			0
$154$	23.6545	+	23.6545i	1.90613	+	1.90613i
$155$	6.68243	−	0.0786099i	0.536746	−	0.00631410i
$156$		0			0
$157$	−2.92797	+	2.92797i	−0.233678	+	0.233678i	−0.814226	−	0.580548i	$-0.802838\pi$
$157$	−2.92797	+	2.92797i	−0.233678	+	0.233678i	0.580548	+	0.814226i	$0.302838\pi$
$158$			18.7523i			1.49185i
$159$		0			0
$160$	10.9365	−	11.1969i	0.864605	−	0.885189i
$161$	6.33252	+	6.33252i	0.499073	+	0.499073i
$162$		0			0
$163$	8.49438			0.665331			0.332666	−	0.943045i	$-0.392052\pi$
$163$	8.49438			0.665331			0.332666	+	0.943045i	$0.392052\pi$
$164$	−4.82302	−	4.82302i	−0.376615	−	0.376615i
$165$		0			0
$166$			9.96651i			0.773551i
$167$			13.2559i			1.02577i	0.858457	+	0.512886i	$0.171424\pi$
$167$			13.2559i			1.02577i	−0.858457	+	0.512886i	$0.828576\pi$
$168$		0			0
$169$	−8.67432	−	9.68277i	−0.667256	−	0.744829i
$170$	13.8910	−	0.163408i	1.06539	−	0.0125329i
$171$		0			0
$172$	3.71224	−	3.71224i	0.283056	−	0.283056i
$173$	−7.94523	+	7.94523i	−0.604065	+	0.604065i	−0.941389	−	0.337324i	$-0.890478\pi$
$173$	−7.94523	+	7.94523i	−0.604065	+	0.604065i	0.337324	+	0.941389i	$0.390478\pi$
$174$		0			0
$175$	−20.5606	+	0.483802i	−1.55423	+	0.0365720i
$176$	−3.41991	+	3.41991i	−0.257785	+	0.257785i
$177$		0			0
$178$	−19.7802	−	19.7802i	−1.48259	−	1.48259i
$179$	1.37631			0.102870			0.0514350	−	0.998676i	$-0.483621\pi$
$179$	1.37631			0.102870			0.0514350	+	0.998676i	$0.483621\pi$
$180$		0			0
$181$			23.4687i			1.74442i	0.489136	+	0.872208i	$0.337312\pi$
$181$			23.4687i			1.74442i	−0.489136	+	0.872208i	$0.662688\pi$
$182$	30.0306	+	13.4159i	2.22602	+	0.994450i
$183$		0			0
$184$	3.13654	−	3.13654i	0.231229	−	0.231229i
$185$	12.5341	+	12.2427i	0.921527	+	0.900098i
$186$		0			0
$187$	−10.2725			−0.751202
$188$		−	18.5359i		−	1.35187i
$189$		0			0
$190$	−0.227763	−	19.3616i	−0.0165237	−	1.40464i
$191$	2.92479			0.211630			0.105815	−	0.994386i	$-0.466255\pi$
$191$	2.92479			0.211630			0.105815	+	0.994386i	$0.466255\pi$
$192$		0			0
$193$	−20.6977			−1.48985			−0.744927	−	0.667146i	$-0.767516\pi$
$193$	−20.6977			−1.48985			−0.744927	+	0.667146i	$0.767516\pi$
$194$	−39.0396			−2.80288
$195$		0			0
$196$	−28.9493			−2.06781
$197$	6.16201			0.439025			0.219513	−	0.975610i	$-0.429553\pi$
$197$	6.16201			0.439025			0.219513	+	0.975610i	$0.429553\pi$
$198$		0			0
$199$	−23.2876			−1.65081			−0.825407	−	0.564538i	$-0.809054\pi$
$199$	−23.2876			−1.65081			−0.825407	+	0.564538i	$0.809054\pi$
$200$	0.239630	+	10.1838i	0.0169444	+	0.720102i
$201$		0			0
$202$			10.3489i			0.728150i
$203$	34.5806			2.42708
$204$		0			0
$205$	−5.22530	+	0.0614687i	−0.364951	+	0.00429316i
$206$	4.61499	−	4.61499i	0.321542	−	0.321542i
$207$		0			0
$208$	−1.93963	+	4.34175i	−0.134489	+	0.301046i
$209$			14.3182i			0.990407i
$210$		0			0
$211$	11.6786			0.803990			0.401995	−	0.915642i	$-0.368317\pi$
$211$	11.6786			0.803990			0.401995	+	0.915642i	$0.368317\pi$
$212$	−15.5267	−	15.5267i	−1.06638	−	1.06638i
$213$		0			0
$214$	3.79718	−	3.79718i	0.259570	−	0.259570i
$215$	−0.0473119	−	4.02187i	−0.00322665	−	0.274289i
$216$		0			0
$217$	8.69260	−	8.69260i	0.590092	−	0.590092i
$218$	−10.5950	+	10.5950i	−0.717583	+	0.717583i
$219$		0			0
$220$	−0.281512	−	23.9307i	−0.0189796	−	1.61341i
$221$	−9.43384	+	3.60768i	−0.634588	+	0.242679i
$222$		0			0
$223$		−	16.7954i		−	1.12470i	−0.826898	−	0.562351i	$-0.809897\pi$
$223$		−	16.7954i		−	1.12470i	0.826898	−	0.562351i	$-0.190103\pi$
$224$		−	28.7913i		−	1.92370i
$225$		0			0
$226$	−4.32517	−	4.32517i	−0.287706	−	0.287706i
$227$	22.2305			1.47549			0.737746	−	0.675078i	$-0.235890\pi$
$227$	22.2305			1.47549			0.737746	+	0.675078i	$0.235890\pi$
$228$		0			0
$229$	−1.99942	−	1.99942i	−0.132125	−	0.132125i	0.637951	−	0.770077i	$-0.279782\pi$
$229$	−1.99942	−	1.99942i	−0.132125	−	0.132125i	−0.770077	+	0.637951i	$0.779782\pi$
$230$	−0.127006	−	10.7965i	−0.00837456	−	0.711901i
$231$		0			0
$232$		−	17.1280i		−	1.12451i
$233$	−7.60402	+	7.60402i	−0.498156	+	0.498156i	−0.910863	−	0.412708i	$-0.864583\pi$
$233$	−7.60402	+	7.60402i	−0.498156	+	0.498156i	0.412708	+	0.910863i	$0.364583\pi$
$234$		0			0
$235$	−10.1591	−	9.92287i	−0.662707	−	0.647296i
$236$	−19.0007	−	19.0007i	−1.23684	−	1.23684i
$237$		0			0
$238$	18.0695	−	18.0695i	1.17127	−	1.17127i
$239$	17.2164	−	17.2164i	1.11363	−	1.11363i	0.120979	−	0.992655i	$-0.461397\pi$
$239$	17.2164	−	17.2164i	1.11363	−	1.11363i	0.992655	−	0.120979i	$-0.0386034\pi$
$240$		0			0
$241$	10.2155	−	10.2155i	0.658040	−	0.658040i	−0.296876	−	0.954916i	$-0.595945\pi$
$241$	10.2155	−	10.2155i	0.658040	−	0.658040i	0.954916	+	0.296876i	$0.0959447\pi$
$242$			5.42825i			0.348941i
$243$		0			0
$244$	22.9076			1.46651
$245$	−15.4975	+	15.8664i	−0.990097	+	1.01367i
$246$		0			0
$247$	5.02849	+	13.1492i	0.319955	+	0.836661i
$248$	−4.30550	−	4.30550i	−0.273400	−	0.273400i
$249$		0			0
$250$	18.1409	+	16.9037i	1.14733	+	1.06908i
$251$		−	18.7574i		−	1.18396i	−0.805954	−	0.591978i	$-0.798347\pi$
$251$		−	18.7574i		−	1.18396i	0.805954	−	0.591978i	$-0.201653\pi$
$252$		0			0
$253$			7.98415i			0.501959i
$254$	9.60860	+	9.60860i	0.602897	+	0.602897i
$255$		0			0
$256$	−6.56189			−0.410118
$257$	1.40078	+	1.40078i	0.0873784	+	0.0873784i	0.749445	−	0.662067i	$-0.230320\pi$
$257$	1.40078	+	1.40078i	0.0873784	+	0.0873784i	−0.662067	+	0.749445i	$0.730320\pi$
$258$		0			0
$259$	32.2300			2.00267
$260$	−8.66291	−	21.8780i	−0.537251	−	1.35682i
$261$		0			0
$262$	−26.0915			−1.61194
$263$	−15.8782	−	15.8782i	−0.979092	−	0.979092i	0.0206938	−	0.999786i	$-0.493413\pi$
$263$	−15.8782	−	15.8782i	−0.979092	−	0.979092i	−0.999786	+	0.0206938i	$0.993413\pi$
$264$		0			0
