LMFDB - Embedded newform 418.2.j.a.111.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(23,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("418.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.j (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			111.3
Character	$\chi$	$=$	418.111
Dual form			418.2.j.a.177.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(0.361908 - 0.131724i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.0315845 + 0.179124i) q^{5} +(-0.361908 - 0.131724i) q^{6} +(-2.25138 - 3.89951i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.18451 + 1.83302i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(0.361908 - 0.131724i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.0315845 + 0.179124i) q^{5} +(-0.361908 - 0.131724i) q^{6} +(-2.25138 - 3.89951i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.18451 + 1.83302i) q^{9} +(0.139334 - 0.116915i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.192567 + 0.333537i) q^{12} +(0.715352 + 0.260367i) q^{13} +(-0.781898 + 4.43436i) q^{14} +(0.0121643 + 0.0689870i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-4.94895 - 4.15266i) q^{17} +2.85167 q^{18} +(-4.35887 - 0.0166052i) q^{19} -0.181888 q^{20} +(-1.32845 - 1.11471i) q^{21} +(-0.939693 + 0.342020i) q^{22} +(-0.621437 - 3.52435i) q^{23} +(0.0668780 - 0.379284i) q^{24} +(4.66738 + 1.69879i) q^{25} +(-0.380631 - 0.659272i) q^{26} +(-1.12684 + 1.95175i) q^{27} +(3.44932 - 2.89432i) q^{28} +(1.98892 - 1.66890i) q^{29} +(0.0350256 - 0.0606662i) q^{30} +(-3.72751 - 6.45624i) q^{31} +(0.939693 + 0.342020i) q^{32} +(0.0668780 - 0.379284i) q^{33} +(1.12184 + 6.36225i) q^{34} +(0.769607 - 0.280114i) q^{35} +(-2.18451 - 1.83302i) q^{36} +2.57990 q^{37} +(3.32841 + 2.81455i) q^{38} +0.293188 q^{39} +(0.139334 + 0.116915i) q^{40} +(-9.71352 + 3.53543i) q^{41} +(0.301136 + 1.70783i) q^{42} +(1.56903 - 8.89839i) q^{43} +(0.939693 + 0.342020i) q^{44} +(-0.259342 - 0.449193i) q^{45} +(-1.78936 + 3.09926i) q^{46} +(-5.75934 + 4.83266i) q^{47} +(-0.295030 + 0.247560i) q^{48} +(-6.63747 + 11.4964i) q^{49} +(-2.48346 - 4.30148i) q^{50} +(-2.33807 - 0.850988i) q^{51} +(-0.132192 + 0.749696i) q^{52} +(0.256460 + 1.45446i) q^{53} +(2.11777 - 0.770805i) q^{54} +(0.139334 + 0.116915i) q^{55} -4.50277 q^{56} +(-1.57970 + 0.568157i) q^{57} -2.59635 q^{58} +(3.39041 + 2.84489i) q^{59} +(-0.0658267 + 0.0239589i) q^{60} +(-0.172833 - 0.980187i) q^{61} +(-1.29455 + 7.34176i) q^{62} +(12.0660 + 4.39168i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.0692321 + 0.119913i) q^{65} +(-0.295030 + 0.247560i) q^{66} +(9.17313 - 7.69717i) q^{67} +(3.23020 - 5.59487i) q^{68} +(-0.689144 - 1.19363i) q^{69} +(-0.769607 - 0.280114i) q^{70} +(-1.29037 + 7.31803i) q^{71} +(0.495188 + 2.80835i) q^{72} +(5.67359 - 2.06502i) q^{73} +(-1.97632 - 1.65833i) q^{74} +1.91293 q^{75} +(-0.740556 - 4.29553i) q^{76} -4.50277 q^{77} +(-0.224595 - 0.188458i) q^{78} +(11.5585 - 4.20697i) q^{79} +(-0.0315845 - 0.179124i) q^{80} +(1.33484 - 7.57026i) q^{81} +(9.71352 + 3.53543i) q^{82} +(6.70102 + 11.6065i) q^{83} +(0.867087 - 1.50184i) q^{84} +(0.900153 - 0.755318i) q^{85} +(-6.92172 + 5.80801i) q^{86} +(0.499973 - 0.865978i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-2.47252 - 0.899923i) q^{89} +(-0.0900685 + 0.510804i) q^{90} +(-0.595229 - 3.37571i) q^{91} +(3.36289 - 1.22399i) q^{92} +(-2.19946 - 1.84556i) q^{93} +7.51829 q^{94} +(0.140647 - 0.780255i) q^{95} +0.385135 q^{96} +(-2.58173 - 2.16633i) q^{97} +(12.4744 - 4.54029i) q^{98} +(0.495188 + 2.80835i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{8}+O(q^{10}) $ 24 * q + 12 * q^8	$ 24 q + 12 q^{8} + 12 q^{11} - 3 q^{12} - 3 q^{13} + 3 q^{14} + 27 q^{15} - 6 q^{18} - 21 q^{19} - 18 q^{20} + 15 q^{21} + 9 q^{23} + 36 q^{25} - 21 q^{27} - 3 q^{28} - 9 q^{30} - 27 q^{31} - 9 q^{34} - 45 q^{35} + 18 q^{37} + 9 q^{38} + 36 q^{39} - 18 q^{41} + 39 q^{42} - 48 q^{43} + 36 q^{45} - 18 q^{46} - 9 q^{47} + 6 q^{49} + 3 q^{50} - 18 q^{51} - 3 q^{52} - 36 q^{53} - 45 q^{54} + 18 q^{58} + 9 q^{59} - 9 q^{60} + 15 q^{61} - 33 q^{62} + 87 q^{63} - 12 q^{64} - 36 q^{65} + 33 q^{67} + 9 q^{68} - 18 q^{69} + 45 q^{70} - 9 q^{71} - 3 q^{73} + 3 q^{74} + 42 q^{75} + 9 q^{76} + 12 q^{78} + 15 q^{79} - 108 q^{81} + 18 q^{82} + 36 q^{83} - 9 q^{84} - 99 q^{85} - 33 q^{86} + 63 q^{87} - 12 q^{88} - 27 q^{89} - 36 q^{90} - 21 q^{91} - 9 q^{92} - 21 q^{93} + 54 q^{94} + 18 q^{95} - 6 q^{96} + 45 q^{97} + 39 q^{98}+O(q^{100}) $ 24 * q + 12 * q^8 + 12 * q^11 - 3 * q^12 - 3 * q^13 + 3 * q^14 + 27 * q^15 - 6 * q^18 - 21 * q^19 - 18 * q^20 + 15 * q^21 + 9 * q^23 + 36 * q^25 - 21 * q^27 - 3 * q^28 - 9 * q^30 - 27 * q^31 - 9 * q^34 - 45 * q^35 + 18 * q^37 + 9 * q^38 + 36 * q^39 - 18 * q^41 + 39 * q^42 - 48 * q^43 + 36 * q^45 - 18 * q^46 - 9 * q^47 + 6 * q^49 + 3 * q^50 - 18 * q^51 - 3 * q^52 - 36 * q^53 - 45 * q^54 + 18 * q^58 + 9 * q^59 - 9 * q^60 + 15 * q^61 - 33 * q^62 + 87 * q^63 - 12 * q^64 - 36 * q^65 + 33 * q^67 + 9 * q^68 - 18 * q^69 + 45 * q^70 - 9 * q^71 - 3 * q^73 + 3 * q^74 + 42 * q^75 + 9 * q^76 + 12 * q^78 + 15 * q^79 - 108 * q^81 + 18 * q^82 + 36 * q^83 - 9 * q^84 - 99 * q^85 - 33 * q^86 + 63 * q^87 - 12 * q^88 - 27 * q^89 - 36 * q^90 - 21 * q^91 - 9 * q^92 - 21 * q^93 + 54 * q^94 + 18 * q^95 - 6 * q^96 + 45 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	0.361908	−	0.131724i	0.208948	−	0.0760508i	−0.235426	−	0.971892i	$-0.575648\pi$
$3$	0.361908	−	0.131724i	0.208948	−	0.0760508i	0.444374	+	0.895842i	$0.353426\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.0315845	+	0.179124i	−0.0141250	+	0.0801069i	−0.991055	−	0.133451i	$-0.957394\pi$
$5$	−0.0315845	+	0.179124i	−0.0141250	+	0.0801069i	0.976930	+	0.213558i	$0.0685052\pi$
$6$	−0.361908	−	0.131724i	−0.147748	−	0.0537760i
$7$	−2.25138	−	3.89951i	−0.850943	−	1.47388i	−0.880358	−	0.474310i	$-0.842698\pi$
$7$	−2.25138	−	3.89951i	−0.850943	−	1.47388i	0.0294144	−	0.999567i	$-0.490636\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−2.18451	+	1.83302i	−0.728169	+	0.611006i
$10$	0.139334	−	0.116915i	0.0440613	−	0.0369718i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	0.192567	+	0.333537i	0.0555894	+	0.0962837i
$13$	0.715352	+	0.260367i	0.198403	+	0.0722128i	0.439310	−	0.898335i	$-0.355223\pi$
$13$	0.715352	+	0.260367i	0.198403	+	0.0722128i	−0.240907	+	0.970548i	$0.577445\pi$
$14$	−0.781898	+	4.43436i	−0.208971	+	1.18513i
$15$	0.0121643	+	0.0689870i	0.00314080	+	0.0178124i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−4.94895	−	4.15266i	−1.20030	−	1.00717i	−0.999622	−	0.0275108i	$-0.991242\pi$
$17$	−4.94895	−	4.15266i	−1.20030	−	1.00717i	−0.200675	−	0.979658i	$-0.564314\pi$
$18$	2.85167			0.672145
$19$	−4.35887	−	0.0166052i	−0.999993	−	0.00380949i
$19$	−4.35887	−	0.0166052i	−0.999993	−	0.00380949i
$20$	−0.181888			−0.0406713
$21$	−1.32845	−	1.11471i	−0.289892	−	0.243249i
$22$	−0.939693	+	0.342020i	−0.200343	+	0.0729189i
$23$	−0.621437	−	3.52435i	−0.129579	−	0.734877i	−0.978483	−	0.206330i	$-0.933848\pi$
$23$	−0.621437	−	3.52435i	−0.129579	−	0.734877i	0.848904	−	0.528547i	$-0.177263\pi$
$24$	0.0668780	−	0.379284i	0.0136514	−	0.0774210i
$25$	4.66738	+	1.69879i	0.933475	+	0.339757i
$26$	−0.380631	−	0.659272i	−0.0746479	−	0.129294i
$27$	−1.12684	+	1.95175i	−0.216861	+	0.375614i
$28$	3.44932	−	2.89432i	0.651861	−	0.546976i
$29$	1.98892	−	1.66890i	0.369333	−	0.309908i	−0.439164	−	0.898407i	$-0.644725\pi$
$29$	1.98892	−	1.66890i	0.369333	−	0.309908i	0.808498	+	0.588499i	$0.200281\pi$
$30$	0.0350256	−	0.0606662i	0.00639478	−	0.0110761i
$31$	−3.72751	−	6.45624i	−0.669481	−	1.15957i	−0.978049	−	0.208373i	$-0.933183\pi$
$31$	−3.72751	−	6.45624i	−0.669481	−	1.15957i	0.308569	−	0.951202i	$-0.400150\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	0.0668780	−	0.379284i	0.0116420	−	0.0660248i
$34$	1.12184	+	6.36225i	0.192393	+	1.09112i
$35$	0.769607	−	0.280114i	0.130087	−	0.0473479i
$36$	−2.18451	−	1.83302i	−0.364084	−	0.305503i
$37$	2.57990			0.424134			0.212067	−	0.977255i	$-0.431981\pi$
$37$	2.57990			0.424134			0.212067	+	0.977255i	$0.431981\pi$
$38$	3.32841	+	2.81455i	0.539940	+	0.456580i
$39$	0.293188			0.0469477
$40$	0.139334	+	0.116915i	0.0220306	+	0.0184859i
$41$	−9.71352	+	3.53543i	−1.51700	+	0.552142i	−0.960396	−	0.278639i	$-0.910117\pi$
$41$	−9.71352	+	3.53543i	−1.51700	+	0.552142i	−0.556601	+	0.830780i	$0.687895\pi$
$42$	0.301136	+	1.70783i	0.0464663	+	0.263523i
$43$	1.56903	−	8.89839i	0.239274	−	1.35699i	−0.594148	−	0.804356i	$-0.702511\pi$
$43$	1.56903	−	8.89839i	0.239274	−	1.35699i	0.833422	−	0.552636i	$-0.186378\pi$
$44$	0.939693	+	0.342020i	0.141664	+	0.0515615i
$45$	−0.259342	−	0.449193i	−0.0386604	−	0.0669618i
$46$	−1.78936	+	3.09926i	−0.263826	+	0.456961i
$47$	−5.75934	+	4.83266i	−0.840086	+	0.704916i	−0.957583	−	0.288157i	$-0.906957\pi$
$47$	−5.75934	+	4.83266i	−0.840086	+	0.704916i	0.117497	+	0.993073i	$0.462513\pi$
$48$	−0.295030	+	0.247560i	−0.0425840	+	0.0357322i
$49$	−6.63747	+	11.4964i	−0.948210	+	1.64235i
$50$	−2.48346	−	4.30148i	−0.351214	−	0.608321i
$51$	−2.33807	−	0.850988i	−0.327395	−	0.119162i
$52$	−0.132192	+	0.749696i	−0.0183317	+	0.103964i
$53$	0.256460	+	1.45446i	0.0352275	+	0.199785i	0.997342	−	0.0728601i	$-0.0232126\pi$
$53$	0.256460	+	1.45446i	0.0352275	+	0.199785i	−0.962115	+	0.272645i	$0.912102\pi$
$54$	2.11777	−	0.770805i	0.288192	−	0.104893i
$55$	0.139334	+	0.116915i	0.0187878	+	0.0157648i
$56$	−4.50277			−0.601708
$57$	−1.57970	+	0.568157i	−0.209236	+	0.0752543i
$58$	−2.59635			−0.340918
$59$	3.39041	+	2.84489i	0.441394	+	0.370373i	0.836231	−	0.548378i	$-0.184754\pi$
