LMFDB - Embedded newform 418.2.j.a.177.3

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			177.3
Character	$\chi$	$=$	418.177
Dual form			418.2.j.a.111.3

$q$-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 $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

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	0.444374	−	0.895842i	$-0.353426\pi$
$3$	0.361908	+	0.131724i	0.208948	+	0.0760508i	−0.235426	+	0.971892i	$0.575648\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.0315845	−	0.179124i	−0.0141250	−	0.0801069i	0.976930	−	0.213558i	$-0.0685052\pi$
$5$	−0.0315845	−	0.179124i	−0.0141250	−	0.0801069i	−0.991055	+	0.133451i	$0.957394\pi$
$6$	−0.361908	+	0.131724i	−0.147748	+	0.0537760i
$7$	−2.25138	+	3.89951i	−0.850943	+	1.47388i	0.0294144	+	0.999567i	$0.490636\pi$
$7$	−2.25138	+	3.89951i	−0.850943	+	1.47388i	−0.880358	+	0.474310i	$0.842698\pi$
$8$	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	−0.240907	−	0.970548i	$-0.577445\pi$
$13$	0.715352	−	0.260367i	0.198403	−	0.0722128i	0.439310	+	0.898335i	$0.355223\pi$
$14$	−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	−0.200675	+	0.979658i	$0.564314\pi$
$17$	−4.94895	+	4.15266i	−1.20030	+	1.00717i	−0.999622	+	0.0275108i	$0.991242\pi$
$18$	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	0.848904	+	0.528547i	$0.177263\pi$
$23$	−0.621437	+	3.52435i	−0.129579	+	0.734877i	−0.978483	+	0.206330i	$0.933848\pi$
$24$	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	0.808498	−	0.588499i	$-0.200281\pi$
$29$	1.98892	+	1.66890i	0.369333	+	0.309908i	−0.439164	+	0.898407i	$0.644725\pi$
$30$	0.0350256	+	0.0606662i	0.00639478	+	0.0110761i
$31$	−3.72751	+	6.45624i	−0.669481	+	1.15957i	0.308569	+	0.951202i	$0.400150\pi$
$31$	−3.72751	+	6.45624i	−0.669481	+	1.15957i	−0.978049	+	0.208373i	$0.933183\pi$
$32$	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	−0.556601	−	0.830780i	$-0.687895\pi$
$41$	−9.71352	−	3.53543i	−1.51700	−	0.552142i	−0.960396	+	0.278639i	$0.910117\pi$
$42$	0.301136	−	1.70783i	0.0464663	−	0.263523i
$43$	1.56903	+	8.89839i	0.239274	+	1.35699i	0.833422	+	0.552636i	$0.186378\pi$
$43$	1.56903	+	8.89839i	0.239274	+	1.35699i	−0.594148	+	0.804356i	$0.702511\pi$
$44$	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	0.117497	−	0.993073i	$-0.462513\pi$
$47$	−5.75934	−	4.83266i	−0.840086	−	0.704916i	−0.957583	+	0.288157i	$0.906957\pi$
$48$	−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	−0.962115	−	0.272645i	$-0.912102\pi$
$53$	0.256460	−	1.45446i	0.0352275	−	0.199785i	0.997342	+	0.0728601i	$0.0232126\pi$
$54$	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	−0.394837	−	0.918751i	$-0.629199\pi$
$59$	3.39041	−	2.84489i	0.441394	−	0.370373i	0.836231	+	0.548378i	$0.184754\pi$
$60$	−0.0658267	−	0.0239589i	−0.00849819	−	0.00309309i
$61$	−0.172833	+	0.980187i	−0.0221291	+	0.125500i	−0.993871	−	0.110545i	$-0.964740\pi$
$61$	−0.172833	+	0.980187i	−0.0221291	+	0.125500i	0.971742	+	0.236045i	$0.0758514\pi$
$62$	−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	0.998638	−	0.0521660i	$-0.0166125\pi$
$67$	9.17313	+	7.69717i	1.12068	+	0.940359i	0.122038	+	0.992525i	$0.461057\pi$
$68$	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	−0.960468	−	0.278390i	$-0.910199\pi$
$71$	−1.29037	−	7.31803i	−0.153138	−	0.868490i	0.807330	−	0.590100i	$-0.200912\pi$
$72$	0.495188	−	2.80835i	0.0583584	−	0.330967i
$73$	5.67359	+	2.06502i	0.664043	+	0.241692i	0.651981	−	0.758235i	$-0.273938\pi$
$73$	5.67359	+	2.06502i	0.664043	+	0.241692i	0.0120621	+	0.999927i	$0.496160\pi$