$265$	−16.8217	+	0.197885i	−1.03335	+	0.0121560i
$266$	−25.1859	−	25.1859i	−1.54424	−	1.54424i
$267$		0			0
$268$	−36.0438			−2.20173
$269$		−	0.349269i		−	0.0212953i	−0.999943	−	0.0106477i	$-0.996611\pi$
$269$		−	0.349269i		−	0.0212953i	0.999943	−	0.0106477i	$-0.00338932\pi$
$270$		0			0
$271$	8.52139	−	8.52139i	0.517637	−	0.517637i	−0.399218	−	0.916856i	$-0.630719\pi$
$271$	8.52139	−	8.52139i	0.517637	−	0.517637i	0.916856	+	0.399218i	$0.130719\pi$
$272$	2.61245	+	2.61245i	0.158403	+	0.158403i
$273$		0			0
$274$		−	27.4272i		−	1.65694i
$275$	−13.2665	−	12.6566i	−0.800003	−	0.763219i
$276$		0			0
$277$	5.27671	+	5.27671i	0.317047	+	0.317047i	0.847632	−	0.530585i	$-0.178028\pi$
$277$	5.27671	+	5.27671i	0.317047	+	0.317047i	−0.530585	+	0.847632i	$0.678028\pi$
$278$			33.6505i			2.01823i
$279$		0			0
$280$	13.4049	+	13.0932i	0.801095	+	0.782467i
$281$	5.98480	−	5.98480i	0.357023	−	0.357023i	−0.505691	−	0.862714i	$-0.668763\pi$
$281$	5.98480	−	5.98480i	0.357023	−	0.357023i	0.862714	+	0.505691i	$0.168763\pi$
$282$		0			0
$283$	2.56174	−	2.56174i	0.152280	−	0.152280i	−0.626856	−	0.779135i	$-0.715658\pi$
$283$	2.56174	−	2.56174i	0.152280	−	0.152280i	0.779135	+	0.626856i	$0.215658\pi$
$284$	22.6376	+	22.6376i	1.34330	+	1.34330i
$285$		0			0
$286$	10.4741	+	27.3891i	0.619346	+	1.61955i
$287$	−6.79714	+	6.79714i	−0.401223	+	0.401223i
$288$		0			0
$289$		−	9.15288i		−	0.538404i
$290$	−29.8255	−	29.1320i	−1.75142	−	1.71069i
$291$		0			0
$292$	15.4087			0.901727
$293$	−5.91537			−0.345579			−0.172790	−	0.984959i	$-0.555278\pi$
$293$	−5.91537			−0.345579			−0.172790	+	0.984959i	$0.555278\pi$
$294$		0			0
$295$	−20.5855	+	0.242161i	−1.19853	+	0.0140991i
$296$		−	15.9637i		−	0.927872i
$297$		0			0
$298$	−14.4986	+	14.4986i	−0.839882	+	0.839882i
$299$	2.80401	+	7.33229i	0.162160	+	0.424037i
$300$		0			0
$301$	−5.23170	−	5.23170i	−0.301550	−	0.301550i
$302$	−5.68122	+	5.68122i	−0.326918	+	0.326918i
$303$		0			0
$304$	3.64130	−	3.64130i	0.208843	−	0.208843i
$305$	12.2631	−	12.5551i	0.702186	−	0.718903i
$306$		0			0
$307$			2.81730i			0.160792i	0.996763	+	0.0803960i	$0.0256185\pi$
$307$			2.81730i			0.160792i	−0.996763	+	0.0803960i	$0.974382\pi$
$308$	−31.1294	−	31.1294i	−1.77376	−	1.77376i
$309$		0			0
$310$	−14.8203	+	0.174341i	−0.841735	+	0.00990189i
$311$			9.18067i			0.520588i	0.965529	+	0.260294i	$0.0838195\pi$
$311$			9.18067i			0.520588i	−0.965529	+	0.260294i	$0.916180\pi$
$312$		0			0
$313$	16.4881	+	16.4881i	0.931960	+	0.931960i	0.997828	−	0.0658683i	$-0.0209817\pi$
$313$	16.4881	+	16.4881i	0.931960	+	0.931960i	−0.0658683	+	0.997828i	$0.520982\pi$
$314$	6.49365	−	6.49365i	0.366458	−	0.366458i
$315$		0			0
$316$		−	24.6781i		−	1.38825i
$317$	−13.3835			−0.751695			−0.375847	−	0.926682i	$-0.622648\pi$
$317$	−13.3835			−0.751695			−0.375847	+	0.926682i	$0.622648\pi$
$318$		0			0
$319$	21.7999	+	21.7999i	1.22056	+	1.22056i
$320$	−20.1336	+	20.6129i	−1.12550	+	1.15230i
$321$		0			0
$322$	−14.0442	−	14.0442i	−0.782655	−	0.782655i
$323$	10.9376			0.608582
$324$		0			0
$325$	−16.6283	−	6.96406i	−0.922375	−	0.386296i
$326$	−18.8388			−1.04339
$327$		0			0
$328$	3.36667	+	3.36667i	0.185893	+	0.185893i
$329$	−26.1229			−1.44020
$330$		0			0
$331$	−13.7828	−	13.7828i	−0.757572	−	0.757572i	0.218308	−	0.975880i	$-0.429946\pi$
$331$	−13.7828	−	13.7828i	−0.757572	−	0.757572i	−0.975880	+	0.218308i	$0.929946\pi$
$332$		−	13.1159i		−	0.719831i
$333$		0			0
$334$		−	29.3989i		−	1.60863i
$335$	−19.2954	+	19.7548i	−1.05422	+	1.07932i
$336$		0			0
$337$	24.8025	+	24.8025i	1.35108	+	1.35108i	0.884459	+	0.466618i	$0.154528\pi$
$337$	24.8025	+	24.8025i	1.35108	+	1.35108i	0.466618	+	0.884459i	$0.345472\pi$
$338$	19.2379	+	21.4744i	1.04640	+	1.16805i
$339$		0			0
$340$	−18.2805	+	0.215046i	−0.991400	+	0.0116625i
$341$	10.9598			0.593506
$342$		0			0
$343$			12.0058i			0.648254i
$344$	−2.59130	+	2.59130i	−0.139713	+	0.139713i
$345$		0			0
$346$	17.6209	−	17.6209i	0.947306	−	0.947306i
$347$	−2.24725	+	2.24725i	−0.120639	+	0.120639i	−0.764849	−	0.644210i	$-0.777186\pi$
$347$	−2.24725	+	2.24725i	−0.120639	+	0.120639i	0.644210	+	0.764849i	$0.277186\pi$
$348$		0			0
$349$	19.2780	+	19.2780i	1.03193	+	1.03193i	0.999473	+	0.0324525i	$0.0103318\pi$
$349$	19.2780	+	19.2780i	1.03193	+	1.03193i	0.0324525	+	0.999473i	$0.489668\pi$
$350$	45.5991	−	1.07297i	2.43738	−	0.0573529i
$351$		0			0
$352$	18.1503	−	18.1503i	0.967415	−	0.967415i
$353$		−	20.5850i		−	1.09563i	−0.836600	−	0.547814i	$-0.815460\pi$
$353$		−	20.5850i		−	1.09563i	0.836600	−	0.547814i	$-0.184540\pi$
$354$		0			0
$355$	24.5258	−	0.288513i	1.30169	−	0.0153127i
$356$	26.0307	+	26.0307i	1.37963	+	1.37963i
$357$		0			0
$358$	−3.05237			−0.161323
$359$	−10.6029	−	10.6029i	−0.559602	−	0.559602i	0.369592	−	0.929194i	$-0.379497\pi$
$359$	−10.6029	−	10.6029i	−0.559602	−	0.559602i	−0.929194	+	0.369592i	$0.879497\pi$
$360$		0			0
$361$			3.75492i			0.197627i
$362$		−	52.0488i		−	2.73563i
$363$		0			0
$364$	−39.5204	−	17.6553i	−2.07143	−	0.925389i
$365$	8.24877	−	8.44515i	0.431760	−	0.442039i
$366$		0			0
$367$	−1.02534	+	1.02534i	−0.0535221	+	0.0535221i	−0.733361	−	0.679839i	$-0.762050\pi$
$367$	−1.02534	+	1.02534i	−0.0535221	+	0.0535221i	0.679839	+	0.733361i	$0.262050\pi$
$368$	2.03048	−	2.03048i	0.105846	−	0.105846i
$369$		0			0
$370$	−27.7981	−	27.1517i	−1.44516	−	1.41155i
$371$	−21.8819	+	21.8819i	−1.13605	+	1.13605i
$372$		0			0
$373$	8.41567	+	8.41567i	0.435747	+	0.435747i	0.890578	−	0.454831i	$-0.150300\pi$
$373$	8.41567	+	8.41567i	0.435747	+	0.435747i	−0.454831	+	0.890578i	$0.650300\pi$
$374$	22.7824			1.17805
$375$		0			0
$376$			12.9388i			0.667270i
$377$	27.6761	+	12.3640i	1.42539	+	0.636779i