$59$	3.39041	+	2.84489i	0.441394	+	0.370373i	−0.394837	+	0.918751i	$0.629199\pi$
$60$	−0.0658267	+	0.0239589i	−0.00849819	+	0.00309309i
$61$	−0.172833	−	0.980187i	−0.0221291	−	0.125500i	0.971742	−	0.236045i	$-0.0758514\pi$
$61$	−0.172833	−	0.980187i	−0.0221291	−	0.125500i	−0.993871	+	0.110545i	$0.964740\pi$
$62$	−1.29455	+	7.34176i	−0.164408	+	0.932405i
$63$	12.0660	+	4.39168i	1.52018	+	0.553300i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.0692321	+	0.119913i	−0.00858718	+	0.0148734i
$66$	−0.295030	+	0.247560i	−0.0363157	+	0.0304725i
$67$	9.17313	−	7.69717i	1.12068	−	0.940359i	0.122038	−	0.992525i	$-0.461057\pi$
$67$	9.17313	−	7.69717i	1.12068	−	0.940359i	0.998638	+	0.0521660i	$0.0166125\pi$
$68$	3.23020	−	5.59487i	0.391719	−	0.678477i
$69$	−0.689144	−	1.19363i	−0.0829632	−	0.143696i
$70$	−0.769607	−	0.280114i	−0.0919856	−	0.0334800i
$71$	−1.29037	+	7.31803i	−0.153138	+	0.868490i	0.807330	+	0.590100i	$0.200912\pi$
$71$	−1.29037	+	7.31803i	−0.153138	+	0.868490i	−0.960468	+	0.278390i	$0.910199\pi$
$72$	0.495188	+	2.80835i	0.0583584	+	0.330967i
$73$	5.67359	−	2.06502i	0.664043	−	0.241692i	0.0120621	−	0.999927i	$-0.496160\pi$
$73$	5.67359	−	2.06502i	0.664043	−	0.241692i	0.651981	+	0.758235i	$0.273938\pi$
$74$	−1.97632	−	1.65833i	−0.229743	−	0.192777i
$75$	1.91293			0.220886
$76$	−0.740556	−	4.29553i	−0.0849477	−	0.492731i
$77$	−4.50277			−0.513138
$78$	−0.224595	−	0.188458i	−0.0254304	−	0.0213387i
$79$	11.5585	−	4.20697i	1.30044	−	0.473321i	0.403299	−	0.915068i	$-0.367864\pi$
$79$	11.5585	−	4.20697i	1.30044	−	0.473321i	0.897139	+	0.441748i	$0.145641\pi$
$80$	−0.0315845	−	0.179124i	−0.00353125	−	0.0200267i
$81$	1.33484	−	7.57026i	0.148316	−	0.841140i
$82$	9.71352	+	3.53543i	1.07268	+	0.390423i
$83$	6.70102	+	11.6065i	0.735532	+	1.27398i	0.954490	+	0.298244i	$0.0964011\pi$
$83$	6.70102	+	11.6065i	0.735532	+	1.27398i	−0.218958	+	0.975734i	$0.570266\pi$
$84$	0.867087	−	1.50184i	0.0946069	−	0.163864i
$85$	0.900153	−	0.755318i	0.0976353	−	0.0819258i
$86$	−6.92172	+	5.80801i	−0.746388	+	0.626294i
$87$	0.499973	−	0.865978i	0.0536027	−	0.0928426i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	−2.47252	−	0.899923i	−0.262086	−	0.0953916i	0.207635	−	0.978206i	$-0.433423\pi$
$89$	−2.47252	−	0.899923i	−0.262086	−	0.0953916i	−0.469721	+	0.882815i	$0.655646\pi$
$90$	−0.0900685	+	0.510804i	−0.00949405	+	0.0538435i
$91$	−0.595229	−	3.37571i	−0.0623969	−	0.353871i
$92$	3.36289	−	1.22399i	0.350606	−	0.127610i
$93$	−2.19946	−	1.84556i	−0.228073	−	0.191376i
$94$	7.51829			0.775452
$95$	0.140647	−	0.780255i	0.0144301	−	0.0800525i
$96$	0.385135			0.0393077
$97$	−2.58173	−	2.16633i	−0.262135	−	0.219958i	0.502242	−	0.864727i	$-0.332509\pi$
$97$	−2.58173	−	2.16633i	−0.262135	−	0.219958i	−0.764377	+	0.644770i	$0.776953\pi$
$98$	12.4744	−	4.54029i	1.26010	−	0.458639i
$99$	0.495188	+	2.80835i	0.0497682	+	0.282250i
$100$	−0.862496	+	4.89146i	−0.0862496	+	0.489146i
$101$	14.8738	+	5.41361i	1.48000	+	0.538675i	0.950795	−	0.309822i	$-0.100269\pi$
$101$	14.8738	+	5.41361i	1.48000	+	0.538675i	0.529201	+	0.848496i	$0.322492\pi$
$102$	1.24406	+	2.15478i	0.123180	+	0.213355i
$103$	8.59925	−	14.8943i	0.847309	−	1.46758i	−0.0362913	−	0.999341i	$-0.511554\pi$
$103$	8.59925	−	14.8943i	0.847309	−	1.46758i	0.883601	−	0.468241i	$-0.155112\pi$
$104$	0.583160	−	0.489330i	0.0571836	−	0.0479827i
$105$	0.241629	−	0.202751i	0.0235806	−	0.0197865i
$106$	0.738447	−	1.27903i	0.0717243	−	0.124230i
$107$	−3.24214	−	5.61554i	−0.313429	−	0.542875i	0.665673	−	0.746243i	$-0.268144\pi$
$107$	−3.24214	−	5.61554i	−0.313429	−	0.542875i	−0.979102	+	0.203368i	$0.934811\pi$
$108$	−2.11777	−	0.770805i	−0.203782	−	0.0741707i
$109$	1.39608	−	7.91754i	0.133720	−	0.758362i	−0.842023	−	0.539442i	$-0.818635\pi$
$109$	1.39608	−	7.91754i	0.133720	−	0.758362i	0.975743	−	0.218921i	$-0.0702536\pi$
$110$	−0.0315845	−	0.179124i	−0.00301146	−	0.0170788i
$111$	0.933689	−	0.339835i	0.0886218	−	0.0322557i
$112$	3.44932	+	2.89432i	0.325930	+	0.273488i
$113$	−7.52691			−0.708072			−0.354036	−	0.935232i	$-0.615191\pi$
$113$	−7.52691			−0.708072			−0.354036	+	0.935232i	$0.615191\pi$
$114$	1.57532	+	0.580176i	0.147543	+	0.0543385i
$115$	0.650924			0.0606990
$116$	1.98892	+	1.66890i	0.184667	+	0.154954i
$117$	−2.03995	+	0.742481i	−0.188593	+	0.0686424i
$118$	−0.768543	−	4.35862i	−0.0707501	−	0.401244i
$119$	−5.05137	+	28.6477i	−0.463058	+	2.62613i
$120$	0.0658267	+	0.0239589i	0.00600913	+	0.00218714i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−0.497654	+	0.861962i	−0.0450555	+	0.0780384i
$123$	−3.04970	+	2.55900i	−0.274982	+	0.230738i
$124$	5.71088	−	4.79200i	0.512852	−	0.430334i
$125$	−0.906430	+	1.56998i	−0.0810735	+	0.140423i
$126$	−6.42021	−	11.1201i	−0.571958	−	0.990660i
$127$	15.5930	+	5.67540i	1.38366	+	0.503610i	0.923285	−	0.384115i	$-0.125493\pi$
$127$	15.5930	+	5.67540i	1.38366	+	0.503610i	0.460373	+	0.887725i	$0.347716\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	−0.604287	−	3.42708i	−0.0532045	−	0.301738i
$130$	0.130114	−	0.0473575i	0.0114117	−	0.00415353i
$131$	5.66616	+	4.75447i	0.495055	+	0.415400i	0.855834	−	0.517251i	$-0.173045\pi$
$131$	5.66616	+	4.75447i	0.495055	+	0.415400i	−0.360779	+	0.932651i	$0.617489\pi$
$132$	0.385135			0.0335217
$133$	9.74874	+	17.0348i	0.845323	+	1.47711i
$134$	−11.9747			−1.03445
$135$	−0.314015	−	0.263490i	−0.0270261	−	0.0226776i
$136$	−6.07079	+	2.20959i	−0.520566	+	0.189470i
$137$	−0.817347	−	4.63541i	−0.0698307	−	0.396030i	−0.999610	−	0.0279130i	$-0.991114\pi$
$137$	−0.817347	−	4.63541i	−0.0698307	−	0.396030i	0.929780	−	0.368117i	$-0.119997\pi$
$138$	−0.239337	+	1.35735i	−0.0203737	+	0.115545i
$139$	−6.65728	−	2.42305i	−0.564663	−	0.205520i	0.0438865	−	0.999037i	$-0.486026\pi$
$139$	−6.65728	−	2.42305i	−0.564663	−	0.205520i	−0.608549	+	0.793516i	$0.708248\pi$
$140$	0.409499	+	0.709273i	0.0346090	+	0.0599445i
$141$	−1.44778	+	2.50762i	−0.121925	+	0.211180i
$142$	5.69242	−	4.77651i	0.477697	−	0.400835i
$143$	0.583160	−	0.489330i	0.0487663	−	0.0409198i
$144$	1.42584	−	2.46962i	0.118820	−	0.205802i
$145$	0.236122	+	0.408976i	0.0196089	+	0.0339636i
$146$	−5.67359	−	2.06502i	−0.469549	−	0.170902i
$147$	−0.887801	+	5.03497i	−0.0732246	+	0.415277i
$148$	0.447996	+	2.54071i	0.0368250	+	0.208845i
$149$	−14.6397	+	5.32842i	−1.19933	+	0.436521i	−0.862991	−	0.505219i	$-0.831412\pi$
$149$	−14.6397	+	5.32842i	−1.19933	+	0.436521i	−0.336341	+	0.941740i	$0.609190\pi$
$150$	−1.46539	−	1.22961i	−0.119649	−	0.100397i
$151$	2.38954			0.194458			0.0972289	−	0.995262i	$-0.469002\pi$
$151$	2.38954			0.194458			0.0972289	+	0.995262i	$0.469002\pi$
$152$	−2.19381	+	3.76659i	−0.177942	+	0.305511i
$153$	18.4229			1.48941
$154$	3.44932	+	2.89432i	0.277954	+	0.233231i
$155$	1.27420	−	0.463771i	0.102346	−	0.0372510i
$156$	0.0509116	+	0.288734i	0.00407619	+	0.0231172i
$157$	−2.08461	+	11.8224i	−0.166370	+	0.943531i	0.781271	+	0.624192i	$0.214572\pi$
$157$	−2.08461	+	11.8224i	−0.166370	+	0.943531i	−0.947641	+	0.319339i	$0.896539\pi$
$158$	−11.5585	−	4.20697i	−0.919549	−	0.334688i
$159$	0.284402	+	0.492598i	0.0225545	+	0.0390656i
$160$	−0.0909438	+	0.157519i	−0.00718974	+	0.0124530i
$161$	−12.3441	+	10.3580i	−0.972854	+	0.816322i
$162$	−5.88862	+	4.94114i	−0.462653	+	0.388212i
$163$	−9.37925	+	16.2453i	−0.734640	+	1.27243i	0.220241	+	0.975445i	$0.429316\pi$
$163$	−9.37925	+	16.2453i	−0.734640	+	1.27243i	−0.954881	+	0.296988i	$0.904018\pi$
$164$	−5.16846	−	8.95203i	−0.403589	−	0.699036i
$165$	0.0658267	+	0.0239589i	0.00512460	+	0.00186520i
$166$	2.32724	−	13.1984i	0.180629	−	1.02440i
$167$	−3.81905	−	21.6589i	−0.295527	−	1.67602i	−0.665053	−	0.746796i	$-0.731591\pi$
$167$	−3.81905	−	21.6589i	−0.295527	−	1.67602i	0.369526	−	0.929220i	$-0.379520\pi$
$168$	−1.62959	+	0.593122i	−0.125726	+	0.0457604i
$169$	−9.51464	−	7.98373i	−0.731895	−	0.614133i
$170$	−1.17507			−0.0901235
$171$	9.55241	−	7.95361i	0.730491	−	0.608228i
$172$	9.03566			0.688963
$173$	−1.99540	−	1.67434i	−0.151708	−	0.127298i	0.563775	−	0.825929i	$-0.309349\pi$
$173$	−1.99540	−	1.67434i	−0.151708	−	0.127298i	−0.715482	+	0.698631i	$0.753793\pi$
$174$	−0.939642	+	0.342002i	−0.0712341	+	0.0259271i
$175$	−3.88362	−	22.0251i	−0.293574	−	1.66494i
$176$	−0.173648	+	0.984808i	−0.0130892	+	0.0742327i
$177$	1.60176	+	0.582992i	0.120395	+	0.0438204i
$178$	1.31560	+	2.27868i	0.0986083	+	0.170795i
$179$	10.1837	−	17.6387i	0.761168	−	1.31838i	−0.181081	−	0.983468i	$-0.557960\pi$
$179$	10.1837	−	17.6387i	0.761168	−	1.31838i	0.942249	−	0.334914i	$-0.108707\pi$
$180$	0.397335	−	0.333404i	0.0296156	−	0.0248504i
$181$	−5.38395	+	4.51767i	−0.400186	+	0.335796i	−0.820566	−	0.571552i	$-0.806341\pi$
$181$	−5.38395	+	4.51767i	−0.400186	+	0.335796i	0.420379	+	0.907348i	$0.361897\pi$
$182$	−1.71389	+	2.96855i	−0.127042	+	0.220044i
$183$	−0.191664	−	0.331972i	−0.0141682	−	0.0245401i
$184$	−3.36289	−	1.22399i	−0.247916	−	0.0902339i
$185$	−0.0814849	+	0.462124i	−0.00599089	+	0.0339760i
$186$	0.498577	+	2.82757i	0.0365574	+	0.207327i
$187$	−6.07079	+	2.20959i	−0.443940	+	0.161581i
$188$	−5.75934	−	4.83266i	−0.420043	−	0.352458i
$189$	10.1478			0.738145
$190$	−0.609280	+	0.507304i	−0.0442018	+	0.0368037i
$191$	6.09687			0.441154			0.220577	−	0.975370i	$-0.429206\pi$
$191$	6.09687			0.441154			0.220577	+	0.975370i	$0.429206\pi$
$192$	−0.295030	−	0.247560i	−0.0212920	−	0.0178661i
$193$	−7.64838	+	2.78378i	−0.550543	+	0.200381i	−0.602288	−	0.798279i	$-0.705744\pi$
$193$	−7.64838	+	2.78378i	−0.550543	+	0.200381i	0.0517449	+	0.998660i	$0.483522\pi$
$194$	0.585232	+	3.31901i	0.0420172	+	0.238291i
$195$	−0.00926020	+	0.0525172i	−0.000663137	+	0.00376083i
