LMFDB - Embedded newform 55.2.j.a.14.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,2,Mod(4,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 2]))

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

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

chi := DirichletCharacter("55.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	55.j (of order $10$, 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:	$0.439177211117$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
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} - 7x^{14} + 25x^{12} - 57x^{10} + 194x^{8} - 303x^{6} + 235x^{4} - 33x^{2} + 121 $ x^16 - 7x^14 + 25x^12 - 57x^10 + 194x^8 - 303x^6 + 235x^4 - 33*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			14.2
Root			$1.17360 - 0.381325i$ of defining polynomial
Character	$\chi$	$=$	55.14
Dual form			55.2.j.a.4.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.725323 - 0.998322i) q^{2} +(-0.346168 + 0.112477i) q^{3} +(0.147481 - 0.453901i) q^{4} +(0.0238439 - 2.23594i) q^{5} +(0.363371 + 0.264005i) q^{6} +(2.45903 + 0.798988i) q^{7} +(-2.90731 + 0.944641i) q^{8} +(-2.31987 + 1.68548i) q^{9} +O(q^{10})$	\(q+(-0.725323 - 0.998322i) q^{2} +(-0.346168 + 0.112477i) q^{3} +(0.147481 - 0.453901i) q^{4} +(0.0238439 - 2.23594i) q^{5} +(0.363371 + 0.264005i) q^{6} +(2.45903 + 0.798988i) q^{7} +(-2.90731 + 0.944641i) q^{8} +(-2.31987 + 1.68548i) q^{9} +(-2.24948 + 1.59798i) q^{10} +(3.12020 + 1.12443i) q^{11} +0.173714i q^{12} +(1.62187 + 2.23232i) q^{13} +(-0.985946 - 3.03443i) q^{14} +(0.243237 + 0.776692i) q^{15} +(2.27957 + 1.65620i) q^{16} +(-2.26370 + 3.11572i) q^{17} +(3.36531 + 1.09346i) q^{18} +(0.0857804 + 0.264005i) q^{19} +(-1.01138 - 0.340583i) q^{20} -0.941105 q^{21} +(-1.14061 - 3.93054i) q^{22} -8.40180i q^{23} +(0.900166 - 0.654009i) q^{24} +(-4.99886 - 0.106627i) q^{25} +(1.05219 - 3.23830i) q^{26} +(1.25532 - 1.72780i) q^{27} +(0.725323 - 0.998322i) q^{28} +(-1.02689 + 3.16043i) q^{29} +(0.598963 - 0.806182i) q^{30} +(-0.456498 + 0.331666i) q^{31} +2.63682i q^{32} +(-1.20659 - 0.0382919i) q^{33} +4.75241 q^{34} +(1.84512 - 5.47920i) q^{35} +(0.422906 + 1.30157i) q^{36} +(0.497006 + 0.161487i) q^{37} +(0.201343 - 0.277125i) q^{38} +(-0.812523 - 0.590333i) q^{39} +(2.04284 + 6.52309i) q^{40} +(-1.57966 - 4.86168i) q^{41} +(0.682605 + 0.939526i) q^{42} +2.54457i q^{43} +(0.970553 - 1.25043i) q^{44} +(3.71333 + 5.22728i) q^{45} +(-8.38769 + 6.09402i) q^{46} +(-4.68373 + 1.52184i) q^{47} +(-0.975398 - 0.316926i) q^{48} +(-0.254663 - 0.185023i) q^{49} +(3.51934 + 5.06781i) q^{50} +(0.433175 - 1.33318i) q^{51} +(1.25245 - 0.406945i) q^{52} +(5.12599 + 7.05533i) q^{53} -2.63541 q^{54} +(2.58856 - 6.94977i) q^{55} -7.90392 q^{56} +(-0.0593888 - 0.0817417i) q^{57} +(3.89995 - 1.26717i) q^{58} +(-2.31987 + 7.13983i) q^{59} +(0.388415 + 0.00414203i) q^{60} +(-11.4711 - 8.33424i) q^{61} +(0.662218 + 0.215168i) q^{62} +(-7.05132 + 2.29111i) q^{63} +(7.19153 - 5.22495i) q^{64} +(5.03000 - 3.57318i) q^{65} +(0.836937 + 1.23233i) q^{66} -3.20618i q^{67} +(1.08037 + 1.48701i) q^{68} +(0.945006 + 2.90843i) q^{69} +(-6.80831 + 2.13216i) q^{70} +(6.79655 + 4.93798i) q^{71} +(5.15239 - 7.09166i) q^{72} +(-12.3973 - 4.02812i) q^{73} +(-0.199274 - 0.613302i) q^{74} +(1.74244 - 0.525345i) q^{75} +0.132483 q^{76} +(6.77427 + 5.25802i) q^{77} +1.23934i q^{78} +(7.85090 - 5.70401i) q^{79} +(3.75753 - 5.05749i) q^{80} +(2.41812 - 7.44221i) q^{81} +(-3.70776 + 5.10330i) q^{82} +(1.93792 - 2.66732i) q^{83} +(-0.138796 + 0.427169i) q^{84} +(6.91259 + 5.13580i) q^{85} +(2.54030 - 1.84564i) q^{86} -1.20954i q^{87} +(-10.1336 - 0.321596i) q^{88} -2.48823 q^{89} +(2.52514 - 7.49856i) q^{90} +(2.20464 + 6.78519i) q^{91} +(-3.81359 - 1.23911i) q^{92} +(0.120720 - 0.166157i) q^{93} +(4.91650 + 3.57205i) q^{94} +(0.592344 - 0.185505i) q^{95} +(-0.296581 - 0.912781i) q^{96} +(-6.40771 - 8.81946i) q^{97} +0.388437i q^{98} +(-9.13367 + 2.65051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{9}+O(q^{10}) $ 16 * q - 4 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^9	$ 16 q - 4 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{9} - 6 q^{11} - 12 q^{14} - 16 q^{15} + 16 q^{16} + 6 q^{19} - 8 q^{20} + 8 q^{21} + 6 q^{24} - 16 q^{25} + 40 q^{26} + 2 q^{29} + 26 q^{30} + 8 q^{31} - 16 q^{34} + 22 q^{35} + 10 q^{36} + 30 q^{39} + 12 q^{40} - 52 q^{41} + 4 q^{44} + 12 q^{45} - 62 q^{46} - 10 q^{49} + 28 q^{50} - 42 q^{51} - 40 q^{54} - 8 q^{55} - 20 q^{56} + 2 q^{59} - 32 q^{60} - 40 q^{61} - 8 q^{64} - 40 q^{65} + 58 q^{66} + 26 q^{69} - 34 q^{70} + 36 q^{71} + 48 q^{74} - 20 q^{75} + 56 q^{76} + 38 q^{79} + 34 q^{80} + 68 q^{81} + 12 q^{84} + 58 q^{85} + 22 q^{86} + 24 q^{89} + 78 q^{90} - 20 q^{91} + 14 q^{94} + 48 q^{95} - 86 q^{96} - 72 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^9 - 6 * q^11 - 12 * q^14 - 16 * q^15 + 16 * q^16 + 6 * q^19 - 8 * q^20 + 8 * q^21 + 6 * q^24 - 16 * q^25 + 40 * q^26 + 2 * q^29 + 26 * q^30 + 8 * q^31 - 16 * q^34 + 22 * q^35 + 10 * q^36 + 30 * q^39 + 12 * q^40 - 52 * q^41 + 4 * q^44 + 12 * q^45 - 62 * q^46 - 10 * q^49 + 28 * q^50 - 42 * q^51 - 40 * q^54 - 8 * q^55 - 20 * q^56 + 2 * q^59 - 32 * q^60 - 40 * q^61 - 8 * q^64 - 40 * q^65 + 58 * q^66 + 26 * q^69 - 34 * q^70 + 36 * q^71 + 48 * q^74 - 20 * q^75 + 56 * q^76 + 38 * q^79 + 34 * q^80 + 68 * q^81 + 12 * q^84 + 58 * q^85 + 22 * q^86 + 24 * q^89 + 78 * q^90 - 20 * q^91 + 14 * q^94 + 48 * q^95 - 86 * q^96 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.725323	−	0.998322i	−0.512881	−	0.705920i	0.471521	−	0.881855i	$-0.343705\pi$
$2$	−0.725323	−	0.998322i	−0.512881	−	0.705920i	−0.984402	+	0.175935i	$0.943705\pi$
$3$	−0.346168	+	0.112477i	−0.199860	+	0.0649385i	−0.407236	−	0.913323i	$-0.633508\pi$
$3$	−0.346168	+	0.112477i	−0.199860	+	0.0649385i	0.207376	+	0.978261i	$0.433508\pi$
$4$	0.147481	−	0.453901i	0.0737407	−	0.226951i
$5$	0.0238439	−	2.23594i	0.0106633	−	0.999943i
$5$	0.0238439	−	2.23594i	0.0106633	−	0.999943i
$6$	0.363371	+	0.264005i	0.148346	+	0.107780i
$7$	2.45903	+	0.798988i	0.929427	+	0.301989i	0.734328	−	0.678795i	$-0.237497\pi$
$7$	2.45903	+	0.798988i	0.929427	+	0.301989i	0.195099	+	0.980784i	$0.437497\pi$
$8$	−2.90731	+	0.944641i	−1.02789	+	0.333981i
$9$	−2.31987	+	1.68548i	−0.773290	+	0.561828i
$10$	−2.24948	+	1.59798i	−0.711349	+	0.505324i
$11$	3.12020	+	1.12443i	0.940776	+	0.339029i
$11$	3.12020	+	1.12443i	0.940776	+	0.339029i
$12$			0.173714i			0.0501470i
$13$	1.62187	+	2.23232i	0.449826	+	0.619133i	0.972360	−	0.233486i	$-0.0750132\pi$
$13$	1.62187	+	2.23232i	0.449826	+	0.619133i	−0.522534	+	0.852619i	$0.675013\pi$
$14$	−0.985946	−	3.03443i	−0.263505	−	0.810985i
$15$	0.243237	+	0.776692i	0.0628036	+	0.200541i
$16$	2.27957	+	1.65620i	0.569892	+	0.414051i
$17$	−2.26370	+	3.11572i	−0.549028	+	0.755673i	−0.989880	−	0.141907i	$-0.954677\pi$
$17$	−2.26370	+	3.11572i	−0.549028	+	0.755673i	0.440852	+	0.897580i	$0.354677\pi$
$18$	3.36531	+	1.09346i	0.793211	+	0.257730i
$19$	0.0857804	+	0.264005i	0.0196794	+	0.0605669i	0.960414	−	0.278577i	$-0.0898627\pi$
$19$	0.0857804	+	0.264005i	0.0196794	+	0.0605669i	−0.940735	+	0.339144i	$0.889863\pi$
$20$	−1.01138	−	0.340583i	−0.226151	−	0.0761566i
$21$	−0.941105			−0.205366
$22$	−1.14061	−	3.93054i	−0.243179	−	0.837994i
$23$		−	8.40180i		−	1.75190i	−0.482406	−	0.875948i	$-0.660237\pi$
$23$		−	8.40180i		−	1.75190i	0.482406	−	0.875948i	$-0.339763\pi$
$24$	0.900166	−	0.654009i	0.183746	−	0.133499i
$25$	−4.99886	−	0.106627i	−0.999773	−	0.0213255i
$26$	1.05219	−	3.23830i	0.206351	−	0.635083i
$27$	1.25532	−	1.72780i	0.241586	−	0.332514i
$28$	0.725323	−	0.998322i	0.137073	−	0.188665i
$29$	−1.02689	+	3.16043i	−0.190688	+	0.586877i	−1.00000		0.000502126i	$-0.999840\pi$
$29$	−1.02689	+	3.16043i	−0.190688	+	0.586877i	0.809312	+	0.587379i	$0.199840\pi$
$30$	0.598963	−	0.806182i	0.109355	−	0.147188i
$31$	−0.456498	+	0.331666i	−0.0819895	+	0.0595689i	−0.628025	−	0.778193i	$-0.716136\pi$
$31$	−0.456498	+	0.331666i	−0.0819895	+	0.0595689i	0.546035	+	0.837762i	$0.316136\pi$
$32$			2.63682i			0.466128i
$33$	−1.20659	−	0.0382919i	−0.210040	−	0.00666576i
$34$	4.75241			0.815031
$35$	1.84512	−	5.47920i	0.311883	−	0.926154i
$36$	0.422906	+	1.30157i	0.0704843	+	0.216928i
$37$	0.497006	+	0.161487i	0.0817073	+	0.0265483i	0.349585	−	0.936905i	$-0.386322\pi$
$37$	0.497006	+	0.161487i	0.0817073	+	0.0265483i	−0.267878	+	0.963453i	$0.586322\pi$
$38$	0.201343	−	0.277125i	0.0326622	−	0.0449556i
$39$	−0.812523	−	0.590333i	−0.130108	−	0.0945289i
$40$	2.04284	+	6.52309i	0.323001	+	1.03139i
$41$	−1.57966	−	4.86168i	−0.246701	−	0.759267i	−0.995352	−	0.0963031i	$-0.969298\pi$
$41$	−1.57966	−	4.86168i	−0.246701	−	0.759267i	0.748651	−	0.662964i	$-0.230702\pi$
$42$	0.682605	+	0.939526i	0.105328	+	0.144972i
$43$			2.54457i			0.388043i	0.980997	+	0.194022i	$0.0621532\pi$
$43$			2.54457i			0.388043i	−0.980997	+	0.194022i	$0.937847\pi$
$44$	0.970553	−	1.25043i	0.146316	−	0.188509i
$45$	3.71333	+	5.22728i	0.553550	+	0.779237i
$46$	−8.38769	+	6.09402i	−1.23670	+	0.898514i
$47$	−4.68373	+	1.52184i	−0.683193	+	0.221983i	−0.629993	−	0.776601i	$-0.716942\pi$
$47$	−4.68373	+	1.52184i	−0.683193	+	0.221983i	−0.0532000	+	0.998584i	$0.516942\pi$
$48$	−0.975398	−	0.316926i	−0.140787	−	0.0457443i
$49$	−0.254663	−	0.185023i	−0.0363804	−	0.0264319i
$50$	3.51934	+	5.06781i	0.497710	+	0.716697i
$51$	0.433175	−	1.33318i	0.0606566	−	0.186682i
$52$	1.25245	−	0.406945i	0.173683	−	0.0564331i
$53$	5.12599	+	7.05533i	0.704109	+	0.969123i	0.999904	+	0.0138718i	$0.00441567\pi$
$53$	5.12599	+	7.05533i	0.704109	+	0.969123i	−0.295794	+	0.955252i	$0.595584\pi$
$54$	−2.63541			−0.358633
$55$	2.58856	−	6.94977i	0.349041	−	0.937107i
$56$	−7.90392			−1.05621
