LMFDB - Embedded newform 418.2.q.a.21.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(21,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 1]))

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

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

chi := DirichletCharacter("418.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.q (of order $18$, degree $6$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			21.2
Character	$\chi$	$=$	418.21
Dual form			418.2.q.a.219.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(-1.64579 + 1.96137i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-3.44031 + 1.25217i) q^{5} +(-1.64579 - 1.96137i) q^{6} +(0.237067 - 0.136871i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.617423 - 3.50158i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(-1.64579 + 1.96137i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-3.44031 + 1.25217i) q^{5} +(-1.64579 - 1.96137i) q^{6} +(0.237067 - 0.136871i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.617423 - 3.50158i) q^{9} +(-0.635743 - 3.60548i) q^{10} +(0.340766 - 3.29907i) q^{11} +(2.21736 - 1.28019i) q^{12} +(-3.77750 + 3.16970i) q^{13} +(0.0936252 + 0.257233i) q^{14} +(3.20604 - 8.80853i) q^{15} +(0.766044 + 0.642788i) q^{16} +(5.78331 + 1.01975i) q^{17} +3.55560 q^{18} +(-0.912144 + 4.26239i) q^{19} +3.66110 q^{20} +(-0.121707 + 0.690237i) q^{21} +(3.18978 + 0.908467i) q^{22} +(0.397637 + 0.144728i) q^{23} +(0.875705 + 2.40598i) q^{24} +(6.43756 - 5.40176i) q^{25} +(-2.46559 - 4.27053i) q^{26} +(1.23196 + 0.711270i) q^{27} +(-0.269583 + 0.0475347i) q^{28} +(-1.03238 - 5.85493i) q^{29} +(8.11798 + 4.68692i) q^{30} +(-1.39534 + 0.805602i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(5.90988 + 6.09794i) q^{33} +(-2.00852 + 5.51837i) q^{34} +(-0.644199 + 0.767726i) q^{35} +(-0.617423 + 3.50158i) q^{36} -11.0389i q^{37} +(-4.03925 - 1.63844i) q^{38} -12.6257i q^{39} +(-0.635743 + 3.60548i) q^{40} +(-7.09476 - 5.95321i) q^{41} +(-0.658617 - 0.239717i) q^{42} +(3.30494 + 9.08025i) q^{43} +(-1.44856 + 2.98357i) q^{44} +(6.50869 + 11.2734i) q^{45} +(-0.211578 + 0.366464i) q^{46} +(-0.930808 - 5.27887i) q^{47} +(-2.52149 + 0.444607i) q^{48} +(-3.46253 + 5.99728i) q^{49} +(4.20182 + 7.27777i) q^{50} +(-11.5182 + 9.66493i) q^{51} +(4.63380 - 1.68656i) q^{52} +(2.33781 - 6.42309i) q^{53} +(-0.914391 + 1.08973i) q^{54} +(2.95866 + 11.7765i) q^{55} -0.273742i q^{56} +(-6.85894 - 8.80404i) q^{57} +5.94525 q^{58} +(-12.1854 - 2.14861i) q^{59} +(-6.02539 + 7.18078i) q^{60} +(0.928920 - 2.55219i) q^{61} +(-0.551064 - 1.51404i) q^{62} +(-0.625635 - 0.745602i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(9.02677 - 15.6348i) q^{65} +(-7.03154 + 4.76120i) q^{66} +(-1.03788 + 0.183006i) q^{67} +(-5.08576 - 2.93626i) q^{68} +(-0.938292 + 0.541723i) q^{69} +(-0.644199 - 0.767726i) q^{70} +(-0.936463 - 2.57291i) q^{71} +(-3.34117 - 1.21609i) q^{72} +(1.56790 - 1.86855i) q^{73} +(10.8712 + 1.91689i) q^{74} +21.5166i q^{75} +(2.31496 - 3.69337i) q^{76} +(-0.370762 - 0.828743i) q^{77} +(12.4339 + 2.19244i) q^{78} +(3.48779 + 2.92660i) q^{79} +(-3.44031 - 1.25217i) q^{80} +(6.60090 - 2.40253i) q^{81} +(7.09476 - 5.95321i) q^{82} +(-9.67636 + 5.58665i) q^{83} +(0.350443 - 0.606985i) q^{84} +(-21.1733 + 3.73342i) q^{85} +(-9.51620 + 1.67796i) q^{86} +(13.1828 + 7.61108i) q^{87} +(-2.68670 - 1.94465i) q^{88} +(-5.35117 - 6.37728i) q^{89} +(-12.2323 + 4.45221i) q^{90} +(-0.461683 + 1.26846i) q^{91} +(-0.324157 - 0.272000i) q^{92} +(0.716352 - 4.06264i) q^{93} +5.36031 q^{94} +(-2.19918 - 15.8061i) q^{95} -2.56039i q^{96} +(-3.37410 - 0.594944i) q^{97} +(-5.30491 - 4.45135i) q^{98} +(-11.7624 + 0.843705i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{3} - 3 q^{6} - 18 q^{7} + 30 q^{8} - 3 q^{9}+O(q^{10}) $ 60 * q - 3 * q^3 - 3 * q^6 - 18 * q^7 + 30 * q^8 - 3 * q^9	$ 60 q - 3 q^{3} - 3 q^{6} - 18 q^{7} + 30 q^{8} - 3 q^{9} + 3 q^{11} + 6 q^{13} - 12 q^{14} + 24 q^{15} - 6 q^{17} + 60 q^{18} - 30 q^{19} - 12 q^{20} + 12 q^{21} + 12 q^{22} + 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} + 6 q^{28} - 3 q^{29} - 9 q^{31} - 42 q^{33} - 6 q^{34} - 24 q^{35} - 3 q^{36} + 6 q^{38} + 15 q^{41} + 6 q^{42} - 3 q^{43} + 12 q^{44} - 48 q^{45} + 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} + 36 q^{50} - 45 q^{51} - 3 q^{52} + 24 q^{53} - 27 q^{54} + 6 q^{55} + 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} + 54 q^{61} - 66 q^{63} - 30 q^{64} - 63 q^{66} + 9 q^{67} - 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} - 6 q^{72} + 12 q^{74} + 18 q^{77} + 36 q^{79} - 93 q^{81} - 15 q^{82} - 36 q^{83} + 24 q^{84} - 60 q^{85} - 3 q^{86} + 54 q^{87} - 3 q^{88} - 3 q^{89} - 24 q^{90} - 12 q^{91} - 102 q^{93} - 12 q^{94} + 24 q^{95} - 6 q^{97} - 18 q^{98} - 78 q^{99}+O(q^{100}) $ 60 * q - 3 * q^3 - 3 * q^6 - 18 * q^7 + 30 * q^8 - 3 * q^9 + 3 * q^11 + 6 * q^13 - 12 * q^14 + 24 * q^15 - 6 * q^17 + 60 * q^18 - 30 * q^19 - 12 * q^20 + 12 * q^21 + 12 * q^22 + 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 + 6 * q^28 - 3 * q^29 - 9 * q^31 - 42 * q^33 - 6 * q^34 - 24 * q^35 - 3 * q^36 + 6 * q^38 + 15 * q^41 + 6 * q^42 - 3 * q^43 + 12 * q^44 - 48 * q^45 + 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 + 36 * q^50 - 45 * q^51 - 3 * q^52 + 24 * q^53 - 27 * q^54 + 6 * q^55 + 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 + 54 * q^61 - 66 * q^63 - 30 * q^64 - 63 * q^66 + 9 * q^67 - 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 - 6 * q^72 + 12 * q^74 + 18 * q^77 + 36 * q^79 - 93 * q^81 - 15 * q^82 - 36 * q^83 + 24 * q^84 - 60 * q^85 - 3 * q^86 + 54 * q^87 - 3 * q^88 - 3 * q^89 - 24 * q^90 - 12 * q^91 - 102 * q^93 - 12 * q^94 + 24 * q^95 - 6 * q^97 - 18 * q^98 - 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$

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 $

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	−1.64579	+	1.96137i	−0.950195	+	1.13240i	0.0408890	+	0.999164i	$0.486981\pi$
$3$	−1.64579	+	1.96137i	−0.950195	+	1.13240i	−0.991084	+	0.133235i	$0.957463\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−3.44031	+	1.25217i	−1.53855	+	0.559987i	−0.965697	−	0.259670i	$-0.916386\pi$
$5$	−3.44031	+	1.25217i	−1.53855	+	0.559987i	−0.572855	+	0.819657i	$0.694164\pi$
$6$	−1.64579	−	1.96137i	−0.671890	−	0.800727i
$7$	0.237067	−	0.136871i	0.0896030	−	0.0517323i	−0.454529	−	0.890732i	$-0.650192\pi$
$7$	0.237067	−	0.136871i	0.0896030	−	0.0517323i	0.544132	+	0.839000i	$0.316859\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−0.617423	−	3.50158i	−0.205808	−	1.16719i
$10$	−0.635743	−	3.60548i	−0.201040	−	1.14015i
$11$	0.340766	−	3.29907i	0.102745	−	0.994708i
$11$	0.340766	−	3.29907i	0.102745	−	0.994708i
$12$	2.21736	−	1.28019i	0.640097	−	0.369560i
$13$	−3.77750	+	3.16970i	−1.04769	+	0.879117i	−0.992849	−	0.119378i	$-0.961910\pi$
$13$	−3.77750	+	3.16970i	−1.04769	+	0.879117i	−0.0548424	+	0.998495i	$0.517466\pi$
$14$	0.0936252	+	0.257233i	0.0250224	+	0.0687484i
$15$	3.20604	−	8.80853i	0.827796	−	2.27435i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	5.78331	+	1.01975i	1.40266	+	0.247327i	0.823235	−	0.567700i	$-0.192167\pi$
$17$	5.78331	+	1.01975i	1.40266	+	0.247327i	0.579423	+	0.815027i	$0.303278\pi$
$18$	3.55560			0.838062
$19$	−0.912144	+	4.26239i	−0.209260	+	0.977860i
$19$	−0.912144	+	4.26239i	−0.209260	+	0.977860i
$20$	3.66110			0.818647
$21$	−0.121707	+	0.690237i	−0.0265587	+	0.150622i
$22$	3.18978	+	0.908467i	0.680063	+	0.193686i
$23$	0.397637	+	0.144728i	0.0829131	+	0.0301779i	0.383144	−	0.923689i	$-0.374841\pi$
$23$	0.397637	+	0.144728i	0.0829131	+	0.0301779i	−0.300231	+	0.953867i	$0.597064\pi$
$24$	0.875705	+	2.40598i	0.178752	+	0.491118i
$25$	6.43756	−	5.40176i	1.28751	−	1.08035i
$26$	−2.46559	−	4.27053i	−0.483542	−	0.837520i
$27$	1.23196	+	0.711270i	0.237090	+	0.136884i
$28$	−0.269583	+	0.0475347i	−0.0509464	+	0.00898322i
$29$	−1.03238	−	5.85493i	−0.191709	−	1.08723i	−0.917029	−	0.398821i	$-0.869419\pi$
$29$	−1.03238	−	5.85493i	−0.191709	−	1.08723i	0.725320	−	0.688412i	$-0.241692\pi$
$30$	8.11798	+	4.68692i	1.48213	+	0.855710i
$31$	−1.39534	+	0.805602i	−0.250611	+	0.144690i	−0.620044	−	0.784567i	$-0.712885\pi$
$31$	−1.39534	+	0.805602i	−0.250611	+	0.144690i	0.369433	+	0.929257i	$0.379552\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	5.90988	+	6.09794i	1.02878	+	1.06151i
$34$	−2.00852	+	5.51837i	−0.344459	+	0.946393i
$35$	−0.644199	+	0.767726i	−0.108889	+	0.129769i
$36$	−0.617423	+	3.50158i	−0.102904	+	0.583596i
$37$		−	11.0389i		−	1.81479i	−0.420279	−	0.907395i	$-0.638068\pi$
$37$		−	11.0389i		−	1.81479i	0.420279	−	0.907395i	$-0.361932\pi$
$38$	−4.03925	−	1.63844i	−0.655252	−	0.265791i
$39$		−	12.6257i		−	2.02174i
$40$	−0.635743	+	3.60548i	−0.100520	+	0.570076i
$41$	−7.09476	−	5.95321i	−1.10801	−	0.929735i	−0.110077	−	0.993923i	$-0.535110\pi$
$41$	−7.09476	−	5.95321i	−1.10801	−	0.929735i	−0.997938	+	0.0641882i	$0.979554\pi$
$42$	−0.658617	−	0.239717i	−0.101627	−	0.0369891i
$43$	3.30494	+	9.08025i	0.503999	+	1.38473i	0.887339	+	0.461118i	$0.152552\pi$
$43$	3.30494	+	9.08025i	0.503999	+	1.38473i	−0.383340	+	0.923607i	$0.625226\pi$
$44$	−1.44856	+	2.98357i	−0.218379	+	0.449789i
$45$	6.50869	+	11.2734i	0.970258	+	1.68054i
$46$	−0.211578	+	0.366464i	−0.0311955	+	0.0540322i
$47$	−0.930808	−	5.27887i	−0.135772	−	0.770003i	−0.974319	−	0.225173i	$-0.927705\pi$
$47$	−0.930808	−	5.27887i	−0.135772	−	0.770003i	0.838547	−	0.544830i	$-0.183406\pi$
$48$	−2.52149	+	0.444607i	−0.363946	+	0.0641735i
$49$	−3.46253	+	5.99728i	−0.494648	+	0.856755i
$50$	4.20182	+	7.27777i	0.594227	+	1.02923i
$51$	−11.5182	+	9.66493i	−1.61287	+	1.35336i
