LMFDB - Embedded newform 300.3.c.d.151.6

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:	8.0.85100625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + x^{5} + 3x^{4} + 2x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + x^5 + 3x^4 + 2x^3 - 8x^2 - 8*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.6
Root			$1.40906 + 0.120653i$ of defining polynomial
Character	$\chi$	$=$	300.151
Dual form			300.3.c.d.151.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.438172 + 1.95141i) q^{2} +1.73205i q^{3} +(-3.61601 - 1.71011i) q^{4} +(-3.37994 - 0.758935i) q^{6} +6.33166i q^{7} +(4.92155 - 6.30701i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-0.438172 + 1.95141i) q^{2} +1.73205i q^{3} +(-3.61601 - 1.71011i) q^{4} +(-3.37994 - 0.758935i) q^{6} +6.33166i q^{7} +(4.92155 - 6.30701i) q^{8} -3.00000 q^{9} +9.27963i q^{11} +(2.96199 - 6.26312i) q^{12} -18.5674 q^{13} +(-12.3557 - 2.77436i) q^{14} +(10.1511 + 12.3675i) q^{16} -13.9110 q^{17} +(1.31451 - 5.85423i) q^{18} -17.2468i q^{19} -10.9668 q^{21} +(-18.1084 - 4.06607i) q^{22} -33.7148i q^{23} +(10.9241 + 8.52438i) q^{24} +(8.13571 - 36.2327i) q^{26} -5.19615i q^{27} +(10.8278 - 22.8954i) q^{28} -28.6177 q^{29} +23.4939i q^{31} +(-28.5820 + 14.3898i) q^{32} -16.0728 q^{33} +(6.09542 - 27.1461i) q^{34} +(10.8480 + 5.13032i) q^{36} +67.3338 q^{37} +(33.6556 + 7.55706i) q^{38} -32.1597i q^{39} -44.0791 q^{41} +(4.80532 - 21.4007i) q^{42} +50.2937i q^{43} +(15.8691 - 33.5552i) q^{44} +(65.7915 + 14.7729i) q^{46} -31.1594i q^{47} +(-21.4212 + 17.5822i) q^{48} +8.91003 q^{49} -24.0946i q^{51} +(67.1400 + 31.7522i) q^{52} -81.6070 q^{53} +(10.1398 + 2.27681i) q^{54} +(39.9338 + 31.1616i) q^{56} +29.8724 q^{57} +(12.5395 - 55.8449i) q^{58} +19.2751i q^{59} -53.1563 q^{61} +(-45.8462 - 10.2943i) q^{62} -18.9950i q^{63} +(-15.5566 - 62.0805i) q^{64} +(7.04264 - 31.3646i) q^{66} -4.49911i q^{67} +(50.3025 + 23.7893i) q^{68} +58.3958 q^{69} +13.3360i q^{71} +(-14.7647 + 18.9210i) q^{72} -40.8904 q^{73} +(-29.5037 + 131.396i) q^{74} +(-29.4939 + 62.3647i) q^{76} -58.7555 q^{77} +(62.7568 + 14.0915i) q^{78} +141.309i q^{79} +9.00000 q^{81} +(19.3142 - 86.0164i) q^{82} +69.8503i q^{83} +(39.6559 + 18.7543i) q^{84} +(-98.1438 - 22.0373i) q^{86} -49.5673i q^{87} +(58.5266 + 45.6702i) q^{88} -46.3079 q^{89} -117.563i q^{91} +(-57.6559 + 121.913i) q^{92} -40.6926 q^{93} +(60.8049 + 13.6532i) q^{94} +(-24.9239 - 49.5055i) q^{96} -68.5543 q^{97} +(-3.90412 + 17.3871i) q^{98} -27.8389i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 10 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 10 * q^4 - 6 * q^6 + 20 * q^8 - 24 * q^9	$ 8 q - 4 q^{2} + 10 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9} - 16 q^{13} - 20 q^{14} + 34 q^{16} + 12 q^{18} - 48 q^{21} - 68 q^{22} + 18 q^{24} - 36 q^{26} - 28 q^{28} + 64 q^{29} + 76 q^{32} - 92 q^{34} - 30 q^{36} + 112 q^{37} + 40 q^{38} - 16 q^{41} - 108 q^{42} + 172 q^{44} + 152 q^{46} - 48 q^{48} - 56 q^{49} + 128 q^{52} - 352 q^{53} + 18 q^{54} + 116 q^{56} - 144 q^{57} + 204 q^{58} - 176 q^{61} + 56 q^{62} - 110 q^{64} + 108 q^{66} + 184 q^{68} - 96 q^{69} - 60 q^{72} + 240 q^{73} + 132 q^{74} - 24 q^{76} + 288 q^{77} + 240 q^{78} + 72 q^{81} - 40 q^{82} - 36 q^{84} - 200 q^{86} - 140 q^{88} + 80 q^{89} - 144 q^{92} - 144 q^{93} - 96 q^{94} - 174 q^{96} - 432 q^{97} - 660 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 10 * q^4 - 6 * q^6 + 20 * q^8 - 24 * q^9 - 16 * q^13 - 20 * q^14 + 34 * q^16 + 12 * q^18 - 48 * q^21 - 68 * q^22 + 18 * q^24 - 36 * q^26 - 28 * q^28 + 64 * q^29 + 76 * q^32 - 92 * q^34 - 30 * q^36 + 112 * q^37 + 40 * q^38 - 16 * q^41 - 108 * q^42 + 172 * q^44 + 152 * q^46 - 48 * q^48 - 56 * q^49 + 128 * q^52 - 352 * q^53 + 18 * q^54 + 116 * q^56 - 144 * q^57 + 204 * q^58 - 176 * q^61 + 56 * q^62 - 110 * q^64 + 108 * q^66 + 184 * q^68 - 96 * q^69 - 60 * q^72 + 240 * q^73 + 132 * q^74 - 24 * q^76 + 288 * q^77 + 240 * q^78 + 72 * q^81 - 40 * q^82 - 36 * q^84 - 200 * q^86 - 140 * q^88 + 80 * q^89 - 144 * q^92 - 144 * q^93 - 96 * q^94 - 174 * q^96 - 432 * q^97 - 660 * q^98

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 $

$2$	−0.438172	+	1.95141i	−0.219086	+	0.975706i
$2$	−0.438172	+	1.95141i	−0.219086	+	0.975706i
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−3.61601	−	1.71011i	−0.904003	−	0.427526i
$5$		0			0
$5$		0			0
$6$	−3.37994	−	0.758935i	−0.563324	−	0.126489i
$7$			6.33166i			0.904523i	0.891885	+	0.452262i	$0.149383\pi$
$7$			6.33166i			0.904523i	−0.891885	+	0.452262i	$0.850617\pi$
$8$	4.92155	−	6.30701i	0.615194	−	0.788376i
$9$	−3.00000			−0.333333
$10$		0			0
$11$			9.27963i			0.843602i	0.906688	+	0.421801i	$0.138602\pi$
$11$			9.27963i			0.843602i	−0.906688	+	0.421801i	$0.861398\pi$
$12$	2.96199	−	6.26312i	0.246833	−	0.521926i
$13$	−18.5674			−1.42826			−0.714131	−	0.700012i	$-0.753178\pi$
$13$	−18.5674			−1.42826			−0.714131	+	0.700012i	$0.753178\pi$
$14$	−12.3557	−	2.77436i	−0.882549	−	0.198168i
$15$		0			0
$16$	10.1511	+	12.3675i	0.634442	+	0.772970i
$17$	−13.9110			−0.818296			−0.409148	−	0.912468i	$-0.634174\pi$
$17$	−13.9110			−0.818296			−0.409148	+	0.912468i	$0.634174\pi$
$18$	1.31451	−	5.85423i	0.0730286	−	0.325235i
$19$		−	17.2468i		−	0.907727i	−0.891071	−	0.453864i	$-0.850045\pi$
$19$		−	17.2468i		−	0.907727i	0.891071	−	0.453864i	$-0.149955\pi$
$20$		0			0
$21$	−10.9668			−0.522227
$22$	−18.1084	−	4.06607i	−0.823108	−	0.184821i
$23$		−	33.7148i		−	1.46586i	−0.680303	−	0.732931i	$-0.738152\pi$
$23$		−	33.7148i		−	1.46586i	0.680303	−	0.732931i	$-0.261848\pi$
$24$	10.9241	+	8.52438i	0.455169	+	0.355183i
$25$		0			0
$26$	8.13571	−	36.2327i	0.312912	−	1.39356i
$27$		−	5.19615i		−	0.192450i
$28$	10.8278	−	22.8954i	0.386708	−	0.817692i
$29$	−28.6177			−0.986817			−0.493409	−	0.869798i	$-0.664249\pi$
$29$	−28.6177			−0.986817			−0.493409	+	0.869798i	$0.664249\pi$
$30$		0			0
$31$			23.4939i			0.757866i	0.925424	+	0.378933i	$0.123709\pi$
$31$			23.4939i			0.757866i	−0.925424	+	0.378933i	$0.876291\pi$
$32$	−28.5820	+	14.3898i	−0.893189	+	0.449682i
$33$	−16.0728			−0.487054
$34$	6.09542	−	27.1461i	0.179277	−	0.798416i
$35$		0			0
$36$	10.8480	+	5.13032i	0.301334	+	0.142509i
$37$	67.3338			1.81983			0.909916	−	0.414793i	$-0.136146\pi$
$37$	67.3338			1.81983			0.909916	+	0.414793i	$0.136146\pi$
$38$	33.6556	+	7.55706i	0.885674	+	0.198870i
$39$		−	32.1597i		−	0.824608i
$40$		0			0
$41$	−44.0791			−1.07510			−0.537550	−	0.843232i	$-0.680650\pi$
$41$	−44.0791			−1.07510			−0.537550	+	0.843232i	$0.680650\pi$
$42$	4.80532	−	21.4007i	0.114412	−	0.509540i
$43$			50.2937i			1.16962i	0.811170	+	0.584811i	$0.198831\pi$
$43$			50.2937i			1.16962i	−0.811170	+	0.584811i	$0.801169\pi$
$44$	15.8691	−	33.5552i	0.360662	−	0.762619i
$45$		0			0
$46$	65.7915	+	14.7729i	1.43025	+	0.321150i
$47$		−	31.1594i		−	0.662967i	−0.943461	−	0.331483i	$-0.892451\pi$
$47$		−	31.1594i		−	0.662967i	0.943461	−	0.331483i	$-0.107549\pi$
$48$	−21.4212	+	17.5822i	−0.446275	+	0.366295i
$49$	8.91003			0.181837
$50$		0			0
$51$		−	24.0946i		−	0.472444i
$52$	67.1400	+	31.7522i	1.29115	+	0.610620i
$53$	−81.6070			−1.53975			−0.769877	−	0.638192i	$-0.779682\pi$
$53$	−81.6070			−1.53975			−0.769877	+	0.638192i	$0.779682\pi$
$54$	10.1398	+	2.27681i	0.187775	+	0.0421631i
$55$		0			0
$56$	39.9338	+	31.1616i	0.713104	+	0.556457i
$57$	29.8724			0.524077
$58$	12.5395	−	55.8449i	0.216198	−	0.962843i
