LMFDB - Embedded newform 300.3.f.b.199.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,3,Mod(199,300)]

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, 1]))

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

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

chi := DirichletCharacter("300.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	300.f (of order $2$, degree $1$, not 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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 5x^{14} + 12x^{12} + 25x^{10} + 53x^{8} + 100x^{6} + 192x^{4} + 320x^{2} + 256 $ x^16 + 5x^14 + 12x^12 + 25x^10 + 53x^8 + 100x^6 + 192x^4 + 320*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{24} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.15
Root			$-1.28061 - 0.600040i$ of defining polynomial
Character	$\chi$	$=$	300.199
Dual form			300.3.f.b.199.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.95141 - 0.438172i) q^{2} -1.73205 q^{3} +(3.61601 - 1.71011i) q^{4} +(-3.37994 + 0.758935i) q^{6} +6.33166 q^{7} +(6.30701 - 4.92155i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(1.95141 - 0.438172i) q^{2} -1.73205 q^{3} +(3.61601 - 1.71011i) q^{4} +(-3.37994 + 0.758935i) q^{6} +6.33166 q^{7} +(6.30701 - 4.92155i) q^{8} +3.00000 q^{9} -9.27963i q^{11} +(-6.26312 + 2.96199i) q^{12} +18.5674i q^{13} +(12.3557 - 2.77436i) q^{14} +(10.1511 - 12.3675i) q^{16} -13.9110i q^{17} +(5.85423 - 1.31451i) q^{18} -17.2468i q^{19} -10.9668 q^{21} +(-4.06607 - 18.1084i) q^{22} +33.7148 q^{23} +(-10.9241 + 8.52438i) q^{24} +(8.13571 + 36.2327i) q^{26} -5.19615 q^{27} +(22.8954 - 10.8278i) q^{28} +28.6177 q^{29} -23.4939i q^{31} +(14.3898 - 28.5820i) q^{32} +16.0728i q^{33} +(-6.09542 - 27.1461i) q^{34} +(10.8480 - 5.13032i) q^{36} +67.3338i q^{37} +(-7.55706 - 33.6556i) q^{38} -32.1597i q^{39} -44.0791 q^{41} +(-21.4007 + 4.80532i) q^{42} -50.2937 q^{43} +(-15.8691 - 33.5552i) q^{44} +(65.7915 - 14.7729i) q^{46} -31.1594 q^{47} +(-17.5822 + 21.4212i) q^{48} -8.91003 q^{49} +24.0946i q^{51} +(31.7522 + 67.1400i) q^{52} +81.6070i q^{53} +(-10.1398 + 2.27681i) q^{54} +(39.9338 - 31.1616i) q^{56} +29.8724i q^{57} +(55.8449 - 12.5395i) q^{58} +19.2751i q^{59} -53.1563 q^{61} +(-10.2943 - 45.8462i) q^{62} +18.9950 q^{63} +(15.5566 - 62.0805i) q^{64} +(7.04264 + 31.3646i) q^{66} -4.49911 q^{67} +(-23.7893 - 50.3025i) q^{68} -58.3958 q^{69} -13.3360i q^{71} +(18.9210 - 14.7647i) q^{72} +40.8904i q^{73} +(29.5037 + 131.396i) q^{74} +(-29.4939 - 62.3647i) q^{76} -58.7555i q^{77} +(-14.0915 - 62.7568i) q^{78} +141.309i q^{79} +9.00000 q^{81} +(-86.0164 + 19.3142i) q^{82} -69.8503 q^{83} +(-39.6559 + 18.7543i) q^{84} +(-98.1438 + 22.0373i) q^{86} -49.5673 q^{87} +(-45.6702 - 58.5266i) q^{88} +46.3079 q^{89} +117.563i q^{91} +(121.913 - 57.6559i) q^{92} +40.6926i q^{93} +(-60.8049 + 13.6532i) q^{94} +(-24.9239 + 49.5055i) q^{96} -68.5543i q^{97} +(-17.3871 + 3.90412i) q^{98} -27.8389i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 20 q^{4} - 12 q^{6} + 48 q^{9}+O(q^{10}) $ 16 * q - 20 * q^4 - 12 * q^6 + 48 * q^9	$ 16 q - 20 q^{4} - 12 q^{6} + 48 q^{9} + 40 q^{14} + 68 q^{16} - 96 q^{21} - 36 q^{24} - 72 q^{26} - 128 q^{29} + 184 q^{34} - 60 q^{36} - 32 q^{41} - 344 q^{44} + 304 q^{46} + 112 q^{49} - 36 q^{54} + 232 q^{56} - 352 q^{61} + 220 q^{64} + 216 q^{66} + 192 q^{69} - 264 q^{74} - 48 q^{76} + 144 q^{81} + 72 q^{84} - 400 q^{86} - 160 q^{89} + 192 q^{94} - 348 q^{96}+O(q^{100}) $ 16 * q - 20 * q^4 - 12 * q^6 + 48 * q^9 + 40 * q^14 + 68 * q^16 - 96 * q^21 - 36 * q^24 - 72 * q^26 - 128 * q^29 + 184 * q^34 - 60 * q^36 - 32 * q^41 - 344 * q^44 + 304 * q^46 + 112 * q^49 - 36 * q^54 + 232 * q^56 - 352 * q^61 + 220 * q^64 + 216 * q^66 + 192 * q^69 - 264 * q^74 - 48 * q^76 + 144 * q^81 + 72 * q^84 - 400 * q^86 - 160 * q^89 + 192 * q^94 - 348 * 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 $

$2$	1.95141	−	0.438172i	0.975706	−	0.219086i
$2$	1.95141	−	0.438172i	0.975706	−	0.219086i
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	3.61601	−	1.71011i	0.904003	−	0.427526i
$5$		0			0
$5$		0			0
$6$	−3.37994	+	0.758935i	−0.563324	+	0.126489i
$7$	6.33166			0.904523			0.452262	−	0.891885i	$-0.350617\pi$
$7$	6.33166			0.904523			0.452262	+	0.891885i	$0.350617\pi$
$8$	6.30701	−	4.92155i	0.788376	−	0.615194i
$9$	3.00000			0.333333
$10$		0			0
$11$		−	9.27963i		−	0.843602i	−0.906688	−	0.421801i	$-0.861398\pi$
$11$		−	9.27963i		−	0.843602i	0.906688	−	0.421801i	$-0.138602\pi$
$12$	−6.26312	+	2.96199i	−0.521926	+	0.246833i
$13$			18.5674i			1.42826i	0.700012	+	0.714131i	$0.253178\pi$
$13$			18.5674i			1.42826i	−0.700012	+	0.714131i	$0.746822\pi$
$14$	12.3557	−	2.77436i	0.882549	−	0.198168i
$15$		0			0
$16$	10.1511	−	12.3675i	0.634442	−	0.772970i
$17$		−	13.9110i		−	0.818296i	−0.912468	−	0.409148i	$-0.865826\pi$
$17$		−	13.9110i		−	0.818296i	0.912468	−	0.409148i	$-0.134174\pi$
$18$	5.85423	−	1.31451i	0.325235	−	0.0730286i
$19$		−	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
$22$	−4.06607	−	18.1084i	−0.184821	−	0.823108i
$23$	33.7148			1.46586			0.732931	−	0.680303i	$-0.238152\pi$
$23$	33.7148			1.46586			0.732931	+	0.680303i	$0.238152\pi$
$24$	−10.9241	+	8.52438i	−0.455169	+	0.355183i
$25$		0			0
$26$	8.13571	+	36.2327i	0.312912	+	1.39356i
$27$	−5.19615			−0.192450
$28$	22.8954	−	10.8278i	0.817692	−	0.386708i
$29$	28.6177			0.986817			0.493409	−	0.869798i	$-0.335751\pi$
$29$	28.6177			0.986817			0.493409	+	0.869798i	$0.335751\pi$
$30$		0			0
$31$		−	23.4939i		−	0.757866i	−0.925424	−	0.378933i	$-0.876291\pi$
$31$		−	23.4939i		−	0.757866i	0.925424	−	0.378933i	$-0.123709\pi$
$32$	14.3898	−	28.5820i	0.449682	−	0.893189i
$33$			16.0728i			0.487054i
$34$	−6.09542	−	27.1461i	−0.179277	−	0.798416i
$35$		0			0
$36$	10.8480	−	5.13032i	0.301334	−	0.142509i
$37$			67.3338i			1.81983i	0.414793	+	0.909916i	$0.363854\pi$
$37$			67.3338i			1.81983i	−0.414793	+	0.909916i	$0.636146\pi$
$38$	−7.55706	−	33.6556i	−0.198870	−	0.885674i
$39$		−	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	$0.680650\pi$
$42$	−21.4007	+	4.80532i	−0.509540	+	0.114412i
$43$	−50.2937			−1.16962			−0.584811	−	0.811170i	$-0.698831\pi$
$43$	−50.2937			−1.16962			−0.584811	+	0.811170i	$0.698831\pi$
$44$	−15.8691	−	33.5552i	−0.360662	−	0.762619i
$45$		0			0
$46$	65.7915	−	14.7729i	1.43025	−	0.321150i
$47$	−31.1594			−0.662967			−0.331483	−	0.943461i	$-0.607549\pi$
$47$	−31.1594			−0.662967			−0.331483	+	0.943461i	$0.607549\pi$
$48$	−17.5822	+	21.4212i	−0.366295	+	0.446275i
$49$	−8.91003			−0.181837
$50$		0			0
$51$			24.0946i			0.472444i
$52$	31.7522	+	67.1400i	0.610620	+	1.29115i
$53$			81.6070i			1.53975i	0.638192	+	0.769877i	$0.279682\pi$