$57$	−0.0593888	−	0.0817417i	−0.00786624	−	0.0108269i
$58$	3.89995	−	1.26717i	0.512088	−	0.166388i
$59$	−2.31987	+	7.13983i	−0.302021	+	0.929526i	0.678751	+	0.734369i	$0.262522\pi$
$59$	−2.31987	+	7.13983i	−0.302021	+	0.929526i	−0.980772	+	0.195157i	$0.937478\pi$
$60$	0.388415	+	0.00414203i	0.0501441	+	0.000534734i
$61$	−11.4711	−	8.33424i	−1.46872	−	1.06709i	−0.980981	−	0.194103i	$-0.937820\pi$
$61$	−11.4711	−	8.33424i	−1.46872	−	1.06709i	−0.487743	−	0.872987i	$-0.662180\pi$
$62$	0.662218	+	0.215168i	0.0841017	+	0.0273263i
$63$	−7.05132	+	2.29111i	−0.888382	+	0.288653i
$64$	7.19153	−	5.22495i	0.898942	−	0.653119i
$65$	5.03000	−	3.57318i	0.623894	−	0.443199i
$66$	0.836937	+	1.23233i	0.103020	+	0.151690i
$67$		−	3.20618i		−	0.391698i	−0.980634	−	0.195849i	$-0.937254\pi$
$67$		−	3.20618i		−	0.391698i	0.980634	−	0.195849i	$-0.0627462\pi$
$68$	1.08037	+	1.48701i	0.131015	+	0.180326i
$69$	0.945006	+	2.90843i	0.113765	+	0.350134i
$70$	−6.80831	+	2.13216i	−0.813749	+	0.254842i
$71$	6.79655	+	4.93798i	0.806602	+	0.586030i	0.912843	−	0.408310i	$-0.133882\pi$
$71$	6.79655	+	4.93798i	0.806602	+	0.586030i	−0.106242	+	0.994340i	$0.533882\pi$
$72$	5.15239	−	7.09166i	0.607216	−	0.835761i
$73$	−12.3973	−	4.02812i	−1.45099	−	0.471455i	−0.525685	−	0.850679i	$-0.676191\pi$
$73$	−12.3973	−	4.02812i	−1.45099	−	0.471455i	−0.925305	+	0.379224i	$0.876191\pi$
$74$	−0.199274	−	0.613302i	−0.0231651	−	0.0712949i
$75$	1.74244	−	0.525345i	0.201199	−	0.0606616i
$76$	0.132483			0.0151969
$77$	6.77427	+	5.25802i	0.771999	+	0.599206i
$78$			1.23934i			0.140328i
$79$	7.85090	−	5.70401i	0.883295	−	0.641752i	−0.0508259	−	0.998708i	$-0.516185\pi$
$79$	7.85090	−	5.70401i	0.883295	−	0.641752i	0.934121	+	0.356956i	$0.116185\pi$
$80$	3.75753	−	5.05749i	0.420104	−	0.565445i
$81$	2.41812	−	7.44221i	0.268680	−	0.826912i
$82$	−3.70776	+	5.10330i	−0.409454	+	0.563565i
$83$	1.93792	−	2.66732i	0.212715	−	0.292776i	−0.689305	−	0.724471i	$-0.742084\pi$
$83$	1.93792	−	2.66732i	0.212715	−	0.292776i	0.902020	+	0.431694i	$0.142084\pi$
$84$	−0.138796	+	0.427169i	−0.0151438	+	0.0466079i
$85$	6.91259	+	5.13580i	0.749775	+	0.557055i
$86$	2.54030	−	1.84564i	0.273928	−	0.199020i
$87$		−	1.20954i		−	0.129676i
$88$	−10.1336	−	0.321596i	−1.08024	−	0.0342823i
$89$	−2.48823			−0.263752			−0.131876	−	0.991266i	$-0.542100\pi$
$89$	−2.48823			−0.263752			−0.131876	+	0.991266i	$0.542100\pi$
$90$	2.52514	−	7.49856i	0.266174	−	0.790418i
$91$	2.20464	+	6.78519i	0.231109	+	0.711281i
$92$	−3.81359	−	1.23911i	−0.397594	−	0.129186i
$93$	0.120720	−	0.166157i	0.0125181	−	0.0172297i
$94$	4.91650	+	3.57205i	0.507099	+	0.368429i
$95$	0.592344	−	0.185505i	0.0607733	−	0.0190324i
$96$	−0.296581	−	0.912781i	−0.0302696	−	0.0931604i
$97$	−6.40771	−	8.81946i	−0.650605	−	0.895480i	0.348521	−	0.937301i	$-0.386684\pi$
$97$	−6.40771	−	8.81946i	−0.650605	−	0.895480i	−0.999125	+	0.0418208i	$0.986684\pi$
$98$			0.388437i			0.0392380i
$99$	−9.13367	+	2.65051i	−0.917969	+	0.266387i
$100$	−0.785638	+	2.25326i	−0.0785638	+	0.225326i
$101$	−11.1954	+	8.13391i	−1.11398	+	0.809355i	−0.983286	−	0.182068i	$-0.941721\pi$
$101$	−11.1954	+	8.13391i	−1.11398	+	0.809355i	−0.130695	+	0.991423i	$0.541721\pi$
$102$	−1.64513	+	0.534535i	−0.162892	+	0.0529269i
$103$	12.7346	+	4.13771i	1.25477	+	0.407700i	0.859629	−	0.510919i	$-0.170695\pi$
$103$	12.7346	+	4.13771i	1.25477	+	0.407700i	0.395144	+	0.918619i	$0.370695\pi$
$104$	−6.82402	−	4.95794i	−0.669150	−	0.486166i
$105$	−0.0224397	+	2.10426i	−0.00218989	+	0.205354i
$106$	3.32548	−	10.2348i	0.322999	−	0.994090i
$107$	9.75728	−	3.17033i	0.943272	−	0.306488i	0.203293	−	0.979118i	$-0.434836\pi$
$107$	9.75728	−	3.17033i	0.943272	−	0.306488i	0.739979	+	0.672630i	$0.234836\pi$
$108$	−0.599112	−	0.824608i	−0.0576496	−	0.0793479i
$109$	4.94262			0.473417			0.236708	−	0.971581i	$-0.423931\pi$
$109$	4.94262			0.473417			0.236708	+	0.971581i	$0.423931\pi$
$110$	−8.81565	+	2.45662i	−0.840540	+	0.234229i
$111$	−0.190211			−0.0180540
$112$	4.28225	+	5.89401i	0.404634	+	0.556931i
$113$	9.43836	−	3.06671i	0.887886	−	0.288492i	0.170658	−	0.985330i	$-0.445411\pi$
$113$	9.43836	−	3.06671i	0.887886	−	0.288492i	0.717228	+	0.696839i	$0.245411\pi$
$114$	−0.0385284	+	0.118578i	−0.00360852	+	0.0111059i
$115$	−18.7859	−	0.200332i	−1.75180	−	0.0186810i
$116$	1.28308	+	0.932209i	0.119131	+	0.0865534i
$117$	−7.52506	−	2.44504i	−0.695692	−	0.226044i
$118$	8.81050	−	2.86270i	0.811072	−	0.263533i
$119$	−8.05594	+	5.85298i	−0.738487	+	0.536542i
$120$	−1.44086	−	2.02831i	−0.131532	−	0.185159i
$121$	8.47131	+	7.01690i	0.770119	+	0.637900i
$122$			17.4969i			1.58409i
$123$	1.09365	+	1.50528i	0.0986113	+	0.135727i
$124$	0.0832183	+	0.256120i	0.00747323	+	0.0230002i
$125$	−0.357605	+	11.1746i	−0.0319852	+	0.999488i
$126$	7.40175	+	5.37769i	0.659400	+	0.479082i
$127$	−6.54543	+	9.00901i	−0.580813	+	0.799420i	−0.993784	−	0.111324i	$-0.964491\pi$
$127$	−6.54543	+	9.00901i	−0.580813	+	0.799420i	0.412972	+	0.910744i	$0.364491\pi$
$128$	−5.41684	−	1.76004i	−0.478786	−	0.155567i
$129$	−0.286205	−	0.880848i	−0.0251989	−	0.0775544i
$130$	−7.21556	−	2.42984i	−0.632846	−	0.213111i
$131$	10.1649			0.888114			0.444057	−	0.895999i	$-0.353539\pi$
$131$	10.1649			0.888114			0.444057	+	0.895999i	$0.353539\pi$
$132$	−0.195330	+	0.542023i	−0.0170013	+	0.0471771i
$133$			0.717734i			0.0622354i
$134$	−3.20080	+	2.32552i	−0.276507	+	0.200894i
$135$	−3.83332	−	2.84801i	−0.329919	−	0.245118i
$136$	3.63804	−	11.1967i	0.311959	−	0.960112i
$137$	2.55455	−	3.51604i	0.218250	−	0.300395i	−0.685827	−	0.727764i	$-0.740559\pi$
$137$	2.55455	−	3.51604i	0.218250	−	0.300395i	0.904077	+	0.427369i	$0.140559\pi$
$138$	2.21811	−	3.05297i	0.188818	−	0.259886i
$139$	2.56560	−	7.89611i	0.217612	−	0.669739i	−0.781346	−	0.624098i	$-0.785467\pi$
$139$	2.56560	−	7.89611i	0.217612	−	0.669739i	0.998958	−	0.0456418i	$-0.0145333\pi$
$140$	−2.21489	−	1.64558i	−0.187193	−	0.139077i
$141$	1.45019	−	1.05362i	0.122128	−	0.0887310i
$142$		−	10.3668i		−	0.869960i
$143$	2.55048	+	8.78896i	0.213282	+	0.734969i
$144$	−8.07981			−0.673318
$145$	7.04205	+	2.37141i	0.584810	+	0.196935i
$146$	4.97067	+	15.2981i	0.411375	+	1.26608i
$147$	0.108967	+	0.0354054i	0.00898743	+	0.00292019i
$148$	0.146598	−	0.201775i	0.0120503	−	0.0165858i
$149$	6.84987	+	4.97672i	0.561163	+	0.407709i	0.831884	−	0.554949i	$-0.187262\pi$
$149$	6.84987	+	4.97672i	0.561163	+	0.407709i	−0.270721	+	0.962658i	$0.587262\pi$
$150$	−1.78829	−	1.35847i	−0.146014	−	0.110919i
$151$	3.43080	+	10.5589i	0.279195	+	0.859273i	0.988079	+	0.153948i	$0.0491988\pi$
$151$	3.43080	+	10.5589i	0.279195	+	0.859273i	−0.708884	+	0.705325i	$0.750801\pi$
$152$	−0.498780	−	0.686511i	−0.0404564	−	0.0556834i
$153$		−	11.0435i		−	0.892814i
$154$	0.335658	−	10.5767i	0.0270481	−	0.852291i
$155$	0.730700	+	1.02861i	0.0586912	+	0.0826201i
$156$	−0.387785	+	0.281742i	−0.0310476	+	0.0225574i
$157$	13.0925	−	4.25400i	1.04489	−	0.339506i	0.264231	−	0.964459i	$-0.414882\pi$
$157$	13.0925	−	4.25400i	1.04489	−	0.339506i	0.780662	+	0.624953i	$0.214882\pi$
$158$	−11.3889	−	3.70047i	−0.906051	−	0.294394i
$159$	−2.56801	−	1.86577i	−0.203657	−	0.147965i
$160$	5.89577	+	0.0628721i	0.466102	+	0.00497048i
$161$	6.71293	−	20.6603i	0.529053	−	1.62826i
$162$	−9.18364	+	2.98395i	−0.721535	+	0.234441i
$163$	−5.25535	−	7.23337i	−0.411631	−	0.566561i	0.551985	−	0.833854i	$-0.313871\pi$
$163$	−5.25535	−	7.23337i	−0.411631	−	0.566561i	−0.963615	+	0.267293i	$0.913871\pi$
$164$	−2.43969			−0.190508
$165$	−0.114388	+	2.69694i	−0.00890511	+	0.209957i
$166$	−4.06846			−0.315774
$167$	−9.94425	−	13.6871i	−0.769509	−	1.05914i	−0.996363	−	0.0852095i	$-0.972844\pi$
$167$	−9.94425	−	13.6871i	−0.769509	−	1.05914i	0.226854	−	0.973929i	$-0.427156\pi$
$168$	2.73608	−	0.889007i	0.211093	−	0.0685883i
$169$	1.66446	−	5.12268i	0.128035	−	0.394052i
$170$	0.113316	−	10.6261i	0.00869095	−	0.814984i
$171$	−0.643975	−	0.467875i	−0.0492460	−	0.0357793i
$172$	1.15498	+	0.375277i	0.0880667	+	0.0286146i
$173$	−3.21447	+	1.04445i	−0.244392	+	0.0794077i	−0.428652	−	0.903470i	$-0.641011\pi$
$173$	−3.21447	+	1.04445i	−0.244392	+	0.0794077i	0.184260	+	0.982878i	$0.441011\pi$
$174$	−1.20751	+	0.877307i	−0.0915410	+	0.0665085i
$175$	−12.2072	−	4.25623i	−0.922775	−	0.321741i
$176$	5.25043	+	7.73091i	0.395766	+	0.582739i
$177$		−	2.73251i		−	0.205388i
$178$	1.80477	+	2.48405i	0.135273	+	0.186188i
$179$	−4.27183	−	13.1473i	−0.319291	−	0.982678i	−0.973952	−	0.226755i	$-0.927188\pi$
$179$	−4.27183	−	13.1473i	−0.319291	−	0.982678i	0.654660	−	0.755923i	$-0.272812\pi$
$180$	2.92032	−	0.914557i	0.217668	−	0.0681671i
$181$	2.10264	+	1.52766i	0.156288	+	0.113550i	0.663181	−	0.748459i	$-0.269206\pi$
$181$	2.10264	+	1.52766i	0.156288	+	0.113550i	−0.506893	+	0.862009i	$0.669206\pi$
$182$	5.17473	−	7.12240i	0.383576	−	0.527947i
$183$	4.90833	+	1.59481i	0.362834	+	0.117892i
$184$	7.93668	+	24.4266i	0.585100	+	1.80075i
$185$	0.372926	−	1.10743i	0.0274181	−	0.0814195i
$186$	−0.253440			−0.0185831
$187$	−10.5666	+	7.17629i	−0.772708	+	0.524782i
$188$			2.35039i			0.171420i
$189$	4.46735	−	3.24572i	0.324952	−	0.236091i
$190$	−0.614835	−	0.456799i	−0.0446048	−	0.0331397i
$191$	0.685498	−	2.10975i	0.0496009	−	0.152656i	−0.923188	−	0.384348i	$-0.874426\pi$
$191$	0.685498	−	2.10975i	0.0496009	−	0.152656i	0.972789	+	0.231692i	$0.0744262\pi$
$192$	−1.90179	+	2.61759i	−0.137250	+	0.188908i
$193$	−6.15791	+	8.47564i	−0.443256	+	0.610090i	−0.970932	−	0.239356i	$-0.923064\pi$
$193$	−6.15791	+	8.47564i	−0.443256	+	0.610090i	0.527676	+	0.849446i	$0.323064\pi$
$194$	−4.15700	+	12.7939i	−0.298455	+	0.918550i
$195$	−1.33932	+	1.80268i	−0.0959109	+	0.129092i
$196$	−0.121540	+	0.0883042i	−0.00868145	+	0.00630744i
$197$			1.32667i			0.0945210i	0.998883	+	0.0472605i	$0.0150491\pi$
