LMFDB - Embedded newform 105.4.b.a.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.a.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} +(96.1838 - 3.11036i) 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} +(2.95091 + 91.2530i) 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} +(398.506 - 302.060i) 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} +(682.896 - 22.0833i) 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} - 74 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} - 1834 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} - 898 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} + 1068 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 - 74 * 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 - 1834 * 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 - 898 * 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 + 1068 * 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	$-0.759329\pi$
$13$		−	64.3163i		−	1.37216i	0.727525	−	0.686082i	$-0.240671\pi$
$14$	−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	$-0.521752\pi$
$17$	−9.57247			−0.136569			−0.0682843	+	0.997666i	$0.521752\pi$
$18$	24.1642	+	8.50080i	0.316420	+	0.111314i
$19$		−	13.8330i		−	0.167027i	−0.996507	−	0.0835134i	$-0.973386\pi$
$19$		−	13.8330i		−	0.167027i	0.996507	−	0.0835134i	$-0.0266141\pi$
$20$	−35.4995			−0.396897
$21$	96.1838	−	3.11036i	0.999478	−	0.0323208i
$22$	−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	$0.205011\pi$
$31$			207.276i			1.20090i	−0.799664	+	0.600448i	$0.794989\pi$
$32$			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	$-0.634233\pi$
$41$	−214.915			−0.818635			−0.409318	+	0.912392i	$0.634233\pi$
$42$	2.95091	+	91.2530i	0.0108413	+	0.335253i
$43$	−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	$-0.859062\pi$
$47$	−582.288			−1.80714			−0.903569	+	0.428443i	$0.859062\pi$
$48$	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	$-0.383304\pi$
$59$	324.893			0.716907			0.358454	+	0.933548i	$0.383304\pi$
$60$	−150.528	+	106.616i	−0.323885	+	0.229402i
$61$		−	32.4225i		−	0.0680538i	−0.999421	−	0.0340269i	$-0.989167\pi$
$61$		−	32.4225i		−	0.0680538i	0.999421	−	0.0340269i	$-0.0108332\pi$
$62$	−196.650			−0.402815
$63$	398.506	−	302.060i	0.796937	−	0.604062i
$64$	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	$0.266198\pi$
$73$			925.788i			1.48432i	−0.670224	+	0.742159i	$0.733802\pi$
$74$		−	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	$-0.472381\pi$
$83$	131.055			0.173315			0.0866575	+	0.996238i	$0.472381\pi$
$84$	682.896	−	22.0833i	0.887024	−	0.0286843i
$85$	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	$-0.402762\pi$
$89$	505.040			0.601508			0.300754	+	0.953702i	$0.402762\pi$
$90$	−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	$0.0143891\pi$
$97$			86.3424i			0.0903788i	−0.998978	+	0.0451894i	$0.985611\pi$
$98$	−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	$-0.354538\pi$
$101$	895.757			0.882486			0.441243	+	0.897388i	$0.354538\pi$
$102$	−27.2754	−	38.5092i	−0.0264771	−	0.0373822i
$103$		−	486.200i		−	0.465114i	−0.972583	−	0.232557i	$-0.925291\pi$
$103$		−	486.200i		−	0.465114i	0.972583	−	0.232557i	$-0.0747092\pi$
$104$	921.383			0.868740
$105$	−480.919	+	15.5518i	−0.446980	+	0.0144543i
$106$	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
$126$	286.575	+	378.077i	0.202620	+	0.267315i
$127$	−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	$-0.239788\pi$
$131$	2187.34			1.45885			0.729424	+	0.684062i	$0.239788\pi$
$132$	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	$0.144000\pi$
$139$			1432.68i			0.874234i	−0.899405	+	0.437117i	$0.856000\pi$
$140$	−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
$147$	1517.94	+	934.020i	0.851682	+	0.524059i
$148$	−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	$0.143732\pi$
