LMFDB - Embedded newform 380.2.bj.a.187.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(23,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 4]))

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

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

chi := DirichletCharacter("380.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bj (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$56$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			187.21
Character	$\chi$	$=$	380.187
Dual form			380.2.bj.a.63.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.675890 - 1.24224i) q^{2} +(2.66706 + 1.24367i) q^{3} +(-1.08634 + 1.67924i) q^{4} +(-1.83931 - 1.27160i) q^{5} +(-0.257697 - 4.15372i) q^{6} +(-0.680480 - 0.182334i) q^{7} +(2.82028 + 0.214521i) q^{8} +(3.63812 + 4.33575i) q^{9} +O(q^{10})$	\(q+(-0.675890 - 1.24224i) q^{2} +(2.66706 + 1.24367i) q^{3} +(-1.08634 + 1.67924i) q^{4} +(-1.83931 - 1.27160i) q^{5} +(-0.257697 - 4.15372i) q^{6} +(-0.680480 - 0.182334i) q^{7} +(2.82028 + 0.214521i) q^{8} +(3.63812 + 4.33575i) q^{9} +(-0.336464 + 3.14433i) q^{10} +(4.42405 + 2.55422i) q^{11} +(-4.98577 + 3.12759i) q^{12} +(4.17611 - 1.94735i) q^{13} +(0.233426 + 0.968561i) q^{14} +(-3.32409 - 5.67891i) q^{15} +(-1.63971 - 3.64847i) q^{16} +(0.0707102 + 0.808222i) q^{17} +(2.92709 - 7.44993i) q^{18} +(1.81574 - 3.96271i) q^{19} +(4.13344 - 1.70725i) q^{20} +(-1.58812 - 1.33259i) q^{21} +(0.182801 - 7.22212i) q^{22} +(-3.22440 + 4.60493i) q^{23} +(7.25506 + 4.07964i) q^{24} +(1.76609 + 4.67771i) q^{25} +(-5.24168 - 3.87155i) q^{26} +(2.02591 + 7.56081i) q^{27} +(1.04542 - 0.944614i) q^{28} +(1.45419 + 1.73304i) q^{29} +(-4.80787 + 7.96765i) q^{30} +(3.69118 - 2.13111i) q^{31} +(-3.42403 + 4.50289i) q^{32} +(8.62258 + 12.3143i) q^{33} +(0.956217 - 0.634109i) q^{34} +(1.01976 + 1.20066i) q^{35} +(-11.2330 + 1.39918i) q^{36} +(-3.00157 - 3.00157i) q^{37} +(-6.14990 + 0.422761i) q^{38} +13.5598 q^{39} +(-4.91457 - 3.98083i) q^{40} +(-11.7506 + 4.27688i) q^{41} +(-0.582008 + 2.87351i) q^{42} +(0.269355 - 0.188604i) q^{43} +(-9.09520 + 4.65428i) q^{44} +(-1.17830 - 12.6010i) q^{45} +(7.89979 + 0.893073i) q^{46} +(0.476448 - 5.44582i) q^{47} +(0.164282 - 11.7699i) q^{48} +(-5.63237 - 3.25185i) q^{49} +(4.61717 - 5.35553i) q^{50} +(-0.816573 + 2.24351i) q^{51} +(-1.26661 + 9.12819i) q^{52} +(-11.1041 - 7.77520i) q^{53} +(8.02308 - 7.62696i) q^{54} +(-4.88923 - 10.3236i) q^{55} +(-1.88003 - 0.660210i) q^{56} +(9.77100 - 8.31060i) q^{57} +(1.16998 - 2.97781i) q^{58} +(2.95310 + 2.47795i) q^{59} +(13.1474 + 0.587296i) q^{60} +(1.71625 + 9.73331i) q^{61} +(-5.14219 - 3.14496i) q^{62} +(-1.68512 - 3.61374i) q^{63} +(7.90796 + 1.21002i) q^{64} +(-10.1574 - 1.72855i) q^{65} +(9.46948 - 19.0345i) q^{66} +(0.477465 - 5.45745i) q^{67} +(-1.43402 - 0.759267i) q^{68} +(-14.3267 + 8.27151i) q^{69} +(0.802275 - 2.07830i) q^{70} +(-0.0829719 - 0.0146302i) q^{71} +(9.33042 + 13.0085i) q^{72} +(2.33355 - 5.00431i) q^{73} +(-1.69995 + 5.75741i) q^{74} +(-1.10726 + 14.6721i) q^{75} +(4.68183 + 7.35394i) q^{76} +(-2.54475 - 2.54475i) q^{77} +(-9.16493 - 16.8446i) q^{78} +(-11.3348 + 4.12554i) q^{79} +(-1.62345 + 8.79570i) q^{80} +(-1.05142 + 5.96291i) q^{81} +(13.2551 + 11.7064i) q^{82} +(0.669912 - 2.50014i) q^{83} +(3.96298 - 1.21918i) q^{84} +(0.897674 - 1.57648i) q^{85} +(-0.416348 - 0.207129i) q^{86} +(1.72309 + 6.43065i) q^{87} +(11.9291 + 8.15268i) q^{88} +(-0.790885 + 2.17294i) q^{89} +(-14.8571 + 9.98063i) q^{90} +(-3.19683 + 0.563687i) q^{91} +(-4.22998 - 10.4171i) q^{92} +(12.4950 - 1.09317i) q^{93} +(-7.08707 + 3.08892i) q^{94} +(-8.37867 + 4.97974i) q^{95} +(-14.7322 + 7.75112i) q^{96} +(-0.610730 - 6.98067i) q^{97} +(-0.232729 + 9.19468i) q^{98} +(5.02076 + 28.4741i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.675890	−	1.24224i	−0.477927	−	0.878400i
$2$	−0.675890	−	1.24224i	−0.477927	−	0.878400i
$3$	2.66706	+	1.24367i	1.53983	+	0.718033i	0.992878	−	0.119133i	$-0.0380115\pi$
$3$	2.66706	+	1.24367i	1.53983	+	0.718033i	0.546949	+	0.837166i	$0.315789\pi$
$4$	−1.08634	+	1.67924i	−0.543172	+	0.839621i
$5$	−1.83931	−	1.27160i	−0.822562	−	0.568675i
$5$	−1.83931	−	1.27160i	−0.822562	−	0.568675i
$6$	−0.257697	−	4.15372i	−0.105204	−	1.69575i
$7$	−0.680480	−	0.182334i	−0.257197	−	0.0689158i	0.127916	−	0.991785i	$-0.459171\pi$
$7$	−0.680480	−	0.182334i	−0.257197	−	0.0689158i	−0.385114	+	0.922869i	$0.625838\pi$
$8$	2.82028	+	0.214521i	0.997120	+	0.0758446i
$9$	3.63812	+	4.33575i	1.21271	+	1.44525i
$10$	−0.336464	+	3.14433i	−0.106399	+	0.994323i
$11$	4.42405	+	2.55422i	1.33390	+	0.770128i	0.985895	−	0.167365i	$-0.0535258\pi$
$11$	4.42405	+	2.55422i	1.33390	+	0.770128i	0.348005	+	0.937493i	$0.386859\pi$
$12$	−4.98577	+	3.12759i	−1.43927	+	0.902856i
$13$	4.17611	−	1.94735i	1.15824	−	0.540098i	0.254038	−	0.967194i	$-0.418241\pi$
$13$	4.17611	−	1.94735i	1.15824	−	0.540098i	0.904206	+	0.427096i	$0.140463\pi$
$14$	0.233426	+	0.968561i	0.0623858	+	0.258859i
$15$	−3.32409	−	5.67891i	−0.858276	−	1.46629i
$16$	−1.63971	−	3.64847i	−0.409928	−	0.912118i
$17$	0.0707102	+	0.808222i	0.0171498	+	0.196023i	0.999936	+	0.0112784i	$0.00359010\pi$
$17$	0.0707102	+	0.808222i	0.0171498	+	0.196023i	−0.982787	+	0.184744i	$0.940854\pi$
$18$	2.92709	−	7.44993i	0.689921	−	1.75597i
$19$	1.81574	−	3.96271i	0.416560	−	0.909108i
$19$	1.81574	−	3.96271i	0.416560	−	0.909108i
$20$	4.13344	−	1.70725i	0.924265	−	0.381753i
$21$	−1.58812	−	1.33259i	−0.346555	−	0.290795i
$22$	0.182801	−	7.22212i	0.0389733	−	1.53976i
$23$	−3.22440	+	4.60493i	−0.672335	+	0.960194i	0.327547	+	0.944835i	$0.393778\pi$
$23$	−3.22440	+	4.60493i	−0.672335	+	0.960194i	−0.999882	+	0.0153588i	$0.995111\pi$
$24$	7.25506	+	4.07964i	1.48093	+	0.832752i
$25$	1.76609	+	4.67771i	0.353217	+	0.935541i
$26$	−5.24168	−	3.87155i	−1.02798	−	0.759274i
$27$	2.02591	+	7.56081i	0.389887	+	1.45508i
$28$	1.04542	−	0.944614i	0.197566	−	0.178515i
$29$	1.45419	+	1.73304i	0.270037	+	0.321817i	0.883973	−	0.467539i	$-0.154859\pi$
$29$	1.45419	+	1.73304i	0.270037	+	0.321817i	−0.613936	+	0.789356i	$0.710415\pi$
$30$	−4.80787	+	7.96765i	−0.877794	+	1.45469i
$31$	3.69118	−	2.13111i	0.662956	−	0.382758i	−0.130446	−	0.991455i	$-0.541641\pi$
$31$	3.69118	−	2.13111i	0.662956	−	0.382758i	0.793402	+	0.608698i	$0.208308\pi$
$32$	−3.42403	+	4.50289i	−0.605288	+	0.796006i
$33$	8.62258	+	12.3143i	1.50100	+	2.14365i
$34$	0.956217	−	0.634109i	0.163990	−	0.108749i
$35$	1.01976	+	1.20066i	0.172370	+	0.202949i
$36$	−11.2330	+	1.39918i	−1.87217	+	0.233197i
$37$	−3.00157	−	3.00157i	−0.493455	−	0.493455i	0.415938	−	0.909393i	$-0.363453\pi$
$37$	−3.00157	−	3.00157i	−0.493455	−	0.493455i	−0.909393	+	0.415938i	$0.863453\pi$
$38$	−6.14990	+	0.422761i	−0.997646	+	0.0685808i
$39$	13.5598			2.17130
$40$	−4.91457	−	3.98083i	−0.777062	−	0.629424i
$41$	−11.7506	+	4.27688i	−1.83514	+	0.667936i	−0.843792	+	0.536671i	$0.819682\pi$
$41$	−11.7506	+	4.27688i	−1.83514	+	0.667936i	−0.991347	+	0.131265i	$0.958096\pi$
$42$	−0.582008	+	2.87351i	−0.0898057	+	0.443393i
$43$	0.269355	−	0.188604i	0.0410763	−	0.0287619i	−0.552858	−	0.833275i	$-0.686463\pi$
$43$	0.269355	−	0.188604i	0.0410763	−	0.0287619i	0.593934	+	0.804514i	$0.297574\pi$
$44$	−9.09520	+	4.65428i	−1.37115	+	0.701659i
$45$	−1.17830	−	12.6010i	−0.175651	−	1.87844i
$46$	7.89979	+	0.893073i	1.16476	+	0.131676i
$47$	0.476448	−	5.44582i	0.0694971	−	0.794355i	−0.878845	−	0.477107i	$-0.841686\pi$
$47$	0.476448	−	5.44582i	0.0694971	−	0.794355i	0.948342	−	0.317248i	$-0.102759\pi$
$48$	0.164282	−	11.7699i	0.0237121	−	1.69885i
$49$	−5.63237	−	3.25185i	−0.804624	−	0.464550i
$50$	4.61717	−	5.35553i	0.652967	−	0.757386i
$51$	−0.816573	+	2.24351i	−0.114343	+	0.314155i
$52$	−1.26661	+	9.12819i	−0.175648	+	1.26585i
$53$	−11.1041	−	7.77520i	−1.52527	−	1.06801i	−0.971993	−	0.235009i	$-0.924488\pi$
$53$	−11.1041	−	7.77520i	−1.52527	−	1.06801i	−0.553277	−	0.832997i	$-0.686623\pi$
$54$	8.02308	−	7.62696i	1.09180	−	1.03790i
$55$	−4.88923	−	10.3236i	−0.659264	−	1.39203i
$56$	−1.88003	−	0.660210i	−0.251230	−	0.0882243i
$57$	9.77100	−	8.31060i	1.29420	−	1.10077i
$58$	1.16998	−	2.97781i	0.153626	−	0.391005i
$59$	2.95310	+	2.47795i	0.384461	+	0.322601i	0.814451	−	0.580232i	$-0.197038\pi$
$59$	2.95310	+	2.47795i	0.384461	+	0.322601i	−0.429989	+	0.902834i	$0.641483\pi$
$60$	13.1474	+	0.587296i	1.69732	+	0.0758196i
$61$	1.71625	+	9.73331i	0.219743	+	1.24622i	0.872484	+	0.488642i	$0.162508\pi$
$61$	1.71625	+	9.73331i	0.219743	+	1.24622i	−0.652741	+	0.757581i	$0.726381\pi$
$62$	−5.14219	−	3.14496i	−0.653059	−	0.399410i
$63$	−1.68512	−	3.61374i	−0.212305	−	0.455289i
$64$	7.90796	+	1.21002i	0.988495	+	0.151252i
$65$	−10.1574	−	1.72855i	−1.25987	−	0.214400i
$66$	9.46948	−	19.0345i	1.16561	−	2.34298i
$67$	0.477465	−	5.45745i	0.0583317	−	0.666734i	−0.909594	−	0.415498i	$-0.863607\pi$
$67$	0.477465	−	5.45745i	0.0583317	−	0.666734i	0.967926	−	0.251236i	$-0.0808371\pi$
$68$	−1.43402	−	0.759267i	−0.173900	−	0.0920747i
$69$	−14.3267	+	8.27151i	−1.72473	+	0.995773i
$70$	0.802275	−	2.07830i	0.0958902	−	0.248405i
$71$	−0.0829719	−	0.0146302i	−0.00984695	−	0.00173628i	0.168723	−	0.985664i	$-0.446036\pi$
$71$	−0.0829719	−	0.0146302i	−0.00984695	−	0.00173628i	−0.178569	+	0.983927i	$0.557147\pi$
$72$	9.33042	+	13.0085i	1.09960	+	1.53306i
$73$	2.33355	−	5.00431i	0.273121	−	0.585710i	−0.721128	−	0.692802i	$-0.756376\pi$
