LMFDB - Embedded newform 322.2.i.b.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (of order $11$, degree $10$, 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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			169.1
Root			$-0.415415 + 0.909632i$ of defining polynomial
Character	$\chi$	$=$	322.169
Dual form			322.2.i.b.141.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 - 0.989821i) q^{2} +(-0.570276 - 1.24873i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.59792 - 1.84410i) q^{5} +(-1.31718 + 0.386758i) q^{6} +(-0.841254 - 0.540641i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.730471 - 0.843008i) q^{9} +O(q^{10})$	\(q+(0.142315 - 0.989821i) q^{2} +(-0.570276 - 1.24873i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.59792 - 1.84410i) q^{5} +(-1.31718 + 0.386758i) q^{6} +(-0.841254 - 0.540641i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.730471 - 0.843008i) q^{9} +(-2.05274 + 1.31921i) q^{10} +(0.245454 + 1.70717i) q^{11} +(0.195368 + 1.35881i) q^{12} +(-2.01722 + 1.29639i) q^{13} +(-0.654861 + 0.755750i) q^{14} +(-1.39153 + 3.04702i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-4.48538 + 1.31703i) q^{17} +(-0.730471 - 0.843008i) q^{18} +(1.11435 + 0.327204i) q^{19} +(1.01365 + 2.21959i) q^{20} +(-0.195368 + 1.35881i) q^{21} +1.72472 q^{22} +(-3.46135 - 3.31949i) q^{23} +1.37279 q^{24} +(-0.135777 + 0.944350i) q^{25} +(0.996114 + 2.18119i) q^{26} +(-5.42079 - 1.59169i) q^{27} +(0.654861 + 0.755750i) q^{28} +(5.04311 - 1.48079i) q^{29} +(2.81797 + 1.81100i) q^{30} +(0.249869 - 0.547137i) q^{31} +(0.654861 - 0.755750i) q^{32} +(1.99182 - 1.28006i) q^{33} +(0.665284 + 4.62715i) q^{34} +(0.347262 + 2.41526i) q^{35} +(-0.938384 + 0.603063i) q^{36} +(5.27613 - 6.08898i) q^{37} +(0.482462 - 1.05645i) q^{38} +(2.76921 + 1.77967i) q^{39} +(2.34125 - 0.687454i) q^{40} +(-8.18535 - 9.44640i) q^{41} +(1.31718 + 0.386758i) q^{42} +(2.29652 + 5.02867i) q^{43} +(0.245454 - 1.70717i) q^{44} -2.72183 q^{45} +(-3.77831 + 2.95371i) q^{46} +6.22277 q^{47} +(0.195368 - 1.35881i) q^{48} +(0.415415 + 0.909632i) q^{49} +(0.915415 + 0.268790i) q^{50} +(4.20251 + 4.84995i) q^{51} +(2.30075 - 0.675560i) q^{52} +(-8.29712 - 5.33224i) q^{53} +(-2.34695 + 5.13910i) q^{54} +(2.75597 - 3.18056i) q^{55} +(0.841254 - 0.540641i) q^{56} +(-0.226900 - 1.57812i) q^{57} +(-0.748008 - 5.20251i) q^{58} +(3.45491 - 2.22034i) q^{59} +(2.19360 - 2.53155i) q^{60} +(3.76039 - 8.23412i) q^{61} +(-0.506008 - 0.325192i) q^{62} +(-1.07028 + 0.314261i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(5.61404 + 1.64843i) q^{65} +(-0.983568 - 2.15371i) q^{66} +(-2.04487 + 14.2224i) q^{67} +4.67474 q^{68} +(-2.17122 + 6.21532i) q^{69} +2.44009 q^{70} +(1.32879 - 9.24194i) q^{71} +(0.463379 + 1.01466i) q^{72} +(-3.05612 - 0.897358i) q^{73} +(-5.27613 - 6.08898i) q^{74} +(1.25667 - 0.368991i) q^{75} +(-0.977031 - 0.627899i) q^{76} +(0.716476 - 1.56886i) q^{77} +(2.15565 - 2.48775i) q^{78} +(6.14561 - 3.94954i) q^{79} +(-0.347262 - 2.41526i) q^{80} +(0.627519 + 4.36449i) q^{81} +(-10.5151 + 6.75767i) q^{82} +(2.66583 - 3.07653i) q^{83} +(0.570276 - 1.24873i) q^{84} +(9.59601 + 6.16698i) q^{85} +(5.30432 - 1.55749i) q^{86} +(-4.72507 - 5.45302i) q^{87} +(-1.65486 - 0.485911i) q^{88} +(-2.00538 - 4.39117i) q^{89} +(-0.387356 + 2.69412i) q^{90} +2.39788 q^{91} +(2.38594 + 4.16021i) q^{92} -0.825721 q^{93} +(0.885593 - 6.15943i) q^{94} +(-1.17725 - 2.57783i) q^{95} +(-1.31718 - 0.386758i) q^{96} +(-0.816541 - 0.942338i) q^{97} +(0.959493 - 0.281733i) q^{98} +(1.61845 + 1.04012i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} + 5 q^{3} - q^{4} + 8 q^{5} - 5 q^{6} + q^{7} + q^{8}+O(q^{10}) $ 10 * q + q^2 + 5 * q^3 - q^4 + 8 * q^5 - 5 * q^6 + q^7 + q^8	\( 10 q + q^{2} + 5 q^{3} - q^{4} + 8 q^{5} - 5 q^{6} + q^{7} + q^{8} + 3 q^{10} + 11 q^{11} + 5 q^{12} - 6 q^{13} - q^{14} + 4 q^{15} - q^{16} - 2 q^{17} - 3 q^{19} + 8 q^{20} - 5 q^{21} - 21 q^{23} + 6 q^{24} - 15 q^{25} - 5 q^{26} - 4 q^{27} + q^{28} + 2 q^{29} - 4 q^{30} + 3 q^{31} + q^{32} - 11 q^{33} + 2 q^{34} + 3 q^{35} - 6 q^{37} - 8 q^{38} + 8 q^{39} + 14 q^{40} - 23 q^{41} + 5 q^{42} - q^{43} + 11 q^{44} - 22 q^{45} - q^{46} + 38 q^{47} + 5 q^{48} - q^{49} + 4 q^{50} + 21 q^{51} + 5 q^{52} - 49 q^{53} + 4 q^{54} + 11 q^{55} - q^{56} - 7 q^{57} - 13 q^{58} + 9 q^{59} + 4 q^{60} + 16 q^{61} - 14 q^{62} - q^{64} + 15 q^{65} + 7 q^{67} - 2 q^{68} - 16 q^{69} + 8 q^{70} - 16 q^{71} + 11 q^{72} - 9 q^{73} + 6 q^{74} - 2 q^{75} - 14 q^{76} + 11 q^{77} - 8 q^{78} + 6 q^{79} - 3 q^{80} - 24 q^{81} - 43 q^{82} - 19 q^{83} - 5 q^{84} + 49 q^{85} + 23 q^{86} - 21 q^{87} - 11 q^{88} + 25 q^{89} - 11 q^{90} + 6 q^{91} + q^{92} - 4 q^{93} - 5 q^{94} + 24 q^{95} - 5 q^{96} + 16 q^{97} + q^{98} - 33 q^{99}+O(q^{100}) \) 10 * q + q^2 + 5 * q^3 - q^4 + 8 * q^5 - 5 * q^6 + q^7 + q^8 + 3 * q^10 + 11 * q^11 + 5 * q^12 - 6 * q^13 - q^14 + 4 * q^15 - q^16 - 2 * q^17 - 3 * q^19 + 8 * q^20 - 5 * q^21 - 21 * q^23 + 6 * q^24 - 15 * q^25 - 5 * q^26 - 4 * q^27 + q^28 + 2 * q^29 - 4 * q^30 + 3 * q^31 + q^32 - 11 * q^33 + 2 * q^34 + 3 * q^35 - 6 * q^37 - 8 * q^38 + 8 * q^39 + 14 * q^40 - 23 * q^41 + 5 * q^42 - q^43 + 11 * q^44 - 22 * q^45 - q^46 + 38 * q^47 + 5 * q^48 - q^49 + 4 * q^50 + 21 * q^51 + 5 * q^52 - 49 * q^53 + 4 * q^54 + 11 * q^55 - q^56 - 7 * q^57 - 13 * q^58 + 9 * q^59 + 4 * q^60 + 16 * q^61 - 14 * q^62 - q^64 + 15 * q^65 + 7 * q^67 - 2 * q^68 - 16 * q^69 + 8 * q^70 - 16 * q^71 + 11 * q^72 - 9 * q^73 + 6 * q^74 - 2 * q^75 - 14 * q^76 + 11 * q^77 - 8 * q^78 + 6 * q^79 - 3 * q^80 - 24 * q^81 - 43 * q^82 - 19 * q^83 - 5 * q^84 + 49 * q^85 + 23 * q^86 - 21 * q^87 - 11 * q^88 + 25 * q^89 - 11 * q^90 + 6 * q^91 + q^92 - 4 * q^93 - 5 * q^94 + 24 * q^95 - 5 * q^96 + 16 * q^97 + q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	0.142315	−	0.989821i	0.100632	−	0.699909i
$2$	0.142315	−	0.989821i	0.100632	−	0.699909i
$3$	−0.570276	−	1.24873i	−0.329249	−	0.720954i	0.670532	−	0.741880i	$-0.266066\pi$
$3$	−0.570276	−	1.24873i	−0.329249	−	0.720954i	−0.999781	+	0.0209260i	$0.993339\pi$
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	−1.59792	−	1.84410i	−0.714612	−	0.824707i	0.276036	−	0.961147i	$-0.410979\pi$
$5$	−1.59792	−	1.84410i	−0.714612	−	0.824707i	−0.990648	+	0.136441i	$0.956434\pi$
$6$	−1.31718	+	0.386758i	−0.537736	+	0.157893i
$7$	−0.841254	−	0.540641i	−0.317964	−	0.204343i
$7$	−0.841254	−	0.540641i	−0.317964	−	0.204343i
$8$	−0.415415	+	0.909632i	−0.146871	+	0.321603i
$9$	0.730471	−	0.843008i	0.243490	−	0.281003i
$10$	−2.05274	+	1.31921i	−0.649133	+	0.417172i
$11$	0.245454	+	1.70717i	0.0740071	+	0.514731i	0.992780	+	0.119945i	$0.0382720\pi$
$11$	0.245454	+	1.70717i	0.0740071	+	0.514731i	−0.918773	+	0.394785i	$0.870819\pi$
$12$	0.195368	+	1.35881i	0.0563978	+	0.392255i
$13$	−2.01722	+	1.29639i	−0.559477	+	0.359554i	−0.789614	−	0.613604i	$-0.789719\pi$
$13$	−2.01722	+	1.29639i	−0.559477	+	0.359554i	0.230137	+	0.973158i	$0.426083\pi$
$14$	−0.654861	+	0.755750i	−0.175019	+	0.201983i
$15$	−1.39153	+	3.04702i	−0.359291	+	0.786737i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	−4.48538	+	1.31703i	−1.08786	+	0.319426i	−0.776020	−	0.630708i	$-0.782765\pi$
$17$	−4.48538	+	1.31703i	−1.08786	+	0.319426i	−0.311843	+	0.950134i	$0.600946\pi$
$18$	−0.730471	−	0.843008i	−0.172174	−	0.198699i
$19$	1.11435	+	0.327204i	0.255650	+	0.0750657i	0.407046	−	0.913407i	$-0.366559\pi$
$19$	1.11435	+	0.327204i	0.255650	+	0.0750657i	−0.151396	+	0.988473i	$0.548377\pi$
$20$	1.01365	+	2.21959i	0.226659	+	0.496315i
$21$	−0.195368	+	1.35881i	−0.0426327	+	0.296517i
$22$	1.72472			0.367712
$23$	−3.46135	−	3.31949i	−0.721742	−	0.692162i
$23$	−3.46135	−	3.31949i	−0.721742	−	0.692162i
$24$	1.37279			0.280219
$25$	−0.135777	+	0.944350i	−0.0271554	+	0.188870i
$26$	0.996114	+	2.18119i	0.195354	+	0.427766i
$27$	−5.42079	−	1.59169i	−1.04323	−	0.306321i
$28$	0.654861	+	0.755750i	0.123757	+	0.142823i
$29$	5.04311	−	1.48079i	0.936481	−	0.274976i	0.222333	−	0.974971i	$-0.428633\pi$
$29$	5.04311	−	1.48079i	0.936481	−	0.274976i	0.714148	+	0.699995i	$0.246814\pi$
$30$	2.81797	+	1.81100i	0.514488	+	0.330642i
$31$	0.249869	−	0.547137i	0.0448778	−	0.0982688i	−0.885865	−	0.463943i	$-0.846434\pi$
$31$	0.249869	−	0.547137i	0.0448778	−	0.0982688i	0.930743	+	0.365674i	$0.119162\pi$
$32$	0.654861	−	0.755750i	0.115764	−	0.133599i
$33$	1.99182	−	1.28006i	0.346731	−	0.222830i
$34$	0.665284	+	4.62715i	0.114095	+	0.793550i
$35$	0.347262	+	2.41526i	0.0586979	+	0.408253i
$36$	−0.938384	+	0.603063i	−0.156397	+	0.100511i
$37$	5.27613	−	6.08898i	0.867391	−	1.00102i	−0.132561	−	0.991175i	$-0.542320\pi$
$37$	5.27613	−	6.08898i	0.867391	−	1.00102i	0.999952	−	0.00984727i	$-0.00313453\pi$
$38$	0.482462	−	1.05645i	0.0782657	−	0.171378i
$39$	2.76921	+	1.77967i	0.443429	+	0.284975i
$40$	2.34125	−	0.687454i	0.370185	−	0.108696i
$41$	−8.18535	−	9.44640i	−1.27834	−	1.47528i	−0.803622	−	0.595140i	$-0.797097\pi$
$41$	−8.18535	−	9.44640i	−1.27834	−	1.47528i	−0.474715	−	0.880140i	$-0.657449\pi$
$42$	1.31718	+	0.386758i	0.203245	+	0.0596781i
$43$	2.29652	+	5.02867i	0.350216	+	0.766866i	0.999977	+	0.00672748i	$0.00214144\pi$
$43$	2.29652	+	5.02867i	0.350216	+	0.766866i	−0.649762	+	0.760138i	$0.725131\pi$
$44$	0.245454	−	1.70717i	0.0370036	−	0.257365i
$45$	−2.72183			−0.405746
$46$	−3.77831	+	2.95371i	−0.557081	+	0.435501i
$47$	6.22277			0.907685			0.453842	−	0.891082i	$-0.350053\pi$
$47$	6.22277			0.907685			0.453842	+	0.891082i	$0.350053\pi$
$48$	0.195368	−	1.35881i	0.0281989	−	0.196128i
$49$	0.415415	+	0.909632i	0.0593450	+	0.129947i
$50$	0.915415	+	0.268790i	0.129459	+	0.0380127i
$51$	4.20251	+	4.84995i	0.588469	+	0.679129i
$52$	2.30075	−	0.675560i	0.319056	−	0.0936833i
