LMFDB - Embedded newform 189.2.bd.a.185.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(47,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 15]))

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

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

chi := DirichletCharacter("189.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.bd (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			185.5
Character	$\chi$	$=$	189.185
Dual form			189.2.bd.a.47.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.63190 + 0.287749i) q^{2} +(1.35485 - 1.07906i) q^{3} +(0.700923 - 0.255115i) q^{4} +(-3.60525 + 1.31220i) q^{5} +(-1.90049 + 2.15078i) q^{6} +(2.03118 - 1.69538i) q^{7} +(1.79971 - 1.03907i) q^{8} +(0.671243 - 2.92394i) q^{9} +O(q^{10})$	\(q+(-1.63190 + 0.287749i) q^{2} +(1.35485 - 1.07906i) q^{3} +(0.700923 - 0.255115i) q^{4} +(-3.60525 + 1.31220i) q^{5} +(-1.90049 + 2.15078i) q^{6} +(2.03118 - 1.69538i) q^{7} +(1.79971 - 1.03907i) q^{8} +(0.671243 - 2.92394i) q^{9} +(5.50583 - 3.17879i) q^{10} +(0.982995 - 2.70076i) q^{11} +(0.674361 - 1.10198i) q^{12} +(-1.44158 - 3.96072i) q^{13} +(-2.82685 + 3.35116i) q^{14} +(-3.46863 + 5.66814i) q^{15} +(-3.78076 + 3.17244i) q^{16} +(-1.59416 - 2.76117i) q^{17} +(-0.254044 + 4.96474i) q^{18} +(-1.96303 - 1.13336i) q^{19} +(-2.19224 + 1.83951i) q^{20} +(0.922531 - 4.48876i) q^{21} +(-0.827014 + 4.69023i) q^{22} +(2.25312 + 0.397286i) q^{23} +(1.31713 - 3.34978i) q^{24} +(7.44573 - 6.24771i) q^{25} +(3.49221 + 6.04869i) q^{26} +(-2.24568 - 4.68582i) q^{27} +(0.991186 - 1.70651i) q^{28} +(0.356349 - 0.979061i) q^{29} +(4.02946 - 10.2479i) q^{30} +(2.96755 + 8.15327i) q^{31} +(2.58538 - 3.08114i) q^{32} +(-1.58248 - 4.71984i) q^{33} +(3.39605 + 4.04725i) q^{34} +(-5.09824 + 8.77758i) q^{35} +(-0.275452 - 2.22070i) q^{36} +0.0244697 q^{37} +(3.52960 + 1.28467i) q^{38} +(-6.22700 - 3.81062i) q^{39} +(-5.12495 + 6.10768i) q^{40} +(-2.99981 + 1.09184i) q^{41} +(-0.213847 + 7.59067i) q^{42} +(-0.110557 - 0.627001i) q^{43} -2.14380i q^{44} +(1.41681 + 11.4223i) q^{45} -3.79119 q^{46} +(10.0976 + 3.67521i) q^{47} +(-1.69911 + 8.37787i) q^{48} +(1.25140 - 6.88723i) q^{49} +(-10.3529 + 12.3382i) q^{50} +(-5.13934 - 2.02078i) q^{51} +(-2.02088 - 2.40839i) q^{52} +(1.91685 + 1.10670i) q^{53} +(5.01308 + 7.00061i) q^{54} +11.0268i q^{55} +(1.89394 - 5.16172i) q^{56} +(-3.88258 + 0.582707i) q^{57} +(-0.299804 + 1.70027i) q^{58} +(-8.38964 - 7.03975i) q^{59} +(-0.985213 + 4.85782i) q^{60} +(-2.60670 + 7.16186i) q^{61} +(-7.18884 - 12.4514i) q^{62} +(-3.59376 - 7.07707i) q^{63} +(1.60294 - 2.77637i) q^{64} +(10.3945 + 12.3877i) q^{65} +(3.94057 + 7.24696i) q^{66} +(-1.88769 + 10.7056i) q^{67} +(-1.82180 - 1.52867i) q^{68} +(3.48134 - 1.89300i) q^{69} +(5.79410 - 15.7912i) q^{70} +(3.88604 + 2.24361i) q^{71} +(-1.83012 - 5.95972i) q^{72} +2.22546i q^{73} +(-0.0399322 + 0.00704112i) q^{74} +(3.34618 - 16.4991i) q^{75} +(-1.66507 - 0.293597i) q^{76} +(-2.58216 - 7.15227i) q^{77} +(11.2584 + 4.42676i) q^{78} +(-2.19643 - 12.4566i) q^{79} +(9.46771 - 16.3986i) q^{80} +(-8.09886 - 3.92535i) q^{81} +(4.58122 - 2.64497i) q^{82} +(4.16888 + 1.51735i) q^{83} +(-0.498526 - 3.38162i) q^{84} +(9.37059 + 7.86286i) q^{85} +(0.360837 + 0.991392i) q^{86} +(-0.573669 - 1.71100i) q^{87} +(-1.03715 - 5.88198i) q^{88} +(2.36580 - 4.09769i) q^{89} +(-5.59885 - 18.2325i) q^{90} +(-9.64302 - 5.60091i) q^{91} +(1.68062 - 0.296338i) q^{92} +(12.8185 + 7.84430i) q^{93} +(-17.5358 - 3.09203i) q^{94} +(8.56442 + 1.51014i) q^{95} +(0.178064 - 6.96428i) q^{96} +(-13.0174 + 2.29533i) q^{97} +(-0.0603728 + 11.5994i) q^{98} +(-7.23702 - 4.68708i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.63190	+	0.287749i	−1.15393	+	0.203469i	−0.717691	−	0.696362i	$-0.754801\pi$
$2$	−1.63190	+	0.287749i	−1.15393	+	0.203469i	−0.436239	+	0.899831i	$0.643690\pi$
$3$	1.35485	−	1.07906i	0.782224	−	0.622998i
$3$	1.35485	−	1.07906i	0.782224	−	0.622998i
$4$	0.700923	−	0.255115i	0.350461	−	0.127558i
$5$	−3.60525	+	1.31220i	−1.61232	+	0.586835i	−0.981896	−	0.189418i	$-0.939340\pi$
$5$	−3.60525	+	1.31220i	−1.61232	+	0.586835i	−0.630420	+	0.776254i	$0.717118\pi$
$6$	−1.90049	+	2.15078i	−0.775870	+	0.878054i
$7$	2.03118	−	1.69538i	0.767715	−	0.640792i
$7$	2.03118	−	1.69538i	0.767715	−	0.640792i
$8$	1.79971	−	1.03907i	0.636295	−	0.367365i
$9$	0.671243	−	2.92394i	0.223748	−	0.974647i
$10$	5.50583	−	3.17879i	1.74110	−	1.00522i
$11$	0.982995	−	2.70076i	0.296384	−	0.814309i	−0.698713	−	0.715402i	$-0.746243\pi$
$11$	0.982995	−	2.70076i	0.296384	−	0.814309i	0.995097	−	0.0989062i	$-0.0315344\pi$
$12$	0.674361	−	1.10198i	0.194671	−	0.318115i
$13$	−1.44158	−	3.96072i	−0.399823	−	1.09851i	−0.962371	−	0.271740i	$-0.912401\pi$
$13$	−1.44158	−	3.96072i	−0.399823	−	1.09851i	0.562547	−	0.826765i	$-0.309821\pi$
$14$	−2.82685	+	3.35116i	−0.755507	+	0.895635i
$15$	−3.46863	+	5.66814i	−0.895595	+	1.46351i
$16$	−3.78076	+	3.17244i	−0.945191	+	0.793109i
$17$	−1.59416	−	2.76117i	−0.386642	−	0.669683i	0.605354	−	0.795957i	$-0.293032\pi$
$17$	−1.59416	−	2.76117i	−0.386642	−	0.669683i	−0.991995	+	0.126273i	$0.959698\pi$
$18$	−0.254044	+	4.96474i	−0.0598788	+	1.17020i
$19$	−1.96303	−	1.13336i	−0.450351	−	0.260010i	0.257628	−	0.966244i	$-0.417059\pi$
$19$	−1.96303	−	1.13336i	−0.450351	−	0.260010i	−0.707978	+	0.706234i	$0.750393\pi$
$20$	−2.19224	+	1.83951i	−0.490200	+	0.411326i
$21$	0.922531	−	4.48876i	0.201313	−	0.979527i
$22$	−0.827014	+	4.69023i	−0.176320	+	0.999960i
$23$	2.25312	+	0.397286i	0.469808	+	0.0828398i	0.403540	−	0.914962i	$-0.367780\pi$
$23$	2.25312	+	0.397286i	0.469808	+	0.0828398i	0.0662680	+	0.997802i	$0.478891\pi$
$24$	1.31713	−	3.34978i	0.268857	−	0.683772i
$25$	7.44573	−	6.24771i	1.48915	−	1.24954i
$26$	3.49221	+	6.04869i	0.684880	+	1.18625i
$27$	−2.24568	−	4.68582i	−0.432182	−	0.901786i
$28$	0.991186	−	1.70651i	0.187317	−	0.322501i
$29$	0.356349	−	0.979061i	0.0661723	−	0.181807i	−0.902199	−	0.431320i	$-0.858048\pi$
$29$	0.356349	−	0.979061i	0.0661723	−	0.181807i	0.968372	+	0.249513i	$0.0802704\pi$
$30$	4.02946	−	10.2479i	0.735676	−	1.87101i
$31$	2.96755	+	8.15327i	0.532988	+	1.46437i	0.855498	+	0.517805i	$0.173251\pi$
$31$	2.96755	+	8.15327i	0.532988	+	1.46437i	−0.322511	+	0.946566i	$0.604527\pi$
$32$	2.58538	−	3.08114i	0.457035	−	0.544673i
$33$	−1.58248	−	4.71984i	−0.275474	−	0.821618i
$34$	3.39605	+	4.04725i	0.582417	+	0.694098i
$35$	−5.09824	+	8.77758i	−0.861760	+	1.48368i
$36$	−0.275452	−	2.22070i	−0.0459086	−	0.370117i
$37$	0.0244697			0.00402279			0.00201140	−	0.999998i	$-0.499360\pi$
$37$	0.0244697			0.00402279			0.00201140	+	0.999998i	$0.499360\pi$
$38$	3.52960	+	1.28467i	0.572577	+	0.208401i
$39$	−6.22700	−	3.81062i	−0.997118	−	0.610188i
$40$	−5.12495	+	6.10768i	−0.810326	+	0.965709i
$41$	−2.99981	+	1.09184i	−0.468492	+	0.170517i	−0.565469	−	0.824770i	$-0.691305\pi$
$41$	−2.99981	+	1.09184i	−0.468492	+	0.170517i	0.0969772	+	0.995287i	$0.469083\pi$
$42$	−0.213847	+	7.59067i	−0.0329974	+	1.17127i
$43$	−0.110557	−	0.627001i	−0.0168598	−	0.0956167i	0.975217	−	0.221252i	$-0.0710143\pi$
$43$	−0.110557	−	0.627001i	−0.0168598	−	0.0956167i	−0.992077	+	0.125635i	$0.959903\pi$
$44$		−	2.14380i		−	0.323190i
$45$	1.41681	+	11.4223i	0.211205	+	1.70274i
$46$	−3.79119			−0.558980
$47$	10.0976	+	3.67521i	1.47288	+	0.536084i	0.948881	−	0.315635i	$-0.102217\pi$
$47$	10.0976	+	3.67521i	1.47288	+	0.536084i	0.523999	+	0.851719i	$0.324440\pi$
$48$	−1.69911	+	8.37787i	−0.245245	+	1.20924i
$49$	1.25140	−	6.88723i	0.178772	−	0.983891i
$50$	−10.3529	+	12.3382i	−1.46413	+	1.74488i
$51$	−5.13934	−	2.02078i	−0.719651	−	0.282965i
$52$	−2.02088	−	2.40839i	−0.280245	−	0.333983i
$53$	1.91685	+	1.10670i	0.263300	+	0.152016i	0.625839	−	0.779952i	$-0.284757\pi$
$53$	1.91685	+	1.10670i	0.263300	+	0.152016i	−0.362539	+	0.931969i	$0.618090\pi$
$54$	5.01308	+	7.00061i	0.682193	+	0.952662i
$55$			11.0268i			1.48685i
$56$	1.89394	−	5.16172i	0.253088	−	0.689764i
$57$	−3.88258	+	0.582707i	−0.514261	+	0.0771814i
$58$	−0.299804	+	1.70027i	−0.0393661	+	0.223257i
$59$	−8.38964	−	7.03975i	−1.09224	−	0.916497i	−0.0953596	−	0.995443i	$-0.530400\pi$
$59$	−8.38964	−	7.03975i	−1.09224	−	0.916497i	−0.996879	+	0.0789460i	$0.974845\pi$
$60$	−0.985213	+	4.85782i	−0.127190	+	0.627142i
$61$	−2.60670	+	7.16186i	−0.333754	+	0.916982i	0.653372	+	0.757037i	$0.273354\pi$
$61$	−2.60670	+	7.16186i	−0.333754	+	0.916982i	−0.987126	+	0.159945i	$0.948868\pi$
$62$	−7.18884	−	12.4514i	−0.912984	−	1.58133i
$63$	−3.59376	−	7.07707i	−0.452772	−	0.891627i
$64$	1.60294	−	2.77637i	0.200367	−	0.347046i
$65$	10.3945	+	12.3877i	1.28928	+	1.53651i
$66$	3.94057	+	7.24696i	0.485051	+	0.892039i
$67$	−1.88769	+	10.7056i	−0.230618	+	1.30790i	0.621031	+	0.783786i	$0.286714\pi$
$67$	−1.88769	+	10.7056i	−0.230618	+	1.30790i	−0.851649	+	0.524113i	$0.824397\pi$
$68$	−1.82180	−	1.52867i	−0.220926	−	0.185379i
$69$	3.48134	−	1.89300i	0.419104	−	0.227890i
$70$	5.79410	−	15.7912i	0.692527	−	1.88741i
$71$	3.88604	+	2.24361i	0.461188	+	0.266267i	0.712544	−	0.701628i	$-0.247543\pi$
$71$	3.88604	+	2.24361i	0.461188	+	0.266267i	−0.251356	+	0.967895i	$0.580876\pi$
$72$	−1.83012	−	5.95972i	−0.215682	−	0.702360i
$73$			2.22546i			0.260470i	0.991483	+	0.130235i	$0.0415732\pi$
