LMFDB - Embedded newform 360.4.k.c.181.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,4,Mod(181,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("360.181");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	360.k (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:	$21.2406876021$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.3
Root			$1.98839 - 0.215211i$ of defining polynomial
Character	$\chi$	$=$	360.181
Dual form			360.4.k.c.181.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.20360 - 1.77318i) q^{2} +(1.71169 + 7.81474i) q^{4} +5.00000i q^{5} +21.5703 q^{7} +(10.0850 - 20.2557i) q^{8} +O(q^{10})$	\(q+(-2.20360 - 1.77318i) q^{2} +(1.71169 + 7.81474i) q^{4} +5.00000i q^{5} +21.5703 q^{7} +(10.0850 - 20.2557i) q^{8} +(8.86588 - 11.0180i) q^{10} -37.2871i q^{11} +24.1097i q^{13} +(-47.5322 - 38.2479i) q^{14} +(-58.1402 + 26.7528i) q^{16} +14.4940 q^{17} -26.6887i q^{19} +(-39.0737 + 8.55846i) q^{20} +(-66.1166 + 82.1658i) q^{22} +8.36366 q^{23} -25.0000 q^{25} +(42.7508 - 53.1282i) q^{26} +(36.9216 + 168.566i) q^{28} +104.553i q^{29} +204.288 q^{31} +(175.555 + 44.1404i) q^{32} +(-31.9389 - 25.7004i) q^{34} +107.851i q^{35} +130.923i q^{37} +(-47.3237 + 58.8111i) q^{38} +(101.278 + 50.4251i) q^{40} +437.963 q^{41} -308.764i q^{43} +(291.389 - 63.8240i) q^{44} +(-18.4301 - 14.8302i) q^{46} -97.1081 q^{47} +122.277 q^{49} +(55.0900 + 44.3294i) q^{50} +(-188.411 + 41.2684i) q^{52} -154.502i q^{53} +186.436 q^{55} +(217.537 - 436.920i) q^{56} +(185.390 - 230.392i) q^{58} +544.088i q^{59} -374.601i q^{61} +(-450.168 - 362.238i) q^{62} +(-308.584 - 408.558i) q^{64} -120.549 q^{65} -19.3982i q^{67} +(24.8092 + 113.267i) q^{68} +(191.240 - 237.661i) q^{70} +955.725 q^{71} +127.417 q^{73} +(232.150 - 288.502i) q^{74} +(208.565 - 45.6828i) q^{76} -804.293i q^{77} +973.871 q^{79} +(-133.764 - 290.701i) q^{80} +(-965.094 - 776.586i) q^{82} -55.0210i q^{83} +72.4698i q^{85} +(-547.493 + 680.392i) q^{86} +(-755.275 - 376.041i) q^{88} +919.812 q^{89} +520.054i q^{91} +(14.3160 + 65.3598i) q^{92} +(213.987 + 172.190i) q^{94} +133.443 q^{95} +297.986 q^{97} +(-269.449 - 216.818i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 40 q^{8}+O(q^{10}) $ 12 * q - 2 * q^2 + 16 * q^4 + 28 * q^7 + 40 * q^8	$ 12 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 40 q^{8} + 30 q^{10} - 68 q^{14} - 56 q^{16} - 20 q^{20} - 164 q^{22} - 604 q^{23} - 300 q^{25} + 308 q^{26} - 436 q^{28} - 264 q^{31} - 72 q^{32} - 180 q^{34} - 820 q^{38} + 120 q^{40} - 40 q^{41} + 472 q^{44} - 1268 q^{46} + 940 q^{47} + 1308 q^{49} + 50 q^{50} + 1024 q^{52} + 440 q^{55} + 728 q^{56} - 360 q^{58} - 592 q^{62} - 2048 q^{64} + 2344 q^{68} + 1160 q^{70} + 1592 q^{71} + 432 q^{73} + 420 q^{74} + 2256 q^{76} + 2016 q^{79} - 1600 q^{80} + 88 q^{82} + 244 q^{86} + 4080 q^{88} + 424 q^{89} + 900 q^{92} + 292 q^{94} + 1520 q^{95} - 1584 q^{97} + 7266 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 + 16 * q^4 + 28 * q^7 + 40 * q^8 + 30 * q^10 - 68 * q^14 - 56 * q^16 - 20 * q^20 - 164 * q^22 - 604 * q^23 - 300 * q^25 + 308 * q^26 - 436 * q^28 - 264 * q^31 - 72 * q^32 - 180 * q^34 - 820 * q^38 + 120 * q^40 - 40 * q^41 + 472 * q^44 - 1268 * q^46 + 940 * q^47 + 1308 * q^49 + 50 * q^50 + 1024 * q^52 + 440 * q^55 + 728 * q^56 - 360 * q^58 - 592 * q^62 - 2048 * q^64 + 2344 * q^68 + 1160 * q^70 + 1592 * q^71 + 432 * q^73 + 420 * q^74 + 2256 * q^76 + 2016 * q^79 - 1600 * q^80 + 88 * q^82 + 244 * q^86 + 4080 * q^88 + 424 * q^89 + 900 * q^92 + 292 * q^94 + 1520 * q^95 - 1584 * q^97 + 7266 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$1$	$1$

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
$3$		0			0
$3$		0			0
$4$	1.71169	+	7.81474i	0.213961	+	0.976842i
$5$			5.00000i			0.447214i
$5$			5.00000i			0.447214i
$6$		0			0
$7$	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
$9$		0			0
$10$	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	$-0.170733\pi$
$12$		0			0
$13$			24.1097i			0.514372i	0.966362	+	0.257186i	$0.0827954\pi$
$13$			24.1097i			0.514372i	−0.966362	+	0.257186i	$0.917205\pi$
$14$	−47.5322	−	38.2479i	−0.907394	−	0.730156i
$15$		0			0
$16$	−58.1402	+	26.7528i	−0.908441	+	0.418013i
$17$	14.4940			0.206783			0.103391	−	0.994641i	$-0.467031\pi$
$17$	14.4940			0.206783			0.103391	+	0.994641i	$0.467031\pi$
$18$		0			0
$19$		−	26.6887i		−	0.322253i	−0.986934	−	0.161126i	$-0.948487\pi$
$19$		−	26.6887i		−	0.322253i	0.986934	−	0.161126i	$-0.0515127\pi$
$20$	−39.0737	+	8.55846i	−0.436857	+	0.0956864i
$21$		0			0
$22$	−66.1166	+	82.1658i	−0.640732	+	0.796264i
$23$	8.36366			0.0758236			0.0379118	−	0.999281i	$-0.487929\pi$
$23$	8.36366			0.0758236			0.0379118	+	0.999281i	$0.487929\pi$
$24$		0			0
$25$	−25.0000			−0.200000
$26$	42.7508	−	53.1282i	0.322466	−	0.400742i
$27$		0			0
$28$	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	$0.891351\pi$
$30$		0			0
$31$	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
$33$		0			0
$34$	−31.9389	−	25.7004i	−0.161102	−	0.129635i
$35$			107.851i			0.520863i
$36$		0			0
$37$			130.923i			0.581720i	0.956766	+	0.290860i	$0.0939414\pi$
$37$			130.923i			0.581720i	−0.956766	+	0.290860i	$0.906059\pi$
$38$	−47.3237	+	58.8111i	−0.202024	+	0.251064i
$39$		0			0
$40$	101.278	+	50.4251i	0.400338	+	0.199323i
$41$	437.963			1.66825			0.834126	−	0.551574i	$-0.185973\pi$
$41$	437.963			1.66825			0.834126	+	0.551574i	$0.185973\pi$
$42$		0			0
$43$		−	308.764i		−	1.09503i	−0.836797	−	0.547513i	$-0.815575\pi$
$43$		−	308.764i		−	1.09503i	0.836797	−	0.547513i	$-0.184425\pi$
$44$	291.389	−	63.8240i	0.998376	−	0.218678i
$45$		0			0
$46$	−18.4301	−	14.8302i	−0.0590734	−	0.0475348i
$47$	−97.1081			−0.301376			−0.150688	−	0.988581i	$-0.548149\pi$
$47$	−97.1081			−0.301376			−0.150688	+	0.988581i	$0.548149\pi$
$48$		0			0
$49$	122.277			0.356492