$52$	4.63380	−	1.68656i	0.642592	−	0.233884i
$53$	2.33781	−	6.42309i	0.321123	−	0.882279i	−0.669148	−	0.743129i	$-0.733341\pi$
$53$	2.33781	−	6.42309i	0.321123	−	0.882279i	0.990271	−	0.139150i	$-0.0444370\pi$
$54$	−0.914391	+	1.08973i	−0.124433	+	0.148293i
$55$	2.95866	+	11.7765i	0.398946	+	1.58795i
$56$		−	0.273742i		−	0.0365803i
$57$	−6.85894	−	8.80404i	−0.908489	−	1.16612i
$58$	5.94525			0.780650
$59$	−12.1854	−	2.14861i	−1.58640	−	0.279725i	−0.690281	−	0.723541i	$-0.742513\pi$
$59$	−12.1854	−	2.14861i	−1.58640	−	0.279725i	−0.896118	+	0.443817i	$0.853624\pi$
$60$	−6.02539	+	7.18078i	−0.777874	+	0.927034i
$61$	0.928920	−	2.55219i	0.118936	−	0.326774i	−0.865911	−	0.500198i	$-0.833261\pi$
$61$	0.928920	−	2.55219i	0.118936	−	0.326774i	0.984847	+	0.173424i	$0.0554829\pi$
$62$	−0.551064	−	1.51404i	−0.0699852	−	0.192283i
$63$	−0.625635	−	0.745602i	−0.0788225	−	0.0939371i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	9.02677	−	15.6348i	1.11963	−	1.93926i
$66$	−7.03154	+	4.76120i	−0.865522	+	0.586063i
$67$	−1.03788	+	0.183006i	−0.126797	+	0.0223578i	−0.236687	−	0.971586i	$-0.576061\pi$
$67$	−1.03788	+	0.183006i	−0.126797	+	0.0223578i	0.109889	+	0.993944i	$0.464950\pi$
$68$	−5.08576	−	2.93626i	−0.616739	−	0.356074i
$69$	−0.938292	+	0.541723i	−0.112957	+	0.0652158i
$70$	−0.644199	−	0.767726i	−0.0769965	−	0.0917608i
$71$	−0.936463	−	2.57291i	−0.111138	−	0.305348i	0.871638	−	0.490150i	$-0.163058\pi$
$71$	−0.936463	−	2.57291i	−0.111138	−	0.305348i	−0.982776	+	0.184802i	$0.940836\pi$
$72$	−3.34117	−	1.21609i	−0.393760	−	0.143317i
$73$	1.56790	−	1.86855i	0.183509	−	0.218698i	−0.666445	−	0.745554i	$-0.732185\pi$
$73$	1.56790	−	1.86855i	0.183509	−	0.218698i	0.849954	+	0.526856i	$0.176629\pi$
$74$	10.8712	+	1.91689i	1.26375	+	0.222834i
$75$			21.5166i			2.48452i
$76$	2.31496	−	3.69337i	0.265544	−	0.423658i
$77$	−0.370762	−	0.828743i	−0.0422523	−	0.0944440i
$78$	12.4339	+	2.19244i	1.40787	+	0.248245i
$79$	3.48779	+	2.92660i	0.392407	+	0.329269i	0.817550	−	0.575858i	$-0.195332\pi$
$79$	3.48779	+	2.92660i	0.392407	+	0.329269i	−0.425143	+	0.905126i	$0.639776\pi$
$80$	−3.44031	−	1.25217i	−0.384638	−	0.139997i
$81$	6.60090	−	2.40253i	0.733433	−	0.266948i
$82$	7.09476	−	5.95321i	0.783485	−	0.657422i
$83$	−9.67636	+	5.58665i	−1.06212	+	0.613215i	−0.926018	−	0.377480i	$-0.876791\pi$
$83$	−9.67636	+	5.58665i	−1.06212	+	0.613215i	−0.136101	+	0.990695i	$0.543457\pi$
$84$	0.350443	−	0.606985i	0.0382364	−	0.0662274i
$85$	−21.1733	+	3.73342i	−2.29656	+	0.404946i
$86$	−9.51620	+	1.67796i	−1.02616	+	0.180939i
$87$	13.1828	+	7.61108i	1.41334	+	0.815993i
$88$	−2.68670	−	1.94465i	−0.286403	−	0.207300i
$89$	−5.35117	−	6.37728i	−0.567223	−	0.675990i	0.403836	−	0.914832i	$-0.367677\pi$
$89$	−5.35117	−	6.37728i	−0.567223	−	0.675990i	−0.971059	+	0.238842i	$0.923232\pi$
$90$	−12.2323	+	4.45221i	−1.28940	+	0.469304i
$91$	−0.461683	+	1.26846i	−0.0483975	+	0.132971i
$92$	−0.324157	−	0.272000i	−0.0337957	−	0.0283579i
$93$	0.716352	−	4.06264i	0.0742823	−	0.421276i
$94$	5.36031			0.552874
$95$	−2.19918	−	15.8061i	−0.225631	−	1.62167i
$96$		−	2.56039i		−	0.261319i
$97$	−3.37410	−	0.594944i	−0.342587	−	0.0604074i	−0.000292476	−	1.00000i	$-0.500093\pi$
$97$	−3.37410	−	0.594944i	−0.342587	−	0.0604074i	−0.342295	+	0.939593i	$0.611204\pi$
$98$	−5.30491	−	4.45135i	−0.535877	−	0.449654i
$99$	−11.7624	+	0.843705i	−1.18216	+	0.0847955i
$100$	−7.89684	+	2.87421i	−0.789684	+	0.287421i
$101$	0.172485	+	0.205559i	0.0171629	+	0.0204539i	0.774558	−	0.632503i	$-0.217973\pi$
$101$	0.172485	+	0.205559i	0.0171629	+	0.0204539i	−0.757395	+	0.652957i	$0.773528\pi$
$102$	−7.51798	−	13.0215i	−0.744391	−	1.28932i
$103$	−5.81928	−	3.35976i	−0.573390	−	0.331047i	0.185112	−	0.982717i	$-0.440735\pi$
$103$	−5.81928	−	3.35976i	−0.573390	−	0.331047i	−0.758502	+	0.651670i	$0.774069\pi$
$104$	0.856291	+	4.85627i	0.0839662	+	0.476196i
$105$	−0.445583	−	2.52703i	−0.0434845	−	0.246613i
$106$	5.91955	+	3.41765i	0.574958	+	0.331952i
$107$	8.42420	+	14.5911i	0.814398	+	1.41058i	0.909759	+	0.415137i	$0.136266\pi$
$107$	8.42420	+	14.5911i	0.814398	+	1.41058i	−0.0953606	+	0.995443i	$0.530400\pi$
$108$	−0.914391	−	1.08973i	−0.0879873	−	0.104859i
$109$	−14.3627	+	5.22759i	−1.37569	+	0.500712i	−0.920870	−	0.389869i	$-0.872520\pi$
$109$	−14.3627	+	5.22759i	−1.37569	+	0.500712i	−0.454824	+	0.890581i	$0.650298\pi$
$110$	−12.1114	+	0.868740i	−1.15477	+	0.0828311i
$111$	21.6515	+	18.1677i	2.05507	+	1.72440i
$112$	0.269583	+	0.0475347i	0.0254732	+	0.00449161i
$113$			11.7408i			1.10449i	0.833683	+	0.552243i	$0.186228\pi$
$113$			11.7408i			1.10449i	−0.833683	+	0.552243i	$0.813772\pi$
$114$	9.86133	−	5.22594i	0.923599	−	0.489454i
$115$	−1.54922			−0.144465
$116$	−1.03238	+	5.85493i	−0.0958543	+	0.543617i
$117$	13.4313	+	11.2702i	1.24172	+	1.04193i
$118$	4.23193	−	11.6271i	0.389581	−	1.07036i
$119$	1.51061	−	0.549816i	0.138477	−	0.0504016i
$120$	−6.02539	−	7.18078i	−0.550040	−	0.655512i
$121$	−10.7678	−	2.24842i	−0.978887	−	0.204402i
$122$	2.35211	+	1.35799i	0.212950	+	0.122947i
$123$	23.3529	−	4.11775i	2.10566	−	0.371285i
$124$	1.58673	−	0.279783i	0.142492	−	0.0251252i
$125$	−6.23053	+	10.7916i	−0.557276	+	0.965230i
$126$	0.842915	−	0.486657i	0.0750929	−	0.0433549i
$127$	0.0940622	−	0.0789275i	0.00834667	−	0.00700369i	−0.638605	−	0.769535i	$-0.720488\pi$
$127$	0.0940622	−	0.0789275i	0.00834667	−	0.00700369i	0.646951	+	0.762531i	$0.276044\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	−23.2490	−	8.46194i	−2.04696	−	0.745032i
$130$	13.8298	+	11.6046i	1.21296	+	1.01779i
$131$	0.553284	+	0.0975590i	0.0483407	+	0.00852377i	0.197766	−	0.980249i	$-0.436631\pi$
$131$	0.553284	+	0.0975590i	0.0483407	+	0.00852377i	−0.149426	+	0.988773i	$0.547742\pi$
$132$	−3.46785	−	7.75149i	−0.301838	−	0.674680i
$133$	0.367158	+	1.13532i	0.0318366	+	0.0984447i
$134$		−	1.05389i		−	0.0910423i
$135$	−5.12894	−	0.904370i	−0.441429	−	0.0778358i
$136$	3.77479	−	4.49862i	0.323685	−	0.385753i
$137$	2.90452	+	1.05716i	0.248149	+	0.0903190i	0.463100	−	0.886306i	$-0.346737\pi$
$137$	2.90452	+	1.05716i	0.248149	+	0.0903190i	−0.214951	+	0.976625i	$0.568959\pi$
$138$	−0.370560	−	1.01811i	−0.0315442	−	0.0866669i
$139$	−0.421179	−	0.501941i	−0.0357239	−	0.0425741i	0.747887	−	0.663826i	$-0.231069\pi$
$139$	−0.421179	−	0.501941i	−0.0357239	−	0.0425741i	−0.783611	+	0.621252i	$0.786624\pi$
$140$	0.867927	−	0.501098i	0.0733532	−	0.0423505i
$141$	11.8857	+	6.86224i	1.00096	+	0.577905i
$142$	2.69644	−	0.475455i	0.226280	−	0.0398993i
$143$	9.16984	+	13.5424i	0.766820	+	1.13247i
$144$	1.77780	−	3.07924i	0.148150	−	0.256603i
$145$	10.8831	+	18.8500i	0.903790	+	1.56541i
$146$	1.56790	+	1.86855i	0.129761	+	0.154643i
$147$	−6.06431	−	16.6616i	−0.500176	−	1.37422i
$148$	−3.77554	+	10.3732i	−0.310347	+	0.852672i
$149$	8.53243	−	10.1686i	0.699004	−	0.833041i	−0.293409	−	0.955987i	$-0.594790\pi$
$149$	8.53243	−	10.1686i	0.699004	−	0.833041i	0.992413	+	0.122946i	$0.0392343\pi$
$150$	−21.1897	−	3.73632i	−1.73013	−	0.305069i
$151$	−11.2435			−0.914985			−0.457492	−	0.889213i	$-0.651252\pi$
$151$	−11.2435			−0.914985			−0.457492	+	0.889213i	$0.651252\pi$
$152$	3.23527	+	2.92114i	0.262415	+	0.236935i
$153$		−	20.8803i		−	1.68807i
$154$	0.880535	−	0.221220i	0.0709555	−	0.0178264i
$155$	3.79166	−	4.51872i	0.304553	−	0.362953i
$156$	−4.31826	+	11.8643i	−0.345738	+	0.949906i
$157$	2.81130	−	1.02323i	0.224366	−	0.0816627i	−0.227391	−	0.973804i	$-0.573020\pi$
$157$	2.81130	−	1.02323i	0.224366	−	0.0816627i	0.451757	+	0.892141i	$0.350797\pi$
$158$	−3.48779	+	2.92660i	−0.277474	+	0.232828i
$159$	8.75053	+	15.1564i	0.693962	+	1.20198i
$160$	1.83055	−	3.17060i	0.144718	−	0.250658i
$161$	0.114076	−	0.0201146i	0.00899043	−	0.00158526i
$162$	1.21980	+	6.91781i	0.0958363	+	0.543515i
$163$	−0.426720	+	0.739101i	−0.0334233	+	0.0578909i	−0.882253	−	0.470775i	$-0.843974\pi$
$163$	−0.426720	+	0.739101i	−0.0334233	+	0.0578909i	0.848830	+	0.528666i	$0.177308\pi$
$164$	4.63077	+	8.02074i	0.361603	+	0.626314i
$165$	−27.9675	−	13.5786i	−2.17726	−	1.05709i
$166$	−3.82149	−	10.4995i	−0.296606	−	0.814917i
$167$	3.01423	+	1.09709i	0.233248	+	0.0848953i	0.456000	−	0.889980i	$-0.349282\pi$
$167$	3.01423	+	1.09709i	0.233248	+	0.0848953i	−0.222752	+	0.974875i	$0.571504\pi$
$168$	0.536909	+	0.450520i	0.0414235	+	0.0347584i
$169$	1.96510	−	11.1446i	0.151162	−	0.857280i
$170$		−	21.4999i		−	1.64897i
$171$	15.4883	+	0.562246i	1.18442	+	0.0429960i
$172$		−	9.66300i		−	0.736797i
$173$	4.36030	−	24.7285i	0.331508	−	1.88007i	−0.127807	−	0.991799i	$-0.540794\pi$
$173$	4.36030	−	24.7285i	0.331508	−	1.88007i	0.459314	−	0.888274i	$-0.348095\pi$
$174$	−9.78462	+	11.6609i	−0.741770	+	0.884007i
$175$	0.786792	−	2.16169i	0.0594759	−	0.163409i
$176$	2.38164	−	2.30820i	0.179523	−	0.173987i
$177$	24.2687	−	20.3639i	1.82415	−	1.53064i
$178$	7.20961	−	4.16247i	0.540383	−	0.311990i
$179$	−11.3225	−	6.53703i	−0.846281	−	0.488601i	0.0131130	−	0.999914i	$-0.495826\pi$
$179$	−11.3225	−	6.53703i	−0.846281	−	0.488601i	−0.859394	+	0.511313i	$0.829159\pi$
$180$	−2.26044	−	12.8196i	−0.168484	−	0.955518i
$181$	−9.55366	+	1.68457i	−0.710118	+	0.125213i	−0.517028	−	0.855968i	$-0.672962\pi$
$181$	−9.55366	+	1.68457i	−0.710118	+	0.125213i	−0.193089	+	0.981181i	$0.561851\pi$
$182$	−1.16902	−	0.674935i	−0.0866537	−	0.0500295i
$183$	3.47698	+	6.02231i	0.257026	+	0.445182i
$184$	0.324157	−	0.272000i	0.0238972	−	0.0200521i
$185$	13.8226	+	37.9773i	1.01626	+	2.79215i
$186$	3.87652	+	1.41094i	0.284240	+	0.103455i
$187$	5.33499	−	18.7321i	0.390133	−	1.36982i
$188$	−0.930808	+	5.27887i	−0.0678861	+	0.385001i
$189$	0.389408			0.0283253
$190$	15.9479	+	0.578929i	1.15698	+	0.0419999i
$191$	−18.0452			−1.30571			−0.652854	−	0.757484i	$-0.726429\pi$