$157$			1716.82i			0.872719i	−0.899772	+	0.436360i	$0.856268\pi$
$158$			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	$-0.442580\pi$
$167$	774.390			0.358827			0.179413	+	0.983774i	$0.442580\pi$
$168$	44.5585	+	1377.91i	0.0204629	+	0.632787i
$169$	−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	$-0.386146\pi$
$173$	1593.30			0.700212			0.350106	+	0.936710i	$0.386146\pi$
$174$	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	$-0.594928\pi$
$181$		−	4655.24i		−	1.91172i	0.293825	−	0.955859i	$-0.405072\pi$
$182$	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
$189$	782.600	−	2477.66i	0.301194	−	0.953563i
$190$	−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	$0.0238296\pi$
$199$			419.925i			0.149586i	−0.997199	+	0.0747931i	$0.976170\pi$
$200$			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
$210$	−14.7546	−	456.265i	−0.00484839	−	0.149930i
$211$	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	$-0.867125\pi$
$223$		−	2700.19i		−	0.810843i	0.914130	−	0.405422i	$-0.132875\pi$
$224$	−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	$-0.355890\pi$
$227$	2992.08			0.874852			0.437426	+	0.899254i	$0.355890\pi$
$228$	−294.965	−	416.452i	−0.0856778	−	0.120966i
$229$		−	3637.31i		−	1.04961i	−0.851224	−	0.524803i	$-0.824139\pi$
$229$		−	3637.31i		−	1.04961i	0.851224	−	0.524803i	$-0.175861\pi$
$230$	638.400			0.183021
$231$	70.5249	+	2180.89i	0.0200874	+	0.621177i
$232$	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	$-0.968923\pi$
$241$		−	729.389i		−	0.194955i	0.995238	−	0.0974773i	$-0.0310774\pi$
$242$			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	$-0.797996\pi$
$251$	−6404.70			−1.61060			−0.805301	+	0.592866i	$0.797996\pi$
$252$	2829.35	−	2144.59i	0.707272	−	0.536098i
$253$	−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	$-0.329759\pi$
$257$	4199.90			1.01939			0.509694	+	0.860356i	$0.329759\pi$
$258$	−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	$-0.853400\pi$
$269$	−7904.46			−1.79161			−0.895805	+	0.444447i	$0.853400\pi$
$270$	−639.969	+	182.635i	−0.144249	+	0.0411659i
$271$		−	2525.75i		−	0.566157i	−0.959097	−	0.283079i	$-0.908644\pi$
$271$		−	2525.75i		−	0.566157i	0.959097	−	0.283079i	$-0.0913557\pi$
$272$	−413.605			−0.0922004
$273$	−200.047	−	6186.18i	−0.0443494	−	1.37145i
$274$	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	$0.0979960\pi$
$283$			2885.26i			0.606047i	−0.952983	+	0.303023i	$0.902004\pi$
$284$			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	$-0.750513\pi$
$293$	−7104.19			−1.41649			−0.708245	+	0.705967i	$0.750513\pi$
$294$	−886.137	+	1440.12i	−0.175784	+	0.285679i
$295$	−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	$0.0480748\pi$
$307$			1618.65i			0.300916i	−0.988616	+	0.150458i	$0.951925\pi$
$308$	−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	$-0.576872\pi$
$311$	−2623.36			−0.478318			−0.239159	+	0.970980i	$0.576872\pi$
$312$	3906.93	−	2767.21i	0.708931	−	0.502123i
$313$			5619.16i			1.01474i	0.861728	+	0.507371i	$0.169382\pi$
$313$			5619.16i			1.01474i	−0.861728	+	0.507371i	$0.830618\pi$
$314$	−1628.81			−0.292735
$315$	−1992.53	+	1510.30i	−0.356401	+	0.270145i
$316$	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
$336$	4155.89	−	134.392i	0.674769	−	0.0218205i
$337$	−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	$0.336327\pi$
$349$			11353.5i			1.74138i	−0.491832	+	0.870690i	$0.663673\pi$
$350$	−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	$-0.0976176\pi$
$353$	12645.6			1.90669			0.953343	+	0.301890i	$0.0976176\pi$
$354$	925.737	+	1307.02i	0.138990	+	0.196235i
$355$		−	1789.69i		−	0.267569i
$356$	3585.74			0.533831
$357$	−920.717	+	29.7739i	−0.136497	+	0.00441400i
$358$	−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	$-0.688049\pi$