$197$			1.32667i			0.0945210i	−0.998883	+	0.0472605i	$0.984951\pi$
$198$	9.27093	+	7.19586i	0.658856	+	0.511388i
$199$	5.20321			0.368846			0.184423	−	0.982847i	$-0.440958\pi$
$199$	5.20321			0.368846			0.184423	+	0.982847i	$0.440958\pi$
$200$	14.6340	−	4.41213i	1.03478	−	0.311985i
$201$	0.360621	+	1.10988i	0.0254362	+	0.0782847i
$202$	16.2405	+	5.27687i	1.14268	+	0.371279i
$203$	−5.05029	+	6.95113i	−0.354461	+	0.487873i
$204$	−0.541245	−	0.393237i	−0.0378947	−	0.0275321i
$205$	−10.9081	+	3.41610i	−0.761855	+	0.238591i
$206$	−5.10590	−	15.7144i	−0.355745	−	1.09487i
$207$	14.1611	+	19.4911i	0.984264	+	1.35472i
$208$			7.77487i			0.539090i
$209$	−0.0292033	+	0.920202i	−0.00202004	+	0.0636517i
$210$	2.11700	−	1.50386i	0.146087	−	0.103776i
$211$	−15.3038	+	11.1189i	−1.05356	+	0.765454i	−0.972886	−	0.231287i	$-0.925706\pi$
$211$	−15.3038	+	11.1189i	−1.05356	+	0.765454i	−0.0806716	+	0.996741i	$0.525706\pi$
$212$	3.95841	−	1.28617i	0.271865	−	0.0883342i
$213$	−2.90815	−	0.944916i	−0.199263	−	0.0647446i
$214$	−10.2422	−	7.44139i	−0.700142	−	0.508683i
$215$	5.68951	+	0.0606726i	0.388021	+	0.00413784i
$216$	−2.01744	+	6.20905i	−0.137270	+	0.422473i
$217$	−1.38754	+	0.450839i	−0.0941924	+	0.0306050i
$218$	−3.58499	−	4.93432i	−0.242806	−	0.334194i
$219$	4.74460			0.320611
$220$	−2.77275	−	2.19991i	−0.186939	−	0.148318i
$221$	−10.6267			−0.714829
$222$	0.137964	+	0.189892i	0.00925956	+	0.0127447i
$223$	−20.8018	+	6.75890i	−1.39299	+	0.452610i	−0.906917	−	0.421309i	$-0.861571\pi$
$223$	−20.8018	+	6.75890i	−1.39299	+	0.452610i	−0.486072	+	0.873919i	$0.661571\pi$
$224$	−2.10679	+	6.48402i	−0.140766	+	0.433232i
$225$	11.7764	−	8.17814i	0.785095	−	0.545210i
$226$	−9.90742	−	7.19816i	−0.659032	−	0.478815i
$227$	2.31929	+	0.753584i	0.153937	+	0.0500171i	0.384972	−	0.922928i	$-0.374211\pi$
$227$	2.31929	+	0.753584i	0.153937	+	0.0500171i	−0.231035	+	0.972945i	$0.574211\pi$
$228$	−0.0458614	+	0.0149013i	−0.00303724	+	0.000986860i
$229$	5.90678	−	4.29153i	0.390331	−	0.283592i	−0.375260	−	0.926920i	$-0.622447\pi$
$229$	5.90678	−	4.29153i	0.390331	−	0.283592i	0.765591	+	0.643327i	$0.222447\pi$
$230$	13.4259	+	18.8997i	0.885275	+	1.24621i
$231$	−2.93644	−	1.05821i	−0.193203	−	0.0696250i
$232$		−	10.1584i		−	0.666930i
$233$	−2.62053	−	3.60685i	−0.171676	−	0.236292i	0.714505	−	0.699630i	$-0.246652\pi$
$233$	−2.62053	−	3.60685i	−0.171676	−	0.236292i	−0.886182	+	0.463338i	$0.846652\pi$
$234$	3.01717	+	9.28588i	0.197238	+	0.607037i
$235$	3.29106	+	10.5088i	0.214685	+	0.685521i
$236$	2.89864	+	2.10598i	0.188685	+	0.137088i
$237$	−2.07616	+	2.85759i	−0.134861	+	0.185620i
$238$	11.6863	+	3.79711i	0.757511	+	0.246130i
$239$	−7.47040	−	22.9915i	−0.483220	−	1.48720i	−0.834542	−	0.550944i	$-0.814268\pi$
$239$	−7.47040	−	22.9915i	−0.483220	−	1.48720i	0.351322	−	0.936255i	$-0.385732\pi$
$240$	−0.731885	+	2.17338i	−0.0472430	+	0.140291i
$241$	−12.0393			−0.775522			−0.387761	−	0.921760i	$-0.626751\pi$
$241$	−12.0393			−0.775522			−0.387761	+	0.921760i	$0.626751\pi$
$242$	0.860691	−	13.5466i	0.0553273	−	0.870809i
$243$			9.25525i			0.593725i
$244$	−5.47470	+	3.97760i	−0.350482	+	0.254640i
$245$	−0.419773	+	0.564999i	−0.0268183	+	0.0360964i
$246$	0.709506	−	2.18363i	0.0452364	−	0.139223i
$247$	−0.450217	+	0.619671i	−0.0286466	+	0.0394287i
$248$	1.01388	−	1.39548i	0.0643812	−	0.0886131i
$249$	−0.370835	+	1.14131i	−0.0235007	+	0.0723277i
$250$	11.4152	−	7.74821i	0.721963	−	0.490040i
$251$	0.433947	−	0.315281i	0.0273905	−	0.0199004i	−0.574006	−	0.818851i	$-0.694611\pi$
$251$	0.433947	−	0.315281i	0.0273905	−	0.0199004i	0.601396	+	0.798951i	$0.294611\pi$
$252$			3.53850i			0.222904i
$253$	9.44724	−	26.2153i	0.593943	−	1.64814i
$254$	13.7414			0.862214
$255$	−2.97057	−	1.00034i	−0.186024	−	0.0626438i
$256$	−3.32196	−	10.2240i	−0.207623	−	0.638997i
$257$	−22.5590	−	7.32987i	−1.40719	−	0.457224i	−0.495683	−	0.868504i	$-0.665082\pi$
$257$	−22.5590	−	7.32987i	−1.40719	−	0.457224i	−0.911509	+	0.411279i	$0.865082\pi$
$258$	−0.671779	+	0.924624i	−0.0418231	+	0.0575646i
$259$	1.09313	+	0.794203i	0.0679236	+	0.0493494i
$260$	−0.880041	−	2.81010i	−0.0545778	−	0.174275i
$261$	−2.94461	−	9.06258i	−0.182267	−	0.560960i
$262$	−7.37286	−	10.1479i	−0.455497	−	0.626937i
$263$		−	4.97643i		−	0.306860i	−0.988160	−	0.153430i	$-0.950968\pi$
$263$		−	4.97643i		−	0.306860i	0.988160	−	0.153430i	$-0.0490320\pi$
$264$	3.54409	−	1.02846i	0.218123	−	0.0632976i
$265$	15.8975	−	11.2932i	0.976576	−	0.693735i
$266$	0.716529	−	0.520589i	0.0439332	−	0.0319194i
$267$	0.861345	−	0.279868i	0.0527134	−	0.0171276i
$268$	−1.45529	−	0.472852i	−0.0888960	−	0.0288841i
$269$	23.3034	+	16.9309i	1.42083	+	1.03230i	0.991633	+	0.129087i	$0.0412047\pi$
$269$	23.3034	+	16.9309i	1.42083	+	1.03230i	0.429201	+	0.903209i	$0.358795\pi$
$270$	−0.0628385	+	5.89261i	−0.00382423	+	0.358613i
$271$	−4.96782	+	15.2894i	−0.301773	+	0.928763i	0.679088	+	0.734057i	$0.262375\pi$
$271$	−4.96782	+	15.2894i	−0.301773	+	0.928763i	−0.980862	+	0.194706i	$0.937625\pi$
$272$	−10.3205	+	3.35334i	−0.625774	+	0.203326i
$273$	−1.52635	−	2.10084i	−0.0923790	−	0.127149i
$274$	−5.36301			−0.323992
$275$	−15.4776	−	5.95358i	−0.933332	−	0.359014i
$276$	1.45951			0.0878522
$277$	10.5824	+	14.5654i	0.635832	+	0.875148i	0.998385	−	0.0568151i	$-0.0180946\pi$
$277$	10.5824	+	14.5654i	0.635832	+	0.875148i	−0.362552	+	0.931963i	$0.618095\pi$
$278$	−9.74375	+	3.16594i	−0.584391	+	0.189880i
$279$	0.500000	−	1.53884i	0.0299342	−	0.0921280i
$280$	−0.188461	+	17.6727i	−0.0112627	+	1.05615i
$281$	−11.0957	−	8.06146i	−0.661911	−	0.480907i	0.205397	−	0.978679i	$-0.434152\pi$
$281$	−11.0957	−	8.06146i	−0.661911	−	0.480907i	−0.867308	+	0.497772i	$0.834152\pi$
$282$	−2.10371	−	0.683536i	−0.125274	−	0.0407040i
$283$	19.5009	−	6.33621i	1.15921	−	0.376649i	0.334602	−	0.942360i	$-0.391398\pi$
$283$	19.5009	−	6.33621i	1.15921	−	0.376649i	0.824604	+	0.565711i	$0.191398\pi$
$284$	3.24372	−	2.35670i	0.192479	−	0.139844i
$285$	−0.184186	+	0.130841i	−0.0109102	+	0.00775034i
$286$	6.92428	−	8.92103i	0.409441	−	0.527512i
$287$		−	13.2172i		−	0.780184i
$288$	−4.44432	−	6.11708i	−0.261884	−	0.360452i
$289$	0.669933	+	2.06184i	0.0394078	+	0.121285i
$290$	−2.74033	−	8.75027i	−0.160918	−	0.513833i
$291$	3.21013	+	2.33229i	0.188181	+	0.136721i
$292$	−3.65673	+	5.03306i	−0.213994	+	0.294538i
$293$	21.3163	+	6.92608i	1.24531	+	0.404626i	0.856238	−	0.516581i	$-0.172796\pi$
$293$	21.3163	+	6.92608i	1.24531	+	0.404626i	0.389073	+	0.921207i	$0.372796\pi$
$294$	−0.0436901	−	0.134464i	−0.00254806	−	0.00784212i
$295$	15.9089	+	5.35733i	0.926253	+	0.311916i
$296$	−1.59750			−0.0928525
$297$	5.85963	−	3.97955i	0.340010	−	0.230917i
$298$		−	10.4481i		−	0.605242i
$299$	18.7555	−	13.6266i	1.08466	−	0.788049i
$300$	0.0185227	−	0.868373i	0.00106941	−	0.0501356i
$301$	−2.03308	+	6.25718i	−0.117185	+	0.360658i
$302$	8.05276	−	11.0837i	0.463384	−	0.637794i
$303$	2.96060	−	4.07492i	0.170082	−	0.234098i
$304$	−0.241704	+	0.743887i	−0.0138627	+	0.0426649i
$305$	−18.9084	+	25.4500i	−1.08269	+	1.45726i
$306$	−11.0250	+	8.01010i	−0.630255	+	0.457907i
$307$			20.3044i			1.15883i	0.815032	+	0.579416i	$0.196719\pi$
$307$			20.3044i			1.15883i	−0.815032	+	0.579416i	$0.803281\pi$
$308$	3.38570	−	2.29939i	0.192918	−	0.131020i
$309$	−4.87369			−0.277254
$310$	0.496892	−	1.47555i	0.0282216	−	0.0838056i
$311$	−2.70662	−	8.33012i	−0.153478	−	0.472358i	0.844525	−	0.535516i	$-0.179883\pi$
$311$	−2.70662	−	8.33012i	−0.153478	−	0.472358i	−0.998004	+	0.0631580i	$0.979883\pi$
$312$	2.91991	+	0.948735i	0.165307	+	0.0537116i
$313$	1.01759	−	1.40060i	0.0575177	−	0.0791664i	−0.779289	−	0.626664i	$-0.784420\pi$
$313$	1.01759	−	1.40060i	0.0575177	−	0.0791664i	0.836807	+	0.547498i	$0.184420\pi$
$314$	−13.7431	−	9.98497i	−0.775570	−	0.563485i
$315$	4.95466	+	15.8210i	0.279163	+	0.891410i
$316$	−1.43120	−	4.40477i	−0.0805111	−	0.247788i
$317$	10.2724	+	14.1387i	0.576954	+	0.794109i	0.993357	−	0.115071i	$-0.0367095\pi$
$317$	10.2724	+	14.1387i	0.576954	+	0.794109i	−0.416403	+	0.909180i	$0.636710\pi$
$318$			3.91699i			0.219654i
$319$	−6.75777	+	8.70651i	−0.378363	+	0.487471i
$320$	−11.5112	−	16.2044i	−0.643496	−	0.905855i
$321$	−3.02107	+	2.19493i	−0.168619	+	0.122509i
$322$	−25.4947	+	8.28372i	−1.42076	+	0.461633i
$323$	−1.01675	−	0.330361i	−0.0565733	−	0.0183818i
$324$	−3.02140	−	2.19518i	−0.167856	−	0.121954i
$325$	−7.86949	−	11.3320i	−0.436521	−	0.628585i
$326$	−3.40940	+	10.4931i	−0.188829	+	0.581157i
$327$	−1.71097	+	0.555929i	−0.0946171	+	0.0307430i
$328$	9.18509	+	12.6422i	0.507162	+	0.698048i
$329$	−12.7334			−0.702014
$330$	2.77538	−	1.84196i	0.152780	−	0.101396i
$331$	12.6193			0.693620			0.346810	−	0.937935i	$-0.387265\pi$
$331$	12.6193			0.693620			0.346810	+	0.937935i	$0.387265\pi$
$332$	−0.924893	−	1.27301i	−0.0507601	−	0.0698653i
$333$	−1.42517	+	0.463067i	−0.0780990	+	0.0253759i
$334$	−6.45132	+	19.8551i	−0.353000	+	1.08642i
$335$	−7.16883	−	0.0764480i	−0.391675	−	0.00417680i
$336$	−2.14531	−	1.55866i	−0.117036	−	0.0850320i
$337$	11.2794	+	3.66490i	0.614428	+	0.199640i	0.599665	−	0.800251i	$-0.295301\pi$
$337$	11.2794	+	3.66490i	0.614428	+	0.199640i	0.0147629	+	0.999891i	$0.495301\pi$
$338$	−6.32135	+	2.05393i	−0.343836	+	0.111719i
$339$	−2.92232	+	2.12319i	−0.158719	+	0.115316i
$340$	3.35062	−	2.38020i	0.181713	−	0.129084i
$341$	−1.79730	+	0.521562i	−0.0973294	+	0.0282442i
$342$			0.982255i			0.0531143i
$343$	−11.1167	−	15.3009i	−0.600248	−	0.826171i
$344$	−2.40371	−	7.39785i	−0.129599	−	0.398865i
$345$	6.52561	−	2.04363i	0.351327	−	0.110025i
$346$	3.37422	+	2.45152i	0.181399	+	0.131794i
$347$	13.1100	−	18.0444i	0.703781	−	0.968672i	−0.296127	−	0.955148i	$-0.595695\pi$
$347$	13.1100	−	18.0444i	0.703781	−	0.968672i	0.999909	−	0.0135232i	$-0.00430468\pi$