$73$	2.33355	−	5.00431i	0.273121	−	0.585710i	0.994249	+	0.107092i	$0.0341538\pi$
$74$	−1.69995	+	5.75741i	−0.197615	+	0.669286i
$75$	−1.10726	+	14.6721i	−0.127856	+	1.69419i
$76$	4.68183	+	7.35394i	0.537043	+	0.843555i
$77$	−2.54475	−	2.54475i	−0.290002	−	0.290002i
$78$	−9.16493	−	16.8446i	−1.03772	−	1.90727i
$79$	−11.3348	+	4.12554i	−1.27527	+	0.464159i	−0.888864	−	0.458171i	$-0.848505\pi$
$79$	−11.3348	+	4.12554i	−1.27527	+	0.464159i	−0.386402	+	0.922330i	$0.626282\pi$
$80$	−1.62345	+	8.79570i	−0.181507	+	0.983390i
$81$	−1.05142	+	5.96291i	−0.116825	+	0.662546i
$82$	13.2551	+	11.7064i	1.46378	+	1.29276i
$83$	0.669912	−	2.50014i	0.0735324	−	0.274426i	−0.919364	−	0.393408i	$-0.871296\pi$
$83$	0.669912	−	2.50014i	0.0735324	−	0.274426i	0.992897	+	0.118981i	$0.0379628\pi$
$84$	3.96298	−	1.21918i	0.432397	−	0.133024i
$85$	0.897674	−	1.57648i	0.0973664	−	0.170993i
$86$	−0.416348	−	0.207129i	−0.0448959	−	0.0223353i
$87$	1.72309	+	6.43065i	0.184734	+	0.689438i
$88$	11.9291	+	8.15268i	1.27165	+	0.869079i
$89$	−0.790885	+	2.17294i	−0.0838336	+	0.230331i	−0.974526	−	0.224276i	$-0.927998\pi$
$89$	−0.790885	+	2.17294i	−0.0838336	+	0.230331i	0.890692	+	0.454607i	$0.150220\pi$
$90$	−14.8571	+	9.98063i	−1.56608	+	1.05205i
$91$	−3.19683	+	0.563687i	−0.335118	+	0.0590904i
$92$	−4.22998	−	10.4171i	−0.441006	−	1.08606i
$93$	12.4950	−	1.09317i	1.29567	−	0.113356i
$94$	−7.08707	+	3.08892i	−0.730976	+	0.318597i
$95$	−8.37867	+	4.97974i	−0.859634	+	0.510911i
$96$	−14.7322	+	7.75112i	−1.50360	+	0.791095i
$97$	−0.610730	−	6.98067i	−0.0620102	−	0.708780i	−0.962032	−	0.272936i	$-0.912005\pi$
$97$	−0.610730	−	6.98067i	−0.0620102	−	0.708780i	0.900022	−	0.435844i	$-0.143550\pi$
$98$	−0.232729	+	9.19468i	−0.0235091	+	0.928803i
$99$	5.02076	+	28.4741i	0.504605	+	2.86176i
$100$	−9.77358	−	2.11591i	−0.977358	−	0.211591i
$101$	4.23081	+	1.53989i	0.420982	+	0.153225i	0.543820	−	0.839202i	$-0.316977\pi$
$101$	4.23081	+	1.53989i	0.420982	+	0.153225i	−0.122838	+	0.992427i	$0.539200\pi$
$102$	3.33891	−	0.501987i	0.330601	−	0.0497041i
$103$	4.49084	−	1.20332i	0.442495	−	0.118566i	−0.0306905	−	0.999529i	$-0.509771\pi$
$103$	4.49084	−	1.20332i	0.442495	−	0.118566i	0.473186	+	0.880963i	$0.343104\pi$
$104$	12.1955	−	4.59621i	1.19587	−	0.450696i
$105$	1.22652	+	4.47048i	0.119696	+	0.436274i
$106$	−2.15352	+	19.0492i	−0.209168	+	1.85023i
$107$	−3.36224	−	0.900909i	−0.325040	−	0.0870941i	0.0926094	−	0.995703i	$-0.470479\pi$
$107$	−3.36224	−	0.900909i	−0.325040	−	0.0870941i	−0.417649	+	0.908608i	$0.637146\pi$
$108$	−14.8973	−	4.81164i	−1.43349	−	0.463001i
$109$	−13.4271	−	2.36757i	−1.28609	−	0.226772i	−0.511524	−	0.859269i	$-0.670919\pi$
$109$	−13.4271	−	2.36757i	−1.28609	−	0.226772i	−0.774563	+	0.632497i	$0.782030\pi$
$110$	−9.51985	+	13.0512i	−0.907682	+	1.24439i
$111$	−4.27240	−	11.7383i	−0.405518	−	1.11415i
$112$	0.450551	+	2.78169i	0.0425731	+	0.262845i
$113$	2.07728	−	2.07728i	0.195414	−	0.195414i	−0.602617	−	0.798031i	$-0.705875\pi$
$113$	2.07728	−	2.07728i	0.195414	−	0.195414i	0.798031	+	0.602617i	$0.205875\pi$
$114$	−16.9279	−	6.52092i	−1.58544	−	0.610740i
$115$	11.7863	−	4.36973i	1.09908	−	0.407479i
$116$	−4.48995	+	0.559265i	−0.416881	+	0.0519265i
$117$	23.6364	+	11.0218i	2.18519	+	1.01897i
$118$	1.08224	−	5.34330i	0.0996286	−	0.491891i
$119$	0.0992495	−	0.562872i	0.00909818	−	0.0515984i
$120$	−8.15662	−	16.7292i	−0.744594	−	1.52716i
$121$	7.54812	+	13.0737i	0.686193	+	1.18852i
$122$	10.9312	−	8.71065i	0.989661	−	0.788625i
$123$	−36.6586	−	3.20721i	−3.30540	−	0.289185i
$124$	−0.431251	+	8.51351i	−0.0387275	+	0.764535i
$125$	2.69978	−	10.8495i	0.241476	−	0.970407i
$126$	−3.35020	+	4.53582i	−0.298459	+	0.404083i
$127$	5.35499	−	2.49707i	0.475178	−	0.221579i	−0.170249	−	0.985401i	$-0.554457\pi$
$127$	5.35499	−	2.49707i	0.475178	−	0.221579i	0.645427	+	0.763822i	$0.276679\pi$
$128$	−3.84178	−	10.6415i	−0.339568	−	0.940581i
$129$	0.952948	−	0.168030i	0.0839024	−	0.0147942i
$130$	4.71800	+	13.7863i	0.413796	+	1.20914i
$131$	−2.21710	+	2.64224i	−0.193709	+	0.230854i	−0.854153	−	0.520022i	$-0.825924\pi$
$131$	−2.21710	+	2.64224i	−0.193709	+	0.230854i	0.660444	+	0.750876i	$0.270368\pi$
$132$	−30.0458	+	1.10182i	−2.61515	+	0.0959008i
$133$	−1.95811	+	2.36547i	−0.169790	+	0.205113i
$134$	−7.10221	+	3.09551i	−0.613537	+	0.267412i
$135$	5.88803	−	16.4828i	0.506761	−	1.41861i
$136$	0.0260422	+	2.29458i	0.00223310	+	0.196759i
$137$	−2.97555	+	4.24953i	−0.254218	+	0.363062i	−0.925894	−	0.377784i	$-0.876686\pi$
$137$	−2.97555	+	4.24953i	−0.254218	+	0.363062i	0.671675	+	0.740846i	$0.265575\pi$
$138$	19.9585	+	12.2066i	1.69898	+	1.03910i
$139$	4.62451	+	1.68318i	0.392245	+	0.142766i	0.530611	−	0.847616i	$-0.321963\pi$
$139$	4.62451	+	1.68318i	0.392245	+	0.142766i	−0.138365	+	0.990381i	$0.544185\pi$
$140$	−3.12401	+	0.408083i	−0.264027	+	0.0344893i
$141$	8.04352	−	13.9318i	0.677387	−	1.17327i
$142$	0.0379056	+	0.112960i	0.00318097	+	0.00947938i
$143$	23.4493	+	2.05155i	1.96093	+	0.171559i
$144$	9.85337	−	20.3830i	0.821114	−	1.69858i
$145$	−0.470978	−	5.03673i	−0.0391126	−	0.418278i
$146$	−7.79380	+	0.483528i	−0.645020	+	0.0400170i
$147$	−10.9776	−	15.6777i	−0.905420	−	1.29307i
$148$	8.30110	−	1.77963i	0.682346	−	0.146284i
$149$	3.46851	+	9.52967i	0.284152	+	0.780701i	0.996856	+	0.0792358i	$0.0252480\pi$
$149$	3.46851	+	9.52967i	0.284152	+	0.780701i	−0.712704	+	0.701465i	$0.752530\pi$
$150$	18.9748	−	8.54127i	1.54928	−	0.697392i
$151$			8.22272i			0.669156i	0.942368	+	0.334578i	$0.108594\pi$
$151$			8.22272i			0.669156i	−0.942368	+	0.334578i	$0.891406\pi$
$152$	5.97099	−	10.7864i	0.484311	−	0.874896i
$153$	−3.24699	+	3.24699i	−0.262504	+	0.262504i
$154$	−1.44123	+	4.88118i	−0.116138	+	0.393337i
$155$	−9.49912	−	0.773940i	−0.762987	−	0.0621643i
$156$	−14.7306	+	22.7702i	−1.17939	+	1.82307i
$157$	−6.04999	+	4.23625i	−0.482842	+	0.338089i	−0.789521	−	0.613724i	$-0.789671\pi$
$157$	−6.04999	+	4.23625i	−0.482842	+	0.338089i	0.306679	+	0.951813i	$0.400782\pi$
$158$	12.7860	+	11.2922i	1.01720	+	0.898360i
$159$	−19.9456	−	34.5468i	−1.58179	−	2.73974i
$160$	12.0237	−	3.92821i	0.950556	−	0.310553i
$161$	3.03378	−	2.54564i	0.239095	−	0.200625i
$162$	8.11804	−	2.72415i	0.637814	−	0.214030i
$163$	−7.91777	+	2.12156i	−0.620167	+	0.166173i	−0.555204	−	0.831714i	$-0.687360\pi$
$163$	−7.91777	+	2.12156i	−0.620167	+	0.166173i	−0.0649635	+	0.997888i	$0.520693\pi$
$164$	5.58330	−	24.3783i	0.435983	−	1.90363i
$165$	−0.200717	−	33.6142i	−0.0156258	−	2.61686i
$166$	−3.55858	+	0.857630i	−0.276199	+	0.0665650i
$167$	17.4576	+	12.2240i	1.35091	+	0.945919i	0.999955	+	0.00952761i	$0.00303278\pi$
$167$	17.4576	+	12.2240i	1.35091	+	0.945919i	0.350958	+	0.936391i	$0.385856\pi$
$168$	−4.19307	−	4.09896i	−0.323502	−	0.316241i
$169$	5.29147	−	6.30612i	0.407036	−	0.485086i
$170$	−2.56510	−	0.0496018i	−0.196735	−	0.00380428i
$171$	23.7872	−	6.54423i	1.81905	−	0.500450i
$172$	0.0241004	+	0.657202i	0.00183764	+	0.0501112i
$173$	−14.4875	+	1.26749i	−1.10146	+	0.0963655i	−0.623357	−	0.781937i	$-0.714232\pi$
$173$	−14.4875	+	1.26749i	−1.10146	+	0.0963655i	−0.478105	+	0.878303i	$0.658676\pi$
$174$	6.82382	−	6.48691i	0.517313	−	0.491772i
$175$	−0.348882	−	3.50510i	−0.0263730	−	0.264961i
$176$	2.06485	−	20.3292i	0.155644	−	1.53237i
$177$	4.79435	+	10.2815i	0.360366	+	0.772806i
$178$	3.23387	−	0.486196i	0.242389	−	0.0364419i
$179$	−11.4097	+	19.7622i	−0.852802	+	1.47710i	0.0258672	+	0.999665i	$0.491765\pi$
$179$	−11.4097	+	19.7622i	−0.852802	+	1.47710i	−0.878669	+	0.477431i	$0.841568\pi$
$180$	22.4402	+	11.7104i	1.67259	+	0.872838i
$181$	8.90541	−	7.47252i	0.661934	−	0.555428i	−0.248732	−	0.968572i	$-0.580014\pi$
$181$	8.90541	−	7.47252i	0.661934	−	0.555428i	0.910666	+	0.413144i	$0.135569\pi$
$182$	2.86094	+	3.59025i	0.212067	+	0.266127i
$183$	−7.52770	+	28.0938i	−0.556464	+	2.07675i
$184$	−10.0816	+	12.2955i	−0.743224	+	0.906435i
$185$	1.70402	+	9.33758i	0.125282	+	0.686513i
$186$	−9.80323	−	14.7830i	−0.718808	−	1.08394i
$187$	−1.75155	+	3.75622i	−0.128086	+	0.274682i
$188$	8.62728	+	6.71611i	0.629209	+	0.489823i
$189$		−	5.51437i		−	0.401112i
$190$	11.8491	+	7.04260i	0.859626	+	0.510924i
$191$			5.73730i			0.415136i	0.978221	+	0.207568i	$0.0665548\pi$
$191$			5.73730i			0.415136i	−0.978221	+	0.207568i	$0.933445\pi$
$192$	19.5861	+	13.0621i	1.41351	+	0.942675i
$193$	4.62205	−	9.91202i	0.332702	−	0.713483i	−0.666793	−	0.745243i	$-0.732334\pi$
$193$	4.62205	−	9.91202i	0.332702	−	0.713483i	0.999496	+	0.0317603i	$0.0101113\pi$
$194$	−8.25892	+	5.47685i	−0.592956	+	0.393215i
$195$	−24.9406	−	17.2426i	−1.78603	−	1.23477i
$196$	11.5793	−	5.92549i	0.827096	−	0.423249i
$197$	1.93254	−	7.21233i	0.137688	−	0.513857i	−0.862285	−	0.506424i	$-0.830967\pi$
$197$	1.93254	−	7.21233i	0.137688	−	0.513857i	0.999972	−	0.00743352i	$-0.00236619\pi$
$198$	31.9784	−	25.4824i	2.27260	−	1.81096i
$199$	4.26586	−	3.57948i	0.302399	−	0.253743i	−0.478943	−	0.877846i	$-0.658980\pi$
$199$	4.26586	−	3.57948i	0.302399	−	0.253743i	0.781342	+	0.624103i	$0.214535\pi$
$200$	3.97740	+	13.5713i	0.281244	+	0.959636i
$201$	8.06070	−	13.9615i	0.568558	−	0.984771i
$202$	−0.946646	−	6.29650i	−0.0666058	−	0.443020i
$203$	−0.673557	−	1.44445i	−0.0472744	−	0.101380i
$204$	−2.88033	−	3.80845i	−0.201663	−	0.266645i
$205$	27.0514	+	7.07556i	1.88935	+	0.494179i
$206$	−4.53013	−	4.76541i	−0.315629	−	0.332022i
$207$	−31.6966	+	2.77309i	−2.20306	+	0.192743i