$53$	−8.29712	−	5.33224i	−1.13970	−	0.732439i	−0.172136	−	0.985073i	$-0.555067\pi$
$53$	−8.29712	−	5.33224i	−1.13970	−	0.732439i	−0.967562	+	0.252634i	$0.918703\pi$
$54$	−2.34695	+	5.13910i	−0.319379	+	0.699342i
$55$	2.75597	−	3.18056i	0.371616	−	0.428867i
$56$	0.841254	−	0.540641i	0.112417	−	0.0722462i
$57$	−0.226900	−	1.57812i	−0.0300536	−	0.209027i
$58$	−0.748008	−	5.20251i	−0.0982183	−	0.683123i
$59$	3.45491	−	2.22034i	0.449791	−	0.289063i	−0.296068	−	0.955167i	$-0.595675\pi$
$59$	3.45491	−	2.22034i	0.449791	−	0.289063i	0.745859	+	0.666103i	$0.232039\pi$
$60$	2.19360	−	2.53155i	0.283193	−	0.326822i
$61$	3.76039	−	8.23412i	0.481469	−	1.05427i	−0.500588	−	0.865686i	$-0.666883\pi$
$61$	3.76039	−	8.23412i	0.481469	−	1.05427i	0.982057	−	0.188585i	$-0.0603900\pi$
$62$	−0.506008	−	0.325192i	−0.0642631	−	0.0412994i
$63$	−1.07028	+	0.314261i	−0.134842	+	0.0395932i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	5.61404	+	1.64843i	0.696336	+	0.204463i
$66$	−0.983568	−	2.15371i	−0.121069	−	0.265104i
$67$	−2.04487	+	14.2224i	−0.249821	+	1.73754i	0.349416	+	0.936968i	$0.386380\pi$
$67$	−2.04487	+	14.2224i	−0.249821	+	1.73754i	−0.599236	+	0.800572i	$0.704529\pi$
$68$	4.67474			0.566895
$69$	−2.17122	+	6.21532i	−0.261384	+	0.748237i
$70$	2.44009			0.291647
$71$	1.32879	−	9.24194i	0.157698	−	1.09682i	−0.745162	−	0.666883i	$-0.767628\pi$
$71$	1.32879	−	9.24194i	0.157698	−	1.09682i	0.902861	−	0.429933i	$-0.141463\pi$
$72$	0.463379	+	1.01466i	0.0546097	+	0.119579i
$73$	−3.05612	−	0.897358i	−0.357692	−	0.105028i	0.0979491	−	0.995191i	$-0.468772\pi$
$73$	−3.05612	−	0.897358i	−0.357692	−	0.105028i	−0.455641	+	0.890164i	$0.650590\pi$
$74$	−5.27613	−	6.08898i	−0.613338	−	0.707830i
$75$	1.25667	−	0.368991i	0.145108	−	0.0426074i
$76$	−0.977031	−	0.627899i	−0.112073	−	0.0720250i
$77$	0.716476	−	1.56886i	0.0816501	−	0.178789i
$78$	2.15565	−	2.48775i	0.244080	−	0.281683i
$79$	6.14561	−	3.94954i	0.691435	−	0.444358i	−0.147161	−	0.989113i	$-0.547013\pi$
$79$	6.14561	−	3.94954i	0.691435	−	0.444358i	0.838596	+	0.544754i	$0.183377\pi$
$80$	−0.347262	−	2.41526i	−0.0388250	−	0.270034i
$81$	0.627519	+	4.36449i	0.0697243	+	0.484943i
$82$	−10.5151	+	6.75767i	−1.16120	+	0.746260i
$83$	2.66583	−	3.07653i	0.292613	−	0.337693i	−0.590340	−	0.807155i	$-0.701006\pi$
$83$	2.66583	−	3.07653i	0.292613	−	0.337693i	0.882953	+	0.469461i	$0.155552\pi$
$84$	0.570276	−	1.24873i	0.0622222	−	0.136248i
$85$	9.59601	+	6.16698i	1.04083	+	0.668903i
$86$	5.30432	−	1.55749i	0.571979	−	0.167948i
$87$	−4.72507	−	5.45302i	−0.506580	−	0.584625i
$88$	−1.65486	−	0.485911i	−0.176409	−	0.0517983i
$89$	−2.00538	−	4.39117i	−0.212570	−	0.465463i	0.773071	−	0.634320i	$-0.218720\pi$
$89$	−2.00538	−	4.39117i	−0.212570	−	0.465463i	−0.985641	+	0.168857i	$0.945992\pi$
$90$	−0.387356	+	2.69412i	−0.0408309	+	0.283985i
$91$	2.39788			0.251366
$92$	2.38594	+	4.16021i	0.248751	+	0.433731i
$93$	−0.825721			−0.0856233
$94$	0.885593	−	6.15943i	0.0913419	−	0.635297i
$95$	−1.17725	−	2.57783i	−0.120784	−	0.264479i
$96$	−1.31718	−	0.386758i	−0.134434	−	0.0394734i
$97$	−0.816541	−	0.942338i	−0.0829071	−	0.0956799i	0.712780	−	0.701387i	$-0.247436\pi$
$97$	−0.816541	−	0.942338i	−0.0829071	−	0.0956799i	−0.795687	+	0.605707i	$0.792890\pi$
$98$	0.959493	−	0.281733i	0.0969234	−	0.0284593i
$99$	1.61845	+	1.04012i	0.162661	+	0.104536i
$100$	0.396331	−	0.867845i	0.0396331	−	0.0867845i
$101$	4.57240	−	5.27683i	0.454971	−	0.525064i	−0.481200	−	0.876611i	$-0.659799\pi$
$101$	4.57240	−	5.27683i	0.454971	−	0.525064i	0.936170	+	0.351547i	$0.114344\pi$
$102$	5.39867	−	3.46951i	0.534548	−	0.343533i
$103$	0.460386	+	3.20206i	0.0453632	+	0.315508i	0.999851	+	0.0172583i	$0.00549376\pi$
$103$	0.460386	+	3.20206i	0.0453632	+	0.315508i	−0.954488	+	0.298250i	$0.903597\pi$
$104$	−0.341254	−	2.37347i	−0.0334627	−	0.232738i
$105$	2.81797	−	1.81100i	0.275006	−	0.176735i
$106$	−6.45877	+	7.45381i	−0.627331	+	0.723978i
$107$	−5.34578	+	11.7056i	−0.516796	+	1.13162i	0.453843	+	0.891082i	$0.350053\pi$
$107$	−5.34578	+	11.7056i	−0.516796	+	1.13162i	−0.970639	+	0.240543i	$0.922675\pi$
$108$	4.75278	+	3.05443i	0.457337	+	0.293912i
$109$	1.40057	−	0.411246i	0.134151	−	0.0393902i	−0.213968	−	0.976841i	$-0.568639\pi$
$109$	1.40057	−	0.411246i	0.134151	−	0.0393902i	0.348119	+	0.937450i	$0.386821\pi$
$110$	−2.75597	−	3.18056i	−0.262772	−	0.303255i
$111$	−10.6123	−	3.11606i	−1.00728	−	0.295764i
$112$	−0.415415	−	0.909632i	−0.0392530	−	0.0859521i
$113$	1.35508	−	9.42477i	0.127475	−	0.886608i	−0.821264	−	0.570548i	$-0.806731\pi$
$113$	1.35508	−	9.42477i	0.127475	−	0.886608i	0.948739	−	0.316060i	$-0.102360\pi$
$114$	−1.59435			−0.149325
$115$	−0.590504	+	11.6874i	−0.0550647	+	1.08985i
$116$	−5.25601			−0.488008
$117$	−0.380655	+	2.64751i	−0.0351915	+	0.244762i
$118$	−1.70605	−	3.73573i	−0.157055	−	0.343902i
$119$	4.48538	+	1.31703i	0.411174	+	0.120732i
$120$	−2.19360	−	2.53155i	−0.200248	−	0.231098i
$121$	7.70024	−	2.26100i	0.700022	−	0.205545i
$122$	−7.61514	−	4.89396i	−0.689443	−	0.443078i
$123$	−7.12809	+	15.6083i	−0.642718	+	1.40736i
$124$	−0.393894	+	0.454578i	−0.0353727	+	0.0408223i
$125$	−8.30525	+	5.33746i	−0.742844	+	0.477397i
$126$	0.158746	+	1.10411i	0.0141423	+	0.0983616i
$127$	0.974945	+	6.78089i	0.0865123	+	0.601707i	0.986248	+	0.165271i	$0.0528500\pi$
$127$	0.974945	+	6.78089i	0.0865123	+	0.601707i	−0.899736	+	0.436435i	$0.856241\pi$
$128$	−0.841254	+	0.540641i	−0.0743570	+	0.0477863i
$129$	4.96981	−	5.73546i	0.437567	−	0.504979i
$130$	2.43061	−	5.32230i	0.213179	−	0.466797i
$131$	13.3471	+	8.57763i	1.16614	+	0.749431i	0.972788	−	0.231699i	$-0.0744283\pi$
$131$	13.3471	+	8.57763i	1.16614	+	0.749431i	0.193350	+	0.981130i	$0.438065\pi$
$132$	−2.27177	+	0.667052i	−0.197732	+	0.0580594i
$133$	−0.760554	−	0.877726i	−0.0659484	−	0.0761085i
$134$	13.7866	+	4.04811i	1.19098	+	0.349703i
$135$	5.72677	+	12.5399i	0.492882	+	1.07926i
$136$	0.665284	−	4.62715i	0.0570477	−	0.396775i
$137$	−8.44398			−0.721418			−0.360709	−	0.932678i	$-0.617465\pi$
$137$	−8.44398			−0.721418			−0.360709	+	0.932678i	$0.617465\pi$
$138$	5.84306	+	3.03366i	0.497394	+	0.258242i
$139$	−9.20419			−0.780690			−0.390345	−	0.920669i	$-0.627644\pi$
$139$	−9.20419			−0.780690			−0.390345	+	0.920669i	$0.627644\pi$
$140$	0.347262	−	2.41526i	0.0293490	−	0.204127i
$141$	−3.54870	−	7.77056i	−0.298854	−	0.654399i
$142$	−8.95876	−	2.63053i	−0.751803	−	0.220749i
$143$	−2.70829	−	3.12554i	−0.226479	−	0.261370i
$144$	1.07028	−	0.314261i	0.0891896	−	0.0261884i
$145$	−10.7892	−	6.93381i	−0.895996	−	0.575821i
$146$	−1.32316	+	2.89731i	−0.109505	+	0.239783i
$147$	0.898983	−	1.03748i	0.0741469	−	0.0855701i
$148$	−6.77787	+	4.35588i	−0.557138	+	0.358051i
$149$	2.44152	+	16.9811i	0.200017	+	1.39115i	0.804227	+	0.594322i	$0.202580\pi$
$149$	2.44152	+	16.9811i	0.200017	+	1.39115i	−0.604210	+	0.796825i	$0.706511\pi$
$150$	−0.186393	−	1.29639i	−0.0152189	−	0.105850i
$151$	4.62658	−	2.97333i	0.376506	−	0.241966i	−0.338677	−	0.940903i	$-0.609979\pi$
$151$	4.62658	−	2.97333i	0.376506	−	0.241966i	0.715183	+	0.698937i	$0.246343\pi$
$152$	−0.760554	+	0.877726i	−0.0616891	+	0.0711930i
$153$	−2.16617	+	4.74326i	−0.175125	+	0.383470i
$154$	−1.45093	−	0.932456i	−0.116919	−	0.0751395i
$155$	−1.40825	+	0.413499i	−0.113113	+	0.0332130i
$156$	−2.15565	−	2.48775i	−0.172590	−	0.199180i
$157$	9.78933	+	2.87441i	0.781274	+	0.229403i	0.647963	−	0.761672i	$-0.275621\pi$
$157$	9.78933	+	2.87441i	0.781274	+	0.229403i	0.133311	+	0.991074i	$0.457439\pi$
$158$	−3.03473	−	6.64513i	−0.241430	−	0.528658i
$159$	−1.92687	+	13.4017i	−0.152811	+	1.06282i
$160$	−2.44009			−0.192906
$161$	1.11722	+	4.66388i	0.0880495	+	0.367566i
$162$	4.40937			0.346433
$163$	−0.581903	+	4.04722i	−0.0455781	+	0.317003i	0.954259	+	0.298980i	$0.0966463\pi$
$163$	−0.581903	+	4.04722i	−0.0455781	+	0.317003i	−0.999838	+	0.0180231i	$0.994263\pi$
$164$	5.19243	+	11.3698i	0.405461	+	0.887835i
$165$	−5.54333	−	1.62767i	−0.431548	−	0.126714i
$166$	−2.66583	−	3.07653i	−0.206909	−	0.238785i
$167$	−0.222325	+	0.0652805i	−0.0172040	+	0.00505156i	−0.290323	−	0.956929i	$-0.593763\pi$
$167$	−0.222325	+	0.0652805i	−0.0172040	+	0.00505156i	0.273119	+	0.961980i	$0.411945\pi$
$168$	−1.15486	−	0.742184i	−0.0890994	−	0.0572607i
$169$	−3.01184	+	6.59500i	−0.231680	+	0.507308i
$170$	7.46986	−	8.62068i	0.572912	−	0.661176i
$171$	1.08984	−	0.700397i	0.0833420	−	0.0535607i
$172$	−0.786752	−	5.47198i	−0.0599893	−	0.417235i
$173$	−2.98685	−	20.7740i	−0.227086	−	1.57942i	−0.710289	−	0.703910i	$-0.751436\pi$
$173$	−2.98685	−	20.7740i	−0.227086	−	1.57942i	0.483203	−	0.875508i	$-0.339473\pi$
$174$	−6.06996	+	3.90093i	−0.460163	+	0.295729i
$175$	0.624777	−	0.721031i	0.0472287	−	0.0545048i
$176$	−0.716476	+	1.56886i	−0.0540064	+	0.118258i
$177$	−4.74286	−	3.04805i	−0.356495	−	0.229105i
$178$	−4.63187	+	1.36004i	−0.347173	+	0.101939i
$179$	4.18240	+	4.82674i	0.312607	+	0.360768i	0.890210	−	0.455550i	$-0.150557\pi$
$179$	4.18240	+	4.82674i	0.312607	+	0.360768i	−0.577603	+	0.816318i	$0.696012\pi$
$180$	2.61157	+	0.766827i	0.194655	+	0.0571559i
$181$	5.70666	+	12.4958i	0.424173	+	0.928809i	0.994237	+	0.107209i	$0.0341913\pi$
$181$	5.70666	+	12.4958i	0.424173	+	0.928809i	−0.570064	+	0.821601i	$0.693081\pi$
$182$	0.341254	−	2.37347i	0.0252954	−	0.175933i
$183$	−12.4266			−0.918604
$184$	4.45741	−	1.76959i	0.328605	−	0.130456i
$185$	−19.6595			−1.44540
$186$	−0.117512	+	0.817316i	−0.00861642	+	0.0599285i
$187$	−3.34934	−	7.33403i	−0.244928	−	0.536317i
$188$	−5.97071	−	1.75316i	−0.435459	−	0.127862i
$189$	3.69973	+	4.26972i	0.269116	+	0.310576i
$190$	−2.71913	+	0.798408i	−0.197266	+	0.0579226i
$191$	−13.1683	−	8.46274i	−0.952824	−	0.612343i	−0.0308205	−	0.999525i	$-0.509812\pi$