$59$			19.2751i			0.326697i	0.986568	+	0.163349i	$0.0522296\pi$
$59$			19.2751i			0.326697i	−0.986568	+	0.163349i	$0.947770\pi$
$60$		0			0
$61$	−53.1563			−0.871415			−0.435707	−	0.900088i	$-0.643502\pi$
$61$	−53.1563			−0.871415			−0.435707	+	0.900088i	$0.643502\pi$
$62$	−45.8462	−	10.2943i	−0.739455	−	0.166038i
$63$		−	18.9950i		−	0.301508i
$64$	−15.5566	−	62.0805i	−0.243072	−	0.970008i
$65$		0			0
$66$	7.04264	−	31.3646i	0.106707	−	0.475221i
$67$		−	4.49911i		−	0.0671509i	−0.999436	−	0.0335754i	$-0.989311\pi$
$67$		−	4.49911i		−	0.0671509i	0.999436	−	0.0335754i	$-0.0106894\pi$
$68$	50.3025	+	23.7893i	0.739742	+	0.349843i
$69$	58.3958			0.846316
$70$		0			0
$71$			13.3360i			0.187832i	0.995580	+	0.0939158i	$0.0299385\pi$
$71$			13.3360i			0.187832i	−0.995580	+	0.0939158i	$0.970062\pi$
$72$	−14.7647	+	18.9210i	−0.205065	+	0.262792i
$73$	−40.8904			−0.560143			−0.280071	−	0.959979i	$-0.590358\pi$
$73$	−40.8904			−0.560143			−0.280071	+	0.959979i	$0.590358\pi$
$74$	−29.5037	+	131.396i	−0.398699	+	1.77562i
$75$		0			0
$76$	−29.4939	+	62.3647i	−0.388077	+	0.820588i
$77$	−58.7555			−0.763058
$78$	62.7568	+	14.0915i	0.804574	+	0.180660i
$79$			141.309i			1.78872i	0.447352	+	0.894358i	$0.352367\pi$
$79$			141.309i			1.78872i	−0.447352	+	0.894358i	$0.647633\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$	19.3142	−	86.0164i	0.235539	−	1.04898i
$83$			69.8503i			0.841570i	0.907160	+	0.420785i	$0.138245\pi$
$83$			69.8503i			0.841570i	−0.907160	+	0.420785i	$0.861755\pi$
$84$	39.6559	+	18.7543i	0.472095	+	0.223266i
$85$		0			0
$86$	−98.1438	−	22.0373i	−1.14121	−	0.256248i
$87$		−	49.5673i		−	0.569739i
$88$	58.5266	+	45.6702i	0.665076	+	0.518979i
$89$	−46.3079			−0.520313			−0.260157	−	0.965566i	$-0.583774\pi$
$89$	−46.3079			−0.520313			−0.260157	+	0.965566i	$0.583774\pi$
$90$		0			0
$91$		−	117.563i		−	1.29190i
$92$	−57.6559	+	121.913i	−0.626695	+	1.32514i
$93$	−40.6926			−0.437554
$94$	60.8049	+	13.6532i	0.646860	+	0.145247i
$95$		0			0
$96$	−24.9239	−	49.5055i	−0.259624	−	0.515683i
$97$	−68.5543			−0.706745			−0.353373	−	0.935483i	$-0.614965\pi$
$97$	−68.5543			−0.706745			−0.353373	+	0.935483i	$0.614965\pi$
$98$	−3.90412	+	17.3871i	−0.0398380	+	0.177420i
$99$		−	27.8389i		−	0.281201i
$100$		0			0
$101$	−43.3949			−0.429653			−0.214826	−	0.976652i	$-0.568919\pi$
$101$	−43.3949			−0.429653			−0.214826	+	0.976652i	$0.568919\pi$
$102$	47.0185	+	10.5576i	0.460966	+	0.103506i
$103$			85.7919i			0.832931i	0.909152	+	0.416465i	$0.136731\pi$
$103$			85.7919i			0.832931i	−0.909152	+	0.416465i	$0.863269\pi$
$104$	−91.3805	+	117.105i	−0.878659	+	1.12601i
$105$		0			0
$106$	35.7579	−	159.249i	0.337338	−	1.50235i
$107$			183.075i			1.71098i	0.517818	+	0.855491i	$0.326745\pi$
$107$			183.075i			1.71098i	−0.517818	+	0.855491i	$0.673255\pi$
$108$	−8.88597	+	18.7893i	−0.0822775	+	0.173975i
$109$	81.4798			0.747521			0.373761	−	0.927525i	$-0.378068\pi$
$109$	81.4798			0.747521			0.373761	+	0.927525i	$0.378068\pi$
$110$		0			0
$111$			116.625i			1.05068i
$112$	−78.3070	+	64.2732i	−0.699170	+	0.573868i
$113$	172.814			1.52933			0.764664	−	0.644429i	$-0.222905\pi$
$113$	172.814			1.52933			0.764664	+	0.644429i	$0.222905\pi$
$114$	−13.0892	+	58.2933i	−0.114818	+	0.511344i
$115$		0			0
$116$	103.482	+	48.9393i	0.892086	+	0.421891i
$117$	55.7022			0.476087
$118$	−37.6137	−	8.44582i	−0.318760	−	0.0715748i
$119$		−	88.0800i		−	0.740168i
$120$		0			0
$121$	34.8885			0.288335
$122$	23.2916	−	103.730i	0.190915	−	0.850244i
$123$		−	76.3472i		−	0.620709i
$124$	40.1770	−	84.9541i	0.324008	−	0.685113i
$125$		0			0
$126$	37.0670	+	8.32307i	0.294183	+	0.0660561i
$127$		−	22.3785i		−	0.176208i	−0.996111	−	0.0881041i	$-0.971919\pi$
$127$		−	22.3785i		−	0.176208i	0.996111	−	0.0881041i	$-0.0280808\pi$
$128$	127.961	−	3.15546i	0.999696	−	0.0246520i
$129$	−87.1113			−0.675282
$130$		0			0
$131$		−	1.75315i		−	0.0133828i	−0.999978	−	0.00669141i	$-0.997870\pi$
$131$		−	1.75315i		−	0.0133828i	0.999978	−	0.00669141i	$-0.00212996\pi$
$132$	58.1194	+	27.4862i	0.440298	+	0.208228i
$133$	109.201			0.821060
$134$	8.77961	+	1.97138i	0.0655195	+	0.0147118i
$135$		0			0
$136$	−68.4639	+	87.7370i	−0.503411	+	0.645125i
$137$	19.5084			0.142397			0.0711987	−	0.997462i	$-0.477318\pi$
$137$	19.5084			0.142397			0.0711987	+	0.997462i	$0.477318\pi$
$138$	−25.5874	+	113.954i	−0.185416	+	0.825755i
$139$			257.370i			1.85158i	0.378038	+	0.925790i	$0.376599\pi$
$139$			257.370i			1.85158i	−0.378038	+	0.925790i	$0.623401\pi$
$140$		0			0
$141$	53.9697			0.382764
$142$	−26.0241	−	5.84348i	−0.183268	−	0.0411512i
$143$		−	172.299i		−	1.20489i
$144$	−30.4532	−	37.1026i	−0.211481	−	0.257657i
$145$		0			0
$146$	17.9170	−	79.7940i	0.122719	−	0.546534i
$147$			15.4326i			0.104984i
$148$	−243.480	−	115.148i	−1.64513	−	0.778026i
$149$	−111.673			−0.749486			−0.374743	−	0.927129i	$-0.622269\pi$
$149$	−111.673			−0.749486			−0.374743	+	0.927129i	$0.622269\pi$
$150$		0			0
$151$			6.45275i			0.0427335i	0.999772	+	0.0213667i	$0.00680176\pi$
$151$			6.45275i			0.0427335i	−0.999772	+	0.0213667i	$0.993198\pi$
$152$	−108.776	−	84.8811i	−0.715630	−	0.558428i
$153$	41.7331			0.272765
$154$	25.7450	−	114.656i	0.167175	−	0.744520i
$155$		0			0
$156$	−54.9965	+	116.290i	−0.352542	+	0.745448i
$157$	75.9075			0.483488			0.241744	−	0.970340i	$-0.422281\pi$
$157$	75.9075			0.483488			0.241744	+	0.970340i	$0.422281\pi$
$158$	−275.751	−	61.9174i	−1.74526	−	0.391882i
$159$		−	141.347i		−	0.888977i
$160$		0			0
$161$	213.471			1.32591
$162$	−3.94354	+	17.5627i	−0.0243429	+	0.108412i
$163$			249.298i			1.52944i	0.644364	+	0.764719i	$0.277122\pi$
$163$			249.298i			1.52944i	−0.644364	+	0.764719i	$0.722878\pi$
$164$	159.391	+	75.3799i	0.971893	+	0.459634i
$165$		0			0
$166$	−136.307	−	30.6064i	−0.821124	−	0.184376i
$167$		−	79.1883i		−	0.474182i	−0.971487	−	0.237091i	$-0.923806\pi$
$167$		−	79.1883i		−	0.474182i	0.971487	−	0.237091i	$-0.0761939\pi$
$168$	−53.9735	+	69.1674i	−0.321271	+	0.411711i
$169$	175.749			1.03993
$170$		0			0
$171$			51.7404i			0.302576i
$172$	86.0076	−	181.863i	0.500044	−	1.05734i
$173$	27.7204			0.160234			0.0801168	−	0.996785i	$-0.474471\pi$
$173$	27.7204			0.160234			0.0801168	+	0.996785i	$0.474471\pi$
$174$	96.7262	+	21.7190i	0.555898	+	0.124822i
$175$		0			0
$176$	−114.766	+	94.1982i	−0.652080	+	0.535217i
$177$	−33.3855			−0.188619
$178$	20.2908	−	90.3657i	0.113993	−	0.507673i
$179$		−	204.324i		−	1.14147i	−0.821133	−	0.570737i	$-0.806658\pi$
$179$		−	204.324i		−	1.14147i	0.821133	−	0.570737i	$-0.193342\pi$
$180$		0			0
$181$	−49.8262			−0.275283			−0.137641	−	0.990482i	$-0.543952\pi$
$181$	−49.8262			−0.275283			−0.137641	+	0.990482i	$0.543952\pi$
$182$	229.413	+	51.5126i	1.26051	+	0.283036i
$183$		−	92.0694i		−	0.503112i
$184$	−212.640	−	165.929i	−1.15565	−	0.901790i
$185$		0			0
$186$	17.8303	−	79.4079i	0.0958620	−	0.426924i
$187$		−	129.089i		−	0.690317i
$188$	−53.2859	+	112.673i	−0.283436	+	0.599324i
$189$	32.9003			0.174076
$190$		0			0
$191$			1.13703i			0.00595301i	0.999996	+	0.00297651i	$0.000947453\pi$
$191$			1.13703i			0.00595301i	−0.999996	+	0.00297651i	$0.999053\pi$
$192$	107.527	−	26.9449i	0.560034	−	0.140338i
$193$	76.6452			0.397126			0.198563	−	0.980088i	$-0.436373\pi$
$193$	76.6452			0.397126			0.198563	+	0.980088i	$0.436373\pi$
$194$	30.0385	−	133.778i	0.154838	−	0.689575i
$195$		0			0
$196$	−32.2188	−	15.2371i	−0.164382	−	0.0777403i