$196$	−12.4744	−	4.54029i	−0.891026	−	0.324307i
$197$	1.24293	+	2.15282i	0.0885550	+	0.153382i	0.906901	−	0.421345i	$-0.138442\pi$
$197$	1.24293	+	2.15282i	0.0885550	+	0.153382i	−0.818346	+	0.574727i	$0.805108\pi$
$198$	1.42584	−	2.46962i	0.101330	−	0.175508i
$199$	4.26695	−	3.58040i	0.302476	−	0.253808i	−0.478898	−	0.877871i	$-0.658964\pi$
$199$	4.26695	−	3.58040i	0.302476	−	0.253808i	0.781374	+	0.624063i	$0.214519\pi$
$200$	3.80488	−	3.19267i	0.269046	−	0.225756i
$201$	2.30593	−	3.99399i	0.162648	−	0.281714i
$202$	−7.91417	−	13.7077i	−0.556839	−	0.964474i
$203$	−10.9857	−	3.99848i	−0.771048	−	0.280638i
$204$	0.432058	−	2.45032i	0.0302501	−	0.171557i
$205$	−0.326486	−	1.85159i	−0.0228028	−	0.129321i
$206$	−16.1613	+	5.88223i	−1.12601	+	0.409835i
$207$	7.81773	+	6.55985i	0.543370	+	0.455941i
$208$	−0.761262			−0.0527840
$209$	−2.19381	+	3.76659i	−0.151749	+	0.260540i
$210$	−0.315425			−0.0217664
$211$	−12.7653	−	10.7114i	−0.878801	−	0.737401i	0.0871314	−	0.996197i	$-0.472230\pi$
$211$	−12.7653	−	10.7114i	−0.878801	−	0.737401i	−0.965932	+	0.258795i	$0.916674\pi$
$212$	−1.38783	+	0.505128i	−0.0953163	+	0.0346923i
$213$	0.496965	+	2.81843i	0.0340515	+	0.193116i
$214$	−1.12598	+	6.38576i	−0.0769706	+	0.436522i
$215$	1.54436	+	0.562102i	0.105325	+	0.0383350i
$216$	1.12684	+	1.95175i	0.0766718	+	0.132800i
$217$	−16.7841	+	29.0710i	−1.13938	+	1.97347i
$218$	−6.15875	+	5.16780i	−0.417123	+	0.350008i
$219$	1.78131	−	1.49469i	0.120370	−	0.101002i
$220$	−0.0909438	+	0.157519i	−0.00613143	+	0.0106200i
$221$	−2.45903	−	4.25916i	−0.165412	−	0.286502i
$222$	−0.933689	−	0.339835i	−0.0626651	−	0.0228082i
$223$	−3.10063	+	17.5845i	−0.207633	+	1.17755i	0.685608	+	0.727971i	$0.259536\pi$
$223$	−3.10063	+	17.5845i	−0.207633	+	1.17755i	−0.893242	+	0.449577i	$0.851575\pi$
$224$	−0.781898	−	4.43436i	−0.0522427	−	0.296283i
$225$	−13.3098	+	4.84438i	−0.887321	+	0.322959i
$226$	5.76595	+	4.83820i	0.383545	+	0.321833i
$227$	−18.1766			−1.20643			−0.603213	−	0.797580i	$-0.706113\pi$
$227$	−18.1766			−1.20643			−0.603213	+	0.797580i	$0.706113\pi$
$228$	−0.833837	−	1.45704i	−0.0552222	−	0.0964948i
$229$	9.36484			0.618846			0.309423	−	0.950925i	$-0.399864\pi$
$229$	9.36484			0.618846			0.309423	+	0.950925i	$0.399864\pi$
$230$	−0.498637	−	0.418406i	−0.0328791	−	0.0275889i
$231$	−1.62959	+	0.593122i	−0.107219	+	0.0390246i
$232$	−0.450852	−	2.55691i	−0.0295999	−	0.167869i
$233$	−4.42030	+	25.0688i	−0.289584	+	1.64231i	0.398854	+	0.917015i	$0.369408\pi$
$233$	−4.42030	+	25.0688i	−0.289584	+	1.64231i	−0.688437	+	0.725296i	$0.741703\pi$
$234$	2.03995	+	0.742481i	0.133356	+	0.0485375i
$235$	−0.683742	−	1.18428i	−0.0446024	−	0.0772536i
$236$	−2.21293	+	3.83291i	−0.144050	+	0.249501i
$237$	3.62898	−	3.04507i	0.235727	−	0.197799i
$238$	22.2840	−	18.6985i	1.44446	−	1.21204i
$239$	−4.17638	+	7.23371i	−0.270148	+	0.467910i	−0.968899	−	0.247455i	$-0.920406\pi$
$239$	−4.17638	+	7.23371i	−0.270148	+	0.467910i	0.698752	+	0.715364i	$0.253739\pi$
$240$	−0.0350256	−	0.0606662i	−0.00226090	−	0.00391599i
$241$	−13.2036	−	4.80571i	−0.850517	−	0.309563i	−0.120266	−	0.992742i	$-0.538375\pi$
$241$	−13.2036	−	4.80571i	−0.850517	−	0.309563i	−0.730251	+	0.683179i	$0.760597\pi$
$242$	−0.173648	+	0.984808i	−0.0111625	+	0.0633058i
$243$	−1.68814	−	9.57390i	−0.108294	−	0.614166i
$244$	0.935284	−	0.340416i	0.0598754	−	0.0217929i
$245$	−1.84965	−	1.55204i	−0.118170	−	0.0991563i
$246$	3.98110			0.253826
$247$	−3.11380	−	1.14678i	−0.198126	−	0.0729681i
$248$	−7.45502			−0.473394
$249$	3.95401	+	3.31781i	0.250575	+	0.210257i
$250$	1.70353	−	0.620034i	0.107741	−	0.0392144i
$251$	−4.53584	−	25.7240i	−0.286299	−	1.62368i	−0.700607	−	0.713548i	$-0.747087\pi$
$251$	−4.53584	−	25.7240i	−0.286299	−	1.62368i	0.414307	−	0.910137i	$-0.364024\pi$
$252$	−2.22972	+	12.6453i	−0.140459	+	0.796582i
$253$	−3.36289	−	1.22399i	−0.211423	−	0.0769518i
$254$	−8.29688	−	14.3706i	−0.520593	−	0.901693i
$255$	0.226280	−	0.391928i	0.0141702	−	0.0245435i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	17.9825	−	15.0891i	1.12172	−	0.941233i	0.123028	−	0.992403i	$-0.460739\pi$
$257$	17.9825	−	15.0891i	1.12172	−	0.941233i	0.998690	+	0.0511698i	$0.0162950\pi$
$258$	−1.73997	+	3.01372i	−0.108326	+	0.187626i
$259$	−5.80836	−	10.0604i	−0.360914	−	0.625121i
$260$	−0.130114	−	0.0473575i	−0.00806931	−	0.00293699i
$261$	−1.28568	+	7.29146i	−0.0795817	+	0.451330i
$262$	−1.28441	−	7.28427i	−0.0793513	−	0.450024i
$263$	6.52915	−	2.37642i	0.402605	−	0.146536i	−0.132778	−	0.991146i	$-0.542390\pi$
$263$	6.52915	−	2.37642i	0.402605	−	0.146536i	0.535383	+	0.844610i	$0.320167\pi$
$264$	−0.295030	−	0.247560i	−0.0181579	−	0.0152363i
$265$	−0.268629			−0.0165017
$266$	3.48182	−	19.3158i	0.213484	−	1.18433i
$267$	−1.01337			−0.0620170
$268$	9.17313	+	7.69717i	0.560338	+	0.470180i
$269$	−9.24302	+	3.36419i	−0.563557	+	0.205118i	−0.608060	−	0.793891i	$-0.708052\pi$
$269$	−9.24302	+	3.36419i	−0.563557	+	0.205118i	0.0445026	+	0.999009i	$0.485830\pi$
$270$	0.0711813	+	0.403689i	0.00433196	+	0.0245678i
$271$	−4.32442	+	24.5250i	−0.262690	+	1.48979i	0.512843	+	0.858482i	$0.328592\pi$
$271$	−4.32442	+	24.5250i	−0.262690	+	1.48979i	−0.775533	+	0.631307i	$0.782519\pi$
$272$	6.07079	+	2.20959i	0.368096	+	0.133976i
$273$	−0.660080	−	1.14329i	−0.0399499	−	0.0691952i
$274$	−2.35346	+	4.07631i	−0.142178	+	0.246259i
$275$	3.80488	−	3.19267i	0.229443	−	0.192525i
$276$	1.05583	−	0.885946i	0.0635535	−	0.0533277i
$277$	15.4424	−	26.7470i	0.927844	−	1.60707i	0.140921	−	0.990021i	$-0.454994\pi$
$277$	15.4424	−	26.7470i	0.927844	−	1.60707i	0.786923	−	0.617051i	$-0.211673\pi$
$278$	3.54226	+	6.13538i	0.212451	+	0.367976i
$279$	19.9772	+	7.27110i	1.19600	+	0.435309i
$280$	0.142218	−	0.806556i	0.00849913	−	0.0482009i
$281$	−4.53569	−	25.7232i	−0.270577	−	1.53452i	−0.752670	−	0.658398i	$-0.771235\pi$
$281$	−4.53569	−	25.7232i	−0.270577	−	1.53452i	0.482094	−	0.876120i	$-0.339877\pi$
$282$	2.72093	−	0.990338i	0.162029	−	0.0589738i
$283$	−18.3653	−	15.4103i	−1.09171	−	0.916050i	−0.0948657	−	0.995490i	$-0.530242\pi$
$283$	−18.3653	−	15.4103i	−1.09171	−	0.916050i	−0.996840	+	0.0794406i	$0.974687\pi$
$284$	−7.43092			−0.440944
$285$	−0.0518769	−	0.300907i	−0.00307292	−	0.0178242i
$286$	−0.761262			−0.0450143
$287$	35.6553	+	29.9184i	2.10467	+	1.76603i
$288$	−2.67969	+	0.975329i	−0.157903	+	0.0574718i
$289$	4.29549	+	24.3609i	0.252676	+	1.43299i
$290$	0.0820044	−	0.465070i	0.00481546	−	0.0273099i
$291$	−1.21971	−	0.443938i	−0.0715006	−	0.0260241i
$292$	3.01885	+	5.22880i	0.176665	+	0.305993i
$293$	−0.0584608	+	0.101257i	−0.00341531	+	0.00591550i	−0.867728	−	0.497039i	$-0.834420\pi$
$293$	−0.0584608	+	0.101257i	−0.00341531	+	0.00591550i	0.864313	+	0.502955i	$0.167754\pi$
$294$	3.91651	−	3.28634i	0.228415	−	0.191663i
$295$	−0.616674	+	0.517451i	−0.0359041	+	0.0301271i
$296$	1.28995	−	2.23426i	0.0749769	−	0.129864i
$297$	1.12684	+	1.95175i	0.0653860	+	0.113252i
$298$	14.6397	+	5.32842i	0.848056	+	0.308667i
$299$	0.473076	−	2.68295i	0.0273587	−	0.155159i
$300$	0.332177	+	1.88387i	0.0191783	+	0.108765i
$301$	−38.2319	+	13.9153i	−2.20365	+	0.802063i
$302$	−1.83049	−	1.53597i	−0.105333	−	0.0883849i
$303$	6.09605			0.350209
$304$	4.10167	−	1.47522i	0.235247	−	0.0846095i
$305$	0.181034			0.0103660
$306$	−14.1128	−	11.8420i	−0.806774	−	0.676964i
$307$	5.45544	−	1.98562i	0.311359	−	0.113325i	−0.181615	−	0.983370i	$-0.558132\pi$
$307$	5.45544	−	1.98562i	0.311359	−	0.113325i	0.492973	+	0.870045i	$0.335910\pi$
$308$	−0.781898	−	4.43436i	−0.0445528	−	0.252671i
$309$	1.15020	−	6.52311i	0.0654326	−	0.371087i
$310$	−1.27420	−	0.463771i	−0.0723698	−	0.0263404i
$311$	−7.17515	−	12.4277i	−0.406865	−	0.704711i	0.587671	−	0.809100i	$-0.300045\pi$
$311$	−7.17515	−	12.4277i	−0.406865	−	0.704711i	−0.994537	+	0.104388i	$0.966711\pi$
$312$	0.146594	−	0.253909i	0.00829926	−	0.0143747i
$313$	14.1272	−	11.8541i	0.798515	−	0.670033i	−0.149322	−	0.988789i	$-0.547709\pi$
$313$	14.1272	−	11.8541i	0.798515	−	0.670033i	0.947837	+	0.318755i	$0.103265\pi$
$314$	9.19620	−	7.71653i	0.518972	−	0.435469i
$315$	−1.16776	+	2.02261i	−0.0657957	+	0.113961i
$316$	6.15017	+	10.6524i	0.345974	+	0.599245i
$317$	−10.2622	−	3.73512i	−0.576380	−	0.209785i	0.0373486	−	0.999302i	$-0.488109\pi$
$317$	−10.2622	−	3.73512i	−0.576380	−	0.209785i	−0.613728	+	0.789517i	$0.710331\pi$
$318$	0.0987717	−	0.560162i	0.00553884	−	0.0314123i
$319$	−0.450852	−	2.55691i	−0.0252429	−	0.143159i
$320$	0.170919	−	0.0622093i	0.00955464	−	0.00347760i
$321$	−1.91306	−	1.60525i	−0.106776	−	0.0895961i
$322$	16.1141			0.898005
$323$	21.5029	+	18.1831i	1.19645	+	1.01173i
$324$	7.68704			0.427058
$325$	2.89651	+	2.43046i	0.160669	+	0.134818i
$326$	17.6272	−	6.41579i	0.976282	−	0.355338i
$327$	−0.537677	−	3.04932i	−0.0297336	−	0.168628i
$328$	−1.79499	+	10.1799i	−0.0991115	+	0.562089i
$329$	31.8115	+	11.5784i	1.75383	+	0.638340i
$330$	−0.0350256	−	0.0606662i	−0.00192810	−	0.00333956i
$331$	4.59558	−	7.95978i	0.252596	−	0.437509i	−0.711644	−	0.702540i	$-0.752049\pi$
$331$	4.59558	−	7.95978i	0.252596	−	0.437509i	0.964240	+	0.265031i	$0.0853823\pi$
$332$	−10.2666	+	8.61466i	−0.563450	+	0.472791i
$333$	−5.63582	+	4.72901i	−0.308841	+	0.259148i
$334$	−10.9965	+	19.0465i	−0.601702	+	1.04218i
$335$	1.08902	+	1.88624i	0.0594997	+	0.103056i
$336$	1.62959	+	0.593122i	0.0889014	+	0.0323575i
$337$	−1.23685	+	7.01451i	−0.0673753	+	0.382105i	0.932410	+	0.361401i	$0.117702\pi$
$337$	−1.23685	+	7.01451i	−0.0673753	+	0.382105i	−0.999786	+	0.0207031i	$0.993410\pi$
$338$	2.15679	+	12.2318i	0.117314	+	0.665321i
$339$	−2.72405	+	0.991474i	−0.147950	+	0.0538495i
$340$	0.900153	+	0.755318i	0.0488177	+	0.0409629i
