LMFDB - Embedded newform 27.4.e.a.25.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,4,Mod(4,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	27.e (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:	$1.59305157015$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.3
Character	$\chi$	$=$	27.25
Dual form			27.4.e.a.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.404735 + 2.29536i) q^{2} +(4.52897 - 2.54724i) q^{3} +(2.41266 + 0.878135i) q^{4} +(-4.78113 + 4.01185i) q^{5} +(4.01380 + 11.4266i) q^{6} +(2.53990 - 0.924448i) q^{7} +(-12.3152 + 21.3306i) q^{8} +(14.0232 - 23.0727i) q^{9} +O(q^{10})$	\(q+(-0.404735 + 2.29536i) q^{2} +(4.52897 - 2.54724i) q^{3} +(2.41266 + 0.878135i) q^{4} +(-4.78113 + 4.01185i) q^{5} +(4.01380 + 11.4266i) q^{6} +(2.53990 - 0.924448i) q^{7} +(-12.3152 + 21.3306i) q^{8} +(14.0232 - 23.0727i) q^{9} +(-7.27356 - 12.5982i) q^{10} +(-30.2808 - 25.4086i) q^{11} +(13.1637 - 2.16856i) q^{12} +(-12.8853 - 73.0761i) q^{13} +(1.09396 + 6.20415i) q^{14} +(-11.4345 + 30.3482i) q^{15} +(-28.2425 - 23.6983i) q^{16} +(29.1160 + 50.4303i) q^{17} +(47.2846 + 41.5266i) q^{18} +(-41.2204 + 71.3959i) q^{19} +(-15.0582 + 5.48072i) q^{20} +(9.14835 - 10.6565i) q^{21} +(70.5777 - 59.2217i) q^{22} +(-25.8401 - 9.40502i) q^{23} +(-1.44124 + 127.975i) q^{24} +(-14.9417 + 84.7386i) q^{25} +172.951 q^{26} +(4.73890 - 140.216i) q^{27} +6.93969 q^{28} +(30.1245 - 170.844i) q^{29} +(-65.0323 - 38.5293i) q^{30} +(149.460 + 54.3991i) q^{31} +(-85.1171 + 71.4217i) q^{32} +(-201.863 - 37.9425i) q^{33} +(-127.540 + 46.4208i) q^{34} +(-8.43485 + 14.6096i) q^{35} +(54.0941 - 43.3523i) q^{36} +(220.701 + 382.265i) q^{37} +(-147.196 - 123.512i) q^{38} +(-244.499 - 298.138i) q^{39} +(-26.6943 - 151.391i) q^{40} +(14.7471 + 83.6352i) q^{41} +(20.7579 + 25.3118i) q^{42} +(-150.412 - 126.210i) q^{43} +(-50.7449 - 87.8928i) q^{44} +(25.5176 + 166.573i) q^{45} +(32.0463 - 55.5058i) q^{46} +(402.616 - 146.540i) q^{47} +(-188.275 - 35.3885i) q^{48} +(-257.157 + 215.780i) q^{49} +(-188.459 - 68.5933i) q^{50} +(260.323 + 154.232i) q^{51} +(33.0829 - 187.623i) q^{52} +448.275 q^{53} +(319.929 + 67.6278i) q^{54} +246.712 q^{55} +(-11.5604 + 65.5623i) q^{56} +(-4.82401 + 428.348i) q^{57} +(379.958 + 138.293i) q^{58} +(-269.039 + 225.751i) q^{59} +(-54.2373 + 63.1788i) q^{60} +(-346.588 + 126.148i) q^{61} +(-185.357 + 321.048i) q^{62} +(14.2879 - 71.5661i) q^{63} +(-276.961 - 479.711i) q^{64} +(354.777 + 297.693i) q^{65} +(168.793 - 447.991i) q^{66} +(-104.831 - 594.527i) q^{67} +(25.9622 + 147.239i) q^{68} +(-140.986 + 23.2257i) q^{69} +(-30.1205 - 25.2741i) q^{70} +(-423.268 - 733.122i) q^{71} +(319.456 + 583.268i) q^{72} +(21.1923 - 36.7062i) q^{73} +(-966.762 + 351.873i) q^{74} +(148.179 + 421.839i) q^{75} +(-162.146 + 136.057i) q^{76} +(-100.399 - 36.5423i) q^{77} +(783.292 - 440.548i) q^{78} +(63.6782 - 361.137i) q^{79} +230.105 q^{80} +(-335.701 - 647.106i) q^{81} -197.942 q^{82} +(-10.0517 + 57.0062i) q^{83} +(31.4297 - 17.6770i) q^{84} +(-341.526 - 124.305i) q^{85} +(350.575 - 294.168i) q^{86} +(-298.748 - 850.483i) q^{87} +(914.895 - 332.995i) q^{88} +(-713.269 + 1235.42i) q^{89} +(-392.672 - 8.84559i) q^{90} +(-100.282 - 173.694i) q^{91} +(-54.0843 - 45.3821i) q^{92} +(815.469 - 134.339i) q^{93} +(173.411 + 983.460i) q^{94} +(-89.3490 - 506.723i) q^{95} +(-203.565 + 540.280i) q^{96} +(875.961 + 735.019i) q^{97} +(-391.214 - 677.602i) q^{98} +(-1010.88 + 342.351i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	−0.404735	+	2.29536i	−0.143095	+	0.811534i	0.825781	+	0.563990i	$0.190734\pi$
$2$	−0.404735	+	2.29536i	−0.143095	+	0.811534i	−0.968877	+	0.247544i	$0.920377\pi$
$3$	4.52897	−	2.54724i	0.871601	−	0.490216i
$3$	4.52897	−	2.54724i	0.871601	−	0.490216i
$4$	2.41266	+	0.878135i	0.301582	+	0.109767i
$5$	−4.78113	+	4.01185i	−0.427637	+	0.358830i	−0.831059	−	0.556184i	$-0.812265\pi$
$5$	−4.78113	+	4.01185i	−0.427637	+	0.358830i	0.403422	+	0.915014i	$0.367821\pi$
$6$	4.01380	+	11.4266i	0.273105	+	0.777481i
$7$	2.53990	−	0.924448i	0.137142	−	0.0499155i	−0.272537	−	0.962145i	$-0.587863\pi$
$7$	2.53990	−	0.924448i	0.137142	−	0.0499155i	0.409679	+	0.912230i	$0.365641\pi$
$8$	−12.3152	+	21.3306i	−0.544261	+	0.942688i
$9$	14.0232	−	23.0727i	0.519377	−	0.854545i
$10$	−7.27356	−	12.5982i	−0.230010	−	0.398389i
$11$	−30.2808	−	25.4086i	−0.830000	−	0.696453i	0.125291	−	0.992120i	$-0.460014\pi$
$11$	−30.2808	−	25.4086i	−0.830000	−	0.696453i	−0.955291	+	0.295667i	$0.904458\pi$
$12$	13.1637	−	2.16856i	0.316669	−	0.0521673i
$13$	−12.8853	−	73.0761i	−0.274903	−	1.55905i	−0.739270	−	0.673409i	$-0.764829\pi$
$13$	−12.8853	−	73.0761i	−0.274903	−	1.55905i	0.464367	−	0.885643i	$-0.346282\pi$
$14$	1.09396	+	6.20415i	0.0208838	+	0.118438i
$15$	−11.4345	+	30.3482i	−0.196825	+	0.522392i
$16$	−28.2425	−	23.6983i	−0.441290	−	0.370286i
$17$	29.1160	+	50.4303i	0.415392	+	0.719479i	0.995469	−	0.0950816i	$-0.0303112\pi$
$17$	29.1160	+	50.4303i	0.415392	+	0.719479i	−0.580078	+	0.814561i	$0.696978\pi$
$18$	47.2846	+	41.5266i	0.619172	+	0.543773i
$19$	−41.2204	+	71.3959i	−0.497717	+	0.862070i	−0.999997	−	0.00263470i	$-0.999161\pi$
$19$	−41.2204	+	71.3959i	−0.497717	+	0.862070i	0.502280	+	0.864705i	$0.332495\pi$
$20$	−15.0582	+	5.48072i	−0.168355	+	0.0612764i
$21$	9.14835	−	10.6565i	0.0950635	−	0.110735i
$22$	70.5777	−	59.2217i	0.683964	−	0.573914i
$23$	−25.8401	−	9.40502i	−0.234262	−	0.0852644i	0.222222	−	0.974996i	$-0.428669\pi$
$23$	−25.8401	−	9.40502i	−0.234262	−	0.0852644i	−0.456484	+	0.889732i	$0.650891\pi$
$24$	−1.44124	+	127.975i	−0.0122580	+	1.08845i
$25$	−14.9417	+	84.7386i	−0.119534	+	0.677909i
$26$	172.951			1.30456
$27$	4.73890	−	140.216i	0.0337778	−	0.999429i
$28$	6.93969			0.0468385
$29$	30.1245	−	170.844i	0.192896	−	1.09397i	−0.722488	−	0.691383i	$-0.757002\pi$
$29$	30.1245	−	170.844i	0.192896	−	1.09397i	0.915384	−	0.402582i	$-0.131887\pi$
$30$	−65.0323	−	38.5293i	−0.395774	−	0.234482i
$31$	149.460	+	54.3991i	0.865931	+	0.315173i	0.736518	−	0.676418i	$-0.236469\pi$
$31$	149.460	+	54.3991i	0.865931	+	0.315173i	0.129413	+	0.991591i	$0.458691\pi$
$32$	−85.1171	+	71.4217i	−0.470210	+	0.394553i
$33$	−201.863	−	37.9425i	−1.06484	−	0.200150i
$34$	−127.540	+	46.4208i	−0.643322	+	0.234150i
$35$	−8.43485	+	14.6096i	−0.0407357	+	0.0705563i
$36$	54.0941	−	43.3523i	0.250435	−	0.200705i
$37$	220.701	+	382.265i	0.980621	+	1.69849i	0.659977	+	0.751286i	$0.270566\pi$
$37$	220.701	+	382.265i	0.980621	+	1.69849i	0.320644	+	0.947200i	$0.396101\pi$
$38$	−147.196	−	123.512i	−0.628378	−	0.527272i
$39$	−244.499	−	298.138i	−1.00388	−	1.22411i
$40$	−26.6943	−	151.391i	−0.105519	−	0.598426i
$41$	14.7471	+	83.6352i	0.0561736	+	0.318576i	0.999927	−	0.0120735i	$-0.00384321\pi$
$41$	14.7471	+	83.6352i	0.0561736	+	0.318576i	−0.943754	+	0.330650i	$0.892732\pi$
$42$	20.7579	+	25.3118i	0.0762624	+	0.0929929i
$43$	−150.412	−	126.210i	−0.533431	−	0.447602i	0.335853	−	0.941914i	$-0.390975\pi$
$43$	−150.412	−	126.210i	−0.533431	−	0.447602i	−0.869284	+	0.494312i	$0.835420\pi$
$44$	−50.7449	−	87.8928i	−0.173866	−	0.301144i
$45$	25.5176	+	166.573i	0.0845319	+	0.551804i
$46$	32.0463	−	55.5058i	0.102717	−	0.177911i
$47$	402.616	−	146.540i	1.24952	−	0.454789i	0.369283	−	0.929317i	$-0.379603\pi$
$47$	402.616	−	146.540i	1.24952	−	0.454789i	0.880240	+	0.474528i	$0.157381\pi$
$48$	−188.275	−	35.3885i	−0.566149	−	0.106414i
$49$	−257.157	+	215.780i	−0.749728	+	0.629097i
$50$	−188.459	−	68.5933i	−0.533041	−	0.194011i
$51$	260.323	+	154.232i	0.714756	+	0.423468i
$52$	33.0829	−	187.623i	0.0882265	−	0.500357i
$53$	448.275			1.16180			0.580899	−	0.813976i	$-0.302701\pi$
$53$	448.275			1.16180			0.580899	+	0.813976i	$0.302701\pi$
$54$	319.929	+	67.6278i	0.806237	+	0.170425i
$55$	246.712			0.604848
$56$	−11.5604	+	65.5623i	−0.0275861	+	0.156449i
$57$	−4.82401	+	428.348i	−0.0112097	+	0.995370i
$58$	379.958	+	138.293i	0.860187	+	0.313083i
$59$	−269.039	+	225.751i	−0.593660	+	0.498140i	−0.889401	−	0.457128i	$-0.848878\pi$
$59$	−269.039	+	225.751i	−0.593660	+	0.498140i	0.295741	+	0.955268i	$0.404434\pi$
$60$	−54.2373	+	63.1788i	−0.116700	+	0.135939i
$61$	−346.588	+	126.148i	−0.727475	+	0.264779i	−0.679096	−	0.734050i	$-0.737628\pi$
$61$	−346.588	+	126.148i	−0.727475	+	0.264779i	−0.0483796	+	0.998829i	$0.515406\pi$
$62$	−185.357	+	321.048i	−0.379684	+	0.657632i
$63$	14.2879	−	71.5661i	0.0285732	−	0.143119i
$64$	−276.961	−	479.711i	−0.540940	−	0.936935i
$65$	354.777	+	297.693i	0.676994	+	0.568065i
$66$	168.793	−	447.991i	0.314802	−	0.835514i
$67$	−104.831	−	594.527i	−0.191152	−	1.08408i	−0.917793	−	0.397059i	$-0.870031\pi$
$67$	−104.831	−	594.527i	−0.191152	−	1.08408i	0.726641	−	0.687017i	$-0.241080\pi$
$68$	25.9622	+	147.239i	0.0462996	+	0.262578i
$69$	−140.986	+	23.2257i	−0.245981	+	0.0405224i
$70$	−30.1205	−	25.2741i	−0.0514297	−	0.0431547i
$71$	−423.268	−	733.122i	−0.707502	−	1.22543i	−0.965781	−	0.259359i	$-0.916489\pi$
$71$	−423.268	−	733.122i	−0.707502	−	1.22543i	0.258279	−	0.966070i	$-0.416845\pi$
$72$	319.456	+	583.268i	0.522893	+	0.954706i
$73$	21.1923	−	36.7062i	0.0339777	−	0.0588512i	−0.848536	−	0.529137i	$-0.822516\pi$
$73$	21.1923	−	36.7062i	0.0339777	−	0.0588512i	0.882514	+	0.470286i	$0.155849\pi$