$197$	−134.496			−0.682719			−0.341359	−	0.939933i	$-0.610887\pi$
$197$	−134.496			−0.682719			−0.341359	+	0.939933i	$0.610887\pi$
$198$	54.3251	+	12.1982i	0.274369	+	0.0616071i
$199$		−	176.014i		−	0.884491i	−0.896894	−	0.442245i	$-0.854182\pi$
$199$		−	176.014i		−	0.884491i	0.896894	−	0.442245i	$-0.145818\pi$
$200$		0			0
$201$	7.79269			0.0387696
$202$	19.0144	−	84.6813i	0.0941308	−	0.419214i
$203$		−	181.198i		−	0.892599i
$204$	−41.2044	+	87.1264i	−0.201982	+	0.427090i
$205$		0			0
$206$	−167.415	−	37.5916i	−0.812695	−	0.182483i
$207$			101.144i			0.488621i
$208$	−188.479	−	229.633i	−0.906150	−	1.10400i
$209$	160.044			0.765761
$210$		0			0
$211$		−	218.087i		−	1.03359i	−0.856110	−	0.516793i	$-0.827126\pi$
$211$		−	218.087i		−	1.03359i	0.856110	−	0.516793i	$-0.172874\pi$
$212$	295.092	+	139.557i	1.39194	+	0.658286i
$213$	−23.0987			−0.108445
$214$	−357.255	−	80.2183i	−1.66941	−	0.374852i
$215$		0			0
$216$	−32.7722	−	25.5731i	−0.151723	−	0.118394i
$217$	−148.755			−0.685508
$218$	−35.7021	+	159.001i	−0.163771	+	0.729361i
$219$		−	70.8243i		−	0.323399i
$220$		0			0
$221$	258.292			1.16874
$222$	−227.584	−	51.1020i	−1.02515	−	0.230189i
$223$		−	328.579i		−	1.47345i	−0.676193	−	0.736724i	$-0.736372\pi$
$223$		−	328.579i		−	1.47345i	0.676193	−	0.736724i	$-0.263628\pi$
$224$	−91.1115	−	180.972i	−0.406748	−	0.807910i
$225$		0			0
$226$	−75.7222	+	337.231i	−0.335054	+	1.49217i
$227$		−	157.649i		−	0.694491i	−0.937774	−	0.347245i	$-0.887117\pi$
$227$		−	157.649i		−	0.694491i	0.937774	−	0.347245i	$-0.112883\pi$
$228$	−108.019	−	51.0849i	−0.473767	−	0.224057i
$229$	−273.148			−1.19279			−0.596393	−	0.802692i	$-0.703400\pi$
$229$	−273.148			−1.19279			−0.596393	+	0.802692i	$0.703400\pi$
$230$		0			0
$231$		−	101.767i		−	0.440552i
$232$	−140.844	+	180.492i	−0.607084	+	0.777983i
$233$	−108.746			−0.466720			−0.233360	−	0.972390i	$-0.574972\pi$
$233$	−108.746			−0.466720			−0.233360	+	0.972390i	$0.574972\pi$
$234$	−24.4071	+	108.698i	−0.104304	+	0.464521i
$235$		0			0
$236$	32.9625	−	69.6992i	0.139672	−	0.295335i
$237$	−244.754			−1.03272
$238$	171.880	+	38.5942i	0.722186	+	0.162160i
$239$		−	178.994i		−	0.748927i	−0.927242	−	0.374464i	$-0.877827\pi$
$239$		−	178.994i		−	0.748927i	0.927242	−	0.374464i	$-0.122173\pi$
$240$		0			0
$241$	358.623			1.48806			0.744032	−	0.668144i	$-0.232911\pi$
$241$	358.623			1.48806			0.744032	+	0.668144i	$0.232911\pi$
$242$	−15.2872	+	68.0819i	−0.0631701	+	0.281330i
$243$			15.5885i			0.0641500i
$244$	192.214	+	90.9029i	0.787762	+	0.372553i
$245$		0			0
$246$	148.985	+	33.4532i	0.605629	+	0.135989i
$247$			320.229i			1.29647i
$248$	148.176	+	115.626i	0.597483	+	0.466235i
$249$	−120.984			−0.485881
$250$		0			0
$251$			306.220i			1.22000i	0.792401	+	0.610000i	$0.208831\pi$
$251$			306.220i			1.22000i	−0.792401	+	0.610000i	$0.791169\pi$
$252$	−32.4834	+	68.6861i	−0.128903	+	0.272564i
$253$	312.861			1.23660
$254$	43.6696	+	9.80560i	0.171927	+	0.0386047i
$255$		0			0
$256$	−49.9113	+	251.087i	−0.194966	+	0.980810i
$257$	251.062			0.976895			0.488447	−	0.872593i	$-0.337563\pi$
$257$	251.062			0.976895			0.488447	+	0.872593i	$0.337563\pi$
$258$	38.1697	−	169.990i	0.147945	−	0.658876i
$259$			426.335i			1.64608i
$260$		0			0
$261$	85.8531			0.328939
$262$	3.42112	+	0.768181i	0.0130577	+	0.00293199i
$263$		−	48.7645i		−	0.185416i	−0.995693	−	0.0927082i	$-0.970448\pi$
$263$		−	48.7645i		−	0.185416i	0.995693	−	0.0927082i	$-0.0295524\pi$
$264$	−79.1031	+	101.371i	−0.299633	+	0.383982i
$265$		0			0
$266$	−47.8488	+	213.096i	−0.179883	+	0.801113i
$267$		−	80.2076i		−	0.300403i
$268$	−7.69395	+	16.2688i	−0.0287088	+	0.0607046i
$269$	148.696			0.552772			0.276386	−	0.961047i	$-0.410863\pi$
$269$	148.696			0.552772			0.276386	+	0.961047i	$0.410863\pi$
$270$		0			0
$271$		−	83.3415i		−	0.307533i	−0.988107	−	0.153767i	$-0.950860\pi$
$271$		−	83.3415i		−	0.307533i	0.988107	−	0.153767i	$-0.0491404\pi$
$272$	−141.212	−	172.045i	−0.519162	−	0.632519i
$273$	203.624			0.745877
$274$	−8.54805	+	38.0690i	−0.0311972	+	0.138938i
$275$		0			0
$276$	−211.160	−	99.8630i	−0.765072	−	0.361822i
$277$	−144.080			−0.520146			−0.260073	−	0.965589i	$-0.583747\pi$
$277$	−144.080			−0.520146			−0.260073	+	0.965589i	$0.583747\pi$
$278$	−502.234	−	112.772i	−1.80660	−	0.405655i
$279$		−	70.4816i		−	0.252622i
$280$		0			0
$281$	−343.671			−1.22303			−0.611514	−	0.791233i	$-0.709439\pi$
$281$	−343.671			−1.22303			−0.611514	+	0.791233i	$0.709439\pi$
$282$	−23.6480	+	105.317i	−0.0838581	+	0.373465i
$283$			314.955i			1.11292i	0.830876	+	0.556458i	$0.187840\pi$
$283$			314.955i			1.11292i	−0.830876	+	0.556458i	$0.812160\pi$
$284$	22.8061	−	48.2233i	0.0803030	−	0.169800i
$285$		0			0
$286$	336.225	+	75.4964i	1.17561	+	0.263973i
$287$		−	279.094i		−	0.972453i
$288$	85.7461	−	43.1695i	0.297730	−	0.149894i
$289$	−95.4831			−0.330391
$290$		0			0
$291$		−	118.740i		−	0.408040i
$292$	147.860	+	69.9269i	0.506371	+	0.239476i
$293$	6.55421			0.0223693			0.0111847	−	0.999937i	$-0.496440\pi$
$293$	6.55421			0.0223693			0.0111847	+	0.999937i	$0.496440\pi$
$294$	−30.1154	−	6.76214i	−0.102433	−	0.0230005i
$295$		0			0
$296$	331.387	−	424.674i	1.11955	−	1.43471i
$297$	48.2184			0.162351
$298$	48.9321	−	217.921i	0.164202	−	0.731278i
$299$			625.997i			2.09364i
$300$		0			0
$301$	−318.443			−1.05795
$302$	−12.5920	−	2.82741i	−0.0416953	−	0.00936229i
$303$		−	75.1622i		−	0.248060i
$304$	213.300	−	175.074i	0.701646	−	0.575900i
$305$		0			0
$306$	−18.2863	+	81.4384i	−0.0597590	+	0.266139i
$307$			354.559i			1.15492i	0.816420	+	0.577458i	$0.195955\pi$
$307$			354.559i			1.15492i	−0.816420	+	0.577458i	$0.804045\pi$
$308$	212.460	+	100.478i	0.689807	+	0.326228i
$309$	−148.596			−0.480893
$310$		0			0
$311$		−	193.387i		−	0.621823i	−0.950439	−	0.310912i	$-0.899366\pi$
$311$		−	193.387i		−	0.621823i	0.950439	−	0.310912i	$-0.100634\pi$
$312$	−202.831	−	158.276i	−0.650101	−	0.507294i
$313$	23.5224			0.0751514			0.0375757	−	0.999294i	$-0.488036\pi$
$313$	23.5224			0.0751514			0.0375757	+	0.999294i	$0.488036\pi$
$314$	−33.2605	+	148.127i	−0.105925	+	0.471742i
$315$		0			0
$316$	241.653	−	510.973i	0.764724	−	1.61700i
$317$	214.004			0.675092			0.337546	−	0.941309i	$-0.390403\pi$
$317$	214.004			0.675092			0.337546	+	0.941309i	$0.390403\pi$
$318$	275.827	+	61.9344i	0.867380	+	0.194762i
$319$		−	265.562i		−	0.832481i
$320$		0			0
$321$	−317.095			−0.987836
$322$	−93.5369	+	416.570i	−0.290487	+	1.29369i
$323$			239.921i			0.742790i
$324$	−32.5441	−	15.3910i	−0.100445	−	0.0475029i
$325$		0			0
$326$	−486.483	−	109.235i	−1.49228	−	0.335078i
$327$			141.127i			0.431582i
$328$	−216.938	+	278.007i	−0.661395	+	0.847583i
$329$	197.291			0.599669
$330$		0			0
$331$			412.454i			1.24609i	0.782188	+	0.623043i	$0.214104\pi$
$331$			412.454i			1.24609i	−0.782188	+	0.623043i	$0.785896\pi$
$332$	119.451	−	252.579i	0.359793	−	0.760782i
$333$	−202.001			−0.606610
$334$	154.529	+	34.6981i	0.462662	+	0.103886i
$335$		0			0
$336$	−111.324	−	135.632i	−0.331323	−	0.403666i
$337$	−103.268			−0.306433			−0.153216	−	0.988193i	$-0.548963\pi$
$337$	−103.268			−0.306433			−0.153216	+	0.988193i	$0.548963\pi$
$338$	−77.0081	+	342.958i	−0.227835	+	1.01467i
$339$			299.323i			0.882958i
$340$		0			0
$341$	−218.014			−0.639338
$342$	−100.967	−	22.6712i	−0.295225	−	0.0662900i
$343$			366.667i			1.06900i
$344$	317.203	+	247.523i	0.922102	+	0.719545i
$345$		0			0
