LMFDB - Embedded newform 180.3.f.h.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,3,Mod(19,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("180.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	180.f (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:	$4.90464475849$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.389136420864.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 24x^{4} + 80x^{2} + 256 $ x^8 + 5x^6 + 24x^4 + 80*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.4
Root			$-0.656712 + 1.88911i$ of defining polynomial
Character	$\chi$	$=$	180.19
Dual form			180.3.f.h.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.656712 + 1.88911i) q^{2} +(-3.13746 - 2.48120i) q^{4} +(3.27492 + 3.77822i) q^{5} +9.55505 q^{7} +(6.74766 - 4.29756i) q^{8} +O(q^{10})$	\(q+(-0.656712 + 1.88911i) q^{2} +(-3.13746 - 2.48120i) q^{4} +(3.27492 + 3.77822i) q^{5} +9.55505 q^{7} +(6.74766 - 4.29756i) q^{8} +(-9.28814 + 3.70547i) q^{10} -9.92480i q^{11} +7.55643i q^{13} +(-6.27492 + 18.0505i) q^{14} +(3.68729 + 15.5693i) q^{16} +17.1903i q^{17} +26.1762i q^{19} +(-0.900407 - 19.9797i) q^{20} +(18.7490 + 6.51774i) q^{22} +1.67451 q^{23} +(-3.54983 + 24.7467i) q^{25} +(-14.2749 - 4.96240i) q^{26} +(-29.9786 - 23.7080i) q^{28} +0.350497 q^{29} -46.0258i q^{31} +(-31.8336 - 3.25887i) q^{32} +(-32.4743 - 11.2890i) q^{34} +(31.2920 + 36.1010i) q^{35} -22.6693i q^{37} +(-49.4498 - 17.1903i) q^{38} +(38.3352 + 11.4200i) q^{40} +77.2990 q^{41} -41.7994 q^{43} +(-24.6254 + 31.1386i) q^{44} +(-1.09967 + 3.16332i) q^{46} -14.0866 q^{47} +42.2990 q^{49} +(-44.4180 - 22.9575i) q^{50} +(18.7490 - 23.7080i) q^{52} +22.6693i q^{53} +(37.4980 - 32.5029i) q^{55} +(64.4743 - 41.0634i) q^{56} +(-0.230175 + 0.662126i) q^{58} -94.7802i q^{59} +38.0000 q^{61} +(86.9478 + 30.2257i) q^{62} +(27.0619 - 57.9970i) q^{64} +(-28.5498 + 24.7467i) q^{65} -29.8477 q^{67} +(42.6525 - 53.9337i) q^{68} +(-88.7486 + 35.4060i) q^{70} -7.19630i q^{71} -34.3805i q^{73} +(42.8248 + 14.8872i) q^{74} +(64.9485 - 82.1269i) q^{76} -94.8320i q^{77} +46.0258i q^{79} +(-46.7487 + 64.9196i) q^{80} +(-50.7632 + 146.026i) q^{82} -24.1336 q^{83} +(-64.9485 + 56.2967i) q^{85} +(27.4502 - 78.9636i) q^{86} +(-42.6525 - 66.9692i) q^{88} -100.199 q^{89} +72.2021i q^{91} +(-5.25370 - 4.15479i) q^{92} +(9.25083 - 26.6111i) q^{94} +(-98.8995 + 85.7250i) q^{95} -131.861i q^{97} +(-27.7783 + 79.9074i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 10 q^{4} - 4 q^{5}+O(q^{10}) $ 8 * q - 10 * q^4 - 4 * q^5	$ 8 q - 10 q^{4} - 4 q^{5} - 42 q^{10} - 20 q^{14} - 46 q^{16} - 52 q^{20} + 32 q^{25} - 84 q^{26} + 184 q^{29} + 12 q^{34} - 6 q^{40} + 256 q^{41} - 348 q^{44} + 112 q^{46} - 24 q^{49} - 72 q^{50} + 244 q^{56} + 304 q^{61} - 10 q^{64} - 168 q^{65} - 104 q^{70} + 252 q^{74} - 24 q^{76} + 308 q^{80} + 24 q^{85} + 280 q^{86} - 560 q^{89} + 376 q^{94}+O(q^{100}) $ 8 * q - 10 * q^4 - 4 * q^5 - 42 * q^10 - 20 * q^14 - 46 * q^16 - 52 * q^20 + 32 * q^25 - 84 * q^26 + 184 * q^29 + 12 * q^34 - 6 * q^40 + 256 * q^41 - 348 * q^44 + 112 * q^46 - 24 * q^49 - 72 * q^50 + 244 * q^56 + 304 * q^61 - 10 * q^64 - 168 * q^65 - 104 * q^70 + 252 * q^74 - 24 * q^76 + 308 * q^80 + 24 * q^85 + 280 * q^86 - 560 * q^89 + 376 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.656712	+	1.88911i	−0.328356	+	0.944554i
$2$	−0.656712	+	1.88911i	−0.328356	+	0.944554i
$3$		0			0
$3$		0			0
$4$	−3.13746	−	2.48120i	−0.784365	−	0.620300i
$5$	3.27492	+	3.77822i	0.654983	+	0.755643i
$5$	3.27492	+	3.77822i	0.654983	+	0.755643i
$6$		0			0
$7$	9.55505			1.36501			0.682504	−	0.730882i	$-0.260891\pi$
$7$	9.55505			1.36501			0.682504	+	0.730882i	$0.260891\pi$
$8$	6.74766	−	4.29756i	0.843458	−	0.537196i
$9$		0			0
$10$	−9.28814	+	3.70547i	−0.928814	+	0.370547i
$11$		−	9.92480i		−	0.902255i	−0.892460	−	0.451127i	$-0.851022\pi$
$11$		−	9.92480i		−	0.902255i	0.892460	−	0.451127i	$-0.148978\pi$
$12$		0			0
$13$			7.55643i			0.581264i	0.956835	+	0.290632i	$0.0938655\pi$
$13$			7.55643i			0.581264i	−0.956835	+	0.290632i	$0.906134\pi$
$14$	−6.27492	+	18.0505i	−0.448208	+	1.28932i
$15$		0			0
$16$	3.68729	+	15.5693i	0.230456	+	0.973083i
$17$			17.1903i			1.01119i	0.862770	+	0.505596i	$0.168727\pi$
$17$			17.1903i			1.01119i	−0.862770	+	0.505596i	$0.831273\pi$
$18$		0			0
$19$			26.1762i			1.37770i	0.724905	+	0.688849i	$0.241884\pi$
$19$			26.1762i			1.37770i	−0.724905	+	0.688849i	$0.758116\pi$
$20$	−0.900407	−	19.9797i	−0.0450204	−	0.998986i
$21$		0			0
$22$	18.7490	+	6.51774i	0.852228	+	0.296261i
$23$	1.67451			0.0728047			0.0364023	−	0.999337i	$-0.488410\pi$
$23$	1.67451			0.0728047			0.0364023	+	0.999337i	$0.488410\pi$
$24$		0			0
$25$	−3.54983	+	24.7467i	−0.141993	+	0.989868i
$26$	−14.2749	−	4.96240i	−0.549035	−	0.190862i
$27$		0			0
$28$	−29.9786	−	23.7080i	−1.07066	−	0.846714i
$29$	0.350497			0.0120861			0.00604305	−	0.999982i	$-0.498076\pi$
$29$	0.350497			0.0120861			0.00604305	+	0.999982i	$0.498076\pi$
$30$		0			0
$31$		−	46.0258i		−	1.48470i	−0.670010	−	0.742352i	$-0.733710\pi$
$31$		−	46.0258i		−	1.48470i	0.670010	−	0.742352i	$-0.266290\pi$
$32$	−31.8336	−	3.25887i	−0.994801	−	0.101840i
$33$		0			0
$34$	−32.4743	−	11.2890i	−0.955125	−	0.332031i
$35$	31.2920	+	36.1010i	0.894057	+	1.03146i
$36$		0			0
$37$		−	22.6693i		−	0.612684i	−0.951922	−	0.306342i	$-0.900895\pi$
$37$		−	22.6693i		−	0.612684i	0.951922	−	0.306342i	$-0.0991051\pi$
$38$	−49.4498	−	17.1903i	−1.30131	−	0.452375i
$39$		0			0
$40$	38.3352	+	11.4200i	0.958379	+	0.285499i
$41$	77.2990			1.88534			0.942671	−	0.333724i	$-0.108305\pi$
$41$	77.2990			1.88534			0.942671	+	0.333724i	$0.108305\pi$
$42$		0			0
$43$	−41.7994			−0.972079			−0.486039	−	0.873937i	$-0.661559\pi$
$43$	−41.7994			−0.972079			−0.486039	+	0.873937i	$0.661559\pi$
$44$	−24.6254	+	31.1386i	−0.559668	+	0.707697i
$45$		0			0
$46$	−1.09967	+	3.16332i	−0.0239058	+	0.0687679i
$47$	−14.0866			−0.299715			−0.149857	−	0.988708i	$-0.547881\pi$
$47$	−14.0866			−0.299715			−0.149857	+	0.988708i	$0.547881\pi$
$48$		0			0
$49$	42.2990			0.863245
$50$	−44.4180	−	22.9575i	−0.888359	−	0.459149i
$51$		0			0
$52$	18.7490	−	23.7080i	0.360558	−	0.455923i
$53$			22.6693i			0.427723i	0.976864	+	0.213861i	$0.0686041\pi$
$53$			22.6693i			0.427723i	−0.976864	+	0.213861i	$0.931396\pi$
$54$		0			0
$55$	37.4980	−	32.5029i	0.681783	−	0.590962i
$56$	64.4743	−	41.0634i	1.15133	−	0.733276i
$57$		0			0
$58$	−0.230175	+	0.662126i	−0.00396854	+	0.0114160i
$59$		−	94.7802i		−	1.60644i	−0.595680	−	0.803222i	$-0.703117\pi$
$59$		−	94.7802i		−	1.60644i	0.595680	−	0.803222i	$-0.296883\pi$
$60$		0			0
$61$	38.0000			0.622951			0.311475	−	0.950254i	$-0.399177\pi$
$61$	38.0000			0.622951			0.311475	+	0.950254i	$0.399177\pi$
$62$	86.9478	+	30.2257i	1.40238	+	0.487512i
$63$		0			0
$64$	27.0619	−	57.9970i	0.422842	−	0.906203i
$65$	−28.5498	+	24.7467i	−0.439228	+	0.380718i
$66$		0			0
$67$	−29.8477			−0.445488			−0.222744	−	0.974877i	$-0.571501\pi$