$378$		0			0
$379$	−5.03557	+	5.03557i	−0.258660	+	0.258660i	−0.824509	−	0.565849i	$-0.808548\pi$
$379$	−5.03557	+	5.03557i	−0.258660	+	0.258660i	0.565849	+	0.824509i	$0.308548\pi$
$380$	0.299737	+	25.4799i	0.0153762	+	1.30709i
$381$		0			0
$382$	−6.48659			−0.331883
$383$			0.483559i			0.0247087i	0.999924	+	0.0123543i	$0.00393261\pi$
$383$			0.483559i			0.0247087i	−0.999924	+	0.0123543i	$0.996067\pi$
$384$		0			0
$385$	−33.7258	+	0.396739i	−1.71883	+	0.0202197i
$386$	45.9033			2.33642
$387$		0			0
$388$	51.3761			2.60823
$389$	−17.5944			−0.892070			−0.446035	−	0.895015i	$-0.647164\pi$
$389$	−17.5944			−0.892070			−0.446035	+	0.895015i	$0.647164\pi$
$390$		0			0
$391$	6.09905			0.308442
$392$	20.2078			1.02065
$393$		0			0
$394$	−13.6661			−0.688488
$395$	−13.5255	−	13.2110i	−0.680540	−	0.664715i
$396$		0			0
$397$			9.63810i			0.483722i	0.970311	+	0.241861i	$0.0777578\pi$
$397$			9.63810i			0.483722i	−0.970311	+	0.241861i	$0.922242\pi$
$398$	51.6472			2.58884
$399$		0			0
$400$	0.155128	+	6.59260i	0.00775638	+	0.329630i
$401$	16.8784	−	16.8784i	0.842865	−	0.842865i	−0.146365	−	0.989231i	$-0.546757\pi$
$401$	16.8784	−	16.8784i	0.842865	−	0.842865i	0.989231	+	0.146365i	$0.0467575\pi$
$402$		0			0
$403$	10.0650	−	3.84904i	0.501372	−	0.191734i
$404$		−	13.6192i		−	0.677582i
$405$		0			0
$406$	−76.6927			−3.80620
$407$	20.3180	+	20.3180i	1.00713	+	1.00713i
$408$		0			0
$409$	−3.65546	+	3.65546i	−0.180751	+	0.180751i	−0.791683	−	0.610932i	$-0.790795\pi$
$409$	−3.65546	+	3.65546i	−0.180751	+	0.180751i	0.610932	+	0.791683i	$0.290795\pi$
$410$	11.5887	−	0.136325i	0.572323	−	0.00673261i
$411$		0			0
$412$	−6.07334	+	6.07334i	−0.299212	+	0.299212i
$413$	−26.7779	+	26.7779i	−1.31765	+	1.31765i
$414$		0			0
$415$	−7.18853	−	7.02137i	−0.352871	−	0.344666i
$416$	10.2941	−	23.0428i	0.504710	−	1.12976i
$417$		0			0
$418$		−	31.7548i		−	1.55318i
$419$			33.9420i			1.65818i	0.559117	+	0.829089i	$0.311140\pi$
$419$			33.9420i			1.65818i	−0.559117	+	0.829089i	$0.688860\pi$
$420$		0			0
$421$	−19.7073	−	19.7073i	−0.960474	−	0.960474i	0.0387742	−	0.999248i	$-0.487655\pi$
$421$	−19.7073	−	19.7073i	−0.960474	−	0.960474i	−0.999248	+	0.0387742i	$0.987655\pi$
$422$	−25.9008			−1.26083
$423$		0			0
$424$	10.8383	+	10.8383i	0.526353	+	0.526353i
$425$	−9.66827	+	10.1342i	−0.468980	+	0.491583i
$426$		0			0
$427$		−	32.2839i		−	1.56233i
$428$	−4.99709	+	4.99709i	−0.241543	+	0.241543i
$429$		0			0
$430$	0.104928	+	8.91969i	0.00506009	+	0.430146i
$431$	−10.7665	−	10.7665i	−0.518606	−	0.518606i	0.398543	−	0.917150i	$-0.369516\pi$
$431$	−10.7665	−	10.7665i	−0.518606	−	0.518606i	−0.917150	+	0.398543i	$0.869516\pi$
$432$		0			0
$433$	−11.8525	+	11.8525i	−0.569594	+	0.569594i	−0.932015	−	0.362421i	$-0.881950\pi$
$433$	−11.8525	+	11.8525i	−0.569594	+	0.569594i	0.362421	+	0.932015i	$0.381950\pi$
$434$	−19.2784	+	19.2784i	−0.925394	+	0.925394i
$435$		0			0
$436$	13.9430	−	13.9430i	0.667749	−	0.667749i
$437$		−	8.50103i		−	0.406659i
$438$		0			0
$439$	−2.02222			−0.0965152			−0.0482576	−	0.998835i	$-0.515367\pi$
$439$	−2.02222			−0.0965152			−0.0482576	+	0.998835i	$0.515367\pi$
$440$	0.196507	+	16.7046i	0.00936812	+	0.796361i
$441$		0			0
$442$	20.9223	−	8.00110i	0.995174	−	0.380573i
$443$	−0.127396	−	0.127396i	−0.00605277	−	0.00605277i	0.704074	−	0.710127i	$-0.251362\pi$
$443$	−0.127396	−	0.127396i	−0.00605277	−	0.00605277i	−0.710127	+	0.704074i	$0.751362\pi$
$444$		0			0
$445$	28.2019	−	0.331758i	1.33690	−	0.0157268i
$446$			37.2488i			1.76378i
$447$		0			0
$448$			53.0035i			2.50418i
$449$	24.8640	+	24.8640i	1.17341	+	1.17341i	0.981392	+	0.192014i	$0.0615019\pi$
$449$	24.8640	+	24.8640i	1.17341	+	1.17341i	0.192014	+	0.981392i	$0.438498\pi$
$450$		0			0
$451$	−8.56996			−0.403544
$452$	5.69192	+	5.69192i	0.267726	+	0.267726i
$453$		0			0
$454$	−49.3028			−2.31390
$455$	−30.8329	+	12.2087i	−1.44547	+	0.572354i
$456$		0			0
$457$	32.3018			1.51101			0.755507	−	0.655140i	$-0.227390\pi$
$457$	32.3018			1.51101			0.755507	+	0.655140i	$0.227390\pi$
$458$	4.43430	+	4.43430i	0.207201	+	0.207201i
$459$		0			0
$460$	0.167141	+	14.2082i	0.00779297	+	0.662462i
$461$	14.5631	+	14.5631i	0.678272	+	0.678272i	0.959609	−	0.281337i	$-0.0907779\pi$
$461$	14.5631	+	14.5631i	0.678272	+	0.678272i	−0.281337	+	0.959609i	$0.590778\pi$
$462$		0			0
$463$	13.2720			0.616800			0.308400	−	0.951257i	$-0.400206\pi$
$463$	13.2720			0.616800			0.308400	+	0.951257i	$0.400206\pi$
$464$		−	11.0880i		−	0.514749i
$465$		0			0
$466$	16.8642	−	16.8642i	0.781217	−	0.781217i
$467$	−21.6107	−	21.6107i	−1.00002	−	1.00002i	−1.00000		2.29542e-5i	$-0.999993\pi$
$467$	−21.6107	−	21.6107i	−1.00002	−	1.00002i	−2.29542e−5	−	1.00000i	$-0.500007\pi$
$468$		0			0
$469$			50.7970i			2.34559i
$470$	22.5308	+	22.0069i	1.03927	+	1.01510i
$471$		0			0
$472$	13.2633	+	13.2633i	0.610491	+	0.610491i
$473$		−	6.59622i		−	0.303295i
$474$		0			0
$475$	14.1254	+	13.4759i	0.648117	+	0.618317i
$476$	−23.7795	+	23.7795i	−1.08993	+	1.08993i
$477$		0			0
$478$	−38.1824	+	38.1824i	−1.74642	+	1.74642i
$479$	−13.5992	−	13.5992i	−0.621361	−	0.621361i	0.324518	−	0.945879i	$-0.394798\pi$
$479$	−13.5992	−	13.5992i	−0.621361	−	0.621361i	−0.945879	+	0.324518i	$0.894798\pi$
$480$		0			0
$481$	25.7948	+	11.5236i	1.17614	+	0.525429i
$482$	−22.6560	+	22.6560i	−1.03195	+	1.03195i
$483$		0			0
$484$		−	7.14359i		−	0.324708i
$485$	27.5032	−	28.1580i	1.24886	−	1.27859i
$486$		0			0
$487$	16.1028			0.729687			0.364844	−	0.931069i	$-0.381122\pi$
$487$	16.1028			0.729687			0.364844	+	0.931069i	$0.381122\pi$
$488$	−15.9904			−0.723853
$489$		0			0
$490$	34.3702	−	35.1885i	1.55269	−	1.58965i
