LMFDB - Embedded newform 845.2.e.o.191.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(146,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("845.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.e (of order $3$, degree $2$, not 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 17 x^{16} - 18 x^{15} + 230 x^{14} - 185 x^{13} + 996 x^{12} - 534 x^{11} + 3020 x^{10} + \cdots + 1 $ x^18 + 17x^16 - 18x^15 + 230x^14 - 185x^13 + 996x^12 - 534x^11 + 3020x^10 - 1485x^9 + 3379x^8 - 1280x^7 + 2595x^6 - 1007x^5 + 541x^4 - 65x^3 + 24*x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.6
Root			$1.03666 + 1.79554i$ of defining polynomial
Character	$\chi$	$=$	845.191
Dual form			845.2.e.o.146.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.135687 - 0.235017i) q^{2} +(0.159809 - 0.276797i) q^{3} +(0.963178 + 1.66827i) q^{4} +1.00000 q^{5} +(-0.0433679 - 0.0751154i) q^{6} +(1.69076 + 2.92848i) q^{7} +1.06551 q^{8} +(1.44892 + 2.50961i) q^{9} +(0.135687 - 0.235017i) q^{10} +(0.876022 - 1.51732i) q^{11} +0.615697 q^{12} +0.917654 q^{14} +(0.159809 - 0.276797i) q^{15} +(-1.78178 + 3.08613i) q^{16} +(-0.977094 - 1.69238i) q^{17} +0.786399 q^{18} +(-3.56631 - 6.17702i) q^{19} +(0.963178 + 1.66827i) q^{20} +1.08079 q^{21} +(-0.237729 - 0.411760i) q^{22} +(-3.80710 + 6.59409i) q^{23} +(0.170278 - 0.294930i) q^{24} +1.00000 q^{25} +1.88505 q^{27} +(-3.25700 + 5.64129i) q^{28} +(-1.99190 + 3.45007i) q^{29} +(-0.0433679 - 0.0751154i) q^{30} -4.86923 q^{31} +(1.54904 + 2.68301i) q^{32} +(-0.279992 - 0.484961i) q^{33} -0.530316 q^{34} +(1.69076 + 2.92848i) q^{35} +(-2.79114 + 4.83440i) q^{36} +(5.25050 - 9.09413i) q^{37} -1.93560 q^{38} +1.06551 q^{40} +(0.455555 - 0.789045i) q^{41} +(0.146649 - 0.254004i) q^{42} +(-2.29276 - 3.97118i) q^{43} +3.37506 q^{44} +(1.44892 + 2.50961i) q^{45} +(1.03315 + 1.78946i) q^{46} +8.58491 q^{47} +(0.569488 + 0.986383i) q^{48} +(-2.21732 + 3.84051i) q^{49} +(0.135687 - 0.235017i) q^{50} -0.624593 q^{51} +11.9646 q^{53} +(0.255777 - 0.443019i) q^{54} +(0.876022 - 1.51732i) q^{55} +(1.80152 + 3.12032i) q^{56} -2.27971 q^{57} +(0.540549 + 0.936259i) q^{58} +(1.91149 + 3.31079i) q^{59} +0.615697 q^{60} +(-3.99238 - 6.91500i) q^{61} +(-0.660691 + 1.14435i) q^{62} +(-4.89955 + 8.48627i) q^{63} -6.28638 q^{64} -0.151965 q^{66} +(0.236374 - 0.409412i) q^{67} +(1.88223 - 3.26012i) q^{68} +(1.21682 + 2.10759i) q^{69} +0.917654 q^{70} +(-2.75156 - 4.76584i) q^{71} +(1.54384 + 2.67401i) q^{72} -2.93857 q^{73} +(-1.42485 - 2.46791i) q^{74} +(0.159809 - 0.276797i) q^{75} +(6.86998 - 11.8992i) q^{76} +5.92456 q^{77} +4.09938 q^{79} +(-1.78178 + 3.08613i) q^{80} +(-4.04552 + 7.00704i) q^{81} +(-0.123626 - 0.214126i) q^{82} +11.7733 q^{83} +(1.04099 + 1.80306i) q^{84} +(-0.977094 - 1.69238i) q^{85} -1.24439 q^{86} +(0.636646 + 1.10270i) q^{87} +(0.933411 - 1.61671i) q^{88} +(-1.92996 + 3.34279i) q^{89} +0.786399 q^{90} -14.6677 q^{92} +(-0.778146 + 1.34779i) q^{93} +(1.16486 - 2.01760i) q^{94} +(-3.56631 - 6.17702i) q^{95} +0.990200 q^{96} +(-3.47888 - 6.02559i) q^{97} +(0.601723 + 1.04221i) q^{98} +5.07715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{2} - 7 q^{3} - 17 q^{4} + 18 q^{5} + 2 q^{6} - 7 q^{7} + 24 q^{8} - 16 q^{9} - 3 q^{10} + 9 q^{11} + 24 q^{12} - 4 q^{14} - 7 q^{15} - 37 q^{16} + q^{17} - 20 q^{18} + 4 q^{19} - 17 q^{20}+ \cdots - 2 q^{99}+O(q^{100}) $ 18 * q - 3 * q^2 - 7 * q^3 - 17 * q^4 + 18 * q^5 + 2 * q^6 - 7 * q^7 + 24 * q^8 - 16 * q^9 - 3 * q^10 + 9 * q^11 + 24 * q^12 - 4 * q^14 - 7 * q^15 - 37 * q^16 + q^17 - 20 * q^18 + 4 * q^19 - 17 * q^20 - 2 * q^21 - 12 * q^22 - 14 * q^23 + 35 * q^24 + 18 * q^25 + 44 * q^27 - 18 * q^28 - 12 * q^29 + 2 * q^30 - 14 * q^31 - 22 * q^32 + 8 * q^33 - 60 * q^34 - 7 * q^35 - 3 * q^36 + 5 * q^37 - 94 * q^38 + 24 * q^40 + 10 * q^41 + 11 * q^42 - 39 * q^43 - 50 * q^44 - 16 * q^45 - 6 * q^46 + 72 * q^47 + 3 * q^48 - 16 * q^49 - 3 * q^50 + 86 * q^51 - 16 * q^53 + 2 * q^54 + 9 * q^55 + 29 * q^56 - 64 * q^57 - 21 * q^58 + 21 * q^59 + 24 * q^60 + 3 * q^61 + 10 * q^62 - 35 * q^63 + 68 * q^64 - 98 * q^66 - q^67 + 20 * q^68 + 13 * q^69 - 4 * q^70 + q^71 + 3 * q^72 + 15 * q^74 - 7 * q^75 + 5 * q^76 - 8 * q^77 + 78 * q^79 - 37 * q^80 - 29 * q^81 + 4 * q^82 + 14 * q^83 - 12 * q^84 + q^85 - 48 * q^86 - 16 * q^87 - 42 * q^88 + 19 * q^89 - 20 * q^90 - 54 * q^92 - 31 * q^93 - 16 * q^94 + 4 * q^95 - 14 * q^96 + 34 * q^97 - 48 * q^98 - 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.135687	−	0.235017i	0.0959451	−	0.166182i	−0.814058	−	0.580784i	$-0.802746\pi$
$2$	0.135687	−	0.235017i	0.0959451	−	0.166182i	0.910003	+	0.414602i	$0.136079\pi$
$3$	0.159809	−	0.276797i	0.0922656	−	0.159809i	−0.816198	−	0.577772i	$-0.803922\pi$
$3$	0.159809	−	0.276797i	0.0922656	−	0.159809i	0.908464	+	0.417963i	$0.137256\pi$
$4$	0.963178	+	1.66827i	0.481589	+	0.834137i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.0433679	−	0.0751154i	−0.0177049	−	0.0306657i
$7$	1.69076	+	2.92848i	0.639046	+	1.10686i	0.985642	+	0.168846i	$0.0540041\pi$
$7$	1.69076	+	2.92848i	0.639046	+	1.10686i	−0.346596	+	0.938014i	$0.612663\pi$
$8$	1.06551			0.376715
$9$	1.44892	+	2.50961i	0.482974	+	0.836536i
$10$	0.135687	−	0.235017i	0.0429080	−	0.0743188i
$11$	0.876022	−	1.51732i	0.264131	−	0.457488i	−0.703205	−	0.710987i	$-0.748248\pi$
$11$	0.876022	−	1.51732i	0.264131	−	0.457488i	0.967335	+	0.253500i	$0.0815817\pi$
$12$	0.615697			0.177736
$13$		0			0
$13$		0			0
$14$	0.917654			0.245253
$15$	0.159809	−	0.276797i	0.0412624	−	0.0714687i
$16$	−1.78178	+	3.08613i	−0.445445	+	0.771534i
$17$	−0.977094	−	1.69238i	−0.236980	−	0.410462i	0.722866	−	0.690988i	$-0.242824\pi$
$17$	−0.977094	−	1.69238i	−0.236980	−	0.410462i	−0.959846	+	0.280526i	$0.909491\pi$
$18$	0.786399			0.185356
$19$	−3.56631	−	6.17702i	−0.818167	−	1.41711i	−0.907031	−	0.421063i	$-0.861657\pi$
$19$	−3.56631	−	6.17702i	−0.818167	−	1.41711i	0.0888645	−	0.996044i	$-0.471676\pi$
$20$	0.963178	+	1.66827i	0.215373	+	0.373037i
$21$	1.08079			0.235848
$22$	−0.237729	−	0.411760i	−0.0506841	−	0.0877874i
$23$	−3.80710	+	6.59409i	−0.793835	+	1.37496i	0.129741	+	0.991548i	$0.458585\pi$
$23$	−3.80710	+	6.59409i	−0.793835	+	1.37496i	−0.923576	+	0.383415i	$0.874748\pi$
$24$	0.170278	−	0.294930i	0.0347578	−	0.0602023i
$25$	1.00000			0.200000
$26$		0			0
$27$	1.88505			0.362779
$28$	−3.25700	+	5.64129i	−0.615515	+	1.06610i
$29$	−1.99190	+	3.45007i	−0.369886	+	0.640662i	−0.989547	−	0.144208i	$-0.953937\pi$
$29$	−1.99190	+	3.45007i	−0.369886	+	0.640662i	0.619661	+	0.784869i	$0.287270\pi$
$30$	−0.0433679	−	0.0751154i	−0.00791786	−	0.0137141i
$31$	−4.86923			−0.874540			−0.437270	−	0.899330i	$-0.644055\pi$
$31$	−4.86923			−0.874540			−0.437270	+	0.899330i	$0.644055\pi$
$32$	1.54904	+	2.68301i	0.273834	+	0.474294i
$33$	−0.279992	−	0.484961i	−0.0487404	−	0.0844208i
$34$	−0.530316			−0.0909484
$35$	1.69076	+	2.92848i	0.285790	+	0.495003i
$36$	−2.79114	+	4.83440i	−0.465190	+	0.805733i
$37$	5.25050	−	9.09413i	0.863176	−	1.49507i	−0.00567044	−	0.999984i	$-0.501805\pi$
$37$	5.25050	−	9.09413i	0.863176	−	1.49507i	0.868847	−	0.495081i	$-0.164862\pi$
$38$	−1.93560			−0.313997
$39$		0			0
$40$	1.06551			0.168472
$41$	0.455555	−	0.789045i	0.0711458	−	0.123228i	−0.828258	−	0.560347i	$-0.810668\pi$
$41$	0.455555	−	0.789045i	0.0711458	−	0.123228i	0.899404	+	0.437119i	$0.144001\pi$
$42$	0.146649	−	0.254004i	0.0226285	−	0.0391937i
$43$	−2.29276	−	3.97118i	−0.349643	−	0.605600i	0.636543	−	0.771241i	$-0.280364\pi$
$43$	−2.29276	−	3.97118i	−0.349643	−	0.605600i	−0.986186	+	0.165642i	$0.947030\pi$
$44$	3.37506			0.508810
$45$	1.44892	+	2.50961i	0.215993	+	0.374110i
$46$	1.03315	+	1.78946i	0.152329	+	0.263842i
$47$	8.58491			1.25224			0.626119	−	0.779728i	$-0.284643\pi$
$47$	8.58491			1.25224			0.626119	+	0.779728i	$0.284643\pi$
$48$	0.569488	+	0.986383i	0.0821986	+	0.142372i
$49$	−2.21732	+	3.84051i	−0.316760	+	0.548644i
$50$	0.135687	−	0.235017i	0.0191890	−	0.0332364i
$51$	−0.624593			−0.0874605
$52$		0			0
$53$	11.9646			1.64347			0.821734	−	0.569871i	$-0.193007\pi$
$53$	11.9646			1.64347			0.821734	+	0.569871i	$0.193007\pi$
$54$	0.255777	−	0.443019i	0.0348069	−	0.0602873i
$55$	0.876022	−	1.51732i	0.118123	−	0.204595i
$56$	1.80152	+	3.12032i	0.240738	+	0.416971i
$57$	−2.27971			−0.301955
$58$	0.540549	+	0.936259i	0.0709776	+	0.122937i
$59$	1.91149	+	3.31079i	0.248854	+	0.431028i	0.963208	−	0.268756i	$-0.0866127\pi$