$341$	−7.45502			−0.403712
$342$	−12.4301	−	0.0473525i	−0.672140	−	0.00256053i
$343$	28.2546			1.52560
$344$	−6.92172	−	5.80801i	−0.373194	−	0.313147i
$345$	0.235575	−	0.0857422i	0.0126829	−	0.00461621i
$346$	0.452321	+	2.56524i	0.0243169	+	0.137908i
$347$	3.98983	−	22.6274i	0.214185	−	1.21470i	−0.668130	−	0.744045i	$-0.732905\pi$
$347$	3.98983	−	22.6274i	0.214185	−	1.21470i	0.882315	−	0.470660i	$-0.155984\pi$
$348$	0.939642	+	0.342002i	0.0503701	+	0.0183332i
$349$	11.6363	+	20.1546i	0.622874	+	1.07885i	0.988948	+	0.148264i	$0.0473686\pi$
$349$	11.6363	+	20.1546i	0.622874	+	1.07885i	−0.366073	+	0.930586i	$0.619298\pi$
$350$	−11.1824	+	19.3686i	−0.597727	+	1.03529i
$351$	−1.31426	+	1.10279i	−0.0701499	+	0.0588628i
$352$	0.766044	−	0.642788i	0.0408303	−	0.0342607i
$353$	0.954373	−	1.65302i	0.0507962	−	0.0879815i	−0.839509	−	0.543345i	$-0.817157\pi$
$353$	0.954373	−	1.65302i	0.0507962	−	0.0879815i	0.890305	+	0.455364i	$0.150491\pi$
$354$	−0.852277	−	1.47619i	−0.0452980	−	0.0784585i
$355$	−1.27008	−	0.462272i	−0.0674090	−	0.0245349i
$356$	0.456903	−	2.59122i	0.0242158	−	0.137335i
$357$	1.94546	+	11.0332i	0.102965	+	0.583941i
$358$	−19.1392	+	6.96608i	−1.01154	+	0.368169i
$359$	−3.99102	−	3.34886i	−0.210638	−	0.176746i	0.531365	−	0.847143i	$-0.321679\pi$
$359$	−3.99102	−	3.34886i	−0.210638	−	0.176746i	−0.742003	+	0.670397i	$0.766124\pi$
$360$	−0.518684			−0.0273370
$361$	18.9994	+	0.144760i	0.999971	+	0.00761893i
$362$	7.02825			0.369397
$363$	−0.295030	−	0.247560i	−0.0154851	−	0.0129935i
$364$	3.22107	−	1.17237i	0.168830	−	0.0614490i
$365$	0.190698	+	1.08150i	0.00998157	+	0.0566083i
$366$	−0.0665642	+	0.377504i	−0.00347937	+	0.0197325i
$367$	2.39581	+	0.872004i	0.125060	+	0.0455182i	0.403792	−	0.914851i	$-0.367692\pi$
$367$	2.39581	+	0.872004i	0.125060	+	0.0455182i	−0.278732	+	0.960369i	$0.589914\pi$
$368$	1.78936	+	3.09926i	0.0932767	+	0.161560i
$369$	14.7387	−	25.5282i	0.767268	−	1.32895i
$370$	0.359468	−	0.301630i	0.0186879	−	0.0156810i
$371$	5.09428	−	4.27461i	0.264482	−	0.221927i
$372$	1.43559	−	2.48652i	0.0744321	−	0.128920i
$373$	−17.0328	−	29.5017i	−0.881924	−	1.52754i	−0.849199	−	0.528073i	$-0.822915\pi$
$373$	−17.0328	−	29.5017i	−0.881924	−	1.52754i	−0.0327256	−	0.999464i	$-0.510419\pi$
$374$	6.07079	+	2.20959i	0.313913	+	0.114255i
$375$	−0.121240	+	0.687588i	−0.00626082	+	0.0355069i
$376$	1.30554	+	7.40407i	0.0673279	+	0.381836i
$377$	1.85731	−	0.676004i	0.0956561	−	0.0348160i
$378$	−7.77368	−	6.52289i	−0.399835	−	0.335501i
$379$	−10.5089			−0.539807			−0.269903	−	0.962887i	$-0.586992\pi$
$379$	−10.5089			−0.539807			−0.269903	+	0.962887i	$0.586992\pi$
$380$	0.792824	+	0.00302028i	0.0406710	+	0.000154937i
$381$	6.39084			0.327412
$382$	−4.67047	−	3.91899i	−0.238962	−	0.200513i
$383$	2.54625	−	0.926759i	0.130107	−	0.0473552i	−0.276146	−	0.961116i	$-0.589057\pi$
$383$	2.54625	−	0.926759i	0.130107	−	0.0473552i	0.406253	+	0.913761i	$0.366835\pi$
$384$	0.0668780	+	0.379284i	0.00341285	+	0.0193552i
$385$	0.142218	−	0.806556i	0.00724808	−	0.0411059i
$386$	7.64838	+	2.78378i	0.389292	+	0.141691i
$387$	12.8834	+	22.3147i	0.654899	+	1.13432i
$388$	1.68511	−	2.91869i	0.0855484	−	0.148174i
$389$	−8.42660	+	7.07076i	−0.427246	+	0.358502i	−0.830911	−	0.556405i	$-0.812180\pi$
$389$	−8.42660	+	7.07076i	−0.427246	+	0.358502i	0.403666	+	0.914907i	$0.367736\pi$
$390$	0.0408511	−	0.0342782i	0.00206858	−	0.00173574i
$391$	−11.5600	+	20.0224i	−0.584612	+	1.01258i
$392$	6.63747	+	11.4964i	0.335243	+	0.580657i
$393$	2.67691	+	0.974314i	0.135032	+	0.0491477i
$394$	0.431665	−	2.44809i	0.0217470	−	0.123333i
$395$	0.388500	+	2.20329i	0.0195476	+	0.110860i
$396$	−2.67969	+	0.975329i	−0.134660	+	0.0490121i
$397$	−13.3541	−	11.2054i	−0.670222	−	0.562383i	0.242909	−	0.970049i	$-0.421898\pi$
$397$	−13.3541	−	11.2054i	−0.670222	−	0.562383i	−0.913131	+	0.407666i	$0.866343\pi$
$398$	−5.57011			−0.279204
$399$	5.77204	+	4.88091i	0.288964	+	0.244351i
$400$	−4.96692			−0.248346
$401$	−9.03054	−	7.57752i	−0.450964	−	0.378403i	0.388830	−	0.921310i	$-0.372879\pi$
$401$	−9.03054	−	7.57752i	−0.450964	−	0.378403i	−0.839793	+	0.542906i	$0.817324\pi$
$402$	−4.33374	+	1.57735i	−0.216147	+	0.0786711i
$403$	−0.985492	−	5.58900i	−0.0490909	−	0.278408i
$404$	−2.74856	+	15.5879i	−0.136746	+	0.775526i
$405$	1.31386	+	0.478205i	0.0652861	+	0.0237622i
$406$	5.84539	+	10.1245i	0.290102	+	0.502471i
$407$	1.28995	−	2.23426i	0.0639405	−	0.110748i
$408$	−1.90601	+	1.59933i	−0.0943617	+	0.0791789i
$409$	6.19038	−	5.19434i	0.306095	−	0.256844i	−0.476781	−	0.879022i	$-0.658197\pi$
$409$	6.19038	−	5.19434i	0.306095	−	0.256844i	0.782876	+	0.622178i	$0.213752\pi$
$410$	−0.940078	+	1.62826i	−0.0464272	+	0.0804142i
$411$	−0.906398	−	1.56993i	−0.0447093	−	0.0774388i
$412$	16.1613	+	5.88223i	0.796210	+	0.289797i
$413$	3.46057	−	19.6259i	0.170284	−	0.965727i
$414$	−1.77213	−	10.0503i	−0.0870957	−	0.493944i
$415$	−2.29066	+	0.833730i	−0.112444	+	0.0409262i
$416$	0.583160	+	0.489330i	0.0285918	+	0.0239914i
$417$	−2.72850			−0.133615
$418$	4.10167	−	1.47522i	0.200619	−	0.0721552i
$419$	−15.7157			−0.767762			−0.383881	−	0.923383i	$-0.625413\pi$
$419$	−15.7157			−0.767762			−0.383881	+	0.923383i	$0.625413\pi$
$420$	0.241629	+	0.202751i	0.0117903	+	0.00989324i
$421$	31.7405	−	11.5526i	1.54694	−	0.563040i	0.579242	−	0.815156i	$-0.303349\pi$
$421$	31.7405	−	11.5526i	1.54694	−	0.563040i	0.967697	+	0.252116i	$0.0811264\pi$
$422$	2.89366	+	16.4108i	0.140861	+	0.798864i
$423$	3.72296	−	21.1140i	0.181017	−	1.02660i
$424$	1.38783	+	0.505128i	0.0673988	+	0.0245312i
$425$	−16.0441	−	27.7892i	−0.778254	−	1.34798i
$426$	1.43095	−	2.47848i	0.0693299	−	0.120083i
$427$	−3.43314	+	2.88075i	−0.166141	+	0.139409i
$428$	4.96724	−	4.16801i	0.240101	−	0.201468i
$429$	0.146594	−	0.253909i	0.00707763	−	0.0122588i
$430$	−0.821738	−	1.42329i	−0.0396277	−	0.0686372i
$431$	−34.8394	−	12.6805i	−1.67815	−	0.610798i	−0.685098	−	0.728451i	$-0.740241\pi$
$431$	−34.8394	−	12.6805i	−1.67815	−	0.610798i	−0.993055	+	0.117654i	$0.962463\pi$
$432$	0.391348	−	2.21944i	0.0188287	−	0.106783i
$433$	6.50176	+	36.8733i	0.312455	+	1.77202i	0.586150	+	0.810202i	$0.300643\pi$
$433$	6.50176	+	36.8733i	0.312455	+	1.77202i	−0.273696	+	0.961816i	$0.588246\pi$
$434$	31.5438	−	11.4810i	1.51415	−	0.551106i
$435$	0.139326	+	0.116909i	0.00668019	+	0.00560535i
$436$	8.03968			0.385031
$437$	2.65024	+	15.3725i	0.126778	+	0.735365i
$438$	−2.32533			−0.111109
$439$	−4.15333	−	3.48505i	−0.198227	−	0.166333i	0.538271	−	0.842772i	$-0.319078\pi$
$439$	−4.15333	−	3.48505i	−0.198227	−	0.166333i	−0.736498	+	0.676439i	$0.763522\pi$
$440$	0.170919	−	0.0622093i	0.00814822	−	0.00296571i
$441$	−6.57358	−	37.2806i	−0.313028	−	1.77527i
$442$	−0.854011	+	4.84334i	−0.0406212	+	0.230374i
$443$	1.24181	+	0.451983i	0.0590003	+	0.0214744i	0.371352	−	0.928492i	$-0.378894\pi$
$443$	1.24181	+	0.451983i	0.0590003	+	0.0214744i	−0.312351	+	0.949967i	$0.601117\pi$
$444$	0.496805	+	0.860492i	0.0235773	+	0.0408371i
$445$	0.239291	−	0.414465i	0.0113435	−	0.0196475i
$446$	13.6783	−	11.4775i	0.647688	−	0.543475i
$447$	−4.59636	+	3.85680i	−0.217400	+	0.182420i
$448$	−2.25138	+	3.89951i	−0.106368	+	0.184235i
$449$	10.0435	+	17.3958i	0.473980	+	0.820958i	0.999556	−	0.0297888i	$-0.00948348\pi$
$449$	10.0435	+	17.3958i	0.473980	+	0.820958i	−0.525576	+	0.850747i	$0.676150\pi$
$450$	13.3098	+	4.84438i	0.627431	+	0.228366i
$451$	−1.79499	+	10.1799i	−0.0845226	+	0.479351i
$452$	−1.30703	−	7.41256i	−0.0614777	−	0.348657i
$453$	0.864794	−	0.314759i	0.0406315	−	0.0147887i
$454$	13.9241	+	11.6837i	0.653491	+	0.548344i
$455$	0.623472			0.0292288
$456$	−0.297810	+	1.65214i	−0.0139462	+	0.0773684i
$457$	23.1189			1.08146			0.540729	−	0.841197i	$-0.318148\pi$
$457$	23.1189			1.08146			0.540729	+	0.841197i	$0.318148\pi$
$458$	−7.17388	−	6.01960i	−0.335213	−	0.281277i
$459$	13.6816	−	4.97970i	0.638604	−	0.232433i
$460$	0.113032	+	0.641035i	0.00527013	+	0.0298884i
$461$	−5.01235	+	28.4264i	−0.233448	+	1.32395i	0.612409	+	0.790541i	$0.290201\pi$
$461$	−5.01235	+	28.4264i	−0.233448	+	1.32395i	−0.845857	+	0.533410i	$0.820910\pi$
$462$	1.62959	+	0.593122i	0.0758154	+	0.0275945i
$463$	13.7600	+	23.8331i	0.639483	+	1.10762i	0.985546	+	0.169406i	$0.0541849\pi$
$463$	13.7600	+	23.8331i	0.639483	+	1.10762i	−0.346063	+	0.938211i	$0.612482\pi$
$464$	−1.29818	+	2.24851i	−0.0602663	+	0.104384i
$465$	0.400054	−	0.335685i	0.0185521	−	0.0155670i
$466$	19.5000	−	16.3625i	0.903322	−	0.757977i
$467$	−1.58685	+	2.74850i	−0.0734306	+	0.127186i	−0.900403	−	0.435057i	$-0.856728\pi$
$467$	−1.58685	+	2.74850i	−0.0734306	+	0.127186i	0.826972	+	0.562243i	$0.190061\pi$
$468$	−1.08543	−	1.88003i	−0.0501742	−	0.0869043i
$469$	−50.6675	−	18.4415i	−2.33961	−	0.851547i
$470$	−0.237461	+	1.34671i	−0.0109533	+	0.0621190i
$471$	0.802856	+	4.55322i	0.0369936	+	0.209801i
$472$	4.15895	−	1.51373i	0.191431	−	0.0696753i
$473$	−6.92172	−	5.80801i	−0.318261	−	0.267053i
$474$	−4.73729			−0.217591
$475$	−20.3163	−	7.48228i	−0.932174	−	0.343311i
$476$	−29.0897			−1.33332
$477$	−3.22629	−	2.70717i	−0.147721	−	0.123953i
$478$	7.84903	−	2.85681i	0.359006	−	0.130668i
$479$	5.05898	+	28.6909i	0.231151	+	1.31092i	0.850570	+	0.525862i	$0.176257\pi$
$479$	5.05898	+	28.6909i	0.231151	+	1.31092i	−0.619419	+	0.785060i	$0.712632\pi$
$480$	−0.0121643	+	0.0689870i	−0.000555221	+	0.00314881i
$481$	1.84554	+	0.671721i	0.0841493	+	0.0306279i
$482$	7.02547	+	12.1685i	0.320002	+	0.554259i
$483$	−3.10306	+	5.37465i	−0.141194	+	0.244555i
$484$	0.766044	−	0.642788i	0.0348202	−	0.0292176i
$485$	0.469586	−	0.394029i	0.0213228	−	0.0178919i
