LMFDB - Embedded newform 77.2.f.b.36.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(15,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("77.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.f (of order $5$, degree $4$, 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:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			36.3
Root			$0.183009 - 0.132964i$ of defining polynomial
Character	$\chi$	$=$	77.36
Dual form			77.2.f.b.15.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.183009 + 0.132964i) q^{2} +(-0.0677147 - 0.208405i) q^{3} +(-0.602221 + 1.85345i) q^{4} +(2.01892 + 1.46683i) q^{5} +(0.0401026 + 0.0291363i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.276036 - 0.849550i) q^{8} +(2.38820 - 1.73513i) q^{9} +O(q^{10})$	\(q+(-0.183009 + 0.132964i) q^{2} +(-0.0677147 - 0.208405i) q^{3} +(-0.602221 + 1.85345i) q^{4} +(2.01892 + 1.46683i) q^{5} +(0.0401026 + 0.0291363i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.276036 - 0.849550i) q^{8} +(2.38820 - 1.73513i) q^{9} -0.564516 q^{10} +(-2.66598 - 1.97296i) q^{11} +0.427046 q^{12} +(-4.15429 + 3.01827i) q^{13} +(0.0699031 + 0.215140i) q^{14} +(0.168984 - 0.520079i) q^{15} +(-2.98979 - 2.17221i) q^{16} +(1.16298 + 0.844956i) q^{17} +(-0.206353 + 0.635089i) q^{18} +(-1.87526 - 5.77147i) q^{19} +(-3.93453 + 2.85860i) q^{20} -0.219130 q^{21} +(0.750229 + 0.00659095i) q^{22} +7.08292 q^{23} +(-0.158358 + 0.115054i) q^{24} +(0.379361 + 1.16755i) q^{25} +(0.358952 - 1.10474i) q^{26} +(-1.05516 - 0.766622i) q^{27} +(1.57664 + 1.14549i) q^{28} +(2.01408 - 6.19869i) q^{29} +(0.0382260 + 0.117648i) q^{30} +(-6.22049 + 4.51945i) q^{31} +2.62252 q^{32} +(-0.230648 + 0.689200i) q^{33} -0.325184 q^{34} +(2.01892 - 1.46683i) q^{35} +(1.77775 + 5.47134i) q^{36} +(-1.23122 + 3.78932i) q^{37} +(1.11058 + 0.806887i) q^{38} +(0.910328 + 0.661392i) q^{39} +(0.688853 - 2.12007i) q^{40} +(2.08556 + 6.41868i) q^{41} +(0.0401026 - 0.0291363i) q^{42} -0.802299 q^{43} +(5.26228 - 3.75309i) q^{44} +7.36674 q^{45} +(-1.29624 + 0.941771i) q^{46} +(2.08655 + 6.42174i) q^{47} +(-0.250246 + 0.770178i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.224669 - 0.163231i) q^{50} +(0.0973416 - 0.299587i) q^{51} +(-3.09240 - 9.51742i) q^{52} +(-5.32469 + 3.86861i) q^{53} +0.295037 q^{54} +(-2.48840 - 7.89379i) q^{55} -0.893270 q^{56} +(-1.07582 + 0.781627i) q^{57} +(0.455607 + 1.40221i) q^{58} +(0.888810 - 2.73548i) q^{59} +(0.862172 + 0.626405i) q^{60} +(0.691986 + 0.502757i) q^{61} +(0.537482 - 1.65420i) q^{62} +(-0.912213 - 2.80750i) q^{63} +(5.49964 - 3.99573i) q^{64} -12.8145 q^{65} +(-0.0494280 - 0.156797i) q^{66} -1.64668 q^{67} +(-2.26645 + 1.64667i) q^{68} +(-0.479618 - 1.47611i) q^{69} +(-0.174445 + 0.536886i) q^{70} +(-3.65738 - 2.65724i) q^{71} +(-2.13331 - 1.54994i) q^{72} +(-4.58827 + 14.1212i) q^{73} +(-0.278517 - 0.857187i) q^{74} +(0.217635 - 0.158121i) q^{75} +11.8264 q^{76} +(-2.70023 + 1.92582i) q^{77} -0.254539 q^{78} +(-1.98444 + 1.44178i) q^{79} +(-2.84989 - 8.77105i) q^{80} +(2.64832 - 8.15069i) q^{81} +(-1.23513 - 0.897372i) q^{82} +(-1.81851 - 1.32122i) q^{83} +(0.131964 - 0.406145i) q^{84} +(1.10856 + 3.41180i) q^{85} +(0.146828 - 0.106677i) q^{86} -1.42822 q^{87} +(-0.940224 + 2.80949i) q^{88} +1.73566 q^{89} +(-1.34818 + 0.979509i) q^{90} +(1.58680 + 4.88366i) q^{91} +(-4.26549 + 13.1278i) q^{92} +(1.36309 + 0.990346i) q^{93} +(-1.23572 - 0.897800i) q^{94} +(4.67976 - 14.4028i) q^{95} +(-0.177584 - 0.546546i) q^{96} +(9.77095 - 7.09901i) q^{97} +0.226211 q^{98} +(-9.79024 - 0.0860098i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} + 3 q^{6} - 4 q^{7} - 5 q^{8} - 12 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 + 3 * q^6 - 4 * q^7 - 5 * q^8 - 12 * q^9	\( 16 q - 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} + 3 q^{6} - 4 q^{7} - 5 q^{8} - 12 q^{9} + 12 q^{10} - 3 q^{11} + 18 q^{12} - 7 q^{13} + 2 q^{14} - 18 q^{15} + 17 q^{16} - 5 q^{17} + 11 q^{18} + 19 q^{19} + q^{20} + 8 q^{21} - 33 q^{22} + 32 q^{23} - 35 q^{24} + 7 q^{25} - 27 q^{26} + 10 q^{27} + 4 q^{28} + 3 q^{29} - 2 q^{30} - 7 q^{31} + 32 q^{32} - 26 q^{33} - 24 q^{34} - 5 q^{35} + 52 q^{36} + 4 q^{37} - 5 q^{38} + 11 q^{39} - 10 q^{40} - 10 q^{41} + 3 q^{42} - 8 q^{43} - 38 q^{44} + 70 q^{45} - 42 q^{46} - 23 q^{47} - 36 q^{48} - 4 q^{49} + 52 q^{50} - 29 q^{51} + 33 q^{52} + 4 q^{53} + 60 q^{54} - 12 q^{55} - 11 q^{57} + 20 q^{58} + 17 q^{59} - 30 q^{60} - 7 q^{61} + 79 q^{62} - 2 q^{63} + 7 q^{64} - 8 q^{65} + 8 q^{66} - 38 q^{67} - 2 q^{68} + 10 q^{69} - 18 q^{70} - 14 q^{71} - 35 q^{73} - 29 q^{74} + 9 q^{75} + 52 q^{76} - 3 q^{77} - 58 q^{78} + 15 q^{79} - 87 q^{80} - 14 q^{81} + 19 q^{82} + 5 q^{83} + 8 q^{84} + 6 q^{85} - 52 q^{86} - 72 q^{87} + 55 q^{88} + 74 q^{89} - 14 q^{90} + 13 q^{91} - 55 q^{92} + 32 q^{93} - 24 q^{94} + 32 q^{95} - 42 q^{96} + 20 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 + 3 * q^6 - 4 * q^7 - 5 * q^8 - 12 * q^9 + 12 * q^10 - 3 * q^11 + 18 * q^12 - 7 * q^13 + 2 * q^14 - 18 * q^15 + 17 * q^16 - 5 * q^17 + 11 * q^18 + 19 * q^19 + q^20 + 8 * q^21 - 33 * q^22 + 32 * q^23 - 35 * q^24 + 7 * q^25 - 27 * q^26 + 10 * q^27 + 4 * q^28 + 3 * q^29 - 2 * q^30 - 7 * q^31 + 32 * q^32 - 26 * q^33 - 24 * q^34 - 5 * q^35 + 52 * q^36 + 4 * q^37 - 5 * q^38 + 11 * q^39 - 10 * q^40 - 10 * q^41 + 3 * q^42 - 8 * q^43 - 38 * q^44 + 70 * q^45 - 42 * q^46 - 23 * q^47 - 36 * q^48 - 4 * q^49 + 52 * q^50 - 29 * q^51 + 33 * q^52 + 4 * q^53 + 60 * q^54 - 12 * q^55 - 11 * q^57 + 20 * q^58 + 17 * q^59 - 30 * q^60 - 7 * q^61 + 79 * q^62 - 2 * q^63 + 7 * q^64 - 8 * q^65 + 8 * q^66 - 38 * q^67 - 2 * q^68 + 10 * q^69 - 18 * q^70 - 14 * q^71 - 35 * q^73 - 29 * q^74 + 9 * q^75 + 52 * q^76 - 3 * q^77 - 58 * q^78 + 15 * q^79 - 87 * q^80 - 14 * q^81 + 19 * q^82 + 5 * q^83 + 8 * q^84 + 6 * q^85 - 52 * q^86 - 72 * q^87 + 55 * q^88 + 74 * q^89 - 14 * q^90 + 13 * q^91 - 55 * q^92 + 32 * q^93 - 24 * q^94 + 32 * q^95 - 42 * q^96 + 20 * q^97 + 2 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.183009	+	0.132964i	−0.129407	+	0.0940195i	−0.650606	−	0.759416i	$-0.725485\pi$
$2$	−0.183009	+	0.132964i	−0.129407	+	0.0940195i	0.521199	+	0.853435i	$0.325485\pi$
$3$	−0.0677147	−	0.208405i	−0.0390951	−	0.120322i	0.929604	−	0.368559i	$-0.120149\pi$
$3$	−0.0677147	−	0.208405i	−0.0390951	−	0.120322i	−0.968699	+	0.248237i	$0.920149\pi$
$4$	−0.602221	+	1.85345i	−0.301111	+	0.926723i
$5$	2.01892	+	1.46683i	0.902889	+	0.655987i	0.939206	−	0.343353i	$-0.111563\pi$
$5$	2.01892	+	1.46683i	0.902889	+	0.655987i	−0.0363174	+	0.999340i	$0.511563\pi$
$6$	0.0401026	+	0.0291363i	0.0163718	+	0.0118948i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	−0.276036	−	0.849550i	−0.0975933	−	0.300361i
$9$	2.38820	−	1.73513i	0.796068	−	0.578377i
$10$	−0.564516			−0.178516
$11$	−2.66598	−	1.97296i	−0.803822	−	0.594870i
$11$	−2.66598	−	1.97296i	−0.803822	−	0.594870i
$12$	0.427046			0.123278
$13$	−4.15429	+	3.01827i	−1.15219	+	0.837117i	−0.988771	−	0.149439i	$-0.952253\pi$
$13$	−4.15429	+	3.01827i	−1.15219	+	0.837117i	−0.163422	+	0.986556i	$0.552253\pi$
$14$	0.0699031	+	0.215140i	0.0186824	+	0.0574985i
$15$	0.168984	−	0.520079i	0.0436314	−	0.134284i
$16$	−2.98979	−	2.17221i	−0.747449	−	0.543053i
$17$	1.16298	+	0.844956i	0.282065	+	0.204932i	0.719817	−	0.694163i	$-0.244226\pi$
$17$	1.16298	+	0.844956i	0.282065	+	0.204932i	−0.437753	+	0.899095i	$0.644226\pi$
$18$	−0.206353	+	0.635089i	−0.0486378	+	0.149692i
$19$	−1.87526	−	5.77147i	−0.430215	−	1.32406i	−0.897912	−	0.440176i	$-0.854916\pi$
$19$	−1.87526	−	5.77147i	−0.430215	−	1.32406i	0.467697	−	0.883889i	$-0.345084\pi$
$20$	−3.93453	+	2.85860i	−0.879788	+	0.639203i
$21$	−0.219130			−0.0478180
$22$	0.750229	+	0.00659095i	0.159949	+	0.00140520i
$23$	7.08292			1.47689			0.738446	−	0.674313i	$-0.235560\pi$
$23$	7.08292			1.47689			0.738446	+	0.674313i	$0.235560\pi$
$24$	−0.158358	+	0.115054i	−0.0323248	+	0.0234853i
$25$	0.379361	+	1.16755i	0.0758722	+	0.233511i
$26$	0.358952	−	1.10474i	0.0703962	−	0.216657i
$27$	−1.05516	−	0.766622i	−0.203067	−	0.147536i
$28$	1.57664	+	1.14549i	0.297956	+	0.216478i
$29$	2.01408	−	6.19869i	0.374004	−	1.15107i	−0.570143	−	0.821545i	$-0.693112\pi$
$29$	2.01408	−	6.19869i	0.374004	−	1.15107i	0.944148	−	0.329522i	$-0.106888\pi$
$30$	0.0382260	+	0.117648i	0.00697909	+	0.0214794i
$31$	−6.22049	+	4.51945i	−1.11723	+	0.811718i	−0.983787	−	0.179338i	$-0.942604\pi$
$31$	−6.22049	+	4.51945i	−1.11723	+	0.811718i	−0.133446	+	0.991056i	$0.542604\pi$
$32$	2.62252			0.463601
$33$	−0.230648	+	0.689200i	−0.0401506	+	0.119974i
$34$	−0.325184			−0.0557687
$35$	2.01892	−	1.46683i	0.341260	−	0.247940i
$36$	1.77775	+	5.47134i	0.296291	+	0.911890i
$37$	−1.23122	+	3.78932i	−0.202412	+	0.622960i	0.797398	+	0.603454i	$0.206209\pi$
$37$	−1.23122	+	3.78932i	−0.202412	+	0.622960i	−0.999810	+	0.0195059i	$0.993791\pi$
$38$	1.11058	+	0.806887i	0.180161	+	0.130894i
$39$	0.910328	+	0.661392i	0.145769	+	0.105907i
$40$	0.688853	−	2.12007i	0.108917	−	0.335213i
$41$	2.08556	+	6.41868i	0.325709	+	1.00243i	0.971120	+	0.238594i	$0.0766864\pi$
$41$	2.08556	+	6.41868i	0.325709	+	1.00243i	−0.645410	+	0.763836i	$0.723314\pi$
$42$	0.0401026	−	0.0291363i	0.00618797	−	0.00449582i
$43$	−0.802299			−0.122349			−0.0611747	−	0.998127i	$-0.519485\pi$
$43$	−0.802299			−0.122349			−0.0611747	+	0.998127i	$0.519485\pi$
$44$	5.26228	−	3.75309i	0.793319	−	0.565799i
$45$	7.36674			1.09817
$46$	−1.29624	+	0.941771i	−0.191120	+	0.138857i
$47$	2.08655	+	6.42174i	0.304355	+	0.936707i	0.979917	+	0.199405i	$0.0639008\pi$
$47$	2.08655	+	6.42174i	0.304355	+	0.936707i	−0.675563	+	0.737303i	$0.736099\pi$
$48$	−0.250246	+	0.770178i	−0.0361199	+	0.111166i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−0.224669	−	0.163231i	−0.0317729	−	0.0230844i