$73$			2.22546i			0.260470i	−0.991483	+	0.130235i	$0.958427\pi$
$74$	−0.0399322	+	0.00704112i	−0.00464202	+	0.000818514i
$75$	3.34618	−	16.4991i	0.386384	−	1.90516i
$76$	−1.66507	−	0.293597i	−0.190997	−	0.0336779i
$77$	−2.58216	−	7.15227i	−0.294264	−	0.815077i
$78$	11.2584	+	4.42676i	1.27476	+	0.501232i
$79$	−2.19643	−	12.4566i	−0.247118	−	1.40147i	−0.815523	−	0.578725i	$-0.803551\pi$
$79$	−2.19643	−	12.4566i	−0.247118	−	1.40147i	0.568405	−	0.822749i	$-0.307561\pi$
$80$	9.46771	−	16.3986i	1.05852	−	1.83342i
$81$	−8.09886	−	3.92535i	−0.899874	−	0.436150i
$82$	4.58122	−	2.64497i	0.505912	−	0.292088i
$83$	4.16888	+	1.51735i	0.457594	+	0.166550i	0.560524	−	0.828138i	$-0.310600\pi$
$83$	4.16888	+	1.51735i	0.457594	+	0.166550i	−0.102931	+	0.994689i	$0.532822\pi$
$84$	−0.498526	−	3.38162i	−0.0543937	−	0.368965i
$85$	9.37059	+	7.86286i	1.01638	+	0.852846i
$86$	0.360837	+	0.991392i	0.0389101	+	0.106905i
$87$	−0.573669	−	1.71100i	−0.0615038	−	0.183439i
$88$	−1.03715	−	5.88198i	−0.110561	−	0.627022i
$89$	2.36580	−	4.09769i	0.250774	−	0.434354i	−0.712965	−	0.701200i	$-0.752648\pi$
$89$	2.36580	−	4.09769i	0.250774	−	0.434354i	0.963739	+	0.266846i	$0.0859814\pi$
$90$	−5.59885	−	18.2325i	−0.590171	−	1.92187i
$91$	−9.64302	−	5.60091i	−1.01086	−	0.587135i
$92$	1.68062	−	0.296338i	0.175216	−	0.0308954i
$93$	12.8185	+	7.84430i	1.32922	+	0.813416i
$94$	−17.5358	−	3.09203i	−1.80868	−	0.318918i
$95$	8.56442	+	1.51014i	0.878691	+	0.154937i
$96$	0.178064	−	6.96428i	0.0181735	−	0.710788i
$97$	−13.0174	+	2.29533i	−1.32172	+	0.233055i	−0.789605	−	0.613616i	$-0.789714\pi$
$97$	−13.0174	+	2.29533i	−1.32172	+	0.233055i	−0.532117	+	0.846671i	$0.678603\pi$
$98$	−0.0603728	+	11.5994i	−0.00609857	+	1.17171i
$99$	−7.23702	−	4.68708i	−0.727348	−	0.471070i
$100$	3.62500	−	6.27868i	0.362500	−	0.627868i
$101$	0.471291	+	2.67282i	0.0468952	+	0.265956i	0.999236	−	0.0390800i	$-0.0124427\pi$
$101$	0.471291	+	2.67282i	0.0468952	+	0.265956i	−0.952341	+	0.305036i	$0.901332\pi$
$102$	8.96838	+	1.81887i	0.888002	+	0.180095i
$103$	3.33939	+	9.17490i	0.329040	+	0.904029i	0.988355	+	0.152163i	$0.0486239\pi$
$103$	3.33939	+	9.17490i	0.329040	+	0.904029i	−0.659316	+	0.751866i	$0.729154\pi$
$104$	−6.70988	−	5.63026i	−0.657958	−	0.552092i
$105$	2.56421	+	17.3936i	0.250241	+	1.69745i
$106$	−3.44657	−	1.25445i	−0.334761	−	0.121843i
$107$	12.2288	−	7.06029i	1.18220	−	0.682544i	0.225678	−	0.974202i	$-0.427540\pi$
$107$	12.2288	−	7.06029i	1.18220	−	0.682544i	0.956523	+	0.291658i	$0.0942070\pi$
$108$	−2.76947	−	2.71149i	−0.266493	−	0.260913i
$109$	2.48897	−	4.31103i	0.238400	−	0.412922i	−0.721855	−	0.692044i	$-0.756710\pi$
$109$	2.48897	−	4.31103i	0.238400	−	0.412922i	0.960255	+	0.279123i	$0.0900436\pi$
$110$	−3.17294	−	17.9947i	−0.302528	−	1.71572i
$111$	0.0331528	−	0.0264044i	0.00314672	−	0.00250619i
$112$	−2.30094	+	12.8536i	−0.217419	+	1.21455i
$113$	7.89136	+	1.39146i	0.742357	+	0.130898i	0.532020	−	0.846732i	$-0.321433\pi$
$113$	7.89136	+	1.39146i	0.742357	+	0.130898i	0.210336	+	0.977629i	$0.432544\pi$
$114$	6.16833	−	2.06813i	0.577717	−	0.193698i
$115$	−8.64438	+	1.52424i	−0.806092	+	0.142136i
$116$		−	0.777156i		−	0.0721571i
$117$	−12.5486	+	1.55650i	−1.16011	+	0.143898i
$118$	15.7168	+	9.07408i	1.44684	+	0.835336i
$119$	−7.91927	−	2.90574i	−0.725958	−	0.266369i
$120$	−0.352972	+	13.8052i	−0.0322218	+	1.26023i
$121$	2.09869	+	1.76101i	0.190790	+	0.160091i
$122$	2.19307	−	12.4375i	0.198551	−	1.12604i
$123$	−2.88613	+	4.71627i	−0.260234	+	0.425252i
$124$	4.16005	+	4.95775i	0.373583	+	0.445219i
$125$	−9.05388	+	15.6818i	−0.809804	+	1.40262i
$126$	7.90109	+	10.5150i	0.703885	+	0.936749i
$127$	−3.39217	−	5.87541i	−0.301006	−	0.521358i	0.675358	−	0.737490i	$-0.263989\pi$
$127$	−3.39217	−	5.87541i	−0.301006	−	0.521358i	−0.976364	+	0.216132i	$0.930656\pi$
$128$	−4.56825	+	12.5512i	−0.403780	+	1.10938i
$129$	−0.826362	−	0.730195i	−0.0727571	−	0.0642900i
$130$	−20.5274	−	17.2246i	−1.80037	−	1.51069i
$131$	3.49094	−	19.7981i	0.305005	−	1.72977i	−0.318478	−	0.947930i	$-0.603172\pi$
$131$	3.49094	−	19.7981i	0.305005	−	1.72977i	0.623482	−	0.781837i	$-0.285717\pi$
$132$	−2.31329	−	2.90453i	−0.201346	−	0.252807i
$133$	−5.90875	+	1.02602i	−0.512353	+	0.0889675i
$134$		−	18.0137i		−	1.55615i
$135$	14.2450	+	13.9468i	1.22601	+	1.20035i
$136$	−5.73808	−	3.31288i	−0.492036	−	0.284077i
$137$	12.0468	+	14.3569i	1.02923	+	1.22659i	0.973629	+	0.228138i	$0.0732636\pi$
$137$	12.0468	+	14.3569i	1.02923	+	1.22659i	0.0556027	+	0.998453i	$0.482292\pi$
$138$	−5.13650	+	4.09094i	−0.437248	+	0.348244i
$139$	8.49230	−	10.1207i	0.720308	−	0.858429i	−0.274353	−	0.961629i	$-0.588464\pi$
$139$	8.49230	−	10.1207i	0.720308	−	0.858429i	0.994661	+	0.103200i	$0.0329081\pi$
$140$	−1.33418	+	7.45304i	−0.112759	+	0.629897i
$141$	17.6465	−	5.91654i	1.48610	−	0.498263i
$142$	−6.98723	−	2.54314i	−0.586355	−	0.213416i
$143$	−12.1140			−1.01302
$144$	6.73821	+	13.1842i	0.561517	+	1.09868i
$145$			3.99736i			0.331963i
$146$	−0.640372	−	3.63173i	−0.0529976	−	0.300564i
$147$	−5.73630	−	10.6815i	−0.473122	−	0.880997i
$148$	0.0171514	−	0.00624259i	0.00140983	−	0.000513138i
$149$	−8.49738	+	10.1268i	−0.696132	+	0.829618i	−0.992083	−	0.125585i	$-0.959919\pi$
$149$	−8.49738	+	10.1268i	−0.696132	+	0.829618i	0.295951	+	0.955203i	$0.404364\pi$
$150$	−0.713040	+	27.8878i	−0.0582195	+	2.27703i
$151$	11.8035	+	4.29612i	0.960556	+	0.349614i	0.774251	−	0.632878i	$-0.218127\pi$
$151$	11.8035	+	4.29612i	0.960556	+	0.349614i	0.186304	+	0.982492i	$0.440349\pi$
$152$	−4.71053			−0.382075
$153$	−9.14358	+	2.80782i	−0.739215	+	0.226999i
$154$	6.27188	+	10.9288i	0.505403	+	0.880668i
$155$	−21.3975	−	25.5006i	−1.71869	−	2.04825i
$156$	−5.33679	−	1.08235i	−0.427285	−	0.0866575i
$157$	11.6576	−	13.8930i	0.930376	−	1.10878i	−0.0634678	−	0.997984i	$-0.520216\pi$
$157$	11.6576	−	13.8930i	0.930376	−	1.10878i	0.993843	−	0.110794i	$-0.0353395\pi$
$158$	7.16872	+	19.6959i	0.570313	+	1.56692i
$159$	3.79125	−	0.568999i	0.300666	−	0.0451246i
$160$	−5.27787	+	14.5008i	−0.417252	+	1.14639i
$161$	5.25004	−	3.01292i	0.413761	−	0.237452i
$162$	14.3461	+	4.07536i	1.12713	+	0.320190i
$163$	2.93944	+	5.09126i	0.230235	+	0.398779i	0.957877	−	0.287178i	$-0.0927172\pi$
$163$	2.93944	+	5.09126i	0.230235	+	0.398779i	−0.727642	+	0.685957i	$0.759384\pi$
$164$	−1.82409	+	1.53059i	−0.142438	+	0.119519i
$165$	11.8986	+	14.9397i	0.926305	+	1.16305i
$166$	−7.23982	−	1.27657i	−0.561919	−	0.0990814i
$167$	−1.43991	+	8.16616i	−0.111424	+	0.631916i	0.877035	+	0.480427i	$0.159518\pi$
$167$	−1.43991	+	8.16616i	−0.111424	+	0.631916i	−0.988459	+	0.151490i	$0.951593\pi$
$168$	−3.00382	−	9.03705i	−0.231750	−	0.697223i
$169$	−3.65055	+	3.06317i	−0.280811	+	0.235629i
$170$	−17.5544	−	10.1350i	−1.34636	−	0.777322i
$171$	−4.63154	+	4.97904i	−0.354183	+	0.380756i
$172$	−0.237449	−	0.411274i	−0.0181053	−	0.0313594i
$173$	−14.9572	+	12.5506i	−1.13718	+	0.954205i	−0.999343	−	0.0362507i	$-0.988459\pi$
$173$	−14.9572	+	12.5506i	−1.13718	+	0.954205i	−0.137834	+	0.990455i	$0.544014\pi$
$174$	1.42851	+	2.62712i	0.108295	+	0.199162i
$175$	4.53142	−	25.3135i	0.342543	−	1.91352i
$176$	4.85151	+	13.3294i	0.365696	+	1.00474i
$177$	−18.9631	−	0.484850i	−1.42535	−	0.0364435i
$178$	−2.68165	+	7.36778i	−0.200998	+	0.552239i
$179$	2.56681	−	1.48195i	0.191853	−	0.110766i	−0.400997	−	0.916079i	$-0.631336\pi$
$179$	2.56681	−	1.48195i	0.191853	−	0.110766i	0.592850	+	0.805313i	$0.298003\pi$
$180$	3.90708	+	7.64473i	0.291217	+	0.569805i
$181$	22.0624	−	12.7377i	1.63988	−	0.946787i	0.659011	−	0.752134i	$-0.270975\pi$
$181$	22.0624	−	12.7377i	1.63988	−	0.946787i	0.980872	−	0.194653i	$-0.0623581\pi$
$182$	17.3481	+	6.36538i	1.28593	+	0.471833i
$183$	4.19640	+	12.5160i	0.310207	+	0.925213i
$184$	4.46778	−	1.62614i	0.329369	−	0.119880i
$185$	−0.0882194	+	0.0321092i	−0.00648602	+	0.00236072i
$186$	−23.1757	−	9.11263i	−1.69933	−	0.668171i
$187$	−9.02431	+	1.59123i	−0.659923	+	0.116362i
$188$	8.01521			0.584569
$189$	−12.5056	−	5.71047i	−0.909650	−	0.415376i
$190$	−14.4108			−1.04547
$191$	−22.3269	+	3.93683i	−1.61552	+	0.284859i	−0.907094	−	0.420929i	$-0.861704\pi$
$191$	−22.3269	+	3.93683i	−1.61552	+	0.284859i	−0.708423	+	0.705788i	$0.750593\pi$
$192$	−0.824137	−	5.49124i	−0.0594770	−	0.396296i
$193$	14.0257	−	5.10496i	1.00960	−	0.367463i	0.216318	−	0.976323i	$-0.430595\pi$
$193$	14.0257	−	5.10496i	1.00960	−	0.367463i	0.793277	+	0.608860i	$0.208373\pi$
$194$	20.5827	−	7.49150i	1.47775	−	0.537859i
$195$	27.4502	+	5.56716i	1.96575	+	0.398673i
$196$	−0.879902	−	5.14667i	−0.0628501	−	0.367619i
$197$	16.5142	−	9.53447i	1.17659	−	0.679303i	0.221364	−	0.975191i	$-0.428949\pi$
$197$	16.5142	−	9.53447i	1.17659	−	0.679303i	0.955222	+	0.295889i	$0.0956158\pi$
$198$	13.1588	+	5.56642i	0.935157	+	0.395588i
$199$	−5.02974	+	2.90392i	−0.356549	+	0.205854i	−0.667566	−	0.744551i	$-0.732664\pi$
$199$	−5.02974	+	2.90392i	−0.356549	+	0.205854i	0.311017	+	0.950404i	$0.399330\pi$
$200$	6.90840	−	18.9807i	0.488498	−	1.34214i
$201$	8.99450	+	16.5414i	0.634423	+	1.16674i
$202$	−1.53820	−	4.22617i	−0.108227	−	0.297352i
$203$	−0.936066	−	2.59280i	−0.0656990	−	0.181979i
$204$	−4.11781	−	0.105285i	−0.288304	−	0.00737140i
$205$	9.38235	−	7.87273i	0.655292	−	0.549855i
$206$	−8.08962	−	14.0116i	−0.563631	−	0.976237i
$207$	2.67403	−	6.32131i	0.185858	−	0.439362i