$486$	−4.86080	+	8.41915i	−0.220490	+	0.381900i
$487$	−6.88402	−	11.9235i	−0.311945	−	0.540304i	0.666839	−	0.745202i	$-0.267647\pi$
$487$	−6.88402	−	11.9235i	−0.311945	−	0.540304i	−0.978783	+	0.204898i	$0.934314\pi$
$488$	−0.935284	−	0.340416i	−0.0423383	−	0.0154099i
$489$	−1.25453	+	7.11480i	−0.0567318	+	0.321742i
$490$	0.419282	+	2.37786i	0.0189412	+	0.107421i
$491$	−3.42804	+	1.24770i	−0.154705	+	0.0563081i	−0.418212	−	0.908349i	$-0.637343\pi$
$491$	−3.42804	+	1.24770i	−0.154705	+	0.0563081i	0.263507	+	0.964658i	$0.415121\pi$
$492$	−3.04970	−	2.55900i	−0.137491	−	0.115369i
$493$	−16.7735			−0.755439
$494$	1.64817	+	2.88000i	0.0741548	+	0.129577i
$495$	−0.518684			−0.0233131
$496$	5.71088	+	4.79200i	0.256426	+	0.215167i
$497$	31.4419	−	11.4439i	1.41036	−	0.513329i
$498$	−0.896300	−	5.08317i	−0.0401642	−	0.227782i
$499$	2.38303	−	13.5149i	0.106679	−	0.605008i	−0.883857	−	0.467757i	$-0.845062\pi$
$499$	2.38303	−	13.5149i	0.106679	−	0.605008i	0.990536	−	0.137251i	$-0.0438267\pi$
$500$	−1.70353	−	0.620034i	−0.0761842	−	0.0277288i
$501$	−4.23514	−	7.33548i	−0.189212	−	0.327725i
$502$	−13.0604	+	22.6213i	−0.582915	+	1.00964i
$503$	−9.98789	+	8.38083i	−0.445338	+	0.373683i	−0.837702	−	0.546127i	$-0.816102\pi$
$503$	−9.98789	+	8.38083i	−0.445338	+	0.373683i	0.392364	+	0.919810i	$0.371657\pi$
$504$	9.83633	−	8.25366i	0.438145	−	0.367647i
$505$	−1.43949	+	2.49327i	−0.0640565	+	0.110949i
$506$	1.78936	+	3.09926i	0.0795466	+	0.137779i
$507$	−4.49508	−	1.63607i	−0.199633	−	0.0726606i
$508$	−2.88148	+	16.3417i	−0.127845	+	0.725044i
$509$	4.96408	+	28.1527i	0.220029	+	1.24785i	0.871964	+	0.489570i	$0.162846\pi$
$509$	4.96408	+	28.1527i	0.220029	+	1.24785i	−0.651935	+	0.758275i	$0.726042\pi$
$510$	−0.425266	+	0.154784i	−0.0188311	+	0.00685396i
$511$	−20.8260	−	17.4751i	−0.921287	−	0.773052i
$512$	−1.00000			−0.0441942
$513$	4.94416	−	8.48869i	0.218290	−	0.374785i
$514$	−23.4745			−1.03542
$515$	2.39634	+	2.01077i	0.105595	+	0.0886049i
$516$	3.27008	−	1.19021i	0.143957	−	0.0523962i
$517$	1.30554	+	7.40407i	0.0574174	+	0.325630i
$518$	−2.01722	+	11.4402i	−0.0886316	+	0.502655i
$519$	−0.942703	−	0.343116i	−0.0413801	−	0.0150611i
$520$	0.0692321	+	0.119913i	0.00303603	+	0.00525855i
$521$	16.1878	−	28.0380i	0.709199	−	1.22837i	−0.255955	−	0.966689i	$-0.582390\pi$
$521$	16.1878	−	28.0380i	0.709199	−	1.22837i	0.965155	−	0.261681i	$-0.0842767\pi$
$522$	5.67175	−	4.75916i	0.248246	−	0.208303i
$523$	−2.12896	+	1.78641i	−0.0930930	+	0.0781143i	−0.688146	−	0.725572i	$-0.741575\pi$
$523$	−2.12896	+	1.78641i	−0.0930930	+	0.0781143i	0.595053	+	0.803686i	$0.297131\pi$
$524$	−3.69832	+	6.40568i	−0.161562	+	0.279833i
$525$	−4.30675	−	7.45951i	−0.187962	−	0.325560i
$526$	−6.52915	−	2.37642i	−0.284685	−	0.103617i
$527$	−8.36331	+	47.4307i	−0.364312	+	2.06611i
$528$	0.0668780	+	0.379284i	0.00291049	+	0.0165062i
$529$	9.57810	−	3.48614i	0.416439	−	0.151571i
$530$	0.205782	+	0.172671i	0.00893858	+	0.00750036i
$531$	−12.6211			−0.547709
$532$	−15.0832	+	12.5587i	−0.653939	+	0.544489i
$533$	−7.86909			−0.340848
$534$	0.776283	+	0.651379i	0.0335931	+	0.0281879i
$535$	1.10828	−	0.403382i	0.0479152	−	0.0174397i
$536$	−2.07938	−	11.7928i	−0.0898156	−	0.509369i
$537$	1.36213	−	7.72505i	0.0587805	−	0.333361i
$538$	9.24302	+	3.36419i	0.398495	+	0.145040i
$539$	6.63747	+	11.4964i	0.285896	+	0.495186i
$540$	0.204959	−	0.354999i	0.00882001	−	0.0152767i
$541$	−6.08773	+	5.10821i	−0.261732	+	0.219619i	−0.764205	−	0.644974i	$-0.776868\pi$
$541$	−6.08773	+	5.10821i	−0.261732	+	0.219619i	0.502473	+	0.864593i	$0.332424\pi$
$542$	19.0771	−	16.0076i	0.819431	−	0.687584i
$543$	−1.35341	+	2.34418i	−0.0580805	+	0.100598i
$544$	−3.23020	−	5.59487i	−0.138494	−	0.239878i
$545$	1.37413	+	0.500142i	0.0588612	+	0.0214237i
$546$	−0.229243	+	1.30010i	−0.00981071	+	0.0556393i
$547$	−5.53318	−	31.3803i	−0.236582	−	1.34172i	−0.839257	−	0.543736i	$-0.817009\pi$
$547$	−5.53318	−	31.3803i	−0.236582	−	1.34172i	0.602675	−	0.797987i	$-0.294102\pi$
$548$	4.42305	−	1.60986i	0.188943	−	0.0687698i
$549$	2.17426	+	1.82442i	0.0927951	+	0.0778643i
$550$	−4.96692			−0.211790
$551$	−8.69716	+	7.24150i	−0.370511	+	0.308498i
$552$	−1.37829			−0.0586638
$553$	−42.4279	−	35.6012i	−1.80422	−	1.51392i
$554$	−29.0222	+	10.5632i	−1.23304	+	0.448788i
$555$	0.0313827	+	0.177980i	0.00133212	+	0.00755483i
$556$	1.23021	−	6.97690i	0.0521727	−	0.295886i
$557$	31.3768	+	11.4202i	1.32948	+	0.483890i	0.906483	−	0.422242i	$-0.138757\pi$
$557$	31.3768	+	11.4202i	1.32948	+	0.483890i	0.422994	+	0.906132i	$0.360979\pi$
$558$	−10.6296	−	18.4111i	−0.449988	−	0.779403i
$559$	3.43925	−	5.95696i	0.145465	−	0.251953i
$560$	−0.627389	+	0.526442i	−0.0265120	+	0.0222462i
$561$	−1.90601	+	1.59933i	−0.0804719	+	0.0675240i
$562$	−13.0600	+	22.6206i	−0.550903	+	0.954192i
$563$	18.2889	+	31.6774i	0.770787	+	1.33504i	0.937132	+	0.348974i	$0.113470\pi$
$563$	18.2889	+	31.6774i	0.770787	+	1.33504i	−0.166346	+	0.986067i	$0.553197\pi$
$564$	−2.72093	−	0.990338i	−0.114572	−	0.0417007i
$565$	0.237733	−	1.34825i	0.0100015	−	0.0567214i
$566$	4.16308	+	23.6100i	0.174987	+	0.992403i
$567$	−32.5256	+	11.8383i	−1.36595	+	0.497163i
$568$	5.69242	+	4.77651i	0.238849	+	0.200418i
$569$	17.8547			0.748507			0.374254	−	0.927326i	$-0.377899\pi$
$569$	17.8547			0.748507			0.374254	+	0.927326i	$0.377899\pi$
$570$	−0.153679	+	0.263854i	−0.00643693	+	0.0110516i
$571$	−23.4937			−0.983182			−0.491591	−	0.870826i	$-0.663584\pi$
$571$	−23.4937			−0.983182			−0.491591	+	0.870826i	$0.663584\pi$
$572$	0.583160	+	0.489330i	0.0243832	+	0.0204599i
$573$	2.20651	−	0.803103i	0.0921782	−	0.0335501i
$574$	−8.08241	−	45.8376i	−0.337353	−	1.91322i
$575$	3.08663	−	17.5051i	0.128721	−	0.730015i
$576$	2.67969	+	0.975329i	0.111654	+	0.0406387i
$577$	−5.77431	−	10.0014i	−0.240388	−	0.416364i	0.720437	−	0.693520i	$-0.243941\pi$
$577$	−5.77431	−	10.0014i	−0.240388	−	0.416364i	−0.960825	+	0.277156i	$0.910608\pi$
$578$	12.3684	−	21.4226i	0.514456	−	0.891064i
$579$	−2.40132	+	2.01495i	−0.0997956	+	0.0837384i
$580$	−0.361760	+	0.303553i	−0.0150213	+	0.0126044i
$581$	30.1731	−	52.2614i	1.25179	−	2.16817i
$582$	0.648993	+	1.12409i	0.0269016	+	0.0465950i
$583$	1.38783	+	0.505128i	0.0574779	+	0.0209202i
$584$	1.04844	−	5.94598i	0.0433846	−	0.246046i
$585$	−0.0685657	−	0.388855i	−0.00283484	−	0.0160772i
$586$	0.109870	−	0.0399895i	0.00453870	−	0.00165195i
$587$	−30.1410	−	25.2913i	−1.24405	−	1.04388i	−0.997196	−	0.0748309i	$-0.976158\pi$
$587$	−30.1410	−	25.2913i	−1.24405	−	1.04388i	−0.246855	−	0.969052i	$-0.579397\pi$
$588$	−5.11264			−0.210842
$589$	16.1405	+	28.2038i	0.665059	+	1.16212i
$590$	0.805010			0.0331417
$591$	0.733404	+	0.615399i	0.0301682	+	0.0253141i
$592$	−2.42432	+	0.882379i	−0.0996388	+	0.0362656i
$593$	−0.201598	−	1.14332i	−0.00827863	−	0.0469504i	0.980389	−	0.197074i	$-0.0631439\pi$
$593$	−0.201598	−	1.14332i	−0.00827863	−	0.0469504i	−0.988667	+	0.150124i	$0.952033\pi$
$594$	0.391348	−	2.21944i	0.0160572	−	0.0910649i
$595$	−4.97196	−	1.80965i	−0.203831	−	0.0741883i
$596$	−7.78963	−	13.4920i	−0.319076	−	0.552655i
$597$	1.07262	−	1.85783i	0.0438995	−	0.0760361i
$598$	−2.08696	+	1.75117i	−0.0853423	+	0.0716107i
$599$	22.2678	−	18.6849i	0.909840	−	0.763446i	−0.0622488	−	0.998061i	$-0.519827\pi$
$599$	22.2678	−	18.6849i	0.909840	−	0.763446i	0.972088	+	0.234615i	$0.0753828\pi$
$600$	0.956466	−	1.65665i	0.0390476	−	0.0676324i
$601$	−0.864177	−	1.49680i	−0.0352505	−	0.0610557i	0.847862	−	0.530217i	$-0.177890\pi$
$601$	−0.864177	−	1.49680i	−0.0352505	−	0.0610557i	−0.883112	+	0.469161i	$0.844556\pi$
$602$	38.2319	+	13.9153i	1.55822	+	0.567144i
$603$	−5.92971	+	33.6291i	−0.241476	+	1.36948i
$604$	0.414939	+	2.35324i	0.0168836	+	0.0957518i
$605$	0.170919	−	0.0622093i	0.00694883	−	0.00252917i
$606$	−4.66984	−	3.91846i	−0.189699	−	0.159177i
$607$	41.5532			1.68659			0.843297	−	0.537448i	$-0.180612\pi$
$607$	41.5532			1.68659			0.843297	+	0.537448i	$0.180612\pi$
$608$	−4.09032	−	1.50642i	−0.165884	−	0.0610936i
$609$	−4.50253			−0.182452
$610$	−0.138680	−	0.116367i	−0.00561500	−	0.00471155i
$611$	−5.37822	+	1.95751i	−0.217580	+	0.0791925i
$612$	3.19911	+	18.1430i	0.129316	+	0.733389i
$613$	6.46110	−	36.6427i	0.260961	−	1.47998i	−0.519333	−	0.854572i	$-0.673820\pi$
$613$	6.46110	−	36.6427i	0.260961	−	1.47998i	0.780294	−	0.625413i	$-0.215069\pi$
$614$	−5.45544	−	1.98562i	−0.220164	−	0.0801331i
$615$	−0.362057	−	0.627101i	−0.0145995	−	0.0252871i
$616$	−2.25138	+	3.89951i	−0.0907109	+	0.157116i
$617$	17.8611	−	14.9873i	0.719062	−	0.603365i	−0.208063	−	0.978115i	$-0.566716\pi$
$617$	17.8611	−	14.9873i	0.719062	−	0.603365i	0.927126	+	0.374750i	$0.122272\pi$
$618$	−5.07408	+	4.25766i	−0.204109	+	0.171268i
$619$	8.94329	−	15.4902i	0.359461	−	0.622605i	−0.628410	−	0.777883i	$-0.716294\pi$
$619$	8.94329	−	15.4902i	0.359461	−	0.622605i	0.987871	+	0.155277i	$0.0496271\pi$
$620$	0.677988	+	1.17431i	0.0272287	+	0.0471614i
$621$	7.57889	+	2.75849i	0.304130	+	0.110694i
$622$	−2.49190	+	14.1323i	−0.0999162	+	0.566653i
$623$	2.05733	+	11.6677i	0.0824251	+	0.467456i
$624$	−0.275507	+	0.100276i	−0.0110291	+	0.00401427i
$625$	18.7718	+	15.7514i	0.750872	+	0.630056i
$626$	−18.4417			−0.737079
$627$	−0.297810	+	1.65214i	−0.0118934	+	0.0659800i
$628$	−12.0048			−0.479043
$629$	−12.7678	−	10.7135i	−0.509086	−	0.427174i
$630$	2.19467	−	0.798793i	0.0874376	−	0.0318247i
$631$	0.918231	+	5.20755i	0.0365542	+	0.207309i	0.997615	−	0.0690290i	$-0.0219901\pi$
$631$	0.918231	+	5.20755i	0.0365542	+	0.207309i	−0.961060	+	0.276338i	$0.910879\pi$
$632$	2.13593	−	12.1135i	0.0849629	−	0.481848i
$633$	−6.03082	−	2.19504i	−0.239704	−	0.0872450i