$67$	−29.8477			−0.445488			−0.222744	+	0.974877i	$0.571501\pi$
$68$	42.6525	−	53.9337i	0.627242	−	0.793143i
$69$		0			0
$70$	−88.7486	+	35.4060i	−1.26784	+	0.505800i
$71$		−	7.19630i		−	0.101356i	−0.998715	−	0.0506782i	$-0.983862\pi$
$71$		−	7.19630i		−	0.101356i	0.998715	−	0.0506782i	$-0.0161383\pi$
$72$		0			0
$73$		−	34.3805i		−	0.470966i	−0.971878	−	0.235483i	$-0.924333\pi$
$73$		−	34.3805i		−	0.470966i	0.971878	−	0.235483i	$-0.0756672\pi$
$74$	42.8248	+	14.8872i	0.578713	+	0.201178i
$75$		0			0
$76$	64.9485	−	82.1269i	0.854586	−	1.08062i
$77$		−	94.8320i		−	1.23158i
$78$		0			0
$79$			46.0258i			0.582606i	0.956631	+	0.291303i	$0.0940887\pi$
$79$			46.0258i			0.582606i	−0.956631	+	0.291303i	$0.905911\pi$
$80$	−46.7487	+	64.9196i	−0.584359	+	0.811495i
$81$		0			0
$82$	−50.7632	+	146.026i	−0.619063	+	1.78081i
$83$	−24.1336			−0.290767			−0.145383	−	0.989375i	$-0.546442\pi$
$83$	−24.1336			−0.290767			−0.145383	+	0.989375i	$0.546442\pi$
$84$		0			0
$85$	−64.9485	+	56.2967i	−0.764100	+	0.662314i
$86$	27.4502	−	78.9636i	0.319188	−	0.918181i
$87$		0			0
$88$	−42.6525	−	66.9692i	−0.484687	−	0.761014i
$89$	−100.199			−1.12584			−0.562918	−	0.826513i	$-0.690321\pi$
$89$	−100.199			−1.12584			−0.562918	+	0.826513i	$0.690321\pi$
$90$		0			0
$91$			72.2021i			0.793430i
$92$	−5.25370	−	4.15479i	−0.0571054	−	0.0451607i
$93$		0			0
$94$	9.25083	−	26.6111i	0.0984131	−	0.283097i
$95$	−98.8995	+	85.7250i	−1.04105	+	0.902369i
$96$		0			0
$97$		−	131.861i		−	1.35939i	−0.733494	−	0.679696i	$-0.762112\pi$
$97$		−	131.861i		−	1.35939i	0.733494	−	0.679696i	$-0.237888\pi$
$98$	−27.7783	+	79.9074i	−0.283452	+	0.815382i
$99$		0			0
$100$	72.5389	−	68.8339i	0.725389	−	0.688339i
$101$	−29.4502			−0.291586			−0.145793	−	0.989315i	$-0.546573\pi$
$101$	−29.4502			−0.291586			−0.145793	+	0.989315i	$0.546573\pi$
$102$		0			0
$103$	143.786			1.39598			0.697991	−	0.716107i	$-0.254078\pi$
$103$	143.786			1.39598			0.697991	+	0.716107i	$0.254078\pi$
$104$	32.4743	+	50.9882i	0.312252	+	0.490272i
$105$		0			0
$106$	−42.8248	−	14.8872i	−0.404007	−	0.140445i
$107$	35.1014			0.328050			0.164025	−	0.986456i	$-0.447552\pi$
$107$	35.1014			0.328050			0.164025	+	0.986456i	$0.447552\pi$
$108$		0			0
$109$	−151.498			−1.38989			−0.694947	−	0.719061i	$-0.744572\pi$
$109$	−151.498			−1.38989			−0.694947	+	0.719061i	$0.744572\pi$
$110$	36.7761	+	92.1829i	0.334328	+	0.838026i
$111$		0			0
$112$	35.2323	+	148.766i	0.314574	+	1.32827i
$113$		−	32.3031i		−	0.285868i	−0.989732	−	0.142934i	$-0.954346\pi$
$113$		−	32.3031i		−	0.285868i	0.989732	−	0.142934i	$-0.0456537\pi$
$114$		0			0
$115$	5.48387	+	6.32665i	0.0476858	+	0.0550143i
$116$	−1.09967	−	0.869652i	−0.00947990	−	0.00749700i
$117$		0			0
$118$	179.050	+	62.2433i	1.51737	+	0.527486i
$119$			164.254i			1.38028i
$120$		0			0
$121$	22.4983			0.185937
$122$	−24.9551	+	71.7861i	−0.204550	+	0.588411i
$123$		0			0
$124$	−114.199	+	144.404i	−0.920962	+	1.16455i
$125$	−105.124	+	67.6313i	−0.840990	+	0.541051i
$126$		0			0
$127$	−192.053			−1.51223			−0.756116	−	0.654438i	$-0.772905\pi$
$127$	−192.053			−1.51223			−0.756116	+	0.654438i	$0.772905\pi$
$128$	91.7908	+	89.2102i	0.717115	+	0.696954i
$129$		0			0
$130$	−28.0002	−	70.1852i	−0.215386	−	0.539886i
$131$		−	42.4277i		−	0.323876i	−0.986801	−	0.161938i	$-0.948226\pi$
$131$		−	42.4277i		−	0.323876i	0.986801	−	0.161938i	$-0.0517744\pi$
$132$		0			0
$133$			250.115i			1.88057i
$134$	19.6013	−	56.3855i	0.146279	−	0.420787i
$135$		0			0
$136$	73.8762	+	115.994i	0.543208	+	0.852897i
$137$		−	206.854i		−	1.50988i	−0.655791	−	0.754942i	$-0.727665\pi$
$137$		−	206.854i		−	1.50988i	0.655791	−	0.754942i	$-0.272335\pi$
$138$		0			0
$139$		−	46.0258i		−	0.331121i	−0.986200	−	0.165561i	$-0.947057\pi$
$139$		−	46.0258i		−	0.331121i	0.986200	−	0.165561i	$-0.0529433\pi$
$140$	−8.60344	−	190.907i	−0.0614531	−	1.36362i
$141$		0			0
$142$	13.5946	+	4.72590i	0.0957366	+	0.0332810i
$143$	74.9961			0.524448
$144$		0			0
$145$	1.14785	+	1.32425i	0.00791619	+	0.00913277i
$146$	64.9485	+	22.5781i	0.444853	+	0.154645i
$147$		0			0
$148$	−56.2471	+	71.1240i	−0.380048	+	0.480567i
$149$	−11.6495			−0.0781846			−0.0390923	−	0.999236i	$-0.512447\pi$
$149$	−11.6495			−0.0781846			−0.0390923	+	0.999236i	$0.512447\pi$
$150$		0			0
$151$		−	125.424i		−	0.830624i	−0.909679	−	0.415312i	$-0.863672\pi$
$151$		−	125.424i		−	0.830624i	0.909679	−	0.415312i	$-0.136328\pi$
$152$	112.494	+	176.628i	0.740093	+	1.16203i
$153$		0			0
$154$	179.148	+	62.2773i	1.16330	+	0.404398i
$155$	173.896	−	150.731i	1.12191	−	0.972457i
$156$		0			0
$157$		−	197.220i		−	1.25618i	−0.778140	−	0.628090i	$-0.783837\pi$
$157$		−	197.220i		−	1.25618i	0.778140	−	0.628090i	$-0.216163\pi$
$158$	−86.9478	−	30.2257i	−0.550303	−	0.191302i
$159$		0			0
$160$	−91.9398	−	130.947i	−0.574624	−	0.818418i
$161$	16.0000			0.0993789
$162$		0			0
$163$	−18.4196			−0.113004			−0.0565018	−	0.998402i	$-0.517995\pi$
$163$	−18.4196			−0.113004			−0.0565018	+	0.998402i	$0.517995\pi$
$164$	−242.522	−	191.794i	−1.47880	−	1.16948i
$165$		0			0
$166$	15.8488	−	45.5910i	0.0954749	−	0.274645i
$167$	−92.8920			−0.556240			−0.278120	−	0.960546i	$-0.589711\pi$
$167$	−92.8920			−0.556240			−0.278120	+	0.960546i	$0.589711\pi$
$168$		0			0
$169$	111.900			0.662132
$170$	−63.6980	−	159.665i	−0.374694	−	0.939209i
$171$		0			0
$172$	131.144	+	103.713i	0.762464	+	0.602981i
$173$			117.501i			0.679198i	0.940570	+	0.339599i	$0.110291\pi$
$173$			117.501i			0.679198i	−0.940570	+	0.339599i	$0.889709\pi$
$174$		0			0
$175$	−33.9189	+	236.456i	−0.193822	+	1.35118i
$176$	154.522	−	36.5956i	0.877968	−	0.207930i
$177$		0			0
$178$	65.8021	−	189.287i	0.369675	−	1.06341i
$179$			231.988i			1.29602i	0.761631	+	0.648011i	$0.224399\pi$
$179$			231.988i			1.29602i	−0.761631	+	0.648011i	$0.775601\pi$
$180$		0			0
$181$	−218.096			−1.20495			−0.602476	−	0.798137i	$-0.705819\pi$
$181$	−218.096			−1.20495			−0.602476	+	0.798137i	$0.705819\pi$
$182$	−136.398	−	47.4160i	−0.749437	−	0.260527i
$183$		0			0
$184$	11.2990	−	7.19630i	0.0614076	−	0.0391103i
$185$	85.6495	−	74.2401i	0.462970	−	0.401298i
$186$		0			0
$187$	170.610			0.912352
$188$	44.1961	+	34.9516i	0.235085	+	0.185913i
$189$		0			0
$190$	−96.9954	−	243.129i	−0.510502	−	1.27962i
$191$		−	137.208i		−	0.718366i	−0.933267	−	0.359183i	$-0.883055\pi$
$191$		−	137.208i		−	0.718366i	0.933267	−	0.359183i	$-0.116945\pi$
$192$		0			0
$193$		−	37.0290i		−	0.191860i	−0.995388	−	0.0959301i	$-0.969417\pi$
$193$		−	37.0290i		−	0.191860i	0.995388	−	0.0959301i	$-0.0305825\pi$
$194$	249.100	+	86.5947i	1.28402	+	0.446364i
$195$		0			0
$196$	−132.711	−	104.952i	−0.677099	−	0.535471i
$197$			194.572i			0.987674i	0.869554	+	0.493837i	$0.164406\pi$
$197$			194.572i			0.987674i	−0.869554	+	0.493837i	$0.835594\pi$
$198$		0			0
$199$		−	176.037i		−	0.884610i	−0.896865	−	0.442305i	$-0.854161\pi$
$199$		−	176.037i		−	0.884610i	0.896865	−	0.442305i	$-0.145839\pi$