$59$	1.91149	+	3.31079i	0.248854	+	0.431028i	−0.714354	+	0.699785i	$0.753279\pi$
$60$	0.615697			0.0794862
$61$	−3.99238	−	6.91500i	−0.511172	−	0.885375i	−0.999916	−	0.0129483i	$-0.995878\pi$
$61$	−3.99238	−	6.91500i	−0.511172	−	0.885375i	0.488745	−	0.872427i	$-0.337455\pi$
$62$	−0.660691	+	1.14435i	−0.0839078	+	0.145333i
$63$	−4.89955	+	8.48627i	−0.617286	+	1.06917i
$64$	−6.28638			−0.785798
$65$		0			0
$66$	−0.151965			−0.0187056
$67$	0.236374	−	0.409412i	0.0288777	−	0.0500177i	−0.851225	−	0.524800i	$-0.824140\pi$
$67$	0.236374	−	0.409412i	0.0288777	−	0.0500177i	0.880103	+	0.474783i	$0.157473\pi$
$68$	1.88223	−	3.26012i	0.228254	−	0.395348i
$69$	1.21682	+	2.10759i	0.146487	+	0.253724i
$70$	0.917654			0.109681
$71$	−2.75156	−	4.76584i	−0.326550	−	0.565602i	0.655275	−	0.755391i	$-0.272553\pi$
$71$	−2.75156	−	4.76584i	−0.326550	−	0.565602i	−0.981825	+	0.189789i	$0.939220\pi$
$72$	1.54384	+	2.67401i	0.181943	+	0.315135i
$73$	−2.93857			−0.343934			−0.171967	−	0.985103i	$-0.555012\pi$
$73$	−2.93857			−0.343934			−0.171967	+	0.985103i	$0.555012\pi$
$74$	−1.42485	−	2.46791i	−0.165635	−	0.286888i
$75$	0.159809	−	0.276797i	0.0184531	−	0.0319618i
$76$	6.86998	−	11.8992i	0.788040	−	1.36493i
$77$	5.92456			0.675167
$78$		0			0
$79$	4.09938			0.461216			0.230608	−	0.973047i	$-0.425928\pi$
$79$	4.09938			0.461216			0.230608	+	0.973047i	$0.425928\pi$
$80$	−1.78178	+	3.08613i	−0.199209	+	0.345040i
$81$	−4.04552	+	7.00704i	−0.449502	+	0.778560i
$82$	−0.123626	−	0.214126i	−0.0136522	−	0.0236463i
$83$	11.7733			1.29229			0.646144	−	0.763215i	$-0.276381\pi$
$83$	11.7733			1.29229			0.646144	+	0.763215i	$0.276381\pi$
$84$	1.04099	+	1.80306i	0.113582	+	0.196729i
$85$	−0.977094	−	1.69238i	−0.105981	−	0.183564i
$86$	−1.24439			−0.134186
$87$	0.636646	+	1.10270i	0.0682556	+	0.118222i
$88$	0.933411	−	1.61671i	0.0995019	−	0.172342i
$89$	−1.92996	+	3.34279i	−0.204576	+	0.354335i	−0.949997	−	0.312258i	$-0.898915\pi$
$89$	−1.92996	+	3.34279i	−0.204576	+	0.354335i	0.745422	+	0.666593i	$0.232248\pi$
$90$	0.786399			0.0828937
$91$		0			0
$92$	−14.6677			−1.52921
$93$	−0.778146	+	1.34779i	−0.0806899	+	0.139759i
$94$	1.16486	−	2.01760i	0.120146	−	0.208099i
$95$	−3.56631	−	6.17702i	−0.365895	−	0.633749i
$96$	0.990200			0.101062
$97$	−3.47888	−	6.02559i	−0.353226	−	0.611806i	0.633586	−	0.773672i	$-0.281582\pi$
$97$	−3.47888	−	6.02559i	−0.353226	−	0.611806i	−0.986813	+	0.161866i	$0.948249\pi$
$98$	0.601723	+	1.04221i	0.0607832	+	0.105280i
$99$	5.07715			0.510273
$100$	0.963178	+	1.66827i	0.0963178	+	0.166827i
$101$	8.94614	−	15.4952i	0.890175	−	1.54183i	0.0505093	−	0.998724i	$-0.483916\pi$
$101$	8.94614	−	15.4952i	0.890175	−	1.54183i	0.839665	−	0.543104i	$-0.182751\pi$
$102$	−0.0847491	+	0.146790i	−0.00839141	+	0.0145343i
$103$	10.2561			1.01056			0.505281	−	0.862955i	$-0.331389\pi$
$103$	10.2561			1.01056			0.505281	+	0.862955i	$0.331389\pi$
$104$		0			0
$105$	1.08079			0.105474
$106$	1.62344	−	2.81189i	0.157683	−	0.273115i
$107$	−6.44930	+	11.1705i	−0.623478	+	1.07990i	0.365355	+	0.930868i	$0.380948\pi$
$107$	−6.44930	+	11.1705i	−0.623478	+	1.07990i	−0.988833	+	0.149027i	$0.952386\pi$
$108$	1.81564	+	3.14479i	0.174710	+	0.302607i
$109$	−10.4476			−1.00070			−0.500348	−	0.865825i	$-0.666794\pi$
$109$	−10.4476			−1.00070			−0.500348	+	0.865825i	$0.666794\pi$
$110$	−0.237729	−	0.411760i	−0.0226666	−	0.0392597i
$111$	−1.67815	−	2.90664i	−0.159283	−	0.275886i
$112$	−12.0502			−1.13864
$113$	9.48828	+	16.4342i	0.892582	+	1.54600i	0.836769	+	0.547557i	$0.184442\pi$
$113$	9.48828	+	16.4342i	0.892582	+	1.54600i	0.0558139	+	0.998441i	$0.482225\pi$
$114$	−0.309327	+	0.535769i	−0.0289711	+	0.0501794i
$115$	−3.80710	+	6.59409i	−0.355014	+	0.614902i
$116$	−7.67421			−0.712533
$117$		0			0
$118$	1.03745			0.0955054
$119$	3.30406	−	5.72280i	0.302883	−	0.524608i
$120$	0.170278	−	0.294930i	0.0155442	−	0.0269233i
$121$	3.96517	+	6.86788i	0.360470	+	0.624352i
$122$	−2.16685			−0.196178
$123$	−0.145603	−	0.252193i	−0.0131286	−	0.0227394i
$124$	−4.68994	−	8.12321i	−0.421169	−	0.729486i
$125$	1.00000			0.0894427
$126$	1.32961	+	2.30295i	0.118451	+	0.205163i
$127$	4.94244	−	8.56056i	0.438571	−	0.759627i	−0.559009	−	0.829162i	$-0.688818\pi$
$127$	4.94244	−	8.56056i	0.438571	−	0.759627i	0.997580	+	0.0695347i	$0.0221515\pi$
$128$	−3.95106	+	6.84343i	−0.349227	+	0.604880i
$129$	−1.46561			−0.129040
$130$		0			0
$131$	−11.4705			−1.00218			−0.501089	−	0.865396i	$-0.667067\pi$
$131$	−11.4705			−1.00218			−0.501089	+	0.865396i	$0.667067\pi$
$132$	0.539365	−	0.934207i	0.0469457	−	0.0813123i
$133$	12.0595	−	20.8877i	1.04569	−	1.81119i
$134$	−0.0641458	−	0.111104i	−0.00554135	−	0.00959790i
$135$	1.88505			0.162240
$136$	−1.04110	−	1.80324i	−0.0892739	−	0.154627i
$137$	−6.54130	−	11.3299i	−0.558861	−	0.967976i	−0.997592	−	0.0693572i	$-0.977905\pi$
$137$	−6.54130	−	11.3299i	−0.558861	−	0.967976i	0.438731	−	0.898619i	$-0.355428\pi$
$138$	0.660424			0.0562190
$139$	−5.98810	−	10.3717i	−0.507904	−	0.879715i	−0.999958	−	0.00915055i	$-0.997087\pi$
$139$	−5.98810	−	10.3717i	−0.507904	−	0.879715i	0.492054	−	0.870564i	$-0.336246\pi$
$140$	−3.25700	+	5.64129i	−0.275267	+	0.476776i
$141$	1.37194	−	2.37628i	0.115538	−	0.200118i
$142$	−1.49340			−0.125324
$143$		0			0
$144$	−10.3266			−0.860554
$145$	−1.99190	+	3.45007i	−0.165418	+	0.286513i
$146$	−0.398726	+	0.690614i	−0.0329988	+	0.0571556i
$147$	0.708694	+	1.22749i	0.0584521	+	0.101242i
$148$	20.2287			1.66278
$149$	8.15261	+	14.1207i	0.667887	+	1.15681i	0.978494	+	0.206276i	$0.0661346\pi$
$149$	8.15261	+	14.1207i	0.667887	+	1.15681i	−0.310606	+	0.950539i	$0.600532\pi$
$150$	−0.0433679	−	0.0751154i	−0.00354098	−	0.00613315i
$151$	−8.75415			−0.712402			−0.356201	−	0.934409i	$-0.615928\pi$
$151$	−8.75415			−0.712402			−0.356201	+	0.934409i	$0.615928\pi$
$152$	−3.79994	−	6.58168i	−0.308216	−	0.533845i
$153$	2.83147	−	4.90424i	0.228911	−	0.396485i
$154$	0.803886	−	1.39237i	0.0647790	−	0.112200i
$155$	−4.86923			−0.391106
$156$		0			0
$157$	6.48821			0.517816			0.258908	−	0.965902i	$-0.416637\pi$
$157$	6.48821			0.517816			0.258908	+	0.965902i	$0.416637\pi$
$158$	0.556232	−	0.963423i	0.0442515	−	0.0766458i
$159$	1.91205	−	3.31177i	0.151636	−	0.262641i
$160$	1.54904	+	2.68301i	0.122462	+	0.212111i
$161$	−25.7475			−2.02919
$162$	1.09785	+	1.90153i	0.0862551	+	0.149398i
$163$	−1.92467	−	3.33362i	−0.150751	−	0.261109i	0.780752	−	0.624840i	$-0.214836\pi$
$163$	−1.92467	−	3.33362i	−0.150751	−	0.261109i	−0.931504	+	0.363731i	$0.881503\pi$
$164$	1.75512			0.137052
$165$	−0.279992	−	0.484961i	−0.0217974	−	0.0377541i
$166$	1.59748	−	2.76692i	0.123989	−	0.214755i
$167$	−3.42947	+	5.94001i	−0.265380	+	0.459652i	−0.967663	−	0.252246i	$-0.918831\pi$
$167$	−3.42947	+	5.94001i	−0.265380	+	0.459652i	0.702283	+	0.711898i	$0.252164\pi$
$168$	1.15159			0.0888474
$169$		0			0
$170$	−0.530316			−0.0406733
$171$	10.3346	−	17.9001i	0.790307	−	1.36885i
$172$	4.41668	−	7.64991i	0.336769	−	0.583300i
$173$	−8.01021	−	13.8741i	−0.609005	−	1.05483i	−0.991405	−	0.130831i	$-0.958235\pi$
$173$	−8.01021	−	13.8741i	−0.609005	−	1.05483i	0.382399	−	0.923997i	$-0.375098\pi$
$174$	0.345538			0.0261952
$175$	1.69076	+	2.92848i	0.127809	+	0.221372i
$176$	3.12176	+	5.40704i	0.235311	+	0.407571i
$177$	1.22189			0.0918428
$178$	0.523741	+	0.907146i	0.0392560	+	0.0679935i
$179$	4.04154	−	7.00016i	0.302079	−	0.523216i	−0.674528	−	0.738250i	$-0.735653\pi$
$179$	4.04154	−	7.00016i	0.302079	−	0.523216i	0.976607	+	0.215033i	$0.0689860\pi$
$180$	−2.79114	+	4.83440i	−0.208039	+	0.360335i
$181$	11.0898			0.824298			0.412149	−	0.911117i	$-0.364778\pi$
$181$	11.0898			0.824298			0.412149	+	0.911117i	$0.364778\pi$
$182$		0			0
$183$	−2.55207			−0.188654
$184$	−4.05650	+	7.02607i	−0.299049	+	0.517969i
$185$	5.25050	−	9.09413i	0.386024	−	0.668613i
$186$	0.211168	+	0.365754i	0.0154836	+	0.0268184i
$187$	−3.42382			−0.250375
$188$	8.26879	+	14.3220i	0.603064	+	1.04454i
$189$	3.18717	+	5.52034i	0.231832	+	0.401546i
$190$	−1.93560			−0.140424
$191$	−10.8766	−	18.8388i	−0.787003	−	1.36313i	−0.927795	−	0.373090i	$-0.878298\pi$
$191$	−10.8766	−	18.8388i	−0.787003	−	1.36313i	0.140792	−	0.990039i	$-0.455035\pi$
$192$	−1.00462	+	1.74005i	−0.0725022	+	0.125577i
$193$	−11.2643	+	19.5103i	−0.810820	+	1.40438i	0.101472	+	0.994838i	$0.467645\pi$
$193$	−11.2643	+	19.5103i	−0.810820	+	1.40438i	−0.912291	+	0.409542i	$0.865688\pi$
$194$	−1.88815			−0.135561
$195$		0			0
$196$	−8.54270			−0.610193