$208$	−13.9525	−	12.0433i	−0.967430	−	0.835054i
$209$	18.1546	−	12.8934i	1.25578	−	0.891855i
$210$	4.72444	−	4.54519i	0.326017	−	0.313648i
$211$	14.9442	−	17.8098i	1.02880	−	1.22607i	0.0550419	−	0.998484i	$-0.482471\pi$
$211$	14.9442	−	17.8098i	1.02880	−	1.22607i	0.973757	−	0.227591i	$-0.0730848\pi$
$212$	25.1194	−	10.2000i	1.72520	−	0.700539i
$213$	−0.203096	−	0.142209i	−0.0139159	−	0.00974401i
$214$	1.15336	+	4.78564i	0.0788417	+	0.327139i
$215$	−0.735255	+	0.00439034i	−0.0501440	+	0.000299419i
$216$	4.09169	+	21.7582i	0.278404	+	1.48046i
$217$	−2.90035	+	0.777146i	−0.196889	+	0.0527561i
$218$	6.13418	+	18.2800i	0.415459	+	1.23808i
$219$	12.4474	−	10.4446i	0.841119	−	0.705782i
$220$	22.6472	+	3.00477i	1.52687	+	0.202582i
$221$	1.86919	+	3.23752i	0.125735	+	0.217779i
$222$	−11.6942	+	13.2412i	−0.784863	+	0.888690i
$223$	11.4667	−	8.02904i	0.767865	−	0.537665i	−0.122742	−	0.992439i	$-0.539169\pi$
$223$	11.4667	−	8.02904i	0.767865	−	0.537665i	0.890607	+	0.454774i	$0.150280\pi$
$224$	3.15101	−	2.43981i	0.210536	−	0.163017i
$225$	−13.8561	+	24.6754i	−0.923740	+	1.64503i
$226$	−3.98450	−	1.17648i	−0.265045	−	0.0782580i
$227$	12.3751	−	12.3751i	0.821364	−	0.821364i	−0.164940	−	0.986304i	$-0.552743\pi$
$227$	12.3751	−	12.3751i	0.821364	−	0.821364i	0.986304	+	0.164940i	$0.0527430\pi$
$228$	3.34084	+	25.4360i	0.221253	+	1.68454i
$229$			20.3283i			1.34333i	0.740855	+	0.671665i	$0.234421\pi$
$229$			20.3283i			1.34333i	−0.740855	+	0.671665i	$0.765579\pi$
$230$	−13.3945	−	11.6880i	−0.883207	−	0.770682i
$231$	−3.62217	−	9.95184i	−0.238321	−	0.654783i
$232$	3.72946	+	5.19961i	0.244851	+	0.341371i
$233$	−10.8312	−	15.4685i	−0.709574	−	1.01338i	−0.998431	−	0.0560039i	$-0.982164\pi$
$233$	−10.8312	−	15.4685i	−0.709574	−	1.01338i	0.288857	−	0.957372i	$-0.406725\pi$
$234$	−2.28380	−	36.8118i	−0.149297	−	2.40646i
$235$	−7.80122	+	9.41068i	−0.508896	+	0.613885i
$236$	−7.36917	+	2.26707i	−0.479692	+	0.147574i
$237$	−35.3614	−	3.09372i	−2.29697	−	0.200959i
$238$	−0.766306	+	0.257147i	−0.0496722	+	0.0166684i
$239$	−3.67958	+	6.37322i	−0.238012	+	0.412249i	−0.960144	−	0.279507i	$-0.909829\pi$
$239$	−3.67958	+	6.37322i	−0.238012	+	0.412249i	0.722132	+	0.691756i	$0.243162\pi$
$240$	−15.2688	+	21.4396i	−0.985596	+	1.38392i
$241$	−20.9429	−	7.62260i	−1.34905	−	0.491015i	−0.436400	−	0.899753i	$-0.643747\pi$
$241$	−20.9429	−	7.62260i	−1.34905	−	0.491015i	−0.912652	+	0.408738i	$0.865969\pi$
$242$	11.1391	−	18.2130i	0.716047	−	1.17078i
$243$	3.24896	−	4.64000i	0.208421	−	0.297656i
$244$	−18.2090	−	7.69173i	−1.16571	−	0.492413i
$245$	6.22461	+	13.1432i	0.397676	+	0.839691i
$246$	20.7931	+	47.7067i	1.32572	+	3.04167i
$247$	−0.134048	−	20.0846i	−0.00852929	−	1.27795i
$248$	10.8673	−	5.21848i	0.690077	−	0.331374i
$249$	4.89605	−	5.83488i	0.310274	−	0.369771i
$250$	−15.3025	+	3.97927i	−0.967813	+	0.251671i
$251$	−6.71269	+	1.18363i	−0.423701	+	0.0747100i	−0.381433	−	0.924396i	$-0.624569\pi$
$251$	−6.71269	+	1.18363i	−0.423701	+	0.0747100i	−0.0422679	+	0.999106i	$0.513458\pi$
$252$	7.89897	+	1.09605i	0.497588	+	0.0690446i
$253$	−26.0269	+	12.1366i	−1.63630	+	0.763019i
$254$	−6.72136	−	4.96446i	−0.421736	−	0.311498i
$255$	4.35477	−	3.08816i	0.272706	−	0.193388i
$256$	−10.6227	+	11.9649i	−0.663918	+	0.747806i
$257$	−8.25697	−	0.722391i	−0.515056	−	0.0450615i	−0.173335	−	0.984863i	$-0.555454\pi$
$257$	−8.25697	−	0.722391i	−0.515056	−	0.0450615i	−0.341721	+	0.939801i	$0.611010\pi$
$258$	−0.852823	−	1.07022i	−0.0530944	−	0.0666292i
$259$	1.49522	+	2.58980i	0.0929084	+	0.160922i
$260$	13.9371	−	15.1789i	0.864340	−	0.941356i
$261$	−2.22349	+	12.6100i	−0.137630	+	0.780541i
$262$	4.78083	+	0.968320i	0.295361	+	0.0598230i
$263$	−21.5425	−	10.0454i	−1.32837	−	0.619428i	−0.376637	−	0.926361i	$-0.622920\pi$
$263$	−21.5425	−	10.0454i	−1.32837	−	0.619428i	−0.951731	+	0.306933i	$0.900697\pi$
$264$	21.6764	+	36.5796i	1.33409	+	2.25132i
$265$	10.5370	+	28.4209i	0.647282	+	1.74588i
$266$	4.26197	+	0.833656i	0.261318	+	0.0511147i
$267$	−4.81176	+	4.81176i	−0.294475	+	0.294475i
$268$	8.64570	+	6.73045i	0.528120	+	0.411128i
$269$	−8.43617	−	23.1782i	−0.514362	−	1.41320i	−0.876648	−	0.481132i	$-0.840226\pi$
$269$	−8.43617	−	23.1782i	−0.514362	−	1.41320i	0.362286	−	0.932067i	$-0.381996\pi$
$270$	−24.4553	+	3.82619i	−1.48830	+	0.232855i
$271$	1.44258	+	0.254365i	0.0876304	+	0.0154516i	0.217291	−	0.976107i	$-0.430278\pi$
$271$	1.44258	+	0.254365i	0.0876304	+	0.0154516i	−0.129661	+	0.991558i	$0.541389\pi$
$272$	2.83283	−	1.58324i	0.171765	−	0.0959978i
$273$	−9.22716	−	2.47241i	−0.558453	−	0.149637i
$274$	7.29010	+	0.824147i	0.440411	+	0.0497886i
$275$	−4.13466	+	25.2054i	−0.249329	+	1.51994i
$276$	1.67383	−	33.0437i	0.100752	−	1.98900i
$277$	−3.22365	+	0.863775i	−0.193691	+	0.0518992i	−0.354360	−	0.935109i	$-0.615301\pi$
$277$	−3.22365	+	0.863775i	−0.193691	+	0.0518992i	0.160670	+	0.987008i	$0.448635\pi$
$278$	−1.03474	−	6.88242i	−0.0620593	−	0.412780i
$279$	22.6689	+	8.25081i	1.35715	+	0.493963i
$280$	2.61843	+	3.60497i	0.156481	+	0.215438i
$281$	1.42616	+	8.08813i	0.0850773	+	0.482497i	0.997340	+	0.0728915i	$0.0232227\pi$
$281$	1.42616	+	8.08813i	0.0850773	+	0.482497i	−0.912263	+	0.409606i	$0.865666\pi$
$282$	−22.7432	−	0.575659i	−1.35434	−	0.0342800i
$283$	−0.354616	−	4.05328i	−0.0210797	−	0.240942i	−0.999423	−	0.0339551i	$-0.989190\pi$
$283$	−0.354616	−	4.05328i	−0.0210797	−	0.240942i	0.978344	−	0.206987i	$-0.0663659\pi$
$284$	0.114704	−	0.123437i	0.00680641	−	0.00732461i
$285$	−28.5396	+	2.86096i	−1.69054	+	0.169469i
$286$	−13.3006	−	30.5164i	−0.786482	−	1.80447i
$287$	8.77588	−	0.767790i	0.518024	−	0.0453212i
$288$	−31.9804	+	1.53636i	−1.88447	+	0.0905309i
$289$	16.0935	−	2.83772i	0.946677	−	0.166925i
$290$	−5.93852	+	3.98935i	−0.348722	+	0.234263i
$291$	7.05280	−	19.3774i	0.413443	−	1.13592i
$292$	5.86842	+	9.35500i	0.343423	+	0.547460i
$293$	5.47848	+	20.4460i	0.320056	+	1.19447i	0.919189	+	0.393817i	$0.128846\pi$
$293$	5.47848	+	20.4460i	0.320056	+	1.19447i	−0.599132	+	0.800650i	$0.704488\pi$
$294$	−12.0558	+	24.2333i	−0.703111	+	1.41332i
$295$	−2.28071	−	8.31286i	−0.132788	−	0.483993i
$296$	−7.82136	−	9.10916i	−0.454608	−	0.529459i
$297$	−10.3493	+	38.6240i	−0.600526	+	2.24119i
$298$	9.49384	−	10.7498i	0.549963	−	0.622717i
$299$	−4.49805	+	25.5097i	−0.260129	+	1.47527i
$300$	−23.4352	−	17.7984i	−1.35303	−	1.02759i
$301$	−0.217680	+	0.0792290i	−0.0125469	+	0.00456668i
$302$	10.2146	−	5.55766i	0.587786	−	0.319807i
$303$	9.36871	+	9.36871i	0.538218	+	0.538218i
$304$	−17.4351	−	0.126979i	−0.999973	−	0.00728273i
$305$	9.22014	−	20.0849i	0.527944	−	1.15006i
$306$	6.22817	+	1.83895i	0.356041	+	0.105126i
$307$	−10.2792	+	22.0439i	−0.586666	+	1.25811i	0.359112	+	0.933295i	$0.383080\pi$
$307$	−10.2792	+	22.0439i	−0.586666	+	1.25811i	−0.945778	+	0.324815i	$0.894698\pi$
$308$	7.03774	−	1.50878i	0.401012	−	0.0859708i
$309$	13.4739	+	2.37580i	0.766501	+	0.135155i
$310$	5.45894	+	12.3233i	0.310047	+	0.699918i
$311$	21.4157	−	12.3643i	1.21437	−	0.701118i	0.250663	−	0.968074i	$-0.419351\pi$
$311$	21.4157	−	12.3643i	1.21437	−	0.701118i	0.963709	+	0.266956i	$0.0860180\pi$
$312$	38.2424	+	2.90886i	2.16505	+	0.164682i
$313$	1.30977	−	14.9707i	0.0740325	−	0.846195i	−0.864866	−	0.502002i	$-0.832597\pi$
$313$	1.30977	−	14.9707i	0.0740325	−	0.846195i	0.938899	−	0.344193i	$-0.111847\pi$
$314$	9.35159	+	4.65233i	0.527740	+	0.262546i
$315$	−1.49578	+	8.78956i	−0.0842776	+	0.495236i
$316$	5.38573	−	23.5157i	0.302971	−	1.32286i
$317$	−5.84729	−	12.5396i	−0.328417	−	0.704292i	0.670889	−	0.741558i	$-0.265913\pi$
$317$	−5.84729	−	12.5396i	−0.328417	−	0.704292i	−0.999305	+	0.0372661i	$0.988135\pi$
$318$	−29.4345	+	48.1272i	−1.65061	+	2.69884i
$319$	2.00684	+	11.3814i	0.112362	+	0.637235i
$320$	−13.0065	−	12.2813i	−0.727085	−	0.686547i
$321$	−7.84685	−	6.58429i	−0.437969	−	0.367499i
$322$	−5.21281	−	2.04812i	−0.290499	−	0.114137i
$323$	3.33114	+	1.18732i	0.185350	+	0.0660642i
$324$	−8.87097	−	8.24337i	−0.492832	−	0.457965i
$325$	16.4845	+	16.0954i	0.914396	+	0.892813i
$326$	7.98704	+	8.40186i	0.442361	+	0.465336i
$327$	−32.8665	−	23.0134i	−1.81752	−	1.27264i
$328$	−34.0575	+	9.54124i	−1.88051	+	0.526827i
$329$	−1.31717	+	3.61890i	−0.0726181	+	0.199517i
$330$	−41.6214	+	22.9689i	−2.29118	+	1.26440i
$331$	19.9339	+	11.5089i	1.09567	+	0.632584i	0.935080	−	0.354437i	$-0.115328\pi$
$331$	19.9339	+	11.5089i	1.09567	+	0.632584i	0.160588	+	0.987021i	$0.448661\pi$
$332$	3.47059	+	3.84096i	0.190474	+	0.210800i
$333$	2.09396	−	23.9341i	0.114749	−	1.31158i
$334$	3.38571	−	29.9487i	0.185258	−	1.63872i
$335$	−7.81788	+	9.43078i	−0.427137	+	0.515259i
$336$	−2.25785	+	7.97926i	−0.123176	+	0.435304i
$337$	18.0287	−	12.6238i	0.982084	−	0.687663i	0.0319454	−	0.999490i	$-0.489830\pi$
$337$	18.0287	−	12.6238i	0.982084	−	0.687663i	0.950139	+	0.311827i	$0.100941\pi$
$338$	−11.4102	−	2.31105i	−0.620633	−	0.125704i
$339$	8.12367	−	2.95678i	0.441217	−	0.160590i
$340$	1.67211	+	3.22001i	0.0906830	+	0.174630i
$341$	21.7733			1.17909
$342$	−24.2071	−	25.1264i	−1.30897	−	1.35868i
$343$	6.72681	+	6.72681i	0.363214	+	0.363214i
$344$	0.800117	−	0.474135i	0.0431394	−	0.0255637i
$345$	36.8692	+	3.00391i	1.98497	+	0.161725i
$346$	11.3665	+	17.1403i	0.611066	+	0.921469i
$347$	5.74370	+	8.20285i	0.308338	+	0.440352i	0.943176	−	0.332293i	$-0.107822\pi$
$347$	5.74370	+	8.20285i	0.308338	+	0.440352i	−0.634838	+	0.772645i	$0.718933\pi$