$191$	−13.1683	−	8.46274i	−0.952824	−	0.612343i	−0.922003	+	0.387182i	$0.873448\pi$
$192$	−0.570276	+	1.24873i	−0.0411561	+	0.0901193i
$193$	10.0630	−	11.6134i	0.724353	−	0.835947i	−0.267471	−	0.963566i	$-0.586188\pi$
$193$	10.0630	−	11.6134i	0.724353	−	0.835947i	0.991823	+	0.127619i	$0.0407333\pi$
$194$	−1.04895	+	0.674121i	−0.0753104	+	0.0483990i
$195$	−1.14311	−	7.95048i	−0.0818595	−	0.569345i
$196$	−0.142315	−	0.989821i	−0.0101653	−	0.0707015i
$197$	9.18681	−	5.90400i	0.654533	−	0.420643i	−0.170787	−	0.985308i	$-0.554631\pi$
$197$	9.18681	−	5.90400i	0.654533	−	0.420643i	0.825320	+	0.564665i	$0.190995\pi$
$198$	1.25986	−	1.45396i	0.0895344	−	0.103328i
$199$	−6.96653	+	15.2546i	−0.493844	+	1.08137i	0.484577	+	0.874748i	$0.338973\pi$
$199$	−6.96653	+	15.2546i	−0.493844	+	1.08137i	−0.978421	+	0.206619i	$0.933754\pi$
$200$	−0.802607	−	0.515804i	−0.0567529	−	0.0364729i
$201$	18.9260	−	5.55719i	1.33494	−	0.391974i
$202$	−4.57240	−	5.27683i	−0.321713	−	0.371276i
$203$	−5.04311	−	1.48079i	−0.353957	−	0.103931i
$204$	−2.66589	−	5.83748i	−0.186650	−	0.408705i
$205$	−4.34055	+	30.1892i	−0.303157	+	2.10851i
$206$	3.23498			0.225392
$207$	−5.32678	+	0.493158i	−0.370237	+	0.0342768i
$208$	−2.39788			−0.166263
$209$	−0.285070	+	1.98270i	−0.0197187	+	0.137146i
$210$	−1.39153	−	3.04702i	−0.0960245	−	0.210264i
$211$	−2.66561	−	0.782694i	−0.183508	−	0.0538829i	0.188687	−	0.982037i	$-0.439577\pi$
$211$	−2.66561	−	0.782694i	−0.183508	−	0.0538829i	−0.372196	+	0.928154i	$0.621395\pi$
$212$	6.45877	+	7.45381i	0.443590	+	0.511930i
$213$	−12.2985	+	3.61115i	−0.842676	+	0.247432i
$214$	10.8257	+	6.95725i	0.740029	+	0.475588i
$215$	5.60372	−	12.2704i	0.382171	−	0.836837i
$216$	3.69973	−	4.26972i	0.251735	−	0.290517i
$217$	−0.506008	+	0.325192i	−0.0343501	+	0.0220754i
$218$	−0.207737	−	1.44485i	−0.0140698	−	0.0978573i
$219$	0.622274	+	4.32801i	0.0420494	+	0.292460i
$220$	−3.54041	+	2.27528i	−0.238694	+	0.153399i
$221$	7.34062	−	8.47153i	0.493784	−	0.569857i
$222$	−4.59464	+	10.0609i	−0.308372	+	0.675241i
$223$	−6.41328	−	4.12157i	−0.429465	−	0.276000i	0.307999	−	0.951387i	$-0.400341\pi$
$223$	−6.41328	−	4.12157i	−0.429465	−	0.276000i	−0.737464	+	0.675386i	$0.763977\pi$
$224$	−0.959493	+	0.281733i	−0.0641088	+	0.0188240i
$225$	0.696914	+	0.804281i	0.0464609	+	0.0536188i
$226$	−9.13599	−	2.68257i	−0.607717	−	0.178442i
$227$	11.9154	+	26.0911i	0.790852	+	1.73172i	0.674196	+	0.738552i	$0.264490\pi$
$227$	11.9154	+	26.0911i	0.790852	+	1.73172i	0.116656	+	0.993172i	$0.462782\pi$
$228$	−0.226900	+	1.57812i	−0.0150268	+	0.104514i
$229$	7.15345			0.472713			0.236357	−	0.971666i	$-0.424047\pi$
$229$	7.15345			0.472713			0.236357	+	0.971666i	$0.424047\pi$
$230$	11.4844	+	2.24778i	0.757257	+	0.148214i
$231$	−2.36768			−0.155782
$232$	−0.748008	+	5.20251i	−0.0491092	+	0.341562i
$233$	−5.52388	−	12.0956i	−0.361881	−	0.792410i	−0.999752	−	0.0222663i	$-0.992912\pi$
$233$	−5.52388	−	12.0956i	−0.361881	−	0.792410i	0.637871	−	0.770144i	$-0.279815\pi$
$234$	2.56639	+	0.753560i	0.167770	+	0.0492618i
$235$	−9.94351	−	11.4754i	−0.648643	−	0.748574i
$236$	−3.94051	+	1.15704i	−0.256505	+	0.0753167i
$237$	−8.43660	−	5.42187i	−0.548016	−	0.352189i
$238$	1.94196	−	4.25229i	0.125878	−	0.275635i
$239$	18.5881	−	21.4518i	1.20236	−	1.38760i	0.301520	−	0.953460i	$-0.402506\pi$
$239$	18.5881	−	21.4518i	1.20236	−	1.38760i	0.900844	−	0.434143i	$-0.142949\pi$
$240$	−2.81797	+	1.81100i	−0.181899	+	0.116899i
$241$	1.82965	+	12.7255i	0.117858	+	0.819721i	0.959907	+	0.280319i	$0.0904404\pi$
$241$	1.82965	+	12.7255i	0.117858	+	0.819721i	−0.842049	+	0.539402i	$0.818651\pi$
$242$	−1.14212	−	7.94364i	−0.0734184	−	0.510637i
$243$	−9.16614	+	5.89072i	−0.588008	+	0.377890i
$244$	−5.92789	+	6.84115i	−0.379494	+	0.437960i
$245$	1.01365	−	2.21959i	0.0647598	−	0.141804i
$246$	14.4350	+	9.27684i	0.920344	+	0.591469i
$247$	−2.67208	+	0.784595i	−0.170021	+	0.0499226i
$248$	0.393894	+	0.454578i	0.0250123	+	0.0288657i
$249$	−5.36202	−	1.57443i	−0.339804	−	0.0997754i
$250$	4.10117	+	8.98032i	0.259381	+	0.567965i
$251$	1.48749	−	10.3457i	0.0938897	−	0.653017i	−0.887474	−	0.460858i	$-0.847542\pi$
$251$	1.48749	−	10.3457i	0.0938897	−	0.653017i	0.981364	−	0.192159i	$-0.0615491\pi$
$252$	1.11546			0.0702674
$253$	4.81733	−	6.72390i	0.302863	−	0.422728i
$254$	6.85062			0.429846
$255$	2.22852	−	15.4997i	0.139555	−	0.970629i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	9.00739	+	2.64481i	0.561866	+	0.164979i	0.550319	−	0.834955i	$-0.314506\pi$
$257$	9.00739	+	2.64481i	0.561866	+	0.164979i	0.0115469	+	0.999933i	$0.496324\pi$
$258$	−4.96981	−	5.73546i	−0.309407	−	0.357074i
$259$	−7.73052	+	2.26988i	−0.480351	+	0.141044i
$260$	−4.92221	−	3.16332i	−0.305263	−	0.196180i
$261$	2.43552	−	5.33305i	0.150755	−	0.330108i
$262$	10.3898	−	11.9905i	0.641884	−	0.740774i
$263$	17.2514	−	11.0868i	1.06377	−	0.683642i	0.113015	−	0.993593i	$-0.463949\pi$
$263$	17.2514	−	11.0868i	1.06377	−	0.683642i	0.950752	+	0.309951i	$0.100313\pi$
$264$	0.336956	+	2.34358i	0.0207382	+	0.144237i
$265$	3.42498	+	23.8212i	0.210395	+	1.46333i
$266$	−0.977031	+	0.627899i	−0.0599056	+	0.0384990i
$267$	−4.33976	+	5.00835i	−0.265589	+	0.306506i
$268$	5.96894	−	13.0702i	0.364611	−	0.798387i
$269$	8.61869	+	5.53890i	0.525491	+	0.337712i	0.776341	−	0.630314i	$-0.217074\pi$
$269$	8.61869	+	5.53890i	0.525491	+	0.337712i	−0.250850	+	0.968026i	$0.580710\pi$
$270$	13.2272	−	3.88387i	0.804985	−	0.236365i
$271$	−8.42350	−	9.72124i	−0.511691	−	0.590523i	0.439840	−	0.898076i	$-0.355035\pi$
$271$	−8.42350	−	9.72124i	−0.511691	−	0.590523i	−0.951531	+	0.307553i	$0.900490\pi$
$272$	−4.48538	−	1.31703i	−0.271966	−	0.0798564i
$273$	−1.36745	−	2.99430i	−0.0827619	−	0.181223i
$274$	−1.20170	+	8.35803i	−0.0725975	+	0.504927i
$275$	−1.64549			−0.0992269
$276$	3.83433	−	5.35185i	0.230800	−	0.322144i
$277$	4.84496			0.291106			0.145553	−	0.989350i	$-0.453504\pi$
$277$	4.84496			0.291106			0.145553	+	0.989350i	$0.453504\pi$
$278$	−1.30989	+	9.11051i	−0.0785622	+	0.546412i
$279$	−0.278719	−	0.610310i	−0.0166865	−	0.0365383i
$280$	−2.34125	−	0.687454i	−0.139917	−	0.0410832i
$281$	−8.30134	−	9.58026i	−0.495216	−	0.571510i	0.452036	−	0.892000i	$-0.350698\pi$
$281$	−8.30134	−	9.58026i	−0.495216	−	0.571510i	−0.947252	+	0.320490i	$0.896153\pi$
$282$	−8.19650	+	2.40671i	−0.488095	+	0.143317i
$283$	5.86944	+	3.77206i	0.348902	+	0.224226i	0.703340	−	0.710854i	$-0.251691\pi$
$283$	5.86944	+	3.77206i	0.348902	+	0.224226i	−0.354438	+	0.935080i	$0.615328\pi$
$284$	−3.87872	+	8.49321i	−0.230160	+	0.503979i
$285$	−2.54765	+	2.94014i	−0.150910	+	0.174159i
$286$	−3.47915	+	2.23592i	−0.205727	+	0.132212i
$287$	1.77885	+	12.3722i	0.105002	+	0.730305i
$288$	−0.158746	−	1.10411i	−0.00935423	−	0.0650601i
$289$	4.08273	−	2.62381i	0.240161	−	0.154342i
$290$	−8.39870	+	9.69261i	−0.493188	+	0.569170i
$291$	−0.711072	+	1.55703i	−0.0416838	+	0.0912748i
$292$	2.67951	+	1.72202i	0.156807	+	0.100773i
$293$	10.0466	−	2.94994i	0.586928	−	0.172338i	0.0252324	−	0.999682i	$-0.491967\pi$
$293$	10.0466	−	2.94994i	0.586928	−	0.172338i	0.561696	+	0.827344i	$0.310149\pi$
$294$	−0.898983	−	1.03748i	−0.0524298	−	0.0605072i
$295$	−9.61521	−	2.82328i	−0.559819	−	0.164378i
$296$	3.34695	+	7.32879i	0.194537	+	0.425977i
$297$	1.38673	−	9.64490i	0.0804660	−	0.559654i
$298$	17.1557			0.993805
$299$	11.2857	+	2.20889i	0.652668	+	0.127743i
$300$	−1.30972			−0.0756168
$301$	0.786752	−	5.47198i	0.0453476	−	0.315400i
$302$	−2.28463	−	5.00264i	−0.131466	−	0.287870i
$303$	−9.19686	−	2.70044i	−0.528346	−	0.155136i
$304$	0.760554	+	0.877726i	0.0436208	+	0.0503411i
$305$	−21.1934	+	6.22293i	−1.21353	+	0.356324i
$306$	4.38670	+	2.81916i	0.250771	+	0.161161i
$307$	10.7211	−	23.4760i	0.611888	−	1.33985i	−0.309388	−	0.950936i	$-0.600124\pi$
$307$	10.7211	−	23.4760i	0.611888	−	1.33985i	0.921275	−	0.388911i	$-0.127149\pi$
$308$	−1.12945	+	1.30346i	−0.0643566	+	0.0742715i
$309$	3.73596	−	2.40095i	0.212531	−	0.136585i
$310$	0.208875	+	1.45276i	0.0118633	+	0.0825113i
$311$	−1.92838	−	13.4122i	−0.109349	−	0.760536i	−0.968536	−	0.248874i	$-0.919939\pi$
$311$	−1.92838	−	13.4122i	−0.109349	−	0.760536i	0.859187	−	0.511661i	$-0.170970\pi$
$312$	−2.76921	+	1.77967i	−0.156776	+	0.100754i
$313$	20.5748	−	23.7446i	1.16296	−	1.34212i	0.233867	−	0.972269i	$-0.424862\pi$
$313$	20.5748	−	23.7446i	1.16296	−	1.34212i	0.929090	−	0.369855i	$-0.120593\pi$
$314$	4.23832	−	9.28062i	0.239182	−	0.523736i
$315$	2.28975	+	1.47153i	0.129013	+	0.0829114i
$316$	−7.00938	+	2.05814i	−0.394309	+	0.115779i
$317$	−1.34629	−	1.55370i	−0.0756153	−	0.0872648i	0.716681	−	0.697401i	$-0.245660\pi$
$317$	−1.34629	−	1.55370i	−0.0756153	−	0.0872648i	−0.792297	+	0.610136i	$0.791115\pi$
$318$	12.9911	+	3.81452i	0.728503	+	0.213908i
$319$	3.76581	+	8.24597i	0.210845	+	0.461686i
$320$	−0.347262	+	2.41526i	−0.0194125	+	0.135017i
$321$	17.6657			0.986004
$322$	4.77541	−	0.442111i	0.266123	−	0.0246379i
$323$	−5.42923			−0.302090
$324$	0.627519	−	4.36449i	0.0348622	−	0.242472i
$325$	−0.950354	−	2.08098i	−0.0527162	−	0.115432i
$326$	3.92321	+	1.15196i	0.217287	+	0.0638011i
$327$	−1.31225	−	1.51442i	−0.0725675	−	0.0837474i
$328$	11.9931	−	3.52148i	0.662206	−	0.194441i
$329$	−5.23493	−	3.36429i	−0.288611	−	0.185479i
$330$	−2.40000	+	5.25527i	−0.132116	+	0.289293i
$331$	12.1885	−	14.0663i	0.669941	−	0.773153i	−0.314427	−	0.949282i	$-0.601812\pi$
$331$	12.1885	−	14.0663i	0.669941	−	0.773153i	0.984367	+	0.176129i	$0.0563577\pi$
$332$	−3.42460	+	2.20086i	−0.187950	+	0.120788i
$333$	−1.27900	−	8.89564i	−0.0700888	−	0.487478i
$334$	0.0329759	+	0.229353i	0.00180436	+	0.0125496i
$335$	29.4950	−	18.9553i	1.61149	−	1.03564i
$336$	−0.898983	+	1.03748i	−0.0490436	+	0.0565993i
$337$	−7.45713	+	16.3288i	−0.406216	+	0.889488i	0.590386	+	0.807121i	$0.298975\pi$