$634$	5.46038	+	9.45765i	0.216859	+	0.375611i
$635$	−1.50910	+	2.61384i	−0.0598868	+	0.103727i
$636$	−0.435729	+	0.365620i	−0.0172778	+	0.0144978i
$637$	−7.74141	+	6.49582i	−0.306726	+	0.257374i
$638$	−1.29818	+	2.24851i	−0.0513953	+	0.0890193i
$639$	−10.5953	−	18.3516i	−0.419143	−	0.725976i
$640$	−0.170919	−	0.0622093i	−0.00675615	−	0.00245904i
$641$	−0.407145	+	2.30903i	−0.0160813	+	0.0912014i	−0.991792	−	0.127861i	$-0.959189\pi$
$641$	−0.407145	+	2.30903i	−0.0160813	+	0.0912014i	0.975711	+	0.219063i	$0.0702999\pi$
$642$	0.433655	+	2.45938i	0.0171150	+	0.0970640i
$643$	−5.43757	+	1.97911i	−0.214437	+	0.0780486i	−0.447005	−	0.894531i	$-0.647509\pi$
$643$	−5.43757	+	1.97911i	−0.214437	+	0.0780486i	0.232568	+	0.972580i	$0.425287\pi$
$644$	−12.3441	−	10.3580i	−0.486427	−	0.408161i
$645$	0.632960			0.0249228
$646$	−4.78429	−	27.7508i	−0.188235	−	1.09184i
$647$	16.1646			0.635495			0.317747	−	0.948175i	$-0.397074\pi$
$647$	16.1646			0.635495			0.317747	+	0.948175i	$0.397074\pi$
$648$	−5.88862	−	4.94114i	−0.231327	−	0.194106i
$649$	4.15895	−	1.51373i	0.163253	−	0.0594193i
$650$	−0.656585	−	3.72368i	−0.0257534	−	0.146055i
$651$	−2.24498	+	12.7319i	−0.0879876	+	0.499002i
$652$	−17.6272	−	6.41579i	−0.690336	−	0.251262i
$653$	4.27768	+	7.40915i	0.167398	+	0.289943i	0.937504	−	0.347973i	$-0.113130\pi$
$653$	4.27768	+	7.40915i	0.167398	+	0.289943i	−0.770106	+	0.637916i	$0.779797\pi$
$654$	−1.54818	+	2.68153i	−0.0605386	+	0.104856i
$655$	−1.03060	+	0.864780i	−0.0402690	+	0.0337897i
$656$	7.91853	−	6.64444i	0.309167	−	0.259422i
$657$	−8.60877	+	14.9108i	−0.335860	+	0.581727i
$658$	−16.9266	−	29.3177i	−0.659866	−	1.14292i
$659$	−26.8037	−	9.75574i	−1.04412	−	0.380030i	−0.237681	−	0.971343i	$-0.576387\pi$
$659$	−26.8037	−	9.75574i	−1.04412	−	0.380030i	−0.806442	+	0.591314i	$0.798610\pi$
$660$	−0.0121643	+	0.0689870i	−0.000473494	+	0.00268532i
$661$	−1.71292	−	9.71447i	−0.0666250	−	0.377849i	−0.999829	−	0.0185017i	$-0.994110\pi$
$661$	−1.71292	−	9.71447i	−0.0666250	−	0.377849i	0.933204	−	0.359348i	$-0.117001\pi$
$662$	−8.63687	+	3.14356i	−0.335681	+	0.122178i
$663$	−1.45097	−	1.21751i	−0.0563512	−	0.0472843i
$664$	13.4020			0.520100
$665$	−3.35926	+	1.20820i	−0.130267	+	0.0468520i
$666$	7.35704			0.285079
$667$	−7.11778	−	5.97253i	−0.275602	−	0.231257i
$668$	20.6667	−	7.52206i	0.799618	−	0.291037i
$669$	1.19416	+	6.77242i	0.0461689	+	0.261837i
$670$	0.378214	−	2.14496i	0.0146117	−	0.0828669i
$671$	−0.935284	−	0.340416i	−0.0361062	−	0.0131416i
$672$	−0.867087	−	1.50184i	−0.0334486	−	0.0579347i
$673$	−19.8233	+	34.3350i	−0.764132	+	1.32352i	0.176572	+	0.984288i	$0.443499\pi$
$673$	−19.8233	+	34.3350i	−0.764132	+	1.32352i	−0.940704	+	0.339228i	$0.889834\pi$
$674$	5.45632	−	4.57839i	0.210170	−	0.176353i
$675$	−8.57499	+	7.19527i	−0.330051	+	0.276946i
$676$	6.21024	−	10.7565i	0.238855	−	0.413710i
$677$	5.55291	+	9.61793i	0.213416	+	0.369647i	0.952781	−	0.303657i	$-0.0982078\pi$
$677$	5.55291	+	9.61793i	0.213416	+	0.369647i	−0.739366	+	0.673304i	$0.764874\pi$
$678$	2.72405	+	0.991474i	0.104617	+	0.0380773i
$679$	−2.63516	+	14.9448i	−0.101128	+	0.573527i
$680$	−0.204048	−	1.15721i	−0.00782489	−	0.0443772i
$681$	−6.57827	+	2.39430i	−0.252080	+	0.0917496i
$682$	5.71088	+	4.79200i	0.218681	+	0.183495i
$683$	19.6159			0.750580			0.375290	−	0.926907i	$-0.377543\pi$
$683$	19.6159			0.750580			0.375290	+	0.926907i	$0.377543\pi$
$684$	9.49154	+	8.02616i	0.362918	+	0.306888i
$685$	0.856130			0.0327110
$686$	−21.6443	−	18.1617i	−0.826382	−	0.693417i
$687$	3.38921	−	1.23357i	0.129307	−	0.0470637i
$688$	1.56903	+	8.89839i	0.0598186	+	0.339248i
$689$	−0.195233	+	1.10722i	−0.00743779	+	0.0421818i
$690$	−0.235575	−	0.0857422i	−0.00896818	−	0.00326415i
$691$	−1.84949	−	3.20340i	−0.0703577	−	0.121863i	0.828700	−	0.559692i	$-0.189081\pi$
$691$	−1.84949	−	3.20340i	−0.0703577	−	0.121863i	−0.899058	+	0.437829i	$0.855747\pi$
$692$	1.30241	−	2.25583i	0.0495100	−	0.0857539i
$693$	9.83633	−	8.25366i	0.373651	−	0.313531i
$694$	−17.6010	+	14.7690i	−0.668126	+	0.560624i
$695$	0.644294	−	1.11595i	0.0244395	−	0.0423304i
$696$	−0.499973	−	0.865978i	−0.0189514	−	0.0328248i
$697$	62.7532	+	22.8403i	2.37695	+	0.865138i
$698$	4.04123	−	22.9189i	0.152963	−	0.867495i
$699$	1.70241	+	9.65486i	0.0643911	+	0.365180i
$700$	21.0161	−	7.64924i	0.794334	−	0.289114i
$701$	−16.3027	−	13.6796i	−0.615744	−	0.516671i	0.280719	−	0.959790i	$-0.409427\pi$
$701$	−16.3027	−	13.6796i	−0.615744	−	0.516671i	−0.896463	+	0.443120i	$0.853872\pi$
$702$	1.71564			0.0647527
$703$	−11.2455	−	0.0428398i	−0.424130	−	0.00161573i
$704$	−1.00000			−0.0376889
$705$	−0.403449	−	0.338534i	−0.0151948	−	0.0127499i
$706$	−1.79363	+	0.652830i	−0.0675043	+	0.0245696i
$707$	−12.3761	−	70.1886i	−0.465453	−	2.63971i
$708$	−0.295993	+	1.67866i	−0.0111241	+	0.0630878i
$709$	26.5424	+	9.66063i	0.996819	+	0.362812i	0.788357	−	0.615218i	$-0.210932\pi$
$709$	26.5424	+	9.66063i	0.996819	+	0.362812i	0.208462	+	0.978030i	$0.433154\pi$
$710$	0.675797	+	1.17051i	0.0253622	+	0.0439286i
$711$	−17.5383	+	30.3772i	−0.657737	+	1.13923i
$712$	−2.01561	+	1.69130i	−0.0755383	+	0.0633842i
$713$	−20.4376	+	17.1492i	−0.765394	+	0.642242i
$714$	5.60172	−	9.70247i	0.209639	−	0.363106i
$715$	0.0692321	+	0.119913i	0.00258913	+	0.00448451i
$716$	19.1392	+	6.96608i	0.715264	+	0.260335i
$717$	−0.558616	+	3.16807i	−0.0208619	+	0.118314i
$718$	0.904690	+	5.13075i	0.0337627	+	0.191478i
$719$	1.23539	−	0.449646i	0.0460723	−	0.0167690i	−0.318881	−	0.947795i	$-0.603307\pi$
$719$	1.23539	−	0.449646i	0.0460723	−	0.0167690i	0.364954	+	0.931026i	$0.381085\pi$
$720$	0.397335	+	0.333404i	0.0148078	+	0.0124252i
$721$	−77.4409			−2.88405
$722$	−14.4614	−	12.3235i	−0.538197	−	0.458633i
$723$	−5.41151			−0.201256
$724$	−5.38395	−	4.51767i	−0.200093	−	0.167898i
$725$	12.1182	−	4.41065i	0.450057	−	0.163807i
$726$	0.0668780	+	0.379284i	0.00248207	+	0.0140765i
$727$	3.59934	−	20.4129i	0.133492	−	0.757072i	−0.842406	−	0.538844i	$-0.818861\pi$
$727$	3.59934	−	20.4129i	0.133492	−	0.757072i	0.975898	−	0.218228i	$-0.0700276\pi$
$728$	−3.22107	−	1.17237i	−0.119381	−	0.0434510i
$729$	9.65850	+	16.7290i	0.357722	+	0.619593i
$730$	0.549092	−	0.951055i	0.0203228	−	0.0352001i
$731$	−44.7171	+	37.5221i	−1.65392	+	1.38780i
$732$	0.293646	−	0.246398i	0.0108535	−	0.00910715i
$733$	10.4331	−	18.0707i	0.385356	−	0.667456i	−0.606463	−	0.795112i	$-0.707412\pi$
$733$	10.4331	−	18.0707i	0.385356	−	0.667456i	0.991819	+	0.127656i	$0.0407453\pi$
$734$	−1.27478	−	2.20799i	−0.0470531	−	0.0814984i
$735$	−0.873845	−	0.318053i	−0.0322322	−	0.0117316i
$736$	0.621437	−	3.52435i	0.0229065	−	0.129909i
$737$	−2.07938	−	11.7928i	−0.0765950	−	0.434392i
$738$	−27.6998	+	10.0819i	−1.01964	+	0.371119i
$739$	−0.317844	−	0.266703i	−0.0116921	−	0.00981082i	0.636923	−	0.770928i	$-0.280207\pi$
$739$	−0.317844	−	0.266703i	−0.0116921	−	0.00981082i	−0.648615	+	0.761117i	$0.724651\pi$
$740$	−0.469253			−0.0172501
$741$	−1.27797	−	0.00486845i	−0.0469474	−	0.000178847i
$742$	−6.65011			−0.244133
$743$	17.1736	+	14.4104i	0.630039	+	0.528665i	0.900941	−	0.433942i	$-0.142878\pi$
$743$	17.1736	+	14.4104i	0.630039	+	0.528665i	−0.270902	+	0.962607i	$0.587322\pi$
$744$	−2.69803	+	0.982004i	−0.0989148	+	0.0360020i
$745$	−0.492063	−	2.79063i	−0.0180278	−	0.102241i
$746$	−5.91543	+	33.5480i	−0.216579	+	1.22828i
$747$	−35.9133	−	13.0714i	−1.31400	−	0.478257i
$748$	−3.23020	−	5.59487i	−0.118108	−	0.204569i
$749$	−14.5986	+	25.2855i	−0.533421	+	0.923912i
$750$	0.534849	−	0.448791i	0.0195299	−	0.0163875i
$751$	−2.90504	+	2.43762i	−0.106006	+	0.0889500i	−0.694250	−	0.719734i	$-0.744264\pi$
$751$	−2.90504	+	2.43762i	−0.106006	+	0.0889500i	0.588244	+	0.808684i	$0.299820\pi$
$752$	3.75914	−	6.51103i	0.137082	−	0.237433i
$753$	−5.03002	−	8.71225i	−0.183304	−	0.317492i
$754$	−1.85731	−	0.676004i	−0.0676391	−	0.0246186i
$755$	−0.0754723	+	0.428024i	−0.00274672	+	0.0155774i
$756$	1.76215	+	9.99364i	0.0640887	+	0.363465i
$757$	12.5662	−	4.57371i	0.456725	−	0.166234i	−0.103404	−	0.994639i	$-0.532974\pi$
$757$	12.5662	−	4.57371i	0.456725	−	0.166234i	0.560130	+	0.828405i	$0.310751\pi$
$758$	8.05030	+	6.75500i	0.292400	+	0.245353i
$759$	−1.37829			−0.0500287
$760$	−0.605397	−	0.511931i	−0.0219601	−	0.0185697i
$761$	−10.8452			−0.393138			−0.196569	−	0.980490i	$-0.562980\pi$
$761$	−10.8452			−0.393138			−0.196569	+	0.980490i	$0.562980\pi$
$762$	−4.89566	−	4.10795i	−0.177351	−	0.148815i
$763$	−34.0176	+	12.3814i	−1.23152	+	0.448237i
$764$	1.05871	+	6.00424i	0.0383028	+	0.217226i
$765$	−0.581878	+	3.30000i	−0.0210379	+	0.119312i
$766$	−2.54625	−	0.926759i	−0.0919997	−	0.0334852i
$767$	1.68462	+	2.91785i	0.0608281	+	0.105357i
$768$	0.192567	−	0.333537i	0.00694868	−	0.0120355i
$769$	−27.6013	+	23.1602i	−0.995328	+	0.835179i	−0.986330	−	0.164780i	$-0.947308\pi$
$769$	−27.6013	+	23.1602i	−0.995328	+	0.835179i	−0.00899751	+	0.999960i	$0.502864\pi$
$770$	−0.627389	+	0.526442i	−0.0226095	+	0.0189717i
$771$	4.52042	−	7.82960i	0.162799	−	0.281976i
$772$	−4.06962	−	7.04879i	−0.146469	−	0.253691i
$773$	11.9235	+	4.33979i	0.428858	+	0.156091i	0.547425	−	0.836855i	$-0.315608\pi$
$773$	11.9235	+	4.33979i	0.428858	+	0.156091i	−0.118568	+	0.992946i	$0.537830\pi$
$774$	4.47435	−	25.3753i	0.160827	−	0.912096i
$775$	−6.42993	−	36.4659i	−0.230970	−	1.30989i
$776$	−3.16697	+	1.15268i	−0.113687	+	0.0413788i
$777$	−3.42728	−	2.87583i	−0.122953	−	0.103170i
$778$	11.0001			0.394374
$779$	42.3986	−	15.2492i	1.51909	−	0.546359i
$780$	−0.0533274			−0.00190943
$781$	5.69242	+	4.77651i	0.203691	+	0.170917i
$782$	21.7256	−	7.90748i	0.776906	−	0.282771i
$783$	1.01608	+	5.76246i	0.0363116	+	0.205933i