$491$			20.7163i			0.934915i	0.884016	+	0.467457i	$0.154830\pi$
$491$			20.7163i			0.934915i	−0.884016	+	0.467457i	$0.845170\pi$
$492$		0			0
$493$	16.6528	−	16.6528i	0.750005	−	0.750005i
$494$	−11.1522	−	29.1622i	−0.501760	−	1.31207i
$495$		0			0
$496$	−2.78722	−	2.78722i	−0.125150	−	0.125150i
$497$	31.9035	−	31.9035i	1.43107	−	1.43107i
$498$		0			0
$499$	−4.09738	+	4.09738i	−0.183424	+	0.183424i	−0.792846	−	0.609422i	$-0.791401\pi$
$499$	−4.09738	+	4.09738i	−0.183424	+	0.183424i	0.609422	+	0.792846i	$0.291401\pi$
$500$	−23.8735	−	22.2453i	−1.06765	−	0.994840i
$501$		0			0
$502$			41.6001i			1.85670i
$503$	23.4993	+	23.4993i	1.04778	+	1.04778i	0.998800	+	0.0489821i	$0.0155977\pi$
$503$	23.4993	+	23.4993i	1.04778	+	1.04778i	0.0489821	+	0.998800i	$0.484402\pi$
$504$		0			0
$505$	−7.46438	−	7.29080i	−0.332160	−	0.324436i
$506$		−	17.7072i		−	0.787182i
$507$		0			0
$508$	−12.6449	−	12.6449i	−0.561028	−	0.561028i
$509$	13.7959	−	13.7959i	0.611492	−	0.611492i	−0.331843	−	0.943335i	$-0.607670\pi$
$509$	13.7959	−	13.7959i	0.611492	−	0.611492i	0.943335	+	0.331843i	$0.107670\pi$
$510$		0			0
$511$		−	21.7157i		−	0.960645i
$512$	−14.6057			−0.645488
$513$		0			0
$514$	−3.10665	−	3.10665i	−0.137029	−	0.137029i
$515$	0.0774037	+	6.57990i	0.00341081	+	0.289945i
$516$		0			0
$517$	−16.4681	−	16.4681i	−0.724266	−	0.724266i
$518$	−71.4795			−3.14063
$519$		0			0
$520$	6.04707	+	15.2718i	0.265181	+	0.669711i
$521$	20.4402			0.895503			0.447752	−	0.894158i	$-0.352225\pi$
$521$	20.4402			0.895503			0.447752	+	0.894158i	$0.352225\pi$
$522$		0			0
$523$	1.95338	+	1.95338i	0.0854154	+	0.0854154i	0.748524	−	0.663108i	$-0.230763\pi$
$523$	1.95338	+	1.95338i	0.0854154	+	0.0854154i	−0.663108	+	0.748524i	$0.730763\pi$
$524$	34.3364			1.49999
$525$		0			0
$526$	35.2146	+	35.2146i	1.53543	+	1.53543i
$527$		−	8.37211i		−	0.364695i
$528$		0			0
$529$			18.2596i			0.793896i
$530$	37.3072	−	0.438869i	1.62052	−	0.0190632i
$531$		0			0
$532$	33.1446	+	33.1446i	1.43700	+	1.43700i
$533$	−7.87027	+	3.00974i	−0.340899	+	0.130366i
$534$		0			0
$535$	0.0636871	+	5.41388i	0.00275343	+	0.234063i
$536$	25.1601			1.08675
$537$		0			0
$538$			0.774608i			0.0333957i
$539$	−25.7198	+	25.7198i	−1.10783	+	1.10783i
$540$		0			0
$541$	28.9135	−	28.9135i	1.24309	−	1.24309i	0.284374	−	0.958714i	$-0.408214\pi$
$541$	28.9135	−	28.9135i	1.24309	−	1.24309i	0.958714	−	0.284374i	$-0.0917856\pi$
$542$	−18.8987	+	18.8987i	−0.811769	+	0.811769i
$543$		0			0
$544$	−13.8649	−	13.8649i	−0.594453	−	0.594453i
$545$	−0.177701	−	15.1060i	−0.00761189	−	0.647068i
$546$		0			0
$547$	−21.7628	+	21.7628i	−0.930509	+	0.930509i	−0.997738	−	0.0672284i	$-0.978584\pi$
$547$	−21.7628	+	21.7628i	−0.930509	+	0.930509i	0.0672284	+	0.997738i	$0.478584\pi$
$548$			36.0942i			1.54187i
$549$		0			0
$550$	29.4225	+	28.0697i	1.25458	+	1.19690i
$551$	−23.2112	−	23.2112i	−0.988830	−	0.988830i
$552$		0			0
$553$	−34.7791			−1.47896
$554$	−11.7027	−	11.7027i	−0.497199	−	0.497199i
$555$		0			0
$556$		−	44.2842i		−	1.87807i
$557$			37.6115i			1.59365i	0.604210	+	0.796825i	$0.293489\pi$
$557$			37.6115i			1.59365i	−0.604210	+	0.796825i	$0.706511\pi$
$558$		0			0
$559$	−2.31657	−	6.05768i	−0.0979805	−	0.256212i
$560$	8.67783	+	8.47604i	0.366705	+	0.358178i
$561$		0			0
$562$	−13.2731	+	13.2731i	−0.559890	+	0.559890i
$563$	27.8463	−	27.8463i	1.17358	−	1.17358i	0.192234	−	0.981349i	$-0.438427\pi$
$563$	27.8463	−	27.8463i	1.17358	−	1.17358i	0.981349	−	0.192234i	$-0.0615733\pi$
$564$		0			0
$565$	6.16667	−	0.0725426i	0.259434	−	0.00305189i
$566$	−5.68142	+	5.68142i	−0.238808	+	0.238808i
$567$		0			0
$568$	−15.8020	−	15.8020i	−0.663037	−	0.663037i
$569$	1.85521			0.0777743			0.0388872	−	0.999244i	$-0.487619\pi$
$569$	1.85521			0.0777743			0.0388872	+	0.999244i	$0.487619\pi$
$570$		0			0
$571$			33.3973i			1.39763i	0.715302	+	0.698816i	$0.246289\pi$
$571$			33.3973i			1.39763i	−0.715302	+	0.698816i	$0.753711\pi$
$572$	−13.7839	−	36.0440i	−0.576335	−	1.50708i
$573$		0			0
$574$	15.0747	−	15.0747i	0.629205	−	0.629205i
$575$	7.87666	+	7.51450i	0.328480	+	0.313376i
$576$		0			0
$577$	−17.7281			−0.738030			−0.369015	−	0.929423i	$-0.620305\pi$
$577$	−17.7281			−0.738030			−0.369015	+	0.929423i	$0.620305\pi$
$578$			20.2992i			0.844336i
$579$		0			0
$580$	39.2504	+	38.3377i	1.62979	+	1.59189i
$581$	−18.4844			−0.766864
$582$		0			0
$583$	−27.5891			−1.14262
$584$	−10.7559			−0.445083
$585$		0			0
$586$	13.1191			0.541944
$587$	33.3826			1.37785			0.688924	−	0.724834i	$-0.258083\pi$
$587$	33.3826			1.37785			0.688924	+	0.724834i	$0.258083\pi$
$588$		0			0
$589$	−11.6693			−0.480825
$590$	45.6544	−	0.537063i	1.87956	−	0.0221105i
$591$		0			0
$592$		−	10.3343i		−	0.424738i
$593$	−26.1087			−1.07216			−0.536078	−	0.844169i	$-0.680095\pi$
$593$	−26.1087			−1.07216			−0.536078	+	0.844169i	$0.680095\pi$
$594$		0			0
$595$	0.303066	+	25.7629i	0.0124245	+	1.05618i
$596$	19.0802	−	19.0802i	0.781555	−	0.781555i
$597$		0			0
$598$	−6.21872	−	16.2615i	−0.254302	−	0.664984i
$599$		−	1.98183i		−	0.0809755i	−0.999180	−	0.0404877i	$-0.987109\pi$
$599$		−	1.98183i		−	0.0809755i	0.999180	−	0.0404877i	$-0.0128912\pi$
$600$		0			0
$601$	−7.83403			−0.319557			−0.159778	−	0.987153i	$-0.551078\pi$
$601$	−7.83403			−0.319557			−0.159778	+	0.987153i	$0.551078\pi$
$602$	11.6029	+	11.6029i	0.472897	+	0.472897i
$603$		0			0
$604$	7.47650	−	7.47650i	0.304214	−	0.304214i
$605$	−3.91523	−	3.82419i	−0.159177	−	0.155475i
$606$		0			0
$607$	15.2335	−	15.2335i	0.618309	−	0.618309i	−0.326788	−	0.945098i	$-0.605966\pi$
$607$	15.2335	−	15.2335i	0.618309	−	0.618309i	0.945098	+	0.326788i	$0.105966\pi$
$608$	−19.3253	+	19.3253i	−0.783745	+	0.783745i
