LMFDB - Embedded newform 105.4.b.b.41.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(41,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("105.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.b (of order $2$, degree $1$, 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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 96 x^{14} + 3618 x^{12} + 68560 x^{10} + 697017 x^{8} + 3791184 x^{6} + 10461796 x^{4} + \cdots + 5760000 $ x^16 + 96x^14 + 3618x^12 + 68560x^10 + 697017x^8 + 3791184x^6 + 10461796x^4 + 13209792*x^2 + 5760000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			41.10
Root			$1.39379i$ of defining polynomial
Character	$\chi$	$=$	105.41
Dual form			105.4.b.b.41.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.39379i q^{2} +(5.17944 + 0.416449i) q^{3} +6.05735 q^{4} +5.00000 q^{5} +(-0.580442 + 7.21904i) q^{6} +(-10.8253 + 15.0271i) q^{7} +19.5930i q^{8} +(26.6531 + 4.31394i) q^{9} +O(q^{10})$	\(q+1.39379i q^{2} +(5.17944 + 0.416449i) q^{3} +6.05735 q^{4} +5.00000 q^{5} +(-0.580442 + 7.21904i) q^{6} +(-10.8253 + 15.0271i) q^{7} +19.5930i q^{8} +(26.6531 + 4.31394i) q^{9} +6.96894i q^{10} -67.7901i q^{11} +(31.3737 + 2.52258i) q^{12} +2.57864i q^{13} +(-20.9446 - 15.0882i) q^{14} +(25.8972 + 2.08225i) q^{15} +21.1504 q^{16} -62.5926 q^{17} +(-6.01273 + 37.1488i) q^{18} +134.611i q^{19} +30.2868 q^{20} +(-62.3269 + 73.3237i) q^{21} +94.4850 q^{22} -58.4546i q^{23} +(-8.15948 + 101.481i) q^{24} +25.0000 q^{25} -3.59408 q^{26} +(136.252 + 33.4435i) q^{27} +(-65.5726 + 91.0244i) q^{28} -91.3578i q^{29} +(-2.90221 + 36.0952i) q^{30} -182.870i q^{31} +186.223i q^{32} +(28.2311 - 351.114i) q^{33} -87.2408i q^{34} +(-54.1264 + 75.1354i) q^{35} +(161.447 + 26.1311i) q^{36} -340.482 q^{37} -187.620 q^{38} +(-1.07387 + 13.3559i) q^{39} +97.9649i q^{40} +67.1808 q^{41} +(-102.198 - 86.8705i) q^{42} -88.7823 q^{43} -410.628i q^{44} +(133.266 + 21.5697i) q^{45} +81.4734 q^{46} +157.841 q^{47} +(109.547 + 8.80805i) q^{48} +(-108.626 - 325.345i) q^{49} +34.8447i q^{50} +(-324.194 - 26.0666i) q^{51} +15.6198i q^{52} -458.943i q^{53} +(-46.6131 + 189.906i) q^{54} -338.950i q^{55} +(-294.425 - 212.100i) q^{56} +(-56.0588 + 697.211i) q^{57} +127.333 q^{58} -589.112 q^{59} +(156.868 + 12.6129i) q^{60} -431.560i q^{61} +254.883 q^{62} +(-353.354 + 353.819i) q^{63} -90.3525 q^{64} +12.8932i q^{65} +(489.379 + 39.3482i) q^{66} +809.483 q^{67} -379.145 q^{68} +(24.3434 - 302.762i) q^{69} +(-104.723 - 75.4408i) q^{70} +80.5430i q^{71} +(-84.5230 + 522.214i) q^{72} +406.079i q^{73} -474.560i q^{74} +(129.486 + 10.4112i) q^{75} +815.389i q^{76} +(1018.69 + 733.847i) q^{77} +(-18.6153 - 1.49675i) q^{78} -657.971 q^{79} +105.752 q^{80} +(691.780 + 229.960i) q^{81} +93.6358i q^{82} -649.146 q^{83} +(-377.536 + 444.147i) q^{84} -312.963 q^{85} -123.744i q^{86} +(38.0459 - 473.182i) q^{87} +1328.21 q^{88} -600.574 q^{89} +(-30.0636 + 185.744i) q^{90} +(-38.7495 - 27.9145i) q^{91} -354.080i q^{92} +(76.1562 - 947.166i) q^{93} +219.996i q^{94} +673.057i q^{95} +(-77.5524 + 964.530i) q^{96} +813.824i q^{97} +(453.462 - 151.402i) q^{98} +(292.443 - 1806.82i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{3} - 64 q^{4} + 80 q^{5} + 28 q^{6} - 4 q^{7} - 22 q^{9}+O(q^{10}) $ 16 * q + 2 * q^3 - 64 * q^4 + 80 * q^5 + 28 * q^6 - 4 * q^7 - 22 * q^9	$ 16 q + 2 q^{3} - 64 q^{4} + 80 q^{5} + 28 q^{6} - 4 q^{7} - 22 q^{9} + 66 q^{12} + 90 q^{14} + 10 q^{15} + 376 q^{16} + 72 q^{17} - 182 q^{18} - 320 q^{20} - 70 q^{21} - 276 q^{22} - 526 q^{24} + 400 q^{25} - 696 q^{26} + 128 q^{27} + 10 q^{28} + 140 q^{30} + 502 q^{33} - 20 q^{35} + 996 q^{36} - 812 q^{37} + 1200 q^{38} - 594 q^{39} + 936 q^{41} - 974 q^{42} - 548 q^{43} - 110 q^{45} + 1224 q^{46} - 912 q^{47} - 1850 q^{48} + 328 q^{49} + 750 q^{51} + 2950 q^{54} - 1254 q^{56} + 432 q^{57} + 576 q^{58} + 552 q^{59} + 330 q^{60} + 1860 q^{62} + 362 q^{63} - 4000 q^{64} - 1378 q^{66} + 1004 q^{67} - 3828 q^{68} - 1988 q^{69} + 450 q^{70} + 1988 q^{72} + 50 q^{75} - 1152 q^{77} + 1446 q^{78} + 1292 q^{79} + 1880 q^{80} - 2950 q^{81} + 1752 q^{83} - 420 q^{84} + 360 q^{85} - 1910 q^{87} - 912 q^{88} - 6096 q^{89} - 910 q^{90} - 552 q^{91} - 1080 q^{93} + 9546 q^{96} + 4824 q^{98} + 2530 q^{99}+O(q^{100}) $ 16 * q + 2 * q^3 - 64 * q^4 + 80 * q^5 + 28 * q^6 - 4 * q^7 - 22 * q^9 + 66 * q^12 + 90 * q^14 + 10 * q^15 + 376 * q^16 + 72 * q^17 - 182 * q^18 - 320 * q^20 - 70 * q^21 - 276 * q^22 - 526 * q^24 + 400 * q^25 - 696 * q^26 + 128 * q^27 + 10 * q^28 + 140 * q^30 + 502 * q^33 - 20 * q^35 + 996 * q^36 - 812 * q^37 + 1200 * q^38 - 594 * q^39 + 936 * q^41 - 974 * q^42 - 548 * q^43 - 110 * q^45 + 1224 * q^46 - 912 * q^47 - 1850 * q^48 + 328 * q^49 + 750 * q^51 + 2950 * q^54 - 1254 * q^56 + 432 * q^57 + 576 * q^58 + 552 * q^59 + 330 * q^60 + 1860 * q^62 + 362 * q^63 - 4000 * q^64 - 1378 * q^66 + 1004 * q^67 - 3828 * q^68 - 1988 * q^69 + 450 * q^70 + 1988 * q^72 + 50 * q^75 - 1152 * q^77 + 1446 * q^78 + 1292 * q^79 + 1880 * q^80 - 2950 * q^81 + 1752 * q^83 - 420 * q^84 + 360 * q^85 - 1910 * q^87 - 912 * q^88 - 6096 * q^89 - 910 * q^90 - 552 * q^91 - 1080 * q^93 + 9546 * q^96 + 4824 * q^98 + 2530 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$			1.39379i			0.492779i	0.969171	+	0.246389i	$0.0792442\pi$
$2$			1.39379i			0.492779i	−0.969171	+	0.246389i	$0.920756\pi$
$3$	5.17944	+	0.416449i	0.996783	+	0.0801457i
$3$	5.17944	+	0.416449i	0.996783	+	0.0801457i
$4$	6.05735			0.757169
$5$	5.00000			0.447214
$5$	5.00000			0.447214
$6$	−0.580442	+	7.21904i	−0.0394941	+	0.491193i
$7$	−10.8253	+	15.0271i	−0.584510	+	0.811386i
$7$	−10.8253	+	15.0271i	−0.584510	+	0.811386i
$8$			19.5930i			0.865895i
$9$	26.6531	+	4.31394i	0.987153	+	0.159776i
$10$			6.96894i			0.220377i
$11$		−	67.7901i		−	1.85813i	−0.369912	−	0.929067i	$-0.620612\pi$
$11$		−	67.7901i		−	1.85813i	0.369912	−	0.929067i	$-0.379388\pi$
$12$	31.3737	+	2.52258i	0.754733	+	0.0606838i
$13$			2.57864i			0.0550144i	0.999622	+	0.0275072i	$0.00875692\pi$
$13$			2.57864i			0.0550144i	−0.999622	+	0.0275072i	$0.991243\pi$
$14$	−20.9446	−	15.0882i	−0.399834	−	0.288034i
$15$	25.8972	+	2.08225i	0.445775	+	0.0358422i
$16$	21.1504			0.330474
$17$	−62.5926			−0.892996			−0.446498	−	0.894785i	$-0.647329\pi$
$17$	−62.5926			−0.892996			−0.446498	+	0.894785i	$0.647329\pi$
$18$	−6.01273	+	37.1488i	−0.0787341	+	0.486448i
$19$			134.611i			1.62537i	0.582705	+	0.812684i	$0.301994\pi$
$19$			134.611i			1.62537i	−0.582705	+	0.812684i	$0.698006\pi$
$20$	30.2868			0.338616
$21$	−62.3269	+	73.3237i	−0.647659	+	0.761930i
$22$	94.4850			0.915649
$23$		−	58.4546i		−	0.529940i	−0.964257	−	0.264970i	$-0.914638\pi$
$23$		−	58.4546i		−	0.529940i	0.964257	−	0.264970i	$-0.0853621\pi$
$24$	−8.15948	+	101.481i	−0.0693978	+	0.863110i
$25$	25.0000			0.200000
$26$	−3.59408			−0.0271099
$27$	136.252	+	33.4435i	0.971172	+	0.238378i
$28$	−65.5726	+	91.0244i	−0.442573	+	0.614357i
$29$		−	91.3578i		−	0.584990i	−0.956267	−	0.292495i	$-0.905514\pi$
$29$		−	91.3578i		−	0.584990i	0.956267	−	0.292495i	$-0.0944855\pi$
$30$	−2.90221	+	36.0952i	−0.0176623	+	0.219668i
$31$		−	182.870i		−	1.05950i	−0.848154	−	0.529750i	$-0.822286\pi$
$31$		−	182.870i		−	1.05950i	0.848154	−	0.529750i	$-0.177714\pi$
$32$			186.223i			1.02875i
$33$	28.2311	−	351.114i	0.148921	−	1.85216i
$34$		−	87.2408i		−	0.440049i
$35$	−54.1264	+	75.1354i	−0.261401	+	0.362863i
$36$	161.447	+	26.1311i	0.747442	+	0.120977i
$37$	−340.482			−1.51284			−0.756418	−	0.654089i	$-0.773052\pi$
$37$	−340.482			−1.51284			−0.756418	+	0.654089i	$0.773052\pi$
$38$	−187.620			−0.800946
$39$	−1.07387	+	13.3559i	−0.00440916	+	0.0548374i
$40$			97.9649i			0.387240i
$41$	67.1808			0.255899			0.127950	−	0.991781i	$-0.459160\pi$
$41$	67.1808			0.255899			0.127950	+	0.991781i	$0.459160\pi$
$42$	−102.198	−	86.8705i	−0.375463	−	0.319153i
$43$	−88.7823			−0.314864			−0.157432	−	0.987530i	$-0.550322\pi$
$43$	−88.7823			−0.314864			−0.157432	+	0.987530i	$0.550322\pi$