$197$	8.63744	−	14.9605i	0.615392	−	1.06589i	−0.374923	−	0.927056i	$-0.622331\pi$
$197$	8.63744	−	14.9605i	0.615392	−	1.06589i	0.990316	−	0.138835i	$-0.0443357\pi$
$198$	0.688903	−	1.19322i	0.0489582	−	0.0847981i
$199$	−8.74503	−	15.1468i	−0.619919	−	1.07373i	−0.989500	−	0.144532i	$-0.953832\pi$
$199$	−8.74503	−	15.1468i	−0.619919	−	1.07373i	0.369581	−	0.929198i	$-0.379501\pi$
$200$	1.06551			0.0753430
$201$	−0.0755494	−	0.130855i	−0.00532884	−	0.00922982i
$202$	−2.42775	−	4.20499i	−0.170816	−	0.295862i
$203$	−13.4713			−0.945498
$204$	−0.601594	−	1.04199i	−0.0421200	−	0.0729540i
$205$	0.455555	−	0.789045i	0.0318174	−	0.0551093i
$206$	1.39162	−	2.41035i	0.0969585	−	0.167937i
$207$	−22.0648			−1.53361
$208$		0			0
$209$	−12.4967			−0.864412
$210$	0.146649	−	0.254004i	0.0101198	−	0.0175279i
$211$	−3.16782	+	5.48682i	−0.218081	+	0.377728i	−0.954221	−	0.299101i	$-0.903313\pi$
$211$	−3.16782	+	5.48682i	−0.218081	+	0.377728i	0.736140	+	0.676829i	$0.236647\pi$
$212$	11.5241	+	19.9603i	0.791476	+	1.37088i
$213$	−1.75889			−0.120517
$214$	1.75017	+	3.03139i	0.119639	+	0.207221i
$215$	−2.29276	−	3.97118i	−0.156365	−	0.270832i
$216$	2.00855			0.136664
$217$	−8.23269	−	14.2594i	−0.558871	−	0.967993i
$218$	−1.41760	+	2.45535i	−0.0960118	+	0.166297i
$219$	−0.469610	+	0.813388i	−0.0317333	+	0.0549637i
$220$	3.37506			0.227547
$221$		0			0
$222$	−0.910812			−0.0611297
$223$	−11.7474	+	20.3471i	−0.786664	+	1.36254i	0.141335	+	0.989962i	$0.454860\pi$
$223$	−11.7474	+	20.3471i	−0.786664	+	1.36254i	−0.928000	+	0.372581i	$0.878473\pi$
$224$	−5.23810	+	9.07265i	−0.349985	+	0.606192i
$225$	1.44892	+	2.50961i	0.0965948	+	0.167307i
$226$	5.14974			0.342556
$227$	−4.79699	−	8.30862i	−0.318387	−	0.551463i	0.661765	−	0.749712i	$-0.269808\pi$
$227$	−4.79699	−	8.30862i	−0.318387	−	0.551463i	−0.980152	+	0.198249i	$0.936475\pi$
$228$	−2.19577	−	3.80318i	−0.145418	−	0.251872i
$229$	−7.23000			−0.477772			−0.238886	−	0.971048i	$-0.576782\pi$
$229$	−7.23000			−0.477772			−0.238886	+	0.971048i	$0.576782\pi$
$230$	1.03315	+	1.78946i	0.0681237	+	0.117994i
$231$	0.946797	−	1.63990i	0.0622947	−	0.107898i
$232$	−2.12239	+	3.67609i	−0.139342	+	0.241347i
$233$	−0.429924			−0.0281652			−0.0140826	−	0.999901i	$-0.504483\pi$
$233$	−0.429924			−0.0281652			−0.0140826	+	0.999901i	$0.504483\pi$
$234$		0			0
$235$	8.58491			0.560017
$236$	−3.68220	+	6.37776i	−0.239691	+	0.415157i
$237$	0.655117	−	1.13470i	0.0425544	−	0.0737064i
$238$	−0.896635	−	1.55302i	−0.0581202	−	0.100667i
$239$	−12.7450			−0.824405			−0.412203	−	0.911092i	$-0.635240\pi$
$239$	−12.7450			−0.824405			−0.412203	+	0.911092i	$0.635240\pi$
$240$	0.569488	+	0.986383i	0.0367603	+	0.0636707i
$241$	−9.56689	−	16.5703i	−0.616258	−	1.06739i	−0.990162	−	0.139922i	$-0.955315\pi$
$241$	−9.56689	−	16.5703i	−0.616258	−	1.06739i	0.373905	−	0.927467i	$-0.378019\pi$
$242$	2.15209			0.138341
$243$	4.12060	+	7.13709i	0.264337	+	0.457845i
$244$	7.69074	−	13.3208i	0.492349	−	0.852774i
$245$	−2.21732	+	3.84051i	−0.141659	+	0.245361i
$246$	−0.0790259			−0.00503851
$247$		0			0
$248$	−5.18821			−0.329452
$249$	1.88148	−	3.25881i	0.119234	−	0.206519i
$250$	0.135687	−	0.235017i	0.00858159	−	0.0148638i
$251$	−0.205908	−	0.356642i	−0.0129968	−	0.0225111i	0.859454	−	0.511213i	$-0.170804\pi$
$251$	−0.205908	−	0.356642i	−0.0129968	−	0.0225111i	−0.872451	+	0.488702i	$0.837470\pi$
$252$	−18.8766			−1.18911
$253$	6.67021	+	11.5531i	0.419352	+	0.726340i
$254$	−1.34125	−	2.32311i	−0.0841575	−	0.145765i
$255$	−0.624593			−0.0391135
$256$	−5.21417	−	9.03121i	−0.325886	−	0.564451i
$257$	1.23778	−	2.14390i	0.0772105	−	0.133733i	−0.824835	−	0.565374i	$-0.808732\pi$
$257$	1.23778	−	2.14390i	0.0772105	−	0.133733i	0.902045	+	0.431641i	$0.142065\pi$
$258$	−0.198865	+	0.344444i	−0.0123808	+	0.0214441i
$259$	35.5093			2.20644
$260$		0			0
$261$	−11.5444			−0.714582
$262$	−1.55639	+	2.69575i	−0.0961542	+	0.166544i
$263$	5.67953	−	9.83724i	0.350215	−	0.606590i	−0.636072	−	0.771630i	$-0.719442\pi$
$263$	5.67953	−	9.83724i	0.350215	−	0.606590i	0.986287	+	0.165039i	$0.0527752\pi$
$264$	−0.298334	−	0.516730i	−0.0183612	−	0.0318026i
$265$	11.9646			0.734981
$266$	−3.27264	−	5.66837i	−0.200658	−	0.347550i
$267$	0.616850	+	1.06841i	0.0377506	+	0.0653859i
$268$	0.910682			0.0556288
$269$	14.8444	+	25.7112i	0.905078	+	1.56764i	0.820812	+	0.571199i	$0.193521\pi$
$269$	14.8444	+	25.7112i	0.905078	+	1.56764i	0.0842665	+	0.996443i	$0.473145\pi$
$270$	0.255777	−	0.443019i	0.0155661	−	0.0269613i
$271$	7.38804	−	12.7965i	0.448792	−	0.777330i	−0.549516	−	0.835483i	$-0.685188\pi$
$271$	7.38804	−	12.7965i	0.448792	−	0.777330i	0.998308	+	0.0581532i	$0.0185212\pi$
$272$	6.96387			0.422247
$273$		0			0
$274$	−3.55028			−0.214480
$275$	0.876022	−	1.51732i	0.0528261	−	0.0914975i
$276$	−2.34402	+	4.05996i	−0.141093	+	0.244381i
$277$	0.973258	+	1.68573i	0.0584774	+	0.101286i	0.893782	−	0.448501i	$-0.148042\pi$
$277$	0.973258	+	1.68573i	0.0584774	+	0.101286i	−0.835305	+	0.549787i	$0.814709\pi$
$278$	−3.25002			−0.194924
$279$	−7.05514	−	12.2199i	−0.422380	−	0.731584i
$280$	1.80152	+	3.12032i	0.107661	+	0.186475i
$281$	18.5256			1.10515			0.552573	−	0.833464i	$-0.313646\pi$
$281$	18.5256			1.10515			0.552573	+	0.833464i	$0.313646\pi$
$282$	−0.372309	−	0.644859i	−0.0221707	−	0.0384008i
$283$	−6.54758	+	11.3407i	−0.389214	+	0.674138i	−0.992344	−	0.123505i	$-0.960587\pi$
$283$	−6.54758	+	11.3407i	−0.389214	+	0.674138i	0.603130	+	0.797643i	$0.293920\pi$
$284$	5.30049	−	9.18072i	0.314526	−	0.544775i
$285$	−2.27971			−0.135038
$286$		0			0
$287$	3.08093			0.181862
$288$	−4.48887	+	7.77496i	−0.264509	+	0.458144i
$289$	6.59057	−	11.4152i	0.387681	−	0.671483i
$290$	0.540549	+	0.936259i	0.0317421	+	0.0549790i
$291$	−2.22382			−0.130363
$292$	−2.83037	−	4.90234i	−0.165635	−	0.286888i
$293$	0.603763	+	1.04575i	0.0352722	+	0.0610933i	0.883123	−	0.469142i	$-0.155437\pi$
$293$	0.603763	+	1.04575i	0.0352722	+	0.0610933i	−0.847850	+	0.530236i	$0.822104\pi$
$294$	0.384642			0.0224328
$295$	1.91149	+	3.31079i	0.111291	+	0.192762i
$296$	5.59446	−	9.68988i	0.325171	−	0.563213i
$297$	1.65135	−	2.86022i	0.0958210	−	0.165967i
$298$	4.42481			0.256322
$299$		0			0
$300$	0.615697			0.0355473
$301$	7.75301	−	13.4286i	0.446876	−	0.774012i
$302$	−1.18782	+	2.05737i	−0.0683515	+	0.118388i
$303$	−2.85934	−	4.95253i	−0.164265	−	0.284515i
$304$	25.4175			1.45779
$305$	−3.99238	−	6.91500i	−0.228603	−	0.395952i
$306$	−0.768386	−	1.33088i	−0.0439257	−	0.0760815i
$307$	−21.9275			−1.25147			−0.625733	−	0.780037i	$-0.715200\pi$
$307$	−21.9275			−1.25147			−0.625733	+	0.780037i	$0.715200\pi$
$308$	5.70641	+	9.88379i	0.325153	+	0.563181i
$309$	1.63901	−	2.83885i	0.0932401	−	0.161497i
$310$	−0.660691	+	1.14435i	−0.0375247	+	0.0649947i
$311$	−12.5966			−0.714288			−0.357144	−	0.934049i	$-0.616249\pi$
$311$	−12.5966			−0.714288			−0.357144	+	0.934049i	$0.616249\pi$
$312$		0			0
$313$	26.8268			1.51634			0.758169	−	0.652058i	$-0.226094\pi$
$313$	26.8268			1.51634			0.758169	+	0.652058i	$0.226094\pi$
$314$	0.880366	−	1.52484i	0.0496819	−	0.0860516i
$315$	−4.89955	+	8.48627i	−0.276058	+	0.478147i
$316$	3.94843	+	6.83889i	0.222117	+	0.384718i
$317$	17.1279			0.961999			0.481000	−	0.876721i	$-0.340274\pi$
$317$	17.1279			0.961999			0.481000	+	0.876721i	$0.340274\pi$
$318$	−0.518881	−	0.898728i	−0.0290974	−	0.0503982i
$319$	3.48990	+	6.04468i	0.195397	+	0.338437i
$320$	−6.28638			−0.351420
$321$	2.06131	+	3.57030i	0.115051	+	0.199274i
$322$	−3.49360	+	6.05110i	−0.194691	+	0.337214i
$323$	−6.96924	+	12.0711i	−0.387779	+	0.671652i
$324$	−15.5862			−0.865901
$325$		0			0
$326$	−1.04461			−0.0578555
$327$	−1.66961	+	2.89185i	−0.0923298	+	0.159920i
$328$	0.485399	−	0.840735i	0.0268017	−	0.0464218i
$329$	14.5150	+	25.1407i	0.800237	+	1.38605i
$330$	−0.151965			−0.00836540
$331$	0.715309	+	1.23895i	0.0393169	+	0.0680989i	0.885014	−	0.465564i	$-0.154148\pi$
$331$	0.715309	+	1.23895i	0.0393169	+	0.0680989i	−0.845697	+	0.533663i	$0.820815\pi$
$332$	11.3398	+	19.6411i	0.622352	+	1.07794i
$333$	30.4302			1.66757
$334$	0.930668	+	1.61196i	0.0509239	+	0.0882028i
$335$	0.236374	−	0.409412i	0.0129145	−	0.0223686i
$336$	−1.92573	+	3.33547i	−0.105057	+	0.181965i
$337$	−7.48872			−0.407937			−0.203968	−	0.978977i	$-0.565384\pi$
$337$	−7.48872			−0.407937			−0.203968	+	0.978977i	$0.565384\pi$
$338$		0			0
$339$	6.06524			0.329419
$340$	1.88223	−	3.26012i	0.102078	−	0.176805i
$341$	−4.26555	+	7.38816i	−0.230993	+	0.400091i
$342$	−2.80454	−	4.85761i	−0.151652	−	0.262669i