$51$	0.0973416	−	0.299587i	0.0136306	−	0.0419505i
$52$	−3.09240	−	9.51742i	−0.428838	−	1.31983i
$53$	−5.32469	+	3.86861i	−0.731402	+	0.531394i	−0.890007	−	0.455948i	$-0.849300\pi$
$53$	−5.32469	+	3.86861i	−0.731402	+	0.531394i	0.158605	+	0.987342i	$0.449300\pi$
$54$	0.295037			0.0401495
$55$	−2.48840	−	7.89379i	−0.335535	−	1.06440i
$56$	−0.893270			−0.119368
$57$	−1.07582	+	0.781627i	−0.142495	+	0.103529i
$58$	0.455607	+	1.40221i	0.0598241	+	0.184120i
$59$	0.888810	−	2.73548i	0.115713	−	0.356129i	−0.876382	−	0.481617i	$-0.840050\pi$
$59$	0.888810	−	2.73548i	0.115713	−	0.356129i	0.992095	+	0.125488i	$0.0400497\pi$
$60$	0.862172	+	0.626405i	0.111306	+	0.0808685i
$61$	0.691986	+	0.502757i	0.0885997	+	0.0643715i	0.631203	−	0.775617i	$-0.282561\pi$
$61$	0.691986	+	0.502757i	0.0885997	+	0.0643715i	−0.542604	+	0.839989i	$0.682561\pi$
$62$	0.537482	−	1.65420i	0.0682603	−	0.210084i
$63$	−0.912213	−	2.80750i	−0.114928	−	0.353712i
$64$	5.49964	−	3.99573i	0.687455	−	0.499466i
$65$	−12.8145			−1.58944
$66$	−0.0494280	−	0.156797i	−0.00608417	−	0.0193004i
$67$	−1.64668			−0.201174			−0.100587	−	0.994928i	$-0.532072\pi$
$67$	−1.64668			−0.201174			−0.100587	+	0.994928i	$0.532072\pi$
$68$	−2.26645	+	1.64667i	−0.274848	+	0.199689i
$69$	−0.479618	−	1.47611i	−0.0577393	−	0.177703i
$70$	−0.174445	+	0.536886i	−0.0208502	+	0.0641702i
$71$	−3.65738	−	2.65724i	−0.434051	−	0.315357i	0.349216	−	0.937042i	$-0.386448\pi$
$71$	−3.65738	−	2.65724i	−0.434051	−	0.315357i	−0.783267	+	0.621686i	$0.786448\pi$
$72$	−2.13331	−	1.54994i	−0.251413	−	0.182662i
$73$	−4.58827	+	14.1212i	−0.537016	+	1.65277i	0.202236	+	0.979337i	$0.435179\pi$
$73$	−4.58827	+	14.1212i	−0.537016	+	1.65277i	−0.739252	+	0.673429i	$0.764821\pi$
$74$	−0.278517	−	0.857187i	−0.0323769	−	0.0996459i
$75$	0.217635	−	0.158121i	0.0251303	−	0.0182583i
$76$	11.8264			1.35658
$77$	−2.70023	+	1.92582i	−0.307720	+	0.219467i
$78$	−0.254539			−0.0288209
$79$	−1.98444	+	1.44178i	−0.223267	+	0.162213i	−0.693796	−	0.720171i	$-0.744063\pi$
$79$	−1.98444	+	1.44178i	−0.223267	+	0.162213i	0.470529	+	0.882385i	$0.344063\pi$
$80$	−2.84989	−	8.77105i	−0.318627	−	0.980633i
$81$	2.64832	−	8.15069i	0.294258	−	0.905633i
$82$	−1.23513	−	0.897372i	−0.136397	−	0.0990982i
$83$	−1.81851	−	1.32122i	−0.199607	−	0.145023i	0.483492	−	0.875349i	$-0.339368\pi$
$83$	−1.81851	−	1.32122i	−0.199607	−	0.145023i	−0.683099	+	0.730326i	$0.739368\pi$
$84$	0.131964	−	0.406145i	0.0143985	−	0.0443140i
$85$	1.10856	+	3.41180i	0.120240	+	0.370061i
$86$	0.146828	−	0.106677i	0.0158328	−	0.0115032i
$87$	−1.42822			−0.153121
$88$	−0.940224	+	2.80949i	−0.100228	+	0.299492i
$89$	1.73566			0.183980			0.0919898	−	0.995760i	$-0.470677\pi$
$89$	1.73566			0.183980			0.0919898	+	0.995760i	$0.470677\pi$
$90$	−1.34818	+	0.979509i	−0.142111	+	0.103249i
$91$	1.58680	+	4.88366i	0.166342	+	0.511947i
$92$	−4.26549	+	13.1278i	−0.444708	+	1.36867i
$93$	1.36309	+	0.990346i	0.141346	+	0.102694i
$94$	−1.23572	−	0.897800i	−0.127454	−	0.0926010i
$95$	4.67976	−	14.4028i	0.480134	−	1.47770i
$96$	−0.177584	−	0.546546i	−0.0181245	−	0.0557816i
$97$	9.77095	−	7.09901i	0.992089	−	0.720795i	0.0317117	−	0.999497i	$-0.489904\pi$
$97$	9.77095	−	7.09901i	0.992089	−	0.720795i	0.960378	+	0.278702i	$0.0899042\pi$
$98$	0.226211			0.0228508
$99$	−9.79024	−	0.0860098i	−0.983956	−	0.00864431i
$100$	−2.39246			−0.239246
$101$	2.98801	−	2.17091i	0.297318	−	0.216014i	−0.429118	−	0.903249i	$-0.641175\pi$
$101$	2.98801	−	2.17091i	0.297318	−	0.216014i	0.726436	+	0.687234i	$0.241175\pi$
$102$	0.0220198	+	0.0677699i	0.00218028	+	0.00671022i
$103$	−0.355853	+	1.09520i	−0.0350632	+	0.107913i	−0.967056	−	0.254563i	$-0.918069\pi$
$103$	−0.355853	+	1.09520i	−0.0350632	+	0.107913i	0.931993	+	0.362476i	$0.118069\pi$
$104$	3.71090	+	2.69613i	0.363884	+	0.264377i
$105$	−0.442405	−	0.321426i	−0.0431743	−	0.0313680i
$106$	0.460080	−	1.41598i	0.0446869	−	0.137532i
$107$	0.360665	+	1.11001i	0.0348668	+	0.107309i	0.966975	−	0.254870i	$-0.0820328\pi$
$107$	0.360665	+	1.11001i	0.0348668	+	0.107309i	−0.932108	+	0.362179i	$0.882033\pi$
$108$	2.05633	−	1.49401i	0.197871	−	0.143762i
$109$	9.30234			0.891003			0.445501	−	0.895281i	$-0.353025\pi$
$109$	9.30234			0.891003			0.445501	+	0.895281i	$0.353025\pi$
$110$	1.50499	+	1.11377i	0.143495	+	0.106194i
$111$	0.873083			0.0828694
$112$	−2.98979	+	2.17221i	−0.282509	+	0.205255i
$113$	1.01893	+	3.13595i	0.0958529	+	0.295005i	0.987475	−	0.157775i	$-0.0504322\pi$
$113$	1.01893	+	3.13595i	0.0958529	+	0.295005i	−0.891622	+	0.452780i	$0.850432\pi$
$114$	0.0929560	−	0.286089i	0.00870613	−	0.0267947i
$115$	14.2999	+	10.3895i	1.33347	+	0.968822i
$116$	10.2760	+	7.46596i	0.954104	+	0.693197i
$117$	−4.68420	+	14.4165i	−0.433054	+	1.33280i
$118$	0.201059	+	0.618796i	0.0185090	+	0.0569648i
$119$	1.16298	−	0.844956i	0.106610	−	0.0774570i
$120$	−0.488478			−0.0445918
$121$	3.21486	+	10.5197i	0.292260	+	0.956339i
$122$	−0.193488			−0.0175176
$123$	1.19646	−	0.869279i	0.107881	−	0.0783802i
$124$	−4.63045	−	14.2511i	−0.415827	−	1.27978i
$125$	2.90909	−	8.95326i	0.260197	−	0.800804i
$126$	0.540239	+	0.392506i	0.0481283	+	0.0349673i
$127$	0.233972	+	0.169990i	0.0207616	+	0.0150842i	0.598118	−	0.801408i	$-0.295916\pi$
$127$	0.233972	+	0.169990i	0.0207616	+	0.0150842i	−0.577356	+	0.816492i	$0.695916\pi$
$128$	−2.09601	+	6.45084i	−0.185262	+	0.570179i
$129$	0.0543275	+	0.167203i	0.00478327	+	0.0147214i
$130$	2.34516	−	1.70386i	0.205684	−	0.149438i
$131$	−16.5059			−1.44212			−0.721062	−	0.692871i	$-0.756346\pi$
$131$	−16.5059			−1.44212			−0.721062	+	0.692871i	$0.756346\pi$
$132$	−1.13849	−	0.842544i	−0.0990932	−	0.0733341i
$133$	−6.06848			−0.526204
$134$	0.301357	−	0.218949i	0.0260333	−	0.0189143i
$135$	−1.00579	−	3.09550i	−0.0865645	−	0.266418i
$136$	0.396808	−	1.22125i	0.0340260	−	0.104721i
$137$	−7.54479	−	5.48161i	−0.644595	−	0.468326i	0.216831	−	0.976209i	$-0.430428\pi$
$137$	−7.54479	−	5.48161i	−0.644595	−	0.468326i	−0.861426	+	0.507883i	$0.830428\pi$
$138$	0.284044	+	0.206370i	0.0241794	+	0.0175674i
$139$	1.49147	−	4.59026i	0.126505	−	0.389341i	−0.867668	−	0.497145i	$-0.834382\pi$
$139$	1.49147	−	4.59026i	0.126505	−	0.389341i	0.994172	+	0.107804i	$0.0343818\pi$
$140$	1.50286	+	4.62532i	0.127015	+	0.390911i
$141$	1.19703	−	0.869693i	0.100808	−	0.0732414i
$142$	1.02265			0.0858189
$143$	17.0302	+	0.149614i	1.42413	+	0.0125114i
$144$	−10.9093			−0.909109
$145$	13.1587	−	9.56035i	1.09277	−	0.793944i
$146$	−1.03792	−	3.19438i	−0.0858987	−	0.264369i
$147$	−0.0677147	+	0.208405i	−0.00558502	+	0.0171889i
$148$	−6.28183	−	4.56401i	−0.516363	−	0.375160i
$149$	−0.745845	−	0.541888i	−0.0611020	−	0.0443932i	0.556815	−	0.830637i	$-0.312023\pi$
$149$	−0.745845	−	0.541888i	−0.0611020	−	0.0443932i	−0.617917	+	0.786243i	$0.712023\pi$
$150$	−0.0188048	+	0.0578751i	−0.00153540	+	0.00472549i
$151$	5.59210	+	17.2107i	0.455079	+	1.40059i	0.871043	+	0.491207i	$0.163444\pi$
$151$	5.59210	+	17.2107i	0.455079	+	1.40059i	−0.415964	+	0.909381i	$0.636556\pi$
$152$	−4.38551	+	3.18626i	−0.355712	+	0.258440i
$153$	4.24355			0.343070
$154$	0.238102	−	0.711474i	0.0191868	−	0.0573322i
$155$	−19.1880			−1.54121
$156$	−1.77407	+	1.28894i	−0.142039	+	0.103198i
$157$	−3.79267	−	11.6726i	−0.302688	−	0.931577i	−0.980530	−	0.196369i	$-0.937085\pi$
$157$	−3.79267	−	11.6726i	−0.302688	−	0.931577i	0.677842	−	0.735207i	$-0.262915\pi$
$158$	0.171466	−	0.527718i	0.0136411	−	0.0419830i
$159$	1.16680	+	0.847727i	0.0925329	+	0.0672291i
$160$	5.29467	+	3.84680i	0.418580	+	0.304116i
$161$	2.18874	−	6.73626i	0.172497	−	0.530892i
$162$	0.599080	+	1.84378i	0.0470682	+	0.144861i
$163$	−6.55233	+	4.76055i	−0.513218	+	0.372875i	−0.814043	−	0.580804i	$-0.802738\pi$
$163$	−6.55233	+	4.76055i	−0.513218	+	0.372875i	0.300825	+	0.953679i	$0.402738\pi$
$164$	−13.1526			−1.02705
$165$	−1.47660	+	1.05312i	−0.114953	+	0.0819852i
$166$	0.508478			0.0394655
$167$	10.5590	−	7.67154i	0.817077	−	0.593641i	−0.0987965	−	0.995108i	$-0.531499\pi$
$167$	10.5590	−	7.67154i	0.817077	−	0.593641i	0.915874	+	0.401466i	$0.131499\pi$
$168$	0.0604875	+	0.186161i	0.00466671	+	0.0143627i
$169$	4.13096	−	12.7138i	0.317766	−	0.977985i
$170$	−0.656522	−	0.476991i	−0.0503529	−	0.0365835i
$171$	−14.4928	−	10.5296i	−1.10829	−	0.805219i
$172$	0.483161	−	1.48702i	0.0368407	−	0.113384i
$173$	1.82697	+	5.62283i	0.138902	+	0.427496i	0.996176	−	0.0873636i	$-0.0278442\pi$
$173$	1.82697	+	5.62283i	0.138902	+	0.427496i	−0.857275	+	0.514859i	$0.827844\pi$
$174$	0.261376	−	0.189901i	0.0198149	−	0.0143964i
$175$	1.22764			0.0928007
$176$	3.68503	+	11.6898i	0.277770	+	0.881153i
$177$	−0.630271			−0.0473741
$178$	−0.317641	+	0.230780i	−0.0238082	+	0.0172977i
$179$	1.33961	+	4.12290i	0.100127	+	0.308160i	0.988556	−	0.150854i	$-0.0482025\pi$
$179$	1.33961	+	4.12290i	0.100127	+	0.308160i	−0.888429	+	0.459015i	$0.848202\pi$
$180$	−4.43641	+	13.6539i	−0.330670	+	1.01770i
$181$	−8.76223	−	6.36613i	−0.651291	−	0.473191i	0.212420	−	0.977179i	$-0.431866\pi$
$181$	−8.76223	−	6.36613i	−0.651291	−	0.473191i	−0.863711	+	0.503988i	$0.831866\pi$
$182$	−0.939748	−	0.682767i	−0.0696587	−	0.0506100i
$183$	0.0579192	−	0.178257i	0.00428151	−	0.0131771i
$184$	−1.95514	−	6.01730i	−0.144135	−	0.443601i
$185$	−8.04404	+	5.84433i	−0.591409	+	0.429684i
$186$	−0.381138			−0.0279464
$187$	−1.43342	−	4.54715i	−0.104822	−	0.332520i
$188$	−13.1589			−0.959713
$189$	−1.05516	+	0.766622i	−0.0767519	+	0.0557635i
$190$	1.05862	+	3.25808i	0.0768000	+	0.236366i
$191$	3.60178	−	11.0851i	0.260616	−	0.802093i	−0.732055	−	0.681245i	$-0.761439\pi$
$191$	3.60178	−	11.0851i	0.260616	−	0.802093i	0.992671	−	0.120848i	$-0.0385613\pi$
$192$	−1.20513	−	0.875581i	−0.0869731	−	0.0631896i