$74$	−966.762	+	351.873i	−1.51870	+	0.552762i
$75$	148.179	+	421.839i	0.228136	+	0.649464i
$76$	−162.146	+	136.057i	−0.244729	+	0.205352i
$77$	−100.399	−	36.5423i	−0.148591	−	0.0540828i
$78$	783.292	−	440.548i	1.13706	−	0.639516i
$79$	63.6782	−	361.137i	0.0906881	−	0.514318i	−0.905295	−	0.424782i	$-0.860351\pi$
$79$	63.6782	−	361.137i	0.0906881	−	0.514318i	0.995984	−	0.0895356i	$-0.0285383\pi$
$80$	230.105			0.321582
$81$	−335.701	−	647.106i	−0.460495	−	0.887662i
$82$	−197.942			−0.266574
$83$	−10.0517	+	57.0062i	−0.0132930	+	0.0753884i	−0.990733	−	0.135827i	$-0.956631\pi$
$83$	−10.0517	+	57.0062i	−0.0132930	+	0.0753884i	0.977440	+	0.211215i	$0.0677421\pi$
$84$	31.4297	−	17.6770i	0.0408245	−	0.0229610i
$85$	−341.526	−	124.305i	−0.435808	−	0.158621i
$86$	350.575	−	294.168i	0.439576	−	0.368848i
$87$	−298.748	−	850.483i	−0.368151	−	1.04806i
$88$	914.895	−	332.995i	1.10827	−	0.403379i
$89$	−713.269	+	1235.42i	−0.849509	+	1.47139i	0.0321377	+	0.999483i	$0.489768\pi$
$89$	−713.269	+	1235.42i	−0.849509	+	1.47139i	−0.881647	+	0.471910i	$0.843565\pi$
$90$	−392.672	−	8.84559i	−0.459903	−	0.0103601i
$91$	−100.282	−	173.694i	−0.115521	−	0.200089i
$92$	−54.0843	−	45.3821i	−0.0612900	−	0.0514284i
$93$	815.469	−	134.339i	0.909249	−	0.149788i
$94$	173.411	+	983.460i	0.190276	+	1.07911i
$95$	−89.3490	−	506.723i	−0.0964948	−	0.547249i
$96$	−203.565	+	540.280i	−0.216419	+	0.574397i
$97$	875.961	+	735.019i	0.916911	+	0.769380i	0.973421	−	0.229022i	$-0.0735528\pi$
$97$	875.961	+	735.019i	0.916911	+	0.769380i	−0.0565098	+	0.998402i	$0.517997\pi$
$98$	−391.214	−	677.602i	−0.403251	−	0.698450i
$99$	−1010.88	+	342.351i	−1.02623	+	0.347551i
$100$	−110.461	+	191.324i	−0.110461	+	0.191324i
$101$	423.836	−	154.264i	0.417557	−	0.151978i	−0.124693	−	0.992195i	$-0.539795\pi$
$101$	423.836	−	154.264i	0.417557	−	0.151978i	0.542250	+	0.840217i	$0.317573\pi$
$102$	−459.381	+	535.114i	−0.445936	+	0.519452i
$103$	−12.2315	+	10.2635i	−0.0117011	+	0.00981835i	−0.648619	−	0.761113i	$-0.724653\pi$
$103$	−12.2315	+	10.2635i	−0.0117011	+	0.00981835i	0.636918	+	0.770931i	$0.280209\pi$
$104$	1717.44	+	625.098i	1.61932	+	0.589383i
$105$	−0.987127	+	87.6520i	−0.000917464	+	0.0814663i
$106$	−181.432	+	1028.95i	−0.166248	+	0.942838i
$107$	190.566			0.172175			0.0860876	−	0.996288i	$-0.472564\pi$
$107$	190.566			0.172175			0.0860876	+	0.996288i	$0.472564\pi$
$108$	134.562	−	334.132i	0.119891	−	0.297702i
$109$	−505.344			−0.444066			−0.222033	−	0.975039i	$-0.571269\pi$
$109$	−505.344			−0.444066			−0.222033	+	0.975039i	$0.571269\pi$
$110$	−99.8528	+	566.294i	−0.0865509	+	0.490854i
$111$	1973.27	+	1169.09i	1.68733	+	0.999686i
$112$	−93.6410	−	34.0826i	−0.0790022	−	0.0287544i
$113$	1505.37	−	1263.16i	1.25322	−	1.05158i	0.256848	−	0.966452i	$-0.417316\pi$
$113$	1505.37	−	1263.16i	1.25322	−	1.05158i	0.996370	−	0.0851232i	$-0.0271284\pi$
$114$	−981.262	−	184.440i	−0.806172	−	0.151530i
$115$	161.276	−	58.6998i	0.130775	−	0.0475981i
$116$	222.704	−	385.735i	0.178255	−	0.308747i
$117$	−1866.76	−	727.461i	−1.47506	−	0.574818i
$118$	−409.291	−	708.912i	−0.319307	−	0.553056i
$119$	120.572	+	101.172i	0.0928807	+	0.0779361i
$120$	−506.527	−	617.649i	−0.385328	−	0.469862i
$121$	40.2037	+	228.006i	0.0302056	+	0.171304i
$122$	−149.279	−	846.601i	−0.110779	−	0.628259i
$123$	279.828	+	341.217i	0.205132	+	0.250134i
$124$	312.826	+	262.492i	0.226554	+	0.190101i
$125$	−658.603	−	1140.73i	−0.471258	−	0.816243i
$126$	158.487	+	61.7613i	0.112057	+	0.0436677i
$127$	478.674	−	829.089i	0.334453	−	0.579289i	−0.648927	−	0.760851i	$-0.724782\pi$
$127$	478.674	−	829.089i	0.334453	−	0.579289i	0.983380	+	0.181562i	$0.0581152\pi$
$128$	377.914	−	137.549i	0.260962	−	0.0949825i
$129$	−1002.70	−	188.469i	−0.684361	−	0.128634i
$130$	−826.904	+	693.855i	−0.557879	+	0.468116i
$131$	−1383.34	−	503.493i	−0.922616	−	0.335805i	−0.163337	−	0.986570i	$-0.552226\pi$
$131$	−1383.34	−	503.493i	−0.922616	−	0.335805i	−0.759279	+	0.650766i	$0.774448\pi$
$132$	−453.706	−	268.805i	−0.299167	−	0.177246i
$133$	−38.6940	+	219.444i	−0.0252270	+	0.143070i
$134$	1407.09			0.907117
$135$	539.868	+	689.403i	0.344181	+	0.439514i
$136$	−1434.28			−0.904326
$137$	−105.061	+	595.832i	−0.0655181	+	0.371572i	0.934366	+	0.356316i	$0.115967\pi$
$137$	−105.061	+	595.832i	−0.0655181	+	0.371572i	−0.999884	+	0.0152557i	$0.995144\pi$
$138$	3.75037	−	333.014i	0.00231342	−	0.205420i
$139$	−896.762	−	326.395i	−0.547211	−	0.199169i	0.0535958	−	0.998563i	$-0.482932\pi$
$139$	−896.762	−	326.395i	−0.547211	−	0.199169i	−0.600807	+	0.799394i	$0.705154\pi$
$140$	−33.1796	+	27.8410i	−0.0200299	+	0.0168071i
$141$	1450.16	−	1689.23i	0.866141	−	1.00893i
$142$	1854.09	−	674.834i	1.09572	−	0.398809i
$143$	−1466.59	+	2540.20i	−0.857637	+	1.48547i
$144$	−942.834	+	319.307i	−0.545622	+	0.184784i
$145$	541.372	+	937.684i	0.310059	+	0.537037i
$146$	75.6768	+	63.5004i	0.0428977	+	0.0359954i
$147$	−615.013	+	1632.30i	−0.345071	+	0.915850i
$148$	196.795	+	1116.08i	0.109300	+	0.619872i
$149$	158.401	+	898.335i	0.0870919	+	0.493923i	0.996886	+	0.0788619i	$0.0251286\pi$
$149$	158.401	+	898.335i	0.0870919	+	0.493923i	−0.909794	+	0.415061i	$0.863760\pi$
$150$	−1028.25	+	169.391i	−0.559707	+	0.0922050i
$151$	−309.263	−	259.503i	−0.166672	−	0.139855i	0.555637	−	0.831425i	$-0.312475\pi$
$151$	−309.263	−	259.503i	−0.166672	−	0.139855i	−0.722309	+	0.691571i	$0.756919\pi$
$152$	−1015.28	−	1758.51i	−0.541775	−	0.938382i
$153$	1571.86	+	35.4088i	0.830573	+	0.0187100i
$154$	124.513	−	215.663i	0.0651528	−	0.112848i
$155$	−932.830	+	339.522i	−0.483398	+	0.175942i
$156$	−328.087	−	934.007i	−0.168385	−	0.479362i
$157$	1879.49	−	1577.08i	0.955412	−	0.801685i	−0.0247890	−	0.999693i	$-0.507891\pi$
$157$	1879.49	−	1577.08i	0.955412	−	0.801685i	0.980201	+	0.198007i	$0.0634470\pi$
$158$	803.169	+	292.329i	0.404409	+	0.147193i
$159$	2030.22	−	1141.86i	1.01262	−	0.569531i
$160$	120.423	−	682.954i	0.0595018	−	0.337451i
$161$	−74.3256			−0.0363831
$162$	1621.21	−	508.650i	0.786262	−	0.246687i
$163$	2510.23			1.20623			0.603117	−	0.797653i	$-0.293925\pi$
$163$	2510.23			1.20623			0.603117	+	0.797653i	$0.293925\pi$
$164$	−37.8632	+	214.733i	−0.0180282	+	0.102243i
$165$	1117.35	−	628.433i	0.527186	−	0.296506i
$166$	−126.782	−	46.1447i	−0.0592781	−	0.0215755i
$167$	−2387.20	+	2003.10i	−1.10615	+	0.928169i	−0.997823	−	0.0659466i	$-0.978993\pi$
$167$	−2387.20	+	2003.10i	−1.10615	+	0.928169i	−0.108325	+	0.994115i	$0.534549\pi$
$168$	114.646	+	326.377i	0.0526496	+	0.149884i
$169$	−3109.59	+	1131.80i	−1.41538	+	0.515156i
$170$	423.553	−	733.616i	0.191089	−	0.330975i
$171$	1069.26	+	1952.26i	0.478176	+	0.873061i
$172$	−252.062	−	436.583i	−0.111741	−	0.193542i
$173$	688.221	+	577.486i	0.302454	+	0.253789i	0.781365	−	0.624075i	$-0.214524\pi$
$173$	688.221	+	577.486i	0.302454	+	0.253789i	−0.478911	+	0.877863i	$0.658968\pi$
$174$	2073.08	−	341.515i	0.903218	−	0.148794i
$175$	40.3860	+	229.040i	0.0174451	+	0.0989362i
$176$	253.066	+	1435.21i	0.108384	+	0.614675i
$177$	−643.431	+	1707.73i	−0.273239	+	0.725201i
$178$	−2547.05	−	2137.23i	−1.07252	−	0.899955i
$179$	907.223	+	1571.36i	0.378821	+	0.656138i	0.990891	−	0.134666i	$-0.0429962\pi$
$179$	907.223	+	1571.36i	0.378821	+	0.656138i	−0.612070	+	0.790804i	$0.709663\pi$
$180$	−84.7081	+	424.290i	−0.0350765	+	0.175693i
$181$	−12.5828	+	21.7941i	−0.00516726	+	0.00894996i	−0.868597	−	0.495518i	$-0.834978\pi$
$181$	−12.5828	+	21.7941i	−0.00516726	+	0.00894996i	0.863430	+	0.504468i	$0.168311\pi$
$182$	439.279	−	159.885i	0.178910	−	0.0651178i
$183$	−1248.36	+	1454.16i	−0.504269	+	0.587402i
$184$	518.841	−	435.359i	0.207877	−	0.174430i
$185$	−2588.79	−	942.242i	−1.02882	−	0.374459i
$186$	−21.6923	+	1926.17i	−0.00855138	+	0.759320i
$187$	399.710	−	2266.87i	0.156308	−	0.886469i
$188$	1100.06			0.426754
$189$	−117.586	−	360.515i	−0.0452547	−	0.138749i
$190$	1199.28			0.457919
$191$	303.311	−	1720.16i	0.114905	−	0.651657i	−0.871893	−	0.489697i	$-0.837107\pi$
$191$	303.311	−	1720.16i	0.114905	−	0.651657i	0.986797	−	0.161960i	$-0.0517816\pi$
$192$	−2476.29	−	1467.11i	−0.930784	−	0.551456i
$193$	−2367.51	−	861.705i	−0.882992	−	0.321383i	−0.139575	−	0.990211i	$-0.544574\pi$
$193$	−2367.51	−	861.705i	−0.882992	−	0.321383i	−0.743417	+	0.668829i	$0.766796\pi$
$194$	−2041.67	+	1713.16i	−0.755584	+	0.634010i
$195$	2365.07	+	444.543i	0.868543	+	0.163253i
$196$	−809.915	+	294.785i	−0.295158	+	0.107429i
$197$	908.545	−	1573.65i	0.328584	−	0.569125i	−0.653647	−	0.756800i	$-0.726762\pi$
$197$	908.545	−	1573.65i	0.328584	−	0.569125i	0.982231	+	0.187675i	$0.0600951\pi$
$198$	−376.683	−	2458.90i	−0.135200	−	0.882556i
$199$	−131.725	−	228.155i	−0.0469234	−	0.0812738i	0.841610	−	0.540086i	$-0.181608\pi$
$199$	−131.725	−	228.155i	−0.0469234	−	0.0812738i	−0.888533	+	0.458812i	$0.848275\pi$
$200$	−1623.51	−	1362.29i	−0.573999	−	0.481642i
$201$	−1989.18	−	2425.57i	−0.698039	−	0.851176i
$202$	182.550	+	1035.29i	0.0635850	+	0.360609i
$203$	−81.4236	−	461.776i	−0.0281518	−	0.159657i
$204$	492.634	+	600.708i	0.169075	+	0.206167i
$205$	−406.040	−	340.708i	−0.138337	−	0.116078i
$206$	−18.6079	−	32.2298i	−0.00629355	−	0.0109008i
$207$	−579.359	+	464.313i	−0.194533	+	0.155903i
$208$	−1367.87	+	2369.22i	−0.455983	+	0.789786i
$209$	3062.26	−	1114.57i	1.01350	−	0.368882i
