LMFDB - Embedded newform 300.3.c.f.151.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,3,Mod(151,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("300.151");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	300.c (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:	$8.17440793081$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.6080256576.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 7x^{6} - 12x^{5} + 12x^{4} - 48x^{3} + 112x^{2} - 192x + 256 $ x^8 - 3x^7 + 7x^6 - 12x^5 + 12x^4 - 48x^3 + 112x^2 - 192*x + 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			151.8
Root			$0.375825 - 1.96437i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.3.c.f.151.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.88911 + 0.656712i) q^{2} -1.73205i q^{3} +(3.13746 + 2.48120i) q^{4} +(1.13746 - 3.27203i) q^{6} +9.55505i q^{7} +(4.29756 + 6.74766i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(1.88911 + 0.656712i) q^{2} -1.73205i q^{3} +(3.13746 + 2.48120i) q^{4} +(1.13746 - 3.27203i) q^{6} +9.55505i q^{7} +(4.29756 + 6.74766i) q^{8} -3.00000 q^{9} +9.92480i q^{11} +(4.29756 - 5.43424i) q^{12} +7.55643 q^{13} +(-6.27492 + 18.0505i) q^{14} +(3.68729 + 15.5693i) q^{16} +17.1903 q^{17} +(-5.66732 - 1.97014i) q^{18} -26.1762i q^{19} +16.5498 q^{21} +(-6.51774 + 18.7490i) q^{22} +1.67451i q^{23} +(11.6873 - 7.44360i) q^{24} +(14.2749 + 4.96240i) q^{26} +5.19615i q^{27} +(-23.7080 + 29.9786i) q^{28} +0.350497 q^{29} -46.0258i q^{31} +(-3.25887 + 31.8336i) q^{32} +17.1903 q^{33} +(32.4743 + 11.2890i) q^{34} +(-9.41238 - 7.44360i) q^{36} +22.6693 q^{37} +(17.1903 - 49.4498i) q^{38} -13.0881i q^{39} -77.2990 q^{41} +(31.2644 + 10.8685i) q^{42} +41.7994i q^{43} +(-24.6254 + 31.1386i) q^{44} +(-1.09967 + 3.16332i) q^{46} +14.0866i q^{47} +(26.9669 - 6.38658i) q^{48} -42.2990 q^{49} -29.7744i q^{51} +(23.7080 + 18.7490i) q^{52} -22.6693 q^{53} +(-3.41238 + 9.81609i) q^{54} +(-64.4743 + 41.0634i) q^{56} -45.3386 q^{57} +(0.662126 + 0.230175i) q^{58} -94.7802i q^{59} +38.0000 q^{61} +(30.2257 - 86.9478i) q^{62} -28.6652i q^{63} +(-27.0619 + 57.9970i) q^{64} +(32.4743 + 11.2890i) q^{66} -29.8477i q^{67} +(53.9337 + 42.6525i) q^{68} +2.90033 q^{69} +7.19630i q^{71} +(-12.8927 - 20.2430i) q^{72} -34.3805 q^{73} +(42.8248 + 14.8872i) q^{74} +(64.9485 - 82.1269i) q^{76} -94.8320 q^{77} +(8.59513 - 24.7249i) q^{78} -46.0258i q^{79} +9.00000 q^{81} +(-146.026 - 50.7632i) q^{82} -24.1336i q^{83} +(51.9244 + 41.0634i) q^{84} +(-27.4502 + 78.9636i) q^{86} -0.607078i q^{87} +(-66.9692 + 42.6525i) q^{88} -100.199 q^{89} +72.2021i q^{91} +(-4.15479 + 5.25370i) q^{92} -79.7191 q^{93} +(-9.25083 + 26.6111i) q^{94} +(55.1375 + 5.64452i) q^{96} +131.861 q^{97} +(-79.9074 - 27.7783i) q^{98} -29.7744i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{4} - 6 q^{6} - 24 q^{9}+O(q^{10}) $ 8 * q + 10 * q^4 - 6 * q^6 - 24 * q^9	$ 8 q + 10 q^{4} - 6 q^{6} - 24 q^{9} - 20 q^{14} - 46 q^{16} + 72 q^{21} + 18 q^{24} + 84 q^{26} + 184 q^{29} - 12 q^{34} - 30 q^{36} - 256 q^{41} - 348 q^{44} + 112 q^{46} + 24 q^{49} + 18 q^{54} - 244 q^{56} + 304 q^{61} + 10 q^{64} - 12 q^{66} + 144 q^{69} + 252 q^{74} - 24 q^{76} + 72 q^{81} + 204 q^{84} - 280 q^{86} - 560 q^{89} - 376 q^{94} + 426 q^{96}+O(q^{100}) $ 8 * q + 10 * q^4 - 6 * q^6 - 24 * q^9 - 20 * q^14 - 46 * q^16 + 72 * q^21 + 18 * q^24 + 84 * q^26 + 184 * q^29 - 12 * q^34 - 30 * q^36 - 256 * q^41 - 348 * q^44 + 112 * q^46 + 24 * q^49 + 18 * q^54 - 244 * q^56 + 304 * q^61 + 10 * q^64 - 12 * q^66 + 144 * q^69 + 252 * q^74 - 24 * q^76 + 72 * q^81 + 204 * q^84 - 280 * q^86 - 560 * q^89 - 376 * q^94 + 426 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	1.88911	+	0.656712i	0.944554	+	0.328356i
$2$	1.88911	+	0.656712i	0.944554	+	0.328356i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	3.13746	+	2.48120i	0.784365	+	0.620300i
$5$		0			0
$5$		0			0
$6$	1.13746	−	3.27203i	0.189576	−	0.545339i
$7$			9.55505i			1.36501i	0.730882	+	0.682504i	$0.239109\pi$
$7$			9.55505i			1.36501i	−0.730882	+	0.682504i	$0.760891\pi$
$8$	4.29756	+	6.74766i	0.537196	+	0.843458i
$9$	−3.00000			−0.333333
$10$		0			0
$11$			9.92480i			0.902255i	0.892460	+	0.451127i	$0.148978\pi$
$11$			9.92480i			0.902255i	−0.892460	+	0.451127i	$0.851022\pi$
$12$	4.29756	−	5.43424i	0.358130	−	0.452853i
$13$	7.55643			0.581264			0.290632	−	0.956835i	$-0.406134\pi$
$13$	7.55643			0.581264			0.290632	+	0.956835i	$0.406134\pi$
$14$	−6.27492	+	18.0505i	−0.448208	+	1.28932i
$15$		0			0
$16$	3.68729	+	15.5693i	0.230456	+	0.973083i
$17$	17.1903			1.01119			0.505596	−	0.862770i	$-0.331273\pi$
$17$	17.1903			1.01119			0.505596	+	0.862770i	$0.331273\pi$
$18$	−5.66732	−	1.97014i	−0.314851	−	0.109452i
$19$		−	26.1762i		−	1.37770i	−0.724905	−	0.688849i	$-0.758116\pi$
$19$		−	26.1762i		−	1.37770i	0.724905	−	0.688849i	$-0.241884\pi$
$20$		0			0
$21$	16.5498			0.788087
$22$	−6.51774	+	18.7490i	−0.296261	+	0.852228i
$23$			1.67451i			0.0728047i	0.999337	+	0.0364023i	$0.0115898\pi$
$23$			1.67451i			0.0728047i	−0.999337	+	0.0364023i	$0.988410\pi$
$24$	11.6873	−	7.44360i	0.486971	−	0.310150i
$25$		0			0
$26$	14.2749	+	4.96240i	0.549035	+	0.190862i
$27$			5.19615i			0.192450i
$28$	−23.7080	+	29.9786i	−0.846714	+	1.07066i
$29$	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	$-0.266290\pi$
$32$	−3.25887	+	31.8336i	−0.101840	+	0.994801i
$33$	17.1903			0.520917
$34$	32.4743	+	11.2890i	0.955125	+	0.332031i
$35$		0			0
$36$	−9.41238	−	7.44360i	−0.261455	−	0.206767i
$37$	22.6693			0.612684			0.306342	−	0.951922i	$-0.400895\pi$
$37$	22.6693			0.612684			0.306342	+	0.951922i	$0.400895\pi$
$38$	17.1903	−	49.4498i	0.452375	−	1.30131i
$39$		−	13.0881i		−	0.335593i
$40$		0			0
$41$	−77.2990			−1.88534			−0.942671	−	0.333724i	$-0.891695\pi$
$41$	−77.2990			−1.88534			−0.942671	+	0.333724i	$0.891695\pi$
$42$	31.2644	+	10.8685i	0.744391	+	0.258773i
$43$			41.7994i			0.972079i	0.873937	+	0.486039i	$0.161559\pi$
$43$			41.7994i			0.972079i	−0.873937	+	0.486039i	$0.838441\pi$
$44$	−24.6254	+	31.1386i	−0.559668	+	0.707697i
$45$		0			0
$46$	−1.09967	+	3.16332i	−0.0239058	+	0.0687679i
$47$			14.0866i			0.299715i	0.988708	+	0.149857i	$0.0478814\pi$
$47$			14.0866i			0.299715i	−0.988708	+	0.149857i	$0.952119\pi$
$48$	26.9669	−	6.38658i	0.561810	−	0.133054i
$49$	−42.2990			−0.863245
$50$		0			0
$51$		−	29.7744i		−	0.583812i
$52$	23.7080	+	18.7490i	0.455923	+	0.360558i
$53$	−22.6693			−0.427723			−0.213861	−	0.976864i	$-0.568604\pi$
$53$	−22.6693			−0.427723			−0.213861	+	0.976864i	$0.568604\pi$
$54$	−3.41238	+	9.81609i	−0.0631921	+	0.181780i
$55$		0			0
$56$	−64.4743	+	41.0634i	−1.15133	+	0.733276i
$57$	−45.3386			−0.795414