$53$			81.6070i			1.53975i	−0.638192	+	0.769877i	$0.720318\pi$
$54$	−10.1398	+	2.27681i	−0.187775	+	0.0421631i
$55$		0			0
$56$	39.9338	−	31.1616i	0.713104	−	0.556457i
$57$			29.8724i			0.524077i
$58$	55.8449	−	12.5395i	0.962843	−	0.216198i
$59$			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	$0.643502\pi$
$62$	−10.2943	−	45.8462i	−0.166038	−	0.739455i
$63$	18.9950			0.301508
$64$	15.5566	−	62.0805i	0.243072	−	0.970008i
$65$		0			0
$66$	7.04264	+	31.3646i	0.106707	+	0.475221i
$67$	−4.49911			−0.0671509			−0.0335754	−	0.999436i	$-0.510689\pi$
$67$	−4.49911			−0.0671509			−0.0335754	+	0.999436i	$0.510689\pi$
$68$	−23.7893	−	50.3025i	−0.349843	−	0.739742i
$69$	−58.3958			−0.846316
$70$		0			0
$71$		−	13.3360i		−	0.187832i	−0.995580	−	0.0939158i	$-0.970062\pi$
$71$		−	13.3360i		−	0.187832i	0.995580	−	0.0939158i	$-0.0299385\pi$
$72$	18.9210	−	14.7647i	0.262792	−	0.205065i
$73$			40.8904i			0.560143i	0.959979	+	0.280071i	$0.0903581\pi$
$73$			40.8904i			0.560143i	−0.959979	+	0.280071i	$0.909642\pi$
$74$	29.5037	+	131.396i	0.398699	+	1.77562i
$75$		0			0
$76$	−29.4939	−	62.3647i	−0.388077	−	0.820588i
$77$		−	58.7555i		−	0.763058i
$78$	−14.0915	−	62.7568i	−0.180660	−	0.804574i
$79$			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
$82$	−86.0164	+	19.3142i	−1.04898	+	0.235539i
$83$	−69.8503			−0.841570			−0.420785	−	0.907160i	$-0.638245\pi$
$83$	−69.8503			−0.841570			−0.420785	+	0.907160i	$0.638245\pi$
$84$	−39.6559	+	18.7543i	−0.472095	+	0.223266i
$85$		0			0
$86$	−98.1438	+	22.0373i	−1.14121	+	0.256248i
$87$	−49.5673			−0.569739
$88$	−45.6702	−	58.5266i	−0.518979	−	0.665076i
$89$	46.3079			0.520313			0.260157	−	0.965566i	$-0.416226\pi$
$89$	46.3079			0.520313			0.260157	+	0.965566i	$0.416226\pi$
$90$		0			0
$91$			117.563i			1.29190i
$92$	121.913	−	57.6559i	1.32514	−	0.626695i
$93$			40.6926i			0.437554i
$94$	−60.8049	+	13.6532i	−0.646860	+	0.145247i
$95$		0			0
$96$	−24.9239	+	49.5055i	−0.259624	+	0.515683i
$97$		−	68.5543i		−	0.706745i	−0.935483	−	0.353373i	$-0.885035\pi$
$97$		−	68.5543i		−	0.706745i	0.935483	−	0.353373i	$-0.114965\pi$
$98$	−17.3871	+	3.90412i	−0.177420	+	0.0398380i
$99$		−	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	$0.568919\pi$
$102$	10.5576	+	47.0185i	0.103506	+	0.460966i
$103$	−85.7919			−0.832931			−0.416465	−	0.909152i	$-0.636731\pi$
$103$	−85.7919			−0.832931			−0.416465	+	0.909152i	$0.636731\pi$
$104$	91.3805	+	117.105i	0.878659	+	1.12601i
$105$		0			0
$106$	35.7579	+	159.249i	0.337338	+	1.50235i
$107$	183.075			1.71098			0.855491	−	0.517818i	$-0.173255\pi$
$107$	183.075			1.71098			0.855491	+	0.517818i	$0.173255\pi$
$108$	−18.7893	+	8.88597i	−0.173975	+	0.0822775i
$109$	−81.4798			−0.747521			−0.373761	−	0.927525i	$-0.621932\pi$
$109$	−81.4798			−0.747521			−0.373761	+	0.927525i	$0.621932\pi$
$110$		0			0
$111$		−	116.625i		−	1.05068i
$112$	64.2732	−	78.3070i	0.573868	−	0.699170i
$113$		−	172.814i		−	1.52933i	−0.644429	−	0.764664i	$-0.722905\pi$
$113$		−	172.814i		−	1.52933i	0.644429	−	0.764664i	$-0.277095\pi$
$114$	13.0892	+	58.2933i	0.114818	+	0.511344i
$115$		0			0
$116$	103.482	−	48.9393i	0.892086	−	0.421891i
$117$			55.7022i			0.476087i
$118$	8.44582	+	37.6137i	0.0715748	+	0.318760i
$119$		−	88.0800i		−	0.740168i
$120$		0			0
$121$	34.8885			0.288335
$122$	−103.730	+	23.2916i	−0.850244	+	0.190915i
$123$	76.3472			0.620709
$124$	−40.1770	−	84.9541i	−0.324008	−	0.685113i
$125$		0			0
$126$	37.0670	−	8.32307i	0.294183	−	0.0660561i
$127$	−22.3785			−0.176208			−0.0881041	−	0.996111i	$-0.528081\pi$
$127$	−22.3785			−0.176208			−0.0881041	+	0.996111i	$0.528081\pi$
$128$	3.15546	−	127.961i	0.0246520	−	0.999696i
$129$	87.1113			0.675282
$130$		0			0
$131$			1.75315i			0.0133828i	0.999978	+	0.00669141i	$0.00212996\pi$
$131$			1.75315i			0.0133828i	−0.999978	+	0.00669141i	$0.997870\pi$
$132$	27.4862	+	58.1194i	0.208228	+	0.440298i
$133$		−	109.201i		−	0.821060i
$134$	−8.77961	+	1.97138i	−0.0655195	+	0.0147118i
$135$		0			0
$136$	−68.4639	−	87.7370i	−0.503411	−	0.645125i
$137$			19.5084i			0.142397i	0.997462	+	0.0711987i	$0.0226824\pi$
$137$			19.5084i			0.142397i	−0.997462	+	0.0711987i	$0.977318\pi$
$138$	−113.954	+	25.5874i	−0.825755	+	0.185416i
$139$			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
$142$	−5.84348	−	26.0241i	−0.0411512	−	0.183268i
$143$	172.299			1.20489
$144$	30.4532	−	37.1026i	0.211481	−	0.257657i
$145$		0			0
$146$	17.9170	+	79.7940i	0.122719	+	0.546534i
$147$	15.4326			0.104984
$148$	115.148	+	243.480i	0.778026	+	1.64513i
$149$	111.673			0.749486			0.374743	−	0.927129i	$-0.377731\pi$
$149$	111.673			0.749486			0.374743	+	0.927129i	$0.377731\pi$
$150$		0			0
$151$		−	6.45275i		−	0.0427335i	−0.999772	−	0.0213667i	$-0.993198\pi$
$151$		−	6.45275i		−	0.0427335i	0.999772	−	0.0213667i	$-0.00680176\pi$
$152$	−84.8811	−	108.776i	−0.558428	−	0.715630i
$153$		−	41.7331i		−	0.272765i
$154$	−25.7450	−	114.656i	−0.167175	−	0.744520i
$155$		0			0
$156$	−54.9965	−	116.290i	−0.352542	−	0.745448i
$157$			75.9075i			0.483488i	0.970340	+	0.241744i	$0.0777193\pi$
$157$			75.9075i			0.483488i	−0.970340	+	0.241744i	$0.922281\pi$
$158$	61.9174	+	275.751i	0.391882	+	1.74526i
$159$		−	141.347i		−	0.888977i
$160$		0			0
$161$	213.471			1.32591
$162$	17.5627	−	3.94354i	0.108412	−	0.0243429i
$163$	−249.298			−1.52944			−0.764719	−	0.644364i	$-0.777122\pi$
$163$	−249.298			−1.52944			−0.764719	+	0.644364i	$0.777122\pi$
$164$	−159.391	+	75.3799i	−0.971893	+	0.459634i
$165$		0			0
$166$	−136.307	+	30.6064i	−0.821124	+	0.184376i
$167$	−79.1883			−0.474182			−0.237091	−	0.971487i	$-0.576194\pi$
$167$	−79.1883			−0.474182			−0.237091	+	0.971487i	$0.576194\pi$
$168$	−69.1674	+	53.9735i	−0.411711	+	0.321271i
$169$	−175.749			−1.03993
$170$		0			0
$171$		−	51.7404i		−	0.302576i
$172$	−181.863	+	86.0076i	−1.05734	+	0.500044i
$173$		−	27.7204i		−	0.160234i	−0.996785	−	0.0801168i	$-0.974471\pi$
$173$		−	27.7204i		−	0.160234i	0.996785	−	0.0801168i	$-0.0255293\pi$
$174$	−96.7262	+	21.7190i	−0.555898	+	0.124822i
$175$		0			0
$176$	−114.766	−	94.1982i	−0.652080	−	0.535217i
$177$		−	33.3855i		−	0.188619i
$178$	90.3657	−	20.2908i	0.507673	−	0.113993i
$179$		−	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	$0.543952\pi$
$182$	51.5126	+	229.413i	0.283036	+	1.26051i
$183$	92.0694			0.503112
$184$	212.640	−	165.929i	1.15565	−	0.901790i
$185$		0			0
$186$	17.8303	+	79.4079i	0.0958620	+	0.426924i
$187$	−129.089			−0.690317
$188$	−112.673	+	53.2859i	−0.599324	+	0.283436i
$189$	−32.9003			−0.174076
$190$		0			0
$191$		−	1.13703i		−	0.00595301i	−0.999996	−	0.00297651i	$-0.999053\pi$
$191$		−	1.13703i		−	0.00595301i	0.999996	−	0.00297651i	$-0.000947453\pi$
$192$	−26.9449	+	107.527i	−0.140338	+	0.560034i