$50$	55.0900	+	44.3294i	0.155818	+	0.125383i
$51$		0			0
$52$	−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	$-0.0641632\pi$
$54$		0			0
$55$	186.436			0.457072
$56$	217.537	−	436.920i	0.519100	−	1.04261i
$57$		0			0
$58$	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	$0.795052\pi$
$60$		0			0
$61$		−	374.601i		−	0.786275i	−0.919480	−	0.393137i	$-0.871390\pi$
$61$		−	374.601i		−	0.786275i	0.919480	−	0.393137i	$-0.128610\pi$
$62$	−450.168	−	362.238i	−0.922120	−	0.742005i
$63$		0			0
$64$	−308.584	−	408.558i	−0.602704	−	0.797965i
$65$	−120.549			−0.230034
$66$		0			0
$67$		−	19.3982i		−	0.0353711i	−0.999844	−	0.0176855i	$-0.994370\pi$
$67$		−	19.3982i		−	0.0353711i	0.999844	−	0.0176855i	$-0.00562977\pi$
$68$	24.8092	+	113.267i	0.0442435	+	0.201994i
$69$		0			0
$70$	191.240	−	237.661i	0.326536	−	0.405799i
$71$	955.725			1.59752			0.798759	−	0.601651i	$-0.205490\pi$
$71$	955.725			1.59752			0.798759	+	0.601651i	$0.205490\pi$
$72$		0			0
$73$	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
$75$		0			0
$76$	208.565	−	45.6828i	0.314790	−	0.0689496i
$77$		−	804.293i		−	1.19036i
$78$		0			0
$79$	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
$81$		0			0
$82$	−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	$-0.0115832\pi$
$84$		0			0
$85$			72.4698i			0.0924760i
$86$	−547.493	+	680.392i	−0.686485	+	0.853123i
$87$		0			0
$88$	−755.275	−	376.041i	−0.914916	−	0.455525i
$89$	919.812			1.09550			0.547752	−	0.836641i	$-0.315484\pi$
$89$	919.812			1.09550			0.547752	+	0.836641i	$0.315484\pi$
$90$		0			0
$91$			520.054i			0.599082i
$92$	14.3160	+	65.3598i	0.0162233	+	0.0740677i
$93$		0			0
$94$	213.987	+	172.190i	0.234799	+	0.188936i
$95$	133.443			0.144116
$96$		0			0
$97$	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
$99$		0			0
$100$	−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	$-0.344806\pi$
$102$		0			0
$103$	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
$105$		0			0
$106$	−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	$-0.00967233\pi$
$108$		0			0
$109$			1459.15i			1.28222i	0.767451	+	0.641108i	$0.221525\pi$
$109$			1459.15i			1.28222i	−0.767451	+	0.641108i	$0.778475\pi$
$110$	−410.829	−	330.583i	−0.356100	−	0.286544i
$111$		0			0
$112$	−1254.10	+	577.066i	−1.05805	+	0.486854i
$113$	−458.263			−0.381502			−0.190751	−	0.981638i	$-0.561092\pi$
$113$	−458.263			−0.381502			−0.190751	+	0.981638i	$0.561092\pi$
$114$		0			0
$115$			41.8183i			0.0339093i
$116$	−817.052	+	178.962i	−0.653978	+	0.143243i
$117$		0			0
$118$	964.764	−	1198.95i	0.752659	−	0.935360i
$119$	312.639			0.240837
$120$		0			0
$121$	−59.3283			−0.0445743
$122$	−664.234	+	825.471i	−0.492926	+	0.612579i
$123$		0			0
$124$	349.678	+	1596.46i	0.253242	+	1.15618i
$125$		−	125.000i		−	0.0894427i
$126$		0			0
$127$	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
$129$		0			0
$130$	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	$0.797094\pi$
$132$		0			0
$133$		−	575.682i		−	0.375323i
$134$	−34.3963	+	42.7457i	−0.0221746	+	0.0275572i
$135$		0			0
$136$	146.172	−	293.585i	0.0921629	−	0.185108i
$137$	−2380.60			−1.48459			−0.742293	−	0.670075i	$-0.766262\pi$
$137$	−2380.60			−1.48459			−0.742293	+	0.670075i	$0.766262\pi$
$138$		0			0
$139$			2858.52i			1.74429i	0.489245	+	0.872146i	$0.337272\pi$
$139$			2858.52i			1.74429i	−0.489245	+	0.872146i	$0.662728\pi$
$140$	−842.830	+	184.608i	−0.508801	+	0.111445i
$141$		0			0
$142$	−2106.04	−	1694.67i	−1.24461	−	1.00150i
$143$	898.983			0.525711
$144$		0			0
$145$	−522.764			−0.299401
$146$	−280.775	−	225.932i	−0.159158	−	0.128070i
$147$		0			0
$148$	−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	$0.920608\pi$
$150$		0			0
$151$	−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
$153$		0			0
$154$	−1426.15	+	1772.34i	−0.746251	+	0.927397i
$155$			1021.44i			0.529316i
$156$		0			0
$157$		−	571.369i		−	0.290447i	−0.989399	−	0.145224i	$-0.953610\pi$
$157$		−	571.369i		−	0.290447i	0.989399	−	0.145224i	$-0.0463901\pi$
$158$	−2146.02	−	1726.85i	−1.08056	−	0.869496i
$159$		0			0
$160$	−220.702	+	877.776i	−0.109050	+	0.433714i
$161$	180.406			0.0883106
$162$		0			0
$163$			236.962i			0.113867i	0.998378	+	0.0569333i	$0.0181322\pi$
$163$			236.962i			0.113867i	−0.998378	+	0.0569333i	$0.981868\pi$
$164$	749.657	+	3422.57i	0.356941	+	1.62962i
$165$		0			0
$166$	−97.5619	+	121.244i	−0.0456161	+	0.0566890i
$167$	−1448.46			−0.671169			−0.335585	−	0.942010i	$-0.608934\pi$
$167$	−1448.46			−0.671169			−0.335585	+	0.942010i	$0.608934\pi$
$168$		0			0
$169$	1615.72			0.735421
$170$	128.502	−	159.694i	0.0579743	−	0.0720471i
$171$		0			0
$172$	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	$0.812383\pi$
$174$		0			0
$175$	−539.257			−0.232937
$176$	997.536	+	2167.88i	0.427228	+	0.928467i
$177$		0			0
$178$	−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	$-0.00940662\pi$
$180$		0			0
$181$		−	3457.79i		−	1.41997i	−0.704215	−	0.709987i	$-0.748701\pi$
$181$		−	3457.79i		−	1.41997i	0.704215	−	0.709987i	$-0.251299\pi$
$182$	922.147	−	1145.99i	0.375572	−	0.466739i
$183$		0			0
$184$	84.3477	−	169.411i	0.0337945	−	0.0678760i
$185$	−654.616			−0.260153
$186$		0			0
$187$		−	540.438i		−	0.211341i
$188$	−166.219	−	758.874i	−0.0644828	−	0.294397i
$189$		0			0
$190$	−294.056	−	236.619i	−0.112279	−	0.0903480i
$191$	1416.99			0.536804			0.268402	−	0.963307i	$-0.413504\pi$
$191$	1416.99			0.536804			0.268402	+	0.963307i	$0.413504\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$	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	$-0.162212\pi$
$198$		0			0
$199$	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
$201$		0			0
$202$	−3180.25	+	3952.22i	−1.10773	+	1.37662i
$203$			2255.23i			0.779735i
$204$		0			0
$205$			2189.81i			0.746065i
$206$	−4592.54	−	3695.50i	−1.55329	−	1.24989i
$207$		0			0
$208$	−645.004	−	1401.75i	−0.215014	−	0.467277i