$74$	−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	0.897139	−	0.441748i	$-0.145641\pi$
$79$	11.5585	+	4.20697i	1.30044	+	0.473321i	0.403299	+	0.915068i	$0.367864\pi$
$80$	−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	−0.218958	−	0.975734i	$-0.570266\pi$
$83$	6.70102	−	11.6065i	0.735532	−	1.27398i	0.954490	−	0.298244i	$-0.0964011\pi$
$84$	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	−0.469721	−	0.882815i	$-0.655646\pi$
$89$	−2.47252	+	0.899923i	−0.262086	+	0.0953916i	0.207635	+	0.978206i	$0.433423\pi$
$90$	−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	−0.764377	−	0.644770i	$-0.776953\pi$
$97$	−2.58173	+	2.16633i	−0.262135	+	0.219958i	0.502242	+	0.864727i	$0.332509\pi$
$98$	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	0.529201	−	0.848496i	$-0.322492\pi$
$101$	14.8738	−	5.41361i	1.48000	−	0.538675i	0.950795	+	0.309822i	$0.100269\pi$
$102$	1.24406	−	2.15478i	0.123180	−	0.213355i
$103$	8.59925	+	14.8943i	0.847309	+	1.46758i	0.883601	+	0.468241i	$0.155112\pi$
$103$	8.59925	+	14.8943i	0.847309	+	1.46758i	−0.0362913	+	0.999341i	$0.511554\pi$
$104$	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	−0.979102	−	0.203368i	$-0.934811\pi$
$107$	−3.24214	+	5.61554i	−0.313429	+	0.542875i	0.665673	+	0.746243i	$0.268144\pi$
$108$	−2.11777	+	0.770805i	−0.203782	+	0.0741707i
$109$	1.39608	+	7.91754i	0.133720	+	0.758362i	0.975743	+	0.218921i	$0.0702536\pi$
$109$	1.39608	+	7.91754i	0.133720	+	0.758362i	−0.842023	+	0.539442i	$0.818635\pi$
$110$	−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	0.460373	−	0.887725i	$-0.347716\pi$
$127$	15.5930	−	5.67540i	1.38366	−	0.503610i	0.923285	+	0.384115i	$0.125493\pi$
$128$	−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	−0.360779	−	0.932651i	$-0.617489\pi$
$131$	5.66616	−	4.75447i	0.495055	−	0.415400i	0.855834	+	0.517251i	$0.173045\pi$
$132$	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	0.929780	+	0.368117i	$0.119997\pi$
$137$	−0.817347	+	4.63541i	−0.0698307	+	0.396030i	−0.999610	+	0.0279130i	$0.991114\pi$
$138$	−0.239337	−	1.35735i	−0.0203737	−	0.115545i
$139$	−6.65728	+	2.42305i	−0.564663	+	0.205520i	−0.608549	−	0.793516i	$-0.708248\pi$
$139$	−6.65728	+	2.42305i	−0.564663	+	0.205520i	0.0438865	+	0.999037i	$0.486026\pi$
$140$	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	−0.336341	−	0.941740i	$-0.609190\pi$
$149$	−14.6397	−	5.32842i	−1.19933	−	0.436521i	−0.862991	+	0.505219i	$0.831412\pi$
$150$	−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	−0.947641	−	0.319339i	$-0.896539\pi$
$157$	−2.08461	−	11.8224i	−0.166370	−	0.943531i	0.781271	−	0.624192i	$-0.214572\pi$
$158$	−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	−0.954881	−	0.296988i	$-0.904018\pi$
$163$	−9.37925	−	16.2453i	−0.734640	−	1.27243i	0.220241	−	0.975445i	$-0.429316\pi$
$164$	−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	0.369526	+	0.929220i	$0.379520\pi$
$167$	−3.81905	+	21.6589i	−0.295527	+	1.67602i	−0.665053	+	0.746796i	$0.731591\pi$
$168$	−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	−0.715482	−	0.698631i	$-0.753793\pi$
$173$	−1.99540	+	1.67434i	−0.151708	+	0.127298i	0.563775	+	0.825929i	$0.309349\pi$
$174$	−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	0.942249	+	0.334914i	$0.108707\pi$
$179$	10.1837	+	17.6387i	0.761168	+	1.31838i	−0.181081	+	0.983468i	$0.557960\pi$
$180$	0.397335	+	0.333404i	0.0296156	+	0.0248504i
$181$	−5.38395	−	4.51767i	−0.400186	−	0.335796i	0.420379	−	0.907348i	$-0.361897\pi$
$181$	−5.38395	−	4.51767i	−0.400186	−	0.335796i	−0.820566	+	0.571552i	$0.806341\pi$
