LMFDB - Embedded newform 40.4.d.a.21.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,4,Mod(21,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("40.21");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	40.d (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:	$2.36007640023$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{11} + 7x^{10} - 12x^{9} + 21x^{8} - 68x^{6} + 336x^{4} - 768x^{3} + 1792x^{2} - 4096x + 4096 $ x^12 - 4x^11 + 7x^10 - 12x^9 + 21x^8 - 68x^6 + 336x^4 - 768x^3 + 1792x^2 - 4096*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.9
Root			$1.98839 - 0.215211i$ of defining polynomial
Character	$\chi$	$=$	40.21
Dual form			40.4.d.a.21.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.20360 - 1.77318i) q^{2} +9.57890i q^{3} +(1.71169 - 7.81474i) q^{4} +5.00000i q^{5} +(16.9851 + 21.1081i) q^{6} +21.5703 q^{7} +(-10.0850 - 20.2557i) q^{8} -64.7554 q^{9} +O(q^{10})$	\(q+(2.20360 - 1.77318i) q^{2} +9.57890i q^{3} +(1.71169 - 7.81474i) q^{4} +5.00000i q^{5} +(16.9851 + 21.1081i) q^{6} +21.5703 q^{7} +(-10.0850 - 20.2557i) q^{8} -64.7554 q^{9} +(8.86588 + 11.0180i) q^{10} -37.2871i q^{11} +(74.8566 + 16.3961i) q^{12} -24.1097i q^{13} +(47.5322 - 38.2479i) q^{14} -47.8945 q^{15} +(-58.1402 - 26.7528i) q^{16} -14.4940 q^{17} +(-142.695 + 114.823i) q^{18} +26.6887i q^{19} +(39.0737 + 8.55846i) q^{20} +206.620i q^{21} +(-66.1166 - 82.1658i) q^{22} -8.36366 q^{23} +(194.027 - 96.6035i) q^{24} -25.0000 q^{25} +(-42.7508 - 53.1282i) q^{26} -361.655i q^{27} +(36.9216 - 168.566i) q^{28} +104.553i q^{29} +(-105.540 + 84.9254i) q^{30} +204.288 q^{31} +(-175.555 + 44.1404i) q^{32} +357.170 q^{33} +(-31.9389 + 25.7004i) q^{34} +107.851i q^{35} +(-110.841 + 506.046i) q^{36} -130.923i q^{37} +(47.3237 + 58.8111i) q^{38} +230.945 q^{39} +(101.278 - 50.4251i) q^{40} -437.963 q^{41} +(366.373 + 455.307i) q^{42} +308.764i q^{43} +(-291.389 - 63.8240i) q^{44} -323.777i q^{45} +(-18.4301 + 14.8302i) q^{46} +97.1081 q^{47} +(256.263 - 556.920i) q^{48} +122.277 q^{49} +(-55.0900 + 44.3294i) q^{50} -138.836i q^{51} +(-188.411 - 41.2684i) q^{52} -154.502i q^{53} +(-641.279 - 796.943i) q^{54} +186.436 q^{55} +(-217.537 - 436.920i) q^{56} -255.648 q^{57} +(185.390 + 230.392i) q^{58} +544.088i q^{59} +(-81.9806 + 374.283i) q^{60} +374.601i q^{61} +(450.168 - 362.238i) q^{62} -1396.79 q^{63} +(-308.584 + 408.558i) q^{64} +120.549 q^{65} +(787.058 - 633.325i) q^{66} +19.3982i q^{67} +(-24.8092 + 113.267i) q^{68} -80.1147i q^{69} +(191.240 + 237.661i) q^{70} -955.725 q^{71} +(653.060 + 1311.66i) q^{72} +127.417 q^{73} +(-232.150 - 288.502i) q^{74} -239.473i q^{75} +(208.565 + 45.6828i) q^{76} -804.293i q^{77} +(508.910 - 409.506i) q^{78} +973.871 q^{79} +(133.764 - 290.701i) q^{80} +1715.87 q^{81} +(-965.094 + 776.586i) q^{82} -55.0210i q^{83} +(1614.68 + 353.669i) q^{84} -72.4698i q^{85} +(547.493 + 680.392i) q^{86} -1001.50 q^{87} +(-755.275 + 376.041i) q^{88} -919.812 q^{89} +(-574.114 - 713.474i) q^{90} -520.054i q^{91} +(-14.3160 + 65.3598i) q^{92} +1956.85i q^{93} +(213.987 - 172.190i) q^{94} -133.443 q^{95} +(-422.816 - 1681.63i) q^{96} +297.986 q^{97} +(269.449 - 216.818i) q^{98} +2414.54i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 16 q^{4} - 36 q^{6} + 28 q^{7} - 40 q^{8} - 108 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 + 16 * q^4 - 36 * q^6 + 28 * q^7 - 40 * q^8 - 108 * q^9	$ 12 q + 2 q^{2} + 16 q^{4} - 36 q^{6} + 28 q^{7} - 40 q^{8} - 108 q^{9} + 30 q^{10} + 188 q^{12} + 68 q^{14} - 60 q^{15} - 56 q^{16} - 206 q^{18} + 20 q^{20} - 164 q^{22} + 604 q^{23} + 360 q^{24} - 300 q^{25} - 308 q^{26} - 436 q^{28} + 40 q^{30} - 264 q^{31} + 72 q^{32} - 232 q^{33} - 180 q^{34} + 440 q^{36} + 820 q^{38} + 600 q^{39} + 120 q^{40} + 40 q^{41} + 884 q^{42} - 472 q^{44} - 1268 q^{46} - 940 q^{47} + 424 q^{48} + 1308 q^{49} - 50 q^{50} + 1024 q^{52} - 1512 q^{54} + 440 q^{55} - 728 q^{56} - 680 q^{57} - 360 q^{58} - 820 q^{60} + 592 q^{62} - 1300 q^{63} - 2048 q^{64} + 2928 q^{66} - 2344 q^{68} + 1160 q^{70} - 1592 q^{71} - 152 q^{72} + 432 q^{73} - 420 q^{74} + 2256 q^{76} + 3320 q^{78} + 2016 q^{79} + 1600 q^{80} + 2508 q^{81} + 88 q^{82} + 1048 q^{84} - 244 q^{86} - 1968 q^{87} + 4080 q^{88} - 424 q^{89} - 2250 q^{90} - 900 q^{92} + 292 q^{94} - 1520 q^{95} - 5920 q^{96} - 1584 q^{97} - 7266 q^{98}+O(q^{100}) $ 12 * q + 2 * q^2 + 16 * q^4 - 36 * q^6 + 28 * q^7 - 40 * q^8 - 108 * q^9 + 30 * q^10 + 188 * q^12 + 68 * q^14 - 60 * q^15 - 56 * q^16 - 206 * q^18 + 20 * q^20 - 164 * q^22 + 604 * q^23 + 360 * q^24 - 300 * q^25 - 308 * q^26 - 436 * q^28 + 40 * q^30 - 264 * q^31 + 72 * q^32 - 232 * q^33 - 180 * q^34 + 440 * q^36 + 820 * q^38 + 600 * q^39 + 120 * q^40 + 40 * q^41 + 884 * q^42 - 472 * q^44 - 1268 * q^46 - 940 * q^47 + 424 * q^48 + 1308 * q^49 - 50 * q^50 + 1024 * q^52 - 1512 * q^54 + 440 * q^55 - 728 * q^56 - 680 * q^57 - 360 * q^58 - 820 * q^60 + 592 * q^62 - 1300 * q^63 - 2048 * q^64 + 2928 * q^66 - 2344 * q^68 + 1160 * q^70 - 1592 * q^71 - 152 * q^72 + 432 * q^73 - 420 * q^74 + 2256 * q^76 + 3320 * q^78 + 2016 * q^79 + 1600 * q^80 + 2508 * q^81 + 88 * q^82 + 1048 * q^84 - 244 * q^86 - 1968 * q^87 + 4080 * q^88 - 424 * q^89 - 2250 * q^90 - 900 * q^92 + 292 * q^94 - 1520 * q^95 - 5920 * q^96 - 1584 * q^97 - 7266 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	2.20360	−	1.77318i	0.779090	−	0.626913i
$2$	2.20360	−	1.77318i	0.779090	−	0.626913i
$3$			9.57890i			1.84346i	0.387831	+	0.921730i	$0.373224\pi$
$3$			9.57890i			1.84346i	−0.387831	+	0.921730i	$0.626776\pi$
$4$	1.71169	−	7.81474i	0.213961	−	0.976842i
$5$			5.00000i			0.447214i
$5$			5.00000i			0.447214i
$6$	16.9851	+	21.1081i	1.15569	+	1.43622i
$7$	21.5703			1.16469			0.582343	−	0.812943i	$-0.302136\pi$
$7$	21.5703			1.16469			0.582343	+	0.812943i	$0.302136\pi$
$8$	−10.0850	−	20.2557i	−0.445699	−	0.895183i
$9$	−64.7554			−2.39835
$10$	8.86588	+	11.0180i	0.280364	+	0.348419i
$11$		−	37.2871i		−	1.02204i	−0.859568	−	0.511022i	$-0.829267\pi$
$11$		−	37.2871i		−	1.02204i	0.859568	−	0.511022i	$-0.170733\pi$
$12$	74.8566	+	16.3961i	1.80077	+	0.394429i
$13$		−	24.1097i		−	0.514372i	−0.966362	−	0.257186i	$-0.917205\pi$
$13$		−	24.1097i		−	0.514372i	0.966362	−	0.257186i	$-0.0827954\pi$
$14$	47.5322	−	38.2479i	0.907394	−	0.730156i
$15$	−47.8945			−0.824421
$16$	−58.1402	−	26.7528i	−0.908441	−	0.418013i
$17$	−14.4940			−0.206783			−0.103391	−	0.994641i	$-0.532969\pi$
$17$	−14.4940			−0.206783			−0.103391	+	0.994641i	$0.532969\pi$
$18$	−142.695	+	114.823i	−1.86853	+	1.50355i
$19$			26.6887i			0.322253i	0.986934	+	0.161126i	$0.0515127\pi$
$19$			26.6887i			0.322253i	−0.986934	+	0.161126i	$0.948487\pi$
$20$	39.0737	+	8.55846i	0.436857	+	0.0956864i
$21$			206.620i			2.14705i
$22$	−66.1166	−	82.1658i	−0.640732	−	0.796264i
$23$	−8.36366			−0.0758236			−0.0379118	−	0.999281i	$-0.512071\pi$
$23$	−8.36366			−0.0758236			−0.0379118	+	0.999281i	$0.512071\pi$
$24$	194.027	−	96.6035i	1.65023	−	0.821630i
$25$	−25.0000			−0.200000
$26$	−42.7508	−	53.1282i	−0.322466	−	0.400742i
$27$		−	361.655i		−	2.57780i
$28$	36.9216	−	168.566i	0.249198	−	1.13771i
$29$			104.553i			0.669481i	0.942310	+	0.334741i	$0.108649\pi$
$29$			104.553i			0.669481i	−0.942310	+	0.334741i	$0.891351\pi$
$30$	−105.540	+	84.9254i	−0.642298	+	0.516840i
$31$	204.288			1.18359			0.591793	−	0.806090i	$-0.298420\pi$
$31$	204.288			1.18359			0.591793	+	0.806090i	$0.298420\pi$
$32$	−175.555	+	44.1404i	−0.969815	+	0.243843i
$33$	357.170			1.88410
$34$	−31.9389	+	25.7004i	−0.161102	+	0.129635i
$35$			107.851i			0.520863i
$36$	−110.841	+	506.046i	−0.513154	+	2.34281i
$37$		−	130.923i		−	0.581720i	−0.956766	−	0.290860i	$-0.906059\pi$
$37$		−	130.923i		−	0.581720i	0.956766	−	0.290860i	$-0.0939414\pi$
$38$	47.3237	+	58.8111i	0.202024	+	0.251064i
$39$	230.945			0.948225
$40$	101.278	−	50.4251i	0.400338	−	0.199323i
$41$	−437.963			−1.66825			−0.834126	−	0.551574i	$-0.814027\pi$
$41$	−437.963			−1.66825			−0.834126	+	0.551574i	$0.814027\pi$
$42$	366.373	+	455.307i	1.34601	+	1.67275i
$43$			308.764i			1.09503i	0.836797	+	0.547513i	$0.184425\pi$
$43$			308.764i			1.09503i	−0.836797	+	0.547513i	$0.815575\pi$
$44$	−291.389	−	63.8240i	−0.998376	−	0.218678i
$45$		−	323.777i		−	1.07257i
$46$	−18.4301	+	14.8302i	−0.0590734	+	0.0475348i
$47$	97.1081			0.301376			0.150688	−	0.988581i	$-0.451851\pi$