$209$	−995.143			−0.329356
$210$		0			0
$211$			152.205i			0.0496598i	0.999692	+	0.0248299i	$0.00790441\pi$
$211$			152.205i			0.0496598i	−0.999692	+	0.0248299i	$0.992096\pi$
$212$	1207.39	−	264.460i	0.391152	−	0.0856754i
$213$		0			0
$214$	−119.254	+	148.201i	−0.0380935	+	0.0473403i
$215$	1543.82			0.489710
$216$		0			0
$217$	4406.54			1.37851
$218$	2587.34	−	3215.39i	0.803837	−	0.998961i
$219$		0			0
$220$	319.120	+	1456.94i	0.0977958	+	0.446487i
$221$			349.446i			0.106363i
$222$		0			0
$223$	−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
$225$		0			0
$226$	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	$0.858556\pi$
$228$		0			0
$229$		−	4949.77i		−	1.42834i	−0.699971	−	0.714171i	$-0.746804\pi$
$229$		−	4949.77i		−	1.42834i	0.699971	−	0.714171i	$-0.253196\pi$
$230$	74.1512	−	92.1507i	0.0212582	−	0.0264184i
$231$		0			0
$232$	2117.79	+	1054.42i	0.599308	+	0.298387i
$233$	−5193.31			−1.46019			−0.730096	−	0.683344i	$-0.760525\pi$
$233$	−5193.31			−1.46019			−0.730096	+	0.683344i	$0.760525\pi$
$234$		0			0
$235$		−	485.540i		−	0.134779i
$236$	−4251.90	+	931.311i	−1.17278	+	0.256878i
$237$		0			0
$238$	−688.930	−	554.364i	−0.187633	−	0.150983i
$239$	2066.30			0.559238			0.279619	−	0.960111i	$-0.409792\pi$
$239$	2066.30			0.559238			0.279619	+	0.960111i	$0.409792\pi$
$240$		0			0
$241$	−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
$243$		0			0
$244$	2927.41	−	641.202i	0.768066	−	0.168232i
$245$			611.384i			0.159428i
$246$		0			0
$247$	643.457			0.165758
$248$	2060.25	−	4137.99i	0.527524	−	1.05953i
$249$		0			0
$250$	−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	$-0.158683\pi$
$252$		0			0
$253$		−	311.857i		−	0.0774951i
$254$	−459.858	−	370.035i	−0.113599	−	0.0914097i
$255$		0			0
$256$	2664.57	−	3110.83i	0.650530	−	0.759480i
$257$	−6168.56			−1.49721			−0.748607	−	0.663013i	$-0.769277\pi$
$257$	−6168.56			−1.49721			−0.748607	+	0.663013i	$0.769277\pi$
$258$		0			0
$259$			2824.05i			0.677521i
$260$	−206.342	−	942.057i	−0.0492185	−	0.224707i
$261$		0			0
$262$	3164.56	−	3932.73i	0.746211	−	0.927347i
$263$	1636.11			0.383599			0.191800	−	0.981434i	$-0.438568\pi$
$263$	1636.11			0.383599			0.191800	+	0.981434i	$0.438568\pi$
$264$		0			0
$265$	772.511			0.179075
$266$	−1020.79	+	1268.57i	−0.235295	+	0.292410i
$267$		0			0
$268$	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	$-0.0825292\pi$
$270$		0			0
$271$	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
$273$		0			0
$274$	5245.88	+	4221.22i	1.15663	+	0.930706i
$275$			932.178i			0.204409i
$276$		0			0
$277$			2139.00i			0.463971i	0.972719	+	0.231986i	$0.0745223\pi$
$277$			2139.00i			0.463971i	−0.972719	+	0.231986i	$0.925478\pi$
$278$	5068.66	−	6299.03i	1.09352	−	1.35896i
$279$		0			0
$280$	2184.60	+	1087.68i	0.466268	+	0.232148i
$281$	1493.53			0.317069			0.158534	−	0.987353i	$-0.449323\pi$
$281$	1493.53			0.317069			0.158534	+	0.987353i	$0.449323\pi$
$282$		0			0
$283$			1090.20i			0.228995i	0.993424	+	0.114498i	$0.0365259\pi$
$283$			1090.20i			0.228995i	−0.993424	+	0.114498i	$0.963474\pi$
$284$	1635.91	+	7468.74i	0.341807	+	1.56052i
$285$		0			0
$286$	−1981.00	−	1594.05i	−0.409576	−	0.329575i
$287$	9446.98			1.94299
$288$		0			0
$289$	−4702.92			−0.957241
$290$	1151.96	+	926.952i	0.233260	+	0.187698i
$291$		0			0
$292$	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	$-0.132905\pi$
$294$		0			0
$295$	−2720.44			−0.536916
$296$	2651.94	+	1320.36i	0.520746	+	0.259272i
$297$		0			0
$298$	1592.12	−	1978.60i	0.309494	−	0.384621i
$299$			201.646i			0.0390016i
$300$		0			0
$301$		−	6660.13i		−	1.27536i
$302$	7561.25	+	6084.33i	1.44073	+	1.15932i
$303$		0			0
$304$	713.998	+	1551.69i	0.134706	+	0.292748i
$305$	1873.01			0.351633
$306$		0			0
$307$		−	6736.05i		−	1.25227i	−0.779715	−	0.626135i	$-0.784636\pi$
$307$		−	6736.05i		−	1.25227i	0.779715	−	0.626135i	$-0.215364\pi$
$308$	6285.34	−	1376.70i	1.16279	−	0.254691i
$309$		0			0
$310$	1811.19	−	2250.84i	0.331835	−	0.412384i
$311$	−3274.35			−0.597014			−0.298507	−	0.954407i	$-0.596489\pi$
$311$	−3274.35			−0.597014			−0.298507	+	0.954407i	$0.596489\pi$
$312$		0			0
$313$	−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
$315$		0			0
$316$	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	$-0.296782\pi$
$318$		0			0
$319$	3898.47			0.684239
$320$	2042.79	−	1542.92i	0.356861	−	0.269537i
$321$		0			0
$322$	−397.543	−	319.892i	−0.0688019	−	0.0553630i
$323$		−	386.825i		−	0.0666362i
$324$		0			0
$325$		−	602.744i		−	0.102874i
$326$	420.175	−	522.168i	0.0713844	−	0.0887123i
$327$		0			0
$328$	4416.87	−	8871.23i	0.743539	−	1.49339i
$329$	−2094.65			−0.351008
$330$		0			0
$331$		−	280.089i		−	0.0465108i	−0.999730	−	0.0232554i	$-0.992597\pi$
$331$		−	280.089i		−	0.0465108i	0.999730	−	0.0232554i	$-0.00740310\pi$
$332$	429.975	−	94.1789i	0.0710781	−	0.0155685i
$333$		0			0
$334$	3191.83	+	2568.38i	0.522901	+	0.420764i
$335$	96.9908			0.0158184
$336$		0			0
$337$	−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
$339$		0			0
$340$	−566.333	+	124.046i	−0.0903344	+	0.0197863i
$341$		−	7617.30i		−	1.20968i
$342$		0			0
$343$	−4761.06			−0.749484
$344$	−6254.23	−	3113.90i	−0.980248	−	0.488052i
$345$		0			0
$346$	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	$0.927692\pi$
$348$		0			0
$349$			5665.17i			0.868910i	0.900693	+	0.434455i	$0.143059\pi$
$349$			5665.17i			0.868910i	−0.900693	+	0.434455i	$0.856941\pi$
$350$	1188.31	+	956.198i	0.181479	+	0.146031i
$351$		0			0
$352$	1645.87	−	6545.95i	0.249219	−	0.991193i
$353$	9428.18			1.42156			0.710781	−	0.703414i	$-0.248342\pi$
$353$	9428.18			1.42156			0.710781	+	0.703414i	$0.248342\pi$
$354$		0			0
$355$			4778.63i			0.714432i
$356$	1574.43	+	7188.09i	0.234396	+	1.07013i
$357$		0			0
$358$	−250.947	+	311.862i	−0.0370474	+	0.0460403i
$359$	−4573.16			−0.672318			−0.336159	−	0.941805i	$-0.609128\pi$