$182$	−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	0.0517449	−	0.998660i	$-0.483522\pi$
$193$	−7.64838	−	2.78378i	−0.550543	−	0.200381i	−0.602288	+	0.798279i	$0.705744\pi$
$194$	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	−0.818346	−	0.574727i	$-0.805108\pi$
$197$	1.24293	−	2.15282i	0.0885550	−	0.153382i	0.906901	+	0.421345i	$0.138442\pi$
$198$	1.42584	+	2.46962i	0.101330	+	0.175508i
$199$	4.26695	+	3.58040i	0.302476	+	0.253808i	0.781374	−	0.624063i	$-0.214519\pi$
$199$	4.26695	+	3.58040i	0.302476	+	0.253808i	−0.478898	+	0.877871i	$0.658964\pi$
$200$	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	−0.965932	−	0.258795i	$-0.916674\pi$
$211$	−12.7653	+	10.7114i	−0.878801	+	0.737401i	0.0871314	+	0.996197i	$0.472230\pi$
$212$	−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	−0.893242	−	0.449577i	$-0.851575\pi$
$223$	−3.10063	−	17.5845i	−0.207633	−	1.17755i	0.685608	−	0.727971i	$-0.259536\pi$
$224$	−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	−0.688437	−	0.725296i	$-0.741703\pi$
$233$	−4.42030	−	25.0688i	−0.289584	−	1.64231i	0.398854	−	0.917015i	$-0.369408\pi$
$234$	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	0.698752	−	0.715364i	$-0.253739\pi$
$239$	−4.17638	−	7.23371i	−0.270148	−	0.467910i	−0.968899	+	0.247455i	$0.920406\pi$
$240$	−0.0350256	+	0.0606662i	−0.00226090	+	0.00391599i
$241$	−13.2036	+	4.80571i	−0.850517	+	0.309563i	−0.730251	−	0.683179i	$-0.760597\pi$
$241$	−13.2036	+	4.80571i	−0.850517	+	0.309563i	−0.120266	+	0.992742i	$0.538375\pi$
$242$	−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	0.414307	+	0.910137i	$0.364024\pi$
$251$	−4.53584	+	25.7240i	−0.286299	+	1.62368i	−0.700607	+	0.713548i	$0.747087\pi$
$252$	−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	0.998690	−	0.0511698i	$-0.0162950\pi$
$257$	17.9825	+	15.0891i	1.12172	+	0.941233i	0.123028	+	0.992403i	$0.460739\pi$
$258$	−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	0.535383	−	0.844610i	$-0.320167\pi$
$263$	6.52915	+	2.37642i	0.402605	+	0.146536i	−0.132778	+	0.991146i	$0.542390\pi$
$264$	−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	0.0445026	−	0.999009i	$-0.485830\pi$
$269$	−9.24302	−	3.36419i	−0.563557	−	0.205118i	−0.608060	+	0.793891i	$0.708052\pi$
$270$	0.0711813	−	0.403689i	0.00433196	−	0.0245678i
$271$	−4.32442	−	24.5250i	−0.262690	−	1.48979i	−0.775533	−	0.631307i	$-0.782519\pi$
$271$	−4.32442	−	24.5250i	−0.262690	−	1.48979i	0.512843	−	0.858482i	$-0.328592\pi$
$272$	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	0.786923	+	0.617051i	$0.211673\pi$
$277$	15.4424	+	26.7470i	0.927844	+	1.60707i	0.140921	+	0.990021i	$0.454994\pi$
$278$	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	0.482094	+	0.876120i	$0.339877\pi$
$281$	−4.53569	+	25.7232i	−0.270577	+	1.53452i	−0.752670	+	0.658398i	$0.771235\pi$
$282$	2.72093	+	0.990338i	0.162029	+	0.0589738i
$283$	−18.3653	+	15.4103i	−1.09171	+	0.916050i	−0.996840	−	0.0794406i	$-0.974687\pi$
$283$	−18.3653	+	15.4103i	−1.09171	+	0.916050i	−0.0948657	+	0.995490i	$0.530242\pi$
$284$	−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	0.864313	−	0.502955i	$-0.167754\pi$
$293$	−0.0584608	−	0.101257i	−0.00341531	−	0.00591550i	−0.867728	+	0.497039i	$0.834420\pi$
$294$	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	0.492973	−	0.870045i	$-0.335910\pi$
$307$	5.45544	+	1.98562i	0.311359	+	0.113325i	−0.181615	+	0.983370i	$0.558132\pi$
$308$	−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	−0.994537	−	0.104388i	$-0.966711\pi$
$311$	−7.17515	+	12.4277i	−0.406865	+	0.704711i	0.587671	+	0.809100i	$0.300045\pi$