$337$	−7.45713	+	16.3288i	−0.406216	+	0.889488i	−0.996602	+	0.0823676i	$0.973752\pi$
$338$	6.09924	+	3.91975i	0.331755	+	0.213206i
$339$	−12.5418	+	3.68259i	−0.681175	+	0.200011i
$340$	−7.46986	−	8.62068i	−0.405110	−	0.467522i
$341$	0.995387	+	0.292272i	0.0539032	+	0.0158274i
$342$	−0.538167	−	1.17842i	−0.0291008	−	0.0637218i
$343$	0.142315	−	0.989821i	0.00768428	−	0.0534453i
$344$	−5.52825			−0.298063
$345$	14.9311	−	5.92765i	0.803865	−	0.319134i
$346$	−20.9876			−1.12830
$347$	2.05847	−	14.3170i	0.110505	−	0.768576i	−0.856926	−	0.515439i	$-0.827629\pi$
$347$	2.05847	−	14.3170i	0.110505	−	0.768576i	0.967431	−	0.253136i	$-0.0814622\pi$
$348$	2.99738	+	6.56334i	0.160676	+	0.351832i
$349$	33.7851	+	9.92021i	1.80848	+	0.531017i	0.998464	−	0.0553954i	$-0.0176419\pi$
$349$	33.7851	+	9.92021i	1.80848	+	0.531017i	0.810013	+	0.586412i	$0.199460\pi$
$350$	−0.624777	−	0.721031i	−0.0333957	−	0.0385407i
$351$	12.9984	−	3.81667i	0.693803	−	0.203719i
$352$	1.45093	+	0.932456i	0.0773348	+	0.0497001i
$353$	−10.5671	+	23.1388i	−0.562431	+	1.23155i	0.388299	+	0.921533i	$0.373063\pi$
$353$	−10.5671	+	23.1388i	−0.562431	+	1.23155i	−0.950730	+	0.310019i	$0.899665\pi$
$354$	−3.69200	+	4.26080i	−0.196228	+	0.226459i
$355$	−19.1664	+	12.3175i	−1.01724	+	0.653744i
$356$	0.687012	+	4.77827i	0.0364116	+	0.253248i
$357$	−0.913293	−	6.35209i	−0.0483366	−	0.336188i
$358$	5.37283	−	3.45291i	0.283963	−	0.182492i
$359$	−6.82436	+	7.87573i	−0.360176	+	0.415665i	−0.906699	−	0.421779i	$-0.861406\pi$
$359$	−6.82436	+	7.87573i	−0.360176	+	0.415665i	0.546523	+	0.837444i	$0.315951\pi$
$360$	1.13069	−	2.47586i	0.0595925	−	0.130489i
$361$	−14.8491	−	9.54293i	−0.781531	−	0.502260i
$362$	13.1808	−	3.87023i	0.692768	−	0.203415i
$363$	−7.21464	−	8.32613i	−0.378670	−	0.437009i
$364$	−2.30075	−	0.675560i	−0.120592	−	0.0354090i
$365$	3.22863	+	7.06970i	0.168994	+	0.370045i
$366$	−1.76850	+	12.3002i	−0.0924408	+	0.642940i
$367$	16.7657			0.875164			0.437582	−	0.899178i	$-0.355835\pi$
$367$	16.7657			0.875164			0.437582	+	0.899178i	$0.355835\pi$
$368$	−1.11722	−	4.66388i	−0.0582393	−	0.243122i
$369$	−13.9426			−0.725820
$370$	−2.79784	+	19.4594i	−0.145453	+	1.01165i
$371$	4.09716	+	8.97153i	0.212714	+	0.465778i
$372$	0.792273	+	0.232632i	0.0410775	+	0.0120614i
$373$	−2.06018	−	2.37757i	−0.106672	−	0.123106i	0.699903	−	0.714238i	$-0.253227\pi$
$373$	−2.06018	−	2.37757i	−0.106672	−	0.123106i	−0.806575	+	0.591132i	$0.798681\pi$
$374$	−7.73604	+	2.27151i	−0.400021	+	0.117457i
$375$	11.4013	+	7.32719i	0.588762	+	0.378375i
$376$	−2.58503	+	5.66043i	−0.133313	+	0.291915i
$377$	−8.25339	+	9.52492i	−0.425071	+	0.490558i
$378$	4.75278	−	3.05443i	0.244457	−	0.157103i
$379$	−2.85172	−	19.8341i	−0.146483	−	1.01881i	−0.921918	−	0.387384i	$-0.873379\pi$
$379$	−2.85172	−	19.8341i	−0.146483	−	1.01881i	0.775436	−	0.631427i	$-0.217530\pi$
$380$	0.403309	+	2.80508i	0.0206893	+	0.143897i
$381$	7.91151	−	5.08442i	0.405319	−	0.260483i
$382$	−10.2506	+	11.8299i	−0.524469	+	0.605269i
$383$	1.23599	−	2.70645i	0.0631563	−	0.138293i	−0.875422	−	0.483360i	$-0.839416\pi$
$383$	1.23599	−	2.70645i	0.0631563	−	0.138293i	0.938578	+	0.345067i	$0.112144\pi$
$384$	1.15486	+	0.742184i	0.0589337	+	0.0378744i
$385$	−4.03802	+	1.18567i	−0.205796	+	0.0604273i
$386$	−10.0630	−	11.6134i	−0.512195	−	0.591104i
$387$	5.91675	+	1.73732i	0.300765	+	0.0883127i
$388$	0.517978	+	1.13421i	0.0262963	+	0.0575809i
$389$	−4.96869	+	34.5580i	−0.251923	+	1.75216i	0.334722	+	0.942317i	$0.391358\pi$
$389$	−4.96869	+	34.5580i	−0.251923	+	1.75216i	−0.586645	+	0.809844i	$0.699552\pi$
$390$	−8.03223			−0.406728
$391$	19.8973	+	10.3305i	1.00625	+	0.522435i
$392$	−1.00000			−0.0505076
$393$	3.09964	−	21.5585i	0.156356	−	1.08748i
$394$	−4.53649	−	9.93353i	−0.228545	−	0.500444i
$395$	−17.1036	−	5.02206i	−0.860573	−	0.252687i
$396$	−1.25986	−	1.45396i	−0.0633104	−	0.0730641i
$397$	−35.3977	+	10.3937i	−1.77656	+	0.521644i	−0.994792	−	0.101928i	$-0.967499\pi$
$397$	−35.3977	+	10.3937i	−1.77656	+	0.521644i	−0.781766	+	0.623572i	$0.785681\pi$
$398$	14.1079	+	9.06657i	0.707163	+	0.454466i
$399$	−0.662317	+	1.45027i	−0.0331573	+	0.0726045i
$400$	−0.624777	+	0.721031i	−0.0312389	+	0.0360516i
$401$	6.08063	−	3.90778i	0.303652	−	0.195145i	−0.379937	−	0.925012i	$-0.624054\pi$
$401$	6.08063	−	3.90778i	0.303652	−	0.195145i	0.683589	+	0.729867i	$0.260418\pi$
$402$	−2.80717	−	19.5243i	−0.140009	−	0.973782i
$403$	0.205262	+	1.42763i	0.0102248	+	0.0711151i
$404$	−5.87384	+	3.77489i	−0.292234	+	0.187808i
$405$	7.04583	−	8.13132i	0.350110	−	0.404049i
$406$	−2.18343	+	4.78104i	−0.108362	+	0.237279i
$407$	11.6900	+	7.51268i	0.579450	+	0.372390i
$408$	−6.15746	+	1.80799i	−0.304840	+	0.0895090i
$409$	21.9734	+	25.3587i	1.08652	+	1.25391i	0.965261	+	0.261286i	$0.0841466\pi$
$409$	21.9734	+	25.3587i	1.08652	+	1.25391i	0.121256	+	0.992621i	$0.461308\pi$
$410$	29.2642	+	8.59275i	1.44526	+	0.424366i
$411$	4.81540	+	10.5442i	0.237526	+	0.520109i
$412$	0.460386	−	3.20206i	0.0226816	−	0.157754i
$413$	−4.10686			−0.202086
$414$	−0.269942	+	5.34274i	−0.0132669	+	0.262581i
$415$	−9.93322			−0.487603
$416$	−0.341254	+	2.37347i	−0.0167313	+	0.116369i
$417$	5.24893	+	11.4936i	0.257041	+	0.562842i
$418$	1.92195	+	0.564336i	0.0940058	+	0.0276026i
$419$	10.2963	+	11.8826i	0.503007	+	0.580501i	0.949294	−	0.314388i	$-0.101799\pi$
$419$	10.2963	+	11.8826i	0.503007	+	0.580501i	−0.446287	+	0.894890i	$0.647254\pi$
$420$	−3.21404	+	0.943727i	−0.156829	+	0.0460492i
$421$	−12.7897	−	8.21944i	−0.623332	−	0.400591i	0.190503	−	0.981687i	$-0.438988\pi$
$421$	−12.7897	−	8.21944i	−0.623332	−	0.400591i	−0.813835	+	0.581095i	$0.802624\pi$
$422$	−1.15408	+	2.52709i	−0.0561799	+	0.123017i
$423$	4.54555	−	5.24585i	0.221012	−	0.255062i
$424$	8.29712	−	5.33224i	0.402944	−	0.258956i
$425$	−0.634722	−	4.41459i	−0.0307885	−	0.214139i
$426$	1.82414	+	12.6872i	0.0883801	+	0.614697i
$427$	−7.61514	+	4.89396i	−0.368523	+	0.236835i
$428$	8.42709	−	9.72538i	0.407339	−	0.470094i
$429$	−2.35848	+	5.16434i	−0.113868	+	0.249337i
$430$	−11.3481	−	7.29295i	−0.547252	−	0.351697i
$431$	−30.9113	+	9.07637i	−1.48894	+	0.437193i	−0.922204	−	0.386703i	$-0.873614\pi$
$431$	−30.9113	+	9.07637i	−1.48894	+	0.437193i	−0.566740	+	0.823897i	$0.691796\pi$
$432$	−3.69973	−	4.26972i	−0.178003	−	0.205427i
$433$	−13.4972	−	3.96314i	−0.648635	−	0.190456i	−0.0591671	−	0.998248i	$-0.518844\pi$
$433$	−13.4972	−	3.96314i	−0.648635	−	0.190456i	−0.589468	+	0.807792i	$0.700663\pi$
$434$	0.249869	+	0.547137i	0.0119941	+	0.0262634i
$435$	−2.50562	+	17.4270i	−0.120135	+	0.835560i
$436$	−1.45970			−0.0699071
$437$	−2.77102	−	4.83166i	−0.132556	−	0.231129i
$438$	4.37252			0.208927
$439$	−0.567997	+	3.95051i	−0.0271090	+	0.188547i	−0.998876	−	0.0473942i	$-0.984908\pi$
$439$	−0.567997	+	3.95051i	−0.0271090	+	0.188547i	0.971767	+	0.235942i	$0.0758174\pi$
$440$	1.74827	+	3.82818i	0.0833455	+	0.182501i
$441$	1.07028	+	0.314261i	0.0509655	+	0.0149648i
$442$	−7.34062	−	8.47153i	−0.349158	−	0.402950i
$443$	−34.8466	+	10.2319i	−1.65561	+	0.486132i	−0.970257	−	0.242077i	$-0.922171\pi$
$443$	−34.8466	+	10.2319i	−1.65561	+	0.486132i	−0.685355	+	0.728209i	$0.740353\pi$
$444$	9.30457	+	5.97968i	0.441575	+	0.283783i
$445$	−4.89331	+	10.7149i	−0.231965	+	0.507933i
$446$	−4.99232	+	5.76144i	−0.236393	+	0.272812i
$447$	19.8125	−	12.7327i	0.937098	−	0.602236i
$448$	0.142315	+	0.989821i	0.00672374	+	0.0467647i
$449$	2.31274	+	16.0855i	0.109145	+	0.759120i	0.968728	+	0.248124i	$0.0798141\pi$
$449$	2.31274	+	16.0855i	0.109145	+	0.759120i	−0.859583	+	0.510996i	$0.829277\pi$
$450$	0.895276	−	0.575359i	0.0422037	−	0.0271227i
$451$	14.1175	−	16.2924i	0.664766	−	0.767181i
$452$	−3.95545	+	8.66123i	−0.186049	+	0.407390i
$453$	−6.35131	−	4.08174i	−0.298411	−	0.191777i
$454$	27.5212	−	8.08096i	1.29164	−	0.379258i
$455$	−3.83162	−	4.42193i	−0.179629	−	0.207303i
$456$	1.52977	+	0.449181i	0.0716380	+	0.0210348i
$457$	−16.9145	−	37.0377i	−0.791229	−	1.73255i	−0.673100	−	0.739551i	$-0.735038\pi$
$457$	−16.9145	−	37.0377i	−0.791229	−	1.73255i	−0.118129	−	0.992998i	$-0.537690\pi$
$458$	1.01804	−	7.08064i	0.0475700	−	0.330856i
$459$	26.4106			1.23274
$460$	3.85930	−	11.0476i	0.179941	−	0.515097i
$461$	−34.1098			−1.58865			−0.794327	−	0.607491i	$-0.792176\pi$
$461$	−34.1098			−1.58865			−0.794327	+	0.607491i	$0.792176\pi$
$462$	−0.336956	+	2.34358i	−0.0156766	+	0.109033i
$463$	−16.8462	−	36.8880i	−0.782910	−	1.71433i	−0.695915	−	0.718124i	$-0.745001\pi$
$463$	−16.8462	−	36.8880i	−0.782910	−	1.71433i	−0.0869947	−	0.996209i	$-0.527726\pi$
$464$	5.04311	+	1.48079i	0.234120	+	0.0687439i
$465$	1.31944	+	1.52271i	0.0611875	+	0.0706141i
$466$	−12.7586	+	3.74627i	−0.591032	+	0.173543i
$467$	−25.9614	−	16.6844i	−1.20135	−	0.772061i	−0.222161	−	0.975010i	$-0.571311\pi$
$467$	−25.9614	−	16.6844i	−1.20135	−	0.772061i	−0.979189	+	0.202949i	$0.934948\pi$
$468$	1.11113	−	2.43303i	0.0513618	−	0.112467i
$469$	9.40945	−	10.8591i	0.434488	−	0.501426i
$470$	−12.7737	+	8.20917i	−0.589208	+	0.378661i
$471$	−1.99326	−	13.8634i	−0.0918446	−	0.638793i
$472$	0.584468	+	4.06506i	0.0269023	+	0.187110i
$473$	−8.02111	+	5.15485i	−0.368811	+	0.237020i
$474$	−6.56734	+	7.57912i	−0.301648	+	0.348120i
$475$	−0.460299	+	1.00791i	−0.0211199	+	0.0462462i
$476$	−3.93264	−	2.52735i	−0.180252	−	0.115841i
$477$	−10.5559	+	3.09950i	−0.483323	+	0.141916i
$478$	−18.5881	−	21.4518i	−0.850200	−	0.981183i
$479$	−1.78388	−	0.523794i	−0.0815075	−	0.0239328i	0.240725	−	0.970593i	$-0.422615\pi$
$479$	−1.78388	−	0.523794i	−0.0815075	−	0.0239328i	−0.322232	+	0.946661i	$0.604433\pi$
$480$	1.39153	+	3.04702i	0.0635142	+	0.139077i
$481$	−2.74944	+	19.1228i	−0.125364	+	0.871923i
$482$	12.8564			0.585591