$193$		−	76.6452i		−	0.397126i	−0.980088	−	0.198563i	$-0.936373\pi$
$193$		−	76.6452i		−	0.397126i	0.980088	−	0.198563i	$-0.0636274\pi$
$194$	−30.0385	−	133.778i	−0.154838	−	0.689575i
$195$		0			0
$196$	−32.2188	+	15.2371i	−0.164382	+	0.0777403i
$197$		−	134.496i		−	0.682719i	−0.939933	−	0.341359i	$-0.889113\pi$
$197$		−	134.496i		−	0.682719i	0.939933	−	0.341359i	$-0.110887\pi$
$198$	−12.1982	−	54.3251i	−0.0616071	−	0.274369i
$199$		−	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
$202$	−84.6813	+	19.0144i	−0.419214	+	0.0941308i
$203$	181.198			0.892599
$204$	41.2044	+	87.1264i	0.201982	+	0.427090i
$205$		0			0
$206$	−167.415	+	37.5916i	−0.812695	+	0.182483i
$207$	101.144			0.488621
$208$	229.633	+	188.479i	1.10400	+	0.906150i
$209$	−160.044			−0.765761
$210$		0			0
$211$			218.087i			1.03359i	0.856110	+	0.516793i	$0.172874\pi$
$211$			218.087i			1.03359i	−0.856110	+	0.516793i	$0.827126\pi$
$212$	139.557	+	295.092i	0.658286	+	1.39194i
$213$			23.0987i			0.108445i
$214$	357.255	−	80.2183i	1.66941	−	0.374852i
$215$		0			0
$216$	−32.7722	+	25.5731i	−0.151723	+	0.118394i
$217$		−	148.755i		−	0.685508i
$218$	−159.001	+	35.7021i	−0.729361	+	0.163771i
$219$		−	70.8243i		−	0.323399i
$220$		0			0
$221$	258.292			1.16874
$222$	−51.1020	−	227.584i	−0.230189	−	1.02515i
$223$	328.579			1.47345			0.736724	−	0.676193i	$-0.236372\pi$
$223$	328.579			1.47345			0.736724	+	0.676193i	$0.236372\pi$
$224$	91.1115	−	180.972i	0.406748	−	0.807910i
$225$		0			0
$226$	−75.7222	−	337.231i	−0.335054	−	1.49217i
$227$	−157.649			−0.694491			−0.347245	−	0.937774i	$-0.612883\pi$
$227$	−157.649			−0.694491			−0.347245	+	0.937774i	$0.612883\pi$
$228$	51.0849	+	108.019i	0.224057	+	0.473767i
$229$	273.148			1.19279			0.596393	−	0.802692i	$-0.296600\pi$
$229$	273.148			1.19279			0.596393	+	0.802692i	$0.296600\pi$
$230$		0			0
$231$			101.767i			0.440552i
$232$	180.492	−	140.844i	0.777983	−	0.607084i
$233$			108.746i			0.466720i	0.972390	+	0.233360i	$0.0749721\pi$
$233$			108.746i			0.466720i	−0.972390	+	0.233360i	$0.925028\pi$
$234$	24.4071	+	108.698i	0.104304	+	0.464521i
$235$		0			0
$236$	32.9625	+	69.6992i	0.139672	+	0.295335i
$237$		−	244.754i		−	1.03272i
$238$	−38.5942	−	171.880i	−0.162160	−	0.722186i
$239$		−	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	$0.232911\pi$
$242$	68.0819	−	15.2872i	0.281330	−	0.0631701i
$243$	−15.5885			−0.0641500
$244$	−192.214	+	90.9029i	−0.787762	+	0.372553i
$245$		0			0
$246$	148.985	−	33.4532i	0.605629	−	0.135989i
$247$	320.229			1.29647
$248$	−115.626	−	148.176i	−0.466235	−	0.597483i
$249$	120.984			0.485881
$250$		0			0
$251$		−	306.220i		−	1.22000i	−0.792401	−	0.610000i	$-0.791169\pi$
$251$		−	306.220i		−	1.22000i	0.792401	−	0.610000i	$-0.208831\pi$
$252$	68.6861	−	32.4834i	0.272564	−	0.128903i
$253$		−	312.861i		−	1.23660i
$254$	−43.6696	+	9.80560i	−0.171927	+	0.0386047i
$255$		0			0
$256$	−49.9113	−	251.087i	−0.194966	−	0.980810i
$257$			251.062i			0.976895i	0.872593	+	0.488447i	$0.162437\pi$
$257$			251.062i			0.976895i	−0.872593	+	0.488447i	$0.837563\pi$
$258$	169.990	−	38.1697i	0.658876	−	0.147945i
$259$			426.335i			1.64608i
$260$		0			0
$261$	85.8531			0.328939
$262$	0.768181	+	3.42112i	0.00293199	+	0.0130577i
$263$	48.7645			0.185416			0.0927082	−	0.995693i	$-0.470448\pi$
$263$	48.7645			0.185416			0.0927082	+	0.995693i	$0.470448\pi$
$264$	79.1031	+	101.371i	0.299633	+	0.383982i
$265$		0			0
$266$	−47.8488	−	213.096i	−0.179883	−	0.801113i
$267$	−80.2076			−0.300403
$268$	−16.2688	+	7.69395i	−0.0607046	+	0.0287088i
$269$	−148.696			−0.552772			−0.276386	−	0.961047i	$-0.589137\pi$
$269$	−148.696			−0.552772			−0.276386	+	0.961047i	$0.589137\pi$
$270$		0			0
$271$			83.3415i			0.307533i	0.988107	+	0.153767i	$0.0491404\pi$
$271$			83.3415i			0.307533i	−0.988107	+	0.153767i	$0.950860\pi$
$272$	−172.045	−	141.212i	−0.632519	−	0.519162i
$273$		−	203.624i		−	0.745877i
$274$	8.54805	+	38.0690i	0.0311972	+	0.138938i
$275$		0			0
$276$	−211.160	+	99.8630i	−0.765072	+	0.361822i
$277$		−	144.080i		−	0.520146i	−0.965589	−	0.260073i	$-0.916253\pi$
$277$		−	144.080i		−	0.520146i	0.965589	−	0.260073i	$-0.0837466\pi$
$278$	112.772	+	502.234i	0.405655	+	1.80660i
$279$		−	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	$0.709439\pi$
$282$	105.317	−	23.6480i	0.373465	−	0.0838581i
$283$	−314.955			−1.11292			−0.556458	−	0.830876i	$-0.687840\pi$
$283$	−314.955			−1.11292			−0.556458	+	0.830876i	$0.687840\pi$
$284$	−22.8061	−	48.2233i	−0.0803030	−	0.169800i
$285$		0			0
$286$	336.225	−	75.4964i	1.17561	−	0.263973i
$287$	−279.094			−0.972453
$288$	43.1695	−	85.7461i	0.149894	−	0.297730i
$289$	95.4831			0.330391
$290$		0			0
$291$			118.740i			0.408040i
$292$	69.9269	+	147.860i	0.239476	+	0.506371i
$293$		−	6.55421i		−	0.0223693i	−0.999937	−	0.0111847i	$-0.996440\pi$
$293$		−	6.55421i		−	0.0223693i	0.999937	−	0.0111847i	$-0.00356026\pi$
$294$	30.1154	−	6.76214i	0.102433	−	0.0230005i
$295$		0			0
$296$	331.387	+	424.674i	1.11955	+	1.43471i
$297$			48.2184i			0.162351i
$298$	217.921	−	48.9321i	0.731278	−	0.164202i
$299$			625.997i			2.09364i
$300$		0			0
$301$	−318.443			−1.05795
$302$	−2.82741	−	12.5920i	−0.00936229	−	0.0416953i
$303$	75.1622			0.248060
$304$	−213.300	−	175.074i	−0.701646	−	0.575900i
$305$		0			0
$306$	−18.2863	−	81.4384i	−0.0597590	−	0.266139i
$307$	354.559			1.15492			0.577458	−	0.816420i	$-0.304045\pi$
$307$	354.559			1.15492			0.577458	+	0.816420i	$0.304045\pi$
$308$	−100.478	−	212.460i	−0.326228	−	0.689807i
$309$	148.596			0.480893
$310$		0			0
$311$			193.387i			0.621823i	0.950439	+	0.310912i	$0.100634\pi$
$311$			193.387i			0.621823i	−0.950439	+	0.310912i	$0.899366\pi$
$312$	−158.276	−	202.831i	−0.507294	−	0.650101i
$313$		−	23.5224i		−	0.0751514i	−0.999294	−	0.0375757i	$-0.988036\pi$
$313$		−	23.5224i		−	0.0751514i	0.999294	−	0.0375757i	$-0.0119635\pi$
$314$	33.2605	+	148.127i	0.105925	+	0.471742i
$315$		0			0
$316$	241.653	+	510.973i	0.764724	+	1.61700i
$317$			214.004i			0.675092i	0.941309	+	0.337546i	$0.109597\pi$
$317$			214.004i			0.675092i	−0.941309	+	0.337546i	$0.890403\pi$
$318$	−61.9344	−	275.827i	−0.194762	−	0.867380i
$319$		−	265.562i		−	0.832481i
$320$		0			0
$321$	−317.095			−0.987836
$322$	416.570	−	93.5369i	1.29369	−	0.290487i
$323$	−239.921			−0.742790
$324$	32.5441	−	15.3910i	0.100445	−	0.0475029i
$325$		0			0
$326$	−486.483	+	109.235i	−1.49228	+	0.335078i
$327$	141.127			0.431582
$328$	−278.007	+	216.938i	−0.847583	+	0.661395i
$329$	−197.291			−0.599669
$330$		0			0
$331$		−	412.454i		−	1.24609i	−0.782188	−	0.623043i	$-0.785896\pi$
$331$		−	412.454i		−	1.24609i	0.782188	−	0.623043i	$-0.214104\pi$
$332$	−252.579	+	119.451i	−0.760782	+	0.359793i