$343$	8.67480			0.468395
$344$	−2.44296	−	4.23134i	−0.131716	−	0.228138i
$345$	1.21682	+	2.10759i	0.0655112	+	0.113469i
$346$	−4.34752			−0.233724
$347$	−3.48406	−	6.03457i	−0.187034	−	0.323953i	0.757226	−	0.653153i	$-0.226554\pi$
$347$	−3.48406	−	6.03457i	−0.187034	−	0.323953i	−0.944260	+	0.329200i	$0.893221\pi$
$348$	−1.22641	+	2.12420i	−0.0657423	+	0.113869i
$349$	10.9869	−	19.0299i	0.588116	−	1.01865i	−0.406363	−	0.913712i	$-0.633203\pi$
$349$	10.9869	−	19.0299i	0.588116	−	1.01865i	0.994479	−	0.104935i	$-0.0334635\pi$
$350$	0.917654			0.0490507
$351$		0			0
$352$	5.42797			0.289312
$353$	6.50920	−	11.2743i	0.346450	−	0.600069i	−0.639166	−	0.769069i	$-0.720720\pi$
$353$	6.50920	−	11.2743i	0.346450	−	0.600069i	0.985616	+	0.169000i	$0.0540538\pi$
$354$	0.165794	−	0.287164i	0.00881187	−	0.0152626i
$355$	−2.75156	−	4.76584i	−0.146038	−	0.252945i
$356$	−7.43559			−0.394085
$357$	−1.05603	−	1.82911i	−0.0558913	−	0.0968066i
$358$	−1.09677	−	1.89966i	−0.0579660	−	0.100400i
$359$	−9.99211			−0.527363			−0.263682	−	0.964610i	$-0.584937\pi$
$359$	−9.99211			−0.527363			−0.263682	+	0.964610i	$0.584937\pi$
$360$	1.54384	+	2.67401i	0.0813676	+	0.140933i
$361$	−15.9371	+	27.6038i	−0.838794	+	1.45283i
$362$	1.50474	−	2.60628i	0.0790873	−	0.136983i
$363$	2.53468			0.133036
$364$		0			0
$365$	−2.93857			−0.153812
$366$	−0.346282	+	0.599778i	−0.0181005	+	0.0313509i
$367$	−12.6441	+	21.9003i	−0.660018	+	1.14318i	0.320593	+	0.947217i	$0.396118\pi$
$367$	−12.6441	+	21.9003i	−0.660018	+	1.14318i	−0.980610	+	0.195967i	$0.937215\pi$
$368$	−13.5668	−	23.4984i	−0.707220	−	1.22494i
$369$	2.64026			0.137446
$370$	−1.42485	−	2.46791i	−0.0740743	−	0.128300i
$371$	20.2293	+	35.0381i	1.05025	+	1.81909i
$372$	−2.99797			−0.155438
$373$	−7.13514	−	12.3584i	−0.369444	−	0.639895i	0.620035	−	0.784574i	$-0.287118\pi$
$373$	−7.13514	−	12.3584i	−0.369444	−	0.639895i	−0.989479	+	0.144679i	$0.953785\pi$
$374$	−0.464568	+	0.804656i	−0.0240222	+	0.0416078i
$375$	0.159809	−	0.276797i	0.00825249	−	0.0142937i
$376$	9.14730			0.471736
$377$		0			0
$378$	1.72983			0.0889728
$379$	3.50670	−	6.07379i	0.180127	−	0.311990i	−0.761796	−	0.647816i	$-0.775682\pi$
$379$	3.50670	−	6.07379i	0.180127	−	0.311990i	0.941924	+	0.335827i	$0.109016\pi$
$380$	6.86998	−	11.8992i	0.352422	−	0.610414i
$381$	−1.57969	−	2.73611i	−0.0809301	−	0.140175i
$382$	−5.90325			−0.302036
$383$	2.34668	+	4.06457i	0.119910	+	0.207690i	0.919732	−	0.392547i	$-0.128406\pi$
$383$	2.34668	+	4.06457i	0.119910	+	0.207690i	−0.799822	+	0.600237i	$0.795073\pi$
$384$	1.26283	+	2.18728i	0.0644434	+	0.111619i
$385$	5.92456			0.301944
$386$	3.05683	+	5.29458i	0.155588	+	0.269487i
$387$	6.64407	−	11.5079i	0.337737	−	0.584978i
$388$	6.70156	−	11.6074i	0.340220	−	0.589278i
$389$	−9.34682			−0.473902			−0.236951	−	0.971522i	$-0.576148\pi$
$389$	−9.34682			−0.473902			−0.236951	+	0.971522i	$0.576148\pi$
$390$		0			0
$391$	14.8796			0.752493
$392$	−2.36258	+	4.09210i	−0.119328	+	0.206682i
$393$	−1.83308	+	3.17499i	−0.0924667	+	0.160157i
$394$	−2.34398	−	4.05989i	−0.118088	−	0.204534i
$395$	4.09938			0.206262
$396$	4.89020	+	8.47008i	0.245742	+	0.425637i
$397$	−10.6067	−	18.3713i	−0.532334	−	0.922029i	−0.999287	−	0.0377472i	$-0.987982\pi$
$397$	−10.6067	−	18.3713i	−0.532334	−	0.922029i	0.466954	−	0.884282i	$-0.345352\pi$
$398$	−4.74634			−0.237913
$399$	−3.85443	−	6.67608i	−0.192963	−	0.334222i
$400$	−1.78178	+	3.08613i	−0.0890890	+	0.154307i
$401$	9.10862	−	15.7766i	0.454863	−	0.787845i	−0.543818	−	0.839203i	$-0.683022\pi$
$401$	9.10862	−	15.7766i	0.454863	−	0.787845i	0.998680	+	0.0513581i	$0.0163550\pi$
$402$	−0.0410042			−0.00204511
$403$		0			0
$404$	34.4669			1.71479
$405$	−4.04552	+	7.00704i	−0.201023	+	0.348183i
$406$	−1.82787	+	3.16597i	−0.0907159	+	0.157125i
$407$	−9.19910	−	15.9333i	−0.455983	−	0.789785i
$408$	−0.665510			−0.0329477
$409$	−2.18068	−	3.77705i	−0.107828	−	0.186763i	0.807062	−	0.590466i	$-0.201056\pi$
$409$	−2.18068	−	3.77705i	−0.107828	−	0.186763i	−0.914890	+	0.403703i	$0.867723\pi$
$410$	−0.123626	−	0.214126i	−0.00610544	−	0.0105749i
$411$	−4.18143			−0.206255
$412$	9.87843	+	17.1099i	0.486675	+	0.842946i
$413$	−6.46372	+	11.1955i	−0.318059	+	0.550894i
$414$	−2.99390	+	5.18559i	−0.147142	+	0.254858i
$415$	11.7733			0.577929
$416$		0			0
$417$	−3.82780			−0.187448
$418$	−1.69563	+	2.93692i	−0.0829361	+	0.143650i
$419$	−8.52773	+	14.7705i	−0.416607	+	0.721584i	−0.995596	−	0.0937512i	$-0.970114\pi$
$419$	−8.52773	+	14.7705i	−0.416607	+	0.721584i	0.578989	+	0.815336i	$0.303448\pi$
$420$	1.04099	+	1.80306i	0.0507953	+	0.0879801i
$421$	−1.27996			−0.0623816			−0.0311908	−	0.999513i	$-0.509930\pi$
$421$	−1.27996			−0.0623816			−0.0311908	+	0.999513i	$0.509930\pi$
$422$	0.859662	+	1.48898i	0.0418477	+	0.0724824i
$423$	12.4389	+	21.5447i	0.604798	+	1.04754i
$424$	12.7484			0.619119
$425$	−0.977094	−	1.69238i	−0.0473960	−	0.0820923i
$426$	−0.238659	+	0.413370i	−0.0115631	+	0.0200278i
$427$	13.5003	−	23.3832i	0.653325	−	1.13159i
$428$	−24.8473			−1.20104
$429$		0			0
$430$	−1.24439			−0.0600099
$431$	−16.4366	+	28.4691i	−0.791725	+	1.37131i	0.133173	+	0.991093i	$0.457483\pi$
$431$	−16.4366	+	28.4691i	−0.791725	+	1.37131i	−0.924898	+	0.380215i	$0.875850\pi$
$432$	−3.35875	+	5.81753i	−0.161598	+	0.279896i
$433$	14.1311	+	24.4758i	0.679097	+	1.17623i	0.975253	+	0.221091i	$0.0709618\pi$
$433$	14.1311	+	24.4758i	0.679097	+	1.17623i	−0.296156	+	0.955140i	$0.595705\pi$
$434$	−4.46827			−0.214484
$435$	0.636646	+	1.10270i	0.0305248	+	0.0528706i
$436$	−10.0629	−	17.4294i	−0.481924	−	0.834717i
$437$	54.3091			2.59796
$438$	0.127440	+	0.220732i	0.00608931	+	0.0105470i
$439$	−13.1310	+	22.7436i	−0.626711	+	1.08549i	0.361497	+	0.932373i	$0.382266\pi$
$439$	−13.1310	+	22.7436i	−0.626711	+	1.08549i	−0.988207	+	0.153121i	$0.951067\pi$
$440$	0.933411	−	1.61671i	0.0444986	−	0.0770739i
$441$	−12.8509			−0.611948
$442$		0			0
$443$	−14.0477			−0.667427			−0.333714	−	0.942674i	$-0.608302\pi$
$443$	−14.0477			−0.667427			−0.333714	+	0.942674i	$0.608302\pi$
$444$	3.23272	−	5.59923i	0.153418	−	0.265728i
$445$	−1.92996	+	3.34279i	−0.0914890	+	0.158464i
$446$	3.18794	+	5.52167i	0.150953	+	0.261459i
$447$	5.21143			0.246492
$448$	−10.6288	−	18.4095i	−0.502161	−	0.869769i
$449$	2.22952	+	3.86164i	0.105218	+	0.182242i	0.913827	−	0.406104i	$-0.133113\pi$
$449$	2.22952	+	3.86164i	0.105218	+	0.182242i	−0.808609	+	0.588346i	$0.799779\pi$
$450$	0.786399			0.0370712
$451$	−0.798153	−	1.38244i	−0.0375836	−	0.0650966i
$452$	−18.2778	+	31.6581i	−0.859716	+	1.48907i
$453$	−1.39899	+	2.42312i	−0.0657303	+	0.113848i
$454$	−2.60355			−0.122191
$455$		0			0
$456$	−2.42905			−0.113751
$457$	−8.20743	+	14.2157i	−0.383927	+	0.664982i	−0.991620	−	0.129191i	$-0.958762\pi$
$457$	−8.20743	+	14.2157i	−0.383927	+	0.664982i	0.607692	+	0.794172i	$0.292095\pi$
$458$	−0.981017	+	1.69917i	−0.0458399	+	0.0793971i
$459$	−1.84188	−	3.19022i	−0.0859714	−	0.148907i
$460$	−14.6677			−0.683883
$461$	−10.2727	−	17.7929i	−0.478449	−	0.828699i	0.521245	−	0.853407i	$-0.325468\pi$
$461$	−10.2727	−	17.7929i	−0.478449	−	0.828699i	−0.999695	+	0.0247082i	$0.992134\pi$
$462$	−0.256936	−	0.445026i	−0.0119537	−	0.0207045i
$463$	1.58359			0.0735958			0.0367979	−	0.999323i	$-0.488284\pi$
$463$	1.58359			0.0735958			0.0367979	+	0.999323i	$0.488284\pi$
$464$	−7.09825	−	12.2945i	−0.329528	−	0.570759i
$465$	−0.778146	+	1.34779i	−0.0360856	+	0.0625022i
$466$	−0.0583350	+	0.101039i	−0.00270232	+	0.00468055i
$467$	5.14277			0.237979			0.118990	−	0.992896i	$-0.462034\pi$
$467$	5.14277			0.237979			0.118990	+	0.992896i	$0.462034\pi$
$468$		0			0
$469$	1.59861			0.0738168
$470$	1.16486	−	2.01760i	0.0537310	−	0.0930647i
$471$	1.03687	−	1.79592i	0.0477766	−	0.0827515i
$472$	2.03671	+	3.52768i	0.0937471	+	0.162375i
$473$	−8.03405			−0.369406
$474$	−0.177782	−	0.307927i	−0.00816578	−	0.0141435i
$475$	−3.56631	−	6.17702i	−0.163633	−	0.283421i
$476$	12.7296			0.583460
$477$	17.3358	+	30.0265i	0.793753	+	1.37482i
$478$	−1.72933	+	2.99529i	−0.0790977	+	0.137001i
$479$	−11.1457	+	19.3049i	−0.509260	+	0.882064i	0.490682	+	0.871338i	$0.336748\pi$
$479$	−11.1457	+	19.3049i	−0.509260	+	0.882064i	−0.999942	+	0.0107258i	$0.996586\pi$
$480$	0.990200			0.0451962
$481$		0			0
$482$	−5.19241			−0.236508
$483$	−4.11468	+	7.12684i	−0.187224	+	0.324282i
$484$	−7.63833	+	13.2300i	−0.347197	+	0.601363i
$485$	−3.47888	−	6.02559i	−0.157968	−	0.273608i
$486$	2.23645			0.101447