$200$	82.3974	+	182.238i	0.411987	+	0.911190i
$201$		0			0
$202$	19.3403	−	55.6345i	0.0957440	−	0.275419i
$203$	3.34901			0.0164976
$204$		0			0
$205$	253.148	+	292.052i	1.23487	+	1.42465i
$206$	−94.4261	+	271.628i	−0.458379	+	1.31858i
$207$		0			0
$208$	−117.649	+	27.8628i	−0.565618	+	0.133956i
$209$	259.794			1.24303
$210$		0			0
$211$			20.7193i			0.0981955i	0.998794	+	0.0490978i	$0.0156346\pi$
$211$			20.7193i			0.0981955i	−0.998794	+	0.0490978i	$0.984365\pi$
$212$	56.2471	−	71.1240i	0.265316	−	0.335490i
$213$		0			0
$214$	−23.0515	+	66.3103i	−0.107717	+	0.309861i
$215$	−136.890	−	157.927i	−0.636696	−	0.734545i
$216$		0			0
$217$		−	439.779i		−	2.02663i
$218$	99.4908	−	286.197i	0.456380	−	1.31283i
$219$		0			0
$220$	−198.295	+	8.93636i	−0.901340	+	0.0406198i
$221$	−129.897			−0.587769
$222$		0			0
$223$	97.0265			0.435096			0.217548	−	0.976050i	$-0.430194\pi$
$223$	97.0265			0.435096			0.217548	+	0.976050i	$0.430194\pi$
$224$	−304.172	−	31.1386i	−1.35791	−	0.139012i
$225$		0			0
$226$	61.0241	+	21.2138i	0.270018	+	0.0938666i
$227$	−407.256			−1.79408			−0.897040	−	0.441948i	$-0.854287\pi$
$227$	−407.256			−1.79408			−0.897040	+	0.441948i	$0.854287\pi$
$228$		0			0
$229$	−7.89702			−0.0344848			−0.0172424	−	0.999851i	$-0.505489\pi$
$229$	−7.89702			−0.0344848			−0.0172424	+	0.999851i	$0.505489\pi$
$230$	−15.5530	+	6.20484i	−0.0676220	+	0.0269776i
$231$		0			0
$232$	2.36503	−	1.50628i	0.0101941	−	0.00649260i
$233$		−	28.1483i		−	0.120808i	−0.998174	−	0.0604042i	$-0.980761\pi$
$233$		−	28.1483i		−	0.120808i	0.998174	−	0.0604042i	$-0.0192390\pi$
$234$		0			0
$235$	−46.1324	−	53.2222i	−0.196308	−	0.226477i
$236$	−235.169	+	297.369i	−0.996477	+	1.26004i
$237$		0			0
$238$	−310.293	−	107.867i	−1.30375	−	0.453225i
$239$		−	296.005i		−	1.23851i	−0.785189	−	0.619257i	$-0.787434\pi$
$239$		−	296.005i		−	1.23851i	0.785189	−	0.619257i	$-0.212566\pi$
$240$		0			0
$241$	465.794			1.93276			0.966378	−	0.257127i	$-0.0827758\pi$
$241$	465.794			1.93276			0.966378	+	0.257127i	$0.0827758\pi$
$242$	−14.7749	+	42.5018i	−0.0610534	+	0.175627i
$243$		0			0
$244$	−119.223	−	94.2856i	−0.488621	−	0.386416i
$245$	138.526	+	159.815i	0.565411	+	0.652305i
$246$		0			0
$247$	−197.799			−0.800806
$248$	−197.799	−	310.567i	−0.797577	−	1.25229i
$249$		0			0
$250$	−58.7268	−	243.004i	−0.234907	−	0.972018i
$251$			141.676i			0.564445i	0.959349	+	0.282223i	$0.0910716\pi$
$251$			141.676i			0.564445i	−0.959349	+	0.282223i	$0.908928\pi$
$252$		0			0
$253$		−	16.6191i		−	0.0656883i
$254$	126.124	−	362.810i	0.496550	−	1.42838i
$255$		0			0
$256$	−228.808	+	114.817i	−0.893780	+	0.448505i
$257$		−	41.7549i		−	0.162470i	−0.996695	−	0.0812352i	$-0.974113\pi$
$257$		−	41.7549i		−	0.162470i	0.996695	−	0.0812352i	$-0.0258865\pi$
$258$		0			0
$259$		−	216.606i		−	0.836318i
$260$	150.975	−	6.80387i	0.580675	−	0.0261687i
$261$		0			0
$262$	80.1505	+	27.8628i	0.305918	+	0.106346i
$263$	203.283			0.772939			0.386469	−	0.922302i	$-0.373694\pi$
$263$	203.283			0.772939			0.386469	+	0.922302i	$0.373694\pi$
$264$		0			0
$265$	−85.6495	+	74.2401i	−0.323206	+	0.280151i
$266$	−472.495	−	164.254i	−1.77630	−	0.617495i
$267$		0			0
$268$	93.6458	+	74.0580i	0.349425	+	0.276336i
$269$	244.048			0.907242			0.453621	−	0.891195i	$-0.350132\pi$
$269$	244.048			0.907242			0.453621	+	0.891195i	$0.350132\pi$
$270$		0			0
$271$			466.585i			1.72172i	0.508845	+	0.860858i	$0.330073\pi$
$271$			466.585i			1.72172i	−0.508845	+	0.860858i	$0.669927\pi$
$272$	−267.641	+	63.3855i	−0.983973	+	0.233035i
$273$		0			0
$274$	390.770	+	135.844i	1.42617	+	0.495780i
$275$	245.606	+	35.2314i	0.893113	+	0.128114i
$276$		0			0
$277$			494.181i			1.78405i	0.451990	+	0.892023i	$0.350714\pi$
$277$			494.181i			1.78405i	−0.451990	+	0.892023i	$0.649286\pi$
$278$	86.9478	+	30.2257i	0.312762	+	0.108726i
$279$		0			0
$280$	366.294	+	109.118i	1.30819	+	0.389708i
$281$	43.4020			0.154455			0.0772277	−	0.997013i	$-0.475393\pi$
$281$	43.4020			0.154455			0.0772277	+	0.997013i	$0.475393\pi$
$282$		0			0
$283$	−310.785			−1.09818			−0.549090	−	0.835763i	$-0.685026\pi$
$283$	−310.785			−1.09818			−0.549090	+	0.835763i	$0.685026\pi$
$284$	−17.8555	+	22.5781i	−0.0628714	+	0.0795003i
$285$		0			0
$286$	−49.2508	+	141.676i	−0.172206	+	0.495370i
$287$	738.596			2.57351
$288$		0			0
$289$	−6.50497			−0.0225085
$290$	−3.25546	+	1.29876i	−0.0112257	+	0.00447847i
$291$		0			0
$292$	−85.3049	+	107.867i	−0.292140	+	0.369409i
$293$			245.207i			0.836886i	0.908243	+	0.418443i	$0.137424\pi$
$293$			245.207i			0.836886i	−0.908243	+	0.418443i	$0.862576\pi$
$294$		0			0
$295$	358.100	−	310.397i	1.21390	−	1.05219i
$296$	−97.4228	−	152.965i	−0.329131	−	0.516773i
$297$		0			0
$298$	7.65037	−	22.0072i	0.0256724	−	0.0738496i
$299$			12.6533i			0.0423187i
$300$		0			0
$301$	−399.395			−1.32689
$302$	236.940	+	82.3676i	0.784569	+	0.272740i
$303$		0			0
$304$	−407.547	+	96.5195i	−1.34061	+	0.317498i
$305$	124.447	+	143.572i	0.408022	+	0.470729i
$306$		0			0
$307$	337.514			1.09939			0.549697	−	0.835364i	$-0.314743\pi$
$307$	337.514			1.09939			0.549697	+	0.835364i	$0.314743\pi$
$308$	−235.297	+	297.531i	−0.763952	+	0.966011i
$309$		0			0
$310$	170.548	+	427.494i	0.550153	+	1.37901i
$311$			427.756i			1.37542i	0.725986	+	0.687710i	$0.241384\pi$
$311$			427.756i			1.37542i	−0.725986	+	0.687710i	$0.758616\pi$
$312$		0			0
$313$			83.8739i			0.267968i	0.990984	+	0.133984i	$0.0427770\pi$
$313$			83.8739i			0.267968i	−0.990984	+	0.133984i	$0.957223\pi$
$314$	372.571	+	129.517i	1.18653	+	0.412475i
$315$		0			0
$316$	114.199	−	144.404i	0.361390	−	0.456975i
$317$		−	112.204i		−	0.353957i	−0.984215	−	0.176978i	$-0.943368\pi$
$317$		−	112.204i		−	0.353957i	0.984215	−	0.176978i	$-0.0566323\pi$
$318$		0			0
$319$		−	3.47861i		−	0.0109047i
$320$	307.751	−	87.6898i	0.961721	−	0.274031i
$321$		0			0
$322$	−10.5074	+	30.2257i	−0.0326317	+	0.0938687i
$323$	−449.976			−1.39312
$324$		0			0
$325$	−186.997	−	26.8241i	−0.575374	−	0.0825356i
$326$	12.0964	−	34.7966i	0.0371054	−	0.106738i
$327$		0			0
$328$	521.588	−	332.197i	1.59021	−	1.01280i
$329$	−134.598			−0.409113
$330$		0			0
$331$		−	132.621i		−	0.400666i	−0.979728	−	0.200333i	$-0.935798\pi$
$331$		−	132.621i		−	0.400666i	0.979728	−	0.200333i	$-0.0642025\pi$
$332$	75.7182	+	59.8803i	0.228067	+	0.180362i
$333$		0			0
$334$	61.0033	−	175.483i	0.182645	−	0.525398i
$335$	−97.7487	−	112.771i	−0.291787	−	0.336630i
$336$		0			0
$337$			20.7739i			0.0616437i	0.999525	+	0.0308219i	$0.00981246\pi$
$337$			20.7739i			0.0616437i	−0.999525	+	0.0308219i	$0.990188\pi$
$338$	−73.4863	+	211.392i	−0.217415	+	0.625420i
$339$		0			0
$340$	343.457	−	15.4782i	1.01017	−	0.0455242i
$341$	−456.797			−1.33958
$342$		0			0
$343$	−64.0283			−0.186672
$344$	−282.048	+	179.636i	−0.819907	+	0.522196i
$345$		0			0
$346$	−221.973	−	77.1645i	−0.641539	−	0.223019i
$347$	−8.89616			−0.0256374			−0.0128187	−	0.999918i	$-0.504080\pi$