$784$	2.30517	−	13.0733i	0.0823274	−	0.466902i
$785$	−2.05184	−	0.746809i	−0.0732333	−	0.0266547i
$786$	−1.42435	−	2.46705i	−0.0508050	−	0.0879968i
$787$	−15.8803	+	27.5056i	−0.566073	+	0.980468i	0.430876	+	0.902411i	$0.358205\pi$
$787$	−15.8803	+	27.5056i	−0.566073	+	0.980468i	−0.996949	+	0.0780563i	$0.975129\pi$
$788$	−1.90428	+	1.59788i	−0.0678371	+	0.0569221i
$789$	2.04992	−	1.72009i	0.0729792	−	0.0612368i
$790$	1.11864	−	1.93754i	0.0397995	−	0.0689347i
$791$	16.9460	+	29.3513i	0.602529	+	1.04361i
$792$	2.67969	+	0.975329i	0.0952188	+	0.0346568i
$793$	0.131572	−	0.746179i	0.00467224	−	0.0264976i
$794$	3.02712	+	17.1677i	0.107429	+	0.609258i
$795$	−0.0972190	+	0.0353848i	−0.00344800	+	0.00125497i
$796$	4.26695	+	3.58040i	0.151238	+	0.126904i
$797$	27.6993			0.981158			0.490579	−	0.871397i	$-0.336785\pi$
$797$	27.6993			0.981158			0.490579	+	0.871397i	$0.336785\pi$
$798$	−1.28425	−	7.44919i	−0.0454621	−	0.263699i
$799$	48.5711			1.71832
$800$	3.80488	+	3.19267i	0.134523	+	0.112878i
$801$	7.05081	−	2.56628i	0.249128	−	0.0906752i
$802$	2.04706	+	11.6094i	0.0722841	+	0.409944i
$803$	1.04844	−	5.94598i	0.0369985	−	0.209829i
$804$	4.33374	+	1.57735i	0.152839	+	0.0556289i
$805$	−1.46548	−	2.53829i	−0.0516514	−	0.0894629i
$806$	−2.83761	+	4.91489i	−0.0999506	+	0.173120i
$807$	−2.90198	+	2.43505i	−0.102155	+	0.0857180i
$808$	12.1252	−	10.1743i	0.426564	−	0.357929i
$809$	−1.77572	+	3.07564i	−0.0624310	+	0.108134i	−0.895552	−	0.444958i	$-0.853219\pi$
$809$	−1.77572	+	3.07564i	−0.0624310	+	0.108134i	0.833121	+	0.553091i	$0.186552\pi$
$810$	−0.699089	−	1.21086i	−0.0245635	−	0.0425452i
$811$	8.65244	+	3.14923i	0.303828	+	0.110584i	0.489435	−	0.872040i	$-0.337203\pi$
$811$	8.65244	+	3.14923i	0.303828	+	0.110584i	−0.185607	+	0.982624i	$0.559425\pi$
$812$	2.03008	−	11.5132i	0.0712419	−	0.404033i
$813$	1.66549	+	9.44544i	0.0584111	+	0.331266i
$814$	−2.42432	+	0.882379i	−0.0849722	+	0.0309274i
$815$	−2.61370	−	2.19315i	−0.0915539	−	0.0768228i
$816$	2.48812			0.0871017
$817$	−6.98694	+	38.7609i	−0.244442	+	1.35607i
$818$	−8.08097			−0.282544
$819$	7.48802	+	6.28320i	0.261653	+	0.219553i
$820$	1.76677	−	0.643051i	0.0616983	−	0.0224563i
$821$	0.0943635	+	0.535162i	0.00329331	+	0.0186773i	0.986410	−	0.164302i	$-0.0525371\pi$
$821$	0.0943635	+	0.535162i	0.00329331	+	0.0186773i	−0.983117	+	0.182979i	$0.941426\pi$
$822$	−0.314789	+	1.78526i	−0.0109795	+	0.0622680i
$823$	22.3983	+	8.15230i	0.780754	+	0.284171i	0.701487	−	0.712682i	$-0.252520\pi$
$823$	22.3983	+	8.15230i	0.780754	+	0.284171i	0.0792671	+	0.996853i	$0.474742\pi$
$824$	−8.59925	−	14.8943i	−0.299569	−	0.518869i
$825$	0.956466	−	1.65665i	0.0332999	−	0.0576771i
$826$	−15.2662	+	12.8099i	−0.531180	+	0.445713i
$827$	−16.5583	+	13.8941i	−0.575789	+	0.483144i	−0.883561	−	0.468316i	$-0.844861\pi$
$827$	−16.5583	+	13.8941i	−0.575789	+	0.483144i	0.307772	+	0.951460i	$0.400416\pi$
$828$	−5.10266	+	8.83806i	−0.177330	+	0.307144i
$829$	17.0505	+	29.5323i	0.592187	+	1.02570i	0.993937	+	0.109949i	$0.0350686\pi$
$829$	17.0505	+	29.5323i	0.592187	+	1.02570i	−0.401750	+	0.915749i	$0.631598\pi$
$830$	2.29066	+	0.833730i	0.0795098	+	0.0289392i
$831$	2.06551	−	11.7141i	0.0716518	−	0.406358i
$832$	−0.132192	−	0.749696i	−0.00458292	−	0.0259910i
$833$	80.5893	−	29.3321i	2.79225	−	1.01630i
$834$	2.09015	+	1.75384i	0.0723760	+	0.0607307i
$835$	4.00026			0.138435
$836$	−4.09032	−	1.50642i	−0.141467	−	0.0521008i
$837$	16.8013			0.580736
$838$	12.0389	+	10.1019i	0.415878	+	0.348963i
$839$	17.5787	−	6.39814i	0.606886	−	0.220888i	−0.0202544	−	0.999795i	$-0.506448\pi$
$839$	17.5787	−	6.39814i	0.606886	−	0.220888i	0.627140	+	0.778907i	$0.284225\pi$
$840$	−0.0547729	−	0.310633i	−0.00188985	−	0.0107178i
$841$	−3.86523	+	21.9208i	−0.133284	+	0.755889i
$842$	−31.7405	−	11.5526i	−1.09385	−	0.398129i
$843$	−5.02986	−	8.71198i	−0.173238	−	0.300057i
$844$	8.33197	−	14.4314i	0.286798	−	0.496749i
$845$	1.73060	−	1.45214i	0.0595343	−	0.0499552i
$846$	−16.4237	+	13.7812i	−0.564660	+	0.473806i
$847$	−2.25138	+	3.89951i	−0.0773585	+	0.133989i
$848$	−0.738447	−	1.27903i	−0.0253584	−	0.0439220i
$849$	−8.67647	−	3.15798i	−0.297776	−	0.108382i
$850$	−5.57207	+	31.6008i	−0.191120	+	1.08390i
$851$	−1.60325	−	9.09247i	−0.0549586	−	0.311686i
$852$	−2.68931	+	0.978830i	−0.0921343	+	0.0335342i
$853$	−14.0743	−	11.8098i	−0.481896	−	0.404358i	0.369216	−	0.929344i	$-0.379626\pi$
$853$	−14.0743	−	11.8098i	−0.481896	−	0.404358i	−0.851111	+	0.524985i	$0.824071\pi$
$854$	4.48164			0.153359
$855$	1.12298	+	1.96228i	0.0384050	+	0.0671086i
$856$	−6.48427			−0.221628
$857$	0.519562	+	0.435964i	0.0177479	+	0.0148923i	0.651618	−	0.758547i	$-0.274090\pi$
$857$	0.519562	+	0.435964i	0.0177479	+	0.0148923i	−0.633871	+	0.773439i	$0.718535\pi$
$858$	−0.275507	+	0.100276i	−0.00940565	+	0.00342338i
$859$	7.46897	+	42.3587i	0.254838	+	1.44526i	0.796488	+	0.604654i	$0.206689\pi$
$859$	7.46897	+	42.3587i	0.254838	+	1.44526i	−0.541650	+	0.840604i	$0.682200\pi$
$860$	−0.285387	+	1.61851i	−0.00973160	+	0.0551907i
$861$	16.8449	+	6.13105i	0.574073	+	0.208946i
$862$	18.5376	+	32.1081i	0.631394	+	1.09361i
$863$	15.7928	−	27.3540i	0.537594	−	0.931141i	−0.461438	−	0.887172i	$-0.652666\pi$
$863$	15.7928	−	27.3540i	0.537594	−	0.931141i	0.999033	−	0.0439686i	$-0.0140002\pi$
$864$	−1.72642	+	1.44864i	−0.0587340	+	0.0492837i
$865$	0.362939	−	0.304542i	0.0123403	−	0.0103547i
$866$	18.7211	−	32.4259i	0.636168	−	1.10188i
$867$	4.76349	+	8.25060i	0.161776	+	0.280205i
$868$	−31.5438	−	11.4810i	−1.07067	−	0.389691i
$869$	2.13593	−	12.1135i	0.0724566	−	0.410922i
$870$	−0.0315828	−	0.179115i	−0.00107076	−	0.00607256i
$871$	8.56611	−	3.11781i	0.290252	−	0.105643i
$872$	−6.15875	−	5.16780i	−0.208562	−	0.175004i
$873$	9.61074			0.325274
$874$	7.85104	−	13.4795i	0.265565	−	0.455952i
$875$	8.16289			0.275956
$876$	1.78131	+	1.49469i	0.0601848	+	0.0505010i
$877$	−30.8246	+	11.2192i	−1.04087	+	0.378846i	−0.805211	−	0.592989i	$-0.797948\pi$
$877$	−30.8246	+	11.2192i	−1.04087	+	0.378846i	−0.235661	+	0.971835i	$0.575726\pi$
$878$	0.941482	+	5.33941i	0.0317735	+	0.180196i
$879$	−0.00781947	+	0.0443464i	−0.000263744	+	0.00149577i
$880$	−0.170919	−	0.0622093i	−0.00576166	−	0.00209707i
$881$	23.6550	+	40.9716i	0.796957	+	1.38037i	0.921589	+	0.388167i	$0.126892\pi$
$881$	23.6550	+	40.9716i	0.796957	+	1.38037i	−0.124632	+	0.992203i	$0.539775\pi$
$882$	−18.9279	+	32.7840i	−0.637335	+	1.10390i
$883$	−7.22845	+	6.06539i	−0.243257	+	0.204116i	−0.756262	−	0.654269i	$-0.772976\pi$
$883$	−7.22845	+	6.06539i	−0.243257	+	0.204116i	0.513005	+	0.858385i	$0.328532\pi$
$884$	3.76745	−	3.16126i	0.126713	−	0.106325i
$885$	−0.155019	+	0.268500i	−0.00521090	+	0.00902554i
$886$	−0.660755	−	1.14446i	−0.0221985	−	0.0384489i
$887$	15.8248	+	5.75976i	0.531345	+	0.193394i	0.593739	−	0.804658i	$-0.297651\pi$
$887$	15.8248	+	5.75976i	0.531345	+	0.193394i	−0.0623935	+	0.998052i	$0.519873\pi$
$888$	0.172539	−	0.978516i	0.00579002	−	0.0328368i
$889$	−12.9746	−	73.5828i	−0.435155	−	2.46789i
$890$	−0.449720	+	0.163685i	−0.0150747	+	0.00548673i
$891$	−5.88862	−	4.94114i	−0.197276	−	0.165534i
$892$	−17.8558			−0.597857
$893$	25.1845	−	20.9693i	0.842766	−	0.701711i
$894$	6.00012			0.200674
$895$	2.83788	+	2.38127i	0.0948599	+	0.0795969i
$896$	4.23122	−	1.54004i	0.141355	−	0.0514491i
$897$	−0.182198	−	1.03330i	−0.00608342	−	0.0345008i
$898$	3.48806	−	19.7818i	0.116398	−	0.660126i
$899$	−18.1886	−	6.62010i	−0.606623	−	0.220793i
$900$	−7.08201	−	12.2664i	−0.236067	−	0.408880i
$901$	4.77066	−	8.26303i	0.158934	−	0.275281i
$902$	7.91853	−	6.64444i	0.263658	−	0.221236i
$903$	−12.0035	+	10.0721i	−0.399450	+	0.335179i
$904$	−3.76345	+	6.51849i	−0.125171	+	0.216802i
$905$	−0.639176	−	1.10709i	−0.0212469	−	0.0368008i
$906$	−0.864794	−	0.314759i	−0.0287308	−	0.0104572i
$907$	−6.87430	+	38.9861i	−0.228257	+	1.29451i	0.628102	+	0.778131i	$0.283832\pi$
$907$	−6.87430	+	38.9861i	−0.228257	+	1.29451i	−0.856359	+	0.516380i	$0.827279\pi$
$908$	−3.15634	−	17.9005i	−0.104747	−	0.594048i
$909$	−42.4151	+	15.4378i	−1.40682	+	0.512041i
$910$	−0.477607	−	0.400760i	−0.0158325	−	0.0132851i
$911$	21.5387			0.713608			0.356804	−	0.934179i	$-0.383866\pi$
$911$	21.5387			0.713608			0.356804	+	0.934179i	$0.383866\pi$
$912$	1.29011	−	1.07418i	0.0427198	−	0.0355697i
$913$	13.4020			0.443542
$914$	−17.7101	−	14.8606i	−0.585799	−	0.491544i
$915$	0.0655178	−	0.0238465i	0.00216595	−	0.000788342i
$916$	1.62619	+	9.22256i	0.0537307	+	0.304722i
$917$	5.78342	−	32.7994i	0.190985	−	1.08313i
$918$	−13.6816	−	4.97970i	−0.451561	−	0.164355i
$919$	8.10496	+	14.0382i	0.267358	+	0.463077i	0.968179	−	0.250260i	$-0.0805161\pi$
$919$	8.10496	+	14.0382i	0.267358	+	0.463077i	−0.700821	+	0.713337i	$0.747183\pi$
$920$	0.325462	−	0.563717i	0.0107302	−	0.0185852i
$921$	1.71282	−	1.43722i	0.0564392	−	0.0473581i
$922$	22.1118	−	18.5540i	0.728215	−	0.611045i
$923$	−2.82844	+	4.89900i	−0.0930992	+	0.161253i
$924$	−0.867087	−	1.50184i	−0.0285251	−	0.0494068i
$925$	12.0414	+	4.38270i	0.395918	+	0.144102i
$926$	4.77881	−	27.1020i	0.157041	−	0.890626i
$927$	8.51648	+	48.2994i	0.279718	+	1.58636i
$928$	2.43977	−	0.888005i	0.0800895	−	0.0291502i
$929$	0.379899	+	0.318773i	0.0124641	+	0.0104586i	0.648998	−	0.760790i	$-0.275188\pi$
$929$	0.379899	+	0.318773i	0.0124641	+	0.0104586i	−0.636534	+	0.771248i	$0.719633\pi$
$930$	−0.522234			−0.0171247
$931$	29.1227	−	50.0012i	0.954459	−	1.63872i
$932$	−25.4555			−0.833823
$933$	−4.23377	−	3.55256i	−0.138608	−	0.116306i
$934$	2.98230	−	1.08547i	0.0975838	−	0.0355176i
$935$	−0.204048	−	1.15721i	−0.00667309	−	0.0378450i
$936$	−0.376967	+	2.13789i	−0.0123216	+	0.0698790i