$483$	5.18681	−	4.05481i	0.236008	−	0.184500i
$484$	−8.02533			−0.364788
$485$	−0.432998	+	3.01157i	−0.0196614	+	0.136748i
$486$	4.52628	+	9.91118i	0.205316	+	0.449580i
$487$	5.28273	+	1.55115i	0.239383	+	0.0702893i	0.399224	−	0.916854i	$-0.369280\pi$
$487$	5.28273	+	1.55115i	0.239383	+	0.0702893i	−0.159840	+	0.987143i	$0.551098\pi$
$488$	5.92789	+	6.84115i	0.268343	+	0.309684i
$489$	5.38573	−	1.58139i	0.243551	−	0.0715131i
$490$	−2.05274	−	1.31921i	−0.0927333	−	0.0595960i
$491$	−16.9424	+	37.0986i	−0.764598	+	1.67424i	−0.0264005	+	0.999651i	$0.508405\pi$
$491$	−16.9424	+	37.0986i	−0.764598	+	1.67424i	−0.738197	+	0.674585i	$0.764323\pi$
$492$	11.2367	−	12.9679i	0.506591	−	0.584637i
$493$	−20.6700	+	13.2838i	−0.930929	+	0.598272i
$494$	0.396331	+	2.75655i	0.0178318	+	0.124023i
$495$	−0.668083	−	4.64662i	−0.0300281	−	0.208850i
$496$	0.506008	−	0.325192i	0.0227204	−	0.0146015i
$497$	−6.11442	+	7.05641i	−0.274269	+	0.316523i
$498$	−2.32150	+	5.08337i	−0.104029	+	0.227791i
$499$	−26.6848	−	17.1493i	−1.19457	−	0.767707i	−0.216566	−	0.976268i	$-0.569486\pi$
$499$	−26.6848	−	17.1493i	−1.19457	−	0.767707i	−0.978009	+	0.208561i	$0.933122\pi$
$500$	9.47257	−	2.78140i	0.423626	−	0.124388i
$501$	0.208304	+	0.240396i	0.00930635	+	0.0107401i
$502$	−10.0287	−	2.94470i	−0.447605	−	0.131429i
$503$	5.60045	+	12.2633i	0.249712	+	0.546793i	0.992430	−	0.122811i	$-0.0391910\pi$
$503$	5.60045	+	12.2633i	0.249712	+	0.546793i	−0.742718	+	0.669604i	$0.766464\pi$
$504$	0.158746	−	1.10411i	0.00707113	−	0.0491808i
$505$	−17.0373			−0.758152
$506$	−5.96988	−	5.72521i	−0.265394	−	0.254517i
$507$	9.95295			0.442026
$508$	0.974945	−	6.78089i	0.0432562	−	0.300853i
$509$	−17.4375	−	38.1827i	−0.772902	−	1.69242i	−0.720157	−	0.693812i	$-0.755930\pi$
$509$	−17.4375	−	38.1827i	−0.772902	−	1.69242i	−0.0527454	−	0.998608i	$-0.516797\pi$
$510$	−15.0248	−	4.41167i	−0.665309	−	0.195352i
$511$	2.08582	+	2.40717i	0.0922715	+	0.106487i
$512$	0.959493	−	0.281733i	0.0424040	−	0.0124509i
$513$	−5.51987	−	3.54741i	−0.243708	−	0.156622i
$514$	3.89977	−	8.53931i	0.172012	−	0.376653i
$515$	5.16925	−	5.96564i	0.227785	−	0.262877i
$516$	−6.38436	+	4.10298i	−0.281056	+	0.180624i
$517$	1.52740	+	10.6233i	0.0671751	+	0.467213i
$518$	1.14661	+	7.97487i	0.0503793	+	0.350396i
$519$	−24.2378	+	15.5767i	−1.06392	+	0.683740i
$520$	−3.83162	+	4.42193i	−0.168028	+	0.193914i
$521$	10.1324	−	22.1869i	0.443909	−	0.972026i	−0.546955	−	0.837162i	$-0.684213\pi$
$521$	10.1324	−	22.1869i	0.443909	−	0.972026i	0.990864	−	0.134864i	$-0.0430597\pi$
$522$	−4.93216	−	3.16971i	−0.215875	−	0.138734i
$523$	−3.31084	+	0.972150i	−0.144773	+	0.0425092i	−0.353316	−	0.935504i	$-0.614946\pi$
$523$	−3.31084	+	0.972150i	−0.144773	+	0.0425092i	0.208543	+	0.978013i	$0.433128\pi$
$524$	−10.3898	−	11.9905i	−0.453881	−	0.523806i
$525$	−1.25667	−	0.368991i	−0.0548455	−	0.0161041i
$526$	−8.51883	−	18.6536i	−0.371439	−	0.813337i
$527$	−0.400164	+	2.78320i	−0.0174314	+	0.121238i
$528$	2.36768			0.103040
$529$	0.961941	+	22.9799i	0.0418235	+	0.999125i
$530$	24.0662			1.04537
$531$	0.651950	−	4.53441i	0.0282922	−	0.196777i
$532$	0.482462	+	1.05645i	0.0209174	+	0.0458027i
$533$	28.7579	+	8.44408i	1.24564	+	0.365754i
$534$	4.33976	+	5.00835i	0.187800	+	0.216733i
$535$	30.1285	−	8.84651i	1.30257	−	0.382468i
$536$	−12.0877	−	7.76827i	−0.522107	−	0.335538i
$537$	3.64218	−	7.97526i	0.157172	−	0.344158i
$538$	6.70909	−	7.74270i	0.289249	−	0.333811i
$539$	−1.45093	+	0.932456i	−0.0624960	+	0.0401637i
$540$	−1.96190	−	13.6453i	−0.0844269	−	0.587202i
$541$	0.780345	+	5.42742i	0.0335496	+	0.233343i	0.999696	−	0.0246513i	$-0.00784756\pi$
$541$	0.780345	+	5.42742i	0.0335496	+	0.233343i	−0.966146	+	0.257994i	$0.916938\pi$
$542$	−10.8211	+	6.95429i	−0.464805	+	0.298712i
$543$	12.3496	−	14.2522i	0.529971	−	0.611619i
$544$	−1.94196	+	4.25229i	−0.0832606	+	0.182315i
$545$	−2.99639	−	1.92566i	−0.128351	−	0.0824863i
$546$	−3.15843	+	0.927399i	−0.135168	+	0.0396890i
$547$	19.7048	+	22.7406i	0.842518	+	0.972317i	0.999884	−	0.0152230i	$-0.00484583\pi$
$547$	19.7048	+	22.7406i	0.842518	+	0.972317i	−0.157366	+	0.987540i	$0.550300\pi$
$548$	8.10194	+	2.37894i	0.346098	+	0.101623i
$549$	−4.19457	−	9.18482i	−0.179020	−	0.391999i
$550$	−0.234178	+	1.62874i	−0.00998538	+	0.0694499i
$551$	6.10432			0.260053
$552$	−4.75170	−	4.55695i	−0.202246	−	0.193957i
$553$	−7.30530			−0.310653
$554$	0.689510	−	4.79565i	0.0292945	−	0.203748i
$555$	11.2114	+	24.5494i	0.475896	+	1.04207i
$556$	8.83136	+	2.59312i	0.374533	+	0.109973i
$557$	3.57276	+	4.12319i	0.151383	+	0.174705i	0.826376	−	0.563119i	$-0.190399\pi$
$557$	3.57276	+	4.12319i	0.151383	+	0.174705i	−0.674993	+	0.737824i	$0.735853\pi$
$558$	−0.643763	+	0.189026i	−0.0272527	+	0.00800211i
$559$	−11.1517	−	7.16677i	−0.471667	−	0.303122i
$560$	−1.01365	+	2.21959i	−0.0428346	+	0.0937947i
$561$	−7.24817	+	8.36483i	−0.306018	+	0.353164i
$562$	−10.6641	+	6.85343i	−0.449840	+	0.289095i
$563$	5.68434	+	39.5354i	0.239566	+	1.66622i	0.654269	+	0.756262i	$0.272977\pi$
$563$	5.68434	+	39.5354i	0.239566	+	1.66622i	−0.414702	+	0.909957i	$0.636114\pi$
$564$	1.21573	+	8.45558i	0.0511914	+	0.356044i
$565$	−19.5455	+	12.5611i	−0.822287	+	0.528452i
$566$	4.56897	−	5.27288i	0.192048	−	0.221635i
$567$	1.83172	−	4.01090i	0.0769250	−	0.168442i
$568$	7.85476	+	5.04795i	0.329579	+	0.211807i
$569$	−18.1447	+	5.32775i	−0.760664	+	0.223351i	−0.638986	−	0.769219i	$-0.720646\pi$
$569$	−18.1447	+	5.32775i	−0.760664	+	0.223351i	−0.121678	+	0.992570i	$0.538828\pi$
$570$	2.54765	+	2.94014i	0.106709	+	0.123149i
$571$	14.2235	+	4.17640i	0.595236	+	0.174777i	0.565455	−	0.824779i	$-0.308701\pi$
$571$	14.2235	+	4.17640i	0.595236	+	0.174777i	0.0297814	+	0.999556i	$0.490519\pi$
$572$	1.71802	+	3.76194i	0.0718341	+	0.157295i
$573$	−3.05812	+	21.2697i	−0.127755	+	0.888556i
$574$	12.4994			0.521714
$575$	3.60474	−	2.81802i	0.150328	−	0.117520i
$576$	−1.11546			−0.0464775
$577$	1.61635	−	11.2420i	0.0672895	−	0.468009i	−0.928118	−	0.372285i	$-0.878574\pi$
$577$	1.61635	−	11.2420i	0.0672895	−	0.468009i	0.995408	−	0.0957236i	$-0.0305165\pi$
$578$	−2.01607	−	4.41458i	−0.0838576	−	0.183622i
$579$	−20.2406	−	5.94319i	−0.841172	−	0.246990i
$580$	8.39870	+	9.69261i	0.348737	+	0.402464i
$581$	−3.90594	+	1.14689i	−0.162046	+	0.0475809i
$582$	1.43999	+	0.925423i	0.0596894	+	0.0383600i
$583$	7.06647	−	15.4734i	0.292663	−	0.640843i
$584$	2.08582	−	2.40717i	0.0863120	−	0.0996094i
$585$	5.49053	−	3.52855i	0.227006	−	0.145888i
$586$	−1.49014	−	10.3641i	−0.0615571	−	0.428139i
$587$	−1.85230	−	12.8830i	−0.0764524	−	0.531738i	−0.991673	−	0.128784i	$-0.958893\pi$
$587$	−1.85230	−	12.8830i	−0.0764524	−	0.531738i	0.915220	−	0.402954i	$-0.132017\pi$
$588$	−1.15486	+	0.742184i	−0.0476257	+	0.0306071i
$589$	0.457468	−	0.527946i	0.0188496	−	0.0217536i
$590$	−4.16293	+	9.11555i	−0.171385	+	0.375281i
$591$	−12.6115	−	8.10493i	−0.518769	−	0.333392i
$592$	7.73052	−	2.26988i	0.317722	−	0.0932917i
$593$	30.6704	+	35.3956i	1.25948	+	1.45352i	0.837048	+	0.547129i	$0.184279\pi$
$593$	30.6704	+	35.3956i	1.25948	+	1.45352i	0.422436	+	0.906393i	$0.361175\pi$
$594$	−9.34937	−	2.74522i	−0.383609	−	0.112638i
$595$	−4.73855	−	10.3760i	−0.194262	−	0.425374i
$596$	2.44152	−	16.9811i	0.100008	−	0.695573i
$597$	23.0217			0.942215
$598$	3.79253	−	10.8565i	0.155088	−	0.443953i
$599$	41.1082			1.67963			0.839817	−	0.542870i	$-0.182662\pi$
$599$	41.1082			1.67963			0.839817	+	0.542870i	$0.182662\pi$
$600$	−0.186393	+	1.29639i	−0.00760945	+	0.0529249i
$601$	7.83210	+	17.1499i	0.319478	+	0.699560i	0.999432	−	0.0336952i	$-0.0107276\pi$
$601$	7.83210	+	17.1499i	0.319478	+	0.699560i	−0.679954	+	0.733255i	$0.738000\pi$
$602$	−5.30432	−	1.55749i	−0.216188	−	0.0634785i
$603$	10.4959	+	12.1129i	0.427425	+	0.493274i
$604$	−5.27686	+	1.54943i	−0.214712	+	0.0630452i
$605$	−16.4739	−	10.5871i	−0.669759	−	0.430428i
$606$	−3.98181	+	8.71894i	−0.161750	+	0.354183i
$607$	−10.2120	+	11.7853i	−0.414492	+	0.478349i	−0.924151	−	0.382027i	$-0.875226\pi$
$607$	−10.2120	+	11.7853i	−0.414492	+	0.478349i	0.509659	+	0.860376i	$0.329771\pi$
$608$	0.977031	−	0.627899i	0.0396238	−	0.0254647i
$609$	1.02686	+	7.14193i	0.0416103	+	0.289406i
$610$	3.14346	+	21.8633i	0.127275	+	0.885217i
$611$	−12.5527	+	8.06714i	−0.507829	+	0.326362i
$612$	3.41476	−	3.94084i	0.138033	−	0.159299i
$613$	19.3685	−	42.4112i	0.782288	−	1.71297i	0.0847739	−	0.996400i	$-0.472983\pi$
$613$	19.3685	−	42.4112i	0.782288	−	1.71297i	0.697514	−	0.716571i	$-0.254290\pi$
$614$	−21.7113	−	13.9530i	−0.876196	−	0.563097i
$615$	40.1735	−	11.7960i	1.61995	−	0.475661i
$616$	1.12945	+	1.30346i	0.0455070	+	0.0525179i
$617$	13.6720	+	4.01446i	0.550414	+	0.161616i	0.545102	−	0.838370i	$-0.316491\pi$
$617$	13.6720	+	4.01446i	0.550414	+	0.161616i	0.00531178	+	0.999986i	$0.498309\pi$
$618$	−1.84483	−	4.03962i	−0.0742101	−	0.162497i
$619$	3.42484	−	23.8203i	0.137656	−	0.957418i	−0.797535	−	0.603273i	$-0.793863\pi$
$619$	3.42484	−	23.8203i	0.137656	−	0.957418i	0.935191	−	0.354145i	$-0.115228\pi$
$620$	1.46770			0.0589442
$621$	13.4797	+	23.5037i	0.540921	+	0.943170i
$622$	−13.5501			−0.543310
$623$	−0.687012	+	4.77827i	−0.0275246	+	0.191437i
$624$	1.36745	+	2.99430i	0.0547419	+	0.119868i
$625$	27.6910	+	8.13082i	1.10764	+	0.325233i
$626$	−20.5748	−	23.7446i	−0.822334	−	0.949025i
$627$	2.63843	−	0.774713i	0.105369	−	0.0309390i
$628$	−8.58298	−	5.51595i	−0.342498	−	0.220110i
$629$	−15.6461	+	34.2602i	−0.623851	+	1.36604i
$630$	1.78242	−	2.05702i	0.0710132	−	0.0819536i
$631$	−0.819195	+	0.526465i	−0.0326116	+	0.0209582i	−0.556845	−	0.830616i	$-0.687988\pi$
$631$	−0.819195	+	0.526465i	−0.0326116	+	0.0209582i	0.524233	+	0.851575i	$0.324352\pi$
$632$	1.03965	+	7.23094i	0.0413551	+	0.287631i