$47$	97.1081			0.301376			0.150688	+	0.988581i	$0.451851\pi$
$48$	256.263	−	556.920i	0.770591	−	1.67468i
$49$	122.277			0.356492
$50$	−55.0900	+	44.3294i	−0.155818	+	0.125383i
$51$		−	138.836i		−	0.381196i
$52$	−188.411	−	41.2684i	−0.502461	−	0.110056i
$53$		−	154.502i		−	0.400425i	−0.979753	−	0.200212i	$-0.935837\pi$
$53$		−	154.502i		−	0.400425i	0.979753	−	0.200212i	$-0.0641632\pi$
$54$	−641.279	−	796.943i	−1.61606	−	2.00834i
$55$	186.436			0.457072
$56$	−217.537	−	436.920i	−0.519100	−	1.04261i
$57$	−255.648			−0.594060
$58$	185.390	+	230.392i	0.419706	+	0.521586i
$59$			544.088i			1.20058i	0.799782	+	0.600290i	$0.204948\pi$
$59$			544.088i			1.20058i	−0.799782	+	0.600290i	$0.795052\pi$
$60$	−81.9806	+	374.283i	−0.176394	+	0.805329i
$61$			374.601i			0.786275i	0.919480	+	0.393137i	$0.128610\pi$
$61$			374.601i			0.786275i	−0.919480	+	0.393137i	$0.871390\pi$
$62$	450.168	−	362.238i	0.922120	−	0.742005i
$63$	−1396.79			−2.79332
$64$	−308.584	+	408.558i	−0.602704	+	0.797965i
$65$	120.549			0.230034
$66$	787.058	−	633.325i	1.46788	−	1.18116i
$67$			19.3982i			0.0353711i	0.999844	+	0.0176855i	$0.00562977\pi$
$67$			19.3982i			0.0353711i	−0.999844	+	0.0176855i	$0.994370\pi$
$68$	−24.8092	+	113.267i	−0.0442435	+	0.201994i
$69$		−	80.1147i		−	0.139778i
$70$	191.240	+	237.661i	0.326536	+	0.405799i
$71$	−955.725			−1.59752			−0.798759	−	0.601651i	$-0.794510\pi$
$71$	−955.725			−1.59752			−0.798759	+	0.601651i	$0.794510\pi$
$72$	653.060	+	1311.66i	1.06894	+	2.14696i
$73$	127.417			0.204287			0.102144	−	0.994770i	$-0.467430\pi$
$73$	127.417			0.204287			0.102144	+	0.994770i	$0.467430\pi$
$74$	−232.150	−	288.502i	−0.364687	−	0.453212i
$75$		−	239.473i		−	0.368692i
$76$	208.565	+	45.6828i	0.314790	+	0.0689496i
$77$		−	804.293i		−	1.19036i
$78$	508.910	−	409.506i	0.738753	−	0.594454i
$79$	973.871			1.38695			0.693475	−	0.720481i	$-0.256079\pi$
$79$	973.871			1.38695			0.693475	+	0.720481i	$0.256079\pi$
$80$	133.764	−	290.701i	0.186941	−	0.406267i
$81$	1715.87			2.35373
$82$	−965.094	+	776.586i	−1.29972	+	1.04585i
$83$		−	55.0210i		−	0.0727631i	−0.999338	−	0.0363816i	$-0.988417\pi$
$83$		−	55.0210i		−	0.0727631i	0.999338	−	0.0363816i	$-0.0115832\pi$
$84$	1614.68	+	353.669i	2.09733	+	0.459386i
$85$		−	72.4698i		−	0.0924760i
$86$	547.493	+	680.392i	0.686485	+	0.853123i
$87$	−1001.50			−1.23416
$88$	−755.275	+	376.041i	−0.914916	+	0.455525i
$89$	−919.812			−1.09550			−0.547752	−	0.836641i	$-0.684516\pi$
$89$	−919.812			−1.09550			−0.547752	+	0.836641i	$0.684516\pi$
$90$	−574.114	−	713.474i	−0.672410	−	0.835631i
$91$		−	520.054i		−	0.599082i
$92$	−14.3160	+	65.3598i	−0.0162233	+	0.0740677i
$93$			1956.85i			2.18189i
$94$	213.987	−	172.190i	0.234799	−	0.188936i
$95$	−133.443			−0.144116
$96$	−422.816	−	1681.63i	−0.449516	−	1.78782i
$97$	297.986			0.311916			0.155958	−	0.987764i	$-0.450154\pi$
$97$	297.986			0.311916			0.155958	+	0.987764i	$0.450154\pi$
$98$	269.449	−	216.818i	0.277739	−	0.223489i
$99$			2414.54i			2.45122i
$100$	−42.7923	+	195.368i	−0.0427923	+	0.195368i
$101$		−	1793.53i		−	1.76696i	−0.468469	−	0.883480i	$-0.655194\pi$
$101$		−	1793.53i		−	1.76696i	0.468469	−	0.883480i	$-0.344806\pi$
$102$	−246.181	−	305.939i	−0.238976	−	0.296986i
$103$	2084.11			1.99372			0.996862	−	0.0791611i	$-0.0252241\pi$
$103$	2084.11			1.99372			0.996862	+	0.0791611i	$0.0252241\pi$
$104$	−488.359	+	243.147i	−0.460457	+	0.229255i
$105$	−1033.10			−0.960191
$106$	−273.960	−	340.461i	−0.251031	−	0.311967i
$107$		−	67.2542i		−	0.0607637i	−0.999538	−	0.0303818i	$-0.990328\pi$
$107$		−	67.2542i		−	0.0607637i	0.999538	−	0.0303818i	$-0.00967233\pi$
$108$	−2826.24	−	619.042i	−2.51810	−	0.551550i
$109$		−	1459.15i		−	1.28222i	−0.767451	−	0.641108i	$-0.778475\pi$
$109$		−	1459.15i		−	1.28222i	0.767451	−	0.641108i	$-0.221525\pi$
$110$	410.829	−	330.583i	0.356100	−	0.286544i
$111$	1254.10			1.07238
$112$	−1254.10	−	577.066i	−1.05805	−	0.486854i
$113$	458.263			0.381502			0.190751	−	0.981638i	$-0.438908\pi$
$113$	458.263			0.381502			0.190751	+	0.981638i	$0.438908\pi$
$114$	−563.346	+	453.309i	−0.462826	+	0.372424i
$115$		−	41.8183i		−	0.0339093i
$116$	817.052	+	178.962i	0.653978	+	0.143243i
$117$			1561.24i			1.23364i
$118$	964.764	+	1198.95i	0.752659	+	0.935360i
$119$	−312.639			−0.240837
$120$	483.018	+	970.136i	0.367444	+	0.738007i
$121$	−59.3283			−0.0445743
$122$	664.234	+	825.471i	0.492926	+	0.612579i
$123$		−	4195.21i		−	3.07536i
$124$	349.678	−	1596.46i	0.253242	−	1.15618i
$125$		−	125.000i		−	0.0894427i
$126$	−3077.97	+	2476.76i	−2.17625	+	1.75117i
$127$	208.685			0.145809			0.0729047	−	0.997339i	$-0.476773\pi$
$127$	208.685			0.145809			0.0729047	+	0.997339i	$0.476773\pi$
$128$	44.4492	+	1447.47i	0.0306937	+	0.999529i
$129$	−2957.62			−2.01864
$130$	265.641	−	213.754i	0.179217	−	0.144211i
$131$			1784.69i			1.19030i	0.803616	+	0.595148i	$0.202906\pi$
$131$			1784.69i			1.19030i	−0.803616	+	0.595148i	$0.797094\pi$
$132$	611.364	−	2791.19i	0.403124	−	1.84047i
$133$			575.682i			0.375323i
$134$	34.3963	+	42.7457i	0.0221746	+	0.0275572i
$135$	1808.28			1.15283
$136$	146.172	+	293.585i	0.0921629	+	0.185108i
$137$	2380.60			1.48459			0.742293	−	0.670075i	$-0.233738\pi$
$137$	2380.60			1.48459			0.742293	+	0.670075i	$0.233738\pi$
$138$	−142.057	−	176.541i	−0.0876285	−	0.108899i
$139$		−	2858.52i		−	1.74429i	−0.489245	−	0.872146i	$-0.662728\pi$
$139$		−	2858.52i		−	1.74429i	0.489245	−	0.872146i	$-0.337272\pi$
$140$	842.830	+	184.608i	0.508801	+	0.111445i
$141$			930.189i			0.555575i
$142$	−2106.04	+	1694.67i	−1.24461	+	1.00150i
$143$	−898.983			−0.525711
$144$	3764.89	+	1732.39i	2.17876	+	1.00254i
$145$	−522.764			−0.299401
$146$	280.775	−	225.932i	0.159158	−	0.128070i
$147$			1171.28i			0.657179i
$148$	−1023.13	−	224.100i	−0.568248	−	0.124466i
$149$			897.894i			0.493680i	0.969056	+	0.246840i	$0.0793922\pi$
$149$			897.894i			0.493680i	−0.969056	+	0.246840i	$0.920608\pi$
$150$	−424.627	−	527.701i	−0.231138	−	0.287244i
$151$	−3431.32			−1.84925			−0.924625	−	0.380878i	$-0.875622\pi$
$151$	−3431.32			−1.84925			−0.924625	+	0.380878i	$0.875622\pi$
$152$	540.597	−	269.156i	0.288475	−	0.143628i
$153$	938.563			0.495937
$154$	−1426.15	−	1772.34i	−0.746251	−	0.927397i
$155$			1021.44i			0.529316i
$156$	395.306	−	1804.77i	0.202884	−	0.926266i
$157$			571.369i			0.290447i	0.989399	+	0.145224i	$0.0463901\pi$
$157$			571.369i			0.290447i	−0.989399	+	0.145224i	$0.953610\pi$
$158$	2146.02	−	1726.85i	1.08056	−	0.869496i
$159$	1479.96			0.738167
$160$	−220.702	−	877.776i	−0.109050	−	0.433714i
$161$	−180.406			−0.0883106
$162$	3781.08	−	3042.53i	1.83376	−	1.47558i
$163$		−	236.962i		−	0.113867i	−0.998378	−	0.0569333i	$-0.981868\pi$
$163$		−	236.962i		−	0.113867i	0.998378	−	0.0569333i	$-0.0181322\pi$
$164$	−749.657	+	3422.57i	−0.356941	+	1.62962i
$165$			1785.85i			0.842594i
$166$	−97.5619	−	121.244i	−0.0456161	−	0.0566890i
$167$	1448.46			0.671169			0.335585	−	0.942010i	$-0.391066\pi$
$167$	1448.46			0.671169			0.335585	+	0.942010i	$0.391066\pi$
$168$	4185.22	−	2083.76i	1.92200	−	0.956940i
$169$	1615.72			0.735421
$170$	−128.502	−	159.694i	−0.0579743	−	0.0720471i
$171$		−	1728.24i		−	0.772874i
$172$	2412.91	+	528.509i	1.06967	+	0.234293i
$173$			2529.74i			1.11175i	0.831266	+	0.555875i	$0.187617\pi$
$173$			2529.74i			1.11175i	−0.831266	+	0.555875i	$0.812383\pi$
$174$	−2206.91	+	1775.84i	−0.961523	+	0.773712i
$175$	−539.257			−0.232937
$176$	−997.536	+	2167.88i	−0.427228	+	0.928467i
$177$	−5211.77			−2.21322
$178$	−2026.90	+	1630.99i	−0.853496	+	0.686785i
$179$		−	141.524i		−	0.0590949i	−0.999563	−	0.0295475i	$-0.990593\pi$
$179$		−	141.524i		−	0.0590949i	0.999563	−	0.0295475i	$-0.00940662\pi$
$180$	−2530.23	−	554.206i	−1.04774	−	0.229489i
$181$			3457.79i			1.41997i	0.704215	+	0.709987i	$0.251299\pi$
$181$			3457.79i			1.41997i	−0.704215	+	0.709987i	$0.748701\pi$
$182$	−922.147	−	1145.99i	−0.375572	−	0.466739i
$183$	−3588.27			−1.44947
$184$	84.3477	+	169.411i	0.0337945	+	0.0678760i
$185$	654.616			0.260153
$186$	3469.85	+	4312.12i	1.36786	+	1.69989i
$187$			540.438i			0.211341i
$188$	166.219	−	758.874i	0.0644828	−	0.294397i
$189$		−	7801.01i		−	3.00233i
$190$	−294.056	+	236.619i	−0.112279	+	0.0903480i
$191$	−1416.99			−0.536804			−0.268402	−	0.963307i	$-0.586496\pi$