$58$	0.662126	+	0.230175i	0.0114160	+	0.00396854i
$59$		−	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	$0.399177\pi$
$62$	30.2257	−	86.9478i	0.487512	−	1.40238i
$63$		−	28.6652i		−	0.455002i
$64$	−27.0619	+	57.9970i	−0.422842	+	0.906203i
$65$		0			0
$66$	32.4743	+	11.2890i	0.492034	+	0.171046i
$67$		−	29.8477i		−	0.445488i	−0.974877	−	0.222744i	$-0.928499\pi$
$67$		−	29.8477i		−	0.445488i	0.974877	−	0.222744i	$-0.0715013\pi$
$68$	53.9337	+	42.6525i	0.793143	+	0.627242i
$69$	2.90033			0.0420338
$70$		0			0
$71$			7.19630i			0.101356i	0.998715	+	0.0506782i	$0.0161383\pi$
$71$			7.19630i			0.101356i	−0.998715	+	0.0506782i	$0.983862\pi$
$72$	−12.8927	−	20.2430i	−0.179065	−	0.281153i
$73$	−34.3805			−0.470966			−0.235483	−	0.971878i	$-0.575667\pi$
$73$	−34.3805			−0.470966			−0.235483	+	0.971878i	$0.575667\pi$
$74$	42.8248	+	14.8872i	0.578713	+	0.201178i
$75$		0			0
$76$	64.9485	−	82.1269i	0.854586	−	1.08062i
$77$	−94.8320			−1.23158
$78$	8.59513	−	24.7249i	0.110194	−	0.316986i
$79$		−	46.0258i		−	0.582606i	−0.956631	−	0.291303i	$-0.905911\pi$
$79$		−	46.0258i		−	0.582606i	0.956631	−	0.291303i	$-0.0940887\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	−146.026	−	50.7632i	−1.78081	−	0.619063i
$83$		−	24.1336i		−	0.290767i	−0.989375	−	0.145383i	$-0.953558\pi$
$83$		−	24.1336i		−	0.290767i	0.989375	−	0.145383i	$-0.0464415\pi$
$84$	51.9244	+	41.0634i	0.618148	+	0.488851i
$85$		0			0
$86$	−27.4502	+	78.9636i	−0.319188	+	0.918181i
$87$		−	0.607078i		−	0.00697791i
$88$	−66.9692	+	42.6525i	−0.761014	+	0.484687i
$89$	−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
$92$	−4.15479	+	5.25370i	−0.0451607	+	0.0571054i
$93$	−79.7191			−0.857195
$94$	−9.25083	+	26.6111i	−0.0984131	+	0.283097i
$95$		0			0
$96$	55.1375	+	5.64452i	0.574349	+	0.0587971i
$97$	131.861			1.35939			0.679696	−	0.733494i	$-0.262112\pi$
$97$	131.861			1.35939			0.679696	+	0.733494i	$0.262112\pi$
$98$	−79.9074	−	27.7783i	−0.815382	−	0.283452i
$99$		−	29.7744i		−	0.300752i
$100$		0			0
$101$	29.4502			0.291586			0.145793	−	0.989315i	$-0.453427\pi$
$101$	29.4502			0.291586			0.145793	+	0.989315i	$0.453427\pi$
$102$	19.5532	−	56.2471i	0.191698	−	0.551442i
$103$		−	143.786i		−	1.39598i	−0.716107	−	0.697991i	$-0.754078\pi$
$103$		−	143.786i		−	1.39598i	0.716107	−	0.697991i	$-0.245922\pi$
$104$	32.4743	+	50.9882i	0.312252	+	0.490272i
$105$		0			0
$106$	−42.8248	−	14.8872i	−0.404007	−	0.140445i
$107$		−	35.1014i		−	0.328050i	−0.986456	−	0.164025i	$-0.947552\pi$
$107$		−	35.1014i		−	0.328050i	0.986456	−	0.164025i	$-0.0524478\pi$
$108$	−12.8927	+	16.3027i	−0.119377	+	0.150951i
$109$	151.498			1.38989			0.694947	−	0.719061i	$-0.255428\pi$
$109$	151.498			1.38989			0.694947	+	0.719061i	$0.255428\pi$
$110$		0			0
$111$		−	39.2644i		−	0.353733i
$112$	−148.766	+	35.2323i	−1.32827	+	0.314574i
$113$	32.3031			0.285868			0.142934	−	0.989732i	$-0.454346\pi$
$113$	32.3031			0.285868			0.142934	+	0.989732i	$0.454346\pi$
$114$	−85.6495	−	29.7744i	−0.751311	−	0.261179i
$115$		0			0
$116$	1.09967	+	0.869652i	0.00947990	+	0.00749700i
$117$	−22.6693			−0.193755
$118$	62.2433	−	179.050i	0.527486	−	1.51737i
$119$			164.254i			1.38028i
$120$		0			0
$121$	22.4983			0.185937
$122$	71.7861	+	24.9551i	0.588411	+	0.204550i
$123$			133.886i			1.08850i
$124$	114.199	−	144.404i	0.920962	−	1.16455i
$125$		0			0
$126$	18.8248	−	54.1516i	0.149403	−	0.429774i
$127$		−	192.053i		−	1.51223i	−0.654438	−	0.756116i	$-0.727095\pi$
$127$		−	192.053i		−	1.51223i	0.654438	−	0.756116i	$-0.272905\pi$
$128$	−89.2102	+	91.7908i	−0.696954	+	0.717115i
$129$	72.3987			0.561230
$130$		0			0
$131$			42.4277i			0.323876i	0.986801	+	0.161938i	$0.0517744\pi$
$131$			42.4277i			0.323876i	−0.986801	+	0.161938i	$0.948226\pi$
$132$	53.9337	+	42.6525i	0.408589	+	0.323125i
$133$	250.115			1.88057
$134$	19.6013	−	56.3855i	0.146279	−	0.420787i
$135$		0			0
$136$	73.8762	+	115.994i	0.543208	+	0.852897i
$137$	−206.854			−1.50988			−0.754942	−	0.655791i	$-0.772335\pi$
$137$	−206.854			−1.50988			−0.754942	+	0.655791i	$0.772335\pi$
$138$	5.47904	+	1.90468i	0.0397032	+	0.0138020i
$139$			46.0258i			0.331121i	0.986200	+	0.165561i	$0.0529433\pi$
$139$			46.0258i			0.331121i	−0.986200	+	0.165561i	$0.947057\pi$
$140$		0			0
$141$	24.3987			0.173040
$142$	−4.72590	+	13.5946i	−0.0332810	+	0.0957366i
$143$			74.9961i			0.524448i
$144$	−11.0619	−	46.7080i	−0.0768186	−	0.324361i
$145$		0			0
$146$	−64.9485	−	22.5781i	−0.444853	−	0.154645i
$147$			73.2640i			0.498395i
$148$	71.1240	+	56.2471i	0.480567	+	0.380048i
$149$	−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	$-0.136328\pi$
$152$	176.628	−	112.494i	1.16203	−	0.740093i
$153$	−51.5708			−0.337064
$154$	−179.148	−	62.2773i	−1.16330	−	0.404398i
$155$		0			0
$156$	32.4743	−	41.0634i	0.208168	−	0.263227i
$157$	197.220			1.25618			0.628090	−	0.778140i	$-0.283837\pi$
$157$	197.220			1.25618			0.628090	+	0.778140i	$0.283837\pi$
$158$	30.2257	−	86.9478i	0.191302	−	0.550303i
$159$			39.2644i			0.246946i
$160$		0			0
$161$	−16.0000			−0.0993789
$162$	17.0020	+	5.91041i	0.104950	+	0.0364840i
$163$			18.4196i			0.113004i	0.998402	+	0.0565018i	$0.0179947\pi$
$163$			18.4196i			0.113004i	−0.998402	+	0.0565018i	$0.982005\pi$
$164$	−242.522	−	191.794i	−1.47880	−	1.16948i
$165$		0			0
$166$	15.8488	−	45.5910i	0.0954749	−	0.274645i
$167$			92.8920i			0.556240i	0.960546	+	0.278120i	$0.0897112\pi$
$167$			92.8920i			0.556240i	−0.960546	+	0.278120i	$0.910289\pi$
$168$	71.1240	+	111.673i	0.423357	+	0.664718i
$169$	−111.900			−0.662132
$170$		0			0
$171$			78.5287i			0.459232i
$172$	−103.713	+	131.144i	−0.602981	+	0.762464i
$173$	−117.501			−0.679198			−0.339599	−	0.940570i	$-0.610291\pi$
$173$	−117.501			−0.679198			−0.339599	+	0.940570i	$0.610291\pi$
$174$	0.398675	−	1.14684i	0.00229124	−	0.00659101i
$175$		0			0
$176$	−154.522	+	36.5956i	−0.877968	+	0.207930i
$177$	−164.164			−0.927481
$178$	−189.287	−	65.8021i	−1.06341	−	0.369675i
$179$			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	$0.705819\pi$
$182$	−47.4160	+	136.398i	−0.260527	+	0.749437i
$183$		−	65.8179i		−	0.359661i
$184$	−11.2990	+	7.19630i	−0.0614076	+	0.0391103i
$185$		0			0
$186$	−150.598	−	52.3525i	−0.809667	−	0.281465i
$187$			170.610i			0.912352i
$188$	−34.9516	+	44.1961i	−0.185913	+	0.235085i
$189$	−49.6495			−0.262696
$190$		0			0
$191$			137.208i			0.718366i	0.933267	+	0.359183i	$0.116945\pi$
$191$			137.208i			0.718366i	−0.933267	+	0.359183i	$0.883055\pi$
$192$	100.454	+	46.8725i	0.523197	+	0.244128i
$193$	−37.0290			−0.191860			−0.0959301	−	0.995388i	$-0.530583\pi$
$193$	−37.0290			−0.191860			−0.0959301	+	0.995388i	$0.530583\pi$
$194$	249.100	+	86.5947i	1.28402	+	0.446364i
$195$		0			0
$196$	−132.711	−	104.952i	−0.677099	−	0.535471i