$210$	−200.794	−	37.7416i	−0.0659813	−	0.0124020i
$211$	2735.26	−	2295.16i	0.892432	−	0.748839i	−0.0762648	−	0.997088i	$-0.524299\pi$
$211$	2735.26	−	2295.16i	0.892432	−	0.748839i	0.968696	+	0.248249i	$0.0798550\pi$
$212$	1081.53	+	393.646i	0.350377	+	0.127527i
$213$	−3784.40	−	2242.12i	−1.21738	−	0.721257i
$214$	−77.1288	+	437.419i	−0.0246375	+	0.139726i
$215$	1225.47			0.388728
$216$	2932.53	+	1827.87i	0.923766	+	0.575792i
$217$	429.903			0.134487
$218$	204.530	−	1159.95i	0.0635438	−	0.360375i
$219$	2.48013	−	220.223i	0.000765259	−	0.0679512i
$220$	595.231	+	216.646i	0.182411	+	0.0663922i
$221$	3310.09	−	2777.49i	1.00751	−	0.845404i
$222$	−3482.14	+	4056.19i	−1.05273	+	1.22628i
$223$	−2659.24	+	967.883i	−0.798546	+	0.290647i	−0.708884	−	0.705325i	$-0.750801\pi$
$223$	−2659.24	+	967.883i	−0.798546	+	0.290647i	−0.0896619	+	0.995972i	$0.528579\pi$
$224$	−150.163	+	260.090i	−0.0447911	+	0.0775804i
$225$	1745.62	+	1533.05i	0.517221	+	0.454237i
$226$	2290.13	+	3966.63i	0.674059	+	1.16750i
$227$	−2392.61	−	2007.64i	−0.699574	−	0.587013i	0.222078	−	0.975029i	$-0.428716\pi$
$227$	−2392.61	−	2007.64i	−0.699574	−	0.587013i	−0.921653	+	0.388016i	$0.873160\pi$
$228$	−387.786	+	1029.22i	−0.112639	+	0.298955i
$229$	−365.834	−	2074.75i	−0.105568	−	0.598704i	−0.990992	−	0.133921i	$-0.957243\pi$
$229$	−365.834	−	2074.75i	−0.105568	−	0.598704i	0.885424	−	0.464784i	$-0.153868\pi$
$230$	69.4632	+	393.946i	0.0199142	+	0.112939i
$231$	−547.786	+	90.2412i	−0.156025	+	0.0257032i
$232$	3273.22	+	2746.56i	0.926282	+	0.777243i
$233$	3081.61	+	5337.51i	0.866451	+	1.50074i	0.865599	+	0.500737i	$0.166938\pi$
$233$	3081.61	+	5337.51i	0.866451	+	1.50074i	0.000851595		1.00000i	$0.499729\pi$
$234$	2425.33	−	3990.46i	0.677558	−	1.11481i
$235$	−1337.06	+	2315.86i	−0.371151	+	0.642852i
$236$	−847.339	+	308.406i	−0.233716	+	0.0850658i
$237$	−631.505	−	1797.78i	−0.173083	−	0.492737i
$238$	−281.026	+	235.808i	−0.0765386	+	0.0642235i
$239$	−540.460	−	196.711i	−0.146274	−	0.0532393i	0.267846	−	0.963462i	$-0.413688\pi$
$239$	−540.460	−	196.711i	−0.146274	−	0.0532393i	−0.414120	+	0.910223i	$0.635910\pi$
$240$	1042.14	−	586.132i	0.280291	−	0.157645i
$241$	−881.084	+	4996.88i	−0.235501	+	1.33559i	0.606057	+	0.795422i	$0.292751\pi$
$241$	−881.084	+	4996.88i	−0.235501	+	1.33559i	−0.841557	+	0.540168i	$0.818361\pi$
$242$	−539.629			−0.143342
$243$	−3168.71	−	2075.61i	−0.836514	−	0.547945i
$244$	−946.971			−0.248457
$245$	363.824	−	2063.35i	0.0948728	−	0.538051i
$246$	−896.474	+	504.205i	−0.232346	+	0.130679i
$247$	5748.47	+	2092.27i	1.48084	+	0.538980i
$248$	−3001.00	+	2518.14i	−0.768402	+	0.644766i
$249$	99.6842	+	283.783i	0.0253704	+	0.0722251i
$250$	2884.96	−	1050.04i	0.729843	−	0.265641i
$251$	909.067	−	1574.55i	0.228605	−	0.395955i	−0.728790	−	0.684737i	$-0.759917\pi$
$251$	909.067	−	1574.55i	0.228605	−	0.395955i	0.957395	+	0.288782i	$0.0932503\pi$
$252$	97.3165	−	160.118i	0.0243268	−	0.0400256i
$253$	543.490	+	941.352i	0.135055	+	0.233922i
$254$	1709.32	+	1434.29i	0.422254	+	0.354313i
$255$	−1863.40	+	306.972i	−0.457609	+	0.0753857i
$256$	−606.730	−	3440.93i	−0.148127	−	0.840072i
$257$	−326.294	−	1850.50i	−0.0791970	−	0.449149i	−0.998459	−	0.0555014i	$-0.982324\pi$
$257$	−326.294	−	1850.50i	−0.0791970	−	0.449149i	0.919262	−	0.393647i	$-0.128787\pi$
$258$	838.431	−	2225.27i	0.202320	−	0.536975i
$259$	913.942	+	766.888i	0.219265	+	0.183985i
$260$	594.539	+	1029.77i	0.141814	+	0.245630i
$261$	−3519.40	−	3090.83i	−0.834658	−	0.733018i
$262$	1715.58	−	2971.48i	0.404539	−	0.700682i
$263$	−3213.45	+	1169.60i	−0.753422	+	0.274223i	−0.690045	−	0.723767i	$-0.742409\pi$
$263$	−3213.45	+	1169.60i	−0.753422	+	0.274223i	−0.0633767	+	0.997990i	$0.520187\pi$
$264$	3295.32	−	3838.58i	0.768230	−	0.894879i
$265$	−2143.26	+	1798.41i	−0.496828	+	0.416888i
$266$	−488.044	−	177.634i	−0.112496	−	0.0409451i
$267$	−83.4735	+	7412.03i	−0.0191329	+	1.69891i
$268$	269.154	−	1526.45i	0.0613476	−	0.347920i
$269$	−55.2438			−0.0125215			−0.00626073	−	0.999980i	$-0.501993\pi$
$269$	−55.2438			−0.0125215			−0.00626073	+	0.999980i	$0.501993\pi$
$270$	−1800.93	+	960.168i	−0.405931	+	0.216422i
$271$	−4176.94			−0.936276			−0.468138	−	0.883655i	$-0.655075\pi$
$271$	−4176.94			−0.936276			−0.468138	+	0.883655i	$0.655075\pi$
$272$	372.805	−	2114.28i	0.0831051	−	0.471313i
$273$	−896.616	−	531.213i	−0.198775	−	0.117767i
$274$	−1325.13	−	482.307i	−0.292168	−	0.106340i
$275$	2605.54	−	2186.31i	0.571345	−	0.479415i
$276$	−360.545	−	67.7689i	−0.0786315	−	0.0147797i
$277$	−1386.58	+	504.673i	−0.300763	+	0.109469i	−0.487994	−	0.872847i	$-0.662271\pi$
$277$	−1386.58	+	504.673i	−0.300763	+	0.109469i	0.187230	+	0.982316i	$0.440049\pi$
$278$	1112.14	−	1926.29i	0.239935	−	0.415580i
$279$	3351.04	−	2685.61i	0.719074	−	0.576283i
$280$	−207.754	−	359.841i	−0.0443417	−	0.0768021i
$281$	924.184	+	775.482i	0.196200	+	0.164631i	0.735595	−	0.677421i	$-0.236903\pi$
$281$	924.184	+	775.482i	0.196200	+	0.164631i	−0.539395	+	0.842053i	$0.681347\pi$
$282$	3290.48	+	4012.35i	0.694841	+	0.847276i
$283$	−255.320	−	1447.99i	−0.0536297	−	0.304149i	0.946180	−	0.323640i	$-0.104907\pi$
$283$	−255.320	−	1447.99i	−0.0536297	−	0.304149i	−0.999810	+	0.0194907i	$0.993796\pi$
$284$	−377.420	−	2140.46i	−0.0788583	−	0.447228i
$285$	−1695.40	−	2067.34i	−0.352375	−	0.429680i
$286$	−5237.11	−	4394.45i	−1.08279	−	0.908565i
$287$	114.773	+	198.792i	0.0236056	+	0.0408862i
$288$	454.282	+	2965.44i	0.0929473	+	0.606738i
$289$	761.021	−	1318.13i	0.154900	−	0.268294i
$290$	−2371.44	+	863.133i	−0.480192	+	0.174776i
$291$	5839.47	+	1097.60i	1.17634	+	0.221108i
$292$	83.3628	−	69.9497i	0.0167070	−	0.0140188i
$293$	2806.00	+	1021.30i	0.559482	+	0.203635i	0.606254	−	0.795271i	$-0.292671\pi$
$293$	2806.00	+	1021.30i	0.559482	+	0.203635i	−0.0467724	+	0.998906i	$0.514894\pi$
$294$	−3497.81	−	2072.33i	−0.693865	−	0.411090i
$295$	380.635	−	2158.69i	0.0751235	−	0.426046i
$296$	−10871.9			−2.13485
$297$	−3706.19	+	4125.44i	−0.724091	+	0.806002i
$298$	−2126.12			−0.413297
$299$	−354.325	+	2009.48i	−0.0685323	+	0.388666i
$300$	−12.9272	+	1147.87i	−0.00248784	+	0.220908i
$301$	−498.705	−	181.514i	−0.0954979	−	0.0347584i
$302$	720.823	−	604.842i	0.137347	−	0.115248i
$303$	1526.59	−	1778.27i	0.289441	−	0.337157i
$304$	2856.13	−	1039.55i	0.538850	−	0.196125i
$305$	1151.00	−	1993.58i	0.216085	−	0.374270i
$306$	−717.463	+	3593.67i	−0.134035	+	0.671360i
$307$	−2609.58	−	4519.93i	−0.485136	−	0.840280i	0.514718	−	0.857359i	$-0.327897\pi$
$307$	−2609.58	−	4519.93i	−0.485136	−	0.840280i	−0.999854	+	0.0170792i	$0.994563\pi$
$308$	−210.139	−	176.328i	−0.0388760	−	0.0326208i
$309$	−29.2528	+	77.6396i	−0.00538554	+	0.0142937i
$310$	−401.779	−	2278.60i	−0.0736113	−	0.417470i
$311$	1619.49	+	9184.59i	0.295283	+	1.67463i	0.666052	+	0.745906i	$0.267983\pi$
$311$	1619.49	+	9184.59i	0.295283	+	1.67463i	−0.370769	+	0.928725i	$0.620906\pi$
$312$	9370.52	−	1543.68i	1.70032	−	0.280108i
$313$	2732.79	+	2293.08i	0.493503	+	0.414098i	0.855280	−	0.518166i	$-0.173385\pi$
$313$	2732.79	+	2293.08i	0.493503	+	0.414098i	−0.361777	+	0.932265i	$0.617830\pi$
$314$	2859.28	+	4952.41i	0.513880	+	0.890066i
$315$	218.800	+	399.488i	0.0391364	+	0.0714558i
$316$	470.761	−	815.382i	0.0838050	−	0.145154i
$317$	504.110	−	183.481i	0.0893175	−	0.0325089i	−0.296975	−	0.954885i	$-0.595978\pi$
$317$	504.110	−	183.481i	0.0893175	−	0.0325089i	0.386292	+	0.922376i	$0.373756\pi$
$318$	1799.29	+	5122.25i	0.317292	+	0.903276i
$319$	−5253.11	+	4407.88i	−0.921999	+	0.773649i
$320$	3248.71	+	1182.43i	0.567527	+	0.206563i
$321$	863.070	−	485.417i	0.150068	−	0.0844030i
$322$	30.0822	−	170.604i	0.00520625	−	0.0295261i
$323$	−4800.69			−0.826989
$324$	−241.685	−	1856.03i	−0.0414412	−	0.318250i
$325$	6384.90			1.08976
$326$	−1015.98	+	5761.88i	−0.172606	+	0.978900i
$327$	−2288.69	+	1287.23i	−0.387048	+	0.217688i
$328$	−1965.60	−	715.421i	−0.330891	−	0.120434i
$329$	887.135	−	744.395i	0.148661	−	0.124741i
$330$	990.253	+	2819.08i	0.165187	+	0.470258i
$331$	7145.60	−	2600.78i	1.18658	−	0.431879i	0.328058	−	0.944658i	$-0.393606\pi$
$331$	7145.60	−	2600.78i	1.18658	−	0.431879i	0.858521	+	0.512778i	$0.171384\pi$
$332$	−74.3104	+	128.709i	−0.0122841	+	0.0212767i
$333$	11914.8	+	268.401i	1.96074	+	0.0441690i
$334$	−3631.65	−	6290.21i	−0.594956	−	1.03049i
$335$	2886.36	+	2421.95i	0.470743	+	0.395000i
$336$	−510.914	+	84.1669i	−0.0829543	+	0.0136657i
$337$	1328.90	+	7536.54i	0.214806	+	1.21822i	0.881243	+	0.472663i	$0.156707\pi$
$337$	1328.90	+	7536.54i	0.214806	+	1.21822i	−0.666438	+	0.745561i	$0.732182\pi$
$338$	−1339.33	−	7595.71i	−0.215532	−	1.22234i
$339$	3600.23	−	9555.35i	0.576808	−	1.53090i
$340$	−714.828	−	599.812i	−0.114021	−	0.0956746i
$341$	−3143.57	−	5444.82i	−0.499220	−	0.864674i
$342$	−4913.92	+	1664.18i	−0.776943	+	0.263125i
$343$	−917.223	+	1588.68i	−0.144389	+	0.250089i
$344$	4544.49	−	1654.06i	0.712275	−	0.259247i
$345$	580.894	−	676.658i	0.0906500	−	0.105594i
$346$	−1604.09	+	1345.99i	−0.249238	+	0.209135i
$347$	−9254.22	−	3368.26i	−1.43168	−	0.521088i	−0.494267	−	0.869310i	$-0.664563\pi$
$347$	−9254.22	−	3368.26i	−1.43168	−	0.521088i	−0.937412	+	0.348222i	$0.886786\pi$
$348$	26.0630	−	2314.26i	0.00401472	−	0.356487i