$191$	−1416.99			−0.536804			−0.268402	+	0.963307i	$0.586496\pi$
$192$	−3913.54	−	2955.90i	−1.47102	−	1.11106i
$193$	−2681.12			−0.999955			−0.499978	−	0.866038i	$-0.666658\pi$
$193$	−2681.12			−0.999955			−0.499978	+	0.866038i	$0.666658\pi$
$194$	656.641	−	528.381i	0.243011	−	0.195544i
$195$			1154.72i			0.424059i
$196$	209.300	−	955.560i	0.0762755	−	0.348236i
$197$		−	2697.74i		−	0.975664i	−0.872938	−	0.487832i	$-0.837788\pi$
$197$		−	2697.74i		−	0.975664i	0.872938	−	0.487832i	$-0.162212\pi$
$198$	4281.41	+	5320.68i	1.53670	+	1.90972i
$199$	3543.25			1.26218			0.631091	−	0.775709i	$-0.282607\pi$
$199$	3543.25			1.26218			0.631091	+	0.775709i	$0.282607\pi$
$200$	252.126	+	506.392i	0.0891399	+	0.179037i
$201$	−185.813			−0.0652052
$202$	−3180.25	−	3952.22i	−1.10773	−	1.37662i
$203$			2255.23i			0.779735i
$204$	−1084.97	−	237.645i	−0.372368	−	0.0815611i
$205$		−	2189.81i		−	0.746065i
$206$	4592.54	−	3695.50i	1.55329	−	1.24989i
$207$	541.592			0.181851
$208$	−645.004	+	1401.75i	−0.215014	+	0.467277i
$209$	995.143			0.329356
$210$	−2276.53	+	1831.86i	−0.748075	+	0.601956i
$211$		−	152.205i		−	0.0496598i	−0.999692	−	0.0248299i	$-0.992096\pi$
$211$		−	152.205i		−	0.0496598i	0.999692	−	0.0248299i	$-0.00790441\pi$
$212$	−1207.39	−	264.460i	−0.391152	−	0.0856754i
$213$		−	9154.80i		−	2.94496i
$214$	−119.254	−	148.201i	−0.0380935	−	0.0473403i
$215$	−1543.82			−0.489710
$216$	−7325.57	+	3647.30i	−2.30760	+	1.14892i
$217$	4406.54			1.37851
$218$	−2587.34	−	3215.39i	−0.803837	−	0.998961i
$219$			1220.51i			0.376596i
$220$	319.120	−	1456.94i	0.0977958	−	0.446487i
$221$			349.446i			0.106363i
$222$	2763.53	−	2223.74i	0.835478	−	0.672287i
$223$	−2065.40			−0.620222			−0.310111	−	0.950700i	$-0.600366\pi$
$223$	−2065.40			−0.620222			−0.310111	+	0.950700i	$0.600366\pi$
$224$	−3786.77	+	952.120i	−1.12953	+	0.284001i
$225$	1618.89			0.479670
$226$	1009.83	−	812.580i	0.297224	−	0.239168i
$227$			2940.45i			0.859757i	0.902887	+	0.429878i	$0.141444\pi$
$227$			2940.45i			0.859757i	−0.902887	+	0.429878i	$0.858556\pi$
$228$	−437.591	+	1997.82i	−0.127106	+	0.580303i
$229$			4949.77i			1.42834i	0.699971	+	0.714171i	$0.253196\pi$
$229$			4949.77i			1.42834i	−0.699971	+	0.714171i	$0.746804\pi$
$230$	−74.1512	−	92.1507i	−0.0212582	−	0.0264184i
$231$	7704.25			2.19438
$232$	2117.79	−	1054.42i	0.599308	−	0.298387i
$233$	5193.31			1.46019			0.730096	−	0.683344i	$-0.239475\pi$
$233$	5193.31			1.46019			0.730096	+	0.683344i	$0.239475\pi$
$234$	2768.35	+	3440.34i	0.773387	+	0.961119i
$235$			485.540i			0.134779i
$236$	4251.90	+	931.311i	1.17278	+	0.256878i
$237$			9328.62i			2.55679i
$238$	−688.930	+	554.364i	−0.187633	+	0.150983i
$239$	−2066.30			−0.559238			−0.279619	−	0.960111i	$-0.590208\pi$
$239$	−2066.30			−0.559238			−0.279619	+	0.960111i	$0.590208\pi$
$240$	2784.60	+	1281.31i	0.748938	+	0.344619i
$241$	−2309.08			−0.617181			−0.308591	−	0.951195i	$-0.599857\pi$
$241$	−2309.08			−0.617181			−0.308591	+	0.951195i	$0.599857\pi$
$242$	−130.736	+	105.200i	−0.0347273	+	0.0279442i
$243$			6671.42i			1.76120i
$244$	2927.41	+	641.202i	0.768066	+	0.168232i
$245$			611.384i			0.159428i
$246$	−7438.84	−	9244.55i	−1.92798	−	2.39598i
$247$	643.457			0.165758
$248$	−2060.25	−	4137.99i	−0.527524	−	1.05953i
$249$	527.041			0.134136
$250$	−221.647	−	275.450i	−0.0560728	−	0.0696839i
$251$		−	3802.60i		−	0.956246i	−0.878293	−	0.478123i	$-0.841317\pi$
$251$		−	3802.60i		−	0.956246i	0.878293	−	0.478123i	$-0.158683\pi$
$252$	−2390.88	+	10915.6i	−0.597663	+	2.72863i
$253$			311.857i			0.0774951i
$254$	459.858	−	370.035i	0.113599	−	0.0914097i
$255$	694.182			0.170476
$256$	2664.57	+	3110.83i	0.650530	+	0.759480i
$257$	6168.56			1.49721			0.748607	−	0.663013i	$-0.230723\pi$
$257$	6168.56			1.49721			0.748607	+	0.663013i	$0.230723\pi$
$258$	−6517.41	+	5244.39i	−1.57270	+	1.26551i
$259$		−	2824.05i		−	0.677521i
$260$	206.342	−	942.057i	0.0492185	−	0.224707i
$261$		−	6770.36i		−	1.60565i
$262$	3164.56	+	3932.73i	0.746211	+	0.927347i
$263$	−1636.11			−0.383599			−0.191800	−	0.981434i	$-0.561432\pi$
$263$	−1636.11			−0.383599			−0.191800	+	0.981434i	$0.561432\pi$
$264$	−3602.07	−	7234.71i	−0.839742	−	1.68661i
$265$	772.511			0.179075
$266$	1020.79	+	1268.57i	0.235295	+	0.292410i
$267$		−	8810.79i		−	2.01952i
$268$	151.591	+	33.2036i	0.0345520	+	0.00756804i
$269$		−	2262.24i		−	0.512756i	−0.966577	−	0.256378i	$-0.917471\pi$
$269$		−	2262.24i		−	0.512756i	0.966577	−	0.256378i	$-0.0825292\pi$
$270$	3984.72	−	3206.39i	0.898156	−	0.722722i
$271$	41.6380			0.00933332			0.00466666	−	0.999989i	$-0.498515\pi$
$271$	41.6380			0.00933332			0.00466666	+	0.999989i	$0.498515\pi$
$272$	842.683	+	387.755i	0.187850	+	0.0864378i
$273$	4981.55			1.10438
$274$	5245.88	−	4221.22i	1.15663	−	0.930706i
$275$			932.178i			0.204409i
$276$	−626.075	−	137.132i	−0.136541	−	0.0299071i
$277$		−	2139.00i		−	0.463971i	−0.972719	−	0.231986i	$-0.925478\pi$
$277$		−	2139.00i		−	0.463971i	0.972719	−	0.231986i	$-0.0745223\pi$
$278$	−5068.66	−	6299.03i	−1.09352	−	1.35896i
$279$	−13228.7			−2.83865
$280$	2184.60	−	1087.68i	0.466268	−	0.232148i
$281$	−1493.53			−0.317069			−0.158534	−	0.987353i	$-0.550677\pi$
$281$	−1493.53			−0.317069			−0.158534	+	0.987353i	$0.550677\pi$
$282$	1649.39	+	2049.76i	0.348297	+	0.432843i
$283$		−	1090.20i		−	0.228995i	−0.993424	−	0.114498i	$-0.963474\pi$
$283$		−	1090.20i		−	0.228995i	0.993424	−	0.114498i	$-0.0365259\pi$
$284$	−1635.91	+	7468.74i	−0.341807	+	1.56052i
$285$		−	1278.24i		−	0.265672i
$286$	−1981.00	+	1594.05i	−0.409576	+	0.329575i
$287$	−9446.98			−1.94299
$288$	11368.1	−	2858.33i	2.32595	−	0.584822i
$289$	−4702.92			−0.957241
$290$	−1151.96	+	926.952i	−0.233260	+	0.187698i
$291$			2854.38i			0.575005i
$292$	218.098	−	995.727i	0.0437096	−	0.199557i
$293$		−	4067.51i		−	0.811011i	−0.914093	−	0.405506i	$-0.867095\pi$
$293$		−	4067.51i		−	0.811011i	0.914093	−	0.405506i	$-0.132905\pi$
$294$	2076.88	+	2581.02i	0.411994	+	0.512001i
$295$	−2720.44			−0.536916
$296$	−2651.94	+	1320.36i	−0.520746	+	0.259272i
$297$	−13485.1			−2.63463
$298$	1592.12	+	1978.60i	0.309494	+	0.384621i
$299$			201.646i			0.0390016i
$300$	−1871.42	−	409.903i	−0.360154	−	0.0788859i
$301$			6660.13i			1.27536i
$302$	−7561.25	+	6084.33i	−1.44073	+	1.15932i
$303$	17180.1			3.25732
$304$	713.998	−	1551.69i	0.134706	−	0.292748i
$305$	−1873.01			−0.351633
$306$	2068.22	−	1664.24i	0.386379	−	0.310909i
$307$			6736.05i			1.25227i	0.779715	+	0.626135i	$0.215364\pi$
$307$			6736.05i			1.25227i	−0.779715	+	0.626135i	$0.784636\pi$
$308$	−6285.34	−	1376.70i	−1.16279	−	0.254691i
$309$			19963.5i			3.67535i
$310$	1811.19	+	2250.84i	0.331835	+	0.412384i
$311$	3274.35			0.597014			0.298507	−	0.954407i	$-0.403511\pi$
$311$	3274.35			0.597014			0.298507	+	0.954407i	$0.403511\pi$
$312$	−2329.09	−	4677.95i	−0.422624	−	0.848835i
$313$	−9357.60			−1.68985			−0.844925	−	0.534885i	$-0.820355\pi$
$313$	−9357.60			−1.68985			−0.844925	+	0.534885i	$0.820355\pi$
$314$	1013.14	+	1259.07i	0.182085	+	0.226284i
$315$		−	6983.96i		−	1.24921i
$316$	1666.97	−	7610.55i	0.296754	−	1.35483i
$317$		−	9064.68i		−	1.60607i	−0.595934	−	0.803033i	$-0.703218\pi$
$317$		−	9064.68i		−	1.60607i	0.595934	−	0.803033i	$-0.296782\pi$
$318$	3261.24	−	2624.23i	0.575098	−	0.462766i
$319$	3898.47			0.684239
$320$	−2042.79	−	1542.92i	−0.356861	−	0.269537i
$321$	644.222			0.112015
$322$	−397.543	+	319.892i	−0.0688019	+	0.0553630i
$323$		−	386.825i		−	0.0666362i
$324$	2937.03	−	13409.0i	0.503606	−	2.29922i
$325$			602.744i			0.102874i
$326$	−420.175	−	522.168i	−0.0713844	−	0.0887123i
$327$	13977.1			2.36371
$328$	4416.87	+	8871.23i	0.743539	+	1.49339i
$329$	2094.65			0.351008
$330$	3166.62	+	3935.29i	0.528233	+	0.656457i
$331$			280.089i			0.0465108i	0.999730	+	0.0232554i	$0.00740310\pi$
$331$			280.089i			0.0465108i	−0.999730	+	0.0232554i	$0.992597\pi$
$332$	−429.975	−	94.1789i	−0.0710781	−	0.0155685i
$333$			8477.98i			1.39517i
$334$	3191.83	−	2568.38i	0.522901	−	0.420764i
$335$	−96.9908			−0.0158184
$336$	5527.66	−	12012.9i	0.897496	−	1.95047i
$337$	−5748.75			−0.929242			−0.464621	−	0.885510i	$-0.653809\pi$
$337$	−5748.75			−0.929242			−0.464621	+	0.885510i	$0.653809\pi$
$338$	3560.40	−	2864.96i	0.572959	−	0.461045i
$339$			4389.65i			0.703284i
$340$	−566.333	−	124.046i	−0.0903344	−	0.0197863i
$341$		−	7617.30i		−	1.20968i