$333$			202.001i			0.606610i
$334$	−154.529	+	34.6981i	−0.462662	+	0.103886i
$335$		0			0
$336$	−111.324	+	135.632i	−0.331323	+	0.403666i
$337$		−	103.268i		−	0.306433i	−0.988193	−	0.153216i	$-0.951037\pi$
$337$		−	103.268i		−	0.306433i	0.988193	−	0.153216i	$-0.0489631\pi$
$338$	−342.958	+	77.0081i	−1.01467	+	0.227835i
$339$			299.323i			0.882958i
$340$		0			0
$341$	−218.014			−0.639338
$342$	−22.6712	−	100.967i	−0.0662900	−	0.295225i
$343$	−366.667			−1.06900
$344$	−317.203	+	247.523i	−0.922102	+	0.719545i
$345$		0			0
$346$	−12.1463	−	54.0939i	−0.0351049	−	0.156341i
$347$	−153.211			−0.441531			−0.220766	−	0.975327i	$-0.570856\pi$
$347$	−153.211			−0.441531			−0.220766	+	0.975327i	$0.570856\pi$
$348$	−179.236	+	84.7654i	−0.515046	+	0.243579i
$349$	84.7317			0.242784			0.121392	−	0.992605i	$-0.461264\pi$
$349$	84.7317			0.242784			0.121392	+	0.992605i	$0.461264\pi$
$350$		0			0
$351$		−	96.4791i		−	0.274869i
$352$	−265.231	−	133.532i	−0.753496	−	0.379353i
$353$			256.065i			0.725396i	0.931907	+	0.362698i	$0.118144\pi$
$353$			256.065i			0.725396i	−0.931907	+	0.362698i	$0.881856\pi$
$354$	−14.6286	−	65.1489i	−0.0413237	−	0.184036i
$355$		0			0
$356$	167.450	−	79.1914i	0.470365	−	0.222448i
$357$			152.559i			0.427336i
$358$	−89.5289	−	398.720i	−0.250081	−	1.11374i
$359$		−	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
$362$	−97.2314	+	21.8324i	−0.268595	+	0.0603106i
$363$	−60.4287			−0.166470
$364$	201.044	+	425.108i	0.552320	+	1.16788i
$365$		0			0
$366$	179.665	−	40.3422i	0.490889	−	0.110225i
$367$	−245.301			−0.668396			−0.334198	−	0.942503i	$-0.608465\pi$
$367$	−245.301			−0.668396			−0.334198	+	0.942503i	$0.608465\pi$
$368$	342.242	−	416.969i	0.930005	−	1.13307i
$369$	−132.237			−0.358367
$370$		0			0
$371$			516.708i			1.39274i
$372$	69.5886	+	147.145i	0.187066	+	0.395550i
$373$			698.787i			1.87342i	0.350101	+	0.936712i	$0.386147\pi$
$373$			698.787i			1.87342i	−0.350101	+	0.936712i	$0.613853\pi$
$374$	−251.906	+	56.5632i	−0.673546	+	0.151239i
$375$		0			0
$376$	−196.523	+	153.353i	−0.522667	+	0.407853i
$377$			531.357i			1.40943i
$378$	−64.2020	+	14.4160i	−0.169847	+	0.0381375i
$379$			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
$382$	−0.498212	−	2.21880i	−0.00130422	−	0.00580839i
$383$	−156.524			−0.408680			−0.204340	−	0.978900i	$-0.565505\pi$
$383$	−156.524			−0.408680			−0.204340	+	0.978900i	$0.565505\pi$
$384$	−5.46541	+	221.635i	−0.0142328	+	0.577175i
$385$		0			0
$386$	−33.5838	−	149.566i	−0.0870046	−	0.387478i
$387$	−150.881			−0.389874
$388$	−117.235	−	247.893i	−0.302152	−	0.638900i
$389$	−386.588			−0.993801			−0.496900	−	0.867808i	$-0.665529\pi$
$389$	−386.588			−0.993801			−0.496900	+	0.867808i	$0.665529\pi$
$390$		0			0
$391$		−	469.008i		−	1.19951i
$392$	−56.1956	+	43.8512i	−0.143356	+	0.111865i
$393$		−	3.03655i		−	0.00772658i
$394$	−58.9322	−	262.456i	−0.149574	−	0.666133i
$395$		0			0
$396$	−47.6074	−	100.666i	−0.120221	−	0.254206i
$397$			561.155i			1.41349i	0.707470	+	0.706744i	$0.249837\pi$
$397$			561.155i			1.41349i	−0.707470	+	0.706744i	$0.750163\pi$
$398$	−77.1242	−	343.475i	−0.193779	−	0.863002i
$399$			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	$0.493279\pi$
$402$	15.2067	−	3.41453i	0.0378277	−	0.00849387i
$403$	436.220			1.08243
$404$	−156.917	+	74.2099i	−0.388407	+	0.183688i
$405$		0			0
$406$	353.591	−	79.3957i	0.870914	−	0.195556i
$407$	624.832			1.53521
$408$	118.583	+	151.965i	0.290644	+	0.372463i
$409$	−258.490			−0.632006			−0.316003	−	0.948758i	$-0.602341\pi$
$409$	−258.490			−0.632006			−0.316003	+	0.948758i	$0.602341\pi$
$410$		0			0
$411$		−	33.7896i		−	0.0822132i
$412$	−310.224	+	146.713i	−0.752972	+	0.356100i
$413$			122.044i			0.295505i
$414$	197.374	−	44.3186i	0.476750	−	0.107050i
$415$		0			0
$416$	530.694	+	267.182i	1.27571	+	0.642264i
$417$		−	445.777i		−	1.06901i
$418$	−312.312	+	70.1267i	−0.747157	+	0.167767i
$419$			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	$0.463071\pi$
$422$	95.5594	+	425.577i	0.226444	+	1.00848i
$423$	−93.4783			−0.220989
$424$	401.633	+	514.696i	0.947248	+	1.21390i
$425$		0			0
$426$	10.1212	+	45.0751i	0.0237587	+	0.105810i
$427$	−336.568			−0.788215
$428$	662.002	−	313.078i	1.54673	−	0.731490i
$429$	−298.430			−0.695641
$430$		0			0
$431$		−	389.968i		−	0.904799i	−0.891815	−	0.452399i	$-0.850568\pi$
$431$		−	389.968i		−	0.904799i	0.891815	−	0.452399i	$-0.149432\pi$
$432$	−52.7465	+	64.2635i	−0.122098	+	0.148758i
$433$			275.893i			0.637166i	0.947895	+	0.318583i	$0.103207\pi$
$433$			275.893i			0.637166i	−0.947895	+	0.318583i	$0.896793\pi$
$434$	−65.1803	−	290.283i	−0.150185	−	0.668854i
$435$		0			0
$436$	−294.632	+	139.339i	−0.675761	+	0.319585i
$437$		−	581.473i		−	1.33060i
$438$	−31.0332	−	138.207i	−0.0708520	−	0.315542i
$439$		−	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
$442$	504.034	−	113.176i	1.14035	−	0.256055i
$443$	−794.679			−1.79386			−0.896929	−	0.442174i	$-0.854207\pi$
$443$	−794.679			−1.79386			−0.896929	+	0.442174i	$0.854207\pi$
$444$	−199.442	−	421.719i	−0.449194	−	0.949818i
$445$		0			0
$446$	641.193	−	143.974i	1.43765	−	0.322812i
$447$	−193.424			−0.432716
$448$	98.4993	−	393.073i	0.219865	−	0.877395i
$449$	750.226			1.67088			0.835441	−	0.549581i	$-0.185212\pi$
$449$	750.226			1.67088			0.835441	+	0.549581i	$0.185212\pi$
$450$		0			0
$451$			409.037i			0.906957i
$452$	−295.530	−	624.898i	−0.653828	−	1.38252i
$453$			11.1765i			0.0246722i
$454$	−307.639	+	69.0775i	−0.677619	+	0.152153i
$455$		0			0
$456$	147.018	+	188.405i	0.322409	+	0.413169i
$457$		−	101.092i		−	0.221209i	−0.993865	−	0.110604i	$-0.964721\pi$
$457$		−	101.092i		−	0.221209i	0.993865	−	0.110604i	$-0.0352787\pi$
$458$	533.024	−	119.686i	1.16381	−	0.261323i
$459$			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	$0.501549\pi$
$462$	44.5916	+	198.590i	0.0965186	+	0.429849i
$463$	515.108			1.11254			0.556272	−	0.831000i	$-0.312231\pi$
$463$	515.108			1.11254			0.556272	+	0.831000i	$0.312231\pi$
$464$	290.500	−	353.930i	0.626079	−	0.762780i
$465$		0			0
$466$	47.6493	+	212.208i	0.102252	+	0.455382i
$467$	295.498			0.632758			0.316379	−	0.948633i	$-0.397533\pi$
$467$	295.498			0.632758			0.316379	+	0.948633i	$0.397533\pi$
$468$	95.2567	+	201.420i	0.203540	+	0.430384i
$469$	−28.4869			−0.0607396
$470$		0			0
$471$		−	131.476i		−	0.279142i
$472$	94.8637	+	121.568i	0.200982	+	0.257560i
$473$			466.707i			0.986696i
$474$	−107.244	−	477.615i	−0.226253	−	1.00763i
$475$		0			0
$476$	−150.626	−	318.498i	−0.316441	−	0.669114i
$477$			244.821i			0.513251i
$478$	−78.4299	−	349.290i	−0.164079	−	0.730732i
$479$			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
$482$	699.822	−	157.139i	1.45191	−	0.326014i