$633$	0.542760	+	3.77498i	0.0215728	+	0.150042i
$634$	−1.72949	+	1.11147i	−0.0686867	+	0.0441423i
$635$	10.9468	−	12.6332i	0.434409	−	0.501334i
$636$	5.62452	−	12.3160i	0.223027	−	0.488360i
$637$	−2.01722	−	1.29639i	−0.0799253	−	0.0513649i
$638$	8.69797	−	2.55395i	0.344356	−	0.101112i
$639$	−6.82039	−	7.87115i	−0.269810	−	0.311378i
$640$	2.34125	+	0.687454i	0.0925462	+	0.0271740i
$641$	14.6795	+	32.1435i	0.579804	+	1.26959i	0.941411	+	0.337263i	$0.109501\pi$
$641$	14.6795	+	32.1435i	0.579804	+	1.26959i	−0.361607	+	0.932331i	$0.617772\pi$
$642$	2.51409	−	17.4859i	0.0992233	−	0.690114i
$643$	32.6259			1.28664			0.643321	−	0.765597i	$-0.277556\pi$
$643$	32.6259			1.28664			0.643321	+	0.765597i	$0.277556\pi$
$644$	0.242000	−	4.78972i	0.00953615	−	0.188741i
$645$	−18.5181			−0.729151
$646$	−0.772660	+	5.37397i	−0.0303999	+	0.211436i
$647$	1.67198	+	3.66114i	0.0657325	+	0.143934i	0.939647	−	0.342146i	$-0.111154\pi$
$647$	1.67198	+	3.66114i	0.0657325	+	0.143934i	−0.873914	+	0.486080i	$0.838426\pi$
$648$	−4.23076	−	1.24226i	−0.166200	−	0.0488007i
$649$	4.63851	+	5.35313i	0.182078	+	0.210129i
$650$	−2.19505	+	0.644526i	−0.0860971	+	0.0252804i
$651$	0.694641	+	0.446418i	0.0272251	+	0.0174965i
$652$	1.69857	−	3.71934i	0.0665210	−	0.145661i
$653$	−19.9507	+	23.0243i	−0.780730	+	0.901010i	−0.997162	−	0.0752877i	$-0.976012\pi$
$653$	−19.9507	+	23.0243i	−0.780730	+	0.901010i	0.216432	+	0.976298i	$0.430558\pi$
$654$	−1.68575	+	1.08337i	−0.0659182	+	0.0423630i
$655$	−5.50954	−	38.3197i	−0.215276	−	1.49727i
$656$	−1.77885	−	12.3722i	−0.0694523	−	0.483051i
$657$	−2.98889	+	1.92084i	−0.116608	+	0.0749392i
$658$	−4.07505	+	4.70286i	−0.158862	+	0.183337i
$659$	−21.0100	+	46.0055i	−0.818434	+	1.79212i	−0.252671	+	0.967552i	$0.581309\pi$
$659$	−21.0100	+	46.0055i	−0.818434	+	1.79212i	−0.565763	+	0.824568i	$0.691418\pi$
$660$	4.86022	+	3.12347i	0.189184	+	0.121581i
$661$	2.45229	−	0.720057i	0.0953830	−	0.0280070i	−0.233693	−	0.972310i	$-0.575081\pi$
$661$	2.45229	−	0.720057i	0.0953830	−	0.0280070i	0.329076	+	0.944304i	$0.393263\pi$
$662$	−12.1885	−	14.0663i	−0.473719	−	0.546701i
$663$	−14.7648	−	4.33535i	−0.573419	−	0.168371i
$664$	1.69109	+	3.70296i	0.0656269	+	0.143703i
$665$	−0.403309	+	2.80508i	−0.0156397	+	0.108776i
$666$	−8.98712			−0.348244
$667$	−22.3714	−	11.6150i	−0.866226	−	0.449735i
$668$	0.231711			0.00896517
$669$	−1.48938	+	10.3589i	−0.0575829	+	0.400498i
$670$	−14.5648	−	31.8924i	−0.562687	−	1.23211i
$671$	14.9800	+	4.39853i	0.578298	+	0.169804i
$672$	0.898983	+	1.03748i	0.0346790	+	0.0400217i
$673$	14.9057	−	4.37671i	0.574573	−	0.168710i	0.0184791	−	0.999829i	$-0.494118\pi$
$673$	14.9057	−	4.37671i	0.574573	−	0.168710i	0.556094	+	0.831119i	$0.312299\pi$
$674$	15.1014	+	9.70506i	0.581683	+	0.373825i
$675$	2.23913	−	4.90301i	0.0861842	−	0.188717i
$676$	4.74786	−	5.47932i	0.182610	−	0.210743i
$677$	25.7202	−	16.5294i	0.988509	−	0.635276i	0.0567630	−	0.998388i	$-0.481922\pi$
$677$	25.7202	−	16.5294i	0.988509	−	0.635276i	0.931746	+	0.363112i	$0.118286\pi$
$678$	1.86023	+	12.9382i	0.0714417	+	0.496888i
$679$	0.177451	+	1.23420i	0.00680995	+	0.0473643i
$680$	−9.59601	+	6.16698i	−0.367990	+	0.236493i
$681$	25.7856	−	29.7582i	0.988107	−	1.14034i
$682$	0.430955	−	0.943661i	0.0165021	−	0.0361346i
$683$	−19.9227	−	12.8036i	−0.762323	−	0.489915i	0.100802	−	0.994907i	$-0.467859\pi$
$683$	−19.9227	−	12.8036i	−0.762323	−	0.489915i	−0.863124	+	0.504992i	$0.831496\pi$
$684$	−1.24302	+	0.364983i	−0.0475279	+	0.0139555i
$685$	13.4928	+	15.5715i	0.515534	+	0.594958i
$686$	−0.959493	−	0.281733i	−0.0366336	−	0.0107566i
$687$	−4.07944	−	8.93272i	−0.155640	−	0.340805i
$688$	−0.786752	+	5.47198i	−0.0299946	+	0.208617i
$689$	23.6498			0.900986
$690$	−3.74239	−	15.6227i	−0.142470	−	0.594747i
$691$	18.5518			0.705745			0.352873	−	0.935671i	$-0.385205\pi$
$691$	18.5518			0.705745			0.352873	+	0.935671i	$0.385205\pi$
$692$	−2.98685	+	20.7740i	−0.113543	+	0.789709i
$693$	−0.799200	−	1.75000i	−0.0303591	−	0.0664772i
$694$	−13.8783	−	4.07504i	−0.526813	−	0.154686i
$695$	14.7076	+	16.9735i	0.557891	+	0.643840i
$696$	6.92310	−	2.03281i	0.262420	−	0.0770533i
$697$	49.1555	+	31.5903i	1.86190	+	1.19657i
$698$	14.6274	−	32.0295i	0.553654	−	1.21233i
$699$	−11.9540	+	13.7957i	−0.452142	+	0.521800i
$700$	−0.802607	+	0.515804i	−0.0303357	+	0.0194956i
$701$	−2.27716	−	15.8380i	−0.0860072	−	0.598193i	−0.986554	−	0.163435i	$-0.947743\pi$
$701$	−2.27716	−	15.8380i	−0.0860072	−	0.598193i	0.900547	−	0.434759i	$-0.143166\pi$
$702$	−1.92796	−	13.4093i	−0.0727662	−	0.506100i
$703$	7.87181	−	5.05891i	0.296891	−	0.190800i
$704$	1.12945	−	1.30346i	0.0425679	−	0.0491260i
$705$	−8.65916	+	18.9609i	−0.326123	+	0.714109i
$706$	21.3994	+	13.7526i	0.805377	+	0.517584i
$707$	−6.69942	+	1.96713i	−0.251957	+	0.0739814i
$708$	3.69200	+	4.26080i	0.138754	+	0.160131i
$709$	29.3401	+	8.61502i	1.10189	+	0.323544i	0.781603	−	0.623777i	$-0.214403\pi$
$709$	29.3401	+	8.61502i	1.10189	+	0.323544i	0.320287	+	0.947321i	$0.396221\pi$
$710$	9.46444	+	20.7242i	0.355194	+	0.777767i
$711$	1.15969	−	8.06582i	0.0434918	−	0.302492i
$712$	4.82741			0.180915
$713$	−2.68110	+	1.06440i	−0.100408	+	0.0398620i
$714$	−6.41741			−0.240166
$715$	−1.43616	+	9.98873i	−0.0537094	+	0.373557i
$716$	−2.65313	−	5.80954i	−0.0991521	−	0.217113i
$717$	−37.3879	−	10.9781i	−1.39628	−	0.409983i
$718$	6.82436	+	7.87573i	0.254683	+	0.293920i
$719$	44.1149	−	12.9533i	1.64521	−	0.483077i	0.677579	−	0.735450i	$-0.263029\pi$
$719$	44.1149	−	12.9533i	1.64521	−	0.483077i	0.967630	+	0.252373i	$0.0812111\pi$
$720$	−2.28975	−	1.47153i	−0.0853338	−	0.0548407i
$721$	1.34386	−	2.94265i	0.0500480	−	0.109590i
$722$	−11.5590	+	13.3399i	−0.430183	+	0.496458i
$723$	14.8473	−	9.54178i	0.552177	−	0.354863i
$724$	−1.95502	−	13.5974i	−0.0726576	−	0.505345i
$725$	0.713646	+	4.96352i	0.0265041	+	0.184340i
$726$	−9.26813	+	5.95627i	−0.343973	+	0.221058i
$727$	1.30281	−	1.50352i	0.0483185	−	0.0557625i	−0.731076	−	0.682296i	$-0.760981\pi$
$727$	1.30281	−	1.50352i	0.0483185	−	0.0557625i	0.779394	+	0.626534i	$0.215527\pi$
$728$	−0.996114	+	2.18119i	−0.0369185	+	0.0808401i
$729$	23.7113	+	15.2384i	0.878198	+	0.564383i
$730$	7.45723	−	2.18964i	0.276004	−	0.0810422i
$731$	−16.9236	−	19.5309i	−0.625943	−	0.722377i
$732$	11.9233	+	3.50099i	0.440697	+	0.129400i
$733$	5.94427	+	13.0161i	0.219557	+	0.480762i	0.987074	−	0.160266i	$-0.0512354\pi$
$733$	5.94427	+	13.0161i	0.219557	+	0.480762i	−0.767517	+	0.641028i	$0.778508\pi$
$734$	2.38601	−	16.5951i	0.0880694	−	0.612536i
$735$	−3.34973			−0.123557
$736$	−4.77541	+	0.442111i	−0.176024	+	0.0162964i
$737$	−24.7819			−0.912854
$738$	−1.98423	+	13.8006i	−0.0730406	+	0.508008i
$739$	−12.6437	−	27.6859i	−0.465107	−	1.01844i	−0.986294	−	0.164999i	$-0.947238\pi$
$739$	−12.6437	−	27.6859i	−0.465107	−	1.01844i	0.521187	−	0.853443i	$-0.325489\pi$
$740$	18.8632	+	5.53873i	0.693425	+	0.203608i
$741$	2.50357	+	2.88927i	0.0919710	+	0.106140i
$742$	9.46330	−	2.77867i	0.347408	−	0.102008i
$743$	−34.2066	−	21.9832i	−1.25492	−	0.806487i	−0.267338	−	0.963603i	$-0.586144\pi$
$743$	−34.2066	−	21.9832i	−1.25492	−	0.806487i	−0.987580	+	0.157116i	$0.949780\pi$
$744$	0.343017	−	0.751102i	0.0125756	−	0.0275367i
$745$	27.4135	−	31.6369i	1.00435	−	1.15909i
$746$	−2.64657	+	1.70084i	−0.0968977	+	0.0622724i
$747$	−0.646231	−	4.49463i	−0.0236443	−	0.164450i
$748$	1.14743	+	7.98056i	0.0419543	+	0.291798i
$749$	10.8257	−	6.95725i	0.395562	−	0.254212i
$750$	8.87519	−	10.2425i	0.324076	−	0.374004i
$751$	−11.7173	+	25.6574i	−0.427571	+	0.936250i	0.566143	+	0.824307i	$0.308435\pi$
$751$	−11.7173	+	25.6574i	−0.427571	+	0.936250i	−0.993715	+	0.111943i	$0.964292\pi$
$752$	5.23493	+	3.36429i	0.190898	+	0.122683i
$753$	−13.7673	+	4.04245i	−0.501709	+	0.147315i
$754$	8.25339	+	9.52492i	0.300571	+	0.346877i
$755$	−12.8760	−	3.78074i	−0.468607	−	0.137595i
$756$	−2.34695	−	5.13910i	−0.0853576	−	0.186907i
$757$	6.81874	−	47.4254i	0.247831	−	1.72370i	−0.362867	−	0.931841i	$-0.618202\pi$
$757$	6.81874	−	47.4254i	0.247831	−	1.72370i	0.610698	−	0.791863i	$-0.290889\pi$
$758$	−20.0381			−0.727816
$759$	−11.1435	−	2.18107i	−0.404485	−	0.0791678i
$760$	2.83392			0.102797
$761$	−0.686432	+	4.77424i	−0.0248831	+	0.173066i	−0.998473	−	0.0552370i	$-0.982409\pi$
$761$	−0.686432	+	4.77424i	−0.0248831	+	0.173066i	0.973590	+	0.228303i	$0.0733177\pi$
$762$	−3.90674	−	8.55457i	−0.141526	−	0.309899i
$763$	−1.40057	−	0.411246i	−0.0507042	−	0.0148881i
$764$	10.2506	+	11.8299i	0.370855	+	0.427990i
$765$	12.2084	−	3.58471i	0.441396	−	0.129606i
$766$	−2.50300	−	1.60858i	−0.0904371	−	0.0581204i
$767$	−4.09091	+	8.95783i	−0.147714	+	0.323449i
$768$	0.898983	−	1.03748i	0.0324393	−	0.0374369i
$769$	−35.3506	+	22.7185i	−1.27478	+	0.819249i	−0.990234	−	0.139415i	$-0.955478\pi$
$769$	−35.3506	+	22.7185i	−1.27478	+	0.819249i	−0.284542	+	0.958664i	$0.591841\pi$
$770$	0.598931	+	4.16565i	0.0215840	+	0.150120i
$771$	−1.83405	−	12.7561i	−0.0660515	−	0.459398i
$772$	−12.9273	+	8.30785i	−0.465262	+	0.299006i
$773$	−16.5353	+	19.0828i	−0.594735	+	0.686361i	−0.970706	−	0.240271i	$-0.922764\pi$
$773$	−16.5353	+	19.0828i	−0.594735	+	0.686361i	0.375971	+	0.926631i	$0.377309\pi$
$774$	2.56167	−	5.60928i	0.0920775	−	0.201621i
$775$	0.482763	+	0.310253i	0.0173413	+	0.0111446i
$776$	1.19638	−	0.351290i	0.0429477	−	0.0126106i
$777$	7.24300	+	8.35886i	0.259841	+	0.299873i
$778$	33.4992	+	9.83624i	1.20100	+	0.352646i
$779$	−6.03048	−	13.2049i	−0.216064	−	0.473115i
$780$	−1.14311	+	7.95048i	−0.0409298	+	0.284673i
$781$	16.1037			0.576236
$782$	13.0570	−	18.2246i	0.466918	−	0.651711i
$783$	−29.6946			−1.06120
$784$	−0.142315	+	0.989821i	−0.00508267	+	0.0353508i
$785$	−10.3419	−	22.6456i	−0.369118	−	0.808256i
$786$	−20.8979	−	6.13618i	−0.745404	−	0.218870i