$487$	11.7093	+	20.2810i	0.530597	+	0.919021i	0.999363	+	0.0356985i	$0.0113656\pi$
$487$	11.7093	+	20.2810i	0.530597	+	0.919021i	−0.468765	+	0.883323i	$0.655301\pi$
$488$	−4.25392	−	7.36801i	−0.192566	−	0.333534i
$489$	−1.23031			−0.0556367
$490$	0.601723	+	1.04221i	0.0271831	+	0.0470824i
$491$	−1.69895	+	2.94267i	−0.0766727	+	0.132801i	−0.901812	−	0.432128i	$-0.857763\pi$
$491$	−1.69895	+	2.94267i	−0.0766727	+	0.132801i	0.825140	+	0.564929i	$0.191096\pi$
$492$	0.280484	−	0.485813i	0.0126452	−	0.0219021i
$493$	7.78509			0.350623
$494$		0			0
$495$	5.07715			0.228201
$496$	8.67590	−	15.0271i	0.389559	−	0.674737i
$497$	9.30445	−	16.1158i	0.417361	−	0.722891i
$498$	−0.510584	−	0.884357i	−0.0228798	−	0.0396290i
$499$	−4.87712			−0.218330			−0.109165	−	0.994024i	$-0.534818\pi$
$499$	−4.87712			−0.218330			−0.109165	+	0.994024i	$0.534818\pi$
$500$	0.963178	+	1.66827i	0.0430746	+	0.0746075i
$501$	1.09612	+	1.89853i	0.0489710	+	0.0848202i
$502$	−0.111756			−0.00498791
$503$	6.99264	+	12.1116i	0.311786	+	0.540030i	0.978749	−	0.205061i	$-0.0657394\pi$
$503$	6.99264	+	12.1116i	0.311786	+	0.540030i	−0.666963	+	0.745091i	$0.732406\pi$
$504$	−5.22052	+	9.04221i	−0.232541	+	0.402772i
$505$	8.94614	−	15.4952i	0.398098	−	0.689526i
$506$	3.62024			0.160939
$507$		0			0
$508$	19.0418			0.844844
$509$	−18.5079	+	32.0566i	−0.820347	+	1.42088i	0.0850772	+	0.996374i	$0.472886\pi$
$509$	−18.5079	+	32.0566i	−0.820347	+	1.42088i	−0.905424	+	0.424508i	$0.860447\pi$
$510$	−0.0847491	+	0.146790i	−0.00375275	+	0.00649996i
$511$	−4.96841	−	8.60555i	−0.219790	−	0.380687i
$512$	−18.6342			−0.823524
$513$	−6.72268	−	11.6440i	−0.296814	−	0.514096i
$514$	−0.335901	−	0.581797i	−0.0148159	−	0.0256620i
$515$	10.2561			0.451937
$516$	−1.41165	−	2.44505i	−0.0621443	−	0.107637i
$517$	7.52057	−	13.0260i	0.330754	−	0.572883i
$518$	4.81814	−	8.34527i	0.211697	−	0.366670i
$519$	−5.12041			−0.224761
$520$		0			0
$521$	21.5328			0.943370			0.471685	−	0.881767i	$-0.343646\pi$
$521$	21.5328			0.943370			0.471685	+	0.881767i	$0.343646\pi$
$522$	−1.56643	+	2.71313i	−0.0685607	+	0.118751i
$523$	−18.0027	+	31.1816i	−0.787204	+	1.36348i	0.140469	+	0.990085i	$0.455139\pi$
$523$	−18.0027	+	31.1816i	−0.787204	+	1.36348i	−0.927673	+	0.373393i	$0.878194\pi$
$524$	−11.0481	−	19.1359i	−0.482638	−	0.835954i
$525$	1.08079			0.0471696
$526$	−1.54128	−	2.66957i	−0.0672029	−	0.116399i
$527$	4.75770	+	8.24057i	0.207248	+	0.358965i
$528$	1.99554			0.0868446
$529$	−17.4880	−	30.2901i	−0.760349	−	1.31696i
$530$	1.62344	−	2.81189i	0.0705179	−	0.122141i
$531$	−5.53919	+	9.59416i	−0.240380	+	0.416351i
$532$	46.4619			2.01438
$533$		0			0
$534$	0.334794			0.0144879
$535$	−6.44930	+	11.1705i	−0.278828	+	0.482944i
$536$	0.251859	−	0.436233i	0.0108787	−	0.0188424i
$537$	−1.29175	−	2.23737i	−0.0557430	−	0.0965498i
$538$	8.05676			0.347351
$539$	3.88484	+	6.72875i	0.167332	+	0.289828i
$540$	1.81564	+	3.14479i	0.0781329	+	0.135330i
$541$	0.123280			0.00530020			0.00265010	−	0.999996i	$-0.499156\pi$
$541$	0.123280			0.00530020			0.00265010	+	0.999996i	$0.499156\pi$
$542$	−2.00492	−	3.47263i	−0.0861188	−	0.149162i
$543$	1.77225	−	3.06962i	0.0760543	−	0.131730i
$544$	3.02711	−	5.24311i	0.129786	−	0.224797i
$545$	−10.4476			−0.447525
$546$		0			0
$547$	2.52166			0.107818			0.0539092	−	0.998546i	$-0.482832\pi$
$547$	2.52166			0.107818			0.0539092	+	0.998546i	$0.482832\pi$
$548$	12.6009	−	21.8254i	0.538283	−	0.932333i
$549$	11.5693	−	20.0386i	0.493765	−	0.855227i
$550$	−0.237729	−	0.411760i	−0.0101368	−	0.0175575i
$551$	28.4149			1.21052
$552$	1.29653	+	2.24566i	0.0551840	+	0.0955815i
$553$	6.93106	+	12.0049i	0.294739	+	0.510502i
$554$	0.528233			0.0224425
$555$	−1.67815	−	2.90664i	−0.0712335	−	0.123380i
$556$	11.5352	−	19.9796i	0.489202	−	0.847322i
$557$	0.487480	−	0.844340i	0.0206552	−	0.0357758i	−0.855513	−	0.517781i	$-0.826758\pi$
$557$	0.487480	−	0.844340i	0.0206552	−	0.0357758i	0.876168	+	0.482005i	$0.160091\pi$
$558$	−3.82916			−0.162101
$559$		0			0
$560$	−12.0502			−0.509215
$561$	−0.547157	+	0.947704i	−0.0231010	+	0.0400121i
$562$	2.51369	−	4.35383i	0.106033	−	0.183655i
$563$	15.7688	+	27.3124i	0.664576	+	1.15108i	0.979400	+	0.201930i	$0.0647213\pi$
$563$	15.7688	+	27.3124i	0.664576	+	1.15108i	−0.314824	+	0.949150i	$0.601945\pi$
$564$	5.28570			0.222568
$565$	9.48828	+	16.4342i	0.399175	+	0.691391i
$566$	1.77684	+	3.07758i	0.0746863	+	0.129360i
$567$	−27.3600			−1.14901
$568$	−2.93182	−	5.07806i	−0.123016	−	0.213071i
$569$	−12.4381	+	21.5434i	−0.521433	+	0.903148i	0.478256	+	0.878220i	$0.341269\pi$
$569$	−12.4381	+	21.5434i	−0.521433	+	0.903148i	−0.999689	+	0.0249279i	$0.992064\pi$
$570$	−0.309327	+	0.535769i	−0.0129563	+	0.0224409i
$571$	−7.92958			−0.331843			−0.165921	−	0.986139i	$-0.553060\pi$
$571$	−7.92958			−0.331843			−0.165921	+	0.986139i	$0.553060\pi$
$572$		0			0
$573$	−6.95271			−0.290453
$574$	0.418042	−	0.724070i	0.0174487	−	0.0302221i
$575$	−3.80710	+	6.59409i	−0.158767	+	0.274993i
$576$	−9.10848	−	15.7764i	−0.379520	−	0.657348i
$577$	19.0769			0.794180			0.397090	−	0.917780i	$-0.370020\pi$
$577$	19.0769			0.794180			0.397090	+	0.917780i	$0.370020\pi$
$578$	−1.78851	−	3.09779i	−0.0743922	−	0.128851i
$579$	3.60026	+	6.23583i	0.149622	+	0.259152i
$580$	−7.67421			−0.318654
$581$	19.9058	+	34.4779i	0.825832	+	1.43038i
$582$	−0.301743	+	0.522635i	−0.0125077	+	0.0216639i
$583$	10.4813	−	18.1541i	0.434090	−	0.751866i
$584$	−3.13108			−0.129565
$585$		0			0
$586$	0.327691			0.0135368
$587$	9.55978	−	16.5580i	0.394574	−	0.683423i	−0.598472	−	0.801143i	$-0.704225\pi$
$587$	9.55978	−	16.5580i	0.394574	−	0.683423i	0.993047	+	0.117721i	$0.0375587\pi$
$588$	−1.36520	+	2.36459i	−0.0562998	+	0.0975141i
$589$	17.3652	+	30.0774i	0.715519	+	1.23932i
$590$	1.03745			0.0427113
$591$	−2.76068	−	4.78164i	−0.113559	−	0.196690i
$592$	18.7105	+	32.4075i	0.768995	+	1.33194i
$593$	−36.9354			−1.51676			−0.758379	−	0.651814i	$-0.774008\pi$
$593$	−36.9354			−1.51676			−0.758379	+	0.651814i	$0.774008\pi$
$594$	−0.448133	−	0.776189i	−0.0183871	−	0.0318474i
$595$	3.30406	−	5.72280i	0.135453	−	0.234612i
$596$	−15.7048	+	27.2015i	−0.643295	+	1.11422i
$597$	−5.59013			−0.228789
$598$		0			0
$599$	−5.19953			−0.212447			−0.106224	−	0.994342i	$-0.533876\pi$
$599$	−5.19953			−0.212447			−0.106224	+	0.994342i	$0.533876\pi$
$600$	0.170278	−	0.294930i	0.00695157	−	0.0120405i
$601$	14.1603	−	24.5264i	0.577613	−	1.00045i	−0.418140	−	0.908383i	$-0.637318\pi$
$601$	14.1603	−	24.5264i	0.577613	−	1.00045i	0.995752	−	0.0920718i	$-0.0293489\pi$
$602$	−2.10396	−	3.64417i	−0.0857512	−	0.148525i
$603$	1.36995			0.0557887
$604$	−8.43180	−	14.6043i	−0.343085	−	0.594241i
$605$	3.96517	+	6.86788i	0.161207	+	0.279219i
$606$	−1.55190			−0.0630417
$607$	−10.0808	−	17.4604i	−0.409166	−	0.708696i	0.585631	−	0.810578i	$-0.300847\pi$
$607$	−10.0808	−	17.4604i	−0.409166	−	0.708696i	−0.994796	+	0.101882i	$0.967514\pi$
$608$	11.0487	−	19.1369i	0.448084	−	0.776104i
$609$	−2.15283	+	3.72881i	−0.0872370	+	0.151099i
$610$	−2.16685			−0.0877333
$611$		0			0
$612$	10.9088			0.440963
$613$	9.40952	−	16.2978i	0.380047	−	0.658260i	−0.611022	−	0.791614i	$-0.709241\pi$
$613$	9.40952	−	16.2978i	0.380047	−	0.658260i	0.991069	+	0.133353i	$0.0425746\pi$
$614$	−2.97527	+	5.15332i	−0.120072	+	0.207971i
$615$	−0.145603	−	0.252193i	−0.00587130	−	0.0101694i
$616$	6.31268			0.254345
$617$	−1.41246	−	2.44645i	−0.0568634	−	0.0984903i	0.836192	−	0.548436i	$-0.184777\pi$
$617$	−1.41246	−	2.44645i	−0.0568634	−	0.0984903i	−0.893056	+	0.449946i	$0.851443\pi$
$618$	−0.444785	−	0.770390i	−0.0178919	−	0.0309896i
$619$	−15.6686			−0.629773			−0.314886	−	0.949129i	$-0.601966\pi$
$619$	−15.6686			−0.629773			−0.314886	+	0.949129i	$0.601966\pi$
$620$	−4.68994	−	8.12321i	−0.188352	−	0.326236i
$621$	−7.17659	+	12.4302i	−0.287987	+	0.498808i
$622$	−1.70919	+	2.96041i	−0.0685324	+	0.118702i
$623$	−13.0524			−0.522933
$624$		0			0
$625$	1.00000			0.0400000
$626$	3.64004	−	6.30474i	0.145485	−	0.251988i
$627$	−1.99708	+	3.45904i	−0.0797555	+	0.138141i
$628$	6.24931	+	10.8241i	0.249374	+	0.431929i
$629$	−20.5209			−0.818223
$630$	1.32961	+	2.30295i	0.0529729	+	0.0917518i
$631$	5.05744	+	8.75974i	0.201333	+	0.348720i	0.948958	−	0.315402i	$-0.102139\pi$
$631$	5.05744	+	8.75974i	0.201333	+	0.348720i	−0.747625	+	0.664121i	$0.768806\pi$
$632$	4.36793			0.173747
$633$	1.01249	+	1.75368i	0.0402429	+	0.0697027i
$634$	2.32403	−	4.02534i	0.0922992	−	0.159867i