$367$		−	11678.2i		−	1.66102i	0.557003	−	0.830510i	$-0.311951\pi$
$368$			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
$378$	2350.65	+	742.480i	0.319852	+	0.101029i
$379$	−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	$-0.288486\pi$
$383$	9244.28			1.23332			0.616659	+	0.787230i	$0.288486\pi$
$384$	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	$0.0939782\pi$
$397$			4603.25i			0.581941i	−0.956732	+	0.290971i	$0.906022\pi$
$398$	−398.397			−0.0501755
$399$	−43.0257	−	1330.51i	−0.00539844	−	0.166940i
$400$	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	$-0.987132\pi$
$409$		−	668.576i		−	0.0808287i	0.999183	−	0.0404143i	$-0.0128678\pi$
$410$			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	$-0.0747621\pi$
$419$	16682.5			1.94509			0.972544	+	0.232719i	$0.0747621\pi$
$420$	−3414.48	+	110.416i	−0.396689	+	0.0128280i
$421$	−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	$-0.871397\pi$
$433$		−	7084.08i		−	0.786233i	0.919489	−	0.393117i	$-0.128603\pi$
$434$	−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	$0.139021\pi$
$439$			7781.46i			0.845989i	−0.906132	+	0.422994i	$0.860979\pi$
$440$	1624.13			0.175971
$441$	9241.65	−	598.333i	0.997911	−	0.0646078i
$442$	−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	$-0.662439\pi$
$461$	−9669.50			−0.976906			−0.488453	+	0.872590i	$0.662439\pi$
$462$	−2069.08	+	66.9094i	−0.208360	+	0.00673790i
$463$	−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	$-0.614302\pi$
$467$	−7093.06			−0.702843			−0.351422	+	0.936217i	$0.614302\pi$
$468$	−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	$-0.441160\pi$
$479$	3853.70			0.367599			0.183800	+	0.982964i	$0.441160\pi$
$480$	−2336.57	−	3298.93i	−0.222186	−	0.313698i
$481$			11028.5i			1.04544i
$482$	691.997			0.0653934
$483$	418.590	+	12944.3i	0.0394338	+	1.21944i
$484$	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	$-0.929990\pi$
$503$	−22018.7			−1.95182			−0.975910	+	0.218174i	$0.929990\pi$
$504$	4327.25	+	5708.92i	0.382442	+	0.504555i
$505$	−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	$-0.390402\pi$
$509$	7752.57			0.675101			0.337551	+	0.941307i	$0.390402\pi$
$510$	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	$-0.417704\pi$
$521$	6080.85			0.511338			0.255669	+	0.966764i	$0.417704\pi$
$522$	1654.52	−	4703.10i	0.138729	−	0.394347i
$523$		−	13407.4i		−	1.12096i	−0.828167	−	0.560482i	$-0.810616\pi$
$523$		−	13407.4i		−	1.12096i	0.828167	−	0.560482i	$-0.189384\pi$
$524$	15529.9			1.29471
$525$	2404.60	−	77.7591i	0.199896	−	0.00646416i
$526$	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
$546$	5869.05	−	189.792i	0.460022	−	0.0148761i
$547$	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	$-0.338935\pi$
$563$	12949.4			0.969366			0.484683	+	0.874690i	$0.338935\pi$
$564$	−17530.2	+	12416.3i	−1.30878	+	0.926986i
$565$			9957.30i			0.741428i
$566$	−2737.35			−0.203285
$567$	−4122.76	−	12856.4i	−0.305361	−	0.952237i
$568$	−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	$0.119657\pi$
$577$			10176.6i			0.734245i	−0.930173	+	0.367122i	$0.880343\pi$
$578$		−	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	$-0.616285\pi$
$587$	−10161.5			−0.714499			−0.357249	+	0.934009i	$0.616285\pi$
$588$	10777.2	+	6631.45i	0.755857	+	0.465096i
$589$	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	$-0.649061\pi$
$593$	−13035.7			−0.902722			−0.451361	+	0.892341i	$0.649061\pi$
$594$	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	$-0.759760\pi$
$601$		−	20188.0i		−	1.37019i	0.728452	−	0.685096i	$-0.240240\pi$
$602$	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	$-0.756672\pi$
$607$		−	20701.4i		−	1.38426i	0.721773	−	0.692130i	$-0.243328\pi$
$608$	2152.41			0.143572
$609$	−605.373	−	18720.4i	−0.0402807	−	1.24563i
$610$	−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	$-0.708842\pi$
