LMFDB - Embedded newform 105.4.b.b.41.9

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			41.9
Root			$0.948735i$ of defining polynomial
Character	$\chi$	$=$	105.41
Dual form			105.4.b.b.41.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.948735i q^{2} +(-4.24029 + 3.00332i) q^{3} +7.09990 q^{4} +5.00000 q^{5} +(-2.84936 - 4.02291i) q^{6} +(15.4514 - 10.2104i) q^{7} +14.3258i q^{8} +(8.96014 - 25.4699i) q^{9} +O(q^{10})$	\(q+0.948735i q^{2} +(-4.24029 + 3.00332i) q^{3} +7.09990 q^{4} +5.00000 q^{5} +(-2.84936 - 4.02291i) q^{6} +(15.4514 - 10.2104i) q^{7} +14.3258i q^{8} +(8.96014 - 25.4699i) q^{9} +4.74368i q^{10} +22.6742i q^{11} +(-30.1056 + 21.3233i) q^{12} +64.3163i q^{13} +(9.68701 + 14.6593i) q^{14} +(-21.2015 + 15.0166i) q^{15} +43.2078 q^{16} +9.57247 q^{17} +(24.1642 + 8.50080i) q^{18} +13.8330i q^{19} +35.4995 q^{20} +(-34.8534 + 89.7009i) q^{21} -21.5118 q^{22} +134.579i q^{23} +(-43.0250 - 60.7456i) q^{24} +25.0000 q^{25} -61.0191 q^{26} +(38.5007 + 134.910i) q^{27} +(109.704 - 72.4931i) q^{28} -194.631i q^{29} +(-14.2468 - 20.1146i) q^{30} -207.276i q^{31} +155.599i q^{32} +(-68.0978 - 96.1450i) q^{33} +9.08174i q^{34} +(77.2572 - 51.0522i) q^{35} +(63.6161 - 180.834i) q^{36} -171.473 q^{37} -13.1239 q^{38} +(-193.162 - 272.720i) q^{39} +71.6291i q^{40} +214.915 q^{41} +(-85.1024 - 33.0666i) q^{42} -322.180 q^{43} +160.984i q^{44} +(44.8007 - 127.350i) q^{45} -127.680 q^{46} +582.288 q^{47} +(-183.214 + 129.767i) q^{48} +(134.494 - 315.532i) q^{49} +23.7184i q^{50} +(-40.5901 + 28.7492i) q^{51} +456.639i q^{52} -534.126i q^{53} +(-127.994 + 36.5270i) q^{54} +113.371i q^{55} +(146.273 + 221.354i) q^{56} +(-41.5450 - 58.6560i) q^{57} +184.653 q^{58} -324.893 q^{59} +(-150.528 + 106.616i) q^{60} +32.4225i q^{61} +196.650 q^{62} +(-121.612 - 485.034i) q^{63} +198.040 q^{64} +321.581i q^{65} +(91.2162 - 64.6067i) q^{66} -781.863 q^{67} +67.9636 q^{68} +(-404.184 - 570.655i) q^{69} +(48.4350 + 73.2966i) q^{70} +357.938i q^{71} +(364.877 + 128.361i) q^{72} -925.788i q^{73} -162.682i q^{74} +(-106.007 + 75.0830i) q^{75} +98.2130i q^{76} +(231.513 + 350.348i) q^{77} +(258.739 - 183.260i) q^{78} +827.285 q^{79} +216.039 q^{80} +(-568.432 - 456.428i) q^{81} +203.897i q^{82} -131.055 q^{83} +(-247.455 + 636.867i) q^{84} +47.8624 q^{85} -305.664i q^{86} +(584.540 + 825.293i) q^{87} -324.826 q^{88} -505.040 q^{89} +(120.821 + 42.5040i) q^{90} +(656.698 + 993.779i) q^{91} +955.499i q^{92} +(622.515 + 878.909i) q^{93} +552.437i q^{94} +69.1650i q^{95} +(-467.314 - 659.786i) q^{96} -86.3424i q^{97} +(299.356 + 127.599i) q^{98} +(577.509 + 203.164i) 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 $

$2$			0.948735i			0.335429i	0.985836	+	0.167714i	$0.0536386\pi$
$2$			0.948735i			0.335429i	−0.985836	+	0.167714i	$0.946361\pi$
$3$	−4.24029	+	3.00332i	−0.816044	+	0.577989i
$3$	−4.24029	+	3.00332i	−0.816044	+	0.577989i
$4$	7.09990			0.887488
$5$	5.00000			0.447214
$5$	5.00000			0.447214
$6$	−2.84936	−	4.02291i	−0.193874	−	0.273725i
$7$	15.4514	−	10.2104i	0.834299	−	0.551312i
$7$	15.4514	−	10.2104i	0.834299	−	0.551312i
$8$			14.3258i			0.633117i
$9$	8.96014	−	25.4699i	0.331857	−	0.943330i
$10$			4.74368i			0.150008i
$11$			22.6742i			0.621501i	0.950491	+	0.310751i	$0.100580\pi$
$11$			22.6742i			0.621501i	−0.950491	+	0.310751i	$0.899420\pi$
$12$	−30.1056	+	21.3233i	−0.724229	+	0.512958i
$13$			64.3163i			1.37216i	0.727525	+	0.686082i	$0.240671\pi$
$13$			64.3163i			1.37216i	−0.727525	+	0.686082i	$0.759329\pi$
$14$	9.68701	+	14.6593i	0.184926	+	0.279848i
$15$	−21.2015	+	15.0166i	−0.364946	+	0.258485i
$16$	43.2078			0.675122
$17$	9.57247			0.136569			0.0682843	−	0.997666i	$-0.478248\pi$
$17$	9.57247			0.136569			0.0682843	+	0.997666i	$0.478248\pi$
$18$	24.1642	+	8.50080i	0.316420	+	0.111314i
$19$			13.8330i			0.167027i	0.996507	+	0.0835134i	$0.0266141\pi$
$19$			13.8330i			0.167027i	−0.996507	+	0.0835134i	$0.973386\pi$
$20$	35.4995			0.396897
$21$	−34.8534	+	89.7009i	−0.362173	+	0.932111i
$22$	−21.5118			−0.208469
$23$			134.579i			1.22007i	0.792373	+	0.610037i	$0.208845\pi$
$23$			134.579i			1.22007i	−0.792373	+	0.610037i	$0.791155\pi$
$24$	−43.0250	−	60.7456i	−0.365935	−	0.516652i
$25$	25.0000			0.200000
$26$	−61.0191			−0.460263
$27$	38.5007	+	134.910i	0.274424	+	0.961609i
$28$	109.704	−	72.4931i	0.740430	−	0.489283i
$29$		−	194.631i		−	1.24628i	−0.782111	−	0.623140i	$-0.785857\pi$
$29$		−	194.631i		−	1.24628i	0.782111	−	0.623140i	$-0.214143\pi$
$30$	−14.2468	−	20.1146i	−0.0867031	−	0.122413i
$31$		−	207.276i		−	1.20090i	−0.799664	−	0.600448i	$-0.794989\pi$
$31$		−	207.276i		−	1.20090i	0.799664	−	0.600448i	$-0.205011\pi$
$32$			155.599i			0.859573i
$33$	−68.0978	−	96.1450i	−0.359221	−	0.507173i
$34$			9.08174i			0.0458090i
$35$	77.2572	−	51.0522i	0.373110	−	0.246554i
$36$	63.6161	−	180.834i	0.294519	−	0.837193i
$37$	−171.473			−0.761891			−0.380946	−	0.924597i	$-0.624401\pi$
$37$	−171.473			−0.761891			−0.380946	+	0.924597i	$0.624401\pi$
$38$	−13.1239			−0.0560256
$39$	−193.162	−	272.720i	−0.793096	−	1.11975i
$40$			71.6291i			0.283139i
$41$	214.915			0.818635			0.409318	−	0.912392i	$-0.365767\pi$
$41$	214.915			0.818635			0.409318	+	0.912392i	$0.365767\pi$
$42$	−85.1024	−	33.0666i	−0.312657	−	0.121483i
$43$	−322.180			−1.14260			−0.571302	−	0.820740i	$-0.693562\pi$
$43$	−322.180			−1.14260			−0.571302	+	0.820740i	$0.693562\pi$
$44$			160.984i			0.551575i
$45$	44.8007	−	127.350i	0.148411	−	0.421870i
$46$	−127.680			−0.409248
$47$	582.288			1.80714			0.903569	−	0.428443i	$-0.140938\pi$
$47$	582.288			1.80714			0.903569	+	0.428443i	$0.140938\pi$
$48$	−183.214	+	129.767i	−0.550930	+	0.390213i
$49$	134.494	−	315.532i	0.392110	−	0.919918i
$50$			23.7184i			0.0670857i
$51$	−40.5901	+	28.7492i	−0.111446	+	0.0789351i
$52$			456.639i			1.21778i
$53$		−	534.126i		−	1.38430i	−0.721754	−	0.692150i	$-0.756664\pi$
$53$		−	534.126i		−	1.38430i	0.721754	−	0.692150i	$-0.243336\pi$
$54$	−127.994	+	36.5270i	−0.322551	+	0.0920498i
$55$			113.371i			0.277944i
$56$	146.273	+	221.354i	0.349045	+	0.528209i
$57$	−41.5450	−	58.6560i	−0.0965397	−	0.136301i
$58$	184.653			0.418038
$59$	−324.893			−0.716907			−0.358454	−	0.933548i	$-0.616696\pi$
$59$	−324.893			−0.716907			−0.358454	+	0.933548i	$0.616696\pi$
$60$	−150.528	+	106.616i	−0.323885	+	0.229402i
$61$			32.4225i			0.0680538i	0.999421	+	0.0340269i	$0.0108332\pi$
$61$			32.4225i			0.0680538i	−0.999421	+	0.0340269i	$0.989167\pi$
$62$	196.650			0.402815
$63$	−121.612	−	485.034i	−0.243201	−	0.969976i
$64$	198.040			0.386797
$65$			321.581i			0.613650i
$66$	91.2162	−	64.6067i	0.170120	−	0.120493i
$67$	−781.863			−1.42567			−0.712834	−	0.701333i	$-0.752589\pi$
$67$	−781.863			−1.42567			−0.712834	+	0.701333i	$0.752589\pi$
$68$	67.9636			0.121203
$69$	−404.184	−	570.655i	−0.705190	−	0.995635i
$70$	48.4350	+	73.2966i	0.0827013	+	0.125152i
$71$			357.938i			0.598302i	0.954206	+	0.299151i	$0.0967034\pi$
$71$			357.938i			0.598302i	−0.954206	+	0.299151i	$0.903297\pi$
$72$	364.877	+	128.361i	0.597238	+	0.210104i
$73$		−	925.788i		−	1.48432i	−0.670224	−	0.742159i	$-0.733802\pi$
$73$		−	925.788i		−	1.48432i	0.670224	−	0.742159i	$-0.266198\pi$
$74$		−	162.682i		−	0.255560i
$75$	−106.007	+	75.0830i	−0.163209	+	0.115598i
$76$			98.2130i			0.148234i
$77$	231.513	+	350.348i	0.342641	+	0.518518i
$78$	258.739	−	183.260i	0.375595	−	0.266027i