$635$	4.94244	−	8.56056i	0.196135	−	0.339716i
$636$	7.36659			0.292104
$637$		0			0
$638$	1.89413			0.0749894
$639$	7.97360	−	13.8107i	0.315431	−	0.546342i
$640$	−3.95106	+	6.84343i	−0.156179	+	0.270510i
$641$	8.80867	+	15.2571i	0.347922	+	0.602618i	0.985880	−	0.167453i	$-0.0535542\pi$
$641$	8.80867	+	15.2571i	0.347922	+	0.602618i	−0.637958	+	0.770071i	$0.720221\pi$
$642$	1.11877			0.0441544
$643$	−9.51562	−	16.4815i	−0.375260	−	0.649969i	0.615106	−	0.788444i	$-0.289113\pi$
$643$	−9.51562	−	16.4815i	−0.375260	−	0.649969i	−0.990366	+	0.138476i	$0.955780\pi$
$644$	−24.7995	−	42.9539i	−0.977235	−	1.69262i
$645$	−1.46561			−0.0577085
$646$	1.89127	+	3.27577i	0.0744109	+	0.128884i
$647$	13.3486	−	23.1204i	0.524787	−	0.908958i	−0.474796	−	0.880096i	$-0.657478\pi$
$647$	13.3486	−	23.1204i	0.524787	−	0.908958i	0.999583	−	0.0288625i	$-0.00918849\pi$
$648$	−4.31054	+	7.46608i	−0.169334	+	0.293295i
$649$	6.69802			0.262920
$650$		0			0
$651$	−5.26262			−0.206258
$652$	3.70759	−	6.42174i	0.145201	−	0.251495i
$653$	1.58038	−	2.73730i	0.0618451	−	0.107119i	−0.833445	−	0.552602i	$-0.813635\pi$
$653$	1.58038	−	2.73730i	0.0618451	−	0.107119i	0.895290	+	0.445483i	$0.146968\pi$
$654$	0.453089	+	0.784773i	0.0177172	+	0.0306871i
$655$	−11.4705			−0.448188
$656$	1.62340	+	2.81181i	0.0633831	+	0.109783i
$657$	−4.25776	−	7.37466i	−0.166111	−	0.287713i
$658$	7.87798			0.307116
$659$	9.00298	+	15.5936i	0.350706	+	0.607441i	0.986373	−	0.164522i	$-0.0526082\pi$
$659$	9.00298	+	15.5936i	0.350706	+	0.607441i	−0.635667	+	0.771963i	$0.719275\pi$
$660$	0.539365	−	0.934207i	0.0209947	−	0.0363639i
$661$	−1.75893	+	3.04656i	−0.0684145	+	0.118497i	−0.898204	−	0.439580i	$-0.855127\pi$
$661$	−1.75893	+	3.04656i	−0.0684145	+	0.118497i	0.829789	+	0.558077i	$0.188461\pi$
$662$	0.388232			0.0150891
$663$		0			0
$664$	12.5446			0.486824
$665$	12.0595	−	20.8877i	0.467648	−	0.809990i
$666$	4.12899	−	7.15161i	0.159995	−	0.277119i
$667$	−15.1667	−	26.2695i	−0.587258	−	1.01716i
$668$	−13.2128			−0.511217
$669$	3.75468	+	6.50329i	0.145164	+	0.251432i
$670$	−0.0641458	−	0.111104i	−0.00247817	−	0.00429231i
$671$	−13.9896			−0.540064
$672$	1.67419	+	2.89978i	0.0645832	+	0.111861i
$673$	13.0016	−	22.5194i	0.501175	−	0.868060i	−0.498824	−	0.866703i	$-0.666235\pi$
$673$	13.0016	−	22.5194i	0.501175	−	0.868060i	0.999999	−	0.00135704i	$-0.000431960\pi$
$674$	−1.01612	+	1.75997i	−0.0391395	+	0.0677917i
$675$	1.88505			0.0725558
$676$		0			0
$677$	−28.5157			−1.09595			−0.547975	−	0.836495i	$-0.684601\pi$
$677$	−28.5157			−1.09595			−0.547975	+	0.836495i	$0.684601\pi$
$678$	0.822974	−	1.42543i	0.0316061	−	0.0547434i
$679$	11.7639	−	20.3756i	0.451456	−	0.781945i
$680$	−1.04110	−	1.80324i	−0.0399245	−	0.0691513i
$681$	−3.06640			−0.117505
$682$	1.15756	+	2.00495i	0.0443252	+	0.0767736i
$683$	−14.4746	−	25.0708i	−0.553857	−	0.959308i	−0.997991	−	0.0633481i	$-0.979822\pi$
$683$	−14.4746	−	25.0708i	−0.553857	−	0.959308i	0.444135	−	0.895960i	$-0.353511\pi$
$684$	39.8163			1.52241
$685$	−6.54130	−	11.3299i	−0.249930	−	0.432892i
$686$	1.17706	−	2.03872i	0.0449402	−	0.0778388i
$687$	−1.15542	+	2.00124i	−0.0440820	+	0.0763522i
$688$	16.3408			0.622987
$689$		0			0
$690$	0.660424			0.0251419
$691$	−10.8283	+	18.7551i	−0.411927	+	0.713478i	−0.995100	−	0.0988692i	$-0.968477\pi$
$691$	−10.8283	+	18.7551i	−0.411927	+	0.713478i	0.583173	+	0.812348i	$0.301811\pi$
$692$	15.4305	−	26.7265i	0.586581	−	1.01599i
$693$	8.58423	+	14.8683i	0.326088	+	0.564801i
$694$	−1.89097			−0.0717801
$695$	−5.98810	−	10.3717i	−0.227141	−	0.393420i
$696$	0.678353	+	1.17494i	0.0257129	+	0.0445360i
$697$	−1.78048			−0.0674405
$698$	−2.98156	−	5.16421i	−0.112854	−	0.195468i
$699$	−0.0687056	+	0.119002i	−0.00259868	+	0.00450105i
$700$	−3.25700	+	5.64129i	−0.123103	+	0.213221i
$701$	25.0376			0.945656			0.472828	−	0.881155i	$-0.343233\pi$
$701$	25.0376			0.945656			0.472828	+	0.881155i	$0.343233\pi$
$702$		0			0
$703$	−74.8995			−2.82489
$704$	−5.50701	+	9.53843i	−0.207553	+	0.359493i
$705$	1.37194	−	2.37628i	0.0516704	−	0.0894957i
$706$	−1.76643	−	3.05954i	−0.0664803	−	0.115147i
$707$	60.5030			2.27545
$708$	1.17690	+	2.03844i	0.0442305	+	0.0766094i
$709$	−12.8123	−	22.1916i	−0.481178	−	0.833424i	0.518589	−	0.855024i	$-0.326457\pi$
$709$	−12.8123	−	22.1916i	−0.481178	−	0.833424i	−0.999767	+	0.0215996i	$0.993124\pi$
$710$	−1.49340			−0.0560464
$711$	5.93968	+	10.2878i	0.222756	+	0.385824i
$712$	−2.05639	+	3.56178i	−0.0770666	+	0.133483i
$713$	18.5376	−	32.1081i	0.694240	−	1.20246i
$714$	−0.573160			−0.0214500
$715$		0			0
$716$	15.5709			0.581912
$717$	−2.03676	+	3.52778i	−0.0760643	+	0.131747i
$718$	−1.35580	+	2.34831i	−0.0505980	+	0.0876382i
$719$	−7.40320	−	12.8227i	−0.276093	−	0.478207i	0.694317	−	0.719669i	$-0.255706\pi$
$719$	−7.40320	−	12.8227i	−0.276093	−	0.478207i	−0.970410	+	0.241462i	$0.922373\pi$
$720$	−10.3266			−0.384851
$721$	17.3405	+	30.0347i	0.645795	+	1.11855i
$722$	4.32491	+	7.49096i	0.160956	+	0.278785i
$723$	−6.11549			−0.227438
$724$	10.6814	+	18.5008i	0.396973	+	0.687577i
$725$	−1.99190	+	3.45007i	−0.0739773	+	0.128132i
$726$	0.343922	−	0.595691i	0.0127642	−	0.0221082i
$727$	−30.1688			−1.11890			−0.559449	−	0.828865i	$-0.688987\pi$
$727$	−30.1688			−1.11890			−0.559449	+	0.828865i	$0.688987\pi$
$728$		0			0
$729$	−21.6391			−0.801447
$730$	−0.398726	+	0.690614i	−0.0147575	+	0.0255608i
$731$	−4.48049	+	7.76044i	−0.165717	+	0.287030i
$732$	−2.45810	−	4.25755i	−0.0908539	−	0.157363i
$733$	−49.8997			−1.84309			−0.921544	−	0.388275i	$-0.873071\pi$
$733$	−49.8997			−1.84309			−0.921544	+	0.388275i	$0.873071\pi$
$734$	3.43128	+	5.94316i	0.126651	+	0.219366i
$735$	0.708694	+	1.22749i	0.0261406	+	0.0452768i
$736$	−23.5894			−0.869516
$737$	−0.414138	−	0.717308i	−0.0152550	−	0.0264224i
$738$	0.358248	−	0.620504i	0.0131873	−	0.0228411i
$739$	−15.7898	+	27.3487i	−0.580836	+	1.00604i	0.414544	+	0.910029i	$0.363941\pi$
$739$	−15.7898	+	27.3487i	−0.580836	+	1.00604i	−0.995380	+	0.0960090i	$0.969392\pi$
$740$	20.2287			0.743620
$741$		0			0
$742$	10.9794			0.403066
$743$	0.802238	−	1.38952i	0.0294312	−	0.0509764i	−0.850935	−	0.525272i	$-0.823964\pi$
$743$	0.802238	−	1.38952i	0.0294312	−	0.0509764i	0.880366	+	0.474295i	$0.157297\pi$
$744$	−0.829122	+	1.43608i	−0.0303971	+	0.0526493i
$745$	8.15261	+	14.1207i	0.298688	+	0.517343i
$746$	−3.87258			−0.141785
$747$	17.0586	+	29.5464i	0.624142	+	1.08105i
$748$	−3.29775	−	5.71188i	−0.120578	−	0.208847i
$749$	−43.6168			−1.59372
$750$	−0.0433679	−	0.0751154i	−0.00158357	−	0.00274283i
$751$	−5.39364	+	9.34206i	−0.196817	+	0.340897i	−0.947495	−	0.319772i	$-0.896394\pi$
$751$	−5.39364	+	9.34206i	−0.196817	+	0.340897i	0.750678	+	0.660668i	$0.229727\pi$
$752$	−15.2964	+	26.4942i	−0.557803	+	0.966143i
$753$	−0.131623			−0.00479662
$754$		0			0
$755$	−8.75415			−0.318596
$756$	−6.13962	+	10.6341i	−0.223296	+	0.386760i
$757$	3.20195	−	5.54593i	0.116377	−	0.201570i	−0.801953	−	0.597388i	$-0.796205\pi$
$757$	3.20195	−	5.54593i	0.116377	−	0.201570i	0.918329	+	0.395817i	$0.129539\pi$
$758$	−0.951628	−	1.64827i	−0.0345647	−	0.0598678i
$759$	4.26383			0.154767
$760$	−3.79994	−	6.58168i	−0.137838	−	0.238743i
$761$	−25.1328	−	43.5312i	−0.911062	−	1.57801i	−0.812567	−	0.582868i	$-0.801930\pi$
$761$	−25.1328	−	43.5312i	−0.911062	−	1.57801i	−0.0984952	−	0.995138i	$-0.531403\pi$
$762$	−0.857374			−0.0310594
$763$	−17.6643	−	30.5955i	−0.639490	−	1.10763i
$764$	20.9522	−	36.2903i	0.758024	−	1.31294i
$765$	2.83147	−	4.90424i	0.102372	−	0.177313i
$766$	1.27366			0.0460191
$767$		0			0
$768$	−3.33308			−0.120272
$769$	−2.05229	+	3.55467i	−0.0740074	+	0.128185i	−0.900654	−	0.434537i	$-0.856912\pi$
$769$	−2.05229	+	3.55467i	−0.0740074	+	0.128185i	0.826647	+	0.562721i	$0.190246\pi$
$770$	0.803886	−	1.39237i	0.0289700	−	0.0501776i
$771$	−0.395616	−	0.685227i	−0.0142478	−	0.0246778i
$772$	−43.3980			−1.56193
$773$	0.589257	+	1.02062i	0.0211941	+	0.0367093i	0.876428	−	0.481533i	$-0.159920\pi$
$773$	0.589257	+	1.02062i	0.0211941	+	0.0367093i	−0.855234	+	0.518242i	$0.826587\pi$
$774$	−1.80303	−	3.12293i	−0.0648085	−	0.112252i
$775$	−4.86923			−0.174908
$776$	−3.70678	−	6.42033i	−0.133066	−	0.230476i
$777$	5.67469	−	9.82885i	0.203578	−	0.352608i
$778$	−1.26824	+	2.19666i	−0.0454686	+	0.0787540i
$779$	−6.49860			−0.232836
$780$		0			0
$781$	−9.64172			−0.345008
$782$	2.01896	−	3.49695i	0.0721980	−	0.125051i
$783$	−3.75484	+	6.50357i	−0.134187	+	0.232419i