$342$	−3064.47	−	3808.34i	−0.484525	−	0.602138i
$343$	−4761.06			−0.749484
$344$	6254.23	−	3113.90i	0.980248	−	0.488052i
$345$	400.573			0.0625106
$346$	4485.68	+	5574.53i	0.696969	+	0.866152i
$347$			2911.52i			0.450428i	0.974309	+	0.225214i	$0.0723081\pi$
$347$			2911.52i			0.450428i	−0.974309	+	0.225214i	$0.927692\pi$
$348$	−1714.26	+	7826.46i	−0.264063	+	1.20558i
$349$		−	5665.17i		−	0.868910i	−0.900693	−	0.434455i	$-0.856941\pi$
$349$		−	5665.17i		−	0.868910i	0.900693	−	0.434455i	$-0.143059\pi$
$350$	−1188.31	+	956.198i	−0.181479	+	0.146031i
$351$	−8719.42			−1.32595
$352$	1645.87	+	6545.95i	0.249219	+	0.991193i
$353$	−9428.18			−1.42156			−0.710781	−	0.703414i	$-0.751658\pi$
$353$	−9428.18			−1.42156			−0.710781	+	0.703414i	$0.751658\pi$
$354$	−11484.6	+	9241.38i	−1.72430	+	1.38750i
$355$		−	4778.63i		−	0.714432i
$356$	−1574.43	+	7188.09i	−0.234396	+	1.07013i
$357$		−	2994.74i		−	0.443973i
$358$	−250.947	−	311.862i	−0.0370474	−	0.0460403i
$359$	4573.16			0.672318			0.336159	−	0.941805i	$-0.390872\pi$
$359$	4573.16			0.672318			0.336159	+	0.941805i	$0.390872\pi$
$360$	−6558.32	+	3265.30i	−0.960150	+	0.478046i
$361$	6146.71			0.896153
$362$	6131.26	+	7619.57i	0.890199	+	1.10629i
$363$		−	568.300i		−	0.0821709i
$364$	−4064.08	−	890.172i	−0.585208	−	0.128180i
$365$			637.083i			0.0913601i
$366$	−7907.10	+	6362.63i	−1.12926	+	0.908689i
$367$	−2717.97			−0.386585			−0.193293	−	0.981141i	$-0.561917\pi$
$367$	−2717.97			−0.386585			−0.193293	+	0.981141i	$0.561917\pi$
$368$	486.265	+	223.751i	0.0688813	+	0.0316952i
$369$	28360.5			4.00105
$370$	1442.51	−	1160.75i	0.202683	−	0.163093i
$371$		−	3332.65i		−	0.466369i
$372$	15292.3	+	3349.53i	2.13137	+	0.466841i
$373$			5627.51i			0.781183i	0.920564	+	0.390592i	$0.127730\pi$
$373$			5627.51i			0.781183i	−0.920564	+	0.390592i	$0.872270\pi$
$374$	958.292	+	1190.91i	0.132492	+	0.164654i
$375$	1197.36			0.164884
$376$	−979.338	−	1966.99i	−0.134323	−	0.269786i
$377$	2520.74			0.344363
$378$	−13832.6	−	17190.3i	−1.88220	−	2.33908i
$379$		−	8066.74i		−	1.09330i	−0.837361	−	0.546650i	$-0.815903\pi$
$379$		−	8066.74i		−	1.09330i	0.837361	−	0.546650i	$-0.184097\pi$
$380$	−228.414	+	1042.82i	−0.0308352	+	0.140778i
$381$			1998.97i			0.268794i
$382$	−3122.47	+	2512.57i	−0.418219	+	0.336529i
$383$	10607.8			1.41523			0.707613	−	0.706600i	$-0.249772\pi$
$383$	10607.8			1.41523			0.707613	+	0.706600i	$0.249772\pi$
$384$	−13865.2	+	425.775i	−1.84259	+	0.0565826i
$385$	4021.47			0.532345
$386$	−5908.11	+	4754.10i	−0.779055	+	0.626884i
$387$		−	19994.1i		−	2.62625i
$388$	510.059	−	2328.68i	0.0667380	−	0.304693i
$389$			8992.58i			1.17209i	0.810280	+	0.586044i	$0.199315\pi$
$389$			8992.58i			1.17209i	−0.810280	+	0.586044i	$0.800685\pi$
$390$	2047.53	+	2544.55i	0.265848	+	0.330380i
$391$	121.223			0.0156790
$392$	−1233.16	−	2476.80i	−0.158888	−	0.319125i
$393$	−17095.3			−2.19426
$394$	−4783.56	−	5944.73i	−0.611656	−	0.760130i
$395$			4869.36i			0.620263i
$396$	18869.0	+	4132.95i	2.39445	+	0.524466i
$397$		−	8977.17i		−	1.13489i	−0.823411	−	0.567445i	$-0.807932\pi$
$397$		−	8977.17i		−	1.13489i	0.823411	−	0.567445i	$-0.192068\pi$
$398$	7807.90	−	6282.81i	0.983353	−	0.791278i
$399$	−5514.40			−0.691893
$400$	1453.51	+	668.821i	0.181688	+	0.0836026i
$401$	−3165.72			−0.394236			−0.197118	−	0.980380i	$-0.563158\pi$
$401$	−3165.72			−0.394236			−0.197118	+	0.980380i	$0.563158\pi$
$402$	−409.457	+	329.479i	−0.0508007	+	0.0408779i
$403$		−	4925.33i		−	0.608804i
$404$	−14016.0	−	3069.97i	−1.72604	−	0.378061i
$405$			8579.33i			1.05262i
$406$	3998.92	+	4969.62i	0.488826	+	0.607483i
$407$	−4881.75			−0.594543
$408$	−2812.22	+	1400.17i	−0.341240	+	0.169899i
$409$	−5417.61			−0.654972			−0.327486	−	0.944856i	$-0.606202\pi$
$409$	−5417.61			−0.654972			−0.327486	+	0.944856i	$0.606202\pi$
$410$	−3882.93	−	4825.47i	−0.467717	−	0.581251i
$411$			22803.5i			2.73678i
$412$	3567.35	−	16286.8i	0.426580	−	1.94755i
$413$			11736.1i			1.39830i
$414$	1193.45	−	960.338i	0.141679	−	0.114005i
$415$	275.105			0.0325407
$416$	1064.21	+	4232.59i	0.125426	+	0.498846i
$417$	27381.5			3.21554
$418$	2192.90	−	1764.56i	0.256598	−	0.206478i
$419$		−	6198.14i		−	0.722670i	−0.932436	−	0.361335i	$-0.882321\pi$
$419$		−	6198.14i		−	0.722670i	0.932436	−	0.361335i	$-0.117679\pi$
$420$	−1768.34	+	8073.39i	−0.205444	+	0.937955i
$421$		−	4344.57i		−	0.502949i	−0.967864	−	0.251474i	$-0.919085\pi$
$421$		−	4344.57i		−	0.502949i	0.967864	−	0.251474i	$-0.0809154\pi$
$422$	−269.886	−	335.398i	−0.0311323	−	0.0386894i
$423$	−6288.27			−0.722804
$424$	−3129.54	+	1558.16i	−0.358453	+	0.178469i
$425$	362.349			0.0413565
$426$	−16233.1	−	20173.5i	−1.84623	−	2.29439i
$427$			8080.25i			0.915763i
$428$	−525.574	−	115.118i	−0.0593565	−	0.0130011i
$429$		−	8611.27i		−	0.969128i
$430$	−3401.96	+	2737.47i	−0.381528	+	0.307006i
$431$	4750.74			0.530940			0.265470	−	0.964119i	$-0.414473\pi$
$431$	4750.74			0.530940			0.265470	+	0.964119i	$0.414473\pi$
$432$	−9675.31	+	21026.7i	−1.07755	+	2.34178i
$433$	4210.26			0.467280			0.233640	−	0.972323i	$-0.424936\pi$
$433$	4210.26			0.467280			0.233640	+	0.972323i	$0.424936\pi$
$434$	9710.25	−	7813.58i	1.07398	−	0.864202i
$435$		−	5007.50i		−	0.551934i
$436$	−11402.9	−	2497.62i	−1.25252	−	0.274345i
$437$		−	223.215i		−	0.0244344i
$438$	2164.18	+	2689.52i	0.236093	+	0.293402i
$439$	−5776.50			−0.628012			−0.314006	−	0.949421i	$-0.601671\pi$
$439$	−5776.50			−0.628012			−0.314006	+	0.949421i	$0.601671\pi$
$440$	−1880.21	−	3776.38i	−0.203717	−	0.409163i
$441$	−7918.08			−0.854992
$442$	619.629	+	770.038i	0.0666804	+	0.0828665i
$443$			11981.6i			1.28502i	0.766278	+	0.642510i	$0.222107\pi$
$443$			11981.6i			1.28502i	−0.766278	+	0.642510i	$0.777893\pi$
$444$	2146.63	−	9800.46i	0.229447	−	1.04754i
$445$		−	4599.06i		−	0.489924i
$446$	−4551.32	+	3662.32i	−0.483209	+	0.388825i
$447$	−8600.84			−0.910080
$448$	−6656.25	+	8812.71i	−0.701961	+	0.929378i
$449$	−5567.58			−0.585190			−0.292595	−	0.956236i	$-0.594519\pi$
$449$	−5567.58			−0.585190			−0.292595	+	0.956236i	$0.594519\pi$
$450$	3567.37	−	2870.57i	0.373706	−	0.300711i
$451$			16330.4i			1.70503i
$452$	784.404	−	3581.20i	0.0816267	−	0.372667i
$453$		−	32868.3i		−	3.40902i
$454$	5213.94	+	6479.58i	0.538992	+	0.669828i
$455$	2600.27			0.267918
$456$	2578.22	+	5178.33i	0.264772	+	0.531792i
$457$	−7283.56			−0.745538			−0.372769	−	0.927924i	$-0.621592\pi$
$457$	−7283.56			−0.745538			−0.372769	+	0.927924i	$0.621592\pi$
$458$	8776.82	+	10907.3i	0.895445	+	1.11281i
$459$			5241.82i			0.533044i
$460$	−326.799	−	71.5800i	−0.0331241	−	0.00725529i
$461$		−	11901.1i		−	1.20236i	−0.799113	−	0.601181i	$-0.794697\pi$
$461$		−	11901.1i		−	1.20236i	0.799113	−	0.601181i	$-0.205303\pi$
$462$	16977.1	−	13661.0i	1.70962	−	1.37569i
$463$	4915.73			0.493419			0.246710	−	0.969089i	$-0.420651\pi$
$463$	4915.73			0.493419			0.246710	+	0.969089i	$0.420651\pi$
$464$	2797.08	−	6078.72i	0.279852	−	0.608184i
$465$	−9784.27			−0.975773
$466$	11444.0	−	9208.65i	1.13762	−	0.915413i
$467$		−	3110.15i		−	0.308181i	−0.988057	−	0.154091i	$-0.950755\pi$
$467$		−	3110.15i		−	0.308181i	0.988057	−	0.154091i	$-0.0492447\pi$
$468$	12200.7	+	2672.35i	1.20508	+	0.263952i
$469$			418.424i			0.0411962i
$470$	860.949	+	1069.94i	0.0844949	+	0.105005i
$471$	−5473.09			−0.535428
$472$	11020.9	−	5487.14i	1.07474	−	0.535098i
$473$	11512.9			1.11916
$474$	16541.3	+	20556.5i	1.60288	+	1.99197i
$475$		−	667.217i		−	0.0644505i
$476$	−535.141	+	2443.19i	−0.0515297	+	0.235259i
$477$			10004.8i			0.960358i
$478$	−4553.30	+	3663.92i	−0.435697	+	0.350594i
$479$	6590.43			0.628652			0.314326	−	0.949315i	$-0.398221\pi$
$479$	6590.43			0.628652			0.314326	+	0.949315i	$0.398221\pi$
$480$	8408.13	−	2114.08i	0.799535	−	0.201030i
$481$	−3156.52			−0.299221
$482$	−5088.28	+	4094.40i	−0.480840	+	0.386919i
$483$		−	1728.10i		−	0.162797i
$484$	−101.552	+	463.635i	−0.00953717	+	0.0435420i
$485$			1489.93i			0.139493i
$486$	11829.6	+	14701.1i	1.10412	+	1.37213i
$487$	3139.99			0.292169			0.146085	−	0.989272i	$-0.453333\pi$
$487$	3139.99			0.292169			0.146085	+	0.989272i	$0.453333\pi$
$488$	7587.80	−	3777.86i	0.703860	−	0.350442i
$489$	2269.83			0.209909
$490$	1084.09	+	1347.24i	0.0999474	+	0.124209i
$491$		−	12057.6i		−	1.10825i	−0.832433	−	0.554126i	$-0.813053\pi$
$491$		−	12057.6i		−	1.10825i	0.832433	−	0.554126i	$-0.186947\pi$