$349$	517.464	−	2934.69i	0.0793674	−	0.450115i	−0.919063	−	0.394110i	$-0.871053\pi$
$349$	517.464	−	2934.69i	0.0793674	−	0.450115i	0.998431	−	0.0560046i	$-0.0178361\pi$
$350$	−542.077			−0.0827863
$351$	−10307.5	+	1460.43i	−1.56745	+	0.222085i
$352$	4392.14			0.665062
$353$	−2152.20	+	12205.8i	−0.324505	+	1.84036i	0.188627	+	0.982049i	$0.439596\pi$
$353$	−2152.20	+	12205.8i	−0.324505	+	1.84036i	−0.513131	+	0.858310i	$0.671515\pi$
$354$	−3659.43	−	2168.08i	−0.549426	−	0.325515i
$355$	4964.87	+	1807.07i	0.742276	+	0.270166i
$356$	−2805.73	+	2354.29i	−0.417707	+	0.350498i
$357$	803.775	+	151.079i	0.119160	+	0.0223976i
$358$	−3974.02	+	1446.42i	−0.586685	+	0.213536i
$359$	5508.78	−	9541.49i	0.809867	−	1.40273i	−0.103088	−	0.994672i	$-0.532872\pi$
$359$	5508.78	−	9541.49i	0.809867	−	1.40273i	0.912955	−	0.408059i	$-0.133794\pi$
$360$	−3867.34	−	1507.07i	−0.566186	−	0.220638i
$361$	31.2529	+	54.1316i	0.00455648	+	0.00789206i
$362$	−44.9327	−	37.7030i	−0.00652378	−	0.00547410i
$363$	762.867	+	930.226i	0.110303	+	0.134502i
$364$	−89.4200	−	507.126i	−0.0128760	−	0.0730237i
$365$	45.9363	+	260.518i	0.00658744	+	0.0373592i
$366$	−2832.57	−	3453.98i	−0.404538	−	0.493286i
$367$	3192.07	+	2678.47i	0.454018	+	0.380967i	0.840924	−	0.541152i	$-0.182012\pi$
$367$	3192.07	+	2678.47i	0.454018	+	0.380967i	−0.386906	+	0.922119i	$0.626456\pi$
$368$	506.906	+	877.987i	0.0718052	+	0.124370i
$369$	2136.49	+	832.575i	0.301413	+	0.117458i
$370$	3210.56	−	5560.85i	0.451105	−	0.781338i
$371$	1138.57	−	414.406i	0.159331	−	0.0579917i
$372$	2085.41	+	391.978i	0.290655	+	0.0546321i
$373$	−8891.59	+	7460.93i	−1.23429	+	1.03569i	−0.236339	+	0.971671i	$0.575948\pi$
$373$	−8891.59	+	7460.93i	−1.23429	+	1.03569i	−0.997949	+	0.0640196i	$0.979608\pi$
$374$	5041.51	+	1834.96i	0.697032	+	0.253699i
$375$	−5888.51	−	3488.73i	−0.810884	−	0.480420i
$376$	−1832.52	+	10392.7i	−0.251342	+	1.42543i
$377$	−12872.8			−1.75858
$378$	875.105	−	123.990i	0.119076	−	0.0168713i
$379$	−7443.38			−1.00881			−0.504407	−	0.863466i	$-0.668289\pi$
$379$	−7443.38			−1.00881			−0.504407	+	0.863466i	$0.668289\pi$
$380$	229.403	−	1301.01i	0.0309687	−	0.175632i
$381$	56.0191	−	4974.22i	0.00753266	−	0.668863i
$382$	3825.64	+	1392.42i	0.512400	+	0.186498i
$383$	5971.10	−	5010.35i	0.796629	−	0.668451i	−0.150747	−	0.988572i	$-0.548168\pi$
$383$	5971.10	−	5010.35i	0.796629	−	0.668451i	0.947377	+	0.320121i	$0.103724\pi$
$384$	1361.19	−	1585.59i	0.180893	−	0.210715i
$385$	626.623	−	228.072i	0.0829498	−	0.0301913i
$386$	2936.14	−	5085.55i	0.387165	−	0.670589i
$387$	−5021.26	+	1700.53i	−0.659548	+	0.223367i
$388$	1467.95	+	2542.56i	0.192072	+	0.332678i
$389$	2589.80	+	2173.10i	0.337553	+	0.283240i	0.795769	−	0.605600i	$-0.207067\pi$
$389$	2589.80	+	2173.10i	0.337553	+	0.283240i	−0.458216	+	0.888841i	$0.651511\pi$
$390$	−1977.61	+	5248.77i	−0.256770	+	0.681491i
$391$	−278.060	−	1576.96i	−0.0359645	−	0.203965i
$392$	−1435.77	−	8142.68i	−0.184994	−	1.04915i
$393$	−7547.61	+	1243.38i	−0.968770	+	0.159593i
$394$	3244.37	+	2722.35i	0.414845	+	0.348096i
$395$	1144.37	+	1982.11i	0.145771	+	0.252483i
$396$	−2739.53	−	61.7124i	−0.347643	−	0.00783123i
$397$	986.308	−	1708.34i	0.124689	−	0.215967i	−0.796923	−	0.604082i	$-0.793540\pi$
$397$	986.308	−	1708.34i	0.124689	−	0.215967i	0.921611	+	0.388114i	$0.126873\pi$
$398$	577.013	−	210.015i	0.0726709	−	0.0264501i
$399$	383.733	+	1092.42i	0.0481470	+	0.137066i
$400$	2430.15	−	2039.14i	0.303769	−	0.254893i
$401$	6067.75	+	2208.48i	0.755634	+	0.275028i	0.690974	−	0.722879i	$-0.257182\pi$
$401$	6067.75	+	2208.48i	0.755634	+	0.275028i	0.0646593	+	0.997907i	$0.479404\pi$
$402$	6372.65	−	3584.18i	0.790644	−	0.444683i
$403$	2049.44	−	11622.9i	0.253324	−	1.43667i
$404$	1158.03			0.142610
$405$	4201.12	+	1747.12i	0.515445	+	0.214358i
$406$	1092.90			0.133595
$407$	3029.82	−	17183.0i	0.368999	−	2.09270i
$408$	−6495.80	+	3653.44i	−0.788211	+	0.443315i
$409$	−2929.07	−	1066.09i	−0.354116	−	0.128888i	0.158836	−	0.987305i	$-0.449226\pi$
$409$	−2929.07	−	1066.09i	−0.354116	−	0.128888i	−0.512952	+	0.858417i	$0.671448\pi$
$410$	946.387	−	794.113i	0.113997	−	0.0956547i
$411$	1041.90	+	2966.12i	0.125045	+	0.355980i
$412$	−38.5232	+	14.0213i	−0.00460655	+	0.00167665i
$413$	−474.638	+	822.097i	−0.0565506	+	0.0979485i
$414$	−831.280	−	1517.76i	−0.0986840	−	0.180179i
$415$	−180.641	−	312.880i	−0.0213671	−	0.0370088i
$416$	6315.98	+	5299.74i	0.744391	+	0.624618i
$417$	−4892.81	+	806.032i	−0.574585	+	0.0946560i
$418$	1318.94	+	7480.10i	0.154334	+	0.875272i
$419$	1908.57	+	10824.0i	0.222529	+	1.26203i	0.867352	+	0.497695i	$0.165820\pi$
$419$	1908.57	+	10824.0i	0.222529	+	1.26203i	−0.644823	+	0.764332i	$0.723069\pi$
$420$	−79.3519	+	210.607i	−0.00921899	+	0.0244680i
$421$	973.947	+	817.239i	0.112749	+	0.0946075i	0.697419	−	0.716664i	$-0.254332\pi$
$421$	973.947	+	817.239i	0.112749	+	0.0946075i	−0.584670	+	0.811271i	$0.698776\pi$
$422$	4161.16	+	7207.35i	0.480005	+	0.831394i
$423$	2264.87	−	11344.4i	0.260335	−	1.30398i
$424$	−5520.60	+	9561.96i	−0.632321	+	1.09521i
$425$	−4708.44	+	1713.73i	−0.537395	+	0.195596i
$426$	6678.17	−	7779.12i	0.759526	−	0.884740i
$427$	−763.681	+	640.804i	−0.0865506	+	0.0726246i
$428$	459.771	+	167.343i	0.0519249	+	0.0188991i
$429$	−171.634	+	15240.2i	−0.0193160	+	1.71516i
$430$	−495.991	+	2812.91i	−0.0556252	+	0.315466i
$431$	9788.90			1.09400			0.547001	−	0.837132i	$-0.315769\pi$
$431$	9788.90			1.09400			0.547001	+	0.837132i	$0.315769\pi$
$432$	−3456.72	+	3847.75i	−0.384981	+	0.428530i
$433$	−554.607			−0.0615536			−0.0307768	−	0.999526i	$-0.509798\pi$
$433$	−554.607			−0.0615536			−0.0307768	+	0.999526i	$0.509798\pi$
$434$	−173.997	+	986.784i	−0.0192445	+	0.109141i
$435$	4840.36	+	2867.74i	0.533512	+	0.316087i
$436$	−1219.22	−	443.760i	−0.133922	−	0.0487437i
$437$	1736.62	−	1457.20i	0.190100	−	0.159513i
$438$	504.489	+	94.8248i	0.0550352	+	0.0103445i
$439$	527.503	−	191.995i	0.0573493	−	0.0208734i	−0.313186	−	0.949692i	$-0.601396\pi$
$439$	527.503	−	191.995i	0.0573493	−	0.0208734i	0.370536	+	0.928818i	$0.379174\pi$
$440$	−3038.31	+	5262.51i	−0.329195	+	0.570182i
$441$	1372.48	+	8959.23i	0.148200	+	0.967415i
$442$	5035.65	+	8722.00i	0.541903	+	0.938604i
$443$	−13469.2	−	11302.0i	−1.44456	−	1.21213i	−0.936431	−	0.350851i	$-0.885892\pi$
$443$	−13469.2	−	11302.0i	−1.44456	−	1.21213i	−0.508130	−	0.861280i	$-0.669663\pi$
$444$	3734.19	+	4553.41i	0.399137	+	0.486701i
$445$	−1546.07	−	8768.22i	−0.164699	−	0.934053i
$446$	−1145.36	−	6495.65i	−0.121602	−	0.689637i
$447$	3005.66	+	3665.05i	0.318038	+	0.387810i
$448$	−1146.92	−	962.381i	−0.120953	−	0.101492i
$449$	−2896.70	−	5017.23i	−0.304463	−	0.527345i	0.672679	−	0.739934i	$-0.265144\pi$
$449$	−2896.70	−	5017.23i	−0.304463	−	0.527345i	−0.977142	+	0.212590i	$0.931810\pi$
$450$	−4225.42	+	3386.36i	−0.442641	+	0.354743i
$451$	1678.50	−	2907.25i	0.175249	−	0.303541i
$452$	4741.17	−	1725.65i	0.493376	−	0.179574i
$453$	−2061.66	−	387.514i	−0.213831	−	0.0401920i
$454$	5576.64	−	4679.36i	0.576486	−	0.483729i
$455$	1176.30	+	428.137i	0.121199	+	0.0441130i
$456$	−9077.51	−	5378.10i	−0.932222	−	0.552308i
$457$	−129.874	+	736.553i	−0.0132938	+	0.0753928i	−0.990733	−	0.135825i	$-0.956632\pi$
$457$	−129.874	+	736.553i	−0.0132938	+	0.0753928i	0.977439	+	0.211217i	$0.0677428\pi$
$458$	4910.37			0.500975
$459$	7209.12	−	3843.54i	0.733100	−	0.390852i
$460$	440.650			0.0446640
$461$	−1984.93	+	11257.1i	−0.200537	+	1.13730i	0.703774	+	0.710424i	$0.251497\pi$
$461$	−1984.93	+	11257.1i	−0.200537	+	1.13730i	−0.904310	+	0.426876i	$0.859614\pi$
$462$	14.5717	−	1293.89i	0.00146739	−	0.130297i
$463$	−6328.14	−	2303.25i	−0.635191	−	0.231191i	0.00429807	−	0.999991i	$-0.498632\pi$
$463$	−6328.14	−	2303.25i	−0.635191	−	0.231191i	−0.639489	+	0.768800i	$0.720854\pi$
$464$	−4899.51	+	4111.18i	−0.490203	+	0.411329i
$465$	−3359.92	+	3913.82i	−0.335080	+	0.390321i
$466$	−13498.8	+	4913.15i	−1.34188	+	0.488406i
$467$	−753.154	+	1304.50i	−0.0746292	+	0.129261i	−0.900925	−	0.433975i	$-0.857111\pi$
$467$	−753.154	+	1304.50i	−0.0746292	+	0.129261i	0.826296	+	0.563236i	$0.190444\pi$
$468$	−3865.04	−	3394.38i	−0.381755	−	0.335267i
$469$	−815.870	−	1413.13i	−0.0803270	−	0.139130i
$470$	−4774.59	−	4006.36i	−0.468586	−	0.393190i
$471$	4494.96	−	11930.1i	0.439739	−	1.16711i
$472$	−1502.12	−	8518.94i	−0.146484	−	0.830754i
$473$	1347.75	+	7643.49i	0.131014	+	0.743019i
$474$	4382.16	−	721.908i	0.424640	−	0.0699543i
$475$	−5434.09	−	4559.74i	−0.524911	−	0.440453i
$476$	202.056	+	349.971i	0.0194563	+	0.0336993i
$477$	6286.23	−	10342.9i	0.603411	−	0.992808i
$478$	670.267	−	1160.94i	0.0641366	−	0.111088i
$479$	−7393.80	+	2691.12i	−0.705285	+	0.256703i	−0.669666	−	0.742663i	$-0.733563\pi$
$479$	−7393.80	+	2691.12i	−0.705285	+	0.256703i	−0.0356191	+	0.999365i	$0.511340\pi$
$480$	−1194.25	−	3399.82i	−0.113562	−	0.323292i
$481$	25090.6	−	21053.6i	2.37845	−	1.99576i
$482$	−11113.0	−	4044.82i	−1.05018	−	0.382233i
$483$	−336.619	+	189.325i	−0.0317116	+	0.0178356i
$484$	−103.223	+	585.405i	−0.00969409	+	0.0549779i
$485$	−7136.87			−0.668183
$486$	6046.78	−	6433.27i	0.564377	−	0.600451i
$487$	−12030.9			−1.11945			−0.559724	−	0.828679i	$-0.689093\pi$
$487$	−12030.9			−1.11945			−0.559724	+	0.828679i	$0.689093\pi$