$784$	−7.90156	−	13.6859i	−0.282198	−	0.488782i
$785$	6.48821			0.231574
$786$	0.497450	+	0.861609i	0.0177435	+	0.0307326i
$787$	−16.7458	−	29.0046i	−0.596923	−	1.03390i	−0.993272	−	0.115801i	$-0.963056\pi$
$787$	−16.7458	−	29.0046i	−0.596923	−	1.03390i	0.396349	−	0.918100i	$-0.370277\pi$
$788$	33.2776			1.18546
$789$	−1.81528	−	3.14416i	−0.0646256	−	0.111935i
$790$	0.556232	−	0.963423i	0.0197899	−	0.0342770i
$791$	−32.0848	+	55.5724i	−1.14080	+	1.97593i
$792$	5.40976			0.192227
$793$		0			0
$794$	−5.75675			−0.204299
$795$	1.91205	−	3.31177i	0.0678135	−	0.117456i
$796$	16.8460	−	29.1782i	0.597092	−	1.03419i
$797$	12.4697	+	21.5982i	0.441700	+	0.765046i	0.997816	−	0.0660582i	$-0.0210423\pi$
$797$	12.4697	+	21.5982i	0.441700	+	0.765046i	−0.556116	+	0.831105i	$0.687709\pi$
$798$	−2.09198			−0.0740555
$799$	−8.38826	−	14.5289i	−0.296755	−	0.513995i
$800$	1.54904	+	2.68301i	0.0547668	+	0.0948589i
$801$	−11.1855			−0.395219
$802$	−2.47184	−	4.28135i	−0.0872837	−	0.151180i
$803$	−2.57426	+	4.45874i	−0.0908435	+	0.157346i
$804$	0.145535	−	0.252074i	0.00513262	−	0.00888996i
$805$	−25.7475			−0.907481
$806$		0			0
$807$	9.48906			0.334031
$808$	9.53221	−	16.5103i	0.335342	−	0.580829i
$809$	−6.41107	+	11.1043i	−0.225401	+	0.390406i	−0.956440	−	0.291930i	$-0.905703\pi$
$809$	−6.41107	+	11.1043i	−0.225401	+	0.390406i	0.731039	+	0.682336i	$0.239036\pi$
$810$	1.09785	+	1.90153i	0.0385744	+	0.0668129i
$811$	29.8424			1.04791			0.523954	−	0.851746i	$-0.324456\pi$
$811$	29.8424			1.04791			0.523954	+	0.851746i	$0.324456\pi$
$812$	−12.9752	−	22.4738i	−0.455341	−	0.788674i
$813$	−2.36135	−	4.08998i	−0.0828161	−	0.143442i
$814$	−4.99279			−0.174997
$815$	−1.92467	−	3.33362i	−0.0674181	−	0.116772i
$816$	1.11289	−	1.92758i	0.0389589	−	0.0674787i
$817$	−16.3534	+	28.3249i	−0.572133	+	0.990963i
$818$	−1.18356			−0.0413822
$819$		0			0
$820$	1.75512			0.0612916
$821$	−9.84590	+	17.0536i	−0.343624	+	0.595175i	−0.985103	−	0.171966i	$-0.944988\pi$
$821$	−9.84590	+	17.0536i	−0.343624	+	0.595175i	0.641479	+	0.767141i	$0.278321\pi$
$822$	−0.567365	+	0.982705i	−0.0197891	+	0.0342758i
$823$	−20.9534	−	36.2924i	−0.730390	−	1.26507i	−0.956716	−	0.291022i	$-0.906005\pi$
$823$	−20.9534	−	36.2924i	−0.730390	−	1.26507i	0.226326	−	0.974052i	$-0.427329\pi$
$824$	10.9280			0.380693
$825$	−0.279992	−	0.484961i	−0.00974807	−	0.0168842i
$826$	1.75408	+	3.03816i	0.0610324	+	0.105711i
$827$	21.7734			0.757134			0.378567	−	0.925574i	$-0.376417\pi$
$827$	21.7734			0.757134			0.378567	+	0.925574i	$0.376417\pi$
$828$	−21.2523	−	36.8101i	−0.738569	−	1.27924i
$829$	2.93841	−	5.08948i	0.102055	−	0.176765i	−0.810476	−	0.585772i	$-0.800791\pi$
$829$	2.93841	−	5.08948i	0.102055	−	0.176765i	0.912531	+	0.409007i	$0.134125\pi$
$830$	1.59748	−	2.76692i	0.0554495	−	0.0960413i
$831$	0.622141			0.0215818
$832$		0			0
$833$	8.66612			0.300263
$834$	−0.519382	+	0.899597i	−0.0179847	+	0.0311505i
$835$	−3.42947	+	5.94001i	−0.118682	+	0.205563i
$836$	−12.0365	−	20.8478i	−0.416291	−	0.721038i
$837$	−9.17876			−0.317265
$838$	2.31420	+	4.00832i	0.0799428	+	0.138465i
$839$	27.0558	+	46.8620i	0.934069	+	1.61786i	0.776285	+	0.630381i	$0.217102\pi$
$839$	27.0558	+	46.8620i	0.934069	+	1.61786i	0.157784	+	0.987474i	$0.449565\pi$
$840$	1.15159			0.0397338
$841$	6.56468	+	11.3704i	0.226368	+	0.392081i
$842$	−0.173674	+	0.300813i	−0.00598521	+	0.0103667i
$843$	2.96056	−	5.12784i	0.101967	−	0.176612i
$844$	−12.2047			−0.420103
$845$		0			0
$846$	6.75116			0.232110
$847$	−13.4083	+	23.2238i	−0.460714	+	0.797980i
$848$	−21.3183	+	36.9244i	−0.732075	+	1.26799i
$849$	2.09272	+	3.62470i	0.0718221	+	0.124399i
$850$	−0.530316			−0.0181897
$851$	39.9783	+	69.2445i	1.37044	+	2.37367i
$852$	−1.69413	−	2.93432i	−0.0580399	−	0.100528i
$853$	10.8001			0.369787			0.184893	−	0.982759i	$-0.440806\pi$
$853$	10.8001			0.369787			0.184893	+	0.982759i	$0.440806\pi$
$854$	−3.66362	−	6.34558i	−0.125367	−	0.217141i
$855$	10.3346	−	17.9001i	0.353436	−	0.612169i
$856$	−6.87180	+	11.9023i	−0.234873	+	0.406812i
$857$	−12.0558			−0.411817			−0.205908	−	0.978571i	$-0.566015\pi$
$857$	−12.0558			−0.411817			−0.205908	+	0.978571i	$0.566015\pi$
$858$		0			0
$859$	−47.6819			−1.62688			−0.813442	−	0.581646i	$-0.802409\pi$
$859$	−47.6819			−1.62688			−0.813442	+	0.581646i	$0.802409\pi$
$860$	4.41668	−	7.64991i	0.150608	−	0.260860i
$861$	0.492360	−	0.852793i	0.0167796	−	0.0290631i
$862$	4.46047	+	7.72577i	0.151924	+	0.263141i
$863$	−46.2292			−1.57366			−0.786831	−	0.617169i	$-0.788279\pi$
$863$	−46.2292			−1.57366			−0.786831	+	0.617169i	$0.788279\pi$
$864$	2.92002	+	5.05763i	0.0993412	+	0.172064i
$865$	−8.01021	−	13.8741i	−0.272355	−	0.471733i
$866$	7.66962			0.260624
$867$	−2.10646	−	3.64850i	−0.0715392	−	0.123910i
$868$	15.8591	−	27.4687i	0.538292	−	0.932350i
$869$	3.59115	−	6.22005i	0.121821	−	0.211001i
$870$	0.345538			0.0117148
$871$		0			0
$872$	−11.1320			−0.376977
$873$	10.0812	−	17.4612i	0.341198	−	0.590973i
$874$	7.36904	−	12.7636i	0.249261	−	0.431734i
$875$	1.69076	+	2.92848i	0.0571580	+	0.0990006i
$876$	−1.80927			−0.0611296
$877$	12.6141	+	21.8482i	0.425947	+	0.737761i	0.996508	−	0.0834935i	$-0.0266078\pi$
$877$	12.6141	+	21.8482i	0.425947	+	0.737761i	−0.570562	+	0.821255i	$0.693274\pi$
$878$	3.56342	+	6.17203i	0.120260	+	0.208296i
$879$	0.385947			0.0130177
$880$	3.12176	+	5.40704i	0.105234	+	0.182271i
$881$	6.25429	−	10.8327i	0.210712	−	0.364964i	−0.741225	−	0.671256i	$-0.765755\pi$
$881$	6.25429	−	10.8327i	0.210712	−	0.364964i	0.951938	+	0.306292i	$0.0990883\pi$
$882$	−1.74370	+	3.02017i	−0.0587134	+	0.101695i
$883$	−11.2289			−0.377881			−0.188941	−	0.981989i	$-0.560505\pi$
$883$	−11.2289			−0.377881			−0.188941	+	0.981989i	$0.560505\pi$
$884$		0			0
$885$	1.22189			0.0410733
$886$	−1.90609	+	3.30145i	−0.0640364	+	0.110914i
$887$	27.2692	−	47.2316i	0.915609	−	1.58588i	0.109602	−	0.993976i	$-0.465042\pi$
$887$	27.2692	−	47.2316i	0.915609	−	1.58588i	0.806007	−	0.591906i	$-0.201624\pi$
$888$	−1.78809	−	3.09706i	−0.0600043	−	0.103930i
$889$	33.4259			1.12107
$890$	0.523741	+	0.907146i	0.0175558	+	0.0304076i
$891$	7.08793	+	12.2767i	0.237455	+	0.411283i
$892$	−45.2594			−1.51540
$893$	−30.6164	−	53.0292i	−1.02454	−	1.77455i
$894$	0.707123	−	1.22477i	0.0236497	−	0.0409625i
$895$	4.04154	−	7.00016i	0.135094	−	0.233989i
$896$	−26.7211			−0.892690
$897$		0			0
$898$	1.21007			0.0403805
$899$	9.69901	−	16.7992i	0.323480	−	0.560284i
$900$	−2.79114	+	4.83440i	−0.0930380	+	0.161147i
$901$	−11.6906	−	20.2487i	−0.389469	−	0.674581i
$902$	−0.433196			−0.0144238
$903$	−2.47800	−	4.29202i	−0.0824626	−	0.142829i
$904$	10.1099	+	17.5108i	0.336249	+	0.582400i
$905$	11.0898			0.368637
$906$	0.379649	+	0.657572i	0.0126130	+	0.0218464i
$907$	−14.4541	+	25.0353i	−0.479942	+	0.831283i	−0.999735	−	0.0230085i	$-0.992676\pi$
$907$	−14.4541	+	25.0353i	−0.479942	+	0.831283i	0.519794	+	0.854292i	$0.326009\pi$
$908$	9.24070	−	16.0054i	0.306664	−	0.531157i
$909$	51.8491			1.71973
$910$		0			0
$911$	−7.04371			−0.233369			−0.116684	−	0.993169i	$-0.537227\pi$
$911$	−7.04371			−0.233369			−0.116684	+	0.993169i	$0.537227\pi$
$912$	4.06194	−	7.03549i	0.134504	−	0.232968i
$913$	10.3137	−	17.8638i	0.341333	−	0.591206i
$914$	2.22728	+	3.85776i	0.0736719	+	0.127604i
$915$	−2.55207			−0.0843688
$916$	−6.96378	−	12.0616i	−0.230090	−	0.398527i
$917$	−19.3938	−	33.5910i	−0.640439	−	1.10927i
$918$	−0.999674			−0.0329942
$919$	8.68191	+	15.0375i	0.286390	+	0.496042i	0.972945	−	0.231036i	$-0.0742114\pi$
$919$	8.68191	+	15.0375i	0.286390	+	0.496042i	−0.686555	+	0.727077i	$0.740878\pi$
$920$	−4.05650	+	7.02607i	−0.133739	+	0.231643i
$921$	−3.50420	+	6.06945i	−0.115467	+	0.199995i
$922$	−5.57551			−0.183620
$923$		0			0
$924$	3.64774			0.120002
$925$	5.25050	−	9.09413i	0.172635	−	0.299013i
$926$	0.214873	−	0.372170i	0.00706115	−	0.0122303i
$927$	14.8603	+	25.7387i	0.488075	+	0.845371i
$928$	−12.3421			−0.405150
$929$	15.4690	+	26.7931i	0.507522	+	0.879055i	0.999962	+	0.00870800i	$0.00277188\pi$
$929$	15.4690	+	26.7931i	0.507522	+	0.879055i	−0.492440	+	0.870347i	$0.663895\pi$
$930$	0.211168	+	0.365754i	0.00692448	+	0.0119936i
$931$	31.6306			1.03665
$932$	−0.414093	−	0.717230i	−0.0135641	−	0.0234937i
$933$	−2.01305	+	3.48670i	−0.0659042	+	0.114149i
$934$	0.697807	−	1.20864i	0.0228329	−	0.0395478i
$935$	−3.42382			−0.111971
$936$		0			0
$937$	30.5009			0.996422			0.498211	−	0.867056i	$-0.333990\pi$
$937$	30.5009			0.996422			0.498211	+	0.867056i	$0.333990\pi$