$193$	−18.1587	−	13.1931i	−1.30709	−	0.949659i	−0.307096	−	0.951679i	$-0.599357\pi$
$193$	−18.1587	−	13.1931i	−1.30709	−	0.949659i	−0.999998	+	0.00201912i	$0.999357\pi$
$194$	−0.844259	+	2.59836i	−0.0606143	+	0.186552i
$195$	0.867729	+	2.67060i	0.0621394	+	0.191245i
$196$	1.57664	−	1.14549i	0.112617	−	0.0818209i
$197$	24.1022			1.71721			0.858604	−	0.512639i	$-0.171332\pi$
$197$	24.1022			1.71721			0.858604	+	0.512639i	$0.171332\pi$
$198$	1.80314	−	1.28601i	0.128143	−	0.0913925i
$199$	18.7205			1.32706			0.663531	−	0.748148i	$-0.269057\pi$
$199$	18.7205			1.32706			0.663531	+	0.748148i	$0.269057\pi$
$200$	0.887178	−	0.644573i	0.0627330	−	0.0455782i
$201$	0.111505	+	0.343176i	0.00786493	+	0.0242058i
$202$	−0.258179	+	0.794593i	−0.0181654	+	0.0559074i
$203$	−5.27292	−	3.83100i	−0.370086	−	0.268883i
$204$	0.496647	+	0.360835i	0.0347722	+	0.0252635i
$205$	−5.20455	+	16.0180i	−0.363502	+	1.11874i
$206$	−0.0804979	−	0.247747i	−0.00560855	−	0.0172614i
$207$	16.9155	−	12.2898i	1.17571	−	0.854200i
$208$	18.9768			1.31580
$209$	−6.38746	+	19.0864i	−0.441830	+	1.32023i
$210$	0.123702			0.00853625
$211$	6.12131	−	4.44739i	0.421408	−	0.306171i	−0.356796	−	0.934182i	$-0.616131\pi$
$211$	6.12131	−	4.44739i	0.421408	−	0.306171i	0.778204	+	0.628011i	$0.216131\pi$
$212$	−3.96362	−	12.1988i	−0.272223	−	0.837815i
$213$	−0.306123	+	0.942149i	−0.0209752	+	0.0645550i
$214$	−0.213596	−	0.155187i	−0.0146011	−	0.0106083i
$215$	−1.61978	−	1.17684i	−0.110468	−	0.0802596i
$216$	−0.360021	+	1.10803i	−0.0244963	+	0.0753919i
$217$	2.37602	+	7.31263i	0.161295	+	0.496414i
$218$	−1.70241	+	1.23687i	−0.115302	+	0.0837717i
$219$	3.25362			0.219859
$220$	16.1293	+	0.141700i	1.08744	+	0.00955340i
$221$	−7.38167			−0.496545
$222$	−0.159782	+	0.116088i	−0.0107239	+	0.00779134i
$223$	5.41533	+	16.6667i	0.362637	+	1.11608i	0.951447	+	0.307811i	$0.0995966\pi$
$223$	5.41533	+	16.6667i	0.362637	+	1.11608i	−0.588810	+	0.808271i	$0.700403\pi$
$224$	0.810404	−	2.49417i	0.0541474	−	0.166649i
$225$	2.93185	+	2.13011i	0.195457	+	0.142008i
$226$	−0.603440	−	0.438425i	−0.0401403	−	0.0291636i
$227$	−7.93471	+	24.4205i	−0.526645	+	1.62085i	0.234394	+	0.972142i	$0.424689\pi$
$227$	−7.93471	+	24.4205i	−0.526645	+	1.62085i	−0.761039	+	0.648706i	$0.775311\pi$
$228$	−0.800823	−	2.46468i	−0.0530358	−	0.163227i
$229$	16.0484	−	11.6598i	1.06051	−	0.770503i	0.0863246	−	0.996267i	$-0.472488\pi$
$229$	16.0484	−	11.6598i	1.06051	−	0.770503i	0.974182	+	0.225764i	$0.0724878\pi$
$230$	−3.99842			−0.263648
$231$	0.584194	+	0.432334i	0.0384372	+	0.0284455i
$232$	−5.82205			−0.382236
$233$	16.3539	−	11.8818i	1.07138	−	0.778405i	0.0952219	−	0.995456i	$-0.469644\pi$
$233$	16.3539	−	11.8818i	1.07138	−	0.778405i	0.976160	+	0.217051i	$0.0696439\pi$
$234$	−1.05962	−	3.26117i	−0.0692695	−	0.213189i
$235$	−5.20704	+	16.0256i	−0.339670	+	1.04540i
$236$	4.53480	+	3.29472i	0.295190	+	0.214468i
$237$	0.434850	+	0.315937i	0.0282465	+	0.0205223i
$238$	−0.100488	+	0.309269i	−0.00651364	+	0.0200469i
$239$	5.28431	+	16.2634i	0.341814	+	1.05199i	0.963267	+	0.268544i	$0.0865424\pi$
$239$	5.28431	+	16.2634i	0.341814	+	1.05199i	−0.621454	+	0.783451i	$0.713458\pi$
$240$	−1.63495	+	1.18786i	−0.105535	+	0.0766760i
$241$	−24.1529			−1.55582			−0.777912	−	0.628373i	$-0.783721\pi$
$241$	−24.1529			−1.55582			−0.777912	+	0.628373i	$0.783721\pi$
$242$	−1.98709	−	1.49774i	−0.127735	−	0.0962786i
$243$	−5.79074			−0.371476
$244$	−1.34856	+	0.979787i	−0.0863328	+	0.0627245i
$245$	−0.771159	−	2.37338i	−0.0492676	−	0.151630i
$246$	−0.103380	+	0.318171i	−0.00659128	+	0.0202859i
$247$	25.2102	+	18.3163i	1.60409	+	1.16544i
$248$	5.55658	+	4.03709i	0.352843	+	0.256356i
$249$	−0.152209	+	0.468452i	−0.00964586	+	0.0296869i
$250$	0.658069	+	2.02533i	0.0416200	+	0.128093i
$251$	−9.62305	+	6.99156i	−0.607402	+	0.441303i	−0.848498	−	0.529198i	$-0.822493\pi$
$251$	−9.62305	+	6.99156i	−0.607402	+	0.441303i	0.241097	+	0.970501i	$0.422493\pi$
$252$	5.75291			0.362399
$253$	−18.8829	−	13.9743i	−1.18716	−	0.878558i
$254$	−0.0654215			−0.00410491
$255$	0.635968	−	0.462058i	0.0398259	−	0.0289352i
$256$	3.72721	+	11.4712i	0.232951	+	0.716949i
$257$	7.09531	−	21.8371i	0.442593	−	1.36216i	−0.442509	−	0.896764i	$-0.645911\pi$
$257$	7.09531	−	21.8371i	0.442593	−	1.36216i	0.885102	−	0.465397i	$-0.154089\pi$
$258$	−0.0321743	−	0.0233760i	−0.00200308	−	0.00145533i
$259$	3.22339	+	2.34193i	0.200291	+	0.145520i
$260$	7.71715	−	23.7509i	0.478597	−	1.47297i
$261$	−5.94552	−	18.2984i	−0.368018	−	1.13264i
$262$	3.02072	−	2.19468i	0.186621	−	0.135588i
$263$	1.93774			0.119486			0.0597432	−	0.998214i	$-0.480972\pi$
$263$	1.93774			0.119486			0.0597432	+	0.998214i	$0.480972\pi$
$264$	0.649177	+	0.00570319i	0.0399541	+	0.000351007i
$265$	−16.4247			−1.00896
$266$	1.11058	−	0.806887i	0.0680943	−	0.0494734i
$267$	−0.117530	−	0.361720i	−0.00719271	−	0.0221369i
$268$	0.991666	−	3.05203i	0.0605756	−	0.186433i
$269$	−5.81421	−	4.22427i	−0.354499	−	0.257558i	0.396255	−	0.918140i	$-0.370310\pi$
$269$	−5.81421	−	4.22427i	−0.354499	−	0.257558i	−0.750754	+	0.660582i	$0.770310\pi$
$270$	0.595657	+	0.432770i	0.0362505	+	0.0263376i
$271$	0.368071	−	1.13281i	0.0223587	−	0.0688130i	−0.939255	−	0.343221i	$-0.888482\pi$
$271$	0.368071	−	1.13281i	0.0223587	−	0.0688130i	0.961613	+	0.274408i	$0.0884819\pi$
$272$	−1.64165	−	5.05249i	−0.0995398	−	0.306352i
$273$	0.910328	−	0.661392i	0.0550955	−	0.0400293i
$274$	2.10962			0.127447
$275$	1.29217	−	3.86113i	0.0779207	−	0.232835i
$276$	3.02473			0.182067
$277$	−8.36543	+	6.07784i	−0.502630	+	0.365182i	−0.810021	−	0.586401i	$-0.800544\pi$
$277$	−8.36543	+	6.07784i	−0.502630	+	0.365182i	0.307391	+	0.951583i	$0.400544\pi$
$278$	0.337387	+	1.03837i	0.0202351	+	0.0622773i
$279$	−7.01396	+	21.5867i	−0.419915	+	1.29236i
$280$	−1.80344	−	1.31028i	−0.107776	−	0.0783040i
$281$	10.6396	+	7.73015i	0.634707	+	0.461142i	0.858028	−	0.513603i	$-0.171690\pi$
$281$	10.6396	+	7.73015i	0.634707	+	0.461142i	−0.223321	+	0.974745i	$0.571690\pi$
$282$	−0.103429	+	0.318323i	−0.00615913	+	0.0189559i
$283$	0.0927146	+	0.285346i	0.00551131	+	0.0169621i	0.953774	−	0.300524i	$-0.0971614\pi$
$283$	0.0927146	+	0.285346i	0.00551131	+	0.0169621i	−0.948263	+	0.317486i	$0.897161\pi$
$284$	7.12761	−	5.17851i	0.422946	−	0.307288i
$285$	−3.31850			−0.196571
$286$	−3.13656	+	2.23701i	−0.185469	+	0.132277i
$287$	6.74900			0.398381
$288$	6.26312	−	4.55042i	0.369058	−	0.268136i
$289$	−4.61471	−	14.2026i	−0.271454	−	0.835448i
$290$	−1.13698	+	3.49926i	−0.0667656	+	0.205483i
$291$	−2.14110	−	1.55560i	−0.125514	−	0.0911910i
$292$	−23.4098	−	17.0082i	−1.36995	−	0.995330i
$293$	4.98880	−	15.3539i	0.291449	−	0.896987i	−0.692942	−	0.720993i	$-0.743686\pi$
$293$	4.98880	−	15.3539i	0.291449	−	0.896987i	0.984391	−	0.175994i	$-0.0563140\pi$
$294$	−0.0153178	−	0.0471435i	−0.000893355	−	0.00274946i
$295$	5.80692	−	4.21898i	0.338092	−	0.245638i
$296$	3.55908			0.206867
$297$	1.30053	+	4.12559i	0.0754644	+	0.239391i
$298$	0.208548			0.0120808
$299$	−29.4245	+	21.3782i	−1.70166	+	1.23633i
$300$	0.162005	+	0.498599i	0.00935334	+	0.0287866i
$301$	−0.247924	+	0.763031i	−0.0142901	+	0.0439804i
$302$	−3.31180	−	2.40617i	−0.190573	−	0.138459i
$303$	−0.654761	−	0.475711i	−0.0376150	−	0.0273289i
$304$	−6.93020	+	21.3290i	−0.397474	+	1.22330i
$305$	0.659605	+	2.03005i	0.0377688	+	0.116241i
$306$	−0.776607	+	0.564238i	−0.0443956	+	0.0322553i
$307$	−28.6376			−1.63443			−0.817217	−	0.576330i	$-0.804484\pi$
$307$	−28.6376			−1.63443			−0.817217	+	0.576330i	$0.804484\pi$
$308$	−1.94326	−	6.16449i	−0.110728	−	0.351255i
$309$	0.252341			0.0143552
$310$	3.51157	−	2.55130i	0.199444	−	0.144904i
$311$	−9.83377	−	30.2652i	−0.557622	−	1.71618i	−0.688916	−	0.724841i	$-0.741913\pi$
$311$	−9.83377	−	30.2652i	−0.557622	−	1.71618i	0.131294	−	0.991343i	$-0.458087\pi$
$312$	0.310603	−	0.955937i	0.0175844	−	0.0541193i
$313$	−0.0276872	−	0.0201159i	−0.00156497	−	0.00113702i	0.587002	−	0.809585i	$-0.300308\pi$
$313$	−0.0276872	−	0.0201159i	−0.00156497	−	0.00113702i	−0.588567	+	0.808448i	$0.700308\pi$
$314$	2.24613	+	1.63191i	0.126756	+	0.0920938i
$315$	2.27645	−	7.00619i	0.128263	−	0.394754i
$316$	−1.47719	−	4.54633i	−0.0830985	−	0.255751i
$317$	−18.1134	+	13.1602i	−1.01735	+	0.739149i	−0.965738	−	0.259518i	$-0.916436\pi$
$317$	−18.1134	+	13.1602i	−1.01735	+	0.739149i	−0.0516132	+	0.998667i	$0.516436\pi$
$318$	−0.326251			−0.0182952
$319$	−17.5992	+	12.5519i	−0.985368	+	0.702770i
$320$	16.9644			0.948339
$321$	0.206909	−	0.150328i	0.0115486	−	0.00839052i
$322$	0.495119	+	1.52382i	0.0275919	+	0.0849191i
$323$	2.69574	−	8.29662i	0.149995	−	0.461636i
$324$	13.5120	+	9.81704i	0.750666	+	0.545391i
$325$	−5.09997	−	3.70534i	−0.282895	−	0.205535i
$326$	0.566155	−	1.74244i	0.0313564	−	0.0965051i
$327$	−0.629906	−	1.93865i	−0.0348339	−	0.107208i
$328$	4.87730	−	3.54357i	0.269304	−	0.195661i
$329$	6.75222			0.372262
$330$	0.130204	−	0.389064i	0.00716751	−	0.0214173i
$331$	10.7577			0.591297			0.295648	−	0.955297i	$-0.404464\pi$
$331$	10.7577			0.591297			0.295648	+	0.955297i	$0.404464\pi$
$332$	3.54396	−	2.57484i	0.194500	−	0.141313i
$333$	3.63455	+	11.1860i	0.199172	+	0.612989i
$334$	−0.912348	+	2.80792i	−0.0499215	+	0.153642i
$335$	−3.32452	−	2.41540i	−0.181638	−	0.131968i
$336$	0.655152	+	0.475996i	0.0357415	+	0.0259677i
$337$	2.31915	−	7.13761i	0.126332	−	0.388810i	−0.867809	−	0.496897i	$-0.834473\pi$
$337$	2.31915	−	7.13761i	0.126332	−	0.388810i	0.994141	+	0.108087i	$0.0344726\pi$
$338$	0.934471	+	2.87601i	0.0508285	+	0.156434i
$339$	0.584549	−	0.424700i	0.0317483	−	0.0230665i
$340$	−6.99118			−0.379150
$341$	25.5004	+	0.224027i	1.38092	+	0.0121318i
$342$	4.05236			0.219126
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	0.221463	+	0.681593i	0.0119405	+	0.0367490i