$609$		0			0
$610$	−27.1972	+	27.8447i	−1.10118	+	1.12740i
$611$	−20.9071	−	9.34003i	−0.845811	−	0.377857i
$612$		0			0
$613$		−	34.9526i		−	1.41172i	−0.708349	−	0.705862i	$-0.750560\pi$
$613$		−	34.9526i		−	1.41172i	0.708349	−	0.705862i	$-0.249440\pi$
$614$		−	6.24821i		−	0.252157i
$615$		0			0
$616$	21.7296	+	21.7296i	0.875510	+	0.875510i
$617$	−12.6145			−0.507842			−0.253921	−	0.967225i	$-0.581720\pi$
$617$	−12.6145			−0.507842			−0.253921	+	0.967225i	$0.581720\pi$
$618$		0			0
$619$	21.5568	+	21.5568i	0.866442	+	0.866442i	0.992077	−	0.125635i	$-0.0400967\pi$
$619$	21.5568	+	21.5568i	0.866442	+	0.866442i	−0.125635	+	0.992077i	$0.540097\pi$
$620$	19.5035	−	0.229433i	0.783280	−	0.00921423i
$621$		0			0
$622$		−	20.3609i		−	0.816396i
$623$	36.6854	−	36.6854i	1.46977	−	1.46977i
$624$		0			0
$625$	−24.9723	+	1.17588i	−0.998893	+	0.0470351i
$626$	−36.5672	−	36.5672i	−1.46152	−	1.46152i
$627$		0			0
$628$	−8.54565	+	8.54565i	−0.341009	+	0.341009i
$629$	15.5208	−	15.5208i	0.618856	−	0.618856i
$630$		0			0
$631$	−25.2174	+	25.2174i	−1.00389	+	1.00389i	−0.00389463	+	0.999992i	$0.501240\pi$
$631$	−25.2174	+	25.2174i	−1.00389	+	1.00389i	−0.999992	+	0.00389463i	$0.998760\pi$
$632$			17.2263i			0.685226i
$633$		0			0
$634$	29.6820			1.17882
$635$	−13.6996	+	0.161158i	−0.543653	+	0.00639534i
$636$		0			0
$637$	−14.5872	+	32.6526i	−0.577966	+	1.29374i
$638$	−48.3478	−	48.3478i	−1.91411	−	1.91411i
$639$		0			0
$640$	22.7792	−	23.3215i	0.900427	−	0.921863i
$641$		−	15.3670i		−	0.606961i	−0.952838	−	0.303481i	$-0.901851\pi$
$641$		−	15.3670i		−	0.606961i	0.952838	−	0.303481i	$-0.0981487\pi$
$642$		0			0
$643$			5.80970i			0.229112i	0.993417	+	0.114556i	$0.0365445\pi$
$643$			5.80970i			0.229112i	−0.993417	+	0.114556i	$0.963455\pi$
$644$	18.4822	+	18.4822i	0.728302	+	0.728302i
$645$		0			0
$646$	−24.2573			−0.954389
$647$	−21.0666	−	21.0666i	−0.828212	−	0.828212i	0.159057	−	0.987269i	$-0.449155\pi$
$647$	−21.0666	−	21.0666i	−0.828212	−	0.828212i	−0.987269	+	0.159057i	$0.949155\pi$
$648$		0			0
$649$	−33.7620			−1.32528
$650$	36.8783	+	15.4449i	1.44649	+	0.605797i
$651$		0			0
$652$	24.7919			0.970926
$653$	9.40721	+	9.40721i	0.368132	+	0.368132i	0.866796	−	0.498663i	$-0.166176\pi$
$653$	9.40721	+	9.40721i	0.368132	+	0.368132i	−0.498663	+	0.866796i	$0.666176\pi$
$654$		0			0
$655$	18.3814	−	18.8190i	0.718220	−	0.735319i
$656$	2.17946	+	2.17946i	0.0850935	+	0.0850935i
$657$		0			0
$658$	57.9353			2.25855
$659$		−	2.27833i		−	0.0887510i	−0.999015	−	0.0443755i	$-0.985870\pi$
$659$		−	2.27833i		−	0.0887510i	0.999015	−	0.0443755i	$-0.0141298\pi$
$660$		0			0
$661$	22.0600	−	22.0600i	0.858036	−	0.858036i	−0.133071	−	0.991107i	$-0.542484\pi$
$661$	22.0600	−	22.0600i	0.858036	−	0.858036i	0.991107	+	0.133071i	$0.0424837\pi$
$662$	30.5675	+	30.5675i	1.18804	+	1.18804i
$663$		0			0
$664$			9.15547i			0.355301i
$665$	35.9091	−	0.422423i	1.39250	−	0.0163808i
$666$		0			0
$667$	−12.9431	−	12.9431i	−0.501160	−	0.501160i
$668$			38.6889i			1.49692i
$669$		0			0
$670$	42.7933	−	43.8121i	1.65325	−	1.69261i
$671$	20.3521	−	20.3521i	0.785682	−	0.785682i
$672$		0			0
$673$	24.7463	−	24.7463i	0.953900	−	0.953900i	−0.0450834	−	0.998983i	$-0.514355\pi$
$673$	24.7463	−	24.7463i	0.953900	−	0.953900i	0.998983	+	0.0450834i	$0.0143554\pi$
$674$	−55.0069	−	55.0069i	−2.11879	−	2.11879i
$675$		0			0
$676$	−25.3171	−	28.2604i	−0.973734	−	1.08694i
$677$	11.5334	−	11.5334i	0.443265	−	0.443265i	−0.449843	−	0.893108i	$-0.648520\pi$
$677$	11.5334	−	11.5334i	0.443265	−	0.443265i	0.893108	+	0.449843i	$0.148520\pi$
$678$		0			0
$679$		−	72.4049i		−	2.77865i
$680$	12.7605	−	0.150111i	0.489345	−	0.00575648i
$681$		0			0
$682$	−24.3066			−0.930747
$683$	−33.8458			−1.29507			−0.647536	−	0.762035i	$-0.724200\pi$
$683$	−33.8458			−1.29507			−0.647536	+	0.762035i	$0.724200\pi$
$684$		0			0
$685$	19.7824	+	19.3223i	0.755845	+	0.738269i
$686$		−	26.6265i		−	1.01660i
$687$		0			0
$688$	−1.67751	+	1.67751i	−0.0639545	+	0.0639545i
$689$	−25.3366	+	9.68921i	−0.965248	+	0.369129i
$690$		0			0
$691$	13.6461	+	13.6461i	0.519121	+	0.519121i	0.917305	−	0.398185i	$-0.130360\pi$
$691$	13.6461	+	13.6461i	0.519121	+	0.519121i	−0.398185	+	0.917305i	$0.630360\pi$
$692$	−23.1891	+	23.1891i	−0.881518	+	0.881518i
$693$		0			0
$694$	4.98395	−	4.98395i	0.189188	−	0.189188i
$695$	−24.2711	−	23.7067i	−0.920655	−	0.899246i
$696$		0			0
$697$			6.54654i			0.247968i
$698$	−42.7546	−	42.7546i	−1.61829	−	1.61829i
$699$		0			0
$700$	−60.0085	+	1.41203i	−2.26811	+	0.0533699i
$701$			36.0430i			1.36133i	0.732597	+	0.680663i	$0.238308\pi$
$701$			36.0430i			1.36133i	−0.732597	+	0.680663i	$0.761692\pi$
$702$		0			0
$703$	−21.6334	−	21.6334i	−0.815919	−	0.815919i
$704$	−33.4139	+	33.4139i	−1.25933	+	1.25933i
$705$		0			0
$706$			45.6533i			1.71819i
$707$	−19.1937			−0.721855
$708$		0			0
$709$	−11.7237	−	11.7237i	−0.440292	−	0.440292i	0.451818	−	0.892110i	$-0.350776\pi$
$709$	−11.7237	−	11.7237i	−0.440292	−	0.440292i	−0.892110	+	0.451818i	$0.850776\pi$
$710$	−54.3932	+	0.639863i	−2.04134	+	0.0240136i
$711$		0			0
$712$	−18.1705	−	18.1705i	−0.680970	−	0.680970i
$713$	−6.50708			−0.243692
$714$		0			0
$715$	−27.1338	−	11.7409i	−1.01475	−	0.439083i
$716$	4.01692			0.150119
$717$		0			0
$718$	23.5152	+	23.5152i	0.877578	+	0.877578i
$719$	15.7258			0.586474			0.293237	−	0.956040i	$-0.405267\pi$
$719$	15.7258			0.586474			0.293237	+	0.956040i	$0.405267\pi$
$720$		0			0
$721$	8.55922	+	8.55922i	0.318762	+	0.318762i
$722$		−	8.32765i		−	0.309923i
$723$		0			0
$724$			68.4963i			2.54565i
$725$	42.0240	−	0.988848i	1.56073	−	0.0367249i
$726$		0			0