$348$	−12.6705	−	4.09242i	−0.679210	−	0.219377i
$349$	−8.06767	+	4.65787i	−0.431852	+	0.249330i	−0.700135	−	0.714010i	$-0.746877\pi$
$349$	−8.06767	+	4.65787i	−0.431852	+	0.249330i	0.268283	+	0.963340i	$0.413544\pi$
$350$	−4.11839	+	2.80246i	−0.220137	+	0.149798i
$351$	23.1840	+	27.6296i	1.23747	+	1.47476i
$352$	−26.6495	+	11.1753i	−1.42042	+	0.595644i
$353$	2.00587	+	7.48601i	0.106762	+	0.398440i	0.998539	−	0.0540342i	$-0.0172080\pi$
$353$	2.00587	+	7.48601i	0.106762	+	0.398440i	−0.891777	+	0.452475i	$0.850541\pi$
$354$	9.53171	−	12.9049i	0.506605	−	0.685890i
$355$	0.134007	+	0.132416i	0.00711235	+	0.00702792i
$356$	−2.78972	−	3.68865i	−0.147855	−	0.195498i
$357$	0.964731	−	1.37778i	0.0510590	−	0.0729197i
$358$	32.2612	+	0.816571i	1.70506	+	0.0431571i
$359$	−17.9823	−	15.0889i	−0.949069	−	0.796364i	0.0300712	−	0.999548i	$-0.490427\pi$
$359$	−17.9823	−	15.0889i	−0.949069	−	0.796364i	−0.979141	+	0.203184i	$0.934871\pi$
$360$	−0.619966	−	35.7911i	−0.0326751	−	1.88636i
$361$	−12.4062	−	14.3905i	−0.652955	−	0.757396i
$362$	−15.3018	−	6.01209i	−0.804244	−	0.315988i
$363$	3.87188	+	44.2558i	0.203221	+	2.32283i
$364$	2.52629	−	5.98061i	0.132413	−	0.313469i
$365$	−10.6556	+	6.23712i	−0.557738	+	0.326466i
$366$	39.9872	−	9.63706i	2.09017	−	0.503737i
$367$	−12.6438	+	5.89589i	−0.659999	+	0.307763i	−0.723607	−	0.690212i	$-0.757517\pi$
$367$	−12.6438	+	5.89589i	−0.659999	+	0.307763i	0.0636077	+	0.997975i	$0.479739\pi$
$368$	22.0880	+	4.21339i	1.15142	+	0.219638i
$369$	−61.2937	−	35.3879i	−3.19082	−	1.84222i
$370$	10.4478	−	8.42799i	0.543157	−	0.438150i
$371$	6.13846	+	7.31553i	0.318693	+	0.379803i
$372$	−11.7382	+	22.1697i	−0.608595	+	1.14944i
$373$	15.4983	+	4.15277i	0.802474	+	0.215022i	0.636670	−	0.771137i	$-0.280311\pi$
$373$	15.4983	+	4.15277i	0.802474	+	0.215022i	0.165804	+	0.986159i	$0.446978\pi$
$374$	5.85000	−	0.362934i	0.302497	−	0.0187669i
$375$	20.6936	−	25.5786i	1.06861	−	1.32087i
$376$	2.51196	−	15.2565i	0.129544	−	0.786796i
$377$	9.44770	+	4.40553i	0.486581	+	0.226897i
$378$	−6.85020	+	3.72711i	−0.352336	+	0.191702i
$379$	34.1285			1.75307			0.876533	−	0.481342i	$-0.159851\pi$
$379$	34.1285			1.75307			0.876533	+	0.481342i	$0.159851\pi$
$380$	0.739925	−	19.4795i	0.0379574	−	0.999279i
$381$	17.3876			0.890794
$382$	7.12713	−	3.87778i	0.364655	−	0.198405i
$383$	17.3805	+	8.10468i	0.888105	+	0.414130i	0.812468	−	0.583006i	$-0.198123\pi$
$383$	17.3805	+	8.10468i	0.888105	+	0.414130i	0.0756363	+	0.997135i	$0.475901\pi$
$384$	2.98822	−	33.1593i	0.152492	−	1.69215i
$385$	1.44468	+	7.91648i	0.0736277	+	0.403461i
$386$	−15.4371	+	0.957721i	−0.785730	+	0.0487467i
$387$	1.79769	+	0.481689i	0.0913817	+	0.0244856i
$388$	12.3857	+	6.55785i	0.628789	+	0.332924i
$389$	−5.35659	−	6.38373i	−0.271590	−	0.323668i	0.612960	−	0.790114i	$-0.289979\pi$
$389$	−5.35659	−	6.38373i	−0.271590	−	0.323668i	−0.884550	+	0.466446i	$0.845534\pi$
$390$	−4.56239	+	42.6364i	−0.231025	+	2.15898i
$391$	−3.94980	−	2.28042i	−0.199750	−	0.115326i
$392$	−15.1873	−	10.3794i	−0.767073	−	0.524238i
$393$	−9.19922	+	4.28967i	−0.464039	+	0.216385i
$394$	−10.2657	+	2.47406i	−0.517177	+	0.124641i
$395$	26.0942	+	6.82519i	1.31294	+	0.343412i
$396$	−53.2693	−	22.5016i	−2.67688	−	1.13075i
$397$	0.832371	+	9.51405i	0.0417755	+	0.477496i	0.988050	+	0.154132i	$0.0492582\pi$
$397$	0.832371	+	9.51405i	0.0417755	+	0.477496i	−0.946275	+	0.323364i	$0.895186\pi$
$398$	−7.32985	−	2.87991i	−0.367412	−	0.144357i
$399$	−8.16427	+	3.87361i	−0.408725	+	0.193923i
$400$	14.1706	−	14.1136i	0.708530	−	0.705681i
$401$	−22.3536	−	18.7569i	−1.11628	−	0.936673i	−0.117873	−	0.993029i	$-0.537607\pi$
$401$	−22.3536	−	18.7569i	−1.11628	−	0.936673i	−0.998411	+	0.0563558i	$0.982052\pi$
$402$	−22.7918	−	0.576889i	−1.13675	−	0.0287726i
$403$	11.2648	−	16.0878i	0.561138	−	0.801388i
$404$	−7.18197	+	5.43171i	−0.357316	+	0.270238i
$405$	9.51630	−	9.63063i	0.472869	−	0.478550i
$406$	−1.33911	+	1.81301i	−0.0664587	+	0.0899782i
$407$	−5.61240	−	20.9458i	−0.278196	−	1.03824i
$408$	−2.78424	+	6.15217i	−0.137841	+	0.304578i
$409$	15.0056	+	17.8830i	0.741979	+	0.884256i	0.996567	−	0.0827937i	$-0.0263843\pi$
$409$	15.0056	+	17.8830i	0.741979	+	0.884256i	−0.254588	+	0.967050i	$0.581940\pi$
$410$	−9.49423	−	38.3868i	−0.468887	−	1.89579i
$411$	−13.2210	+	7.63313i	−0.652143	+	0.376515i
$412$	−2.85793	+	8.84842i	−0.140800	+	0.435930i
$413$	−1.55771	−	2.22465i	−0.0766501	−	0.109468i
$414$	24.8683	+	37.5006i	1.22221	+	1.84305i
$415$	−4.41135	+	3.74667i	−0.216544	+	0.183917i
$416$	−5.53040	+	25.4723i	−0.271150	+	1.24888i
$417$	10.2405	+	10.2405i	0.501480	+	0.501480i
$418$	−28.2873	−	13.8379i	−1.38358	−	0.676834i
$419$	−25.0045			−1.22155			−0.610774	−	0.791805i	$-0.709142\pi$
$419$	−25.0045			−1.22155			−0.610774	+	0.791805i	$0.709142\pi$
$420$	−8.83944	−	2.79686i	−0.431320	−	0.136473i
$421$	−2.32011	+	0.844451i	−0.113075	+	0.0411560i	−0.397938	−	0.917412i	$-0.630274\pi$
$421$	−2.32011	+	0.844451i	−0.113075	+	0.0411560i	0.284863	+	0.958568i	$0.408052\pi$
$422$	−32.2247	−	6.52686i	−1.56867	−	0.317723i
$423$	25.3451	−	17.7468i	1.23232	−	0.862880i
$424$	−29.6488	−	24.3103i	−1.43987	−	1.18061i
$425$	−3.65574	+	1.75815i	−0.177330	+	0.0852829i
$426$	−0.0393881	+	0.348412i	−0.00190836	+	0.0168806i
$427$	0.606844	−	6.93626i	0.0293672	−	0.335669i
$428$	5.16539	−	4.66732i	0.249679	−	0.225603i
$429$	59.9891	+	34.6347i	2.89630	+	1.67218i
$430$	0.502406	+	0.910399i	0.0242282	+	0.0439034i
$431$	6.10896	−	16.7842i	0.294258	−	0.808468i	−0.701173	−	0.712991i	$-0.747340\pi$
$431$	6.10896	−	16.7842i	0.294258	−	0.808468i	0.995432	−	0.0954770i	$-0.0304376\pi$
$432$	24.2635	−	19.7891i	1.16738	−	0.952101i
$433$	−13.6927	−	9.58772i	−0.658028	−	0.460756i	0.196263	−	0.980551i	$-0.437119\pi$
$433$	−13.6927	−	9.58772i	−0.658028	−	0.460756i	−0.854291	+	0.519795i	$0.826008\pi$
$434$	2.92572	+	3.07768i	0.140439	+	0.147733i
$435$	5.00791	−	14.0190i	0.240111	−	0.672160i
$436$	18.5622	−	19.9754i	0.888969	−	0.956650i
$437$	12.3933	+	21.1387i	0.592852	+	1.01120i
$438$	−21.3879	−	8.40332i	−1.02195	−	0.401526i
$439$	1.70107	+	1.42737i	0.0811879	+	0.0681247i	0.682478	−	0.730906i	$-0.260902\pi$
$439$	1.70107	+	1.42737i	0.0811879	+	0.0681247i	−0.601291	+	0.799030i	$0.705347\pi$
$440$	−11.5744	−	30.1643i	−0.551787	−	1.43803i
$441$	−6.39206	−	36.2512i	−0.304384	−	1.72625i
$442$	2.75843	−	4.51020i	0.131205	−	0.214528i
$443$	11.0740	+	23.7482i	0.526139	+	1.12831i	0.972381	+	0.233397i	$0.0749843\pi$
$443$	11.0740	+	23.7482i	0.526139	+	1.12831i	−0.446242	+	0.894912i	$0.647238\pi$
$444$	24.3528	+	5.57746i	1.15573	+	0.264694i
$445$	4.21778	−	2.99101i	0.199942	−	0.141788i
$446$	−17.7242	−	8.81765i	−0.839267	−	0.417528i
$447$	−2.60103	+	29.7299i	−0.123024	+	1.40617i
$448$	−5.16058	−	2.26528i	−0.243815	−	0.107025i
$449$	24.0138	−	13.8644i	1.13328	−	0.654300i	0.188523	−	0.982069i	$-0.439630\pi$
$449$	24.0138	−	13.8644i	1.13328	−	0.654300i	0.944758	+	0.327769i	$0.106297\pi$
$450$	40.0181	+	0.534818i	1.88647	+	0.0252116i
$451$	−62.9094	−	11.0926i	−2.96229	−	0.522331i
$452$	1.23162	+	5.74489i	0.0579303	+	0.270217i
$453$	−10.2264	+	21.9305i	−0.480476	+	1.03038i
$454$	−23.7371	−	7.00869i	−1.11404	−	0.328934i
$455$	6.59672	+	3.02828i	0.309259	+	0.141968i
$456$	29.3397	−	21.3421i	1.37396	−	0.999437i
$457$	−15.1424	−	15.1424i	−0.708330	−	0.708330i	0.257854	−	0.966184i	$-0.416985\pi$
$457$	−15.1424	−	15.1424i	−0.708330	−	0.708330i	−0.966184	+	0.257854i	$0.916985\pi$
$458$	25.2527	−	13.7397i	1.17998	−	0.642014i
$459$	−5.96756	+	2.17201i	−0.278542	+	0.101381i
$460$	−5.46611	+	24.5390i	−0.254859	+	1.14414i
$461$	−6.64904	+	37.7086i	−0.309677	+	1.75626i	0.290954	+	0.956737i	$0.406027\pi$
$461$	−6.64904	+	37.7086i	−0.309677	+	1.75626i	−0.600630	+	0.799527i	$0.705084\pi$
$462$	−9.91443	+	11.2260i	−0.461261	+	0.522280i
$463$	−8.35844	+	31.1941i	−0.388449	+	1.44971i	0.444207	+	0.895924i	$0.353485\pi$
$463$	−8.35844	+	31.1941i	−0.388449	+	1.44971i	−0.832657	+	0.553789i	$0.813181\pi$
$464$	3.93848	−	8.14726i	0.182840	−	0.378227i
$465$	−24.3722	−	13.8779i	−1.13023	−	0.643573i
$466$	−11.8950	+	23.9100i	−0.551025	+	1.10761i
$467$	9.50422	+	35.4702i	0.439803	+	1.64137i	0.729304	+	0.684189i	$0.239844\pi$
$467$	9.50422	+	35.4702i	0.439803	+	1.64137i	−0.289502	+	0.957178i	$0.593490\pi$
$468$	−44.1856	+	27.7178i	−2.04248	+	1.28125i
$469$	−1.31999	+	3.62663i	−0.0609513	+	0.167462i
$470$	16.9631	+	3.33043i	0.782452	+	0.153621i
$471$	−21.4042	+	3.77413i	−0.986252	+	0.173903i
$472$	7.79701	+	7.62201i	0.358886	+	0.350832i
$473$	1.67338	−	0.146402i	0.0769420	−	0.00673155i
$474$	20.0573	+	46.0186i	0.921262	+	2.11370i
$475$	21.7432	+	1.49502i	0.997645	+	0.0685963i
$476$	0.837379	+	0.778136i	0.0383812	+	0.0356658i
$477$	−6.68692	−	76.4319i	−0.306173	−	3.49957i
$478$	10.4041	+	0.263340i	0.475872	+	0.0120449i
$479$	−2.21937	−	12.5867i	−0.101405	−	0.575099i	−0.992595	−	0.121468i	$-0.961240\pi$
$479$	−2.21937	−	12.5867i	−0.101405	−	0.575099i	0.891190	−	0.453631i	$-0.149871\pi$
$480$	36.9533	+	4.47673i	1.68668	+	0.204334i
$481$	−18.3800	−	6.68977i	−0.838055	−	0.305027i
$482$	4.68599	+	31.1683i	0.213441	+	1.41968i
$483$	11.2572	−	3.01636i	0.512220	−	0.137249i
$484$	−30.1538	−	1.52744i	−1.37063	−	0.0694291i
$485$	−7.75328	+	13.6162i	−0.352058	+	0.618279i
$486$	−7.95996	−	0.899875i	−0.361071	−	0.0408192i
$487$	7.46506	+	2.00026i	0.338274	+	0.0906402i	0.423957	−	0.905682i	$-0.360641\pi$