$488$	1577.50	−	8946.45i	0.146332	−	0.829891i
$489$	11368.7	−	6394.14i	1.05135	−	0.591315i
$490$	4588.88	+	1670.22i	0.423070	+	0.153985i
$491$	−8360.94	+	7015.66i	−0.768481	+	0.644832i	−0.940319	−	0.340293i	$-0.889474\pi$
$491$	−8360.94	+	7015.66i	−0.768481	+	0.644832i	0.171839	+	0.985125i	$0.445029\pi$
$492$	375.494	+	1068.97i	0.0344077	+	0.0979527i
$493$	9492.84	−	3455.11i	0.867213	−	0.315640i
$494$	−7129.13	+	12348.0i	−0.649301	+	1.12462i
$495$	3459.68	−	5692.32i	0.314144	−	0.516870i
$496$	−2931.97	−	5078.32i	−0.265422	−	0.459725i
$497$	−1752.79	−	1470.77i	−0.158196	−	0.132742i
$498$	−691.732	+	113.954i	−0.0622435	+	0.0102539i
$499$	2712.48	+	15383.2i	0.243341	+	1.38006i	0.824314	+	0.566133i	$0.191561\pi$
$499$	2712.48	+	15383.2i	0.243341	+	1.38006i	−0.580973	+	0.813923i	$0.697328\pi$
$500$	−587.264	−	3330.54i	−0.0525265	−	0.297893i
$501$	−5709.19	+	15152.7i	−0.509117	+	1.35124i
$502$	3246.23	+	2723.91i	0.288619	+	0.242180i
$503$	9728.26	+	16849.8i	0.862349	+	1.49363i	0.869656	+	0.493659i	$0.164341\pi$
$503$	9728.26	+	16849.8i	0.862349	+	1.49363i	−0.00730688	+	0.999973i	$0.502326\pi$
$504$	1350.59	+	1186.12i	0.119365	+	0.104829i
$505$	−1407.53	+	2437.92i	−0.124028	+	0.214824i
$506$	−2380.71	+	866.509i	−0.209161	+	0.0761285i
$507$	−11200.3	+	13046.7i	−0.981108	+	1.14285i
$508$	1882.93	−	1579.96i	0.164452	−	0.137991i
$509$	−12484.3	−	4543.90i	−1.08714	−	0.395687i	−0.264580	−	0.964364i	$-0.585233\pi$
$509$	−12484.3	−	4543.90i	−1.08714	−	0.395687i	−0.822561	+	0.568677i	$0.807456\pi$
$510$	49.5682	−	4401.42i	0.00430376	−	0.382153i
$511$	19.8934	−	112.821i	0.00172218	−	0.00976696i
$512$	11361.1			0.980653
$513$	9815.51	+	6118.10i	0.844767	+	0.526551i
$514$	4379.64			0.375832
$515$	17.3051	−	98.1420i	0.00148069	−	0.00839739i
$516$	−2253.66	−	1335.21i	−0.192271	−	0.113914i
$517$	−15914.9	−	5792.56i	−1.35384	−	0.492759i
$518$	−2130.19	+	1787.44i	−0.180686	+	0.151613i
$519$	4587.93	+	862.356i	0.388030	+	0.0729350i
$520$	−10719.1	+	3901.44i	−0.903970	+	0.329018i
$521$	1678.81	−	2907.79i	0.141171	−	0.244516i	−0.786767	−	0.617250i	$-0.788247\pi$
$521$	1678.81	−	2907.79i	0.141171	−	0.244516i	0.927938	+	0.372735i	$0.121580\pi$
$522$	8519.01	−	6827.35i	0.714305	−	0.572461i
$523$	5383.99	+	9325.34i	0.450144	+	0.779672i	0.998395	−	0.0566419i	$-0.0180393\pi$
$523$	5383.99	+	9325.34i	0.450144	+	0.779672i	−0.548251	+	0.836314i	$0.684706\pi$
$524$	−2895.38	−	2429.51i	−0.241384	−	0.202545i
$525$	766.327	+	934.445i	0.0637053	+	0.0776810i
$526$	−1384.06	−	7849.42i	−0.114730	−	0.650667i
$527$	1608.32	+	9121.21i	0.132940	+	0.753940i
$528$	4801.94	+	5855.39i	0.395791	+	0.482620i
$529$	−8741.21	−	7334.74i	−0.718436	−	0.602839i
$530$	−3260.55	−	5647.44i	−0.267225	−	0.462847i
$531$	1435.90	+	9373.21i	0.117350	+	0.766032i
$532$	−286.057	+	495.465i	−0.0233123	+	0.0403781i
$533$	5921.72	−	2155.33i	0.481235	−	0.175155i
$534$	−16979.5	−	3191.51i	−1.37599	−	0.258633i
$535$	−911.123	+	764.523i	−0.0736285	+	0.0617817i
$536$	13972.6	+	5085.62i	1.12598	+	0.409824i
$537$	8111.40	+	4805.72i	0.651830	+	0.386186i
$538$	22.3591	−	126.805i	0.00179176	−	0.0101616i
$539$	13269.6			1.06041
$540$	697.127	+	2137.37i	0.0555547	+	0.170329i
$541$	10631.7			0.844900			0.422450	−	0.906386i	$-0.361170\pi$
$541$	10631.7			0.844900			0.422450	+	0.906386i	$0.361170\pi$
$542$	1690.55	−	9587.59i	0.133977	−	0.759819i
$543$	−1.47256	+	130.756i	−0.000116379	+	0.0103339i
$544$	−6080.09	−	2212.97i	−0.479194	−	0.174412i
$545$	2416.12	−	2027.36i	0.189899	−	0.159344i
$546$	1582.22	−	1843.06i	0.124016	−	0.144461i
$547$	7239.72	−	2635.04i	0.565901	−	0.205971i	−0.0431962	−	0.999067i	$-0.513754\pi$
$547$	7239.72	−	2635.04i	0.565901	−	0.205971i	0.609097	+	0.793095i	$0.291532\pi$
$548$	−776.697	+	1345.28i	−0.0605453	+	0.104868i
$549$	−1949.69	+	9765.71i	−0.151568	+	0.759181i
$550$	3963.82	+	6865.53i	0.307305	+	0.532268i
$551$	10955.8	+	9193.04i	0.847068	+	0.710774i
$552$	1240.85	−	3293.34i	0.0956779	−	0.253938i
$553$	−172.116	−	976.119i	−0.0132353	−	0.0750612i
$554$	−597.213	−	3386.96i	−0.0457999	−	0.259744i
$555$	−14124.7	+	2326.87i	−1.08029	+	0.177964i
$556$	−1876.96	−	1574.96i	−0.143167	−	0.120131i
$557$	−7812.89	−	13532.3i	−0.594332	−	1.02941i	−0.993641	−	0.112597i	$-0.964083\pi$
$557$	−7812.89	−	13532.3i	−0.594332	−	1.02941i	0.399309	−	0.916817i	$-0.369250\pi$
$558$	4808.16	+	8778.82i	0.364777	+	0.666016i
$559$	−7284.86	+	12617.7i	−0.551193	+	0.954694i
$560$	584.444	−	212.720i	0.0441023	−	0.0160519i
$561$	−3963.97	−	11284.7i	−0.298323	−	0.849272i
$562$	−2154.06	+	1807.47i	−0.161679	+	0.135665i
$563$	−3110.45	−	1132.11i	−0.232842	−	0.0847475i	0.222964	−	0.974827i	$-0.428427\pi$
$563$	−3110.45	−	1132.11i	−0.232842	−	0.0847475i	−0.455806	+	0.890079i	$0.650649\pi$
$564$	4982.12	−	2802.10i	0.371960	−	0.209202i
$565$	−2129.79	+	12078.7i	−0.158586	+	0.899386i
$566$	3427.01			0.254502
$567$	−1450.86	−	1333.25i	−0.107461	−	0.0987496i
$568$	20850.5			1.54026
$569$	2333.03	−	13231.3i	0.171891	−	0.974840i	−0.769781	−	0.638308i	$-0.779635\pi$
$569$	2333.03	−	13231.3i	0.171891	−	0.974840i	0.941672	−	0.336532i	$-0.109254\pi$
$570$	5431.49	−	3054.84i	0.399123	−	0.224479i
$571$	20350.2	+	7406.86i	1.49147	+	0.542850i	0.953836	−	0.300328i	$-0.0970962\pi$
$571$	20350.2	+	7406.86i	1.49147	+	0.542850i	0.537633	+	0.843179i	$0.319318\pi$
$572$	−5769.00	+	4840.77i	−0.421703	+	0.353851i
$573$	−3007.97	−	8563.17i	−0.219302	−	0.624313i
$574$	−502.753	+	182.987i	−0.0365583	+	0.0133062i
$575$	1183.06	−	2049.13i	0.0858037	−	0.148616i
$576$	−14952.1	−	336.821i	−1.08160	−	0.0243649i
$577$	−6942.37	−	12024.5i	−0.500892	−	0.867570i	−0.999999	−	0.00103001i	$-0.999672\pi$
$577$	−6942.37	−	12024.5i	−0.500892	−	0.867570i	0.499108	−	0.866540i	$-0.333661\pi$
$578$	2717.57	+	2280.31i	0.195564	+	0.164098i
$579$	−12917.4	+	2127.98i	−0.927164	+	0.152739i
$580$	482.732	+	2737.71i	0.0345592	+	0.195995i
$581$	27.1688	+	154.082i	0.00194002	+	0.0110024i
$582$	−4882.83	+	12959.5i	−0.347766	+	0.923003i
$583$	−13574.1	−	11390.0i	−0.964292	−	0.809137i
$584$	521.976	+	904.090i	0.0369855	+	0.0640608i
$585$	11843.7	−	4011.06i	0.837053	−	0.283482i
$586$	−3479.94	+	6027.43i	−0.245316	+	0.424899i
$587$	3702.30	−	1347.53i	0.260324	−	0.0947501i	−0.208561	−	0.978009i	$-0.566878\pi$
$587$	3702.30	−	1347.53i	0.260324	−	0.0947501i	0.468885	+	0.883259i	$0.344656\pi$
$588$	−2917.19	+	3398.12i	−0.204597	+	0.238326i
$589$	−10044.7	+	8428.49i	−0.702689	+	0.589626i
$590$	4800.92	+	1747.39i	0.335001	+	0.121930i
$591$	106.327	−	9441.28i	0.00740049	−	0.657127i
$592$	2825.88	−	16026.4i	0.196187	−	1.11263i
$593$	12075.4			0.836219			0.418109	−	0.908397i	$-0.362693\pi$
$593$	12075.4			0.836219			0.418109	+	0.908397i	$0.362693\pi$
$594$	−7969.37	−	10176.8i	−0.550484	−	0.702959i
$595$	−982.355			−0.0676851
$596$	−406.693	+	2306.47i	−0.0279510	+	0.158518i
$597$	−1177.75	−	697.772i	−0.0807402	−	0.0478357i
$598$	−4469.08	−	1626.61i	−0.305609	−	0.111233i
$599$	3521.24	−	2954.67i	0.240190	−	0.201544i	−0.514744	−	0.857344i	$-0.672113\pi$
$599$	3521.24	−	2954.67i	0.240190	−	0.201544i	0.754935	+	0.655800i	$0.227669\pi$
$600$	−10822.9	−	2034.30i	−0.736407	−	0.138417i
$601$	−12007.3	+	4370.29i	−0.814954	+	0.296619i	−0.715669	−	0.698440i	$-0.753878\pi$
$601$	−12007.3	+	4370.29i	−0.814954	+	0.296619i	−0.0992853	+	0.995059i	$0.531656\pi$
$602$	618.483	−	1071.24i	0.0418729	−	0.0725260i
$603$	−15187.4	−	5918.42i	−1.02567	−	0.399696i
$604$	−518.268	−	897.666i	−0.0349139	−	0.0604727i
$605$	−1106.95	−	928.837i	−0.0743863	−	0.0624175i
$606$	3463.90	+	4223.81i	0.232197	+	0.283137i
$607$	4788.12	+	27154.8i	0.320171	+	1.81578i	0.541637	+	0.840612i	$0.317805\pi$
$607$	4788.12	+	27154.8i	0.320171	+	1.81578i	−0.221466	+	0.975168i	$0.571084\pi$
$608$	−1590.65	−	9021.04i	−0.106101	−	0.601730i
$609$	−1545.02	−	1883.97i	−0.102803	−	0.125357i
$610$	4110.15	+	3448.83i	0.272812	+	0.228916i
$611$	−15896.4	−	27533.4i	−1.05254	−	1.82305i
$612$	3761.27	+	1465.74i	0.248432	+	0.0968119i
$613$	13671.0	−	23678.9i	0.900760	−	1.56016i	0.0742512	−	0.997240i	$-0.476343\pi$
$613$	13671.0	−	23678.9i	0.900760	−	1.56016i	0.826509	−	0.562923i	$-0.190323\pi$
$614$	11431.1	−	4160.57i	0.751336	−	0.273464i
$615$	−2706.81	−	508.777i	−0.177478	−	0.0333591i
$616$	2015.90	−	1691.54i	0.131856	−	0.110640i
$617$	−11248.8	−	4094.25i	−0.733973	−	0.267144i	−0.0521276	−	0.998640i	$-0.516600\pi$
$617$	−11248.8	−	4094.25i	−0.733973	−	0.267144i	−0.681846	+	0.731496i	$0.738822\pi$
$618$	−166.371	−	98.5692i	−0.0108292	−	0.00641591i
$619$	−3036.42	+	17220.4i	−0.197163	+	1.11817i	0.712141	+	0.702036i	$0.247726\pi$
$619$	−3036.42	+	17220.4i	−0.197163	+	1.11817i	−0.909304	+	0.416132i	$0.863386\pi$
$620$	−2548.74			−0.165097
$621$	−1441.19	+	3578.62i	−0.0931286	+	0.231248i
$622$	−21737.4			−1.40127
$623$	−669.551	+	3797.22i	−0.0430578	+	0.244193i
$624$	−160.081	+	14214.4i	−0.0102698	+	0.911909i
$625$	−2381.77	−	866.893i	−0.152433	−	0.0554811i
$626$	−6369.52	+	5344.66i	−0.406673	+	0.341239i
$627$	11029.8	−	12848.1i	0.702532	−	0.818350i
$628$	5919.45	−	2154.50i	0.376133	−	0.136901i
$629$	−12851.8	+	22260.0i	−0.814684	+	1.41107i
$630$	−1005.53	+	340.538i	−0.0635891	+	0.0215355i
$631$	7837.35	+	13574.7i	0.494453	+	0.856418i	0.999980	−	0.00639327i	$-0.00203505\pi$