$79$	827.285			1.17819			0.589094	−	0.808064i	$-0.299485\pi$
$79$	827.285			1.17819			0.589094	+	0.808064i	$0.299485\pi$
$80$	216.039			0.301924
$81$	−568.432	−	456.428i	−0.779742	−	0.626101i
$82$			203.897i			0.274594i
$83$	−131.055			−0.173315			−0.0866575	−	0.996238i	$-0.527619\pi$
$83$	−131.055			−0.173315			−0.0866575	+	0.996238i	$0.527619\pi$
$84$	−247.455	+	636.867i	−0.321424	+	0.827237i
$85$	47.8624			0.0610753
$86$		−	305.664i		−	0.383262i
$87$	584.540	+	825.293i	0.720336	+	1.01702i
$88$	−324.826			−0.393483
$89$	−505.040			−0.601508			−0.300754	−	0.953702i	$-0.597238\pi$
$89$	−505.040			−0.601508			−0.300754	+	0.953702i	$0.597238\pi$
$90$	120.821	+	42.5040i	0.141507	+	0.0497813i
$91$	656.698	+	993.779i	0.756490	+	1.14479i
$92$			955.499i			1.08280i
$93$	622.515	+	878.909i	0.694105	+	0.979985i
$94$			552.437i			0.606166i
$95$			69.1650i			0.0746967i
$96$	−467.314	−	659.786i	−0.496824	−	0.701449i
$97$		−	86.3424i		−	0.0903788i	−0.998978	−	0.0451894i	$-0.985611\pi$
$97$		−	86.3424i		−	0.0903788i	0.998978	−	0.0451894i	$-0.0143891\pi$
$98$	299.356	+	127.599i	0.308567	+	0.131525i
$99$	577.509	+	203.164i	0.586281	+	0.206250i
$100$	177.498			0.177498
$101$	−895.757			−0.882486			−0.441243	−	0.897388i	$-0.645462\pi$
$101$	−895.757			−0.882486			−0.441243	+	0.897388i	$0.645462\pi$
$102$	−27.2754	−	38.5092i	−0.0264771	−	0.0373822i
$103$			486.200i			0.465114i	0.972583	+	0.232557i	$0.0747092\pi$
$103$			486.200i			0.465114i	−0.972583	+	0.232557i	$0.925291\pi$
$104$	−921.383			−0.868740
$105$	−174.267	+	448.504i	−0.161969	+	0.416853i
$106$	506.744			0.464334
$107$			728.790i			0.658456i	0.944250	+	0.329228i	$0.106788\pi$
$107$			728.790i			0.658456i	−0.944250	+	0.329228i	$0.893212\pi$
$108$	273.351	+	957.847i	0.243548	+	0.853416i
$109$	−1064.25			−0.935197			−0.467599	−	0.883941i	$-0.654881\pi$
$109$	−1064.25			−0.935197			−0.467599	+	0.883941i	$0.654881\pi$
$110$	−107.559			−0.0932303
$111$	727.095	−	514.988i	0.621737	−	0.440365i
$112$	667.623	−	441.171i	0.563254	−	0.372203i
$113$		−	1991.46i		−	1.65788i	−0.559335	−	0.828941i	$-0.688944\pi$
$113$		−	1991.46i		−	1.65788i	0.559335	−	0.828941i	$-0.311056\pi$
$114$	55.6490	−	39.4152i	0.0457194	−	0.0323822i
$115$			672.896i			0.545634i
$116$		−	1381.86i		−	1.10606i
$117$	1638.13	+	576.283i	1.29440	+	0.455362i
$118$		−	308.238i		−	0.240471i
$119$	147.908	−	97.7392i	0.113939	−	0.0752919i
$120$	−215.125	−	303.728i	−0.163651	−	0.231054i
$121$	816.883			0.613736
$122$	−30.7604			−0.0228272
$123$	−911.301	+	645.458i	−0.668043	+	0.473162i
$124$		−	1471.64i		−	1.06578i
$125$	125.000			0.0894427
$126$	460.168	−	115.378i	0.325358	−	0.0815766i
$127$	−1019.14			−0.712081			−0.356041	−	0.934471i	$-0.615874\pi$
$127$	−1019.14			−0.712081			−0.356041	+	0.934471i	$0.615874\pi$
$128$			1432.68i			0.989315i
$129$	1366.14	−	967.610i	0.932416	−	0.660413i
$130$	−305.096			−0.205836
$131$	−2187.34			−1.45885			−0.729424	−	0.684062i	$-0.760212\pi$
$131$	−2187.34			−1.45885			−0.729424	+	0.684062i	$0.760212\pi$
$132$	−483.487	−	682.620i	−0.318804	−	0.450110i
$133$	141.241	+	213.740i	0.0920839	+	0.139350i
$134$		−	741.781i		−	0.478210i
$135$	192.503	+	674.550i	0.122726	+	0.430044i
$136$			137.133i			0.0864639i
$137$		−	2492.50i		−	1.55437i	−0.629274	−	0.777184i	$-0.716647\pi$
$137$		−	2492.50i		−	1.55437i	0.629274	−	0.777184i	$-0.283353\pi$
$138$	541.401	−	383.464i	0.333964	−	0.236541i
$139$		−	1432.68i		−	0.874234i	−0.899405	−	0.437117i	$-0.856000\pi$
$139$		−	1432.68i		−	0.874234i	0.899405	−	0.437117i	$-0.144000\pi$
$140$	548.518	−	362.466i	0.331130	−	0.218814i
$141$	−2469.07	+	1748.80i	−1.47470	+	1.04451i
$142$	−339.588			−0.200688
$143$	−1458.32			−0.852802
$144$	387.148	−	1100.50i	0.224044	−	0.636863i
$145$		−	973.156i		−	0.557353i
$146$	878.327			0.497883
$147$	377.351	+	1741.88i	0.211724	+	0.977330i
$148$	−1217.44			−0.676169
$149$		−	1519.04i		−	0.835198i	−0.908632	−	0.417599i	$-0.862872\pi$
$149$		−	1519.04i		−	0.835198i	0.908632	−	0.417599i	$-0.137128\pi$
$150$	−71.2339	−	100.573i	−0.0387748	−	0.0547449i
$151$	83.5248			0.0450142			0.0225071	−	0.999747i	$-0.492835\pi$
$151$	83.5248			0.0450142			0.0225071	+	0.999747i	$0.492835\pi$
$152$	−198.169			−0.105748
$153$	85.7707	−	243.810i	0.0453212	−	0.128829i
$154$	−332.388	+	219.645i	−0.173926	+	0.114932i
$155$		−	1036.38i		−	0.537057i
$156$	−1371.43	−	1936.28i	−0.703863	−	0.993761i
$157$		−	1716.82i		−	0.872719i	−0.899772	−	0.436360i	$-0.856268\pi$
$157$		−	1716.82i		−	0.872719i	0.899772	−	0.436360i	$-0.143732\pi$
$158$			784.875i			0.395198i
$159$	1604.15	+	2264.85i	0.800110	+	1.12965i
$160$			777.996i			0.384413i
$161$	1374.11	+	2079.44i	0.672642	+	1.01791i
$162$	433.029	−	539.291i	0.210012	−	0.261548i
$163$	2329.29			1.11929			0.559643	−	0.828734i	$-0.310938\pi$
$163$	2329.29			1.11929			0.559643	+	0.828734i	$0.310938\pi$
$164$	1525.87			0.726529
$165$	−340.489	−	480.725i	−0.160649	−	0.226815i
$166$		−	124.336i		−	0.0581348i
$167$	−774.390			−0.358827			−0.179413	−	0.983774i	$-0.557420\pi$
$167$	−774.390			−0.358827			−0.179413	+	0.983774i	$0.557420\pi$
$168$	−1285.04	−	499.303i	−0.590136	−	0.229298i
$169$	−1939.58			−0.882832
$170$			45.4087i			0.0204864i
$171$	352.325	+	123.946i	0.157561	+	0.0554290i
$172$	−2287.45			−1.01405
$173$	−1593.30			−0.700212			−0.350106	−	0.936710i	$-0.613854\pi$
$173$	−1593.30			−0.700212			−0.350106	+	0.936710i	$0.613854\pi$
$174$	−782.984	+	554.573i	−0.341137	+	0.241621i
$175$	386.286	−	255.261i	0.166860	−	0.110262i
$176$			979.701i			0.419589i
$177$	1377.64	−	975.759i	0.585028	−	0.414365i
$178$		−	479.150i		−	0.201763i
$179$			1433.50i			0.598576i	0.954163	+	0.299288i	$0.0967492\pi$
$179$			1433.50i			0.598576i	−0.954163	+	0.299288i	$0.903251\pi$
$180$	318.080	−	904.169i	0.131713	−	0.374404i
$181$			4655.24i			1.91172i	0.293825	+	0.955859i	$0.405072\pi$
$181$			4655.24i			1.91172i	−0.293825	+	0.955859i	$0.594928\pi$
$182$	−942.833	+	623.032i	−0.383997	+	0.253748i
$183$	−97.3752	−	137.481i	−0.0393343	−	0.0555349i
$184$	−1927.96			−0.772450
$185$	−857.365			−0.340728
$186$	−833.852	+	590.602i	−0.328715	+	0.232823i
$187$			217.048i			0.0848775i
$188$	4134.19			1.60381
$189$	1972.38	+	1691.44i	0.759098	+	0.650976i
$190$	−65.6193			−0.0250554
$191$		−	1104.23i		−	0.418322i	−0.977881	−	0.209161i	$-0.932927\pi$
$191$		−	1104.23i		−	0.418322i	0.977881	−	0.209161i	$-0.0670732\pi$
$192$	−839.747	+	594.777i	−0.315643	+	0.223564i
$193$	1575.84			0.587726			0.293863	−	0.955848i	$-0.405059\pi$
$193$	1575.84			0.587726			0.293863	+	0.955848i	$0.405059\pi$
$194$	81.9161			0.0303156
$195$	−965.812	−	1363.60i	−0.354683	−	0.500766i
$196$	954.892	−	2240.25i	0.347993	−	0.816416i
$197$			373.569i			0.135105i	0.997716	+	0.0675525i	$0.0215190\pi$
$197$			373.569i			0.135105i	−0.997716	+	0.0675525i	$0.978481\pi$
$198$	−192.748	+	547.903i	−0.0691820	+	0.196655i
$199$		−	419.925i		−	0.149586i	−0.997199	−	0.0747931i	$-0.976170\pi$
$199$		−	419.925i		−	0.149586i	0.997199	−	0.0747931i	$-0.0238296\pi$
$200$			358.145i			0.126623i
$201$	3315.33	−	2348.18i	1.16341	−	0.824021i
$202$		−	849.836i		−	0.296011i
$203$	−1987.27	−	3007.33i	−0.687089	−	1.03977i
$204$	−288.185	+	204.116i	−0.0989069	+	0.0700540i
$205$	1074.57			0.366105
$206$	−461.275			−0.156013
$207$	3427.72	+	1205.85i	1.15093	+	0.404890i
$208$			2778.96i			0.926378i
$209$	−313.652			−0.103807
$210$	−425.512	−	165.333i	−0.139824	−	0.0543289i
$211$	5139.58			1.67689			0.838443	−	0.544989i	$-0.183466\pi$