$208$	18.0154	+	10.4012i	1.24914	+	0.721194i
$209$	−4.99057	+	4.18759i	−0.345205	+	0.289662i
$210$	−9.18954	−	27.6469i	−0.634138	−	1.90782i
$211$	0.180568	−	1.02405i	0.0124308	−	0.0704985i	−0.977961	−	0.208786i	$-0.933049\pi$
$211$	0.180568	−	1.02405i	0.0124308	−	0.0704985i	0.990392	+	0.138288i	$0.0441599\pi$
$212$	1.62590	+	0.286690i	0.111667	+	0.0196900i
$213$	7.68600	−	1.15353i	0.526636	−	0.0790387i
$214$	−17.9246	+	15.0405i	−1.22530	+	1.02815i
$215$	1.22134	+	2.11542i	0.0832946	+	0.144271i
$216$	−8.91046	−	6.09972i	−0.606280	−	0.415034i
$217$	19.8505	+	11.5297i	1.34754	+	0.782685i
$218$	−2.82127	+	7.75138i	−0.191081	+	0.524990i
$219$	2.40141	+	3.01516i	0.162272	+	0.203746i
$220$	2.81310	+	7.72893i	0.189659	+	0.521084i
$221$	−8.63811	+	10.2945i	−0.581062	+	0.692483i
$222$	−0.0465043	+	0.0526290i	−0.00312117	+	0.00353223i
$223$	4.95104	+	5.90042i	0.331546	+	0.395122i	0.905904	−	0.423483i	$-0.139193\pi$
$223$	4.95104	+	5.90042i	0.331546	+	0.395122i	−0.574358	+	0.818604i	$0.694748\pi$
$224$	0.0276935	−	10.6415i	0.00185035	−	0.711018i
$225$	−13.2700	−	25.9646i	−0.884669	−	1.73097i
$226$	−13.2783			−0.883261
$227$	3.04716	+	1.10908i	0.202247	+	0.0736119i	0.441158	−	0.897430i	$-0.354568\pi$
$227$	3.04716	+	1.10908i	0.202247	+	0.0736119i	−0.238910	+	0.971042i	$0.576790\pi$
$228$	−2.57273	+	1.39894i	−0.170383	+	0.0926469i
$229$	−14.0510	+	16.7453i	−0.928514	+	1.10656i	0.0655597	+	0.997849i	$0.479117\pi$
$229$	−14.0510	+	16.7453i	−0.928514	+	1.10656i	−0.994073	+	0.108711i	$0.965328\pi$
$230$	13.6682	−	4.97481i	0.901254	−	0.328030i
$231$	−11.2162	−	6.90395i	−0.737971	−	0.454247i
$232$	−0.375982	−	2.13230i	−0.0246844	−	0.139992i
$233$			9.31495i			0.610243i	0.952313	+	0.305121i	$0.0986970\pi$
$233$			9.31495i			0.610243i	−0.952313	+	0.305121i	$0.901303\pi$
$234$	20.0302	−	6.15089i	1.30941	−	0.402096i
$235$	−41.2268			−2.68934
$236$	−7.67644	−	2.79399i	−0.499693	−	0.181874i
$237$	−16.4173	−	14.5067i	−1.06642	−	0.942312i
$238$	13.7596	+	2.46313i	0.891902	+	0.159661i
$239$	−3.92573	+	4.67850i	−0.253934	+	0.302627i	−0.877919	−	0.478810i	$-0.841068\pi$
$239$	−3.92573	+	4.67850i	−0.253934	+	0.302627i	0.623984	+	0.781437i	$0.285513\pi$
$240$	−4.86775	−	32.4339i	−0.314212	−	2.09360i
$241$	0.213906	+	0.254923i	0.0137789	+	0.0164210i	0.772890	−	0.634540i	$-0.218810\pi$
$241$	0.213906	+	0.254923i	0.0137789	+	0.0164210i	−0.759111	+	0.650961i	$0.774366\pi$
$242$	−3.93158	−	2.26990i	−0.252731	−	0.145915i
$243$	−15.2085	+	3.42092i	−0.975623	+	0.219452i
$244$			5.68492i			0.363939i
$245$	4.52584	+	26.4723i	0.289145	+	1.69125i
$246$	3.35279	−	8.52698i	0.213766	−	0.543660i
$247$	−1.65903	+	9.40885i	−0.105562	+	0.598671i
$248$	13.8125	+	11.5901i	0.877096	+	0.735971i
$249$	7.28552	−	2.44270i	0.461701	−	0.154800i
$250$	10.2626	−	28.1964i	0.649067	−	1.78330i
$251$	6.85299	+	11.8697i	0.432557	+	0.749210i	0.997093	−	0.0761982i	$-0.0242782\pi$
$251$	6.85299	+	11.8697i	0.432557	+	0.749210i	−0.564536	+	0.825409i	$0.690945\pi$
$252$	−4.32442	−	4.04365i	−0.272413	−	0.254726i
$253$	3.28778	−	5.69460i	0.206701	−	0.358016i
$254$	7.22633	+	8.61200i	0.453420	+	0.540365i
$255$	21.1803	+	0.541540i	1.32636	+	0.0339125i
$256$	2.72997	−	15.4824i	0.170623	−	0.967652i
$257$	0.0315889	+	0.0265062i	0.00197046	+	0.00165341i	0.643772	−	0.765217i	$-0.277368\pi$
$257$	0.0315889	+	0.0265062i	0.00197046	+	0.00165341i	−0.641802	+	0.766871i	$0.721813\pi$
$258$	1.55866	+	0.953822i	0.0970376	+	0.0593824i
$259$	0.0497024	−	0.0414853i	0.00308836	−	0.00257777i
$260$	10.4461	+	6.03104i	0.647837	+	0.374029i
$261$	−2.62352	−	1.69913i	−0.162392	−	0.105174i
$262$			33.3131i			2.05809i
$263$	13.7378	−	2.42234i	0.847109	−	0.149368i	0.266787	−	0.963755i	$-0.414038\pi$
$263$	13.7378	−	2.42234i	0.847109	−	0.149368i	0.580322	+	0.814387i	$0.302927\pi$
$264$	−7.75222	−	6.85006i	−0.477116	−	0.421592i
$265$	−8.36295	−	1.47461i	−0.513732	−	0.0905848i
$266$	9.34726	−	3.37460i	0.573117	−	0.206910i
$267$	−1.21636	−	8.10461i	−0.0744399	−	0.495994i
$268$	1.40804	+	7.98538i	0.0860096	+	0.487785i
$269$	−11.2526	+	19.4900i	−0.686081	+	1.18833i	0.287015	+	0.957926i	$0.407337\pi$
$269$	−11.2526	+	19.4900i	−0.686081	+	1.18833i	−0.973096	+	0.230401i	$0.925996\pi$
$270$	−27.2596	−	18.6608i	−1.65897	−	1.13566i
$271$	5.53035	−	3.19295i	0.335945	−	0.193958i	−0.322533	−	0.946558i	$-0.604534\pi$
$271$	5.53035	−	3.19295i	0.335945	−	0.193958i	0.658477	+	0.752601i	$0.271201\pi$
$272$	14.7868	+	5.38196i	0.896582	+	0.326329i
$273$	−19.1086	+	2.81703i	−1.15651	+	0.170495i
$274$	−23.7905	−	19.9626i	−1.43723	−	1.20598i
$275$	−9.55442	−	26.2506i	−0.576153	−	1.58297i
$276$	1.95722	−	2.21499i	0.117811	−	0.133326i
$277$	1.08917	+	6.17699i	0.0654418	+	0.371139i	0.999887	+	0.0150321i	$0.00478504\pi$
$277$	1.08917	+	6.17699i	0.0654418	+	0.371139i	−0.934445	+	0.356107i	$0.884104\pi$
$278$	−10.9464	+	18.9597i	−0.656521	+	1.13713i
$279$	25.8316	−	3.20411i	1.54650	−	0.191825i
$280$	−0.0548963	+	21.0945i	−0.00328068	+	1.26064i
$281$	−6.25888	+	1.10361i	−0.373373	+	0.0658358i	−0.357186	−	0.934033i	$-0.616264\pi$
$281$	−6.25888	+	1.10361i	−0.373373	+	0.0658358i	−0.0161870	+	0.999869i	$0.505153\pi$
$282$	−27.0948	+	14.7330i	−1.61347	+	0.877335i
$283$	−0.572909	−	0.101019i	−0.0340559	−	0.00600498i	0.156594	−	0.987663i	$-0.449949\pi$
$283$	−0.572909	−	0.101019i	−0.0340559	−	0.00600498i	−0.190650	+	0.981658i	$0.561060\pi$
$284$	3.29619	+	0.581207i	0.195593	+	0.0344883i
$285$	13.2331	−	7.19554i	0.783858	−	0.426227i
$286$	19.7689	−	3.48579i	1.16896	−	0.206119i
$287$	−4.24208	+	7.30354i	−0.250402	+	0.431114i
$288$	−7.27365	−	9.62770i	−0.428604	−	0.567318i
$289$	3.41728	−	5.91890i	0.201016	−	0.348170i
$290$	−1.15023	−	6.52331i	−0.0675441	−	0.383062i
$291$	−15.1599	+	17.1565i	−0.888689	+	1.00573i
$292$	0.567747	+	1.55987i	0.0332249	+	0.0912847i
$293$	−7.63328	−	6.40508i	−0.445941	−	0.374189i	0.391986	−	0.919971i	$-0.371788\pi$
$293$	−7.63328	−	6.40508i	−0.445941	−	0.374189i	−0.837927	+	0.545782i	$0.816233\pi$
$294$	12.4347	+	15.7806i	0.725205	+	0.920343i
$295$	39.4843	+	14.3711i	2.29887	+	0.836719i
$296$	0.0440385	−	0.0254256i	0.00255968	−	0.00147783i
$297$	−14.8627	+	1.45891i	−0.862424	+	0.0846544i
$298$	10.9529	−	18.9710i	0.634486	−	1.09896i
$299$	−1.67452	−	9.49669i	−0.0968401	−	0.549208i
$300$	−1.86376	−	12.4183i	−0.107604	−	0.716969i
$301$	−1.28756	−	1.08612i	−0.0742139	−	0.0626027i
$302$	−20.4984	−	3.61442i	−1.17955	−	0.207986i
$303$	3.52267	+	3.11272i	0.202372	+	0.178821i
$304$	11.0173	−	1.94264i	0.631884	−	0.111418i
$305$		−	29.2408i		−	1.67432i
$306$	14.1135	−	7.21315i	0.806815	−	0.412348i
$307$	1.93850	+	1.11920i	0.110636	+	0.0638759i	0.554297	−	0.832319i	$-0.312987\pi$
$307$	1.93850	+	1.11920i	0.110636	+	0.0638759i	−0.443661	+	0.896195i	$0.646320\pi$
$308$	−3.63454	−	4.35444i	−0.207097	−	0.248117i
$309$	14.4247	+	8.82721i	0.820591	+	0.502162i
$310$	42.2564	+	35.4573i	2.40000	+	2.01384i
$311$	0.646712	−	3.66769i	0.0366717	−	0.207976i	−0.960966	−	0.276665i	$-0.910771\pi$
$311$	0.646712	−	3.66769i	0.0366717	−	0.207976i	0.997638	+	0.0686896i	$0.0218818\pi$
$312$	−15.1663	−	0.387774i	−0.858623	−	0.0219534i
$313$	−9.35374	−	11.1474i	−0.528705	−	0.630086i	0.433911	−	0.900956i	$-0.357133\pi$
$313$	−9.35374	−	11.1474i	−0.528705	−	0.630086i	−0.962616	+	0.270870i	$0.912689\pi$
$314$	−15.0263	+	26.0264i	−0.847986	+	1.46875i
$315$	22.2430	+	20.7988i	1.25325	+	1.17188i
$316$	−4.71738	−	8.17075i	−0.265374	−	0.459641i
$317$	−0.419059	+	1.15136i	−0.0235367	+	0.0646666i	−0.950905	−	0.309484i	$-0.899844\pi$
$317$	−0.419059	+	1.15136i	−0.0235367	+	0.0646666i	0.927368	+	0.374151i	$0.122066\pi$
$318$	−6.02322	+	2.01948i	−0.337765	+	0.113247i
$319$	−2.29391	−	1.92482i	−0.128435	−	0.107769i
$320$	−2.13583	+	12.1129i	−0.119396	+	0.677131i
$321$	8.94967	−	22.7613i	0.499522	−	1.27041i
$322$	−7.70060	+	6.42749i	−0.429138	+	0.358190i
$323$			7.22704i			0.402123i
$324$	−6.67809	−	0.685227i	−0.371005	−	0.0380681i
$325$	−35.4790	−	20.4838i	−1.96802	−	1.13624i
$326$	−6.26189	−	7.46263i	−0.346814	−	0.413317i
$327$	−1.27969	−	8.52656i	−0.0707668	−	0.471520i
$328$	−4.26431	+	5.08200i	−0.235457	+	0.280607i
$329$	26.7408	−	9.65413i	1.47427	−	0.532249i
$330$	−23.7162	−	20.9563i	−1.30554	−	1.15360i
$331$	−19.2551	−	7.00827i	−1.05835	−	0.385210i	−0.246545	−	0.969131i	$-0.579295\pi$
$331$	−19.2551	−	7.00827i	−1.05835	−	0.385210i	−0.811810	+	0.583922i	$0.801517\pi$
$332$	3.30916			0.181614
$333$	0.0164251	−	0.0715480i	0.000900091	−	0.00392080i
$334$		−	13.7407i		−	0.751858i
$335$	−7.24235	−	41.0734i	−0.395692	−	2.24408i
$336$	10.7524	+	19.8976i	0.586593	+	1.08550i
$337$	18.8694	−	6.86790i	1.02788	−	0.374119i	0.227608	−	0.973753i	$-0.426909\pi$
$337$	18.8694	−	6.86790i	1.02788	−	0.374119i	0.800274	+	0.599634i	$0.204687\pi$
$338$	5.07591	−	6.04924i	0.276093	−	0.329035i
$339$	12.1931	−	6.63006i	0.662238	−	0.360095i
$340$	8.57399	+	3.12068i	0.464990	+	0.169242i
$341$	24.9371			1.35042
$342$	6.12552	−	9.45802i	0.331230	−	0.511431i
$343$	−9.13463	−	16.1108i	−0.493224	−	0.869903i
$344$	−0.850466	−	1.01355i	−0.0458540	−	0.0546467i
$345$	−10.0671	+	11.3929i	−0.541994	+	0.613376i
$346$	20.7973	−	24.7853i	1.11807	−	1.33247i
$347$	−0.215717	−	0.592678i	−0.0115803	−	0.0318166i	0.933768	−	0.357879i	$-0.116500\pi$