$191$	−18.0452			−1.30571			−0.652854	+	0.757484i	$0.726429\pi$
$192$	2.52149	+	0.444607i	0.181973	+	0.0320867i
$193$	8.71634	+	7.31387i	0.627416	+	0.526464i	0.900125	−	0.435632i	$-0.143475\pi$
$193$	8.71634	+	7.31387i	0.627416	+	0.526464i	−0.272709	+	0.962097i	$0.587920\pi$
$194$	1.17181	−	3.21952i	0.0841311	−	0.231148i
$195$	15.8096	+	43.4365i	1.13215	+	3.11055i
$196$	5.30491	−	4.45135i	0.378922	−	0.317953i
$197$	−8.45276	+	4.88020i	−0.602234	+	0.347700i	−0.769920	−	0.638140i	$-0.779704\pi$
$197$	−8.45276	+	4.88020i	−0.602234	+	0.347700i	0.167686	+	0.985840i	$0.446371\pi$
$198$	1.21162	−	11.7302i	0.0861064	−	0.833627i
$199$	−0.0144800	−	0.0821203i	−0.00102646	−	0.00582135i	0.984290	−	0.176558i	$-0.0564963\pi$
$199$	−0.0144800	−	0.0821203i	−0.00102646	−	0.00582135i	−0.985317	+	0.170737i	$0.945385\pi$
$200$	−1.45928	−	8.27597i	−0.103186	−	0.585200i
$201$	1.34918	−	2.33686i	0.0951642	−	0.164829i
$202$	−0.232388	+	0.134169i	−0.0163508	+	0.00944011i
$203$	−1.04611	−	1.24671i	−0.0734227	−	0.0875018i
$204$	14.1292	−	5.14260i	0.989240	−	0.360054i
$205$	31.8626	+	11.5970i	2.22538	+	0.809971i
$206$	4.31923	−	5.14745i	0.300935	−	0.358640i
$207$	0.261266	−	1.48172i	0.0181593	−	0.102986i
$208$	−4.93118			−0.341916
$209$	13.7511	+	4.46171i	0.951185	+	0.308623i
$210$	2.56601			0.177072
$211$	−3.13056	+	17.7543i	−0.215517	+	1.22226i	0.664491	+	0.747296i	$0.268648\pi$
$211$	−3.13056	+	17.7543i	−0.215517	+	1.22226i	−0.880008	+	0.474959i	$0.842463\pi$
$212$	−4.39365	+	5.23615i	−0.301757	+	0.359620i
$213$	6.58765	+	2.39771i	0.451378	+	0.164288i
$214$	−15.8323	+	5.76249i	−1.08228	+	0.393916i
$215$	−22.7400	−	27.1005i	−1.55086	−	1.84824i
$216$	1.23196	−	0.711270i	0.0838240	−	0.0483958i
$217$	−0.220527	+	0.381964i	−0.0149703	+	0.0259294i
$218$	−2.65411	−	15.0522i	−0.179759	−	1.01947i
$219$	1.08450	+	6.15048i	0.0732834	+	0.415611i
$220$	1.24758	−	12.0782i	0.0841116	−	0.814314i
$221$	−25.0788	+	14.4793i	−1.68698	+	0.973980i
$222$	−21.6515	+	18.1677i	−1.45315	+	1.21934i
$223$	−1.19401	−	3.28052i	−0.0799570	−	0.219680i	0.893272	−	0.449516i	$-0.148403\pi$
$223$	−1.19401	−	3.28052i	−0.0799570	−	0.219680i	−0.973229	+	0.229836i	$0.926181\pi$
$224$	−0.0936252	+	0.257233i	−0.00625560	+	0.0171871i
$225$	−22.8894	−	19.2065i	−1.52596	−	1.28043i
$226$	−11.5625	−	2.03878i	−0.769124	−	0.135617i
$227$	19.2754			1.27936			0.639678	−	0.768643i	$-0.279068\pi$
$227$	19.2754			1.27936			0.639678	+	0.768643i	$0.279068\pi$
$228$	3.43414	+	10.6190i	0.227431	+	0.703260i
$229$	17.0800			1.12868			0.564338	−	0.825544i	$-0.309132\pi$
$229$	17.0800			1.12868			0.564338	+	0.825544i	$0.309132\pi$
$230$	0.269019	−	1.52568i	0.0177386	−	0.100600i
$231$	2.23567	+	0.636731i	0.147096	+	0.0418938i
$232$	−5.58671	−	2.03340i	−0.366785	−	0.133499i
$233$	−2.56192	−	7.03883i	−0.167837	−	0.461129i	0.827049	−	0.562130i	$-0.190018\pi$
$233$	−2.56192	−	7.03883i	−0.167837	−	0.461129i	−0.994886	+	0.101001i	$0.967796\pi$
$234$	−13.4313	+	11.2702i	−0.878030	+	0.736755i
$235$	9.81231	+	16.9954i	0.640084	+	1.10866i
$236$	10.7156	+	6.18667i	0.697528	+	0.402718i
$237$	−11.4803	+	2.02429i	−0.745727	+	0.131492i
$238$	0.279149	+	1.58313i	0.0180946	+	0.102619i
$239$	−14.5032	−	8.37340i	−0.938132	−	0.541631i	−0.0487574	−	0.998811i	$-0.515526\pi$
$239$	−14.5032	−	8.37340i	−0.938132	−	0.541631i	−0.889374	+	0.457180i	$0.848859\pi$
$240$	8.11798	−	4.68692i	0.524014	−	0.302539i
$241$	5.52057	−	4.63231i	0.355611	−	0.298393i	−0.447427	−	0.894320i	$-0.647660\pi$
$241$	5.52057	−	4.63231i	0.355611	−	0.298393i	0.803039	+	0.595927i	$0.203215\pi$
$242$	4.08406	−	10.2137i	0.262534	−	0.656564i
$243$	−7.61103	+	20.9111i	−0.488248	+	1.34145i
$244$	−1.74580	+	2.08056i	−0.111763	+	0.133194i
$245$	4.40256	−	24.9682i	0.281269	−	1.59516i
$246$			23.7132i			1.51190i
$247$	−10.0649	−	18.9924i	−0.640414	−	1.20846i
$248$			1.61120i			0.102312i
$249$	4.96773	−	28.1734i	0.314817	−	1.78542i
$250$	−9.54573	−	8.00982i	−0.603725	−	0.506586i
$251$	3.78996	+	1.37943i	0.239220	+	0.0870691i	0.458848	−	0.888515i	$-0.348262\pi$
$251$	3.78996	+	1.37943i	0.239220	+	0.0870691i	−0.219628	+	0.975584i	$0.570484\pi$
$252$	0.332893	+	0.914617i	0.0209703	+	0.0576154i
$253$	0.612969	−	1.26252i	0.0385371	−	0.0793737i
$254$	0.0613947	+	0.106339i	0.00385225	+	0.00667229i
$255$	27.5241	−	47.6731i	1.72362	−	2.98540i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−20.7820	+	3.66443i	−1.29635	+	0.228581i	−0.778907	−	0.627139i	$-0.784226\pi$
$257$	−20.7820	+	3.66443i	−1.29635	+	0.228581i	−0.517439	+	0.855720i	$0.673115\pi$
$258$	12.3705	−	21.4264i	0.770155	−	1.33395i
$259$	−1.51091	−	2.61697i	−0.0938833	−	0.162611i
$260$	−13.8298	+	11.6046i	−0.857689	+	0.719686i
$261$	−19.8641	+	7.22993i	−1.22956	+	0.447522i
$262$	−0.192154	+	0.527938i	−0.0118713	+	0.0326161i
$263$	−14.1553	+	16.8697i	−0.872856	+	1.04023i	0.125982	+	0.992033i	$0.459792\pi$
$263$	−14.1553	+	16.8697i	−0.872856	+	1.04023i	−0.998838	+	0.0481968i	$0.984653\pi$
$264$	8.23591	−	2.06914i	0.506885	−	0.127347i
$265$			25.0247i			1.53726i
$266$	−1.18183	+	0.164434i	−0.0724625	+	0.0100821i
$267$	21.3151			1.30446
$268$	1.03788	+	0.183006i	0.0633986	+	0.0111789i
$269$	15.4558	−	18.4195i	0.942354	−	1.12305i	−0.0498904	−	0.998755i	$-0.515887\pi$
$269$	15.4558	−	18.4195i	0.942354	−	1.12305i	0.992245	−	0.124299i	$-0.0396683\pi$
$270$	1.78126	−	4.89397i	0.108404	−	0.297838i
$271$	−3.63179	−	9.97827i	−0.220616	−	0.606137i	0.779170	−	0.626812i	$-0.215641\pi$
$271$	−3.63179	−	9.97827i	−0.220616	−	0.606137i	−0.999786	+	0.0206753i	$0.993418\pi$
$272$	3.77479	+	4.49862i	0.228880	+	0.272769i
$273$	−1.72810	−	2.99315i	−0.104589	−	0.181154i
$274$	−1.54546	+	2.67682i	−0.0933647	+	0.161712i
$275$	−15.6271	−	23.0787i	−0.942349	−	1.39170i
$276$	1.06699	−	0.188138i	0.0642250	−	0.0113246i
$277$	−18.6035	−	10.7408i	−1.11778	−	0.645350i	−0.176946	−	0.984221i	$-0.556622\pi$
$277$	−18.6035	−	10.7408i	−1.11778	−	0.645350i	−0.940833	+	0.338871i	$0.889955\pi$
$278$	0.567452	−	0.327619i	0.0340335	−	0.0196493i
$279$	3.68239	+	4.38851i	0.220459	+	0.262733i
$280$	0.342771	+	0.941756i	0.0204845	+	0.0562807i
$281$	26.3722	+	9.59869i	1.57323	+	0.572610i	0.973718	−	0.227755i	$-0.0731385\pi$
$281$	26.3722	+	9.59869i	1.57323	+	0.572610i	0.599514	+	0.800365i	$0.295361\pi$
$282$	−8.82193	+	10.5136i	−0.525338	+	0.626073i
$283$	9.36052	+	1.65051i	0.556425	+	0.0981128i	0.444787	−	0.895636i	$-0.353279\pi$
$283$	9.36052	+	1.65051i	0.556425	+	0.0981128i	0.111638	+	0.993749i	$0.464390\pi$
$284$			2.73803i			0.162472i
$285$	34.6210	+	21.7001i	2.05077	+	1.28540i
$286$	−14.9290	+	6.67891i	−0.882769	+	0.394932i
$287$	−2.49676	−	0.440245i	−0.147379	−	0.0259869i
$288$	2.72374	+	2.28549i	0.160498	+	0.134674i
$289$	16.4320	+	5.98076i	0.966589	+	0.351810i
$290$	−20.4535	+	7.44446i	−1.20107	+	0.437154i
$291$	6.71995	−	5.63871i	0.393930	−	0.330547i
$292$	−2.11243	+	1.21961i	−0.123621	+	0.0713724i
$293$	−8.90517	+	15.4242i	−0.520245	+	0.901091i	0.479478	+	0.877554i	$0.340826\pi$
$293$	−8.90517	+	15.4242i	−0.520245	+	0.901091i	−0.999723	+	0.0235372i	$0.992507\pi$
$294$	17.4615	−	3.07893i	1.01838	−	0.179567i
$295$	44.6118	−	7.86626i	2.59740	−	0.457992i
$296$	−9.56000	−	5.51947i	−0.555664	−	0.320813i
$297$	2.76634	−	3.82193i	0.160519	−	0.221771i
$298$	8.53243	+	10.1686i	0.494271	+	0.589049i
$299$	−1.96082	+	0.713681i	−0.113397	+	0.0412732i
$300$	7.35911	−	20.2190i	0.424878	−	1.16734i
$301$	2.02632	+	1.70028i	0.116795	+	0.0980025i
$302$	1.95242	−	11.0727i	0.112349	−	0.637163i
$303$	−0.687051			−0.0394701
$304$	−3.43856	+	2.67887i	−0.197215	+	0.153644i
$305$			9.94347i			0.569362i
$306$	20.5631	+	3.62583i	1.17551	+	0.207275i
$307$	−10.4982	−	8.80907i	−0.599166	−	0.502760i	0.292011	−	0.956415i	$-0.405676\pi$
$307$	−10.4982	−	8.80907i	−0.599166	−	0.502760i	−0.891178	+	0.453655i	$0.850120\pi$
$308$	0.0649560	+	0.905572i	0.00370121	+	0.0515997i
$309$	16.1670	−	5.88432i	0.919710	−	0.334747i
$310$	3.79166	+	4.51872i	0.215352	+	0.256646i
$311$	14.7635	+	25.5711i	0.837162	+	1.45001i	0.892258	+	0.451525i	$0.149120\pi$
$311$	14.7635	+	25.5711i	0.837162	+	1.45001i	−0.0550967	+	0.998481i	$0.517547\pi$
$312$	−10.9342	−	6.31287i	−0.619028	−	0.357396i
$313$	−1.72983	−	9.81033i	−0.0977755	−	0.554512i	−0.993861	−	0.110632i	$-0.964713\pi$
$313$	−1.72983	−	9.81033i	−0.0977755	−	0.554512i	0.896086	−	0.443881i	$-0.146399\pi$
$314$	0.519508	+	2.94628i	0.0293175	+	0.166268i
$315$	3.08600	+	1.78170i	0.173876	+	0.100387i
$316$	−2.27649	−	3.94300i	−0.128063	−	0.221811i
$317$	−15.4094	−	18.3642i	−0.865480	−	1.03144i	−0.999183	−	0.0404173i	$-0.987131\pi$
$317$	−15.4094	−	18.3642i	−0.865480	−	1.03144i	0.133703	−	0.991021i	$-0.457313\pi$
$318$	−16.4456	+	5.98571i	−0.922224	+	0.335662i
$319$	−19.6676	+	1.41074i	−1.10118	+	0.0789865i
$320$	2.80456	+	2.35331i	0.156780	+	0.131554i
$321$	−42.4831	−	7.49092i	−2.37118	−	0.418102i
$322$			0.115836i			0.00645527i
$323$	−9.62180	+	23.7206i	−0.535372	+	1.31985i
$324$	−7.02453			−0.390252
$325$	−7.19596	+	40.8103i	−0.399160	+	2.26375i
$326$	−0.653774	−	0.548581i	−0.0362092	−	0.0303831i
$327$	13.3847	−	36.7740i	0.740173	−	2.03361i
$328$	−8.70301	+	3.16764i	−0.480543	+	0.174903i
$329$	−0.943188	−	1.12405i	−0.0519996	−	0.0619708i
$330$	18.2288	−	25.1847i	1.00346	−	1.38637i
$331$	9.56321	+	5.52132i	0.525641	+	0.303479i	0.739240	−	0.673442i	$-0.235185\pi$
$331$	9.56321	+	5.52132i	0.525641	+	0.303479i	−0.213598	+	0.976922i	$0.568518\pi$
$332$	11.0036	−	1.94022i	0.603899	−	0.106484i
$333$	−38.6537	+	6.81569i	−2.11821	+	0.373497i
$334$	−1.60384	+	2.77793i	−0.0877581	+	0.152001i
$335$	3.34147	−	1.92920i	0.182564	−	0.105403i
$336$	−0.536909	+	0.450520i	−0.0292908	+	0.0245779i
$337$	−7.59852	+	2.76563i	−0.413918	+	0.150654i	−0.540581	−	0.841292i	$-0.681795\pi$