$347$	−8.89616			−0.0256374			−0.0128187	+	0.999918i	$0.504080\pi$
$348$		0			0
$349$	19.4020			0.0555931			0.0277965	−	0.999614i	$-0.491151\pi$
$349$	19.4020			0.0555931			0.0277965	+	0.999614i	$0.491151\pi$
$350$	−424.416	−	219.360i	−1.21262	−	0.626742i
$351$		0			0
$352$	−32.3436	+	315.942i	−0.0918853	+	0.897564i
$353$		−	80.2902i		−	0.227451i	−0.993512	−	0.113726i	$-0.963722\pi$
$353$		−	80.2902i		−	0.227451i	0.993512	−	0.113726i	$-0.0362784\pi$
$354$		0			0
$355$	27.1892	−	23.5673i	0.0765892	−	0.0663867i
$356$	314.371	+	248.615i	0.883065	+	0.698356i
$357$		0			0
$358$	−438.251	−	152.349i	−1.22416	−	0.425557i
$359$		−	314.115i		−	0.874972i	−0.899225	−	0.437486i	$-0.855869\pi$
$359$		−	314.115i		−	0.874972i	0.899225	−	0.437486i	$-0.144131\pi$
$360$		0			0
$361$	−324.196			−0.898050
$362$	143.227	−	412.008i	0.395653	−	1.13814i
$363$		0			0
$364$	179.148	−	226.531i	0.492164	−	0.622338i
$365$	129.897	−	112.593i	0.355882	−	0.308475i
$366$		0			0
$367$	−476.800			−1.29918			−0.649592	−	0.760283i	$-0.725060\pi$
$367$	−476.800			−1.29918			−0.649592	+	0.760283i	$0.725060\pi$
$368$	6.17440	+	26.0709i	0.0167783	+	0.0708450i
$369$		0			0
$370$	84.0005	+	210.556i	0.227028	+	0.569069i
$371$			216.606i			0.583844i
$372$		0			0
$373$		−	86.1333i		−	0.230920i	−0.993312	−	0.115460i	$-0.963166\pi$
$373$		−	86.1333i		−	0.230920i	0.993312	−	0.115460i	$-0.0368343\pi$
$374$	−112.042	+	322.300i	−0.299576	+	0.861766i
$375$		0			0
$376$	−95.0515	+	60.5380i	−0.252797	+	0.161005i
$377$			2.64850i			0.00702521i
$378$		0			0
$379$			638.035i			1.68347i	0.539891	+	0.841735i	$0.318466\pi$
$379$			638.035i			1.68347i	−0.539891	+	0.841735i	$0.681534\pi$
$380$	522.994	−	23.5693i	1.37630	−	0.0620244i
$381$		0			0
$382$	259.201	+	90.1061i	0.678535	+	0.235880i
$383$	−216.742			−0.565907			−0.282953	−	0.959134i	$-0.591314\pi$
$383$	−216.742			−0.565907			−0.282953	+	0.959134i	$0.591314\pi$
$384$		0			0
$385$	358.296	−	310.567i	0.930638	−	0.806667i
$386$	69.9518	+	24.3174i	0.181222	+	0.0629985i
$387$		0			0
$388$	−327.174	+	413.708i	−0.843231	+	1.06626i
$389$	−476.640			−1.22529			−0.612647	−	0.790356i	$-0.709895\pi$
$389$	−476.640			−1.22529			−0.612647	+	0.790356i	$0.709895\pi$
$390$		0			0
$391$			28.7852i			0.0736195i
$392$	285.419	−	181.783i	0.728111	−	0.463731i
$393$		0			0
$394$	−367.567	−	127.778i	−0.932912	−	0.324309i
$395$	−173.896	+	150.731i	−0.440242	+	0.381597i
$396$		0			0
$397$			43.0792i			0.108512i	0.998527	+	0.0542559i	$0.0172787\pi$
$397$			43.0792i			0.108512i	−0.998527	+	0.0542559i	$0.982721\pi$
$398$	332.554	+	115.606i	0.835562	+	0.290467i
$399$		0			0
$400$	−398.379	+	35.9798i	−0.995946	+	0.0899494i
$401$	168.694			0.420684			0.210342	−	0.977628i	$-0.432542\pi$
$401$	168.694			0.420684			0.210342	+	0.977628i	$0.432542\pi$
$402$		0			0
$403$	347.791			0.863005
$404$	92.3987	+	73.0718i	0.228710	+	0.180871i
$405$		0			0
$406$	−2.19934	+	6.32665i	−0.00541709	+	0.0155829i
$407$	−224.988			−0.552797
$408$		0			0
$409$	373.890			0.914157			0.457079	−	0.889426i	$-0.348896\pi$
$409$	373.890			0.914157			0.457079	+	0.889426i	$0.348896\pi$
$410$	−717.964	+	286.429i	−1.75113	+	0.698608i
$411$		0			0
$412$	−451.123	−	356.762i	−1.09496	−	0.865927i
$413$		−	905.630i		−	2.19281i
$414$		0			0
$415$	−79.0356	−	91.1820i	−0.190447	−	0.219716i
$416$	24.6254	−	240.549i	0.0591957	−	0.578242i
$417$		0			0
$418$	−170.610	+	490.779i	−0.408158	+	1.17411i
$419$		−	87.5839i		−	0.209031i	−0.994523	−	0.104515i	$-0.966671\pi$
$419$		−	87.5839i		−	0.209031i	0.994523	−	0.104515i	$-0.0333291\pi$
$420$		0			0
$421$	70.3023			0.166989			0.0834944	−	0.996508i	$-0.473392\pi$
$421$	70.3023			0.166989			0.0834944	+	0.996508i	$0.473392\pi$
$422$	−39.1409	−	13.6066i	−0.0927510	−	0.0322431i
$423$		0			0
$424$	97.4228	+	152.965i	0.229771	+	0.360766i
$425$	−425.402	−	61.0226i	−1.00095	−	0.143583i
$426$		0			0
$427$	363.092			0.850332
$428$	−110.129	−	87.0935i	−0.257311	−	0.203490i
$429$		0			0
$430$	388.238	−	154.887i	0.902880	−	0.360201i
$431$		−	247.370i		−	0.573944i	−0.957939	−	0.286972i	$-0.907351\pi$
$431$		−	247.370i		−	0.573944i	0.957939	−	0.286972i	$-0.0926487\pi$
$432$		0			0
$433$		−	636.247i		−	1.46939i	−0.678397	−	0.734696i	$-0.737325\pi$
$433$		−	636.247i		−	1.46939i	0.678397	−	0.734696i	$-0.262675\pi$
$434$	830.791	+	288.808i	1.91426	+	0.665457i
$435$		0			0
$436$	475.320	+	375.898i	1.09018	+	0.862151i
$437$			43.8323i			0.100303i
$438$		0			0
$439$			769.786i			1.75350i	0.480947	+	0.876750i	$0.340293\pi$
$439$			769.786i			1.75350i	−0.480947	+	0.876750i	$0.659707\pi$
$440$	113.341	−	380.469i	0.257593	−	0.864702i
$441$		0			0
$442$	85.3049	−	245.390i	0.192998	−	0.555180i
$443$	612.214			1.38197			0.690986	−	0.722868i	$-0.257177\pi$
$443$	612.214			1.38197			0.690986	+	0.722868i	$0.257177\pi$
$444$		0			0
$445$	−328.145	−	378.575i	−0.737403	−	0.850730i
$446$	−63.7185	+	183.294i	−0.142867	+	0.410972i
$447$		0			0
$448$	258.578	−	554.165i	0.577182	−	1.23697i
$449$	−175.897			−0.391753			−0.195876	−	0.980629i	$-0.562755\pi$
$449$	−175.897			−0.391753			−0.195876	+	0.980629i	$0.562755\pi$
$450$		0			0
$451$		−	767.177i		−	1.70106i
$452$	−80.1505	+	101.350i	−0.177324	+	0.224225i
$453$		0			0
$454$	267.450	−	769.351i	0.589097	−	1.69461i
$455$	−272.795	+	236.456i	−0.599550	+	0.519683i
$456$		0			0
$457$			365.357i			0.799469i	0.916631	+	0.399734i	$0.130898\pi$
$457$			365.357i			0.799469i	−0.916631	+	0.399734i	$0.869102\pi$
$458$	5.18607	−	14.9183i	0.0113233	−	0.0325728i
$459$		0			0
$460$	−1.50774	−	33.4562i	−0.00327769	−	0.0727308i
$461$	−308.350			−0.668873			−0.334437	−	0.942418i	$-0.608546\pi$
$461$	−308.350			−0.668873			−0.334437	+	0.942418i	$0.608546\pi$
$462$		0			0
$463$	−92.6302			−0.200065			−0.100033	−	0.994984i	$-0.531895\pi$
$463$	−92.6302			−0.200065			−0.100033	+	0.994984i	$0.531895\pi$
$464$	1.29238	+	5.45700i	0.00278531	+	0.0117608i
$465$		0			0
$466$	53.1752	+	18.4854i	0.114110	+	0.0396681i
$467$	−606.103			−1.29786			−0.648932	−	0.760846i	$-0.724784\pi$
$467$	−606.103			−1.29786			−0.648932	+	0.760846i	$0.724784\pi$
$468$		0			0
$469$	−285.196			−0.608094
$470$	130.838	−	52.1974i	0.278379	−	0.111058i
$471$		0			0
$472$	−407.324	−	639.545i	−0.862975	−	1.35497i
$473$			414.851i			0.877063i
$474$		0			0
$475$	−647.776	−	92.9214i	−1.36374	−	0.195624i
$476$	407.547	−	515.339i	0.856190	−	1.08265i
$477$		0			0
$478$	559.185	+	194.390i	1.16984	+	0.406673i
$479$			138.947i			0.290078i	0.989426	+	0.145039i	$0.0463307\pi$
$479$			138.947i			0.290078i	−0.989426	+	0.145039i	$0.953669\pi$
$480$		0			0
$481$	171.299			0.356131
$482$	−305.893	+	879.935i	−0.634632	+	1.82559i
$483$		0			0
$484$	−70.5876	−	55.8229i	−0.145842	−	0.115337i
$485$	498.199	−	431.834i	1.02722	−	0.890379i
$486$		0			0
$487$	−201.243			−0.413230			−0.206615	−	0.978422i	$-0.566245\pi$
$487$	−201.243			−0.413230			−0.206615	+	0.978422i	$0.566245\pi$
$488$	256.411	−	163.307i	0.525433	−	0.334646i
$489$		0			0