$787$	−11.1158	−	12.8283i	−0.396236	−	0.457281i	0.522216	−	0.852813i	$-0.325105\pi$
$787$	−11.1158	−	12.8283i	−0.396236	−	0.457281i	−0.918452	+	0.395533i	$0.870560\pi$
$788$	−10.4780	+	3.07663i	−0.373264	+	0.109600i
$789$	−23.6825	−	15.2198i	−0.843119	−	0.541840i
$790$	−7.40503	+	16.2148i	−0.263459	+	0.576895i
$791$	−6.23538	+	7.19601i	−0.221705	+	0.255861i
$792$	−1.61845	+	1.04012i	−0.0575093	+	0.0369590i
$793$	3.08907	+	21.4850i	0.109696	+	0.762954i
$794$	5.25029	+	36.5165i	0.186326	+	1.29592i
$795$	27.7931	−	17.8615i	0.985719	−	0.633483i
$796$	10.9820	−	12.6740i	0.389248	−	0.449216i
$797$	7.84819	−	17.1851i	0.277997	−	0.608729i	−0.718202	−	0.695835i	$-0.755035\pi$
$797$	7.84819	−	17.1851i	0.277997	−	0.608729i	0.996199	+	0.0871058i	$0.0277618\pi$
$798$	1.34125	+	0.861971i	0.0474799	+	0.0305135i
$799$	−27.9115	+	8.19555i	−0.987437	+	0.289938i
$800$	0.624777	+	0.721031i	0.0220892	+	0.0254923i
$801$	−5.16666	−	1.51707i	−0.182555	−	0.0536030i
$802$	−3.00264	−	6.57487i	−0.106027	−	0.232167i
$803$	0.781805	−	5.43758i	0.0275893	−	0.191888i
$804$	−19.7250			−0.695649
$805$	6.81543	−	9.51279i	0.240213	−	0.335282i
$806$	1.44231			0.0508031
$807$	2.00155	−	13.9211i	0.0704580	−	0.490046i
$808$	2.90053	+	6.35127i	0.102040	+	0.223437i
$809$	9.13723	+	2.68293i	0.321248	+	0.0943269i	0.438381	−	0.898789i	$-0.355552\pi$
$809$	9.13723	+	2.68293i	0.321248	+	0.0943269i	−0.117133	+	0.993116i	$0.537370\pi$
$810$	−7.04583	−	8.13132i	−0.247565	−	0.285706i
$811$	9.74369	−	2.86101i	0.342147	−	0.100463i	−0.106145	−	0.994351i	$-0.533851\pi$
$811$	9.74369	−	2.86101i	0.342147	−	0.100463i	0.448292	+	0.893887i	$0.352033\pi$
$812$	4.42164	+	2.84161i	0.155169	+	0.0997211i
$813$	−7.33548	+	16.0625i	−0.257267	+	0.563335i
$814$	9.09987	−	10.5018i	0.318950	−	0.368088i
$815$	8.39332	−	5.39406i	0.294005	−	0.188946i
$816$	0.913293	+	6.35209i	0.0319716	+	0.222368i
$817$	0.913733	+	6.35515i	0.0319675	+	0.222339i
$818$	28.2277	−	18.1409i	0.986960	−	0.634281i
$819$	1.75158	−	2.02143i	0.0612051	−	0.0706345i
$820$	12.6700	−	27.7435i	0.442456	−	0.968844i
$821$	−39.4304	−	25.3404i	−1.37613	−	0.884386i	−0.377007	−	0.926210i	$-0.623047\pi$
$821$	−39.4304	−	25.3404i	−1.37613	−	0.884386i	−0.999125	+	0.0418243i	$0.986683\pi$
$822$	11.1222	−	3.26578i	0.387932	−	0.113907i
$823$	−32.3256	−	37.3058i	−1.12680	−	1.30040i	−0.948626	−	0.316399i	$-0.897526\pi$
$823$	−32.3256	−	37.3058i	−1.12680	−	1.30040i	−0.178175	−	0.983999i	$-0.557019\pi$
$824$	−3.10395	−	0.911401i	−0.108131	−	0.0317501i
$825$	0.938384	+	2.05478i	0.0326704	+	0.0715381i
$826$	−0.584468	+	4.06506i	−0.0203362	+	0.141442i
$827$	19.4439			0.676130			0.338065	−	0.941123i	$-0.390228\pi$
$827$	19.4439			0.676130			0.338065	+	0.941123i	$0.390228\pi$
$828$	5.24994	+	1.02755i	0.182448	+	0.0357097i
$829$	−8.95771			−0.311114			−0.155557	−	0.987827i	$-0.549717\pi$
$829$	−8.95771			−0.311114			−0.155557	+	0.987827i	$0.549717\pi$
$830$	−1.41365	+	9.83212i	−0.0490683	+	0.341278i
$831$	−2.76297	−	6.05005i	−0.0958462	−	0.209874i
$832$	2.30075	+	0.675560i	0.0797640	+	0.0234208i
$833$	−3.06130	−	3.53293i	−0.106068	−	0.122409i
$834$	12.1236	−	3.55980i	0.419805	−	0.123266i
$835$	0.475642	+	0.305677i	0.0164603	+	0.0105784i
$836$	0.832115	−	1.82208i	0.0287793	−	0.0630178i
$837$	−2.22536	+	2.56820i	−0.0769198	+	0.0887701i
$838$	13.2269	−	8.50044i	0.456917	−	0.293643i
$839$	−2.92458	−	20.3409i	−0.100968	−	0.702245i	−0.975935	−	0.218063i	$-0.930026\pi$
$839$	−2.92458	−	20.3409i	−0.100968	−	0.702245i	0.874967	−	0.484182i	$-0.160883\pi$
$840$	0.476716	+	3.31563i	0.0164483	+	0.114400i
$841$	−1.15617	+	0.743028i	−0.0398681	+	0.0256216i
$842$	−9.95595	+	11.4898i	−0.343105	+	0.395964i
$843$	−7.22910	+	15.8295i	−0.248983	+	0.545198i
$844$	2.33713	+	1.50198i	0.0804472	+	0.0517003i
$845$	16.9745	−	4.98417i	0.583941	−	0.171461i
$846$	−4.54555	−	5.24585i	−0.156279	−	0.180356i
$847$	−7.70024	−	2.26100i	−0.264584	−	0.0776887i
$848$	−4.09716	−	8.97153i	−0.140697	−	0.308083i
$849$	1.36308	−	9.48045i	0.0467809	−	0.325368i
$850$	−4.45998			−0.152976
$851$	−38.4749	+	3.56204i	−1.31890	+	0.122105i
$852$	12.8177			0.439126
$853$	4.07327	−	28.3302i	0.139466	−	0.970009i	−0.793121	−	0.609064i	$-0.791545\pi$
$853$	4.07327	−	28.3302i	0.139466	−	0.970009i	0.932587	−	0.360945i	$-0.117546\pi$
$854$	3.76039	+	8.23412i	0.128678	+	0.281766i
$855$	−3.03308	−	0.890592i	−0.103729	−	0.0304576i
$856$	−8.42709	−	9.72538i	−0.288032	−	0.332407i
$857$	26.3909	−	7.74906i	0.901495	−	0.264703i	0.202038	−	0.979378i	$-0.435243\pi$
$857$	26.3909	−	7.74906i	0.901495	−	0.264703i	0.699457	+	0.714675i	$0.253425\pi$
$858$	4.77613	+	3.06943i	0.163054	+	0.104789i
$859$	−9.25592	+	20.2676i	−0.315808	+	0.691523i	−0.999260	−	0.0384726i	$-0.987751\pi$
$859$	−9.25592	+	20.2676i	−0.315808	+	0.691523i	0.683452	+	0.729996i	$0.260478\pi$
$860$	−8.83371	+	10.1946i	−0.301227	+	0.347635i
$861$	14.4350	−	9.27684i	0.491945	−	0.316154i
$862$	4.58485	+	31.8884i	0.156161	+	1.08612i
$863$	3.21348	+	22.3503i	0.109388	+	0.760811i	0.968498	+	0.249021i	$0.0801087\pi$
$863$	3.21348	+	22.3503i	0.109388	+	0.760811i	−0.859110	+	0.511791i	$0.828982\pi$
$864$	−4.75278	+	3.05443i	−0.161693	+	0.103914i
$865$	−33.5366	+	38.7033i	−1.14028	+	1.31595i
$866$	−5.84366	+	12.7958i	−0.198576	+	0.434820i
$867$	−5.60472	−	3.60193i	−0.190346	−	0.122328i
$868$	0.577128	−	0.169460i	0.0195890	−	0.00575185i
$869$	8.25100	+	9.52216i	0.279896	+	0.323017i
$870$	16.8930	+	4.96024i	0.572727	+	0.168168i
$871$	−14.3128	−	31.3407i	−0.484971	−	1.06194i
$872$	−0.207737	+	1.44485i	−0.00703488	+	0.0489286i
$873$	−1.39086			−0.0470734
$874$	−5.17683	+	2.05520i	−0.175109	+	0.0695182i
$875$	9.87247			0.333751
$876$	0.622274	−	4.32801i	0.0210247	−	0.146230i
$877$	5.09453	+	11.1555i	0.172030	+	0.376693i	0.975934	−	0.218066i	$-0.0699747\pi$
$877$	5.09453	+	11.1555i	0.172030	+	0.376693i	−0.803904	+	0.594759i	$0.797247\pi$
$878$	3.82946	+	1.12443i	0.129238	+	0.0379477i
$879$	−9.41301	−	10.8632i	−0.317493	−	0.366406i
$880$	4.03802	−	1.18567i	0.136122	−	0.0399689i
$881$	−11.1979	−	7.19642i	−0.377265	−	0.242454i	0.338242	−	0.941059i	$-0.390168\pi$
$881$	−11.1979	−	7.19642i	−0.377265	−	0.242454i	−0.715507	+	0.698606i	$0.753804\pi$
$882$	0.463379	−	1.01466i	0.0156028	−	0.0341653i
$883$	−13.5336	+	15.6186i	−0.455442	+	0.525609i	−0.936305	−	0.351187i	$-0.885778\pi$
$883$	−13.5336	+	15.6186i	−0.455442	+	0.525609i	0.480863	+	0.876796i	$0.340324\pi$
$884$	−9.42998	+	6.06028i	−0.317165	+	0.203829i
$885$	1.95781	+	13.6168i	0.0658110	+	0.457725i
$886$	5.16855	+	35.9481i	0.173641	+	1.20770i
$887$	−23.9409	+	15.3859i	−0.803856	+	0.516607i	−0.876872	−	0.480724i	$-0.840374\pi$
$887$	−23.9409	+	15.3859i	−0.803856	+	0.516607i	0.0730163	+	0.997331i	$0.476737\pi$
$888$	7.24300	−	8.35886i	0.243059	−	0.280505i
$889$	2.84585	−	6.23154i	0.0954467	−	0.208999i
$890$	9.90941	+	6.36839i	0.332164	+	0.213469i
$891$	−7.29689	+	2.14256i	−0.244455	+	0.0717785i
$892$	4.99232	+	5.76144i	0.167155	+	0.192907i
$893$	6.93437	+	2.03612i	0.232050	+	0.0681360i
$894$	−9.78350	−	21.4229i	−0.327209	−	0.716488i
$895$	2.21785	−	15.4255i	0.0741347	−	0.515618i
$896$	1.00000			0.0334077
$897$	−3.67764	−	15.3524i	−0.122793	−	0.512603i
$898$	16.2509			0.542298
$899$	0.449922	−	3.12927i	0.0150057	−	0.104367i
$900$	−0.442092	−	0.968046i	−0.0147364	−	0.0322682i
$901$	44.2384	+	12.9896i	1.47379	+	0.432745i
$902$	−14.1175	−	16.2924i	−0.470060	−	0.542479i
$903$	−7.28169	+	2.13810i	−0.242319	+	0.0711514i
$904$	8.01015	+	5.14781i	0.266414	+	0.171214i
$905$	13.9248	−	30.4911i	0.462876	−	1.01356i
$906$	−4.94408	+	5.70577i	−0.164256	+	0.189562i
$907$	24.0963	−	15.4858i	0.800106	−	0.514197i	−0.0755447	−	0.997142i	$-0.524070\pi$
$907$	24.0963	−	15.4858i	0.800106	−	0.514197i	0.875650	+	0.482946i	$0.160433\pi$
$908$	−4.08203	−	28.3911i	−0.135467	−	0.942193i
$909$	−1.10841	−	7.70914i	−0.0367635	−	0.255696i
$910$	−4.92221	+	3.16332i	−0.163170	+	0.104863i
$911$	3.65917	−	4.22291i	0.121234	−	0.139911i	−0.691888	−	0.722005i	$-0.743221\pi$
$911$	3.65917	−	4.22291i	0.121234	−	0.139911i	0.813122	+	0.582094i	$0.197766\pi$
$912$	0.662317	−	1.45027i	0.0219315	−	0.0480233i
$913$	5.90650	+	3.79588i	0.195477	+	0.125625i
$914$	−39.0679	+	11.4714i	−1.29225	+	0.379439i
$915$	19.8568	+	22.9160i	0.656446	+	0.757579i
$916$	−6.86368	−	2.01536i	−0.226782	−	0.0665893i
$917$	−6.59084	−	14.4319i	−0.217649	−	0.476584i
$918$	3.75862	−	26.1418i	0.124053	−	0.862807i
$919$	1.00321			0.0330928			0.0165464	−	0.999863i	$-0.494733\pi$
$919$	1.00321			0.0330928			0.0165464	+	0.999863i	$0.494733\pi$
$920$	−10.3859	−	5.39225i	−0.342413	−	0.177777i
$921$	−35.4292			−1.16743
$922$	−4.85434	+	33.7626i	−0.159869	+	1.11191i
$923$	9.30069	+	20.3657i	0.306136	+	0.670344i
$924$	2.27177	+	0.667052i	0.0747357	+	0.0219444i
$925$	5.03375	+	5.80926i	0.165509	+	0.191007i
$926$	−38.9100	+	11.4250i	−1.27866	+	0.375449i
$927$	3.03566	+	1.95090i	0.0997041	+	0.0640760i
$928$	2.18343	−	4.78104i	0.0716745	−	0.156945i
$929$	−27.2164	+	31.4094i	−0.892941	+	1.03051i	0.106404	+	0.994323i	$0.466066\pi$
$929$	−27.2164	+	31.4094i	−0.892941	+	1.03051i	−0.999345	+	0.0361856i	$0.988479\pi$
$930$	1.69499	−	1.08930i	0.0555809	−	0.0357197i
$931$	0.165284	+	1.14958i	0.00541697	+	0.0376759i
$932$	1.89240	+	13.1619i	0.0619875	+	0.431133i
$933$	−15.6485	+	10.0567i	−0.512309	+	0.329241i
$934$	−20.2093	+	23.3227i	−0.661267	+	0.763143i
$935$	−8.17270	+	17.8957i	−0.267276	+	0.585252i
$936$	−2.25013	−	1.44607i	−0.0735478	−	0.0472663i
$937$	−6.01570	+	1.76637i	−0.196524	+	0.0577047i	−0.378513	−	0.925596i	$-0.623565\pi$
$937$	−6.01570	+	1.76637i	−0.196524	+	0.0577047i	0.181989	+	0.983301i	$0.441746\pi$
$938$	−9.40945	−	10.8591i	−0.307229	−	0.354562i
$939$	−41.3839	−	12.1514i	−1.35051	−	0.396546i