$312$	0.146594	+	0.253909i	0.00829926	+	0.0143747i
$313$	14.1272	+	11.8541i	0.798515	+	0.670033i	0.947837	−	0.318755i	$-0.103265\pi$
$313$	14.1272	+	11.8541i	0.798515	+	0.670033i	−0.149322	+	0.988789i	$0.547709\pi$
$314$	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	−0.613728	−	0.789517i	$-0.710331\pi$
$317$	−10.2622	+	3.73512i	−0.576380	+	0.209785i	0.0373486	+	0.999302i	$0.488109\pi$
$318$	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	0.964240	−	0.265031i	$-0.0853823\pi$
$331$	4.59558	+	7.95978i	0.252596	+	0.437509i	−0.711644	+	0.702540i	$0.752049\pi$
$332$	−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	−0.999786	−	0.0207031i	$-0.993410\pi$
$337$	−1.23685	−	7.01451i	−0.0673753	−	0.382105i	0.932410	−	0.361401i	$-0.117702\pi$
$338$	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	0.882315	+	0.470660i	$0.155984\pi$
$347$	3.98983	+	22.6274i	0.214185	+	1.21470i	−0.668130	+	0.744045i	$0.732905\pi$
$348$	0.939642	−	0.342002i	0.0503701	−	0.0183332i
$349$	11.6363	−	20.1546i	0.622874	−	1.07885i	−0.366073	−	0.930586i	$-0.619298\pi$
$349$	11.6363	−	20.1546i	0.622874	−	1.07885i	0.988948	−	0.148264i	$-0.0473686\pi$
$350$	−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	0.890305	−	0.455364i	$-0.150491\pi$
$353$	0.954373	+	1.65302i	0.0507962	+	0.0879815i	−0.839509	+	0.543345i	$0.817157\pi$
$354$	−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	−0.742003	−	0.670397i	$-0.766124\pi$
$359$	−3.99102	+	3.34886i	−0.210638	+	0.176746i	0.531365	+	0.847143i	$0.321679\pi$
$360$	−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	−0.278732	−	0.960369i	$-0.589914\pi$
$367$	2.39581	−	0.872004i	0.125060	−	0.0455182i	0.403792	+	0.914851i	$0.367692\pi$
$368$	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	−0.0327256	+	0.999464i	$0.510419\pi$
$373$	−17.0328	+	29.5017i	−0.881924	+	1.52754i	−0.849199	+	0.528073i	$0.822915\pi$
$374$	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	0.406253	−	0.913761i	$-0.366835\pi$
$383$	2.54625	+	0.926759i	0.130107	+	0.0473552i	−0.276146	+	0.961116i	$0.589057\pi$
$384$	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	0.403666	−	0.914907i	$-0.367736\pi$
$389$	−8.42660	−	7.07076i	−0.427246	−	0.358502i	−0.830911	+	0.556405i	$0.812180\pi$
$390$	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	−0.913131	−	0.407666i	$-0.866343\pi$
$397$	−13.3541	+	11.2054i	−0.670222	+	0.562383i	0.242909	+	0.970049i	$0.421898\pi$
$398$	−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	−0.839793	−	0.542906i	$-0.817324\pi$
$401$	−9.03054	+	7.57752i	−0.450964	+	0.378403i	0.388830	+	0.921310i	$0.372879\pi$
$402$	−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	0.782876	−	0.622178i	$-0.213752\pi$
$409$	6.19038	+	5.19434i	0.306095	+	0.256844i	−0.476781	+	0.879022i	$0.658197\pi$
$410$	−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	0.967697	−	0.252116i	$-0.0811264\pi$
$421$	31.7405	+	11.5526i	1.54694	+	0.563040i	0.579242	+	0.815156i	$0.303349\pi$
$422$	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	−0.993055	−	0.117654i	$-0.962463\pi$
$431$	−34.8394	+	12.6805i	−1.67815	+	0.610798i	−0.685098	+	0.728451i	$0.740241\pi$
$432$	0.391348	+	2.21944i	0.0188287	+	0.106783i
$433$	6.50176	−	36.8733i	0.312455	−	1.77202i	−0.273696	−	0.961816i	$-0.588246\pi$
$433$	6.50176	−	36.8733i	0.312455	−	1.77202i	0.586150	−	0.810202i	$-0.300643\pi$
$434$	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	−0.736498	−	0.676439i	$-0.763522\pi$
$439$	−4.15333	+	3.48505i	−0.198227	+	0.166333i	0.538271	+	0.842772i	$0.319078\pi$