$359$	−4573.16			−0.672318			−0.336159	+	0.941805i	$0.609128\pi$
$360$		0			0
$361$	6146.71			0.896153
$362$	−6131.26	+	7619.57i	−0.890199	+	1.10629i
$363$		0			0
$364$	−4064.08	+	890.172i	−0.585208	+	0.128180i
$365$			637.083i			0.0913601i
$366$		0			0
$367$	−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
$369$		0			0
$370$	1442.51	+	1160.75i	0.202683	+	0.163093i
$371$		−	3332.65i		−	0.466369i
$372$		0			0
$373$		−	5627.51i		−	0.781183i	−0.920564	−	0.390592i	$-0.872270\pi$
$373$		−	5627.51i		−	0.781183i	0.920564	−	0.390592i	$-0.127730\pi$
$374$	−958.292	+	1190.91i	−0.132492	+	0.164654i
$375$		0			0
$376$	−979.338	+	1966.99i	−0.134323	+	0.269786i
$377$	−2520.74			−0.344363
$378$		0			0
$379$			8066.74i			1.09330i	0.837361	+	0.546650i	$0.184097\pi$
$379$			8066.74i			1.09330i	−0.837361	+	0.546650i	$0.815903\pi$
$380$	228.414	+	1042.82i	0.0308352	+	0.140778i
$381$		0			0
$382$	−3122.47	−	2512.57i	−0.418219	−	0.336529i
$383$	−10607.8			−1.41523			−0.707613	−	0.706600i	$-0.750228\pi$
$383$	−10607.8			−1.41523			−0.707613	+	0.706600i	$0.750228\pi$
$384$		0			0
$385$	4021.47			0.532345
$386$	5908.11	+	4754.10i	0.779055	+	0.626884i
$387$		0			0
$388$	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	$0.800685\pi$
$390$		0			0
$391$	121.223			0.0156790
$392$	1233.16	−	2476.80i	0.158888	−	0.319125i
$393$		0			0
$394$	−4783.56	+	5944.73i	−0.611656	+	0.760130i
$395$			4869.36i			0.620263i
$396$		0			0
$397$			8977.17i			1.13489i	0.823411	+	0.567445i	$0.192068\pi$
$397$			8977.17i			1.13489i	−0.823411	+	0.567445i	$0.807932\pi$
$398$	−7807.90	−	6282.81i	−0.983353	−	0.791278i
$399$		0			0
$400$	1453.51	−	668.821i	0.181688	−	0.0836026i
$401$	3165.72			0.394236			0.197118	−	0.980380i	$-0.436842\pi$
$401$	3165.72			0.394236			0.197118	+	0.980380i	$0.436842\pi$
$402$		0			0
$403$			4925.33i			0.608804i
$404$	14016.0	−	3069.97i	1.72604	−	0.378061i
$405$		0			0
$406$	3998.92	−	4969.62i	0.488826	−	0.607483i
$407$	4881.75			0.594543
$408$		0			0
$409$	−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
$411$		0			0
$412$	3567.35	+	16286.8i	0.426580	+	1.94755i
$413$			11736.1i			1.39830i
$414$		0			0
$415$	275.105			0.0325407
$416$	−1064.21	+	4232.59i	−0.125426	+	0.498846i
$417$		0			0
$418$	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	$-0.117679\pi$
$420$		0			0
$421$			4344.57i			0.502949i	0.967864	+	0.251474i	$0.0809154\pi$
$421$			4344.57i			0.502949i	−0.967864	+	0.251474i	$0.919085\pi$
$422$	269.886	−	335.398i	0.0311323	−	0.0386894i
$423$		0			0
$424$	−3129.54	−	1558.16i	−0.358453	−	0.178469i
$425$	−362.349			−0.0413565
$426$		0			0
$427$		−	8080.25i		−	0.915763i
$428$	525.574	−	115.118i	0.0593565	−	0.0130011i
$429$		0			0
$430$	−3401.96	−	2737.47i	−0.381528	−	0.307006i
$431$	−4750.74			−0.530940			−0.265470	−	0.964119i	$-0.585527\pi$
$431$	−4750.74			−0.530940			−0.265470	+	0.964119i	$0.585527\pi$
$432$		0			0
$433$	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
$435$		0			0
$436$	−11402.9	+	2497.62i	−1.25252	+	0.274345i
$437$		−	223.215i		−	0.0244344i
$438$		0			0
$439$	−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
$441$		0			0
$442$	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	$0.777893\pi$
$444$		0			0
$445$			4599.06i			0.489924i
$446$	4551.32	+	3662.32i	0.483209	+	0.388825i
$447$		0			0
$448$	−6656.25	−	8812.71i	−0.701961	−	0.929378i
$449$	5567.58			0.585190			0.292595	−	0.956236i	$-0.405481\pi$
$449$	5567.58			0.585190			0.292595	+	0.956236i	$0.405481\pi$
$450$		0			0
$451$		−	16330.4i		−	1.70503i
$452$	−784.404	−	3581.20i	−0.0816267	−	0.372667i
$453$		0			0
$454$	5213.94	−	6479.58i	0.538992	−	0.669828i
$455$	−2600.27			−0.267918
$456$		0			0
$457$	−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
$459$		0			0
$460$	−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	$-0.205303\pi$
$462$		0			0
$463$	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
$465$		0			0
$466$	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	$-0.0492447\pi$
$468$		0			0
$469$		−	418.424i		−	0.0411962i
$470$	−860.949	+	1069.94i	−0.0844949	+	0.105005i
$471$		0			0
$472$	11020.9	+	5487.14i	1.07474	+	0.535098i
$473$	−11512.9			−1.11916
$474$		0			0
$475$			667.217i			0.0644505i
$476$	535.141	+	2443.19i	0.0515297	+	0.235259i
$477$		0			0
$478$	−4553.30	−	3663.92i	−0.435697	−	0.350594i
$479$	−6590.43			−0.628652			−0.314326	−	0.949315i	$-0.601779\pi$
$479$	−6590.43			−0.628652			−0.314326	+	0.949315i	$0.601779\pi$
$480$		0			0
$481$	−3156.52			−0.299221
$482$	5088.28	+	4094.40i	0.480840	+	0.386919i
$483$		0			0
$484$	−101.552	−	463.635i	−0.00953717	−	0.0435420i
$485$			1489.93i			0.139493i
$486$		0			0
$487$	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
$489$		0			0
$490$	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	$-0.186947\pi$
$492$		0			0
$493$			1515.38i			0.138437i
$494$	−1417.92	−	1140.96i	−0.129140	−	0.103916i
$495$		0			0
$496$	−11877.3	+	5465.28i	−1.07522	+	0.494754i
$497$	20615.3			1.86061
$498$		0			0
$499$		−	8458.64i		−	0.758839i	−0.925225	−	0.379420i	$-0.876124\pi$
$499$		−	8458.64i		−	0.758839i	0.925225	−	0.379420i	$-0.123876\pi$
$500$	976.842	−	213.961i	0.0873714	−	0.0191373i
$501$		0			0
$502$	−6742.67	+	8379.40i	−0.599483	+	0.745001i
$503$	−16896.2			−1.49774			−0.748869	−	0.662718i	$-0.769403\pi$
$503$	−16896.2			−1.49774			−0.748869	+	0.662718i	$0.769403\pi$
$504$		0			0
$505$	8967.65			0.790208
$506$	−552.977	+	687.207i	−0.0485826	+	0.0603756i
$507$		0			0
$508$	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	$0.903609\pi$
$510$		0			0
$511$	2748.41			0.237931
$512$	−11387.7	+	2130.27i	−0.982949	+	0.183878i
$513$		0			0
$514$	13593.0	+	10937.9i	1.16646	+	0.938623i
$515$			10420.6i			0.891620i
$516$		0			0
$517$			3620.88i			0.308019i
$518$	5007.54	−	6223.07i	0.424746	−	0.527849i
$519$		0			0