$492$	−32784.4	−	7180.90i	−3.00414	−	0.658008i
$493$		−	1515.38i		−	0.138437i
$494$	1417.92	−	1140.96i	0.129140	−	0.103916i
$495$	−12072.7			−1.09622
$496$	−11877.3	−	5465.28i	−1.07522	−	0.494754i
$497$	−20615.3			−1.86061
$498$	1161.39	−	934.536i	0.104504	−	0.0840915i
$499$			8458.64i			0.758839i	0.925225	+	0.379420i	$0.123876\pi$
$499$			8458.64i			0.758839i	−0.925225	+	0.379420i	$0.876124\pi$
$500$	−976.842	−	213.961i	−0.0873714	−	0.0191373i
$501$			13874.7i			1.23727i
$502$	−6742.67	−	8379.40i	−0.599483	−	0.745001i
$503$	16896.2			1.49774			0.748869	−	0.662718i	$-0.230597\pi$
$503$	16896.2			1.49774			0.748869	+	0.662718i	$0.230597\pi$
$504$	14086.7	+	28293.0i	1.24498	+	2.50053i
$505$	8967.65			0.790208
$506$	552.977	+	687.207i	0.0485826	+	0.0603756i
$507$			15476.8i			1.35572i
$508$	357.204	−	1630.82i	0.0311976	−	0.142433i
$509$			6849.13i			0.596429i	0.954499	+	0.298214i	$0.0963910\pi$
$509$			6849.13i			0.596429i	−0.954499	+	0.298214i	$0.903609\pi$
$510$	1529.70	−	1230.91i	0.132816	−	0.106873i
$511$	2748.41			0.237931
$512$	11387.7	+	2130.27i	0.982949	+	0.183878i
$513$	9652.10			0.830703
$514$	13593.0	−	10937.9i	1.16646	−	0.938623i
$515$			10420.6i			0.891620i
$516$	−5062.54	+	23113.0i	−0.431910	+	1.97189i
$517$		−	3620.88i		−	0.308019i
$518$	−5007.54	−	6223.07i	−0.424746	−	0.527849i
$519$	−24232.1			−2.04947
$520$	−1215.74	−	2441.80i	−0.102526	−	0.205923i
$521$	11044.1			0.928696			0.464348	−	0.885653i	$-0.346289\pi$
$521$	11044.1			0.928696			0.464348	+	0.885653i	$0.346289\pi$
$522$	−12005.0	−	14919.1i	−1.00660	−	1.25094i
$523$			3115.75i			0.260502i	0.991481	+	0.130251i	$0.0415782\pi$
$523$			3115.75i			0.260502i	−0.991481	+	0.130251i	$0.958422\pi$
$524$	13946.8	+	3054.83i	1.16273	+	0.254677i
$525$		−	5165.49i		−	0.429410i
$526$	−3605.32	+	2901.10i	−0.298858	+	0.240483i
$527$	−2960.94			−0.244745
$528$	−20765.9	−	9555.30i	−1.71159	−	0.787578i
$529$	−12097.0			−0.994251
$530$	1702.30	−	1369.80i	0.139516	−	0.112265i
$531$		−	35232.6i		−	2.87941i
$532$	4498.80	+	985.390i	0.366631	+	0.0803046i
$533$			10559.2i			0.858103i
$534$	−15623.1	−	19415.4i	−1.26606	−	1.57339i
$535$	336.271			0.0271743
$536$	392.923	−	195.631i	0.0316636	−	0.0157649i
$537$	1355.64			0.108939
$538$	−4011.36	−	4985.07i	−0.321453	−	0.399483i
$539$		−	4559.35i		−	0.364350i
$540$	3095.21	−	14131.2i	0.246661	−	1.12613i
$541$			14840.6i			1.17938i	0.807629	+	0.589691i	$0.200751\pi$
$541$			14840.6i			1.17938i	−0.807629	+	0.589691i	$0.799249\pi$
$542$	91.7535	−	73.8316i	0.00727150	−	0.00585118i
$543$	−33121.8			−2.61767
$544$	2544.49	−	639.769i	0.200541	−	0.0504226i
$545$	7295.76			0.573424
$546$	10977.3	−	8833.16i	0.860414	−	0.692352i
$547$			12622.8i			0.986679i	0.869837	+	0.493340i	$0.164224\pi$
$547$			12622.8i			0.986679i	−0.869837	+	0.493340i	$0.835776\pi$
$548$	4074.85	−	18603.8i	0.317644	−	1.45021i
$549$		−	24257.5i		−	1.88576i
$550$	1652.92	+	2054.15i	0.128146	+	0.159253i
$551$	−2790.37			−0.215742
$552$	−1622.78	+	807.958i	−0.125127	+	0.0622989i
$553$	21006.7			1.61536
$554$	−3792.83	−	4713.50i	−0.290870	−	0.361475i
$555$			6270.50i			0.479582i
$556$	−22338.6	−	4892.91i	−1.70390	−	0.373211i
$557$			13382.1i			1.01798i	0.860771	+	0.508992i	$0.169982\pi$
$557$			13382.1i			1.01798i	−0.860771	+	0.508992i	$0.830018\pi$
$558$	−29150.8	+	23456.9i	−2.21156	+	1.77959i
$559$	7444.23			0.563251
$560$	2885.33	−	6270.50i	0.217728	−	0.473173i
$561$	−5176.80			−0.389599
$562$	−3291.13	+	2648.28i	−0.247025	+	0.198774i
$563$		−	153.895i		−	0.0115203i	−0.999983	−	0.00576014i	$-0.998166\pi$
$563$		−	153.895i		−	0.0115203i	0.999983	−	0.00576014i	$-0.00183352\pi$
$564$	7269.18	+	1592.20i	0.542709	+	0.118872i
$565$			2291.31i			0.170613i
$566$	−1933.12	−	2402.37i	−0.143560	−	0.178408i
$567$	37011.7			2.74135
$568$	9638.52	+	19358.9i	0.712013	+	1.43007i
$569$	−5395.71			−0.397539			−0.198770	−	0.980046i	$-0.563695\pi$
$569$	−5395.71			−0.397539			−0.198770	+	0.980046i	$0.563695\pi$
$570$	−2266.55	−	2816.73i	−0.166553	−	0.206982i
$571$		−	22390.5i		−	1.64100i	−0.571646	−	0.820500i	$-0.693695\pi$
$571$		−	22390.5i		−	1.64100i	0.571646	−	0.820500i	$-0.306305\pi$
$572$	−1538.78	+	7025.31i	−0.112482	+	0.513537i
$573$		−	13573.2i		−	0.989578i
$574$	−20817.4	+	16751.2i	−1.51376	+	1.21808i
$575$	209.091			0.0151647
$576$	19982.5	−	26456.3i	1.44549	−	1.91380i
$577$	−1935.38			−0.139638			−0.0698188	−	0.997560i	$-0.522242\pi$
$577$	−1935.38			−0.139638			−0.0698188	+	0.997560i	$0.522242\pi$
$578$	−10363.4	+	8339.12i	−0.745777	+	0.600106i
$579$		−	25682.2i		−	1.84338i
$580$	−894.810	+	4085.26i	−0.0640603	+	0.292468i
$581$		−	1186.82i		−	0.0847461i
$582$	5061.31	+	6289.90i	0.360478	+	0.447981i
$583$	−5760.94			−0.409252
$584$	−1285.00	−	2580.91i	−0.0910508	−	0.182875i
$585$	−7806.18			−0.551702
$586$	−7212.41	−	8963.15i	−0.508433	−	0.631851i
$587$		−	7905.44i		−	0.555865i	−0.960601	−	0.277932i	$-0.910351\pi$
$587$		−	7905.44i		−	0.555865i	0.960601	−	0.277932i	$-0.0896491\pi$
$588$	9153.22	+	2004.86i	0.641960	+	0.140611i
$589$			5452.17i			0.381414i
$590$	−5994.76	+	4823.82i	−0.418306	+	0.336599i
$591$	25841.4			1.79860
$592$	−3502.57	+	7611.90i	−0.243166	+	0.528458i
$593$	−11141.6			−0.771552			−0.385776	−	0.922592i	$-0.626066\pi$
$593$	−11141.6			−0.771552			−0.385776	+	0.922592i	$0.626066\pi$
$594$	−29715.7	+	23911.4i	−2.05261	+	1.65168i
$595$		−	1563.19i		−	0.107705i
$596$	7016.81	+	1536.92i	0.482248	+	0.105629i
$597$			33940.4i			2.32678i
$598$	357.553	+	444.346i	0.0244506	+	0.0303857i
$599$	278.847			0.0190207			0.00951033	−	0.999955i	$-0.496973\pi$
$599$	278.847			0.0190207			0.00951033	+	0.999955i	$0.496973\pi$
$600$	−4850.68	+	2415.09i	−0.330047	+	0.164326i
$601$	18890.7			1.28214			0.641071	−	0.767482i	$-0.278490\pi$
$601$	18890.7			1.28214			0.641071	+	0.767482i	$0.278490\pi$
$602$	11809.6	+	14676.2i	0.799539	+	0.993620i
$603$		−	1256.14i		−	0.0848321i
$604$	−5873.36	+	26814.9i	−0.395668	+	1.80643i
$605$		−	296.642i		−	0.0199342i
$606$	37857.9	−	30463.3i	2.53774	−	2.04206i
$607$	5398.05			0.360956			0.180478	−	0.983579i	$-0.442236\pi$
$607$	5398.05			0.360956			0.180478	+	0.983579i	$0.442236\pi$
$608$	−1178.05	−	4685.34i	−0.0785792	−	0.312525i
$609$	−21602.6			−1.43741
$610$	−4127.35	+	3321.17i	−0.273953	+	0.220443i
$611$		−	2341.25i		−	0.155019i
$612$	1606.53	−	7334.62i	0.106111	−	0.484452i
$613$		−	14412.8i		−	0.949635i	−0.880084	−	0.474817i	$-0.842514\pi$
$613$		−	14412.8i		−	0.949635i	0.880084	−	0.474817i	$-0.157486\pi$
$614$	11944.2	+	14843.5i	0.785063	+	0.975630i
$615$	20976.0			1.37534
$616$	−16291.5	+	8111.32i	−1.06559	+	0.530543i
$617$	13226.3			0.863001			0.431500	−	0.902113i	$-0.357984\pi$
$617$	13226.3			0.863001			0.431500	+	0.902113i	$0.357984\pi$
$618$	35398.8	+	43991.5i	2.30412	+	2.86343i
$619$			14179.4i			0.920705i	0.887736	+	0.460352i	$0.152277\pi$
$619$			14179.4i			0.920705i	−0.887736	+	0.460352i	$0.847723\pi$
$620$	7982.28	+	1748.39i	0.517058	+	0.113253i
$621$			3024.76i			0.195458i
$622$	7215.35	−	5806.00i	0.465127	−	0.374275i
$623$	−19840.6			−1.27592
$624$	−13427.2	−	6178.43i	−0.861407	−	0.396371i
$625$	625.000			0.0400000
$626$	−20620.4	+	16592.7i	−1.31654	+	1.05939i
$627$			9532.38i			0.607156i
$628$	4465.10	+	978.007i	0.283721	+	0.0621444i
$629$			1897.60i			0.120290i
$630$	−12383.8	−	15389.8i	−0.783146	−	0.973247i
$631$	1533.79			0.0967657			0.0483828	−	0.998829i	$-0.484593\pi$
$631$	1533.79			0.0967657			0.0483828	+	0.998829i	$0.484593\pi$
$632$	−9821.52	−	19726.4i	−0.618163	−	1.24157i
$633$	1457.96			0.0915459
$634$	−16073.3	−	19974.9i	−1.00686	−	1.25127i
$635$			1043.42i			0.0652079i
$636$	2533.24	−	11565.5i	0.157939	−	0.721073i
$637$		−	2948.06i		−	0.183370i
$638$	8590.66	−	6912.67i	0.533084	−	0.428958i
$639$	61888.4			3.83140
$640$	−7237.36	+	222.246i	−0.447003	+	0.0137266i
$641$	−26682.6			−1.64415			−0.822074	−	0.569381i	$-0.807183\pi$
$641$	−26682.6			−1.64415			−0.822074	+	0.569381i	$0.807183\pi$
$642$	1419.61	−	1142.32i	0.0872701	−	0.0702239i
$643$		−	16498.3i		−	1.01186i	−0.862574	−	0.505931i	$-0.831149\pi$
$643$		−	16498.3i		−	1.01186i	0.862574	−	0.505931i	$-0.168851\pi$
$644$	−308.800	+	1409.83i	−0.0188951	+	0.0862655i
$645$		−	14788.1i		−	0.902762i
$646$	−685.909	−	852.406i	−0.0417751	−	0.0519156i
$647$	−20127.5			−1.22302			−0.611510	−	0.791236i	$-0.709438\pi$