$487$	7.46506	+	2.00026i	0.338274	+	0.0906402i	−0.0856833	+	0.996322i	$0.527307\pi$
$488$	2.75229	+	27.8188i	0.124591	+	1.25930i
$489$	−23.7557	−	4.18876i	−1.07427	−	0.189422i
$490$	12.1200	−	16.6159i	0.547525	−	0.750629i
$491$	2.85243	+	7.83700i	0.128729	+	0.353679i	0.987267	−	0.159070i	$-0.0508495\pi$
$491$	2.85243	+	7.83700i	0.128729	+	0.353679i	−0.858539	+	0.512749i	$0.828627\pi$
$492$	45.2096	−	58.0746i	2.03820	−	2.61820i
$493$	−1.29785	+	1.29785i	−0.0584524	+	0.0584524i
$494$	−24.8594	+	13.7415i	−1.11848	+	0.618260i
$495$	26.9729	−	58.7570i	1.21234	−	2.64093i
$496$	−13.8278	−	9.97277i	−0.620885	−	0.447791i
$497$	0.0537931	+	0.0250841i	0.00241295	+	0.00112518i
$498$	−10.5575	−	2.13835i	−0.473095	−	0.0958217i
$499$	0.0149988	−	0.0850623i	0.000671437	−	0.00380791i	−0.984470	−	0.175552i	$-0.943829\pi$
$499$	0.0149988	−	0.0850623i	0.000671437	−	0.00380791i	0.985142	+	0.171744i	$0.0549402\pi$
$500$	15.2860	+	16.3199i	0.683612	+	0.729846i
$501$	31.3580	+	54.3136i	1.40097	+	2.42655i
$502$	6.00740	+	7.53880i	0.268123	+	0.336473i
$503$	−19.0067	−	1.66287i	−0.847467	−	0.0741438i	−0.344855	−	0.938656i	$-0.612072\pi$
$503$	−19.0067	−	1.66287i	−0.847467	−	0.0741438i	−0.502612	+	0.864512i	$0.667628\pi$
$504$	−3.97728	−	10.5533i	−0.177162	−	0.470080i
$505$	−5.82364	−	8.21221i	−0.259149	−	0.365439i
$506$	32.6679	+	24.1288i	1.45227	+	1.07266i
$507$	21.9554	−	10.2380i	0.975073	−	0.454684i
$508$	−1.62417	+	11.7050i	−0.0720609	+	0.519326i
$509$	13.5536	−	2.38987i	0.600755	−	0.105929i	0.135004	−	0.990845i	$-0.456895\pi$
$509$	13.5536	−	2.38987i	0.600755	−	0.105929i	0.465751	+	0.884916i	$0.345784\pi$
$510$	−6.77960	−	3.32243i	−0.300206	−	0.147120i
$511$	−2.50039	+	2.97985i	−0.110611	+	0.131821i
$512$	22.0431	+	5.10901i	0.974176	+	0.225789i
$513$	33.6399	+	5.70039i	1.48524	+	0.251678i
$514$	4.68342	+	10.7454i	0.206577	+	0.473961i
$515$	−9.79015	−	3.49726i	−0.431406	−	0.154108i
$516$	−0.753065	+	1.78277i	−0.0331518	+	0.0784820i
$517$	16.0177	−	22.8756i	0.704457	−	1.00607i
$518$	2.20656	−	3.60785i	0.0969505	−	0.158520i
$519$	−40.2153	−	14.6372i	−1.76526	−	0.642500i
$520$	−28.2759	−	7.05396i	−1.23998	−	0.309337i
$521$	−0.130227	+	0.225560i	−0.00570536	+	0.00988197i	−0.868864	−	0.495051i	$-0.835149\pi$
$521$	−0.130227	+	0.225560i	−0.00570536	+	0.00988197i	0.863159	+	0.504933i	$0.168483\pi$
$522$	17.1676	−	5.76088i	0.751404	−	0.252147i
$523$	−33.2356	−	2.90774i	−1.45329	−	0.127147i	−0.667026	−	0.745035i	$-0.732433\pi$
$523$	−33.2356	−	2.90774i	−1.45329	−	0.127147i	−0.786266	+	0.617888i	$0.787988\pi$
$524$	−2.02843	−	6.59344i	−0.0886123	−	0.288036i
$525$	3.42870	−	9.78221i	0.149641	−	0.426931i
$526$	2.08149	+	33.5507i	0.0907571	+	1.46288i
$527$	1.98341	+	2.83260i	0.0863987	+	0.123390i
$528$	30.7899	−	51.6512i	1.33996	−	2.24783i
$529$	−2.94210	−	8.08336i	−0.127918	−	0.351451i
$530$	28.1839	−	32.2990i	1.22423	−	1.40298i
$531$			21.8190i			0.946864i
$532$	−1.84502	−	5.85787i	−0.0799917	−	0.253971i
$533$	−40.7433	+	40.7433i	−1.76479	+	1.76479i
$534$	9.22960	+	2.72516i	0.399404	+	0.117929i
$535$	5.03859	+	5.93245i	0.217837	+	0.256482i
$536$	2.51732	−	15.2891i	0.108732	−	0.660390i
$537$	−55.0080	+	38.5170i	−2.37377	+	1.66213i
$538$	−23.0911	+	26.1457i	−0.995526	+	1.12722i
$539$	−16.6119	−	28.7727i	−0.715526	−	1.23933i
$540$	21.2822	+	27.7934i	0.915839	+	1.19604i
$541$	−8.80613	+	7.38922i	−0.378605	+	0.317687i	−0.812155	−	0.583442i	$-0.801705\pi$
$541$	−8.80613	+	7.38922i	−0.378605	+	0.317687i	0.433549	+	0.901130i	$0.357261\pi$
$542$	−0.659041	−	1.96396i	−0.0283082	−	0.0843592i
$543$	33.0446	−	8.85427i	1.41808	−	0.379973i
$544$	−3.88145	−	2.44897i	−0.166416	−	0.104999i
$545$	21.6860	+	21.4286i	0.928927	+	0.917899i
$546$	3.16521	+	13.1335i	0.135459	+	0.562061i
$547$	−31.8044	−	22.2697i	−1.35986	−	0.952183i	−0.999815	−	0.0192482i	$-0.993873\pi$
$547$	−31.8044	−	22.2697i	−1.35986	−	0.952183i	−0.360044	−	0.932935i	$-0.617238\pi$
$548$	−3.90352	−	9.61312i	−0.166750	−	0.410652i
$549$	−35.9573	+	42.8522i	−1.53462	+	1.82889i
$550$	34.1058	−	11.8998i	1.45428	−	0.507410i
$551$	9.50797	−	2.61579i	0.405053	−	0.111436i
$552$	−42.1797	+	20.2546i	−1.79529	+	0.862094i
$553$	8.46534	−	0.740621i	0.359983	−	0.0314944i
$554$	3.25186	+	3.42075i	0.138158	+	0.145334i
$555$	−7.06815	+	27.0231i	−0.300026	+	1.14707i
$556$	−7.85028	+	5.93715i	−0.332926	+	0.251791i
$557$	3.20483	+	6.87277i	0.135793	+	0.291209i	0.962432	−	0.271524i	$-0.0875277\pi$
$557$	3.20483	+	6.87277i	0.135793	+	0.291209i	−0.826639	+	0.562733i	$0.809750\pi$
$558$	−5.07218	−	33.7370i	−0.214722	−	1.42820i
$559$	0.757577	−	1.31216i	0.0320421	−	0.0554985i
$560$	2.70848	−	5.68929i	0.114454	−	0.240416i
$561$	−9.34300	+	7.83970i	−0.394462	+	0.330993i
$562$	9.08351	−	7.23833i	0.383165	−	0.305330i
$563$	−0.556474	+	2.07679i	−0.0234526	+	0.0875263i	−0.976660	−	0.214790i	$-0.931093\pi$
$563$	−0.556474	+	2.07679i	−0.0234526	+	0.0875263i	0.953208	+	0.302316i	$0.0977599\pi$
$564$	14.6568	+	28.6417i	0.617164	+	1.20603i
$565$	−6.46221	+	1.17929i	−0.271867	+	0.0496131i
$566$	−4.79548	+	3.18009i	−0.201569	+	0.133669i
$567$	1.80271	−	3.86593i	0.0757069	−	0.162354i
$568$	−0.230866	−	0.0590604i	−0.00968690	−	0.00247812i
$569$			29.6206i			1.24176i	0.783906	+	0.620879i	$0.213224\pi$
$569$			29.6206i			1.24176i	−0.783906	+	0.620879i	$0.786776\pi$
$570$	22.8436	+	33.5194i	0.956815	+	1.40397i
$571$			31.0883i			1.30101i	0.759504	+	0.650503i	$0.225442\pi$
$571$			31.0883i			1.30101i	−0.759504	+	0.650503i	$0.774558\pi$
$572$	−28.9190	+	37.1483i	−1.20916	+	1.55325i
$573$	−7.13530	+	15.3017i	−0.298081	+	0.639238i
$574$	−6.88532	−	10.3829i	−0.287388	−	0.433372i
$575$	−27.2351	−	6.95011i	−1.13578	−	0.289840i
$576$	23.5238	+	38.6891i	0.980159	+	1.61205i
$577$	10.8807	−	40.6071i	0.452967	−	1.69050i	−0.241028	−	0.970518i	$-0.577485\pi$
$577$	10.8807	−	40.6071i	0.452967	−	1.69050i	0.693996	−	0.719979i	$-0.255849\pi$
$578$	−14.4026	−	18.0741i	−0.599069	−	0.751783i
$579$	24.6546	−	20.6876i	1.02461	−	0.859748i
$580$	8.96954	+	4.68074i	0.372440	+	0.194357i
$581$	−0.911723	+	1.57915i	−0.0378246	+	0.0655142i
$582$	−28.8384	+	4.33570i	−1.19539	+	0.179721i
$583$	−29.2656	−	62.7603i	−1.21206	−	2.59927i
$584$	7.65479	−	13.6130i	0.316757	−	0.563308i
$585$	−29.4593	−	50.3285i	−1.21799	−	2.08083i
$586$	21.6961	−	20.6249i	0.896256	−	0.852005i
$587$	36.2290	−	3.16963i	1.49533	−	0.130825i	0.690069	−	0.723743i	$-0.257580\pi$
$587$	36.2290	−	3.16963i	1.49533	−	0.130825i	0.805262	+	0.592919i	$0.202025\pi$
$588$	38.2521	−	1.40275i	1.57749	−	0.0578485i
$589$	−1.74271	−	18.4966i	−0.0718072	−	0.762140i
$590$	−8.78510	+	8.45178i	−0.361677	+	0.347954i
$591$	14.1240	−	16.8323i	0.580982	−	0.692387i
$592$	−6.02942	+	15.8728i	−0.247808	+	0.652370i
$593$	20.7598	+	14.5362i	0.852502	+	0.596929i	0.916056	−	0.401050i	$-0.131355\pi$
$593$	20.7598	+	14.5362i	0.852502	+	0.596929i	−0.0635539	+	0.997978i	$0.520243\pi$
$594$	54.9755	−	13.2493i	2.25567	−	0.543624i
$595$	−0.898295	+	0.909087i	−0.0368265	+	0.0372690i
$596$	−19.7706	−	4.52802i	−0.809836	−	0.185475i
$597$	15.8290	−	4.24137i	0.647838	−	0.173588i
$598$	34.7295	−	11.6541i	1.42020	−	0.476571i
$599$	18.9868	−	15.9318i	0.775778	−	0.650955i	−0.166404	−	0.986058i	$-0.553216\pi$
$599$	18.9868	−	15.9318i	0.775778	−	0.650955i	0.942182	+	0.335103i	$0.108771\pi$
$600$	−6.27028	+	41.1420i	−0.255983	+	1.67962i
$601$	24.3395	+	42.1572i	0.992827	+	1.71963i	0.599953	+	0.800036i	$0.295186\pi$
$601$	24.3395	+	42.1572i	0.992827	+	1.71963i	0.392875	+	0.919592i	$0.371481\pi$
$602$	0.245549	+	0.216861i	0.0100078	+	0.00883861i
$603$	25.3992	−	17.7847i	1.03434	−	0.724250i
$604$	−13.8080	−	8.93271i	−0.561838	−	0.363467i
$605$	2.74120	−	33.6448i	0.111446	−	1.36785i
$606$	5.30601	−	17.9705i	0.215542	−	0.730000i
$607$	−1.38444	+	1.38444i	−0.0561929	+	0.0561929i	−0.734645	−	0.678452i	$-0.762651\pi$
$607$	−1.38444	+	1.38444i	−0.0561929	+	0.0561929i	0.678452	+	0.734645i	$0.262651\pi$
$608$	11.6265	+	21.7445i	0.471517	+	0.881857i
$609$		−	4.69011i		−	0.190053i
$610$	−31.1822	+	2.12152i	−1.26253	+	0.0858980i
$611$	−8.61524	−	23.6702i	−0.348535	−	0.957592i
$612$	−1.92514	−	8.97984i	−0.0778191	−	0.362988i
$613$	−8.11233	−	11.5856i	−0.327654	−	0.467939i	0.621201	−	0.783652i	$-0.286645\pi$
$613$	−8.11233	−	11.5856i	−0.327654	−	0.467939i	−0.948855	+	0.315713i	$0.897756\pi$
$614$	34.3315	−	2.12993i	1.38551	−	0.0859569i
$615$	63.3481	+	52.5140i	2.55444	+	2.11757i
$616$	−6.63101	−	7.72282i	−0.267171	−	0.311161i
$617$	31.4710	+	2.75336i	1.26697	+	0.110846i	0.700751	−	0.713406i	$-0.252848\pi$
$617$	31.4710	+	2.75336i	1.26697	+	0.110846i	0.566223	+	0.824252i	$0.308404\pi$
$618$	−6.15552	−	18.3436i	−0.247611	−	0.737888i
$619$	6.20493	−	10.7473i	0.249397	−	0.431968i	−0.713962	−	0.700185i	$-0.753101\pi$
$619$	6.20493	−	10.7473i	0.249397	−	0.431968i	0.963359	+	0.268216i	$0.0864342\pi$
$620$	11.6189	−	15.1106i	0.466628	−	0.606855i
$621$	−41.3494	−	15.0499i	−1.65929	−	0.603933i
$622$	−29.8342	−	18.2466i	−1.19624	−	0.731621i
$623$	0.934382	−	1.33444i	0.0374352	−	0.0534631i
$624$	−22.2342	−	49.4725i	−0.890079	−	1.98048i
$625$	−18.7619	+	16.5225i	−0.750475	+	0.660899i
$626$	−19.4826	+	8.49152i	−0.778680	+	0.339389i
$627$	64.4545	−	11.8091i	2.57406	−	0.471612i
$628$	−0.541319	−	14.7614i	−0.0216010	−	0.589045i
$629$	2.21369	−	2.63817i	0.0882656	−	0.105191i
$630$	11.9298	−	4.08266i	0.475293	−	0.162657i