$520$	−1215.74	+	2441.80i	−0.102526	+	0.205923i
$521$	−11044.1			−0.928696			−0.464348	−	0.885653i	$-0.653711\pi$
$521$	−11044.1			−0.928696			−0.464348	+	0.885653i	$0.653711\pi$
$522$		0			0
$523$		−	3115.75i		−	0.260502i	−0.991481	−	0.130251i	$-0.958422\pi$
$523$		−	3115.75i		−	0.260502i	0.991481	−	0.130251i	$-0.0415782\pi$
$524$	−13946.8	+	3054.83i	−1.16273	+	0.254677i
$525$		0			0
$526$	−3605.32	−	2901.10i	−0.298858	−	0.240483i
$527$	2960.94			0.244745
$528$		0			0
$529$	−12097.0			−0.994251
$530$	−1702.30	−	1369.80i	−0.139516	−	0.112265i
$531$		0			0
$532$	4498.80	−	985.390i	0.366631	−	0.0803046i
$533$			10559.2i			0.858103i
$534$		0			0
$535$	336.271			0.0271743
$536$	−392.923	−	195.631i	−0.0316636	−	0.0157649i
$537$		0			0
$538$	−4011.36	+	4985.07i	−0.321453	+	0.399483i
$539$		−	4559.35i		−	0.364350i
$540$		0			0
$541$		−	14840.6i		−	1.17938i	−0.807629	−	0.589691i	$-0.799249\pi$
$541$		−	14840.6i		−	1.17938i	0.807629	−	0.589691i	$-0.200751\pi$
$542$	−91.7535	−	73.8316i	−0.00727150	−	0.00585118i
$543$		0			0
$544$	2544.49	+	639.769i	0.200541	+	0.0504226i
$545$	−7295.76			−0.573424
$546$		0			0
$547$		−	12622.8i		−	0.986679i	−0.869837	−	0.493340i	$-0.835776\pi$
$547$		−	12622.8i		−	0.986679i	0.869837	−	0.493340i	$-0.164224\pi$
$548$	−4074.85	−	18603.8i	−0.317644	−	1.45021i
$549$		0			0
$550$	1652.92	−	2054.15i	0.128146	−	0.159253i
$551$	2790.37			0.215742
$552$		0			0
$553$	21006.7			1.61536
$554$	3792.83	−	4713.50i	0.290870	−	0.361475i
$555$		0			0
$556$	−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	$0.830018\pi$
$558$		0			0
$559$	7444.23			0.563251
$560$	−2885.33	−	6270.50i	−0.217728	−	0.473173i
$561$		0			0
$562$	−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	$-0.00183352\pi$
$564$		0			0
$565$		−	2291.31i		−	0.170613i
$566$	1933.12	−	2402.37i	0.143560	−	0.178408i
$567$		0			0
$568$	9638.52	−	19358.9i	0.712013	−	1.43007i
$569$	5395.71			0.397539			0.198770	−	0.980046i	$-0.436305\pi$
$569$	5395.71			0.397539			0.198770	+	0.980046i	$0.436305\pi$
$570$		0			0
$571$			22390.5i			1.64100i	0.571646	+	0.820500i	$0.306305\pi$
$571$			22390.5i			1.64100i	−0.571646	+	0.820500i	$0.693695\pi$
$572$	1538.78	+	7025.31i	0.112482	+	0.513537i
$573$		0			0
$574$	−20817.4	−	16751.2i	−1.51376	−	1.21808i
$575$	−209.091			−0.0151647
$576$		0			0
$577$	−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
$579$		0			0
$580$	−894.810	−	4085.26i	−0.0640603	−	0.292468i
$581$		−	1186.82i		−	0.0847461i
$582$		0			0
$583$	−5760.94			−0.409252
$584$	1285.00	−	2580.91i	0.0910508	−	0.182875i
$585$		0			0
$586$	−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	$-0.0896491\pi$
$588$		0			0
$589$		−	5452.17i		−	0.381414i
$590$	5994.76	+	4823.82i	0.418306	+	0.336599i
$591$		0			0
$592$	−3502.57	−	7611.90i	−0.243166	−	0.528458i
$593$	11141.6			0.771552			0.385776	−	0.922592i	$-0.373934\pi$
$593$	11141.6			0.771552			0.385776	+	0.922592i	$0.373934\pi$
$594$		0			0
$595$			1563.19i			0.107705i
$596$	−7016.81	+	1536.92i	−0.482248	+	0.105629i
$597$		0			0
$598$	357.553	−	444.346i	0.0244506	−	0.0303857i
$599$	−278.847			−0.0190207			−0.00951033	−	0.999955i	$-0.503027\pi$
$599$	−278.847			−0.0190207			−0.00951033	+	0.999955i	$0.503027\pi$
$600$		0			0
$601$	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
$603$		0			0
$604$	−5873.36	−	26814.9i	−0.395668	−	1.80643i
$605$		−	296.642i		−	0.0199342i
$606$		0			0
$607$	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
$609$		0			0
$610$	−4127.35	−	3321.17i	−0.273953	−	0.220443i
$611$		−	2341.25i		−	0.155019i
$612$		0			0
$613$			14412.8i			0.949635i	0.880084	+	0.474817i	$0.157486\pi$
$613$			14412.8i			0.949635i	−0.880084	+	0.474817i	$0.842514\pi$
$614$	−11944.2	+	14843.5i	−0.785063	+	0.975630i
$615$		0			0
$616$	−16291.5	−	8111.32i	−1.06559	−	0.530543i
$617$	−13226.3			−0.863001			−0.431500	−	0.902113i	$-0.642016\pi$
$617$	−13226.3			−0.863001			−0.431500	+	0.902113i	$0.642016\pi$
$618$		0			0
$619$		−	14179.4i		−	0.920705i	−0.887736	−	0.460352i	$-0.847723\pi$
$619$		−	14179.4i		−	0.920705i	0.887736	−	0.460352i	$-0.152277\pi$
$620$	−7982.28	+	1748.39i	−0.517058	+	0.113253i
$621$		0			0
$622$	7215.35	+	5806.00i	0.465127	+	0.374275i
$623$	19840.6			1.27592
$624$		0			0
$625$	625.000			0.0400000
$626$	20620.4	+	16592.7i	1.31654	+	1.05939i
$627$		0			0
$628$	4465.10	−	978.007i	0.283721	−	0.0621444i
$629$			1897.60i			0.120290i
$630$		0			0
$631$	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
$633$		0			0
$634$	−16073.3	+	19974.9i	−1.00686	+	1.25127i
$635$			1043.42i			0.0652079i
$636$		0			0
$637$			2948.06i			0.183370i
$638$	−8590.66	−	6912.67i	−0.533084	−	0.428958i
$639$		0			0
$640$	−7237.36	−	222.246i	−0.447003	−	0.0137266i
$641$	26682.6			1.64415			0.822074	−	0.569381i	$-0.192817\pi$
$641$	26682.6			1.64415			0.822074	+	0.569381i	$0.192817\pi$
$642$		0			0
$643$			16498.3i			1.01186i	0.862574	+	0.505931i	$0.168851\pi$
$643$			16498.3i			1.01186i	−0.862574	+	0.505931i	$0.831149\pi$
$644$	308.800	+	1409.83i	0.0188951	+	0.0862655i
$645$		0			0
$646$	−685.909	+	852.406i	−0.0417751	+	0.0519156i
$647$	20127.5			1.22302			0.611510	−	0.791236i	$-0.290562\pi$
$647$	20127.5			1.22302			0.611510	+	0.791236i	$0.290562\pi$
$648$		0			0
$649$	20287.5			1.22705
$650$	−1068.77	+	1328.20i	−0.0644933	+	0.0801484i
$651$		0			0
$652$	−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	$0.777835\pi$
$654$		0			0
$655$	−8923.43			−0.532316
$656$	−25463.3	+	11716.7i	−1.51551	+	0.697351i
$657$		0			0
$658$	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	$-0.194397\pi$
$660$		0			0
$661$			9326.38i			0.548796i	0.961616	+	0.274398i	$0.0884786\pi$
$661$			9326.38i			0.548796i	−0.961616	+	0.274398i	$0.911521\pi$
$662$	−496.647	+	617.204i	−0.0291582	+	0.0362361i
$663$		0			0
$664$	−1114.49	−	554.888i	−0.0651363	−	0.0324305i
$665$	2878.41			0.167850