$348$	−0.549011	−	0.178385i	−0.0294301	−	0.00956242i
$349$	−4.93434	−	15.1863i	−0.264129	−	0.812906i	−0.991893	−	0.127078i	$-0.959440\pi$
$349$	−4.93434	−	15.1863i	−0.264129	−	0.812906i	0.727763	−	0.685828i	$-0.240560\pi$
$350$	4.60506	+	15.2738i	0.246151	+	0.816420i
$351$	5.89295			0.314542
$352$	−2.96492	+	8.22740i	−0.158031	+	0.438522i
$353$			24.1406i			1.28488i	0.766337	+	0.642439i	$0.222077\pi$
$353$			24.1406i			1.28488i	−0.766337	+	0.642439i	$0.777923\pi$
$354$	−2.72792	+	1.98195i	−0.144987	+	0.105340i
$355$	11.2031	−	15.0789i	0.594598	−	0.800307i
$356$	−0.366968	+	1.12941i	−0.0194492	+	0.0598586i
$357$	2.13038	−	2.93222i	0.112752	−	0.155189i
$358$	−10.0268	+	13.8007i	−0.529934	+	0.729391i
$359$	−6.29726	+	19.3810i	−0.332357	+	1.02289i	0.635653	+	0.771975i	$0.280731\pi$
$359$	−6.29726	+	19.3810i	−0.332357	+	1.02289i	−0.968010	+	0.250913i	$0.919269\pi$
$360$	−15.7337	−	11.6895i	−0.829238	−	0.616093i
$361$	15.3090	−	11.1226i	0.805736	−	0.585401i
$362$		−	3.20716i		−	0.168564i
$363$	−3.72173	−	1.47620i	−0.195340	−	0.0774804i
$364$	3.40495			0.178468
$365$	−9.30223	+	27.6235i	−0.486901	+	1.44588i
$366$	−1.96799	−	6.05685i	−0.102869	−	0.316597i
$367$	5.13979	+	1.67002i	0.268295	+	0.0871744i	0.440075	−	0.897961i	$-0.354952\pi$
$367$	5.13979	+	1.67002i	0.268295	+	0.0871744i	−0.171780	+	0.985135i	$0.554952\pi$
$368$	13.9151	−	19.1525i	0.725374	−	0.998392i
$369$	11.8589	+	8.61599i	0.617349	+	0.448530i
$370$	−1.37606	+	0.430941i	−0.0715379	+	0.0224036i
$371$	6.96786	+	21.4449i	0.361753	+	1.11336i
$372$	−0.0576150	−	0.0793003i	−0.00298720	−	0.00411153i
$373$			17.0982i			0.885311i	0.896692	+	0.442656i	$0.145964\pi$
$373$			17.0982i			0.885311i	−0.896692	+	0.442656i	$0.854036\pi$
$374$	14.8285	+	5.34375i	0.766761	+	0.276319i
$375$	−1.13309	−	3.90852i	−0.0585127	−	0.201835i
$376$	12.1795	−	8.84889i	0.628108	−	0.456347i
$377$	−8.72055	+	2.83348i	−0.449131	+	0.145932i
$378$	−6.48055	−	2.10566i	−0.333323	−	0.108303i
$379$	−6.95104	−	5.05023i	−0.357051	−	0.259413i	0.394770	−	0.918780i	$-0.370824\pi$
$379$	−6.95104	−	5.05023i	−0.357051	−	0.259413i	−0.751821	+	0.659367i	$0.770824\pi$
$380$	0.00315892	−	0.296224i	0.000162049	−	0.0151960i
$381$	1.25251	−	3.85484i	0.0641681	−	0.197489i
$382$	−2.60341	+	0.845900i	−0.133202	+	0.0432800i
$383$	−5.68364	−	7.82286i	−0.290420	−	0.399729i	0.638730	−	0.769431i	$-0.279460\pi$
$383$	−5.68364	−	7.82286i	−0.290420	−	0.399729i	−0.929151	+	0.369701i	$0.879460\pi$
$384$	2.07310			0.105792
$385$	11.9181	−	15.0215i	0.607404	−	0.765566i
$386$	12.9279			0.658012
$387$	−4.28883	−	5.90307i	−0.218014	−	0.300070i
$388$	−4.94818	+	1.60776i	−0.251206	+	0.0816217i
$389$	8.45759	−	26.0298i	0.428817	−	1.31976i	−0.470475	−	0.882414i	$-0.655917\pi$
$389$	8.45759	−	26.0298i	0.428817	−	1.31976i	0.899292	−	0.437350i	$-0.144083\pi$
$390$	2.77109	+	0.0295508i	0.140320	+	0.00149636i
$391$	26.1776	+	19.0192i	1.32386	+	0.961840i
$392$	0.915163	+	0.297354i	0.0462227	+	0.0150187i
$393$	−3.51877	+	1.14332i	−0.177498	+	0.0576727i
$394$	1.32444	−	0.962262i	0.0667243	−	0.0484780i
$395$	−12.5666	−	17.6902i	−0.632296	−	0.890088i
$396$	−0.143975	+	4.53669i	−0.00723503	+	0.227977i
$397$		−	10.6518i		−	0.534596i	−0.963614	−	0.267298i	$-0.913869\pi$
$397$		−	10.6518i		−	0.534596i	0.963614	−	0.267298i	$-0.0861308\pi$
$398$	−3.77401	−	5.19448i	−0.189174	−	0.260376i
$399$	−0.0807283	−	0.248456i	−0.00404147	−	0.0124384i
$400$	−11.2187	−	8.52220i	−0.560933	−	0.426110i
$401$	−11.0953	−	8.06124i	−0.554075	−	0.402559i	0.275210	−	0.961384i	$-0.411252\pi$
$401$	−11.0953	−	8.06124i	−0.554075	−	0.402559i	−0.829286	+	0.558825i	$0.811252\pi$
$402$	0.846448	−	1.16504i	0.0422170	−	0.0581067i
$403$	−1.48076	−	0.481129i	−0.0737621	−	0.0239668i
$404$	2.04088	+	6.28119i	0.101538	+	0.312501i
$405$	−16.5827	−	5.58423i	−0.824000	−	0.277482i
$406$	10.6026			0.526196
$407$	1.36918	+	1.06272i	0.0678676	+	0.0526771i
$408$			4.28514i			0.212146i
$409$	−18.0478	+	13.1125i	−0.892408	+	0.648372i	−0.936505	−	0.350655i	$-0.885959\pi$
$409$	−18.0478	+	13.1125i	−0.892408	+	0.648372i	0.0440970	+	0.999027i	$0.485959\pi$
$410$	11.3223	+	8.41202i	0.559167	+	0.415440i
$411$	−0.488831	+	1.50447i	−0.0241123	+	0.0742099i
$412$	3.75622	−	5.16999i	0.185056	−	0.254707i
$413$	−11.4093	+	15.7035i	−0.561413	+	0.772719i
$414$	9.18699	−	28.2747i	0.451516	−	1.38962i
$415$	−5.91776	−	4.39668i	−0.290492	−	0.215824i
$416$	−5.88621	+	4.27658i	−0.288595	+	0.209677i
$417$			3.02195i			0.147986i
$418$	0.939840	−	0.638290i	0.0459691	−	0.0312198i
$419$	0.510725			0.0249506			0.0124753	−	0.999922i	$-0.496029\pi$
$419$	0.510725			0.0249506			0.0124753	+	0.999922i	$0.496029\pi$
$420$	0.951815	+	0.320524i	0.0464438	+	0.0156400i
$421$	4.08365	+	12.5682i	0.199025	+	0.612536i	0.999906	+	0.0137124i	$0.00436492\pi$
$421$	4.08365	+	12.5682i	0.199025	+	0.612536i	−0.800881	+	0.598824i	$0.795635\pi$
$422$	22.2004	+	7.21335i	1.08070	+	0.351140i
$423$	8.30062	−	11.4248i	0.403590	−	0.555494i
$424$	−21.5676	−	15.6698i	−1.04741	−	0.760991i
$425$	11.6482	−	15.3337i	0.565019	−	0.743793i
$426$	1.16602	+	3.58864i	0.0564939	+	0.173870i
$427$	−21.5488	−	29.6594i	−1.04282	−	1.43532i
$428$		−	4.89641i		−	0.236677i
$429$	−1.87145	−	2.75558i	−0.0903543	−	0.133041i
$430$	−4.06616	−	5.72397i	−0.196088	−	0.276034i
$431$	23.7902	−	17.2846i	1.14594	−	0.832571i	0.158000	−	0.987439i	$-0.449495\pi$
$431$	23.7902	−	17.2846i	1.14594	−	0.832571i	0.987935	+	0.154868i	$0.0494952\pi$
$432$	5.72316	−	1.85957i	0.275356	−	0.0894685i
$433$	−9.71650	−	3.15708i	−0.466945	−	0.151720i	0.0660883	−	0.997814i	$-0.478948\pi$
$433$	−9.71650	−	3.15708i	−0.466945	−	0.151720i	−0.533034	+	0.846094i	$0.678948\pi$
$434$	1.45650	+	1.05821i	0.0699142	+	0.0507956i
$435$	−2.70446	−	0.0288402i	−0.129669	−	0.00138278i
$436$	0.728944	−	2.24346i	0.0349101	−	0.107442i
$437$	2.21811	−	0.720709i	0.106107	−	0.0344762i
$438$	−3.44137	−	4.73664i	−0.164435	−	0.226325i
$439$	1.53306			0.0731691			0.0365846	−	0.999331i	$-0.488352\pi$
$439$	1.53306			0.0731691			0.0365846	+	0.999331i	$0.488352\pi$
$440$	−0.960695	+	22.6504i	−0.0457993	+	1.07981i
$441$	0.902638			0.0429827
$442$	7.70779	+	10.6089i	0.366622	+	0.504612i
$443$	−3.22650	+	1.04835i	−0.153296	+	0.0498088i	−0.384660	−	0.923058i	$-0.625681\pi$
$443$	−3.22650	+	1.04835i	−0.153296	+	0.0498088i	0.231364	+	0.972867i	$0.425681\pi$
$444$	−0.0280526	+	0.0863370i	−0.00133132	+	0.00409737i
$445$	−0.0593292	+	5.56353i	−0.00281247	+	0.263737i
$446$	21.8356	+	15.8645i	1.03394	+	0.751204i
$447$	−2.93097	−	0.952329i	−0.138630	−	0.0450436i
$448$	21.8589	−	7.10238i	1.03274	−	0.335556i
$449$	−26.1718	+	19.0149i	−1.23512	+	0.897368i	−0.997263	−	0.0739317i	$-0.976445\pi$
$449$	−26.1718	+	19.0149i	−1.23512	+	0.897368i	−0.237858	+	0.971300i	$0.576445\pi$
$450$	−16.7061	−	5.82487i	−0.787535	−	0.274587i
$451$	0.537783	−	16.9456i	0.0253232	−	0.797939i
$452$		−	4.73637i		−	0.222780i
$453$	−2.37527	−	3.26927i	−0.111600	−	0.153604i
$454$	−0.929918	−	2.86199i	−0.0436432	−	0.134320i
$455$	15.2239	−	4.76766i	0.713705	−	0.223512i
$456$	0.249878	+	0.181547i	0.0117016	+	0.00850171i
$457$	−7.15509	+	9.84814i	−0.334701	+	0.460676i	−0.942884	−	0.333120i	$-0.891899\pi$
$457$	−7.15509	+	9.84814i	−0.334701	+	0.460676i	0.608183	+	0.793797i	$0.291899\pi$
$458$	−8.56865	−	2.78412i	−0.400387	−	0.130094i
$459$	2.54166	+	7.82243i	0.118635	+	0.365120i
$460$	−2.86151	+	8.49741i	−0.133418	+	0.396194i
$461$	−16.5699			−0.771739			−0.385869	−	0.922553i	$-0.626098\pi$
$461$	−16.5699			−0.771739			−0.385869	+	0.922553i	$0.626098\pi$
$462$	1.07343	+	3.69905i	0.0499407	+	0.172095i
$463$			14.6302i			0.679924i	0.940439	+	0.339962i	$0.110414\pi$
$463$			14.6302i			0.679924i	−0.940439	+	0.339962i	$0.889586\pi$
$464$	−7.57517	+	5.50368i	−0.351669	+	0.255502i
$465$	−0.368640	−	0.273885i	−0.0170953	−	0.0127011i
$466$	−1.70006	+	5.23226i	−0.0787539	+	0.242380i
$467$	−17.9188	+	24.6632i	−0.829185	+	1.14128i	0.158889	+	0.987296i	$0.449209\pi$
$467$	−17.9188	+	24.6632i	−0.829185	+	1.14128i	−0.988074	+	0.153979i	$0.950791\pi$
$468$	−2.21961	+	3.05504i	−0.102602	+	0.141219i
$469$	2.56170	−	7.88411i	0.118288	−	0.364054i
$470$	8.10412	−	10.9078i	0.373815	−	0.503141i
$471$	−4.05372	+	2.94520i	−0.186785	+	0.135707i
$472$		−	22.9491i		−	1.05632i
$473$	−2.86120	+	7.93957i	−0.131558	+	0.365062i
$474$	4.35868			0.200201
$475$	−0.400654	−	1.32887i	−0.0183833	−	0.0609728i
$476$	1.46857	+	4.51981i	0.0673120	+	0.207165i
$477$	−23.7833	−	7.72766i	−1.08896	−	0.353825i
$478$	−17.5345	+	24.1342i	−0.802009	+	1.10387i
$479$	11.3257	+	8.22857i	0.517482	+	0.375973i	0.815655	−	0.578539i	$-0.196377\pi$
$479$	11.3257	+	8.22857i	0.517482	+	0.375973i	−0.298172	+	0.954512i	$0.596377\pi$
$480$	−2.04800	+	0.641373i	−0.0934778	+	0.0292745i
$481$	0.445590	+	1.37138i	0.0203172	+	0.0625298i
$482$	8.73241	+	12.0191i	0.397750	+	0.547456i
$483$			7.90697i			0.359780i
$484$	4.43434	−	2.81027i	0.201561	−	0.127740i
$485$	−19.8726	+	14.1170i	−0.902367	+	0.641019i
$486$	9.23972	−	6.71305i	0.419122	−	0.304510i
$487$	32.4606	−	10.5471i	1.47093	−	0.477934i	0.539541	−	0.841960i	$-0.318598\pi$
$487$	32.4606	−	10.5471i	1.47093	−	0.477934i	0.931389	+	0.364026i	$0.118598\pi$
$488$	41.2229	+	13.3941i	1.86607	+	0.606324i
$489$	2.63282	+	1.91285i	0.119060	+	0.0865022i
$490$	0.868522	+	0.00926186i	0.0392358	+	0.000418408i
$491$	−0.987097	+	3.03797i	−0.0445470	+	0.137102i	−0.970856	−	0.239662i	$-0.922963\pi$
$491$	−0.987097	+	3.03797i	−0.0445470	+	0.137102i	0.926309	+	0.376764i	$0.122963\pi$
$492$	0.844543	−	0.274409i	0.0380750	−	0.0123713i
$493$	−7.52244	−	10.3538i	−0.338794	−	0.466310i
$494$	0.945184			0.0425258
$495$	5.70861	+	20.4855i	0.256583	+	0.920757i
$496$	−1.58993			−0.0713898
$497$	12.7675	+	17.5730i	0.572702	+	0.788257i