$490$	−392.879	+	156.738i	−0.801794	+	0.319873i
$491$		−	347.368i		−	0.707470i	−0.935346	−	0.353735i	$-0.884911\pi$
$491$		−	347.368i		−	0.707470i	0.935346	−	0.353735i	$-0.115089\pi$
$492$		0			0
$493$			6.02513i			0.0122214i
$494$	129.897	−	373.664i	0.262949	−	0.756404i
$495$		0			0
$496$	716.591	−	169.711i	1.44474	−	0.342159i
$497$		−	68.7610i		−	0.138352i
$498$		0			0
$499$		−	672.277i		−	1.34725i	−0.739074	−	0.673625i	$-0.764736\pi$
$499$		−	672.277i		−	1.34725i	0.739074	−	0.673625i	$-0.235264\pi$
$500$	497.628	+	48.6426i	0.995257	+	0.0972852i
$501$		0			0
$502$	−267.641	−	93.0401i	−0.533149	−	0.185339i
$503$	−436.350			−0.867496			−0.433748	−	0.901034i	$-0.642809\pi$
$503$	−436.350			−0.867496			−0.433748	+	0.901034i	$0.642809\pi$
$504$		0			0
$505$	−96.4469	−	111.269i	−0.190984	−	0.220335i
$506$	31.3954	+	10.9140i	0.0620462	+	0.0215692i
$507$		0			0
$508$	602.559	+	476.523i	1.18614	+	0.938037i
$509$	109.547			0.215219			0.107610	−	0.994193i	$-0.465680\pi$
$509$	109.547			0.215219			0.107610	+	0.994193i	$0.465680\pi$
$510$		0			0
$511$		−	328.508i		−	0.642872i
$512$	−66.6415	−	507.644i	−0.130159	−	0.991493i
$513$		0			0
$514$	78.8796	+	27.4210i	0.153462	+	0.0533482i
$515$	470.888	+	543.255i	0.914345	+	1.05486i
$516$		0			0
$517$			139.807i			0.270419i
$518$	409.193	+	142.248i	0.789947	+	0.274610i
$519$		0			0
$520$	−86.2941	+	289.677i	−0.165950	+	0.557071i
$521$	743.100			1.42629			0.713147	−	0.701014i	$-0.247269\pi$
$521$	743.100			1.42629			0.713147	+	0.701014i	$0.247269\pi$
$522$		0			0
$523$	−366.211			−0.700212			−0.350106	−	0.936710i	$-0.613854\pi$
$523$	−366.211			−0.700212			−0.350106	+	0.936710i	$0.613854\pi$
$524$	−105.272	+	133.115i	−0.200900	+	0.254037i
$525$		0			0
$526$	−133.498	+	384.023i	−0.253799	+	0.730083i
$527$	791.196			1.50132
$528$		0			0
$529$	−526.196			−0.994699
$530$	−84.0005	−	210.556i	−0.158491	−	0.397275i
$531$		0			0
$532$	620.586	−	784.727i	1.16652	−	1.47505i
$533$			584.105i			1.09588i
$534$		0			0
$535$	114.954	+	132.621i	0.214867	+	0.247889i
$536$	−201.402	+	128.272i	−0.375750	+	0.239314i
$537$		0			0
$538$	−160.269	+	461.033i	−0.297898	+	0.856939i
$539$		−	419.809i		−	0.778867i
$540$		0			0
$541$	170.688			0.315504			0.157752	−	0.987479i	$-0.449575\pi$
$541$	170.688			0.315504			0.157752	+	0.987479i	$0.449575\pi$
$542$	−881.430	−	306.412i	−1.62625	−	0.565336i
$543$		0			0
$544$	56.0208	−	547.228i	0.102979	−	1.00593i
$545$	−496.145	−	572.393i	−0.910357	−	1.05026i
$546$		0			0
$547$	507.600			0.927971			0.463986	−	0.885843i	$-0.346419\pi$
$547$	507.600			0.927971			0.463986	+	0.885843i	$0.346419\pi$
$548$	−513.247	+	648.997i	−0.936581	+	1.18430i
$549$		0			0
$550$	−227.848	+	440.839i	−0.414270	+	0.801526i
$551$			9.17469i			0.0166510i
$552$		0			0
$553$			439.779i			0.795261i
$554$	−933.561	−	324.534i	−1.68513	−	0.585802i
$555$		0			0
$556$	−114.199	+	144.404i	−0.205394	+	0.259720i
$557$			788.492i			1.41561i	0.706410	+	0.707803i	$0.250314\pi$
$557$			788.492i			1.41561i	−0.706410	+	0.707803i	$0.749686\pi$
$558$		0			0
$559$		−	315.854i		−	0.565035i
$560$	−446.686	+	620.310i	−0.797654	+	1.10770i
$561$		0			0
$562$	−28.5026	+	81.9910i	−0.0507164	+	0.145892i
$563$	936.102			1.66270			0.831351	−	0.555747i	$-0.187568\pi$
$563$	936.102			1.66270			0.831351	+	0.555747i	$0.187568\pi$
$564$		0			0
$565$	122.048	−	105.790i	0.216014	−	0.187239i
$566$	204.096	−	587.107i	0.360594	−	1.03729i
$567$		0			0
$568$	−30.9266	−	48.5582i	−0.0544482	−	0.0854898i
$569$	95.4983			0.167835			0.0839177	−	0.996473i	$-0.473257\pi$
$569$	95.4983			0.167835			0.0839177	+	0.996473i	$0.473257\pi$
$570$		0			0
$571$			889.123i			1.55713i	0.627562	+	0.778566i	$0.284053\pi$
$571$			889.123i			1.55713i	−0.627562	+	0.778566i	$0.715947\pi$
$572$	−235.297	−	186.080i	−0.411359	−	0.325315i
$573$		0			0
$574$	−485.045	+	1395.29i	−0.845026	+	2.43081i
$575$	−5.94422	+	41.4385i	−0.0103378	+	0.0720670i
$576$		0			0
$577$			522.147i			0.904934i	0.891781	+	0.452467i	$0.149456\pi$
$577$			522.147i			0.904934i	−0.891781	+	0.452467i	$0.850544\pi$
$578$	4.27189	−	12.2886i	0.00739081	−	0.0212605i
$579$		0			0
$580$	−0.315590	−	7.00283i	−0.000544120	−	0.0120738i
$581$	−230.598			−0.396898
$582$		0			0
$583$	224.988			0.385915
$584$	−147.752	−	231.988i	−0.253001	−	0.397240i
$585$		0			0
$586$	−463.223	−	161.031i	−0.790484	−	0.274796i
$587$	−95.8440			−0.163278			−0.0816388	−	0.996662i	$-0.526015\pi$
$587$	−95.8440			−0.163278			−0.0816388	+	0.996662i	$0.526015\pi$
$588$		0			0
$589$	1204.78			2.04547
$590$	351.205	+	880.331i	0.595263	+	1.49209i
$591$		0			0
$592$	352.946	−	83.5883i	0.596192	−	0.141197i
$593$		−	878.624i		−	1.48166i	−0.671693	−	0.740829i	$-0.734433\pi$
$593$		−	878.624i		−	1.48166i	0.671693	−	0.740829i	$-0.265567\pi$
$594$		0			0
$595$	−620.586	+	537.918i	−1.04300	+	0.904063i
$596$	36.5498	+	28.9047i	0.0613252	+	0.0484979i
$597$		0			0
$598$	−23.9034	−	8.30957i	−0.0399723	−	0.0138956i
$599$			967.652i			1.61545i	0.589563	+	0.807723i	$0.299300\pi$
$599$			967.652i			1.61545i	−0.589563	+	0.807723i	$0.700700\pi$
$600$		0			0
$601$	279.704			0.465398			0.232699	−	0.972549i	$-0.425244\pi$
$601$	279.704			0.465398			0.232699	+	0.972549i	$0.425244\pi$
$602$	262.288	−	754.501i	0.435694	−	1.25332i
$603$		0			0
$604$	−311.203	+	393.513i	−0.515236	+	0.651512i
$605$	73.6802	+	85.0036i	0.121785	+	0.140502i
$606$		0			0
$607$	747.564			1.23157			0.615786	−	0.787914i	$-0.288839\pi$
$607$	747.564			1.23157			0.615786	+	0.787914i	$0.288839\pi$
$608$	85.3049	−	833.285i	0.140304	−	1.37053i
$609$		0			0
$610$	−352.949	+	140.808i	−0.578605	+	0.230833i
$611$		−	106.444i		−	0.174213i
$612$		0			0
$613$			457.152i			0.745761i	0.927879	+	0.372881i	$0.121630\pi$
$613$			457.152i			0.745761i	−0.927879	+	0.372881i	$0.878370\pi$
$614$	−221.650	+	637.600i	−0.360993	+	1.03844i
$615$		0			0
$616$	−407.547	−	639.894i	−0.661601	−	1.03879i
$617$			764.888i			1.23969i	0.784725	+	0.619844i	$0.212804\pi$
$617$			764.888i			1.23969i	−0.784725	+	0.619844i	$0.787196\pi$
$618$		0			0
$619$			365.359i			0.590240i	0.955460	+	0.295120i	$0.0953597\pi$
$619$			365.359i			0.590240i	−0.955460	+	0.295120i	$0.904640\pi$
$620$	−919.584	+	41.4420i	−1.48320	+	0.0668420i
$621$		0			0
$622$	−808.077	−	280.912i	−1.29916	−	0.451627i
$623$	−957.410			−1.53677
$624$		0			0
$625$	−599.797	−	175.693i	−0.959676	−	0.281109i
$626$	−158.447	−	55.0810i	−0.253110	−	0.0879888i
$627$		0			0
$628$	−489.343	+	618.771i	−0.779209	+	0.985304i
$629$	389.691			0.619541
$630$		0			0
$631$		−	62.1578i		−	0.0985067i	−0.998786	−	0.0492534i	$-0.984316\pi$
$631$		−	62.1578i		−	0.0985067i	0.998786	−	0.0492534i	$-0.0156842\pi$
$632$	197.799	+	310.567i	0.312973	+	0.491403i
$633$		0			0
$634$	211.966	+	73.6859i	0.334331	+	0.116224i
$635$	−628.959	−	725.619i	−0.990486	−	1.14271i
$636$		0			0
$637$			319.630i			0.501773i
$638$	6.57147	+	2.28444i	0.0103001	+	0.00358063i
$639$		0			0
$640$	−36.4480	+	638.961i	−0.0569501	+	0.998377i