$483$	−369.743			−0.765512
$484$	126.157	−	59.6631i	0.260656	−	0.123271i
$485$		0			0
$486$	−30.4195	+	6.83042i	−0.0625915	+	0.0140544i
$487$	−357.751			−0.734601			−0.367301	−	0.930102i	$-0.619718\pi$
$487$	−357.751			−0.734601			−0.367301	+	0.930102i	$0.619718\pi$
$488$	−335.257	+	261.612i	−0.687002	+	0.536089i
$489$	431.797			0.883021
$490$		0			0
$491$			422.379i			0.860242i	0.902771	+	0.430121i	$0.141529\pi$
$491$			422.379i			0.860242i	−0.902771	+	0.430121i	$0.858471\pi$
$492$	276.072	−	130.562i	0.561123	−	0.265370i
$493$		−	398.102i		−	0.807509i
$494$	624.898	−	140.315i	1.26498	−	0.284039i
$495$		0			0
$496$	−290.561	−	238.488i	−0.585808	−	0.480822i
$497$		−	84.4394i		−	0.169898i
$498$	236.090	−	53.0119i	0.474076	−	0.106450i
$499$		−	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
$502$	−134.177	−	597.562i	−0.267285	−	1.19036i
$503$	702.853			1.39732			0.698661	−	0.715452i	$-0.253779\pi$
$503$	702.853			1.39732			0.698661	+	0.715452i	$0.253779\pi$
$504$	119.802	−	93.4849i	0.237701	−	0.185486i
$505$		0			0
$506$	−137.087	−	610.520i	−0.270923	−	1.20656i
$507$	304.406			0.600406
$508$	−80.9207	+	38.2695i	−0.159293	+	0.0753337i
$509$	389.029			0.764300			0.382150	−	0.924100i	$-0.375184\pi$
$509$	389.029			0.764300			0.382150	+	0.924100i	$0.375184\pi$
$510$		0			0
$511$			258.904i			0.506662i
$512$	−207.417	−	468.105i	−0.405111	−	0.914267i
$513$			89.6171i			0.174692i
$514$	110.008	+	489.925i	0.214024	+	0.953162i
$515$		0			0
$516$	314.996	−	148.970i	0.610457	−	0.288701i
$517$			289.148i			0.559280i
$518$	186.808	+	831.954i	0.360633	+	1.60609i
$519$			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	$0.546523\pi$
$522$	167.535	−	37.6184i	0.320948	−	0.0720659i
$523$	557.762			1.06647			0.533234	−	0.845968i	$-0.320977\pi$
$523$	557.762			1.06647			0.533234	+	0.845968i	$0.320977\pi$
$524$	2.99807	+	6.33941i	0.00572151	+	0.0120981i
$525$		0			0
$526$	95.1596	−	21.3672i	0.180912	−	0.0406221i
$527$	−326.824			−0.620159
$528$	198.781	+	163.156i	0.376478	+	0.309008i
$529$	607.689			1.14875
$530$		0			0
$531$			57.8254i			0.108899i
$532$	−186.745	−	394.872i	−0.351025	−	0.742241i
$533$		−	818.435i		−	1.53552i
$534$	−156.518	+	35.1447i	−0.293105	+	0.0658141i
$535$		0			0
$536$	−28.3759	+	22.1426i	−0.0529401	+	0.0413108i
$537$			353.899i			0.659030i
$538$	−290.166	+	65.1542i	−0.539342	+	0.121104i
$539$			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	$0.397949\pi$
$542$	36.5179	+	162.633i	0.0673761	+	0.300062i
$543$	86.3015			0.158935
$544$	−397.606	−	200.177i	−0.730893	−	0.367973i
$545$		0			0
$546$	−89.2224	−	397.355i	−0.163411	−	0.727756i
$547$	113.651			0.207771			0.103885	−	0.994589i	$-0.466872\pi$
$547$	113.651			0.207771			0.103885	+	0.994589i	$0.466872\pi$
$548$	33.3615	+	70.5428i	0.0608787	+	0.128728i
$549$	−159.469			−0.290472
$550$		0			0
$551$		−	493.564i		−	0.895761i
$552$	−368.303	+	287.398i	−0.667215	+	0.520649i
$553$			894.718i			1.61794i
$554$	−63.1319	−	281.160i	−0.113957	−	0.507509i
$555$		0			0
$556$	440.129	+	930.651i	0.791599	+	1.67383i
$557$		−	233.232i		−	0.418728i	−0.977838	−	0.209364i	$-0.932861\pi$
$557$		−	233.232i		−	0.418728i	0.977838	−	0.209364i	$-0.0671394\pi$
$558$	−30.8830	−	137.539i	−0.0553459	−	0.246485i
$559$		−	933.825i		−	1.67053i
$560$		0			0
$561$	223.589			0.398554
$562$	−670.644	+	150.587i	−1.19332	+	0.267948i
$563$	−167.786			−0.298021			−0.149011	−	0.988836i	$-0.547609\pi$
$563$	−167.786			−0.298021			−0.149011	+	0.988836i	$0.547609\pi$
$564$	195.155	−	92.2939i	0.346020	−	0.163642i
$565$		0			0
$566$	−614.607	+	138.004i	−1.08588	+	0.243824i
$567$	56.9850			0.100503
$568$	−65.6341	−	84.1105i	−0.115553	−	0.148082i
$569$	−381.089			−0.669752			−0.334876	−	0.942262i	$-0.608694\pi$
$569$	−381.089			−0.669752			−0.334876	+	0.942262i	$0.608694\pi$
$570$		0			0
$571$		−	453.871i		−	0.794870i	−0.917630	−	0.397435i	$-0.869900\pi$
$571$		−	453.871i		−	0.794870i	0.917630	−	0.397435i	$-0.130100\pi$
$572$	623.034	−	294.649i	1.08922	−	0.515120i
$573$			1.96939i			0.00343697i
$574$	−544.627	+	122.291i	−0.948828	+	0.213051i
$575$		0			0
$576$	46.6699	−	186.242i	0.0810241	−	0.323336i
$577$		−	688.294i		−	1.19288i	−0.802656	−	0.596442i	$-0.796581\pi$
$577$		−	688.294i		−	1.19288i	0.802656	−	0.596442i	$-0.203419\pi$
$578$	186.327	−	41.8380i	0.322365	−	0.0723841i
$579$			132.753i			0.229281i
$580$		0			0
$581$	−442.269			−0.761220
$582$	52.0283	+	231.710i	0.0893957	+	0.398127i
$583$	757.282			1.29894
$584$	201.244	+	257.896i	0.344597	+	0.441603i
$585$		0			0
$586$	−2.87187	−	12.7900i	−0.00490080	−	0.0218259i
$587$	−249.163			−0.424468			−0.212234	−	0.977219i	$-0.568074\pi$
$587$	−249.163			−0.424468			−0.212234	+	0.977219i	$0.568074\pi$
$588$	55.8046	−	26.3914i	0.0949057	−	0.0448834i
$589$	−405.194			−0.687936
$590$		0			0
$591$			232.953i			0.394168i
$592$	832.752	+	683.510i	1.40668	+	1.15458i
$593$		−	163.937i		−	0.276454i	−0.990401	−	0.138227i	$-0.955860\pi$
$593$		−	163.937i		−	0.276454i	0.990401	−	0.138227i	$-0.0441404\pi$
$594$	21.1279	+	94.0938i	0.0355689	+	0.158407i
$595$		0			0
$596$	403.812	−	190.973i	0.677538	−	0.320425i
$597$			304.865i			0.510661i
$598$	274.294	+	1221.58i	0.458686	+	2.04277i
$599$			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	$0.118348\pi$
$602$	−621.413	+	139.533i	−1.03225	+	0.231782i
$603$	−13.4973			−0.0223836
$604$	−11.0349	−	23.3332i	−0.0182697	−	0.0386312i
$605$		0			0
$606$	146.672	−	32.9339i	0.242034	−	0.0543464i
$607$	−660.957			−1.08889			−0.544445	−	0.838796i	$-0.683260\pi$
$607$	−660.957			−1.08889			−0.544445	+	0.838796i	$0.683260\pi$
$608$	−492.949	−	248.179i	−0.810772	−	0.408189i
$609$	−313.844			−0.515342
$610$		0			0
$611$		−	578.550i		−	0.946890i
$612$	−71.3680	−	150.907i	−0.116614	−	0.246581i
$613$		−	179.315i		−	0.292520i	−0.989246	−	0.146260i	$-0.953276\pi$
$613$		−	179.315i		−	0.292520i	0.989246	−	0.146260i	$-0.0467236\pi$
$614$	691.891	−	155.358i	1.12686	−	0.253026i
$615$		0			0
$616$	−289.168	−	370.571i	−0.469429	−	0.601576i
$617$			63.6752i			0.103201i	0.998668	+	0.0516007i	$0.0164323\pi$
$617$			63.6752i			0.103201i	−0.998668	+	0.0516007i	$0.983568\pi$
$618$	289.972	−	65.1105i	0.469210	−	0.105357i
$619$		−	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
$622$	84.7367	+	377.378i	0.136233	+	0.606716i
$623$	293.206			0.470636
$624$	−397.736	−	326.456i	−0.637397	−	0.523166i
$625$		0			0
$626$	−10.3068	−	45.9019i	−0.0164646	−	0.0733257i
$627$	277.204			0.442112
$628$	129.810	+	274.483i	0.206704	+	0.437074i
$629$	936.682			1.48916
$630$		0			0
$631$		−	340.783i		−	0.540068i	−0.962851	−	0.270034i	$-0.912965\pi$
$631$		−	340.783i		−	0.540068i	0.962851	−	0.270034i	$-0.0870349\pi$
$632$	695.458	+	891.234i	1.10041	+	1.41018i