$727$	−29.7923	−	29.7923i	−1.10494	−	1.10494i	−0.993806	−	0.111131i	$-0.964553\pi$
$727$	−29.7923	−	29.7923i	−1.10494	−	1.10494i	−0.111131	−	0.993806i	$-0.535447\pi$
$728$	27.5868	+	12.3241i	1.02244	+	0.456763i
$729$		0			0
$730$	−18.2941	+	18.7296i	−0.677095	+	0.693214i
$731$	−5.03881			−0.186367
$732$		0			0
$733$			21.4923i			0.793836i	0.917854	+	0.396918i	$0.129920\pi$
$733$			21.4923i			0.793836i	−0.917854	+	0.396918i	$0.870080\pi$
$734$	2.27399	−	2.27399i	0.0839344	−	0.0839344i
$735$		0			0
$736$	−10.7763	+	10.7763i	−0.397219	+	0.397219i
$737$	−32.0229	+	32.0229i	−1.17958	+	1.17958i
$738$		0			0
$739$	−0.314385	−	0.314385i	−0.0115649	−	0.0115649i	0.701301	−	0.712866i	$-0.252603\pi$
$739$	−0.314385	−	0.314385i	−0.0115649	−	0.0115649i	−0.712866	+	0.701301i	$0.752603\pi$
$740$	36.5824	+	35.7317i	1.34479	+	1.31352i
$741$		0			0
$742$	48.5297	−	48.5297i	1.78158	−	1.78158i
$743$			22.1368i			0.812122i	0.913846	+	0.406061i	$0.133098\pi$
$743$			22.1368i			0.812122i	−0.913846	+	0.406061i	$0.866902\pi$
$744$		0			0
$745$	−0.243174	−	20.6716i	−0.00890920	−	0.757350i
$746$	−18.6642	−	18.6642i	−0.683347	−	0.683347i
$747$		0			0
$748$	−29.9816			−1.09624
$749$	7.04245	+	7.04245i	0.257326	+	0.257326i
$750$		0			0
$751$			0.516848i			0.0188600i	0.999956	+	0.00943002i	$0.00300171\pi$
$751$			0.516848i			0.0188600i	−0.999956	+	0.00943002i	$0.996998\pi$
$752$			8.37613i			0.305446i
$753$		0			0
$754$	−61.3800	−	27.4209i	−2.23533	−	0.998609i
$755$	−0.0952867	−	8.10010i	−0.00346784	−	0.294793i
$756$		0			0
$757$	−24.0375	+	24.0375i	−0.873657	+	0.873657i	−0.992869	−	0.119212i	$-0.961963\pi$
$757$	−24.0375	+	24.0375i	−0.873657	+	0.873657i	0.119212	+	0.992869i	$0.461963\pi$
$758$	11.1679	−	11.1679i	0.405635	−	0.405635i
$759$		0			0
$760$	−0.209229	−	17.7860i	−0.00758952	−	0.645167i
$761$	36.2711	−	36.2711i	1.31483	−	1.31483i	0.397015	−	0.917812i	$-0.370046\pi$
$761$	36.2711	−	36.2711i	1.31483	−	1.31483i	0.917812	−	0.397015i	$-0.129954\pi$
$762$		0			0
$763$	−19.6500	−	19.6500i	−0.711379	−	0.711379i
$764$	8.53636			0.308835
$765$		0			0
$766$		−	1.07243i		−	0.0387486i
$767$	−31.0055	+	11.8571i	−1.11955	+	0.428136i
$768$		0			0
$769$	5.51342	−	5.51342i	0.198819	−	0.198819i	−0.600675	−	0.799494i	$-0.705101\pi$
$769$	5.51342	−	5.51342i	0.198819	−	0.198819i	0.799494	+	0.600675i	$0.205101\pi$
$770$	74.7970	−	0.879886i	2.69550	−	0.0317089i
$771$		0			0
$772$	−60.4088			−2.17416
$773$			37.1946i			1.33780i	0.743353	+	0.668899i	$0.233234\pi$
$773$			37.1946i			1.33780i	−0.743353	+	0.668899i	$0.766766\pi$
$774$		0			0
$775$	10.3151	−	10.8122i	0.370529	−	0.388387i
$776$	−35.8627			−1.28739
$777$		0			0
$778$	39.0208			1.39896
$779$	9.12476			0.326928
$780$		0			0
$781$	40.2244			1.43934
$782$	−13.5264			−0.483705
$783$		0			0
$784$	13.0818			0.467207
$785$	0.108913	+	9.25843i	0.00388727	+	0.330447i
$786$		0			0
$787$			16.6120i			0.592154i	0.955164	+	0.296077i	$0.0956785\pi$
$787$			16.6120i			0.592154i	−0.955164	+	0.296077i	$0.904321\pi$
$788$	17.9846			0.640674
$789$		0			0
$790$	29.9967	+	29.2992i	1.06724	+	1.04242i
$791$	8.02169	−	8.02169i	0.285219	−	0.285219i
$792$		0			0
$793$	11.5428	−	25.8380i	0.409899	−	0.917534i
$794$		−	21.3753i		−	0.758582i
$795$		0			0
$796$	−67.9677			−2.40905
$797$	−23.0821	−	23.0821i	−0.817611	−	0.817611i	0.168150	−	0.985761i	$-0.446221\pi$
$797$	−23.0821	−	23.0821i	−0.817611	−	0.817611i	−0.985761	+	0.168150i	$0.946221\pi$
$798$		0			0
$799$	−12.5799	+	12.5799i	−0.445044	+	0.445044i
$800$	−0.823302	−	34.9886i	−0.0291081	−	1.23703i
$801$		0			0
$802$	−37.4328	+	37.4328i	−1.32180	+	1.32180i
$803$	13.6897	−	13.6897i	0.483101	−	0.483101i
$804$		0			0
$805$	20.0238	−	0.235553i	0.705746	−	0.00830216i
$806$	−22.3221	+	8.53639i	−0.786262	+	0.300681i
$807$		0			0
$808$			9.50678i			0.334448i
$809$		−	10.9372i		−	0.384533i	−0.981343	−	0.192267i	$-0.938416\pi$
$809$		−	10.9372i		−	0.384533i	0.981343	−	0.192267i	$-0.0615838\pi$
$810$		0			0
$811$	17.0726	+	17.0726i	0.599501	+	0.599501i	0.940180	−	0.340679i	$-0.110657\pi$
$811$	17.0726	+	17.0726i	0.599501	+	0.599501i	−0.340679	+	0.940180i	$0.610657\pi$
$812$	100.928			3.54187
$813$		0			0
$814$	−45.0613	−	45.0613i	−1.57940	−	1.57940i
$815$	13.2719	−	13.5879i	0.464894	−	0.475962i
$816$		0			0
$817$			7.02325i			0.245712i
$818$	8.10707	−	8.10707i	0.283457	−	0.283457i
$819$		0			0
$820$	−15.2507	+	0.179404i	−0.532577	+	0.00626506i
$821$	7.58466	+	7.58466i	0.264706	+	0.264706i	0.826963	−	0.562256i	$-0.190067\pi$
$821$	7.58466	+	7.58466i	0.264706	+	0.264706i	−0.562256	+	0.826963i	$0.690067\pi$
$822$		0			0
$823$	20.2348	−	20.2348i	0.705341	−	0.705341i	−0.260211	−	0.965552i	$-0.583792\pi$
$823$	20.2348	−	20.2348i	0.705341	−	0.705341i	0.965552	+	0.260211i	$0.0837922\pi$
$824$	4.23944	−	4.23944i	0.147688	−	0.147688i
$825$		0			0
$826$	59.3879	−	59.3879i	2.06637	−	2.06637i
$827$		−	0.322011i		−	0.0111974i	−0.999984	−	0.00559871i	$-0.998218\pi$
$827$		−	0.322011i		−	0.0111974i	0.999984	−	0.00559871i	$-0.00178213\pi$
$828$		0			0
$829$	2.29166			0.0795925			0.0397963	−	0.999208i	$-0.487329\pi$
$829$	2.29166			0.0795925			0.0397963	+	0.999208i	$0.487329\pi$
$830$	15.9427	+	15.5720i	0.553380	+	0.540511i
$831$		0			0
$832$	−18.9510	+	42.4207i	−0.657007	+	1.47067i
$833$	19.6472	+	19.6472i	0.680735	+	0.680735i
$834$		0			0
$835$	21.2045	+	20.7114i	0.733812	+	0.716748i
$836$			41.7893i			1.44531i
$837$		0			0
$838$		−	75.2766i		−	2.60039i
$839$	−0.488256	−	0.488256i	−0.0168565	−	0.0168565i	0.698628	−	0.715485i	$-0.253794\pi$
$839$	−0.488256	−	0.488256i	−0.0168565	−	0.0168565i	−0.715485	+	0.698628i	$0.753794\pi$
$840$		0			0
$841$	−41.6797			−1.43723
$842$	43.7067	+	43.7067i	1.50623	+	1.50623i