$197$	194.572			0.987674			0.493837	−	0.869554i	$-0.335594\pi$
$197$	194.572			0.987674			0.493837	+	0.869554i	$0.335594\pi$
$198$	19.5532	−	56.2471i	0.0987536	−	0.284076i
$199$			176.037i			0.884610i	0.896865	+	0.442305i	$0.145839\pi$
$199$			176.037i			0.884610i	−0.896865	+	0.442305i	$0.854161\pi$
$200$		0			0
$201$	−51.6977			−0.257202
$202$	55.6345	+	19.3403i	0.275419	+	0.0957440i
$203$			3.34901i			0.0164976i
$204$	73.8762	−	93.4159i	0.362138	−	0.457921i
$205$		0			0
$206$	94.4261	−	271.628i	0.458379	−	1.31858i
$207$		−	5.02352i		−	0.0242682i
$208$	27.8628	+	117.649i	0.133956	+	0.565618i
$209$	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	$0.984365\pi$
$212$	−71.1240	−	56.2471i	−0.335490	−	0.265316i
$213$	12.4644			0.0585181
$214$	23.0515	−	66.3103i	0.107717	−	0.309861i
$215$		0			0
$216$	−35.0619	+	22.3308i	−0.162324	+	0.103383i
$217$	439.779			2.02663
$218$	286.197	+	99.4908i	1.31283	+	0.456380i
$219$			59.5488i			0.271912i
$220$		0			0
$221$	129.897			0.587769
$222$	25.7854	−	74.1746i	0.116150	−	0.334120i
$223$		−	97.0265i		−	0.435096i	−0.976050	−	0.217548i	$-0.930194\pi$
$223$		−	97.0265i		−	0.435096i	0.976050	−	0.217548i	$-0.0698059\pi$
$224$	−304.172	−	31.1386i	−1.35791	−	0.139012i
$225$		0			0
$226$	61.0241	+	21.2138i	0.270018	+	0.0938666i
$227$			407.256i			1.79408i	0.441948	+	0.897040i	$0.354287\pi$
$227$			407.256i			1.79408i	−0.441948	+	0.897040i	$0.645713\pi$
$228$	−142.248	−	112.494i	−0.623895	−	0.493395i
$229$	7.89702			0.0344848			0.0172424	−	0.999851i	$-0.494511\pi$
$229$	7.89702			0.0344848			0.0172424	+	0.999851i	$0.494511\pi$
$230$		0			0
$231$			164.254i			0.711055i
$232$	1.50628	+	2.36503i	0.00649260	+	0.0101941i
$233$	28.1483			0.120808			0.0604042	−	0.998174i	$-0.480761\pi$
$233$	28.1483			0.120808			0.0604042	+	0.998174i	$0.480761\pi$
$234$	−42.8248	−	14.8872i	−0.183012	−	0.0636205i
$235$		0			0
$236$	235.169	−	297.369i	0.996477	−	1.26004i
$237$	−79.7191			−0.336368
$238$	−107.867	+	310.293i	−0.453225	+	1.30375i
$239$		−	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	$0.0827758\pi$
$242$	42.5018	+	14.7749i	0.175627	+	0.0610534i
$243$		−	15.5885i		−	0.0641500i
$244$	119.223	+	94.2856i	0.488621	+	0.386416i
$245$		0			0
$246$	−87.9244	+	252.925i	−0.357416	+	1.02815i
$247$		−	197.799i		−	0.800806i
$248$	310.567	−	197.799i	1.25229	−	0.797577i
$249$	−41.8007			−0.167874
$250$		0			0
$251$		−	141.676i		−	0.564445i	−0.959349	−	0.282223i	$-0.908928\pi$
$251$		−	141.676i		−	0.564445i	0.959349	−	0.282223i	$-0.0910716\pi$
$252$	71.1240	−	89.9357i	0.282238	−	0.356888i
$253$	−16.6191			−0.0656883
$254$	126.124	−	362.810i	0.496550	−	1.42838i
$255$		0			0
$256$	−228.808	+	114.817i	−0.893780	+	0.448505i
$257$	−41.7549			−0.162470			−0.0812352	−	0.996695i	$-0.525887\pi$
$257$	−41.7549			−0.162470			−0.0812352	+	0.996695i	$0.525887\pi$
$258$	136.769	+	47.5451i	0.530112	+	0.184283i
$259$			216.606i			0.836318i
$260$		0			0
$261$	−1.05149			−0.00402870
$262$	−27.8628	+	80.1505i	−0.106346	+	0.305918i
$263$			203.283i			0.772939i	0.922302	+	0.386469i	$0.126306\pi$
$263$			203.283i			0.772939i	−0.922302	+	0.386469i	$0.873694\pi$
$264$	73.8762	+	115.994i	0.279834	+	0.439371i
$265$		0			0
$266$	472.495	+	164.254i	1.77630	+	0.617495i
$267$			173.550i			0.650001i
$268$	74.0580	−	93.6458i	0.276336	−	0.349425i
$269$	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	$0.669927\pi$
$272$	63.3855	+	267.641i	0.233035	+	0.983973i
$273$	125.058			0.458087
$274$	−390.770	−	135.844i	−1.42617	−	0.495780i
$275$		0			0
$276$	9.09967	+	7.19630i	0.0329698	+	0.0260736i
$277$	−494.181			−1.78405			−0.892023	−	0.451990i	$-0.850714\pi$
$277$	−494.181			−1.78405			−0.892023	+	0.451990i	$0.850714\pi$
$278$	−30.2257	+	86.9478i	−0.108726	+	0.312762i
$279$			138.078i			0.494902i
$280$		0			0
$281$	−43.4020			−0.154455			−0.0772277	−	0.997013i	$-0.524607\pi$
$281$	−43.4020			−0.154455			−0.0772277	+	0.997013i	$0.524607\pi$
$282$	46.0917	+	16.0229i	0.163446	+	0.0568188i
$283$			310.785i			1.09818i	0.835763	+	0.549090i	$0.185026\pi$
$283$			310.785i			1.09818i	−0.835763	+	0.549090i	$0.814974\pi$
$284$	−17.8555	+	22.5781i	−0.0628714	+	0.0795003i
$285$		0			0
$286$	−49.2508	+	141.676i	−0.172206	+	0.495370i
$287$		−	738.596i		−	2.57351i
$288$	9.77660	−	95.5009i	0.0339465	−	0.331600i
$289$	6.50497			0.0225085
$290$		0			0
$291$		−	228.390i		−	0.784845i
$292$	−107.867	−	85.3049i	−0.369409	−	0.292140i
$293$	−245.207			−0.836886			−0.418443	−	0.908243i	$-0.637424\pi$
$293$	−245.207			−0.836886			−0.418443	+	0.908243i	$0.637424\pi$
$294$	−48.1134	+	138.404i	−0.163651	+	0.470761i
$295$		0			0
$296$	97.4228	+	152.965i	0.329131	+	0.516773i
$297$	−51.5708			−0.173639
$298$	−22.0072	−	7.65037i	−0.0738496	−	0.0256724i
$299$			12.6533i			0.0423187i
$300$		0			0
$301$	−399.395			−1.32689
$302$	82.3676	−	236.940i	0.272740	−	0.784569i
$303$		−	51.0092i		−	0.168347i
$304$	407.547	−	96.5195i	1.34061	−	0.317498i
$305$		0			0
$306$	−97.4228	−	33.8671i	−0.318375	−	0.110677i
$307$			337.514i			1.09939i	0.835364	+	0.549697i	$0.185257\pi$
$307$			337.514i			1.09939i	−0.835364	+	0.549697i	$0.814743\pi$
$308$	−297.531	−	235.297i	−0.966011	−	0.763952i
$309$	−249.045			−0.805970
$310$		0			0
$311$		−	427.756i		−	1.37542i	−0.725986	−	0.687710i	$-0.758616\pi$
$311$		−	427.756i		−	1.37542i	0.725986	−	0.687710i	$-0.241384\pi$
$312$	88.3142	−	56.2471i	0.283058	−	0.180279i
$313$	83.8739			0.267968			0.133984	−	0.990984i	$-0.457223\pi$
$313$	83.8739			0.267968			0.133984	+	0.990984i	$0.457223\pi$
$314$	372.571	+	129.517i	1.18653	+	0.412475i
$315$		0			0
$316$	114.199	−	144.404i	0.361390	−	0.456975i
$317$	−112.204			−0.353957			−0.176978	−	0.984215i	$-0.556632\pi$
$317$	−112.204			−0.353957			−0.176978	+	0.984215i	$0.556632\pi$
$318$	−25.7854	+	74.1746i	−0.0810861	+	0.233254i
$319$			3.47861i			0.0109047i
$320$		0			0
$321$	−60.7974			−0.189400
$322$	−30.2257	−	10.5074i	−0.0938687	−	0.0326317i
$323$		−	449.976i		−	1.39312i
$324$	28.2371	+	22.3308i	0.0871516	+	0.0689222i
$325$		0			0
$326$	−12.0964	+	34.7966i	−0.0371054	+	0.106738i
$327$		−	262.403i		−	0.802455i
$328$	−332.197	−	521.588i	−1.01280	−	1.59021i
$329$	−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	$-0.0642025\pi$
$332$	59.8803	−	75.7182i	0.180362	−	0.228067i
$333$	−68.0079			−0.204228
$334$	−61.0033	+	175.483i	−0.182645	+	0.525398i
$335$		0			0
$336$	61.0241	+	257.670i	0.181619	+	0.766874i
$337$	−20.7739			−0.0616437			−0.0308219	−	0.999525i	$-0.509812\pi$
$337$	−20.7739			−0.0616437			−0.0308219	+	0.999525i	$0.509812\pi$
$338$	−211.392	−	73.4863i	−0.625420	−	0.217415i
$339$		−	55.9506i		−	0.165046i
$340$		0			0
$341$	456.797			1.33958
$342$	−51.5708	+	148.349i	−0.150792	+	0.433770i