$631$	7837.35	+	13574.7i	0.494453	+	0.856418i	−0.505527	+	0.862811i	$0.668702\pi$
$632$	6919.06	+	5805.78i	0.435483	+	0.365414i
$633$	6541.61	−	17362.0i	0.410752	−	1.09017i
$634$	217.125	+	1231.38i	0.0136012	+	0.0771360i
$635$	1037.57	+	5884.35i	0.0648420	+	0.367737i
$636$	5900.94	−	972.109i	0.367905	−	0.0606079i
$637$	19081.9	+	16011.6i	1.18690	+	0.995925i
$638$	−7991.58	−	13841.8i	−0.495909	−	0.858939i
$639$	−22850.7	−	514.749i	−1.41465	−	0.0318672i
$640$	−1255.03	+	2173.77i	−0.0775146	+	0.134259i
$641$	−11192.7	+	4073.82i	−0.689682	+	0.251024i	−0.662999	−	0.748620i	$-0.730717\pi$
$641$	−11192.7	+	4073.82i	−0.689682	+	0.251024i	−0.0266830	+	0.999644i	$0.508494\pi$
$642$	764.896	+	2177.52i	0.0470218	+	0.133863i
$643$	−1791.00	+	1502.83i	−0.109845	+	0.0921707i	−0.696056	−	0.717988i	$-0.745063\pi$
$643$	−1791.00	+	1502.83i	−0.109845	+	0.0921707i	0.586211	+	0.810158i	$0.300619\pi$
$644$	−179.322	−	65.2679i	−0.0109725	−	0.00399366i
$645$	5550.14	−	3121.57i	0.338816	−	0.190561i
$646$	1943.01	−	11019.3i	0.118338	−	0.671130i
$647$	27544.4			1.67370			0.836850	−	0.547433i	$-0.184395\pi$
$647$	27544.4			1.67370			0.836850	+	0.547433i	$0.184395\pi$
$648$	17937.4	+	808.548i	1.08742	+	0.0490166i
$649$	13882.7			0.839669
$650$	−2584.19	+	14655.7i	−0.155939	+	0.884373i
$651$	1947.02	−	1095.06i	0.117219	−	0.0659277i
$652$	6056.31	+	2204.32i	0.363778	+	0.132405i
$653$	14617.2	−	12265.3i	0.875983	−	0.735037i	−0.0893659	−	0.995999i	$-0.528484\pi$
$653$	14617.2	−	12265.3i	0.875983	−	0.735037i	0.965349	+	0.260962i	$0.0840396\pi$
$654$	−2028.35	−	5774.36i	−0.121277	−	0.345253i
$655$	8633.85	−	3142.47i	0.515042	−	0.187460i
$656$	1565.52	−	2711.55i	0.0931755	−	0.161385i
$657$	−549.728	−	1003.70i	−0.0326437	−	0.0596015i
$658$	1349.60	+	2337.58i	0.0799590	+	0.138493i
$659$	−4300.20	−	3608.30i	−0.254191	−	0.213292i	0.506783	−	0.862073i	$-0.330834\pi$
$659$	−4300.20	−	3608.30i	−0.254191	−	0.213292i	−0.760975	+	0.648782i	$0.775279\pi$
$660$	3247.63	−	535.008i	0.191536	−	0.0315533i
$661$	−3251.84	−	18442.1i	−0.191349	−	1.08519i	−0.917523	−	0.397683i	$-0.869814\pi$
$661$	−3251.84	−	18442.1i	−0.191349	−	1.08519i	0.726174	−	0.687511i	$-0.241297\pi$
$662$	3077.68	+	17454.4i	0.180691	+	1.02475i
$663$	7916.36	−	21010.8i	0.463719	−	1.23075i
$664$	−1092.19	−	916.452i	−0.0638329	−	0.0535621i
$665$	−695.376	−	1204.43i	−0.0405497	−	0.0702341i
$666$	−5438.42	+	27240.2i	−0.316418	+	1.58489i
$667$	−2385.21	+	4131.31i	−0.138464	+	0.239827i
$668$	−7518.47	+	2736.50i	−0.435477	+	0.158501i
$669$	−9578.18	+	11157.2i	−0.553533	+	0.644788i
$670$	−6727.46	+	5645.01i	−0.387917	+	0.325501i
$671$	13700.2	+	4986.46i	0.788211	+	0.286885i
$672$	−17.5735	+	1560.44i	−0.00100880	+	0.0895765i
$673$	1039.78	−	5896.87i	0.0595550	−	0.337753i	−0.940443	−	0.339952i	$-0.889589\pi$
$673$	1039.78	−	5896.87i	0.0595550	−	0.337753i	0.999998	+	0.00219950i	$0.000700122\pi$
$674$	−17836.9			−1.01937
$675$	11810.9	+	2496.63i	0.673485	+	0.142364i
$676$	−8496.23			−0.483400
$677$	−3572.70	+	20261.8i	−0.202821	+	1.15026i	0.698010	+	0.716088i	$0.254069\pi$
$677$	−3572.70	+	20261.8i	−0.202821	+	1.15026i	−0.900832	+	0.434169i	$0.857042\pi$
$678$	20475.9	+	12131.2i	1.15984	+	0.687164i
$679$	2904.34	+	1057.09i	0.164151	+	0.0597460i
$680$	6857.47	−	5754.10i	0.386724	−	0.324500i
$681$	−15950.0	−	2998.00i	−0.897513	−	0.168698i
$682$	13770.2	−	5011.93i	0.773148	−	0.281403i
$683$	−5457.83	+	9453.24i	−0.305766	+	0.529602i	−0.977432	−	0.211252i	$-0.932246\pi$
$683$	−5457.83	+	9453.24i	−0.305766	+	0.529602i	0.671666	+	0.740854i	$0.265579\pi$
$684$	865.395	+	5649.09i	0.0483760	+	0.315787i
$685$	−1888.07	−	3270.24i	−0.105313	−	0.182408i
$686$	−3275.36	−	2748.35i	−0.182294	−	0.152963i
$687$	−6941.73	−	8464.62i	−0.385507	−	0.470080i
$688$	1257.03	+	7129.00i	0.0696570	+	0.395044i
$689$	−5776.15	−	32758.2i	−0.319381	−	1.81130i
$690$	1318.07	+	1607.23i	0.0727218	+	0.0886756i
$691$	648.624	+	544.261i	0.0357089	+	0.0299633i	0.660467	−	0.750855i	$-0.270358\pi$
$691$	648.624	+	544.261i	0.0357089	+	0.0299633i	−0.624759	+	0.780818i	$0.714803\pi$
$692$	1153.33	+	1997.63i	0.0633570	+	0.109737i
$693$	−2251.04	+	1804.04i	−0.123391	+	0.0988887i
$694$	11476.9	−	19878.5i	0.627747	−	1.08729i
$695$	5596.98	−	2037.13i	0.305476	−	0.111184i
$696$	21820.5	+	4101.42i	1.18837	+	0.223368i
$697$	−3788.38	+	3178.82i	−0.205875	+	0.172750i
$698$	6526.74	+	2375.54i	0.353926	+	0.128819i
$699$	27552.4	+	16323.8i	1.49088	+	0.883296i
$700$	−103.691	+	588.060i	−0.00559878	+	0.0317523i
$701$	−17623.2			−0.949529			−0.474765	−	0.880113i	$-0.657467\pi$
$701$	−17623.2			−0.949529			−0.474765	+	0.880113i	$0.657467\pi$
$702$	819.599	−	24250.6i	0.0440652	−	1.30382i
$703$	−36389.5			−1.95229
$704$	−3802.18	+	21563.2i	−0.203551	+	1.15440i
$705$	−156.476	+	13894.3i	−0.00835919	+	0.742254i
$706$	−27145.6	−	9880.18i	−1.44708	−	0.526693i
$707$	933.891	−	783.628i	0.0496784	−	0.0416851i
$708$	−3051.99	+	3555.13i	−0.162007	+	0.188715i
$709$	−2260.60	+	822.791i	−0.119744	+	0.0435833i	−0.401197	−	0.915992i	$-0.631406\pi$
$709$	−2260.60	+	822.791i	−0.119744	+	0.0435833i	0.281453	+	0.959575i	$0.409184\pi$
$710$	−6157.33	+	10664.8i	−0.325465	+	0.563722i
$711$	−7439.45	−	6533.52i	−0.392407	−	0.344622i
$712$	−17568.1	−	30428.9i	−0.924709	−	1.60164i
$713$	−3350.44	−	2811.35i	−0.175982	−	0.147666i
$714$	−672.097	+	1783.81i	−0.0352277	+	0.0934977i
$715$	−3178.96	−	18028.8i	−0.166274	−	0.942989i
$716$	808.954	+	4587.80i	0.0422235	+	0.239461i
$717$	−2948.80	+	485.779i	−0.153591	+	0.0253023i
$718$	19671.6	+	16506.4i	1.02248	+	0.857959i
$719$	2183.22	+	3781.44i	0.113241	+	0.196139i	0.917075	−	0.398714i	$-0.130543\pi$
$719$	2183.22	+	3781.44i	0.113241	+	0.196139i	−0.803834	+	0.594853i	$0.797210\pi$
$720$	3226.81	−	5309.16i	0.167022	−	0.274806i
$721$	−21.5788	+	37.3756i	−0.00111461	+	0.00193057i
$722$	−136.901	+	49.8279i	−0.00705668	+	0.00256842i
$723$	8737.82	+	24875.0i	0.449465	+	1.27955i
$724$	−49.4962	+	41.5322i	−0.00254076	+	0.00213195i
$725$	14027.0	+	5105.41i	0.718552	+	0.261531i
$726$	−2443.97	+	1374.56i	−0.124937	+	0.0702683i
$727$	−390.362	+	2213.85i	−0.0199143	+	0.112940i	−0.993145	−	0.116893i	$-0.962707\pi$
$727$	−390.362	+	2213.85i	−0.0199143	+	0.112940i	0.973230	+	0.229832i	$0.0738178\pi$
$728$	4940.00			0.251495
$729$	−19638.1	−	1328.94i	−0.997718	−	0.0675171i
$730$	−616.575			−0.0312609
$731$	1985.45	−	11260.0i	0.100458	−	0.569723i
$732$	−4288.81	+	2412.16i	−0.216556	+	0.121798i
$733$	11697.6	+	4257.58i	0.589442	+	0.214539i	0.619484	−	0.785009i	$-0.287342\pi$
$733$	11697.6	+	4257.58i	0.589442	+	0.214539i	−0.0300420	+	0.999549i	$0.509564\pi$
$734$	−7439.99	+	6242.90i	−0.374135	+	0.313937i
$735$	−3608.08	−	10271.6i	−0.181070	−	0.515474i
$736$	2871.15	−	1045.01i	0.143794	−	0.0523366i
$737$	−11931.7	+	20666.4i	−0.596352	+	1.03291i
$738$	−2775.78	+	4567.06i	−0.138452	+	0.227799i
$739$	−18843.7	−	32638.3i	−0.937993	−	1.62465i	−0.769207	−	0.639000i	$-0.779348\pi$
$739$	−18843.7	−	32638.3i	−0.937993	−	1.62465i	−0.168787	−	0.985653i	$-0.553985\pi$
$740$	−5418.44	−	4546.61i	−0.269170	−	0.225860i
$741$	31364.2	−	5166.87i	1.55491	−	0.256154i
$742$	490.394	+	2781.16i	0.0242627	+	0.137601i
$743$	−1559.46	−	8844.15i	−0.0770001	−	0.436689i	−0.998798	−	0.0490183i	$-0.984391\pi$
$743$	−1559.46	−	8844.15i	−0.0770001	−	0.436689i	0.921798	−	0.387671i	$-0.126720\pi$
$744$	−7177.15	+	19048.8i	−0.353666	+	0.938661i
$745$	−4361.32	−	3659.58i	−0.214478	−	0.179969i
$746$	−13526.8	−	23429.1i	−0.663877	−	1.14987i
$747$	1174.33	+	1031.33i	0.0575187	+	0.0505145i
$748$	2954.98	−	5118.17i	0.144445	−	0.250186i
$749$	484.019	−	176.169i	0.0236124	−	0.00859421i
$750$	10391.2	−	12104.3i	0.505911	−	0.589314i
$751$	−14919.1	+	12518.6i	−0.724908	+	0.608270i	−0.928738	−	0.370736i	$-0.879105\pi$
$751$	−14919.1	+	12518.6i	−0.724908	+	0.608270i	0.203830	+	0.979006i	$0.434661\pi$
$752$	−14843.7	−	5402.65i	−0.719804	−	0.261987i
$753$	106.388	−	9446.70i	0.00514872	−	0.457180i
$754$	5210.07	−	29547.8i	0.251644	−	1.42714i
$755$	2519.71			0.121459
$756$	32.8865	−	973.056i	0.00158210	−	0.0468118i
$757$	4304.01			0.206647			0.103324	−	0.994648i	$-0.467052\pi$
$757$	4304.01			0.206647			0.103324	+	0.994648i	$0.467052\pi$
$758$	3012.59	−	17085.3i	0.144357	−	0.818687i
$759$	4859.29	+	2878.96i	0.232386	+	0.137681i
$760$	11909.1	+	4334.54i	0.568404	+	0.206882i
$761$	26645.0	−	22357.8i	1.26922	−	1.06501i	0.274590	−	0.961562i	$-0.411458\pi$
$761$	26645.0	−	22357.8i	1.26922	−	1.06501i	0.994635	−	0.103445i	$-0.0329864\pi$
$762$	11395.0	+	2141.82i	0.541727	+	0.101824i
$763$	−1283.52	+	467.164i	−0.0609000	+	0.0221658i
$764$	2242.32	−	3883.81i	0.106184	−	0.183915i
$765$	−7657.34	+	6136.78i	−0.361898	+	0.290034i
$766$	9083.86	+	15733.7i	0.428477	+	0.742144i
$767$	19963.6	+	16751.5i	0.939825	+	0.788606i
$768$	−11512.7	−	14038.4i	−0.540925	−	0.659593i
$769$	−3797.53	−	21536.9i	−0.178079	−	1.00993i	−0.934530	−	0.355884i	$-0.884180\pi$
$769$	−3797.53	−	21536.9i	−0.178079	−	1.00993i	0.756451	−	0.654050i	$-0.226931\pi$
$770$	269.893	+	1530.64i	0.0126315	+	0.0716368i
$771$	−6191.44	−	7549.73i	−0.289208	−	0.352655i
$772$	−4955.30	−	4157.99i	−0.231017	−	0.193846i
$773$	3355.81	+	5812.44i	0.156145	+	0.270451i	0.933475	−	0.358641i	$-0.116760\pi$
$773$	3355.81	+	5812.44i	0.156145	+	0.270451i	−0.777330	+	0.629093i	$0.783427\pi$