$498$	1.40837	−	0.457607i	0.0631106	−	0.0205059i
$499$	−2.01742	+	6.20897i	−0.0903120	+	0.277952i	−0.986004	−	0.166724i	$-0.946681\pi$
$499$	−2.01742	+	6.20897i	−0.0903120	+	0.277952i	0.895692	+	0.444676i	$0.146681\pi$
$500$	5.01943	+	1.81037i	0.224476	+	0.0809620i
$501$	4.98186	+	3.61953i	0.222573	+	0.161709i
$502$	−0.629504	−	0.204538i	−0.0280961	−	0.00912898i
$503$	−0.954737	+	0.310213i	−0.0425696	+	0.0138317i	−0.330224	−	0.943902i	$-0.607124\pi$
$503$	−0.954737	+	0.310213i	−0.0425696	+	0.0138317i	0.287655	+	0.957734i	$0.407124\pi$
$504$	18.3361	−	13.3219i	0.816753	−	0.593406i
$505$	17.9200	+	25.2261i	0.797430	+	1.12255i
$506$	−33.0236	+	9.58317i	−1.46808	+	0.426024i
$507$			1.96052i			0.0870697i
$508$	3.12387	+	4.29964i	0.138599	+	0.190766i
$509$	1.32074	+	4.06483i	0.0585409	+	0.180170i	0.976051	−	0.217542i	$-0.0698041\pi$
$509$	1.32074	+	4.06483i	0.0585409	+	0.180170i	−0.917510	+	0.397713i	$0.869804\pi$
$510$	1.15596	+	3.69116i	0.0511869	+	0.163447i
$511$	−27.2669	−	19.8105i	−1.20621	−	0.876366i
$512$	−14.4929	+	19.9477i	−0.640501	+	0.881574i
$513$	0.563828	+	0.183199i	0.0248936	+	0.00808842i
$514$	9.04501	+	27.8377i	0.398958	+	1.22787i
$515$	9.55531	−	28.3750i	0.421057	−	1.25035i
$516$	−0.442028			−0.0194592
$517$	−16.3254	−	0.518099i	−0.717990	−	0.0227860i
$518$		−	1.66735i		−	0.0732590i
$519$	0.995271	−	0.723107i	0.0436875	−	0.0317409i
$520$	−11.2484	+	15.1399i	−0.493273	+	0.663928i
$521$	−3.05561	+	9.40421i	−0.133869	+	0.412006i	−0.995412	−	0.0956779i	$-0.969498\pi$
$521$	−3.05561	+	9.40421i	−0.133869	+	0.412006i	0.861544	+	0.507684i	$0.169498\pi$
$522$	−6.91158	+	9.51297i	−0.302512	+	0.416371i
$523$	25.9607	−	35.7318i	1.13518	−	1.56244i	0.357351	−	0.933970i	$-0.383680\pi$
$523$	25.9607	−	35.7318i	1.13518	−	1.56244i	0.777831	−	0.628474i	$-0.216320\pi$
$524$	1.49914	−	4.61387i	0.0654901	−	0.201558i
$525$	4.70446	+	0.100347i	0.205319	+	0.00437952i
$526$	−4.96808	+	3.60952i	−0.216619	+	0.157383i
$527$		−	2.17311i		−	0.0946623i
$528$	−2.68708	−	2.08564i	−0.116940	−	0.0907659i
$529$	−47.5902			−2.06914
$530$	−22.8051	−	7.67962i	−0.990589	−	0.333581i
$531$	−6.65227	−	20.4736i	−0.288684	−	0.888477i
$532$	0.325780	+	0.105852i	0.0141244	+	0.00458928i
$533$	8.29081	−	11.4113i	0.359115	−	0.494279i
$534$	−0.904152	−	0.656905i	−0.0391265	−	0.0284270i
$535$	−6.85602	−	21.8923i	−0.296412	−	0.946486i
$536$	3.02869	+	9.32135i	0.130820	+	0.402621i
$537$	2.95754	+	4.07070i	0.127627	+	0.175664i
$538$		−	35.5447i		−	1.53244i
$539$	−0.586552	−	0.863660i	−0.0252646	−	0.0372005i
$540$	−1.85806	+	1.31992i	−0.0799581	+	0.0568002i
$541$	17.2074	−	12.5019i	0.739805	−	0.537499i	−0.152845	−	0.988250i	$-0.548844\pi$
$541$	17.2074	−	12.5019i	0.739805	−	0.537499i	0.892650	+	0.450751i	$0.148844\pi$
$542$	18.8670	−	6.13026i	0.810406	−	0.263317i
$543$	−0.899692	−	0.292328i	−0.0386095	−	0.0125450i
$544$	−8.21558	−	5.96897i	−0.352240	−	0.255918i
$545$	0.117851	−	11.0514i	0.00504820	−	0.473390i
$546$	−0.990219	+	3.04758i	−0.0423775	+	0.130424i
$547$	3.93160	−	1.27746i	0.168103	−	0.0546201i	−0.223756	−	0.974645i	$-0.571832\pi$
$547$	3.93160	−	1.27746i	0.168103	−	0.0546201i	0.391859	+	0.920025i	$0.371832\pi$
$548$	−1.21919	−	1.67806i	−0.0520810	−	0.0716834i
$549$	40.6587			1.73527
$550$	5.28265	+	19.7699i	0.225253	+	0.842989i
$551$	−0.922455			−0.0392979
$552$	−5.49485	−	7.56301i	−0.233876	−	0.321903i
$553$	23.8631	−	7.75358i	1.01476	−	0.329716i
$554$	6.86529	−	21.1292i	0.291678	−	0.897694i
$555$	−0.00453538	+	0.425300i	−0.000192516	+	0.0180530i
$556$	−3.20568	−	2.32906i	−0.135951	−	0.0987742i
$557$	−30.1172	−	9.78568i	−1.27611	−	0.414633i	−0.408900	−	0.912579i	$-0.634088\pi$
$557$	−30.1172	−	9.78568i	−1.27611	−	0.414633i	−0.867208	+	0.497947i	$0.834088\pi$
$558$	−1.89892	+	0.616997i	−0.0803877	+	0.0261196i
$559$	−5.68028	+	4.12697i	−0.240250	+	0.174552i
$560$	13.2808	−	9.43431i	0.561214	−	0.398673i
$561$	2.85066	−	3.67270i	0.120355	−	0.155061i
$562$			16.9242i			0.713904i
$563$	7.49233	+	10.3123i	0.315764	+	0.434612i	0.937168	−	0.348879i	$-0.113437\pi$
$563$	7.49233	+	10.3123i	0.315764	+	0.434612i	−0.621404	+	0.783490i	$0.713437\pi$
$564$	−0.264365	−	0.813631i	−0.0111318	−	0.0342600i
$565$	−6.63193	−	21.1767i	−0.279007	−	0.890912i
$566$	−20.4700	−	14.8723i	−0.860419	−	0.625131i
$567$	11.8925	−	16.3686i	0.499437	−	0.687416i
$568$	−24.4243	−	7.93592i	−1.02482	−	0.332984i
$569$	−4.83153	−	14.8699i	−0.202548	−	0.623380i	−0.999805	−	0.0197396i	$-0.993716\pi$
$569$	−4.83153	−	14.8699i	−0.202548	−	0.623380i	0.797257	−	0.603640i	$-0.206284\pi$
$570$	0.264215	+	0.0889746i	0.0110668	+	0.00372674i
$571$	−3.61999			−0.151492			−0.0757460	−	0.997127i	$-0.524134\pi$
$571$	−3.61999			−0.151492			−0.0757460	+	0.997127i	$0.524134\pi$
$572$	4.36547	+	0.138541i	0.182529	+	0.00579271i
$573$			0.807429i			0.0337308i
$574$	−13.1950	+	9.58671i	−0.550748	+	0.400142i
$575$	−0.895861	+	41.9994i	−0.0373600	+	1.75150i
$576$	−7.87684	+	24.2424i	−0.328202	+	1.01010i
$577$	14.0100	−	19.2831i	0.583243	−	0.802765i	−0.410803	−	0.911724i	$-0.634752\pi$
$577$	14.0100	−	19.2831i	0.583243	−	0.802765i	0.994046	+	0.108959i	$0.0347516\pi$
$578$	1.57246	−	2.16431i	0.0654058	−	0.0900234i
$579$	1.17836	−	3.62661i	0.0489709	−	0.150717i
$580$	2.11496	−	2.84665i	0.0878189	−	0.118201i
$581$	6.89657	−	5.01065i	0.286118	−	0.207877i
$582$		−	4.89641i		−	0.202963i
$583$	8.06090	+	27.7779i	0.333848	+	1.15044i
$584$	39.8478			1.64891
$585$	−5.64640	+	16.7673i	−0.233450	+	0.693242i
$586$	−8.54674	−	26.3042i	−0.353063	−	1.08661i
$587$	1.18595	+	0.385338i	0.0489493	+	0.0159046i	0.333389	−	0.942789i	$-0.391808\pi$
$587$	1.18595	+	0.385338i	0.0489493	+	0.0159046i	−0.284440	+	0.958694i	$0.591808\pi$
$588$	0.0321412	−	0.0442385i	0.00132548	−	0.00182436i
$589$	−0.126720	−	0.0920674i	−0.00522140	−	0.00379357i
$590$	−6.19076	−	19.7680i	−0.254870	−	0.813836i
$591$	−0.149219	−	0.459249i	−0.00613805	−	0.0188910i
$592$	0.865504	+	1.19126i	0.0355720	+	0.0489606i
$593$		−	18.5288i		−	0.760886i	−0.924804	−	0.380443i	$-0.875772\pi$
$593$		−	18.5288i		−	0.760886i	0.924804	−	0.380443i	$-0.124228\pi$
$594$	−8.22300	−	2.96333i	−0.337394	−	0.121587i
$595$	12.8948	+	18.1522i	0.528637	+	0.744166i
$596$	3.26917	−	2.37519i	0.133910	−	0.0972915i
$597$	−1.80118	+	0.585240i	−0.0737176	+	0.0239523i
$598$	−27.2075	−	8.84026i	−1.11260	−	0.361505i
$599$	27.3738	+	19.8882i	1.11846	+	0.812611i	0.983975	−	0.178304i	$-0.0570612\pi$
$599$	27.3738	+	19.8882i	1.11846	+	0.812611i	0.134488	+	0.990915i	$0.457061\pi$
$600$	−4.56954	+	3.17332i	−0.186551	+	0.129550i
$601$	−6.58286	+	20.2600i	−0.268520	+	0.826421i	0.722341	+	0.691537i	$0.243066\pi$
$601$	−6.58286	+	20.2600i	−0.268520	+	0.826421i	−0.990861	+	0.134884i	$0.956934\pi$
$602$	7.72132	−	2.50881i	0.314698	−	0.102251i
$603$	5.40397	+	7.43793i	0.220067	+	0.302896i
$604$	5.29869			0.215601
$605$	15.8914	−	18.7740i	0.646076	−	0.763273i
$606$	−6.21547			−0.252486
$607$	−22.0185	−	30.3059i	−0.893704	−	1.23008i	−0.972433	−	0.233182i	$-0.925086\pi$
$607$	−22.0185	−	30.3059i	−0.893704	−	1.23008i	0.0787287	−	0.996896i	$-0.474914\pi$
$608$	−0.696133	+	0.226187i	−0.0282319	+	0.00917310i
$609$	0.966407	−	2.97430i	0.0391608	−	0.120525i
$610$	39.1220	+	0.417194i	1.58400	+	0.0168917i
$611$	−10.9936	−	7.98734i	−0.444755	−	0.323133i
$612$	−5.01266	−	1.62871i	−0.202625	−	0.0658367i
$613$	−19.0256	+	6.18180i	−0.768437	+	0.249680i	−0.666896	−	0.745151i	$-0.732377\pi$
$613$	−19.0256	+	6.18180i	−0.768437	+	0.249680i	−0.101541	+	0.994831i	$0.532377\pi$
$614$	20.2703	−	14.7272i	0.818043	−	0.594343i
$615$	3.39180	−	2.40945i	0.136771	−	0.0971584i
$616$	−24.6618	−	8.88741i	−0.993652	−	0.358084i
$617$			34.7932i			1.40072i	0.713790	+	0.700360i	$0.246977\pi$
$617$			34.7932i			1.40072i	−0.713790	+	0.700360i	$0.753023\pi$
$618$	3.53500	+	4.86551i	0.142198	+	0.195719i
$619$	14.2407	+	43.8285i	0.572384	+	1.76162i	0.644920	+	0.764250i	$0.276891\pi$
$619$	14.2407	+	43.8285i	0.572384	+	1.76162i	−0.0725362	+	0.997366i	$0.523109\pi$
$620$	0.574653	−	0.179964i	0.0230786	−	0.00722754i
$621$	−14.5166	−	10.5469i	−0.582530	−	0.423233i
$622$	−6.35297	+	8.74411i	−0.254731	+	0.350607i
$623$	−6.11864	−	1.98807i	−0.245138	−	0.0796502i
$624$	−0.874492	−	2.69141i	−0.0350077	−	0.107743i
$625$	24.9773	+	1.06603i	0.999090	+	0.0426412i
$626$	−2.13633			−0.0853849
$627$	−0.0933921	−	0.321829i	−0.00372972	−	0.0128526i
$628$		−	6.57008i		−	0.262175i
$629$	−1.62822	+	1.18297i	−0.0649214	+	0.0471682i
$630$	12.2007	−	16.4216i	0.486086	−	0.654254i
$631$	−6.34658	+	19.5328i	−0.252653	+	0.777587i	0.741629	+	0.670810i	$0.234053\pi$
$631$	−6.34658	+	19.5328i	−0.252653	+	0.777587i	−0.994283	+	0.106778i	$0.965947\pi$
$632$	−17.4367	+	23.9996i	−0.693596	+	0.954653i
$633$	4.04707	−	5.57031i	0.160857	−	0.221400i
$634$	6.66419	−	20.5103i	0.264669	−	0.814567i
$635$	19.9875	+	14.8500i	0.793181	+	0.589304i
$636$	−1.22561	+	0.890458i	−0.0485986	+	0.0353090i
$637$		−	0.868571i		−	0.0344140i
$638$	13.5935	+	0.431399i	0.538171	+	0.0170793i
$639$	−24.0900			−0.952985
$640$	−4.06450	+	12.0698i	−0.160664	+	0.477100i
$641$	4.91631	+	15.1309i	0.194183	+	0.597633i	0.999985	+	0.00544856i	$0.00173434\pi$
$641$	4.91631	+	15.1309i	0.194183	+	0.597633i	−0.805802	+	0.592185i	$0.798266\pi$
$642$	4.38250	+	1.42396i	0.172963	+	0.0561992i
$643$	−24.8656	+	34.2246i	−0.980603	+	1.34968i	−0.0440996	+	0.999027i	$0.514042\pi$
$643$	−24.8656	+	34.2246i	−0.980603	+	1.34968i	−0.936504	+	0.350658i	$0.885958\pi$
$644$	−8.38769	−	6.09402i	−0.330521	−	0.240138i
$645$	−1.97635	+	0.618935i	−0.0778187	+	0.0243705i
$646$	0.407663	+	1.25466i	0.0160393	+	0.0493639i
$647$	4.40187	+	6.05866i	0.173055	+	0.238190i	0.886731	−	0.462286i	$-0.152971\pi$
$647$	4.40187	+	6.05866i	0.173055	+	0.238190i	−0.713675	+	0.700477i	$0.752971\pi$