$44$		−	410.628i		−	1.40692i
$45$	133.266	+	21.5697i	0.441468	+	0.0714539i
$46$	81.4734			0.261143
$47$	157.841			0.489860			0.244930	−	0.969541i	$-0.421235\pi$
$47$	157.841			0.489860			0.244930	+	0.969541i	$0.421235\pi$
$48$	109.547	+	8.80805i	0.329411	+	0.0264861i
$49$	−108.626	−	325.345i	−0.316695	−	0.948527i
$50$			34.8447i			0.0985557i
$51$	−324.194	−	26.0666i	−0.890123	−	0.0715697i
$52$			15.6198i			0.0416552i
$53$		−	458.943i		−	1.18945i	−0.803931	−	0.594723i	$-0.797262\pi$
$53$		−	458.943i		−	1.18945i	0.803931	−	0.594723i	$-0.202738\pi$
$54$	−46.6131	+	189.906i	−0.117467	+	0.478573i
$55$		−	338.950i		−	0.830983i
$56$	−294.425	−	212.100i	−0.702576	−	0.506125i
$57$	−56.0588	+	697.211i	−0.130266	+	1.62014i
$58$	127.333			0.288271
$59$	−589.112			−1.29993			−0.649965	−	0.759964i	$-0.725216\pi$
$59$	−589.112			−1.29993			−0.649965	+	0.759964i	$0.725216\pi$
$60$	156.868	+	12.6129i	0.337527	+	0.0271386i
$61$		−	431.560i		−	0.905829i	−0.891554	−	0.452915i	$-0.850384\pi$
$61$		−	431.560i		−	0.905829i	0.891554	−	0.452915i	$-0.149616\pi$
$62$	254.883			0.522099
$63$	−353.354	+	353.819i	−0.706641	+	0.707572i
$64$	−90.3525			−0.176470
$65$			12.8932i			0.0246032i
$66$	489.379	+	39.3482i	0.912703	+	0.0733853i
$67$	809.483			1.47603			0.738016	−	0.674783i	$-0.235763\pi$
$67$	809.483			1.47603			0.738016	+	0.674783i	$0.235763\pi$
$68$	−379.145			−0.676149
$69$	24.3434	−	302.762i	0.0424724	−	0.528236i
$70$	−104.723	−	75.4408i	−0.178811	−	0.128813i
$71$			80.5430i			0.134629i	0.997732	+	0.0673147i	$0.0214432\pi$
$71$			80.5430i			0.134629i	−0.997732	+	0.0673147i	$0.978557\pi$
$72$	−84.5230	+	522.214i	−0.138349	+	0.854772i
$73$			406.079i			0.651068i	0.945530	+	0.325534i	$0.105544\pi$
$73$			406.079i			0.651068i	−0.945530	+	0.325534i	$0.894456\pi$
$74$		−	474.560i		−	0.745493i
$75$	129.486	+	10.4112i	0.199357	+	0.0160291i
$76$			815.389i			1.23068i
$77$	1018.69	+	733.847i	1.50766	+	1.08610i
$78$	−18.6153	−	1.49675i	−0.0270227	−	0.00217274i
$79$	−657.971			−0.937058			−0.468529	−	0.883448i	$-0.655216\pi$
$79$	−657.971			−0.937058			−0.468529	+	0.883448i	$0.655216\pi$
$80$	105.752			0.147793
$81$	691.780	+	229.960i	0.948943	+	0.315446i
$82$			93.6358i			0.126102i
$83$	−649.146			−0.858471			−0.429235	−	0.903193i	$-0.641217\pi$
$83$	−649.146			−0.858471			−0.429235	+	0.903193i	$0.641217\pi$
$84$	−377.536	+	444.147i	−0.490388	+	0.576910i
$85$	−312.963			−0.399360
$86$		−	123.744i		−	0.155158i
$87$	38.0459	−	473.182i	0.0468844	−	0.583108i
$88$	1328.21			1.60895
$89$	−600.574			−0.715289			−0.357644	−	0.933858i	$-0.616420\pi$
$89$	−600.574			−0.715289			−0.357644	+	0.933858i	$0.616420\pi$
$90$	−30.0636	+	185.744i	−0.0352109	+	0.217546i
$91$	−38.7495	−	27.9145i	−0.0446379	−	0.0321565i
$92$		−	354.080i		−	0.401255i
$93$	76.1562	−	947.166i	0.0849144	−	1.05609i
$94$			219.996i			0.241392i
$95$			673.057i			0.726886i
$96$	−77.5524	+	964.530i	−0.0824496	+	1.02544i
$97$			813.824i			0.851869i	0.904754	+	0.425934i	$0.140055\pi$
$97$			813.824i			0.851869i	−0.904754	+	0.425934i	$0.859945\pi$
$98$	453.462	−	151.402i	0.467414	−	0.156061i
$99$	292.443	−	1806.82i	0.296885	−	1.83426i
$100$	151.434			0.151434
$101$	293.929			0.289575			0.144787	−	0.989463i	$-0.453750\pi$
$101$	293.929			0.289575			0.144787	+	0.989463i	$0.453750\pi$
$102$	36.3314	−	451.858i	0.0352680	−	0.438634i
$103$			658.984i			0.630405i	0.949025	+	0.315202i	$0.102072\pi$
$103$			658.984i			0.630405i	−0.949025	+	0.315202i	$0.897928\pi$
$104$	−50.5233			−0.0476367
$105$	−311.634	+	366.618i	−0.289642	+	0.340746i
$106$	639.669			0.586133
$107$			514.453i			0.464804i	0.972620	+	0.232402i	$0.0746585\pi$
$107$			514.453i			0.464804i	−0.972620	+	0.232402i	$0.925341\pi$
$108$	825.325	+	202.579i	0.735342	+	0.180492i
$109$	1628.10			1.43068			0.715340	−	0.698777i	$-0.246272\pi$
$109$	1628.10			1.43068			0.715340	+	0.698777i	$0.246272\pi$
$110$	472.425			0.409491
$111$	−1763.51	−	141.794i	−1.50797	−	0.121247i
$112$	−228.959	+	317.828i	−0.193166	+	0.268142i
$113$			771.780i			0.642504i	0.946994	+	0.321252i	$0.104104\pi$
$113$			771.780i			0.642504i	−0.946994	+	0.321252i	$0.895896\pi$
$114$	−971.765	−	78.1341i	−0.798370	−	0.0641924i
$115$		−	292.273i		−	0.236997i
$116$		−	553.386i		−	0.442937i
$117$	−11.1241	+	68.7289i	−0.00878996	+	0.0543076i
$118$		−	821.098i		−	0.640578i
$119$	677.582	−	940.584i	0.521965	−	0.724564i
$120$	−40.7974	+	507.403i	−0.0310356	+	0.385995i
$121$	−3264.49			−2.45266
$122$	601.503			0.446373
$123$	347.959	+	27.9774i	0.255076	+	0.0205092i
$124$		−	1107.71i		−	0.802221i
$125$	125.000			0.0894427
$126$	−493.149	−	492.501i	−0.348676	−	0.348218i
$127$	1500.54			1.04844			0.524218	−	0.851584i	$-0.324358\pi$
$127$	1500.54			1.04844			0.524218	+	0.851584i	$0.324358\pi$
$128$			1363.85i			0.941786i
$129$	−459.842	−	36.9733i	−0.313852	−	0.0252350i
$130$	−17.9704			−0.0121239
$131$	1840.55			1.22756			0.613778	−	0.789479i	$-0.289649\pi$
$131$	1840.55			1.22756			0.613778	+	0.789479i	$0.289649\pi$
$132$	171.006	−	2126.82i	0.112759	−	1.40240i
$133$	−2022.82	−	1457.21i	−1.31880	−	0.950044i
$134$			1128.25i			0.727357i
$135$	681.259	+	167.217i	0.434322	+	0.106606i
$136$		−	1226.37i		−	0.773241i
$137$			1789.29i			1.11583i	0.829897	+	0.557916i	$0.188399\pi$
$137$			1789.29i			1.11583i	−0.829897	+	0.557916i	$0.811601\pi$
$138$	421.986	+	33.9295i	0.260303	+	0.0209295i
$139$			2246.13i			1.37061i	0.728258	+	0.685303i	$0.240330\pi$
$139$			2246.13i			1.37061i	−0.728258	+	0.685303i	$0.759670\pi$
$140$	−327.863	+	455.122i	−0.197925	+	0.274749i
$141$	817.525	+	65.7325i	0.488284	+	0.0392601i
$142$	−112.260			−0.0663425
$143$	174.806			0.102224
$144$	563.723	+	91.2415i	0.326229	+	0.0528018i
$145$		−	456.789i		−	0.261616i
$146$	−565.989			−0.320833
$147$	−427.134	−	1730.34i	−0.239656	−	0.970858i
$148$	−2062.42			−1.14547
$149$			293.931i			0.161609i	0.996730	+	0.0808046i	$0.0257490\pi$
$149$			293.931i			0.161609i	−0.996730	+	0.0808046i	$0.974251\pi$
$150$	−14.5111	+	180.476i	−0.00789882	+	0.0982387i
$151$	−951.272			−0.512672			−0.256336	−	0.966588i	$-0.582515\pi$
$151$	−951.272			−0.512672			−0.256336	+	0.966588i	$0.582515\pi$
$152$	−2637.44			−1.40740
$153$	−1668.29	−	270.021i	−0.881524	−	0.142679i
$154$	−1022.83	+	1419.83i	−0.535206	+	0.742945i
$155$		−	914.352i		−	0.473823i
$156$	−6.50483	+	80.9015i	−0.00333848	+	0.0415212i
$157$		−	1703.52i		−	0.865960i	−0.901404	−	0.432980i	$-0.857462\pi$
$157$		−	1703.52i		−	0.865960i	0.901404	−	0.432980i	$-0.142538\pi$
$158$		−	917.073i		−	0.461762i
$159$	191.126	−	2377.06i	0.0953289	−	1.18562i
$160$			931.115i			0.460069i
$161$	878.402	+	632.788i	0.429986	+	0.309756i
$162$	−320.516	+	964.195i	−0.155445	+	0.467619i
$163$	1738.35			0.835325			0.417663	−	0.908602i	$-0.362849\pi$
$163$	1738.35			0.835325			0.417663	+	0.908602i	$0.362849\pi$
$164$	406.938			0.193759
$165$	141.156	−	1755.57i	0.0665997	−	0.828310i
$166$		−	904.773i		−	0.423036i
$167$	1674.27			0.775802			0.387901	−	0.921701i	$-0.373200\pi$
$167$	1674.27			0.775802			0.387901	+	0.921701i	$0.373200\pi$
$168$	−1436.63	−	1221.17i	−0.659752	−	0.560805i
$169$	2190.35			0.996973
$170$		−	436.204i		−	0.196796i
$171$	−580.706	+	3587.82i	−0.259694	+	1.60449i
$172$	−537.786			−0.238406
$173$	−1741.35			−0.765275			−0.382638	−	0.923899i	$-0.624984\pi$
$173$	−1741.35			−0.765275			−0.382638	+	0.923899i	$0.624984\pi$
$174$	659.516	+	53.0279i	0.287343	+	0.0231036i
$175$	−270.632	+	375.677i	−0.116902	+	0.162277i
$176$		−	1433.78i		−	0.614066i
$177$	−3051.27	−	245.335i	−1.29575	−	0.104184i
$178$		−	837.073i		−	0.352479i
$179$			1666.76i			0.695976i	0.937499	+	0.347988i	$0.113135\pi$
$179$			1666.76i			0.695976i	−0.937499	+	0.347988i	$0.886865\pi$
$180$	807.237	+	130.655i	0.334266	+	0.0541027i
$181$		−	4189.97i		−	1.72065i	−0.509746	−	0.860325i	$-0.670260\pi$
$181$		−	4189.97i		−	1.72065i	0.509746	−	0.860325i	$-0.329740\pi$
$182$	38.9070	−	54.0086i	0.0158460	−	0.0219966i
$183$	179.723	−	2235.24i	0.0725983	−	0.902915i
$184$	1145.30			0.458873