$347$	−0.215717	−	0.592678i	−0.0115803	−	0.0318166i	−0.945348	+	0.326063i	$0.894278\pi$
$348$	−0.838601	−	1.05293i	−0.0449537	−	0.0564430i
$349$	−0.582328	+	1.59993i	−0.0311713	+	0.0856425i	−0.954302	−	0.298844i	$-0.903399\pi$
$349$	−0.582328	+	1.59993i	−0.0311713	+	0.0856425i	0.923131	+	0.384486i	$0.125621\pi$
$350$	−0.110896	+	42.6132i	−0.00592765	+	2.27777i
$351$	−15.3219	+	15.6495i	−0.817821	+	0.835310i
$352$	−5.77999	−	10.0112i	−0.308074	−	0.533600i
$353$	18.3149	−	15.3681i	0.974806	−	0.817960i	−0.00849145	−	0.999964i	$-0.502703\pi$
$353$	18.3149	−	15.3681i	0.974806	−	0.817960i	0.983298	+	0.182004i	$0.0582585\pi$
$354$	31.0854	−	4.66536i	1.65217	−	0.247961i
$355$	−16.9542	−	2.98948i	−0.899836	−	0.158665i
$356$	0.612862	−	3.47571i	0.0324816	−	0.184212i
$357$	−13.8649	+	4.60855i	−0.733809	+	0.243910i
$358$	−3.76236	+	3.15700i	−0.198847	+	0.166852i
$359$	−10.8355	−	6.25585i	−0.571873	−	0.330171i	0.186024	−	0.982545i	$-0.440440\pi$
$359$	−10.8355	−	6.25585i	−0.571873	−	0.330171i	−0.757897	+	0.652374i	$0.773773\pi$
$360$	14.4184	+	19.0848i	0.759917	+	1.00586i
$361$	−6.93100	−	12.0048i	−0.364789	−	0.631834i
$362$	−32.3384	+	27.1351i	−1.69967	+	1.42619i
$363$	4.74364	+	0.121286i	0.248977	+	0.00636587i
$364$	−8.18789	−	1.46573i	−0.429162	−	0.0768250i
$365$	−2.92025	−	8.02333i	−0.152853	−	0.419960i
$366$	−10.4496	−	19.2175i	−0.546209	−	1.00451i
$367$	−4.50874	+	12.3877i	−0.235354	+	0.646630i	0.764643	+	0.644454i	$0.222915\pi$
$367$	−4.50874	+	12.3877i	−0.235354	+	0.646630i	−0.999998	+	0.00217674i	$0.999307\pi$
$368$	−9.77888	+	5.64584i	−0.509759	+	0.294310i
$369$	1.17888	+	9.50416i	0.0613700	+	0.494767i
$370$	0.134726	−	0.0777842i	0.00700408	−	0.00404381i
$371$	5.76975	−	1.00189i	0.299550	−	0.0520154i
$372$	10.9860	+	2.22806i	0.569596	+	0.115519i
$373$	10.5249	−	3.83075i	0.544959	−	0.198349i	−0.0548464	−	0.998495i	$-0.517467\pi$
$373$	10.5249	−	3.83075i	0.544959	−	0.198349i	0.599805	+	0.800146i	$0.295245\pi$
$374$	14.2689	−	5.19347i	0.737829	−	0.268548i
$375$	4.65498	+	31.0162i	0.240382	+	1.60167i
$376$	21.9915	−	3.87769i	1.13412	−	0.199977i
$377$	−4.39149			−0.226173
$378$	22.0511	+	5.72047i	1.13419	+	0.294229i
$379$	−6.24758			−0.320917			−0.160458	−	0.987043i	$-0.551297\pi$
$379$	−6.24758			−0.320917			−0.160458	+	0.987043i	$0.551297\pi$
$380$	6.38826	−	1.12642i	0.327711	−	0.0577842i
$381$	−10.9358	−	4.29994i	−0.560259	−	0.220292i
$382$	35.3025	−	12.8491i	1.80623	−	0.657415i
$383$	−13.4741	+	4.90417i	−0.688494	+	0.250591i	−0.662490	−	0.749070i	$-0.730500\pi$
$383$	−13.4741	+	4.90417i	−0.688494	+	0.250591i	−0.0260038	+	0.999662i	$0.508278\pi$
$384$	7.35420	+	21.9344i	0.375293	+	1.11933i
$385$	18.6946	+	22.3974i	0.952763	+	1.14148i
$386$	−21.4197	+	12.3667i	−1.09023	+	0.629447i
$387$	−1.90752	−	0.0976075i	−0.0969649	−	0.00496167i
$388$	−8.53865	+	4.92979i	−0.433484	+	0.250272i
$389$	−2.95313	+	8.11366i	−0.149730	+	0.411379i	−0.991769	−	0.128037i	$-0.959133\pi$
$389$	−2.95313	+	8.11366i	−0.149730	+	0.411379i	0.842040	+	0.539415i	$0.181355\pi$
$390$	−46.3980	−	1.18631i	−2.34945	−	0.0600712i
$391$	−2.49487	−	6.85459i	−0.126171	−	0.346652i
$392$	−4.90412	−	13.6953i	−0.247696	−	0.691719i
$393$	−16.6337	−	30.5904i	−0.839059	−	1.54308i
$394$	−24.2060	+	20.3113i	−1.21948	+	1.02327i
$395$	24.2642	+	42.0269i	1.22087	+	2.11460i
$396$	−6.26834	−	1.43901i	−0.314996	−	0.0723130i
$397$	0.00629478	+	0.00363429i	0.000315926	+	0.000182400i	0.500158	−	0.865934i	$-0.333275\pi$
$397$	0.00629478	+	0.00363429i	0.000315926	+	0.000182400i	−0.499842	+	0.866117i	$0.666609\pi$
$398$	7.37245	−	6.18622i	0.369548	−	0.310087i
$399$	−6.89833	+	7.76602i	−0.345348	+	0.388787i
$400$	−8.33008	+	47.2422i	−0.416504	+	2.36211i
$401$	14.9200	+	2.63081i	0.745071	+	0.131376i	0.533280	−	0.845939i	$-0.320959\pi$
$401$	14.9200	+	2.63081i	0.745071	+	0.131376i	0.211791	+	0.977315i	$0.432070\pi$
$402$	−19.4379	−	24.4059i	−0.969475	−	1.21725i
$403$	28.0148	−	23.5072i	1.39552	−	1.17098i
$404$	1.01222	+	1.75321i	0.0503596	+	0.0872254i
$405$	34.3493	+	3.52452i	1.70683	+	0.175135i
$406$	2.27364	+	3.96184i	0.112839	+	0.196623i
$407$	0.0240536	−	0.0660867i	0.00119229	−	0.00327580i
$408$	−11.3491	+	1.70329i	−0.561862	+	0.0843255i
$409$	3.50114	+	9.61931i	0.173120	+	0.475644i	0.995660	−	0.0930631i	$-0.0296658\pi$
$409$	3.50114	+	9.61931i	0.173120	+	0.475644i	−0.822540	+	0.568708i	$0.807444\pi$
$410$	−13.0457	+	15.5473i	−0.644282	+	0.767826i
$411$	31.8137	+	6.45211i	1.56925	+	0.318259i
$412$	4.68131	+	5.57897i	0.230631	+	0.274856i
$413$	−28.9759	−	0.0754068i	−1.42581	−	0.00371052i
$414$	−2.54481	+	11.0852i	−0.125071	+	0.544809i
$415$	−17.0209			−0.835524
$416$	−15.9306	−	5.79825i	−0.781060	−	0.284283i
$417$	0.584892	−	22.8758i	0.0286423	−	1.12023i
$418$	6.93916	−	8.26977i	0.339405	−	0.404488i
$419$	−37.4662	+	13.6366i	−1.83034	+	0.666190i	−0.837548	+	0.546363i	$0.816012\pi$
$419$	−37.4662	+	13.6366i	−1.83034	+	0.666190i	−0.992795	+	0.119827i	$0.961766\pi$
$420$	6.23469	+	11.5374i	0.304222	+	0.562969i
$421$	3.81518	+	21.6370i	0.185940	+	1.05452i	0.924741	+	0.380597i	$0.124281\pi$
$421$	3.81518	+	21.6370i	0.185940	+	1.05452i	−0.738801	+	0.673924i	$0.764608\pi$
$422$			1.72311i			0.0838795i
$423$	17.5240	−	27.0577i	0.852046	−	1.31559i
$424$	4.59972			0.223382
$425$	−29.1207	−	10.5991i	−1.41256	−	0.514131i
$426$	−12.2109	+	4.09409i	−0.591619	+	0.198359i
$427$	6.84735	+	18.9664i	0.331367	+	0.917847i
$428$	6.77024	−	8.06846i	0.327252	−	0.390004i
$429$	−16.4127	+	13.0718i	−0.792411	+	0.631111i
$430$	−2.60182	−	3.10072i	−0.125471	−	0.149530i
$431$	5.61933	+	3.24432i	0.270673	+	0.156273i	0.629194	−	0.777249i	$-0.283385\pi$
$431$	5.61933	+	3.24432i	0.270673	+	0.156273i	−0.358520	+	0.933522i	$0.616719\pi$
$432$	23.3559	+	10.5917i	1.12371	+	0.509593i
$433$			1.48559i			0.0713927i	0.999363	+	0.0356963i	$0.0113649\pi$
$433$			1.48559i			0.0713927i	−0.999363	+	0.0356963i	$0.988635\pi$
$434$	−35.7117	−	13.1034i	−1.71422	−	0.628981i
$435$	4.31341	+	5.41583i	0.206812	+	0.259669i
$436$	0.644770	−	3.65667i	0.0308789	−	0.175123i
$437$	−3.97268	−	3.33348i	−0.190039	−	0.159462i
$438$	−4.78648	−	4.22945i	−0.228707	−	0.202091i
$439$	4.31238	−	11.8482i	0.205819	−	0.565483i	−0.793238	−	0.608912i	$-0.791606\pi$
$439$	4.31238	−	11.8482i	0.205819	−	0.565483i	0.999056	+	0.0434295i	$0.0138284\pi$
$440$	11.4576	+	19.8451i	0.546217	+	0.946076i
$441$	−19.2979	−	8.28203i	−0.918946	−	0.394382i
$442$	11.1343	−	19.2852i	0.529606	−	0.917305i
$443$	−0.999759	−	1.19147i	−0.0475000	−	0.0566083i	0.741771	−	0.670653i	$-0.233986\pi$
$443$	−0.999759	−	1.19147i	−0.0475000	−	0.0566083i	−0.789271	+	0.614045i	$0.789542\pi$
$444$	0.0165014	−	0.0269652i	0.000783122	−	0.00127971i
$445$	−3.15230	+	17.8776i	−0.149434	+	0.847480i
$446$	−9.77746	−	8.20426i	−0.462976	−	0.388483i
$447$	−0.585241	+	22.8895i	−0.0276810	+	1.08264i
$448$	−1.45113	−	8.35689i	−0.0685595	−	0.394826i
$449$	−3.71332	−	2.14388i	−0.175242	−	0.101176i	0.409813	−	0.912169i	$-0.365594\pi$
$449$	−3.71332	−	2.14388i	−0.175242	−	0.101176i	−0.585055	+	0.810993i	$0.698927\pi$
$450$	29.1267	+	38.5533i	1.37305	+	1.81742i
$451$			9.17503i			0.432035i
$452$	5.88622	−	1.03790i	0.276864	−	0.0488186i
$453$	20.6278	−	6.91612i	0.969178	−	0.324948i
$454$	−5.29180	−	0.933088i	−0.248357	−	0.0437920i
$455$	42.1151	+	7.53908i	1.97438	+	0.353438i
$456$	−6.38207	+	5.08296i	−0.298868	+	0.238032i
$457$	2.62834	+	14.9061i	0.122949	+	0.697277i	0.982505	+	0.186236i	$0.0596288\pi$
$457$	2.62834	+	14.9061i	0.122949	+	0.697277i	−0.859556	+	0.511041i	$0.829260\pi$
$458$	18.1114	−	31.3698i	0.846289	−	1.46582i
$459$	−9.35837	+	13.6707i	−0.436812	+	0.638093i
$460$	−5.67019	+	3.27368i	−0.264374	+	0.152636i
$461$	−6.54769	−	2.38316i	−0.304956	−	0.110995i	0.185009	−	0.982737i	$-0.440768\pi$
$461$	−6.54769	−	2.38316i	−0.304956	−	0.110995i	−0.489966	+	0.871742i	$0.662991\pi$
$462$	20.2903	+	8.03914i	0.943992	+	0.374015i
$463$	−30.9400	−	25.9617i	−1.43790	−	1.20654i	−0.940851	−	0.338822i	$-0.889972\pi$
$463$	−30.9400	−	25.9617i	−1.43790	−	1.20654i	−0.497051	−	0.867721i	$-0.665584\pi$
$464$	1.75874	+	4.83209i	0.0816473	+	0.224324i
$465$	−56.5072	−	11.4602i	−2.62046	−	0.531454i
$466$	−2.68036	−	15.2011i	−0.124165	−	0.704177i
$467$	4.21489	−	7.30040i	0.195042	−	0.337822i	−0.751872	−	0.659309i	$-0.770849\pi$
$467$	4.21489	−	7.30040i	0.195042	−	0.337822i	0.946914	+	0.321486i	$0.104182\pi$
$468$	−8.39848	+	4.29231i	−0.388220	+	0.198412i
$469$	14.3158	+	24.9454i	0.661042	+	1.15187i
$470$	67.2782	−	11.8630i	3.10331	−	0.547197i
$471$	0.802894	−	31.4021i	0.0369954	−	1.44693i
$472$	−22.4137	−	3.95214i	−1.03167	−	0.181912i
$473$	−1.80205	−	0.317751i	−0.0828585	−	0.0146102i
$474$	30.9657	+	18.9495i	1.42230	+	0.870379i
$475$	−21.6971	+	3.82578i	−0.995531	+	0.175539i
$476$	−6.29209	−	0.0163745i	−0.288398	−	0.000750525i
$477$	4.52259	−	4.86191i	0.207075	−	0.222611i
$478$	5.06018	−	8.76448i	0.231447	−	0.400878i
$479$	3.99718	+	22.6691i	0.182636	+	1.03578i	0.928956	+	0.370191i	$0.120708\pi$
$479$	3.99718	+	22.6691i	0.182636	+	1.03578i	−0.746320	+	0.665588i	$0.768181\pi$
$480$	8.49659	+	25.3416i	0.387814	+	1.15668i
$481$	−0.0352751	−	0.0969176i	−0.00160841	−	0.00441906i
$482$	−0.422427	−	0.354458i	−0.0192410	−	0.0161451i
$483$	3.86189	−	9.74720i	0.175722	−	0.443513i
$484$	1.92028	+	0.698923i	0.0872852	+	0.0317692i