$440$	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	−0.312351	−	0.949967i	$-0.601117\pi$
$443$	1.24181	−	0.451983i	0.0590003	−	0.0214744i	0.371352	+	0.928492i	$0.378894\pi$
$444$	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	−0.525576	−	0.850747i	$-0.676150\pi$
$449$	10.0435	−	17.3958i	0.473980	−	0.820958i	0.999556	+	0.0297888i	$0.00948348\pi$
$450$	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	−0.845857	−	0.533410i	$-0.820910\pi$
$461$	−5.01235	−	28.4264i	−0.233448	−	1.32395i	0.612409	−	0.790541i	$-0.290201\pi$
$462$	1.62959	−	0.593122i	0.0758154	−	0.0275945i
$463$	13.7600	−	23.8331i	0.639483	−	1.10762i	−0.346063	−	0.938211i	$-0.612482\pi$
$463$	13.7600	−	23.8331i	0.639483	−	1.10762i	0.985546	−	0.169406i	$-0.0541849\pi$
$464$	−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	0.826972	−	0.562243i	$-0.190061\pi$
$467$	−1.58685	−	2.74850i	−0.0734306	−	0.127186i	−0.900403	+	0.435057i	$0.856728\pi$
$468$	−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	−0.619419	−	0.785060i	$-0.712632\pi$
$479$	5.05898	−	28.6909i	0.231151	−	1.31092i	0.850570	−	0.525862i	$-0.176257\pi$
$480$	−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	−0.978783	−	0.204898i	$-0.934314\pi$
$487$	−6.88402	+	11.9235i	−0.311945	+	0.540304i	0.666839	+	0.745202i	$0.267647\pi$
$488$	−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	0.263507	−	0.964658i	$-0.415121\pi$
$491$	−3.42804	−	1.24770i	−0.154705	−	0.0563081i	−0.418212	+	0.908349i	$0.637343\pi$
$492$	−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	0.990536	+	0.137251i	$0.0438267\pi$
$499$	2.38303	+	13.5149i	0.106679	+	0.605008i	−0.883857	+	0.467757i	$0.845062\pi$
$500$	−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	0.392364	−	0.919810i	$-0.371657\pi$
$503$	−9.98789	−	8.38083i	−0.445338	−	0.373683i	−0.837702	+	0.546127i	$0.816102\pi$
$504$	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	−0.651935	−	0.758275i	$-0.726042\pi$
$509$	4.96408	−	28.1527i	0.220029	−	1.24785i	0.871964	−	0.489570i	$-0.162846\pi$
$510$	−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	0.965155	+	0.261681i	$0.0842767\pi$
$521$	16.1878	+	28.0380i	0.709199	+	1.22837i	−0.255955	+	0.966689i	$0.582390\pi$
$522$	5.67175	+	4.75916i	0.248246	+	0.208303i
$523$	−2.12896	−	1.78641i	−0.0930930	−	0.0781143i	0.595053	−	0.803686i	$-0.297131\pi$
$523$	−2.12896	−	1.78641i	−0.0930930	−	0.0781143i	−0.688146	+	0.725572i	$0.741575\pi$
$524$	−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	0.502473	−	0.864593i	$-0.332424\pi$
$541$	−6.08773	−	5.10821i	−0.261732	−	0.219619i	−0.764205	+	0.644974i	$0.776868\pi$
$542$	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	0.602675	+	0.797987i	$0.294102\pi$
$547$	−5.53318	+	31.3803i	−0.236582	+	1.34172i	−0.839257	+	0.543736i	$0.817009\pi$
$548$	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	0.422994	−	0.906132i	$-0.360979\pi$
$557$	31.3768	−	11.4202i	1.32948	−	0.483890i	0.906483	+	0.422242i	$0.138757\pi$
$558$	−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	−0.166346	−	0.986067i	$-0.553197\pi$
$563$	18.2889	−	31.6774i	0.770787	−	1.33504i	0.937132	−	0.348974i	$-0.113470\pi$
$564$	−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	−0.960825	−	0.277156i	$-0.910608\pi$
$577$	−5.77431	+	10.0014i	−0.240388	+	0.416364i	0.720437	+	0.693520i	$0.243941\pi$
$578$	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	−0.246855	+	0.969052i	$0.579397\pi$
$587$	−30.1410	+	25.2913i	−1.24405	+	1.04388i	−0.997196	+	0.0748309i	$0.976158\pi$
$588$	−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	−0.988667	−	0.150124i	$-0.952033\pi$