$337$	−7.59852	+	2.76563i	−0.413918	+	0.150654i	0.126663	+	0.991946i	$0.459573\pi$
$338$	10.6341	+	3.87049i	0.578418	+	0.210527i
$339$	−23.0282	−	19.3229i	−1.25072	−	1.04948i
$340$	21.1733	+	3.73342i	1.14828	+	0.202473i
$341$	2.18225	+	4.87786i	0.118176	+	0.264151i
$342$	−3.24322	+	15.1553i	−0.175373	+	0.819507i
$343$			3.81187i			0.205822i
$344$	9.51620	+	1.67796i	0.513079	+	0.0904697i
$345$	2.54968	−	3.03859i	0.137270	−	0.163592i
$346$	23.5957	+	8.58812i	1.26851	+	0.461700i
$347$	−0.786873	−	2.16192i	−0.0422416	−	0.116058i	0.916778	−	0.399396i	$-0.130780\pi$
$347$	−0.786873	−	2.16192i	−0.0422416	−	0.116058i	−0.959020	+	0.283338i	$0.908558\pi$
$348$	−9.78462	−	11.6609i	−0.524510	−	0.625087i
$349$	−18.3193	+	10.5767i	−0.980612	+	0.566157i	−0.902455	−	0.430784i	$-0.858237\pi$
$349$	−18.3193	+	10.5767i	−0.980612	+	0.566157i	−0.0781571	+	0.996941i	$0.524904\pi$
$350$	1.99223	+	1.15021i	0.106489	+	0.0614815i
$351$	−6.90823	+	1.21811i	−0.368734	+	0.0650178i
$352$	1.85956	+	2.74628i	0.0991149	+	0.146377i
$353$	−0.686635	+	1.18929i	−0.0365459	+	0.0632993i	−0.883720	−	0.468016i	$-0.844969\pi$
$353$	−0.686635	+	1.18929i	−0.0365459	+	0.0632993i	0.847174	+	0.531316i	$0.178302\pi$
$354$	15.8403	+	27.4362i	0.841902	+	1.45822i
$355$	6.44344	+	7.67899i	0.341982	+	0.407558i
$356$	2.84730	+	7.82289i	0.150906	+	0.414612i
$357$	−1.40774	+	3.86775i	−0.0745057	+	0.204703i
$358$	8.40385	−	10.0153i	0.444157	−	0.529326i
$359$	−19.9448	−	3.51680i	−1.05264	−	0.185610i	−0.379554	−	0.925170i	$-0.623922\pi$
$359$	−19.9448	−	3.51680i	−1.05264	−	0.185610i	−0.673091	+	0.739560i	$0.735034\pi$
$360$	13.0174			0.686076
$361$	−17.3360	−	7.77583i	−0.912420	−	0.409254i
$362$		−	9.70104i		−	0.509875i
$363$	22.1314	−	17.4192i	1.16160	−	0.914269i
$364$	0.867680	−	1.03406i	0.0454788	−	0.0541995i
$365$	−3.05432	+	8.39168i	−0.159870	+	0.439240i
$366$	−6.53459	+	2.37840i	−0.341569	+	0.124321i
$367$	10.7171	−	8.99268i	0.559426	−	0.469414i	−0.318692	−	0.947858i	$-0.603244\pi$
$367$	10.7171	−	8.99268i	0.559426	−	0.469414i	0.878118	+	0.478444i	$0.158799\pi$
$368$	0.211578	+	0.366464i	0.0110293	+	0.0191033i
$369$	−16.4652	+	28.5185i	−0.857142	+	1.48461i
$370$	−39.8006	+	7.01793i	−2.06914	+	0.364845i
$371$	−0.324915	−	1.84268i	−0.0168687	−	0.0956673i
$372$	−2.06265	+	3.57262i	−0.106944	+	0.185232i
$373$	−3.51785	−	6.09310i	−0.182148	−	0.315489i	0.760464	−	0.649380i	$-0.224972\pi$
$373$	−3.51785	−	6.09310i	−0.182148	−	0.315489i	−0.942612	+	0.333891i	$0.891638\pi$
$374$	17.5211	+	8.50673i	0.905993	+	0.439873i
$375$	−10.9122	−	29.9811i	−0.563505	−	1.54822i
$376$	−5.03704	−	1.83333i	−0.259766	−	0.0945470i
$377$	22.4582	+	18.8447i	1.15666	+	0.970550i
$378$	−0.0676201	+	0.383492i	−0.00347800	+	0.0197247i
$379$			13.4097i			0.688810i	0.938821	+	0.344405i	$0.111919\pi$
$379$			13.4097i			0.688810i	−0.938821	+	0.344405i	$0.888081\pi$
$380$	−3.33945	+	15.6050i	−0.171310	+	0.800522i
$381$			0.314389i			0.0161066i
$382$	3.13352	−	17.7711i	0.160325	−	0.909248i
$383$	−2.99121	+	3.56479i	−0.152844	+	0.182152i	−0.837033	−	0.547152i	$-0.815712\pi$
$383$	−2.99121	+	3.56479i	−0.152844	+	0.182152i	0.684189	+	0.729305i	$0.260156\pi$
$384$	−0.875705	+	2.40598i	−0.0446881	+	0.122780i
$385$	2.31326	+	2.38687i	0.117895	+	0.121646i
$386$	−8.71634	+	7.31387i	−0.443650	+	0.372266i
$387$	29.7547	−	17.1789i	1.51251	−	0.873251i
$388$	2.96713	+	1.71307i	0.150633	+	0.0869681i
$389$	0.373133	+	2.11614i	0.0189186	+	0.107293i	0.992805	−	0.119744i	$-0.0382074\pi$
$389$	0.373133	+	2.11614i	0.0189186	+	0.107293i	−0.973886	+	0.227037i	$0.927096\pi$
$390$	−45.5219	+	8.02673i	−2.30509	+	0.406449i
$391$	2.15207	+	1.24250i	0.108835	+	0.0628359i
$392$	3.46253	+	5.99728i	0.174884	+	0.302909i
$393$	−1.10194	+	0.924636i	−0.0555854	+	0.0466417i
$394$	−3.33826	−	9.17178i	−0.168179	−	0.462068i
$395$	−15.6637	−	5.70111i	−0.788125	−	0.286854i
$396$	11.3416	+	3.23014i	0.569935	+	0.162321i
$397$	−3.65930	+	20.7529i	−0.183655	+	1.04156i	0.744016	+	0.668162i	$0.232919\pi$
$397$	−3.65930	+	20.7529i	−0.183655	+	1.04156i	−0.927671	+	0.373398i	$0.878193\pi$
$398$	0.0833871			0.00417982
$399$	−2.83105	−	1.14836i	−0.141730	−	0.0574900i
$400$	8.40364			0.420182
$401$	−2.63453	−	0.464538i	−0.131562	−	0.0231979i	0.107479	−	0.994207i	$-0.465722\pi$
$401$	−2.63453	−	0.464538i	−0.131562	−	0.0231979i	−0.239041	+	0.971009i	$0.576833\pi$
$402$	2.06707	+	1.73448i	0.103096	+	0.0865079i
$403$	2.71740	−	7.46599i	0.135363	−	0.371907i
$404$	−0.0917772	−	0.252156i	−0.00456608	−	0.0125452i
$405$	−19.7007	+	16.5309i	−0.978938	+	0.821426i
$406$	1.40942	−	0.813732i	0.0699486	−	0.0403848i
$407$	−36.4182	−	3.76169i	−1.80519	−	0.186460i
$408$	2.61097	+	14.8075i	0.129262	+	0.733082i
$409$	−5.83852	−	33.1119i	−0.288696	−	1.63728i	−0.691776	−	0.722112i	$-0.743171\pi$
$409$	−5.83852	−	33.1119i	−0.288696	−	1.63728i	0.403080	−	0.915165i	$-0.367940\pi$
$410$	−16.9537	+	29.3647i	−0.837284	+	1.45022i
$411$	−6.85369	+	3.95698i	−0.338068	+	0.195183i
$412$	4.31923	+	5.14745i	0.212793	+	0.253597i
$413$	−3.18283	+	1.15846i	−0.156617	+	0.0570039i
$414$	1.41384	+	0.514594i	0.0694863	+	0.0252909i
$415$	26.2942	−	31.3362i	1.29073	−	1.53824i
$416$	0.856291	−	4.85627i	0.0419831	−	0.238098i
$417$	1.67766			0.0821556
$418$	−6.78178	+	12.7674i	−0.331708	+	0.624476i
$419$	−24.9436			−1.21858			−0.609288	−	0.792949i	$-0.708545\pi$
$419$	−24.9436			−1.21858			−0.609288	+	0.792949i	$0.708545\pi$
$420$	−0.445583	+	2.52703i	−0.0217422	+	0.123306i
$421$	−24.9895	+	29.7813i	−1.21791	+	1.45145i	−0.363709	+	0.931513i	$0.618490\pi$
$421$	−24.9895	+	29.7813i	−1.21791	+	1.45145i	−0.854204	+	0.519939i	$0.825955\pi$
$422$	−16.9409	−	6.16600i	−0.824672	−	0.300156i
$423$	−17.9097	+	6.51859i	−0.870799	+	0.316945i
$424$	−4.39365	−	5.23615i	−0.213375	−	0.254290i
$425$	42.7389	−	24.6753i	2.07314	−	1.19693i
$426$	−3.50522	+	6.07121i	−0.169828	+	0.294151i
$427$	−0.129103	−	0.732182i	−0.00624775	−	0.0354328i
$428$	−2.92570	−	16.5924i	−0.141419	−	0.802026i
$429$	−41.6533	−	4.30242i	−2.01104	−	0.207723i
$430$	30.6376	−	17.6886i	1.47747	−	0.853020i
$431$	−11.2679	+	9.45486i	−0.542754	+	0.455425i	−0.872479	−	0.488652i	$-0.837489\pi$
$431$	−11.2679	+	9.45486i	−0.542754	+	0.455425i	0.329724	+	0.944077i	$0.393044\pi$
$432$	0.486537	+	1.33675i	0.0234085	+	0.0643144i
$433$	−4.80305	+	13.1963i	−0.230820	+	0.634172i	−0.999988	−	0.00487402i	$-0.998449\pi$
$433$	−4.80305	+	13.1963i	−0.230820	+	0.634172i	0.769168	+	0.639046i	$0.220671\pi$
$434$	−0.337867	−	0.283504i	−0.0162181	−	0.0136086i
$435$	−54.8832	−	9.67738i	−2.63145	−	0.463995i
$436$	15.2844			0.731992
$437$	−0.979590	+	1.56287i	−0.0468602	+	0.0747623i
$438$	−6.24536			−0.298415
$439$	−3.28920	+	18.6540i	−0.156985	+	0.890305i	0.799964	+	0.600048i	$0.204852\pi$
$439$	−3.28920	+	18.6540i	−0.156985	+	0.890305i	−0.956949	+	0.290257i	$0.906259\pi$
$440$	11.6781	+	3.32599i	0.556731	+	0.158560i
$441$	23.1378	+	8.42147i	1.10180	+	0.401022i
$442$	−9.90439	−	27.2121i	−0.471104	−	1.29435i
$443$	−17.8522	+	14.9798i	−0.848184	+	0.711711i	−0.959389	−	0.282086i	$-0.908974\pi$
$443$	−17.8522	+	14.9798i	−0.848184	+	0.711711i	0.111205	+	0.993798i	$0.464529\pi$
$444$	−14.1320	−	24.4773i	−0.670674	−	1.16164i
$445$	26.3951	+	15.2392i	1.25125	+	0.722408i
$446$	3.43802	−	0.606216i	0.162795	−	0.0287052i
$447$	5.90176	+	33.4706i	0.279144	+	1.58310i
$448$	−0.237067	−	0.136871i	−0.0112004	−	0.00646654i
$449$	−8.08644	+	4.66871i	−0.381623	+	0.220330i	−0.678524	−	0.734578i	$-0.737380\pi$
$449$	−8.08644	+	4.66871i	−0.381623	+	0.220330i	0.296901	+	0.954908i	$0.404047\pi$
$450$	22.8894	−	19.2065i	1.07902	−	0.905401i
$451$	−22.0577	+	21.3775i	−1.03866	+	1.00663i
$452$	4.01560	−	11.0328i	0.188878	−	0.518939i
$453$	18.5044	−	22.0527i	0.869415	−	1.03613i
$454$	−3.34714	+	18.9826i	−0.157089	+	0.890897i
$455$		−	4.94201i		−	0.231685i
$456$	−11.0540	+	1.53800i	−0.517651	+	0.0720234i
$457$		−	22.9944i		−	1.07563i	−0.843061	−	0.537817i	$-0.819249\pi$
$457$		−	22.9944i		−	1.07563i	0.843061	−	0.537817i	$-0.180751\pi$
$458$	−2.96590	+	16.8205i	−0.138588	+	0.785969i
$459$	6.39946	+	5.36979i	0.298701	+	0.250640i
$460$	1.45579	+	0.529864i	0.0678765	+	0.0247050i
$461$	1.55459	+	4.27120i	0.0724044	+	0.198929i	0.970616	−	0.240634i	$-0.0773554\pi$
$461$	1.55459	+	4.27120i	0.0724044	+	0.198929i	−0.898212	+	0.439564i	$0.855133\pi$
$462$	−1.01528	+	2.09114i	−0.0472350	+	0.0972885i
$463$	−3.08388	−	5.34144i	−0.143320	−	0.248238i	0.785425	−	0.618957i	$-0.212445\pi$
$463$	−3.08388	−	5.34144i	−0.143320	−	0.248238i	−0.928745	+	0.370719i	$0.879111\pi$
$464$	2.97263	−	5.14874i	0.138001	−	0.239024i
$465$	2.62264	+	14.8737i	0.121622	+	0.689752i
$466$	7.37677	−	1.30072i	0.341722	−	0.0602548i
$467$	20.0081	−	34.6551i	0.925866	−	1.60365i	0.135704	−	0.990749i	$-0.456670\pi$
$467$	20.0081	−	34.6551i	0.925866	−	1.60365i	0.790162	−	0.612898i	$-0.209996\pi$
$468$	−8.76664	−	15.1843i	−0.405238	−	0.701893i
$469$	−0.220999	+	0.185440i	−0.0102048	+	0.00856283i
$470$	−18.4411	+	6.71201i	−0.850625	+	0.309602i
$471$	−2.61987	+	7.19803i	−0.120717	+	0.331668i
$472$	−7.95343	+	9.47853i	−0.366086	+	0.436285i
$473$	31.0826	−	7.80900i	1.42918	−	0.359058i
$474$		−	11.6574i		−	0.535443i
$475$	17.1524	+	32.3666i	0.787007	+	1.48508i
$476$	−1.60756			−0.0736822
$477$	−23.9344	−	4.22027i	−1.09588	−	0.193233i
$478$	10.7646	−	12.8288i	0.492363	−	0.586776i
$479$	−10.5180	+	28.8980i	−0.480581	+	1.32038i	0.428416	+	0.903581i	$0.359072\pi$
$479$	−10.5180	+	28.8980i	−0.480581	+	1.32038i	−0.908997	+	0.416803i	$0.863151\pi$
$480$	3.20604	+	8.80853i	0.146335	+	0.402052i
$481$	34.9901	+	41.6996i	1.59541	+	1.90134i
$482$	3.60330	+	6.24109i	0.164126	+	0.284274i
$483$	−0.148292	+	0.256850i	−0.00674753	+	0.0116871i