$485$	43.9192	−	25.3568i	1.99427	−	1.15139i
$486$	23.8344	−	9.95883i	1.08115	−	0.451742i
$487$	−13.2168	+	22.8922i	−0.598912	+	1.03735i	0.394070	+	0.919080i	$0.371067\pi$
$487$	−13.2168	+	22.8922i	−0.598912	+	1.03735i	−0.992982	+	0.118265i	$0.962267\pi$
$488$	2.75032	+	15.5978i	0.124501	+	0.706080i
$489$	9.47631	+	3.72606i	0.428533	+	0.168498i
$490$	−15.0031	−	41.8979i	−0.677771	−	1.89275i
$491$	−12.8648	−	2.26841i	−0.580580	−	0.102372i	−0.124357	−	0.992238i	$-0.539687\pi$
$491$	−12.8648	−	2.26841i	−0.580580	−	0.102372i	−0.456223	+	0.889866i	$0.650798\pi$
$492$	−0.819763	+	4.04204i	−0.0369578	+	0.182229i
$493$	−3.27144	+	0.576843i	−0.147338	+	0.0259797i
$494$		−	15.8317i		−	0.712303i
$495$	32.2417	+	7.40166i	1.44916	+	0.332680i
$496$	−37.0854	−	21.4112i	−1.66518	−	0.961393i
$497$	11.6970	−	2.03113i	0.524682	−	0.0911084i
$498$	−11.1864	+	6.08265i	−0.501274	+	0.272570i
$499$	19.8121	+	16.6244i	0.886913	+	0.744208i	0.967589	−	0.252532i	$-0.0812633\pi$
$499$	19.8121	+	16.6244i	0.886913	+	0.744208i	−0.0806756	+	0.996740i	$0.525708\pi$
$500$	−2.34541	+	13.3015i	−0.104890	+	0.594861i
$501$	6.86093	+	12.6177i	0.306524	+	0.563717i
$502$	−14.5989	−	17.3983i	−0.651581	−	0.776524i
$503$	11.7401	−	20.3345i	0.523467	−	0.906672i	−0.476160	−	0.879359i	$-0.657972\pi$
$503$	11.7401	−	20.3345i	0.523467	−	0.906672i	0.999627	−	0.0273131i	$-0.00869510\pi$
$504$	−13.8213	−	9.00254i	−0.615649	−	0.401005i
$505$	−5.20641	−	9.01776i	−0.231682	−	0.401285i
$506$	−3.72672	+	10.2391i	−0.165673	+	0.455183i
$507$	−1.64059	+	8.08931i	−0.0728611	+	0.359259i
$508$	−3.87655	−	3.25281i	−0.171994	−	0.144320i
$509$	4.92895	−	27.9535i	0.218472	−	1.23902i	−0.656307	−	0.754494i	$-0.727882\pi$
$509$	4.92895	−	27.9535i	0.218472	−	1.23902i	0.874779	−	0.484522i	$-0.161007\pi$
$510$	−34.7200	+	5.21085i	−1.53743	+	0.230740i
$511$	3.77299	+	4.52031i	0.166907	+	0.199967i
$512$		−	0.661943i		−	0.0292540i
$513$	−0.902358	+	11.7436i	−0.0398401	+	0.518492i
$514$	−0.0591771	−	0.0341659i	−0.00261019	−	0.00150699i
$515$	−24.0787	−	28.6958i	−1.06103	−	1.26449i
$516$	−0.765500	−	0.300993i	−0.0336992	−	0.0132505i
$517$	19.8517	−	23.6583i	0.873076	−	1.04049i
$518$	−0.0691722	+	0.0820018i	−0.00303925	+	0.00360295i
$519$	−6.72192	+	33.1440i	−0.295059	+	1.45486i
$520$	31.5789	+	11.4938i	1.38482	+	0.504035i
$521$	−15.0773			−0.660549			−0.330275	−	0.943885i	$-0.607141\pi$
$521$	−15.0773			−0.660549			−0.330275	+	0.943885i	$0.607141\pi$
$522$	4.77025	+	2.01790i	0.208788	+	0.0883213i
$523$			4.77566i			0.208825i	0.994534	+	0.104412i	$0.0332962\pi$
$523$			4.77566i			0.208825i	−0.994534	+	0.104412i	$0.966704\pi$
$524$	−2.60391	−	14.7675i	−0.113752	−	0.645122i
$525$	−21.1755	−	39.1858i	−0.924176	−	1.71021i
$526$	−21.7217	+	7.90606i	−0.947112	+	0.344721i
$527$	17.7818	−	21.1916i	0.774590	−	0.923120i
$528$	20.9564	+	12.8243i	0.912008	+	0.558105i
$529$	−16.6942	−	6.07620i	−0.725836	−	0.264183i
$530$	14.0718			0.611242
$531$	−26.2153	+	19.8054i	−1.13765	+	0.859483i
$532$	−3.87982	+	2.22657i	−0.168212	+	0.0965342i
$533$	8.64896	+	10.3074i	0.374628	+	0.446464i
$534$	4.31707	+	12.8759i	0.186818	+	0.557196i
$535$	−34.8233	+	41.5008i	−1.50554	+	1.79423i
$536$	7.72653	+	21.2285i	0.333735	+	0.916930i
$537$	1.87853	−	4.77758i	0.0810646	−	0.206168i
$538$	12.7549	−	35.0437i	0.549902	−	1.51084i
$539$	−17.3706	−	10.1498i	−0.748206	−	0.437185i
$540$	13.5427	+	6.14149i	0.582784	+	0.264287i
$541$	−10.3759	−	17.9716i	−0.446094	−	0.772657i	0.552034	−	0.833822i	$-0.313852\pi$
$541$	−10.3759	−	17.9716i	−0.446094	−	0.772657i	−0.998128	+	0.0611643i	$0.980519\pi$
$542$	−8.10622	+	6.80193i	−0.348192	+	0.292168i
$543$	16.1464	−	41.0644i	0.692909	−	1.76224i
$544$	−12.6291	−	2.22685i	−0.541468	−	0.0954753i
$545$	−3.31642	+	18.8084i	−0.142060	+	0.805662i
$546$	30.3728	−	10.0956i	1.29984	−	0.432052i
$547$	−9.38962	+	7.87883i	−0.401471	+	0.336874i	−0.821062	−	0.570839i	$-0.806618\pi$
$547$	−9.38962	+	7.87883i	−0.401471	+	0.336874i	0.419591	+	0.907713i	$0.362174\pi$
$548$	12.1066	+	6.98973i	0.517167	+	0.298586i
$549$	19.1911	+	12.4292i	0.819057	+	0.530465i
$550$	23.1454	+	40.0891i	0.986925	+	1.70940i
$551$	−1.80915	+	1.51806i	−0.0770724	+	0.0646714i
$552$	4.29847	−	7.02419i	0.182955	−	0.298969i
$553$	−25.5799	−	21.5778i	−1.08777	−	0.917581i
$554$	−3.55484	−	9.76683i	−0.151031	−	0.414953i
$555$	−0.0848762	+	0.138698i	−0.00360280	+	0.00588738i
$556$	3.37050	−	9.26036i	0.142941	−	0.392727i
$557$	−18.6030	+	10.7404i	−0.788233	+	0.455086i	−0.839340	−	0.543607i	$-0.817058\pi$
$557$	−18.6030	+	10.7404i	−0.788233	+	0.455086i	0.0511072	+	0.998693i	$0.483725\pi$
$558$	−41.2328	+	12.6618i	−1.74552	+	0.536017i
$559$	−2.32400	+	1.34176i	−0.0982945	+	0.0567504i
$560$	−8.57108	−	49.3598i	−0.362194	−	2.08583i
$561$	−10.5096	+	11.8937i	−0.443714	+	0.502152i
$562$	9.89631	−	3.60196i	0.417451	−	0.151940i
$563$	−15.1623	+	5.51864i	−0.639016	+	0.232583i	−0.641151	−	0.767415i	$-0.721543\pi$
$563$	−15.1623	+	5.51864i	−0.639016	+	0.232583i	0.00213467	+	0.999998i	$0.499321\pi$
$564$	10.8594	−	8.64892i	0.457264	−	0.364185i
$565$	−30.2762	+	5.33851i	−1.27373	+	0.224593i
$566$	0.964001			0.0405200
$567$	−23.1052	+	5.75752i	−0.970328	+	0.241793i
$568$	9.32501			0.391269
$569$	26.1637	−	4.61337i	1.09684	−	0.193403i	0.404190	−	0.914675i	$-0.367554\pi$
$569$	26.1637	−	4.61337i	1.09684	−	0.193403i	0.692651	+	0.721272i	$0.256442\pi$
$570$	−19.5246	+	15.5502i	−0.817794	+	0.651327i
$571$	−27.8574	+	10.1393i	−1.16580	+	0.424315i	−0.851164	−	0.524899i	$-0.824103\pi$
$571$	−27.8574	+	10.1393i	−1.16580	+	0.424315i	−0.314631	+	0.949214i	$0.601881\pi$
$572$	−8.49098	+	3.09046i	−0.355026	+	0.129219i
$573$	−26.0015	+	29.4260i	−1.08623	+	1.22929i
$574$	4.82108	−	13.1393i	0.201228	−	0.548424i
$575$	19.2582	−	11.1187i	0.803124	−	0.463684i
$576$	−7.04198	−	6.55051i	−0.293416	−	0.272938i
$577$	31.4355	−	18.1493i	1.30868	−	0.755564i	0.326800	−	0.945093i	$-0.394029\pi$
$577$	31.4355	−	18.1493i	1.30868	−	0.755564i	0.981875	+	0.189529i	$0.0606962\pi$
$578$	−3.87351	+	10.6424i	−0.161117	+	0.442665i
$579$	13.4942	−	22.0511i	0.560801	−	0.916414i
$580$	1.01979	+	2.80184i	0.0423443	+	0.116340i
$581$	11.0402	−	3.98581i	0.458026	−	0.165359i
$582$	19.8027	−	32.3600i	0.820850	−	1.34136i
$583$	4.87317	−	4.08908i	0.201826	−	0.169352i
$584$	2.31240	+	4.00519i	0.0956876	+	0.165736i
$585$	43.1983	−	22.0778i	1.78603	−	0.912806i
$586$	14.2998	+	8.25601i	0.590720	+	0.341053i
$587$	27.4601	−	23.0418i	1.13340	−	0.951035i	0.134196	−	0.990955i	$-0.457155\pi$
$587$	27.4601	−	23.0418i	1.13340	−	0.951035i	0.999203	+	0.0399198i	$0.0127102\pi$
$588$	−6.74572	−	6.02350i	−0.278189	−	0.248405i
$589$	3.41518	−	19.3684i	0.140720	−	0.798063i
$590$	−68.5699	−	12.0907i	−2.82298	−	0.497767i
$591$	12.0860	−	30.7376i	0.497150	−	1.26438i
$592$	−0.0925142	+	0.0776286i	−0.00380231	+	0.00319052i
$593$	9.90996	+	17.1646i	0.406953	+	0.704864i	0.994547	−	0.104293i	$-0.0332578\pi$
$593$	9.90996	+	17.1646i	0.406953	+	0.704864i	−0.587593	+	0.809156i	$0.699924\pi$
$594$	23.8348	−	6.65753i	0.977952	−	0.273162i
$595$	32.3639	+	0.0842236i	1.32679	+	0.00345283i
$596$	−3.37251	+	9.26590i	−0.138143	+	0.379546i
$597$	−3.68103	+	9.36179i	−0.150655	+	0.383153i
$598$	5.46532	+	15.0158i	0.223493	+	0.614043i
$599$	11.8996	−	14.1814i	0.486205	−	0.579436i	−0.466043	−	0.884762i	$-0.654321\pi$
$599$	11.8996	−	14.1814i	0.486205	−	0.579436i	0.952248	+	0.305326i	$0.0987654\pi$
$600$	−11.1215	−	33.1706i	−0.454034	−	1.35418i
$601$	27.1016	+	32.2984i	1.10550	+	1.31748i	0.943755	+	0.330646i	$0.107266\pi$
$601$	27.1016	+	32.2984i	1.10550	+	1.31748i	0.161741	+	0.986833i	$0.448289\pi$
$602$	2.41371	+	1.40194i	0.0983754	+	0.0571389i
$603$	30.0355	+	12.7056i	1.22314	+	0.517410i
$604$	9.36935			0.381234
$605$	−9.87708	−	3.59496i	−0.401561	−	0.146156i
$606$	−6.64434	−	4.06602i	−0.269908	−	0.165171i
$607$	26.4848	−	31.5633i	1.07498	−	1.28111i	0.117360	−	0.993089i	$-0.462557\pi$
$607$	26.4848	−	31.5633i	1.07498	−	1.28111i	0.957623	−	0.288025i	$-0.0929988\pi$
$608$	−8.56722	+	3.11821i	−0.347447	+	0.126460i
$609$	−4.06602	−	2.50278i	−0.164764	−	0.101418i
$610$	8.41400	+	47.7182i	0.340673	+	1.93205i
$611$		−	45.2917i		−	1.83231i
$612$	−5.69263	+	4.30073i	−0.230111	+	0.173847i
$613$	−33.7892			−1.36473			−0.682366	−	0.731011i	$-0.739049\pi$
$613$	−33.7892			−1.36473			−0.682366	+	0.731011i	$0.739049\pi$
$614$	−3.48550	−	1.26862i	−0.140663	−	0.0511972i
$615$	4.21652	−	20.7905i	0.170026	−	0.838355i
$616$	−12.0788	−	10.1890i	−0.486669	−	0.410527i
$617$	12.0622	−	14.3752i	0.485607	−	0.578724i	−0.466487	−	0.884528i	$-0.654481\pi$
$617$	12.0622	−	14.3752i	0.485607	−	0.578724i	0.952095	+	0.305803i	$0.0989251\pi$
$618$	−26.0797	−	10.2545i	−1.04908	−	0.412495i
$619$	−9.30674	−	11.0913i	−0.374069	−	0.445798i	0.545864	−	0.837874i	$-0.316202\pi$
$619$	−9.30674	−	11.0913i	−0.374069	−	0.445798i	−0.919933	+	0.392076i	$0.871757\pi$
$620$	−21.5036	−	12.4151i	−0.863605	−	0.498602i
$621$	−3.19818	−	11.4499i	−0.128339	−	0.459468i
$622$			6.17140i			0.247451i
$623$	−2.14175	−	12.3341i	−0.0858074	−	0.494154i
$624$	35.6318	−	5.34770i	1.42641	−	0.214079i
$625$	3.62476	−	20.5571i	0.144991	−	0.822282i
$626$	18.4720	+	15.4999i	0.738291	+	0.619500i
$627$	−2.24281	+	11.0587i	−0.0895692	+	0.441642i
$628$	4.62676	−	12.7119i	0.184628	−	0.507260i