$211$	5139.58			1.67689			0.838443	+	0.544989i	$0.183466\pi$
$212$		−	3792.24i		−	1.22855i
$213$	−1075.00	−	1517.76i	−0.345812	−	0.488241i
$214$	−691.429			−0.220865
$215$	−1610.90			−0.510988
$216$	−1932.69	+	551.553i	−0.608811	+	0.173743i
$217$	−2116.37	−	3202.71i	−0.662069	−	1.00191i
$218$		−	1009.69i		−	0.313692i
$219$	2780.44	+	3925.61i	0.857920	+	1.21127i
$220$			804.921i			0.246672i
$221$			615.666i			0.187394i
$222$	488.587	+	689.821i	0.147711	+	0.208548i
$223$			2700.19i			0.810843i	0.914130	+	0.405422i	$0.132875\pi$
$223$			2700.19i			0.810843i	−0.914130	+	0.405422i	$0.867125\pi$
$224$	1588.74	+	2404.23i	0.473893	+	0.717141i
$225$	224.003	−	636.748i	0.0663714	−	0.188666i
$226$	1889.37			0.556101
$227$	−2992.08			−0.874852			−0.437426	−	0.899254i	$-0.644110\pi$
$227$	−2992.08			−0.874852			−0.437426	+	0.899254i	$0.644110\pi$
$228$	−294.965	−	416.452i	−0.0856778	−	0.120966i
$229$			3637.31i			1.04961i	0.851224	+	0.524803i	$0.175861\pi$
$229$			3637.31i			1.04961i	−0.851224	+	0.524803i	$0.824139\pi$
$230$	−638.400			−0.183021
$231$	−2033.89	−	790.271i	−0.579308	−	0.225091i
$232$	2788.25			0.789041
$233$			6001.00i			1.68729i	0.536901	+	0.843645i	$0.319595\pi$
$233$			6001.00i			1.68729i	−0.536901	+	0.843645i	$0.680405\pi$
$234$	−546.740	+	1554.15i	−0.152741	+	0.434180i
$235$	2911.44			0.808176
$236$	−2306.71			−0.636246
$237$	−3507.93	+	2484.60i	−0.961454	+	0.680980i
$238$	92.7286	+	140.326i	0.0252551	+	0.0382184i
$239$			5173.92i			1.40031i	0.713992	+	0.700153i	$0.246885\pi$
$239$			5173.92i			1.40031i	−0.713992	+	0.700153i	$0.753115\pi$
$240$	−916.068	+	648.834i	−0.246383	+	0.174509i
$241$			729.389i			0.194955i	0.995238	+	0.0974773i	$0.0310774\pi$
$241$			729.389i			0.194955i	−0.995238	+	0.0974773i	$0.968923\pi$
$242$			775.005i			0.205865i
$243$	3781.11	+	228.203i	0.998184	+	0.0602439i
$244$			230.197i			0.0603969i
$245$	672.469	−	1577.66i	0.175357	−	0.411400i
$246$	−612.369	−	864.584i	−0.158712	−	0.224081i
$247$	−889.688			−0.229188
$248$	2969.39			0.760308
$249$	555.711	−	393.600i	0.141433	−	0.100174i
$250$			118.592i			0.0300016i
$251$	6404.70			1.61060			0.805301	−	0.592866i	$-0.202004\pi$
$251$	6404.70			1.61060			0.805301	+	0.592866i	$0.202004\pi$
$252$	−863.433	−	3443.69i	−0.215838	−	0.860842i
$253$	−3051.47			−0.758278
$254$		−	966.897i		−	0.238852i
$255$	−202.950	+	143.746i	−0.0498402	+	0.0353009i
$256$	225.084			0.0549521
$257$	−4199.90			−1.01939			−0.509694	−	0.860356i	$-0.670241\pi$
$257$	−4199.90			−1.01939			−0.509694	+	0.860356i	$0.670241\pi$
$258$	918.006	+	1296.10i	0.221521	+	0.312759i
$259$	−2649.50	+	1750.81i	−0.635645	+	0.420040i
$260$			2283.20i			0.544607i
$261$	−4957.24	−	1743.92i	−1.17565	−	0.413586i
$262$		−	2075.21i		−	0.489339i
$263$		−	1003.82i		−	0.235353i	−0.993052	−	0.117677i	$-0.962455\pi$
$263$		−	1003.82i		−	0.235353i	0.993052	−	0.117677i	$-0.0375447\pi$
$264$	1377.36	−	975.556i	0.321100	−	0.227429i
$265$		−	2670.63i		−	0.619077i
$266$	−202.783	+	134.000i	−0.0467421	+	0.0308876i
$267$	2141.52	−	1516.80i	0.490857	−	0.347665i
$268$	−5551.15			−1.26526
$269$	7904.46			1.79161			0.895805	−	0.444447i	$-0.146600\pi$
$269$	7904.46			1.79161			0.895805	+	0.444447i	$0.146600\pi$
$270$	−639.969	+	182.635i	−0.144249	+	0.0411659i
$271$			2525.75i			0.566157i	0.959097	+	0.283079i	$0.0913557\pi$
$271$			2525.75i			0.566157i	−0.959097	+	0.283079i	$0.908644\pi$
$272$	413.605			0.0922004
$273$	−5769.22	−	2241.64i	−1.27901	−	0.496960i
$274$	2364.72			0.521379
$275$			566.854i			0.124300i
$276$	−2869.67	−	4051.59i	−0.625847	−	0.883614i
$277$	329.076			0.0713801			0.0356900	−	0.999363i	$-0.488637\pi$
$277$	329.076			0.0713801			0.0356900	+	0.999363i	$0.488637\pi$
$278$	1359.24			0.293243
$279$	−5279.29	−	1857.22i	−1.13284	−	0.398526i
$280$	731.364	+	1106.77i	0.156098	+	0.236222i
$281$		−	445.607i		−	0.0946002i	−0.998881	−	0.0473001i	$-0.984938\pi$
$281$		−	445.607i		−	0.0946002i	0.998881	−	0.0473001i	$-0.0150617\pi$
$282$	−1659.15	−	2342.50i	−0.350357	−	0.494658i
$283$		−	2885.26i		−	0.606047i	−0.952983	−	0.303023i	$-0.902004\pi$
$283$		−	2885.26i		−	0.606047i	0.952983	−	0.303023i	$-0.0979960\pi$
$284$			2541.32i			0.530985i
$285$	−207.725	−	293.280i	−0.0431739	−	0.0609558i
$286$		−	1383.56i		−	0.286054i
$287$	3320.74	−	2194.37i	0.682987	−	0.451324i
$288$	3963.10	+	1394.19i	0.810860	+	0.285255i
$289$	−4821.37			−0.981349
$290$	923.267			0.186952
$291$	259.314	+	366.117i	0.0522379	+	0.0737531i
$292$		−	6573.00i		−	1.31731i
$293$	7104.19			1.41649			0.708245	−	0.705967i	$-0.249487\pi$
$293$	7104.19			1.41649			0.708245	+	0.705967i	$0.249487\pi$
$294$	−1652.58	+	358.006i	−0.327824	+	0.0710181i
$295$	−1624.47			−0.320611
$296$		−	2456.49i		−	0.482366i
$297$	−3058.97	+	872.970i	−0.597641	+	0.170555i
$298$	1441.17			0.280149
$299$	−8655.63			−1.67414
$300$	−752.641	+	533.082i	−0.144846	+	0.102592i
$301$	−4978.14	+	3289.60i	−0.953274	+	0.629932i
$302$			79.2429i			0.0150991i
$303$	3798.27	−	2690.24i	0.720148	−	0.510068i
$304$			597.694i			0.112763i
$305$			162.113i			0.0304346i
$306$	231.311	+	81.3737i	0.0432130	+	0.0152020i
$307$		−	1618.65i		−	0.300916i	−0.988616	−	0.150458i	$-0.951925\pi$
$307$		−	1618.65i		−	0.300916i	0.988616	−	0.150458i	$-0.0480748\pi$
$308$	1643.72	+	2487.44i	0.304090	+	0.460178i
$309$	−1460.22	−	2061.63i	−0.268831	−	0.379554i
$310$	983.248			0.180144
$311$	2623.36			0.478318			0.239159	−	0.970980i	$-0.423128\pi$
$311$	2623.36			0.478318			0.239159	+	0.970980i	$0.423128\pi$
$312$	3906.93	−	2767.21i	0.708931	−	0.502123i
$313$		−	5619.16i		−	1.01474i	−0.861728	−	0.507371i	$-0.830618\pi$
$313$		−	5619.16i		−	1.01474i	0.861728	−	0.507371i	$-0.169382\pi$
$314$	1628.81			0.292735
$315$	−608.060	−	2425.17i	−0.108763	−	0.433786i
$316$	5873.64			1.04563
$317$		−	2281.14i		−	0.404169i	−0.979368	−	0.202084i	$-0.935228\pi$
$317$		−	2281.14i		−	0.404169i	0.979368	−	0.202084i	$-0.0647715\pi$
$318$	−2148.74	+	1521.92i	−0.378917	+	0.268380i
$319$	4413.10			0.774564
$320$	990.200			0.172981
$321$	−2188.79	−	3090.28i	−0.380581	−	0.537329i
$322$	−1972.84	+	1303.67i	−0.341435	+	0.225623i
$323$			132.416i			0.0228106i
$324$	−4035.81	−	3240.59i	−0.692011	−	0.555657i
$325$			1607.91i			0.274433i
$326$			2209.88i			0.375441i
$327$	4512.72	−	3196.28i	0.763162	−	0.540534i
$328$			3078.83i			0.518292i
$329$	8997.19	−	5945.42i	1.50769	−	0.996297i
$330$	456.081	−	323.034i	0.0760801	−	0.0538861i
$331$	−270.671			−0.0449468			−0.0224734	−	0.999747i	$-0.507154\pi$
$331$	−270.671			−0.0449468			−0.0224734	+	0.999747i	$0.507154\pi$
$332$	−930.477			−0.153815
$333$	−1536.42	+	4367.40i	−0.252839	+	0.718715i
$334$		−	734.691i		−	0.120361i
$335$	−3909.31			−0.637578
$336$	−1505.94	+	3875.78i	−0.244511	+	0.629289i
$337$	−4842.16			−0.782698			−0.391349	−	0.920242i	$-0.627991\pi$
$337$	−4842.16			−0.782698			−0.391349	+	0.920242i	$0.627991\pi$
$338$		−	1840.15i		−	0.296127i
$339$	5980.99	+	8444.37i	0.958238	+	1.35291i
$340$	339.818			0.0542036
$341$	4699.80			0.746359
$342$	−117.592	+	334.264i	−0.0185925	+	0.0528506i
$343$	−1143.60	−	6248.66i	−0.180025	−	0.983662i
$344$		−	4615.49i		−	0.723403i
$345$	−2020.92	−	2853.28i	−0.315370	−	0.445261i
$346$		−	1511.62i		−	0.234871i
$347$			9182.70i			1.42061i	0.703892	+	0.710307i	$0.251444\pi$
$347$			9182.70i			1.42061i	−0.703892	+	0.710307i	$0.748556\pi$
$348$	4150.17	+	5859.50i	0.639289	+	0.902592i