$593$	−0.201598	+	1.14332i	−0.00827863	+	0.0469504i	0.980389	+	0.197074i	$0.0631439\pi$
$594$	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	0.972088	−	0.234615i	$-0.0753828\pi$
$599$	22.2678	+	18.6849i	0.909840	+	0.763446i	−0.0622488	+	0.998061i	$0.519827\pi$
$600$	0.956466	+	1.65665i	0.0390476	+	0.0676324i
$601$	−0.864177	+	1.49680i	−0.0352505	+	0.0610557i	−0.883112	−	0.469161i	$-0.844556\pi$
$601$	−0.864177	+	1.49680i	−0.0352505	+	0.0610557i	0.847862	+	0.530217i	$0.177890\pi$
$602$	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	0.780294	+	0.625413i	$0.215069\pi$
$613$	6.46110	+	36.6427i	0.260961	+	1.47998i	−0.519333	+	0.854572i	$0.673820\pi$
$614$	−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	0.927126	−	0.374750i	$-0.122272\pi$
$617$	17.8611	+	14.9873i	0.719062	+	0.603365i	−0.208063	+	0.978115i	$0.566716\pi$
$618$	−5.07408	−	4.25766i	−0.204109	−	0.171268i
$619$	8.94329	+	15.4902i	0.359461	+	0.622605i	0.987871	−	0.155277i	$-0.0496271\pi$
$619$	8.94329	+	15.4902i	0.359461	+	0.622605i	−0.628410	+	0.777883i	$0.716294\pi$
$620$	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	−0.961060	−	0.276338i	$-0.910879\pi$
$631$	0.918231	−	5.20755i	0.0365542	−	0.207309i	0.997615	+	0.0690290i	$0.0219901\pi$
$632$	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	0.975711	−	0.219063i	$-0.0702999\pi$
$641$	−0.407145	−	2.30903i	−0.0160813	−	0.0912014i	−0.991792	+	0.127861i	$0.959189\pi$
$642$	0.433655	−	2.45938i	0.0171150	−	0.0970640i
$643$	−5.43757	−	1.97911i	−0.214437	−	0.0780486i	0.232568	−	0.972580i	$-0.425287\pi$
$643$	−5.43757	−	1.97911i	−0.214437	−	0.0780486i	−0.447005	+	0.894531i	$0.647509\pi$
$644$	−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	−0.770106	−	0.637916i	$-0.779797\pi$
$653$	4.27768	−	7.40915i	0.167398	−	0.289943i	0.937504	+	0.347973i	$0.113130\pi$
$654$	−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	−0.806442	−	0.591314i	$-0.798610\pi$
$659$	−26.8037	+	9.75574i	−1.04412	+	0.380030i	−0.237681	+	0.971343i	$0.576387\pi$
$660$	−0.0121643	−	0.0689870i	−0.000473494	−	0.00268532i
$661$	−1.71292	+	9.71447i	−0.0666250	+	0.377849i	0.933204	+	0.359348i	$0.117001\pi$
$661$	−1.71292	+	9.71447i	−0.0666250	+	0.377849i	−0.999829	+	0.0185017i	$0.994110\pi$
$662$	−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	−0.940704	−	0.339228i	$-0.889834\pi$
$673$	−19.8233	−	34.3350i	−0.764132	−	1.32352i	0.176572	−	0.984288i	$-0.443499\pi$
$674$	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	−0.739366	−	0.673304i	$-0.764874\pi$
$677$	5.55291	−	9.61793i	0.213416	−	0.369647i	0.952781	+	0.303657i	$0.0982078\pi$
$678$	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	−0.899058	−	0.437829i	$-0.855747\pi$
$691$	−1.84949	+	3.20340i	−0.0703577	+	0.121863i	0.828700	+	0.559692i	$0.189081\pi$
$692$	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	−0.896463	−	0.443120i	$-0.853872\pi$
$701$	−16.3027	+	13.6796i	−0.615744	+	0.516671i	0.280719	+	0.959790i	$0.409427\pi$
$702$	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	0.208462	−	0.978030i	$-0.433154\pi$
$709$	26.5424	−	9.66063i	0.996819	−	0.362812i	0.788357	+	0.615218i	$0.210932\pi$
$710$	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	0.364954	−	0.931026i	$-0.381085\pi$
$719$	1.23539	+	0.449646i	0.0460723	+	0.0167690i	−0.318881	+	0.947795i	$0.603307\pi$
$720$	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	0.975898	+	0.218228i	$0.0700276\pi$
$727$	3.59934	+	20.4129i	0.133492	+	0.757072i	−0.842406	+	0.538844i	$0.818861\pi$