$346$	−12.1463	+	54.0939i	−0.0351049	+	0.156341i
$347$		−	153.211i		−	0.441531i	−0.975327	−	0.220766i	$-0.929144\pi$
$347$		−	153.211i		−	0.441531i	0.975327	−	0.220766i	$-0.0708556\pi$
$348$	−84.7654	+	179.236i	−0.243579	+	0.515046i
$349$	−84.7317			−0.242784			−0.121392	−	0.992605i	$-0.538736\pi$
$349$	−84.7317			−0.242784			−0.121392	+	0.992605i	$0.538736\pi$
$350$		0			0
$351$			96.4791i			0.274869i
$352$	−133.532	−	265.231i	−0.379353	−	0.753496i
$353$	−256.065			−0.725396			−0.362698	−	0.931907i	$-0.618144\pi$
$353$	−256.065			−0.725396			−0.362698	+	0.931907i	$0.618144\pi$
$354$	14.6286	−	65.1489i	0.0413237	−	0.184036i
$355$		0			0
$356$	167.450	+	79.1914i	0.470365	+	0.222448i
$357$	152.559			0.427336
$358$	398.720	+	89.5289i	1.11374	+	0.250081i
$359$		−	667.258i		−	1.85866i	−0.369253	−	0.929329i	$-0.620386\pi$
$359$		−	667.258i		−	1.85866i	0.369253	−	0.929329i	$-0.379614\pi$
$360$		0			0
$361$	63.5473			0.176031
$362$	21.8324	−	97.2314i	0.0603106	−	0.268595i
$363$			60.4287i			0.166470i
$364$	−201.044	+	425.108i	−0.552320	+	1.16788i
$365$		0			0
$366$	179.665	+	40.3422i	0.490889	+	0.110225i
$367$		−	245.301i		−	0.668396i	−0.942503	−	0.334198i	$-0.891535\pi$
$367$		−	245.301i		−	0.668396i	0.942503	−	0.334198i	$-0.108465\pi$
$368$	416.969	−	342.242i	1.13307	−	0.930005i
$369$	132.237			0.358367
$370$		0			0
$371$		−	516.708i		−	1.39274i
$372$	147.145	+	69.5886i	0.395550	+	0.187066i
$373$	−698.787			−1.87342			−0.936712	−	0.350101i	$-0.886147\pi$
$373$	−698.787			−1.87342			−0.936712	+	0.350101i	$0.886147\pi$
$374$	251.906	+	56.5632i	0.673546	+	0.151239i
$375$		0			0
$376$	−196.523	−	153.353i	−0.522667	−	0.407853i
$377$	531.357			1.40943
$378$	−14.4160	+	64.2020i	−0.0381375	+	0.169847i
$379$			208.691i			0.550636i	0.961353	+	0.275318i	$0.0887831\pi$
$379$			208.691i			0.550636i	−0.961353	+	0.275318i	$0.911217\pi$
$380$		0			0
$381$	38.7606			0.101734
$382$	−2.21880	−	0.498212i	−0.00580839	−	0.00130422i
$383$			156.524i			0.408680i	0.978900	+	0.204340i	$0.0655048\pi$
$383$			156.524i			0.408680i	−0.978900	+	0.204340i	$0.934495\pi$
$384$	5.46541	+	221.635i	0.0142328	+	0.577175i
$385$		0			0
$386$	−33.5838	+	149.566i	−0.0870046	+	0.387478i
$387$		−	150.881i		−	0.389874i
$388$	247.893	+	117.235i	0.638900	+	0.302152i
$389$	386.588			0.993801			0.496900	−	0.867808i	$-0.334471\pi$
$389$	386.588			0.993801			0.496900	+	0.867808i	$0.334471\pi$
$390$		0			0
$391$			469.008i			1.19951i
$392$	43.8512	−	56.1956i	0.111865	−	0.143356i
$393$	3.03655			0.00772658
$394$	58.9322	−	262.456i	0.149574	−	0.666133i
$395$		0			0
$396$	−47.6074	+	100.666i	−0.120221	+	0.254206i
$397$	561.155			1.41349			0.706744	−	0.707470i	$-0.250163\pi$
$397$	561.155			1.41349			0.706744	+	0.707470i	$0.250163\pi$
$398$	343.475	+	77.1242i	0.863002	+	0.193779i
$399$			189.142i			0.474039i
$400$		0			0
$401$	16.9333			0.0422276			0.0211138	−	0.999777i	$-0.493279\pi$
$401$	16.9333			0.0422276			0.0211138	+	0.999777i	$0.493279\pi$
$402$	−3.41453	+	15.2067i	−0.00849387	+	0.0378277i
$403$		−	436.220i		−	1.08243i
$404$	156.917	+	74.2099i	0.388407	+	0.183688i
$405$		0			0
$406$	353.591	+	79.3957i	0.870914	+	0.195556i
$407$			624.832i			1.53521i
$408$	−151.965	−	118.583i	−0.372463	−	0.290644i
$409$	258.490			0.632006			0.316003	−	0.948758i	$-0.397659\pi$
$409$	258.490			0.632006			0.316003	+	0.948758i	$0.397659\pi$
$410$		0			0
$411$			33.7896i			0.0822132i
$412$	146.713	−	310.224i	0.356100	−	0.752972i
$413$	−122.044			−0.295505
$414$	−197.374	−	44.3186i	−0.476750	−	0.107050i
$415$		0			0
$416$	530.694	−	267.182i	1.27571	−	0.642264i
$417$	−445.777			−1.06901
$418$	−70.1267	+	312.312i	−0.167767	+	0.747157i
$419$			258.917i			0.617941i	0.951072	+	0.308970i	$0.0999844\pi$
$419$			258.917i			0.617941i	−0.951072	+	0.308970i	$0.900016\pi$
$420$		0			0
$421$	97.4654			0.231509			0.115755	−	0.993278i	$-0.463071\pi$
$421$	97.4654			0.231509			0.115755	+	0.993278i	$0.463071\pi$
$422$	425.577	+	95.5594i	1.00848	+	0.226444i
$423$			93.4783i			0.220989i
$424$	−401.633	+	514.696i	−0.947248	+	1.21390i
$425$		0			0
$426$	10.1212	−	45.0751i	0.0237587	−	0.105810i
$427$		−	336.568i		−	0.788215i
$428$	313.078	−	662.002i	0.731490	−	1.54673i
$429$	298.430			0.695641
$430$		0			0
$431$			389.968i			0.904799i	0.891815	+	0.452399i	$0.149432\pi$
$431$			389.968i			0.904799i	−0.891815	+	0.452399i	$0.850568\pi$
$432$	64.2635	−	52.7465i	0.148758	−	0.122098i
$433$	−275.893			−0.637166			−0.318583	−	0.947895i	$-0.603207\pi$
$433$	−275.893			−0.637166			−0.318583	+	0.947895i	$0.603207\pi$
$434$	65.1803	−	290.283i	0.150185	−	0.668854i
$435$		0			0
$436$	−294.632	−	139.339i	−0.675761	−	0.319585i
$437$	−581.473			−1.33060
$438$	138.207	+	31.0332i	0.315542	+	0.0708520i
$439$		−	446.143i		−	1.01627i	−0.861277	−	0.508136i	$-0.830335\pi$
$439$		−	446.143i		−	1.01627i	0.861277	−	0.508136i	$-0.169665\pi$
$440$		0			0
$441$	−26.7301			−0.0606125
$442$	−113.176	+	504.034i	−0.256055	+	1.14035i
$443$			794.679i			1.79386i	0.442174	+	0.896929i	$0.354207\pi$
$443$			794.679i			1.79386i	−0.442174	+	0.896929i	$0.645793\pi$
$444$	199.442	−	421.719i	0.449194	−	0.949818i
$445$		0			0
$446$	641.193	+	143.974i	1.43765	+	0.322812i
$447$		−	193.424i		−	0.432716i
$448$	393.073	−	98.4993i	0.877395	−	0.219865i
$449$	−750.226			−1.67088			−0.835441	−	0.549581i	$-0.814788\pi$
$449$	−750.226			−1.67088			−0.835441	+	0.549581i	$0.814788\pi$
$450$		0			0
$451$		−	409.037i		−	0.906957i
$452$	−624.898	−	295.530i	−1.38252	−	0.653828i
$453$	−11.1765			−0.0246722
$454$	307.639	+	69.0775i	0.677619	+	0.152153i
$455$		0			0
$456$	147.018	−	188.405i	0.322409	−	0.413169i
$457$	−101.092			−0.221209			−0.110604	−	0.993865i	$-0.535279\pi$
$457$	−101.092			−0.221209			−0.110604	+	0.993865i	$0.535279\pi$
$458$	119.686	−	533.024i	0.261323	−	1.16381i
$459$			72.2839i			0.157481i
$460$		0			0
$461$	−4.48690			−0.00973297			−0.00486648	−	0.999988i	$-0.501549\pi$
$461$	−4.48690			−0.00973297			−0.00486648	+	0.999988i	$0.501549\pi$
$462$	198.590	+	44.5916i	0.429849	+	0.0965186i
$463$		−	515.108i		−	1.11254i	−0.831000	−	0.556272i	$-0.812231\pi$
$463$		−	515.108i		−	1.11254i	0.831000	−	0.556272i	$-0.187769\pi$
$464$	−290.500	−	353.930i	−0.626079	−	0.762780i
$465$		0			0
$466$	47.6493	−	212.208i	0.102252	−	0.455382i
$467$			295.498i			0.632758i	0.948633	+	0.316379i	$0.102467\pi$
$467$			295.498i			0.632758i	−0.948633	+	0.316379i	$0.897533\pi$
$468$	−201.420	−	95.2567i	−0.430384	−	0.203540i
$469$	28.4869			0.0607396
$470$		0			0
$471$			131.476i			0.279142i
$472$	121.568	+	94.8637i	0.257560	+	0.200982i
$473$	−466.707			−0.986696
$474$	107.244	−	477.615i	0.226253	−	1.00763i
$475$		0			0
$476$	−150.626	+	318.498i	−0.316441	+	0.669114i
$477$	244.821			0.513251
$478$	349.290	+	78.4299i	0.730732	+	0.164079i
$479$			273.155i			0.570260i	0.958489	+	0.285130i	$0.0920368\pi$
$479$			273.155i			0.570260i	−0.958489	+	0.285130i	$0.907963\pi$
$480$		0			0
$481$	−1250.21			−2.59920
$482$	−157.139	+	699.822i	−0.326014	+	1.45191i
$483$			369.743i			0.765512i
$484$	−126.157	−	59.6631i	−0.260656	−	0.123271i
$485$		0			0
$486$	−30.4195	−	6.83042i	−0.0625915	−	0.0140544i
$487$		−	357.751i		−	0.734601i	−0.930102	−	0.367301i	$-0.880282\pi$
$487$		−	357.751i		−	0.734601i	0.930102	−	0.367301i	$-0.119718\pi$
$488$	−261.612	+	335.257i	−0.536089	+	0.687002i
$489$	−431.797			−0.883021
$490$		0			0
$491$		−	422.379i		−	0.860242i	−0.902771	−	0.430121i	$-0.858471\pi$