$349$		−	11353.5i		−	1.74138i	−0.491832	−	0.870690i	$-0.663673\pi$
$349$		−	11353.5i		−	1.74138i	0.491832	−	0.870690i	$-0.336327\pi$
$350$	242.175	+	366.483i	0.0369852	+	0.0559696i
$351$	−8676.91	+	2476.22i	−1.31948	+	0.376555i
$352$	−3528.08			−0.534226
$353$	−12645.6			−1.90669			−0.953343	−	0.301890i	$-0.902382\pi$
$353$	−12645.6			−1.90669			−0.953343	+	0.301890i	$0.902382\pi$
$354$	925.737	+	1307.02i	0.138990	+	0.196235i
$355$			1789.69i			0.267569i
$356$	−3585.74			−0.533831
$357$	−333.633	+	858.659i	−0.0494614	+	0.127297i
$358$	−1360.02			−0.200780
$359$			1779.92i			0.261673i	0.991404	+	0.130836i	$0.0417663\pi$
$359$			1779.92i			0.261673i	−0.991404	+	0.130836i	$0.958234\pi$
$360$	1824.38	+	641.806i	0.267093	+	0.0939615i
$361$	6667.65			0.972102
$362$	−4416.59			−0.641245
$363$	−3463.82	+	2453.36i	−0.500836	+	0.354733i
$364$	4662.49	+	7055.73i	0.671376	+	1.01599i
$365$		−	4628.94i		−	0.663807i
$366$	130.433	−	92.3833i	0.0186280	−	0.0131939i
$367$			11678.2i			1.66102i	0.557003	+	0.830510i	$0.311951\pi$
$367$			11678.2i			1.66102i	−0.557003	+	0.830510i	$0.688049\pi$
$368$			5814.87i			0.823699i
$369$	1925.67	−	5473.86i	0.271670	−	0.772243i
$370$		−	813.412i		−	0.114290i
$371$	−5453.66	−	8253.01i	−0.763181	−	1.15492i
$372$	4419.79	+	6240.16i	0.616010	+	0.869724i
$373$	−3272.51			−0.454273			−0.227137	−	0.973863i	$-0.572936\pi$
$373$	−3272.51			−0.454273			−0.227137	+	0.973863i	$0.572936\pi$
$374$	−205.921			−0.0284704
$375$	−530.036	+	375.415i	−0.0729892	+	0.0516969i
$376$			8341.75i			1.14413i
$377$	12517.9			1.71010
$378$	−1604.73	+	1871.27i	−0.218356	+	0.254623i
$379$	−617.624			−0.0837077			−0.0418538	−	0.999124i	$-0.513326\pi$
$379$	−617.624			−0.0837077			−0.0418538	+	0.999124i	$0.513326\pi$
$380$			491.065i			0.0662924i
$381$	4321.46	−	3060.81i	0.581090	−	0.411575i
$382$	1047.62			0.140317
$383$	−9244.28			−1.23332			−0.616659	−	0.787230i	$-0.711514\pi$
$383$	−9244.28			−1.23332			−0.616659	+	0.787230i	$0.711514\pi$
$384$	−4302.80	−	6074.99i	−0.571814	−	0.807325i
$385$	1157.57	+	1751.74i	0.153234	+	0.231888i
$386$			1495.05i			0.197140i
$387$	−2886.78	+	8205.89i	−0.379181	+	1.07785i
$388$		−	613.022i		−	0.0802100i
$389$		−	1016.89i		−	0.132541i	−0.997802	−	0.0662706i	$-0.978890\pi$
$389$		−	1016.89i		−	0.132541i	0.997802	−	0.0662706i	$-0.0211101\pi$
$390$	1293.69	−	916.300i	0.167971	−	0.118971i
$391$			1288.26i			0.166624i
$392$	4520.25	+	1926.73i	0.582416	+	0.248252i
$393$	9274.98	−	6569.29i	1.19049	−	0.843199i
$394$	−354.418			−0.0453181
$395$	4136.43			0.526902
$396$	4100.25	+	1442.44i	0.520317	+	0.183044i
$397$		−	4603.25i		−	0.581941i	−0.956732	−	0.290971i	$-0.906022\pi$
$397$		−	4603.25i		−	0.581941i	0.956732	−	0.290971i	$-0.0939782\pi$
$398$	398.397			0.0501755
$399$	−1240.83	−	482.127i	−0.155688	−	0.0604926i
$400$	1080.20			0.135024
$401$			6522.49i			0.812263i	0.913815	+	0.406132i	$0.133123\pi$
$401$			6522.49i			0.812263i	−0.913815	+	0.406132i	$0.866877\pi$
$402$	2227.81	+	3145.37i	0.276400	+	0.390240i
$403$	13331.2			1.64783
$404$	−6359.78			−0.783196
$405$	−2842.16	−	2282.14i	−0.348711	−	0.280001i
$406$	2853.16	−	1885.39i	0.348768	−	0.230469i
$407$		−	3888.00i		−	0.473516i
$408$	−411.855	−	581.486i	−0.0499752	−	0.0705584i
$409$			668.576i			0.0808287i	0.999183	+	0.0404143i	$0.0128678\pi$
$409$			668.576i			0.0808287i	−0.999183	+	0.0404143i	$0.987132\pi$
$410$			1019.49i			0.122802i
$411$	7485.77	+	10568.9i	0.898408	+	1.26843i
$412$			3451.97i			0.412783i
$413$	−5020.07	+	3317.31i	−0.598115	+	0.395240i
$414$	−1144.03	+	3252.00i	−0.135812	+	0.386056i
$415$	−655.274			−0.0775088
$416$	−10007.6			−1.17947
$417$	4302.80	+	6074.99i	0.505298	+	0.713414i
$418$		−	297.573i		−	0.0348200i
$419$	−16682.5			−1.94509			−0.972544	−	0.232719i	$-0.925238\pi$
$419$	−16682.5			−1.94509			−0.972544	+	0.232719i	$0.925238\pi$
$420$	−1237.28	+	3184.34i	−0.143745	+	0.369952i
$421$	−2711.43			−0.313888			−0.156944	−	0.987608i	$-0.550164\pi$
$421$	−2711.43			−0.313888			−0.156944	+	0.987608i	$0.550164\pi$
$422$			4876.10i			0.562476i
$423$	5217.38	−	14830.8i	0.599711	−	1.70473i
$424$	7651.79			0.876424
$425$	239.312			0.0273137
$426$	1439.95	−	1019.89i	0.163770	−	0.115995i
$427$	331.048	+	500.975i	0.0375189	+	0.0567772i
$428$			5174.34i			0.584372i
$429$	6183.69	−	4379.79i	0.695924	−	0.492910i
$430$		−	1528.32i		−	0.171400i
$431$			2719.42i			0.303921i	0.988387	+	0.151961i	$0.0485587\pi$
$431$			2719.42i			0.303921i	−0.988387	+	0.151961i	$0.951441\pi$
$432$	1663.53	+	5829.16i	0.185270	+	0.649203i
$433$			7084.08i			0.786233i	0.919489	+	0.393117i	$0.128603\pi$
$433$			7084.08i			0.786233i	−0.919489	+	0.393117i	$0.871397\pi$
$434$	3038.52	−	2007.88i	0.336068	−	0.222077i
$435$	2922.70	+	4126.46i	0.322144	+	0.454825i
$436$	−7556.06			−0.829976
$437$	−1861.64			−0.203785
$438$	−3724.36	+	2637.90i	−0.406295	+	0.287771i
$439$		−	7781.46i		−	0.845989i	−0.906132	−	0.422994i	$-0.860979\pi$
$439$		−	7781.46i		−	0.845989i	0.906132	−	0.422994i	$-0.139021\pi$
$440$	−1624.13			−0.175971
$441$	−6831.49	−	6252.75i	−0.737662	−	0.675170i
$442$	−584.104			−0.0628574
$443$		−	15917.2i		−	1.70710i	−0.521008	−	0.853552i	$-0.674444\pi$
$443$		−	15917.2i		−	1.70710i	0.521008	−	0.853552i	$-0.325556\pi$
$444$	5162.30	−	3656.36i	0.551784	−	0.390818i
$445$	−2525.20			−0.269002
$446$	−2561.77			−0.271980
$447$	4562.16	+	6441.16i	0.482735	+	0.681558i
$448$	3060.00	−	2022.08i	0.322704	−	0.213246i
$449$			362.637i			0.0381156i	0.999818	+	0.0190578i	$0.00606665\pi$
$449$			362.637i			0.0381156i	−0.999818	+	0.0190578i	$0.993933\pi$
$450$	604.105	+	212.520i	0.0632840	+	0.0222629i
$451$			4873.01i			0.508783i
$452$		−	14139.2i		−	1.47135i
$453$	−354.169	+	250.852i	−0.0367336	+	0.0260177i
$454$		−	2838.69i		−	0.293450i
$455$	3283.49	+	4968.89i	0.338313	+	0.511968i
$456$	840.295	−	595.165i	0.0862947	−	0.0611210i
$457$	10948.8			1.12071			0.560355	−	0.828252i	$-0.310665\pi$
$457$	10948.8			1.12071			0.560355	+	0.828252i	$0.310665\pi$
$458$	−3450.84			−0.352068
$459$	368.547	+	1291.42i	0.0374777	+	0.131325i
$460$			4777.50i			0.484243i
$461$	9669.50			0.976906			0.488453	−	0.872590i	$-0.337561\pi$
$461$	9669.50			0.976906			0.488453	+	0.872590i	$0.337561\pi$
$462$	749.758	−	1929.62i	0.0755019	−	0.194317i
$463$	−2566.64			−0.257628			−0.128814	−	0.991669i	$-0.541117\pi$
$463$	−2566.64			−0.257628			−0.128814	+	0.991669i	$0.541117\pi$
$464$		−	8409.58i		−	0.841390i
$465$	3112.57	+	4394.54i	0.310413	+	0.438263i
$466$	−5693.36			−0.565966
$467$	7093.06			0.702843			0.351422	−	0.936217i	$-0.385698\pi$
$467$	7093.06			0.702843			0.351422	+	0.936217i	$0.385698\pi$
$468$	11630.6	+	4091.55i	1.14877	+	0.404128i
$469$	−12080.9	+	7983.16i	−1.18943	+	0.785988i
$470$			2762.19i			0.271086i
$471$	5156.15	+	7279.80i	0.504422	+	0.712178i
$472$		−	4654.36i		−	0.453886i
$473$		−	7305.16i		−	0.710130i
$474$	−2357.23	−	3328.10i	−0.228420	−	0.322499i
$475$			345.825i			0.0334054i
$476$	1050.14	−	693.938i	0.101119	−	0.0668206i
$477$	−13604.1	−	4785.84i	−1.30585	−	0.459389i
$478$	−4908.69			−0.469703
$479$	−3853.70			−0.367599			−0.183800	−	0.982964i	$-0.558840\pi$
$479$	−3853.70			−0.367599			−0.183800	+	0.982964i	$0.558840\pi$
$480$	−2336.57	−	3298.93i	−0.222186	−	0.313698i
$481$		−	11028.5i		−	1.04544i
$482$	−691.997			−0.0653934
$483$	−12071.9	−	4690.54i	−1.13724	−	0.441878i
$484$	5799.79			0.544683
$485$		−	431.712i		−	0.0404186i