$843$		0			0
$844$	34.0855			1.17327
$845$	−29.0419	−	1.25297i	−0.999071	−	0.0431034i
$846$		0			0
$847$	−10.0675			−0.345925
$848$	7.01629	+	7.01629i	0.240940	+	0.240940i
$849$		0			0
$850$	21.4423	−	22.4757i	0.735463	−	0.770909i
$851$	−12.0633	−	12.0633i	−0.413525	−	0.413525i
$852$		0			0
$853$	−2.53904			−0.0869352			−0.0434676	−	0.999055i	$-0.513841\pi$
$853$	−2.53904			−0.0869352			−0.0434676	+	0.999055i	$0.513841\pi$
$854$			71.5992i			2.45007i
$855$		0			0
$856$	3.48817	−	3.48817i	0.119223	−	0.119223i
$857$	3.15552	+	3.15552i	0.107791	+	0.107791i	0.758945	−	0.651155i	$-0.225715\pi$
$857$	3.15552	+	3.15552i	0.107791	+	0.107791i	−0.651155	+	0.758945i	$0.725715\pi$
$858$		0			0
$859$			36.8208i			1.25631i	0.778088	+	0.628155i	$0.216190\pi$
$859$			36.8208i			1.25631i	−0.778088	+	0.628155i	$0.783810\pi$
$860$	−0.138086	−	11.7383i	−0.00470868	−	0.400274i
$861$		0			0
$862$	23.8780	+	23.8780i	0.813288	+	0.813288i
$863$			11.3029i			0.384754i	0.981321	+	0.192377i	$0.0616196\pi$
$863$			11.3029i			0.384754i	−0.981321	+	0.192377i	$0.938380\pi$
$864$		0			0
$865$	0.295542	+	25.1233i	0.0100487	+	0.854217i
$866$	26.2864	−	26.2864i	0.893248	−	0.893248i
$867$		0			0
$868$	25.3704	−	25.3704i	0.861129	−	0.861129i
$869$	−21.9250	−	21.9250i	−0.743756	−	0.743756i
$870$		0			0
$871$	−18.1620	+	40.6547i	−0.615397	+	1.37753i
$872$	−9.73279	+	9.73279i	−0.329594	+	0.329594i
$873$		0			0
$874$			18.8536i			0.637731i
$875$	−31.3505	+	33.6451i	−1.05984	+	1.13741i
$876$		0			0
$877$	11.1316			0.375889			0.187944	−	0.982180i	$-0.439818\pi$
$877$	11.1316			0.375889			0.187944	+	0.982180i	$0.439818\pi$
$878$	4.48487			0.151357
$879$		0			0
$880$	0.127212	+	10.8139i	0.00428830	+	0.364538i
$881$			25.7462i			0.867410i	0.901055	+	0.433705i	$0.142794\pi$
$881$			25.7462i			0.867410i	−0.901055	+	0.433705i	$0.857206\pi$
$882$		0			0
$883$	3.65379	−	3.65379i	0.122960	−	0.122960i	−0.642949	−	0.765909i	$-0.722289\pi$
$883$	3.65379	−	3.65379i	0.122960	−	0.122960i	0.765909	+	0.642949i	$0.222289\pi$
$884$	−27.5338	+	10.5295i	−0.926062	+	0.354144i
$885$		0			0
$886$	0.282539	+	0.282539i	0.00949208	+	0.00949208i
$887$	9.40170	−	9.40170i	0.315678	−	0.315678i	−0.531426	−	0.847105i	$-0.678344\pi$
$887$	9.40170	−	9.40170i	0.315678	−	0.315678i	0.847105	+	0.531426i	$0.178344\pi$
$888$		0			0
$889$	−17.8206	+	17.8206i	−0.597685	+	0.597685i
$890$	−62.5461	+	0.735771i	−2.09655	+	0.0246631i
$891$		0			0
$892$		−	49.0194i		−	1.64129i
$893$	17.5342	+	17.5342i	0.586760	+	0.586760i
$894$		0			0
$895$	2.15038	−	2.20158i	0.0718794	−	0.0735907i
$896$		−	59.9684i		−	2.00340i
$897$		0			0
$898$	−55.1434	−	55.1434i	−1.84016	−	1.84016i
$899$	−17.7669	+	17.7669i	−0.592560	+	0.592560i
$900$		0			0
$901$			21.0752i			0.702115i
$902$	19.0064			0.632845
$903$		0			0
$904$	−3.97320	−	3.97320i	−0.132147	−	0.132147i
$905$	37.5412	+	36.6682i	1.24791	+	1.21889i
$906$		0			0
$907$	−0.772139	−	0.772139i	−0.0256384	−	0.0256384i	0.694171	−	0.719810i	$-0.255771\pi$
$907$	−0.772139	−	0.772139i	−0.0256384	−	0.0256384i	−0.719810	+	0.694171i	$0.755771\pi$
$908$	64.8825			2.15320
$909$		0			0
$910$	68.3812	−	27.0765i	2.26681	−	0.897577i
$911$	6.21262			0.205833			0.102917	−	0.994690i	$-0.467182\pi$
$911$	6.21262			0.205833			0.102917	+	0.994690i	$0.467182\pi$
$912$		0			0
$913$	−11.6528	−	11.6528i	−0.385650	−	0.385650i
$914$	−71.6388			−2.36960
$915$		0			0
$916$	−5.83555	−	5.83555i	−0.192812	−	0.192812i
$917$		−	48.3907i		−	1.59800i
$918$		0			0
$919$			29.9003i			0.986320i	0.869939	+	0.493160i	$0.164158\pi$
$919$			29.9003i			0.986320i	−0.869939	+	0.493160i	$0.835842\pi$
$920$	−0.116671	−	9.91792i	−0.00384653	−	0.326984i
$921$		0			0
$922$	−32.2980	−	32.2980i	−1.06368	−	1.06368i
$923$	36.9403	−	14.1267i	1.21591	−	0.464986i
$924$		0			0
$925$	39.1674	−	0.921631i	1.28782	−	0.0303030i
$926$	−29.4345			−0.967278
$927$		0			0
$928$			58.8470i			1.93175i
$929$	−16.4364	+	16.4364i	−0.539260	+	0.539260i	−0.923312	−	0.384052i	$-0.874528\pi$
$929$	−16.4364	+	16.4364i	−0.539260	+	0.539260i	0.384052	+	0.923312i	$0.374528\pi$
$930$		0			0
$931$	27.3848	−	27.3848i	0.897501	−	0.897501i
$932$	−22.1933	+	22.1933i	−0.726964	+	0.726964i
$933$		0			0
$934$	47.9281	+	47.9281i	1.56826	+	1.56826i
$935$	−16.0501	+	16.4322i	−0.524895	+	0.537391i
$936$		0			0
$937$	15.7357	−	15.7357i	0.514064	−	0.514064i	−0.401705	−	0.915769i	$-0.631582\pi$
$937$	15.7357	−	15.7357i	0.514064	−	0.514064i	0.915769	+	0.401705i	$0.131582\pi$
$938$		−	112.657i		−	3.67839i
$939$		0			0
$940$	−29.6506	−	28.9611i	−0.967096	−	0.944607i
$941$	6.42421	+	6.42421i	0.209423	+	0.209423i	0.804022	−	0.594599i	$-0.202689\pi$
$941$	6.42421	+	6.42421i	0.209423	+	0.209423i	−0.594599	+	0.804022i	$0.702689\pi$
$942$		0			0
$943$	5.08819			0.165694
$944$	8.58615	+	8.58615i	0.279455	+	0.279455i
$945$		0			0
$946$			14.6291i			0.475633i
$947$		−	12.4887i		−	0.405827i	−0.979197	−	0.202914i	$-0.934959\pi$
$947$		−	12.4887i		−	0.405827i	0.979197	−	0.202914i	$-0.0650411\pi$
$948$		0			0
$949$	7.76426	−	17.3799i	0.252039	−	0.564174i
$950$	−31.3272	−	29.8868i	−1.01639	−	0.969657i
$951$		0			0
$952$	16.5991	−	16.5991i	0.537980	−	0.537980i
$953$	30.2555	−	30.2555i	0.980072	−	0.980072i	−0.0197332	−	0.999805i	$-0.506282\pi$
$953$	30.2555	−	30.2555i	0.980072	−	0.980072i	0.999805	+	0.0197332i	$0.00628169\pi$
$954$		0			0
$955$	4.56978	−	4.67858i	0.147875	−	0.151395i
$956$	50.2481	−	50.2481i	1.62514	−	1.62514i
$957$		0			0
$958$	30.1602	+	30.1602i	0.974431	+	0.974431i
$959$	50.8679			1.64261
$960$		0			0
$961$		−	22.0678i		−	0.711864i
$962$	−57.2077	−	25.5569i	−1.84445	−	0.823988i
$963$		0			0
$964$	29.8153	−	29.8153i	0.960286	−	0.960286i