$343$			64.0283i			0.186672i
$344$	−282.048	+	179.636i	−0.819907	+	0.522196i
$345$		0			0
$346$	−221.973	−	77.1645i	−0.641539	−	0.223019i
$347$			8.89616i			0.0256374i	0.999918	+	0.0128187i	$0.00408042\pi$
$347$			8.89616i			0.0256374i	−0.999918	+	0.0128187i	$0.995920\pi$
$348$	1.50628	−	1.90468i	0.00432840	−	0.00547323i
$349$	−19.4020			−0.0555931			−0.0277965	−	0.999614i	$-0.508849\pi$
$349$	−19.4020			−0.0555931			−0.0277965	+	0.999614i	$0.508849\pi$
$350$		0			0
$351$			39.2644i			0.111864i
$352$	−315.942	−	32.3436i	−0.897564	−	0.0918853i
$353$	80.2902			0.227451			0.113726	−	0.993512i	$-0.463722\pi$
$353$	80.2902			0.227451			0.113726	+	0.993512i	$0.463722\pi$
$354$	−310.124	−	107.809i	−0.876056	−	0.304544i
$355$		0			0
$356$	−314.371	−	248.615i	−0.883065	−	0.698356i
$357$	284.496			0.796907
$358$	−152.349	+	438.251i	−0.425557	+	1.22416i
$359$		−	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
$362$	−412.008	−	143.227i	−1.13814	−	0.395653i
$363$		−	38.9683i		−	0.107351i
$364$	−179.148	+	226.531i	−0.492164	+	0.622338i
$365$		0			0
$366$	43.2234	−	124.337i	0.118097	−	0.339719i
$367$		−	476.800i		−	1.29918i	−0.760283	−	0.649592i	$-0.774940\pi$
$367$		−	476.800i		−	1.29918i	0.760283	−	0.649592i	$-0.225060\pi$
$368$	−26.0709	+	6.17440i	−0.0708450	+	0.0167783i
$369$	231.897			0.628447
$370$		0			0
$371$		−	216.606i		−	0.583844i
$372$	−250.115	−	197.799i	−0.672353	−	0.531718i
$373$	−86.1333			−0.230920			−0.115460	−	0.993312i	$-0.536834\pi$
$373$	−86.1333			−0.230920			−0.115460	+	0.993312i	$0.536834\pi$
$374$	−112.042	+	322.300i	−0.299576	+	0.861766i
$375$		0			0
$376$	−95.0515	+	60.5380i	−0.252797	+	0.161005i
$377$	2.64850			0.00702521
$378$	−93.7933	−	32.6054i	−0.248130	−	0.0862577i
$379$		−	638.035i		−	1.68347i	−0.539891	−	0.841735i	$-0.681534\pi$
$379$		−	638.035i		−	1.68347i	0.539891	−	0.841735i	$-0.318466\pi$
$380$		0			0
$381$	−332.646			−0.873087
$382$	−90.1061	+	259.201i	−0.235880	+	0.678535i
$383$		−	216.742i		−	0.565907i	−0.959134	−	0.282953i	$-0.908686\pi$
$383$		−	216.742i		−	0.565907i	0.959134	−	0.282953i	$-0.0913142\pi$
$384$	158.986	+	154.517i	0.414027	+	0.402387i
$385$		0			0
$386$	−69.9518	−	24.3174i	−0.181222	−	0.0629985i
$387$		−	125.398i		−	0.324026i
$388$	413.708	+	327.174i	1.06626	+	0.843231i
$389$	−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
$392$	−181.783	−	285.419i	−0.463731	−	0.728111i
$393$	73.4869			0.186990
$394$	367.567	+	127.778i	0.932912	+	0.324309i
$395$		0			0
$396$	73.8762	−	93.4159i	0.186556	−	0.235899i
$397$	−43.0792			−0.108512			−0.0542559	−	0.998527i	$-0.517279\pi$
$397$	−43.0792			−0.108512			−0.0542559	+	0.998527i	$0.517279\pi$
$398$	−115.606	+	332.554i	−0.290467	+	0.835562i
$399$		−	433.213i		−	1.08575i
$400$		0			0
$401$	−168.694			−0.420684			−0.210342	−	0.977628i	$-0.567458\pi$
$401$	−168.694			−0.420684			−0.210342	+	0.977628i	$0.567458\pi$
$402$	−97.6625	−	33.9505i	−0.242942	−	0.0844540i
$403$		−	347.791i		−	0.863005i
$404$	92.3987	+	73.0718i	0.228710	+	0.180871i
$405$		0			0
$406$	−2.19934	+	6.32665i	−0.00541709	+	0.0155829i
$407$			224.988i			0.552797i
$408$	200.908	−	127.957i	0.492421	−	0.313621i
$409$	−373.890			−0.914157			−0.457079	−	0.889426i	$-0.651104\pi$
$409$	−373.890			−0.914157			−0.457079	+	0.889426i	$0.651104\pi$
$410$		0			0
$411$			358.282i			0.871732i
$412$	356.762	−	451.123i	0.865927	−	1.09496i
$413$	905.630			2.19281
$414$	3.29901	−	9.48997i	0.00796862	−	0.0229226i
$415$		0			0
$416$	−24.6254	+	240.549i	−0.0591957	+	0.578242i
$417$	79.7191			0.191173
$418$	490.779	+	170.610i	1.17411	+	0.408158i
$419$		−	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	$0.473392\pi$
$422$	−13.6066	+	39.1409i	−0.0322431	+	0.0927510i
$423$		−	42.2597i		−	0.0999048i
$424$	−97.4228	−	152.965i	−0.229771	−	0.360766i
$425$		0			0
$426$	23.5465	+	8.18550i	0.0552735	+	0.0192148i
$427$			363.092i			0.850332i
$428$	87.0935	−	110.129i	0.203490	−	0.257311i
$429$	129.897			0.302790
$430$		0			0
$431$			247.370i			0.573944i	0.957939	+	0.286972i	$0.0926487\pi$
$431$			247.370i			0.573944i	−0.957939	+	0.286972i	$0.907351\pi$
$432$	−80.9006	+	19.1597i	−0.187270	+	0.0443512i
$433$	−636.247			−1.46939			−0.734696	−	0.678397i	$-0.762675\pi$
$433$	−636.247			−1.46939			−0.734696	+	0.678397i	$0.762675\pi$
$434$	830.791	+	288.808i	1.91426	+	0.665457i
$435$		0			0
$436$	475.320	+	375.898i	1.09018	+	0.862151i
$437$	43.8323			0.100303
$438$	−39.1064	+	112.494i	−0.0892840	+	0.256836i
$439$		−	769.786i		−	1.75350i	−0.480947	−	0.876750i	$-0.659707\pi$
$439$		−	769.786i		−	1.75350i	0.480947	−	0.876750i	$-0.340293\pi$
$440$		0			0
$441$	126.897			0.287748
$442$	245.390	+	85.3049i	0.555180	+	0.192998i
$443$			612.214i			1.38197i	0.722868	+	0.690986i	$0.242823\pi$
$443$			612.214i			1.38197i	−0.722868	+	0.690986i	$0.757177\pi$
$444$	97.4228	−	123.190i	0.219421	−	0.277456i
$445$		0			0
$446$	63.7185	−	183.294i	0.142867	−	0.410972i
$447$			20.1775i			0.0451399i
$448$	−554.165	−	258.578i	−1.23697	−	0.577182i
$449$	−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
$452$	101.350	+	80.1505i	0.224225	+	0.177324i
$453$	−217.241			−0.479561
$454$	−267.450	+	769.351i	−0.589097	+	1.69461i
$455$		0			0
$456$	−194.846	−	305.929i	−0.427293	−	0.670898i
$457$	−365.357			−0.799469			−0.399734	−	0.916631i	$-0.630898\pi$
$457$	−365.357			−0.799469			−0.399734	+	0.916631i	$0.630898\pi$
$458$	14.9183	+	5.18607i	0.0325728	+	0.0113233i
$459$			89.3232i			0.194604i
$460$		0			0
$461$	308.350			0.668873			0.334437	−	0.942418i	$-0.391454\pi$
$461$	308.350			0.668873			0.334437	+	0.942418i	$0.391454\pi$
$462$	−107.867	+	310.293i	−0.233479	+	0.671630i
$463$			92.6302i			0.200065i	0.994984	+	0.100033i	$0.0318947\pi$
$463$			92.6302i			0.200065i	−0.994984	+	0.100033i	$0.968105\pi$
$464$	1.29238	+	5.45700i	0.00278531	+	0.0117608i
$465$		0			0
$466$	53.1752	+	18.4854i	0.114110	+	0.0396681i
$467$			606.103i			1.29786i	0.760846	+	0.648932i	$0.224784\pi$
$467$			606.103i			1.29786i	−0.760846	+	0.648932i	$0.775216\pi$
$468$	−71.1240	−	56.2471i	−0.151974	−	0.120186i
$469$	285.196			0.608094
$470$		0			0
$471$		−	341.596i		−	0.725256i
$472$	639.545	−	407.324i	1.35497	−	0.862975i
$473$	−414.851			−0.877063
$474$	−150.598	−	52.3525i	−0.317717	−	0.110448i
$475$		0			0
$476$	−407.547	+	515.339i	−0.856190	+	1.08265i
$477$	68.0079			0.142574
$478$	194.390	−	559.185i	0.406673	−	1.16984i
$479$			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
$482$	879.935	+	305.893i	1.82559	+	0.634632i
$483$			27.7128i			0.0573764i
$484$	70.5876	+	55.8229i	0.145842	+	0.115337i
$485$		0			0
$486$	10.2371	−	29.4483i	0.0210640	−	0.0605932i
$487$		−	201.243i		−	0.413230i	−0.978422	−	0.206615i	$-0.933755\pi$