$486$	−216.505	+	3587.28i	−0.0202075	+	0.334819i
$487$	−15436.4			−1.43632			−0.718162	−	0.695876i	$-0.755016\pi$
$487$	−15436.4			−1.43632			−0.718162	+	0.695876i	$0.755016\pi$
$488$	−464.479			−0.0430860
$489$	−9876.85	+	6995.59i	−0.913387	+	0.646935i
$490$	1496.78	+	637.995i	0.137995	+	0.0588197i
$491$		−	11840.5i		−	1.08829i	−0.838990	−	0.544147i	$-0.816853\pi$
$491$		−	11840.5i		−	1.08829i	0.838990	−	0.544147i	$-0.183147\pi$
$492$	−6470.15	+	4582.69i	−0.592880	+	0.419926i
$493$		−	1863.10i		−	0.170203i
$494$		−	844.078i		−	0.0768762i
$495$	2887.54	+	1015.82i	0.262193	+	0.0922376i
$496$		−	8955.92i		−	0.810752i
$497$	3654.71	+	5530.66i	0.329851	+	0.499163i
$498$	373.422	+	527.223i	0.0336013	+	0.0474406i
$499$	4648.67			0.417040			0.208520	−	0.978018i	$-0.433135\pi$
$499$	4648.67			0.417040			0.208520	+	0.978018i	$0.433135\pi$
$500$	887.488			0.0793793
$501$	3283.64	−	2325.74i	0.292819	−	0.207398i
$502$			6076.37i			0.540242i
$503$	22018.7			1.95182			0.975910	−	0.218174i	$-0.0700101\pi$
$503$	22018.7			1.95182			0.975910	+	0.218174i	$0.0700101\pi$
$504$	6948.50	−	1742.19i	0.614109	−	0.153975i
$505$	−4478.78			−0.394660
$506$		−	2895.04i		−	0.254348i
$507$	8224.40	−	5825.19i	0.720430	−	0.510268i
$508$	−7235.81			−0.631963
$509$	−7752.57			−0.675101			−0.337551	−	0.941307i	$-0.609598\pi$
$509$	−7752.57			−0.675101			−0.337551	+	0.941307i	$0.609598\pi$
$510$	−136.377	−	192.546i	−0.0118409	−	0.0167178i
$511$	−9452.70	−	14304.7i	−0.818323	−	1.23837i
$512$			11675.0i			1.00775i
$513$	−1866.21	+	532.580i	−0.160614	+	0.0458362i
$514$		−	3984.60i		−	0.341932i
$515$			2431.00i			0.208005i
$516$	9699.44	−	6869.93i	0.827508	−	0.586109i
$517$			13202.9i			1.12314i
$518$	−1661.06	−	2513.68i	−0.140893	−	0.213214i
$519$	6756.08	−	4785.20i	0.571404	−	0.404715i
$520$	−4606.91			−0.388513
$521$	−6080.85			−0.511338			−0.255669	−	0.966764i	$-0.582296\pi$
$521$	−6080.85			−0.511338			−0.255669	+	0.966764i	$0.582296\pi$
$522$	1654.52	−	4703.10i	0.138729	−	0.394347i
$523$			13407.4i			1.12096i	0.828167	+	0.560482i	$0.189384\pi$
$523$			13407.4i			1.12096i	−0.828167	+	0.560482i	$0.810616\pi$
$524$	−15529.9			−1.29471
$525$	−871.334	+	2242.52i	−0.0724346	+	0.186422i
$526$	952.356			0.0789443
$527$		−	1984.14i		−	0.164005i
$528$	−2942.35	−	4154.22i	−0.242518	−	0.342404i
$529$	−5944.57			−0.488581
$530$	2533.72			0.207656
$531$	−2911.09	+	8275.00i	−0.237911	+	0.676280i
$532$	1002.80	+	1517.53i	0.0817233	+	0.123672i
$533$			13822.5i			1.12330i
$534$	1439.04	+	2031.73i	0.116617	+	0.164647i
$535$			3643.95i			0.294471i
$536$		−	11200.8i		−	0.902615i
$537$	−4305.27	−	6078.48i	−0.345971	−	0.488465i
$538$			7499.24i			0.600957i
$539$	7154.42	+	3049.53i	0.571731	+	0.243697i
$540$	1366.75	+	4789.24i	0.108918	+	0.381659i
$541$	20040.7			1.59264			0.796321	−	0.604875i	$-0.206777\pi$
$541$	20040.7			1.59264			0.796321	+	0.604875i	$0.206777\pi$
$542$	−2396.27			−0.189905
$543$	−13981.2	−	19739.6i	−1.10495	−	1.56005i
$544$			1489.47i			0.117391i
$545$	−5321.24			−0.418233
$546$	2126.72	−	5473.47i	0.166695	−	0.429016i
$547$	3820.80			0.298657			0.149329	−	0.988788i	$-0.452289\pi$
$547$	3820.80			0.298657			0.149329	+	0.988788i	$0.452289\pi$
$548$		−	17696.5i		−	1.37948i
$549$	825.799	+	290.510i	0.0641971	+	0.0225841i
$550$	−537.794			−0.0416939
$551$	2692.33			0.208162
$552$	8175.10	−	5790.27i	0.630354	−	0.446468i
$553$	12782.7	−	8446.95i	0.982961	−	0.649549i
$554$			312.206i			0.0239429i
$555$	3635.48	−	2574.94i	0.278049	−	0.196937i
$556$		−	10171.9i		−	0.775872i
$557$			14135.0i			1.07526i	0.843182	+	0.537629i	$0.180680\pi$
$557$			14135.0i			1.07526i	−0.843182	+	0.537629i	$0.819320\pi$
$558$	1762.01	−	5008.65i	0.133677	−	0.379987i
$559$		−	20721.4i		−	1.56784i
$560$	3338.11	−	2205.85i	0.251895	−	0.166454i
$561$	−651.864	−	920.346i	−0.0490583	−	0.0692638i
$562$	422.763			0.0317316
$563$	−12949.4			−0.969366			−0.484683	−	0.874690i	$-0.661065\pi$
$563$	−12949.4			−0.969366			−0.484683	+	0.874690i	$0.661065\pi$
$564$	−17530.2	+	12416.3i	−1.30878	+	0.926986i
$565$		−	9957.30i		−	0.741428i
$566$	2737.35			0.203285
$567$	−13443.4	−	1248.52i	−0.995715	−	0.0924745i
$568$	−5127.75			−0.378795
$569$			18520.3i			1.36452i	0.731109	+	0.682260i	$0.239003\pi$
$569$			18520.3i			1.36452i	−0.731109	+	0.682260i	$0.760997\pi$
$570$	278.245	−	197.076i	0.0204463	−	0.0144818i
$571$	−13858.2			−1.01567			−0.507835	−	0.861455i	$-0.669554\pi$
$571$	−13858.2			−1.01567			−0.507835	+	0.861455i	$0.669554\pi$
$572$	−10353.9			−0.756851
$573$	3316.36	+	4682.26i	0.241785	+	0.341369i
$574$	2081.88	+	3150.51i	0.151387	+	0.229093i
$575$			3364.48i			0.244015i
$576$	1774.47	−	5044.06i	0.128361	−	0.364877i
$577$		−	10176.6i		−	0.734245i	−0.930173	−	0.367122i	$-0.880343\pi$
$577$		−	10176.6i		−	0.734245i	0.930173	−	0.367122i	$-0.119657\pi$
$578$		−	4574.20i		−	0.329173i
$579$	−6682.00	+	4732.74i	−0.479610	+	0.339699i
$580$		−	6909.31i		−	0.494644i
$581$	−2024.99	+	1338.13i	−0.144597	+	0.0955506i
$582$	−347.348	+	246.020i	−0.0247389	+	0.0175221i
$583$	12110.9			0.860344
$584$	13262.7			0.939748
$585$	8190.65	+	2881.41i	0.578874	+	0.203644i
$586$			6740.00i			0.475131i
$587$	10161.5			0.714499			0.357249	−	0.934009i	$-0.383715\pi$
$587$	10161.5			0.714499			0.357249	+	0.934009i	$0.383715\pi$
$588$	2679.15	+	12367.1i	0.187902	+	0.867368i
$589$	2867.24			0.200582
$590$		−	1541.19i		−	0.107542i
$591$	−1121.95	−	1584.04i	−0.0780892	−	0.110252i
$592$	−7408.97			−0.514369
$593$	13035.7			0.902722			0.451361	−	0.892341i	$-0.350939\pi$
$593$	13035.7			0.902722			0.451361	+	0.892341i	$0.350939\pi$
$594$	−828.218	−	2902.15i	−0.0572091	−	0.200466i
$595$	739.542	−	488.696i	0.0509551	−	0.0336716i
$596$		−	10785.0i		−	0.741228i
$597$	1261.17	+	1780.60i	0.0864592	+	0.122069i
$598$		−	8211.91i		−	0.561555i
$599$		−	26428.7i		−	1.80275i	−0.433039	−	0.901375i	$-0.642559\pi$
$599$		−	26428.7i		−	1.80275i	0.433039	−	0.901375i	$-0.357441\pi$
$600$	−1075.62	−	1518.64i	−0.0731870	−	0.103330i
$601$			20188.0i			1.37019i	0.728452	+	0.685096i	$0.240240\pi$
$601$			20188.0i			1.37019i	−0.728452	+	0.685096i	$0.759760\pi$
$602$	−3120.96	−	4722.94i	−0.211297	−	0.319755i
$603$	−7005.60	+	19914.0i	−0.473118	+	1.34487i
$604$	593.017			0.0399496
$605$	4084.41			0.274471
$606$	2552.33	+	3603.55i	0.171091	+	0.241558i
$607$			20701.4i			1.38426i	0.721773	+	0.692130i	$0.243328\pi$
$607$			20701.4i			1.38426i	−0.721773	+	0.692130i	$0.756672\pi$
$608$	−2152.41			−0.143572
$609$	17458.6	+	6783.55i	1.16167	+	0.451368i
$610$	−153.802			−0.0102086
$611$			37450.6i			2.47969i
$612$	608.963	−	1731.03i	0.0402220	−	0.114334i
$613$	10042.5			0.661686			0.330843	−	0.943686i	$-0.392667\pi$
$613$	10042.5			0.661686			0.330843	+	0.943686i	$0.392667\pi$
$614$	1535.67			0.100936
$615$	−4556.51	+	3227.29i	−0.298758	+	0.211605i
$616$	−5019.02	+	3316.61i	−0.328283	+	0.216932i
$617$		−	19935.4i		−	1.30076i	−0.759609	−	0.650380i	$-0.774610\pi$
$617$		−	19935.4i		−	1.30076i	0.759609	−	0.650380i	$-0.225390\pi$
$618$	1955.94	−	1385.36i	0.127313	−	0.0901736i
$619$			24406.2i			1.58476i	0.610027	+	0.792380i	$0.291158\pi$
$619$			24406.2i			1.58476i	−0.610027	+	0.792380i	$0.708842\pi$
$620$		−	7358.18i		−	0.476632i
$621$	−18156.1	+	5181.39i	−1.17323	+	0.334818i
$622$			2488.87i			0.160442i
$623$	−7803.60	+	5156.69i	−0.501837	+	0.331618i
$624$	−8346.12	−	11783.6i	−0.535436	−	0.755965i
$625$	625.000			0.0400000
$626$	5331.10			0.340373