$619$		−	24406.2i		−	1.58476i	0.610027	−	0.792380i	$-0.291158\pi$
$620$		−	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
$630$	−1432.87	−	1890.38i	−0.0906143	−	0.119547i
$631$	−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	$0.0276015\pi$
$643$			2824.13i			0.173208i	−0.996243	+	0.0866039i	$0.972399\pi$
$644$	−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	$-0.470960\pi$
$647$	2998.63			0.182208			0.0911039	+	0.995841i	$0.470960\pi$
$648$	6538.70	−	8143.25i	0.396395	−	0.493668i
$649$			7366.69i			0.445559i
$650$	1525.48			0.0920526
$651$	644.702	+	19936.6i	0.0388139	+	1.20027i
$652$	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	$0.000993215\pi$
$661$			106.053i			0.00624055i	−0.999995	+	0.00312027i	$0.999007\pi$
$662$		−	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
$672$	483.970	+	14966.1i	0.0277821	+	0.859123i
$673$	−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	$-0.536525\pi$
$677$	−4033.61			−0.228987			−0.114494	+	0.993424i	$0.536525\pi$
$678$	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	$0.146914\pi$
$691$			16178.2i			0.890663i	−0.895366	+	0.445332i	$0.853086\pi$
$692$	11312.3			0.621430
$693$	6848.95	+	9035.79i	0.375426	+	0.495298i
$694$	−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
$714$	−28.2475	−	873.517i	−0.00148058	−	0.0457851i
$715$	−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	$-0.682493\pi$
$719$	−20915.2			−1.08485			−0.542423	+	0.840106i	$0.682493\pi$
$720$	−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	$0.371207\pi$
$727$			36038.5i			1.83851i	−0.393666	+	0.919253i	$0.628793\pi$
$728$	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	$-0.819259\pi$
$733$		−	21345.1i		−	1.07558i	0.843079	−	0.537790i	$-0.180741\pi$
$734$	11079.5			0.557154
$735$	−7589.68	−	4670.10i	−0.380884	−	0.234366i
$736$	−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
$756$	5556.38	−	17591.2i	0.267306	−	0.846275i
$757$	−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	$-0.387852\pi$
$761$	14488.6			0.690160			0.345080	+	0.938573i	$0.387852\pi$
$762$	−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	$-0.868484\pi$
$769$		−	17124.6i		−	0.803031i	0.915852	−	0.401515i	$-0.131516\pi$
$770$	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	$-0.592515\pi$
$773$	−12317.6			−0.573137			−0.286569	+	0.958060i	$0.592515\pi$
$774$	−7785.22	−	2738.79i	−0.361543	−	0.127188i
$775$			5181.89i			0.240179i
$776$	−1236.92			−0.0572204
$777$	−16492.9	+	533.343i	−0.761493	+	0.0246249i
$778$	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	$0.0399441\pi$
$787$			5526.55i			0.250318i	−0.992137	+	0.125159i	$0.960056\pi$
$788$			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	$-0.244936\pi$
$797$	32322.3			1.43653			0.718266	+	0.695769i	$0.244936\pi$
$798$	1262.30	−	40.8200i	0.0559963	−	0.00181079i
$799$	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	$-0.961910\pi$
$811$		−	5514.22i		−	0.238755i	0.992849	−	0.119378i	$-0.0380899\pi$
$812$	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
$819$	−19427.3	−	25630.4i	−0.828872	−	1.09353i
$820$	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	$-0.898661\pi$
$829$		−	14942.6i		−	0.626027i	0.949749	−	0.313013i	$-0.101339\pi$
$830$		−	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	$-0.310601\pi$
$839$	27243.7			1.12104			0.560522	+	0.828140i	$0.310601\pi$
$840$	−222.792	−	6889.56i	−0.00915127	−	0.282991i
$841$	−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	$-0.737636\pi$
$853$		−	36573.7i		−	1.46807i	0.679114	−	0.734033i	$-0.262364\pi$
$854$	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	$-0.384609\pi$
$857$	17793.8			0.709245			0.354623	+	0.935010i	$0.384609\pi$
$858$	4155.27	+	5866.69i	0.165336	+	0.233433i
$859$			18563.7i			0.737353i	0.929558	+	0.368676i	$0.120189\pi$