$774$	−1871.07	−	12213.9i	−0.0868917	−	0.567208i
$775$	−6842.89	+	11852.2i	−0.317166	+	0.549348i
$776$	−26466.0	+	9632.85i	−1.22432	+	0.445617i
$777$	6092.66	+	1145.19i	0.281304	+	0.0528744i
$778$	−6036.24	+	5065.00i	−0.278161	+	0.233405i
$779$	−6579.09	−	2394.59i	−0.302594	−	0.110135i
$780$	5315.72	+	3149.38i	0.244017	+	0.144572i
$781$	−5810.71	+	32954.1i	−0.266227	+	1.50985i
$782$	3732.24			0.170671
$783$	−23812.4	−	5033.55i	−1.08683	−	0.229737i
$784$	12376.4			0.563793
$785$	−2659.09	+	15080.4i	−0.120901	+	0.685661i
$786$	200.774	−	17827.7i	0.00911116	−	0.809026i
$787$	5480.97	+	1994.91i	0.248253	+	0.0903568i	0.463150	−	0.886280i	$-0.346719\pi$
$787$	5480.97	+	1994.91i	0.248253	+	0.0903568i	−0.214896	+	0.976637i	$0.568941\pi$
$788$	3573.88	−	2998.84i	0.161566	−	0.135570i
$789$	−11574.4	+	13482.5i	−0.522255	+	0.608352i
$790$	−5012.84	+	1824.52i	−0.225758	+	0.0821691i
$791$	2655.77	−	4599.94i	0.119379	−	0.206770i
$792$	5146.64	−	25778.8i	0.230907	−	1.15658i
$793$	13684.3	+	23701.8i	0.612790	+	1.06138i
$794$	3522.06	+	2955.36i	0.157422	+	0.132093i
$795$	−5125.79	+	13604.3i	−0.228671	+	0.606913i
$796$	−117.457	−	666.132i	−0.00523009	−	0.0296613i
$797$	3430.37	+	19454.6i	0.152459	+	0.864638i	0.961072	+	0.276297i	$0.0891074\pi$
$797$	3430.37	+	19454.6i	0.152459	+	0.864638i	−0.808613	+	0.588341i	$0.799781\pi$
$798$	−2662.81	+	438.666i	−0.118123	+	0.0194594i
$799$	19112.6	+	16037.4i	0.846253	+	0.710091i
$800$	−4780.39	−	8279.87i	−0.211265	−	0.365922i
$801$	18502.2	+	33781.5i	0.816157	+	1.49015i
$802$	−7525.10	+	13033.9i	−0.331322	+	0.573867i
$803$	−1574.37	+	573.025i	−0.0691886	+	0.0251826i
$804$	−2669.23	−	7598.83i	−0.117085	−	0.333321i
$805$	355.361	−	298.183i	0.0155588	−	0.0130554i
$806$	25849.4	+	9408.40i	1.12966	+	0.411162i
$807$	−250.198	+	140.719i	−0.0109137	+	0.00613822i
$808$	−1929.10	+	10940.5i	−0.0839918	+	0.476341i
$809$	−5722.03			−0.248672			−0.124336	−	0.992240i	$-0.539680\pi$
$809$	−5722.03			−0.248672			−0.124336	+	0.992240i	$0.539680\pi$
$810$	−5710.61	+	8935.98i	−0.247716	+	0.387628i
$811$	43726.0			1.89325			0.946626	−	0.322335i	$-0.104468\pi$
$811$	43726.0			1.89325			0.946626	+	0.322335i	$0.104468\pi$
$812$	209.055	−	1185.61i	0.00903495	−	0.0512397i
$813$	−18917.2	+	10639.6i	−0.816059	+	0.458977i
$814$	38214.9	+	13909.1i	1.64549	+	0.598911i
$815$	−12001.7	+	10070.6i	−0.515831	+	0.432833i
$816$	−3697.15	−	10525.1i	−0.158610	−	0.451536i
$817$	15210.9	−	5536.32i	0.651362	−	0.237076i
$818$	3632.57	−	6291.80i	0.155269	−	0.268934i
$819$	−5413.88	−	121.956i	−0.230984	−	0.00520330i
$820$	−680.447	−	1178.57i	−0.0289783	−	0.0501919i
$821$	−4899.18	−	4110.90i	−0.208261	−	0.174752i	0.532691	−	0.846310i	$-0.321181\pi$
$821$	−4899.18	−	4110.90i	−0.208261	−	0.174752i	−0.740952	+	0.671558i	$0.765625\pi$
$822$	−7230.02	+	1191.06i	−0.306783	+	0.0505389i
$823$	1941.36	+	11010.0i	0.0822255	+	0.466324i	0.997921	+	0.0644510i	$0.0205296\pi$
$823$	1941.36	+	11010.0i	0.0822255	+	0.466324i	−0.915695	+	0.401873i	$0.868359\pi$
$824$	−68.2919	−	387.303i	−0.00288721	−	0.0163742i
$825$	6231.37	−	16538.6i	0.262968	−	0.697941i
$826$	−1694.91	−	1422.20i	−0.0713964	−	0.0599087i
$827$	17539.0	+	30378.5i	0.737474	+	1.27734i	0.953629	+	0.300984i	$0.0973151\pi$
$827$	17539.0	+	30378.5i	0.737474	+	1.27734i	−0.216155	+	0.976359i	$0.569352\pi$
$828$	−1805.52	+	611.471i	−0.0757805	+	0.0256644i
$829$	−9332.94	+	16165.1i	−0.391009	+	0.677247i	−0.992583	−	0.121570i	$-0.961207\pi$
$829$	−9332.94	+	16165.1i	−0.391009	+	0.677247i	0.601574	+	0.798817i	$0.294541\pi$
$830$	791.285	−	288.004i	0.0330915	−	0.0120443i
$831$	−4994.25	+	5817.59i	−0.208482	+	0.242852i
$832$	−31486.7	+	26420.5i	−1.31202	+	1.10092i
$833$	−18369.2	−	6685.85i	−0.764053	−	0.278093i
$834$	130.154	−	11557.0i	0.00540391	−	0.479840i
$835$	3377.39	−	19154.1i	0.139975	−	0.793840i
$836$	8366.91			0.346143
$837$	8335.90	−	20698.9i	0.344242	−	0.854791i
$838$	−25617.6			−1.05602
$839$	7858.90	−	44570.0i	0.323384	−	1.83400i	−0.197411	−	0.980321i	$-0.563253\pi$
$839$	7858.90	−	44570.0i	0.323384	−	1.83400i	0.520795	−	0.853682i	$-0.325635\pi$
$840$	−1857.51	−	1100.51i	−0.0762979	−	0.0452038i
$841$	−5362.15	−	1951.66i	−0.219859	−	0.0800222i
$842$	−2270.05	+	1904.80i	−0.0929110	+	0.0779616i
$843$	6160.94	+	1158.02i	0.251713	+	0.0473125i
$844$	8614.70	−	3135.49i	0.351339	−	0.127877i
$845$	10326.7	−	17886.5i	0.420415	−	0.728181i
$846$	25122.9	+	9790.18i	1.02097	+	0.397865i
$847$	312.893	+	541.947i	0.0126932	+	0.0219853i
$848$	−12660.4	−	10623.3i	−0.512689	−	0.430197i
$849$	−4844.72	−	5907.56i	−0.195842	−	0.238807i
$850$	−2027.97	−	11501.2i	−0.0818339	−	0.464103i
$851$	−2107.72	−	11953.4i	−0.0849019	−	0.481503i
$852$	−7161.57	−	8732.69i	−0.287971	−	0.351147i
$853$	−18695.5	−	15687.4i	−0.750436	−	0.629691i	0.185182	−	0.982704i	$-0.440713\pi$
$853$	−18695.5	−	15687.4i	−0.750436	−	0.629691i	−0.935618	+	0.353014i	$0.885157\pi$
$854$	−1161.79	−	2012.28i	−0.0465523	−	0.0806310i
$855$	−12944.4	−	5044.34i	−0.517767	−	0.201769i
$856$	−2346.87	+	4064.89i	−0.0937082	+	0.162307i
$857$	45437.0	−	16537.7i	1.81108	−	0.659181i	0.814175	−	0.580619i	$-0.197189\pi$
$857$	45437.0	−	16537.7i	1.81108	−	0.659181i	0.996909	−	0.0785619i	$-0.0250328\pi$
$858$	−34912.4	−	6562.21i	−1.38915	−	0.261108i
$859$	21344.3	−	17910.0i	0.847799	−	0.711388i	−0.111505	−	0.993764i	$-0.535567\pi$
$859$	21344.3	−	17910.0i	0.847799	−	0.711388i	0.959304	+	0.282376i	$0.0911226\pi$
$860$	2956.65	+	1076.13i	0.117233	+	0.0426695i
$861$	1026.17	+	607.971i	0.0406177	+	0.0240646i
$862$	−3961.91	+	22469.1i	−0.156546	+	0.887819i
$863$	−3754.16			−0.148080			−0.0740401	−	0.997255i	$-0.523589\pi$
$863$	−3754.16			−0.148080			−0.0740401	+	0.997255i	$0.523589\pi$
$864$	9611.11	+	12273.2i	0.378445	+	0.483269i
$865$	−5607.26			−0.220408
$866$	224.469	−	1273.03i	0.00880804	−	0.0499529i
$867$	89.0620	−	7908.27i	0.00348870	−	0.309779i
$868$	1037.21	+	377.513i	0.0405589	+	0.0147622i
$869$	−11104.2	+	9317.55i	−0.433469	+	0.363724i
$870$	−8541.57	+	9949.72i	−0.332858	+	0.387732i
$871$	−42095.0	+	15321.3i	−1.63758	+	0.596031i
$872$	6223.43	−	10779.3i	0.241688	−	0.418616i
$873$	29242.6	−	9903.52i	1.13369	−	0.383944i
$874$	2641.93	+	4575.95i	0.102248	+	0.177098i
$875$	−2727.33	−	2288.50i	−0.105372	−	0.0884178i
$876$	199.369	−	529.145i	0.00768957	−	0.0204088i
$877$	−1377.74	−	7813.57i	−0.0530480	−	0.300850i	0.946728	−	0.322036i	$-0.104367\pi$
$877$	−1377.74	−	7813.57i	−0.0530480	−	0.300850i	−0.999776	+	0.0211854i	$0.993256\pi$
$878$	227.200	+	1288.52i	0.00873308	+	0.0495278i
$879$	15309.8	−	2522.10i	0.587470	−	0.0967786i
$880$	−6967.77	−	5846.65i	−0.266913	−	0.223967i
$881$	−133.462	−	231.163i	−0.00510381	−	0.00884006i	0.863462	−	0.504414i	$-0.168291\pi$
$881$	−133.462	−	231.163i	−0.00510381	−	0.00884006i	−0.868566	+	0.495573i	$0.834958\pi$
$882$	−21120.2	−	475.767i	−0.806297	−	0.0181631i
$883$	11596.0	−	20084.9i	0.441946	−	0.765472i	−0.555888	−	0.831257i	$-0.687622\pi$
$883$	11596.0	−	20084.9i	0.441946	−	0.765472i	0.997834	+	0.0657848i	$0.0209551\pi$
$884$	10425.1	−	3794.43i	0.396645	−	0.144367i
$885$	−3774.80	−	10746.2i	−0.143377	−	0.408169i
$886$	31393.6	−	26342.4i	1.19040	−	0.998860i
$887$	−21544.6	−	7841.59i	−0.815555	−	0.296838i	−0.0996383	−	0.995024i	$-0.531769\pi$
$887$	−21544.6	−	7841.59i	−0.815555	−	0.296838i	−0.715916	+	0.698186i	$0.753991\pi$
$888$	−49238.6	+	27693.3i	−1.86074	+	1.04654i
$889$	449.336	−	2548.31i	0.0169519	−	0.0961390i
$890$	20752.0			0.781583
$891$	−6276.76	+	28124.6i	−0.236004	+	1.05747i
$892$	−7265.75			−0.272730
$893$	−6133.64	+	34785.6i	−0.229848	+	1.30353i
$894$	−9629.12	+	5415.72i	−0.360230	+	0.202605i
$895$	−10641.6	−	3873.22i	−0.397440	−	0.144656i
$896$	832.705	−	698.723i	0.0310477	−	0.0260521i
$897$	3513.89	+	10003.4i	0.130797	+	0.372357i
$898$	12688.8	−	4618.33i	0.471525	−	0.171621i
$899$	13796.2	−	23895.7i	0.511823	−	0.886503i
$900$	2865.36	+	5231.61i	0.106124	+	0.193763i
$901$	13051.9	+	22606.6i	0.482601	+	0.835889i
$902$	5993.84	+	5029.43i	0.221256	+	0.185656i
$903$	−2720.98	+	448.248i	−0.100275	+	0.0165191i
$904$	8404.90	+	47666.6i	0.309229	+	1.75372i
$905$	−27.2744	−	154.681i	−0.00100180	−	0.00568151i
$906$	1723.91	−	4575.42i	0.0632153	−	0.167779i
$907$	−40735.9	−	34181.5i	−1.49130	−	1.25135i	−0.892978	−	0.450100i	$-0.851388\pi$
$907$	−40735.9	−	34181.5i	−1.49130	−	1.25135i	−0.598326	−	0.801253i	$-0.704167\pi$
$908$	−4009.57	−	6944.79i	−0.146544	−	0.253822i
$909$	2384.24	−	11942.3i	0.0869970	−	0.435755i
$910$	−1458.82	+	2526.75i	−0.0531422	+	0.0920450i
$911$	−21425.6	+	7798.27i	−0.779210	+	0.283609i	−0.700843	−	0.713315i	$-0.747193\pi$
$911$	−21425.6	+	7798.27i	−0.779210	+	0.283609i	−0.0783671	+	0.996925i	$0.524971\pi$
$912$	10287.4	−	11983.3i	0.373518	−	0.435096i
$913$	1752.82	−	1470.79i	0.0635377	−	0.0533144i
$914$	−1638.09	−	596.217i	−0.0592815	−	0.0215767i
$915$	134.701	−	11960.7i	0.00486674	−	0.432142i
$916$	939.277	−	5326.91i	0.0338806	−	0.192146i
$917$	−3978.99			−0.143291
$918$	5904.55	+	18103.2i	0.212287	+	0.650864i
$919$	37480.2			1.34533			0.672665	−	0.739948i	$-0.265150\pi$
$919$	37480.2			1.34533			0.672665	+	0.739948i	$0.265150\pi$
$920$	−734.052	+	4163.02i	−0.0263054	+	0.149185i
$921$	−23332.1	−	13823.4i	−0.834764	−	0.494568i