$185$	−1702.41			−0.676561
$186$	1320.15	+	106.146i	0.520420	+	0.0418440i
$187$			4243.15i			1.65931i
$188$	956.096			0.370907
$189$	−1977.52	+	1685.43i	−0.761077	+	0.648662i
$190$	−938.099			−0.358194
$191$			3858.58i			1.46176i	0.682504	+	0.730882i	$0.260891\pi$
$191$			3858.58i			1.46176i	−0.682504	+	0.730882i	$0.739109\pi$
$192$	−467.975	−	37.6272i	−0.175902	−	0.0141433i
$193$	1129.53			0.421272			0.210636	−	0.977565i	$-0.432447\pi$
$193$	1129.53			0.421272			0.210636	+	0.977565i	$0.432447\pi$
$194$	−1134.30			−0.419783
$195$	−5.36937	+	66.7796i	−0.00197184	+	0.0245240i
$196$	−657.989	−	1970.73i	−0.239792	−	0.718196i
$197$		−	3793.36i		−	1.37191i	−0.727646	−	0.685953i	$-0.759385\pi$
$197$		−	3793.36i		−	1.37191i	0.727646	−	0.685953i	$-0.240615\pi$
$198$	2518.32	+	407.603i	0.903886	+	0.146298i
$199$			2716.52i			0.967684i	0.875155	+	0.483842i	$0.160759\pi$
$199$			2716.52i			0.967684i	−0.875155	+	0.483842i	$0.839241\pi$
$200$			489.824i			0.173179i
$201$	4192.67	+	337.109i	1.47128	+	0.118298i
$202$			409.675i			0.142696i
$203$	1372.84	+	988.974i	0.474653	+	0.341933i
$204$	−1963.76	−	157.895i	−0.673974	−	0.0541904i
$205$	335.904			0.114442
$206$	−918.485			−0.310650
$207$	252.170	−	1558.00i	0.0846716	−	0.523132i
$208$			54.5392i			0.0181808i
$209$	9125.32			3.02015
$210$	−510.988	−	434.353i	−0.167912	−	0.142729i
$211$	2986.43			0.974379			0.487190	−	0.873296i	$-0.338022\pi$
$211$	2986.43			0.974379			0.487190	+	0.873296i	$0.338022\pi$
$212$		−	2779.98i		−	0.900611i
$213$	−33.5421	+	417.167i	−0.0107900	+	0.134196i
$214$	−717.038			−0.229046
$215$	−443.911			−0.140812
$216$	−655.257	+	2669.58i	−0.206410	+	0.840934i
$217$	2748.01	+	1979.62i	0.859664	+	0.619289i
$218$			2269.23i			0.705009i
$219$	−169.111	+	2103.26i	−0.0521803	+	0.648974i
$220$		−	2053.14i		−	0.629195i
$221$		−	161.404i		−	0.0491276i
$222$	197.630	−	2457.95i	0.0597481	−	0.743095i
$223$			5668.92i			1.70233i	0.524900	+	0.851164i	$0.324103\pi$
$223$			5668.92i			1.70233i	−0.524900	+	0.851164i	$0.675897\pi$
$224$	−2798.39	−	2015.92i	−0.834710	−	0.601313i
$225$	666.329	+	107.849i	0.197431	+	0.0319551i
$226$	−1075.70			−0.316612
$227$	−1778.27			−0.519946			−0.259973	−	0.965616i	$-0.583714\pi$
$227$	−1778.27			−0.519946			−0.259973	+	0.965616i	$0.583714\pi$
$228$	−339.568	+	4223.26i	−0.0986335	+	1.22672i
$229$			1353.76i			0.390650i	0.980739	+	0.195325i	$0.0625762\pi$
$229$			1353.76i			0.390650i	−0.980739	+	0.195325i	$0.937424\pi$
$230$	407.367			0.116787
$231$	4970.61	+	4225.14i	1.41577	+	1.20344i
$232$	1789.97			0.506540
$233$		−	2216.62i		−	0.623242i	−0.950206	−	0.311621i	$-0.899128\pi$
$233$		−	2216.62i		−	0.623242i	0.950206	−	0.311621i	$-0.100872\pi$
$234$	−95.7936	−	15.5047i	−0.0267616	−	0.00433151i
$235$	789.203			0.219072
$236$	−3568.46			−0.984267
$237$	−3407.92	−	274.012i	−0.934044	−	0.0751011i
$238$	1310.97	+	944.406i	0.357050	+	0.257213i
$239$			4546.46i			1.23048i	0.788338	+	0.615242i	$0.210942\pi$
$239$			4546.46i			1.23048i	−0.788338	+	0.615242i	$0.789058\pi$
$240$	547.735	+	44.0402i	0.147317	+	0.0118449i
$241$		−	35.5837i		−	0.00951099i	−0.999989	−	0.00475549i	$-0.998486\pi$
$241$		−	35.5837i		−	0.00951099i	0.999989	−	0.00475549i	$-0.00151373\pi$
$242$		−	4550.01i		−	1.20862i
$243$	3487.26	+	1479.16i	0.920609	+	0.390485i
$244$		−	2614.11i		−	0.685866i
$245$	−543.132	−	1626.72i	−0.141630	−	0.424194i
$246$	−38.9945	+	484.981i	−0.0101065	+	0.125696i
$247$	−347.115			−0.0894186
$248$	3582.98			0.917416
$249$	−3362.21	−	270.336i	−0.855709	−	0.0688027i
$250$			174.224i			0.0440755i
$251$	−555.734			−0.139752			−0.0698758	−	0.997556i	$-0.522260\pi$
$251$	−555.734			−0.139752			−0.0698758	+	0.997556i	$0.522260\pi$
$252$	−2140.39	+	2143.21i	−0.535047	+	0.535752i
$253$	−3962.64			−0.984700
$254$			2091.43i			0.516647i
$255$	−1620.97	−	130.333i	−0.398075	−	0.0320070i
$256$	−2623.74			−0.640562
$257$	−5009.10			−1.21580			−0.607898	−	0.794016i	$-0.707987\pi$
$257$	−5009.10			−1.21580			−0.607898	+	0.794016i	$0.707987\pi$
$258$	51.5330	−	640.923i	0.0124353	−	0.154659i
$259$	3685.82	−	5116.45i	0.884268	−	1.22749i
$260$			78.0988i			0.0186288i
$261$	394.112	−	2434.97i	0.0934672	−	0.577475i
$262$			2565.34i			0.604913i
$263$		−	334.413i		−	0.0784061i	−0.999231	−	0.0392031i	$-0.987518\pi$
$263$		−	334.413i		−	0.0784061i	0.999231	−	0.0392031i	$-0.0124819\pi$
$264$	6879.38	+	553.132i	1.60377	+	0.128950i
$265$		−	2294.71i		−	0.531936i
$266$	2031.04	−	2819.38i	0.468162	−	0.649877i
$267$	−3110.64	−	250.108i	−0.712988	−	0.0573273i
$268$	4903.33			1.11761
$269$	−5366.63			−1.21639			−0.608195	−	0.793787i	$-0.708106\pi$
$269$	−5366.63			−1.21639			−0.608195	+	0.793787i	$0.708106\pi$
$270$	−233.066	+	949.530i	−0.0525331	+	0.214024i
$271$		−	2497.86i		−	0.559905i	−0.960014	−	0.279953i	$-0.909681\pi$
$271$		−	2497.86i		−	0.559905i	0.960014	−	0.279953i	$-0.0903188\pi$
$272$	−1323.86			−0.295112
$273$	−189.076	−	160.719i	−0.0419171	−	0.0356306i
$274$	−2493.89			−0.549858
$275$		−	1694.75i		−	0.371627i
$276$	147.456	−	1833.94i	0.0321588	−	0.399964i
$277$	−2734.48			−0.593136			−0.296568	−	0.955012i	$-0.595842\pi$
$277$	−2734.48			−0.593136			−0.296568	+	0.955012i	$0.595842\pi$
$278$	−3130.63			−0.675405
$279$	788.893	−	4874.07i	0.169282	−	1.04589i
$280$	−1472.13	−	1060.50i	−0.314201	−	0.226346i
$281$			561.914i			0.119292i	0.998220	+	0.0596459i	$0.0189972\pi$
$281$			561.914i			0.119292i	−0.998220	+	0.0596459i	$0.981003\pi$
$282$	−91.6173	+	1139.46i	−0.0193466	+	0.240616i
$283$		−	312.314i		−	0.0656012i	−0.999462	−	0.0328006i	$-0.989557\pi$
$283$		−	312.314i		−	0.0656012i	0.999462	−	0.0328006i	$-0.0104426\pi$
$284$			487.877i			0.101937i
$285$	−280.294	+	3486.06i	−0.0582568	+	0.724548i
$286$			243.643i			0.0503738i
$287$	−727.251	+	1009.53i	−0.149576	+	0.207633i
$288$	−803.355	+	4963.43i	−0.164369	+	1.01553i
$289$	−995.171			−0.202559
$290$	636.667			0.128919
$291$	−338.916	+	4215.15i	−0.0682736	+	0.849128i
$292$			2459.77i			0.492969i
$293$	−5189.02			−1.03463			−0.517313	−	0.855796i	$-0.673068\pi$
$293$	−5189.02			−1.03463			−0.517313	+	0.855796i	$0.673068\pi$
$294$	2411.73	−	595.335i	0.478418	−	0.118097i
$295$	−2945.56			−0.581346
$296$		−	6671.06i		−	1.30996i
$297$	2267.14	−	9236.51i	0.442938	−	1.80457i
$298$	−409.678			−0.0796375
$299$	150.734			0.0291543
$300$	784.342	+	63.0645i	0.150947	+	0.0121368i
$301$	961.093	−	1334.14i	0.184042	−	0.255477i
$302$		−	1325.87i		−	0.252634i
$303$	1522.39	+	122.406i	0.288643	+	0.0232082i
$304$			2847.08i			0.537142i
$305$		−	2157.80i		−	0.405099i
$306$	376.352	−	2325.24i	0.0703092	−	0.434396i
$307$		−	324.556i		−	0.0603367i	−0.999545	−	0.0301684i	$-0.990396\pi$
$307$		−	324.556i		−	0.0603367i	0.999545	−	0.0301684i	$-0.00960434\pi$
$308$	6170.55	+	4445.17i	1.14156	+	0.822360i
$309$	−274.433	+	3413.17i	−0.0505242	+	0.628377i
$310$	1274.41			0.233490
$311$	6882.09			1.25481			0.627407	−	0.778691i	$-0.284116\pi$
$311$	6882.09			1.25481			0.627407	+	0.778691i	$0.284116\pi$
$312$	−261.682	−	21.0404i	−0.0474835	−	0.00381788i
$313$		−	10414.6i		−	1.88072i	−0.340181	−	0.940360i	$-0.610488\pi$
$313$		−	10414.6i		−	1.88072i	0.340181	−	0.940360i	$-0.389512\pi$
$314$	2374.35			0.426727
$315$	−1766.77	+	1769.10i	−0.316020	+	0.316436i
$316$	−3985.57			−0.709511
$317$		−	2351.44i		−	0.416625i	−0.978062	−	0.208312i	$-0.933203\pi$
$317$		−	2351.44i		−	0.416625i	0.978062	−	0.208312i	$-0.0667971\pi$
$318$	3313.12	+	266.390i	0.584248	+	0.0469760i
$319$	−6193.15			−1.08699
$320$	−451.763			−0.0789197
$321$	−214.243	+	2664.58i	−0.0372520	+	0.463309i
$322$	−881.972	+	1224.31i	−0.152641	+	0.211888i
$323$		−	8425.68i		−	1.45145i
$324$	4190.35	+	1392.95i	0.718511	+	0.238846i
$325$			64.4661i			0.0110029i
$326$			2422.89i			0.411631i
$327$	8432.66	+	678.023i	1.42608	+	0.114663i
$328$			1316.27i			0.221582i
$329$	−1708.67	+	2371.88i	−0.286328	+	0.397465i
$330$	2446.90	+	196.741i	0.408173	+	0.0328189i
$331$	116.712			0.0193809			0.00969047	−	0.999953i	$-0.496915\pi$