$859$			18563.7i			0.737353i	−0.929558	+	0.368676i	$0.879811\pi$
$860$	11437.2			0.453496
$861$	−20671.3	+	668.463i	−0.818208	+	0.0264589i
$862$	−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	$-0.672552\pi$
$881$	−26982.4			−1.03185			−0.515925	+	0.856634i	$0.672552\pi$
$882$	567.660	+	8767.88i	0.0216713	+	0.334728i
$883$	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	$-0.646803\pi$
$887$	−23512.3			−0.890040			−0.445020	+	0.895521i	$0.646803\pi$
$888$	−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
$903$	−30988.5	+	1002.10i	−1.14201	+	0.0369299i
$904$	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
$924$	500.720	+	15484.1i	0.0178273	+	0.551287i
$925$	−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	$-0.747520\pi$
$929$	−39730.9			−1.40315			−0.701576	+	0.712595i	$0.747520\pi$
$930$	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	$-0.863555\pi$
$937$		−	23843.3i		−	0.831297i	0.909525	−	0.415648i	$-0.136445\pi$
$938$	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	$-0.516146\pi$
$941$	−2927.06			−0.101402			−0.0507011	+	0.998714i	$0.516146\pi$
$942$	−6906.61	+	4891.82i	−0.238885	+	0.169198i
$943$		−	28923.1i		−	0.998796i
$944$	14037.9			0.484000
$945$	−3913.00	+	12388.3i	−0.134698	+	0.426446i
$946$	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
$966$	−12280.8	+	397.131i	−0.409034	+	0.0132272i
$967$	−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	$-0.418927\pi$
$971$	15246.9			0.503909			0.251955	+	0.967739i	$0.418927\pi$
$972$	−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	$-0.334870\pi$
$983$	30561.8			0.991629			0.495815	+	0.868428i	$0.334870\pi$
$984$	−9246.71	−	13055.1i	−0.299567	−	0.422950i
$985$		−	1867.84i		−	0.0604208i
$986$	−1767.59			−0.0570908
$987$	−56006.7	+	1811.13i	−1.80619	+	0.0584081i
$988$	−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	$0.176983\pi$
$997$			33231.0i			1.05560i	−0.849368	+	0.527801i	$0.823017\pi$
$998$			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.a.41.9	yes	16
3.2	odd	2		105.4.b.b.41.8	yes	16
7.6	odd	2		105.4.b.b.41.9	yes	16
21.20	even	2	inner	105.4.b.a.41.8	✓	16

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

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} +(96.1838 - 3.11036i) 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} +(2.95091 + 91.2530i) 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} +(398.506 - 302.060i) 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} +(682.896 - 22.0833i) 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	\( 16 q - 2 q^{3} - 64 q^{4} - 80 q^{5} - 28 q^{6} - 4 q^{7} - 22 q^{9} - 66 q^{12} - 90 q^{14} + 10 q^{15} + 376 q^{16} - 72 q^{17} - 182 q^{18} + 320 q^{20} - 74 q^{21} - 276 q^{22} + 526 q^{24} + 400 q^{25} + 696 q^{26} - 128 q^{27} + 10 q^{28} + 140 q^{30} - 502 q^{33} + 20 q^{35} + 996 q^{36} - 812 q^{37} - 1200 q^{38} - 594 q^{39} - 936 q^{41} - 1834 q^{42} - 548 q^{43} + 110 q^{45} + 1224 q^{46} + 912 q^{47} + 1850 q^{48} + 328 q^{49} + 750 q^{51} - 2950 q^{54} + 1254 q^{56} + 432 q^{57} + 576 q^{58} - 552 q^{59} + 330 q^{60} - 1860 q^{62} - 898 q^{63} - 4000 q^{64} + 1378 q^{66} + 1004 q^{67} + 3828 q^{68} + 1988 q^{69} + 450 q^{70} + 1988 q^{72} - 50 q^{75} + 1152 q^{77} + 1446 q^{78} + 1292 q^{79} - 1880 q^{80} - 2950 q^{81} - 1752 q^{83} + 1068 q^{84} + 360 q^{85} + 1910 q^{87} - 912 q^{88} + 6096 q^{89} + 910 q^{90} - 552 q^{91} - 1080 q^{93} - 9546 q^{96} - 4824 q^{98} + 2530 q^{99}+O(q^{100}) \) 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 - 74 * 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 - 1834 * 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 - 898 * 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 + 1068 * 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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