$629$	−0.0390087	−	0.0675651i	−0.00155538	−	0.00269400i
$630$	−42.2832	−	27.5413i	−1.68460	−	1.09727i
$631$	3.09835	−	5.36650i	0.123343	−	0.213637i	−0.797741	−	0.603001i	$-0.793972\pi$
$631$	3.09835	−	5.36650i	0.123343	−	0.213637i	0.921084	+	0.389363i	$0.127305\pi$
$632$	−16.8961	−	20.1360i	−0.672092	−	0.800968i
$633$	−0.860372	−	1.58228i	−0.0341967	−	0.0628899i
$634$	0.352563	−	1.99948i	0.0140021	−	0.0794097i
$635$	19.9393	+	16.7311i	0.791269	+	0.663953i
$636$	2.51221	−	1.36603i	0.0996157	−	0.0541666i
$637$	−29.0824	+	4.97208i	−1.15229	+	0.197001i
$638$	4.29731	+	2.48105i	0.170132	+	0.0982259i
$639$	9.16865	−	9.85654i	0.362706	−	0.389919i
$640$		−	51.2445i		−	2.02562i
$641$	−8.28416	+	1.46072i	−0.327205	+	0.0576950i	−0.334838	−	0.942276i	$-0.608681\pi$
$641$	−8.28416	+	1.46072i	−0.327205	+	0.0576950i	0.00763285	+	0.999971i	$0.497570\pi$
$642$	−8.05548	+	39.7194i	−0.317924	+	1.56760i
$643$	−12.6614	−	2.23255i	−0.499317	−	0.0880430i	−0.0816827	−	0.996658i	$-0.526029\pi$
$643$	−12.6614	−	2.23255i	−0.499317	−	0.0880430i	−0.417634	+	0.908615i	$0.637141\pi$
$644$	2.91123	−	3.45119i	0.114719	−	0.135996i
$645$	3.93741	+	1.54818i	0.155035	+	0.0609595i
$646$	−2.07957	−	11.7938i	−0.0818196	−	0.464022i
$647$	−3.45841	+	5.99014i	−0.135964	+	0.235497i	−0.925965	−	0.377609i	$-0.876747\pi$
$647$	−3.45841	+	5.99014i	−0.135964	+	0.235497i	0.790001	+	0.613105i	$0.210080\pi$
$648$	−18.6543	+	1.35074i	−0.732812	+	0.0530620i
$649$	−27.2596	+	15.7383i	−1.07003	+	0.617784i
$650$	63.7926	+	23.2186i	2.50215	+	0.910708i
$651$	39.3357	−	5.79896i	1.54169	−	0.227279i
$652$	3.35918	+	2.81869i	0.131556	+	0.110388i
$653$	2.61548	+	7.18597i	0.102352	+	0.281209i	0.980290	−	0.197565i	$-0.0633035\pi$
$653$	2.61548	+	7.18597i	0.102352	+	0.281209i	−0.877938	+	0.478774i	$0.841081\pi$
$654$	4.54183	+	13.5463i	0.177600	+	0.529702i
$655$	13.3934	+	75.9579i	0.523325	+	2.96792i
$656$	7.87778	−	13.6447i	0.307576	−	0.532736i
$657$	6.50711	+	1.49382i	0.253866	+	0.0582796i
$658$	−40.8605	+	23.4492i	−1.59291	+	0.914146i
$659$	−5.58789	+	0.985295i	−0.217673	+	0.0383817i	−0.281421	−	0.959584i	$-0.590806\pi$
$659$	−5.58789	+	0.985295i	−0.217673	+	0.0383817i	0.0637479	+	0.997966i	$0.479695\pi$
$660$	12.1513	+	7.43603i	0.472990	+	0.289447i
$661$	47.1559	+	8.31485i	1.83415	+	0.323410i	0.980362	−	0.197208i	$-0.0631874\pi$
$661$	47.1559	+	8.31485i	1.83415	+	0.323410i	0.853790	+	0.520618i	$0.174298\pi$
$662$	33.4390	+	5.89620i	1.29965	+	0.229162i
$663$	−0.594934	+	23.2686i	−0.0231053	+	0.903677i
$664$	9.07941	−	1.60094i	0.352349	−	0.0621287i
$665$	19.9562	−	11.4526i	0.773866	−	0.444111i
$666$	−0.00621639	+	0.121486i	−0.000240880	+	0.00470747i
$667$	1.19186	−	2.06437i	0.0461491	−	0.0799327i
$668$	1.07404	+	6.09119i	0.0415559	+	0.235675i
$669$	13.0749	+	2.65170i	0.505503	+	0.102521i
$670$	23.6376	+	64.9439i	0.913202	+	2.50900i
$671$	16.7800	+	14.0801i	0.647787	+	0.543557i
$672$	−11.4454	−	14.4476i	−0.441515	−	0.557328i
$673$	−17.7107	−	6.44618i	−0.682699	−	0.248482i	−0.0226931	−	0.999742i	$-0.507224\pi$
$673$	−17.7107	−	6.44618i	−0.682699	−	0.248482i	−0.660006	+	0.751260i	$0.729446\pi$
$674$	−28.8168	+	16.6374i	−1.10998	+	0.640849i
$675$	−45.9964	−	20.8590i	−1.77040	−	0.802862i
$676$	−1.77729	+	3.07836i	−0.0683573	+	0.118398i
$677$	−2.26261	−	12.8319i	−0.0869591	−	0.493169i	−0.996917	−	0.0784680i	$-0.974997\pi$
$677$	−2.26261	−	12.8319i	−0.0869591	−	0.493169i	0.909958	−	0.414701i	$-0.136114\pi$
$678$	−17.9902	+	14.3282i	−0.690908	+	0.550270i
$679$	−22.5494	+	26.7317i	−0.865365	+	1.02587i
$680$	25.0344	+	4.41424i	0.960025	+	0.169278i
$681$	5.32521	−	1.78545i	0.204063	−	0.0684185i
$682$	−40.6949	+	7.17561i	−1.55829	+	0.274768i
$683$			41.4953i			1.58777i	0.608066	+	0.793886i	$0.291946\pi$
$683$			41.4953i			1.58777i	−0.608066	+	0.793886i	$0.708054\pi$
$684$	−1.97613	+	4.67150i	−0.0755592	+	0.178619i
$685$	−62.2710	−	35.9522i	−2.37925	−	1.37366i
$686$	19.5427	+	23.6628i	0.746143	+	0.903451i
$687$	−0.967735	+	37.8493i	−0.0369214	+	1.44404i
$688$	2.40711	+	2.01981i	0.0917703	+	0.0770044i
$689$	1.62001	−	9.18751i	0.0617173	−	0.350016i
$690$	13.1502	−	21.4890i	0.500620	−	0.818071i
$691$	−4.14114	−	4.93522i	−0.157536	−	0.187745i	0.681503	−	0.731815i	$-0.261327\pi$
$691$	−4.14114	−	4.93522i	−0.157536	−	0.187745i	−0.839039	+	0.544071i	$0.816882\pi$
$692$	−7.28201	+	12.6128i	−0.276821	+	0.479467i
$693$	−22.6461	+	2.74916i	−0.860253	+	0.104432i
$694$	0.522571	+	0.905120i	0.0198365	+	0.0343579i
$695$	−17.3364	+	47.6314i	−0.657608	+	1.80676i
$696$	−2.81029	−	2.48324i	−0.106524	−	0.0941269i
$697$	7.79696	+	6.54243i	0.295331	+	0.247812i
$698$	0.489925	−	2.77850i	0.0185439	−	0.105168i
$699$	10.0514	+	12.6204i	0.380180	+	0.477346i
$700$	−3.28169	−	18.8989i	−0.124036	−	0.714310i
$701$			10.7905i			0.407550i	0.979018	+	0.203775i	$0.0653211\pi$
$701$			10.7905i			0.407550i	−0.979018	+	0.203775i	$0.934679\pi$
$702$	20.5007	−	29.9473i	0.773748	−	1.13029i
$703$	−0.0480348	−	0.0277329i	−0.00181167	−	0.00104597i
$704$	−5.92261	−	7.05830i	−0.223217	−	0.266020i
$705$	−55.8562	+	44.4864i	−2.10367	+	1.67545i
$706$	−25.4661	+	30.3493i	−0.958428	+	1.14221i
$707$	5.48871	+	4.62997i	0.206424	+	0.174128i
$708$	−13.4153	+	4.49792i	−0.504179	+	0.169042i
$709$	−43.7116	−	15.9097i	−1.64163	−	0.597503i	−0.654303	−	0.756232i	$-0.727038\pi$
$709$	−43.7116	−	15.9097i	−1.64163	−	0.597503i	−0.987322	+	0.158730i	$0.949260\pi$
$710$	28.5278			1.07063
$711$	−37.8966	−	1.93916i	−1.42123	−	0.0727241i
$712$		−	9.83289i		−	0.368503i
$713$	3.44706	+	19.5493i	0.129093	+	0.732126i
$714$	21.3001	−	11.5103i	0.797135	−	0.430763i
$715$	43.6740	−	15.8960i	1.63332	−	0.594478i
$716$	1.42107	−	1.69357i	0.0531079	−	0.0632915i
$717$	−0.270378	+	10.5748i	−0.0100974	+	0.394923i
$718$	19.4825	+	7.09106i	0.727081	+	0.264636i
$719$	−15.8232			−0.590106			−0.295053	−	0.955481i	$-0.595337\pi$
$719$	−15.8232			−0.590106			−0.295053	+	0.955481i	$0.595337\pi$
$720$	−41.5933	−	38.6905i	−1.55009	−	1.44191i
$721$	22.3378	+	12.9744i	0.831903	+	0.483191i
$722$	14.7651	+	17.5964i	0.549500	+	0.654869i
$723$	0.564889	+	0.114565i	0.0210084	+	0.00426071i
$724$	12.2144	−	14.5566i	0.453946	−	0.540992i
$725$	−3.46361	−	9.51619i	−0.128635	−	0.353422i
$726$	−7.77607	+	1.16705i	−0.288597	+	0.0433133i
$727$	−11.4600	+	31.4861i	−0.425028	+	1.16775i	0.523767	+	0.851862i	$0.324526\pi$
$727$	−11.4600	+	31.4861i	−0.425028	+	1.16775i	−0.948795	+	0.315893i	$0.897696\pi$
$728$	−23.1744	−	0.0603089i	−0.858900	−	0.00223520i
$729$	−16.9138	+	21.0457i	−0.626437	+	0.779472i
$730$	7.07427	+	12.2530i	0.261831	+	0.453504i
$731$	−1.55501	+	1.30481i	−0.0575142	+	0.0482601i
$732$	6.13439	+	7.70222i	0.226733	+	0.284682i
$733$	5.74109	+	1.01231i	0.212052	+	0.0373905i	0.278665	−	0.960388i	$-0.410108\pi$
$733$	5.74109	+	1.01231i	0.212052	+	0.0373905i	−0.0666128	+	0.997779i	$0.521219\pi$
$734$	3.79329	−	21.5128i	0.140013	−	0.794053i
$735$	34.6971	+	30.9823i	1.27982	+	1.14280i
$736$	7.04927	−	5.91504i	0.259839	−	0.218031i
$737$	27.0576	+	15.6217i	0.996681	+	0.575434i
$738$	−4.65862	−	15.1707i	−0.171486	−	0.558439i
$739$	22.7016	+	39.3204i	0.835093	+	1.44642i	0.893955	+	0.448157i	$0.147919\pi$
$739$	22.7016	+	39.3204i	0.835093	+	1.44642i	−0.0588624	+	0.998266i	$0.518747\pi$
$740$	−0.0536434	+	0.0450122i	−0.00197197	+	0.00165468i
$741$	7.90500	+	14.5378i	0.290398	+	0.534059i
$742$	−9.12737	+	3.29522i	−0.335076	+	0.120971i
$743$	8.03623	+	22.0794i	0.294821	+	0.810013i	0.995344	+	0.0963839i	$0.0307276\pi$
$743$	8.03623	+	22.0794i	0.294821	+	0.810013i	−0.700524	+	0.713629i	$0.747050\pi$
$744$	31.2203	+	0.798246i	1.14459	+	0.0292651i
$745$	17.3468	−	47.6599i	0.635537	−	1.74612i
$746$	−16.0733	+	9.27994i	−0.588486	+	0.339763i
$747$	7.23496	−	11.1710i	0.264713	−	0.408727i
$748$	−5.91940	+	3.41757i	−0.216435	+	0.124959i
$749$	12.8690	−	35.0731i	0.470224	−	1.28154i
$750$	−16.5213	−	49.2760i	−0.603274	−	1.79930i
$751$	−21.6249	+	7.87082i	−0.789103	+	0.287210i	−0.704963	−	0.709244i	$-0.749037\pi$
$751$	−21.6249	+	7.87082i	−0.789103	+	0.287210i	−0.0841402	+	0.996454i	$0.526814\pi$
$752$	−49.8358	+	18.1388i	−1.81733	+	0.661452i
$753$	22.0930	+	8.68690i	0.805112	+	0.316568i
$754$	7.16649	−	1.26364i	0.260988	−	0.0460192i
$755$	−48.1920			−1.75389
$756$	−10.2223	−	0.812230i	−0.371781	−	0.0295405i
$757$	−0.0748603			−0.00272084			−0.00136042	−	0.999999i	$-0.500433\pi$
$757$	−0.0748603			−0.00272084			−0.00136042	+	0.999999i	$0.500433\pi$
$758$	10.1954	−	1.79773i	0.370315	−	0.0652966i
$759$	−1.69038	−	11.2630i	−0.0613570	−	0.408823i
$760$	16.9826	−	6.18118i	0.616025	−	0.224215i
$761$	2.80845	−	1.02219i	0.101806	−	0.0370544i	−0.290615	−	0.956840i	$-0.593860\pi$
$761$	2.80845	−	1.02219i	0.101806	−	0.0370544i	0.392421	+	0.919786i	$0.371638\pi$
$762$	19.0835	+	3.87031i	0.691322	+	0.140207i
$763$	−2.25326	−	12.9762i	−0.0815734	−	0.469771i
$764$	−14.6451	+	8.45534i	−0.529840	+	0.305903i
$765$	29.2805	−	22.1212i	1.05864	−	0.799792i
$766$	20.5772	−	11.8803i	0.743486	−	0.429252i
$767$	−15.7881	+	43.3774i	−0.570074	+	1.56627i
$768$	−13.0078	−	23.9222i	−0.469380	−	0.863219i
$769$	5.62460	+	15.4535i	0.202828	+	0.557266i	0.998847	−	0.0480060i	$-0.0152867\pi$
$769$	5.62460	+	15.4535i	0.202828	+	0.557266i	−0.796019	+	0.605272i	$0.793064\pi$
$770$	−36.9525	−	31.1711i	−1.33168	−	1.12333i