$487$		−	201.243i		−	0.413230i	0.978422	−	0.206615i	$-0.0662447\pi$
$488$	163.307	+	256.411i	0.334646	+	0.525433i
$489$	31.9036			0.0652426
$490$		0			0
$491$			347.368i			0.707470i	0.935346	+	0.353735i	$0.115089\pi$
$491$			347.368i			0.707470i	−0.935346	+	0.353735i	$0.884911\pi$
$492$	−332.197	+	420.061i	−0.675198	+	0.853783i
$493$	6.02513			0.0122214
$494$	129.897	−	373.664i	0.262949	−	0.756404i
$495$		0			0
$496$	716.591	−	169.711i	1.44474	−	0.342159i
$497$	−68.7610			−0.138352
$498$	−78.9660	−	27.4510i	−0.158566	−	0.0551225i
$499$			672.277i			1.34725i	0.739074	+	0.673625i	$0.235264\pi$
$499$			672.277i			1.34725i	−0.739074	+	0.673625i	$0.764736\pi$
$500$		0			0
$501$	160.894			0.321145
$502$	93.0401	−	267.641i	0.185339	−	0.533149i
$503$		−	436.350i		−	0.867496i	−0.901034	−	0.433748i	$-0.857191\pi$
$503$		−	436.350i		−	0.867496i	0.901034	−	0.433748i	$-0.142809\pi$
$504$	193.423	−	123.190i	0.383775	−	0.244425i
$505$		0			0
$506$	−31.3954	−	10.9140i	−0.0620462	−	0.0215692i
$507$			193.817i			0.382282i
$508$	476.523	−	602.559i	0.938037	−	1.18614i
$509$	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
$512$	−507.644	+	66.6415i	−0.991493	+	0.130159i
$513$	136.016			0.265138
$514$	−78.8796	−	27.4210i	−0.153462	−	0.0533482i
$515$		0			0
$516$	227.148	+	179.636i	0.440209	+	0.348131i
$517$	−139.807			−0.270419
$518$	−142.248	+	409.193i	−0.274610	+	0.789947i
$519$			203.518i			0.392135i
$520$		0			0
$521$	−743.100			−1.42629			−0.713147	−	0.701014i	$-0.752731\pi$
$521$	−743.100			−1.42629			−0.713147	+	0.701014i	$0.752731\pi$
$522$	−1.98638	−	0.690526i	−0.00380532	−	0.00132285i
$523$			366.211i			0.700212i	0.936710	+	0.350106i	$0.113854\pi$
$523$			366.211i			0.700212i	−0.936710	+	0.350106i	$0.886146\pi$
$524$	−105.272	+	133.115i	−0.200900	+	0.254037i
$525$		0			0
$526$	−133.498	+	384.023i	−0.253799	+	0.730083i
$527$		−	791.196i		−	1.50132i
$528$	63.3855	+	267.641i	0.120048	+	0.506895i
$529$	526.196			0.994699
$530$		0			0
$531$			284.341i			0.535481i
$532$	784.727	+	620.586i	1.47505	+	1.16652i
$533$	−584.105			−1.09588
$534$	−113.973	+	327.855i	−0.213432	+	0.613961i
$535$		0			0
$536$	201.402	−	128.272i	0.375750	−	0.239314i
$537$	401.815			0.748259
$538$	461.033	+	160.269i	0.856939	+	0.297898i
$539$		−	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	$0.449575\pi$
$542$	−306.412	+	881.430i	−0.565336	+	1.62625i
$543$			377.754i			0.695680i
$544$	−56.0208	+	547.228i	−0.102979	+	1.00593i
$545$		0			0
$546$	236.248	+	82.1269i	0.432688	+	0.150416i
$547$			507.600i			0.927971i	0.885843	+	0.463986i	$0.153581\pi$
$547$			507.600i			0.927971i	−0.885843	+	0.463986i	$0.846419\pi$
$548$	−648.997	−	513.247i	−1.18430	−	0.936581i
$549$	−114.000			−0.207650
$550$		0			0
$551$		−	9.17469i		−	0.0166510i
$552$	12.4644	+	19.5705i	0.0225804	+	0.0354537i
$553$	439.779			0.795261
$554$	−933.561	−	324.534i	−1.68513	−	0.585802i
$555$		0			0
$556$	−114.199	+	144.404i	−0.205394	+	0.259720i
$557$	788.492			1.41561			0.707803	−	0.706410i	$-0.249686\pi$
$557$	788.492			1.41561			0.707803	+	0.706410i	$0.249686\pi$
$558$	−90.6772	+	260.843i	−0.162504	+	0.467461i
$559$			315.854i			0.565035i
$560$		0			0
$561$	295.505			0.526747
$562$	−81.9910	−	28.5026i	−0.145892	−	0.0507164i
$563$			936.102i			1.66270i	0.555747	+	0.831351i	$0.312432\pi$
$563$			936.102i			1.66270i	−0.555747	+	0.831351i	$0.687568\pi$
$564$	76.5498	+	60.5380i	0.135727	+	0.107337i
$565$		0			0
$566$	−204.096	+	587.107i	−0.360594	+	1.03729i
$567$			85.9955i			0.151667i
$568$	−48.5582	+	30.9266i	−0.0854898	+	0.0544482i
$569$	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	$0.715947\pi$
$572$	−186.080	+	235.297i	−0.325315	+	0.411359i
$573$	237.651			0.414749
$574$	485.045	−	1395.29i	0.845026	−	2.43081i
$575$		0			0
$576$	81.1856	−	173.991i	0.140947	−	0.302068i
$577$	−522.147			−0.904934			−0.452467	−	0.891781i	$-0.649456\pi$
$577$	−522.147			−0.904934			−0.452467	+	0.891781i	$0.649456\pi$
$578$	12.2886	+	4.27189i	0.0212605	+	0.00739081i
$579$			64.1361i			0.110771i
$580$		0			0
$581$	230.598			0.396898
$582$	149.986	−	431.453i	0.257709	−	0.741329i
$583$		−	224.988i		−	0.385915i
$584$	−147.752	−	231.988i	−0.253001	−	0.397240i
$585$		0			0
$586$	−463.223	−	161.031i	−0.790484	−	0.274796i
$587$			95.8440i			0.163278i	0.996662	+	0.0816388i	$0.0260154\pi$
$587$			95.8440i			0.163278i	−0.996662	+	0.0816388i	$0.973985\pi$
$588$	−181.783	+	229.863i	−0.309154	+	0.390923i
$589$	−1204.78			−2.04547
$590$		0			0
$591$		−	337.008i		−	0.570234i
$592$	83.5883	+	352.946i	0.141197	+	0.596192i
$593$	878.624			1.48166			0.740829	−	0.671693i	$-0.234433\pi$
$593$	878.624			1.48166			0.740829	+	0.671693i	$0.234433\pi$
$594$	−97.4228	−	33.8671i	−0.164011	−	0.0570154i
$595$		0			0
$596$	−36.5498	−	28.9047i	−0.0613252	−	0.0484979i
$597$	304.906			0.510730
$598$	−8.30957	+	23.9034i	−0.0138956	+	0.0399723i
$599$			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	$0.425244\pi$
$602$	−754.501	−	262.288i	−1.25332	−	0.435694i
$603$			89.5430i			0.148496i
$604$	311.203	−	393.513i	0.515236	−	0.651512i
$605$		0			0
$606$	33.4983	−	96.3619i	0.0552778	−	0.159013i
$607$			747.564i			1.23157i	0.787914	+	0.615786i	$0.211161\pi$
$607$			747.564i			1.23157i	−0.787914	+	0.615786i	$0.788839\pi$
$608$	833.285	+	85.3049i	1.37053	+	0.140304i
$609$	5.80066			0.00952490
$610$		0			0
$611$			106.444i			0.174213i
$612$	−161.801	−	127.957i	−0.264381	−	0.209081i
$613$	457.152			0.745761			0.372881	−	0.927879i	$-0.378370\pi$
$613$	457.152			0.745761			0.372881	+	0.927879i	$0.378370\pi$
$614$	−221.650	+	637.600i	−0.360993	+	1.03844i
$615$		0			0
$616$	−407.547	−	639.894i	−0.661601	−	1.03879i
$617$	764.888			1.23969			0.619844	−	0.784725i	$-0.287196\pi$
$617$	764.888			1.23969			0.619844	+	0.784725i	$0.287196\pi$
$618$	−470.473	−	163.551i	−0.761283	−	0.264645i
$619$		−	365.359i		−	0.590240i	−0.955460	−	0.295120i	$-0.904640\pi$
$619$		−	365.359i		−	0.590240i	0.955460	−	0.295120i	$-0.0953597\pi$
$620$		0			0
$621$	−8.70099			−0.0140113
$622$	280.912	−	808.077i	0.451627	−	1.29916i
$623$		−	957.410i		−	1.53677i
$624$	203.773	−	48.2598i	0.326560	−	0.0773393i
$625$		0			0
$626$	158.447	+	55.0810i	0.253110	+	0.0879888i
$627$		−	449.976i		−	0.717666i
$628$	618.771	+	489.343i	0.985304	+	0.779209i
$629$	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	$-0.0156842\pi$
$632$	310.567	−	197.799i	0.491403	−	0.312973i
$633$	35.8868			0.0566932
$634$	−211.966	−	73.6859i	−0.334331	−	0.116224i
$635$		0			0
$636$	−97.4228	+	123.190i	−0.153180	+	0.193696i
$637$	−319.630			−0.501773
$638$	−2.28444	+	6.57147i	−0.00358063	+	0.0103001i
$639$		−	21.5889i		−	0.0337855i
$640$		0			0
$641$	−1111.69			−1.73431			−0.867154	−	0.498041i	$-0.834053\pi$