$331$	116.712			0.0193809			0.00969047	+	0.999953i	$0.496915\pi$
$332$	−3932.11			−0.650008
$333$	−9074.92	−	1468.82i	−1.49340	−	0.241714i
$334$			2333.58i			0.382298i
$335$	4047.42			0.660101
$336$	−1318.24	+	1550.82i	−0.214035	+	0.251798i
$337$	−482.498			−0.0779921			−0.0389961	−	0.999239i	$-0.512416\pi$
$337$	−482.498			−0.0779921			−0.0389961	+	0.999239i	$0.512416\pi$
$338$			3052.89i			0.491287i
$339$	−321.407	+	3997.39i	−0.0514939	+	0.640437i
$340$	−1895.73			−0.302383
$341$	−12396.8			−1.96869
$342$	−5000.66	−	809.382i	−0.790657	−	0.127972i
$343$	6064.90	+	1889.61i	0.954734	+	0.297462i
$344$		−	1739.51i		−	0.272640i
$345$	121.717	−	1513.81i	0.0189942	−	0.236234i
$346$		−	2427.08i		−	0.377111i
$347$			1524.90i			0.235911i	0.993019	+	0.117955i	$0.0376340\pi$
$347$			1524.90i			0.235911i	−0.993019	+	0.117955i	$0.962366\pi$
$348$	230.457	−	2866.23i	0.0354994	−	0.441512i
$349$			2797.89i			0.429133i	0.976709	+	0.214567i	$0.0688339\pi$
$349$			2797.89i			0.429133i	−0.976709	+	0.214567i	$0.931166\pi$
$350$	−523.614	−	377.204i	−0.0799668	−	0.0576069i
$351$	−86.2388	+	351.345i	−0.0131142	+	0.0534285i
$352$	12624.1			1.91155
$353$	6871.80			1.03612			0.518058	−	0.855346i	$-0.326655\pi$
$353$	6871.80			1.03612			0.518058	+	0.855346i	$0.326655\pi$
$354$	341.945	−	4252.82i	0.0513395	−	0.638517i
$355$			402.715i			0.0602081i
$356$	−3637.89			−0.541595
$357$	3901.20	−	4589.52i	0.578357	−	0.680400i
$358$	−2323.11			−0.342962
$359$		−	9204.67i		−	1.35321i	−0.736344	−	0.676607i	$-0.763450\pi$
$359$		−	9204.67i		−	1.35321i	0.736344	−	0.676607i	$-0.236550\pi$
$360$	−422.615	+	2611.07i	−0.0618716	+	0.382265i
$361$	−11261.2			−1.64182
$362$	5839.93			0.847900
$363$	−16908.2	−	1359.50i	−2.44477	−	0.196570i
$364$	−234.719	−	169.088i	−0.0337984	−	0.0243479i
$365$			2030.40i			0.291167i
$366$	3115.45	+	250.495i	0.444937	+	0.0357749i
$367$		−	3102.52i		−	0.441281i	−0.975355	−	0.220641i	$-0.929185\pi$
$367$		−	3102.52i		−	0.441281i	0.975355	−	0.220641i	$-0.0708148\pi$
$368$		−	1236.34i		−	0.175132i
$369$	1790.58	+	289.814i	0.252612	+	0.0408865i
$370$		−	2372.80i		−	0.333395i
$371$	6896.57	+	4968.18i	0.965100	+	0.695243i
$372$	461.305	−	5737.32i	0.0642945	−	0.799640i
$373$	−6036.54			−0.837963			−0.418981	−	0.907995i	$-0.637613\pi$
$373$	−6036.54			−0.837963			−0.418981	+	0.907995i	$0.637613\pi$
$374$	−5914.06			−0.817670
$375$	647.430	+	52.0561i	0.0891550	+	0.00716845i
$376$			3092.57i			0.424167i
$377$	235.579			0.0321829
$378$	−2349.13	−	2756.25i	−0.319647	−	0.375042i
$379$	8484.08			1.14986			0.574931	−	0.818202i	$-0.305029\pi$
$379$	8484.08			1.14986			0.574931	+	0.818202i	$0.305029\pi$
$380$			4076.95i			0.550376i
$381$	7771.95	+	624.898i	1.04506	+	0.0840276i
$382$	−5378.04			−0.720326
$383$	−6784.15			−0.905101			−0.452551	−	0.891739i	$-0.649486\pi$
$383$	−6784.15			−0.905101			−0.452551	+	0.891739i	$0.649486\pi$
$384$	−567.975	+	7063.98i	−0.0754800	+	0.938756i
$385$	5093.43	+	3669.23i	0.674248	+	0.485718i
$386$			1574.33i			0.207594i
$387$	−2366.33	−	383.002i	−0.310819	−	0.0503077i
$388$			4929.62i			0.645009i
$389$			2023.40i			0.263729i	0.991268	+	0.131865i	$0.0420964\pi$
$389$			2023.40i			0.263729i	−0.991268	+	0.131865i	$0.957904\pi$
$390$	−93.0766	−	7.48376i	−0.0120849	−	0.000971680i
$391$			3658.82i			0.473234i
$392$	6374.48	−	2128.32i	0.821326	−	0.274225i
$393$	9533.03	+	766.497i	1.22361	+	0.0983833i
$394$	5287.14			0.676046
$395$	−3289.86			−0.419065
$396$	1771.43	−	10944.5i	0.224792	−	1.38885i
$397$		−	792.398i		−	0.100175i	−0.998745	−	0.0500873i	$-0.984050\pi$
$397$		−	792.398i		−	0.100175i	0.998745	−	0.0500873i	$-0.0159500\pi$
$398$	−3786.26			−0.476854
$399$	−9870.20	−	8389.91i	−1.23842	−	1.05268i
$400$	528.759			0.0660949
$401$			13954.2i			1.73776i	0.495024	+	0.868880i	$0.335159\pi$
$401$			13954.2i			1.73776i	−0.495024	+	0.868880i	$0.664841\pi$
$402$	−469.858	+	5843.69i	−0.0582945	+	0.725017i
$403$	471.558			0.0582877
$404$	1780.43			0.219257
$405$	3458.90	+	1149.80i	0.424380	+	0.141072i
$406$	−1378.42	+	1913.45i	−0.168497	+	0.233899i
$407$			23081.3i			2.81105i
$408$	510.723	−	6351.93i	0.0619719	−	0.770754i
$409$			2366.91i			0.286152i	0.989712	+	0.143076i	$0.0456993\pi$
$409$			2366.91i			0.286152i	−0.989712	+	0.143076i	$0.954301\pi$
$410$			468.179i			0.0563944i
$411$	−745.146	+	9267.49i	−0.0894291	+	1.11224i
$412$			3991.70i			0.477323i
$413$	6377.31	−	8852.63i	0.759822	−	1.05474i
$414$	2171.52	+	351.472i	0.257788	+	0.0417244i
$415$	−3245.73			−0.383920
$416$	−480.203			−0.0565958
$417$	−935.399	+	11633.7i	−0.109848	+	1.36620i
$418$			12718.8i			1.48827i
$419$	15398.7			1.79541			0.897703	−	0.440600i	$-0.145234\pi$
$419$	15398.7			1.79541			0.897703	+	0.440600i	$0.145234\pi$
$420$	−1887.68	+	2220.74i	−0.219308	+	0.258002i
$421$	4342.52			0.502711			0.251356	−	0.967895i	$-0.419124\pi$
$421$	4342.52			0.502711			0.251356	+	0.967895i	$0.419124\pi$
$422$			4162.45i			0.480153i
$423$	4206.95	+	680.915i	0.483567	+	0.0782677i
$424$	8992.05			1.02994
$425$	−1564.81			−0.178599
$426$	−581.443	−	46.7505i	−0.0661291	−	0.00531707i
$427$	6485.08	+	4671.76i	0.734977	+	0.529467i
$428$			3116.22i			0.351935i
$429$	905.399	+	72.7980i	0.101895	+	0.00819282i
$430$		−	618.719i		−	0.0693890i
$431$		−	3165.86i		−	0.353814i	−0.984228	−	0.176907i	$-0.943391\pi$
$431$		−	3165.86i		−	0.353814i	0.984228	−	0.176907i	$-0.0566092\pi$
$432$	2881.77	+	707.342i	0.320948	+	0.0787778i
$433$		−	11822.9i		−	1.31217i	−0.754685	−	0.656087i	$-0.772210\pi$
$433$		−	11822.9i		−	1.31217i	0.754685	−	0.656087i	$-0.227790\pi$
$434$	−2759.18	+	3830.14i	−0.305172	+	0.423624i
$435$	190.229	−	2365.91i	0.0209674	−	0.260774i
$436$	9862.00			1.08327
$437$	7868.66			0.861348
$438$	−2931.50	−	235.705i	−0.319800	−	0.0257133i
$439$		−	11914.9i		−	1.29537i	−0.761909	−	0.647684i	$-0.775738\pi$
$439$		−	11914.9i		−	1.29537i	0.761909	−	0.647684i	$-0.224262\pi$
$440$	6641.05			0.719544
$441$	−1491.72	−	9140.07i	−0.161075	−	0.986942i
$442$	224.963			0.0242090
$443$		−	8026.37i		−	0.860823i	−0.902633	−	0.430411i	$-0.858368\pi$
$443$		−	8026.37i		−	0.860823i	0.902633	−	0.430411i	$-0.141632\pi$
$444$	−10682.2	−	858.893i	−1.14179	−	0.0918047i
$445$	−3002.87			−0.319887
$446$	−7901.28			−0.838871
$447$	−122.407	+	1522.40i	−0.0129523	+	0.161089i
$448$	978.092	−	1357.74i	0.103148	−	0.143185i
$449$		−	15264.8i		−	1.60443i	−0.597036	−	0.802214i	$-0.703655\pi$
$449$		−	15264.8i		−	1.60443i	0.597036	−	0.802214i	$-0.296345\pi$
$450$	−150.318	+	928.721i	−0.0157468	+	0.0972896i
$451$		−	4554.19i		−	0.475495i
$452$			4674.95i			0.486484i
$453$	−4927.06	−	396.157i	−0.511023	−	0.0410884i
$454$		−	2478.53i		−	0.256218i
$455$	−193.747	−	139.573i	−0.0199627	−	0.0143808i
$456$	−13660.4	−	1098.36i	−1.40287	−	0.112797i
$457$	−1121.90			−0.114836			−0.0574180	−	0.998350i	$-0.518287\pi$
$457$	−1121.90			−0.114836			−0.0574180	+	0.998350i	$0.518287\pi$
$458$	−1886.85			−0.192504
$459$	−8528.35	−	2093.31i	−0.867253	−	0.212870i
$460$		−	1770.40i		−	0.179446i
$461$	7671.75			0.775074			0.387537	−	0.921854i	$-0.373326\pi$
$461$	7671.75			0.775074			0.387537	+	0.921854i	$0.373326\pi$
$462$	−5888.96	+	6927.99i	−0.593028	+	0.697660i
$463$	3491.25			0.350436			0.175218	−	0.984530i	$-0.443937\pi$
$463$	3491.25			0.350436			0.175218	+	0.984530i	$0.443937\pi$
$464$		−	1932.25i		−	0.193324i
$465$	380.781	−	4735.83i	0.0379749	−	0.472299i
$466$	3089.50			0.307121
$467$	4518.50			0.447733			0.223866	−	0.974620i	$-0.428132\pi$
$467$	4518.50			0.447733			0.223866	+	0.974620i	$0.428132\pi$
$468$	−67.3827	+	416.315i	−0.00665549	+	0.0411201i
$469$	−8762.89	+	12164.2i	−0.862756	+	1.19763i
$470$			1099.98i			0.107954i
$471$	709.430	−	8823.28i	0.0694030	−	0.863174i
$472$		−	11542.5i		−	1.12560i
$473$			6018.56i			0.585060i
$474$	381.914	−	4749.92i	0.0370082	−	0.460277i
$475$			3365.29i			0.325073i
$476$	4104.36	−	5697.45i	0.395216	−	0.548618i
$477$	1979.85	−	12232.3i	0.190044	−	1.17416i
$478$	−6336.80			−0.606357
$479$	−18591.3			−1.77340			−0.886698	−	0.462348i	$-0.847007\pi$