$633$		−	377.737i		−	0.596742i
$634$	93.7705	+	417.610i	0.147903	+	0.658691i
$635$		0			0
$636$	−241.719	−	511.114i	−0.380061	−	0.803638i
$637$		−	165.436i		−	0.259712i
$638$	−116.362	−	518.220i	−0.182385	−	0.812257i
$639$		−	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	$0.296094\pi$
$642$	−618.783	+	138.942i	−0.963837	+	0.216421i
$643$	−1163.47			−1.80943			−0.904717	−	0.426014i	$-0.859917\pi$
$643$	−1163.47			−1.80943			−0.904717	+	0.426014i	$0.859917\pi$
$644$	771.913	−	365.058i	1.19862	−	0.566860i
$645$		0			0
$646$	−468.185	+	105.127i	−0.724744	+	0.162735i
$647$	740.530			1.14456			0.572279	−	0.820059i	$-0.306059\pi$
$647$	740.530			1.14456			0.572279	+	0.820059i	$0.306059\pi$
$648$	56.7630	−	44.2940i	0.0875973	−	0.0683549i
$649$	178.866			0.275603
$650$		0			0
$651$			257.652i			0.395778i
$652$	−901.465	+	426.326i	−1.38262	+	0.653875i
$653$			109.569i			0.167793i	0.996474	+	0.0838967i	$0.0267366\pi$
$653$			109.569i			0.167793i	−0.996474	+	0.0838967i	$0.973263\pi$
$654$	275.397	−	61.8379i	0.421097	−	0.0945534i
$655$		0			0
$656$	−447.450	+	545.149i	−0.682089	+	0.831020i
$657$			122.671i			0.186714i
$658$	−384.996	+	86.4473i	−0.585100	+	0.131379i
$659$			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	$0.322285\pi$
$662$	−180.726	−	804.868i	−0.273000	−	1.21581i
$663$	−447.375			−0.674773
$664$	−440.546	+	343.772i	−0.663473	+	0.517729i
$665$		0			0
$666$	88.5112	+	394.188i	0.132900	+	0.591873i
$667$	964.841			1.44654
$668$	−286.346	+	135.420i	−0.428662	+	0.202725i
$669$	−569.116			−0.850696
$670$		0			0
$671$			493.271i			0.735128i
$672$	−157.810	+	313.452i	−0.234836	+	0.466447i
$673$		−	1221.18i		−	1.81454i	−0.420552	−	0.907269i	$-0.638163\pi$
$673$		−	1221.18i		−	1.81454i	0.420552	−	0.907269i	$-0.361837\pi$
$674$	−45.2490	−	201.518i	−0.0671350	−	0.298988i
$675$		0			0
$676$	−635.509	+	300.549i	−0.940103	+	0.444599i
$677$		−	989.373i		−	1.46141i	−0.682695	−	0.730704i	$-0.739192\pi$
$677$		−	989.373i		−	1.46141i	0.682695	−	0.730704i	$-0.260808\pi$
$678$	131.155	+	584.102i	0.193444	+	0.861507i
$679$		−	434.063i		−	0.639268i
$680$		0			0
$681$	273.057			0.400965
$682$	−425.435	+	95.5276i	−0.623806	+	0.140070i
$683$	−307.312			−0.449945			−0.224972	−	0.974365i	$-0.572229\pi$
$683$	−307.312			−0.449945			−0.224972	+	0.974365i	$0.572229\pi$
$684$	−88.4816	−	187.094i	−0.129359	−	0.273529i
$685$		0			0
$686$	−715.518	+	160.663i	−1.04303	+	0.234203i
$687$	−473.107			−0.688656
$688$	−510.536	+	622.009i	−0.742058	+	0.904083i
$689$	−1515.23			−2.19917
$690$		0			0
$691$			893.378i			1.29288i	0.762966	+	0.646438i	$0.223742\pi$
$691$			893.378i			1.29288i	−0.762966	+	0.646438i	$0.776258\pi$
$692$	−47.4048	−	100.237i	−0.0685041	−	0.144852i
$693$		−	176.266i		−	0.254353i
$694$	−298.978	+	67.1329i	−0.430805	+	0.0967332i
$695$		0			0
$696$	−312.621	+	243.948i	−0.449169	+	0.350500i
$697$			613.186i			0.879750i
$698$	165.346	−	37.1270i	0.236886	−	0.0531906i
$699$		−	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	$0.202622\pi$
$702$	−42.2744	−	188.270i	−0.0602199	−	0.268191i
$703$	1161.29			1.65191
$704$	−576.084	−	144.360i	−0.818301	−	0.205056i
$705$		0			0
$706$	112.200	+	499.688i	0.158924	+	0.707773i
$707$	−274.762			−0.388631
$708$	−57.0928	−	120.722i	−0.0806395	−	0.170512i
$709$	−1093.27			−1.54199			−0.770997	−	0.636839i	$-0.780242\pi$
$709$	−1093.27			−1.54199			−0.770997	+	0.636839i	$0.780242\pi$
$710$		0			0
$711$			423.926i			0.596239i
$712$	292.064	−	227.907i	0.410202	−	0.320094i
$713$		−	792.091i		−	1.11093i
$714$	66.8470	+	297.705i	0.0936233	+	0.416954i
$715$		0			0
$716$	−349.415	−	738.837i	−0.488010	−	1.03190i
$717$			310.026i			0.432393i
$718$	−292.374	−	1302.10i	−0.407206	−	1.81350i
$719$			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
$722$	124.007	−	27.8446i	0.171755	−	0.0385660i
$723$	−621.154			−0.859134
$724$	−180.172	+	85.2081i	−0.248857	+	0.117691i
$725$		0			0
$726$	−117.921	+	26.4782i	−0.162426	+	0.0364713i
$727$	295.050			0.405846			0.202923	−	0.979195i	$-0.434956\pi$
$727$	295.050			0.405846			0.202923	+	0.979195i	$0.434956\pi$
$728$	578.591	+	741.468i	0.794767	+	1.01850i
$729$	27.0000			0.0370370
$730$		0			0
$731$			699.638i			0.957097i
$732$	332.924	−	157.448i	0.454814	−	0.215094i
$733$			261.200i			0.356344i	0.983999	+	0.178172i	$0.0570184\pi$
$733$			261.200i			0.356344i	−0.983999	+	0.178172i	$0.942982\pi$
$734$	−478.684	+	107.484i	−0.652158	+	0.146436i
$735$		0			0
$736$	485.150	−	963.638i	0.659172	−	1.30929i
$737$			41.7501i			0.0566487i
$738$	−258.049	+	57.9426i	−0.349660	+	0.0785130i
$739$			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
$742$	226.407	+	1008.31i	0.305130	+	1.35891i
$743$	23.7067			0.0319067			0.0159534	−	0.999873i	$-0.494922\pi$
$743$	23.7067			0.0319067			0.0159534	+	0.999873i	$0.494922\pi$
$744$	200.271	+	256.648i	0.269181	+	0.344957i
$745$		0			0
$746$	306.189	+	1363.62i	0.410441	+	1.82791i
$747$	−209.551			−0.280523
$748$	−466.788	+	220.756i	−0.624048	+	0.295129i
$749$	1159.17			1.54762
$750$		0			0
$751$		−	395.508i		−	0.526642i	−0.964708	−	0.263321i	$-0.915182\pi$
$751$		−	395.508i		−	0.526642i	0.964708	−	0.263321i	$-0.0848179\pi$
$752$	−316.302	+	385.365i	−0.420614	+	0.512453i
$753$			530.389i			0.704368i
$754$	232.825	+	1036.90i	0.308787	+	1.37519i
$755$		0			0
$756$	−118.968	+	56.2630i	−0.157365	+	0.0744219i
$757$		−	393.940i		−	0.520396i	−0.965555	−	0.260198i	$-0.916212\pi$
$757$		−	393.940i		−	0.520396i	0.965555	−	0.260198i	$-0.0837879\pi$
$758$	91.4425	+	407.242i	0.120637	+	0.537259i
$759$			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	$0.578025\pi$
$762$	75.6379	−	16.9838i	0.0992623	−	0.0222885i
$763$	−515.903			−0.676150
$764$	−1.94443	−	4.11150i	−0.00254507	−	0.00538154i
$765$		0			0
$766$	−305.444	+	68.5846i	−0.398751	+	0.0895360i
$767$	−357.890			−0.466610
$768$	86.4490	+	434.896i	0.112564	+	0.566271i
$769$	873.491			1.13588			0.567940	−	0.823070i	$-0.307741\pi$
$769$	873.491			1.13588			0.567940	+	0.823070i	$0.307741\pi$
$770$		0			0
$771$		−	434.852i		−	0.564010i
$772$	−131.071	−	277.150i	−0.169782	−	0.359003i
$773$		−	1176.93i		−	1.52254i	−0.648432	−	0.761272i	$-0.724575\pi$
$773$		−	1176.93i		−	1.52254i	0.648432	−	0.761272i	$-0.275425\pi$
$774$	−294.431	+	66.1119i	−0.380402	+	0.0854159i
$775$		0			0
$776$	−337.394	−	432.372i	−0.434786	−	0.557181i
$777$		−	738.433i		−	0.950365i
$778$	−754.393	+	169.392i	−0.969657	+	0.217728i
$779$			760.224i			0.975897i
$780$		0			0
$781$	−123.754			−0.158455
$782$	−205.506	−	915.228i	−0.262795	−	1.17037i
$783$	−148.702			−0.189913
$784$	−90.4464	+	110.195i	−0.115365	+	0.140555i
$785$		0			0
$786$	−1.33053	−	5.92555i	−0.00169278	−	0.00753887i