$631$	23.5150	−	4.14632i	0.936116	−	0.165063i	0.315276	−	0.949000i	$-0.397903\pi$
$631$	23.5150	−	4.14632i	0.936116	−	0.165063i	0.620840	+	0.783937i	$0.286792\pi$
$632$	−32.8524	+	9.20361i	−1.30680	+	0.366100i
$633$	62.0064	−	28.9141i	2.46453	−	1.14923i
$634$	−11.6251	+	15.7391i	−0.461691	+	0.625081i
$635$	−13.0247	−	2.21650i	−0.516870	−	0.0879593i
$636$	79.6802	+	4.03620i	3.15953	+	0.160046i
$637$	−29.8539	−	2.61188i	−1.18285	−	0.103486i
$638$	12.7820	−	10.1856i	0.506046	−	0.403250i
$639$	−0.238429	−	0.412972i	−0.00943211	−	0.0163369i
$640$	−6.46544	+	24.4581i	−0.255569	+	0.966791i
$641$	3.17020	−	17.9791i	0.125215	−	0.710132i	−0.855964	−	0.517035i	$-0.827036\pi$
$641$	3.17020	−	17.9791i	0.125215	−	0.710132i	0.981180	−	0.193097i	$-0.0618531\pi$
$642$	−2.87569	+	14.1980i	−0.113494	+	0.560349i
$643$	−28.7806	−	13.4206i	−1.13499	−	0.529257i	−0.237985	−	0.971269i	$-0.576487\pi$
$643$	−28.7806	−	13.4206i	−1.13499	−	0.529257i	−0.897009	+	0.442012i	$0.854265\pi$
$644$	0.979024	+	7.85989i	0.0385790	+	0.309723i
$645$	−1.96643	−	0.902705i	−0.0774280	−	0.0355440i
$646$	−0.776545	−	4.94059i	−0.0305528	−	0.194385i
$647$	−20.5581	+	20.5581i	−0.808221	+	0.808221i	−0.984365	−	0.176143i	$-0.943638\pi$
$647$	−20.5581	+	20.5581i	−0.808221	+	0.808221i	0.176143	+	0.984365i	$0.443638\pi$
$648$	−4.24447	+	16.5915i	−0.166739	+	0.651777i
$649$	6.73543	+	18.5055i	0.264389	+	0.726403i
$650$	8.85272	−	31.3565i	0.347232	−	1.22990i
$651$	−8.70191	−	1.53438i	−0.341055	−	0.0601372i
$652$	5.03881	−	15.6006i	0.197335	−	0.610966i
$653$	−5.92048	−	1.58639i	−0.231686	−	0.0620802i	0.141108	−	0.989994i	$-0.454934\pi$
$653$	−5.92048	−	1.58639i	−0.231686	−	0.0620802i	−0.372794	+	0.927914i	$0.621600\pi$
$654$	−6.37408	+	56.3827i	−0.249246	+	2.20474i
$655$	7.43779	−	2.04063i	0.290619	−	0.0797339i
$656$	34.8717	+	35.8590i	1.36151	+	1.40006i
$657$	30.1872	−	8.08862i	1.17771	−	0.315567i
$658$	5.38583	−	0.809731i	0.209961	−	0.0315666i
$659$	27.5649	+	10.0328i	1.07378	+	0.390822i	0.817587	−	0.575805i	$-0.195311\pi$
$659$	27.5649	+	10.0328i	1.07378	+	0.390822i	0.256188	+	0.966627i	$0.417533\pi$
$660$	56.6645	+	36.1796i	2.20566	+	1.40829i
$661$	3.27858	+	18.5938i	0.127522	+	0.723214i	0.979778	+	0.200088i	$0.0641229\pi$
$661$	3.27858	+	18.5938i	0.127522	+	0.723214i	−0.852256	+	0.523125i	$0.824766\pi$
$662$	0.823667	−	32.5416i	0.0320127	−	1.26476i
$663$	0.958816	+	10.9593i	0.0372373	+	0.425625i
$664$	2.42567	−	6.90740i	0.0941343	−	0.268059i
$665$	6.60950	−	1.86090i	0.256305	−	0.0721625i
$666$	−31.1473	+	13.5756i	−1.20693	+	0.526045i
$667$	−12.6694	+	1.10843i	−0.490562	+	0.0429186i
$668$	−39.4920	+	16.0362i	−1.52799	+	0.620458i
$669$	40.5677	−	7.15319i	1.56844	−	0.276558i
$670$	16.9994	+	3.33755i	0.656743	+	0.128941i
$671$	−17.2683	+	47.4443i	−0.666636	+	1.83157i
$672$	11.4383	−	2.58830i	0.441240	−	0.0998458i
$673$	−1.87829	−	7.00988i	−0.0724028	−	0.270211i	0.920229	−	0.391380i	$-0.128002\pi$
$673$	−1.87829	−	7.00988i	−0.0724028	−	0.270211i	−0.992632	+	0.121169i	$0.961336\pi$
$674$	−27.8673	−	13.8637i	−1.07341	−	0.534010i
$675$	−31.7893	+	22.8297i	−1.22357	+	0.878715i
$676$	4.84116	+	15.7363i	0.186198	+	0.605241i
$677$	1.84209	−	6.87476i	0.0707971	−	0.264218i	−0.921450	−	0.388496i	$-0.872995\pi$
$677$	1.84209	−	6.87476i	0.0707971	−	0.264218i	0.992247	+	0.124278i	$0.0396614\pi$
$678$	−9.16375	−	8.09313i	−0.351932	−	0.310815i
$679$	−0.857225	+	4.86157i	−0.0328973	+	0.186570i
$680$	2.86988	−	4.25355i	0.110055	−	0.163116i
$681$	48.3956	−	17.6146i	1.85452	−	0.674992i
$682$	−14.7164	−	27.0477i	−0.563518	−	1.03571i
$683$	−19.5269	−	19.5269i	−0.747177	−	0.747177i	0.226771	−	0.973948i	$-0.427183\pi$
$683$	−19.5269	−	19.5269i	−0.747177	−	0.747177i	−0.973948	+	0.226771i	$0.927183\pi$
$684$	−14.8517	+	47.0538i	−0.567871	+	1.79915i
$685$	10.8766	−	4.03248i	0.415575	−	0.154073i
$686$	3.80976	−	12.9029i	0.145457	−	0.492636i
$687$	−25.2817	+	54.2167i	−0.964556	+	2.06850i
$688$	−1.12978	−	0.673477i	−0.0430726	−	0.0256761i
$689$	−61.5131	−	10.8464i	−2.34346	−	0.413216i
$690$	−21.1879	−	47.8308i	−0.806611	−	1.82089i
$691$	−30.9878	+	17.8908i	−1.17883	+	0.680599i	−0.955744	−	0.294199i	$-0.904947\pi$
$691$	−30.9878	+	17.8908i	−1.17883	+	0.680599i	−0.223089	+	0.974798i	$0.571614\pi$
$692$	13.6100	−	25.7049i	0.517373	−	0.977155i
$693$	1.77528	−	20.2915i	0.0674373	−	0.770812i
$694$	6.30784	−	12.6793i	0.239442	−	0.481300i
$695$	−6.36555	−	8.97639i	−0.241459	−	0.340494i
$696$	3.48008	+	18.5059i	0.131912	+	0.701463i
$697$	−4.28755	−	9.19469i	−0.162403	−	0.348274i
$698$	11.2391	+	6.87381i	0.425405	+	0.260177i
$699$	−9.64964	−	54.7258i	−0.364983	−	2.06992i
$700$	6.26493	+	3.22189i	0.236792	+	0.121776i
$701$	33.2096	+	27.8662i	1.25431	+	1.05249i	0.996264	+	0.0863589i	$0.0275232\pi$
$701$	33.2096	+	27.8662i	1.25431	+	1.05249i	0.258046	+	0.966133i	$0.416921\pi$
$702$	18.6529	−	47.4748i	0.704008	−	1.79182i
$703$	−17.3444	+	6.44427i	−0.654157	+	0.243050i
$704$	31.8945	+	25.5519i	1.20207	+	0.963023i
$705$	−32.5101	+	15.3967i	−1.22440	+	0.579873i
$706$	7.94371	−	7.55151i	0.298966	−	0.284205i
$707$	−2.59821	−	1.81929i	−0.0977157	−	0.0684213i
$708$	−22.4735	−	3.11839i	−0.844605	−	0.117196i
$709$	5.74816	−	15.7929i	0.215877	−	0.593116i	−0.783732	−	0.621100i	$-0.786686\pi$
$709$	5.74816	−	15.7929i	0.215877	−	0.593116i	0.999608	+	0.0279832i	$0.00890848\pi$
$710$	0.0739192	−	0.255968i	0.00277414	−	0.00960632i
$711$	−59.1247	−	34.1357i	−2.21735	−	1.28019i
$712$	−2.69666	+	5.95863i	−0.101062	+	0.223309i
$713$	−2.08828	+	23.8692i	−0.0782068	+	0.893908i
$714$	−2.36359	−	0.267204i	−0.0884551	−	0.00999987i
$715$	−40.5216	−	33.5914i	−1.51542	−	1.25625i
$716$	−20.7907	−	40.6282i	−0.776984	−	1.51835i
$717$	−17.7398	+	12.4216i	−0.662506	+	0.463892i
$718$	−6.59009	+	32.5369i	−0.245940	+	1.21427i
$719$	6.21319	−	2.26142i	0.231713	−	0.0843367i	−0.223554	−	0.974692i	$-0.571766\pi$
$719$	6.21319	−	2.26142i	0.231713	−	0.0843367i	0.455267	+	0.890355i	$0.349544\pi$
$720$	−44.0423	+	24.9610i	−1.64136	+	0.930242i
$721$	−3.27533			−0.121980
$722$	−9.49136	+	25.1379i	−0.353232	+	0.935536i
$723$	−46.3760	−	46.3760i	−1.72474	−	1.72474i
$724$	2.87385	+	23.0721i	0.106806	+	0.857467i
$725$	−5.53842	+	9.86298i	−0.205692	+	0.366302i
$726$	52.3596	−	34.7219i	1.94325	−	1.28865i
$727$	13.8781	+	19.8200i	0.514712	+	0.735084i	0.989423	−	0.145057i	$-0.0463366\pi$
$727$	13.8781	+	19.8200i	0.514712	+	0.735084i	−0.474712	+	0.880141i	$0.657448\pi$
$728$	−9.13687	+	0.903969i	−0.338635	+	0.0335033i
$729$	30.1669	−	17.4169i	1.11729	−	0.645069i
$730$	14.9500	+	9.02121i	0.553325	+	0.333890i
$731$	0.171480	+	0.204362i	0.00634243	+	0.00755862i
$732$	−38.9986	−	43.1603i	−1.44143	−	1.59525i
$733$	−9.43318	−	35.2051i	−0.348423	−	1.30033i	−0.888563	−	0.458756i	$-0.848295\pi$
$733$	−9.43318	−	35.2051i	−0.348423	−	1.30033i	0.540140	−	0.841575i	$-0.318371\pi$
$734$	15.8699	+	11.7217i	0.585770	+	0.432655i
$735$	0.255537	+	42.7952i	0.00942564	+	1.57852i
$736$	−9.69504	−	30.2865i	−0.357364	−	1.11638i
$737$	16.0519	−	22.9245i	0.591279	−	0.844434i
$738$	−2.53265	+	100.060i	−0.0932280	+	3.68326i
$739$	10.7763	+	9.04242i	0.396414	+	0.332631i	0.819106	−	0.573643i	$-0.194470\pi$
$739$	10.7763	+	9.04242i	0.396414	+	0.332631i	−0.422692	+	0.906274i	$0.638915\pi$
$740$	−17.5312	−	7.28237i	−0.644460	−	0.267705i
$741$	24.6211	−	53.7335i	0.904479	−	1.97395i
$742$	4.93875	−	12.5700i	0.181307	−	0.461458i
$743$	2.23319	+	25.5255i	0.0819278	+	0.936440i	0.920267	+	0.391291i	$0.127971\pi$
$743$	2.23319	+	25.5255i	0.0819278	+	0.936440i	−0.838339	+	0.545149i	$0.816473\pi$
$744$	35.4739	−	0.402609i	1.30054	−	0.0147604i
$745$	5.73823	−	21.9385i	0.210232	−	0.803765i
$746$	−5.31643	−	22.0595i	−0.194648	−	0.807658i
$747$	13.2772	−	6.19127i	0.485788	−	0.226527i
$748$	−4.40482	−	7.02183i	−0.161056	−	0.256744i
$749$	2.12367	+	1.22610i	0.0775972	+	0.0448008i
$750$	−45.7615	−	8.41825i	−1.67097	−	0.307391i
$751$	−17.2884	−	20.6035i	−0.630862	−	0.751832i	0.352035	−	0.935987i	$-0.385490\pi$
$751$	−17.2884	−	20.6035i	−0.630862	−	0.751832i	−0.982897	+	0.184155i	$0.941045\pi$
$752$	−20.6502	+	7.19128i	−0.753034	+	0.262239i
$753$	−19.3752	−	5.19156i	−0.706071	−	0.189191i
$754$	−0.912858	−	14.7140i	−0.0332443	−	0.535853i
$755$	10.4560	−	15.1241i	0.380532	−	0.550422i
$756$	9.25997	+	5.99051i	0.336782	+	0.217873i
$757$	19.1761	+	8.94196i	0.696967	+	0.325001i	0.738612	−	0.674131i	$-0.235482\pi$
$757$	19.1761	+	8.94196i	0.696967	+	0.325001i	−0.0416442	+	0.999133i	$0.513260\pi$
$758$	−23.0672	−	42.3960i	−0.837837	−	1.53989i
$759$	−84.5092			−3.06749
$760$	−24.6985	+	12.2469i	−0.895908	+	0.444241i
$761$	−33.1675			−1.20232			−0.601161	−	0.799128i	$-0.705295\pi$
$761$	−33.1675			−1.20232			−0.601161	+	0.799128i	$0.705295\pi$
$762$	−11.7521	−	21.5997i	−0.425734	−	0.782473i
$763$	8.70521	+	4.05931i	0.315150	+	0.146957i
$764$	−9.63431	−	6.23268i	−0.348557	−	0.225490i
$765$	10.1011	−	1.84335i	0.365205	−	0.0666464i
$766$	−1.67935	−	27.0688i	−0.0606773	−	0.978034i
$767$	17.1579	+	4.59745i	0.619537	+	0.166004i
$768$	−43.2117	+	18.7000i	−1.55927	+	0.674777i
$769$	11.7149	+	13.9612i	0.422448	+	0.503454i	0.934728	−	0.355364i	$-0.115643\pi$
$769$	11.7149	+	13.9612i	0.422448	+	0.503454i	−0.512279	+	0.858819i	$0.671199\pi$
$770$	8.85775	−	7.14532i	0.319211	−	0.257499i
$771$	−21.1234	−	12.1956i	−0.760741	−	0.439214i
$772$	11.6235	+	18.5294i	0.418341	+	0.666888i