$345$	1.19690	−	3.68368i	0.0644389	−	0.198322i
$346$	−1.08198	−	0.786107i	−0.0581678	−	0.0422614i
$347$	22.3950	+	16.2710i	1.20223	+	0.873471i	0.994502	−	0.104716i	$-0.0333934\pi$
$347$	22.3950	+	16.2710i	1.20223	+	0.873471i	0.207727	+	0.978187i	$0.433393\pi$
$348$	0.860103	−	2.64712i	0.0461063	−	0.141901i
$349$	−3.41788	−	10.5192i	−0.182955	−	0.563078i	0.816952	−	0.576706i	$-0.195662\pi$
$349$	−3.41788	−	10.5192i	−0.182955	−	0.563078i	−0.999907	+	0.0136278i	$0.995662\pi$
$350$	−0.224669	+	0.163231i	−0.0120090	+	0.00872508i
$351$	6.69733			0.357477
$352$	−6.99159	−	5.17413i	−0.372653	−	0.275782i
$353$	31.9202			1.69894			0.849469	−	0.527638i	$-0.176922\pi$
$353$	31.9202			1.69894			0.849469	+	0.527638i	$0.176922\pi$
$354$	0.115345	−	0.0838032i	0.00613053	−	0.00445409i
$355$	−3.48623	−	10.7295i	−0.185030	−	0.569464i
$356$	−1.04525	+	3.21695i	−0.0553982	+	0.170498i
$357$	−0.254844	−	0.185155i	−0.0134878	−	0.00979943i
$358$	−0.793358	−	0.576408i	−0.0419303	−	0.0304641i
$359$	1.10574	−	3.40313i	0.0583590	−	0.179610i	−0.917628	−	0.397441i	$-0.869898\pi$
$359$	1.10574	−	3.40313i	0.0583590	−	0.179610i	0.975986	+	0.217831i	$0.0698982\pi$
$360$	−2.03348	−	6.25842i	−0.107174	−	0.329847i
$361$	−14.4219	+	10.4781i	−0.759046	+	0.551479i
$362$	2.45003			0.128771
$363$	1.97467	−	1.38233i	0.103643	−	0.0725536i
$364$	−10.0072			−0.524520
$365$	−29.9768	+	21.7794i	−1.56906	+	1.13999i
$366$	0.0131020	+	0.0403238i	0.000684852	+	0.00210776i
$367$	0.708875	−	2.18169i	0.0370030	−	0.113883i	−0.930849	−	0.365404i	$-0.880931\pi$
$367$	0.708875	−	2.18169i	0.0370030	−	0.113883i	0.967852	+	0.251521i	$0.0809307\pi$
$368$	−21.1765	−	15.3856i	−1.10390	−	0.802031i
$369$	16.1180	+	11.7104i	0.839069	+	0.609619i
$370$	0.695045	−	2.13913i	0.0361337	−	0.111208i
$371$	2.03385	+	6.25954i	0.105592	+	0.324979i
$372$	−2.65644	+	1.93001i	−0.137730	+	0.100067i
$373$	7.96856			0.412596			0.206298	−	0.978489i	$-0.433858\pi$
$373$	7.96856			0.412596			0.206298	+	0.978489i	$0.433858\pi$
$374$	0.866934	+	0.641576i	0.0448281	+	0.0331751i
$375$	−2.06289			−0.106527
$376$	4.87963	−	3.54526i	0.251648	−	0.182833i
$377$	10.3423	+	31.8302i	0.532653	+	1.63934i
$378$	0.0911715	−	0.280597i	0.00468936	−	0.0144324i
$379$	9.40174	+	6.83077i	0.482935	+	0.350873i	0.802461	−	0.596705i	$-0.203524\pi$
$379$	9.40174	+	6.83077i	0.482935	+	0.350873i	−0.319526	+	0.947578i	$0.603524\pi$
$380$	23.8766	+	17.3474i	1.22484	+	0.889902i
$381$	0.0195835	−	0.0602717i	0.00100329	−	0.00308781i
$382$	0.814764	+	2.50759i	0.0416869	+	0.128299i
$383$	−10.1762	+	7.39343i	−0.519979	+	0.377787i	−0.816596	−	0.577210i	$-0.804141\pi$
$383$	−10.1762	+	7.39343i	−0.519979	+	0.377787i	0.296617	+	0.954996i	$0.404141\pi$
$384$	1.48632			0.0758482
$385$	−8.27640	−	0.0727103i	−0.421804	−	0.00370566i
$386$	5.07741			0.258433
$387$	−1.91605	+	1.39209i	−0.0973984	+	0.0707641i
$388$	7.27336	+	22.3851i	0.369249	+	1.13643i
$389$	−0.135440	+	0.416842i	−0.00686709	+	0.0211347i	−0.954431	−	0.298431i	$-0.903537\pi$
$389$	−0.135440	+	0.416842i	−0.00686709	+	0.0211347i	0.947564	+	0.319565i	$0.103537\pi$
$390$	−0.513894	−	0.373366i	−0.0260221	−	0.0189061i
$391$	8.23731	+	5.98476i	0.416579	+	0.302662i
$392$	−0.276036	+	0.849550i	−0.0139419	+	0.0429088i
$393$	1.11769	+	3.43990i	0.0563800	+	0.173520i
$394$	−4.41091	+	3.20471i	−0.222218	+	0.161451i
$395$	−6.12128			−0.307995
$396$	6.05530	−	18.0939i	0.304290	−	0.909252i
$397$	16.8147			0.843905			0.421952	−	0.906618i	$-0.361345\pi$
$397$	16.8147			0.843905			0.421952	+	0.906618i	$0.361345\pi$
$398$	−3.42602	+	2.48915i	−0.171731	+	0.124770i
$399$	0.410925	+	1.26470i	0.0205720	+	0.0633141i
$400$	1.40196	−	4.31480i	0.0700981	−	0.215740i
$401$	−29.8211	−	21.6663i	−1.48919	−	1.08196i	−0.974446	−	0.224621i	$-0.927886\pi$
$401$	−29.8211	−	21.6663i	−1.48919	−	1.08196i	−0.514747	−	0.857342i	$-0.672114\pi$
$402$	−0.0660362	−	0.0479781i	−0.00329359	−	0.00239293i
$403$	12.2008	−	37.5502i	0.607766	−	1.87051i
$404$	2.22423	+	6.84548i	0.110660	+	0.340575i
$405$	17.3024	−	12.5710i	0.859766	−	0.624656i
$406$	1.47437			0.0731720
$407$	10.7586	−	7.67308i	0.533283	−	0.380340i
$408$	−0.281384			−0.0139306
$409$	−13.1659	+	9.56556i	−0.651010	+	0.472986i	−0.863615	−	0.504152i	$-0.831805\pi$
$409$	−13.1659	+	9.56556i	−0.651010	+	0.472986i	0.212605	+	0.977138i	$0.431805\pi$
$410$	−1.17733	−	3.62345i	−0.0581441	−	0.178949i
$411$	−0.631499	+	1.94356i	−0.0311496	+	0.0958685i
$412$	−1.81559	−	1.31911i	−0.0894479	−	0.0649877i
$413$	−2.32694	−	1.69062i	−0.114501	−	0.0831898i
$414$	−1.46158	+	4.49828i	−0.0718328	+	0.221079i
$415$	−1.73341	−	5.33489i	−0.0850898	−	0.261879i
$416$	−10.8947	+	7.91548i	−0.534158	+	0.388088i
$417$	−1.05763			−0.0517922
$418$	−1.36884	−	4.34228i	−0.0669520	−	0.212388i
$419$	5.56352			0.271796			0.135898	−	0.990723i	$-0.456608\pi$
$419$	5.56352			0.271796			0.135898	+	0.990723i	$0.456608\pi$
$420$	0.862172	−	0.626405i	0.0420697	−	0.0305654i
$421$	6.64120	+	20.4395i	0.323672	+	0.996161i	0.972036	+	0.234831i	$0.0754536\pi$
$421$	6.64120	+	20.4395i	0.323672	+	0.996161i	−0.648364	+	0.761331i	$0.724546\pi$
$422$	−0.528912	+	1.62782i	−0.0257470	+	0.0792412i
$423$	16.1257	+	11.7160i	0.784057	+	0.569651i
$424$	4.75638	+	3.45571i	0.230990	+	0.167824i
$425$	−0.545341	+	1.67839i	−0.0264529	+	0.0814137i
$426$	−0.0692485	−	0.213125i	−0.00335510	−	0.0103259i
$427$	0.691986	−	0.502757i	0.0334875	−	0.0243301i
$428$	−2.27455			−0.109944
$429$	−1.12201	−	3.55930i	−0.0541713	−	0.171844i
$430$	0.452910			0.0218413
$431$	22.4249	−	16.2927i	1.08017	−	0.784791i	0.102459	−	0.994737i	$-0.467329\pi$
$431$	22.4249	−	16.2927i	1.08017	−	0.784791i	0.977713	+	0.209947i	$0.0673290\pi$
$432$	1.48946	+	4.58408i	0.0716616	+	0.220552i
$433$	2.87019	−	8.83352i	0.137932	−	0.424512i	−0.858102	−	0.513479i	$-0.828356\pi$
$433$	2.87019	−	8.83352i	0.137932	−	0.424512i	0.996035	+	0.0889667i	$0.0283565\pi$
$434$	−1.40715	−	1.02235i	−0.0675452	−	0.0490744i
$435$	−2.88346	−	2.09496i	−0.138251	−	0.100445i
$436$	−5.60207	+	17.2414i	−0.268290	+	0.825713i
$437$	−13.2823	−	40.8788i	−0.635380	−	1.95550i
$438$	−0.595442	+	0.432614i	−0.0284513	+	0.0206711i
$439$	−14.7118			−0.702156			−0.351078	−	0.936346i	$-0.614185\pi$
$439$	−14.7118			−0.702156			−0.351078	+	0.936346i	$0.614185\pi$
$440$	−6.01928	+	4.29298i	−0.286958	+	0.204660i
$441$	−2.95198			−0.140571
$442$	1.35091	−	0.981494i	0.0642563	−	0.0466849i
$443$	0.755067	+	2.32386i	0.0358743	+	0.110410i	0.967390	−	0.253291i	$-0.0815130\pi$
$443$	0.755067	+	2.32386i	0.0358743	+	0.110410i	−0.931516	+	0.363701i	$0.881513\pi$
$444$	−0.525789	+	1.61821i	−0.0249528	+	0.0767970i
$445$	3.50416	+	2.54592i	0.166113	+	0.120688i
$446$	−3.20712	−	2.33011i	−0.151861	−	0.110334i
$447$	−0.0624272	+	0.192131i	−0.00295271	+	0.00908750i
$448$	−2.10068	−	6.46522i	−0.0992477	−	0.305453i
$449$	−3.85849	+	2.80335i	−0.182093	+	0.132298i	−0.675098	−	0.737728i	$-0.735899\pi$
$449$	−3.85849	+	2.80335i	−0.182093	+	0.132298i	0.493005	+	0.870027i	$0.335899\pi$
$450$	−0.819782			−0.0386449
$451$	7.10376	−	21.2268i	0.334503	−	0.999530i
$452$	−6.42593			−0.302250
$453$	3.20812	−	2.33084i	0.150731	−	0.109512i
$454$	−1.79492	−	5.52420i	−0.0842398	−	0.259264i
$455$	−3.95989	+	12.1873i	−0.185643	+	0.571349i
$456$	0.960995	+	0.698203i	0.0450027	+	0.0326964i
$457$	−25.1503	−	18.2728i	−1.17648	−	0.854764i	−0.184712	−	0.982793i	$-0.559135\pi$
$457$	−25.1503	−	18.2728i	−1.17648	−	0.854764i	−0.991770	+	0.128028i	$0.959135\pi$
$458$	−1.38666	+	4.26770i	−0.0647944	+	0.199417i
$459$	−0.579376	−	1.78313i	−0.0270429	−	0.0832296i
$460$	−27.8680	+	20.2473i	−1.29935	+	0.944034i
$461$	29.7215			1.38427			0.692134	−	0.721769i	$-0.256671\pi$
$461$	29.7215			1.38427			0.692134	+	0.721769i	$0.256671\pi$
$462$	−0.164397	−	0.00144427i	−0.00764846	−	6.71937e-5i
$463$	−25.4553			−1.18301			−0.591505	−	0.806302i	$-0.701466\pi$
$463$	−25.4553			−1.18301			−0.591505	+	0.806302i	$0.701466\pi$
$464$	−19.4865	+	14.1578i	−0.904640	+	0.657259i
$465$	1.29931	+	3.99886i	0.0602540	+	0.185443i
$466$	−1.41306	+	4.34896i	−0.0654589	+	0.201462i
$467$	2.57665	+	1.87204i	0.119233	+	0.0866279i	0.645804	−	0.763503i	$-0.276522\pi$
$467$	2.57665	+	1.87204i	0.119233	+	0.0866279i	−0.526571	+	0.850131i	$0.676522\pi$
$468$	−23.8992	−	17.3638i	−1.10474	−	0.802643i
$469$	−0.508852	+	1.56609i	−0.0234966	+	0.0723151i
$470$	−1.17789	−	3.62517i	−0.0543320	−	0.167217i
$471$	−2.17581	+	1.58082i	−0.100256	+	0.0728402i
$472$	−2.56927			−0.118260
$473$	2.13891	+	1.58290i	0.0983472	+	0.0727820i
$474$	−0.121590			−0.00558479
$475$	6.02709	−	4.37894i	0.276542	−	0.200920i
$476$	0.865708	+	2.66437i	0.0396796	+	0.122121i
$477$	−6.00389	+	18.4781i	−0.274899	+	0.846052i
$478$	−3.12952	−	2.27373i	−0.143141	−	0.103998i
$479$	−2.61599	−	1.90062i	−0.119527	−	0.0868418i	0.526416	−	0.850227i	$-0.323536\pi$
$479$	−2.61599	−	1.90062i	−0.119527	−	0.0868418i	−0.645943	+	0.763386i	$0.723536\pi$
$480$	0.443164	−	1.36392i	0.0202276	−	0.0622541i
$481$	−6.32232	−	19.4581i	−0.288273	−	0.887213i
$482$	4.42019	−	3.21146i	0.201334	−	0.146278i
$483$	−1.55208			−0.0706220
$484$	−21.4338	−	0.376632i	−0.974264	−	0.0171196i
$485$	30.1398			1.36858
$486$	1.05976	−	0.769958i	0.0480715	−	0.0349260i
$487$	3.05029	+	9.38784i	0.138222	+	0.425404i	0.996077	−	0.0884878i	$-0.0282034\pi$
$487$	3.05029	+	9.38784i	0.138222	+	0.425404i	−0.857855	+	0.513891i	$0.828203\pi$
$488$	0.236105	−	0.726655i	0.0106880	−	0.0328941i
$489$	1.43581	+	1.04318i	0.0649296	+	0.0471741i
$490$	0.456703	+	0.331814i	0.0206317	+	0.0149898i
$491$	1.30591	−	4.01917i	0.0589348	−	0.181383i	−0.917255	−	0.398300i	$-0.869600\pi$
$491$	1.30591	−	4.01917i	0.0589348	−	0.181383i	0.976190	+	0.216918i	$0.0696003\pi$
$492$	0.890628	+	2.74107i	0.0401526	+	0.123577i
$493$	7.57995	−	5.50716i	0.341384	−	0.248030i