$771$	0.0714001	+	0.00182557i	0.00257141	+	6.57462e-5i
$772$	8.52862	−	7.15636i	0.306952	−	0.257563i
$773$	−19.5197	−	33.8091i	−0.702074	−	1.21603i	−0.967737	−	0.251962i	$-0.918924\pi$
$773$	−19.5197	−	33.8091i	−0.702074	−	1.21603i	0.265663	−	0.964066i	$-0.414409\pi$
$774$	3.14098	−	0.389601i	0.112900	−	0.0140039i
$775$	73.0348	+	42.1667i	2.62349	+	1.51467i
$776$	−21.0427	+	17.6569i	−0.755388	+	0.633846i
$777$	0.0225740	−	0.109839i	0.000809840	−	0.00394044i
$778$	2.48453	−	14.0905i	0.0890747	−	0.505168i
$779$	7.12618	+	1.25654i	0.255322	+	0.0450201i
$780$	20.6607	−	3.10081i	0.739773	−	0.111027i
$781$	9.87939	−	8.28979i	0.353512	−	0.296632i
$782$	6.04378	+	10.4681i	0.216125	+	0.374340i
$783$	−5.38795	+	0.528874i	−0.192550	+	0.0189004i
$784$	17.1181	+	30.0090i	0.611360	+	1.07175i
$785$	−23.7981	+	65.3847i	−0.849390	+	2.33368i
$786$	35.9469	+	45.1343i	1.28218	+	1.60989i
$787$	1.64760	+	4.52676i	0.0587308	+	0.161361i	0.965588	−	0.260076i	$-0.0837478\pi$
$787$	1.64760	+	4.52676i	0.0587308	+	0.161361i	−0.906857	+	0.421438i	$0.861526\pi$
$788$	9.14278	−	10.8959i	0.325698	−	0.388152i
$789$	15.9988	−	18.1059i	0.569573	−	0.644586i
$790$	−51.6900	−	61.6018i	−1.83905	−	2.19169i
$791$	18.3878	−	10.5525i	0.653796	−	0.375204i
$792$	−17.8948	−	0.915670i	−0.635862	−	0.0325369i
$793$	32.1239			1.14075
$794$	−0.0113182	−	0.00411950i	−0.000401669	−	0.000146196i
$795$	−12.9218	+	7.02627i	−0.458287	+	0.249196i
$796$	−2.78463	+	3.31859i	−0.0986984	+	0.117624i
$797$	16.1079	−	5.86280i	0.570572	−	0.207671i	−0.0405913	−	0.999176i	$-0.512924\pi$
$797$	16.1079	−	5.86280i	0.570572	−	0.207671i	0.611163	+	0.791505i	$0.290702\pi$
$798$	9.02274	−	14.6584i	0.319401	−	0.518901i
$799$	−5.94927	−	33.7400i	−0.210470	−	1.19364i
$800$		−	39.0940i		−	1.38218i
$801$	−10.3934	−	9.66801i	−0.367232	−	0.341602i
$802$	−25.1051			−0.886491
$803$	6.01042	+	2.18761i	0.212103	+	0.0771992i
$804$	10.5244	+	9.29964i	0.371168	+	0.327973i
$805$	−14.9742	+	17.7515i	−0.527769	+	0.625657i
$806$	−38.9533	+	46.4228i	−1.37207	+	1.63517i
$807$	5.78541	+	38.5483i	0.203656	+	1.35696i
$808$	3.62542	+	4.32061i	0.127542	+	0.151999i
$809$	−1.45376	−	0.839326i	−0.0511113	−	0.0295091i	0.474227	−	0.880403i	$-0.342728\pi$
$809$	−1.45376	−	0.839326i	−0.0511113	−	0.0295091i	−0.525338	+	0.850894i	$0.676061\pi$
$810$	−57.0689	+	4.13229i	−2.00520	+	0.145194i
$811$			24.2899i			0.852933i	0.904503	+	0.426467i	$0.140242\pi$
$811$			24.2899i			0.852933i	−0.904503	+	0.426467i	$0.859758\pi$
$812$	−1.31757	−	1.57855i	−0.0462377	−	0.0553961i
$813$	4.04740	−	10.2936i	0.141949	−	0.361011i
$814$	−0.0202368	+	0.114768i	−0.000709299	+	0.00402263i
$815$	−17.2782	−	14.4981i	−0.605229	−	0.507848i
$816$	25.8414	−	8.66416i	0.904630	−	0.303306i
$817$	−0.493589	+	1.35612i	−0.0172685	+	0.0474448i
$818$	−8.48147	−	14.6903i	−0.296548	−	0.513636i
$819$	−22.8496	+	24.4361i	−0.798428	+	0.853865i
$820$	4.56785	−	7.91175i	0.159516	−	0.276290i
$821$	1.25319	+	1.49349i	0.0437366	+	0.0521233i	0.787469	−	0.616354i	$-0.211391\pi$
$821$	1.25319	+	1.49349i	0.0437366	+	0.0521233i	−0.743733	+	0.668477i	$0.766946\pi$
$822$	−53.7734	−	1.37489i	−1.87556	−	0.0479546i
$823$	4.76626	−	27.0308i	0.166141	−	0.942234i	−0.781739	−	0.623606i	$-0.785667\pi$
$823$	4.76626	−	27.0308i	0.166141	−	0.942234i	0.947880	−	0.318628i	$-0.103222\pi$
$824$	15.5433	+	13.0423i	0.541475	+	0.454352i
$825$	−41.2708	−	25.2558i	−1.43687	−	0.879293i
$826$	47.3076	−	8.21472i	1.64604	−	0.285827i
$827$	−39.0581	−	22.5502i	−1.35818	−	0.784147i	−0.368804	−	0.929507i	$-0.620233\pi$
$827$	−39.0581	−	22.5502i	−1.35818	−	0.784147i	−0.989379	+	0.145360i	$0.953566\pi$
$828$	0.261628	−	5.11294i	0.00909219	−	0.177687i
$829$			35.8296i			1.24441i	0.782853	+	0.622207i	$0.213764\pi$
$829$			35.8296i			1.24441i	−0.782853	+	0.622207i	$0.786236\pi$
$830$	27.7765	−	4.89774i	0.964136	−	0.170003i
$831$	8.14102	+	7.19361i	0.282409	+	0.249544i
$832$	−13.3072	−	2.34641i	−0.461343	−	0.0813473i
$833$	−21.0118	+	7.52405i	−0.728016	+	0.260693i
$834$	5.62800	+	37.4994i	0.194882	+	1.29850i
$835$	−5.52441	−	31.3305i	−0.191180	−	1.08424i
$836$	−2.42969	+	4.20835i	−0.0840326	+	0.145549i
$837$	31.5406	−	32.2151i	1.09020	−	1.11352i
$838$	57.2173	−	33.0344i	1.97654	−	1.14115i
$839$	−30.2589	−	11.0133i	−1.04465	−	0.380222i	−0.238010	−	0.971263i	$-0.576495\pi$
$839$	−30.2589	−	11.0133i	−1.04465	−	0.380222i	−0.806642	+	0.591040i	$0.798717\pi$
$840$	22.6880	+	28.6392i	0.782809	+	0.988146i
$841$	21.3837	+	17.9431i	0.737369	+	0.618726i
$842$	−12.4520	−	34.2116i	−0.429124	−	1.17901i
$843$	−7.28898	+	8.24895i	−0.251046	+	0.284109i
$844$	−0.134686	−	0.763845i	−0.00463610	−	0.0262926i
$845$	9.14163	−	15.8338i	0.314482	−	0.544698i
$846$	−20.8117	+	49.1980i	−0.715520	+	1.69146i
$847$	7.24838	+	0.0188631i	0.249057	+	0.000648145i
$848$	−10.7581	+	1.89694i	−0.369435	+	0.0651413i
$849$	−0.885213	+	0.481339i	−0.0303804	+	0.0165195i
$850$	50.5721	+	8.91722i	1.73461	+	0.305858i
$851$	0.0551332	+	0.00972146i	0.00188994	+	0.000333247i
$852$	5.09301	−	2.76935i	0.174484	−	0.0948764i
$853$	29.8196	−	5.25801i	1.02100	−	0.180031i	0.362007	−	0.932175i	$-0.382092\pi$
$853$	29.8196	−	5.25801i	1.02100	−	0.180031i	0.658998	+	0.752145i	$0.270981\pi$
$854$	−16.6318	−	28.9810i	−0.569127	−	0.991708i
$855$	10.1644	−	24.0282i	0.347614	−	0.821747i
$856$	14.6722	−	25.4130i	0.501485	−	0.868598i
$857$	8.06670	+	45.7485i	0.275553	+	1.56274i	0.737199	+	0.675675i	$0.236148\pi$
$857$	8.06670	+	45.7485i	0.275553	+	1.56274i	−0.461646	+	0.887064i	$0.652741\pi$
$858$	23.0225	−	26.0546i	0.785975	−	0.889489i
$859$	−15.7677	−	43.3213i	−0.537986	−	1.47810i	−0.849359	−	0.527816i	$-0.823011\pi$
$859$	−15.7677	−	43.3213i	−0.537986	−	1.47810i	0.311373	−	0.950288i	$-0.399211\pi$
$860$	1.39574	+	1.17116i	0.0475943	+	0.0399364i
$861$	2.13360	+	14.4727i	0.0727127	+	0.493228i
$862$	−10.1037	−	3.67746i	−0.344135	−	0.125255i
$863$	2.45633	−	1.41816i	0.0836143	−	0.0482748i	−0.457610	−	0.889153i	$-0.651294\pi$
$863$	2.45633	−	1.41816i	0.0836143	−	0.0482748i	0.541224	+	0.840878i	$0.317961\pi$
$864$	−20.2436	−	5.19537i	−0.688702	−	0.176750i
$865$	37.4556	−	64.8750i	1.27353	−	2.20582i
$866$	−0.427475	−	2.42433i	−0.0145262	−	0.0823821i
$867$	−1.75697	−	11.7067i	−0.0596697	−	0.397580i
$868$	16.8551	+	3.01725i	0.572098	+	0.102412i
$869$	−35.8012	−	6.31272i	−1.21447	−	0.214144i
$870$	−8.59746	−	7.59693i	−0.291481	−	0.257560i
$871$	45.1232	−	7.95643i	1.52894	−	0.269593i
$872$		−	10.3448i		−	0.350320i
$873$	−2.02647	+	39.6030i	−0.0685857	+	1.34036i
$874$	7.44223	+	4.29678i	0.251737	+	0.145341i
$875$	8.19644	+	47.2023i	0.277090	+	1.59573i
$876$	2.45242	+	1.50076i	0.0828595	+	0.0507060i
$877$	−37.7331	−	31.6619i	−1.27416	−	1.06915i	−0.994021	−	0.109185i	$-0.965176\pi$
$877$	−37.7331	−	31.6619i	−1.27416	−	1.06915i	−0.280136	−	0.959960i	$-0.590380\pi$
$878$	−3.62810	+	20.5760i	−0.122442	+	0.694405i
$879$	−17.2534	−	0.441138i	−0.581944	−	0.0148792i
$880$	−34.9818	−	41.6897i	−1.17924	−	1.40536i
$881$	13.9157	−	24.1027i	0.468833	−	0.812042i	−0.530533	−	0.847664i	$-0.678008\pi$
$881$	13.9157	−	24.1027i	0.468833	−	0.812042i	0.999365	+	0.0356225i	$0.0113414\pi$
$882$	33.8754	+	7.96254i	1.14064	+	0.268113i
$883$	20.7815	+	35.9946i	0.699354	+	1.21132i	0.968691	+	0.248270i	$0.0798621\pi$
$883$	20.7815	+	35.9946i	0.699354	+	1.21132i	−0.269337	+	0.963046i	$0.586805\pi$
$884$	−3.42837	+	9.41936i	−0.115308	+	0.316807i
$885$	69.0028	−	23.1354i	2.31950	−	0.777687i
$886$	1.97435	+	1.65668i	0.0663297	+	0.0556572i
$887$	4.60475	−	26.1148i	0.154612	−	0.876850i	−0.804527	−	0.593916i	$-0.797581\pi$
$887$	4.60475	−	26.1148i	0.154612	−	0.876850i	0.959139	−	0.282934i	$-0.0913078\pi$
$888$	0.0322297	−	0.0819682i	0.00108156	−	0.00275067i
$889$	−16.8511	−	6.18302i	−0.565169	−	0.207372i
$890$		−	30.0816i		−	1.00834i
$891$	−18.5626	+	18.0145i	−0.621869	+	0.603507i
$892$	4.97559	+	2.87266i	0.166595	+	0.0961836i
$893$	−15.6565	−	18.6587i	−0.523925	−	0.624389i
$894$	−5.63136	−	37.5218i	−0.188341	−	1.25492i
$895$	−7.30939	+	8.71099i	−0.244326	+	0.291176i
$896$	12.0000	+	33.2386i	0.400891	+	1.11042i
$897$	−12.5163	−	11.0597i	−0.417906	−	0.369272i
$898$	6.67667	+	2.43011i	0.222803	+	0.0810938i
$899$	9.04003			0.301502
$900$	−15.9252	−	14.8138i	−0.530841	−	0.493793i
$901$		−	7.05703i		−	0.235104i
$902$	−2.64010	−	14.9728i	−0.0879058	−	0.498538i
$903$	−2.91645	−	0.0821633i	−0.0970533	−	0.00273422i
$904$	15.6480	−	5.69541i	0.520445	−	0.189426i
$905$	−62.8259	+	74.8730i	−2.08840	+	2.48886i
$906$	−31.6724	+	17.2221i	−1.05225	+	0.572165i
$907$	12.1012	+	4.40449i	0.401815	+	0.146249i	0.535019	−	0.844840i	$-0.320304\pi$
$907$	12.1012	+	4.40449i	0.401815	+	0.146249i	−0.133204	+	0.991089i	$0.542527\pi$
$908$	2.41877			0.0802695
$909$	8.13152	+	0.416088i	0.269706	+	0.0138008i
$910$	−70.8970	−	0.184502i	−2.35021	−	0.00611619i
$911$	−1.43534	−	1.71057i	−0.0475550	−	0.0566738i	0.741743	−	0.670685i	$-0.234000\pi$
$911$	−1.43534	−	1.71057i	−0.0475550	−	0.0566738i	−0.789298	+	0.614011i	$0.789555\pi$
$912$	12.8305	−	14.5203i	0.424861	−	0.480816i
$913$	8.19597	−	9.76757i	0.271247	−	0.323260i
$914$	−8.57840	−	23.5690i	−0.283748	−	0.779592i
$915$	−31.5527	−	39.6169i	−1.04310	−	1.30970i
$916$	−5.57667	+	15.3218i	−0.184258	+	0.506245i
$917$	−26.4745	−	46.1320i	−0.874265	−	1.52341i
$918$	11.3382	−	25.0021i	0.374218	−	0.825192i