$787$	−603.482			−0.766814			−0.383407	−	0.923580i	$-0.625249\pi$
$787$	−603.482			−0.766814			−0.383407	+	0.923580i	$0.625249\pi$
$788$	−230.002	−	486.338i	−0.291880	−	0.617180i
$789$	−84.4626			−0.107050
$790$		0			0
$791$		−	1094.20i		−	1.38331i
$792$	−137.011	−	175.580i	−0.172993	−	0.221692i
$793$		−	986.975i		−	1.24461i
$794$	245.882	+	1095.04i	0.309675	+	1.37915i
$795$		0			0
$796$	−301.002	−	636.467i	−0.378143	−	0.799582i
$797$		−	860.121i		−	1.07920i	−0.841922	−	0.539599i	$-0.818576\pi$
$797$		−	860.121i		−	1.07920i	0.841922	−	0.539599i	$-0.181424\pi$
$798$	82.8765	+	369.093i	0.103855	+	0.462523i
$799$			433.460i			0.542503i
$800$		0			0
$801$	138.924			0.173438
$802$	33.0437	−	7.41967i	0.0412017	−	0.00925146i
$803$	379.448			0.472538
$804$	28.1784	−	13.3263i	0.0350478	−	0.0165750i
$805$		0			0
$806$	851.245	−	191.139i	1.05614	−	0.237145i
$807$	257.548			0.319143
$808$	−273.692	+	213.570i	−0.338728	+	0.264320i
$809$	−941.012			−1.16318			−0.581589	−	0.813483i	$-0.697569\pi$
$809$	−941.012			−1.16318			−0.581589	+	0.813483i	$0.697569\pi$
$810$		0			0
$811$		−	1105.29i		−	1.36287i	−0.731878	−	0.681436i	$-0.761356\pi$
$811$		−	1105.29i		−	1.36287i	0.731878	−	0.681436i	$-0.238644\pi$
$812$	655.213	−	309.867i	0.806912	−	0.381610i
$813$		−	144.352i		−	0.177554i
$814$	1219.30	−	273.784i	1.49792	−	0.336344i
$815$		0			0
$816$	297.991	+	244.586i	0.365185	+	0.299738i
$817$			867.407i			1.06170i
$818$	−504.421	+	113.263i	−0.616652	+	0.138463i
$819$			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	$0.537534\pi$
$822$	−14.8057	−	65.9374i	−0.0180117	−	0.0802159i
$823$	178.778			0.217227			0.108614	−	0.994084i	$-0.465359\pi$
$823$	178.778			0.217227			0.108614	+	0.994084i	$0.465359\pi$
$824$	−541.090	+	422.229i	−0.656662	+	0.512414i
$825$		0			0
$826$	53.4761	+	238.158i	0.0647410	+	0.288326i
$827$	1558.61			1.88465			0.942326	−	0.334697i	$-0.108634\pi$
$827$	1558.61			1.88465			0.942326	+	0.334697i	$0.108634\pi$
$828$	365.740	−	172.968i	0.441714	−	0.208898i
$829$	565.477			0.682119			0.341059	−	0.940042i	$-0.389214\pi$
$829$	565.477			0.682119			0.341059	+	0.940042i	$0.389214\pi$
$830$		0			0
$831$			249.554i			0.300306i
$832$	1152.67	+	288.846i	1.38543	+	0.347171i
$833$			123.948i			0.148797i
$834$	−195.327	−	869.895i	−0.234205	−	1.04304i
$835$		0			0
$836$	−578.721	+	273.692i	−0.692250	+	0.327383i
$837$			122.078i			0.145851i
$838$	113.450	+	505.254i	0.135382	+	0.602928i
$839$		−	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
$842$	190.195	−	42.7066i	0.225885	−	0.0507204i
$843$	595.256			0.706116
$844$	372.952	+	788.604i	0.441886	+	0.934365i
$845$		0			0
$846$	−182.415	+	40.9595i	−0.215620	+	0.0484155i
$847$	220.903			0.260806
$848$	1009.28	+	828.398i	1.19018	+	0.976885i
$849$	545.518			0.642542
$850$		0			0
$851$			2270.15i			2.66762i
$852$	39.5012	+	83.5252i	0.0463630	+	0.0980343i
$853$			120.366i			0.141109i	0.997508	+	0.0705546i	$0.0224769\pi$
$853$			120.366i			0.141109i	−0.997508	+	0.0705546i	$0.977523\pi$
$854$	−656.782	+	147.474i	−0.769066	+	0.172687i
$855$		0			0
$856$	1154.66	−	901.014i	1.34890	−	1.05259i
$857$			717.784i			0.837554i	0.908089	+	0.418777i	$0.137541\pi$
$857$			717.784i			0.837554i	−0.908089	+	0.418777i	$0.862459\pi$
$858$	−582.360	+	130.764i	−0.678741	+	0.152405i
$859$		−	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
$862$	−170.873	−	760.989i	−0.198229	−	0.882817i
$863$	−1234.73			−1.43075			−0.715373	−	0.698743i	$-0.753743\pi$
$863$	−1234.73			−1.43075			−0.715373	+	0.698743i	$0.753743\pi$
$864$	−74.7717	+	148.517i	−0.0865413	+	0.171894i
$865$		0			0
$866$	120.888	+	538.381i	0.139594	+	0.621687i
$867$	−165.382			−0.190752
$868$	−254.387	−	537.901i	−0.293073	−	0.619701i
$869$	1311.29			1.50897
$870$		0			0
$871$		−	83.5368i		−	0.0959091i
$872$	−513.894	+	401.007i	−0.589327	+	0.459871i
$873$		−	205.663i		−	0.235582i
$874$	−254.785	−	1134.69i	−0.291516	−	1.29828i
$875$		0			0
$876$	−121.117	−	256.101i	−0.138261	−	0.292353i
$877$			685.723i			0.781896i	0.920413	+	0.390948i	$0.127853\pi$
$877$			685.723i			0.781896i	−0.920413	+	0.390948i	$0.872147\pi$
$878$	−195.487	−	870.609i	−0.222651	−	0.991582i
$879$			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	$0.583785\pi$
$882$	−52.1614	+	11.7124i	−0.0591399	+	0.0132793i
$883$	771.505			0.873732			0.436866	−	0.899527i	$-0.356088\pi$
$883$	771.505			0.873732			0.436866	+	0.899527i	$0.356088\pi$
$884$	933.986	−	441.707i	1.05655	−	0.499668i
$885$		0			0
$886$	−1550.75	+	348.206i	−1.75028	+	0.393009i
$887$	−1161.05			−1.30896			−0.654480	−	0.756080i	$-0.727112\pi$
$887$	−1161.05			−1.30896			−0.654480	+	0.756080i	$0.727112\pi$
$888$	−573.979	−	735.558i	−0.646372	−	0.828331i
$889$	−141.693			−0.159385
$890$		0			0
$891$		−	83.5166i		−	0.0937336i
$892$	1188.15	−	561.905i	1.33200	−	0.629938i
$893$			537.401i			0.601793i
$894$	−377.450	+	84.7529i	−0.422203	+	0.0948019i
$895$		0			0
$896$	19.9793	−	810.207i	0.0222983	−	0.904248i
$897$		−	1084.26i		−	1.20876i
$898$	1464.00	−	328.728i	1.63029	−	0.366066i
$899$		−	672.340i		−	0.747876i
$900$		0			0
$901$	1135.24			1.25997
$902$	179.229	+	798.200i	0.198701	+	0.884923i
$903$	551.560			0.610808
$904$	−850.514	−	1089.94i	−0.940834	−	1.20569i
$905$		0			0
$906$	4.89722	+	21.8099i	0.00540532	+	0.0240728i
$907$	392.544			0.432793			0.216397	−	0.976306i	$-0.430570\pi$
$907$	392.544			0.432793			0.216397	+	0.976306i	$0.430570\pi$
$908$	−570.062	+	269.597i	−0.627822	+	0.296913i
$909$	−130.185			−0.143218
$910$		0			0
$911$			1013.40i			1.11240i	0.831048	+	0.556201i	$0.187741\pi$
$911$			1013.40i			1.11240i	−0.831048	+	0.556201i	$0.812259\pi$
$912$	369.447	+	303.237i	0.405096	+	0.332496i
$913$			648.185i			0.709950i
$914$	−44.2958	−	197.273i	−0.0484637	−	0.215835i
$915$		0			0
$916$	987.707	−	467.112i	1.07828	−	0.509948i
$917$			11.1004i			0.0121051i
$918$	31.6727	+	141.056i	0.0345019	+	0.153655i
$919$			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
$922$	−8.75578	+	1.96603i	−0.00949651	+	0.00213236i
$923$	247.616			0.268273
$924$	174.033	+	367.992i	0.188348	+	0.398260i
$925$		0			0
$926$	1005.19	−	225.706i	1.08552	−	0.243743i
$927$	−257.376			−0.277644
$928$	411.804	−	817.952i	0.443754	−	0.881414i
$929$	−980.857			−1.05582			−0.527910	−	0.849300i	$-0.677024\pi$
$929$	−980.857			−1.05582			−0.527910	+	0.849300i	$0.677024\pi$
$930$		0			0
$931$			153.670i			0.165059i
$932$	185.967	+	393.226i	0.199535	+	0.421917i
$933$		−	334.956i		−	0.359010i
$934$	576.638	−	129.479i	0.617386	−	0.138628i
$935$		0			0
$936$	274.141	+	351.314i	0.292886	+	0.375336i
$937$		−	964.666i		−	1.02953i	−0.857333	−	0.514763i	$-0.827880\pi$
$937$		−	964.666i		−	1.02953i	0.857333	−	0.514763i	$-0.172120\pi$