$479$	−18591.3			−1.77340			−0.886698	+	0.462348i	$0.847007\pi$
$480$	−387.762	+	4822.65i	−0.0368726	+	0.458589i
$481$		−	877.982i		−	0.0832277i
$482$	49.5962			0.00468681
$483$	4286.11	+	3643.29i	0.403778	+	0.343221i
$484$	−19774.2			−1.85708
$485$			4069.12i			0.380967i
$486$	−2061.63	+	4860.51i	−0.192423	+	0.453657i
$487$	62.4942			0.00581495			0.00290748	−	0.999996i	$-0.499075\pi$
$487$	62.4942			0.00581495			0.00290748	+	0.999996i	$0.499075\pi$
$488$	8455.54			0.784353
$489$	9003.67	+	723.934i	0.832638	+	0.0669477i
$490$	2267.31	−	757.011i	0.209034	−	0.0697924i
$491$		−	11712.0i		−	1.07649i	−0.842789	−	0.538244i	$-0.819088\pi$
$491$		−	11712.0i		−	1.07649i	0.842789	−	0.538244i	$-0.180912\pi$
$492$	2107.71	+	169.469i	0.193136	+	0.0155290i
$493$			5718.32i			0.522394i
$494$		−	483.805i		−	0.0440636i
$495$	1462.21	−	9034.09i	0.132771	−	0.820307i
$496$		−	3867.78i		−	0.350138i
$497$	−1210.33	−	871.901i	−0.109236	−	0.0786923i
$498$	376.792	−	4686.21i	0.0339045	−	0.421675i
$499$	−10826.2			−0.971237			−0.485618	−	0.874171i	$-0.661405\pi$
$499$	−10826.2			−0.971237			−0.485618	+	0.874171i	$0.661405\pi$
$500$	757.169			0.0677233
$501$	8671.77	+	697.248i	0.773306	+	0.0621771i
$502$		−	774.576i		−	0.0688666i
$503$	−11386.8			−1.00937			−0.504684	−	0.863304i	$-0.668391\pi$
$503$	−11386.8			−1.00937			−0.504684	+	0.863304i	$0.668391\pi$
$504$	−6932.37	−	6923.25i	−0.612683	−	0.611877i
$505$	1469.65			0.129502
$506$		−	5523.08i		−	0.485239i
$507$	11344.8	+	912.170i	0.993766	+	0.0799031i
$508$	9089.29			0.793843
$509$	−755.673			−0.0658047			−0.0329024	−	0.999459i	$-0.510475\pi$
$509$	−755.673			−0.0658047			−0.0329024	+	0.999459i	$0.510475\pi$
$510$	181.657	−	2259.29i	0.0157723	−	0.196163i
$511$	−6102.19	−	4395.92i	−0.528268	−	0.380556i
$512$			7253.87i			0.626131i
$513$	−4501.87	+	18341.0i	−0.387452	+	1.57851i
$514$		−	6981.63i		−	0.599118i
$515$			3294.92i			0.281925i
$516$	−2785.43	−	223.960i	−0.237639	−	0.0191072i
$517$		−	10700.0i		−	0.910225i
$518$	7131.26	+	5137.25i	0.604883	+	0.435749i
$519$	−9019.23	−	725.185i	−0.762813	−	0.0613335i
$520$	−252.616			−0.0213038
$521$	−14676.3			−1.23413			−0.617064	−	0.786913i	$-0.711678\pi$
$521$	−14676.3			−1.23413			−0.617064	+	0.786913i	$0.711678\pi$
$522$	3393.84	+	549.309i	0.284567	+	0.0460587i
$523$			10547.2i			0.881832i	0.897548	+	0.440916i	$0.145346\pi$
$523$			10547.2i			0.881832i	−0.897548	+	0.440916i	$0.854654\pi$
$524$	11148.9			0.929468
$525$	−1558.17	+	1833.09i	−0.129532	+	0.152386i
$526$	466.101			0.0386369
$527$			11446.3i			0.946129i
$528$	597.098	−	7426.20i	0.0492147	−	0.612090i
$529$	8750.06			0.719163
$530$	3198.34			0.262127
$531$	−15701.7	−	2541.40i	−1.28323	−	0.207697i
$532$	−12252.9	−	8826.82i	−0.998555	−	0.719344i
$533$			173.235i			0.0140781i
$534$	348.598	−	4335.57i	0.0282497	−	0.351345i
$535$			2572.26i			0.207867i
$536$			15860.2i			1.27809i
$537$	−694.121	+	8632.89i	−0.0557794	+	0.693737i
$538$		−	7479.95i		−	0.599411i
$539$	−22055.2	+	7363.79i	−1.76249	+	0.588462i
$540$	4126.62	+	1012.89i	0.328855	+	0.0807186i
$541$	7767.39			0.617276			0.308638	−	0.951180i	$-0.400127\pi$
$541$	7767.39			0.617276			0.308638	+	0.951180i	$0.400127\pi$
$542$	3481.49			0.275909
$543$	1744.91	−	21701.7i	0.137903	−	1.71512i
$544$		−	11656.2i		−	0.918666i
$545$	8140.52			0.639820
$546$	224.008	−	263.531i	0.0175580	−	0.0206559i
$547$	−10163.9			−0.794473			−0.397237	−	0.917716i	$-0.630031\pi$
$547$	−10163.9			−0.794473			−0.397237	+	0.917716i	$0.630031\pi$
$548$			10838.3i			0.844874i
$549$	1861.72	−	11502.4i	0.144729	−	0.894192i
$550$	2362.13			0.183130
$551$	12297.8			0.950824
$552$	5932.01	+	476.959i	0.457397	+	0.0367767i
$553$	7122.73	−	9887.39i	0.547720	−	0.760316i
$554$		−	3811.28i		−	0.292285i
$555$	−8817.53	−	708.968i	−0.674384	−	0.0542234i
$556$			13605.6i			1.03778i
$557$		−	16917.4i		−	1.28692i	−0.765480	−	0.643460i	$-0.777498\pi$
$557$		−	16917.4i		−	1.28692i	0.765480	−	0.643460i	$-0.222502\pi$
$558$	6793.43	+	1099.55i	0.515392	+	0.0834188i
$559$		−	228.938i		−	0.0173221i
$560$	−1144.79	+	1589.14i	−0.0863863	+	0.119917i
$561$	−1767.06	+	21977.1i	−0.132986	+	1.65397i
$562$	−783.190			−0.0587845
$563$	13413.1			1.00408			0.502038	−	0.864846i	$-0.332584\pi$
$563$	13413.1			1.00408			0.502038	+	0.864846i	$0.332584\pi$
$564$	4952.04	+	398.165i	0.369713	+	0.0297266i
$565$			3858.90i			0.287337i
$566$	435.300			0.0323269
$567$	−10944.3	+	7906.05i	−0.810616	+	0.585578i
$568$	−1578.08			−0.116575
$569$			8625.40i			0.635493i	0.948176	+	0.317747i	$0.102926\pi$
$569$			8625.40i			0.635493i	−0.948176	+	0.317747i	$0.897074\pi$
$570$	−4858.83	−	390.671i	−0.357042	−	0.0287077i
$571$	17682.5			1.29596			0.647978	−	0.761659i	$-0.275615\pi$
$571$	17682.5			1.29596			0.647978	+	0.761659i	$0.275615\pi$
$572$	1058.86			0.0774009
$573$	−1606.90	+	19985.3i	−0.117154	+	1.45706i
$574$	−1407.07	−	1013.63i	−0.102317	−	0.0737078i
$575$		−	1461.37i		−	0.105988i
$576$	−2408.18	−	389.776i	−0.174203	−	0.0281956i
$577$			22409.4i			1.61684i	0.588606	+	0.808420i	$0.299677\pi$
$577$			22409.4i			1.61684i	−0.588606	+	0.808420i	$0.700323\pi$
$578$		−	1387.06i		−	0.0998166i
$579$	5850.33	+	470.392i	0.419916	+	0.0337631i
$580$		−	2766.93i		−	0.198087i
$581$	7027.19	−	9754.78i	0.501785	−	0.696551i
$582$	−5875.02	−	472.377i	−0.418432	−	0.0336438i
$583$	−31111.7			−2.21015
$584$	−7956.30			−0.563757
$585$	−55.6206	+	343.645i	−0.00393099	+	0.0242871i
$586$		−	7232.39i		−	0.509842i
$587$	−273.325			−0.0192186			−0.00960930	−	0.999954i	$-0.503059\pi$
$587$	−273.325			−0.0192186			−0.00960930	+	0.999954i	$0.503059\pi$
$588$	−2587.30	−	10481.3i	−0.181460	−	0.735104i
$589$	24616.5			1.72208
$590$		−	4105.49i		−	0.286475i
$591$	1579.74	−	19647.5i	0.109952	−	1.36749i
$592$	−7201.32			−0.499954
$593$	−21856.6			−1.51356			−0.756780	−	0.653669i	$-0.773229\pi$
$593$	−21856.6			−1.51356			−0.756780	+	0.653669i	$0.773229\pi$
$594$	12873.7	+	3159.91i	0.889253	+	0.218270i
$595$	3387.91	−	4702.92i	0.233430	−	0.324035i
$596$			1780.44i			0.122365i
$597$	−1131.29	+	14070.1i	−0.0775557	+	0.964571i
$598$			210.091i			0.0143666i
$599$		−	11295.6i		−	0.770493i	−0.922814	−	0.385246i	$-0.874116\pi$
$599$		−	11295.6i		−	0.770493i	0.922814	−	0.385246i	$-0.125884\pi$
$600$	−203.987	+	2537.02i	−0.0138796	+	0.172622i
$601$			4883.39i			0.331443i	0.986173	+	0.165722i	$0.0529953\pi$
$601$			4883.39i			0.331443i	−0.986173	+	0.165722i	$0.947005\pi$
$602$	1859.51	+	1339.56i	0.125893	+	0.0906917i
$603$	21575.3	+	3492.07i	1.45707	+	0.235834i
$604$	−5762.19			−0.388179
$605$	−16322.5			−1.09686
$606$	−170.609	+	2121.89i	−0.0114365	+	0.142237i
$607$		−	11389.4i		−	0.761583i	−0.924661	−	0.380792i	$-0.875652\pi$
$607$		−	11389.4i		−	0.761583i	0.924661	−	0.380792i	$-0.124348\pi$
$608$	−25067.7			−1.67209
$609$	6698.69	+	5694.05i	0.445722	+	0.378874i
$610$	3007.52			0.199624
$611$			407.014i			0.0269493i
$612$	−10105.4	−	1635.61i	−0.667463	−	0.108032i
$613$	−683.834			−0.0450567			−0.0225284	−	0.999746i	$-0.507172\pi$
$613$	−683.834			−0.0450567			−0.0225284	+	0.999746i	$0.507172\pi$
$614$	452.362			0.0297326
$615$	1739.79	+	139.887i	0.114074	+	0.00917200i
$616$	−14378.2	+	19959.1i	−0.940448	+	1.30548i
$617$		−	7945.11i		−	0.518409i	−0.965822	−	0.259204i	$-0.916540\pi$
$617$		−	7945.11i		−	0.518409i	0.965822	−	0.259204i	$-0.0834603\pi$
$618$	−4757.24	−	382.502i	−0.309651	−	0.0248972i
$619$			18920.0i			1.22853i	0.789100	+	0.614264i	$0.210547\pi$
$619$			18920.0i			1.22853i	−0.789100	+	0.614264i	$0.789453\pi$
$620$		−	5538.56i		−	0.358764i
$621$	1954.93	−	7964.54i	0.126326	−	0.514664i
$622$			9592.17i			0.618346i
$623$	6501.38	−	9024.87i	0.418094	−	0.580376i
$624$	−22.7128	+	282.483i	−0.00145712	+	0.0181224i
$625$	625.000			0.0400000
$626$	14515.7			0.926779
$627$	47264.0	+	3800.23i	3.01044	+	0.242052i
$628$		−	10318.8i		−	0.655678i
$629$	21311.7			1.35096
$630$	−2465.75	−	2462.50i	−0.155933	−	0.155728i
$631$	−1816.54			−0.114604			−0.0573022	−	0.998357i	$-0.518250\pi$