$484$	9.34938	+	5.79561i	0.424972	+	0.263437i
$485$	12.3529	−	2.17815i	0.560916	−	0.0989046i
$486$	−19.2718	−	11.1266i	−0.874186	−	0.504712i
$487$	−12.1487	+	7.01403i	−0.550508	+	0.317836i	−0.749327	−	0.662200i	$-0.769623\pi$
$487$	−12.1487	+	7.01403i	−0.550508	+	0.317836i	0.198819	+	0.980036i	$0.436290\pi$
$488$	−1.74580	−	2.08056i	−0.0790286	−	0.0941826i
$489$	−0.747362	−	2.05336i	−0.0337969	−	0.0928562i
$490$	23.8244	+	8.67136i	1.07627	+	0.391732i
$491$	4.39189	−	5.23405i	0.198203	−	0.236209i	−0.657784	−	0.753207i	$-0.728506\pi$
$491$	4.39189	−	5.23405i	0.198203	−	0.236209i	0.855987	+	0.516997i	$0.172950\pi$
$492$	−23.3529	−	4.11775i	−1.05283	−	0.185642i
$493$		−	34.9137i		−	1.57243i
$494$	20.4516	−	6.61398i	0.920163	−	0.297577i
$495$	39.4097	−	17.6311i	1.77133	−	0.792457i
$496$	−1.58673	−	0.279783i	−0.0712461	−	0.0125626i
$497$	−0.574161	−	0.481778i	−0.0257546	−	0.0216107i
$498$	26.8827	+	9.78452i	1.20464	+	0.438455i
$499$	19.8646	−	7.23013i	0.889262	−	0.323665i	0.143320	−	0.989676i	$-0.454222\pi$
$499$	19.8646	−	7.23013i	0.889262	−	0.323665i	0.745942	+	0.666011i	$0.232000\pi$
$500$	9.54573	−	8.00982i	0.426898	−	0.358210i
$501$	−7.11258	+	4.10645i	−0.317767	+	0.183463i
$502$	−2.01660	+	3.49285i	−0.0900051	+	0.155893i
$503$	−22.0931	+	3.89562i	−0.985085	+	0.173697i	−0.642912	−	0.765940i	$-0.722274\pi$
$503$	−22.0931	+	3.89562i	−0.985085	+	0.173697i	−0.342173	+	0.939637i	$0.611163\pi$
$504$	−0.958528	+	0.169014i	−0.0426962	+	0.00752850i
$505$	−0.850795	−	0.491207i	−0.0378599	−	0.0218584i
$506$	1.13689	+	0.822891i	0.0505411	+	0.0365819i
$507$	18.6246	+	22.1960i	0.827149	+	0.985758i
$508$	−0.115384	+	0.0419965i	−0.00511935	+	0.00186329i
$509$	11.4258	−	31.3921i	0.506440	−	1.39143i	−0.378446	−	0.925623i	$-0.623541\pi$
$509$	11.4258	−	31.3921i	0.506440	−	1.39143i	0.884886	−	0.465808i	$-0.154236\pi$
$510$	42.1693	+	35.3843i	1.86729	+	1.56684i
$511$	0.115948	−	0.657573i	0.00512923	−	0.0290893i
$512$	−1.00000			−0.0441942
$513$	−4.15543	+	4.60230i	−0.183467	+	0.203196i
$514$		−	21.1026i		−	0.930797i
$515$	24.2271	+	4.27189i	1.06757	+	0.188242i
$516$	18.9527	+	15.9032i	0.834348	+	0.700101i
$517$	−17.7326	+	1.27194i	−0.779878	+	0.0559400i
$518$	2.83958	−	1.03352i	0.124764	−	0.0454104i
$519$	41.3257	+	49.2500i	1.81400	+	2.16184i
$520$	−9.02677	−	15.6348i	−0.395850	−	0.685633i
$521$	−6.29891	−	3.63668i	−0.275960	−	0.159326i	0.355633	−	0.934626i	$-0.384265\pi$
$521$	−6.29891	−	3.63668i	−0.275960	−	0.159326i	−0.631593	+	0.775300i	$0.717599\pi$
$522$	−3.67073	−	20.8178i	−0.160664	−	0.911169i
$523$	−1.06086	−	6.01643i	−0.0463881	−	0.263080i	0.952789	−	0.303632i	$-0.0981994\pi$
$523$	−1.06086	−	6.01643i	−0.0463881	−	0.263080i	−0.999177	+	0.0405521i	$0.987088\pi$
$524$	−0.486550	−	0.280910i	−0.0212550	−	0.0122716i
$525$	2.94500	+	5.10088i	0.128530	+	0.222621i
$526$	−14.1553	−	16.8697i	−0.617202	−	0.735553i
$527$	−8.89122	+	3.23614i	−0.387308	+	0.140968i
$528$	0.607553	+	8.47009i	0.0264404	+	0.368613i
$529$	−17.4819	−	14.6690i	−0.760081	−	0.637783i
$530$	−24.6446	−	4.34550i	−1.07049	−	0.188756i
$531$			43.9946i			1.90920i
$532$	0.0432867	−	1.19243i	0.00187672	−	0.0516983i
$533$	45.6704			1.97820
$534$	−3.70133	+	20.9913i	−0.160172	+	0.908381i
$535$	−47.2524	−	39.6495i	−2.04290	−	1.71420i
$536$	−0.360452	+	0.990333i	−0.0155691	+	0.0427759i
$537$	31.4559	−	11.4490i	1.35742	−	0.494062i
$538$	15.4558	+	18.4195i	0.666345	+	0.794119i
$539$	18.6056	+	13.4668i	0.801398	+	0.580057i
$540$	4.51031	+	2.60403i	0.194093	+	0.112060i
$541$	22.6471	−	3.99330i	0.973676	−	0.171685i	0.335892	−	0.941901i	$-0.390962\pi$
$541$	22.6471	−	3.99330i	0.973676	−	0.171685i	0.637784	+	0.770215i	$0.279851\pi$
$542$	10.4573	−	1.84391i	0.449181	−	0.0792027i
$543$	12.4192	−	21.5107i	0.532960	−	0.923113i
$544$	−5.08576	+	2.93626i	−0.218050	+	0.125891i
$545$	42.8662	−	35.9690i	1.83619	−	1.54074i
$546$	3.24776	−	1.18209i	0.138991	−	0.0505887i
$547$	30.1464	+	10.9724i	1.28897	+	0.469145i	0.893388	−	0.449286i	$-0.148322\pi$
$547$	30.1464	+	10.9724i	1.28897	+	0.469145i	0.395579	+	0.918432i	$0.370544\pi$
$548$	−2.36778	−	1.98681i	−0.101147	−	0.0848721i
$549$	−9.51022	−	1.67691i	−0.405886	−	0.0715687i
$550$	25.4417	−	11.3821i	1.08484	−	0.485334i
$551$	25.8977	+	0.940122i	1.10328	+	0.0400505i
$552$			1.08345i			0.0461145i
$553$	1.22741	+	0.216425i	0.0521947	+	0.00920333i
$554$	13.8081	−	16.4558i	0.586648	−	0.699140i
$555$	−97.2368	−	35.3913i	−4.12747	−	1.50228i
$556$	0.224104	+	0.615722i	0.00950415	+	0.0261124i
$557$	−8.02903	−	9.56862i	−0.340201	−	0.405436i	0.568635	−	0.822590i	$-0.307472\pi$
$557$	−8.02903	−	9.56862i	−0.340201	−	0.405436i	−0.908836	+	0.417155i	$0.863027\pi$
$558$	−4.96128	+	2.86439i	−0.210028	+	0.121259i
$559$	−41.2661	−	23.8250i	−1.74537	−	1.00769i
$560$	−0.986970	+	0.174029i	−0.0417071	+	0.00735408i
$561$	27.9603	+	41.2929i	1.18048	+	1.74339i
$562$	−14.0323	+	24.3047i	−0.591919	+	1.02523i
$563$	8.08017	+	13.9953i	0.340539	+	0.589830i	0.984533	−	0.175200i	$-0.0560573\pi$
$563$	8.08017	+	13.9953i	0.340539	+	0.589830i	−0.643994	+	0.765030i	$0.722724\pi$
$564$	−8.82193	−	10.5136i	−0.371470	−	0.442701i
$565$	−14.7015	−	40.3921i	−0.618498	−	1.69931i
$566$	−3.25087	+	8.93171i	−0.136644	+	0.375428i
$567$	1.23602	−	1.47303i	0.0519080	−	0.0618615i
$568$	−2.69644	−	0.475455i	−0.113140	−	0.0199496i
$569$	3.19198			0.133815			0.0669074	−	0.997759i	$-0.478687\pi$
$569$	3.19198			0.133815			0.0669074	+	0.997759i	$0.478687\pi$
$570$	−27.3823	+	30.3269i	−1.14692	+	1.27025i
$571$		−	31.8000i		−	1.33079i	−0.746492	−	0.665394i	$-0.768263\pi$
$571$		−	31.8000i		−	1.33079i	0.746492	−	0.665394i	$-0.231737\pi$
$572$	−3.98506	−	15.8620i	−0.166624	−	0.663221i
$573$	29.6986	−	35.3934i	1.24068	−	1.47858i
$574$	0.867114	−	2.38238i	0.0361926	−	0.0994385i
$575$	3.34160	−	1.21624i	0.139354	−	0.0507208i
$576$	−2.72374	+	2.28549i	−0.113489	+	0.0952289i
$577$	3.00903	+	5.21178i	0.125267	+	0.216969i	0.921837	−	0.387577i	$-0.126688\pi$
$577$	3.00903	+	5.21178i	0.125267	+	0.216969i	−0.796570	+	0.604546i	$0.793354\pi$
$578$	−8.74329	+	15.1438i	−0.363673	+	0.629900i
$579$	−28.6905	+	5.05890i	−1.19233	+	0.210241i
$580$	−3.77965	−	21.4355i	−0.156942	−	0.890060i
$581$	−1.52930	+	2.64882i	−0.0634460	+	0.109892i
$582$	4.38613	+	7.59701i	0.181811	+	0.314906i
$583$	−20.3936	−	9.90138i	−0.844616	−	0.410073i
$584$	−0.834263	−	2.29212i	−0.0345221	−	0.0948486i
$585$	−60.3199	−	21.9546i	−2.49392	−	0.907713i
$586$	−13.6435	−	11.4483i	−0.563608	−	0.472923i
$587$	−0.927553	+	5.26041i	−0.0382842	+	0.217120i	−0.997948	−	0.0640297i	$-0.979605\pi$
$587$	−0.927553	+	5.26041i	−0.0382842	+	0.217120i	0.959664	+	0.281150i	$0.0907159\pi$
$588$			17.7309i			0.731209i
$589$	−2.16104	−	6.68233i	−0.0890440	−	0.275340i
$590$			45.3000i			1.86497i
$591$	4.33954	−	24.6108i	0.178505	−	1.01235i
$592$	7.09569	−	8.45632i	0.291631	−	0.347552i
$593$	1.30854	−	3.59518i	0.0537352	−	0.147636i	−0.909921	−	0.414781i	$-0.863858\pi$
$593$	1.30854	−	3.59518i	0.0537352	−	0.147636i	0.963656	+	0.267145i	$0.0860803\pi$
$594$	3.28350	+	3.38798i	0.134724	+	0.139011i
$595$	−4.50849	+	3.78308i	−0.184830	+	0.155091i
$596$	−11.4957	+	6.63705i	−0.470883	+	0.271864i
$597$	0.184899	+	0.106752i	0.00756743	+	0.00436906i
$598$	−0.362345	−	2.05496i	−0.0148174	−	0.0840336i
$599$	43.5935	−	7.68672i	1.78118	−	0.314071i	0.816473	−	0.577384i	$-0.195926\pi$
$599$	43.5935	−	7.68672i	1.78118	−	0.314071i	0.964710	+	0.263313i	$0.0848152\pi$
$600$	18.6339	+	10.7583i	0.760727	+	0.439206i
$601$	−21.8213	−	37.7956i	−0.890109	−	1.54171i	−0.839743	−	0.542984i	$-0.817294\pi$
$601$	−21.8213	−	37.7956i	−0.890109	−	1.54171i	−0.0503663	−	0.998731i	$-0.516039\pi$
$602$	−2.02632	+	1.70028i	−0.0825864	+	0.0692983i
$603$	1.28162	+	3.52122i	0.0521916	+	0.143395i
$604$	10.5655	+	3.84551i	0.429902	+	0.156472i
$605$	39.8598	−	5.74780i	1.62053	−	0.233681i
$606$	0.119305	−	0.676613i	0.00484644	−	0.0274855i
$607$	26.4392			1.07313			0.536567	−	0.843858i	$-0.319721\pi$
$607$	26.4392			1.07313			0.536567	+	0.843858i	$0.319721\pi$
$608$	−2.04107	−	3.85150i	−0.0827763	−	0.156199i
$609$	4.16694			0.168853
$610$	−9.79241	−	1.72667i	−0.396483	−	0.0699107i
$611$	20.2486	+	16.9906i	0.819170	+	0.687366i
$612$	−7.14149	+	19.6211i	−0.288678	+	0.793136i
$613$	5.23484	+	14.3826i	0.211433	+	0.580908i	0.999394	−	0.0348178i	$-0.0110851\pi$
$613$	5.23484	+	14.3826i	0.211433	+	0.580908i	−0.787960	+	0.615726i	$0.788863\pi$
$614$	10.4982	−	8.80907i	0.423675	−	0.355505i
$615$	−75.1851	+	43.4081i	−3.03175	+	1.75038i
$616$	−0.903094	−	0.0932818i	−0.0363867	−	0.00375843i
$617$	3.47080	+	19.6839i	0.139729	+	0.792442i	0.971449	+	0.237247i	$0.0762452\pi$
$617$	3.47080	+	19.6839i	0.139729	+	0.792442i	−0.831720	+	0.555195i	$0.812644\pi$
$618$	2.98755	+	16.9432i	0.120177	+	0.681556i
$619$	24.5812	−	42.5758i	0.988000	−	1.71127i	0.360241	−	0.932859i	$-0.382694\pi$
$619$	24.5812	−	42.5758i	0.988000	−	1.71127i	0.627759	−	0.778408i	$-0.283972\pi$
$620$	−5.10849	+	2.94939i	−0.205162	+	0.118450i
$621$	0.386931	+	0.461126i	0.0155270	+	0.0185043i
$622$	−27.7463	+	10.0988i	−1.11253	+	0.404926i
$623$	−2.14145	−	0.779424i	−0.0857954	−	0.0312270i
$624$	8.11567	−	9.67188i	0.324887	−	0.387185i
$625$	0.625652	−	3.54825i	0.0250261	−	0.141930i
$626$	9.96167			0.398148
$627$	−31.3825	+	19.6280i	−1.25330	+	0.783868i
$628$	−2.99173			−0.119383
$629$	11.2570	−	63.8416i	0.448846	−	2.54553i
$630$	−2.29051	+	2.72972i	−0.0912561	+	0.108755i
$631$	6.50770	+	2.36861i	0.259067	+	0.0942928i	0.468289	−	0.883575i	$-0.344871\pi$
$631$	6.50770	+	2.36861i	0.259067	+	0.0942928i	−0.209221	+	0.977868i	$0.567093\pi$
$632$	4.27841	−	1.55721i	0.170186	−	0.0619426i
$633$	−29.6705	−	35.3600i	−1.17930	−	1.40543i