$938$	−55.5896	+	12.4821i	−0.0592639	+	0.0133072i
$939$			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	$0.817514\pi$
$942$	−57.6089	−	256.563i	−0.0611560	−	0.272360i
$943$	−1486.12			−1.57595
$944$	238.386	+	195.663i	0.252527	+	0.207271i
$945$		0			0
$946$	204.498	+	910.738i	0.216171	+	0.962725i
$947$	−1245.27			−1.31497			−0.657483	−	0.753469i	$-0.728379\pi$
$947$	−1245.27			−1.31497			−0.657483	+	0.753469i	$0.728379\pi$
$948$	−418.555	−	885.032i	−0.441513	−	0.933578i
$949$	−759.229			−0.800031
$950$		0			0
$951$		−	370.666i		−	0.389765i
$952$	−433.490	−	555.521i	−0.455347	−	0.583530i
$953$			1106.52i			1.16109i	0.814228	+	0.580546i	$0.197161\pi$
$953$			1106.52i			1.16109i	−0.814228	+	0.580546i	$0.802839\pi$
$954$	107.274	+	477.746i	0.112446	+	0.500782i
$955$		0			0
$956$	−306.098	−	647.243i	−0.320186	−	0.677032i
$957$			459.966i			0.480633i
$958$	119.689	+	533.037i	0.124936	+	0.556406i
$959$			123.521i			0.128802i
$960$		0			0
$961$	409.039			0.425638
$962$	−2439.68	+	547.808i	−2.53605	+	0.569447i
$963$	549.225			0.570327
$964$	1296.79	−	613.284i	1.34521	−	0.636187i
$965$		0			0
$966$	−721.520	+	162.011i	−0.746915	+	0.167713i
$967$	406.453			0.420324			0.210162	−	0.977667i	$-0.432601\pi$
$967$	406.453			0.420324			0.210162	+	0.977667i	$0.432601\pi$
$968$	220.042	−	171.706i	0.227316	−	0.177382i
$969$	415.555			0.428850
$970$		0			0
$971$		−	1815.22i		−	1.86943i	−0.355393	−	0.934717i	$-0.615653\pi$
$971$		−	1815.22i		−	1.86943i	0.355393	−	0.934717i	$-0.384347\pi$
$972$	−56.3680	+	26.6579i	−0.0579918	+	0.0274258i
$973$			1629.58i			1.67480i
$974$	−698.119	+	156.756i	−0.716754	+	0.160941i
$975$		0			0
$976$	−539.594	+	657.412i	−0.552862	+	0.673578i
$977$			1457.74i			1.49205i	0.665916	+	0.746027i	$0.268041\pi$
$977$			1457.74i			1.49205i	−0.665916	+	0.746027i	$0.731959\pi$
$978$	842.614	−	189.201i	0.861568	−	0.193457i
$979$		−	429.720i		−	0.438938i
$980$		0			0
$981$	−244.439			−0.249174
$982$	185.074	+	824.235i	0.188467	+	0.839343i
$983$	−19.9496			−0.0202946			−0.0101473	−	0.999949i	$-0.503230\pi$
$983$	−19.9496			−0.0202946			−0.0101473	+	0.999949i	$0.503230\pi$
$984$	481.522	−	375.747i	0.489352	−	0.381857i
$985$		0			0
$986$	−174.437	−	776.860i	−0.176914	−	0.787891i
$987$	341.718			0.346219
$988$	1157.95	−	547.625i	1.17201	−	0.554276i
$989$	−1695.65			−1.71450
$990$		0			0
$991$			605.720i			0.611221i	0.952157	+	0.305611i	$0.0988605\pi$
$991$			605.720i			0.611221i	−0.952157	+	0.305611i	$0.901139\pi$
$992$	−671.502	−	338.073i	−0.676918	−	0.340799i
$993$			714.392i			0.719428i
$994$	−36.9989	−	164.776i	−0.0372223	−	0.165771i
$995$		0			0
$996$	437.481	−	206.896i	0.439237	−	0.207727i
$997$		−	1238.47i		−	1.24220i	−0.783732	−	0.621099i	$-0.786686\pi$
$997$		−	1238.47i		−	1.24220i	0.783732	−	0.621099i	$-0.213314\pi$
$998$	−90.7434	−	404.129i	−0.0909253	−	0.404939i
$999$		−	349.876i		−	0.350227i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.c.a.31.3	✓	8	20.7	even	4
60.3.c.a.31.4	yes	8	5.2	odd	4
180.3.c.b.91.5		8	15.2	even	4
180.3.c.b.91.6		8	60.47	odd	4
300.3.c.d.151.5		8	5.3	odd	4
300.3.c.d.151.6		8	20.3	even	4
300.3.f.b.199.1		16	4.3	odd	2	inner
300.3.f.b.199.2		16	5.4	even	2	inner
300.3.f.b.199.15		16	1.1	even	1	trivial
300.3.f.b.199.16		16	20.19	odd	2	inner
900.3.c.u.451.3		8	60.23	odd	4
900.3.c.u.451.4		8	15.8	even	4
900.3.f.f.199.1		16	60.59	even	2
900.3.f.f.199.2		16	3.2	odd	2
900.3.f.f.199.15		16	15.14	odd	2
900.3.f.f.199.16		16	12.11	even	2
960.3.e.c.511.2		8	40.37	odd	4
960.3.e.c.511.5		8	40.27	even	4
2880.3.e.j.2431.5		8	120.107	odd	4
2880.3.e.j.2431.8		8	120.77	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.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.95141 - 0.438172i) q^{2} -1.73205 q^{3} +(3.61601 - 1.71011i) q^{4} +(-3.37994 + 0.758935i) q^{6} +6.33166 q^{7} +(6.30701 - 4.92155i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(1.95141 - 0.438172i) q^{2} -1.73205 q^{3} +(3.61601 - 1.71011i) q^{4} +(-3.37994 + 0.758935i) q^{6} +6.33166 q^{7} +(6.30701 - 4.92155i) q^{8} +3.00000 q^{9} -9.27963i q^{11} +(-6.26312 + 2.96199i) q^{12} +18.5674i q^{13} +(12.3557 - 2.77436i) q^{14} +(10.1511 - 12.3675i) q^{16} -13.9110i q^{17} +(5.85423 - 1.31451i) q^{18} -17.2468i q^{19} -10.9668 q^{21} +(-4.06607 - 18.1084i) q^{22} +33.7148 q^{23} +(-10.9241 + 8.52438i) q^{24} +(8.13571 + 36.2327i) q^{26} -5.19615 q^{27} +(22.8954 - 10.8278i) q^{28} +28.6177 q^{29} -23.4939i q^{31} +(14.3898 - 28.5820i) q^{32} +16.0728i q^{33} +(-6.09542 - 27.1461i) q^{34} +(10.8480 - 5.13032i) q^{36} +67.3338i q^{37} +(-7.55706 - 33.6556i) q^{38} -32.1597i q^{39} -44.0791 q^{41} +(-21.4007 + 4.80532i) q^{42} -50.2937 q^{43} +(-15.8691 - 33.5552i) q^{44} +(65.7915 - 14.7729i) q^{46} -31.1594 q^{47} +(-17.5822 + 21.4212i) q^{48} -8.91003 q^{49} +24.0946i q^{51} +(31.7522 + 67.1400i) q^{52} +81.6070i q^{53} +(-10.1398 + 2.27681i) q^{54} +(39.9338 - 31.1616i) q^{56} +29.8724i q^{57} +(55.8449 - 12.5395i) q^{58} +19.2751i q^{59} -53.1563 q^{61} +(-10.2943 - 45.8462i) q^{62} +18.9950 q^{63} +(15.5566 - 62.0805i) q^{64} +(7.04264 + 31.3646i) q^{66} -4.49911 q^{67} +(-23.7893 - 50.3025i) q^{68} -58.3958 q^{69} -13.3360i q^{71} +(18.9210 - 14.7647i) q^{72} +40.8904i q^{73} +(29.5037 + 131.396i) q^{74} +(-29.4939 - 62.3647i) q^{76} -58.7555i q^{77} +(-14.0915 - 62.7568i) q^{78} +141.309i q^{79} +9.00000 q^{81} +(-86.0164 + 19.3142i) q^{82} -69.8503 q^{83} +(-39.6559 + 18.7543i) q^{84} +(-98.1438 + 22.0373i) q^{86} -49.5673 q^{87} +(-45.6702 - 58.5266i) q^{88} +46.3079 q^{89} +117.563i q^{91} +(121.913 - 57.6559i) q^{92} +40.6926i q^{93} +(-60.8049 + 13.6532i) q^{94} +(-24.9239 + 49.5055i) q^{96} -68.5543i q^{97} +(-17.3871 + 3.90412i) q^{98} -27.8389i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 20 q^{4} - 12 q^{6} + 48 q^{9}+O(q^{10}) \) 16 * q - 20 * q^4 - 12 * q^6 + 48 * q^9	\( 16 q - 20 q^{4} - 12 q^{6} + 48 q^{9} + 40 q^{14} + 68 q^{16} - 96 q^{21} - 36 q^{24} - 72 q^{26} - 128 q^{29} + 184 q^{34} - 60 q^{36} - 32 q^{41} - 344 q^{44} + 304 q^{46} + 112 q^{49} - 36 q^{54} + 232 q^{56} - 352 q^{61} + 220 q^{64} + 216 q^{66} + 192 q^{69} - 264 q^{74} - 48 q^{76} + 144 q^{81} + 72 q^{84} - 400 q^{86} - 160 q^{89} + 192 q^{94} - 348 q^{96}+O(q^{100}) \) 16 * q - 20 * q^4 - 12 * q^6 + 48 * q^9 + 40 * q^14 + 68 * q^16 - 96 * q^21 - 36 * q^24 - 72 * q^26 - 128 * q^29 + 184 * q^34 - 60 * q^36 - 32 * q^41 - 344 * q^44 + 304 * q^46 + 112 * q^49 - 36 * q^54 + 232 * q^56 - 352 * q^61 + 220 * q^64 + 216 * q^66 + 192 * q^69 - 264 * q^74 - 48 * q^76 + 144 * q^81 + 72 * q^84 - 400 * q^86 - 160 * q^89 + 192 * q^94 - 348 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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