$627$	1329.98	−	941.997i	0.0847115	−	0.0599996i
$628$		−	12189.2i		−	0.774528i
$629$	−1641.42			−0.104050
$630$	2300.84	−	576.888i	0.145504	−	0.0364822i
$631$	−321.373			−0.0202752			−0.0101376	−	0.999949i	$-0.503227\pi$
$631$	−321.373			−0.0202752			−0.0101376	+	0.999949i	$0.503227\pi$
$632$			11851.5i			0.745931i
$633$	−21793.3	+	15435.8i	−1.36841	+	0.969223i
$634$	2164.20			0.135570
$635$	−5095.71			−0.318452
$636$	11389.3	+	16080.2i	0.710088	+	1.00255i
$637$	20293.8	+	8650.14i	1.26228	+	0.538039i
$638$			4186.86i			0.259811i
$639$	9116.65	+	3207.17i	0.564396	+	0.198551i
$640$			7163.41i			0.442435i
$641$			21926.6i			1.35109i	0.737318	+	0.675546i	$0.236092\pi$
$641$			21926.6i			1.35109i	−0.737318	+	0.675546i	$0.763908\pi$
$642$	2931.86	−	2076.58i	0.180236	−	0.127658i
$643$		−	2824.13i		−	0.173208i	−0.996243	−	0.0866039i	$-0.972399\pi$
$643$		−	2824.13i		−	0.173208i	0.996243	−	0.0866039i	$-0.0276015\pi$
$644$	9756.07	+	14763.8i	0.596961	+	0.903380i
$645$	6830.69	−	4838.05i	0.416989	−	0.295346i
$646$	−125.628			−0.00765133
$647$	−2998.63			−0.182208			−0.0911039	−	0.995841i	$-0.529040\pi$
$647$	−2998.63			−0.182208			−0.0911039	+	0.995841i	$0.529040\pi$
$648$	6538.70	−	8143.25i	0.396395	−	0.493668i
$649$		−	7366.69i		−	0.445559i
$650$	−1525.48			−0.0920526
$651$	18592.8	+	7224.25i	1.11937	+	0.434932i
$652$	16537.7			0.993353
$653$			19590.2i			1.17400i	0.809585	+	0.587002i	$0.199692\pi$
$653$			19590.2i			1.17400i	−0.809585	+	0.587002i	$0.800308\pi$
$654$	3032.42	+	4281.38i	0.181311	+	0.255987i
$655$	−10936.7			−0.652417
$656$	9286.00			0.552679
$657$	−23579.7	−	8295.18i	−1.40020	−	0.492581i
$658$	5640.63	+	8535.95i	0.334186	+	0.505723i
$659$			4145.27i			0.245033i	0.992466	+	0.122517i	$0.0390965\pi$
$659$			4145.27i			0.245033i	−0.992466	+	0.122517i	$0.960904\pi$
$660$	−2417.44	−	3413.10i	−0.142574	−	0.201295i
$661$		−	106.053i		−	0.00624055i	−0.999995	−	0.00312027i	$-0.999007\pi$
$661$		−	106.053i		−	0.00624055i	0.999995	−	0.00312027i	$-0.000993215\pi$
$662$		−	256.795i		−	0.0150765i
$663$	−1849.04	−	2610.60i	−0.108312	−	0.152922i
$664$		−	1877.47i		−	0.109729i
$665$	706.206	+	1068.70i	0.0411812	+	0.0623194i
$666$	−4143.51	−	1457.66i	−0.241077	−	0.0848094i
$667$	26193.3			1.52055
$668$	−5498.09			−0.318454
$669$	−8109.53	−	11449.6i	−0.468659	−	0.661684i
$670$		−	3708.90i		−	0.213862i
$671$	−735.153			−0.0422955
$672$	−13957.4	−	5423.16i	−0.801217	−	0.311314i
$673$	−2113.29			−0.121042			−0.0605209	−	0.998167i	$-0.519276\pi$
$673$	−2113.29			−0.121042			−0.0605209	+	0.998167i	$0.519276\pi$
$674$		−	4593.93i		−	0.262539i
$675$	962.517	+	3372.75i	0.0548849	+	0.192322i
$676$	−13770.8			−0.783503
$677$	4033.61			0.228987			0.114494	−	0.993424i	$-0.463475\pi$
$677$	4033.61			0.228987			0.114494	+	0.993424i	$0.463475\pi$
$678$	−8011.47	+	5674.38i	−0.453803	+	0.321421i
$679$	−881.594	−	1334.11i	−0.0498269	−	0.0754029i
$680$			685.667i			0.0386678i
$681$	12687.3	−	8986.18i	0.713918	−	0.505655i
$682$			4458.87i			0.250350i
$683$			649.189i			0.0363697i	0.999835	+	0.0181849i	$0.00578874\pi$
$683$			649.189i			0.0363697i	−0.999835	+	0.0181849i	$0.994211\pi$
$684$	2501.48	+	880.002i	0.139834	+	0.0491926i
$685$		−	12462.5i		−	0.695134i
$686$	5928.33	−	1084.97i	0.329948	−	0.0603855i
$687$	−10924.0	−	15423.2i	−0.606661	−	0.856526i
$688$	−13920.7			−0.771398
$689$	34353.0			1.89948
$690$	2707.00	−	1917.32i	0.149353	−	0.105784i
$691$		−	16178.2i		−	0.890663i	−0.895366	−	0.445332i	$-0.853086\pi$
$691$		−	16178.2i		−	0.890663i	0.895366	−	0.445332i	$-0.146914\pi$
$692$	−11312.3			−0.621430
$693$	10997.7	−	2757.45i	0.602841	−	0.151150i
$694$	−8711.96			−0.476515
$695$		−	7163.41i		−	0.390969i
$696$	−11823.0	+	8374.00i	−0.643892	+	0.456057i
$697$	2057.27			0.111800
$698$	10771.5			0.584109
$699$	−18022.9	−	25446.0i	−0.975236	−	1.37690i
$700$	2742.59	−	1812.33i	0.148086	−	0.0978565i
$701$		−	2026.49i		−	0.109186i	−0.998509	−	0.0545932i	$-0.982614\pi$
$701$		−	2026.49i		−	0.109186i	0.998509	−	0.0545932i	$-0.0173862\pi$
$702$	−2349.28	−	8232.09i	−0.126307	−	0.442593i
$703$		−	2371.99i		−	0.127256i
$704$			4490.39i			0.240395i
$705$	−12345.4	+	8743.99i	−0.659508	+	0.467117i
$706$		−	11997.4i		−	0.639557i
$707$	−13840.7	+	9146.07i	−0.736258	+	0.486525i
$708$	9781.13	−	6927.79i	0.519205	−	0.367743i
$709$	821.533			0.0435167			0.0217583	−	0.999763i	$-0.493074\pi$
$709$	821.533			0.0435167			0.0217583	+	0.999763i	$0.493074\pi$
$710$	−1697.94			−0.0897502
$711$	7412.59	−	21070.9i	0.390990	−	1.11142i
$712$		−	7235.11i		−	0.380825i
$713$	27895.0			1.46518
$714$	−814.640	−	316.529i	−0.0426991	−	0.0165908i
$715$	−7291.59			−0.381384
$716$			10177.7i			0.531229i
$717$	−15539.0	−	21938.9i	−0.809362	−	1.14271i
$718$	−1688.67			−0.0877725
$719$	20915.2			1.08485			0.542423	−	0.840106i	$-0.317507\pi$
$719$	20915.2			1.08485			0.542423	+	0.840106i	$0.317507\pi$
$720$	1935.74	−	5502.49i	0.100195	−	0.284814i
$721$	4964.32	+	7512.49i	0.256423	+	0.388044i
$722$			6325.83i			0.326071i
$723$	−2190.59	−	3092.82i	−0.112682	−	0.159092i
$724$			33051.7i			1.69663i
$725$		−	4865.78i		−	0.249256i
$726$	−2327.59	−	3286.25i	−0.118988	−	0.167995i
$727$		−	36038.5i		−	1.83851i	−0.393666	−	0.919253i	$-0.628793\pi$
$727$		−	36038.5i		−	1.83851i	0.393666	−	0.919253i	$-0.371207\pi$
$728$	−14236.7	+	9407.72i	−0.724789	+	0.478947i
$729$	−16718.4	+	10388.2i	−0.849383	+	0.527778i
$730$	4391.64			0.222660
$731$	−3084.06			−0.156044
$732$	−691.354	−	976.101i	−0.0349087	−	0.0492865i
$733$			21345.1i			1.07558i	0.843079	+	0.537790i	$0.180741\pi$
$733$			21345.1i			1.07558i	−0.843079	+	0.537790i	$0.819259\pi$
$734$	−11079.5			−0.557154
$735$	1886.75	+	8709.38i	0.0946857	+	0.437075i
$736$	−20940.4			−1.04874
$737$		−	17728.1i		−	0.886055i
$738$	5193.24	+	1826.95i	0.259032	+	0.0911258i
$739$	−5664.66			−0.281973			−0.140986	−	0.990012i	$-0.545027\pi$
$739$	−5664.66			−0.281973			−0.140986	+	0.990012i	$0.545027\pi$
$740$	−6087.20			−0.302392
$741$	3772.53	−	2672.02i	0.187028	−	0.132468i
$742$	7829.93	−	5174.08i	0.387393	−	0.255993i
$743$		−	9650.55i		−	0.476506i	−0.971203	−	0.238253i	$-0.923425\pi$
$743$		−	9650.55i		−	0.476506i	0.971203	−	0.238253i	$-0.0765748\pi$
$744$	−12591.1	+	8918.03i	−0.620445	+	0.439450i
$745$		−	7595.19i		−	0.373512i
$746$		−	3104.74i		−	0.152376i
$747$	−1174.27	+	3337.96i	−0.0575158	+	0.163493i
$748$			1541.02i			0.0753278i
$749$	7441.27	+	11260.9i	0.363015	+	0.549349i
$750$	−356.169	−	502.864i	−0.0173406	−	0.0244827i
$751$	−25540.0			−1.24097			−0.620484	−	0.784219i	$-0.713064\pi$
$751$	−25540.0			−1.24097			−0.620484	+	0.784219i	$0.713064\pi$
$752$	25159.4			1.22004
$753$	−27157.8	+	19235.4i	−1.31432	+	0.930911i
$754$			11876.2i			0.573616i
$755$	417.624			0.0201310
$756$	14003.7	+	12009.1i	0.673690	+	0.577733i
$757$	−6554.94			−0.314721			−0.157360	−	0.987541i	$-0.550298\pi$
$757$	−6554.94			−0.314721			−0.157360	+	0.987541i	$0.550298\pi$
$758$		−	585.962i		−	0.0280780i
$759$	12939.1	−	9164.54i	0.618788	−	0.438276i
$760$	−990.845			−0.0472918
$761$	−14488.6			−0.690160			−0.345080	−	0.938573i	$-0.612148\pi$
$761$	−14488.6			−0.690160			−0.345080	+	0.938573i	$0.612148\pi$
$762$	2903.90	+	4099.92i	0.138054	+	0.194914i
$763$	−16444.2	+	10866.4i	−0.780234	+	0.515585i
$764$		−	7839.94i		−	0.371255i
$765$	428.853	−	1219.05i	0.0202683	−	0.0576142i
$766$		−	8770.38i		−	0.413690i
$767$		−	20895.9i		−	0.983714i
$768$	−954.421	+	675.999i	−0.0448434	+	0.0317617i