$648$			23.9210i			0.939707i
$649$	−15.2667	+	19.6692i	−0.599271	+	0.772082i
$650$	−5.60503	+	16.0756i	−0.219847	+	0.630538i
$651$	0.429613	−	0.312132i	0.0168379	−	0.0122334i
$652$	−4.05830	+	1.31862i	−0.158935	+	0.0516412i
$653$	−15.6641	−	5.08959i	−0.612985	−	0.199171i	−0.0139618	−	0.999903i	$-0.504444\pi$
$653$	−15.6641	−	5.08959i	−0.612985	−	0.199171i	−0.599023	+	0.800732i	$0.704444\pi$
$654$	1.79601	+	1.30487i	0.0702294	+	0.0510246i
$655$	0.242372	−	22.7282i	0.00947025	−	0.888063i
$656$	4.45100	−	13.6988i	0.173782	−	0.534847i
$657$	35.5494	−	11.5507i	1.38691	−	0.450635i
$658$	9.23581	+	12.7120i	0.360050	+	0.495566i
$659$	−23.7359			−0.924619			−0.462310	−	0.886719i	$-0.652979\pi$
$659$	−23.7359			−0.924619			−0.462310	+	0.886719i	$0.652979\pi$
$660$	1.20727	+	0.449670i	0.0469931	+	0.0175034i
$661$	13.4183			0.521911			0.260956	−	0.965351i	$-0.415962\pi$
$661$	13.4183			0.521911			0.260956	+	0.965351i	$0.415962\pi$
$662$	−9.15308	−	12.5981i	−0.355745	−	0.489640i
$663$	3.67862	−	1.19526i	0.142866	−	0.0464199i
$664$	−3.11447	+	9.58536i	−0.120865	+	0.371984i
$665$	1.60481	+	0.0171136i	0.0622319	+	0.000663637i
$666$	1.49600	+	1.08691i	0.0579688	+	0.0421168i
$667$	26.5533	+	8.62768i	1.02815	+	0.334065i
$668$	−7.67918	+	2.49512i	−0.297116	+	0.0965389i
$669$	6.44068	−	4.67943i	0.249011	−	0.180917i
$670$	5.12340	+	7.21225i	0.197934	+	0.278634i
$671$	−26.4209	−	38.9030i	−1.01997	−	1.50183i
$672$		−	2.48152i		−	0.0957268i
$673$	28.3824	+	39.0650i	1.09406	+	1.50585i	0.843030	+	0.537867i	$0.180770\pi$
$673$	28.3824	+	39.0650i	1.09406	+	1.50585i	0.251031	+	0.967979i	$0.419230\pi$
$674$	−4.52246	−	13.9187i	−0.174199	−	0.536128i
$675$	−6.45939	+	8.50316i	−0.248622	+	0.327287i
$676$	−2.07971	−	1.51100i	−0.0799889	−	0.0581154i
$677$	14.3206	−	19.7107i	0.550387	−	0.757543i	−0.439678	−	0.898156i	$-0.644907\pi$
$677$	14.3206	−	19.7107i	0.550387	−	0.757543i	0.990065	+	0.140613i	$0.0449073\pi$
$678$	4.23926	+	1.37742i	0.162808	+	0.0528994i
$679$	−8.71013	−	26.8070i	−0.334264	−	1.02876i
$680$	−24.9485	−	8.40142i	−0.956731	−	0.322180i
$681$	−0.887625			−0.0340139
$682$	1.82431	+	1.41598i	0.0698565	+	0.0542209i
$683$		−	38.9856i		−	1.49174i	−0.666090	−	0.745871i	$-0.732034\pi$
$683$		−	38.9856i		−	1.49174i	0.666090	−	0.745871i	$-0.267966\pi$
$684$	−0.307344	+	0.223298i	−0.0117516	+	0.00853802i
$685$	−7.80074	−	5.79566i	−0.298051	−	0.221441i
$686$	−7.21198	+	22.1962i	−0.275355	+	0.847454i
$687$	−1.56204	+	2.14996i	−0.0595956	+	0.0820263i
$688$	−4.21433	+	5.80053i	−0.160670	+	0.221143i
$689$	−7.43600	+	22.8857i	−0.283289	+	0.871875i
$690$	−6.77338	−	5.03237i	−0.257858	−	0.191579i
$691$	−4.78820	+	3.47883i	−0.182152	+	0.132341i	−0.675125	−	0.737704i	$-0.735910\pi$
$691$	−4.78820	+	3.47883i	−0.182152	+	0.132341i	0.492973	+	0.870045i	$0.335910\pi$
$692$			1.61309i			0.0613205i
$693$	−24.5777	−	0.779993i	−0.933630	−	0.0296295i
$694$	−27.5230			−1.04476
$695$	−17.5941	−	5.92481i	−0.667381	−	0.224741i
$696$	1.14258	+	3.51650i	0.0433094	+	0.133293i
$697$	18.7235	+	6.08364i	0.709203	+	0.230434i
$698$	−11.5819	+	15.9411i	−0.438380	+	0.603378i
$699$	1.31283	+	0.953826i	0.0496557	+	0.0360770i
$700$	−3.73224	+	4.91313i	−0.141065	+	0.185699i
$701$	3.69808	+	11.3815i	0.139675	+	0.429874i	0.996288	−	0.0860851i	$-0.0274357\pi$
$701$	3.69808	+	11.3815i	0.139675	+	0.429874i	−0.856613	+	0.515959i	$0.827436\pi$
$702$	−4.27429	−	5.88306i	−0.161323	−	0.222042i
$703$			0.145064i			0.00547120i
$704$	28.3141	−	8.21652i	1.06713	−	0.309672i
$705$	−2.32126	−	3.26765i	−0.0874236	−	0.123067i
$706$	24.1001	−	17.5098i	0.907021	−	0.658989i
$707$	−34.0287	+	11.0566i	−1.27978	+	0.415826i
$708$	−1.24029	−	0.402994i	−0.0466129	−	0.0151455i
$709$	5.50819	+	4.00194i	0.206865	+	0.150296i	0.686394	−	0.727230i	$-0.259193\pi$
$709$	5.50819	+	4.00194i	0.206865	+	0.150296i	−0.479529	+	0.877526i	$0.659193\pi$
$710$	−23.1795	−	0.247185i	−0.869911	−	0.00927668i
$711$	−8.59904	+	26.4651i	−0.322489	+	0.992520i
$712$	7.23405	−	2.35048i	0.271107	−	0.0880881i
$713$	2.78659	+	3.83541i	0.104358	+	0.143637i
$714$	−4.47251			−0.167380
$715$	19.7124	−	5.49316i	0.737202	−	0.205433i
$716$	−6.59761			−0.246564
$717$	5.17202	+	7.11868i	0.193153	+	0.265852i
$718$	23.9160	−	7.77077i	0.892537	−	0.290003i
$719$	2.86277	−	8.81069i	0.106763	−	0.328583i	−0.883377	−	0.468663i	$-0.844736\pi$
$719$	2.86277	−	8.81069i	0.106763	−	0.328583i	0.990140	+	0.140080i	$0.0447359\pi$
$720$	−0.192655	+	18.0660i	−0.00717981	+	0.673279i
$721$	28.0087	+	20.3495i	1.04310	+	0.757855i
$722$	−22.2079	−	7.21579i	−0.826493	−	0.268544i
$723$	4.16763	−	1.35414i	0.154996	−	0.0503612i
$724$	1.00351	−	0.729090i	0.0372950	−	0.0270964i
$725$	5.47025	−	15.6891i	0.203160	−	0.582677i
$726$	1.22574	+	4.78621i	0.0454913	+	0.177633i
$727$			19.4121i			0.719956i	0.932961	+	0.359978i	$0.117216\pi$
$727$			19.4121i			0.719956i	−0.932961	+	0.359978i	$0.882784\pi$
$728$	−12.8191	−	17.6440i	−0.475109	−	0.653931i
$729$	6.21336	+	19.1228i	0.230125	+	0.708250i
$730$	34.3243	−	10.7494i	1.27040	−	0.397851i
$731$	−7.92817	−	5.76015i	−0.293234	−	0.213047i
$732$	1.44778	−	1.99269i	0.0535114	−	0.0736521i
$733$	−10.9962	−	3.57287i	−0.406152	−	0.131967i	0.0988140	−	0.995106i	$-0.468495\pi$
$733$	−10.9962	−	3.57287i	−0.406152	−	0.131967i	−0.504966	+	0.863139i	$0.668495\pi$
$734$	−2.06079	−	6.34247i	−0.0760653	−	0.234105i
$735$	0.0817627	−	0.242799i	0.00301586	−	0.00895578i
$736$	22.1540			0.816608
$737$	3.60513	−	10.0039i	0.132797	−	0.368500i
$738$		−	18.0884i		−	0.665842i
$739$	7.36801	−	5.35317i	0.271037	−	0.196920i	−0.443962	−	0.896046i	$-0.646427\pi$
$739$	7.36801	−	5.35317i	0.271037	−	0.196920i	0.714998	+	0.699126i	$0.246427\pi$
$740$	−0.447662	−	0.332596i	−0.0164564	−	0.0122265i
$741$	0.0861521	−	0.265149i	0.00316488	−	0.00974049i
$742$	16.3549	−	22.5106i	0.600409	−	0.826391i
$743$	−0.0429676	+	0.0591398i	−0.00157633	+	0.00216963i	−0.809804	−	0.586700i	$-0.800427\pi$
$743$	−0.0429676	+	0.0591398i	−0.00157633	+	0.00216963i	0.808228	+	0.588870i	$0.200427\pi$
$744$	−0.194012	+	0.597108i	−0.00711283	+	0.0218910i
$745$	11.2910	−	15.1972i	0.413669	−	0.556783i
$746$	17.0695	−	12.4017i	0.624959	−	0.454059i
$747$			9.45417i			0.345910i
$748$	1.69895	+	5.85457i	0.0621197	+	0.214064i
$749$	26.5265			0.969258
$750$	−3.08010	+	3.96613i	−0.112469	+	0.144823i
$751$	−11.9045	−	36.6384i	−0.434403	−	1.33695i	−0.893697	−	0.448670i	$-0.851898\pi$
$751$	−11.9045	−	36.6384i	−0.434403	−	1.33695i	0.459295	−	0.888284i	$-0.348102\pi$
$752$	−13.1974	−	4.28808i	−0.481258	−	0.156370i
$753$	−0.114757	+	0.157949i	−0.00418197	+	0.00575598i
$754$	9.15394	+	6.65073i	0.333367	+	0.242205i
$755$	23.6909	−	7.41930i	0.862201	−	0.270016i
$756$	−0.814385	−	2.50642i	−0.0296189	−	0.0911576i
$757$	−16.5530	−	22.7833i	−0.601630	−	0.828073i	0.394226	−	0.919013i	$-0.371013\pi$
$757$	−16.5530	−	22.7833i	−0.601630	−	0.828073i	−0.995856	+	0.0909407i	$0.971013\pi$
$758$			10.6024i			0.385097i
$759$	−0.321721	+	10.1375i	−0.0116777	+	0.367967i
$760$	−1.54689	+	1.09887i	−0.0561116	+	0.0398603i
$761$	23.8575	−	17.3335i	0.864832	−	0.628337i	−0.0643631	−	0.997927i	$-0.520502\pi$
$761$	23.8575	−	17.3335i	0.864832	−	0.628337i	0.929195	+	0.369589i	$0.120502\pi$
$762$	−4.75684	+	1.54559i	−0.172322	+	0.0559909i
$763$	12.1541	+	3.94909i	0.440006	+	0.142967i
$764$	−0.856518	−	0.622297i	−0.0309877	−	0.0225139i
$765$	−24.6926	−	0.263321i	−0.892763	−	0.00952037i
$766$	−3.68725	+	11.3482i	−0.133226	+	0.410027i
$767$	−19.7009	+	6.40120i	−0.711357	+	0.231134i
$768$	2.29991	+	3.16556i	0.0829910	+	0.114227i
$769$	−8.42410			−0.303781			−0.151890	−	0.988397i	$-0.548536\pi$
$769$	−8.42410			−0.303781			−0.151890	+	0.988397i	$0.548536\pi$
$770$	−23.6408	−	1.00270i	−0.851955	−	0.0361348i
$771$	8.63364			0.310933
$772$	2.93892	+	4.04508i	0.105774	+	0.145586i
$773$	0.853557	−	0.277338i	0.0307003	−	0.00997514i	−0.293627	−	0.955920i	$-0.594862\pi$
$773$	0.853557	−	0.277338i	0.0307003	−	0.00997514i	0.324327	+	0.945945i	$0.394862\pi$
$774$	−2.78238	+	8.56327i	−0.100010	+	0.307800i
$775$	2.31734	−	1.60928i	0.0832412	−	0.0578069i
$776$	26.9604	+	19.5879i	0.967822	+	0.703164i
$777$	−0.467735	−	0.151976i	−0.0167799	−	0.00545212i
$778$	−32.1206	+	10.4366i	−1.15158	+	0.374171i
$779$	1.14800	−	0.834074i	0.0411315	−	0.0298838i
$780$	0.620713	+	0.873782i	0.0222251	+	0.0312864i
$781$	15.6542	+	23.0497i	0.560150	+	0.824785i
$782$		−	39.9287i		−	1.42785i
$783$	4.17151	+	5.74159i	0.149077	+	0.205188i
$784$	−0.274085	−	0.843546i	−0.00978874	−	0.0301267i
$785$	−9.19952	−	29.3754i	−0.328345	−	1.04845i
$786$	3.69364	+	2.68359i	0.131748	+	0.0957205i
$787$	−22.2187	+	30.5814i	−0.792010	+	1.09011i	0.201844	+	0.979418i	$0.435306\pi$
$787$	−22.2187	+	30.5814i	−0.792010	+	1.09011i	−0.993855	+	0.110691i	$0.964694\pi$
$788$	0.602175	+	0.195659i	0.0214516	+	0.00697005i
$789$	0.559733	+	1.72268i	0.0199270	+	0.0613290i
$790$	−8.54559	+	25.3766i	−0.304039	+	0.902860i
$791$	25.6595			0.912346
$792$	24.0506	−	16.3339i	0.854601	−	0.580400i
$793$		−	39.1242i		−	1.38934i
$794$	−10.6339	+	7.72596i	−0.377382	+	0.274184i
$795$	−4.23299	+	5.69744i	−0.150129	+	0.202067i
$796$	0.767377	−	2.36174i	0.0271990	−	0.0837098i
$797$	8.92880	−	12.2894i	0.316274	−	0.435314i	−0.621051	−	0.783770i	$-0.713294\pi$
$797$	8.92880	−	12.2894i	0.316274	−	0.435314i	0.937325	+	0.348456i	$0.113294\pi$
$798$	−0.189485	+	0.260804i	−0.00670770	+	0.00923236i
$799$	5.86096	−	18.0382i	0.207346	−	0.638145i
$800$	0.281157	−	13.1811i	0.00994039	−	0.466022i
$801$	5.77237	−	4.19387i	0.203957	−	0.148183i
$802$			16.9237i			0.597598i
$803$	−34.1526	−	26.5084i	−1.20522	−	0.935461i
$804$	0.556959			0.0196424
$805$	−46.0351	−	15.5023i	−1.62252	−	0.546386i
$806$	0.593711	+	1.82725i	0.0209126	+	0.0643623i
$807$	−9.97122	−	3.23985i	−0.351004	−	0.114048i