$922$	−25035.8	−	9112.27i	−0.894261	−	0.325484i
$923$	−48119.8	+	40377.3i	−1.71601	+	1.43991i
$924$	−1400.86	−	263.309i	−0.0498756	−	0.00937472i
$925$	−35690.3	+	12990.2i	−1.26864	+	0.461746i
$926$	7848.02	−	13593.2i	0.278512	−	0.482397i
$927$	65.2813	+	426.141i	0.00231297	+	0.0150985i
$928$	9637.89	+	16693.3i	0.340926	+	0.590501i
$929$	3364.31	+	2822.99i	0.118815	+	0.0996978i	0.700259	−	0.713889i	$-0.253068\pi$
$929$	3364.31	+	2822.99i	0.118815	+	0.0996978i	−0.581444	+	0.813586i	$0.697512\pi$
$930$	−7623.78	−	9296.29i	−0.268810	−	0.327782i
$931$	−4805.70	−	27254.5i	−0.169173	−	0.959430i
$932$	2747.82	+	15583.6i	0.0965748	+	0.547703i
$933$	30729.9	+	37471.5i	1.07830	+	1.31486i
$934$	−2689.48	−	2256.74i	−0.0942210	−	0.0790608i
$935$	7183.25	+	12441.8i	0.251249	+	0.435176i
$936$	38506.7	−	30860.2i	1.34469	−	1.07767i
$937$	18588.8	−	32196.8i	0.648101	−	1.12254i	−0.335475	−	0.942049i	$-0.608897\pi$
$937$	18588.8	−	32196.8i	0.648101	−	1.12254i	0.983576	−	0.180495i	$-0.0577698\pi$
$938$	3573.85	−	1300.78i	0.124404	−	0.0452792i
$939$	18217.8	+	3424.25i	0.633135	+	0.119005i
$940$	−5259.51	+	4413.26i	−0.182496	+	0.153132i
$941$	−8919.73	−	3246.51i	−0.309006	−	0.112469i	0.182862	−	0.983139i	$-0.441464\pi$
$941$	−8919.73	−	3246.51i	−0.309006	−	0.112469i	−0.491869	+	0.870669i	$0.663686\pi$
$942$	25564.5	+	15146.1i	0.884223	+	0.523870i
$943$	405.523	−	2299.84i	0.0140039	−	0.0794200i
$944$	12948.3			0.446430
$945$	2008.53	+	1251.93i	0.0691401	+	0.0430957i
$946$	−18090.1			−0.621733
$947$	7470.95	−	42369.9i	0.256360	−	1.45389i	−0.536196	−	0.844094i	$-0.680139\pi$
$947$	7470.95	−	42369.9i	0.256360	−	1.45389i	0.792556	−	0.609799i	$-0.208750\pi$
$948$	55.0929	−	4891.98i	0.00188748	−	0.167599i
$949$	−2955.42	−	1075.68i	−0.101093	−	0.0367947i
$950$	12665.6	−	10627.7i	0.432555	−	0.362957i
$951$	1815.73	−	2115.07i	0.0619128	−	0.0721197i
$952$	−3642.92	+	1325.91i	−0.124021	+	0.0451399i
$953$	−8469.02	+	14668.8i	−0.287868	+	0.498603i	−0.973301	−	0.229534i	$-0.926280\pi$
$953$	−8469.02	+	14668.8i	−0.287868	+	0.498603i	0.685432	+	0.728136i	$0.259613\pi$
$954$	21196.5	+	18615.3i	0.719352	+	0.631754i
$955$	5450.86	+	9441.16i	0.184697	+	0.319904i
$956$	−1131.20	−	949.193i	−0.0382696	−	0.0321120i
$957$	−12563.3	+	33344.1i	−0.424360	+	1.12629i
$958$	−3184.58	−	18060.7i	−0.107400	−	0.609095i
$959$	283.970	+	1610.48i	0.00956192	+	0.0542283i
$960$	17725.3	−	2920.03i	0.595917	−	0.0981702i
$961$	−3442.13	−	2888.29i	−0.115543	−	0.0969517i
$962$	38170.5	+	66113.3i	1.27928	+	2.21578i
$963$	2672.34	−	4396.88i	0.0894238	−	0.147131i
$964$	−6513.68	+	11282.0i	−0.217626	+	0.376940i
$965$	14776.4	−	5378.18i	0.492922	−	0.179409i
$966$	−298.328	−	849.289i	−0.00993640	−	0.0282872i
$967$	23871.0	−	20030.1i	0.793836	−	0.666107i	−0.152856	−	0.988248i	$-0.548847\pi$
$967$	23871.0	−	20030.1i	0.793836	−	0.666107i	0.946692	+	0.322141i	$0.104403\pi$
$968$	−5358.62	−	1950.38i	−0.177926	−	0.0647599i
$969$	−21742.2	+	12228.5i	−0.720805	+	0.405403i
$970$	2888.54	−	16381.7i	0.0956138	−	0.542253i
$971$	−52849.2			−1.74667			−0.873333	−	0.487124i	$-0.838046\pi$
$971$	−52849.2			−1.74667			−0.873333	+	0.487124i	$0.838046\pi$
$972$	−5822.34	−	7790.30i	−0.192131	−	0.257072i
$973$	−2579.42			−0.0849870
$974$	4869.31	−	27615.2i	0.160188	−	0.908470i
$975$	28917.0	−	16263.8i	0.949832	−	0.534215i
$976$	12778.0	+	4650.81i	0.419071	+	0.152530i
$977$	−22129.5	+	18568.9i	−0.724653	+	0.608056i	−0.928668	−	0.370912i	$-0.879045\pi$
$977$	−22129.5	+	18568.9i	−0.724653	+	0.608056i	0.204015	+	0.978968i	$0.434601\pi$
$978$	10075.6	+	28683.3i	0.329428	+	0.937824i
$979$	52988.6	−	19286.3i	1.72985	−	0.629614i
$980$	2689.68	−	4658.66i	0.0876720	−	0.151852i
$981$	−7086.53	+	11659.7i	−0.230638	+	0.379475i
$982$	−12719.5	−	22030.9i	−0.413337	−	0.715920i
$983$	−1432.25	−	1201.80i	−0.0464716	−	0.0389943i	0.619256	−	0.785189i	$-0.287434\pi$
$983$	−1432.25	−	1201.80i	−0.0464716	−	0.0389943i	−0.665728	+	0.746195i	$0.731879\pi$
$984$	−10724.5	+	1766.73i	−0.347444	+	0.0572372i
$985$	1969.35	+	11168.8i	0.0637043	+	0.361285i
$986$	4088.66	+	23187.9i	0.132058	+	0.748939i
$987$	2121.66	−	5631.09i	0.0684227	−	0.181600i
$988$	12031.8	+	10095.9i	0.387431	+	0.325093i
$989$	2699.64	+	4675.91i	0.0867982	+	0.150339i
$990$	11665.7	+	10245.1i	0.374505	+	0.328900i
$991$	−19703.8	+	34128.0i	−0.631597	+	1.09396i	0.355628	+	0.934627i	$0.384267\pi$
$991$	−19703.8	+	34128.0i	−0.631597	+	1.09396i	−0.987225	+	0.159331i	$0.949066\pi$
$992$	−16606.9	+	6044.42i	−0.531522	+	0.193458i
$993$	25737.4	−	29980.4i	0.822509	−	0.958106i
$994$	4085.36	−	3428.02i	0.130362	−	0.109387i
$995$	1545.12	+	562.377i	0.0492297	+	0.0179182i
$996$	−8.69652	+	772.208i	−0.000276666	+	0.0245666i
$997$	−971.013	+	5506.89i	−0.0308448	+	0.174930i	−0.996338	−	0.0854971i	$-0.972752\pi$
$997$	−971.013	+	5506.89i	−0.0308448	+	0.174930i	0.965494	+	0.260427i	$0.0838633\pi$
$998$	−36407.9			−1.15478
$999$	54645.6	−	29134.3i	1.73064	−	0.922690i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.4.e.a.25.3	yes	48
3.2	odd	2		81.4.e.a.73.6		48
9.2	odd	6		243.4.e.a.55.3		48
9.4	even	3		243.4.e.c.136.3		48
9.5	odd	6		243.4.e.b.136.6		48
9.7	even	3		243.4.e.d.55.6		48
27.4	even	9		243.4.e.c.109.3		48
27.5	odd	18		243.4.e.a.190.3		48
27.11	odd	18		729.4.a.c.1.18		24
27.13	even	9	inner	27.4.e.a.13.3	✓	48
27.14	odd	18		81.4.e.a.10.6		48
27.16	even	9		729.4.a.d.1.7		24
27.22	even	9		243.4.e.d.190.6		48
27.23	odd	18		243.4.e.b.109.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.13.3	✓	48	27.13	even	9	inner
27.4.e.a.25.3	yes	48	1.1	even	1	trivial
81.4.e.a.10.6		48	27.14	odd	18
81.4.e.a.73.6		48	3.2	odd	2
243.4.e.a.55.3		48	9.2	odd	6
243.4.e.a.190.3		48	27.5	odd	18
243.4.e.b.109.6		48	27.23	odd	18
243.4.e.b.136.6		48	9.5	odd	6
243.4.e.c.109.3		48	27.4	even	9
243.4.e.c.136.3		48	9.4	even	3
243.4.e.d.55.6		48	9.7	even	3
243.4.e.d.190.6		48	27.22	even	9
729.4.a.c.1.18		24	27.11	odd	18
729.4.a.d.1.7		24	27.16	even	9

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.404735 + 2.29536i) q^{2} +(4.52897 - 2.54724i) q^{3} +(2.41266 + 0.878135i) q^{4} +(-4.78113 + 4.01185i) q^{5} +(4.01380 + 11.4266i) q^{6} +(2.53990 - 0.924448i) q^{7} +(-12.3152 + 21.3306i) q^{8} +(14.0232 - 23.0727i) q^{9} +O(q^{10})\)	\(q+(-0.404735 + 2.29536i) q^{2} +(4.52897 - 2.54724i) q^{3} +(2.41266 + 0.878135i) q^{4} +(-4.78113 + 4.01185i) q^{5} +(4.01380 + 11.4266i) q^{6} +(2.53990 - 0.924448i) q^{7} +(-12.3152 + 21.3306i) q^{8} +(14.0232 - 23.0727i) q^{9} +(-7.27356 - 12.5982i) q^{10} +(-30.2808 - 25.4086i) q^{11} +(13.1637 - 2.16856i) q^{12} +(-12.8853 - 73.0761i) q^{13} +(1.09396 + 6.20415i) q^{14} +(-11.4345 + 30.3482i) q^{15} +(-28.2425 - 23.6983i) q^{16} +(29.1160 + 50.4303i) q^{17} +(47.2846 + 41.5266i) q^{18} +(-41.2204 + 71.3959i) q^{19} +(-15.0582 + 5.48072i) q^{20} +(9.14835 - 10.6565i) q^{21} +(70.5777 - 59.2217i) q^{22} +(-25.8401 - 9.40502i) q^{23} +(-1.44124 + 127.975i) q^{24} +(-14.9417 + 84.7386i) q^{25} +172.951 q^{26} +(4.73890 - 140.216i) q^{27} +6.93969 q^{28} +(30.1245 - 170.844i) q^{29} +(-65.0323 - 38.5293i) q^{30} +(149.460 + 54.3991i) q^{31} +(-85.1171 + 71.4217i) q^{32} +(-201.863 - 37.9425i) q^{33} +(-127.540 + 46.4208i) q^{34} +(-8.43485 + 14.6096i) q^{35} +(54.0941 - 43.3523i) q^{36} +(220.701 + 382.265i) q^{37} +(-147.196 - 123.512i) q^{38} +(-244.499 - 298.138i) q^{39} +(-26.6943 - 151.391i) q^{40} +(14.7471 + 83.6352i) q^{41} +(20.7579 + 25.3118i) q^{42} +(-150.412 - 126.210i) q^{43} +(-50.7449 - 87.8928i) q^{44} +(25.5176 + 166.573i) q^{45} +(32.0463 - 55.5058i) q^{46} +(402.616 - 146.540i) q^{47} +(-188.275 - 35.3885i) q^{48} +(-257.157 + 215.780i) q^{49} +(-188.459 - 68.5933i) q^{50} +(260.323 + 154.232i) q^{51} +(33.0829 - 187.623i) q^{52} +448.275 q^{53} +(319.929 + 67.6278i) q^{54} +246.712 q^{55} +(-11.5604 + 65.5623i) q^{56} +(-4.82401 + 428.348i) q^{57} +(379.958 + 138.293i) q^{58} +(-269.039 + 225.751i) q^{59} +(-54.2373 + 63.1788i) q^{60} +(-346.588 + 126.148i) q^{61} +(-185.357 + 321.048i) q^{62} +(14.2879 - 71.5661i) q^{63} +(-276.961 - 479.711i) q^{64} +(354.777 + 297.693i) q^{65} +(168.793 - 447.991i) q^{66} +(-104.831 - 594.527i) q^{67} +(25.9622 + 147.239i) q^{68} +(-140.986 + 23.2257i) q^{69} +(-30.1205 - 25.2741i) q^{70} +(-423.268 - 733.122i) q^{71} +(319.456 + 583.268i) q^{72} +(21.1923 - 36.7062i) q^{73} +(-966.762 + 351.873i) q^{74} +(148.179 + 421.839i) q^{75} +(-162.146 + 136.057i) q^{76} +(-100.399 - 36.5423i) q^{77} +(783.292 - 440.548i) q^{78} +(63.6782 - 361.137i) q^{79} +230.105 q^{80} +(-335.701 - 647.106i) q^{81} -197.942 q^{82} +(-10.0517 + 57.0062i) q^{83} +(31.4297 - 17.6770i) q^{84} +(-341.526 - 124.305i) q^{85} +(350.575 - 294.168i) q^{86} +(-298.748 - 850.483i) q^{87} +(914.895 - 332.995i) q^{88} +(-713.269 + 1235.42i) q^{89} +(-392.672 - 8.84559i) q^{90} +(-100.282 - 173.694i) q^{91} +(-54.0843 - 45.3821i) q^{92} +(815.469 - 134.339i) q^{93} +(173.411 + 983.460i) q^{94} +(-89.3490 - 506.723i) q^{95} +(-203.565 + 540.280i) q^{96} +(875.961 + 735.019i) q^{97} +(-391.214 - 677.602i) q^{98} +(-1010.88 + 342.351i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Introduction

L-functions

Modular forms

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