$494$	−7.04910			−0.317154
$495$	−19.6396	−	14.5343i	−0.882733	−	0.653267i
$496$	28.4152			1.27588
$497$	−3.65738	+	2.65724i	−0.164056	+	0.119194i
$498$	−0.0344314	−	0.105969i	−0.00154291	−	0.00474859i
$499$	−6.30249	+	19.3971i	−0.282138	+	0.868332i	0.705104	+	0.709104i	$0.250900\pi$
$499$	−6.30249	+	19.3971i	−0.282138	+	0.868332i	−0.987242	+	0.159228i	$0.949100\pi$
$500$	14.8425	+	10.7837i	0.663776	+	0.482261i
$501$	−2.31378	−	1.68106i	−0.103372	−	0.0751042i
$502$	0.831480	−	2.55903i	0.0371108	−	0.114215i
$503$	−7.40382	−	22.7866i	−0.330120	−	1.01600i	−0.969076	−	0.246762i	$-0.920634\pi$
$503$	−7.40382	−	22.7866i	−0.330120	−	1.01600i	0.638956	−	0.769243i	$-0.279366\pi$
$504$	−2.13331	+	1.54994i	−0.0950252	+	0.0690398i
$505$	9.21692			0.410147
$506$	5.31381	+	0.0466832i	0.236228	+	0.00207532i
$507$	−2.92934			−0.130097
$508$	−0.455971	+	0.331282i	−0.0202304	+	0.0146983i
$509$	1.14133	+	3.51264i	0.0505884	+	0.155695i	0.973159	−	0.230132i	$-0.0739159\pi$
$509$	1.14133	+	3.51264i	0.0505884	+	0.155695i	−0.922571	+	0.385828i	$0.873916\pi$
$510$	−0.0549509	+	0.169121i	−0.00243327	+	0.00748882i
$511$	12.0122	+	8.72740i	0.531390	+	0.386078i
$512$	−13.1822	−	9.57742i	−0.582576	−	0.423266i
$513$	−2.44582	+	7.52746i	−0.107986	+	0.332346i
$514$	1.60504	+	4.93980i	0.0707952	+	0.217885i
$515$	−2.32491	+	1.68915i	−0.102448	+	0.0744328i
$516$	−0.342618			−0.0150829
$517$	7.10714	−	21.2369i	0.312572	−	0.933997i
$518$	−0.901299			−0.0396008
$519$	1.04811	−	0.761497i	0.0460069	−	0.0334260i
$520$	3.53725	+	10.8865i	0.155119	+	0.477406i
$521$	−0.0736294	+	0.226608i	−0.00322576	+	0.00992787i	−0.952656	−	0.304049i	$-0.901661\pi$
$521$	−0.0736294	+	0.226608i	−0.00322576	+	0.00992787i	0.949431	+	0.313977i	$0.101661\pi$
$522$	3.52111	+	2.55823i	0.154115	+	0.111971i
$523$	17.7914	+	12.9262i	0.777966	+	0.565225i	0.904368	−	0.426754i	$-0.140343\pi$
$523$	17.7914	+	12.9262i	0.777966	+	0.565225i	−0.126402	+	0.991979i	$0.540343\pi$
$524$	9.94018	−	30.5927i	0.434239	−	1.33645i
$525$	−0.0831292	−	0.255845i	−0.00362806	−	0.0111660i
$526$	−0.354624	+	0.257649i	−0.0154623	+	0.0112340i
$527$	−11.0531			−0.481479
$528$	2.18668	−	1.55955i	0.0951630	−	0.0678707i
$529$	27.1678			1.18121
$530$	3.00587	−	2.18389i	0.130567	−	0.0948622i
$531$	−2.62375	−	8.07508i	−0.113861	−	0.350429i
$532$	3.65457	−	11.2476i	0.158446	−	0.487645i
$533$	−28.0373	−	20.3703i	−1.21443	−	0.882336i
$534$	0.0696046	+	0.0505707i	0.00301208	+	0.00218841i
$535$	−0.900048	+	2.77006i	−0.0389125	+	0.119760i
$536$	0.454542	+	1.39894i	0.0196332	+	0.0604249i
$537$	0.768521	−	0.558363i	0.0331641	−	0.0240951i
$538$	1.62573			0.0700900
$539$	0.997144	+	3.16318i	0.0429500	+	0.136248i
$540$	6.34305			0.272961
$541$	−23.1629	+	16.8288i	−0.995851	+	0.723528i	−0.961195	−	0.275871i	$-0.911034\pi$
$541$	−23.1629	+	16.8288i	−0.995851	+	0.723528i	−0.0346561	+	0.999399i	$0.511034\pi$
$542$	0.0832618	+	0.256253i	0.00357640	+	0.0110070i
$543$	−0.733399	+	2.25717i	−0.0314731	+	0.0968644i
$544$	3.04995	+	2.21592i	0.130765	+	0.0950066i
$545$	18.7807	+	13.6450i	0.804477	+	0.584486i
$546$	−0.0786569	+	0.242081i	−0.00336621	+	0.0103601i
$547$	1.98033	+	6.09482i	0.0846727	+	0.260596i	0.984425	−	0.175805i	$-0.0562529\pi$
$547$	1.98033	+	6.09482i	0.0846727	+	0.260596i	−0.899752	+	0.436401i	$0.856253\pi$
$548$	14.7035	−	10.6827i	0.628103	−	0.456343i
$549$	2.52495			0.107762
$550$	0.276913	+	0.878433i	0.0118076	+	0.0374565i
$551$	−39.5524			−1.68499
$552$	−1.12164	+	0.814919i	−0.0477402	+	0.0346853i
$553$	0.757990	+	2.33285i	0.0322330	+	0.0992030i
$554$	0.722815	−	2.22460i	0.0307095	−	0.0945141i
$555$	1.76269	+	1.28067i	0.0748218	+	0.0543612i
$556$	7.60961	+	5.52871i	0.322719	+	0.234469i
$557$	−6.95884	+	21.4171i	−0.294855	+	0.907471i	0.688415	+	0.725317i	$0.258307\pi$
$557$	−6.95884	+	21.4171i	−0.294855	+	0.907471i	−0.983270	+	0.182154i	$0.941693\pi$
$558$	−1.58664	−	4.88317i	−0.0671677	−	0.206721i
$559$	3.33298	−	2.42155i	0.140970	−	0.102421i
$560$	−9.22243			−0.389719
$561$	−0.850583	+	0.606640i	−0.0359116	+	0.0256124i
$562$	−2.97498			−0.125492
$563$	24.1303	−	17.5317i	1.01697	−	0.738873i	0.0513116	−	0.998683i	$-0.483660\pi$
$563$	24.1303	−	17.5317i	1.01697	−	0.738873i	0.965660	+	0.259810i	$0.0836598\pi$
$564$	0.891053	+	2.74238i	0.0375201	+	0.115475i
$565$	−2.54277	+	7.82583i	−0.106975	+	0.329235i
$566$	−0.0549082	−	0.0398932i	−0.00230797	−	0.00167684i
$567$	−6.93339	−	5.03741i	−0.291175	−	0.211551i
$568$	−1.24789	+	3.84062i	−0.0523604	+	0.161149i
$569$	9.04690	+	27.8435i	0.379266	+	1.16726i	0.940555	+	0.339640i	$0.110305\pi$
$569$	9.04690	+	27.8435i	0.379266	+	1.16726i	−0.561290	+	0.827619i	$0.689695\pi$
$570$	0.607316	−	0.441241i	0.0254376	−	0.0184815i
$571$	37.9252			1.58712			0.793559	−	0.608493i	$-0.208226\pi$
$571$	37.9252			1.58712			0.793559	+	0.608493i	$0.208226\pi$
$572$	−10.5332	+	31.4744i	−0.440416	+	1.31601i
$573$	−2.55409			−0.106699
$574$	−1.23513	+	0.897372i	−0.0515532	+	0.0374556i
$575$	2.68699	+	8.26969i	0.112055	+	0.344870i
$576$	6.20116	−	19.0852i	0.258382	−	0.795217i
$577$	−7.09721	−	5.15642i	−0.295461	−	0.214665i	0.430172	−	0.902747i	$-0.358453\pi$
$577$	−7.09721	−	5.15642i	−0.295461	−	0.214665i	−0.725633	+	0.688082i	$0.758453\pi$
$578$	2.73297	+	1.98562i	0.113676	+	0.0825908i
$579$	−1.51989	+	4.67773i	−0.0631643	+	0.194400i
$580$	9.79515	+	30.1464i	0.406721	+	1.25176i
$581$	−1.81851	+	1.32122i	−0.0754444	+	0.0548136i
$582$	0.598679			0.0248161
$583$	21.8281	+	0.191765i	0.904027	+	0.00794211i
$584$	13.2632			0.548836
$585$	−30.6036	+	22.2348i	−1.26530	+	0.919296i
$586$	1.12852	+	3.47324i	0.0466189	+	0.143478i
$587$	2.83372	−	8.72130i	0.116960	−	0.359966i	−0.875391	−	0.483416i	$-0.839396\pi$
$587$	2.83372	−	8.72130i	0.116960	−	0.359966i	0.992351	+	0.123450i	$0.0393958\pi$
$588$	−0.345487	−	0.251011i	−0.0142477	−	0.0103515i
$589$	37.7489	+	27.4262i	1.55542	+	1.13008i
$590$	−0.501747	+	1.54422i	−0.0206566	+	0.0635745i
$591$	−1.63207	−	5.02300i	−0.0671345	−	0.206619i
$592$	11.9123	−	8.65480i	0.489593	−	0.355710i
$593$	7.25596			0.297967			0.148983	−	0.988840i	$-0.452400\pi$
$593$	7.25596			0.297967			0.148983	+	0.988840i	$0.452400\pi$
$594$	−0.786562	−	0.582097i	−0.0322730	−	0.0238837i
$595$	3.58738			0.147068
$596$	1.45352	−	1.05605i	0.0595386	−	0.0432573i
$597$	−1.26766	−	3.90144i	−0.0518817	−	0.159675i
$598$	2.54243	−	7.82479i	0.103968	−	0.319979i
$599$	16.1949	+	11.7663i	0.661708	+	0.480759i	0.867239	−	0.497892i	$-0.165892\pi$
$599$	16.1949	+	11.7663i	0.661708	+	0.480759i	−0.205532	+	0.978650i	$0.565892\pi$
$600$	−0.194407	−	0.141245i	−0.00793663	−	0.00576630i
$601$	−3.48280	+	10.7189i	−0.142066	+	0.437235i	−0.996622	−	0.0821246i	$-0.973829\pi$
$601$	−3.48280	+	10.7189i	−0.142066	+	0.437235i	0.854556	+	0.519360i	$0.173829\pi$
$602$	−0.0560832	−	0.172606i	−0.00228578	−	0.00703491i
$603$	−3.93261	+	2.85721i	−0.160148	+	0.116354i
$604$	−35.2668			−1.43499
$605$	−8.94012	+	25.9542i	−0.363468	+	1.05519i
$606$	0.183079			0.00743709
$607$	10.9428	−	7.95040i	0.444154	−	0.322697i	−0.343129	−	0.939288i	$-0.611487\pi$
$607$	10.9428	−	7.95040i	0.444154	−	0.322697i	0.787283	+	0.616591i	$0.211487\pi$
$608$	−4.91792	−	15.1358i	−0.199448	−	0.613838i
$609$	−0.441343	+	1.35832i	−0.0178841	+	0.0550417i
$610$	−0.390637	−	0.283814i	−0.0158164	−	0.0114913i
$611$	−28.0507	−	20.3800i	−1.13481	−	0.824487i
$612$	−2.55555	+	7.86519i	−0.103302	+	0.317931i
$613$	−9.51673	−	29.2895i	−0.384377	−	1.18299i	−0.936931	−	0.349514i	$-0.886347\pi$
$613$	−9.51673	−	29.2895i	−0.384377	−	1.18299i	0.552554	−	0.833477i	$-0.313653\pi$
$614$	5.24093	−	3.80776i	0.211507	−	0.153669i
$615$	3.69064			0.148821
$616$	2.38144	+	1.76239i	0.0959508	+	0.0710085i
$617$	23.6896			0.953707			0.476853	−	0.878983i	$-0.341777\pi$
$617$	23.6896			0.953707			0.476853	+	0.878983i	$0.341777\pi$
$618$	−0.0461807	+	0.0335522i	−0.00185766	+	0.00134967i
$619$	−10.0393	−	30.8977i	−0.403513	−	1.24188i	−0.922131	−	0.386878i	$-0.873553\pi$
$619$	−10.0393	−	30.8977i	−0.403513	−	1.24188i	0.518618	−	0.855006i	$-0.326447\pi$
$620$	11.5554	−	35.5639i	0.464076	−	1.42828i
$621$	−7.47365	−	5.42992i	−0.299907	−	0.217895i
$622$	5.82385	+	4.23127i	0.233515	+	0.169659i
$623$	0.536349	−	1.65071i	0.0214884	−	0.0661344i
$624$	−1.28501	−	3.95485i	−0.0514415	−	0.158321i
$625$	23.9721	−	17.4167i	0.958882	−	0.696669i
$626$	0.00774169			0.000309420
$627$	4.41022	+	0.0387449i	0.176127	+	0.00154732i
$628$	23.9186			0.954456
$629$	−4.63370	+	3.36658i	−0.184758	+	0.134234i
$630$	0.514958	+	1.58488i	0.0205164	+	0.0631431i
$631$	−4.67646	+	14.3927i	−0.186167	+	0.572962i	−0.999967	−	0.00818299i	$-0.997395\pi$
$631$	−4.67646	+	14.3927i	−0.186167	+	0.572962i	0.813800	+	0.581145i	$0.197395\pi$
$632$	1.77264	+	1.28790i	0.0705119	+	0.0512299i
$633$	−1.34136	−	0.974555i	−0.0533143	−	0.0387351i
$634$	1.56509	−	4.81686i	0.0621577	−	0.191302i
$635$	0.223023	+	0.686395i	0.00885041	+	0.0272387i
$636$	−2.27388	+	1.65207i	−0.0901654	+	0.0655090i
$637$	5.13499			0.203456
$638$	1.55187	−	4.63716i	0.0614393	−	0.183587i
$639$	−13.3452			−0.527929
$640$	−13.6940	+	9.94925i	−0.541302	+	0.393279i
$641$	−5.11431	−	15.7402i	−0.202003	−	0.621701i	−0.999823	−	0.0188056i	$-0.994014\pi$
$641$	−5.11431	−	15.7402i	−0.202003	−	0.621701i	0.797820	−	0.602895i	$-0.205986\pi$
$642$	−0.0178780	+	0.0550229i	−0.000705589	+	0.00217158i
$643$	−1.61403	−	1.17266i	−0.0636513	−	0.0462454i	0.555505	−	0.831513i	$-0.312525\pi$
$643$	−1.61403	−	1.17266i	−0.0636513	−	0.0462454i	−0.619156	+	0.785268i	$0.712525\pi$
$644$	11.1672	+	8.11343i	0.440049	+	0.319714i
$645$	−0.135575	+	0.417258i	−0.00533828	+	0.0164295i
$646$	0.609806	+	1.87679i	0.0239925	+	0.0738413i
$647$	−32.7261	+	23.7769i	−1.28660	+	0.934767i	−0.999731	−	0.0232039i	$-0.992613\pi$