$631$	−1816.54			−0.114604			−0.0573022	+	0.998357i	$0.518250\pi$
$632$		−	12891.6i		−	0.811394i
$633$	15468.0	+	1243.69i	0.971245	+	0.0780923i
$634$	3277.41			0.205304
$635$	7502.69			0.468875
$636$	1157.72	−	14398.7i	0.0721801	−	0.897714i
$637$	838.948	−	280.109i	0.0521826	−	0.0174228i
$638$		−	8631.94i		−	0.535646i
$639$	−347.458	+	2146.72i	−0.0215105	+	0.132900i
$640$			6819.26i			0.421179i
$641$		−	15359.9i		−	0.946457i	−0.880940	−	0.473229i	$-0.843088\pi$
$641$		−	15359.9i		−	0.946457i	0.880940	−	0.473229i	$-0.156912\pi$
$642$	−3713.86	−	298.610i	−0.228309	−	0.0183570i
$643$			11392.9i			0.698745i	0.936984	+	0.349373i	$0.113605\pi$
$643$			11392.9i			0.698745i	−0.936984	+	0.349373i	$0.886395\pi$
$644$	5320.79	+	3833.02i	0.325572	+	0.234537i
$645$	−2299.21	−	184.866i	−0.140359	−	0.0112854i
$646$	11743.6			0.715242
$647$	4600.01			0.279513			0.139757	−	0.990186i	$-0.455368\pi$
$647$	4600.01			0.279513			0.139757	+	0.990186i	$0.455368\pi$
$648$	−4505.61	+	13554.0i	−0.273143	+	0.821686i
$649$			39935.9i			2.41544i
$650$	−89.8521			−0.00542198
$651$	13408.7	+	11397.7i	0.807265	+	0.686195i
$652$	10529.8			0.632483
$653$		−	19253.3i		−	1.15381i	−0.816810	−	0.576907i	$-0.804259\pi$
$653$		−	19253.3i		−	1.15381i	0.816810	−	0.576907i	$-0.195741\pi$
$654$	−945.020	+	11753.4i	−0.0565034	+	0.702741i
$655$	9202.76			0.548980
$656$	1420.90			0.0845682
$657$	−1751.80	+	10823.3i	−0.104025	+	0.642704i
$658$	−3305.90	−	2381.52i	−0.195862	−	0.141096i
$659$			1117.61i			0.0660635i	0.999454	+	0.0330317i	$0.0105162\pi$
$659$			1117.61i			0.0660635i	−0.999454	+	0.0330317i	$0.989484\pi$
$660$	855.029	−	10634.1i	0.0504272	−	0.627171i
$661$			15114.5i			0.889390i	0.895682	+	0.444695i	$0.146688\pi$
$661$			15114.5i			0.889390i	−0.895682	+	0.444695i	$0.853312\pi$
$662$			162.672i			0.00955051i
$663$	67.2165	−	835.981i	0.00393736	−	0.0489696i
$664$		−	12718.7i		−	0.743346i
$665$	−10114.1	−	7286.04i	−0.589786	−	0.424873i
$666$	2047.23	−	12648.5i	0.119112	−	0.735916i
$667$	−5340.28			−0.310010
$668$	10141.6			0.587413
$669$	−2360.82	+	29361.8i	−0.136434	+	1.69685i
$670$			5641.24i			0.325284i
$671$	−29255.5			−1.68315
$672$	−13654.5	−	11606.7i	−0.783833	−	0.666277i
$673$	20340.5			1.16503			0.582516	−	0.812819i	$-0.302068\pi$
$673$	20340.5			1.16503			0.582516	+	0.812819i	$0.302068\pi$
$674$		−	672.500i		−	0.0384329i
$675$	3406.29	+	836.087i	0.194234	+	0.0476756i
$676$	13267.7			0.754878
$677$	−28057.2			−1.59280			−0.796399	−	0.604772i	$-0.793264\pi$
$677$	−28057.2			−1.59280			−0.796399	+	0.604772i	$0.793264\pi$
$678$	−5571.51	−	447.974i	−0.315594	−	0.0253751i
$679$	−12229.4	−	8809.87i	−0.691194	−	0.497926i
$680$		−	6131.87i		−	0.345804i
$681$	−9210.42	−	740.557i	−0.518273	−	0.0416714i
$682$		−	17278.5i		−	0.970130i
$683$			19325.6i			1.08268i	0.840802	+	0.541342i	$0.182084\pi$
$683$			19325.6i			1.08268i	−0.840802	+	0.541342i	$0.817916\pi$
$684$	−3517.54	+	21732.7i	−0.196632	+	1.21487i
$685$			8946.43i			0.499015i
$686$	−2633.72	+	8453.18i	−0.146583	+	0.470472i
$687$	−563.772	+	7011.71i	−0.0313089	+	0.389393i
$688$	−1877.78			−0.104055
$689$	1183.45			0.0654366
$690$	2109.93	+	169.648i	0.116411	+	0.00935996i
$691$			13253.9i			0.729669i	0.931072	+	0.364835i	$0.118874\pi$
$691$			13253.9i			0.729669i	−0.931072	+	0.364835i	$0.881126\pi$
$692$	−10548.0			−0.579443
$693$	23985.4	+	23953.9i	1.31476	+	1.31303i
$694$	−2125.39			−0.116252
$695$			11230.7i			0.612954i
$696$	9271.04	+	745.432i	0.504911	+	0.0405970i
$697$	−4205.02			−0.228517
$698$	−3899.66			−0.211468
$699$	923.109	−	11480.8i	0.0499502	−	0.621238i
$700$	−1639.31	+	2275.61i	−0.0885147	+	0.122871i
$701$			3313.99i			0.178556i	0.996007	+	0.0892779i	$0.0284559\pi$
$701$			3313.99i			0.178556i	−0.996007	+	0.0892779i	$0.971544\pi$
$702$	−489.700	−	120.199i	−0.0263284	−	0.00646240i
$703$		−	45832.8i		−	2.45891i
$704$			6125.00i			0.327905i
$705$	4087.62	+	328.663i	0.218367	+	0.0175577i
$706$			9577.83i			0.510576i
$707$	−3181.87	+	4416.90i	−0.169259	+	0.234957i
$708$	−18482.6	−	1486.08i	−0.981100	−	0.0788847i
$709$	1427.42			0.0756104			0.0378052	−	0.999285i	$-0.487963\pi$
$709$	1427.42			0.0756104			0.0378052	+	0.999285i	$0.487963\pi$
$710$	−561.299			−0.0296693
$711$	−17537.0	−	2838.45i	−0.925020	−	0.149719i
$712$		−	11767.0i		−	0.619365i
$713$	−10689.6			−0.561472
$714$	6396.81	+	5437.45i	0.335287	+	0.285002i
$715$	874.032			0.0457160
$716$			10096.2i			0.526971i
$717$	−1893.37	+	23548.1i	−0.0986180	+	1.22653i
$718$	12829.4			0.666835
$719$	25522.1			1.32380			0.661902	−	0.749591i	$-0.269750\pi$
$719$	25522.1			1.32380			0.661902	+	0.749591i	$0.269750\pi$
$720$	2818.62	+	456.207i	0.145894	+	0.0236137i
$721$	−9902.61	−	7133.69i	−0.511502	−	0.368478i
$722$		−	15695.8i		−	0.809054i
$723$	14.8188	−	184.304i	0.000762265	−	0.00948039i
$724$		−	25380.1i		−	1.30282i
$725$		−	2283.94i		−	0.116998i
$726$	1894.85	−	23566.5i	0.0968656	−	1.20473i
$727$		−	28266.9i		−	1.44204i	−0.692916	−	0.721018i	$-0.743674\pi$
$727$		−	28266.9i		−	1.44204i	0.692916	−	0.721018i	$-0.256326\pi$
$728$	546.929	−	759.218i	0.0278442	−	0.0386518i
$729$	17446.1	+	9113.46i	0.886352	+	0.463012i
$730$	−2829.94			−0.143481
$731$	5557.11			0.281173
$732$	1088.64	−	13539.6i	0.0549692	−	0.683659i
$733$		−	24004.4i		−	1.20958i	−0.796385	−	0.604790i	$-0.793257\pi$
$733$		−	24004.4i		−	1.20958i	0.796385	−	0.604790i	$-0.206743\pi$
$734$	4324.26			0.217454
$735$	−2135.67	−	8651.70i	−0.107177	−	0.434181i
$736$	10885.6			0.545174
$737$		−	54874.9i		−	2.74266i
$738$	−403.939	+	2495.69i	−0.0201480	+	0.124482i
$739$	12241.0			0.609324			0.304662	−	0.952460i	$-0.401456\pi$
$739$	12241.0			0.609324			0.304662	+	0.952460i	$0.401456\pi$
$740$	−10312.1			−0.512271
$741$	−1797.86	−	144.556i	−0.0891309	−	0.00716651i
$742$	−6924.60	+	9612.36i	−0.342601	+	0.475580i
$743$			33949.2i			1.67628i	0.545455	+	0.838140i	$0.316357\pi$
$743$			33949.2i			1.67628i	−0.545455	+	0.838140i	$0.683643\pi$
$744$	18557.8	+	1492.13i	0.914465	+	0.0735270i
$745$			1469.65i			0.0722738i
$746$		−	8413.66i		−	0.412930i
$747$	−17301.8	−	2800.38i	−0.847442	−	0.137163i
$748$			25702.3i			1.25638i
$749$	−7730.73	−	5569.10i	−0.377136	−	0.271683i
$750$	−72.5553	+	902.380i	−0.00353246	+	0.0439337i
$751$	−14152.1			−0.687640			−0.343820	−	0.939036i	$-0.611721\pi$
$751$	−14152.1			−0.687640			−0.343820	+	0.939036i	$0.611721\pi$
$752$	3338.38			0.161886
$753$	−2878.39	−	231.435i	−0.139302	−	0.0112005i
$754$			328.348i			0.0158590i
$755$	−4756.36			−0.229274
$756$	−11978.5	+	10209.2i	−0.576264	+	0.491147i
$757$	−17424.1			−0.836579			−0.418290	−	0.908314i	$-0.637370\pi$
$757$	−17424.1			−0.836579			−0.418290	+	0.908314i	$0.637370\pi$
$758$			11825.0i			0.566628i
$759$	−20524.3	−	1650.24i	−0.981533	−	0.0789195i
$760$	−13187.2			−0.629408
$761$	10979.4			0.522999			0.261500	−	0.965204i	$-0.415783\pi$
$761$	10979.4			0.522999			0.261500	+	0.965204i	$0.415783\pi$
$762$	−870.976	+	10832.4i	−0.0414070	+	0.514985i
$763$	−17624.7	+	24465.7i	−0.836247	+	1.16083i
$764$			23372.8i			1.10680i
$765$	−8341.44	−	1350.10i	−0.394229	−	0.0638080i
$766$		−	9455.67i		−	0.446015i
$767$		−	1519.11i		−	0.0715148i
$768$	−13589.5	−	1092.65i	−0.638501	−	0.0513382i
$769$		−	20853.1i		−	0.977868i	−0.872321	−	0.488934i	$-0.837386\pi$
$769$		−	20853.1i		−	0.977868i	0.872321	−	0.488934i	$-0.162614\pi$
$770$	−5114.14	+	7099.17i	−0.239352	+	0.332255i
$771$	−25944.3	−	2086.04i	−1.21188	−	0.0974407i
$772$	6841.97			0.318974
$773$	7220.83			0.335983			0.167992	−	0.985788i	$-0.446272\pi$
$773$	7220.83			0.335983			0.167992	+	0.985788i	$0.446272\pi$
$774$	533.823	−	3298.16i	0.0247906	−	0.153165i
$775$		−	4571.76i		−	0.211900i
$776$	−15945.2			−0.737629
$777$	21221.2	−	24965.4i	0.979802	−	1.15268i
$778$	−2820.20			−0.129960
$779$			9043.30i			0.415930i
$780$	−32.5242	+	404.508i	−0.00149302	+	0.0185688i
$781$	5460.01			0.250160
$782$	−5099.63			−0.233200
$783$	3055.32	−	12447.7i	0.139449	−	0.568126i
$784$	−2297.49	−	6881.16i	−0.104660	−	0.313464i
$785$		−	8517.60i		−	0.387269i