$666$		0			0
$667$			874.443i			0.0507625i
$668$	−2479.32	−	11319.3i	−0.143604	−	0.655626i
$669$		0			0
$670$	−213.729	−	171.982i	−0.0123240	−	0.00991677i
$671$	−13967.8			−0.803608
$672$		0			0
$673$	−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
$675$		0			0
$676$	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	$0.911049\pi$
$678$		0			0
$679$	6427.63			0.363284
$680$	1467.93	+	730.860i	0.0827829	+	0.0412165i
$681$		0			0
$682$	−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	$0.895846\pi$
$684$		0			0
$685$		−	11903.0i		−	0.663927i
$686$	10491.5	+	8442.20i	0.583916	+	0.469861i
$687$		0			0
$688$	8260.32	+	17951.6i	0.457735	+	0.994766i
$689$	3725.01			0.205967
$690$		0			0
$691$			28412.6i			1.56421i	0.623149	+	0.782103i	$0.285853\pi$
$691$			28412.6i			1.56421i	−0.623149	+	0.782103i	$0.714147\pi$
$692$	−19769.3	+	4330.13i	−1.08600	+	0.237871i
$693$		0			0
$694$	5162.64	−	6415.82i	0.282379	−	0.350924i
$695$	−14292.6			−0.780071
$696$		0			0
$697$	6347.82			0.344965
$698$	10045.3	−	12483.8i	0.544731	−	0.676959i
$699$		0			0
$700$	−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	$-0.107428\pi$
$702$		0			0
$703$	3494.17			0.187461
$704$	−15233.9	+	11506.2i	−0.815555	+	0.615990i
$705$		0			0
$706$	−20775.9	−	16717.8i	−1.10752	−	0.891195i
$707$		−	38686.9i		−	2.05795i
$708$		0			0
$709$			12774.2i			0.676650i	0.941029	+	0.338325i	$0.109860\pi$
$709$			12774.2i			0.676650i	−0.941029	+	0.338325i	$0.890140\pi$
$710$	8473.35	−	10530.2i	0.447886	−	0.556606i
$711$		0			0
$712$	9276.33	−	18631.4i	0.488266	−	0.980676i
$713$	1708.59			0.0897438
$714$		0			0
$715$			4494.91i			0.235105i
$716$	1105.97	−	242.245i	0.0577264	−	0.0126440i
$717$		0			0
$718$	10077.4	+	8109.02i	0.523796	+	0.421485i
$719$	15748.6			0.816861			0.408430	−	0.912790i	$-0.366076\pi$
$719$	15748.6			0.816861			0.408430	+	0.912790i	$0.366076\pi$
$720$		0			0
$721$	44954.8			2.32206
$722$	−13544.9	−	10899.2i	−0.698184	−	0.561810i
$723$		0			0
$724$	27021.7	−	5918.66i	1.38709	−	0.303820i
$725$		−	2613.82i		−	0.133896i
$726$		0			0
$727$	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
$729$		0			0
$730$	1129.66	−	1403.88i	0.0572748	−	0.0711777i
$731$		−	4475.22i		−	0.226432i
$732$		0			0
$733$			34913.5i			1.75929i	0.475631	+	0.879645i	$0.342220\pi$
$733$			34913.5i			1.75929i	−0.475631	+	0.879645i	$0.657780\pi$
$734$	5989.31	+	4819.43i	0.301184	+	0.242355i
$735$		0			0
$736$	1468.28	+	369.175i	0.0735348	+	0.0184891i
$737$	−723.301			−0.0361508
$738$		0			0
$739$		−	19324.3i		−	0.961918i	−0.876743	−	0.480959i	$-0.840289\pi$
$739$		−	19324.3i		−	0.961918i	0.876743	−	0.480959i	$-0.159711\pi$
$740$	−1120.50	−	5115.65i	−0.0556627	−	0.254128i
$741$		0			0
$742$	−5909.38	+	7343.83i	−0.292372	+	0.363343i
$743$	7053.57			0.348278			0.174139	−	0.984721i	$-0.444286\pi$
$743$	7053.57			0.348278			0.174139	+	0.984721i	$0.444286\pi$
$744$		0			0
$745$	−4489.47			−0.220781
$746$	−9978.56	+	12400.8i	−0.489733	+	0.608612i
$747$		0			0
$748$	4223.38	−	925.063i	0.206447	−	0.0452188i
$749$		−	1450.69i		−	0.0707705i
$750$		0			0
$751$	−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
$753$		0			0
$754$	5554.70	+	4469.72i	0.268289	+	0.215885i
$755$		−	17156.6i		−	0.827010i
$756$		0			0
$757$			28515.3i			1.36910i	0.728967	+	0.684549i	$0.240001\pi$
$757$			28515.3i			1.36910i	−0.728967	+	0.684549i	$0.759999\pi$
$758$	14303.8	−	17775.9i	0.685403	−	0.851779i
$759$		0			0
$760$	1345.78	−	2702.98i	0.0642323	−	0.129010i
$761$	−1517.92			−0.0723057			−0.0361528	−	0.999346i	$-0.511510\pi$
$761$	−1517.92			−0.0723057			−0.0361528	+	0.999346i	$0.511510\pi$
$762$		0			0
$763$			31474.3i			1.49338i
$764$	2425.44	+	11073.4i	0.114855	+	0.524373i
$765$		0			0
$766$	23375.3	+	18809.4i	1.10259	+	0.887223i
$767$	−13117.8			−0.617545
$768$		0			0
$769$	−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
$771$		0			0
$772$	−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	$0.722421\pi$
$774$		0			0
$775$	−5107.19			−0.236717
$776$	3005.19	−	6035.90i	0.139021	−	0.279222i
$777$		0			0
$778$	15945.4	−	19816.0i	0.734796	−	0.913161i
$779$		−	11688.6i		−	0.537599i
$780$		0			0
$781$		−	35636.2i		−	1.63273i
$782$	−267.126	−	214.949i	−0.0122153	−	0.00982936i
$783$		0			0
$784$	−7109.20	+	3271.25i	−0.323852	+	0.149018i
$785$	2856.84			0.129892
$786$		0			0
$787$		−	35511.6i		−	1.60845i	−0.594324	−	0.804226i	$-0.702580\pi$
$787$		−	35511.6i		−	1.60845i	0.594324	−	0.804226i	$-0.297420\pi$
$788$	21082.1	−	4617.69i	0.953070	−	0.208754i
$789$		0			0
$790$	8634.23	−	10730.1i	0.388851	−	0.483240i
$791$	−9884.85			−0.444330
$792$		0			0
$793$	9031.54			0.404438
$794$	15918.1	−	19782.1i	0.711477	−	0.884181i
$795$		0			0
$796$	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	$-0.168237\pi$
$798$		0			0
$799$	−1407.48			−0.0623193
$800$	−4388.88	−	1103.51i	−0.193963	−	0.0487687i
$801$		0			0
$802$	−6975.98	−	5613.39i	−0.307145	−	0.247152i
$803$		−	4751.00i		−	0.208791i
$804$		0			0
$805$			902.032i			0.0394937i
$806$	8733.47	−	10853.4i	0.381667	−	0.474313i
$807$		0			0
$808$	−36329.2	−	18087.8i	−1.58175	−	0.787533i
$809$	22716.0			0.987209			0.493604	−	0.869687i	$-0.335679\pi$
$809$	22716.0			0.987209			0.493604	+	0.869687i	$0.335679\pi$
$810$		0			0
$811$		−	17237.0i		−	0.746327i	−0.927766	−	0.373164i	$-0.878273\pi$
$811$		−	17237.0i		−	0.746327i	0.927766	−	0.373164i	$-0.121727\pi$
$812$	−17624.0	+	3860.26i	−0.761678	+	0.166833i
$813$		0			0
$814$	−10757.4	−	8656.20i	−0.463203	−	0.372727i
$815$	−1184.81			−0.0509227
$816$		0			0
$817$	−8240.51			−0.352875
$818$	11938.2	+	9606.38i	0.510282	+	0.410610i
$819$		0			0
$820$	−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	$0.891734\pi$
$822$		0			0
$823$	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
$825$		0			0
$826$	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	$0.975129\pi$