$647$	−20127.5			−1.22302			−0.611510	+	0.791236i	$0.709438\pi$
$648$	−17304.6	−	34756.0i	−1.04905	−	2.10701i
$649$	20287.5			1.22705
$650$	1068.77	+	1328.20i	0.0644933	+	0.0801484i
$651$			42209.9i			2.54122i
$652$	−1851.79	−	405.605i	−0.111230	−	0.0243631i
$653$			21447.4i			1.28530i	0.766160	+	0.642650i	$0.222165\pi$
$653$			21447.4i			1.28530i	−0.766160	+	0.642650i	$0.777835\pi$
$654$	30799.9	−	24783.8i	1.84155	−	1.48184i
$655$	−8923.43			−0.532316
$656$	25463.3	+	11716.7i	1.51551	+	0.697351i
$657$	−8250.91			−0.489953
$658$	4615.76	−	3714.18i	0.273467	−	0.220051i
$659$		−	19402.5i		−	1.14691i	−0.819237	−	0.573455i	$-0.805603\pi$
$659$		−	19402.5i		−	1.14691i	0.819237	−	0.573455i	$-0.194397\pi$
$660$	13955.9	+	3056.82i	0.823082	+	0.180283i
$661$		−	9326.38i		−	0.548796i	−0.961616	−	0.274398i	$-0.911521\pi$
$661$		−	9326.38i		−	0.548796i	0.961616	−	0.274398i	$-0.0884786\pi$
$662$	496.647	+	617.204i	0.0291582	+	0.0362361i
$663$	−3347.31			−0.196076
$664$	−1114.49	+	554.888i	−0.0651363	+	0.0324305i
$665$	−2878.41			−0.167850
$666$	15033.0	+	18682.1i	0.874648	+	1.08696i
$667$		−	874.443i		−	0.0507625i
$668$	2479.32	−	11319.3i	0.143604	−	0.655626i
$669$		−	19784.3i		−	1.14336i
$670$	−213.729	+	171.982i	−0.0123240	+	0.00991677i
$671$	13967.8			0.803608
$672$	−9120.27	−	36273.1i	−0.523545	−	2.08224i
$673$	−15027.4			−0.860718			−0.430359	−	0.902658i	$-0.641613\pi$
$673$	−15027.4			−0.860718			−0.430359	+	0.902658i	$0.641613\pi$
$674$	−12667.9	+	10193.6i	−0.723963	+	0.582553i
$675$			9041.38i			0.515560i
$676$	2765.61	−	12626.4i	0.157352	−	0.718390i
$677$			9717.31i			0.551649i	0.961208	+	0.275825i	$0.0889509\pi$
$677$			9717.31i			0.551649i	−0.961208	+	0.275825i	$0.911049\pi$
$678$	7783.63	+	9673.03i	0.440898	+	0.547921i
$679$	6427.63			0.363284
$680$	−1467.93	+	730.860i	−0.0827829	+	0.0412165i
$681$	−28166.3			−1.58493
$682$	−13506.8	−	16785.5i	−0.758362	−	0.942447i
$683$			11473.9i			0.642804i	0.946943	+	0.321402i	$0.104154\pi$
$683$			11473.9i			0.642804i	−0.946943	+	0.321402i	$0.895846\pi$
$684$	−13505.7	−	2958.21i	−0.754976	−	0.165365i
$685$			11903.0i			0.663927i
$686$	−10491.5	+	8442.20i	−0.583916	+	0.469861i
$687$	−47413.4			−2.63309
$688$	8260.32	−	17951.6i	0.457735	−	0.994766i
$689$	−3725.01			−0.205967
$690$	882.703	−	710.287i	0.0487013	−	0.0391886i
$691$		−	28412.6i		−	1.56421i	−0.623149	−	0.782103i	$-0.714147\pi$
$691$		−	28412.6i		−	1.56421i	0.623149	−	0.782103i	$-0.285853\pi$
$692$	19769.3	+	4330.13i	1.08600	+	0.237871i
$693$			52082.3i			2.85490i
$694$	5162.64	+	6415.82i	0.282379	+	0.350924i
$695$	14292.6			0.780071
$696$	10100.2	+	20286.1i	0.550066	+	1.10480i
$697$	6347.82			0.344965
$698$	−10045.3	−	12483.8i	−0.544731	−	0.676959i
$699$			49746.2i			2.69181i
$700$	−923.041	+	4214.15i	−0.0498395	+	0.227543i
$701$		−	12291.3i		−	0.662250i	−0.943587	−	0.331125i	$-0.892572\pi$
$701$		−	12291.3i		−	0.662250i	0.943587	−	0.331125i	$-0.107428\pi$
$702$	−19214.1	+	15461.1i	−1.03303	+	0.831254i
$703$	3494.17			0.187461
$704$	15233.9	+	11506.2i	0.815555	+	0.615990i
$705$	−4650.94			−0.248461
$706$	−20775.9	+	16717.8i	−1.10752	+	0.891195i
$707$		−	38686.9i		−	2.05795i
$708$	−8920.94	+	40728.6i	−0.473544	+	2.16197i
$709$		−	12774.2i		−	0.676650i	−0.941029	−	0.338325i	$-0.890140\pi$
$709$		−	12774.2i		−	0.676650i	0.941029	−	0.338325i	$-0.109860\pi$
$710$	−8473.35	−	10530.2i	−0.447886	−	0.556606i
$711$	−63063.4			−3.32639
$712$	9276.33	+	18631.4i	0.488266	+	0.980676i
$713$	−1708.59			−0.0897438
$714$	−5310.20	−	6599.20i	−0.278332	−	0.345895i
$715$		−	4494.91i		−	0.235105i
$716$	−1105.97	−	242.245i	−0.0577264	−	0.0126440i
$717$		−	19792.9i		−	1.03093i
$718$	10077.4	−	8109.02i	0.523796	−	0.421485i
$719$	−15748.6			−0.816861			−0.408430	−	0.912790i	$-0.633924\pi$
$719$	−15748.6			−0.816861			−0.408430	+	0.912790i	$0.633924\pi$
$720$	−8661.95	+	18824.5i	−0.448350	+	0.974370i
$721$	44954.8			2.32206
$722$	13544.9	−	10899.2i	0.698184	−	0.561810i
$723$		−	22118.4i		−	1.13775i
$724$	27021.7	+	5918.66i	1.38709	+	0.303820i
$725$		−	2613.82i		−	0.133896i
$726$	−1007.70	−	1252.31i	−0.0515140	−	0.0640185i
$727$	9536.44			0.486502			0.243251	−	0.969963i	$-0.421786\pi$
$727$	9536.44			0.486502			0.243251	+	0.969963i	$0.421786\pi$
$728$	−10534.0	+	5244.76i	−0.536288	+	0.267010i
$729$	−17576.5			−0.892980
$730$	1129.66	+	1403.88i	0.0572748	+	0.0711777i
$731$		−	4475.22i		−	0.226432i
$732$	−6142.01	+	28041.4i	−0.310130	+	1.41590i
$733$		−	34913.5i		−	1.75929i	−0.475631	−	0.879645i	$-0.657780\pi$
$733$		−	34913.5i		−	1.75929i	0.475631	−	0.879645i	$-0.342220\pi$
$734$	−5989.31	+	4819.43i	−0.301184	+	0.242355i
$735$	−5856.38			−0.293899
$736$	1468.28	−	369.175i	0.0735348	−	0.0184891i
$737$	723.301			0.0361508
$738$	62495.1	−	50288.1i	3.11718	−	2.50831i
$739$			19324.3i			0.961918i	0.876743	+	0.480959i	$0.159711\pi$
$739$			19324.3i			0.961918i	−0.876743	+	0.480959i	$0.840289\pi$
$740$	1120.50	−	5115.65i	0.0556627	−	0.254128i
$741$			6163.61i			0.305568i
$742$	−5909.38	−	7343.83i	−0.292372	−	0.363343i
$743$	−7053.57			−0.348278			−0.174139	−	0.984721i	$-0.555714\pi$
$743$	−7053.57			−0.348278			−0.174139	+	0.984721i	$0.555714\pi$
$744$	39637.4	−	19734.9i	1.95319	−	0.972469i
$745$	−4489.47			−0.220781
$746$	9978.56	+	12400.8i	0.489733	+	0.608612i
$747$			3562.91i			0.174511i
$748$	4223.38	+	925.063i	0.206447	+	0.0452188i
$749$		−	1450.69i		−	0.0707705i
$750$	2638.51	−	2123.14i	0.128460	−	0.103368i
$751$	−36810.6			−1.78860			−0.894299	−	0.447471i	$-0.852325\pi$
$751$	−36810.6			−1.78860			−0.894299	+	0.447471i	$0.852325\pi$
$752$	−5645.89	−	2597.92i	−0.273782	−	0.125979i
$753$	36424.7			1.76280
$754$	5554.70	−	4469.72i	0.268289	−	0.215885i
$755$		−	17156.6i		−	0.827010i
$756$	−60962.8	−	13352.9i	−2.93280	−	0.642382i
$757$		−	28515.3i		−	1.36910i	−0.728967	−	0.684549i	$-0.759999\pi$
$757$		−	28515.3i		−	1.36910i	0.728967	−	0.684549i	$-0.240001\pi$
$758$	−14303.8	−	17775.9i	−0.685403	−	0.851779i
$759$	−2987.24			−0.142859
$760$	1345.78	+	2702.98i	0.0642323	+	0.129010i
$761$	1517.92			0.0723057			0.0361528	−	0.999346i	$-0.488490\pi$
$761$	1517.92			0.0723057			0.0361528	+	0.999346i	$0.488490\pi$
$762$	3544.53	+	4404.93i	0.168510	+	0.209415i
$763$		−	31474.3i		−	1.49338i
$764$	−2425.44	+	11073.4i	−0.114855	+	0.524373i
$765$			4692.81i			0.221790i
$766$	23375.3	−	18809.4i	1.10259	−	0.887223i
$767$	13117.8			0.617545
$768$	−29798.4	+	25523.7i	−1.40007	+	1.19923i
$769$	−10413.9			−0.488341			−0.244171	−	0.969732i	$-0.578516\pi$
$769$	−10413.9			−0.488341			−0.244171	+	0.969732i	$0.578516\pi$
$770$	8861.69	−	7130.77i	0.414745	−	0.333734i
$771$			59088.0i			2.76006i
$772$	−4589.25	+	20952.3i	−0.213952	+	0.976798i
$773$			32909.8i			1.53129i	0.643266	+	0.765643i	$0.277579\pi$
$773$			32909.8i			1.53129i	−0.643266	+	0.765643i	$0.722421\pi$
$774$	−35453.2	−	44059.1i	−1.64643	−	2.04609i
$775$	−5107.19			−0.236717
$776$	−3005.19	−	6035.90i	−0.139021	−	0.279222i
$777$	27051.3			1.24898
$778$	15945.4	+	19816.0i	0.734796	+	0.913161i
$779$		−	11688.6i		−	0.537599i
$780$	9023.87	+	1976.53i	0.414239	+	0.0907323i
$781$			35636.2i			1.63273i
$782$	267.126	−	214.949i	0.0122153	−	0.00982936i
$783$	37812.1			1.72579
$784$	−7109.20	−	3271.25i	−0.323852	−	0.149018i
$785$	−2856.84			−0.129892
$786$	−37671.2	+	30313.0i	−1.70953	+	1.37561i
$787$			35511.6i			1.60845i	0.594324	+	0.804226i	$0.297420\pi$
$787$			35511.6i			1.60845i	−0.594324	+	0.804226i	$0.702580\pi$
$788$	−21082.1	−	4617.69i	−0.953070	−	0.208754i
$789$		−	15672.1i		−	0.707150i
$790$	8634.23	+	10730.1i	0.388851	+	0.483240i
$791$	9884.85			0.444330
$792$	48908.2	−	24350.7i	2.19429	−	1.09251i
$793$	9031.54			0.404438
$794$	−15918.1	−	19782.1i	−0.711477	−	0.884181i
$795$			7399.81i			0.330118i
$796$	6064.95	−	27689.6i	0.270058	−	1.23295i
$797$		−	22692.3i		−	1.00853i	−0.863548	−	0.504267i	$-0.831763\pi$
$797$		−	22692.3i		−	1.00853i	0.863548	−	0.504267i	$-0.168237\pi$
$798$	−12151.5	+	9778.01i	−0.539047	+	0.433757i
$799$	−1407.48			−0.0623193
$800$	4388.88	−	1103.51i	0.193963	−	0.0487687i
$801$	59562.8			2.62740
$802$	−6975.98	+	5613.39i	−0.307145	+	0.247152i
$803$		−	4751.00i		−	0.208791i
$804$	−318.055	+	1452.08i	−0.0139514	+	0.0636952i
$805$		−	902.032i		−	0.0394937i
$806$	−8733.47	−	10853.4i	−0.381667	−	0.474313i
$807$	21669.8			0.945246
$808$	−36329.2	+	18087.8i	−1.58175	+	0.787533i