$937$	−29.2713	−	10.6539i	−0.956251	−	0.348047i	−0.183688	−	0.982985i	$-0.558803\pi$
$937$	−29.2713	−	10.6539i	−0.956251	−	0.348047i	−0.772563	+	0.634938i	$0.781026\pi$
$938$	26.9596	+	46.6954i	0.880262	+	1.52466i
$939$	3.55127	−	6.15098i	0.115891	−	0.200730i
$940$	1.04755	−	0.879002i	0.0341674	−	0.0286699i
$941$	34.8223	−	29.2194i	1.13518	−	0.952525i	0.135905	−	0.990722i	$-0.456606\pi$
$941$	34.8223	−	29.2194i	1.13518	−	0.952525i	0.999270	+	0.0381967i	$0.0121614\pi$
$942$	2.31173	−	4.00403i	0.0753203	−	0.130459i
$943$	18.4964	+	32.0368i	0.602327	+	1.04326i
$944$	−4.15895	−	1.51373i	−0.135362	−	0.0492679i
$945$	−0.320513	+	1.81772i	−0.0104263	+	0.0591305i
$946$	1.56903	+	8.89839i	0.0510135	+	0.289312i
$947$	−44.8602	+	16.3278i	−1.45776	+	0.530581i	−0.944747	−	0.327800i	$-0.893693\pi$
$947$	−44.8602	+	16.3278i	−1.45776	+	0.530581i	−0.513013	+	0.858381i	$0.671471\pi$
$948$	3.62898	+	3.04507i	0.117864	+	0.0988994i
$949$	4.59627			0.149201
$950$	10.7536	+	18.7908i	0.348894	+	0.609654i
$951$	−4.20596			−0.136388
$952$	22.2840	+	18.6985i	0.722228	+	0.606021i
$953$	−0.951952	+	0.346482i	−0.0308367	+	0.0112237i	−0.357392	−	0.933954i	$-0.616334\pi$
$953$	−0.951952	+	0.346482i	−0.0308367	+	0.0112237i	0.326556	+	0.945178i	$0.394112\pi$
$954$	0.731340	+	4.14763i	0.0236780	+	0.134285i
$955$	−0.192566	+	1.09210i	−0.00623130	+	0.0353395i
$956$	−7.84903	−	2.85681i	−0.253856	−	0.0923960i
$957$	−0.499973	−	0.865978i	−0.0161618	−	0.0279931i
$958$	14.5668	−	25.2304i	0.470631	−	0.815156i
$959$	−16.2357	+	13.6233i	−0.524277	+	0.439921i
$960$	0.0536624	−	0.0450281i	0.00173195	−	0.00145328i
$961$	−12.2887	+	21.2846i	−0.396409	+	0.686601i
$962$	−0.981991	−	1.70086i	−0.0316607	−	0.0548379i
$963$	17.3759	+	6.32430i	0.559930	+	0.203798i
$964$	2.43992	−	13.8375i	0.0785846	−	0.445675i
$965$	−0.257074	−	1.45794i	−0.00827549	−	0.0469326i
$966$	5.83184	−	2.12262i	0.187636	−	0.0682940i
$967$	29.0426	+	24.3697i	0.933948	+	0.783676i	0.976522	−	0.215418i	$-0.0691112\pi$
$967$	29.0426	+	24.3697i	0.933948	+	0.783676i	−0.0425736	+	0.999093i	$0.513556\pi$
$968$	−1.00000			−0.0321412
$969$	10.1772	+	3.74817i	0.326939	+	0.120409i
$970$	−0.613000			−0.0196823
$971$	15.6260	+	13.1117i	0.501461	+	0.420776i	0.858113	−	0.513462i	$-0.171637\pi$
$971$	15.6260	+	13.1117i	0.501461	+	0.420776i	−0.356651	+	0.934238i	$0.616082\pi$
$972$	9.13531	−	3.32498i	0.293015	−	0.106649i
$973$	5.53937	+	31.4154i	0.177584	+	1.00713i
$974$	−2.39079	+	13.5589i	−0.0766060	+	0.434454i
$975$	1.36842	+	0.498064i	0.0438245	+	0.0159508i
$976$	0.497654	+	0.861962i	0.0159295	+	0.0275907i
$977$	26.6142	−	46.0972i	0.851464	−	1.47478i	−0.0284235	−	0.999596i	$-0.509049\pi$
$977$	26.6142	−	46.0972i	0.851464	−	1.47478i	0.879887	−	0.475183i	$-0.157618\pi$
$978$	5.53433	−	4.64385i	0.176968	−	0.148494i
$979$	−2.01561	+	1.69130i	−0.0644193	+	0.0540542i
$980$	1.20727	−	2.09106i	0.0385649	−	0.0667964i
$981$	11.4633	+	19.8549i	0.365994	+	0.633920i
$982$	3.42804	+	1.24770i	0.109393	+	0.0398158i
$983$	6.38772	−	36.2266i	0.203737	−	1.15545i	−0.695679	−	0.718353i	$-0.744896\pi$
$983$	6.38772	−	36.2266i	0.203737	−	1.15545i	0.899415	−	0.437095i	$-0.143993\pi$
$984$	0.691311	+	3.92062i	0.0220382	+	0.124985i
$985$	−0.424879	+	0.154643i	−0.0135378	+	0.00492735i
$986$	12.8492	+	10.7818i	0.409203	+	0.343362i
$987$	13.0380			0.415005
$988$	0.588655	−	3.26563i	0.0187276	−	0.103894i
$989$	−32.3361			−1.02823
$990$	0.397335	+	0.333404i	0.0126281	+	0.0105963i
$991$	−51.1795	+	18.6278i	−1.62577	+	0.591732i	−0.984469	−	0.175557i	$-0.943827\pi$
$991$	−51.1795	+	18.6278i	−1.62577	+	0.591732i	−0.641302	+	0.767289i	$0.721605\pi$
$992$	−1.29455	−	7.34176i	−0.0411020	−	0.233101i
$993$	0.614686	−	3.48606i	0.0195065	−	0.110627i
$994$	−31.4419	−	11.4439i	−0.997275	−	0.362979i
$995$	0.506567	+	0.877400i	0.0160593	+	0.0278154i
$996$	−2.58079	+	4.47007i	−0.0817756	+	0.141639i
$997$	10.8540	−	9.10761i	0.343750	−	0.288441i	−0.454524	−	0.890734i	$-0.650191\pi$
$997$	10.8540	−	9.10761i	0.343750	−	0.288441i	0.798275	+	0.602294i	$0.205746\pi$
$998$	−10.5127	+	8.82120i	−0.332773	+	0.279230i
$999$	−2.90714	+	5.03532i	−0.0919779	+	0.159310i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.j.a.111.3	✓	24
19.5	even	9		7942.2.a.bt.1.6		12
19.6	even	9	inner	418.2.j.a.177.3	yes	24
19.14	odd	18		7942.2.a.bx.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.j.a.111.3	✓	24	1.1	even	1	trivial
418.2.j.a.177.3	yes	24	19.6	even	9	inner
7942.2.a.bt.1.6		12	19.5	even	9
7942.2.a.bx.1.7		12	19.14	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.j (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.361908 - 0.131724i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.0315845 + 0.179124i) q^{5} +(-0.361908 - 0.131724i) q^{6} +(-2.25138 - 3.89951i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.18451 + 1.83302i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.361908 - 0.131724i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.0315845 + 0.179124i) q^{5} +(-0.361908 - 0.131724i) q^{6} +(-2.25138 - 3.89951i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.18451 + 1.83302i) q^{9} +(0.139334 - 0.116915i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.192567 + 0.333537i) q^{12} +(0.715352 + 0.260367i) q^{13} +(-0.781898 + 4.43436i) q^{14} +(0.0121643 + 0.0689870i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-4.94895 - 4.15266i) q^{17} +2.85167 q^{18} +(-4.35887 - 0.0166052i) q^{19} -0.181888 q^{20} +(-1.32845 - 1.11471i) q^{21} +(-0.939693 + 0.342020i) q^{22} +(-0.621437 - 3.52435i) q^{23} +(0.0668780 - 0.379284i) q^{24} +(4.66738 + 1.69879i) q^{25} +(-0.380631 - 0.659272i) q^{26} +(-1.12684 + 1.95175i) q^{27} +(3.44932 - 2.89432i) q^{28} +(1.98892 - 1.66890i) q^{29} +(0.0350256 - 0.0606662i) q^{30} +(-3.72751 - 6.45624i) q^{31} +(0.939693 + 0.342020i) q^{32} +(0.0668780 - 0.379284i) q^{33} +(1.12184 + 6.36225i) q^{34} +(0.769607 - 0.280114i) q^{35} +(-2.18451 - 1.83302i) q^{36} +2.57990 q^{37} +(3.32841 + 2.81455i) q^{38} +0.293188 q^{39} +(0.139334 + 0.116915i) q^{40} +(-9.71352 + 3.53543i) q^{41} +(0.301136 + 1.70783i) q^{42} +(1.56903 - 8.89839i) q^{43} +(0.939693 + 0.342020i) q^{44} +(-0.259342 - 0.449193i) q^{45} +(-1.78936 + 3.09926i) q^{46} +(-5.75934 + 4.83266i) q^{47} +(-0.295030 + 0.247560i) q^{48} +(-6.63747 + 11.4964i) q^{49} +(-2.48346 - 4.30148i) q^{50} +(-2.33807 - 0.850988i) q^{51} +(-0.132192 + 0.749696i) q^{52} +(0.256460 + 1.45446i) q^{53} +(2.11777 - 0.770805i) q^{54} +(0.139334 + 0.116915i) q^{55} -4.50277 q^{56} +(-1.57970 + 0.568157i) q^{57} -2.59635 q^{58} +(3.39041 + 2.84489i) q^{59} +(-0.0658267 + 0.0239589i) q^{60} +(-0.172833 - 0.980187i) q^{61} +(-1.29455 + 7.34176i) q^{62} +(12.0660 + 4.39168i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.0692321 + 0.119913i) q^{65} +(-0.295030 + 0.247560i) q^{66} +(9.17313 - 7.69717i) q^{67} +(3.23020 - 5.59487i) q^{68} +(-0.689144 - 1.19363i) q^{69} +(-0.769607 - 0.280114i) q^{70} +(-1.29037 + 7.31803i) q^{71} +(0.495188 + 2.80835i) q^{72} +(5.67359 - 2.06502i) q^{73} +(-1.97632 - 1.65833i) q^{74} +1.91293 q^{75} +(-0.740556 - 4.29553i) q^{76} -4.50277 q^{77} +(-0.224595 - 0.188458i) q^{78} +(11.5585 - 4.20697i) q^{79} +(-0.0315845 - 0.179124i) q^{80} +(1.33484 - 7.57026i) q^{81} +(9.71352 + 3.53543i) q^{82} +(6.70102 + 11.6065i) q^{83} +(0.867087 - 1.50184i) q^{84} +(0.900153 - 0.755318i) q^{85} +(-6.92172 + 5.80801i) q^{86} +(0.499973 - 0.865978i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-2.47252 - 0.899923i) q^{89} +(-0.0900685 + 0.510804i) q^{90} +(-0.595229 - 3.37571i) q^{91} +(3.36289 - 1.22399i) q^{92} +(-2.19946 - 1.84556i) q^{93} +7.51829 q^{94} +(0.140647 - 0.780255i) q^{95} +0.385135 q^{96} +(-2.58173 - 2.16633i) q^{97} +(12.4744 - 4.54029i) q^{98} +(0.495188 + 2.80835i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{8}+O(q^{10}) \) 24 * q + 12 * q^8	\( 24 q + 12 q^{8} + 12 q^{11} - 3 q^{12} - 3 q^{13} + 3 q^{14} + 27 q^{15} - 6 q^{18} - 21 q^{19} - 18 q^{20} + 15 q^{21} + 9 q^{23} + 36 q^{25} - 21 q^{27} - 3 q^{28} - 9 q^{30} - 27 q^{31} - 9 q^{34} - 45 q^{35} + 18 q^{37} + 9 q^{38} + 36 q^{39} - 18 q^{41} + 39 q^{42} - 48 q^{43} + 36 q^{45} - 18 q^{46} - 9 q^{47} + 6 q^{49} + 3 q^{50} - 18 q^{51} - 3 q^{52} - 36 q^{53} - 45 q^{54} + 18 q^{58} + 9 q^{59} - 9 q^{60} + 15 q^{61} - 33 q^{62} + 87 q^{63} - 12 q^{64} - 36 q^{65} + 33 q^{67} + 9 q^{68} - 18 q^{69} + 45 q^{70} - 9 q^{71} - 3 q^{73} + 3 q^{74} + 42 q^{75} + 9 q^{76} + 12 q^{78} + 15 q^{79} - 108 q^{81} + 18 q^{82} + 36 q^{83} - 9 q^{84} - 99 q^{85} - 33 q^{86} + 63 q^{87} - 12 q^{88} - 27 q^{89} - 36 q^{90} - 21 q^{91} - 9 q^{92} - 21 q^{93} + 54 q^{94} + 18 q^{95} - 6 q^{96} + 45 q^{97} + 39 q^{98}+O(q^{100}) \) 24 * q + 12 * q^8 + 12 * q^11 - 3 * q^12 - 3 * q^13 + 3 * q^14 + 27 * q^15 - 6 * q^18 - 21 * q^19 - 18 * q^20 + 15 * q^21 + 9 * q^23 + 36 * q^25 - 21 * q^27 - 3 * q^28 - 9 * q^30 - 27 * q^31 - 9 * q^34 - 45 * q^35 + 18 * q^37 + 9 * q^38 + 36 * q^39 - 18 * q^41 + 39 * q^42 - 48 * q^43 + 36 * q^45 - 18 * q^46 - 9 * q^47 + 6 * q^49 + 3 * q^50 - 18 * q^51 - 3 * q^52 - 36 * q^53 - 45 * q^54 + 18 * q^58 + 9 * q^59 - 9 * q^60 + 15 * q^61 - 33 * q^62 + 87 * q^63 - 12 * q^64 - 36 * q^65 + 33 * q^67 + 9 * q^68 - 18 * q^69 + 45 * q^70 - 9 * q^71 - 3 * q^73 + 3 * q^74 + 42 * q^75 + 9 * q^76 + 12 * q^78 + 15 * q^79 - 108 * q^81 + 18 * q^82 + 36 * q^83 - 9 * q^84 - 99 * q^85 - 33 * q^86 + 63 * q^87 - 12 * q^88 - 27 * q^89 - 36 * q^90 - 21 * q^91 - 9 * q^92 - 21 * q^93 + 54 * q^94 + 18 * q^95 - 6 * q^96 + 45 * q^97 + 39 * q^98

Introduction

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