$634$	20.7611	−	11.9864i	0.824527	−	0.476041i
$635$	−0.224772	+	0.389317i	−0.00891981	+	0.0154496i
$636$	−3.03903	−	17.2352i	−0.120505	−	0.683419i
$637$	−5.92987	−	33.6300i	−0.234950	−	1.33247i
$638$	2.02594	−	19.6138i	0.0802076	−	0.776518i
$639$	−8.43105	+	4.86767i	−0.333527	+	0.192562i
$640$	−2.80456	+	2.35331i	−0.110860	+	0.0930227i
$641$	−8.18749	−	22.4949i	−0.323386	−	0.888497i	−0.989742	−	0.142863i	$-0.954369\pi$
$641$	−8.18749	−	22.4949i	−0.323386	−	0.888497i	0.666356	−	0.745634i	$-0.267853\pi$
$642$	14.7542	−	40.5369i	0.582303	−	1.59986i
$643$	14.5196	+	12.1834i	0.572598	+	0.480467i	0.882507	−	0.470299i	$-0.155854\pi$
$643$	14.5196	+	12.1834i	0.572598	+	0.480467i	−0.309909	+	0.950766i	$0.600299\pi$
$644$	−0.114076	−	0.0201146i	−0.00449522	−	0.000792628i
$645$	90.5794			3.56656
$646$	−21.6894	−	13.5947i	−0.853358	−	0.534875i
$647$	−32.2823			−1.26915			−0.634574	−	0.772862i	$-0.718824\pi$
$647$	−32.2823			−1.26915			−0.634574	+	0.772862i	$0.718824\pi$
$648$	1.21980	−	6.91781i	0.0479181	−	0.271757i
$649$	−11.2408	+	39.4682i	−0.441239	+	1.54926i
$650$	−38.9408	−	14.1733i	−1.52738	−	0.555922i
$651$	−0.386233	−	1.06117i	−0.0151377	−	0.0415904i
$652$	0.653774	−	0.548581i	0.0256037	−	0.0214841i
$653$	25.2798	+	43.7858i	0.989273	+	1.71347i	0.621142	+	0.783698i	$0.286669\pi$
$653$	25.2798	+	43.7858i	0.989273	+	1.71347i	0.368132	+	0.929774i	$0.379997\pi$
$654$	33.8911	+	19.5671i	1.32525	+	0.765132i
$655$	−2.02563	+	0.357173i	−0.0791479	+	0.0139559i
$656$	−1.60825	−	9.12084i	−0.0627916	−	0.356109i
$657$	−7.51094	−	4.33644i	−0.293030	−	0.169181i
$658$	1.27075	−	0.733670i	0.0495391	−	0.0286014i
$659$	−15.2502	+	12.7964i	−0.594062	+	0.498477i	−0.889531	−	0.456875i	$-0.848969\pi$
$659$	−15.2502	+	12.7964i	−0.594062	+	0.498477i	0.295469	+	0.955352i	$0.404524\pi$
$660$	21.6367	+	22.3252i	0.842206	+	0.869005i
$661$	−7.40288	+	20.3392i	−0.287939	+	0.791105i	0.708416	+	0.705795i	$0.249410\pi$
$661$	−7.40288	+	20.3392i	−0.287939	+	0.791105i	−0.996354	+	0.0853096i	$0.972812\pi$
$662$	−7.09807	+	8.45915i	−0.275874	+	0.328774i
$663$	12.8752	−	73.0186i	0.500030	−	2.83581i
$664$			11.1733i			0.433608i
$665$	−2.68475	−	3.44610i	−0.104110	−	0.133634i
$666$		−	39.2500i		−	1.52091i
$667$	0.436859	−	2.47755i	0.0169153	−	0.0959312i
$668$	−2.45722	−	2.06185i	−0.0950728	−	0.0797755i
$669$	8.39941	+	3.05714i	0.324740	+	0.118196i
$670$	1.31965	+	3.62571i	0.0509825	+	0.140073i
$671$	−8.10331	−	3.93427i	−0.312825	−	0.151881i
$672$	−0.350443	−	0.606985i	−0.0135186	−	0.0234149i
$673$	−4.82206	+	8.35206i	−0.185877	+	0.321948i	−0.943872	−	0.330312i	$-0.892846\pi$
$673$	−4.82206	+	8.35206i	−0.185877	+	0.321948i	0.757995	+	0.652261i	$0.226179\pi$
$674$	−1.40415	−	7.96333i	−0.0540858	−	0.306736i
$675$	11.7729	−	2.07588i	0.453139	−	0.0799007i
$676$	−5.65828	+	9.80043i	−0.217626	+	0.376940i
$677$	14.6422	+	25.3611i	0.562746	+	0.974705i	0.997255	+	0.0740380i	$0.0235886\pi$
$677$	14.6422	+	25.3611i	0.562746	+	0.974705i	−0.434509	+	0.900668i	$0.643078\pi$
$678$	23.0282	−	19.3229i	0.884391	−	0.742092i
$679$	−0.881318	+	0.320774i	−0.0338219	+	0.0123102i
$680$	−7.35340	+	20.2033i	−0.281990	+	0.774761i
$681$	−31.7233	+	37.8063i	−1.21564	+	1.44874i
$682$	−5.18270	+	1.30207i	−0.198456	+	0.0498588i
$683$		−	33.9838i		−	1.30035i	−0.759783	−	0.650176i	$-0.774695\pi$
$683$		−	33.9838i		−	1.30035i	0.759783	−	0.650176i	$-0.225305\pi$
$684$	−14.3619	−	5.82564i	−0.549142	−	0.222749i
$685$	−11.3162			−0.432368
$686$	−3.75396	−	0.661924i	−0.143327	−	0.0252724i
$687$	−28.1100	+	33.5002i	−1.07246	+	1.27811i
$688$	−3.30494	+	9.08025i	−0.126000	+	0.346181i
$689$	11.5282	+	31.6734i	0.439189	+	1.20666i
$690$	2.54968	+	3.03859i	0.0970647	+	0.115677i
$691$	−23.5710	−	40.8261i	−0.896681	−	1.55310i	−0.831710	−	0.555211i	$-0.812638\pi$
$691$	−23.5710	−	40.8261i	−0.896681	−	1.55310i	−0.0649717	−	0.997887i	$-0.520696\pi$
$692$	−12.5550	+	21.7459i	−0.477269	+	0.826654i
$693$	−2.67299	+	1.80994i	−0.101539	+	0.0687539i
$694$	2.26571	−	0.399506i	0.0860052	−	0.0151650i
$695$	2.07750	+	1.19944i	0.0788040	+	0.0454975i
$696$	13.1828	−	7.61108i	0.499692	−	0.288497i
$697$	−34.9604	−	41.6642i	−1.32422	−	1.57814i
$698$	−7.23487	−	19.8777i	−0.273844	−	0.752380i
$699$	18.0221	+	6.55953i	0.681660	+	0.248104i
$700$	−1.47869	+	1.76223i	−0.0558891	+	0.0666060i
$701$	−25.3475	−	4.46946i	−0.957364	−	0.168809i	−0.326927	−	0.945050i	$-0.606013\pi$
$701$	−25.3475	−	4.46946i	−0.957364	−	0.168809i	−0.630437	+	0.776241i	$0.717124\pi$
$702$		−	7.01480i		−	0.264757i
$703$	47.0523	+	10.0691i	1.77461	+	0.379763i
$704$	−3.02746	+	1.35442i	−0.114102	+	0.0510468i
$705$	−49.4833	−	8.72524i	−1.86365	−	0.328612i
$706$	−1.05199	−	0.882721i	−0.0395920	−	0.0332216i
$707$	0.0690255	+	0.0251232i	0.00259597	+	0.000944857i
$708$	−29.7700	+	10.8354i	−1.11882	+	0.407219i
$709$	−8.68909	+	7.29101i	−0.326326	+	0.273820i	−0.791201	−	0.611557i	$-0.790544\pi$
$709$	−8.68909	+	7.29101i	−0.326326	+	0.273820i	0.464875	+	0.885376i	$0.346099\pi$
$710$	−8.68122	+	5.01210i	−0.325800	+	0.188101i
$711$	8.09429	−	14.0197i	0.303560	−	0.525781i
$712$	−8.19847	+	1.44561i	−0.307251	+	0.0541766i
$713$	−0.671433	+	0.118392i	−0.0251454	+	0.00443381i
$714$	−3.56453	−	2.05798i	−0.133399	−	0.0770181i
$715$	−48.5044	−	35.1078i	−1.81396	−	1.31296i
$716$	8.40385	+	10.0153i	0.314067	+	0.374290i
$717$	40.2925	−	14.6653i	1.50475	−	0.547684i
$718$	6.92674	−	19.0311i	0.258504	−	0.710233i
$719$	−10.6803	−	8.96185i	−0.398309	−	0.334221i	0.421531	−	0.906814i	$-0.361493\pi$
$719$	−10.6803	−	8.96185i	−0.398309	−	0.334221i	−0.819839	+	0.572593i	$0.805937\pi$
$720$	−2.26044	+	12.8196i	−0.0842418	+	0.477759i
$721$	−1.83941			−0.0685033
$722$	10.6681	−	15.7224i	0.397024	−	0.585125i
$723$			18.4517i			0.686225i
$724$	9.55366	+	1.68457i	0.355059	+	0.0626064i
$725$	−38.2729	−	32.1148i	−1.42142	−	1.19271i
$726$	13.3114	+	24.8200i	0.494034	+	0.921157i
$727$	−34.0014	+	12.3755i	−1.26104	+	0.458982i	−0.884119	−	0.467262i	$-0.845241\pi$
$727$	−34.0014	+	12.3755i	−1.26104	+	0.458982i	−0.376924	+	0.926244i	$0.623018\pi$
$728$	0.867680	+	1.03406i	0.0321584	+	0.0383248i
$729$	−17.9516	−	31.0930i	−0.664873	−	1.15159i
$730$	−7.73381	−	4.46512i	−0.286241	−	0.165261i
$731$	9.85388	+	55.8841i	0.364459	+	2.06695i
$732$	−1.20754	−	6.84832i	−0.0446321	−	0.253121i
$733$	5.27004	+	3.04266i	0.194653	+	0.112383i	0.594159	−	0.804348i	$-0.297485\pi$
$733$	5.27004	+	3.04266i	0.194653	+	0.112383i	−0.399506	+	0.916731i	$0.630818\pi$
$734$	6.99507	+	12.1158i	0.258193	+	0.447203i
$735$	41.7262	+	49.7274i	1.53909	+	1.83422i
$736$	−0.397637	+	0.144728i	−0.0146571	+	0.00533475i
$737$	0.250077	+	3.48640i	0.00921170	+	0.128423i
$738$	−25.2261	−	21.1672i	−0.928585	−	0.779175i
$739$	48.3218	+	8.52044i	1.77755	+	0.313430i	0.963568	−	0.267464i	$-0.0861858\pi$
$739$	48.3218	+	8.52044i	1.77755	+	0.313430i	0.813979	+	0.580894i	$0.197297\pi$
$740$		−	40.4146i		−	1.48567i
$741$	53.8159	+	11.5165i	1.97698	+	0.423069i
$742$	1.87111			0.0686906
$743$	3.30348	−	18.7350i	0.121193	−	0.687320i	−0.862303	−	0.506392i	$-0.830979\pi$
$743$	3.30348	−	18.7350i	0.121193	−	0.687320i	0.983496	−	0.180928i	$-0.0579100\pi$
$744$	−3.16017	−	2.65170i	−0.115857	−	0.0972159i
$745$	−16.6214	+	45.6670i	−0.608962	+	1.67311i
$746$	6.61140	−	2.40635i	0.242061	−	0.0881028i
$747$	25.5365	+	30.4332i	0.934332	+	1.11349i
$748$	−11.4200	+	15.7777i	−0.417557	+	0.576890i
$749$	3.99421	+	2.30606i	0.145945	+	0.0842614i
$750$	31.4205	−	5.54028i	1.14731	−	0.202302i
$751$	41.6647	−	7.34661i	1.52037	−	0.268082i	0.649790	−	0.760114i	$-0.274857\pi$
$751$	41.6647	−	7.34661i	1.52037	−	0.268082i	0.870577	+	0.492032i	$0.163746\pi$
$752$	2.68015	−	4.64216i	0.0977352	−	0.169282i
$753$	−8.94305	+	5.16327i	−0.325903	+	0.188160i
$754$	−22.4582	+	18.8447i	−0.817880	+	0.686283i
$755$	38.6812	−	14.0788i	1.40775	−	0.512380i
$756$	−0.365924	−	0.133186i	−0.0133085	−	0.00484391i
$757$	25.8360	+	21.6790i	0.939026	+	0.787937i	0.977416	−	0.211326i	$-0.0677782\pi$
$757$	25.8360	+	21.6790i	0.939026	+	0.787937i	−0.0383893	+	0.999263i	$0.512223\pi$
$758$	−13.2060	−	2.32857i	−0.479663	−	0.0845775i
$759$	1.46745	+	3.28009i	0.0532649	+	0.119060i
$760$	−14.7881	−	5.99850i	−0.536420	−	0.217589i
$761$			38.7722i			1.40549i	0.711442	+	0.702745i	$0.248042\pi$
$761$			38.7722i			1.40549i	−0.711442	+	0.702745i	$0.751958\pi$
$762$	−0.309613	−	0.0545930i	−0.0112161	−	0.00197770i
$763$	−2.68942	+	3.20512i	−0.0973634	+	0.116033i
$764$	16.9570	+	6.17184i	0.613482	+	0.223289i
$765$	26.1457	+	71.8348i	0.945300	+	2.59719i
$766$	−2.99121	−	3.56479i	−0.108077	−	0.128801i
$767$	52.8407	−	30.5076i	1.90797	−	1.10157i
$768$	−2.21736	−	1.28019i	−0.0800122	−	0.0461951i
$769$	8.61018	−	1.51821i	0.310491	−	0.0547480i	−0.0162314	−	0.999868i	$-0.505167\pi$
$769$	8.61018	−	1.51821i	0.310491	−	0.0547480i	0.326723	+	0.945120i	$0.394056\pi$
$770$	−2.75230	+	1.86364i	−0.0991862	+	0.0671611i
$771$	27.0155	−	46.7922i	0.972938	−	1.68518i
$772$	−5.68918	−	9.85396i	−0.204758	−	0.354652i
$773$	5.41312	+	6.45111i	0.194697	+	0.232030i	0.854557	−	0.519358i	$-0.173829\pi$
$773$	5.41312	+	6.45111i	0.194697	+	0.232030i	−0.659860	+	0.751388i	$0.729384\pi$
$774$	11.7510	+	32.2857i	0.422382	+	1.16049i
$775$	−4.63095	+	12.7234i	−0.166348	+	0.457039i
$776$	−2.20228	+	2.62458i	−0.0790574	+	0.0942169i
$777$	7.61949	+	1.34352i	0.273348	+	0.0481985i
$778$	−2.14879			−0.0770377
$779$	31.8464	−	24.8105i	1.14101	−	0.888927i
$780$		−	46.2241i		−	1.65509i
$781$	−8.80733	+	2.21270i	−0.315151	+	0.0791766i
$782$	−1.59733	+	1.90362i	−0.0571203	+	0.0680733i
$783$	2.89259	−	7.94732i	0.103373	−	0.284014i
$784$	−6.50743	+	2.36851i	−0.232408	+	0.0845897i
$785$	−8.39049	+	7.04046i	−0.299469	+	0.251285i
$786$	−0.719239	−	1.24576i	−0.0256544	−	0.0444347i