$828$		0			0
$829$		−	22469.6i		−	0.941376i	−0.882300	−	0.470688i	$-0.844006\pi$
$829$		−	22469.6i		−	0.941376i	0.882300	−	0.470688i	$-0.155994\pi$
$830$	−606.221	−	487.810i	−0.0253521	−	0.0204001i
$831$		0			0
$832$	9850.23	−	7439.89i	0.410451	−	0.310014i
$833$	1772.27			0.0737163
$834$		0			0
$835$		−	7242.30i		−	0.300156i
$836$	−1703.38	−	7776.78i	−0.0704696	−	0.321729i
$837$		0			0
$838$	−10990.4	+	13658.2i	−0.453051	+	0.563025i
$839$	31935.2			1.31409			0.657046	−	0.753850i	$-0.271806\pi$
$839$	31935.2			1.31409			0.657046	+	0.753850i	$0.271806\pi$
$840$		0			0
$841$	13457.7			0.551795
$842$	7703.69	−	9573.69i	0.315305	−	0.391842i
$843$		0			0
$844$	−1189.44	+	260.528i	−0.0485098	+	0.0106253i
$845$			8078.60i			0.328890i
$846$		0			0
$847$	−1279.73			−0.0519150
$848$	4133.37	+	8982.79i	0.167383	+	0.363762i
$849$		0			0
$850$	798.472	+	642.509i	0.0322204	+	0.0259269i
$851$			1095.00i			0.0441081i
$852$		0			0
$853$		−	14782.2i		−	0.593355i	−0.954978	−	0.296678i	$-0.904121\pi$
$853$		−	14782.2i		−	0.593355i	0.954978	−	0.296678i	$-0.0958787\pi$
$854$	−14327.7	+	17805.6i	−0.574103	+	0.713461i
$855$		0			0
$856$	−1362.28	−	678.261i	−0.0543946	−	0.0270823i
$857$	7222.91			0.287900			0.143950	−	0.989585i	$-0.454020\pi$
$857$	7222.91			0.287900			0.143950	+	0.989585i	$0.454020\pi$
$858$		0			0
$859$		−	4646.96i		−	0.184578i	−0.995732	−	0.0922889i	$-0.970582\pi$
$859$		−	4646.96i		−	0.184578i	0.995732	−	0.0922889i	$-0.0294183\pi$
$860$	2642.54	+	12064.6i	0.104779	+	0.478370i
$861$		0			0
$862$	10468.7	+	8423.90i	0.413650	+	0.332853i
$863$	−8122.19			−0.320374			−0.160187	−	0.987087i	$-0.551210\pi$
$863$	−8122.19			−0.320374			−0.160187	+	0.987087i	$0.551210\pi$
$864$		0			0
$865$	−12648.7			−0.497189
$866$	−9277.73	−	7465.54i	−0.364053	−	0.292944i
$867$		0			0
$868$	7542.64	+	34436.0i	0.294947	+	1.34658i
$869$		−	36312.8i		−	1.41752i
$870$		0			0
$871$	467.685			0.0181939
$872$	29556.1	+	14715.6i	1.14782	+	0.571483i
$873$		0			0
$874$	−395.799	+	491.876i	−0.0153182	+	0.0190366i
$875$		−	2696.28i		−	0.104173i
$876$		0			0
$877$		−	31986.1i		−	1.23158i	−0.787910	−	0.615790i	$-0.788837\pi$
$877$		−	31986.1i		−	1.23158i	0.787910	−	0.615790i	$-0.211163\pi$
$878$	12729.1	+	10242.8i	0.489278	+	0.393709i
$879$		0			0
$880$	−10839.4	+	4987.68i	−0.415223	+	0.191062i
$881$	29450.6			1.12624			0.563118	−	0.826376i	$-0.309602\pi$
$881$	29450.6			1.12624			0.563118	+	0.826376i	$0.309602\pi$
$882$		0			0
$883$		−	46156.5i		−	1.75911i	−0.475801	−	0.879553i	$-0.657842\pi$
$883$		−	46156.5i		−	1.75911i	0.475801	−	0.879553i	$-0.342158\pi$
$884$	−2730.83	+	598.143i	−0.103900	+	0.0227576i
$885$		0			0
$886$	21245.5	−	26402.7i	0.805595	−	1.00115i
$887$	−41051.2			−1.55396			−0.776982	−	0.629523i	$-0.783250\pi$
$887$	−41051.2			−1.55396			−0.776982	+	0.629523i	$0.783250\pi$
$888$		0			0
$889$	4501.39			0.169822
$890$	8154.94	−	10134.5i	0.307140	−	0.381695i
$891$		0			0
$892$	−3535.33	−	16140.6i	−0.132704	−	0.605859i
$893$			2591.69i			0.0971192i
$894$		0			0
$895$	707.620			0.0264281
$896$	−958.782	+	31222.4i	−0.0357485	+	1.16414i
$897$		0			0
$898$	−12268.7	−	9872.31i	−0.455916	−	0.366863i
$899$			21358.8i			0.792389i
$900$		0			0
$901$		−	2239.35i		−	0.0828008i
$902$	−28956.6	+	35985.6i	−1.06890	+	1.32837i
$903$		0			0
$904$	−4621.59	+	9282.42i	−0.170035	+	0.341514i
$905$	17288.9			0.635031
$906$		0			0
$907$			27915.8i			1.02197i	0.859588	+	0.510987i	$0.170720\pi$
$907$			27915.8i			1.02197i	−0.859588	+	0.510987i	$0.829280\pi$
$908$	−22978.9	+	5033.15i	−0.839847	+	0.183955i
$909$		0			0
$910$	5729.95	+	4610.74i	0.208732	+	0.167961i
$911$	6557.22			0.238475			0.119237	−	0.992866i	$-0.461955\pi$
$911$	6557.22			0.238475			0.119237	+	0.992866i	$0.461955\pi$
$912$		0			0
$913$	−2051.57			−0.0743671
$914$	16050.0	+	12915.0i	0.580841	+	0.467387i
$915$		0			0
$916$	38681.2	−	8472.48i	1.39526	−	0.305610i
$917$			38496.2i			1.38632i
$918$		0			0
$919$	−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
$921$		0			0
$922$	−21102.7	+	26225.2i	−0.753776	+	0.936748i
$923$			23042.3i			0.821719i
$924$		0			0
$925$		−	3273.08i		−	0.116344i
$926$	−10832.3	−	8716.45i	−0.384418	−	0.309331i
$927$		0			0
$928$	−4615.00	+	18354.8i	−0.163249	+	0.649273i
$929$	−56597.2			−1.99881			−0.999405	−	0.0345020i	$-0.989015\pi$
$929$	−56597.2			−1.99881			−0.999405	+	0.0345020i	$0.989015\pi$
$930$		0			0
$931$		−	3263.40i		−	0.114880i
$932$	−8889.34	−	40584.3i	−0.312425	−	1.42638i
$933$		0			0
$934$	−5514.84	+	6853.52i	−0.193203	+	0.240101i
$935$	2702.19			0.0945145
$936$		0			0
$937$	−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
$939$		0			0
$940$	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	$-0.0245591\pi$
$942$		0			0
$943$	3662.97			0.126493
$944$	−14555.9	−	31633.4i	−0.501858	−	1.09066i
$945$		0			0
$946$	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	$0.998770\pi$
$948$		0			0
$949$			3071.98i			0.105080i
$950$	1183.09	−	1470.28i	0.0404049	−	0.0502127i
$951$		0			0
$952$	3152.97	−	6332.71i	0.107341	−	0.215593i
$953$	−4845.81			−0.164713			−0.0823563	−	0.996603i	$-0.526245\pi$
$953$	−4845.81			−0.164713			−0.0823563	+	0.996603i	$0.526245\pi$
$954$		0			0
$955$			7084.94i			0.240066i
$956$	3536.87	+	16147.6i	0.119655	+	0.546288i
$957$		0			0
$958$	14522.7	+	11686.0i	0.489777	+	0.394110i
$959$	−51350.2			−1.72908
$960$		0			0
$961$	11942.5			0.400876
$962$	6955.71	+	5597.07i	0.233120	+	0.187585i
$963$		0			0
$964$	−3952.43	−	18044.8i	−0.132053	−	0.602889i
$965$		−	13405.6i		−	0.447194i
$966$		0			0
$967$	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
$969$		0			0
$970$	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	$0.840521\pi$
$972$		0			0
$973$			61659.1i			2.03155i
$974$	−6919.28	−	5567.75i	−0.227626	−	0.183165i
$975$		0			0
$976$	10021.6	+	21779.4i	0.328673	+	0.714284i