$809$	−22716.0			−0.987209			−0.493604	−	0.869687i	$-0.664321\pi$
$809$	−22716.0			−0.987209			−0.493604	+	0.869687i	$0.664321\pi$
$810$	15212.7	+	18905.4i	0.659900	+	0.820084i
$811$			17237.0i			0.746327i	0.927766	+	0.373164i	$0.121727\pi$
$811$			17237.0i			0.746327i	−0.927766	+	0.373164i	$0.878273\pi$
$812$	17624.0	+	3860.26i	0.761678	+	0.166833i
$813$			398.847i			0.0172056i
$814$	−10757.4	+	8656.20i	−0.463203	+	0.372727i
$815$	1184.81			0.0509227
$816$	−3714.26	+	8071.98i	−0.159345	+	0.346294i
$817$	−8240.51			−0.352875
$818$	−11938.2	+	9606.38i	−0.510282	+	0.410610i
$819$			33676.3i			1.43681i
$820$	−17112.8	−	3748.29i	−0.728788	−	0.159629i
$821$			15695.7i			0.667217i	0.942712	+	0.333609i	$0.108266\pi$
$821$			15695.7i			0.667217i	−0.942712	+	0.333609i	$0.891734\pi$
$822$	40434.7	+	50249.8i	1.71572	+	2.13219i
$823$	16856.0			0.713927			0.356963	−	0.934118i	$-0.383812\pi$
$823$	16856.0			0.713927			0.356963	+	0.934118i	$0.383812\pi$
$824$	−21018.3	−	42215.1i	−0.888602	−	1.78475i
$825$	−8929.24			−0.376820
$826$	20810.2	+	25861.7i	0.876611	+	1.08940i
$827$			3712.67i			0.156109i	0.996949	+	0.0780544i	$0.0248708\pi$
$827$			3712.67i			0.156109i	−0.996949	+	0.0780544i	$0.975129\pi$
$828$	927.038	−	4232.40i	0.0389092	−	0.177640i
$829$			22469.6i			0.941376i	0.882300	+	0.470688i	$0.155994\pi$
$829$			22469.6i			0.941376i	−0.882300	+	0.470688i	$0.844006\pi$
$830$	606.221	−	487.810i	0.0253521	−	0.0204001i
$831$	20489.3			0.855313
$832$	9850.23	+	7439.89i	0.410451	+	0.310014i
$833$	−1772.27			−0.0737163
$834$	60337.8	−	48552.2i	2.50519	−	2.01586i
$835$			7242.30i			0.300156i
$836$	1703.38	−	7776.78i	0.0704696	−	0.321729i
$837$		−	73881.8i		−	3.05105i
$838$	−10990.4	−	13658.2i	−0.453051	−	0.563025i
$839$	−31935.2			−1.31409			−0.657046	−	0.753850i	$-0.728194\pi$
$839$	−31935.2			−1.31409			−0.657046	+	0.753850i	$0.728194\pi$
$840$	10418.8	+	20926.1i	0.427957	+	0.859546i
$841$	13457.7			0.551795
$842$	−7703.69	−	9573.69i	−0.315305	−	0.391842i
$843$		−	14306.3i		−	0.584504i
$844$	−1189.44	−	260.528i	−0.0485098	−	0.0106253i
$845$			8078.60i			0.328890i
$846$	−13856.8	+	11150.2i	−0.563129	+	0.453135i
$847$	−1279.73			−0.0519150
$848$	−4133.37	+	8982.79i	−0.167383	+	0.363762i
$849$	10442.9			0.422144
$850$	798.472	−	642.509i	0.0322204	−	0.0259269i
$851$			1095.00i			0.0441081i
$852$	−71542.4	−	15670.2i	−2.87676	−	0.630108i
$853$			14782.2i			0.593355i	0.954978	+	0.296678i	$0.0958787\pi$
$853$			14782.2i			0.593355i	−0.954978	+	0.296678i	$0.904121\pi$
$854$	14327.7	+	17805.6i	0.574103	+	0.713461i
$855$	8641.18			0.345640
$856$	−1362.28	+	678.261i	−0.0543946	+	0.0270823i
$857$	−7222.91			−0.287900			−0.143950	−	0.989585i	$-0.545980\pi$
$857$	−7222.91			−0.287900			−0.143950	+	0.989585i	$0.545980\pi$
$858$	−15269.3	−	18975.8i	−0.607559	−	0.755038i
$859$			4646.96i			0.184578i	0.995732	+	0.0922889i	$0.0294183\pi$
$859$			4646.96i			0.184578i	−0.995732	+	0.0922889i	$0.970582\pi$
$860$	−2642.54	+	12064.6i	−0.104779	+	0.478370i
$861$		−	90491.7i		−	3.58182i
$862$	10468.7	−	8423.90i	0.413650	−	0.332853i
$863$	8122.19			0.320374			0.160187	−	0.987087i	$-0.448790\pi$
$863$	8122.19			0.320374			0.160187	+	0.987087i	$0.448790\pi$
$864$	15963.6	+	63490.5i	0.628580	+	2.49999i
$865$	−12648.7			−0.497189
$866$	9277.73	−	7465.54i	0.364053	−	0.292944i
$867$		−	45048.9i		−	1.76464i
$868$	7542.64	−	34436.0i	0.294947	−	1.34658i
$869$		−	36312.8i		−	1.41752i
$870$	−8879.19	−	11034.5i	−0.346015	−	0.430006i
$871$	467.685			0.0181939
$872$	−29556.1	+	14715.6i	−1.14782	+	0.571483i
$873$	−19296.2			−0.748083
$874$	−395.799	−	491.876i	−0.0153182	−	0.0190366i
$875$		−	2696.28i		−	0.104173i
$876$	9537.98	+	2089.14i	0.367875	+	0.0805770i
$877$			31986.1i			1.23158i	0.787910	+	0.615790i	$0.211163\pi$
$877$			31986.1i			1.23158i	−0.787910	+	0.615790i	$0.788837\pi$
$878$	−12729.1	+	10242.8i	−0.489278	+	0.393709i
$879$	38962.3			1.49507
$880$	−10839.4	−	4987.68i	−0.415223	−	0.191062i
$881$	−29450.6			−1.12624			−0.563118	−	0.826376i	$-0.690398\pi$
$881$	−29450.6			−1.12624			−0.563118	+	0.826376i	$0.690398\pi$
$882$	−17448.3	+	14040.1i	−0.666115	+	0.536005i
$883$			46156.5i			1.75911i	0.475801	+	0.879553i	$0.342158\pi$
$883$			46156.5i			1.75911i	−0.475801	+	0.879553i	$0.657842\pi$
$884$	2730.83	+	598.143i	0.103900	+	0.0227576i
$885$		−	26058.8i		−	0.989783i
$886$	21245.5	+	26402.7i	0.805595	+	1.00115i
$887$	41051.2			1.55396			0.776982	−	0.629523i	$-0.216750\pi$
$887$	41051.2			1.55396			0.776982	+	0.629523i	$0.216750\pi$
$888$	−12647.6	−	25402.6i	−0.477958	−	0.959974i
$889$	4501.39			0.169822
$890$	−8154.94	−	10134.5i	−0.307140	−	0.381695i
$891$		−	63979.7i		−	2.40561i
$892$	−3535.33	+	16140.6i	−0.132704	+	0.605859i
$893$			2591.69i			0.0971192i
$894$	−18952.8	+	15250.8i	−0.709034	+	0.570541i
$895$	707.620			0.0264281
$896$	958.782	+	31222.4i	0.0357485	+	1.16414i
$897$	−1931.54			−0.0718979
$898$	−12268.7	+	9872.31i	−0.455916	+	0.366863i
$899$			21358.8i			0.792389i
$900$	2771.03	−	12651.2i	0.102631	−	0.468562i
$901$			2239.35i			0.0828008i
$902$	28956.6	+	35985.6i	1.06890	+	1.32837i
$903$	−63796.7			−2.35108
$904$	−4621.59	−	9282.42i	−0.170035	−	0.341514i
$905$	−17288.9			−0.635031
$906$	−58281.3	−	72428.5i	−2.13716	−	2.65593i
$907$		−	27915.8i		−	1.02197i	−0.859588	−	0.510987i	$-0.829280\pi$
$907$		−	27915.8i		−	1.02197i	0.859588	−	0.510987i	$-0.170720\pi$
$908$	22978.9	+	5033.15i	0.839847	+	0.183955i
$909$			116141.i			4.23778i
$910$	5729.95	−	4610.74i	0.208732	−	0.167961i
$911$	−6557.22			−0.238475			−0.119237	−	0.992866i	$-0.538045\pi$
$911$	−6557.22			−0.238475			−0.119237	+	0.992866i	$0.538045\pi$
$912$	14863.4	+	6839.31i	0.539669	+	0.248325i
$913$	−2051.57			−0.0743671
$914$	−16050.0	+	12915.0i	−0.580841	+	0.467387i
$915$		−	17941.3i		−	0.648221i
$916$	38681.2	+	8472.48i	1.39526	+	0.305610i
$917$			38496.2i			1.38632i
$918$	9294.67	+	11550.9i	0.334172	+	0.415289i
$919$	−11493.0			−0.412534			−0.206267	−	0.978496i	$-0.566131\pi$
$919$	−11493.0			−0.412534			−0.206267	+	0.978496i	$0.566131\pi$
$920$	−847.057	+	421.738i	−0.0303551	+	0.0151134i
$921$	−64524.0			−2.30851
$922$	−21102.7	−	26225.2i	−0.753776	−	0.936748i
$923$			23042.3i			0.821719i
$924$	13187.3	−	60206.7i	0.469513	−	2.14356i
$925$			3273.08i			0.116344i
$926$	10832.3	−	8716.45i	0.384418	−	0.309331i
$927$	−134957.			−4.78164
$928$	−4615.00	−	18354.8i	−0.163249	−	0.649273i
$929$	56597.2			1.99881			0.999405	−	0.0345020i	$-0.0109845\pi$
$929$	56597.2			1.99881			0.999405	+	0.0345020i	$0.0109845\pi$
$930$	−21560.6	+	17349.2i	−0.760215	+	0.611724i
$931$			3263.40i			0.114880i
$932$	8889.34	−	40584.3i	0.312425	−	1.42638i
$933$			31364.7i			1.10057i
$934$	−5514.84	−	6853.52i	−0.193203	−	0.240101i
$935$	−2702.19			−0.0945145
$936$	31623.9	−	15745.1i	1.10434	−	0.549834i
$937$	−37901.5			−1.32144			−0.660720	−	0.750633i	$-0.729749\pi$
$937$	−37901.5			−1.32144			−0.660720	+	0.750633i	$0.729749\pi$
$938$	741.939	+	922.037i	0.0258264	+	0.0320955i
$939$		−	89635.5i		−	3.11517i
$940$	3794.37	+	831.095i	0.131658	+	0.0288376i
$941$		−	4449.85i		−	0.154156i	−0.997025	−	0.0770781i	$-0.975441\pi$
$941$		−	4449.85i		−	0.154156i	0.997025	−	0.0770781i	$-0.0245591\pi$
$942$	−12060.5	+	9704.75i	−0.417146	+	0.335666i
$943$	3662.97			0.126493
$944$	14555.9	−	31633.4i	0.501858	−	1.09066i
$945$	39005.0			1.34268
$946$	25369.9	−	20414.4i	0.871929	−	0.701618i
$947$			225.160i			0.00772620i	0.999993	+	0.00386310i	$0.00122967\pi$
$947$			225.160i			0.00772620i	−0.999993	+	0.00386310i	$0.998770\pi$
$948$	72900.7	+	15967.7i	2.49758	+	0.547054i
$949$		−	3071.98i		−	0.105080i
$950$	−1183.09	−	1470.28i	−0.0404049	−	0.0502127i
$951$	86829.7			2.96072
$952$	3152.97	+	6332.71i	0.107341	+	0.215593i
$953$	4845.81			0.164713			0.0823563	−	0.996603i	$-0.473755\pi$
$953$	4845.81			0.164713			0.0823563	+	0.996603i	$0.473755\pi$
$954$	17740.4	+	22046.7i	0.602060	+	0.748205i
$955$		−	7084.94i		−	0.240066i
$956$	−3536.87	+	16147.6i	−0.119655	+	0.546288i
$957$			37343.1i			1.26137i
$958$	14522.7	−	11686.0i	0.489777	−	0.394110i
$959$	51350.2			1.72908
$960$	14779.5	−	19567.7i	0.496882	−	0.657859i
$961$	11942.5			0.400876
$962$	−6955.71	+	5597.07i	−0.233120	+	0.187585i
$963$			4355.07i			0.145732i
$964$	−3952.43	+	18044.8i	−0.132053	+	0.602889i
$965$		−	13405.6i		−	0.447194i