$769$			17124.6i			0.803031i	0.915852	+	0.401515i	$0.131516\pi$
$769$			17124.6i			0.803031i	−0.915852	+	0.401515i	$0.868484\pi$
$770$	−1661.94	+	1098.22i	−0.0777820	+	0.0513990i
$771$	17808.8	−	12613.6i	0.831866	−	0.589195i
$772$	11188.3			0.521600
$773$	12317.6			0.573137			0.286569	−	0.958060i	$-0.407485\pi$
$773$	12317.6			0.573137			0.286569	+	0.958060i	$0.407485\pi$
$774$	−7785.22	−	2738.79i	−0.361543	−	0.127188i
$775$		−	5181.89i		−	0.240179i
$776$	1236.92			0.0572204
$777$	5976.41	−	15381.3i	0.275936	−	0.710167i
$778$	964.763			0.0444581
$779$			2972.92i			0.136734i
$780$	−6857.17	−	9681.42i	−0.314777	−	0.444423i
$781$	−8115.94			−0.371845
$782$	−1222.21			−0.0558904
$783$	26257.7	−	7493.43i	1.19843	−	0.342009i
$784$	5811.18	−	13633.4i	0.264722	−	0.621057i
$785$		−	8584.09i		−	0.390292i
$786$	6232.52	+	8799.50i	0.282833	+	0.399323i
$787$		−	5526.55i		−	0.250318i	−0.992137	−	0.125159i	$-0.960056\pi$
$787$		−	5526.55i		−	0.250318i	0.992137	−	0.125159i	$-0.0399441\pi$
$788$			2652.30i			0.119904i
$789$	3014.78	+	4256.47i	0.136032	+	0.192059i
$790$			3924.37i			0.176738i
$791$	−20333.7	−	30770.9i	−0.914011	−	1.38317i
$792$	−2910.48	+	8273.28i	−0.130580	+	0.371185i
$793$	−2085.30			−0.0933809
$794$	4367.27			0.195200
$795$	8020.76	+	11324.2i	0.357820	+	0.505195i
$796$		−	2981.42i		−	0.132756i
$797$	−32322.3			−1.43653			−0.718266	−	0.695769i	$-0.755064\pi$
$797$	−32322.3			−1.43653			−0.718266	+	0.695769i	$0.755064\pi$
$798$	457.411	−	1177.22i	0.0202909	−	0.0522221i
$799$	5573.94			0.246798
$800$			3889.98i			0.171915i
$801$	−4525.23	+	12863.3i	−0.199614	+	0.567420i
$802$	−6188.12			−0.272456
$803$	20991.5			0.922506
$804$	23538.5	−	16671.9i	1.03251	−	0.731308i
$805$	6870.57	+	10397.2i	0.300814	+	0.455222i
$806$			12647.8i			0.552728i
$807$	−33517.2	+	23739.6i	−1.46203	+	1.03553i
$808$		−	12832.4i		−	0.558717i
$809$			23348.8i			1.01471i	0.861737	+	0.507355i	$0.169377\pi$
$809$			23348.8i			1.01471i	−0.861737	+	0.507355i	$0.830623\pi$
$810$	2165.15	−	2696.46i	0.0939203	−	0.116968i
$811$			5514.22i			0.238755i	0.992849	+	0.119378i	$0.0380899\pi$
$811$			5514.22i			0.238755i	−0.992849	+	0.119378i	$0.961910\pi$
$812$	−14109.4	−	21351.7i	−0.609783	−	0.922783i
$813$	−7585.65	−	10709.9i	−0.327233	−	0.462009i
$814$	3688.69			0.158831
$815$	11646.4			0.500560
$816$	−1753.81	+	1242.19i	−0.0752396	+	0.0532908i
$817$		−	4456.72i		−	0.190846i
$818$	−634.301			−0.0271123
$819$	31195.5	−	7821.63i	1.33097	−	0.333712i
$820$	7629.37			0.324914
$821$		−	23388.8i		−	0.994244i	−0.867681	−	0.497122i	$-0.834390\pi$
$821$		−	23388.8i		−	0.994244i	0.867681	−	0.497122i	$-0.165610\pi$
$822$	−10027.1	+	7102.01i	−0.425469	+	0.301352i
$823$	−25766.4			−1.09132			−0.545662	−	0.838005i	$-0.683722\pi$
$823$	−25766.4			−1.09132			−0.545662	+	0.838005i	$0.683722\pi$
$824$	−6965.21			−0.294472
$825$	−1702.44	−	2403.63i	−0.0718442	−	0.101435i
$826$	−3147.25	−	4762.72i	−0.132575	−	0.200625i
$827$			1204.96i			0.0506657i	0.999679	+	0.0253329i	$0.00806456\pi$
$827$			1204.96i			0.0506657i	−0.999679	+	0.0253329i	$0.991935\pi$
$828$	24336.5	+	8561.40i	1.02144	+	0.359335i
$829$			14942.6i			0.626027i	0.949749	+	0.313013i	$0.101339\pi$
$829$			14942.6i			0.626027i	−0.949749	+	0.313013i	$0.898661\pi$
$830$		−	621.682i		−	0.0259987i
$831$	−1395.38	+	988.321i	−0.0582493	+	0.0412569i
$832$			12737.2i			0.530748i
$833$	1287.44	−	3020.42i	0.0535499	−	0.125632i
$834$	−5763.56	+	4082.22i	−0.239299	+	0.169491i
$835$	−3871.95			−0.160472
$836$	−2226.90			−0.0921278
$837$	27963.5	−	7980.25i	1.15479	−	0.329555i
$838$		−	15827.2i		−	0.652438i
$839$	−27243.7			−1.12104			−0.560522	−	0.828140i	$-0.689399\pi$
$839$	−27243.7			−1.12104			−0.560522	+	0.828140i	$0.689399\pi$
$840$	−6425.19	−	2496.51i	−0.263917	−	0.102545i
$841$	−13492.3			−0.553211
$842$		−	2572.43i		−	0.105287i
$843$	1338.30	+	1889.50i	0.0546779	+	0.0771980i
$844$	36490.5			1.48822
$845$	−9697.91			−0.394815
$846$	14070.5	+	4949.92i	0.571814	+	0.201160i
$847$	12622.0	−	8340.73i	0.512039	−	0.338360i
$848$		−	23078.4i		−	0.934571i
$849$	8665.37	+	12234.4i	0.350288	+	0.494561i
$850$			227.044i			0.00916180i
$851$		−	23076.7i		−	0.929564i
$852$	−7632.41	−	10776.0i	−0.306904	−	0.433308i
$853$			36573.7i			1.46807i	0.679114	+	0.734033i	$0.262364\pi$
$853$			36573.7i			1.46807i	−0.679114	+	0.734033i	$0.737636\pi$
$854$	−475.292	+	314.077i	−0.0190447	+	0.0125849i
$855$	1761.63	+	619.728i	0.0704636	+	0.0247886i
$856$	−10440.5			−0.416880
$857$	−17793.8			−0.709245			−0.354623	−	0.935010i	$-0.615391\pi$
$857$	−17793.8			−0.709245			−0.354623	+	0.935010i	$0.615391\pi$
$858$	4155.27	+	5866.69i	0.165336	+	0.233433i
$859$		−	18563.7i		−	0.737353i	−0.929558	−	0.368676i	$-0.879811\pi$
$859$		−	18563.7i		−	0.737353i	0.929558	−	0.368676i	$-0.120189\pi$
$860$	−11437.2			−0.453496
$861$	−7490.50	+	19278.0i	−0.296487	+	0.763059i
$862$	−2580.01			−0.101944
$863$		−	9471.58i		−	0.373599i	−0.982398	−	0.186800i	$-0.940188\pi$
$863$		−	9471.58i		−	0.373599i	0.982398	−	0.186800i	$-0.0598115\pi$
$864$	−20991.9	+	5990.68i	−0.826572	+	0.235888i
$865$	−7966.52			−0.313144
$866$	−6720.92			−0.263725
$867$	20444.0	−	14480.1i	0.800824	−	0.567209i
$868$	−15026.1	−	22738.9i	−0.587578	−	0.889180i
$869$			18758.0i			0.732246i
$870$	−3914.92	+	2772.87i	−0.152561	+	0.108056i
$871$		−	50286.5i		−	1.95625i
$872$		−	15246.2i		−	0.592090i
$873$	−2199.13	−	773.640i	−0.0852570	−	0.0299928i
$874$		−	1766.20i		−	0.0683554i
$875$	1931.43	−	1276.31i	0.0746220	−	0.0493108i
$876$	19740.8	+	27871.4i	0.761393	+	1.07499i
$877$	19182.6			0.738596			0.369298	−	0.929311i	$-0.379598\pi$
$877$	19182.6			0.738596			0.369298	+	0.929311i	$0.379598\pi$
$878$	7382.55			0.283769
$879$	−30123.8	+	21336.2i	−1.15592	+	0.818716i
$880$			4898.50i			0.187646i
$881$	26982.4			1.03185			0.515925	−	0.856634i	$-0.327448\pi$
$881$	26982.4			1.03185			0.515925	+	0.856634i	$0.327448\pi$
$882$	5932.21	−	6481.27i	0.226471	−	0.247433i
$883$	36699.9			1.39870			0.699349	−	0.714781i	$-0.253473\pi$
$883$	36699.9			1.39870			0.699349	+	0.714781i	$0.253473\pi$
$884$			4371.17i			0.166310i
$885$	6888.21	−	4878.79i	0.261633	−	0.185309i
$886$	15101.2			0.572611
$887$	23512.3			0.890040			0.445020	−	0.895521i	$-0.353197\pi$
$887$	23512.3			0.890040			0.445020	+	0.895521i	$0.353197\pi$
$888$	7377.62	+	10416.2i	0.278803	+	0.393632i
$889$	−15747.2	+	10405.9i	−0.594089	+	0.392579i
$890$		−	2395.75i		−	0.0902311i
$891$	10349.1	−	12888.7i	0.389123	−	0.484611i
$892$			19171.1i			0.719613i
$893$			8054.80i			0.301840i
$894$	−6110.96	+	4328.28i	−0.228614	+	0.161923i
$895$			7167.52i			0.267691i
$896$	14628.3	+	22137.0i	0.545421	+	0.825385i
$897$	36702.4	−	25995.6i	1.36617	−	0.967636i
$898$	−344.047			−0.0127851
$899$	−40342.3			−1.49665
$900$	1590.40	−	4520.84i	0.0589038	−	0.167439i
$901$		−	5112.91i		−	0.189052i
$902$	−4623.20			−0.170660
$903$	11229.1	−	28899.8i	0.413820	−	1.06503i
$904$	28529.3			1.04963
$905$			23276.2i			0.854947i
$906$	−237.992	−	336.013i	−0.00872709	−	0.0123215i
$907$	−11736.3			−0.429655			−0.214828	−	0.976652i	$-0.568919\pi$
$907$	−11736.3			−0.429655			−0.214828	+	0.976652i	$0.568919\pi$
$908$	−21243.5			−0.776420
$909$	−8026.10	+	22814.8i	−0.292859	+	0.832476i
$910$	−4714.17	+	3115.16i	−0.171729	+	0.113480i
$911$			8694.31i			0.316197i	0.987423	+	0.158098i	$0.0505363\pi$
$911$			8694.31i			0.316197i	−0.987423	+	0.158098i	$0.949464\pi$