$940$	6.30773	+	13.8120i	0.205735	+	0.450498i
$941$	0.779520	−	5.42168i	0.0254116	−	0.176742i	−0.973163	−	0.230117i	$-0.926089\pi$
$941$	0.779520	−	5.42168i	0.0254116	−	0.176742i	0.998575	+	0.0533756i	$0.0169981\pi$
$942$	−14.0060			−0.456340
$943$	−3.02485	+	59.8685i	−0.0985027	+	1.94959i
$944$	4.10686			0.133667
$945$	1.96190	−	13.6453i	0.0638208	−	0.443883i
$946$	3.96086	+	8.67307i	0.128779	+	0.281986i
$947$	11.9940	+	3.52176i	0.389753	+	0.114442i	0.470737	−	0.882274i	$-0.343988\pi$
$947$	11.9940	+	3.52176i	0.389753	+	0.114442i	−0.0809840	+	0.996715i	$0.525806\pi$
$948$	6.56734	+	7.57912i	0.213297	+	0.246158i
$949$	7.32821	−	2.15176i	0.237884	−	0.0698489i
$950$	0.932147	+	0.599054i	0.0302428	+	0.0194359i
$951$	−1.17240	+	2.56720i	−0.0380176	+	0.0832470i
$952$	−3.06130	+	3.53293i	−0.0992173	+	0.114503i
$953$	17.5075	−	11.2514i	0.567122	−	0.364467i	−0.225441	−	0.974257i	$-0.572382\pi$
$953$	17.5075	−	11.2514i	0.567122	−	0.364467i	0.792563	+	0.609790i	$0.208746\pi$
$954$	1.56569	+	10.8896i	0.0506910	+	0.352563i
$955$	5.43575	+	37.8064i	0.175897	+	1.22339i
$956$	−23.8788	+	15.3460i	−0.772297	+	0.496325i
$957$	8.14944	−	9.40495i	0.263434	−	0.304019i
$958$	−0.772335	+	1.69118i	−0.0249530	+	0.0546395i
$959$	7.10353	+	4.56516i	0.229385	+	0.147417i
$960$	3.21404	−	0.943727i	0.103733	−	0.0304587i
$961$	20.0638	+	23.1548i	0.647218	+	0.746929i
$962$	18.5368	+	5.44290i	0.597651	+	0.175486i
$963$	5.96300	+	13.0571i	0.192155	+	0.420760i
$964$	1.82965	−	12.7255i	0.0589290	−	0.409861i
$965$	−37.4961			−1.20704
$966$	−3.27538	−	5.71107i	−0.105384	−	0.183751i
$967$	29.0368			0.933761			0.466881	−	0.884320i	$-0.345378\pi$
$967$	29.0368			0.933761			0.466881	+	0.884320i	$0.345378\pi$
$968$	−1.14212	+	7.94364i	−0.0367092	+	0.255318i
$969$	3.09616	+	6.77964i	0.0994629	+	0.217793i
$970$	2.91929	+	0.857181i	0.0937328	+	0.0275224i
$971$	5.09296	+	5.87759i	0.163441	+	0.188621i	0.831562	−	0.555431i	$-0.187447\pi$
$971$	5.09296	+	5.87759i	0.163441	+	0.188621i	−0.668122	+	0.744052i	$0.732901\pi$
$972$	10.4545	−	3.06970i	0.335327	−	0.0984608i
$973$	7.74306	+	4.97616i	0.248231	+	0.159528i
$974$	2.28717	−	5.00820i	0.0732857	−	0.160473i
$975$	−2.05662	+	2.37347i	−0.0658647	+	0.0760119i
$976$	7.61514	−	4.89396i	0.243755	−	0.156652i
$977$	0.617531	+	4.29503i	0.0197566	+	0.137410i	0.997312	−	0.0732666i	$-0.0233424\pi$
$977$	0.617531	+	4.29503i	0.0197566	+	0.137410i	−0.977556	+	0.210677i	$0.932433\pi$
$978$	−0.798828	−	5.55597i	−0.0255437	−	0.177660i
$979$	7.00424	−	4.50135i	0.223856	−	0.143864i
$980$	−1.59792	+	1.84410i	−0.0510437	+	0.0589076i
$981$	0.676395	−	1.48110i	0.0215956	−	0.0472879i
$982$	34.3098	+	22.0496i	1.09487	+	0.703631i
$983$	−31.7505	+	9.32279i	−1.01268	+	0.297351i	−0.745651	−	0.666337i	$-0.767861\pi$
$983$	−31.7505	+	9.32279i	−1.01268	+	0.297351i	−0.267033	+	0.963687i	$0.586043\pi$
$984$	−11.2367	−	12.9679i	−0.358214	−	0.413401i
$985$	−25.5674	−	7.50726i	−0.814644	−	0.239201i
$986$	10.2069	+	22.3501i	0.325055	+	0.711772i
$987$	−1.21573	+	8.45558i	−0.0386971	+	0.269144i
$988$	2.78489			0.0885992
$989$	8.74358	−	25.0293i	0.278030	−	0.795885i
$990$	−4.69440			−0.149198
$991$	3.64980	−	25.3849i	0.115940	−	0.806379i	−0.846013	−	0.533162i	$-0.821003\pi$
$991$	3.64980	−	25.3849i	0.115940	−	0.806379i	0.961953	−	0.273216i	$-0.0880874\pi$
$992$	−0.249869	−	0.547137i	−0.00793336	−	0.0173716i
$993$	−24.5158	−	7.19848i	−0.777985	−	0.228437i
$994$	6.11442	+	7.05641i	0.193938	+	0.223816i
$995$	39.2629	−	11.5286i	1.24472	−	0.365482i
$996$	4.70125	+	3.02131i	0.148965	+	0.0957338i
$997$	−14.2864	+	31.2828i	−0.452453	+	0.990735i	0.536690	+	0.843780i	$0.319675\pi$
$997$	−14.2864	+	31.2828i	−0.452453	+	0.990735i	−0.989143	+	0.146955i	$0.953053\pi$
$998$	−20.7724	+	23.9726i	−0.657537	+	0.758839i
$999$	−38.2926	+	24.6091i	−1.21152	+	0.778599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.b.169.1	yes	10
23.3	even	11	inner	322.2.i.b.141.1	✓	10
23.7	odd	22		7406.2.a.be.1.3		5
23.16	even	11		7406.2.a.bf.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.b.141.1	✓	10	23.3	even	11	inner
322.2.i.b.169.1	yes	10	1.1	even	1	trivial
7406.2.a.be.1.3		5	23.7	odd	22
7406.2.a.bf.1.3		5	23.16	even	11

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 - 0.989821i) q^{2} +(-0.570276 - 1.24873i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.59792 - 1.84410i) q^{5} +(-1.31718 + 0.386758i) q^{6} +(-0.841254 - 0.540641i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.730471 - 0.843008i) q^{9} +O(q^{10})\)	\(q+(0.142315 - 0.989821i) q^{2} +(-0.570276 - 1.24873i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.59792 - 1.84410i) q^{5} +(-1.31718 + 0.386758i) q^{6} +(-0.841254 - 0.540641i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.730471 - 0.843008i) q^{9} +(-2.05274 + 1.31921i) q^{10} +(0.245454 + 1.70717i) q^{11} +(0.195368 + 1.35881i) q^{12} +(-2.01722 + 1.29639i) q^{13} +(-0.654861 + 0.755750i) q^{14} +(-1.39153 + 3.04702i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-4.48538 + 1.31703i) q^{17} +(-0.730471 - 0.843008i) q^{18} +(1.11435 + 0.327204i) q^{19} +(1.01365 + 2.21959i) q^{20} +(-0.195368 + 1.35881i) q^{21} +1.72472 q^{22} +(-3.46135 - 3.31949i) q^{23} +1.37279 q^{24} +(-0.135777 + 0.944350i) q^{25} +(0.996114 + 2.18119i) q^{26} +(-5.42079 - 1.59169i) q^{27} +(0.654861 + 0.755750i) q^{28} +(5.04311 - 1.48079i) q^{29} +(2.81797 + 1.81100i) q^{30} +(0.249869 - 0.547137i) q^{31} +(0.654861 - 0.755750i) q^{32} +(1.99182 - 1.28006i) q^{33} +(0.665284 + 4.62715i) q^{34} +(0.347262 + 2.41526i) q^{35} +(-0.938384 + 0.603063i) q^{36} +(5.27613 - 6.08898i) q^{37} +(0.482462 - 1.05645i) q^{38} +(2.76921 + 1.77967i) q^{39} +(2.34125 - 0.687454i) q^{40} +(-8.18535 - 9.44640i) q^{41} +(1.31718 + 0.386758i) q^{42} +(2.29652 + 5.02867i) q^{43} +(0.245454 - 1.70717i) q^{44} -2.72183 q^{45} +(-3.77831 + 2.95371i) q^{46} +6.22277 q^{47} +(0.195368 - 1.35881i) q^{48} +(0.415415 + 0.909632i) q^{49} +(0.915415 + 0.268790i) q^{50} +(4.20251 + 4.84995i) q^{51} +(2.30075 - 0.675560i) q^{52} +(-8.29712 - 5.33224i) q^{53} +(-2.34695 + 5.13910i) q^{54} +(2.75597 - 3.18056i) q^{55} +(0.841254 - 0.540641i) q^{56} +(-0.226900 - 1.57812i) q^{57} +(-0.748008 - 5.20251i) q^{58} +(3.45491 - 2.22034i) q^{59} +(2.19360 - 2.53155i) q^{60} +(3.76039 - 8.23412i) q^{61} +(-0.506008 - 0.325192i) q^{62} +(-1.07028 + 0.314261i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(5.61404 + 1.64843i) q^{65} +(-0.983568 - 2.15371i) q^{66} +(-2.04487 + 14.2224i) q^{67} +4.67474 q^{68} +(-2.17122 + 6.21532i) q^{69} +2.44009 q^{70} +(1.32879 - 9.24194i) q^{71} +(0.463379 + 1.01466i) q^{72} +(-3.05612 - 0.897358i) q^{73} +(-5.27613 - 6.08898i) q^{74} +(1.25667 - 0.368991i) q^{75} +(-0.977031 - 0.627899i) q^{76} +(0.716476 - 1.56886i) q^{77} +(2.15565 - 2.48775i) q^{78} +(6.14561 - 3.94954i) q^{79} +(-0.347262 - 2.41526i) q^{80} +(0.627519 + 4.36449i) q^{81} +(-10.5151 + 6.75767i) q^{82} +(2.66583 - 3.07653i) q^{83} +(0.570276 - 1.24873i) q^{84} +(9.59601 + 6.16698i) q^{85} +(5.30432 - 1.55749i) q^{86} +(-4.72507 - 5.45302i) q^{87} +(-1.65486 - 0.485911i) q^{88} +(-2.00538 - 4.39117i) q^{89} +(-0.387356 + 2.69412i) q^{90} +2.39788 q^{91} +(2.38594 + 4.16021i) q^{92} -0.825721 q^{93} +(0.885593 - 6.15943i) q^{94} +(-1.17725 - 2.57783i) q^{95} +(-1.31718 - 0.386758i) q^{96} +(-0.816541 - 0.942338i) q^{97} +(0.959493 - 0.281733i) q^{98} +(1.61845 + 1.04012i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} + 5 q^{3} - q^{4} + 8 q^{5} - 5 q^{6} + q^{7} + q^{8}+O(q^{10}) \) 10 * q + q^2 + 5 * q^3 - q^4 + 8 * q^5 - 5 * q^6 + q^7 + q^8	\( 10 q + q^{2} + 5 q^{3} - q^{4} + 8 q^{5} - 5 q^{6} + q^{7} + q^{8} + 3 q^{10} + 11 q^{11} + 5 q^{12} - 6 q^{13} - q^{14} + 4 q^{15} - q^{16} - 2 q^{17} - 3 q^{19} + 8 q^{20} - 5 q^{21} - 21 q^{23} + 6 q^{24} - 15 q^{25} - 5 q^{26} - 4 q^{27} + q^{28} + 2 q^{29} - 4 q^{30} + 3 q^{31} + q^{32} - 11 q^{33} + 2 q^{34} + 3 q^{35} - 6 q^{37} - 8 q^{38} + 8 q^{39} + 14 q^{40} - 23 q^{41} + 5 q^{42} - q^{43} + 11 q^{44} - 22 q^{45} - q^{46} + 38 q^{47} + 5 q^{48} - q^{49} + 4 q^{50} + 21 q^{51} + 5 q^{52} - 49 q^{53} + 4 q^{54} + 11 q^{55} - q^{56} - 7 q^{57} - 13 q^{58} + 9 q^{59} + 4 q^{60} + 16 q^{61} - 14 q^{62} - q^{64} + 15 q^{65} + 7 q^{67} - 2 q^{68} - 16 q^{69} + 8 q^{70} - 16 q^{71} + 11 q^{72} - 9 q^{73} + 6 q^{74} - 2 q^{75} - 14 q^{76} + 11 q^{77} - 8 q^{78} + 6 q^{79} - 3 q^{80} - 24 q^{81} - 43 q^{82} - 19 q^{83} - 5 q^{84} + 49 q^{85} + 23 q^{86} - 21 q^{87} - 11 q^{88} + 25 q^{89} - 11 q^{90} + 6 q^{91} + q^{92} - 4 q^{93} - 5 q^{94} + 24 q^{95} - 5 q^{96} + 16 q^{97} + q^{98} - 33 q^{99}+O(q^{100}) \) 10 * q + q^2 + 5 * q^3 - q^4 + 8 * q^5 - 5 * q^6 + q^7 + q^8 + 3 * q^10 + 11 * q^11 + 5 * q^12 - 6 * q^13 - q^14 + 4 * q^15 - q^16 - 2 * q^17 - 3 * q^19 + 8 * q^20 - 5 * q^21 - 21 * q^23 + 6 * q^24 - 15 * q^25 - 5 * q^26 - 4 * q^27 + q^28 + 2 * q^29 - 4 * q^30 + 3 * q^31 + q^32 - 11 * q^33 + 2 * q^34 + 3 * q^35 - 6 * q^37 - 8 * q^38 + 8 * q^39 + 14 * q^40 - 23 * q^41 + 5 * q^42 - q^43 + 11 * q^44 - 22 * q^45 - q^46 + 38 * q^47 + 5 * q^48 - q^49 + 4 * q^50 + 21 * q^51 + 5 * q^52 - 49 * q^53 + 4 * q^54 + 11 * q^55 - q^56 - 7 * q^57 - 13 * q^58 + 9 * q^59 + 4 * q^60 + 16 * q^61 - 14 * q^62 - q^64 + 15 * q^65 + 7 * q^67 - 2 * q^68 - 16 * q^69 + 8 * q^70 - 16 * q^71 + 11 * q^72 - 9 * q^73 + 6 * q^74 - 2 * q^75 - 14 * q^76 + 11 * q^77 - 8 * q^78 + 6 * q^79 - 3 * q^80 - 24 * q^81 - 43 * q^82 - 19 * q^83 - 5 * q^84 + 49 * q^85 + 23 * q^86 - 21 * q^87 - 11 * q^88 + 25 * q^89 - 11 * q^90 + 6 * q^91 + q^92 - 4 * q^93 - 5 * q^94 + 24 * q^95 - 5 * q^96 + 16 * q^97 + q^98 - 33 * q^99

Introduction

L-functions

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