$965$	−32.3387	+	33.1086i	−1.04102	+	1.06580i
$966$		0			0
$967$	35.6086			1.14510			0.572548	−	0.819871i	$-0.305955\pi$
$967$	35.6086			1.14510			0.572548	+	0.819871i	$0.305955\pi$
$968$			4.98652i			0.160273i
$969$		0			0
$970$	−60.9966	+	62.4488i	−1.95848	+	2.00511i
$971$	28.4165			0.911929			0.455964	−	0.889998i	$-0.349294\pi$
$971$	28.4165			0.911929			0.455964	+	0.889998i	$0.349294\pi$
$972$		0			0
$973$	−62.4102			−2.00078
$974$	−35.7127			−1.14431
$975$		0			0
$976$	−10.3516			−0.331347
$977$	42.8927			1.37226			0.686130	−	0.727479i	$-0.259308\pi$
$977$	42.8927			1.37226			0.686130	+	0.727479i	$0.259308\pi$
$978$		0			0
$979$	46.2536			1.47827
$980$	−45.2313	+	46.3081i	−1.44486	+	1.47926i
$981$		0			0
$982$		−	45.9446i		−	1.46615i
$983$	−39.1642			−1.24914			−0.624572	−	0.780967i	$-0.714727\pi$
$983$	−39.1642			−1.24914			−0.624572	+	0.780967i	$0.714727\pi$
$984$		0			0
$985$	9.62772	−	9.85693i	0.306765	−	0.314068i
$986$	−36.9326	+	36.9326i	−1.17617	+	1.17617i
$987$		0			0
$988$	14.6763	+	38.3774i	0.466914	+	1.22095i
$989$			3.91633i			0.124532i
$990$		0			0
$991$	7.60282			0.241512			0.120756	−	0.992682i	$-0.461468\pi$
$991$	7.60282			0.241512			0.120756	+	0.992682i	$0.461468\pi$
$992$	14.7925	+	14.7925i	0.469662	+	0.469662i
$993$		0			0
$994$	−70.7554	+	70.7554i	−2.24422	+	2.24422i
$995$	−36.3853	+	37.2515i	−1.15349	+	1.18095i
$996$		0			0
$997$	−1.06259	+	1.06259i	−0.0336527	+	0.0336527i	−0.723733	−	0.690080i	$-0.757575\pi$
$997$	−1.06259	+	1.06259i	−0.0336527	+	0.0336527i	0.690080	+	0.723733i	$0.257575\pi$
$998$	9.08715	−	9.08715i	0.287649	−	0.287649i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.w.g.73.2		28
3.2	odd	2		195.2.t.a.73.13	yes	28
5.2	odd	4		585.2.n.g.307.2		28
13.5	odd	4		585.2.n.g.343.13		28
15.2	even	4		195.2.k.a.112.13	✓	28
15.8	even	4		975.2.k.d.307.2		28
15.14	odd	2		975.2.t.d.268.2		28
39.5	even	4		195.2.k.a.148.2	yes	28
65.57	even	4	inner	585.2.w.g.577.2		28
195.44	even	4		975.2.k.d.343.13		28
195.83	odd	4		975.2.t.d.382.2		28
195.122	odd	4		195.2.t.a.187.13	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.k.a.112.13	✓	28	15.2	even	4
195.2.k.a.148.2	yes	28	39.5	even	4
195.2.t.a.73.13	yes	28	3.2	odd	2
195.2.t.a.187.13	yes	28	195.122	odd	4
585.2.n.g.307.2		28	5.2	odd	4
585.2.n.g.343.13		28	13.5	odd	4
585.2.w.g.73.2		28	1.1	even	1	trivial
585.2.w.g.577.2		28	65.57	even	4	inner
975.2.k.d.307.2		28	15.8	even	4
975.2.k.d.343.13		28	195.44	even	4
975.2.t.d.268.2		28	15.14	odd	2
975.2.t.d.382.2		28	195.83	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.21780 q^{2} +2.91862 q^{4} +(1.56243 - 1.59963i) q^{5} -4.11325i q^{7} -2.03732 q^{8} +O(q^{10})\)	\(q-2.21780 q^{2} +2.91862 q^{4} +(1.56243 - 1.59963i) q^{5} -4.11325i q^{7} -2.03732 q^{8} +(-3.46515 + 3.54765i) q^{10} +(2.59303 - 2.59303i) q^{11} +(1.47066 - 3.29198i) q^{13} +9.12235i q^{14} -1.31889 q^{16} +(-1.98080 - 1.98080i) q^{17} +(-2.76089 + 2.76089i) q^{19} +(4.56015 - 4.66871i) q^{20} +(-5.75081 + 5.75081i) q^{22} +(-1.53954 + 1.53954i) q^{23} +(-0.117620 - 4.99862i) q^{25} +(-3.26162 + 7.30095i) q^{26} -12.0050i q^{28} +8.40712i q^{29} +(2.11332 + 2.11332i) q^{31} +6.99966 q^{32} +(4.39301 + 4.39301i) q^{34} +(-6.57967 - 6.42667i) q^{35} +7.83564i q^{37} +(6.12310 - 6.12310i) q^{38} +(-3.18317 + 3.25895i) q^{40} +(-1.65250 - 1.65250i) q^{41} +(1.27192 - 1.27192i) q^{43} +(7.56807 - 7.56807i) q^{44} +(3.41439 - 3.41439i) q^{46} -6.35092i q^{47} -9.91882 q^{49} +(0.260858 + 11.0859i) q^{50} +(4.29230 - 9.60806i) q^{52} +(-5.31987 - 5.31987i) q^{53} +(-0.0964538 - 8.19931i) q^{55} +8.38000i q^{56} -18.6453i q^{58} +(-6.51015 - 6.51015i) q^{59} +7.84876 q^{61} +(-4.68691 - 4.68691i) q^{62} -12.8861 q^{64} +(-2.96815 - 7.49601i) q^{65} -12.3496 q^{67} +(-5.78120 - 5.78120i) q^{68} +(14.5924 + 14.2530i) q^{70} +(7.75627 + 7.75627i) q^{71} +5.27944 q^{73} -17.3779i q^{74} +(-8.05801 + 8.05801i) q^{76} +(-10.6658 - 10.6658i) q^{77} -8.45538i q^{79} +(-2.06067 + 2.10973i) q^{80} +(3.66491 + 3.66491i) q^{82} -4.49388i q^{83} +(-6.26340 + 0.0736805i) q^{85} +(-2.82085 + 2.82085i) q^{86} +(-5.28283 + 5.28283i) q^{88} +(8.91884 + 8.91884i) q^{89} +(-13.5408 - 6.04919i) q^{91} +(-4.49334 + 4.49334i) q^{92} +14.0850i q^{94} +(0.102698 + 8.73011i) q^{95} +17.6029 q^{97} +21.9979 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} + 28 q^{4} + 4 q^{5} + 12 q^{8}+O(q^{10}) \) 28 * q + 4 * q^2 + 28 * q^4 + 4 * q^5 + 12 * q^8	\( 28 q + 4 q^{2} + 28 q^{4} + 4 q^{5} + 12 q^{8} + 8 q^{11} + 28 q^{16} - 28 q^{17} - 12 q^{20} - 32 q^{22} + 8 q^{23} + 4 q^{25} - 16 q^{31} + 68 q^{32} - 28 q^{34} - 48 q^{40} - 4 q^{41} + 40 q^{44} - 16 q^{46} + 28 q^{49} - 4 q^{50} + 48 q^{52} - 20 q^{53} - 8 q^{55} + 32 q^{59} + 8 q^{61} + 72 q^{62} + 28 q^{64} - 64 q^{65} + 32 q^{67} - 60 q^{68} - 16 q^{70} - 40 q^{71} + 56 q^{73} - 40 q^{76} - 48 q^{77} + 12 q^{80} - 4 q^{82} + 44 q^{85} - 16 q^{86} - 72 q^{88} - 36 q^{89} - 56 q^{91} + 32 q^{92} + 56 q^{95} + 48 q^{97} + 12 q^{98}+O(q^{100}) \) 28 * q + 4 * q^2 + 28 * q^4 + 4 * q^5 + 12 * q^8 + 8 * q^11 + 28 * q^16 - 28 * q^17 - 12 * q^20 - 32 * q^22 + 8 * q^23 + 4 * q^25 - 16 * q^31 + 68 * q^32 - 28 * q^34 - 48 * q^40 - 4 * q^41 + 40 * q^44 - 16 * q^46 + 28 * q^49 - 4 * q^50 + 48 * q^52 - 20 * q^53 - 8 * q^55 + 32 * q^59 + 8 * q^61 + 72 * q^62 + 28 * q^64 - 64 * q^65 + 32 * q^67 - 60 * q^68 - 16 * q^70 - 40 * q^71 + 56 * q^73 - 40 * q^76 - 48 * q^77 + 12 * q^80 - 4 * q^82 + 44 * q^85 - 16 * q^86 - 72 * q^88 - 36 * q^89 - 56 * q^91 + 32 * q^92 + 56 * q^95 + 48 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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