$912$	−1795.07	−	2534.40i	−0.0651761	−	0.0920200i
$913$		−	2971.56i		−	0.107716i
$914$			10387.5i			0.375918i
$915$	−486.876	−	687.405i	−0.0175908	−	0.0248360i
$916$			25824.5i			0.931513i
$917$	−33797.6	+	22333.7i	−1.21712	+	0.804281i
$918$	−1225.22	+	349.653i	−0.0440503	+	0.0125711i
$919$	−44592.6			−1.60063			−0.800313	−	0.599583i	$-0.795333\pi$
$919$	−44592.6			−1.60063			−0.800313	+	0.599583i	$0.795333\pi$
$920$	−9639.78			−0.345450
$921$	4861.32	+	6863.54i	0.173926	+	0.245561i
$922$			9173.80i			0.327682i
$923$	−23021.2			−0.820968
$924$	−14440.4	−	5610.84i	−0.514129	−	0.199765i
$925$	−4286.82			−0.152378
$926$		−	2435.06i		−	0.0864159i
$927$	12383.5	+	4356.42i	0.438756	+	0.154351i
$928$	30284.5			1.07127
$929$	39730.9			1.40315			0.701576	−	0.712595i	$-0.252480\pi$
$929$	39730.9			1.40315			0.701576	+	0.712595i	$0.252480\pi$
$930$	−4169.26	+	2953.01i	−0.147006	+	0.104121i
$931$	4364.76	+	1860.45i	0.153651	+	0.0654929i
$932$			42606.5i			1.49745i
$933$	−11123.8	+	7878.78i	−0.390329	+	0.276463i
$934$			6729.44i			0.235754i
$935$			1085.24i			0.0379584i
$936$	−8255.72	+	23467.5i	−0.288298	+	0.819509i
$937$			23843.3i			0.831297i	0.909525	+	0.415648i	$0.136445\pi$
$937$			23843.3i			0.831297i	−0.909525	+	0.415648i	$0.863555\pi$
$938$	−7573.91	−	11461.6i	−0.263643	−	0.398970i
$939$	16876.2	+	23826.9i	0.586509	+	0.828074i
$940$	20670.9			0.717247
$941$	2927.06			0.101402			0.0507011	−	0.998714i	$-0.483854\pi$
$941$	2927.06			0.101402			0.0507011	+	0.998714i	$0.483854\pi$
$942$	−6906.61	+	4891.82i	−0.238885	+	0.169198i
$943$			28923.1i			0.998796i
$944$	−14037.9			−0.484000
$945$	9861.91	+	8457.22i	0.339479	+	0.291125i
$946$	6930.67			0.238198
$947$		−	11812.3i		−	0.405330i	−0.979248	−	0.202665i	$-0.935040\pi$
$947$		−	11812.3i		−	0.405330i	0.979248	−	0.202665i	$-0.0649602\pi$
$948$	−24906.0	+	17640.4i	−0.853278	+	0.604361i
$949$	59543.2			2.03673
$950$	−328.097			−0.0112051
$951$	6850.99	+	9672.69i	0.233605	+	0.329820i
$952$	1400.19	+	2118.91i	0.0476686	+	0.0721368i
$953$		−	2528.03i		−	0.0859297i	−0.999077	−	0.0429648i	$-0.986320\pi$
$953$		−	2528.03i		−	0.0859297i	0.999077	−	0.0429648i	$-0.0136803\pi$
$954$	4540.50	−	12906.7i	0.154092	−	0.438020i
$955$		−	5521.16i		−	0.187079i
$956$			36734.4i			1.24276i
$957$	−18712.8	+	13253.9i	−0.632079	+	0.447690i
$958$		−	3656.14i		−	0.123303i
$959$	−25449.5	−	38512.7i	−0.856942	−	1.29681i
$960$	−4198.73	+	2973.89i	−0.141160	+	0.0999810i
$961$	−13172.2			−0.442152
$962$	10463.1			0.350670
$963$	18562.2	+	6530.06i	0.621141	+	0.218513i
$964$			5178.59i			0.173020i
$965$	7879.18			0.262839
$966$	4450.08	−	11453.0i	0.148218	−	0.381464i
$967$	−6480.21			−0.215501			−0.107751	−	0.994178i	$-0.534365\pi$
$967$	−6480.21			−0.215501			−0.107751	+	0.994178i	$0.534365\pi$
$968$			11702.5i			0.388567i
$969$	−397.688	−	561.483i	−0.0131843	−	0.0186145i
$970$	409.580			0.0135576
$971$	−15246.9			−0.503909			−0.251955	−	0.967739i	$-0.581073\pi$
$971$	−15246.9			−0.503909			−0.251955	+	0.967739i	$0.581073\pi$
$972$	26845.5	+	1620.22i	0.885876	+	0.0534657i
$973$	−14628.3	−	22137.0i	−0.481976	−	0.729373i
$974$		−	14645.0i		−	0.481784i
$975$	−4829.06	−	6817.99i	−0.158619	−	0.223949i
$976$			1400.91i			0.0459446i
$977$			11247.9i			0.368324i	0.982896	+	0.184162i	$0.0589571\pi$
$977$			11247.9i			0.368324i	−0.982896	+	0.184162i	$0.941043\pi$
$978$	−6636.96	−	9370.51i	−0.217001	−	0.306376i
$979$		−	11451.4i		−	0.373838i
$980$	4774.46	−	11201.2i	0.155627	−	0.365112i
$981$	−9535.81	+	27106.3i	−0.310352	+	0.882199i
$982$	11233.5			0.365045
$983$	−30561.8			−0.991629			−0.495815	−	0.868428i	$-0.665130\pi$
$983$	−30561.8			−0.991629			−0.495815	+	0.868428i	$0.665130\pi$
$984$	−9246.71	−	13055.1i	−0.299567	−	0.422950i
$985$			1867.84i			0.0604208i
$986$	1767.59			0.0570908
$987$	−20294.7	+	52231.7i	−0.654496	+	1.68445i
$988$	−6316.69			−0.203402
$989$		−	43358.7i		−	1.39406i
$990$	−963.742	+	2739.51i	−0.0309391	+	0.0879469i
$991$	13827.0			0.443218			0.221609	−	0.975136i	$-0.428869\pi$
$991$	13827.0			0.443218			0.221609	+	0.975136i	$0.428869\pi$
$992$	32251.9			1.03226
$993$	1147.72	−	812.910i	0.0366786	−	0.0259788i
$994$	−5247.13	+	3467.35i	−0.167433	+	0.110641i
$995$		−	2099.62i		−	0.0668970i
$996$	3945.49	−	2794.52i	0.125520	−	0.0889034i
$997$		−	33231.0i		−	1.05560i	−0.849368	−	0.527801i	$-0.823017\pi$
$997$		−	33231.0i		−	1.05560i	0.849368	−	0.527801i	$-0.176983\pi$
$998$			4410.36i			0.139887i
$999$	−6601.82	−	23133.4i	−0.209081	−	0.732641i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.b.b.41.9	yes	16
3.2	odd	2		105.4.b.a.41.8	✓	16
7.6	odd	2		105.4.b.a.41.9	yes	16
21.20	even	2	inner	105.4.b.b.41.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.b.a.41.8	✓	16	3.2	odd	2
105.4.b.a.41.9	yes	16	7.6	odd	2
105.4.b.b.41.8	yes	16	21.20	even	2	inner
105.4.b.b.41.9	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)

\(f(q)\)	\(=\)	\(q+0.948735i q^{2} +(-4.24029 + 3.00332i) q^{3} +7.09990 q^{4} +5.00000 q^{5} +(-2.84936 - 4.02291i) q^{6} +(15.4514 - 10.2104i) q^{7} +14.3258i q^{8} +(8.96014 - 25.4699i) q^{9} +O(q^{10})\)	\(q+0.948735i q^{2} +(-4.24029 + 3.00332i) q^{3} +7.09990 q^{4} +5.00000 q^{5} +(-2.84936 - 4.02291i) q^{6} +(15.4514 - 10.2104i) q^{7} +14.3258i q^{8} +(8.96014 - 25.4699i) q^{9} +4.74368i q^{10} +22.6742i q^{11} +(-30.1056 + 21.3233i) q^{12} +64.3163i q^{13} +(9.68701 + 14.6593i) q^{14} +(-21.2015 + 15.0166i) q^{15} +43.2078 q^{16} +9.57247 q^{17} +(24.1642 + 8.50080i) q^{18} +13.8330i q^{19} +35.4995 q^{20} +(-34.8534 + 89.7009i) q^{21} -21.5118 q^{22} +134.579i q^{23} +(-43.0250 - 60.7456i) q^{24} +25.0000 q^{25} -61.0191 q^{26} +(38.5007 + 134.910i) q^{27} +(109.704 - 72.4931i) q^{28} -194.631i q^{29} +(-14.2468 - 20.1146i) q^{30} -207.276i q^{31} +155.599i q^{32} +(-68.0978 - 96.1450i) q^{33} +9.08174i q^{34} +(77.2572 - 51.0522i) q^{35} +(63.6161 - 180.834i) q^{36} -171.473 q^{37} -13.1239 q^{38} +(-193.162 - 272.720i) q^{39} +71.6291i q^{40} +214.915 q^{41} +(-85.1024 - 33.0666i) q^{42} -322.180 q^{43} +160.984i q^{44} +(44.8007 - 127.350i) q^{45} -127.680 q^{46} +582.288 q^{47} +(-183.214 + 129.767i) q^{48} +(134.494 - 315.532i) q^{49} +23.7184i q^{50} +(-40.5901 + 28.7492i) q^{51} +456.639i q^{52} -534.126i q^{53} +(-127.994 + 36.5270i) q^{54} +113.371i q^{55} +(146.273 + 221.354i) q^{56} +(-41.5450 - 58.6560i) q^{57} +184.653 q^{58} -324.893 q^{59} +(-150.528 + 106.616i) q^{60} +32.4225i q^{61} +196.650 q^{62} +(-121.612 - 485.034i) q^{63} +198.040 q^{64} +321.581i q^{65} +(91.2162 - 64.6067i) q^{66} -781.863 q^{67} +67.9636 q^{68} +(-404.184 - 570.655i) q^{69} +(48.4350 + 73.2966i) q^{70} +357.938i q^{71} +(364.877 + 128.361i) q^{72} -925.788i q^{73} -162.682i q^{74} +(-106.007 + 75.0830i) q^{75} +98.2130i q^{76} +(231.513 + 350.348i) q^{77} +(258.739 - 183.260i) q^{78} +827.285 q^{79} +216.039 q^{80} +(-568.432 - 456.428i) q^{81} +203.897i q^{82} -131.055 q^{83} +(-247.455 + 636.867i) q^{84} +47.8624 q^{85} -305.664i q^{86} +(584.540 + 825.293i) q^{87} -324.826 q^{88} -505.040 q^{89} +(120.821 + 42.5040i) q^{90} +(656.698 + 993.779i) q^{91} +955.499i q^{92} +(622.515 + 878.909i) q^{93} +552.437i q^{94} +69.1650i q^{95} +(-467.314 - 659.786i) q^{96} -86.3424i q^{97} +(299.356 + 127.599i) q^{98} +(577.509 + 203.164i) 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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