$787$	−24.3600	+	42.1927i	−0.868339	+	1.50401i	−0.00464555	+	0.999989i	$0.501479\pi$
$787$	−24.3600	+	42.1927i	−0.868339	+	1.50401i	−0.863693	+	0.504018i	$0.831855\pi$
$788$	9.61212	−	1.69488i	0.342418	−	0.0603775i
$789$	−9.79105	−	55.5278i	−0.348571	−	1.97684i
$790$	8.33447	−	14.4357i	0.296527	−	0.513600i
$791$	1.60698	+	2.78337i	0.0571376	+	0.0989652i
$792$	−5.15051	+	10.6084i	−0.183015	+	0.376951i
$793$	4.58067	+	12.5853i	0.162665	+	0.446917i
$794$	−19.8022	−	7.20742i	−0.702754	−	0.255782i
$795$	−49.0828	−	41.1854i	−1.74079	−	1.46069i
$796$	−0.0144800	+	0.0821203i	−0.000513231	+	0.00291068i
$797$			9.32254i			0.330221i	0.986275	+	0.165111i	$0.0527981\pi$
$797$			9.32254i			0.330221i	−0.986275	+	0.165111i	$0.947202\pi$
$798$	1.62252	−	2.58863i	0.0574366	−	0.0916364i
$799$		−	31.4786i		−	1.11363i
$800$	−1.45928	+	8.27597i	−0.0515932	+	0.292600i
$801$	−19.0266	+	22.6750i	−0.672272	+	0.801182i
$802$	0.914962	−	2.51384i	0.0323084	−	0.0887667i
$803$	−5.63020	−	5.80936i	−0.198686	−	0.205008i
$804$	−2.06707	+	1.73448i	−0.0729000	+	0.0611703i
$805$	−0.367269	+	0.212043i	−0.0129445	+	0.00747353i
$806$	6.88069	+	3.97257i	0.242362	+	0.139928i
$807$	10.6905	+	60.6290i	0.376324	+	2.13424i
$808$	0.264262	−	0.0465965i	0.00929670	−	0.00163926i
$809$	22.7913	+	13.1586i	0.801301	+	0.462631i	0.843926	−	0.536460i	$-0.180239\pi$
$809$	22.7913	+	13.1586i	0.801301	+	0.462631i	−0.0426251	+	0.999091i	$0.513572\pi$
$810$	−12.8587	−	22.2720i	−0.451810	−	0.782558i
$811$	−12.8334	+	10.7685i	−0.450641	+	0.378133i	−0.839674	−	0.543091i	$-0.817254\pi$
$811$	−12.8334	+	10.7685i	−0.450641	+	0.378133i	0.389033	+	0.921224i	$0.372809\pi$
$812$	0.556625	+	1.52932i	0.0195337	+	0.0536684i
$813$	25.5483	+	9.29881i	0.896017	+	0.326123i
$814$	10.0285	−	35.2118i	0.351499	−	1.23417i
$815$	0.542569	−	3.07706i	0.0190054	−	0.107785i
$816$	−15.0360			−0.526364
$817$	−41.7182	+	5.80446i	−1.45953	+	0.203072i
$818$	33.6227			1.17559
$819$	4.72668	+	0.833440i	0.165163	+	0.0291228i
$820$	−25.9746	−	21.7953i	−0.907072	−	0.761124i
$821$	−17.3966	+	47.7967i	−0.607144	+	1.66811i	0.129291	+	0.991607i	$0.458730\pi$
$821$	−17.3966	+	47.7967i	−0.607144	+	1.66811i	−0.736435	+	0.676508i	$0.763492\pi$
$822$	−2.70673	−	7.43669i	−0.0944082	−	0.259384i
$823$	−23.2223	+	19.4859i	−0.809480	+	0.679234i	−0.950484	−	0.310775i	$-0.899411\pi$
$823$	−23.2223	+	19.4859i	−0.809480	+	0.679234i	0.141004	+	0.990009i	$0.454967\pi$
$824$	−5.81928	+	3.35976i	−0.202724	+	0.117043i
$825$	70.9848	+	7.33212i	2.47137	+	0.255272i
$826$	−0.588163	−	3.33564i	−0.0204648	−	0.116062i
$827$	−4.08309	−	23.1564i	−0.141983	−	0.805226i	−0.969740	−	0.244139i	$-0.921495\pi$
$827$	−4.08309	−	23.1564i	−0.141983	−	0.805226i	0.827757	−	0.561086i	$-0.189616\pi$
$828$	−0.752287	+	1.30300i	−0.0261438	+	0.0452823i
$829$	40.8005	−	23.5562i	1.41706	−	0.818140i	0.421020	−	0.907051i	$-0.361672\pi$
$829$	40.8005	−	23.5562i	1.41706	−	0.818140i	0.996040	+	0.0889114i	$0.0283388\pi$
$830$	26.2942	+	31.3362i	0.912686	+	1.08770i
$831$	51.6841	−	18.8115i	1.79290	−	0.652563i
$832$	4.63380	+	1.68656i	0.160648	+	0.0584711i
$833$	−26.1407	+	31.1532i	−0.905720	+	1.07940i
$834$	−0.291323	+	1.65218i	−0.0100877	+	0.0572102i
$835$	−11.7436			−0.406405
$836$	−11.3958	−	8.89579i	−0.394133	−	0.307667i
$837$	−2.29200			−0.0792232
$838$	4.33141	−	24.5647i	0.149626	−	0.848572i
$839$	1.13985	−	1.35842i	0.0393519	−	0.0468978i	−0.746009	−	0.665935i	$-0.768033\pi$
$839$	1.13985	−	1.35842i	0.0393519	−	0.0468978i	0.785361	+	0.619037i	$0.212477\pi$
$840$	−2.41126	−	0.877627i	−0.0831964	−	0.0302810i
$841$	−5.96330	+	2.17046i	−0.205631	+	0.0748436i
$842$	−24.9895	−	29.7813i	−0.861194	−	1.02633i
$843$	−62.2296	+	35.9283i	−2.14330	+	1.23744i
$844$	9.01409	−	15.6129i	0.310278	−	0.537417i
$845$	7.19442	+	40.8016i	0.247496	+	1.40362i
$846$	−3.30958	−	18.7695i	−0.113786	−	0.645310i
$847$	−2.86043	+	0.940765i	−0.0982854	+	0.0323251i
$848$	5.91955	−	3.41765i	0.203278	−	0.117363i
$849$	−18.6427	+	15.6431i	−0.639815	+	0.536869i
$850$	16.8789	+	46.3744i	0.578942	+	1.59063i
$851$	1.59764	−	4.38949i	0.0547665	−	0.150470i
$852$	−5.37030	−	4.50622i	−0.183984	−	0.154381i
$853$	22.4033	+	3.95031i	0.767074	+	0.135256i	0.543475	−	0.839425i	$-0.317108\pi$
$853$	22.4033	+	3.95031i	0.767074	+	0.135256i	0.223599	+	0.974681i	$0.428219\pi$
$854$	0.743477			0.0254413
$855$	−53.9885	+	17.4597i	−1.84637	+	0.597107i
$856$	16.8484			0.575867
$857$	−4.23257	+	24.0041i	−0.144582	+	0.819965i	0.823120	+	0.567868i	$0.192231\pi$
$857$	−4.23257	+	24.0041i	−0.144582	+	0.819965i	−0.967702	+	0.252097i	$0.918880\pi$
$858$	11.4701	−	40.2733i	0.391582	−	1.37491i
$859$	−38.9837	−	14.1889i	−1.33011	−	0.484120i	−0.423424	−	0.905932i	$-0.639172\pi$
$859$	−38.9837	−	14.1889i	−1.33011	−	0.484120i	−0.906683	+	0.421812i	$0.861394\pi$
$860$	12.0997	+	33.2437i	0.412597	+	1.13360i
$861$	4.97261	−	4.17252i	0.169466	−	0.142199i
$862$	−7.35458	−	12.7385i	−0.250498	−	0.433875i
$863$	−9.59165	−	5.53774i	−0.326504	−	0.188507i	0.327784	−	0.944753i	$-0.393698\pi$
$863$	−9.59165	−	5.53774i	−0.326504	−	0.188507i	−0.654288	+	0.756246i	$0.727031\pi$
$864$	−1.40093	+	0.247021i	−0.0476605	+	0.00840384i
$865$	15.9635	+	90.5335i	0.542775	+	3.07823i
$866$	−12.1617	−	7.02159i	−0.413273	−	0.238603i
$867$	−38.7741	+	22.3862i	−1.31684	+	0.760276i
$868$	0.337867	−	0.283504i	0.0114679	−	0.00962275i
$869$	10.8436	−	10.5092i	0.367844	−	0.356500i
$870$	19.0607	−	52.3689i	0.646219	−	1.77547i
$871$	3.34052	−	3.98108i	0.113189	−	0.134894i
$872$	−2.65411	+	15.0522i	−0.0898797	+	0.509733i
$873$			12.1820i			0.412298i
$874$	−1.36903	−	1.23610i	−0.0463080	−	0.0418116i
$875$			3.41111i			0.115317i
$876$	1.08450	−	6.15048i	0.0366417	−	0.207805i
$877$	6.02211	+	5.05315i	0.203352	+	0.170633i	0.738777	−	0.673950i	$-0.235404\pi$
$877$	6.02211	+	5.05315i	0.203352	+	0.170633i	−0.535424	+	0.844583i	$0.679848\pi$
$878$	−17.7994	−	6.47845i	−0.600701	−	0.218637i
$879$	−15.5966	−	42.8513i	−0.526060	−	1.44534i
$880$	−5.30334	+	10.9231i	−0.178775	+	0.368219i
$881$	−19.8951	−	34.4593i	−0.670282	−	1.16096i	−0.977824	−	0.209429i	$-0.932840\pi$
$881$	−19.8951	−	34.4593i	−0.670282	−	1.16096i	0.307542	−	0.951535i	$-0.400494\pi$
$882$	−12.3114	+	21.3239i	−0.414545	+	0.718013i
$883$	2.08153	+	11.8049i	0.0700490	+	0.397267i	0.999592	+	0.0285544i	$0.00909039\pi$
$883$	2.08153	+	11.8049i	0.0700490	+	0.397267i	−0.929543	+	0.368713i	$0.879799\pi$
$884$	28.5186	−	5.02859i	0.959183	−	0.169130i
$885$	−57.9928	+	100.447i	−1.94941	+	3.37647i
$886$	−11.6522	−	20.1822i	−0.391464	−	0.678035i
$887$	−2.70931	+	2.27338i	−0.0909698	+	0.0763327i	−0.687138	−	0.726527i	$-0.741133\pi$
$887$	−2.70931	+	2.27338i	−0.0909698	+	0.0763327i	0.596169	+	0.802859i	$0.296689\pi$
$888$	26.5594	−	9.66685i	0.891277	−	0.324398i
$889$	0.0114962	−	0.0315855i	0.000385570	−	0.00105934i
$890$	−19.5912	+	23.3478i	−0.656697	+	0.782621i
$891$	−5.67676	−	22.5955i	−0.190179	−	0.756979i
$892$			3.49106i			0.116889i
$893$	23.3497	+	0.847625i	0.781367	+	0.0283647i
$894$	−33.9869			−1.13669
$895$	47.1383	+	8.31175i	1.57566	+	0.277831i
$896$	0.175958	−	0.209698i	0.00587834	−	0.00700553i
$897$	1.82730	−	5.02047i	0.0610118	−	0.167628i
$898$	−3.19359	−	8.77430i	−0.106571	−	0.292802i
$899$	6.15727	+	7.33795i	0.205356	+	0.244734i
$900$	14.9400	+	25.8768i	0.497999	+	0.862560i
$901$	20.0703	−	34.7627i	0.668638	−	1.15811i
$902$	−17.2224	−	25.4348i	−0.573444	−	0.846885i
$903$	−6.66977	+	1.17606i	−0.221956	+	0.0391368i
$904$	10.1679	+	5.87042i	0.338178	+	0.195247i
$905$	30.7581	−	17.7582i	1.02244	−	0.590303i
$906$	18.5044	+	22.0527i	0.614769	+	0.732653i
$907$	10.1349	+	27.8454i	0.336524	+	0.924591i	0.986372	+	0.164527i	$0.0526099\pi$
$907$	10.1349	+	27.8454i	0.336524	+	0.924591i	−0.649849	+	0.760063i	$0.725168\pi$
$908$	−18.1130	−	6.59259i	−0.601100	−	0.218783i
$909$	0.613286	−	0.730885i	0.0203414	−	0.0242419i
$910$	4.86693	+	0.858171i	0.161337	+	0.0284481i
$911$			22.4146i			0.742629i	0.928507	+	0.371315i	$0.121093\pi$
$911$			22.4146i			0.742629i	−0.928507	+	0.371315i	$0.878907\pi$
$912$	0.404874	−	11.1531i	0.0134067	−	0.369317i
$913$	15.1334	+	33.8268i	0.500842	+	1.11950i
$914$	22.6451	+	3.99294i	0.749034	+	0.132075i
$915$	−19.5029	−	16.3648i	−0.644744	−	0.541005i
$916$	−16.0499	−	5.84169i	−0.530304	−	0.193015i
$917$	0.144519	−	0.0526005i	0.00477243	−	0.00173702i
$918$	−6.39946	+	5.36979i	−0.211214	+	0.177229i
$919$	27.5401	−	15.9003i	0.908464	−	0.524502i	0.0285270	−	0.999593i	$-0.490918\pi$
$919$	27.5401	−	15.9003i	0.908464	−	0.524502i	0.879936	+	0.475091i	$0.157585\pi$
$920$	−0.774609	+	1.34166i	−0.0255381	+	0.0442333i
$921$	34.5557	−	6.09311i	1.13865	−	0.200775i
$922$	−4.47626	+	0.789285i	−0.147418	+	0.0259937i
$923$	11.6929	+	6.75087i	0.384875	+	0.222208i
$924$	−1.88307	−	1.36298i	−0.0619484	−	0.0448386i
$925$	−59.6296	−	71.0638i	−1.96061	−	2.33656i
$926$	5.79581	−	2.10950i	0.190462	−	0.0693225i
$927$	−8.17151	+	22.4510i	−0.268388	+	0.737389i
$928$	4.55433	+	3.82153i	0.149503	+	0.125448i
$929$	−6.53858	+	37.0821i	−0.214524	+	1.21662i	0.667207	+	0.744872i	$0.267490\pi$
$929$	−6.53858	+	37.0821i	−0.214524	+	1.21662i	−0.881731	+	0.471753i	$0.843622\pi$
$930$	−15.1032			−0.495252
$931$	−22.4044	−	20.2291i	−0.734276	−	0.662981i
$932$			7.49057i			0.245362i
$933$	−74.4521	−	13.1279i	−2.43745	−	0.429789i
$934$	30.6542	+	25.7220i	1.00304	+	0.841648i
$935$	5.10170	+	71.1244i	0.166843	+	2.32602i
$936$	16.4759	−	5.99674i	0.538532	−	0.196009i
$937$	−3.92148	−	4.67344i	−0.128109	−	0.152675i	0.698177	−	0.715925i	$-0.253995\pi$
$937$	−3.92148	−	4.67344i	−0.128109	−	0.152675i	−0.826286	+	0.563251i	$0.809551\pi$
$938$	−0.144247	−	0.249843i	−0.00470983	−	0.00815766i
$939$	22.0886	+	12.7529i	0.720835	+	0.416174i