$491$		−	422.379i		−	0.860242i	0.902771	−	0.430121i	$-0.141529\pi$
$492$	−130.562	+	276.072i	−0.265370	+	0.561123i
$493$	398.102			0.807509
$494$	−624.898	−	140.315i	−1.26498	−	0.284039i
$495$		0			0
$496$	−290.561	+	238.488i	−0.585808	+	0.480822i
$497$	−84.4394			−0.169898
$498$	53.0119	−	236.090i	0.106450	−	0.474076i
$499$		−	207.096i		−	0.415021i	−0.978233	−	0.207511i	$-0.933464\pi$
$499$		−	207.096i		−	0.415021i	0.978233	−	0.207511i	$-0.0665362\pi$
$500$		0			0
$501$	137.158			0.273769
$502$	−597.562	−	134.177i	−1.19036	−	0.267285i
$503$		−	702.853i		−	1.39732i	−0.715452	−	0.698661i	$-0.753779\pi$
$503$		−	702.853i		−	1.39732i	0.715452	−	0.698661i	$-0.246221\pi$
$504$	−119.802	−	93.4849i	−0.237701	−	0.185486i
$505$		0			0
$506$	−137.087	+	610.520i	−0.270923	+	1.20656i
$507$			304.406i			0.600406i
$508$	−38.2695	+	80.9207i	−0.0753337	+	0.159293i
$509$	−389.029			−0.764300			−0.382150	−	0.924100i	$-0.624816\pi$
$509$	−389.029			−0.764300			−0.382150	+	0.924100i	$0.624816\pi$
$510$		0			0
$511$		−	258.904i		−	0.506662i
$512$	−468.105	−	207.417i	−0.914267	−	0.405111i
$513$	−89.6171			−0.174692
$514$	−110.008	+	489.925i	−0.214024	+	0.953162i
$515$		0			0
$516$	314.996	+	148.970i	0.610457	+	0.288701i
$517$	289.148			0.559280
$518$	−831.954	−	186.808i	−1.60609	−	0.360633i
$519$			48.0132i			0.0925109i
$520$		0			0
$521$	−151.753			−0.291273			−0.145637	−	0.989338i	$-0.546523\pi$
$521$	−151.753			−0.291273			−0.145637	+	0.989338i	$0.546523\pi$
$522$	−37.6184	+	167.535i	−0.0720659	+	0.320948i
$523$		−	557.762i		−	1.06647i	−0.845968	−	0.533234i	$-0.820977\pi$
$523$		−	557.762i		−	1.06647i	0.845968	−	0.533234i	$-0.179023\pi$
$524$	−2.99807	+	6.33941i	−0.00572151	+	0.0120981i
$525$		0			0
$526$	95.1596	+	21.3672i	0.180912	+	0.0406221i
$527$		−	326.824i		−	0.620159i
$528$	−163.156	−	198.781i	−0.309008	−	0.376478i
$529$	−607.689			−1.14875
$530$		0			0
$531$		−	57.8254i		−	0.108899i
$532$	−394.872	−	186.745i	−0.742241	−	0.351025i
$533$	818.435			1.53552
$534$	156.518	+	35.1447i	0.293105	+	0.0658141i
$535$		0			0
$536$	−28.3759	−	22.1426i	−0.0529401	−	0.0413108i
$537$	353.899			0.659030
$538$	−65.1542	+	290.166i	−0.121104	+	0.539342i
$539$			82.6818i			0.153398i
$540$		0			0
$541$	340.979			0.630275			0.315137	−	0.949046i	$-0.397949\pi$
$541$	340.979			0.630275			0.315137	+	0.949046i	$0.397949\pi$
$542$	162.633	+	36.5179i	0.300062	+	0.0673761i
$543$		−	86.3015i		−	0.158935i
$544$	397.606	−	200.177i	0.730893	−	0.367973i
$545$		0			0
$546$	−89.2224	+	397.355i	−0.163411	+	0.727756i
$547$			113.651i			0.207771i	0.994589	+	0.103885i	$0.0331275\pi$
$547$			113.651i			0.207771i	−0.994589	+	0.103885i	$0.966872\pi$
$548$	−70.5428	−	33.3615i	−0.128728	−	0.0608787i
$549$	159.469			0.290472
$550$		0			0
$551$			493.564i			0.895761i
$552$	287.398	−	368.303i	0.520649	−	0.667215i
$553$	−894.718			−1.61794
$554$	63.1319	−	281.160i	0.113957	−	0.507509i
$555$		0			0
$556$	440.129	−	930.651i	0.791599	−	1.67383i
$557$	−233.232			−0.418728			−0.209364	−	0.977838i	$-0.567139\pi$
$557$	−233.232			−0.418728			−0.209364	+	0.977838i	$0.567139\pi$
$558$	137.539	+	30.8830i	0.246485	+	0.0553459i
$559$		−	933.825i		−	1.67053i
$560$		0			0
$561$	223.589			0.398554
$562$	150.587	−	670.644i	0.267948	−	1.19332i
$563$			167.786i			0.298021i	0.988836	+	0.149011i	$0.0476088\pi$
$563$			167.786i			0.298021i	−0.988836	+	0.149011i	$0.952391\pi$
$564$	−195.155	−	92.2939i	−0.346020	−	0.163642i
$565$		0			0
$566$	−614.607	−	138.004i	−1.08588	−	0.243824i
$567$			56.9850i			0.100503i
$568$	84.1105	+	65.6341i	0.148082	+	0.115553i
$569$	381.089			0.669752			0.334876	−	0.942262i	$-0.391306\pi$
$569$	381.089			0.669752			0.334876	+	0.942262i	$0.391306\pi$
$570$		0			0
$571$			453.871i			0.794870i	0.917630	+	0.397435i	$0.130100\pi$
$571$			453.871i			0.794870i	−0.917630	+	0.397435i	$0.869900\pi$
$572$	−294.649	+	623.034i	−0.515120	+	1.08922i
$573$	−1.96939			−0.00343697
$574$	544.627	+	122.291i	0.948828	+	0.213051i
$575$		0			0
$576$	46.6699	+	186.242i	0.0810241	+	0.323336i
$577$	−688.294			−1.19288			−0.596442	−	0.802656i	$-0.703419\pi$
$577$	−688.294			−1.19288			−0.596442	+	0.802656i	$0.703419\pi$
$578$	41.8380	−	186.327i	0.0723841	−	0.322365i
$579$			132.753i			0.229281i
$580$		0			0
$581$	−442.269			−0.761220
$582$	231.710	+	52.0283i	0.398127	+	0.0893957i
$583$		−	757.282i		−	1.29894i
$584$	−201.244	+	257.896i	−0.344597	+	0.441603i
$585$		0			0
$586$	−2.87187	+	12.7900i	−0.00490080	+	0.0218259i
$587$		−	249.163i		−	0.424468i	−0.977219	−	0.212234i	$-0.931926\pi$
$587$		−	249.163i		−	0.424468i	0.977219	−	0.212234i	$-0.0680739\pi$
$588$	26.3914	−	55.8046i	0.0448834	−	0.0949057i
$589$	405.194			0.687936
$590$		0			0
$591$		−	232.953i		−	0.394168i
$592$	683.510	+	832.752i	1.15458	+	1.40668i
$593$	163.937			0.276454			0.138227	−	0.990401i	$-0.455860\pi$
$593$	163.937			0.276454			0.138227	+	0.990401i	$0.455860\pi$
$594$	−21.1279	+	94.0938i	−0.0355689	+	0.158407i
$595$		0			0
$596$	403.812	+	190.973i	0.677538	+	0.320425i
$597$	304.865			0.510661
$598$	−1221.58	−	274.294i	−2.04277	−	0.458686i
$599$			170.412i			0.284494i	0.989831	+	0.142247i	$0.0454327\pi$
$599$			170.412i			0.284494i	−0.989831	+	0.142247i	$0.954567\pi$
$600$		0			0
$601$	1119.87			1.86335			0.931674	−	0.363295i	$-0.118348\pi$
$601$	1119.87			1.86335			0.931674	+	0.363295i	$0.118348\pi$
$602$	139.533	−	621.413i	0.231782	−	1.03225i
$603$			13.4973i			0.0223836i
$604$	11.0349	−	23.3332i	0.0182697	−	0.0386312i
$605$		0			0
$606$	146.672	+	32.9339i	0.242034	+	0.0543464i
$607$		−	660.957i		−	1.08889i	−0.838796	−	0.544445i	$-0.816740\pi$
$607$		−	660.957i		−	1.08889i	0.838796	−	0.544445i	$-0.183260\pi$
$608$	248.179	+	492.949i	0.408189	+	0.810772i
$609$	313.844			0.515342
$610$		0			0
$611$			578.550i			0.946890i
$612$	−150.907	−	71.3680i	−0.246581	−	0.116614i
$613$	179.315			0.292520			0.146260	−	0.989246i	$-0.453276\pi$
$613$	179.315			0.292520			0.146260	+	0.989246i	$0.453276\pi$
$614$	−691.891	−	155.358i	−1.12686	−	0.253026i
$615$		0			0
$616$	−289.168	+	370.571i	−0.469429	+	0.601576i
$617$	63.6752			0.103201			0.0516007	−	0.998668i	$-0.483568\pi$
$617$	63.6752			0.103201			0.0516007	+	0.998668i	$0.483568\pi$
$618$	65.1105	−	289.972i	0.105357	−	0.469210i
$619$		−	872.350i		−	1.40929i	−0.709561	−	0.704644i	$-0.751107\pi$
$619$		−	872.350i		−	1.40929i	0.709561	−	0.704644i	$-0.248893\pi$
$620$		0			0
$621$	−175.187			−0.282105
$622$	377.378	+	84.7367i	0.606716	+	0.136233i
$623$		−	293.206i		−	0.470636i
$624$	397.736	−	326.456i	0.637397	−	0.523166i
$625$		0			0
$626$	−10.3068	+	45.9019i	−0.0164646	+	0.0733257i
$627$			277.204i			0.442112i
$628$	−274.483	−	129.810i	−0.437074	−	0.206704i
$629$	−936.682			−1.48916
$630$		0			0
$631$			340.783i			0.540068i	0.962851	+	0.270034i	$0.0870349\pi$
$631$			340.783i			0.540068i	−0.962851	+	0.270034i	$0.912965\pi$
$632$	891.234	+	695.458i	1.41018	+	1.10041i
$633$	377.737			0.596742
$634$	−93.7705	+	417.610i	−0.147903	+	0.658691i
$635$		0			0
$636$	−241.719	+	511.114i	−0.380061	+	0.803638i
$637$	−165.436			−0.259712
$638$	518.220	+	116.362i	0.812257	+	0.182385i
$639$		−	40.0081i		−	0.0626105i
$640$		0			0
$641$	766.210			1.19534			0.597668	−	0.801744i	$-0.296094\pi$
$641$	766.210			1.19534			0.597668	+	0.801744i	$0.296094\pi$
$642$	138.942	−	618.783i	0.216421	−	0.963837i
$643$			1163.47i			1.80943i	0.426014	+	0.904717i	$0.359917\pi$