$977$	−42580.5			−1.39434			−0.697170	−	0.716906i	$-0.745558\pi$
$977$	−42580.5			−1.39434			−0.697170	+	0.716906i	$0.745558\pi$
$978$		0			0
$979$		−	34297.1i		−	1.11965i
$980$	−4777.80	+	1046.50i	−0.155736	+	0.0341114i
$981$		0			0
$982$	−21380.2	+	26570.1i	−0.694777	+	0.863427i
$983$	40586.0			1.31688			0.658440	−	0.752633i	$-0.271217\pi$
$983$	40586.0			1.31688			0.658440	+	0.752633i	$0.271217\pi$
$984$		0			0
$985$	13488.7			0.436330
$986$	2687.04	−	3339.30i	0.0867879	−	0.107855i
$987$		0			0
$988$	1101.40	+	5028.45i	0.0354658	+	0.161919i
$989$		−	2582.40i		−	0.0830288i
$990$		0			0
$991$	−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
$993$		0			0
$994$	−45427.8	−	36554.5i	−1.44958	−	1.16644i
$995$			17716.2i			0.564465i
$996$		0			0
$997$		−	22467.5i		−	0.713694i	−0.934163	−	0.356847i	$-0.883852\pi$
$997$		−	22467.5i		−	0.713694i	0.934163	−	0.356847i	$-0.116148\pi$
$998$	−14998.7	+	18639.5i	−0.475726	+	0.591204i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.4.k.c.181.3		12
3.2	odd	2		40.4.d.a.21.10	yes	12
4.3	odd	2		1440.4.k.c.721.8		12
8.3	odd	2		1440.4.k.c.721.2		12
8.5	even	2	inner	360.4.k.c.181.4		12
12.11	even	2		160.4.d.a.81.12		12
15.2	even	4		200.4.f.b.149.4		12
15.8	even	4		200.4.f.c.149.9		12
15.14	odd	2		200.4.d.b.101.3		12
24.5	odd	2		40.4.d.a.21.9	✓	12
24.11	even	2		160.4.d.a.81.1		12
48.5	odd	4		1280.4.a.bb.1.1		6
48.11	even	4		1280.4.a.bd.1.6		6
48.29	odd	4		1280.4.a.bc.1.6		6
48.35	even	4		1280.4.a.ba.1.1		6
60.23	odd	4		800.4.f.b.49.2		12
60.47	odd	4		800.4.f.c.49.11		12
60.59	even	2		800.4.d.d.401.1		12
120.29	odd	2		200.4.d.b.101.4		12
120.53	even	4		200.4.f.b.149.3		12
120.59	even	2		800.4.d.d.401.12		12
120.77	even	4		200.4.f.c.149.10		12
120.83	odd	4		800.4.f.c.49.12		12
120.107	odd	4		800.4.f.b.49.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.d.a.21.9	✓	12	24.5	odd	2
40.4.d.a.21.10	yes	12	3.2	odd	2
160.4.d.a.81.1		12	24.11	even	2
160.4.d.a.81.12		12	12.11	even	2
200.4.d.b.101.3		12	15.14	odd	2
200.4.d.b.101.4		12	120.29	odd	2
200.4.f.b.149.3		12	120.53	even	4
200.4.f.b.149.4		12	15.2	even	4
200.4.f.c.149.9		12	15.8	even	4
200.4.f.c.149.10		12	120.77	even	4
360.4.k.c.181.3		12	1.1	even	1	trivial
360.4.k.c.181.4		12	8.5	even	2	inner
800.4.d.d.401.1		12	60.59	even	2
800.4.d.d.401.12		12	120.59	even	2
800.4.f.b.49.1		12	120.107	odd	4
800.4.f.b.49.2		12	60.23	odd	4
800.4.f.c.49.11		12	60.47	odd	4
800.4.f.c.49.12		12	120.83	odd	4
1280.4.a.ba.1.1		6	48.35	even	4
1280.4.a.bb.1.1		6	48.5	odd	4
1280.4.a.bc.1.6		6	48.29	odd	4
1280.4.a.bd.1.6		6	48.11	even	4
1440.4.k.c.721.2		12	8.3	odd	2
1440.4.k.c.721.8		12	4.3	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	360.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.20360 - 1.77318i) q^{2} +(1.71169 + 7.81474i) q^{4} +5.00000i q^{5} +21.5703 q^{7} +(10.0850 - 20.2557i) q^{8} +O(q^{10})\)	\(q+(-2.20360 - 1.77318i) q^{2} +(1.71169 + 7.81474i) q^{4} +5.00000i q^{5} +21.5703 q^{7} +(10.0850 - 20.2557i) q^{8} +(8.86588 - 11.0180i) q^{10} -37.2871i q^{11} +24.1097i q^{13} +(-47.5322 - 38.2479i) q^{14} +(-58.1402 + 26.7528i) q^{16} +14.4940 q^{17} -26.6887i q^{19} +(-39.0737 + 8.55846i) q^{20} +(-66.1166 + 82.1658i) q^{22} +8.36366 q^{23} -25.0000 q^{25} +(42.7508 - 53.1282i) q^{26} +(36.9216 + 168.566i) q^{28} +104.553i q^{29} +204.288 q^{31} +(175.555 + 44.1404i) q^{32} +(-31.9389 - 25.7004i) q^{34} +107.851i q^{35} +130.923i q^{37} +(-47.3237 + 58.8111i) q^{38} +(101.278 + 50.4251i) q^{40} +437.963 q^{41} -308.764i q^{43} +(291.389 - 63.8240i) q^{44} +(-18.4301 - 14.8302i) q^{46} -97.1081 q^{47} +122.277 q^{49} +(55.0900 + 44.3294i) q^{50} +(-188.411 + 41.2684i) q^{52} -154.502i q^{53} +186.436 q^{55} +(217.537 - 436.920i) q^{56} +(185.390 - 230.392i) q^{58} +544.088i q^{59} -374.601i q^{61} +(-450.168 - 362.238i) q^{62} +(-308.584 - 408.558i) q^{64} -120.549 q^{65} -19.3982i q^{67} +(24.8092 + 113.267i) q^{68} +(191.240 - 237.661i) q^{70} +955.725 q^{71} +127.417 q^{73} +(232.150 - 288.502i) q^{74} +(208.565 - 45.6828i) q^{76} -804.293i q^{77} +973.871 q^{79} +(-133.764 - 290.701i) q^{80} +(-965.094 - 776.586i) q^{82} -55.0210i q^{83} +72.4698i q^{85} +(-547.493 + 680.392i) q^{86} +(-755.275 - 376.041i) q^{88} +919.812 q^{89} +520.054i q^{91} +(14.3160 + 65.3598i) q^{92} +(213.987 + 172.190i) q^{94} +133.443 q^{95} +297.986 q^{97} +(-269.449 - 216.818i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 40 q^{8}+O(q^{10}) \) 12 * q - 2 * q^2 + 16 * q^4 + 28 * q^7 + 40 * q^8	\( 12 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 40 q^{8} + 30 q^{10} - 68 q^{14} - 56 q^{16} - 20 q^{20} - 164 q^{22} - 604 q^{23} - 300 q^{25} + 308 q^{26} - 436 q^{28} - 264 q^{31} - 72 q^{32} - 180 q^{34} - 820 q^{38} + 120 q^{40} - 40 q^{41} + 472 q^{44} - 1268 q^{46} + 940 q^{47} + 1308 q^{49} + 50 q^{50} + 1024 q^{52} + 440 q^{55} + 728 q^{56} - 360 q^{58} - 592 q^{62} - 2048 q^{64} + 2344 q^{68} + 1160 q^{70} + 1592 q^{71} + 432 q^{73} + 420 q^{74} + 2256 q^{76} + 2016 q^{79} - 1600 q^{80} + 88 q^{82} + 244 q^{86} + 4080 q^{88} + 424 q^{89} + 900 q^{92} + 292 q^{94} + 1520 q^{95} - 1584 q^{97} + 7266 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 + 16 * q^4 + 28 * q^7 + 40 * q^8 + 30 * q^10 - 68 * q^14 - 56 * q^16 - 20 * q^20 - 164 * q^22 - 604 * q^23 - 300 * q^25 + 308 * q^26 - 436 * q^28 - 264 * q^31 - 72 * q^32 - 180 * q^34 - 820 * q^38 + 120 * q^40 - 40 * q^41 + 472 * q^44 - 1268 * q^46 + 940 * q^47 + 1308 * q^49 + 50 * q^50 + 1024 * q^52 + 440 * q^55 + 728 * q^56 - 360 * q^58 - 592 * q^62 - 2048 * q^64 + 2344 * q^68 + 1160 * q^70 + 1592 * q^71 + 432 * q^73 + 420 * q^74 + 2256 * q^76 + 2016 * q^79 - 1600 * q^80 + 88 * q^82 + 244 * q^86 + 4080 * q^88 + 424 * q^89 + 900 * q^92 + 292 * q^94 + 1520 * q^95 - 1584 * q^97 + 7266 * q^98

Introduction

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