$808$	24.8647	−	34.2234i	0.874739	−	1.20397i
$809$	−32.1268	−	23.3415i	−1.12952	−	0.820643i	−0.143893	−	0.989593i	$-0.545962\pi$
$809$	−32.1268	−	23.3415i	−1.12952	−	0.820643i	−0.985625	+	0.168951i	$0.945962\pi$
$810$	6.45295	+	20.6052i	0.226734	+	0.723994i
$811$	2.72454	+	8.38527i	0.0956715	+	0.294447i	0.987428	−	0.158069i	$-0.0505268\pi$
$811$	2.72454	+	8.38527i	0.0956715	+	0.294447i	−0.891757	+	0.452515i	$0.850527\pi$
$812$	2.41030	+	3.31749i	0.0845850	+	0.116421i
$813$		−	5.85145i		−	0.205219i
$814$	0.0678414	−	2.13770i	0.00237784	−	0.0749262i
$815$	−16.2987	+	11.5782i	−0.570918	+	0.405566i
$816$	3.19546	−	2.32164i	0.111864	−	0.0812736i
$817$	−0.671779	+	0.218274i	−0.0235026	+	0.00763645i
$818$	26.1810	+	8.50673i	0.915398	+	0.297431i
$819$	−16.5508	−	12.0249i	−0.578332	−	0.420183i
$820$	−0.0581719	+	5.45501i	−0.00203145	+	0.190497i
$821$	−2.60214	+	8.00856i	−0.0908153	+	0.279501i	−0.986141	−	0.165912i	$-0.946943\pi$
$821$	−2.60214	+	8.00856i	−0.0908153	+	0.279501i	0.895325	+	0.445413i	$0.146943\pi$
$822$	1.85650	−	0.603214i	0.0647530	−	0.0210395i
$823$	14.0504	+	19.3388i	0.489767	+	0.674107i	0.980345	−	0.197291i	$-0.0632143\pi$
$823$	14.0504	+	19.3388i	0.489767	+	0.674107i	−0.490578	+	0.871397i	$0.663214\pi$
$824$	−40.9319			−1.42593
$825$	6.02747	+	0.320071i	0.209850	+	0.0111434i
$826$	23.9526			0.833416
$827$	27.9268	+	38.4379i	0.971109	+	1.33662i	0.941485	+	0.337055i	$0.109431\pi$
$827$	27.9268	+	38.4379i	0.971109	+	1.33662i	0.0296239	+	0.999561i	$0.490569\pi$
$828$	10.9355	−	3.55317i	0.380036	−	0.123481i
$829$	8.71437	−	26.8201i	0.302663	−	0.931500i	−0.677876	−	0.735176i	$-0.737100\pi$
$829$	8.71437	−	26.8201i	0.302663	−	0.931500i	0.980539	−	0.196324i	$-0.0629004\pi$
$830$	−0.0970082	+	9.09685i	−0.00336720	+	0.315756i
$831$	−5.30154	−	3.85179i	−0.183908	−	0.133617i
$832$	23.3275	+	7.57956i	0.808735	+	0.262774i
$833$	1.15296	−	0.374620i	0.0399477	−	0.0129798i
$834$	3.01688	−	2.19189i	0.104466	−	0.0758990i
$835$	−30.8406	+	21.9084i	−1.06728	+	0.758171i
$836$	0.413374	+	0.148968i	0.0142968	+	0.00515217i
$837$			1.20508i			0.0416537i
$838$	−0.370441	−	0.509868i	−0.0127967	−	0.0176131i
$839$	−6.90363	−	21.2472i	−0.238340	−	0.733535i	−0.996661	−	0.0816534i	$-0.973980\pi$
$839$	−6.90363	−	21.2472i	−0.238340	−	0.733535i	0.758321	−	0.651881i	$-0.226020\pi$
$840$	−1.92253	−	6.13891i	−0.0663335	−	0.211813i
$841$	14.5277	+	10.5550i	0.500954	+	0.363965i
$842$	9.58513	−	13.1928i	0.330325	−	0.454654i
$843$	4.74768	+	1.54262i	0.163519	+	0.0531305i
$844$	2.78984	+	8.58624i	0.0960302	+	0.295551i
$845$	−11.4143	−	3.84377i	−0.392664	−	0.132230i
$846$	−17.4263			−0.599128
$847$	15.2248	+	24.0233i	0.523130	+	0.825449i
$848$			24.5728i			0.843833i
$849$	−6.03789	+	4.38679i	−0.207220	+	0.150554i
$850$	−23.7566	−	0.506736i	−0.814845	−	0.0173809i
$851$	1.35678	−	4.17574i	0.0465098	−	0.143143i
$852$	−0.857797	+	1.18066i	−0.0293876	+	0.0404486i
$853$	4.79201	−	6.59563i	0.164075	−	0.225830i	−0.719061	−	0.694947i	$-0.755428\pi$
$853$	4.79201	−	6.59563i	0.164075	−	0.225830i	0.883136	+	0.469117i	$0.155428\pi$
$854$	−13.9798	+	43.0254i	−0.478378	+	1.47230i
$855$	−1.06150	+	1.42873i	−0.0363024	+	0.0488617i
$856$	−25.3726	+	18.4343i	−0.867217	+	0.630070i
$857$			4.42433i			0.151132i	0.997141	+	0.0755662i	$0.0240764\pi$
$857$			4.42433i			0.151132i	−0.997141	+	0.0755662i	$0.975924\pi$
$858$	−1.39355	+	3.86699i	−0.0475752	+	0.132017i
$859$	−2.90501			−0.0991176			−0.0495588	−	0.998771i	$-0.515782\pi$
$859$	−2.90501			−0.0991176			−0.0495588	+	0.998771i	$0.515782\pi$
$860$	0.866637	−	2.57353i	0.0295521	−	0.0877566i
$861$	1.48662	+	4.57535i	0.0506640	+	0.155928i
$862$	−34.5112	−	11.2134i	−1.17546	−	0.381929i
$863$	10.4097	−	14.3277i	0.354351	−	0.487722i	−0.594213	−	0.804308i	$-0.702536\pi$
$863$	10.4097	−	14.3277i	0.354351	−	0.487722i	0.948564	+	0.316586i	$0.102536\pi$
$864$	4.55588	+	3.31004i	0.154994	+	0.112610i
$865$	2.25867	+	7.21227i	0.0767972	+	0.245225i
$866$	3.89582	+	11.9901i	0.132385	+	0.407440i
$867$	−0.463818	−	0.638391i	−0.0157521	−	0.0216809i
$868$			0.696297i			0.0236339i
$869$	30.9102	−	8.96987i	1.04856	−	0.304282i
$870$	1.93281	+	2.72084i	0.0655285	+	0.0922450i
$871$	7.15721	−	5.20002i	0.242513	−	0.176196i
$872$	−14.3697	+	4.66900i	−0.486619	+	0.158112i
$873$	29.7301	+	9.65990i	1.00621	+	0.326938i
$874$	−2.32835	−	1.69164i	−0.0787576	−	0.0572207i
$875$	−9.80775	+	27.1930i	−0.331562	+	0.919292i
$876$	0.699741	−	2.15358i	0.0236421	−	0.0727628i
$877$	−48.8651	+	15.8772i	−1.65006	+	0.536136i	−0.978753	−	0.205045i	$-0.934266\pi$
$877$	−48.8651	+	15.8772i	−1.65006	+	0.536136i	−0.671305	+	0.741181i	$0.734266\pi$
$878$	−1.11197	−	1.53049i	−0.0375270	−	0.0516516i
$879$	−8.15803			−0.275164
$880$	17.4110	−	11.5553i	0.586926	−	0.389529i
$881$	33.6727			1.13446			0.567231	−	0.823559i	$-0.308015\pi$
$881$	33.6727			1.13446			0.567231	+	0.823559i	$0.308015\pi$
$882$	−0.654704	−	0.901123i	−0.0220450	−	0.0303424i
$883$	−13.2297	+	4.29860i	−0.445216	+	0.144660i	−0.523041	−	0.852308i	$-0.675203\pi$
$883$	−13.2297	+	4.29860i	−0.445216	+	0.144660i	0.0778247	+	0.996967i	$0.475203\pi$
$884$	−1.56724	+	4.82347i	−0.0527120	+	0.162231i
$885$	−6.10973	−	0.0651538i	−0.205376	−	0.00219012i
$886$	3.38685	+	2.46069i	0.113783	+	0.0826685i
$887$	42.5128	+	13.8133i	1.42744	+	0.463804i	0.917958	−	0.396677i	$-0.129837\pi$
$887$	42.5128	+	13.8133i	1.42744	+	0.463804i	0.509483	+	0.860481i	$0.329837\pi$
$888$	0.553001	−	0.179681i	0.0185575	−	0.00602970i
$889$	−23.2935	+	16.9237i	−0.781239	+	0.567603i
$890$	5.59723	−	3.97613i	0.187620	−	0.133280i
$891$	15.9133	−	20.5022i	0.533115	−	0.686849i
$892$			10.4388i			0.349516i
$893$	−0.803545	−	1.10598i	−0.0268896	−	0.0370104i
$894$	1.17517	+	3.61680i	0.0393035	+	0.120964i
$895$	−29.4985	+	9.23807i	−0.986027	+	0.308795i
$896$	−11.9139	−	8.65598i	−0.398017	−	0.289176i
$897$	−4.95985	+	6.82665i	−0.165605	+	0.227935i
$898$	37.9660	+	12.3359i	1.26694	+	0.411654i
$899$	−0.579434	−	1.78331i	−0.0193252	−	0.0594768i
$900$	−1.97526	−	6.55146i	−0.0658421	−	0.218382i
$901$	−33.5861			−1.11892
$902$	−17.3073	+	11.7542i	−0.576269	+	0.391372i
$903$		−	2.39471i		−	0.0796909i
$904$	−24.5433	+	17.8317i	−0.816297	+	0.593074i
$905$	3.46589	−	4.66495i	0.115210	−	0.155068i
$906$	−1.54095	+	4.74256i	−0.0511947	+	0.157561i
$907$	13.4003	−	18.4440i	0.444950	−	0.612421i	−0.526353	−	0.850266i	$-0.676441\pi$
$907$	13.4003	−	18.4440i	0.444950	−	0.612421i	0.971303	+	0.237845i	$0.0764410\pi$
$908$	0.684106	−	0.941591i	0.0227028	−	0.0312478i
$909$	12.2622	−	37.7392i	0.406712	−	1.25173i
$910$	−15.8019	−	11.7402i	−0.523827	−	0.389184i
$911$	−30.3887	+	22.0787i	−1.00682	+	0.731499i	−0.963540	−	0.267564i	$-0.913781\pi$
$911$	−30.3887	+	22.0787i	−1.00682	+	0.731499i	−0.0432817	+	0.999063i	$0.513781\pi$
$912$		−	0.284696i		−	0.00942722i
$913$	9.04593	−	6.14352i	0.299376	−	0.203321i
$914$	15.0214			0.496863
$915$	3.68294	−	10.9367i	0.121754	−	0.361557i
$916$	−1.07679	−	3.31402i	−0.0355781	−	0.109498i
$917$	24.9959	+	8.12165i	0.825437	+	0.268201i
$918$	5.96577	−	8.21118i	0.196900	−	0.271009i
$919$	32.1280	+	23.3424i	1.05981	+	0.769994i	0.974053	−	0.226322i	$-0.0726701\pi$
$919$	32.1280	+	23.3424i	1.05981	+	0.769994i	0.0857538	+	0.996316i	$0.472670\pi$
$920$	54.8057	−	17.1635i	1.80689	−	0.565865i
$921$	−2.28377	−	7.02872i	−0.0752528	−	0.231604i
$922$	12.0186	+	16.5421i	0.395810	+	0.544786i
$923$			23.1808i			0.763005i
$924$	−0.913392	+	1.17679i	−0.0300484	+	0.0387134i
$925$	−2.46724	−	0.860246i	−0.0811225	−	0.0282847i
$926$	14.6057	−	10.6116i	0.479972	−	0.348720i
$927$	−36.5165	+	11.8649i	−1.19936	+	0.389696i
$928$	−8.33348	−	2.70771i	−0.273560	−	0.0888850i
$929$	16.7708	+	12.1847i	0.550231	+	0.399766i	0.827871	−	0.560919i	$-0.189552\pi$
$929$	16.7708	+	12.1847i	0.550231	+	0.399766i	−0.277640	+	0.960685i	$0.589552\pi$
$930$	−0.00604300	+	0.566676i	−0.000198158	+	0.0185821i
$931$	0.0270020	−	0.0831035i	0.000884954	−	0.00272361i
$932$	−2.02363	+	0.657518i	−0.0662862	+	0.0215377i
$933$	1.87389	+	2.57919i	0.0613484	+	0.0844388i
$934$	37.6187			1.23092
$935$	15.7938	+	23.7974i	0.516513	+	0.778260i
$936$	24.1874			0.790588
$937$	−32.8282	−	45.1841i	−1.07245	−	1.47610i	−0.867572	−	0.497312i	$-0.834320\pi$
$937$	−32.8282	−	45.1841i	−1.07245	−	1.47610i	−0.204877	−	0.978788i	$-0.565680\pi$
$938$	−9.72893	+	3.16112i	−0.317661	+	0.103214i
$939$	−0.194723	+	0.599297i	−0.00635455	+	0.0195573i
$940$	5.25534	+	0.0560427i	0.171410	+	0.00182791i
$941$	10.8120	+	7.85541i	0.352462	+	0.256079i	0.749901	−	0.661550i	$-0.230101\pi$
$941$	10.8120	+	7.85541i	0.352462	+	0.256079i	−0.397439	+	0.917629i	$0.630101\pi$
$942$	5.88051	+	1.91069i	0.191597	+	0.0622537i
$943$	−40.8469	+	13.2720i	−1.33016	+	0.432194i
$944$	−17.1133	+	12.4336i	−0.556991	+	0.404678i
$945$	−7.15072	−	10.0661i	−0.232613	−	0.327451i
$946$	10.0015	−	2.90236i	0.325178	−	0.0943639i
$947$		−	42.2245i		−	1.37211i	−0.727550	−	0.686055i	$-0.759341\pi$
$947$		−	42.2245i		−	1.37211i	0.727550	−	0.686055i	$-0.240659\pi$
$948$	0.990868	+	1.36381i	0.0321819	+	0.0442946i
$949$	−11.1148	−	34.2077i	−0.360800	−	1.11043i
$950$	−1.03604	+	1.36384i	−0.0336135	+	0.0442489i
$951$	−5.14624	−	3.73896i	−0.166878	−	0.121244i
$952$	17.8921	−	24.6264i	0.579887	−	0.798146i
$953$	−13.9985	−	4.54837i	−0.453454	−	0.147336i	0.0733803	−	0.997304i	$-0.476621\pi$
$953$	−13.9985	−	4.54837i	−0.453454	−	0.147336i	−0.526835	+	0.849968i	$0.676621\pi$
$954$	9.53588	+	29.3484i	0.308735	+	0.950190i
$955$	−4.70092	−	1.58304i	−0.152118	−	0.0512259i
$956$	−11.5376			−0.373154
$957$	1.36004	−	3.77401i	0.0439640	−	0.121996i
$958$		−	17.2750i		−	0.558131i
$959$	9.09100	−	6.60500i	0.293564	−	0.213286i
$960$	5.80743	+	4.31471i	0.187434	+	0.139257i
$961$	−9.48114	+	29.1799i	−0.305843	+	0.941288i