$643$			1163.47i			1.80943i	−0.426014	+	0.904717i	$0.640083\pi$
$644$	−771.913	−	365.058i	−1.19862	−	0.566860i
$645$		0			0
$646$	−468.185	−	105.127i	−0.724744	−	0.162735i
$647$			740.530i			1.14456i	0.820059	+	0.572279i	$0.193941\pi$
$647$			740.530i			1.14456i	−0.820059	+	0.572279i	$0.806059\pi$
$648$	44.2940	−	56.7630i	0.0683549	−	0.0875973i
$649$	−178.866			−0.275603
$650$		0			0
$651$		−	257.652i		−	0.395778i
$652$	426.326	−	901.465i	0.653875	−	1.38262i
$653$	−109.569			−0.167793			−0.0838967	−	0.996474i	$-0.526737\pi$
$653$	−109.569			−0.167793			−0.0838967	+	0.996474i	$0.526737\pi$
$654$	−275.397	−	61.8379i	−0.421097	−	0.0945534i
$655$		0			0
$656$	−447.450	−	545.149i	−0.682089	−	0.831020i
$657$	122.671			0.186714
$658$	−86.4473	+	384.996i	−0.131379	+	0.585100i
$659$			723.214i			1.09744i	0.836006	+	0.548721i	$0.184885\pi$
$659$			723.214i			1.09744i	−0.836006	+	0.548721i	$0.815115\pi$
$660$		0			0
$661$	700.333			1.05951			0.529753	−	0.848152i	$-0.322285\pi$
$661$	700.333			1.05951			0.529753	+	0.848152i	$0.322285\pi$
$662$	−804.868	−	180.726i	−1.21581	−	0.273000i
$663$			447.375i			0.674773i
$664$	440.546	+	343.772i	0.663473	+	0.517729i
$665$		0			0
$666$	88.5112	−	394.188i	0.132900	−	0.591873i
$667$			964.841i			1.44654i
$668$	−135.420	+	286.346i	−0.202725	+	0.428662i
$669$	569.116			0.850696
$670$		0			0
$671$		−	493.271i		−	0.735128i
$672$	313.452	−	157.810i	0.466447	−	0.234836i
$673$	1221.18			1.81454			0.907269	−	0.420552i	$-0.138163\pi$
$673$	1221.18			1.81454			0.907269	+	0.420552i	$0.138163\pi$
$674$	45.2490	−	201.518i	0.0671350	−	0.298988i
$675$		0			0
$676$	−635.509	−	300.549i	−0.940103	−	0.444599i
$677$	−989.373			−1.46141			−0.730704	−	0.682695i	$-0.760808\pi$
$677$	−989.373			−1.46141			−0.730704	+	0.682695i	$0.760808\pi$
$678$	−584.102	−	131.155i	−0.861507	−	0.193444i
$679$		−	434.063i		−	0.639268i
$680$		0			0
$681$	273.057			0.400965
$682$	95.5276	−	425.435i	0.140070	−	0.623806i
$683$			307.312i			0.449945i	0.974365	+	0.224972i	$0.0722292\pi$
$683$			307.312i			0.449945i	−0.974365	+	0.224972i	$0.927771\pi$
$684$	88.4816	−	187.094i	0.129359	−	0.273529i
$685$		0			0
$686$	−715.518	−	160.663i	−1.04303	−	0.234203i
$687$		−	473.107i		−	0.688656i
$688$	−622.009	+	510.536i	−0.904083	+	0.742058i
$689$	1515.23			2.19917
$690$		0			0
$691$		−	893.378i		−	1.29288i	−0.762966	−	0.646438i	$-0.776258\pi$
$691$		−	893.378i		−	1.29288i	0.762966	−	0.646438i	$-0.223742\pi$
$692$	−100.237	−	47.4048i	−0.144852	−	0.0685041i
$693$	176.266			0.254353
$694$	298.978	+	67.1329i	0.430805	+	0.0967332i
$695$		0			0
$696$	−312.621	−	243.948i	−0.449169	−	0.350500i
$697$	613.186			0.879750
$698$	37.1270	−	165.346i	0.0531906	−	0.236886i
$699$		−	188.353i		−	0.269461i
$700$		0			0
$701$	1127.42			1.60830			0.804149	−	0.594428i	$-0.202622\pi$
$701$	1127.42			1.60830			0.804149	+	0.594428i	$0.202622\pi$
$702$	−188.270	−	42.2744i	−0.268191	−	0.0602199i
$703$		−	1161.29i		−	1.65191i
$704$	576.084	−	144.360i	0.818301	−	0.205056i
$705$		0			0
$706$	112.200	−	499.688i	0.158924	−	0.707773i
$707$		−	274.762i		−	0.388631i
$708$	120.722	+	57.0928i	0.170512	+	0.0806395i
$709$	1093.27			1.54199			0.770997	−	0.636839i	$-0.219758\pi$
$709$	1093.27			1.54199			0.770997	+	0.636839i	$0.219758\pi$
$710$		0			0
$711$		−	423.926i		−	0.596239i
$712$	−227.907	+	292.064i	−0.320094	+	0.410202i
$713$	792.091			1.11093
$714$	−66.8470	+	297.705i	−0.0936233	+	0.416954i
$715$		0			0
$716$	−349.415	+	738.837i	−0.488010	+	1.03190i
$717$	310.026			0.432393
$718$	1302.10	+	292.374i	1.81350	+	0.407206i
$719$			769.690i			1.07050i	0.844693	+	0.535251i	$0.179783\pi$
$719$			769.690i			1.07050i	−0.844693	+	0.535251i	$0.820217\pi$
$720$		0			0
$721$	−543.205			−0.753405
$722$	−27.8446	+	124.007i	−0.0385660	+	0.171755i
$723$			621.154i			0.859134i
$724$	180.172	+	85.2081i	0.248857	+	0.117691i
$725$		0			0
$726$	−117.921	−	26.4782i	−0.162426	−	0.0364713i
$727$			295.050i			0.405846i	0.979195	+	0.202923i	$0.0650441\pi$
$727$			295.050i			0.405846i	−0.979195	+	0.202923i	$0.934956\pi$
$728$	−741.468	−	578.591i	−1.01850	−	0.794767i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$		−	699.638i		−	0.957097i
$732$	−157.448	+	332.924i	−0.215094	+	0.454814i
$733$	−261.200			−0.356344			−0.178172	−	0.983999i	$-0.557018\pi$
$733$	−261.200			−0.356344			−0.178172	+	0.983999i	$0.557018\pi$
$734$	478.684	+	107.484i	0.652158	+	0.146436i
$735$		0			0
$736$	485.150	+	963.638i	0.659172	+	1.30929i
$737$	41.7501			0.0566487
$738$	−57.9426	+	258.049i	−0.0785130	+	0.349660i
$739$			482.679i			0.653151i	0.945171	+	0.326576i	$0.105895\pi$
$739$			482.679i			0.653151i	−0.945171	+	0.326576i	$0.894105\pi$
$740$		0			0
$741$	−554.652			−0.748519
$742$	1008.31	+	226.407i	1.35891	+	0.305130i
$743$		−	23.7067i		−	0.0319067i	−0.999873	−	0.0159534i	$-0.994922\pi$
$743$		−	23.7067i		−	0.0319067i	0.999873	−	0.0159534i	$-0.00507833\pi$
$744$	−200.271	+	256.648i	−0.269181	+	0.344957i
$745$		0			0
$746$	306.189	−	1363.62i	0.410441	−	1.82791i
$747$		−	209.551i		−	0.280523i
$748$	−220.756	+	466.788i	−0.295129	+	0.624048i
$749$	−1159.17			−1.54762
$750$		0			0
$751$			395.508i			0.526642i	0.964708	+	0.263321i	$0.0848179\pi$
$751$			395.508i			0.526642i	−0.964708	+	0.263321i	$0.915182\pi$
$752$	385.365	−	316.302i	0.512453	−	0.420614i
$753$	−530.389			−0.704368
$754$	−232.825	+	1036.90i	−0.308787	+	1.37519i
$755$		0			0
$756$	−118.968	−	56.2630i	−0.157365	−	0.0744219i
$757$	−393.940			−0.520396			−0.260198	−	0.965555i	$-0.583788\pi$
$757$	−393.940			−0.520396			−0.260198	+	0.965555i	$0.583788\pi$
$758$	−407.242	−	91.4425i	−0.537259	−	0.120637i
$759$			541.891i			0.713954i
$760$		0			0
$761$	−369.354			−0.485354			−0.242677	−	0.970107i	$-0.578025\pi$
$761$	−369.354			−0.485354			−0.242677	+	0.970107i	$0.578025\pi$
$762$	−16.9838	+	75.6379i	−0.0222885	+	0.0992623i
$763$			515.903i			0.676150i
$764$	1.94443	−	4.11150i	0.00254507	−	0.00538154i
$765$		0			0
$766$	−305.444	−	68.5846i	−0.398751	−	0.0895360i
$767$		−	357.890i		−	0.466610i
$768$	−434.896	−	86.4490i	−0.566271	−	0.112564i
$769$	−873.491			−1.13588			−0.567940	−	0.823070i	$-0.692259\pi$
$769$	−873.491			−1.13588			−0.567940	+	0.823070i	$0.692259\pi$
$770$		0			0
$771$			434.852i			0.564010i
$772$	−277.150	−	131.071i	−0.359003	−	0.169782i
$773$	1176.93			1.52254			0.761272	−	0.648432i	$-0.224575\pi$
$773$	1176.93			1.52254			0.761272	+	0.648432i	$0.224575\pi$
$774$	294.431	+	66.1119i	0.380402	+	0.0854159i
$775$		0			0
$776$	−337.394	+	432.372i	−0.434786	+	0.557181i
$777$	−738.433			−0.950365
$778$	−169.392	+	754.393i	−0.217728	+	0.969657i
$779$			760.224i			0.975897i
$780$		0			0
$781$	−123.754			−0.158455
$782$	−915.228	−	205.506i	−1.17037	−	0.262795i
$783$			148.702i			0.189913i
$784$	90.4464	+	110.195i	0.115365	+	0.140555i
$785$		0			0
$786$	−1.33053	+	5.92555i	−0.00169278	+	0.00753887i
$787$		−	603.482i		−	0.766814i	−0.923580	−	0.383407i	$-0.874751\pi$
$787$		−	603.482i		−	0.766814i	0.923580	−	0.383407i	$-0.125249\pi$
$788$	486.338	+	230.002i	0.617180	+	0.291880i
$789$	84.4626			0.107050
$790$		0			0
$791$			1094.20i			1.38331i
$792$	−175.580	−	137.011i	−0.221692	−	0.172993i
$793$	986.975			1.24461
$794$	−245.882	+	1095.04i	−0.309675	+	1.37915i
$795$		0			0
$796$	−301.002	+	636.467i	−0.378143	+	0.799582i
$797$	−860.121			−1.07920			−0.539599	−	0.841922i	$-0.681424\pi$
$797$	−860.121			−1.07920			−0.539599	+	0.841922i	$0.681424\pi$