$641$	−1111.69			−1.73431			−0.867154	+	0.498041i	$0.834053\pi$
$642$	−114.853	−	39.9264i	−0.178898	−	0.0621906i
$643$		−	468.983i		−	0.729367i	−0.931132	−	0.364683i	$-0.881177\pi$
$643$		−	468.983i		−	0.729367i	0.931132	−	0.364683i	$-0.118823\pi$
$644$	−50.1993	−	39.6992i	−0.0779493	−	0.0616447i
$645$		0			0
$646$	295.505	−	850.054i	0.457438	−	1.31587i
$647$		−	96.7647i		−	0.149559i	−0.997200	−	0.0747795i	$-0.976175\pi$
$647$		−	96.7647i		−	0.149559i	0.997200	−	0.0747795i	$-0.0238253\pi$
$648$	38.6781	+	60.7290i	0.0596884	+	0.0937175i
$649$	940.675			1.44942
$650$		0			0
$651$		−	761.720i		−	1.17008i
$652$	−45.7027	+	57.7907i	−0.0700961	+	0.0886360i
$653$	−920.353			−1.40942			−0.704712	−	0.709494i	$-0.748924\pi$
$653$	−920.353			−1.40942			−0.704712	+	0.709494i	$0.748924\pi$
$654$	172.323	−	495.707i	0.263491	−	0.757962i
$655$		0			0
$656$	−285.024	−	1203.49i	−0.434488	−	1.83459i
$657$	103.142			0.156989
$658$	−254.270	−	88.3921i	−0.386429	−	0.134335i
$659$		−	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	$0.574400\pi$
$662$	87.0935	−	250.535i	0.131561	−	0.378451i
$663$		−	224.988i		−	0.339349i
$664$	162.846	−	103.716i	0.245249	−	0.156198i
$665$		0			0
$666$	−128.474	−	44.6616i	−0.192904	−	0.0670595i
$667$			0.586909i			0.000879924i
$668$	−230.484	+	291.445i	−0.345035	+	0.436295i
$669$	−168.055			−0.251203
$670$		0			0
$671$			377.142i			0.562060i
$672$	−53.9337	+	526.841i	−0.0802585	+	0.783990i
$673$	−556.892			−0.827476			−0.413738	−	0.910396i	$-0.635777\pi$
$673$	−556.892			−0.827476			−0.413738	+	0.910396i	$0.635777\pi$
$674$	−39.2442	−	13.6425i	−0.0582258	−	0.0202411i
$675$		0			0
$676$	−351.083	−	277.647i	−0.519353	−	0.410721i
$677$	58.1920			0.0859557			0.0429779	−	0.999076i	$-0.486316\pi$
$677$	58.1920			0.0859557			0.0429779	+	0.999076i	$0.486316\pi$
$678$	36.7435	−	105.697i	0.0541939	−	0.155895i
$679$			1259.94i			1.85558i
$680$		0			0
$681$	705.389			1.03581
$682$	862.940	+	299.984i	1.26531	+	0.439860i
$683$			357.274i			0.523096i	0.965191	+	0.261548i	$0.0842329\pi$
$683$			357.274i			0.523096i	−0.965191	+	0.261548i	$0.915767\pi$
$684$	−194.846	+	246.381i	−0.284862	+	0.360206i
$685$		0			0
$686$	−42.0482	+	120.956i	−0.0612947	+	0.176321i
$687$		−	13.6780i		−	0.0199098i
$688$	−650.788	+	154.127i	−0.945913	+	0.224021i
$689$	−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	$0.853276\pi$
$692$	−368.655	−	291.544i	−0.532739	−	0.421307i
$693$	284.496			0.410528
$694$	−5.84222	+	16.8058i	−0.00841818	+	0.0242159i
$695$		0			0
$696$	4.09636	−	2.60896i	0.00588557	−	0.00374850i
$697$	−1328.79			−1.90644
$698$	−36.6524	−	12.7415i	−0.0525107	−	0.0182543i
$699$		−	48.7543i		−	0.0697487i
$700$		0			0
$701$	−886.028			−1.26395			−0.631975	−	0.774989i	$-0.717755\pi$
$701$	−886.028			−1.26395			−0.631975	+	0.774989i	$0.717755\pi$
$702$	−25.7854	+	74.1746i	−0.0367313	+	0.105662i
$703$		−	593.397i		−	0.844093i
$704$	−575.609	−	268.584i	−0.817626	−	0.381511i
$705$		0			0
$706$	151.677	+	52.7276i	0.214840	+	0.0746849i
$707$			281.398i			0.398017i
$708$	−515.058	−	407.324i	−0.727483	−	0.575316i
$709$	760.887			1.07318			0.536592	−	0.843842i	$-0.319712\pi$
$709$	760.887			1.07318			0.536592	+	0.843842i	$0.319712\pi$
$710$		0			0
$711$			138.078i			0.194202i
$712$	−430.613	−	676.111i	−0.604794	−	0.949594i
$713$	77.0706			0.108093
$714$	537.444	+	186.832i	0.752722	+	0.261669i
$715$		0			0
$716$	−575.609	+	727.853i	−0.803923	+	1.01655i
$717$	−512.695			−0.715056
$718$	206.283	−	593.397i	0.287302	−	0.826458i
$719$			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
$722$	−612.441	−	212.903i	−0.848257	−	0.294880i
$723$		−	806.779i		−	1.11588i
$724$	−684.268	−	541.141i	−0.945122	−	0.747432i
$725$		0			0
$726$	25.5909	−	73.6153i	0.0352492	−	0.101398i
$727$		−	327.332i		−	0.450250i	−0.974330	−	0.225125i	$-0.927721\pi$
$727$		−	327.332i		−	0.450250i	0.974330	−	0.225125i	$-0.0722790\pi$
$728$	−487.195	+	310.293i	−0.669224	+	0.426227i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$			718.542i			0.982958i
$732$	163.307	−	206.501i	0.223098	−	0.282105i
$733$	−947.567			−1.29272			−0.646362	−	0.763031i	$-0.723710\pi$
$733$	−947.567			−1.29272			−0.646362	+	0.763031i	$0.723710\pi$
$734$	313.120	−	900.727i	0.426595	−	1.22715i
$735$		0			0
$736$	−53.3056	−	5.45700i	−0.0724261	−	0.00741440i
$737$	296.232			0.401943
$738$	438.079	+	152.290i	0.593602	+	0.206354i
$739$		−	183.234i		−	0.247948i	−0.992285	−	0.123974i	$-0.960436\pi$
$739$		−	183.234i		−	0.247948i	0.992285	−	0.123974i	$-0.0395640\pi$
$740$		0			0
$741$	−342.598			−0.462345
$742$	142.248	−	409.193i	0.191709	−	0.551473i
$743$			183.712i			0.247258i	0.992329	+	0.123629i	$0.0394532\pi$
$743$			183.712i			0.247258i	−0.992329	+	0.123629i	$0.960547\pi$
$744$	−342.598	−	537.918i	−0.460481	−	0.723008i
$745$		0			0
$746$	−162.715	−	56.5648i	−0.218117	−	0.0758241i
$747$			72.4009i			0.0969222i
$748$	−423.317	+	535.281i	−0.565932	+	0.715617i
$749$	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	$-0.0739354\pi$
$752$	−219.319	+	51.9414i	−0.291647	+	0.0690710i
$753$	−245.390			−0.325882
$754$	5.00331	+	1.73930i	0.00663569	+	0.00230677i
$755$		0			0
$756$	−155.773	−	123.190i	−0.206049	−	0.162950i
$757$	−549.335			−0.725674			−0.362837	−	0.931853i	$-0.618192\pi$
$757$	−549.335			−0.725674			−0.362837	+	0.931853i	$0.618192\pi$
$758$	419.005	−	1205.32i	0.552778	−	1.59013i
$759$			28.7852i			0.0379252i
$760$		0			0
$761$	251.485			0.330467			0.165233	−	0.986255i	$-0.447162\pi$
$761$	251.485			0.330467			0.165233	+	0.986255i	$0.447162\pi$
$762$	−628.405	−	218.453i	−0.824678	−	0.286683i
$763$			1447.57i			1.89721i
$764$	−340.440	+	430.484i	−0.445602	+	0.563461i
$765$		0			0
$766$	142.337	−	409.450i	0.185819	−	0.534529i
$767$		−	716.200i		−	0.933768i
$768$	198.869	+	396.307i	0.258945	+	0.516024i
$769$	−583.691			−0.759026			−0.379513	−	0.925186i	$-0.623908\pi$
$769$	−583.691			−0.759026			−0.379513	+	0.925186i	$0.623908\pi$
$770$		0			0
$771$			72.3216i			0.0938024i
$772$	−116.177	−	91.8764i	−0.150488	−	0.119011i
$773$	1328.04			1.71803			0.859015	−	0.511951i	$-0.171077\pi$
$773$	1328.04			1.71803			0.859015	+	0.511951i	$0.171077\pi$
$774$	82.3505	−	236.891i	0.106396	−	0.306060i
$775$		0			0
$776$	566.681	+	889.753i	0.730259	+	1.14659i
$777$	375.173			0.482848
$778$	−900.424	−	313.015i	−1.15736	−	0.402333i
$779$			2023.40i			2.59743i
$780$		0			0
$781$	−71.4219			−0.0914492
$782$	−18.9036	+	54.3784i	−0.0241734	+	0.0695376i
$783$			1.82123i			0.00232597i
$784$	−155.969	−	658.567i	−0.198940	−	0.840009i
$785$		0			0
$786$	138.825	+	48.2598i	0.176622	+	0.0613992i
$787$		−	1318.83i		−	1.67577i	−0.545850	−	0.837883i	$-0.683793\pi$