$966$	−3064.22	−	3808.03i	−0.102060	−	0.126834i
$967$	40394.8			1.34334			0.671670	−	0.740851i	$-0.265577\pi$
$967$	40394.8			1.34334			0.671670	+	0.740851i	$0.265577\pi$
$968$	598.328	+	1201.74i	0.0198667	+	0.0399021i
$969$	3705.36			0.122841
$970$	2641.91	+	3283.20i	0.0874500	+	0.108678i
$971$			29066.2i			0.960637i	0.877094	+	0.480318i	$0.159479\pi$
$971$			29066.2i			0.960637i	−0.877094	+	0.480318i	$0.840521\pi$
$972$	52135.4	+	11419.4i	1.72042	+	0.376829i
$973$		−	61659.1i		−	2.03155i
$974$	6919.28	−	5567.75i	0.227626	−	0.183165i
$975$	−5773.62			−0.189645
$976$	10021.6	−	21779.4i	0.328673	−	0.714284i
$977$	42580.5			1.39434			0.697170	−	0.716906i	$-0.254442\pi$
$977$	42580.5			1.39434			0.697170	+	0.716906i	$0.254442\pi$
$978$	5001.80	−	4024.81i	0.163538	−	0.131594i
$979$			34297.1i			1.11965i
$980$	4777.80	+	1046.50i	0.155736	+	0.0341114i
$981$			94488.0i			3.07520i
$982$	−21380.2	−	26570.1i	−0.694777	−	0.863427i
$983$	−40586.0			−1.31688			−0.658440	−	0.752633i	$-0.728783\pi$
$983$	−40586.0			−1.31688			−0.658440	+	0.752633i	$0.728783\pi$
$984$	−84976.7	+	42308.8i	−2.75301	+	1.37068i
$985$	13488.7			0.436330
$986$	−2687.04	−	3339.30i	−0.0867879	−	0.107855i
$987$			20064.4i			0.647070i
$988$	1101.40	−	5028.45i	0.0354658	−	0.161919i
$989$		−	2582.40i		−	0.0830288i
$990$	−26603.4	+	21407.0i	−0.854052	+	0.687233i
$991$	−50370.4			−1.61460			−0.807299	−	0.590142i	$-0.799072\pi$
$991$	−50370.4			−1.61460			−0.807299	+	0.590142i	$0.799072\pi$
$992$	−35863.8	+	9017.34i	−1.14786	+	0.288610i
$993$	−2682.95			−0.0857409
$994$	−45427.8	+	36554.5i	−1.44958	+	1.16644i
$995$			17716.2i			0.564465i
$996$	902.131	−	4118.69i	0.0286999	−	0.131030i
$997$			22467.5i			0.713694i	0.934163	+	0.356847i	$0.116148\pi$
$997$			22467.5i			0.713694i	−0.934163	+	0.356847i	$0.883852\pi$
$998$	14998.7	+	18639.5i	0.475726	+	0.591204i
$999$	−47349.1			−1.49956

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.4.d.a.21.9	✓	12
3.2	odd	2		360.4.k.c.181.4		12
4.3	odd	2		160.4.d.a.81.1		12
5.2	odd	4		200.4.f.c.149.10		12
5.3	odd	4		200.4.f.b.149.3		12
5.4	even	2		200.4.d.b.101.4		12
8.3	odd	2		160.4.d.a.81.12		12
8.5	even	2	inner	40.4.d.a.21.10	yes	12
12.11	even	2		1440.4.k.c.721.2		12
16.3	odd	4		1280.4.a.bd.1.6		6
16.5	even	4		1280.4.a.bc.1.6		6
16.11	odd	4		1280.4.a.ba.1.1		6
16.13	even	4		1280.4.a.bb.1.1		6
20.3	even	4		800.4.f.c.49.12		12
20.7	even	4		800.4.f.b.49.1		12
20.19	odd	2		800.4.d.d.401.12		12
24.5	odd	2		360.4.k.c.181.3		12
24.11	even	2		1440.4.k.c.721.8		12
40.3	even	4		800.4.f.b.49.2		12
40.13	odd	4		200.4.f.c.149.9		12
40.19	odd	2		800.4.d.d.401.1		12
40.27	even	4		800.4.f.c.49.11		12
40.29	even	2		200.4.d.b.101.3		12
40.37	odd	4		200.4.f.b.149.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.d.a.21.9	✓	12	1.1	even	1	trivial
40.4.d.a.21.10	yes	12	8.5	even	2	inner
160.4.d.a.81.1		12	4.3	odd	2
160.4.d.a.81.12		12	8.3	odd	2
200.4.d.b.101.3		12	40.29	even	2
200.4.d.b.101.4		12	5.4	even	2
200.4.f.b.149.3		12	5.3	odd	4
200.4.f.b.149.4		12	40.37	odd	4
200.4.f.c.149.9		12	40.13	odd	4
200.4.f.c.149.10		12	5.2	odd	4
360.4.k.c.181.3		12	24.5	odd	2
360.4.k.c.181.4		12	3.2	odd	2
800.4.d.d.401.1		12	40.19	odd	2
800.4.d.d.401.12		12	20.19	odd	2
800.4.f.b.49.1		12	20.7	even	4
800.4.f.b.49.2		12	40.3	even	4
800.4.f.c.49.11		12	40.27	even	4
800.4.f.c.49.12		12	20.3	even	4
1280.4.a.ba.1.1		6	16.11	odd	4
1280.4.a.bb.1.1		6	16.13	even	4
1280.4.a.bc.1.6		6	16.5	even	4
1280.4.a.bd.1.6		6	16.3	odd	4
1440.4.k.c.721.2		12	12.11	even	2
1440.4.k.c.721.8		12	24.11	even	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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	40.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.20360 - 1.77318i) q^{2} +9.57890i q^{3} +(1.71169 - 7.81474i) q^{4} +5.00000i q^{5} +(16.9851 + 21.1081i) q^{6} +21.5703 q^{7} +(-10.0850 - 20.2557i) q^{8} -64.7554 q^{9} +O(q^{10})\)	\(q+(2.20360 - 1.77318i) q^{2} +9.57890i q^{3} +(1.71169 - 7.81474i) q^{4} +5.00000i q^{5} +(16.9851 + 21.1081i) q^{6} +21.5703 q^{7} +(-10.0850 - 20.2557i) q^{8} -64.7554 q^{9} +(8.86588 + 11.0180i) q^{10} -37.2871i q^{11} +(74.8566 + 16.3961i) q^{12} -24.1097i q^{13} +(47.5322 - 38.2479i) q^{14} -47.8945 q^{15} +(-58.1402 - 26.7528i) q^{16} -14.4940 q^{17} +(-142.695 + 114.823i) q^{18} +26.6887i q^{19} +(39.0737 + 8.55846i) q^{20} +206.620i q^{21} +(-66.1166 - 82.1658i) q^{22} -8.36366 q^{23} +(194.027 - 96.6035i) q^{24} -25.0000 q^{25} +(-42.7508 - 53.1282i) q^{26} -361.655i q^{27} +(36.9216 - 168.566i) q^{28} +104.553i q^{29} +(-105.540 + 84.9254i) q^{30} +204.288 q^{31} +(-175.555 + 44.1404i) q^{32} +357.170 q^{33} +(-31.9389 + 25.7004i) q^{34} +107.851i q^{35} +(-110.841 + 506.046i) q^{36} -130.923i q^{37} +(47.3237 + 58.8111i) q^{38} +230.945 q^{39} +(101.278 - 50.4251i) q^{40} -437.963 q^{41} +(366.373 + 455.307i) q^{42} +308.764i q^{43} +(-291.389 - 63.8240i) q^{44} -323.777i q^{45} +(-18.4301 + 14.8302i) q^{46} +97.1081 q^{47} +(256.263 - 556.920i) q^{48} +122.277 q^{49} +(-55.0900 + 44.3294i) q^{50} -138.836i q^{51} +(-188.411 - 41.2684i) q^{52} -154.502i q^{53} +(-641.279 - 796.943i) q^{54} +186.436 q^{55} +(-217.537 - 436.920i) q^{56} -255.648 q^{57} +(185.390 + 230.392i) q^{58} +544.088i q^{59} +(-81.9806 + 374.283i) q^{60} +374.601i q^{61} +(450.168 - 362.238i) q^{62} -1396.79 q^{63} +(-308.584 + 408.558i) q^{64} +120.549 q^{65} +(787.058 - 633.325i) q^{66} +19.3982i q^{67} +(-24.8092 + 113.267i) q^{68} -80.1147i q^{69} +(191.240 + 237.661i) q^{70} -955.725 q^{71} +(653.060 + 1311.66i) q^{72} +127.417 q^{73} +(-232.150 - 288.502i) q^{74} -239.473i q^{75} +(208.565 + 45.6828i) q^{76} -804.293i q^{77} +(508.910 - 409.506i) q^{78} +973.871 q^{79} +(133.764 - 290.701i) q^{80} +1715.87 q^{81} +(-965.094 + 776.586i) q^{82} -55.0210i q^{83} +(1614.68 + 353.669i) q^{84} -72.4698i q^{85} +(547.493 + 680.392i) q^{86} -1001.50 q^{87} +(-755.275 + 376.041i) q^{88} -919.812 q^{89} +(-574.114 - 713.474i) q^{90} -520.054i q^{91} +(-14.3160 + 65.3598i) q^{92} +1956.85i q^{93} +(213.987 - 172.190i) q^{94} -133.443 q^{95} +(-422.816 - 1681.63i) q^{96} +297.986 q^{97} +(269.449 - 216.818i) q^{98} +2414.54i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 16 q^{4} - 36 q^{6} + 28 q^{7} - 40 q^{8} - 108 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 + 16 * q^4 - 36 * q^6 + 28 * q^7 - 40 * q^8 - 108 * q^9	\( 12 q + 2 q^{2} + 16 q^{4} - 36 q^{6} + 28 q^{7} - 40 q^{8} - 108 q^{9} + 30 q^{10} + 188 q^{12} + 68 q^{14} - 60 q^{15} - 56 q^{16} - 206 q^{18} + 20 q^{20} - 164 q^{22} + 604 q^{23} + 360 q^{24} - 300 q^{25} - 308 q^{26} - 436 q^{28} + 40 q^{30} - 264 q^{31} + 72 q^{32} - 232 q^{33} - 180 q^{34} + 440 q^{36} + 820 q^{38} + 600 q^{39} + 120 q^{40} + 40 q^{41} + 884 q^{42} - 472 q^{44} - 1268 q^{46} - 940 q^{47} + 424 q^{48} + 1308 q^{49} - 50 q^{50} + 1024 q^{52} - 1512 q^{54} + 440 q^{55} - 728 q^{56} - 680 q^{57} - 360 q^{58} - 820 q^{60} + 592 q^{62} - 1300 q^{63} - 2048 q^{64} + 2928 q^{66} - 2344 q^{68} + 1160 q^{70} - 1592 q^{71} - 152 q^{72} + 432 q^{73} - 420 q^{74} + 2256 q^{76} + 3320 q^{78} + 2016 q^{79} + 1600 q^{80} + 2508 q^{81} + 88 q^{82} + 1048 q^{84} - 244 q^{86} - 1968 q^{87} + 4080 q^{88} - 424 q^{89} - 2250 q^{90} - 900 q^{92} + 292 q^{94} - 1520 q^{95} - 5920 q^{96} - 1584 q^{97} - 7266 q^{98}+O(q^{100}) \) 12 * q + 2 * q^2 + 16 * q^4 - 36 * q^6 + 28 * q^7 - 40 * q^8 - 108 * q^9 + 30 * q^10 + 188 * q^12 + 68 * q^14 - 60 * q^15 - 56 * q^16 - 206 * q^18 + 20 * q^20 - 164 * q^22 + 604 * q^23 + 360 * q^24 - 300 * q^25 - 308 * q^26 - 436 * q^28 + 40 * q^30 - 264 * q^31 + 72 * q^32 - 232 * q^33 - 180 * q^34 + 440 * q^36 + 820 * q^38 + 600 * q^39 + 120 * q^40 + 40 * q^41 + 884 * q^42 - 472 * q^44 - 1268 * q^46 - 940 * q^47 + 424 * q^48 + 1308 * q^49 - 50 * q^50 + 1024 * q^52 - 1512 * q^54 + 440 * q^55 - 728 * q^56 - 680 * q^57 - 360 * q^58 - 820 * q^60 + 592 * q^62 - 1300 * q^63 - 2048 * q^64 + 2928 * q^66 - 2344 * q^68 + 1160 * q^70 - 1592 * q^71 - 152 * q^72 + 432 * q^73 - 420 * q^74 + 2256 * q^76 + 3320 * q^78 + 2016 * q^79 + 1600 * q^80 + 2508 * q^81 + 88 * q^82 + 1048 * q^84 - 244 * q^86 - 1968 * q^87 + 4080 * q^88 - 424 * q^89 - 2250 * q^90 - 900 * q^92 + 292 * q^94 - 1520 * q^95 - 5920 * q^96 - 1584 * q^97 - 7266 * q^98

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