$728$	−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	0.991819	−	0.127656i	$-0.0407453\pi$
$733$	10.4331	+	18.0707i	0.385356	+	0.667456i	−0.606463	+	0.795112i	$0.707412\pi$
$734$	−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	−0.648615	−	0.761117i	$-0.724651\pi$
$739$	−0.317844	+	0.266703i	−0.0116921	+	0.00981082i	0.636923	+	0.770928i	$0.280207\pi$
$740$	−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	−0.270902	−	0.962607i	$-0.587322\pi$
$743$	17.1736	−	14.4104i	0.630039	−	0.528665i	0.900941	+	0.433942i	$0.142878\pi$
$744$	−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	0.588244	−	0.808684i	$-0.299820\pi$
$751$	−2.90504	−	2.43762i	−0.106006	−	0.0889500i	−0.694250	+	0.719734i	$0.744264\pi$
$752$	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	0.560130	−	0.828405i	$-0.310751\pi$
$757$	12.5662	+	4.57371i	0.456725	+	0.166234i	−0.103404	+	0.994639i	$0.532974\pi$
$758$	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	−0.00899751	−	0.999960i	$-0.502864\pi$
$769$	−27.6013	−	23.1602i	−0.995328	−	0.835179i	−0.986330	+	0.164780i	$0.947308\pi$
$770$	−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	−0.118568	−	0.992946i	$-0.537830\pi$
$773$	11.9235	−	4.33979i	0.428858	−	0.156091i	0.547425	+	0.836855i	$0.315608\pi$
$774$	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	−0.996949	−	0.0780563i	$-0.975129\pi$
$787$	−15.8803	−	27.5056i	−0.566073	−	0.980468i	0.430876	−	0.902411i	$-0.358205\pi$
$788$	−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	0.833121	−	0.553091i	$-0.186552\pi$
$809$	−1.77572	−	3.07564i	−0.0624310	−	0.108134i	−0.895552	+	0.444958i	$0.853219\pi$
$810$	−0.699089	+	1.21086i	−0.0245635	+	0.0425452i
$811$	8.65244	−	3.14923i	0.303828	−	0.110584i	−0.185607	−	0.982624i	$-0.559425\pi$
$811$	8.65244	−	3.14923i	0.303828	−	0.110584i	0.489435	+	0.872040i	$0.337203\pi$
$812$	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	−0.983117	−	0.182979i	$-0.941426\pi$
$821$	0.0943635	−	0.535162i	0.00329331	−	0.0186773i	0.986410	+	0.164302i	$0.0525371\pi$
$822$	−0.314789	−	1.78526i	−0.0109795	−	0.0622680i
$823$	22.3983	−	8.15230i	0.780754	−	0.284171i	0.0792671	−	0.996853i	$-0.474742\pi$
$823$	22.3983	−	8.15230i	0.780754	−	0.284171i	0.701487	+	0.712682i	$0.252520\pi$
$824$	−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	0.307772	−	0.951460i	$-0.400416\pi$
$827$	−16.5583	−	13.8941i	−0.575789	−	0.483144i	−0.883561	+	0.468316i	$0.844861\pi$
$828$	−5.10266	−	8.83806i	−0.177330	−	0.307144i
$829$	17.0505	−	29.5323i	0.592187	−	1.02570i	−0.401750	−	0.915749i	$-0.631598\pi$
$829$	17.0505	−	29.5323i	0.592187	−	1.02570i	0.993937	−	0.109949i	$-0.0350686\pi$
$830$	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	0.627140	−	0.778907i	$-0.284225\pi$
$839$	17.5787	+	6.39814i	0.606886	+	0.220888i	−0.0202544	+	0.999795i	$0.506448\pi$
$840$	−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	−0.851111	−	0.524985i	$-0.824071\pi$
$853$	−14.0743	+	11.8098i	−0.481896	+	0.404358i	0.369216	+	0.929344i	$0.379626\pi$
$854$	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	−0.633871	−	0.773439i	$-0.718535\pi$
$857$	0.519562	−	0.435964i	0.0177479	−	0.0148923i	0.651618	+	0.758547i	$0.274090\pi$
$858$	−0.275507	−	0.100276i	−0.00940565	−	0.00342338i
$859$	7.46897	−	42.3587i	0.254838	−	1.44526i	−0.541650	−	0.840604i	$-0.682200\pi$
$859$	7.46897	−	42.3587i	0.254838	−	1.44526i	0.796488	−	0.604654i	$-0.206689\pi$
$860$	−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	0.999033	+	0.0439686i	$0.0140002\pi$
$863$	15.7928	+	27.3540i	0.537594	+	0.931141i	−0.461438	+	0.887172i	$0.652666\pi$