$647$	−32.7261	+	23.7769i	−1.28660	+	0.934767i	−0.286866	+	0.957971i	$0.592613\pi$
$648$	−7.65545			−0.300735
$649$	−7.76653	+	5.53913i	−0.304863	+	0.217430i
$650$	1.42602			0.0559329
$651$	1.36309	−	0.990346i	0.0534239	−	0.0388147i
$652$	−4.87747	−	15.0113i	−0.191016	−	0.587888i
$653$	−12.8198	+	39.4552i	−0.501676	+	1.54400i	0.304611	+	0.952477i	$0.401473\pi$
$653$	−12.8198	+	39.4552i	−0.501676	+	1.54400i	−0.806288	+	0.591524i	$0.798527\pi$
$654$	0.373048	+	0.271036i	0.0145873	+	0.0105983i
$655$	−33.3240	−	24.2113i	−1.30208	−	0.946015i
$656$	7.70736	−	23.7208i	0.300922	−	0.926142i
$657$	13.5445	+	41.6856i	0.528421	+	1.62631i
$658$	−1.23572	+	0.897800i	−0.0481732	+	0.0349999i
$659$	−51.1359			−1.99197			−0.995985	−	0.0895158i	$-0.971468\pi$
$659$	−51.1359			−1.99197			−0.995985	+	0.0895158i	$0.971468\pi$
$660$	−1.06266	−	3.37101i	−0.0413639	−	0.131216i
$661$	−42.8840			−1.66800			−0.833998	−	0.551768i	$-0.813954\pi$
$661$	−42.8840			−1.66800			−0.833998	+	0.551768i	$0.813954\pi$
$662$	−1.96875	+	1.43038i	−0.0765178	+	0.0555934i
$663$	0.499848	+	1.53837i	0.0194125	+	0.0597455i
$664$	−0.620472	+	1.90962i	−0.0240790	+	0.0741075i
$665$	−12.2518	−	8.90144i	−0.475104	−	0.345183i
$666$	−2.15249	−	1.56387i	−0.0834072	−	0.0605988i
$667$	14.2655	−	43.9048i	0.552364	−	1.70000i
$668$	7.85995	+	24.1904i	0.304111	+	0.935956i
$669$	3.10671	−	2.25716i	0.120112	−	0.0872668i
$670$	0.929577			0.0359127
$671$	−0.852898	−	2.70560i	−0.0329258	−	0.104448i
$672$	−0.574672			−0.0221685
$673$	20.2313	−	14.6989i	0.779858	−	0.566600i	−0.125078	−	0.992147i	$-0.539918\pi$
$673$	20.2313	−	14.6989i	0.779858	−	0.566600i	0.904936	+	0.425547i	$0.139918\pi$
$674$	0.524618	+	1.61461i	0.0202075	+	0.0621923i
$675$	0.494784	−	1.52279i	0.0190442	−	0.0586121i
$676$	21.0766	+	15.3130i	0.810638	+	0.588963i
$677$	8.02456	+	5.83018i	0.308409	+	0.224072i	0.731213	−	0.682149i	$-0.238954\pi$
$677$	8.02456	+	5.83018i	0.308409	+	0.224072i	−0.422805	+	0.906221i	$0.638954\pi$
$678$	−0.0505080	+	0.155448i	−0.00193975	+	0.00596993i
$679$	−3.73217	−	11.4864i	−0.143228	−	0.440809i
$680$	2.59249	−	1.88356i	0.0994175	−	0.0722310i
$681$	5.62665			0.215614
$682$	−4.69658	+	3.34963i	−0.179841	+	0.128264i
$683$	−39.8980			−1.52666			−0.763328	−	0.646011i	$-0.776436\pi$
$683$	−39.8980			−1.52666			−0.763328	+	0.646011i	$0.776436\pi$
$684$	28.2439	−	20.5204i	1.07993	−	0.784617i
$685$	−7.19174	−	22.1339i	−0.274782	−	0.845692i
$686$	0.0699031	−	0.215140i	0.00266891	−	0.00821407i
$687$	−3.51667	−	2.55501i	−0.134169	−	0.0974798i
$688$	2.39871	+	1.74276i	0.0914499	+	0.0664422i
$689$	10.4438	−	32.1427i	0.397877	−	1.22454i
$690$	0.270752	+	0.833289i	0.0103074	+	0.0317228i
$691$	5.35084	−	3.88762i	0.203556	−	0.147892i	−0.481338	−	0.876535i	$-0.659849\pi$
$691$	5.35084	−	3.88762i	0.203556	−	0.147892i	0.684893	+	0.728643i	$0.259849\pi$
$692$	−11.5218			−0.437995
$693$	−3.10715	+	9.28449i	−0.118031	+	0.352689i
$694$	−6.26194			−0.237700
$695$	9.74430	−	7.07965i	0.369622	−	0.268546i
$696$	0.394239	+	1.21334i	0.0149436	+	0.0459916i
$697$	−2.99804	+	9.22701i	−0.113559	+	0.349498i
$698$	2.02417	+	1.47065i	0.0766159	+	0.0556647i
$699$	−3.58363	−	2.60366i	−0.135545	−	0.0984795i
$700$	−0.739310	+	2.27536i	−0.0279433	+	0.0860006i
$701$	4.51215	+	13.8870i	0.170421	+	0.524503i	0.999395	−	0.0347848i	$-0.0110746\pi$
$701$	4.51215	+	13.8870i	0.170421	+	0.524503i	−0.828973	+	0.559288i	$0.811075\pi$
$702$	−1.22567	+	0.890502i	−0.0462600	+	0.0336098i
$703$	24.1788			0.911920
$704$	−22.5453	−	0.198066i	−0.849709	−	0.00746491i
$705$	3.69240			0.139064
$706$	−5.84167	+	4.24422i	−0.219854	+	0.159733i
$707$	−1.14132	−	3.51261i	−0.0429237	−	0.132105i
$708$	0.379563	−	1.16817i	0.0142648	−	0.0439027i
$709$	3.35261	+	2.43582i	0.125910	+	0.0914790i	0.648958	−	0.760824i	$-0.275205\pi$
$709$	3.35261	+	2.43582i	0.125910	+	0.0914790i	−0.523048	+	0.852303i	$0.675205\pi$
$710$	2.06465	+	1.50006i	0.0774849	+	0.0562961i
$711$	−2.23757	+	6.88654i	−0.0839155	+	0.258265i
$712$	−0.479104	−	1.47453i	−0.0179552	−	0.0552604i
$713$	−44.0593	+	32.0109i	−1.65003	+	1.19882i
$714$	0.0712575			0.00266674
$715$	34.1631	+	25.2824i	1.27763	+	0.945510i
$716$	−8.44832			−0.315729
$717$	3.03155	−	2.20255i	0.113215	−	0.0822557i
$718$	0.250132	+	0.769827i	0.00933484	+	0.0287297i
$719$	5.26017	−	16.1891i	0.196171	−	0.603753i	−0.803790	−	0.594914i	$-0.797186\pi$
$719$	5.26017	−	16.1891i	0.196171	−	0.603753i	0.999961	−	0.00883941i	$-0.00281371\pi$
$720$	−22.0250	−	16.0021i	−0.820825	−	0.596364i
$721$	0.931634	+	0.676872i	0.0346959	+	0.0252080i
$722$	1.24612	−	3.83517i	0.0463759	−	0.142730i
$723$	1.63551	+	5.03357i	0.0608252	+	0.187201i
$724$	17.0761	−	12.4065i	0.634627	−	0.461084i
$725$	8.00136			0.297163
$726$	−0.177581	+	0.515538i	−0.00659066	+	0.0191334i
$727$	−21.6199			−0.801837			−0.400918	−	0.916114i	$-0.631309\pi$
$727$	−21.6199			−0.801837			−0.400918	+	0.916114i	$0.631309\pi$
$728$	3.71090	−	2.69613i	0.137535	−	0.0999252i
$729$	−7.55284	−	23.2453i	−0.279735	−	0.860936i
$730$	2.59015	−	7.97166i	0.0958657	−	0.295044i
$731$	−0.933059	−	0.677907i	−0.0345104	−	0.0250733i
$732$	0.295510	+	0.214700i	0.0109224	+	0.00793555i
$733$	−14.9047	+	45.8719i	−0.550517	+	1.69432i	0.156981	+	0.987602i	$0.449824\pi$
$733$	−14.9047	+	45.8719i	−0.550517	+	1.69432i	−0.707498	+	0.706715i	$0.750176\pi$
$734$	0.160355	+	0.493523i	0.00591883	+	0.0182163i
$735$	−0.442405	+	0.321426i	−0.0163184	+	0.0118560i
$736$	18.5751			0.684688
$737$	4.39001	+	3.24883i	0.161708	+	0.119672i
$738$	−4.50679			−0.165897
$739$	6.60439	−	4.79837i	0.242946	−	0.176511i	−0.459649	−	0.888101i	$-0.652025\pi$
$739$	6.60439	−	4.79837i	0.242946	−	0.176511i	0.702595	+	0.711590i	$0.252025\pi$
$740$	−5.98787	−	18.4288i	−0.220118	−	0.677455i
$741$	2.11010	−	6.49421i	0.0775163	−	0.238571i
$742$	−1.20450	−	0.875124i	−0.0442187	−	0.0321268i
$743$	−15.8254	−	11.4978i	−0.580577	−	0.421814i	0.258355	−	0.966050i	$-0.416820\pi$
$743$	−15.8254	−	11.4978i	−0.580577	−	0.421814i	−0.838932	+	0.544236i	$0.816820\pi$
$744$	0.465086	−	1.43139i	0.0170509	−	0.0524772i
$745$	−0.710943	−	2.18806i	−0.0260469	−	0.0801642i
$746$	−1.45832	+	1.05953i	−0.0533927	+	0.0387921i
$747$	−6.63546			−0.242779
$748$	9.29113	+	0.0816249i	0.339717	+	0.00298450i
$749$	1.16714			0.0426462
$750$	0.377527	−	0.274289i	0.0137853	−	0.0100156i
$751$	0.344955	+	1.06166i	0.0125876	+	0.0387406i	0.957153	−	0.289583i	$-0.0935165\pi$
$751$	0.344955	+	1.06166i	0.0125876	+	0.0387406i	−0.944565	+	0.328323i	$0.893516\pi$
$752$	7.71103	−	23.7321i	0.281192	−	0.865421i
$753$	2.10869	+	1.53206i	0.0768451	+	0.0558312i
$754$	−6.12498	−	4.45006i	−0.223059	−	0.162062i
$755$	−13.9552	+	42.9497i	−0.507882	+	1.56310i
$756$	−0.785450	−	2.41737i	−0.0285665	−	0.0879188i
$757$	21.5015	−	15.6218i	0.781485	−	0.567782i	−0.123939	−	0.992290i	$-0.539553\pi$
$757$	21.5015	−	15.6218i	0.781485	−	0.567782i	0.905424	+	0.424508i	$0.139553\pi$
$758$	−2.62885			−0.0954840
$759$	−1.63366	+	4.88155i	−0.0592981	+	0.177189i
$760$	−13.5277			−0.490701
$761$	−5.09683	+	3.70306i	−0.184760	+	0.134236i	−0.676321	−	0.736607i	$-0.736427\pi$
$761$	−5.09683	+	3.70306i	−0.184760	+	0.134236i	0.491561	+	0.870843i	$0.336427\pi$
$762$	0.00443000	+	0.0136341i	0.000160482	+	0.000493913i
$763$	2.87458	−	8.84705i	0.104067	−	0.320285i
$764$	18.3766	+	13.3514i	0.664844	+	0.483037i
$765$	8.56739	+	6.22457i	0.309755	+	0.225050i
$766$	0.879273	−	2.70613i	0.0317694	−	0.0977763i
$767$	4.56403	+	14.0466i	0.164797	+	0.507195i
$768$	2.13826	−	1.55354i	0.0771578	−	0.0560584i
$769$	13.1916			0.475700			0.237850	−	0.971302i	$-0.423557\pi$
$769$	13.1916			0.475700			0.237850	+	0.971302i	$0.423557\pi$
$770$	1.52432	−	1.08715i	0.0549327	−	0.0391783i
$771$	−5.03141			−0.181202
$772$	35.3883	−	25.7111i	1.27365	−	0.925362i
$773$	14.1585	+	43.5753i	0.509245	+	1.56729i	0.793515	+	0.608550i	$0.208249\pi$
$773$	14.1585	+	43.5753i	0.509245	+	1.56729i	−0.284270	+	0.958744i	$0.591751\pi$
$774$	0.165557	−	0.509531i	0.00595081	−	0.0183147i
$775$	−7.63652	−	5.54825i	−0.274312	−	0.199299i
$776$	−8.72809	−	6.34133i	−0.313320	−	0.227640i
$777$	0.269797	−	0.830351i	0.00967893	−	0.0297887i
$778$	−0.0306381	−	0.0942944i	−0.00109843	−	0.00338062i
$779$	33.1342	−	24.0734i	1.18716	−	0.862520i
$780$	−5.47237			−0.195942
$781$	4.50786	+	14.3000i	0.161304	+	0.511695i
$782$	−2.30326			−0.0823643
$783$	−6.87723	+	4.99660i	−0.245772	+	0.178564i
$784$	1.14200	+	3.51471i	0.0407857	+	0.125526i
$785$	9.46469	−	29.1293i	0.337809	−	1.03967i
$786$	−0.661929	−	0.480919i	−0.0236102	−	0.0171538i
$787$	15.2483	+	11.0785i	0.543543	+	0.394907i	0.825399	−	0.564549i	$-0.190950\pi$
$787$	15.2483	+	11.0785i	0.543543	+	0.394907i	−0.281856	+	0.959457i	$0.590950\pi$
$788$	−14.5148	+	44.6721i	−0.517070	+	1.59138i
$789$	−0.131214	−	0.403834i	−0.00467133	−	0.0143769i
$790$	1.12025	−	0.813909i	0.0398567	−	0.0289576i
$791$	3.29733			0.117240
$792$	2.62938	+	8.34104i	0.0934311	+	0.296386i
$793$	−4.39217			−0.155970
$794$	−3.07724	+	2.23574i	−0.109207	+	0.0793435i
$795$	1.11220	+	3.42299i	0.0394455	+	0.121401i
$796$	−11.2739	+	34.6975i	−0.399593	+	1.22982i
$797$	22.7830	+	16.5528i	0.807016	+	0.586331i	0.912964	−	0.408040i	$-0.133788\pi$
$797$	22.7830	+	16.5528i	0.807016	+	0.586331i	−0.105948	+	0.994372i	$0.533788\pi$
$798$	−0.243362	−	0.176813i	−0.00861492	−	0.00625911i
$799$	−2.99947	+	9.23141i	−0.106114	+	0.326584i
$800$	0.994884	+	3.06194i	0.0351744	+	0.108256i
$801$	4.14511	−	3.01160i	0.146460	−	0.106410i
$802$	8.33835			0.294437
$803$	40.0928	−	28.5944i	1.41485	−	1.00907i
$804$	−0.703208			−0.0248002
$805$	14.2999	−	10.3895i	0.504004	−	0.366180i
$806$	2.75996	+	8.49429i	0.0972155	+	0.299199i
$807$	−0.486649	+	1.49775i	−0.0171309	+	0.0527234i
$808$	−2.66910	−	1.93921i	−0.0938985	−	0.0682213i