$787$		−	1318.83i		−	1.67577i	0.545850	−	0.837883i	$-0.316207\pi$
$788$	610.461	+	482.772i	0.774697	+	0.612654i
$789$	352.096			0.446256
$790$		0			0
$791$			308.658i			0.390212i
$792$	200.908	−	127.957i	0.253671	−	0.161562i
$793$	287.144			0.362099
$794$	−81.3812	−	28.2906i	−0.102495	−	0.0356305i
$795$		0			0
$796$	−436.784	+	552.310i	−0.548724	+	0.693857i
$797$	−1277.40			−1.60276			−0.801381	−	0.598154i	$-0.795901\pi$
$797$	−1277.40			−1.60276			−0.801381	+	0.598154i	$0.795901\pi$
$798$	284.496	−	818.385i	0.356511	−	1.02555i
$799$			242.152i			0.303069i
$800$		0			0
$801$	300.598			0.375278
$802$	−318.682	−	110.784i	−0.397359	−	0.138134i
$803$		−	341.220i		−	0.424931i
$804$	−162.199	−	128.272i	−0.201740	−	0.159543i
$805$		0			0
$806$	228.399	−	657.015i	0.283373	−	0.815155i
$807$		−	422.704i		−	0.523797i
$808$	126.564	+	198.720i	0.156639	+	0.245940i
$809$	−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	$-0.198437\pi$
$812$	−8.30957	+	10.5074i	−0.0102335	+	0.0129401i
$813$	808.149			0.994033
$814$	−147.752	+	425.027i	−0.181514	+	0.522146i
$815$		0			0
$816$	463.567	−	109.787i	0.568097	−	0.134543i
$817$	1094.15			1.33923
$818$	−706.319	−	245.538i	−0.863471	−	0.300169i
$819$		−	216.606i		−	0.264477i
$820$		0			0
$821$	1169.34			1.42429			0.712144	−	0.702033i	$-0.247724\pi$
$821$	1169.34			1.42429			0.712144	+	0.702033i	$0.247724\pi$
$822$	−235.288	+	676.833i	−0.286239	+	0.823398i
$823$			1251.71i			1.52091i	0.649389	+	0.760457i	$0.275025\pi$
$823$			1251.71i			1.52091i	−0.649389	+	0.760457i	$0.724975\pi$
$824$	970.220	−	617.930i	1.17745	−	0.749915i
$825$		0			0
$826$	1710.83	+	594.738i	2.07123	+	0.720022i
$827$		−	892.104i		−	1.07872i	−0.842074	−	0.539362i	$-0.818666\pi$
$827$		−	892.104i		−	1.07872i	0.842074	−	0.539362i	$-0.181334\pi$
$828$	12.4644	−	15.7611i	0.0150536	−	0.0190351i
$829$	−998.688			−1.20469			−0.602345	−	0.798236i	$-0.705767\pi$
$829$	−998.688			−1.20469			−0.602345	+	0.798236i	$0.705767\pi$
$830$		0			0
$831$			855.946i			1.03002i
$832$	−204.491	+	438.251i	−0.245783	+	0.526743i
$833$	−727.131			−0.872906
$834$	150.598	+	52.3525i	0.180573	+	0.0627728i
$835$		0			0
$836$	815.093	+	644.601i	0.974992	+	0.771054i
$837$	239.157			0.285732
$838$	57.5174	−	165.455i	0.0686365	−	0.197441i
$839$		−	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
$842$	132.809	+	46.1684i	0.157730	+	0.0548318i
$843$			75.1744i			0.0891749i
$844$	−51.4086	+	65.0058i	−0.0609107	+	0.0770211i
$845$		0			0
$846$	27.7525	−	79.8332i	0.0328044	−	0.0943655i
$847$			214.973i			0.253805i
$848$	−83.5883	−	352.946i	−0.0985712	−	0.416209i
$849$	538.296			0.634035
$850$		0			0
$851$			37.9599i			0.0446062i
$852$	39.1064	+	30.9266i	0.0458995	+	0.0362988i
$853$	−832.689			−0.976189			−0.488094	−	0.872791i	$-0.662308\pi$
$853$	−832.689			−0.976189			−0.488094	+	0.872791i	$0.662308\pi$
$854$	−238.447	+	685.920i	−0.279212	+	0.803185i
$855$		0			0
$856$	236.852	−	150.850i	0.276696	−	0.176227i
$857$	149.415			0.174347			0.0871735	−	0.996193i	$-0.472217\pi$
$857$	149.415			0.174347			0.0871735	+	0.996193i	$0.472217\pi$
$858$	245.390	+	85.3049i	0.286002	+	0.0994230i
$859$			394.144i			0.458840i	0.973327	+	0.229420i	$0.0736830\pi$
$859$			394.144i			0.458840i	−0.973327	+	0.229420i	$0.926317\pi$
$860$		0			0
$861$	−1279.29			−1.48581
$862$	−162.451	+	467.308i	−0.188458	+	0.542121i
$863$		−	1409.58i		−	1.63335i	−0.577095	−	0.816677i	$-0.695814\pi$
$863$		−	1409.58i		−	1.63335i	0.577095	−	0.816677i	$-0.304186\pi$
$864$	−165.412	−	16.9336i	−0.191450	−	0.0195990i
$865$		0			0
$866$	−1201.94	−	417.831i	−1.38792	−	0.482484i
$867$		−	11.2669i		−	0.0129953i
$868$	1379.79	+	1091.18i	1.58962	+	1.25712i
$869$	456.797			0.525659
$870$		0			0
$871$		−	225.542i		−	0.258946i
$872$	651.074	+	1022.26i	0.746644	+	1.17232i
$873$	−395.583			−0.453131
$874$	82.8040	+	28.7852i	0.0947414	+	0.0329350i
$875$		0			0
$876$	−147.752	+	186.832i	−0.168667	+	0.213278i
$877$	872.780			0.995189			0.497594	−	0.867410i	$-0.334217\pi$
$877$	872.780			0.995189			0.497594	+	0.867410i	$0.334217\pi$
$878$	505.528	−	1454.21i	0.575772	−	1.65627i
$879$			424.712i			0.483176i
$880$		0			0
$881$	1103.38			1.25241			0.626206	−	0.779657i	$-0.284607\pi$
$881$	1103.38			1.25241			0.626206	+	0.779657i	$0.284607\pi$
$882$	239.722	+	83.3348i	0.271794	+	0.0944839i
$883$		−	536.884i		−	0.608023i	−0.952668	−	0.304011i	$-0.901674\pi$
$883$		−	536.884i		−	0.608023i	0.952668	−	0.304011i	$-0.0983261\pi$
$884$	407.547	+	322.300i	0.461025	+	0.364593i
$885$		0			0
$886$	−402.048	+	1156.54i	−0.453779	+	1.30535i
$887$			888.945i			1.00219i	0.865392	+	0.501096i	$0.167070\pi$
$887$			888.945i			1.00219i	−0.865392	+	0.501096i	$0.832930\pi$
$888$	264.943	−	168.741i	0.298359	−	0.190024i
$889$	1835.08			2.06421
$890$		0			0
$891$			89.3232i			0.100251i
$892$	240.742	−	304.417i	0.269890	−	0.341274i
$893$	368.734			0.412916
$894$	−13.2508	+	38.1175i	−0.0148220	+	0.0426371i
$895$		0			0
$896$	−877.066	−	852.408i	−0.978868	−	0.951348i
$897$	21.9162			0.0244327
$898$	−332.288	−	115.514i	−0.370032	−	0.128634i
$899$		−	16.1319i		−	0.0179443i
$900$		0			0
$901$	−389.691			−0.432510
$902$	503.814	−	1449.28i	0.558553	−	1.60674i
$903$			691.773i			0.766083i
$904$	138.825	+	217.971i	0.153567	+	0.241118i
$905$		0			0
$906$	−410.392	−	142.665i	−0.452971	−	0.157467i
$907$			1668.40i			1.83947i	0.392543	+	0.919734i	$0.371595\pi$
$907$			1668.40i			1.83947i	−0.392543	+	0.919734i	$0.628405\pi$
$908$	−1010.48	+	1277.75i	−1.11287	+	1.40721i
$909$	−88.3505			−0.0971953
$910$		0			0
$911$		−	1498.13i		−	1.64449i	−0.569131	−	0.822247i	$-0.692720\pi$
$911$		−	1498.13i		−	1.64449i	0.569131	−	0.822247i	$-0.307280\pi$
$912$	−167.177	−	705.891i	−0.183308	−	0.774004i
$913$	239.521			0.262345
$914$	−690.199	−	239.935i	−0.755142	−	0.262510i
$915$		0			0
$916$	24.7766	+	19.5941i	0.0270487	+	0.0213909i
$917$	−405.399			−0.442093
$918$	−58.6596	+	168.741i	−0.0638994	+	0.183814i
$919$		−	1094.82i		−	1.19131i	−0.803240	−	0.595656i	$-0.796892\pi$
$919$		−	1094.82i		−	1.19131i	0.803240	−	0.595656i	$-0.203108\pi$
$920$		0			0
$921$	584.591			0.634735
$922$	582.507	+	202.497i	0.631787	+	0.219629i
$923$			54.3784i			0.0589148i
$924$	−407.547	+	515.339i	−0.441068	+	0.557727i
$925$		0			0
$926$	−60.8314	+	174.988i	−0.0656926	+	0.188972i
$927$			431.358i			0.465327i
$928$	−1.14222	+	11.1576i	−0.00123084	+	0.0120233i
$929$	−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
$932$	88.3142	+	69.8417i	0.0947578	+	0.0749374i
$933$	−740.894			−0.794099
$934$	−398.035	+	1144.99i	−0.426162	+	1.22590i
$935$		0			0
$936$	−97.4228	−	152.965i	−0.104084	−	0.163424i
$937$	−1272.49			−1.35805			−0.679025	−	0.734115i	$-0.737597\pi$
$937$	−1272.49			−1.35805			−0.679025	+	0.734115i	$0.737597\pi$