$641$	1111.69			1.73431			0.867154	−	0.498041i	$-0.165947\pi$
$641$	1111.69			1.73431			0.867154	+	0.498041i	$0.165947\pi$
$642$		0			0
$643$	468.983			0.729367			0.364683	−	0.931132i	$-0.381177\pi$
$643$	468.983			0.729367			0.364683	+	0.931132i	$0.381177\pi$
$644$	−50.1993	−	39.6992i	−0.0779493	−	0.0616447i
$645$		0			0
$646$	295.505	−	850.054i	0.457438	−	1.31587i
$647$	96.7647			0.149559			0.0747795	−	0.997200i	$-0.476175\pi$
$647$	96.7647			0.149559			0.0747795	+	0.997200i	$0.476175\pi$
$648$		0			0
$649$	−940.675			−1.44942
$650$	173.477	−	335.641i	0.266887	−	0.516371i
$651$		0			0
$652$	57.7907	+	45.7027i	0.0886360	+	0.0700961i
$653$			920.353i			1.40942i	0.709494	+	0.704712i	$0.248924\pi$
$653$			920.353i			1.40942i	−0.709494	+	0.704712i	$0.751076\pi$
$654$		0			0
$655$	160.301	−	138.947i	0.244734	−	0.212133i
$656$	285.024	+	1203.49i	0.434488	+	1.83459i
$657$		0			0
$658$	88.3921	−	254.270i	0.134335	−	0.386429i
$659$		−	591.020i		−	0.896844i	−0.893822	−	0.448422i	$-0.851986\pi$
$659$		−	591.020i		−	0.896844i	0.893822	−	0.448422i	$-0.148014\pi$
$660$		0			0
$661$	−306.193			−0.463226			−0.231613	−	0.972808i	$-0.574400\pi$
$661$	−306.193			−0.463226			−0.231613	+	0.972808i	$0.574400\pi$
$662$	250.535	+	87.0935i	0.378451	+	0.131561i
$663$		0			0
$664$	−162.846	+	103.716i	−0.245249	+	0.156198i
$665$	−944.990	+	819.107i	−1.42104	+	1.23174i
$666$		0			0
$667$	0.586909			0.000879924
$668$	291.445	+	230.484i	0.436295	+	0.345035i
$669$		0			0
$670$	277.229	−	110.600i	0.413775	−	0.165074i
$671$		−	377.142i		−	0.562060i
$672$		0			0
$673$		−	556.892i		−	0.827476i	−0.910396	−	0.413738i	$-0.864223\pi$
$673$		−	556.892i		−	0.827476i	0.910396	−	0.413738i	$-0.135777\pi$
$674$	−39.2442	−	13.6425i	−0.0582258	−	0.0202411i
$675$		0			0
$676$	−351.083	−	277.647i	−0.519353	−	0.410721i
$677$			58.1920i			0.0859557i	0.999076	+	0.0429779i	$0.0136845\pi$
$677$			58.1920i			0.0859557i	−0.999076	+	0.0429779i	$0.986316\pi$
$678$		0			0
$679$		−	1259.94i		−	1.85558i
$680$	−196.312	+	658.991i	−0.288694	+	0.969105i
$681$		0			0
$682$	299.984	−	862.940i	0.439860	−	1.26531i
$683$	357.274			0.523096			0.261548	−	0.965191i	$-0.415767\pi$
$683$	357.274			0.523096			0.261548	+	0.965191i	$0.415767\pi$
$684$		0			0
$685$	781.540	−	677.430i	1.14093	−	0.988949i
$686$	42.0482	−	120.956i	0.0612947	−	0.176321i
$687$		0			0
$688$	−154.127	−	650.788i	−0.224021	−	0.945913i
$689$	−171.299			−0.248620
$690$		0			0
$691$			614.707i			0.889590i	0.895632	+	0.444795i	$0.146724\pi$
$691$			614.707i			0.889590i	−0.895632	+	0.444795i	$0.853276\pi$
$692$	291.544	−	368.655i	0.421307	−	0.532739i
$693$		0			0
$694$	5.84222	−	16.8058i	0.00841818	−	0.0242159i
$695$	173.896	−	150.731i	0.250210	−	0.216879i
$696$		0			0
$697$			1328.79i			1.90644i
$698$	−12.7415	+	36.6524i	−0.0182543	+	0.0525107i
$699$		0			0
$700$	693.113	−	657.711i	0.990162	−	0.939587i
$701$	886.028			1.26395			0.631975	−	0.774989i	$-0.282245\pi$
$701$	886.028			1.26395			0.631975	+	0.774989i	$0.282245\pi$
$702$		0			0
$703$	593.397			0.844093
$704$	−575.609	−	268.584i	−0.817626	−	0.381511i
$705$		0			0
$706$	151.677	+	52.7276i	0.214840	+	0.0746849i
$707$	−281.398			−0.398017
$708$		0			0
$709$	−760.887			−1.07318			−0.536592	−	0.843842i	$-0.680288\pi$
$709$	−760.887			−1.07318			−0.536592	+	0.843842i	$0.680288\pi$
$710$	26.6657	+	66.8402i	0.0375573	+	0.0941412i
$711$		0			0
$712$	−676.111	+	430.613i	−0.949594	+	0.604794i
$713$		−	77.0706i		−	0.108093i
$714$		0			0
$715$	245.606	+	283.351i	0.343505	+	0.396296i
$716$	575.609	−	727.853i	0.803923	−	1.01655i
$717$		0			0
$718$	593.397	+	206.283i	0.826458	+	0.287302i
$719$			575.877i			0.800942i	0.916309	+	0.400471i	$0.131154\pi$
$719$			575.877i			0.800942i	−0.916309	+	0.400471i	$0.868846\pi$
$720$		0			0
$721$	1373.88			1.90553
$722$	212.903	−	612.441i	0.294880	−	0.848257i
$723$		0			0
$724$	684.268	+	541.141i	0.945122	+	0.747432i
$725$	−1.24421	+	8.67363i	−0.00171615	+	0.0119636i
$726$		0			0
$727$	−327.332			−0.450250			−0.225125	−	0.974330i	$-0.572279\pi$
$727$	−327.332			−0.450250			−0.225125	+	0.974330i	$0.572279\pi$
$728$	310.293	+	487.195i	0.426227	+	0.669224i
$729$		0			0
$730$	127.396	+	319.331i	0.174515	+	0.437440i
$731$		−	718.542i		−	0.982958i
$732$		0			0
$733$		−	947.567i		−	1.29272i	−0.763031	−	0.646362i	$-0.776290\pi$
$733$		−	947.567i		−	1.29272i	0.763031	−	0.646362i	$-0.223710\pi$
$734$	313.120	−	900.727i	0.426595	−	1.22715i
$735$		0			0
$736$	−53.3056	−	5.45700i	−0.0724261	−	0.00741440i
$737$			296.232i			0.401943i
$738$		0			0
$739$			183.234i			0.247948i	0.992285	+	0.123974i	$0.0395640\pi$
$739$			183.234i			0.247948i	−0.992285	+	0.123974i	$0.960436\pi$
$740$	−452.926	+	20.4116i	−0.612062	+	0.0275832i
$741$		0			0
$742$	−409.193	−	142.248i	−0.551473	−	0.191709i
$743$	183.712			0.247258			0.123629	−	0.992329i	$-0.460547\pi$
$743$	183.712			0.247258			0.123629	+	0.992329i	$0.460547\pi$
$744$		0			0
$745$	−38.1512	−	44.0143i	−0.0512096	−	0.0590797i
$746$	162.715	+	56.5648i	0.218117	+	0.0758241i
$747$		0			0
$748$	−535.281	−	423.317i	−0.715617	−	0.565932i
$749$	335.395			0.447791
$750$		0			0
$751$		−	345.748i		−	0.460384i	−0.973145	−	0.230192i	$-0.926065\pi$
$751$		−	345.748i		−	0.460384i	0.973145	−	0.230192i	$-0.0739354\pi$
$752$	−51.9414	−	219.319i	−0.0690710	−	0.291647i
$753$		0			0
$754$	−5.00331	−	1.73930i	−0.00663569	−	0.00230677i
$755$	473.880	−	410.754i	0.627656	−	0.544045i
$756$		0			0
$757$			549.335i			0.725674i	0.931853	+	0.362837i	$0.118192\pi$
$757$			549.335i			0.725674i	−0.931853	+	0.362837i	$0.881808\pi$
$758$	−1205.32	−	419.005i	−1.59013	−	0.552778i
$759$		0			0
$760$	−298.932	+	1003.47i	−0.393331	+	1.32036i
$761$	−251.485			−0.330467			−0.165233	−	0.986255i	$-0.552838\pi$
$761$	−251.485			−0.330467			−0.165233	+	0.986255i	$0.552838\pi$
$762$		0			0
$763$	−1447.57			−1.89721
$764$	−340.440	+	430.484i	−0.445602	+	0.563461i
$765$		0			0
$766$	142.337	−	409.450i	0.185819	−	0.534529i
$767$	716.200			0.933768
$768$		0			0
$769$	583.691			0.759026			0.379513	−	0.925186i	$-0.376092\pi$
$769$	583.691			0.759026			0.379513	+	0.925186i	$0.376092\pi$
$770$	351.397	+	880.812i	0.456360	+	1.14391i
$771$		0			0
$772$	−91.8764	+	116.177i	−0.119011	+	0.150488i
$773$		−	1328.04i		−	1.71803i	−0.511951	−	0.859015i	$-0.671077\pi$
$773$		−	1328.04i		−	1.71803i	0.511951	−	0.859015i	$-0.328923\pi$
$774$		0			0
$775$	1138.99	+	163.384i	1.46966	+	0.210818i
$776$	−566.681	−	889.753i	−0.730259	−	1.14659i
$777$		0			0
$778$	313.015	−	900.424i	0.402333	−	1.15736i
$779$			2023.40i			2.59743i
$780$		0			0
$781$	−71.4219			−0.0914492
$782$	−54.3784	−	18.9036i	−0.0695376	−	0.0241734i
$783$		0			0
$784$	155.969	+	658.567i	0.198940	+	0.840009i
$785$	745.141	−	645.880i	0.949224	−	0.822778i
$786$		0			0
$787$	−1318.83			−1.67577			−0.837883	−	0.545850i	$-0.816207\pi$
$787$	−1318.83			−1.67577			−0.837883	+	0.545850i	$0.816207\pi$
$788$	482.772	−	610.461i	0.612654	−	0.774697i
$789$		0			0