$809$	5.29544	+	3.84736i	0.186178	+	0.135266i	0.676970	−	0.736011i	$-0.263293\pi$
$809$	5.29544	+	3.84736i	0.186178	+	0.135266i	−0.490792	+	0.871277i	$0.663293\pi$
$810$	−1.49502	+	4.60119i	−0.0525296	+	0.161670i
$811$	5.81096	+	17.8843i	0.204050	+	0.628002i	0.999751	+	0.0223122i	$0.00710279\pi$
$811$	5.81096	+	17.8843i	0.204050	+	0.628002i	−0.795701	+	0.605690i	$0.792897\pi$
$812$	10.2760	−	7.46596i	0.360617	−	0.262004i
$813$	−0.261006			−0.00915387
$814$	−0.948675	+	2.83474i	−0.0332511	+	0.0993576i
$815$	−20.2116			−0.707980
$816$	−0.941797	+	0.684256i	−0.0329695	+	0.0239537i
$817$	1.50452	+	4.63044i	0.0526365	+	0.161999i
$818$	1.13760	−	3.50116i	0.0397751	−	0.122415i
$819$	12.2634	+	8.90988i	0.428518	+	0.311336i
$820$	−26.5542	−	19.2927i	−0.927311	−	0.673731i
$821$	−3.58089	+	11.0208i	−0.124974	+	0.384630i	−0.993896	−	0.110318i	$-0.964813\pi$
$821$	−3.58089	+	11.0208i	−0.124974	+	0.384630i	0.868922	+	0.494948i	$0.164813\pi$
$822$	−0.142852	−	0.439654i	−0.00498255	−	0.0153347i
$823$	−9.98844	+	7.25702i	−0.348175	+	0.252964i	−0.748103	−	0.663583i	$-0.769035\pi$
$823$	−9.98844	+	7.25702i	−0.348175	+	0.252964i	0.399928	+	0.916547i	$0.369035\pi$
$824$	1.02866			0.0358349
$825$	−0.892177	−	0.00783800i	−0.0310616	−	0.000272884i
$826$	0.650640			0.0226387
$827$	3.63717	−	2.64256i	0.126477	−	0.0918907i	−0.522748	−	0.852487i	$-0.675093\pi$
$827$	3.63717	−	2.64256i	0.126477	−	0.0918907i	0.649225	+	0.760596i	$0.275093\pi$
$828$	12.5916	+	38.7531i	0.437590	+	1.34676i
$829$	−6.13796	+	18.8907i	−0.213180	+	0.656101i	0.786098	+	0.618102i	$0.212098\pi$
$829$	−6.13796	+	18.8907i	−0.213180	+	0.656101i	−0.999278	+	0.0379987i	$0.987902\pi$
$830$	1.02658	+	0.745851i	0.0356330	+	0.0258889i
$831$	1.83311	+	1.33183i	0.0635900	+	0.0462008i
$832$	−10.7869	+	33.1988i	−0.373970	+	1.15096i
$833$	−0.444220	−	1.36717i	−0.0153913	−	0.0473695i
$834$	0.193555	−	0.140626i	0.00670226	−	0.00486947i
$835$	32.5706			1.12715
$836$	−31.5290	−	23.3331i	−1.09045	−	0.806991i
$837$	10.0284			0.346631
$838$	−1.01817	+	0.739747i	−0.0351722	+	0.0255541i
$839$	−13.5513	−	41.7065i	−0.467842	−	1.43987i	−0.855373	−	0.518012i	$-0.826672\pi$
$839$	−13.5513	−	41.7065i	−0.467842	−	1.43987i	0.387532	−	0.921856i	$-0.373328\pi$
$840$	−0.150948	+	0.464570i	−0.00520820	+	0.0160292i
$841$	−10.9057	−	7.92348i	−0.376060	−	0.273224i
$842$	−3.93311	−	2.85757i	−0.135544	−	0.0984785i
$843$	0.890538	−	2.74079i	0.0306717	−	0.0943979i
$844$	4.55662	+	14.0238i	0.156845	+	0.482720i
$845$	26.9891	−	19.6087i	0.928453	−	0.674561i
$846$	−4.50894			−0.155021
$847$	10.9983	+	0.193261i	0.377906	+	0.00664052i
$848$	24.3232			0.835261
$849$	0.0531893	−	0.0386443i	0.00182545	−	0.00132627i
$850$	−0.123362	−	0.379670i	−0.00423129	−	0.0130226i
$851$	−8.72066	+	26.8394i	−0.298940	+	0.920044i
$852$	−1.56187	−	1.13476i	−0.0535088	−	0.0388764i
$853$	−31.6655	−	23.0063i	−1.08421	−	0.787721i	−0.105794	−	0.994388i	$-0.533738\pi$
$853$	−31.6655	−	23.0063i	−1.08421	−	0.787721i	−0.978411	+	0.206667i	$0.933738\pi$
$854$	−0.0597911	+	0.184018i	−0.00204601	+	0.00629697i
$855$	−13.8146	−	42.5169i	−0.472449	−	1.45405i
$856$	0.843455	−	0.612806i	0.0288287	−	0.0209453i
$857$	35.0524			1.19737			0.598684	−	0.800986i	$-0.295691\pi$
$857$	35.0524			1.19737			0.598684	+	0.800986i	$0.295691\pi$
$858$	0.678595	+	0.502195i	0.0231669	+	0.0171447i
$859$	−32.5206			−1.10959			−0.554794	−	0.831988i	$-0.687203\pi$
$859$	−32.5206			−1.10959			−0.554794	+	0.831988i	$0.687203\pi$
$860$	3.15667	−	2.29345i	0.107642	−	0.0782061i
$861$	−0.457007	−	1.40652i	−0.0155748	−	0.0479342i
$862$	−1.93763	+	5.96341i	−0.0659959	+	0.203114i
$863$	−10.2696	−	7.46132i	−0.349582	−	0.253986i	0.399111	−	0.916902i	$-0.369319\pi$
$863$	−10.2696	−	7.46132i	−0.349582	−	0.253986i	−0.748694	+	0.662916i	$0.769319\pi$
$864$	−2.76719	−	2.01048i	−0.0941418	−	0.0683981i
$865$	−4.55924	+	14.0319i	−0.155019	+	0.477099i
$866$	0.649269	+	1.99824i	0.0220630	+	0.0679031i
$867$	−2.64741	+	1.92345i	−0.0899107	+	0.0653239i
$868$	−14.9844			−0.508605
$869$	8.13505	+	0.0714685i	0.275963	+	0.00242440i
$870$	0.806251			0.0273345
$871$	6.84079	−	4.97012i	0.231791	−	0.168406i
$872$	−2.56778	−	7.90281i	−0.0869559	−	0.267623i
$873$	11.0173	−	33.9078i	0.372879	−	1.14760i
$874$	7.86619	+	5.71512i	0.266078	+	0.193317i
$875$	−7.61610	−	5.53342i	−0.257471	−	0.187064i
$876$	−1.95940	+	6.03041i	−0.0662020	+	0.203749i
$877$	−8.69388	−	26.7570i	−0.293571	−	0.903520i	−0.983698	−	0.179831i	$-0.942445\pi$
$877$	−8.69388	−	26.7570i	−0.293571	−	0.903520i	0.690126	−	0.723689i	$-0.257555\pi$
$878$	2.69239	−	1.95614i	0.0908638	−	0.0660164i
$879$	−3.53765			−0.119322
$880$	−9.70720	+	29.0061i	−0.327230	+	0.977797i
$881$	−36.7964			−1.23970			−0.619850	−	0.784720i	$-0.712807\pi$
$881$	−36.7964			−1.23970			−0.619850	+	0.784720i	$0.712807\pi$
$882$	0.540239	−	0.392506i	0.0181908	−	0.0132164i
$883$	−0.705855	−	2.17240i	−0.0237539	−	0.0731070i	0.938477	−	0.345342i	$-0.112237\pi$
$883$	−0.705855	−	2.17240i	−0.0237539	−	0.0731070i	−0.962231	+	0.272235i	$0.912237\pi$
$884$	4.44540	−	13.6815i	0.149515	−	0.460159i
$885$	−1.27247	−	0.924502i	−0.0427735	−	0.0310768i
$886$	−0.447173	−	0.324890i	−0.0150231	−	0.0109149i
$887$	13.0614	−	40.1989i	0.438560	−	1.34975i	−0.450835	−	0.892607i	$-0.648874\pi$
$887$	13.0614	−	40.1989i	0.438560	−	1.34975i	0.889395	−	0.457140i	$-0.151126\pi$
$888$	−0.241002	−	0.741728i	−0.00808750	−	0.0248908i
$889$	0.233972	−	0.169990i	0.00784716	−	0.00570130i
$890$	−0.979808			−0.0328432
$891$	−23.1413	+	16.5045i	−0.775264	+	0.552922i
$892$	−34.1520			−1.14349
$893$	33.1500	−	24.0849i	1.10932	−	0.805971i
$894$	−0.0141217	−	0.0434623i	−0.000472302	−	0.00145360i
$895$	−3.34304	+	10.2888i	−0.111745	+	0.343917i
$896$	5.48741	+	3.98684i	0.183322	+	0.133191i
$897$	6.44778	+	4.68459i	0.215285	+	0.156414i
$898$	0.333393	−	1.02608i	0.0111255	−	0.0342406i
$899$	15.4861	+	47.6614i	0.516491	+	1.58960i
$900$	−5.71367	+	4.15123i	−0.190456	+	0.138374i
$901$	−9.46132			−0.315202
$902$	1.52234	+	4.82923i	0.0506884	+	0.160796i
$903$	0.175807			0.00585050
$904$	2.38288	−	1.73127i	0.0792535	−	0.0575810i
$905$	−8.35220	−	25.7054i	−0.277636	−	0.854477i
$906$	−0.277198	+	0.853128i	−0.00920929	+	0.0283433i
$907$	−31.9793	−	23.2343i	−1.06185	−	0.771483i	−0.0874240	−	0.996171i	$-0.527864\pi$
$907$	−31.9793	−	23.2343i	−1.06185	−	0.771483i	−0.974431	+	0.224689i	$0.927864\pi$
$908$	−40.4837	−	29.4131i	−1.34350	−	0.976108i
$909$	3.36915	−	10.3692i	0.111748	−	0.343924i
$910$	−0.895772	−	2.75690i	−0.0296946	−	0.0913905i
$911$	28.5013	−	20.7074i	0.944291	−	0.686067i	−0.00515893	−	0.999987i	$-0.501642\pi$
$911$	28.5013	−	20.7074i	0.944291	−	0.686067i	0.949450	+	0.313919i	$0.101642\pi$
$912$	4.91433			0.162730
$913$	2.24138	+	7.11019i	0.0741788	+	0.235313i
$914$	7.03234			0.232609
$915$	0.378408	−	0.274929i	0.0125098	−	0.00908888i
$916$	11.9462	+	36.7666i	0.394713	+	1.21480i
$917$	−5.10059	+	15.6980i	−0.168436	+	0.518394i
$918$	0.343123	+	0.249293i	0.0113247	+	0.00822791i
$919$	32.0455	+	23.2824i	1.05708	+	0.768017i	0.973547	−	0.228488i	$-0.0733780\pi$
$919$	32.0455	+	23.2824i	1.05708	+	0.768017i	0.0835379	+	0.996505i	$0.473378\pi$
$920$	4.87909	−	15.0163i	0.160859	−	0.495073i
$921$	1.93919	+	5.96821i	0.0638984	+	0.196659i
$922$	−5.43930	+	3.95188i	−0.179134	+	0.130148i
$923$	23.2141			0.764101
$924$	−1.15312	+	0.822412i	−0.0379349	+	0.0270554i
$925$	−4.89131			−0.160825
$926$	4.65855	−	3.38463i	0.153089	−	0.111226i
$927$	1.05047	+	3.23302i	0.0345020	+	0.106186i
$928$	5.28196	−	16.2562i	0.173389	−	0.533636i
$929$	−2.11685	−	1.53798i	−0.0694516	−	0.0504595i	0.552518	−	0.833501i	$-0.313667\pi$
$929$	−2.11685	−	1.53798i	−0.0694516	−	0.0504595i	−0.621969	+	0.783042i	$0.713667\pi$
$930$	−0.769488	−	0.559066i	−0.0252325	−	0.0183325i
$931$	−1.87526	+	5.77147i	−0.0614593	+	0.189152i
$932$	12.1736	+	37.4666i	0.398761	+	1.22726i
$933$	−5.64152	+	4.09881i	−0.184695	+	0.134189i
$934$	−0.720463			−0.0235743
$935$	3.77594	−	11.2829i	0.123487	−	0.368991i
$936$	13.5405			0.442586
$937$	−43.5575	+	31.6464i	−1.42296	+	1.03384i	−0.431689	+	0.902022i	$0.642082\pi$
$937$	−43.5575	+	31.6464i	−1.42296	+	1.03384i	−0.991274	+	0.131820i	$0.957918\pi$
$938$	−0.115108	−	0.354266i	−0.00375841	−	0.0115672i
$939$	−0.00231742	+	0.00713228i	−7.56261e−5	+	0.000232753i
$940$	−26.5668	−	19.3019i	−0.866514	−	0.629559i
$941$	−23.9854	−	17.4264i	−0.781902	−	0.568085i	0.123647	−	0.992326i	$-0.460541\pi$
$941$	−23.9854	−	17.4264i	−0.781902	−	0.568085i	−0.905549	+	0.424241i	$0.860541\pi$
$942$	0.188001	−	0.578607i	0.00612540	−	0.0188520i
$943$	14.7718	+	45.4630i	0.481037	+	1.48048i
$944$	−8.59940	+	6.24783i	−0.279887	+	0.203349i
$945$	−3.25480			−0.105879
$946$	−0.601908	−	0.00528791i	−0.0195697	−	0.000171925i
$947$	−15.7861			−0.512980			−0.256490	−	0.966547i	$-0.582566\pi$
$947$	−15.7861			−0.512980			−0.256490	+	0.966547i	$0.582566\pi$
$948$	−0.847448	+	0.615707i	−0.0275238	+	0.0199972i
$949$	−23.5607	−	72.5123i	−0.764812	−	2.35385i
$950$	−0.520771	+	1.60277i	−0.0168961	+	0.0520007i
$951$	3.96919	+	2.88378i	0.128710	+	0.0935131i
$952$	−1.03886	−	0.754773i	−0.0336695	−	0.0244623i
$953$	−10.8502	+	33.3934i	−0.351472	+	1.08172i	0.606555	+	0.795041i	$0.292551\pi$
$953$	−10.8502	+	33.3934i	−0.351472	+	1.08172i	−0.958027	+	0.286678i	$0.907449\pi$
$954$	−1.35815	−	4.17995i	−0.0439716	−	0.135331i
$955$	23.5318	−	17.0968i	0.761470	−	0.553240i
$956$	−33.3257			−1.07783
$957$	3.80759	+	2.81782i	0.123082	+	0.0910870i
$958$	0.731463			0.0236325
$959$	−7.54479	+	5.48161i	−0.243634	+	0.177011i
$960$	−1.14874	−	3.53546i	−0.0370754	−	0.114106i
$961$	8.68955	−	26.7437i	0.280308	−	0.862700i
$962$	3.74426	+	2.72036i	0.120720	+	0.0877080i
$963$	2.78736	+	2.02514i	0.0898214	+	0.0652591i