$864$	−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	−0.235661	−	0.971835i	$-0.575726\pi$
$877$	−30.8246	−	11.2192i	−1.04087	−	0.378846i	−0.805211	+	0.592989i	$0.797948\pi$
$878$	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	−0.124632	−	0.992203i	$-0.539775\pi$
$881$	23.6550	−	40.9716i	0.796957	−	1.38037i	0.921589	−	0.388167i	$-0.126892\pi$
$882$	−18.9279	−	32.7840i	−0.637335	−	1.10390i
$883$	−7.22845	−	6.06539i	−0.243257	−	0.204116i	0.513005	−	0.858385i	$-0.328532\pi$
$883$	−7.22845	−	6.06539i	−0.243257	−	0.204116i	−0.756262	+	0.654269i	$0.772976\pi$
$884$	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	−0.0623935	−	0.998052i	$-0.519873\pi$
$887$	15.8248	−	5.75976i	0.531345	−	0.193394i	0.593739	+	0.804658i	$0.297651\pi$
$888$	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	−0.856359	−	0.516380i	$-0.827279\pi$
$907$	−6.87430	−	38.9861i	−0.228257	−	1.29451i	0.628102	−	0.778131i	$-0.283832\pi$
$908$	−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	−0.700821	−	0.713337i	$-0.747183\pi$
$919$	8.10496	−	14.0382i	0.267358	−	0.463077i	0.968179	+	0.250260i	$0.0805161\pi$
$920$	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	−0.636534	−	0.771248i	$-0.719633\pi$
$929$	0.379899	−	0.318773i	0.0124641	−	0.0104586i	0.648998	+	0.760790i	$0.275188\pi$
$930$	−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	−0.772563	−	0.634938i	$-0.781026\pi$
$937$	−29.2713	+	10.6539i	−0.956251	+	0.348047i	−0.183688	+	0.982985i	$0.558803\pi$
$938$	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	0.999270	−	0.0381967i	$-0.0121614\pi$
$941$	34.8223	+	29.2194i	1.13518	+	0.952525i	0.135905	+	0.990722i	$0.456606\pi$
$942$	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	−0.513013	−	0.858381i	$-0.671471\pi$
$947$	−44.8602	−	16.3278i	−1.45776	−	0.530581i	−0.944747	+	0.327800i	$0.893693\pi$
$948$	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	0.326556	−	0.945178i	$-0.394112\pi$
$953$	−0.951952	−	0.346482i	−0.0308367	−	0.0112237i	−0.357392	+	0.933954i	$0.616334\pi$
$954$	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	−0.0425736	−	0.999093i	$-0.513556\pi$
$967$	29.0426	−	24.3697i	0.933948	−	0.783676i	0.976522	+	0.215418i	$0.0691112\pi$
$968$	−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	−0.356651	−	0.934238i	$-0.616082\pi$
$971$	15.6260	−	13.1117i	0.501461	−	0.420776i	0.858113	+	0.513462i	$0.171637\pi$
$972$	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	0.879887	+	0.475183i	$0.157618\pi$
$977$	26.6142	+	46.0972i	0.851464	+	1.47478i	−0.0284235	+	0.999596i	$0.509049\pi$
$978$	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	0.899415	+	0.437095i	$0.143993\pi$
$983$	6.38772	+	36.2266i	0.203737	+	1.15545i	−0.695679	+	0.718353i	$0.744896\pi$
$984$	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	−0.641302	−	0.767289i	$-0.721605\pi$
$991$	−51.1795	−	18.6278i	−1.62577	−	0.591732i	−0.984469	+	0.175557i	$0.943827\pi$
$992$	−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	0.798275	−	0.602294i	$-0.205746\pi$
$997$	10.8540	+	9.10761i	0.343750	+	0.288441i	−0.454524	+	0.890734i	$0.650191\pi$
$998$	−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.177.3	yes	24
19.4	even	9		7942.2.a.bt.1.6		12
19.15	odd	18		7942.2.a.bx.1.7		12
19.16	even	9	inner	418.2.j.a.111.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.j.a.111.3	✓	24	19.16	even	9	inner
418.2.j.a.177.3	yes	24	1.1	even	1	trivial
7942.2.a.bt.1.6		12	19.4	even	9
7942.2.a.bx.1.7		12	19.15	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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