$773$	34.7208	−	16.1906i	1.24882	−	0.582334i	0.318096	−	0.948059i	$-0.396957\pi$
$773$	34.7208	−	16.1906i	1.24882	−	0.582334i	0.930723	+	0.365725i	$0.119179\pi$
$774$	−0.616665	−	2.55874i	−0.0221656	−	0.0919720i
$775$	16.4876	+	13.5026i	0.592253	+	0.485026i
$776$	−0.224929	−	19.8185i	−0.00807447	−	0.711442i
$777$	0.766986	+	8.76669i	0.0275155	+	0.314503i
$778$	−4.30969	+	10.9689i	−0.154510	+	0.393254i
$779$	−4.38809	+	54.3300i	−0.157220	+	1.94658i
$780$	56.0485	−	23.1499i	2.00686	−	0.828901i
$781$	−0.329703	−	0.276653i	−0.0117977	−	0.00989944i
$782$	−0.163205	+	6.44793i	−0.00583620	+	0.230578i
$783$	−10.1571	+	14.5059i	−0.362986	+	0.518397i
$784$	−2.62881	+	25.8816i	−0.0938861	+	0.924344i
$785$	16.5146	−	0.0986114i	0.589430	−	0.00351959i
$786$	11.5465	+	8.52834i	0.411849	+	0.304196i
$787$	4.75003	+	17.7273i	0.169320	+	0.631912i	0.997450	+	0.0713746i	$0.0227386\pi$
$787$	4.75003	+	17.7273i	0.169320	+	0.631912i	−0.828129	+	0.560537i	$0.810595\pi$
$788$	10.0119	+	11.0803i	0.356658	+	0.394718i
$789$	−44.9619	−	53.5835i	−1.60069	−	1.90762i
$790$	−9.15827	−	37.0285i	−0.325837	−	1.31741i
$791$	−1.79231	+	1.03479i	−0.0637270	+	0.0367928i
$792$	8.05165	+	81.3821i	0.286103	+	2.89179i
$793$	26.1214	+	37.3052i	0.927598	+	1.32475i
$794$	11.2562	−	7.46446i	0.399467	−	0.264904i
$795$	−7.24352	+	88.9048i	−0.256901	+	3.15313i
$796$	1.37663	+	11.0520i	0.0487933	+	0.391727i
$797$	−0.548120	−	0.548120i	−0.0194154	−	0.0194154i	0.697332	−	0.716748i	$-0.254370\pi$
$797$	−0.548120	−	0.548120i	−0.0194154	−	0.0194154i	−0.716748	+	0.697332i	$0.754370\pi$
$798$	10.3301	+	7.52389i	0.365682	+	0.266343i
$799$	4.43512			0.156903
$800$	−27.1103	−	8.06409i	−0.958495	−	0.285109i
$801$	−12.2987	+	4.47634i	−0.434551	+	0.158164i
$802$	−8.19206	+	40.4462i	−0.289272	+	1.42820i
$803$	23.1059	−	16.1789i	0.815388	−	0.570941i
$804$	14.6881	+	28.7029i	0.518010	+	1.01227i
$805$	−8.81707	+	0.824473i	−0.310761	+	0.0290588i
$806$	−27.5987	−	3.12004i	−0.972122	−	0.109899i
$807$	6.32625	−	72.3094i	0.222695	−	2.54541i
$808$	11.6017	+	5.25052i	0.408148	+	0.184713i
$809$	11.3717	+	6.56544i	0.399807	+	0.230829i	0.686401	−	0.727223i	$-0.259190\pi$
$809$	11.3717	+	6.56544i	0.399807	+	0.230829i	−0.286594	+	0.958052i	$0.592523\pi$
$810$	−18.3956	−	5.31232i	−0.646355	−	0.186656i
$811$	−16.1992	+	44.5070i	−0.568832	+	1.56285i	0.237498	+	0.971388i	$0.423673\pi$
$811$	−16.1992	+	44.5070i	−0.568832	+	1.56285i	−0.806330	+	0.591466i	$0.798550\pi$
$812$	3.15729	+	0.438101i	0.110799	+	0.0153743i
$813$	3.53109	+	2.47250i	0.123841	+	0.0867143i
$814$	−22.2264	+	21.1290i	−0.779035	+	0.740571i
$815$	17.2610	+	6.16600i	0.604625	+	0.215986i
$816$	9.52434	−	0.699479i	0.333419	−	0.0244867i
$817$	−0.258305	−	1.40983i	−0.00903696	−	0.0493238i
$818$	12.0729	−	30.7275i	0.422119	−	1.07436i
$819$	−14.0745	−	11.8099i	−0.491801	−	0.412670i
$820$	−41.2688	+	37.7394i	−1.44117	+	1.31792i
$821$	−2.20410	−	12.5001i	−0.0769237	−	0.436256i	−0.998809	−	0.0487928i	$-0.984463\pi$
$821$	−2.20410	−	12.5001i	−0.0769237	−	0.436256i	0.921885	−	0.387463i	$-0.126649\pi$
$822$	18.4182	+	11.2645i	0.642407	+	0.392895i
$823$	4.94826	+	10.6116i	0.172485	+	0.369896i	0.973479	−	0.228777i	$-0.0734726\pi$
$823$	4.94826	+	10.6116i	0.172485	+	0.369896i	−0.800993	+	0.598673i	$0.795695\pi$
$824$	12.9236	−	2.43031i	0.450213	−	0.0846639i
$825$	−42.3745	+	62.0821i	−1.47529	+	2.16142i
$826$	−1.71071	+	3.43868i	−0.0595232	+	0.119647i
$827$	1.52982	−	17.4859i	0.0531971	−	0.608046i	−0.922071	−	0.387021i	$-0.873504\pi$
$827$	1.52982	−	17.4859i	0.0531971	−	0.608046i	0.975268	−	0.221025i	$-0.0709402\pi$
$828$	29.7767	−	56.2388i	1.03481	−	1.95443i
$829$	−24.6638	+	14.2397i	−0.856611	+	0.494564i	−0.862876	−	0.505416i	$-0.831339\pi$
$829$	−24.6638	+	14.2397i	−0.856611	+	0.494564i	0.00626510	+	0.999980i	$0.498006\pi$
$830$	7.63587	+	2.94763i	0.265045	+	0.102314i
$831$	−9.67192	−	1.70542i	−0.335515	−	0.0591604i
$832$	35.3808	−	10.3464i	1.22661	−	0.358697i
$833$	2.22995	−	4.78214i	0.0772632	−	0.165691i
$834$	5.79975	−	19.6427i	0.200829	−	0.680170i
$835$	−16.5660	−	44.6827i	−0.573289	−	1.54631i
$836$	1.92902	+	44.4926i	0.0667166	+	1.53881i
$837$	23.5909	+	23.5909i	0.815421	+	0.815421i
$838$	16.9003	+	31.0617i	0.583810	+	1.07301i
$839$	−5.55667	+	2.02246i	−0.191838	+	0.0698232i	−0.436152	−	0.899873i	$-0.643659\pi$
$839$	−5.55667	+	2.02246i	−0.191838	+	0.0698232i	0.244315	+	0.969696i	$0.421437\pi$
$840$	2.50011	+	12.8711i	0.0862621	+	0.444096i
$841$	4.14705	−	23.5191i	0.143002	−	0.811003i
$842$	2.61716	+	2.31139i	0.0901932	+	0.0796557i
$843$	−6.25532	+	23.3452i	−0.215445	+	0.804051i
$844$	13.6724	+	44.4424i	0.470624	+	1.52977i
$845$	−17.7515	+	4.87028i	−0.610669	+	0.167543i
$846$	−39.1764	−	19.4899i	−1.34691	−	0.670077i
$847$	−2.75256	−	10.2727i	−0.0945791	−	0.352974i
$848$	−10.1600	+	53.2622i	−0.348896	+	1.82903i
$849$	4.09516	−	11.2514i	0.140545	−	0.386145i
$850$	4.65494	+	3.35301i	0.159663	+	0.115007i
$851$	23.5003	−	4.14373i	0.805579	−	0.142045i
$852$	0.459436	−	0.186559i	0.0157400	−	0.00639141i
$853$	−38.8154	+	3.39591i	−1.32901	+	0.116274i	−0.729439	−	0.684046i	$-0.760219\pi$
$853$	−38.8154	+	3.39591i	−1.32901	+	0.116274i	−0.599574	+	0.800319i	$0.704663\pi$
$854$	−9.02669	+	3.93430i	−0.308887	+	0.134629i
$855$	−52.0736	−	18.2109i	−1.78088	−	0.622799i
$856$	−9.28919	−	3.26209i	−0.317498	−	0.111496i
$857$	2.33408	+	26.6787i	0.0797308	+	0.911327i	0.925740	+	0.378160i	$0.123443\pi$
$857$	2.33408	+	26.6787i	0.0797308	+	0.911327i	−0.846010	+	0.533168i	$0.821001\pi$
$858$	2.47874	−	97.9305i	0.0846228	−	3.34329i
$859$	1.78145	+	10.1031i	0.0607823	+	0.344714i	0.999999	+	0.00138887i	$0.000442090\pi$
$859$	1.78145	+	10.1031i	0.0607823	+	0.344714i	−0.939217	+	0.343325i	$0.888447\pi$
$860$	0.791367	−	1.23944i	0.0269854	−	0.0422646i
$861$	24.3607	+	8.86656i	0.830210	+	0.302172i
$862$	−24.9791	+	3.75548i	−0.850792	+	0.127912i
$863$	27.5601	−	7.38471i	0.938157	−	0.251378i	0.242828	−	0.970069i	$-0.421925\pi$
$863$	27.5601	−	7.38471i	0.938157	−	0.251378i	0.695330	+	0.718691i	$0.255258\pi$
$864$	−40.9823	−	16.7660i	−1.39425	−	0.570390i
$865$	28.2586	+	16.0909i	0.960822	+	0.547108i
$866$	−2.65554	+	23.4899i	−0.0902389	+	0.798219i
$867$	46.4515	+	12.4466i	1.57758	+	0.422710i
$868$	1.84576	−	5.71464i	0.0626492	−	0.193967i
$869$	−60.6833	−	10.7001i	−2.05854	−	0.362976i
$870$	−20.7998	+	3.25427i	−0.705180	+	0.110330i
$871$	−8.63363	−	23.7207i	−0.292540	−	0.803746i
$872$	−37.3604	−	9.55760i	−1.26518	−	0.323661i
$873$	28.0445	−	28.0445i	0.949163	−	0.949163i
$874$	17.8830	−	29.6830i	0.604901	−	1.00404i
$875$	−3.81537	+	6.89059i	−0.128983	+	0.232945i
$876$	4.01688	+	32.2487i	0.135718	+	1.08958i
$877$	46.0281	+	21.4633i	1.55426	+	0.724763i	0.994583	−	0.103948i	$-0.0331477\pi$
$877$	46.0281	+	21.4633i	1.55426	+	0.724763i	0.559676	+	0.828711i	$0.310925\pi$
$878$	0.623404	−	3.07790i	0.0210389	−	0.103874i
$879$	−10.8166	+	61.3441i	−0.364835	+	2.06908i
$880$	−29.6484	+	34.7660i	−0.999448	+	1.17196i
$881$	−22.4755	−	38.9287i	−0.757219	−	1.31154i	−0.944264	−	0.329190i	$-0.893224\pi$
$881$	−22.4755	−	38.9287i	−0.757219	−	1.31154i	0.187045	−	0.982351i	$-0.440109\pi$
$882$	−40.7125	+	32.4423i	−1.37086	+	1.09239i
$883$	17.1969	+	1.50454i	0.578723	+	0.0506317i	0.372760	−	0.927928i	$-0.378412\pi$
$883$	17.1969	+	1.50454i	0.578723	+	0.0506317i	0.205964	+	0.978560i	$0.433967\pi$
$884$	−7.46717	−	0.378249i	−0.251148	−	0.0127219i
$885$	4.25566	−	25.0073i	0.143053	−	0.840612i
$886$	22.0163	−	29.8077i	0.739651	−	1.00141i
$887$	12.0517	−	5.61978i	0.404655	−	0.188694i	−0.209625	−	0.977782i	$-0.567224\pi$
$887$	12.0517	−	5.61978i	0.404655	−	0.188694i	0.614280	+	0.789088i	$0.289447\pi$
$888$	−9.53125	−	34.0219i	−0.319848	−	1.14170i
$889$	−4.09926	+	0.722811i	−0.137485	+	0.0242423i
$890$	−6.56633	−	3.21792i	−0.220104	−	0.107865i
$891$	−19.8822	+	23.6946i	−0.666077	+	0.793800i
$892$	1.02597	+	27.9776i	0.0343521	+	0.936760i
$893$	−20.7151	−	11.7762i	−0.693205	−	0.394077i
$894$	38.6898	−	16.8630i	1.29398	−	0.563984i
$895$	46.1155	−	21.8402i	1.54147	−	0.730037i
$896$	0.673951	+	7.94179i	0.0225151	+	0.265317i
$897$	−43.7222	+	62.4418i	−1.45984	+	2.08487i
$898$	−33.4536	−	20.4602i	−1.11636	−	0.682766i
$899$	9.06098	+	3.29793i	0.302201	+	0.109992i
$900$	−26.3835	−	50.0737i	−0.879449	−	1.66912i
$901$	5.49891	−	9.52439i	0.183195	−	0.317303i
$902$	28.7401	+	85.6463i	0.956941	+	2.85171i
$903$	−0.679099	−	0.0594135i	−0.0225990	−	0.00197716i
$904$	6.30413	−	5.41289i	0.209672	−	0.180030i
$905$	−25.8818	+	2.42017i	−0.860340	+	0.0804493i
$906$	34.1549	−	2.11897i	1.13472	−	0.0703982i
$907$	13.5536	+	19.3565i	0.450040	+	0.642723i	0.978503	−	0.206233i	$-0.0661205\pi$
$907$	13.5536	+	19.3565i	0.450040	+	0.642723i	−0.528463	+	0.848956i	$0.677232\pi$
$908$	7.33718	+	34.2244i	0.243493	+	1.13578i
$909$	8.71565	+	23.9460i	0.289080	+	0.794240i
$910$	−0.696797	−	10.2415i	−0.0230986	−	0.339503i
$911$			2.67570i			0.0886498i	0.999017	+	0.0443249i	$0.0141137\pi$
$911$			2.67570i			0.0886498i	−0.999017	+	0.0443249i	$0.985886\pi$
$912$	−46.3426	−	22.0222i	−1.53456	−	0.729228i
$913$	9.34965	−	9.34965i	0.309428	−	0.309428i
$914$	−8.57594	+	29.0451i	−0.283667	+	0.960727i
$915$	49.5697	−	42.1008i	1.63872	−	1.39181i
$916$	−34.1361	−	22.0835i	−1.12789	−	0.729660i
$917$	1.99047	−	1.39374i	0.0657310	−	0.0460253i
$918$	6.73159	+	5.94513i	0.222176	+	0.196218i
$919$	10.5688	+	18.3057i	0.348633	+	0.603850i	0.986007	−	0.166705i	$-0.0533127\pi$