$962$	1.04589	−	1.43954i	0.0337207	−	0.0464126i
$963$	−17.2921	+	23.8005i	−0.557229	+	0.766960i
$964$	−1.77558	+	5.46467i	−0.0571875	+	0.176005i
$965$	18.8042	+	13.9708i	0.605328	+	0.449736i
$966$	7.89370	−	5.73511i	0.253976	−	0.184524i
$967$		−	32.2786i		−	1.03801i	−0.854771	−	0.519005i	$-0.826303\pi$
$967$		−	32.2786i		−	1.03801i	0.854771	−	0.519005i	$-0.173697\pi$
$968$	−31.2571	−	12.3979i	−1.00464	−	0.398485i
$969$	0.389123			0.0125004
$970$	28.5073	+	9.59985i	0.915315	+	0.308233i
$971$	−13.2262	−	40.7060i	−0.424448	−	1.30632i	−0.903522	−	0.428542i	$-0.859027\pi$
$971$	−13.2262	−	40.7060i	−0.424448	−	1.30632i	0.479074	−	0.877775i	$-0.340973\pi$
$972$	4.20097	+	1.36498i	0.134746	+	0.0437817i
$973$	12.6178	−	17.3669i	0.404508	−	0.556757i
$974$	−34.0738	−	24.7561i	−1.09179	−	0.793235i
$975$	3.99875	+	3.03763i	0.128062	+	0.0972820i
$976$	−12.3460	−	37.9970i	−0.395185	−	1.21625i
$977$	−7.16932	−	9.86772i	−0.229367	−	0.315696i	0.678785	−	0.734337i	$-0.262507\pi$
$977$	−7.16932	−	9.86772i	−0.229367	−	0.315696i	−0.908152	+	0.418640i	$0.862507\pi$
$978$		−	4.01584i		−	0.128412i
$979$	−7.76378	−	2.79784i	−0.248131	−	0.0894195i
$980$	0.194545	+	0.273862i	0.00621451	+	0.00874821i
$981$	−11.4662	+	8.33070i	−0.366088	+	0.265979i
$982$	3.74884	−	1.21807i	0.119630	−	0.0388702i
$983$	−13.3786	−	4.34697i	−0.426711	−	0.138647i	0.0877853	−	0.996139i	$-0.472021\pi$
$983$	−13.3786	−	4.34697i	−0.426711	−	0.138647i	−0.514496	+	0.857493i	$0.672021\pi$
$984$	−4.60153	−	3.34321i	−0.146692	−	0.106578i
$985$	2.96635	+	0.0316329i	0.0945157	+	0.00100791i
$986$	−4.88018	+	15.0196i	−0.155416	+	0.478323i
$987$	4.40788	−	1.43221i	0.140305	−	0.0455877i
$988$	0.214871	+	0.295744i	0.00683595	+	0.00940887i
$989$	21.3790			0.679811
$990$	16.3106	−	20.5577i	0.518384	−	0.653366i
$991$	−22.9455			−0.728887			−0.364444	−	0.931225i	$-0.618741\pi$
$991$	−22.9455			−0.728887			−0.364444	+	0.931225i	$0.618741\pi$
$992$	−0.874542	−	1.20370i	−0.0277667	−	0.0382176i
$993$	−4.36840	+	1.41938i	−0.138627	+	0.0450426i
$994$	8.28292	−	25.4922i	0.262718	−	0.808564i
$995$	0.124065	−	11.6341i	0.00393313	−	0.368825i
$996$	0.463351	+	0.336645i	0.0146819	+	0.0106670i
$997$	3.45659	+	1.12311i	0.109471	+	0.0355694i	0.363240	−	0.931695i	$-0.381670\pi$
$997$	3.45659	+	1.12311i	0.109471	+	0.0355694i	−0.253769	+	0.967265i	$0.581670\pi$
$998$	7.66183	−	2.48948i	0.242531	−	0.0788031i
$999$	0.902916	−	0.656007i	0.0285670	−	0.0207551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.2.j.a.14.2	yes	16
3.2	odd	2		495.2.ba.a.289.3		16
4.3	odd	2		880.2.cd.c.289.3		16
5.2	odd	4		275.2.h.d.201.3		16
5.3	odd	4		275.2.h.d.201.2		16
5.4	even	2	inner	55.2.j.a.14.3	yes	16
11.2	odd	10		605.2.b.f.364.3		8
11.3	even	5		605.2.j.h.269.2		16
11.4	even	5	inner	55.2.j.a.4.3	yes	16
11.5	even	5		605.2.j.h.9.3		16
11.6	odd	10		605.2.j.g.9.2		16
11.7	odd	10		605.2.j.d.444.2		16
11.8	odd	10		605.2.j.g.269.3		16
11.9	even	5		605.2.b.g.364.6		8
11.10	odd	2		605.2.j.d.124.3		16
15.14	odd	2		495.2.ba.a.289.2		16
20.19	odd	2		880.2.cd.c.289.2		16
33.26	odd	10		495.2.ba.a.334.2		16
44.15	odd	10		880.2.cd.c.609.2		16
55.2	even	20		3025.2.a.bk.1.6		8
55.4	even	10	inner	55.2.j.a.4.2	✓	16
55.9	even	10		605.2.b.g.364.3		8
55.13	even	20		3025.2.a.bk.1.3		8
55.14	even	10		605.2.j.h.269.3		16
55.19	odd	10		605.2.j.g.269.2		16
55.24	odd	10		605.2.b.f.364.6		8
55.29	odd	10		605.2.j.d.444.3		16
55.37	odd	20		275.2.h.d.26.3		16
55.39	odd	10		605.2.j.g.9.3		16
55.42	odd	20		3025.2.a.bl.1.3		8
55.48	odd	20		275.2.h.d.26.2		16
55.49	even	10		605.2.j.h.9.2		16
55.53	odd	20		3025.2.a.bl.1.6		8
55.54	odd	2		605.2.j.d.124.2		16
165.59	odd	10		495.2.ba.a.334.3		16
220.59	odd	10		880.2.cd.c.609.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.4.2	✓	16	55.4	even	10	inner
55.2.j.a.4.3	yes	16	11.4	even	5	inner
55.2.j.a.14.2	yes	16	1.1	even	1	trivial
55.2.j.a.14.3	yes	16	5.4	even	2	inner
275.2.h.d.26.2		16	55.48	odd	20
275.2.h.d.26.3		16	55.37	odd	20
275.2.h.d.201.2		16	5.3	odd	4
275.2.h.d.201.3		16	5.2	odd	4
495.2.ba.a.289.2		16	15.14	odd	2
495.2.ba.a.289.3		16	3.2	odd	2
495.2.ba.a.334.2		16	33.26	odd	10
495.2.ba.a.334.3		16	165.59	odd	10
605.2.b.f.364.3		8	11.2	odd	10
605.2.b.f.364.6		8	55.24	odd	10
605.2.b.g.364.3		8	55.9	even	10
605.2.b.g.364.6		8	11.9	even	5
605.2.j.d.124.2		16	55.54	odd	2
605.2.j.d.124.3		16	11.10	odd	2
605.2.j.d.444.2		16	11.7	odd	10
605.2.j.d.444.3		16	55.29	odd	10
605.2.j.g.9.2		16	11.6	odd	10
605.2.j.g.9.3		16	55.39	odd	10
605.2.j.g.269.2		16	55.19	odd	10
605.2.j.g.269.3		16	11.8	odd	10
605.2.j.h.9.2		16	55.49	even	10
605.2.j.h.9.3		16	11.5	even	5
605.2.j.h.269.2		16	11.3	even	5
605.2.j.h.269.3		16	55.14	even	10
880.2.cd.c.289.2		16	20.19	odd	2
880.2.cd.c.289.3		16	4.3	odd	2
880.2.cd.c.609.2		16	44.15	odd	10
880.2.cd.c.609.3		16	220.59	odd	10
3025.2.a.bk.1.3		8	55.13	even	20
3025.2.a.bk.1.6		8	55.2	even	20
3025.2.a.bl.1.3		8	55.42	odd	20
3025.2.a.bl.1.6		8	55.53	odd	20

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:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	55.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.725323 - 0.998322i) q^{2} +(-0.346168 + 0.112477i) q^{3} +(0.147481 - 0.453901i) q^{4} +(0.0238439 - 2.23594i) q^{5} +(0.363371 + 0.264005i) q^{6} +(2.45903 + 0.798988i) q^{7} +(-2.90731 + 0.944641i) q^{8} +(-2.31987 + 1.68548i) q^{9} +O(q^{10})\)	\(q+(-0.725323 - 0.998322i) q^{2} +(-0.346168 + 0.112477i) q^{3} +(0.147481 - 0.453901i) q^{4} +(0.0238439 - 2.23594i) q^{5} +(0.363371 + 0.264005i) q^{6} +(2.45903 + 0.798988i) q^{7} +(-2.90731 + 0.944641i) q^{8} +(-2.31987 + 1.68548i) q^{9} +(-2.24948 + 1.59798i) q^{10} +(3.12020 + 1.12443i) q^{11} +0.173714i q^{12} +(1.62187 + 2.23232i) q^{13} +(-0.985946 - 3.03443i) q^{14} +(0.243237 + 0.776692i) q^{15} +(2.27957 + 1.65620i) q^{16} +(-2.26370 + 3.11572i) q^{17} +(3.36531 + 1.09346i) q^{18} +(0.0857804 + 0.264005i) q^{19} +(-1.01138 - 0.340583i) q^{20} -0.941105 q^{21} +(-1.14061 - 3.93054i) q^{22} -8.40180i q^{23} +(0.900166 - 0.654009i) q^{24} +(-4.99886 - 0.106627i) q^{25} +(1.05219 - 3.23830i) q^{26} +(1.25532 - 1.72780i) q^{27} +(0.725323 - 0.998322i) q^{28} +(-1.02689 + 3.16043i) q^{29} +(0.598963 - 0.806182i) q^{30} +(-0.456498 + 0.331666i) q^{31} +2.63682i q^{32} +(-1.20659 - 0.0382919i) q^{33} +4.75241 q^{34} +(1.84512 - 5.47920i) q^{35} +(0.422906 + 1.30157i) q^{36} +(0.497006 + 0.161487i) q^{37} +(0.201343 - 0.277125i) q^{38} +(-0.812523 - 0.590333i) q^{39} +(2.04284 + 6.52309i) q^{40} +(-1.57966 - 4.86168i) q^{41} +(0.682605 + 0.939526i) q^{42} +2.54457i q^{43} +(0.970553 - 1.25043i) q^{44} +(3.71333 + 5.22728i) q^{45} +(-8.38769 + 6.09402i) q^{46} +(-4.68373 + 1.52184i) q^{47} +(-0.975398 - 0.316926i) q^{48} +(-0.254663 - 0.185023i) q^{49} +(3.51934 + 5.06781i) q^{50} +(0.433175 - 1.33318i) q^{51} +(1.25245 - 0.406945i) q^{52} +(5.12599 + 7.05533i) q^{53} -2.63541 q^{54} +(2.58856 - 6.94977i) q^{55} -7.90392 q^{56} +(-0.0593888 - 0.0817417i) q^{57} +(3.89995 - 1.26717i) q^{58} +(-2.31987 + 7.13983i) q^{59} +(0.388415 + 0.00414203i) q^{60} +(-11.4711 - 8.33424i) q^{61} +(0.662218 + 0.215168i) q^{62} +(-7.05132 + 2.29111i) q^{63} +(7.19153 - 5.22495i) q^{64} +(5.03000 - 3.57318i) q^{65} +(0.836937 + 1.23233i) q^{66} -3.20618i q^{67} +(1.08037 + 1.48701i) q^{68} +(0.945006 + 2.90843i) q^{69} +(-6.80831 + 2.13216i) q^{70} +(6.79655 + 4.93798i) q^{71} +(5.15239 - 7.09166i) q^{72} +(-12.3973 - 4.02812i) q^{73} +(-0.199274 - 0.613302i) q^{74} +(1.74244 - 0.525345i) q^{75} +0.132483 q^{76} +(6.77427 + 5.25802i) q^{77} +1.23934i q^{78} +(7.85090 - 5.70401i) q^{79} +(3.75753 - 5.05749i) q^{80} +(2.41812 - 7.44221i) q^{81} +(-3.70776 + 5.10330i) q^{82} +(1.93792 - 2.66732i) q^{83} +(-0.138796 + 0.427169i) q^{84} +(6.91259 + 5.13580i) q^{85} +(2.54030 - 1.84564i) q^{86} -1.20954i q^{87} +(-10.1336 - 0.321596i) q^{88} -2.48823 q^{89} +(2.52514 - 7.49856i) q^{90} +(2.20464 + 6.78519i) q^{91} +(-3.81359 - 1.23911i) q^{92} +(0.120720 - 0.166157i) q^{93} +(4.91650 + 3.57205i) q^{94} +(0.592344 - 0.185505i) q^{95} +(-0.296581 - 0.912781i) q^{96} +(-6.40771 - 8.81946i) q^{97} +0.388437i q^{98} +(-9.13367 + 2.65051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{9}+O(q^{10}) \) 16 * q - 4 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^9	\( 16 q - 4 q^{4} - 2 q^{5} - 18 q^{6} + 2 q^{9} - 6 q^{11} - 12 q^{14} - 16 q^{15} + 16 q^{16} + 6 q^{19} - 8 q^{20} + 8 q^{21} + 6 q^{24} - 16 q^{25} + 40 q^{26} + 2 q^{29} + 26 q^{30} + 8 q^{31} - 16 q^{34} + 22 q^{35} + 10 q^{36} + 30 q^{39} + 12 q^{40} - 52 q^{41} + 4 q^{44} + 12 q^{45} - 62 q^{46} - 10 q^{49} + 28 q^{50} - 42 q^{51} - 40 q^{54} - 8 q^{55} - 20 q^{56} + 2 q^{59} - 32 q^{60} - 40 q^{61} - 8 q^{64} - 40 q^{65} + 58 q^{66} + 26 q^{69} - 34 q^{70} + 36 q^{71} + 48 q^{74} - 20 q^{75} + 56 q^{76} + 38 q^{79} + 34 q^{80} + 68 q^{81} + 12 q^{84} + 58 q^{85} + 22 q^{86} + 24 q^{89} + 78 q^{90} - 20 q^{91} + 14 q^{94} + 48 q^{95} - 86 q^{96} - 72 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 2 * q^5 - 18 * q^6 + 2 * q^9 - 6 * q^11 - 12 * q^14 - 16 * q^15 + 16 * q^16 + 6 * q^19 - 8 * q^20 + 8 * q^21 + 6 * q^24 - 16 * q^25 + 40 * q^26 + 2 * q^29 + 26 * q^30 + 8 * q^31 - 16 * q^34 + 22 * q^35 + 10 * q^36 + 30 * q^39 + 12 * q^40 - 52 * q^41 + 4 * q^44 + 12 * q^45 - 62 * q^46 - 10 * q^49 + 28 * q^50 - 42 * q^51 - 40 * q^54 - 8 * q^55 - 20 * q^56 + 2 * q^59 - 32 * q^60 - 40 * q^61 - 8 * q^64 - 40 * q^65 + 58 * q^66 + 26 * q^69 - 34 * q^70 + 36 * q^71 + 48 * q^74 - 20 * q^75 + 56 * q^76 + 38 * q^79 + 34 * q^80 + 68 * q^81 + 12 * q^84 + 58 * q^85 + 22 * q^86 + 24 * q^89 + 78 * q^90 - 20 * q^91 + 14 * q^94 + 48 * q^95 - 86 * q^96 - 72 * q^99

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