$938$	538.766	+	187.292i	0.574378	+	0.199671i
$939$		−	145.274i		−	0.154711i
$940$		0			0
$941$	707.360			0.751711			0.375856	−	0.926678i	$-0.377349\pi$
$941$	707.360			0.751711			0.375856	+	0.926678i	$0.377349\pi$
$942$	224.330	−	645.311i	0.238142	−	0.685044i
$943$		−	129.438i		−	0.137262i
$944$	1475.66	−	349.482i	1.56320	−	0.370214i
$945$		0			0
$946$	−783.698	−	272.437i	−0.828433	−	0.287989i
$947$			284.977i			0.300926i	0.988616	+	0.150463i	$0.0480765\pi$
$947$			284.977i			0.300926i	−0.988616	+	0.150463i	$0.951924\pi$
$948$	−250.115	−	197.799i	−0.263835	−	0.208649i
$949$	−259.794			−0.273756
$950$		0			0
$951$			194.343i			0.204357i
$952$	−1108.33	+	705.891i	−1.16421	+	0.741482i
$953$	−295.247			−0.309808			−0.154904	−	0.987930i	$-0.549507\pi$
$953$	−295.247			−0.309808			−0.154904	+	0.987930i	$0.549507\pi$
$954$	128.474	+	44.6616i	0.134669	+	0.0468151i
$955$		0			0
$956$	734.447	−	928.702i	0.768250	−	0.971446i
$957$	6.02513			0.00629585
$958$	−91.2483	+	262.486i	−0.0952487	+	0.273994i
$959$		−	1976.50i		−	2.06100i
$960$		0			0
$961$	−1157.38			−1.20435
$962$	323.602	+	112.494i	0.336385	+	0.116938i
$963$			105.304i			0.109350i
$964$	1461.41	+	1155.73i	1.51598	+	1.19889i
$965$		0			0
$966$	−18.1993	+	52.3525i	−0.0188399	+	0.0541951i
$967$			348.013i			0.359889i	0.983677	+	0.179945i	$0.0575918\pi$
$967$			348.013i			0.359889i	−0.983677	+	0.179945i	$0.942408\pi$
$968$	96.6881	+	151.811i	0.0998844	+	0.156830i
$969$	−779.382			−0.804316
$970$		0			0
$971$		−	798.691i		−	0.822545i	−0.911513	−	0.411272i	$-0.865085\pi$
$971$		−	798.691i		−	0.822545i	0.911513	−	0.411272i	$-0.134915\pi$
$972$	38.6781	−	48.9081i	0.0397923	−	0.0503170i
$973$	−439.779			−0.451983
$974$	132.159	−	380.170i	0.135687	−	0.390318i
$975$		0			0
$976$	140.117	+	591.634i	0.143563	+	0.606183i
$977$	−721.834			−0.738827			−0.369413	−	0.929265i	$-0.620441\pi$
$977$	−721.834			−0.738827			−0.369413	+	0.929265i	$0.620441\pi$
$978$	60.2694	+	20.9515i	0.0616252	+	0.0214228i
$979$		−	994.458i		−	1.01579i
$980$		0			0
$981$	−454.495			−0.463298
$982$	−228.121	+	656.216i	−0.232302	+	0.668244i
$983$			1717.25i			1.74695i	0.486870	+	0.873474i	$0.338139\pi$
$983$			1717.25i			1.74695i	−0.486870	+	0.873474i	$0.661861\pi$
$984$	−903.416	+	575.383i	−0.918106	+	0.584739i
$985$		0			0
$986$	11.3821	+	3.95677i	0.0115437	+	0.00401296i
$987$			233.131i			0.236201i
$988$	490.779	−	620.586i	0.496740	−	0.628124i
$989$	−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	$0.944754\pi$
$992$	1465.17	+	149.992i	1.47699	+	0.151202i
$993$	−229.706			−0.231325
$994$	−129.897	−	45.1562i	−0.130681	−	0.0454288i
$995$		0			0
$996$	−131.148	−	103.716i	−0.131675	−	0.104132i
$997$	1586.05			1.59082			0.795410	−	0.606072i	$-0.207256\pi$
$997$	1586.05			1.59082			0.795410	+	0.606072i	$0.207256\pi$
$998$	−441.493	+	1270.00i	−0.442377	+	1.27255i
$999$			117.793i			0.117911i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.f.b.19.3	✓	8	20.3	even	4
60.3.f.b.19.4	yes	8	5.2	odd	4
60.3.f.b.19.5	yes	8	5.3	odd	4
60.3.f.b.19.6	yes	8	20.7	even	4
180.3.f.h.19.3		8	60.47	odd	4
180.3.f.h.19.4		8	15.8	even	4
180.3.f.h.19.5		8	15.2	even	4
180.3.f.h.19.6		8	60.23	odd	4
300.3.c.f.151.1		8	5.4	even	2	inner
300.3.c.f.151.2		8	20.19	odd	2	inner
300.3.c.f.151.7		8	4.3	odd	2	inner
300.3.c.f.151.8		8	1.1	even	1	trivial
900.3.c.r.451.1		8	3.2	odd	2
900.3.c.r.451.2		8	12.11	even	2
900.3.c.r.451.7		8	60.59	even	2
900.3.c.r.451.8		8	15.14	odd	2
960.3.j.e.319.3		8	40.27	even	4
960.3.j.e.319.4		8	40.13	odd	4
960.3.j.e.319.7		8	40.37	odd	4
960.3.j.e.319.8		8	40.3	even	4

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	300.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.88911 + 0.656712i) q^{2} -1.73205i q^{3} +(3.13746 + 2.48120i) q^{4} +(1.13746 - 3.27203i) q^{6} +9.55505i q^{7} +(4.29756 + 6.74766i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(1.88911 + 0.656712i) q^{2} -1.73205i q^{3} +(3.13746 + 2.48120i) q^{4} +(1.13746 - 3.27203i) q^{6} +9.55505i q^{7} +(4.29756 + 6.74766i) q^{8} -3.00000 q^{9} +9.92480i q^{11} +(4.29756 - 5.43424i) q^{12} +7.55643 q^{13} +(-6.27492 + 18.0505i) q^{14} +(3.68729 + 15.5693i) q^{16} +17.1903 q^{17} +(-5.66732 - 1.97014i) q^{18} -26.1762i q^{19} +16.5498 q^{21} +(-6.51774 + 18.7490i) q^{22} +1.67451i q^{23} +(11.6873 - 7.44360i) q^{24} +(14.2749 + 4.96240i) q^{26} +5.19615i q^{27} +(-23.7080 + 29.9786i) q^{28} +0.350497 q^{29} -46.0258i q^{31} +(-3.25887 + 31.8336i) q^{32} +17.1903 q^{33} +(32.4743 + 11.2890i) q^{34} +(-9.41238 - 7.44360i) q^{36} +22.6693 q^{37} +(17.1903 - 49.4498i) q^{38} -13.0881i q^{39} -77.2990 q^{41} +(31.2644 + 10.8685i) q^{42} +41.7994i q^{43} +(-24.6254 + 31.1386i) q^{44} +(-1.09967 + 3.16332i) q^{46} +14.0866i q^{47} +(26.9669 - 6.38658i) q^{48} -42.2990 q^{49} -29.7744i q^{51} +(23.7080 + 18.7490i) q^{52} -22.6693 q^{53} +(-3.41238 + 9.81609i) q^{54} +(-64.4743 + 41.0634i) q^{56} -45.3386 q^{57} +(0.662126 + 0.230175i) q^{58} -94.7802i q^{59} +38.0000 q^{61} +(30.2257 - 86.9478i) q^{62} -28.6652i q^{63} +(-27.0619 + 57.9970i) q^{64} +(32.4743 + 11.2890i) q^{66} -29.8477i q^{67} +(53.9337 + 42.6525i) q^{68} +2.90033 q^{69} +7.19630i q^{71} +(-12.8927 - 20.2430i) q^{72} -34.3805 q^{73} +(42.8248 + 14.8872i) q^{74} +(64.9485 - 82.1269i) q^{76} -94.8320 q^{77} +(8.59513 - 24.7249i) q^{78} -46.0258i q^{79} +9.00000 q^{81} +(-146.026 - 50.7632i) q^{82} -24.1336i q^{83} +(51.9244 + 41.0634i) q^{84} +(-27.4502 + 78.9636i) q^{86} -0.607078i q^{87} +(-66.9692 + 42.6525i) q^{88} -100.199 q^{89} +72.2021i q^{91} +(-4.15479 + 5.25370i) q^{92} -79.7191 q^{93} +(-9.25083 + 26.6111i) q^{94} +(55.1375 + 5.64452i) q^{96} +131.861 q^{97} +(-79.9074 - 27.7783i) q^{98} -29.7744i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{4} - 6 q^{6} - 24 q^{9}+O(q^{10}) \) 8 * q + 10 * q^4 - 6 * q^6 - 24 * q^9	\( 8 q + 10 q^{4} - 6 q^{6} - 24 q^{9} - 20 q^{14} - 46 q^{16} + 72 q^{21} + 18 q^{24} + 84 q^{26} + 184 q^{29} - 12 q^{34} - 30 q^{36} - 256 q^{41} - 348 q^{44} + 112 q^{46} + 24 q^{49} + 18 q^{54} - 244 q^{56} + 304 q^{61} + 10 q^{64} - 12 q^{66} + 144 q^{69} + 252 q^{74} - 24 q^{76} + 72 q^{81} + 204 q^{84} - 280 q^{86} - 560 q^{89} - 376 q^{94} + 426 q^{96}+O(q^{100}) \) 8 * q + 10 * q^4 - 6 * q^6 - 24 * q^9 - 20 * q^14 - 46 * q^16 + 72 * q^21 + 18 * q^24 + 84 * q^26 + 184 * q^29 - 12 * q^34 - 30 * q^36 - 256 * q^41 - 348 * q^44 + 112 * q^46 + 24 * q^49 + 18 * q^54 - 244 * q^56 + 304 * q^61 + 10 * q^64 - 12 * q^66 + 144 * q^69 + 252 * q^74 - 24 * q^76 + 72 * q^81 + 204 * q^84 - 280 * q^86 - 560 * q^89 - 376 * q^94 + 426 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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