$919$	10.5688	+	18.3057i	0.348633	+	0.603850i	−0.637374	+	0.770555i	$0.719979\pi$
$920$	34.1780	−	9.79545i	1.12681	−	0.322946i
$921$	−54.8306	+	46.0083i	−1.80673	+	1.51602i
$922$	51.3373	−	17.2271i	1.69070	−	0.567346i
$923$	−0.374990	+	0.100478i	−0.0123429	+	0.00330728i
$924$	20.6465	+	4.72861i	0.679219	+	0.155560i
$925$	8.73942	−	19.3415i	0.287350	−	0.635944i
$926$	44.4001	−	10.7006i	1.45908	−	0.351643i
$927$	21.5555	+	15.0933i	0.707975	+	0.495730i
$928$	−12.7829	+	0.614098i	−0.419619	+	0.0201588i
$929$	22.8621	−	27.2459i	0.750080	−	0.893910i	−0.247098	−	0.968991i	$-0.579477\pi$
$929$	22.8621	−	27.2459i	0.750080	−	0.893910i	0.997178	+	0.0750801i	$0.0239213\pi$
$930$	−0.766837	+	39.6562i	−0.0251456	+	1.30038i
$931$	−23.1131	+	16.4149i	−0.757501	+	0.537978i
$932$	37.7418	−	1.38404i	1.23627	−	0.0453356i
$933$	72.4940	−	6.34241i	2.37335	−	0.207641i
$934$	37.6389	−	35.7806i	1.23158	−	1.17078i
$935$	7.99804	−	4.68157i	0.261564	−	0.153104i
$936$	64.2969	+	36.1552i	2.10161	+	1.18177i
$937$	−13.3108	−	28.5451i	−0.434844	−	0.932526i	−0.994592	−	0.103863i	$-0.966880\pi$
$937$	−13.3108	−	28.5451i	−0.434844	−	0.932526i	0.559747	−	0.828663i	$-0.310898\pi$
$938$	5.39733	−	0.811460i	0.176229	−	0.0264951i
$939$	22.1119	−	38.2989i	0.721593	−	1.24984i
$940$	−7.32801	−	23.3234i	−0.239013	−	0.760725i
$941$	9.94008	−	8.34072i	0.324037	−	0.271900i	−0.466228	−	0.884665i	$-0.654387\pi$
$941$	9.94008	−	8.34072i	0.324037	−	0.271900i	0.790265	+	0.612765i	$0.209943\pi$
$942$	19.1553	+	24.0383i	0.624112	+	0.783210i
$943$	18.1941	−	67.9011i	0.592480	−	2.21117i
$944$	4.19848	−	14.8374i	0.136649	−	0.482918i
$945$	−7.01206	+	10.1426i	−0.228102	+	0.329939i
$946$	−1.31289	−	1.97979i	−0.0426856	−	0.0643686i
$947$	22.5163	−	48.2864i	0.731682	−	1.56910i	−0.0878957	−	0.996130i	$-0.528014\pi$
$947$	22.5163	−	48.2864i	0.731682	−	1.56910i	0.819578	−	0.572968i	$-0.194208\pi$
$948$	43.6098	−	56.0196i	1.41638	−	1.81943i
$949$		−	25.4428i		−	0.825908i
$950$	−12.8388	−	28.0208i	−0.416546	−	0.909115i
$951$		−	40.7159i		−	1.32030i
$952$	0.400659	−	1.56616i	0.0129854	−	0.0507597i
$953$	−14.6314	+	31.3771i	−0.473956	+	1.01640i	0.513438	+	0.858126i	$0.328371\pi$
$953$	−14.6314	+	31.3771i	−0.473956	+	1.01640i	−0.987395	+	0.158276i	$0.949406\pi$
$954$	−90.4275	+	59.9664i	−2.92770	+	1.94148i
$955$	7.29552	−	10.5526i	0.236078	−	0.341475i
$956$	−6.70489	−	13.1024i	−0.216852	−	0.423762i
$957$	−8.80231	+	32.8506i	−0.284538	+	1.06191i
$958$	−14.1357	+	11.2642i	−0.456702	+	0.363930i
$959$	2.79964	−	2.34917i	0.0904050	−	0.0758588i
$960$	−19.4152	−	48.9308i	−0.626622	−	1.57923i
$961$	−6.41678	+	11.1142i	−0.206993	+	0.358522i
$962$	4.11253	+	27.3540i	0.132593	+	0.881928i
$963$	−8.32612	−	17.8554i	−0.268306	−	0.575383i
$964$	35.5514	−	26.8875i	1.14503	−	0.865988i
$965$	−21.1054	+	12.3538i	−0.679408	+	0.397684i
$966$	−11.3557	−	11.9455i	−0.365363	−	0.384339i
$967$	−35.5103	+	3.10675i	−1.14193	+	0.0999063i	−0.642387	−	0.766380i	$-0.722056\pi$
$967$	−35.5103	+	3.10675i	−1.14193	+	0.0999063i	−0.499547	+	0.866287i	$0.666500\pi$
$968$	18.4832	+	38.4908i	0.594074	+	1.23714i
$969$	7.40771	+	7.30949i	0.237970	+	0.234815i
$970$	22.1550	+	0.428415i	0.711355	+	0.0137556i
$971$	2.10197	−	2.50504i	0.0674556	−	0.0803904i	−0.731261	−	0.682097i	$-0.761068\pi$
$971$	2.10197	−	2.50504i	0.0674556	−	0.0803904i	0.798717	+	0.601707i	$0.205512\pi$
$972$	4.26219	+	10.4964i	0.136710	+	0.336673i
$973$	−2.83998	−	1.98858i	−0.0910457	−	0.0637509i
$974$	−2.56075	−	10.6254i	−0.0820518	−	0.340459i
$975$	23.9478	+	63.4287i	0.766942	+	2.03134i
$976$	32.6976	−	22.2215i	1.04662	−	0.711293i
$977$	−21.5677	+	5.77906i	−0.690013	+	0.184888i	−0.586753	−	0.809766i	$-0.699594\pi$
$977$	−21.5677	+	5.77906i	−0.690013	+	0.184888i	−0.103260	+	0.994654i	$0.532927\pi$
$978$	10.8528	+	32.3415i	0.347033	+	1.03417i
$979$	−9.04909	+	7.59308i	−0.289210	+	0.242676i
$980$	−28.8328	−	3.82546i	−0.921029	−	0.122200i
$981$	−38.5844	−	66.8302i	−1.23191	−	2.13372i
$982$	7.80754	−	8.84037i	0.249148	−	0.282108i
$983$	−11.8968	+	8.33023i	−0.379449	+	0.265693i	−0.747705	−	0.664031i	$-0.768844\pi$
$983$	−11.8968	+	8.33023i	−0.379449	+	0.265693i	0.368255	+	0.929725i	$0.379955\pi$
$984$	−102.700	−	16.9093i	−3.27394	−	0.539048i
$985$	−12.7257	+	10.8083i	−0.405474	+	0.344380i
$986$	2.48946	+	0.735045i	0.0792805	+	0.0234086i
$987$	−8.01370	+	8.01370i	−0.255079	+	0.255079i
$988$	33.8725	+	21.5937i	1.07763	+	0.686987i
$989$			1.84850i			0.0587788i
$990$	−91.2213	+	6.20637i	−2.89920	+	0.197251i
$991$	3.80088	+	10.4428i	0.120739	+	0.331728i	0.985308	−	0.170786i	$-0.0546307\pi$
$991$	3.80088	+	10.4428i	0.120739	+	0.331728i	−0.864569	+	0.502514i	$0.832409\pi$
$992$	−3.04257	+	23.9180i	−0.0966018	+	0.759396i
$993$	38.8517	+	55.4860i	1.23292	+	1.76080i
$994$	−0.00519761	−	0.0837784i	−0.000164858	−	0.00265729i
$995$	−12.3979	+	1.15931i	−0.393039	+	0.0367526i
$996$	4.47939	+	14.5603i	0.141935	+	0.461362i
$997$	−1.28175	−	0.112139i	−0.0405935	−	0.00355147i	0.0668409	−	0.997764i	$-0.478708\pi$
$997$	−1.28175	−	0.112139i	−0.0405935	−	0.00355147i	−0.107434	+	0.994212i	$0.534264\pi$
$998$	−0.115806	+	0.0388606i	−0.00366576	+	0.00123011i
$999$	16.6134	−	28.7752i	0.525624	−	0.910408i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bj.a.187.21	yes	672
4.3	odd	2	inner	380.2.bj.a.187.34	yes	672
5.3	odd	4	inner	380.2.bj.a.263.9	yes	672
19.6	even	9	inner	380.2.bj.a.367.6	yes	672
20.3	even	4	inner	380.2.bj.a.263.6	yes	672
76.63	odd	18	inner	380.2.bj.a.367.9	yes	672
95.63	odd	36	inner	380.2.bj.a.63.34	yes	672
380.63	even	36	inner	380.2.bj.a.63.21	✓	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bj.a.63.21	✓	672	380.63	even	36	inner
380.2.bj.a.63.34	yes	672	95.63	odd	36	inner
380.2.bj.a.187.21	yes	672	1.1	even	1	trivial
380.2.bj.a.187.34	yes	672	4.3	odd	2	inner
380.2.bj.a.263.6	yes	672	20.3	even	4	inner
380.2.bj.a.263.9	yes	672	5.3	odd	4	inner
380.2.bj.a.367.6	yes	672	19.6	even	9	inner
380.2.bj.a.367.9	yes	672	76.63	odd	18	inner

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bj (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.675890 - 1.24224i) q^{2} +(2.66706 + 1.24367i) q^{3} +(-1.08634 + 1.67924i) q^{4} +(-1.83931 - 1.27160i) q^{5} +(-0.257697 - 4.15372i) q^{6} +(-0.680480 - 0.182334i) q^{7} +(2.82028 + 0.214521i) q^{8} +(3.63812 + 4.33575i) q^{9} +O(q^{10})\)	\(q+(-0.675890 - 1.24224i) q^{2} +(2.66706 + 1.24367i) q^{3} +(-1.08634 + 1.67924i) q^{4} +(-1.83931 - 1.27160i) q^{5} +(-0.257697 - 4.15372i) q^{6} +(-0.680480 - 0.182334i) q^{7} +(2.82028 + 0.214521i) q^{8} +(3.63812 + 4.33575i) q^{9} +(-0.336464 + 3.14433i) q^{10} +(4.42405 + 2.55422i) q^{11} +(-4.98577 + 3.12759i) q^{12} +(4.17611 - 1.94735i) q^{13} +(0.233426 + 0.968561i) q^{14} +(-3.32409 - 5.67891i) q^{15} +(-1.63971 - 3.64847i) q^{16} +(0.0707102 + 0.808222i) q^{17} +(2.92709 - 7.44993i) q^{18} +(1.81574 - 3.96271i) q^{19} +(4.13344 - 1.70725i) q^{20} +(-1.58812 - 1.33259i) q^{21} +(0.182801 - 7.22212i) q^{22} +(-3.22440 + 4.60493i) q^{23} +(7.25506 + 4.07964i) q^{24} +(1.76609 + 4.67771i) q^{25} +(-5.24168 - 3.87155i) q^{26} +(2.02591 + 7.56081i) q^{27} +(1.04542 - 0.944614i) q^{28} +(1.45419 + 1.73304i) q^{29} +(-4.80787 + 7.96765i) q^{30} +(3.69118 - 2.13111i) q^{31} +(-3.42403 + 4.50289i) q^{32} +(8.62258 + 12.3143i) q^{33} +(0.956217 - 0.634109i) q^{34} +(1.01976 + 1.20066i) q^{35} +(-11.2330 + 1.39918i) q^{36} +(-3.00157 - 3.00157i) q^{37} +(-6.14990 + 0.422761i) q^{38} +13.5598 q^{39} +(-4.91457 - 3.98083i) q^{40} +(-11.7506 + 4.27688i) q^{41} +(-0.582008 + 2.87351i) q^{42} +(0.269355 - 0.188604i) q^{43} +(-9.09520 + 4.65428i) q^{44} +(-1.17830 - 12.6010i) q^{45} +(7.89979 + 0.893073i) q^{46} +(0.476448 - 5.44582i) q^{47} +(0.164282 - 11.7699i) q^{48} +(-5.63237 - 3.25185i) q^{49} +(4.61717 - 5.35553i) q^{50} +(-0.816573 + 2.24351i) q^{51} +(-1.26661 + 9.12819i) q^{52} +(-11.1041 - 7.77520i) q^{53} +(8.02308 - 7.62696i) q^{54} +(-4.88923 - 10.3236i) q^{55} +(-1.88003 - 0.660210i) q^{56} +(9.77100 - 8.31060i) q^{57} +(1.16998 - 2.97781i) q^{58} +(2.95310 + 2.47795i) q^{59} +(13.1474 + 0.587296i) q^{60} +(1.71625 + 9.73331i) q^{61} +(-5.14219 - 3.14496i) q^{62} +(-1.68512 - 3.61374i) q^{63} +(7.90796 + 1.21002i) q^{64} +(-10.1574 - 1.72855i) q^{65} +(9.46948 - 19.0345i) q^{66} +(0.477465 - 5.45745i) q^{67} +(-1.43402 - 0.759267i) q^{68} +(-14.3267 + 8.27151i) q^{69} +(0.802275 - 2.07830i) q^{70} +(-0.0829719 - 0.0146302i) q^{71} +(9.33042 + 13.0085i) q^{72} +(2.33355 - 5.00431i) q^{73} +(-1.69995 + 5.75741i) q^{74} +(-1.10726 + 14.6721i) q^{75} +(4.68183 + 7.35394i) q^{76} +(-2.54475 - 2.54475i) q^{77} +(-9.16493 - 16.8446i) q^{78} +(-11.3348 + 4.12554i) q^{79} +(-1.62345 + 8.79570i) q^{80} +(-1.05142 + 5.96291i) q^{81} +(13.2551 + 11.7064i) q^{82} +(0.669912 - 2.50014i) q^{83} +(3.96298 - 1.21918i) q^{84} +(0.897674 - 1.57648i) q^{85} +(-0.416348 - 0.207129i) q^{86} +(1.72309 + 6.43065i) q^{87} +(11.9291 + 8.15268i) q^{88} +(-0.790885 + 2.17294i) q^{89} +(-14.8571 + 9.98063i) q^{90} +(-3.19683 + 0.563687i) q^{91} +(-4.22998 - 10.4171i) q^{92} +(12.4950 - 1.09317i) q^{93} +(-7.08707 + 3.08892i) q^{94} +(-8.37867 + 4.97974i) q^{95} +(-14.7322 + 7.75112i) q^{96} +(-0.610730 - 6.98067i) q^{97} +(-0.232729 + 9.19468i) q^{98} +(5.02076 + 28.4741i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Introduction

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