$790$	−170.548	−	427.494i	−0.215883	−	0.541132i
$791$		−	308.658i		−	0.390212i
$792$		0			0
$793$			287.144i			0.362099i
$794$	−81.3812	−	28.2906i	−0.102495	−	0.0356305i
$795$		0			0
$796$	−436.784	+	552.310i	−0.548724	+	0.693857i
$797$		−	1277.40i		−	1.60276i	−0.598154	−	0.801381i	$-0.704099\pi$
$797$		−	1277.40i		−	1.60276i	0.598154	−	0.801381i	$-0.295901\pi$
$798$		0			0
$799$		−	242.152i		−	0.303069i
$800$	193.650	−	776.208i	0.242063	−	0.970261i
$801$		0			0
$802$	−110.784	+	318.682i	−0.138134	+	0.397359i
$803$	−341.220			−0.424931
$804$		0			0
$805$	52.3987	+	60.4515i	0.0650915	+	0.0750950i
$806$	−228.399	+	657.015i	−0.283373	+	0.815155i
$807$		0			0
$808$	−198.720	+	126.564i	−0.245940	+	0.156639i
$809$	−321.093			−0.396901			−0.198451	−	0.980111i	$-0.563591\pi$
$809$	−321.093			−0.396901			−0.198451	+	0.980111i	$0.563591\pi$
$810$		0			0
$811$		−	946.932i		−	1.16761i	−0.811894	−	0.583805i	$-0.801563\pi$
$811$		−	946.932i		−	1.16761i	0.811894	−	0.583805i	$-0.198437\pi$
$812$	−10.5074	−	8.30957i	−0.0129401	−	0.0102335i
$813$		0			0
$814$	147.752	−	425.027i	0.181514	−	0.522146i
$815$	−60.3226	−	69.5931i	−0.0740154	−	0.0853904i
$816$		0			0
$817$		−	1094.15i		−	1.33923i
$818$	−245.538	+	706.319i	−0.300169	+	0.863471i
$819$		0			0
$820$	−69.6006	−	1544.41i	−0.0848788	−	1.88343i
$821$	−1169.34			−1.42429			−0.712144	−	0.702033i	$-0.752276\pi$
$821$	−1169.34			−1.42429			−0.712144	+	0.702033i	$0.752276\pi$
$822$		0			0
$823$	−1251.71			−1.52091			−0.760457	−	0.649389i	$-0.775025\pi$
$823$	−1251.71			−1.52091			−0.760457	+	0.649389i	$0.775025\pi$
$824$	970.220	−	617.930i	1.17745	−	0.749915i
$825$		0			0
$826$	1710.83	+	594.738i	2.07123	+	0.720022i
$827$	892.104			1.07872			0.539362	−	0.842074i	$-0.318666\pi$
$827$	892.104			1.07872			0.539362	+	0.842074i	$0.318666\pi$
$828$		0			0
$829$	998.688			1.20469			0.602345	−	0.798236i	$-0.294233\pi$
$829$	998.688			1.20469			0.602345	+	0.798236i	$0.294233\pi$
$830$	224.156	−	89.4265i	0.270068	−	0.107743i
$831$		0			0
$832$	438.251	+	204.491i	0.526743	+	0.245783i
$833$			727.131i			0.872906i
$834$		0			0
$835$	−304.214	−	350.966i	−0.364328	−	0.420319i
$836$	−815.093	−	644.601i	−0.974992	−	0.771054i
$837$		0			0
$838$	165.455	+	57.5174i	0.197441	+	0.0686365i
$839$		−	610.359i		−	0.727484i	−0.931500	−	0.363742i	$-0.881499\pi$
$839$		−	610.359i		−	0.727484i	0.931500	−	0.363742i	$-0.118501\pi$
$840$		0			0
$841$	−840.877			−0.999854
$842$	−46.1684	+	132.809i	−0.0548318	+	0.157730i
$843$		0			0
$844$	51.4086	−	65.0058i	0.0609107	−	0.0770211i
$845$	366.464	+	422.784i	0.433686	+	0.500336i
$846$		0			0
$847$	214.973			0.253805
$848$	−352.946	+	83.5883i	−0.416209	+	0.0985712i
$849$		0			0
$850$	394.645	−	763.556i	0.464288	−	0.898301i
$851$		−	37.9599i		−	0.0446062i
$852$		0			0
$853$		−	832.689i		−	0.976189i	−0.872791	−	0.488094i	$-0.837692\pi$
$853$		−	832.689i		−	0.976189i	0.872791	−	0.488094i	$-0.162308\pi$
$854$	−238.447	+	685.920i	−0.279212	+	0.803185i
$855$		0			0
$856$	236.852	−	150.850i	0.276696	−	0.176227i
$857$			149.415i			0.174347i	0.996193	+	0.0871735i	$0.0277834\pi$
$857$			149.415i			0.174347i	−0.996193	+	0.0871735i	$0.972217\pi$
$858$		0			0
$859$		−	394.144i		−	0.458840i	−0.973327	−	0.229420i	$-0.926317\pi$
$859$		−	394.144i		−	0.458840i	0.973327	−	0.229420i	$-0.0736830\pi$
$860$	37.6365	+	835.140i	0.0437633	+	0.971093i
$861$		0			0
$862$	467.308	+	162.451i	0.542121	+	0.188458i
$863$	−1409.58			−1.63335			−0.816677	−	0.577095i	$-0.804186\pi$
$863$	−1409.58			−1.63335			−0.816677	+	0.577095i	$0.804186\pi$
$864$		0			0
$865$	−443.945	+	384.807i	−0.513231	+	0.444864i
$866$	1201.94	+	417.831i	1.38792	+	0.482484i
$867$		0			0
$868$	−1091.18	+	1379.79i	−1.25712	+	1.58962i
$869$	456.797			0.525659
$870$		0			0
$871$		−	225.542i		−	0.258946i
$872$	−1022.26	+	651.074i	−1.17232	+	0.746644i
$873$		0			0
$874$	−82.8040	−	28.7852i	−0.0947414	−	0.0329350i
$875$	−1004.46	+	646.221i	−1.14796	+	0.738538i
$876$		0			0
$877$		−	872.780i		−	0.995189i	−0.867410	−	0.497594i	$-0.834217\pi$
$877$		−	872.780i		−	0.995189i	0.867410	−	0.497594i	$-0.165783\pi$
$878$	−1454.21	−	505.528i	−1.65627	−	0.575772i
$879$		0			0
$880$	644.314	+	463.971i	0.732175	+	0.527240i
$881$	−1103.38			−1.25241			−0.626206	−	0.779657i	$-0.715393\pi$
$881$	−1103.38			−1.25241			−0.626206	+	0.779657i	$0.715393\pi$
$882$		0			0
$883$	536.884			0.608023			0.304011	−	0.952668i	$-0.401674\pi$
$883$	536.884			0.608023			0.304011	+	0.952668i	$0.401674\pi$
$884$	407.547	+	322.300i	0.461025	+	0.364593i
$885$		0			0
$886$	−402.048	+	1156.54i	−0.453779	+	1.30535i
$887$	−888.945			−1.00219			−0.501096	−	0.865392i	$-0.667070\pi$
$887$	−888.945			−1.00219			−0.501096	+	0.865392i	$0.667070\pi$
$888$		0			0
$889$	−1835.08			−2.06421
$890$	930.665	−	371.286i	1.04569	−	0.417175i
$891$		0			0
$892$	−304.417	−	240.742i	−0.341274	−	0.269890i
$893$		−	368.734i		−	0.412916i
$894$		0			0
$895$	−876.501	+	759.742i	−0.979331	+	0.848874i
$896$	877.066	+	852.408i	0.978868	+	0.951348i
$897$		0			0
$898$	115.514	−	332.288i	0.128634	−	0.370032i
$899$		−	16.1319i		−	0.0179443i
$900$		0			0
$901$	−389.691			−0.432510
$902$	1449.28	+	503.814i	1.60674	+	0.558553i
$903$		0			0
$904$	−138.825	−	217.971i	−0.153567	−	0.241118i
$905$	−714.248	−	824.015i	−0.789224	−	0.910514i
$906$		0			0
$907$	1668.40			1.83947			0.919734	−	0.392543i	$-0.128405\pi$
$907$	1668.40			1.83947			0.919734	+	0.392543i	$0.128405\pi$
$908$	1277.75	+	1010.48i	1.40721	+	1.11287i
$909$		0			0
$910$	−267.543	−	670.623i	−0.294003	−	0.736948i
$911$			1498.13i			1.64449i	0.569131	+	0.822247i	$0.307280\pi$
$911$			1498.13i			1.64449i	−0.569131	+	0.822247i	$0.692720\pi$
$912$		0			0
$913$			239.521i			0.262345i
$914$	−690.199	−	239.935i	−0.755142	−	0.262510i
$915$		0			0
$916$	24.7766	+	19.5941i	0.0270487	+	0.0213909i
$917$		−	405.399i		−	0.442093i
$918$		0			0
$919$			1094.82i			1.19131i	0.803240	+	0.595656i	$0.203108\pi$
$919$			1094.82i			1.19131i	−0.803240	+	0.595656i	$0.796892\pi$
$920$	64.1925	+	19.1228i	0.0697745	+	0.0207856i
$921$		0			0
$922$	202.497	−	582.507i	0.219629	−	0.631787i
$923$	54.3784			0.0589148
$924$		0			0
$925$	560.990	+	80.4723i	0.606476	+	0.0869970i
$926$	60.8314	−	174.988i	0.0656926	−	0.188972i
$927$		0			0
$928$	−11.1576	−	1.14222i	−0.0120233	−	0.00123084i
$929$	−1145.90			−1.23348			−0.616740	−	0.787167i	$-0.711547\pi$
$929$	−1145.90			−1.23348			−0.616740	+	0.787167i	$0.711547\pi$
$930$		0			0
$931$			1107.23i			1.18929i
$932$	−69.8417	+	88.3142i	−0.0749374	+	0.0947578i
$933$		0			0
$934$	398.035	−	1144.99i	0.426162	−	1.22590i
$935$	558.733	+	644.601i	0.597576	+	0.689413i
$936$		0			0
$937$			1272.49i			1.35805i	0.734115	+	0.679025i	$0.237597\pi$
$937$			1272.49i			1.35805i	−0.734115	+	0.679025i	$0.762403\pi$
$938$	187.292	−	538.766i	0.199671	−	0.574378i
$939$		0			0
$940$	12.6837	+	281.446i	0.0134933	+	0.299411i
$941$	−707.360			−0.751711			−0.375856	−	0.926678i	$-0.622651\pi$