$798$	−369.093	−	82.8765i	−0.462523	−	0.103855i
$799$			433.460i			0.542503i
$800$		0			0
$801$	138.924			0.173438
$802$	−7.41967	+	33.0437i	−0.00925146	+	0.0412017i
$803$		−	379.448i		−	0.472538i
$804$	−28.1784	−	13.3263i	−0.0350478	−	0.0165750i
$805$		0			0
$806$	851.245	+	191.139i	1.05614	+	0.237145i
$807$			257.548i			0.319143i
$808$	−213.570	+	273.692i	−0.264320	+	0.338728i
$809$	941.012			1.16318			0.581589	−	0.813483i	$-0.302431\pi$
$809$	941.012			1.16318			0.581589	+	0.813483i	$0.302431\pi$
$810$		0			0
$811$			1105.29i			1.36287i	0.731878	+	0.681436i	$0.238644\pi$
$811$			1105.29i			1.36287i	−0.731878	+	0.681436i	$0.761356\pi$
$812$	−309.867	+	655.213i	−0.381610	+	0.806912i
$813$	144.352			0.177554
$814$	−1219.30	−	273.784i	−1.49792	−	0.336344i
$815$		0			0
$816$	297.991	−	244.586i	0.365185	−	0.299738i
$817$	867.407			1.06170
$818$	−113.263	+	504.421i	−0.138463	+	0.616652i
$819$			352.688i			0.430632i
$820$		0			0
$821$	−193.170			−0.235286			−0.117643	−	0.993056i	$-0.537534\pi$
$821$	−193.170			−0.235286			−0.117643	+	0.993056i	$0.537534\pi$
$822$	−65.9374	−	14.8057i	−0.0802159	−	0.0180117i
$823$		−	178.778i		−	0.217227i	−0.994084	−	0.108614i	$-0.965359\pi$
$823$		−	178.778i		−	0.217227i	0.994084	−	0.108614i	$-0.0346411\pi$
$824$	541.090	+	422.229i	0.656662	+	0.512414i
$825$		0			0
$826$	53.4761	−	238.158i	0.0647410	−	0.288326i
$827$			1558.61i			1.88465i	0.334697	+	0.942326i	$0.391366\pi$
$827$			1558.61i			1.88465i	−0.334697	+	0.942326i	$0.608634\pi$
$828$	172.968	−	365.740i	0.208898	−	0.441714i
$829$	−565.477			−0.682119			−0.341059	−	0.940042i	$-0.610786\pi$
$829$	−565.477			−0.682119			−0.341059	+	0.940042i	$0.610786\pi$
$830$		0			0
$831$		−	249.554i		−	0.300306i
$832$	288.846	+	1152.67i	0.347171	+	1.38543i
$833$	−123.948			−0.148797
$834$	195.327	−	869.895i	0.234205	−	1.04304i
$835$		0			0
$836$	−578.721	−	273.692i	−0.692250	−	0.327383i
$837$	122.078			0.145851
$838$	−505.254	−	113.450i	−0.602928	−	0.135382i
$839$		−	1280.25i		−	1.52592i	−0.646443	−	0.762962i	$-0.723744\pi$
$839$		−	1280.25i		−	1.52592i	0.646443	−	0.762962i	$-0.276256\pi$
$840$		0			0
$841$	−22.0271			−0.0261915
$842$	−42.7066	+	190.195i	−0.0507204	+	0.225885i
$843$		−	595.256i		−	0.706116i
$844$	−372.952	+	788.604i	−0.441886	+	0.934365i
$845$		0			0
$846$	−182.415	−	40.9595i	−0.215620	−	0.0484155i
$847$			220.903i			0.260806i
$848$	−828.398	−	1009.28i	−0.976885	−	1.19018i
$849$	−545.518			−0.642542
$850$		0			0
$851$		−	2270.15i		−	2.66762i
$852$	83.5252	+	39.5012i	0.0980343	+	0.0463630i
$853$	−120.366			−0.141109			−0.0705546	−	0.997508i	$-0.522477\pi$
$853$	−120.366			−0.141109			−0.0705546	+	0.997508i	$0.522477\pi$
$854$	656.782	+	147.474i	0.769066	+	0.172687i
$855$		0			0
$856$	1154.66	+	901.014i	1.34890	+	1.05259i
$857$	717.784			0.837554			0.418777	−	0.908089i	$-0.362459\pi$
$857$	717.784			0.837554			0.418777	+	0.908089i	$0.362459\pi$
$858$	−130.764	+	582.360i	−0.152405	+	0.678741i
$859$		−	252.894i		−	0.294405i	−0.989106	−	0.147203i	$-0.952973\pi$
$859$		−	252.894i		−	0.294405i	0.989106	−	0.147203i	$-0.0470269\pi$
$860$		0			0
$861$	483.405			0.561446
$862$	−760.989	−	170.873i	−0.882817	−	0.198229i
$863$			1234.73i			1.43075i	0.698743	+	0.715373i	$0.253743\pi$
$863$			1234.73i			1.43075i	−0.698743	+	0.715373i	$0.746257\pi$
$864$	74.7717	+	148.517i	0.0865413	+	0.171894i
$865$		0			0
$866$	120.888	−	538.381i	0.139594	−	0.621687i
$867$		−	165.382i		−	0.190752i
$868$	537.901	+	254.387i	0.619701	+	0.293073i
$869$	−1311.29			−1.50897
$870$		0			0
$871$			83.5368i			0.0959091i
$872$	401.007	−	513.894i	0.459871	−	0.589327i
$873$	205.663			0.235582
$874$	254.785	−	1134.69i	0.291516	−	1.29828i
$875$		0			0
$876$	−121.117	+	256.101i	−0.138261	+	0.292353i
$877$	685.723			0.781896			0.390948	−	0.920413i	$-0.372147\pi$
$877$	685.723			0.781896			0.390948	+	0.920413i	$0.372147\pi$
$878$	870.609	+	195.487i	0.991582	+	0.222651i
$879$			11.3522i			0.0129149i
$880$		0			0
$881$	−458.454			−0.520379			−0.260189	−	0.965558i	$-0.583785\pi$
$881$	−458.454			−0.520379			−0.260189	+	0.965558i	$0.583785\pi$
$882$	11.7124	−	52.1614i	0.0132793	−	0.0591399i
$883$		−	771.505i		−	0.873732i	−0.899527	−	0.436866i	$-0.856088\pi$
$883$		−	771.505i		−	0.873732i	0.899527	−	0.436866i	$-0.143912\pi$
$884$	−933.986	−	441.707i	−1.05655	−	0.499668i
$885$		0			0
$886$	−1550.75	−	348.206i	−1.75028	−	0.393009i
$887$		−	1161.05i		−	1.30896i	−0.756080	−	0.654480i	$-0.772888\pi$
$887$		−	1161.05i		−	1.30896i	0.756080	−	0.654480i	$-0.227112\pi$
$888$	735.558	+	573.979i	0.828331	+	0.646372i
$889$	141.693			0.159385
$890$		0			0
$891$			83.5166i			0.0937336i
$892$	−561.905	+	1188.15i	−0.629938	+	1.33200i
$893$	−537.401			−0.601793
$894$	377.450	+	84.7529i	0.422203	+	0.0948019i
$895$		0			0
$896$	19.9793	+	810.207i	0.0222983	+	0.904248i
$897$	−1084.26			−1.20876
$898$	328.728	−	1464.00i	0.366066	−	1.63029i
$899$		−	672.340i		−	0.747876i
$900$		0			0
$901$	1135.24			1.25997
$902$	798.200	+	179.229i	0.884923	+	0.198701i
$903$		−	551.560i		−	0.610808i
$904$	850.514	−	1089.94i	0.940834	−	1.20569i
$905$		0			0
$906$	4.89722	−	21.8099i	0.00540532	−	0.0240728i
$907$			392.544i			0.432793i	0.976306	+	0.216397i	$0.0694304\pi$
$907$			392.544i			0.432793i	−0.976306	+	0.216397i	$0.930570\pi$
$908$	−269.597	+	570.062i	−0.296913	+	0.627822i
$909$	130.185			0.143218
$910$		0			0
$911$		−	1013.40i		−	1.11240i	−0.831048	−	0.556201i	$-0.812259\pi$
$911$		−	1013.40i		−	1.11240i	0.831048	−	0.556201i	$-0.187741\pi$
$912$	303.237	+	369.447i	0.332496	+	0.405096i
$913$	−648.185			−0.709950
$914$	44.2958	−	197.273i	0.0484637	−	0.215835i
$915$		0			0
$916$	987.707	+	467.112i	1.07828	+	0.509948i
$917$	11.1004			0.0121051
$918$	−141.056	−	31.6727i	−0.153655	−	0.0345019i
$919$			970.018i			1.05551i	0.849395	+	0.527757i	$0.176967\pi$
$919$			970.018i			1.05551i	−0.849395	+	0.527757i	$0.823033\pi$
$920$		0			0
$921$	−614.115			−0.666791
$922$	1.96603	−	8.75578i	0.00213236	−	0.00949651i
$923$		−	247.616i		−	0.268273i
$924$	−174.033	+	367.992i	−0.188348	+	0.398260i
$925$		0			0
$926$	1005.19	+	225.706i	1.08552	+	0.243743i
$927$		−	257.376i		−	0.277644i
$928$	817.952	−	411.804i	0.881414	−	0.443754i
$929$	980.857			1.05582			0.527910	−	0.849300i	$-0.322976\pi$
$929$	980.857			1.05582			0.527910	+	0.849300i	$0.322976\pi$
$930$		0			0
$931$		−	153.670i		−	0.165059i
$932$	393.226	+	185.967i	0.421917	+	0.199535i
$933$	334.956			0.359010
$934$	−576.638	−	129.479i	−0.617386	−	0.138628i
$935$		0			0
$936$	274.141	−	351.314i	0.292886	−	0.375336i
$937$	−964.666			−1.02953			−0.514763	−	0.857333i	$-0.672120\pi$
$937$	−964.666			−1.02953			−0.514763	+	0.857333i	$0.672120\pi$
$938$	−12.4821	+	55.5896i	−0.0133072	+	0.0592639i
$939$			40.7420i			0.0433887i
$940$		0			0
$941$	−1581.10			−1.68023			−0.840117	−	0.542405i	$-0.817514\pi$
$941$	−1581.10			−1.68023			−0.840117	+	0.542405i	$0.817514\pi$
$942$	−256.563	−	57.6089i	−0.272360	−	0.0611560i
$943$			1486.12i			1.57595i
$944$	−238.386	+	195.663i	−0.252527	+	0.207271i
$945$		0			0
$946$	204.498	−	910.738i	0.216171	−	0.962725i
$947$		−	1245.27i		−	1.31497i	−0.753469	−	0.657483i	$-0.771621\pi$
$947$		−	1245.27i		−	1.31497i	0.753469	−	0.657483i	$-0.228379\pi$
$948$	885.032	+	418.555i	0.933578	+	0.441513i
$949$	759.229			0.800031
$950$		0			0
$951$			370.666i			0.389765i
$952$	−555.521	−	433.490i	−0.583530	−	0.455347i
$953$	−1106.52			−1.16109			−0.580546	−	0.814228i	$-0.697161\pi$