$786$	−1068.33	+	13287.0i	−0.0484812	+	0.602967i
$787$			6781.22i			0.307147i	0.988137	+	0.153573i	$0.0490781\pi$
$787$			6781.22i			0.307147i	−0.988137	+	0.153573i	$0.950922\pi$
$788$		−	22977.7i		−	1.03877i
$789$	139.266	−	1732.07i	0.00628391	−	0.0781539i
$790$		−	4585.37i		−	0.206506i
$791$	−11597.6	−	8354.74i	−0.521319	−	0.375550i
$792$	35400.9	+	5729.82i	1.58828	+	0.257071i
$793$	1112.84			0.0498336
$794$	1104.44			0.0493639
$795$	955.631	−	11885.3i	0.0426324	−	0.530225i
$796$			16454.9i			0.732701i
$797$	−13204.8			−0.586873			−0.293436	−	0.955979i	$-0.594799\pi$
$797$	−13204.8			−0.586873			−0.293436	+	0.955979i	$0.594799\pi$
$798$	11693.8	−	13757.0i	0.518740	−	0.610265i
$799$	−9879.64			−0.437443
$800$			4655.57i			0.205749i
$801$	−16007.2	−	2590.84i	−0.706100	−	0.114286i
$802$	−19449.3			−0.856331
$803$	27528.1			1.20977
$804$	25396.5	+	2041.99i	1.11401	+	0.0895713i
$805$	4392.01	+	3163.94i	0.192296	+	0.138527i
$806$			657.252i			0.0287230i
$807$	−27796.1	−	2234.93i	−1.21248	−	0.0974885i
$808$			5758.95i			0.250741i
$809$		−	14180.1i		−	0.616248i	−0.951346	−	0.308124i	$-0.900299\pi$
$809$		−	14180.1i		−	0.616248i	0.951346	−	0.308124i	$-0.0997012\pi$
$810$	−1602.58	+	4820.97i	−0.0695172	+	0.209126i
$811$			4883.94i			0.211465i	0.994395	+	0.105733i	$0.0337188\pi$
$811$			4883.94i			0.211465i	−0.994395	+	0.105733i	$0.966281\pi$
$812$	8315.78	+	5990.57i	0.359393	+	0.258901i
$813$	1040.23	−	12937.5i	0.0448740	−	0.558104i
$814$	−32170.5			−1.38523
$815$	8691.75			0.373569
$816$	−6856.82	−	551.318i	−0.294163	−	0.0236520i
$817$		−	11951.1i		−	0.511770i
$818$	−3298.97			−0.141009
$819$	−912.374	−	911.173i	−0.0389266	−	0.0388754i
$820$	2034.69			0.0866517
$821$		−	5023.86i		−	0.213561i	−0.994283	−	0.106781i	$-0.965946\pi$
$821$		−	5023.86i		−	0.213561i	0.994283	−	0.106781i	$-0.0340543\pi$
$822$	−12916.9	−	1038.58i	−0.548089	−	0.0440688i
$823$	8525.75			0.361104			0.180552	−	0.983565i	$-0.442212\pi$
$823$	8525.75			0.361104			0.180552	+	0.983565i	$0.442212\pi$
$824$	−12911.5			−0.545864
$825$	705.778	−	8777.86i	0.0297843	−	0.370431i
$826$	12338.7	+	8888.62i	0.519756	+	0.374424i
$827$		−	12413.7i		−	0.521965i	−0.965344	−	0.260983i	$-0.915953\pi$
$827$		−	12413.7i		−	0.521965i	0.965344	−	0.260983i	$-0.0840465\pi$
$828$	1527.48	−	9437.35i	0.0641107	−	0.396100i
$829$		−	33996.1i		−	1.42429i	−0.702034	−	0.712144i	$-0.747725\pi$
$829$		−	33996.1i		−	1.42429i	0.702034	−	0.712144i	$-0.252275\pi$
$830$		−	4523.86i		−	0.189187i
$831$	−14163.1	−	1138.77i	−0.591228	−	0.0475373i
$832$		−	232.987i		−	0.00970838i
$833$	6799.21	+	20364.2i	0.282807	+	0.847031i
$834$	−16214.9	−	1303.75i	−0.673233	−	0.0541308i
$835$	8371.35			0.346949
$836$	55275.3			2.28676
$837$	6115.82	−	24916.4i	0.252561	−	1.02896i
$838$			21462.5i			0.884738i
$839$	31623.9			1.30129			0.650643	−	0.759384i	$-0.274500\pi$
$839$	31623.9			1.30129			0.650643	+	0.759384i	$0.274500\pi$
$840$	−7183.14	−	6105.85i	−0.295050	−	0.250800i
$841$	16042.8			0.657786
$842$			6052.55i			0.247725i
$843$	−234.009	+	2910.40i	−0.00956072	+	0.118908i
$844$	18089.8			0.737770
$845$	10951.8			0.445860
$846$	−949.052	+	5863.59i	−0.0385686	+	0.238291i
$847$	35339.1	−	49055.8i	1.43361	−	1.99006i
$848$		−	9706.80i		−	0.393081i
$849$	130.063	−	1617.61i	0.00525765	−	0.0653902i
$850$		−	2181.02i		−	0.0880098i
$851$			19902.8i			0.801713i
$852$	−203.176	+	2526.93i	−0.00816983	+	0.101609i
$853$			8122.18i			0.326024i	0.986624	+	0.163012i	$0.0521209\pi$
$853$			8122.18i			0.326024i	−0.986624	+	0.163012i	$0.947879\pi$
$854$	−6511.44	+	9038.84i	−0.260910	+	0.362181i
$855$	−2903.53	+	17939.1i	−0.116139	+	0.717548i
$856$	−10079.7			−0.402472
$857$	−32466.5			−1.29409			−0.647045	−	0.762451i	$-0.723996\pi$
$857$	−32466.5			−1.29409			−0.647045	+	0.762451i	$0.723996\pi$
$858$	−101.465	+	1261.93i	−0.00403725	+	0.0502118i
$859$		−	36463.5i		−	1.44833i	−0.689625	−	0.724166i	$-0.742225\pi$
$859$		−	36463.5i		−	1.44833i	0.689625	−	0.724166i	$-0.257775\pi$
$860$	−2688.93			−0.106618
$861$	−4187.17	+	4925.94i	−0.165736	+	0.194977i
$862$	4412.53			0.174352
$863$			27677.6i			1.09172i	0.837876	+	0.545860i	$0.183797\pi$
$863$			27677.6i			1.09172i	−0.837876	+	0.545860i	$0.816203\pi$
$864$	−6227.94	+	25373.2i	−0.245230	+	0.999090i
$865$	−8706.76			−0.342241
$866$	16478.6			0.646612
$867$	−5154.43	−	414.438i	−0.201907	−	0.0162342i
$868$	16645.7	+	11991.3i	0.650911	+	0.468906i
$869$			44603.9i			1.74118i
$870$	3297.58	+	265.140i	0.128504	+	0.0103323i
$871$			2087.37i			0.0812030i
$872$			31899.4i			1.23882i
$873$	−3510.79	+	21691.0i	−0.136108	+	0.840925i
$874$			10967.2i			0.424454i
$875$	−1353.16	+	1878.39i	−0.0522802	+	0.0725726i
$876$	−1024.37	+	12740.2i	−0.0395093	+	0.491383i
$877$	21309.8			0.820504			0.410252	−	0.911972i	$-0.365441\pi$
$877$	21309.8			0.820504			0.410252	+	0.911972i	$0.365441\pi$
$878$	16606.8			0.638330
$879$	−26876.2	−	2160.96i	−1.03130	−	0.0829208i
$880$		−	7168.92i		−	0.274618i
$881$	7499.34			0.286787			0.143393	−	0.989666i	$-0.454199\pi$
$881$	7499.34			0.286787			0.143393	+	0.989666i	$0.454199\pi$
$882$	12739.3	−	2079.14i	0.486344	−	0.0793743i
$883$	−21250.7			−0.809902			−0.404951	−	0.914338i	$-0.632711\pi$
$883$	−21250.7			−0.809902			−0.404951	+	0.914338i	$0.632711\pi$
$884$		−	977.680i		−	0.0371979i
$885$	−15256.3	−	1226.68i	−0.579476	−	0.0465924i
$886$	11187.1			0.424195
$887$	24278.0			0.919024			0.459512	−	0.888171i	$-0.348024\pi$
$887$	24278.0			0.919024			0.459512	+	0.888171i	$0.348024\pi$
$888$	2778.16	−	34552.3i	0.104987	−	1.30574i
$889$	−16243.8	+	22548.7i	−0.612821	+	0.850686i
$890$		−	4185.37i		−	0.157633i
$891$	15589.0	−	46895.8i	0.586141	−	1.76326i
$892$			34338.7i			1.28895i
$893$			21247.1i			0.796202i
$894$	−2121.90	−	170.610i	−0.0793813	−	0.00638260i
$895$			8333.81i			0.311250i
$896$	−20494.7	−	14764.1i	−0.764152	−	0.550484i
$897$	780.715	+	62.7729i	0.0290606	+	0.00233659i
$898$	21275.8			0.790628
$899$	−16706.6			−0.619797
$900$	4036.19	+	653.277i	0.149488	+	0.0241954i
$901$			28726.4i			1.06217i
$902$	6347.57			0.234314
$903$	5533.52	−	6509.84i	0.203925	−	0.239905i
$904$	−15121.5			−0.556342
$905$		−	20949.8i		−	0.769498i
$906$	552.158	−	6867.27i	0.0202475	−	0.251821i
$907$	−38164.2			−1.39716			−0.698579	−	0.715533i	$-0.746184\pi$
$907$	−38164.2			−1.39716			−0.698579	+	0.715533i	$0.746184\pi$
$908$	−10771.6			−0.393687
$909$	7834.13	+	1267.99i	0.285855	+	0.0462670i
$910$	194.535	−	270.043i	0.00708656	−	0.00983718i
$911$		−	27030.1i		−	0.983038i	−0.870867	−	0.491519i	$-0.836442\pi$
$911$		−	27030.1i		−	0.983038i	0.870867	−	0.491519i	$-0.163558\pi$
$912$	−1185.66	+	14746.3i	−0.0430496	+	0.535414i
$913$			44005.7i			1.59515i
$914$		−	1563.69i		−	0.0565888i
$915$	898.613	−	11176.2i	0.0324669	−	0.403796i
$916$			8200.19i			0.295788i
$917$	−19924.5	+	27658.1i	−0.717519	+	0.996022i
$918$	2917.64	−	11886.7i	0.104898	−	0.427364i
$919$	14738.9			0.529045			0.264523	−	0.964380i	$-0.414786\pi$
$919$	14738.9			0.529045			0.264523	+	0.964380i	$0.414786\pi$
$920$	5726.50			0.205214
$921$	135.161	−	1681.02i	0.00483573	−	0.0601426i
$922$			10692.8i			0.381940i
$923$	−207.692			−0.00740656
$924$	30108.8	+	25593.2i	1.07198	+	0.911206i
$925$	−8512.06			−0.302567
$926$			4866.06i			0.172688i
$927$	−2842.82	+	17564.0i	−0.100723	+	0.622306i
$928$	17012.9			0.601806
$929$	28651.5			1.01187			0.505933	−	0.862573i	$-0.331148\pi$
$929$	28651.5			1.01187			0.505933	+	0.862573i	$0.331148\pi$
$930$	6600.75	+	530.729i	0.232739	+	0.0187132i
$931$	43795.1	−	14622.4i	1.54171	−	0.514746i
$932$		−	13426.8i		−	0.471900i
$933$	35645.3	+	2866.04i	1.25078	+	0.100568i
$934$			6297.83i			0.220633i
$935$			21215.8i			0.742064i
$936$	−1346.60	−	217.955i	−0.0470247	−	0.00761119i
$937$			40156.3i			1.40005i	0.714117	+	0.700026i	$0.246828\pi$
$937$			40156.3i			1.40005i	−0.714117	+	0.700026i	$0.753172\pi$
$938$	−16954.3	−	12213.6i	−0.590167	−	0.425148i
$939$	4337.13	−	53941.5i	0.150732	−	1.87467i
$940$	4780.48			0.165874