$938$	0.216910	−	0.375699i	0.00708236	−	0.0122670i
$939$	4.28715	−	7.42557i	0.139906	−	0.242324i
$940$	8.26879	+	14.3220i	0.269698	+	0.467131i
$941$	32.0423			1.04455			0.522275	−	0.852777i	$-0.325083\pi$
$941$	32.0423			1.04455			0.522275	+	0.852777i	$0.325083\pi$
$942$	−0.281380	−	0.487365i	−0.00916787	−	0.0158792i
$943$	3.46869	+	6.00794i	0.112956	+	0.195646i
$944$	−13.6234			−0.443404
$945$	3.18717	+	5.52034i	0.103679	+	0.179577i
$946$	−1.09011	+	1.88813i	−0.0354427	+	0.0613885i
$947$	−4.31698	+	7.47722i	−0.140283	+	0.242977i	−0.927603	−	0.373567i	$-0.878135\pi$
$947$	−4.31698	+	7.47722i	−0.140283	+	0.242977i	0.787320	+	0.616544i	$0.211468\pi$
$948$	2.52398			0.0819750
$949$		0			0
$950$	−1.93560			−0.0627993
$951$	2.73719	−	4.74095i	0.0887595	−	0.153736i
$952$	3.52051	−	6.09770i	0.114100	−	0.197628i
$953$	16.2130	+	28.0818i	0.525191	+	0.909657i	0.999570	+	0.0293364i	$0.00933941\pi$
$953$	16.2130	+	28.0818i	0.525191	+	0.909657i	−0.474379	+	0.880321i	$0.657327\pi$
$954$	9.40897			0.304627
$955$	−10.8766	−	18.8388i	−0.351959	−	0.609610i
$956$	−12.2757	−	21.2621i	−0.397025	−	0.687667i
$957$	2.23086			0.0721136
$958$	3.02465	+	5.23885i	0.0977220	+	0.169260i
$959$	22.1195	−	38.3121i	0.714276	−	1.23716i
$960$	−1.00462	+	1.74005i	−0.0324240	+	0.0561599i
$961$	−7.29060			−0.235181
$962$		0			0
$963$	−37.3782			−1.20449
$964$	18.4292	−	31.9204i	0.593566	−	1.02809i
$965$	−11.2643	+	19.5103i	−0.362610	+	0.628058i
$966$	1.11662	+	1.93404i	0.0359265	+	0.0622266i
$967$	27.0744			0.870656			0.435328	−	0.900272i	$-0.356632\pi$
$967$	27.0744			0.870656			0.435328	+	0.900272i	$0.356632\pi$
$968$	4.22493	+	7.31779i	0.135794	+	0.235203i
$969$	2.22749	+	3.85813i	0.0715573	+	0.123941i
$970$	−1.88815			−0.0606249
$971$	−15.9019	−	27.5430i	−0.510317	−	0.883896i	−0.999929	−	0.0119548i	$-0.996195\pi$
$971$	−15.9019	−	27.5430i	−0.510317	−	0.883896i	0.489611	−	0.871941i	$-0.337139\pi$
$972$	−7.93775	+	13.7486i	−0.254603	+	0.440986i
$973$	20.2488	−	35.0720i	0.649148	−	1.12436i
$974$	6.35517			0.203633
$975$		0			0
$976$	28.4542			0.910796
$977$	−15.6836	+	27.1648i	−0.501763	+	0.869079i	0.498235	+	0.867042i	$0.333982\pi$
$977$	−15.6836	+	27.1648i	−0.501763	+	0.869079i	−0.999998	+	0.00203688i	$0.999352\pi$
$978$	−0.166937	+	0.289144i	−0.00533807	+	0.00924581i
$979$	3.38138	+	5.85672i	0.108069	+	0.187182i
$980$	−8.54270			−0.272886
$981$	−15.1377	−	26.2193i	−0.483310	−	0.837117i
$982$	0.461051	+	0.798564i	0.0147127	+	0.0254832i
$983$	−35.5044			−1.13241			−0.566207	−	0.824263i	$-0.691590\pi$
$983$	−35.5044			−1.13241			−0.566207	+	0.824263i	$0.691590\pi$
$984$	−0.155142	−	0.268714i	−0.00494575	−	0.00856628i
$985$	8.63744	−	14.9605i	0.275212	−	0.476681i
$986$	1.05633	−	1.82963i	0.0336406	−	0.0582672i
$987$	9.27849			0.295338
$988$		0			0
$989$	34.9151			1.11024
$990$	0.688903	−	1.19322i	0.0218948	−	0.0379229i
$991$	20.5319	−	35.5623i	0.652217	−	1.12967i	−0.330367	−	0.943853i	$-0.607172\pi$
$991$	20.5319	−	35.5623i	0.652217	−	1.12967i	0.982584	−	0.185820i	$-0.0594943\pi$
$992$	−7.54263	−	13.0642i	−0.239479	−	0.414789i
$993$	0.457250			0.0145104
$994$	−2.52498	−	4.37340i	−0.0800876	−	0.138716i
$995$	−8.74503	−	15.1468i	−0.277236	−	0.480187i
$996$	7.24879			0.229687
$997$	22.3952	+	38.7897i	0.709264	+	1.22848i	0.965131	+	0.261769i	$0.0843058\pi$
$997$	22.3952	+	38.7897i	0.709264	+	1.22848i	−0.255867	+	0.966712i	$0.582361\pi$
$998$	−0.661761	+	1.14620i	−0.0209477	+	0.0362825i
$999$	9.89747	−	17.1429i	0.313142	−	0.542378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.e.o.191.6		18
13.2	odd	12		845.2.m.j.361.11		36
13.3	even	3	inner	845.2.e.o.146.6		18
13.4	even	6		845.2.a.n.1.6	✓	9
13.5	odd	4		845.2.m.j.316.8		36
13.6	odd	12		845.2.c.h.506.11		18
13.7	odd	12		845.2.c.h.506.8		18
13.8	odd	4		845.2.m.j.316.11		36
13.9	even	3		845.2.a.o.1.4	yes	9
13.10	even	6		845.2.e.p.146.4		18
13.11	odd	12		845.2.m.j.361.8		36
13.12	even	2		845.2.e.p.191.4		18
39.17	odd	6		7605.2.a.cs.1.4		9
39.35	odd	6		7605.2.a.cp.1.6		9
65.4	even	6		4225.2.a.bt.1.4		9
65.9	even	6		4225.2.a.bs.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.a.n.1.6	✓	9	13.4	even	6
845.2.a.o.1.4	yes	9	13.9	even	3
845.2.c.h.506.8		18	13.7	odd	12
845.2.c.h.506.11		18	13.6	odd	12
845.2.e.o.146.6		18	13.3	even	3	inner
845.2.e.o.191.6		18	1.1	even	1	trivial
845.2.e.p.146.4		18	13.10	even	6
845.2.e.p.191.4		18	13.12	even	2
845.2.m.j.316.8		36	13.5	odd	4
845.2.m.j.316.11		36	13.8	odd	4
845.2.m.j.361.8		36	13.11	odd	12
845.2.m.j.361.11		36	13.2	odd	12
4225.2.a.bs.1.6		9	65.9	even	6
4225.2.a.bt.1.4		9	65.4	even	6
7605.2.a.cp.1.6		9	39.35	odd	6
7605.2.a.cs.1.4		9	39.17	odd	6

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.135687 - 0.235017i) q^{2} +(0.159809 - 0.276797i) q^{3} +(0.963178 + 1.66827i) q^{4} +1.00000 q^{5} +(-0.0433679 - 0.0751154i) q^{6} +(1.69076 + 2.92848i) q^{7} +1.06551 q^{8} +(1.44892 + 2.50961i) q^{9} +(0.135687 - 0.235017i) q^{10} +(0.876022 - 1.51732i) q^{11} +0.615697 q^{12} +0.917654 q^{14} +(0.159809 - 0.276797i) q^{15} +(-1.78178 + 3.08613i) q^{16} +(-0.977094 - 1.69238i) q^{17} +0.786399 q^{18} +(-3.56631 - 6.17702i) q^{19} +(0.963178 + 1.66827i) q^{20} +1.08079 q^{21} +(-0.237729 - 0.411760i) q^{22} +(-3.80710 + 6.59409i) q^{23} +(0.170278 - 0.294930i) q^{24} +1.00000 q^{25} +1.88505 q^{27} +(-3.25700 + 5.64129i) q^{28} +(-1.99190 + 3.45007i) q^{29} +(-0.0433679 - 0.0751154i) q^{30} -4.86923 q^{31} +(1.54904 + 2.68301i) q^{32} +(-0.279992 - 0.484961i) q^{33} -0.530316 q^{34} +(1.69076 + 2.92848i) q^{35} +(-2.79114 + 4.83440i) q^{36} +(5.25050 - 9.09413i) q^{37} -1.93560 q^{38} +1.06551 q^{40} +(0.455555 - 0.789045i) q^{41} +(0.146649 - 0.254004i) q^{42} +(-2.29276 - 3.97118i) q^{43} +3.37506 q^{44} +(1.44892 + 2.50961i) q^{45} +(1.03315 + 1.78946i) q^{46} +8.58491 q^{47} +(0.569488 + 0.986383i) q^{48} +(-2.21732 + 3.84051i) q^{49} +(0.135687 - 0.235017i) q^{50} -0.624593 q^{51} +11.9646 q^{53} +(0.255777 - 0.443019i) q^{54} +(0.876022 - 1.51732i) q^{55} +(1.80152 + 3.12032i) q^{56} -2.27971 q^{57} +(0.540549 + 0.936259i) q^{58} +(1.91149 + 3.31079i) q^{59} +0.615697 q^{60} +(-3.99238 - 6.91500i) q^{61} +(-0.660691 + 1.14435i) q^{62} +(-4.89955 + 8.48627i) q^{63} -6.28638 q^{64} -0.151965 q^{66} +(0.236374 - 0.409412i) q^{67} +(1.88223 - 3.26012i) q^{68} +(1.21682 + 2.10759i) q^{69} +0.917654 q^{70} +(-2.75156 - 4.76584i) q^{71} +(1.54384 + 2.67401i) q^{72} -2.93857 q^{73} +(-1.42485 - 2.46791i) q^{74} +(0.159809 - 0.276797i) q^{75} +(6.86998 - 11.8992i) q^{76} +5.92456 q^{77} +4.09938 q^{79} +(-1.78178 + 3.08613i) q^{80} +(-4.04552 + 7.00704i) q^{81} +(-0.123626 - 0.214126i) q^{82} +11.7733 q^{83} +(1.04099 + 1.80306i) q^{84} +(-0.977094 - 1.69238i) q^{85} -1.24439 q^{86} +(0.636646 + 1.10270i) q^{87} +(0.933411 - 1.61671i) q^{88} +(-1.92996 + 3.34279i) q^{89} +0.786399 q^{90} -14.6677 q^{92} +(-0.778146 + 1.34779i) q^{93} +(1.16486 - 2.01760i) q^{94} +(-3.56631 - 6.17702i) q^{95} +0.990200 q^{96} +(-3.47888 - 6.02559i) q^{97} +(0.601723 + 1.04221i) q^{98} +5.07715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{2} - 7 q^{3} - 17 q^{4} + 18 q^{5} + 2 q^{6} - 7 q^{7} + 24 q^{8} - 16 q^{9} - 3 q^{10} + 9 q^{11} + 24 q^{12} - 4 q^{14} - 7 q^{15} - 37 q^{16} + q^{17} - 20 q^{18} + 4 q^{19} - 17 q^{20}+ \cdots - 2 q^{99}+O(q^{100}) \) 18 * q - 3 * q^2 - 7 * q^3 - 17 * q^4 + 18 * q^5 + 2 * q^6 - 7 * q^7 + 24 * q^8 - 16 * q^9 - 3 * q^10 + 9 * q^11 + 24 * q^12 - 4 * q^14 - 7 * q^15 - 37 * q^16 + q^17 - 20 * q^18 + 4 * q^19 - 17 * q^20 - 2 * q^21 - 12 * q^22 - 14 * q^23 + 35 * q^24 + 18 * q^25 + 44 * q^27 - 18 * q^28 - 12 * q^29 + 2 * q^30 - 14 * q^31 - 22 * q^32 + 8 * q^33 - 60 * q^34 - 7 * q^35 - 3 * q^36 + 5 * q^37 - 94 * q^38 + 24 * q^40 + 10 * q^41 + 11 * q^42 - 39 * q^43 - 50 * q^44 - 16 * q^45 - 6 * q^46 + 72 * q^47 + 3 * q^48 - 16 * q^49 - 3 * q^50 + 86 * q^51 - 16 * q^53 + 2 * q^54 + 9 * q^55 + 29 * q^56 - 64 * q^57 - 21 * q^58 + 21 * q^59 + 24 * q^60 + 3 * q^61 + 10 * q^62 - 35 * q^63 + 68 * q^64 - 98 * q^66 - q^67 + 20 * q^68 + 13 * q^69 - 4 * q^70 + q^71 + 3 * q^72 + 15 * q^74 - 7 * q^75 + 5 * q^76 - 8 * q^77 + 78 * q^79 - 37 * q^80 - 29 * q^81 + 4 * q^82 + 14 * q^83 - 12 * q^84 + q^85 - 48 * q^86 - 16 * q^87 - 42 * q^88 + 19 * q^89 - 20 * q^90 - 54 * q^92 - 31 * q^93 - 16 * q^94 + 4 * q^95 - 14 * q^96 + 34 * q^97 - 48 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

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