$953$	−1106.52			−1.16109			−0.580546	+	0.814228i	$0.697161\pi$
$954$	−107.274	+	477.746i	−0.112446	+	0.500782i
$955$		0			0
$956$	−306.098	+	647.243i	−0.320186	+	0.677032i
$957$	459.966			0.480633
$958$	−533.037	−	119.689i	−0.556406	−	0.124936i
$959$			123.521i			0.128802i
$960$		0			0
$961$	409.039			0.425638
$962$	547.808	−	2439.68i	0.569447	−	2.53605i
$963$		−	549.225i		−	0.570327i
$964$	−1296.79	−	613.284i	−1.34521	−	0.636187i
$965$		0			0
$966$	−721.520	−	162.011i	−0.746915	−	0.167713i
$967$			406.453i			0.420324i	0.977667	+	0.210162i	$0.0673992\pi$
$967$			406.453i			0.420324i	−0.977667	+	0.210162i	$0.932601\pi$
$968$	171.706	−	220.042i	0.177382	−	0.227316i
$969$	−415.555			−0.428850
$970$		0			0
$971$			1815.22i			1.86943i	0.355393	+	0.934717i	$0.384347\pi$
$971$			1815.22i			1.86943i	−0.355393	+	0.934717i	$0.615653\pi$
$972$	26.6579	−	56.3680i	0.0274258	−	0.0579918i
$973$	−1629.58			−1.67480
$974$	698.119	+	156.756i	0.716754	+	0.160941i
$975$		0			0
$976$	−539.594	−	657.412i	−0.552862	−	0.673578i
$977$	1457.74			1.49205			0.746027	−	0.665916i	$-0.231959\pi$
$977$	1457.74			1.49205			0.746027	+	0.665916i	$0.231959\pi$
$978$	189.201	−	842.614i	0.193457	−	0.861568i
$979$		−	429.720i		−	0.438938i
$980$		0			0
$981$	−244.439			−0.249174
$982$	824.235	+	185.074i	0.839343	+	0.188467i
$983$			19.9496i			0.0202946i	0.999949	+	0.0101473i	$0.00323004\pi$
$983$			19.9496i			0.0202946i	−0.999949	+	0.0101473i	$0.996770\pi$
$984$	−481.522	−	375.747i	−0.489352	−	0.381857i
$985$		0			0
$986$	−174.437	+	776.860i	−0.176914	+	0.787891i
$987$			341.718i			0.346219i
$988$	547.625	−	1157.95i	0.554276	−	1.17201i
$989$	1695.65			1.71450
$990$		0			0
$991$		−	605.720i		−	0.611221i	−0.952157	−	0.305611i	$-0.901139\pi$
$991$		−	605.720i		−	0.611221i	0.952157	−	0.305611i	$-0.0988605\pi$
$992$	−338.073	−	671.502i	−0.340799	−	0.676918i
$993$	−714.392			−0.719428
$994$	36.9989	−	164.776i	0.0372223	−	0.165771i
$995$		0			0
$996$	437.481	+	206.896i	0.439237	+	0.207727i
$997$	−1238.47			−1.24220			−0.621099	−	0.783732i	$-0.713314\pi$
$997$	−1238.47			−1.24220			−0.621099	+	0.783732i	$0.713314\pi$
$998$	404.129	+	90.7434i	0.404939	+	0.0909253i
$999$		−	349.876i		−	0.350227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.3.c.d.151.6		8
3.2	odd	2		900.3.c.u.451.3		8
4.3	odd	2	inner	300.3.c.d.151.5		8
5.2	odd	4		300.3.f.b.199.1		16
5.3	odd	4		300.3.f.b.199.16		16
5.4	even	2		60.3.c.a.31.3	✓	8
12.11	even	2		900.3.c.u.451.4		8
15.2	even	4		900.3.f.f.199.16		16
15.8	even	4		900.3.f.f.199.1		16
15.14	odd	2		180.3.c.b.91.6		8
20.3	even	4		300.3.f.b.199.2		16
20.7	even	4		300.3.f.b.199.15		16
20.19	odd	2		60.3.c.a.31.4	yes	8
40.19	odd	2		960.3.e.c.511.2		8
40.29	even	2		960.3.e.c.511.5		8
60.23	odd	4		900.3.f.f.199.15		16
60.47	odd	4		900.3.f.f.199.2		16
60.59	even	2		180.3.c.b.91.5		8
120.29	odd	2		2880.3.e.j.2431.5		8
120.59	even	2		2880.3.e.j.2431.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.c.a.31.3	✓	8	5.4	even	2
60.3.c.a.31.4	yes	8	20.19	odd	2
180.3.c.b.91.5		8	60.59	even	2
180.3.c.b.91.6		8	15.14	odd	2
300.3.c.d.151.5		8	4.3	odd	2	inner
300.3.c.d.151.6		8	1.1	even	1	trivial
300.3.f.b.199.1		16	5.2	odd	4
300.3.f.b.199.2		16	20.3	even	4
300.3.f.b.199.15		16	20.7	even	4
300.3.f.b.199.16		16	5.3	odd	4
900.3.c.u.451.3		8	3.2	odd	2
900.3.c.u.451.4		8	12.11	even	2
900.3.f.f.199.1		16	15.8	even	4
900.3.f.f.199.2		16	60.47	odd	4
900.3.f.f.199.15		16	60.23	odd	4
900.3.f.f.199.16		16	15.2	even	4
960.3.e.c.511.2		8	40.19	odd	2
960.3.e.c.511.5		8	40.29	even	2
2880.3.e.j.2431.5		8	120.29	odd	2
2880.3.e.j.2431.8		8	120.59	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	300.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.438172 + 1.95141i) q^{2} +1.73205i q^{3} +(-3.61601 - 1.71011i) q^{4} +(-3.37994 - 0.758935i) q^{6} +6.33166i q^{7} +(4.92155 - 6.30701i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-0.438172 + 1.95141i) q^{2} +1.73205i q^{3} +(-3.61601 - 1.71011i) q^{4} +(-3.37994 - 0.758935i) q^{6} +6.33166i q^{7} +(4.92155 - 6.30701i) q^{8} -3.00000 q^{9} +9.27963i q^{11} +(2.96199 - 6.26312i) q^{12} -18.5674 q^{13} +(-12.3557 - 2.77436i) q^{14} +(10.1511 + 12.3675i) q^{16} -13.9110 q^{17} +(1.31451 - 5.85423i) q^{18} -17.2468i q^{19} -10.9668 q^{21} +(-18.1084 - 4.06607i) q^{22} -33.7148i q^{23} +(10.9241 + 8.52438i) q^{24} +(8.13571 - 36.2327i) q^{26} -5.19615i q^{27} +(10.8278 - 22.8954i) q^{28} -28.6177 q^{29} +23.4939i q^{31} +(-28.5820 + 14.3898i) q^{32} -16.0728 q^{33} +(6.09542 - 27.1461i) q^{34} +(10.8480 + 5.13032i) q^{36} +67.3338 q^{37} +(33.6556 + 7.55706i) q^{38} -32.1597i q^{39} -44.0791 q^{41} +(4.80532 - 21.4007i) q^{42} +50.2937i q^{43} +(15.8691 - 33.5552i) q^{44} +(65.7915 + 14.7729i) q^{46} -31.1594i q^{47} +(-21.4212 + 17.5822i) q^{48} +8.91003 q^{49} -24.0946i q^{51} +(67.1400 + 31.7522i) q^{52} -81.6070 q^{53} +(10.1398 + 2.27681i) q^{54} +(39.9338 + 31.1616i) q^{56} +29.8724 q^{57} +(12.5395 - 55.8449i) q^{58} +19.2751i q^{59} -53.1563 q^{61} +(-45.8462 - 10.2943i) q^{62} -18.9950i q^{63} +(-15.5566 - 62.0805i) q^{64} +(7.04264 - 31.3646i) q^{66} -4.49911i q^{67} +(50.3025 + 23.7893i) q^{68} +58.3958 q^{69} +13.3360i q^{71} +(-14.7647 + 18.9210i) q^{72} -40.8904 q^{73} +(-29.5037 + 131.396i) q^{74} +(-29.4939 + 62.3647i) q^{76} -58.7555 q^{77} +(62.7568 + 14.0915i) q^{78} +141.309i q^{79} +9.00000 q^{81} +(19.3142 - 86.0164i) q^{82} +69.8503i q^{83} +(39.6559 + 18.7543i) q^{84} +(-98.1438 - 22.0373i) q^{86} -49.5673i q^{87} +(58.5266 + 45.6702i) q^{88} -46.3079 q^{89} -117.563i q^{91} +(-57.6559 + 121.913i) q^{92} -40.6926 q^{93} +(60.8049 + 13.6532i) q^{94} +(-24.9239 - 49.5055i) q^{96} -68.5543 q^{97} +(-3.90412 + 17.3871i) q^{98} -27.8389i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 10 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 10 * q^4 - 6 * q^6 + 20 * q^8 - 24 * q^9	\( 8 q - 4 q^{2} + 10 q^{4} - 6 q^{6} + 20 q^{8} - 24 q^{9} - 16 q^{13} - 20 q^{14} + 34 q^{16} + 12 q^{18} - 48 q^{21} - 68 q^{22} + 18 q^{24} - 36 q^{26} - 28 q^{28} + 64 q^{29} + 76 q^{32} - 92 q^{34} - 30 q^{36} + 112 q^{37} + 40 q^{38} - 16 q^{41} - 108 q^{42} + 172 q^{44} + 152 q^{46} - 48 q^{48} - 56 q^{49} + 128 q^{52} - 352 q^{53} + 18 q^{54} + 116 q^{56} - 144 q^{57} + 204 q^{58} - 176 q^{61} + 56 q^{62} - 110 q^{64} + 108 q^{66} + 184 q^{68} - 96 q^{69} - 60 q^{72} + 240 q^{73} + 132 q^{74} - 24 q^{76} + 288 q^{77} + 240 q^{78} + 72 q^{81} - 40 q^{82} - 36 q^{84} - 200 q^{86} - 140 q^{88} + 80 q^{89} - 144 q^{92} - 144 q^{93} - 96 q^{94} - 174 q^{96} - 432 q^{97} - 660 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 10 * q^4 - 6 * q^6 + 20 * q^8 - 24 * q^9 - 16 * q^13 - 20 * q^14 + 34 * q^16 + 12 * q^18 - 48 * q^21 - 68 * q^22 + 18 * q^24 - 36 * q^26 - 28 * q^28 + 64 * q^29 + 76 * q^32 - 92 * q^34 - 30 * q^36 + 112 * q^37 + 40 * q^38 - 16 * q^41 - 108 * q^42 + 172 * q^44 + 152 * q^46 - 48 * q^48 - 56 * q^49 + 128 * q^52 - 352 * q^53 + 18 * q^54 + 116 * q^56 - 144 * q^57 + 204 * q^58 - 176 * q^61 + 56 * q^62 - 110 * q^64 + 108 * q^66 + 184 * q^68 - 96 * q^69 - 60 * q^72 + 240 * q^73 + 132 * q^74 - 24 * q^76 + 288 * q^77 + 240 * q^78 + 72 * q^81 - 40 * q^82 - 36 * q^84 - 200 * q^86 - 140 * q^88 + 80 * q^89 - 144 * q^92 - 144 * q^93 - 96 * q^94 - 174 * q^96 - 432 * q^97 - 660 * q^98

Introduction

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