$941$	−16366.2			−0.566973			−0.283487	−	0.958976i	$-0.591491\pi$
$941$	−16366.2			−0.566973			−0.283487	+	0.958976i	$0.591491\pi$
$942$	12297.8	+	988.795i	0.425354	+	0.0342003i
$943$		−	3927.03i		−	0.135611i
$944$	−12459.9			−0.429593
$945$	−9887.61	+	8427.15i	−0.340364	+	0.290090i
$946$	−8388.59			−0.288305
$947$			33729.1i			1.15739i	0.815544	+	0.578695i	$0.196438\pi$
$947$			33729.1i			1.15739i	−0.815544	+	0.578695i	$0.803562\pi$
$948$	−20643.0	−	1659.79i	−0.707229	−	0.0568643i
$949$	−1047.13			−0.0358181
$950$	−4690.50			−0.160189
$951$	979.255	−	12179.1i	0.0333907	−	0.415285i
$952$	18428.8	+	13275.9i	0.627397	+	0.451967i
$953$		−	4151.70i		−	0.141120i	−0.997508	−	0.0705598i	$-0.977521\pi$
$953$		−	4151.70i		−	0.141120i	0.997508	−	0.0705598i	$-0.0224785\pi$
$954$	17049.2	+	2759.50i	0.578603	+	0.0936499i
$955$			19292.9i			0.653721i
$956$			27539.5i			0.931685i
$957$	−32077.0	−	2579.13i	−1.08349	−	0.0871176i
$958$		−	25912.3i		−	0.873892i
$959$	−26887.7	−	19369.5i	−0.905371	−	0.652215i
$960$	−2339.88	−	188.136i	−0.0786658	−	0.00632507i
$961$	−3650.61			−0.122541
$962$	1223.72			0.0410129
$963$	−2219.32	+	13711.8i	−0.0742644	+	0.458833i
$964$		−	215.543i		−	0.00720143i
$965$	5647.65			0.188398
$966$	−5077.98	+	5973.92i	−0.169132	+	0.198973i
$967$	−50915.8			−1.69322			−0.846609	−	0.532216i	$-0.821360\pi$
$967$	−50915.8			−1.69322			−0.846609	+	0.532216i	$0.821360\pi$
$968$		−	63961.1i		−	2.12375i
$969$	3508.87	−	43640.3i	0.116327	−	1.44678i
$970$	−5671.49			−0.187733
$971$	22112.0			0.730801			0.365400	−	0.930850i	$-0.380932\pi$
$971$	22112.0			0.730801			0.365400	+	0.930850i	$0.380932\pi$
$972$	21123.6	+	8959.77i	0.697057	+	0.295663i
$973$	−33752.8	−	24315.0i	−1.11209	−	0.801134i
$974$			87.1037i			0.00286548i
$975$	−26.8468	+	333.898i	−0.000881833	+	0.0109675i
$976$		−	9127.64i		−	0.299353i
$977$		−	14762.3i		−	0.483407i	−0.970350	−	0.241704i	$-0.922294\pi$
$977$		−	14762.3i		−	0.483407i	0.970350	−	0.241704i	$-0.0777061\pi$
$978$	−1009.01	+	12549.2i	−0.0329904	+	0.410306i
$979$			40712.9i			1.32910i
$980$	−3289.94	−	9853.65i	−0.107238	−	0.321187i
$981$	43394.1	+	7023.55i	1.41230	+	0.228588i
$982$	16324.1			0.530471
$983$	−21515.6			−0.698110			−0.349055	−	0.937102i	$-0.613497\pi$
$983$	−21515.6			−0.698110			−0.349055	+	0.937102i	$0.613497\pi$
$984$	−548.160	+	6817.54i	−0.0177588	+	0.220869i
$985$		−	18966.8i		−	0.613535i
$986$	−7970.13			−0.257424
$987$	−9837.71	+	11573.4i	−0.317262	+	0.373239i
$988$	−2102.60			−0.0677050
$989$			5189.73i			0.166859i
$990$	12591.6	+	2038.02i	0.404230	+	0.0654266i
$991$	−25694.9			−0.823639			−0.411820	−	0.911265i	$-0.635107\pi$
$991$	−25694.9			−0.823639			−0.411820	+	0.911265i	$0.635107\pi$
$992$	34054.7			1.08996
$993$	604.504	+	48.6047i	0.0193186	+	0.00155330i
$994$	1215.25	−	1686.94i	0.0387779	−	0.0538294i
$995$			13582.6i			0.432761i
$996$	−20366.1	−	1637.52i	−0.647917	−	0.0520953i
$997$		−	37820.6i		−	1.20140i	−0.799476	−	0.600698i	$-0.794890\pi$
$997$		−	37820.6i		−	1.20140i	0.799476	−	0.600698i	$-0.205110\pi$
$998$		−	15089.4i		−	0.478605i
$999$	−46391.3	−	11386.9i	−1.46922	−	0.360627i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.b.b.41.10	yes	16
3.2	odd	2		105.4.b.a.41.7	✓	16
7.6	odd	2		105.4.b.a.41.10	yes	16
21.20	even	2	inner	105.4.b.b.41.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.b.a.41.7	✓	16	3.2	odd	2
105.4.b.a.41.10	yes	16	7.6	odd	2
105.4.b.b.41.7	yes	16	21.20	even	2	inner
105.4.b.b.41.10	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.39379i q^{2} +(5.17944 + 0.416449i) q^{3} +6.05735 q^{4} +5.00000 q^{5} +(-0.580442 + 7.21904i) q^{6} +(-10.8253 + 15.0271i) q^{7} +19.5930i q^{8} +(26.6531 + 4.31394i) q^{9} +O(q^{10})\)	\(q+1.39379i q^{2} +(5.17944 + 0.416449i) q^{3} +6.05735 q^{4} +5.00000 q^{5} +(-0.580442 + 7.21904i) q^{6} +(-10.8253 + 15.0271i) q^{7} +19.5930i q^{8} +(26.6531 + 4.31394i) q^{9} +6.96894i q^{10} -67.7901i q^{11} +(31.3737 + 2.52258i) q^{12} +2.57864i q^{13} +(-20.9446 - 15.0882i) q^{14} +(25.8972 + 2.08225i) q^{15} +21.1504 q^{16} -62.5926 q^{17} +(-6.01273 + 37.1488i) q^{18} +134.611i q^{19} +30.2868 q^{20} +(-62.3269 + 73.3237i) q^{21} +94.4850 q^{22} -58.4546i q^{23} +(-8.15948 + 101.481i) q^{24} +25.0000 q^{25} -3.59408 q^{26} +(136.252 + 33.4435i) q^{27} +(-65.5726 + 91.0244i) q^{28} -91.3578i q^{29} +(-2.90221 + 36.0952i) q^{30} -182.870i q^{31} +186.223i q^{32} +(28.2311 - 351.114i) q^{33} -87.2408i q^{34} +(-54.1264 + 75.1354i) q^{35} +(161.447 + 26.1311i) q^{36} -340.482 q^{37} -187.620 q^{38} +(-1.07387 + 13.3559i) q^{39} +97.9649i q^{40} +67.1808 q^{41} +(-102.198 - 86.8705i) q^{42} -88.7823 q^{43} -410.628i q^{44} +(133.266 + 21.5697i) q^{45} +81.4734 q^{46} +157.841 q^{47} +(109.547 + 8.80805i) q^{48} +(-108.626 - 325.345i) q^{49} +34.8447i q^{50} +(-324.194 - 26.0666i) q^{51} +15.6198i q^{52} -458.943i q^{53} +(-46.6131 + 189.906i) q^{54} -338.950i q^{55} +(-294.425 - 212.100i) q^{56} +(-56.0588 + 697.211i) q^{57} +127.333 q^{58} -589.112 q^{59} +(156.868 + 12.6129i) q^{60} -431.560i q^{61} +254.883 q^{62} +(-353.354 + 353.819i) q^{63} -90.3525 q^{64} +12.8932i q^{65} +(489.379 + 39.3482i) q^{66} +809.483 q^{67} -379.145 q^{68} +(24.3434 - 302.762i) q^{69} +(-104.723 - 75.4408i) q^{70} +80.5430i q^{71} +(-84.5230 + 522.214i) q^{72} +406.079i q^{73} -474.560i q^{74} +(129.486 + 10.4112i) q^{75} +815.389i q^{76} +(1018.69 + 733.847i) q^{77} +(-18.6153 - 1.49675i) q^{78} -657.971 q^{79} +105.752 q^{80} +(691.780 + 229.960i) q^{81} +93.6358i q^{82} -649.146 q^{83} +(-377.536 + 444.147i) q^{84} -312.963 q^{85} -123.744i q^{86} +(38.0459 - 473.182i) q^{87} +1328.21 q^{88} -600.574 q^{89} +(-30.0636 + 185.744i) q^{90} +(-38.7495 - 27.9145i) q^{91} -354.080i q^{92} +(76.1562 - 947.166i) q^{93} +219.996i q^{94} +673.057i q^{95} +(-77.5524 + 964.530i) q^{96} +813.824i q^{97} +(453.462 - 151.402i) q^{98} +(292.443 - 1806.82i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3} - 64 q^{4} + 80 q^{5} + 28 q^{6} - 4 q^{7} - 22 q^{9}+O(q^{10}) \) 16 * q + 2 * q^3 - 64 * q^4 + 80 * q^5 + 28 * q^6 - 4 * q^7 - 22 * q^9	\( 16 q + 2 q^{3} - 64 q^{4} + 80 q^{5} + 28 q^{6} - 4 q^{7} - 22 q^{9} + 66 q^{12} + 90 q^{14} + 10 q^{15} + 376 q^{16} + 72 q^{17} - 182 q^{18} - 320 q^{20} - 70 q^{21} - 276 q^{22} - 526 q^{24} + 400 q^{25} - 696 q^{26} + 128 q^{27} + 10 q^{28} + 140 q^{30} + 502 q^{33} - 20 q^{35} + 996 q^{36} - 812 q^{37} + 1200 q^{38} - 594 q^{39} + 936 q^{41} - 974 q^{42} - 548 q^{43} - 110 q^{45} + 1224 q^{46} - 912 q^{47} - 1850 q^{48} + 328 q^{49} + 750 q^{51} + 2950 q^{54} - 1254 q^{56} + 432 q^{57} + 576 q^{58} + 552 q^{59} + 330 q^{60} + 1860 q^{62} + 362 q^{63} - 4000 q^{64} - 1378 q^{66} + 1004 q^{67} - 3828 q^{68} - 1988 q^{69} + 450 q^{70} + 1988 q^{72} + 50 q^{75} - 1152 q^{77} + 1446 q^{78} + 1292 q^{79} + 1880 q^{80} - 2950 q^{81} + 1752 q^{83} - 420 q^{84} + 360 q^{85} - 1910 q^{87} - 912 q^{88} - 6096 q^{89} - 910 q^{90} - 552 q^{91} - 1080 q^{93} + 9546 q^{96} + 4824 q^{98} + 2530 q^{99}+O(q^{100}) \) 16 * q + 2 * q^3 - 64 * q^4 + 80 * q^5 + 28 * q^6 - 4 * q^7 - 22 * q^9 + 66 * q^12 + 90 * q^14 + 10 * q^15 + 376 * q^16 + 72 * q^17 - 182 * q^18 - 320 * q^20 - 70 * q^21 - 276 * q^22 - 526 * q^24 + 400 * q^25 - 696 * q^26 + 128 * q^27 + 10 * q^28 + 140 * q^30 + 502 * q^33 - 20 * q^35 + 996 * q^36 - 812 * q^37 + 1200 * q^38 - 594 * q^39 + 936 * q^41 - 974 * q^42 - 548 * q^43 - 110 * q^45 + 1224 * q^46 - 912 * q^47 - 1850 * q^48 + 328 * q^49 + 750 * q^51 + 2950 * q^54 - 1254 * q^56 + 432 * q^57 + 576 * q^58 + 552 * q^59 + 330 * q^60 + 1860 * q^62 + 362 * q^63 - 4000 * q^64 - 1378 * q^66 + 1004 * q^67 - 3828 * q^68 - 1988 * q^69 + 450 * q^70 + 1988 * q^72 + 50 * q^75 - 1152 * q^77 + 1446 * q^78 + 1292 * q^79 + 1880 * q^80 - 2950 * q^81 + 1752 * q^83 - 420 * q^84 + 360 * q^85 - 1910 * q^87 - 912 * q^88 - 6096 * q^89 - 910 * q^90 - 552 * q^91 - 1080 * q^93 + 9546 * q^96 + 4824 * q^98 + 2530 * q^99

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