$941$	−707.360			−0.751711			−0.375856	+	0.926678i	$0.622651\pi$
$942$		0			0
$943$	129.438			0.137262
$944$	1475.66	−	349.482i	1.56320	−	0.370214i
$945$		0			0
$946$	−783.698	−	272.437i	−0.828433	−	0.287989i
$947$	−284.977			−0.300926			−0.150463	−	0.988616i	$-0.548076\pi$
$947$	−284.977			−0.300926			−0.150463	+	0.988616i	$0.548076\pi$
$948$		0			0
$949$	259.794			0.273756
$950$	600.940	−	1162.70i	0.632569	−	1.22389i
$951$		0			0
$952$	705.891	+	1108.33i	0.741482	+	1.16421i
$953$			295.247i			0.309808i	0.987930	+	0.154904i	$0.0495068\pi$
$953$			295.247i			0.309808i	−0.987930	+	0.154904i	$0.950493\pi$
$954$		0			0
$955$	518.401	−	449.344i	0.542828	−	0.470518i
$956$	−734.447	+	928.702i	−0.768250	+	0.971446i
$957$		0			0
$958$	−262.486	−	91.2483i	−0.273994	−	0.0952487i
$959$		−	1976.50i		−	2.06100i
$960$		0			0
$961$	−1157.38			−1.20435
$962$	−112.494	+	323.602i	−0.116938	+	0.336385i
$963$		0			0
$964$	−1461.41	−	1155.73i	−1.51598	−	1.19889i
$965$	139.904	−	121.267i	0.144978	−	0.125665i
$966$		0			0
$967$	348.013			0.359889			0.179945	−	0.983677i	$-0.442408\pi$
$967$	348.013			0.359889			0.179945	+	0.983677i	$0.442408\pi$
$968$	151.811	−	96.6881i	0.156830	−	0.0998844i
$969$		0			0
$970$	488.607	+	1224.74i	0.503719	+	1.26262i
$971$			798.691i			0.822545i	0.911513	+	0.411272i	$0.134915\pi$
$971$			798.691i			0.822545i	−0.911513	+	0.411272i	$0.865085\pi$
$972$		0			0
$973$		−	439.779i		−	0.451983i
$974$	132.159	−	380.170i	0.135687	−	0.390318i
$975$		0			0
$976$	140.117	+	591.634i	0.143563	+	0.606183i
$977$		−	721.834i		−	0.738827i	−0.929265	−	0.369413i	$-0.879559\pi$
$977$		−	721.834i		−	0.738827i	0.929265	−	0.369413i	$-0.120441\pi$
$978$		0			0
$979$			994.458i			1.01579i
$980$	−38.0863	−	845.122i	−0.0388636	−	0.862370i
$981$		0			0
$982$	656.216	+	228.121i	0.668244	+	0.232302i
$983$	1717.25			1.74695			0.873474	−	0.486870i	$-0.161861\pi$
$983$	1717.25			1.74695			0.873474	+	0.486870i	$0.161861\pi$
$984$		0			0
$985$	−735.135	+	637.207i	−0.746330	+	0.646910i
$986$	−11.3821	−	3.95677i	−0.0115437	−	0.00401296i
$987$		0			0
$988$	620.586	+	490.779i	0.628124	+	0.496740i
$989$	−69.9934			−0.0707719
$990$		0			0
$991$			342.270i			0.345378i	0.984976	+	0.172689i	$0.0552456\pi$
$991$			342.270i			0.345378i	−0.984976	+	0.172689i	$0.944754\pi$
$992$	−149.992	+	1465.17i	−0.151202	+	1.47699i
$993$		0			0
$994$	129.897	+	45.1562i	0.130681	+	0.0454288i
$995$	665.108	−	576.508i	0.668450	−	0.579405i
$996$		0			0
$997$		−	1586.05i		−	1.59082i	−0.606072	−	0.795410i	$-0.707256\pi$
$997$		−	1586.05i		−	1.59082i	0.606072	−	0.795410i	$-0.292744\pi$
$998$	1270.00	+	441.493i	1.27255	+	0.442377i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.3.f.h.19.4		8
3.2	odd	2		60.3.f.b.19.5	yes	8
4.3	odd	2	inner	180.3.f.h.19.6		8
5.2	odd	4		900.3.c.r.451.1		8
5.3	odd	4		900.3.c.r.451.8		8
5.4	even	2	inner	180.3.f.h.19.5		8
12.11	even	2		60.3.f.b.19.3	✓	8
15.2	even	4		300.3.c.f.151.8		8
15.8	even	4		300.3.c.f.151.1		8
15.14	odd	2		60.3.f.b.19.4	yes	8
20.3	even	4		900.3.c.r.451.7		8
20.7	even	4		900.3.c.r.451.2		8
20.19	odd	2	inner	180.3.f.h.19.3		8
24.5	odd	2		960.3.j.e.319.4		8
24.11	even	2		960.3.j.e.319.8		8
60.23	odd	4		300.3.c.f.151.2		8
60.47	odd	4		300.3.c.f.151.7		8
60.59	even	2		60.3.f.b.19.6	yes	8
120.29	odd	2		960.3.j.e.319.7		8
120.59	even	2		960.3.j.e.319.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.f.b.19.3	✓	8	12.11	even	2
60.3.f.b.19.4	yes	8	15.14	odd	2
60.3.f.b.19.5	yes	8	3.2	odd	2
60.3.f.b.19.6	yes	8	60.59	even	2
180.3.f.h.19.3		8	20.19	odd	2	inner
180.3.f.h.19.4		8	1.1	even	1	trivial
180.3.f.h.19.5		8	5.4	even	2	inner
180.3.f.h.19.6		8	4.3	odd	2	inner
300.3.c.f.151.1		8	15.8	even	4
300.3.c.f.151.2		8	60.23	odd	4
300.3.c.f.151.7		8	60.47	odd	4
300.3.c.f.151.8		8	15.2	even	4
900.3.c.r.451.1		8	5.2	odd	4
900.3.c.r.451.2		8	20.7	even	4
900.3.c.r.451.7		8	20.3	even	4
900.3.c.r.451.8		8	5.3	odd	4
960.3.j.e.319.3		8	120.59	even	2
960.3.j.e.319.4		8	24.5	odd	2
960.3.j.e.319.7		8	120.29	odd	2
960.3.j.e.319.8		8	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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	180.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.656712 + 1.88911i) q^{2} +(-3.13746 - 2.48120i) q^{4} +(3.27492 + 3.77822i) q^{5} +9.55505 q^{7} +(6.74766 - 4.29756i) q^{8} +O(q^{10})\)	\(q+(-0.656712 + 1.88911i) q^{2} +(-3.13746 - 2.48120i) q^{4} +(3.27492 + 3.77822i) q^{5} +9.55505 q^{7} +(6.74766 - 4.29756i) q^{8} +(-9.28814 + 3.70547i) q^{10} -9.92480i q^{11} +7.55643i q^{13} +(-6.27492 + 18.0505i) q^{14} +(3.68729 + 15.5693i) q^{16} +17.1903i q^{17} +26.1762i q^{19} +(-0.900407 - 19.9797i) q^{20} +(18.7490 + 6.51774i) q^{22} +1.67451 q^{23} +(-3.54983 + 24.7467i) q^{25} +(-14.2749 - 4.96240i) q^{26} +(-29.9786 - 23.7080i) q^{28} +0.350497 q^{29} -46.0258i q^{31} +(-31.8336 - 3.25887i) q^{32} +(-32.4743 - 11.2890i) q^{34} +(31.2920 + 36.1010i) q^{35} -22.6693i q^{37} +(-49.4498 - 17.1903i) q^{38} +(38.3352 + 11.4200i) q^{40} +77.2990 q^{41} -41.7994 q^{43} +(-24.6254 + 31.1386i) q^{44} +(-1.09967 + 3.16332i) q^{46} -14.0866 q^{47} +42.2990 q^{49} +(-44.4180 - 22.9575i) q^{50} +(18.7490 - 23.7080i) q^{52} +22.6693i q^{53} +(37.4980 - 32.5029i) q^{55} +(64.4743 - 41.0634i) q^{56} +(-0.230175 + 0.662126i) q^{58} -94.7802i q^{59} +38.0000 q^{61} +(86.9478 + 30.2257i) q^{62} +(27.0619 - 57.9970i) q^{64} +(-28.5498 + 24.7467i) q^{65} -29.8477 q^{67} +(42.6525 - 53.9337i) q^{68} +(-88.7486 + 35.4060i) q^{70} -7.19630i q^{71} -34.3805i q^{73} +(42.8248 + 14.8872i) q^{74} +(64.9485 - 82.1269i) q^{76} -94.8320i q^{77} +46.0258i q^{79} +(-46.7487 + 64.9196i) q^{80} +(-50.7632 + 146.026i) q^{82} -24.1336 q^{83} +(-64.9485 + 56.2967i) q^{85} +(27.4502 - 78.9636i) q^{86} +(-42.6525 - 66.9692i) q^{88} -100.199 q^{89} +72.2021i q^{91} +(-5.25370 - 4.15479i) q^{92} +(9.25083 - 26.6111i) q^{94} +(-98.8995 + 85.7250i) q^{95} -131.861i q^{97} +(-27.7783 + 79.9074i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 10 q^{4} - 4 q^{5}+O(q^{10}) \) 8 * q - 10 * q^4 - 4 * q^5	\( 8 q - 10 q^{4} - 4 q^{5} - 42 q^{10} - 20 q^{14} - 46 q^{16} - 52 q^{20} + 32 q^{25} - 84 q^{26} + 184 q^{29} + 12 q^{34} - 6 q^{40} + 256 q^{41} - 348 q^{44} + 112 q^{46} - 24 q^{49} - 72 q^{50} + 244 q^{56} + 304 q^{61} - 10 q^{64} - 168 q^{65} - 104 q^{70} + 252 q^{74} - 24 q^{76} + 308 q^{80} + 24 q^{85} + 280 q^{86} - 560 q^{89} + 376 q^{94}+O(q^{100}) \) 8 * q - 10 * q^4 - 4 * q^5 - 42 * q^10 - 20 * q^14 - 46 * q^16 - 52 * q^20 + 32 * q^25 - 84 * q^26 + 184 * q^29 + 12 * q^34 - 6 * q^40 + 256 * q^41 - 348 * q^44 + 112 * q^46 - 24 * q^49 - 72 * q^50 + 244 * q^56 + 304 * q^61 - 10 * q^64 - 168 * q^65 - 104 * q^70 + 252 * q^74 - 24 * q^76 + 308 * q^80 + 24 * q^85 + 280 * q^86 - 560 * q^89 + 376 * q^94

Introduction

L-functions

Modular forms

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Database

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