$964$	14.5454	−	44.7661i	0.468475	−	1.44182i
$965$	−17.3090	−	53.2716i	−0.557196	−	1.71487i
$966$	0.284044	−	0.206370i	0.00913896	−	0.00663984i
$967$	−49.2820			−1.58480			−0.792401	−	0.610001i	$-0.791169\pi$
$967$	−49.2820			−1.58480			−0.792401	+	0.610001i	$0.791169\pi$
$968$	8.04962	−	5.63500i	0.258725	−	0.181116i
$969$	−1.91160			−0.0614093
$970$	−5.51585	+	4.00750i	−0.177103	+	0.128673i
$971$	11.5394	+	35.5148i	0.370318	+	1.13972i	0.946583	+	0.322460i	$0.104510\pi$
$971$	11.5394	+	35.5148i	0.370318	+	1.13972i	−0.576265	+	0.817263i	$0.695490\pi$
$972$	3.48730	−	10.7328i	0.111855	−	0.344255i
$973$	−3.90471	−	2.83694i	−0.125179	−	0.0909481i
$974$	−1.80647	−	1.31248i	−0.0578831	−	0.0420545i
$975$	−0.426867	+	1.31376i	−0.0136707	+	0.0420741i
$976$	−0.976800	−	3.00628i	−0.0312666	−	0.0962287i
$977$	−32.3999	+	23.5399i	−1.03656	+	0.753108i	−0.969612	−	0.244648i	$-0.921328\pi$
$977$	−32.3999	+	23.5399i	−1.03656	+	0.753108i	−0.0669524	+	0.997756i	$0.521328\pi$
$978$	−0.401470			−0.0128376
$979$	−4.62723	−	3.42439i	−0.147887	−	0.109444i
$980$	4.86335			0.155354
$981$	22.2159	−	16.1408i	0.709299	−	0.515336i
$982$	0.295411	+	0.909181i	0.00942694	+	0.0290131i
$983$	−16.0817	+	49.4944i	−0.512926	+	1.57862i	0.274098	+	0.961702i	$0.411621\pi$
$983$	−16.0817	+	49.4944i	−0.512926	+	1.57862i	−0.787024	+	0.616923i	$0.788379\pi$
$984$	−1.06876	−	0.776500i	−0.0340709	−	0.0247539i
$985$	48.6604	+	35.3538i	1.55045	+	1.12647i
$986$	−0.654946	+	2.01572i	−0.0208577	+	0.0641935i
$987$	−0.457225	−	1.40719i	−0.0145536	−	0.0447915i
$988$	−49.1304	+	35.6953i	−1.56305	+	1.13562i
$989$	−5.68262			−0.180697
$990$	5.52674	+	0.0485539i	0.175651	+	0.00154314i
$991$	45.4828			1.44481			0.722404	−	0.691471i	$-0.243037\pi$
$991$	45.4828			1.44481			0.722404	+	0.691471i	$0.243037\pi$
$992$	−16.3134	+	11.8524i	−0.517951	+	0.376313i
$993$	−0.728455	−	2.24195i	−0.0231168	−	0.0711463i
$994$	0.316016	−	0.972598i	0.0100234	−	0.0308489i
$995$	37.7953	+	27.4599i	1.19819	+	0.870536i
$996$	−0.776586	−	0.564223i	−0.0246071	−	0.0178781i
$997$	8.63992	−	26.5909i	0.273629	−	0.842143i	−0.715950	−	0.698152i	$-0.754006\pi$
$997$	8.63992	−	26.5909i	0.273629	−	0.842143i	0.989579	−	0.143992i	$-0.0459939\pi$
$998$	−1.42569	−	4.38783i	−0.0451296	−	0.138894i
$999$	4.20412	−	3.05447i	0.133012	−	0.0966392i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.f.b.36.3	yes	16
3.2	odd	2		693.2.m.i.190.2		16
7.2	even	3		539.2.q.g.410.2		32
7.3	odd	6		539.2.q.f.520.3		32
7.4	even	3		539.2.q.g.520.3		32
7.5	odd	6		539.2.q.f.410.2		32
7.6	odd	2		539.2.f.e.344.3		16
11.2	odd	10		847.2.a.o.1.5		8
11.3	even	5		847.2.f.w.148.2		16
11.4	even	5	inner	77.2.f.b.15.3	✓	16
11.5	even	5		847.2.f.w.372.2		16
11.6	odd	10		847.2.f.v.372.3		16
11.7	odd	10		847.2.f.x.323.2		16
11.8	odd	10		847.2.f.v.148.3		16
11.9	even	5		847.2.a.p.1.4		8
11.10	odd	2		847.2.f.x.729.2		16
33.2	even	10		7623.2.a.cw.1.4		8
33.20	odd	10		7623.2.a.ct.1.5		8
33.26	odd	10		693.2.m.i.631.2		16
77.4	even	15		539.2.q.g.422.2		32
77.13	even	10		5929.2.a.bs.1.5		8
77.20	odd	10		5929.2.a.bt.1.4		8
77.26	odd	30		539.2.q.f.312.3		32
77.37	even	15		539.2.q.g.312.3		32
77.48	odd	10		539.2.f.e.246.3		16
77.59	odd	30		539.2.q.f.422.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.15.3	✓	16	11.4	even	5	inner
77.2.f.b.36.3	yes	16	1.1	even	1	trivial
539.2.f.e.246.3		16	77.48	odd	10
539.2.f.e.344.3		16	7.6	odd	2
539.2.q.f.312.3		32	77.26	odd	30
539.2.q.f.410.2		32	7.5	odd	6
539.2.q.f.422.2		32	77.59	odd	30
539.2.q.f.520.3		32	7.3	odd	6
539.2.q.g.312.3		32	77.37	even	15
539.2.q.g.410.2		32	7.2	even	3
539.2.q.g.422.2		32	77.4	even	15
539.2.q.g.520.3		32	7.4	even	3
693.2.m.i.190.2		16	3.2	odd	2
693.2.m.i.631.2		16	33.26	odd	10
847.2.a.o.1.5		8	11.2	odd	10
847.2.a.p.1.4		8	11.9	even	5
847.2.f.v.148.3		16	11.8	odd	10
847.2.f.v.372.3		16	11.6	odd	10
847.2.f.w.148.2		16	11.3	even	5
847.2.f.w.372.2		16	11.5	even	5
847.2.f.x.323.2		16	11.7	odd	10
847.2.f.x.729.2		16	11.10	odd	2
5929.2.a.bs.1.5		8	77.13	even	10
5929.2.a.bt.1.4		8	77.20	odd	10
7623.2.a.ct.1.5		8	33.20	odd	10
7623.2.a.cw.1.4		8	33.2	even	10

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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.183009 + 0.132964i) q^{2} +(-0.0677147 - 0.208405i) q^{3} +(-0.602221 + 1.85345i) q^{4} +(2.01892 + 1.46683i) q^{5} +(0.0401026 + 0.0291363i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.276036 - 0.849550i) q^{8} +(2.38820 - 1.73513i) q^{9} +O(q^{10})\)	\(q+(-0.183009 + 0.132964i) q^{2} +(-0.0677147 - 0.208405i) q^{3} +(-0.602221 + 1.85345i) q^{4} +(2.01892 + 1.46683i) q^{5} +(0.0401026 + 0.0291363i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.276036 - 0.849550i) q^{8} +(2.38820 - 1.73513i) q^{9} -0.564516 q^{10} +(-2.66598 - 1.97296i) q^{11} +0.427046 q^{12} +(-4.15429 + 3.01827i) q^{13} +(0.0699031 + 0.215140i) q^{14} +(0.168984 - 0.520079i) q^{15} +(-2.98979 - 2.17221i) q^{16} +(1.16298 + 0.844956i) q^{17} +(-0.206353 + 0.635089i) q^{18} +(-1.87526 - 5.77147i) q^{19} +(-3.93453 + 2.85860i) q^{20} -0.219130 q^{21} +(0.750229 + 0.00659095i) q^{22} +7.08292 q^{23} +(-0.158358 + 0.115054i) q^{24} +(0.379361 + 1.16755i) q^{25} +(0.358952 - 1.10474i) q^{26} +(-1.05516 - 0.766622i) q^{27} +(1.57664 + 1.14549i) q^{28} +(2.01408 - 6.19869i) q^{29} +(0.0382260 + 0.117648i) q^{30} +(-6.22049 + 4.51945i) q^{31} +2.62252 q^{32} +(-0.230648 + 0.689200i) q^{33} -0.325184 q^{34} +(2.01892 - 1.46683i) q^{35} +(1.77775 + 5.47134i) q^{36} +(-1.23122 + 3.78932i) q^{37} +(1.11058 + 0.806887i) q^{38} +(0.910328 + 0.661392i) q^{39} +(0.688853 - 2.12007i) q^{40} +(2.08556 + 6.41868i) q^{41} +(0.0401026 - 0.0291363i) q^{42} -0.802299 q^{43} +(5.26228 - 3.75309i) q^{44} +7.36674 q^{45} +(-1.29624 + 0.941771i) q^{46} +(2.08655 + 6.42174i) q^{47} +(-0.250246 + 0.770178i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-0.224669 - 0.163231i) q^{50} +(0.0973416 - 0.299587i) q^{51} +(-3.09240 - 9.51742i) q^{52} +(-5.32469 + 3.86861i) q^{53} +0.295037 q^{54} +(-2.48840 - 7.89379i) q^{55} -0.893270 q^{56} +(-1.07582 + 0.781627i) q^{57} +(0.455607 + 1.40221i) q^{58} +(0.888810 - 2.73548i) q^{59} +(0.862172 + 0.626405i) q^{60} +(0.691986 + 0.502757i) q^{61} +(0.537482 - 1.65420i) q^{62} +(-0.912213 - 2.80750i) q^{63} +(5.49964 - 3.99573i) q^{64} -12.8145 q^{65} +(-0.0494280 - 0.156797i) q^{66} -1.64668 q^{67} +(-2.26645 + 1.64667i) q^{68} +(-0.479618 - 1.47611i) q^{69} +(-0.174445 + 0.536886i) q^{70} +(-3.65738 - 2.65724i) q^{71} +(-2.13331 - 1.54994i) q^{72} +(-4.58827 + 14.1212i) q^{73} +(-0.278517 - 0.857187i) q^{74} +(0.217635 - 0.158121i) q^{75} +11.8264 q^{76} +(-2.70023 + 1.92582i) q^{77} -0.254539 q^{78} +(-1.98444 + 1.44178i) q^{79} +(-2.84989 - 8.77105i) q^{80} +(2.64832 - 8.15069i) q^{81} +(-1.23513 - 0.897372i) q^{82} +(-1.81851 - 1.32122i) q^{83} +(0.131964 - 0.406145i) q^{84} +(1.10856 + 3.41180i) q^{85} +(0.146828 - 0.106677i) q^{86} -1.42822 q^{87} +(-0.940224 + 2.80949i) q^{88} +1.73566 q^{89} +(-1.34818 + 0.979509i) q^{90} +(1.58680 + 4.88366i) q^{91} +(-4.26549 + 13.1278i) q^{92} +(1.36309 + 0.990346i) q^{93} +(-1.23572 - 0.897800i) q^{94} +(4.67976 - 14.4028i) q^{95} +(-0.177584 - 0.546546i) q^{96} +(9.77095 - 7.09901i) q^{97} +0.226211 q^{98} +(-9.79024 - 0.0860098i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} + 3 q^{6} - 4 q^{7} - 5 q^{8} - 12 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 + 3 * q^6 - 4 * q^7 - 5 * q^8 - 12 * q^9	\( 16 q - 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} + 3 q^{6} - 4 q^{7} - 5 q^{8} - 12 q^{9} + 12 q^{10} - 3 q^{11} + 18 q^{12} - 7 q^{13} + 2 q^{14} - 18 q^{15} + 17 q^{16} - 5 q^{17} + 11 q^{18} + 19 q^{19} + q^{20} + 8 q^{21} - 33 q^{22} + 32 q^{23} - 35 q^{24} + 7 q^{25} - 27 q^{26} + 10 q^{27} + 4 q^{28} + 3 q^{29} - 2 q^{30} - 7 q^{31} + 32 q^{32} - 26 q^{33} - 24 q^{34} - 5 q^{35} + 52 q^{36} + 4 q^{37} - 5 q^{38} + 11 q^{39} - 10 q^{40} - 10 q^{41} + 3 q^{42} - 8 q^{43} - 38 q^{44} + 70 q^{45} - 42 q^{46} - 23 q^{47} - 36 q^{48} - 4 q^{49} + 52 q^{50} - 29 q^{51} + 33 q^{52} + 4 q^{53} + 60 q^{54} - 12 q^{55} - 11 q^{57} + 20 q^{58} + 17 q^{59} - 30 q^{60} - 7 q^{61} + 79 q^{62} - 2 q^{63} + 7 q^{64} - 8 q^{65} + 8 q^{66} - 38 q^{67} - 2 q^{68} + 10 q^{69} - 18 q^{70} - 14 q^{71} - 35 q^{73} - 29 q^{74} + 9 q^{75} + 52 q^{76} - 3 q^{77} - 58 q^{78} + 15 q^{79} - 87 q^{80} - 14 q^{81} + 19 q^{82} + 5 q^{83} + 8 q^{84} + 6 q^{85} - 52 q^{86} - 72 q^{87} + 55 q^{88} + 74 q^{89} - 14 q^{90} + 13 q^{91} - 55 q^{92} + 32 q^{93} - 24 q^{94} + 32 q^{95} - 42 q^{96} + 20 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 + 3 * q^6 - 4 * q^7 - 5 * q^8 - 12 * q^9 + 12 * q^10 - 3 * q^11 + 18 * q^12 - 7 * q^13 + 2 * q^14 - 18 * q^15 + 17 * q^16 - 5 * q^17 + 11 * q^18 + 19 * q^19 + q^20 + 8 * q^21 - 33 * q^22 + 32 * q^23 - 35 * q^24 + 7 * q^25 - 27 * q^26 + 10 * q^27 + 4 * q^28 + 3 * q^29 - 2 * q^30 - 7 * q^31 + 32 * q^32 - 26 * q^33 - 24 * q^34 - 5 * q^35 + 52 * q^36 + 4 * q^37 - 5 * q^38 + 11 * q^39 - 10 * q^40 - 10 * q^41 + 3 * q^42 - 8 * q^43 - 38 * q^44 + 70 * q^45 - 42 * q^46 - 23 * q^47 - 36 * q^48 - 4 * q^49 + 52 * q^50 - 29 * q^51 + 33 * q^52 + 4 * q^53 + 60 * q^54 - 12 * q^55 - 11 * q^57 + 20 * q^58 + 17 * q^59 - 30 * q^60 - 7 * q^61 + 79 * q^62 - 2 * q^63 + 7 * q^64 - 8 * q^65 + 8 * q^66 - 38 * q^67 - 2 * q^68 + 10 * q^69 - 18 * q^70 - 14 * q^71 - 35 * q^73 - 29 * q^74 + 9 * q^75 + 52 * q^76 - 3 * q^77 - 58 * q^78 + 15 * q^79 - 87 * q^80 - 14 * q^81 + 19 * q^82 + 5 * q^83 + 8 * q^84 + 6 * q^85 - 52 * q^86 - 72 * q^87 + 55 * q^88 + 74 * q^89 - 14 * q^90 + 13 * q^91 - 55 * q^92 + 32 * q^93 - 24 * q^94 + 32 * q^95 - 42 * q^96 + 20 * q^97 + 2 * q^98 + 16 * q^99

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