$919$	−9.06589	−	15.7026i	−0.299056	−	0.517980i	0.676864	−	0.736108i	$-0.263338\pi$
$919$	−9.06589	−	15.7026i	−0.299056	−	0.517980i	−0.975920	+	0.218128i	$0.930005\pi$
$920$	−13.9736	+	11.7253i	−0.460697	+	0.386570i
$921$	3.83407	−	0.575425i	0.126337	−	0.0189609i
$922$	11.3709	+	2.00500i	0.374482	+	0.0660313i
$923$	3.28424	−	18.6258i	0.108102	−	0.613077i
$924$	−9.62299	−	1.97772i	−0.316573	−	0.0650622i
$925$	0.182195	−	0.152880i	0.00599053	−	0.00502665i
$926$	57.9615	+	33.4641i	1.90473	+	1.09970i
$927$	29.0684	−	3.60559i	0.954732	−	0.118423i
$928$	−2.09532	−	3.62921i	−0.0687824	−	0.119135i
$929$	14.7593	−	12.3845i	0.484237	−	0.406323i	−0.367719	−	0.929937i	$-0.619861\pi$
$929$	14.7593	−	12.3845i	0.484237	−	0.406323i	0.851956	+	0.523614i	$0.175417\pi$
$930$	95.5119	+	2.44206i	3.13196	+	0.0800783i
$931$	−10.2622	+	12.1016i	−0.336331	+	0.396613i
$932$	2.37638	+	6.52906i	0.0778410	+	0.213866i
$933$	−3.08147	−	5.66702i	−0.100883	−	0.185530i
$934$	−4.77761	+	13.1264i	−0.156328	+	0.429508i
$935$	30.4469	−	17.5785i	0.995720	−	0.574879i
$936$	−20.9665	+	15.8400i	−0.685312	+	0.517747i
$937$	26.1439	−	15.0942i	0.854085	−	0.493106i	−0.00794190	−	0.999968i	$-0.502528\pi$
$937$	26.1439	−	15.0942i	0.854085	−	0.493106i	0.862027	+	0.506862i	$0.169195\pi$
$938$	−30.5400	−	36.5891i	−0.997166	−	1.19468i
$939$	−24.7016	−	5.00973i	−0.806107	−	0.163486i
$940$	−28.8968	+	10.5176i	−0.942510	+	0.343046i
$941$	2.92209	−	1.06355i	0.0952573	−	0.0346708i	−0.293952	−	0.955820i	$-0.594971\pi$
$941$	2.92209	−	1.06355i	0.0952573	−	0.0346708i	0.389209	+	0.921149i	$0.372748\pi$
$942$	7.72568	+	51.4763i	0.251716	+	1.67719i
$943$	−7.19271	+	1.26827i	−0.234227	+	0.0413005i
$944$	54.0524			1.75926
$945$	52.5792	+	4.17777i	1.71040	+	0.135903i
$946$	3.03221			0.0985856
$947$	49.0430	−	8.64760i	1.59368	−	0.281009i	0.694802	−	0.719201i	$-0.255492\pi$
$947$	49.0430	−	8.64760i	1.59368	−	0.281009i	0.898881	+	0.438192i	$0.144381\pi$
$948$	−15.2081	−	5.97979i	−0.493936	−	0.194215i
$949$	8.81441	−	3.20818i	0.286128	−	0.104142i
$950$	34.3067	−	12.4866i	1.11306	−	0.405119i
$951$	0.674623	+	2.01211i	0.0218762	+	0.0652471i
$952$	−17.2717	+	2.99914i	−0.559778	+	0.0972026i
$953$	−24.6725	+	14.2447i	−0.799222	+	0.461431i	−0.843199	−	0.537602i	$-0.819330\pi$
$953$	−24.6725	+	14.2447i	−0.799222	+	0.461431i	0.0439773	+	0.999033i	$0.485997\pi$
$954$	−5.98142	+	9.23553i	−0.193656	+	0.299011i
$955$	75.3281	−	43.4907i	2.43756	−	1.40733i
$956$	−1.55808	+	4.28078i	−0.0503918	+	0.138450i
$957$	−5.18492	−	0.132569i	−0.167605	−	0.00428534i
$958$	−13.0460	−	35.8436i	−0.421498	−	1.15806i
$959$	48.8096	+	8.73749i	1.57615	+	0.282148i
$960$	10.1768	+	18.7158i	0.328456	+	0.604051i
$961$	−33.9221	+	28.4641i	−1.09426	+	0.918196i
$962$	0.0854535	+	0.148010i	0.00275513	+	0.00477202i
$963$	−12.4354	−	40.4954i	−0.400725	−	1.30495i
$964$	0.214966	+	0.124111i	0.00692359	+	0.00399734i
$965$	−43.8676	+	36.8093i	−1.41215	+	1.18493i
$966$	−3.49749	+	17.0177i	−0.112530	+	0.547536i
$967$	0.546444	−	3.09904i	0.0175725	−	0.0996584i	−0.974760	−	0.223255i	$-0.928332\pi$
$967$	0.546444	−	3.09904i	0.0175725	−	0.0996584i	0.992333	+	0.123597i	$0.0394429\pi$
$968$	5.60683	+	0.988636i	0.180210	+	0.0317760i
$969$	7.79843	+	9.79156i	0.250522	+	0.314550i
$970$	−64.3755	+	54.0175i	−2.06697	+	1.73440i
$971$	11.2478	+	19.4817i	0.360958	+	0.625197i	0.988119	−	0.153693i	$-0.0491165\pi$
$971$	11.2478	+	19.4817i	0.360958	+	0.625197i	−0.627161	+	0.778890i	$0.715783\pi$
$972$	−9.78723	+	6.27771i	−0.313925	+	0.201358i
$973$	0.0909659	−	34.9547i	0.00291623	−	1.12060i
$974$	14.9814	−	41.1610i	0.480034	−	1.31888i
$975$	−70.1722	+	10.5316i	−2.24731	+	0.337281i
$976$	−12.8652	−	35.3469i	−0.411805	−	1.13143i
$977$	−28.7374	+	34.2480i	−0.919392	+	1.09569i	0.0757387	+	0.997128i	$0.475869\pi$
$977$	−28.7374	+	34.2480i	−0.919392	+	1.09569i	−0.995131	+	0.0985613i	$0.968576\pi$
$978$	−16.5366	−	3.35377i	−0.528782	−	0.107242i
$979$	−8.74128	−	10.4175i	−0.279373	−	0.332943i
$980$	9.92575	+	17.4004i	0.317066	+	0.555836i
$981$	−10.9345	−	10.1714i	−0.349111	−	0.324747i
$982$	21.6468			0.690778
$983$	−0.767586	−	0.279378i	−0.0244822	−	0.00891078i	0.329750	−	0.944068i	$-0.393036\pi$
$983$	−0.767586	−	0.279378i	−0.0244822	−	0.00891078i	−0.354232	+	0.935157i	$0.615258\pi$
$984$	−0.293696	+	11.4868i	−0.00936270	+	0.366186i
$985$	−47.0266	+	56.0441i	−1.49839	+	1.78571i
$986$	5.17268	−	1.88270i	0.164732	−	0.0599574i
$987$	25.8124	−	41.9350i	0.821618	−	1.33480i
$988$	1.23748	+	7.01812i	0.0393696	+	0.223276i
$989$		−	1.45663i		−	0.0463181i
$990$	−54.7451	−	2.80129i	−1.73991	−	0.0890309i
$991$	−10.8376			−0.344267			−0.172134	−	0.985074i	$-0.555066\pi$
$991$	−10.8376			−0.344267			−0.172134	+	0.985074i	$0.555066\pi$
$992$	32.7936	+	11.9359i	1.04120	+	0.378965i
$993$	−33.6501	+	11.2823i	−1.06785	+	0.358032i
$994$	−18.5039	+	6.68040i	−0.586909	+	0.211889i
$995$	14.3229	−	17.0694i	0.454068	−	0.541137i
$996$	4.48342	−	3.57079i	0.142063	−	0.113145i
$997$	32.7273	+	39.0028i	1.03648	+	1.23523i	0.971424	+	0.237351i	$0.0762790\pi$
$997$	32.7273	+	39.0028i	1.03648	+	1.23523i	0.0650587	+	0.997881i	$0.479277\pi$
$998$	−37.1151	−	21.4284i	−1.17486	−	0.678305i
$999$	−0.0549512	−	0.114661i	−0.00173858	−	0.00362770i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.bd.a.185.5	yes	132
3.2	odd	2		567.2.bd.a.17.18		132
7.5	odd	6		189.2.ba.a.131.18	yes	132
21.5	even	6		567.2.ba.a.341.5		132
27.7	even	9		567.2.ba.a.143.5		132
27.20	odd	18		189.2.ba.a.101.18	✓	132
189.47	even	18	inner	189.2.bd.a.47.5	yes	132
189.61	odd	18		567.2.bd.a.467.18		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.18	✓	132	27.20	odd	18
189.2.ba.a.131.18	yes	132	7.5	odd	6
189.2.bd.a.47.5	yes	132	189.47	even	18	inner
189.2.bd.a.185.5	yes	132	1.1	even	1	trivial
567.2.ba.a.143.5		132	27.7	even	9
567.2.ba.a.341.5		132	21.5	even	6
567.2.bd.a.17.18		132	3.2	odd	2
567.2.bd.a.467.18		132	189.61	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.bd (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.63190 + 0.287749i) q^{2} +(1.35485 - 1.07906i) q^{3} +(0.700923 - 0.255115i) q^{4} +(-3.60525 + 1.31220i) q^{5} +(-1.90049 + 2.15078i) q^{6} +(2.03118 - 1.69538i) q^{7} +(1.79971 - 1.03907i) q^{8} +(0.671243 - 2.92394i) q^{9} +O(q^{10})\)	\(q+(-1.63190 + 0.287749i) q^{2} +(1.35485 - 1.07906i) q^{3} +(0.700923 - 0.255115i) q^{4} +(-3.60525 + 1.31220i) q^{5} +(-1.90049 + 2.15078i) q^{6} +(2.03118 - 1.69538i) q^{7} +(1.79971 - 1.03907i) q^{8} +(0.671243 - 2.92394i) q^{9} +(5.50583 - 3.17879i) q^{10} +(0.982995 - 2.70076i) q^{11} +(0.674361 - 1.10198i) q^{12} +(-1.44158 - 3.96072i) q^{13} +(-2.82685 + 3.35116i) q^{14} +(-3.46863 + 5.66814i) q^{15} +(-3.78076 + 3.17244i) q^{16} +(-1.59416 - 2.76117i) q^{17} +(-0.254044 + 4.96474i) q^{18} +(-1.96303 - 1.13336i) q^{19} +(-2.19224 + 1.83951i) q^{20} +(0.922531 - 4.48876i) q^{21} +(-0.827014 + 4.69023i) q^{22} +(2.25312 + 0.397286i) q^{23} +(1.31713 - 3.34978i) q^{24} +(7.44573 - 6.24771i) q^{25} +(3.49221 + 6.04869i) q^{26} +(-2.24568 - 4.68582i) q^{27} +(0.991186 - 1.70651i) q^{28} +(0.356349 - 0.979061i) q^{29} +(4.02946 - 10.2479i) q^{30} +(2.96755 + 8.15327i) q^{31} +(2.58538 - 3.08114i) q^{32} +(-1.58248 - 4.71984i) q^{33} +(3.39605 + 4.04725i) q^{34} +(-5.09824 + 8.77758i) q^{35} +(-0.275452 - 2.22070i) q^{36} +0.0244697 q^{37} +(3.52960 + 1.28467i) q^{38} +(-6.22700 - 3.81062i) q^{39} +(-5.12495 + 6.10768i) q^{40} +(-2.99981 + 1.09184i) q^{41} +(-0.213847 + 7.59067i) q^{42} +(-0.110557 - 0.627001i) q^{43} -2.14380i q^{44} +(1.41681 + 11.4223i) q^{45} -3.79119 q^{46} +(10.0976 + 3.67521i) q^{47} +(-1.69911 + 8.37787i) q^{48} +(1.25140 - 6.88723i) q^{49} +(-10.3529 + 12.3382i) q^{50} +(-5.13934 - 2.02078i) q^{51} +(-2.02088 - 2.40839i) q^{52} +(1.91685 + 1.10670i) q^{53} +(5.01308 + 7.00061i) q^{54} +11.0268i q^{55} +(1.89394 - 5.16172i) q^{56} +(-3.88258 + 0.582707i) q^{57} +(-0.299804 + 1.70027i) q^{58} +(-8.38964 - 7.03975i) q^{59} +(-0.985213 + 4.85782i) q^{60} +(-2.60670 + 7.16186i) q^{61} +(-7.18884 - 12.4514i) q^{62} +(-3.59376 - 7.07707i) q^{63} +(1.60294 - 2.77637i) q^{64} +(10.3945 + 12.3877i) q^{65} +(3.94057 + 7.24696i) q^{66} +(-1.88769 + 10.7056i) q^{67} +(-1.82180 - 1.52867i) q^{68} +(3.48134 - 1.89300i) q^{69} +(5.79410 - 15.7912i) q^{70} +(3.88604 + 2.24361i) q^{71} +(-1.83012 - 5.95972i) q^{72} +2.22546i q^{73} +(-0.0399322 + 0.00704112i) q^{74} +(3.34618 - 16.4991i) q^{75} +(-1.66507 - 0.293597i) q^{76} +(-2.58216 - 7.15227i) q^{77} +(11.2584 + 4.42676i) q^{78} +(-2.19643 - 12.4566i) q^{79} +(9.46771 - 16.3986i) q^{80} +(-8.09886 - 3.92535i) q^{81} +(4.58122 - 2.64497i) q^{82} +(4.16888 + 1.51735i) q^{83} +(-0.498526 - 3.38162i) q^{84} +(9.37059 + 7.86286i) q^{85} +(0.360837 + 0.991392i) q^{86} +(-0.573669 - 1.71100i) q^{87} +(-1.03715 - 5.88198i) q^{88} +(2.36580 - 4.09769i) q^{89} +(-5.59885 - 18.2325i) q^{90} +(-9.64302 - 5.60091i) q^{91} +(1.68062 - 0.296338i) q^{92} +(12.8185 + 7.84430i) q^{93} +(-17.5358 - 3.09203i) q^{94} +(8.56442 + 1.51014i) q^{95} +(0.178064 - 6.96428i) q^{96} +(-13.0174 + 2.29533i) q^{97} +(-0.0603728 + 11.5994i) q^{98} +(-7.23702 - 4.68708i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Introduction

L-functions

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