$940$	−3.40778	−	19.3265i	−0.111150	−	0.630360i
$941$	−5.75552	−	32.6412i	−0.187625	−	1.06407i	−0.922537	−	0.385909i	$-0.873888\pi$
$941$	−5.75552	−	32.6412i	−0.187625	−	1.06407i	0.734912	−	0.678162i	$-0.237223\pi$
$942$	−6.63374	−	3.82999i	−0.216139	−	0.124788i
$943$	−1.95954	−	3.39403i	−0.0638115	−	0.110525i
$944$	−7.95343	−	9.47853i	−0.258862	−	0.308500i
$945$	−1.33968	+	0.487605i	−0.0435800	+	0.0158618i
$946$	2.29293	+	31.9664i	0.0745495	+	1.03932i
$947$	26.5685	+	22.2936i	0.863361	+	0.724446i	0.962689	−	0.270609i	$-0.0872250\pi$
$947$	26.5685	+	22.2936i	0.863361	+	0.724446i	−0.0993284	+	0.995055i	$0.531669\pi$
$948$	11.4803	+	2.02429i	0.372863	+	0.0657459i
$949$			12.0283i			0.390454i
$950$	−34.8534	+	11.2714i	−1.13079	+	0.365694i
$951$	61.3798			1.99037
$952$	0.279149	−	1.58313i	0.00904728	−	0.0513096i
$953$	15.5245	+	13.0266i	0.502886	+	0.421972i	0.858618	−	0.512616i	$-0.171324\pi$
$953$	15.5245	+	13.0266i	0.502886	+	0.421972i	−0.355731	+	0.934588i	$0.615768\pi$
$954$	8.31232	−	22.8379i	0.269121	−	0.739404i
$955$	62.0812	−	22.5957i	2.00890	−	0.731180i
$956$	10.7646	+	12.8288i	0.348153	+	0.414913i
$957$	29.6017	−	40.8973i	0.956888	−	1.32202i
$958$	−26.6326	−	15.3763i	−0.860459	−	0.496786i
$959$	0.833259	−	0.146926i	0.0269074	−	0.00474449i
$960$	−9.23143	+	1.62775i	−0.297943	+	0.0525354i
$961$	−14.2020	+	24.5986i	−0.458129	+	0.793503i
$962$	−47.1421	+	27.2175i	−1.51992	+	0.877527i
$963$	45.8907	−	38.5069i	1.47881	−	1.24087i
$964$	−6.77198	+	2.46480i	−0.218111	+	0.0793858i
$965$	−39.1451	−	14.2476i	−1.26012	−	0.458648i
$966$	−0.227197	−	0.190641i	−0.00730994	−	0.00613376i
$967$	1.43104	+	0.252332i	0.0460193	+	0.00811444i	0.196610	−	0.980482i	$-0.437007\pi$
$967$	1.43104	+	0.252332i	0.0460193	+	0.00811444i	−0.150591	+	0.988596i	$0.548118\pi$
$968$	−7.33107	+	8.20094i	−0.235629	+	0.263588i
$969$	−30.6895	−	57.9110i	−0.985887	−	1.86037i
$970$			12.5435i			0.402746i
$971$	−19.7620	−	3.48457i	−0.634192	−	0.111825i	−0.152696	−	0.988273i	$-0.548795\pi$
$971$	−19.7620	−	3.48457i	−0.634192	−	0.111825i	−0.481496	+	0.876448i	$0.659907\pi$
$972$	14.3040	−	17.0469i	0.458803	−	0.546780i
$973$	−0.168549	−	0.0613467i	−0.00540343	−	0.00196669i
$974$	−4.79788	−	13.1821i	−0.153734	−	0.422381i
$975$	−68.2012	−	81.2791i	−2.18419	−	2.60301i
$976$	2.35211	−	1.35799i	0.0752891	−	0.0434682i
$977$	−0.109546	−	0.0632462i	−0.00350468	−	0.00202343i	0.498247	−	0.867035i	$-0.333977\pi$
$977$	−0.109546	−	0.0632462i	−0.00350468	−	0.00202343i	−0.501751	+	0.865012i	$0.667311\pi$
$978$	2.15194	−	0.379446i	0.0688116	−	0.0121333i
$979$	−22.8626	+	15.4807i	−0.730691	+	0.494767i
$980$	−12.6767	+	21.9566i	−0.404941	+	0.701379i
$981$	27.1726	+	47.0644i	0.867555	+	1.50265i
$982$	4.39189	+	5.23405i	0.140151	+	0.167025i
$983$	−10.9350	−	30.0437i	−0.348773	−	0.958247i	−0.982757	−	0.184900i	$-0.940804\pi$
$983$	−10.9350	−	30.0437i	−0.348773	−	0.958247i	0.633984	−	0.773346i	$-0.281419\pi$
$984$	8.11038	−	22.2831i	0.258550	−	0.710359i
$985$	22.9692	−	27.3737i	0.731861	−	0.872198i
$986$	34.3832	+	6.06269i	1.09499	+	0.193075i
$987$	3.75696			0.119585
$988$	2.96211	+	21.2894i	0.0942372	+	0.677308i
$989$			4.08896i			0.130021i
$990$	10.5198	+	41.8725i	0.334341	+	1.33080i
$991$	−13.3223	+	15.8770i	−0.423198	+	0.504348i	−0.934947	−	0.354787i	$-0.884553\pi$
$991$	−13.3223	+	15.8770i	−0.423198	+	0.504348i	0.511749	+	0.859135i	$0.328998\pi$
$992$	0.551064	−	1.51404i	0.0174963	−	0.0480707i
$993$	−26.5684	+	9.67009i	−0.843121	+	0.306871i
$994$	0.574161	−	0.481778i	0.0182113	−	0.0152811i
$995$	0.152644	+	0.264388i	0.00483915	+	0.00838165i
$996$	−14.3040	+	24.7753i	−0.453240	+	0.785034i
$997$	−27.1211	+	4.78219i	−0.858935	+	0.151453i	−0.585734	−	0.810503i	$-0.699194\pi$
$997$	−27.1211	+	4.78219i	−0.858935	+	0.151453i	−0.273201	+	0.961957i	$0.588083\pi$
$998$	3.67083	+	20.8183i	0.116198	+	0.658992i
$999$	7.85166	−	13.5995i	0.248416	−	0.430268i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.q.a.21.2	✓	60
11.10	odd	2		418.2.q.b.21.2	yes	60
19.10	odd	18		418.2.q.b.219.2	yes	60
209.10	even	18	inner	418.2.q.a.219.2	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.q.a.21.2	✓	60	1.1	even	1	trivial
418.2.q.a.219.2	yes	60	209.10	even	18	inner
418.2.q.b.21.2	yes	60	11.10	odd	2
418.2.q.b.219.2	yes	60	19.10	odd	18

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.q (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-1.64579 + 1.96137i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-3.44031 + 1.25217i) q^{5} +(-1.64579 - 1.96137i) q^{6} +(0.237067 - 0.136871i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.617423 - 3.50158i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-1.64579 + 1.96137i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-3.44031 + 1.25217i) q^{5} +(-1.64579 - 1.96137i) q^{6} +(0.237067 - 0.136871i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.617423 - 3.50158i) q^{9} +(-0.635743 - 3.60548i) q^{10} +(0.340766 - 3.29907i) q^{11} +(2.21736 - 1.28019i) q^{12} +(-3.77750 + 3.16970i) q^{13} +(0.0936252 + 0.257233i) q^{14} +(3.20604 - 8.80853i) q^{15} +(0.766044 + 0.642788i) q^{16} +(5.78331 + 1.01975i) q^{17} +3.55560 q^{18} +(-0.912144 + 4.26239i) q^{19} +3.66110 q^{20} +(-0.121707 + 0.690237i) q^{21} +(3.18978 + 0.908467i) q^{22} +(0.397637 + 0.144728i) q^{23} +(0.875705 + 2.40598i) q^{24} +(6.43756 - 5.40176i) q^{25} +(-2.46559 - 4.27053i) q^{26} +(1.23196 + 0.711270i) q^{27} +(-0.269583 + 0.0475347i) q^{28} +(-1.03238 - 5.85493i) q^{29} +(8.11798 + 4.68692i) q^{30} +(-1.39534 + 0.805602i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(5.90988 + 6.09794i) q^{33} +(-2.00852 + 5.51837i) q^{34} +(-0.644199 + 0.767726i) q^{35} +(-0.617423 + 3.50158i) q^{36} -11.0389i q^{37} +(-4.03925 - 1.63844i) q^{38} -12.6257i q^{39} +(-0.635743 + 3.60548i) q^{40} +(-7.09476 - 5.95321i) q^{41} +(-0.658617 - 0.239717i) q^{42} +(3.30494 + 9.08025i) q^{43} +(-1.44856 + 2.98357i) q^{44} +(6.50869 + 11.2734i) q^{45} +(-0.211578 + 0.366464i) q^{46} +(-0.930808 - 5.27887i) q^{47} +(-2.52149 + 0.444607i) q^{48} +(-3.46253 + 5.99728i) q^{49} +(4.20182 + 7.27777i) q^{50} +(-11.5182 + 9.66493i) q^{51} +(4.63380 - 1.68656i) q^{52} +(2.33781 - 6.42309i) q^{53} +(-0.914391 + 1.08973i) q^{54} +(2.95866 + 11.7765i) q^{55} -0.273742i q^{56} +(-6.85894 - 8.80404i) q^{57} +5.94525 q^{58} +(-12.1854 - 2.14861i) q^{59} +(-6.02539 + 7.18078i) q^{60} +(0.928920 - 2.55219i) q^{61} +(-0.551064 - 1.51404i) q^{62} +(-0.625635 - 0.745602i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(9.02677 - 15.6348i) q^{65} +(-7.03154 + 4.76120i) q^{66} +(-1.03788 + 0.183006i) q^{67} +(-5.08576 - 2.93626i) q^{68} +(-0.938292 + 0.541723i) q^{69} +(-0.644199 - 0.767726i) q^{70} +(-0.936463 - 2.57291i) q^{71} +(-3.34117 - 1.21609i) q^{72} +(1.56790 - 1.86855i) q^{73} +(10.8712 + 1.91689i) q^{74} +21.5166i q^{75} +(2.31496 - 3.69337i) q^{76} +(-0.370762 - 0.828743i) q^{77} +(12.4339 + 2.19244i) q^{78} +(3.48779 + 2.92660i) q^{79} +(-3.44031 - 1.25217i) q^{80} +(6.60090 - 2.40253i) q^{81} +(7.09476 - 5.95321i) q^{82} +(-9.67636 + 5.58665i) q^{83} +(0.350443 - 0.606985i) q^{84} +(-21.1733 + 3.73342i) q^{85} +(-9.51620 + 1.67796i) q^{86} +(13.1828 + 7.61108i) q^{87} +(-2.68670 - 1.94465i) q^{88} +(-5.35117 - 6.37728i) q^{89} +(-12.2323 + 4.45221i) q^{90} +(-0.461683 + 1.26846i) q^{91} +(-0.324157 - 0.272000i) q^{92} +(0.716352 - 4.06264i) q^{93} +5.36031 q^{94} +(-2.19918 - 15.8061i) q^{95} -2.56039i q^{96} +(-3.37410 - 0.594944i) q^{97} +(-5.30491 - 4.45135i) q^{98} +(-11.7624 + 0.843705i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{3} - 3 q^{6} - 18 q^{7} + 30 q^{8} - 3 q^{9}+O(q^{10}) \) 60 * q - 3 * q^3 - 3 * q^6 - 18 * q^7 + 30 * q^8 - 3 * q^9	\( 60 q - 3 q^{3} - 3 q^{6} - 18 q^{7} + 30 q^{8} - 3 q^{9} + 3 q^{11} + 6 q^{13} - 12 q^{14} + 24 q^{15} - 6 q^{17} + 60 q^{18} - 30 q^{19} - 12 q^{20} + 12 q^{21} + 12 q^{22} + 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} + 6 q^{28} - 3 q^{29} - 9 q^{31} - 42 q^{33} - 6 q^{34} - 24 q^{35} - 3 q^{36} + 6 q^{38} + 15 q^{41} + 6 q^{42} - 3 q^{43} + 12 q^{44} - 48 q^{45} + 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} + 36 q^{50} - 45 q^{51} - 3 q^{52} + 24 q^{53} - 27 q^{54} + 6 q^{55} + 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} + 54 q^{61} - 66 q^{63} - 30 q^{64} - 63 q^{66} + 9 q^{67} - 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} - 6 q^{72} + 12 q^{74} + 18 q^{77} + 36 q^{79} - 93 q^{81} - 15 q^{82} - 36 q^{83} + 24 q^{84} - 60 q^{85} - 3 q^{86} + 54 q^{87} - 3 q^{88} - 3 q^{89} - 24 q^{90} - 12 q^{91} - 102 q^{93} - 12 q^{94} + 24 q^{95} - 6 q^{97} - 18 q^{98} - 78 q^{99}+O(q^{100}) \) 60 * q - 3 * q^3 - 3 * q^6 - 18 * q^7 + 30 * q^8 - 3 * q^9 + 3 * q^11 + 6 * q^13 - 12 * q^14 + 24 * q^15 - 6 * q^17 + 60 * q^18 - 30 * q^19 - 12 * q^20 + 12 * q^21 + 12 * q^22 + 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 + 6 * q^28 - 3 * q^29 - 9 * q^31 - 42 * q^33 - 6 * q^34 - 24 * q^35 - 3 * q^36 + 6 * q^38 + 15 * q^41 + 6 * q^42 - 3 * q^43 + 12 * q^44 - 48 * q^45 + 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 + 36 * q^50 - 45 * q^51 - 3 * q^52 + 24 * q^53 - 27 * q^54 + 6 * q^55 + 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 + 54 * q^61 - 66 * q^63 - 30 * q^64 - 63 * q^66 + 9 * q^67 - 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 - 6 * q^72 + 12 * q^74 + 18 * q^77 + 36 * q^79 - 93 * q^81 - 15 * q^82 - 36 * q^83 + 24 * q^84 - 60 * q^85 - 3 * q^86 + 54 * q^87 - 3 * q^88 - 3 * q^89 - 24 * q^90 - 12 * q^91 - 102 * q^93 - 12 * q^94 + 24 * q^95 - 6 * q^97 - 18 * q^98 - 78 * q^99

Introduction

L-functions

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